LMFDB - Embedded newform 300.2.r.a.179.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(59,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("300.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.r (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			179.15
Character	$\chi$	$=$	300.179
Dual form			300.2.r.a.119.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02850 - 0.970662i) q^{2} +(-0.992477 - 1.41950i) q^{3} +(0.115630 + 1.99665i) q^{4} +(-1.30960 - 1.81244i) q^{5} +(-0.357093 + 2.42332i) q^{6} -1.82094 q^{7} +(1.81915 - 2.16580i) q^{8} +(-1.02998 + 2.81765i) q^{9} +O(q^{10})$	\(q+(-1.02850 - 0.970662i) q^{2} +(-0.992477 - 1.41950i) q^{3} +(0.115630 + 1.99665i) q^{4} +(-1.30960 - 1.81244i) q^{5} +(-0.357093 + 2.42332i) q^{6} -1.82094 q^{7} +(1.81915 - 2.16580i) q^{8} +(-1.02998 + 2.81765i) q^{9} +(-0.412349 + 3.13528i) q^{10} +(0.247309 - 0.761138i) q^{11} +(2.71950 - 2.14577i) q^{12} +(-3.23099 + 1.04981i) q^{13} +(1.87284 + 1.76751i) q^{14} +(-1.27303 + 3.65779i) q^{15} +(-3.97326 + 0.461748i) q^{16} +(-0.461404 + 0.335230i) q^{17} +(3.79432 - 1.89820i) q^{18} +(4.02541 + 5.54050i) q^{19} +(3.46740 - 2.82439i) q^{20} +(1.80724 + 2.58482i) q^{21} +(-0.993166 + 0.542779i) q^{22} +(-1.85496 - 0.602713i) q^{23} +(-4.87983 - 0.432783i) q^{24} +(-1.56991 + 4.74714i) q^{25} +(4.34210 + 2.05647i) q^{26} +(5.02189 - 1.33440i) q^{27} +(-0.210555 - 3.63578i) q^{28} +(-1.66916 + 2.29741i) q^{29} +(4.85978 - 2.52636i) q^{30} +(-2.38209 - 3.27867i) q^{31} +(4.53470 + 3.38178i) q^{32} +(-1.32589 + 0.404357i) q^{33} +(0.799949 + 0.103083i) q^{34} +(2.38469 + 3.30035i) q^{35} +(-5.74497 - 1.73070i) q^{36} +(3.42585 - 1.11313i) q^{37} +(1.23781 - 9.60572i) q^{38} +(4.69690 + 3.54449i) q^{39} +(-6.30775 - 0.460786i) q^{40} +(-10.0468 + 3.26439i) q^{41} +(0.650244 - 4.41271i) q^{42} +5.23402 q^{43} +(1.54833 + 0.405780i) q^{44} +(6.45569 - 1.82321i) q^{45} +(1.32280 + 2.42043i) q^{46} +(-6.91025 + 9.51115i) q^{47} +(4.59882 + 5.18178i) q^{48} -3.68419 q^{49} +(6.22253 - 3.35859i) q^{50} +(0.933792 + 0.322256i) q^{51} +(-2.46972 - 6.32979i) q^{52} +(-6.16323 - 4.47785i) q^{53} +(-6.46027 - 3.50213i) q^{54} +(-1.70340 + 0.548551i) q^{55} +(-3.31256 + 3.94378i) q^{56} +(3.86963 - 11.2129i) q^{57} +(3.94674 - 0.742693i) q^{58} +(-2.59431 - 7.98448i) q^{59} +(-7.45054 - 2.11884i) q^{60} +(4.03533 - 12.4195i) q^{61} +(-0.732495 + 5.68433i) q^{62} +(1.87552 - 5.13076i) q^{63} +(-1.38138 - 7.87983i) q^{64} +(6.13403 + 4.48116i) q^{65} +(1.75617 + 0.871106i) q^{66} +(-7.80141 + 5.66806i) q^{67} +(-0.722690 - 0.882502i) q^{68} +(0.985452 + 3.23130i) q^{69} +(0.750862 - 5.70914i) q^{70} +(-9.89629 - 7.19008i) q^{71} +(4.22878 + 7.35645i) q^{72} +(-12.0129 - 3.90322i) q^{73} +(-4.60397 - 2.18049i) q^{74} +(8.29669 - 2.48294i) q^{75} +(-10.5970 + 8.67800i) q^{76} +(-0.450334 + 1.38598i) q^{77} +(-1.39027 - 8.20461i) q^{78} +(0.222877 - 0.306764i) q^{79} +(6.04026 + 6.59661i) q^{80} +(-6.87829 - 5.80423i) q^{81} +(13.5017 + 6.39458i) q^{82} +(-3.26571 - 4.49487i) q^{83} +(-4.95203 + 3.90731i) q^{84} +(1.21184 + 0.397254i) q^{85} +(-5.38320 - 5.08046i) q^{86} +(4.91779 + 0.0892587i) q^{87} +(-1.19858 - 1.92025i) q^{88} +(12.8868 + 4.18717i) q^{89} +(-8.40940 - 4.39112i) q^{90} +(5.88343 - 1.91164i) q^{91} +(0.988920 - 3.77340i) q^{92} +(-2.28991 + 6.63540i) q^{93} +(16.3393 - 3.07471i) q^{94} +(4.77019 - 14.5517i) q^{95} +(0.299861 - 9.79337i) q^{96} +(-0.331073 + 0.455683i) q^{97} +(3.78920 + 3.57610i) q^{98} +(1.88990 + 1.48078i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 6 q^{4} - 7 q^{6} - 6 q^{9}+O(q^{10}) $ 224 * q - 6 * q^4 - 7 * q^6 - 6 * q^9	$ 224 q - 6 q^{4} - 7 q^{6} - 6 q^{9} - 5 q^{12} - 20 q^{13} + 6 q^{16} - 24 q^{21} - 10 q^{22} - 28 q^{24} - 20 q^{25} - 50 q^{28} - 25 q^{30} - 10 q^{33} - 14 q^{34} - 25 q^{36} - 60 q^{37} - 20 q^{40} - 85 q^{42} - 30 q^{45} + 6 q^{46} - 70 q^{48} + 88 q^{49} + 40 q^{52} - 46 q^{54} + 50 q^{58} + 10 q^{60} - 28 q^{61} + 18 q^{64} + 64 q^{66} - 42 q^{69} - 40 q^{70} - 5 q^{72} - 20 q^{73} - 80 q^{76} - 85 q^{78} + 18 q^{81} - 48 q^{84} - 20 q^{85} + 50 q^{88} - 60 q^{90} + 60 q^{94} + 44 q^{96} - 120 q^{97}+O(q^{100}) $ 224 * q - 6 * q^4 - 7 * q^6 - 6 * q^9 - 5 * q^12 - 20 * q^13 + 6 * q^16 - 24 * q^21 - 10 * q^22 - 28 * q^24 - 20 * q^25 - 50 * q^28 - 25 * q^30 - 10 * q^33 - 14 * q^34 - 25 * q^36 - 60 * q^37 - 20 * q^40 - 85 * q^42 - 30 * q^45 + 6 * q^46 - 70 * q^48 + 88 * q^49 + 40 * q^52 - 46 * q^54 + 50 * q^58 + 10 * q^60 - 28 * q^61 + 18 * q^64 + 64 * q^66 - 42 * q^69 - 40 * q^70 - 5 * q^72 - 20 * q^73 - 80 * q^76 - 85 * q^78 + 18 * q^81 - 48 * q^84 - 20 * q^85 + 50 * q^88 - 60 * q^90 + 60 * q^94 + 44 * q^96 - 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.02850	−	0.970662i	−0.727260	−	0.686362i
$2$	−1.02850	−	0.970662i	−0.727260	−	0.686362i
$3$	−0.992477	−	1.41950i	−0.573007	−	0.819550i
$3$	−0.992477	−	1.41950i	−0.573007	−	0.819550i
$4$	0.115630	+	1.99665i	0.0578152	+	0.998327i
$5$	−1.30960	−	1.81244i	−0.585669	−	0.810550i
$5$	−1.30960	−	1.81244i	−0.585669	−	0.810550i
$6$	−0.357093	+	2.42332i	−0.145783	+	0.989317i
$7$	−1.82094			−0.688249			−0.344125	−	0.938924i	$-0.611824\pi$
$7$	−1.82094			−0.688249			−0.344125	+	0.938924i	$0.611824\pi$
$8$	1.81915	−	2.16580i	0.643167	−	0.765726i
$9$	−1.02998	+	2.81765i	−0.343326	+	0.939216i
$10$	−0.412349	+	3.13528i	−0.130396	+	0.991462i
$11$	0.247309	−	0.761138i	0.0745664	−	0.229492i	−0.906826	−	0.421506i	$-0.861502\pi$
$11$	0.247309	−	0.761138i	0.0745664	−	0.229492i	0.981392	+	0.192014i	$0.0615018\pi$
$12$	2.71950	−	2.14577i	0.785051	−	0.619431i
$13$	−3.23099	+	1.04981i	−0.896116	+	0.291166i	−0.720633	−	0.693317i	$-0.756149\pi$
$13$	−3.23099	+	1.04981i	−0.896116	+	0.291166i	−0.175483	+	0.984482i	$0.556149\pi$
$14$	1.87284	+	1.76751i	0.500536	+	0.472388i
$15$	−1.27303	+	3.65779i	−0.328694	+	0.944437i
$16$	−3.97326	+	0.461748i	−0.993315	+	0.115437i
$17$	−0.461404	+	0.335230i	−0.111907	+	0.0813051i	−0.642331	−	0.766427i	$-0.722033\pi$
$17$	−0.461404	+	0.335230i	−0.111907	+	0.0813051i	0.530424	+	0.847732i	$0.322033\pi$
$18$	3.79432	−	1.89820i	0.894329	−	0.447409i
$19$	4.02541	+	5.54050i	0.923492	+	1.27108i	0.962345	+	0.271833i	$0.0876298\pi$
$19$	4.02541	+	5.54050i	0.923492	+	1.27108i	−0.0388525	+	0.999245i	$0.512370\pi$
$20$	3.46740	−	2.82439i	0.775334	−	0.631552i
$21$	1.80724	+	2.58482i	0.394372	+	0.564055i
$22$	−0.993166	+	0.542779i	−0.211744	+	0.115721i
$23$	−1.85496	−	0.602713i	−0.386786	−	0.125674i	0.109168	−	0.994023i	$-0.465181\pi$
$23$	−1.85496	−	0.602713i	−0.386786	−	0.125674i	−0.495954	+	0.868349i	$0.665181\pi$
$24$	−4.87983	−	0.432783i	−0.996090	−	0.0883414i
$25$	−1.56991	+	4.74714i	−0.313982	+	0.949429i
$26$	4.34210	+	2.05647i	0.851555	+	0.403307i
$27$	5.02189	−	1.33440i	0.966463	−	0.256805i
$28$	−0.210555	−	3.63578i	−0.0397912	−	0.687098i
$29$	−1.66916	+	2.29741i	−0.309956	+	0.426618i	−0.935368	−	0.353677i	$-0.884931\pi$
$29$	−1.66916	+	2.29741i	−0.309956	+	0.426618i	0.625411	+	0.780295i	$0.284931\pi$
$30$	4.85978	−	2.52636i	0.887271	−	0.461248i
$31$	−2.38209	−	3.27867i	−0.427837	−	0.588867i	0.539618	−	0.841910i	$-0.318569\pi$
$31$	−2.38209	−	3.27867i	−0.427837	−	0.588867i	−0.967455	+	0.253043i	$0.918569\pi$
$32$	4.53470	+	3.38178i	0.801630	+	0.597821i
$33$	−1.32589	+	0.404357i	−0.230807	+	0.0703895i
$34$	0.799949	+	0.103083i	0.137190	+	0.0176786i
$35$	2.38469	+	3.30035i	0.403087	+	0.557860i
$36$	−5.74497	−	1.73070i	−0.957495	−	0.288451i
$37$	3.42585	−	1.11313i	0.563207	−	0.182997i	−0.0135567	−	0.999908i	$-0.504315\pi$
$37$	3.42585	−	1.11313i	0.563207	−	0.182997i	0.576764	+	0.816911i	$0.304315\pi$
$38$	1.23781	−	9.60572i	0.200800	−	1.55825i
$39$	4.69690	+	3.54449i	0.752106	+	0.567572i
$40$	−6.30775	−	0.460786i	−0.997342	−	0.0728566i
$41$	−10.0468	+	3.26439i	−1.56904	+	0.509812i	−0.959204	−	0.282716i	$-0.908765\pi$
$41$	−10.0468	+	3.26439i	−1.56904	+	0.509812i	−0.609836	+	0.792528i	$0.708765\pi$
$42$	0.650244	−	4.41271i	0.100335	−	0.680896i
$43$	5.23402			0.798181			0.399090	−	0.916912i	$-0.369326\pi$
$43$	5.23402			0.798181			0.399090	+	0.916912i	$0.369326\pi$
$44$	1.54833	+	0.405780i	0.233419	+	0.0611736i
$45$	6.45569	−	1.82321i	0.962357	−	0.271788i
$46$	1.32280	+	2.42043i	0.195036	+	0.356873i
$47$	−6.91025	+	9.51115i	−1.00796	+	1.38734i	−0.0876549	+	0.996151i	$0.527937\pi$
$47$	−6.91025	+	9.51115i	−1.00796	+	1.38734i	−0.920309	+	0.391192i	$0.872063\pi$
$48$	4.59882	+	5.18178i	0.663783	+	0.747925i
$49$	−3.68419			−0.526313
$50$	6.22253	−	3.35859i	0.879999	−	0.474976i
$51$	0.933792	+	0.322256i	0.130757	+	0.0451249i
$52$	−2.46972	−	6.32979i	−0.342488	−	0.877784i
$53$	−6.16323	−	4.47785i	−0.846585	−	0.615080i	0.0776171	−	0.996983i	$-0.475269\pi$
$53$	−6.16323	−	4.47785i	−0.846585	−	0.615080i	−0.924202	+	0.381903i	$0.875269\pi$
$54$	−6.46027	−	3.50213i	−0.879131	−	0.476579i
$55$	−1.70340	+	0.548551i	−0.229686	+	0.0739666i
$56$	−3.31256	+	3.94378i	−0.442659	+	0.527010i
$57$	3.86963	−	11.2129i	0.512545	−	1.48518i
$58$	3.94674	−	0.742693i	0.518233	−	0.0975203i
$59$	−2.59431	−	7.98448i	−0.337751	−	1.03949i	−0.965351	−	0.260955i	$-0.915963\pi$
$59$	−2.59431	−	7.98448i	−0.337751	−	1.03949i	0.627600	−	0.778536i	$-0.284037\pi$
$60$	−7.45054	−	2.11884i	−0.961860	−	0.273541i
$61$	4.03533	−	12.4195i	0.516671	−	1.59015i	−0.263550	−	0.964646i	$-0.584893\pi$
$61$	4.03533	−	12.4195i	0.516671	−	1.59015i	0.780221	−	0.625504i	$-0.215107\pi$
$62$	−0.732495	+	5.68433i	−0.0930269	+	0.721910i
$63$	1.87552	−	5.13076i	0.236294	−	0.646415i
$64$	−1.38138	−	7.87983i	−0.172672	−	0.984979i
$65$	6.13403	+	4.48116i	0.760832	+	0.555820i
$66$	1.75617	+	0.871106i	0.216170	+	0.107226i
$67$	−7.80141	+	5.66806i	−0.953094	+	0.692464i	−0.951537	−	0.307535i	$-0.900496\pi$
$67$	−7.80141	+	5.66806i	−0.953094	+	0.692464i	−0.00155776	+	0.999999i	$0.500496\pi$
$68$	−0.722690	−	0.882502i	−0.0876390	−	0.107019i
$69$	0.985452	+	3.23130i	0.118635	+	0.389003i
$70$	0.750862	−	5.70914i	0.0897451	−	0.682373i
$71$	−9.89629	−	7.19008i	−1.17447	−	0.853305i	−0.182936	−	0.983125i	$-0.558560\pi$
$71$	−9.89629	−	7.19008i	−1.17447	−	0.853305i	−0.991538	+	0.129819i	$0.958560\pi$
$72$	4.22878	+	7.35645i	0.498367	+	0.866966i
$73$	−12.0129	−	3.90322i	−1.40600	−	0.456837i	−0.494874	−	0.868965i	$-0.664786\pi$
$73$	−12.0129	−	3.90322i	−1.40600	−	0.456837i	−0.911126	+	0.412128i	$0.864786\pi$
$74$	−4.60397	−	2.18049i	−0.535200	−	0.253477i
$75$	8.29669	−	2.48294i	0.958019	−	0.286705i
$76$	−10.5970	+	8.67800i	−1.21556	+	0.995435i
$77$	−0.450334	+	1.38598i	−0.0513203	+	0.157948i
$78$	−1.39027	−	8.20461i	−0.157417	−	0.928990i
$79$	0.222877	−	0.306764i	0.0250756	−	0.0345136i	−0.796295	−	0.604908i	$-0.793210\pi$
$79$	0.222877	−	0.306764i	0.0250756	−	0.0345136i	0.821371	+	0.570395i	$0.193210\pi$
$80$	6.04026	+	6.59661i	0.675322	+	0.737523i
$81$	−6.87829	−	5.80423i	−0.764255	−	0.644914i
$82$	13.5017	+	6.39458i	1.49102	+	0.706163i
$83$	−3.26571	−	4.49487i	−0.358459	−	0.493376i	0.591260	−	0.806481i	$-0.298631\pi$
$83$	−3.26571	−	4.49487i	−0.358459	−	0.493376i	−0.949719	+	0.313105i	$0.898631\pi$
$84$	−4.95203	+	3.90731i	−0.540311	+	0.426323i
$85$	1.21184	+	0.397254i	0.131442	+	0.0430882i
$86$	−5.38320	−	5.08046i	−0.580485	−	0.547841i
$87$	4.91779	+	0.0892587i	0.527242	+	0.00956954i
$88$	−1.19858	−	1.92025i	−0.127769	−	0.204699i
$89$	12.8868	+	4.18717i	1.36600	+	0.443839i	0.898041	−	0.439912i	$-0.144991\pi$
$89$	12.8868	+	4.18717i	1.36600	+	0.443839i	0.467956	+	0.883752i	$0.344991\pi$
$90$	−8.40940	−	4.39112i	−0.886429	−	0.462865i
$91$	5.88343	−	1.91164i	0.616751	−	0.200395i
$92$	0.988920	−	3.77340i	0.103102	−	0.393405i
$93$	−2.28991	+	6.63540i	−0.237452	+	0.688058i
$94$	16.3393	−	3.07471i	1.68527	−	0.317132i
$95$	4.77019	−	14.5517i	0.489411	−	1.49297i
$96$	0.299861	−	9.79337i	0.0306045	−	0.999532i
$97$	−0.331073	+	0.455683i	−0.0336153	+	0.0462676i	−0.825494	−	0.564411i	$-0.809103\pi$
$97$	−0.331073	+	0.455683i	−0.0336153	+	0.0462676i	0.791879	+	0.610679i	$0.209103\pi$
$98$	3.78920	+	3.57610i	0.382767	+	0.361241i
$99$	1.88990	+	1.48078i	0.189942	+	0.148824i
$100$	−9.65994	−	2.58566i	−0.965994	−	0.258566i
$101$		−	1.23431i		−	0.122818i	−0.998113	−	0.0614091i	$-0.980441\pi$
$101$		−	1.23431i		−	0.122818i	0.998113	−	0.0614091i	$-0.0195594\pi$
$102$	−0.647605	−	1.23784i	−0.0641224	−	0.122564i
$103$	−4.93809	−	3.58773i	−0.486564	−	0.353510i	0.317297	−	0.948326i	$-0.397225\pi$
$103$	−4.93809	−	3.58773i	−0.486564	−	0.353510i	−0.803862	+	0.594816i	$0.797225\pi$
$104$	−3.60398	+	8.90745i	−0.353399	+	0.873448i
$105$	2.31810	−	6.66060i	0.226223	−	0.650008i
$106$	1.99241	+	10.5879i	0.193520	+	1.02839i
$107$		−	1.00404i		−	0.0970639i	−0.998822	−	0.0485319i	$-0.984546\pi$
$107$		−	1.00404i		−	0.0970639i	0.998822	−	0.0485319i	$-0.0154543\pi$
$108$	3.24501	+	9.87268i	0.312252	+	0.949999i
$109$	6.02193	+	18.5336i	0.576796	+	1.77520i	0.629979	+	0.776612i	$0.283064\pi$
$109$	6.02193	+	18.5336i	0.576796	+	1.77520i	−0.0531824	+	0.998585i	$0.516936\pi$
$110$	2.28440	+	1.08924i	0.217809	+	0.103855i
$111$	−4.98017	−	3.75826i	−0.472697	−	0.356718i
$112$	7.23505	−	0.840813i	0.683648	−	0.0794494i
$113$	3.24909	+	9.99968i	0.305649	+	0.940691i	0.979434	+	0.201764i	$0.0646673\pi$
$113$	3.24909	+	9.99968i	0.305649	+	0.940691i	−0.673785	+	0.738927i	$0.735333\pi$
$114$	−14.8639	+	7.77638i	−1.39213	+	0.728325i
$115$	1.33687	+	4.15132i	0.124663	+	0.387113i
$116$	−4.78014	−	3.06709i	−0.443824	−	0.284773i
$117$	0.369844	−	10.1851i	0.0341921	−	0.941612i
$118$	−5.08198	+	10.7303i	−0.467834	+	0.987800i
$119$	0.840187	−	0.610432i	0.0770198	−	0.0559582i
$120$	5.60621	+	9.41119i	0.511775	+	0.859120i
$121$	8.38102	+	6.08917i	0.761911	+	0.553560i
$122$	−16.2054	+	8.85650i	−1.46717	+	0.801830i
$123$	14.6050	+	11.0216i	1.31689	+	0.993781i
$124$	6.27093	−	5.13533i	0.563146	−	0.461166i
$125$	10.6599	−	3.37146i	0.953449	−	0.301553i
$126$	−6.90921	+	3.45649i	−0.615521	+	0.307929i
$127$	−0.355933	+	1.09545i	−0.0315839	+	0.0972053i	−0.965606	−	0.260011i	$-0.916274\pi$
$127$	−0.355933	+	1.09545i	−0.0315839	+	0.0972053i	0.934022	+	0.357216i	$0.116274\pi$
$128$	−6.22790	+	9.44527i	−0.550474	+	0.834852i
$129$	−5.19465	−	7.42971i	−0.457363	−	0.654149i
$130$	−1.95916	−	10.5630i	−0.171830	−	0.926432i
$131$	1.69523	−	1.23165i	0.148113	−	0.107610i	−0.511261	−	0.859425i	$-0.670822\pi$
$131$	1.69523	−	1.23165i	0.148113	−	0.107610i	0.659374	+	0.751815i	$0.270822\pi$
$132$	−0.960674	−	2.60058i	−0.0836159	−	0.226352i
$133$	−7.33001	−	10.0889i	−0.635593	−	0.874818i
$134$	13.5255	+	1.74293i	1.16843	+	0.150566i
$135$	−8.99517	−	7.35438i	−0.774181	−	0.632964i
$136$	−0.113323	+	1.60914i	−0.00971738	+	0.137983i
$137$	−0.813605	−	2.50402i	−0.0695110	−	0.213933i	0.910267	−	0.414023i	$-0.135877\pi$
$137$	−0.813605	−	2.50402i	−0.0695110	−	0.213933i	−0.979778	+	0.200090i	$0.935877\pi$
$138$	2.12296	−	4.27994i	0.180718	−	0.364332i
$139$	−10.9638	−	3.56235i	−0.929936	−	0.302155i	−0.195400	−	0.980724i	$-0.562600\pi$
$139$	−10.9638	−	3.56235i	−0.929936	−	0.302155i	−0.734537	+	0.678569i	$0.762600\pi$
$140$	−6.31391	+	5.14303i	−0.533623	+	0.434665i
$141$	20.3594	+	0.369526i	1.71457	+	0.0311197i
$142$	3.19922	+	17.0010i	0.268472	+	1.42669i
$143$			2.71886i			0.227363i
$144$	2.79132	−	11.6708i	0.232610	−	0.972570i
$145$	6.34986	+	0.0165905i	0.527327	+	0.00137777i
$146$	8.56655	+	15.6749i	0.708973	+	1.29726i
$147$	3.65648	+	5.22972i	0.301581	+	0.431340i
$148$	2.61866	+	6.71154i	0.215253	+	0.551685i
$149$			7.95239i			0.651485i	0.945459	+	0.325742i	$0.105614\pi$
$149$			7.95239i			0.651485i	−0.945459	+	0.325742i	$0.894386\pi$
$150$	−10.9432	−	5.49957i	−0.893512	−	0.449038i
$151$		−	13.9119i		−	1.13213i	−0.824360	−	0.566065i	$-0.808465\pi$
$151$		−	13.9119i		−	1.13213i	0.824360	−	0.566065i	$-0.191535\pi$
$152$	19.3224	+	1.36077i	1.56726	+	0.110373i
$153$	−0.469324	−	1.64535i	−0.0379426	−	0.133019i
$154$	1.80849	−	0.988365i	0.145732	−	0.0796447i
$155$	−2.82283	+	8.61115i	−0.226735	+	0.691664i
$156$	−6.53402	+	9.78794i	−0.523140	+	0.783662i
$157$		−	9.44912i		−	0.754122i	−0.926188	−	0.377061i	$-0.876935\pi$
$157$		−	9.44912i		−	0.754122i	0.926188	−	0.377061i	$-0.123065\pi$
$158$	−0.526993	+	0.0991688i	−0.0419253	+	0.00788945i
$159$	−0.239454	+	13.1929i	−0.0189899	+	1.04626i
$160$	0.190663	−	12.6477i	0.0150732	−	0.999886i
$161$	3.37776	+	1.09750i	0.266205	+	0.0864952i
$162$	1.44039	+	12.6462i	0.113168	+	0.993576i
$163$	6.32363	+	19.4621i	0.495305	+	1.52439i	0.816480	+	0.577373i	$0.195922\pi$
$163$	6.32363	+	19.4621i	0.495305	+	1.52439i	−0.321175	+	0.947020i	$0.604078\pi$
$164$	−7.67957	−	19.6824i	−0.599674	−	1.53694i
$165$	2.46925	+	1.87355i	0.192231	+	0.145856i
$166$	−1.00421	+	7.79289i	−0.0779417	+	0.604845i
$167$	−0.0489748	−	0.0674080i	−0.00378978	−	0.00521619i	0.807118	−	0.590390i	$-0.201026\pi$
$167$	−0.0489748	−	0.0674080i	−0.00378978	−	0.00521619i	−0.810908	+	0.585174i	$0.801026\pi$
$168$	8.88585	+	0.788069i	0.685558	+	0.0608009i
$169$	−1.18001	+	0.857329i	−0.0907701	+	0.0659484i
$170$	−0.860778	−	1.58486i	−0.0660187	−	0.121553i
$171$	−19.7573	+	5.63560i	−1.51088	+	0.430965i
$172$	0.605211	+	10.4505i	0.0461469	+	0.796845i
$173$	2.07273	−	6.37921i	0.157587	−	0.485002i	−0.840827	−	0.541304i	$-0.817931\pi$
$173$	2.07273	−	6.37921i	0.157587	−	0.485002i	0.998414	+	0.0563017i	$0.0179309\pi$
$174$	−4.97131	−	4.86531i	−0.376874	−	0.368838i
$175$	2.85871	−	8.64425i	0.216098	−	0.653444i
$176$	−0.631168	+	3.13839i	−0.0475761	+	0.236565i
$177$	−8.75919	+	11.6071i	−0.658381	+	0.872440i
$178$	−9.18975	−	16.8152i	−0.688801	−	1.26035i
$179$	−9.23271	−	6.70796i	−0.690085	−	0.501376i	0.186603	−	0.982435i	$-0.440252\pi$
$179$	−9.23271	−	6.70796i	−0.690085	−	0.501376i	−0.876688	+	0.481059i	$0.840252\pi$
$180$	4.38679	+	12.6790i	0.326972	+	0.945034i
$181$	5.93997	−	4.31564i	0.441515	−	0.320779i	−0.344722	−	0.938705i	$-0.612027\pi$
$181$	5.93997	−	4.31564i	0.441515	−	0.320779i	0.786237	+	0.617926i	$0.212027\pi$
$182$	−7.90668	−	3.74470i	−0.586082	−	0.277575i
$183$	−21.6344	+	6.59788i	−1.59926	+	0.487729i
$184$	−4.67981	+	2.92105i	−0.345000	+	0.215342i
$185$	−6.50397	−	4.75142i	−0.478181	−	0.349332i
$186$	8.79590	−	4.60179i	0.644947	−	0.337419i
$187$	0.141047	+	0.434097i	0.0103144	+	0.0317444i
$188$	−19.7895	−	12.6976i	−1.44330	−	0.926068i
$189$	−9.14454	+	2.42985i	−0.665168	+	0.176746i
$190$	−19.0309	+	10.3362i	−1.38065	+	0.749863i
$191$	7.52546	+	23.1610i	0.544523	+	1.67587i	0.722120	+	0.691767i	$0.243168\pi$
$191$	7.52546	+	23.1610i	0.544523	+	1.67587i	−0.177597	+	0.984103i	$0.556832\pi$
$192$	−9.81446	+	9.78143i	−0.708298	+	0.705914i
$193$		−	2.22720i		−	0.160317i	−0.996782	−	0.0801586i	$-0.974457\pi$
$193$		−	2.22720i		−	0.160317i	0.996782	−	0.0801586i	$-0.0255427\pi$
$194$	0.782823	−	0.147310i	0.0562034	−	0.0105763i
$195$	0.273144	−	13.1547i	0.0195602	−	0.942029i
$196$	−0.426004	−	7.35606i	−0.0304289	−	0.525433i
$197$	−3.52656	−	2.56220i	−0.251257	−	0.182549i	0.455027	−	0.890478i	$-0.349630\pi$
$197$	−3.52656	−	2.56220i	−0.251257	−	0.182549i	−0.706284	+	0.707929i	$0.749630\pi$
$198$	−0.506421	−	3.35744i	−0.0359898	−	0.238603i
$199$		−	22.2330i		−	1.57605i	−0.615642	−	0.788026i	$-0.711103\pi$
$199$		−	22.2330i		−	1.57605i	0.615642	−	0.788026i	$-0.288897\pi$
$200$	7.42546	+	12.0359i	0.525059	+	0.851066i
$201$	15.7886	+	5.44871i	1.11364	+	0.384322i
$202$	−1.19810	+	1.26949i	−0.0842978	+	0.0893209i
$203$	3.03944	−	4.18343i	0.213327	−	0.293619i
$204$	−0.535460	+	1.90172i	−0.0374897	+	0.133147i
$205$	19.0737	+	13.9342i	1.33217	+	0.973204i
$206$	1.59636	+	8.48320i	0.111223	+	0.591053i
$207$	3.60880	−	4.60584i	0.250829	−	0.320128i
$208$	12.3528	−	5.66308i	0.856514	−	0.392664i
$209$	5.21261	−	1.69368i	0.360563	−	0.117154i
$210$	−8.84936	+	4.60034i	−0.610664	+	0.317454i
$211$	9.80805	+	3.18683i	0.675214	+	0.219390i	0.626499	−	0.779422i	$-0.284487\pi$
$211$	9.80805	+	3.18683i	0.675214	+	0.219390i	0.0487152	+	0.998813i	$0.484487\pi$
$212$	8.22807	−	12.8236i	0.565106	−	0.880730i
$213$	−0.384490	+	21.1838i	−0.0263448	+	1.45149i
$214$	−0.974580	+	1.03265i	−0.0666209	+	0.0705907i
$215$	−6.85446	−	9.48637i	−0.467470	−	0.646965i
$216$	6.24554	−	13.3039i	0.424955	−	0.905214i
$217$	4.33764	+	5.97025i	0.294458	+	0.405287i
$218$	11.7963	−	24.9071i	0.798946	−	1.68692i
$219$	6.38187	+	20.9262i	0.431247	+	1.41406i
$220$	−1.29223	−	3.33766i	−0.0871222	−	0.225025i
$221$	1.13886	−	1.56751i	0.0766083	−	0.105442i
$222$	1.47412	+	8.69943i	0.0989362	+	0.583868i
$223$	−1.98071	+	6.09600i	−0.132638	+	0.408218i	−0.995215	−	0.0977075i	$-0.968849\pi$
$223$	−1.98071	+	6.09600i	−0.132638	+	0.408218i	0.862577	+	0.505926i	$0.168849\pi$
$224$	−8.25741	−	6.15801i	−0.551721	−	0.411450i
$225$	−11.7588	−	9.31291i	−0.783921	−	0.620861i
$226$	6.36461	−	13.4385i	0.423368	−	0.893913i
$227$	−6.19562	−	2.01308i	−0.411218	−	0.133613i	0.0961004	−	0.995372i	$-0.469363\pi$
$227$	−6.19562	−	2.01308i	−0.411218	−	0.133613i	−0.507318	+	0.861759i	$0.669363\pi$
$228$	22.8357	+	6.42976i	1.51233	+	0.425821i
$229$	−12.7239	−	9.24448i	−0.840821	−	0.610892i	0.0817789	−	0.996650i	$-0.473940\pi$
$229$	−12.7239	−	9.24448i	−0.840821	−	0.610892i	−0.922600	+	0.385758i	$0.873940\pi$
$230$	2.65456	−	5.56728i	0.175037	−	0.367096i
$231$	2.41435	−	0.736308i	0.158853	−	0.0484455i
$232$	1.93926	+	7.79441i	0.127319	+	0.511728i
$233$	18.0172	−	13.0903i	1.18035	−	0.857573i	0.188137	−	0.982143i	$-0.439755\pi$
$233$	18.0172	−	13.0903i	1.18035	−	0.857573i	0.992211	+	0.124570i	$0.0397551\pi$
$234$	−10.2667	+	10.1164i	−0.671153	+	0.661329i
$235$	26.2881	+	0.0686840i	1.71484	+	0.00448045i
$236$	15.6423	−	6.10320i	1.01822	−	0.397284i
$237$	−0.656653	−	0.0119184i	−0.0426542	−	0.000774181i
$238$	−1.45666	−	0.187708i	−0.0944210	−	0.0121673i
$239$	0.384409	−	1.18309i	0.0248653	−	0.0765276i	−0.937854	−	0.347031i	$-0.887190\pi$
$239$	0.384409	−	1.18309i	0.0248653	−	0.0765276i	0.962719	+	0.270503i	$0.0871900\pi$
$240$	3.36909	−	15.1212i	0.217474	−	0.976066i
$241$	−3.61439	−	11.1239i	−0.232823	−	0.716556i	−0.997403	−	0.0720267i	$-0.977053\pi$
$241$	−3.61439	−	11.1239i	−0.232823	−	0.716556i	0.764579	−	0.644529i	$-0.222947\pi$
$242$	−2.70937	−	14.3979i	−0.174165	−	0.925529i
$243$	−1.41257	+	15.5243i	−0.0906165	+	0.995886i
$244$	25.2640	+	6.62109i	1.61736	+	0.423872i
$245$	4.82481	+	6.67739i	0.308245	+	0.426603i
$246$	−4.32303	−	25.5122i	−0.275627	−	1.62660i
$247$	−18.8226	−	13.6754i	−1.19765	−	0.870144i
$248$	−11.4343	−	0.805258i	−0.726081	−	0.0511339i
$249$	−3.13933	+	9.09675i	−0.198947	+	0.576483i
$250$	−14.2363	−	6.87959i	−0.900380	−	0.435104i
$251$	23.4563			1.48055			0.740273	−	0.672307i	$-0.234696\pi$
$251$	23.4563			1.48055			0.740273	+	0.672307i	$0.234696\pi$
$252$	10.4612	+	3.15150i	0.658995	+	0.198526i
$253$	−0.917496	+	1.26282i	−0.0576825	+	0.0793931i
$254$	1.42939	−	0.781179i	0.0896877	−	0.0490156i
$255$	−0.638819	−	2.11447i	−0.0400044	−	0.132413i
$256$	15.5736	−	3.66929i	0.973349	−	0.229330i
$257$	−25.9997			−1.62182			−0.810908	−	0.585174i	$-0.801026\pi$
$257$	−25.9997			−1.62182			−0.810908	+	0.585174i	$0.801026\pi$
$258$	−1.86903	+	12.6837i	−0.116361	+	0.789653i
$259$	−6.23826	+	2.02693i	−0.387627	+	0.125948i
$260$	−8.23806	+	12.7657i	−0.510903	+	0.791695i
$261$	−4.75409	−	7.06940i	−0.294271	−	0.437585i
$262$	−2.93906	−	0.378734i	−0.181576	−	0.0233983i
$263$	−6.97976	+	2.26786i	−0.430391	+	0.139842i	−0.516198	−	0.856469i	$-0.672653\pi$
$263$	−6.97976	+	2.26786i	−0.430391	+	0.139842i	0.0858073	+	0.996312i	$0.472653\pi$
$264$	−1.53623	+	3.60719i	−0.0945485	+	0.222007i
$265$	−0.0445073	+	17.0347i	−0.00273406	+	1.04643i
$266$	−2.25398	+	17.4914i	−0.138200	+	1.07247i
$267$	−6.84614	−	22.4485i	−0.418977	−	1.37383i
$268$	−12.2192	−	14.9213i	−0.746409	−	0.911465i
$269$	−12.1764	−	16.7593i	−0.742406	−	1.02183i	−0.998477	−	0.0551761i	$-0.982428\pi$
$269$	−12.1764	−	16.7593i	−0.742406	−	1.02183i	0.256071	−	0.966658i	$-0.417572\pi$
$270$	2.11293	+	16.2953i	0.128589	+	0.991698i
$271$	1.70072	−	2.34083i	0.103311	−	0.142196i	−0.754231	−	0.656609i	$-0.771990\pi$
$271$	1.70072	−	2.34083i	0.103311	−	0.142196i	0.857542	+	0.514413i	$0.171990\pi$
$272$	1.67849	−	1.54501i	0.101773	−	0.0936798i
$273$	−8.55276	−	6.45429i	−0.517636	−	0.390631i
$274$	−1.59376	+	3.36512i	−0.0962827	+	0.203294i
$275$	3.22498	+	2.36893i	0.194474	+	0.142852i
$276$	−6.33784	+	2.34124i	−0.381493	+	0.140926i
$277$	−18.9590	−	6.16014i	−1.13913	−	0.370127i	−0.322093	−	0.946708i	$-0.604386\pi$
$277$	−18.9590	−	6.16014i	−1.13913	−	0.370127i	−0.817040	+	0.576581i	$0.804386\pi$
$278$	7.81843	+	14.3060i	0.468918	+	0.858018i
$279$	11.6916	−	3.33495i	0.699961	−	0.199658i
$280$	11.4860	+	0.839061i	0.686420	+	0.0501435i
$281$	−1.88448	−	2.59377i	−0.112419	−	0.154731i	0.749100	−	0.662457i	$-0.230486\pi$
$281$	−1.88448	−	2.59377i	−0.112419	−	0.154731i	−0.861519	+	0.507726i	$0.830486\pi$
$282$	−20.5810	−	20.1421i	−1.22558	−	1.19945i
$283$	11.2107	−	8.14505i	0.666407	−	0.484173i	−0.202414	−	0.979300i	$-0.564879\pi$
$283$	11.2107	−	8.14505i	0.666407	−	0.484173i	0.868820	+	0.495127i	$0.164879\pi$
$284$	13.2118	−	20.5909i	0.783976	−	1.22184i
$285$	−25.3904	+	7.67089i	−1.50400	+	0.454384i
$286$	2.63910	−	2.79635i	0.156053	−	0.165352i
$287$	18.2945	−	5.94425i	1.07989	−	0.350878i
$288$	−14.1993	+	9.29404i	−0.836703	+	0.547657i
$289$	−5.15277	+	15.8586i	−0.303104	+	0.932859i
$290$	−6.51473	−	6.18063i	−0.382558	−	0.362939i
$291$	0.975425	+	0.0177041i	0.0571804	+	0.00103784i
$292$	6.40433	−	24.4369i	0.374785	−	1.43006i
$293$	−30.5925			−1.78723			−0.893617	−	0.448830i	$-0.851841\pi$
$293$	−30.5925			−1.78723			−0.893617	+	0.448830i	$0.851841\pi$
$294$	1.31560	−	8.92798i	0.0767274	−	0.520690i
$295$	−11.0739	+	15.1585i	−0.644749	+	0.882562i
$296$	3.82133	−	9.44466i	0.222111	−	0.548960i
$297$	0.226297	−	4.15236i	0.0131311	−	0.240944i
$298$	7.71908	−	8.17904i	0.447154	−	0.473799i
$299$	6.62610			0.383197
$300$	5.91692	+	16.2785i	0.341613	+	0.939841i
$301$	−9.53082			−0.549347
$302$	−13.5037	+	14.3084i	−0.777051	+	0.823354i
$303$	−1.75210	+	1.22502i	−0.100656	+	0.0703757i
$304$	−18.5523	−	20.1551i	−1.06405	−	1.15598i
$305$	−27.7943	+	8.95068i	−1.59149	+	0.512515i
$306$	−1.11438	+	2.14780i	−0.0637050	+	0.122782i
$307$	3.72232			0.212444			0.106222	−	0.994342i	$-0.466125\pi$
$307$	3.72232			0.212444			0.106222	+	0.994342i	$0.466125\pi$
$308$	−2.81940	−	0.738899i	−0.160650	−	0.0421027i
$309$	−0.191854	+	10.5704i	−0.0109142	+	0.601328i
$310$	11.2618	−	6.11657i	0.639627	−	0.347398i
$311$	−7.40049	+	22.7764i	−0.419644	+	1.29153i	0.488387	+	0.872627i	$0.337585\pi$
$311$	−7.40049	+	22.7764i	−0.419644	+	1.29153i	−0.908031	+	0.418903i	$0.862415\pi$
$312$	16.2210	−	3.72459i	0.918335	−	0.210863i
$313$	27.7968	−	9.03173i	1.57117	−	0.510503i	0.611406	−	0.791317i	$-0.290604\pi$
$313$	27.7968	−	9.03173i	1.57117	−	0.510503i	0.959762	+	0.280814i	$0.0906043\pi$
$314$	−9.17190	+	9.71843i	−0.517600	+	0.548443i
$315$	−11.7554	+	3.31994i	−0.662342	+	0.187058i
$316$	0.638273	+	0.409537i	0.0359057	+	0.0230383i
$317$	−1.16402	+	0.845712i	−0.0653780	+	0.0474999i	−0.619994	−	0.784606i	$-0.712865\pi$
$317$	−1.16402	+	0.845712i	−0.0653780	+	0.0474999i	0.554616	+	0.832106i	$0.312865\pi$
$318$	13.0521	−	13.3365i	0.731927	−	0.747873i
$319$	1.33585	+	1.83863i	0.0747930	+	0.102944i
$320$	−12.4727	+	12.8231i	−0.697246	+	0.716832i
$321$	−1.42523	+	0.996484i	−0.0795487	+	0.0556183i
$322$	−2.40873	−	4.40745i	−0.134233	−	0.245617i
$323$	−3.71468	−	1.20697i	−0.206690	−	0.0671577i
$324$	10.7937	−	14.4047i	0.599650	−	0.800262i
$325$	0.0887613	−	16.9861i	0.00492359	−	0.942220i
$326$	12.3873	−	26.1550i	0.686069	−	1.44859i
$327$	20.3319	−	26.9423i	1.12436	−	1.48991i
$328$	−11.2066	+	27.6977i	−0.618778	+	1.52935i
$329$	12.5831	−	17.3192i	0.693730	−	0.954838i
$330$	−0.721043	−	4.32376i	−0.0396921	−	0.238015i
$331$	−15.0265	−	20.6822i	−0.825929	−	1.13679i	−0.988667	−	0.150125i	$-0.952032\pi$
$331$	−15.0265	−	20.6822i	−0.825929	−	1.13679i	0.162738	−	0.986669i	$-0.447968\pi$
$332$	8.59709	−	7.04025i	0.471827	−	0.386384i
$333$	−0.392150	+	10.7994i	−0.0214897	+	0.591801i
$334$	−0.0150598	+	0.116867i	−0.000824033	+	0.00639469i
$335$	20.4898	+	6.71676i	1.11947	+	0.366976i
$336$	−8.37416	−	9.43569i	−0.456848	−	0.514759i
$337$	20.3797	−	6.62178i	1.11016	−	0.360711i	0.304153	−	0.952623i	$-0.401627\pi$
$337$	20.3797	−	6.62178i	1.11016	−	0.360711i	0.806003	+	0.591912i	$0.201627\pi$
$338$	2.04582	+	0.263629i	0.111278	+	0.0143395i
$339$	10.9699	−	14.5366i	0.595805	−	0.789517i
$340$	−0.653053	+	2.46556i	−0.0354168	+	0.133714i
$341$	−3.08463	+	1.00226i	−0.167042	+	0.0542753i
$342$	25.7906	+	13.3814i	1.39460	+	0.723583i
$343$	19.4552			1.05048
$344$	9.52147	−	11.3358i	0.513363	−	0.611188i
$345$	4.56601	−	6.01778i	0.245825	−	0.323986i
$346$	−8.32386	+	4.54910i	−0.447494	+	0.244561i
$347$	−7.86215	+	10.8213i	−0.422062	+	0.580919i	−0.966109	−	0.258136i	$-0.916892\pi$
$347$	−7.86215	+	10.8213i	−0.422062	+	0.580919i	0.544046	+	0.839055i	$0.316892\pi$
$348$	0.390426	+	9.82944i	0.0209290	+	0.526913i
$349$	−12.3010			−0.658459			−0.329229	−	0.944250i	$-0.606789\pi$
$349$	−12.3010			−0.658459			−0.329229	+	0.944250i	$0.606789\pi$
$350$	−11.3308	+	6.11578i	−0.605658	+	0.326902i
$351$	−14.8248	+	9.58348i	−0.791291	+	0.511528i
$352$	3.69548	−	2.61519i	0.196970	−	0.139390i
$353$	15.1176	+	10.9836i	0.804629	+	0.584597i	0.912268	−	0.409593i	$-0.134329\pi$
$353$	15.1176	+	10.9836i	0.804629	+	0.584597i	−0.107640	+	0.994190i	$0.534329\pi$
$354$	20.2754	−	3.43565i	1.07762	−	0.182603i
$355$	−0.0714653	+	27.3526i	−0.00379298	+	1.45172i
$356$	−6.87023	+	26.2146i	−0.364122	+	1.38937i
$357$	−1.70038	−	0.586809i	−0.0899935	−	0.0310572i
$358$	2.98470	+	15.8610i	0.157746	+	0.838279i
$359$	6.92004	+	21.2977i	0.365225	+	1.12405i	0.949840	+	0.312737i	$0.101246\pi$
$359$	6.92004	+	21.2977i	0.365225	+	1.12405i	−0.584614	+	0.811311i	$0.698754\pi$
$360$	7.79517	−	17.2984i	0.410842	−	0.911707i
$361$	−8.62190	+	26.5355i	−0.453784	+	1.39660i
$362$	−10.2983	−	1.32706i	−0.541267	−	0.0697488i
$363$	0.325619	−	17.9402i	0.0170905	−	0.941618i
$364$	4.49719	+	11.5261i	0.235717	+	0.604134i
$365$	8.65765	+	26.8843i	0.453162	+	1.40719i
$366$	28.6554	+	14.2138i	1.49784	+	0.742968i
$367$	−20.4151	+	14.8325i	−1.06566	+	0.774248i	−0.975127	−	0.221646i	$-0.928857\pi$
$367$	−20.4151	+	14.8325i	−1.06566	+	0.774248i	−0.0905333	+	0.995893i	$0.528857\pi$
$368$	7.64854	+	1.53821i	0.398707	+	0.0801848i
$369$	1.15003	−	31.6705i	0.0598681	−	1.64870i
$370$	2.07732	+	11.2000i	0.107994	+	0.582260i
$371$	11.2229	+	8.15388i	0.582662	+	0.423329i
$372$	−13.5134	−	3.80490i	−0.700636	−	0.197275i
$373$	5.54492	+	1.80165i	0.287105	+	0.0932862i	0.449029	−	0.893517i	$-0.351770\pi$
$373$	5.54492	+	1.80165i	0.287105	+	0.0932862i	−0.161924	+	0.986803i	$0.551770\pi$
$374$	0.276295	−	0.583379i	0.0142869	−	0.0301658i
$375$	−15.3655	−	11.7856i	−0.793471	−	0.608608i
$376$	8.02845	+	32.2684i	0.414036	+	1.66412i
$377$	2.98121	−	9.17522i	0.153540	−	0.472548i
$378$	11.7637	+	6.37715i	0.605061	+	0.328005i
$379$	6.83449	−	9.40687i	0.351064	−	0.483199i	−0.596568	−	0.802563i	$-0.703469\pi$
$379$	6.83449	−	9.40687i	0.351064	−	0.483199i	0.947632	+	0.319364i	$0.103469\pi$
$380$	29.6062	+	7.84180i	1.51877	+	0.402276i
$381$	1.90825	−	0.581960i	0.0977624	−	0.0298147i
$382$	14.7415	−	31.1258i	0.754243	−	1.59253i
$383$	−7.25747	−	9.98905i	−0.370839	−	0.510416i	0.582289	−	0.812982i	$-0.302157\pi$
$383$	−7.25747	−	9.98905i	−0.370839	−	0.510416i	−0.953129	+	0.302565i	$0.902157\pi$
$384$	19.5886	−	0.533691i	0.999629	−	0.0272348i
$385$	3.10178	−	0.998876i	0.158081	−	0.0509074i
$386$	−2.16186	+	2.29068i	−0.110036	+	0.116592i
$387$	−5.39092	+	14.7476i	−0.274036	+	0.749664i
$388$	−0.948123	−	0.608347i	−0.0481336	−	0.0308841i
$389$	11.4198	+	3.71053i	0.579009	+	0.188131i	0.583857	−	0.811857i	$-0.301543\pi$
$389$	11.4198	+	3.71053i	0.579009	+	0.188131i	−0.00484763	+	0.999988i	$0.501543\pi$
$390$	−13.0497	+	13.2645i	−0.660798	+	0.671675i
$391$	1.05793	−	0.343743i	0.0535020	−	0.0173838i
$392$	−6.70210	+	7.97922i	−0.338507	+	0.403012i
$393$	−3.43081	−	1.18399i	−0.173061	−	0.0597244i
$394$	1.14005	+	6.05833i	0.0574348	+	0.305214i
$395$	−0.847872	−	0.00221527i	−0.0426610	−	0.000111462i
$396$	−2.73809	+	3.94470i	−0.137594	+	0.198229i
$397$	−8.27856	+	11.3945i	−0.415489	+	0.571872i	−0.964546	−	0.263913i	$-0.914987\pi$
$397$	−8.27856	+	11.3945i	−0.415489	+	0.571872i	0.549057	+	0.835785i	$0.314987\pi$
$398$	−21.5807	+	22.8666i	−1.08174	+	1.14620i
$399$	−7.04635	+	20.4180i	−0.352759	+	1.02218i
$400$	4.04569	−	19.5865i	0.202284	−	0.979327i
$401$		−	17.2299i		−	0.860422i	−0.902728	−	0.430211i	$-0.858439\pi$
$401$		−	17.2299i		−	0.860422i	0.902728	−	0.430211i	$-0.141561\pi$
$402$	−10.9497	−	20.9294i	−0.546121	−	1.04386i
$403$	11.1385	+	8.09261i	0.554849	+	0.403122i
$404$	2.46449	−	0.142723i	0.122613	−	0.00710076i
$405$	−1.51206	+	20.0677i	−0.0751346	+	0.997173i
$406$	−7.18677	+	1.35240i	−0.356673	+	0.0671183i
$407$		−	2.88284i		−	0.142897i
$408$	2.39665	−	1.43617i	0.118652	−	0.0711012i
$409$	1.46342	+	4.50396i	0.0723617	+	0.222706i	0.980696	−	0.195538i	$-0.0626454\pi$
$409$	1.46342	+	4.50396i	0.0723617	+	0.222706i	−0.908334	+	0.418245i	$0.862645\pi$
$410$	−6.09200	−	32.8454i	−0.300862	−	1.62212i
$411$	−2.74698	+	3.64010i	−0.135498	+	0.179553i
$412$	6.59247	−	10.2745i	0.324788	−	0.506189i
$413$	4.72408	+	14.5392i	0.232457	+	0.715429i
$414$	−8.18237	+	1.23419i	−0.402142	+	0.0606572i
$415$	−3.86994	+	11.8054i	−0.189968	+	0.579504i
$416$	−18.2018	−	6.16593i	−0.892419	−	0.302309i
$417$	5.82454	+	19.0987i	0.285229	+	0.935267i
$418$	−7.00516	−	3.31773i	−0.342634	−	0.162275i
$419$	25.6302	−	18.6215i	1.25212	−	0.909717i	0.253776	−	0.967263i	$-0.418327\pi$
$419$	25.6302	−	18.6215i	1.25212	−	0.909717i	0.998343	+	0.0575456i	$0.0183275\pi$
$420$	13.5670	+	3.85827i	0.662000	+	0.188265i
$421$	−17.3178	−	12.5821i	−0.844020	−	0.613216i	0.0794709	−	0.996837i	$-0.474677\pi$
$421$	−17.3178	−	12.5821i	−0.844020	−	0.613216i	−0.923491	+	0.383621i	$0.874677\pi$
$422$	−6.99426	−	12.7980i	−0.340475	−	0.622995i
$423$	−19.6817	−	29.2669i	−0.956956	−	1.42301i
$424$	−20.9100	+	5.20245i	−1.01548	+	0.252653i
$425$	−0.867019	−	2.71663i	−0.0420566	−	0.131776i
$426$	20.9578	−	21.4144i	1.01541	−	1.03753i
$427$	−7.34808	+	22.6151i	−0.355598	+	1.09442i
$428$	2.00471	−	0.116097i	0.0969015	−	0.00561176i
$429$	3.85943	−	2.69841i	0.186335	−	0.130280i
$430$	−2.15824	+	16.4101i	−0.104080	+	0.791366i
$431$	0.503603	−	0.365889i	0.0242577	−	0.0176243i	−0.575590	−	0.817738i	$-0.695228\pi$
$431$	0.503603	−	0.365889i	0.0242577	−	0.0176243i	0.599848	+	0.800114i	$0.295228\pi$
$432$	−19.3371	+	7.62075i	−0.930358	+	0.366654i
$433$	4.45711	+	6.13469i	0.214195	+	0.294814i	0.902572	−	0.430539i	$-0.141676\pi$
$433$	4.45711	+	6.13469i	0.214195	+	0.294814i	−0.688377	+	0.725353i	$0.741676\pi$
$434$	1.33383	−	10.3508i	0.0640257	−	0.496854i
$435$	−6.27854	−	9.03011i	−0.301033	−	0.432961i
$436$	−36.3089	+	14.1668i	−1.73888	+	0.678465i
$437$	−4.12764	−	12.7036i	−0.197452	−	0.607694i
$438$	13.7485	−	27.7172i	0.656927	−	1.32438i
$439$	−8.83207	−	2.86971i	−0.421532	−	0.136964i	0.0905673	−	0.995890i	$-0.471132\pi$
$439$	−8.83207	−	2.86971i	−0.421532	−	0.136964i	−0.512099	+	0.858926i	$0.671132\pi$
$440$	−1.91068	+	4.68711i	−0.0910883	+	0.223449i
$441$	3.79463	−	10.3808i	0.180697	−	0.494322i
$442$	−2.69285	+	0.506736i	−0.128086	+	0.0241030i
$443$			35.1121i			1.66823i	0.551593	+	0.834114i	$0.314020\pi$
$443$			35.1121i			1.66823i	−0.551593	+	0.834114i	$0.685980\pi$
$444$	6.92808	−	10.3782i	0.328792	−	0.492530i
$445$	−9.28748	−	28.8401i	−0.440269	−	1.36715i
$446$	7.95432	−	4.34714i	0.376648	−	0.205843i
$447$	11.2884	−	7.89256i	0.533925	−	0.373305i
$448$	2.51540	+	14.3487i	0.118842	+	0.677911i
$449$			10.5162i			0.496290i	0.968723	+	0.248145i	$0.0798210\pi$
$449$			10.5162i			0.496290i	−0.968723	+	0.248145i	$0.920179\pi$
$450$	3.05426	+	20.9922i	0.143979	+	0.989581i
$451$			8.45429i			0.398097i
$452$	−19.5902	+	7.64358i	−0.921446	+	0.359524i
$453$	−19.7479	+	13.8072i	−0.927838	+	0.648719i
$454$	4.41818	+	8.08430i	0.207356	+	0.379415i
$455$	−11.1697	−	8.15992i	−0.523642	−	0.382543i
$456$	−17.2455	−	28.7788i	−0.807593	−	1.34769i
$457$			35.6181i			1.66614i	0.553165	+	0.833072i	$0.313420\pi$
$457$			35.6181i			1.66614i	−0.553165	+	0.833072i	$0.686580\pi$
$458$	4.11332	+	21.8586i	0.192203	+	1.02139i
$459$	−1.86979	+	2.29918i	−0.0872744	+	0.107317i
$460$	−8.13417	+	3.14928i	−0.379258	+	0.146836i
$461$	30.8965	+	10.0389i	1.43899	+	0.467557i	0.921583	−	0.388182i	$-0.126897\pi$
$461$	30.8965	+	10.0389i	1.43899	+	0.467557i	0.517409	+	0.855739i	$0.326897\pi$
$462$	−3.19787	−	1.58623i	−0.148779	−	0.0737980i
$463$	−1.66383	−	5.12073i	−0.0773245	−	0.237980i	0.904921	−	0.425579i	$-0.139930\pi$
$463$	−1.66383	−	5.12073i	−0.0773245	−	0.237980i	−0.982246	+	0.187599i	$0.939930\pi$
$464$	5.57120	−	9.89893i	0.258636	−	0.459546i
$465$	15.0251	−	4.53936i	0.696774	−	0.210508i
$466$	−31.2370	−	4.02527i	−1.44703	−	0.186467i
$467$	6.84008	+	9.41456i	0.316521	+	0.435654i	0.937401	−	0.348252i	$-0.113225\pi$
$467$	6.84008	+	9.41456i	0.316521	+	0.435654i	−0.620880	+	0.783906i	$0.713225\pi$
$468$	20.3789	−	0.439254i	0.942014	−	0.0203045i
$469$	14.2059	−	10.3212i	0.655967	−	0.476588i
$470$	−26.9707	−	25.5875i	−1.24406	−	1.18026i
$471$	−13.4131	+	9.37804i	−0.618041	+	0.432117i
$472$	−22.0122	−	8.90621i	−1.01320	−	0.409941i
$473$	1.29442	−	3.98381i	0.0595175	−	0.183176i
$474$	0.663799	+	0.649646i	0.0304893	+	0.0298392i
$475$	−32.6211	+	10.4111i	−1.49676	+	0.477694i
$476$	1.31597	+	1.60698i	0.0603175	+	0.0736558i
$477$	18.9650	−	12.7537i	0.868348	−	0.583954i
$478$	−1.54374	+	0.843677i	−0.0706092	+	0.0385889i
$479$	−12.5883	−	9.14595i	−0.575175	−	0.417889i	0.261806	−	0.965120i	$-0.415682\pi$
$479$	−12.5883	−	9.14595i	−0.575175	−	0.417889i	−0.836981	+	0.547231i	$0.815682\pi$
$480$	−18.1426	+	12.2819i	−0.828094	+	0.560589i
$481$	−9.90033	+	7.19301i	−0.451416	+	0.327973i
$482$	−7.08019	+	14.9493i	−0.322494	+	0.680924i
$483$	−1.79445	−	5.88399i	−0.0816501	−	0.267731i
$484$	−11.1889	+	17.4381i	−0.508585	+	0.792640i
$485$	1.25947	+	0.00329068i	0.0571896	+	0.000149422i
$486$	16.5217	−	14.5957i	0.749440	−	0.662073i
$487$	−3.42465	−	10.5400i	−0.155186	−	0.477613i	0.842994	−	0.537923i	$-0.180791\pi$
$487$	−3.42465	−	10.5400i	−0.155186	−	0.477613i	−0.998180	+	0.0603102i	$0.980791\pi$
$488$	−19.5572	−	31.3326i	−0.885313	−	1.41836i
$489$	21.3505	−	28.2922i	0.965503	−	1.27942i
$490$	1.51917	−	11.5510i	0.0686293	−	0.521819i
$491$	−9.09567	−	27.9936i	−0.410482	−	1.26333i	−0.916230	−	0.400652i	$-0.868784\pi$
$491$	−9.09567	−	27.9936i	−0.410482	−	1.26333i	0.505748	−	0.862681i	$-0.331216\pi$
$492$	−20.3175	+	30.4355i	−0.915983	+	1.37214i
$493$		−	1.61959i		−	0.0729425i
$494$	6.08485	+	32.3355i	0.273770	+	1.45484i
$495$	0.208836	−	5.36457i	0.00938648	−	0.241119i
$496$	10.9786	+	11.9271i	0.492953	+	0.535542i
$497$	18.0205	+	13.0927i	0.808331	+	0.587287i
$498$	12.0587	−	6.30879i	0.540362	−	0.282704i
$499$		−	7.05232i		−	0.315705i	−0.987463	−	0.157853i	$-0.949543\pi$
$499$		−	7.05232i		−	0.315705i	0.987463	−	0.157853i	$-0.0504571\pi$
$500$	7.96426	+	20.8943i	0.356172	+	0.934420i
$501$	−0.0470795	+	0.136421i	−0.00210336	+	0.00609483i
$502$	−24.1248	−	22.7681i	−1.07674	−	1.01619i
$503$	−3.33390	+	4.58871i	−0.148651	+	0.204601i	−0.876849	−	0.480767i	$-0.840358\pi$
$503$	−3.33390	+	4.58871i	−0.148651	+	0.204601i	0.728197	+	0.685367i	$0.240358\pi$
$504$	−7.70034	−	13.3956i	−0.343000	−	0.596689i
$505$	−2.23712	+	1.61645i	−0.0995503	+	0.0719309i
$506$	2.16942	−	0.408239i	0.0964425	−	0.0181484i
$507$	2.38812	+	0.824151i	0.106060	+	0.0366018i
$508$	−2.22839	−	0.584007i	−0.0988687	−	0.0259111i
$509$	−20.5138	+	6.66534i	−0.909259	+	0.295436i	−0.726053	−	0.687638i	$-0.758647\pi$
$509$	−20.5138	+	6.66534i	−0.909259	+	0.295436i	−0.183206	+	0.983075i	$0.558647\pi$
$510$	−1.39541	+	2.79482i	−0.0617899	+	0.123757i
$511$	21.8747	+	7.10751i	0.967678	+	0.314418i
$512$	−19.5791	−	11.3428i	−0.865281	−	0.501286i
$513$	27.6084	+	22.4523i	1.21894	+	0.991293i
$514$	26.7407	+	25.2369i	1.17948	+	1.11315i
$515$	−0.0356600	+	13.6485i	−0.00157137	+	0.601425i
$516$	14.2339	−	11.2310i	0.626612	−	0.494418i
$517$	5.53033	+	7.61185i	0.243224	+	0.334769i
$518$	8.38353	+	3.97054i	0.368351	+	0.174455i
$519$	−11.1124	+	3.38897i	−0.487782	+	0.148759i
$520$	20.8640	−	5.13316i	0.914948	−	0.225104i
$521$	−9.57343	+	13.1767i	−0.419420	+	0.577282i	−0.965484	−	0.260461i	$-0.916125\pi$
$521$	−9.57343	+	13.1767i	−0.419420	+	0.577282i	0.546065	+	0.837743i	$0.316125\pi$
$522$	−1.97241	+	11.8855i	−0.0863301	+	0.520214i
$523$	7.50639	−	23.1023i	0.328231	−	1.01019i	−0.641729	−	0.766931i	$-0.721783\pi$
$523$	7.50639	−	23.1023i	0.328231	−	1.01019i	0.969961	−	0.243261i	$-0.0782173\pi$
$524$	2.65521	+	3.24237i	0.115993	+	0.141643i
$525$	−15.1077	+	4.52127i	−0.659356	+	0.197324i
$526$	9.38002	+	4.44249i	0.408988	+	0.193702i
$527$	2.19821	+	0.714243i	0.0957557	+	0.0311129i
$528$	5.08138	−	2.21884i	0.221139	−	0.0965626i
$529$	−15.5298	−	11.2830i	−0.675208	−	0.490567i
$530$	16.5807	−	17.4770i	0.720220	−	0.759153i
$531$	25.1695	+	0.913965i	1.09227	+	0.0396627i
$532$	19.2965	−	15.8021i	0.836608	−	0.685107i
$533$	29.0340	−	21.0944i	1.25760	−	0.913702i
$534$	−14.7486	+	29.7336i	−0.638236	+	1.28670i
$535$	−1.81976	+	1.31488i	−0.0786751	+	0.0568474i
$536$	−1.91607	+	27.2074i	−0.0827615	+	1.17518i
$537$	−0.358709	+	19.7634i	−0.0154794	+	0.852852i
$538$	−3.74424	+	29.0561i	−0.161425	+	1.25270i
$539$	−0.911133	+	2.80418i	−0.0392453	+	0.120785i
$540$	13.6440	−	18.8106i	0.587146	−	0.809481i
$541$	−3.44912	−	10.6153i	−0.148289	−	0.456387i	0.849130	−	0.528184i	$-0.177127\pi$
$541$	−3.44912	−	10.6153i	−0.148289	−	0.456387i	−0.997419	+	0.0717967i	$0.977127\pi$
$542$	−4.02135	+	0.756731i	−0.172732	+	0.0325044i
$543$	−12.0214	−	4.14863i	−0.515886	−	0.178035i
$544$	−3.22600	−	0.0402015i	−0.138314	−	0.00172363i
$545$	25.7048	−	35.1860i	1.10107	−	1.50720i
$546$	2.53159	+	14.9401i	0.108342	+	0.639376i
$547$	1.81953	+	1.32197i	0.0777977	+	0.0565233i	0.626004	−	0.779820i	$-0.284689\pi$
$547$	1.81953	+	1.32197i	0.0777977	+	0.0565233i	−0.548207	+	0.836343i	$0.684689\pi$
$548$	4.90558	−	1.91403i	0.209556	−	0.0817632i
$549$	30.8374	+	24.1619i	1.31611	+	1.03121i
$550$	−1.01746	−	5.56681i	−0.0433849	−	0.237370i
$551$	−19.4479			−0.828506
$552$	8.79103	+	3.74393i	0.374171	+	0.159352i
$553$	−0.405845	+	0.558597i	−0.0172583	+	0.0237540i
$554$	13.5199	+	24.7385i	0.574406	+	1.05104i
$555$	−0.289617	+	13.9481i	−0.0122935	+	0.592063i
$556$	5.84504	−	22.3028i	0.247885	−	0.945850i
$557$	16.9838			0.719626			0.359813	−	0.933024i	$-0.382840\pi$
$557$	16.9838			0.719626			0.359813	+	0.933024i	$0.382840\pi$
$558$	−15.2620	−	7.91864i	−0.646091	−	0.335223i
$559$	−16.9111	+	5.49474i	−0.715263	+	0.232403i
$560$	−10.9989	−	12.0120i	−0.464790	−	0.507600i
$561$	0.476217	−	0.631048i	0.0201059	−	0.0266429i
$562$	−0.579479	+	4.49689i	−0.0244439	+	0.189690i
$563$	32.4238	−	10.5351i	1.36650	−	0.444003i	0.468293	−	0.883573i	$-0.344869\pi$
$563$	32.4238	−	10.5351i	1.36650	−	0.444003i	0.898208	+	0.439570i	$0.144869\pi$
$564$	1.61634	+	40.6934i	0.0680604	+	1.71350i
$565$	13.8689	−	18.9844i	0.583468	−	0.798678i
$566$	−19.4363	−	2.50460i	−0.816969	−	0.105276i
$567$	12.5249	+	10.5691i	0.525998	+	0.443862i
$568$	−33.5751	+	8.35356i	−1.40878	+	0.350507i
$569$	−17.1184	−	23.5614i	−0.717640	−	0.987747i	−0.999599	−	0.0283201i	$-0.990984\pi$
$569$	−17.1184	−	23.5614i	−0.717640	−	0.987747i	0.281959	−	0.959426i	$-0.409016\pi$
$570$	33.5599	+	16.7560i	1.40567	+	0.701831i
$571$	16.1661	−	22.2507i	0.676529	−	0.931162i	−0.323357	−	0.946277i	$-0.604812\pi$
$571$	16.1661	−	22.2507i	0.676529	−	0.931162i	0.999886	+	0.0151153i	$0.00481154\pi$
$572$	−5.42863	+	0.314383i	−0.226982	+	0.0131450i
$573$	25.4082	−	33.6692i	1.06144	−	1.40655i
$574$	−24.5858	−	11.6441i	−1.02619	−	0.486016i
$575$	5.77329	−	7.85955i	0.240763	−	0.327766i
$576$	23.6254	+	4.22381i	0.984392	+	0.175992i
$577$	−12.8350	−	4.17033i	−0.534326	−	0.173613i	0.0294110	−	0.999567i	$-0.490637\pi$
$577$	−12.8350	−	4.17033i	−0.534326	−	0.173613i	−0.563737	+	0.825954i	$0.690637\pi$
$578$	20.6930	−	11.3090i	0.860715	−	0.470392i
$579$	−3.16151	+	2.21044i	−0.131388	+	0.0918629i
$580$	0.701111	+	12.6804i	0.0291120	+	0.526525i
$581$	5.94666	+	8.18487i	0.246709	+	0.339566i
$582$	−0.986041	−	0.965017i	−0.0408727	−	0.0400012i
$583$	−4.93249	+	3.58366i	−0.204283	+	0.148420i
$584$	−30.3068	+	18.9169i	−1.25410	+	0.782788i
$585$	−18.9443	+	12.6680i	−0.783249	+	0.523759i
$586$	31.4645	+	29.6950i	1.29978	+	1.22669i
$587$	−19.9702	+	6.48872i	−0.824259	+	0.267818i	−0.690625	−	0.723213i	$-0.742665\pi$
$587$	−19.9702	+	6.48872i	−0.824259	+	0.267818i	−0.133634	+	0.991031i	$0.542665\pi$
$588$	−10.0191	+	7.90543i	−0.413183	+	0.326015i
$589$	8.57657	−	26.3960i	0.353392	−	1.08763i
$590$	26.1033	−	4.84150i	1.07466	−	0.199322i
$591$	−0.137014	+	7.54889i	−0.00563600	+	0.310520i
$592$	−13.0978	+	6.00462i	−0.538317	+	0.246789i
$593$	−25.7697			−1.05824			−0.529118	−	0.848548i	$-0.677477\pi$
$593$	−25.7697			−1.05824			−0.529118	+	0.848548i	$0.677477\pi$
$594$	−4.26329	+	4.05105i	−0.174925	+	0.166217i
$595$	−2.20668	−	0.723373i	−0.0904651	−	0.0296554i
$596$	−15.8782	+	0.919537i	−0.650395	+	0.0376657i
$597$	−31.5597	+	22.0657i	−1.29165	+	0.903089i
$598$	−6.81495	−	6.43170i	−0.278684	−	0.263012i
$599$	33.3719			1.36354			0.681770	−	0.731566i	$-0.261210\pi$
$599$	33.3719			1.36354			0.681770	+	0.731566i	$0.261210\pi$
$600$	9.71538	−	22.4858i	0.396629	−	0.917979i
$601$	−23.8413			−0.972507			−0.486254	−	0.873818i	$-0.661637\pi$
$601$	−23.8413			−0.972507			−0.486254	+	0.873818i	$0.661637\pi$
$602$	9.80246	+	9.25120i	0.399518	+	0.377051i
$603$	−7.93532	−	27.8196i	−0.323151	−	1.13290i
$604$	27.7772	−	1.60863i	1.13024	−	0.0654543i
$605$	0.0605228	−	23.1645i	0.00246060	−	0.941770i
$606$	2.99113	+	0.440763i	0.121506	+	0.0179048i
$607$	35.6213			1.44583			0.722913	−	0.690940i	$-0.242803\pi$
$607$	35.6213			1.44583			0.722913	+	0.690940i	$0.242803\pi$
$608$	−0.482737	+	38.7376i	−0.0195776	+	1.57102i
$609$	−8.95497	−	0.162534i	−0.362874	−	0.00658623i
$610$	37.2745	+	17.7730i	1.50920	+	0.719609i
$611$	12.3420	−	37.9849i	0.499306	−	1.53671i
$612$	3.23093	−	1.12733i	0.130603	−	0.0455696i
$613$	13.0452	−	4.23863i	0.526889	−	0.171197i	−0.0334802	−	0.999439i	$-0.510659\pi$
$613$	13.0452	−	4.23863i	0.526889	−	0.171197i	0.560370	+	0.828243i	$0.310659\pi$
$614$	−3.82841	−	3.61312i	−0.154502	−	0.145814i
$615$	0.849339	−	40.9046i	0.0342486	−	1.64943i
$616$	2.18254	+	3.49665i	0.0879371	+	0.140884i
$617$	15.5169	−	11.2737i	0.624686	−	0.453861i	−0.229869	−	0.973222i	$-0.573830\pi$
$617$	15.5169	−	11.2737i	0.624686	−	0.453861i	0.854555	+	0.519361i	$0.173830\pi$
$618$	10.4576	−	10.6854i	0.420666	−	0.429831i
$619$	−4.26674	−	5.87266i	−0.171495	−	0.236042i	0.714615	−	0.699518i	$-0.246602\pi$
$619$	−4.26674	−	5.87266i	−0.171495	−	0.236042i	−0.886109	+	0.463476i	$0.846602\pi$
$620$	−17.5199	−	4.64050i	−0.703616	−	0.186367i
$621$	−10.1197	−	0.551506i	−0.406088	−	0.0221312i
$622$	29.7196	−	16.2422i	1.19165	−	0.651251i
$623$	−23.4660	−	7.62457i	−0.940146	−	0.305472i
$624$	−20.2987	−	11.9144i	−0.812597	−	0.476957i
$625$	−20.0708	−	14.9052i	−0.802830	−	0.596208i
$626$	−37.3558	−	17.6922i	−1.49304	−	0.707121i
$627$	−7.57757	−	5.71837i	−0.302619	−	0.228370i
$628$	18.8666	−	1.09260i	0.752860	−	0.0435997i
$629$	−1.20755	+	1.66205i	−0.0481481	+	0.0662702i
$630$	15.3130	+	7.99595i	0.610084	+	0.318566i
$631$	11.1723	+	15.3773i	0.444761	+	0.612162i	0.971262	−	0.238013i	$-0.0764962\pi$
$631$	11.1723	+	15.3773i	0.444761	+	0.612162i	−0.526501	+	0.850175i	$0.676496\pi$
$632$	−0.258942	−	1.04076i	−0.0103002	−	0.0413991i
$633$	−5.21056	−	17.0854i	−0.207101	−	0.679084i
$634$	2.01810	+	0.260057i	0.0801490	+	0.0103282i
$635$	2.45157	−	0.789487i	0.0972875	−	0.0313298i
$636$	−26.3693	+	1.04739i	−1.04561	+	0.0415318i
$637$	11.9036	−	3.86771i	0.471638	−	0.153244i
$638$	0.410773	−	3.18769i	0.0162627	−	0.126202i
$639$	30.4521	−	20.4787i	1.20467	−	0.810124i
$640$	25.2751	−	1.08177i	0.999085	−	0.0427606i
$641$	−14.5392	+	4.72407i	−0.574263	+	0.186589i	−0.581729	−	0.813383i	$-0.697624\pi$
$641$	−14.5392	+	4.72407i	−0.574263	+	0.186589i	0.00746563	+	0.999972i	$0.497624\pi$
$642$	2.43310	+	0.358535i	0.0960269	+	0.0141502i
$643$	−14.5941			−0.575536			−0.287768	−	0.957700i	$-0.592913\pi$
$643$	−14.5941			−0.575536			−0.287768	+	0.957700i	$0.592913\pi$
$644$	−1.80076	+	6.87113i	−0.0709599	+	0.270760i
$645$	−6.66304	+	19.1449i	−0.262357	+	0.753831i
$646$	2.64899	+	4.84707i	0.104223	+	0.190705i
$647$	25.2315	−	34.7282i	0.991952	−	1.36531i	0.0618172	−	0.998087i	$-0.480310\pi$
$647$	25.2315	−	34.7282i	0.991952	−	1.36531i	0.930135	−	0.367218i	$-0.119690\pi$
$648$	−25.0835	+	4.33824i	−0.985371	+	0.170422i
$649$	−6.71889			−0.263740
$650$	−16.5791	+	17.3841i	−0.650284	+	0.681860i
$651$	4.16978	−	12.0826i	0.163426	−	0.473556i
$652$	−38.1280	+	14.8765i	−1.49321	+	0.582610i
$653$	−0.112789	−	0.0819458i	−0.00441377	−	0.00320679i	0.585576	−	0.810617i	$-0.300868\pi$
$653$	−0.112789	−	0.0819458i	−0.00441377	−	0.00320679i	−0.589990	+	0.807411i	$0.700868\pi$
$654$	−47.0633	+	7.97485i	−1.84032	+	0.311841i
$655$	−4.45237	−	1.45953i	−0.173968	−	0.0570287i
$656$	38.4110	−	17.6093i	1.49970	−	0.687529i
$657$	23.3709	−	29.8278i	0.911785	−	1.16369i
$658$	−29.7528	+	5.59885i	−1.15989	+	0.218266i
$659$	6.59221	+	20.2887i	0.256796	+	0.790337i	0.993470	+	0.114089i	$0.0363950\pi$
$659$	6.59221	+	20.2887i	0.256796	+	0.790337i	−0.736674	+	0.676248i	$0.763605\pi$
$660$	−3.45532	+	5.14688i	−0.134498	+	0.200342i
$661$	−5.23008	+	16.0965i	−0.203427	+	0.626083i	0.796348	+	0.604839i	$0.206763\pi$
$661$	−5.23008	+	16.0965i	−0.203427	+	0.626083i	−0.999774	+	0.0212437i	$0.993237\pi$
$662$	−4.62064	+	35.8573i	−0.179586	+	1.39363i
$663$	−3.35539	−	0.0609009i	−0.130312	−	0.00236519i
$664$	−15.6758	−	1.10396i	−0.608340	−	0.0428421i
$665$	−8.68621	+	26.4976i	−0.336837	+	1.02753i
$666$	10.8858	−	10.7265i	0.421818	−	0.415644i
$667$	4.48091	−	3.25557i	0.173502	−	0.126056i
$668$	0.128928	−	0.105580i	0.00498835	−	0.00408502i
$669$	10.6191	−	3.23852i	0.410558	−	0.125208i
$670$	−14.5540	−	26.7968i	−0.562271	−	1.03525i
$671$	−8.45496	−	6.14289i	−0.326400	−	0.237144i
$672$	−0.546029	+	17.8331i	−0.0210635	+	0.687927i
$673$	17.7151	+	5.75598i	0.682866	+	0.221877i	0.629850	−	0.776717i	$-0.283117\pi$
$673$	17.7151	+	5.75598i	0.682866	+	0.221877i	0.0530162	+	0.998594i	$0.483117\pi$
$674$	−27.3881	−	12.9713i	−1.05495	−	0.499637i
$675$	−1.54935	+	25.9345i	−0.0596346	+	0.998220i
$676$	−1.84823	−	2.25694i	−0.0710859	−	0.0868055i
$677$	−2.93522	+	9.03368i	−0.112810	+	0.347193i	−0.991484	−	0.130229i	$-0.958429\pi$
$677$	−2.93522	+	9.03368i	−0.112810	+	0.347193i	0.878674	+	0.477422i	$0.158429\pi$
$678$	−25.3927	+	4.30278i	−0.975199	+	0.165247i
$679$	0.602862	−	0.829769i	0.0231357	−	0.0318436i
$680$	3.06489	−	1.90194i	0.117533	−	0.0729359i
$681$	3.29144	+	10.7926i	0.126128	+	0.413575i
$682$	4.14541	+	1.96331i	0.158736	+	0.0751792i
$683$	1.42535	+	1.96183i	0.0545395	+	0.0750672i	0.835416	−	0.549619i	$-0.185227\pi$
$683$	1.42535	+	1.96183i	0.0545395	+	0.0750672i	−0.780876	+	0.624686i	$0.785227\pi$
$684$	−13.5369	−	38.7968i	−0.517596	−	1.48343i
$685$	−3.47290	+	4.75387i	−0.132693	+	0.181636i
$686$	−20.0097	−	18.8845i	−0.763975	−	0.721012i
$687$	−0.494349	+	27.2366i	−0.0188606	+	1.03914i
$688$	−20.7961	+	2.41680i	−0.792845	+	0.0921395i
$689$	24.6143	+	7.99766i	0.937729	+	0.304687i
$690$	−10.5374	+	1.75724i	−0.401151	+	0.0668971i
$691$	4.66222	−	1.51485i	0.177359	−	0.0576275i	−0.218991	−	0.975727i	$-0.570277\pi$
$691$	4.66222	−	1.51485i	0.177359	−	0.0576275i	0.396350	+	0.918099i	$0.370277\pi$
$692$	12.9767	+	3.40090i	0.493302	+	0.129283i
$693$	−3.44138	−	2.69641i	−0.130727	−	0.102428i
$694$	18.5901	−	3.49825i	0.705670	−	0.132792i
$695$	7.90158	+	24.5365i	0.299724	+	0.930723i
$696$	9.13951	−	10.4886i	0.346432	−	0.397568i
$697$	3.54129	−	4.87417i	0.134136	−	0.184622i
$698$	12.6516	+	11.9401i	0.478871	+	0.451941i
$699$	−36.4634	−	12.5837i	−1.37917	−	0.475959i
$700$	17.5901	+	4.70832i	0.664844	+	0.177958i
$701$			2.98414i			0.112710i	0.998411	+	0.0563548i	$0.0179478\pi$
$701$			2.98414i			0.112710i	−0.998411	+	0.0563548i	$0.982052\pi$
$702$	24.5497	+	4.53328i	0.926568	+	0.171098i
$703$	19.9577	+	14.5001i	0.752721	+	0.546883i
$704$	−6.33927	−	0.897331i	−0.238920	−	0.0338195i
$705$	−25.9928	−	37.3842i	−0.978946	−	1.40797i
$706$	−4.88713	−	25.9707i	−0.183930	−	0.977421i
$707$			2.24760i			0.0845296i
$708$	−24.1881	−	16.1470i	−0.909045	−	0.606840i
$709$	−1.13807	−	3.50262i	−0.0427411	−	0.131544i	0.927409	−	0.374049i	$-0.122031\pi$
$709$	−1.13807	−	3.50262i	−0.0427411	−	0.131544i	−0.970150	+	0.242505i	$0.922031\pi$
$710$	26.6236	−	28.0628i	0.999167	−	1.05318i
$711$	0.634795	+	0.943949i	0.0238067	+	0.0354009i
$712$	32.5116	−	20.2931i	1.21842	−	0.760517i
$713$	2.44259	+	7.51752i	0.0914757	+	0.281533i
$714$	1.17925	+	2.25402i	0.0441322	+	0.0843547i
$715$	4.92779	−	3.56061i	0.184289	−	0.133159i
$716$	12.3259	−	19.2102i	0.460640	−	0.717918i
$717$	−2.06091	+	0.628519i	−0.0769663	+	0.0234725i
$718$	13.5556	−	28.6217i	0.505890	−	1.06815i
$719$	−37.7629	+	27.4363i	−1.40832	+	1.02320i	−0.414753	+	0.909934i	$0.636132\pi$
$719$	−37.7629	+	27.4363i	−1.40832	+	1.02320i	−0.993564	+	0.113268i	$0.963868\pi$
$720$	−24.8083	+	10.2250i	−0.924549	+	0.381062i
$721$	8.99194	+	6.53303i	0.334878	+	0.243303i
$722$	34.6246	−	18.9228i	1.28859	−	0.704234i
$723$	−12.2033	+	16.1709i	−0.453845	+	0.601402i
$724$	9.30369	+	11.3611i	0.345769	+	0.422230i
$725$	−8.28568	−	11.5305i	−0.307723	−	0.428232i
$726$	−17.7488	+	18.1355i	−0.658720	+	0.673071i
$727$	−1.82280	+	5.61001i	−0.0676040	+	0.208064i	−0.979152	−	0.203131i	$-0.934888\pi$
$727$	−1.82280	+	5.61001i	−0.0676040	+	0.208064i	0.911548	+	0.411195i	$0.134888\pi$
$728$	6.56261	−	16.2199i	0.243227	−	0.601150i
$729$	23.4388	−	13.4024i	0.868103	−	0.496385i
$730$	17.1912	−	36.0542i	0.636274	−	1.33443i
$731$	−2.41500	+	1.75460i	−0.0893219	+	0.0648962i
$732$	−15.6753	−	42.4336i	−0.579375	−	1.56839i
$733$	0.998702	+	1.37460i	0.0368879	+	0.0507718i	0.827063	−	0.562110i	$-0.190010\pi$
$733$	0.998702	+	1.37460i	0.0368879	+	0.0507718i	−0.790175	+	0.612882i	$0.790010\pi$
$734$	35.3943	+	4.56098i	1.30643	+	0.168349i
$735$	4.69007	−	13.4760i	0.172996	−	0.497069i
$736$	−6.37345	−	9.00620i	−0.234928	−	0.331973i
$737$	2.38482	+	7.33972i	0.0878459	+	0.270362i
$738$	−31.9241	+	31.4568i	−1.17514	+	1.15794i
$739$	−27.5191	−	8.94150i	−1.01231	−	0.328918i	−0.244534	−	0.969641i	$-0.578635\pi$
$739$	−27.5191	−	8.94150i	−1.01231	−	0.328918i	−0.767773	+	0.640722i	$0.778635\pi$
$740$	8.73489	−	13.5356i	0.321101	−	0.497578i
$741$	−0.731293	+	40.2912i	−0.0268647	+	1.48013i
$742$	−3.62806	−	19.2799i	−0.133190	−	0.707787i
$743$		−	14.8662i		−	0.545390i	−0.962101	−	0.272695i	$-0.912085\pi$
$743$		−	14.8662i		−	0.545390i	0.962101	−	0.272695i	$-0.0879149\pi$
$744$	10.2053	+	17.0303i	0.374143	+	0.624360i
$745$	14.4133	−	10.4144i	0.528061	−	0.381555i
$746$	−3.95416	−	7.23525i	−0.144772	−	0.264901i
$747$	16.0286	−	4.57202i	0.586455	−	0.167282i
$748$	−0.850433	+	0.331817i	−0.0310949	+	0.0121324i
$749$			1.82829i			0.0668041i
$750$	4.36357	+	27.0363i	0.159335	+	0.987225i
$751$			25.3737i			0.925901i	0.886384	+	0.462950i	$0.153209\pi$
$751$			25.3737i			0.925901i	−0.886384	+	0.462950i	$0.846791\pi$
$752$	23.0645	−	40.9810i	0.841075	−	1.49442i
$753$	−23.2798	−	33.2962i	−0.848363	−	1.21338i
$754$	−11.9722	+	6.54298i	−0.436002	+	0.238281i
$755$	−25.2145	+	18.2189i	−0.917649	+	0.663054i
$756$	−5.90896	−	17.9775i	−0.214907	−	0.653836i
$757$			3.24743i			0.118030i	0.998257	+	0.0590150i	$0.0187960\pi$
$757$			3.24743i			0.118030i	−0.998257	+	0.0590150i	$0.981204\pi$
$758$	−16.1602	+	3.04100i	−0.586964	+	0.110454i
$759$	2.70318	+	0.0490632i	0.0981191	+	0.00178088i
$760$	−22.8383	−	36.8029i	−0.828431	−	1.33498i
$761$	−27.5057	−	8.93716i	−0.997082	−	0.323972i	−0.235383	−	0.971903i	$-0.575635\pi$
$761$	−27.5057	−	8.93716i	−0.997082	−	0.323972i	−0.761699	+	0.647931i	$0.775635\pi$
$762$	−2.52752	−	1.25372i	−0.0915624	−	0.0454173i
$763$	−10.9656	−	33.7485i	−0.396980	−	1.22178i
$764$	−45.3743	+	17.7039i	−1.64159	+	0.640503i
$765$	−2.36749	+	3.00537i	−0.0855967	+	0.108659i
$766$	−2.23167	+	17.3183i	−0.0806336	+	0.625736i
$767$	16.7644	+	23.0743i	0.605328	+	0.833163i
$768$	−20.6650	−	18.4651i	−0.745683	−	0.666300i
$769$	13.1748	−	9.57208i	0.475097	−	0.345178i	−0.324328	−	0.945945i	$-0.605138\pi$
$769$	13.1748	−	9.57208i	0.475097	−	0.345178i	0.799424	+	0.600767i	$0.205138\pi$
$770$	−4.15975	−	1.98343i	−0.149907	−	0.0714779i
$771$	25.8041	+	36.9066i	0.929312	+	1.32916i
$772$	4.44695	−	0.257532i	0.160049	−	0.00926877i
$773$	8.38178	−	25.7965i	0.301472	−	0.927835i	−0.679498	−	0.733677i	$-0.737803\pi$
$773$	8.38178	−	25.7965i	0.301472	−	0.927835i	0.980970	−	0.194158i	$-0.0621974\pi$
$774$	19.8595	−	9.93520i	0.713836	−	0.357113i
$775$	19.3040	−	6.16092i	0.693420	−	0.221307i
$776$	0.384646	+	1.54599i	0.0138080	+	0.0554979i
$777$	9.06857	+	6.84354i	0.325333	+	0.245511i
$778$	−8.14365	−	14.9011i	−0.291964	−	0.534230i
$779$	−58.5287	−	42.5236i	−2.09701	−	1.52356i
$780$	26.2970	−	0.975712i	0.941585	−	0.0349361i
$781$	−7.92009	+	5.75428i	−0.283403	+	0.205904i
$782$	−1.42174	−	0.673355i	−0.0508415	−	0.0240791i
$783$	−5.31671	+	13.7647i	−0.190004	+	0.491909i
$784$	14.6382	−	1.70117i	0.522795	−	0.0607560i
$785$	−17.1260	+	12.3745i	−0.611253	+	0.441666i
$786$	2.37934	+	4.54789i	0.0848682	+	0.162218i
$787$	2.84743	+	8.76347i	0.101500	+	0.312384i	0.988893	−	0.148629i	$-0.0474861\pi$
$787$	2.84743	+	8.76347i	0.101500	+	0.312384i	−0.887393	+	0.461013i	$0.847486\pi$
$788$	4.70805	−	7.33760i	0.167717	−	0.261391i
$789$	10.1465	+	7.65699i	0.361225	+	0.272596i
$790$	0.869887	+	0.825275i	0.0309492	+	0.0293620i
$791$	−5.91639	−	18.2088i	−0.210363	−	0.647430i
$792$	6.64509	−	1.39937i	0.236123	−	0.0497245i
$793$			44.3636i			1.57540i
$794$	19.5747	−	3.68353i	0.694679	−	0.130724i
$795$	24.2250	−	16.8434i	0.859172	−	0.597373i
$796$	44.3915	−	2.57080i	1.57342	−	0.0911197i
$797$	26.7271	+	19.4184i	0.946721	+	0.687833i	0.950029	−	0.312161i	$-0.101053\pi$
$797$	26.7271	+	19.4184i	0.946721	+	0.687833i	−0.00330770	+	0.999995i	$0.501053\pi$
$798$	27.0661	−	14.1603i	0.958131	−	0.501269i
$799$		−	6.70500i		−	0.237206i
$800$	−23.1729	+	16.2178i	−0.819286	+	0.573385i
$801$	−25.0711	+	31.9978i	−0.885843	+	1.13059i
$802$	−16.7244	+	17.7210i	−0.590561	+	0.625751i
$803$	−5.94178	+	8.17815i	−0.209681	+	0.288601i
$804$	−9.05356	+	32.1543i	−0.319294	+	1.13400i
$805$	−2.43435	−	7.55929i	−0.0857994	−	0.266430i
$806$	−3.60080	−	19.1350i	−0.126833	−	0.674002i
$807$	−11.7051	+	33.9176i	−0.412041	+	1.19396i
$808$	−2.67327	−	2.24539i	−0.0940451	−	0.0789927i
$809$	−43.7227	+	14.2064i	−1.53721	+	0.499469i	−0.950604	−	0.310405i	$-0.899535\pi$
$809$	−43.7227	+	14.2064i	−1.53721	+	0.499469i	−0.586604	+	0.809874i	$0.699535\pi$
$810$	21.0341	−	19.1720i	0.739064	−	0.673635i
$811$	−19.3987	−	6.30303i	−0.681182	−	0.221329i	−0.0520692	−	0.998643i	$-0.516582\pi$
$811$	−19.3987	−	6.30303i	−0.681182	−	0.221329i	−0.629113	+	0.777314i	$0.716582\pi$
$812$	8.70432	+	5.58498i	0.305462	+	0.195995i
$813$	−5.01074	−	0.0909459i	−0.175734	−	0.00318961i
$814$	−2.79826	+	2.96500i	−0.0980789	+	0.103923i
$815$	26.9927	−	36.9488i	0.945511	−	1.29426i
$816$	−3.85900	−	0.849232i	−0.135092	−	0.0297291i
$817$	21.0691	+	28.9991i	0.737113	+	1.01455i
$818$	2.86669	−	6.05282i	0.100231	−	0.211632i
$819$	−0.673463	+	18.5464i	−0.0235327	+	0.648064i
$820$	−25.6162	+	39.6949i	−0.894557	+	1.38620i
$821$	3.92568	−	5.40323i	0.137007	−	0.188574i	−0.735000	−	0.678067i	$-0.762818\pi$
$821$	3.92568	−	5.40323i	0.137007	−	0.188574i	0.872007	+	0.489493i	$0.162818\pi$
$822$	6.35857	−	1.07746i	0.221781	−	0.0375806i
$823$	−5.42342	+	16.6916i	−0.189048	+	0.581831i	−0.999995	−	0.00328953i	$-0.998953\pi$
$823$	−5.42342	+	16.6916i	−0.189048	+	0.581831i	0.810946	+	0.585121i	$0.198953\pi$
$824$	−16.7534	+	4.16829i	−0.583634	+	0.145209i
$825$	0.161985	−	6.92898i	0.00563960	−	0.241236i
$826$	9.25395	−	19.5391i	0.321986	−	0.679852i
$827$	−52.2944	−	16.9915i	−1.81845	−	0.590852i	−0.999864	−	0.0164732i	$-0.994756\pi$
$827$	−52.2944	−	16.9915i	−1.81845	−	0.590852i	−0.818590	−	0.574378i	$-0.805244\pi$
$828$	9.61357	+	6.67295i	0.334095	+	0.231901i
$829$	5.51800	+	4.00906i	0.191648	+	0.139241i	0.679472	−	0.733702i	$-0.262209\pi$
$829$	5.51800	+	4.00906i	0.191648	+	0.139241i	−0.487824	+	0.872942i	$0.662209\pi$
$830$	15.4393	−	8.38547i	0.535905	−	0.291064i
$831$	10.0720	+	33.0261i	0.349394	+	1.14566i
$832$	12.7356	+	24.0095i	0.441527	+	0.832380i
$833$	1.69990	−	1.23505i	0.0588981	−	0.0427919i
$834$	12.5478	−	25.2967i	0.434495	−	0.875953i
$835$	−0.0580361	+	0.177041i	−0.00200842	+	0.00612677i
$836$	3.98443	+	10.2119i	0.137804	+	0.353187i
$837$	−16.3377	−	13.2865i	−0.564712	−	0.459247i
$838$	−44.4359	−	5.72610i	−1.53501	−	0.197805i
$839$	−15.1216	+	46.5395i	−0.522055	+	1.60672i	0.248012	+	0.968757i	$0.420223\pi$
$839$	−15.1216	+	46.5395i	−0.522055	+	1.60672i	−0.770067	+	0.637963i	$0.779777\pi$
$840$	−10.2086	−	17.1372i	−0.352228	−	0.591288i
$841$	6.46952	+	19.9111i	0.223087	+	0.686591i
$842$	5.59841	+	29.7505i	0.192934	+	1.02527i
$843$	−1.81156	+	5.24929i	−0.0623933	+	0.180795i
$844$	−5.22889	+	19.9518i	−0.179986	+	0.686769i
$845$	3.09920	+	1.01595i	0.106616	+	0.0349498i
$846$	−8.16568	+	49.2053i	−0.280742	+	1.69171i
$847$	−15.2613	−	11.0880i	−0.524384	−	0.380988i
$848$	26.5558	+	14.9458i	0.911929	+	0.513241i
$849$	−22.6883	−	7.82984i	−0.778660	−	0.268719i
$850$	−1.74520	+	3.63564i	−0.0598599	+	0.124702i
$851$	−7.02572			−0.240838
$852$	−42.3412	+	1.68180i	−1.45059	+	0.0576174i
$853$	9.90539	−	13.6336i	0.339154	−	0.466806i	−0.605040	−	0.796195i	$-0.706843\pi$
$853$	9.90539	−	13.6336i	0.339154	−	0.466806i	0.944194	+	0.329389i	$0.106843\pi$
$854$	29.5091	−	16.1271i	1.00978	−	0.551859i
$855$	36.0883	+	28.4286i	1.23419	+	0.972237i
$856$	−2.17454	−	1.82649i	−0.0743243	−	0.0624283i
$857$	22.3994			0.765150			0.382575	−	0.923924i	$-0.375037\pi$
$857$	22.3994			0.765150			0.382575	+	0.923924i	$0.375037\pi$
$858$	−6.58867	−	0.970887i	−0.224934	−	0.0331455i
$859$	−23.1034	+	7.50675i	−0.788278	+	0.256127i	−0.675370	−	0.737479i	$-0.736016\pi$
$859$	−23.1034	+	7.50675i	−0.788278	+	0.256127i	−0.112907	+	0.993606i	$0.536016\pi$
$860$	18.1484	−	14.7829i	0.618856	−	0.504092i
$861$	−26.5948	−	20.0696i	−0.906347	−	0.683969i
$862$	−0.873112	−	0.112511i	−0.0297383	−	0.00383214i
$863$	33.1359	−	10.7665i	1.12796	−	0.366496i	0.315159	−	0.949039i	$-0.397942\pi$
$863$	33.1359	−	10.7665i	1.12796	−	0.366496i	0.812800	+	0.582543i	$0.197942\pi$
$864$	27.2854	+	10.9319i	0.928269	+	0.371909i
$865$	−14.2764	+	4.59748i	−0.485412	+	0.156319i
$866$	1.37056	−	10.6359i	0.0465736	−	0.361422i
$867$	27.6254	−	8.42493i	0.938206	−	0.286126i
$868$	−11.4190	+	9.35111i	−0.387585	+	0.317397i
$869$	−0.178370	−	0.245506i	−0.00605080	−	0.00832821i
$870$	−2.30770	+	15.3818i	−0.0782382	+	0.521492i
$871$	19.2559	−	26.5035i	0.652462	−	0.898037i
$872$	51.0949	+	20.6731i	1.73029	+	0.700080i
$873$	−0.942956	−	1.40219i	−0.0319142	−	0.0474569i
$874$	−8.08559	+	17.0722i	−0.273499	+	0.577475i
$875$	−19.4110	+	6.13922i	−0.656211	+	0.207544i
$876$	−41.0444	+	15.1621i	−1.38676	+	0.512280i
$877$	16.7709	+	5.44918i	0.566311	+	0.184006i	0.578159	−	0.815924i	$-0.303771\pi$
$877$	16.7709	+	5.44918i	0.566311	+	0.184006i	−0.0118476	+	0.999930i	$0.503771\pi$
$878$	6.29828	+	11.5245i	0.212557	+	0.388932i
$879$	30.3624	+	43.4262i	1.02410	+	1.46473i
$880$	6.51474	−	2.96607i	0.219612	−	0.0999863i
$881$	11.5775	+	15.9351i	0.390056	+	0.536866i	0.958214	−	0.286054i	$-0.0923436\pi$
$881$	11.5775	+	15.9351i	0.390056	+	0.536866i	−0.568158	+	0.822920i	$0.692344\pi$
$882$	−13.9790	+	6.99332i	−0.470697	+	0.235477i
$883$	0.877936	−	0.637858i	0.0295449	−	0.0214656i	−0.572915	−	0.819615i	$-0.694187\pi$
$883$	0.877936	−	0.637858i	0.0295449	−	0.0214656i	0.602460	+	0.798149i	$0.294187\pi$
$884$	3.26147	+	2.09267i	0.109695	+	0.0703840i
$885$	32.5082	+	0.674997i	1.09275	+	0.0226898i
$886$	34.0820	−	36.1129i	1.14501	−	1.21324i
$887$	21.9230	−	7.12322i	0.736103	−	0.239174i	0.0831120	−	0.996540i	$-0.473514\pi$
$887$	21.9230	−	7.12322i	0.736103	−	0.239174i	0.652991	+	0.757366i	$0.273514\pi$
$888$	−17.1993	+	3.94922i	−0.577171	+	0.132527i
$889$	0.648131	−	1.99474i	0.0217376	−	0.0669015i
$890$	−18.4418	+	38.6771i	−0.618171	+	1.29646i
$891$	−6.11888	+	3.79990i	−0.204990	+	0.127301i
$892$	−12.4006	−	3.24991i	−0.415204	−	0.108815i
$893$	−80.5131			−2.69427
$894$	−19.2712	−	2.83974i	−0.644525	−	0.0949752i
$895$	−0.0666733	+	25.5185i	−0.00222864	+	0.852990i
$896$	11.3406	−	17.1992i	0.378863	−	0.574586i
$897$	−6.57625	−	9.40576i	−0.219575	−	0.314049i
$898$	10.2077	−	10.8159i	0.340635	−	0.360932i
$899$	11.5086			0.383832
$900$	17.2350	−	24.5551i	0.574500	−	0.818505i
$901$	4.34485			0.144748
$902$	8.20625	−	8.69524i	0.273238	−	0.289520i
$903$	9.45912	+	13.5290i	0.314780	+	0.450218i
$904$	27.5679	+	11.1540i	0.916895	+	0.370978i
$905$	−15.6008	−	5.11412i	−0.518589	−	0.169999i
$906$	33.7129	+	4.96783i	1.12004	+	0.165045i
$907$	−1.65243			−0.0548681			−0.0274341	−	0.999624i	$-0.508734\pi$
$907$	−1.65243			−0.0548681			−0.0274341	+	0.999624i	$0.508734\pi$
$908$	3.30302	−	12.6033i	0.109615	−	0.418255i
$909$	3.47785	+	1.27131i	0.115353	+	0.0421667i
$910$	3.56750	+	19.2345i	0.118262	+	0.637616i
$911$	−6.28831	+	19.3534i	−0.208341	+	0.641208i	0.791219	+	0.611533i	$0.209447\pi$
$911$	−6.28831	+	19.3534i	−0.208341	+	0.641208i	−0.999560	+	0.0296742i	$0.990553\pi$
$912$	−10.1975	+	46.3385i	−0.337673	+	1.53442i
$913$	−4.22886	+	1.37404i	−0.139955	+	0.0454741i
$914$	34.5731	−	36.6332i	1.14358	−	1.21172i
$915$	40.2907	+	30.5707i	1.33197	+	1.01064i
$916$	16.9868	−	26.4742i	0.561258	−	0.874733i
$917$	−3.08690	+	2.24276i	−0.101938	+	0.0740626i
$918$	4.15481	−	0.549777i	0.137129	−	0.0181454i
$919$	−14.6259	−	20.1308i	−0.482463	−	0.664053i	0.496513	−	0.868029i	$-0.334614\pi$
$919$	−14.6259	−	20.1308i	−0.482463	−	0.664053i	−0.978976	+	0.203976i	$0.934614\pi$
$920$	11.4229	+	4.65650i	0.376602	+	0.153520i
$921$	−3.69432	−	5.28385i	−0.121732	−	0.174109i
$922$	−22.0327	−	40.3150i	−0.725608	−	1.32770i
$923$	39.5231	+	12.8418i	1.30092	+	0.422694i
$924$	1.74933	+	4.73549i	0.0575486	+	0.155786i
$925$	−0.0941144	+	18.0105i	−0.00309446	+	0.592183i
$926$	−3.25925	+	6.88169i	−0.107106	+	0.226146i
$927$	15.1951	−	10.2185i	0.499072	−	0.335620i
$928$	−15.3385	+	4.77331i	−0.503511	+	0.156692i
$929$	−18.5106	+	25.4777i	−0.607315	+	0.835897i	−0.996353	−	0.0853246i	$-0.972807\pi$
$929$	−18.5106	+	25.4777i	−0.607315	+	0.835897i	0.389039	+	0.921221i	$0.372807\pi$
$930$	−19.8596	−	9.91560i	−0.651221	−	0.325145i
$931$	−14.8304	−	20.4123i	−0.486046	−	0.668985i
$932$	28.2201	+	34.4605i	0.924380	+	1.12879i
$933$	39.6760	−	12.1000i	1.29893	−	0.396137i
$934$	2.10333	−	16.3223i	0.0688229	−	0.534082i
$935$	0.602063	−	0.824132i	0.0196896	−	0.0269520i
$936$	−21.3861	−	19.3292i	−0.699025	−	0.631795i
$937$	−36.4068	+	11.8293i	−1.18936	+	0.386446i	−0.835836	−	0.548979i	$-0.815017\pi$
$937$	−36.4068	+	11.8293i	−1.18936	+	0.386446i	−0.353524	+	0.935426i	$0.615017\pi$
$938$	−24.6291	−	3.17376i	−0.804170	−	0.103627i
$939$	−40.4083	−	30.4939i	−1.31867	−	0.995129i
$940$	2.90256	+	52.4961i	0.0946711	+	1.71224i
$941$	−2.32449	+	0.755274i	−0.0757763	+	0.0246212i	−0.346660	−	0.937991i	$-0.612684\pi$
$941$	−2.32449	+	0.755274i	−0.0757763	+	0.0246212i	0.270884	+	0.962612i	$0.412684\pi$
$942$	22.8982	+	3.37422i	0.746065	+	0.109938i
$943$	20.6038			0.670953
$944$	13.9947	+	30.5265i	0.455489	+	0.993553i
$945$	16.3796	+	13.3919i	0.532830	+	0.435637i
$946$	−5.19825	+	2.84091i	−0.169010	+	0.0923661i
$947$	−12.8379	+	17.6699i	−0.417176	+	0.574193i	−0.964950	−	0.262433i	$-0.915475\pi$
$947$	−12.8379	+	17.6699i	−0.417176	+	0.574193i	0.547774	+	0.836626i	$0.315475\pi$
$948$	−0.0521321	−	1.31249i	−0.00169317	−	0.0426276i
$949$	42.9111			1.39295
$950$	43.6565	+	20.9562i	1.41640	+	0.679910i
$951$	2.35576	+	0.812984i	0.0763907	+	0.0263628i
$952$	0.206354	−	2.93014i	0.00668798	−	0.0949665i
$953$	−4.38238	−	3.18398i	−0.141959	−	0.103139i	0.514539	−	0.857467i	$-0.327963\pi$
$953$	−4.38238	−	3.18398i	−0.141959	−	0.103139i	−0.656498	+	0.754328i	$0.727963\pi$
$954$	−31.8851	−	5.29137i	−1.03232	−	0.171314i
$955$	32.1227	−	43.9710i	1.03947	−	1.42287i
$956$	2.40667	+	0.630731i	0.0778372	+	0.0203993i
$957$	1.28415	−	3.72104i	0.0415107	−	0.120284i
$958$	4.06948	+	21.6256i	0.131479	+	0.698692i
$959$	1.48152	+	4.55966i	0.0478409	+	0.147239i
$960$	30.5813	+	4.97844i	0.987007	+	0.160678i
$961$	4.50422	−	13.8625i	0.145297	−	0.447179i
$962$	17.1645	+	2.21185i	0.553406	+	0.0713130i
$963$	2.82902	+	1.03414i	0.0911640	+	0.0333245i
$964$	21.7927	−	8.50295i	0.701897	−	0.273862i
$965$	−4.03667	+	2.91673i	−0.129945	+	0.0938929i
$966$	−3.86578	+	7.79349i	−0.124379	+	0.250752i
$967$	27.8413	−	20.2279i	0.895315	−	0.650485i	−0.0419431	−	0.999120i	$-0.513355\pi$
$967$	27.8413	−	20.2279i	0.895315	−	0.650485i	0.937258	+	0.348635i	$0.113355\pi$
$968$	28.4342	−	7.07450i	0.913911	−	0.227383i
$969$	1.97343	+	6.47089i	0.0633958	+	0.207875i
$970$	−1.29217	−	1.22591i	−0.0414892	−	0.0393615i
$971$	16.9238	+	12.2958i	0.543110	+	0.394592i	0.825239	−	0.564784i	$-0.191041\pi$
$971$	16.9238	+	12.2958i	0.543110	+	0.394592i	−0.282129	+	0.959377i	$0.591041\pi$
$972$	−31.1600	−	1.02533i	−0.999459	−	0.0328876i
$973$	19.9644	+	6.48681i	0.640028	+	0.207958i
$974$	−6.70852	+	14.1646i	−0.214955	+	0.453863i
$975$	−24.1999	+	16.7323i	−0.775018	+	0.535863i
$976$	−10.2987	+	51.2091i	−0.329655	+	1.63916i
$977$	−10.1982	+	31.3867i	−0.326268	+	1.00415i	0.644597	+	0.764523i	$0.277025\pi$
$977$	−10.1982	+	31.3867i	−0.326268	+	1.00415i	−0.970865	+	0.239628i	$0.922975\pi$
$978$	−49.4212	+	8.37439i	−1.58031	+	0.267784i
$979$	6.37403	−	8.77310i	0.203715	−	0.280390i
$980$	−12.7746	+	10.4056i	−0.408068	+	0.332394i
$981$	−58.4236	−	2.12150i	−1.86532	−	0.0677342i
$982$	−17.8174	+	37.6203i	−0.568576	+	1.20051i
$983$	−13.0632	−	17.9799i	−0.416651	−	0.573470i	0.548174	−	0.836364i	$-0.315323\pi$
$983$	−13.0632	−	17.9799i	−0.416651	−	0.573470i	−0.964825	+	0.262894i	$0.915323\pi$
$984$	50.4392	−	11.5816i	1.60794	−	0.369208i
$985$	−0.0254668	+	9.74715i	−0.000811440	+	0.310570i
$986$	−1.57207	+	1.66575i	−0.0500649	+	0.0530482i
$987$	−37.0731	−	0.672884i	−1.18005	−	0.0214181i
$988$	25.1286	−	39.1634i	0.799446	−	1.24595i
$989$	−9.70889	−	3.15461i	−0.308725	−	0.100311i
$990$	−5.42197	+	5.31476i	−0.172322	+	0.168914i
$991$	−45.2796	+	14.7122i	−1.43835	+	0.467349i	−0.921384	−	0.388655i	$-0.872940\pi$
$991$	−45.2796	+	14.7122i	−1.43835	+	0.467349i	−0.516970	+	0.856004i	$0.672940\pi$
$992$	0.285666	−	22.9235i	0.00906992	−	0.727823i
$993$	−14.4450	+	41.8567i	−0.458397	+	1.32828i
$994$	−5.82557	−	30.9577i	−0.184776	−	0.981918i
$995$	−40.2960	+	29.1162i	−1.27747	+	0.923046i
$996$	−18.5261	−	5.21631i	−0.587021	−	0.165285i
$997$	−0.0218001	+	0.0300053i	−0.000690416	+	0.000950276i	−0.809362	−	0.587310i	$-0.800187\pi$
$997$	−0.0218001	+	0.0300053i	−0.000690416	+	0.000950276i	0.808672	+	0.588260i	$0.200187\pi$
$998$	−6.84542	+	7.25332i	−0.216688	+	0.229600i
$999$	15.7189	−	10.1615i	0.497324	−	0.321494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.r.a.179.15	yes	224
3.2	odd	2	inner	300.2.r.a.179.42	yes	224
4.3	odd	2	inner	300.2.r.a.179.53	yes	224
12.11	even	2	inner	300.2.r.a.179.4	yes	224
25.19	even	10	inner	300.2.r.a.119.4	✓	224
75.44	odd	10	inner	300.2.r.a.119.53	yes	224
100.19	odd	10	inner	300.2.r.a.119.42	yes	224
300.119	even	10	inner	300.2.r.a.119.15	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.r.a.119.4	✓	224	25.19	even	10	inner
300.2.r.a.119.15	yes	224	300.119	even	10	inner
300.2.r.a.119.42	yes	224	100.19	odd	10	inner
300.2.r.a.119.53	yes	224	75.44	odd	10	inner
300.2.r.a.179.4	yes	224	12.11	even	2	inner
300.2.r.a.179.15	yes	224	1.1	even	1	trivial
300.2.r.a.179.42	yes	224	3.2	odd	2	inner
300.2.r.a.179.53	yes	224	4.3	odd	2	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02850 - 0.970662i) q^{2} +(-0.992477 - 1.41950i) q^{3} +(0.115630 + 1.99665i) q^{4} +(-1.30960 - 1.81244i) q^{5} +(-0.357093 + 2.42332i) q^{6} -1.82094 q^{7} +(1.81915 - 2.16580i) q^{8} +(-1.02998 + 2.81765i) q^{9} +O(q^{10})\)	\(q+(-1.02850 - 0.970662i) q^{2} +(-0.992477 - 1.41950i) q^{3} +(0.115630 + 1.99665i) q^{4} +(-1.30960 - 1.81244i) q^{5} +(-0.357093 + 2.42332i) q^{6} -1.82094 q^{7} +(1.81915 - 2.16580i) q^{8} +(-1.02998 + 2.81765i) q^{9} +(-0.412349 + 3.13528i) q^{10} +(0.247309 - 0.761138i) q^{11} +(2.71950 - 2.14577i) q^{12} +(-3.23099 + 1.04981i) q^{13} +(1.87284 + 1.76751i) q^{14} +(-1.27303 + 3.65779i) q^{15} +(-3.97326 + 0.461748i) q^{16} +(-0.461404 + 0.335230i) q^{17} +(3.79432 - 1.89820i) q^{18} +(4.02541 + 5.54050i) q^{19} +(3.46740 - 2.82439i) q^{20} +(1.80724 + 2.58482i) q^{21} +(-0.993166 + 0.542779i) q^{22} +(-1.85496 - 0.602713i) q^{23} +(-4.87983 - 0.432783i) q^{24} +(-1.56991 + 4.74714i) q^{25} +(4.34210 + 2.05647i) q^{26} +(5.02189 - 1.33440i) q^{27} +(-0.210555 - 3.63578i) q^{28} +(-1.66916 + 2.29741i) q^{29} +(4.85978 - 2.52636i) q^{30} +(-2.38209 - 3.27867i) q^{31} +(4.53470 + 3.38178i) q^{32} +(-1.32589 + 0.404357i) q^{33} +(0.799949 + 0.103083i) q^{34} +(2.38469 + 3.30035i) q^{35} +(-5.74497 - 1.73070i) q^{36} +(3.42585 - 1.11313i) q^{37} +(1.23781 - 9.60572i) q^{38} +(4.69690 + 3.54449i) q^{39} +(-6.30775 - 0.460786i) q^{40} +(-10.0468 + 3.26439i) q^{41} +(0.650244 - 4.41271i) q^{42} +5.23402 q^{43} +(1.54833 + 0.405780i) q^{44} +(6.45569 - 1.82321i) q^{45} +(1.32280 + 2.42043i) q^{46} +(-6.91025 + 9.51115i) q^{47} +(4.59882 + 5.18178i) q^{48} -3.68419 q^{49} +(6.22253 - 3.35859i) q^{50} +(0.933792 + 0.322256i) q^{51} +(-2.46972 - 6.32979i) q^{52} +(-6.16323 - 4.47785i) q^{53} +(-6.46027 - 3.50213i) q^{54} +(-1.70340 + 0.548551i) q^{55} +(-3.31256 + 3.94378i) q^{56} +(3.86963 - 11.2129i) q^{57} +(3.94674 - 0.742693i) q^{58} +(-2.59431 - 7.98448i) q^{59} +(-7.45054 - 2.11884i) q^{60} +(4.03533 - 12.4195i) q^{61} +(-0.732495 + 5.68433i) q^{62} +(1.87552 - 5.13076i) q^{63} +(-1.38138 - 7.87983i) q^{64} +(6.13403 + 4.48116i) q^{65} +(1.75617 + 0.871106i) q^{66} +(-7.80141 + 5.66806i) q^{67} +(-0.722690 - 0.882502i) q^{68} +(0.985452 + 3.23130i) q^{69} +(0.750862 - 5.70914i) q^{70} +(-9.89629 - 7.19008i) q^{71} +(4.22878 + 7.35645i) q^{72} +(-12.0129 - 3.90322i) q^{73} +(-4.60397 - 2.18049i) q^{74} +(8.29669 - 2.48294i) q^{75} +(-10.5970 + 8.67800i) q^{76} +(-0.450334 + 1.38598i) q^{77} +(-1.39027 - 8.20461i) q^{78} +(0.222877 - 0.306764i) q^{79} +(6.04026 + 6.59661i) q^{80} +(-6.87829 - 5.80423i) q^{81} +(13.5017 + 6.39458i) q^{82} +(-3.26571 - 4.49487i) q^{83} +(-4.95203 + 3.90731i) q^{84} +(1.21184 + 0.397254i) q^{85} +(-5.38320 - 5.08046i) q^{86} +(4.91779 + 0.0892587i) q^{87} +(-1.19858 - 1.92025i) q^{88} +(12.8868 + 4.18717i) q^{89} +(-8.40940 - 4.39112i) q^{90} +(5.88343 - 1.91164i) q^{91} +(0.988920 - 3.77340i) q^{92} +(-2.28991 + 6.63540i) q^{93} +(16.3393 - 3.07471i) q^{94} +(4.77019 - 14.5517i) q^{95} +(0.299861 - 9.79337i) q^{96} +(-0.331073 + 0.455683i) q^{97} +(3.78920 + 3.57610i) q^{98} +(1.88990 + 1.48078i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 6 q^{4} - 7 q^{6} - 6 q^{9}+O(q^{10}) \) 224 * q - 6 * q^4 - 7 * q^6 - 6 * q^9	\( 224 q - 6 q^{4} - 7 q^{6} - 6 q^{9} - 5 q^{12} - 20 q^{13} + 6 q^{16} - 24 q^{21} - 10 q^{22} - 28 q^{24} - 20 q^{25} - 50 q^{28} - 25 q^{30} - 10 q^{33} - 14 q^{34} - 25 q^{36} - 60 q^{37} - 20 q^{40} - 85 q^{42} - 30 q^{45} + 6 q^{46} - 70 q^{48} + 88 q^{49} + 40 q^{52} - 46 q^{54} + 50 q^{58} + 10 q^{60} - 28 q^{61} + 18 q^{64} + 64 q^{66} - 42 q^{69} - 40 q^{70} - 5 q^{72} - 20 q^{73} - 80 q^{76} - 85 q^{78} + 18 q^{81} - 48 q^{84} - 20 q^{85} + 50 q^{88} - 60 q^{90} + 60 q^{94} + 44 q^{96} - 120 q^{97}+O(q^{100}) \) 224 * q - 6 * q^4 - 7 * q^6 - 6 * q^9 - 5 * q^12 - 20 * q^13 + 6 * q^16 - 24 * q^21 - 10 * q^22 - 28 * q^24 - 20 * q^25 - 50 * q^28 - 25 * q^30 - 10 * q^33 - 14 * q^34 - 25 * q^36 - 60 * q^37 - 20 * q^40 - 85 * q^42 - 30 * q^45 + 6 * q^46 - 70 * q^48 + 88 * q^49 + 40 * q^52 - 46 * q^54 + 50 * q^58 + 10 * q^60 - 28 * q^61 + 18 * q^64 + 64 * q^66 - 42 * q^69 - 40 * q^70 - 5 * q^72 - 20 * q^73 - 80 * q^76 - 85 * q^78 + 18 * q^81 - 48 * q^84 - 20 * q^85 + 50 * q^88 - 60 * q^90 + 60 * q^94 + 44 * q^96 - 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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