LMFDB - Embedded newform 861.2.bw.a.236.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(236,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 21]))

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

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

chi := DirichletCharacter("861.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.bw (of order $30$, degree $8$, 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:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$864$
Relative dimension:	$108$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			236.17
Character	$\chi$	$=$	861.236
Dual form			861.2.bw.a.332.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.859146 - 1.92967i) q^{2} +(1.58756 - 0.692569i) q^{3} +(-1.64725 + 1.82945i) q^{4} +(-2.32162 - 0.493476i) q^{5} +(-2.70038 - 2.46846i) q^{6} +(2.60017 + 0.488991i) q^{7} +(0.927655 + 0.301413i) q^{8} +(2.04070 - 2.19899i) q^{9} +O(q^{10})$	\(q+(-0.859146 - 1.92967i) q^{2} +(1.58756 - 0.692569i) q^{3} +(-1.64725 + 1.82945i) q^{4} +(-2.32162 - 0.493476i) q^{5} +(-2.70038 - 2.46846i) q^{6} +(2.60017 + 0.488991i) q^{7} +(0.927655 + 0.301413i) q^{8} +(2.04070 - 2.19899i) q^{9} +(1.04236 + 4.90394i) q^{10} +(3.82123 - 0.812227i) q^{11} +(-1.34808 + 4.04520i) q^{12} +(-2.12311 - 1.54253i) q^{13} +(-1.29033 - 5.43759i) q^{14} +(-4.02748 + 0.824461i) q^{15} +(0.299289 + 2.84754i) q^{16} +(-1.07581 - 5.06127i) q^{17} +(-5.99659 - 2.04862i) q^{18} +(0.0540963 + 0.514692i) q^{19} +(4.72707 - 3.43442i) q^{20} +(4.46659 - 1.02450i) q^{21} +(-4.85032 - 6.67590i) q^{22} +(-2.72822 - 6.12768i) q^{23} +(1.68146 - 0.163953i) q^{24} +(0.578681 + 0.257645i) q^{25} +(-1.15252 + 5.42216i) q^{26} +(1.71678 - 4.90435i) q^{27} +(-5.17771 + 3.95140i) q^{28} +(0.169272 + 0.520964i) q^{29} +(5.05113 + 7.06339i) q^{30} +(0.404258 + 1.90188i) q^{31} +(6.92712 - 3.99938i) q^{32} +(5.50391 - 3.93592i) q^{33} +(-8.84233 + 6.42433i) q^{34} +(-5.79531 - 2.41837i) q^{35} +(0.661419 + 7.35564i) q^{36} +(-2.16515 - 0.460216i) q^{37} +(0.946711 - 0.546584i) q^{38} +(-4.43887 - 0.978458i) q^{39} +(-2.00492 - 1.15754i) q^{40} +(-5.76396 + 2.78869i) q^{41} +(-5.81439 - 7.73887i) q^{42} +(-6.12990 - 4.45363i) q^{43} +(-4.80857 + 8.32869i) q^{44} +(-5.82287 + 4.09819i) q^{45} +(-9.48049 + 10.5291i) q^{46} +(4.32120 + 9.70558i) q^{47} +(2.44726 + 4.31336i) q^{48} +(6.52178 + 2.54292i) q^{49} -1.33802i q^{50} +(-5.21319 - 7.29001i) q^{51} +(6.31927 - 1.34320i) q^{52} +(-2.93882 + 3.26389i) q^{53} +(-10.9388 + 0.900739i) q^{54} -9.27226 q^{55} +(2.26467 + 1.23734i) q^{56} +(0.442341 + 0.779639i) q^{57} +(0.859862 - 0.774223i) q^{58} +(-0.358430 + 3.41023i) q^{59} +(5.12594 - 8.72617i) q^{60} +(13.6382 - 1.43343i) q^{61} +(3.32270 - 2.41408i) q^{62} +(6.38144 - 4.71987i) q^{63} +(-9.03610 - 6.56511i) q^{64} +(4.16785 + 4.62887i) q^{65} +(-12.3237 - 7.23921i) q^{66} +(-10.2493 - 9.22849i) q^{67} +(11.0315 + 6.36903i) q^{68} +(-8.57506 - 7.83859i) q^{69} +(0.312344 + 13.2608i) q^{70} +(4.75666 - 14.6395i) q^{71} +(2.55587 - 1.42481i) q^{72} +(3.33086 - 1.92307i) q^{73} +(0.972111 + 4.57342i) q^{74} +(1.09713 + 0.00825104i) q^{75} +(-1.03071 - 0.748858i) q^{76} +(10.3330 - 0.243384i) q^{77} +(1.92553 + 9.40621i) q^{78} +(11.1101 + 6.41445i) q^{79} +(0.710358 - 6.75860i) q^{80} +(-0.671119 - 8.97494i) q^{81} +(10.3333 + 8.72666i) q^{82} -11.8609 q^{83} +(-5.48331 + 9.85901i) q^{84} +12.2812i q^{85} +(-3.32758 + 15.6550i) q^{86} +(0.629533 + 0.709830i) q^{87} +(3.78960 + 0.398303i) q^{88} +(3.13164 - 0.329149i) q^{89} +(12.9109 + 7.71530i) q^{90} +(-4.76616 - 5.04902i) q^{91} +(15.7044 + 5.10265i) q^{92} +(1.95897 + 2.73938i) q^{93} +(15.0161 - 16.6770i) q^{94} +(0.128397 - 1.22162i) q^{95} +(8.22738 - 11.1468i) q^{96} +(1.18877 + 3.65867i) q^{97} +(-0.696153 - 14.7696i) q^{98} +(6.01188 - 10.0604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9}+O(q^{10}) $ 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9	$ 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9} - 18 q^{10} - 15 q^{12} - 50 q^{15} + 82 q^{16} - 15 q^{18} - 30 q^{19} - 14 q^{21} + 30 q^{24} + 78 q^{25} + 15 q^{30} - 18 q^{31} + 36 q^{33} + 16 q^{36} - 10 q^{37} - 2 q^{39} - 144 q^{40} - 24 q^{42} - 8 q^{43} + 69 q^{45} - 12 q^{46} + 52 q^{49} - 18 q^{51} - 30 q^{52} + 15 q^{54} - 38 q^{57} - 10 q^{58} - 126 q^{61} + 65 q^{63} - 16 q^{64} - 70 q^{67} - 260 q^{70} - 33 q^{72} - 48 q^{73} + 60 q^{75} - 2 q^{78} + 68 q^{81} - 150 q^{82} + 115 q^{84} - 138 q^{87} + 30 q^{88} + 64 q^{91} - 15 q^{93} + 60 q^{94} - 30 q^{99}+O(q^{100}) $ 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9 - 18 * q^10 - 15 * q^12 - 50 * q^15 + 82 * q^16 - 15 * q^18 - 30 * q^19 - 14 * q^21 + 30 * q^24 + 78 * q^25 + 15 * q^30 - 18 * q^31 + 36 * q^33 + 16 * q^36 - 10 * q^37 - 2 * q^39 - 144 * q^40 - 24 * q^42 - 8 * q^43 + 69 * q^45 - 12 * q^46 + 52 * q^49 - 18 * q^51 - 30 * q^52 + 15 * q^54 - 38 * q^57 - 10 * q^58 - 126 * q^61 + 65 * q^63 - 16 * q^64 - 70 * q^67 - 260 * q^70 - 33 * q^72 - 48 * q^73 + 60 * q^75 - 2 * q^78 + 68 * q^81 - 150 * q^82 + 115 * q^84 - 138 * q^87 + 30 * q^88 + 64 * q^91 - 15 * q^93 + 60 * q^94 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.859146	−	1.92967i	−0.607508	−	1.36449i	−0.911299	−	0.411746i	$-0.864919\pi$
$2$	−0.859146	−	1.92967i	−0.607508	−	1.36449i	0.303791	−	0.952739i	$-0.401748\pi$
$3$	1.58756	−	0.692569i	0.916578	−	0.399855i
$3$	1.58756	−	0.692569i	0.916578	−	0.399855i
$4$	−1.64725	+	1.82945i	−0.823623	+	0.914726i
$5$	−2.32162	−	0.493476i	−1.03826	−	0.220689i	−0.342916	−	0.939366i	$-0.611415\pi$
$5$	−2.32162	−	0.493476i	−1.03826	−	0.220689i	−0.695344	+	0.718677i	$0.744748\pi$
$6$	−2.70038	−	2.46846i	−1.10242	−	1.00774i
$7$	2.60017	+	0.488991i	0.982772	+	0.184821i
$7$	2.60017	+	0.488991i	0.982772	+	0.184821i
$8$	0.927655	+	0.301413i	0.327976	+	0.106566i
$9$	2.04070	−	2.19899i	0.680232	−	0.732997i
$10$	1.04236	+	4.90394i	0.329625	+	1.55076i
$11$	3.82123	−	0.812227i	1.15214	−	0.244896i	0.408043	−	0.912963i	$-0.366212\pi$
$11$	3.82123	−	0.812227i	1.15214	−	0.244896i	0.744101	+	0.668067i	$0.232878\pi$
$12$	−1.34808	+	4.04520i	−0.389157	+	1.16775i
$13$	−2.12311	−	1.54253i	−0.588844	−	0.427821i	0.253057	−	0.967451i	$-0.418564\pi$
$13$	−2.12311	−	1.54253i	−0.588844	−	0.427821i	−0.841902	+	0.539631i	$0.818564\pi$
$14$	−1.29033	−	5.43759i	−0.344856	−	1.45326i
$15$	−4.02748	+	0.824461i	−1.03989	+	0.212875i
$16$	0.299289	+	2.84754i	0.0748221	+	0.711885i
$17$	−1.07581	−	5.06127i	−0.260921	−	1.22754i	−0.892077	−	0.451883i	$-0.850753\pi$
$17$	−1.07581	−	5.06127i	−0.260921	−	1.22754i	0.631156	−	0.775656i	$-0.282581\pi$
$18$	−5.99659	−	2.04862i	−1.41341	−	0.482865i
$19$	0.0540963	+	0.514692i	0.0124105	+	0.118078i	0.998973	−	0.0453049i	$-0.0144259\pi$
$19$	0.0540963	+	0.514692i	0.0124105	+	0.118078i	−0.986563	+	0.163383i	$0.947759\pi$
$20$	4.72707	−	3.43442i	1.05701	−	0.767960i
$21$	4.46659	−	1.02450i	0.974689	−	0.223563i
$22$	−4.85032	−	6.67590i	−1.03409	−	1.42331i
$23$	−2.72822	−	6.12768i	−0.568873	−	1.27771i	−0.937452	−	0.348114i	$-0.886822\pi$
$23$	−2.72822	−	6.12768i	−0.568873	−	1.27771i	0.368579	−	0.929596i	$-0.379844\pi$
$24$	1.68146	−	0.163953i	0.343226	−	0.0334668i
$25$	0.578681	+	0.257645i	0.115736	+	0.0515291i
$26$	−1.15252	+	5.42216i	−0.226027	+	1.06337i
$27$	1.71678	−	4.90435i	0.330394	−	0.943843i
$28$	−5.17771	+	3.95140i	−0.978495	+	0.746744i
$29$	0.169272	+	0.520964i	0.0314330	+	0.0967407i	0.965542	−	0.260247i	$-0.0838039\pi$
$29$	0.169272	+	0.520964i	0.0314330	+	0.0967407i	−0.934109	+	0.356987i	$0.883804\pi$
$30$	5.05113	+	7.06339i	0.922207	+	1.28959i
$31$	0.404258	+	1.90188i	0.0726069	+	0.341589i	0.999424	−	0.0339234i	$-0.0108002\pi$
$31$	0.404258	+	1.90188i	0.0726069	+	0.341589i	−0.926818	+	0.375512i	$0.877467\pi$
$32$	6.92712	−	3.99938i	1.22455	−	0.706997i
$33$	5.50391	−	3.93592i	0.958107	−	0.685156i
$34$	−8.84233	+	6.42433i	−1.51645	+	1.10176i
$35$	−5.79531	−	2.41837i	−0.979586	−	0.408780i
$36$	0.661419	+	7.35564i	0.110237	+	1.22594i
$37$	−2.16515	−	0.460216i	−0.355948	−	0.0756591i	0.0264671	−	0.999650i	$-0.491574\pi$
$37$	−2.16515	−	0.460216i	−0.355948	−	0.0756591i	−0.382415	+	0.923991i	$0.624908\pi$
$38$	0.946711	−	0.546584i	0.153577	−	0.0886676i
$39$	−4.43887	−	0.978458i	−0.710788	−	0.156679i
$40$	−2.00492	−	1.15754i	−0.317006	−	0.183024i
$41$	−5.76396	+	2.78869i	−0.900179	+	0.435520i
$41$	−5.76396	+	2.78869i	−0.900179	+	0.435520i
$42$	−5.81439	−	7.73887i	−0.897180	−	1.19413i
$43$	−6.12990	−	4.45363i	−0.934801	−	0.679172i	0.0123629	−	0.999924i	$-0.496065\pi$
$43$	−6.12990	−	4.45363i	−0.934801	−	0.679172i	−0.947163	+	0.320751i	$0.896065\pi$
$44$	−4.80857	+	8.32869i	−0.724920	+	1.25560i
$45$	−5.82287	+	4.09819i	−0.868023	+	0.610922i
$46$	−9.48049	+	10.5291i	−1.39782	+	1.55244i
$47$	4.32120	+	9.70558i	0.630312	+	1.41570i	0.892660	+	0.450731i	$0.148837\pi$
$47$	4.32120	+	9.70558i	0.630312	+	1.41570i	−0.262347	+	0.964974i	$0.584497\pi$
$48$	2.44726	+	4.31336i	0.353231	+	0.622581i
$49$	6.52178	+	2.54292i	0.931682	+	0.363274i
$50$		−	1.33802i		−	0.189225i
$51$	−5.21319	−	7.29001i	−0.729992	−	1.02080i
$52$	6.31927	−	1.34320i	0.876325	−	0.186269i
$53$	−2.93882	+	3.26389i	−0.403677	+	0.448329i	−0.910368	−	0.413799i	$-0.864202\pi$
$53$	−2.93882	+	3.26389i	−0.403677	+	0.448329i	0.506691	+	0.862128i	$0.330868\pi$
$54$	−10.9388	+	0.900739i	−1.48858	+	0.122575i
$55$	−9.27226			−1.25027
$56$	2.26467	+	1.23734i	0.302630	+	0.165347i
$57$	0.442341	+	0.779639i	0.0585895	+	0.103266i
$58$	0.859862	−	0.774223i	0.112905	−	0.101661i
$59$	−0.358430	+	3.41023i	−0.0466636	+	0.443974i	0.946099	+	0.323878i	$0.104987\pi$
$59$	−0.358430	+	3.41023i	−0.0466636	+	0.443974i	−0.992762	+	0.120096i	$0.961680\pi$
$60$	5.12594	−	8.72617i	0.661756	−	1.12654i
$61$	13.6382	−	1.43343i	1.74619	−	0.183532i	0.823045	−	0.567977i	$-0.192274\pi$
$61$	13.6382	−	1.43343i	1.74619	−	0.183532i	0.923148	+	0.384444i	$0.125607\pi$
$62$	3.32270	−	2.41408i	0.421983	−	0.306589i
$63$	6.38144	−	4.71987i	0.803986	−	0.594648i
$64$	−9.03610	−	6.56511i	−1.12951	−	0.820639i
$65$	4.16785	+	4.62887i	0.516959	+	0.574141i
$66$	−12.3237	−	7.23921i	−1.51694	−	0.891085i
$67$	−10.2493	−	9.22849i	−1.25215	−	1.12744i	−0.986568	−	0.163351i	$-0.947770\pi$
$67$	−10.2493	−	9.22849i	−1.25215	−	1.12744i	−0.265580	−	0.964089i	$-0.585564\pi$
$68$	11.0315	+	6.36903i	1.33776	+	0.772358i
$69$	−8.57506	−	7.83859i	−1.03232	−	0.943655i
$70$	0.312344	+	13.2608i	0.0373323	+	1.58497i
$71$	4.75666	−	14.6395i	0.564511	−	1.73739i	−0.104887	−	0.994484i	$-0.533448\pi$
$71$	4.75666	−	14.6395i	0.564511	−	1.73739i	0.669399	−	0.742903i	$-0.266552\pi$
$72$	2.55587	−	1.42481i	0.301212	−	0.167916i
$73$	3.33086	−	1.92307i	0.389848	−	0.225079i	−0.292246	−	0.956343i	$-0.594403\pi$
$73$	3.33086	−	1.92307i	0.389848	−	0.225079i	0.682094	+	0.731264i	$0.261069\pi$
$74$	0.972111	+	4.57342i	0.113006	+	0.531649i
$75$	1.09713	+	0.00825104i	0.126685	+	0.000952748i
$76$	−1.03071	−	0.748858i	−0.118231	−	0.0858999i
$77$	10.3330	−	0.243384i	1.17756	−	0.0277361i
$78$	1.92553	+	9.40621i	0.218024	+	1.06504i
$79$	11.1101	+	6.41445i	1.24999	+	0.721682i	0.971107	−	0.238644i	$-0.0767028\pi$
$79$	11.1101	+	6.41445i	1.24999	+	0.721682i	0.278882	+	0.960325i	$0.410036\pi$
$80$	0.710358	−	6.75860i	0.0794204	−	0.755635i
$81$	−0.671119	−	8.97494i	−0.0745687	−	0.997216i
$82$	10.3333	+	8.72666i	1.14113	+	0.963699i
$83$	−11.8609			−1.30190			−0.650949	−	0.759121i	$-0.725629\pi$
$83$	−11.8609			−1.30190			−0.650949	+	0.759121i	$0.725629\pi$
$84$	−5.48331	+	9.85901i	−0.598278	+	1.07571i
$85$			12.2812i			1.33209i
$86$	−3.32758	+	15.6550i	−0.358822	+	1.68812i
$87$	0.629533	+	0.709830i	0.0674930	+	0.0761018i
$88$	3.78960	+	0.398303i	0.403972	+	0.0424592i
$89$	3.13164	−	0.329149i	0.331953	−	0.0348897i	0.0629141	−	0.998019i	$-0.479961\pi$
$89$	3.13164	−	0.329149i	0.331953	−	0.0348897i	0.269039	+	0.963129i	$0.413294\pi$
$90$	12.9109	+	7.71530i	1.36092	+	0.813264i
$91$	−4.76616	−	5.04902i	−0.499630	−	0.529281i
$92$	15.7044	+	5.10265i	1.63729	+	0.531988i
$93$	1.95897	+	2.73938i	0.203136	+	0.284060i
$94$	15.0161	−	16.6770i	1.54879	−	1.72010i
$95$	0.128397	−	1.22162i	0.0131732	−	0.125335i
$96$	8.22738	−	11.1468i	0.839704	−	1.13766i
$97$	1.18877	+	3.65867i	0.120702	+	0.371482i	0.993094	−	0.117326i	$-0.0374321\pi$
$97$	1.18877	+	3.65867i	0.120702	+	0.371482i	−0.872392	+	0.488807i	$0.837432\pi$
$98$	−0.696153	−	14.7696i	−0.0703221	−	1.49196i
$99$	6.01188	−	10.0604i	0.604217	−	1.01110i
$100$	−1.42458	+	0.634264i	−0.142458	+	0.0634264i
$101$	−4.61097	+	10.3564i	−0.458809	+	1.03050i	0.524971	+	0.851120i	$0.324076\pi$
$101$	−4.61097	+	10.3564i	−0.458809	+	1.03050i	−0.983780	+	0.179381i	$0.942591\pi$
$102$	−9.58844	+	16.3229i	−0.949397	+	1.61621i
$103$	3.47994	−	0.365757i	0.342889	−	0.0360391i	0.0684809	−	0.997652i	$-0.478185\pi$
$103$	3.47994	−	0.365757i	0.342889	−	0.0360391i	0.274408	+	0.961613i	$0.411518\pi$
$104$	−1.50457	−	2.07087i	−0.147536	−	0.203065i
$105$	−10.8753	+	0.174337i	−1.06132	+	0.0170135i
$106$	8.82310	+	2.86680i	0.856976	+	0.278448i
$107$	2.09901	−	0.220615i	0.202919	−	0.0213276i	−0.00252372	−	0.999997i	$-0.500803\pi$
$107$	2.09901	−	0.220615i	0.202919	−	0.0213276i	0.205442	+	0.978669i	$0.434137\pi$
$108$	6.14433	+	11.2194i	0.591238	+	1.07959i
$109$	8.25874	−	4.76818i	0.791043	−	0.456709i	−0.0492863	−	0.998785i	$-0.515695\pi$
$109$	8.25874	−	4.76818i	0.791043	−	0.456709i	0.840330	+	0.542076i	$0.182361\pi$
$110$	7.96622	+	17.8924i	0.759550	+	1.70598i
$111$	−3.75603	+	0.768893i	−0.356507	+	0.0729801i
$112$	−0.614220	+	7.55044i	−0.0580383	+	0.713450i
$113$	−8.95115	−	2.90841i	−0.842054	−	0.273600i	−0.143940	−	0.989586i	$-0.545977\pi$
$113$	−8.95115	−	2.90841i	−0.842054	−	0.273600i	−0.698114	+	0.715987i	$0.745977\pi$
$114$	1.12441	−	1.52340i	0.105311	−	0.142679i
$115$	3.31003	+	15.5725i	0.308662	+	1.45214i
$116$	−1.23191	−	0.548482i	−0.114380	−	0.0509253i
$117$	−7.72463	+	1.52086i	−0.714142	+	0.140604i
$118$	6.88857	−	2.23823i	0.634145	−	0.206046i
$119$	−0.322365	−	13.6862i	−0.0295512	−	1.25461i
$120$	−3.98462	−	0.449122i	−0.363744	−	0.0409990i
$121$	3.89307	−	1.73330i	0.353915	−	0.157573i
$122$	−14.4833	−	25.0857i	−1.31125	−	2.27116i
$123$	−7.21927	+	8.41915i	−0.650940	+	0.759129i
$124$	−4.14532	−	2.39330i	−0.372261	−	0.214925i
$125$	8.38462	+	6.09179i	0.749944	+	0.544866i
$126$	−14.5904	−	8.25905i	−1.29982	−	0.735774i
$127$	2.14263	+	6.59433i	0.190127	+	0.585152i	0.999999	−	0.00145529i	$-0.000463233\pi$
$127$	2.14263	+	6.59433i	0.190127	+	0.585152i	−0.809872	+	0.586607i	$0.800463\pi$
$128$	−1.57912	+	7.42920i	−0.139576	+	0.656654i
$129$	−12.8160	−	2.82503i	−1.12839	−	0.248730i
$130$	5.35141	−	12.0195i	0.469350	−	1.05418i
$131$	−12.4679	−	13.8470i	−1.08932	−	1.20982i	−0.976345	−	0.216218i	$-0.930628\pi$
$131$	−12.4679	−	13.8470i	−1.08932	−	1.20982i	−0.112977	−	0.993598i	$-0.536039\pi$
$132$	−1.86570	+	16.5526i	−0.162389	+	1.44072i
$133$	−0.111020	+	1.36474i	−0.00962666	+	0.118338i
$134$	−9.00235	+	27.7064i	−0.777684	+	2.39347i
$135$	−6.40588	+	10.5389i	−0.551331	+	0.907041i
$136$	0.527558	−	5.01938i	0.0452377	−	0.430408i
$137$	9.54682	+	16.5356i	0.815640	+	1.41273i	0.908867	+	0.417085i	$0.136948\pi$
$137$	9.54682	+	16.5356i	0.815640	+	1.41273i	−0.0932274	+	0.995645i	$0.529718\pi$
$138$	−7.75868	+	23.2815i	−0.660463	+	1.98186i
$139$	4.53559	+	6.24271i	0.384704	+	0.529499i	0.956823	−	0.290671i	$-0.0938785\pi$
$139$	4.53559	+	6.24271i	0.384704	+	0.529499i	−0.572119	+	0.820171i	$0.693879\pi$
$140$	13.9706	−	6.61858i	1.18073	−	0.559372i
$141$	13.5820	+	12.4155i	1.14381	+	1.04557i
$142$	−32.3361	+	3.39866i	−2.71358	+	0.285209i
$143$	−9.36576	−	4.16991i	−0.783205	−	0.348705i
$144$	6.87247	+	5.15283i	0.572706	+	0.429403i
$145$	−0.135901	−	1.29301i	−0.0112860	−	0.107379i
$146$	−6.57260	−	4.77528i	−0.543952	−	0.395205i
$147$	12.1149	−	0.479742i	0.999217	−	0.0395685i
$148$	4.40848	−	3.20295i	0.362374	−	0.263280i
$149$	20.6211	+	4.38315i	1.68934	+	0.359081i	0.949517	−	0.313715i	$-0.101574\pi$
$149$	20.6211	+	4.38315i	1.68934	+	0.359081i	0.739828	+	0.672797i	$0.234907\pi$
$150$	−0.926672	−	2.12419i	−0.0756624	−	0.173439i
$151$	12.9293	+	1.35892i	1.05217	+	0.110587i	0.614791	−	0.788690i	$-0.289241\pi$
$151$	12.9293	+	1.35892i	1.05217	+	0.110587i	0.437378	+	0.899278i	$0.355907\pi$
$152$	−0.104952	+	0.493762i	−0.00851276	+	0.0400494i
$153$	−13.3251	−	7.96283i	−1.07727	−	0.643757i
$154$	−9.34722	−	19.7302i	−0.753220	−	1.58991i
$155$		−	4.61495i		−	0.370682i
$156$	9.10196	−	6.50894i	0.728740	−	0.521132i
$157$	−2.76746	−	1.23215i	−0.220867	−	0.0983364i	0.293320	−	0.956014i	$-0.405240\pi$
$157$	−2.76746	−	1.23215i	−0.220867	−	0.0983364i	−0.514187	+	0.857678i	$0.671906\pi$
$158$	2.83255	−	26.9499i	0.225345	−	2.14402i
$159$	−2.40508	+	7.21695i	−0.190735	+	0.572341i
$160$	−18.0558	+	5.86667i	−1.42743	+	0.463801i
$161$	−4.09746	−	17.2671i	−0.322925	−	1.36084i
$162$	−16.7421	+	9.00583i	−1.31539	+	0.707564i
$163$	6.39416	−	11.0750i	0.500829	−	0.867461i	−0.499171	−	0.866504i	$-0.666362\pi$
$163$	6.39416	−	11.0750i	0.500829	−	0.867461i	1.00000		0.000957403i	$-0.000304751\pi$
$164$	4.39288	−	15.1385i	0.343027	−	1.18212i
$165$	−14.7203	+	6.42168i	−1.14597	+	0.499927i
$166$	10.1902	+	22.8876i	0.790914	+	1.77642i
$167$		−	5.52225i		−	0.427324i	−0.976908	−	0.213662i	$-0.931461\pi$
$167$		−	5.52225i		−	0.427324i	0.976908	−	0.213662i	$-0.0685392\pi$
$168$	4.45225	+	0.395911i	0.343499	+	0.0305452i
$169$	−1.88903	−	5.81382i	−0.145310	−	0.447217i
$170$	23.6988	−	10.5514i	1.81761	−	0.809254i
$171$	1.24220	+	0.931372i	0.0949932	+	0.0712238i
$172$	18.2452	−	3.87813i	1.39118	−	0.295704i
$173$	−6.20539	+	10.7481i	−0.471787	+	0.817160i	−0.999479	−	0.0322763i	$-0.989724\pi$
$173$	−6.20539	+	10.7481i	−0.471787	+	0.817160i	0.527692	+	0.849436i	$0.323058\pi$
$174$	0.828880	−	1.82464i	0.0628372	−	0.138326i
$175$	1.37868	+	0.952892i	0.104219	+	0.0720319i
$176$	3.45650	+	10.6380i	0.260543	+	0.801870i
$177$	1.79279	+	5.66218i	0.134754	+	0.425596i
$178$	−3.32568	−	5.76026i	−0.249271	−	0.431749i
$179$	8.90775	−	9.89305i	0.665796	−	0.739442i	−0.311750	−	0.950164i	$-0.600915\pi$
$179$	8.90775	−	9.89305i	0.665796	−	0.739442i	0.977546	+	0.210723i	$0.0675817\pi$
$180$	2.09426	−	17.4034i	0.156097	−	1.29717i
$181$	4.57906	−	14.0929i	0.340359	−	1.04752i	−0.623663	−	0.781693i	$-0.714356\pi$
$181$	4.57906	−	14.0929i	0.340359	−	1.04752i	0.964022	−	0.265823i	$-0.0856437\pi$
$182$	−5.64813	+	13.5350i	−0.418667	+	1.00328i
$183$	20.6587	−	11.7211i	1.52714	−	0.866446i
$184$	−0.683882	−	6.50670i	−0.0504164	−	0.479680i
$185$	4.79955	+	2.13690i	0.352870	+	0.157108i
$186$	3.60307	−	6.13370i	0.264190	−	0.449745i
$187$	−8.22180	−	18.4665i	−0.601238	−	1.35040i
$188$	−24.8740	−	8.08205i	−1.81412	−	0.589444i
$189$	6.86209	−	11.9127i	0.499144	−	0.866519i
$190$	−2.46763	+	0.801781i	−0.179021	+	0.0581673i
$191$	−6.35192	+	11.0018i	−0.459609	+	0.796066i	−0.998940	−	0.0460278i	$-0.985344\pi$
$191$	−6.35192	+	11.0018i	−0.459609	+	0.796066i	0.539331	+	0.842094i	$0.318677\pi$
$192$	−18.8922	−	4.16439i	−1.36342	−	0.300539i
$193$	−9.29288	−	8.36735i	−0.668916	−	0.602295i	0.263075	−	0.964775i	$-0.415263\pi$
$193$	−9.29288	−	8.36735i	−0.668916	−	0.602295i	−0.931991	+	0.362480i	$0.881930\pi$
$194$	6.03871	−	5.43728i	0.433554	−	0.390374i
$195$	9.82253	+	4.46209i	0.703406	+	0.319537i
$196$	−15.3951	+	7.74246i	−1.09965	+	0.553033i
$197$	12.3769	+	4.02150i	0.881817	+	0.286520i	0.714712	−	0.699419i	$-0.246558\pi$
$197$	12.3769	+	4.02150i	0.881817	+	0.286520i	0.167106	+	0.985939i	$0.446558\pi$
$198$	−24.5783	−	2.95766i	−1.74670	−	0.210192i
$199$	1.04238	−	9.91758i	0.0738924	−	0.703039i	−0.893381	−	0.449301i	$-0.851673\pi$
$199$	1.04238	−	9.91758i	0.0738924	−	0.703039i	0.967273	−	0.253738i	$-0.0816602\pi$
$200$	0.459159	+	0.413428i	0.0324674	+	0.0292338i
$201$	−22.6627	−	7.55245i	−1.59850	−	0.532709i
$202$	23.9460			1.68483
$203$	0.185388	+	1.43737i	0.0130117	+	0.100884i
$204$	21.9241	+	2.47115i	1.53500	+	0.173015i
$205$	14.7579	−	3.62991i	1.03074	−	0.253524i
$206$	−3.69557	−	6.40091i	−0.257483	−	0.445973i
$207$	−19.0422	−	6.50541i	−1.32352	−	0.452157i
$208$	3.75699	−	6.50730i	0.260500	−	0.451200i
$209$	0.624761	+	1.92282i	0.0432156	+	0.133004i
$210$	9.67988	+	20.8360i	0.667975	+	1.43782i
$211$	2.53552	−	3.48984i	0.174552	−	0.240251i	−0.712773	−	0.701395i	$-0.752561\pi$
$211$	2.53552	−	3.48984i	0.174552	−	0.240251i	0.887325	+	0.461144i	$0.152561\pi$
$212$	−1.13017	−	10.7528i	−0.0776204	−	0.738509i
$213$	−2.58737	−	26.5354i	−0.177284	−	1.81817i
$214$	−2.22907	−	3.86086i	−0.152376	−	0.263923i
$215$	12.0335	+	13.3646i	0.820681	+	0.911458i
$216$	3.07081	−	4.03209i	0.208942	−	0.274349i
$217$	0.121136	+	5.14290i	0.00822323	+	0.349123i
$218$	−16.2965	−	11.8401i	−1.10374	−	0.801913i
$219$	3.95608	−	5.35985i	0.267327	−	0.362185i
$220$	15.2737	−	16.9632i	1.02975	−	1.14366i
$221$	−5.52310	+	12.4051i	−0.371524	+	0.834457i
$222$	4.71069	+	6.58733i	0.316161	+	0.442113i
$223$	−3.98503	+	5.48492i	−0.266857	+	0.367298i	−0.921326	−	0.388792i	$-0.872893\pi$
$223$	−3.98503	+	5.48492i	−0.266857	+	0.367298i	0.654468	+	0.756089i	$0.272893\pi$
$224$	19.9674	−	7.01176i	1.33413	−	0.468493i
$225$	1.74747	−	0.746738i	0.116498	−	0.0497825i
$226$	2.07807	+	19.7716i	0.138231	+	1.31518i
$227$	1.37080	−	3.07887i	0.0909832	−	0.204352i	−0.862322	−	0.506360i	$-0.830991\pi$
$227$	1.37080	−	3.07887i	0.0909832	−	0.204352i	0.953305	+	0.302009i	$0.0976572\pi$
$228$	−2.15496	−	0.475016i	−0.142715	−	0.0314587i
$229$	16.2369	+	18.0329i	1.07296	+	1.19165i	0.980620	+	0.195921i	$0.0627696\pi$
$229$	16.2369	+	18.0329i	1.07296	+	1.19165i	0.0923452	+	0.995727i	$0.470564\pi$
$230$	27.2060	−	19.7663i	1.79391	−	1.30335i
$231$	16.2357	−	7.54271i	1.06823	−	0.496274i
$232$			0.534296i			0.0350783i
$233$	8.66834	−	3.85939i	0.567882	−	0.252837i	−0.102651	−	0.994717i	$-0.532732\pi$
$233$	8.66834	−	3.85939i	0.567882	−	0.252837i	0.670532	+	0.741880i	$0.266066\pi$
$234$	9.57135	+	13.5994i	0.625699	+	0.889018i
$235$	−5.24273	−	24.6651i	−0.341998	−	1.60897i
$236$	−5.64843	−	6.27322i	−0.367682	−	0.408352i
$237$	22.0805	+	2.48878i	1.43428	+	0.161663i
$238$	−26.1330	+	12.3805i	−1.69395	+	0.802511i
$239$	18.6848	−	13.5753i	1.20862	−	0.878112i	0.213513	−	0.976940i	$-0.431509\pi$
$239$	18.6848	−	13.5753i	1.20862	−	0.878112i	0.995104	+	0.0988284i	$0.0315095\pi$
$240$	−3.55306	−	11.2217i	−0.229349	−	0.724355i
$241$	9.83713	+	8.85740i	0.633666	+	0.570555i	0.922103	−	0.386944i	$-0.126469\pi$
$241$	9.83713	+	8.85740i	0.633666	+	0.570555i	−0.288438	+	0.957499i	$0.593136\pi$
$242$	−6.68942	−	6.02318i	−0.430012	−	0.387185i
$243$	−7.28121	−	13.7835i	−0.467090	−	0.884210i
$244$	−19.8431	+	27.3117i	−1.27032	+	1.74845i
$245$	−13.8862	−	9.12204i	−0.887158	−	0.582785i
$246$	22.4486	+	6.69755i	1.43127	+	0.427020i
$247$	0.679075	−	1.17619i	0.0432085	−	0.0748393i
$248$	−0.198242	+	1.88614i	−0.0125884	+	0.119770i
$249$	−18.8298	+	8.21446i	−1.19329	+	0.520571i
$250$	4.55154	−	21.4133i	0.287865	−	1.35430i
$251$	6.88059	+	21.1763i	0.434299	+	1.33663i	0.893803	+	0.448459i	$0.148027\pi$
$251$	6.88059	+	21.1763i	0.434299	+	1.33663i	−0.459504	+	0.888175i	$0.651973\pi$
$252$	−1.87704	+	19.4493i	−0.118242	+	1.22519i
$253$	−15.4022	−	21.1993i	−0.968329	−	1.33279i
$254$	10.8841	−	9.80006i	0.682927	−	0.614910i
$255$	8.50561	+	19.4972i	0.532642	+	1.22096i
$256$	−6.15771	+	1.30886i	−0.384857	+	0.0818038i
$257$	0.0760768	−	0.0684998i	0.00474554	−	0.00427290i	−0.666754	−	0.745277i	$-0.732317\pi$
$257$	0.0760768	−	0.0684998i	0.00474554	−	0.00427290i	0.671500	+	0.741005i	$0.265650\pi$
$258$	5.55945	+	27.1579i	0.346116	+	1.69077i
$259$	−5.40471	−	2.25538i	−0.335832	−	0.140142i
$260$	−15.3338			−0.950961
$261$	1.49103	+	0.690904i	0.0922923	+	0.0427659i
$262$	−16.0084	+	35.9555i	−0.989003	+	2.22134i
$263$	13.1511	−	2.79534i	0.810929	−	0.172368i	0.216257	−	0.976336i	$-0.430615\pi$
$263$	13.1511	−	2.79534i	0.810929	−	0.172368i	0.594672	+	0.803968i	$0.297282\pi$
$264$	6.29207	−	1.99223i	0.387250	−	0.122613i
$265$	8.43347	−	6.12727i	0.518064	−	0.376395i
$266$	2.72888	−	0.958278i	0.167319	−	0.0587558i
$267$	4.74371	−	2.69142i	0.290310	−	0.164712i
$268$	33.7662	−	3.54897i	2.06260	−	0.216788i
$269$	0.160900	−	1.53086i	0.00981025	−	0.0933383i	−0.988521	−	0.151082i	$-0.951724\pi$
$269$	0.160900	−	1.53086i	0.00981025	−	0.0933383i	0.998331	+	0.0577442i	$0.0183908\pi$
$270$	25.8402	+	3.30684i	1.57258	+	0.201248i
$271$	−14.3076	+	1.50379i	−0.869123	+	0.0913485i	−0.528583	−	0.848882i	$-0.677276\pi$
$271$	−14.3076	+	1.50379i	−0.869123	+	0.0913485i	−0.340540	+	0.940230i	$0.610610\pi$
$272$	14.0902	−	4.57818i	0.854344	−	0.277593i
$273$	−11.0634	−	4.71473i	−0.669585	−	0.285348i
$274$	23.7062	−	32.6287i	1.43214	−	1.97117i
$275$	2.42054	+	0.514501i	0.145964	+	0.0310256i
$276$	28.4656	−	2.77558i	1.71342	−	0.167070i
$277$	3.13383	−	0.666115i	0.188293	−	0.0400230i	−0.112800	−	0.993618i	$-0.535982\pi$
$277$	3.13383	−	0.666115i	0.188293	−	0.0400230i	0.301093	+	0.953595i	$0.402649\pi$
$278$	8.14965	−	14.1156i	0.488783	−	0.846598i
$279$	5.00719	+	2.99221i	0.299773	+	0.179139i
$280$	−4.64712	−	3.99020i	−0.277718	−	0.238460i
$281$	−20.4884	−	14.8857i	−1.22224	−	0.888007i	−0.225953	−	0.974138i	$-0.572550\pi$
$281$	−20.4884	−	14.8857i	−1.22224	−	0.888007i	−0.996284	+	0.0861312i	$0.972550\pi$
$282$	12.2889	−	36.8754i	0.731794	−	2.19590i
$283$	11.8946	+	10.7100i	0.707062	+	0.636641i	0.942095	−	0.335346i	$-0.108853\pi$
$283$	11.8946	+	10.7100i	0.707062	+	0.636641i	−0.235033	+	0.971987i	$0.575520\pi$
$284$	18.9469	+	32.8169i	1.12429	+	1.94733i
$285$	−0.642215	−	2.02831i	−0.0380415	−	0.120147i
$286$			21.6554i			1.28051i
$287$	−16.3509	+	4.43255i	−0.965164	+	0.261645i
$288$	5.34156	−	23.3942i	0.314755	−	1.37852i
$289$	−8.92884	+	3.97538i	−0.525226	+	0.233846i
$290$	−2.37834	+	1.37313i	−0.139661	+	0.0806331i
$291$	4.42113	+	4.98505i	0.259171	+	0.292229i
$292$	−1.96858	+	9.26143i	−0.115202	+	0.541984i
$293$	−6.94504	+	9.55902i	−0.405733	+	0.558444i	−0.962171	−	0.272445i	$-0.912168\pi$
$293$	−6.94504	+	9.55902i	−0.405733	+	0.558444i	0.556438	+	0.830889i	$0.312168\pi$
$294$	−11.3342	−	22.9656i	−0.661023	−	1.33938i
$295$	2.51500	−	7.74039i	0.146429	−	0.450663i
$296$	−1.86980	−	1.07953i	−0.108680	−	0.0627462i
$297$	2.57674	−	20.1351i	0.149518	−	1.16835i
$298$	−9.25848	−	43.5577i	−0.536329	−	2.52323i
$299$	−3.65982	+	17.2181i	−0.211653	+	0.995748i
$300$	−1.82234	+	1.99355i	−0.105213	+	0.115098i
$301$	−13.7610	−	14.5777i	−0.793171	−	0.840243i
$302$	−8.48585	−	26.1168i	−0.488306	−	1.50285i
$303$	−0.147665	+	19.6348i	−0.00848315	+	1.12799i
$304$	−1.44942	+	0.308083i	−0.0831297	+	0.0176698i
$305$	−32.3701	−	3.40224i	−1.85351	−	0.194811i
$306$	−3.91747	+	32.5543i	−0.223947	+	1.86101i
$307$	−3.34668	−	4.60631i	−0.191005	−	0.262896i	0.702764	−	0.711423i	$-0.251949\pi$
$307$	−3.34668	−	4.60631i	−0.191005	−	0.262896i	−0.893769	+	0.448527i	$0.851949\pi$
$308$	−16.5758	+	19.3047i	−0.944492	+	1.09999i
$309$	5.27131	−	2.99076i	0.299874	−	0.170139i
$310$	−8.90534	+	3.96491i	−0.505789	+	0.225192i
$311$	2.99722	+	14.1008i	0.169957	+	0.799585i	0.977693	+	0.210040i	$0.0673595\pi$
$311$	2.99722	+	14.1008i	0.169957	+	0.799585i	−0.807736	+	0.589545i	$0.799307\pi$
$312$	−3.82282	−	2.24561i	−0.216425	−	0.127132i
$313$	10.9118	+	2.31937i	0.616771	+	0.131099i	0.505694	−	0.862713i	$-0.331237\pi$
$313$	10.9118	+	2.31937i	0.616771	+	0.131099i	0.111077	+	0.993812i	$0.464570\pi$
$314$			6.39889i			0.361110i
$315$	−17.1444	+	7.80866i	−0.965980	+	0.439968i
$316$	−30.0361	+	9.75931i	−1.68966	+	0.549004i
$317$	−3.70892	−	4.11917i	−0.208314	−	0.231356i	0.629930	−	0.776652i	$-0.283084\pi$
$317$	−3.70892	−	4.11917i	−0.208314	−	0.231356i	−0.838243	+	0.545297i	$0.816417\pi$
$318$	15.9927	−	1.55939i	0.896824	−	0.0874463i
$319$	1.06997	+	1.85324i	0.0599066	+	0.103761i
$320$	17.7387	+	19.7008i	0.991623	+	1.10131i
$321$	3.17951	−	1.80395i	0.177463	−	0.100686i
$322$	−29.7995	+	22.7417i	−1.66066	+	1.26735i
$323$	2.54680	−	0.827505i	0.141708	−	0.0460436i
$324$	17.5247	+	13.5562i	0.973596	+	0.753120i
$325$	−0.831177	−	1.43964i	−0.0461054	−	0.0798569i
$326$	−26.8646	−	2.82359i	−1.48790	−	0.156384i
$327$	9.80895	−	13.2895i	0.542436	−	0.734912i
$328$	−6.18751	+	0.849608i	−0.341648	+	0.0469118i
$329$	6.48993	+	27.3492i	0.357801	+	1.50781i
$330$	25.0386	+	22.8882i	1.37833	+	1.25995i
$331$	27.8854	+	16.0996i	1.53272	+	0.884916i	0.999235	+	0.0391063i	$0.0124511\pi$
$331$	27.8854	+	16.0996i	1.53272	+	0.884916i	0.533485	+	0.845810i	$0.320882\pi$
$332$	19.5378	−	21.6989i	1.07227	−	1.19088i
$333$	−5.43042	+	3.82198i	−0.297585	+	0.209443i
$334$	−10.6561	+	4.74442i	−0.583078	+	0.259603i
$335$	19.2409	+	26.4828i	1.05124	+	1.44691i
$336$	4.25409	+	12.4122i	0.232080	+	0.677139i
$337$	6.95676			0.378959			0.189479	−	0.981885i	$-0.439320\pi$
$337$	6.95676			0.378959			0.189479	+	0.981885i	$0.439320\pi$
$338$	−9.59583	+	8.64012i	−0.521944	+	0.469961i
$339$	−16.2248	+	1.58202i	−0.881209	+	0.0859236i
$340$	−22.4680	−	20.2302i	−1.21850	−	1.09714i
$341$	3.08952	+	6.93918i	0.167307	+	0.375778i
$342$	0.730016	−	3.19722i	0.0394748	−	0.172886i
$343$	15.7143	+	9.80111i	0.848491	+	0.529210i
$344$	−4.34405	−	5.97907i	−0.234215	−	0.322370i
$345$	16.0399	+	22.4298i	0.863558	+	1.20758i
$346$	26.0716	+	2.74023i	1.40162	+	0.147316i
$347$	−2.68417	−	1.19507i	−0.144094	−	0.0641546i	0.333423	−	0.942777i	$-0.391796\pi$
$347$	−2.68417	−	1.19507i	−0.144094	−	0.0641546i	−0.477517	+	0.878623i	$0.658463\pi$
$348$	−2.33560	−	0.0175650i	−0.125201	−	0.000941584i
$349$	−3.76638	−	5.18398i	−0.201610	−	0.277492i	0.696226	−	0.717823i	$-0.254861\pi$
$349$	−3.76638	−	5.18398i	−0.201610	−	0.277492i	−0.897836	+	0.440331i	$0.854861\pi$
$350$	0.654280	−	3.47908i	0.0349727	−	0.185965i
$351$	−11.2100	+	7.76430i	−0.598346	+	0.414428i
$352$	23.2217	−	20.9089i	1.23772	−	1.11445i
$353$	3.56007	+	1.58504i	0.189483	+	0.0843634i	0.499285	−	0.866438i	$-0.333596\pi$
$353$	3.56007	+	1.58504i	0.189483	+	0.0843634i	−0.309802	+	0.950801i	$0.600263\pi$
$354$	9.38590	−	8.32414i	0.498855	−	0.442423i
$355$	−18.2674	+	31.6401i	−0.969532	+	1.67928i
$356$	−4.55642	+	6.27137i	−0.241490	+	0.332382i
$357$	−9.99044	−	21.5045i	−0.528750	−	1.13814i
$358$	−26.7434	−	8.68946i	−1.41343	−	0.459252i
$359$	−4.63766	+	4.17576i	−0.244766	+	0.220388i	−0.782378	−	0.622804i	$-0.785993\pi$
$359$	−4.63766	+	4.17576i	−0.244766	+	0.220388i	0.537612	+	0.843193i	$0.319327\pi$
$360$	−6.63687	+	2.04661i	−0.349794	+	0.107866i
$361$	18.3228	−	3.89464i	0.964359	−	0.204981i
$362$	−31.1288	+	3.27176i	−1.63609	+	0.171960i
$363$	4.98004	−	5.44794i	0.261384	−	0.285943i
$364$	17.0880	−	0.402490i	0.895654	−	0.0210962i
$365$	−8.68199	+	2.82095i	−0.454436	+	0.147655i
$366$	−40.3667	−	29.7945i	−2.11000	−	1.55738i
$367$	1.63813	+	0.172174i	0.0855095	+	0.00898741i	0.147187	−	0.989109i	$-0.452978\pi$
$367$	1.63813	+	0.172174i	0.0855095	+	0.00898741i	−0.0616771	+	0.998096i	$0.519645\pi$
$368$	16.6323	−	9.60266i	0.867019	−	0.500573i
$369$	−5.63018	+	18.3658i	−0.293096	+	0.956083i
$370$		−	11.0975i		−	0.576930i
$371$	−9.23743	+	7.04961i	−0.479584	+	0.365997i
$372$	−8.23847	−	0.928590i	−0.427145	−	0.0481452i
$373$	−2.18229	−	0.463860i	−0.112995	−	0.0240178i	0.151067	−	0.988523i	$-0.451729\pi$
$373$	−2.18229	−	0.463860i	−0.112995	−	0.0240178i	−0.264062	+	0.964506i	$0.585062\pi$
$374$	−28.5705	+	31.7308i	−1.47735	+	1.64076i
$375$	17.5301	+	3.86415i	0.905249	+	0.199544i
$376$	1.08319	+	10.3059i	0.0558615	+	0.531486i
$377$	0.444221	−	1.36717i	0.0228785	−	0.0704129i
$378$	−28.8831	−	3.00688i	−1.48559	−	0.154657i
$379$	1.09397	−	3.36691i	0.0561937	−	0.172946i	−0.919020	−	0.394210i	$-0.871018\pi$
$379$	1.09397	−	3.36691i	0.0561937	−	0.172946i	0.975214	+	0.221264i	$0.0710182\pi$
$380$	2.02339	+	2.24720i	0.103797	+	0.115279i
$381$	7.96858	+	8.98498i	0.408243	+	0.460314i
$382$	26.6872	+	2.80494i	1.36544	+	0.143513i
$383$	−7.09790	−	4.09798i	−0.362686	−	0.209397i	0.307572	−	0.951525i	$-0.400483\pi$
$383$	−7.09790	−	4.09798i	−0.362686	−	0.209397i	−0.670258	+	0.742128i	$0.733817\pi$
$384$	2.63828	+	12.8880i	0.134634	+	0.657686i
$385$	−24.1095	−	4.53405i	−1.22873	−	0.231077i
$386$	−8.16231	+	25.1210i	−0.415451	+	1.27863i
$387$	−22.3027	+	4.39108i	−1.13371	+	0.223211i
$388$	−8.65157	−	3.85193i	−0.439217	−	0.195552i
$389$	−8.07373	+	18.1339i	−0.409354	+	0.919425i	0.584772	+	0.811198i	$0.301184\pi$
$389$	−8.07373	+	18.1339i	−0.409354	+	0.919425i	−0.994126	+	0.108227i	$0.965483\pi$
$390$	0.171378	−	22.7879i	0.00867805	−	1.15391i
$391$	−28.0788	+	20.4005i	−1.42001	+	1.03170i
$392$	5.28349	+	4.32470i	0.266857	+	0.218431i
$393$	−29.3835	−	13.3480i	−1.48220	−	0.673320i
$394$	−2.87338	−	27.3384i	−0.144759	−	1.37729i
$395$	−22.6282	−	20.3745i	−1.13855	−	1.02515i
$396$	8.50188	+	27.5703i	0.427235	+	1.38546i
$397$	−8.06434	+	3.59047i	−0.404738	+	0.180201i	−0.599000	−	0.800749i	$-0.704435\pi$
$397$	−8.06434	+	3.59047i	−0.404738	+	0.180201i	0.194263	+	0.980950i	$0.437769\pi$
$398$	−20.0333	+	6.50920i	−1.00418	+	0.326277i
$399$	0.768925	+	2.24350i	0.0384944	+	0.112315i
$400$	−0.560463	+	1.72493i	−0.0280232	+	0.0862464i
$401$	1.53920	+	0.888660i	0.0768642	+	0.0443776i	0.537940	−	0.842983i	$-0.319203\pi$
$401$	1.53920	+	0.888660i	0.0768642	+	0.0443776i	−0.461075	+	0.887361i	$0.652536\pi$
$402$	4.89681	+	50.2203i	0.244231	+	2.50476i
$403$	2.07543	−	4.66149i	0.103384	−	0.232205i
$404$	−11.3512	−	25.4951i	−0.564741	−	1.26843i
$405$	−2.87083	+	21.1676i	−0.142653	+	1.05183i
$406$	2.61438	−	1.59265i	0.129749	−	0.0790418i
$407$	−8.64732			−0.428632
$408$	−2.63874	−	8.33394i	−0.130637	−	0.412591i
$409$	25.5162	−	14.7318i	1.26169	−	0.728440i	0.288292	−	0.957542i	$-0.406913\pi$
$409$	25.5162	−	14.7318i	1.26169	−	0.728440i	0.973402	+	0.229103i	$0.0735792\pi$
$410$	−19.6837	−	25.3593i	−0.972109	−	1.25240i
$411$	26.6082	+	19.6394i	1.31249	+	0.968740i
$412$	−5.06319	+	6.96888i	−0.249445	+	0.343332i
$413$	−2.59955	+	8.69191i	−0.127915	+	0.427701i
$414$	3.80670	+	42.3343i	0.187089	+	2.08062i
$415$	27.5364	+	5.85305i	1.35171	+	0.287315i
$416$	−20.8762	−	2.19418i	−1.02354	−	0.107578i
$417$	11.5240	+	6.76946i	0.564334	+	0.331502i
$418$	3.17365	−	2.85756i	0.155228	−	0.139768i
$419$	−26.8445			−1.31144			−0.655720	−	0.755004i	$-0.727635\pi$
$419$	−26.8445			−1.31144			−0.655720	+	0.755004i	$0.727635\pi$
$420$	17.5953	−	20.1830i	0.858565	−	0.984830i
$421$	−21.8918	−	7.11306i	−1.06694	−	0.346669i	−0.277644	−	0.960684i	$-0.589554\pi$
$421$	−21.8918	−	7.11306i	−1.06694	−	0.346669i	−0.789295	+	0.614015i	$0.789554\pi$
$422$	−8.91264	−	1.89444i	−0.433860	−	0.0922199i
$423$	30.1608	+	10.3039i	1.46647	+	0.500991i
$424$	−3.70999	+	2.14196i	−0.180173	+	0.104023i
$425$	0.681465	−	3.20604i	0.0330559	−	0.155516i
$426$	−48.9817	+	27.7906i	−2.37317	+	1.34646i
$427$	36.1626	+	2.94179i	1.75003	+	0.142363i
$428$	−3.05398	+	4.20344i	−0.147620	+	0.203181i
$429$	−17.7567	−	0.133540i	−0.857300	−	0.00644739i
$430$	15.4507	−	34.7029i	0.745101	−	1.67352i
$431$	3.41368	−	7.66725i	0.164431	−	0.369318i	−0.812472	−	0.583000i	$-0.801879\pi$
$431$	3.41368	−	7.66725i	0.164431	−	0.369318i	0.976903	+	0.213682i	$0.0685455\pi$
$432$	14.4792	+	3.42077i	0.696629	+	0.164582i
$433$	−9.49752	+	13.0722i	−0.456422	+	0.628211i	−0.973762	−	0.227569i	$-0.926922\pi$
$433$	−9.49752	+	13.0722i	−0.456422	+	0.628211i	0.517340	+	0.855780i	$0.326922\pi$
$434$	9.82005	−	4.65226i	0.471378	−	0.223315i
$435$	−1.11125	−	1.95862i	−0.0532805	−	0.0939085i
$436$	−4.88101	+	22.9633i	−0.233758	+	1.09974i
$437$	3.00628	−	1.73568i	0.143810	−	0.0830287i
$438$	−13.7416	−	3.02906i	−0.656600	−	0.144734i
$439$	−33.6913	−	7.16130i	−1.60800	−	0.341790i	−0.685584	−	0.727994i	$-0.740453\pi$
$439$	−33.6913	−	7.16130i	−1.60800	−	0.341790i	−0.922414	+	0.386204i	$0.873786\pi$
$440$	−8.60146	−	2.79478i	−0.410058	−	0.133236i
$441$	18.9008	−	9.15200i	0.900039	−	0.435809i
$442$	28.6829			1.36431
$443$	−16.9410	+	15.2537i	−0.804891	+	0.724727i	−0.964965	−	0.262378i	$-0.915493\pi$
$443$	−16.9410	+	15.2537i	−0.804891	+	0.724727i	0.160074	+	0.987105i	$0.448827\pi$
$444$	4.78046	−	8.13804i	0.226871	−	0.386214i
$445$	−7.43291	−	0.781230i	−0.352354	−	0.0370339i
$446$	14.0078	+	2.97746i	0.663290	+	0.140987i
$447$	35.7728	−	7.32301i	1.69200	−	0.346367i
$448$	−20.2851	−	21.4890i	−0.958382	−	1.01526i
$449$	8.59559	−	11.8308i	0.405651	−	0.558331i	−0.556500	−	0.830848i	$-0.687856\pi$
$449$	8.59559	−	11.8308i	0.405651	−	0.558331i	0.962151	+	0.272517i	$0.0878561\pi$
$450$	−2.94229	−	2.73049i	−0.138701	−	0.128717i
$451$	−19.7603	+	15.3379i	−0.930478	+	0.722232i
$452$	20.0655	−	11.5848i	0.943804	−	0.544905i
$453$	21.4671	−	6.79704i	1.00861	−	0.319353i
$454$	−7.11892			−0.334108
$455$	8.57366	+	14.0739i	0.401939	+	0.659795i
$456$	0.175346	+	0.856564i	0.00821133	+	0.0401123i
$457$	7.06820	+	15.8754i	0.330636	+	0.742621i	1.00000		0.000313720i	$-9.98601e-5\pi$
$457$	7.06820	+	15.8754i	0.330636	+	0.742621i	−0.669364	+	0.742935i	$0.733433\pi$
$458$	20.8478	−	46.8248i	0.974152	−	2.18798i
$459$	−26.6692	−	3.41293i	−1.24481	−	0.159302i
$460$	−33.9415	−	19.5962i	−1.58253	−	0.913675i
$461$	−6.94697	+	21.3806i	−0.323552	+	0.995792i	0.648537	+	0.761183i	$0.275381\pi$
$461$	−6.94697	+	21.3806i	−0.323552	+	0.995792i	−0.972090	+	0.234609i	$0.924619\pi$
$462$	−28.5038	−	24.8494i	−1.32612	−	1.15610i
$463$	21.9343	−	7.12688i	1.01937	−	0.331214i	0.248792	−	0.968557i	$-0.419966\pi$
$463$	21.9343	−	7.12688i	1.01937	−	0.331214i	0.770581	+	0.637342i	$0.219966\pi$
$464$	−1.43281	+	0.637927i	−0.0665164	+	0.0296150i
$465$	−3.19617	−	7.32651i	−0.148219	−	0.339759i
$466$	−14.8947	−	13.4113i	−0.689985	−	0.621266i
$467$	−0.225467	−	2.14517i	−0.0104334	−	0.0992668i	0.988066	−	0.154032i	$-0.0492258\pi$
$467$	−0.225467	−	2.14517i	−0.0104334	−	0.0992668i	−0.998499	+	0.0547648i	$0.982559\pi$
$468$	9.94201	−	16.6371i	0.459570	−	0.769049i
$469$	−22.1372	−	29.0075i	−1.02220	−	1.33944i
$470$	−43.0913	+	31.3077i	−1.98765	+	1.44412i
$471$	−5.24686	−	0.0394594i	−0.241762	−	0.00181819i
$472$	−1.36039	+	3.05548i	−0.0626170	+	0.140640i
$473$	−27.0411	−	12.0395i	−1.24335	−	0.553575i
$474$	−14.1678	−	44.7463i	−0.650750	−	2.05527i
$475$	−0.101304	+	0.311780i	−0.00464812	+	0.0143055i
$476$	25.5693	+	21.9548i	1.17197	+	1.00630i
$477$	1.18002	+	13.1230i	0.0540296	+	0.600862i
$478$	−42.2488	−	24.3924i	−1.93242	−	1.11568i
$479$	31.4409	+	3.30458i	1.43657	+	0.150990i	0.790583	−	0.612355i	$-0.209778\pi$
$479$	31.4409	+	3.30458i	1.43657	+	0.150990i	0.645991	+	0.763345i	$0.276445\pi$
$480$	−24.6015	+	21.8186i	−1.12290	+	0.995876i
$481$	3.88695	+	4.31689i	0.177230	+	0.196833i
$482$	8.64035	−	26.5923i	0.393557	−	1.21124i
$483$	−18.4636	−	24.5748i	−0.840124	−	1.11819i
$484$	−3.24184	+	9.97736i	−0.147356	+	0.453516i
$485$	−0.954418	−	9.08068i	−0.0433379	−	0.412333i
$486$	−20.3420	+	25.8924i	−0.922730	+	1.17450i
$487$	−20.2055	+	22.4405i	−0.915600	+	1.01688i	0.0841912	+	0.996450i	$0.473169\pi$
$487$	−20.2055	+	22.4405i	−0.915600	+	1.01688i	−0.999791	+	0.0204273i	$0.993497\pi$
$488$	13.0836	+	2.78101i	0.592267	+	0.125890i
$489$	2.48090	−	22.0106i	0.112190	−	0.995355i
$490$	−5.67225	+	34.6330i	−0.256246	+	1.56456i
$491$			31.4654i			1.42001i	0.704195	+	0.710007i	$0.251308\pi$
$491$			31.4654i			1.42001i	−0.704195	+	0.710007i	$0.748692\pi$
$492$	−3.51052	−	27.0757i	−0.158267	−	1.22067i
$493$	2.45464	−	1.41719i	0.110551	−	0.0638269i
$494$	−2.85309	−	0.299872i	−0.128367	−	0.0134919i
$495$	−18.9219	+	20.3896i	−0.850474	+	0.916445i
$496$	−5.29470	+	1.72035i	−0.237739	+	0.0772462i
$497$	19.5267	−	35.7392i	0.875892	−	1.60312i
$498$	32.0288	+	29.2780i	1.43525	+	1.31198i
$499$	21.3951	−	2.24871i	0.957775	−	0.100666i	0.387275	−	0.921964i	$-0.373416\pi$
$499$	21.3951	−	2.24871i	0.957775	−	0.100666i	0.570500	+	0.821298i	$0.306750\pi$
$500$	−24.9562	+	5.30460i	−1.11607	+	0.237229i
$501$	−3.82454	−	8.76690i	−0.170868	−	0.391676i
$502$	34.9519	−	31.4708i	1.55998	−	1.40461i
$503$	24.2742	+	7.88715i	1.08233	+	0.351671i	0.795279	−	0.606244i	$-0.207324\pi$
$503$	24.2742	+	7.88715i	1.08233	+	0.351671i	0.287053	+	0.957915i	$0.407324\pi$
$504$	7.34241	−	2.45496i	0.327057	−	0.109353i
$505$	15.8156	−	21.7683i	0.703783	−	0.968675i
$506$	−27.6750	+	47.9346i	−1.23031	+	2.13095i
$507$	−7.02541	−	7.92151i	−0.312010	−	0.351807i
$508$	−15.5934	−	6.94265i	−0.691847	−	0.308030i
$509$	23.1151	−	20.8129i	1.02456	−	0.922516i	0.0275349	−	0.999621i	$-0.491234\pi$
$509$	23.1151	−	20.8129i	1.02456	−	0.922516i	0.997023	+	0.0771047i	$0.0245676\pi$
$510$	30.3157	−	33.1640i	1.34240	−	1.46853i
$511$	9.60118	−	3.37156i	0.424731	−	0.149149i
$512$	16.7447	+	23.0471i	0.740018	+	1.01855i
$513$	2.61710	+	0.618303i	0.115548	+	0.0272987i
$514$	−0.197543	−	0.0879520i	−0.00871327	−	0.00387940i
$515$	−8.25960	−	0.868119i	−0.363962	−	0.0382539i
$516$	26.2794	−	18.7928i	1.15689	−	0.827307i
$517$	24.3954	+	33.5774i	1.07291	+	1.47673i
$518$	0.291293	+	12.3670i	0.0127987	+	0.543376i
$519$	−2.40767	+	21.3609i	−0.105685	+	0.937638i
$520$	2.47113	+	5.55024i	0.108366	+	0.243394i
$521$	15.1846	+	13.6723i	0.665249	+	0.598993i	0.930987	−	0.365053i	$-0.118949\pi$
$521$	15.1846	+	13.6723i	0.665249	+	0.598993i	−0.265738	+	0.964045i	$0.585616\pi$
$522$	0.0522075	−	3.47078i	0.00228506	−	0.151912i
$523$	−24.3214	+	21.8991i	−1.06350	+	0.957579i	−0.999186	−	0.0403507i	$-0.987152\pi$
$523$	−24.3214	+	21.8991i	−1.06350	+	0.957579i	−0.0643136	+	0.997930i	$0.520486\pi$
$524$	45.8700			2.00384
$525$	2.84869	+	0.557940i	0.124327	+	0.0243505i
$526$	−16.6928	−	22.9756i	−0.727840	−	1.00179i
$527$	9.19105	−	4.09212i	0.400369	−	0.178256i
$528$	12.8550	+	14.4946i	0.559440	+	0.630797i
$529$	−14.7153	+	16.3430i	−0.639796	+	0.710565i
$530$	−19.0692	−	11.0096i	−0.828314	−	0.478227i
$531$	6.76762	+	7.74743i	0.293690	+	0.336210i
$532$	−2.31385	−	2.45117i	−0.100318	−	0.106272i
$533$	16.5391	+	2.97038i	0.716390	+	0.128661i
$534$	−9.26910	−	6.84149i	−0.401113	−	0.296060i
$535$	−4.98197	−	0.523626i	−0.215389	−	0.0226383i
$536$	−6.72620	−	11.6501i	−0.290528	−	0.503209i
$537$	7.28996	−	21.8751i	0.314585	−	0.943978i
$538$	−3.09230	+	1.00475i	−0.133319	+	0.0433178i
$539$	26.9866	+	4.41991i	1.16240	+	0.190379i
$540$	−8.72828	−	29.0794i	−0.375606	−	1.25138i
$541$	−7.69650	−	8.54783i	−0.330898	−	0.367500i	0.554620	−	0.832103i	$-0.312863\pi$
$541$	−7.69650	−	8.54783i	−0.330898	−	0.367500i	−0.885519	+	0.464604i	$0.846197\pi$
$542$	15.1941	+	26.3170i	0.652643	+	1.13041i
$543$	−2.49077	−	25.5446i	−0.106889	−	1.09622i
$544$	−27.6942	−	30.7575i	−1.18738	−	1.31872i
$545$	−21.5266	+	6.99443i	−0.922100	+	0.299609i
$546$	0.407165	+	25.3993i	0.0174251	+	1.08699i
$547$			3.52767i			0.150832i	0.997152	+	0.0754161i	$0.0240285\pi$
$547$			3.52767i			0.150832i	−0.997152	+	0.0754161i	$0.975972\pi$
$548$	−45.9770	−	9.77272i	−1.96404	−	0.417470i
$549$	24.6793	−	32.9155i	1.05329	−	1.40480i
$550$	−1.08678	−	5.11288i	−0.0463403	−	0.218014i
$551$	−0.258979	+	0.115305i	−0.0110329	+	0.00491216i
$552$	−5.59204	−	9.85614i	−0.238013	−	0.419505i
$553$	25.7517	+	22.1114i	1.09507	+	0.940273i
$554$	−3.97780	−	5.47497i	−0.169000	−	0.232609i
$555$	9.09952	+	0.0684336i	0.386253	+	0.00290485i
$556$	−18.8920	−	1.98563i	−0.801198	−	0.0842093i
$557$	11.5203	−	2.44871i	0.488129	−	0.103755i	0.0427289	−	0.999087i	$-0.486395\pi$
$557$	11.5203	−	2.44871i	0.488129	−	0.103755i	0.445400	+	0.895332i	$0.353062\pi$
$558$	1.47208	−	12.2330i	0.0623179	−	0.517864i
$559$	6.14458	+	18.9111i	0.259888	+	0.799854i
$560$	5.15195	−	17.2262i	0.217709	−	0.727938i
$561$	−25.8419	−	23.6225i	−1.09105	−	0.997342i
$562$	−11.1220	+	52.3250i	−0.469154	+	2.20720i
$563$	6.97551	+	32.8172i	0.293983	+	1.38308i	0.838761	+	0.544500i	$0.183280\pi$
$563$	6.97551	+	32.8172i	0.293983	+	1.38308i	−0.544778	+	0.838580i	$0.683386\pi$
$564$	−45.0863	+	4.39622i	−1.89848	+	0.185114i
$565$	19.3460	+	11.1694i	0.813891	+	0.469900i
$566$	10.4475	−	32.1542i	0.439142	−	1.35154i
$567$	2.64364	−	23.6646i	0.111023	−	0.993818i
$568$	8.82508	−	12.1467i	0.370292	−	0.509663i
$569$	−4.76730	+	22.4284i	−0.199856	+	0.940246i	0.757835	+	0.652446i	$0.226257\pi$
$569$	−4.76730	+	22.4284i	−0.199856	+	0.940246i	−0.957691	+	0.287800i	$0.907076\pi$
$570$	−3.36222	+	2.98188i	−0.140828	+	0.124897i
$571$	−6.40475	+	3.69779i	−0.268031	+	0.154748i	−0.627992	−	0.778220i	$-0.716123\pi$
$571$	−6.40475	+	3.69779i	−0.268031	+	0.154748i	0.359962	+	0.932967i	$0.382790\pi$
$572$	23.0564	−	10.2654i	0.964035	−	0.429216i
$573$	−2.46452	+	21.8652i	−0.102957	+	0.913434i
$574$	22.6012	+	27.7437i	0.943356	+	1.15800i
$575$		−	4.24889i		−	0.177191i
$576$	−32.8766	+	6.47290i	−1.36986	+	0.269704i
$577$	6.82004	+	11.8127i	0.283922	+	0.491767i	0.972347	−	0.233540i	$-0.0750310\pi$
$577$	6.82004	+	11.8127i	0.283922	+	0.491767i	−0.688425	+	0.725307i	$0.741698\pi$
$578$	15.3424	+	13.8143i	0.638158	+	0.574600i
$579$	−20.5480	−	6.84771i	−0.853945	−	0.284581i
$580$	2.58937	+	1.88129i	0.107518	+	0.0781162i
$581$	−30.8403	−	5.79985i	−1.27947	−	0.240618i
$582$	5.82113	−	12.8142i	0.241293	−	0.531167i
$583$	−8.57887	+	14.8590i	−0.355300	+	0.615398i
$584$	3.66953	−	0.779983i	0.151846	−	0.0322759i
$585$	18.6842	+	0.281047i	0.772495	+	0.0116199i
$586$	24.4126	+	5.18906i	1.00847	+	0.214358i
$587$	26.6851	−	36.7289i	1.10141	−	1.51596i	0.267914	−	0.963443i	$-0.413666\pi$
$587$	26.6851	−	36.7289i	1.10141	−	1.51596i	0.833499	−	0.552521i	$-0.186334\pi$
$588$	−19.0785	+	22.9538i	−0.786784	+	0.946599i
$589$	−0.957016	+	0.310953i	−0.0394331	+	0.0128126i
$590$	−17.0972	+	1.79699i	−0.703880	+	0.0739807i
$591$	22.4342	−	2.18749i	0.922821	−	0.0899811i
$592$	0.662481	−	6.30308i	0.0272278	−	0.259055i
$593$	11.8067	−	1.24093i	0.484842	−	0.0509589i	0.141045	−	0.990003i	$-0.454954\pi$
$593$	11.8067	−	1.24093i	0.484842	−	0.0509589i	0.343796	+	0.939044i	$0.388287\pi$
$594$	−41.0679	+	12.3267i	−1.68504	+	0.505770i
$595$	−6.00542	+	31.9333i	−0.246198	+	1.30914i
$596$	−41.9868	+	30.5052i	−1.71984	+	1.24954i
$597$	−5.21377	−	16.4667i	−0.213385	−	0.673937i
$598$	36.3696	−	7.73060i	1.48726	−	0.316128i
$599$	−11.8344	+	26.5805i	−0.483541	+	1.08605i	0.492865	+	0.870106i	$0.335950\pi$
$599$	−11.8344	+	26.5805i	−0.483541	+	1.08605i	−0.976406	+	0.215944i	$0.930717\pi$
$600$	1.01527	+	0.338343i	0.0414482	+	0.0138128i
$601$	−6.36225			−0.259522			−0.129761	−	0.991545i	$-0.541421\pi$
$601$	−6.36225			−0.259522			−0.129761	+	0.991545i	$0.541421\pi$
$602$	−16.3074	+	39.0786i	−0.664641	+	1.59272i
$603$	−41.2090	+	3.70552i	−1.67816	+	0.150900i
$604$	−23.7838	+	21.4150i	−0.967748	+	0.871364i
$605$	−9.89357	+	2.10294i	−0.402231	+	0.0854968i
$606$	38.0157	−	16.5842i	1.54428	−	0.673689i
$607$	11.9178	−	10.7308i	0.483729	−	0.435551i	−0.390836	−	0.920460i	$-0.627814\pi$
$607$	11.9178	−	10.7308i	0.483729	−	0.435551i	0.874565	+	0.484909i	$0.161147\pi$
$608$	2.43318	+	3.34898i	0.0986784	+	0.135819i
$609$	1.28979	+	2.15352i	0.0522650	+	0.0872649i
$610$	21.2454	+	65.3868i	0.860203	+	2.64743i
$611$	5.79676	−	27.2716i	0.234512	−	1.10329i
$612$	36.5173	−	11.2609i	1.47612	−	0.455193i
$613$	−2.62591	+	24.9839i	−0.106059	+	1.00909i	0.804005	+	0.594622i	$0.202698\pi$
$613$	−2.62591	+	24.9839i	−0.106059	+	1.00909i	−0.910065	+	0.414466i	$0.863968\pi$
$614$	−6.01339	+	10.4155i	−0.242680	+	0.420335i
$615$	20.9151	−	15.9836i	0.843377	−	0.644519i
$616$	9.65883	+	2.88873i	0.389166	+	0.116390i
$617$	23.6047	−	32.4891i	0.950290	−	1.30796i	−0.00110793	−	0.999999i	$-0.500353\pi$
$617$	23.6047	−	32.4891i	0.950290	−	1.30796i	0.951398	−	0.307963i	$-0.0996473\pi$
$618$	−10.3000	−	7.60240i	−0.414327	−	0.305813i
$619$	0.993174	+	0.894258i	0.0399190	+	0.0359433i	0.688849	−	0.724905i	$-0.258116\pi$
$619$	0.993174	+	0.894258i	0.0399190	+	0.0359433i	−0.648930	+	0.760848i	$0.724783\pi$
$620$	8.44283	+	7.60196i	0.339072	+	0.305302i
$621$	−34.7361	+	2.86030i	−1.39391	+	0.114780i
$622$	24.6350	−	17.8983i	0.987772	−	0.717658i
$623$	8.30375	+	0.675501i	0.332683	+	0.0270634i
$624$	1.45770	−	12.9327i	0.0583545	−	0.517723i
$625$	−18.5791	−	20.6341i	−0.743163	−	0.825366i
$626$	−4.89919	−	23.0489i	−0.195811	−	0.921218i
$627$	2.32353	+	2.61990i	0.0927928	+	0.104629i
$628$	6.81285	−	3.03327i	0.271862	−	0.121041i
$629$			11.4535i			0.456681i
$630$	29.7977	+	26.3744i	1.18717	+	1.05078i
$631$	−34.3348	+	24.9457i	−1.36685	+	0.993072i	−0.368870	+	0.929481i	$0.620255\pi$
$631$	−34.3348	+	24.9457i	−1.36685	+	0.993072i	−0.997976	+	0.0635909i	$0.979745\pi$
$632$	8.37299	+	9.29914i	0.333060	+	0.369900i
$633$	1.60833	−	7.29636i	0.0639255	−	0.290004i
$634$	−4.76215	+	10.6960i	−0.189129	+	0.424791i
$635$	−1.72023	−	16.3669i	−0.0682651	−	0.649499i
$636$	−9.24130	−	16.2881i	−0.366441	−	0.645864i
$637$	−9.92391	−	15.4589i	−0.393200	−	0.612505i
$638$	2.65688	−	3.65689i	0.105187	−	0.144778i
$639$	−22.4852	−	40.3346i	−0.889501	−	1.59561i
$640$	7.33226	−	16.4685i	0.289833	−	0.650976i
$641$	23.9158	−	26.5611i	0.944616	−	1.04910i	−0.0541049	−	0.998535i	$-0.517231\pi$
$641$	23.9158	−	26.5611i	0.944616	−	1.04910i	0.998721	−	0.0505668i	$-0.0161028\pi$
$642$	−6.21269	−	4.58556i	−0.245195	−	0.180978i
$643$	−36.0587	−	26.1982i	−1.42202	−	1.03316i	−0.991435	−	0.130604i	$-0.958308\pi$
$643$	−36.0587	−	26.1982i	−1.42202	−	1.03316i	−0.430582	−	0.902551i	$-0.641692\pi$
$644$	38.3389	+	20.9471i	1.51076	+	0.825430i
$645$	28.3599	+	12.8831i	1.11667	+	0.507270i
$646$	−3.78489	−	4.20354i	−0.148914	−	0.165386i
$647$	21.9432	+	38.0067i	0.862675	+	1.49420i	0.869337	+	0.494220i	$0.164546\pi$
$647$	21.9432	+	38.0067i	0.862675	+	1.49420i	−0.00666154	+	0.999978i	$0.502120\pi$
$648$	2.08260	−	8.52794i	0.0818123	−	0.335009i
$649$	1.40024	+	13.3224i	0.0549642	+	0.522950i
$650$	−2.06394	+	2.84076i	−0.0809542	+	0.111424i
$651$	3.75413	+	8.08078i	0.147136	+	0.316711i
$652$	9.72844	+	29.9411i	0.380995	+	1.17258i
$653$	−15.5911	+	27.0047i	−0.610129	+	1.05677i	0.381090	+	0.924538i	$0.375549\pi$
$653$	−15.5911	+	27.0047i	−0.610129	+	1.05677i	−0.991218	+	0.132236i	$0.957784\pi$
$654$	−34.0718	−	7.51042i	−1.33231	−	0.293681i
$655$	22.1125	+	38.3000i	0.864008	+	1.49651i
$656$	−9.66599	−	15.5785i	−0.377394	−	0.608237i
$657$	2.56846	−	11.2489i	0.100205	−	0.438863i
$658$	47.1992	−	36.0204i	1.84002	−	1.40422i
$659$	3.09258			0.120470			0.0602350	−	0.998184i	$-0.480815\pi$
$659$	3.09258			0.120470			0.0602350	+	0.998184i	$0.480815\pi$
$660$	12.4998	−	37.5081i	0.486552	−	1.46000i
$661$	−3.59771	−	3.23939i	−0.139935	−	0.125998i	0.596191	−	0.802843i	$-0.296680\pi$
$661$	−3.59771	−	3.23939i	−0.139935	−	0.125998i	−0.736126	+	0.676845i	$0.763347\pi$
$662$	7.10942	−	67.6416i	0.276316	−	2.62897i
$663$	−0.176876	+	23.5190i	−0.00686930	+	0.913401i
$664$	−11.0028	−	3.57502i	−0.426991	−	0.138738i
$665$	0.931212	−	3.11362i	0.0361109	−	0.120741i
$666$	12.0407	+	7.19530i	0.466567	+	0.278812i
$667$	2.73049	−	2.45855i	0.105725	−	0.0951954i
$668$	10.1027	+	9.09650i	0.390885	+	0.351954i
$669$	−2.52779	+	11.4676i	−0.0977299	+	0.443361i
$670$	34.5725	−	59.8813i	1.33565	−	2.31342i
$671$	50.9504	−	16.5548i	1.96692	−	0.639091i
$672$	26.8433	−	24.9604i	1.03550	−	0.962867i
$673$	5.24093	+	1.70288i	0.202023	+	0.0656413i	0.408281	−	0.912856i	$-0.366128\pi$
$673$	5.24093	+	1.70288i	0.202023	+	0.0656413i	−0.206258	+	0.978498i	$0.566128\pi$
$674$	−5.97687	−	13.4243i	−0.230220	−	0.517084i
$675$	2.25705	−	2.39574i	0.0868739	−	0.0922120i
$676$	13.7478	+	6.12091i	0.528761	+	0.235420i
$677$	1.45038	+	13.7994i	0.0557426	+	0.530356i	0.986388	+	0.164434i	$0.0525797\pi$
$677$	1.45038	+	13.7994i	0.0557426	+	0.530356i	−0.930645	+	0.365922i	$0.880754\pi$
$678$	16.9922	+	29.9493i	0.652583	+	1.15020i
$679$	1.30196	+	10.0945i	0.0499646	+	0.387390i
$680$	−3.70173	+	11.3928i	−0.141955	+	0.436892i
$681$	0.0438995	−	5.83726i	0.00168223	−	0.223684i
$682$	10.7360	−	11.9235i	0.411103	−	0.456576i
$683$	−16.5674	−	28.6955i	−0.633932	−	1.09800i	−0.986740	−	0.162307i	$-0.948106\pi$
$683$	−16.5674	−	28.6955i	−0.633932	−	1.09800i	0.352808	−	0.935696i	$-0.385227\pi$
$684$	−3.75011	+	0.738340i	−0.143389	+	0.0282311i
$685$	−14.0042	−	43.1005i	−0.535073	−	1.64678i
$686$	5.41210	−	38.7440i	0.206635	−	1.47925i
$687$	38.2661	+	17.3832i	1.45994	+	0.663209i
$688$	10.8473	−	18.7881i	0.413549	−	0.716288i
$689$	11.2741	−	2.39638i	0.429508	−	0.0912947i
$690$	29.5016	−	50.2222i	1.12311	−	1.91193i
$691$	0.0912953	−	0.0406473i	0.00347304	−	0.00154630i	−0.404999	−	0.914317i	$-0.632728\pi$
$691$	0.0912953	−	0.0406473i	0.00347304	−	0.00154630i	0.408472	+	0.912771i	$0.366062\pi$
$692$	−9.44125	−	29.0572i	−0.358902	−	1.10459i
$693$	20.5513	−	23.2189i	0.780681	−	0.882012i
$694$			6.20631i			0.235588i
$695$	−7.44930	−	16.7314i	−0.282568	−	0.634658i
$696$	0.370037	+	0.848227i	0.0140262	+	0.0321520i
$697$	20.3152	+	26.1729i	0.769494	+	0.991368i
$698$	−6.76751	+	11.7217i	−0.256154	+	0.443672i
$699$	11.0886	−	12.1304i	0.419410	−	0.458816i
$700$	−4.01430	+	0.952588i	−0.151726	+	0.0360044i
$701$	−19.6979	+	6.40023i	−0.743979	+	0.241734i	−0.656389	−	0.754423i	$-0.727917\pi$
$701$	−19.6979	+	6.40023i	−0.743979	+	0.241734i	−0.0875907	+	0.996157i	$0.527917\pi$
$702$	24.6136	+	14.9610i	0.928980	+	0.564666i
$703$	0.119743	−	1.13928i	0.00451620	−	0.0429688i
$704$	−39.8614	−	17.7474i	−1.50233	−	0.668881i
$705$	−25.4054	−	35.5264i	−0.956824	−	1.33800i
$706$		−	8.23155i		−	0.309799i
$707$	−17.0535	+	24.6737i	−0.641363	+	0.927950i
$708$	−13.3119	−	6.04719i	−0.500291	−	0.227267i
$709$	−0.403205	+	1.89693i	−0.0151427	+	0.0712408i	−0.985070	−	0.172153i	$-0.944928\pi$
$709$	−0.403205	+	1.89693i	−0.0151427	+	0.0712408i	0.969927	+	0.243394i	$0.0782609\pi$
$710$	76.7493	+	8.06668i	2.88035	+	0.302737i
$711$	36.7777	−	11.3412i	1.37927	−	0.425327i
$712$	3.00429	+	0.638582i	0.112591	+	0.0239319i
$713$	10.5512	−	7.66593i	0.395147	−	0.287091i
$714$	−32.9133	+	37.7537i	−1.23175	+	1.41290i
$715$	19.6860	+	14.3027i	0.736215	+	0.534892i
$716$	3.42562	+	32.5926i	0.128021	+	1.21804i
$717$	20.2614	−	34.4921i	0.756675	−	1.28813i
$718$	12.0423	+	5.36157i	0.449414	+	0.200092i
$719$	−21.3997	+	2.24920i	−0.798074	+	0.0838809i	−0.494782	−	0.869017i	$-0.664752\pi$
$719$	−21.3997	+	2.24920i	−0.798074	+	0.0838809i	−0.303291	+	0.952898i	$0.598086\pi$
$720$	−13.4125	−	15.3543i	−0.499854	−	0.572222i
$721$	9.22730	+	0.750630i	0.343643	+	0.0279549i
$722$	−23.2574	−	32.0110i	−0.865549	−	1.19133i
$723$	21.7514	+	7.24876i	0.808943	+	0.269584i
$724$	18.2394	+	31.5916i	0.677863	+	1.17409i
$725$	−0.0362698	+	0.345084i	−0.00134703	+	0.0128161i
$726$	−14.7913	−	4.92928i	−0.548958	−	0.182943i
$727$	−2.70266	+	8.31795i	−0.100236	+	0.308496i	−0.988583	−	0.150678i	$-0.951854\pi$
$727$	−2.70266	+	8.31795i	−0.100236	+	0.308496i	0.888347	+	0.459173i	$0.151854\pi$
$728$	−2.89951	−	6.12034i	−0.107463	−	0.226835i
$729$	−21.1054	−	16.8393i	−0.781680	−	0.623680i
$730$	12.9026	+	14.3298i	0.477547	+	0.530370i
$731$	−15.9465	+	35.8163i	−0.589801	+	1.32471i
$732$	−12.5869	+	57.1016i	−0.465224	+	2.11054i
$733$	0.709159	−	3.33633i	0.0261934	−	0.123230i	−0.963108	−	0.269114i	$-0.913269\pi$
$733$	0.709159	−	3.33633i	0.0261934	−	0.123230i	0.989302	+	0.145884i	$0.0466025\pi$
$734$	−1.07515	−	3.30897i	−0.0396845	−	0.122136i
$735$	−28.3629	−	4.86461i	−1.04618	−	0.179434i
$736$	−43.4056	−	31.5360i	−1.59995	−	1.16243i
$737$	−46.6604	−	26.9394i	−1.71876	−	0.992326i
$738$	40.2771	−	4.91445i	1.48262	−	0.180903i
$739$	11.3765	+	19.7047i	0.418492	+	0.724849i	0.995788	−	0.0916859i	$-0.0292256\pi$
$739$	11.3765	+	19.7047i	0.418492	+	0.724849i	−0.577296	+	0.816535i	$0.695892\pi$
$740$	−11.8154	+	5.26055i	−0.434342	+	0.193382i
$741$	0.263478	−	2.33758i	0.00967911	−	0.0858732i
$742$	21.5397	+	11.7686i	0.790749	+	0.432038i
$743$	30.8807	−	10.0337i	1.13290	−	0.368102i	0.318224	−	0.948015i	$-0.396913\pi$
$743$	30.8807	−	10.0337i	1.13290	−	0.368102i	0.814678	+	0.579913i	$0.196913\pi$
$744$	0.991563	+	3.13166i	0.0363525	+	0.114812i
$745$	−45.7114	−	20.3520i	−1.67473	−	0.745640i
$746$	0.979807	+	4.60963i	0.0358733	+	0.168770i
$747$	−24.2044	+	26.0819i	−0.885593	+	0.954287i
$748$	47.3269	+	15.3774i	1.73044	+	0.562255i
$749$	5.56566	+	0.452760i	0.203365	+	0.0165435i
$750$	−7.60436	−	37.1472i	−0.277672	−	1.35642i
$751$	−18.3771	−	41.2756i	−0.670588	−	1.50617i	−0.852432	−	0.522839i	$-0.824873\pi$
$751$	−18.3771	−	41.2756i	−0.670588	−	1.50617i	0.181843	−	0.983328i	$-0.441794\pi$
$752$	−26.3438	+	15.2096i	−0.960658	+	0.554636i
$753$	25.5894	+	28.8533i	0.932529	+	1.05147i
$754$	−3.01984	+	0.317398i	−0.109976	+	0.0115590i
$755$	−29.3463	−	9.53518i	−1.06802	−	0.347021i
$756$	10.4901	+	32.1770i	0.381521	+	1.17027i
$757$	−27.3692	−	37.6705i	−0.994752	−	1.36916i	−0.928491	−	0.371356i	$-0.878893\pi$
$757$	−27.3692	−	37.6705i	−0.994752	−	1.36916i	−0.0662611	−	0.997802i	$-0.521107\pi$
$758$	−7.43692	+	0.781651i	−0.270121	+	0.0283909i
$759$	−39.1340	−	22.9881i	−1.42047	−	0.834416i
$760$	0.487319	−	1.09454i	0.0176769	−	0.0397030i
$761$	−9.79619	+	4.36154i	−0.355111	+	0.158106i	−0.576536	−	0.817072i	$-0.695596\pi$
$761$	−9.79619	+	4.36154i	−0.355111	+	0.158106i	0.221425	+	0.975177i	$0.428929\pi$
$762$	10.4919	−	23.0962i	0.380081	−	0.836686i
$763$	23.8057	−	8.35965i	0.861825	−	0.302639i
$764$	−9.66418	−	29.7433i	−0.349638	−	1.07607i
$765$	27.0063	+	25.0623i	0.976416	+	0.906129i
$766$	−1.80962	+	17.2174i	−0.0653843	+	0.622090i
$767$	6.02136	−	6.68740i	0.217419	−	0.241468i
$768$	−8.86925	+	6.34253i	−0.320042	+	0.228866i
$769$	−38.5592	−	12.5286i	−1.39048	−	0.451794i	−0.484379	−	0.874858i	$-0.660955\pi$
$769$	−38.5592	−	12.5286i	−1.39048	−	0.451794i	−0.906100	+	0.423064i	$0.860955\pi$
$770$	11.9643	+	50.4188i	0.431164	+	1.81697i
$771$	0.0733356	−	0.161436i	0.00264112	−	0.00581398i
$772$	30.6153	−	3.21780i	1.10187	−	0.115811i
$773$	−47.1267	−	4.95321i	−1.69503	−	0.178155i	−0.792820	−	0.609456i	$-0.791388\pi$
$773$	−47.1267	−	4.95321i	−1.69503	−	0.178155i	−0.902208	+	0.431301i	$0.858055\pi$
$774$	27.6347	+	39.2644i	0.993307	+	1.41133i
$775$	−0.256075	+	1.20474i	−0.00919850	+	0.0432755i
$776$			3.75230i			0.134700i
$777$	−10.1423	+	0.162587i	−0.363853	+	0.00583277i
$778$	41.9290			1.50323
$779$	−1.74712	−	2.81580i	−0.0625972	−	0.100887i
$780$	−24.3433	+	10.6197i	−0.871630	+	0.380246i
$781$	6.28568	−	59.8043i	0.224919	−	2.13997i
$782$	63.4901	+	36.6560i	2.27040	+	1.31082i
$783$	2.84560	+	0.0642112i	0.101693	+	0.00229472i
$784$	−5.28917	+	19.3321i	−0.188899	+	0.690432i
$785$	5.81695	+	4.22626i	0.207616	+	0.150842i
$786$	−0.512666	+	68.1684i	−0.0182862	+	2.43149i
$787$	−2.28520	−	10.7510i	−0.0814584	−	0.383232i	0.918466	−	0.395499i	$-0.129428\pi$
$787$	−2.28520	−	10.7510i	−0.0814584	−	0.383232i	−0.999925	+	0.0122674i	$0.996095\pi$
$788$	−27.7449	+	16.0185i	−0.988372	+	0.570637i
$789$	18.9421	−	13.5458i	0.674358	−	0.482243i
$790$	−19.8752	+	61.1697i	−0.707129	+	2.17632i
$791$	−21.8523	−	11.9394i	−0.776980	−	0.424516i
$792$	8.60928	−	7.52047i	0.305917	−	0.267228i
$793$	−31.1665	−	17.9940i	−1.10675	−	0.638985i
$794$	13.8569	+	12.4768i	0.491763	+	0.442785i
$795$	9.14508	−	15.5682i	0.324343	−	0.552146i
$796$	16.4267	+	18.2437i	0.582229	+	0.646630i
$797$	−24.9683	−	18.1405i	−0.884422	−	0.642570i	0.0499957	−	0.998749i	$-0.484079\pi$
$797$	−24.9683	−	18.1405i	−0.884422	−	0.642570i	−0.934418	+	0.356179i	$0.884079\pi$
$798$	3.66859	−	3.41126i	0.129867	−	0.120757i
$799$	44.4738	−	32.3121i	1.57337	−	1.14312i
$800$	5.03902	−	0.529622i	0.178156	−	0.0187250i
$801$	5.66693	−	7.55814i	0.200231	−	0.267054i
$802$	0.392423	−	3.73365i	0.0138569	−	0.131840i
$803$	11.1660	−	10.0539i	0.394040	−	0.354795i
$804$	51.1479	−	29.0196i	1.80385	−	1.02344i
$805$	0.991850	+	42.1097i	0.0349581	+	1.48417i
$806$	−10.7782			−0.379647
$807$	−0.804789	−	2.54177i	−0.0283299	−	0.0894745i
$808$	−7.39895	+	8.21737i	−0.260294	+	0.289086i
$809$	−7.98978	+	1.69828i	−0.280906	+	0.0597084i	−0.346210	−	0.938157i	$-0.612532\pi$
$809$	−7.98978	+	1.69828i	−0.280906	+	0.0597084i	0.0653042	+	0.997865i	$0.479198\pi$
$810$	43.3130	−	12.6463i	1.52186	−	0.444345i
$811$			27.6300i			0.970219i	0.874453	+	0.485109i	$0.161220\pi$
$811$			27.6300i			0.970219i	−0.874453	+	0.485109i	$0.838780\pi$
$812$	−2.93498	−	2.02854i	−0.102998	−	0.0711879i
$813$	−21.6727	+	12.2963i	−0.760093	+	0.431251i
$814$	7.42931	+	16.6865i	0.260397	+	0.584862i
$815$	−20.3101	+	22.5566i	−0.711430	+	0.790123i
$816$	19.1983	−	17.0266i	0.672076	−	0.596050i
$817$	1.96064	−	3.39593i	0.0685942	−	0.118809i
$818$	−50.3497	−	36.5812i	−1.76043	−	1.27903i
$819$	−20.8290	+	0.177233i	−0.727825	+	0.00619304i
$820$	−17.6691	+	32.9782i	−0.617032	+	1.15165i
$821$	−28.3230	−	16.3523i	−0.988479	−	0.570699i	−0.0836598	−	0.996494i	$-0.526661\pi$
$821$	−28.3230	−	16.3523i	−0.988479	−	0.570699i	−0.904819	+	0.425796i	$0.859994\pi$
$822$	15.0373	−	68.2182i	0.524486	−	2.37938i
$823$	−22.4711	+	12.9737i	−0.783294	+	0.452235i	−0.837597	−	0.546289i	$-0.816040\pi$
$823$	−22.4711	+	12.9737i	−0.783294	+	0.452235i	0.0543022	+	0.998525i	$0.482707\pi$
$824$	3.33843	+	0.709606i	0.116300	+	0.0247203i
$825$	4.19908	−	0.859588i	0.146193	−	0.0299270i
$826$	19.0059	−	2.45134i	0.661301	−	0.0852930i
$827$	9.19718	−	6.68214i	0.319817	−	0.232361i	−0.416280	−	0.909236i	$-0.636666\pi$
$827$	9.19718	−	6.68214i	0.319817	−	0.232361i	0.736098	+	0.676876i	$0.236666\pi$
$828$	43.2685	−	24.1208i	1.50368	−	0.838254i
$829$	−41.2335	+	23.8062i	−1.43210	+	0.826822i	−0.997281	−	0.0736972i	$-0.976520\pi$
$829$	−41.2335	+	23.8062i	−1.43210	+	0.826822i	−0.434817	+	0.900519i	$0.643187\pi$
$830$	−12.3633	−	58.1649i	−0.429138	−	2.01893i
$831$	4.51381	−	3.22789i	0.156582	−	0.111974i
$832$	9.05775	+	27.8769i	0.314021	+	0.966458i
$833$	5.85424	−	35.7442i	0.202837	−	1.23846i
$834$	3.16203	−	28.0536i	0.109492	−	0.971416i
$835$	−2.72510	+	12.8206i	−0.0943059	+	0.443674i
$836$	−4.54684	−	2.02438i	−0.157256	−	0.0700147i
$837$	10.0215	+	1.28248i	0.346395	+	0.0443292i
$838$	23.0634	+	51.8012i	0.796711	+	1.78944i
$839$	30.7925	+	42.3823i	1.06308	+	1.46320i	0.876894	+	0.480684i	$0.159612\pi$
$839$	30.7925	+	42.3823i	1.06308	+	1.46320i	0.186183	+	0.982515i	$0.440388\pi$
$840$	−10.1411	−	3.11623i	−0.349900	−	0.107520i
$841$	23.2187	−	16.8694i	0.800646	−	0.581704i
$842$	5.08232	+	48.3551i	0.175148	+	1.66643i
$843$	−42.8360	−	9.44232i	−1.47535	−	0.325211i
$844$	2.20788	+	10.3872i	0.0759982	+	0.357544i
$845$	1.51662	+	14.4297i	0.0521733	+	0.496396i
$846$	−6.02940	−	67.0529i	−0.207295	−	2.30533i
$847$	10.9702	−	2.60321i	0.376941	−	0.0894475i
$848$	−10.1736	−	7.39155i	−0.349363	−	0.253827i
$849$	26.3008	+	8.76487i	0.902642	+	0.300810i
$850$	−6.77209	+	1.43945i	−0.232281	+	0.0493728i
$851$	3.08694	+	14.5229i	0.105819	+	0.497839i
$852$	52.8073	+	38.9768i	1.80915	+	1.33532i
$853$	−41.3135	−	13.4236i	−1.41455	−	0.459615i	−0.500683	−	0.865631i	$-0.666918\pi$
$853$	−41.3135	−	13.4236i	−1.41455	−	0.459615i	−0.913866	+	0.406016i	$0.866918\pi$
$854$	−25.3923	−	72.3094i	−0.868905	−	2.47438i
$855$	−2.42430	−	2.77529i	−0.0829093	−	0.0949129i
$856$	2.01365	+	0.428015i	0.0688252	+	0.0146292i
$857$	−1.85032	+	2.05498i	−0.0632056	+	0.0701969i	−0.773918	−	0.633285i	$-0.781706\pi$
$857$	−1.85032	+	2.05498i	−0.0632056	+	0.0701969i	0.710713	+	0.703482i	$0.248373\pi$
$858$	14.9979	+	34.3793i	0.512019	+	1.17369i
$859$	−18.3444	−	41.2022i	−0.625903	−	1.40580i	−0.896472	−	0.443101i	$-0.853878\pi$
$859$	−18.3444	−	41.2022i	−0.625903	−	1.40580i	0.270569	−	0.962701i	$-0.412788\pi$
$860$	−44.2721			−1.50967
$861$	−22.8882	+	18.3611i	−0.780029	+	0.625744i
$862$	−17.7281			−0.603822
$863$	2.04474	+	4.59256i	0.0696037	+	0.156332i	0.944997	−	0.327079i	$-0.106064\pi$
$863$	2.04474	+	4.59256i	0.0696037	+	0.156332i	−0.875393	+	0.483411i	$0.839398\pi$
$864$	−7.72204	−	40.8391i	−0.262709	−	1.38937i
$865$	19.7105	−	21.8907i	0.670177	−	0.744307i
$866$	33.3849	+	7.09617i	1.13446	+	0.241138i
$867$	−11.4219	+	12.4950i	−0.387907	+	0.424352i
$868$	−9.60824	−	8.25002i	−0.326125	−	0.280024i
$869$	47.6644	+	15.4871i	1.61690	+	0.525364i
$870$	−2.82476	+	3.82709i	−0.0957684	+	0.129751i
$871$	7.52512	+	35.4029i	0.254979	+	1.19958i
$872$	9.09846	−	1.93394i	0.308113	−	0.0654913i
$873$	10.4713	+	4.85213i	0.354400	+	0.164220i
$874$	−5.93213	−	4.30994i	−0.200657	−	0.145786i
$875$	18.8226	+	19.9397i	0.636321	+	0.674084i
$876$	3.28894	+	16.0665i	0.111123	+	0.542835i
$877$	1.01547	+	9.66154i	0.0342899	+	0.326247i	0.998198	+	0.0600106i	$0.0191135\pi$
$877$	1.01547	+	9.66154i	0.0342899	+	0.326247i	−0.963908	+	0.266236i	$0.914220\pi$
$878$	15.1268	+	71.1658i	0.510503	+	2.40173i
$879$	−4.40538	+	19.9854i	−0.148590	+	0.674092i
$880$	−2.77508	−	26.4031i	−0.0935480	−	0.890049i
$881$	24.0782	−	17.4939i	0.811216	−	0.589383i	−0.102967	−	0.994685i	$-0.532834\pi$
$881$	24.0782	−	17.4939i	0.811216	−	0.589383i	0.914183	+	0.405302i	$0.132834\pi$
$882$	−33.8989	−	28.6095i	−1.14144	−	0.963332i
$883$	−26.0379	−	35.8380i	−0.876243	−	1.20605i	−0.977447	−	0.211180i	$-0.932269\pi$
$883$	−26.0379	−	35.8380i	−0.876243	−	1.20605i	0.101204	−	0.994866i	$-0.467731\pi$
$884$	−13.5966	−	30.5385i	−0.457304	−	1.02712i
$885$	−1.36803	−	14.0301i	−0.0459859	−	0.471618i
$886$	43.9895	+	19.5854i	1.47786	+	0.657984i
$887$	4.32941	−	20.3683i	0.145367	−	0.683900i	−0.843746	−	0.536743i	$-0.819654\pi$
$887$	4.32941	−	20.3683i	0.145367	−	0.683900i	0.989113	−	0.147157i	$-0.0470123\pi$
$888$	−3.71606	−	0.418852i	−0.124703	−	0.0140557i
$889$	2.34663	+	18.1941i	0.0787034	+	0.610211i
$890$	4.87843	+	15.0143i	0.163526	+	0.503280i
$891$	−9.85419	−	33.7502i	−0.330128	−	1.13067i
$892$	−3.47008	−	16.3254i	−0.116187	−	0.546616i
$893$	−4.76162	+	2.74912i	−0.159342	+	0.0919960i
$894$	−44.8651	−	62.7384i	−1.50051	−	2.09828i
$895$	−25.5624	+	18.5722i	−0.854457	+	0.620799i
$896$	−7.73880	+	18.5450i	−0.258535	+	0.619545i
$897$	6.11454	+	29.8694i	0.204158	+	0.997312i
$898$	−30.2145	−	6.42228i	−1.00827	−	0.214314i
$899$	−0.922385	+	0.532539i	−0.0307633	+	0.0177612i
$900$	−1.51239	+	4.42698i	−0.0504132	+	0.147566i
$901$	19.6810	+	11.3628i	0.655670	+	0.378551i
$902$	46.5741	+	24.9535i	1.55075	+	0.830862i
$903$	−31.9425	−	13.6125i	−1.06298	−	0.452995i
$904$	−7.42695	−	5.39600i	−0.247017	−	0.179468i
$905$	−17.5853	+	30.4587i	−0.584557	+	1.01248i
$906$	−31.5595	−	35.5849i	−1.04849	−	1.18223i
$907$	20.0736	−	22.2940i	0.666534	−	0.740261i	−0.311146	−	0.950362i	$-0.600713\pi$
$907$	20.0736	−	22.2940i	0.666534	−	0.740261i	0.977680	+	0.210101i	$0.0673793\pi$
$908$	3.37459	+	7.57946i	0.111990	+	0.251533i
$909$	13.3641	+	31.2738i	0.443258	+	1.03729i
$910$	19.7920	−	28.6359i	0.656099	−	0.949271i
$911$		−	27.3092i		−	0.904793i	−0.891817	−	0.452396i	$-0.850569\pi$
$911$		−	27.3092i		−	0.904793i	0.891817	−	0.452396i	$-0.149431\pi$
$912$	−2.08767	+	1.49292i	−0.0691295	+	0.0494355i
$913$	−45.3230	+	9.63371i	−1.49997	+	0.318829i
$914$	24.5618	−	27.2786i	0.812431	−	0.902296i
$915$	−53.7458	+	17.0173i	−1.77678	+	0.562574i
$916$	−59.7365			−1.97375
$917$	−25.6475	−	42.1012i	−0.846956	−	1.39030i
$918$	16.3269	+	54.3950i	0.538867	+	1.79530i
$919$	−28.2504	+	25.4368i	−0.931894	+	0.839082i	−0.987216	−	0.159387i	$-0.949048\pi$
$919$	−28.2504	+	25.4368i	−0.931894	+	0.839082i	0.0553217	+	0.998469i	$0.482382\pi$
$920$	−1.62318	+	15.4436i	−0.0535148	+	0.509160i
$921$	−8.50324	−	4.99499i	−0.280191	−	0.164590i
$922$	47.2260	−	4.96365i	1.55530	−	0.163469i
$923$	−32.6807	+	23.7439i	−1.07570	+	0.781541i
$924$	−12.9452	+	42.1272i	−0.425866	+	1.38588i
$925$	−1.13436	−	0.824159i	−0.0372974	−	0.0270982i
$926$	−32.5973	−	36.2030i	−1.07121	−	1.18970i
$927$	6.29721	−	8.39876i	0.206828	−	0.275851i
$928$	3.25610	+	2.93180i	0.106887	+	0.0962412i
$929$	5.92668	+	3.42177i	0.194448	+	0.112265i	0.594063	−	0.804418i	$-0.297523\pi$
$929$	5.92668	+	3.42177i	0.194448	+	0.112265i	−0.399615	+	0.916683i	$0.630856\pi$
$930$	−11.3918	+	12.4621i	−0.373552	+	0.408649i
$931$	−0.956016	+	3.49427i	−0.0313322	+	0.114520i
$932$	−7.21831	+	22.2157i	−0.236444	+	0.727699i
$933$	14.5241	+	20.3101i	0.475497	+	0.664924i
$934$	−3.94577	+	2.27809i	−0.129110	+	0.0745415i
$935$	9.97516	+	46.9294i	0.326223	+	1.53476i
$936$	−7.62420	−	0.917469i	−0.249205	−	0.0299884i
$937$	16.8055	+	12.2099i	0.549013	+	0.398881i	0.827421	−	0.561582i	$-0.189807\pi$
$937$	16.8055	+	12.2099i	0.549013	+	0.398881i	−0.278409	+	0.960463i	$0.589807\pi$
$938$	−36.9558	+	67.6392i	−1.20665	+	2.20850i
$939$	18.9295	−	3.87503i	0.617739	−	0.126457i
$940$	53.7597	+	31.0382i	1.75345	+	1.01235i
$941$	1.30100	−	12.3781i	0.0424112	−	0.403516i	−0.952636	−	0.304113i	$-0.901640\pi$
$941$	1.30100	−	12.3781i	0.0424112	−	0.403516i	0.995047	−	0.0994031i	$-0.0316933\pi$
$942$	4.43167	+	10.1586i	0.144392	+	0.330986i
$943$	32.8136	+	27.7115i	1.06856	+	0.902412i
$944$	−9.81804			−0.319550
$945$	−21.8098	+	24.2704i	−0.709473	+	0.789517i
$946$			62.5241i			2.03283i
$947$	−2.28052	+	10.7290i	−0.0741070	+	0.348646i	−0.999542	−	0.0302602i	$-0.990366\pi$
$947$	−2.28052	+	10.7290i	−0.0741070	+	0.348646i	0.925435	+	0.378906i	$0.123700\pi$
$948$	−40.9251	+	36.2956i	−1.32918	+	1.17882i
$949$	−10.0382	−	1.05506i	−0.325853	−	0.0342485i
$950$	0.688668	−	0.0723820i	0.0223433	−	0.00234838i
$951$	−8.74094	−	3.97075i	−0.283444	−	0.128760i
$952$	3.82617	−	12.7933i	0.124007	−	0.414632i
$953$	−25.2226	−	8.19532i	−0.817040	−	0.265473i	−0.129464	−	0.991584i	$-0.541326\pi$
$953$	−25.2226	−	8.19532i	−0.817040	−	0.265473i	−0.687577	+	0.726112i	$0.741326\pi$
$954$	24.3093	−	13.5517i	0.787044	−	0.438751i
$955$	20.1759	−	22.4076i	0.652877	−	0.725093i
$956$	−5.94309	+	56.5447i	−0.192213	+	1.82879i
$957$	2.98213	+	2.20110i	0.0963986	+	0.0711514i
$958$	−20.6356	−	63.5099i	−0.666706	−	2.05191i
$959$	16.7376	+	47.6636i	0.540486	+	1.53914i
$960$	41.8054	+	18.9910i	1.34926	+	0.612931i
$961$	24.8662	−	11.0711i	0.802134	−	0.357133i
$962$	4.99074	−	11.2094i	0.160908	−	0.361405i
$963$	3.79831	−	5.06591i	0.122399	−	0.163247i
$964$	−32.4084	+	3.40626i	−1.04380	+	0.109708i
$965$	17.4455	+	24.0116i	0.561590	+	0.772962i
$966$	−31.5584	+	56.7421i	−1.01537	+	1.82565i
$967$	7.31377	+	2.37639i	0.235195	+	0.0764195i	0.424243	−	0.905548i	$-0.360540\pi$
$967$	7.31377	+	2.37639i	0.235195	+	0.0764195i	−0.189048	+	0.981968i	$0.560540\pi$
$968$	4.13386	−	0.434487i	0.132867	−	0.0139649i
$969$	3.47009	−	3.07755i	0.111475	−	0.0988651i
$970$	−16.7028	+	9.64335i	−0.536294	+	0.309629i
$971$	−18.1390	−	40.7408i	−0.582107	−	1.30743i	−0.929191	−	0.369600i	$-0.879495\pi$
$971$	−18.1390	−	40.7408i	−0.582107	−	1.30743i	0.347084	−	0.937834i	$-0.387172\pi$
$972$	37.2101	+	9.38414i	1.19352	+	0.300996i
$973$	8.74069	+	18.4500i	0.280214	+	0.591479i
$974$	60.6624	+	19.7104i	1.94375	+	0.631562i
$975$	−2.31660	−	1.70987i	−0.0741904	−	0.0547597i
$976$	8.16352	+	38.4063i	0.261308	+	1.22936i
$977$	24.7643	+	11.0258i	0.792281	+	0.352746i	0.762647	−	0.646815i	$-0.223899\pi$
$977$	24.7643	+	11.0258i	0.792281	+	0.352746i	0.0296334	+	0.999561i	$0.490566\pi$
$978$	−44.6048	+	14.1230i	−1.42630	+	0.451604i
$979$	11.6994	−	3.80135i	0.373913	−	0.121492i
$980$	39.5624	−	10.3779i	1.26377	−	0.331511i
$981$	6.36838	−	27.8913i	0.203327	−	0.890501i
$982$	60.7179	−	27.0334i	1.93759	−	0.862669i
$983$	−2.57532	−	4.46059i	−0.0821401	−	0.142271i	0.822029	−	0.569446i	$-0.192842\pi$
$983$	−2.57532	−	4.46059i	−0.0821401	−	0.142271i	−0.904169	+	0.427175i	$0.859509\pi$
$984$	−9.23464	+	5.63409i	−0.294390	+	0.179608i
$985$	−26.7500	−	15.4441i	−0.852324	−	0.492090i
$986$	−4.84360	−	3.51908i	−0.154252	−	0.112070i
$987$	29.2444	+	38.9238i	0.930858	+	1.23896i
$988$	1.03318	+	3.17981i	0.0328700	+	0.101163i
$989$	−10.5667	+	49.7125i	−0.336002	+	1.58077i
$990$	55.6019	+	18.9954i	1.76715	+	0.603712i
$991$	21.9600	−	49.3230i	0.697583	−	1.56680i	−0.121157	−	0.992633i	$-0.538661\pi$
$991$	21.9600	−	49.3230i	0.697583	−	1.56680i	0.818740	−	0.574164i	$-0.194673\pi$
$992$	10.4067	+	11.5578i	0.330413	+	0.366961i
$993$	55.4199	+	6.24659i	1.75870	+	0.198229i
$994$	−85.7413	−	6.97496i	−2.71955	−	0.221232i
$995$	−7.31410	+	22.5105i	−0.231873	+	0.713630i
$996$	15.9894	−	47.9795i	0.506643	−	1.52029i
$997$	2.80966	−	26.7321i	0.0889828	−	0.846614i	−0.855445	−	0.517894i	$-0.826716\pi$
$997$	2.80966	−	26.7321i	0.0889828	−	0.846614i	0.944427	−	0.328720i	$-0.106617\pi$
$998$	−22.7208	−	39.3535i	−0.719213	−	1.24571i
$999$	−5.97414	+	9.82856i	−0.189013	+	0.310962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.bw.a.236.17	✓	864
3.2	odd	2	inner	861.2.bw.a.236.92	yes	864
7.3	odd	6	inner	861.2.bw.a.605.92	yes	864
21.17	even	6	inner	861.2.bw.a.605.17	yes	864
41.4	even	10	inner	861.2.bw.a.824.17	yes	864
123.86	odd	10	inner	861.2.bw.a.824.92	yes	864
287.45	odd	30	inner	861.2.bw.a.332.92	yes	864
861.332	even	30	inner	861.2.bw.a.332.17	yes	864

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.bw.a.236.17	✓	864	1.1	even	1	trivial
861.2.bw.a.236.92	yes	864	3.2	odd	2	inner
861.2.bw.a.332.17	yes	864	861.332	even	30	inner
861.2.bw.a.332.92	yes	864	287.45	odd	30	inner
861.2.bw.a.605.17	yes	864	21.17	even	6	inner
861.2.bw.a.605.92	yes	864	7.3	odd	6	inner
861.2.bw.a.824.17	yes	864	41.4	even	10	inner
861.2.bw.a.824.92	yes	864	123.86	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.bw (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.859146 - 1.92967i) q^{2} +(1.58756 - 0.692569i) q^{3} +(-1.64725 + 1.82945i) q^{4} +(-2.32162 - 0.493476i) q^{5} +(-2.70038 - 2.46846i) q^{6} +(2.60017 + 0.488991i) q^{7} +(0.927655 + 0.301413i) q^{8} +(2.04070 - 2.19899i) q^{9} +O(q^{10})\)	\(q+(-0.859146 - 1.92967i) q^{2} +(1.58756 - 0.692569i) q^{3} +(-1.64725 + 1.82945i) q^{4} +(-2.32162 - 0.493476i) q^{5} +(-2.70038 - 2.46846i) q^{6} +(2.60017 + 0.488991i) q^{7} +(0.927655 + 0.301413i) q^{8} +(2.04070 - 2.19899i) q^{9} +(1.04236 + 4.90394i) q^{10} +(3.82123 - 0.812227i) q^{11} +(-1.34808 + 4.04520i) q^{12} +(-2.12311 - 1.54253i) q^{13} +(-1.29033 - 5.43759i) q^{14} +(-4.02748 + 0.824461i) q^{15} +(0.299289 + 2.84754i) q^{16} +(-1.07581 - 5.06127i) q^{17} +(-5.99659 - 2.04862i) q^{18} +(0.0540963 + 0.514692i) q^{19} +(4.72707 - 3.43442i) q^{20} +(4.46659 - 1.02450i) q^{21} +(-4.85032 - 6.67590i) q^{22} +(-2.72822 - 6.12768i) q^{23} +(1.68146 - 0.163953i) q^{24} +(0.578681 + 0.257645i) q^{25} +(-1.15252 + 5.42216i) q^{26} +(1.71678 - 4.90435i) q^{27} +(-5.17771 + 3.95140i) q^{28} +(0.169272 + 0.520964i) q^{29} +(5.05113 + 7.06339i) q^{30} +(0.404258 + 1.90188i) q^{31} +(6.92712 - 3.99938i) q^{32} +(5.50391 - 3.93592i) q^{33} +(-8.84233 + 6.42433i) q^{34} +(-5.79531 - 2.41837i) q^{35} +(0.661419 + 7.35564i) q^{36} +(-2.16515 - 0.460216i) q^{37} +(0.946711 - 0.546584i) q^{38} +(-4.43887 - 0.978458i) q^{39} +(-2.00492 - 1.15754i) q^{40} +(-5.76396 + 2.78869i) q^{41} +(-5.81439 - 7.73887i) q^{42} +(-6.12990 - 4.45363i) q^{43} +(-4.80857 + 8.32869i) q^{44} +(-5.82287 + 4.09819i) q^{45} +(-9.48049 + 10.5291i) q^{46} +(4.32120 + 9.70558i) q^{47} +(2.44726 + 4.31336i) q^{48} +(6.52178 + 2.54292i) q^{49} -1.33802i q^{50} +(-5.21319 - 7.29001i) q^{51} +(6.31927 - 1.34320i) q^{52} +(-2.93882 + 3.26389i) q^{53} +(-10.9388 + 0.900739i) q^{54} -9.27226 q^{55} +(2.26467 + 1.23734i) q^{56} +(0.442341 + 0.779639i) q^{57} +(0.859862 - 0.774223i) q^{58} +(-0.358430 + 3.41023i) q^{59} +(5.12594 - 8.72617i) q^{60} +(13.6382 - 1.43343i) q^{61} +(3.32270 - 2.41408i) q^{62} +(6.38144 - 4.71987i) q^{63} +(-9.03610 - 6.56511i) q^{64} +(4.16785 + 4.62887i) q^{65} +(-12.3237 - 7.23921i) q^{66} +(-10.2493 - 9.22849i) q^{67} +(11.0315 + 6.36903i) q^{68} +(-8.57506 - 7.83859i) q^{69} +(0.312344 + 13.2608i) q^{70} +(4.75666 - 14.6395i) q^{71} +(2.55587 - 1.42481i) q^{72} +(3.33086 - 1.92307i) q^{73} +(0.972111 + 4.57342i) q^{74} +(1.09713 + 0.00825104i) q^{75} +(-1.03071 - 0.748858i) q^{76} +(10.3330 - 0.243384i) q^{77} +(1.92553 + 9.40621i) q^{78} +(11.1101 + 6.41445i) q^{79} +(0.710358 - 6.75860i) q^{80} +(-0.671119 - 8.97494i) q^{81} +(10.3333 + 8.72666i) q^{82} -11.8609 q^{83} +(-5.48331 + 9.85901i) q^{84} +12.2812i q^{85} +(-3.32758 + 15.6550i) q^{86} +(0.629533 + 0.709830i) q^{87} +(3.78960 + 0.398303i) q^{88} +(3.13164 - 0.329149i) q^{89} +(12.9109 + 7.71530i) q^{90} +(-4.76616 - 5.04902i) q^{91} +(15.7044 + 5.10265i) q^{92} +(1.95897 + 2.73938i) q^{93} +(15.0161 - 16.6770i) q^{94} +(0.128397 - 1.22162i) q^{95} +(8.22738 - 11.1468i) q^{96} +(1.18877 + 3.65867i) q^{97} +(-0.696153 - 14.7696i) q^{98} +(6.01188 - 10.0604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9}+O(q^{10}) \) 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9	\( 864 q - 110 q^{4} - 20 q^{7} - 12 q^{9} - 18 q^{10} - 15 q^{12} - 50 q^{15} + 82 q^{16} - 15 q^{18} - 30 q^{19} - 14 q^{21} + 30 q^{24} + 78 q^{25} + 15 q^{30} - 18 q^{31} + 36 q^{33} + 16 q^{36} - 10 q^{37} - 2 q^{39} - 144 q^{40} - 24 q^{42} - 8 q^{43} + 69 q^{45} - 12 q^{46} + 52 q^{49} - 18 q^{51} - 30 q^{52} + 15 q^{54} - 38 q^{57} - 10 q^{58} - 126 q^{61} + 65 q^{63} - 16 q^{64} - 70 q^{67} - 260 q^{70} - 33 q^{72} - 48 q^{73} + 60 q^{75} - 2 q^{78} + 68 q^{81} - 150 q^{82} + 115 q^{84} - 138 q^{87} + 30 q^{88} + 64 q^{91} - 15 q^{93} + 60 q^{94} - 30 q^{99}+O(q^{100}) \) 864 * q - 110 * q^4 - 20 * q^7 - 12 * q^9 - 18 * q^10 - 15 * q^12 - 50 * q^15 + 82 * q^16 - 15 * q^18 - 30 * q^19 - 14 * q^21 + 30 * q^24 + 78 * q^25 + 15 * q^30 - 18 * q^31 + 36 * q^33 + 16 * q^36 - 10 * q^37 - 2 * q^39 - 144 * q^40 - 24 * q^42 - 8 * q^43 + 69 * q^45 - 12 * q^46 + 52 * q^49 - 18 * q^51 - 30 * q^52 + 15 * q^54 - 38 * q^57 - 10 * q^58 - 126 * q^61 + 65 * q^63 - 16 * q^64 - 70 * q^67 - 260 * q^70 - 33 * q^72 - 48 * q^73 + 60 * q^75 - 2 * q^78 + 68 * q^81 - 150 * q^82 + 115 * q^84 - 138 * q^87 + 30 * q^88 + 64 * q^91 - 15 * q^93 + 60 * q^94 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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