LMFDB - Embedded newform 95.2.r.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(2,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("95.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.r (of order $36$, degree $12$, 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:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			33.2
Character	$\chi$	$=$	95.33
Dual form			95.2.r.a.72.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66970 - 0.778592i) q^{2} +(0.823960 + 1.17674i) q^{3} +(0.896104 + 1.06793i) q^{4} +(-0.649562 - 2.13964i) q^{5} +(-0.459565 - 2.60632i) q^{6} +(4.27404 + 1.14523i) q^{7} +(0.288912 + 1.07824i) q^{8} +(0.320261 - 0.879909i) q^{9} +O(q^{10})$	\(q+(-1.66970 - 0.778592i) q^{2} +(0.823960 + 1.17674i) q^{3} +(0.896104 + 1.06793i) q^{4} +(-0.649562 - 2.13964i) q^{5} +(-0.459565 - 2.60632i) q^{6} +(4.27404 + 1.14523i) q^{7} +(0.288912 + 1.07824i) q^{8} +(0.320261 - 0.879909i) q^{9} +(-0.581337 + 4.07830i) q^{10} +(1.77494 - 3.07428i) q^{11} +(-0.518325 + 1.93441i) q^{12} +(-1.25440 - 0.878342i) q^{13} +(-6.24468 - 5.23991i) q^{14} +(1.98258 - 2.52734i) q^{15} +(0.841272 - 4.77109i) q^{16} +(-2.08055 + 4.46175i) q^{17} +(-1.21983 + 1.21983i) q^{18} +(-0.520647 + 4.32769i) q^{19} +(1.70292 - 2.61103i) q^{20} +(2.17401 + 5.97304i) q^{21} +(-5.35721 + 3.75116i) q^{22} +(-2.61743 - 0.228995i) q^{23} +(-1.03075 + 1.22840i) q^{24} +(-4.15614 + 2.77966i) q^{25} +(1.41060 + 2.44323i) q^{26} +(5.46205 - 1.46355i) q^{27} +(2.60696 + 5.59063i) q^{28} +(-2.05733 - 0.748808i) q^{29} +(-5.27808 + 2.67627i) q^{30} +(-5.90309 + 3.40815i) q^{31} +(-3.83887 + 5.48247i) q^{32} +(5.08010 - 0.444451i) q^{33} +(6.94776 - 5.82986i) q^{34} +(-0.325881 - 9.88881i) q^{35} +(1.22667 - 0.446472i) q^{36} +(-1.62447 - 1.62447i) q^{37} +(4.23883 - 6.82056i) q^{38} -2.19982i q^{39} +(2.11937 - 1.31855i) q^{40} +(3.31265 + 0.584109i) q^{41} +(1.02063 - 11.6658i) q^{42} +(-0.476636 - 5.44797i) q^{43} +(4.87366 - 0.859357i) q^{44} +(-2.09072 - 0.113688i) q^{45} +(4.19201 + 2.42026i) q^{46} +(-5.62428 + 2.62265i) q^{47} +(6.30749 - 2.94123i) q^{48} +(10.8937 + 6.28948i) q^{49} +(9.10371 - 1.40525i) q^{50} +(-6.96459 + 1.22805i) q^{51} +(-0.186063 - 2.12670i) q^{52} +(-0.296214 + 3.38574i) q^{53} +(-10.2595 - 1.80902i) q^{54} +(-7.73079 - 1.80079i) q^{55} +4.93929i q^{56} +(-5.52155 + 2.95318i) q^{57} +(2.85211 + 2.85211i) q^{58} +(-1.77821 + 0.647217i) q^{59} +(4.47564 - 0.147492i) q^{60} +(7.98682 - 6.70174i) q^{61} +(12.5099 - 1.09448i) q^{62} +(2.37650 - 3.39400i) q^{63} +(2.28709 - 1.32045i) q^{64} +(-1.06453 + 3.25451i) q^{65} +(-8.82826 - 3.21322i) q^{66} +(1.21739 + 2.61071i) q^{67} +(-6.62924 + 1.77630i) q^{68} +(-1.88719 - 3.26871i) q^{69} +(-7.15523 + 16.7650i) q^{70} +(2.76573 - 3.29607i) q^{71} +(1.04128 + 0.0910999i) q^{72} +(-10.7658 + 7.53828i) q^{73} +(1.44757 + 3.97716i) q^{74} +(-6.69542 - 2.60035i) q^{75} +(-5.08825 + 3.32204i) q^{76} +(11.1069 - 11.1069i) q^{77} +(-1.71276 + 3.67303i) q^{78} +(-0.548448 + 3.11040i) q^{79} +(-10.7549 + 1.29910i) q^{80} +(4.07080 + 3.41581i) q^{81} +(-5.07633 - 3.55449i) q^{82} +(0.251741 - 0.939512i) q^{83} +(-4.43068 + 7.67416i) q^{84} +(10.8980 + 1.55344i) q^{85} +(-3.44591 + 9.46756i) q^{86} +(-0.814011 - 3.03793i) q^{87} +(3.82760 + 1.02560i) q^{88} +(1.53879 + 8.72693i) q^{89} +(3.40235 + 1.81764i) q^{90} +(-4.35546 - 5.19064i) q^{91} +(-2.10093 - 3.00044i) q^{92} +(-8.87441 - 4.13820i) q^{93} +11.4328 q^{94} +(9.59791 - 1.69711i) q^{95} -9.61450 q^{96} +(-4.20551 - 1.96106i) q^{97} +(-13.2922 - 18.9833i) q^{98} +(-2.13664 - 2.54635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8}+O(q^{10}) $ 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8	$ 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} + 6 q^{15} + 12 q^{16} - 30 q^{17} - 84 q^{20} + 24 q^{21} - 24 q^{22} + 12 q^{25} - 48 q^{26} - 18 q^{27} - 6 q^{30} - 36 q^{31} + 18 q^{32} + 90 q^{33} - 30 q^{35} + 24 q^{36} + 54 q^{38} + 54 q^{40} + 12 q^{41} + 24 q^{42} + 48 q^{43} + 12 q^{45} - 36 q^{46} - 24 q^{47} + 60 q^{48} + 126 q^{50} - 96 q^{51} - 30 q^{53} + 18 q^{55} - 66 q^{57} + 120 q^{58} + 84 q^{60} - 48 q^{61} + 60 q^{62} - 126 q^{63} + 72 q^{65} + 72 q^{66} + 108 q^{67} + 18 q^{68} + 36 q^{70} - 24 q^{71} + 48 q^{72} + 6 q^{73} + 60 q^{76} + 168 q^{77} - 138 q^{78} - 60 q^{80} - 120 q^{81} + 60 q^{82} - 36 q^{85} - 180 q^{86} - 6 q^{87} - 198 q^{88} - 270 q^{90} - 24 q^{91} - 72 q^{92} - 90 q^{93} - 24 q^{95} - 192 q^{96} - 72 q^{97} - 90 q^{98}+O(q^{100}) $ 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8 - 12 * q^10 - 12 * q^11 - 18 * q^12 - 12 * q^13 + 6 * q^15 + 12 * q^16 - 30 * q^17 - 84 * q^20 + 24 * q^21 - 24 * q^22 + 12 * q^25 - 48 * q^26 - 18 * q^27 - 6 * q^30 - 36 * q^31 + 18 * q^32 + 90 * q^33 - 30 * q^35 + 24 * q^36 + 54 * q^38 + 54 * q^40 + 12 * q^41 + 24 * q^42 + 48 * q^43 + 12 * q^45 - 36 * q^46 - 24 * q^47 + 60 * q^48 + 126 * q^50 - 96 * q^51 - 30 * q^53 + 18 * q^55 - 66 * q^57 + 120 * q^58 + 84 * q^60 - 48 * q^61 + 60 * q^62 - 126 * q^63 + 72 * q^65 + 72 * q^66 + 108 * q^67 + 18 * q^68 + 36 * q^70 - 24 * q^71 + 48 * q^72 + 6 * q^73 + 60 * q^76 + 168 * q^77 - 138 * q^78 - 60 * q^80 - 120 * q^81 + 60 * q^82 - 36 * q^85 - 180 * q^86 - 6 * q^87 - 198 * q^88 - 270 * q^90 - 24 * q^91 - 72 * q^92 - 90 * q^93 - 24 * q^95 - 192 * q^96 - 72 * q^97 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.66970	−	0.778592i	−1.18065	−	0.550548i	−0.269655	−	0.962957i	$-0.586910\pi$
$2$	−1.66970	−	0.778592i	−1.18065	−	0.550548i	−0.910999	+	0.412409i	$0.864687\pi$
$3$	0.823960	+	1.17674i	0.475714	+	0.679389i	0.983254	−	0.182238i	$-0.0583342\pi$
$3$	0.823960	+	1.17674i	0.475714	+	0.679389i	−0.507541	+	0.861628i	$0.669445\pi$
$4$	0.896104	+	1.06793i	0.448052	+	0.533967i
$5$	−0.649562	−	2.13964i	−0.290493	−	0.956877i
$5$	−0.649562	−	2.13964i	−0.290493	−	0.956877i
$6$	−0.459565	−	2.60632i	−0.187617	−	1.06403i
$7$	4.27404	+	1.14523i	1.61543	+	0.432855i	0.949656	−	0.313295i	$-0.101433\pi$
$7$	4.27404	+	1.14523i	1.61543	+	0.432855i	0.665779	+	0.746149i	$0.268099\pi$
$8$	0.288912	+	1.07824i	0.102146	+	0.381214i
$9$	0.320261	−	0.879909i	0.106754	−	0.293303i
$10$	−0.581337	+	4.07830i	−0.183835	+	1.28967i
$11$	1.77494	−	3.07428i	0.535163	−	0.926930i	−0.463992	−	0.885839i	$-0.653583\pi$
$11$	1.77494	−	3.07428i	0.535163	−	0.926930i	0.999155	−	0.0410908i	$-0.0130833\pi$
$12$	−0.518325	+	1.93441i	−0.149627	+	0.558417i
$13$	−1.25440	−	0.878342i	−0.347909	−	0.243608i	0.386540	−	0.922273i	$-0.373670\pi$
$13$	−1.25440	−	0.878342i	−0.347909	−	0.243608i	−0.734448	+	0.678665i	$0.762559\pi$
$14$	−6.24468	−	5.23991i	−1.66896	−	1.40043i
$15$	1.98258	−	2.52734i	0.511901	−	0.652557i
$16$	0.841272	−	4.77109i	0.210318	−	1.19277i
$17$	−2.08055	+	4.46175i	−0.504607	+	1.08213i	0.474774	+	0.880108i	$0.342530\pi$
$17$	−2.08055	+	4.46175i	−0.504607	+	1.08213i	−0.979380	+	0.202025i	$0.935248\pi$
$18$	−1.21983	+	1.21983i	−0.287516	+	0.287516i
$19$	−0.520647	+	4.32769i	−0.119445	+	0.992841i
$19$	−0.520647	+	4.32769i	−0.119445	+	0.992841i
$20$	1.70292	−	2.61103i	0.380785	−	0.583844i
$21$	2.17401	+	5.97304i	0.474408	+	1.30342i
$22$	−5.35721	+	3.75116i	−1.14216	+	0.799750i
$23$	−2.61743	−	0.228995i	−0.545771	−	0.0477488i	−0.189063	−	0.981965i	$-0.560545\pi$
$23$	−2.61743	−	0.228995i	−0.545771	−	0.0477488i	−0.356708	+	0.934216i	$0.616101\pi$
$24$	−1.03075	+	1.22840i	−0.210401	+	0.250746i
$25$	−4.15614	+	2.77966i	−0.831228	+	0.555932i
$26$	1.41060	+	2.44323i	0.276641	+	0.479157i
$27$	5.46205	−	1.46355i	1.05117	−	0.281661i
$28$	2.60696	+	5.59063i	0.492668	+	1.05653i
$29$	−2.05733	−	0.748808i	−0.382037	−	0.139050i	0.143860	−	0.989598i	$-0.454048\pi$
$29$	−2.05733	−	0.748808i	−0.382037	−	0.139050i	−0.525898	+	0.850548i	$0.676271\pi$
$30$	−5.27808	+	2.67627i	−0.963641	+	0.488618i
$31$	−5.90309	+	3.40815i	−1.06023	+	0.612122i	−0.925495	−	0.378760i	$-0.876350\pi$
$31$	−5.90309	+	3.40815i	−1.06023	+	0.612122i	−0.134731	+	0.990882i	$0.543017\pi$
$32$	−3.83887	+	5.48247i	−0.678622	+	0.969173i
$33$	5.08010	−	0.444451i	0.884331	−	0.0773689i
$34$	6.94776	−	5.82986i	1.19153	−	0.999813i
$35$	−0.325881	−	9.88881i	−0.0550839	−	1.67151i
$36$	1.22667	−	0.446472i	0.204445	−	0.0744120i
$37$	−1.62447	−	1.62447i	−0.267061	−	0.267061i	0.560854	−	0.827915i	$-0.310473\pi$
$37$	−1.62447	−	1.62447i	−0.267061	−	0.267061i	−0.827915	+	0.560854i	$0.810473\pi$
$38$	4.23883	−	6.82056i	0.687629	−	1.10644i
$39$		−	2.19982i		−	0.352253i
$40$	2.11937	−	1.31855i	0.335102	−	0.208481i
$41$	3.31265	+	0.584109i	0.517349	+	0.0912225i	0.426225	−	0.904617i	$-0.359843\pi$
$41$	3.31265	+	0.584109i	0.517349	+	0.0912225i	0.0911234	+	0.995840i	$0.470954\pi$
$42$	1.02063	−	11.6658i	0.157486	−	1.80008i
$43$	−0.476636	−	5.44797i	−0.0726863	−	0.830808i	−0.941795	−	0.336187i	$-0.890863\pi$
$43$	−0.476636	−	5.44797i	−0.0726863	−	0.830808i	0.869109	−	0.494621i	$-0.164693\pi$
$44$	4.87366	−	0.859357i	0.734731	−	0.129553i
$45$	−2.09072	−	0.113688i	−0.311666	−	0.0169476i
$46$	4.19201	+	2.42026i	0.618078	+	0.356848i
$47$	−5.62428	+	2.62265i	−0.820386	+	0.382552i	−0.787048	−	0.616892i	$-0.788392\pi$
$47$	−5.62428	+	2.62265i	−0.820386	+	0.382552i	−0.0333378	+	0.999444i	$0.510614\pi$
$48$	6.30749	−	2.94123i	0.910408	−	0.424530i
$49$	10.8937	+	6.28948i	1.55624	+	0.898497i
$50$	9.10371	−	1.40525i	1.28746	−	0.198733i
$51$	−6.96459	+	1.22805i	−0.975238	+	0.171961i
$52$	−0.186063	−	2.12670i	−0.0258022	−	0.294921i
$53$	−0.296214	+	3.38574i	−0.0406881	+	0.465067i	0.948331	+	0.317282i	$0.102770\pi$
$53$	−0.296214	+	3.38574i	−0.0406881	+	0.465067i	−0.989019	+	0.147786i	$0.952785\pi$
$54$	−10.2595	−	1.80902i	−1.39614	−	0.246177i
$55$	−7.73079	−	1.80079i	−1.04242	−	0.242819i
$56$			4.93929i			0.660041i
$57$	−5.52155	+	2.95318i	−0.731347	+	0.391159i
$58$	2.85211	+	2.85211i	0.374500	+	0.374500i
$59$	−1.77821	+	0.647217i	−0.231504	+	0.0842604i	−0.455167	−	0.890406i	$-0.650421\pi$
$59$	−1.77821	+	0.647217i	−0.231504	+	0.0842604i	0.223664	+	0.974666i	$0.428198\pi$
$60$	4.47564	−	0.147492i	0.577802	−	0.0190412i
$61$	7.98682	−	6.70174i	1.02261	−	0.858070i	0.0326549	−	0.999467i	$-0.489604\pi$
$61$	7.98682	−	6.70174i	1.02261	−	0.858070i	0.989953	+	0.141397i	$0.0451593\pi$
$62$	12.5099	−	1.09448i	1.58876	−	0.138999i
$63$	2.37650	−	3.39400i	0.299411	−	0.427603i
$64$	2.28709	−	1.32045i	0.285887	−	0.165057i
$65$	−1.06453	+	3.25451i	−0.132038	+	0.403672i
$66$	−8.82826	−	3.21322i	−1.08668	−	0.395521i
$67$	1.21739	+	2.61071i	0.148728	+	0.318949i	0.966531	−	0.256550i	$-0.0825857\pi$
$67$	1.21739	+	2.61071i	0.148728	+	0.318949i	−0.817803	+	0.575499i	$0.804808\pi$
$68$	−6.62924	+	1.77630i	−0.803913	+	0.215408i
$69$	−1.88719	−	3.26871i	−0.227191	−	0.393506i
$70$	−7.15523	+	16.7650i	−0.855213	+	2.00380i
$71$	2.76573	−	3.29607i	0.328232	−	0.391172i	−0.576539	−	0.817069i	$-0.695597\pi$
$71$	2.76573	−	3.29607i	0.328232	−	0.391172i	0.904771	+	0.425898i	$0.140042\pi$
$72$	1.04128	+	0.0910999i	0.122716	+	0.0107362i
$73$	−10.7658	+	7.53828i	−1.26004	+	0.882290i	−0.996600	−	0.0823864i	$-0.973746\pi$
$73$	−10.7658	+	7.53828i	−1.26004	+	0.882290i	−0.263440	+	0.964676i	$0.584857\pi$
$74$	1.44757	+	3.97716i	0.168276	+	0.462336i
$75$	−6.69542	−	2.60035i	−0.773121	−	0.300263i
$76$	−5.08825	+	3.32204i	−0.583662	+	0.381065i
$77$	11.1069	−	11.1069i	1.26575	−	1.26575i
$78$	−1.71276	+	3.67303i	−0.193932	+	0.415889i
$79$	−0.548448	+	3.11040i	−0.0617052	+	0.349948i	0.938286	+	0.345859i	$0.112413\pi$
$79$	−0.548448	+	3.11040i	−0.0617052	+	0.349948i	−0.999992	+	0.00408857i	$0.998699\pi$
$80$	−10.7549	+	1.29910i	−1.20243	+	0.145244i
$81$	4.07080	+	3.41581i	0.452311	+	0.379534i
$82$	−5.07633	−	3.55449i	−0.560587	−	0.392527i
$83$	0.251741	−	0.939512i	0.0276322	−	0.103125i	−0.950732	−	0.310012i	$-0.899667\pi$
$83$	0.251741	−	0.939512i	0.0276322	−	0.103125i	0.978365	+	0.206888i	$0.0663334\pi$
$84$	−4.43068	+	7.67416i	−0.483427	+	0.837320i
$85$	10.8980	+	1.55344i	1.18205	+	0.168495i
$86$	−3.44591	+	9.46756i	−0.371582	+	1.02091i
$87$	−0.814011	−	3.03793i	−0.0872711	−	0.325700i
$88$	3.82760	+	1.02560i	0.408024	+	0.109330i
$89$	1.53879	+	8.72693i	0.163112	+	0.925052i	0.950990	+	0.309221i	$0.100068\pi$
$89$	1.53879	+	8.72693i	0.163112	+	0.925052i	−0.787878	+	0.615831i	$0.788820\pi$
$90$	3.40235	+	1.81764i	0.358639	+	0.191596i
$91$	−4.35546	−	5.19064i	−0.456577	−	0.544127i
$92$	−2.10093	−	3.00044i	−0.219037	−	0.312818i
$93$	−8.87441	−	4.13820i	−0.920233	−	0.429112i
$94$	11.4328			1.17920
$95$	9.59791	−	1.69711i	0.984725	−	0.174120i
$96$	−9.61450			−0.981276
$97$	−4.20551	−	1.96106i	−0.427005	−	0.199115i	0.197222	−	0.980359i	$-0.436808\pi$
$97$	−4.20551	−	1.96106i	−0.427005	−	0.199115i	−0.624227	+	0.781243i	$0.714586\pi$
$98$	−13.2922	−	18.9833i	−1.34272	−	1.91760i
$99$	−2.13664	−	2.54635i	−0.214741	−	0.255918i
$100$	−6.69283	−	1.94762i	−0.669283	−	0.194762i
$101$	1.16186	+	6.58921i	0.115609	+	0.655651i	0.986447	+	0.164081i	$0.0524658\pi$
$101$	1.16186	+	6.58921i	0.115609	+	0.655651i	−0.870838	+	0.491570i	$0.836423\pi$
$102$	12.5849	+	3.37211i	1.24609	+	0.333889i
$103$	−3.25567	−	12.1503i	−0.320791	−	1.19721i	−0.918476	−	0.395477i	$-0.870579\pi$
$103$	−3.25567	−	12.1503i	−0.320791	−	1.19721i	0.597685	−	0.801731i	$-0.296087\pi$
$104$	0.584647	−	1.60631i	0.0573294	−	0.157511i
$105$	11.3680	−	8.53146i	1.10940	−	0.832585i
$106$	3.13070	−	5.42253i	0.304080	−	0.526682i
$107$	−3.20832	+	11.9736i	−0.310160	+	1.15753i	0.618252	+	0.785980i	$0.287841\pi$
$107$	−3.20832	+	11.9736i	−0.310160	+	1.15753i	−0.928412	+	0.371552i	$0.878826\pi$
$108$	6.45754	+	4.52162i	0.621377	+	0.435093i
$109$	−8.87524	−	7.44721i	−0.850094	−	0.713313i	0.109717	−	0.993963i	$-0.465006\pi$
$109$	−8.87524	−	7.44721i	−0.850094	−	0.713313i	−0.959810	+	0.280650i	$0.909450\pi$
$110$	11.5060	+	9.02591i	1.09705	+	0.860587i
$111$	0.573074	−	3.25007i	0.0543938	−	0.308483i
$112$	9.05961	−	19.4284i	0.856052	−	1.83581i
$113$	−9.15180	+	9.15180i	−0.860929	+	0.860929i	−0.991446	−	0.130517i	$-0.958336\pi$
$113$	−9.15180	+	9.15180i	−0.860929	+	0.860929i	0.130517	+	0.991446i	$0.458336\pi$
$114$	11.5186	−	0.631883i	1.07882	−	0.0591813i
$115$	1.21021	+	5.74910i	0.112853	+	0.536107i
$116$	−1.04391	−	2.86811i	−0.0969242	−	0.266297i
$117$	−1.17460	+	0.822461i	−0.108591	+	0.0760366i
$118$	3.47299	+	0.303847i	0.319715	+	0.0279714i
$119$	−14.0020	+	16.6870i	−1.28357	+	1.52969i
$120$	3.29787	+	1.40751i	0.301053	+	0.128488i
$121$	−0.800797	−	1.38702i	−0.0727998	−	0.126093i
$122$	−18.5535	+	4.97139i	−1.67975	+	0.450089i
$123$	2.04215	+	4.37940i	0.184134	+	0.394877i
$124$	−8.92946	−	3.25006i	−0.801889	−	0.291864i
$125$	8.64715	+	7.08709i	0.773425	+	0.633888i
$126$	−6.61057	+	3.81662i	−0.588917	+	0.340011i
$127$	8.83254	−	12.6142i	0.783761	−	1.11933i	−0.206273	−	0.978495i	$-0.566133\pi$
$127$	8.83254	−	12.6142i	0.783761	−	1.11933i	0.990033	−	0.140832i	$-0.0449778\pi$
$128$	8.48794	−	0.742599i	0.750235	−	0.0656371i
$129$	6.01810	−	5.04979i	0.529864	−	0.444609i
$130$	4.31137	−	4.60521i	0.378132	−	0.403904i
$131$	5.69354	−	2.07228i	0.497447	−	0.181056i	−0.0810982	−	0.996706i	$-0.525843\pi$
$131$	5.69354	−	2.07228i	0.497447	−	0.181056i	0.578546	+	0.815650i	$0.303621\pi$
$132$	5.02694	+	5.02694i	0.437539	+	0.437539i
$133$	−7.18145	+	17.9005i	−0.622711	+	1.55217i
$134$		−	5.30695i		−	0.458450i
$135$	−6.67942	−	10.7362i	−0.574873	−	0.924022i
$136$	−5.41191	−	0.954266i	−0.464068	−	0.0818276i
$137$	0.180064	−	2.05814i	0.0153839	−	0.175839i	−0.984615	−	0.174735i	$-0.944093\pi$
$137$	0.180064	−	2.05814i	0.0153839	−	0.175839i	0.999999	−	0.00110380i	$-0.000351351\pi$
$138$	0.606042	+	6.92709i	0.0515897	+	0.589673i
$139$	8.12095	−	1.43194i	0.688810	−	0.121456i	0.181722	−	0.983350i	$-0.441833\pi$
$139$	8.12095	−	1.43194i	0.688810	−	0.121456i	0.507088	+	0.861894i	$0.330722\pi$
$140$	10.2686	−	9.20942i	0.867853	−	0.778338i
$141$	−7.72035	−	4.45734i	−0.650170	−	0.375376i
$142$	−7.18423	+	3.35006i	−0.602887	+	0.281131i
$143$	−4.92675	+	2.29738i	−0.411996	+	0.192117i
$144$	−3.92870	−	2.26824i	−0.327392	−	0.189020i
$145$	−0.265816	+	4.88836i	−0.0220748	+	0.405956i
$146$	23.8448	−	4.20449i	1.97341	−	0.347966i
$147$	1.57491	+	18.0013i	0.129896	+	1.48472i
$148$	0.279134	−	3.19051i	0.0229447	−	0.262259i
$149$	4.20634	+	0.741691i	0.344597	+	0.0607617i	0.343268	−	0.939237i	$-0.388466\pi$
$149$	4.20634	+	0.741691i	0.344597	+	0.0607617i	0.00132850	+	0.999999i	$0.499577\pi$
$150$	9.15470	+	9.55480i	0.747479	+	0.780146i
$151$		−	21.5441i		−	1.75323i	−0.481192	−	0.876615i	$-0.659796\pi$
$151$		−	21.5441i		−	1.75323i	0.481192	−	0.876615i	$-0.340204\pi$
$152$	−4.81670	+	0.688945i	−0.390686	+	0.0558808i
$153$	3.25961	+	3.25961i	0.263524	+	0.263524i
$154$	−27.1929	+	9.89739i	−2.19126	+	0.797555i
$155$	11.1266	+	10.4167i	0.893713	+	0.836689i
$156$	2.34926	−	1.97127i	0.188092	−	0.157828i
$157$	5.98609	−	0.523715i	0.477742	−	0.0417970i	0.154258	−	0.988031i	$-0.450701\pi$
$157$	5.98609	−	0.523715i	0.477742	−	0.0417970i	0.323484	+	0.946234i	$0.395146\pi$
$158$	3.33748	−	4.76641i	0.265515	−	0.379195i
$159$	−4.22820	+	2.44115i	−0.335318	+	0.193596i
$160$	14.2241	+	4.65260i	1.12451	+	0.367820i
$161$	−10.9247	−	3.97628i	−0.860989	−	0.313375i
$162$	−4.13748	−	8.87285i	−0.325071	−	0.697117i
$163$	0.798670	−	0.214003i	0.0625567	−	0.0167620i	−0.227405	−	0.973800i	$-0.573024\pi$
$163$	0.798670	−	0.214003i	0.0625567	−	0.0167620i	0.289962	+	0.957038i	$0.406357\pi$
$164$	2.34468	+	4.06111i	0.183089	+	0.317120i
$165$	−4.25080	−	10.5809i	−0.330925	−	0.823721i
$166$	−1.15183	+	1.37270i	−0.0893992	+	0.106542i
$167$	12.4974	+	1.09338i	0.967081	+	0.0846086i	0.559741	−	0.828668i	$-0.310901\pi$
$167$	12.4974	+	1.09338i	0.967081	+	0.0846086i	0.407340	+	0.913276i	$0.366456\pi$
$168$	−5.81225	+	4.06978i	−0.448425	+	0.313990i
$169$	−3.64422	−	10.0124i	−0.280325	−	0.770186i
$170$	−16.9868	−	11.0789i	−1.30283	−	0.849710i
$171$	3.64123	+	1.84411i	0.278452	+	0.141023i
$172$	5.39096	−	5.39096i	0.411057	−	0.411057i
$173$	10.1904	−	21.8534i	0.774764	−	1.66149i	0.0250847	−	0.999685i	$-0.492014\pi$
$173$	10.1904	−	21.8534i	0.774764	−	1.66149i	0.749679	−	0.661801i	$-0.230208\pi$
$174$	−1.00616	+	5.70620i	−0.0762766	+	0.432586i
$175$	−20.9468	+	7.12066i	−1.58343	+	0.538272i
$176$	−13.1745	−	11.0547i	−0.993063	−	0.833279i
$177$	−2.22678	−	1.55921i	−0.167375	−	0.117197i
$178$	4.22540	−	15.7694i	0.316707	−	1.18197i
$179$	10.9968	−	19.0471i	0.821942	−	1.42365i	−0.0822924	−	0.996608i	$-0.526224\pi$
$179$	10.9968	−	19.0471i	0.821942	−	1.42365i	0.904234	−	0.427037i	$-0.140443\pi$
$180$	−1.75209	−	2.33463i	−0.130593	−	0.174013i
$181$	−3.89772	+	10.7089i	−0.289715	+	0.795986i	0.706391	+	0.707822i	$0.250322\pi$
$181$	−3.89772	+	10.7089i	−0.289715	+	0.795986i	−0.996106	+	0.0881640i	$0.971900\pi$
$182$	3.23091	+	12.0579i	0.239491	+	0.893792i
$183$	14.4670	+	3.87642i	1.06943	+	0.286553i
$184$	−0.509296	−	2.88836i	−0.0375458	−	0.212933i
$185$	−2.42059	+	4.53097i	−0.177965	+	0.333124i
$186$	11.5956	+	13.8191i	0.850230	+	1.01326i
$187$	10.0238	+	14.3155i	0.733014	+	1.04685i
$188$	−7.84075	−	3.65620i	−0.571846	−	0.266656i
$189$	25.0211			1.82002
$190$	−17.3469	−	4.63920i	−1.25848	−	0.336563i
$191$	−9.67077			−0.699752			−0.349876	−	0.936796i	$-0.613776\pi$
$191$	−9.67077			−0.699752			−0.349876	+	0.936796i	$0.613776\pi$
$192$	3.43830	+	1.60331i	0.248138	+	0.115709i
$193$	7.75033	+	11.0686i	0.557881	+	0.796737i	0.994701	−	0.102812i	$-0.0327841\pi$
$193$	7.75033	+	11.0686i	0.557881	+	0.796737i	−0.436820	+	0.899549i	$0.643895\pi$
$194$	5.49505	+	6.54875i	0.394522	+	0.470173i
$195$	−4.70683	+	1.42892i	−0.337063	+	0.102327i
$196$	3.04513	+	17.2698i	0.217509	+	1.23356i
$197$	−17.5116	−	4.69221i	−1.24765	−	0.334306i	−0.426220	−	0.904619i	$-0.640155\pi$
$197$	−17.5116	−	4.69221i	−1.24765	−	0.334306i	−0.821427	+	0.570313i	$0.806822\pi$
$198$	1.58498	+	5.91521i	0.112639	+	0.420376i
$199$	5.21800	−	14.3363i	0.369894	−	1.01628i	−0.605507	−	0.795840i	$-0.707030\pi$
$199$	5.21800	−	14.3363i	0.369894	−	1.01628i	0.975401	−	0.220436i	$-0.0707479\pi$
$200$	−4.19789	−	3.67822i	−0.296836	−	0.260089i
$201$	−2.06904	+	3.58368i	−0.145939	+	0.252773i
$202$	3.19036	−	11.9066i	0.224473	−	0.837745i
$203$	−7.93557	−	5.55655i	−0.556968	−	0.389993i
$204$	−7.55247	−	6.33727i	−0.528778	−	0.443698i
$205$	−0.901985	−	7.46730i	−0.0629974	−	0.521539i
$206$	−4.02417	+	22.8222i	−0.280377	+	1.59010i
$207$	−1.03975	+	2.22976i	−0.0722679	+	0.154979i
$208$	−5.24594	+	5.24594i	−0.363741	+	0.363741i
$209$	12.3804	+	9.28199i	0.856372	+	0.642049i
$210$	−25.6237	+	5.39390i	−1.76820	+	0.372214i
$211$	5.24953	+	14.4230i	0.361393	+	0.992918i	0.978538	+	0.206069i	$0.0660671\pi$
$211$	5.24953	+	14.4230i	0.361393	+	0.992918i	−0.617145	+	0.786850i	$0.711711\pi$
$212$	−3.88119	+	2.71764i	−0.266561	+	0.186648i
$213$	6.15746	+	0.538708i	0.421902	+	0.0369117i
$214$	14.6795	−	17.4943i	1.00347	−	1.19589i
$215$	−11.3471	+	4.55863i	−0.773866	+	0.310896i
$216$	3.15611	+	5.46654i	0.214746	+	0.371951i
$217$	−29.1331	+	7.80620i	−1.97769	+	0.529919i
$218$	9.02061	+	19.3448i	0.610953	+	1.31019i
$219$	−17.7412	−	6.45725i	−1.19884	−	0.436341i
$220$	−5.00446	−	9.86968i	−0.337401	−	0.665413i
$221$	6.52878	−	3.76939i	0.439173	−	0.253557i
$222$	−3.48733	+	4.98043i	−0.234055	+	0.334265i
$223$	−16.2183	+	1.41892i	−1.08606	+	0.0950179i	−0.616098	−	0.787669i	$-0.711288\pi$
$223$	−16.2183	+	1.41892i	−1.08606	+	0.0950179i	−0.469961	+	0.882687i	$0.655732\pi$
$224$	−22.6861	+	19.0359i	−1.51578	+	1.27189i
$225$	1.11480	+	4.54724i	0.0743201	+	0.303149i
$226$	22.4062	−	8.15520i	1.49044	−	0.542476i
$227$	−11.7879	−	11.7879i	−0.782393	−	0.782393i	0.197841	−	0.980234i	$-0.436607\pi$
$227$	−11.7879	−	11.7879i	−0.782393	−	0.782393i	−0.980234	+	0.197841i	$0.936607\pi$
$228$	−8.10168	−	3.25030i	−0.536547	−	0.215256i
$229$			15.2871i			1.01020i	0.863061	+	0.505100i	$0.168544\pi$
$229$			15.2871i			1.01020i	−0.863061	+	0.505100i	$0.831456\pi$
$230$	2.45552	−	10.5415i	0.161912	−	0.695087i
$231$	22.2215	+	3.91825i	1.46207	+	0.257802i
$232$	0.213003	−	2.43463i	0.0139843	−	0.159841i
$233$	0.724390	+	8.27981i	0.0474563	+	0.542428i	0.982293	+	0.187351i	$0.0599901\pi$
$233$	0.724390	+	8.27981i	0.0474563	+	0.542428i	−0.934837	+	0.355078i	$0.884454\pi$
$234$	2.60158	−	0.458729i	0.170071	−	0.0299880i
$235$	9.26484	+	10.3304i	0.604372	+	0.673880i
$236$	−2.28465	−	1.31904i	−0.148718	−	0.0858623i
$237$	−4.11203	+	1.91747i	−0.267105	+	0.124553i
$238$	36.3715	−	16.9603i	2.35761	−	1.09937i
$239$	12.7842	+	7.38094i	0.826938	+	0.477433i	0.852803	−	0.522232i	$-0.174901\pi$
$239$	12.7842	+	7.38094i	0.826938	+	0.477433i	−0.0258648	+	0.999665i	$0.508234\pi$
$240$	−10.3903	−	11.5853i	−0.670691	−	0.747826i
$241$	−9.86754	+	1.73991i	−0.635624	+	0.112078i	−0.482170	−	0.876078i	$-0.660151\pi$
$241$	−9.86754	+	1.73991i	−0.635624	+	0.112078i	−0.153455	+	0.988156i	$0.549040\pi$
$242$	0.257164	+	2.93940i	0.0165311	+	0.188952i
$243$	0.813197	−	9.29488i	0.0521666	−	0.596267i
$244$	14.3140	+	2.52395i	0.916363	+	0.161579i
$245$	6.38110	−	27.3940i	0.407674	−	1.75014i
$246$		−	8.90226i		−	0.567587i
$247$	4.45429	−	4.97136i	0.283420	−	0.316320i
$248$	−5.38027	−	5.38027i	−0.341647	−	0.341647i
$249$	1.31298	−	0.477887i	0.0832070	−	0.0302849i
$250$	−8.92016	−	18.5659i	−0.564160	−	1.17421i
$251$	−1.57049	+	1.31780i	−0.0991285	+	0.0831787i	−0.691005	−	0.722850i	$-0.742832\pi$
$251$	−1.57049	+	1.31780i	−0.0991285	+	0.0831787i	0.591876	+	0.806029i	$0.298387\pi$
$252$	5.75416	−	0.503423i	0.362478	−	0.0317127i
$253$	−5.34976	+	7.64025i	−0.336337	+	0.480338i
$254$	−24.5689	+	14.1849i	−1.54159	+	0.890039i
$255$	7.15151	+	14.1040i	0.447845	+	0.883229i
$256$	−19.7137	−	7.17522i	−1.23211	−	0.448451i
$257$	1.57579	+	3.37930i	0.0982952	+	0.210795i	0.949306	−	0.314353i	$-0.101788\pi$
$257$	1.57579	+	3.37930i	0.0982952	+	0.210795i	−0.851011	+	0.525148i	$0.824010\pi$
$258$	−13.9801	+	3.74596i	−0.870364	+	0.233213i
$259$	−5.08265	−	8.80341i	−0.315821	−	0.547018i
$260$	−4.42953	+	1.77953i	−0.274708	+	0.110362i
$261$	−1.31777	+	1.57045i	−0.0815677	+	0.0972086i
$262$	−11.1199	−	0.972869i	−0.686993	−	0.0601041i
$263$	16.3675	−	11.4607i	1.00927	−	0.706696i	0.0528196	−	0.998604i	$-0.483179\pi$
$263$	16.3675	−	11.4607i	1.00927	−	0.706696i	0.956446	+	0.291909i	$0.0942903\pi$
$264$	1.94693	+	5.34913i	0.119825	+	0.329216i
$265$	7.43668	−	1.56546i	0.456832	−	0.0961652i
$266$	25.9280	−	24.2969i	1.58975	−	1.48974i
$267$	−9.00139	+	9.00139i	−0.550876	+	0.550876i
$268$	−1.69716	+	3.63957i	−0.103670	+	0.222322i
$269$	2.25210	−	12.7723i	0.137313	−	0.778740i	−0.835908	−	0.548869i	$-0.815058\pi$
$269$	2.25210	−	12.7723i	0.137313	−	0.778740i	0.973221	−	0.229871i	$-0.0738304\pi$
$270$	2.79350	+	23.1267i	0.170007	+	1.40744i
$271$	16.0539	+	13.4709i	0.975208	+	0.818297i	0.983360	−	0.181670i	$-0.0581503\pi$
$271$	16.0539	+	13.4709i	0.975208	+	0.818297i	−0.00815153	+	0.999967i	$0.502595\pi$
$272$	19.5371	+	13.6800i	1.18461	+	0.829473i
$273$	2.51929	−	9.40212i	0.152474	−	0.569042i
$274$	−1.90310	+	3.29627i	−0.114971	+	0.199135i
$275$	1.16857	+	17.7109i	0.0704676	+	1.06800i
$276$	1.79965	−	4.94449i	0.108326	−	0.297623i
$277$	−1.74816	−	6.52420i	−0.105036	−	0.392001i	0.893313	−	0.449435i	$-0.148375\pi$
$277$	−1.74816	−	6.52420i	−0.105036	−	0.392001i	−0.998349	+	0.0574339i	$0.981708\pi$
$278$	−14.6744	−	3.93200i	−0.880113	−	0.235826i
$279$	1.10833	+	6.28568i	0.0663543	+	0.376314i
$280$	10.5683	−	3.20838i	0.631578	−	0.191737i
$281$	−6.33637	−	7.55139i	−0.377996	−	0.450478i	0.543184	−	0.839613i	$-0.317218\pi$
$281$	−6.33637	−	7.55139i	−0.377996	−	0.450478i	−0.921181	+	0.389135i	$0.872774\pi$
$282$	9.42018	+	13.4534i	0.560963	+	0.801139i
$283$	29.1570	+	13.5961i	1.73320	+	0.808205i	0.990324	+	0.138777i	$0.0443172\pi$
$283$	29.1570	+	13.5961i	1.73320	+	0.808205i	0.742877	+	0.669428i	$0.233461\pi$
$284$	5.99837			0.355938
$285$	9.90534	+	9.89586i	0.586742	+	0.586180i
$286$	10.0149			0.592193
$287$	13.4894	+	6.29023i	0.796257	+	0.371301i
$288$	3.59464	+	5.13367i	0.211816	+	0.302505i
$289$	−4.65112	−	5.54299i	−0.273595	−	0.326058i
$290$	4.24987	−	7.95511i	0.249561	−	0.467140i
$291$	−1.15752	−	6.56461i	−0.0678549	−	0.384824i
$292$	−17.6977	−	4.74207i	−1.03568	−	0.277509i
$293$	−5.95902	−	22.2394i	−0.348130	−	1.29924i	−0.888913	−	0.458076i	$-0.848539\pi$
$293$	−5.95902	−	22.2394i	−0.348130	−	1.29924i	0.540784	−	0.841162i	$-0.318128\pi$
$294$	11.3860	−	31.2829i	0.664047	−	1.82446i
$295$	2.53987	+	3.38433i	0.147877	+	0.197043i
$296$	1.28223	−	2.22089i	0.0745281	−	0.129086i
$297$	5.19542	−	19.3896i	0.301469	−	1.12510i
$298$	−6.44583	−	4.51342i	−0.373397	−	0.261455i
$299$	3.08217	+	2.58625i	0.178246	+	0.149567i
$300$	−3.22278	−	9.48046i	−0.186068	−	0.547354i
$301$	4.20200	−	23.8307i	0.242199	−	1.37358i
$302$	−16.7740	+	35.9720i	−0.965237	+	2.06996i
$303$	−6.79645	+	6.79645i	−0.390446	+	0.390446i
$304$	20.2098	+	6.12482i	1.15911	+	0.351283i
$305$	−19.5273	−	12.7357i	−1.11813	−	0.729247i
$306$	−2.90466	−	7.98047i	−0.166048	−	0.456213i
$307$	−3.05271	+	2.13753i	−0.174227	+	0.121995i	−0.657437	−	0.753509i	$-0.728360\pi$
$307$	−3.05271	+	2.13753i	−0.174227	+	0.121995i	0.483210	+	0.875504i	$0.339471\pi$
$308$	21.8144	+	1.90851i	1.24299	+	0.108747i
$309$	11.6152	−	13.8425i	0.660765	−	0.787470i
$310$	−10.4678	−	26.0558i	−0.594529	−	1.47987i
$311$	−6.16899	−	10.6850i	−0.349812	−	0.605891i	0.636404	−	0.771356i	$-0.280421\pi$
$311$	−6.16899	−	10.6850i	−0.349812	−	0.605891i	−0.986216	+	0.165464i	$0.947088\pi$
$312$	2.37192	−	0.635555i	0.134284	−	0.0359812i
$313$	6.60915	+	14.1734i	0.373571	+	0.801126i	0.999770	+	0.0214623i	$0.00683220\pi$
$313$	6.60915	+	14.1734i	0.373571	+	0.801126i	−0.626198	+	0.779664i	$0.715390\pi$
$314$	−10.4027	−	3.78628i	−0.587059	−	0.213672i
$315$	−8.80562	−	2.88025i	−0.496141	−	0.162284i
$316$	−3.81318	+	2.20154i	−0.214508	+	0.123846i
$317$	13.7178	−	19.5910i	0.770466	−	1.10034i	−0.221663	−	0.975123i	$-0.571148\pi$
$317$	13.7178	−	19.5910i	0.770466	−	1.10034i	0.992129	−	0.125217i	$-0.0399626\pi$
$318$	8.96046	−	0.783939i	0.502478	−	0.0439611i
$319$	−5.95368	+	4.99573i	−0.333342	+	0.279707i
$320$	−4.31091	−	4.03585i	−0.240987	−	0.225611i
$321$	−16.7333	+	6.09043i	−0.933962	+	0.339935i
$322$	15.1451	+	15.1451i	0.844002	+	0.844002i
$323$	−18.2258	−	11.3270i	−1.01411	−	0.630249i
$324$			7.40827i			0.411570i
$325$	7.65496	+	0.163698i	0.424621	+	0.00908033i
$326$	−1.50016	−	0.264518i	−0.0830860	−	0.0146503i
$327$	1.45056	−	16.5800i	0.0802164	−	0.916878i
$328$	0.327258	+	3.74057i	0.0180698	+	0.206539i
$329$	−27.0419	+	4.76822i	−1.49087	+	0.262880i
$330$	−1.14065	+	20.9765i	−0.0627906	+	1.15472i
$331$	7.63848	+	4.41008i	0.419849	+	0.242400i	0.695013	−	0.718997i	$-0.255399\pi$
$331$	7.63848	+	4.41008i	0.419849	+	0.242400i	−0.275164	+	0.961397i	$0.588732\pi$
$332$	1.22892	−	0.573057i	0.0674460	−	0.0314506i
$333$	−1.94964	+	0.909130i	−0.106839	+	0.0498200i
$334$	−20.0156	−	11.5560i	−1.09521	−	0.632318i
$335$	4.79522	−	4.30061i	0.261991	−	0.234967i
$336$	30.3269	−	5.34744i	1.65447	−	0.291727i
$337$	−0.0238979	−	0.273154i	−0.00130180	−	0.0148796i	0.995516	−	0.0945931i	$-0.0301550\pi$
$337$	−0.0238979	−	0.273154i	−0.00130180	−	0.0148796i	−0.996818	+	0.0797135i	$0.974599\pi$
$338$	−1.71085	+	19.5551i	−0.0930577	+	1.06365i
$339$	−18.3100	−	3.22854i	−0.994461	−	0.175350i
$340$	8.10675	+	13.0304i	0.439650	+	0.706672i
$341$			24.1970i			1.31034i
$342$	−4.64394	−	5.91414i	−0.251116	−	0.319800i
$343$	17.4555	+	17.4555i	0.942509	+	0.942509i
$344$	5.73649	−	2.08791i	0.309291	−	0.112573i
$345$	−5.76801	+	6.16113i	−0.310539	+	0.331704i
$346$	−34.0298	+	28.5544i	−1.82946	+	1.53510i
$347$	−11.2290	+	0.982411i	−0.602805	+	0.0527386i	−0.384473	−	0.923136i	$-0.625617\pi$
$347$	−11.2290	+	0.982411i	−0.602805	+	0.0527386i	−0.218331	+	0.975875i	$0.570061\pi$
$348$	2.51487	−	3.59161i	0.134811	−	0.192530i
$349$	−20.6735	+	11.9359i	−1.10663	+	0.638912i	−0.937954	−	0.346759i	$-0.887282\pi$
$349$	−20.6735	+	11.9359i	−1.10663	+	0.638912i	−0.168675	+	0.985672i	$0.553949\pi$
$350$	40.5189	+	4.41970i	2.16583	+	0.236243i
$351$	−8.13710	−	2.96166i	−0.434327	−	0.158082i
$352$	10.0409	+	21.5328i	0.535182	+	1.14770i
$353$	10.2142	−	2.73689i	0.543648	−	0.145670i	0.0234648	−	0.999725i	$-0.492530\pi$
$353$	10.2142	−	2.73689i	0.543648	−	0.145670i	0.520183	+	0.854055i	$0.325864\pi$
$354$	2.50406	+	4.33716i	0.133089	+	0.230517i
$355$	−8.84893	−	3.77668i	−0.469652	−	0.200445i
$356$	−7.94087	+	9.46356i	−0.420865	+	0.501568i
$357$	−31.1733	−	2.72731i	−1.64987	−	0.144345i
$358$	−33.1913	+	23.2408i	−1.75421	+	1.22831i
$359$	9.08655	+	24.9651i	0.479570	+	1.31761i	0.909860	+	0.414916i	$0.136189\pi$
$359$	9.08655	+	24.9651i	0.479570	+	1.31761i	−0.430290	+	0.902691i	$0.641589\pi$
$360$	−0.481453	−	2.28714i	−0.0253748	−	0.120543i
$361$	−18.4579	−	4.50640i	−0.971466	−	0.237179i
$362$	14.8459	−	14.8459i	0.780281	−	0.780281i
$363$	0.972335	−	2.08518i	0.0510343	−	0.109443i
$364$	1.64032	−	9.30270i	0.0859760	−	0.487594i
$365$	23.1223	+	18.1383i	1.21028	+	0.949405i
$366$	−21.1374	−	17.7363i	−1.10487	−	0.927094i
$367$	17.7491	+	12.4280i	0.926494	+	0.648738i	0.936295	−	0.351214i	$-0.114231\pi$
$367$	17.7491	+	12.4280i	0.926494	+	0.648738i	−0.00980114	+	0.999952i	$0.503120\pi$
$368$	−3.29452	+	12.2953i	−0.171739	+	0.640939i
$369$	1.57487	−	2.72776i	0.0819847	−	0.142002i
$370$	7.56942	−	5.68069i	0.393515	−	0.295325i
$371$	−5.14347	+	14.1316i	−0.267035	+	0.733674i
$372$	−3.53306	−	13.1855i	−0.183180	−	0.683639i
$373$	−18.5179	−	4.96186i	−0.958821	−	0.256915i	−0.254720	−	0.967015i	$-0.581983\pi$
$373$	−18.5179	−	4.96186i	−0.958821	−	0.256915i	−0.704101	+	0.710100i	$0.748650\pi$
$374$	−5.59080	−	31.7070i	−0.289093	−	1.63953i
$375$	−1.21473	+	16.0149i	−0.0627285	+	0.827006i
$376$	−4.45276	−	5.30659i	−0.229633	−	0.273666i
$377$	1.92301	+	2.74635i	0.0990403	+	0.141444i
$378$	−41.7776	−	19.4812i	−2.14881	−	1.00201i
$379$	−8.71753			−0.447789			−0.223895	−	0.974613i	$-0.571877\pi$
$379$	−8.71753			−0.447789			−0.223895	+	0.974613i	$0.571877\pi$
$380$	10.4131	+	8.72915i	0.534182	+	0.447796i
$381$	22.1212			1.13330
$382$	16.1472	+	7.52958i	0.826165	+	0.385247i
$383$	1.18720	+	1.69550i	0.0606633	+	0.0866361i	0.848338	−	0.529456i	$-0.177604\pi$
$383$	1.18720	+	1.69550i	0.0606633	+	0.0866361i	−0.787674	+	0.616092i	$0.788715\pi$
$384$	7.86757	+	9.37620i	0.401490	+	0.478477i
$385$	−30.9794	−	16.5502i	−1.57886	−	0.843474i
$386$	−4.32276	−	24.5156i	−0.220023	−	1.24781i
$387$	−4.94637	−	1.32538i	−0.251438	−	0.0673726i
$388$	−1.67429	−	6.24852i	−0.0849990	−	0.317220i
$389$	6.97523	−	19.1643i	0.353658	−	0.971667i	−0.627527	−	0.778595i	$-0.715933\pi$
$389$	6.97523	−	19.1643i	0.353658	−	0.971667i	0.981185	−	0.193072i	$-0.0618452\pi$
$390$	8.97152	+	1.27884i	0.454290	+	0.0647564i
$391$	6.46740	−	11.2019i	0.327070	−	0.566502i
$392$	−3.63422	+	13.5631i	−0.183556	+	0.685039i
$393$	7.12978	+	4.99233i	0.359650	+	0.251830i
$394$	25.5857	+	21.4689i	1.28899	+	1.08159i
$395$	7.01140	−	0.846918i	0.352782	−	0.0426130i
$396$	0.804685	−	4.56359i	0.0404369	−	0.229329i
$397$	−4.28466	+	9.18848i	−0.215041	+	0.461156i	−0.984006	−	0.178134i	$-0.942994\pi$
$397$	−4.28466	+	9.18848i	−0.215041	+	0.461156i	0.768965	+	0.639290i	$0.220772\pi$
$398$	−19.8746	+	19.8746i	−0.996225	+	0.996225i
$399$	−26.9814	+	6.29860i	−1.35076	+	0.315324i
$400$	9.76557	+	22.1678i	0.488279	+	1.10839i
$401$	5.50246	+	15.1179i	0.274780	+	0.754951i	0.997933	+	0.0642633i	$0.0204697\pi$
$401$	5.50246	+	15.1179i	0.274780	+	0.754951i	−0.723153	+	0.690687i	$0.757308\pi$
$402$	6.24488	−	4.37271i	0.311466	−	0.218091i
$403$	10.3984	+	0.909739i	0.517979	+	0.0453173i
$404$	−5.99571	+	7.14541i	−0.298298	+	0.355497i
$405$	4.66437	−	10.9288i	0.231774	−	0.543058i
$406$	8.92371	+	15.4563i	0.442876	+	0.767084i
$407$	−7.87739	+	2.11074i	−0.390468	+	0.104626i
$408$	−3.33628	−	7.15467i	−0.165170	−	0.354209i
$409$	−0.573185	−	0.208622i	−0.0283422	−	0.0103157i	0.327810	−	0.944744i	$-0.393689\pi$
$409$	−0.573185	−	0.208622i	−0.0283422	−	0.0103157i	−0.356152	+	0.934428i	$0.615912\pi$
$410$	−4.30794	+	13.1704i	−0.212754	+	0.650439i
$411$	2.57026	−	1.48394i	0.126781	−	0.0731973i
$412$	10.0583	−	14.3648i	0.495539	−	0.707703i
$413$	−8.34136	+	0.729775i	−0.410452	+	0.0359099i
$414$	3.47214	−	2.91348i	0.170647	−	0.143190i
$415$	−2.17374	+	0.0716346i	−0.106705	+	0.00351640i
$416$	9.63097	−	3.50538i	0.472197	−	0.171866i
$417$	8.37636	+	8.37636i	0.410192	+	0.410192i
$418$	−13.4447	−	25.1374i	−0.657600	−	1.22951i
$419$		−	31.1162i		−	1.52013i	−0.649850	−	0.760063i	$-0.725168\pi$
$419$		−	31.1162i		−	1.52013i	0.649850	−	0.760063i	$-0.274832\pi$
$420$	19.2980	+	4.49523i	0.941644	+	0.219345i
$421$	−27.9327	−	4.92528i	−1.36135	−	0.240044i	−0.555184	−	0.831727i	$-0.687352\pi$
$421$	−27.9327	−	4.92528i	−1.36135	−	0.240044i	−0.806170	+	0.591684i	$0.798463\pi$
$422$	2.46449	−	28.1692i	0.119969	−	1.37126i
$423$	0.506453	+	5.78879i	0.0246246	+	0.281460i
$424$	−3.73621	+	0.658794i	−0.181446	+	0.0319939i
$425$	−3.75510	−	24.3269i	−0.182149	−	1.18003i
$426$	−9.86166	−	5.69363i	−0.477799	−	0.275857i
$427$	41.8110	−	19.4968i	2.02338	−	0.943516i
$428$	−15.6620	+	7.30332i	−0.757052	+	0.353019i
$429$	−6.76286	−	3.90454i	−0.326514	−	0.188513i
$430$	22.4955	+	1.22325i	1.08483	+	0.0589902i
$431$	−27.5436	+	4.85668i	−1.32673	+	0.233938i	−0.791708	−	0.610900i	$-0.790808\pi$
$431$	−27.5436	+	4.85668i	−1.32673	+	0.233938i	−0.535022	+	0.844838i	$0.679697\pi$
$432$	−2.38767	−	27.2912i	−0.114877	−	1.31305i
$433$	1.62433	−	18.5662i	0.0780604	−	0.892234i	−0.851691	−	0.524045i	$-0.824422\pi$
$433$	1.62433	−	18.5662i	0.0780604	−	0.892234i	0.929751	−	0.368189i	$-0.120022\pi$
$434$	54.7213	+	9.64884i	2.62671	+	0.463159i
$435$	−5.97133	+	3.71502i	−0.286303	+	0.178121i
$436$		−	16.1516i		−	0.773524i
$437$	2.35377	−	11.2082i	0.112596	−	0.536161i
$438$	24.5948	+	24.5948i	1.17518	+	1.17518i
$439$	−13.3596	+	4.86248i	−0.637617	+	0.232074i	−0.640543	−	0.767922i	$-0.721291\pi$
$439$	−13.3596	+	4.86248i	−0.637617	+	0.232074i	0.00292604	+	0.999996i	$0.499069\pi$
$440$	−0.291841	−	8.85589i	−0.0139130	−	0.422188i
$441$	9.02299	−	7.57119i	0.429666	−	0.360533i
$442$	−13.8359	+	1.21048i	−0.658107	+	0.0575769i
$443$	−4.01515	+	5.73422i	−0.190765	+	0.272441i	−0.903129	−	0.429369i	$-0.858736\pi$
$443$	−4.01515	+	5.73422i	−0.190765	+	0.272441i	0.712364	+	0.701811i	$0.247625\pi$
$444$	3.98439	−	2.30039i	0.189091	−	0.109172i
$445$	17.6730	−	8.96115i	0.837779	−	0.424799i
$446$	28.1844	+	10.2583i	1.33457	+	0.485744i
$447$	2.59308	+	5.56088i	0.122648	+	0.263021i
$448$	11.2873	−	3.02444i	0.533277	−	0.142891i
$449$	8.43938	+	14.6174i	0.398279	+	0.689839i	0.993514	−	0.113713i	$-0.0362743\pi$
$449$	8.43938	+	14.6174i	0.398279	+	0.689839i	−0.595235	+	0.803552i	$0.702941\pi$
$450$	1.67907	−	8.46048i	0.0791519	−	0.398831i
$451$	7.67545	−	9.14725i	0.361423	−	0.430727i
$452$	−17.9745	−	1.57256i	−0.845448	−	0.0739671i
$453$	25.3517	−	17.7514i	1.19113	−	0.834036i
$454$	10.5043	+	28.8603i	0.492990	+	1.35448i
$455$	−8.27697	+	12.6908i	−0.388030	+	0.594953i
$456$	−4.77947	−	5.10032i	−0.223819	−	0.238844i
$457$	−6.78033	+	6.78033i	−0.317170	+	0.317170i	−0.847679	−	0.530509i	$-0.822001\pi$
$457$	−6.78033	+	6.78033i	−0.317170	+	0.317170i	0.530509	+	0.847679i	$0.322001\pi$
$458$	11.9024	−	25.5248i	0.556163	−	1.19270i
$459$	−4.83405	+	27.4153i	−0.225634	+	1.27964i
$460$	−5.05519	+	6.44422i	−0.235699	+	0.300463i
$461$	21.7316	+	18.2350i	1.01214	+	0.849287i	0.988620	−	0.150436i	$-0.0480678\pi$
$461$	21.7316	+	18.2350i	1.01214	+	0.849287i	0.0235214	+	0.999723i	$0.492512\pi$
$462$	−34.0525	−	23.8438i	−1.58426	−	1.10931i
$463$	4.25510	−	15.8802i	0.197751	−	0.738017i	−0.793786	−	0.608197i	$-0.791893\pi$
$463$	4.25510	−	15.8802i	0.197751	−	0.738017i	0.991538	−	0.129821i	$-0.0414401\pi$
$464$	−5.30341	+	9.18578i	−0.246205	+	0.426439i
$465$	−3.08980	+	21.6761i	−0.143286	+	1.00520i
$466$	5.23708	−	14.3888i	0.242603	−	0.666547i
$467$	−7.23029	−	26.9838i	−0.334578	−	1.24866i	−0.904326	−	0.426842i	$-0.859626\pi$
$467$	−7.23029	−	26.9838i	−0.334578	−	1.24866i	0.569749	−	0.821819i	$-0.307041\pi$
$468$	−1.93090	−	0.517382i	−0.0892557	−	0.0239160i
$469$	2.21334	+	12.5525i	0.102203	+	0.579619i
$470$	−7.42632	−	24.4621i	−0.342550	−	1.12835i
$471$	5.54857	+	6.61253i	0.255665	+	0.304689i
$472$	−1.21160	−	1.73034i	−0.0557684	−	0.0796456i
$473$	−17.5946	−	8.20449i	−0.809000	−	0.377243i
$474$	8.35876			0.383931
$475$	−9.86564	−	19.4337i	−0.452667	−	0.891680i
$476$	−30.3679			−1.39191
$477$	2.88428	+	1.34496i	0.132062	+	0.0615815i
$478$	−15.5989	−	22.2776i	−0.713478	−	1.01895i
$479$	5.94529	+	7.08532i	0.271647	+	0.323736i	0.884571	−	0.466406i	$-0.154451\pi$
$479$	5.94529	+	7.08532i	0.271647	+	0.323736i	−0.612924	+	0.790142i	$0.710007\pi$
$480$	6.24521	+	20.5716i	0.285054	+	0.938960i
$481$	0.610897	+	3.46457i	0.0278545	+	0.157971i
$482$	17.8305	+	4.77766i	0.812156	+	0.217617i
$483$	−4.32251	−	16.1318i	−0.196681	−	0.734024i
$484$	0.763651	−	2.09811i	0.0347114	−	0.0953688i
$485$	−1.46423	+	10.2721i	−0.0664872	+	0.466433i
$486$	−8.59471	+	14.8865i	−0.389864	+	0.675264i
$487$	−4.88464	+	18.2297i	−0.221344	+	0.826067i	0.762492	+	0.646997i	$0.223975\pi$
$487$	−4.88464	+	18.2297i	−0.221344	+	0.826067i	−0.983836	+	0.179070i	$0.942691\pi$
$488$	9.53355	+	6.67546i	0.431564	+	0.302184i
$489$	0.909897	+	0.763495i	0.0411470	+	0.0345264i
$490$	−31.9833	+	40.7714i	−1.44486	+	1.84186i
$491$	2.48979	−	14.1203i	0.112362	−	0.637239i	−0.875660	−	0.482928i	$-0.839573\pi$
$491$	2.48979	−	14.1203i	0.112362	−	0.637239i	0.988022	−	0.154311i	$-0.0493157\pi$
$492$	−2.84694	+	6.10527i	−0.128350	+	0.275247i
$493$	7.62137	−	7.62137i	0.343249	−	0.343249i
$494$	−11.3080	+	4.83258i	−0.508770	+	0.217428i
$495$	−4.06040	+	6.22567i	−0.182502	+	0.279823i
$496$	11.2945	+	31.0314i	0.507138	+	1.39335i
$497$	15.5956	−	10.9202i	0.699558	−	0.489836i
$498$	−2.56436	−	0.224353i	−0.114912	−	0.0100535i
$499$	0.682333	−	0.813172i	0.0305454	−	0.0364026i	−0.750555	−	0.660807i	$-0.770214\pi$
$499$	0.682333	−	0.813172i	0.0305454	−	0.0364026i	0.781101	+	0.624405i	$0.214658\pi$
$500$	0.180195	+	15.5854i	0.00805855	+	0.696998i
$501$	9.01077	+	15.6071i	0.402571	+	0.697274i
$502$	3.64827	−	0.977551i	0.162830	−	0.0436302i
$503$	1.52362	+	3.26741i	0.0679348	+	0.145687i	0.937343	−	0.348408i	$-0.113278\pi$
$503$	1.52362	+	3.26741i	0.0679348	+	0.145687i	−0.869408	+	0.494094i	$0.835500\pi$
$504$	4.34613	+	1.58186i	0.193592	+	0.0704617i
$505$	13.3439	−	6.76606i	0.593794	−	0.301086i
$506$	14.8811	−	8.59161i	0.661546	−	0.381944i
$507$	8.77929	−	12.5381i	0.389902	−	0.556838i
$508$	21.3860	−	1.87103i	0.948849	−	0.0830136i
$509$	−24.2515	+	20.3494i	−1.07493	+	0.901971i	−0.995490	−	0.0948686i	$-0.969757\pi$
$509$	−24.2515	+	20.3494i	−1.07493	+	0.901971i	−0.0794377	+	0.996840i	$0.525312\pi$
$510$	−0.959555	−	29.1176i	−0.0424898	−	1.28935i
$511$	−54.6464	+	19.8897i	−2.41742	+	0.879867i
$512$	15.2798	+	15.2798i	0.675277	+	0.675277i
$513$	3.49001	+	24.4001i	0.154088	+	1.07729i
$514$		−	6.86930i		−	0.302992i
$515$	−23.8826	+	14.8584i	−1.05239	+	0.654738i
$516$	10.7857	+	1.90181i	0.474813	+	0.0837224i
$517$	−1.91999	+	21.9456i	−0.0844413	+	0.965168i
$518$	1.63222	+	18.6563i	0.0717155	+	0.819712i
$519$	34.1123	−	6.01491i	1.49736	−	0.264025i
$520$	−3.81668	−	0.207541i	−0.167373	−	0.00910129i
$521$	35.0712	+	20.2484i	1.53650	+	0.887098i	0.999040	+	0.0438085i	$0.0139492\pi$
$521$	35.0712	+	20.2484i	1.53650	+	0.887098i	0.537459	+	0.843290i	$0.319384\pi$
$522$	3.42301	−	1.59618i	0.149821	−	0.0698627i
$523$	24.9322	−	11.6261i	1.09021	−	0.508373i	0.207472	−	0.978241i	$-0.433476\pi$
$523$	24.9322	−	11.6261i	1.09021	−	0.508373i	0.882737	+	0.469868i	$0.155699\pi$
$524$	7.31507	+	4.22336i	0.319560	+	0.184498i
$525$	−25.6385	−	18.7818i	−1.11896	−	0.819704i
$526$	−36.2520	+	6.39221i	−1.58066	+	0.278713i
$527$	−2.92465	−	33.4289i	−0.127400	−	1.45619i
$528$	2.15323	−	24.6115i	0.0937072	−	1.07108i
$529$	−15.8521	−	2.79515i	−0.689222	−	0.121528i
$530$	−13.6359	−	3.17631i	−0.592304	−	0.137970i
$531$			1.77194i			0.0768958i
$532$	−25.5519	+	8.37136i	−1.10781	+	0.362944i
$533$	−3.64234	−	3.64234i	−0.157767	−	0.157767i
$534$	22.0380	−	8.02118i	0.953678	−	0.347110i
$535$	27.7032	−	0.912946i	1.19772	−	0.0394701i
$536$	−2.46324	+	2.06691i	−0.106396	+	0.0892767i
$537$	31.4743	−	2.75365i	1.35822	−	0.118829i
$538$	−13.7047	+	19.5724i	−0.590853	+	0.843825i
$539$	38.6712	−	22.3268i	1.66569	−	0.961685i
$540$	5.48007	−	16.7539i	0.235825	−	0.720973i
$541$	11.1396	+	4.05450i	0.478931	+	0.174317i	0.570194	−	0.821510i	$-0.306868\pi$
$541$	11.1396	+	4.05450i	0.478931	+	0.174317i	−0.0912630	+	0.995827i	$0.529090\pi$
$542$	−16.3169	−	34.9917i	−0.700871	−	1.50302i
$543$	−15.8131	+	4.23711i	−0.678606	+	0.181832i
$544$	−16.4745	−	28.5346i	−0.706336	−	1.22341i
$545$	−10.1693	+	23.8273i	−0.435607	+	1.02065i
$546$	−11.5269	+	13.7372i	−0.493304	+	0.587897i
$547$	1.37232	+	0.120063i	0.0586762	+	0.00513350i	0.116456	−	0.993196i	$-0.462847\pi$
$547$	1.37232	+	0.120063i	0.0586762	+	0.00513350i	−0.0577798	+	0.998329i	$0.518402\pi$
$548$	2.35932	−	1.65201i	0.100785	−	0.0705704i
$549$	−3.33906	−	9.17398i	−0.142507	−	0.391536i
$550$	11.8384	−	30.4816i	0.504790	−	1.29974i
$551$	4.31176	−	8.51365i	0.183687	−	0.362693i
$552$	2.97920	−	2.97920i	0.126803	−	0.126803i
$553$	−5.90620	+	12.6659i	−0.251157	+	0.538609i
$554$	−2.16081	+	12.2545i	−0.0918038	+	0.520645i
$555$	−7.32623	+	0.884945i	−0.310981	+	0.0375638i
$556$	8.80644	+	7.38948i	0.373476	+	0.313384i
$557$	−22.6324	−	15.8474i	−0.958966	−	0.671475i	−0.0144346	−	0.999896i	$-0.504595\pi$
$557$	−22.6324	−	15.8474i	−0.958966	−	0.671475i	−0.944532	+	0.328420i	$0.893484\pi$
$558$	3.04340	−	11.3581i	0.128837	−	0.480827i
$559$	−4.18729	+	7.25260i	−0.177103	+	0.306752i
$560$	−47.4546	−	6.76437i	−2.00532	−	0.285847i
$561$	−8.58635	+	23.5908i	−0.362516	+	0.996004i
$562$	4.70036	+	17.5420i	0.198273	+	0.739964i
$563$	−11.4662	−	3.07235i	−0.483241	−	0.129484i	0.00897027	−	0.999960i	$-0.497145\pi$
$563$	−11.4662	−	3.07235i	−0.483241	−	0.129484i	−0.492211	+	0.870476i	$0.663811\pi$
$564$	−2.15808	−	12.2391i	−0.0908715	−	0.515358i
$565$	25.5262	+	13.6369i	1.07390	+	0.573709i
$566$	−38.0974	−	45.4027i	−1.60135	−	1.90842i
$567$	13.4869	+	19.2613i	0.566396	+	0.808898i
$568$	4.35300	+	2.02984i	0.182648	+	0.0851700i
$569$	36.4460			1.52789			0.763947	−	0.645279i	$-0.223259\pi$
$569$	36.4460			1.52789			0.763947	+	0.645279i	$0.223259\pi$
$570$	−8.83407	−	24.2353i	−0.370018	−	1.01511i
$571$	2.73728			0.114551			0.0572757	−	0.998358i	$-0.481759\pi$
$571$	2.73728			0.114551			0.0572757	+	0.998358i	$0.481759\pi$
$572$	−6.86833	−	3.20276i	−0.287179	−	0.133914i
$573$	−7.96833	−	11.3800i	−0.332882	−	0.475404i
$574$	−17.6258	−	21.0056i	−0.735685	−	0.876755i
$575$	11.5149	−	6.32382i	0.480205	−	0.263722i
$576$	−0.429413	−	2.43532i	−0.0178922	−	0.101472i
$577$	−16.5385	−	4.43149i	−0.688508	−	0.184485i	−0.102431	−	0.994740i	$-0.532662\pi$
$577$	−16.5385	−	4.43149i	−0.688508	−	0.184485i	−0.586078	+	0.810255i	$0.699329\pi$
$578$	3.45023	+	12.8764i	0.143511	+	0.535589i
$579$	−6.63889	+	18.2402i	−0.275903	+	0.758037i
$580$	−5.45864	+	4.09660i	−0.226658	+	0.170102i
$581$	2.15191	−	3.72721i	0.0892761	−	0.154631i
$582$	−3.17845	+	11.8621i	−0.131751	+	0.491701i
$583$	9.88295	+	6.92012i	0.409310	+	0.286602i
$584$	−11.2384	−	9.43015i	−0.465049	−	0.390223i
$585$	2.52275	+	1.97898i	0.104303	+	0.0818206i
$586$	−7.36564	+	41.7726i	−0.304272	+	1.72561i
$587$	1.51219	−	3.24291i	0.0624148	−	0.133849i	−0.872626	−	0.488389i	$-0.837585\pi$
$587$	1.51219	−	3.24291i	0.0624148	−	0.133849i	0.935041	+	0.354540i	$0.115363\pi$
$588$	−17.8129	+	17.8129i	−0.734592	+	0.734592i
$589$	−11.6760	−	27.3212i	−0.481101	−	1.12575i
$590$	−1.60580	−	7.62833i	−0.0661097	−	0.314053i
$591$	−8.90733	−	24.4727i	−0.366399	−	1.00667i
$592$	−9.11710	+	6.38386i	−0.374710	+	0.262375i
$593$	23.4296	+	2.04982i	0.962138	+	0.0841762i	0.557389	−	0.830252i	$-0.311803\pi$
$593$	23.4296	+	2.04982i	0.962138	+	0.0841762i	0.404749	+	0.914428i	$0.367359\pi$
$594$	−23.7713	+	28.3296i	−0.975350	+	1.16238i
$595$	44.7994	+	19.1201i	1.83660	+	0.783849i
$596$	2.97724	+	5.15673i	0.121952	+	0.211228i
$597$	21.1695	−	5.67235i	0.866410	−	0.232154i
$598$	−3.13265	−	6.71800i	−0.128104	−	0.274719i
$599$	−18.8495	−	6.86065i	−0.770169	−	0.280319i	−0.0731021	−	0.997324i	$-0.523290\pi$
$599$	−18.8495	−	6.86065i	−0.770169	−	0.280319i	−0.697067	+	0.717006i	$0.745512\pi$
$600$	0.869403	−	7.97052i	0.0354932	−	0.325395i
$601$	24.9750	−	14.4193i	1.01875	−	0.588176i	0.105009	−	0.994471i	$-0.466513\pi$
$601$	24.9750	−	14.4193i	1.01875	−	0.588176i	0.913742	+	0.406295i	$0.133179\pi$
$602$	−25.5704	+	36.5184i	−1.04217	+	1.48838i
$603$	2.68707	−	0.235088i	0.109426	−	0.00957354i
$604$	23.0076	−	19.3057i	0.936168	−	0.785538i
$605$	−2.44756	+	2.61438i	−0.0995076	+	0.106290i
$606$	16.6397	−	6.05634i	0.675940	−	0.246022i
$607$	18.7707	+	18.7707i	0.761880	+	0.761880i	0.976662	−	0.214782i	$-0.0689042\pi$
$607$	18.7707	+	18.7707i	0.761880	+	0.761880i	−0.214782	+	0.976662i	$0.568904\pi$
$608$	−21.7278	−	19.4679i	−0.881177	−	0.789526i
$609$		−	13.9165i		−	0.563923i
$610$	22.6886	+	36.4686i	0.918636	+	1.47657i
$611$	9.35869	+	1.65019i	0.378612	+	0.0667595i
$612$	−0.560103	+	6.40201i	−0.0226408	+	0.258786i
$613$	−1.84410	−	21.0781i	−0.0744823	−	0.851337i	−0.937913	−	0.346870i	$-0.887245\pi$
$613$	−1.84410	−	21.0781i	−0.0744823	−	0.851337i	0.863431	−	0.504467i	$-0.168311\pi$
$614$	6.76136	−	1.19221i	0.272866	−	0.0481137i
$615$	8.04384	−	7.21415i	0.324359	−	0.290903i
$616$	15.1848	+	8.76693i	0.611812	+	0.353230i
$617$	−8.70269	+	4.05813i	−0.350357	+	0.163374i	−0.589827	−	0.807530i	$-0.700804\pi$
$617$	−8.70269	+	4.05813i	−0.350357	+	0.163374i	0.239470	+	0.970904i	$0.423026\pi$
$618$	−30.1715	+	14.0692i	−1.21367	+	0.565946i
$619$	7.50172	+	4.33112i	0.301519	+	0.174082i	0.643125	−	0.765761i	$-0.277637\pi$
$619$	7.50172	+	4.33112i	0.301519	+	0.174082i	−0.341606	+	0.939843i	$0.610971\pi$
$620$	−1.15372	+	21.2170i	−0.0463346	+	0.852094i
$621$	−14.6317	+	2.57996i	−0.587148	+	0.103530i
$622$	1.98108	+	22.6439i	0.0794341	+	0.907936i
$623$	−3.41744	+	39.0615i	−0.136917	+	1.56497i
$624$	−10.4955	−	1.85065i	−0.420158	−	0.0740852i
$625$	9.54697	−	23.1053i	0.381879	−	0.924212i
$626$		−	28.8110i		−	1.15152i
$627$	−0.721488	+	22.2165i	−0.0288135	+	0.887241i
$628$	5.92345	+	5.92345i	0.236371	+	0.236371i
$629$	10.6277	−	3.86818i	0.423756	−	0.154234i
$630$	12.4602	+	11.6651i	0.496425	+	0.464750i
$631$	26.3688	−	22.1260i	1.04972	−	0.880823i	0.0566590	−	0.998394i	$-0.481955\pi$
$631$	26.3688	−	22.1260i	1.04972	−	0.880823i	0.993064	+	0.117571i	$0.0375108\pi$
$632$	−3.51220	+	0.307278i	−0.139708	+	0.0122229i
$633$	−12.6466	+	18.0613i	−0.502659	+	0.717871i
$634$	−38.1579	+	22.0305i	−1.51544	+	0.874942i
$635$	−32.7271	−	10.7048i	−1.29874	−	0.424806i
$636$	−6.39589	−	2.32791i	−0.253613	−	0.0923078i
$637$	−8.14076	−	17.4579i	−0.322549	−	0.691708i
$638$	13.8305	−	3.70587i	0.547554	−	0.146717i
$639$	−2.01449	−	3.48920i	−0.0796919	−	0.138030i
$640$	−7.10234	−	17.6788i	−0.280745	−	0.698816i
$641$	−30.8378	+	36.7510i	−1.21802	+	1.45158i	−0.363951	+	0.931418i	$0.618573\pi$
$641$	−30.8378	+	36.7510i	−1.21802	+	1.45158i	−0.854068	+	0.520161i	$0.825872\pi$
$642$	32.6815	+	2.85926i	1.28984	+	0.112846i
$643$	−3.43496	+	2.40519i	−0.135462	+	0.0948513i	−0.639343	−	0.768921i	$-0.720794\pi$
$643$	−3.43496	+	2.40519i	−0.135462	+	0.0948513i	0.503882	+	0.863773i	$0.331905\pi$
$644$	−5.54329	−	15.2301i	−0.218436	−	0.600148i
$645$	−14.7139	−	9.59643i	−0.579358	−	0.377859i
$646$	21.6125	+	33.1031i	0.850334	+	1.30242i
$647$	−16.6468	+	16.6468i	−0.654452	+	0.654452i	−0.954062	−	0.299610i	$-0.903144\pi$
$647$	−16.6468	+	16.6468i	−0.654452	+	0.654452i	0.299610	+	0.954062i	$0.403144\pi$
$648$	−2.50694	+	5.37615i	−0.0984820	+	0.211195i
$649$	−1.16649	+	6.61549i	−0.0457887	+	0.259681i
$650$	−12.6540	−	6.23342i	−0.496331	−	0.244495i
$651$	−33.1904	−	27.8500i	−1.30083	−	1.09153i
$652$	0.944232	+	0.661158i	0.0369790	+	0.0258930i
$653$	−1.83108	+	6.83370i	−0.0716559	+	0.267423i	−0.992454	−	0.122616i	$-0.960872\pi$
$653$	−1.83108	+	6.83370i	−0.0716559	+	0.267423i	0.920798	+	0.390039i	$0.127538\pi$
$654$	−15.3311	+	26.5542i	−0.599493	+	1.03835i
$655$	−8.13225	−	10.8361i	−0.317753	−	0.423400i
$656$	5.57368	−	15.3135i	0.217615	−	0.597894i
$657$	3.18515	+	11.8871i	0.124264	+	0.463761i
$658$	48.8643	+	13.0931i	1.90493	+	0.510424i
$659$	−3.04945	−	17.2943i	−0.118790	−	0.673689i	−0.984804	−	0.173670i	$-0.944437\pi$
$659$	−3.04945	−	17.2943i	−0.118790	−	0.673689i	0.866014	−	0.500019i	$-0.166674\pi$
$660$	7.49054	−	14.0212i	0.291569	−	0.545773i
$661$	29.9904	+	35.7412i	1.16649	+	1.39017i	0.905241	+	0.424899i	$0.139690\pi$
$661$	29.9904	+	35.7412i	1.16649	+	1.39017i	0.261250	+	0.965271i	$0.415865\pi$
$662$	−9.32029	−	13.3108i	−0.362243	−	0.517337i
$663$	9.81504	+	4.57683i	0.381185	+	0.177749i
$664$	1.08575			0.0421352
$665$	42.9654	+	3.73826i	1.66613	+	0.144964i
$666$	3.96314			0.153569
$667$	5.21345	+	2.43107i	0.201865	+	0.0941314i
$668$	10.0313	+	14.3262i	0.388124	+	0.554299i
$669$	−15.0329	−	17.9156i	−0.581207	−	0.692656i
$670$	−11.3550	+	3.44719i	−0.438681	+	0.133177i
$671$	−6.42692	−	36.4489i	−0.248109	−	1.40709i
$672$	−41.0928	−	11.0108i	−1.58519	−	0.424750i
$673$	2.84741	+	10.6267i	0.109759	+	0.409628i	0.998842	−	0.0481200i	$-0.0153230\pi$
$673$	2.84741	+	10.6267i	0.109759	+	0.409628i	−0.889082	+	0.457748i	$0.848656\pi$
$674$	−0.172773	+	0.474691i	−0.00665498	+	0.0182844i
$675$	−18.6329	+	21.2654i	−0.717179	+	0.818504i
$676$	7.42701	−	12.8640i	0.285654	−	0.494767i
$677$	0.890582	−	3.32370i	0.0342278	−	0.127740i	−0.946698	−	0.322123i	$-0.895604\pi$
$677$	0.890582	−	3.32370i	0.0342278	−	0.127740i	0.980926	+	0.194383i	$0.0622703\pi$
$678$	28.0584	+	19.6467i	1.07758	+	0.754526i
$679$	−15.7286	−	13.1979i	−0.603610	−	0.506489i
$680$	1.47358	+	12.1994i	0.0565094	+	0.467826i
$681$	4.15851	−	23.5841i	0.159354	−	0.903744i
$682$	18.8396	−	40.4016i	0.721405	−	1.54706i
$683$	9.79318	−	9.79318i	0.374725	−	0.374725i	−0.494470	−	0.869195i	$-0.664638\pi$
$683$	9.79318	−	9.79318i	0.374725	−	0.374725i	0.869195	+	0.494470i	$0.164638\pi$
$684$	1.29353	+	5.54111i	0.0494594	+	0.211870i
$685$	−4.52065	+	0.951618i	−0.172725	+	0.0363595i
$686$	−15.5547	−	42.7361i	−0.593880	−	1.63167i
$687$	−17.9889	+	12.5960i	−0.686319	+	0.480566i
$688$	−26.3938	−	2.30915i	−1.00625	−	0.0880357i
$689$	3.34541	−	3.98690i	0.127450	−	0.151889i
$690$	14.4278	−	5.79629i	0.549258	−	0.220661i
$691$	0.178187	+	0.308629i	0.00677856	+	0.0117408i	0.869395	−	0.494118i	$-0.164509\pi$
$691$	0.178187	+	0.308629i	0.00677856	+	0.0117408i	−0.862616	+	0.505859i	$0.831176\pi$
$692$	32.4697	−	8.70024i	1.23431	−	0.330733i
$693$	−6.21595	−	13.3302i	−0.236125	−	0.506371i
$694$	19.5139	+	7.10249i	0.740739	+	0.269607i
$695$	−8.33891	−	16.4458i	−0.316313	−	0.623825i
$696$	3.04043	−	1.75539i	0.115247	−	0.0665379i
$697$	−9.49826	+	13.5649i	−0.359772	+	0.513808i
$698$	43.8117	−	3.83302i	1.65830	−	0.145082i
$699$	−9.14629	+	7.67465i	−0.345945	+	0.290282i
$700$	−26.3749	−	15.9890i	−0.996879	−	0.604327i
$701$	13.0486	−	4.74928i	0.492837	−	0.179378i	−0.0836325	−	0.996497i	$-0.526652\pi$
$701$	13.0486	−	4.74928i	0.492837	−	0.179378i	0.576470	+	0.817119i	$0.304430\pi$
$702$	11.2806	+	11.2806i	0.425757	+	0.425757i
$703$	7.87597	−	6.18442i	0.297048	−	0.233250i
$704$		−	9.37489i		−	0.353329i
$705$	−4.52228	+	19.4141i	−0.170319	+	0.731177i
$706$	−19.1856	−	3.38293i	−0.722058	−	0.127318i
$707$	−2.58032	+	29.4932i	−0.0970428	+	1.10920i
$708$	−0.330293	−	3.77527i	−0.0124132	−	0.141883i
$709$	−23.0076	+	4.05687i	−0.864070	+	0.152359i	−0.588081	−	0.808802i	$-0.700116\pi$
$709$	−23.0076	+	4.05687i	−0.864070	+	0.152359i	−0.275989	+	0.961161i	$0.589005\pi$
$710$	11.8345	+	13.1956i	0.444142	+	0.495222i
$711$	2.56123	+	1.47873i	0.0960535	+	0.0554565i
$712$	−8.96511	+	4.18050i	−0.335982	+	0.156671i
$713$	16.2313	−	7.56880i	0.607869	−	0.283454i
$714$	49.9265	+	28.8251i	1.86845	+	1.07875i
$715$	8.11581	+	9.04919i	0.303514	+	0.338421i
$716$	30.1953	−	5.32425i	1.12845	−	0.198977i
$717$	1.84821	+	21.1252i	0.0690228	+	0.788935i
$718$	4.26584	−	48.7588i	0.159200	−	1.81966i
$719$	14.5612	+	2.56753i	0.543040	+	0.0957526i	0.438438	−	0.898762i	$-0.355532\pi$
$719$	14.5612	+	2.56753i	0.543040	+	0.0957526i	0.104602	+	0.994514i	$0.466643\pi$
$720$	−2.30128	+	9.87937i	−0.0857636	+	0.368183i
$721$		−	55.6595i		−	2.07287i
$722$	27.3104	+	21.8954i	1.01639	+	0.814864i
$723$	−10.1779	−	10.1779i	−0.378520	−	0.378520i
$724$	−14.9292	+	5.43377i	−0.554838	+	0.201944i
$725$	10.6320	−	2.60654i	0.394862	−	0.0968044i
$726$	−3.24701	+	2.72456i	−0.120508	+	0.101118i
$727$	−23.9580	+	2.09606i	−0.888554	+	0.0777384i	−0.522286	−	0.852771i	$-0.674920\pi$
$727$	−23.9580	+	2.09606i	−0.888554	+	0.0777384i	−0.366269	+	0.930509i	$0.619365\pi$
$728$	4.33839	−	6.19586i	0.160791	−	0.229634i
$729$	25.4140	−	14.6728i	0.941259	−	0.543436i
$730$	−24.4848	−	48.2883i	−0.906223	−	1.78723i
$731$	25.2991	+	9.20813i	0.935722	+	0.340575i
$732$	8.82417	+	18.9235i	0.326151	+	0.699433i
$733$	−29.4230	+	7.88388i	−1.08676	+	0.291198i	−0.757364	−	0.652993i	$-0.773513\pi$
$733$	−29.4230	+	7.88388i	−1.08676	+	0.291198i	−0.329400	+	0.944190i	$0.606847\pi$
$734$	−19.9592	−	34.5703i	−0.736707	−	1.27601i
$735$	37.4933	−	15.0627i	1.38296	−	0.555596i
$736$	11.3034	−	13.4709i	0.416649	−	0.496543i
$737$	10.1869	+	0.891234i	0.375238	+	0.0328290i
$738$	−4.75337	+	3.32835i	−0.174974	+	0.122518i
$739$	5.15140	+	14.1534i	0.189497	+	0.520640i	0.997664	−	0.0683142i	$-0.0217620\pi$
$739$	5.15140	+	14.1534i	0.189497	+	0.520640i	−0.808166	+	0.588954i	$0.799540\pi$
$740$	−7.00787	+	1.47519i	−0.257615	+	0.0542291i
$741$	9.52014	+	1.14533i	0.349731	+	0.0420747i
$742$	19.5907	−	19.5907i	0.719199	−	0.719199i
$743$	7.40046	−	15.8703i	0.271496	−	0.582226i	−0.722533	−	0.691336i	$-0.757022\pi$
$743$	7.40046	−	15.8703i	0.271496	−	0.582226i	0.994030	+	0.109110i	$0.0348001\pi$
$744$	1.89803	−	10.7643i	0.0695853	−	0.394638i
$745$	−1.14532	−	9.48184i	−0.0419614	−	0.347388i
$746$	27.0560	+	22.7027i	0.990591	+	0.831205i
$747$	−0.746062	−	0.522398i	−0.0272970	−	0.0191136i
$748$	−6.30564	+	23.5330i	−0.230557	+	0.860450i
$749$	−27.4250	+	47.5014i	−1.00209	+	1.73566i
$750$	14.4973	−	25.7942i	0.529367	−	0.941872i
$751$	8.77625	−	24.1126i	0.320250	−	0.879880i	−0.670221	−	0.742161i	$-0.733801\pi$
$751$	8.77625	−	24.1126i	0.320250	−	0.879880i	0.990471	−	0.137719i	$-0.0439769\pi$
$752$	7.78133	+	29.0403i	0.283756	+	1.05899i
$753$	−2.84472	−	0.762241i	−0.103668	−	0.0277776i
$754$	−1.07256	−	6.08281i	−0.0390605	−	0.221523i
$755$	−46.0966	+	13.9942i	−1.67763	+	0.509301i
$756$	22.4215	+	26.7209i	0.815462	+	0.971830i
$757$	−11.9533	−	17.0711i	−0.434450	−	0.620459i	0.540909	−	0.841081i	$-0.318080\pi$
$757$	−11.9533	−	17.0711i	−0.434450	−	0.620459i	−0.975359	+	0.220622i	$0.929191\pi$
$758$	14.5556	+	6.78740i	0.528684	+	0.246529i
$759$	−13.3986			−0.486337
$760$	4.60284	+	9.85849i	0.166962	+	0.357605i
$761$	−3.66132			−0.132723			−0.0663614	−	0.997796i	$-0.521139\pi$
$761$	−3.66132			−0.132723			−0.0663614	+	0.997796i	$0.521139\pi$
$762$	−36.9357	−	17.2234i	−1.33804	−	0.623938i
$763$	−29.4044	−	41.9938i	−1.06451	−	1.52028i
$764$	−8.66601	−	10.3277i	−0.313525	−	0.373645i
$765$	4.85709	−	9.09173i	0.175608	−	0.328712i
$766$	−0.662164	−	3.75532i	−0.0239250	−	0.135685i
$767$	2.79907	+	0.750009i	0.101069	+	0.0270813i
$768$	−7.80000	−	29.1100i	−0.281458	−	1.05042i
$769$	−17.1222	+	47.0428i	−0.617441	+	1.69641i	0.0957227	+	0.995408i	$0.469484\pi$
$769$	−17.1222	+	47.0428i	−0.617441	+	1.69641i	−0.713164	+	0.700997i	$0.752738\pi$
$770$	38.8403	+	51.7540i	1.39971	+	1.86509i
$771$	−2.67815	+	4.63870i	−0.0964514	+	0.167059i
$772$	−4.87547	+	18.1955i	−0.175472	+	0.654870i
$773$	13.9531	+	9.77003i	0.501856	+	0.351404i	0.796931	−	0.604071i	$-0.206456\pi$
$773$	13.9531	+	9.77003i	0.501856	+	0.351404i	−0.295074	+	0.955474i	$0.595344\pi$
$774$	7.22700	+	6.06418i	0.259769	+	0.217972i
$775$	15.0606	−	30.5733i	0.540991	−	1.09823i
$776$	0.899462	−	5.10110i	0.0322888	−	0.183119i
$777$	6.17140	−	13.2346i	0.221398	−	0.474789i
$778$	−26.5677	+	26.5677i	−0.952497	+	0.952497i
$779$	−4.25256	+	14.0320i	−0.152364	+	0.502749i
$780$	−5.74380	−	3.74612i	−0.205661	−	0.134133i
$781$	−5.22405	−	14.3530i	−0.186931	−	0.513589i
$782$	−19.5203	+	13.6682i	−0.698043	+	0.488775i
$783$	−12.3332	−	1.07901i	−0.440752	−	0.0385608i
$784$	39.1722	−	46.6836i	1.39901	−	1.66727i
$785$	−5.00890	−	12.4679i	−0.178775	−	0.444999i
$786$	−8.01758	−	13.8869i	−0.285978	−	0.495328i
$787$	−32.8993	+	8.81535i	−1.17273	+	0.314233i	−0.792041	−	0.610468i	$-0.790981\pi$
$787$	−32.8993	+	8.81535i	−1.17273	+	0.314233i	−0.380694	+	0.924701i	$0.624315\pi$
$788$	−10.6812	−	22.9059i	−0.380502	−	0.815989i
$789$	26.9724	+	9.81715i	0.960243	+	0.349500i
$790$	−12.3663	−	4.04493i	−0.439974	−	0.143912i
$791$	−49.5960	+	28.6343i	−1.76343	+	1.01812i
$792$	2.12827	−	3.03948i	0.0756247	−	0.108003i
$793$	−15.9051	+	1.39152i	−0.564807	+	0.0494142i
$794$	14.3081	−	12.0060i	0.507777	−	0.426076i
$795$	7.96966	+	7.46115i	0.282655	+	0.264620i
$796$	19.9861	−	7.27436i	0.708389	−	0.257833i
$797$	−3.26737	−	3.26737i	−0.115736	−	0.115736i	0.646867	−	0.762603i	$-0.276079\pi$
$797$	−3.26737	−	3.26737i	−0.115736	−	0.115736i	−0.762603	+	0.646867i	$0.776079\pi$
$798$	49.9547	+	10.4907i	1.76838	+	0.371368i
$799$		−	30.5507i		−	1.08080i
$800$	0.715456	−	33.4567i	0.0252952	−	1.18287i
$801$	8.17172	+	1.44089i	0.288733	+	0.0509115i
$802$	2.58323	−	29.5264i	0.0912169	−	1.04261i
$803$	4.06621	+	46.4770i	0.143494	+	1.64014i
$804$	−5.68120	+	1.00175i	−0.200361	+	0.0353290i
$805$	−1.41152	+	25.9579i	−0.0497496	+	0.914894i
$806$	−16.6538	−	9.61507i	−0.586605	−	0.338676i
$807$	16.8853	−	7.87373i	0.594389	−	0.277168i
$808$	−6.76905	+	3.15646i	−0.238134	+	0.111044i
$809$	−28.5222	−	16.4673i	−1.00279	−	0.578959i	−0.0937143	−	0.995599i	$-0.529874\pi$
$809$	−28.5222	−	16.4673i	−1.00279	−	0.578959i	−0.909071	+	0.416641i	$0.863207\pi$
$810$	−16.2972	+	14.6162i	−0.572625	+	0.513561i
$811$	24.2723	−	4.27986i	0.852316	−	0.150286i	0.269610	−	0.962969i	$-0.413105\pi$
$811$	24.2723	−	4.27986i	0.852316	−	0.150286i	0.582706	+	0.812683i	$0.301994\pi$
$812$	−1.17706	−	13.4539i	−0.0413069	−	0.472140i
$813$	−2.62385	+	29.9907i	−0.0920224	+	1.05182i
$814$	14.7963	+	2.60898i	0.518608	+	0.0914446i
$815$	−0.976675	−	1.56986i	−0.0342114	−	0.0549898i
$816$			34.2618i			1.19940i
$817$	23.8253	+	0.773735i	0.833542	+	0.0270696i
$818$	0.794612	+	0.794612i	0.0277830	+	0.0277830i
$819$	−5.96218	+	2.17005i	−0.208335	+	0.0758278i
$820$	7.16631	−	7.65473i	0.250258	−	0.267315i
$821$	−32.8651	+	27.5771i	−1.14700	+	0.962446i	−0.999645	−	0.0266382i	$-0.991520\pi$
$821$	−32.8651	+	27.5771i	−1.14700	+	0.962446i	−0.147353	+	0.989084i	$0.547075\pi$
$822$	−5.44693	+	0.476545i	−0.189984	+	0.0166214i
$823$	−11.0868	+	15.8336i	−0.386462	+	0.551924i	−0.964499	−	0.264086i	$-0.914930\pi$
$823$	−11.0868	+	15.8336i	−0.386462	+	0.551924i	0.578038	+	0.816010i	$0.303819\pi$
$824$	12.1603	−	7.02076i	0.423625	−	0.244580i
$825$	−19.8782	+	15.9681i	−0.692069	+	0.555939i
$826$	14.4957	+	5.27602i	0.504371	+	0.183576i
$827$	−11.9632	−	25.6551i	−0.416000	−	0.892115i	−0.996940	−	0.0781685i	$-0.975093\pi$
$827$	−11.9632	−	25.6551i	−0.416000	−	0.892115i	0.580940	−	0.813946i	$-0.302685\pi$
$828$	−3.31296	+	0.887706i	−0.115133	+	0.0308499i
$829$	8.14109	+	14.1008i	0.282752	+	0.489741i	0.972062	−	0.234726i	$-0.0754194\pi$
$829$	8.14109	+	14.1008i	0.282752	+	0.489741i	−0.689310	+	0.724467i	$0.742086\pi$
$830$	3.68526	+	1.57285i	0.127917	+	0.0545944i
$831$	6.23686	−	7.43280i	0.216354	−	0.257841i
$832$	−4.02874	−	0.352470i	−0.139672	−	0.0122197i
$833$	−50.7269	+	35.5194i	−1.75758	+	1.23067i
$834$	−7.46421	−	20.5077i	−0.258464	−	0.710125i
$835$	−5.77841	−	27.4503i	−0.199970	−	0.949956i
$836$	1.18158	+	21.5391i	0.0408658	+	0.744946i
$837$	−27.2550	+	27.2550i	−0.942069	+	0.942069i
$838$	−24.2268	+	51.9546i	−0.836902	+	1.79474i
$839$	3.24114	−	18.3814i	0.111896	−	0.634596i	−0.876344	−	0.481686i	$-0.840024\pi$
$839$	3.24114	−	18.3814i	0.111896	−	0.634596i	0.988240	−	0.152910i	$-0.0488644\pi$
$840$	12.4833	+	9.79256i	0.430714	+	0.337875i
$841$	−18.5434	−	15.5597i	−0.639427	−	0.536543i
$842$	42.8043	+	29.9719i	1.47513	+	1.03290i
$843$	3.66509	−	13.6783i	0.126232	−	0.471105i
$844$	−10.6987	+	18.5306i	−0.368263	+	0.637851i
$845$	−19.0558	+	14.3010i	−0.655541	+	0.491970i
$846$	3.66148	−	10.0598i	0.125884	−	0.345864i
$847$	−1.83419	−	6.84528i	−0.0630234	−	0.235207i
$848$	15.9045	+	4.26159i	0.546162	+	0.146344i
$849$	8.02512	+	45.5127i	0.275421	+	1.56199i
$850$	−12.6708	+	43.5421i	−0.434605	+	1.49348i
$851$	3.87993	+	4.62392i	0.133002	+	0.158506i
$852$	4.94242	+	7.05851i	0.169324	+	0.241820i
$853$	39.5534	+	18.4441i	1.35428	+	0.631513i	0.958041	−	0.286633i	$-0.0925360\pi$
$853$	39.5534	+	18.4441i	1.35428	+	0.631513i	0.396243	+	0.918146i	$0.370314\pi$
$854$	−84.9917			−2.90836
$855$	1.58053	−	8.98880i	0.0540531	−	0.307411i
$856$	−13.8373			−0.472949
$857$	−32.1530	−	14.9932i	−1.09832	−	0.512157i	−0.212963	−	0.977060i	$-0.568311\pi$
$857$	−32.1530	−	14.9932i	−1.09832	−	0.512157i	−0.885362	+	0.464903i	$0.846089\pi$
$858$	8.25188	+	11.7849i	0.281714	+	0.402330i
$859$	−2.82588	−	3.36775i	−0.0964177	−	0.114906i	0.715678	−	0.698430i	$-0.246118\pi$
$859$	−2.82588	−	3.36775i	−0.0964177	−	0.114906i	−0.812096	+	0.583524i	$0.801673\pi$
$860$	−15.0365	−	8.03297i	−0.512740	−	0.273922i
$861$	3.71282	+	21.0564i	0.126532	+	0.717601i
$862$	49.7708	+	13.3361i	1.69520	+	0.454228i
$863$	−1.84578	−	6.88853i	−0.0628310	−	0.234488i	0.927368	−	0.374150i	$-0.122065\pi$
$863$	−1.84578	−	6.88853i	−0.0628310	−	0.234488i	−0.990199	+	0.139661i	$0.955399\pi$
$864$	−12.9442	+	35.5639i	−0.440371	+	1.20991i
$865$	−53.3779	−	7.60871i	−1.81490	−	0.258704i
$866$	−17.1676	+	29.7352i	−0.583380	+	1.01044i
$867$	2.69030	−	10.0404i	0.0913675	−	0.340988i
$868$	−34.4428	−	24.1171i	−1.16907	−	0.818588i
$869$	8.58879	+	7.20685i	0.291355	+	0.244476i
$870$	12.8628	−	1.55371i	0.436089	−	0.0526759i
$871$	0.765994	−	4.34417i	0.0259547	−	0.147197i
$872$	5.46568	−	11.7212i	0.185091	−	0.396930i
$873$	−3.07241	+	3.07241i	−0.103985	+	0.103985i
$874$	−12.6567	+	16.8816i	−0.428119	+	0.571030i
$875$	28.8419	+	40.1934i	0.975036	+	1.35879i
$876$	−9.00199	−	24.7328i	−0.304149	−	0.835643i
$877$	6.45780	−	4.52180i	0.218064	−	0.152690i	−0.459441	−	0.888208i	$-0.651950\pi$
$877$	6.45780	−	4.52180i	0.218064	−	0.152690i	0.677505	+	0.735518i	$0.263061\pi$
$878$	26.0923	+	2.28278i	0.880573	+	0.0770401i
$879$	21.2599	−	25.3365i	0.717078	−	0.854580i
$880$	−15.0954	+	35.3694i	−0.508867	+	1.19230i
$881$	5.25281	+	9.09814i	0.176972	+	0.306524i	0.940842	−	0.338846i	$-0.110037\pi$
$881$	5.25281	+	9.09814i	0.176972	+	0.306524i	−0.763870	+	0.645370i	$0.776703\pi$
$882$	−20.9605	+	5.61635i	−0.705777	+	0.189112i
$883$	−16.0757	−	34.4744i	−0.540990	−	1.16016i	−0.966845	−	0.255365i	$-0.917804\pi$
$883$	−16.0757	−	34.4744i	−0.540990	−	1.16016i	0.425855	−	0.904792i	$-0.359973\pi$
$884$	9.87593	+	3.59454i	0.332163	+	0.120898i
$885$	−1.88972	+	5.77732i	−0.0635221	+	0.194202i
$886$	11.1687	−	6.44825i	0.375219	−	0.216633i
$887$	18.2360	−	26.0438i	0.612306	−	0.874464i	−0.386551	−	0.922268i	$-0.626334\pi$
$887$	18.2360	−	26.0438i	0.612306	−	0.874464i	0.998857	+	0.0478044i	$0.0152224\pi$
$888$	3.66991	−	0.321075i	0.123154	−	0.0107746i
$889$	52.1967	−	43.7982i	1.75062	−	1.46894i
$890$	−36.4855	+	1.20236i	−1.22300	+	0.0403033i
$891$	17.7266	−	6.45194i	0.593862	−	0.216148i
$892$	−16.0486	−	16.0486i	−0.537347	−	0.537347i
$893$	−8.42174	−	25.7056i	−0.281823	−	0.860206i
$894$		−	11.3039i		−	0.378060i
$895$	−47.8970	−	11.1570i	−1.60102	−	0.372939i
$896$	37.1282	+	6.54671i	1.24037	+	0.218710i
$897$	−0.503748	+	5.75787i	−0.0168197	+	0.192250i
$898$	−2.71018	−	30.9775i	−0.0904399	−	1.03373i
$899$	14.6967	−	2.59142i	0.490162	−	0.0864287i
$900$	−3.85718	+	5.26533i	−0.128573	+	0.175511i
$901$	−14.4900	−	8.36582i	−0.482733	−	0.278706i
$902$	−19.9376	+	9.29708i	−0.663851	+	0.309559i
$903$	31.5047	−	14.6909i	1.04841	−	0.488883i
$904$	−12.5119	−	7.22373i	−0.416138	−	0.240258i
$905$	25.4450	+	1.38363i	0.845821	+	0.0459935i
$906$	−56.1507	+	9.90089i	−1.86548	+	0.328935i
$907$	−3.87264	−	44.2645i	−0.128589	−	1.46978i	−0.736858	−	0.676048i	$-0.763691\pi$
$907$	−3.87264	−	44.2645i	−0.128589	−	1.46978i	0.608269	−	0.793731i	$-0.291864\pi$
$908$	2.02553	−	23.1520i	0.0672197	−	0.768325i
$909$	6.17001	+	1.08794i	0.204646	+	0.0360846i
$910$	23.7010	−	14.7454i	0.785679	−	0.488804i
$911$			30.5111i			1.01088i	0.862863	+	0.505438i	$0.168669\pi$
$911$			30.5111i			1.01088i	−0.862863	+	0.505438i	$0.831331\pi$
$912$	9.44478	+	28.8282i	0.312748	+	0.954599i
$913$	−2.44150	−	2.44150i	−0.0808018	−	0.0808018i
$914$	16.6002	−	6.04198i	0.549086	−	0.199851i
$915$	−1.10306	−	33.4722i	−0.0364660	−	1.10656i
$916$	−16.3256	+	13.6988i	−0.539414	+	0.452622i
$917$	26.7077	−	2.33662i	0.881965	−	0.0771619i
$918$	29.4167	−	42.0114i	0.970896	−	1.38658i
$919$	44.4140	−	25.6425i	1.46508	−	0.845867i	0.465845	−	0.884867i	$-0.345751\pi$
$919$	44.4140	−	25.6425i	1.46508	−	0.845867i	0.999239	+	0.0389999i	$0.0124172\pi$
$920$	−5.84924	+	2.96588i	−0.192844	+	0.0977823i
$921$	−5.03062	−	1.83100i	−0.165765	−	0.0603334i
$922$	−22.0875	−	47.3669i	−0.727415	−	1.55995i
$923$	−6.36442	+	1.70534i	−0.209487	+	0.0561320i
$924$	15.7283	+	27.2423i	0.517425	+	0.896206i
$925$	11.2670	+	2.23604i	0.370456	+	0.0735206i
$926$	−19.4689	+	23.2022i	−0.639789	+	0.762471i
$927$	−11.7338	−	1.02658i	−0.385390	−	0.0337173i
$928$	12.0032	−	8.40470i	0.394023	−	0.275898i
$929$	−12.0267	−	33.0430i	−0.394582	−	1.08411i	−0.964885	−	0.262672i	$-0.915396\pi$
$929$	−12.0267	−	33.0430i	−0.394582	−	1.08411i	0.570303	−	0.821434i	$-0.306826\pi$
$930$	22.0358	−	33.7868i	0.722584	−	1.10791i
$931$	−32.8907	+	43.8700i	−1.07795	+	1.43778i
$932$	−8.19317	+	8.19317i	−0.268376	+	0.268376i
$933$	7.49044	−	16.0633i	0.245226	−	0.525889i
$934$	−8.93699	+	50.6842i	−0.292427	+	1.65844i
$935$	24.1190	−	30.7462i	0.788774	−	1.00551i
$936$	−1.22616	−	1.02887i	−0.0400784	−	0.0336298i
$937$	37.3205	+	26.1321i	1.21921	+	0.853698i	0.992735	−	0.120319i	$-0.0383918\pi$
$937$	37.3205	+	26.1321i	1.21921	+	0.853698i	0.226472	+	0.974018i	$0.427281\pi$
$938$	6.07765	−	22.6821i	0.198442	−	0.740597i
$939$	−11.2326	+	19.4555i	−0.366564	+	0.634907i
$940$	−2.72991	+	19.1513i	−0.0890399	+	0.624648i
$941$	6.71949	−	18.4616i	0.219049	−	0.601832i	−0.780684	−	0.624926i	$-0.785129\pi$
$941$	6.71949	−	18.4616i	0.219049	−	0.601832i	0.999733	+	0.0230935i	$0.00735154\pi$
$942$	−4.11597	−	15.3610i	−0.134105	−	0.500488i
$943$	−8.53685	−	2.28744i	−0.277998	−	0.0744894i
$944$	1.59197	+	9.02850i	0.0518142	+	0.293853i
$945$	−16.2528	−	53.5362i	−0.528702	−	1.74153i
$946$	22.9897	+	27.3980i	0.747458	+	0.890786i
$947$	26.7171	+	38.1560i	0.868190	+	1.23990i	0.969510	+	0.245050i	$0.0788045\pi$
$947$	26.7171	+	38.1560i	0.868190	+	1.23990i	−0.101320	+	0.994854i	$0.532307\pi$
$948$	−5.73254	−	2.67313i	−0.186184	−	0.0868191i
$949$	20.1258			0.653312
$950$	1.34168	+	40.1297i	0.0435300	+	1.30198i
$951$	34.3563			1.11408
$952$	−22.0379	−	10.2764i	−0.714252	−	0.333061i
$953$	28.3766	+	40.5260i	0.919209	+	1.31277i	0.949677	+	0.313231i	$0.101411\pi$
$953$	28.3766	+	40.5260i	0.919209	+	1.31277i	−0.0304677	+	0.999536i	$0.509700\pi$
$954$	−3.76869	−	4.49135i	−0.122016	−	0.145413i
$955$	6.28176	+	20.6920i	0.203273	+	0.669577i
$956$	3.57357	+	20.2667i	0.115578	+	0.655473i
$957$	−10.7843	−	2.88963i	−0.348606	−	0.0934086i
$958$	−4.41025	−	16.4593i	−0.142489	−	0.531775i
$959$	3.12664	−	8.59036i	0.100964	−	0.277397i
$960$	1.19711	−	8.39818i	0.0386366	−	0.271050i
$961$	7.73097	−	13.3904i	0.249386	−	0.431949i
$962$	1.67747	−	6.26042i	0.0540839	−	0.201844i
$963$	9.50819	+	6.65770i	0.306397	+	0.214542i
$964$	−10.7005	−	8.97875i	−0.344638	−	0.289186i
$965$	18.6486	−	23.7727i	0.600319	−	0.765270i
$966$	−5.34283	+	30.3007i	−0.171903	+	0.974910i
$967$	−12.1230	+	25.9978i	−0.389848	+	0.836032i	0.609225	+	0.792997i	$0.291481\pi$
$967$	−12.1230	+	25.9978i	−0.389848	+	0.836032i	−0.999074	+	0.0430352i	$0.986297\pi$
$968$	1.26418	−	1.26418i	0.0406322	−	0.0406322i
$969$	−1.68851	−	30.7800i	−0.0542428	−	0.988796i
$970$	10.4426	−	16.0113i	0.335292	−	0.514091i
$971$	5.31587	+	14.6052i	0.170594	+	0.468704i	0.995298	−	0.0968611i	$-0.0308802\pi$
$971$	5.31587	+	14.6052i	0.170594	+	0.468704i	−0.824704	+	0.565565i	$0.808658\pi$
$972$	10.6550	−	7.46074i	0.341760	−	0.239303i
$973$	36.3492	+	3.18014i	1.16530	+	0.101951i
$974$	22.3494	−	26.6349i	0.716120	−	0.853438i
$975$	6.11475	+	9.14276i	0.195829	+	0.292803i
$976$	−25.2555	−	43.7439i	−0.808410	−	1.40021i
$977$	37.3527	−	10.0086i	1.19502	−	0.320204i	0.394150	−	0.919046i	$-0.371039\pi$
$977$	37.3527	−	10.0086i	1.19502	−	0.320204i	0.800867	+	0.598842i	$0.204372\pi$
$978$	−0.924801	−	1.98324i	−0.0295719	−	0.0634171i
$979$	29.5603	+	10.7591i	0.944750	+	0.343861i
$980$	34.9731	−	17.7333i	1.11718	−	0.566469i
$981$	−9.39526	+	5.42435i	−0.299968	+	0.173186i
$982$	−15.1511	+	21.6380i	−0.483492	+	0.690497i
$983$	−9.73496	+	0.851699i	−0.310497	+	0.0271650i	−0.241339	−	0.970441i	$-0.577587\pi$
$983$	−9.73496	+	0.851699i	−0.310497	+	0.0271650i	−0.0691576	+	0.997606i	$0.522031\pi$
$984$	−4.13202	+	3.46718i	−0.131724	+	0.110530i
$985$	1.33520	+	40.5164i	0.0425429	+	1.29096i
$986$	−18.6593	+	6.79144i	−0.594234	+	0.216283i
$987$	−27.8924	−	27.8924i	−0.887825	−	0.887825i
$988$	9.30060	+	0.302040i	0.295891	+	0.00960917i
$989$			14.3688i			0.456902i
$990$	11.6269	−	7.23358i	0.369527	−	0.229898i
$991$	−23.1600	−	4.08373i	−0.735701	−	0.129724i	−0.206771	−	0.978389i	$-0.566295\pi$
$991$	−23.1600	−	4.08373i	−0.735701	−	0.129724i	−0.528930	+	0.848666i	$0.677407\pi$
$992$	3.97609	−	45.4469i	0.126241	−	1.44294i
$993$	1.10430	+	12.6222i	0.0350439	+	0.400554i
$994$	−34.5422	+	6.09073i	−1.09561	+	0.193186i
$995$	−34.0640	−	1.85231i	−1.07990	−	0.0587223i
$996$	1.68692	+	0.973944i	0.0534521	+	0.0308606i
$997$	−28.1198	+	13.1125i	−0.890563	+	0.415276i	−0.813375	−	0.581740i	$-0.802372\pi$
$997$	−28.1198	+	13.1125i	−0.890563	+	0.415276i	−0.0771884	+	0.997017i	$0.524594\pi$
$998$	−1.77242	+	0.826492i	−0.0561049	+	0.0261621i
$999$	−11.2504	−	6.49543i	−0.355947	−	0.205506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.r.a.33.2	✓	96
3.2	odd	2		855.2.dl.a.793.7		96
5.2	odd	4	inner	95.2.r.a.52.7	yes	96
5.3	odd	4		475.2.bb.b.432.2		96
5.4	even	2		475.2.bb.b.318.7		96
15.2	even	4		855.2.dl.a.622.2		96
19.15	odd	18	inner	95.2.r.a.53.7	yes	96
57.53	even	18		855.2.dl.a.433.2		96
95.34	odd	18		475.2.bb.b.243.2		96
95.53	even	36		475.2.bb.b.357.7		96
95.72	even	36	inner	95.2.r.a.72.2	yes	96
285.167	odd	36		855.2.dl.a.262.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.33.2	✓	96	1.1	even	1	trivial
95.2.r.a.52.7	yes	96	5.2	odd	4	inner
95.2.r.a.53.7	yes	96	19.15	odd	18	inner
95.2.r.a.72.2	yes	96	95.72	even	36	inner
475.2.bb.b.243.2		96	95.34	odd	18
475.2.bb.b.318.7		96	5.4	even	2
475.2.bb.b.357.7		96	95.53	even	36
475.2.bb.b.432.2		96	5.3	odd	4
855.2.dl.a.262.7		96	285.167	odd	36
855.2.dl.a.433.2		96	57.53	even	18
855.2.dl.a.622.2		96	15.2	even	4
855.2.dl.a.793.7		96	3.2	odd	2

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.66970 - 0.778592i) q^{2} +(0.823960 + 1.17674i) q^{3} +(0.896104 + 1.06793i) q^{4} +(-0.649562 - 2.13964i) q^{5} +(-0.459565 - 2.60632i) q^{6} +(4.27404 + 1.14523i) q^{7} +(0.288912 + 1.07824i) q^{8} +(0.320261 - 0.879909i) q^{9} +O(q^{10})\)	\(q+(-1.66970 - 0.778592i) q^{2} +(0.823960 + 1.17674i) q^{3} +(0.896104 + 1.06793i) q^{4} +(-0.649562 - 2.13964i) q^{5} +(-0.459565 - 2.60632i) q^{6} +(4.27404 + 1.14523i) q^{7} +(0.288912 + 1.07824i) q^{8} +(0.320261 - 0.879909i) q^{9} +(-0.581337 + 4.07830i) q^{10} +(1.77494 - 3.07428i) q^{11} +(-0.518325 + 1.93441i) q^{12} +(-1.25440 - 0.878342i) q^{13} +(-6.24468 - 5.23991i) q^{14} +(1.98258 - 2.52734i) q^{15} +(0.841272 - 4.77109i) q^{16} +(-2.08055 + 4.46175i) q^{17} +(-1.21983 + 1.21983i) q^{18} +(-0.520647 + 4.32769i) q^{19} +(1.70292 - 2.61103i) q^{20} +(2.17401 + 5.97304i) q^{21} +(-5.35721 + 3.75116i) q^{22} +(-2.61743 - 0.228995i) q^{23} +(-1.03075 + 1.22840i) q^{24} +(-4.15614 + 2.77966i) q^{25} +(1.41060 + 2.44323i) q^{26} +(5.46205 - 1.46355i) q^{27} +(2.60696 + 5.59063i) q^{28} +(-2.05733 - 0.748808i) q^{29} +(-5.27808 + 2.67627i) q^{30} +(-5.90309 + 3.40815i) q^{31} +(-3.83887 + 5.48247i) q^{32} +(5.08010 - 0.444451i) q^{33} +(6.94776 - 5.82986i) q^{34} +(-0.325881 - 9.88881i) q^{35} +(1.22667 - 0.446472i) q^{36} +(-1.62447 - 1.62447i) q^{37} +(4.23883 - 6.82056i) q^{38} -2.19982i q^{39} +(2.11937 - 1.31855i) q^{40} +(3.31265 + 0.584109i) q^{41} +(1.02063 - 11.6658i) q^{42} +(-0.476636 - 5.44797i) q^{43} +(4.87366 - 0.859357i) q^{44} +(-2.09072 - 0.113688i) q^{45} +(4.19201 + 2.42026i) q^{46} +(-5.62428 + 2.62265i) q^{47} +(6.30749 - 2.94123i) q^{48} +(10.8937 + 6.28948i) q^{49} +(9.10371 - 1.40525i) q^{50} +(-6.96459 + 1.22805i) q^{51} +(-0.186063 - 2.12670i) q^{52} +(-0.296214 + 3.38574i) q^{53} +(-10.2595 - 1.80902i) q^{54} +(-7.73079 - 1.80079i) q^{55} +4.93929i q^{56} +(-5.52155 + 2.95318i) q^{57} +(2.85211 + 2.85211i) q^{58} +(-1.77821 + 0.647217i) q^{59} +(4.47564 - 0.147492i) q^{60} +(7.98682 - 6.70174i) q^{61} +(12.5099 - 1.09448i) q^{62} +(2.37650 - 3.39400i) q^{63} +(2.28709 - 1.32045i) q^{64} +(-1.06453 + 3.25451i) q^{65} +(-8.82826 - 3.21322i) q^{66} +(1.21739 + 2.61071i) q^{67} +(-6.62924 + 1.77630i) q^{68} +(-1.88719 - 3.26871i) q^{69} +(-7.15523 + 16.7650i) q^{70} +(2.76573 - 3.29607i) q^{71} +(1.04128 + 0.0910999i) q^{72} +(-10.7658 + 7.53828i) q^{73} +(1.44757 + 3.97716i) q^{74} +(-6.69542 - 2.60035i) q^{75} +(-5.08825 + 3.32204i) q^{76} +(11.1069 - 11.1069i) q^{77} +(-1.71276 + 3.67303i) q^{78} +(-0.548448 + 3.11040i) q^{79} +(-10.7549 + 1.29910i) q^{80} +(4.07080 + 3.41581i) q^{81} +(-5.07633 - 3.55449i) q^{82} +(0.251741 - 0.939512i) q^{83} +(-4.43068 + 7.67416i) q^{84} +(10.8980 + 1.55344i) q^{85} +(-3.44591 + 9.46756i) q^{86} +(-0.814011 - 3.03793i) q^{87} +(3.82760 + 1.02560i) q^{88} +(1.53879 + 8.72693i) q^{89} +(3.40235 + 1.81764i) q^{90} +(-4.35546 - 5.19064i) q^{91} +(-2.10093 - 3.00044i) q^{92} +(-8.87441 - 4.13820i) q^{93} +11.4328 q^{94} +(9.59791 - 1.69711i) q^{95} -9.61450 q^{96} +(-4.20551 - 1.96106i) q^{97} +(-13.2922 - 18.9833i) q^{98} +(-2.13664 - 2.54635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8}+O(q^{10}) \) 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8	\( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} + 6 q^{15} + 12 q^{16} - 30 q^{17} - 84 q^{20} + 24 q^{21} - 24 q^{22} + 12 q^{25} - 48 q^{26} - 18 q^{27} - 6 q^{30} - 36 q^{31} + 18 q^{32} + 90 q^{33} - 30 q^{35} + 24 q^{36} + 54 q^{38} + 54 q^{40} + 12 q^{41} + 24 q^{42} + 48 q^{43} + 12 q^{45} - 36 q^{46} - 24 q^{47} + 60 q^{48} + 126 q^{50} - 96 q^{51} - 30 q^{53} + 18 q^{55} - 66 q^{57} + 120 q^{58} + 84 q^{60} - 48 q^{61} + 60 q^{62} - 126 q^{63} + 72 q^{65} + 72 q^{66} + 108 q^{67} + 18 q^{68} + 36 q^{70} - 24 q^{71} + 48 q^{72} + 6 q^{73} + 60 q^{76} + 168 q^{77} - 138 q^{78} - 60 q^{80} - 120 q^{81} + 60 q^{82} - 36 q^{85} - 180 q^{86} - 6 q^{87} - 198 q^{88} - 270 q^{90} - 24 q^{91} - 72 q^{92} - 90 q^{93} - 24 q^{95} - 192 q^{96} - 72 q^{97} - 90 q^{98}+O(q^{100}) \) 96 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 12 * q^6 - 18 * q^8 - 12 * q^10 - 12 * q^11 - 18 * q^12 - 12 * q^13 + 6 * q^15 + 12 * q^16 - 30 * q^17 - 84 * q^20 + 24 * q^21 - 24 * q^22 + 12 * q^25 - 48 * q^26 - 18 * q^27 - 6 * q^30 - 36 * q^31 + 18 * q^32 + 90 * q^33 - 30 * q^35 + 24 * q^36 + 54 * q^38 + 54 * q^40 + 12 * q^41 + 24 * q^42 + 48 * q^43 + 12 * q^45 - 36 * q^46 - 24 * q^47 + 60 * q^48 + 126 * q^50 - 96 * q^51 - 30 * q^53 + 18 * q^55 - 66 * q^57 + 120 * q^58 + 84 * q^60 - 48 * q^61 + 60 * q^62 - 126 * q^63 + 72 * q^65 + 72 * q^66 + 108 * q^67 + 18 * q^68 + 36 * q^70 - 24 * q^71 + 48 * q^72 + 6 * q^73 + 60 * q^76 + 168 * q^77 - 138 * q^78 - 60 * q^80 - 120 * q^81 + 60 * q^82 - 36 * q^85 - 180 * q^86 - 6 * q^87 - 198 * q^88 - 270 * q^90 - 24 * q^91 - 72 * q^92 - 90 * q^93 - 24 * q^95 - 192 * q^96 - 72 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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