LMFDB - Embedded newform 49.6.e.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(8,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([12]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("49.8");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	49.e (of order $7$, degree $6$, 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:	$7.85880717084$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	49.8
Dual form			49.6.e.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.59749 - 8.27300i) q^{2} +(25.4427 - 12.2525i) q^{3} +(-17.7949 + 77.9644i) q^{4} +(45.4620 - 21.8934i) q^{5} +(-269.223 - 129.651i) q^{6} +(124.236 - 37.0458i) q^{7} +(457.324 - 220.236i) q^{8} +(345.696 - 433.489i) q^{9} +O(q^{10})$	\(q+(-6.59749 - 8.27300i) q^{2} +(25.4427 - 12.2525i) q^{3} +(-17.7949 + 77.9644i) q^{4} +(45.4620 - 21.8934i) q^{5} +(-269.223 - 129.651i) q^{6} +(124.236 - 37.0458i) q^{7} +(457.324 - 220.236i) q^{8} +(345.696 - 433.489i) q^{9} +(-481.059 - 231.666i) q^{10} +(145.000 + 181.825i) q^{11} +(502.513 + 2201.65i) q^{12} +(-102.069 - 127.991i) q^{13} +(-1126.13 - 783.396i) q^{14} +(888.426 - 1114.05i) q^{15} +(-2533.60 - 1220.12i) q^{16} +(155.585 + 681.660i) q^{17} -5866.99 q^{18} -1914.46 q^{19} +(897.912 + 3934.01i) q^{20} +(2706.99 - 2464.75i) q^{21} +(547.597 - 2399.18i) q^{22} +(-1066.62 + 4673.15i) q^{23} +(8937.09 - 11206.8i) q^{24} +(-360.929 + 452.590i) q^{25} +(-385.466 + 1688.84i) q^{26} +(1957.12 - 8574.70i) q^{27} +(677.487 + 10345.2i) q^{28} +(-354.349 - 1552.50i) q^{29} -15077.9 q^{30} +550.336 q^{31} +(3007.00 + 13174.5i) q^{32} +(5917.02 + 2849.48i) q^{33} +(4612.91 - 5784.40i) q^{34} +(4836.97 - 4404.12i) q^{35} +(27645.1 + 34665.9i) q^{36} +(-1364.68 - 5979.07i) q^{37} +(12630.7 + 15838.4i) q^{38} +(-4165.12 - 2005.82i) q^{39} +(15969.2 - 20024.7i) q^{40} +(-3575.24 + 1721.75i) q^{41} +(-38250.2 - 6133.76i) q^{42} +(-16157.5 - 7781.04i) q^{43} +(-16756.1 + 8069.33i) q^{44} +(6225.52 - 27275.8i) q^{45} +(45697.9 - 22007.0i) q^{46} +(-557.884 - 699.565i) q^{47} -79411.2 q^{48} +(14062.2 - 9204.85i) q^{49} +6125.51 q^{50} +(12310.6 + 15436.9i) q^{51} +(11795.0 - 5680.19i) q^{52} +(-2324.84 + 10185.8i) q^{53} +(-83850.6 + 40380.3i) q^{54} +(10572.8 + 5091.58i) q^{55} +(48657.4 - 44303.1i) q^{56} +(-48709.1 + 23457.0i) q^{57} +(-10506.0 + 13174.2i) q^{58} +(10244.7 + 4933.58i) q^{59} +(71046.9 + 89090.0i) q^{60} +(6501.09 + 28483.1i) q^{61} +(-3630.84 - 4552.93i) q^{62} +(26889.0 - 66661.6i) q^{63} +(33048.4 - 41441.4i) q^{64} +(-7442.42 - 3584.08i) q^{65} +(-15463.7 - 67750.9i) q^{66} +14606.6 q^{67} -55913.9 q^{68} +(30120.4 + 131966. i) q^{69} +(-68347.2 - 10960.1i) q^{70} +(2657.84 - 11644.7i) q^{71} +(62625.4 - 274380. i) q^{72} +(-27824.8 + 34891.2i) q^{73} +(-40461.3 + 50736.9i) q^{74} +(-3637.61 + 15937.4i) q^{75} +(34067.6 - 149260. i) q^{76} +(24750.1 + 17217.6i) q^{77} +(10885.3 + 47691.4i) q^{78} +17346.6 q^{79} -141895. q^{80} +(-25286.8 - 110789. i) q^{81} +(37831.6 + 18218.8i) q^{82} +(68570.5 - 85984.6i) q^{83} +(143992. + 254909. i) q^{84} +(21997.0 + 27583.4i) q^{85} +(42226.5 + 185006. i) q^{86} +(-28037.7 - 35158.1i) q^{87} +(106357. + 51218.6i) q^{88} +(-24228.4 + 30381.4i) q^{89} +(-266725. + 128448. i) q^{90} +(-17422.2 - 12119.8i) q^{91} +(-345359. - 166316. i) q^{92} +(14002.0 - 6743.01i) q^{93} +(-2106.86 + 9230.75i) q^{94} +(-87035.4 + 41914.0i) q^{95} +(237928. + 298352. i) q^{96} +149268. q^{97} +(-168927. - 55607.8i) q^{98} +128945. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9}+O(q^{10}) $ 138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9	\( 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9} - 771 q^{10} + 410 q^{11} - 1316 q^{12} + 483 q^{13} + 2597 q^{14} + 2557 q^{15} - 7357 q^{16} - 1422 q^{17} - 2480 q^{18} - 6758 q^{19} - 3647 q^{20} - 399 q^{21} - 857 q^{22} - 2392 q^{23} - 3571 q^{24} - 8066 q^{25} - 343 q^{26} + 16396 q^{27} + 32102 q^{28} + 30341 q^{29} + 13716 q^{30} - 32712 q^{31} - 26993 q^{32} - 16775 q^{33} + 35163 q^{34} - 12019 q^{35} + 35461 q^{36} - 34872 q^{37} + 13383 q^{38} - 20671 q^{39} + 165169 q^{40} + 51233 q^{41} - 13741 q^{42} - 17203 q^{43} - 4267 q^{44} + 30777 q^{45} - 74611 q^{46} + 64264 q^{47} - 247084 q^{48} - 70350 q^{49} - 263036 q^{50} - 57453 q^{51} - 36043 q^{52} + 124590 q^{53} + 144840 q^{54} + 90977 q^{55} + 404404 q^{56} - 103899 q^{57} + 24861 q^{58} - 8079 q^{59} + 72065 q^{60} - 236659 q^{61} - 173227 q^{62} - 119805 q^{63} + 105381 q^{64} - 33383 q^{65} + 536577 q^{66} + 19716 q^{67} - 256340 q^{68} - 202795 q^{69} + 194803 q^{70} + 61778 q^{71} - 392108 q^{72} - 157760 q^{73} - 328319 q^{74} + 355167 q^{75} - 61334 q^{76} - 24402 q^{77} + 497217 q^{78} - 73876 q^{79} - 1340760 q^{80} - 815116 q^{81} + 248976 q^{82} + 303107 q^{83} + 1250354 q^{84} + 205487 q^{85} + 1083219 q^{86} + 197027 q^{87} + 1052915 q^{88} + 219783 q^{89} + 82170 q^{90} - 837235 q^{91} + 35936 q^{92} + 138365 q^{93} - 571908 q^{94} - 610016 q^{95} - 1054494 q^{96} + 762020 q^{97} - 2160767 q^{98} - 1090772 q^{99}+O(q^{100}) \) 138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9 - 771 * q^10 + 410 * q^11 - 1316 * q^12 + 483 * q^13 + 2597 * q^14 + 2557 * q^15 - 7357 * q^16 - 1422 * q^17 - 2480 * q^18 - 6758 * q^19 - 3647 * q^20 - 399 * q^21 - 857 * q^22 - 2392 * q^23 - 3571 * q^24 - 8066 * q^25 - 343 * q^26 + 16396 * q^27 + 32102 * q^28 + 30341 * q^29 + 13716 * q^30 - 32712 * q^31 - 26993 * q^32 - 16775 * q^33 + 35163 * q^34 - 12019 * q^35 + 35461 * q^36 - 34872 * q^37 + 13383 * q^38 - 20671 * q^39 + 165169 * q^40 + 51233 * q^41 - 13741 * q^42 - 17203 * q^43 - 4267 * q^44 + 30777 * q^45 - 74611 * q^46 + 64264 * q^47 - 247084 * q^48 - 70350 * q^49 - 263036 * q^50 - 57453 * q^51 - 36043 * q^52 + 124590 * q^53 + 144840 * q^54 + 90977 * q^55 + 404404 * q^56 - 103899 * q^57 + 24861 * q^58 - 8079 * q^59 + 72065 * q^60 - 236659 * q^61 - 173227 * q^62 - 119805 * q^63 + 105381 * q^64 - 33383 * q^65 + 536577 * q^66 + 19716 * q^67 - 256340 * q^68 - 202795 * q^69 + 194803 * q^70 + 61778 * q^71 - 392108 * q^72 - 157760 * q^73 - 328319 * q^74 + 355167 * q^75 - 61334 * q^76 - 24402 * q^77 + 497217 * q^78 - 73876 * q^79 - 1340760 * q^80 - 815116 * q^81 + 248976 * q^82 + 303107 * q^83 + 1250354 * q^84 + 205487 * q^85 + 1083219 * q^86 + 197027 * q^87 + 1052915 * q^88 + 219783 * q^89 + 82170 * q^90 - 837235 * q^91 + 35936 * q^92 + 138365 * q^93 - 571908 * q^94 - 610016 * q^95 - 1054494 * q^96 + 762020 * q^97 - 2160767 * q^98 - 1090772 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−6.59749	−	8.27300i	−1.16628	−	1.46247i	−0.859825	−	0.510589i	$-0.829427\pi$
$2$	−6.59749	−	8.27300i	−1.16628	−	1.46247i	−0.306458	−	0.951884i	$-0.599144\pi$
$3$	25.4427	−	12.2525i	1.63215	−	0.786001i	0.632210	−	0.774797i	$-0.282148\pi$
$3$	25.4427	−	12.2525i	1.63215	−	0.786001i	0.999937	−	0.0112041i	$-0.00356645\pi$
$4$	−17.7949	+	77.9644i	−0.556090	+	2.43639i
$5$	45.4620	−	21.8934i	0.813249	−	0.391640i	0.0194432	−	0.999811i	$-0.493811\pi$
$5$	45.4620	−	21.8934i	0.813249	−	0.391640i	0.793806	+	0.608171i	$0.208096\pi$
$6$	−269.223	−	129.651i	−3.05305	−	1.47027i
$7$	124.236	−	37.0458i	0.958303	−	0.285755i
$7$	124.236	−	37.0458i	0.958303	−	0.285755i
$8$	457.324	−	220.236i	2.52638	−	1.21664i
$9$	345.696	−	433.489i	1.42262	−	1.78391i
$10$	−481.059	−	231.666i	−1.52124	−	0.732592i
$11$	145.000	+	181.825i	0.361316	+	0.453077i	0.928950	−	0.370205i	$-0.120712\pi$
$11$	145.000	+	181.825i	0.361316	+	0.453077i	−0.567634	+	0.823281i	$0.692141\pi$
$12$	502.513	+	2201.65i	1.00738	+	4.41363i
$13$	−102.069	−	127.991i	−0.167508	−	0.210049i	0.690991	−	0.722863i	$-0.257174\pi$
$13$	−102.069	−	127.991i	−0.167508	−	0.210049i	−0.858500	+	0.512814i	$0.828603\pi$
$14$	−1126.13	−	783.396i	−1.53556	−	1.06822i
$15$	888.426	−	1114.05i	1.01951	−	1.27843i
$16$	−2533.60	−	1220.12i	−2.47422	−	1.19152i
$17$	155.585	+	681.660i	0.130570	+	0.572065i	0.997310	+	0.0733042i	$0.0233544\pi$
$17$	155.585	+	681.660i	0.130570	+	0.572065i	−0.866739	+	0.498761i	$0.833788\pi$
$18$	−5866.99			−4.26809
$19$	−1914.46			−1.21664			−0.608322	−	0.793691i	$-0.708157\pi$
$19$	−1914.46			−1.21664			−0.608322	+	0.793691i	$0.708157\pi$
$20$	897.912	+	3934.01i	0.501948	+	2.19918i
$21$	2706.99	−	2464.75i	1.33949	−	1.21962i
$22$	547.597	−	2399.18i	0.241215	−	1.05683i
$23$	−1066.62	+	4673.15i	−0.420425	+	1.84200i	0.109541	+	0.993982i	$0.465062\pi$
$23$	−1066.62	+	4673.15i	−0.420425	+	1.84200i	−0.529966	+	0.848019i	$0.677795\pi$
$24$	8937.09	−	11206.8i	3.16715	−	3.97148i
$25$	−360.929	+	452.590i	−0.115497	+	0.144829i
$26$	−385.466	+	1688.84i	−0.111829	+	0.489953i
$27$	1957.12	−	8574.70i	0.516664	−	2.26365i
$28$	677.487	+	10345.2i	0.163307	+	2.49370i
$29$	−354.349	−	1552.50i	−0.0782413	−	0.342797i	0.920623	−	0.390454i	$-0.127682\pi$
$29$	−354.349	−	1552.50i	−0.0782413	−	0.342797i	−0.998864	+	0.0476564i	$0.984825\pi$
$30$	−15077.9			−3.05871
$31$	550.336			0.102855			0.0514273	−	0.998677i	$-0.483623\pi$
$31$	550.336			0.102855			0.0514273	+	0.998677i	$0.483623\pi$
$32$	3007.00	+	13174.5i	0.519109	+	2.27437i
$33$	5917.02	+	2849.48i	0.945840	+	0.455493i
$34$	4612.91	−	5784.40i	0.684348	−	0.858146i
$35$	4836.97	−	4404.12i	0.667426	−	0.607700i
$36$	27645.1	+	34665.9i	3.55519	+	4.45806i
$37$	−1364.68	−	5979.07i	−0.163881	−	0.718008i	−0.988362	−	0.152119i	$-0.951390\pi$
$37$	−1364.68	−	5979.07i	−0.163881	−	0.718008i	0.824481	−	0.565889i	$-0.191467\pi$
$38$	12630.7	+	15838.4i	1.41895	+	1.77931i
$39$	−4165.12	−	2005.82i	−0.438497	−	0.211169i
$40$	15969.2	−	20024.7i	1.57809	−	1.97887i
$41$	−3575.24	+	1721.75i	−0.332159	+	0.159959i	−0.592528	−	0.805550i	$-0.701870\pi$
$41$	−3575.24	+	1721.75i	−0.332159	+	0.159959i	0.260369	+	0.965509i	$0.416156\pi$
$42$	−38250.2	−	6133.76i	−3.34589	−	0.536542i
$43$	−16157.5	−	7781.04i	−1.33261	−	0.641751i	−0.374254	−	0.927326i	$-0.622101\pi$
$43$	−16157.5	−	7781.04i	−1.33261	−	0.641751i	−0.958356	+	0.285575i	$0.907815\pi$
$44$	−16756.1	+	8069.33i	−1.30479	+	0.628356i
$45$	6225.52	−	27275.8i	0.458294	−	2.00792i
$46$	45697.9	−	22007.0i	3.18421	−	1.53344i
$47$	−557.884	−	699.565i	−0.0368383	−	0.0461938i	0.763071	−	0.646315i	$-0.223691\pi$
$47$	−557.884	−	699.565i	−0.0368383	−	0.0461938i	−0.799909	+	0.600121i	$0.795119\pi$
$48$	−79411.2			−4.97483
$49$	14062.2	−	9204.85i	0.836688	−	0.547679i
$50$	6125.51			0.346511
$51$	12310.6	+	15436.9i	0.662754	+	0.831067i
$52$	11795.0	−	5680.19i	0.604910	−	0.291309i
$53$	−2324.84	+	10185.8i	−0.113685	+	0.498086i	0.885740	+	0.464181i	$0.153651\pi$
$53$	−2324.84	+	10185.8i	−0.113685	+	0.498086i	−0.999425	+	0.0339045i	$0.989206\pi$
$54$	−83850.6	+	40380.3i	−3.91311	+	1.88445i
$55$	10572.8	+	5091.58i	0.471283	+	0.226958i
$56$	48657.4	−	44303.1i	2.07338	−	1.88784i
$57$	−48709.1	+	23457.0i	−1.98574	+	0.956283i
$58$	−10506.0	+	13174.2i	−0.410080	+	0.514225i
$59$	10244.7	+	4933.58i	0.383150	+	0.184515i	0.615537	−	0.788108i	$-0.288939\pi$
$59$	10244.7	+	4933.58i	0.383150	+	0.184515i	−0.232387	+	0.972623i	$0.574654\pi$
$60$	71046.9	+	89090.0i	2.54781	+	3.19485i
$61$	6501.09	+	28483.1i	0.223698	+	0.980084i	0.954668	+	0.297674i	$0.0962109\pi$
$61$	6501.09	+	28483.1i	0.223698	+	0.980084i	−0.730970	+	0.682410i	$0.760932\pi$
$62$	−3630.84	−	4552.93i	−0.119958	−	0.150422i
$63$	26889.0	−	66661.6i	0.853539	−	2.11604i
$64$	33048.4	−	41441.4i	1.00856	−	1.26469i
$65$	−7442.42	−	3584.08i	−0.218490	−	0.105219i
$66$	−15463.7	−	67750.9i	−0.436972	−	1.91450i
$67$	14606.6			0.397523			0.198761	−	0.980048i	$-0.436308\pi$
$67$	14606.6			0.397523			0.198761	+	0.980048i	$0.436308\pi$
$68$	−55913.9			−1.46638
$69$	30120.4	+	131966.i	0.761619	+	3.33687i
$70$	−68347.2	−	10960.1i	−1.66715	−	0.267342i
$71$	2657.84	−	11644.7i	0.0625723	−	0.274147i	−0.933957	−	0.357384i	$-0.883669\pi$
$71$	2657.84	−	11644.7i	0.0625723	−	0.274147i	0.996530	+	0.0832370i	$0.0265258\pi$
$72$	62625.4	−	274380.i	1.42370	−	6.23765i
$73$	−27824.8	+	34891.2i	−0.611118	+	0.766318i	−0.987065	−	0.160324i	$-0.948746\pi$
$73$	−27824.8	+	34891.2i	−0.611118	+	0.766318i	0.375946	+	0.926641i	$0.377318\pi$
$74$	−40461.3	+	50736.9i	−0.858936	+	1.07707i
$75$	−3637.61	+	15937.4i	−0.0746729	+	0.327163i
$76$	34067.6	−	149260.i	0.676563	−	2.96421i
$77$	24750.1	+	17217.6i	0.475719	+	0.330937i
$78$	10885.3	+	47691.4i	0.202583	+	0.887573i
$79$	17346.6			0.312713			0.156357	−	0.987701i	$-0.450025\pi$
$79$	17346.6			0.312713			0.156357	+	0.987701i	$0.450025\pi$
$80$	−141895.			−2.47881
$81$	−25286.8	−	110789.i	−0.428234	−	1.87622i
$82$	37831.6	+	18218.8i	0.621327	+	0.299216i
$83$	68570.5	−	85984.6i	1.09255	−	1.37002i	0.169414	−	0.985545i	$-0.445812\pi$
$83$	68570.5	−	85984.6i	1.09255	−	1.37002i	0.923137	−	0.384471i	$-0.125616\pi$
$84$	143992.	+	254909.i	2.22659	+	3.94173i
$85$	21997.0	+	27583.4i	0.330230	+	0.414095i
$86$	42226.5	+	185006.i	0.615657	+	2.69737i
$87$	−28037.7	−	35158.1i	−0.397140	−	0.497998i
$88$	106357.	+	51218.6i	1.46406	+	0.705052i
$89$	−24228.4	+	30381.4i	−0.324227	+	0.406568i	−0.917055	−	0.398761i	$-0.869440\pi$
$89$	−24228.4	+	30381.4i	−0.324227	+	0.406568i	0.592828	+	0.805329i	$0.298012\pi$
$90$	−266725.	+	128448.i	−3.47102	+	1.67156i
$91$	−17422.2	−	12119.8i	−0.220546	−	0.153424i
$92$	−345359.	−	166316.i	−4.25404	−	2.04864i
$93$	14002.0	−	6743.01i	0.167874	−	0.0808438i
$94$	−2106.86	+	9230.75i	−0.0245932	+	0.107750i
$95$	−87035.4	+	41914.0i	−0.989434	+	0.476486i
$96$	237928.	+	298352.i	2.63492	+	3.30408i
$97$	149268.			1.61078			0.805392	−	0.592743i	$-0.201955\pi$
$97$	149268.			1.61078			0.805392	+	0.592743i	$0.201955\pi$
$98$	−168927.	−	55607.8i	−1.77678	−	0.584885i
$99$	128945.			1.32226
$100$	−28863.3	−	36193.4i	−0.288633	−	0.361934i
$101$	99599.2	−	47964.4i	0.971521	−	0.467860i	0.120341	−	0.992733i	$-0.461601\pi$
$101$	99599.2	−	47964.4i	0.971521	−	0.467860i	0.851181	+	0.524873i	$0.175887\pi$
$102$	46491.0	−	203690.i	0.442454	−	1.93852i
$103$	−77639.0	+	37389.0i	−0.721086	+	0.347257i	−0.758171	−	0.652055i	$-0.773907\pi$
$103$	−77639.0	+	37389.0i	−0.721086	+	0.347257i	0.0370855	+	0.999312i	$0.488193\pi$
$104$	−74866.8	−	36054.0i	−0.678744	−	0.326866i
$105$	69103.7	−	171318.i	0.611685	−	1.51645i
$106$	99604.9	−	47967.2i	0.861026	−	0.414648i
$107$	−57427.2	+	72011.4i	−0.484907	+	0.608054i	−0.962751	−	0.270391i	$-0.912847\pi$
$107$	−57427.2	+	72011.4i	−0.484907	+	0.608054i	0.477844	+	0.878445i	$0.341418\pi$
$108$	633695.	+	305171.i	5.22782	+	2.51759i
$109$	−68264.5	−	85600.9i	−0.550337	−	0.690100i	0.426402	−	0.904534i	$-0.359781\pi$
$109$	−68264.5	−	85600.9i	−0.550337	−	0.690100i	−0.976739	+	0.214433i	$0.931210\pi$
$110$	−27631.2	−	121060.i	−0.217730	−	0.953937i
$111$	−107980.	−	135403.i	−0.831833	−	1.04309i
$112$	−359965.	−	57723.5i	−2.71154	−	0.434818i
$113$	−85031.3	+	106626.i	−0.626445	+	0.785537i	−0.989235	−	0.146334i	$-0.953253\pi$
$113$	−85031.3	+	106626.i	−0.626445	+	0.785537i	0.362790	+	0.931871i	$0.381824\pi$
$114$	515418.	+	248212.i	3.71447	+	1.78880i
$115$	53820.4	+	235803.i	0.379492	+	1.66266i
$116$	127346.			0.878697
$117$	−90767.6			−0.613008
$118$	−26773.8	−	117303.i	−0.177013	−	0.775543i
$119$	44581.8	+	78923.1i	0.288596	+	0.510901i
$120$	160945.	−	705145.i	1.02029	−	4.47018i
$121$	23802.1	−	104284.i	0.147792	−	0.647520i
$122$	192750.	−	241701.i	1.17245	−	1.47021i
$123$	−69867.9	+	87611.6i	−0.416404	+	0.522154i
$124$	−9793.15	+	42906.6i	−0.0571963	+	0.250594i
$125$	−41587.9	+	182209.i	−0.238063	+	1.04302i
$126$	−728892.	+	217347.i	−4.09013	+	1.21963i
$127$	−11383.0	−	49872.3i	−0.0626251	−	0.274378i	0.933915	−	0.357496i	$-0.116369\pi$
$127$	−11383.0	−	49872.3i	−0.0626251	−	0.274378i	−0.996540	+	0.0831177i	$0.973512\pi$
$128$	−128454.			−0.692982
$129$	−506428.			−2.67943
$130$	19450.2	+	85217.1i	0.100941	+	0.442250i
$131$	73418.3	+	35356.4i	0.373789	+	0.180007i	0.611340	−	0.791368i	$-0.290631\pi$
$131$	73418.3	+	35356.4i	0.373789	+	0.180007i	−0.237552	+	0.971375i	$0.576345\pi$
$132$	−327451.	+	410610.i	−1.63573	+	2.05114i
$133$	−237846.	+	70922.8i	−1.16591	+	0.347662i
$134$	−96366.9	−	120840.i	−0.463624	−	0.581366i
$135$	−98754.4	−	432671.i	−0.466361	−	2.04326i
$136$	221278.	+	277474.i	1.02587	+	1.28640i
$137$	387764.	+	186737.i	1.76509	+	0.850022i	0.969842	+	0.243735i	$0.0783728\pi$
$137$	387764.	+	186737.i	1.76509	+	0.850022i	0.795246	+	0.606286i	$0.207341\pi$
$138$	893036.	−	1.11983e6i	3.99182	−	5.00559i
$139$	−13391.8	+	6449.13i	−0.0587896	+	0.0283116i	−0.463048	−	0.886333i	$-0.653244\pi$
$139$	−13391.8	+	6449.13i	−0.0587896	+	0.0283116i	0.404258	+	0.914645i	$0.367530\pi$
$140$	257292.	+	455482.i	1.10944	+	1.96404i
$141$	−22765.5	−	10963.3i	−0.0964339	−	0.0464401i
$142$	−113872.	+	54837.8i	−0.473910	+	0.228223i
$143$	8471.81	−	37117.4i	0.0346447	−	0.151788i
$144$	−1.40477e6	+	676500.i	−5.64544	+	2.71870i
$145$	−50098.9	−	62822.1i	−0.197883	−	0.248137i
$146$	472229.			1.83346
$147$	244998.	−	406494.i	0.935122	−	1.55153i
$148$	490439.			1.84048
$149$	−294233.	−	368957.i	−1.08574	−	1.36148i	−0.927392	−	0.374092i	$-0.877954\pi$
$149$	−294233.	−	368957.i	−1.08574	−	1.36148i	−0.158349	−	0.987383i	$-0.550617\pi$
$150$	155849.	−	75053.0i	0.565557	−	0.272358i
$151$	26489.8	−	116059.i	0.0945446	−	0.414227i	−0.905402	−	0.424555i	$-0.860431\pi$
$151$	26489.8	−	116059.i	0.0945446	−	0.414227i	0.999947	+	0.0103283i	$0.00328766\pi$
$152$	−875530.	+	421633.i	−3.07371	+	1.48022i
$153$	349278.	+	168203.i	1.20626	+	0.580906i
$154$	−20848.1	−	318351.i	−0.0708378	−	1.08169i
$155$	25019.4	−	12048.7i	0.0836464	−	0.0402820i
$156$	230500.	−	289038.i	0.758333	−	0.950920i
$157$	−482068.	−	232152.i	−1.56084	−	0.751663i	−0.563614	−	0.826038i	$-0.690589\pi$
$157$	−482068.	−	232152.i	−1.56084	−	0.751663i	−0.997230	+	0.0743756i	$0.976304\pi$
$158$	−114444.	−	143508.i	−0.364712	−	0.457335i
$159$	65651.5	+	287638.i	0.205945	+	0.902306i
$160$	425139.	+	533108.i	1.31290	+	1.64632i
$161$	40608.2	+	620087.i	0.123467	+	1.88533i
$162$	−749725.	+	940125.i	−2.24447	+	2.81448i
$163$	−96468.4	−	46456.7i	−0.284391	−	0.136956i	0.286250	−	0.958155i	$-0.407591\pi$
$163$	−96468.4	−	46456.7i	−0.284391	−	0.136956i	−0.570641	+	0.821199i	$0.693305\pi$
$164$	−70613.9	−	309380.i	−0.205013	−	0.898219i
$165$	331384.			0.947593
$166$	−1.16374e6			−3.27784
$167$	101656.	+	445386.i	0.282061	+	1.23579i	0.895145	+	0.445774i	$0.147072\pi$
$167$	101656.	+	445386.i	0.282061	+	1.23579i	−0.613084	+	0.790018i	$0.710071\pi$
$168$	695147.	−	1.72337e6i	1.90022	−	4.71090i
$169$	76657.0	−	335856.i	0.206459	−	0.904558i
$170$	83072.1	−	363963.i	0.220462	−	0.965905i
$171$	−661823.	+	829900.i	−1.73082	+	2.17038i
$172$	894165.	−	1.12125e6i	2.30461	−	2.88988i
$173$	98025.2	−	429476.i	0.249013	−	1.09100i	−0.683525	−	0.729927i	$-0.739554\pi$
$173$	98025.2	−	429476.i	0.249013	−	1.09100i	0.932538	−	0.361071i	$-0.117589\pi$
$174$	−105885.	+	463911.i	−0.265131	+	1.16161i
$175$	−28073.8	+	69599.0i	−0.0692957	+	0.171794i
$176$	−145526.	−	637590.i	−0.354126	−	1.55153i
$177$	321101.			0.770386
$178$	411192.			0.972735
$179$	106467.	+	466460.i	0.248359	+	1.08813i	0.933177	+	0.359418i	$0.117025\pi$
$179$	106467.	+	466460.i	0.248359	+	1.08813i	−0.684817	+	0.728715i	$0.740118\pi$
$180$	2.01576e6	+	970737.i	4.63721	+	2.23316i
$181$	24271.7	−	30435.7i	0.0550685	−	0.0690537i	−0.753534	−	0.657408i	$-0.771653\pi$
$181$	24271.7	−	30435.7i	0.0550685	−	0.0690537i	0.808603	+	0.588355i	$0.200224\pi$
$182$	14675.5	+	224094.i	0.0328408	+	0.501479i
$183$	514396.	+	645032.i	1.13545	+	1.42382i
$184$	541405.	+	2.37205e6i	1.17890	+	5.16511i
$185$	−192943.	−	241943.i	−0.414477	−	0.519738i
$186$	−148163.	−	71351.6i	−0.314020	−	0.151224i
$187$	−101383.	+	127130.i	−0.212012	+	0.265855i
$188$	64468.6	−	31046.5i	0.133031	−	0.0640645i
$189$	−74511.5	−	1.13779e6i	−0.151729	−	2.31690i
$190$	920971.	+	443516.i	1.85081	+	0.891303i
$191$	558490.	−	268955.i	1.10773	−	0.533453i	0.211646	−	0.977346i	$-0.432117\pi$
$191$	558490.	−	268955.i	1.10773	−	0.533453i	0.896079	+	0.443894i	$0.146403\pi$
$192$	333077.	−	1.45931e6i	0.652066	−	2.85689i
$193$	−509887.	+	245548.i	−0.985327	+	0.474508i	−0.855934	−	0.517085i	$-0.827017\pi$
$193$	−509887.	+	245548.i	−0.985327	+	0.474508i	−0.129393	+	0.991593i	$0.541303\pi$
$194$	−984794.	−	1.23489e6i	−1.87863	−	2.35573i
$195$	−233269.			−0.439310
$196$	467415.	+	1.26015e6i	0.869086	+	2.34306i
$197$	−160015.			−0.293762			−0.146881	−	0.989154i	$-0.546923\pi$
$197$	−160015.			−0.293762			−0.146881	+	0.989154i	$0.546923\pi$
$198$	−850716.	−	1.06676e6i	−1.54213	−	1.93377i
$199$	−387560.	+	186639.i	−0.693755	+	0.334095i	−0.747315	−	0.664470i	$-0.768657\pi$
$199$	−387560.	+	186639.i	−0.693755	+	0.334095i	0.0535604	+	0.998565i	$0.482943\pi$
$200$	−65384.9	+	286470.i	−0.115585	+	0.506412i
$201$	371631.	−	178968.i	0.648816	−	0.312453i
$202$	−1.05391e6	−	507539.i	−1.81730	−	0.875166i
$203$	−101537.	−	179750.i	−0.172935	−	0.306146i
$204$	−1.42260e6	+	685087.i	−2.39335	+	1.15258i
$205$	−124843.	+	156548.i	−0.207481	+	0.260174i
$206$	821542.	+	395634.i	1.34884	+	0.649569i
$207$	1.65704e6	+	2.07786e6i	2.68786	+	3.37046i
$208$	102439.	+	448814.i	0.164175	+	0.719297i
$209$	−277598.	−	348097.i	−0.439593	−	0.551232i
$210$	−1.87322e6	+	558573.i	−2.93117	+	0.874041i
$211$	204506.	−	256442.i	0.316228	−	0.396537i	−0.598160	−	0.801377i	$-0.704101\pi$
$211$	204506.	−	256442.i	0.316228	−	0.396537i	0.914388	+	0.404840i	$0.132673\pi$
$212$	−752757.	−	362509.i	−1.15031	−	0.553961i
$213$	−75055.2	−	328838.i	−0.113353	−	0.496631i
$214$	974626.			1.45480
$215$	−904906.			−1.33508
$216$	−993417.	−	4.35244e6i	−1.44876	−	6.34744i
$217$	68371.6	−	20387.6i	0.0985658	−	0.0293912i
$218$	−257802.	+	1.12950e6i	−0.367405	+	1.60971i
$219$	−280431.	+	1.22865e6i	−0.395108	+	1.73108i
$220$	−585103.	+	733696.i	−0.815034	+	1.02202i
$221$	71365.8	−	89489.9i	0.0982901	−	0.123252i
$222$	−407788.	+	1.78664e6i	−0.555331	+	2.43307i
$223$	−85434.8	+	374315.i	−0.115046	+	0.504051i	0.884266	+	0.466983i	$0.154659\pi$
$223$	−85434.8	+	374315.i	−0.115046	+	0.504051i	−0.999313	+	0.0370682i	$0.988198\pi$
$224$	861639.	+	1.52536e6i	1.14737	+	2.03119i
$225$	71421.4	+	312918.i	0.0940529	+	0.412073i
$226$	1.44311e6			1.87944
$227$	−68714.2			−0.0885078			−0.0442539	−	0.999020i	$-0.514091\pi$
$227$	−68714.2			−0.0885078			−0.0442539	+	0.999020i	$0.514091\pi$
$228$	−962044.	−	4.21499e6i	−1.22563	−	5.36982i
$229$	−472470.	−	227530.i	−0.595368	−	0.286714i	0.111832	−	0.993727i	$-0.464328\pi$
$229$	−472470.	−	227530.i	−0.595368	−	0.286714i	−0.707201	+	0.707013i	$0.750042\pi$
$230$	1.59571e6	−	2.00096e6i	1.98900	−	2.49413i
$231$	840668.	+	134808.i	1.03656	+	0.166221i
$232$	−503969.	−	631957.i	−0.614729	−	0.770846i
$233$	−259262.	−	1.13590e6i	−0.312859	−	1.37073i	−0.849800	−	0.527106i	$-0.823277\pi$
$233$	−259262.	−	1.13590e6i	−0.312859	−	1.37073i	0.536940	−	0.843620i	$-0.319580\pi$
$234$	598839.	+	750920.i	0.714941	+	0.896508i
$235$	−40678.4	−	19589.7i	−0.0480501	−	0.0231397i
$236$	−566946.	+	710928.i	−0.662616	+	0.830894i
$237$	441344.	−	212540.i	0.510395	−	0.245793i
$238$	358802.	−	889520.i	0.410594	−	1.01792i
$239$	223990.	+	107868.i	0.253649	+	0.122151i	0.556388	−	0.830922i	$-0.312187\pi$
$239$	223990.	+	107868.i	0.253649	+	0.122151i	−0.302739	+	0.953074i	$0.597901\pi$
$240$	−3.61019e6	+	1.73858e6i	−4.04578	+	1.94834i
$241$	290428.	−	1.27245e6i	0.322104	−	1.41123i	−0.511697	−	0.859166i	$-0.670983\pi$
$241$	290428.	−	1.27245e6i	0.322104	−	1.41123i	0.833801	−	0.552064i	$-0.186160\pi$
$242$	−1.01977e6	+	491097.i	−1.11935	+	0.539050i
$243$	−668260.	−	837972.i	−0.725989	−	0.910361i
$244$	−2.33636e6			−2.51226
$245$	437772.	−	726340.i	0.465943	−	0.773081i
$246$	1.18576e6			1.24928
$247$	195408.	+	245034.i	0.203798	+	0.255554i
$248$	251682.	−	121204.i	0.259850	−	0.125137i
$249$	691085.	−	3.02784e6i	0.706371	−	3.09481i
$250$	1.78179e6	−	858064.i	1.80304	−	0.868300i
$251$	−200370.	−	96493.2i	−0.200747	−	0.0966746i	0.330809	−	0.943698i	$-0.392678\pi$
$251$	−200370.	−	96493.2i	−0.200747	−	0.0966746i	−0.531556	+	0.847023i	$0.678393\pi$
$252$	4.71875e6	+	3.28262e6i	4.68086	+	3.25626i
$253$	−1.00435e6	+	483672.i	−0.986474	+	0.475061i
$254$	−337494.	+	423204.i	−0.328232	+	0.411590i
$255$	897629.	+	432276.i	0.864463	+	0.416304i
$256$	−210075.	−	263426.i	−0.200343	−	0.251223i
$257$	192943.	+	845339.i	0.182220	+	0.798359i	0.980571	+	0.196166i	$0.0628491\pi$
$257$	192943.	+	845339.i	0.182220	+	0.798359i	−0.798351	+	0.602193i	$0.794294\pi$
$258$	3.34115e6	+	4.18967e6i	3.12498	+	3.91860i
$259$	−391042.	−	692261.i	−0.362222	−	0.641240i
$260$	411868.	−	516466.i	0.377854	−	0.473814i
$261$	−795491.	−	383088.i	−0.722826	−	0.348095i
$262$	−191873.	−	840653.i	−0.172688	−	0.756595i
$263$	−968976.			−0.863821			−0.431911	−	0.901916i	$-0.642160\pi$
$263$	−968976.			−0.863821			−0.431911	+	0.901916i	$0.642160\pi$
$264$	3.33355e6			2.94373
$265$	117309.	+	513964.i	0.102616	+	0.449592i
$266$	2.15593e6	+	1.49978e6i	1.86823	+	1.29964i
$267$	−244185.	+	1.06984e6i	−0.209624	+	0.918422i
$268$	−259922.	+	1.13879e6i	−0.221058	+	0.968520i
$269$	641495.	−	804409.i	0.540521	−	0.677792i	−0.434303	−	0.900767i	$-0.643005\pi$
$269$	641495.	−	804409.i	0.540521	−	0.677792i	0.974824	+	0.222975i	$0.0715768\pi$
$270$	−2.92796e6	+	3.67154e6i	−2.44430	+	3.06506i
$271$	−182269.	+	798573.i	−0.150761	+	0.660528i	0.841903	+	0.539628i	$0.181435\pi$
$271$	−182269.	+	798573.i	−0.150761	+	0.660528i	−0.992665	+	0.120900i	$0.961422\pi$
$272$	437517.	−	1.91689e6i	0.358569	−	1.57099i
$273$	−591766.	−	94894.8i	−0.480555	−	0.0770612i
$274$	−1.01339e6	−	4.43997e6i	−0.815459	−	3.57276i
$275$	−134627.			−0.107350
$276$	−1.08246e7			−8.55345
$277$	−273794.	−	1.19957e6i	−0.214400	−	0.939346i	−0.961537	−	0.274676i	$-0.911429\pi$
$277$	−273794.	−	1.19957e6i	−0.214400	−	0.939346i	0.747137	−	0.664670i	$-0.231428\pi$
$278$	141706.	+	68241.9i	0.109970	+	0.0529589i
$279$	190249.	−	238565.i	0.146323	−	0.183483i
$280$	1.24212e6	−	3.07938e6i	0.946820	−	2.34730i
$281$	1.02565e6	+	1.28612e6i	0.774877	+	0.971665i	0.999996	−	0.00266657i	$-0.000848798\pi$
$281$	1.02565e6	+	1.28612e6i	0.774877	+	0.971665i	−0.225120	+	0.974331i	$0.572277\pi$
$282$	59496.1	+	260669.i	0.0445518	+	0.195194i
$283$	−464945.	−	583023.i	−0.345093	−	0.432732i	0.578750	−	0.815505i	$-0.303541\pi$
$283$	−464945.	−	583023.i	−0.345093	−	0.432732i	−0.923843	+	0.382773i	$0.874969\pi$
$284$	860579.	+	414433.i	0.633133	+	0.304901i
$285$	−1.70086e6	+	2.13281e6i	−1.24038	+	1.55539i
$286$	−362965.	+	174795.i	−0.262392	+	0.126361i
$287$	−380391.	+	346351.i	−0.272600	+	0.248205i
$288$	6.75053e6	+	3.25089e6i	4.79575	+	2.30951i
$289$	838793.	−	403941.i	0.590759	−	0.284494i
$290$	−189199.	+	828936.i	−0.132107	+	0.578797i
$291$	3.79777e6	−	1.82891e6i	2.62904	−	1.26608i
$292$	−2.22513e6	−	2.79023e6i	−1.52721	−	1.91506i
$293$	1.18638e6			0.807339			0.403670	−	0.914905i	$-0.367735\pi$
$293$	1.18638e6			0.807339			0.403670	+	0.914905i	$0.367735\pi$
$294$	−4.97929e6	+	654976.i	−3.35969	+	0.441934i
$295$	573757.			0.383860
$296$	−1.94091e6	−	2.43382e6i	−1.28758	−	1.61458i
$297$	1.84288e6	−	887483.i	1.21229	−	0.583806i
$298$	−1.11118e6	+	4.86838e6i	−0.724840	+	3.17573i
$299$	706988.	−	340468.i	0.457335	−	0.220241i
$300$	−1.17782e6	−	567208.i	−0.755572	−	0.363864i
$301$	−2.29560e6	−	368119.i	−1.46043	−	0.234192i
$302$	−1.13493e6	+	546552.i	−0.716061	+	0.344837i
$303$	1.94638e6	−	2.44069e6i	1.21793	−	1.52723i
$304$	4.85049e6	+	2.33587e6i	3.01024	+	1.44966i
$305$	919144.	+	1.15257e6i	0.565763	+	0.709444i
$306$	−912812.	−	3.99929e6i	−0.557286	−	2.44163i
$307$	413832.	+	518930.i	0.250599	+	0.314241i	0.891180	−	0.453649i	$-0.149878\pi$
$307$	413832.	+	518930.i	0.250599	+	0.314241i	−0.640582	+	0.767890i	$0.721307\pi$
$308$	−1.78278e6	+	1.62325e6i	−1.07083	+	0.975007i
$309$	−1.51723e6	+	1.90255e6i	−0.903974	+	1.13355i
$310$	−264744.	−	127494.i	−0.156467	−	0.0753504i
$311$	−55643.5	−	243790.i	−0.0326222	−	0.142927i	0.955994	−	0.293386i	$-0.0947821\pi$
$311$	−55643.5	−	243790.i	−0.0326222	−	0.142927i	−0.988616	+	0.150459i	$0.951925\pi$
$312$	−2.34656e6			−1.36473
$313$	702474.			0.405293			0.202647	−	0.979252i	$-0.435046\pi$
$313$	702474.			0.405293			0.202647	+	0.979252i	$0.435046\pi$
$314$	1.25985e6	+	5.51977e6i	0.721100	+	3.15934i
$315$	−237018.	−	3.61926e6i	−0.134588	−	2.05515i
$316$	−308680.	+	1.35242e6i	−0.173897	+	0.761891i
$317$	−225783.	+	989221.i	−0.126195	+	0.552898i	0.871814	+	0.489837i	$0.162944\pi$
$317$	−225783.	+	989221.i	−0.126195	+	0.552898i	−0.998010	+	0.0630617i	$0.979914\pi$
$318$	1.94649e6	−	2.44083e6i	1.07941	−	1.35353i
$319$	230903.	−	289543.i	0.127044	−	0.159308i
$320$	595156.	−	2.60755e6i	0.324905	−	1.42350i
$321$	−578778.	+	2.53579e6i	−0.313509	+	1.37357i
$322$	4.86207e6	−	4.42697e6i	2.61325	−	2.37940i
$323$	−297861.	−	1.30501e6i	−0.158857	−	0.695999i
$324$	9.08755e6			4.80933
$325$	94767.1			0.0497679
$326$	252113.	+	1.10458e6i	0.131387	+	0.575643i
$327$	−2.78566e6	−	1.34150e6i	−1.44065	−	0.693781i
$328$	−1.25585e6	+	1.57479e6i	−0.644547	+	0.808236i
$329$	−95225.3	−	66243.9i	−0.0485023	−	0.0337409i
$330$	−2.18631e6	−	2.74154e6i	−1.10516	−	1.38583i
$331$	544649.	+	2.38626e6i	0.273242	+	1.19715i	0.906161	+	0.422932i	$0.138999\pi$
$331$	544649.	+	2.38626e6i	0.273242	+	1.19715i	−0.632920	+	0.774217i	$0.718144\pi$
$332$	5.48354e6	+	6.87614e6i	2.73033	+	3.42373i
$333$	−3.06363e6	−	1.47537e6i	−1.51400	−	0.729104i
$334$	3.01400e6	−	3.77943e6i	1.47835	−	1.85379i
$335$	664045.	−	319787.i	0.323285	−	0.155686i
$336$	−9.86573e6	+	2.94185e6i	−4.76740	+	1.42158i
$337$	−616732.	−	297002.i	−0.295816	−	0.142457i	0.280089	−	0.959974i	$-0.409636\pi$
$337$	−616732.	−	297002.i	−0.295816	−	0.142457i	−0.575905	+	0.817517i	$0.695350\pi$
$338$	−3.28428e6	+	1.58163e6i	−1.56368	+	0.753030i
$339$	−856985.	+	3.75470e6i	−0.405018	+	1.77450i
$340$	−2.54196e6	+	1.22414e6i	−1.19253	+	0.574294i
$341$	79799.0	+	100065.i	0.0371630	+	0.0466010i
$342$	1.12321e7			5.19275
$343$	1.40603e6	−	1.66452e6i	0.645299	−	0.763930i
$344$	−9.10288e6			−4.14746
$345$	4.25852e6	+	5.34001e6i	1.92624	+	2.41543i
$346$	−4.19978e6	+	2.02251e6i	−1.88598	+	0.908238i
$347$	678983.	−	2.97482e6i	0.302716	−	1.32628i	−0.563293	−	0.826257i	$-0.690466\pi$
$347$	678983.	−	2.97482e6i	0.302716	−	1.32628i	0.866009	−	0.500028i	$-0.166677\pi$
$348$	3.24001e6	−	1.56031e6i	1.43416	−	0.690656i
$349$	−3.90973e6	−	1.88282e6i	−1.71824	−	0.827459i	−0.989820	−	0.142323i	$-0.954543\pi$
$349$	−3.90973e6	−	1.88282e6i	−1.71824	−	0.827459i	−0.728415	−	0.685136i	$-0.759743\pi$
$350$	761009.	−	226924.i	0.332062	−	0.0990172i
$351$	−1.29724e6	+	624720.i	−0.562023	+	0.270656i
$352$	−1.95944e6	+	2.45706e6i	−0.842899	+	1.05696i
$353$	1.73380e6	+	834955.i	0.740564	+	0.356637i	0.765829	−	0.643044i	$-0.222329\pi$
$353$	1.73380e6	+	834955.i	0.740564	+	0.356637i	−0.0252651	+	0.999681i	$0.508043\pi$
$354$	−2.11846e6	−	2.65647e6i	−0.898488	−	1.12667i
$355$	−134112.	−	587582.i	−0.0564802	−	0.247456i
$356$	−1.93753e6	−	2.42958e6i	−0.810258	−	1.01603i
$357$	2.10129e6	+	1.46177e6i	0.872600	+	0.607029i
$358$	3.15661e6	−	3.95827e6i	1.30171	−	1.63229i
$359$	−1.26760e6	−	610445.i	−0.519095	−	0.249983i	0.155943	−	0.987766i	$-0.450159\pi$
$359$	−1.26760e6	−	610445.i	−0.519095	−	0.249983i	−0.675038	+	0.737783i	$0.735873\pi$
$360$	−3.16002e6	−	1.38449e7i	−1.28509	−	5.63034i
$361$	1.18907e6			0.480221
$362$	−411927.			−0.165215
$363$	−672152.	−	2.94489e6i	−0.267733	−	1.17301i
$364$	1.25494e6	−	1.14264e6i	0.496444	−	0.452019i
$365$	−501087.	+	2.19540e6i	−0.196871	+	0.862546i
$366$	1.94262e6	−	8.51119e6i	0.758029	−	3.32114i
$367$	−876193.	+	1.09871e6i	−0.339574	+	0.425813i	−0.922071	−	0.387020i	$-0.873504\pi$
$367$	−876193.	+	1.09871e6i	−0.339574	+	0.425813i	0.582497	+	0.812833i	$0.302076\pi$
$368$	8.40418e6	−	1.05385e7i	3.23501	−	4.05657i
$369$	−489589.	+	2.14503e6i	−0.187183	+	0.820102i
$370$	−728653.	+	3.19244e6i	−0.276705	+	1.21232i
$371$	88511.2	+	1.35157e6i	0.0333859	+	0.509803i
$372$	276551.	+	1.21165e6i	0.103614	+	0.453962i
$373$	−1.05288e6			−0.391839			−0.195920	−	0.980620i	$-0.562769\pi$
$373$	−1.05288e6			−0.391839			−0.195920	+	0.980620i	$0.562769\pi$
$374$	1.72062e6			0.636072
$375$	1.17441e6	+	5.14543e6i	0.431263	+	1.88949i
$376$	−409203.	−	197062.i	−0.149269	−	0.0718841i
$377$	−162538.	+	203816.i	−0.0588981	+	0.0738559i
$378$	−8.92135e6	+	8.12300e6i	−3.21145	+	2.92407i
$379$	2.15986e6	+	2.70838e6i	0.772376	+	0.968528i	0.999986	−	0.00522389i	$-0.00166282\pi$
$379$	2.15986e6	+	2.70838e6i	0.772376	+	0.968528i	−0.227611	+	0.973752i	$0.573091\pi$
$380$	−1.71902e6	−	7.53152e6i	−0.610692	−	2.67562i
$381$	−900676.	−	1.12941e6i	−0.317875	−	0.398603i
$382$	−5.90970e6	−	2.84596e6i	−2.07208	−	0.997862i
$383$	1.81465e6	−	2.27550e6i	0.632115	−	0.792647i	−0.357877	−	0.933769i	$-0.616499\pi$
$383$	1.81465e6	−	2.27550e6i	0.632115	−	0.792647i	0.989992	+	0.141121i	$0.0450708\pi$
$384$	−3.26821e6	+	1.57388e6i	−1.13105	+	0.544684i
$385$	1.50214e6	+	240881.i	0.516487	+	0.0828231i
$386$	5.39540e6	+	2.59829e6i	1.84313	+	0.887603i
$387$	−8.95859e6	+	4.31423e6i	−3.04062	+	1.46429i
$388$	−2.65620e6	+	1.16376e7i	−0.895740	+	3.92449i
$389$	−3.77681e6	+	1.81882e6i	−1.26547	+	0.609417i	−0.941615	−	0.336691i	$-0.890692\pi$
$389$	−3.77681e6	+	1.81882e6i	−1.26547	+	0.609417i	−0.323852	+	0.946108i	$0.604978\pi$
$390$	1.53899e6	+	1.92983e6i	0.512359	+	0.642478i
$391$	−3.35145e6			−1.10864
$392$	4.40376e6	−	7.30660e6i	1.44746	−	2.40160i
$393$	2.30116e6			0.751564
$394$	1.05570e6	+	1.32381e6i	0.342610	+	0.429619i
$395$	788611.	−	379775.i	0.254314	−	0.122471i
$396$	−2.29457e6	+	1.00531e7i	−0.735296	+	3.22154i
$397$	−5.49702e6	+	2.64722e6i	−1.75046	+	0.842975i	−0.772254	+	0.635314i	$0.780871\pi$
$397$	−5.49702e6	+	2.64722e6i	−1.75046	+	0.842975i	−0.978201	+	0.207661i	$0.933415\pi$
$398$	4.10099e6	+	1.97493e6i	1.29772	+	0.624948i
$399$	−5.18244e6	+	4.71868e6i	−1.62968	+	1.48384i
$400$	1.46666e6	−	706308.i	0.458333	−	0.220721i
$401$	−1.00643e6	+	1.26203e6i	−0.312553	+	0.391929i	−0.913151	−	0.407623i	$-0.866358\pi$
$401$	−1.00643e6	+	1.26203e6i	−0.312553	+	0.391929i	0.600598	+	0.799551i	$0.294929\pi$
$402$	−3.93243e6	−	1.89376e6i	−1.21366	−	0.584467i
$403$	−56172.3	−	70437.9i	−0.0172290	−	0.0216045i
$404$	1.96716e6	+	8.61871e6i	0.599636	+	2.62717i
$405$	−3.57512e6	−	4.48306e6i	−1.08306	−	1.35812i
$406$	−817183.	+	2.02591e6i	−0.246039	+	0.609965i
$407$	889264.	−	1.11510e6i	0.266100	−	0.333679i
$408$	9.02968e6	+	4.34846e6i	2.68548	+	1.29326i
$409$	−205576.	−	900687.i	−0.0607665	−	0.266235i	0.935414	−	0.353555i	$-0.115027\pi$
$409$	−205576.	−	900687.i	−0.0607665	−	0.266235i	−0.996180	+	0.0873192i	$0.972170\pi$
$410$	2.11877e6			0.622479
$411$	1.21538e7			3.54900
$412$	−1.53343e6	−	6.71841e6i	−0.445064	−	1.94995i
$413$	1.45553e6	+	233406.i	0.419900	+	0.0673345i
$414$	6.25782e6	−	2.74173e7i	1.79441	−	7.86183i
$415$	1.23486e6	−	5.41027e6i	0.351963	−	1.54205i
$416$	1.37930e6	−	1.72958e6i	0.390773	−	0.490014i
$417$	−261704.	+	328166.i	−0.0737004	+	0.0924174i
$418$	−1.04835e6	+	4.59314e6i	−0.293472	+	1.28579i
$419$	−1.15839e6	+	5.07524e6i	−0.322344	+	1.41228i	0.511025	+	0.859566i	$0.329266\pi$
$419$	−1.15839e6	+	5.07524e6i	−0.322344	+	1.41228i	−0.833369	+	0.552717i	$0.813591\pi$
$420$	1.21270e7	+	8.43621e6i	3.35452	+	2.33359i
$421$	−551350.	−	2.41562e6i	−0.151608	−	0.664238i	−0.992418	−	0.122908i	$-0.960778\pi$
$421$	−551350.	−	2.41562e6i	−0.151608	−	0.664238i	0.840810	−	0.541330i	$-0.182079\pi$
$422$	−3.47077e6			−0.948735
$423$	−496113.			−0.134812
$424$	1.18007e6	+	5.17021e6i	0.318780	+	1.39667i
$425$	−364668.	−	175615.i	−0.0979321	−	0.0471616i
$426$	−2.22530e6	+	2.79044e6i	−0.594108	+	0.744987i
$427$	1.86285e6	+	3.29780e6i	0.494434	+	0.875294i
$428$	−4.59242e6	−	5.75871e6i	−1.21180	−	1.51955i
$429$	−239237.	−	1.04817e6i	−0.0627604	−	0.274971i
$430$	5.97011e6	+	7.48629e6i	1.55708	+	1.95252i
$431$	272290.	+	131128.i	0.0706055	+	0.0340018i	0.468853	−	0.883276i	$-0.344667\pi$
$431$	272290.	+	131128.i	0.0706055	+	0.0340018i	−0.398248	+	0.917278i	$0.630382\pi$
$432$	−1.54207e7	+	1.93370e7i	−3.97553	+	4.98516i
$433$	4.61076e6	−	2.22043e6i	1.18182	−	0.569137i	0.263382	−	0.964692i	$-0.415162\pi$
$433$	4.61076e6	−	2.22043e6i	1.18182	−	0.569137i	0.918442	+	0.395555i	$0.129448\pi$
$434$	−619748.	−	431131.i	−0.157939	−	0.109871i
$435$	−2.04438e6	−	984521.i	−0.518010	−	0.249461i
$436$	7.88859e6	−	3.79894e6i	1.98739	−	0.957076i
$437$	2.04200e6	−	8.94657e6i	0.511507	−	2.24106i
$438$	1.20148e7	−	5.78600e6i	2.99247	−	1.44110i
$439$	3.71573e6	+	4.65938e6i	0.920202	+	1.15390i	0.987729	+	0.156179i	$0.0499176\pi$
$439$	3.71573e6	+	4.65938e6i	0.920202	+	1.15390i	−0.0675273	+	0.997717i	$0.521511\pi$
$440$	5.95653e6			1.46677
$441$	871054.	−	9.27791e6i	0.213279	−	2.27171i
$442$	−1.21119e6			−0.294887
$443$	−1.56256e6	−	1.95938e6i	−0.378291	−	0.474362i	0.555841	−	0.831288i	$-0.312396\pi$
$443$	−1.56256e6	−	1.95938e6i	−0.378291	−	0.474362i	−0.934133	+	0.356926i	$0.883825\pi$
$444$	1.24781e7	−	6.00913e6i	3.00393	−	1.44662i
$445$	−436320.	+	1.91164e6i	−0.104449	+	0.457622i
$446$	3.66036e6	−	1.76274e6i	0.871338	−	0.419614i
$447$	−1.20067e7	−	5.78214e6i	−2.84221	−	1.36874i
$448$	2.57057e6	−	6.37282e6i	0.605111	−	1.50016i
$449$	1.91499e6	−	922211.i	0.448282	−	0.215881i	−0.196102	−	0.980584i	$-0.562828\pi$
$449$	1.91499e6	−	922211.i	0.448282	−	0.215881i	0.644384	+	0.764702i	$0.277114\pi$
$450$	2.11757e6	−	2.65534e6i	0.492953	−	0.618143i
$451$	−831468.	−	400414.i	−0.192488	−	0.0926974i
$452$	−6.79991e6	−	8.52681e6i	−1.56551	−	1.96309i
$453$	−748052.	−	3.27743e6i	−0.171272	−	0.750391i
$454$	453341.	+	568472.i	0.103225	+	0.129440i
$455$	−1.05739e6	−	169562.i	−0.239446	−	0.0383972i
$456$	−1.71097e7	+	2.14549e7i	−3.85329	+	4.83187i
$457$	3.37011e6	+	1.62296e6i	0.754837	+	0.363510i	0.771398	−	0.636352i	$-0.219558\pi$
$457$	3.37011e6	+	1.62296e6i	0.754837	+	0.363510i	−0.0165612	+	0.999863i	$0.505272\pi$
$458$	1.23477e6	+	5.40987e6i	0.275056	+	1.20510i
$459$	6.14953e6			1.36242
$460$	−1.93419e7			−4.26192
$461$	449021.	+	1.96729e6i	0.0984045	+	0.431138i	0.999999	−	0.00144407i	$-0.000459663\pi$
$461$	449021.	+	1.96729e6i	0.0984045	+	0.431138i	−0.901594	+	0.432582i	$0.857603\pi$
$462$	−4.43104e6	−	7.84424e6i	−0.965829	−	1.70980i
$463$	−1.10528e6	+	4.84254e6i	−0.239618	+	1.04984i	0.701742	+	0.712431i	$0.252406\pi$
$463$	−1.10528e6	+	4.84254e6i	−0.239618	+	1.04984i	−0.941360	+	0.337404i	$0.890451\pi$
$464$	−996459.	+	4.36577e6i	−0.214864	+	0.941383i
$465$	488932.	−	613102.i	0.104862	−	0.131492i
$466$	−7.68683e6	+	9.63898e6i	−1.63977	+	2.05620i
$467$	1.36325e6	−	5.97281e6i	0.289258	−	1.26732i	−0.596289	−	0.802770i	$-0.703359\pi$
$467$	1.36325e6	−	5.97281e6i	0.289258	−	1.26732i	0.885547	−	0.464550i	$-0.153784\pi$
$468$	1.61520e6	−	7.07664e6i	0.340887	−	1.49353i
$469$	1.81467e6	−	541113.i	0.380947	−	0.113594i
$470$	106310.	+	465775.i	0.0221988	+	0.0972594i
$471$	−1.51096e7			−3.13834
$472$	5.77169e6			1.19247
$473$	−928059.	−	4.06609e6i	−0.190732	−	0.835650i
$474$	−4.67010e6	−	2.24900e6i	−0.954730	−	0.459774i
$475$	690985.	−	866468.i	0.140519	−	0.176205i
$476$	−6.94652e6	+	2.07137e6i	−1.40524	+	0.419026i
$477$	3.61174e6	+	4.52897e6i	0.726809	+	0.911389i
$478$	−585382.	−	2.56472e6i	−0.117184	−	0.513418i
$479$	−2.85027e6	−	3.57412e6i	−0.567605	−	0.711755i	0.412338	−	0.911031i	$-0.364712\pi$
$479$	−2.85027e6	−	3.57412e6i	−0.567605	−	0.711755i	−0.979943	+	0.199276i	$0.936141\pi$
$480$	1.73486e7	+	8.35464e6i	3.43686	+	1.65510i
$481$	−625974.	+	784946.i	−0.123365	+	0.154695i
$482$	−1.24431e7	+	5.99227e6i	−2.43955	+	1.17483i
$483$	8.63083e6	+	1.52791e7i	1.68339	+	2.98010i
$484$	7.70687e6	+	3.71143e6i	1.49542	+	0.720158i
$485$	6.78602e6	−	3.26798e6i	1.30997	−	0.630848i
$486$	−2.52369e6	+	1.10570e7i	−0.484670	+	2.12348i
$487$	7.17122e6	−	3.45348e6i	1.37016	−	0.659834i	0.403282	−	0.915076i	$-0.367870\pi$
$487$	7.17122e6	−	3.45348e6i	1.37016	−	0.659834i	0.966877	+	0.255242i	$0.0821552\pi$
$488$	9.24611e6	+	1.15943e7i	1.75756	+	2.20391i
$489$	−3.02363e6			−0.571815
$490$	−8.89721e6	+	1.17034e6i	−1.67403	+	0.220202i
$491$	8.53899e6			1.59846			0.799231	−	0.601023i	$-0.205240\pi$
$491$	8.53899e6			1.59846			0.799231	+	0.601023i	$0.205240\pi$
$492$	−5.58730e6	−	7.00625e6i	−1.04061	−	1.30489i
$493$	1.00315e6	−	483091.i	0.185887	−	0.0895182i
$494$	737961.	−	3.23322e6i	0.136055	−	0.596098i
$495$	5.86212e6	−	2.82305e6i	1.07533	−	0.517851i
$496$	−1.39433e6	−	671475.i	−0.254485	−	0.122553i
$497$	−101189.	−	1.54516e6i	−0.0183757	−	0.280596i
$498$	−2.96087e7	+	1.42588e7i	−5.34991	+	2.57638i
$499$	2.51275e6	−	3.15089e6i	0.451750	−	0.566477i	−0.502848	−	0.864375i	$-0.667714\pi$
$499$	2.51275e6	−	3.15089e6i	0.451750	−	0.566477i	0.954598	+	0.297899i	$0.0962857\pi$
$500$	−1.34657e7	−	6.48476e6i	−2.40882	−	1.16003i
$501$	8.04352e6	+	1.00863e7i	1.43170	+	1.79529i
$502$	523654.	+	2.29428e6i	0.0927438	+	0.406337i
$503$	−1.56854e6	−	1.96689e6i	−0.276424	−	0.346625i	0.624168	−	0.781290i	$-0.285438\pi$
$503$	−1.56854e6	−	1.96689e6i	−0.276424	−	0.346625i	−0.900592	+	0.434665i	$0.856867\pi$
$504$	−2.38428e6	−	3.64079e7i	−0.418100	−	6.38439i
$505$	3.47788e6	−	4.36112e6i	0.606856	−	0.760974i
$506$	1.06276e7	+	5.11800e6i	1.84527	+	0.888636i
$507$	−2.16473e6	−	9.48432e6i	−0.374011	−	1.63865i
$508$	4.09082e6			0.703317
$509$	−7.63430e6			−1.30609			−0.653047	−	0.757317i	$-0.726510\pi$
$509$	−7.63430e6			−1.30609			−0.653047	+	0.757317i	$0.726510\pi$
$510$	−2.34589e6	−	1.02780e7i	−0.399376	−	1.74978i
$511$	−2.16427e6	+	5.36554e6i	−0.366657	+	0.908994i
$512$	−1.70803e6	+	7.48336e6i	−0.287952	+	1.26160i
$513$	−3.74684e6	+	1.64160e7i	−0.628595	+	2.75406i
$514$	5.72055e6	−	7.17334e6i	0.955058	−	1.19760i
$515$	−2.71106e6	+	3.39956e6i	−0.450423	+	0.564813i
$516$	9.01181e6	−	3.94833e7i	1.49001	−	6.52814i
$517$	46304.8	−	202874.i	0.00761903	−	0.0333811i
$518$	−3.14717e6	+	7.80228e6i	−0.515343	+	1.27761i
$519$	−2.76816e6	−	1.21281e7i	−0.451099	−	1.97640i
$520$	−4.19294e6			−0.680002
$521$	−7.80949e6			−1.26046			−0.630229	−	0.776409i	$-0.717039\pi$
$521$	−7.80949e6			−1.26046			−0.630229	+	0.776409i	$0.717039\pi$
$522$	2.07896e6	+	9.10852e6i	0.333941	+	1.46309i
$523$	−4.26070e6	−	2.05185e6i	−0.681125	−	0.328013i	0.0611302	−	0.998130i	$-0.480530\pi$
$523$	−4.26070e6	−	2.05185e6i	−0.681125	−	0.328013i	−0.742255	+	0.670117i	$0.766244\pi$
$524$	−4.06301e6	+	5.09485e6i	−0.646427	+	0.810594i
$525$	138491.	+	2.11476e6i	0.0219293	+	0.334859i
$526$	6.39282e6	+	8.01634e6i	1.00746	+	1.26332i
$527$	85623.7	+	375142.i	0.0134297	+	0.0588395i
$528$	−1.15147e7	−	1.44389e7i	−1.79749	−	2.25398i
$529$	−1.49017e7	−	7.17628e6i	−2.31524	−	1.11496i
$530$	3.47808e6	−	4.36137e6i	0.537836	−	0.674425i
$531$	5.68020e6	−	2.73544e6i	0.874234	−	0.421009i
$532$	−1.29702e6	−	1.98056e7i	−0.198687	−	3.03395i
$533$	585290.	+	281861.i	0.0892386	+	0.0429751i
$534$	1.04618e7	−	5.03815e6i	1.58765	−	0.764571i
$535$	−1.03418e6	+	4.53106e6i	−0.156212	+	0.684408i
$536$	6.67995e6	−	3.21689e6i	1.00429	−	0.483643i
$537$	8.42411e6	+	1.05635e7i	1.26063	+	1.58078i
$538$	−1.08871e7			−1.62165
$539$	3.71270e6	+	1.22215e6i	0.550450	+	0.181198i
$540$	3.54903e7			5.23751
$541$	−1.63871e6	−	2.05488e6i	−0.240719	−	0.301852i	0.646766	−	0.762688i	$-0.276121\pi$
$541$	−1.63871e6	−	2.05488e6i	−0.240719	−	0.301852i	−0.887485	+	0.460837i	$0.847549\pi$
$542$	7.80911e6	−	3.76067e6i	1.14183	−	0.549879i
$543$	244621.	−	1.07175e6i	0.0356036	−	0.155990i
$544$	−8.51271e6	+	4.09951e6i	−1.23331	+	0.593929i
$545$	−4.97753e6	−	2.39705e6i	−0.717832	−	0.345690i
$546$	3.11911e6	+	5.52175e6i	0.447764	+	0.792674i
$547$	9.68775e6	−	4.66537e6i	1.38438	−	0.666681i	0.414449	−	0.910072i	$-0.363974\pi$
$547$	9.68775e6	−	4.66537e6i	1.38438	−	0.666681i	0.969928	+	0.243391i	$0.0782599\pi$
$548$	−2.14591e7	+	2.69089e7i	−3.05253	+	3.82775i
$549$	1.45945e7	+	7.02836e6i	2.06662	+	0.995230i
$550$	888201.	+	1.11377e6i	0.125200	+	0.156996i
$551$	678388.	+	2.97221e6i	0.0951917	+	0.417062i
$552$	4.28384e7	+	5.37177e7i	5.98392	+	7.50360i
$553$	2.15507e6	−	642618.i	0.299674	−	0.0893594i
$554$	−8.11768e6	+	1.01792e7i	−1.12372	+	1.40910i
$555$	−7.87341e6	−	3.79163e6i	−1.08500	−	0.522509i
$556$	−264498.	−	1.15884e6i	−0.0362857	−	0.158978i
$557$	−6.49229e6			−0.886666			−0.443333	−	0.896357i	$-0.646204\pi$
$557$	−6.49229e6			−0.886666			−0.443333	+	0.896357i	$0.646204\pi$
$558$	−3.22881e6			−0.438993
$559$	653282.	+	2.86222e6i	0.0884242	+	0.387412i
$560$	−1.76285e7	+	5.25662e6i	−2.37545	+	0.708331i
$561$	−1.02178e6	+	4.47673e6i	−0.137073	+	0.600556i
$562$	3.87338e6	−	1.69704e7i	0.517308	−	2.26647i
$563$	−601184.	+	753862.i	−0.0799350	+	0.100235i	−0.820191	−	0.572090i	$-0.806133\pi$
$563$	−601184.	+	753862.i	−0.0799350	+	0.100235i	0.740256	+	0.672325i	$0.234704\pi$
$564$	1.25986e6	−	1.57981e6i	0.166772	−	0.209125i
$565$	−1.53130e6	+	6.70905e6i	−0.201808	+	0.884179i
$566$	−1.75587e6	+	7.69298e6i	−0.230384	+	1.00938i
$567$	−7.24579e6	−	1.28272e7i	−0.946516	−	1.67561i
$568$	−1.34909e6	−	5.91077e6i	−0.175457	−	0.768729i
$569$	9.90573e6			1.28264			0.641322	−	0.767272i	$-0.278386\pi$
$569$	9.90573e6			1.28264			0.641322	+	0.767272i	$0.278386\pi$
$570$	2.88661e7			3.72136
$571$	−958171.	−	4.19802e6i	−0.122985	−	0.538833i	−0.998455	−	0.0555609i	$-0.982305\pi$
$571$	−958171.	−	4.19802e6i	−0.122985	−	0.538833i	0.875470	−	0.483272i	$-0.160552\pi$
$572$	2.74309e6	+	1.32100e6i	0.350549	+	0.168816i
$573$	1.09141e7	−	1.36859e7i	1.38868	−	1.74135i
$574$	5.37498e6	+	861925.i	0.680922	+	0.109192i
$575$	−1.73005e6	−	2.16941e6i	−0.218217	−	0.273636i
$576$	−6.53969e6	−	2.86523e7i	−0.821298	−	3.59834i
$577$	3.73257e6	+	4.68050e6i	0.466733	+	0.585265i	0.958368	−	0.285537i	$-0.0921718\pi$
$577$	3.73257e6	+	4.68050e6i	0.466733	+	0.585265i	−0.491634	+	0.870802i	$0.663600\pi$
$578$	−8.87574e6	−	4.27433e6i	−1.10506	−	0.532168i
$579$	−9.96428e6	+	1.24948e7i	−1.23523	+	1.54894i
$580$	5.78939e6	−	2.78802e6i	0.714600	−	0.344133i
$581$	5.33356e6	−	1.32226e7i	0.655506	−	1.62509i
$582$	−4.01864e7	−	1.93527e7i	−4.91781	−	2.36829i
$583$	−2.18913e6	+	1.05423e6i	−0.266747	+	0.128459i
$584$	−5.04067e6	+	2.20846e7i	−0.611584	+	2.67952i
$585$	−4.12648e6	+	1.98721e6i	−0.498528	+	0.240079i
$586$	−7.82716e6	−	9.81495e6i	−0.941586	−	1.18071i
$587$	2.52545e6			0.302513			0.151257	−	0.988495i	$-0.451668\pi$
$587$	2.52545e6			0.302513			0.151257	+	0.988495i	$0.451668\pi$
$588$	2.73323e7	+	2.63346e7i	3.26012	+	3.14111i
$589$	−1.05360e6			−0.125137
$590$	−3.78536e6	−	4.74669e6i	−0.447689	−	0.561385i
$591$	−4.07121e6	+	1.96059e6i	−0.479463	+	0.230897i
$592$	−3.83761e6	+	1.68137e7i	−0.450046	+	1.97178i
$593$	−5.27888e6	+	2.54217e6i	−0.616460	+	0.296872i	−0.715933	−	0.698169i	$-0.753999\pi$
$593$	−5.27888e6	+	2.54217e6i	−0.616460	+	0.296872i	0.0994732	+	0.995040i	$0.468284\pi$
$594$	−1.95005e7	−	9.39095e6i	−2.26767	−	1.09205i
$595$	3.75467e6	+	2.61196e6i	0.434790	+	0.302464i
$596$	3.40013e7	−	1.63742e7i	3.92085	−	1.88818i
$597$	−7.57375e6	+	9.49718e6i	−0.869711	+	1.09058i
$598$	−7.48104e6	−	3.60268e6i	−0.855478	−	0.411977i
$599$	5.88497e6	+	7.37951e6i	0.670158	+	0.840351i	0.994406	−	0.105621i	$-0.0336830\pi$
$599$	5.88497e6	+	7.37951e6i	0.670158	+	0.840351i	−0.324249	+	0.945972i	$0.605112\pi$
$600$	1.84642e6	+	8.08969e6i	0.209388	+	0.917389i
$601$	2.04946e6	+	2.56994e6i	0.231448	+	0.290227i	0.883970	−	0.467543i	$-0.154861\pi$
$601$	2.04946e6	+	2.56994e6i	0.231448	+	0.290227i	−0.652522	+	0.757769i	$0.726289\pi$
$602$	1.20998e7	+	2.14202e7i	1.36077	+	2.40897i
$603$	5.04945e6	−	6.33181e6i	0.565523	−	0.709144i
$604$	8.57713e6	+	4.13053e6i	0.956642	+	0.460695i
$605$	−1.20103e6	−	5.26206e6i	−0.133403	−	0.584477i
$606$	−3.30330e7			−3.65399
$607$	−1.26755e7			−1.39635			−0.698174	−	0.715928i	$-0.746004\pi$
$607$	−1.26755e7			−1.39635			−0.698174	+	0.715928i	$0.746004\pi$
$608$	−5.75680e6	−	2.52222e7i	−0.631571	−	2.76709i
$609$	−4.78575e6	−	3.32923e6i	−0.522886	−	0.363748i
$610$	3.47116e6	−	1.52082e7i	0.377703	−	1.65482i
$611$	−32595.0	+	142808.i	−0.00353222	+	0.0154757i
$612$	−1.93292e7	+	2.42381e7i	−2.08610	+	2.61589i
$613$	−8.66093e6	+	1.08605e7i	−0.930923	+	1.16734i	0.0547212	+	0.998502i	$0.482573\pi$
$613$	−8.66093e6	+	1.08605e7i	−0.930923	+	1.16734i	−0.985644	+	0.168838i	$0.945998\pi$
$614$	1.56284e6	−	6.84727e6i	0.167300	−	0.732987i
$615$	−1.25823e6	+	5.51264e6i	−0.134144	+	0.587722i
$616$	1.51108e7	+	2.42314e6i	1.60448	+	0.257292i
$617$	−2.86092e6	−	1.25345e7i	−0.302547	−	1.32555i	−0.866267	−	0.499581i	$-0.833487\pi$
$617$	−2.86092e6	−	1.25345e7i	−0.302547	−	1.32555i	0.563720	−	0.825966i	$-0.309370\pi$
$618$	2.57497e7			2.71207
$619$	3.32266e6			0.348545			0.174272	−	0.984697i	$-0.444243\pi$
$619$	3.32266e6			0.348545			0.174272	+	0.984697i	$0.444243\pi$
$620$	494153.	+	2.16503e6i	0.0516276	+	0.226195i
$621$	3.79834e7	+	1.82918e7i	3.95243	+	1.90339i
$622$	−1.64977e6	+	2.06874e6i	−0.170981	+	0.214403i
$623$	−1.88454e6	+	4.67203e6i	−0.194529	+	0.482265i
$624$	8.10543e6	+	1.01639e7i	0.833326	+	1.04496i
$625$	1.69594e6	+	7.43041e6i	0.173665	+	0.760874i
$626$	−4.63457e6	−	5.81156e6i	−0.472687	−	0.592730i
$627$	−1.13279e7	−	5.45524e6i	−1.15075	−	0.554172i
$628$	2.66779e7	−	3.34531e7i	2.69931	−	3.38483i
$629$	3.86337e6	−	1.86050e6i	0.389350	−	0.187501i
$630$	−2.83784e7	+	2.58389e7i	−2.84864	+	2.59372i
$631$	6.41272e6	+	3.08820e6i	0.641163	+	0.308768i	0.726070	−	0.687621i	$-0.241345\pi$
$631$	6.41272e6	+	3.08820e6i	0.641163	+	0.308768i	−0.0849065	+	0.996389i	$0.527059\pi$
$632$	7.93301e6	−	3.82034e6i	0.790034	−	0.380460i
$633$	2.06111e6	−	9.03029e6i	0.204452	−	0.895762i
$634$	9.67343e6	−	4.65848e6i	0.955779	−	0.460279i
$635$	−1.60937e6	−	2.01808e6i	−0.158387	−	0.198612i
$636$	−2.35938e7			−2.31289
$637$	−2.61346e6	−	860303.i	−0.255192	−	0.0840045i
$638$	−3.91877e6			−0.381152
$639$	−4.12907e6	−	5.17769e6i	−0.400037	−	0.501630i
$640$	−5.83977e6	+	2.81228e6i	−0.563567	+	0.271400i
$641$	3.84502e6	−	1.68461e7i	0.369618	−	1.61940i	−0.358209	−	0.933642i	$-0.616612\pi$
$641$	3.84502e6	−	1.68461e7i	0.369618	−	1.61940i	0.727827	−	0.685761i	$-0.240530\pi$
$642$	2.47971e7	−	1.19416e7i	2.37445	−	1.14347i
$643$	8.38278e6	+	4.03694e6i	0.799578	+	0.385057i	0.788618	−	0.614883i	$-0.210797\pi$
$643$	8.38278e6	+	4.03694e6i	0.799578	+	0.385057i	0.0109601	+	0.999940i	$0.496511\pi$
$644$	−4.90674e7	−	7.86838e6i	−4.66206	−	0.747602i
$645$	−2.30232e7	+	1.10874e7i	−2.17905	+	1.04937i
$646$	−8.83124e6	+	1.10740e7i	−0.832608	+	1.04406i
$647$	−5.65566e6	−	2.72362e6i	−0.531156	−	0.255791i	0.149027	−	0.988833i	$-0.452386\pi$
$647$	−5.65566e6	−	2.72362e6i	−0.531156	−	0.255791i	−0.680184	+	0.733042i	$0.738100\pi$
$648$	−3.59639e7	−	4.50973e7i	−3.36456	−	4.21903i
$649$	588437.	+	2.57811e6i	0.0548388	+	0.240265i
$650$	−625226.	−	784008.i	−0.0580435	−	0.0727842i
$651$	1.48975e6	−	1.35644e6i	0.137772	−	0.125444i
$652$	5.33861e6	−	6.69441e6i	0.491824	−	0.616728i
$653$	−1.38067e7	−	6.64897e6i	−1.26709	−	0.610199i	−0.325050	−	0.945697i	$-0.605381\pi$
$653$	−1.38067e7	−	6.64897e6i	−1.26709	−	0.610199i	−0.942041	+	0.335498i	$0.891096\pi$
$654$	7.28012e6	+	3.18963e7i	0.665571	+	2.91606i
$655$	4.11181e6			0.374481
$656$	1.11590e7			1.01243
$657$	5.50604e6	+	2.41235e7i	0.497652	+	2.18036i
$658$	80212.4	+	1.22484e6i	0.00722232	+	0.110285i
$659$	513959.	−	2.25180e6i	0.0461015	−	0.201984i	−0.946632	−	0.322316i	$-0.895539\pi$
$659$	513959.	−	2.25180e6i	0.0461015	−	0.201984i	0.992734	+	0.120332i	$0.0383959\pi$
$660$	−5.89694e6	+	2.58362e7i	−0.526947	+	2.30871i
$661$	1.23291e7	−	1.54601e7i	1.09755	−	1.37629i	0.177675	−	0.984089i	$-0.443143\pi$
$661$	1.23291e7	−	1.54601e7i	1.09755	−	1.37629i	0.919880	−	0.392200i	$-0.128286\pi$
$662$	1.61482e7	−	2.02492e7i	1.43212	−	1.79582i
$663$	719258.	−	3.15127e6i	0.0635478	−	0.278421i
$664$	1.24220e7	−	5.44245e7i	1.09338	−	4.79043i
$665$	−9.26020e6	+	8.43153e6i	−0.812019	+	0.739354i
$666$	8.00658e6	+	3.50791e7i	0.699458	+	3.06453i
$667$	7.63303e6			0.664328
$668$	−3.65332e7			−3.16772
$669$	2.41261e6	+	1.05704e7i	0.208412	+	0.913112i
$670$	−7.02664e6	−	3.38385e6i	−0.604729	−	0.291222i
$671$	−4.23628e6	+	5.31213e6i	−0.363227	+	0.455473i
$672$	4.06119e7	+	2.82519e7i	3.46920	+	2.41337i
$673$	−1.00451e7	−	1.25961e7i	−0.854900	−	1.07201i	−0.996624	−	0.0821040i	$-0.973836\pi$
$673$	−1.00451e7	−	1.25961e7i	−0.854900	−	1.07201i	0.141724	−	0.989906i	$-0.454735\pi$
$674$	1.61178e6	+	7.06169e6i	0.136665	+	0.598769i
$675$	3.17445e6	+	3.98063e6i	0.268169	+	0.336273i
$676$	2.48207e7	+	1.19530e7i	2.08904	+	1.00603i
$677$	244110.	−	306104.i	0.0204698	−	0.0256683i	−0.771491	−	0.636240i	$-0.780489\pi$
$677$	244110.	−	306104.i	0.0204698	−	0.0256683i	0.791961	+	0.610572i	$0.209060\pi$
$678$	3.67166e7	−	1.76818e7i	3.06752	−	1.47724i
$679$	1.85445e7	−	5.52975e6i	1.54362	−	0.460289i
$680$	1.61346e7	+	7.77002e6i	1.33809	+	0.644391i
$681$	−1.74827e6	+	841923.i	−0.144458	+	0.0695672i
$682$	301362.	−	1.32035e6i	0.0248100	−	0.108700i
$683$	−626587.	+	301748.i	−0.0513960	+	0.0247510i	−0.459405	−	0.888227i	$-0.651937\pi$
$683$	−626587.	+	301748.i	−0.0513960	+	0.0247510i	0.408009	+	0.912978i	$0.366223\pi$
$684$	−5.29256e7	−	6.63666e7i	−4.32539	−	5.42387i
$685$	2.17169e7			1.76836
$686$	−2.30469e7	−	650459.i	−1.86983	−	0.0527728i
$687$	−1.48087e7			−1.19709
$688$	3.14429e7	+	3.94281e7i	2.53251	+	3.17567i
$689$	1.54098e6	−	742096.i	0.123665	−	0.0595542i
$690$	1.60823e7	−	7.04614e7i	1.28596	−	5.63415i
$691$	−4.33548e6	+	2.08786e6i	−0.345416	+	0.166344i	−0.598545	−	0.801089i	$-0.704254\pi$
$691$	−4.33548e6	+	2.08786e6i	−0.345416	+	0.166344i	0.253129	+	0.967432i	$0.418540\pi$
$692$	3.17395e7	+	1.52850e7i	2.51962	+	1.21339i
$693$	1.60197e7	−	4.77688e6i	1.26713	−	0.377843i
$694$	−2.90903e7	+	1.40091e7i	−2.29271	+	1.10411i
$695$	−467623.	+	586381.i	−0.0367227	+	0.0460488i
$696$	−2.05654e7	−	9.90376e6i	−1.60921	−	0.774956i
$697$	−1.72990e6	−	2.16922e6i	−0.134877	−	0.169131i
$698$	1.02178e7	+	4.47671e7i	0.793814	+	3.47792i
$699$	−2.05140e7	−	2.57237e7i	−1.58802	−	1.99132i
$700$	−4.92667e6	−	3.42726e6i	−0.380022	−	0.264364i
$701$	282941.	−	354797.i	0.0217471	−	0.0272700i	−0.770839	−	0.637030i	$-0.780163\pi$
$701$	282941.	−	354797.i	0.0217471	−	0.0272700i	0.792586	+	0.609760i	$0.208734\pi$
$702$	1.37269e7	+	6.61051e6i	1.05130	+	0.506282i
$703$	2.61264e6	+	1.14467e7i	0.199384	+	0.873560i
$704$	1.23271e7			0.937409
$705$	−1.27499e6			−0.0966126
$706$	−4.53117e6	−	1.98524e7i	−0.342136	−	1.49900i
$707$	1.05969e7	−	9.64864e6i	0.797318	−	0.725968i
$708$	−5.71395e6	+	2.50344e7i	−0.428404	+	1.87696i
$709$	−4.95581e6	+	2.17128e7i	−0.370253	+	1.62219i	0.355811	+	0.934558i	$0.384205\pi$
$709$	−4.95581e6	+	2.17128e7i	−0.370253	+	1.62219i	−0.726064	+	0.687627i	$0.758652\pi$
$710$	−3.97626e6	+	4.98608e6i	−0.296026	+	0.371204i
$711$	5.99666e6	−	7.51957e6i	0.444872	−	0.557852i
$712$	−4.38915e6	+	1.92301e7i	−0.324474	+	1.42161i
$713$	−586997.	+	2.57180e6i	−0.0432426	+	0.189458i
$714$	−1.77001e6	−	2.70280e7i	−0.129936	−	1.98412i
$715$	−427480.	−	1.87291e6i	−0.0312716	−	0.137010i
$716$	−3.82619e7			−2.78922
$717$	7.02055e6			0.510004
$718$	3.31279e6	+	1.45143e7i	0.239819	+	1.05071i
$719$	1.08739e7	+	5.23661e6i	0.784449	+	0.377771i	0.782836	−	0.622228i	$-0.213772\pi$
$719$	1.08739e7	+	5.23661e6i	0.784449	+	0.377771i	0.00161279	+	0.999999i	$0.499487\pi$
$720$	−4.90527e7	+	6.15101e7i	−3.52640	+	4.42196i
$721$	−8.26046e6	+	7.52126e6i	−0.591788	+	0.538831i
$722$	−7.84491e6	−	9.83720e6i	−0.560073	−	0.702310i
$723$	−8.20147e6	−	3.59330e7i	−0.583507	−	2.55651i
$724$	1.94099e6	+	2.43393e6i	0.137619	+	0.172568i
$725$	830543.	+	399968.i	0.0586836	+	0.0282605i
$726$	−1.99286e7	+	2.49896e7i	−1.40325	+	1.75962i
$727$	−1.55264e7	+	7.47714e6i	−1.08952	+	0.524686i	−0.890349	−	0.455279i	$-0.849540\pi$
$727$	−1.55264e7	+	7.47714e6i	−1.08952	+	0.524686i	−0.199172	+	0.979964i	$0.563825\pi$
$728$	−1.06368e7	−	1.70570e6i	−0.743846	−	0.119282i
$729$	−2.39026e6	−	1.15109e6i	−0.166581	−	0.0802214i
$730$	2.14685e7	−	1.03387e7i	1.49106	−	0.718055i
$731$	2.79017e6	−	1.22245e7i	0.193125	−	0.846134i
$732$	−5.94432e7	+	2.86263e7i	−4.10038	+	1.97464i
$733$	−2.98945e6	−	3.74865e6i	−0.205509	−	0.257700i	0.668386	−	0.743814i	$-0.266985\pi$
$733$	−2.98945e6	−	3.74865e6i	−0.205509	−	0.257700i	−0.873895	+	0.486114i	$0.838414\pi$
$734$	1.48703e7			1.01878
$735$	2.23857e6	−	2.38438e7i	0.152846	−	1.62801i
$736$	−6.47739e7			−4.40763
$737$	2.11796e6	+	2.65584e6i	0.143632	+	0.180108i
$738$	2.09759e7	−	1.01015e7i	1.41768	−	0.682721i
$739$	−5.45085e6	+	2.38817e7i	−0.367158	+	1.60862i	0.367389	+	0.930067i	$0.380252\pi$
$739$	−5.45085e6	+	2.38817e7i	−0.367158	+	1.60862i	−0.734547	+	0.678558i	$0.762605\pi$
$740$	2.22964e7	−	1.07374e7i	1.49677	−	0.720806i
$741$	7.97398e6	+	3.84007e6i	0.533494	+	0.256917i
$742$	1.05975e7	−	9.64920e6i	0.706636	−	0.643401i
$743$	1.58380e7	−	7.62718e6i	1.05252	−	0.506865i	0.174083	−	0.984731i	$-0.444304\pi$
$743$	1.58380e7	−	7.62718e6i	1.05252	−	0.506865i	0.878433	+	0.477866i	$0.158590\pi$
$744$	4.91840e6	−	6.16748e6i	0.325755	−	0.408484i
$745$	−2.14541e7	−	1.03318e7i	−1.41619	−	0.681999i
$746$	6.94639e6	+	8.71050e6i	0.456996	+	0.573055i
$747$	−1.35689e7	−	5.94492e7i	−0.889698	−	3.89802i
$748$	−8.10754e6	−	1.01665e7i	−0.529828	−	0.664383i
$749$	−4.46681e6	+	1.10739e7i	−0.290933	+	0.721264i
$750$	3.48200e7	−	4.36629e7i	2.26035	−	2.83439i
$751$	2.71463e7	+	1.30730e7i	1.75635	+	0.845812i	0.975156	+	0.221520i	$0.0711017\pi$
$751$	2.71463e7	+	1.30730e7i	1.75635	+	0.845812i	0.781191	+	0.624292i	$0.214613\pi$
$752$	559905.	+	2.45310e6i	0.0361052	+	0.158187i
$753$	−6.28024e6			−0.403635
$754$	2.75851e6			0.176704
$755$	−1.33665e6	−	5.85625e6i	−0.0853396	−	0.373897i
$756$	9.00331e7	+	1.44376e7i	5.72925	+	0.918735i
$757$	−2.59496e6	+	1.13693e7i	−0.164585	+	0.721096i	0.823516	+	0.567293i	$0.192009\pi$
$757$	−2.59496e6	+	1.13693e7i	−0.164585	+	0.721096i	−0.988102	+	0.153803i	$0.950848\pi$
$758$	8.15676e6	−	3.57371e7i	0.515638	−	2.25916i
$759$	−1.96272e7	+	2.46118e7i	−1.23667	+	1.55074i
$760$	−3.05724e7	+	3.83366e7i	−1.91998	+	2.40757i
$761$	−3.63404e6	+	1.59218e7i	−0.227472	+	0.996620i	0.724221	+	0.689568i	$0.242200\pi$
$761$	−3.63404e6	+	1.59218e7i	−0.227472	+	0.996620i	−0.951693	+	0.307052i	$0.900658\pi$
$762$	−3.40142e6	+	1.49026e7i	−0.212213	+	0.929767i
$763$	−1.16521e7	−	8.10582e6i	−0.724589	−	0.504064i
$764$	1.10306e7	+	4.83284e7i	0.683703	+	2.99550i
$765$	1.95614e7			1.20850
$766$	−3.07974e7			−1.89645
$767$	−414214.	−	1.81479e6i	−0.0254236	−	0.111388i
$768$	−8.57251e6	−	4.12830e6i	−0.524451	−	0.252562i
$769$	−9.78114e6	+	1.22652e7i	−0.596450	+	0.747924i	−0.984820	−	0.173579i	$-0.944467\pi$
$769$	−9.78114e6	+	1.22652e7i	−0.596450	+	0.747924i	0.388370	+	0.921503i	$0.373038\pi$
$770$	−7.91756e6	−	1.40164e7i	−0.481243	−	0.851943i
$771$	1.52665e7	+	1.91436e7i	0.924921	+	1.15981i
$772$	−1.00707e7	−	4.41225e7i	−0.608157	−	2.66451i
$773$	−4.43276e6	−	5.55850e6i	−0.266824	−	0.334587i	0.630311	−	0.776343i	$-0.282927\pi$
$773$	−4.43276e6	−	5.55850e6i	−0.266824	−	0.334587i	−0.897135	+	0.441756i	$0.854356\pi$
$774$	9.47959e7	+	4.56513e7i	5.68770	+	2.73905i
$775$	−198632.	+	249077.i	−0.0118794	+	0.0148963i
$776$	6.82638e7	−	3.28741e7i	4.06945	−	1.95975i
$777$	−1.84311e7	−	1.28217e7i	−1.09521	−	0.761891i
$778$	3.99645e7	+	1.92459e7i	2.36715	+	1.13996i
$779$	6.84467e6	−	3.29622e6i	0.404119	−	0.194613i
$780$	4.15099e6	−	1.81867e7i	0.244296	−	1.07033i
$781$	2.50269e6	−	1.20523e6i	0.146818	−	0.0707039i
$782$	2.21112e7	+	2.77265e7i	1.29299	+	1.62136i
$783$	−1.40058e7			−0.816398
$784$	−4.68591e7	+	6.16384e6i	−2.72272	+	0.358147i
$785$	−2.69984e7			−1.56374
$786$	−1.51819e7	−	1.90375e7i	−0.876536	−	1.09914i
$787$	−3.10711e7	+	1.49631e7i	−1.78822	+	0.861159i	−0.840664	+	0.541556i	$0.817835\pi$
$787$	−3.10711e7	+	1.49631e7i	−1.78822	+	0.861159i	−0.947552	+	0.319603i	$0.896450\pi$
$788$	2.84745e6	−	1.24755e7i	0.163358	−	0.715718i
$789$	−2.46533e7	+	1.18724e7i	−1.40988	+	0.678964i
$790$	−8.34474e6	−	4.01861e6i	−0.475713	−	0.229091i
$791$	−6.61392e6	+	1.63968e7i	−0.375853	+	0.931792i
$792$	5.89698e7	−	2.83984e7i	3.34054	−	1.60872i
$793$	2.98202e6	−	3.73933e6i	0.168394	−	0.211160i
$794$	5.81670e7	+	2.80118e7i	3.27435	+	1.57685i
$795$	9.28202e6	+	1.16393e7i	0.520864	+	0.653143i
$796$	−7.65462e6	−	3.35371e7i	−0.428194	−	1.87604i
$797$	−1.31922e7	−	1.65425e7i	−0.735650	−	0.922476i	0.263459	−	0.964670i	$-0.415137\pi$
$797$	−1.31922e7	−	1.65425e7i	−0.735650	−	0.922476i	−0.999109	+	0.0421945i	$0.986565\pi$
$798$	7.32287e7	+	1.17429e7i	4.07075	+	0.652780i
$799$	390067.	−	489129.i	0.0216159	−	0.0271054i
$800$	−7.04798e6	−	3.39413e6i	−0.389350	−	0.187501i
$801$	4.79437e6	+	2.10055e7i	0.264028	+	1.15678i
$802$	1.70807e7			0.937711
$803$	−1.03787e7			−0.568008
$804$	7.34001e6	+	3.21587e7i	0.400458	+	1.75452i
$805$	1.54219e7	+	2.73014e7i	0.838782	+	1.48489i
$806$	−212136.	+	929427.i	−0.0115021	+	0.0503939i
$807$	6.46528e6	−	2.83262e7i	0.349465	−	1.53111i
$808$	3.49856e7	−	4.38706e7i	1.88522	−	2.36399i
$809$	3.27968e6	−	4.11259e6i	0.176182	−	0.220925i	−0.685898	−	0.727698i	$-0.740590\pi$
$809$	3.27968e6	−	4.11259e6i	0.176182	−	0.220925i	0.862079	+	0.506773i	$0.169162\pi$
$810$	−1.35015e7	+	5.91540e7i	−0.723053	+	3.16790i
$811$	−5.57327e6	+	2.44181e7i	−0.297549	+	1.30365i	0.576216	+	0.817298i	$0.304529\pi$
$811$	−5.57327e6	+	2.44181e7i	−0.297549	+	1.30365i	−0.873765	+	0.486349i	$0.838328\pi$
$812$	1.58209e7	−	4.71762e6i	0.842057	−	0.251092i
$813$	5.14714e6	+	2.25511e7i	0.273111	+	1.19658i
$814$	−1.50922e7			−0.798344
$815$	−5.40274e6			−0.284918
$816$	−1.23551e7	−	5.41314e7i	−0.649565	−	2.84593i
$817$	3.09330e7	+	1.48965e7i	1.62131	+	0.780782i
$818$	−6.09510e6	+	7.64301e6i	−0.318491	+	0.399375i
$819$	−1.12766e7	+	3.36256e6i	−0.587447	+	0.175170i
$820$	−9.98362e6	−	1.25191e7i	−0.518505	−	0.650185i
$821$	−1.74754e6	−	7.65649e6i	−0.0904837	−	0.396435i	0.909323	−	0.416091i	$-0.136600\pi$
$821$	−1.74754e6	−	7.65649e6i	−0.0904837	−	0.396435i	−0.999807	+	0.0196558i	$0.993743\pi$
$822$	−8.01844e7	−	1.00548e8i	−4.13914	−	5.19032i
$823$	−9.13823e6	−	4.40074e6i	−0.470287	−	0.226478i	0.183703	−	0.982982i	$-0.441192\pi$
$823$	−9.13823e6	−	4.40074e6i	−0.470287	−	0.226478i	−0.653989	+	0.756504i	$0.726906\pi$
$824$	−2.72718e7	+	3.41978e7i	−1.39925	+	1.75461i
$825$	−3.42527e6	+	1.64952e6i	−0.175210	+	0.0843769i
$826$	−7.67187e6	−	1.35815e7i	−0.391247	−	0.692623i
$827$	1.85274e7	+	8.92234e6i	0.942001	+	0.453644i	0.840875	−	0.541230i	$-0.182041\pi$
$827$	1.85274e7	+	8.92234e6i	0.942001	+	0.453644i	0.101127	+	0.994874i	$0.467755\pi$
$828$	−1.91486e8	+	9.22146e7i	−9.70645	+	4.67438i
$829$	3.37868e6	−	1.48030e7i	0.170750	−	0.748104i	−0.814941	−	0.579544i	$-0.803231\pi$
$829$	3.37868e6	−	1.48030e7i	0.170750	−	0.748104i	0.985691	−	0.168561i	$-0.0539120\pi$
$830$	−5.29062e7	+	2.54783e7i	−2.66570	+	1.28373i
$831$	−2.16638e7	−	2.71656e7i	−1.08826	−	1.36463i
$832$	−8.67733e6			−0.434588
$833$	8.46244e6	+	8.15353e6i	0.422555	+	0.407130i
$834$	4.44151e6			0.221114
$835$	1.43725e7	+	1.80225e7i	0.713372	+	0.894540i
$836$	3.20790e7	−	1.54484e7i	1.58747	−	0.764485i
$837$	1.07707e6	−	4.71896e6i	0.0531412	−	0.232827i
$838$	4.96299e7	−	2.39005e7i	2.44137	−	1.17570i
$839$	5.62016e6	+	2.70652e6i	0.275641	+	0.132742i	0.566598	−	0.823995i	$-0.308259\pi$
$839$	5.62016e6	+	2.70652e6i	0.275641	+	0.132742i	−0.290957	+	0.956736i	$0.593974\pi$
$840$	−6.12750e6	−	9.35668e7i	−0.299630	−	4.57534i
$841$	1.61952e7	−	7.79920e6i	0.789581	−	0.380242i
$842$	−1.63469e7	+	2.04984e7i	−0.794613	+	0.996413i
$843$	4.18535e7	+	2.01556e7i	2.02844	+	0.976846i
$844$	1.63542e7	+	2.05075e7i	0.790267	+	0.990963i
$845$	−3.86804e6	−	1.69470e7i	−0.186358	−	0.816489i
$846$	3.27310e6	+	4.10434e6i	0.157229	+	0.197159i
$847$	−906194.	−	1.38376e7i	−0.0434023	−	0.662752i
$848$	1.83181e7	−	2.29701e7i	0.874762	−	1.09692i
$849$	−1.89730e7	−	9.13689e6i	−0.903370	−	0.435040i
$850$	953034.	+	4.17551e6i	0.0452440	+	0.198227i
$851$	2.93967e7			1.39147
$852$	2.69733e7			1.27302
$853$	1.60881e6	+	7.04868e6i	0.0757065	+	0.331692i	0.998572	−	0.0534317i	$-0.0170159\pi$
$853$	1.60881e6	+	7.04868e6i	0.0757065	+	0.331692i	−0.922865	+	0.385124i	$0.874159\pi$
$854$	1.49925e7	−	3.71686e7i	0.703445	−	1.74394i
$855$	−1.19185e7	+	5.22185e7i	−0.557580	+	2.44292i
$856$	−1.04034e7	+	4.55801e7i	−0.485276	+	2.12613i
$857$	−2.47754e7	+	3.10673e7i	−1.15231	+	1.44495i	−0.277336	+	0.960773i	$0.589452\pi$
$857$	−2.47754e7	+	3.10673e7i	−1.15231	+	1.44495i	−0.874971	+	0.484175i	$0.839120\pi$
$858$	−7.09312e6	+	8.89449e6i	−0.328942	+	0.412480i
$859$	−3.03886e6	+	1.33141e7i	−0.140517	+	0.615643i	0.854799	+	0.518960i	$0.173681\pi$
$859$	−3.03886e6	+	1.33141e7i	−0.140517	+	0.615643i	−0.995315	+	0.0966834i	$0.969177\pi$
$860$	1.61027e7	−	7.05505e7i	0.742424	−	3.25277i
$861$	−5.43448e6	+	1.34728e7i	−0.249833	+	0.619371i
$862$	−711610.	−	3.11777e6i	−0.0326193	−	0.142914i
$863$	−9.64777e6			−0.440961			−0.220480	−	0.975391i	$-0.570762\pi$
$863$	−9.64777e6			−0.440961			−0.220480	+	0.975391i	$0.570762\pi$
$864$	1.18853e8			5.41658
$865$	−4.94626e6	−	2.16710e7i	−0.224769	−	0.984778i
$866$	−4.87891e7	−	2.34956e7i	−2.21069	−	1.06461i
$867$	1.63918e7	−	2.05547e7i	0.740592	−	0.928674i
$868$	372845.	+	5.69334e6i	0.0167969	+	0.256489i
$869$	2.51527e6	+	3.15404e6i	0.112989	+	0.141683i
$870$	5.34284e6	+	2.34085e7i	0.239317	+	1.04852i
$871$	−1.49088e6	−	1.86951e6i	−0.0665884	−	0.0834992i
$872$	−5.00714e7	−	2.41131e7i	−2.22997	−	1.07389i
$873$	5.16014e7	−	6.47061e7i	2.29153	−	2.87349i
$874$	−8.74870e7	+	4.21315e7i	−3.87405	+	1.86564i
$875$	1.58334e6	+	2.41776e7i	0.0699123	+	1.06756i
$876$	−9.08008e7	−	4.37273e7i	−3.99787	−	1.92527i
$877$	1.14801e7	−	5.52854e6i	0.504020	−	0.242723i	−0.164555	−	0.986368i	$-0.552619\pi$
$877$	1.14801e7	−	5.52854e6i	0.504020	−	0.242723i	0.668575	+	0.743645i	$0.266905\pi$
$878$	1.40325e7	−	6.14805e7i	0.614326	−	2.69154i
$879$	3.01848e7	−	1.45362e7i	1.31770	−	0.634569i
$880$	−2.05749e7	−	2.58001e7i	−0.895634	−	1.12309i
$881$	4.02257e6			0.174608			0.0873039	−	0.996182i	$-0.472175\pi$
$881$	4.02257e6			0.174608			0.0873039	+	0.996182i	$0.472175\pi$
$882$	−8.25029e7	+	5.40047e7i	−3.57106	+	2.33755i
$883$	4.63991e6			0.200266			0.100133	−	0.994974i	$-0.468073\pi$
$883$	4.63991e6			0.200266			0.100133	+	0.994974i	$0.468073\pi$
$884$	5.70708e6	+	7.15646e6i	0.245631	+	0.308012i
$885$	1.45979e7	−	7.02998e6i	0.626516	−	0.301714i
$886$	−5.90101e6	+	2.58540e7i	−0.252547	+	1.10648i
$887$	−2.50657e7	+	1.20710e7i	−1.06972	+	0.515150i	−0.884016	−	0.467456i	$-0.845171\pi$
$887$	−2.50657e7	+	1.20710e7i	−1.06972	+	0.515150i	−0.185703	+	0.982606i	$0.559456\pi$
$888$	−7.92023e7	−	3.81418e7i	−3.37059	−	1.62319i
$889$	−3.26174e6	−	5.77424e6i	−0.138419	−	0.245042i
$890$	1.86936e7	−	9.00237e6i	0.791076	−	0.380962i
$891$	1.64775e7	−	2.06622e7i	0.695341	−	0.871931i
$892$	−2.76629e7	−	1.33218e7i	−1.16409	−	0.560595i
$893$	1.06805e6	+	1.33929e6i	0.0448191	+	0.0562013i
$894$	3.13788e7	+	1.37479e8i	1.31308	+	5.75299i
$895$	1.50526e7	+	1.88753e7i	0.628135	+	0.787656i
$896$	−1.59586e7	+	4.75867e6i	−0.664086	+	0.198023i
$897$	1.38161e7	−	1.73248e7i	0.573328	−	0.718931i
$898$	−2.02636e7	−	9.75843e6i	−0.838544	−	0.403821i
$899$	−195011.	−	854398.i	−0.00804747	−	0.0352583i
$900$	−2.56674e7			−1.05627
$901$	−7.30494e6			−0.299781
$902$	2.17298e6	+	9.52046e6i	0.0889283	+	0.389620i
$903$	−6.29166e7	+	1.87610e7i	−2.56771	+	0.765661i
$904$	−1.54040e7	+	6.74895e7i	−0.626922	+	2.74673i
$905$	437099.	−	1.91506e6i	0.0177402	−	0.0777249i
$906$	−2.21789e7	+	2.78115e7i	−0.897676	+	1.12565i
$907$	2.56268e7	−	3.21350e7i	1.03437	−	1.29706i	0.0805283	−	0.996752i	$-0.474339\pi$
$907$	2.56268e7	−	3.21350e7i	1.03437	−	1.29706i	0.953842	−	0.300308i	$-0.0970893\pi$
$908$	1.22276e6	−	5.35726e6i	0.0492183	−	0.215639i
$909$	1.36390e7	−	5.97563e7i	0.547485	−	2.39869i
$910$	5.57336e6	+	9.86649e6i	0.223107	+	0.394966i
$911$	−3.69134e6	−	1.61728e7i	−0.147363	−	0.645638i	−0.993612	−	0.112851i	$-0.964002\pi$
$911$	−3.69134e6	−	1.61728e7i	−0.147363	−	0.645638i	0.846249	−	0.532787i	$-0.178855\pi$
$912$	1.52030e8			6.05259
$913$	2.55769e7			1.01548
$914$	−8.80754e6	−	3.85884e7i	−0.348730	−	1.52789i
$915$	3.75074e7	+	1.80626e7i	1.48103	+	0.713227i
$916$	2.61468e7	−	3.27870e7i	1.02963	−	1.29111i
$917$	1.04310e7	+	1.67270e6i	0.409640	+	0.0656894i
$918$	−4.05715e7	−	5.08751e7i	−1.58897	−	1.99250i
$919$	−4.03418e6	−	1.76749e7i	−0.157567	−	0.690347i	−0.990562	−	0.137066i	$-0.956233\pi$
$919$	−4.03418e6	−	1.76749e7i	−0.157567	−	0.690347i	0.832995	−	0.553281i	$-0.186624\pi$
$920$	7.65455e7	+	9.59850e7i	2.98160	+	3.73881i
$921$	1.68872e7	+	8.13245e6i	0.656007	+	0.315916i
$922$	1.33130e7	−	1.66940e7i	0.515760	−	0.646743i
$923$	−1.76170e6	+	848391.i	−0.0680657	+	0.0327787i
$924$	−2.54698e7	+	6.31433e7i	−0.981401	+	2.43303i
$925$	3.19862e6	+	1.54038e6i	0.122916	+	0.0591933i
$926$	4.73544e7	−	2.28047e7i	1.81482	−	0.873970i
$927$	−1.06318e7	+	4.65809e7i	−0.406356	+	1.78036i
$928$	1.93880e7	−	9.33676e6i	0.739031	−	0.355899i
$929$	−1.70411e7	−	2.13689e7i	−0.647826	−	0.812348i	0.344131	−	0.938922i	$-0.388174\pi$
$929$	−1.70411e7	−	2.13689e7i	−0.647826	−	0.812348i	−0.991957	+	0.126573i	$0.959602\pi$
$930$	−8.29792e6			−0.314602
$931$	−2.69216e7	+	1.76223e7i	−1.01795	+	0.666330i
$932$	9.31734e7			3.51360
$933$	−4.40277e6	−	5.52090e6i	−0.165585	−	0.207637i
$934$	−5.84071e7	+	2.81274e7i	−2.19078	+	1.05502i
$935$	−1.82577e6	+	7.99921e6i	−0.0682993	+	0.299239i
$936$	−4.15102e7	+	1.99903e7i	−1.54869	+	0.745811i
$937$	−1.84415e7	−	8.88094e6i	−0.686193	−	0.330453i	0.0580956	−	0.998311i	$-0.481497\pi$
$937$	−1.84415e7	−	8.88094e6i	−0.686193	−	0.330453i	−0.744289	+	0.667858i	$0.767211\pi$
$938$	−1.64489e7	−	1.14427e7i	−0.610421	−	0.424642i
$939$	1.78728e7	−	8.60709e6i	0.661498	−	0.318561i
$940$	2.25116e6	−	2.82287e6i	0.0830974	−	0.104201i
$941$	−953040.	−	458960.i	−0.0350862	−	0.0168966i	0.416258	−	0.909246i	$-0.363341\pi$
$941$	−953040.	−	458960.i	−0.0350862	−	0.0168966i	−0.451345	+	0.892350i	$0.649055\pi$
$942$	9.96852e7	+	1.25001e8i	3.66019	+	4.58973i
$943$	−4.23256e6	−	1.85441e7i	−0.154997	−	0.679088i
$944$	−1.99364e7	−	2.49995e7i	−0.728143	−	0.913063i
$945$	−2.82975e7	−	5.00950e7i	−1.03079	−	1.82480i
$946$	−2.75159e7	+	3.45038e7i	−0.999668	+	1.25354i
$947$	1.10371e7	+	5.31517e6i	0.399925	+	0.192594i	0.623025	−	0.782202i	$-0.285903\pi$
$947$	1.10371e7	+	5.31517e6i	0.399925	+	0.192594i	−0.223100	+	0.974796i	$0.571618\pi$
$948$	8.71690e6	+	3.81912e7i	0.315022	+	1.38020i
$949$	7.30581e6			0.263332
$950$	−1.17271e7			−0.421580
$951$	6.37595e6	+	2.79348e7i	0.228609	+	1.00160i
$952$	3.77700e7	+	2.62749e7i	1.35069	+	0.939612i
$953$	−6.35603e6	+	2.78476e7i	−0.226701	+	0.993242i	0.725608	+	0.688108i	$0.241558\pi$
$953$	−6.35603e6	+	2.78476e7i	−0.226701	+	0.993242i	−0.952309	+	0.305134i	$0.901299\pi$
$954$	1.36398e7	−	5.97598e7i	0.485217	−	2.12588i
$955$	1.95018e7	−	2.44545e7i	0.691936	−	0.867660i
$956$	−1.23957e7	+	1.55437e7i	−0.438659	+	0.550061i
$957$	2.32715e6	−	1.01959e7i	0.0821380	−	0.359870i
$958$	−1.07641e7	+	4.71605e7i	−0.378933	+	1.66022i
$959$	5.50922e7	+	8.83450e6i	1.93439	+	0.310196i
$960$	−1.68067e7	−	7.36351e7i	−0.588580	−	2.57874i
$961$	−2.83263e7			−0.989421
$962$	1.06237e7			0.370117
$963$	1.13638e7	+	4.97882e7i	0.394874	+	1.73006i
$964$	9.40376e7	+	4.52861e7i	3.25919	+	1.56954i
$965$	−1.78046e7	+	2.23263e7i	−0.615480	+	0.771787i
$966$	6.94623e7	−	1.72207e8i	2.39500	−	5.93755i
$967$	7.82125e6	+	9.80754e6i	0.268974	+	0.337283i	0.897914	−	0.440171i	$-0.145082\pi$
$967$	7.82125e6	+	9.80754e6i	0.268974	+	0.337283i	−0.628940	+	0.777454i	$0.716511\pi$
$968$	−1.20817e7	−	5.29335e7i	−0.414420	−	1.81569i
$969$	−2.35681e7	−	2.95535e7i	−0.806335	−	1.01111i
$970$	−7.18067e7	−	3.45803e7i	−2.45039	−	1.18005i
$971$	−1.27195e7	+	1.59497e7i	−0.432933	+	0.542881i	−0.949665	−	0.313266i	$-0.898577\pi$
$971$	−1.27195e7	+	1.59497e7i	−0.432933	+	0.542881i	0.516732	+	0.856147i	$0.327148\pi$
$972$	7.72236e7	−	3.71889e7i	2.62171	−	1.26255i
$973$	−1.42483e6	+	1.29732e6i	−0.0482481	+	0.0439305i
$974$	−7.58827e7	−	3.65432e7i	−2.56298	−	1.23427i
$975$	2.41113e6	−	1.16114e6i	0.0812286	−	0.0391176i
$976$	1.82816e7	−	8.00971e7i	0.614314	−	2.69149i
$977$	−1.65678e7	+	7.97865e6i	−0.555302	+	0.267420i	−0.690418	−	0.723410i	$-0.742574\pi$
$977$	−1.65678e7	+	7.97865e6i	−0.555302	+	0.267420i	0.135116	+	0.990830i	$0.456859\pi$
$978$	1.99484e7	+	2.50144e7i	0.666899	+	0.836265i
$979$	−9.03722e6			−0.301355
$980$	4.88386e7	+	4.70558e7i	1.62442	+	1.56512i
$981$	−6.07059e7			−2.01399
$982$	−5.63359e7	−	7.06430e7i	−1.86426	−	2.33771i
$983$	6.97881e6	−	3.36082e6i	0.230355	−	0.110933i	−0.315146	−	0.949043i	$-0.602054\pi$
$983$	6.97881e6	−	3.36082e6i	0.230355	−	0.110933i	0.545501	+	0.838110i	$0.316339\pi$
$984$	−1.26571e7	+	5.54543e7i	−0.416721	+	1.82578i
$985$	−7.27462e6	+	3.50327e6i	−0.238902	+	0.115049i
$986$	−1.06149e7	−	5.11186e6i	−0.347714	−	0.167450i
$987$	−3.23444e6	−	518671.i	−0.105683	−	0.0169472i
$988$	−2.25812e7	+	1.08745e7i	−0.735960	+	0.354419i
$989$	5.35958e7	−	6.72070e7i	1.74237	−	2.18486i
$990$	−6.20303e7	−	2.98722e7i	−2.01148	−	0.968679i
$991$	−3.29118e7	−	4.12701e7i	−1.06455	−	1.33491i	−0.939420	−	0.342768i	$-0.888636\pi$
$991$	−3.29118e7	−	4.12701e7i	−1.06455	−	1.33491i	−0.125133	−	0.992140i	$-0.539936\pi$
$992$	1.65486e6	+	7.25042e6i	0.0533927	+	0.233929i
$993$	4.30951e7	+	5.40396e7i	1.38693	+	1.73916i
$994$	−1.21155e7	+	1.10313e7i	−0.388933	+	0.354129i
$995$	−1.35331e7	+	1.69700e7i	−0.433351	+	0.543404i
$996$	2.23766e8	+	1.07760e8i	7.14736	+	3.44199i
$997$	5.17956e6	+	2.26931e7i	0.165027	+	0.723030i	0.987937	+	0.154858i	$0.0494921\pi$
$997$	5.17956e6	+	2.26931e7i	0.165027	+	0.723030i	−0.822910	+	0.568172i	$0.807651\pi$
$998$	−4.26452e7			−1.35533
$999$	−5.39396e7			−1.70999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.6.e.a.8.2	✓	138
49.43	even	7	inner	49.6.e.a.43.2	yes	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.6.e.a.8.2	✓	138	1.1	even	1	trivial
49.6.e.a.43.2	yes	138	49.43	even	7	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	49.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.59749 - 8.27300i) q^{2} +(25.4427 - 12.2525i) q^{3} +(-17.7949 + 77.9644i) q^{4} +(45.4620 - 21.8934i) q^{5} +(-269.223 - 129.651i) q^{6} +(124.236 - 37.0458i) q^{7} +(457.324 - 220.236i) q^{8} +(345.696 - 433.489i) q^{9} +O(q^{10})\)	\(q+(-6.59749 - 8.27300i) q^{2} +(25.4427 - 12.2525i) q^{3} +(-17.7949 + 77.9644i) q^{4} +(45.4620 - 21.8934i) q^{5} +(-269.223 - 129.651i) q^{6} +(124.236 - 37.0458i) q^{7} +(457.324 - 220.236i) q^{8} +(345.696 - 433.489i) q^{9} +(-481.059 - 231.666i) q^{10} +(145.000 + 181.825i) q^{11} +(502.513 + 2201.65i) q^{12} +(-102.069 - 127.991i) q^{13} +(-1126.13 - 783.396i) q^{14} +(888.426 - 1114.05i) q^{15} +(-2533.60 - 1220.12i) q^{16} +(155.585 + 681.660i) q^{17} -5866.99 q^{18} -1914.46 q^{19} +(897.912 + 3934.01i) q^{20} +(2706.99 - 2464.75i) q^{21} +(547.597 - 2399.18i) q^{22} +(-1066.62 + 4673.15i) q^{23} +(8937.09 - 11206.8i) q^{24} +(-360.929 + 452.590i) q^{25} +(-385.466 + 1688.84i) q^{26} +(1957.12 - 8574.70i) q^{27} +(677.487 + 10345.2i) q^{28} +(-354.349 - 1552.50i) q^{29} -15077.9 q^{30} +550.336 q^{31} +(3007.00 + 13174.5i) q^{32} +(5917.02 + 2849.48i) q^{33} +(4612.91 - 5784.40i) q^{34} +(4836.97 - 4404.12i) q^{35} +(27645.1 + 34665.9i) q^{36} +(-1364.68 - 5979.07i) q^{37} +(12630.7 + 15838.4i) q^{38} +(-4165.12 - 2005.82i) q^{39} +(15969.2 - 20024.7i) q^{40} +(-3575.24 + 1721.75i) q^{41} +(-38250.2 - 6133.76i) q^{42} +(-16157.5 - 7781.04i) q^{43} +(-16756.1 + 8069.33i) q^{44} +(6225.52 - 27275.8i) q^{45} +(45697.9 - 22007.0i) q^{46} +(-557.884 - 699.565i) q^{47} -79411.2 q^{48} +(14062.2 - 9204.85i) q^{49} +6125.51 q^{50} +(12310.6 + 15436.9i) q^{51} +(11795.0 - 5680.19i) q^{52} +(-2324.84 + 10185.8i) q^{53} +(-83850.6 + 40380.3i) q^{54} +(10572.8 + 5091.58i) q^{55} +(48657.4 - 44303.1i) q^{56} +(-48709.1 + 23457.0i) q^{57} +(-10506.0 + 13174.2i) q^{58} +(10244.7 + 4933.58i) q^{59} +(71046.9 + 89090.0i) q^{60} +(6501.09 + 28483.1i) q^{61} +(-3630.84 - 4552.93i) q^{62} +(26889.0 - 66661.6i) q^{63} +(33048.4 - 41441.4i) q^{64} +(-7442.42 - 3584.08i) q^{65} +(-15463.7 - 67750.9i) q^{66} +14606.6 q^{67} -55913.9 q^{68} +(30120.4 + 131966. i) q^{69} +(-68347.2 - 10960.1i) q^{70} +(2657.84 - 11644.7i) q^{71} +(62625.4 - 274380. i) q^{72} +(-27824.8 + 34891.2i) q^{73} +(-40461.3 + 50736.9i) q^{74} +(-3637.61 + 15937.4i) q^{75} +(34067.6 - 149260. i) q^{76} +(24750.1 + 17217.6i) q^{77} +(10885.3 + 47691.4i) q^{78} +17346.6 q^{79} -141895. q^{80} +(-25286.8 - 110789. i) q^{81} +(37831.6 + 18218.8i) q^{82} +(68570.5 - 85984.6i) q^{83} +(143992. + 254909. i) q^{84} +(21997.0 + 27583.4i) q^{85} +(42226.5 + 185006. i) q^{86} +(-28037.7 - 35158.1i) q^{87} +(106357. + 51218.6i) q^{88} +(-24228.4 + 30381.4i) q^{89} +(-266725. + 128448. i) q^{90} +(-17422.2 - 12119.8i) q^{91} +(-345359. - 166316. i) q^{92} +(14002.0 - 6743.01i) q^{93} +(-2106.86 + 9230.75i) q^{94} +(-87035.4 + 41914.0i) q^{95} +(237928. + 298352. i) q^{96} +149268. q^{97} +(-168927. - 55607.8i) q^{98} +128945. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9}+O(q^{10}) \) 138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9	\( 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9} - 771 q^{10} + 410 q^{11} - 1316 q^{12} + 483 q^{13} + 2597 q^{14} + 2557 q^{15} - 7357 q^{16} - 1422 q^{17} - 2480 q^{18} - 6758 q^{19} - 3647 q^{20} - 399 q^{21} - 857 q^{22} - 2392 q^{23} - 3571 q^{24} - 8066 q^{25} - 343 q^{26} + 16396 q^{27} + 32102 q^{28} + 30341 q^{29} + 13716 q^{30} - 32712 q^{31} - 26993 q^{32} - 16775 q^{33} + 35163 q^{34} - 12019 q^{35} + 35461 q^{36} - 34872 q^{37} + 13383 q^{38} - 20671 q^{39} + 165169 q^{40} + 51233 q^{41} - 13741 q^{42} - 17203 q^{43} - 4267 q^{44} + 30777 q^{45} - 74611 q^{46} + 64264 q^{47} - 247084 q^{48} - 70350 q^{49} - 263036 q^{50} - 57453 q^{51} - 36043 q^{52} + 124590 q^{53} + 144840 q^{54} + 90977 q^{55} + 404404 q^{56} - 103899 q^{57} + 24861 q^{58} - 8079 q^{59} + 72065 q^{60} - 236659 q^{61} - 173227 q^{62} - 119805 q^{63} + 105381 q^{64} - 33383 q^{65} + 536577 q^{66} + 19716 q^{67} - 256340 q^{68} - 202795 q^{69} + 194803 q^{70} + 61778 q^{71} - 392108 q^{72} - 157760 q^{73} - 328319 q^{74} + 355167 q^{75} - 61334 q^{76} - 24402 q^{77} + 497217 q^{78} - 73876 q^{79} - 1340760 q^{80} - 815116 q^{81} + 248976 q^{82} + 303107 q^{83} + 1250354 q^{84} + 205487 q^{85} + 1083219 q^{86} + 197027 q^{87} + 1052915 q^{88} + 219783 q^{89} + 82170 q^{90} - 837235 q^{91} + 35936 q^{92} + 138365 q^{93} - 571908 q^{94} - 610016 q^{95} - 1054494 q^{96} + 762020 q^{97} - 2160767 q^{98} - 1090772 q^{99}+O(q^{100}) \) 138 * q - 5 * q^2 + 13 * q^3 - 389 * q^4 + 67 * q^5 + 331 * q^6 - 56 * q^7 + 305 * q^8 - 918 * q^9 - 771 * q^10 + 410 * q^11 - 1316 * q^12 + 483 * q^13 + 2597 * q^14 + 2557 * q^15 - 7357 * q^16 - 1422 * q^17 - 2480 * q^18 - 6758 * q^19 - 3647 * q^20 - 399 * q^21 - 857 * q^22 - 2392 * q^23 - 3571 * q^24 - 8066 * q^25 - 343 * q^26 + 16396 * q^27 + 32102 * q^28 + 30341 * q^29 + 13716 * q^30 - 32712 * q^31 - 26993 * q^32 - 16775 * q^33 + 35163 * q^34 - 12019 * q^35 + 35461 * q^36 - 34872 * q^37 + 13383 * q^38 - 20671 * q^39 + 165169 * q^40 + 51233 * q^41 - 13741 * q^42 - 17203 * q^43 - 4267 * q^44 + 30777 * q^45 - 74611 * q^46 + 64264 * q^47 - 247084 * q^48 - 70350 * q^49 - 263036 * q^50 - 57453 * q^51 - 36043 * q^52 + 124590 * q^53 + 144840 * q^54 + 90977 * q^55 + 404404 * q^56 - 103899 * q^57 + 24861 * q^58 - 8079 * q^59 + 72065 * q^60 - 236659 * q^61 - 173227 * q^62 - 119805 * q^63 + 105381 * q^64 - 33383 * q^65 + 536577 * q^66 + 19716 * q^67 - 256340 * q^68 - 202795 * q^69 + 194803 * q^70 + 61778 * q^71 - 392108 * q^72 - 157760 * q^73 - 328319 * q^74 + 355167 * q^75 - 61334 * q^76 - 24402 * q^77 + 497217 * q^78 - 73876 * q^79 - 1340760 * q^80 - 815116 * q^81 + 248976 * q^82 + 303107 * q^83 + 1250354 * q^84 + 205487 * q^85 + 1083219 * q^86 + 197027 * q^87 + 1052915 * q^88 + 219783 * q^89 + 82170 * q^90 - 837235 * q^91 + 35936 * q^92 + 138365 * q^93 - 571908 * q^94 - 610016 * q^95 - 1054494 * q^96 + 762020 * q^97 - 2160767 * q^98 - 1090772 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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