LMFDB - Embedded newform 45.4.l.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,4,Mod(2,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("45.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	45.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.65508595026$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.1
Character	$\chi$	$=$	45.2
Dual form			45.4.l.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41347 - 5.27515i) q^{2} +(4.81992 - 1.94123i) q^{3} +(-18.9011 + 10.9125i) q^{4} +(-3.32298 - 10.6751i) q^{5} +(-17.0531 - 22.6819i) q^{6} +(-4.22008 + 1.13077i) q^{7} +(53.3880 + 53.3880i) q^{8} +(19.4633 - 18.7131i) q^{9} +O(q^{10})$	\(q+(-1.41347 - 5.27515i) q^{2} +(4.81992 - 1.94123i) q^{3} +(-18.9011 + 10.9125i) q^{4} +(-3.32298 - 10.6751i) q^{5} +(-17.0531 - 22.6819i) q^{6} +(-4.22008 + 1.13077i) q^{7} +(53.3880 + 53.3880i) q^{8} +(19.4633 - 18.7131i) q^{9} +(-51.6158 + 32.6182i) q^{10} +(-5.91593 - 3.41556i) q^{11} +(-69.9180 + 89.2889i) q^{12} +(24.4368 + 6.54783i) q^{13} +(11.9299 + 20.6632i) q^{14} +(-36.7393 - 45.0025i) q^{15} +(118.867 - 205.883i) q^{16} +(36.0612 - 36.0612i) q^{17} +(-126.225 - 76.2213i) q^{18} -59.8443i q^{19} +(179.300 + 165.509i) q^{20} +(-18.1454 + 13.6423i) q^{21} +(-9.65561 + 36.0352i) q^{22} +(13.6398 - 50.9044i) q^{23} +(360.964 + 153.688i) q^{24} +(-102.916 + 70.9463i) q^{25} -138.163i q^{26} +(57.4851 - 127.978i) q^{27} +(67.4245 - 67.4245i) q^{28} +(-22.1046 + 38.2863i) q^{29} +(-185.465 + 257.415i) q^{30} +(67.9692 + 117.726i) q^{31} +(-670.646 - 179.699i) q^{32} +(-35.1447 - 4.97859i) q^{33} +(-241.199 - 139.257i) q^{34} +(26.0943 + 41.2922i) q^{35} +(-163.669 + 566.092i) q^{36} +(233.330 + 233.330i) q^{37} +(-315.688 + 84.5883i) q^{38} +(130.494 - 15.8774i) q^{39} +(392.515 - 747.330i) q^{40} +(335.678 - 193.804i) q^{41} +(97.6133 + 76.4365i) q^{42} +(82.0769 + 306.315i) q^{43} +149.090 q^{44} +(-264.440 - 145.589i) q^{45} -287.808 q^{46} +(84.9338 + 316.977i) q^{47} +(173.263 - 1223.09i) q^{48} +(-280.516 + 161.956i) q^{49} +(519.720 + 442.615i) q^{50} +(103.809 - 243.815i) q^{51} +(-533.336 + 142.907i) q^{52} +(43.1181 + 43.1181i) q^{53} +(-756.358 - 122.349i) q^{54} +(-16.8030 + 74.5030i) q^{55} +(-285.671 - 164.932i) q^{56} +(-116.171 - 288.445i) q^{57} +(233.210 + 62.4884i) q^{58} +(-248.925 - 431.152i) q^{59} +(1185.50 + 449.677i) q^{60} +(36.3039 - 62.8801i) q^{61} +(524.950 - 524.950i) q^{62} +(-60.9764 + 100.979i) q^{63} +1889.88i q^{64} +(-11.3043 - 282.624i) q^{65} +(23.4132 + 192.431i) q^{66} +(-47.7525 + 178.215i) q^{67} +(-288.076 + 1075.11i) q^{68} +(-33.0742 - 271.833i) q^{69} +(180.939 - 196.017i) q^{70} +563.835i q^{71} +(2038.16 + 40.0503i) q^{72} +(84.7460 - 84.7460i) q^{73} +(901.044 - 1560.65i) q^{74} +(-358.322 + 541.738i) q^{75} +(653.054 + 1131.12i) q^{76} +(28.8279 + 7.72441i) q^{77} +(-268.206 - 665.935i) q^{78} +(-186.138 - 107.467i) q^{79} +(-2592.82 - 584.770i) q^{80} +(28.6389 - 728.437i) q^{81} +(-1496.82 - 1496.82i) q^{82} +(-930.125 + 249.226i) q^{83} +(194.095 - 455.867i) q^{84} +(-504.787 - 265.126i) q^{85} +(1499.84 - 865.935i) q^{86} +(-32.2201 + 227.447i) q^{87} +(-133.490 - 498.190i) q^{88} -288.322 q^{89} +(-394.226 + 1600.75i) q^{90} -110.529 q^{91} +(297.690 + 1110.99i) q^{92} +(556.139 + 435.487i) q^{93} +(1552.05 - 896.076i) q^{94} +(-638.844 + 198.861i) q^{95} +(-3581.30 + 435.740i) q^{96} +(1588.58 - 425.658i) q^{97} +(1250.84 + 1250.84i) q^{98} +(-179.059 + 44.2274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) $ 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.41347	−	5.27515i	−0.499738	−	1.86505i	−0.501689	−	0.865048i	$-0.667288\pi$
$2$	−1.41347	−	5.27515i	−0.499738	−	1.86505i	0.00195086	−	0.999998i	$-0.499379\pi$
$3$	4.81992	−	1.94123i	0.927594	−	0.373589i
$3$	4.81992	−	1.94123i	0.927594	−	0.373589i
$4$	−18.9011	+	10.9125i	−2.36264	+	1.36407i
$5$	−3.32298	−	10.6751i	−0.297216	−	0.954810i
$5$	−3.32298	−	10.6751i	−0.297216	−	0.954810i
$6$	−17.0531	−	22.6819i	−1.16031	−	1.54331i
$7$	−4.22008	+	1.13077i	−0.227863	+	0.0610556i	−0.370944	−	0.928655i	$-0.620966\pi$
$7$	−4.22008	+	1.13077i	−0.227863	+	0.0610556i	0.143081	+	0.989711i	$0.454299\pi$
$8$	53.3880	+	53.3880i	2.35944	+	2.35944i
$9$	19.4633	−	18.7131i	0.720862	−	0.693078i
$10$	−51.6158	+	32.6182i	−1.63224	+	1.03148i
$11$	−5.91593	−	3.41556i	−0.162156	−	0.0936210i	0.416726	−	0.909032i	$-0.363178\pi$
$11$	−5.91593	−	3.41556i	−0.162156	−	0.0936210i	−0.578882	+	0.815411i	$0.696511\pi$
$12$	−69.9180	+	89.2889i	−1.68197	+	2.14796i
$13$	24.4368	+	6.54783i	0.521351	+	0.139696i	0.509891	−	0.860239i	$-0.329686\pi$
$13$	24.4368	+	6.54783i	0.521351	+	0.139696i	0.0114594	+	0.999934i	$0.496352\pi$
$14$	11.9299	+	20.6632i	0.227743	+	0.394463i
$15$	−36.7393	−	45.0025i	−0.632403	−	0.774640i
$16$	118.867	−	205.883i	1.85729	−	3.21693i
$17$	36.0612	−	36.0612i	0.514477	−	0.514477i	−0.401418	−	0.915895i	$-0.631482\pi$
$17$	36.0612	−	36.0612i	0.514477	−	0.514477i	0.915895	+	0.401418i	$0.131482\pi$
$18$	−126.225	−	76.2213i	−1.65287	−	0.998085i
$19$		−	59.8443i		−	0.722591i	−0.932451	−	0.361296i	$-0.882335\pi$
$19$		−	59.8443i		−	0.722591i	0.932451	−	0.361296i	$-0.117665\pi$
$20$	179.300	+	165.509i	2.00464	+	1.85044i
$21$	−18.1454	+	13.6423i	−0.188554	+	0.141762i
$22$	−9.65561	+	36.0352i	−0.0935719	+	0.349215i
$23$	13.6398	−	50.9044i	0.123656	−	0.461491i	−0.876132	−	0.482071i	$-0.839885\pi$
$23$	13.6398	−	50.9044i	0.123656	−	0.461491i	0.999788	+	0.0205799i	$0.00655126\pi$
$24$	360.964	+	153.688i	3.07006	+	1.30714i
$25$	−102.916	+	70.9463i	−0.823325	+	0.567570i
$26$		−	138.163i		−	1.04215i
$27$	57.4851	−	127.978i	0.409741	−	0.912202i
$28$	67.4245	−	67.4245i	0.455073	−	0.455073i
$29$	−22.1046	+	38.2863i	−0.141542	+	0.245158i	−0.928077	−	0.372387i	$-0.878539\pi$
$29$	−22.1046	+	38.2863i	−0.141542	+	0.245158i	0.786535	+	0.617545i	$0.211873\pi$
$30$	−185.465	+	257.415i	−1.12870	+	1.56658i
$31$	67.9692	+	117.726i	0.393794	+	0.682072i	0.992946	−	0.118563i	$-0.0378289\pi$
$31$	67.9692	+	117.726i	0.393794	+	0.682072i	−0.599152	+	0.800635i	$0.704496\pi$
$32$	−670.646	−	179.699i	−3.70483	−	0.992706i
$33$	−35.1447	−	4.97859i	−0.185391	−	0.0262625i
$34$	−241.199	−	139.257i	−1.21663	−	0.702421i
$35$	26.0943	+	41.2922i	0.126021	+	0.199419i
$36$	−163.669	+	566.092i	−0.757729	+	2.62080i
$37$	233.330	+	233.330i	1.03674	+	1.03674i	0.999299	+	0.0374360i	$0.0119190\pi$
$37$	233.330	+	233.330i	1.03674	+	1.03674i	0.0374360	+	0.999299i	$0.488081\pi$
$38$	−315.688	+	84.5883i	−1.34767	+	0.361106i
$39$	130.494	−	15.8774i	0.535791	−	0.0651902i
$40$	392.515	−	747.330i	1.55155	−	2.95408i
$41$	335.678	−	193.804i	1.27864	−	0.738221i	0.302039	−	0.953295i	$-0.402333\pi$
$41$	335.678	−	193.804i	1.27864	−	0.738221i	0.976598	+	0.215074i	$0.0689993\pi$
$42$	97.6133	+	76.4365i	0.358620	+	0.280819i
$43$	82.0769	+	306.315i	0.291084	+	1.08634i	0.944278	+	0.329149i	$0.106762\pi$
$43$	82.0769	+	306.315i	0.291084	+	1.08634i	−0.653194	+	0.757191i	$0.726571\pi$
$44$	149.090			0.510822
$45$	−264.440	−	145.589i	−0.876010	−	0.482293i
$46$	−287.808			−0.922499
$47$	84.9338	+	316.977i	0.263593	+	0.983742i	0.963106	+	0.269122i	$0.0867335\pi$
$47$	84.9338	+	316.977i	0.263593	+	0.983742i	−0.699513	+	0.714620i	$0.746600\pi$
$48$	173.263	−	1223.09i	0.521007	−	3.67787i
$49$	−280.516	+	161.956i	−0.817832	+	0.472175i
$50$	519.720	+	442.615i	1.46999	+	1.25190i
$51$	103.809	−	243.815i	0.285023	−	0.669430i
$52$	−533.336	+	142.907i	−1.42232	+	0.381108i
$53$	43.1181	+	43.1181i	0.111749	+	0.111749i	0.760770	−	0.649021i	$-0.224821\pi$
$53$	43.1181	+	43.1181i	0.111749	+	0.111749i	−0.649021	+	0.760770i	$0.724821\pi$
$54$	−756.358	−	122.349i	−1.90606	−	0.308325i
$55$	−16.8030	+	74.5030i	−0.0411948	+	0.182654i
$56$	−285.671	−	164.932i	−0.681685	−	0.393571i
$57$	−116.171	−	288.445i	−0.269952	−	0.670271i
$58$	233.210	+	62.4884i	0.527965	+	0.141468i
$59$	−248.925	−	431.152i	−0.549277	−	0.951376i	−0.998324	−	0.0578676i	$-0.981570\pi$
$59$	−248.925	−	431.152i	−0.549277	−	0.951376i	0.449047	−	0.893508i	$-0.351763\pi$
$60$	1185.50	+	449.677i	2.55080	+	0.967551i
$61$	36.3039	−	62.8801i	0.0762006	−	0.131983i	−0.825407	−	0.564538i	$-0.809054\pi$
$61$	36.3039	−	62.8801i	0.0762006	−	0.131983i	0.901608	+	0.432555i	$0.142388\pi$
$62$	524.950	−	524.950i	1.07530	−	1.07530i
$63$	−60.9764	+	100.979i	−0.121941	+	0.201939i
$64$			1889.88i			3.69118i
$65$	−11.3043	−	282.624i	−0.0215712	−	0.539311i
$66$	23.4132	+	192.431i	0.0436662	+	0.358887i
$67$	−47.7525	+	178.215i	−0.0870730	+	0.324961i	−0.995699	−	0.0926506i	$-0.970466\pi$
$67$	−47.7525	+	178.215i	−0.0870730	+	0.324961i	0.908626	+	0.417612i	$0.137133\pi$
$68$	−288.076	+	1075.11i	−0.513740	+	1.91730i
$69$	−33.0742	−	271.833i	−0.0577053	−	0.474273i
$70$	180.939	−	196.017i	0.308948	−	0.334692i
$71$			563.835i			0.942464i	0.882009	+	0.471232i	$0.156191\pi$
$71$			563.835i			0.942464i	−0.882009	+	0.471232i	$0.843809\pi$
$72$	2038.16	+	40.0503i	3.33611	+	0.0655552i
$73$	84.7460	−	84.7460i	0.135874	−	0.135874i	−0.635899	−	0.771772i	$-0.719370\pi$
$73$	84.7460	−	84.7460i	0.135874	−	0.135874i	0.771772	+	0.635899i	$0.219370\pi$
$74$	901.044	−	1560.65i	1.41546	−	2.45165i
$75$	−358.322	+	541.738i	−0.551674	+	0.834060i
$76$	653.054	+	1131.12i	0.985663	+	1.70722i
$77$	28.8279	+	7.72441i	0.0426655	+	0.0114322i
$78$	−268.206	−	665.935i	−0.389338	−	0.966697i
$79$	−186.138	−	107.467i	−0.265091	−	0.153050i	0.361564	−	0.932347i	$-0.382243\pi$
$79$	−186.138	−	107.467i	−0.265091	−	0.153050i	−0.626655	+	0.779297i	$0.715576\pi$
$80$	−2592.82	−	584.770i	−3.62357	−	0.817240i
$81$	28.6389	−	728.437i	0.0392852	−	0.999228i
$82$	−1496.82	−	1496.82i	−2.01580	−	2.01580i
$83$	−930.125	+	249.226i	−1.23005	+	0.329592i	−0.814601	−	0.580022i	$-0.803044\pi$
$83$	−930.125	+	249.226i	−1.23005	+	0.329592i	−0.415454	+	0.909614i	$0.636377\pi$
$84$	194.095	−	455.867i	0.252113	−	0.592133i
$85$	−504.787	−	265.126i	−0.644139	−	0.338317i
$86$	1499.84	−	865.935i	1.88061	−	1.08577i
$87$	−32.2201	+	227.447i	−0.0397052	+	0.280286i
$88$	−133.490	−	498.190i	−0.161705	−	0.603491i
$89$	−288.322			−0.343394			−0.171697	−	0.985150i	$-0.554925\pi$
$89$	−288.322			−0.343394			−0.171697	+	0.985150i	$0.554925\pi$
$90$	−394.226	+	1600.75i	−0.461723	+	1.87482i
$91$	−110.529			−0.127326
$92$	297.690	+	1110.99i	0.337351	+	1.25901i
$93$	556.139	+	435.487i	0.620096	+	0.485569i
$94$	1552.05	−	896.076i	1.70300	−	0.983226i
$95$	−638.844	+	198.861i	−0.689937	+	0.214766i
$96$	−3581.30	+	435.740i	−3.80744	+	0.463255i
$97$	1588.58	−	425.658i	1.66284	−	0.445556i	0.699673	−	0.714463i	$-0.253329\pi$
$97$	1588.58	−	425.658i	1.66284	−	0.445556i	0.963166	+	0.268907i	$0.0866623\pi$
$98$	1250.84	+	1250.84i	1.28933	+	1.28933i
$99$	−179.059	+	44.2274i	−0.181779	+	0.0448992i
$100$	1171.01	−	2464.03i	1.17101	−	2.46403i
$101$	−1256.46	−	725.417i	−1.23785	−	0.714670i	−0.269192	−	0.963087i	$-0.586757\pi$
$101$	−1256.46	−	725.417i	−1.23785	−	0.714670i	−0.968653	+	0.248416i	$0.920090\pi$
$102$	−1432.89	−	202.983i	−1.39095	−	0.197042i
$103$	315.242	+	84.4689i	0.301570	+	0.0808055i	0.406431	−	0.913681i	$-0.366773\pi$
$103$	315.242	+	84.4689i	0.301570	+	0.0808055i	−0.104861	+	0.994487i	$0.533440\pi$
$104$	955.059	+	1654.21i	0.900492	+	1.55970i
$105$	205.930	+	148.371i	0.191397	+	0.137900i
$106$	166.508	−	288.400i	0.152573	−	0.264263i
$107$	−1233.98	+	1233.98i	−1.11489	+	1.11489i	−0.122409	+	0.992480i	$0.539062\pi$
$107$	−1233.98	+	1233.98i	−1.11489	+	1.11489i	−0.992480	+	0.122409i	$0.960938\pi$
$108$	310.038	+	3046.24i	0.276236	+	2.71411i
$109$			577.196i			0.507205i	0.967308	+	0.253603i	$0.0816156\pi$
$109$			577.196i			0.507205i	−0.967308	+	0.253603i	$0.918384\pi$
$110$	416.765	−	16.6697i	0.361245	−	0.0144490i
$111$	1577.58	+	671.686i	1.34898	+	0.574357i
$112$	−268.821	+	1003.25i	−0.226797	+	0.846417i
$113$	491.221	−	1833.26i	0.408940	−	1.52618i	−0.387732	−	0.921772i	$-0.626741\pi$
$113$	491.221	−	1833.26i	0.408940	−	1.52618i	0.796672	−	0.604412i	$-0.206592\pi$
$114$	−1357.38	+	1020.53i	−1.11518	+	0.838433i
$115$	−588.734	+	23.5481i	−0.477389	+	0.0190945i
$116$		−	964.869i		−	0.772292i
$117$	598.152	−	329.847i	0.472642	−	0.260636i
$118$	−1922.54	+	1922.54i	−1.49987	+	1.49987i
$119$	−111.404	+	192.958i	−0.0858185	+	0.148642i
$120$	441.157	−	4364.03i	0.335599	−	3.31983i
$121$	−642.168	−	1112.27i	−0.482470	−	0.835663i
$122$	−383.017	−	102.629i	−0.284235	−	0.0761606i
$123$	1241.73	−	1585.75i	0.910265	−	1.16245i
$124$	−2569.38	−	1483.43i	−1.86078	−	1.07432i
$125$	1099.35	+	862.882i	0.786627	+	0.617428i
$126$	618.869	+	178.928i	0.437565	+	0.126510i
$127$	1405.14	+	1405.14i	0.981780	+	0.981780i	0.999837	−	0.0180574i	$-0.00574816\pi$
$127$	1405.14	+	1405.14i	0.981780	+	0.981780i	−0.0180574	+	0.999837i	$0.505748\pi$
$128$	4604.25	−	1233.71i	3.17939	−	0.851916i
$129$	990.231	+	1317.09i	0.675853	+	0.898937i
$130$	−1474.91	+	459.113i	−0.995060	+	0.309745i
$131$	−1336.30	+	771.513i	−0.891244	+	0.514560i	−0.874349	−	0.485297i	$-0.838711\pi$
$131$	−1336.30	+	771.513i	−0.891244	+	0.514560i	−0.0168950	+	0.999857i	$0.505378\pi$
$132$	718.602	−	289.417i	0.473835	−	0.190837i
$133$	67.6700	+	252.548i	0.0441183	+	0.164652i
$134$	1007.61			0.649581
$135$	−1557.20	−	188.390i	−0.992761	−	0.120104i
$136$	3850.47			2.42776
$137$	32.0003	+	119.427i	0.0199560	+	0.0744767i	0.975186	−	0.221388i	$-0.0710588\pi$
$137$	32.0003	+	119.427i	0.0199560	+	0.0744767i	−0.955230	+	0.295865i	$0.904392\pi$
$138$	−1387.21	+	558.700i	−0.855704	+	0.344635i
$139$	308.354	−	178.028i	0.188160	−	0.108634i	−0.402961	−	0.915217i	$-0.632019\pi$
$139$	308.354	−	178.028i	0.188160	−	0.108634i	0.591121	+	0.806583i	$0.298686\pi$
$140$	−943.814	−	495.713i	−0.569763	−	0.299253i
$141$	1024.70	+	1362.93i	0.612022	+	0.814038i
$142$	2974.32	−	796.965i	1.75774	−	0.470985i
$143$	−122.202	−	122.202i	−0.0714619	−	0.0714619i
$144$	−1539.18	−	6231.54i	−0.890729	−	3.60621i
$145$	482.163	+	108.744i	0.276148	+	0.0622808i
$146$	−566.834	−	327.262i	−0.321312	−	0.185509i
$147$	−1037.67	+	1325.16i	−0.582217	+	0.743520i
$148$	−6956.41	−	1863.96i	−3.86360	−	1.03525i
$149$	601.701	+	1042.18i	0.330827	+	0.573009i	0.982674	−	0.185341i	$-0.0593390\pi$
$149$	601.701	+	1042.18i	0.330827	+	0.573009i	−0.651847	+	0.758350i	$0.726006\pi$
$150$	3364.23	+	1124.47i	1.83125	+	0.612085i
$151$	−820.064	+	1420.39i	−0.441959	+	0.765496i	−0.997835	−	0.0657697i	$-0.979050\pi$
$151$	−820.064	+	1420.39i	−0.441959	+	0.765496i	0.555876	+	0.831265i	$0.312383\pi$
$152$	3194.97	−	3194.97i	1.70491	−	1.70491i
$153$	27.0521	−	1376.69i	0.0142944	−	0.727441i
$154$		−	162.990i		−	0.0852862i
$155$	1030.88	−	1116.78i	0.534207	−	0.578722i
$156$	−2293.22	+	1724.13i	−1.17695	+	0.884876i
$157$	907.102	−	3385.35i	0.461112	−	1.72089i	−0.208355	−	0.978053i	$-0.566811\pi$
$157$	907.102	−	3385.35i	0.461112	−	1.72089i	0.669467	−	0.742842i	$-0.266522\pi$
$158$	−303.803	+	1133.81i	−0.152970	+	0.570892i
$159$	291.528	+	124.124i	0.145407	+	0.0619098i
$160$	310.237	+	7756.35i	0.153290	+	3.83246i
$161$			230.244i			0.112707i
$162$	−3883.09	+	878.551i	−1.88324	+	0.426083i
$163$	1206.55	−	1206.55i	0.579781	−	0.579781i	−0.355062	−	0.934843i	$-0.615540\pi$
$163$	1206.55	−	1206.55i	0.579781	−	0.579781i	0.934843	+	0.355062i	$0.115540\pi$
$164$	−4229.79	+	7326.20i	−2.01397	+	3.48830i
$165$	63.6381	+	391.717i	0.0300256	+	0.184819i
$166$	2629.41	+	4554.27i	1.22941	+	2.12940i
$167$	329.658	+	88.3316i	0.152753	+	0.0409299i	0.334385	−	0.942437i	$-0.391471\pi$
$167$	329.658	+	88.3316i	0.152753	+	0.0409299i	−0.181632	+	0.983367i	$0.558138\pi$
$168$	−1697.08	−	240.408i	−0.779361	−	0.110404i
$169$	−1348.37	−	778.483i	−0.613734	−	0.354339i
$170$	−685.077	+	3037.57i	−0.309077	+	1.37042i
$171$	−1119.87	−	1164.77i	−0.500812	−	0.520889i
$172$	−4894.02	−	4894.02i	−2.16957	−	2.16957i
$173$	716.558	−	192.001i	0.314907	−	0.0843790i	−0.0979039	−	0.995196i	$-0.531214\pi$
$173$	716.558	−	192.001i	0.314907	−	0.0843790i	0.412811	+	0.910817i	$0.364547\pi$
$174$	1245.36	−	151.524i	0.542588	−	0.0660172i
$175$	354.088	−	415.772i	0.152952	−	0.179597i
$176$	−1406.42	+	811.995i	−0.602344	+	0.347764i
$177$	−2036.76	−	1594.90i	−0.864930	−	0.677287i
$178$	407.535	+	1520.94i	0.171607	+	0.640445i
$179$	2527.65			1.05545			0.527725	−	0.849416i	$-0.323045\pi$
$179$	2527.65			1.05545			0.527725	+	0.849416i	$0.323045\pi$
$180$	6586.96	−	133.923i	2.72757	−	0.0554559i
$181$	−2223.82			−0.913232			−0.456616	−	0.889664i	$-0.650939\pi$
$181$	−2223.82			−0.913232			−0.456616	+	0.889664i	$0.650939\pi$
$182$	156.230	+	583.059i	0.0636294	+	0.237468i
$183$	52.9172	−	373.551i	0.0213757	−	0.150895i
$184$	3445.89	−	1989.48i	1.38062	−	0.797101i
$185$	1715.47	−	3266.17i	0.681751	−	1.29802i
$186$	1511.17	−	3549.26i	0.595723	−	1.39916i
$187$	−336.505	+	90.1661i	−0.131592	+	0.0352599i
$188$	−5064.37	−	5064.37i	−1.96466	−	1.96466i
$189$	−97.8781	+	605.081i	−0.0376698	+	0.232874i
$190$	1952.01	+	3088.91i	0.745336	+	1.17944i
$191$	−2292.92	−	1323.82i	−0.868639	−	0.501509i	−0.00174321	−	0.999998i	$-0.500555\pi$
$191$	−2292.92	−	1323.82i	−0.868639	−	0.501509i	−0.866896	+	0.498490i	$0.833888\pi$
$192$	3668.69	+	9109.09i	1.37898	+	3.42392i
$193$	992.559	+	265.955i	0.370186	+	0.0991911i	0.439116	−	0.898430i	$-0.355292\pi$
$193$	992.559	+	265.955i	0.370186	+	0.0991911i	−0.0689296	+	0.997622i	$0.521958\pi$
$194$	−4490.81	−	7778.32i	−1.66197	−	2.87861i
$195$	−603.123	−	1340.28i	−0.221490	−	0.492203i
$196$	3534.71	−	6122.29i	1.28816	−	2.23116i
$197$	−1735.07	+	1735.07i	−0.627507	+	0.627507i	−0.947440	−	0.319933i	$-0.896340\pi$
$197$	−1735.07	+	1735.07i	−0.627507	+	0.627507i	0.319933	+	0.947440i	$0.396340\pi$
$198$	486.401	+	882.050i	0.174581	+	0.316589i
$199$		−	764.080i		−	0.272182i	−0.990696	−	0.136091i	$-0.956546\pi$
$199$		−	764.080i		−	0.272182i	0.990696	−	0.136091i	$-0.0434539\pi$
$200$	−9282.14	−	1706.78i	−3.28173	−	0.603438i
$201$	115.792	+	951.679i	0.0406334	+	0.333961i
$202$	−2050.71	+	7653.36i	−0.714295	+	2.66579i
$203$	49.9902	−	186.566i	0.0172839	−	0.0645043i
$204$	698.536	+	5741.19i	0.239742	+	1.97041i
$205$	−3184.33	−	2939.39i	−1.08489	−	1.00144i
$206$		−	1782.34i		−	0.602824i
$207$	−687.105	−	1246.01i	−0.230710	−	0.418375i
$208$	4252.82	−	4252.82i	1.41769	−	1.41769i
$209$	−204.402	+	354.035i	−0.0676497	+	0.117173i
$210$	491.600	−	1296.03i	0.161541	−	0.425878i
$211$	1529.60	+	2649.34i	0.499061	+	0.864398i	0.999999	−	0.00108439i	$-0.000345174\pi$
$211$	1529.60	+	2649.34i	0.499061	+	0.864398i	−0.500939	+	0.865483i	$0.667012\pi$
$212$	−1285.51	−	344.450i	−0.416457	−	0.111589i
$213$	1094.53	+	2717.64i	0.352094	+	0.874224i
$214$	8253.61	+	4765.22i	2.63647	+	1.52217i
$215$	2997.21	−	1894.06i	0.950734	−	0.600808i
$216$	9901.53	−	3763.49i	3.11904	−	1.18552i
$217$	−419.956	−	419.956i	−0.131375	−	0.131375i
$218$	3044.80	−	815.851i	0.945962	−	0.253470i
$219$	243.958	−	572.980i	0.0752747	−	0.176796i
$220$	−495.423	−	1591.55i	−0.151825	−	0.487738i
$221$	1117.34	−	645.099i	0.340093	−	0.196353i
$222$	1313.38	−	9271.36i	0.397064	−	2.80294i
$223$	1124.39	+	4196.27i	0.337644	+	1.26010i	0.900975	+	0.433872i	$0.142853\pi$
$223$	1124.39	+	4196.27i	0.337644	+	1.26010i	−0.563331	+	0.826231i	$0.690480\pi$
$224$	3033.37			0.904803
$225$	−675.450	+	3306.72i	−0.200133	+	0.979769i
$226$	−10365.1			−3.05077
$227$	694.451	+	2591.73i	0.203050	+	0.757793i	0.990035	+	0.140821i	$0.0449742\pi$
$227$	694.451	+	2591.73i	0.203050	+	0.757793i	−0.786985	+	0.616972i	$0.788359\pi$
$228$	5343.43	+	4184.20i	1.55209	+	1.21537i
$229$	−4176.87	+	2411.52i	−1.20531	+	0.695884i	−0.961731	−	0.273997i	$-0.911654\pi$
$229$	−4176.87	+	2411.52i	−1.20531	+	0.695884i	−0.243577	+	0.969882i	$0.578321\pi$
$230$	956.379	+	3072.38i	0.274182	+	0.880811i
$231$	153.943	−	18.7304i	0.0438472	−	0.00533493i
$232$	−3224.15	+	863.908i	−0.912395	+	0.244475i
$233$	−1004.66	−	1004.66i	−0.282479	−	0.282479i	0.551618	−	0.834097i	$-0.314011\pi$
$233$	−1004.66	−	1004.66i	−0.282479	−	0.282479i	−0.834097	+	0.551618i	$0.814011\pi$
$234$	−2585.46	−	2689.11i	−0.722295	−	0.751250i
$235$	3101.53	−	1959.98i	0.860943	−	0.544065i
$236$	9409.92	+	5432.82i	2.59548	+	1.49850i
$237$	−1105.79	−	156.646i	−0.303075	−	0.0429335i
$238$	1175.35	+	314.933i	0.320111	+	0.0857735i
$239$	3310.25	+	5733.51i	0.895908	+	1.55176i	0.832677	+	0.553759i	$0.186807\pi$
$239$	3310.25	+	5733.51i	0.895908	+	1.55176i	0.0632311	+	0.997999i	$0.479859\pi$
$240$	−13632.4	+	2214.70i	−3.66652	+	0.595660i
$241$	−1226.12	+	2123.69i	−0.327722	+	0.567631i	−0.982059	−	0.188571i	$-0.939614\pi$
$241$	−1226.12	+	2123.69i	−0.327722	+	0.567631i	0.654337	+	0.756203i	$0.272948\pi$
$242$	−4959.69	+	4959.69i	−1.31744	+	1.31744i
$243$	−1276.02	−	3566.60i	−0.336860	−	0.941555i
$244$			1584.67i			0.415771i
$245$	2661.05	+	2456.36i	0.693911	+	0.640536i
$246$	−10120.2	−	4308.88i	−2.62293	−	1.11676i
$247$	391.851	−	1462.41i	0.100943	−	0.376723i
$248$	−2656.42	+	9913.90i	−0.680173	+	2.53844i
$249$	−3999.33	+	3006.83i	−1.01786	+	0.765262i
$250$	2997.94	−	7018.87i	0.758424	−	1.77565i
$251$		−	6563.11i		−	1.65044i	−0.564814	−	0.825219i	$-0.691052\pi$
$251$		−	6563.11i		−	1.65044i	0.564814	−	0.825219i	$-0.308948\pi$
$252$	50.5801	−	2574.02i	0.0126438	−	0.643446i
$253$	−254.559	+	254.559i	−0.0632569	+	0.0632569i
$254$	5426.20	−	9398.45i	1.34043	−	2.32170i
$255$	−2947.70	−	297.981i	−0.723892	−	0.0731777i
$256$	−5456.43	−	9450.81i	−1.33214	−	2.30733i
$257$	3014.35	+	807.694i	0.731635	+	0.196041i	0.605357	−	0.795954i	$-0.293030\pi$
$257$	3014.35	+	807.694i	0.731635	+	0.196041i	0.126278	+	0.991995i	$0.459697\pi$
$258$	5548.16	−	7085.28i	1.33881	−	1.70973i
$259$	−1248.51	−	720.829i	−0.299532	−	0.172935i
$260$	3297.81	+	5218.54i	0.786622	+	1.24477i
$261$	286.227	+	1158.82i	0.0678813	+	0.274825i
$262$	5958.66	+	5958.66i	1.40507	+	1.40507i
$263$	−4536.33	+	1215.51i	−1.06358	+	0.284986i	−0.747854	−	0.663863i	$-0.768916\pi$
$263$	−4536.33	+	1215.51i	−1.06358	+	0.284986i	−0.315729	+	0.948849i	$0.602249\pi$
$264$	−1610.51	−	2142.10i	−0.375454	−	0.499384i
$265$	317.009	−	603.570i	0.0734858	−	0.139913i
$266$	1236.58	−	713.938i	0.285035	−	0.164565i
$267$	−1389.69	+	559.698i	−0.318530	+	0.128288i
$268$	−1042.20	−	3889.55i	−0.237547	−	0.886538i
$269$	4107.03			0.930893			0.465446	−	0.885076i	$-0.345894\pi$
$269$	4107.03			0.930893			0.465446	+	0.885076i	$0.345894\pi$
$270$	1207.28	+	8480.77i	0.272121	+	1.91157i
$271$	−358.244			−0.0803017			−0.0401508	−	0.999194i	$-0.512784\pi$
$271$	−358.244			−0.0803017			−0.0401508	+	0.999194i	$0.512784\pi$
$272$	−3137.92	−	11710.9i	−0.699501	−	2.61057i
$273$	−532.743	+	214.563i	−0.118107	+	0.0475675i
$274$	584.762	−	337.612i	0.128930	−	0.0744376i
$275$	851.163	−	68.1984i	0.186644	−	0.0149546i
$276$	3591.53	+	4777.02i	0.783278	+	1.04182i
$277$	−1618.41	+	433.653i	−0.351051	+	0.0940637i	−0.430035	−	0.902812i	$-0.641499\pi$
$277$	−1618.41	+	433.653i	−0.351051	+	0.0940637i	0.0789846	+	0.996876i	$0.474832\pi$
$278$	−1374.97	−	1374.97i	−0.296638	−	0.296638i
$279$	3525.92	+	1019.42i	0.756601	+	0.218750i
$280$	−811.390	+	3597.63i	−0.173178	+	0.767856i
$281$	3329.19	+	1922.11i	0.706771	+	0.408054i	0.809864	−	0.586617i	$-0.199541\pi$
$281$	3329.19	+	1922.11i	0.706771	+	0.408054i	−0.103094	+	0.994672i	$0.532874\pi$
$282$	5741.27	−	7331.90i	1.21237	−	1.54826i
$283$	−1096.06	−	293.688i	−0.230226	−	0.0616888i	0.141862	−	0.989886i	$-0.454691\pi$
$283$	−1096.06	−	293.688i	−0.230226	−	0.0616888i	−0.372087	+	0.928198i	$0.621358\pi$
$284$	−6152.88	−	10657.1i	−1.28559	−	2.22670i
$285$	−2693.14	+	2198.64i	−0.559748	+	0.456969i
$286$	−471.905	+	817.363i	−0.0975676	+	0.168992i
$287$	−1197.44	+	1197.44i	−0.246281	+	0.246281i
$288$	−16415.7	+	9052.33i	−3.35869	+	1.85213i
$289$			2312.18i			0.470626i
$290$	−107.881	−	2697.19i	−0.0218449	−	0.546153i
$291$	6830.51	−	5135.42i	1.37599	−	1.03451i
$292$	−676.997	+	2526.59i	−0.135679	+	0.506360i
$293$	116.545	−	434.952i	0.0232377	−	0.0867241i	−0.953333	−	0.301920i	$-0.902372\pi$
$293$	116.545	−	434.952i	0.0232377	−	0.0867241i	0.976571	+	0.215196i	$0.0690391\pi$
$294$	8457.14	+	3600.80i	1.67766	+	0.714296i
$295$	−3775.41	+	4090.01i	−0.745129	+	0.807220i
$296$			24914.0i			4.89223i
$297$	−777.196	+	560.767i	−0.151843	+	0.109559i
$298$	4647.15	−	4647.15i	0.903362	−	0.903362i
$299$	666.627	−	1154.63i	0.128937	−	0.223325i
$300$	860.942	−	14149.6i	0.165688	−	2.72310i
$301$	−692.742	−	1199.86i	−0.132654	−	0.229764i
$302$	8651.91	+	2318.27i	1.64855	+	0.441727i
$303$	−7464.23	−	1057.38i	−1.41521	−	0.200479i
$304$	−12321.0	−	7113.51i	−2.32452	−	1.34206i
$305$	−791.889	−	178.598i	−0.148667	−	0.0335295i
$306$	−7300.46	+	1803.20i	−1.36385	+	0.336870i
$307$	1217.81	+	1217.81i	0.226398	+	0.226398i	0.811186	−	0.584788i	$-0.198822\pi$
$307$	1217.81	+	1217.81i	0.226398	+	0.226398i	−0.584788	+	0.811186i	$0.698822\pi$
$308$	−629.171	+	168.586i	−0.116397	+	0.0311886i
$309$	1683.42	−	204.823i	0.309923	−	0.0377086i
$310$	−7348.29	−	3859.50i	−1.34631	−	0.707112i
$311$	−4660.61	+	2690.81i	−0.849772	+	0.490616i	−0.860574	−	0.509326i	$-0.829895\pi$
$311$	−4660.61	+	2690.81i	−0.849772	+	0.490616i	0.0108020	+	0.999942i	$0.496562\pi$
$312$	7814.50	+	6119.18i	1.41798	+	1.11035i
$313$	1248.92	+	4661.02i	0.225537	+	0.841714i	0.982189	+	0.187896i	$0.0601669\pi$
$313$	1248.92	+	4661.02i	0.225537	+	0.841714i	−0.756652	+	0.653817i	$0.773166\pi$
$314$	−19140.4			−3.43998
$315$	1280.59	+	315.378i	0.229057	+	0.0564112i
$316$	4690.95			0.835084
$317$	−997.303	−	3721.99i	−0.176701	−	0.659456i	−0.996256	−	0.0864556i	$-0.972446\pi$
$317$	−997.303	−	3721.99i	−0.176701	−	0.659456i	0.819555	−	0.573001i	$-0.194221\pi$
$318$	242.705	−	1713.30i	0.0427995	−	0.302129i
$319$	261.538	−	150.999i	0.0459039	−	0.0265026i
$320$	20174.7	−	6280.05i	3.52438	−	1.09708i
$321$	−3552.25	+	8343.11i	−0.617654	+	1.45068i
$322$	1214.57	−	325.443i	0.210203	−	0.0563238i
$323$	−2158.06	−	2158.06i	−0.371757	−	0.371757i
$324$	7407.80	+	14080.8i	1.27020	+	2.41440i
$325$	−2979.48	+	1059.83i	−0.508528	+	0.180888i
$326$	−8070.15	−	4659.30i	−1.37106	−	0.791579i
$327$	1120.47	+	2782.04i	0.189486	+	0.470481i
$328$	28268.0	+	7574.39i	4.75865	+	1.27508i
$329$	−716.854	−	1241.63i	−0.120126	−	0.208064i
$330$	1976.41	−	889.381i	0.329691	−	0.148360i
$331$	2384.56	−	4130.18i	0.395974	−	0.685847i	−0.597251	−	0.802054i	$-0.703740\pi$
$331$	2384.56	−	4130.18i	0.395974	−	0.685847i	0.993225	+	0.116207i	$0.0370737\pi$
$332$	14860.7	−	14860.7i	2.45658	−	2.45658i
$333$	8907.69	+	175.038i	1.46588	+	0.0288049i
$334$		−	1863.85i		−	0.305345i
$335$	2061.14	−	82.4410i	0.336156	−	0.0134455i
$336$	651.846	+	5357.45i	0.105837	+	0.869860i
$337$	2610.76	−	9743.49i	0.422009	−	1.57496i	−0.348359	−	0.937361i	$-0.613261\pi$
$337$	2610.76	−	9743.49i	0.422009	−	1.57496i	0.770368	−	0.637599i	$-0.220072\pi$
$338$	−2200.73	+	8213.23i	−0.354153	+	1.32172i
$339$	−1191.13	−	9789.75i	−0.190835	−	1.56846i
$340$	12434.2	−	497.341i	1.98335	−	0.0793298i
$341$		−	928.612i		−	0.147470i
$342$	−4561.41	+	7553.86i	−0.721207	+	1.19435i
$343$	2060.30	−	2060.30i	0.324332	−	0.324332i
$344$	−11971.6	+	20735.5i	−1.87636	+	3.24995i
$345$	−2791.94	+	1256.37i	−0.435690	+	0.196059i
$346$	−2025.67	−	3508.56i	−0.314742	−	0.545148i
$347$	−9703.39	−	2600.02i	−1.50117	−	0.402237i	−0.587677	−	0.809095i	$-0.699958\pi$
$347$	−9703.39	−	2600.02i	−1.50117	−	0.402237i	−0.913491	+	0.406858i	$0.866624\pi$
$348$	−1873.03	−	4650.59i	−0.288520	−	0.716373i
$349$	−5945.55	−	3432.67i	−0.911914	−	0.526494i	−0.0308677	−	0.999523i	$-0.509827\pi$
$349$	−5945.55	−	3432.67i	−0.911914	−	0.526494i	−0.881047	+	0.473030i	$0.843160\pi$
$350$	−2693.75	−	1280.19i	−0.411392	−	0.195511i
$351$	2242.74	−	2750.98i	0.341050	−	0.418338i
$352$	3353.72	+	3353.72i	0.507823	+	0.507823i
$353$	8645.22	−	2316.48i	1.30351	−	0.349274i	0.460733	−	0.887539i	$-0.347587\pi$
$353$	8645.22	−	2316.48i	1.30351	−	0.349274i	0.842776	+	0.538265i	$0.180920\pi$
$354$	−5534.41	+	12998.6i	−0.830933	+	1.95160i
$355$	6019.00	−	1873.61i	0.899874	−	0.280116i
$356$	5449.59	−	3146.32i	0.811314	−	0.468412i
$357$	−162.385	+	1146.30i	−0.0240737	+	0.169940i
$358$	−3572.76	−	13333.7i	−0.527448	−	1.96846i
$359$	−2589.44			−0.380684			−0.190342	−	0.981718i	$-0.560960\pi$
$359$	−2589.44			−0.380684			−0.190342	+	0.981718i	$0.560960\pi$
$360$	−6345.23	−	21890.7i	−0.928952	−	3.20483i
$361$	3277.66			0.477862
$362$	3143.30	+	11731.0i	0.456376	+	1.70322i
$363$	−5254.36	−	4114.45i	−0.759731	−	0.594911i
$364$	2089.13	−	1206.16i	0.300824	−	0.173681i
$365$	−1186.28	−	623.063i	−0.170117	−	0.0893496i
$366$	−2045.34	+	248.858i	−0.292108	+	0.0355410i
$367$	7645.28	−	2048.55i	1.08741	−	0.291371i	0.329783	−	0.944057i	$-0.393024\pi$
$367$	7645.28	−	2048.55i	1.08741	−	0.291371i	0.757629	+	0.652686i	$0.226358\pi$
$368$	−8859.06	−	8859.06i	−1.25492	−	1.25492i
$369$	2906.73	−	10053.6i	0.410076	−	1.41835i
$370$	−19654.3	−	4432.72i	−2.76156	−	0.622827i
$371$	−230.718	−	133.205i	−0.0322865	−	0.0186406i
$372$	−15263.9	−	2162.28i	−2.12741	−	0.301369i
$373$	−5841.25	−	1565.16i	−0.810854	−	0.217268i	−0.170510	−	0.985356i	$-0.554542\pi$
$373$	−5841.25	−	1565.16i	−0.810854	−	0.217268i	−0.640344	+	0.768088i	$0.721208\pi$
$374$	951.279	+	1647.66i	0.131523	+	0.227804i
$375$	6973.81	+	2024.95i	0.960335	+	0.278847i
$376$	−12388.3	+	21457.2i	−1.69915	+	2.94301i
$377$	−790.858	+	790.858i	−0.108040	+	0.108040i
$378$	3330.24	−	338.943i	0.453146	−	0.0461200i
$379$		−	13501.8i		−	1.82992i	−0.403542	−	0.914961i	$-0.632221\pi$
$379$		−	13501.8i		−	1.82992i	0.403542	−	0.914961i	$-0.367779\pi$
$380$	9904.76	−	10730.1i	1.33711	−	1.44853i
$381$	9500.36	+	4044.97i	1.27748	+	0.543911i
$382$	−3742.36	+	13966.7i	−0.501246	+	1.87067i
$383$	−2499.74	+	9329.14i	−0.333500	+	1.24464i	0.571986	+	0.820263i	$0.306173\pi$
$383$	−2499.74	+	9329.14i	−0.333500	+	1.24464i	−0.905486	+	0.424376i	$0.860494\pi$
$384$	19797.2	−	14884.3i	2.63092	−	1.97802i
$385$	−13.3356	−	333.409i	−0.00176531	−	0.0441353i
$386$		−	5611.82i		−	0.739984i
$387$	7329.59	+	4425.98i	0.962750	+	0.581358i
$388$	−25380.8	+	25380.8i	−3.32091	+	3.32091i
$389$	2925.52	−	5067.16i	0.381311	−	0.660450i	−0.609939	−	0.792448i	$-0.708806\pi$
$389$	2925.52	−	5067.16i	0.381311	−	0.660450i	0.991250	+	0.131998i	$0.0421394\pi$
$390$	−6217.69	+	5076.01i	−0.807294	+	0.659061i
$391$	−1343.81	−	2327.54i	−0.173809	−	0.301045i
$392$	−23622.7	−	6329.69i	−3.04369	−	0.815555i
$393$	−4943.18	+	6312.69i	−0.634479	+	0.810262i
$394$	11605.2	+	6700.29i	1.48392	+	0.856741i
$395$	−528.687	+	2344.16i	−0.0673447	+	0.298601i
$396$	2901.78	−	2789.94i	0.368232	−	0.354039i
$397$	4637.81	+	4637.81i	0.586309	+	0.586309i	0.936630	−	0.350321i	$-0.113927\pi$
$397$	4637.81	+	4637.81i	0.586309	+	0.586309i	−0.350321	+	0.936630i	$0.613927\pi$
$398$	−4030.64	+	1080.01i	−0.507632	+	0.136020i
$399$	816.416	+	1085.90i	0.102436	+	0.136248i
$400$	2373.41	+	29621.8i	0.296676	+	3.70272i
$401$	−5746.08	+	3317.50i	−0.715576	+	0.413138i	−0.813122	−	0.582093i	$-0.802234\pi$
$401$	−5746.08	+	3317.50i	−0.715576	+	0.413138i	0.0975465	+	0.995231i	$0.468901\pi$
$402$	4856.58	−	1955.99i	0.602548	−	0.242676i
$403$	890.102	+	3321.90i	0.110023	+	0.410610i
$404$	31664.6			3.89944
$405$	−7871.31	+	2114.86i	−0.965749	+	0.259477i
$406$	−1054.82			−0.128941
$407$	−583.410	−	2177.32i	−0.0710530	−	0.265173i
$408$	18559.0	−	7474.63i	2.25197	−	0.906983i
$409$	−4763.16	+	2750.01i	−0.575851	+	0.332468i	−0.759483	−	0.650527i	$-0.774548\pi$
$409$	−4763.16	+	2750.01i	−0.575851	+	0.332468i	0.183632	+	0.982995i	$0.441215\pi$
$410$	−11004.8	+	20952.5i	−1.32558	+	2.52384i
$411$	386.073	+	513.507i	0.0463347	+	0.0616288i
$412$	−6880.19	+	1843.54i	−0.822725	+	0.220448i
$413$	1538.02	+	1538.02i	0.183247	+	0.183247i
$414$	−5601.68	+	5385.78i	−0.664995	+	0.639364i
$415$	5751.30	+	9101.01i	0.680290	+	1.07651i
$416$	−15211.8	−	8782.55i	−1.79284	−	1.03510i
$417$	1140.65	−	1456.67i	0.133952	−	0.171063i
$418$	2156.50	+	577.833i	0.252340	+	0.0676142i
$419$	−393.101	−	680.870i	−0.0458335	−	0.0793859i	0.842199	−	0.539167i	$-0.181261\pi$
$419$	−393.101	−	680.870i	−0.0458335	−	0.0793859i	−0.888032	+	0.459782i	$0.847928\pi$
$420$	−5511.40	−	557.143i	−0.640306	−	0.0647281i
$421$	7854.61	−	13604.6i	0.909289	−	1.57493i	0.0942338	−	0.995550i	$-0.469960\pi$
$421$	7854.61	−	13604.6i	0.909289	−	1.57493i	0.815055	−	0.579384i	$-0.196707\pi$
$422$	11813.6	−	11813.6i	1.36274	−	1.36274i
$423$	7584.72	+	4580.04i	0.871824	+	0.526452i
$424$			4603.98i			0.527332i
$425$	−1152.85	+	6269.66i	−0.131580	+	0.715584i
$426$	12788.9	−	9615.13i	1.45451	−	1.09356i
$427$	−82.1024	+	306.410i	−0.00930495	+	0.0347265i
$428$	9857.68	−	36789.3i	1.11329	−	4.15486i
$429$	−826.226	−	351.783i	−0.0929851	−	0.0395903i
$430$	−14227.9	−	13133.5i	−1.59565	−	1.47292i
$431$			1343.42i			0.150140i	0.997178	+	0.0750702i	$0.0239181\pi$
$431$			1343.42i			0.150140i	−0.997178	+	0.0750702i	$0.976082\pi$
$432$	−19515.5	−	27047.6i	−2.17348	−	3.01234i
$433$	−4364.85	+	4364.85i	−0.484437	+	0.484437i	−0.906545	−	0.422108i	$-0.861290\pi$
$433$	−4364.85	+	4364.85i	−0.484437	+	0.484437i	0.422108	+	0.906545i	$0.361290\pi$
$434$	−1621.73	+	2808.93i	−0.179368	+	0.310675i
$435$	2535.08	−	411.848i	0.279421	−	0.0453945i
$436$	−6298.68	−	10909.6i	−0.691863	−	1.19834i
$437$	−3046.34	−	816.264i	−0.333470	−	0.0893529i
$438$	−3367.38	−	477.023i	−0.367351	−	0.0520389i
$439$	6104.30	+	3524.32i	0.663649	+	0.383158i	0.793666	−	0.608354i	$-0.208170\pi$
$439$	6104.30	+	3524.32i	0.663649	+	0.383158i	−0.130017	+	0.991512i	$0.541503\pi$
$440$	−4874.65	+	3080.49i	−0.528158	+	0.333765i
$441$	−2429.06	+	8401.53i	−0.262290	+	0.907195i
$442$	−4982.32	−	4982.32i	−0.536165	−	0.536165i
$443$	−5676.94	+	1521.13i	−0.608848	+	0.163140i	−0.550053	−	0.835130i	$-0.685392\pi$
$443$	−5676.94	+	1521.13i	−0.608848	+	0.163140i	−0.0587949	+	0.998270i	$0.518726\pi$
$444$	−37147.7	+	4519.80i	−3.97061	+	0.483109i
$445$	958.087	+	3077.86i	0.102062	+	0.327876i
$446$	20546.7	−	11862.6i	2.18142	−	1.25944i
$447$	4923.25	+	3855.17i	0.520943	+	0.407927i
$448$	−2137.02	−	7975.46i	−0.225367	−	0.841083i
$449$	−9280.82			−0.975477			−0.487738	−	0.872990i	$-0.662178\pi$
$449$	−9280.82			−0.975477			−0.487738	+	0.872990i	$0.662178\pi$
$450$	18398.2	−	1110.85i	1.92733	−	0.116369i
$451$	−2647.80			−0.276452
$452$	10720.9	+	40011.1i	1.11564	+	4.16364i
$453$	−1195.34	+	8438.11i	−0.123978	+	0.875181i
$454$	12690.2	−	7326.67i	1.31185	−	0.757395i
$455$	367.287	+	1179.91i	0.0378433	+	0.121572i
$456$	9197.34	−	21601.7i	0.944529	−	2.21840i
$457$	−2950.39	+	790.554i	−0.301999	+	0.0809203i	−0.406636	−	0.913590i	$-0.633298\pi$
$457$	−2950.39	+	790.554i	−0.301999	+	0.0809203i	0.104638	+	0.994510i	$0.466632\pi$
$458$	18625.0	+	18625.0i	1.90019	+	1.90019i
$459$	−2542.07	−	6688.03i	−0.258504	−	0.680110i
$460$	10870.7	−	6869.67i	1.10185	−	0.696305i
$461$	6729.62	+	3885.35i	0.679890	+	0.392535i	0.799814	−	0.600248i	$-0.204932\pi$
$461$	6729.62	+	3885.35i	0.679890	+	0.392535i	−0.119923	+	0.992783i	$0.538265\pi$
$462$	−316.400	−	785.597i	−0.0318620	−	0.0791110i
$463$	−3695.76	−	990.276i	−0.370965	−	0.0993997i	0.0685201	−	0.997650i	$-0.478172\pi$
$463$	−3695.76	−	990.276i	−0.370965	−	0.0993997i	−0.439485	+	0.898250i	$0.644839\pi$
$464$	5255.00	+	9101.94i	0.525770	+	0.910661i
$465$	2800.83	−	7383.96i	0.279323	−	0.736393i
$466$	−3879.68	+	6719.80i	−0.385671	+	0.668002i
$467$	−3050.23	+	3050.23i	−0.302243	+	0.302243i	−0.841891	−	0.539648i	$-0.818557\pi$
$467$	−3050.23	+	3050.23i	−0.302243	+	0.302243i	0.539648	+	0.841891i	$0.318557\pi$
$468$	−7706.24	+	12761.8i	−0.761156	+	1.26050i
$469$		−	806.077i		−	0.0793628i
$470$	−14723.1	−	13590.6i	−1.44495	−	1.33381i
$471$	−2199.57	−	18078.0i	−0.215182	−	1.76856i
$472$	9728.69	−	36308.0i	0.948727	−	3.54070i
$473$	560.678	−	2092.48i	0.0545032	−	0.203409i
$474$	736.671	+	6054.62i	0.0713849	+	0.586704i
$475$	4245.73	+	6158.92i	0.410121	+	0.594927i
$476$		−	4862.81i		−	0.468249i
$477$	1646.09	+	32.3460i	0.158007	+	0.00310487i
$478$	25566.2	−	25566.2i	2.44638	−	2.44638i
$479$	−1094.98	+	1896.57i	−0.104449	+	0.180911i	−0.913513	−	0.406810i	$-0.866641\pi$
$479$	−1094.98	+	1896.57i	−0.104449	+	0.180911i	0.809064	+	0.587721i	$0.199975\pi$
$480$	16552.1	+	36782.7i	1.57395	+	3.49770i
$481$	4174.04	+	7229.65i	0.395675	+	0.685330i
$482$	12935.9	+	3466.16i	1.22243	+	0.327550i
$483$	446.956	+	1109.76i	0.0421060	+	0.104546i
$484$	24275.3	+	14015.4i	2.27980	+	1.31624i
$485$	−9822.74	−	15543.8i	−0.919645	−	1.45527i
$486$	−17010.7	+	11772.5i	−1.58770	+	1.09879i
$487$	−1824.01	−	1824.01i	−0.169721	−	0.169721i	0.617136	−	0.786857i	$-0.288293\pi$
$487$	−1824.01	−	1824.01i	−0.169721	−	0.169721i	−0.786857	+	0.617136i	$0.788293\pi$
$488$	5295.24	−	1418.85i	0.491197	−	0.131616i
$489$	3473.29	−	8157.66i	0.321201	−	0.754401i
$490$	9196.36	−	17509.4i	0.847856	−	1.61428i
$491$	−2339.22	+	1350.55i	−0.215005	+	0.124133i	−0.603635	−	0.797260i	$-0.706282\pi$
$491$	−2339.22	+	1350.55i	−0.215005	+	0.124133i	0.388630	+	0.921394i	$0.372948\pi$
$492$	−6165.42	+	43522.7i	−0.564957	+	3.98812i
$493$	583.530	+	2177.76i	0.0533081	+	0.198948i
$494$	−8268.28			−0.753052
$495$	1067.14	+	1764.51i	0.0968979	+	0.160220i
$496$	32317.1			2.92557
$497$	−637.566	−	2379.43i	−0.0575428	−	0.214753i
$498$	21514.4	+	16847.0i	1.93591	+	1.51592i
$499$	−14609.9	+	8435.02i	−1.31068	+	0.756720i	−0.982208	−	0.187795i	$-0.939866\pi$
$499$	−14609.9	+	8435.02i	−1.31068	+	0.756720i	−0.328469	+	0.944515i	$0.606533\pi$
$500$	−30195.0	−	4312.74i	−2.70073	−	0.385744i
$501$	1760.40	−	214.189i	0.156983	−	0.0191003i
$502$	−34621.4	+	9276.77i	−3.07814	+	0.824786i
$503$	−3851.44	−	3851.44i	−0.341406	−	0.341406i	0.515490	−	0.856896i	$-0.327610\pi$
$503$	−3851.44	−	3851.44i	−0.341406	−	0.341406i	−0.856896	+	0.515490i	$0.827610\pi$
$504$	−8646.49	+	2135.67i	−0.764177	+	0.188751i
$505$	−3568.71	+	15823.4i	−0.314467	+	1.39432i
$506$	1702.65	+	983.026i	0.149589	+	0.0863653i
$507$	−8010.26	−	1134.73i	−0.701673	−	0.0993989i
$508$	−41892.3	−	11225.0i	−3.65880	−	0.980373i
$509$	−1119.01	−	1938.18i	−0.0974443	−	0.168779i	0.813182	−	0.582010i	$-0.197733\pi$
$509$	−1119.01	−	1938.18i	−0.0974443	−	0.168779i	−0.910626	+	0.413231i	$0.864400\pi$
$510$	2594.60	+	15970.8i	0.225276	+	1.38666i
$511$	−261.807	+	453.463i	−0.0226647	+	0.0392564i
$512$	−15177.5	+	15177.5i	−1.31007	+	1.31007i
$513$	−7658.78	−	3440.16i	−0.659149	−	0.296075i
$514$		−	17042.8i		−	1.46250i
$515$	−145.829	−	3645.93i	−0.0124777	−	0.311959i
$516$	−33089.2	−	14088.4i	−2.82300	−	1.20195i
$517$	580.193	−	2165.31i	0.0493557	−	0.184198i
$518$	−2037.74	+	7604.96i	−0.172844	+	0.645063i
$519$	3081.03	−	2316.43i	0.260583	−	0.195915i
$520$	14485.2	−	15692.3i	1.22158	−	1.32337i
$521$			11295.2i			0.949810i	0.880037	+	0.474905i	$0.157518\pi$
$521$			11295.2i			0.949810i	−0.880037	+	0.474905i	$0.842482\pi$
$522$	5708.38	−	3147.85i	0.478638	−	0.263942i
$523$	7883.52	−	7883.52i	0.659125	−	0.659125i	−0.296048	−	0.955173i	$-0.595669\pi$
$523$	7883.52	−	7883.52i	0.659125	−	0.659125i	0.955173	+	0.296048i	$0.0956690\pi$
$524$	16838.3	−	29164.8i	1.40379	−	2.43144i
$525$	899.570	−	2691.36i	0.0747818	−	0.223734i
$526$	12824.0	+	22211.7i	1.06302	+	1.84121i
$527$	6696.39	+	1794.29i	0.553509	+	0.148312i
$528$	−5202.55	+	6643.92i	−0.428811	+	0.547613i
$529$	8131.72	+	4694.85i	0.668342	+	0.385867i
$530$	−3632.01	−	819.142i	−0.297668	−	0.0671344i
$531$	−12913.1	−	3733.46i	−1.05533	−	0.305119i
$532$	−4034.97	−	4034.97i	−0.328831	−	0.328831i
$533$	9471.91	−	2537.99i	0.769745	−	0.206252i
$534$	4916.77	+	6539.69i	0.398445	+	0.529963i
$535$	17273.3	+	9072.36i	1.39587	+	0.733144i
$536$	−12063.9	+	6965.12i	−0.972169	+	0.561282i
$537$	12183.1	−	4906.74i	0.979029	−	0.394304i
$538$	−5805.17	−	21665.2i	−0.465202	−	1.73616i
$539$	2212.69			0.176822
$540$	31488.7	−	13432.3i	2.50936	−	1.07043i
$541$	−9200.65			−0.731177			−0.365588	−	0.930777i	$-0.619132\pi$
$541$	−9200.65			−0.731177			−0.365588	+	0.930777i	$0.619132\pi$
$542$	506.367	+	1889.79i	0.0401298	+	0.149766i
$543$	−10718.6	+	4316.93i	−0.847109	+	0.341173i
$544$	−30664.4	+	17704.1i	−2.41678	+	1.39533i
$545$	6161.63	−	1918.01i	0.484285	−	0.150750i
$546$	1884.87	+	2507.02i	0.147738	+	0.196503i
$547$	−17231.7	+	4617.23i	−1.34694	+	0.360911i	−0.859004	−	0.511969i	$-0.828916\pi$
$547$	−17231.7	+	4617.23i	−1.34694	+	0.360911i	−0.487934	+	0.872880i	$0.662249\pi$
$548$	−1908.09	−	1908.09i	−0.148740	−	0.148740i
$549$	−470.091	−	1903.21i	−0.0365446	−	0.147955i
$550$	−1562.85	−	4393.62i	−0.121164	−	0.340626i
$551$	2291.22	+	1322.83i	0.177149	+	0.102277i
$552$	12746.9	−	16278.4i	0.982867	−	1.25517i
$553$	907.038	+	243.040i	0.0697490	+	0.0186892i
$554$	4575.16	+	7924.41i	0.350866	+	0.607719i
$555$	1928.06	−	19072.8i	0.147462	−	1.45873i
$556$	−3885.48	+	6729.85i	−0.296369	+	0.513326i
$557$	9243.69	−	9243.69i	0.703174	−	0.703174i	−0.261917	−	0.965091i	$-0.584355\pi$
$557$	9243.69	−	9243.69i	0.703174	−	0.703174i	0.965091	+	0.261917i	$0.0843545\pi$
$558$	393.804	−	20040.7i	0.0298764	−	1.52041i
$559$			8022.80i			0.607027i
$560$	11603.1	−	464.100i	0.875575	−	0.0350211i
$561$	−1446.89	+	1087.82i	−0.108891	+	0.0818681i
$562$	5433.68	−	20278.8i	0.407840	−	1.52208i
$563$	3955.94	−	14763.8i	0.296133	−	1.10518i	−0.644180	−	0.764874i	$-0.722801\pi$
$563$	3955.94	−	14763.8i	0.296133	−	1.10518i	0.940313	−	0.340310i	$-0.110532\pi$
$564$	−34240.9	−	14578.8i	−2.55639	−	1.08843i
$565$	−21202.6	+	848.056i	−1.57876	+	0.0631469i
$566$			6196.99i			0.460210i
$567$	702.834	+	3106.45i	0.0520569	+	0.230085i
$568$	−30102.1	+	30102.1i	−2.22369	+	2.22369i
$569$	−7749.24	+	13422.1i	−0.570941	+	0.988898i	0.425529	+	0.904945i	$0.360088\pi$
$569$	−7749.24	+	13422.1i	−0.570941	+	0.988898i	−0.996470	+	0.0839534i	$0.973245\pi$
$570$	15404.8	+	11099.0i	1.13199	+	0.815591i
$571$	986.984	+	1709.51i	0.0723362	+	0.125290i	0.899925	−	0.436045i	$-0.143621\pi$
$571$	986.984	+	1709.51i	0.0723362	+	0.125290i	−0.827589	+	0.561335i	$0.810288\pi$
$572$	3643.29	+	976.216i	0.266317	+	0.0713595i
$573$	−13621.5	−	1929.63i	−0.993103	−	0.140683i
$574$	8009.23	+	4624.13i	0.582402	+	0.336250i
$575$	2207.73	+	6206.55i	0.160120	+	0.450141i
$576$	35365.6	+	36783.4i	2.55828	+	2.66083i
$577$	−2600.22	−	2600.22i	−0.187606	−	0.187606i	0.607055	−	0.794660i	$-0.292351\pi$
$577$	−2600.22	−	2600.22i	−0.187606	−	0.187606i	−0.794660	+	0.607055i	$0.792351\pi$
$578$	12197.1	−	3268.21i	0.877739	−	0.235189i
$579$	5300.34	−	644.897i	0.380439	−	0.0462884i
$580$	−10300.1	+	3206.24i	−0.737392	+	0.229538i
$581$	3643.38	−	2103.51i	0.260160	−	0.150203i
$582$	−36744.8	−	28773.2i	−2.61705	−	2.04929i
$583$	−107.811	−	402.356i	−0.00765879	−	0.0285830i
$584$	9048.84			0.641171
$585$	−5508.80	−	5289.25i	−0.389334	−	0.373818i
$586$	−2459.17			−0.173357
$587$	−5436.85	−	20290.6i	−0.382288	−	1.42672i	−0.842398	−	0.538856i	$-0.818857\pi$
$587$	−5436.85	−	20290.6i	−0.382288	−	1.42672i	0.460110	−	0.887862i	$-0.347810\pi$
$588$	5152.26	−	36370.6i	0.361353	−	2.55085i
$589$	7045.24	−	4067.57i	0.492859	−	0.284552i
$590$	26911.9	+	14134.7i	1.87787	+	0.986302i
$591$	−4994.75	+	11731.1i	−0.347642	+	0.816502i
$592$	75774.0	−	20303.6i	5.26063	−	1.40958i
$593$	−1706.61	−	1706.61i	−0.118182	−	0.118182i	0.645542	−	0.763725i	$-0.276631\pi$
$593$	−1706.61	−	1706.61i	−0.118182	−	0.118182i	−0.763725	+	0.645542i	$0.776631\pi$
$594$	4056.67	+	3307.20i	0.280214	+	0.228444i
$595$	2430.04	+	548.057i	0.167432	+	0.0377616i
$596$	−22745.6	−	13132.2i	−1.56325	−	0.902541i
$597$	−1483.25	−	3682.81i	−0.101684	−	0.252474i
$598$	−7033.11	−	1884.52i	−0.480945	−	0.128869i
$599$	6939.25	+	12019.1i	0.473339	+	0.819847i	0.999534	−	0.0305164i	$-0.00971517\pi$
$599$	6939.25	+	12019.1i	0.473339	+	0.819847i	−0.526195	+	0.850364i	$0.676382\pi$
$600$	−48052.4	+	9792.19i	−3.26955	+	0.666274i
$601$	11793.6	−	20427.2i	0.800454	−	1.38643i	−0.118864	−	0.992911i	$-0.537925\pi$
$601$	11793.6	−	20427.2i	0.800454	−	1.38643i	0.919318	−	0.393516i	$-0.128741\pi$
$602$	−5350.29	+	5350.29i	−0.362228	+	0.362228i
$603$	2405.53	+	4362.24i	0.162456	+	0.294601i
$604$		−	35795.9i		−	2.41145i
$605$	−9739.66	+	10551.2i	−0.654501	+	0.709040i
$606$	4972.63	+	40869.5i	0.333332	+	2.73962i
$607$	−6898.66	+	25746.1i	−0.461298	+	1.72159i	0.207583	+	0.978218i	$0.433440\pi$
$607$	−6898.66	+	25746.1i	−0.461298	+	1.72159i	−0.668881	+	0.743370i	$0.733226\pi$
$608$	−10754.0	+	40134.3i	−0.717320	+	2.67708i
$609$	−121.218	−	996.276i	−0.00806568	−	0.0662909i
$610$	177.181	+	4429.77i	0.0117604	+	0.294027i
$611$			8302.05i			0.549697i
$612$	14511.8	+	26316.0i	0.958506	+	1.73818i
$613$	2171.14	−	2171.14i	0.143053	−	0.143053i	−0.631953	−	0.775006i	$-0.717747\pi$
$613$	2171.14	−	2171.14i	0.143053	−	0.143053i	0.775006	+	0.631953i	$0.217747\pi$
$614$	4702.80	−	8145.49i	0.309103	−	0.535383i
$615$	−21054.2	−	7986.14i	−1.38047	−	0.523630i
$616$	1126.67	+	1951.45i	0.0736931	+	0.127640i
$617$	934.234	+	250.327i	0.0609576	+	0.0163335i	0.289169	−	0.957278i	$-0.406621\pi$
$617$	934.234	+	250.327i	0.0609576	+	0.0163335i	−0.228211	+	0.973612i	$0.573288\pi$
$618$	−3459.93	−	8590.76i	−0.225209	−	0.559176i
$619$	5225.86	+	3017.15i	0.339330	+	0.195912i	0.659976	−	0.751287i	$-0.270567\pi$
$619$	5225.86	+	3017.15i	0.339330	+	0.195912i	−0.320646	+	0.947199i	$0.603900\pi$
$620$	−7297.80	+	32357.8i	−0.472721	+	2.09600i
$621$	−5730.58	−	4671.84i	−0.370306	−	0.301892i
$622$	20782.0	+	20782.0i	1.33968	+	1.33968i
$623$	1216.74	−	326.025i	0.0782466	−	0.0209661i
$624$	12242.6	−	28753.9i	0.785409	−	1.84468i
$625$	5558.25	−	14603.0i	0.355728	−	0.934590i
$626$	22822.3	−	13176.4i	1.45713	−	0.841272i
$627$	−297.941	+	2103.21i	−0.0189770	+	0.133962i
$628$	19797.6	+	73885.6i	1.25798	+	4.69484i
$629$	16828.3			1.06675
$630$	−146.409	−	7201.06i	−0.00925885	−	0.455392i
$631$	−15462.3			−0.975505			−0.487753	−	0.872982i	$-0.662183\pi$
$631$	−15462.3			−0.975505			−0.487753	+	0.872982i	$0.662183\pi$
$632$	−4200.10	−	15675.0i	−0.264353	−	0.986579i
$633$	12515.5	+	9800.31i	0.785856	+	0.615367i
$634$	−18224.4	+	10521.8i	−1.14161	+	0.659110i
$635$	10330.8	−	19669.3i	0.645612	−	1.22921i
$636$	−6864.69	+	835.234i	−0.427992	+	0.0520742i
$637$	−7915.39	+	2120.92i	−0.492338	+	0.131922i
$638$	−1166.22	−	1166.22i	−0.0723685	−	0.0723685i
$639$	10551.1	+	10974.1i	0.653201	+	0.679387i
$640$	−28469.8	−	45051.3i	−1.75839	−	2.78251i
$641$	1917.34	+	1106.98i	0.118144	+	0.0682105i	0.557908	−	0.829903i	$-0.311604\pi$
$641$	1917.34	+	1106.98i	0.118144	+	0.0682105i	−0.439763	+	0.898114i	$0.644938\pi$
$642$	49032.1	+	6945.88i	3.01424	+	0.426997i
$643$	−5494.59	−	1472.27i	−0.336991	−	0.0902965i	0.0863552	−	0.996264i	$-0.472478\pi$
$643$	−5494.59	−	1472.27i	−0.336991	−	0.0902965i	−0.423346	+	0.905968i	$0.639145\pi$
$644$	−2512.55	−	4351.86i	−0.153740	−	0.266285i
$645$	10769.5	−	14947.5i	0.657440	−	0.912490i
$646$	−8333.71	+	14434.4i	−0.507563	+	0.879125i
$647$	−8395.00	+	8395.00i	−0.510110	+	0.510110i	−0.914560	−	0.404450i	$-0.867463\pi$
$647$	−8395.00	+	8395.00i	−0.510110	+	0.510110i	0.404450	+	0.914560i	$0.367463\pi$
$648$	40418.8	−	37360.8i	2.45031	−	2.26493i
$649$			3400.88i			0.205695i
$650$	9802.16	+	14219.1i	0.591496	+	0.858032i
$651$	−2839.38	−	1208.93i	−0.170944	−	0.0727827i
$652$	−9638.56	+	35971.6i	−0.578950	+	2.16067i
$653$	1089.10	−	4064.57i	0.0652676	−	0.243582i	−0.925583	−	0.378544i	$-0.876425\pi$
$653$	1089.10	−	4064.57i	0.0652676	−	0.243582i	0.990851	+	0.134962i	$0.0430914\pi$
$654$	13091.9	−	9842.97i	0.782775	−	0.588518i
$655$	12676.5	+	11701.4i	0.756200	+	0.698033i
$656$		−	92147.4i		−	5.48438i
$657$	63.5743	−	3235.30i	0.00377514	−	0.192117i
$658$	−5536.52	+	5536.52i	−0.328018	+	0.328018i
$659$	−15566.0	+	26961.1i	−0.920129	+	1.59371i	−0.120915	+	0.992663i	$0.538583\pi$
$659$	−15566.0	+	26961.1i	−0.920129	+	1.59371i	−0.799214	+	0.601047i	$0.794751\pi$
$660$	−5477.46	−	6709.42i	−0.323045	−	0.395703i
$661$	7194.58	+	12461.4i	0.423354	+	0.733270i	0.996265	−	0.0863471i	$-0.0275194\pi$
$661$	7194.58	+	12461.4i	0.423354	+	0.733270i	−0.572911	+	0.819617i	$0.694186\pi$
$662$	−25157.8	−	6741.02i	−1.47702	−	0.395766i
$663$	4133.23	−	5278.34i	0.242113	−	0.309191i
$664$	−62963.2	−	36351.8i	−3.67989	−	2.12459i
$665$	2471.11	−	1561.59i	0.144098	−	0.0910617i
$666$	−11667.4	−	47236.8i	−0.678834	−	2.74833i
$667$	1647.44	+	1647.44i	0.0956357	+	0.0956357i
$668$	−7194.81	+	1927.84i	−0.416730	+	0.111662i
$669$	13565.4	+	18043.0i	0.783957	+	1.04272i
$670$	−3348.25	−	10756.3i	−0.193066	−	0.620227i
$671$	−429.542	+	247.996i	−0.0247128	+	0.0142679i
$672$	14620.6	−	5888.46i	0.839290	−	0.338024i
$673$	−4887.41	−	18240.0i	−0.279934	−	1.04473i	−0.952462	−	0.304657i	$-0.901458\pi$
$673$	−4887.41	−	18240.0i	−0.279934	−	1.04473i	0.672528	−	0.740072i	$-0.265208\pi$
$674$	−55088.6			−3.14827
$675$	3163.47	+	17249.3i	0.180388	+	0.983595i
$676$	33980.9			1.93337
$677$	−5586.18	−	20847.9i	−0.317126	−	1.18353i	−0.921994	−	0.387205i	$-0.873441\pi$
$677$	−5586.18	−	20847.9i	−0.317126	−	1.18353i	0.604867	−	0.796326i	$-0.293226\pi$
$678$	−49958.8	+	20120.9i	−2.82987	+	1.13973i
$679$	−6222.59	+	3592.62i	−0.351695	+	0.203051i
$680$	−12795.0	−	41104.1i	−0.721569	−	2.31805i
$681$	8378.33	+	11143.8i	0.471451	+	0.627067i
$682$	−4898.57	+	1312.57i	−0.275038	+	0.0736962i
$683$	13485.0	+	13485.0i	0.755474	+	0.755474i	0.975495	−	0.220021i	$-0.0706126\pi$
$683$	13485.0	+	13485.0i	0.755474	+	0.755474i	−0.220021	+	0.975495i	$0.570613\pi$
$684$	33877.4	+	9794.69i	1.89376	+	0.547528i
$685$	1168.56	−	738.459i	0.0651799	−	0.0411899i
$686$	−13780.6	−	7956.21i	−0.766974	−	0.442813i
$687$	−15450.9	+	19731.6i	−0.858061	+	1.09579i
$688$	72821.4	+	19512.4i	4.03531	+	1.08126i
$689$	771.339	+	1336.00i	0.0426498	+	0.0738716i
$690$	10573.8	+	12952.1i	0.583391	+	0.714604i
$691$	9014.75	−	15614.0i	0.496291	−	0.859602i	−0.503700	−	0.863879i	$-0.668028\pi$
$691$	9014.75	−	15614.0i	0.496291	−	0.859602i	0.999991	+	0.00427721i	$0.00136148\pi$
$692$	−11448.5	+	11448.5i	−0.628911	+	0.628911i
$693$	705.633	−	389.117i	0.0386794	−	0.0213295i
$694$			54861.9i			3.00076i
$695$	−2925.12	−	2700.13i	−0.159649	−	0.147369i
$696$	−13863.1	+	10422.8i	−0.754999	+	0.567635i
$697$	5116.15	−	19093.7i	0.278032	−	1.03763i
$698$	−9703.95	+	36215.6i	−0.526218	+	1.96387i
$699$	−6792.67	−	2892.12i	−0.367557	−	0.156495i
$700$	−2155.52	+	11722.6i	−0.116387	+	0.632958i
$701$		−	5187.88i		−	0.279520i	−0.990185	−	0.139760i	$-0.955367\pi$
$701$		−	5187.88i		−	0.279520i	0.990185	−	0.139760i	$-0.0446331\pi$
$702$	−17681.9	−	7942.33i	−0.950655	−	0.427014i
$703$	13963.5	−	13963.5i	0.749135	−	0.749135i
$704$	6455.02	−	11180.4i	0.345572	−	0.598548i
$705$	11144.4	−	15467.7i	0.595349	−	0.826310i
$706$	−24439.5	−	42330.5i	−1.30282	−	2.25656i
$707$	6122.63	+	1640.55i	0.325694	+	0.0872693i
$708$	55901.4	+	7918.99i	2.96738	+	0.420358i
$709$	3337.90	+	1927.14i	0.176809	+	0.102081i	0.585793	−	0.810461i	$-0.300783\pi$
$709$	3337.90	+	1927.14i	0.176809	+	0.102081i	−0.408984	+	0.912542i	$0.634117\pi$
$710$	−18391.3	−	29102.8i	−0.972130	−	1.53832i
$711$	−5633.90	+	1391.57i	−0.297170	+	0.0734005i
$712$	−15392.9	−	15392.9i	−0.810217	−	0.810217i
$713$	6919.86	−	1854.17i	0.363465	−	0.0973903i
$714$	6276.44	−	763.660i	0.328977	−	0.0400270i
$715$	−898.445	+	1710.60i	−0.0469929	+	0.0894722i
$716$	−47775.3	+	27583.1i	−2.49364	+	1.43970i
$717$	27085.2	+	21209.2i	1.41076	+	1.10470i
$718$	3660.11	+	13659.7i	0.190242	+	0.709994i
$719$	9734.47			0.504916			0.252458	−	0.967608i	$-0.418761\pi$
$719$	9734.47			0.504916			0.252458	+	0.967608i	$0.418761\pi$
$720$	−61407.6	+	37138.2i	−3.17851	+	1.92230i
$721$	−1425.86			−0.0736503
$722$	−4632.88	−	17290.1i	−0.238806	−	0.891235i
$723$	−1787.21	+	12616.2i	−0.0919323	+	0.648965i
$724$	42032.5	−	24267.5i	2.15763	−	1.24571i
$725$	−441.361	−	5508.49i	−0.0226093	−	0.282180i
$726$	−14277.4	+	33533.2i	−0.729870	+	1.71423i
$727$	−11626.5	+	3115.30i	−0.593125	+	0.158927i	−0.542881	−	0.839810i	$-0.682666\pi$
$727$	−11626.5	+	3115.30i	−0.593125	+	0.158927i	−0.0502438	+	0.998737i	$0.516000\pi$
$728$	−5900.95	−	5900.95i	−0.300417	−	0.300417i
$729$	−13073.9	−	14713.7i	−0.664224	−	0.747534i
$730$	−1609.98	+	7138.49i	−0.0816272	+	0.361928i
$731$	14005.9	+	8086.29i	0.708654	+	0.409141i
$732$	3076.20	+	7637.99i	0.155327	+	0.385667i
$733$	25193.6	+	6750.61i	1.26951	+	0.340163i	0.829842	−	0.557999i	$-0.188431\pi$
$733$	25193.6	+	6750.61i	1.26951	+	0.340163i	0.439664	+	0.898162i	$0.355097\pi$
$734$	−21612.8	−	37434.4i	−1.08684	−	1.88246i
$735$	17594.4	+	6673.78i	0.882965	+	0.334920i
$736$	−18294.9	+	31687.8i	−0.916250	+	1.58699i
$737$	891.204	−	891.204i	0.0445426	−	0.0445426i
$738$	−57143.0	−	1122.87i	−2.85022	−	0.0560074i
$739$		−	24108.3i		−	1.20005i	−0.799981	−	0.600025i	$-0.795157\pi$
$739$		−	24108.3i		−	1.20005i	0.799981	−	0.600025i	$-0.204843\pi$
$740$	3217.99	+	80454.3i	0.159859	+	3.99670i
$741$	−950.172	−	7809.35i	−0.0471058	−	0.387158i
$742$	−376.563	+	1405.35i	−0.0186308	+	0.0695312i
$743$	−430.808	+	1607.80i	−0.0212716	+	0.0793867i	−0.975746	−	0.218907i	$-0.929751\pi$
$743$	−430.808	+	1607.80i	−0.0212716	+	0.0793867i	0.954474	+	0.298294i	$0.0964175\pi$
$744$	6441.38	+	52940.9i	0.317409	+	2.60875i
$745$	9125.90	−	9886.35i	0.448788	−	0.486185i
$746$			33025.8i			1.62086i
$747$	−13439.5	+	22256.3i	−0.658267	+	1.09011i
$748$	5376.36	−	5376.36i	0.262806	−	0.262806i
$749$	3812.14	−	6602.82i	0.185971	−	0.322112i
$750$	824.607	−	39650.1i	0.0401472	−	1.93042i
$751$	−11016.0	−	19080.3i	−0.535259	−	0.927096i	−0.999151	−	0.0412042i	$-0.986881\pi$
$751$	−11016.0	−	19080.3i	−0.535259	−	0.927096i	0.463892	−	0.885892i	$-0.346453\pi$
$752$	75356.1	+	20191.6i	3.65420	+	0.979139i
$753$	−12740.5	−	31633.7i	−0.616585	−	1.53094i
$754$	5289.75	+	3054.04i	0.255492	+	0.147509i
$755$	17887.9	+	4034.33i	0.862261	+	0.194469i
$756$	−4752.97	−	12504.8i	−0.228656	−	0.601580i
$757$	−25360.2	−	25360.2i	−1.21761	−	1.21761i	−0.968466	−	0.249145i	$-0.919851\pi$
$757$	−25360.2	−	25360.2i	−1.21761	−	1.21761i	−0.249145	−	0.968466i	$-0.580149\pi$
$758$	−71224.0	+	19084.4i	−3.41289	+	0.914481i
$759$	−732.799	+	1721.11i	−0.0350447	+	0.0823089i
$760$	−44723.4	−	23489.8i	−2.13459	−	1.12114i
$761$	−14614.3	+	8437.57i	−0.696147	+	0.401921i	−0.805911	−	0.592037i	$-0.798324\pi$
$761$	−14614.3	+	8437.57i	−0.696147	+	0.401921i	0.109763	+	0.993958i	$0.464991\pi$
$762$	7909.33	−	55833.2i	0.376017	−	2.65436i
$763$	−652.674	−	2435.81i	−0.0309678	−	0.115573i
$764$	57784.9			2.73637
$765$	−14786.2	+	4285.91i	−0.698816	+	0.202559i
$766$	52745.9			2.48797
$767$	−3259.84	−	12165.9i	−0.153463	−	0.572732i
$768$	−44645.7	−	34960.0i	−2.09767	−	1.64259i
$769$	4117.86	−	2377.45i	0.193100	−	0.111486i	−0.400333	−	0.916370i	$-0.631106\pi$
$769$	4117.86	−	2377.45i	0.193100	−	0.111486i	0.593433	+	0.804883i	$0.297772\pi$
$770$	−1739.93	+	541.611i	−0.0814322	+	0.0253485i
$771$	16096.9	−	1958.52i	0.751900	−	0.0914844i
$772$	−21662.7	+	5804.50i	−1.00992	+	0.270607i
$773$	15286.0	+	15286.0i	0.711252	+	0.711252i	0.966797	−	0.255545i	$-0.0822549\pi$
$773$	15286.0	+	15286.0i	0.711252	+	0.711252i	−0.255545	+	0.966797i	$0.582255\pi$
$774$	12987.5	−	44920.7i	0.603137	−	2.08610i
$775$	−15347.3	−	7293.69i	−0.711344	−	0.338061i
$776$	107536.	+	62085.9i	4.97463	+	2.87210i
$777$	−7417.02	−	1050.69i	−0.342451	−	0.0485115i
$778$	−30865.1	−	8270.29i	−1.42233	−	0.381111i
$779$	−11598.1	−	20088.4i	−0.533432	−	0.923932i
$780$	26025.6	+	18751.2i	1.19470	+	0.860768i
$781$	1925.82	−	3335.61i	0.0882345	−	0.152827i
$782$	−10378.7	+	10378.7i	−0.474605	+	0.474605i
$783$	3629.13	+	5029.80i	0.165638	+	0.229566i
$784$			77004.9i			3.50788i
$785$	−39153.3	+	1566.04i	−1.78018	+	0.0712032i
$786$	40287.4	+	17153.2i	1.82825	+	0.778414i
$787$	1584.58	−	5913.74i	0.0717716	−	0.267855i	−0.920710	−	0.390247i	$-0.872390\pi$
$787$	1584.58	−	5913.74i	0.0717716	−	0.267855i	0.992482	+	0.122392i	$0.0390564\pi$
$788$	13860.7	−	51728.8i	0.626608	−	2.33853i
$789$	−19505.2	+	14664.7i	−0.880106	+	0.661695i
$790$	13113.1	−	524.493i	0.590559	−	0.0236210i
$791$			8291.97i			0.372729i
$792$	−11920.8	−	7198.41i	−0.534834	−	0.322960i
$793$	1298.88	−	1298.88i	0.0581647	−	0.0581647i
$794$	17909.7	−	31020.5i	0.800493	−	1.38649i
$795$	356.294	−	3524.55i	0.0158949	−	0.157236i
$796$	8338.06	+	14441.9i	0.371275	+	0.643067i
$797$	5099.67	+	1366.45i	0.226649	+	0.0607305i	0.370356	−	0.928890i	$-0.379236\pi$
$797$	5099.67	+	1366.45i	0.226649	+	0.0607305i	−0.143707	+	0.989620i	$0.545902\pi$
$798$	4574.29	−	5841.60i	0.202917	−	0.259136i
$799$	14493.4	+	8367.75i	0.641726	+	0.370500i
$800$	81768.9	−	29086.0i	3.61371	−	1.28543i
$801$	−5611.69	+	5395.40i	−0.247540	+	0.237999i
$802$	25622.2	+	25622.2i	1.12812	+	1.12812i
$803$	−790.807	+	211.896i	−0.0347534	+	0.00931214i
$804$	−12573.8	−	16724.2i	−0.551548	−	0.733602i
$805$	2457.88	−	765.096i	0.107613	−	0.0334982i
$806$	16265.4	−	9390.83i	0.710824	−	0.410395i
$807$	19795.6	−	7972.68i	0.863491	−	0.347771i
$808$	−28351.3	−	105808.i	−1.23440	−	4.60684i
$809$	−5052.91			−0.219593			−0.109797	−	0.993954i	$-0.535020\pi$
$809$	−5052.91			−0.219593			−0.109797	+	0.993954i	$0.535020\pi$
$810$	22282.1	+	38533.0i	0.966558	+	1.67150i
$811$	−35887.2			−1.55385			−0.776923	−	0.629595i	$-0.783221\pi$
$811$	−35887.2			−1.55385			−0.776923	+	0.629595i	$0.783221\pi$
$812$	1091.04	+	4071.82i	0.0471528	+	0.175977i
$813$	−1726.71	+	695.432i	−0.0744874	+	0.0299998i
$814$	−10661.0	+	6155.15i	−0.459053	+	0.265034i
$815$	−16889.4	−	8870.70i	−0.725901	−	0.381260i
$816$	−37858.0	−	50354.1i	−1.62414	−	2.16023i
$817$	18331.2	−	4911.84i	0.784979	−	0.210335i
$818$	21239.3	+	21239.3i	0.907843	+	0.907843i
$819$	−2151.27	+	2068.35i	−0.0917843	+	0.0882466i
$820$	92263.5	+	20808.6i	3.92924	+	0.886179i
$821$	−34969.2	−	20189.5i	−1.48652	−	0.858243i	−0.486638	−	0.873604i	$-0.661777\pi$
$821$	−34969.2	−	20189.5i	−1.48652	−	0.858243i	−0.999882	+	0.0153613i	$0.995110\pi$
$822$	2163.12	−	2762.42i	0.0917854	−	0.117215i
$823$	−42407.7	−	11363.1i	−1.79616	−	0.481280i	−0.802793	−	0.596258i	$-0.796653\pi$
$823$	−42407.7	−	11363.1i	−1.79616	−	0.481280i	−0.993368	+	0.114979i	$0.963320\pi$
$824$	12320.5	+	21339.8i	0.520881	+	0.902192i
$825$	3970.15	−	1981.01i	0.167543	−	0.0835999i
$826$	5939.32	−	10287.2i	0.250188	−	0.433339i
$827$	−104.564	+	104.564i	−0.00439667	+	0.00439667i	−0.709302	−	0.704905i	$-0.750990\pi$
$827$	−104.564	+	104.564i	−0.00439667	+	0.00439667i	0.704905	+	0.709302i	$0.250990\pi$
$828$	26584.2	+	16052.9i	1.11578	+	0.673763i
$829$			22880.1i			0.958575i	0.877658	+	0.479288i	$0.159105\pi$
$829$			22880.1i			0.958575i	−0.877658	+	0.479288i	$0.840895\pi$
$830$	39879.9	−	43203.0i	1.66777	−	1.80674i
$831$	−6958.81	+	5231.88i	−0.290491	+	0.218402i
$832$	−12374.6	+	46182.8i	−0.515641	+	1.92440i
$833$	−4275.42	+	15956.1i	−0.177832	+	0.663680i
$834$	−9296.41	−	3958.13i	−0.385981	−	0.164339i
$835$	−152.498	−	3812.66i	−0.00632024	−	0.158015i
$836$		−	8922.19i		−	0.369115i
$837$	18973.6	−	1931.09i	0.783541	−	0.0797468i
$838$	−3036.06	+	3036.06i	−0.125154	+	0.125154i
$839$	8316.09	−	14403.9i	0.342197	−	0.592703i	−0.642643	−	0.766165i	$-0.722162\pi$
$839$	8316.09	−	14403.9i	0.342197	−	0.592703i	0.984840	+	0.173463i	$0.0554956\pi$
$840$	3072.98	+	18915.4i	0.126224	+	0.776956i
$841$	11217.3	+	19428.9i	0.459932	+	0.796625i
$842$	−82868.5	−	22204.5i	−3.39173	−	0.908812i
$843$	19777.7	+	2801.70i	0.808041	+	0.114467i
$844$	−57822.1	−	33383.6i	−2.35820	−	1.36151i
$845$	−3829.78	+	16980.9i	−0.155915	+	0.691314i
$846$	13439.6	−	46484.3i	0.546174	−	1.88908i
$847$	3967.71	+	3967.71i	0.160959	+	0.160959i
$848$	14002.6	−	3751.99i	0.567042	−	0.151938i
$849$	−5853.03	+	712.143i	−0.236602	+	0.0287876i
$850$	34702.9	−	2780.53i	1.40035	−	0.112202i
$851$	15060.1	−	8694.95i	0.606643	−	0.350246i
$852$	−50344.2	−	39422.3i	−2.02437	−	1.58519i
$853$	6235.35	+	23270.6i	0.250286	+	0.934081i	0.970652	+	0.240487i	$0.0773071\pi$
$853$	6235.35	+	23270.6i	0.250286	+	0.934081i	−0.720366	+	0.693594i	$0.756026\pi$
$854$	1732.41			0.0694166
$855$	−8712.69	+	15825.3i	−0.348500	+	0.632997i
$856$	−131759.			−5.26103
$857$	5842.65	+	21805.1i	0.232883	+	0.869133i	0.979092	+	0.203420i	$0.0652057\pi$
$857$	5842.65	+	21805.1i	0.232883	+	0.869133i	−0.746208	+	0.665713i	$0.768128\pi$
$858$	−687.858	+	4855.70i	−0.0273696	+	0.193206i
$859$	−5394.56	+	3114.55i	−0.214272	+	0.123710i	−0.603295	−	0.797518i	$-0.706146\pi$
$859$	−5394.56	+	3114.55i	−0.214272	+	0.123710i	0.389023	+	0.921228i	$0.372813\pi$
$860$	−35981.4	+	68506.9i	−1.42669	+	2.71635i
$861$	−3447.07	+	8096.07i	−0.136441	+	0.320457i
$862$	7086.77	−	1898.89i	0.280019	−	0.0750308i
$863$	−27165.1	−	27165.1i	−1.07151	−	1.07151i	−0.997238	−	0.0742697i	$-0.976337\pi$
$863$	−27165.1	−	27165.1i	−1.07151	−	1.07151i	−0.0742697	−	0.997238i	$-0.523663\pi$
$864$	−61549.7	+	75498.1i	−2.42357	+	2.97280i
$865$	−4430.74	−	7011.31i	−0.174161	−	0.275597i
$866$	29194.8	+	16855.6i	1.14559	+	0.661406i
$867$	4488.47	+	11144.5i	0.175821	+	0.436550i
$868$	12520.4	+	3354.83i	0.489597	+	0.131187i
$869$	734.121	+	1271.53i	0.0286575	+	0.0496362i
$870$	−5755.83	−	12790.8i	−0.224300	−	0.498447i
$871$	−2333.84	+	4042.33i	−0.0907912	+	0.157255i
$872$	−30815.4	+	30815.4i	−1.19672	+	1.19672i
$873$	22953.5	−	38011.9i	0.889873	−	1.47366i
$874$			17223.7i			0.666589i
$875$	−5615.04	−	2398.33i	−0.216941	−	0.0926608i
$876$	1641.60	+	13492.1i	0.0633158	+	0.520385i
$877$	−10071.2	+	37586.2i	−0.387777	+	1.44720i	0.445966	+	0.895050i	$0.352860\pi$
$877$	−10071.2	+	37586.2i	−0.387777	+	1.44720i	−0.833743	+	0.552153i	$0.813806\pi$
$878$	9963.04	−	37182.6i	0.382957	−	1.42922i
$879$	−282.602	−	2322.67i	−0.0108441	−	0.0891261i
$880$	13341.6	+	12315.4i	0.511075	+	0.471764i
$881$			1863.97i			0.0712812i	0.999365	+	0.0356406i	$0.0113472\pi$
$881$			1863.97i			0.0712812i	−0.999365	+	0.0356406i	$0.988653\pi$
$882$	47752.7	+	938.351i	1.82304	+	0.0358230i
$883$	5893.85	−	5893.85i	0.224625	−	0.224625i	−0.585818	−	0.810443i	$-0.699227\pi$
$883$	5893.85	−	5893.85i	0.224625	−	0.224625i	0.810443	+	0.585818i	$0.199227\pi$
$884$	−14079.3	+	24386.1i	−0.535678	+	0.927821i
$885$	−10257.6	+	27042.5i	−0.389609	+	1.02714i
$886$	16048.4	+	27796.6i	0.608528	+	1.05400i
$887$	30642.0	+	8210.50i	1.15993	+	0.310802i	0.786938	−	0.617032i	$-0.211665\pi$
$887$	30642.0	+	8210.50i	1.15993	+	0.310802i	0.372992	+	0.927835i	$0.378332\pi$
$888$	48363.8	+	120084.i	1.82768	+	4.53800i
$889$	−7518.68	−	4340.91i	−0.283654	−	0.163768i
$890$	14882.0	−	9404.52i	0.560499	−	0.354203i
$891$	−2657.45	+	4211.57i	−0.0999191	+	0.158353i
$892$	−67044.1	−	67044.1i	−2.51659	−	2.51659i
$893$	18969.3	−	5082.80i	0.710843	−	0.190470i
$894$	13377.7	−	31420.0i	0.500467	−	1.17544i
$895$	−8399.33	−	26982.9i	−0.313697	−	1.00775i
$896$	−18035.3	+	10412.7i	−0.672451	+	0.388240i
$897$	971.689	−	6859.31i	0.0361692	−	0.255324i
$898$	13118.2	+	48957.7i	0.487482	+	1.81931i
$899$	−6009.72			−0.222954
$900$	−23318.0	−	69871.4i	−0.863629	−	2.58783i
$901$	3109.78			0.114985
$902$	3742.59	+	13967.5i	0.138154	+	0.515596i
$903$	−5668.17	−	4438.48i	−0.208887	−	0.163570i
$904$	124100.	−	71648.9i	4.56581	−	2.63607i
$905$	7389.69	+	23739.5i	0.271427	+	0.871963i
$906$	46201.8	−	5621.42i	1.69421	−	0.206136i
$907$	40756.7	−	10920.7i	1.49207	−	0.399798i	0.581633	−	0.813452i	$-0.302414\pi$
$907$	40756.7	−	10920.7i	1.49207	−	0.399798i	0.910434	+	0.413653i	$0.135747\pi$
$908$	−41408.2	−	41408.2i	−1.51341	−	1.51341i
$909$	−38029.6	+	9393.26i	−1.38764	+	0.342745i
$910$	5705.07	−	3605.27i	0.207825	−	0.131333i
$911$	16299.0	+	9410.22i	0.592766	+	0.342233i	0.766190	−	0.642614i	$-0.222150\pi$
$911$	16299.0	+	9410.22i	0.592766	+	0.342233i	−0.173425	+	0.984847i	$0.555483\pi$
$912$	−73195.0	−	10368.8i	−2.65760	−	0.376475i
$913$	6353.80	+	1702.50i	0.230318	+	0.0617135i
$914$	8340.58	+	14446.3i	0.301840	+	0.522802i
$915$	−4163.54	+	676.406i	−0.150429	+	0.0244386i
$916$	52631.6	−	91160.6i	1.89847	−	3.28824i
$917$	4766.89	−	4766.89i	0.171665	−	0.171665i
$918$	−31687.2	+	22863.1i	−1.13925	+	0.821999i
$919$		−	44356.0i		−	1.59213i	−0.605211	−	0.796065i	$-0.706911\pi$
$919$		−	44356.0i		−	1.59213i	0.605211	−	0.796065i	$-0.293089\pi$
$920$	−32688.5	−	30174.2i	−1.17142	−	1.08132i
$921$	8233.81	+	3505.71i	0.294586	+	0.125426i
$922$	10983.7	−	40991.5i	0.392329	−	1.46419i
$923$	−3691.90	+	13778.4i	−0.131658	+	0.491354i
$924$	−2705.29	+	2033.93i	−0.0963177	+	0.0724151i
$925$	−40567.2	−	7459.40i	−1.44199	−	0.265150i
$926$			20895.4i			0.741540i
$927$	7716.33	−	4255.12i	0.273395	−	0.150762i
$928$	21704.3	−	21704.3i	0.767758	−	0.767758i
$929$	−13518.2	+	23414.2i	−0.477415	+	0.826907i	−0.999665	−	0.0258858i	$-0.991759\pi$
$929$	−13518.2	+	23414.2i	−0.477415	+	0.826907i	0.522250	+	0.852792i	$0.325093\pi$
$930$	−42910.3	−	4337.78i	−1.51300	−	0.152948i
$931$	9692.16	+	16787.3i	0.341190	+	0.590958i
$932$	29952.6	+	8025.78i	1.05272	+	0.282074i
$933$	−17240.3	+	22016.8i	−0.604955	+	0.772558i
$934$	20401.8	+	11779.0i	0.714740	+	0.412656i
$935$	2080.73	+	3292.60i	0.0727777	+	0.115165i
$936$	49544.0	+	14324.2i	1.73012	+	0.500216i
$937$	37452.3	+	37452.3i	1.30578	+	1.30578i	0.924432	+	0.381346i	$0.124539\pi$
$937$	37452.3	+	37452.3i	1.30578	+	1.30578i	0.381346	+	0.924432i	$0.375461\pi$
$938$	−4252.17	+	1139.37i	−0.148015	+	0.0396606i
$939$	15067.8	+	20041.3i	0.523661	+	0.696511i
$940$	−37233.8	+	70891.4i	−1.29195	+	2.45981i
$941$	−6297.33	+	3635.77i	−0.218158	+	0.125954i	−0.605097	−	0.796152i	$-0.706866\pi$
$941$	−6297.33	+	3635.77i	−0.218158	+	0.125954i	0.386939	+	0.922105i	$0.373532\pi$
$942$	−92255.2	+	37155.8i	−3.19091	+	1.28514i
$943$	−5286.89	−	19730.9i	−0.182571	−	0.681366i
$944$	−118356.			−4.08068
$945$	6784.55	−	965.812i	0.233546	−	0.0332464i
$946$	−11830.6			−0.406604
$947$	8758.51	+	32687.2i	0.300542	+	1.12164i	0.936715	+	0.350092i	$0.113850\pi$
$947$	8758.51	+	32687.2i	0.300542	+	1.12164i	−0.636173	+	0.771546i	$0.719484\pi$
$948$	22610.0	−	9106.20i	0.774620	−	0.311978i
$949$	2625.83	−	1516.02i	0.0898187	−	0.0518569i
$950$	26488.0	−	31102.3i	0.904614	−	1.06220i
$951$	−12032.1	−	16003.7i	−0.410272	−	0.545694i
$952$	−16249.3	+	4353.98i	−0.553195	+	0.148228i
$953$	−14114.4	−	14114.4i	−0.479760	−	0.479760i	0.425295	−	0.905055i	$-0.360170\pi$
$953$	−14114.4	−	14114.4i	−0.479760	−	0.479760i	−0.905055	+	0.425295i	$0.860170\pi$
$954$	−2156.07	−	8729.10i	−0.0731714	−	0.296242i
$955$	−6512.57	+	28876.2i	−0.220672	+	0.978442i
$956$	−125134.	−	72246.4i	−4.23341	−	2.44416i
$957$	967.471	−	1235.51i	0.0326791	−	0.0417329i
$958$	11552.4	+	3095.45i	0.389604	+	0.104394i
$959$	−270.087	−	467.805i	−0.00909445	−	0.0157520i
$960$	85049.5	−	69433.0i	2.85933	−	2.33431i
$961$	5655.88	−	9796.27i	0.189852	−	0.328833i
$962$	32237.6	−	32237.6i	1.08044	−	1.08044i
$963$	−925.698	+	47108.8i	−0.0309763	+	1.57639i
$964$		−	53520.1i		−	1.78814i
$965$	−459.152	−	11479.4i	−0.0153167	−	0.382939i
$966$	5222.38	−	3926.37i	0.173941	−	0.130775i
$967$	6670.89	−	24896.1i	0.221842	−	0.827926i	−0.761803	−	0.647809i	$-0.775686\pi$
$967$	6670.89	−	24896.1i	0.221842	−	0.827926i	0.983645	−	0.180117i	$-0.0576477\pi$
$968$	25097.7	−	93665.8i	0.833337	−	3.11005i
$969$	−14590.9	−	6212.39i	−0.483724	−	0.205955i
$970$	−68111.5	+	73787.1i	−2.25456	+	2.44243i
$971$		−	33741.6i		−	1.11516i	−0.830124	−	0.557579i	$-0.811730\pi$
$971$		−	33741.6i		−	1.11516i	0.830124	−	0.557579i	$-0.188270\pi$
$972$	63039.0	+	53488.0i	2.08022	+	1.76505i
$973$	−1099.97	+	1099.97i	−0.0362419	+	0.0362419i
$974$	−7043.75	+	12200.1i	−0.231721	+	0.401353i
$975$	−12303.5	+	10892.1i	−0.404130	+	0.357772i
$976$	−8630.65	−	14948.7i	−0.283054	−	0.490264i
$977$	18357.4	+	4918.86i	0.601132	+	0.161073i	0.546536	−	0.837436i	$-0.315946\pi$
$977$	18357.4	+	4918.86i	0.601132	+	0.161073i	0.0545961	+	0.998509i	$0.482613\pi$
$978$	−47942.2	−	6791.49i	−1.56751	−	0.222053i
$979$	1705.69	+	984.781i	0.0556835	+	0.0321489i
$980$	−77101.9	−	17389.1i	−2.51319	−	0.566811i
$981$	10801.1	+	11234.1i	0.351533	+	0.365625i
$982$	10430.8	+	10430.8i	0.338961	+	0.338961i
$983$	25071.7	−	6717.95i	0.813493	−	0.217975i	0.171994	−	0.985098i	$-0.444979\pi$
$983$	25071.7	−	6717.95i	0.813493	−	0.217975i	0.641500	+	0.767123i	$0.278313\pi$
$984$	150953.	−	18366.6i	4.89046	−	0.595027i
$985$	24287.7	+	12756.5i	0.785655	+	0.412645i
$986$	10663.2	−	6156.42i	0.344408	−	0.198844i
$987$	−5865.46	−	4592.97i	−0.189159	−	0.148122i
$988$	8552.17	+	31917.1i	0.275385	+	1.02775i
$989$	16712.3			0.537331
$990$	7799.67	−	8123.42i	0.250394	−	0.260787i
$991$	15779.5			0.505806			0.252903	−	0.967492i	$-0.418615\pi$
$991$	15779.5			0.505806			0.252903	+	0.967492i	$0.418615\pi$
$992$	−24428.0	−	91166.5i	−0.781844	−	2.91788i
$993$	3475.78	−	24536.1i	0.111078	−	0.784119i
$994$	−11650.7	+	6726.51i	−0.371767	+	0.214640i
$995$	−8156.63	+	2539.02i	−0.259882	+	0.0808969i
$996$	42779.4	−	100475.i	1.36096	−	3.19646i
$997$	−54082.7	+	14491.4i	−1.71797	+	0.460329i	−0.977356	−	0.211603i	$-0.932132\pi$
$997$	−54082.7	+	14491.4i	−1.71797	+	0.460329i	−0.740614	+	0.671931i	$0.765465\pi$
$998$	65146.6	+	65146.6i	2.06631	+	2.06631i
$999$	43274.2	−	16448.2i	1.37050	−	0.520918i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.4.l.a.2.1	✓	64
3.2	odd	2		135.4.m.a.62.16		64
5.2	odd	4		225.4.p.b.218.16		64
5.3	odd	4	inner	45.4.l.a.38.1	yes	64
5.4	even	2		225.4.p.b.182.16		64
9.4	even	3		135.4.m.a.17.16		64
9.5	odd	6	inner	45.4.l.a.32.1	yes	64
15.8	even	4		135.4.m.a.8.16		64
45.13	odd	12		135.4.m.a.98.16		64
45.14	odd	6		225.4.p.b.32.16		64
45.23	even	12	inner	45.4.l.a.23.1	yes	64
45.32	even	12		225.4.p.b.68.16		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.l.a.2.1	✓	64	1.1	even	1	trivial
45.4.l.a.23.1	yes	64	45.23	even	12	inner
45.4.l.a.32.1	yes	64	9.5	odd	6	inner
45.4.l.a.38.1	yes	64	5.3	odd	4	inner
135.4.m.a.8.16		64	15.8	even	4
135.4.m.a.17.16		64	9.4	even	3
135.4.m.a.62.16		64	3.2	odd	2
135.4.m.a.98.16		64	45.13	odd	12
225.4.p.b.32.16		64	45.14	odd	6
225.4.p.b.68.16		64	45.32	even	12
225.4.p.b.182.16		64	5.4	even	2
225.4.p.b.218.16		64	5.2	odd	4

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41347 - 5.27515i) q^{2} +(4.81992 - 1.94123i) q^{3} +(-18.9011 + 10.9125i) q^{4} +(-3.32298 - 10.6751i) q^{5} +(-17.0531 - 22.6819i) q^{6} +(-4.22008 + 1.13077i) q^{7} +(53.3880 + 53.3880i) q^{8} +(19.4633 - 18.7131i) q^{9} +O(q^{10})\)	\(q+(-1.41347 - 5.27515i) q^{2} +(4.81992 - 1.94123i) q^{3} +(-18.9011 + 10.9125i) q^{4} +(-3.32298 - 10.6751i) q^{5} +(-17.0531 - 22.6819i) q^{6} +(-4.22008 + 1.13077i) q^{7} +(53.3880 + 53.3880i) q^{8} +(19.4633 - 18.7131i) q^{9} +(-51.6158 + 32.6182i) q^{10} +(-5.91593 - 3.41556i) q^{11} +(-69.9180 + 89.2889i) q^{12} +(24.4368 + 6.54783i) q^{13} +(11.9299 + 20.6632i) q^{14} +(-36.7393 - 45.0025i) q^{15} +(118.867 - 205.883i) q^{16} +(36.0612 - 36.0612i) q^{17} +(-126.225 - 76.2213i) q^{18} -59.8443i q^{19} +(179.300 + 165.509i) q^{20} +(-18.1454 + 13.6423i) q^{21} +(-9.65561 + 36.0352i) q^{22} +(13.6398 - 50.9044i) q^{23} +(360.964 + 153.688i) q^{24} +(-102.916 + 70.9463i) q^{25} -138.163i q^{26} +(57.4851 - 127.978i) q^{27} +(67.4245 - 67.4245i) q^{28} +(-22.1046 + 38.2863i) q^{29} +(-185.465 + 257.415i) q^{30} +(67.9692 + 117.726i) q^{31} +(-670.646 - 179.699i) q^{32} +(-35.1447 - 4.97859i) q^{33} +(-241.199 - 139.257i) q^{34} +(26.0943 + 41.2922i) q^{35} +(-163.669 + 566.092i) q^{36} +(233.330 + 233.330i) q^{37} +(-315.688 + 84.5883i) q^{38} +(130.494 - 15.8774i) q^{39} +(392.515 - 747.330i) q^{40} +(335.678 - 193.804i) q^{41} +(97.6133 + 76.4365i) q^{42} +(82.0769 + 306.315i) q^{43} +149.090 q^{44} +(-264.440 - 145.589i) q^{45} -287.808 q^{46} +(84.9338 + 316.977i) q^{47} +(173.263 - 1223.09i) q^{48} +(-280.516 + 161.956i) q^{49} +(519.720 + 442.615i) q^{50} +(103.809 - 243.815i) q^{51} +(-533.336 + 142.907i) q^{52} +(43.1181 + 43.1181i) q^{53} +(-756.358 - 122.349i) q^{54} +(-16.8030 + 74.5030i) q^{55} +(-285.671 - 164.932i) q^{56} +(-116.171 - 288.445i) q^{57} +(233.210 + 62.4884i) q^{58} +(-248.925 - 431.152i) q^{59} +(1185.50 + 449.677i) q^{60} +(36.3039 - 62.8801i) q^{61} +(524.950 - 524.950i) q^{62} +(-60.9764 + 100.979i) q^{63} +1889.88i q^{64} +(-11.3043 - 282.624i) q^{65} +(23.4132 + 192.431i) q^{66} +(-47.7525 + 178.215i) q^{67} +(-288.076 + 1075.11i) q^{68} +(-33.0742 - 271.833i) q^{69} +(180.939 - 196.017i) q^{70} +563.835i q^{71} +(2038.16 + 40.0503i) q^{72} +(84.7460 - 84.7460i) q^{73} +(901.044 - 1560.65i) q^{74} +(-358.322 + 541.738i) q^{75} +(653.054 + 1131.12i) q^{76} +(28.8279 + 7.72441i) q^{77} +(-268.206 - 665.935i) q^{78} +(-186.138 - 107.467i) q^{79} +(-2592.82 - 584.770i) q^{80} +(28.6389 - 728.437i) q^{81} +(-1496.82 - 1496.82i) q^{82} +(-930.125 + 249.226i) q^{83} +(194.095 - 455.867i) q^{84} +(-504.787 - 265.126i) q^{85} +(1499.84 - 865.935i) q^{86} +(-32.2201 + 227.447i) q^{87} +(-133.490 - 498.190i) q^{88} -288.322 q^{89} +(-394.226 + 1600.75i) q^{90} -110.529 q^{91} +(297.690 + 1110.99i) q^{92} +(556.139 + 435.487i) q^{93} +(1552.05 - 896.076i) q^{94} +(-638.844 + 198.861i) q^{95} +(-3581.30 + 435.740i) q^{96} +(1588.58 - 425.658i) q^{97} +(1250.84 + 1250.84i) q^{98} +(-179.059 + 44.2274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 64 q - 6 q^{2} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 8 q^{10} - 36 q^{11} - 138 q^{12} - 2 q^{13} - 96 q^{15} + 316 q^{16} - 480 q^{18} + 378 q^{20} + 480 q^{21} - 34 q^{22} + 306 q^{23} - 146 q^{25} + 180 q^{27} - 232 q^{28} - 1170 q^{30} - 4 q^{31} - 1770 q^{32} - 294 q^{33} - 216 q^{36} + 136 q^{37} + 114 q^{38} + 126 q^{40} + 1992 q^{41} + 1698 q^{42} - 2 q^{43} + 1134 q^{45} - 952 q^{46} + 3462 q^{47} + 4326 q^{48} + 666 q^{50} - 2496 q^{51} - 242 q^{52} + 284 q^{55} - 7128 q^{56} - 2544 q^{57} + 534 q^{58} + 1818 q^{60} + 32 q^{61} - 4038 q^{63} - 2094 q^{65} + 2892 q^{66} + 610 q^{67} - 2694 q^{68} + 498 q^{70} - 1854 q^{72} - 8 q^{73} - 6408 q^{75} + 1368 q^{76} - 6486 q^{77} + 1434 q^{78} + 3012 q^{81} - 3784 q^{82} + 2814 q^{83} - 1658 q^{85} + 12480 q^{86} + 4830 q^{87} - 1338 q^{88} + 13914 q^{90} + 992 q^{91} + 13152 q^{92} + 8310 q^{93} + 4284 q^{95} - 7932 q^{96} + 358 q^{97}+O(q^{100}) \) 64 * q - 6 * q^2 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 8 * q^10 - 36 * q^11 - 138 * q^12 - 2 * q^13 - 96 * q^15 + 316 * q^16 - 480 * q^18 + 378 * q^20 + 480 * q^21 - 34 * q^22 + 306 * q^23 - 146 * q^25 + 180 * q^27 - 232 * q^28 - 1170 * q^30 - 4 * q^31 - 1770 * q^32 - 294 * q^33 - 216 * q^36 + 136 * q^37 + 114 * q^38 + 126 * q^40 + 1992 * q^41 + 1698 * q^42 - 2 * q^43 + 1134 * q^45 - 952 * q^46 + 3462 * q^47 + 4326 * q^48 + 666 * q^50 - 2496 * q^51 - 242 * q^52 + 284 * q^55 - 7128 * q^56 - 2544 * q^57 + 534 * q^58 + 1818 * q^60 + 32 * q^61 - 4038 * q^63 - 2094 * q^65 + 2892 * q^66 + 610 * q^67 - 2694 * q^68 + 498 * q^70 - 1854 * q^72 - 8 * q^73 - 6408 * q^75 + 1368 * q^76 - 6486 * q^77 + 1434 * q^78 + 3012 * q^81 - 3784 * q^82 + 2814 * q^83 - 1658 * q^85 + 12480 * q^86 + 4830 * q^87 - 1338 * q^88 + 13914 * q^90 + 992 * q^91 + 13152 * q^92 + 8310 * q^93 + 4284 * q^95 - 7932 * q^96 + 358 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more