LMFDB - Embedded newform 91.8.f.a.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.f (of order $3$, degree $2$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.3
Character	$\chi$	$=$	91.22
Dual form			91.8.f.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.35205 + 16.1982i) q^{2} +(31.2473 - 54.1220i) q^{3} +(-110.922 - 192.122i) q^{4} -263.837 q^{5} +(584.454 + 1012.30i) q^{6} +(171.500 + 297.047i) q^{7} +1755.26 q^{8} +(-859.293 - 1488.34i) q^{9} +O(q^{10})$	\(q+(-9.35205 + 16.1982i) q^{2} +(31.2473 - 54.1220i) q^{3} +(-110.922 - 192.122i) q^{4} -263.837 q^{5} +(584.454 + 1012.30i) q^{6} +(171.500 + 297.047i) q^{7} +1755.26 q^{8} +(-859.293 - 1488.34i) q^{9} +(2467.42 - 4273.70i) q^{10} +(-1948.08 + 3374.18i) q^{11} -13864.0 q^{12} +(-6646.59 + 4309.45i) q^{13} -6415.51 q^{14} +(-8244.22 + 14279.4i) q^{15} +(-2217.28 + 3840.44i) q^{16} +(9637.35 + 16692.4i) q^{17} +32144.6 q^{18} +(-6794.19 - 11767.9i) q^{19} +(29265.3 + 50689.0i) q^{20} +21435.7 q^{21} +(-36437.1 - 63110.9i) q^{22} +(47517.0 - 82301.8i) q^{23} +(54847.1 - 94998.0i) q^{24} -8514.81 q^{25} +(-7646.17 - 147965. i) q^{26} +29273.3 q^{27} +(38046.2 - 65897.9i) q^{28} +(77004.8 - 133376. i) q^{29} +(-154201. - 267083. i) q^{30} +194632. q^{31} +(70864.3 + 122741. i) q^{32} +(121745. + 210868. i) q^{33} -360516. q^{34} +(-45248.1 - 78372.0i) q^{35} +(-190629. + 330178. i) q^{36} +(132813. - 230039. i) q^{37} +254158. q^{38} +(25547.6 + 494386. i) q^{39} -463103. q^{40} +(6341.88 - 10984.5i) q^{41} +(-200468. + 347220. i) q^{42} +(-144154. - 249682. i) q^{43} +864338. q^{44} +(226714. + 392680. i) q^{45} +(888763. + 1.53938e6i) q^{46} -336075. q^{47} +(138568. + 240007. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(79630.9 - 137925. i) q^{50} +1.20457e6 q^{51} +(1.56519e6 + 798945. i) q^{52} +1.05564e6 q^{53} +(-273766. + 474176. i) q^{54} +(513977. - 890234. i) q^{55} +(301027. + 521393. i) q^{56} -849201. q^{57} +(1.44031e6 + 2.49468e6i) q^{58} +(109343. + 189388. i) q^{59} +3.65785e6 q^{60} +(-423470. - 733472. i) q^{61} +(-1.82020e6 + 3.15269e6i) q^{62} +(294738. - 510501. i) q^{63} -3.21853e6 q^{64} +(1.75362e6 - 1.13699e6i) q^{65} -4.55425e6 q^{66} +(1.10077e6 - 1.90658e6i) q^{67} +(2.13798e6 - 3.70309e6i) q^{68} +(-2.96956e6 - 5.14343e6i) q^{69} +1.69265e6 q^{70} +(2.77325e6 + 4.80340e6i) q^{71} +(-1.50828e6 - 2.61242e6i) q^{72} -885041. q^{73} +(2.48415e6 + 4.30268e6i) q^{74} +(-266065. + 460839. i) q^{75} +(-1.50725e6 + 2.61063e6i) q^{76} -1.33638e6 q^{77} +(-8.24709e6 - 4.20969e6i) q^{78} -4.26864e6 q^{79} +(585001. - 1.01325e6i) q^{80} +(2.79399e6 - 4.83933e6i) q^{81} +(118619. + 205455. i) q^{82} +5.87649e6 q^{83} +(-2.37768e6 - 4.11827e6i) q^{84} +(-2.54269e6 - 4.40407e6i) q^{85} +5.39255e6 q^{86} +(-4.81239e6 - 8.33530e6i) q^{87} +(-3.41938e6 + 5.92255e6i) q^{88} +(4.82611e6 - 8.35907e6i) q^{89} -8.48095e6 q^{90} +(-2.42000e6 - 1.23528e6i) q^{91} -2.10827e7 q^{92} +(6.08172e6 - 1.05338e7i) q^{93} +(3.14299e6 - 5.44382e6i) q^{94} +(1.79256e6 + 3.10481e6i) q^{95} +8.85729e6 q^{96} +(6.78921e6 + 1.17593e7i) q^{97} +(-1.10026e6 - 1.90571e6i) q^{98} +6.69589e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−9.35205	+	16.1982i	−0.826612	+	1.43173i	0.0740684	+	0.997253i	$0.476402\pi$
$2$	−9.35205	+	16.1982i	−0.826612	+	1.43173i	−0.900681	+	0.434481i	$0.856932\pi$
$3$	31.2473	−	54.1220i	0.668173	−	1.15731i	−0.310242	−	0.950658i	$-0.600410\pi$
$3$	31.2473	−	54.1220i	0.668173	−	1.15731i	0.978415	−	0.206651i	$-0.0662566\pi$
$4$	−110.922	−	192.122i	−0.866576	−	1.50095i
$5$	−263.837			−0.943933			−0.471967	−	0.881616i	$-0.656456\pi$
$5$	−263.837			−0.943933			−0.471967	+	0.881616i	$0.656456\pi$
$6$	584.454	+	1012.30i	1.10464	+	1.91329i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$7$	171.500	+	297.047i	0.188982	+	0.327327i
$8$	1755.26			1.21206
$9$	−859.293	−	1488.34i	−0.392910	−	0.680539i
$10$	2467.42	−	4273.70i	0.780267	−	1.35146i
$11$	−1948.08	+	3374.18i	−0.441299	+	0.764352i	−0.997786	−	0.0665043i	$-0.978815\pi$
$11$	−1948.08	+	3374.18i	−0.441299	+	0.764352i	0.556487	+	0.830856i	$0.312149\pi$
$12$	−13864.0			−2.31609
$13$	−6646.59	+	4309.45i	−0.839068	+	0.544026i
$13$	−6646.59	+	4309.45i	−0.839068	+	0.544026i
$14$	−6415.51			−0.624860
$15$	−8244.22	+	14279.4i	−0.630711	+	1.09242i
$16$	−2217.28	+	3840.44i	−0.135332	+	0.234402i
$17$	9637.35	+	16692.4i	0.475758	+	0.824037i	0.999614	−	0.0277695i	$-0.00884044\pi$
$17$	9637.35	+	16692.4i	0.475758	+	0.824037i	−0.523856	+	0.851807i	$0.675507\pi$
$18$	32144.6			1.29914
$19$	−6794.19	−	11767.9i	−0.227248	−	0.393605i	0.729744	−	0.683721i	$-0.239639\pi$
$19$	−6794.19	−	11767.9i	−0.227248	−	0.393605i	−0.956991	+	0.290116i	$0.906306\pi$
$20$	29265.3	+	50689.0i	0.817990	+	1.41680i
$21$	21435.7			0.505091
$22$	−36437.1	−	63110.9i	−0.729566	−	1.26365i
$23$	47517.0	−	82301.8i	0.814332	−	1.41046i	−0.0954746	−	0.995432i	$-0.530437\pi$
$23$	47517.0	−	82301.8i	0.814332	−	1.41046i	0.909807	−	0.415032i	$-0.136230\pi$
$24$	54847.1	−	94998.0i	0.809869	−	1.40273i
$25$	−8514.81			−0.108990
$26$	−7646.17	−	147965.i	−0.0853173	−	1.65102i
$27$	29273.3			0.286219
$28$	38046.2	−	65897.9i	0.327535	−	0.567307i
$29$	77004.8	−	133376.i	0.586306	−	1.01551i	−0.408405	−	0.912801i	$-0.633915\pi$
$29$	77004.8	−	133376.i	0.586306	−	1.01551i	0.994711	−	0.102712i	$-0.0327519\pi$
$30$	−154201.	−	267083.i	−1.04271	−	1.80602i
$31$	194632.			1.17340			0.586702	−	0.809803i	$-0.300426\pi$
$31$	194632.			1.17340			0.586702	+	0.809803i	$0.300426\pi$
$32$	70864.3	+	122741.i	0.382299	+	0.662160i
$33$	121745.	+	210868.i	0.589727	+	1.02144i
$34$	−360516.			−1.57307
$35$	−45248.1	−	78372.0i	−0.178387	−	0.308975i
$36$	−190629.	+	330178.i	−0.680972	+	1.17948i
$37$	132813.	−	230039.i	0.431058	−	0.746614i	−0.565907	−	0.824469i	$-0.691474\pi$
$37$	132813.	−	230039.i	0.431058	−	0.746614i	0.996965	+	0.0778553i	$0.0248072\pi$
$38$	254158.			0.751384
$39$	25547.6	+	494386.i	0.0689642	+	1.33456i
$40$	−463103.			−1.14411
$41$	6341.88	−	10984.5i	0.0143706	−	0.0248906i	−0.858751	−	0.512394i	$-0.828759\pi$
$41$	6341.88	−	10984.5i	0.0143706	−	0.0248906i	0.873121	+	0.487503i	$0.162092\pi$
$42$	−200468.	+	347220.i	−0.417515	+	0.723156i
$43$	−144154.	−	249682.i	−0.276495	−	0.478904i	0.694016	−	0.719960i	$-0.255840\pi$
$43$	−144154.	−	249682.i	−0.276495	−	0.478904i	−0.970511	+	0.241056i	$0.922506\pi$
$44$	864338.			1.52968
$45$	226714.	+	392680.i	0.370881	+	0.642384i
$46$	888763.	+	1.53938e6i	1.34627	+	2.33181i
$47$	−336075.			−0.472165			−0.236083	−	0.971733i	$-0.575864\pi$
$47$	−336075.			−0.472165			−0.236083	+	0.971733i	$0.575864\pi$
$48$	138568.	+	240007.i	0.180850	+	0.313242i
$49$	−58824.5	+	101887.i	−0.0714286	+	0.123718i
$50$	79630.9	−	137925.i	0.0900921	−	0.156044i
$51$	1.20457e6			1.27155
$52$	1.56519e6	+	798945.i	1.54367	+	0.787962i
$53$	1.05564e6			0.973981			0.486990	−	0.873407i	$-0.338095\pi$
$53$	1.05564e6			0.973981			0.486990	+	0.873407i	$0.338095\pi$
$54$	−273766.	+	474176.i	−0.236593	+	0.409790i
$55$	513977.	−	890234.i	0.416557	−	0.721497i
$56$	301027.	+	521393.i	0.229059	+	0.396741i
$57$	−849201.			−0.607363
$58$	1.44031e6	+	2.49468e6i	0.969296	+	1.67887i
$59$	109343.	+	189388.i	0.0693122	+	0.120052i	0.898599	−	0.438771i	$-0.144586\pi$
$59$	109343.	+	189388.i	0.0693122	+	0.120052i	−0.829287	+	0.558824i	$0.811253\pi$
$60$	3.65785e6			2.18623
$61$	−423470.	−	733472.i	−0.238874	−	0.413742i	0.721518	−	0.692396i	$-0.243445\pi$
$61$	−423470.	−	733472.i	−0.238874	−	0.413742i	−0.960391	+	0.278654i	$0.910112\pi$
$62$	−1.82020e6	+	3.15269e6i	−0.969950	+	1.68000i
$63$	294738.	−	510501.i	0.148506	−	0.257220i
$64$	−3.21853e6			−1.53471
$65$	1.75362e6	−	1.13699e6i	0.792024	−	0.513525i
$66$	−4.55425e6			−1.94990
$67$	1.10077e6	−	1.90658e6i	0.447129	−	0.774451i	−0.551068	−	0.834460i	$-0.685780\pi$
$67$	1.10077e6	−	1.90658e6i	0.447129	−	0.774451i	0.998198	+	0.0600093i	$0.0191130\pi$
$68$	2.13798e6	−	3.70309e6i	0.824561	−	1.42818i
$69$	−2.96956e6	−	5.14343e6i	−1.08823	−	1.88487i
$70$	1.69265e6			0.589826
$71$	2.77325e6	+	4.80340e6i	0.919569	+	1.59274i	0.800071	+	0.599905i	$0.204795\pi$
$71$	2.77325e6	+	4.80340e6i	0.919569	+	1.59274i	0.119498	+	0.992834i	$0.461872\pi$
$72$	−1.50828e6	−	2.61242e6i	−0.476232	−	0.824858i
$73$	−885041.			−0.266277			−0.133138	−	0.991097i	$-0.542505\pi$
$73$	−885041.			−0.266277			−0.133138	+	0.991097i	$0.542505\pi$
$74$	2.48415e6	+	4.30268e6i	0.712635	+	1.23432i
$75$	−266065.	+	460839.i	−0.0728239	+	0.126135i
$76$	−1.50725e6	+	2.61063e6i	−0.393855	+	0.682177i
$77$	−1.33638e6			−0.333590
$78$	−8.24709e6	−	4.20969e6i	−1.96775	−	1.00443i
$79$	−4.26864e6			−0.974080			−0.487040	−	0.873380i	$-0.661923\pi$
$79$	−4.26864e6			−0.974080			−0.487040	+	0.873380i	$0.661923\pi$
$80$	585001.	−	1.01325e6i	0.127744	−	0.221260i
$81$	2.79399e6	−	4.83933e6i	0.584154	−	1.01178i
$82$	118619.	+	205455.i	0.0237578	+	0.0411498i
$83$	5.87649e6			1.12809			0.564046	−	0.825743i	$-0.309244\pi$
$83$	5.87649e6			1.12809			0.564046	+	0.825743i	$0.309244\pi$
$84$	−2.37768e6	−	4.11827e6i	−0.437700	−	0.758118i
$85$	−2.54269e6	−	4.40407e6i	−0.449084	−	0.777836i
$86$	5.39255e6			0.914218
$87$	−4.81239e6	−	8.33530e6i	−0.783508	−	1.35708i
$88$	−3.41938e6	+	5.92255e6i	−0.534883	+	0.926444i
$89$	4.82611e6	−	8.35907e6i	0.725658	−	1.25688i	−0.233044	−	0.972466i	$-0.574869\pi$
$89$	4.82611e6	−	8.35907e6i	0.725658	−	1.25688i	0.958702	−	0.284411i	$-0.0917980\pi$
$90$	−8.48095e6			−1.22630
$91$	−2.42000e6	−	1.23528e6i	−0.336643	−	0.171838i
$92$	−2.10827e7			−2.82272
$93$	6.08172e6	−	1.05338e7i	0.784036	−	1.35799i
$94$	3.14299e6	−	5.44382e6i	0.390298	−	0.676015i
$95$	1.79256e6	+	3.10481e6i	0.214507	+	0.371537i
$96$	8.85729e6			1.02177
$97$	6.78921e6	+	1.17593e7i	0.755298	+	1.30821i	0.945226	+	0.326416i	$0.105841\pi$
$97$	6.78921e6	+	1.17593e7i	0.755298	+	1.30821i	−0.189928	+	0.981798i	$0.560826\pi$
$98$	−1.10026e6	−	1.90571e6i	−0.118087	−	0.204534i
$99$	6.69589e6			0.693562
$100$	944478.	+	1.63588e6i	0.0944478	+	0.163588i
$101$	7.91784e6	−	1.37141e7i	0.764683	−	1.32447i	−0.175730	−	0.984438i	$-0.556229\pi$
$101$	7.91784e6	−	1.37141e7i	0.764683	−	1.32447i	0.940414	−	0.340032i	$-0.110438\pi$
$102$	−1.12652e7	+	1.95118e7i	−1.05108	+	1.82053i
$103$	6.31195e6			0.569159			0.284579	−	0.958652i	$-0.408146\pi$
$103$	6.31195e6			0.569159			0.284579	+	0.958652i	$0.408146\pi$
$104$	−1.16665e7	+	7.56419e6i	−1.01700	+	0.659395i
$105$	−5.65553e6			−0.476772
$106$	−9.87240e6	+	1.70995e7i	−0.805104	+	1.39448i
$107$	−900242.	+	1.55926e6i	−0.0710421	+	0.123049i	−0.899358	−	0.437212i	$-0.855966\pi$
$107$	−900242.	+	1.55926e6i	−0.0710421	+	0.123049i	0.828316	+	0.560261i	$0.189299\pi$
$108$	−3.24705e6	−	5.62406e6i	−0.248031	−	0.429602i
$109$	808642.			0.0598086			0.0299043	−	0.999553i	$-0.490480\pi$
$109$	808642.			0.0598086			0.0299043	+	0.999553i	$0.490480\pi$
$110$	9.61347e6	+	1.66510e7i	0.688662	+	1.19280i
$111$	−8.30012e6	−	1.43762e7i	−0.576042	−	0.997734i
$112$	−1.52105e6			−0.102301
$113$	6.37121e6	+	1.10353e7i	0.415382	+	0.719462i	0.995468	−	0.0950926i	$-0.0303147\pi$
$113$	6.37121e6	+	1.10353e7i	0.415382	+	0.719462i	−0.580087	+	0.814555i	$0.696981\pi$
$114$	7.94177e6	−	1.37556e7i	0.502054	−	0.869583i
$115$	−1.25368e7	+	2.17143e7i	−0.768675	+	1.33138i
$116$	−3.41660e7			−2.03232
$117$	1.21253e7	+	6.18931e6i	0.699909	+	0.357266i
$118$	−4.09033e6			−0.229177
$119$	−3.30561e6	+	5.72548e6i	−0.179820	+	0.311457i
$120$	−1.44707e7	+	2.50640e7i	−0.764462	+	1.32409i
$121$	2.15355e6	+	3.73005e6i	0.110511	+	0.191411i
$122$	1.58413e7			0.789824
$123$	−396334.	−	686471.i	−0.0192041	−	0.0332624i
$124$	−2.15889e7	−	3.73930e7i	−1.01684	−	1.76122i
$125$	2.28588e7			1.04681
$126$	5.51280e6	+	9.54845e6i	0.245514	+	0.425242i
$127$	−1.42720e7	+	2.47198e7i	−0.618260	+	1.07086i	0.371543	+	0.928416i	$0.378829\pi$
$127$	−1.42720e7	+	2.47198e7i	−0.618260	+	1.07086i	−0.989803	+	0.142442i	$0.954505\pi$
$128$	2.10292e7	−	3.64237e7i	0.886315	−	1.53514i
$129$	−1.80177e7			−0.738986
$130$	2.01735e6	+	3.90388e7i	0.0805339	+	1.55845i
$131$	3.26447e7			1.26871			0.634357	−	0.773040i	$-0.281265\pi$
$131$	3.26447e7			1.26871			0.634357	+	0.773040i	$0.281265\pi$
$132$	2.70083e7	−	4.67797e7i	1.02209	−	1.77031i
$133$	2.33041e6	−	4.03638e6i	0.0858916	−	0.148769i
$134$	2.05888e7	+	3.56609e7i	0.739205	+	1.28034i
$135$	−7.72340e6			−0.270172
$136$	1.69160e7	+	2.92994e7i	0.576650	+	0.998787i
$137$	−1.82604e7	−	3.16279e7i	−0.606719	−	1.05087i	−0.991777	−	0.127976i	$-0.959152\pi$
$137$	−1.82604e7	−	3.16279e7i	−0.606719	−	1.05087i	0.385058	−	0.922892i	$-0.374181\pi$
$138$	1.11086e8			3.59817
$139$	−2.30619e7	−	3.99444e7i	−0.728355	−	1.26155i	−0.957578	−	0.288174i	$-0.906952\pi$
$139$	−2.30619e7	−	3.99444e7i	−0.728355	−	1.26155i	0.229223	−	0.973374i	$-0.426382\pi$
$140$	−1.00380e7	+	1.73863e7i	−0.309171	+	0.535500i
$141$	−1.05015e7	+	1.81891e7i	−0.315488	+	0.546441i
$142$	−1.03742e8			−3.04051
$143$	−1.59274e6	−	3.08219e7i	−0.0455478	−	0.881421i
$144$	7.62116e6			0.212693
$145$	−2.03167e7	+	3.51896e7i	−0.553434	+	0.958576i
$146$	8.27695e6	−	1.43361e7i	0.220108	−	0.381238i
$147$	3.67622e6	+	6.36740e6i	0.0954532	+	0.165330i
$148$	−5.89275e7			−1.49418
$149$	1.56331e7	+	2.70772e7i	0.387161	+	0.670583i	0.992066	−	0.125715i	$-0.0401223\pi$
$149$	1.56331e7	+	2.70772e7i	0.387161	+	0.670583i	−0.604905	+	0.796297i	$0.706789\pi$
$150$	−4.97651e6	−	8.61957e6i	−0.120394	−	0.208529i
$151$	−6.32910e7			−1.49597			−0.747985	−	0.663716i	$-0.768978\pi$
$151$	−6.32910e7			−1.49597			−0.747985	+	0.663716i	$0.768978\pi$
$152$	−1.19255e7	−	2.06557e7i	−0.275439	−	0.477075i
$153$	1.65626e7	−	2.86873e7i	0.373860	−	0.647544i
$154$	1.24979e7	−	2.16470e7i	0.275750	−	0.477613i
$155$	−5.13511e7			−1.10761
$156$	9.21486e7	−	5.97464e7i	1.94336	−	1.26001i
$157$	3.04050e7			0.627041			0.313520	−	0.949581i	$-0.398492\pi$
$157$	3.04050e7			0.627041			0.313520	+	0.949581i	$0.398492\pi$
$158$	3.99205e7	−	6.91444e7i	0.805186	−	1.39462i
$159$	3.29860e7	−	5.71333e7i	0.650787	−	1.12720i
$160$	−1.86967e7	−	3.23836e7i	−0.360864	−	0.625035i
$161$	3.25967e7			0.615577
$162$	5.22591e7	+	9.05153e7i	0.965737	+	1.67271i
$163$	−1.15769e7	−	2.00517e7i	−0.209380	−	0.362657i	0.742139	−	0.670246i	$-0.233811\pi$
$163$	−1.15769e7	−	2.00517e7i	−0.209380	−	0.362657i	−0.951519	+	0.307589i	$0.900478\pi$
$164$	−2.81381e6			−0.0498129
$165$	−3.21208e7	−	5.56349e7i	−0.556663	−	0.964169i
$166$	−5.49572e7	+	9.51887e7i	−0.932495	+	1.61513i
$167$	−5.53031e6	+	9.57877e6i	−0.0918844	+	0.159148i	−0.908304	−	0.418311i	$-0.862622\pi$
$167$	−5.53031e6	+	9.57877e6i	−0.0918844	+	0.159148i	0.816420	+	0.577459i	$0.195956\pi$
$168$	3.76251e7			0.612203
$169$	2.56058e7	−	5.72863e7i	0.408071	−	0.912950i
$170$	9.51176e7			1.48487
$171$	−1.16764e7	+	2.02241e7i	−0.178576	+	0.309302i
$172$	−3.19797e7	+	5.53904e7i	−0.479208	+	0.830013i
$173$	−1.97392e7	−	3.41892e7i	−0.289846	−	0.502028i	0.683927	−	0.729551i	$-0.260271\pi$
$173$	−1.97392e7	−	3.41892e7i	−0.289846	−	0.502028i	−0.973773	+	0.227523i	$0.926937\pi$
$174$	1.80023e8			2.59063
$175$	−1.46029e6	−	2.52930e6i	−0.0205971	−	0.0356752i
$176$	−8.63887e6	−	1.49630e7i	−0.119444	−	0.206882i
$177$	1.36667e7			0.185250
$178$	9.02680e7	+	1.56349e8i	1.19968	+	2.07790i
$179$	−1.71981e7	+	2.97879e7i	−0.224127	+	0.388199i	−0.956057	−	0.293180i	$-0.905286\pi$
$179$	−1.71981e7	+	2.97879e7i	−0.224127	+	0.388199i	0.731930	+	0.681380i	$0.238620\pi$
$180$	5.02950e7	−	8.71134e7i	0.642792	−	1.11335i
$181$	2.23272e7			0.279872			0.139936	−	0.990161i	$-0.455310\pi$
$181$	2.23272e7			0.279872			0.139936	+	0.990161i	$0.455310\pi$
$182$	4.26413e7	−	2.76473e7i	0.524300	−	0.339940i
$183$	−5.29293e7			−0.638436
$184$	8.34045e7	−	1.44461e8i	0.987023	−	1.70957i
$185$	−3.50411e7	+	6.06930e7i	−0.406890	+	0.704754i
$186$	1.13753e8	+	1.97026e8i	1.29619	+	2.24506i
$187$	−7.50973e7			−0.839806
$188$	3.72780e7	+	6.45675e7i	0.409167	+	0.708698i
$189$	5.02038e6	+	8.69555e6i	0.0540904	+	0.0936873i
$190$	−6.70565e7			−0.709256
$191$	−7.49556e6	−	1.29827e7i	−0.0778372	−	0.134818i	0.824479	−	0.565892i	$-0.191468\pi$
$191$	−7.49556e6	−	1.29827e7i	−0.0778372	−	0.134818i	−0.902317	+	0.431074i	$0.858135\pi$
$192$	−1.00570e8	+	1.74193e8i	−1.02545	+	1.77614i
$193$	1.76415e7	−	3.05560e7i	0.176638	−	0.305947i	−0.764089	−	0.645111i	$-0.776811\pi$
$193$	1.76415e7	−	3.05560e7i	0.176638	−	0.305947i	0.940727	+	0.339165i	$0.110144\pi$
$194$	−2.53972e8			−2.49735
$195$	−6.74041e6	−	1.30437e8i	−0.0650977	−	1.25974i
$196$	2.60997e7			0.247593
$197$	−8.14319e7	+	1.41044e8i	−0.758862	+	1.31439i	0.184569	+	0.982820i	$0.440911\pi$
$197$	−8.14319e7	+	1.41044e8i	−0.758862	+	1.31439i	−0.943431	+	0.331569i	$0.892422\pi$
$198$	−6.26203e7	+	1.08462e8i	−0.573307	+	0.992997i
$199$	−7.92533e6	−	1.37271e7i	−0.0712905	−	0.123479i	0.828177	−	0.560467i	$-0.189378\pi$
$199$	−7.92533e6	−	1.37271e7i	−0.0712905	−	0.123479i	−0.899467	+	0.436988i	$0.856045\pi$
$200$	−1.49457e7			−0.132102
$201$	−6.87920e7	−	1.19151e8i	−0.597519	−	1.03493i
$202$	1.48096e8	+	2.56510e8i	1.26419	+	2.18965i
$203$	5.28253e7			0.443206
$204$	−1.33613e8	−	2.31424e8i	−1.10190	−	1.90854i
$205$	−1.67323e6	+	2.89811e6i	−0.0135649	+	0.0234951i
$206$	−5.90297e7	+	1.02242e8i	−0.470474	+	0.814884i
$207$	−1.63324e8			−1.27984
$208$	−1.81283e6	−	3.50810e7i	−0.0139680	−	0.270303i
$209$	5.29425e7			0.401137
$210$	5.28908e7	−	9.16096e7i	0.394106	−	0.682612i
$211$	−1.32625e8	+	2.29712e8i	−0.971930	+	1.68343i	−0.282217	+	0.959351i	$0.591070\pi$
$211$	−1.32625e8	+	2.29712e8i	−0.971930	+	1.68343i	−0.689714	+	0.724082i	$0.742264\pi$
$212$	−1.17093e8	−	2.02812e8i	−0.844028	−	1.46190i
$213$	3.46626e8			2.45772
$214$	−1.68382e7	−	2.91646e7i	−0.117449	−	0.203427i
$215$	3.80333e7	+	6.58756e7i	0.260993	+	0.452053i
$216$	5.13823e7			0.346917
$217$	3.33793e7	+	5.78147e7i	0.221752	+	0.384086i
$218$	−7.56246e6	+	1.30986e7i	−0.0494385	+	0.0856300i
$219$	−2.76552e7	+	4.79002e7i	−0.177919	+	0.308165i
$220$	−2.28045e8			−1.44391
$221$	−1.35990e8	−	6.94157e7i	−0.847491	−	0.432598i
$222$	3.10493e8			1.90465
$223$	9.63947e7	−	1.66960e8i	0.582085	−	1.00820i	−0.413147	−	0.910664i	$-0.635571\pi$
$223$	9.63947e7	−	1.66960e8i	0.582085	−	1.00820i	0.995232	−	0.0975359i	$-0.0310961\pi$
$224$	−2.43065e7	+	4.21000e7i	−0.144495	+	0.250273i
$225$	7.31672e6	+	1.26729e7i	0.0428231	+	0.0741717i
$226$	−2.38335e8			−1.37344
$227$	−7.26905e7	−	1.25904e8i	−0.412465	−	0.714411i	0.582694	−	0.812692i	$-0.301999\pi$
$227$	−7.26905e7	−	1.25904e8i	−0.412465	−	0.714411i	−0.995159	+	0.0982814i	$0.968665\pi$
$228$	9.41949e7	+	1.63150e8i	0.526326	+	0.911624i
$229$	1.52646e8			0.839967			0.419983	−	0.907532i	$-0.362036\pi$
$229$	1.52646e8			0.839967			0.419983	+	0.907532i	$0.362036\pi$
$230$	−2.34489e8	−	4.06147e8i	−1.27079	−	2.20108i
$231$	−4.17584e7	+	7.23277e7i	−0.222896	+	0.386067i
$232$	1.35163e8	−	2.34110e8i	0.710641	−	1.23087i
$233$	3.72130e8			1.92730			0.963648	−	0.267175i	$-0.0860903\pi$
$233$	3.72130e8			1.92730			0.963648	+	0.267175i	$0.0860903\pi$
$234$	−2.13652e8	+	1.38526e8i	−1.09006	+	0.706764i
$235$	8.86692e7			0.445692
$236$	2.42571e7	−	4.20145e7i	0.120129	−	0.208069i
$237$	−1.33384e8	+	2.31027e8i	−0.650853	+	1.12731i
$238$	−6.18285e7	−	1.07090e8i	−0.297282	−	0.514908i
$239$	3.61510e8			1.71288			0.856441	−	0.516245i	$-0.172671\pi$
$239$	3.61510e8			1.71288			0.856441	+	0.516245i	$0.172671\pi$
$240$	−3.65594e7	−	6.33228e7i	−0.170710	−	0.295679i
$241$	−1.11416e8	−	1.92978e8i	−0.512730	−	0.888074i	−0.999891	−	0.0147620i	$-0.995301\pi$
$241$	−1.11416e8	−	1.92978e8i	−0.512730	−	0.888074i	0.487161	−	0.873312i	$-0.338032\pi$
$242$	−8.05603e7			−0.365399
$243$	−1.42599e8	−	2.46989e8i	−0.637521	−	1.10422i
$244$	−9.39441e7	+	1.62716e8i	−0.414005	+	0.717077i
$245$	1.55201e7	−	2.68816e7i	0.0674238	−	0.116781i
$246$	1.48261e7			0.0634973
$247$	9.58712e7	+	4.89371e7i	0.404808	+	0.206632i
$248$	3.41628e8			1.42224
$249$	1.83625e8	−	3.18047e8i	0.753760	−	1.30555i
$250$	−2.13777e8	+	3.70272e8i	−0.865308	+	1.49876i
$251$	−2.36299e8	−	4.09282e8i	−0.943200	−	1.63367i	−0.759315	−	0.650723i	$-0.774466\pi$
$251$	−2.36299e8	−	4.09282e8i	−0.943200	−	1.63367i	−0.183886	−	0.982948i	$-0.558868\pi$
$252$	−1.30771e8			−0.514766
$253$	1.85134e8	+	3.20661e8i	0.718727	+	1.24487i
$254$	−2.66945e8	−	4.62361e8i	−1.02212	−	1.77037i
$255$	−3.17810e8			−1.20026
$256$	1.87347e8	+	3.24494e8i	0.697921	+	1.20884i
$257$	−5.38767e6	+	9.33172e6i	−0.0197986	+	0.0342922i	−0.875755	−	0.482756i	$-0.839636\pi$
$257$	−5.38767e6	+	9.33172e6i	−0.0197986	+	0.0342922i	0.855956	+	0.517048i	$0.172969\pi$
$258$	1.68503e8	−	2.91856e8i	0.610855	−	1.05803i
$259$	9.11099e7			0.325849
$260$	−4.12956e8	−	2.10792e8i	−1.45713	−	0.743784i
$261$	−2.64679e8			−0.921462
$262$	−3.05295e8	+	5.28787e8i	−1.04873	+	1.81646i
$263$	−1.70691e8	+	2.95645e8i	−0.578583	+	1.00213i	0.417059	+	0.908879i	$0.363061\pi$
$263$	−1.70691e8	+	2.95645e8i	−0.578583	+	1.00213i	−0.995642	+	0.0932555i	$0.970273\pi$
$264$	2.13693e8	+	3.70128e8i	0.714788	+	1.23805i
$265$	−2.78517e8			−0.919373
$266$	4.35881e7	+	7.54969e7i	0.141998	+	0.245948i
$267$	−3.01606e8	−	5.22397e8i	−0.969730	−	1.67962i
$268$	−4.88395e8			−1.54989
$269$	1.12760e8	+	1.95307e8i	0.353202	+	0.611764i	0.986809	−	0.161891i	$-0.0517594\pi$
$269$	1.12760e8	+	1.95307e8i	0.353202	+	0.611764i	−0.633606	+	0.773656i	$0.718426\pi$
$270$	7.22297e7	−	1.25105e8i	0.223328	−	0.386815i
$271$	−2.46569e8	+	4.27070e8i	−0.752568	+	1.30349i	0.194007	+	0.981000i	$0.437852\pi$
$271$	−2.46569e8	+	4.27070e8i	−0.752568	+	1.30349i	−0.946574	+	0.322485i	$0.895482\pi$
$272$	−8.54746e7			−0.257541
$273$	−1.42474e8	+	9.23760e7i	−0.423806	+	0.274783i
$274$	6.83088e8			2.00609
$275$	1.65875e7	−	2.87305e7i	0.0480970	−	0.0833064i
$276$	−6.58777e8	+	1.14104e9i	−1.88607	+	3.26676i
$277$	1.28319e8	+	2.22254e8i	0.362752	+	0.628306i	0.988413	−	0.151790i	$-0.0485037\pi$
$277$	1.28319e8	+	2.22254e8i	0.362752	+	0.628306i	−0.625660	+	0.780096i	$0.715170\pi$
$278$	8.62704e8			2.40827
$279$	−1.67246e8	−	2.89678e8i	−0.461041	−	0.798547i
$280$	−7.94221e7	−	1.37563e8i	−0.216216	−	0.374497i
$281$	−5.61215e8			−1.50889			−0.754444	−	0.656365i	$-0.772093\pi$
$281$	−5.61215e8			−1.50889			−0.754444	+	0.656365i	$0.772093\pi$
$282$	−1.96420e8	−	3.40210e8i	−0.521572	−	0.903390i
$283$	2.01887e8	−	3.49679e8i	0.529489	−	0.917102i	−0.469919	−	0.882709i	$-0.655717\pi$
$283$	2.01887e8	−	3.49679e8i	0.529489	−	0.917102i	0.999408	−	0.0343925i	$-0.0109496\pi$
$284$	6.15226e8	−	1.06560e9i	1.59375	−	2.76046i
$285$	2.24051e8			0.573311
$286$	5.14156e8	+	2.62449e8i	1.29961	+	0.663381i
$287$	4.35053e6			0.0108632
$288$	1.21786e8	−	2.10940e8i	0.300418	−	0.520338i
$289$	1.94125e7	−	3.36234e7i	0.0473085	−	0.0819407i
$290$	−3.80006e8	−	6.58190e8i	−0.914951	−	1.58474i
$291$	8.48579e8			2.01868
$292$	9.81703e7	+	1.70036e8i	0.230749	+	0.399669i
$293$	−1.40380e8	−	2.43145e8i	−0.326038	−	0.564715i	0.655684	−	0.755036i	$-0.272381\pi$
$293$	−1.40380e8	−	2.43145e8i	−0.326038	−	0.564715i	−0.981722	+	0.190321i	$0.939047\pi$
$294$	−1.37521e8			−0.315611
$295$	−2.88488e7	−	4.99676e7i	−0.0654261	−	0.113321i
$296$	2.33121e8	−	4.03778e8i	0.522470	−	0.904944i
$297$	−5.70268e7	+	9.87734e7i	−0.126308	+	0.218772i
$298$	−5.84805e8			−1.28013
$299$	3.88495e7	+	7.51799e8i	0.0840498	+	1.62649i
$300$	1.18050e8			0.252430
$301$	4.94449e7	−	8.56411e7i	0.104505	−	0.181009i
$302$	5.91901e8	−	1.02520e9i	1.23659	−	2.14183i
$303$	−4.94823e8	−	8.57058e8i	−1.02188	−	1.76995i
$304$	6.02584e7			0.123015
$305$	1.11727e8	+	1.93517e8i	0.225481	+	0.390545i
$306$	3.09789e8	+	5.36570e8i	0.618074	+	1.07054i
$307$	−2.47115e7			−0.0487433			−0.0243716	−	0.999703i	$-0.507758\pi$
$307$	−2.47115e7			−0.0487433			−0.0243716	+	0.999703i	$0.507758\pi$
$308$	1.48234e8	+	2.56749e8i	0.289081	+	0.500704i
$309$	1.97232e8	−	3.41615e8i	0.380296	−	0.658693i
$310$	4.80238e8	−	8.31797e8i	0.915568	−	1.58581i
$311$	4.46299e8			0.841327			0.420663	−	0.907217i	$-0.361797\pi$
$311$	4.46299e8			0.841327			0.420663	+	0.907217i	$0.361797\pi$
$312$	4.48426e7	+	8.67774e8i	0.0835891	+	1.61758i
$313$	−5.22539e8			−0.963194			−0.481597	−	0.876393i	$-0.659943\pi$
$313$	−5.22539e8			−0.963194			−0.481597	+	0.876393i	$0.659943\pi$
$314$	−2.84349e8	+	4.92507e8i	−0.518320	+	0.897756i
$315$	−7.77628e7	+	1.34689e8i	−0.140180	+	0.242798i
$316$	4.73485e8	+	8.20099e8i	0.844114	+	1.46205i
$317$	4.74003e8			0.835744			0.417872	−	0.908506i	$-0.362776\pi$
$317$	4.74003e8			0.835744			0.417872	+	0.908506i	$0.362776\pi$
$318$	6.16973e8	+	1.06863e9i	1.07590	+	1.86351i
$319$	3.00023e8	+	5.19655e8i	0.517472	+	0.896289i
$320$	8.49168e8			1.44867
$321$	5.62603e7	+	9.74457e7i	0.0949368	+	0.164435i
$322$	−3.04846e8	+	5.28008e8i	−0.508844	+	0.881343i
$323$	1.30956e8	−	2.26822e8i	0.216230	−	0.374521i
$324$	−1.23966e9			−2.02485
$325$	5.65945e7	−	3.66941e7i	0.0914497	−	0.0592932i
$326$	4.33070e8			0.692304
$327$	2.52679e7	−	4.37653e7i	0.0399625	−	0.0692170i
$328$	1.11316e7	−	1.92806e7i	0.0174181	−	0.0301690i
$329$	−5.76369e7	−	9.98300e7i	−0.0892308	−	0.154552i
$330$	1.20158e9			1.84058
$331$	3.12848e8	+	5.41869e8i	0.474172	+	0.821290i	0.999563	−	0.0295714i	$-0.00941423\pi$
$331$	3.12848e8	+	5.41869e8i	0.474172	+	0.821290i	−0.525391	+	0.850861i	$0.676081\pi$
$332$	−6.51830e8	−	1.12900e9i	−0.977577	−	1.69321i
$333$	−4.56502e8			−0.677467
$334$	−1.03439e8	−	1.79162e8i	−0.151906	−	0.263108i
$335$	−2.90423e8	+	5.03028e8i	−0.422060	+	0.731030i
$336$	−4.75288e7	+	8.23224e7i	−0.0683549	+	0.118394i
$337$	7.39525e7			0.105256			0.0526282	−	0.998614i	$-0.483240\pi$
$337$	7.39525e7			0.105256			0.0526282	+	0.998614i	$0.483240\pi$
$338$	6.88469e8	+	9.50513e8i	0.969786	+	1.33890i
$339$	7.96333e8			1.11019
$340$	−5.64080e8	+	9.77015e8i	−0.778331	+	1.34811i
$341$	−3.79158e8	+	6.56721e8i	−0.517821	+	0.896893i
$342$	−2.18397e8	−	3.78274e8i	−0.295226	−	0.511346i
$343$	−4.03536e7			−0.0539949
$344$	−2.53028e8	−	4.38257e8i	−0.335130	−	0.580462i
$345$	7.83481e8	+	1.35703e9i	1.02722	+	1.77919i
$346$	7.38407e8			0.958361
$347$	8.30802e7	+	1.43899e8i	0.106744	+	0.184886i	0.914449	−	0.404700i	$-0.132624\pi$
$347$	8.30802e7	+	1.43899e8i	0.106744	+	0.184886i	−0.807705	+	0.589586i	$0.799291\pi$
$348$	−1.06760e9	+	1.84913e9i	−1.35794	+	2.35202i
$349$	3.15199e8	−	5.45940e8i	0.396913	−	0.687474i	−0.596430	−	0.802665i	$-0.703415\pi$
$349$	3.15199e8	−	5.45940e8i	0.396913	−	0.687474i	0.993343	+	0.115191i	$0.0367481\pi$
$350$	5.46268e7			0.0681033
$351$	−1.94568e8	+	1.26152e8i	−0.240158	+	0.155711i
$352$	−5.52198e8			−0.674831
$353$	3.11203e8	−	5.39019e8i	0.376558	−	0.652217i	−0.614001	−	0.789305i	$-0.710441\pi$
$353$	3.11203e8	−	5.39019e8i	0.376558	−	0.652217i	0.990559	+	0.137088i	$0.0437743\pi$
$354$	−1.27812e8	+	2.21377e8i	−0.153130	+	0.265229i
$355$	−7.31686e8	−	1.26732e9i	−0.868012	−	1.50344i
$356$	−2.14128e9			−2.51535
$357$	2.06583e8	+	3.57812e8i	0.240301	+	0.416214i
$358$	−3.21674e8	−	5.57156e8i	−0.370532	−	0.641780i
$359$	−2.72199e8			−0.310496			−0.155248	−	0.987875i	$-0.549618\pi$
$359$	−2.72199e8			−0.310496			−0.155248	+	0.987875i	$0.549618\pi$
$360$	3.97941e8	+	6.89254e8i	0.449531	+	0.778611i
$361$	3.54614e8	−	6.14209e8i	0.396717	−	0.687134i
$362$	−2.08805e8	+	3.61661e8i	−0.231345	+	0.400702i
$363$	2.69171e8			0.295362
$364$	3.11062e7	+	6.01954e8i	0.0338059	+	0.654197i
$365$	2.33507e8			0.251348
$366$	4.94998e8	−	8.57361e8i	0.527739	−	0.914071i
$367$	6.70686e8	−	1.16166e9i	0.708253	−	1.22673i	−0.257252	−	0.966344i	$-0.582817\pi$
$367$	6.70686e8	−	1.16166e9i	0.708253	−	1.22673i	0.965505	−	0.260386i	$-0.0838497\pi$
$368$	2.10717e8	+	3.64972e8i	0.220410	+	0.381761i
$369$	−2.17982e7			−0.0225854
$370$	−6.55412e8	−	1.13521e9i	−0.672680	−	1.16512i
$371$	1.81042e8	+	3.13574e8i	0.184065	+	0.318810i
$372$	−2.69838e9			−2.71771
$373$	4.10747e8	+	7.11434e8i	0.409820	+	0.709829i	0.994869	−	0.101168i	$-0.0322581\pi$
$373$	4.10747e8	+	7.11434e8i	0.409820	+	0.709829i	−0.585049	+	0.810998i	$0.698925\pi$
$374$	7.02314e8	−	1.21644e9i	0.694194	−	1.20238i
$375$	7.14278e8	−	1.23717e9i	0.699452	−	1.21149i
$376$	−5.89898e8			−0.572295
$377$	6.29585e7	+	1.21835e9i	0.0605146	+	1.17105i
$378$	−1.87803e8			−0.178847
$379$	−4.93875e8	+	8.55416e8i	−0.465993	+	0.807124i	−0.999246	−	0.0388320i	$-0.987636\pi$
$379$	−4.93875e8	+	8.55416e8i	−0.465993	+	0.807124i	0.533252	+	0.845956i	$0.320970\pi$
$380$	3.97668e8	−	6.88781e8i	0.371773	−	0.643930i
$381$	8.91923e8	+	1.54486e9i	0.826209	+	1.43104i
$382$	2.80395e8			0.257365
$383$	−7.95762e8	−	1.37830e9i	−0.723748	−	1.25357i	−0.959487	−	0.281752i	$-0.909084\pi$
$383$	−7.95762e8	−	1.37830e9i	−0.723748	−	1.25357i	0.235739	−	0.971816i	$-0.424249\pi$
$384$	−1.31421e9	−	2.27629e9i	−1.18442	−	2.05148i
$385$	3.52588e8			0.314887
$386$	3.29969e8	+	5.71522e8i	0.292023	+	0.505799i
$387$	−2.47741e8	+	4.29101e8i	−0.217275	+	0.376332i
$388$	1.50614e9	−	2.60871e9i	1.30905	−	2.26733i
$389$	−8.64280e8			−0.744442			−0.372221	−	0.928144i	$-0.621404\pi$
$389$	−8.64280e8			−0.744442			−0.372221	+	0.928144i	$0.621404\pi$
$390$	2.17589e9	+	1.11067e9i	1.85742	+	0.948114i
$391$	1.83175e9			1.54970
$392$	−1.03252e8	+	1.78838e8i	−0.0865761	+	0.149954i
$393$	1.02006e9	−	1.76680e9i	0.847720	−	1.46829i
$394$	−1.52311e9	−	2.63811e9i	−1.25457	−	2.17298i
$395$	1.12623e9			0.919466
$396$	−7.42720e8	−	1.28643e9i	−0.601024	−	1.04100i
$397$	−1.01372e9	−	1.75581e9i	−0.813113	−	1.40835i	−0.910675	−	0.413124i	$-0.864438\pi$
$397$	−1.01372e9	−	1.75581e9i	−0.813113	−	1.40835i	0.0975615	−	0.995229i	$-0.468896\pi$
$398$	2.96472e8			0.235718
$399$	−1.45638e8	−	2.52252e8i	−0.114781	−	0.198806i
$400$	1.88797e7	−	3.27006e7i	0.0147498	−	0.0255473i
$401$	4.63049e8	−	8.02024e8i	0.358609	−	0.621129i	−0.629120	−	0.777308i	$-0.716584\pi$
$401$	4.63049e8	−	8.02024e8i	0.358609	−	0.621129i	0.987729	+	0.156179i	$0.0499178\pi$
$402$	2.57339e9			1.97567
$403$	−1.29364e9	+	8.38755e8i	−0.984565	+	0.638362i
$404$	−3.51304e9			−2.65063
$405$	−7.37159e8	+	1.27680e9i	−0.551402	+	0.955057i
$406$	−4.94025e8	+	8.55676e8i	−0.366360	+	0.634553i
$407$	5.17462e8	+	8.96270e8i	0.380450	+	0.658959i
$408$	2.11432e9			1.54121
$409$	6.16170e8	+	1.06724e9i	0.445316	+	0.771311i	0.998074	−	0.0620313i	$-0.0197579\pi$
$409$	6.16170e8	+	1.06724e9i	0.445316	+	0.771311i	−0.552758	+	0.833342i	$0.686425\pi$
$410$	−3.12962e7	−	5.42066e7i	−0.0224258	−	0.0388426i
$411$	−2.28235e9			−1.62157
$412$	−7.00133e8	−	1.21267e9i	−0.493219	−	0.854281i
$413$	−3.75047e7	+	6.49600e7i	−0.0261975	+	0.0453755i
$414$	1.52742e9	−	2.64556e9i	1.05793	−	1.83238i
$415$	−1.55044e9			−1.06484
$416$	−9.99950e8	−	5.10420e8i	−0.681007	−	0.347617i
$417$	−2.88249e9			−1.94667
$418$	−4.95121e8	+	8.57575e8i	−0.331585	+	0.574321i
$419$	−2.59046e8	+	4.48681e8i	−0.172040	+	0.297981i	−0.939133	−	0.343554i	$-0.888369\pi$
$419$	−2.59046e8	+	4.48681e8i	−0.172040	+	0.297981i	0.767093	+	0.641536i	$0.221702\pi$
$420$	6.27322e8	+	1.08655e9i	0.413160	+	0.715613i
$421$	6.80136e8			0.444231			0.222115	−	0.975020i	$-0.428704\pi$
$421$	6.80136e8			0.444231			0.222115	+	0.975020i	$0.428704\pi$
$422$	−2.48062e9	−	4.29656e9i	−1.60682	−	2.78309i
$423$	2.88787e8	+	5.00194e8i	0.185518	+	0.321327i
$424$	1.85292e9			1.18053
$425$	−8.20602e7	−	1.42132e8i	−0.0518527	−	0.0898115i
$426$	−3.24167e9	+	5.61473e9i	−2.03158	+	3.51881i
$427$	1.45250e8	−	2.51581e8i	0.0902859	−	0.156380i
$428$	3.99425e8			0.246254
$429$	−1.71791e9	−	8.76901e8i	−1.05051	−	0.536229i
$430$	−1.42276e9			−0.862961
$431$	9.52346e7	−	1.64951e8i	0.0572960	−	0.0992395i	−0.835955	−	0.548798i	$-0.815085\pi$
$431$	9.52346e7	−	1.64951e8i	0.0572960	−	0.0992395i	0.893251	+	0.449559i	$0.148419\pi$
$432$	−6.49071e7	+	1.12422e8i	−0.0387346	+	0.0670903i
$433$	4.69606e8	+	8.13382e8i	0.277988	+	0.481490i	0.970885	−	0.239548i	$-0.0769991\pi$
$433$	4.69606e8	+	8.13382e8i	0.277988	+	0.481490i	−0.692897	+	0.721037i	$0.743666\pi$
$434$	−1.24866e9			−0.733213
$435$	1.26969e9	+	2.19917e9i	0.739579	+	1.28099i
$436$	−8.96959e7	−	1.55358e8i	−0.0518287	−	0.0897699i
$437$	−1.29136e9			−0.740221
$438$	−5.17265e8	−	8.95930e8i	−0.294140	−	0.509465i
$439$	4.68990e7	−	8.12314e7i	0.0264568	−	0.0458245i	−0.852494	−	0.522737i	$-0.824911\pi$
$439$	4.68990e7	−	8.12314e7i	0.0264568	−	0.0458245i	0.878951	+	0.476913i	$0.158244\pi$
$440$	9.02161e8	−	1.56259e9i	0.504894	−	0.874501i
$441$	2.02190e8			0.112260
$442$	2.39620e9	−	1.55362e9i	1.31991	−	0.855792i
$443$	5.07289e8			0.277232			0.138616	−	0.990346i	$-0.455735\pi$
$443$	5.07289e8			0.277232			0.138616	+	0.990346i	$0.455735\pi$
$444$	−1.84133e9	+	3.18927e9i	−0.998368	+	1.72922i
$445$	−1.27331e9	+	2.20543e9i	−0.684973	+	1.18641i
$446$	1.80298e9	+	3.12285e9i	0.962317	+	1.66678i
$447$	1.95397e9			1.03476
$448$	−5.51978e8	−	9.56054e8i	−0.290034	−	0.502353i
$449$	−1.51465e9	−	2.62344e9i	−0.789676	−	1.36776i	−0.926165	−	0.377118i	$-0.876915\pi$
$449$	−1.51465e9	−	2.62344e9i	−0.789676	−	1.36776i	0.136489	−	0.990642i	$-0.456418\pi$
$450$	−2.73705e8			−0.141592
$451$	2.47090e7	+	4.27973e7i	0.0126834	+	0.0219684i
$452$	1.41341e9	−	2.44810e9i	0.719919	−	1.24694i
$453$	−1.97768e9	+	3.42544e9i	−0.999566	+	1.73130i
$454$	2.71922e9			1.36380
$455$	6.38486e8	+	3.25912e8i	0.317769	+	0.162204i
$456$	−1.49057e9			−0.736164
$457$	1.13130e9	−	1.95946e9i	0.554459	−	0.960352i	−0.443486	−	0.896281i	$-0.646258\pi$
$457$	1.13130e9	−	1.95946e9i	0.554459	−	0.960352i	0.997945	−	0.0640704i	$-0.0204082\pi$
$458$	−1.42756e9	+	2.47260e9i	−0.694327	+	1.20261i
$459$	2.82117e8	+	4.88642e8i	0.136171	+	0.235856i
$460$	5.56240e9			2.66446
$461$	1.74731e9	+	3.02643e9i	0.830646	+	1.43872i	0.897527	+	0.440960i	$0.145362\pi$
$461$	1.74731e9	+	3.02643e9i	0.830646	+	1.43872i	−0.0668803	+	0.997761i	$0.521305\pi$
$462$	−7.81054e8	−	1.35283e9i	−0.368497	−	0.638256i
$463$	−7.00571e8			−0.328034			−0.164017	−	0.986458i	$-0.552445\pi$
$463$	−7.00571e8			−0.328034			−0.164017	+	0.986458i	$0.552445\pi$
$464$	3.41482e8	+	5.91464e8i	0.158692	+	0.274862i
$465$	−1.60459e9	+	2.77922e9i	−0.740078	+	1.28185i
$466$	−3.48017e9	+	6.02784e9i	−1.59313	+	2.75938i
$467$	3.62938e9			1.64901			0.824506	−	0.565853i	$-0.191453\pi$
$467$	3.62938e9			1.64901			0.824506	+	0.565853i	$0.191453\pi$
$468$	−1.55857e8	−	3.01606e9i	−0.0702853	−	1.36013i
$469$	7.55125e8			0.337998
$470$	−8.29239e8	+	1.43628e9i	−0.368415	+	0.638113i
$471$	9.50075e8	−	1.64558e9i	0.418972	−	0.725680i
$472$	1.91925e8	+	3.32424e8i	0.0840108	+	0.145511i
$473$	1.12330e9			0.488068
$474$	−2.49482e9	−	4.32116e9i	−1.07601	−	1.86370i
$475$	5.78512e7	+	1.00201e8i	0.0247677	+	0.0428988i
$476$	1.46666e9			0.623310
$477$	−9.07105e8	−	1.57115e9i	−0.382686	−	0.662832i
$478$	−3.38086e9	+	5.85582e9i	−1.41589	+	2.45239i
$479$	−1.95097e9	+	3.37917e9i	−0.811102	+	1.40487i	0.100991	+	0.994887i	$0.467799\pi$
$479$	−1.95097e9	+	3.37917e9i	−0.811102	+	1.40487i	−0.912093	+	0.409983i	$0.865535\pi$
$480$	−2.33688e9			−0.964479
$481$	1.08587e8	+	2.10133e9i	0.0444908	+	0.860967i
$482$	4.16788e9			1.69532
$483$	1.01856e9	−	1.76420e9i	0.411312	−	0.712413i
$484$	4.77750e8	−	8.27488e8i	0.191532	−	0.331744i
$485$	−1.79125e9	−	3.10253e9i	−0.712951	−	1.23487i
$486$	5.33438e9			2.10793
$487$	8.32461e8	+	1.44186e9i	0.326597	+	0.565683i	0.981834	−	0.189740i	$-0.0607646\pi$
$487$	8.32461e8	+	1.44186e9i	0.326597	+	0.565683i	−0.655237	+	0.755423i	$0.727431\pi$
$488$	−7.43300e8	−	1.28743e9i	−0.289531	−	0.501482i
$489$	−1.44699e9			−0.559608
$490$	2.90290e8	+	5.02796e8i	0.111467	+	0.193066i
$491$	1.02718e9	−	1.77913e9i	0.391617	−	0.678301i	−0.601046	−	0.799215i	$-0.705249\pi$
$491$	1.02718e9	−	1.77913e9i	0.391617	−	0.678301i	0.992663	+	0.120914i	$0.0385824\pi$
$492$	−8.79241e7	+	1.52289e8i	−0.0332836	+	0.0576489i
$493$	2.96849e9			1.11576
$494$	−1.68929e9	+	1.09528e9i	−0.630462	+	0.408772i
$495$	−1.76663e9			−0.654676
$496$	−4.31552e8	+	7.47470e8i	−0.158799	+	0.275048i
$497$	−9.51223e8	+	1.64757e9i	−0.347564	+	0.601999i
$498$	3.43453e9	+	5.94879e9i	1.24614	+	2.15837i
$499$	1.53723e9			0.553842			0.276921	−	0.960893i	$-0.410686\pi$
$499$	1.53723e9			0.553842			0.276921	+	0.960893i	$0.410686\pi$
$500$	−2.53554e9	−	4.39168e9i	−0.907142	−	1.57122i
$501$	3.45615e8	+	5.98623e8i	0.122789	+	0.212677i
$502$	8.83952e9			3.11864
$503$	8.72036e8	+	1.51041e9i	0.305525	+	0.529185i	0.977378	−	0.211500i	$-0.0678348\pi$
$503$	8.72036e8	+	1.51041e9i	0.305525	+	0.529185i	−0.671853	+	0.740684i	$0.734501\pi$
$504$	5.17340e8	−	8.96060e8i	0.179999	−	0.311767i
$505$	−2.08902e9	+	3.61829e9i	−0.721810	+	1.25021i
$506$	−6.92553e9			−2.37644
$507$	−2.30033e9	−	3.17588e9i	−0.783904	−	1.08227i
$508$	6.33229e9			2.14308
$509$	6.22882e8	−	1.07886e9i	0.209360	−	0.362622i	−0.742153	−	0.670230i	$-0.766195\pi$
$509$	6.22882e8	−	1.07886e9i	0.209360	−	0.362622i	0.951513	+	0.307608i	$0.0995286\pi$
$510$	2.97217e9	−	5.14795e9i	0.992152	−	1.71846i
$511$	−1.51785e8	−	2.62899e8i	−0.0503216	−	0.0871596i
$512$	−1.62483e9			−0.535011
$513$	−1.98889e8	−	3.44485e8i	−0.0650428	−	0.112657i
$514$	−1.00772e8	−	1.74541e8i	−0.0327316	−	0.0566928i
$515$	−1.66533e9			−0.537248
$516$	1.99856e9	+	3.46161e9i	0.640388	+	1.10918i
$517$	6.54702e8	−	1.13398e9i	0.208366	−	0.360900i
$518$	−8.52064e8	+	1.47582e9i	−0.269351	+	0.466529i
$519$	−2.46719e9			−0.774669
$520$	3.07805e9	−	1.99572e9i	0.959985	−	0.622425i
$521$	3.27846e8			0.101564			0.0507818	−	0.998710i	$-0.483829\pi$
$521$	3.27846e8			0.101564			0.0507818	+	0.998710i	$0.483829\pi$
$522$	2.47529e9	−	4.28733e9i	0.761692	−	1.31929i
$523$	2.51641e9	−	4.35855e9i	0.769175	−	1.33225i	−0.168835	−	0.985644i	$-0.554001\pi$
$523$	2.51641e9	−	4.35855e9i	0.769175	−	1.33225i	0.938011	−	0.346606i	$-0.112666\pi$
$524$	−3.62101e9	−	6.27177e9i	−1.09944	−	1.90428i
$525$	−1.82521e8			−0.0550497
$526$	−3.19262e9	−	5.52978e9i	−0.956527	−	1.65675i
$527$	1.87573e9	+	3.24886e9i	0.558256	+	0.966928i
$528$	−1.07977e9			−0.319236
$529$	−2.81332e9	−	4.87281e9i	−0.826273	−	1.43115i
$530$	2.60471e9	−	4.51149e9i	0.759965	−	1.31630i
$531$	1.87916e8	−	3.25479e8i	0.0544668	−	0.0943393i
$532$	−1.03397e9			−0.297726
$533$	5.18508e6	+	1.00339e8i	0.00148324	+	0.0287029i
$534$	1.12825e10			3.20636
$535$	2.37517e8	−	4.11392e8i	0.0670590	−	0.116150i
$536$	1.93213e9	−	3.34654e9i	0.541950	−	0.938684i
$537$	1.07479e9	+	1.86159e9i	0.299511	+	0.518768i
$538$	−4.21816e9			−1.16785
$539$	−2.29190e8	−	3.96968e8i	−0.0630427	−	0.109193i
$540$	8.56693e8	+	1.48384e9i	0.234125	+	0.405516i
$541$	−1.63075e9			−0.442790			−0.221395	−	0.975184i	$-0.571061\pi$
$541$	−1.63075e9			−0.442790			−0.221395	+	0.975184i	$0.571061\pi$
$542$	−4.61185e9	−	7.98796e9i	−1.24416	−	2.15495i
$543$	6.97666e8	−	1.20839e9i	0.187003	−	0.323898i
$544$	−1.36589e9	+	2.36579e9i	−0.363763	+	0.630056i
$545$	−2.13350e8			−0.0564553
$546$	−1.63901e8	−	3.17173e9i	−0.0430930	−	0.833916i
$547$	4.69795e9			1.22730			0.613652	−	0.789576i	$-0.289700\pi$
$547$	4.69795e9			1.22730			0.613652	+	0.789576i	$0.289700\pi$
$548$	−4.05094e9	+	7.01644e9i	−1.05154	+	1.82131i
$549$	−7.27771e8	+	1.26054e9i	−0.187712	+	0.325126i
$550$	3.10255e8	+	5.37378e8i	0.0795151	+	0.137724i
$551$	−2.09274e9			−0.532948
$552$	−5.21234e9	−	9.02804e9i	−1.31900	−	2.28458i
$553$	−7.32071e8	−	1.26798e9i	−0.184084	−	0.318842i
$554$	−4.80017e9			−1.19942
$555$	2.18988e9	+	3.79299e9i	0.543745	+	0.941794i
$556$	−5.11613e9	+	8.86140e9i	−1.26235	+	2.18645i
$557$	−3.67038e8	+	6.35728e8i	−0.0899948	+	0.155876i	−0.907509	−	0.420033i	$-0.862018\pi$
$557$	−3.67038e8	+	6.35728e8i	−0.0899948	+	0.155876i	0.817514	+	0.575909i	$0.195352\pi$
$558$	6.25636e9			1.52441
$559$	2.03413e9	+	1.03831e9i	0.492535	+	0.251412i
$560$	4.01310e8			0.0965656
$561$	−2.34659e9	+	4.06442e9i	−0.561135	+	0.971915i
$562$	5.24851e9	−	9.09068e9i	1.24727	−	2.16033i
$563$	−9.34971e8	−	1.61942e9i	−0.220810	−	0.382454i	0.734244	−	0.678886i	$-0.237537\pi$
$563$	−9.34971e8	−	1.61942e9i	−0.220810	−	0.382454i	−0.955054	+	0.296431i	$0.904203\pi$
$564$	4.65936e9			1.09358
$565$	−1.68096e9	−	2.91151e9i	−0.392093	−	0.679124i
$566$	3.77612e9	+	6.54044e9i	0.875364	+	1.51618i
$567$	1.91668e9			0.441579
$568$	4.86776e9	+	8.43121e9i	1.11458	+	1.93050i
$569$	−8.92618e6	+	1.54606e7i	−0.00203129	+	0.00351830i	−0.867039	−	0.498240i	$-0.833980\pi$
$569$	−8.92618e6	+	1.54606e7i	−0.00203129	+	0.00351830i	0.865008	+	0.501758i	$0.167313\pi$
$570$	−2.09534e9	+	3.62923e9i	−0.473906	+	0.820829i
$571$	−1.60257e9			−0.360238			−0.180119	−	0.983645i	$-0.557648\pi$
$571$	−1.60257e9			−0.360238			−0.180119	+	0.983645i	$0.557648\pi$
$572$	−5.74490e9	+	3.72482e9i	−1.28350	+	0.832184i
$573$	−9.36865e8			−0.208035
$574$	−4.06864e7	+	7.04709e7i	−0.00897961	+	0.0155531i
$575$	−4.04598e8	+	7.00785e8i	−0.0887537	+	0.153726i
$576$	2.76566e9	+	4.79026e9i	0.603004	+	1.04443i
$577$	−7.14670e9			−1.54878			−0.774391	−	0.632708i	$-0.781944\pi$
$577$	−7.14670e9			−1.54878			−0.774391	+	0.632708i	$0.781944\pi$
$578$	3.63093e8	+	6.28896e8i	0.0782115	+	0.135466i
$579$	−1.10250e9	−	1.90959e9i	−0.236050	−	0.408851i
$580$	9.01427e9			1.91837
$581$	1.00782e9	+	1.74559e9i	0.213189	+	0.369255i
$582$	−7.93596e9	+	1.37455e10i	−1.66866	+	2.89021i
$583$	−2.05647e9	+	3.56191e9i	−0.429816	+	0.744464i
$584$	−1.55347e9			−0.322745
$585$	−3.19911e9	−	1.63297e9i	−0.660668	−	0.337235i
$586$	5.25136e9			1.07803
$587$	−2.97255e9	+	5.14861e9i	−0.606592	+	1.05065i	0.385206	+	0.922831i	$0.374130\pi$
$587$	−2.97255e9	+	5.14861e9i	−0.606592	+	1.05065i	−0.991798	+	0.127817i	$0.959203\pi$
$588$	8.15545e8	−	1.41257e9i	0.165435	−	0.286542i
$589$	−1.32236e9	−	2.29040e9i	−0.266653	−	0.461857i
$590$	1.07918e9			0.216328
$591$	5.08906e9	+	8.81452e9i	1.01410	+	1.75648i
$592$	5.88967e8	+	1.02012e9i	0.116672	+	0.202081i
$593$	−8.30046e9			−1.63460			−0.817298	−	0.576215i	$-0.804529\pi$
$593$	−8.30046e9			−1.63460			−0.817298	+	0.576215i	$0.804529\pi$
$594$	−1.06664e9	−	1.84747e9i	−0.208816	−	0.361680i
$595$	8.72143e8	−	1.51060e9i	0.169738	−	0.293994i
$596$	3.46809e9	−	6.00691e9i	0.671009	−	1.16222i
$597$	−9.90582e8			−0.190537
$598$	−1.25411e10	−	6.40157e9i	−2.39818	−	1.22414i
$599$	7.14852e9			1.35901			0.679505	−	0.733671i	$-0.262195\pi$
$599$	7.14852e9			1.35901			0.679505	+	0.733671i	$0.262195\pi$
$600$	−4.67013e8	+	8.08890e8i	−0.0882673	+	0.152883i
$601$	4.17936e9	−	7.23887e9i	0.785325	−	1.36022i	−0.143480	−	0.989653i	$-0.545829\pi$
$601$	4.17936e9	−	7.23887e9i	0.785325	−	1.36022i	0.928805	−	0.370570i	$-0.120838\pi$
$602$	9.24822e8	+	1.60184e9i	0.172771	+	0.299248i
$603$	−3.78352e9			−0.702726
$604$	7.02035e9	+	1.21596e10i	1.29637	+	2.24538i
$605$	−5.68186e8	−	9.84128e8i	−0.104315	−	0.180679i
$606$	1.85104e10			3.37880
$607$	−4.68056e9	−	8.10696e9i	−0.849449	−	1.47129i	−0.881701	−	0.471809i	$-0.843601\pi$
$607$	−4.68056e9	−	8.10696e9i	−0.849449	−	1.47129i	0.0322523	−	0.999480i	$-0.489732\pi$
$608$	9.62931e8	−	1.66784e9i	0.173753	−	0.300949i
$609$	1.65065e9	−	2.85901e9i	0.296138	−	0.512926i
$610$	−4.17952e9			−0.745542
$611$	2.23375e9	−	1.44830e9i	0.396179	−	0.256870i
$612$	−7.34861e9			−1.29591
$613$	−3.21643e8	+	5.57102e8i	−0.0563978	+	0.0976838i	−0.892846	−	0.450362i	$-0.851295\pi$
$613$	−3.21643e8	+	5.57102e8i	−0.0563978	+	0.0976838i	0.836448	+	0.548046i	$0.184628\pi$
$614$	2.31103e8	−	4.00282e8i	0.0402918	−	0.0697874i
$615$	1.04568e8	+	1.81117e8i	0.0181274	+	0.0313975i
$616$	−2.34570e9			−0.404333
$617$	−5.41481e9	−	9.37873e9i	−0.928080	−	1.60748i	−0.786531	−	0.617551i	$-0.788125\pi$
$617$	−5.41481e9	−	9.37873e9i	−0.928080	−	1.60748i	−0.141549	−	0.989931i	$-0.545208\pi$
$618$	3.68904e9	+	6.38961e9i	0.628715	+	1.08897i
$619$	9.18688e9			1.55686			0.778432	−	0.627728i	$-0.216015\pi$
$619$	9.18688e9			1.55686			0.778432	+	0.627728i	$0.216015\pi$
$620$	5.69595e9	+	9.86568e9i	0.959832	+	1.66248i
$621$	1.39098e9	−	2.40925e9i	0.233078	−	0.403702i
$622$	−4.17381e9	+	7.22926e9i	−0.695451	+	1.20456i
$623$	3.31071e9			0.548546
$624$	−1.95530e9	−	9.98076e8i	−0.322157	−	0.164444i
$625$	−5.36579e9			−0.879132
$626$	4.88681e9	−	8.46421e9i	0.796188	−	1.37904i
$627$	1.65431e9	−	2.86535e9i	0.268029	−	0.464239i
$628$	−3.37257e9	−	5.84147e9i	−0.543378	−	0.941159i
$629$	5.11987e9			0.820317
$630$	−1.45448e9	−	2.51924e9i	−0.231748	−	0.401400i
$631$	6.09028e9	+	1.05487e10i	0.965016	+	1.67146i	0.709573	+	0.704632i	$0.248888\pi$
$631$	6.09028e9	+	1.05487e10i	0.965016	+	1.67146i	0.255443	+	0.966824i	$0.417779\pi$
$632$	−7.49256e9			−1.18065
$633$	8.28833e9	+	1.43558e10i	1.29883	+	2.24965i
$634$	−4.43290e9	+	7.67800e9i	−0.690837	+	1.19656i
$635$	3.76548e9	−	6.52201e9i	0.583596	−	1.01082i
$636$	−1.46354e10			−2.25583
$637$	−4.80945e7	−	9.30703e8i	−0.00737237	−	0.142667i
$638$	−1.12233e10			−1.71100
$639$	4.76606e9	−	8.25506e9i	0.722615	−	1.25161i
$640$	−5.54830e9	+	9.60993e9i	−0.836623	+	1.44907i
$641$	4.30143e9	+	7.45030e9i	0.645074	+	1.11730i	0.984284	+	0.176591i	$0.0565070\pi$
$641$	4.30143e9	+	7.45030e9i	0.645074	+	1.11730i	−0.339210	+	0.940711i	$0.610160\pi$
$642$	−2.10460e9			−0.313904
$643$	−5.73387e9	−	9.93136e9i	−0.850569	−	1.47323i	−0.880695	−	0.473683i	$-0.842924\pi$
$643$	−5.73387e9	−	9.93136e9i	−0.850569	−	1.47323i	0.0301264	−	0.999546i	$-0.490409\pi$
$644$	−3.61568e9	−	6.26254e9i	−0.533444	−	0.923953i
$645$	4.75376e9			0.697554
$646$	2.44941e9	+	4.24250e9i	0.357477	+	0.619168i
$647$	5.54996e9	−	9.61282e9i	0.805610	−	1.39536i	−0.110268	−	0.993902i	$-0.535171\pi$
$647$	5.54996e9	−	9.61282e9i	0.805610	−	1.39536i	0.915878	−	0.401456i	$-0.131496\pi$
$648$	4.90417e9	−	8.49427e9i	0.708032	−	1.22635i
$649$	−8.52037e8			−0.122349
$650$	6.51057e7	+	1.25990e9i	0.00929870	+	0.179944i
$651$	4.17206e9			0.592676
$652$	−2.56826e9	+	4.44835e9i	−0.362887	+	0.628539i
$653$	4.44932e9	−	7.70645e9i	0.625313	−	1.08307i	−0.363167	−	0.931724i	$-0.618305\pi$
$653$	4.44932e9	−	7.70645e9i	0.625313	−	1.08307i	0.988480	−	0.151350i	$-0.0483621\pi$
$654$	4.72614e8	+	8.18591e8i	0.0660669	+	0.114431i
$655$	−8.61290e9			−1.19758
$656$	2.81234e7	+	4.87112e7i	0.00388960	+	0.00673698i
$657$	7.60510e8	+	1.31724e9i	0.104623	+	0.181212i
$658$	2.15609e9			0.295037
$659$	−2.34934e9	−	4.06917e9i	−0.319776	−	0.553869i	0.660665	−	0.750681i	$-0.270274\pi$
$659$	−2.34934e9	−	4.06917e9i	−0.319776	−	0.553869i	−0.980441	+	0.196812i	$0.936941\pi$
$660$	−7.12579e9	+	1.23422e10i	−0.964782	+	1.67105i
$661$	−1.51661e9	+	2.62685e9i	−0.204253	+	0.353777i	−0.949895	−	0.312571i	$-0.898810\pi$
$661$	−1.51661e9	+	2.62685e9i	−0.204253	+	0.353777i	0.745641	+	0.666347i	$0.232143\pi$
$662$	−1.17031e10			−1.56783
$663$	−8.00626e9	+	5.19101e9i	−1.06692	+	0.691759i
$664$	1.03147e10			1.36732
$665$	−6.14848e8	+	1.06495e9i	−0.0810760	+	0.140428i
$666$	4.26923e9	−	7.39453e9i	0.560002	−	0.969953i
$667$	−7.31807e9	−	1.26753e10i	−0.954896	−	1.65393i
$668$	2.45373e9			0.318499
$669$	−6.02416e9	−	1.04341e10i	−0.777866	−	1.34730i
$670$	−5.43211e9	−	9.40868e9i	−0.697761	−	1.20856i
$671$	3.29982e9			0.421659
$672$	1.51902e9	+	2.63103e9i	0.193096	+	0.334451i
$673$	−5.65291e9	+	9.79113e9i	−0.714857	+	1.23817i	0.248157	+	0.968720i	$0.420175\pi$
$673$	−5.65291e9	+	9.79113e9i	−0.714857	+	1.23817i	−0.963015	+	0.269449i	$0.913158\pi$
$674$	−6.91607e8	+	1.19790e9i	−0.0870062	+	0.150699i
$675$	−2.49257e8			−0.0311949
$676$	−1.38462e10	+	1.43485e9i	−1.72392	+	0.178646i
$677$	−4.97612e9			−0.616355			−0.308177	−	0.951329i	$-0.599719\pi$
$677$	−4.97612e9			−0.616355			−0.308177	+	0.951329i	$0.599719\pi$
$678$	−7.44735e9	+	1.28992e10i	−0.917694	+	1.58949i
$679$	−2.32870e9	+	4.03343e9i	−0.285476	+	0.494458i
$680$	−4.46308e9	−	7.73028e9i	−0.544319	−	0.942788i
$681$	−9.08554e9			−1.10239
$682$	−7.09181e9	−	1.22834e10i	−0.856075	−	1.48277i
$683$	−6.16136e9	−	1.06718e10i	−0.739953	−	1.28164i	−0.952516	−	0.304489i	$-0.901514\pi$
$683$	−6.16136e9	−	1.06718e10i	−0.739953	−	1.28164i	0.212563	−	0.977147i	$-0.431819\pi$
$684$	5.18066e9			0.618998
$685$	4.81777e9	+	8.34462e9i	0.572702	+	0.991949i
$686$	3.77389e8	−	6.53657e8i	0.0446329	−	0.0773064i
$687$	4.76979e9	−	8.26152e9i	0.561243	−	0.972101i
$688$	1.27852e9			0.149674
$689$	−7.01641e9	+	4.54923e9i	−0.817236	+	0.529871i
$690$	−2.93086e10			−3.39644
$691$	1.93565e9	−	3.35265e9i	0.223179	−	0.386558i	−0.732592	−	0.680668i	$-0.761690\pi$
$691$	1.93565e9	−	3.35265e9i	0.223179	−	0.386558i	0.955772	+	0.294110i	$0.0950231\pi$
$692$	−4.37900e9	+	7.58466e9i	−0.502347	+	0.870091i
$693$	1.14835e9	+	1.98899e9i	0.131071	+	0.227021i
$694$	−3.10788e9			−0.352944
$695$	6.08459e9	+	1.05388e10i	0.687519	+	1.19082i
$696$	−8.44698e9	−	1.46306e10i	−0.949663	−	1.64486i
$697$	2.44476e8			0.0273477
$698$	5.89551e9	+	1.02113e10i	0.656187	+	1.13655i
$699$	1.16281e10	−	2.01404e10i	1.28777	−	2.23048i
$700$	−3.23956e8	+	5.61108e8i	−0.0356979	+	0.0618306i
$701$	1.49272e10			1.63669			0.818345	−	0.574727i	$-0.194892\pi$
$701$	1.49272e10			1.63669			0.818345	+	0.574727i	$0.194892\pi$
$702$	−2.23829e8	−	4.33144e9i	−0.0244195	−	0.472555i
$703$	−3.60943e9			−0.391828
$704$	6.26996e9	−	1.08599e10i	0.677267	−	1.17306i
$705$	2.77068e9	−	4.79895e9i	0.297800	−	0.515804i
$706$	5.82076e9	+	1.00819e10i	0.622535	+	1.07826i
$707$	5.43164e9			0.578046
$708$	−1.51594e9	−	2.62568e9i	−0.160533	−	0.278052i
$709$	8.99721e9	+	1.55836e10i	0.948082	+	1.64213i	0.749459	+	0.662051i	$0.230314\pi$
$709$	8.99721e9	+	1.55836e10i	0.948082	+	1.64213i	0.198624	+	0.980076i	$0.436353\pi$
$710$	2.73711e10			2.87004
$711$	3.66801e9	+	6.35318e9i	0.382725	+	0.662900i
$712$	8.47106e9	−	1.46723e10i	0.879545	−	1.52342i
$713$	9.24830e9	−	1.60185e10i	0.955540	−	1.65504i
$714$	−7.72790e9			−0.794544
$715$	4.20223e8	+	8.13198e9i	0.0429941	+	0.832003i
$716$	7.63055e9			0.776892
$717$	1.12962e10	−	1.95656e10i	1.14450	−	1.98233i
$718$	2.54562e9	−	4.40915e9i	0.256660	−	0.444549i
$719$	6.67279e9	+	1.15576e10i	0.669509	+	1.15962i	0.978042	+	0.208409i	$0.0668286\pi$
$719$	6.67279e9	+	1.15576e10i	0.669509	+	1.15962i	−0.308533	+	0.951214i	$0.599838\pi$
$720$	−2.01075e9			−0.200768
$721$	1.08250e9	+	1.87494e9i	0.107561	+	0.186301i
$722$	6.63274e9	+	1.14882e10i	0.655862	+	1.13599i
$723$	−1.39258e10			−1.37037
$724$	−2.47657e9	−	4.28955e9i	−0.242530	−	0.420075i
$725$	−6.55681e8	+	1.13567e9i	−0.0639013	+	0.110680i
$726$	−2.51730e9	+	4.36009e9i	−0.244150	+	0.422880i
$727$	−9.77716e9			−0.943718			−0.471859	−	0.881674i	$-0.656417\pi$
$727$	−9.77716e9			−0.943718			−0.471859	+	0.881674i	$0.656417\pi$
$728$	−4.24772e9	−	2.16823e9i	−0.408034	−	0.208279i
$729$	−5.60246e9			−0.535590
$730$	−2.18377e9	+	3.78240e9i	−0.207767	+	0.359863i
$731$	2.77853e9	−	4.81255e9i	0.263090	−	0.455685i
$732$	5.87101e9	+	1.01689e10i	0.553253	+	0.958263i
$733$	−1.71524e9			−0.160865			−0.0804323	−	0.996760i	$-0.525630\pi$
$733$	−1.71524e9			−0.160865			−0.0804323	+	0.996760i	$0.525630\pi$
$734$	1.25446e10	+	2.17279e10i	1.17090	+	2.02806i
$735$	−9.69924e8	−	1.67996e9i	−0.0901015	−	0.156060i
$736$	1.34690e10			1.24527
$737$	4.28876e9	+	7.42835e9i	0.394635	+	0.683528i
$738$	2.03857e8	−	3.53091e8i	0.0186694	−	0.0323363i
$739$	9.18315e9	−	1.59057e10i	0.837021	−	1.44976i	−0.0553535	−	0.998467i	$-0.517629\pi$
$739$	9.18315e9	−	1.59057e10i	0.837021	−	1.44976i	0.892374	−	0.451296i	$-0.149038\pi$
$740$	1.55473e10			1.41040
$741$	5.64429e9	−	3.65959e9i	0.509619	−	0.330422i
$742$	−6.77247e9			−0.608602
$743$	2.13382e9	−	3.69588e9i	0.190852	−	0.330565i	−0.754681	−	0.656092i	$-0.772208\pi$
$743$	2.13382e9	−	3.69588e9i	0.190852	−	0.330565i	0.945533	+	0.325527i	$0.105542\pi$
$744$	1.06750e10	−	1.84896e10i	0.950303	−	1.64597i
$745$	−4.12458e9	−	7.14399e9i	−0.365454	−	0.632986i
$746$	−1.53653e10			−1.35505
$747$	−5.04963e9	−	8.74621e9i	−0.443238	−	0.767711i
$748$	8.32992e9	+	1.44279e10i	0.727755	+	1.26051i
$749$	−6.17566e8			−0.0537028
$750$	1.33599e10	+	2.31401e10i	1.15635	+	2.00286i
$751$	3.78857e9	−	6.56200e9i	0.326389	−	0.565323i	−0.655403	−	0.755279i	$-0.727501\pi$
$751$	3.78857e9	−	6.56200e9i	0.326389	−	0.565323i	0.981793	+	0.189956i	$0.0608346\pi$
$752$	7.45172e8	−	1.29068e9i	0.0638990	−	0.110676i
$753$	−2.95349e10			−2.52088
$754$	−2.03238e10	−	1.03742e10i	−1.72666	−	0.881364i
$755$	1.66985e10			1.41210
$756$	1.11374e9	−	1.92905e9i	0.0937469	−	0.162374i
$757$	−6.25087e9	+	1.08268e10i	−0.523727	+	0.907121i	0.475892	+	0.879504i	$0.342125\pi$
$757$	−6.25087e9	+	1.08268e10i	−0.523727	+	0.907121i	−0.999619	+	0.0276172i	$0.991208\pi$
$758$	−9.23749e9	−	1.59998e10i	−0.770392	−	1.33436i
$759$	2.31398e10			1.92094
$760$	3.14641e9	+	5.44973e9i	0.259996	+	0.450327i
$761$	−1.38684e9	−	2.40207e9i	−0.114072	−	0.197579i	0.803336	−	0.595526i	$-0.203056\pi$
$761$	−1.38684e9	−	2.40207e9i	−0.114072	−	0.197579i	−0.917408	+	0.397947i	$0.869723\pi$
$762$	−3.33652e10			−2.73182
$763$	1.38682e8	+	2.40204e8i	0.0113028	+	0.0195770i
$764$	−1.66284e9	+	2.88012e9i	−0.134904	+	0.233660i
$765$	−4.36984e9	+	7.56878e9i	−0.352899	+	0.611239i
$766$	2.97680e10			2.39304
$767$	−1.54292e9	−	7.87575e8i	−0.123469	−	0.0630243i
$768$	2.34164e10			1.86533
$769$	−6.36593e9	+	1.10261e10i	−0.504801	+	0.874340i	0.495184	+	0.868788i	$0.335101\pi$
$769$	−6.36593e9	+	1.10261e10i	−0.504801	+	0.874340i	−0.999985	+	0.00555218i	$0.998233\pi$
$770$	−3.29742e9	+	5.71130e9i	−0.260290	+	0.450835i
$771$	3.36701e8	+	5.83183e8i	0.0264578	+	0.0458263i
$772$	−7.82731e9			−0.612282
$773$	−1.00441e10	−	1.73970e10i	−0.782140	−	1.35471i	−0.930693	−	0.365802i	$-0.880795\pi$
$773$	−1.00441e10	−	1.73970e10i	−0.782140	−	1.35471i	0.148552	−	0.988905i	$-0.452539\pi$
$774$	−4.63378e9	−	8.02595e9i	−0.359205	−	0.622161i
$775$	−1.65725e9			−0.127889
$776$	1.19168e10	+	2.06405e10i	0.915470	+	1.58564i
$777$	2.84694e9	−	4.93105e9i	0.217723	−	0.377108i
$778$	8.08279e9	−	1.39998e10i	0.615365	−	1.06584i
$779$	−1.72352e8			−0.0130628
$780$	−2.43122e10	+	1.57633e10i	−1.83440	+	1.18937i
$781$	−2.16100e10			−1.62322
$782$	−1.71306e10	+	2.96711e10i	−1.28100	+	2.21876i
$783$	2.25419e9	−	3.90437e9i	0.167812	−	0.290659i
$784$	−2.60860e8	−	4.51823e8i	−0.0193331	−	0.0334859i
$785$	−8.02197e9			−0.591885
$786$	1.90793e10	+	3.30464e10i	1.40147	+	2.42742i
$787$	−2.97163e9	−	5.14701e9i	−0.217312	−	0.376395i	0.736674	−	0.676249i	$-0.236395\pi$
$787$	−2.97163e9	−	5.14701e9i	−0.217312	−	0.376395i	−0.953985	+	0.299854i	$0.903062\pi$
$788$	3.61303e10			2.63045
$789$	1.06673e10	+	1.84763e10i	0.773186	+	1.33920i
$790$	−1.05325e10	+	1.82429e10i	−0.760042	+	1.31643i
$791$	−2.18532e9	+	3.78509e9i	−0.156999	+	0.271931i
$792$	1.17530e10			0.840642
$793$	5.97550e9	+	3.05017e9i	0.425518	+	0.217204i
$794$	3.79214e10			2.68852
$795$	−8.70293e9	+	1.50739e10i	−0.614300	+	1.06400i
$796$	−1.75818e9	+	3.04526e9i	−0.123557	+	0.214007i
$797$	1.01908e10	+	1.76510e10i	0.713025	+	1.23500i	0.963716	+	0.266929i	$0.0860090\pi$
$797$	1.01908e10	+	1.76510e10i	0.713025	+	1.23500i	−0.250691	+	0.968067i	$0.580658\pi$
$798$	5.44806e9			0.379517
$799$	−3.23887e9	−	5.60989e9i	−0.224636	−	0.389082i
$800$	−6.03396e8	−	1.04511e9i	−0.0416666	−	0.0721686i
$801$	−1.65882e10			−1.14047
$802$	8.66091e9	+	1.50011e10i	0.592861	+	1.02687i
$803$	1.72413e9	−	2.98628e9i	0.117508	−	0.203529i
$804$	−1.52611e10	+	2.64329e10i	−1.03559	+	1.79370i
$805$	−8.60022e9			−0.581064
$806$	−1.48819e9	−	2.87987e10i	−0.100112	−	1.93731i
$807$	1.40939e10			0.944001
$808$	1.38978e10	−	2.40718e10i	0.926846	−	1.60534i
$809$	−1.15373e10	+	1.99832e10i	−0.766097	+	1.32692i	0.173568	+	0.984822i	$0.444470\pi$
$809$	−1.15373e10	+	1.99832e10i	−0.766097	+	1.32692i	−0.939665	+	0.342096i	$0.888863\pi$
$810$	−1.37879e10	−	2.38813e10i	−0.911592	−	1.57892i
$811$	−1.17859e10			−0.775873			−0.387936	−	0.921686i	$-0.626812\pi$
$811$	−1.17859e10			−0.775873			−0.387936	+	0.921686i	$0.626812\pi$
$812$	−5.85947e9	−	1.01489e10i	−0.384072	−	0.665232i
$813$	1.54092e10	+	2.66896e10i	1.00569	+	1.74191i
$814$	−1.93573e10			−1.25794
$815$	3.05442e9	+	5.29040e9i	0.197641	+	0.342324i
$816$	−2.67086e9	+	4.62606e9i	−0.172082	+	0.298054i
$817$	−1.95882e9	+	3.39278e9i	−0.125666	+	0.217660i
$818$	−2.30498e10			−1.47242
$819$	2.40975e8	+	4.66324e9i	0.0153278	+	0.296616i
$820$	7.42389e8			0.0470200
$821$	−1.46328e10	+	2.53447e10i	−0.922839	+	1.59840i	−0.127840	+	0.991795i	$0.540804\pi$
$821$	−1.46328e10	+	2.53447e10i	−0.922839	+	1.59840i	−0.795000	+	0.606610i	$0.792529\pi$
$822$	2.13447e10	−	3.69701e10i	1.34041	−	2.32166i
$823$	−1.54158e10	−	2.67009e10i	−0.963975	−	1.66965i	−0.712343	−	0.701832i	$-0.752366\pi$
$823$	−1.54158e10	−	2.67009e10i	−0.963975	−	1.66965i	−0.251633	−	0.967823i	$-0.580968\pi$
$824$	1.10791e10			0.689857
$825$	−1.03663e9	−	1.79550e9i	−0.0642741	−	0.111326i
$826$	−7.01492e8	−	1.21502e9i	−0.0433104	−	0.0750158i
$827$	6.40534e9			0.393797			0.196899	−	0.980424i	$-0.436913\pi$
$827$	6.40534e9			0.393797			0.196899	+	0.980424i	$0.436913\pi$
$828$	1.81162e10	+	3.13782e10i	1.10907	+	1.92097i
$829$	−5.83279e9	+	1.01027e10i	−0.355578	+	0.615880i	−0.987217	−	0.159383i	$-0.949049\pi$
$829$	−5.83279e9	+	1.01027e10i	−0.355578	+	0.615880i	0.631638	+	0.775263i	$0.282383\pi$
$830$	1.44998e10	−	2.51143e10i	0.880213	−	1.52457i
$831$	1.60385e10			0.969525
$832$	2.13922e10	−	1.38701e10i	1.28773	−	0.834925i
$833$	−2.26765e9			−0.135931
$834$	2.69572e10	−	4.66913e10i	1.60914	−	2.78711i
$835$	1.45910e9	−	2.52724e9i	0.0867327	−	0.150226i
$836$	−5.87247e9	−	1.01714e10i	−0.347615	−	0.602088i
$837$	5.69752e9			0.335851
$838$	−4.84523e9	−	8.39218e9i	−0.284420	−	0.492630i
$839$	1.36549e10	+	2.36511e10i	0.798221	+	1.38256i	0.920774	+	0.390097i	$0.127558\pi$
$839$	1.36549e10	+	2.36511e10i	0.798221	+	1.38256i	−0.122553	+	0.992462i	$0.539108\pi$
$840$	−9.92692e9			−0.577879
$841$	−3.23453e9	−	5.60238e9i	−0.187511	−	0.324778i
$842$	−6.36067e9	+	1.10170e10i	−0.367206	+	0.636020i
$843$	−1.75365e10	+	3.03741e10i	−1.00820	+	1.74625i
$844$	5.88438e10			3.36901
$845$	−6.75578e9	+	1.51143e10i	−0.385192	+	0.861764i
$846$	−1.08030e10			−0.613407
$847$	−7.38667e8	+	1.27941e9i	−0.0417692	+	0.0723464i
$848$	−2.34065e9	+	4.05412e9i	−0.131811	+	0.228303i
$849$	−1.26169e10	−	2.18531e10i	−0.707580	−	1.22556i
$850$	3.06972e9			0.171448
$851$	−1.26218e10	−	2.18616e10i	−0.702048	−	1.21598i
$852$	−3.84484e10	−	6.65946e10i	−2.12980	−	3.68893i
$853$	−2.14396e10			−1.18276			−0.591378	−	0.806395i	$-0.701416\pi$
$853$	−2.14396e10			−1.18276			−0.591378	+	0.806395i	$0.701416\pi$
$854$	2.71678e9	+	4.70560e9i	0.149263	+	0.258531i
$855$	3.08067e9	−	5.33588e9i	0.168564	−	0.291961i
$856$	−1.58016e9	+	2.73691e9i	−0.0861077	+	0.149143i
$857$	5.63385e9			0.305754			0.152877	−	0.988245i	$-0.451146\pi$
$857$	5.63385e9			0.305754			0.152877	+	0.988245i	$0.451146\pi$
$858$	3.02702e10	−	1.96263e10i	1.63610	−	1.06080i
$859$	−1.08192e10			−0.582398			−0.291199	−	0.956663i	$-0.594054\pi$
$859$	−1.08192e10			−0.582398			−0.291199	+	0.956663i	$0.594054\pi$
$860$	8.43743e9	−	1.46141e10i	0.452341	−	0.783477i
$861$	1.35943e8	−	2.35459e8i	0.00725846	−	0.0125720i
$862$	1.78128e9	+	3.08526e9i	0.0947231	+	0.164065i
$863$	−4.04426e9			−0.214191			−0.107095	−	0.994249i	$-0.534155\pi$
$863$	−4.04426e9			−0.214191			−0.107095	+	0.994249i	$0.534155\pi$
$864$	2.07444e9	+	3.59303e9i	0.109421	+	0.189523i
$865$	5.20793e9	+	9.02040e9i	0.273595	+	0.473881i
$866$	−1.75671e10			−0.919154
$867$	−1.21318e9	−	2.10129e9i	−0.0632204	−	0.109501i
$868$	7.40498e9	−	1.28258e10i	0.384331	−	0.665680i
$869$	8.31565e9	−	1.44031e10i	0.429860	−	0.744539i
$870$	−4.74968e10			−2.44538
$871$	8.99978e8	+	1.74160e10i	0.0461496	+	0.893067i
$872$	1.41937e9			0.0724919
$873$	1.16678e10	−	2.02093e10i	0.593528	−	1.02802i
$874$	1.20768e10	−	2.09177e10i	0.611876	−	1.05980i
$875$	3.92029e9	+	6.79014e9i	0.197829	+	0.342650i
$876$	1.22702e10			0.616721
$877$	−8.65395e9	−	1.49891e10i	−0.433227	−	0.750372i	0.563922	−	0.825828i	$-0.309292\pi$
$877$	−8.65395e9	−	1.49891e10i	−0.433227	−	0.750372i	−0.997149	+	0.0754563i	$0.975959\pi$
$878$	8.77203e8	+	1.51936e9i	0.0437390	+	0.0757583i
$879$	−1.75460e10			−0.871400
$880$	2.27926e9	+	3.94779e9i	0.112747	+	0.195283i
$881$	−1.06596e9	+	1.84629e9i	−0.0525199	+	0.0909672i	−0.891090	−	0.453826i	$-0.850059\pi$
$881$	−1.06596e9	+	1.84629e9i	−0.0525199	+	0.0909672i	0.838570	+	0.544794i	$0.183392\pi$
$882$	−1.89089e9	+	3.27512e9i	−0.0927954	+	0.160726i
$883$	−6.38251e9			−0.311982			−0.155991	−	0.987758i	$-0.549857\pi$
$883$	−6.38251e9			−0.311982			−0.155991	+	0.987758i	$0.549857\pi$
$884$	1.74800e9	+	3.38265e10i	0.0851056	+	1.64692i
$885$	−3.60580e9			−0.174864
$886$	−4.74419e9	+	8.21719e9i	−0.229163	+	0.396922i
$887$	−1.80199e10	+	3.12113e10i	−0.866999	+	1.50169i	−0.00195122	+	0.999998i	$0.500621\pi$
$887$	−1.80199e10	+	3.12113e10i	−0.866999	+	1.50169i	−0.865048	+	0.501689i	$0.832712\pi$
$888$	−1.45689e10	−	2.52340e10i	−0.698200	−	1.20932i
$889$	−9.79058e9			−0.467361
$890$	−2.38161e10	−	4.12507e10i	−1.13241	−	1.96140i
$891$	1.08858e10	+	1.88548e10i	0.515572	+	0.892998i
$892$	−4.27691e10			−2.01768
$893$	2.28336e9	+	3.95489e9i	0.107299	+	0.185846i
$894$	−1.82736e10	+	3.16508e10i	−0.855347	+	1.48151i
$895$	4.53749e9	−	7.85917e9i	0.211561	−	0.366434i
$896$	1.44260e10			0.669991
$897$	4.19028e10	+	2.13891e10i	1.93852	+	0.989507i
$898$	5.66602e10			2.61102
$899$	1.49876e10	−	2.59592e10i	0.687974	−	1.19161i
$900$	1.62317e9	−	2.81141e9i	0.0742189	−	0.128551i
$901$	1.01736e10	+	1.76211e10i	0.463379	+	0.802596i
$902$	−9.24320e8			−0.0419372
$903$	−3.09004e9	−	5.35211e9i	−0.139655	−	0.241890i
$904$	1.11831e10	+	1.93697e10i	0.503469	+	0.872035i
$905$	−5.89075e9			−0.264180
$906$	−3.69907e10	−	6.40697e10i	−1.65251	−	2.86223i
$907$	9.01003e9	−	1.56058e10i	0.400960	−	0.694483i	−0.592882	−	0.805289i	$-0.702010\pi$
$907$	9.01003e9	−	1.56058e10i	0.400960	−	0.694483i	0.993842	+	0.110806i	$0.0353434\pi$
$908$	−1.61259e10	+	2.79309e10i	−0.714865	+	1.23818i
$909$	−2.72150e10			−1.20181
$910$	−1.12504e10	+	7.29439e9i	−0.494905	+	0.320881i
$911$	−3.15050e10			−1.38059			−0.690295	−	0.723528i	$-0.742519\pi$
$911$	−3.15050e10			−1.38059			−0.690295	+	0.723528i	$0.742519\pi$
$912$	1.88291e9	−	3.26130e9i	0.0821956	−	0.142367i
$913$	−1.14479e10	+	1.98283e10i	−0.497825	+	0.862259i
$914$	2.11599e10	+	3.66500e10i	0.916646	+	1.58768i
$915$	1.39647e10			0.602641
$916$	−1.69318e10	−	2.93267e10i	−0.727895	−	1.26075i
$917$	5.59857e9	+	9.69701e9i	0.239764	+	0.415284i
$918$	−1.05535e10			−0.450243
$919$	1.66745e9	+	2.88810e9i	0.0708675	+	0.122746i	0.899282	−	0.437370i	$-0.144090\pi$
$919$	1.66745e9	+	2.88810e9i	0.0708675	+	0.122746i	−0.828414	+	0.560116i	$0.810757\pi$
$920$	−2.20052e10	+	3.81142e10i	−0.931684	+	1.61372i
$921$	−7.72168e8	+	1.33743e9i	−0.0325689	+	0.0564110i
$922$	−6.53636e10			−2.74649
$923$	−3.91326e10	−	1.99751e10i	−1.63807	−	0.836147i
$924$	1.85277e10			0.772625
$925$	−1.13088e9	+	1.95874e9i	−0.0469808	+	0.0813731i
$926$	6.55178e9	−	1.13480e10i	0.271157	−	0.469658i
$927$	−5.42382e9	−	9.39433e9i	−0.223628	−	0.387335i
$928$	2.18276e10			0.896576
$929$	1.19765e10	+	2.07439e10i	0.490090	+	0.848860i	0.999935	−	0.0114060i	$-0.00363073\pi$
$929$	1.19765e10	+	2.07439e10i	0.490090	+	0.848860i	−0.509845	+	0.860266i	$0.670297\pi$
$930$	−3.00123e10	−	5.19829e10i	−1.22352	−	2.11919i
$931$	1.59866e9			0.0649280
$932$	−4.12772e10	−	7.14943e10i	−1.67015	−	2.89278i
$933$	1.39457e10	−	2.41546e10i	0.562152	−	0.973675i
$934$	−3.39422e10	+	5.87896e10i	−1.36309	+	2.36095i
$935$	1.98135e10			0.792721
$936$	2.12830e10	+	1.08638e10i	0.848336	+	0.433029i
$937$	2.59766e10			1.03156			0.515779	−	0.856722i	$-0.327503\pi$
$937$	2.59766e10			1.03156			0.515779	+	0.856722i	$0.327503\pi$
$938$	−7.06197e9	+	1.22317e10i	−0.279393	+	0.483923i
$939$	−1.63280e10	+	2.82809e10i	−0.643580	+	1.11471i
$940$	−9.83534e9	−	1.70353e10i	−0.386226	−	0.668964i
$941$	3.86257e10			1.51117			0.755583	−	0.655052i	$-0.227353\pi$
$941$	3.86257e10			1.51117			0.755583	+	0.655052i	$0.227353\pi$
$942$	1.77703e10	+	3.07790e10i	0.692654	+	1.19971i
$943$	−6.02694e8	−	1.04390e9i	−0.0234049	−	0.0405384i
$944$	−9.69776e8			−0.0375206
$945$	−1.32456e9	−	2.29421e9i	−0.0510577	−	0.0884346i
$946$	−1.05051e10	+	1.81954e10i	−0.403443	+	0.698784i
$947$	−2.55424e9	+	4.42407e9i	−0.0977320	+	0.169277i	−0.910746	−	0.412968i	$-0.864492\pi$
$947$	−2.55424e9	+	4.42407e9i	−0.0977320	+	0.169277i	0.813014	+	0.582245i	$0.197825\pi$
$948$	5.91806e10			2.25606
$949$	5.88251e9	−	3.81404e9i	0.223424	−	0.144862i
$950$	−2.16411e9			−0.0818930
$951$	1.48113e10	−	2.56540e10i	0.558422	−	0.967214i
$952$	−5.80220e9	+	1.00497e10i	−0.217953	+	0.377506i
$953$	1.99743e10	+	3.45966e10i	0.747562	+	1.29482i	0.948988	+	0.315312i	$0.102109\pi$
$953$	1.99743e10	+	3.45966e10i	0.747562	+	1.29482i	−0.201426	+	0.979504i	$0.564557\pi$
$954$	3.39332e10			1.26533
$955$	1.97761e9	+	3.42532e9i	0.0734732	+	0.127259i
$956$	−4.00993e10	−	6.94540e10i	−1.48434	−	2.57096i
$957$	3.74997e10			1.38304
$958$	−3.64911e10	−	6.32044e10i	−1.34093	−	2.32257i
$959$	6.26331e9	−	1.08484e10i	0.229318	−	0.397191i
$960$	2.65343e10	−	4.59587e10i	0.967961	−	1.67656i
$961$	1.03688e10			0.376875
$962$	−3.50533e10	−	1.78928e10i	−1.26945	−	0.647987i
$963$	3.09429e9			0.111653
$964$	−2.47169e10	+	4.28110e10i	−0.888639	+	1.53917i
$965$	−4.65449e9	+	8.06181e9i	−0.166735	+	0.288793i
$966$	1.90512e10	+	3.29977e10i	0.679991	+	1.17778i
$967$	−1.31064e10			−0.466114			−0.233057	−	0.972463i	$-0.574873\pi$
$967$	−1.31064e10			−0.466114			−0.233057	+	0.972463i	$0.574873\pi$
$968$	3.78003e9	+	6.54720e9i	0.133947	+	0.232002i
$969$	−8.18404e9	−	1.41752e10i	−0.288958	−	0.500490i
$970$	6.70074e10			2.35734
$971$	−1.05880e10	−	1.83390e10i	−0.371149	−	0.642848i	0.618594	−	0.785711i	$-0.287703\pi$
$971$	−1.05880e10	−	1.83390e10i	−0.371149	−	0.642848i	−0.989743	+	0.142863i	$0.954369\pi$
$972$	−3.16347e10	+	5.47929e10i	−1.10492	+	1.91378i
$973$	7.91023e9	−	1.37009e10i	0.275292	−	0.476820i
$974$	−3.11409e10			−1.07988
$975$	−2.17533e8	−	4.20960e9i	−0.00751638	−	0.145454i
$976$	3.75580e9			0.129309
$977$	−2.44330e10	+	4.23192e10i	−0.838196	+	1.45180i	0.0532050	+	0.998584i	$0.483056\pi$
$977$	−2.44330e10	+	4.23192e10i	−0.838196	+	1.45180i	−0.891401	+	0.453215i	$0.850277\pi$
$978$	1.35323e10	−	2.34386e10i	0.462579	−	0.801210i
$979$	1.88033e10	+	3.25683e10i	0.640464	+	1.10932i
$980$	−6.88607e9			−0.233711
$981$	−6.94861e8	−	1.20353e9i	−0.0234994	−	0.0407021i
$982$	1.92125e10	+	3.32770e10i	0.647431	+	1.12138i
$983$	9.77577e8			0.0328257			0.0164128	−	0.999865i	$-0.494775\pi$
$983$	9.77577e8			0.0328257			0.0164128	+	0.999865i	$0.494775\pi$
$984$	−6.95668e8	−	1.20493e9i	−0.0232766	−	0.0403162i
$985$	2.14848e10	−	3.72128e10i	0.716316	−	1.24069i
$986$	−2.77614e10	+	4.80842e10i	−0.922301	+	1.59747i
$987$	−7.20400e9			−0.238486
$988$	−1.23231e9	−	2.38472e10i	−0.0406510	−	0.786661i
$989$	−2.73991e10			−0.900636
$990$	1.65216e10	−	2.86162e10i	0.541164	−	0.937323i
$991$	−1.52316e10	+	2.63818e10i	−0.497149	+	0.861087i	−0.999995	−	0.00328911i	$-0.998953\pi$
$991$	−1.52316e10	+	2.63818e10i	−0.497149	+	0.861087i	0.502846	+	0.864376i	$0.332286\pi$
$992$	1.37924e10	+	2.38892e10i	0.448590	+	0.776981i
$993$	3.91027e10			1.26731
$994$	−1.77918e10	−	3.08163e10i	−0.574602	−	0.995240i
$995$	2.09100e9	+	3.62171e9i	0.0672935	+	0.116556i
$996$	−8.14719e10			−2.61276
$997$	−1.08032e10	−	1.87117e10i	−0.345238	−	0.597970i	0.640159	−	0.768243i	$-0.278869\pi$
$997$	−1.08032e10	−	1.87117e10i	−0.345238	−	0.597970i	−0.985397	+	0.170273i	$0.945535\pi$
$998$	−1.43762e10	+	2.49004e10i	−0.457813	+	0.792955i
$999$	3.88789e9	−	6.73402e9i	0.123377	−	0.213695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.f.a.22.3	✓	48
13.3	even	3	inner	91.8.f.a.29.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.f.a.22.3	✓	48	1.1	even	1	trivial
91.8.f.a.29.3	yes	48	13.3	even	3	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.35205 + 16.1982i) q^{2} +(31.2473 - 54.1220i) q^{3} +(-110.922 - 192.122i) q^{4} -263.837 q^{5} +(584.454 + 1012.30i) q^{6} +(171.500 + 297.047i) q^{7} +1755.26 q^{8} +(-859.293 - 1488.34i) q^{9} +O(q^{10})\)	\(q+(-9.35205 + 16.1982i) q^{2} +(31.2473 - 54.1220i) q^{3} +(-110.922 - 192.122i) q^{4} -263.837 q^{5} +(584.454 + 1012.30i) q^{6} +(171.500 + 297.047i) q^{7} +1755.26 q^{8} +(-859.293 - 1488.34i) q^{9} +(2467.42 - 4273.70i) q^{10} +(-1948.08 + 3374.18i) q^{11} -13864.0 q^{12} +(-6646.59 + 4309.45i) q^{13} -6415.51 q^{14} +(-8244.22 + 14279.4i) q^{15} +(-2217.28 + 3840.44i) q^{16} +(9637.35 + 16692.4i) q^{17} +32144.6 q^{18} +(-6794.19 - 11767.9i) q^{19} +(29265.3 + 50689.0i) q^{20} +21435.7 q^{21} +(-36437.1 - 63110.9i) q^{22} +(47517.0 - 82301.8i) q^{23} +(54847.1 - 94998.0i) q^{24} -8514.81 q^{25} +(-7646.17 - 147965. i) q^{26} +29273.3 q^{27} +(38046.2 - 65897.9i) q^{28} +(77004.8 - 133376. i) q^{29} +(-154201. - 267083. i) q^{30} +194632. q^{31} +(70864.3 + 122741. i) q^{32} +(121745. + 210868. i) q^{33} -360516. q^{34} +(-45248.1 - 78372.0i) q^{35} +(-190629. + 330178. i) q^{36} +(132813. - 230039. i) q^{37} +254158. q^{38} +(25547.6 + 494386. i) q^{39} -463103. q^{40} +(6341.88 - 10984.5i) q^{41} +(-200468. + 347220. i) q^{42} +(-144154. - 249682. i) q^{43} +864338. q^{44} +(226714. + 392680. i) q^{45} +(888763. + 1.53938e6i) q^{46} -336075. q^{47} +(138568. + 240007. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(79630.9 - 137925. i) q^{50} +1.20457e6 q^{51} +(1.56519e6 + 798945. i) q^{52} +1.05564e6 q^{53} +(-273766. + 474176. i) q^{54} +(513977. - 890234. i) q^{55} +(301027. + 521393. i) q^{56} -849201. q^{57} +(1.44031e6 + 2.49468e6i) q^{58} +(109343. + 189388. i) q^{59} +3.65785e6 q^{60} +(-423470. - 733472. i) q^{61} +(-1.82020e6 + 3.15269e6i) q^{62} +(294738. - 510501. i) q^{63} -3.21853e6 q^{64} +(1.75362e6 - 1.13699e6i) q^{65} -4.55425e6 q^{66} +(1.10077e6 - 1.90658e6i) q^{67} +(2.13798e6 - 3.70309e6i) q^{68} +(-2.96956e6 - 5.14343e6i) q^{69} +1.69265e6 q^{70} +(2.77325e6 + 4.80340e6i) q^{71} +(-1.50828e6 - 2.61242e6i) q^{72} -885041. q^{73} +(2.48415e6 + 4.30268e6i) q^{74} +(-266065. + 460839. i) q^{75} +(-1.50725e6 + 2.61063e6i) q^{76} -1.33638e6 q^{77} +(-8.24709e6 - 4.20969e6i) q^{78} -4.26864e6 q^{79} +(585001. - 1.01325e6i) q^{80} +(2.79399e6 - 4.83933e6i) q^{81} +(118619. + 205455. i) q^{82} +5.87649e6 q^{83} +(-2.37768e6 - 4.11827e6i) q^{84} +(-2.54269e6 - 4.40407e6i) q^{85} +5.39255e6 q^{86} +(-4.81239e6 - 8.33530e6i) q^{87} +(-3.41938e6 + 5.92255e6i) q^{88} +(4.82611e6 - 8.35907e6i) q^{89} -8.48095e6 q^{90} +(-2.42000e6 - 1.23528e6i) q^{91} -2.10827e7 q^{92} +(6.08172e6 - 1.05338e7i) q^{93} +(3.14299e6 - 5.44382e6i) q^{94} +(1.79256e6 + 3.10481e6i) q^{95} +8.85729e6 q^{96} +(6.78921e6 + 1.17593e7i) q^{97} +(-1.10026e6 - 1.90571e6i) q^{98} +6.69589e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9	\( 48 q - 8 q^{2} + 41 q^{3} - 1472 q^{4} + 526 q^{5} - 519 q^{6} + 8232 q^{7} + 474 q^{8} - 15427 q^{9} + 17800 q^{10} - 11735 q^{11} + 30484 q^{12} - 5622 q^{13} - 5488 q^{14} + 3465 q^{15} - 110364 q^{16} - 3506 q^{17} - 196096 q^{18} - 25291 q^{19} - 13351 q^{20} + 28126 q^{21} + 91579 q^{22} + 82970 q^{23} - 97143 q^{24} + 1263842 q^{25} - 51951 q^{26} - 1080760 q^{27} + 504896 q^{28} + 209315 q^{29} + 1063844 q^{30} + 948356 q^{31} - 495024 q^{32} - 143209 q^{33} + 436128 q^{34} + 90209 q^{35} - 469485 q^{36} - 377142 q^{37} - 198346 q^{38} + 647900 q^{39} - 4780340 q^{40} - 1895174 q^{41} + 178017 q^{42} - 1366459 q^{43} + 8096352 q^{44} - 2154733 q^{45} + 2854528 q^{46} + 2557720 q^{47} - 4102289 q^{48} - 2823576 q^{49} - 2378593 q^{50} - 4369338 q^{51} + 4270295 q^{52} - 4295420 q^{53} + 1447259 q^{54} - 560241 q^{55} + 81291 q^{56} + 15936670 q^{57} - 384326 q^{58} + 6714194 q^{59} + 5267974 q^{60} - 987536 q^{61} + 8520899 q^{62} + 5291461 q^{63} - 8211866 q^{64} - 11284709 q^{65} - 20326376 q^{66} - 1296682 q^{67} - 8400264 q^{68} - 1147530 q^{69} + 12210800 q^{70} - 7723282 q^{71} + 26270290 q^{72} + 15769600 q^{73} + 58033 q^{74} - 928389 q^{75} - 9095520 q^{76} - 8050210 q^{77} - 30641513 q^{78} - 24665908 q^{79} + 16716608 q^{80} - 5846292 q^{81} - 9977079 q^{82} + 32429868 q^{83} + 5228006 q^{84} + 17821519 q^{85} + 89024148 q^{86} - 16967309 q^{87} + 28910709 q^{88} - 27957029 q^{89} - 155228046 q^{90} - 5184102 q^{91} - 5073264 q^{92} + 11673603 q^{93} - 9670145 q^{94} + 38478411 q^{95} + 111942976 q^{96} - 28714467 q^{97} - 941192 q^{98} + 42173094 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 + 41 * q^3 - 1472 * q^4 + 526 * q^5 - 519 * q^6 + 8232 * q^7 + 474 * q^8 - 15427 * q^9 + 17800 * q^10 - 11735 * q^11 + 30484 * q^12 - 5622 * q^13 - 5488 * q^14 + 3465 * q^15 - 110364 * q^16 - 3506 * q^17 - 196096 * q^18 - 25291 * q^19 - 13351 * q^20 + 28126 * q^21 + 91579 * q^22 + 82970 * q^23 - 97143 * q^24 + 1263842 * q^25 - 51951 * q^26 - 1080760 * q^27 + 504896 * q^28 + 209315 * q^29 + 1063844 * q^30 + 948356 * q^31 - 495024 * q^32 - 143209 * q^33 + 436128 * q^34 + 90209 * q^35 - 469485 * q^36 - 377142 * q^37 - 198346 * q^38 + 647900 * q^39 - 4780340 * q^40 - 1895174 * q^41 + 178017 * q^42 - 1366459 * q^43 + 8096352 * q^44 - 2154733 * q^45 + 2854528 * q^46 + 2557720 * q^47 - 4102289 * q^48 - 2823576 * q^49 - 2378593 * q^50 - 4369338 * q^51 + 4270295 * q^52 - 4295420 * q^53 + 1447259 * q^54 - 560241 * q^55 + 81291 * q^56 + 15936670 * q^57 - 384326 * q^58 + 6714194 * q^59 + 5267974 * q^60 - 987536 * q^61 + 8520899 * q^62 + 5291461 * q^63 - 8211866 * q^64 - 11284709 * q^65 - 20326376 * q^66 - 1296682 * q^67 - 8400264 * q^68 - 1147530 * q^69 + 12210800 * q^70 - 7723282 * q^71 + 26270290 * q^72 + 15769600 * q^73 + 58033 * q^74 - 928389 * q^75 - 9095520 * q^76 - 8050210 * q^77 - 30641513 * q^78 - 24665908 * q^79 + 16716608 * q^80 - 5846292 * q^81 - 9977079 * q^82 + 32429868 * q^83 + 5228006 * q^84 + 17821519 * q^85 + 89024148 * q^86 - 16967309 * q^87 + 28910709 * q^88 - 27957029 * q^89 - 155228046 * q^90 - 5184102 * q^91 - 5073264 * q^92 + 11673603 * q^93 - 9670145 * q^94 + 38478411 * q^95 + 111942976 * q^96 - 28714467 * q^97 - 941192 * q^98 + 42173094 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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