LMFDB - Embedded newform 570.2.bi.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	570.17
Dual form			570.2.bi.a.503.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 - 0.819152i) q^{2} +(-1.61147 - 0.634960i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.56453 - 1.59758i) q^{5} +(0.404170 + 1.68423i) q^{6} +(0.997670 - 3.72335i) q^{7} +(0.965926 - 0.258819i) q^{8} +(2.19365 + 2.04644i) q^{9} +O(q^{10})$	\(q+(-0.573576 - 0.819152i) q^{2} +(-1.61147 - 0.634960i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.56453 - 1.59758i) q^{5} +(0.404170 + 1.68423i) q^{6} +(0.997670 - 3.72335i) q^{7} +(0.965926 - 0.258819i) q^{8} +(2.19365 + 2.04644i) q^{9} +(-2.20604 - 0.365253i) q^{10} +(5.37905 + 3.10559i) q^{11} +(1.14782 - 1.29711i) q^{12} +(0.0148851 - 0.170138i) q^{13} +(-3.62223 + 1.31839i) q^{14} +(-3.53558 + 1.58103i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-1.03580 - 1.47927i) q^{17} +(0.418116 - 2.97072i) q^{18} +(4.29655 + 0.734629i) q^{19} +(0.966132 + 2.01658i) q^{20} +(-3.97189 + 5.36658i) q^{21} +(-0.541341 - 6.18755i) q^{22} +(3.12265 + 6.69654i) q^{23} +(-1.72090 - 0.196246i) q^{24} +(-0.104510 - 4.99891i) q^{25} +(-0.147906 + 0.0853938i) q^{26} +(-2.23559 - 4.69064i) q^{27} +(3.15759 + 2.21097i) q^{28} +(-1.14890 - 6.51574i) q^{29} +(3.32303 + 1.98934i) q^{30} +(-0.994699 - 1.72287i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(-6.69623 - 8.42004i) q^{33} +(-0.617641 + 1.69695i) q^{34} +(-4.38747 - 7.41914i) q^{35} +(-2.67329 + 1.36143i) q^{36} +(-5.60123 - 5.60123i) q^{37} +(-1.86263 - 3.94089i) q^{38} +(-0.132018 + 0.264720i) q^{39} +(1.09773 - 1.94807i) q^{40} +(-2.31503 + 2.75895i) q^{41} +(6.67423 + 0.175441i) q^{42} +(2.27061 - 4.86935i) q^{43} +(-4.75805 + 3.99248i) q^{44} +(6.70137 - 0.302824i) q^{45} +(3.69441 - 6.39890i) q^{46} +(2.67672 + 1.87426i) q^{47} +(0.826310 + 1.52224i) q^{48} +(-6.80584 - 3.92936i) q^{49} +(-4.03492 + 2.95287i) q^{50} +(0.729875 + 3.04149i) q^{51} +(0.154786 + 0.0721779i) q^{52} +(2.65654 + 5.69696i) q^{53} +(-2.56007 + 4.52173i) q^{54} +(13.3771 - 3.73466i) q^{55} -3.85470i q^{56} +(-6.45728 - 3.91197i) q^{57} +(-4.67840 + 4.67840i) q^{58} +(-0.280178 + 1.58897i) q^{59} +(-0.276443 - 3.86310i) q^{60} +(-6.41592 - 2.33520i) q^{61} +(-0.840756 + 1.80301i) q^{62} +(9.80814 - 6.12607i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-0.248520 - 0.289965i) q^{65} +(-3.05650 + 10.3148i) q^{66} +(-4.90506 + 7.00516i) q^{67} +(1.74433 - 0.467391i) q^{68} +(-0.780005 - 12.7740i) q^{69} +(-3.56086 + 7.84945i) q^{70} +(-1.55270 - 4.26601i) q^{71} +(2.64856 + 1.40895i) q^{72} +(-14.9298 + 1.30619i) q^{73} +(-1.37552 + 7.80099i) q^{74} +(-3.00569 + 8.12193i) q^{75} +(-2.15983 + 3.78618i) q^{76} +(16.9297 - 16.9297i) q^{77} +(0.292568 - 0.0436945i) q^{78} +(-1.71816 + 2.04762i) q^{79} +(-2.22540 + 0.218157i) q^{80} +(0.624204 + 8.97833i) q^{81} +(3.58785 + 0.313896i) q^{82} +(-3.17731 + 11.8579i) q^{83} +(-3.68447 - 5.56784i) q^{84} +(-3.98379 - 0.659595i) q^{85} +(-5.29111 + 0.932965i) q^{86} +(-2.28582 + 11.2294i) q^{87} +(5.99955 + 1.60757i) q^{88} +(4.82625 - 4.04970i) q^{89} +(-4.09180 - 5.31574i) q^{90} +(-0.618632 - 0.225164i) q^{91} +(-7.36070 + 0.643978i) q^{92} +(0.508970 + 3.40794i) q^{93} -3.26768i q^{94} +(7.89569 - 5.71472i) q^{95} +(0.772993 - 1.54999i) q^{96} +(11.5127 - 8.06126i) q^{97} +(0.684932 + 7.82881i) q^{98} +(5.44435 + 17.8205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$3$	−1.61147	−	0.634960i	−0.930381	−	0.366595i
$3$	−1.61147	−	0.634960i	−0.930381	−	0.366595i
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	1.56453	−	1.59758i	0.699678	−	0.714459i
$5$	1.56453	−	1.59758i	0.699678	−	0.714459i
$6$	0.404170	+	1.68423i	0.165002	+	0.687586i
$7$	0.997670	−	3.72335i	0.377084	−	1.40730i	−0.473193	−	0.880959i	$-0.656899\pi$
$7$	0.997670	−	3.72335i	0.377084	−	1.40730i	0.850276	−	0.526337i	$-0.176435\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	2.19365	+	2.04644i	0.731217	+	0.682145i
$10$	−2.20604	−	0.365253i	−0.697610	−	0.115503i
$11$	5.37905	+	3.10559i	1.62184	+	0.936372i	0.986427	+	0.164203i	$0.0525052\pi$
$11$	5.37905	+	3.10559i	1.62184	+	0.936372i	0.635417	+	0.772169i	$0.280828\pi$
$12$	1.14782	−	1.29711i	0.331348	−	0.374445i
$13$	0.0148851	−	0.170138i	0.00412839	−	0.0471877i	−0.993851	−	0.110725i	$-0.964683\pi$
$13$	0.0148851	−	0.170138i	0.00412839	−	0.0471877i	0.997979	+	0.0635374i	$0.0202382\pi$
$14$	−3.62223	+	1.31839i	−0.968083	+	0.352353i
$15$	−3.53558	+	1.58103i	−0.912883	+	0.408220i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−1.03580	−	1.47927i	−0.251218	−	0.358777i	0.673659	−	0.739042i	$-0.264722\pi$
$17$	−1.03580	−	1.47927i	−0.251218	−	0.358777i	−0.924877	+	0.380265i	$0.875833\pi$
$18$	0.418116	−	2.97072i	0.0985508	−	0.700205i
$19$	4.29655	+	0.734629i	0.985696	+	0.168535i
$19$	4.29655	+	0.734629i	0.985696	+	0.168535i
$20$	0.966132	+	2.01658i	0.216034	+	0.450921i
$21$	−3.97189	+	5.36658i	−0.866738	+	1.17108i
$22$	−0.541341	−	6.18755i	−0.115414	−	1.31919i
$23$	3.12265	+	6.69654i	0.651117	+	1.39633i	0.903454	+	0.428686i	$0.141023\pi$
$23$	3.12265	+	6.69654i	0.651117	+	1.39633i	−0.252337	+	0.967640i	$0.581199\pi$
$24$	−1.72090	−	0.196246i	−0.351277	−	0.0400586i
$25$	−0.104510	−	4.99891i	−0.0209020	−	0.999782i
$26$	−0.147906	+	0.0853938i	−0.0290068	+	0.0167471i
$27$	−2.23559	−	4.69064i	−0.430239	−	0.902715i
$28$	3.15759	+	2.21097i	0.596728	+	0.417833i
$29$	−1.14890	−	6.51574i	−0.213346	−	1.20994i	−0.883754	−	0.467951i	$-0.844992\pi$
$29$	−1.14890	−	6.51574i	−0.213346	−	1.20994i	0.670409	−	0.741992i	$-0.266119\pi$
$30$	3.32303	+	1.98934i	0.606700	+	0.363202i
$31$	−0.994699	−	1.72287i	−0.178653	−	0.309436i	0.762766	−	0.646674i	$-0.223841\pi$
$31$	−0.994699	−	1.72287i	−0.178653	−	0.309436i	−0.941419	+	0.337238i	$0.890507\pi$
$32$	−0.0871557	+	0.996195i	−0.0154071	+	0.176104i
$33$	−6.69623	−	8.42004i	−1.16566	−	1.46574i
$34$	−0.617641	+	1.69695i	−0.105925	+	0.291025i
$35$	−4.38747	−	7.41914i	−0.741617	−	1.25406i
$36$	−2.67329	+	1.36143i	−0.445549	+	0.226906i
$37$	−5.60123	−	5.60123i	−0.920836	−	0.920836i	0.0762525	−	0.997089i	$-0.475704\pi$
$37$	−5.60123	−	5.60123i	−0.920836	−	0.920836i	−0.997089	+	0.0762525i	$0.975704\pi$
$38$	−1.86263	−	3.94089i	−0.302158	−	0.639297i
$39$	−0.132018	+	0.264720i	−0.0211397	+	0.0423891i
$40$	1.09773	−	1.94807i	0.173567	−	0.308017i
$41$	−2.31503	+	2.75895i	−0.361547	+	0.430875i	−0.915900	−	0.401407i	$-0.868521\pi$
$41$	−2.31503	+	2.75895i	−0.361547	+	0.430875i	0.554353	+	0.832282i	$0.312966\pi$
$42$	6.67423	+	0.175441i	1.02986	+	0.0270712i
$43$	2.27061	−	4.86935i	0.346265	−	0.742569i	−0.653633	−	0.756812i	$-0.726756\pi$
$43$	2.27061	−	4.86935i	0.346265	−	0.742569i	0.999899	+	0.0142429i	$0.00453382\pi$
$44$	−4.75805	+	3.99248i	−0.717303	+	0.601888i
$45$	6.70137	−	0.302824i	0.998981	−	0.0451423i
$46$	3.69441	−	6.39890i	0.544711	−	0.943466i
$47$	2.67672	+	1.87426i	0.390440	+	0.273389i	0.752270	−	0.658855i	$-0.228959\pi$
$47$	2.67672	+	1.87426i	0.390440	+	0.273389i	−0.361830	+	0.932244i	$0.617848\pi$
$48$	0.826310	+	1.52224i	0.119268	+	0.219716i
$49$	−6.80584	−	3.92936i	−0.972263	−	0.561337i
$50$	−4.03492	+	2.95287i	−0.570624	+	0.417598i
$51$	0.729875	+	3.04149i	0.102203	+	0.425894i
$52$	0.154786	+	0.0721779i	0.0214650	+	0.0100093i
$53$	2.65654	+	5.69696i	0.364903	+	0.782538i	0.999949	+	0.0100634i	$0.00320333\pi$
$53$	2.65654	+	5.69696i	0.364903	+	0.782538i	−0.635046	+	0.772474i	$0.719019\pi$
$54$	−2.56007	+	4.52173i	−0.348381	+	0.615330i
$55$	13.3771	−	3.73466i	1.80377	−	0.503582i
$56$		−	3.85470i		−	0.515106i
$57$	−6.45728	−	3.91197i	−0.855288	−	0.518153i
$58$	−4.67840	+	4.67840i	−0.614304	+	0.614304i
$59$	−0.280178	+	1.58897i	−0.0364761	+	0.206866i	−0.997599	−	0.0692547i	$-0.977938\pi$
$59$	−0.280178	+	1.58897i	−0.0364761	+	0.206866i	0.961123	+	0.276121i	$0.0890490\pi$
$60$	−0.276443	−	3.86310i	−0.0356886	−	0.498725i
$61$	−6.41592	−	2.33520i	−0.821474	−	0.298992i	−0.103119	−	0.994669i	$-0.532882\pi$
$61$	−6.41592	−	2.33520i	−0.821474	−	0.298992i	−0.718355	+	0.695677i	$0.755105\pi$
$62$	−0.840756	+	1.80301i	−0.106776	+	0.228982i
$63$	9.80814	−	6.12607i	1.23571	−	0.771812i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−0.248520	−	0.289965i	−0.0308251	−	0.0359657i
$66$	−3.05650	+	10.3148i	−0.376229	+	1.26966i
$67$	−4.90506	+	7.00516i	−0.599249	+	0.855816i	−0.998126	−	0.0611883i	$-0.980511\pi$
$67$	−4.90506	+	7.00516i	−0.599249	+	0.855816i	0.398877	+	0.917004i	$0.369400\pi$
$68$	1.74433	−	0.467391i	0.211531	−	0.0566795i
$69$	−0.780005	−	12.7740i	−0.0939016	−	1.53781i
$70$	−3.56086	+	7.84945i	−0.425604	+	0.938189i
$71$	−1.55270	−	4.26601i	−0.184272	−	0.506282i	0.812818	−	0.582517i	$-0.197932\pi$
$71$	−1.55270	−	4.26601i	−0.184272	−	0.506282i	−0.997090	+	0.0762354i	$0.975710\pi$
$72$	2.64856	+	1.40895i	0.312136	+	0.166046i
$73$	−14.9298	+	1.30619i	−1.74741	+	0.152878i	−0.915574	−	0.402150i	$-0.868263\pi$
$73$	−14.9298	+	1.30619i	−1.74741	+	0.152878i	−0.831831	+	0.555028i	$0.812707\pi$
$74$	−1.37552	+	7.80099i	−0.159901	+	0.906846i
$75$	−3.00569	+	8.12193i	−0.347068	+	0.937840i
$76$	−2.15983	+	3.78618i	−0.247750	+	0.434304i
$77$	16.9297	−	16.9297i	1.92932	−	1.92932i
$78$	0.292568	−	0.0436945i	0.0331268	−	0.00494743i
$79$	−1.71816	+	2.04762i	−0.193308	+	0.230376i	−0.853989	−	0.520292i	$-0.825823\pi$
$79$	−1.71816	+	2.04762i	−0.193308	+	0.230376i	0.660681	+	0.750667i	$0.270268\pi$
$80$	−2.22540	+	0.218157i	−0.248807	+	0.0243907i
$81$	0.624204	+	8.97833i	0.0693560	+	0.997592i
$82$	3.58785	+	0.313896i	0.396211	+	0.0346640i
$83$	−3.17731	+	11.8579i	−0.348756	+	1.30157i	0.539407	+	0.842045i	$0.318648\pi$
$83$	−3.17731	+	11.8579i	−0.348756	+	1.30157i	−0.888163	+	0.459529i	$0.848018\pi$
$84$	−3.68447	−	5.56784i	−0.402008	−	0.607501i
$85$	−3.98379	−	0.659595i	−0.432103	−	0.0715432i
$86$	−5.29111	+	0.932965i	−0.570555	+	0.100604i
$87$	−2.28582	+	11.2294i	−0.245066	+	1.20392i
$88$	5.99955	+	1.60757i	0.639554	+	0.171368i
$89$	4.82625	−	4.04970i	0.511581	−	0.429268i	−0.350104	−	0.936711i	$-0.613854\pi$
$89$	4.82625	−	4.04970i	0.511581	−	0.429268i	0.861685	+	0.507443i	$0.169409\pi$
$90$	−4.09180	−	5.31574i	−0.431314	−	0.560329i
$91$	−0.618632	−	0.225164i	−0.0648503	−	0.0236036i
$92$	−7.36070	+	0.643978i	−0.767406	+	0.0671393i
$93$	0.508970	+	3.40794i	0.0527778	+	0.353387i
$94$		−	3.26768i		−	0.337035i
$95$	7.89569	−	5.71472i	0.810081	−	0.586318i
$96$	0.772993	−	1.54999i	0.0788933	−	0.158196i
$97$	11.5127	−	8.06126i	1.16894	−	0.818497i	0.182590	−	0.983189i	$-0.441552\pi$
$97$	11.5127	−	8.06126i	1.16894	−	0.818497i	0.986345	+	0.164692i	$0.0526629\pi$
$98$	0.684932	+	7.82881i	0.0691886	+	0.790829i
$99$	5.44435	+	17.8205i	0.547178	+	1.79102i
$100$	4.73318	+	1.61152i	0.473318	+	0.161152i
$101$	−4.28641	−	5.10834i	−0.426514	−	0.508299i	0.509399	−	0.860530i	$-0.329868\pi$
$101$	−4.28641	−	5.10834i	−0.426514	−	0.508299i	−0.935913	+	0.352231i	$0.885423\pi$
$102$	2.07281	−	2.34241i	0.205238	−	0.231933i
$103$	−1.66814	−	6.22560i	−0.164367	−	0.613426i	−0.998120	−	0.0612886i	$-0.980479\pi$
$103$	−1.66814	−	6.22560i	−0.164367	−	0.613426i	0.833753	−	0.552138i	$-0.186188\pi$
$104$	−0.0296569	−	0.168193i	−0.00290810	−	0.0164927i
$105$	2.35939	+	14.7416i	0.230253	+	1.43863i
$106$	3.14295	−	5.44375i	0.305270	−	0.528744i
$107$	4.27944	+	1.14667i	0.413709	+	0.110853i	0.459669	−	0.888090i	$-0.347968\pi$
$107$	4.27944	+	1.14667i	0.413709	+	0.110853i	−0.0459598	+	0.998943i	$0.514635\pi$
$108$	5.17238	−	0.496472i	0.497713	−	0.0477730i
$109$	4.88460	+	13.4203i	0.467860	+	1.28544i	0.919449	+	0.393209i	$0.128635\pi$
$109$	4.88460	+	13.4203i	0.467860	+	1.28544i	−0.451589	+	0.892226i	$0.649143\pi$
$110$	−10.7320	−	8.81576i	−1.02326	−	0.840550i
$111$	5.46963	+	12.5827i	0.519155	+	1.19430i
$112$	−3.15759	+	2.21097i	−0.298364	+	0.208917i
$113$	9.98092	+	9.98092i	0.938926	+	0.938926i	0.998239	−	0.0593137i	$-0.0188912\pi$
$113$	9.98092	+	9.98092i	0.938926	+	0.938926i	−0.0593137	+	0.998239i	$0.518891\pi$
$114$	0.499249	+	7.53331i	0.0467589	+	0.705559i
$115$	15.5837	+	5.48824i	1.45319	+	0.511781i
$116$	6.51574	+	1.14890i	0.604971	+	0.106673i
$117$	0.380828	−	0.342761i	0.0352076	−	0.0316883i
$118$	1.46231	−	0.681887i	0.134617	−	0.0627728i
$119$	−6.54125	+	2.38082i	−0.599635	+	0.218249i
$120$	−3.00591	+	2.44223i	−0.274401	+	0.222944i
$121$	13.7894	+	23.8840i	1.25358	+	2.17127i
$122$	1.76713	+	6.59503i	0.159989	+	0.597086i
$123$	5.48242	−	2.97600i	0.494333	−	0.268337i
$124$	1.95917	−	0.345455i	0.175939	−	0.0310228i
$125$	−8.14965	−	7.65396i	−0.728927	−	0.684591i
$126$	−10.6439	−	4.52059i	−0.948234	−	0.402726i
$127$	8.54313	+	0.747427i	0.758080	+	0.0663234i	0.459641	−	0.888105i	$-0.347978\pi$
$127$	8.54313	+	0.747427i	0.758080	+	0.0663234i	0.298440	+	0.954428i	$0.403534\pi$
$128$	−0.906308	−	0.422618i	−0.0801070	−	0.0373545i
$129$	−6.75086	+	6.40504i	−0.594380	+	0.563933i
$130$	−0.0949803	+	0.369893i	−0.00833032	+	0.0324417i
$131$	0.600560	+	0.105895i	0.0524712	+	0.00925209i	0.199822	−	0.979832i	$-0.435964\pi$
$131$	0.600560	+	0.105895i	0.0524712	+	0.00925209i	−0.147351	+	0.989084i	$0.547075\pi$
$132$	10.2025	−	3.41257i	0.888013	−	0.297026i
$133$	7.02182	−	15.2647i	0.608869	−	1.32361i
$134$	8.55172			0.738756
$135$	−10.9913	−	3.76711i	−0.945981	−	0.324221i
$136$	−1.38337	−	1.16079i	−0.118623	−	0.0995365i
$137$	4.97504	−	2.31990i	0.425046	−	0.198202i	−0.198312	−	0.980139i	$-0.563546\pi$
$137$	4.97504	−	2.31990i	0.425046	−	0.198202i	0.623358	+	0.781937i	$0.285768\pi$
$138$	−10.0165	+	7.96581i	−0.852658	+	0.678095i
$139$	−10.3222	−	12.3015i	−0.875520	−	1.04340i	−0.998698	−	0.0510191i	$-0.983753\pi$
$139$	−10.3222	−	12.3015i	−0.875520	−	1.04340i	0.123178	−	0.992385i	$-0.460691\pi$
$140$	8.47232	−	1.58537i	0.716041	−	0.133989i
$141$	−3.12337	−	4.71992i	−0.263035	−	0.397489i
$142$	−2.60392	+	3.71878i	−0.218516	+	0.312073i
$143$	0.608446	−	0.868951i	0.0508808	−	0.0726654i
$144$	−0.365010	−	2.97771i	−0.0304175	−	0.248143i
$145$	−12.2069	−	8.35860i	−1.01373	−	0.694144i
$146$	9.63337	+	11.4806i	0.797264	+	0.950142i
$147$	8.47241	+	10.6535i	0.698792	+	0.878683i
$148$	7.17916	−	3.34770i	0.590124	−	0.275179i
$149$	−10.0722	−	8.45159i	−0.825148	−	0.692382i	0.129023	−	0.991642i	$-0.458816\pi$
$149$	−10.0722	−	8.45159i	−0.825148	−	0.692382i	−0.954172	+	0.299260i	$0.903260\pi$
$150$	8.37709	−	2.19643i	0.683987	−	0.179338i
$151$	−6.57039			−0.534691			−0.267345	−	0.963601i	$-0.586146\pi$
$151$	−6.57039			−0.534691			−0.267345	+	0.963601i	$0.586146\pi$
$152$	4.34028	−	0.402431i	0.352043	−	0.0326415i
$153$	0.755059	−	5.36471i	0.0610429	−	0.433711i
$154$	−23.5785	−	4.15753i	−1.90001	−	0.335023i
$155$	−4.30865	−	1.10637i	−0.346079	−	0.0888655i
$156$	−0.203603	−	0.214595i	−0.0163012	−	0.0171814i
$157$	−7.93586	−	3.70055i	−0.633351	−	0.295336i	0.0793048	−	0.996850i	$-0.474730\pi$
$157$	−7.93586	−	3.70055i	−0.633351	−	0.295336i	−0.712656	+	0.701514i	$0.752508\pi$
$158$	2.66281	+	0.232966i	0.211842	+	0.0185338i
$159$	−0.663575	−	10.8673i	−0.0526249	−	0.861830i
$160$	1.45514	+	1.69781i	0.115039	+	0.134224i
$161$	28.0490	−	4.94579i	2.21057	−	0.389783i
$162$	6.99659	−	5.66107i	0.549704	−	0.444776i
$163$	4.64177	+	17.3233i	0.363571	+	1.35687i	0.869347	+	0.494202i	$0.164540\pi$
$163$	4.64177	+	17.3233i	0.363571	+	1.35687i	−0.505776	+	0.862665i	$0.668794\pi$
$164$	−1.80078	−	3.11903i	−0.140617	−	0.243556i
$165$	−23.9281	−	2.47564i	−1.86280	−	0.192729i
$166$	11.5359	−	4.19871i	0.895356	−	0.325883i
$167$	2.15685	−	1.00576i	0.166902	−	0.0778277i	−0.337372	−	0.941371i	$-0.609538\pi$
$167$	2.15685	−	1.00576i	0.166902	−	0.0778277i	0.504274	+	0.863544i	$0.331760\pi$
$168$	−2.44758	+	6.21172i	−0.188835	+	0.479245i
$169$	12.7738	+	2.25236i	0.982598	+	0.173259i
$170$	1.74470	+	3.64166i	0.133812	+	0.279303i
$171$	7.92175	+	10.4041i	0.605791	+	0.795623i
$172$	3.79909	+	3.79909i	0.289678	+	0.289678i
$173$	0.901575	−	0.631290i	0.0685455	−	0.0479961i	−0.538801	−	0.842433i	$-0.681123\pi$
$173$	0.901575	−	0.631290i	0.0685455	−	0.0479961i	0.607347	+	0.794437i	$0.292234\pi$
$174$	10.5097	−	4.56849i	0.796737	−	0.346336i
$175$	−18.7170	−	4.59813i	−1.41487	−	0.347586i
$176$	−2.12435	−	5.83661i	−0.160129	−	0.439951i
$177$	1.46043	−	2.38267i	0.109773	−	0.179092i
$178$	−6.08554	−	1.63062i	−0.456131	−	0.122220i
$179$	−6.73663	+	11.6682i	−0.503520	+	0.872122i	0.496472	+	0.868053i	$0.334629\pi$
$179$	−6.73663	+	11.6682i	−0.503520	+	0.872122i	−0.999992	+	0.00406900i	$0.998705\pi$
$180$	−2.00744	+	6.40080i	−0.149626	+	0.477087i
$181$	1.39404	+	7.90599i	0.103618	+	0.587648i	0.991763	+	0.128085i	$0.0408829\pi$
$181$	1.39404	+	7.90599i	0.103618	+	0.587648i	−0.888145	+	0.459563i	$0.848006\pi$
$182$	0.170390	+	0.635903i	0.0126301	+	0.0471362i
$183$	8.85627	+	7.83695i	0.654675	+	0.579324i
$184$	4.74944	+	5.66016i	0.350133	+	0.417273i
$185$	−17.7117	+	0.185125i	−1.30219	+	0.0136107i
$186$	2.49969	−	2.37164i	0.183286	−	0.173897i
$187$	−0.977586	−	11.1739i	−0.0714882	−	0.817114i
$188$	−2.67672	+	1.87426i	−0.195220	+	0.136695i
$189$	−19.6953	+	3.64418i	−1.43262	+	0.265075i
$190$	−9.21001	−	3.18994i	−0.668164	−	0.231423i
$191$			8.80171i			0.636870i	0.947945	+	0.318435i	$0.103157\pi$
$191$			8.80171i			0.636870i	−0.947945	+	0.318435i	$0.896843\pi$
$192$	−1.71305	+	0.255841i	−0.123629	+	0.0184638i
$193$	−17.9812	+	1.57316i	−1.29432	+	0.113238i	−0.713419	−	0.700737i	$-0.752855\pi$
$193$	−17.9812	+	1.57316i	−1.29432	+	0.113238i	−0.580899	+	0.813976i	$0.697299\pi$
$194$	−13.2068	−	4.80688i	−0.948193	−	0.345114i
$195$	0.216365	+	0.625070i	0.0154942	+	0.0447622i
$196$	6.02012	−	5.05148i	0.430009	−	0.360820i
$197$	3.99189	+	1.06962i	0.284410	+	0.0762075i	0.398204	−	0.917297i	$-0.369634\pi$
$197$	3.99189	+	1.06962i	0.284410	+	0.0762075i	−0.113794	+	0.993504i	$0.536300\pi$
$198$	11.4749	−	14.6811i	0.815487	−	1.04334i
$199$	9.94814	−	1.75412i	0.705205	−	0.124347i	0.190466	−	0.981694i	$-0.439000\pi$
$199$	9.94814	−	1.75412i	0.705205	−	0.124347i	0.514739	+	0.857347i	$0.327889\pi$
$200$	−1.39476	−	4.80152i	−0.0986245	−	0.339519i
$201$	12.3523	−	8.17405i	0.871267	−	0.576553i
$202$	−1.72593	+	6.44125i	−0.121436	+	0.453205i
$203$	−25.4066	−	2.22279i	−1.78320	−	0.156009i
$204$	−3.10770	−	0.354394i	−0.217583	−	0.0248125i
$205$	0.785704	+	8.01489i	0.0548759	+	0.559784i
$206$	−4.14290	+	4.93732i	−0.288650	+	0.343999i
$207$	−6.85404	+	21.0802i	−0.476389	+	1.46517i
$208$	−0.120765	+	0.120765i	−0.00837355	+	0.00837355i
$209$	20.8299	+	17.2949i	1.44083	+	1.19632i
$210$	10.7223	−	10.3881i	0.739909	−	0.716848i
$211$	0.459303	−	2.60484i	0.0316197	−	0.179324i	−0.964908	−	0.262589i	$-0.915424\pi$
$211$	0.459303	−	2.60484i	0.0316197	−	0.179324i	0.996527	+	0.0832647i	$0.0265347\pi$
$212$	−6.26198	+	0.547852i	−0.430075	+	0.0376266i
$213$	−0.206622	+	7.86043i	−0.0141575	+	0.538588i
$214$	−1.51529	−	4.16322i	−0.103583	−	0.284592i
$215$	−4.22673	−	11.2457i	−0.288260	−	0.766951i
$216$	−3.37344	−	3.95220i	−0.229534	−	0.268913i
$217$	−7.40723	+	1.98476i	−0.502836	+	0.134734i
$218$	8.19161	−	11.6988i	0.554806	−	0.792344i
$219$	24.8883	+	7.37497i	1.68180	+	0.498354i
$220$	−1.06580	+	13.8477i	−0.0718564	+	0.933611i
$221$	−0.267098	+	0.154209i	−0.0179670	+	0.0103732i
$222$	7.16993	−	11.6976i	0.481214	−	0.785093i
$223$	9.87853	−	21.1846i	0.661515	−	1.41862i	−0.233397	−	0.972382i	$-0.574984\pi$
$223$	9.87853	−	21.1846i	0.661515	−	1.41862i	0.894912	−	0.446242i	$-0.147238\pi$
$224$	3.62223	+	1.31839i	0.242021	+	0.0880883i
$225$	10.0007	−	11.1797i	0.666712	−	0.745315i
$226$	2.45107	−	13.9007i	0.163043	−	0.924661i
$227$	−10.2843	+	10.2843i	−0.682593	+	0.682593i	−0.960584	−	0.277991i	$-0.910332\pi$
$227$	−10.2843	+	10.2843i	−0.682593	+	0.682593i	0.277991	+	0.960584i	$0.410332\pi$
$228$	5.88457	−	4.72989i	0.389715	−	0.313245i
$229$		−	0.885181i		−	0.0584944i	−0.999572	−	0.0292472i	$-0.990689\pi$
$229$		−	0.885181i		−	0.0584944i	0.999572	−	0.0292472i	$-0.00931100\pi$
$230$	−4.44274	−	15.9134i	−0.292946	−	1.04930i
$231$	−38.0314	+	16.5320i	−2.50228	+	1.08773i
$232$	−2.79615	−	5.99637i	−0.183576	−	0.393681i
$233$	−12.4239	−	5.79336i	−0.813916	−	0.379535i	−0.0293415	−	0.999569i	$-0.509341\pi$
$233$	−12.4239	−	5.79336i	−0.813916	−	0.379535i	−0.784575	+	0.620034i	$0.787119\pi$
$234$	−0.499208	−	0.115357i	−0.0326342	−	0.00754111i
$235$	7.18208	−	1.34394i	0.468508	−	0.0876690i
$236$	−1.39732	−	0.806741i	−0.0909576	−	0.0525144i
$237$	4.06892	−	2.20871i	0.264304	−	0.143471i
$238$	5.70216	+	3.99270i	0.369616	+	0.258808i
$239$	10.9711	−	19.0025i	0.709660	−	1.22917i	−0.255323	−	0.966856i	$-0.582182\pi$
$239$	10.9711	−	19.0025i	0.709660	−	1.22917i	0.964983	−	0.262312i	$-0.0844850\pi$
$240$	3.72468	+	1.06149i	0.240427	+	0.0685188i
$241$	−5.12338	+	4.29903i	−0.330026	+	0.276925i	−0.792710	−	0.609598i	$-0.791331\pi$
$241$	−5.12338	+	4.29903i	−0.330026	+	0.276925i	0.462684	+	0.886523i	$0.346886\pi$
$242$	11.6553	−	24.9949i	0.749233	−	1.60674i
$243$	4.69500	−	14.8646i	0.301184	−	0.953566i
$244$	4.38874	−	5.23030i	0.280961	−	0.334836i
$245$	−16.9254	+	4.72528i	−1.08132	+	0.301887i
$246$	−5.58238	−	2.78397i	−0.355920	−	0.177500i
$247$	0.188943	−	0.720070i	0.0120221	−	0.0458169i
$248$	−1.40672	−	1.40672i	−0.0893266	−	0.0893266i
$249$	12.6494	−	17.0911i	0.801625	−	1.08311i
$250$	−1.59531	+	11.0659i	−0.100896	+	0.699871i
$251$	−1.08580	+	2.98322i	−0.0685354	+	0.188299i	−0.969232	−	0.246149i	$-0.920835\pi$
$251$	−1.08580	+	2.98322i	−0.0685354	+	0.188299i	0.900697	+	0.434449i	$0.143057\pi$
$252$	2.40204	+	11.3119i	0.151314	+	0.712581i
$253$	−3.99987	+	45.7187i	−0.251469	+	2.87431i
$254$	−4.28788	−	7.42683i	−0.269046	−	0.466001i
$255$	6.00093	+	3.59247i	0.375793	+	0.224969i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−25.0358	−	17.5303i	−1.56169	−	1.09351i	−0.954196	−	0.299184i	$-0.903286\pi$
$257$	−25.0358	−	17.5303i	−1.56169	−	1.09351i	−0.607495	−	0.794324i	$-0.707825\pi$
$258$	9.11884	+	1.85620i	0.567714	+	0.115562i
$259$	−26.4435	+	15.2672i	−1.64312	+	0.948656i
$260$	0.357477	−	0.134359i	0.0221698	−	0.00833256i
$261$	10.8138	−	16.6444i	0.669355	−	1.03026i
$262$	−0.257723	−	0.552689i	−0.0159222	−	0.0341452i
$263$	0.177627	+	2.03029i	0.0109530	+	0.125193i	0.999703	−	0.0243870i	$-0.00776338\pi$
$263$	0.177627	+	2.03029i	0.0109530	+	0.125193i	−0.988750	+	0.149580i	$0.952208\pi$
$264$	−8.64733	−	6.40003i	−0.532206	−	0.393894i
$265$	13.2576	+	4.66902i	0.814405	+	0.286816i
$266$	−16.5316	+	3.00351i	−1.01362	+	0.184157i
$267$	−10.3487	+	3.46148i	−0.633333	+	0.211839i
$268$	−4.90506	−	7.00516i	−0.299624	−	0.427908i
$269$	17.6386	+	14.8005i	1.07544	+	0.902403i	0.995534	−	0.0943990i	$-0.0300929\pi$
$269$	17.6386	+	14.8005i	1.07544	+	0.902403i	0.0799079	+	0.996802i	$0.474537\pi$
$270$	3.21852	+	11.1643i	0.195873	+	0.679436i
$271$	6.89457	−	2.50942i	0.418815	−	0.152436i	−0.124012	−	0.992281i	$-0.539576\pi$
$271$	6.89457	−	2.50942i	0.418815	−	0.152436i	0.542827	+	0.839844i	$0.317354\pi$
$272$	−0.157391	+	1.79899i	−0.00954324	+	0.109080i
$273$	0.853935	+	0.755651i	0.0516825	+	0.0457341i
$274$	−4.75392	−	2.74467i	−0.287195	−	0.165812i
$275$	14.9624	−	27.2139i	0.902268	−	1.64106i
$276$	12.2704	+	3.63600i	0.738593	+	0.218862i
$277$	−21.3346	+	5.71659i	−1.28187	+	0.343477i	−0.834568	−	0.550905i	$-0.814283\pi$
$277$	−21.3346	+	5.71659i	−1.28187	+	0.343477i	−0.447305	+	0.894382i	$0.647616\pi$
$278$	−4.15625	+	15.5113i	−0.249276	+	0.930309i
$279$	1.34372	−	5.81496i	0.0804463	−	0.348132i
$280$	−6.15818	−	6.03078i	−0.368022	−	0.360408i
$281$	−1.92582	+	5.29115i	−0.114885	+	0.315643i	−0.983787	−	0.179340i	$-0.942604\pi$
$281$	−1.92582	+	5.29115i	−0.114885	+	0.315643i	0.868902	+	0.494984i	$0.164826\pi$
$282$	−2.07484	+	5.26575i	−0.123555	+	0.313571i
$283$	3.70622	+	5.29303i	0.220312	+	0.314638i	0.914059	−	0.405580i	$-0.132931\pi$
$283$	3.70622	+	5.29303i	0.220312	+	0.314638i	−0.693747	+	0.720218i	$0.744042\pi$
$284$	4.53979			0.269387
$285$	−16.3523	+	4.19563i	−0.968625	+	0.248528i
$286$	−1.06079			−0.0627261
$287$	7.96290	+	11.3722i	0.470035	+	0.671280i
$288$	−2.22984	+	2.00694i	−0.131394	+	0.118260i
$289$	4.69897	−	12.9103i	0.276410	−	0.759430i
$290$	0.154625	+	14.7936i	0.00907990	+	0.868710i
$291$	−23.6709	+	5.68036i	−1.38761	+	0.332989i
$292$	3.87889	−	14.4762i	0.226995	−	0.847156i
$293$	−12.4950	+	3.34801i	−0.729963	+	0.195593i	−0.604613	−	0.796519i	$-0.706672\pi$
$293$	−12.4950	+	3.34801i	−0.729963	+	0.195593i	−0.125350	+	0.992113i	$0.540006\pi$
$294$	3.86724	−	13.0508i	0.225542	−	0.761136i
$295$	2.10016	+	2.93359i	0.122276	+	0.170800i
$296$	−6.86007	−	3.96067i	−0.398734	−	0.230209i
$297$	2.54190	−	32.1740i	0.147496	−	1.86693i
$298$	−1.14595	+	13.0983i	−0.0663833	+	0.758765i
$299$	1.18581	−	0.431601i	0.0685774	−	0.0249601i
$300$	−6.60411	−	5.60229i	−0.381289	−	0.323449i
$301$	−15.8650	−	13.3123i	−0.914442	−	0.767308i
$302$	3.76862	+	5.38215i	0.216860	+	0.309708i
$303$	3.66381	+	10.9536i	0.210480	+	0.629269i
$304$	−2.81914	−	3.32453i	−0.161689	−	0.190675i
$305$	−13.7685	+	6.59644i	−0.788384	+	0.377711i
$306$	−4.82760	+	2.45856i	−0.275975	+	0.140547i
$307$	2.28004	+	26.0610i	0.130129	+	1.48738i	0.727885	+	0.685700i	$0.240504\pi$
$307$	2.28004	+	26.0610i	0.130129	+	1.48738i	−0.597756	+	0.801678i	$0.703941\pi$
$308$	10.1184	+	21.6991i	0.576552	+	1.23642i
$309$	−1.26485	+	11.0915i	−0.0719548	+	0.630976i
$310$	1.56506	+	4.16402i	0.0888893	+	0.236501i
$311$	9.19721	−	5.31001i	0.521526	−	0.301103i	−0.216033	−	0.976386i	$-0.569312\pi$
$311$	9.19721	−	5.31001i	0.521526	−	0.301103i	0.737559	+	0.675283i	$0.235978\pi$
$312$	−0.0590047	+	0.289868i	−0.00334048	+	0.0164106i
$313$	26.8251	+	18.7832i	1.51625	+	1.06169i	0.975368	+	0.220586i	$0.0707968\pi$
$313$	26.8251	+	18.7832i	1.51625	+	1.06169i	0.540878	+	0.841101i	$0.318092\pi$
$314$	1.52051	+	8.62323i	0.0858072	+	0.486637i
$315$	5.55823	−	25.2537i	0.313171	−	1.42288i
$316$	−1.33649	−	2.31487i	−0.0751835	−	0.130222i
$317$	−1.63939	+	18.7384i	−0.0920776	+	1.05245i	0.799828	+	0.600229i	$0.204924\pi$
$317$	−1.63939	+	18.7384i	−0.0920776	+	1.05245i	−0.891905	+	0.452222i	$0.850632\pi$
$318$	−8.52132	+	6.77677i	−0.477852	+	0.380022i
$319$	14.0553	−	38.6165i	0.786943	−	2.16211i
$320$	0.556131	−	2.16581i	0.0310887	−	0.121072i
$321$	−6.16809	−	4.56510i	−0.344269	−	0.254799i
$322$	−20.1396	−	20.1396i	−1.12233	−	1.12233i
$323$	−3.36364	−	7.11670i	−0.187158	−	0.395984i
$324$	−8.65036	−	2.48421i	−0.480575	−	0.138012i
$325$	−0.852058	−	0.0566282i	−0.0472637	−	0.00314117i
$326$	11.5280	−	13.7386i	0.638478	−	0.760908i
$327$	0.650008	−	24.7280i	0.0359455	−	1.36746i
$328$	−1.52208	+	3.26411i	−0.0840429	+	0.180231i
$329$	9.64902	−	8.09649i	0.531968	−	0.446374i
$330$	11.6967	+	21.0207i	0.643880	+	1.15715i
$331$	6.78745	−	11.7562i	0.373072	−	0.646180i	−0.616964	−	0.786991i	$-0.711638\pi$
$331$	6.78745	−	11.7562i	0.373072	−	0.646180i	0.990036	+	0.140811i	$0.0449711\pi$
$332$	−10.0561	−	7.04134i	−0.551899	−	0.386444i
$333$	−0.824584	−	23.7497i	−0.0451869	−	1.30147i
$334$	−2.06099	−	1.18991i	−0.112772	−	0.0651090i
$335$	3.51718	+	18.7960i	0.192164	+	1.02693i
$336$	6.49222	−	1.55795i	0.354180	−	0.0849934i
$337$	16.3935	+	7.64443i	0.893012	+	0.416418i	0.814277	−	0.580477i	$-0.197134\pi$
$337$	16.3935	+	7.64443i	0.893012	+	0.416418i	0.0787356	+	0.996896i	$0.474912\pi$
$338$	−5.48171	−	11.7556i	−0.298166	−	0.639418i
$339$	−9.74643	−	22.4214i	−0.529353	−	1.21776i
$340$	1.98235	−	3.51795i	0.107508	−	0.190787i
$341$		−	12.3565i		−	0.669143i
$342$	3.97883	−	12.4567i	0.215151	−	0.673580i
$343$	−2.34058	+	2.34058i	−0.126379	+	0.126379i
$344$	0.932965	−	5.29111i	0.0503021	−	0.285277i
$345$	−21.6278	−	18.7392i	−1.16440	−	1.00888i
$346$	−1.03424	−	0.376434i	−0.0556013	−	0.0202372i
$347$	−3.89392	+	8.35055i	−0.209037	+	0.448281i	−0.982673	−	0.185350i	$-0.940658\pi$
$347$	−3.89392	+	8.35055i	−0.209037	+	0.448281i	0.773636	+	0.633630i	$0.218436\pi$
$348$	−9.77039	−	5.98865i	−0.523748	−	0.321026i
$349$	7.08477	−	4.09039i	0.379239	−	0.218954i	−0.298248	−	0.954488i	$-0.596402\pi$
$349$	7.08477	−	4.09039i	0.379239	−	0.218954i	0.677487	+	0.735535i	$0.263069\pi$
$350$	6.96905	+	17.9694i	0.372511	+	0.960506i
$351$	−0.831332	+	0.310537i	−0.0443732	+	0.0165752i
$352$	−3.56259	+	5.08791i	−0.189887	+	0.271186i
$353$	4.67972	−	1.25393i	0.249076	−	0.0667398i	−0.132121	−	0.991234i	$-0.542179\pi$
$353$	4.67972	−	1.25393i	0.249076	−	0.0667398i	0.381197	+	0.924494i	$0.375512\pi$
$354$	−2.78944	+	0.170328i	−0.148257	+	0.00905285i
$355$	−9.24452	−	4.19372i	−0.490648	−	0.222580i
$356$	2.15480	+	5.92027i	0.114204	+	0.313774i
$357$	12.0527	+	0.316823i	0.637898	+	0.0167680i
$358$	13.4220	−	1.17427i	0.709375	−	0.0620622i
$359$	1.82848	−	10.3698i	0.0965032	−	0.547297i	−0.897773	−	0.440458i	$-0.854816\pi$
$359$	1.82848	−	10.3698i	0.0965032	−	0.547297i	0.994276	−	0.106839i	$-0.0340729\pi$
$360$	6.39465	−	2.02695i	0.337027	−	0.106829i
$361$	17.9206	+	6.31274i	0.943192	+	0.332249i
$362$	5.67662	−	5.67662i	0.298357	−	0.298357i
$363$	−7.05582	−	47.2440i	−0.370334	−	2.47967i
$364$	0.423169	−	0.504314i	0.0221801	−	0.0264332i
$365$	−21.2714	+	25.8951i	−1.11340	+	1.35541i
$366$	1.33991	−	11.7497i	0.0700381	−	0.614168i
$367$	0.451928	+	0.0395385i	0.0235904	+	0.00206390i	0.0989448	−	0.995093i	$-0.468453\pi$
$367$	0.451928	+	0.0395385i	0.0235904	+	0.00206390i	−0.0753544	+	0.997157i	$0.524009\pi$
$368$	1.91237	−	7.13705i	0.0996890	−	0.372044i
$369$	−10.7244	+	1.31460i	−0.558289	+	0.0684355i
$370$	10.3106	+	14.4024i	0.536025	+	0.748743i
$371$	23.8621	−	4.20754i	1.23886	−	0.218445i
$372$	−3.37649	−	0.687308i	−0.175063	−	0.0356353i
$373$	−5.05851	−	1.35542i	−0.261920	−	0.0701811i	0.125469	−	0.992097i	$-0.459956\pi$
$373$	−5.05851	−	1.35542i	−0.261920	−	0.0701811i	−0.387389	+	0.921916i	$0.626623\pi$
$374$	−8.59237	+	7.20986i	−0.444301	+	0.372813i
$375$	8.27293	+	17.5088i	0.427212	+	0.904151i
$376$	3.07061	+	1.11761i	0.158355	+	0.0576364i
$377$	−1.12567	+	0.0984838i	−0.0579752	+	0.00507217i
$378$	14.2819	+	14.0432i	0.734582	+	0.722306i
$379$			35.1801i			1.80708i	0.428502	+	0.903541i	$0.359041\pi$
$379$			35.1801i			1.80708i	−0.428502	+	0.903541i	$0.640959\pi$
$380$	2.66960	+	9.37407i	0.136947	+	0.480880i
$381$	−13.2924	−	6.62900i	−0.680990	−	0.339614i
$382$	7.20994	−	5.04846i	0.368893	−	0.258301i
$383$	−1.24815	−	14.2664i	−0.0637776	−	0.728981i	−0.959008	−	0.283378i	$-0.908545\pi$
$383$	−1.24815	−	14.2664i	−0.0637776	−	0.728981i	0.895231	−	0.445603i	$-0.147011\pi$
$384$	1.19214	+	1.25650i	0.0608361	+	0.0641207i
$385$	−0.559542	−	53.5336i	−0.0285169	−	2.72833i
$386$	11.6023	+	13.8271i	0.590540	+	0.703778i
$387$	14.9457	−	6.03498i	0.759735	−	0.306775i
$388$	3.63754	+	13.5755i	0.184668	+	0.689191i
$389$	3.68583	+	20.9034i	0.186879	+	1.05984i	0.923518	+	0.383556i	$0.125301\pi$
$389$	3.68583	+	20.9034i	0.186879	+	1.05984i	−0.736639	+	0.676286i	$0.763588\pi$
$390$	0.387925	−	0.535761i	0.0196433	−	0.0271293i
$391$	6.67159	−	11.5555i	0.337397	−	0.584388i
$392$	−7.59093	−	2.03398i	−0.383400	−	0.102732i
$393$	−0.900544	−	0.551978i	−0.0454264	−	0.0278436i
$394$	−1.41347	−	3.88347i	−0.0712095	−	0.195647i
$395$	0.583130	+	5.94845i	0.0293404	+	0.299299i
$396$	−18.6078	−	0.978941i	−0.935079	−	0.0491936i
$397$	−8.26843	+	5.78962i	−0.414980	+	0.290572i	−0.762361	−	0.647152i	$-0.775960\pi$
$397$	−8.26843	+	5.78962i	−0.414980	+	0.290572i	0.347381	+	0.937724i	$0.387071\pi$
$398$	−7.14291	−	7.14291i	−0.358042	−	0.358042i
$399$	−21.0079	+	20.1399i	−1.05171	+	1.00826i
$400$	−3.13318	+	3.89656i	−0.156659	+	0.194828i
$401$	−28.6872	−	5.05833i	−1.43257	−	0.252601i	−0.597115	−	0.802156i	$-0.703686\pi$
$401$	−28.6872	−	5.05833i	−1.43257	−	0.252601i	−0.835458	+	0.549555i	$0.814797\pi$
$402$	−13.7808	−	5.43000i	−0.687324	−	0.270824i
$403$	−0.307931	+	0.143591i	−0.0153391	+	0.00715276i
$404$	6.26631	−	2.28075i	0.311761	−	0.113472i
$405$	15.3202	+	13.0496i	0.761265	+	0.648441i
$406$	12.7518	+	22.0868i	0.632863	+	1.09615i
$407$	−12.7341	−	47.5244i	−0.631207	−	2.35570i
$408$	1.49220	+	2.74895i	0.0738750	+	0.136093i
$409$	30.1159	−	5.31025i	1.48914	−	0.262575i	0.630915	−	0.775852i	$-0.282680\pi$
$409$	30.1159	−	5.31025i	1.48914	−	0.262575i	0.858223	+	0.513277i	$0.171569\pi$
$410$	6.11476	−	5.24077i	0.301986	−	0.258823i
$411$	−9.49016	+	0.579487i	−0.468115	+	0.0285840i
$412$	6.42068	+	0.561737i	0.316324	+	0.0276748i
$413$	5.63677	+	2.62847i	0.277367	+	0.129339i
$414$	21.1992	−	6.47659i	1.04188	−	0.318307i
$415$	13.9729	+	23.6280i	0.685904	+	1.15985i
$416$	0.168193	+	0.0296569i	0.00824634	+	0.00145405i
$417$	8.82292	+	26.3777i	0.432060	+	1.29172i
$418$	2.21966	−	26.9828i	0.108567	−	1.31977i
$419$	−19.8165			−0.968097			−0.484049	−	0.875041i	$-0.660834\pi$
$419$	−19.8165			−0.968097			−0.484049	+	0.875041i	$0.660834\pi$
$420$	−14.6595	−	2.82481i	−0.715311	−	0.137837i
$421$	−17.2290	−	14.4568i	−0.839690	−	0.704583i	0.117804	−	0.993037i	$-0.462415\pi$
$421$	−17.2290	−	14.4568i	−0.839690	−	0.704583i	−0.957494	+	0.288453i	$0.906859\pi$
$422$	−2.39720	+	1.11783i	−0.116694	+	0.0544153i
$423$	2.03624	+	9.58922i	0.0990053	+	0.466244i
$424$	4.04050	+	4.81528i	0.196224	+	0.233851i
$425$	−7.28651	+	5.33246i	−0.353447	+	0.258663i
$426$	6.55740	−	4.33930i	0.317707	−	0.210240i
$427$	−15.0958	+	21.5590i	−0.730535	+	1.04331i
$428$	−2.54118	+	3.62918i	−0.122832	+	0.175423i
$429$	−1.53224	+	1.01395i	−0.0739773	+	0.0489538i
$430$	−6.78760	+	9.91260i	−0.327327	+	0.478028i
$431$	15.7255	+	18.7409i	0.757470	+	0.902718i	0.997685	−	0.0680021i	$-0.0216624\pi$
$431$	15.7255	+	18.7409i	0.757470	+	0.902718i	−0.240215	+	0.970720i	$0.577218\pi$
$432$	−1.30253	+	5.03025i	−0.0626679	+	0.242018i
$433$	22.2793	−	10.3890i	1.07068	−	0.499264i	0.194324	−	0.980937i	$-0.437749\pi$
$433$	22.2793	−	10.3890i	1.07068	−	0.499264i	0.876351	+	0.481673i	$0.159971\pi$
$434$	5.87443	+	4.92924i	0.281982	+	0.236611i
$435$	14.3636	+	21.2205i	0.688683	+	1.01744i
$436$	−14.2816			−0.683966
$437$	8.49713	+	31.0660i	0.406473	+	1.48609i
$438$	−8.23413	−	24.6174i	−0.393442	−	1.17627i
$439$	−15.6147	−	2.75329i	−0.745247	−	0.131407i	−0.211886	−	0.977294i	$-0.567960\pi$
$439$	−15.6147	−	2.75329i	−0.745247	−	0.131407i	−0.533362	+	0.845887i	$0.679072\pi$
$440$	11.9547	−	7.06965i	0.569917	−	0.337032i
$441$	−6.88847	−	22.5474i	−0.328022	−	1.07368i
$442$	0.279522	+	0.130343i	0.0132955	+	0.00619980i
$443$	34.3850	+	3.00830i	1.63368	+	0.142929i	0.866730	−	0.498778i	$-0.166218\pi$
$443$	34.3850	+	3.00830i	1.63368	+	0.142929i	0.766951	+	0.641706i	$0.221773\pi$
$444$	−13.6946	+	0.836220i	−0.649919	+	0.0396853i
$445$	1.08108	−	14.0462i	0.0512481	−	0.665853i
$446$	−23.0195	+	4.05896i	−1.09000	+	0.192197i
$447$	10.8646	+	20.0149i	0.513879	+	0.946673i
$448$	−0.997670	−	3.72335i	−0.0471355	−	0.175912i
$449$	13.7522	+	23.8196i	0.649008	+	1.12411i	0.983360	+	0.181667i	$0.0581491\pi$
$449$	13.7522	+	23.8196i	0.649008	+	1.12411i	−0.334352	+	0.942448i	$0.608518\pi$
$450$	−14.8941	−	1.77965i	−0.702112	−	0.0838936i
$451$	−21.0208	+	7.65096i	−0.989833	+	0.360270i
$452$	−12.7927	+	5.96532i	−0.601716	+	0.280585i
$453$	10.5880	+	4.17194i	0.497466	+	0.196015i
$454$	14.3232	+	2.52557i	0.672223	+	0.118531i
$455$	−1.32758	+	0.636039i	−0.0622381	+	0.0298179i
$456$	−7.24975	−	2.10740i	−0.339501	−	0.0986882i
$457$	−14.0461	−	14.0461i	−0.657048	−	0.657048i	0.297633	−	0.954681i	$-0.403803\pi$
$457$	−14.0461	−	14.0461i	−0.657048	−	0.657048i	−0.954681	+	0.297633i	$0.903803\pi$
$458$	−0.725098	+	0.507719i	−0.0338816	+	0.0237242i
$459$	−4.62313	+	8.16562i	−0.215789	+	0.381138i
$460$	−10.4872	+	12.7668i	−0.488969	+	0.595256i
$461$	−12.2137	−	33.5568i	−0.568847	−	1.56289i	−0.806307	−	0.591497i	$-0.798537\pi$
$461$	−12.2137	−	33.5568i	−0.568847	−	1.56289i	0.237460	−	0.971397i	$-0.423685\pi$
$462$	35.3562	+	21.6712i	1.64492	+	1.00823i
$463$	5.88103	+	1.57582i	0.273315	+	0.0732344i	0.392873	−	0.919593i	$-0.371481\pi$
$463$	5.88103	+	1.57582i	0.273315	+	0.0732344i	−0.119558	+	0.992827i	$0.538148\pi$
$464$	−3.30813	+	5.72985i	−0.153576	+	0.266001i
$465$	6.24075	+	4.51869i	0.289408	+	0.209549i
$466$	2.38041	+	13.5000i	0.110271	+	0.625375i
$467$	5.50776	+	20.5553i	0.254869	+	0.951184i	0.968163	+	0.250319i	$0.0805356\pi$
$467$	5.50776	+	20.5553i	0.254869	+	0.951184i	−0.713294	+	0.700865i	$0.752798\pi$
$468$	0.191839	+	0.475093i	0.00886776	+	0.0219612i
$469$	21.1890	+	25.2521i	0.978419	+	1.16603i
$470$	−5.22037	−	5.11237i	−0.240798	−	0.235816i
$471$	10.4387	+	11.0023i	0.480989	+	0.506958i
$472$	0.140624	+	1.60734i	0.00647275	+	0.0739839i
$473$	27.3360	−	19.1408i	1.25691	−	0.880097i
$474$	−4.14311	−	2.06620i	−0.190299	−	0.0949035i
$475$	3.22331	−	21.5548i	0.147896	−	0.989003i
$476$		−	6.96105i		−	0.319059i
$477$	−5.83095	+	17.9336i	−0.266981	+	0.821122i
$478$	−21.8587	+	1.91239i	−0.999792	+	0.0874705i
$479$	33.1324	+	12.0592i	1.51386	+	0.550999i	0.959605	−	0.281351i	$-0.0907824\pi$
$479$	33.1324	+	12.0592i	1.51386	+	0.550999i	0.554251	+	0.832349i	$0.313005\pi$
$480$	−1.26687	−	3.65992i	−0.0578244	−	0.167052i
$481$	−1.03635	+	0.869605i	−0.0472537	+	0.0396506i
$482$	6.46021	+	1.73101i	0.294254	+	0.0788452i
$483$	−48.3404	−	9.84001i	−2.19956	−	0.447736i
$484$	−27.1599	+	4.78902i	−1.23454	+	0.217683i
$485$	5.13340	−	31.0045i	0.233096	−	1.40784i
$486$	−14.8693	+	4.68008i	−0.674486	+	0.212293i
$487$	−4.83858	+	18.0578i	−0.219257	+	0.818278i	0.765368	+	0.643593i	$0.222557\pi$
$487$	−4.83858	+	18.0578i	−0.219257	+	0.818278i	−0.984624	+	0.174685i	$0.944109\pi$
$488$	−6.80169	−	0.595071i	−0.307898	−	0.0269376i
$489$	3.51956	−	30.8633i	0.159160	−	1.39569i
$490$	13.5787	+	11.1541i	0.613424	+	0.503893i
$491$	8.29760	−	9.88870i	0.374466	−	0.446271i	−0.545594	−	0.838050i	$-0.683696\pi$
$491$	8.29760	−	9.88870i	0.374466	−	0.446271i	0.920059	+	0.391779i	$0.128140\pi$
$492$	0.921426	+	6.16964i	0.0415411	+	0.278149i
$493$	−8.44854	+	8.44854i	−0.380503	+	0.380503i
$494$	−0.698219	+	0.258242i	−0.0314144	+	0.0116189i
$495$	36.9874	+	19.1828i	1.66246	+	0.862204i
$496$	−0.345455	+	1.95917i	−0.0155114	+	0.0879695i
$497$	−17.4329	+	1.52518i	−0.781974	+	0.0684139i
$498$	−21.2557	−	0.558734i	−0.952489	−	0.0250375i
$499$	3.49017	+	9.58915i	0.156241	+	0.429269i	0.992973	−	0.118344i	$-0.0377586\pi$
$499$	3.49017	+	9.58915i	0.156241	+	0.429269i	−0.836731	+	0.547614i	$0.815536\pi$
$500$	9.97972	−	5.04036i	0.446307	−	0.225412i
$501$	−4.11431	+	0.251227i	−0.183814	+	0.0112240i
$502$	3.06651	−	0.821668i	0.136865	−	0.0366728i
$503$	−17.1913	+	24.5517i	−0.766523	+	1.09471i	0.226176	+	0.974086i	$0.427378\pi$
$503$	−17.1913	+	24.5517i	−0.766523	+	1.09471i	−0.992699	+	0.120621i	$0.961511\pi$
$504$	7.88839	−	8.45586i	0.351377	−	0.376654i
$505$	−14.8672	−	1.14427i	−0.661581	−	0.0509193i
$506$	39.7448	−	22.9467i	1.76687	−	1.02010i
$507$	−19.1544	−	11.7404i	−0.850675	−	0.521412i
$508$	−3.62427	+	7.77228i	−0.160801	+	0.344839i
$509$	5.22986	+	1.90351i	0.231809	+	0.0843718i	0.455313	−	0.890331i	$-0.349527\pi$
$509$	5.22986	+	1.90351i	0.231809	+	0.0843718i	−0.223504	+	0.974703i	$0.571749\pi$
$510$	−0.499217	−	6.97623i	−0.0221057	−	0.308913i
$511$	−10.0316	+	56.8922i	−0.443773	+	2.51676i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−6.15943	−	21.7959i	−0.271945	−	0.962313i
$514$			30.5631i			1.34808i
$515$	−12.5557	−	7.07512i	−0.553272	−	0.311767i
$516$	−3.70984	−	8.53439i	−0.163317	−	0.375706i
$517$	8.57752	+	18.3946i	0.377239	+	0.808992i
$518$	27.6735	+	12.9044i	1.21590	+	0.566986i
$519$	−1.85370	+	0.444838i	−0.0813685	+	0.0195262i
$520$	−0.315100	−	0.215763i	−0.0138181	−	0.00946184i
$521$	−1.21902	−	0.703804i	−0.0534064	−	0.0308342i	0.473059	−	0.881031i	$-0.343150\pi$
$521$	−1.21902	−	0.703804i	−0.0534064	−	0.0308342i	−0.526465	+	0.850197i	$0.676483\pi$
$522$	−19.8368	+	0.688730i	−0.868234	+	0.0301449i
$523$	−32.9449	−	23.0683i	−1.44058	−	1.00870i	−0.993454	−	0.114234i	$-0.963559\pi$
$523$	−32.9449	−	23.0683i	−1.44058	−	1.00870i	−0.447126	−	0.894471i	$-0.647552\pi$
$524$	−0.304912	+	0.528124i	−0.0133202	+	0.0230712i
$525$	27.2421	+	19.2943i	1.18894	+	0.842071i
$526$	1.56123	−	1.31003i	0.0680730	−	0.0571201i
$527$	−1.51829	+	3.25598i	−0.0661377	+	0.141833i
$528$	−0.282694	+	10.7544i	−0.0123027	+	0.468024i
$529$	−20.3086	+	24.2029i	−0.882983	+	1.05230i
$530$	−3.77958	−	13.5380i	−0.164175	−	0.588053i
$531$	−3.86634	+	2.91228i	−0.167785	+	0.126382i
$532$	11.9425	+	11.8192i	0.517772	+	0.512426i
$533$	0.434941	+	0.434941i	0.0188394	+	0.0188394i
$534$	8.77127	+	6.49176i	0.379570	+	0.280926i
$535$	8.52721	−	5.04274i	0.368663	−	0.218017i
$536$	−2.92486	+	8.03598i	−0.126335	+	0.347102i
$537$	18.2647	−	14.5254i	0.788180	−	0.626818i
$538$	2.00681	−	22.9379i	0.0865195	−	0.988923i
$539$	−24.4060	−	42.2724i	−1.05124	−	1.82080i
$540$	7.29918	−	9.04002i	0.314107	−	0.389021i
$541$	−3.87507	−	21.9766i	−0.166602	−	0.944849i	−0.947397	−	0.320061i	$-0.896296\pi$
$541$	−3.87507	−	21.9766i	−0.166602	−	0.944849i	0.780794	−	0.624788i	$-0.214815\pi$
$542$	−6.01016	−	4.20836i	−0.258158	−	0.180765i
$543$	2.77354	−	13.6254i	0.119024	−	0.584722i
$544$	1.56392	−	0.902931i	0.0670526	−	0.0387128i
$545$	29.0821	+	13.1929i	1.24574	+	0.565124i
$546$	0.129196	−	1.13293i	0.00552907	−	0.0484848i
$547$	−0.818057	−	1.75433i	−0.0349776	−	0.0750097i	0.888043	−	0.459761i	$-0.152065\pi$
$547$	−0.818057	−	1.75433i	−0.0349776	−	0.0750097i	−0.923020	+	0.384751i	$0.874287\pi$
$548$	0.478428	+	5.46846i	0.0204374	+	0.233601i
$549$	−9.29543	−	18.2524i	−0.396719	−	0.778992i
$550$	−30.8744	+	3.35278i	−1.31649	+	0.142963i
$551$	−0.149655	−	28.8392i	−0.00637550	−	1.22859i
$552$	−4.05958	−	12.1369i	−0.172787	−	0.516579i
$553$	5.90987	+	8.44017i	0.251313	+	0.358912i
$554$	16.9198	+	14.1974i	0.718853	+	0.603190i
$555$	28.6593	+	10.9479i	1.21652	+	0.464712i
$556$	15.0901	−	5.49234i	0.639962	−	0.232927i
$557$	0.486210	−	5.55741i	0.0206014	−	0.235475i	−0.978912	−	0.204282i	$-0.934514\pi$
$557$	0.486210	−	5.55741i	0.0206014	−	0.235475i	0.999513	−	0.0311926i	$-0.00993053\pi$
$558$	−5.53406	+	2.23461i	−0.234275	+	0.0945987i
$559$	−0.794661	−	0.458798i	−0.0336106	−	0.0194051i
$560$	−1.40794	+	8.50360i	−0.0594963	+	0.359343i
$561$	−5.51961	+	18.6270i	−0.233038	+	0.786434i
$562$	5.43886	−	1.45734i	0.229424	−	0.0614741i
$563$	−5.83241	+	21.7669i	−0.245807	+	0.917364i	0.727169	+	0.686458i	$0.240836\pi$
$563$	−5.83241	+	21.7669i	−0.245807	+	0.917364i	−0.972976	+	0.230906i	$0.925831\pi$
$564$	5.50353	−	1.32070i	0.231741	−	0.0556114i
$565$	31.5607	−	0.329878i	1.32777	−	0.0138781i
$566$	2.21000	−	6.07192i	0.0928931	−	0.255222i
$567$	34.0522	+	6.63328i	1.43006	+	0.278571i
$568$	−2.60392	−	3.71878i	−0.109258	−	0.156036i
$569$	−18.7453			−0.785845			−0.392923	−	0.919571i	$-0.628536\pi$
$569$	−18.7453			−0.785845			−0.392923	+	0.919571i	$0.628536\pi$
$570$	12.8161	+	10.9885i	0.536809	+	0.460257i
$571$	−15.0821			−0.631164			−0.315582	−	0.948898i	$-0.602200\pi$
$571$	−15.0821			−0.631164			−0.315582	+	0.948898i	$0.602200\pi$
$572$	0.608446	+	0.868951i	0.0254404	+	0.0363327i
$573$	5.58874	−	14.1837i	0.233473	−	0.592531i
$574$	4.74823	−	13.0457i	0.198187	−	0.544515i
$575$	33.1490	−	16.3097i	1.38241	−	0.680161i
$576$	2.92297	+	0.675440i	0.121791	+	0.0281433i
$577$	−6.20810	+	23.1689i	−0.258447	+	0.964536i	0.707694	+	0.706519i	$0.249736\pi$
$577$	−6.20810	+	23.1689i	−0.258447	+	0.964536i	−0.966140	+	0.258017i	$0.916931\pi$
$578$	−13.2707	+	3.55588i	−0.551989	+	0.147905i
$579$	29.9751	+	8.88229i	1.24572	+	0.369136i
$580$	12.0295	−	8.61192i	0.499498	−	0.357590i
$581$	40.9812	+	23.6605i	1.70019	+	0.981604i
$582$	18.2301	+	16.1319i	0.755664	+	0.668690i
$583$	−3.40281	+	38.8943i	−0.140930	+	1.61084i
$584$	−14.0830	+	5.12581i	−0.582761	+	0.212108i
$585$	0.0482289	−	1.14466i	0.00199402	−	0.0473260i
$586$	9.90935	+	8.31493i	0.409351	+	0.343487i
$587$	−8.01473	−	11.4462i	−0.330803	−	0.472436i	0.618952	−	0.785429i	$-0.287557\pi$
$587$	−8.01473	−	11.4462i	−0.330803	−	0.472436i	−0.949756	+	0.312993i	$0.898668\pi$
$588$	−12.9087	+	4.31776i	−0.532347	+	0.178061i
$589$	−3.00810	−	8.13312i	−0.123947	−	0.335119i
$590$	1.19846	−	3.40299i	0.0493397	−	0.140099i
$591$	−5.75362	−	4.25835i	−0.236672	−	0.175165i
$592$	0.690389	+	7.89119i	0.0283748	+	0.324326i
$593$	1.77958	+	3.81631i	0.0730784	+	0.156717i	0.939453	−	0.342677i	$-0.111334\pi$
$593$	1.77958	+	3.81631i	0.0730784	+	0.156717i	−0.866375	+	0.499394i	$0.833556\pi$
$594$	−27.8134	+	16.3721i	−1.14120	+	0.671754i
$595$	−6.43042	+	14.1750i	−0.263621	+	0.581119i
$596$	11.3868	−	6.57417i	0.466422	−	0.269289i
$597$	−17.1449	−	3.48996i	−0.701694	−	0.142835i
$598$	−1.03370	−	0.723806i	−0.0422712	−	0.0295986i
$599$	2.85741	+	16.2052i	0.116751	+	0.662126i	0.985869	+	0.167521i	$0.0535762\pi$
$599$	2.85741	+	16.2052i	0.116751	+	0.662126i	−0.869118	+	0.494605i	$0.835313\pi$
$600$	−0.801167	+	8.62312i	−0.0327075	+	0.352037i
$601$	0.487378	+	0.844164i	0.0198806	+	0.0344342i	0.875795	−	0.482684i	$-0.160338\pi$
$601$	0.487378	+	0.844164i	0.0198806	+	0.0344342i	−0.855914	+	0.517118i	$0.827005\pi$
$602$	−1.80502	+	20.6315i	−0.0735671	+	0.840875i
$603$	−25.0956	+	5.32897i	−1.02197	+	0.217012i
$604$	2.24721	−	6.17415i	0.0914375	−	0.251223i
$605$	59.7305	+	15.3375i	2.42839	+	0.623557i
$606$	6.87121	−	9.28396i	0.279124	−	0.377135i
$607$	22.7741	+	22.7741i	0.924373	+	0.924373i	0.997335	−	0.0729620i	$-0.0232452\pi$
$607$	22.7741	+	22.7741i	0.924373	+	0.924373i	−0.0729620	+	0.997335i	$0.523245\pi$
$608$	−1.10630	+	4.21617i	−0.0448665	+	0.170988i
$609$	39.5306	+	19.7142i	1.60186	+	0.798858i
$610$	13.3008	+	7.49497i	0.538534	+	0.303462i
$611$	0.358726	−	0.427513i	0.0145125	−	0.0172953i
$612$	4.78293	+	2.54436i	0.193339	+	0.102850i
$613$	4.28488	−	9.18896i	0.173065	−	0.371139i	−0.800574	−	0.599234i	$-0.795472\pi$
$613$	4.28488	−	9.18896i	0.173065	−	0.371139i	0.973639	+	0.228095i	$0.0732498\pi$
$614$	20.0401	−	16.8157i	0.808753	−	0.678625i
$615$	3.82301	−	13.4146i	0.154158	−	0.540930i
$616$	11.9711	−	20.7346i	0.482331	−	0.835421i
$617$	−16.3189	−	11.4266i	−0.656976	−	0.460019i	0.196950	−	0.980413i	$-0.436896\pi$
$617$	−16.3189	−	11.4266i	−0.656976	−	0.460019i	−0.853926	+	0.520394i	$0.825785\pi$
$618$	9.81115	−	5.32574i	0.394662	−	0.214233i
$619$	2.50509	+	1.44631i	0.100688	+	0.0581322i	0.549498	−	0.835495i	$-0.314819\pi$
$619$	2.50509	+	1.44631i	0.100688	+	0.0581322i	−0.448810	+	0.893627i	$0.648152\pi$
$620$	2.51329	−	3.67041i	0.100936	−	0.147407i
$621$	24.4301	−	29.6179i	0.980347	−	1.18853i
$622$	−9.62501	−	4.48822i	−0.385928	−	0.179961i
$623$	−10.2635	−	22.0101i	−0.411197	−	0.881816i
$624$	0.271290	−	0.117928i	0.0108603	−	0.00472089i
$625$	−24.9782	+	1.04487i	−0.999126	+	0.0417950i
$626$		−	32.7474i		−	1.30885i
$627$	−22.5850	−	41.0964i	−0.901960	−	1.64123i
$628$	6.19161	−	6.19161i	0.247072	−	0.247072i
$629$	−2.48401	+	14.0875i	−0.0990438	+	0.561705i
$630$	−23.8747	+	9.93188i	−0.951190	+	0.395695i
$631$	−30.4987	−	11.1006i	−1.21414	−	0.441909i	−0.345999	−	0.938235i	$-0.612460\pi$
$631$	−30.4987	−	11.1006i	−1.21414	−	0.441909i	−0.868137	+	0.496325i	$0.834682\pi$
$632$	−1.12965	+	2.42254i	−0.0449351	+	0.0963636i
$633$	−2.39412	+	3.90597i	−0.0951578	+	0.155248i
$634$	16.2899	−	9.40497i	0.646954	−	0.373519i
$635$	14.5600	−	12.4789i	0.577797	−	0.495212i
$636$	10.4388	+	3.09326i	0.413927	+	0.122656i
$637$	−0.769837	+	1.09944i	−0.0305021	+	0.0435615i
$638$	−39.6946	+	10.6361i	−1.57152	+	0.421088i
$639$	5.32403	−	12.5356i	0.210615	−	0.495902i
$640$	−2.09311	+	0.786700i	−0.0827374	+	0.0310970i
$641$	10.0191	+	27.5272i	0.395729	+	1.08726i	0.964344	+	0.264653i	$0.0852574\pi$
$641$	10.0191	+	27.5272i	0.395729	+	1.08726i	−0.568614	+	0.822604i	$0.692520\pi$
$642$	−0.201644	+	7.67104i	−0.00795824	+	0.302752i
$643$	−22.0909	+	1.93270i	−0.871179	+	0.0762183i	−0.513972	−	0.857807i	$-0.671827\pi$
$643$	−22.0909	+	1.93270i	−0.871179	+	0.0762183i	−0.357207	+	0.934025i	$0.616271\pi$
$644$	−4.94579	+	28.0490i	−0.194891	+	1.10528i
$645$	−0.329354	+	20.8059i	−0.0129683	+	0.819231i
$646$	−3.90036	+	6.83731i	−0.153457	+	0.269010i
$647$	−12.6179	+	12.6179i	−0.496060	+	0.496060i	−0.910209	−	0.414149i	$-0.864079\pi$
$647$	−12.6179	+	12.6179i	−0.496060	+	0.496060i	0.414149	+	0.910209i	$0.364079\pi$
$648$	2.92670	+	8.51084i	0.114972	+	0.334337i
$649$	−6.44179	+	7.67702i	−0.252862	+	0.301350i
$650$	0.442333	+	0.730446i	0.0173497	+	0.0286504i
$651$	13.1968	+	1.50492i	0.517222	+	0.0589825i
$652$	−17.8662	−	1.56309i	−0.699693	−	0.0612152i
$653$	−8.71012	+	32.5066i	−0.340853	+	1.27208i	0.556529	+	0.830828i	$0.312133\pi$
$653$	−8.71012	+	32.5066i	−0.340853	+	1.27208i	−0.897383	+	0.441253i	$0.854534\pi$
$654$	−20.6288	+	13.6509i	−0.806650	+	0.533793i
$655$	1.10877	−	0.793766i	0.0433232	−	0.0310150i
$656$	3.54684	−	0.625403i	0.138481	−	0.0244179i
$657$	−35.4239	−	27.6876i	−1.38202	−	1.08020i
$658$	−12.1667	−	3.26006i	−0.474308	−	0.127090i
$659$	−21.8138	+	18.3040i	−0.849746	+	0.713021i	−0.959734	−	0.280912i	$-0.909363\pi$
$659$	−21.8138	+	18.3040i	−0.849746	+	0.713021i	0.109988	+	0.993933i	$0.464919\pi$
$660$	10.5102	−	21.6383i	0.409110	−	0.842271i
$661$	26.6217	+	9.68952i	1.03547	+	0.376878i	0.803159	−	0.595764i	$-0.203151\pi$
$661$	26.6217	+	9.68952i	1.03547	+	0.376878i	0.232306	+	0.972643i	$0.425373\pi$
$662$	−13.5232	+	1.18313i	−0.525596	+	0.0459837i
$663$	0.528337	−	0.0789063i	0.0205189	−	0.00306447i
$664$			12.2762i			0.476409i
$665$	−13.4006	−	35.0999i	−0.519655	−	1.36111i
$666$	−18.9816	+	14.2977i	−0.735524	+	0.554025i
$667$	40.0453	−	28.0400i	1.55056	−	1.08571i
$668$	0.207415	+	2.37077i	0.00802513	+	0.0917277i
$669$	−29.3703	+	27.8658i	−1.13552	+	1.07735i
$670$	13.3794	−	13.6620i	0.516891	−	0.527810i
$671$	−27.2593	−	32.4864i	−1.05233	−	1.25412i
$672$	−4.99999	−	4.42451i	−0.192879	−	0.170679i
$673$	−6.23196	−	23.2580i	−0.240224	−	0.896530i	−0.975724	−	0.219004i	$-0.929719\pi$
$673$	−6.23196	−	23.2580i	−0.240224	−	0.896530i	0.735499	−	0.677525i	$-0.236948\pi$
$674$	−3.14099	−	17.8135i	−0.120986	−	0.686149i
$675$	−23.2145	+	11.6657i	−0.893525	+	0.449014i
$676$	−6.48542	+	11.2331i	−0.249439	+	0.432041i
$677$	−18.8373	−	5.04743i	−0.723975	−	0.193989i	−0.122030	−	0.992526i	$-0.538941\pi$
$677$	−18.8373	−	5.04743i	−0.723975	−	0.193989i	−0.601945	+	0.798538i	$0.705607\pi$
$678$	−12.7762	+	20.8442i	−0.490668	+	0.800516i
$679$	−18.5291	−	50.9083i	−0.711081	−	1.95368i
$680$	−4.01876	+	0.393961i	−0.154113	+	0.0151077i
$681$	23.1029	−	10.0427i	0.885306	−	0.384837i
$682$	−10.1219	+	7.08741i	−0.387586	+	0.271391i
$683$	−6.67662	−	6.67662i	−0.255474	−	0.255474i	0.567737	−	0.823210i	$-0.307819\pi$
$683$	−6.67662	−	6.67662i	−0.255474	−	0.255474i	−0.823210	+	0.567737i	$0.807819\pi$
$684$	−12.4861	+	3.88559i	−0.477417	+	0.148569i
$685$	4.07737	−	11.5776i	0.155788	−	0.442356i
$686$	3.25979	+	0.574789i	0.124459	+	0.0219455i
$687$	−0.562055	+	1.42644i	−0.0214437	+	0.0544221i
$688$	−4.86935	+	2.27061i	−0.185642	+	0.0865664i
$689$	1.00881	−	0.367177i	0.0384326	−	0.0139883i
$690$	−2.94502	+	28.4648i	−0.112115	+	1.08364i
$691$	10.0500	+	17.4071i	0.382319	+	0.662196i	0.991393	−	0.130917i	$-0.0417921\pi$
$691$	10.0500	+	17.4071i	0.382319	+	0.662196i	−0.609074	+	0.793113i	$0.708459\pi$
$692$	0.284861	+	1.06312i	0.0108288	+	0.0404137i
$693$	71.7836	−	2.49231i	2.72683	−	0.0946750i
$694$	9.07383	−	1.59996i	0.344438	−	0.0607337i
$695$	−35.8021	−	2.75555i	−1.35805	−	0.104524i
$696$	0.698450	+	11.4384i	0.0264747	+	0.433571i
$697$	6.47915	+	0.566852i	0.245415	+	0.0214711i
$698$	−7.41431	−	3.45735i	−0.280636	−	0.130863i
$699$	16.3421	+	17.2245i	0.618117	+	0.651490i
$700$	10.7224	−	16.0155i	0.405269	−	0.605331i
$701$	8.57744	+	1.51243i	0.323965	+	0.0571238i	0.333266	−	0.942833i	$-0.391849\pi$
$701$	8.57744	+	1.51243i	0.323965	+	0.0571238i	−0.00930044	+	0.999957i	$0.502960\pi$
$702$	0.731210	+	0.502871i	0.0275977	+	0.0189796i
$703$	−19.9511	−	28.1808i	−0.752470	−	1.06286i
$704$	6.21119			0.234093
$705$	−12.4270	−	2.39462i	−0.468029	−	0.0901868i
$706$	−3.71133	−	3.11418i	−0.139678	−	0.117204i
$707$	−23.2966	+	10.8634i	−0.876159	+	0.408559i
$708$	1.73948	+	2.18728i	0.0653737	+	0.0822029i
$709$	−28.0795	−	33.4638i	−1.05455	−	1.25676i	−0.965409	−	0.260741i	$-0.916033\pi$
$709$	−28.0795	−	33.4638i	−1.05455	−	1.25676i	−0.0891384	−	0.996019i	$-0.528411\pi$
$710$	1.86714	+	9.97809i	0.0700725	+	0.374471i
$711$	−7.95937	+	0.975666i	−0.298500	+	0.0365903i
$712$	3.61366	−	5.16084i	0.135428	−	0.193411i
$713$	8.43117	−	12.0410i	0.315750	−	0.450937i
$714$	−6.65364	−	10.0547i	−0.249006	−	0.376289i
$715$	−0.436287	−	2.33154i	−0.0163162	−	0.0871946i
$716$	−8.66045	−	10.3211i	−0.323656	−	0.385718i
$717$	−29.7454	+	23.6557i	−1.11086	+	0.883437i
$718$	−9.54321	+	4.45007i	−0.356150	+	0.166075i
$719$	4.23694	+	3.55521i	0.158011	+	0.132587i	0.718365	−	0.695666i	$-0.244891\pi$
$719$	4.23694	+	3.55521i	0.158011	+	0.132587i	−0.560354	+	0.828253i	$0.689335\pi$
$720$	−5.32819	−	4.07558i	−0.198570	−	0.151888i
$721$	−24.8444			−0.925252
$722$	−5.10777	−	18.3006i	−0.190091	−	0.681077i
$723$	10.9859	−	3.67460i	0.408569	−	0.136660i
$724$	−7.90599	−	1.39404i	−0.293824	−	0.0518091i
$725$	−32.4515	+	6.42421i	−1.20522	+	0.238589i
$726$	−34.6530	+	32.8778i	−1.28609	+	1.22021i
$727$	−5.02995	−	2.34550i	−0.186551	−	0.0869899i	0.327099	−	0.944990i	$-0.393929\pi$
$727$	−5.02995	−	2.34550i	−0.186551	−	0.0869899i	−0.513649	+	0.858000i	$0.671707\pi$
$728$	−0.655830	−	0.0573777i	−0.0243067	−	0.00212656i
$729$	−17.0043	+	20.9727i	−0.629788	+	0.776767i
$730$	33.4128	+	2.57166i	1.23666	+	0.0951813i
$731$	−9.55500	+	1.68481i	−0.353405	+	0.0623148i
$732$	−10.3934	+	5.64178i	−0.384149	+	0.208526i
$733$	6.56460	+	24.4994i	0.242469	+	0.904907i	0.974639	+	0.223784i	$0.0718412\pi$
$733$	6.56460	+	24.4994i	0.242469	+	0.904907i	−0.732170	+	0.681122i	$0.761492\pi$
$734$	−0.226827	−	0.392876i	−0.00837234	−	0.0145013i
$735$	30.2751	+	3.13231i	1.11671	+	0.115537i
$736$	−6.94321	+	2.52712i	−0.255930	+	0.0931510i
$737$	−48.1397	+	22.4479i	−1.77325	+	0.826880i
$738$	7.22811	+	8.03087i	0.266070	+	0.295621i
$739$	22.1066	+	3.89798i	0.813203	+	0.143390i	0.564758	−	0.825257i	$-0.308970\pi$
$739$	22.1066	+	3.89798i	0.813203	+	0.143390i	0.248445	+	0.968646i	$0.420081\pi$
$740$	5.88379	−	16.7068i	0.216292	−	0.614156i
$741$	−0.761691	+	1.04040i	−0.0279814	+	0.0382199i
$742$	−17.1334	−	17.1334i	−0.628986	−	0.628986i
$743$	18.4258	−	12.9019i	0.675976	−	0.473323i	−0.184488	−	0.982835i	$-0.559063\pi$
$743$	18.4258	−	12.9019i	0.675976	−	0.473323i	0.860464	+	0.509511i	$0.170174\pi$
$744$	1.37367	+	3.16009i	0.0503611	+	0.115854i
$745$	−29.2603	+	2.86840i	−1.07202	+	0.105090i
$746$	1.79114	+	4.92113i	0.0655784	+	0.180175i
$747$	−31.2363	+	19.5099i	−1.14288	+	0.713830i
$748$	10.8343	+	2.90306i	0.396143	+	0.106146i
$749$	8.53894	−	14.7899i	0.312006	−	0.540411i
$750$	9.59722	−	16.8194i	0.350441	−	0.614159i
$751$	1.71747	+	9.74024i	0.0626713	+	0.355426i	0.999976	+	0.00691575i	$0.00220137\pi$
$751$	1.71747	+	9.74024i	0.0626713	+	0.355426i	−0.937305	+	0.348511i	$0.886688\pi$
$752$	−0.845737	−	3.15633i	−0.0308408	−	0.115100i
$753$	3.64397	−	4.11792i	0.132794	−	0.150065i
$754$	0.726334	+	0.865611i	0.0264515	+	0.0315237i
$755$	−10.2796	+	10.4967i	−0.374111	+	0.382015i
$756$	3.31179	−	19.7539i	0.120449	−	0.718443i
$757$	−2.32341	−	26.5566i	−0.0844456	−	0.965218i	−0.913711	−	0.406364i	$-0.866797\pi$
$757$	−2.32341	−	26.5566i	−0.0844456	−	0.965218i	0.829266	−	0.558854i	$-0.188759\pi$
$758$	28.8179	−	20.1785i	1.04671	−	0.732916i
$759$	35.4752	−	71.1344i	1.28767	−	2.58201i
$760$	6.14757	−	7.56355i	0.222996	−	0.274359i
$761$			22.9301i			0.831215i	0.909544	+	0.415607i	$0.136431\pi$
$761$			22.9301i			0.831215i	−0.909544	+	0.415607i	$0.863569\pi$
$762$	2.19404	+	14.6907i	0.0794815	+	0.532189i
$763$	54.8419	−	4.79804i	1.98541	−	0.173701i
$764$	−8.27091	−	3.01036i	−0.299231	−	0.108911i
$765$	−7.38923	−	9.59950i	−0.267158	−	0.347071i
$766$	−10.9705	+	9.20533i	−0.396380	+	0.332602i
$767$	0.266173	+	0.0713209i	0.00961095	+	0.00257525i
$768$	0.345486	−	1.69724i	0.0124666	−	0.0612440i
$769$	−30.4540	+	5.36986i	−1.09820	+	0.193642i	−0.693250	−	0.720697i	$-0.743822\pi$
$769$	−30.4540	+	5.36986i	−1.09820	+	0.193642i	−0.404949	+	0.914339i	$0.632711\pi$
$770$	−43.5312	+	31.1640i	−1.56876	+	1.12307i
$771$	29.2133	+	44.1462i	1.05209	+	1.58989i
$772$	4.67167	−	17.4349i	0.168137	−	0.627496i
$773$	36.1265	+	3.16066i	1.29938	+	0.113681i	0.715761	−	0.698346i	$-0.246080\pi$
$773$	36.1265	+	3.16066i	1.29938	+	0.113681i	0.583620	+	0.812027i	$0.301636\pi$
$774$	−13.5161	−	8.78131i	−0.485826	−	0.315638i
$775$	−8.50851	+	5.15246i	−0.305635	+	0.185082i
$776$	9.03398	−	10.7663i	0.324301	−	0.386487i
$777$	52.3069	−	7.81195i	1.87650	−	0.280252i
$778$	15.0089	−	15.0089i	0.538096	−	0.538096i
$779$	−11.9735	+	10.1533i	−0.428993	+	0.363778i
$780$	−0.661375	−	0.0104695i	−0.0236810	−	0.000374867i
$781$	4.89644	−	27.7691i	0.175209	−	0.993657i
$782$	−13.2924	+	1.16293i	−0.475335	+	0.0415864i
$783$	−27.9946	+	19.9556i	−1.00044	+	0.713155i
$784$	2.68784	+	7.38477i	0.0959942	+	0.263742i
$785$	−18.3278	+	6.88854i	−0.654147	+	0.245863i
$786$	0.0643765	+	1.05428i	0.00229624	+	0.0376051i
$787$	47.3730	−	12.6936i	1.68867	−	0.452477i	0.718621	−	0.695402i	$-0.244774\pi$
$787$	47.3730	−	12.6936i	1.68867	−	0.452477i	0.970045	+	0.242926i	$0.0781072\pi$
$788$	−2.37042	+	3.38531i	−0.0844428	+	0.120597i
$789$	1.00291	−	3.38453i	0.0357047	−	0.120493i
$790$	4.53822	−	3.88956i	0.161463	−	0.138385i
$791$	47.1201	−	27.2048i	1.67540	−	0.967292i
$792$	9.87111	+	15.8041i	0.350755	+	0.561576i
$793$	−0.492808	+	1.05683i	−0.0175001	+	0.0375291i
$794$	9.48515	+	3.45231i	0.336615	+	0.122518i
$795$	−18.3995	−	15.9420i	−0.652562	−	0.565405i
$796$	−1.75412	+	9.94814i	−0.0621733	+	0.352602i
$797$	−9.79981	+	9.79981i	−0.347127	+	0.347127i	−0.859038	−	0.511911i	$-0.828938\pi$
$797$	−9.79981	+	9.79981i	−0.347127	+	0.347127i	0.511911	+	0.859038i	$0.328938\pi$
$798$	28.5473	+	5.65688i	1.01056	+	0.200251i
$799$		−	5.90097i		−	0.208761i
$800$	4.98899	+	0.331571i	0.176388	+	0.0117228i
$801$	18.8746	+	0.992973i	0.666900	+	0.0350850i
$802$	12.3108	+	26.4006i	0.434709	+	0.932236i
$803$	−84.3648	−	39.3400i	−2.97717	−	1.38828i
$804$	3.45635	+	14.4031i	0.121896	+	0.507958i
$805$	35.9821	−	52.5482i	1.26820	−	1.85208i
$806$	0.294245	+	0.169882i	0.0103643	+	0.00598384i
$807$	−19.0262	−	35.0503i	−0.669755	−	1.23383i
$808$	−5.46249	−	3.82488i	−0.192170	−	0.134559i
$809$	2.88895	−	5.00381i	0.101570	−	0.175924i	−0.810762	−	0.585376i	$-0.800947\pi$
$809$	2.88895	−	5.00381i	0.101570	−	0.175924i	0.912332	+	0.409452i	$0.134280\pi$
$810$	1.90234	−	20.0345i	0.0668415	−	0.703940i
$811$	−13.8117	+	11.5894i	−0.484994	+	0.406958i	−0.852228	−	0.523170i	$-0.824749\pi$
$811$	−13.8117	+	11.5894i	−0.484994	+	0.406958i	0.367234	+	0.930128i	$0.380305\pi$
$812$	10.7783	−	23.1142i	0.378245	−	0.811149i
$813$	−12.7038	−	0.333936i	−0.445540	−	0.0117116i
$814$	−31.6257	+	37.6901i	−1.10848	+	1.32104i
$815$	34.9375	+	19.6872i	1.22381	+	0.689613i
$816$	1.39592	−	2.79907i	0.0488669	−	0.0979872i
$817$	13.3330	−	19.2533i	0.466461	−	0.673589i
$818$	−21.6237	−	21.6237i	−0.756055	−	0.756055i
$819$	−0.896280	−	1.75992i	−0.0313186	−	0.0614966i
$820$	−7.80026	−	2.00294i	−0.272397	−	0.0699455i
$821$	2.86843	−	7.88095i	0.100109	−	0.275047i	−0.879520	−	0.475861i	$-0.842136\pi$
$821$	2.86843	−	7.88095i	0.100109	−	0.275047i	0.979629	+	0.200814i	$0.0643587\pi$
$822$	5.91802	+	7.44150i	0.206415	+	0.259552i
$823$	4.23304	−	48.3838i	0.147554	−	1.68655i	−0.456588	−	0.889678i	$-0.650929\pi$
$823$	4.23304	−	48.3838i	0.147554	−	1.68655i	0.604143	−	0.796876i	$-0.293516\pi$
$824$	−3.22261	−	5.58172i	−0.112265	−	0.194448i
$825$	−41.3912	+	34.3538i	−1.44106	+	1.19605i
$826$	−1.08000	−	6.12500i	−0.0375781	−	0.213116i
$827$	23.7965	+	16.6625i	0.827487	+	0.579413i	0.908779	−	0.417278i	$-0.137016\pi$
$827$	23.7965	+	16.6625i	0.827487	+	0.579413i	−0.0812920	+	0.996690i	$0.525905\pi$
$828$	−17.4647	−	13.6505i	−0.606939	−	0.474389i
$829$	9.79697	−	5.65628i	0.340263	−	0.196451i	−0.320125	−	0.947375i	$-0.603725\pi$
$829$	9.79697	−	5.65628i	0.340263	−	0.196451i	0.660388	+	0.750924i	$0.270392\pi$
$830$	11.3404	−	24.9984i	0.393631	−	0.867708i
$831$	38.0098	+	4.33454i	1.31855	+	0.150364i
$832$	−0.0721779	−	0.154786i	−0.00250232	−	0.00536624i
$833$	1.23689	+	14.1377i	0.0428558	+	0.489844i
$834$	16.5468	−	22.3570i	0.572967	−	0.774158i
$835$	1.76768	−	5.01927i	0.0611730	−	0.173699i
$836$	−23.3762	+	13.6585i	−0.808481	+	0.472388i
$837$	−5.85763	+	8.51740i	−0.202469	+	0.294405i
$838$	11.3663	+	16.2327i	0.392641	+	0.560749i
$839$	17.4298	+	14.6253i	0.601744	+	0.504923i	0.892006	−	0.452024i	$-0.149298\pi$
$839$	17.4298	+	14.6253i	0.601744	+	0.504923i	−0.290262	+	0.956947i	$0.593742\pi$
$840$	6.09440	+	13.6286i	0.210277	+	0.470232i
$841$	−13.8838	+	5.05330i	−0.478753	+	0.174252i
$842$	−1.96021	+	22.4053i	−0.0675532	+	0.772137i
$843$	6.46307	−	7.30369i	0.222600	−	0.251552i
$844$	2.29066	+	1.32251i	0.0788477	+	0.0455227i
$845$	23.5832	−	16.8832i	0.811288	−	0.580800i
$846$	6.68709	−	7.16814i	0.229907	−	0.246446i
$847$	102.686	−	27.5146i	3.52833	−	0.945413i
$848$	1.62691	−	6.07171i	0.0558683	−	0.208503i
$849$	−2.61159	−	10.8829i	−0.0896294	−	0.373498i
$850$	8.54747	+	2.91018i	0.293176	+	0.0998184i
$851$	20.0182	−	54.9995i	0.686214	−	1.88536i
$852$	−7.31572	−	2.88259i	−0.250632	−	0.0987558i
$853$	−24.3457	−	34.7693i	−0.833582	−	1.19048i	−0.979552	−	0.201189i	$-0.935519\pi$
$853$	−24.3457	−	34.7693i	−0.833582	−	1.19048i	0.145971	−	0.989289i	$-0.453369\pi$
$854$	26.3186			0.900605
$855$	29.0152	+	3.62192i	0.992299	+	0.123867i
$856$	4.43041			0.151428
$857$	24.9026	+	35.5646i	0.850658	+	1.21487i	0.974907	+	0.222614i	$0.0714589\pi$
$857$	24.9026	+	35.5646i	0.850658	+	1.21487i	−0.124249	+	0.992251i	$0.539652\pi$
$858$	1.70943	+	0.673562i	0.0583591	+	0.0229950i
$859$	11.9361	−	32.7941i	0.407253	−	1.11892i	−0.551375	−	0.834258i	$-0.685897\pi$
$859$	11.9361	−	32.7941i	0.407253	−	1.11892i	0.958628	−	0.284661i	$-0.0918811\pi$
$860$	12.0131	−	0.125563i	0.409645	−	0.00428167i
$861$	−5.61105	−	23.3821i	−0.191224	−	0.796858i
$862$	6.33188	−	23.6309i	0.215665	−	0.804872i
$863$	−3.86885	+	1.03666i	−0.131697	+	0.0352881i	−0.324066	−	0.946035i	$-0.605050\pi$
$863$	−3.86885	+	1.03666i	−0.131697	+	0.0352881i	0.192368	+	0.981323i	$0.438383\pi$
$864$	4.86764	−	1.81827i	0.165600	−	0.0618586i
$865$	0.402004	−	2.42801i	0.0136686	−	0.0825547i
$866$	−21.2891	−	12.2912i	−0.723432	−	0.417674i
$867$	−15.7698	+	17.8209i	−0.535569	+	0.605229i
$868$	0.668356	−	7.63935i	0.0226855	−	0.259296i
$869$	−15.6011	+	5.67835i	−0.529233	+	0.192625i
$870$	9.14417	−	23.9376i	0.310017	−	0.811559i
$871$	1.11883	+	0.938809i	0.0379101	+	0.0318103i
$872$	8.19161	+	11.6988i	0.277403	+	0.396172i
$873$	41.7516	+	5.87636i	1.41308	+	0.198885i
$874$	20.5740	−	24.7792i	0.695926	−	0.838168i
$875$	−36.6291	+	22.7079i	−1.23829	+	0.767668i
$876$	−15.4425	+	20.8650i	−0.521754	+	0.704962i
$877$	−2.03643	−	23.2765i	−0.0687655	−	0.785993i	−0.949783	−	0.312909i	$-0.898696\pi$
$877$	−2.03643	−	23.2765i	−0.0687655	−	0.785993i	0.881018	−	0.473084i	$-0.156859\pi$
$878$	6.70084	+	14.3700i	0.226143	+	0.484964i
$879$	22.2611	+	2.53859i	0.750847	+	0.0856246i
$880$	−12.6480	−	5.73771i	−0.426365	−	0.193418i
$881$	−39.2740	+	22.6749i	−1.32318	+	0.763936i	−0.984234	−	0.176872i	$-0.943402\pi$
$881$	−39.2740	+	22.6749i	−1.32318	+	0.763936i	−0.338942	+	0.940807i	$0.610069\pi$
$882$	−14.5186	+	18.5753i	−0.488868	+	0.625464i
$883$	−5.15208	−	3.60752i	−0.173381	−	0.121403i	0.483665	−	0.875253i	$-0.339305\pi$
$883$	−5.15208	−	3.60752i	−0.173381	−	0.121403i	−0.657046	+	0.753850i	$0.728194\pi$
$884$	−0.0535563	−	0.303733i	−0.00180129	−	0.0102156i
$885$	−1.52162	−	6.06090i	−0.0511486	−	0.203735i
$886$	−17.2582	−	29.8920i	−0.579800	−	1.00424i
$887$	3.83746	−	43.8624i	0.128849	−	1.47275i	−0.606509	−	0.795077i	$-0.707431\pi$
$887$	3.83746	−	43.8624i	0.128849	−	1.47275i	0.735358	−	0.677678i	$-0.237014\pi$
$888$	8.53991	+	10.7384i	0.286581	+	0.360356i
$889$	11.3062	−	31.0634i	0.379196	−	1.04183i
$890$	−12.1260	+	7.17099i	−0.406466	+	0.240372i
$891$	−24.5254	+	50.2334i	−0.821633	+	1.68288i
$892$	16.5283	+	16.5283i	0.553409	+	0.553409i
$893$	10.1238	+	10.0193i	0.338779	+	0.335281i
$894$	10.1636	−	20.3799i	0.339921	−	0.681604i
$895$	8.10120	+	29.0175i	0.270793	+	0.969948i
$896$	−2.47775	+	2.95287i	−0.0827759	+	0.0986485i
$897$	−2.18495	−	0.0574344i	−0.0729534	−	0.00191768i
$898$	11.6239	−	24.9275i	0.387894	−	0.831842i
$899$	−10.0830	+	8.46061i	−0.336285	+	0.282177i
$900$	7.08507	+	13.2213i	0.236169	+	0.440709i
$901$	5.67573	−	9.83065i	0.189086	−	0.327507i
$902$	18.3244	+	12.8309i	0.610134	+	0.427221i
$903$	17.1131	+	31.5260i	0.569489	+	1.04912i
$904$	12.2241	+	7.05757i	0.406567	+	0.234731i
$905$	14.8114	+	10.1420i	0.492349	+	0.337133i
$906$	−2.65556	−	11.0661i	−0.0882250	−	0.367646i
$907$	−29.7560	−	13.8755i	−0.988033	−	0.460727i	−0.139702	−	0.990194i	$-0.544614\pi$
$907$	−29.7560	−	13.8755i	−0.988033	−	0.460727i	−0.848331	+	0.529466i	$0.822392\pi$
$908$	−6.14664	−	13.1815i	−0.203984	−	0.437444i
$909$	1.05101	−	19.9778i	0.0348599	−	0.662621i
$910$	1.28248	+	0.722676i	0.0425139	+	0.0239565i
$911$			50.2090i			1.66350i	0.555152	+	0.831749i	$0.312660\pi$
$911$			50.2090i			1.66350i	−0.555152	+	0.831749i	$0.687340\pi$
$912$	2.43200	+	7.14740i	0.0805316	+	0.236674i
$913$	−53.9168	+	53.9168i	−1.78438	+	1.78438i
$914$	−3.44937	+	19.5624i	−0.114095	+	0.647066i
$915$	26.3760	−	1.88746i	0.871964	−	0.0623975i
$916$	0.831798	+	0.302750i	0.0274834	+	0.0100031i
$917$	0.993445	−	2.13045i	0.0328064	−	0.0703537i
$918$	9.34060	−	0.896559i	0.308286	−	0.0295909i
$919$	−42.1101	+	24.3123i	−1.38908	+	0.801988i	−0.993212	−	0.116317i	$-0.962891\pi$
$919$	−42.1101	+	24.3123i	−1.38908	+	0.801988i	−0.395872	+	0.918306i	$0.629558\pi$
$920$	16.4732	+	1.26788i	0.543104	+	0.0418006i
$921$	12.8735	−	43.4441i	0.424195	−	1.43153i
$922$	−20.4826	+	29.2522i	−0.674559	+	0.963371i
$923$	−0.748921	+	0.200673i	−0.0246510	+	0.00660522i
$924$	−2.52748	−	41.3921i	−0.0831480	−	1.36170i
$925$	−27.4146	+	28.5854i	−0.901387	+	0.939882i
$926$	−2.08239	−	5.72131i	−0.0684315	−	0.188014i
$927$	9.08096	−	17.0705i	0.298258	−	0.560670i
$928$	6.59108	−	0.576645i	0.216363	−	0.0189293i
$929$	4.03035	−	22.8572i	0.132231	−	0.749921i	−0.844516	−	0.535530i	$-0.820112\pi$
$929$	4.03035	−	22.8572i	0.132231	−	0.749921i	0.976748	−	0.214392i	$-0.0687769\pi$
$930$	0.121952	−	7.70394i	0.00399897	−	0.252622i
$931$	−26.3550	−	21.8824i	−0.863751	−	0.717168i
$932$	9.69320	−	9.69320i	0.317511	−	0.317511i
$933$	−18.1926	+	2.71704i	−0.595600	+	0.0889520i
$934$	13.6788	−	16.3017i	0.447583	−	0.533408i
$935$	−19.3806	−	15.9200i	−0.633813	−	0.520641i
$936$	0.279139	−	0.429647i	0.00912394	−	0.0140435i
$937$	25.8117	+	2.25823i	0.843230	+	0.0737731i	0.500580	−	0.865690i	$-0.333120\pi$
$937$	25.8117	+	2.25823i	0.843230	+	0.0737731i	0.342650	+	0.939463i	$0.388676\pi$
$938$	8.53179	−	31.8411i	0.278573	−	1.03965i
$939$	−31.3012	−	47.3013i	−1.02148	−	1.54362i
$940$	−1.19353	+	7.20861i	−0.0389285	+	0.235119i
$941$	−8.54721	+	1.50710i	−0.278631	+	0.0491302i	−0.311217	−	0.950339i	$-0.600737\pi$
$941$	−8.54721	+	1.50710i	−0.278631	+	0.0491302i	0.0325864	+	0.999469i	$0.489626\pi$
$942$	3.02516	−	14.8615i	0.0985651	−	0.484214i
$943$	−25.7044	−	6.88748i	−0.837052	−	0.224287i
$944$	1.23600	−	1.03713i	0.0402283	−	0.0337556i
$945$	−24.9920	+	37.1662i	−0.812989	+	1.20902i
$946$	−31.3585	−	11.4136i	−1.01955	−	0.371087i
$947$	−42.7305	+	3.73843i	−1.38855	+	0.121483i	−0.756780	−	0.653670i	$-0.773229\pi$
$947$	−42.7305	+	3.73843i	−1.38855	+	0.121483i	−0.631774	+	0.775152i	$0.717673\pi$
$948$	0.683859	+	4.57895i	0.0222107	+	0.148718i
$949$			2.55957i			0.0830872i
$950$	−19.5055	+	9.72296i	−0.632842	+	0.315454i
$951$	14.5399	−	29.1553i	0.471490	−	0.945425i
$952$	−5.70216	+	3.99270i	−0.184808	+	0.129404i
$953$	0.467856	+	5.34762i	0.0151553	+	0.173226i	1.00000		0.000212580i	$-6.76664e-5\pi$
$953$	0.467856	+	5.34762i	0.0151553	+	0.173226i	−0.984845	+	0.173439i	$0.944512\pi$
$954$	18.0348	−	5.50984i	0.583899	−	0.178388i
$955$	14.0614	+	13.7705i	0.455017	+	0.445604i
$956$	14.1042	+	16.8087i	0.456161	+	0.543631i
$957$	−47.1695	+	53.3047i	−1.52477	+	1.72310i
$958$	−9.12563	−	34.0573i	−0.294836	−	1.10034i
$959$	−3.67436	−	20.8383i	−0.118651	−	0.672905i
$960$	−2.27139	+	3.13700i	−0.0733088	+	0.101246i
$961$	13.5211	−	23.4193i	0.436166	−	0.755462i
$962$	1.30677	+	0.350147i	0.0421319	+	0.0112892i
$963$	7.04101	+	11.2730i	0.226893	+	0.363268i
$964$	−2.28747	−	6.28476i	−0.0736743	−	0.202418i
$965$	−25.6189	+	31.1877i	−0.824702	+	1.00397i
$966$	19.6664	+	45.2421i	0.632757	+	1.45564i
$967$	−5.14625	+	3.60344i	−0.165492	+	0.115879i	−0.653389	−	0.757023i	$-0.726653\pi$
$967$	−5.14625	+	3.60344i	−0.165492	+	0.115879i	0.487896	+	0.872902i	$0.337764\pi$
$968$	19.5012	+	19.5012i	0.626792	+	0.626792i
$969$	0.901574	+	13.6041i	0.0289627	+	0.437027i
$970$	−28.3418	+	13.5784i	−0.909999	+	0.435976i
$971$	−0.906767	−	0.159888i	−0.0290995	−	0.00513104i	0.159079	−	0.987266i	$-0.449147\pi$
$971$	−0.906767	−	0.159888i	−0.0290995	−	0.00513104i	−0.188179	+	0.982135i	$0.560259\pi$
$972$	12.3624	+	9.49586i	0.396524	+	0.304580i
$973$	−56.1012	+	26.1604i	−1.79852	+	0.838664i
$974$	17.5674	−	6.39401i	0.562896	−	0.204877i
$975$	1.33711	+	0.632278i	0.0428217	+	0.0202491i
$976$	3.41384	+	5.91294i	0.109274	+	0.189269i
$977$	−8.17534	−	30.5108i	−0.261552	−	0.976127i	−0.964327	−	0.264714i	$-0.914722\pi$
$977$	−8.17534	−	30.5108i	−0.261552	−	0.976127i	0.702775	−	0.711413i	$-0.251944\pi$
$978$	−27.3005	+	14.8194i	−0.872972	+	0.473872i
$979$	38.5373	−	6.79517i	1.23166	−	0.217175i
$980$	1.34851	−	17.5208i	0.0430765	−	0.559681i
$981$	−16.7487	+	39.4356i	−0.534746	+	1.25908i
$982$	−12.8597	−	1.12507i	−0.410368	−	0.0359026i
$983$	40.5514	+	18.9094i	1.29339	+	0.603117i	0.942783	−	0.333407i	$-0.108198\pi$
$983$	40.5514	+	18.9094i	1.29339	+	0.603117i	0.350605	+	0.936524i	$0.385976\pi$
$984$	4.52537	−	4.29355i	0.144263	−	0.136873i
$985$	7.95422	−	4.70390i	0.253443	−	0.149879i
$986$	11.7665	+	2.07476i	0.374722	+	0.0660737i
$987$	−20.6900	+	6.92048i	−0.658571	+	0.220281i
$988$	0.612022	+	0.423826i	0.0194710	+	0.0134837i
$989$	39.6981			1.26233
$990$	−5.50146	−	41.3011i	−0.174848	−	1.31264i
$991$	−15.3076	−	12.8446i	−0.486262	−	0.408022i	0.366422	−	0.930449i	$-0.380583\pi$
$991$	−15.3076	−	12.8446i	−0.486262	−	0.408022i	−0.852684	+	0.522426i	$0.825027\pi$
$992$	1.80301	−	0.840756i	0.0572455	−	0.0266940i
$993$	−18.4025	+	14.6350i	−0.583985	+	0.464427i
$994$	11.2485	+	13.4054i	0.356780	+	0.425194i
$995$	12.7618	−	18.6373i	0.404576	−	0.590842i
$996$	11.7341	+	17.7321i	0.371808	+	0.561863i
$997$	−4.22162	+	6.02910i	−0.133700	+	0.190944i	−0.880420	−	0.474196i	$-0.842739\pi$
$997$	−4.22162	+	6.02910i	−0.133700	+	0.190944i	0.746719	+	0.665139i	$0.231628\pi$
$998$	5.85310	−	8.35909i	0.185276	−	0.264602i
$999$	−13.7513	+	38.7954i	−0.435073	+	1.22743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.17.3	✓	480
3.2	odd	2	inner	570.2.bi.a.17.24	yes	480
5.3	odd	4	inner	570.2.bi.a.473.13	yes	480
15.8	even	4	inner	570.2.bi.a.473.28	yes	480
19.9	even	9	inner	570.2.bi.a.47.28	yes	480
57.47	odd	18	inner	570.2.bi.a.47.13	yes	480
95.28	odd	36	inner	570.2.bi.a.503.24	yes	480
285.218	even	36	inner	570.2.bi.a.503.3	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.3	✓	480	1.1	even	1	trivial
570.2.bi.a.17.24	yes	480	3.2	odd	2	inner
570.2.bi.a.47.13	yes	480	57.47	odd	18	inner
570.2.bi.a.47.28	yes	480	19.9	even	9	inner
570.2.bi.a.473.13	yes	480	5.3	odd	4	inner
570.2.bi.a.473.28	yes	480	15.8	even	4	inner
570.2.bi.a.503.3	yes	480	285.218	even	36	inner
570.2.bi.a.503.24	yes	480	95.28	odd	36	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 - 0.819152i) q^{2} +(-1.61147 - 0.634960i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.56453 - 1.59758i) q^{5} +(0.404170 + 1.68423i) q^{6} +(0.997670 - 3.72335i) q^{7} +(0.965926 - 0.258819i) q^{8} +(2.19365 + 2.04644i) q^{9} +O(q^{10})\)	\(q+(-0.573576 - 0.819152i) q^{2} +(-1.61147 - 0.634960i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.56453 - 1.59758i) q^{5} +(0.404170 + 1.68423i) q^{6} +(0.997670 - 3.72335i) q^{7} +(0.965926 - 0.258819i) q^{8} +(2.19365 + 2.04644i) q^{9} +(-2.20604 - 0.365253i) q^{10} +(5.37905 + 3.10559i) q^{11} +(1.14782 - 1.29711i) q^{12} +(0.0148851 - 0.170138i) q^{13} +(-3.62223 + 1.31839i) q^{14} +(-3.53558 + 1.58103i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-1.03580 - 1.47927i) q^{17} +(0.418116 - 2.97072i) q^{18} +(4.29655 + 0.734629i) q^{19} +(0.966132 + 2.01658i) q^{20} +(-3.97189 + 5.36658i) q^{21} +(-0.541341 - 6.18755i) q^{22} +(3.12265 + 6.69654i) q^{23} +(-1.72090 - 0.196246i) q^{24} +(-0.104510 - 4.99891i) q^{25} +(-0.147906 + 0.0853938i) q^{26} +(-2.23559 - 4.69064i) q^{27} +(3.15759 + 2.21097i) q^{28} +(-1.14890 - 6.51574i) q^{29} +(3.32303 + 1.98934i) q^{30} +(-0.994699 - 1.72287i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(-6.69623 - 8.42004i) q^{33} +(-0.617641 + 1.69695i) q^{34} +(-4.38747 - 7.41914i) q^{35} +(-2.67329 + 1.36143i) q^{36} +(-5.60123 - 5.60123i) q^{37} +(-1.86263 - 3.94089i) q^{38} +(-0.132018 + 0.264720i) q^{39} +(1.09773 - 1.94807i) q^{40} +(-2.31503 + 2.75895i) q^{41} +(6.67423 + 0.175441i) q^{42} +(2.27061 - 4.86935i) q^{43} +(-4.75805 + 3.99248i) q^{44} +(6.70137 - 0.302824i) q^{45} +(3.69441 - 6.39890i) q^{46} +(2.67672 + 1.87426i) q^{47} +(0.826310 + 1.52224i) q^{48} +(-6.80584 - 3.92936i) q^{49} +(-4.03492 + 2.95287i) q^{50} +(0.729875 + 3.04149i) q^{51} +(0.154786 + 0.0721779i) q^{52} +(2.65654 + 5.69696i) q^{53} +(-2.56007 + 4.52173i) q^{54} +(13.3771 - 3.73466i) q^{55} -3.85470i q^{56} +(-6.45728 - 3.91197i) q^{57} +(-4.67840 + 4.67840i) q^{58} +(-0.280178 + 1.58897i) q^{59} +(-0.276443 - 3.86310i) q^{60} +(-6.41592 - 2.33520i) q^{61} +(-0.840756 + 1.80301i) q^{62} +(9.80814 - 6.12607i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-0.248520 - 0.289965i) q^{65} +(-3.05650 + 10.3148i) q^{66} +(-4.90506 + 7.00516i) q^{67} +(1.74433 - 0.467391i) q^{68} +(-0.780005 - 12.7740i) q^{69} +(-3.56086 + 7.84945i) q^{70} +(-1.55270 - 4.26601i) q^{71} +(2.64856 + 1.40895i) q^{72} +(-14.9298 + 1.30619i) q^{73} +(-1.37552 + 7.80099i) q^{74} +(-3.00569 + 8.12193i) q^{75} +(-2.15983 + 3.78618i) q^{76} +(16.9297 - 16.9297i) q^{77} +(0.292568 - 0.0436945i) q^{78} +(-1.71816 + 2.04762i) q^{79} +(-2.22540 + 0.218157i) q^{80} +(0.624204 + 8.97833i) q^{81} +(3.58785 + 0.313896i) q^{82} +(-3.17731 + 11.8579i) q^{83} +(-3.68447 - 5.56784i) q^{84} +(-3.98379 - 0.659595i) q^{85} +(-5.29111 + 0.932965i) q^{86} +(-2.28582 + 11.2294i) q^{87} +(5.99955 + 1.60757i) q^{88} +(4.82625 - 4.04970i) q^{89} +(-4.09180 - 5.31574i) q^{90} +(-0.618632 - 0.225164i) q^{91} +(-7.36070 + 0.643978i) q^{92} +(0.508970 + 3.40794i) q^{93} -3.26768i q^{94} +(7.89569 - 5.71472i) q^{95} +(0.772993 - 1.54999i) q^{96} +(11.5127 - 8.06126i) q^{97} +(0.684932 + 7.82881i) q^{98} +(5.44435 + 17.8205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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