LMFDB - Embedded newform 966.2.t.a.41.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(41,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("966.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.t (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			41.11
Character	$\chi$	$=$	966.41
Dual form			966.2.t.a.377.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281733 + 0.959493i) q^{2} +(-0.781340 + 1.54580i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.0180311 + 0.125409i) q^{5} +(-1.26306 - 1.18519i) q^{6} +(2.64141 - 0.151432i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-1.77902 - 2.41559i) q^{9} +O(q^{10})$	\(q+(-0.281733 + 0.959493i) q^{2} +(-0.781340 + 1.54580i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.0180311 + 0.125409i) q^{5} +(-1.26306 - 1.18519i) q^{6} +(2.64141 - 0.151432i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-1.77902 - 2.41559i) q^{9} +(-0.115249 - 0.0526324i) q^{10} +(0.317591 + 1.08162i) q^{11} +(1.49303 - 0.877989i) q^{12} +(2.03300 + 0.928439i) q^{13} +(-0.598874 + 2.57708i) q^{14} +(-0.179769 - 0.125859i) q^{15} +(0.415415 + 0.909632i) q^{16} +(4.76211 - 3.06042i) q^{17} +(2.81895 - 1.02640i) q^{18} +(3.58759 - 5.58240i) q^{19} +(0.0829698 - 0.0957522i) q^{20} +(-1.82976 + 4.20143i) q^{21} -1.12728 q^{22} +(-2.25699 + 4.23155i) q^{23} +(0.421789 + 1.67991i) q^{24} +(4.78206 + 1.40414i) q^{25} +(-1.46359 + 1.68908i) q^{26} +(5.12405 - 0.862611i) q^{27} +(-2.30397 - 1.30066i) q^{28} +(1.85215 + 2.88200i) q^{29} +(0.171408 - 0.137028i) q^{30} +(-6.20212 + 5.37417i) q^{31} +(-0.989821 + 0.142315i) q^{32} +(-1.92011 - 0.354176i) q^{33} +(1.59481 + 5.43143i) q^{34} +(-0.0286365 + 0.333987i) q^{35} +(0.190635 + 2.99394i) q^{36} +(0.128937 + 0.896779i) q^{37} +(4.34553 + 5.01501i) q^{38} +(-3.02365 + 2.41719i) q^{39} +(0.0684983 + 0.106585i) q^{40} +(1.09194 - 7.59460i) q^{41} +(-3.51574 - 2.93932i) q^{42} +(2.39542 - 2.76446i) q^{43} +(0.317591 - 1.08162i) q^{44} +(0.335014 - 0.179549i) q^{45} +(-3.42427 - 3.35773i) q^{46} +8.76363 q^{47} +(-1.73069 - 0.0685815i) q^{48} +(6.95414 - 0.799991i) q^{49} +(-2.69453 + 4.19276i) q^{50} +(1.00999 + 9.75252i) q^{51} +(-1.20831 - 1.88017i) q^{52} +(-6.88240 + 3.14309i) q^{53} +(-0.615943 + 5.15952i) q^{54} +(-0.141371 + 0.0203260i) q^{55} +(1.89708 - 1.84420i) q^{56} +(5.82617 + 9.90746i) q^{57} +(-3.28707 + 0.965170i) q^{58} +(-2.75302 + 6.02828i) q^{59} +(0.0831865 + 0.203070i) q^{60} +(-3.49548 + 3.02885i) q^{61} +(-3.40914 - 7.46497i) q^{62} +(-5.06492 - 6.11119i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.153091 + 0.238215i) q^{65} +(0.880787 - 1.74255i) q^{66} +(-6.84609 - 2.01019i) q^{67} -5.66073 q^{68} +(-4.77766 - 6.79514i) q^{69} +(-0.312390 - 0.121572i) q^{70} +(-1.46816 + 5.00010i) q^{71} +(-2.92637 - 0.660576i) q^{72} +(-2.43192 + 3.78414i) q^{73} +(-0.896779 - 0.128937i) q^{74} +(-5.90694 + 6.29502i) q^{75} +(-6.03615 + 2.75662i) q^{76} +(1.00268 + 2.80890i) q^{77} +(-1.46742 - 3.58217i) q^{78} +(-6.99561 + 15.3182i) q^{79} +(-0.121566 + 0.0356950i) q^{80} +(-2.67020 + 8.59477i) q^{81} +(6.97933 + 3.18735i) q^{82} +(-2.02520 - 14.0856i) q^{83} +(3.81075 - 2.54522i) q^{84} +(0.297938 + 0.652393i) q^{85} +(1.97762 + 3.07723i) q^{86} +(-5.90216 + 0.611237i) q^{87} +(0.948327 + 0.609453i) q^{88} +(5.38431 - 6.21382i) q^{89} +(0.0778911 + 0.372028i) q^{90} +(5.51058 + 2.14453i) q^{91} +(4.18645 - 2.33958i) q^{92} +(-3.46145 - 13.7863i) q^{93} +(-2.46900 + 8.40864i) q^{94} +(0.635393 + 0.550571i) q^{95} +(0.553396 - 1.64127i) q^{96} +(11.4832 + 1.65104i) q^{97} +(-1.19162 + 6.89783i) q^{98} +(2.04775 - 2.69138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q + 64 q^{4} + 8 q^{9}+O(q^{10}) $ 640 * q + 64 * q^4 + 8 * q^9	$ 640 q + 64 q^{4} + 8 q^{9} + 8 q^{15} - 64 q^{16} + 20 q^{18} + 54 q^{21} - 8 q^{22} - 56 q^{25} - 44 q^{30} - 8 q^{36} + 20 q^{37} - 16 q^{39} - 4 q^{42} - 28 q^{43} + 24 q^{46} - 68 q^{49} - 40 q^{51} + 32 q^{57} - 80 q^{58} - 8 q^{60} + 86 q^{63} + 64 q^{64} + 24 q^{67} + 72 q^{70} - 64 q^{72} - 8 q^{78} - 144 q^{79} + 20 q^{81} + 34 q^{84} + 32 q^{85} + 8 q^{88} - 40 q^{91} + 16 q^{93} + 68 q^{99}+O(q^{100}) $ 640 * q + 64 * q^4 + 8 * q^9 + 8 * q^15 - 64 * q^16 + 20 * q^18 + 54 * q^21 - 8 * q^22 - 56 * q^25 - 44 * q^30 - 8 * q^36 + 20 * q^37 - 16 * q^39 - 4 * q^42 - 28 * q^43 + 24 * q^46 - 68 * q^49 - 40 * q^51 + 32 * q^57 - 80 * q^58 - 8 * q^60 + 86 * q^63 + 64 * q^64 + 24 * q^67 + 72 * q^70 - 64 * q^72 - 8 * q^78 - 144 * q^79 + 20 * q^81 + 34 * q^84 + 32 * q^85 + 8 * q^88 - 40 * q^91 + 16 * q^93 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.281733	+	0.959493i	−0.199215	+	0.678464i
$2$	−0.281733	+	0.959493i	−0.199215	+	0.678464i
$3$	−0.781340	+	1.54580i	−0.451107	+	0.892470i
$3$	−0.781340	+	1.54580i	−0.451107	+	0.892470i
$4$	−0.841254	−	0.540641i	−0.420627	−	0.270320i
$5$	−0.0180311	+	0.125409i	−0.00806373	+	0.0560845i	−0.993456	−	0.114215i	$-0.963565\pi$
$5$	−0.0180311	+	0.125409i	−0.00806373	+	0.0560845i	0.985392	+	0.170300i	$0.0544737\pi$
$6$	−1.26306	−	1.18519i	−0.515642	−	0.483853i
$7$	2.64141	−	0.151432i	0.998361	−	0.0572360i
$7$	2.64141	−	0.151432i	0.998361	−	0.0572360i
$8$	0.755750	−	0.654861i	0.267198	−	0.231528i
$9$	−1.77902	−	2.41559i	−0.593006	−	0.805198i
$10$	−0.115249	−	0.0526324i	−0.0364449	−	0.0166438i
$11$	0.317591	+	1.08162i	0.0957573	+	0.326119i	0.993415	−	0.114575i	$-0.0365505\pi$
$11$	0.317591	+	1.08162i	0.0957573	+	0.326119i	−0.897657	+	0.440694i	$0.854732\pi$
$12$	1.49303	−	0.877989i	0.431000	−	0.253453i
$13$	2.03300	+	0.928439i	0.563852	+	0.257503i	0.676885	−	0.736089i	$-0.263329\pi$
$13$	2.03300	+	0.928439i	0.563852	+	0.257503i	−0.113033	+	0.993591i	$0.536057\pi$
$14$	−0.598874	+	2.57708i	−0.160056	+	0.688754i
$15$	−0.179769	−	0.125859i	−0.0464161	−	0.0324967i
$16$	0.415415	+	0.909632i	0.103854	+	0.227408i
$17$	4.76211	−	3.06042i	1.15498	−	0.742262i	0.184357	−	0.982859i	$-0.440980\pi$
$17$	4.76211	−	3.06042i	1.15498	−	0.742262i	0.970625	+	0.240598i	$0.0773434\pi$
$18$	2.81895	−	1.02640i	0.664434	−	0.241925i
$19$	3.58759	−	5.58240i	0.823050	−	1.28069i	−0.134063	−	0.990973i	$-0.542802\pi$
$19$	3.58759	−	5.58240i	0.823050	−	1.28069i	0.957112	−	0.289717i	$-0.0935613\pi$
$20$	0.0829698	−	0.0957522i	0.0185526	−	0.0214108i
$21$	−1.82976	+	4.20143i	−0.399286	+	0.916827i
$22$	−1.12728			−0.240337
$23$	−2.25699	+	4.23155i	−0.470615	+	0.882339i
$23$	−2.25699	+	4.23155i	−0.470615	+	0.882339i
$24$	0.421789	+	1.67991i	0.0860973	+	0.342910i
$25$	4.78206	+	1.40414i	0.956413	+	0.280828i
$26$	−1.46359	+	1.68908i	−0.287034	+	0.331255i
$27$	5.12405	−	0.862611i	0.986124	−	0.166010i
$28$	−2.30397	−	1.30066i	−0.435409	−	0.245802i
$29$	1.85215	+	2.88200i	0.343935	+	0.535174i	0.969529	−	0.244975i	$-0.0787797\pi$
$29$	1.85215	+	2.88200i	0.343935	+	0.535174i	−0.625594	+	0.780149i	$0.715143\pi$
$30$	0.171408	−	0.137028i	0.0312946	−	0.0250178i
$31$	−6.20212	+	5.37417i	−1.11393	+	0.965229i	−0.999602	−	0.0282135i	$-0.991018\pi$
$31$	−6.20212	+	5.37417i	−1.11393	+	0.965229i	−0.114332	+	0.993443i	$0.536473\pi$
$32$	−0.989821	+	0.142315i	−0.174977	+	0.0251579i
$33$	−1.92011	−	0.354176i	−0.334249	−	0.0616541i
$34$	1.59481	+	5.43143i	0.273508	+	0.931483i
$35$	−0.0286365	+	0.333987i	−0.00484046	+	0.0564541i
$36$	0.190635	+	2.99394i	0.0317725	+	0.498989i
$37$	0.128937	+	0.896779i	0.0211972	+	0.147429i	0.997671	−	0.0682049i	$-0.0217272\pi$
$37$	0.128937	+	0.896779i	0.0211972	+	0.147429i	−0.976474	+	0.215634i	$0.930818\pi$
$38$	4.34553	+	5.01501i	0.704938	+	0.813542i
$39$	−3.02365	+	2.41719i	−0.484171	+	0.387060i
$40$	0.0684983	+	0.106585i	0.0108305	+	0.0168526i
$41$	1.09194	−	7.59460i	0.170532	−	1.18608i	−0.707231	−	0.706983i	$-0.750056\pi$
$41$	1.09194	−	7.59460i	0.170532	−	1.18608i	0.877763	−	0.479095i	$-0.159035\pi$
$42$	−3.51574	−	2.93932i	−0.542490	−	0.453547i
$43$	2.39542	−	2.76446i	0.365298	−	0.421577i	−0.543109	−	0.839662i	$-0.682753\pi$
$43$	2.39542	−	2.76446i	0.365298	−	0.421577i	0.908408	+	0.418085i	$0.137299\pi$
$44$	0.317591	−	1.08162i	0.0478786	−	0.163060i
$45$	0.335014	−	0.179549i	0.0499410	−	0.0267655i
$46$	−3.42427	−	3.35773i	−0.504881	−	0.495071i
$47$	8.76363			1.27831			0.639153	−	0.769079i	$-0.279285\pi$
$47$	8.76363			1.27831			0.639153	+	0.769079i	$0.279285\pi$
$48$	−1.73069	−	0.0685815i	−0.249804	−	0.00989889i
$49$	6.95414	−	0.799991i	0.993448	−	0.114284i
$50$	−2.69453	+	4.19276i	−0.381063	+	0.592946i
$51$	1.00999	+	9.75252i	0.141426	+	1.36563i
$52$	−1.20831	−	1.88017i	−0.167563	−	0.260733i
$53$	−6.88240	+	3.14309i	−0.945370	+	0.431736i	−0.827608	−	0.561306i	$-0.810299\pi$
$53$	−6.88240	+	3.14309i	−0.945370	+	0.431736i	−0.117761	+	0.993042i	$0.537572\pi$
$54$	−0.615943	+	5.15952i	−0.0838193	+	0.702121i
$55$	−0.141371	+	0.0203260i	−0.0190624	+	0.00274076i
$56$	1.89708	−	1.84420i	0.253508	−	0.246442i
$57$	5.82617	+	9.90746i	0.771694	+	1.31227i
$58$	−3.28707	+	0.965170i	−0.431613	+	0.126733i
$59$	−2.75302	+	6.02828i	−0.358413	+	0.784816i	0.641431	+	0.767181i	$0.278341\pi$
$59$	−2.75302	+	6.02828i	−0.358413	+	0.784816i	−0.999844	+	0.0176350i	$0.994386\pi$
$60$	0.0831865	+	0.203070i	0.0107393	+	0.0262162i
$61$	−3.49548	+	3.02885i	−0.447551	+	0.387805i	−0.849271	−	0.527958i	$-0.822958\pi$
$61$	−3.49548	+	3.02885i	−0.447551	+	0.387805i	0.401720	+	0.915763i	$0.368412\pi$
$62$	−3.40914	−	7.46497i	−0.432961	−	0.948052i
$63$	−5.06492	−	6.11119i	−0.638120	−	0.769937i
$64$	0.142315	−	0.989821i	0.0177894	−	0.123728i
$65$	−0.153091	+	0.238215i	−0.0189887	+	0.0295469i
$66$	0.880787	−	1.74255i	0.108417	−	0.214493i
$67$	−6.84609	−	2.01019i	−0.836383	−	0.245584i	−0.164626	−	0.986356i	$-0.552642\pi$
$67$	−6.84609	−	2.01019i	−0.836383	−	0.245584i	−0.671757	+	0.740772i	$0.734460\pi$
$68$	−5.66073			−0.686465
$69$	−4.77766	−	6.79514i	−0.575163	−	0.818039i
$70$	−0.312390	−	0.121572i	−0.0373378	−	0.0145306i
$71$	−1.46816	+	5.00010i	−0.174239	+	0.593402i	0.825347	+	0.564625i	$0.190979\pi$
$71$	−1.46816	+	5.00010i	−0.174239	+	0.593402i	−0.999586	+	0.0287767i	$0.990839\pi$
$72$	−2.92637	−	0.660576i	−0.344876	−	0.0778497i
$73$	−2.43192	+	3.78414i	−0.284635	+	0.442900i	−0.953901	−	0.300123i	$-0.902972\pi$
$73$	−2.43192	+	3.78414i	−0.284635	+	0.442900i	0.669266	+	0.743023i	$0.266609\pi$
$74$	−0.896779	−	0.128937i	−0.104248	−	0.0149887i
$75$	−5.90694	+	6.29502i	−0.682075	+	0.726886i
$76$	−6.03615	+	2.75662i	−0.692393	+	0.316205i
$77$	1.00268	+	2.80890i	0.114266	+	0.320104i
$78$	−1.46742	−	3.58217i	−0.166152	−	0.405601i
$79$	−6.99561	+	15.3182i	−0.787067	+	1.72344i	−0.102206	+	0.994763i	$0.532590\pi$
$79$	−6.99561	+	15.3182i	−0.787067	+	1.72344i	−0.684861	+	0.728673i	$0.740137\pi$
$80$	−0.121566	+	0.0356950i	−0.0135915	+	0.00399083i
$81$	−2.67020	+	8.59477i	−0.296689	+	0.954974i
$82$	6.97933	+	3.18735i	0.770738	+	0.351984i
$83$	−2.02520	−	14.0856i	−0.222294	−	1.54609i	−0.729327	−	0.684165i	$-0.760167\pi$
$83$	−2.02520	−	14.0856i	−0.222294	−	1.54609i	0.507033	−	0.861927i	$-0.330742\pi$
$84$	3.81075	−	2.54522i	0.415787	−	0.277707i
$85$	0.297938	+	0.652393i	0.0323159	+	0.0707620i
$86$	1.97762	+	3.07723i	0.213252	+	0.331826i
$87$	−5.90216	+	0.611237i	−0.632778	+	0.0655315i
$88$	0.948327	+	0.609453i	0.101092	+	0.0649679i
$89$	5.38431	−	6.21382i	0.570735	−	0.658664i	−0.394851	−	0.918745i	$-0.629204\pi$
$89$	5.38431	−	6.21382i	0.570735	−	0.658664i	0.965587	+	0.260081i	$0.0837494\pi$
$90$	0.0778911	+	0.372028i	0.00821045	+	0.0392152i
$91$	5.51058	+	2.14453i	0.577666	+	0.224808i
$92$	4.18645	−	2.33958i	0.436467	−	0.243918i
$93$	−3.46145	−	13.7863i	−0.358935	−	1.42957i
$94$	−2.46900	+	8.40864i	−0.254658	+	0.867285i
$95$	0.635393	+	0.550571i	0.0651900	+	0.0564874i
$96$	0.553396	−	1.64127i	0.0564807	−	0.167511i
$97$	11.4832	+	1.65104i	1.16595	+	0.167638i	0.697986	−	0.716112i	$-0.254080\pi$
$97$	11.4832	+	1.65104i	1.16595	+	0.167638i	0.467961	+	0.883749i	$0.344989\pi$
$98$	−1.19162	+	6.89783i	−0.120372	+	0.696786i
$99$	2.04775	−	2.69138i	0.205806	−	0.270494i
$100$	−3.26379	−	3.76662i	−0.326379	−	0.376662i
$101$	0.765610	+	5.32493i	0.0761810	+	0.529851i	0.991800	+	0.127803i	$0.0407924\pi$
$101$	0.765610	+	5.32493i	0.0761810	+	0.529851i	−0.915619	+	0.402048i	$0.868298\pi$
$102$	−9.64202	−	1.77853i	−0.954702	−	0.176100i
$103$	1.32971	+	4.52856i	0.131020	+	0.446213i	0.998704	−	0.0509041i	$-0.0162103\pi$
$103$	1.32971	+	4.52856i	0.131020	+	0.446213i	−0.867684	+	0.497117i	$0.834392\pi$
$104$	2.14444	−	0.629663i	0.210279	−	0.0617435i
$105$	−0.493903	−	0.305224i	−0.0482000	−	0.0297868i
$106$	−1.07677	−	7.48912i	−0.104585	−	0.727408i
$107$	−10.3563	+	8.97380i	−1.00118	+	0.867530i	−0.991194	−	0.132421i	$-0.957725\pi$
$107$	−10.3563	+	8.97380i	−1.00118	+	0.867530i	−0.00998891	+	0.999950i	$0.503180\pi$
$108$	−4.77699	−	2.04460i	−0.459666	−	0.196741i
$109$	−4.54252	+	2.91930i	−0.435095	+	0.279618i	−0.739798	−	0.672829i	$-0.765079\pi$
$109$	−4.54252	+	2.91930i	−0.435095	+	0.279618i	0.304703	+	0.952447i	$0.401443\pi$
$110$	0.0203260	−	0.141371i	0.00193801	−	0.0134792i
$111$	−1.48699	−	0.501377i	−0.141139	−	0.0475886i
$112$	1.23503	+	2.33981i	0.116699	+	0.221091i
$113$	2.60839	−	8.88336i	0.245377	−	0.835677i	−0.741046	−	0.671454i	$-0.765670\pi$
$113$	2.60839	−	8.88336i	0.245377	−	0.835677i	0.986423	−	0.164223i	$-0.0525116\pi$
$114$	−11.1476	+	2.79891i	−1.04406	+	0.262142i
$115$	−0.489977	−	0.359346i	−0.0456906	−	0.0335091i
$116$		−	3.42584i		−	0.318081i
$117$	−1.37401	−	6.56261i	−0.127027	−	0.606713i
$118$	−5.00848	−	4.33987i	−0.461068	−	0.399518i
$119$	12.1153	−	8.80498i	1.11060	−	0.807152i
$120$	−0.218281	+	0.0226055i	−0.0199262	+	0.00206359i
$121$	8.18476	−	5.26003i	0.744069	−	0.478184i
$122$	−1.92137	−	4.20722i	−0.173953	−	0.380904i
$123$	10.8866	+	7.62189i	0.981611	+	0.687242i
$124$	8.12305	−	1.16792i	0.729472	−	0.104882i
$125$	−0.525479	+	1.15064i	−0.0470003	+	0.102916i
$126$	7.29059	−	3.13803i	0.649498	−	0.279558i
$127$	13.9805	−	4.10505i	1.24057	−	0.364265i	0.405341	−	0.914165i	$-0.367153\pi$
$127$	13.9805	−	4.10505i	1.24057	−	0.364265i	0.835230	+	0.549901i	$0.185335\pi$
$128$	0.909632	+	0.415415i	0.0804009	+	0.0367178i
$129$	2.40168	+	5.86284i	0.211456	+	0.516194i
$130$	−0.185435	−	0.214003i	−0.0162637	−	0.0187693i
$131$	2.33259	+	5.10767i	0.203800	+	0.446259i	0.983741	−	0.179594i	$-0.0574783\pi$
$131$	2.33259	+	5.10767i	0.203800	+	0.446259i	−0.779941	+	0.625853i	$0.784751\pi$
$132$	1.42382	+	1.33604i	0.123928	+	0.116288i
$133$	8.63095	−	15.2887i	0.748399	−	1.32570i
$134$	3.85753	−	6.00244i	0.333240	−	0.518532i
$135$	0.0157869	+	0.658154i	0.00135872	+	0.0566449i
$136$	1.59481	−	5.43143i	0.136754	−	0.465742i
$137$		−	9.50443i		−	0.812018i	−0.913869	−	0.406009i	$-0.866920\pi$
$137$		−	9.50443i		−	0.812018i	0.913869	−	0.406009i	$-0.133080\pi$
$138$	7.86591	−	2.66972i	0.669591	−	0.227262i
$139$			1.04387i			0.0885398i	0.999020	+	0.0442699i	$0.0140961\pi$
$139$			1.04387i			0.0885398i	−0.999020	+	0.0442699i	$0.985904\pi$
$140$	0.204657	−	0.265485i	0.0172967	−	0.0224376i
$141$	−6.84737	+	13.5468i	−0.576653	+	1.14085i
$142$	−4.38393	−	2.81738i	−0.367891	−	0.236429i
$143$	−0.358552	+	2.49379i	−0.0299837	+	0.208541i
$144$	1.45827	−	2.62173i	0.121523	−	0.218477i
$145$	−0.394824	+	0.180310i	−0.0327883	+	0.0149739i
$146$	−2.94571	−	3.39953i	−0.243788	−	0.281347i
$147$	−4.19691	+	11.3748i	−0.346156	+	0.938177i
$148$	0.376366	−	0.824127i	0.0309371	−	0.0677428i
$149$	−6.33494	−	21.5748i	−0.518979	−	1.76748i	−0.633162	−	0.774019i	$-0.718243\pi$
$149$	−6.33494	−	21.5748i	−0.518979	−	1.76748i	0.114184	−	0.993460i	$-0.463575\pi$
$150$	−4.37585	−	7.44118i	−0.357287	−	0.607570i
$151$	−2.81972	+	6.17433i	−0.229466	+	0.502459i	−0.988983	−	0.148027i	$-0.952708\pi$
$151$	−2.81972	+	6.17433i	−0.229466	+	0.502459i	0.759518	+	0.650487i	$0.225435\pi$
$152$	−0.944374	−	6.56827i	−0.0765989	−	0.532757i
$153$	−15.8646	−	6.05879i	−1.28258	−	0.489824i
$154$	−2.97761	+	0.170706i	−0.239943	+	0.0137559i
$155$	−0.562137	−	0.874702i	−0.0451519	−	0.0702577i
$156$	3.85048	−	0.398762i	0.308285	−	0.0319265i
$157$	−6.32591	+	9.84330i	−0.504862	+	0.785581i	−0.996355	−	0.0853005i	$-0.972815\pi$
$157$	−6.32591	+	9.84330i	−0.504862	+	0.785581i	0.491493	+	0.870882i	$0.336451\pi$
$158$	−12.7269	−	11.0279i	−1.01249	−	0.877331i
$159$	0.518897	−	13.0946i	0.0411512	−	1.03847i
$160$		−	0.126698i		−	0.0100164i
$161$	−5.32085	+	11.5190i	−0.419342	+	0.907828i
$162$	−7.49434	−	4.98346i	−0.588811	−	0.391538i
$163$	13.6684	+	4.01341i	1.07059	+	0.314355i	0.769110	−	0.639117i	$-0.220700\pi$
$163$	13.6684	+	4.01341i	1.07059	+	0.314355i	0.301484	+	0.953471i	$0.402518\pi$
$164$	−5.02455	+	5.79864i	−0.392351	+	0.452798i
$165$	0.0790384	−	0.234413i	0.00615313	−	0.0182490i
$166$	14.0856	+	2.02520i	1.09325	+	0.157186i
$167$	0.359697	−	0.231164i	0.0278342	−	0.0178880i	−0.526650	−	0.850082i	$-0.676552\pi$
$167$	0.359697	−	0.231164i	0.0278342	−	0.0178880i	0.554484	+	0.832194i	$0.312916\pi$
$168$	1.36851	+	4.37346i	0.105583	+	0.337420i
$169$	−5.24211	−	6.04972i	−0.403239	−	0.465363i
$170$	−0.709905	+	0.102069i	−0.0544473	+	0.00782833i
$171$	−19.8672	+	1.26502i	−1.51928	+	0.0967384i
$172$	−3.50974	+	1.03055i	−0.267615	+	0.0785789i
$173$	3.90463	−	1.14650i	0.296863	−	0.0871670i	−0.129909	−	0.991526i	$-0.541469\pi$
$173$	3.90463	−	1.14650i	0.296863	−	0.0871670i	0.426773	+	0.904359i	$0.359650\pi$
$174$	1.07635	−	5.83529i	0.0815981	−	0.442372i
$175$	12.8440	+	2.98476i	0.970918	+	0.225626i
$176$	−0.851940	+	0.738210i	−0.0642174	+	0.0556447i
$177$	−7.16749	−	8.96577i	−0.538742	−	0.673909i
$178$	4.44518	+	6.91684i	0.333181	+	0.518439i
$179$	20.3538	+	2.92643i	1.52131	+	0.218732i	0.851721	−	0.523996i	$-0.175559\pi$
$179$	20.3538	+	2.92643i	1.52131	+	0.218732i	0.669593	+	0.742728i	$0.266469\pi$
$180$	−0.378903	−	0.0300765i	−0.0282418	−	0.00224177i
$181$	5.39226	+	4.67242i	0.400803	+	0.347298i	0.831820	−	0.555046i	$-0.187299\pi$
$181$	5.39226	+	4.67242i	0.400803	+	0.347298i	−0.431016	+	0.902344i	$0.641845\pi$
$182$	−3.61017	+	4.68318i	−0.267604	+	0.347141i
$183$	−1.95085	−	7.76989i	−0.144211	−	0.574367i
$184$	1.06535	+	4.67600i	0.0785389	+	0.344720i
$185$	−0.114789			−0.00843943
$186$	14.2031	+	0.562820i	1.04142	+	0.0412679i
$187$	4.82261	+	4.17881i	0.352664	+	0.305585i
$188$	−7.37243	−	4.73798i	−0.537690	−	0.345552i
$189$	13.4041	−	3.05446i	0.975006	−	0.222179i
$190$	−0.707280	+	0.454542i	−0.0513115	+	0.0329759i
$191$	5.86503	−	2.67847i	0.424379	−	0.193807i	−0.191765	−	0.981441i	$-0.561421\pi$
$191$	5.86503	−	2.67847i	0.424379	−	0.193807i	0.616144	+	0.787634i	$0.288694\pi$
$192$	1.41887	+	0.993377i	0.102398	+	0.0716908i
$193$	−1.61871	−	11.2584i	−0.116517	−	0.810397i	−0.961343	−	0.275355i	$-0.911205\pi$
$193$	−1.61871	−	11.2584i	−0.116517	−	0.810397i	0.844825	−	0.535042i	$-0.179704\pi$
$194$	−4.81936	+	10.5529i	−0.346010	+	0.757657i
$195$	−0.248617	−	0.422776i	−0.0178038	−	0.0302756i
$196$	−6.28270	−	3.08670i	−0.448764	−	0.220478i
$197$	5.09706	+	2.32775i	0.363151	+	0.165845i	0.588630	−	0.808403i	$-0.299667\pi$
$197$	5.09706	+	2.32775i	0.363151	+	0.165845i	−0.225479	+	0.974248i	$0.572395\pi$
$198$	2.00545	+	2.72305i	0.142521	+	0.193519i
$199$	7.64563	−	6.62498i	0.541985	−	0.469632i	−0.340321	−	0.940309i	$-0.610536\pi$
$199$	7.64563	−	6.62498i	0.541985	−	0.469632i	0.882306	+	0.470677i	$0.155990\pi$
$200$	4.53356	−	2.07041i	0.320571	−	0.146400i
$201$	8.45648	−	9.01207i	0.596474	−	0.635662i
$202$	−5.32493	−	0.765610i	−0.374661	−	0.0538681i
$203$	5.32872	+	7.33208i	0.374003	+	0.514611i
$204$	4.42296	−	8.75038i	0.309669	−	0.612649i
$205$	0.932740	+	0.273877i	0.0651454	+	0.0191284i
$206$	−4.71975			−0.328840
$207$	14.2369	−	2.07602i	0.989535	−	0.144293i
$208$			2.23497i			0.154967i
$209$	7.17740	+	2.10747i	0.496471	+	0.145777i
$210$	0.432008	−	0.387905i	0.0298114	−	0.0267680i
$211$	22.7295	+	14.6073i	1.56476	+	1.00561i	0.981074	+	0.193632i	$0.0620267\pi$
$211$	22.7295	+	14.6073i	1.56476	+	1.00561i	0.583687	+	0.811979i	$0.301610\pi$
$212$	7.48912	+	1.07677i	0.514355	+	0.0739531i
$213$	−6.58203	−	6.17626i	−0.450994	−	0.423190i
$214$	−5.69258	−	12.4650i	−0.389137	−	0.852091i
$215$	0.303496	+	0.350253i	0.0206982	+	0.0238871i
$216$	3.30761	−	4.00746i	0.225054	−	0.272673i
$217$	−15.5685	+	15.1346i	−1.05686	+	1.02740i
$218$	−1.52127	−	5.18098i	−0.103034	−	0.350900i
$219$	−3.94939	−	6.71597i	−0.266875	−	0.453823i
$220$	0.129918	+	0.0593313i	0.00875904	+	0.00400012i
$221$	12.5228	−	1.80050i	0.842373	−	0.121115i
$222$	0.900000	−	1.28550i	0.0604041	−	0.0862771i
$223$	23.6029	−	10.7791i	1.58057	−	0.721822i	0.584584	−	0.811333i	$-0.301258\pi$
$223$	23.6029	−	10.7791i	1.58057	−	0.721822i	0.995986	+	0.0895115i	$0.0285306\pi$
$224$	−2.59298	+	0.525803i	−0.173251	+	0.0351317i
$225$	−5.11554	−	14.0495i	−0.341036	−	0.936634i
$226$	7.78866	+	5.00547i	0.518094	+	0.332959i
$227$	−7.23542	+	8.35012i	−0.480231	+	0.554217i	−0.943229	−	0.332143i	$-0.892228\pi$
$227$	−7.23542	+	8.35012i	−0.480231	+	0.554217i	0.462998	+	0.886360i	$0.346774\pi$
$228$	0.455094	−	11.4845i	0.0301393	−	0.760583i
$229$			4.09503i			0.270607i	0.990804	+	0.135304i	$0.0432010\pi$
$229$			4.09503i			0.270607i	−0.990804	+	0.135304i	$0.956799\pi$
$230$	0.482832	−	0.368890i	0.0318370	−	0.0243239i
$231$	−5.12544	−	0.644758i	−0.337229	−	0.0424220i
$232$	3.28707	+	0.965170i	0.215807	+	0.0633665i
$233$	−2.21691	−	1.92097i	−0.145235	−	0.125847i	0.579213	−	0.815176i	$-0.303360\pi$
$233$	−2.21691	−	1.92097i	−0.145235	−	0.125847i	−0.724448	+	0.689329i	$0.757905\pi$
$234$	6.68388	+	0.530552i	0.436939	+	0.0346833i
$235$	−0.158017	+	1.09904i	−0.0103079	+	0.0716932i
$236$	5.57513	−	3.58292i	0.362910	−	0.233228i
$237$	−18.2130	−	22.7826i	−1.18306	−	1.47989i
$238$	5.03506	+	14.1052i	0.326374	+	0.914302i
$239$	−7.61131	+	1.09434i	−0.492334	+	0.0707870i	−0.384011	−	0.923329i	$-0.625457\pi$
$239$	−7.61131	+	1.09434i	−0.492334	+	0.0707870i	−0.108324	+	0.994116i	$0.534548\pi$
$240$	0.0398069	−	0.215807i	0.00256953	−	0.0139303i
$241$	−3.16443	−	10.7771i	−0.203839	−	0.694212i	−0.996427	−	0.0844550i	$-0.973085\pi$
$241$	−3.16443	−	10.7771i	−0.203839	−	0.694212i	0.792588	−	0.609757i	$-0.208733\pi$
$242$	2.74104	+	9.33514i	0.176201	+	0.600086i
$243$	−11.1995	−	10.8430i	−0.718448	−	0.695581i
$244$	4.57811	−	0.658233i	0.293083	−	0.0421390i
$245$	−0.0250646	+	0.886534i	−0.00160132	+	0.0566386i
$246$	−10.3803	+	8.29827i	−0.661821	+	0.529078i
$247$	12.4765	−	8.01815i	0.793859	−	0.510182i
$248$	−1.16792	+	8.12305i	−0.0741629	+	0.515814i
$249$	23.3559	+	7.87505i	1.48012	+	0.499061i
$250$	−0.955985	−	0.828366i	−0.0604618	−	0.0523904i
$251$	−29.5794	−	8.68529i	−1.86703	−	0.548211i	−0.998628	−	0.0523560i	$-0.983327\pi$
$251$	−29.5794	−	8.68529i	−1.86703	−	0.548211i	−0.868406	−	0.495855i	$-0.834855\pi$
$252$	0.956925	+	7.87936i	0.0602806	+	0.496353i
$253$	−5.29371	−	1.09730i	−0.332813	−	0.0689864i
$254$			14.5707i			0.914250i
$255$	−1.24126	−	0.0491870i	−0.0777308	−	0.00308021i
$256$	−0.654861	+	0.755750i	−0.0409288	+	0.0472343i
$257$	−18.4636	−	11.8658i	−1.15173	−	0.740171i	−0.181746	−	0.983346i	$-0.558175\pi$
$257$	−18.4636	−	11.8658i	−1.15173	−	0.740171i	−0.969983	+	0.243175i	$0.921811\pi$
$258$	−6.30198	+	0.652644i	−0.392344	+	0.0406318i
$259$	0.476378	+	2.34924i	0.0296007	+	0.145975i
$260$	0.257577	−	0.117632i	0.0159743	−	0.00729521i
$261$	3.66674	−	9.60116i	0.226965	−	0.594297i
$262$	−5.55794	+	0.799111i	−0.343371	+	0.0493693i
$263$	−4.78554	−	2.18548i	−0.295089	−	0.134763i	0.262369	−	0.964968i	$-0.415496\pi$
$263$	−4.78554	−	2.18548i	−0.295089	−	0.134763i	−0.557458	+	0.830205i	$0.688223\pi$
$264$	−1.68306	+	0.989738i	−0.103585	+	0.0609141i
$265$	−0.270073	−	0.919786i	−0.0165905	−	0.0565020i
$266$	12.2378	+	12.5887i	0.750347	+	0.771861i
$267$	5.39837	+	13.1782i	0.330375	+	0.806492i
$268$	4.67250	+	5.39236i	0.285419	+	0.329391i
$269$	−5.02765	−	11.0090i	−0.306541	−	0.671232i	0.692183	−	0.721722i	$-0.256649\pi$
$269$	−5.02765	−	11.0090i	−0.306541	−	0.671232i	−0.998725	+	0.0504898i	$0.983922\pi$
$270$	−0.635942	−	0.170276i	−0.0387022	−	0.0103627i
$271$	−0.551143	−	0.0792424i	−0.0334795	−	0.00481363i	0.125555	−	0.992087i	$-0.459929\pi$
$271$	−0.551143	−	0.0792424i	−0.0334795	−	0.00481363i	−0.159034	+	0.987273i	$0.550838\pi$
$272$	4.76211	+	3.06042i	0.288745	+	0.185565i
$273$	−7.62066	+	6.84267i	−0.461223	+	0.414138i
$274$	9.11944	+	2.67771i	0.550925	+	0.161766i
$275$			5.61830i			0.338796i
$276$	0.345497	+	8.29944i	0.0207965	+	0.499567i
$277$	−19.8559			−1.19303			−0.596514	−	0.802603i	$-0.703448\pi$
$277$	−19.8559			−1.19303			−0.596514	+	0.802603i	$0.703448\pi$
$278$	−1.00158	−	0.294092i	−0.0600710	−	0.0176384i
$279$	24.0155	+	5.42108i	1.43777	+	0.324551i
$280$	0.197073	+	0.271163i	0.0117774	+	0.0162051i
$281$	−8.99921	−	1.29389i	−0.536848	−	0.0771871i	−0.131442	−	0.991324i	$-0.541961\pi$
$281$	−8.99921	−	1.29389i	−0.536848	−	0.0771871i	−0.405406	+	0.914137i	$0.632870\pi$
$282$	−11.0690	−	10.3866i	−0.659148	−	0.618512i
$283$	−23.8291	+	10.8824i	−1.41649	+	0.646891i	−0.968924	−	0.247359i	$-0.920437\pi$
$283$	−23.8291	+	10.8824i	−1.41649	+	0.646891i	−0.447569	+	0.894249i	$0.647710\pi$
$284$	3.93835	−	3.41260i	0.233698	−	0.202501i
$285$	−1.34753	+	0.552010i	−0.0798210	+	0.0326983i
$286$	−2.29175	−	1.04661i	−0.135514	−	0.0618873i
$287$	1.73420	−	20.2258i	0.102366	−	1.19389i
$288$	2.10468	+	2.13783i	0.124020	+	0.125973i
$289$	6.24946	−	13.6844i	0.367616	−	0.804966i
$290$	−0.0617715	−	0.429630i	−0.00362735	−	0.0252287i
$291$	−11.5245	+	16.4608i	−0.675578	+	0.964950i
$292$	4.09172	−	1.86863i	0.239450	−	0.109353i
$293$	24.5877	−	15.8015i	1.43643	−	0.923136i	0.436705	−	0.899605i	$-0.356145\pi$
$293$	24.5877	−	15.8015i	1.43643	−	0.923136i	0.999723	−	0.0235316i	$-0.00749104\pi$
$294$	−9.73163	−	7.23156i	−0.567560	−	0.421753i
$295$	−0.706359	−	0.453950i	−0.0411258	−	0.0264300i
$296$	0.684709	+	0.593304i	0.0397979	+	0.0344851i
$297$	2.56037	+	5.26830i	0.148568	+	0.305698i
$298$	22.4857			1.30256
$299$	−8.51719	+	6.50725i	−0.492562	+	0.376324i
$300$	8.37258	−	2.10217i	0.483391	−	0.121369i
$301$	5.90867	−	7.66484i	0.340570	−	0.441794i
$302$	−5.12981	−	4.44501i	−0.295188	−	0.255782i
$303$	−8.82950	−	2.97710i	−0.507242	−	0.171030i
$304$	6.56827	+	0.944374i	0.376716	+	0.0541636i
$305$	−0.316817	−	0.492977i	−0.0181409	−	0.0282278i
$306$	10.2829	−	13.5150i	0.587837	−	0.772603i
$307$	−17.3987	+	15.0761i	−0.992996	+	0.860436i	−0.990214	−	0.139560i	$-0.955431\pi$
$307$	−17.3987	+	15.0761i	−0.992996	+	0.860436i	−0.00278275	+	0.999996i	$0.500886\pi$
$308$	0.675098	−	2.90509i	0.0384673	−	0.165533i
$309$	−8.03922	−	1.48288i	−0.457335	−	0.0843582i
$310$	0.997643	−	0.292934i	0.0566623	−	0.0166375i
$311$	21.5107	−	6.31610i	1.21976	−	0.358153i	0.392382	−	0.919802i	$-0.371651\pi$
$311$	21.5107	−	6.31610i	1.21976	−	0.358153i	0.827376	+	0.561649i	$0.189833\pi$
$312$	−0.702197	+	3.80686i	−0.0397541	+	0.215521i
$313$	−23.3924	+	3.36333i	−1.32222	+	0.190106i	−0.767027	−	0.641615i	$-0.778265\pi$
$313$	−23.3924	+	3.36333i	−1.32222	+	0.190106i	−0.555193	+	0.831722i	$0.687355\pi$
$314$	−7.66236	−	8.84284i	−0.432412	−	0.499030i
$315$	0.857722	−	0.524994i	0.0483271	−	0.0295801i
$316$	14.1667	−	9.10441i	0.796942	−	0.512163i
$317$	−13.1154	−	1.88571i	−0.736635	−	0.105912i	−0.236222	−	0.971699i	$-0.575909\pi$
$317$	−13.1154	−	1.88571i	−0.736635	−	0.105912i	−0.500413	+	0.865787i	$0.666818\pi$
$318$	12.4180	+	4.18707i	0.696369	+	0.234799i
$319$	−2.52899	+	2.91861i	−0.141596	+	0.163411i
$320$	0.121566	+	0.0356950i	0.00679575	+	0.00199541i
$321$	−5.77993	−	23.0204i	−0.322604	−	1.28487i
$322$	−9.55339	−	8.35061i	−0.532390	−	0.465362i
$323$		−	37.5636i		−	2.09009i
$324$	6.89300	−	5.78676i	0.382944	−	0.321487i
$325$	8.41826	+	7.29447i	0.466961	+	0.404624i
$326$	−7.70168	+	11.9840i	−0.426557	+	0.663735i
$327$	−0.963415	−	9.30281i	−0.0532769	−	0.514447i
$328$	−4.14817	−	6.45469i	−0.229045	−	0.356400i
$329$	23.1484	−	1.32710i	1.27621	−	0.0731652i
$330$	0.202650	+	0.141878i	0.0111555	+	0.00781015i
$331$	0.531616	+	3.69747i	0.0292202	+	0.203231i	0.999202	−	0.0399473i	$-0.0127190\pi$
$331$	0.531616	+	3.69747i	0.0292202	+	0.203231i	−0.969982	+	0.243178i	$0.921810\pi$
$332$	−5.91153	+	12.9444i	−0.324437	+	0.710419i
$333$	1.93687	−	1.90684i	0.106140	−	0.104494i
$334$	0.120461	+	0.410253i	0.00659135	+	0.0224481i
$335$	0.375538	−	0.822313i	0.0205178	−	0.0449278i
$336$	−4.58186	+	0.0809306i	−0.249961	+	0.00441512i
$337$	−22.7381	−	26.2411i	−1.23862	−	1.42945i	−0.864930	−	0.501893i	$-0.832637\pi$
$337$	−22.7381	−	26.2411i	−1.23862	−	1.42945i	−0.373692	−	0.927553i	$-0.621908\pi$
$338$	7.28153	−	3.32536i	0.396063	−	0.180876i
$339$	11.6939	+	10.9730i	0.635125	+	0.595971i
$340$	0.102069	−	0.709905i	0.00553547	−	0.0385000i
$341$	−7.78252	−	5.00152i	−0.421447	−	0.270848i
$342$	4.38346	−	19.4188i	0.237030	−	1.05005i
$343$	18.2476	−	3.16619i	0.985278	−	0.170958i
$344$		−	3.65791i		−	0.197221i
$345$	0.938316	−	0.476637i	0.0505172	−	0.0256613i
$346$			4.06947i			0.218776i
$347$	−9.71212	+	33.0765i	−0.521374	+	1.77564i	0.103188	+	0.994662i	$0.467096\pi$
$347$	−9.71212	+	33.0765i	−0.521374	+	1.77564i	−0.624562	+	0.780975i	$0.714722\pi$
$348$	5.29567	+	2.67674i	0.283878	+	0.143489i
$349$	3.28867	−	5.11727i	0.176038	−	0.273921i	−0.742011	−	0.670388i	$-0.766128\pi$
$349$	3.28867	−	5.11727i	0.176038	−	0.273921i	0.918049	+	0.396467i	$0.129764\pi$
$350$	−6.48244	+	11.4829i	−0.346501	+	0.613785i
$351$	11.2181	+	3.00368i	0.598776	+	0.160325i
$352$	−0.468288	−	1.02541i	−0.0249599	−	0.0546545i
$353$	11.1348	+	12.8503i	0.592646	+	0.683950i	0.970275	−	0.242007i	$-0.0778057\pi$
$353$	11.1348	+	12.8503i	0.592646	+	0.683950i	−0.377628	+	0.925957i	$0.623260\pi$
$354$	10.6219	−	4.35121i	0.564548	−	0.231264i
$355$	−0.600583	−	0.274277i	−0.0318756	−	0.0145571i
$356$	−7.88901	+	2.31642i	−0.418117	+	0.122770i
$357$	4.14464	+	25.6075i	0.219358	+	1.35529i
$358$	−8.54222	+	18.7048i	−0.451470	+	0.988582i
$359$	−0.551320	+	0.0792678i	−0.0290975	+	0.00418360i	−0.156848	−	0.987623i	$-0.550133\pi$
$359$	−0.551320	+	0.0792678i	−0.0290975	+	0.00418360i	0.127751	+	0.991806i	$0.459224\pi$
$360$	0.135608	−	0.355081i	0.00714715	−	0.0187144i
$361$	−10.3995	−	22.7717i	−0.547341	−	1.19851i
$362$	−6.00233	+	3.85746i	−0.315475	+	0.202744i
$363$	1.73589	+	16.7619i	0.0911106	+	0.879771i
$364$	−3.47638	−	4.78334i	−0.182212	−	0.250715i
$365$	−0.430714	−	0.373216i	−0.0225446	−	0.0195350i
$366$	8.00477	+	0.317202i	0.418416	+	0.0165804i
$367$		−	0.367551i		−	0.0191860i	−0.999954	−	0.00959301i	$-0.996946\pi$
$367$		−	0.367551i		−	0.0191860i	0.999954	−	0.00959301i	$-0.00305360\pi$
$368$	−4.78674	−	0.295183i	−0.249526	−	0.0153875i
$369$	−20.2881	+	10.8732i	−1.05615	+	0.566038i
$370$	0.0323397	−	0.110139i	0.00168126	−	0.00572585i
$371$	−17.7033	+	9.34441i	−0.919109	+	0.485137i
$372$	−4.54149	+	13.4692i	−0.235465	+	0.698345i
$373$	−4.05489	+	28.2024i	−0.209954	+	1.46027i	0.563344	+	0.826223i	$0.309515\pi$
$373$	−4.05489	+	28.2024i	−0.209954	+	1.46027i	−0.773298	+	0.634043i	$0.781394\pi$
$374$	−5.36823	+	3.44995i	−0.277584	+	0.178393i
$375$	−1.36808	−	1.71133i	−0.0706475	−	0.0883725i
$376$	6.62311	−	5.73896i	0.341561	−	0.295964i
$377$	1.08965	+	7.57870i	0.0561200	+	0.390323i
$378$	−0.845644	+	13.7217i	−0.0434952	+	0.705768i
$379$	−16.6798	+	4.89763i	−0.856783	+	0.251574i	−0.680485	−	0.732762i	$-0.738231\pi$
$379$	−16.6798	+	4.89763i	−0.856783	+	0.251574i	−0.176299	+	0.984337i	$0.556412\pi$
$380$	−0.236866	−	0.806690i	−0.0121509	−	0.0413823i
$381$	−4.57793	+	24.8186i	−0.234535	+	1.27149i
$382$	0.917603	+	6.38207i	0.0469486	+	0.326535i
$383$	−15.5815	−	17.9820i	−0.796177	−	0.918837i	0.201988	−	0.979388i	$-0.435260\pi$
$383$	−15.5815	−	17.9820i	−0.796177	−	0.918837i	−0.998165	+	0.0605509i	$0.980714\pi$
$384$	−1.35288	+	1.08153i	−0.0690389	+	0.0551917i
$385$	−0.370340	+	0.0750975i	−0.0188743	+	0.00382732i
$386$	11.2584	+	1.61871i	0.573037	+	0.0823903i
$387$	−10.9393	−	0.868340i	−0.556077	−	0.0441402i
$388$	−8.76770	−	7.59725i	−0.445112	−	0.385692i
$389$	0.478529	−	1.62972i	0.0242624	−	0.0826300i	−0.946472	−	0.322786i	$-0.895380\pi$
$389$	0.478529	−	1.62972i	0.0242624	−	0.0826300i	0.970734	+	0.240156i	$0.0771987\pi$
$390$	0.475694	−	0.119437i	0.0240877	−	0.00604790i
$391$	2.20228	+	27.0585i	0.111374	+	1.36840i
$392$	4.73170	−	5.15858i	0.238987	−	0.260548i
$393$	−9.71800	−	0.385092i	−0.490208	−	0.0194253i
$394$	−3.66947	+	4.23479i	−0.184865	+	0.213346i
$395$	−1.79490	−	1.15351i	−0.0903114	−	0.0580396i
$396$	−3.17775	+	1.15704i	−0.159688	+	0.0581435i
$397$	−12.1323	−	18.8783i	−0.608904	−	0.947473i	−0.999636	−	0.0269690i	$-0.991414\pi$
$397$	−12.1323	−	18.8783i	−0.608904	−	0.947473i	0.390732	−	0.920504i	$-0.372222\pi$
$398$	4.20260	+	9.20240i	0.210657	+	0.461275i
$399$	16.8896	+	25.2874i	0.845539	+	1.26595i
$400$	0.709290	+	4.93322i	0.0354645	+	0.246661i
$401$	26.9624	+	12.3133i	1.34644	+	0.614897i	0.952584	−	0.304276i	$-0.0984145\pi$
$401$	26.9624	+	12.3133i	1.34644	+	0.614897i	0.393853	+	0.919173i	$0.371142\pi$
$402$	6.26455	+	10.6529i	0.312447	+	0.531320i
$403$	−17.5985	+	5.16738i	−0.876643	+	0.257406i
$404$	2.23480	−	4.89354i	0.111186	−	0.243463i
$405$	−1.02971	−	0.489839i	−0.0511668	−	0.0243403i
$406$	−8.53635	+	3.04718i	−0.423652	+	0.151229i
$407$	−0.929020	+	0.424269i	−0.0460498	+	0.0210303i
$408$	7.14984	+	6.70906i	0.353970	+	0.332148i
$409$	−18.9628	−	2.72645i	−0.937652	−	0.134814i	−0.343487	−	0.939157i	$-0.611608\pi$
$409$	−18.9628	−	2.72645i	−0.937652	−	0.134814i	−0.594165	+	0.804343i	$0.702517\pi$
$410$	−0.525567	+	0.817798i	−0.0259559	+	0.0403882i
$411$	14.6920	+	7.42619i	0.724702	+	0.366307i
$412$	1.32971	−	4.52856i	0.0655099	−	0.223106i
$413$	−6.35900	+	16.3401i	−0.312906	+	0.804043i
$414$	−2.01908	+	14.2451i	−0.0992324	+	0.700109i
$415$	1.80297			0.0885043
$416$	−2.14444	−	0.629663i	−0.105140	−	0.0308718i
$417$	−1.61362	−	0.815616i	−0.0790191	−	0.0399409i
$418$	−4.04421	+	6.29292i	−0.197809	+	0.307797i
$419$	4.50619	−	31.3412i	0.220142	−	1.53112i	−0.517357	−	0.855770i	$-0.673084\pi$
$419$	4.50619	−	31.3412i	0.220142	−	1.53112i	0.737498	−	0.675349i	$-0.236007\pi$
$420$	0.250481	+	0.523795i	0.0122222	+	0.0255586i
$421$	−13.0117	−	28.4917i	−0.634153	−	1.38860i	−0.904765	−	0.425912i	$-0.859953\pi$
$421$	−13.0117	−	28.4917i	−0.634153	−	1.38860i	0.270612	−	0.962688i	$-0.412774\pi$
$422$	−20.4193	+	17.6934i	−0.993995	+	0.861301i
$423$	−15.5906	−	21.1694i	−0.758043	−	1.02929i
$424$	−3.14309	+	6.88240i	−0.152642	+	0.334239i
$425$	27.0700	−	7.94846i	1.31309	−	0.385557i
$426$	7.78045	−	4.57536i	0.376964	−	0.221677i
$427$	−8.77435	+	8.52978i	−0.424621	+	0.412785i
$428$	13.5639	−	1.95019i	0.655635	−	0.0942661i
$429$	−3.57475	−	2.50275i	−0.172591	−	0.120834i
$430$	−0.421570	+	0.192525i	−0.0203299	+	0.00928436i
$431$	−7.65973	−	11.9188i	−0.368956	−	0.574107i	0.606286	−	0.795247i	$-0.292659\pi$
$431$	−7.65973	−	11.9188i	−0.368956	−	0.574107i	−0.975242	+	0.221140i	$0.929022\pi$
$432$	2.91327	+	4.30266i	0.140165	+	0.207012i
$433$	−1.05640	+	1.64379i	−0.0507673	+	0.0789955i	−0.865709	−	0.500547i	$-0.833132\pi$
$433$	−1.05640	+	1.64379i	−0.0507673	+	0.0789955i	0.814942	+	0.579542i	$0.196769\pi$
$434$	−10.1354	−	19.2018i	−0.486514	−	0.921717i
$435$	0.0297677	−	0.751204i	0.00142725	−	0.0360175i
$436$	5.39971			0.258599
$437$	15.5250	+	27.7805i	0.742663	+	1.32892i
$438$	7.55660	−	1.89730i	0.361068	−	0.0906565i
$439$	3.44543	−	11.7340i	0.164441	−	0.560035i	−0.835503	−	0.549486i	$-0.814824\pi$
$439$	3.44543	−	11.7340i	0.164441	−	0.560035i	0.999944	−	0.0105496i	$-0.00335810\pi$
$440$	−0.0935300	+	0.107939i	−0.00445887	+	0.00514581i
$441$	−14.3040	−	15.3752i	−0.681142	−	0.732151i
$442$	−1.80050	+	12.5228i	−0.0856412	+	0.595648i
$443$	14.1710	+	22.0506i	0.673287	+	1.04765i	0.994908	+	0.100786i	$0.0321359\pi$
$443$	14.1710	+	22.0506i	0.673287	+	1.04765i	−0.321621	+	0.946868i	$0.604228\pi$
$444$	0.979869	+	1.22571i	0.0465025	+	0.0581697i
$445$	0.682182	+	0.787280i	0.0323385	+	0.0373207i
$446$	3.69275	+	25.6837i	0.174857	+	1.21616i
$447$	38.3002	+	7.06469i	1.81154	+	0.334149i
$448$	0.226022	−	2.63608i	0.0106785	−	0.124543i
$449$	9.88815	+	33.6760i	0.466651	+	1.58927i	0.771084	+	0.636733i	$0.219715\pi$
$449$	9.88815	+	33.6760i	0.466651	+	1.58927i	−0.304433	+	0.952534i	$0.598467\pi$
$450$	14.9216	−	0.950115i	0.703412	−	0.0447889i
$451$	8.56123	−	1.23092i	0.403133	−	0.0579617i
$452$	−6.99703	+	6.06296i	−0.329112	+	0.285178i
$453$	−7.34114	−	9.18298i	−0.344917	−	0.431454i
$454$	−5.97342	−	9.29483i	−0.280347	−	0.436228i
$455$	−0.368304	+	0.652407i	−0.0172664	+	0.0305853i
$456$	10.8911	+	3.67223i	0.510024	+	0.171968i
$457$	16.5927	−	19.1489i	0.776171	−	0.895750i	−0.220655	−	0.975352i	$-0.570820\pi$
$457$	16.5927	−	19.1489i	0.776171	−	0.895750i	0.996827	+	0.0796022i	$0.0253650\pi$
$458$	−3.92915	−	1.15370i	−0.183597	−	0.0539090i
$459$	21.7614	−	19.7896i	1.01573	−	0.923700i
$460$	0.217918	+	0.567202i	0.0101605	+	0.0264459i
$461$	0.868429			0.0404468			0.0202234	−	0.999795i	$-0.493562\pi$
$461$	0.868429			0.0404468			0.0202234	+	0.999795i	$0.493562\pi$
$462$	2.06265	−	4.73618i	0.0959629	−	0.220347i
$463$	−27.2010	+	31.3917i	−1.26414	+	1.45889i	−0.434423	+	0.900709i	$0.643048\pi$
$463$	−27.2010	+	31.3917i	−1.26414	+	1.45889i	−0.829716	+	0.558185i	$0.811498\pi$
$464$	−1.85215	+	2.88200i	−0.0859838	+	0.133793i
$465$	1.79134	−	0.185514i	0.0830713	−	0.00860300i
$466$	2.46773	−	1.58591i	0.114315	−	0.0734661i
$467$	−3.52059	−	7.70901i	−0.162913	−	0.356730i	0.810517	−	0.585716i	$-0.199187\pi$
$467$	−3.52059	−	7.70901i	−0.162913	−	0.356730i	−0.973430	+	0.228985i	$0.926459\pi$
$468$	−2.39213	+	6.26366i	−0.110576	+	0.289538i
$469$	−18.3878	−	4.27303i	−0.849068	−	0.197310i
$470$	−1.01000	−	0.461251i	−0.0465877	−	0.0212759i
$471$	−10.2731	−	17.4696i	−0.473361	−	0.804955i
$472$	1.86709	+	6.35872i	0.0859397	+	0.292684i
$473$	3.75085	+	1.71296i	0.172464	+	0.0787618i
$474$	26.9909	−	11.0567i	1.23973	−	0.507851i
$475$	24.9945	−	21.6579i	1.14683	−	0.993733i
$476$	−14.9523	+	0.857218i	−0.685339	+	0.0392905i
$477$	19.8363	+	11.0335i	0.908243	+	0.505188i
$478$	1.09434	−	7.61131i	0.0500540	−	0.348133i
$479$	0.106656	+	0.0685435i	0.00487323	+	0.00313183i	0.543075	−	0.839684i	$-0.317260\pi$
$479$	0.106656	+	0.0685435i	0.00487323	+	0.00313183i	−0.538202	+	0.842816i	$0.680896\pi$
$480$	0.195851	+	0.0989944i	0.00893932	+	0.00451846i
$481$	−0.570475	+	1.94286i	−0.0260114	+	0.0885868i
$482$	11.2320			0.511606
$483$	−13.6488	−	17.2253i	−0.621042	−	0.783778i
$484$	−9.72924			−0.442238
$485$	−0.414110	+	1.41033i	−0.0188038	+	0.0640397i
$486$	13.5591	−	7.69100i	0.615052	−	0.348871i
$487$	−27.4287	−	17.6273i	−1.24291	−	0.798771i	−0.257061	−	0.966395i	$-0.582754\pi$
$487$	−27.4287	−	17.6273i	−1.24291	−	0.798771i	−0.985851	+	0.167624i	$0.946391\pi$
$488$	−0.658233	+	4.57811i	−0.0297968	+	0.207241i
$489$	−16.8836	+	17.9929i	−0.763504	+	0.813665i
$490$	−0.843562	−	0.273815i	−0.0381082	−	0.0123697i
$491$	−16.1853	+	14.0247i	−0.730433	+	0.632924i	−0.938535	−	0.345183i	$-0.887817\pi$
$491$	−16.1853	+	14.0247i	−0.730433	+	0.632924i	0.208102	+	0.978107i	$0.433271\pi$
$492$	−5.03768	−	12.2977i	−0.227116	−	0.554422i
$493$	17.6403	+	8.05604i	0.794478	+	0.362826i
$494$	4.17832	+	14.2301i	0.187992	+	0.640241i
$495$	0.300600	+	0.305334i	0.0135110	+	0.0137237i
$496$	−7.46497	−	3.40914i	−0.335187	−	0.153075i
$497$	−3.12084	+	13.4296i	−0.139989	+	0.602402i
$498$	−14.1362	+	20.1912i	−0.633457	+	0.904787i
$499$	−12.6709	−	27.7455i	−0.567229	−	1.24206i	−0.948259	−	0.317497i	$-0.897158\pi$
$499$	−12.6709	−	27.7455i	−0.567229	−	1.24206i	0.381030	−	0.924563i	$-0.375569\pi$
$500$	1.06414	−	0.683883i	0.0475899	−	0.0305842i
$501$	0.0762875	+	0.736639i	0.00340828	+	0.0329106i
$502$	16.6669	−	25.9343i	0.743882	−	1.15750i
$503$	1.33342	−	1.53885i	0.0594543	−	0.0686140i	−0.725243	−	0.688493i	$-0.758273\pi$
$503$	1.33342	−	1.53885i	0.0594543	−	0.0686140i	0.784698	+	0.619879i	$0.212818\pi$
$504$	−7.82979	−	1.30171i	−0.348766	−	0.0579827i
$505$	−0.681598			−0.0303307
$506$	2.54426	−	4.77013i	0.113106	−	0.212058i
$507$	13.4475	−	3.37639i	0.597226	−	0.149951i
$508$	−13.9805	−	4.10505i	−0.620286	−	0.182132i
$509$	−9.66369	+	11.1525i	−0.428336	+	0.494326i	−0.928358	−	0.371687i	$-0.878780\pi$
$509$	−9.66369	+	11.1525i	−0.428336	+	0.494326i	0.500023	+	0.866012i	$0.333325\pi$
$510$	0.396899	−	1.17712i	0.0175750	−	0.0521240i
$511$	−5.85067	+	10.3638i	−0.258818	+	0.458466i
$512$	−0.540641	−	0.841254i	−0.0238932	−	0.0371785i
$513$	13.5676	−	31.6992i	0.599022	−	1.39955i
$514$	16.5870	−	14.3727i	0.731621	−	0.633953i
$515$	−0.591897	+	0.0851020i	−0.0260821	+	0.00375004i
$516$	1.14927	−	6.23058i	0.0505936	−	0.274286i
$517$	2.78325	+	9.47888i	0.122407	+	0.416881i
$518$	−2.38829	−	0.204776i	−0.104935	−	0.00899732i
$519$	−1.27857	+	6.93160i	−0.0561232	+	0.304263i
$520$	0.0402988	+	0.280284i	0.00176722	+	0.0122913i
$521$	21.9379	+	25.3177i	0.961118	+	1.10919i	0.993962	+	0.109729i	$0.0349982\pi$
$521$	21.9379	+	25.3177i	0.961118	+	1.10919i	−0.0328437	+	0.999461i	$0.510456\pi$
$522$	8.17921	+	6.22317i	0.357994	+	0.272381i
$523$	−11.6851	−	18.1824i	−0.510954	−	0.795060i	0.485925	−	0.874000i	$-0.338483\pi$
$523$	−11.6851	−	18.1824i	−0.510954	−	0.795060i	−0.996879	+	0.0789401i	$0.974846\pi$
$524$	0.799111	−	5.55794i	0.0349093	−	0.242800i
$525$	−14.6494	+	17.5223i	−0.639352	+	0.764734i
$526$	3.44520	−	3.97597i	0.150218	−	0.173361i
$527$	−13.0880	+	44.5735i	−0.570121	+	1.94165i
$528$	−0.475474	−	1.89373i	−0.0206923	−	0.0824138i
$529$	−12.8120	−	19.1011i	−0.557043	−	0.830484i
$530$	0.958616			0.0416396
$531$	19.4596	−	4.07423i	0.844473	−	0.176806i
$532$	−15.5265	+	8.19543i	−0.673160	+	0.355317i
$533$	9.27103	−	14.4260i	0.401573	−	0.624860i
$534$	−14.1653	+	1.46698i	−0.612991	+	0.0634824i
$535$	−0.938657	−	1.46058i	−0.0405817	−	0.0631463i
$536$	−6.49033	+	2.96403i	−0.280339	+	0.128027i
$537$	−20.4269	+	29.1764i	−0.881486	+	1.25906i
$538$	11.9795	−	1.72240i	0.516474	−	0.0742578i
$539$	3.07385	+	7.26763i	0.132400	+	0.313039i
$540$	0.342544	−	0.562210i	0.0147408	−	0.0241937i
$541$	−1.15704	+	0.339739i	−0.0497452	+	0.0146065i	−0.306510	−	0.951867i	$-0.599161\pi$
$541$	−1.15704	+	0.339739i	−0.0497452	+	0.0146065i	0.256765	+	0.966474i	$0.417343\pi$
$542$	0.231307	−	0.506493i	0.00993550	−	0.0217557i
$543$	−11.4358	+	4.68463i	−0.490758	+	0.201037i
$544$	−4.27810	+	3.70699i	−0.183422	+	0.158936i
$545$	−0.284199	−	0.622310i	−0.0121738	−	0.0266568i
$546$	−4.41851	−	9.23977i	−0.189095	−	0.395426i
$547$	0.697368	−	4.85030i	0.0298173	−	0.207384i	−0.969467	−	0.245224i	$-0.921139\pi$
$547$	0.697368	−	4.85030i	0.0298173	−	0.207384i	0.999284	+	0.0378399i	$0.0120477\pi$
$548$	−5.13848	+	7.99564i	−0.219505	+	0.341557i
$549$	13.5350	+	3.05529i	0.577660	+	0.130397i
$550$	−5.39072	−	1.58286i	−0.229861	−	0.0674932i
$551$	22.7332			0.968468
$552$	−8.06059	−	2.00672i	−0.343081	−	0.0854117i
$553$	−16.1586	+	41.5212i	−0.687134	+	1.76566i
$554$	5.59406	−	19.0516i	0.237669	−	0.809426i
$555$	0.0896890	−	0.177441i	0.00380708	−	0.00753194i
$556$	0.564358	−	0.878158i	0.0239341	−	0.0372422i
$557$	9.95632	+	1.43150i	0.421863	+	0.0606547i	0.349977	−	0.936758i	$-0.386189\pi$
$557$	9.95632	+	1.43150i	0.421863	+	0.0606547i	0.0718856	+	0.997413i	$0.477098\pi$
$558$	−11.9674	+	21.5154i	−0.506622	+	0.910820i
$559$	7.43652	−	3.39615i	0.314531	−	0.143642i
$560$	−0.315701	+	0.112694i	−0.0133408	+	0.00476221i
$561$	−10.2277	+	4.18973i	−0.431814	+	0.176891i
$562$	3.77685	−	8.27015i	0.159317	−	0.348855i
$563$	−7.15181	+	2.09996i	−0.301413	+	0.0885028i	−0.428942	−	0.903332i	$-0.641114\pi$
$563$	−7.15181	+	2.09996i	−0.301413	+	0.0885028i	0.127529	+	0.991835i	$0.459295\pi$
$564$	13.0844	−	7.69437i	0.550951	−	0.323991i
$565$	1.06702	+	0.487291i	0.0448898	+	0.0205005i
$566$	−3.72814	−	25.9298i	−0.156705	−	1.08991i
$567$	−5.75157	+	23.1067i	−0.241543	+	0.970390i
$568$	2.16480	+	4.74026i	0.0908332	+	0.198897i
$569$	−2.82204	−	4.39118i	−0.118306	−	0.184088i	0.777050	−	0.629439i	$-0.216715\pi$
$569$	−2.82204	−	4.39118i	−0.118306	−	0.184088i	−0.895356	+	0.445351i	$0.853079\pi$
$570$	−0.150006	−	1.44847i	−0.00628305	−	0.0606696i
$571$	25.6907	+	16.5104i	1.07512	+	0.690939i	0.953426	−	0.301628i	$-0.0975302\pi$
$571$	25.6907	+	16.5104i	1.07512	+	0.690939i	0.121696	+	0.992567i	$0.461167\pi$
$572$	1.64988	−	1.90406i	0.0689848	−	0.0796127i
$573$	−0.442193	+	11.1590i	−0.0184729	+	0.466173i
$574$	18.9180	+	7.36223i	0.789621	+	0.307293i
$575$	−16.7348	+	17.0664i	−0.697888	+	0.711718i
$576$	−2.64419	+	1.41713i	−0.110175	+	0.0590473i
$577$	1.81843	−	6.19301i	0.0757023	−	0.257818i	−0.912943	−	0.408087i	$-0.866196\pi$
$577$	1.81843	−	6.19301i	0.0757023	−	0.257818i	0.988645	+	0.150269i	$0.0480140\pi$
$578$	11.3694	+	9.85166i	0.472906	+	0.409775i
$579$	18.6680	+	6.29442i	0.775817	+	0.261587i
$580$	0.429630	+	0.0617715i	0.0178394	+	0.00256492i
$581$	−7.48240	−	36.8991i	−0.310422	−	1.53083i
$582$	−12.5472	−	15.6952i	−0.520098	−	0.650588i
$583$	−5.58540	−	6.44589i	−0.231324	−	0.266962i
$584$	0.640163	+	4.45243i	0.0264901	+	0.184243i
$585$	0.847783	−	0.0539815i	0.0350515	−	0.00223186i
$586$	8.23432	+	28.0435i	0.340157	+	1.15847i
$587$	−3.11502	+	0.914653i	−0.128571	+	0.0377518i	−0.345385	−	0.938461i	$-0.612252\pi$
$587$	−3.11502	+	0.914653i	−0.128571	+	0.0377518i	0.216814	+	0.976213i	$0.430433\pi$
$588$	9.68035	−	7.30006i	0.399211	−	0.301049i
$589$	7.75008	+	53.9030i	0.319337	+	2.22104i
$590$	0.634566	−	0.549854i	0.0261247	−	0.0226371i
$591$	−7.58079	+	6.06030i	−0.311832	+	0.249287i
$592$	−0.762176	+	0.489821i	−0.0313252	+	0.0201315i
$593$	4.62946	−	32.1986i	0.190109	−	1.32224i	−0.641605	−	0.767035i	$-0.721731\pi$
$593$	4.62946	−	32.1986i	0.190109	−	1.32224i	0.831714	−	0.555204i	$-0.187360\pi$
$594$	−5.77623	+	0.972402i	−0.237002	+	0.0398982i
$595$	0.885771	+	1.67812i	0.0363131	+	0.0687963i
$596$	−6.33494	+	21.5748i	−0.259489	+	0.883739i
$597$	4.26708	+	16.9950i	0.174640	+	0.695559i
$598$	−3.84409	−	10.0055i	−0.157196	−	0.409155i
$599$		−	27.7163i		−	1.13246i	−0.824248	−	0.566229i	$-0.808402\pi$
$599$		−	27.7163i		−	1.13246i	0.824248	−	0.566229i	$-0.191598\pi$
$600$	−0.341807	+	8.62568i	−0.0139542	+	0.352142i
$601$	−31.8182	−	27.5707i	−1.29789	−	1.12463i	−0.984571	−	0.174983i	$-0.944013\pi$
$601$	−31.8182	−	27.5707i	−1.29789	−	1.12463i	−0.313321	−	0.949647i	$-0.601442\pi$
$602$	5.68969	+	7.82876i	0.231895	+	0.319077i
$603$	7.32350	+	20.1135i	0.298236	+	0.819087i
$604$	5.71019	−	3.66972i	0.232344	−	0.149319i
$605$	0.512073	+	1.12128i	0.0208187	+	0.0455867i
$606$	5.34406	−	7.63310i	0.217088	−	0.310074i
$607$	−44.8799	+	6.45276i	−1.82162	+	0.261909i	−0.966527	−	0.256565i	$-0.917409\pi$
$607$	−44.8799	+	6.45276i	−1.82162	+	0.261909i	−0.855093	+	0.518474i	$0.826500\pi$
$608$	−2.75662	+	6.03615i	−0.111796	+	0.244798i
$609$	−15.4975	+	2.50831i	−0.627990	+	0.101642i
$610$	0.562266	−	0.165096i	0.0227655	−	0.00668455i
$611$	17.8164	+	8.13649i	0.720776	+	0.329167i
$612$	10.0705	+	13.6740i	0.407078	+	0.552740i
$613$	1.38438	+	1.59766i	0.0559147	+	0.0645290i	0.783018	−	0.621999i	$-0.213679\pi$
$613$	1.38438	+	1.59766i	0.0559147	+	0.0645290i	−0.727103	+	0.686528i	$0.759134\pi$
$614$	−9.56359	−	20.9413i	−0.385955	−	0.845124i
$615$	−1.15215	+	1.22784i	−0.0464591	+	0.0495114i
$616$	2.59721	+	1.46621i	0.104645	+	0.0590753i
$617$	−0.192335	+	0.299279i	−0.00774311	+	0.0120485i	−0.845104	−	0.534603i	$-0.820461\pi$
$617$	−0.192335	+	0.299279i	−0.00774311	+	0.0120485i	0.837360	+	0.546651i	$0.184098\pi$
$618$	3.68772	−	7.29580i	0.148342	−	0.293480i
$619$	11.3376	−	38.6124i	0.455698	−	1.55196i	−0.336491	−	0.941687i	$-0.609240\pi$
$619$	11.3376	−	38.6124i	0.455698	−	1.55196i	0.792188	−	0.610277i	$-0.208942\pi$
$620$			1.03976i			0.0417578i
$621$	−7.91476	+	23.6296i	−0.317608	+	0.948222i
$622$			22.4188i			0.898911i
$623$	13.2812	−	17.2286i	0.532100	−	0.690250i
$624$	−3.45482	−	1.74627i	−0.138304	−	0.0699067i
$625$	20.8290	+	13.3860i	0.833160	+	0.535439i
$626$	3.36333	−	23.3924i	0.134426	−	0.934950i
$627$	−8.86572	+	9.44819i	−0.354063	+	0.377324i
$628$	10.6434	−	4.86067i	0.424717	−	0.193962i
$629$	3.35854	+	3.87596i	0.133914	+	0.154545i
$630$	0.262080	+	0.970886i	0.0104415	+	0.0386810i
$631$	−2.46243	+	5.39198i	−0.0980280	+	0.214651i	−0.952292	−	0.305188i	$-0.901281\pi$
$631$	−2.46243	+	5.39198i	−0.0980280	+	0.214651i	0.854264	+	0.519839i	$0.174008\pi$
$632$	4.74439	+	16.1579i	0.188722	+	0.642727i
$633$	−40.3395	+	23.7220i	−1.60335	+	0.942865i
$634$	5.50437	−	12.0529i	0.218606	−	0.478681i
$635$	0.262726	+	1.82730i	0.0104260	+	0.0725141i
$636$	−7.51603	+	10.7354i	−0.298030	+	0.425686i
$637$	14.8805	+	4.83011i	0.589586	+	0.191376i
$638$	−2.08789	−	3.24882i	−0.0826602	−	0.128622i
$639$	14.6901	−	5.34877i	0.581131	−	0.211594i
$640$	−0.0684983	+	0.106585i	−0.00270763	+	0.00421316i
$641$	10.2841	+	8.91121i	0.406197	+	0.351972i	0.833869	−	0.551962i	$-0.186121\pi$
$641$	10.2841	+	8.91121i	0.406197	+	0.351972i	−0.427672	+	0.903934i	$0.640666\pi$
$642$	23.7163	+	0.939797i	0.936008	+	0.0370908i
$643$		−	18.8386i		−	0.742922i	−0.928449	−	0.371461i	$-0.878857\pi$
$643$		−	18.8386i		−	0.742922i	0.928449	−	0.371461i	$-0.121143\pi$
$644$	10.7039	−	6.81377i	0.421791	−	0.268500i
$645$	−0.778556	+	0.195479i	−0.0306556	+	0.00769696i
$646$	36.0420	+	10.5829i	1.41805	+	0.416378i
$647$	−13.9303	+	16.0765i	−0.547658	+	0.632031i	−0.960336	−	0.278846i	$-0.910048\pi$
$647$	−13.9303	+	16.0765i	−0.547658	+	0.632031i	0.412678	+	0.910877i	$0.364594\pi$
$648$	3.61038	+	8.24410i	0.141829	+	0.323859i
$649$	−7.39462	−	1.06319i	−0.290264	−	0.0417337i
$650$	−9.37069	+	6.02218i	−0.367549	+	0.236209i
$651$	−11.2308	−	35.8912i	−0.440170	−	1.40669i
$652$	−9.32880	−	10.7660i	−0.365344	−	0.421629i
$653$	−24.1512	+	3.47242i	−0.945109	+	0.135886i	−0.597603	−	0.801792i	$-0.703880\pi$
$653$	−24.1512	+	3.47242i	−0.945109	+	0.135886i	−0.347505	+	0.937678i	$0.612971\pi$
$654$	9.19741	+	1.69652i	0.359647	+	0.0663390i
$655$	−0.682605	+	0.200431i	−0.0266716	+	0.00783149i
$656$	7.36190	−	2.16165i	0.287434	−	0.0843982i
$657$	13.4674	−	0.857518i	0.525413	−	0.0334550i
$658$	−5.24831	+	22.5846i	−0.204600	+	0.880439i
$659$	22.8488	−	19.7986i	0.890063	−	0.771244i	−0.0842496	−	0.996445i	$-0.526849\pi$
$659$	22.8488	−	19.7986i	0.890063	−	0.771244i	0.974312	+	0.225201i	$0.0723038\pi$
$660$	−0.193224	+	0.154469i	−0.00752125	+	0.00601270i
$661$	−11.2994	−	17.5821i	−0.439494	−	0.683866i	0.548881	−	0.835900i	$-0.315054\pi$
$661$	−11.2994	−	17.5821i	−0.439494	−	0.683866i	−0.988375	+	0.152034i	$0.951418\pi$
$662$	−3.69747	−	0.531616i	−0.143706	−	0.0206618i
$663$	−7.00132	+	20.7646i	−0.271909	+	0.806429i
$664$	−10.7546	−	9.31894i	−0.417361	−	0.361645i
$665$	1.76171	+	1.35807i	0.0683162	+	0.0526636i
$666$	1.28392	+	2.39564i	0.0497510	+	0.0928290i
$667$	−16.3756	+	1.33281i	−0.634066	+	0.0516065i
$668$	−0.427573			−0.0165433
$669$	−1.77954	+	44.9076i	−0.0688009	+	1.73623i
$670$	0.683203	+	0.591998i	0.0263944	+	0.0228709i
$671$	−4.38619	−	2.81883i	−0.169327	−	0.108820i
$672$	1.21321	−	4.41906i	0.0468005	−	0.170469i
$673$	−8.34092	+	5.36038i	−0.321519	+	0.206628i	−0.691437	−	0.722437i	$-0.743022\pi$
$673$	−8.34092	+	5.36038i	−0.321519	+	0.206628i	0.369918	+	0.929064i	$0.379386\pi$
$674$	31.5842	−	14.4240i	1.21658	−	0.555593i
$675$	25.7148	+	3.06983i	0.989762	+	0.118158i
$676$	1.13922	+	7.92344i	0.0438161	+	0.304748i
$677$	−6.18127	+	13.5351i	−0.237565	+	0.520196i	−0.990436	−	0.137973i	$-0.955941\pi$
$677$	−6.18127	+	13.5351i	−0.237565	+	0.520196i	0.752871	+	0.658169i	$0.228669\pi$
$678$	−13.8231	+	8.12876i	−0.530871	+	0.312183i
$679$	30.5820	+	2.62215i	1.17363	+	0.100629i
$680$	0.652393	+	0.297938i	0.0250181	+	0.0114254i
$681$	−7.25432	−	17.7088i	−0.277986	−	0.678603i
$682$	6.99152	−	6.05818i	0.267719	−	0.231980i
$683$	−17.2069	+	7.85812i	−0.658403	+	0.300683i	−0.716458	−	0.697631i	$-0.754238\pi$
$683$	−17.2069	+	7.85812i	−0.658403	+	0.300683i	0.0580542	+	0.998313i	$0.481510\pi$
$684$	17.3973	+	9.67682i	0.665201	+	0.370002i
$685$	1.19194	+	0.171375i	0.0455416	+	0.00654790i
$686$	−2.10301	+	18.4005i	−0.0802933	+	0.702533i
$687$	−6.33011	−	3.19961i	−0.241509	−	0.122073i
$688$	3.50974	+	1.03055i	0.133808	+	0.0392894i
$689$	−16.9101			−0.644222
$690$	0.192976	+	1.03459i	0.00734646	+	0.0393862i
$691$		−	4.85786i		−	0.184802i	−0.995722	−	0.0924009i	$-0.970546\pi$
$691$		−	4.85786i		−	0.184802i	0.995722	−	0.0924009i	$-0.0294541\pi$
$692$	−3.90463	−	1.14650i	−0.148432	−	0.0435835i
$693$	5.00138	−	7.41915i	0.189987	−	0.281830i
$694$	−29.0004	−	18.6374i	−1.10084	−	0.707467i
$695$	−0.130910	−	0.0188220i	−0.00496571	−	0.000713961i
$696$	−4.06028	+	4.32704i	−0.153905	+	0.164016i
$697$	−18.0428	−	39.5081i	−0.683418	−	1.49648i
$698$	3.98346	+	4.59715i	0.150776	+	0.174005i
$699$	4.70160	−	1.92599i	0.177831	−	0.0728475i
$700$	−9.19141	−	9.45495i	−0.347403	−	0.357364i
$701$	−7.83258	−	26.6753i	−0.295833	−	1.00751i	−0.964529	−	0.263977i	$-0.914966\pi$
$701$	−7.83258	−	26.6753i	−0.295833	−	1.00751i	0.668696	−	0.743536i	$-0.266853\pi$
$702$	−6.04251	+	9.91742i	−0.228060	+	0.374309i
$703$	5.46875	+	2.49749i	0.206258	+	0.0941948i
$704$	1.11580	−	0.160428i	0.0420535	−	0.00604637i
$705$	−1.57543	−	1.10298i	−0.0593340	−	0.0415408i
$706$	−15.4668	+	7.06344i	−0.582100	+	0.265836i
$707$	2.82866	+	13.9494i	0.106383	+	0.524622i
$708$	1.18242	+	11.4175i	0.0444380	+	0.429097i
$709$	25.7974	+	16.5790i	0.968842	+	0.622637i	0.926431	−	0.376464i	$-0.122860\pi$
$709$	25.7974	+	16.5790i	0.968842	+	0.622637i	0.0424101	+	0.999100i	$0.486496\pi$
$710$	0.432371	−	0.498982i	0.0162266	−	0.0187265i
$711$	49.4480	−	10.3529i	1.85444	−	0.388263i
$712$		−	8.22206i		−	0.308135i
$713$	−8.74292	−	38.3740i	−0.327425	−	1.43712i
$714$	−25.7379	−	3.23771i	−0.963217	−	0.121168i
$715$	−0.306277	−	0.0899312i	−0.0114541	−	0.00336323i
$716$	−15.5405	−	13.4660i	−0.580778	−	0.503247i
$717$	4.25538	−	12.6206i	0.158920	−	0.471326i
$718$	0.0792678	−	0.551320i	0.00295825	−	0.0205751i
$719$	7.17096	−	4.60850i	0.267432	−	0.171868i	−0.400052	−	0.916493i	$-0.631008\pi$
$719$	7.17096	−	4.60850i	0.267432	−	0.171868i	0.667483	+	0.744625i	$0.267371\pi$
$720$	0.302493	+	0.230152i	0.0112732	+	0.00857728i
$721$	4.19807	+	11.7604i	0.156344	+	0.437982i
$722$	24.7792	−	3.56271i	0.922185	−	0.132590i
$723$	19.1317	+	3.52896i	0.711517	+	0.131243i
$724$	−2.01016	−	6.84596i	−0.0747069	−	0.254428i
$725$	4.81036	+	16.3826i	0.178652	+	0.608434i
$726$	−16.5720	−	3.05680i	−0.615044	−	0.113448i
$727$	18.4909	−	2.65859i	0.685789	−	0.0986016i	0.209392	−	0.977832i	$-0.432852\pi$
$727$	18.4909	−	2.65859i	0.685789	−	0.0986016i	0.476397	+	0.879230i	$0.341942\pi$
$728$	5.56899	−	1.98794i	0.206401	−	0.0736779i
$729$	25.5118	−	8.84012i	0.944882	−	0.327412i
$730$	0.479444	−	0.308120i	0.0177450	−	0.0114040i
$731$	2.94684	−	20.4957i	0.108993	−	0.758061i
$732$	−2.55956	+	7.59116i	−0.0946040	+	0.280577i
$733$	3.65075	+	3.16339i	0.134843	+	0.116842i	0.719671	−	0.694315i	$-0.244293\pi$
$733$	3.65075	+	3.16339i	0.134843	+	0.116842i	−0.584828	+	0.811157i	$0.698838\pi$
$734$	0.352663	+	0.103551i	0.0130170	+	0.00382214i
$735$	−1.35082	−	0.731429i	−0.0498259	−	0.0269792i
$736$	1.63181	−	4.50968i	0.0601492	−	0.166229i
$737$		−	8.04326i		−	0.296277i
$738$	−4.71699	−	22.5296i	−0.173635	−	0.829326i
$739$	−24.4657	+	28.2349i	−0.899985	+	1.03864i	0.0990654	+	0.995081i	$0.468415\pi$
$739$	−24.4657	+	28.2349i	−0.899985	+	1.03864i	−0.999051	+	0.0435577i	$0.986131\pi$
$740$	0.0965664	+	0.0620595i	0.00354985	+	0.00228135i
$741$	2.64611	+	25.5511i	0.0972073	+	0.938642i
$742$	−3.97830	−	19.6188i	−0.146048	−	0.720229i
$743$	−9.12924	+	4.16919i	−0.334919	+	0.152953i	−0.575775	−	0.817608i	$-0.695299\pi$
$743$	−9.12924	+	4.16919i	−0.334919	+	0.152953i	0.240855	+	0.970561i	$0.422572\pi$
$744$	−11.6441	−	8.15223i	−0.426893	−	0.298875i
$745$	2.81990	−	0.405440i	0.103313	−	0.0148542i
$746$	−25.9176	−	11.8362i	−0.948911	−	0.433353i
$747$	−30.4222	+	29.9505i	−1.11309	+	1.09583i
$748$	−1.79780	−	6.12274i	−0.0657340	−	0.223869i
$749$	−25.9964	+	25.2718i	−0.949887	+	0.923411i
$750$	2.02744	−	0.830530i	0.0740316	−	0.0303267i
$751$	23.8167	+	27.4860i	0.869085	+	1.00298i	0.999933	+	0.0115751i	$0.00368456\pi$
$751$	23.8167	+	27.4860i	0.869085	+	1.00298i	−0.130848	+	0.991402i	$0.541770\pi$
$752$	3.64054	+	7.97168i	0.132757	+	0.290697i
$753$	36.5373	−	38.9378i	1.33149	−	1.41897i
$754$	−7.57870	−	1.08965i	−0.276000	−	0.0396828i
$755$	−0.723472	−	0.464947i	−0.0263298	−	0.0169212i
$756$	−12.9276	−	4.67724i	−0.470173	−	0.170109i
$757$	21.5011	+	6.31330i	0.781472	+	0.229461i	0.648049	−	0.761598i	$-0.275585\pi$
$757$	21.5011	+	6.31330i	0.781472	+	0.229461i	0.133423	+	0.991059i	$0.457403\pi$
$758$		−	17.3840i		−	0.631414i
$759$	5.83239	−	7.32567i	0.211702	−	0.265905i
$760$	0.840746			0.0304971
$761$	9.47996	+	2.78357i	0.343648	+	0.100904i	0.449003	−	0.893530i	$-0.351779\pi$
$761$	9.47996	+	2.78357i	0.343648	+	0.100904i	−0.105354	+	0.994435i	$0.533598\pi$
$762$	−22.5235	−	11.3847i	−0.815941	−	0.412424i
$763$	−11.5566	+	8.39897i	−0.418377	+	0.304063i
$764$	−6.38207	−	0.917603i	−0.230895	−	0.0331977i
$765$	1.04588	−	1.88032i	0.0378139	−	0.0679830i
$766$	21.6434	−	9.88421i	0.782008	−	0.357131i
$767$	−11.1938	+	9.69947i	−0.404184	+	0.350228i
$768$	−0.656572	−	1.60278i	−0.0236920	−	0.0578355i
$769$	−15.7124	−	7.17561i	−0.566603	−	0.258759i	0.111452	−	0.993770i	$-0.464450\pi$
$769$	−15.7124	−	7.17561i	−0.566603	−	0.258759i	−0.678056	+	0.735011i	$0.737177\pi$
$770$	0.0322814	−	0.376496i	0.00116334	−	0.0135680i
$771$	32.7686	−	19.2699i	1.18013	−	0.693987i
$772$	−4.72500	+	10.3463i	−0.170056	+	0.372372i
$773$	−1.13046	−	7.86251i	−0.0406597	−	0.282795i	−1.00000		0.000542102i	$-0.999827\pi$
$773$	−1.13046	−	7.86251i	−0.0406597	−	0.282795i	0.959340	−	0.282253i	$-0.0910816\pi$
$774$	3.91513	−	10.2516i	0.140726	−	0.368485i
$775$	−37.2050	+	16.9910i	−1.33644	+	0.610333i
$776$	9.75966	−	6.27215i	0.350351	−	0.225157i
$777$	−4.00367	−	1.09917i	−0.143631	−	0.0394324i
$778$	1.42889	+	0.918290i	0.0512281	+	0.0329223i
$779$	−38.4787	−	33.3420i	−1.37864	−	1.19460i
$780$	−0.0194200	+	0.490074i	−0.000695347	+	0.0175475i
$781$	−5.87446			−0.210205
$782$	−26.5828	−	5.51017i	−0.950601	−	0.197043i
$783$	11.9765	+	13.1698i	0.428007	+	0.470651i
$784$	3.61655	+	5.99338i	0.129162	+	0.214049i
$785$	−1.12037	−	0.970809i	−0.0399878	−	0.0346496i
$786$	3.10737	−	9.21586i	0.110836	−	0.328719i
$787$	−16.6864	−	2.39914i	−0.594805	−	0.0855201i	−0.161664	−	0.986846i	$-0.551686\pi$
$787$	−16.6864	−	2.39914i	−0.594805	−	0.0855201i	−0.433142	+	0.901326i	$0.642595\pi$
$788$	−3.02945	−	4.71391i	−0.107920	−	0.167926i
$789$	7.11746	−	5.68990i	0.253388	−	0.202566i
$790$	1.61247	−	1.39721i	0.0573691	−	0.0497106i
$791$	5.54461	−	23.8596i	0.197144	−	0.848351i
$792$	−0.214899	−	3.37500i	−0.00763610	−	0.119925i
$793$	−9.91841	+	2.91231i	−0.352213	+	0.103419i
$794$	21.5316	−	6.32226i	0.764129	−	0.224369i
$795$	1.63283	+	0.301184i	0.0579104	+	0.0106819i
$796$	−10.0136	+	1.43975i	−0.354924	+	0.0510304i
$797$	10.8875	+	12.5648i	0.385655	+	0.445070i	0.915071	−	0.403293i	$-0.132134\pi$
$797$	10.8875	+	12.5648i	0.385655	+	0.445070i	−0.529416	+	0.848362i	$0.677589\pi$
$798$	−29.0215	+	9.08118i	−1.02735	+	0.321470i
$799$	41.7334	−	26.8204i	1.47642	−	0.948838i
$800$	−4.93322	−	0.709290i	−0.174416	−	0.0250772i
$801$	−24.5888	−	1.95181i	−0.868804	−	0.0689638i
$802$	−19.4107	+	22.4012i	−0.685416	+	0.791012i
$803$	−4.86534	−	1.42859i	−0.171694	−	0.0504140i
$804$	−11.9863	+	3.00951i	−0.422726	+	0.106137i
$805$	−1.34865	−	0.874982i	−0.0475336	−	0.0308391i
$806$		−	18.3414i		−	0.646050i
$807$	20.9461	+	0.830023i	0.737337	+	0.0292182i
$808$	4.06570	+	3.52295i	0.143031	+	0.123937i
$809$	8.68526	−	13.5145i	0.305358	−	0.475146i	−0.654332	−	0.756207i	$-0.727050\pi$
$809$	8.68526	−	13.5145i	0.305358	−	0.475146i	0.959690	+	0.281062i	$0.0906865\pi$
$810$	0.760100	−	0.849998i	0.0267072	−	0.0298659i
$811$	22.5420	+	35.0761i	0.791558	+	1.23169i	0.968879	+	0.247536i	$0.0796207\pi$
$811$	22.5420	+	35.0761i	0.791558	+	1.23169i	−0.177320	+	0.984153i	$0.556743\pi$
$812$	−0.518783	−	9.04906i	−0.0182057	−	0.317560i
$813$	0.553123	−	0.790043i	0.0193989	−	0.0277080i
$814$	−0.145348	−	1.01092i	−0.00509445	−	0.0354327i
$815$	−0.749773	+	1.64177i	−0.0262634	+	0.0575088i
$816$	−8.45164	+	4.97006i	−0.295867	+	0.173987i
$817$	−6.83855	−	23.2900i	−0.239251	−	0.814813i
$818$	7.95846	−	17.4266i	0.278261	−	0.609306i
$819$	−4.62311	−	17.1265i	−0.161544	−	0.598448i
$820$	−0.636602	−	0.734678i	−0.0222311	−	0.0256561i
$821$	14.9190	−	6.81327i	0.520676	−	0.237785i	−0.137700	−	0.990474i	$-0.543971\pi$
$821$	14.9190	−	6.81327i	0.520676	−	0.237785i	0.658376	+	0.752689i	$0.271244\pi$
$822$	−11.2646	+	12.0047i	−0.392898	+	0.418710i
$823$	6.99550	−	48.6548i	0.243848	−	1.69600i	−0.388609	−	0.921403i	$-0.627044\pi$
$823$	6.99550	−	48.6548i	0.243848	−	1.69600i	0.632457	−	0.774596i	$-0.282047\pi$
$824$	3.97050	+	2.55169i	0.138319	+	0.0888922i
$825$	−8.68478	−	4.38980i	−0.302365	−	0.152833i
$826$	−13.8867	−	10.7050i	−0.483179	−	0.372473i
$827$			24.7926i			0.862122i	0.902323	+	0.431061i	$0.141861\pi$
$827$			24.7926i			0.862122i	−0.902323	+	0.431061i	$0.858139\pi$
$828$	−13.0992	−	5.95061i	−0.455230	−	0.206798i
$829$			3.95911i			0.137506i	0.997634	+	0.0687528i	$0.0219020\pi$
$829$			3.95911i			0.137506i	−0.997634	+	0.0687528i	$0.978098\pi$
$830$	−0.507955	+	1.72994i	−0.0176314	+	0.0600470i
$831$	15.5142	−	30.6934i	0.538183	−	1.06474i
$832$	1.20831	−	1.88017i	0.0418908	−	0.0651833i
$833$	30.6681	−	25.0923i	1.06259	−	0.869395i
$834$	1.23719	−	1.31847i	0.0428402	−	0.0456548i
$835$	0.0225042	+	0.0492773i	0.000778790	+	0.00170531i
$836$	−4.89862	−	5.65331i	−0.169422	−	0.195524i
$837$	−27.1442	+	32.8875i	−0.938240	+	1.13676i
$838$	28.8021	+	13.1535i	0.994953	+	0.454380i
$839$	−29.2504	+	8.58869i	−1.00984	+	0.296515i	−0.744486	−	0.667638i	$-0.767306\pi$
$839$	−29.2504	+	8.58869i	−1.00984	+	0.296515i	−0.265350	+	0.964152i	$0.585487\pi$
$840$	−0.573146	+	0.0927652i	−0.0197754	+	0.00320070i
$841$	7.17157	−	15.7035i	0.247296	−	0.541502i
$842$	31.0034	−	4.45762i	1.06845	−	0.153620i
$843$	9.03154	−	12.9000i	0.311063	−	0.444301i
$844$	−11.2239	−	24.5770i	−0.386343	−	0.845974i
$845$	0.853208	−	0.548323i	0.0293512	−	0.0188629i
$846$	24.7043	−	8.99501i	0.849350	−	0.309255i
$847$	20.8228	−	15.1333i	0.715480	−	0.519988i
$848$	−5.71810	−	4.95476i	−0.196360	−	0.170147i
$849$	1.79659	−	45.3379i	0.0616588	−	1.55599i
$850$			28.2128i			0.967691i
$851$	−4.08577	−	1.47842i	−0.140058	−	0.0506795i
$852$	2.19802	+	8.75432i	0.0753029	+	0.299918i
$853$	10.7841	−	36.7273i	0.369240	−	1.25752i	−0.540148	−	0.841570i	$-0.681632\pi$
$853$	10.7841	−	36.7273i	0.369240	−	1.25752i	0.909389	−	0.415948i	$-0.136550\pi$
$854$	−5.71225	−	10.8220i	−0.195469	−	0.370323i
$855$	0.199582	−	2.51433i	0.00682556	−	0.0859882i
$856$	−1.95019	+	13.5639i	−0.0666562	+	0.463604i
$857$	27.1843	−	17.4703i	0.928599	−	0.596774i	0.0134586	−	0.999909i	$-0.495716\pi$
$857$	27.1843	−	17.4703i	0.928599	−	0.596774i	0.915141	+	0.403135i	$0.132080\pi$
$858$	3.40849	−	2.72484i	0.116364	−	0.0930247i
$859$	22.0360	−	19.0943i	0.751857	−	0.651488i	−0.192168	−	0.981362i	$-0.561552\pi$
$859$	22.0360	−	19.0943i	0.751857	−	0.651488i	0.944025	+	0.329874i	$0.107006\pi$
$860$	−0.0659560	−	0.458734i	−0.00224908	−	0.0156427i
$861$	29.9102	+	18.4840i	1.01934	+	0.629932i
$862$	13.5940	−	3.99155i	0.463013	−	0.135953i
$863$	2.76992	+	9.43348i	0.0942892	+	0.321120i	0.993108	−	0.117200i	$-0.0373919\pi$
$863$	2.76992	+	9.43348i	0.0942892	+	0.321120i	−0.898819	+	0.438320i	$0.855574\pi$
$864$	−4.94913	+	1.58306i	−0.168373	+	0.0538568i
$865$	0.0733768	+	0.510347i	0.00249489	+	0.0173523i
$866$	−1.27958	−	1.47672i	−0.0434820	−	0.0501809i
$867$	16.2705	+	20.3526i	0.552574	+	0.691211i
$868$	21.2795	−	4.31505i	0.722273	−	0.146462i
$869$	−18.7902	−	2.70162i	−0.637414	−	0.0916462i
$870$	0.712388	+	0.240200i	0.0241522	+	0.00814356i
$871$	−12.0517	−	10.4429i	−0.408358	−	0.353844i
$872$	−1.52127	+	5.18098i	−0.0515168	+	0.175450i
$873$	−16.4406	−	30.6761i	−0.556431	−	1.03823i
$874$	−31.0291	+	7.06949i	−1.04957	+	0.239129i
$875$	−1.21376	+	3.11889i	−0.0410327	+	0.105438i
$876$	−0.308495	+	7.78503i	−0.0104231	+	0.263032i
$877$	−26.5892	+	30.6856i	−0.897854	+	1.03618i	0.101292	+	0.994857i	$0.467702\pi$
$877$	−26.5892	+	30.6856i	−0.897854	+	1.03618i	−0.999146	+	0.0413216i	$0.986843\pi$
$878$	10.2880	+	6.61172i	0.347205	+	0.223135i
$879$	5.21475	+	50.3541i	0.175889	+	1.69840i
$880$	−0.0772166	−	0.120151i	−0.00260297	−	0.00405030i
$881$	14.5643	+	31.8914i	0.490685	+	1.07445i	0.979386	+	0.201998i	$0.0647436\pi$
$881$	14.5643	+	31.8914i	0.490685	+	1.07445i	−0.488701	+	0.872451i	$0.662529\pi$
$882$	18.7823	−	9.39288i	0.632432	−	0.316275i
$883$	−3.15009	−	21.9094i	−0.106009	−	0.737309i	−0.971612	−	0.236578i	$-0.923974\pi$
$883$	−3.15009	−	21.9094i	−0.106009	−	0.737309i	0.865603	−	0.500730i	$-0.166935\pi$
$884$	−11.5083	−	5.25565i	−0.387065	−	0.176767i
$885$	1.25362	−	0.737204i	0.0421401	−	0.0247808i
$886$	−25.1498	+	7.38465i	−0.844925	+	0.248092i
$887$	9.59991	−	21.0209i	0.322333	−	0.705811i	−0.677217	−	0.735783i	$-0.736814\pi$
$887$	9.59991	−	21.0209i	0.322333	−	0.705811i	0.999551	+	0.0299715i	$0.00954164\pi$
$888$	−1.45212	+	0.594854i	−0.0487300	+	0.0199620i
$889$	36.3067	−	12.9602i	1.21769	−	0.434673i
$890$	−0.947583	+	0.432747i	−0.0317631	+	0.0145057i
$891$	−10.1443	−	0.158506i	−0.339846	−	0.00531016i
$892$	−25.6837	−	3.69275i	−0.859953	−	0.123643i
$893$	31.4403	−	48.9221i	1.05211	−	1.63711i
$894$	−17.5689	+	34.7584i	−0.587593	+	1.16249i
$895$	−0.734000	+	2.49978i	−0.0245349	+	0.0835583i
$896$	2.46562	+	0.959535i	0.0823706	+	0.0320558i
$897$	−3.40411	−	18.2503i	−0.113660	−	0.609359i
$898$	−35.0977			−1.17122
$899$	−26.9756	−	7.92075i	−0.899686	−	0.264172i
$900$	−3.29228	+	14.5849i	−0.109743	+	0.486162i
$901$	−23.1556	+	36.0308i	−0.771424	+	1.20036i
$902$	−1.23092	+	8.56123i	−0.0409851	+	0.285058i
$903$	7.23166	+	15.1225i	0.240654	+	0.503245i
$904$	−3.84608	−	8.42173i	−0.127919	−	0.280103i
$905$	−0.683190	+	0.591987i	−0.0227100	+	0.0196783i
$906$	10.8792	−	4.45662i	0.361439	−	0.148061i
$907$	1.50614	−	3.29798i	0.0500104	−	0.109507i	−0.882977	−	0.469416i	$-0.844465\pi$
$907$	1.50614	−	3.29798i	0.0500104	−	0.109507i	0.932988	+	0.359908i	$0.117192\pi$
$908$	10.6012	−	3.11280i	0.351814	−	0.103302i
$909$	11.5009	−	11.3226i	0.381459	−	0.375545i
$910$	−0.522217	−	0.537190i	−0.0173113	−	0.0178077i
$911$	−10.4537	+	1.50301i	−0.346346	+	0.0497970i	−0.313293	−	0.949657i	$-0.601432\pi$
$911$	−10.4537	+	1.50301i	−0.346346	+	0.0497970i	−0.0330531	+	0.999454i	$0.510523\pi$
$912$	−6.59186	+	9.41537i	−0.218278	+	0.311774i
$913$	14.5920	−	6.66394i	0.482924	−	0.220544i
$914$	13.6986	+	21.3154i	0.453109	+	0.705051i
$915$	1.00959	−	0.104555i	0.0333759	−	0.00345647i
$916$	2.21394	−	3.44496i	0.0731506	−	0.113825i
$917$	6.93481	+	13.1382i	0.229008	+	0.433863i
$918$	12.8571	+	26.4552i	0.424348	+	0.873153i
$919$	26.8799			0.886685			0.443343	−	0.896352i	$-0.353793\pi$
$919$	26.8799			0.886685			0.443343	+	0.896352i	$0.353793\pi$
$920$	−0.605621	+	0.0492914i	−0.0199667	+	0.00162509i
$921$	−9.71033	−	38.6745i	−0.319966	−	1.27437i
$922$	−0.244665	+	0.833252i	−0.00805761	+	0.0274417i
$923$	−7.62705	+	8.80209i	−0.251047	+	0.289724i
$924$	3.96322	+	3.31343i	0.130380	+	0.109004i
$925$	−0.642617	+	4.46950i	−0.0211291	+	0.146956i
$926$	−22.4567	−	34.9433i	−0.737972	−	1.14831i
$927$	8.57360	−	11.2684i	0.281594	−	0.370103i
$928$	−2.24345	−	2.58908i	−0.0736448	−	0.0849906i
$929$	2.41163	+	16.7732i	0.0791229	+	0.550312i	0.990369	+	0.138450i	$0.0442121\pi$
$929$	2.41163	+	16.7732i	0.0791229	+	0.550312i	−0.911247	+	0.411861i	$0.864879\pi$
$930$	−0.326679	+	1.77104i	−0.0107122	+	0.0580747i
$931$	20.4827	−	41.6908i	0.671294	−	1.36636i
$932$	0.826433	+	2.81457i	0.0270707	+	0.0921944i
$933$	−7.04368	+	38.1863i	−0.230600	+	1.25016i
$934$	8.38861	−	1.20610i	0.274484	−	0.0394648i
$935$	−0.611016	+	0.529448i	−0.0199824	+	0.0173148i
$936$	−5.33600	−	4.05991i	−0.174413	−	0.132702i
$937$	−1.35940	−	2.11526i	−0.0444096	−	0.0691027i	0.818339	−	0.574736i	$-0.194895\pi$
$937$	−1.35940	−	2.11526i	−0.0444096	−	0.0691027i	−0.862748	+	0.505633i	$0.831259\pi$
$938$	9.28038	−	16.4391i	0.303015	−	0.536755i
$939$	13.0784	−	38.7880i	0.426798	−	1.26580i
$940$	0.727116	−	0.839137i	0.0237159	−	0.0273696i
$941$	−39.5164	−	11.6031i	−1.28820	−	0.378249i	−0.435281	−	0.900295i	$-0.643351\pi$
$941$	−39.5164	−	11.6031i	−1.28820	−	0.378249i	−0.852918	+	0.522045i	$0.825169\pi$
$942$	19.6562	−	4.93525i	0.640434	−	0.160799i
$943$	29.6724	+	21.7615i	0.966267	+	0.708653i
$944$	−6.62717			−0.215696
$945$	0.141365	+	1.73607i	0.00459862	+	0.0564743i
$946$	−2.70031	+	3.11632i	−0.0877946	+	0.101320i
$947$	4.45835	−	6.93733i	0.144877	−	0.225433i	−0.761230	−	0.648482i	$-0.775404\pi$
$947$	4.45835	−	6.93733i	0.144877	−	0.225433i	0.906107	+	0.423049i	$0.139040\pi$
$948$	3.00460	+	29.0126i	0.0975848	+	0.942287i
$949$	−8.45744	+	5.43526i	−0.274540	+	0.176436i
$950$	13.7388	+	30.0838i	0.445746	+	0.976048i
$951$	13.1625	−	18.8005i	0.426824	−	0.609647i
$952$	3.39007	−	14.5882i	0.109873	−	0.472805i
$953$	−16.0278	−	7.31965i	−0.519191	−	0.237107i	0.138543	−	0.990356i	$-0.455758\pi$
$953$	−16.0278	−	7.31965i	−0.519191	−	0.237107i	−0.657735	+	0.753250i	$0.728485\pi$
$954$	−16.1751	+	15.9243i	−0.523688	+	0.515569i
$955$	0.230151	+	0.783821i	0.00744750	+	0.0253639i
$956$	6.99468	+	3.19436i	0.226224	+	0.103313i
$957$	−2.53560	−	6.18975i	−0.0819642	−	0.200086i
$958$	−0.0958154	+	0.0830245i	−0.00309566	+	0.00268240i
$959$	−1.43928	−	25.1051i	−0.0464767	−	0.810687i
$960$	−0.150162	+	0.160027i	−0.00484646	+	0.00516486i
$961$	5.17286	−	35.9780i	0.166866	−	1.16058i
$962$	−1.70344	−	1.09473i	−0.0549211	−	0.0352956i
$963$	40.1011	+	9.05212i	1.29224	+	0.291701i
$964$	−3.16443	+	10.7771i	−0.101920	+	0.347106i
$965$	1.44109			0.0463903
$966$	20.3728	−	8.24300i	0.655486	−	0.265214i
$967$	−35.8318			−1.15227			−0.576136	−	0.817354i	$-0.695440\pi$
$967$	−35.8318			−1.15227			−0.576136	+	0.817354i	$0.695440\pi$
$968$	2.74104	−	9.33514i	0.0881005	−	0.300043i
$969$	58.0659	+	29.3499i	1.86534	+	0.942854i
$970$	−1.23653	−	0.794671i	−0.0397026	−	0.0255153i
$971$	−3.65850	+	25.4454i	−0.117407	+	0.816582i	0.842987	+	0.537935i	$0.180795\pi$
$971$	−3.65850	+	25.4454i	−0.117407	+	0.816582i	−0.960393	+	0.278648i	$0.910114\pi$
$972$	3.55943	+	15.1766i	0.114169	+	0.486791i
$973$	0.158075	+	2.75729i	0.00506766	+	0.0883946i
$974$	24.6409	−	21.3514i	0.789544	−	0.684144i
$975$	−17.8533	+	7.31353i	−0.571764	+	0.234220i
$976$	−4.20722	−	1.92137i	−0.134670	−	0.0615016i
$977$	−9.77432	−	33.2883i	−0.312708	−	1.06499i	−0.954526	−	0.298129i	$-0.903638\pi$
$977$	−9.77432	−	33.2883i	−0.312708	−	1.06499i	0.641818	−	0.766857i	$-0.278181\pi$
$978$	−12.5074	−	21.2689i	−0.399941	−	0.680104i
$979$	8.43097	+	3.85030i	0.269455	+	0.123056i
$980$	0.500382	−	0.732249i	0.0159841	−	0.0233908i
$981$	15.1331	+	5.77941i	0.483162	+	0.184522i
$982$	−8.89663	−	19.4809i	−0.283903	−	0.621661i
$983$	2.05032	−	1.31766i	0.0653949	−	0.0420268i	−0.507535	−	0.861631i	$-0.669443\pi$
$983$	2.05032	−	1.31766i	0.0653949	−	0.0420268i	0.572930	+	0.819604i	$0.305807\pi$
$984$	13.2188	−	1.36896i	0.421400	−	0.0436409i
$985$	−0.383826	+	0.597245i	−0.0122297	+	0.0190298i
$986$	−12.6996	+	14.6561i	−0.404436	+	0.466744i
$987$	−16.0353	+	36.8197i	−0.510409	+	1.17199i
$988$	−14.8308			−0.471831
$989$	6.29151	+	16.3757i	0.200059	+	0.520717i
$990$	−0.377654	+	0.202401i	−0.0120026	+	0.00643273i
$991$	3.71361	+	1.09041i	0.117967	+	0.0346382i	0.340183	−	0.940359i	$-0.389511\pi$
$991$	3.71361	+	1.09041i	0.117967	+	0.0346382i	−0.222216	+	0.974997i	$0.571329\pi$
$992$	5.37417	−	6.20212i	0.170630	−	0.196918i
$993$	−6.13093	−	2.06720i	−0.194559	−	0.0656007i
$994$	−12.0064	−	6.77800i	−0.380820	−	0.214985i
$995$	0.692971	+	1.07828i	0.0219687	+	0.0341839i
$996$	−15.3907	−	19.2521i	−0.487671	−	0.610025i
$997$	29.8455	−	25.8613i	0.945218	−	0.819036i	−0.0384074	−	0.999262i	$-0.512228\pi$
$997$	29.8455	−	25.8613i	0.945218	−	0.819036i	0.983625	+	0.180226i	$0.0576830\pi$
$998$	30.1914	−	4.34087i	0.955693	−	0.137408i
$999$	1.43425	+	4.48392i	0.0453777	+	0.141865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.t.a.41.11	✓	640
3.2	odd	2	inner	966.2.t.a.41.59	yes	640
7.6	odd	2	inner	966.2.t.a.41.22	yes	640
21.20	even	2	inner	966.2.t.a.41.38	yes	640
23.9	even	11	inner	966.2.t.a.377.38	yes	640
69.32	odd	22	inner	966.2.t.a.377.22	yes	640
161.55	odd	22	inner	966.2.t.a.377.59	yes	640
483.377	even	22	inner	966.2.t.a.377.11	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.t.a.41.11	✓	640	1.1	even	1	trivial
966.2.t.a.41.22	yes	640	7.6	odd	2	inner
966.2.t.a.41.38	yes	640	21.20	even	2	inner
966.2.t.a.41.59	yes	640	3.2	odd	2	inner
966.2.t.a.377.11	yes	640	483.377	even	22	inner
966.2.t.a.377.22	yes	640	69.32	odd	22	inner
966.2.t.a.377.38	yes	640	23.9	even	11	inner
966.2.t.a.377.59	yes	640	161.55	odd	22	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281733 + 0.959493i) q^{2} +(-0.781340 + 1.54580i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.0180311 + 0.125409i) q^{5} +(-1.26306 - 1.18519i) q^{6} +(2.64141 - 0.151432i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-1.77902 - 2.41559i) q^{9} +O(q^{10})\)	\(q+(-0.281733 + 0.959493i) q^{2} +(-0.781340 + 1.54580i) q^{3} +(-0.841254 - 0.540641i) q^{4} +(-0.0180311 + 0.125409i) q^{5} +(-1.26306 - 1.18519i) q^{6} +(2.64141 - 0.151432i) q^{7} +(0.755750 - 0.654861i) q^{8} +(-1.77902 - 2.41559i) q^{9} +(-0.115249 - 0.0526324i) q^{10} +(0.317591 + 1.08162i) q^{11} +(1.49303 - 0.877989i) q^{12} +(2.03300 + 0.928439i) q^{13} +(-0.598874 + 2.57708i) q^{14} +(-0.179769 - 0.125859i) q^{15} +(0.415415 + 0.909632i) q^{16} +(4.76211 - 3.06042i) q^{17} +(2.81895 - 1.02640i) q^{18} +(3.58759 - 5.58240i) q^{19} +(0.0829698 - 0.0957522i) q^{20} +(-1.82976 + 4.20143i) q^{21} -1.12728 q^{22} +(-2.25699 + 4.23155i) q^{23} +(0.421789 + 1.67991i) q^{24} +(4.78206 + 1.40414i) q^{25} +(-1.46359 + 1.68908i) q^{26} +(5.12405 - 0.862611i) q^{27} +(-2.30397 - 1.30066i) q^{28} +(1.85215 + 2.88200i) q^{29} +(0.171408 - 0.137028i) q^{30} +(-6.20212 + 5.37417i) q^{31} +(-0.989821 + 0.142315i) q^{32} +(-1.92011 - 0.354176i) q^{33} +(1.59481 + 5.43143i) q^{34} +(-0.0286365 + 0.333987i) q^{35} +(0.190635 + 2.99394i) q^{36} +(0.128937 + 0.896779i) q^{37} +(4.34553 + 5.01501i) q^{38} +(-3.02365 + 2.41719i) q^{39} +(0.0684983 + 0.106585i) q^{40} +(1.09194 - 7.59460i) q^{41} +(-3.51574 - 2.93932i) q^{42} +(2.39542 - 2.76446i) q^{43} +(0.317591 - 1.08162i) q^{44} +(0.335014 - 0.179549i) q^{45} +(-3.42427 - 3.35773i) q^{46} +8.76363 q^{47} +(-1.73069 - 0.0685815i) q^{48} +(6.95414 - 0.799991i) q^{49} +(-2.69453 + 4.19276i) q^{50} +(1.00999 + 9.75252i) q^{51} +(-1.20831 - 1.88017i) q^{52} +(-6.88240 + 3.14309i) q^{53} +(-0.615943 + 5.15952i) q^{54} +(-0.141371 + 0.0203260i) q^{55} +(1.89708 - 1.84420i) q^{56} +(5.82617 + 9.90746i) q^{57} +(-3.28707 + 0.965170i) q^{58} +(-2.75302 + 6.02828i) q^{59} +(0.0831865 + 0.203070i) q^{60} +(-3.49548 + 3.02885i) q^{61} +(-3.40914 - 7.46497i) q^{62} +(-5.06492 - 6.11119i) q^{63} +(0.142315 - 0.989821i) q^{64} +(-0.153091 + 0.238215i) q^{65} +(0.880787 - 1.74255i) q^{66} +(-6.84609 - 2.01019i) q^{67} -5.66073 q^{68} +(-4.77766 - 6.79514i) q^{69} +(-0.312390 - 0.121572i) q^{70} +(-1.46816 + 5.00010i) q^{71} +(-2.92637 - 0.660576i) q^{72} +(-2.43192 + 3.78414i) q^{73} +(-0.896779 - 0.128937i) q^{74} +(-5.90694 + 6.29502i) q^{75} +(-6.03615 + 2.75662i) q^{76} +(1.00268 + 2.80890i) q^{77} +(-1.46742 - 3.58217i) q^{78} +(-6.99561 + 15.3182i) q^{79} +(-0.121566 + 0.0356950i) q^{80} +(-2.67020 + 8.59477i) q^{81} +(6.97933 + 3.18735i) q^{82} +(-2.02520 - 14.0856i) q^{83} +(3.81075 - 2.54522i) q^{84} +(0.297938 + 0.652393i) q^{85} +(1.97762 + 3.07723i) q^{86} +(-5.90216 + 0.611237i) q^{87} +(0.948327 + 0.609453i) q^{88} +(5.38431 - 6.21382i) q^{89} +(0.0778911 + 0.372028i) q^{90} +(5.51058 + 2.14453i) q^{91} +(4.18645 - 2.33958i) q^{92} +(-3.46145 - 13.7863i) q^{93} +(-2.46900 + 8.40864i) q^{94} +(0.635393 + 0.550571i) q^{95} +(0.553396 - 1.64127i) q^{96} +(11.4832 + 1.65104i) q^{97} +(-1.19162 + 6.89783i) q^{98} +(2.04775 - 2.69138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q + 64 q^{4} + 8 q^{9}+O(q^{10}) \) 640 * q + 64 * q^4 + 8 * q^9	\( 640 q + 64 q^{4} + 8 q^{9} + 8 q^{15} - 64 q^{16} + 20 q^{18} + 54 q^{21} - 8 q^{22} - 56 q^{25} - 44 q^{30} - 8 q^{36} + 20 q^{37} - 16 q^{39} - 4 q^{42} - 28 q^{43} + 24 q^{46} - 68 q^{49} - 40 q^{51} + 32 q^{57} - 80 q^{58} - 8 q^{60} + 86 q^{63} + 64 q^{64} + 24 q^{67} + 72 q^{70} - 64 q^{72} - 8 q^{78} - 144 q^{79} + 20 q^{81} + 34 q^{84} + 32 q^{85} + 8 q^{88} - 40 q^{91} + 16 q^{93} + 68 q^{99}+O(q^{100}) \) 640 * q + 64 * q^4 + 8 * q^9 + 8 * q^15 - 64 * q^16 + 20 * q^18 + 54 * q^21 - 8 * q^22 - 56 * q^25 - 44 * q^30 - 8 * q^36 + 20 * q^37 - 16 * q^39 - 4 * q^42 - 28 * q^43 + 24 * q^46 - 68 * q^49 - 40 * q^51 + 32 * q^57 - 80 * q^58 - 8 * q^60 + 86 * q^63 + 64 * q^64 + 24 * q^67 + 72 * q^70 - 64 * q^72 - 8 * q^78 - 144 * q^79 + 20 * q^81 + 34 * q^84 + 32 * q^85 + 8 * q^88 - 40 * q^91 + 16 * q^93 + 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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