LMFDB - Embedded newform 33.8.f.a.2.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(2,33)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("33.2");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.f (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			2.11
Character	$\chi$	$=$	33.2
Dual form			33.8.f.a.17.11

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997925 + 3.07130i) q^{2} +(-46.7172 - 2.12148i) q^{3} +(95.1172 + 69.1067i) q^{4} +(-23.9618 + 7.78566i) q^{5} +(53.1360 - 141.365i) q^{6} +(-324.042 + 446.006i) q^{7} +(-641.580 + 466.135i) q^{8} +(2178.00 + 198.219i) q^{9} +O(q^{10})$	\(q+(-0.997925 + 3.07130i) q^{2} +(-46.7172 - 2.12148i) q^{3} +(95.1172 + 69.1067i) q^{4} +(-23.9618 + 7.78566i) q^{5} +(53.1360 - 141.365i) q^{6} +(-324.042 + 446.006i) q^{7} +(-641.580 + 466.135i) q^{8} +(2178.00 + 198.219i) q^{9} -81.3633i q^{10} +(-1081.78 - 4279.83i) q^{11} +(-4297.00 - 3430.26i) q^{12} +(-13171.3 - 4279.61i) q^{13} +(-1046.45 - 1440.31i) q^{14} +(1135.95 - 312.890i) q^{15} +(3859.04 + 11876.9i) q^{16} +(-11599.8 - 35700.6i) q^{17} +(-2782.27 + 6491.47i) q^{18} +(-3836.92 - 5281.07i) q^{19} +(-2817.22 - 915.370i) q^{20} +(16084.5 - 20148.7i) q^{21} +(14224.2 + 948.474i) q^{22} +12864.0i q^{23} +(30961.7 - 20415.4i) q^{24} +(-62690.9 + 45547.6i) q^{25} +(26287.9 - 36182.2i) q^{26} +(-101330. - 13880.8i) q^{27} +(-61643.9 + 20029.3i) q^{28} +(61174.6 + 44446.0i) q^{29} +(-172.610 + 3801.07i) q^{30} +(47326.4 - 145656. i) q^{31} -141837. q^{32} +(41458.3 + 202237. i) q^{33} +121223. q^{34} +(4292.18 - 13210.0i) q^{35} +(193467. + 169368. i) q^{36} +(316626. + 230043. i) q^{37} +(20048.7 - 6514.21i) q^{38} +(606247. + 227874. i) q^{39} +(11744.2 - 16164.6i) q^{40} +(-507001. + 368358. i) q^{41} +(45831.5 + 69507.3i) q^{42} -135615. i q^{43} +(192869. - 481843. i) q^{44} +(-53732.0 + 12207.5i) q^{45} +(-39509.2 - 12837.3i) q^{46} +(-370039. - 509314. i) q^{47} +(-155087. - 563043. i) q^{48} +(160571. + 494187. i) q^{49} +(-77329.4 - 237996. i) q^{50} +(466174. + 1.69244e6i) q^{51} +(-957066. - 1.31729e6i) q^{52} +(-1.49230e6 - 484877. i) q^{53} +(143751. - 297361. i) q^{54} +(59242.7 + 94129.9i) q^{55} -437196. i q^{56} +(168047. + 254857. i) q^{57} +(-197554. + 143532. i) q^{58} +(941193. - 1.29544e6i) q^{59} +(129671. + 48740.2i) q^{60} +(-357604. + 116193. i) q^{61} +(400124. + 290707. i) q^{62} +(-794170. + 907168. i) q^{63} +(-352415. + 1.08462e6i) q^{64} +348927. q^{65} +(-662501. - 74486.3i) q^{66} +347077. q^{67} +(1.36381e6 - 4.19737e6i) q^{68} +(27290.7 - 600970. i) q^{69} +(36288.5 + 26365.1i) q^{70} +(-4.57923e6 + 1.48788e6i) q^{71} +(-1.48976e6 + 888068. i) q^{72} +(198818. - 273650. i) q^{73} +(-1.02250e6 + 742889. i) q^{74} +(3.02537e6 - 1.99486e6i) q^{75} -767477. i q^{76} +(2.25937e6 + 904363. i) q^{77} +(-1.30486e6 + 1.63456e6i) q^{78} +(965104. + 313581. i) q^{79} +(-184939. - 254547. i) q^{80} +(4.70439e6 + 863442. i) q^{81} +(-625388. - 1.92475e6i) q^{82} +(1.44530e6 + 4.44817e6i) q^{83} +(2.92233e6 - 804938. i) q^{84} +(555906. + 765139. i) q^{85} +(416513. + 135333. i) q^{86} +(-2.76362e6 - 2.20617e6i) q^{87} +(2.68903e6 + 2.24159e6i) q^{88} +7.70725e6i q^{89} +(16127.8 - 177209. i) q^{90} +(6.17678e6 - 4.48770e6i) q^{91} +(-888988. + 1.22359e6i) q^{92} +(-2.51997e6 + 6.70423e6i) q^{93} +(1.93353e6 - 628241. i) q^{94} +(133056. + 96670.9i) q^{95} +(6.62624e6 + 300905. i) q^{96} +(-4.41852e6 + 1.35988e7i) q^{97} -1.67803e6 q^{98} +(-1.50777e6 - 9.53589e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 42 q^{3} - 1542 q^{4} - 1725 q^{6} - 10 q^{7} + 550 q^{9}+O(q^{10}) $ 104 * q - 42 * q^3 - 1542 * q^4 - 1725 * q^6 - 10 * q^7 + 550 * q^9	$ 104 q - 42 q^{3} - 1542 q^{4} - 1725 q^{6} - 10 q^{7} + 550 q^{9} + 12942 q^{12} - 10 q^{13} - 21762 q^{15} - 40042 q^{16} + 60435 q^{18} + 10460 q^{19} - 218044 q^{22} + 330875 q^{24} + 462276 q^{25} - 294096 q^{27} - 1044930 q^{28} + 243010 q^{30} + 412 q^{31} + 32138 q^{33} + 720380 q^{34} + 166067 q^{36} - 494526 q^{37} + 1075280 q^{39} + 363510 q^{40} - 1090804 q^{42} - 3105552 q^{45} + 706710 q^{46} + 3640214 q^{48} + 3722248 q^{49} + 53970 q^{51} - 3236270 q^{52} + 1380424 q^{55} - 3039180 q^{57} - 1651930 q^{58} - 12139486 q^{60} + 3921710 q^{61} + 459870 q^{63} + 3705878 q^{64} + 15158784 q^{66} - 15866932 q^{67} + 8740364 q^{69} + 14057584 q^{70} - 28129160 q^{72} - 26920980 q^{73} - 16391598 q^{75} + 43716808 q^{78} + 59786450 q^{79} - 17715062 q^{81} + 23865872 q^{82} + 71482920 q^{84} - 2864030 q^{85} - 108977170 q^{88} - 54544280 q^{90} - 56013610 q^{91} - 71700158 q^{93} + 53266890 q^{94} + 34615450 q^{96} + 71130138 q^{97} + 46642084 q^{99}+O(q^{100}) $ 104 * q - 42 * q^3 - 1542 * q^4 - 1725 * q^6 - 10 * q^7 + 550 * q^9 + 12942 * q^12 - 10 * q^13 - 21762 * q^15 - 40042 * q^16 + 60435 * q^18 + 10460 * q^19 - 218044 * q^22 + 330875 * q^24 + 462276 * q^25 - 294096 * q^27 - 1044930 * q^28 + 243010 * q^30 + 412 * q^31 + 32138 * q^33 + 720380 * q^34 + 166067 * q^36 - 494526 * q^37 + 1075280 * q^39 + 363510 * q^40 - 1090804 * q^42 - 3105552 * q^45 + 706710 * q^46 + 3640214 * q^48 + 3722248 * q^49 + 53970 * q^51 - 3236270 * q^52 + 1380424 * q^55 - 3039180 * q^57 - 1651930 * q^58 - 12139486 * q^60 + 3921710 * q^61 + 459870 * q^63 + 3705878 * q^64 + 15158784 * q^66 - 15866932 * q^67 + 8740364 * q^69 + 14057584 * q^70 - 28129160 * q^72 - 26920980 * q^73 - 16391598 * q^75 + 43716808 * q^78 + 59786450 * q^79 - 17715062 * q^81 + 23865872 * q^82 + 71482920 * q^84 - 2864030 * q^85 - 108977170 * q^88 - 54544280 * q^90 - 56013610 * q^91 - 71700158 * q^93 + 53266890 * q^94 + 34615450 * q^96 + 71130138 * q^97 + 46642084 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.997925	+	3.07130i	−0.0882049	+	0.271467i	−0.985423	−	0.170120i	$-0.945584\pi$
$2$	−0.997925	+	3.07130i	−0.0882049	+	0.271467i	0.897218	+	0.441587i	$0.145584\pi$
$3$	−46.7172	−	2.12148i	−0.998971	−	0.0453643i
$3$	−46.7172	−	2.12148i	−0.998971	−	0.0453643i
$4$	95.1172	+	69.1067i	0.743103	+	0.539896i
$5$	−23.9618	+	7.78566i	−0.0857283	+	0.0278548i	−0.351567	−	0.936163i	$-0.614351\pi$
$5$	−23.9618	+	7.78566i	−0.0857283	+	0.0278548i	0.265839	+	0.964017i	$0.414351\pi$
$6$	53.1360	−	141.365i	0.100429	−	0.267186i
$7$	−324.042	+	446.006i	−0.357074	+	0.491470i	−0.949331	−	0.314279i	$-0.898237\pi$
$7$	−324.042	+	446.006i	−0.357074	+	0.491470i	0.592257	+	0.805749i	$0.298237\pi$
$8$	−641.580	+	466.135i	−0.443033	+	0.321882i
$9$	2178.00	+	198.219i	0.995884	+	0.0906352i
$10$		−	81.3633i		−	0.0257293i
$11$	−1081.78	−	4279.83i	−0.245056	−	0.969509i
$11$	−1081.78	−	4279.83i	−0.245056	−	0.969509i
$12$	−4297.00	−	3430.26i	−0.717846	−	0.573050i
$13$	−13171.3	−	4279.61i	−1.66275	−	0.540260i	−0.681303	−	0.732001i	$-0.738587\pi$
$13$	−13171.3	−	4279.61i	−1.66275	−	0.540260i	−0.981445	+	0.191741i	$0.938587\pi$
$14$	−1046.45	−	1440.31i	−0.101922	−	0.140284i
$15$	1135.95	−	312.890i	0.0869037	−	0.0239371i
$16$	3859.04	+	11876.9i	0.235537	+	0.724909i
$17$	−11599.8	−	35700.6i	−0.572639	−	1.76240i	−0.644082	−	0.764957i	$-0.722760\pi$
$17$	−11599.8	−	35700.6i	−0.572639	−	1.76240i	0.0714426	−	0.997445i	$-0.477240\pi$
$18$	−2782.27	+	6491.47i	−0.112446	+	0.262355i
$19$	−3836.92	−	5281.07i	−0.128335	−	0.176638i	0.740014	−	0.672591i	$-0.234819\pi$
$19$	−3836.92	−	5281.07i	−0.128335	−	0.176638i	−0.868349	+	0.495953i	$0.834819\pi$
$20$	−2817.22	−	915.370i	−0.0787436	−	0.0255854i
$21$	16084.5	−	20148.7i	0.379002	−	0.474766i
$22$	14224.2	+	948.474i	0.284805	+	0.0189909i
$23$			12864.0i			0.220459i	0.993906	+	0.110230i	$0.0351586\pi$
$23$			12864.0i			0.220459i	−0.993906	+	0.110230i	$0.964841\pi$
$24$	30961.7	−	20415.4i	0.457179	−	0.301453i
$25$	−62690.9	+	45547.6i	−0.802444	+	0.583009i
$26$	26287.9	−	36182.2i	0.293325	−	0.403728i
$27$	−101330.	−	13880.8i	−0.990747	−	0.135719i
$28$	−61643.9	+	20029.3i	−0.530685	+	0.172430i
$29$	61174.6	+	44446.0i	0.465777	+	0.338407i	0.795793	−	0.605568i	$-0.207054\pi$
$29$	61174.6	+	44446.0i	0.465777	+	0.338407i	−0.330016	+	0.943975i	$0.607054\pi$
$30$	−172.610	+	3801.07i	−0.00116719	+	0.0257028i
$31$	47326.4	−	145656.i	0.285324	−	0.878136i	−0.700978	−	0.713183i	$-0.747253\pi$
$31$	47326.4	−	145656.i	0.285324	−	0.878136i	0.986301	−	0.164953i	$-0.0527473\pi$
$32$	−141837.			−0.765183
$33$	41458.3	+	202237.i	0.200822	+	0.979628i
$34$	121223.			0.528943
$35$	4292.18	−	13210.0i	0.0169215	−	0.0520791i
$36$	193467.	+	169368.i	0.691111	+	0.605025i
$37$	316626.	+	230043.i	1.02764	+	0.746624i	0.967835	−	0.251586i	$-0.0809521\pi$
$37$	316626.	+	230043.i	1.02764	+	0.746624i	0.0598051	+	0.998210i	$0.480952\pi$
$38$	20048.7	−	6514.21i	0.0592712	−	0.0192584i
$39$	606247.	+	227874.i	1.63653	+	0.615133i
$40$	11744.2	−	16164.6i	0.0290145	−	0.0399350i
$41$	−507001.	+	368358.i	−1.14886	+	0.834693i	−0.988328	−	0.152338i	$-0.951320\pi$
$41$	−507001.	+	368358.i	−1.14886	+	0.834693i	−0.160528	+	0.987031i	$0.551320\pi$
$42$	45831.5	+	69507.3i	0.0954534	+	0.144763i
$43$		−	135615.i		−	0.260116i	−0.991506	−	0.130058i	$-0.958484\pi$
$43$		−	135615.i		−	0.260116i	0.991506	−	0.130058i	$-0.0415164\pi$
$44$	192869.	−	481843.i	0.341332	−	0.852749i
$45$	−53732.0	+	12207.5i	−0.0879001	+	0.0199702i
$46$	−39509.2	−	12837.3i	−0.0598474	−	0.0194456i
$47$	−370039.	−	509314.i	−0.519882	−	0.715556i	0.465665	−	0.884961i	$-0.345815\pi$
$47$	−370039.	−	509314.i	−0.519882	−	0.715556i	−0.985546	+	0.169406i	$0.945815\pi$
$48$	−155087.	−	563043.i	−0.202410	−	0.734848i
$49$	160571.	+	494187.i	0.194976	+	0.600074i
$50$	−77329.4	−	237996.i	−0.0874883	−	0.269261i
$51$	466174.	+	1.69244e6i	0.492099	+	1.78656i
$52$	−957066.	−	1.31729e6i	−0.943909	−	1.29918i
$53$	−1.49230e6	−	484877.i	−1.37686	−	0.447369i	−0.475225	−	0.879864i	$-0.657633\pi$
$53$	−1.49230e6	−	484877.i	−1.37686	−	0.447369i	−0.901636	+	0.432495i	$0.857633\pi$
$54$	143751.	−	297361.i	0.124232	−	0.256984i
$55$	59242.7	+	94129.9i	0.0480137	+	0.0762884i
$56$		−	437196.i		−	0.332673i
$57$	168047.	+	254857.i	0.120190	+	0.182278i
$58$	−197554.	+	143532.i	−0.132950	+	0.0965939i
$59$	941193.	−	1.29544e6i	0.596619	−	0.821175i	−0.398775	−	0.917049i	$-0.630565\pi$
$59$	941193.	−	1.29544e6i	0.596619	−	0.821175i	0.995393	+	0.0958739i	$0.0305645\pi$
$60$	129671.	+	48740.2i	0.0775019	+	0.0291312i
$61$	−357604.	+	116193.i	−0.201720	+	0.0655427i	−0.408134	−	0.912922i	$-0.633820\pi$
$61$	−357604.	+	116193.i	−0.201720	+	0.0655427i	0.206415	+	0.978465i	$0.433820\pi$
$62$	400124.	+	290707.i	0.213218	+	0.154912i
$63$	−794170.	+	907168.i	−0.400149	+	0.457084i
$64$	−352415.	+	1.08462e6i	−0.168044	+	0.517188i
$65$	348927.			0.157593
$66$	−662501.	−	74486.3i	−0.283650	−	0.0318913i
$67$	347077.			0.140982			0.0704910	−	0.997512i	$-0.477543\pi$
$67$	347077.			0.140982			0.0704910	+	0.997512i	$0.477543\pi$
$68$	1.36381e6	−	4.19737e6i	0.525984	−	1.61881i
$69$	27290.7	−	600970.i	0.0100010	−	0.220232i
$70$	36288.5	+	26365.1i	0.0126452	+	0.00918728i
$71$	−4.57923e6	+	1.48788e6i	−1.51841	+	0.493360i	−0.945323	−	0.326136i	$-0.894253\pi$
$71$	−4.57923e6	+	1.48788e6i	−1.51841	+	0.493360i	−0.573084	+	0.819497i	$0.694253\pi$
$72$	−1.48976e6	+	888068.i	−0.470383	+	0.280403i
$73$	198818.	−	273650.i	0.0598172	−	0.0823313i	−0.778060	−	0.628189i	$-0.783796\pi$
$73$	198818.	−	273650.i	0.0598172	−	0.0823313i	0.837878	+	0.545858i	$0.183796\pi$
$74$	−1.02250e6	+	742889.i	−0.293327	+	0.213114i
$75$	3.02537e6	−	1.99486e6i	0.828065	−	0.546007i
$76$		−	767477.i		−	0.200548i
$77$	2.25937e6	+	904363.i	0.563988	+	0.225749i
$78$	−1.30486e6	+	1.63456e6i	−0.311338	+	0.390006i
$79$	965104.	+	313581.i	0.220231	+	0.0715575i	0.417054	−	0.908882i	$-0.363062\pi$
$79$	965104.	+	313581.i	0.220231	+	0.0715575i	−0.196823	+	0.980439i	$0.563062\pi$
$80$	−184939.	−	254547.i	−0.0403844	−	0.0555844i
$81$	4.70439e6	+	863442.i	0.983571	+	0.180524i
$82$	−625388.	−	1.92475e6i	−0.125257	−	0.385500i
$83$	1.44530e6	+	4.44817e6i	0.277449	+	0.853901i	0.988561	+	0.150822i	$0.0481921\pi$
$83$	1.44530e6	+	4.44817e6i	0.277449	+	0.853901i	−0.711112	+	0.703079i	$0.751808\pi$
$84$	2.92233e6	−	804938.i	0.537961	−	0.148178i
$85$	555906.	+	765139.i	0.0981827	+	0.135137i
$86$	416513.	+	135333.i	0.0706129	+	0.0229435i
$87$	−2.76362e6	−	2.20617e6i	−0.449946	−	0.359188i
$88$	2.68903e6	+	2.24159e6i	0.420635	+	0.350645i
$89$			7.70725e6i			1.15887i	0.815019	+	0.579435i	$0.196727\pi$
$89$			7.70725e6i			1.15887i	−0.815019	+	0.579435i	$0.803273\pi$
$90$	16127.8	−	177209.i	0.00233198	−	0.0256234i
$91$	6.17678e6	−	4.48770e6i	0.859246	−	0.624279i
$92$	−888988.	+	1.22359e6i	−0.119025	+	0.163824i
$93$	−2.51997e6	+	6.70423e6i	−0.324866	+	0.864289i
$94$	1.93353e6	−	628241.i	0.240106	−	0.0780151i
$95$	133056.	+	96670.9i	0.0159222	+	0.0115681i
$96$	6.62624e6	+	300905.i	0.764395	+	0.0347120i
$97$	−4.41852e6	+	1.35988e7i	−0.491560	+	1.51286i	0.330691	+	0.943739i	$0.392718\pi$
$97$	−4.41852e6	+	1.35988e7i	−0.491560	+	1.51286i	−0.822250	+	0.569126i	$0.807282\pi$
$98$	−1.67803e6			−0.180098
$99$	−1.50777e6	−	9.53589e6i	−0.156176	−	0.987729i
$100$	−9.11062e6			−0.911062
$101$	−1.32169e6	+	4.06773e6i	−0.127645	+	0.392851i	−0.994374	−	0.105929i	$-0.966218\pi$
$101$	−1.32169e6	+	4.06773e6i	−0.127645	+	0.392851i	0.866729	+	0.498780i	$0.166218\pi$
$102$	−5.66321e6	−	257172.i	−0.528399	−	0.0239951i
$103$	140274.	+	101915.i	0.0126487	+	0.00918981i	0.594092	−	0.804397i	$-0.297512\pi$
$103$	140274.	+	101915.i	0.0126487	+	0.00918981i	−0.581443	+	0.813587i	$0.697512\pi$
$104$	1.04453e7	−	3.39389e6i	0.910552	−	0.295856i
$105$	−228543.	+	608028.i	−0.0192667	+	0.0512579i
$106$	2.97841e6	−	4.09942e6i	0.242892	−	0.334312i
$107$	8.88813e6	−	6.45761e6i	0.701403	−	0.509599i	−0.178986	−	0.983852i	$-0.557282\pi$
$107$	8.88813e6	−	6.45761e6i	0.701403	−	0.509599i	0.880389	+	0.474253i	$0.157282\pi$
$108$	−8.67892e6	−	8.32285e6i	−0.662953	−	0.635754i
$109$		−	1.07275e7i		−	0.793424i	−0.917943	−	0.396712i	$-0.870151\pi$
$109$		−	1.07275e7i		−	0.793424i	0.917943	−	0.396712i	$-0.129849\pi$
$110$	−348221.	+	88017.3i	−0.0249448	+	0.00630512i
$111$	−1.43039e7	−	1.14187e7i	−0.992712	−	0.792474i
$112$	−6.54766e6	−	2.12747e6i	−0.440376	−	0.143087i
$113$	270454.	+	372249.i	0.0176327	+	0.0242694i	0.817742	−	0.575584i	$-0.195225\pi$
$113$	270454.	+	372249.i	0.0176327	+	0.0242694i	−0.800110	+	0.599854i	$0.795225\pi$
$114$	−950439.	+	261793.i	−0.0600838	+	0.0165497i
$115$	−100155.	−	308244.i	−0.00614085	−	0.0188996i
$116$	2.74724e6	+	8.45515e6i	0.163416	+	0.502942i
$117$	−2.78388e7	−	1.19318e7i	−1.60694	−	0.688740i
$118$	3.03945e6	+	4.18344e6i	0.170297	+	0.234394i
$119$	1.96815e7	+	6.39492e6i	1.07064	+	0.347873i
$120$	−582951.	+	730248.i	−0.0307962	+	0.0385777i
$121$	−1.71467e7	+	9.25967e6i	−0.879895	+	0.475168i
$122$		−	1.21426e6i		−	0.0605414i
$123$	2.44672e7	−	1.61331e7i	1.18554	−	0.781717i
$124$	1.45673e7	−	1.05838e7i	0.686127	−	0.498500i
$125$	2.30454e6	−	3.17192e6i	0.105536	−	0.145257i
$126$	−1.99366e6	−	3.34442e6i	−0.0887881	−	0.148944i
$127$	−2.10594e7	+	6.84262e6i	−0.912290	+	0.296421i	−0.727300	−	0.686319i	$-0.759225\pi$
$127$	−2.10594e7	+	6.84262e6i	−0.912290	+	0.296421i	−0.184990	+	0.982740i	$0.559225\pi$
$128$	−1.76673e7	−	1.28361e7i	−0.744623	−	0.541000i
$129$	−287704.	+	6.33555e6i	−0.0118000	+	0.259848i
$130$	−348203.	+	1.07166e6i	−0.0139005	+	0.0427814i
$131$	−1.60362e7			−0.623236			−0.311618	−	0.950207i	$-0.600871\pi$
$131$	−1.60362e7			−0.623236			−0.311618	+	0.950207i	$0.600871\pi$
$132$	−1.00325e7	+	2.21012e7i	−0.379665	+	0.836387i
$133$	3.59871e6			0.132637
$134$	−346356.	+	1.06598e6i	−0.0124353	+	0.0382719i
$135$	2.53611e6	−	456308.i	0.0887155	−	0.0159621i
$136$	2.40836e7	+	1.74977e7i	0.820983	+	0.596479i
$137$	1.49365e7	−	4.85316e6i	0.496279	−	0.161251i	−0.0501739	−	0.998740i	$-0.515978\pi$
$137$	1.49365e7	−	4.85316e6i	0.496279	−	0.161251i	0.546453	+	0.837490i	$0.315978\pi$
$138$	1.81852e6	+	683541.i	0.0589037	+	0.0221405i
$139$	2.20698e7	−	3.03764e7i	0.697021	−	0.959367i	−0.302959	−	0.953004i	$-0.597974\pi$
$139$	2.20698e7	−	3.03764e7i	0.697021	−	0.959367i	0.999980	−	0.00636339i	$-0.00202554\pi$
$140$	1.32116e6	−	959877.i	0.0406918	−	0.0295643i
$141$	1.62067e7	+	2.45788e7i	0.486886	+	0.738403i
$142$		−	1.55490e7i		−	0.455714i
$143$	−4.06754e6	+	6.10005e7i	−0.116320	+	1.74444i
$144$	6.05076e6	+	2.66328e7i	0.168866	+	0.743274i
$145$	−1.81189e6	−	588720.i	−0.0493566	−	0.0160369i
$146$	642054.	+	883712.i	0.0170741	+	0.0235004i
$147$	−6.45303e6	−	2.34277e7i	−0.167553	−	0.608301i
$148$	1.42191e7	+	4.37620e7i	0.360543	+	1.10964i
$149$	−5.61257e6	−	1.72737e7i	−0.138998	−	0.427793i	0.857192	−	0.514997i	$-0.172207\pi$
$149$	−5.61257e6	−	1.72737e7i	−0.138998	−	0.427793i	−0.996191	+	0.0872037i	$0.972207\pi$
$150$	3.10771e6	+	1.12825e7i	0.0751833	+	0.272953i
$151$	−3.03344e7	−	4.17517e7i	−0.716994	−	0.986857i	−0.999618	−	0.0276268i	$-0.991205\pi$
$151$	−3.03344e7	−	4.17517e7i	−0.716994	−	0.986857i	0.282624	−	0.959231i	$-0.408795\pi$
$152$	4.92338e6	+	1.59970e6i	0.113713	+	0.0369477i
$153$	−1.81879e7	−	8.00553e7i	−0.410546	−	1.80705i
$154$	−5.03225e6	+	6.03671e6i	−0.111030	+	0.133192i
$155$			3.85864e6i			0.0832288i
$156$	4.19169e7	+	6.35705e7i	0.884001	+	1.34066i
$157$	4.07849e6	−	2.96320e6i	0.0841106	−	0.0611100i	−0.544935	−	0.838478i	$-0.683446\pi$
$157$	4.07849e6	−	2.96320e6i	0.0841106	−	0.0611100i	0.629046	+	0.777368i	$0.283446\pi$
$158$	−1.92620e6	+	2.65119e6i	−0.0388510	+	0.0534738i
$159$	6.86874e7	+	2.58180e7i	1.35515	+	0.509369i
$160$	3.39867e6	−	1.10430e6i	0.0655978	−	0.0213140i
$161$	−5.73742e6	−	4.16848e6i	−0.108349	−	0.0787203i
$162$	−7.34651e6	+	1.35869e7i	−0.135762	+	0.251084i
$163$	−5.07550e6	+	1.56208e7i	−0.0917956	+	0.282518i	−0.986405	−	0.164330i	$-0.947454\pi$
$163$	−5.07550e6	+	1.56208e7i	−0.0917956	+	0.282518i	0.894610	+	0.446848i	$0.147454\pi$
$164$	−7.36805e7			−1.30437
$165$	−2.56796e6	−	4.52317e6i	−0.0445035	−	0.0783879i
$166$	−1.51039e7			−0.256278
$167$	1.55598e7	−	4.78882e7i	0.258522	−	0.795648i	−0.734593	−	0.678507i	$-0.762627\pi$
$167$	1.55598e7	−	4.78882e7i	0.258522	−	0.795648i	0.993115	−	0.117141i	$-0.0373729\pi$
$168$	−927501.	+	2.04246e7i	−0.0150915	+	0.332331i
$169$	1.04403e8	+	7.58534e7i	1.66384	+	1.20885i
$170$	−2.90472e6	+	943801.i	−0.0453454	+	0.0147336i
$171$	−7.31000e6	−	1.22627e7i	−0.111797	−	0.187543i
$172$	9.37188e6	−	1.28993e7i	0.140436	−	0.193293i
$173$	−1.00453e7	+	7.29833e6i	−0.147503	+	0.107167i	−0.659089	−	0.752065i	$-0.729058\pi$
$173$	−1.00453e7	+	7.29833e6i	−0.147503	+	0.107167i	0.511586	+	0.859232i	$0.329058\pi$
$174$	9.53370e6	−	6.28630e6i	0.137195	−	0.0904633i
$175$		−	4.27198e7i		−	0.602555i
$176$	4.66565e7	−	2.93643e7i	0.645086	−	0.405999i
$177$	−4.67182e7	+	5.85227e7i	−0.633256	+	0.793264i
$178$	−2.36713e7	−	7.69126e6i	−0.314595	−	0.102218i
$179$	−2.36298e7	−	3.25236e7i	−0.307946	−	0.423851i	0.626794	−	0.779185i	$-0.284367\pi$
$179$	−2.36298e7	−	3.25236e7i	−0.307946	−	0.423851i	−0.934739	+	0.355335i	$0.884367\pi$
$180$	−5.95445e6	−	2.55210e6i	−0.0761006	−	0.0326170i
$181$	−2.05802e7	−	6.33393e7i	−0.257973	−	0.793960i	−0.993229	−	0.116170i	$-0.962938\pi$
$181$	−2.05802e7	−	6.33393e7i	−0.257973	−	0.793960i	0.735256	−	0.677789i	$-0.237062\pi$
$182$	7.61908e6	+	2.34491e7i	0.0936813	+	0.288321i
$183$	1.69528e7	−	4.66955e6i	0.204485	−	0.0563243i
$184$	−5.99636e6	−	8.25328e6i	−0.0709619	−	0.0976707i
$185$	−9.37797e6	−	3.04709e6i	−0.108895	−	0.0353821i
$186$	−1.80760e7	−	1.44299e7i	−0.205971	−	0.164425i
$187$	−1.40244e8	+	8.82656e7i	−1.56834	+	0.987065i
$188$		−	7.40167e7i		−	0.812413i
$189$	3.90260e7	−	4.06956e7i	0.420472	−	0.438461i
$190$	−429685.	+	312184.i	−0.00454478	+	0.00330197i
$191$	7.72259e7	−	1.06292e8i	0.801948	−	1.10379i	−0.190568	−	0.981674i	$-0.561033\pi$
$191$	7.72259e7	−	1.06292e8i	0.801948	−	1.10379i	0.992516	−	0.122113i	$-0.0389671\pi$
$192$	1.87648e7	−	4.99228e7i	0.191333	−	0.509032i
$193$	−3.39636e7	+	1.10354e7i	−0.340066	+	0.110494i	−0.474071	−	0.880487i	$-0.657216\pi$
$193$	−3.39636e7	+	1.10354e7i	−0.340066	+	0.110494i	0.134005	+	0.990981i	$0.457216\pi$
$194$	−3.73567e7	−	2.71412e7i	−0.367335	−	0.266884i
$195$	−1.63009e7	−	740242.i	−0.157431	−	0.00714912i
$196$	−1.88785e7	+	5.81022e7i	−0.179090	+	0.551183i
$197$	−1.38115e8			−1.28709			−0.643547	−	0.765407i	$-0.722538\pi$
$197$	−1.38115e8			−1.28709			−0.643547	+	0.765407i	$0.722538\pi$
$198$	3.07922e7	+	4.88528e6i	0.281911	+	0.0447261i
$199$	−8.96092e7			−0.806059			−0.403030	−	0.915187i	$-0.632043\pi$
$199$	−8.96092e7			−0.806059			−0.403030	+	0.915187i	$0.632043\pi$
$200$	1.89899e7	−	5.84449e7i	0.167848	−	0.516584i
$201$	−1.62145e7	−	736316.i	−0.140837	−	0.00639555i
$202$	−1.11743e7	−	8.11858e6i	−0.0953870	−	0.0693027i
$203$	−3.96463e7	+	1.28819e7i	−0.332634	+	0.108079i
$204$	−7.26180e7	+	1.93196e8i	−0.598878	+	1.59328i
$205$	9.28075e6	−	1.27739e7i	0.0752393	−	0.103558i
$206$	−452993.	+	329119.i	−0.00361041	+	0.00262311i
$207$	−2.54989e6	+	2.80178e7i	−0.0199814	+	0.219552i
$208$		−	1.72950e8i		−	1.33259i
$209$	−1.84513e7	+	2.21343e7i	−0.139803	+	0.167708i
$210$	−1.63936e6	−	1.30869e6i	−0.0122154	−	0.00975146i
$211$	1.94154e8	+	6.30844e7i	1.42284	+	0.462310i	0.916504	−	0.400025i	$-0.130998\pi$
$211$	1.94154e8	+	6.30844e7i	1.42284	+	0.462310i	0.506339	+	0.862334i	$0.330998\pi$
$212$	−1.08435e8	−	1.49248e8i	−0.781617	−	1.07580i
$213$	2.17085e8	−	5.97950e7i	1.53922	−	0.423971i
$214$	1.09635e7	+	3.37423e7i	0.0764720	+	0.235357i
$215$	1.05585e6	+	3.24957e6i	0.00724549	+	0.0222993i
$216$	7.14813e7	−	3.83276e7i	0.482619	−	0.258776i
$217$	4.96276e7	+	6.83065e7i	0.329696	+	0.453788i
$218$	3.29473e7	+	1.07052e7i	0.215388	+	0.0699840i
$219$	−9.86878e6	+	1.23624e7i	−0.0634905	+	0.0795330i
$220$	−870010.	+	1.30474e7i	−0.00550864	+	0.0826125i
$221$			5.19866e8i			3.23980i
$222$	4.93443e7	−	3.25365e7i	0.302693	−	0.199588i
$223$	2.15481e8	−	1.56556e8i	1.30119	−	0.945373i	0.301228	−	0.953552i	$-0.402603\pi$
$223$	2.15481e8	−	1.56556e8i	1.30119	−	0.945373i	0.999967	+	0.00817871i	$0.00260339\pi$
$224$	4.59612e7	−	6.32602e7i	0.273227	−	0.376065i
$225$	−1.45569e8	+	8.67761e7i	−0.851982	+	0.507880i
$226$	−1.41318e6	+	459170.i	−0.00814362	+	0.00264602i
$227$	1.75145e8	+	1.27250e8i	0.993816	+	0.722050i	0.960754	−	0.277403i	$-0.0894739\pi$
$227$	1.75145e8	+	1.27250e8i	0.993816	+	0.722050i	0.0330628	+	0.999453i	$0.489474\pi$
$228$	−1.62819e6	+	3.58544e7i	−0.00909771	+	0.200341i
$229$	−2.86144e6	+	8.80660e6i	−0.0157456	+	0.0484601i	−0.958621	−	0.284687i	$-0.908110\pi$
$229$	−2.86144e6	+	8.80660e6i	−0.0157456	+	0.0484601i	0.942875	+	0.333147i	$0.108110\pi$
$230$	1.04666e6			0.00567227
$231$	−1.03633e8	−	4.70426e7i	−0.553166	−	0.251101i
$232$	−5.99662e7			−0.315282
$233$	1.69322e7	−	5.21121e7i	0.0876937	−	0.269894i	−0.897587	−	0.440837i	$-0.854682\pi$
$233$	1.69322e7	−	5.21121e7i	0.0876937	−	0.269894i	0.985281	+	0.170944i	$0.0546816\pi$
$234$	6.44271e7	−	7.35941e7i	0.328710	−	0.375480i
$235$	1.28321e7	+	9.32309e6i	0.0645002	+	0.0468622i
$236$	1.79047e8	−	5.81760e7i	0.886698	−	0.288106i
$237$	−4.44217e7	−	1.66971e7i	−0.216759	−	0.0814745i
$238$	−3.92814e7	+	5.40662e7i	−0.188872	+	0.259960i
$239$	−1.72588e8	+	1.25393e8i	−0.817746	+	0.594127i	−0.916066	−	0.401027i	$-0.868653\pi$
$239$	−1.72588e8	+	1.25393e8i	−0.817746	+	0.594127i	0.0983198	+	0.995155i	$0.468653\pi$
$240$	8.09983e6	+	1.22841e7i	0.0378213	+	0.0573592i
$241$		−	1.19968e8i		−	0.552087i	−0.961145	−	0.276043i	$-0.910977\pi$
$241$		−	1.19968e8i		−	0.552087i	0.961145	−	0.276043i	$-0.0890233\pi$
$242$	−1.13281e7	−	6.19030e7i	−0.0513812	−	0.280775i
$243$	−2.17944e8	−	5.03179e7i	−0.974369	−	0.224957i
$244$	−4.20440e7	−	1.36609e7i	−0.185285	−	0.0602026i
$245$	−7.69514e6	−	1.05914e7i	−0.0334299	−	0.0460123i
$246$	2.51331e7	+	9.12455e7i	0.107640	+	0.390786i
$247$	2.79363e7	+	8.59790e7i	0.117958	+	0.363039i
$248$	3.75316e7	+	1.15510e8i	0.156249	+	0.480884i
$249$	−5.80836e7	−	2.10872e8i	−0.238427	−	0.865609i
$250$	7.44216e6	+	1.02433e7i	0.0301238	+	0.0414618i
$251$	3.87414e8	+	1.25879e8i	1.54638	+	0.502451i	0.953129	−	0.302563i	$-0.0978424\pi$
$251$	3.87414e8	+	1.25879e8i	1.54638	+	0.502451i	0.593256	+	0.805014i	$0.297842\pi$
$252$	−1.38231e8	+	3.14048e7i	−0.544129	+	0.123622i
$253$	5.50557e7	−	1.39160e7i	0.213737	−	0.0540249i
$254$		−	7.15081e7i		−	0.273802i
$255$	−2.43472e7	−	3.69245e7i	−0.0919513	−	0.139452i
$256$	−6.10430e7	+	4.43503e7i	−0.227403	+	0.165218i
$257$	−1.32692e8	+	1.82635e8i	−0.487616	+	0.671146i	−0.979946	−	0.199263i	$-0.936145\pi$
$257$	−1.32692e8	+	1.82635e8i	−0.487616	+	0.671146i	0.492330	+	0.870409i	$0.336145\pi$
$258$	−1.91712e7	−	7.20602e6i	−0.0694994	−	0.0261232i
$259$	−2.05201e8	+	6.66737e7i	−0.733887	+	0.238454i
$260$	3.31890e7	+	2.41132e7i	0.117108	+	0.0850841i
$261$	1.24428e8	+	1.08929e8i	0.433189	+	0.379230i
$262$	1.60029e7	−	4.92520e7i	0.0549725	−	0.169188i
$263$	1.37218e8			0.465121			0.232560	−	0.972582i	$-0.425290\pi$
$263$	1.37218e8			0.465121			0.232560	+	0.972582i	$0.425290\pi$
$264$	−1.20868e8	−	1.10426e8i	−0.404296	−	0.369366i
$265$	3.95332e7			0.130497
$266$	−3.59124e6	+	1.10527e7i	−0.0116993	+	0.0360067i
$267$	1.63508e7	−	3.60061e8i	0.0525713	−	1.15768i
$268$	3.30129e7	+	2.39853e7i	0.104764	+	0.0761156i
$269$	−2.64390e8	+	8.59054e7i	−0.828155	+	0.269084i	−0.692268	−	0.721641i	$-0.743388\pi$
$269$	−2.64390e8	+	8.59054e7i	−0.828155	+	0.269084i	−0.135887	+	0.990724i	$0.543388\pi$
$270$	−1.12939e6	+	8.24450e6i	−0.00349197	+	0.0254913i
$271$	5.47934e7	−	7.54166e7i	0.167238	−	0.230184i	−0.717169	−	0.696899i	$-0.754563\pi$
$271$	5.47934e7	−	7.54166e7i	0.167238	−	0.230184i	0.884408	+	0.466715i	$0.154563\pi$
$272$	3.79249e8	−	2.75541e8i	1.14270	−	0.830223i
$273$	−2.98083e8	+	1.96549e8i	−0.886681	+	0.584657i
$274$			5.07175e7i			0.148947i
$275$	2.62754e8	+	2.19034e8i	0.761876	+	0.635106i
$276$	4.41269e7	−	5.52766e7i	0.126334	−	0.158256i
$277$	3.70001e8	+	1.20221e8i	1.04598	+	0.339860i	0.781090	−	0.624419i	$-0.214664\pi$
$277$	3.70001e8	+	1.20221e8i	1.04598	+	0.339860i	0.264891	+	0.964278i	$0.414664\pi$
$278$	7.12711e7	+	9.80962e7i	0.198956	+	0.273839i
$279$	1.31949e8	−	3.07857e8i	0.363739	−	0.848662i
$280$	3.40386e6	+	1.04760e7i	0.00926655	+	0.0285195i
$281$	−2.13233e7	−	6.56263e7i	−0.0573300	−	0.176443i	0.918291	−	0.395906i	$-0.129570\pi$
$281$	−2.13233e7	−	6.56263e7i	−0.0573300	−	0.176443i	−0.975621	+	0.219463i	$0.929570\pi$
$282$	−9.16618e7	+	2.52477e7i	−0.243398	+	0.0670426i
$283$	−3.04423e8	−	4.19002e8i	−0.798407	−	1.09891i	−0.993010	−	0.118031i	$-0.962342\pi$
$283$	−3.04423e8	−	4.19002e8i	−0.798407	−	1.09891i	0.194603	−	0.980882i	$-0.437658\pi$
$284$	−5.38386e8	−	1.74932e8i	−1.39470	−	0.453164i
$285$	−6.01093e6	−	4.79847e6i	−0.0153810	−	0.0122785i
$286$	−1.83291e8	−	7.33665e7i	−0.463299	−	0.185446i
$287$		−	3.45489e8i		−	0.862676i
$288$	−3.08921e8	−	2.81149e7i	−0.762034	−	0.0693525i
$289$	−8.08009e8	+	5.87053e8i	−1.96913	+	1.43065i
$290$	3.61627e6	−	4.97737e6i	0.00870698	−	0.0119841i
$291$	2.35271e8	−	6.25925e8i	0.559684	−	1.48901i
$292$	3.78220e7	−	1.22891e7i	0.0889007	−	0.0288856i
$293$	−4.05172e8	−	2.94375e8i	−0.941028	−	0.683697i	0.00763968	−	0.999971i	$-0.497568\pi$
$293$	−4.05172e8	−	2.94375e8i	−0.941028	−	0.683697i	−0.948668	+	0.316274i	$0.897568\pi$
$294$	7.83930e7	+	3.55991e6i	0.179913	+	0.00817002i
$295$	−1.24668e7	+	3.83689e7i	−0.0282734	+	0.0870166i
$296$	−3.10372e8			−0.695603
$297$	5.02089e7	+	4.48689e8i	0.111207	+	0.993797i
$298$	5.86537e7			0.128392
$299$	5.50529e7	−	1.69435e8i	0.119105	−	0.366568i
$300$	4.25623e8	+	1.93280e7i	0.910124	+	0.0413297i
$301$	6.04850e7	+	4.39449e7i	0.127839	+	0.0928807i
$302$	1.58503e8	−	5.15008e7i	0.331142	−	0.107594i
$303$	7.03751e7	−	1.87229e8i	0.145335	−	0.386656i
$304$	4.79160e7	−	6.59507e7i	0.0978189	−	0.134636i
$305$	7.66420e6	−	5.56837e6i	0.0154674	−	0.0112377i
$306$	2.64024e8	+	2.40287e7i	0.526766	+	0.0479409i
$307$		−	4.42604e8i		−	0.873035i	−0.899696	−	0.436517i	$-0.856212\pi$
$307$		−	4.42604e8i		−	0.873035i	0.899696	−	0.436517i	$-0.143788\pi$
$308$	1.52407e8	+	2.42158e8i	0.297220	+	0.472249i
$309$	−6.33698e6	−	5.05876e6i	−0.0122188	−	0.00975415i
$310$	−1.18510e7	−	3.85064e6i	−0.0225939	−	0.00734119i
$311$	2.25257e8	+	3.10040e8i	0.424636	+	0.584462i	0.966712	−	0.255868i	$-0.0823613\pi$
$311$	2.25257e8	+	3.10040e8i	0.424636	+	0.584462i	−0.542075	+	0.840330i	$0.682361\pi$
$312$	−4.95176e8	+	1.36394e8i	−0.923036	+	0.254245i
$313$	2.27680e8	+	7.00728e8i	0.419682	+	1.29165i	0.907995	+	0.418980i	$0.137612\pi$
$313$	2.27680e8	+	7.00728e8i	0.419682	+	1.29165i	−0.488313	+	0.872668i	$0.662388\pi$
$314$	5.03083e6	+	1.54833e7i	0.00917036	+	0.0282235i
$315$	1.19668e7	−	2.79205e7i	0.0215721	−	0.0503311i
$316$	7.01274e7	+	9.65221e7i	0.125021	+	0.172077i
$317$	3.19413e8	+	1.03783e8i	0.563177	+	0.182987i	0.576750	−	0.816921i	$-0.304321\pi$
$317$	3.19413e8	+	1.03783e8i	0.563177	+	0.182987i	−0.0135734	+	0.999908i	$0.504321\pi$
$318$	−1.47840e8	+	1.85195e8i	−0.257808	+	0.322949i
$319$	1.24043e8	−	3.09898e8i	0.213947	−	0.534504i
$320$		−	2.87332e7i		−	0.0490185i
$321$	−4.28929e8	+	2.82826e8i	−0.723798	+	0.477256i
$322$	1.85281e7	−	1.34615e7i	0.0309269	−	0.0224697i
$323$	−1.44030e8	+	1.98240e8i	−0.237817	+	0.327328i
$324$	3.87798e8	+	4.07233e8i	0.633430	+	0.665174i
$325$	1.02065e9	−	3.31628e8i	1.64924	−	0.535870i
$326$	−4.29111e7	−	3.11767e7i	−0.0685974	−	0.0498390i
$327$	−2.27581e7	+	5.01159e8i	−0.0359931	+	0.792608i
$328$	1.53577e8	−	4.72662e8i	0.240308	−	0.739593i
$329$	3.47065e8			0.537311
$330$	1.64546e7	−	3.37318e6i	0.0252052	−	0.00516703i
$331$	5.64590e8			0.855727			0.427864	−	0.903843i	$-0.359266\pi$
$331$	5.64590e8			0.855727			0.427864	+	0.903843i	$0.359266\pi$
$332$	−1.69925e8	+	5.22977e8i	−0.254844	+	0.784330i
$333$	6.44013e8	+	5.63794e8i	0.955740	+	0.836692i
$334$	1.31551e8	+	9.55777e7i	0.193189	+	0.140360i
$335$	−8.31658e6	+	2.70222e6i	−0.0120861	+	0.00392703i
$336$	3.01375e8	+	1.13280e8i	0.433431	+	0.162917i
$337$	−6.57054e8	+	9.04357e8i	−0.935182	+	1.28717i	0.0226215	+	0.999744i	$0.492799\pi$
$337$	−6.57054e8	+	9.04357e8i	−0.935182	+	1.28717i	−0.957804	+	0.287424i	$0.907201\pi$
$338$	−3.37155e8	+	2.44957e8i	−0.474921	+	0.345050i
$339$	−1.18452e7	−	1.79642e7i	−0.0165136	−	0.0250443i
$340$			1.11195e8i			0.153429i
$341$	−6.74579e8	−	4.49812e7i	−0.921281	−	0.0614315i
$342$	4.49573e7	−	1.02139e7i	0.0607727	−	0.0138070i
$343$	−7.04235e8	−	2.28820e8i	−0.942297	−	0.306171i
$344$	6.32148e7	+	8.70077e7i	0.0837267	+	0.115240i
$345$	4.02501e6	+	1.46128e7i	0.00527716	+	0.0191587i
$346$	−1.23909e7	−	3.81353e7i	−0.0160819	−	0.0494949i
$347$	−3.78631e8	−	1.16531e9i	−0.486477	−	1.49722i	−0.829830	−	0.558017i	$-0.811562\pi$
$347$	−3.78631e8	−	1.16531e9i	−0.486477	−	1.49722i	0.343352	−	0.939207i	$-0.388438\pi$
$348$	−1.10406e8	−	4.00829e8i	−0.140432	−	0.509838i
$349$	−5.35044e8	−	7.36425e8i	−0.673753	−	0.927341i	0.326085	−	0.945340i	$-0.394270\pi$
$349$	−5.35044e8	−	7.36425e8i	−0.673753	−	0.927341i	−0.999838	+	0.0179992i	$0.994270\pi$
$350$	1.31205e8	+	4.26312e7i	0.163574	+	0.0531483i
$351$	1.27524e9	+	6.16480e8i	1.57404	+	0.760928i
$352$	1.53437e8	+	6.07039e8i	0.187513	+	0.741852i
$353$		−	1.26540e9i		−	1.53114i	−0.643352	−	0.765571i	$-0.722457\pi$
$353$		−	1.26540e9i		−	1.53114i	0.643352	−	0.765571i	$-0.277543\pi$
$354$	−1.33119e8	−	2.01887e8i	−0.159489	−	0.241878i
$355$	9.81424e7	−	7.13046e7i	0.116428	−	0.0845899i
$356$	−5.32623e8	+	7.33092e8i	−0.625669	+	0.861159i
$357$	−9.05900e8	−	3.40507e8i	−1.05376	−	0.396084i
$358$	1.23470e8	−	4.01180e7i	0.142224	−	0.0462113i
$359$	5.10594e8	+	3.70968e8i	0.582432	+	0.423162i	0.839600	−	0.543205i	$-0.182789\pi$
$359$	5.10594e8	+	3.70968e8i	0.582432	+	0.423162i	−0.257168	+	0.966367i	$0.582789\pi$
$360$	2.87831e7	−	3.28784e7i	0.0325146	−	0.0371409i
$361$	2.63054e8	−	8.09596e8i	0.294286	−	0.905719i
$362$	2.15071e8			0.238288
$363$	8.20689e8	−	3.96210e8i	0.900545	−	0.434763i
$364$	8.97648e8			0.975554
$365$	−2.63350e6	+	8.10507e6i	−0.00283470	+	0.00872432i
$366$	−2.57603e6	+	5.67269e7i	−0.00274642	+	0.0604791i
$367$	−1.09832e9	−	7.97977e8i	−1.15984	−	0.842673i	−0.170082	−	0.985430i	$-0.554403\pi$
$367$	−1.09832e9	−	7.97977e8i	−1.15984	−	0.842673i	−0.989758	+	0.142757i	$0.954403\pi$
$368$	−1.52785e8	+	4.96427e7i	−0.159813	+	0.0519264i
$369$	−1.17726e9	+	7.01786e8i	−1.21978	+	0.727131i
$370$	1.87170e7	−	2.57618e7i	0.0192101	−	0.0264405i
$371$	6.99826e8	−	5.08453e8i	0.711510	−	0.516943i
$372$	−7.02999e8	+	4.63541e8i	−0.708035	+	0.466862i
$373$			1.32826e9i			1.32526i	0.748945	+	0.662632i	$0.230561\pi$
$373$			1.32826e9i			1.32526i	−0.748945	+	0.662632i	$0.769439\pi$
$374$	−1.31137e8	−	5.18814e8i	−0.129621	−	0.512815i
$375$	−1.14391e8	+	1.43294e8i	−0.112016	+	0.140320i
$376$	4.74819e8	+	1.54278e8i	0.460649	+	0.149674i
$377$	−6.15537e8	−	8.47214e8i	−0.591643	−	0.814326i
$378$	8.60432e7	+	1.60471e8i	0.0819399	+	0.152819i
$379$	−1.72376e8	−	5.30518e8i	−0.162644	−	0.500567i	0.836211	−	0.548408i	$-0.184766\pi$
$379$	−1.72376e8	−	5.30518e8i	−0.162644	−	0.500567i	−0.998855	+	0.0478408i	$0.984766\pi$
$380$	5.97531e6	+	1.83901e7i	0.00558622	+	0.0171926i
$381$	9.98354e8	−	2.74991e8i	0.924798	−	0.254731i
$382$	2.49390e8	+	3.43256e8i	0.228906	+	0.315062i
$383$	−1.59124e9	−	5.17026e8i	−1.44724	−	0.470237i	−0.523095	−	0.852275i	$-0.675223\pi$
$383$	−1.59124e9	−	5.17026e8i	−1.44724	−	0.470237i	−0.924147	+	0.382037i	$0.875223\pi$
$384$	7.98138e8	+	6.37147e8i	0.719314	+	0.574223i
$385$	−6.11796e7	−	4.07949e6i	−0.0546379	−	0.00364328i
$386$		−	1.15325e8i		−	0.102063i
$387$	2.68814e7	−	2.95369e8i	0.0235757	−	0.259046i
$388$	−1.36005e9	+	9.88132e8i	−1.18207	+	0.858823i
$389$	2.61969e8	−	3.60569e8i	0.225645	−	0.310574i	−0.681151	−	0.732143i	$-0.738520\pi$
$389$	2.61969e8	−	3.60569e8i	0.225645	−	0.310574i	0.906796	+	0.421569i	$0.138520\pi$
$390$	1.85406e7	−	4.93263e7i	0.0158270	−	0.0421068i
$391$	4.59253e8	−	1.49220e8i	0.388538	−	0.126244i
$392$	−3.33377e8	−	2.42212e8i	−0.279534	−	0.203093i
$393$	7.49168e8	+	3.40205e7i	0.622594	+	0.0282727i
$394$	1.37829e8	−	4.24193e8i	0.113528	−	0.349403i
$395$	−2.55671e7			−0.0208733
$396$	5.15578e8	−	1.01122e9i	0.417216	−	0.818303i
$397$	4.32300e8			0.346752			0.173376	−	0.984856i	$-0.444532\pi$
$397$	4.32300e8			0.346752			0.173376	+	0.984856i	$0.444532\pi$
$398$	8.94233e7	−	2.75217e8i	0.0710984	−	0.218818i
$399$	−1.68122e8	−	7.63459e6i	−0.132501	−	0.00601700i
$400$	−7.82892e8	−	5.68804e8i	−0.611634	−	0.444378i
$401$	−7.83869e8	+	2.54695e8i	−0.607070	+	0.197249i	−0.596391	−	0.802694i	$-0.703399\pi$
$401$	−7.83869e8	+	2.54695e8i	−0.607070	+	0.197249i	−0.0106786	+	0.999943i	$0.503399\pi$
$402$	1.84423e7	−	4.90646e7i	0.0141587	−	0.0376684i
$403$	−1.24670e9	+	1.71594e9i	−0.948844	+	1.30597i
$404$	−4.06822e8	+	2.95574e8i	−0.306952	+	0.223013i
$405$	−1.19448e8	+	1.59371e7i	−0.0893483	+	0.0119211i
$406$		−	1.34621e8i		−	0.0998322i
$407$	6.42022e8	−	1.60396e9i	0.472030	−	1.17927i
$408$	−1.08800e9	−	8.68538e8i	−0.793079	−	0.633109i
$409$	−1.13444e9	−	3.68603e8i	−0.819881	−	0.266396i	−0.131104	−	0.991369i	$-0.541852\pi$
$409$	−1.13444e9	−	3.68603e8i	−0.819881	−	0.266396i	−0.688777	+	0.724973i	$0.741852\pi$
$410$	2.99708e7	+	4.12513e7i	0.0214761	+	0.0295593i
$411$	−7.08087e8	+	1.95039e8i	−0.503084	+	0.138572i
$412$	6.29944e6	+	1.93877e7i	0.00443774	+	0.0136579i
$413$	2.72788e8	+	8.39555e8i	0.190546	+	0.586441i
$414$	−8.35063e7	−	3.57911e7i	−0.0578386	−	0.0247899i
$415$	−6.92638e7	−	9.53334e7i	−0.0475705	−	0.0654752i
$416$	1.86818e9	+	6.07008e8i	1.27231	+	0.413398i
$417$	−1.09548e9	+	1.37228e9i	−0.739824	+	0.926760i
$418$	−4.95680e7	−	7.87580e7i	−0.0331959	−	0.0527445i
$419$			1.33007e9i			0.883334i	0.897179	+	0.441667i	$0.145613\pi$
$419$			1.33007e9i			0.883334i	−0.897179	+	0.441667i	$0.854387\pi$
$420$	−6.37572e7	+	4.20400e7i	−0.0419910	+	0.0276879i
$421$	9.72010e8	−	7.06206e8i	0.634868	−	0.461258i	−0.223215	−	0.974769i	$-0.571655\pi$
$421$	9.72010e8	−	7.06206e8i	0.634868	−	0.461258i	0.858083	+	0.513511i	$0.171655\pi$
$422$	−3.87502e8	+	5.33350e8i	−0.251004	+	0.345477i
$423$	−7.04988e8	−	1.18263e9i	−0.452887	−	0.759730i
$424$	1.18345e9	−	3.84525e8i	0.753995	−	0.244988i
$425$	2.35328e9	+	1.70976e9i	1.48701	+	1.08037i
$426$	−3.29868e7	+	7.26405e8i	−0.0206732	+	0.455245i
$427$	6.40562e7	−	1.97145e8i	0.0398166	−	0.122543i
$428$	1.29168e9			0.796345
$429$	3.19435e8	−	2.84114e9i	0.195336	−	1.73737i
$430$	−1.10341e7			−0.00669262
$431$	−4.13162e8	+	1.27158e9i	−0.248571	+	0.765022i	0.746458	+	0.665433i	$0.231753\pi$
$431$	−4.13162e8	+	1.27158e9i	−0.248571	+	0.765022i	−0.995029	+	0.0995892i	$0.968247\pi$
$432$	−2.26174e8	−	1.25705e9i	−0.134974	−	0.750169i
$433$	1.25788e9	+	9.13901e8i	0.744613	+	0.540993i	0.894152	−	0.447763i	$-0.147779\pi$
$433$	1.25788e9	+	9.13901e8i	0.744613	+	0.540993i	−0.149540	+	0.988756i	$0.547779\pi$
$434$	−2.59314e8	+	8.42563e7i	−0.152269	+	0.0494753i
$435$	8.33977e7	+	3.13473e7i	0.0485782	+	0.0182594i
$436$	7.41341e8	−	1.02037e9i	0.428367	−	0.589596i
$437$	6.79356e7	−	4.93581e7i	0.0389415	−	0.0282927i
$438$	−2.81202e7	−	4.26467e7i	−0.0159904	−	0.0242508i
$439$			9.96191e8i			0.561975i	0.959711	+	0.280987i	$0.0906619\pi$
$439$			9.96191e8i			0.561975i	−0.959711	+	0.280987i	$0.909338\pi$
$440$	−8.18862e7	−	3.27768e7i	−0.0458275	−	0.0183435i
$441$	2.51766e8	+	1.10817e9i	0.139786	+	0.615276i
$442$	−1.59666e9	−	5.18788e8i	−0.879500	−	0.285767i
$443$	6.45536e8	+	8.88505e8i	0.352783	+	0.485564i	0.948120	−	0.317912i	$-0.102982\pi$
$443$	6.45536e8	+	8.88505e8i	0.352783	+	0.485564i	−0.595337	+	0.803476i	$0.702982\pi$
$444$	−5.71438e8	−	2.07460e9i	−0.309834	−	1.12485i
$445$	−6.00060e7	−	1.84680e8i	−0.0322801	−	0.0993479i
$446$	2.65797e8	+	8.18038e8i	0.141866	+	0.436618i
$447$	2.25558e8	+	8.18887e8i	0.119449	+	0.433658i
$448$	−3.69550e8	−	5.08642e8i	−0.194178	−	0.267263i
$449$	−2.08307e9	−	6.76831e8i	−1.08603	−	0.352873i	−0.289319	−	0.957233i	$-0.593429\pi$
$449$	−2.08307e9	−	6.76831e8i	−1.08603	−	0.352873i	−0.796712	+	0.604360i	$0.793429\pi$
$450$	−1.21248e8	−	5.33682e8i	−0.0627236	−	0.276082i
$451$	2.12497e9	+	1.77140e9i	1.09078	+	0.909280i
$452$			5.40974e7i			0.0275545i
$453$	1.32856e9	+	2.01488e9i	0.671488	+	1.01837i
$454$	−5.65604e8	+	4.10935e8i	−0.283672	+	0.206100i
$455$	−1.13067e8	+	1.55624e8i	−0.0562725	+	0.0774525i
$456$	−2.26613e8	−	8.51786e7i	−0.111920	−	0.0420682i
$457$	4.90449e8	−	1.59357e8i	0.240374	−	0.0781022i	−0.186353	−	0.982483i	$-0.559667\pi$
$457$	4.90449e8	−	1.59357e8i	0.240374	−	0.0781022i	0.426727	+	0.904381i	$0.359667\pi$
$458$	−2.41922e7	−	1.75767e7i	−0.0117665	−	0.00854884i
$459$	6.79852e8	+	3.77855e9i	0.328148	+	1.82381i
$460$	1.17753e7	−	3.62407e7i	0.00564053	−	0.0173598i
$461$	3.66520e9			1.74238			0.871192	−	0.490942i	$-0.163347\pi$
$461$	3.66520e9			1.74238			0.871192	+	0.490942i	$0.163347\pi$
$462$	2.47900e8	−	2.71343e8i	0.116958	−	0.128018i
$463$	3.39685e9			1.59053			0.795267	−	0.606260i	$-0.207331\pi$
$463$	3.39685e9			1.59053			0.795267	+	0.606260i	$0.207331\pi$
$464$	−2.91805e8	+	8.98085e8i	−0.135606	+	0.417354i
$465$	8.18603e6	−	1.80265e8i	0.00377562	−	0.0831431i
$466$	1.43155e8	+	1.04008e8i	0.0655321	+	0.0476119i
$467$	−1.63739e9	+	5.32019e8i	−0.743947	+	0.241723i	−0.656375	−	0.754435i	$-0.727911\pi$
$467$	−1.63739e9	+	5.32019e8i	−0.743947	+	0.241723i	−0.0875726	+	0.996158i	$0.527911\pi$
$468$	−1.82338e9	−	3.05876e9i	−0.822273	−	1.37938i
$469$	−1.12467e8	+	1.54798e8i	−0.0503410	+	0.0692885i
$470$	−4.14395e7	+	3.01076e7i	−0.0184108	+	0.0133762i
$471$	−1.96822e8	+	1.29780e8i	−0.0867963	+	0.0572314i
$472$			1.26985e9i			0.555848i
$473$	−5.80408e8	+	1.46706e8i	−0.252185	+	0.0637430i
$474$	9.56113e7	−	1.19770e8i	0.0412368	−	0.0516563i
$475$	4.81080e8	+	1.56312e8i	0.205963	+	0.0669215i
$476$	1.43012e9	+	1.96839e9i	0.607782	+	0.836541i
$477$	−3.15411e9	−	1.35186e9i	−1.33065	−	0.570320i
$478$	−2.12888e8	−	6.55202e8i	−0.0891567	−	0.274396i
$479$	−8.74177e7	−	2.69044e8i	−0.0363434	−	0.111853i	0.931239	−	0.364409i	$-0.118729\pi$
$479$	−8.74177e7	−	2.69044e8i	−0.0363434	−	0.111853i	−0.967582	+	0.252556i	$0.918729\pi$
$480$	−1.61119e8	+	4.43794e7i	−0.0664972	+	0.0183163i
$481$	−3.18589e9	−	4.38500e9i	−1.30534	−	1.79664i
$482$	3.68459e8	+	1.19719e8i	0.149873	+	0.0486968i
$483$	2.59193e8	+	2.06911e8i	0.104667	+	0.0835545i
$484$	−2.27085e9	−	3.04195e8i	−0.910394	−	0.121953i
$485$		−	3.60253e8i		−	0.143388i
$486$	3.72033e8	−	6.19158e8i	0.147013	−	0.244666i
$487$	−3.18996e9	+	2.31764e9i	−1.25151	+	0.909274i	−0.998308	−	0.0581395i	$-0.981483\pi$
$487$	−3.18996e9	+	2.31764e9i	−1.25151	+	0.909274i	−0.253200	+	0.967414i	$0.581483\pi$
$488$	1.75270e8	−	2.41239e8i	0.0682714	−	0.0939675i
$489$	2.70252e8	−	7.18992e8i	0.104517	−	0.278063i
$490$	4.02087e7	−	1.30646e7i	0.0154395	−	0.00501660i
$491$	−9.47255e7	−	6.88221e7i	−0.0361145	−	0.0262387i	0.569582	−	0.821935i	$-0.307105\pi$
$491$	−9.47255e7	−	6.88221e7i	−0.0361145	−	0.0262387i	−0.605696	+	0.795696i	$0.707105\pi$
$492$	3.44215e9	+	1.56312e8i	1.30302	+	0.0591716i
$493$	8.77134e8	−	2.69954e9i	0.329687	−	1.01467i
$494$	−2.91945e8			−0.108958
$495$	1.10372e8	+	2.16758e8i	0.0409017	+	0.0803261i
$496$	1.91258e9			0.703774
$497$	8.20259e8	−	2.52450e9i	0.299712	−	0.922418i
$498$	7.05614e8	+	3.20427e7i	0.256015	+	0.0116259i
$499$	1.81606e9	+	1.31944e9i	0.654301	+	0.475378i	0.864734	−	0.502231i	$-0.167487\pi$
$499$	1.81606e9	+	1.31944e9i	0.654301	+	0.475378i	−0.210433	+	0.977608i	$0.567487\pi$
$500$	4.38402e8	−	1.42445e8i	0.156847	−	0.0509628i
$501$	−8.28506e8	+	2.20420e9i	−0.294350	+	0.783102i
$502$	−7.73221e8	+	1.06425e9i	−0.272798	+	0.375474i
$503$	−1.44729e9	+	1.05151e9i	−0.507068	+	0.368407i	−0.811710	−	0.584060i	$-0.801463\pi$
$503$	−1.44729e9	+	1.05151e9i	−0.507068	+	0.368407i	0.304642	+	0.952467i	$0.401463\pi$
$504$	8.66606e7	−	9.52212e8i	0.0301519	−	0.331304i
$505$		−	1.07760e8i		−	0.0372339i
$506$	−1.22012e7	+	1.82980e8i	−0.00418673	+	0.0627879i
$507$	−4.71651e9	−	3.76515e9i	−1.60728	−	1.28308i
$508$	−2.47598e9	−	8.04495e8i	−0.837962	−	0.272270i
$509$	−1.38804e9	−	1.91047e9i	−0.466541	−	0.642139i	0.509308	−	0.860584i	$-0.329901\pi$
$509$	−1.38804e9	−	1.91047e9i	−0.466541	−	0.642139i	−0.975849	+	0.218446i	$0.929901\pi$
$510$	1.37703e8	−	3.79295e7i	0.0459671	−	0.0126614i
$511$	5.76239e7	+	1.77348e8i	0.0191042	+	0.0587968i
$512$	−9.39083e8	−	2.89020e9i	−0.309214	−	0.951662i
$513$	3.15488e8	+	5.88388e8i	0.103174	+	0.192421i
$514$	−4.28509e8	−	5.89792e8i	−0.139184	−	0.191570i
$515$	−4.15468e6	−	1.34994e6i	−0.00134033	−	0.000435500i
$516$	−4.65194e8	+	5.82737e8i	−0.149060	+	0.186723i
$517$	−1.77948e9	+	2.13467e9i	−0.566338	+	0.679381i
$518$		−	6.96767e8i		−	0.220259i
$519$	4.84771e8	−	3.19647e8i	0.152213	−	0.100366i
$520$	−2.23865e8	+	1.62647e8i	−0.0698191	+	0.0507265i
$521$	−3.46092e8	+	4.76354e8i	−0.107216	+	0.147570i	−0.859253	−	0.511551i	$-0.829071\pi$
$521$	−3.46092e8	+	4.76354e8i	−0.107216	+	0.147570i	0.752037	+	0.659121i	$0.229071\pi$
$522$	−4.58724e8	+	2.73453e8i	−0.141158	+	0.0841464i
$523$	7.06949e8	−	2.29702e8i	0.216089	−	0.0702115i	−0.198972	−	0.980005i	$-0.563760\pi$
$523$	7.06949e8	−	2.29702e8i	0.216089	−	0.0702115i	0.415061	+	0.909794i	$0.363760\pi$
$524$	−1.52532e9	−	1.10821e9i	−0.463128	−	0.336482i
$525$	−9.06292e7	+	1.99575e9i	−0.0273345	+	0.601934i
$526$	−1.36933e8	+	4.21437e8i	−0.0410260	+	0.126265i
$527$	−5.74899e9			−1.71102
$528$	−2.24196e9	+	1.27284e9i	−0.662840	+	0.376317i
$529$	3.23934e9			0.951398
$530$	−3.94512e7	+	1.21418e8i	−0.0115105	+	0.0354257i
$531$	2.30670e9	−	2.63491e9i	0.668590	−	0.763720i
$532$	3.42299e8	+	2.48695e8i	0.0985633	+	0.0716104i
$533$	8.25429e9	−	2.68198e9i	2.36121	−	0.767204i
$534$	1.08954e9	+	4.09532e8i	0.309634	+	0.116384i
$535$	−1.62699e8	+	2.23936e8i	−0.0459353	+	0.0632245i
$536$	−2.22677e8	+	1.61785e8i	−0.0624596	+	0.0453796i
$537$	1.03492e9	+	1.56954e9i	0.288401	+	0.437384i
$538$		−	8.97746e8i		−	0.248551i
$539$	1.94133e9	−	1.22182e9i	0.533997	−	0.336082i
$540$	2.72761e8	+	1.31859e8i	0.0745426	+	0.0360357i
$541$	7.08462e7	+	2.30193e7i	0.0192365	+	0.00625032i	0.318619	−	0.947883i	$-0.396781\pi$
$541$	7.08462e7	+	2.30193e7i	0.0192365	+	0.00625032i	−0.299383	+	0.954133i	$0.596781\pi$
$542$	1.76947e8	+	2.43547e8i	0.0477360	+	0.0657030i
$543$	8.27077e8	+	3.00270e9i	0.221690	+	0.804845i
$544$	1.64529e9	+	5.06368e9i	0.438174	+	1.34856i
$545$	8.35206e7	+	2.57050e8i	0.0221007	+	0.0680189i
$546$	−3.06196e8	−	1.11164e9i	−0.0805053	−	0.292274i
$547$	−3.74005e9	−	5.14773e9i	−0.977060	−	1.34481i	−0.938398	−	0.345556i	$-0.887690\pi$
$547$	−3.74005e9	−	5.14773e9i	−0.977060	−	1.34481i	−0.0386621	−	0.999252i	$-0.512310\pi$
$548$	1.75610e9	+	5.70592e8i	0.455845	+	0.148113i
$549$	−8.01893e8	+	1.82183e8i	−0.206830	+	0.0469900i
$550$	−9.34926e8	+	5.88416e8i	−0.239612	+	0.150805i
$551$		−	4.93603e8i		−	0.125703i
$552$	2.62624e8	+	3.98292e8i	0.0664581	+	0.100789i
$553$	−4.52593e8	+	3.28828e8i	−0.113807	+	0.0826859i
$554$	−7.38466e8	+	1.01641e9i	−0.184521	+	0.253972i
$555$	4.31648e8	+	1.62247e8i	0.107178	+	0.0402856i
$556$	4.19843e9	−	1.36415e9i	1.03592	−	0.336590i
$557$	−3.44261e9	−	2.50120e9i	−0.844102	−	0.613276i	0.0794113	−	0.996842i	$-0.474696\pi$
$557$	−3.44261e9	−	2.50120e9i	−0.844102	−	0.613276i	−0.923514	+	0.383566i	$0.874696\pi$
$558$	8.13846e8	+	7.12472e8i	0.198300	+	0.173599i
$559$	−5.80379e8	+	1.78622e9i	−0.140530	+	0.432508i
$560$	1.73457e8			0.0417383
$561$	6.73907e9	−	3.82600e9i	1.61150	−	0.914903i
$562$	2.22837e8			0.0529553
$563$	−2.24934e9	+	6.92275e9i	−0.531221	+	1.63493i	0.220455	+	0.975397i	$0.429246\pi$
$563$	−2.24934e9	+	6.92275e9i	−0.531221	+	1.63493i	−0.751676	+	0.659533i	$0.770754\pi$
$564$	−1.57025e8	+	3.45785e9i	−0.0368546	+	0.811577i
$565$	−9.37877e6	−	6.81408e6i	−0.00218764	−	0.00158942i
$566$	1.59067e9	−	5.16840e8i	0.368742	−	0.119812i
$567$	−1.90952e9	+	1.81839e9i	−0.439930	+	0.418935i
$568$	2.24439e9	−	3.08913e9i	0.513900	−	0.707323i
$569$	1.99424e9	−	1.44890e9i	0.453821	−	0.329720i	−0.337281	−	0.941404i	$-0.609507\pi$
$569$	1.99424e9	−	1.44890e9i	0.453821	−	0.329720i	0.791103	+	0.611683i	$0.209507\pi$
$570$	2.07360e7	−	1.36728e7i	0.00468989	−	0.00309240i
$571$		−	6.44960e9i		−	1.44979i	−0.688857	−	0.724897i	$-0.741887\pi$
$571$		−	6.44960e9i		−	1.44979i	0.688857	−	0.724897i	$-0.258113\pi$
$572$	−4.60243e9	+	5.52110e9i	−1.02826	+	1.23350i
$573$	−3.83328e9	+	4.80185e9i	−0.851195	+	1.06627i
$574$	1.06110e9	+	3.44772e8i	0.234188	+	0.0760923i
$575$	−5.85924e8	−	8.06456e8i	−0.128530	−	0.176906i
$576$	−9.82551e8	+	2.29245e9i	−0.214228	+	0.499828i
$577$	2.56491e8	+	7.89398e8i	0.0555849	+	0.171073i	0.974995	−	0.222228i	$-0.0713330\pi$
$577$	2.56491e8	+	7.89398e8i	0.0555849	+	0.171073i	−0.919410	+	0.393301i	$0.871333\pi$
$578$	−9.96682e8	−	3.06747e9i	−0.214689	−	0.660744i
$579$	1.61010e9	−	4.43492e8i	0.344728	−	0.0949534i
$580$	−1.31658e8	−	1.81211e8i	−0.0280187	−	0.0385645i
$581$	−2.45224e9	−	7.96783e8i	−0.518737	−	0.168548i
$582$	1.68762e9	+	1.34721e9i	0.354850	+	0.283273i
$583$	−4.60850e8	+	6.91131e9i	−0.0963207	+	1.44451i
$584$			2.68244e8i			0.0557296i
$585$	7.59963e8	+	6.91641e7i	0.156945	+	0.0142835i
$586$	1.30844e9	−	9.50640e8i	0.268604	−	0.195153i
$587$	3.11767e9	−	4.29110e9i	0.636204	−	0.875660i	−0.362202	−	0.932100i	$-0.617975\pi$
$587$	3.11767e9	−	4.29110e9i	0.636204	−	0.875660i	0.998406	+	0.0564400i	$0.0179750\pi$
$588$	1.00522e9	−	2.67432e9i	0.203910	−	0.542492i
$589$	−9.50806e8	+	3.08936e8i	−0.191729	+	0.0622966i
$590$	−1.05401e8	−	7.65786e7i	−0.0211283	−	0.0153506i
$591$	6.45237e9	+	2.93009e8i	1.28577	+	0.0583881i
$592$	−1.51032e9	+	4.64829e9i	−0.299187	+	0.920804i
$593$	−6.89279e8			−0.135739			−0.0678694	−	0.997694i	$-0.521620\pi$
$593$	−6.89279e8			−0.135739			−0.0678694	+	0.997694i	$0.521620\pi$
$594$	−1.42816e9	−	2.93552e8i	−0.279592	−	0.0574688i
$595$	−5.21393e8			−0.101474
$596$	6.59877e8	−	2.03089e9i	0.127674	−	0.392939i
$597$	4.18630e9	+	1.90104e8i	0.805230	+	0.0365663i
$598$	4.65448e8	+	3.38168e8i	0.0890055	+	0.0646663i
$599$	−9.28054e9	+	3.01543e9i	−1.76433	+	0.573265i	−0.997634	−	0.0687485i	$-0.978099\pi$
$599$	−9.28054e9	+	3.01543e9i	−1.76433	+	0.573265i	−0.766694	+	0.642013i	$0.778099\pi$
$600$	−1.01114e9	+	2.69010e9i	−0.191110	+	0.508438i
$601$	−3.44857e9	+	4.74655e9i	−0.648005	+	0.891903i	−0.999011	−	0.0444707i	$-0.985840\pi$
$601$	−3.44857e9	+	4.74655e9i	−0.648005	+	0.891903i	0.351005	+	0.936373i	$0.385840\pi$
$602$	−1.95327e8	+	1.41914e8i	−0.0364901	+	0.0265116i
$603$	7.55933e8	+	6.87973e7i	0.140402	+	0.0127779i
$604$		−	6.06761e9i		−	1.12044i
$605$	3.38772e8	−	3.55376e8i	0.0621962	−	0.0652446i
$606$	5.04807e8	+	4.02984e8i	0.0921450	+	0.0735586i
$607$	6.44239e9	+	2.09326e9i	1.16919	+	0.379894i	0.828342	−	0.560222i	$-0.189284\pi$
$607$	6.44239e9	+	2.09326e9i	1.16919	+	0.379894i	0.340853	+	0.940117i	$0.389284\pi$
$608$	5.44218e8	+	7.49052e8i	0.0981998	+	0.135160i
$609$	1.87949e9	−	5.17696e8i	0.337194	−	0.0928783i
$610$	9.45381e6	+	2.90958e7i	0.00168637	+	0.00519011i
$611$	2.69422e9	+	8.29195e9i	0.477847	+	1.47066i
$612$	3.80237e9	−	8.87153e9i	0.670540	−	1.56448i
$613$	6.19070e8	+	8.52077e8i	0.108550	+	0.149406i	0.859835	−	0.510571i	$-0.170566\pi$
$613$	6.19070e8	+	8.52077e8i	0.108550	+	0.149406i	−0.751286	+	0.659977i	$0.770566\pi$
$614$	1.35937e9	+	4.41686e8i	0.237000	+	0.0770060i
$615$	−4.60670e8	+	5.77070e8i	−0.0798597	+	0.100038i
$616$	−1.87112e9	+	4.72950e8i	−0.322530	+	0.0815235i
$617$		−	2.02342e9i		−	0.346808i	−0.984851	−	0.173404i	$-0.944523\pi$
$617$		−	2.02342e9i		−	0.346808i	0.984851	−	0.173404i	$-0.0554766\pi$
$618$	2.18608e7	−	1.44145e7i	0.00372568	−	0.00245663i
$619$	−1.06147e9	+	7.71205e8i	−0.179883	+	0.130693i	−0.674083	−	0.738655i	$-0.735461\pi$
$619$	−1.06147e9	+	7.71205e8i	−0.179883	+	0.130693i	0.494200	+	0.869348i	$0.335461\pi$
$620$	−2.66658e8	+	3.67023e8i	−0.0449349	+	0.0618475i
$621$	1.78563e8	−	1.30350e9i	0.0299206	−	0.218419i
$622$	−1.17701e9	+	3.82435e8i	−0.196117	+	0.0637223i
$623$	−3.43748e9	−	2.49747e9i	−0.569550	−	0.413802i
$624$	−3.66909e8	+	8.07972e9i	−0.0604522	+	1.33122i
$625$	1.84024e9	−	5.66368e9i	0.301505	−	0.927937i
$626$	−2.37935e9			−0.387658
$627$	9.08953e8	−	9.94910e8i	0.147267	−	0.161193i
$628$	5.92711e8			0.0954959
$629$	4.53985e9	−	1.39722e10i	0.727385	−	2.23866i
$630$	7.38102e7	+	6.46163e7i	0.0117605	+	0.0102956i
$631$	2.71040e9	+	1.96922e9i	0.429467	+	0.312026i	0.781436	−	0.623985i	$-0.214488\pi$
$631$	2.71040e9	+	1.96922e9i	0.429467	+	0.312026i	−0.351968	+	0.936012i	$0.614488\pi$
$632$	−7.65363e8	+	2.48681e8i	−0.120603	+	0.0391862i
$633$	−8.93649e9	−	3.35902e9i	−1.40041	−	0.526380i
$634$	−6.37500e8	+	8.77443e8i	−0.0993499	+	0.136743i
$635$	4.51347e8	−	3.27923e8i	0.0699524	−	0.0508234i
$636$	4.74916e9	+	7.20249e9i	0.732009	+	1.11015i
$637$		−	7.19626e9i		−	1.10311i
$638$	8.28002e8	+	6.90229e8i	0.126229	+	0.105225i
$639$	−1.02685e10	+	2.33291e9i	−1.55687	+	0.353709i
$640$	5.23279e8	+	1.70024e8i	0.0789047	+	0.0256377i
$641$	1.78512e8	+	2.45701e8i	0.0267710	+	0.0368472i	0.822193	−	0.569209i	$-0.192751\pi$
$641$	1.78512e8	+	2.45701e8i	0.0267710	+	0.0368472i	−0.795422	+	0.606056i	$0.792751\pi$
$642$	−4.40603e8	−	1.59961e9i	−0.0657165	−	0.238584i
$643$	−2.46877e8	−	7.59811e8i	−0.0366221	−	0.112711i	0.931074	−	0.364830i	$-0.118873\pi$
$643$	−2.46877e8	−	7.59811e8i	−0.0366221	−	0.112711i	−0.967696	+	0.252118i	$0.918873\pi$
$644$	−2.57657e8	−	7.92987e8i	−0.0380138	−	0.116995i
$645$	−4.24325e7	−	1.54051e8i	−0.00622644	−	0.0226050i
$646$	−4.65123e8	−	6.40187e8i	−0.0678820	−	0.0934315i
$647$	4.07880e9	+	1.32528e9i	0.592062	+	0.192372i	0.589697	−	0.807625i	$-0.299247\pi$
$647$	4.07880e9	+	1.32528e9i	0.592062	+	0.192372i	0.00236483	+	0.999997i	$0.499247\pi$
$648$	−3.42072e9	+	1.63891e9i	−0.493861	+	0.236616i
$649$	−6.56243e9	−	2.62676e9i	−0.942341	−	0.377193i
$650$			3.46565e9i			0.494980i
$651$	−2.17355e9	−	3.29637e9i	−0.308771	−	0.468277i
$652$	−1.56227e9	+	1.13505e9i	−0.220744	+	0.160380i
$653$	6.04927e9	−	8.32610e9i	0.850172	−	1.17016i	−0.133653	−	0.991028i	$-0.542671\pi$
$653$	6.04927e9	−	8.32610e9i	0.850172	−	1.17016i	0.983825	−	0.179133i	$-0.0573293\pi$
$654$	−1.51650e9	−	5.70016e8i	−0.211992	−	0.0796829i
$655$	3.84257e8	−	1.24853e8i	0.0534290	−	0.0173601i
$656$	−6.33150e9	−	4.60010e9i	−0.875675	−	0.636215i
$657$	4.87268e8	−	5.56599e8i	0.0670331	−	0.0765709i
$658$	−3.46345e8	+	1.06594e9i	−0.0473934	+	0.145862i
$659$	−8.11241e7			−0.0110421			−0.00552104	−	0.999985i	$-0.501757\pi$
$659$	−8.11241e7			−0.0110421			−0.00552104	+	0.999985i	$0.501757\pi$
$660$	6.83243e7	−	6.07694e8i	0.00925063	−	0.0822776i
$661$	−1.10801e10			−1.49224			−0.746121	−	0.665810i	$-0.768086\pi$
$661$	−1.10801e10			−1.49224			−0.746121	+	0.665810i	$0.768086\pi$
$662$	−5.63419e8	+	1.73402e9i	−0.0754794	+	0.232302i
$663$	1.10289e9	−	2.42867e10i	0.146971	−	3.23647i
$664$	−3.00072e9	−	2.18015e9i	−0.397775	−	0.289000i
$665$	−8.62315e7	+	2.80183e7i	−0.0113708	+	0.00369459i
$666$	−2.37425e9	+	1.41533e9i	−0.311435	+	0.185651i
$667$	−5.71753e8	+	7.86950e8i	−0.0746050	+	0.102685i
$668$	4.78940e9	−	3.47970e9i	0.621675	−	0.451674i
$669$	−1.03988e10	+	6.85673e9i	−1.34274	+	0.885372i
$670$		−	2.82393e7i		−	0.00362737i
$671$	8.84134e8	+	1.40479e9i	0.112977	+	0.179507i
$672$	−2.28139e9	+	2.85784e9i	−0.290006	+	0.363283i
$673$	−4.31206e6	−	1.40107e6i	−0.000545295	−	0.000177177i	0.308744	−	0.951145i	$-0.400091\pi$
$673$	−4.31206e6	−	1.40107e6i	−0.000545295	−	0.000177177i	−0.309290	+	0.950968i	$0.600091\pi$
$674$	−2.12186e9	−	2.92049e9i	−0.266936	−	0.367406i
$675$	6.98468e9	−	3.74512e9i	0.874145	−	0.468708i
$676$	4.68856e9	+	1.44299e10i	0.583749	+	1.79660i
$677$	4.19398e9	+	1.29078e10i	0.519477	+	1.59879i	0.774985	+	0.631979i	$0.217757\pi$
$677$	4.19398e9	+	1.29078e10i	0.519477	+	1.59879i	−0.255508	+	0.966807i	$0.582243\pi$
$678$	6.69939e7	−	1.84531e7i	0.00825527	−	0.00227387i
$679$	−4.63336e9	−	6.37728e9i	−0.568005	−	0.781792i
$680$	−7.13316e8	−	2.31771e8i	−0.0869963	−	0.0282668i
$681$	−7.91231e9	−	6.31633e9i	−0.960038	−	0.766390i
$682$	8.11330e8	−	2.02694e9i	0.0979382	−	0.244679i
$683$			1.19787e10i			1.43859i	0.694702	+	0.719297i	$0.255536\pi$
$683$			1.19787e10i			1.43859i	−0.694702	+	0.719297i	$0.744464\pi$
$684$	1.52129e8	−	1.67156e9i	0.0181767	−	0.199722i
$685$	−3.20120e8	+	2.32581e8i	−0.0380536	+	0.0276475i
$686$	1.40555e9	−	1.93457e9i	0.166231	−	0.228797i
$687$	1.52362e8	−	4.05350e8i	0.0179278	−	0.0476959i
$688$	1.61069e9	−	5.23343e8i	0.188561	−	0.0612671i
$689$	1.75804e10	+	1.27729e10i	2.04768	+	1.48773i
$690$	−4.88969e7	−	2.22046e6i	−0.00566643	−	0.000257319i
$691$	3.38794e8	−	1.04270e9i	0.0390628	−	0.120223i	−0.929624	−	0.368511i	$-0.879868\pi$
$691$	3.38794e8	−	1.04270e9i	0.0390628	−	0.120223i	0.968686	+	0.248288i	$0.0798678\pi$
$692$	−1.45984e9			−0.167469
$693$	4.74164e9	+	2.41755e9i	0.541206	+	0.275937i
$694$	3.95684e9			0.449356
$695$	−2.92331e8	+	8.99701e8i	−0.0330314	+	0.101660i
$696$	2.80146e9	+	1.27217e8i	0.314957	+	0.0143025i
$697$	1.90318e10	+	1.38274e10i	2.12894	+	1.54677i
$698$	2.79571e9	−	9.08383e8i	0.311171	−	0.101106i
$699$	−9.01582e8	+	2.39861e9i	−0.0998470	+	0.265638i
$700$	2.95223e9	−	4.06339e9i	0.325317	−	0.447760i
$701$	−9.69081e9	+	7.04078e9i	−1.06254	+	0.771983i	−0.974557	−	0.224138i	$-0.928043\pi$
$701$	−9.69081e9	+	7.04078e9i	−1.06254	+	0.771983i	−0.0879867	+	0.996122i	$0.528043\pi$
$702$	−3.16598e9	+	3.30143e9i	−0.345405	+	0.360182i
$703$		−	2.55478e9i		−	0.277338i
$704$	5.02323e9	+	3.34951e8i	0.542598	+	0.0361807i
$705$	−5.79703e8	−	4.62772e8i	−0.0623080	−	0.0497399i
$706$	3.88641e9	+	1.26277e9i	0.415654	+	0.135054i
$707$	−1.38595e9	−	1.90760e9i	−0.147496	−	0.203010i
$708$	−8.48801e9	+	2.33798e9i	−0.898855	+	0.247585i
$709$	−1.62590e9	−	5.00402e9i	−0.171330	−	0.527299i	0.828117	−	0.560555i	$-0.189412\pi$
$709$	−1.62590e9	−	5.00402e9i	−0.171330	−	0.527299i	−0.999447	+	0.0332563i	$0.989412\pi$
$710$	1.21059e8	+	3.72581e8i	0.0126938	+	0.0390676i
$711$	2.03984e9	+	8.74282e8i	0.212839	+	0.0912237i
$712$	−3.59262e9	−	4.94482e9i	−0.373019	−	0.513417i
$713$	1.87372e9	+	6.08807e8i	0.193593	+	0.0629023i
$714$	1.94982e9	−	2.44249e9i	0.200470	−	0.251124i
$715$	−3.77463e8	−	1.49335e9i	−0.0386192	−	0.152788i
$716$		−	4.72653e9i		−	0.481223i
$717$	8.32886e9	−	5.49186e9i	0.843857	−	0.556419i
$718$	−1.64889e9	+	1.19799e9i	−0.166248	+	0.120786i
$719$	−3.51234e9	+	4.83432e9i	−0.352408	+	0.485048i	−0.948014	−	0.318229i	$-0.896912\pi$
$719$	−3.51234e9	+	4.83432e9i	−0.352408	+	0.485048i	0.595606	+	0.803277i	$0.296912\pi$
$720$	−3.52341e8	−	5.91061e8i	−0.0351803	−	0.0590159i
$721$	−9.09091e7	+	2.95381e7i	−0.00903304	+	0.00293501i
$722$	2.22400e9	+	1.61583e9i	0.219915	+	0.159778i
$723$	−2.54510e8	+	5.60459e9i	−0.0250450	+	0.551518i
$724$	2.41964e9	−	7.44688e9i	0.236955	−	0.729272i
$725$	−5.85950e9			−0.571054
$726$	3.97893e8	+	2.91597e9i	0.0385912	+	0.282816i
$727$	4.17977e9			0.403443			0.201721	−	0.979443i	$-0.435346\pi$
$727$	4.17977e9			0.403443			0.201721	+	0.979443i	$0.435346\pi$
$728$	−1.87103e9	+	5.75843e9i	−0.179730	+	0.553152i
$729$	1.00750e10	+	2.81308e9i	0.963160	+	0.268927i
$730$	−2.22650e7	−	1.61765e7i	−0.00211833	−	0.00153906i
$731$	−4.84153e9	+	1.57311e9i	−0.458429	+	0.148953i
$732$	1.93520e9	+	7.27395e8i	0.182363	+	0.0685460i
$733$	−6.12030e9	+	8.42387e9i	−0.573996	+	0.790037i	−0.993021	−	0.117937i	$-0.962372\pi$
$733$	−6.12030e9	+	8.42387e9i	−0.573996	+	0.790037i	0.419025	+	0.907975i	$0.362372\pi$
$734$	3.54687e9	−	2.57695e9i	0.331061	−	0.240530i
$735$	3.37026e8	+	5.11128e8i	0.0313082	+	0.0474815i
$736$		−	1.82459e9i		−	0.168692i
$737$	−3.75461e8	−	1.48543e9i	−0.0345485	−	0.136683i
$738$	−9.80572e8	−	4.31606e9i	−0.0898013	−	0.395266i
$739$	8.95244e9	+	2.90883e9i	0.815992	+	0.265132i	0.687134	−	0.726531i	$-0.258869\pi$
$739$	8.95244e9	+	2.90883e9i	0.815992	+	0.265132i	0.128859	+	0.991663i	$0.458869\pi$
$740$	−6.81432e8	−	9.37910e8i	−0.0618175	−	0.0850845i
$741$	−1.12270e9	−	4.07597e9i	−0.101368	−	0.368016i
$742$	8.63237e8	+	2.65677e9i	0.0775741	+	0.238748i
$743$	1.69655e9	+	5.22145e9i	0.151742	+	0.467015i	0.997816	−	0.0660508i	$-0.0210400\pi$
$743$	1.69655e9	+	5.22145e9i	0.151742	+	0.467015i	−0.846074	+	0.533065i	$0.821040\pi$
$744$	−1.50832e9	−	5.47595e9i	−0.134273	−	0.487477i
$745$	2.68975e8	+	3.70212e8i	0.0238322	+	0.0328022i
$746$	−4.07949e9	−	1.32551e9i	−0.359766	−	0.116895i
$747$	2.26614e9	+	9.97459e9i	0.198914	+	0.875534i
$748$	−1.94394e10	−	1.29623e9i	−1.69835	−	0.113247i
$749$			6.05670e9i			0.526683i
$750$	−3.25946e8	−	4.94325e8i	−0.0282119	−	0.0427857i
$751$	−6.75114e9	+	4.90499e9i	−0.581617	+	0.422570i	−0.839307	−	0.543658i	$-0.817039\pi$
$751$	−6.75114e9	+	4.90499e9i	−0.581617	+	0.422570i	0.257690	+	0.966228i	$0.417039\pi$
$752$	4.62109e9	−	6.36038e9i	0.396262	−	0.545407i
$753$	−1.78319e10	−	6.70259e9i	−1.52200	−	0.572084i
$754$	3.21631e9	−	1.04504e9i	0.273249	−	0.0887838i
$755$	1.05193e9	+	7.64272e8i	0.0889554	+	0.0646299i
$756$	6.52437e9	−	1.17389e9i	0.549177	−	0.0988104i
$757$	3.82669e9	−	1.17773e10i	0.320618	−	0.986761i	−0.652762	−	0.757563i	$-0.726390\pi$
$757$	3.82669e9	−	1.17773e10i	0.320618	−	0.986761i	0.973380	−	0.229198i	$-0.0736102\pi$
$758$	1.80140e9			0.150234
$759$	−2.60157e9	+	5.33319e8i	−0.215968	+	0.0442732i
$760$	−1.30428e8			−0.0107776
$761$	2.60986e9	−	8.03234e9i	0.214670	−	0.660687i	−0.784507	−	0.620120i	$-0.787084\pi$
$761$	2.60986e9	−	8.03234e9i	0.214670	−	0.660687i	0.999177	−	0.0405665i	$-0.0129163\pi$
$762$	−1.51703e8	+	3.34066e9i	−0.0124209	+	0.273521i
$763$	4.78452e9	+	3.47616e9i	0.389945	+	0.283311i
$764$	1.46910e10	−	4.77340e9i	1.19186	−	0.387259i
$765$	1.05910e9	+	1.77666e9i	0.0855305	+	0.143480i
$766$	3.17588e9	−	4.37123e9i	0.255308	−	0.351401i
$767$	−1.79407e10	+	1.30347e10i	−1.43567	+	1.04308i
$768$	2.94585e9	−	1.94242e9i	0.234664	−	0.154732i
$769$		−	1.23440e10i		−	0.978847i	−0.872046	−	0.489423i	$-0.837207\pi$
$769$		−	1.23440e10i		−	0.978847i	0.872046	−	0.489423i	$-0.162793\pi$
$770$	7.35820e7	−	1.83830e8i	0.00580837	−	0.0145110i
$771$	6.58645e9	−	8.25068e9i	0.517560	−	0.648335i
$772$	−3.99314e9	−	1.29745e9i	−0.312359	−	0.101492i
$773$	6.11959e9	+	8.42290e9i	0.476535	+	0.655894i	0.977834	−	0.209380i	$-0.0671446\pi$
$773$	6.11959e9	+	8.42290e9i	0.476535	+	0.655894i	−0.501300	+	0.865274i	$0.667145\pi$
$774$	8.80340e8	+	3.77317e8i	0.0682428	+	0.0292491i
$775$	3.66734e9	+	1.12869e10i	0.283005	+	0.871001i
$776$	−3.50405e9	−	1.07844e10i	−0.269187	−	0.828473i
$777$	9.72785e9	−	2.67948e9i	0.743949	−	0.204917i
$778$	8.45991e8	+	1.16441e9i	0.0644076	+	0.0886494i
$779$	3.89065e9	+	1.26415e9i	0.294877	+	0.0958113i
$780$	−1.49934e9	−	1.19691e9i	−0.113128	−	0.0903090i
$781$	1.13216e10	+	1.79887e10i	0.850412	+	1.35121i
$782$			1.55941e9i			0.116610i
$783$	−5.58185e9	−	5.35284e9i	−0.415539	−	0.398491i
$784$	−5.24976e9	+	3.81418e9i	−0.389075	+	0.282680i
$785$	−7.46575e7	+	1.02757e8i	−0.00550846	+	0.00758174i
$786$	−8.52100e8	+	2.26697e9i	−0.0625910	+	0.166520i
$787$	−3.72547e9	+	1.21048e9i	−0.272439	+	0.0885207i	−0.442050	−	0.896990i	$-0.645749\pi$
$787$	−3.72547e9	+	1.21048e9i	−0.272439	+	0.0885207i	0.169611	+	0.985511i	$0.445749\pi$
$788$	−1.31371e10	−	9.54469e9i	−0.956443	−	0.694897i
$789$	−6.41044e9	−	2.91105e8i	−0.464642	−	0.0210999i
$790$	2.55140e7	−	7.85240e7i	0.00184113	−	0.00566641i
$791$	−2.53664e8			−0.0182239
$792$	5.41237e9	+	5.41521e9i	0.387123	+	0.387326i
$793$	5.20737e9			0.370819
$794$	−4.31403e8	+	1.32772e9i	−0.0305852	+	0.0941316i
$795$	−1.84688e9	−	8.38689e7i	−0.130363	−	0.00591992i
$796$	−8.52338e9	−	6.19260e9i	−0.598985	−	0.435188i
$797$	4.45856e9	−	1.44867e9i	0.311954	−	0.101360i	−0.148856	−	0.988859i	$-0.547559\pi$
$797$	4.45856e9	−	1.44867e9i	0.311954	−	0.101360i	0.460810	+	0.887499i	$0.347559\pi$
$798$	1.91221e8	−	5.08733e8i	0.0133207	−	0.0354389i
$799$	−1.38905e10	+	1.91186e10i	−0.963392	+	1.32600i
$800$	8.89190e9	−	6.46035e9i	0.614016	−	0.446109i
$801$	−1.52773e9	+	1.67864e10i	−0.105034	+	1.15410i
$802$		−	2.66166e9i		−	0.182198i
$803$	−1.38625e9	−	5.54878e8i	−0.0944795	−	0.0378175i
$804$	−1.49139e9	−	1.19056e9i	−0.101203	−	0.0807898i
$805$	1.69933e8	+	5.52146e7i	0.0114813	+	0.00373051i
$806$	−4.02604e9	−	5.54137e9i	−0.270835	−	0.372773i
$807$	1.25338e10	−	3.45237e9i	0.839509	−	0.231238i
$808$	−1.04815e9	−	3.22586e9i	−0.0699007	−	0.215132i
$809$	−8.47776e9	−	2.60919e10i	−0.562939	−	1.73255i	−0.673997	−	0.738734i	$-0.735424\pi$
$809$	−8.47776e9	−	2.60919e10i	−0.562939	−	1.73255i	0.111058	−	0.993814i	$-0.464576\pi$
$810$	7.02525e7	−	3.82764e8i	0.00464477	−	0.0253066i
$811$	−1.21969e10	−	1.67876e10i	−0.802928	−	1.10514i	−0.992376	−	0.123245i	$-0.960670\pi$
$811$	−1.21969e10	−	1.67876e10i	−0.802928	−	1.10514i	0.189448	−	0.981891i	$-0.439330\pi$
$812$	−4.66127e9	−	1.51454e9i	−0.305533	−	0.0992736i
$813$	−2.71979e9	+	3.40701e9i	−0.177508	+	0.222360i
$814$	4.28555e9	+	3.57247e9i	0.278498	+	0.232158i
$815$		−	4.13818e8i		−	0.0267767i
$816$	−1.83020e10	+	1.20679e10i	−1.17919	+	0.777530i
$817$	−7.16191e8	+	5.20343e8i	−0.0459464	+	0.0333820i
$818$	2.26418e9	−	3.11637e9i	0.144635	−	0.199073i
$819$	1.43426e10	−	8.54984e9i	0.912291	−	0.543831i
$820$	1.76552e9	−	5.73651e8i	0.111821	−	0.0363329i
$821$	−8.66578e9	−	6.29606e9i	−0.546520	−	0.397070i	0.279980	−	0.960006i	$-0.409672\pi$
$821$	−8.66578e9	−	6.29606e9i	−0.546520	−	0.397070i	−0.826501	+	0.562935i	$0.809672\pi$
$822$	1.07596e8	−	2.36938e9i	0.00675686	−	0.148793i
$823$	−3.33286e9	+	1.02575e10i	−0.208409	+	0.641418i	0.791147	+	0.611626i	$0.209484\pi$
$823$	−3.33286e9	+	1.02575e10i	−0.208409	+	0.641418i	−0.999556	+	0.0297915i	$0.990516\pi$
$824$	−1.37503e8			−0.00856182
$825$	−1.18105e10	−	1.07901e10i	−0.732281	−	0.669014i
$826$	−2.85075e9			−0.176006
$827$	−2.54201e9	+	7.82351e9i	−0.156282	+	0.480986i	−0.998289	−	0.0584811i	$-0.981374\pi$
$827$	−2.54201e9	+	7.82351e9i	−0.156282	+	0.480986i	0.842007	+	0.539467i	$0.181374\pi$
$828$	−2.17875e9	+	2.48876e9i	−0.133383	+	0.152362i
$829$	−2.10350e10	−	1.52828e10i	−1.28233	−	0.931671i	−0.282714	−	0.959204i	$-0.591235\pi$
$829$	−2.10350e10	−	1.52828e10i	−1.28233	−	0.931671i	−0.999621	+	0.0275333i	$0.991235\pi$
$830$	3.61917e8	−	1.17594e8i	0.0219703	−	0.00713859i
$831$	−1.70304e10	−	6.40132e9i	−1.02949	−	0.386960i
$832$	9.28351e9	−	1.27777e10i	0.558831	−	0.769165i
$833$	1.57802e10	−	1.14650e10i	0.945920	−	0.687251i
$834$	−3.12148e9	−	4.73398e9i	−0.186328	−	0.282583i
$835$			1.26863e9i			0.0754107i
$836$	−3.28467e9	+	8.30242e8i	−0.194433	+	0.0491454i
$837$	−6.81739e9	+	1.41023e10i	−0.401864	+	0.831287i
$838$	−4.08504e9	−	1.32731e9i	−0.239796	−	0.0779144i
$839$	−2.04436e9	−	2.81382e9i	−0.119506	−	0.164486i	0.745073	−	0.666983i	$-0.232415\pi$
$839$	−2.04436e9	−	2.81382e9i	−0.119506	−	0.164486i	−0.864579	+	0.502497i	$0.832415\pi$
$840$	−1.36794e8	−	4.96630e8i	−0.00796324	−	0.0289105i
$841$	−3.56361e9	−	1.09677e10i	−0.206588	−	0.635812i
$842$	1.19898e9	+	3.69007e9i	0.0692179	+	0.213031i
$843$	8.56939e8	+	3.11111e9i	0.0492667	+	0.178863i
$844$	1.41078e10	+	1.94177e10i	0.807720	+	1.11173i
$845$	−3.09226e9	−	1.00474e9i	−0.176310	−	0.0572866i
$846$	4.33575e9	−	9.85046e8i	0.246188	−	0.0559320i
$847$	1.42638e9	−	1.06480e10i	0.0806570	−	0.602112i
$848$		−	1.95951e10i		−	1.10347i
$849$	1.33329e10	+	2.02204e10i	0.747734	+	1.13400i
$850$	−7.59958e9	+	5.52142e9i	−0.424447	+	0.308379i
$851$	−2.95927e9	+	4.07308e9i	−0.164600	+	0.226553i
$852$	2.47808e10	+	9.31452e9i	1.37270	+	0.515967i
$853$	2.20515e10	−	7.16496e9i	1.21651	−	0.395269i	0.370701	−	0.928752i	$-0.379117\pi$
$853$	2.20515e10	−	7.16496e9i	1.21651	−	0.395269i	0.845810	+	0.533484i	$0.179117\pi$
$854$	5.41567e8	+	3.93471e8i	0.0297543	+	0.0216178i
$855$	2.70634e8	+	2.36923e8i	0.0148082	+	0.0129636i
$856$	−2.69233e9	+	8.28614e9i	−0.146714	+	0.451538i
$857$	−4.98424e9			−0.270499			−0.135250	−	0.990812i	$-0.543184\pi$
$857$	−4.98424e9			−0.270499			−0.135250	+	0.990812i	$0.543184\pi$
$858$	8.40722e9	+	3.81633e9i	0.454409	+	0.206272i
$859$	1.62303e10			0.873674			0.436837	−	0.899541i	$-0.356099\pi$
$859$	1.62303e10			0.873674			0.436837	+	0.899541i	$0.356099\pi$
$860$	−1.24138e8	+	3.82056e8i	−0.00665517	+	0.0204825i
$861$	−7.32948e8	+	1.61403e10i	−0.0391347	+	0.861788i
$862$	−3.49310e9	−	2.53789e9i	−0.185753	−	0.134957i
$863$	−1.59938e10	+	5.19669e9i	−0.847057	+	0.275226i	−0.700213	−	0.713934i	$-0.746912\pi$
$863$	−1.59938e10	+	5.19669e9i	−0.847057	+	0.275226i	−0.146844	+	0.989160i	$0.546912\pi$
$864$	1.43723e10	+	1.96882e9i	0.758103	+	0.103850i
$865$	1.83881e8	−	2.53090e8i	0.00966006	−	0.0132959i
$866$	−4.06213e9	+	2.95131e9i	−0.212540	+	0.154419i
$867$	3.89934e10	−	2.57113e10i	2.03200	−	1.33985i
$868$			9.92671e9i			0.515213i
$869$	2.98042e8	−	4.46971e9i	0.0154067	−	0.231052i
$870$	−1.79501e8	+	2.24857e8i	−0.00924167	+	0.0115768i
$871$	−4.57145e9	−	1.48535e9i	−0.234418	−	0.0761669i
$872$	5.00046e9	+	6.88255e9i	0.255389	+	0.351513i
$873$	−1.23191e10	+	2.87424e10i	−0.626655	+	1.46209i
$874$	8.37988e7	+	2.57906e8i	0.00424569	+	0.0130669i
$875$	6.67929e8	+	2.05567e9i	0.0337056	+	0.103735i
$876$	−1.79301e9	+	4.93875e8i	−0.0901195	+	0.0248229i
$877$	3.53880e9	+	4.87074e9i	0.177157	+	0.243835i	0.888356	−	0.459155i	$-0.151848\pi$
$877$	3.53880e9	+	4.87074e9i	0.177157	+	0.243835i	−0.711200	+	0.702990i	$0.751848\pi$
$878$	−3.05960e9	−	9.94124e8i	−0.152557	−	0.0495689i
$879$	1.83040e10	+	1.46119e10i	0.909044	+	0.725682i
$880$	−8.89353e8	+	1.06687e9i	−0.0439931	+	0.0527744i
$881$		−	1.74908e10i		−	0.861776i	−0.902405	−	0.430888i	$-0.858200\pi$
$881$		−	1.74908e10i		−	0.861776i	0.902405	−	0.430888i	$-0.141800\pi$
$882$	−3.65475e9	−	3.32618e8i	−0.179357	−	0.0163232i
$883$	2.00083e10	−	1.45369e10i	0.978019	−	0.710572i	0.0207538	−	0.999785i	$-0.493393\pi$
$883$	2.00083e10	−	1.45369e10i	0.978019	−	0.710572i	0.957265	+	0.289212i	$0.0933934\pi$
$884$	−3.59262e10	+	4.94482e10i	−1.74916	+	2.40751i
$885$	6.63814e8	−	1.76604e9i	0.0321918	−	0.0856445i
$886$	−3.37306e9	+	1.09597e9i	−0.162932	+	0.0529397i
$887$	−6.66113e9	−	4.83959e9i	−0.320490	−	0.232850i	0.415894	−	0.909413i	$-0.363469\pi$
$887$	−6.66113e9	−	4.83959e9i	−0.320490	−	0.232850i	−0.736385	+	0.676563i	$0.763469\pi$
$888$	1.44997e10	+	6.58448e8i	0.694887	+	0.0315556i
$889$	3.77229e9	−	1.16099e10i	0.180073	−	0.554208i
$890$	6.27087e8			0.0298169
$891$	−1.39374e9	−	2.10680e10i	−0.0660098	−	0.997819i
$892$	3.13150e10			1.47732
$893$	−1.26992e9	+	3.90840e9i	−0.0596753	+	0.183662i
$894$	−2.74014e9	−	1.24432e8i	−0.128260	−	0.00582442i
$895$	8.19429e8	+	5.95350e8i	0.0382059	+	0.0277582i
$896$	1.14499e10	−	3.72031e9i	0.531771	−	0.172783i
$897$	−2.93137e9	+	7.79876e9i	−0.135612	+	0.360788i
$898$	4.15750e9	−	5.72231e9i	0.191587	−	0.263696i
$899$	9.36899e9	−	6.80697e9i	0.430065	−	0.312460i
$900$	−1.98429e10	−	1.80590e9i	−0.907313	−	0.0825743i
$901$			5.89005e10i			2.68276i
$902$	−7.56105e9	+	4.75871e9i	−0.343051	+	0.215907i
$903$	−2.73246e9	−	2.18130e9i	−0.123494	−	0.0985845i
$904$	−3.47036e8	−	1.12759e8i	−0.0156237	−	0.00507646i
$905$	9.86277e8	+	1.35749e9i	0.0442312	+	0.0608790i
$906$	−7.51409e9	+	2.06971e9i	−0.335682	+	0.0924616i
$907$	−1.07046e10	−	3.29454e10i	−0.476371	−	1.46612i	−0.844100	−	0.536186i	$-0.819865\pi$
$907$	−1.07046e10	−	3.29454e10i	−0.476371	−	1.46612i	0.367729	−	0.929933i	$-0.380135\pi$
$908$	7.86543e9	+	2.42073e10i	0.348676	+	1.07311i
$909$	−3.68493e9	+	8.59753e9i	−0.162726	+	0.379665i
$910$	−3.65134e8	−	5.02563e8i	−0.0160623	−	0.0221078i
$911$	−7.24459e9	−	2.35391e9i	−0.317468	−	0.103151i	0.145949	−	0.989292i	$-0.453377\pi$
$911$	−7.24459e9	−	2.35391e9i	−0.317468	−	0.103151i	−0.463416	+	0.886141i	$0.653377\pi$
$912$	−2.37841e9	+	2.97938e9i	−0.103826	+	0.130060i
$913$	1.74739e10	−	1.09976e10i	0.759874	−	0.478243i
$914$			1.66534e9i			0.0721426i
$915$	−3.69863e8	+	2.43879e8i	−0.0159613	+	0.0105245i
$916$	−8.80767e8	+	6.39915e8i	−0.0378640	+	0.0275098i
$917$	5.19641e9	−	7.15224e9i	0.222541	−	0.306302i
$918$	−1.22835e10	−	1.68268e9i	−0.524049	−	0.0717879i
$919$	−8.35684e9	+	2.71530e9i	−0.355171	+	0.115402i	−0.481168	−	0.876629i	$-0.659787\pi$
$919$	−8.35684e9	+	2.71530e9i	−0.355171	+	0.115402i	0.125996	+	0.992031i	$0.459787\pi$
$920$	2.07941e8	+	1.51078e8i	0.00880404	+	0.00639651i
$921$	−9.38976e8	+	2.06773e10i	−0.0396046	+	0.872136i
$922$	−3.65759e9	+	1.12569e10i	−0.153687	+	0.473000i
$923$	6.66819e10			2.79127
$924$	−6.60631e9	−	1.16363e10i	−0.275491	−	0.485246i
$925$	−3.03275e10			−1.25991
$926$	−3.38980e9	+	1.04327e10i	−0.140293	+	0.431777i
$927$	2.85314e8	+	2.49775e8i	0.0117637	+	0.0102984i
$928$	−8.67684e9	−	6.30409e9i	−0.356405	−	0.258943i
$929$	−2.65879e10	+	8.63894e9i	−1.08800	+	0.353513i	−0.797474	−	0.603354i	$-0.793831\pi$
$929$	−2.65879e10	+	8.63894e9i	−1.08800	+	0.353513i	−0.290527	+	0.956867i	$0.593831\pi$
$930$	5.45479e8	+	2.05033e8i	0.0222376	+	0.00835859i
$931$	1.99374e9	−	2.74414e9i	0.0809736	−	0.111451i
$932$	5.21184e9	−	3.78662e9i	0.210880	−	0.153213i
$933$	−9.86564e9	−	1.49621e10i	−0.397685	−	0.603123i
$934$		−	5.55982e9i		−	0.223278i
$935$	2.67329e9	−	3.20689e9i	0.106956	−	0.128305i
$936$	2.34226e10	−	5.32142e9i	0.933619	−	0.212111i
$937$	−2.09050e10	−	6.79244e9i	−0.830159	−	0.269735i	−0.137047	−	0.990565i	$-0.543761\pi$
$937$	−2.09050e10	−	6.79244e9i	−0.830159	−	0.269735i	−0.693112	+	0.720829i	$0.743761\pi$
$938$	−3.63197e8	−	4.99898e8i	−0.0143692	−	0.0197775i
$939$	−9.15001e9	−	3.32191e10i	−0.360655	−	1.30936i
$940$	5.76268e8	+	1.77357e9i	0.0226296	+	0.0696468i
$941$	−1.12869e10	−	3.47374e10i	−0.441580	−	1.35904i	−0.886191	−	0.463320i	$-0.846658\pi$
$941$	−1.12869e10	−	3.47374e10i	−0.441580	−	1.35904i	0.444611	−	0.895724i	$-0.353342\pi$
$942$	−2.02179e8	−	7.34010e8i	−0.00788058	−	0.0286104i
$943$	−4.73856e9	−	6.52206e9i	−0.184016	−	0.253276i
$944$	1.90180e10	+	6.17931e9i	0.735803	+	0.239077i
$945$	−6.18290e8	+	1.27898e9i	−0.0238331	+	0.0493007i
$946$	1.28627e8	−	1.92901e9i	0.00493985	−	0.0740823i
$947$			3.48352e9i			0.133289i	0.997777	+	0.0666444i	$0.0212293\pi$
$947$			3.48352e9i			0.133289i	−0.997777	+	0.0666444i	$0.978771\pi$
$948$	−3.07139e9	−	4.65802e9i	−0.117086	−	0.177571i
$949$	−3.78981e9	+	2.75346e9i	−0.143941	+	0.104579i
$950$	−9.60164e8	+	1.32155e9i	−0.0363340	+	0.0500094i
$951$	−1.47019e10	−	5.52610e9i	−0.554296	−	0.208347i
$952$	−1.56082e10	+	5.07140e9i	−0.586304	+	0.190502i
$953$	3.50652e10	+	2.54764e10i	1.31236	+	0.953482i	0.999994	+	0.00351899i	$0.00112013\pi$
$953$	3.50652e10	+	2.54764e10i	1.31236	+	0.953482i	0.312362	+	0.949963i	$0.398880\pi$
$954$	7.29955e9	−	8.33816e9i	0.272193	−	0.310922i
$955$	−1.02292e9	+	3.14821e9i	−0.0380039	+	0.116964i
$956$	−2.50816e10			−0.928436
$957$	−6.45241e9	+	1.42144e10i	−0.237974	+	0.524248i
$958$	9.13551e8			0.0335702
$959$	−2.67551e9	+	8.23438e9i	−0.0979585	+	0.301485i
$960$	−6.09569e7	+	1.34234e9i	−0.00222369	+	0.0489680i
$961$	3.28235e9	+	2.38476e9i	0.119303	+	0.0866790i
$962$	1.66469e10	−	5.40891e9i	0.602866	−	0.195883i
$963$	2.06384e10	−	1.23029e10i	0.744703	−	0.443930i
$964$	8.29062e9	−	1.14111e10i	0.298069	−	0.410257i
$965$	7.27910e8	−	5.28857e8i	0.0260755	−	0.0189449i
$966$	−8.94142e8	+	5.89576e8i	−0.0319144	+	0.0210436i
$967$			1.87214e10i			0.665802i	0.942962	+	0.332901i	$0.108028\pi$
$967$			1.87214e10i			0.665802i	−0.942962	+	0.332901i	$0.891972\pi$
$968$	6.68470e9	−	1.39335e10i	0.236874	−	0.493737i
$969$	7.14924e9	−	8.95567e9i	0.252422	−	0.316202i
$970$	1.10644e9	+	3.59506e8i	0.0389250	+	0.0126475i
$971$	−1.61843e10	−	2.22757e10i	−0.567317	−	0.780845i	0.424917	−	0.905232i	$-0.360303\pi$
$971$	−1.61843e10	−	2.22757e10i	−0.567317	−	0.780845i	−0.992234	+	0.124388i	$0.960303\pi$
$972$	−1.72529e10	−	1.98475e10i	−0.602602	−	0.693224i
$973$	6.39652e9	+	1.96865e10i	0.222612	+	0.685130i
$974$	−3.93483e9	−	1.21101e10i	−0.136449	−	0.419946i
$975$	−4.83853e10	+	1.33275e10i	−1.67185	+	0.460502i
$976$	−2.76002e9	−	3.79884e9i	−0.0950250	−	0.130791i
$977$	9.91549e8	+	3.22174e8i	0.0340160	+	0.0110525i	0.325976	−	0.945378i	$-0.394307\pi$
$977$	9.91549e8	+	3.22174e8i	0.0340160	+	0.0110525i	−0.291960	+	0.956431i	$0.594307\pi$
$978$	1.93855e9	+	1.54753e9i	0.0662659	+	0.0528995i
$979$	3.29857e10	−	8.33756e9i	1.12353	−	0.283988i
$980$		−	1.53921e9i		−	0.0522405i
$981$	2.12640e9	−	2.33645e10i	0.0719122	−	0.790159i
$982$	3.05902e8	−	2.22251e8i	0.0103084	−	0.00748951i
$983$	1.29800e10	−	1.78654e10i	0.435849	−	0.599894i	−0.533434	−	0.845841i	$-0.679099\pi$
$983$	1.29800e10	−	1.78654e10i	0.435849	−	0.599894i	0.969283	+	0.245947i	$0.0790989\pi$
$984$	−8.17745e9	+	2.17557e10i	−0.273612	+	0.727930i
$985$	3.30949e9	−	1.07532e9i	0.110340	−	0.0358518i
$986$	7.41578e9	+	5.38788e9i	0.246370	+	0.178998i
$987$	−1.62139e10	−	7.36291e8i	−0.536757	−	0.0243747i
$988$	−3.28450e9	+	1.01087e10i	−0.108348	+	0.333461i
$989$	1.74455e9			0.0573450
$990$	−7.75871e8	+	1.22677e8i	−0.0254136	+	0.00401829i
$991$	−3.48375e9			−0.113708			−0.0568538	−	0.998383i	$-0.518107\pi$
$991$	−3.48375e9			−0.113708			−0.0568538	+	0.998383i	$0.518107\pi$
$992$	−6.71265e9	+	2.06594e10i	−0.218325	+	0.671935i
$993$	−2.63761e10	−	1.19777e9i	−0.854846	−	0.0388195i
$994$	6.93493e9	+	5.03852e9i	0.223970	+	0.162724i
$995$	2.14720e9	−	6.97667e8i	0.0691021	−	0.0224526i
$996$	9.04793e9	−	2.40715e10i	0.290163	−	0.771962i
$997$	−1.63465e10	+	2.24990e10i	−0.522387	+	0.719004i	−0.985946	−	0.167062i	$-0.946572\pi$
$997$	−1.63465e10	+	2.24990e10i	−0.522387	+	0.719004i	0.463560	+	0.886066i	$0.346572\pi$
$998$	−5.86469e9	+	4.26095e9i	−0.186762	+	0.135690i
$999$	−2.88904e10	−	2.77051e10i	−0.916800	−	0.879187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.f.a.2.11	✓	104
3.2	odd	2	inner	33.8.f.a.2.16	yes	104
11.6	odd	10	inner	33.8.f.a.17.16	yes	104
33.17	even	10	inner	33.8.f.a.17.11	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.f.a.2.11	✓	104	1.1	even	1	trivial
33.8.f.a.2.16	yes	104	3.2	odd	2	inner
33.8.f.a.17.11	yes	104	33.17	even	10	inner
33.8.f.a.17.16	yes	104	11.6	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997925 + 3.07130i) q^{2} +(-46.7172 - 2.12148i) q^{3} +(95.1172 + 69.1067i) q^{4} +(-23.9618 + 7.78566i) q^{5} +(53.1360 - 141.365i) q^{6} +(-324.042 + 446.006i) q^{7} +(-641.580 + 466.135i) q^{8} +(2178.00 + 198.219i) q^{9} +O(q^{10})\)	\(q+(-0.997925 + 3.07130i) q^{2} +(-46.7172 - 2.12148i) q^{3} +(95.1172 + 69.1067i) q^{4} +(-23.9618 + 7.78566i) q^{5} +(53.1360 - 141.365i) q^{6} +(-324.042 + 446.006i) q^{7} +(-641.580 + 466.135i) q^{8} +(2178.00 + 198.219i) q^{9} -81.3633i q^{10} +(-1081.78 - 4279.83i) q^{11} +(-4297.00 - 3430.26i) q^{12} +(-13171.3 - 4279.61i) q^{13} +(-1046.45 - 1440.31i) q^{14} +(1135.95 - 312.890i) q^{15} +(3859.04 + 11876.9i) q^{16} +(-11599.8 - 35700.6i) q^{17} +(-2782.27 + 6491.47i) q^{18} +(-3836.92 - 5281.07i) q^{19} +(-2817.22 - 915.370i) q^{20} +(16084.5 - 20148.7i) q^{21} +(14224.2 + 948.474i) q^{22} +12864.0i q^{23} +(30961.7 - 20415.4i) q^{24} +(-62690.9 + 45547.6i) q^{25} +(26287.9 - 36182.2i) q^{26} +(-101330. - 13880.8i) q^{27} +(-61643.9 + 20029.3i) q^{28} +(61174.6 + 44446.0i) q^{29} +(-172.610 + 3801.07i) q^{30} +(47326.4 - 145656. i) q^{31} -141837. q^{32} +(41458.3 + 202237. i) q^{33} +121223. q^{34} +(4292.18 - 13210.0i) q^{35} +(193467. + 169368. i) q^{36} +(316626. + 230043. i) q^{37} +(20048.7 - 6514.21i) q^{38} +(606247. + 227874. i) q^{39} +(11744.2 - 16164.6i) q^{40} +(-507001. + 368358. i) q^{41} +(45831.5 + 69507.3i) q^{42} -135615. i q^{43} +(192869. - 481843. i) q^{44} +(-53732.0 + 12207.5i) q^{45} +(-39509.2 - 12837.3i) q^{46} +(-370039. - 509314. i) q^{47} +(-155087. - 563043. i) q^{48} +(160571. + 494187. i) q^{49} +(-77329.4 - 237996. i) q^{50} +(466174. + 1.69244e6i) q^{51} +(-957066. - 1.31729e6i) q^{52} +(-1.49230e6 - 484877. i) q^{53} +(143751. - 297361. i) q^{54} +(59242.7 + 94129.9i) q^{55} -437196. i q^{56} +(168047. + 254857. i) q^{57} +(-197554. + 143532. i) q^{58} +(941193. - 1.29544e6i) q^{59} +(129671. + 48740.2i) q^{60} +(-357604. + 116193. i) q^{61} +(400124. + 290707. i) q^{62} +(-794170. + 907168. i) q^{63} +(-352415. + 1.08462e6i) q^{64} +348927. q^{65} +(-662501. - 74486.3i) q^{66} +347077. q^{67} +(1.36381e6 - 4.19737e6i) q^{68} +(27290.7 - 600970. i) q^{69} +(36288.5 + 26365.1i) q^{70} +(-4.57923e6 + 1.48788e6i) q^{71} +(-1.48976e6 + 888068. i) q^{72} +(198818. - 273650. i) q^{73} +(-1.02250e6 + 742889. i) q^{74} +(3.02537e6 - 1.99486e6i) q^{75} -767477. i q^{76} +(2.25937e6 + 904363. i) q^{77} +(-1.30486e6 + 1.63456e6i) q^{78} +(965104. + 313581. i) q^{79} +(-184939. - 254547. i) q^{80} +(4.70439e6 + 863442. i) q^{81} +(-625388. - 1.92475e6i) q^{82} +(1.44530e6 + 4.44817e6i) q^{83} +(2.92233e6 - 804938. i) q^{84} +(555906. + 765139. i) q^{85} +(416513. + 135333. i) q^{86} +(-2.76362e6 - 2.20617e6i) q^{87} +(2.68903e6 + 2.24159e6i) q^{88} +7.70725e6i q^{89} +(16127.8 - 177209. i) q^{90} +(6.17678e6 - 4.48770e6i) q^{91} +(-888988. + 1.22359e6i) q^{92} +(-2.51997e6 + 6.70423e6i) q^{93} +(1.93353e6 - 628241. i) q^{94} +(133056. + 96670.9i) q^{95} +(6.62624e6 + 300905. i) q^{96} +(-4.41852e6 + 1.35988e7i) q^{97} -1.67803e6 q^{98} +(-1.50777e6 - 9.53589e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 42 q^{3} - 1542 q^{4} - 1725 q^{6} - 10 q^{7} + 550 q^{9}+O(q^{10}) \) 104 * q - 42 * q^3 - 1542 * q^4 - 1725 * q^6 - 10 * q^7 + 550 * q^9	\( 104 q - 42 q^{3} - 1542 q^{4} - 1725 q^{6} - 10 q^{7} + 550 q^{9} + 12942 q^{12} - 10 q^{13} - 21762 q^{15} - 40042 q^{16} + 60435 q^{18} + 10460 q^{19} - 218044 q^{22} + 330875 q^{24} + 462276 q^{25} - 294096 q^{27} - 1044930 q^{28} + 243010 q^{30} + 412 q^{31} + 32138 q^{33} + 720380 q^{34} + 166067 q^{36} - 494526 q^{37} + 1075280 q^{39} + 363510 q^{40} - 1090804 q^{42} - 3105552 q^{45} + 706710 q^{46} + 3640214 q^{48} + 3722248 q^{49} + 53970 q^{51} - 3236270 q^{52} + 1380424 q^{55} - 3039180 q^{57} - 1651930 q^{58} - 12139486 q^{60} + 3921710 q^{61} + 459870 q^{63} + 3705878 q^{64} + 15158784 q^{66} - 15866932 q^{67} + 8740364 q^{69} + 14057584 q^{70} - 28129160 q^{72} - 26920980 q^{73} - 16391598 q^{75} + 43716808 q^{78} + 59786450 q^{79} - 17715062 q^{81} + 23865872 q^{82} + 71482920 q^{84} - 2864030 q^{85} - 108977170 q^{88} - 54544280 q^{90} - 56013610 q^{91} - 71700158 q^{93} + 53266890 q^{94} + 34615450 q^{96} + 71130138 q^{97} + 46642084 q^{99}+O(q^{100}) \) 104 * q - 42 * q^3 - 1542 * q^4 - 1725 * q^6 - 10 * q^7 + 550 * q^9 + 12942 * q^12 - 10 * q^13 - 21762 * q^15 - 40042 * q^16 + 60435 * q^18 + 10460 * q^19 - 218044 * q^22 + 330875 * q^24 + 462276 * q^25 - 294096 * q^27 - 1044930 * q^28 + 243010 * q^30 + 412 * q^31 + 32138 * q^33 + 720380 * q^34 + 166067 * q^36 - 494526 * q^37 + 1075280 * q^39 + 363510 * q^40 - 1090804 * q^42 - 3105552 * q^45 + 706710 * q^46 + 3640214 * q^48 + 3722248 * q^49 + 53970 * q^51 - 3236270 * q^52 + 1380424 * q^55 - 3039180 * q^57 - 1651930 * q^58 - 12139486 * q^60 + 3921710 * q^61 + 459870 * q^63 + 3705878 * q^64 + 15158784 * q^66 - 15866932 * q^67 + 8740364 * q^69 + 14057584 * q^70 - 28129160 * q^72 - 26920980 * q^73 - 16391598 * q^75 + 43716808 * q^78 + 59786450 * q^79 - 17715062 * q^81 + 23865872 * q^82 + 71482920 * q^84 - 2864030 * q^85 - 108977170 * q^88 - 54544280 * q^90 - 56013610 * q^91 - 71700158 * q^93 + 53266890 * q^94 + 34615450 * q^96 + 71130138 * q^97 + 46642084 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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