LMFDB - Embedded newform 175.2.x.a.103.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.6
Character	$\chi$	$=$	175.103
Dual form			175.2.x.a.17.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22592 - 0.0642475i) q^{2} +(0.158411 + 0.195621i) q^{3} +(-0.490303 - 0.0515330i) q^{4} +(-2.14702 + 0.624757i) q^{5} +(-0.181630 - 0.249992i) q^{6} +(2.13484 - 1.56284i) q^{7} +(3.02273 + 0.478753i) q^{8} +(0.610561 - 2.87247i) q^{9} +(2.67220 - 0.627958i) q^{10} +(6.21946 - 1.32199i) q^{11} +(-0.0675884 - 0.104077i) q^{12} +(-3.08865 - 1.57374i) q^{13} +(-2.71754 + 1.77875i) q^{14} +(-0.462326 - 0.321033i) q^{15} +(-2.71039 - 0.576111i) q^{16} +(1.38605 + 3.61079i) q^{17} +(-0.933045 + 3.48217i) q^{18} +(-0.630632 - 6.00007i) q^{19} +(1.08488 - 0.195678i) q^{20} +(0.643905 + 0.170048i) q^{21} +(-7.70946 + 1.22106i) q^{22} +(-0.0931944 + 1.77825i) q^{23} +(0.385178 + 0.667148i) q^{24} +(4.21936 - 2.68272i) q^{25} +(3.68531 + 2.12772i) q^{26} +(1.33148 - 0.678422i) q^{27} +(-1.12726 + 0.656251i) q^{28} +(1.19010 - 1.63804i) q^{29} +(0.546147 + 0.423263i) q^{30} +(0.613319 - 1.37754i) q^{31} +(-2.62656 - 0.703784i) q^{32} +(1.24384 + 1.00724i) q^{33} +(-1.46720 - 4.51558i) q^{34} +(-3.60714 + 4.68920i) q^{35} +(-0.447387 + 1.37692i) q^{36} +(-6.46577 + 4.19892i) q^{37} +(0.387613 + 7.39609i) q^{38} +(-0.181418 - 0.853502i) q^{39} +(-6.78895 + 0.860578i) q^{40} +(2.44960 - 0.795924i) q^{41} +(-0.778448 - 0.249834i) q^{42} +(4.23024 + 4.23024i) q^{43} +(-3.11755 + 0.327667i) q^{44} +(0.483706 + 6.54868i) q^{45} +(0.228497 - 2.17400i) q^{46} +(-2.45246 - 0.941409i) q^{47} +(-0.316655 - 0.621471i) q^{48} +(2.11506 - 6.67282i) q^{49} +(-5.34493 + 3.01771i) q^{50} +(-0.486781 + 0.843129i) q^{51} +(1.43327 + 0.930780i) q^{52} +(2.37094 - 1.91995i) q^{53} +(-1.67587 + 0.746144i) q^{54} +(-12.5274 + 6.72397i) q^{55} +(7.20125 - 3.70198i) q^{56} +(1.07384 - 1.07384i) q^{57} +(-1.56421 + 1.93163i) q^{58} +(-8.64305 + 9.59907i) q^{59} +(0.210136 + 0.181229i) q^{60} +(-0.0639241 + 0.0575575i) q^{61} +(-0.840380 + 1.64934i) q^{62} +(-3.18575 - 7.08646i) q^{63} +(8.44536 + 2.74406i) q^{64} +(7.61459 + 1.44920i) q^{65} +(-1.46013 - 1.31470i) q^{66} +(-1.23771 + 0.475111i) q^{67} +(-0.493512 - 1.84181i) q^{68} +(-0.362627 + 0.263464i) q^{69} +(4.72331 - 5.51681i) q^{70} +(1.14755 + 0.833741i) q^{71} +(3.22076 - 8.39037i) q^{72} +(7.23837 - 11.1461i) q^{73} +(8.19625 - 4.73211i) q^{74} +(1.19319 + 0.400423i) q^{75} +2.97435i q^{76} +(11.2115 - 12.5422i) q^{77} +(0.167567 + 1.05798i) q^{78} +(1.79663 + 4.03530i) q^{79} +(6.17917 - 0.456413i) q^{80} +(-7.70462 - 3.43032i) q^{81} +(-3.05414 + 0.818354i) q^{82} +(0.0358492 - 0.226343i) q^{83} +(-0.306946 - 0.116558i) q^{84} +(-5.23175 - 6.88648i) q^{85} +(-4.91413 - 5.45770i) q^{86} +(0.508959 - 0.0266734i) q^{87} +(19.4326 - 1.01842i) q^{88} +(8.63680 + 9.59214i) q^{89} +(-0.172246 - 8.05921i) q^{90} +(-9.05327 + 1.46737i) q^{91} +(0.137332 - 0.867081i) q^{92} +(0.366631 - 0.0982386i) q^{93} +(2.94602 + 1.31165i) q^{94} +(5.10256 + 12.4883i) q^{95} +(-0.278400 - 0.625297i) q^{96} +(0.0559772 + 0.353426i) q^{97} +(-3.02160 + 8.04442i) q^{98} -18.6723i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−1.22592	−	0.0642475i	−0.866853	−	0.0454298i	−0.386277	−	0.922383i	$-0.626239\pi$
$2$	−1.22592	−	0.0642475i	−0.866853	−	0.0454298i	−0.480576	+	0.876953i	$0.659572\pi$
$3$	0.158411	+	0.195621i	0.0914585	+	0.112942i	0.820821	−	0.571186i	$-0.193516\pi$
$3$	0.158411	+	0.195621i	0.0914585	+	0.112942i	−0.729362	+	0.684128i	$0.760183\pi$
$4$	−0.490303	−	0.0515330i	−0.245152	−	0.0257665i
$5$	−2.14702	+	0.624757i	−0.960175	+	0.279400i
$5$	−2.14702	+	0.624757i	−0.960175	+	0.279400i
$6$	−0.181630	−	0.249992i	−0.0741501	−	0.102059i
$7$	2.13484	−	1.56284i	0.806893	−	0.590698i
$7$	2.13484	−	1.56284i	0.806893	−	0.590698i
$8$	3.02273	+	0.478753i	1.06870	+	0.169265i
$9$	0.610561	−	2.87247i	0.203520	−	0.957489i
$10$	2.67220	−	0.627958i	0.845024	−	0.198578i
$11$	6.21946	−	1.32199i	1.87524	−	0.398594i	0.878390	−	0.477944i	$-0.158618\pi$
$11$	6.21946	−	1.32199i	1.87524	−	0.398594i	0.996847	+	0.0793499i	$0.0252844\pi$
$12$	−0.0675884	−	0.104077i	−0.0195111	−	0.0300444i
$13$	−3.08865	−	1.57374i	−0.856637	−	0.436478i	−0.0302242	−	0.999543i	$-0.509622\pi$
$13$	−3.08865	−	1.57374i	−0.856637	−	0.436478i	−0.826413	+	0.563065i	$0.809622\pi$
$14$	−2.71754	+	1.77875i	−0.726293	+	0.475391i
$15$	−0.462326	−	0.321033i	−0.119372	−	0.0828904i
$16$	−2.71039	−	0.576111i	−0.677597	−	0.144028i
$17$	1.38605	+	3.61079i	0.336167	+	0.875746i	0.992608	+	0.121368i	$0.0387281\pi$
$17$	1.38605	+	3.61079i	0.336167	+	0.875746i	−0.656440	+	0.754378i	$0.727939\pi$
$18$	−0.933045	+	3.48217i	−0.219921	+	0.820756i
$19$	−0.630632	−	6.00007i	−0.144677	−	1.37651i	−0.790237	−	0.612801i	$-0.790043\pi$
$19$	−0.630632	−	6.00007i	−0.144677	−	1.37651i	0.645560	−	0.763709i	$-0.276624\pi$
$20$	1.08488	−	0.195678i	0.242588	−	0.0437550i
$21$	0.643905	+	0.170048i	0.140512	+	0.0371076i
$22$	−7.70946	+	1.22106i	−1.64366	+	0.260331i
$23$	−0.0931944	+	1.77825i	−0.0194324	+	0.370792i	0.971553	+	0.236822i	$0.0761058\pi$
$23$	−0.0931944	+	1.77825i	−0.0194324	+	0.370792i	−0.990985	+	0.133970i	$0.957228\pi$
$24$	0.385178	+	0.667148i	0.0786242	+	0.136181i
$25$	4.21936	−	2.68272i	0.843872	−	0.536545i
$26$	3.68531	+	2.12772i	0.722749	+	0.417279i
$27$	1.33148	−	0.678422i	0.256243	−	0.130562i
$28$	−1.12726	+	0.656251i	−0.213031	+	0.124020i
$29$	1.19010	−	1.63804i	0.220997	−	0.304176i	−0.684095	−	0.729393i	$-0.739802\pi$
$29$	1.19010	−	1.63804i	0.220997	−	0.304176i	0.905091	+	0.425218i	$0.139802\pi$
$30$	0.546147	+	0.423263i	0.0997123	+	0.0772769i
$31$	0.613319	−	1.37754i	0.110155	−	0.247413i	−0.850053	−	0.526697i	$-0.823430\pi$
$31$	0.613319	−	1.37754i	0.110155	−	0.247413i	0.960209	+	0.279284i	$0.0900970\pi$
$32$	−2.62656	−	0.703784i	−0.464314	−	0.124413i
$33$	1.24384	+	1.00724i	0.216524	+	0.175338i
$34$	−1.46720	−	4.51558i	−0.251623	−	0.774415i
$35$	−3.60714	+	4.68920i	−0.609717	+	0.792619i
$36$	−0.447387	+	1.37692i	−0.0745645	+	0.229486i
$37$	−6.46577	+	4.19892i	−1.06297	+	0.690298i	−0.952795	−	0.303615i	$-0.901806\pi$
$37$	−6.46577	+	4.19892i	−1.06297	+	0.690298i	−0.110171	+	0.993913i	$0.535140\pi$
$38$	0.387613	+	7.39609i	0.0628791	+	1.19980i
$39$	−0.181418	−	0.853502i	−0.0290501	−	0.136670i
$40$	−6.78895	+	0.860578i	−1.07343	+	0.136069i
$41$	2.44960	−	0.795924i	0.382563	−	0.124302i	−0.111421	−	0.993773i	$-0.535540\pi$
$41$	2.44960	−	0.795924i	0.382563	−	0.124302i	0.493984	+	0.869471i	$0.335540\pi$
$42$	−0.778448	−	0.249834i	−0.120117	−	0.0385503i
$43$	4.23024	+	4.23024i	0.645106	+	0.645106i	0.951806	−	0.306701i	$-0.0992250\pi$
$43$	4.23024	+	4.23024i	0.645106	+	0.645106i	−0.306701	+	0.951806i	$0.599225\pi$
$44$	−3.11755	+	0.327667i	−0.469988	+	0.0493977i
$45$	0.483706	+	6.54868i	0.0721067	+	0.976220i
$46$	0.228497	−	2.17400i	0.0336900	−	0.320539i
$47$	−2.45246	−	0.941409i	−0.357727	−	0.137319i	0.172866	−	0.984945i	$-0.444697\pi$
$47$	−2.45246	−	0.941409i	−0.357727	−	0.137319i	−0.530593	+	0.847627i	$0.678031\pi$
$48$	−0.316655	−	0.621471i	−0.0457052	−	0.0897016i
$49$	2.11506	−	6.67282i	0.302152	−	0.953260i
$50$	−5.34493	+	3.01771i	−0.755888	+	0.426769i
$51$	−0.486781	+	0.843129i	−0.0681630	+	0.118062i
$52$	1.43327	+	0.930780i	0.198759	+	0.129076i
$53$	2.37094	−	1.91995i	0.325674	−	0.263726i	−0.452514	−	0.891758i	$-0.649473\pi$
$53$	2.37094	−	1.91995i	0.325674	−	0.263726i	0.778188	+	0.628032i	$0.216139\pi$
$54$	−1.67587	+	0.746144i	−0.228057	+	0.101537i
$55$	−12.5274	+	6.72397i	−1.68919	+	0.906660i
$56$	7.20125	−	3.70198i	0.962307	−	0.494698i
$57$	1.07384	−	1.07384i	0.142234	−	0.142234i
$58$	−1.56421	+	1.93163i	−0.205390	+	0.253636i
$59$	−8.64305	+	9.59907i	−1.12523	+	1.24969i	−0.160332	+	0.987063i	$0.551257\pi$
$59$	−8.64305	+	9.59907i	−1.12523	+	1.24969i	−0.964897	+	0.262630i	$0.915410\pi$
$60$	0.210136	+	0.181229i	0.0271285	+	0.0233965i
$61$	−0.0639241	+	0.0575575i	−0.00818465	+	0.00736949i	−0.673213	−	0.739449i	$-0.735086\pi$
$61$	−0.0639241	+	0.0575575i	−0.00818465	+	0.00736949i	0.665028	+	0.746818i	$0.268420\pi$
$62$	−0.840380	+	1.64934i	−0.106728	+	0.209466i
$63$	−3.18575	−	7.08646i	−0.401367	−	0.892810i
$64$	8.44536	+	2.74406i	1.05567	+	0.343008i
$65$	7.61459	+	1.44920i	0.944473	+	0.179752i
$66$	−1.46013	−	1.31470i	−0.179729	−	0.161829i
$67$	−1.23771	+	0.475111i	−0.151210	+	0.0580440i	−0.432796	−	0.901492i	$-0.642473\pi$
$67$	−1.23771	+	0.475111i	−0.151210	+	0.0580440i	0.281586	+	0.959536i	$0.409140\pi$
$68$	−0.493512	−	1.84181i	−0.0598471	−	0.223352i
$69$	−0.362627	+	0.263464i	−0.0436551	+	0.0317173i
$70$	4.72331	−	5.51681i	0.564544	−	0.659385i
$71$	1.14755	+	0.833741i	0.136189	+	0.0989469i	0.653794	−	0.756673i	$-0.273176\pi$
$71$	1.14755	+	0.833741i	0.136189	+	0.0989469i	−0.517605	+	0.855620i	$0.673176\pi$
$72$	3.22076	−	8.39037i	0.379570	−	0.988815i
$73$	7.23837	−	11.1461i	0.847187	−	1.30455i	−0.103572	−	0.994622i	$-0.533027\pi$
$73$	7.23837	−	11.1461i	0.847187	−	1.30455i	0.950759	−	0.309931i	$-0.100306\pi$
$74$	8.19625	−	4.73211i	0.952795	−	0.550096i
$75$	1.19319	+	0.400423i	0.137778	+	0.0462368i
$76$			2.97435i			0.341182i
$77$	11.2115	−	12.5422i	1.27767	−	1.42932i
$78$	0.167567	+	1.05798i	0.0189732	+	0.119792i
$79$	1.79663	+	4.03530i	0.202137	+	0.454007i	0.985961	−	0.166976i	$-0.0534002\pi$
$79$	1.79663	+	4.03530i	0.202137	+	0.454007i	−0.783824	+	0.620983i	$0.786734\pi$
$80$	6.17917	−	0.456413i	0.690853	−	0.0510285i
$81$	−7.70462	−	3.43032i	−0.856069	−	0.381147i
$82$	−3.05414	+	0.818354i	−0.337273	+	0.0903721i
$83$	0.0358492	−	0.226343i	0.00393496	−	0.0248444i	−0.985643	−	0.168844i	$-0.945996\pi$
$83$	0.0358492	−	0.226343i	0.00393496	−	0.0248444i	0.989578	+	0.144000i	$0.0459965\pi$
$84$	−0.306946	−	0.116558i	−0.0334905	−	0.0127175i
$85$	−5.23175	−	6.88648i	−0.567462	−	0.746944i
$86$	−4.91413	−	5.45770i	−0.529905	−	0.588519i
$87$	0.508959	−	0.0266734i	0.0545662	−	0.00285969i
$88$	19.4326	−	1.01842i	2.07153	−	0.108564i
$89$	8.63680	+	9.59214i	0.915499	+	1.01677i	0.999793	+	0.0203242i	$0.00646983\pi$
$89$	8.63680	+	9.59214i	0.915499	+	1.01677i	−0.0842940	+	0.996441i	$0.526863\pi$
$90$	−0.172246	−	8.05921i	−0.0181564	−	0.849515i
$91$	−9.05327	+	1.46737i	−0.949041	+	0.153822i
$92$	0.137332	−	0.867081i	0.0143179	−	0.0903995i
$93$	0.366631	−	0.0982386i	0.0380179	−	0.0101869i
$94$	2.94602	+	1.31165i	0.303859	+	0.135287i
$95$	5.10256	+	12.4883i	0.523512	+	1.28127i
$96$	−0.278400	−	0.625297i	−0.0284141	−	0.0638191i
$97$	0.0559772	+	0.353426i	0.00568363	+	0.0358850i	0.990367	−	0.138466i	$-0.0442172\pi$
$97$	0.0559772	+	0.353426i	0.00568363	+	0.0358850i	−0.984684	+	0.174351i	$0.944217\pi$
$98$	−3.02160	+	8.04442i	−0.305228	+	0.812609i
$99$		−	18.6723i		−	1.87664i
$100$	−2.20701	+	1.09791i	−0.220701	+	0.109791i
$101$	−3.72935	+	2.15314i	−0.371084	+	0.214246i	−0.673932	−	0.738793i	$-0.735396\pi$
$101$	−3.72935	+	2.15314i	−0.371084	+	0.214246i	0.302848	+	0.953039i	$0.402063\pi$
$102$	0.650921	−	1.00233i	0.0644508	−	0.0992455i
$103$	−3.88521	+	10.1213i	−0.382822	+	0.997284i	0.597847	+	0.801610i	$0.296023\pi$
$103$	−3.88521	+	10.1213i	−0.382822	+	0.997284i	−0.980669	+	0.195674i	$0.937310\pi$
$104$	−8.58271	−	6.23570i	−0.841604	−	0.611461i
$105$	−1.48871	+	0.0371874i	−0.145284	+	0.00362912i
$106$	−3.02993	+	2.20137i	−0.294293	+	0.213816i
$107$	−2.57778	−	9.62039i	−0.249203	−	0.930038i	−0.971224	−	0.238167i	$-0.923453\pi$
$107$	−2.57778	−	9.62039i	−0.249203	−	0.930038i	0.722021	−	0.691871i	$-0.243213\pi$
$108$	−0.687790	+	0.264018i	−0.0661826	+	0.0254051i
$109$	−2.12717	−	1.91531i	−0.203746	−	0.183454i	0.560941	−	0.827856i	$-0.310440\pi$
$109$	−2.12717	−	1.91531i	−0.203746	−	0.183454i	−0.764687	+	0.644402i	$0.777106\pi$
$110$	15.7895	−	7.43817i	1.50547	−	0.709202i
$111$	−1.84564	−	0.599686i	−0.175181	−	0.0569197i
$112$	−6.68661	+	3.00600i	−0.631825	+	0.284040i
$113$	−4.40329	+	8.64195i	−0.414227	+	0.812966i	0.585770	+	0.810477i	$0.300792\pi$
$113$	−4.40329	+	8.64195i	−0.414227	+	0.812966i	−0.999997	+	0.00248866i	$0.999208\pi$
$114$	−1.38543	+	1.24745i	−0.129757	+	0.116834i
$115$	−0.910886	−	3.87616i	−0.0849406	−	0.361454i
$116$	−0.667924	+	0.741805i	−0.0620152	+	0.0688749i
$117$	−6.40634	+	7.91117i	−0.592266	+	0.731388i
$118$	11.2124	−	11.2124i	1.03218	−	1.03218i
$119$	8.60209	+	5.54228i	0.788552	+	0.508060i
$120$	−1.24379	−	1.19174i	−0.113542	−	0.108790i
$121$	26.8850	−	11.9700i	2.44409	−	1.08818i
$122$	0.0820635	−	0.0664537i	0.00742968	−	0.00601644i
$123$	0.543742	+	0.353110i	0.0490276	+	0.0318389i
$124$	−0.371701	+	0.643805i	−0.0333797	+	0.0578154i
$125$	−7.38298	+	8.39593i	−0.660354	+	0.750954i
$126$	3.45018	+	8.89207i	0.307366	+	0.792169i
$127$	3.47660	+	6.82321i	0.308498	+	0.605462i	0.992251	−	0.124252i	$-0.0396532\pi$
$127$	3.47660	+	6.82321i	0.308498	+	0.605462i	−0.683753	+	0.729714i	$0.739653\pi$
$128$	−5.09979	−	1.95763i	−0.450762	−	0.173031i
$129$	−0.157408	+	1.49764i	−0.0138590	+	0.131860i
$130$	−9.24173	−	2.26582i	−0.810553	−	0.198725i
$131$	−8.45350	+	0.888499i	−0.738586	+	0.0776285i	−0.466348	−	0.884601i	$-0.654430\pi$
$131$	−8.45350	+	0.888499i	−0.738586	+	0.0776285i	−0.272238	+	0.962230i	$0.587764\pi$
$132$	−0.557951	−	0.557951i	−0.0485634	−	0.0485634i
$133$	−10.7234	−	11.8236i	−0.929840	−	1.02524i
$134$	1.54785	−	0.502926i	0.133714	−	0.0434462i
$135$	−2.43486	+	2.28843i	−0.209559	+	0.196957i
$136$	2.46098	+	11.5780i	0.211028	+	0.992807i
$137$	0.894429	+	17.0667i	0.0764163	+	1.45811i	0.720660	+	0.693289i	$0.243839\pi$
$137$	0.894429	+	17.0667i	0.0764163	+	1.45811i	−0.644244	+	0.764820i	$0.722828\pi$
$138$	0.461477	−	0.299686i	0.0392835	−	0.0255110i
$139$	−4.98856	+	15.3532i	−0.423124	+	1.30224i	0.481656	+	0.876361i	$0.340036\pi$
$139$	−4.98856	+	15.3532i	−0.423124	+	1.30224i	−0.904779	+	0.425880i	$0.859964\pi$
$140$	2.01024	−	2.11324i	0.169896	−	0.178602i
$141$	−0.204336	−	0.628881i	−0.0172082	−	0.0529613i
$142$	−1.35323	−	1.09582i	−0.113560	−	0.0919594i
$143$	−21.2902	−	5.70469i	−1.78038	−	0.477050i
$144$	−3.30972	+	7.43374i	−0.275810	+	0.619479i
$145$	−1.53180	+	4.26042i	−0.127209	+	0.353808i
$146$	−9.58974	+	13.1991i	−0.793652	+	1.09237i
$147$	1.64039	−	0.643295i	0.135297	−	0.0530581i
$148$	3.38657	−	1.72554i	0.278374	−	0.141839i
$149$	13.1522	+	7.59345i	1.07747	+	0.622080i	0.930214	−	0.367018i	$-0.119621\pi$
$149$	13.1522	+	7.59345i	1.07747	+	0.622080i	0.147260	+	0.989098i	$0.452955\pi$
$150$	−1.43702	−	0.567543i	−0.117332	−	0.0463397i
$151$	−7.07212	−	12.2493i	−0.575521	−	0.996832i	−0.995985	−	0.0895225i	$-0.971466\pi$
$151$	−7.07212	−	12.2493i	−0.575521	−	0.996832i	0.420464	−	0.907309i	$-0.361867\pi$
$152$	0.966320	−	18.4385i	0.0783789	−	1.49556i
$153$	11.2181	−	1.77678i	0.906934	−	0.143644i
$154$	−14.5501	+	14.6554i	−1.17248	+	1.18097i
$155$	−0.456181	+	3.34077i	−0.0366413	+	0.268337i
$156$	0.0449661	+	0.427824i	0.00360017	+	0.0342533i
$157$	1.19002	−	4.44121i	0.0949739	−	0.354447i	−0.902042	−	0.431649i	$-0.857932\pi$
$157$	1.19002	−	4.44121i	0.0949739	−	0.354447i	0.997015	+	0.0772018i	$0.0245986\pi$
$158$	−1.94326	−	5.06237i	−0.154598	−	0.402740i
$159$	0.751166	+	0.159665i	0.0595713	+	0.0126623i
$160$	6.07896	−	0.129923i	0.480584	−	0.0102713i
$161$	2.58017	+	3.94193i	0.203346	+	0.310668i
$162$	9.22483	+	4.70028i	0.724771	+	0.369289i
$163$	−5.30627	−	8.17094i	−0.415619	−	0.639997i	0.567412	−	0.823434i	$-0.307945\pi$
$163$	−5.30627	−	8.17094i	−0.415619	−	0.639997i	−0.983032	+	0.183436i	$0.941278\pi$
$164$	−1.24206	+	0.264009i	−0.0969889	+	0.0206156i
$165$	−3.29982	−	1.38546i	−0.256890	−	0.107858i
$166$	−0.0584901	+	0.275174i	−0.00453971	+	0.0213577i
$167$	17.9190	+	2.83810i	1.38662	+	0.219618i	0.804725	−	0.593648i	$-0.202313\pi$
$167$	17.9190	+	2.83810i	1.38662	+	0.219618i	0.581892	+	0.813266i	$0.302313\pi$
$168$	1.86494	+	0.822281i	0.143883	+	0.0634404i
$169$	−0.578133	−	0.795732i	−0.0444718	−	0.0612101i
$170$	5.97124	+	8.77837i	0.457973	+	0.673271i
$171$	−17.6200	−	1.85194i	−1.34744	−	0.141621i
$172$	−1.85610	−	2.29210i	−0.141527	−	0.174771i
$173$	−12.5015	−	0.655177i	−0.950474	−	0.0498122i	−0.429207	−	0.903206i	$-0.641207\pi$
$173$	−12.5015	−	0.655177i	−0.950474	−	0.0498122i	−0.521267	+	0.853394i	$0.674540\pi$
$174$	−0.625655			−0.0474308
$175$	4.81498	−	12.3214i	0.363978	−	0.931408i
$176$	−17.6187			−1.32806
$177$	−3.24693	−	0.170164i	−0.244054	−	0.0127903i
$178$	−9.97172	−	12.3140i	−0.747412	−	0.922977i
$179$	−15.9599	−	1.67745i	−1.19290	−	0.125379i	−0.512805	−	0.858505i	$-0.671394\pi$
$179$	−15.9599	−	1.67745i	−1.19290	−	0.125379i	−0.680092	+	0.733127i	$0.738060\pi$
$180$	0.100310	−	3.23577i	0.00747668	−	0.241180i
$181$	8.02423	+	11.0444i	0.596436	+	0.820924i	0.995376	−	0.0960528i	$-0.0306218\pi$
$181$	8.02423	+	11.0444i	0.596436	+	0.820924i	−0.398940	+	0.916977i	$0.630622\pi$
$182$	11.1928	−	1.21722i	0.829667	−	0.0902267i
$183$	−0.0213857	−	0.00338717i	−0.00158088	−	0.000250387i
$184$	−1.13305	+	5.33056i	−0.0835292	+	0.392974i
$185$	11.2588	−	13.0547i	0.827764	−	0.959799i
$186$	−0.455770	+	0.0968770i	−0.0334187	+	0.00710337i
$187$	13.3939	+	20.6248i	0.979460	+	1.50824i
$188$	1.15393	+	0.587958i	0.0841592	+	0.0428813i
$189$	1.78223	−	3.52921i	0.129638	−	0.256712i
$190$	−5.45297	−	15.6374i	−0.395600	−	1.13445i
$191$	−1.08796	−	0.231253i	−0.0787220	−	0.0167329i	0.168382	−	0.985722i	$-0.446146\pi$
$191$	−1.08796	−	0.231253i	−0.0787220	−	0.0167329i	−0.247104	+	0.968989i	$0.579479\pi$
$192$	0.801039	+	2.08678i	0.0578100	+	0.150600i
$193$	−2.73020	+	10.1893i	−0.196524	+	0.733438i	0.795343	+	0.606160i	$0.207291\pi$
$193$	−2.73020	+	10.1893i	−0.196524	+	0.733438i	−0.991867	+	0.127278i	$0.959376\pi$
$194$	−0.0459166	−	0.436867i	−0.00329662	−	0.0313652i
$195$	0.922738	+	1.71914i	0.0660786	+	0.123110i
$196$	−1.38089	+	3.16271i	−0.0986352	+	0.225908i
$197$	0.109704	−	0.0173753i	0.00781605	−	0.00123794i	−0.152525	−	0.988300i	$-0.548741\pi$
$197$	0.109704	−	0.0173753i	0.00781605	−	0.00123794i	0.160341	+	0.987062i	$0.448741\pi$
$198$	−1.19965	+	22.8907i	−0.0852555	+	1.62677i
$199$	9.56773	+	16.5718i	0.678239	+	1.17474i	0.975511	+	0.219951i	$0.0705897\pi$
$199$	9.56773	+	16.5718i	0.678239	+	1.17474i	−0.297272	+	0.954793i	$0.596077\pi$
$200$	14.0383	−	6.08912i	0.992660	−	0.430565i
$201$	−0.289007	−	0.166858i	−0.0203850	−	0.0117693i
$202$	4.71020	−	2.39997i	0.331409	−	0.168861i
$203$	−0.0193115	−	5.35688i	−0.00135541	−	0.375979i
$204$	0.282119	−	0.388304i	0.0197523	−	0.0271867i
$205$	−4.76207	+	3.23926i	−0.332598	+	0.226240i
$206$	5.41321	−	12.1583i	0.377156	−	0.847107i
$207$	5.05107	+	1.35343i	0.351074	+	0.0940700i
$208$	7.46478	+	6.04486i	0.517589	+	0.419136i
$209$	−11.8542	−	36.4835i	−0.819972	−	2.52362i
$210$	1.82743	+	0.0500576i	0.126104	+	0.00345430i
$211$	−5.50057	+	16.9290i	−0.378675	+	1.16544i	0.562290	+	0.826940i	$0.309920\pi$
$211$	−5.50057	+	16.9290i	−0.378675	+	1.16544i	−0.940966	+	0.338502i	$0.890080\pi$
$212$	−1.26142	+	0.819177i	−0.0866348	+	0.0562613i
$213$	0.0186864	+	0.356558i	0.00128037	+	0.0244309i
$214$	2.54205	+	11.9594i	0.173771	+	0.817528i
$215$	−11.7253	−	6.43952i	−0.799656	−	0.439172i
$216$	4.34949	−	1.41324i	0.295946	−	0.0961585i
$217$	−0.843533	−	3.89934i	−0.0572628	−	0.264704i
$218$	2.48468	+	2.48468i	0.168283	+	0.168283i
$219$	3.32705	−	0.349687i	0.224821	−	0.0236296i
$220$	6.48871	−	2.65122i	0.437469	−	0.178745i
$221$	1.40143	−	13.3338i	0.0942707	−	0.896926i
$222$	2.22407	+	0.853742i	0.149270	+	0.0572994i
$223$	−3.11940	−	6.12217i	−0.208891	−	0.409971i	0.762661	−	0.646798i	$-0.223892\pi$
$223$	−3.11940	−	6.12217i	−0.208891	−	0.409971i	−0.971552	+	0.236827i	$0.923892\pi$
$224$	−6.70718	+	2.60243i	−0.448142	+	0.173882i
$225$	−5.12986	−	13.7579i	−0.341991	−	0.917195i
$226$	5.95329	−	10.3114i	0.396007	−	0.685904i
$227$	−7.16835	−	4.65518i	−0.475780	−	0.308975i	0.284379	−	0.958712i	$-0.408213\pi$
$227$	−7.16835	−	4.65518i	−0.475780	−	0.308975i	−0.760159	+	0.649737i	$0.774879\pi$
$228$	−0.581845	+	0.471169i	−0.0385337	+	0.0312039i
$229$	8.16658	−	3.63599i	0.539663	−	0.240273i	−0.118758	−	0.992923i	$-0.537891\pi$
$229$	8.16658	−	3.63599i	0.539663	−	0.240273i	0.658421	+	0.752650i	$0.271225\pi$
$230$	0.867635	+	4.81037i	0.0572102	+	0.317187i
$231$	4.22954	+	0.206375i	0.278284	+	0.0135784i
$232$	4.38157	−	4.38157i	0.287664	−	0.287664i
$233$	−3.94085	+	4.86654i	−0.258174	+	0.318818i	−0.889708	−	0.456530i	$-0.849092\pi$
$233$	−3.94085	+	4.86654i	−0.258174	+	0.318818i	0.631534	+	0.775348i	$0.282425\pi$
$234$	8.36190	−	9.28683i	0.546635	−	0.607099i
$235$	5.85361	+	0.489034i	0.381848	+	0.0319011i
$236$	4.73238	−	4.26106i	0.308052	−	0.277371i
$237$	−0.504784	+	0.990694i	−0.0327892	+	0.0643525i
$238$	−10.1894	−	7.34702i	−0.660478	−	0.476237i
$239$	22.1170	+	7.18624i	1.43063	+	0.464839i	0.918963	−	0.394345i	$-0.129028\pi$
$239$	22.1170	+	7.18624i	1.43063	+	0.464839i	0.511666	+	0.859184i	$0.329028\pi$
$240$	1.06813	+	1.13648i	0.0689476	+	0.0733592i
$241$	2.77782	+	2.50116i	0.178935	+	0.161114i	0.753731	−	0.657183i	$-0.228252\pi$
$241$	2.77782	+	2.50116i	0.178935	+	0.161114i	−0.574796	+	0.818296i	$0.694919\pi$
$242$	−33.7278	+	12.9469i	−2.16810	+	0.832257i
$243$	−1.70975	−	6.38089i	−0.109681	−	0.409334i
$244$	0.0343083	−	0.0249265i	0.00219637	−	0.00159575i
$245$	−0.372189	+	15.6481i	−0.0237783	+	0.999717i
$246$	−0.643896	−	0.467817i	−0.0410533	−	0.0298270i
$247$	−7.49477	+	19.5246i	−0.476881	+	1.24232i
$248$	2.51340	−	3.87029i	0.159601	−	0.245764i
$249$	0.0499564	−	0.0288423i	0.00316586	−	0.00182781i
$250$	9.59033	−	9.81836i	0.606546	−	0.620967i
$251$			7.23085i			0.456407i	0.973613	+	0.228204i	$0.0732852\pi$
$251$			7.23085i			0.456407i	−0.973613	+	0.228204i	$0.926715\pi$
$252$	1.19680	+	3.63869i	0.0753913	+	0.229216i
$253$	1.77121	+	11.1830i	0.111355	+	0.703068i
$254$	−3.82364	−	8.58803i	−0.239916	−	0.538861i
$255$	0.518376	−	2.11433i	0.0324620	−	0.132405i
$256$	−10.0984	−	4.49609i	−0.631150	−	0.281006i
$257$	20.6651	−	5.53721i	1.28906	−	0.345401i	0.451754	−	0.892143i	$-0.350798\pi$
$257$	20.6651	−	5.53721i	1.28906	−	0.345401i	0.837302	+	0.546741i	$0.184132\pi$
$258$	0.289189	−	1.82587i	0.0180041	−	0.113673i
$259$	−7.24113	+	19.0690i	−0.449942	+	1.18489i
$260$	−3.65878	−	1.10295i	−0.226908	−	0.0684021i
$261$	−3.97857	−	4.41865i	−0.246267	−	0.273508i
$262$	10.4204	−	0.546108i	0.643772	−	0.0337387i
$263$	−16.2964	+	0.854059i	−1.00488	+	0.0526635i	−0.547669	−	0.836695i	$-0.684485\pi$
$263$	−16.2964	+	0.854059i	−1.00488	+	0.0526635i	−0.457211	+	0.889359i	$0.651151\pi$
$264$	3.27756	+	3.64010i	0.201720	+	0.224033i
$265$	−3.89095	+	5.60343i	−0.239019	+	0.344216i
$266$	12.3864	+	15.1837i	0.759459	+	0.930971i
$267$	−0.508262	+	3.20904i	−0.0311051	+	0.196390i
$268$	0.631335	−	0.169166i	0.0385649	−	0.0103334i
$269$	−13.7743	−	6.13271i	−0.839833	−	0.373918i	−0.0586947	−	0.998276i	$-0.518694\pi$
$269$	−13.7743	−	6.13271i	−0.839833	−	0.373918i	−0.781138	+	0.624358i	$0.785361\pi$
$270$	3.13196	−	2.64899i	0.190605	−	0.161213i
$271$	2.08583	+	4.68484i	0.126705	+	0.284584i	0.965748	−	0.259481i	$-0.0835513\pi$
$271$	2.08583	+	4.68484i	0.126705	+	0.284584i	−0.839043	+	0.544065i	$0.816885\pi$
$272$	−1.67653	−	10.5852i	−0.101654	−	0.641820i
$273$	−1.72118	−	1.53856i	−0.104171	−	0.0931180i
$274$		−	20.9798i		−	1.26744i
$275$	22.6956	−	22.2630i	1.36860	−	1.34251i
$276$	0.191374	−	0.110490i	0.0115194	−	0.00665071i
$277$	−0.155664	+	0.239701i	−0.00935293	+	0.0144022i	−0.843316	−	0.537418i	$-0.819400\pi$
$277$	−0.155664	+	0.239701i	−0.00935293	+	0.0144022i	0.833963	+	0.551820i	$0.186066\pi$
$278$	7.10195	−	18.5012i	0.425947	−	1.10963i
$279$	−3.58246	−	2.60281i	−0.214476	−	0.155826i
$280$	−13.1484	+	12.4472i	−0.785765	+	0.743864i
$281$	−0.915304	+	0.665008i	−0.0546025	+	0.0396710i	−0.614752	−	0.788721i	$-0.710744\pi$
$281$	−0.915304	+	0.665008i	−0.0546025	+	0.0396710i	0.560149	+	0.828392i	$0.310744\pi$
$282$	0.210094	+	0.784083i	0.0125109	+	0.0466915i
$283$	2.93029	−	1.12483i	0.174188	−	0.0668644i	−0.269711	−	0.962941i	$-0.586928\pi$
$283$	2.93029	−	1.12483i	0.174188	−	0.0668644i	0.443899	+	0.896077i	$0.353595\pi$
$284$	−0.519681	−	0.467923i	−0.0308374	−	0.0277661i
$285$	−1.63466	+	2.97644i	−0.0968291	+	0.176309i
$286$	25.7335	+	8.36131i	1.52165	+	0.494414i
$287$	3.98560	−	5.52750i	0.235262	−	0.326278i
$288$	−3.62527	+	7.11500i	−0.213621	+	0.419255i
$289$	1.51678	−	1.36572i	0.0892225	−	0.0803363i
$290$	2.15157	−	5.12449i	0.126345	−	0.300921i
$291$	−0.0602702	+	0.0669369i	−0.00353310	+	0.00392391i
$292$	−4.12339	+	5.09196i	−0.241303	+	0.297984i
$293$	−1.98002	+	1.98002i	−0.115674	+	0.115674i	−0.762575	−	0.646900i	$-0.776065\pi$
$293$	−1.98002	+	1.98002i	−0.115674	+	0.115674i	0.646900	+	0.762575i	$0.276065\pi$
$294$	−2.05231	+	0.683234i	−0.119693	+	0.0398470i
$295$	12.5597	−	26.0092i	0.731253	−	1.51431i
$296$	−21.5545	+	9.59668i	−1.25283	+	0.557796i
$297$	7.38421	−	5.97962i	0.428475	−	0.346973i
$298$	−15.6357	−	10.1539i	−0.905750	−	0.588201i
$299$	3.08636	−	5.34574i	0.178489	−	0.309152i
$300$	−0.564390	−	0.257817i	−0.0325850	−	0.0148851i
$301$	15.6421	+	2.41969i	0.901594	+	0.139469i
$302$	7.88284	+	15.4709i	0.453606	+	0.890253i
$303$	−1.01197	−	0.388458i	−0.0581361	−	0.0223163i
$304$	−1.74744	+	16.6258i	−0.100223	+	0.953556i
$305$	0.101287	−	0.163514i	0.00579966	−	0.00936278i
$306$	−13.8667	+	1.45744i	−0.792704	+	0.0833165i
$307$	18.7431	+	18.7431i	1.06973	+	1.06973i	0.997379	+	0.0723483i	$0.0230493\pi$
$307$	18.7431	+	18.7431i	1.06973	+	1.06973i	0.0723483	+	0.997379i	$0.476951\pi$
$308$	−6.14337	+	5.57174i	−0.350051	+	0.317480i
$309$	−2.59540	+	0.843298i	−0.147647	+	0.0479735i
$310$	0.773875	−	4.06619i	0.0439531	−	0.230944i
$311$	−6.29041	−	29.5941i	−0.356697	−	1.67813i	−0.681087	−	0.732202i	$-0.738492\pi$
$311$	−6.29041	−	29.5941i	−0.356697	−	1.67813i	0.324390	−	0.945923i	$-0.394841\pi$
$312$	−0.139759	−	2.66676i	−0.00791229	−	0.150975i
$313$	16.7280	−	10.8633i	0.945521	−	0.614029i	0.0229007	−	0.999738i	$-0.492710\pi$
$313$	16.7280	−	10.8633i	0.945521	−	0.614029i	0.922620	+	0.385709i	$0.126043\pi$
$314$	−1.74420	+	5.36809i	−0.0984308	+	0.302939i
$315$	11.2672	+	13.2244i	0.634834	+	0.745112i
$316$	−0.672944	−	2.07111i	−0.0378561	−	0.116509i
$317$	−13.4747	−	10.9116i	−0.756815	−	0.612857i	0.171270	−	0.985224i	$-0.445213\pi$
$317$	−13.4747	−	10.9116i	−0.756815	−	0.612857i	−0.928085	+	0.372367i	$0.878546\pi$
$318$	−0.910607	−	0.243997i	−0.0510643	−	0.0136826i
$319$	5.23633	−	11.7610i	0.293178	−	0.658490i
$320$	−19.8467	−	0.615256i	−1.10946	−	0.0343939i
$321$	1.47360	−	2.02824i	0.0822485	−	0.113205i
$322$	−2.90981	−	4.99824i	−0.162158	−	0.278541i
$323$	20.7909	−	10.5935i	1.15684	−	0.589438i
$324$	3.60083	+	2.07894i	0.200046	+	0.115497i
$325$	−17.2540	+	1.64580i	−0.957082	+	0.0912925i
$326$	5.98007	+	10.3578i	0.331206	+	0.573665i
$327$	0.0377087	−	0.719525i	0.00208530	−	0.0397898i
$328$	7.78553	−	1.23311i	0.429884	−	0.0680869i
$329$	−6.70687	+	1.82304i	−0.369761	+	0.100507i
$330$	3.95628	+	1.91047i	0.217786	+	0.105168i
$331$	0.656739	+	6.24845i	0.0360976	+	0.343446i	0.997633	+	0.0687646i	$0.0219057\pi$
$331$	0.656739	+	6.24845i	0.0360976	+	0.343446i	−0.961535	+	0.274681i	$0.911428\pi$
$332$	−0.0292411	+	0.109129i	−0.00160482	+	0.00598925i
$333$	8.11350	+	21.1364i	0.444617	+	1.15827i
$334$	−21.7849	−	4.63052i	−1.19202	−	0.253371i
$335$	2.36055	−	1.79333i	0.128970	−	0.0979803i
$336$	−1.64727	−	0.831858i	−0.0898657	−	0.0453816i
$337$	−28.1439	−	14.3400i	−1.53310	−	0.781152i	−0.535123	−	0.844774i	$-0.679735\pi$
$337$	−28.1439	−	14.3400i	−1.53310	−	0.781152i	−0.997974	+	0.0636218i	$0.979735\pi$
$338$	0.657618	+	1.01264i	0.0357697	+	0.0550805i
$339$	−2.38807	+	0.507601i	−0.129702	+	0.0275691i
$340$	2.21026	+	3.64607i	0.119868	+	0.197736i
$341$	1.99343	−	9.37833i	0.107950	−	0.507865i
$342$	21.4817	+	3.40236i	1.16160	+	0.183979i
$343$	−5.91323	−	17.5509i	−0.319284	−	0.947659i
$344$	10.7616	+	14.8121i	0.580228	+	0.798615i
$345$	0.613965	−	0.792214i	0.0330548	−	0.0426514i
$346$	15.2837	+	1.60638i	0.821658	+	0.0863597i
$347$	−7.99465	−	9.87257i	−0.429175	−	0.529987i	0.515983	−	0.856599i	$-0.327427\pi$
$347$	−7.99465	−	9.87257i	−0.429175	−	0.529987i	−0.945159	+	0.326611i	$0.894093\pi$
$348$	−0.250919	−	0.0131501i	−0.0134507	−	0.000704920i
$349$	18.9164			1.01257			0.506287	−	0.862365i	$-0.331018\pi$
$349$	18.9164			1.01257			0.506287	+	0.862365i	$0.331018\pi$
$350$	−6.69437	+	14.7956i	−0.357829	+	0.790858i
$351$	−5.18013			−0.276495
$352$	−17.2662	−	0.904881i	−0.920290	−	0.0482303i
$353$	18.0348	+	22.2711i	0.959893	+	1.18537i	0.982620	+	0.185628i	$0.0594319\pi$
$353$	18.0348	+	22.2711i	0.959893	+	1.18537i	−0.0227268	+	0.999742i	$0.507235\pi$
$354$	3.96953	+	0.417214i	0.210978	+	0.0221747i
$355$	−2.98469	−	1.07312i	−0.158411	−	0.0569552i
$356$	−3.74034	−	5.14814i	−0.198238	−	0.272851i
$357$	0.278478	+	2.56070i	0.0147386	+	0.135527i
$358$	19.4577	+	3.08179i	1.02837	+	0.162878i
$359$	−6.59062	+	31.0064i	−0.347839	+	1.63646i	0.362061	+	0.932154i	$0.382073\pi$
$359$	−6.59062	+	31.0064i	−0.347839	+	1.63646i	−0.709901	+	0.704302i	$0.751260\pi$
$360$	−1.67309	+	20.0265i	−0.0881796	+	1.05549i
$361$	−17.0183	+	3.61735i	−0.895700	+	0.190387i
$362$	−9.12745	−	14.0550i	−0.479728	−	0.738717i
$363$	6.60045	+	3.36310i	0.346434	+	0.176517i
$364$	4.51447	−	0.252916i	0.236622	−	0.0132564i
$365$	−8.57729	+	28.4531i	−0.448956	+	1.48930i
$366$	0.0259995	+	0.00552636i	0.00135901	+	0.000288867i
$367$	−4.76320	−	12.4085i	−0.248637	−	0.647721i	0.751288	−	0.659974i	$-0.229433\pi$
$367$	−4.76320	−	12.4085i	−0.248637	−	0.647721i	−0.999925	+	0.0122534i	$0.996100\pi$
$368$	1.27706	−	4.76607i	0.0665716	−	0.248448i
$369$	−0.790631	−	7.52235i	−0.0411586	−	0.391598i
$370$	−14.6411	+	15.2806i	−0.761153	+	0.794399i
$371$	2.06100	−	7.80419i	0.107002	−	0.405173i
$372$	−0.184823	+	0.0292731i	−0.00958263	+	0.00151774i
$373$	−1.19300	+	22.7639i	−0.0617714	+	1.17867i	0.775307	+	0.631585i	$0.217595\pi$
$373$	−1.19300	+	22.7639i	−0.0617714	+	1.17867i	−0.837078	+	0.547084i	$0.815738\pi$
$374$	−15.0947	−	26.1448i	−0.780529	−	1.35192i
$375$	−2.81196	−	0.114261i	−0.145209	−	0.00590043i
$376$	−6.96240	−	4.01974i	−0.359058	−	0.207302i
$377$	−6.25366	+	3.18640i	−0.322080	+	0.164108i
$378$	−2.41160	+	4.21201i	−0.124039	+	0.216642i
$379$	8.90518	−	12.2569i	0.457428	−	0.629596i	−0.516545	−	0.856260i	$-0.672782\pi$
$379$	8.90518	−	12.2569i	0.457428	−	0.629596i	0.973973	+	0.226664i	$0.0727820\pi$
$380$	−1.85825	−	6.38598i	−0.0953260	−	0.327594i
$381$	−0.784032	+	1.76096i	−0.0401672	+	0.0902169i
$382$	1.31889	+	0.353395i	0.0674802	+	0.0180813i
$383$	−2.72652	−	2.20789i	−0.139318	−	0.112818i	0.557128	−	0.830427i	$-0.311903\pi$
$383$	−2.72652	−	2.20789i	−0.139318	−	0.112818i	−0.696446	+	0.717609i	$0.745237\pi$
$384$	−0.424909	−	1.30773i	−0.0216835	−	0.0667350i
$385$	−16.2354	+	33.9328i	−0.827432	+	1.72938i
$386$	4.00163	−	12.3158i	0.203678	−	0.626855i
$387$	14.7340	−	9.56840i	0.748973	−	0.486389i
$388$	−0.00923272	−	0.176171i	−0.000468720	−	0.00894372i
$389$	0.825989	+	3.88598i	0.0418793	+	0.197027i	0.994114	−	0.108341i	$-0.0345539\pi$
$389$	0.825989	+	3.88598i	0.0418793	+	0.197027i	−0.952234	+	0.305368i	$0.901221\pi$
$390$	−1.02075	−	2.16681i	−0.0516876	−	0.109720i
$391$	−6.55008	+	2.12825i	−0.331252	+	0.107630i
$392$	9.58789	−	19.1575i	0.484262	−	0.967601i
$393$	−1.51293	−	1.51293i	−0.0763174	−	0.0763174i
$394$	−0.135604	+	0.0142525i	−0.00683161	+	0.000718031i
$395$	−6.37848	−	7.54140i	−0.320936	−	0.379449i
$396$	−0.962241	+	9.15511i	−0.0483544	+	0.460062i
$397$	−30.1058	−	11.5565i	−1.51097	−	0.580006i	−0.544946	−	0.838471i	$-0.683450\pi$
$397$	−30.1058	−	11.5565i	−1.51097	−	0.580006i	−0.966021	+	0.258465i	$0.916783\pi$
$398$	−10.6645	−	20.9303i	−0.534565	−	1.04914i
$399$	0.614234	−	3.97071i	0.0307502	−	0.198784i
$400$	−12.9816	+	4.84041i	−0.649082	+	0.242020i
$401$	7.36782	−	12.7614i	0.367932	−	0.637276i	−0.621310	−	0.783565i	$-0.713399\pi$
$401$	7.36782	−	12.7614i	0.367932	−	0.637276i	0.989242	+	0.146288i	$0.0467327\pi$
$402$	0.343578	+	0.223122i	0.0171361	+	0.0111283i
$403$	−4.06222	+	3.28952i	−0.202353	+	0.163863i
$404$	1.93947	−	0.863508i	0.0964923	−	0.0429611i
$405$	18.6851	+	2.55144i	0.928469	+	0.126782i
$406$	−0.320492	+	6.56833i	−0.0159058	+	0.325981i
$407$	−34.6627	+	34.6627i	−1.71816	+	1.71816i
$408$	−1.87506	+	2.31550i	−0.0928291	+	0.114634i
$409$	10.9932	−	12.2091i	0.543577	−	0.603703i	−0.407292	−	0.913298i	$-0.633527\pi$
$409$	10.9932	−	12.2091i	0.543577	−	0.603703i	0.950869	+	0.309595i	$0.100193\pi$
$410$	6.04601	−	3.66511i	0.298591	−	0.181007i
$411$	−3.19692	+	2.87852i	−0.157693	+	0.141987i
$412$	2.42652	−	4.76230i	0.119546	−	0.234622i
$413$	−3.44968	+	34.0002i	−0.169748	+	1.67304i
$414$	−6.10523	−	1.98371i	−0.300056	−	0.0974941i
$415$	0.0644405	+	0.508359i	0.00316326	+	0.0249544i
$416$	7.00494	+	6.30728i	0.343445	+	0.309240i
$417$	−3.79365	+	1.45624i	−0.185776	+	0.0713126i
$418$	12.1883	+	45.4873i	0.596148	+	2.22485i
$419$	−7.57258	+	5.50180i	−0.369945	+	0.268781i	−0.757188	−	0.653197i	$-0.773427\pi$
$419$	−7.57258	+	5.50180i	−0.369945	+	0.268781i	0.387243	+	0.921978i	$0.373427\pi$
$420$	0.731838	+	0.0584847i	0.0357100	+	0.00285376i
$421$	−9.78581	−	7.10980i	−0.476931	−	0.346511i	0.323205	−	0.946329i	$-0.395240\pi$
$421$	−9.78581	−	7.10980i	−0.476931	−	0.346511i	−0.800136	+	0.599818i	$0.795240\pi$
$422$	7.83089	−	20.4002i	0.381202	−	0.993064i
$423$	−4.20154	+	6.46981i	−0.204286	+	0.314573i
$424$	8.08590	−	4.66840i	0.392686	−	0.226717i
$425$	15.5350	+	11.5168i	0.753559	+	0.558648i
$426$		−	0.438310i		−	0.0212362i
$427$	−0.0465144	+	0.222779i	−0.00225099	+	0.0107810i
$428$	0.768125	+	4.84975i	0.0371287	+	0.234422i
$429$	−2.25664	−	5.06849i	−0.108951	−	0.244709i
$430$	13.9605	+	8.64763i	0.673233	+	0.417026i
$431$	24.8448	+	11.0616i	1.19673	+	0.532820i	0.905711	−	0.423896i	$-0.139338\pi$
$431$	24.8448	+	11.0616i	1.19673	+	0.532820i	0.291023	+	0.956716i	$0.406004\pi$
$432$	−3.99967	+	1.07171i	−0.192434	+	0.0515626i
$433$	4.60452	−	29.0718i	0.221279	−	1.39710i	−0.587612	−	0.809143i	$-0.699932\pi$
$433$	4.60452	−	29.0718i	0.221279	−	1.39710i	0.808891	−	0.587959i	$-0.200068\pi$
$434$	0.783577	+	4.83445i	0.0376129	+	0.232061i
$435$	−1.07608	+	0.375244i	−0.0515941	+	0.0179916i
$436$	0.944257	+	1.04870i	0.0452217	+	0.0502238i
$437$	10.7284	−	0.562253i	0.513210	−	0.0268962i
$438$	−4.10114	+	0.214932i	−0.195960	+	0.0102698i
$439$	1.51578	+	1.68345i	0.0723443	+	0.0803465i	0.778230	−	0.627979i	$-0.216118\pi$
$439$	1.51578	+	1.68345i	0.0723443	+	0.0803465i	−0.705886	+	0.708325i	$0.749451\pi$
$440$	−41.0859	+	14.3272i	−1.95869	+	0.683024i
$441$	−17.8761	−	10.1496i	−0.851241	−	0.483315i
$442$	−2.57470	+	16.2560i	−0.122466	+	0.773220i
$443$	14.5039	−	3.88631i	0.689102	−	0.184644i	0.102758	−	0.994706i	$-0.467233\pi$
$443$	14.5039	−	3.88631i	0.689102	−	0.184644i	0.586344	+	0.810062i	$0.300567\pi$
$444$	0.874021	+	0.389139i	0.0414792	+	0.0184677i
$445$	−24.5361	−	15.1986i	−1.16312	−	0.720482i
$446$	3.43079	+	7.70568i	0.162453	+	0.364875i
$447$	0.598018	+	3.77574i	0.0282853	+	0.178586i
$448$	22.3180	−	7.34061i	1.05443	−	0.346811i
$449$		−	16.3116i		−	0.769793i	−0.922960	−	0.384897i	$-0.874237\pi$
$449$		−	16.3116i		−	0.769793i	0.922960	−	0.384897i	$-0.125763\pi$
$450$	5.40486	+	17.1956i	0.254787	+	0.810610i
$451$	14.1830	−	8.18855i	0.667851	−	0.385584i
$452$	2.60429	−	4.01026i	0.122496	−	0.188627i
$453$	1.27591	−	3.32387i	0.0599477	−	0.156169i
$454$	8.48871	+	6.16741i	0.398395	+	0.289451i
$455$	18.5208	−	8.80656i	0.868267	−	0.412858i
$456$	3.76003	−	2.73182i	0.176079	−	0.127929i
$457$	−0.344436	−	1.28545i	−0.0161121	−	0.0601310i	0.957402	−	0.288759i	$-0.0932427\pi$
$457$	−0.344436	−	1.28545i	−0.0161121	−	0.0601310i	−0.973514	+	0.228628i	$0.926576\pi$
$458$	−10.2451	+	3.93274i	−0.478724	+	0.183765i
$459$	4.29514	+	3.86736i	0.200480	+	0.180513i
$460$	0.246860	+	1.94744i	0.0115099	+	0.0907997i
$461$	−24.7473	−	8.04087i	−1.15259	−	0.374501i	−0.330474	−	0.943815i	$-0.607209\pi$
$461$	−24.7473	−	8.04087i	−1.15259	−	0.374501i	−0.822120	+	0.569314i	$0.807209\pi$
$462$	−5.17180	−	0.524735i	−0.240614	−	0.0244129i
$463$	14.0944	−	27.6618i	0.655023	−	1.28555i	−0.289522	−	0.957171i	$-0.593496\pi$
$463$	14.0944	−	27.6618i	0.655023	−	1.28555i	0.944545	−	0.328383i	$-0.106504\pi$
$464$	−4.16933	+	3.75408i	−0.193556	+	0.174279i
$465$	−0.725788	+	0.439975i	−0.0336576	+	0.0204034i
$466$	5.14381	−	5.71278i	0.238282	−	0.264639i
$467$	−4.55740	+	5.62793i	−0.210892	+	0.260429i	−0.871605	−	0.490209i	$-0.836921\pi$
$467$	−4.55740	+	5.62793i	−0.210892	+	0.260429i	0.660713	+	0.750638i	$0.270254\pi$
$468$	3.54874	−	3.54874i	0.164040	−	0.164040i
$469$	−1.89978	+	2.94862i	−0.0877236	+	0.136155i
$470$	−7.14461	−	0.975594i	−0.329556	−	0.0450008i
$471$	1.05731	−	0.470743i	0.0487181	−	0.0216907i
$472$	−30.7212	+	24.8775i	−1.41406	+	1.14508i
$473$	31.9021	+	20.7175i	1.46686	+	0.952591i
$474$	0.682472	−	1.18208i	0.0313470	−	0.0542946i
$475$	−18.7574	−	23.6246i	−0.860648	−	1.08397i
$476$	−3.93202	−	3.16069i	−0.180224	−	0.144870i
$477$	−4.06739	−	7.98270i	−0.186233	−	0.365503i
$478$	−26.6518	−	10.2307i	−1.21903	−	0.467941i
$479$	−1.88857	+	17.9685i	−0.0862908	+	0.821002i	0.862704	+	0.505710i	$0.168769\pi$
$479$	−1.88857	+	17.9685i	−0.0862908	+	0.821002i	−0.948995	+	0.315292i	$0.897897\pi$
$480$	0.988388	+	1.16859i	0.0451135	+	0.0533386i
$481$	26.5785	−	2.79351i	1.21188	−	0.127373i
$482$	−3.24467	−	3.24467i	−0.147791	−	0.147791i
$483$	−0.362398	+	1.12918i	−0.0164897	+	0.0513795i
$484$	−13.7987	+	4.48346i	−0.627212	+	0.203793i
$485$	−0.340990	−	0.723840i	−0.0154835	−	0.0328679i
$486$	1.68606	+	7.93228i	0.0764811	+	0.359815i
$487$	−1.14928	−	21.9295i	−0.0520786	−	0.993720i	−0.892291	−	0.451462i	$-0.850903\pi$
$487$	−1.14928	−	21.9295i	−0.0520786	−	0.993720i	0.840212	−	0.542258i	$-0.182431\pi$
$488$	−0.220781	+	0.143377i	−0.00999429	+	0.00649037i
$489$	0.757837	−	2.33238i	0.0342706	−	0.105474i
$490$	1.46162	−	19.1593i	0.0660293	−	0.865528i
$491$	0.143207	+	0.440744i	0.00646282	+	0.0198905i	0.954236	−	0.299055i	$-0.0966714\pi$
$491$	0.143207	+	0.440744i	0.00646282	+	0.0198905i	−0.947773	+	0.318945i	$0.896671\pi$
$492$	−0.248402	−	0.201152i	−0.0111988	−	0.00906863i
$493$	7.56416	+	2.02681i	0.340673	+	0.0912829i
$494$	10.4424	−	23.4539i	0.469824	−	1.05524i
$495$	11.6657	+	40.0898i	0.524333	+	1.80190i
$496$	−2.45594	+	3.38032i	−0.110275	+	0.151781i
$497$	3.75283	−	0.0135289i	0.168337	−	0.000606856i
$498$	−0.0630953	+	0.0321487i	−0.00282737	+	0.00144062i
$499$	7.05051	+	4.07061i	0.315624	+	0.182226i	0.649440	−	0.760412i	$-0.275003\pi$
$499$	7.05051	+	4.07061i	0.315624	+	0.182226i	−0.333816	+	0.942638i	$0.608337\pi$
$500$	4.05257	−	3.73608i	0.181236	−	0.167083i
$501$	2.28338	+	3.95492i	0.102014	+	0.176693i
$502$	0.464564	−	8.86441i	0.0207345	−	0.395638i
$503$	−20.1887	+	3.19758i	−0.900171	+	0.142573i	−0.589334	−	0.807890i	$-0.700610\pi$
$503$	−20.1887	+	3.19758i	−0.900171	+	0.142573i	−0.310838	+	0.950463i	$0.600610\pi$
$504$	−6.23700	−	22.9456i	−0.277818	−	1.02208i
$505$	6.66179	−	6.95277i	0.296446	−	0.309394i
$506$	−1.45287	−	13.8232i	−0.0645882	−	0.614515i
$507$	0.0640793	−	0.239147i	0.00284586	−	0.0106209i
$508$	−1.35297	−	3.52460i	−0.0600282	−	0.156379i
$509$	39.8393	+	8.46811i	1.76585	+	0.375342i	0.972404	−	0.233304i	$-0.0749536\pi$
$509$	39.8393	+	8.46811i	1.76585	+	0.375342i	0.793442	+	0.608646i	$0.208287\pi$
$510$	−0.771326	+	2.55869i	−0.0341549	+	0.113301i
$511$	−1.96684	−	35.1075i	−0.0870080	−	1.55307i
$512$	21.8254	+	11.1206i	0.964554	+	0.491465i
$513$	−4.91025	−	7.56113i	−0.216793	−	0.333832i
$514$	−25.6895	+	5.46046i	−1.13311	+	0.240851i
$515$	2.01825	−	24.1580i	0.0889348	−	1.06453i
$516$	0.154356	−	0.726186i	0.00679512	−	0.0319685i
$517$	−16.4975	−	2.61294i	−0.725558	−	0.114917i
$518$	10.1021	−	22.9117i	0.443863	−	1.00668i
$519$	−1.85221	−	2.54935i	−0.0813030	−	0.111904i
$520$	22.3230	+	8.02605i	0.978929	+	0.351966i
$521$	14.1070	+	1.48270i	0.618039	+	0.0649585i	0.408374	−	0.912815i	$-0.366096\pi$
$521$	14.1070	+	1.48270i	0.618039	+	0.0649585i	0.209665	+	0.977773i	$0.432763\pi$
$522$	4.59351	+	5.67251i	0.201052	+	0.248279i
$523$	−20.5799	−	1.07854i	−0.899894	−	0.0471615i	−0.403225	−	0.915101i	$-0.632111\pi$
$523$	−20.5799	−	1.07854i	−0.899894	−	0.0471615i	−0.496670	+	0.867940i	$0.665444\pi$
$524$	4.19057			0.183066
$525$	3.17306	−	1.00993i	0.138484	−	0.0440768i
$526$	20.0329			0.873475
$527$	5.82409	+	0.305228i	0.253701	+	0.0132959i
$528$	−2.79100	−	3.44660i	−0.121463	−	0.149994i
$529$	19.7205	+	2.07271i	0.857413	+	0.0901177i
$530$	5.12998	−	6.61935i	0.222832	−	0.287526i
$531$	22.2959	+	30.6877i	0.967560	+	1.33173i
$532$	4.64843	+	6.34976i	0.201535	+	0.275297i
$533$	−8.81854	−	1.39672i	−0.381973	−	0.0604986i
$534$	0.829258	−	3.90135i	0.0358855	−	0.168828i
$535$	11.5449	+	19.0447i	0.499131	+	0.823372i
$536$	−3.96871	+	0.843575i	−0.171422	+	0.0364369i
$537$	−2.20007	−	3.38781i	−0.0949401	−	0.146195i
$538$	16.4921	+	8.40314i	0.711025	+	0.362285i
$539$	4.33317	−	44.2974i	0.186643	−	1.90802i
$540$	1.31175	−	0.996551i	0.0564487	−	0.0428847i
$541$	17.8436	+	3.79278i	0.767158	+	0.163065i	0.574838	−	0.818268i	$-0.305065\pi$
$541$	17.8436	+	3.79278i	0.767158	+	0.163065i	0.192321	+	0.981332i	$0.438399\pi$
$542$	−2.25606	−	5.87723i	−0.0969060	−	0.252449i
$543$	−0.889393	+	3.31926i	−0.0381675	+	0.142443i
$544$	−1.09933	−	10.4594i	−0.0471335	−	0.448445i
$545$	5.76367	+	2.78324i	0.246889	+	0.119221i
$546$	2.01118	+	1.99673i	0.0860704	+	0.0854521i
$547$	29.6025	−	4.68857i	1.26571	−	0.200469i	0.512752	−	0.858537i	$-0.328626\pi$
$547$	29.6025	−	4.68857i	1.26571	−	0.200469i	0.752959	+	0.658068i	$0.228626\pi$
$548$	0.440957	−	8.41397i	0.0188368	−	0.359427i
$549$	0.126302	+	0.218762i	0.00539046	+	0.00933655i
$550$	−29.2532	+	25.8345i	−1.24736	+	1.10158i
$551$	−10.5788	−	6.10770i	−0.450674	−	0.260197i
$552$	−1.22226	+	0.622770i	−0.0520227	+	0.0265069i
$553$	10.1421	+	5.80687i	0.431284	+	0.246933i
$554$	0.206231	−	0.283852i	0.00876190	−	0.0120597i
$555$	4.33728	+	0.134458i	0.184107	+	0.00570741i
$556$	3.23710	−	7.27065i	0.137284	−	0.308344i
$557$	23.0513	+	6.17658i	0.976716	+	0.261710i	0.711661	−	0.702523i	$-0.247943\pi$
$557$	23.0513	+	6.17658i	0.976716	+	0.261710i	0.265055	+	0.964233i	$0.414610\pi$
$558$	4.22457	+	3.42099i	0.178840	+	0.144822i
$559$	−6.40840	−	19.7230i	−0.271047	−	0.834196i
$560$	12.4782	−	10.6314i	0.527302	−	0.449260i
$561$	−1.91291	+	5.88733i	−0.0807630	+	0.248563i
$562$	1.16481	−	0.756437i	0.0491346	−	0.0319084i
$563$	−0.192031	−	3.66418i	−0.00809316	−	0.154427i	−0.999687	−	0.0250340i	$-0.992031\pi$
$563$	−0.192031	−	3.66418i	−0.00809316	−	0.154427i	0.991593	−	0.129393i	$-0.0413027\pi$
$564$	0.0677784	+	0.318872i	0.00285399	+	0.0134270i
$565$	4.05483	−	21.3054i	0.170588	−	0.896324i
$566$	−3.66456	+	1.19069i	−0.154033	+	0.0500483i
$567$	−21.8092	+	4.71792i	−0.915899	+	0.198134i
$568$	3.06956	+	3.06956i	0.128796	+	0.128796i
$569$	−40.5200	+	4.25882i	−1.69869	+	0.178539i	−0.903722	−	0.428119i	$-0.859176\pi$
$569$	−40.5200	+	4.25882i	−1.69869	+	0.178539i	−0.794963	+	0.606658i	$0.792510\pi$
$570$	2.19519	−	3.54384i	0.0919463	−	0.148435i
$571$	−1.11155	+	10.5756i	−0.0465167	+	0.442577i	0.946332	+	0.323197i	$0.104758\pi$
$571$	−1.11155	+	10.5756i	−0.0465167	+	0.442577i	−0.992849	+	0.119381i	$0.961909\pi$
$572$	10.1447	+	3.89417i	0.424170	+	0.162824i
$573$	−0.127107	−	0.249461i	−0.00530995	−	0.0104214i
$574$	−5.24113	+	6.52018i	−0.218761	+	0.272147i
$575$	4.37735	+	7.75311i	0.182548	+	0.323327i
$576$	13.0386	−	22.5836i	0.543277	−	0.940983i
$577$	−27.5115	−	17.8662i	−1.14532	−	0.743779i	−0.174753	−	0.984612i	$-0.555913\pi$
$577$	−27.5115	−	17.8662i	−1.14532	−	0.743779i	−0.970567	+	0.240833i	$0.922579\pi$
$578$	−1.94719	+	1.57680i	−0.0809925	+	0.0655864i
$579$	−2.42572	+	1.08000i	−0.100810	+	0.0448834i
$580$	0.970597	−	2.00996i	0.0403019	−	0.0834590i
$581$	−0.277206	−	0.539232i	−0.0115004	−	0.0223711i
$582$	0.0781867	−	0.0781867i	0.00324094	−	0.00324094i
$583$	12.2078	−	15.0754i	0.505597	−	0.624360i
$584$	27.2158	−	30.2263i	1.12620	−	1.25077i
$585$	8.81196	−	20.9878i	0.364330	−	0.867739i
$586$	2.55455	−	2.30013i	0.105528	−	0.0950174i
$587$	14.7169	−	28.8836i	0.607433	−	1.19215i	−0.358541	−	0.933514i	$-0.616726\pi$
$587$	14.7169	−	28.8836i	0.607433	−	1.19215i	0.965974	−	0.258640i	$-0.0832742\pi$
$588$	−0.837440	+	0.230876i	−0.0345355	+	0.00952115i
$589$	−8.65209	−	2.81124i	−0.356503	−	0.115835i
$590$	−17.0681	+	31.0781i	−0.702683	+	1.27947i
$591$	0.0207772	+	0.0187079i	0.000854660	+	0.000769539i
$592$	19.9438	−	7.65570i	0.819684	−	0.314647i
$593$	10.1549	+	37.8985i	0.417011	+	1.55631i	0.780773	+	0.624815i	$0.214826\pi$
$593$	10.1549	+	37.8985i	0.417011	+	1.55631i	−0.363762	+	0.931492i	$0.618508\pi$
$594$	−9.43659	+	6.85609i	−0.387188	+	0.281309i
$595$	−21.9314	−	6.52515i	−0.899100	−	0.267505i
$596$	−6.05727	−	4.40087i	−0.248116	−	0.180267i
$597$	−1.72616	+	4.49680i	−0.0706470	+	0.184042i
$598$	−4.12707	+	6.35513i	−0.168768	+	0.259881i
$599$	−24.9966	+	14.4318i	−1.02133	+	0.589668i	−0.914490	−	0.404608i	$-0.867408\pi$
$599$	−24.9966	+	14.4318i	−1.02133	+	0.589668i	−0.106845	+	0.994276i	$0.534075\pi$
$600$	3.41498	+	1.78161i	0.139416	+	0.0727340i
$601$			4.29834i			0.175333i	0.996150	+	0.0876666i	$0.0279410\pi$
$601$			4.29834i			0.175333i	−0.996150	+	0.0876666i	$0.972059\pi$
$602$	−19.0204	−	3.97130i	−0.775213	−	0.161858i
$603$	0.609044	+	3.84535i	0.0248022	+	0.156595i
$604$	2.83624	+	6.37031i	0.115405	+	0.259204i
$605$	−50.2442	+	42.4963i	−2.04272	+	1.72772i
$606$	1.21563	+	0.541233i	0.0493816	+	0.0219861i
$607$	−6.68738	+	1.79188i	−0.271432	+	0.0727301i	−0.391968	−	0.919979i	$-0.628206\pi$
$607$	−6.68738	+	1.79188i	−0.271432	+	0.0727301i	0.120535	+	0.992709i	$0.461539\pi$
$608$	−2.56636	+	16.2034i	−0.104080	+	0.657133i
$609$	1.04486	−	0.852365i	0.0423398	−	0.0345396i
$610$	−0.134674	+	0.193947i	−0.00545280	+	0.00785268i
$611$	6.09323	+	6.76722i	0.246506	+	0.273772i
$612$	−5.59186	+	0.293057i	−0.226038	+	0.0118461i
$613$	−9.69734	+	0.508216i	−0.391672	+	0.0205266i	−0.247156	−	0.968976i	$-0.579496\pi$
$613$	−9.69734	+	0.508216i	−0.391672	+	0.0205266i	−0.144516	+	0.989502i	$0.546163\pi$
$614$	−21.7733	−	24.1817i	−0.878699	−	0.975894i
$615$	−1.38803	−	0.418427i	−0.0559708	−	0.0168726i
$616$	39.8939	−	32.5443i	1.60737	−	1.31125i
$617$	−0.775761	+	4.89796i	−0.0312310	+	0.197184i	−0.998371	−	0.0570609i	$-0.981827\pi$
$617$	−0.775761	+	4.89796i	−0.0312310	+	0.197184i	0.967140	+	0.254245i	$0.0818271\pi$
$618$	3.23592	−	0.867063i	0.130168	−	0.0348784i
$619$	31.6155	+	14.0761i	1.27073	+	0.565767i	0.927619	−	0.373527i	$-0.121852\pi$
$619$	31.6155	+	14.0761i	1.27073	+	0.565767i	0.343113	+	0.939294i	$0.388518\pi$
$620$	0.395827	−	1.61448i	0.0158968	−	0.0648391i
$621$	1.08232	+	2.43093i	0.0434320	+	0.0975500i
$622$	5.81017	+	36.6840i	0.232967	+	1.47089i
$623$	33.4292	+	6.97973i	1.33931	+	0.279637i
$624$			2.41784i			0.0967910i
$625$	10.6060	−	22.6388i	0.424239	−	0.905550i
$626$	−21.2050	+	12.2427i	−0.847523	+	0.489318i
$627$	5.25910	−	8.09830i	0.210028	−	0.323415i
$628$	−0.812339	+	2.11622i	−0.0324159	+	0.0844462i
$629$	−24.1233	−	17.5266i	−0.961860	−	0.698832i
$630$	−12.9630	−	16.9359i	−0.516457	−	0.674743i
$631$	−31.6801	+	23.0169i	−1.26116	+	0.916289i	−0.998814	−	0.0486840i	$-0.984497\pi$
$631$	−31.6801	+	23.0169i	−1.26116	+	0.916289i	−0.262349	+	0.964973i	$0.584497\pi$
$632$	3.49882	+	13.0578i	0.139175	+	0.519410i
$633$	−4.18302	+	1.60571i	−0.166260	+	0.0638213i
$634$	15.8178	+	14.2424i	0.628205	+	0.565639i
$635$	−11.7272	−	12.4775i	−0.465378	−	0.495155i
$636$	−0.360071	−	0.116994i	−0.0142777	−	0.00463912i
$637$	−17.0340	+	17.2814i	−0.674912	+	0.684715i
$638$	−7.17492	+	14.0816i	−0.284058	+	0.557495i
$639$	3.09554	−	2.78724i	0.122458	−	0.110261i
$640$	12.1724	+	1.01693i	0.481155	+	0.0401976i
$641$	−13.7378	+	15.2574i	−0.542612	+	0.602632i	−0.950624	−	0.310345i	$-0.899555\pi$
$641$	−13.7378	+	15.2574i	−0.542612	+	0.602632i	0.408012	+	0.912977i	$0.366222\pi$
$642$	−1.93682	+	2.39177i	−0.0764402	+	0.0943958i
$643$	−33.0301	+	33.0301i	−1.30258	+	1.30258i	−0.375934	+	0.926646i	$0.622678\pi$
$643$	−33.0301	+	33.0301i	−1.30258	+	1.30258i	−0.926646	+	0.375934i	$0.877322\pi$
$644$	−1.06193	−	2.06571i	−0.0418458	−	0.0814002i
$645$	−0.597702	−	3.31380i	−0.0235345	−	0.130481i
$646$	−26.1685	+	11.6510i	−1.02959	+	0.458401i
$647$	3.69138	−	2.98922i	0.145123	−	0.117518i	−0.554010	−	0.832510i	$-0.686903\pi$
$647$	3.69138	−	2.98922i	0.145123	−	0.117518i	0.699133	+	0.714992i	$0.253570\pi$
$648$	−21.6467	−	14.0575i	−0.850363	−	0.552232i
$649$	−41.0652	+	71.1270i	−1.61195	+	2.79198i
$650$	21.2577	−	0.909082i	0.833797	−	0.0356571i
$651$	0.629167	−	0.782709i	0.0246590	−	0.0306768i
$652$	2.18061	+	4.27969i	0.0853992	+	0.167605i
$653$	−5.59675	−	2.14839i	−0.219018	−	0.0840731i	0.246385	−	0.969172i	$-0.420757\pi$
$653$	−5.59675	−	2.14839i	−0.219018	−	0.0840731i	−0.465403	+	0.885099i	$0.654091\pi$
$654$	−0.0924553	+	0.879654i	−0.00361529	+	0.0343972i
$655$	17.5947	−	7.18900i	0.687482	−	0.280898i
$656$	−7.09791	+	0.746020i	−0.277127	+	0.0291272i
$657$	−27.5973	−	27.5973i	−1.07668	−	1.07668i
$658$	8.33917	−	1.80399i	0.325095	−	0.0703269i
$659$	−27.7363	+	9.01207i	−1.08045	+	0.351060i	−0.794550	−	0.607198i	$-0.792293\pi$
$659$	−27.7363	+	9.01207i	−1.08045	+	0.351060i	−0.285903	+	0.958259i	$0.592293\pi$
$660$	1.54651	+	0.849347i	0.0601980	+	0.0330608i
$661$	4.20939	+	19.8036i	0.163726	+	0.770271i	0.980998	+	0.194018i	$0.0621521\pi$
$661$	4.20939	+	19.8036i	0.163726	+	0.770271i	−0.817272	+	0.576252i	$0.804515\pi$
$662$	−0.403659	−	7.70227i	−0.0156886	−	0.299357i
$663$	2.83037	−	1.83806i	0.109922	−	0.0713844i
$664$	0.216725	−	0.667011i	0.00841056	−	0.0258850i
$665$	30.4103	+	18.6859i	1.17926	+	0.724608i
$666$	−8.58850	−	26.4327i	−0.332798	−	1.02425i
$667$	2.80193	+	2.26896i	0.108491	+	0.0878546i
$668$	−8.63951	−	2.31495i	−0.334273	−	0.0895681i
$669$	0.703478	−	1.58004i	0.0271980	−	0.0610878i
$670$	−3.00905	+	2.04682i	−0.116250	+	0.0790754i
$671$	−0.321483	+	0.442484i	−0.0124107	+	0.0170819i
$672$	−1.57158	−	0.899813i	−0.0606249	−	0.0347110i
$673$	−3.57412	+	1.82110i	−0.137772	+	0.0701984i	−0.521518	−	0.853240i	$-0.674634\pi$
$673$	−3.57412	+	1.82110i	−0.137772	+	0.0701984i	0.383746	+	0.923439i	$0.374634\pi$
$674$	33.5808	+	19.3879i	1.29348	+	0.746792i
$675$	3.79797	−	6.43450i	0.146184	−	0.247664i
$676$	0.242454	+	0.419943i	0.00932516	+	0.0161517i
$677$	−2.59575	+	49.5298i	−0.0997627	+	1.90359i	0.252361	+	0.967633i	$0.418793\pi$
$677$	−2.59575	+	49.5298i	−0.0997627	+	1.90359i	−0.352124	+	0.935953i	$0.614540\pi$
$678$	2.96019	−	0.468848i	0.113685	−	0.0180060i
$679$	0.671851	+	0.667025i	0.0257833	+	0.0255981i
$680$	−12.5172	−	23.3207i	−0.480013	−	0.894307i
$681$	−0.224893	−	2.13971i	−0.00861790	−	0.0819939i
$682$	−3.04631	+	11.3690i	−0.116649	+	0.435340i
$683$	5.20036	+	13.5474i	0.198986	+	0.518377i	0.996373	−	0.0850917i	$-0.0271183\pi$
$683$	5.20036	+	13.5474i	0.198986	+	0.518377i	−0.797387	+	0.603468i	$0.793785\pi$
$684$	8.54372	+	1.81602i	0.326677	+	0.0694374i
$685$	−12.5829	−	36.0837i	−0.480768	−	1.37869i
$686$	6.12152	+	21.8958i	0.233721	+	0.835986i
$687$	2.00495	+	1.02157i	0.0764936	+	0.0389754i
$688$	−9.02850	−	13.9027i	−0.344208	−	0.530034i
$689$	−10.3445	+	2.19880i	−0.394095	+	0.0837675i
$690$	−0.803567	+	0.931742i	−0.0305913	+	0.0354708i
$691$	0.631401	−	2.97051i	0.0240196	−	0.113003i	−0.964505	−	0.264066i	$-0.914936\pi$
$691$	0.631401	−	2.97051i	0.0240196	−	0.113003i	0.988524	+	0.151063i	$0.0482696\pi$
$692$	6.09578	+	0.965477i	0.231727	+	0.0367019i
$693$	−29.1819	−	39.8624i	−1.10853	−	1.51425i
$694$	9.16648	+	12.6166i	0.347955	+	0.478919i
$695$	1.11850	−	36.0802i	0.0424272	−	1.36860i
$696$	1.55122	+	0.163039i	0.0587987	+	0.00617999i
$697$	6.26919	+	7.74181i	0.237463	+	0.293242i
$698$	−23.1900	−	1.21533i	−0.877753	−	0.0460011i
$699$	−1.57627			−0.0596200
$700$	−2.99576	+	5.79308i	−0.113229	+	0.218958i
$701$	−14.2658			−0.538811			−0.269405	−	0.963027i	$-0.586827\pi$
$701$	−14.2658			−0.538811			−0.269405	+	0.963027i	$0.586827\pi$
$702$	6.35040	+	0.332811i	0.239681	+	0.0125611i
$703$	29.2713	+	36.1471i	1.10399	+	1.36331i
$704$	56.1532	+	5.90194i	2.11635	+	0.222438i
$705$	0.831610	+	1.22256i	0.0313202	+	0.0460442i
$706$	−20.6782	−	28.4611i	−0.778235	−	1.07115i
$707$	−4.59654	+	10.4250i	−0.172871	+	0.392072i
$708$	1.58321	+	0.250756i	0.0595008	+	0.00942399i
$709$	1.30679	−	6.14796i	0.0490775	−	0.230891i	−0.946772	−	0.321904i	$-0.895677\pi$
$709$	1.30679	−	6.14796i	0.0490775	−	0.230891i	0.995850	+	0.0910129i	$0.0290104\pi$
$710$	3.59003	+	1.50731i	0.134731	+	0.0565684i
$711$	12.6882	−	2.69697i	0.475846	−	0.101144i
$712$	21.5144	+	33.1293i	0.806288	+	1.24157i
$713$	2.39245	+	1.21902i	0.0895981	+	0.0456525i
$714$	−0.176871	−	3.15710i	−0.00661924	−	0.118151i
$715$	49.2744	−	1.05312i	1.84276	−	0.0393846i
$716$	7.73874	+	1.64492i	0.289210	+	0.0614735i
$717$	2.09779	+	5.46492i	0.0783433	+	0.204091i
$718$	10.0716	−	37.5878i	0.375870	−	1.40276i
$719$	−3.53563	−	33.6393i	−0.131857	−	1.25453i	−0.837686	−	0.546152i	$-0.816092\pi$
$719$	−3.53563	−	33.6393i	−0.131857	−	1.25453i	0.705830	−	0.708382i	$-0.250574\pi$
$720$	2.46173	−	18.0281i	0.0917434	−	0.671869i
$721$	7.52371	+	27.6794i	0.280198	+	1.03083i
$722$	21.0954	−	3.34118i	0.785090	−	0.124346i
$723$	−0.0492428	+	0.939609i	−0.00183136	+	0.0349444i
$724$	−3.36516	−	5.82862i	−0.125065	−	0.216619i
$725$	0.627071	−	10.1042i	0.0232888	−	0.375260i
$726$	−7.87552	−	4.54694i	−0.292288	−	0.168753i
$727$	0.691104	−	0.352135i	0.0256316	−	0.0130600i	−0.441128	−	0.897444i	$-0.645421\pi$
$727$	0.691104	−	0.352135i	0.0256316	−	0.0130600i	0.466759	+	0.884384i	$0.345421\pi$
$728$	−28.0681	+	0.101185i	−1.04027	+	0.00375018i
$729$	−13.8943	+	19.1239i	−0.514605	+	0.708293i
$730$	12.3431	−	34.3300i	0.456838	−	1.27061i
$731$	−9.41118	+	21.1379i	−0.348085	+	0.781812i
$732$	0.0103109	+	0.00276281i	0.000381103	+	0.000102116i
$733$	−34.3674	−	27.8302i	−1.26939	−	1.02793i	−0.997852	−	0.0655020i	$-0.979135\pi$
$733$	−34.3674	−	27.8302i	−1.26939	−	1.02793i	−0.271536	−	0.962428i	$-0.587532\pi$
$734$	5.04206	+	15.5179i	0.186106	+	0.572774i
$735$	−3.12005	+	2.40601i	−0.115085	+	0.0887470i
$736$	1.49629	−	4.60510i	0.0551539	−	0.169746i
$737$	−7.06977	+	4.59116i	−0.260418	+	0.169118i
$738$	0.485955	+	9.27257i	0.0178882	+	0.341328i
$739$	0.989564	+	4.65553i	0.0364017	+	0.171257i	0.992593	−	0.121485i	$-0.0387657\pi$
$739$	0.989564	+	4.65553i	0.0364017	+	0.171257i	−0.956192	+	0.292742i	$0.905432\pi$
$740$	−6.19298	+	5.82055i	−0.227658	+	0.213968i
$741$	−5.00666	+	1.62676i	−0.183924	+	0.0597607i
$742$	−3.02801	+	9.43486i	−0.111162	+	0.346365i
$743$	−11.1811	−	11.1811i	−0.410196	−	0.410196i	0.471611	−	0.881807i	$-0.343673\pi$
$743$	−11.1811	−	11.1811i	−0.410196	−	0.410196i	−0.881807	+	0.471611i	$0.843673\pi$
$744$	1.15526	−	0.121423i	0.0423538	−	0.00445157i
$745$	−32.9821	−	8.08631i	−1.20837	−	0.296260i
$746$	2.92504	−	27.8299i	0.107093	−	1.01893i
$747$	−0.628275	−	0.241172i	−0.0229874	−	0.00882402i
$748$	−5.50423	−	10.8027i	−0.201254	−	0.394984i
$749$	−20.5383	−	16.5093i	−0.750452	−	0.603237i
$750$	3.43989	+	0.320736i	0.125607	+	0.0117116i
$751$	−25.2501	+	43.7345i	−0.921390	+	1.59589i	−0.124124	+	0.992267i	$0.539612\pi$
$751$	−25.2501	+	43.7345i	−0.921390	+	1.59589i	−0.797266	+	0.603628i	$0.793721\pi$
$752$	6.10475	+	3.96447i	0.222617	+	0.144569i
$753$	−1.41451	+	1.14544i	−0.0515475	+	0.0417423i
$754$	7.87118	−	3.50447i	0.286651	−	0.127625i
$755$	22.8368	+	21.8810i	0.831115	+	0.796333i
$756$	−1.05570	+	1.63854i	−0.0383955	+	0.0595931i
$757$	−6.78176	+	6.78176i	−0.246487	+	0.246487i	−0.819527	−	0.573040i	$-0.805764\pi$
$757$	−6.78176	+	6.78176i	−0.246487	+	0.246487i	0.573040	+	0.819527i	$0.305764\pi$
$758$	−11.7045	+	14.4538i	−0.425126	+	0.524986i
$759$	−1.90705	+	2.11799i	−0.0692214	+	0.0768782i
$760$	9.44486	+	40.1914i	0.342601	+	1.45790i
$761$	−2.48012	+	2.23311i	−0.0899043	+	0.0809502i	−0.712858	−	0.701309i	$-0.752599\pi$
$761$	−2.48012	+	2.23311i	−0.0899043	+	0.0809502i	0.622953	+	0.782259i	$0.285933\pi$
$762$	1.07429	−	2.10842i	0.0389176	−	0.0763800i
$763$	−7.53449	−	0.764455i	−0.272767	−	0.0276751i
$764$	0.521513	+	0.169450i	0.0188677	+	0.00613048i
$765$	−22.9755	+	10.8234i	−0.830681	+	0.391320i
$766$	3.20063	+	2.88186i	0.115643	+	0.104126i
$767$	41.8018	−	16.0462i	1.50938	−	0.579395i
$768$	−0.720163	−	2.68769i	−0.0259867	−	0.0969835i
$769$	−17.4313	+	12.6646i	−0.628589	+	0.456697i	−0.855911	−	0.517123i	$-0.827003\pi$
$769$	−17.4313	+	12.6646i	−0.628589	+	0.456697i	0.227322	+	0.973820i	$0.427003\pi$
$770$	22.0833	−	40.5557i	0.795827	−	1.46153i
$771$	4.35677	+	3.16538i	0.156905	+	0.113998i
$772$	1.86371	−	4.85513i	0.0670764	−	0.174740i
$773$	7.13291	−	10.9837i	0.256553	−	0.395057i	−0.686801	−	0.726846i	$-0.740985\pi$
$773$	7.13291	−	10.9837i	0.256553	−	0.395057i	0.943354	+	0.331789i	$0.107652\pi$
$774$	−18.6774	+	10.7834i	−0.671346	+	0.387602i
$775$	−1.10774	−	7.45769i	−0.0397912	−	0.267888i
$776$			1.09511i			0.0393122i
$777$	−4.87736	+	1.60421i	−0.174974	+	0.0575508i
$778$	−0.762929	−	4.81694i	−0.0273523	−	0.172696i
$779$	−6.32039	−	14.1958i	−0.226452	−	0.508619i
$780$	−0.363829	−	0.890452i	−0.0130272	−	0.0318833i
$781$	8.23931	+	3.66838i	0.294826	+	0.131265i
$782$	8.16658	−	2.18823i	0.292036	−	0.0782509i
$783$	0.473317	−	2.98840i	0.0169150	−	0.106797i
$784$	−9.57692	+	16.8674i	−0.342033	+	0.602408i
$785$	0.219685	+	10.2788i	0.00784091	+	0.366867i
$786$	1.75753	+	1.95193i	0.0626889	+	0.0696231i
$787$	4.71433	−	0.247068i	0.168048	−	0.00880701i	0.0318735	−	0.999492i	$-0.489853\pi$
$787$	4.71433	−	0.247068i	0.168048	−	0.00880701i	0.136174	+	0.990685i	$0.456519\pi$
$788$	−0.0546834	+	0.00286584i	−0.00194802	+	0.000102091i
$789$	−2.74860	−	3.05263i	−0.0978527	−	0.108676i
$790$	7.33496	+	9.65492i	0.260966	+	0.343507i
$791$	4.10567	+	25.3308i	0.145981	+	0.900659i
$792$	8.93944	−	56.4414i	0.317649	−	2.00556i
$793$	0.288020	−	0.0771747i	0.0102279	−	0.00274056i
$794$	36.1647	+	16.1016i	1.28344	+	0.571423i
$795$	−1.71252	+	0.126492i	−0.0607367	+	0.00448620i
$796$	−3.83710	−	8.61826i	−0.136002	−	0.305466i
$797$	4.95326	+	31.2737i	0.175453	+	1.10777i	0.905492	+	0.424363i	$0.139502\pi$
$797$	4.95326	+	31.2737i	0.175453	+	1.10777i	−0.730038	+	0.683406i	$0.760498\pi$
$798$	−1.00811	+	4.82830i	−0.0356866	+	0.170920i
$799$		−	10.1602i		−	0.359440i
$800$	−12.9705	+	4.07682i	−0.458575	+	0.144137i
$801$	32.8264	−	18.9523i	1.15986	−	0.669648i
$802$	−9.85222	+	15.1711i	−0.347894	+	0.535710i
$803$	30.2837	−	78.8918i	1.06869	−	2.78403i
$804$	0.133103	+	0.0967047i	0.00469417	+	0.00341051i
$805$	−8.00242	−	6.85141i	−0.282048	−	0.241481i
$806$	5.19128	−	3.77168i	0.182855	−	0.132852i
$807$	−0.982308	−	3.66602i	−0.0345789	−	0.129050i
$808$	−12.3036	+	4.72292i	−0.432840	+	0.166152i
$809$	−3.07651	−	2.77010i	−0.108164	−	0.0973915i	0.613274	−	0.789870i	$-0.289852\pi$
$809$	−3.07651	−	2.77010i	−0.108164	−	0.0973915i	−0.721438	+	0.692479i	$0.756519\pi$
$810$	−22.7424	−	4.32832i	−0.799086	−	0.152082i
$811$	−9.90122	−	3.21710i	−0.347679	−	0.112968i	0.129972	−	0.991518i	$-0.458511\pi$
$811$	−9.90122	−	3.21710i	−0.347679	−	0.112968i	−0.477650	+	0.878550i	$0.658511\pi$
$812$	−0.266588	+	2.62749i	−0.00935539	+	0.0922069i
$813$	−0.586036	+	1.15016i	−0.0205532	+	0.0403379i
$814$	44.7205	−	40.2665i	1.56745	−	1.41134i
$815$	16.4975	+	14.2280i	0.577882	+	0.498385i
$816$	1.80510	−	2.00477i	0.0631912	−	0.0701809i
$817$	22.7140	−	28.0495i	0.794662	−	0.981326i
$818$	−14.2611	+	14.2611i	−0.498627	+	0.498627i
$819$	−1.31260	+	26.9011i	−0.0458660	+	0.940002i
$820$	2.50179	−	1.34282i	0.0873663	−	0.0468933i
$821$	2.27831	−	1.01437i	0.0795137	−	0.0354018i	−0.366594	−	0.930381i	$-0.619476\pi$
$821$	2.27831	−	1.01437i	0.0795137	−	0.0354018i	0.446108	+	0.894979i	$0.352810\pi$
$822$	4.10409	−	3.32343i	0.143147	−	0.115918i
$823$	−8.34005	−	5.41609i	−0.290716	−	0.188793i	0.391038	−	0.920374i	$-0.372116\pi$
$823$	−8.34005	−	5.41609i	−0.290716	−	0.188793i	−0.681754	+	0.731581i	$0.738783\pi$
$824$	−16.5896	+	28.7340i	−0.577925	+	1.00099i
$825$	7.95034	+	0.913032i	0.276795	+	0.0317877i
$826$	6.41344	−	41.4597i	0.223152	−	1.44257i
$827$	19.3343	+	37.9457i	0.672319	+	1.31950i	0.935010	+	0.354621i	$0.115390\pi$
$827$	19.3343	+	37.9457i	0.672319	+	1.31950i	−0.262691	+	0.964880i	$0.584610\pi$
$828$	−2.40681	−	0.923889i	−0.0836425	−	0.0321073i
$829$	3.04559	−	28.9768i	0.105778	−	1.00641i	−0.804934	−	0.593364i	$-0.797799\pi$
$829$	3.04559	−	28.9768i	0.105778	−	1.00641i	0.910712	−	0.413043i	$-0.135534\pi$
$830$	−0.0463377	−	0.627346i	−0.00160841	−	0.0217755i
$831$	−0.0715494	+	0.00752014i	−0.00248202	+	0.000260871i
$832$	−21.7663	−	21.7663i	−0.754610	−	0.754610i
$833$	27.0258	−	1.61183i	0.936387	−	0.0558465i
$834$	4.74425	−	1.54150i	0.164280	−	0.0533778i
$835$	−40.2456	+	5.10159i	−1.39276	+	0.176548i
$836$	3.93205	+	18.4989i	0.135993	+	0.639796i
$837$	−0.117931	−	2.25025i	−0.00407628	−	0.0777800i
$838$	9.63682	−	6.25823i	0.332898	−	0.216187i
$839$	−4.65064	+	14.3132i	−0.160558	+	0.494146i	−0.998682	−	0.0513340i	$-0.983653\pi$
$839$	−4.65064	+	14.3132i	−0.160558	+	0.494146i	0.838124	+	0.545480i	$0.183653\pi$
$840$	−4.51778	−	0.600319i	−0.155878	−	0.0207130i
$841$	7.69467	+	23.6818i	0.265334	+	0.816613i
$842$	11.5398	+	9.34473i	0.397687	+	0.322041i
$843$	−0.275083	−	0.0737084i	−0.00947438	−	0.00253865i
$844$	3.56935	−	8.01690i	0.122862	−	0.275953i
$845$	1.73840	+	1.34726i	0.0598028	+	0.0463470i
$846$	5.56640	−	7.66150i	0.191377	−	0.263408i
$847$	38.6880	−	67.5709i	1.32933	−	2.32176i
$848$	−7.53228	+	3.83789i	−0.258660	+	0.131794i
$849$	0.684231	+	0.395041i	0.0234827	+	0.0135578i
$850$	−18.3047	−	15.1167i	−0.627846	−	0.518500i
$851$	−6.86417	−	11.8891i	−0.235301	−	0.407553i
$852$	0.00921247	−	0.175784i	0.000315614	−	0.00602227i
$853$	42.2494	−	6.69165i	1.44659	−	0.229118i	0.616769	−	0.787144i	$-0.288441\pi$
$853$	42.2494	−	6.69165i	1.44659	−	0.229118i	0.829823	+	0.558026i	$0.188441\pi$
$854$	0.0713357	−	0.270120i	0.00244106	−	0.00924331i
$855$	38.9875	−	7.03208i	1.33334	−	0.240492i
$856$	−3.18612	−	30.3139i	−0.108899	−	1.03611i
$857$	10.1139	−	37.7457i	0.345486	−	1.28937i	−0.546558	−	0.837421i	$-0.684062\pi$
$857$	10.1139	−	37.7457i	0.345486	−	1.28937i	0.892044	−	0.451949i	$-0.149271\pi$
$858$	2.44081	+	6.35852i	0.0833278	+	0.217076i
$859$	−20.7705	−	4.41492i	−0.708682	−	0.150635i	−0.160551	−	0.987028i	$-0.551327\pi$
$859$	−20.7705	−	4.41492i	−0.708682	−	0.150635i	−0.548131	+	0.836393i	$0.684660\pi$
$860$	5.41709	+	3.76156i	0.184721	+	0.128268i
$861$	1.71266	−	0.0959488i	0.0583672	−	0.00326993i
$862$	−29.7470	−	15.1568i	−1.01319	−	0.516244i
$863$	1.46772	+	2.26009i	0.0499618	+	0.0769345i	0.862769	−	0.505599i	$-0.168728\pi$
$863$	1.46772	+	2.26009i	0.0499618	+	0.0769345i	−0.812807	+	0.582533i	$0.802062\pi$
$864$	−3.97467	+	0.844842i	−0.135221	+	0.0287421i
$865$	27.2503	−	6.40374i	0.926539	−	0.217734i
$866$	−7.51255	+	35.3437i	−0.255287	+	1.20103i
$867$	0.507438	+	0.0803702i	0.0172335	+	0.00272952i
$868$	0.212643	+	1.95533i	0.00721756	+	0.0663681i
$869$	16.5087	+	22.7223i	0.560019	+	0.770800i
$870$	1.34329	−	0.390882i	0.0455418	−	0.0132521i
$871$	4.57054	+	0.480383i	0.154867	+	0.0162772i
$872$	−5.51289	−	6.80785i	−0.186690	−	0.230543i
$873$	1.04938	+	0.0549958i	0.0355162	+	0.00186133i
$874$	−13.1883			−0.446099
$875$	−2.63998	+	29.4624i	−0.0892477	+	0.996009i
$876$	−1.64928			−0.0557241
$877$	4.75949	+	0.249434i	0.160717	+	0.00842280i	0.132525	−	0.991180i	$-0.457692\pi$
$877$	4.75949	+	0.249434i	0.160717	+	0.00842280i	0.0281921	+	0.999603i	$0.491025\pi$
$878$	−1.75006	−	2.16115i	−0.0590617	−	0.0729352i
$879$	−0.700991	−	0.0736771i	−0.0236438	−	0.00248507i
$880$	37.8277	−	11.0074i	1.27517	−	0.371060i
$881$	−2.62989	−	3.61974i	−0.0886034	−	0.121952i	0.762414	−	0.647089i	$-0.224014\pi$
$881$	−2.62989	−	3.61974i	−0.0886034	−	0.121952i	−0.851018	+	0.525137i	$0.824014\pi$
$882$	21.2625	+	13.5911i	0.715944	+	0.457635i
$883$	−21.7304	−	3.44176i	−0.731288	−	0.115825i	−0.220324	−	0.975427i	$-0.570711\pi$
$883$	−21.7304	−	3.44176i	−0.731288	−	0.115825i	−0.510964	+	0.859602i	$0.670711\pi$
$884$	−1.37426	+	6.46537i	−0.0462212	+	0.217454i
$885$	7.07753	−	1.66320i	0.237908	−	0.0559077i
$886$	−18.0303	+	3.83245i	−0.605738	+	0.128754i
$887$	−8.68914	−	13.3801i	−0.291753	−	0.449260i	0.662152	−	0.749370i	$-0.269643\pi$
$887$	−8.68914	−	13.3801i	−0.291753	−	0.449260i	−0.953905	+	0.300110i	$0.902977\pi$
$888$	−5.29177	−	2.69629i	−0.177580	−	0.0904817i
$889$	18.0855	+	9.13307i	0.606570	+	0.306313i
$890$	29.1027	+	20.2086i	0.975526	+	0.677393i
$891$	−52.4534	−	11.1493i	−1.75726	−	0.373516i
$892$	1.21396	+	3.16247i	0.0406464	+	0.105887i
$893$	−4.10192	+	15.3086i	−0.137266	+	0.512282i
$894$	−0.490538	−	4.66715i	−0.0164060	−	0.156093i
$895$	35.3141	−	6.36952i	1.18042	−	0.212910i
$896$	−13.9467	+	3.79094i	−0.465926	+	0.126646i
$897$	1.53465	−	0.243065i	0.0512405	−	0.00811570i
$898$	−1.04798	+	19.9967i	−0.0349716	+	0.667297i
$899$	−1.52654	−	2.64405i	−0.0509131	−	0.0881840i
$900$	1.80620	+	7.00992i	0.0602067	+	0.233664i
$901$	10.2188	+	5.89983i	0.340438	+	0.196552i
$902$	−17.9132	+	9.12725i	−0.596446	+	0.303904i
$903$	2.00453	+	3.44322i	0.0667065	+	0.114583i
$904$	−17.4473	+	24.0142i	−0.580289	+	0.798699i
$905$	−24.1282	−	18.6993i	−0.802049	−	0.621587i
$906$	−1.77771	+	3.99281i	−0.0590606	+	0.132652i
$907$	−17.5182	−	4.69398i	−0.581681	−	0.155861i	−0.0440328	−	0.999030i	$-0.514021\pi$
$907$	−17.5182	−	4.69398i	−0.581681	−	0.155861i	−0.537649	+	0.843169i	$0.680687\pi$
$908$	3.27477	+	2.65186i	0.108677	+	0.0880050i
$909$	3.90783	+	12.0271i	0.129614	+	0.398912i
$910$	−23.2707	+	9.60619i	−0.771416	+	0.318442i
$911$	9.28514	−	28.5767i	0.307631	−	0.946789i	−0.671052	−	0.741410i	$-0.734157\pi$
$911$	9.28514	−	28.5767i	0.307631	−	0.946789i	0.978682	−	0.205379i	$-0.0658427\pi$
$912$	−3.52917	+	2.29187i	−0.116863	+	0.0758914i
$913$	−0.0762598	−	1.45512i	−0.00252383	−	0.0481576i
$914$	0.339663	+	1.59799i	0.0112350	+	0.0528567i
$915$	0.0480317	−	0.00608857i	0.00158788	−	0.000201282i
$916$	−4.19147	+	1.36189i	−0.138490	+	0.0449982i
$917$	−16.6583	+	15.1083i	−0.550105	+	0.498919i
$918$	−5.01701	−	5.01701i	−0.165586	−	0.165586i
$919$	−4.66527	+	0.490339i	−0.153893	+	0.0161748i	−0.181162	−	0.983453i	$-0.557986\pi$
$919$	−4.66527	+	0.490339i	−0.153893	+	0.0161748i	0.0272686	+	0.999628i	$0.491319\pi$
$920$	−0.897635	−	12.1527i	−0.0295941	−	0.400662i
$921$	−0.697437	+	6.63567i	−0.0229813	+	0.218653i
$922$	29.8214	+	11.4474i	0.982116	+	0.376999i
$923$	−2.23227	−	4.38108i	−0.0734761	−	0.144205i
$924$	−2.06312	−	0.319147i	−0.0678718	−	0.0104992i
$925$	−16.0168	+	35.0626i	−0.526631	+	1.15285i
$926$	−19.0558	+	33.0055i	−0.626211	+	1.08463i
$927$	26.7010	+	17.3398i	0.876976	+	0.569515i
$928$	−4.27870	+	3.46482i	−0.140455	+	0.113738i
$929$	42.5286	−	18.9349i	1.39532	−	0.621235i	0.435073	−	0.900395i	$-0.356723\pi$
$929$	42.5286	−	18.9349i	1.39532	−	0.621235i	0.960245	+	0.279160i	$0.0900559\pi$
$930$	0.918022	−	0.492742i	0.0301031	−	0.0161576i
$931$	−41.3712	−	8.48243i	−1.35589	−	0.278000i
$932$	2.18300	−	2.18300i	0.0715065	−	0.0715065i
$933$	4.79275	−	5.91855i	0.156908	−	0.193765i
$934$	5.94857	−	6.60656i	0.194643	−	0.216173i
$935$	−41.6425	−	35.9139i	−1.36185	−	1.17451i
$936$	−23.1521	+	20.8463i	−0.756750	+	0.681381i
$937$	20.7360	−	40.6967i	0.677416	−	1.32950i	−0.254586	−	0.967050i	$-0.581939\pi$
$937$	20.7360	−	40.6967i	0.677416	−	1.32950i	0.932002	−	0.362453i	$-0.118061\pi$
$938$	2.51841	−	3.49270i	0.0822290	−	0.114041i
$939$	4.77498	+	1.55148i	0.155825	+	0.0506307i
$940$	−2.84484	−	0.541429i	−0.0927886	−	0.0176595i
$941$	−16.8199	−	15.1447i	−0.548312	−	0.493702i	0.347777	−	0.937577i	$-0.386937\pi$
$941$	−16.8199	−	15.1447i	−0.548312	−	0.493702i	−0.896089	+	0.443875i	$0.853603\pi$
$942$	−1.32641	+	0.509162i	−0.0432168	+	0.0165894i
$943$	1.18707	+	4.43019i	0.0386562	+	0.144267i
$944$	28.9561	−	21.0379i	0.942442	−	0.684724i
$945$	−1.62157	+	8.69073i	−0.0527497	+	0.282709i
$946$	−37.7783	−	27.4475i	−1.22828	−	0.892395i
$947$	−9.95173	+	25.9251i	−0.323388	+	0.842454i	0.671457	+	0.741044i	$0.265669\pi$
$947$	−9.95173	+	25.9251i	−0.323388	+	0.842454i	−0.994845	+	0.101410i	$0.967665\pi$
$948$	0.298551	−	0.459728i	0.00969648	−	0.0149313i
$949$	−39.8979	+	23.0351i	−1.29514	+	0.747750i
$950$	21.4772	+	30.1669i	0.696811	+	0.978743i
$951$		−	4.36445i		−	0.141527i
$952$	23.3484	+	20.8711i	0.756726	+	0.676435i
$953$	−5.18936	−	32.7643i	−0.168100	−	1.06134i	−0.917067	−	0.398734i	$-0.869450\pi$
$953$	−5.18936	−	32.7643i	−0.168100	−	1.06134i	0.748967	−	0.662608i	$-0.230550\pi$
$954$	4.47341	+	10.0474i	0.144832	+	0.325298i
$955$	2.48034	−	0.183206i	0.0802621	−	0.00592841i
$956$	−10.4737	−	4.66319i	−0.338744	−	0.150818i
$957$	3.13019	−	0.838732i	0.101185	−	0.0271123i
$958$	3.46965	−	21.9065i	0.112099	−	0.707768i
$959$	28.5820	+	35.0368i	0.922962	+	1.13140i
$960$	−3.02357	−	3.97989i	−0.0975854	−	0.128451i
$961$	19.2216	+	21.3478i	0.620052	+	0.688637i
$962$	−32.7625	+	1.71701i	−1.05630	+	0.0553586i
$963$	−29.2081	+	1.53073i	−0.941219	+	0.0493272i
$964$	−1.23308	−	1.36947i	−0.0397148	−	0.0441078i
$965$	−0.504013	−	23.5822i	−0.0162248	−	0.759138i
$966$	0.516816	−	1.36100i	0.0166283	−	0.0437893i
$967$	0.999105	−	6.30810i	0.0321290	−	0.202855i	−0.966402	−	0.257035i	$-0.917254\pi$
$967$	0.999105	−	6.30810i	0.0321290	−	0.202855i	0.998531	+	0.0541800i	$0.0172545\pi$
$968$	86.9967	−	23.3107i	2.79618	−	0.749234i
$969$	5.36581	+	2.38901i	0.172375	+	0.0767462i
$970$	0.371519	+	0.909274i	0.0119288	+	0.0291950i
$971$	−16.6648	−	37.4298i	−0.534799	−	1.20118i	−0.955773	−	0.294105i	$-0.904978\pi$
$971$	−16.6648	−	37.4298i	−0.534799	−	1.20118i	0.420974	−	0.907073i	$-0.361688\pi$
$972$	0.509472	+	3.21668i	0.0163413	+	0.103175i
$973$	13.3448	+	40.5729i	0.427816	+	1.30071i
$974$			26.9575i			0.863775i
$975$	−3.05518	−	3.11454i	−0.0978440	−	0.0997451i
$976$	0.206419	−	0.119176i	0.00660730	−	0.00381473i
$977$	−0.474987	+	0.731416i	−0.0151962	+	0.0234001i	−0.846187	−	0.532886i	$-0.821107\pi$
$977$	−0.474987	+	0.731416i	−0.0151962	+	0.0234001i	0.830991	+	0.556286i	$0.187774\pi$
$978$	−1.07889	+	2.81061i	−0.0344992	+	0.0898735i
$979$	66.3969	+	48.2402i	2.12205	+	1.54176i
$980$	0.988876	−	7.65311i	0.0315885	−	0.244470i
$981$	−6.80044	+	4.94081i	−0.217121	+	0.157748i
$982$	−0.147242	−	0.549516i	−0.00469869	−	0.0175358i
$983$	30.0868	−	11.5492i	0.959621	−	0.368364i	0.172394	−	0.985028i	$-0.444850\pi$
$983$	30.0868	−	11.5492i	0.959621	−	0.368364i	0.787226	+	0.616664i	$0.211516\pi$
$984$	1.47453	+	1.32767i	0.0470064	+	0.0423247i
$985$	−0.224680	+	0.105843i	−0.00715890	+	0.00337244i
$986$	−9.14280	−	2.97068i	−0.291166	−	0.0946056i
$987$	−1.41906	−	1.02321i	−0.0451693	−	0.0325693i
$988$	4.68087	−	9.18673i	0.148918	−	0.292269i
$989$	−7.91668	+	7.12821i	−0.251736	+	0.226664i
$990$	−11.7254	−	49.8962i	−0.372659	−	1.58581i
$991$	−10.3485	+	11.4931i	−0.328730	+	0.365091i	−0.884741	−	0.466084i	$-0.845665\pi$
$991$	−10.3485	+	11.4931i	−0.328730	+	0.365091i	0.556011	+	0.831175i	$0.312331\pi$
$992$	−2.58041	+	3.18654i	−0.0819280	+	0.101173i
$993$	−1.11829	+	1.11829i	−0.0354880	+	0.0354880i
$994$	−4.60152	−	0.224525i	−0.145951	−	0.00712149i
$995$	−30.8954	−	29.6024i	−0.979451	−	0.938460i
$996$	−0.0259801	+	0.0115671i	−0.000823211	+	0.000366517i
$997$	10.4333	−	8.44870i	0.330425	−	0.267573i	−0.449723	−	0.893168i	$-0.648477\pi$
$997$	10.4333	−	8.44870i	0.330425	−	0.267573i	0.780148	+	0.625595i	$0.215144\pi$
$998$	−8.38180	−	5.44320i	−0.265321	−	0.172302i
$999$	−5.76039	+	9.97729i	−0.182251	+	0.315668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.103.6	yes	288
5.2	odd	4		875.2.bb.b.257.13		288
5.3	odd	4		875.2.bb.a.257.6		288
5.4	even	2		875.2.bb.c.243.13		288
7.3	odd	6	inner	175.2.x.a.3.13	✓	288
25.6	even	5		875.2.bb.b.768.13		288
25.8	odd	20		875.2.bb.c.607.6		288
25.17	odd	20	inner	175.2.x.a.117.13	yes	288
25.19	even	10		875.2.bb.a.768.6		288
35.3	even	12		875.2.bb.a.507.6		288
35.17	even	12		875.2.bb.b.507.13		288
35.24	odd	6		875.2.bb.c.493.6		288
175.17	even	60	inner	175.2.x.a.17.6	yes	288
175.31	odd	30		875.2.bb.b.143.13		288
175.94	odd	30		875.2.bb.a.143.6		288
175.108	even	60		875.2.bb.c.857.13		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.13	✓	288	7.3	odd	6	inner
175.2.x.a.17.6	yes	288	175.17	even	60	inner
175.2.x.a.103.6	yes	288	1.1	even	1	trivial
175.2.x.a.117.13	yes	288	25.17	odd	20	inner
875.2.bb.a.143.6		288	175.94	odd	30
875.2.bb.a.257.6		288	5.3	odd	4
875.2.bb.a.507.6		288	35.3	even	12
875.2.bb.a.768.6		288	25.19	even	10
875.2.bb.b.143.13		288	175.31	odd	30
875.2.bb.b.257.13		288	5.2	odd	4
875.2.bb.b.507.13		288	35.17	even	12
875.2.bb.b.768.13		288	25.6	even	5
875.2.bb.c.243.13		288	5.4	even	2
875.2.bb.c.493.6		288	35.24	odd	6
875.2.bb.c.607.6		288	25.8	odd	20
875.2.bb.c.857.13		288	175.108	even	60

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22592 - 0.0642475i) q^{2} +(0.158411 + 0.195621i) q^{3} +(-0.490303 - 0.0515330i) q^{4} +(-2.14702 + 0.624757i) q^{5} +(-0.181630 - 0.249992i) q^{6} +(2.13484 - 1.56284i) q^{7} +(3.02273 + 0.478753i) q^{8} +(0.610561 - 2.87247i) q^{9} +(2.67220 - 0.627958i) q^{10} +(6.21946 - 1.32199i) q^{11} +(-0.0675884 - 0.104077i) q^{12} +(-3.08865 - 1.57374i) q^{13} +(-2.71754 + 1.77875i) q^{14} +(-0.462326 - 0.321033i) q^{15} +(-2.71039 - 0.576111i) q^{16} +(1.38605 + 3.61079i) q^{17} +(-0.933045 + 3.48217i) q^{18} +(-0.630632 - 6.00007i) q^{19} +(1.08488 - 0.195678i) q^{20} +(0.643905 + 0.170048i) q^{21} +(-7.70946 + 1.22106i) q^{22} +(-0.0931944 + 1.77825i) q^{23} +(0.385178 + 0.667148i) q^{24} +(4.21936 - 2.68272i) q^{25} +(3.68531 + 2.12772i) q^{26} +(1.33148 - 0.678422i) q^{27} +(-1.12726 + 0.656251i) q^{28} +(1.19010 - 1.63804i) q^{29} +(0.546147 + 0.423263i) q^{30} +(0.613319 - 1.37754i) q^{31} +(-2.62656 - 0.703784i) q^{32} +(1.24384 + 1.00724i) q^{33} +(-1.46720 - 4.51558i) q^{34} +(-3.60714 + 4.68920i) q^{35} +(-0.447387 + 1.37692i) q^{36} +(-6.46577 + 4.19892i) q^{37} +(0.387613 + 7.39609i) q^{38} +(-0.181418 - 0.853502i) q^{39} +(-6.78895 + 0.860578i) q^{40} +(2.44960 - 0.795924i) q^{41} +(-0.778448 - 0.249834i) q^{42} +(4.23024 + 4.23024i) q^{43} +(-3.11755 + 0.327667i) q^{44} +(0.483706 + 6.54868i) q^{45} +(0.228497 - 2.17400i) q^{46} +(-2.45246 - 0.941409i) q^{47} +(-0.316655 - 0.621471i) q^{48} +(2.11506 - 6.67282i) q^{49} +(-5.34493 + 3.01771i) q^{50} +(-0.486781 + 0.843129i) q^{51} +(1.43327 + 0.930780i) q^{52} +(2.37094 - 1.91995i) q^{53} +(-1.67587 + 0.746144i) q^{54} +(-12.5274 + 6.72397i) q^{55} +(7.20125 - 3.70198i) q^{56} +(1.07384 - 1.07384i) q^{57} +(-1.56421 + 1.93163i) q^{58} +(-8.64305 + 9.59907i) q^{59} +(0.210136 + 0.181229i) q^{60} +(-0.0639241 + 0.0575575i) q^{61} +(-0.840380 + 1.64934i) q^{62} +(-3.18575 - 7.08646i) q^{63} +(8.44536 + 2.74406i) q^{64} +(7.61459 + 1.44920i) q^{65} +(-1.46013 - 1.31470i) q^{66} +(-1.23771 + 0.475111i) q^{67} +(-0.493512 - 1.84181i) q^{68} +(-0.362627 + 0.263464i) q^{69} +(4.72331 - 5.51681i) q^{70} +(1.14755 + 0.833741i) q^{71} +(3.22076 - 8.39037i) q^{72} +(7.23837 - 11.1461i) q^{73} +(8.19625 - 4.73211i) q^{74} +(1.19319 + 0.400423i) q^{75} +2.97435i q^{76} +(11.2115 - 12.5422i) q^{77} +(0.167567 + 1.05798i) q^{78} +(1.79663 + 4.03530i) q^{79} +(6.17917 - 0.456413i) q^{80} +(-7.70462 - 3.43032i) q^{81} +(-3.05414 + 0.818354i) q^{82} +(0.0358492 - 0.226343i) q^{83} +(-0.306946 - 0.116558i) q^{84} +(-5.23175 - 6.88648i) q^{85} +(-4.91413 - 5.45770i) q^{86} +(0.508959 - 0.0266734i) q^{87} +(19.4326 - 1.01842i) q^{88} +(8.63680 + 9.59214i) q^{89} +(-0.172246 - 8.05921i) q^{90} +(-9.05327 + 1.46737i) q^{91} +(0.137332 - 0.867081i) q^{92} +(0.366631 - 0.0982386i) q^{93} +(2.94602 + 1.31165i) q^{94} +(5.10256 + 12.4883i) q^{95} +(-0.278400 - 0.625297i) q^{96} +(0.0559772 + 0.353426i) q^{97} +(-3.02160 + 8.04442i) q^{98} -18.6723i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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