LMFDB - Embedded newform 175.2.x.a.52.12

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			52.12
Character	$\chi$	$=$	175.52
Dual form			175.2.x.a.138.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.228917 + 0.596349i) q^{2} +(-0.00257832 + 0.0491972i) q^{3} +(1.18306 - 1.06523i) q^{4} +(-1.84817 - 1.25868i) q^{5} +(-0.0299289 + 0.00972449i) q^{6} +(1.91442 + 1.82620i) q^{7} +(2.04438 + 1.04166i) q^{8} +(2.98115 + 0.313332i) q^{9} +(0.327538 - 1.39028i) q^{10} +(-0.367849 - 3.49985i) q^{11} +(0.0493562 + 0.0609498i) q^{12} +(0.0915228 + 0.577852i) q^{13} +(-0.650809 + 1.55971i) q^{14} +(0.0666889 - 0.0876793i) q^{15} +(0.179610 - 1.70887i) q^{16} +(0.00260736 - 0.00169324i) q^{17} +(0.495581 + 1.84953i) q^{18} +(-4.41097 + 4.89888i) q^{19} +(-3.52728 + 0.479626i) q^{20} +(-0.0947799 + 0.0894755i) q^{21} +(2.00293 - 1.02054i) q^{22} +(-4.16186 + 1.59759i) q^{23} +(-0.0565180 + 0.0978920i) q^{24} +(1.83143 + 4.65251i) q^{25} +(-0.323650 + 0.186860i) q^{26} +(-0.0462215 + 0.291831i) q^{27} +(4.21020 + 0.121204i) q^{28} +(-7.69230 - 2.49938i) q^{29} +(0.0675536 + 0.0196986i) q^{30} +(0.916502 - 4.31180i) q^{31} +(5.49276 - 1.47178i) q^{32} +(0.173131 - 0.00907344i) q^{33} +(0.00160663 + 0.00116728i) q^{34} +(-1.23955 - 5.78477i) q^{35} +(3.86066 - 2.80493i) q^{36} +(-0.945787 + 0.765883i) q^{37} +(-3.93119 - 1.50904i) q^{38} +(-0.0286647 + 0.00301278i) q^{39} +(-2.46723 - 4.49839i) q^{40} +(-2.00472 + 2.75926i) q^{41} +(-0.0750553 - 0.0360394i) q^{42} +(-6.51520 + 6.51520i) q^{43} +(-4.16335 - 3.74869i) q^{44} +(-5.11528 - 4.33142i) q^{45} +(-1.90544 - 2.11621i) q^{46} +(0.0408626 - 0.0629228i) q^{47} +(0.0836086 + 0.0132423i) q^{48} +(0.329993 + 6.99222i) q^{49} +(-2.35527 + 2.15721i) q^{50} +(7.65801e-5 + 0.000132641i) q^{51} +(0.723824 + 0.586142i) q^{52} +(4.95277 + 0.259564i) q^{53} +(-0.184614 + 0.0392409i) q^{54} +(-3.72536 + 6.93131i) q^{55} +(2.01151 + 5.72762i) q^{56} +(-0.229638 - 0.229638i) q^{57} +(-0.270395 - 5.15944i) q^{58} +(0.931010 - 0.414512i) q^{59} +(-0.0145018 - 0.174769i) q^{60} +(3.41172 - 7.66284i) q^{61} +(2.78114 - 0.440489i) q^{62} +(5.13497 + 6.04403i) q^{63} +(0.115113 + 0.158439i) q^{64} +(0.558184 - 1.18317i) q^{65} +(0.0450436 + 0.101170i) q^{66} +(-1.07397 - 1.65377i) q^{67} +(0.00128097 - 0.00478065i) q^{68} +(-0.0678664 - 0.208871i) q^{69} +(3.16598 - 2.06344i) q^{70} +(2.56775 - 7.90273i) q^{71} +(5.76822 + 3.74593i) q^{72} +(4.59745 - 5.67738i) q^{73} +(-0.673240 - 0.388695i) q^{74} +(-0.233613 + 0.0781056i) q^{75} +10.4944i q^{76} +(5.68721 - 7.37195i) q^{77} +(-0.00835850 - 0.0164045i) q^{78} +(2.35530 + 11.0808i) q^{79} +(-2.48288 + 2.93221i) q^{80} +(8.78197 + 1.86667i) q^{81} +(-2.10440 - 0.563871i) q^{82} +(-6.86085 + 13.4652i) q^{83} +(-0.0168181 + 0.206818i) q^{84} +(-0.00695009 - 0.000152456i) q^{85} +(-5.37677 - 2.39389i) q^{86} +(0.142796 - 0.371995i) q^{87} +(2.89365 - 7.53820i) q^{88} +(1.15239 + 0.513075i) q^{89} +(1.41206 - 4.04202i) q^{90} +(-0.880061 + 1.27339i) q^{91} +(-3.22193 + 6.32340i) q^{92} +(0.209766 + 0.0562065i) q^{93} +(0.0468781 + 0.00996424i) q^{94} +(14.3183 - 3.50192i) q^{95} +(0.0582454 + 0.274023i) q^{96} +(-6.42245 - 12.6048i) q^{97} +(-4.09426 + 1.79743i) q^{98} -10.5489i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	0.228917	+	0.596349i	0.161869	+	0.421682i	0.990395	−	0.138268i	$-0.0441536\pi$
$2$	0.228917	+	0.596349i	0.161869	+	0.421682i	−0.828526	+	0.559950i	$0.810820\pi$
$3$	−0.00257832	+	0.0491972i	−0.00148859	+	0.0284040i	−0.999273	−	0.0381287i	$-0.987860\pi$
$3$	−0.00257832	+	0.0491972i	−0.00148859	+	0.0284040i	0.997784	+	0.0665327i	$0.0211937\pi$
$4$	1.18306	−	1.06523i	0.591530	−	0.532616i
$5$	−1.84817	−	1.25868i	−0.826525	−	0.562901i
$5$	−1.84817	−	1.25868i	−0.826525	−	0.562901i
$6$	−0.0299289	+	0.00972449i	−0.0122184	+	0.00397001i
$7$	1.91442	+	1.82620i	0.723582	+	0.690238i
$7$	1.91442	+	1.82620i	0.723582	+	0.690238i
$8$	2.04438	+	1.04166i	0.722797	+	0.368284i
$9$	2.98115	+	0.313332i	0.993717	+	0.104444i
$10$	0.327538	−	1.39028i	0.103577	−	0.439647i
$11$	−0.367849	−	3.49985i	−0.110911	−	1.05525i	−0.898479	−	0.439017i	$-0.855327\pi$
$11$	−0.367849	−	3.49985i	−0.110911	−	1.05525i	0.787568	−	0.616228i	$-0.211340\pi$
$12$	0.0493562	+	0.0609498i	0.0142479	+	0.0175947i
$13$	0.0915228	+	0.577852i	0.0253839	+	0.160267i	0.997124	−	0.0757850i	$-0.0241463\pi$
$13$	0.0915228	+	0.577852i	0.0253839	+	0.160267i	−0.971740	+	0.236052i	$0.924146\pi$
$14$	−0.650809	+	1.55971i	−0.173936	+	0.416850i
$15$	0.0666889	−	0.0876793i	0.0172190	−	0.0226387i
$16$	0.179610	−	1.70887i	0.0449024	−	0.427218i
$17$	0.00260736	−	0.00169324i	0.000632378	−	0.000410671i	−0.544323	−	0.838876i	$-0.683213\pi$
$17$	0.00260736	−	0.00169324i	0.000632378	−	0.000410671i	0.544955	+	0.838465i	$0.316547\pi$
$18$	0.495581	+	1.84953i	0.116810	+	0.435939i
$19$	−4.41097	+	4.89888i	−1.01195	+	1.12388i	−0.0196734	+	0.999806i	$0.506263\pi$
$19$	−4.41097	+	4.89888i	−1.01195	+	1.12388i	−0.992273	+	0.124074i	$0.960404\pi$
$20$	−3.52728	+	0.479626i	−0.788725	+	0.107248i
$21$	−0.0947799	+	0.0894755i	−0.0206827	+	0.0195252i
$22$	2.00293	−	1.02054i	0.427025	−	0.217580i
$23$	−4.16186	+	1.59759i	−0.867809	+	0.333121i	−0.751214	−	0.660059i	$-0.770531\pi$
$23$	−4.16186	+	1.59759i	−0.867809	+	0.333121i	−0.116595	+	0.993180i	$0.537198\pi$
$24$	−0.0565180	+	0.0978920i	−0.0115367	+	0.0199821i
$25$	1.83143	+	4.65251i	0.366286	+	0.930502i
$26$	−0.323650	+	0.186860i	−0.0634731	+	0.0366462i
$27$	−0.0462215	+	0.291831i	−0.00889533	+	0.0561629i
$28$	4.21020	+	0.121204i	0.795653	+	0.0229054i
$29$	−7.69230	−	2.49938i	−1.42842	−	0.464123i	−0.510156	−	0.860082i	$-0.670412\pi$
$29$	−7.69230	−	2.49938i	−1.42842	−	0.464123i	−0.918268	+	0.395959i	$0.870412\pi$
$30$	0.0675536	+	0.0196986i	0.0123335	+	0.00359645i
$31$	0.916502	−	4.31180i	0.164609	−	0.774423i	−0.815938	−	0.578139i	$-0.803779\pi$
$31$	0.916502	−	4.31180i	0.164609	−	0.774423i	0.980547	−	0.196284i	$-0.0628875\pi$
$32$	5.49276	−	1.47178i	0.970991	−	0.260176i
$33$	0.173131	−	0.00907344i	0.0301383	−	0.00157948i
$34$	0.00160663	+	0.00116728i	0.000275535	+	0.000200188i
$35$	−1.23955	−	5.78477i	−0.209523	−	0.977804i
$36$	3.86066	−	2.80493i	0.643443	−	0.467488i
$37$	−0.945787	+	0.765883i	−0.155486	+	0.125910i	−0.703907	−	0.710292i	$-0.748563\pi$
$37$	−0.945787	+	0.765883i	−0.155486	+	0.125910i	0.548420	+	0.836203i	$0.315229\pi$
$38$	−3.93119	−	1.50904i	−0.637723	−	0.244799i
$39$	−0.0286647	+	0.00301278i	−0.00459003	+	0.000482431i
$40$	−2.46723	−	4.49839i	−0.390103	−	0.711258i
$41$	−2.00472	+	2.75926i	−0.313085	+	0.430924i	−0.936340	−	0.351094i	$-0.885810\pi$
$41$	−2.00472	+	2.75926i	−0.313085	+	0.430924i	0.623255	+	0.782018i	$0.285810\pi$
$42$	−0.0750553	−	0.0360394i	−0.0115813	−	0.00556100i
$43$	−6.51520	+	6.51520i	−0.993558	+	0.993558i	−0.999979	−	0.00642125i	$-0.997956\pi$
$43$	−6.51520	+	6.51520i	−0.993558	+	0.993558i	0.00642125	+	0.999979i	$0.497956\pi$
$44$	−4.16335	−	3.74869i	−0.627648	−	0.565137i
$45$	−5.11528	−	4.33142i	−0.762540	−	0.645690i
$46$	−1.90544	−	2.11621i	−0.280942	−	0.312018i
$47$	0.0408626	−	0.0629228i	0.00596042	−	0.00917824i	−0.835678	−	0.549220i	$-0.814925\pi$
$47$	0.0408626	−	0.0629228i	0.00596042	−	0.00917824i	0.841638	+	0.540042i	$0.181592\pi$
$48$	0.0836086	+	0.0132423i	0.0120679	+	0.00191136i
$49$	0.329993	+	6.99222i	0.0471419	+	0.998888i
$50$	−2.35527	+	2.15721i	−0.333086	+	0.305075i
$51$	7.65801e−5	0	0.000132641i	1.07234e−5	0	1.85734e-5i
$52$	0.723824	+	0.586142i	0.100376	+	0.0812832i
$53$	4.95277	+	0.259564i	0.680315	+	0.0356538i	0.389364	−	0.921084i	$-0.372695\pi$
$53$	4.95277	+	0.259564i	0.680315	+	0.0356538i	0.290951	+	0.956738i	$0.406028\pi$
$54$	−0.184614	+	0.0392409i	−0.0251228	+	0.00534001i
$55$	−3.72536	+	6.93131i	−0.502328	+	0.934618i
$56$	2.01151	+	5.72762i	0.268800	+	0.765386i
$57$	−0.229638	−	0.229638i	−0.0304163	−	0.0304163i
$58$	−0.270395	−	5.15944i	−0.0355046	−	0.677468i
$59$	0.931010	−	0.414512i	0.121207	−	0.0539649i	−0.345237	−	0.938515i	$-0.612202\pi$
$59$	0.931010	−	0.414512i	0.121207	−	0.0539649i	0.466444	+	0.884551i	$0.345535\pi$
$60$	−0.0145018	−	0.174769i	−0.00187218	−	0.0225626i
$61$	3.41172	−	7.66284i	0.436826	−	0.981127i	−0.552245	−	0.833682i	$-0.686229\pi$
$61$	3.41172	−	7.66284i	0.436826	−	0.981127i	0.989070	−	0.147445i	$-0.0471048\pi$
$62$	2.78114	−	0.440489i	0.353205	−	0.0559422i
$63$	5.13497	+	6.04403i	0.646945	+	0.761476i
$64$	0.115113	+	0.158439i	0.0143891	+	0.0198048i
$65$	0.558184	−	1.18317i	0.0692342	−	0.146754i
$66$	0.0450436	+	0.101170i	0.00554449	+	0.0124531i
$67$	−1.07397	−	1.65377i	−0.131206	−	0.202040i	0.766961	−	0.641693i	$-0.221768\pi$
$67$	−1.07397	−	1.65377i	−0.131206	−	0.202040i	−0.898167	+	0.439654i	$0.855101\pi$
$68$	0.00128097	−	0.00478065i	0.000155341	−	0.000579739i
$69$	−0.0678664	−	0.208871i	−0.00817015	−	0.0251451i
$70$	3.16598	−	2.06344i	0.378407	−	0.246628i
$71$	2.56775	−	7.90273i	0.304736	−	0.937882i	−0.675039	−	0.737782i	$-0.735873\pi$
$71$	2.56775	−	7.90273i	0.304736	−	0.937882i	0.979776	−	0.200100i	$-0.0641266\pi$
$72$	5.76822	+	3.74593i	0.679791	+	0.441462i
$73$	4.59745	−	5.67738i	0.538091	−	0.664487i	−0.433500	−	0.901154i	$-0.642722\pi$
$73$	4.59745	−	5.67738i	0.538091	−	0.664487i	0.971591	+	0.236666i	$0.0760549\pi$
$74$	−0.673240	−	0.388695i	−0.0782626	−	0.0451849i
$75$	−0.233613	+	0.0781056i	−0.0269753	+	0.00901885i
$76$			10.4944i			1.20379i
$77$	5.68721	−	7.37195i	0.648118	−	0.840112i
$78$	−0.00835850	−	0.0164045i	−0.000946414	−	0.00185744i
$79$	2.35530	+	11.0808i	0.264992	+	1.24669i	0.886296	+	0.463120i	$0.153270\pi$
$79$	2.35530	+	11.0808i	0.264992	+	1.24669i	−0.621303	+	0.783570i	$0.713397\pi$
$80$	−2.48288	+	2.93221i	−0.277594	+	0.327831i
$81$	8.78197	+	1.86667i	0.975774	+	0.207407i
$82$	−2.10440	−	0.563871i	−0.232392	−	0.0622692i
$83$	−6.86085	+	13.4652i	−0.753076	+	1.47800i	0.121232	+	0.992624i	$0.461316\pi$
$83$	−6.86085	+	13.4652i	−0.753076	+	1.47800i	−0.874308	+	0.485371i	$0.838684\pi$
$84$	−0.0168181	+	0.206818i	−0.00183501	+	0.0225657i
$85$	−0.00695009		0.000152456i	−0.000753843		1.65362e-5i
$86$	−5.37677	−	2.39389i	−0.579792	−	0.258140i
$87$	0.142796	−	0.371995i	0.0153093	−	0.0398821i
$88$	2.89365	−	7.53820i	0.308464	−	0.803575i
$89$	1.15239	+	0.513075i	0.122153	+	0.0543859i	0.466903	−	0.884309i	$-0.345370\pi$
$89$	1.15239	+	0.513075i	0.122153	+	0.0543859i	−0.344750	+	0.938694i	$0.612036\pi$
$90$	1.41206	−	4.04202i	0.148844	−	0.426066i
$91$	−0.880061	+	1.27339i	−0.0922554	+	0.133488i
$92$	−3.22193	+	6.32340i	−0.335910	+	0.659260i
$93$	0.209766	+	0.0562065i	0.0217517	+	0.00582835i
$94$	0.0468781	+	0.00996424i	0.00483510	+	0.00102773i
$95$	14.3183	−	3.50192i	1.46903	−	0.359290i
$96$	0.0582454	+	0.274023i	0.00594464	+	0.0279674i
$97$	−6.42245	−	12.6048i	−0.652101	−	1.27982i	−0.946057	−	0.324002i	$-0.894972\pi$
$97$	−6.42245	−	12.6048i	−0.652101	−	1.27982i	0.293955	−	0.955819i	$-0.405028\pi$
$98$	−4.09426	+	1.79743i	−0.413583	+	0.181568i
$99$		−	10.5489i		−	1.06020i
$100$	7.12270	+	3.55331i	0.712270	+	0.355331i
$101$	−9.59110	−	5.53743i	−0.954351	−	0.550995i	−0.0599208	−	0.998203i	$-0.519085\pi$
$101$	−9.59110	−	5.53743i	−0.954351	−	0.550995i	−0.894430	+	0.447209i	$0.852418\pi$
$102$	−6.15695e−5	0	7.60321e-5i	−6.09629e−6	0	7.52830e-6i
$103$	7.68569	+	4.99114i	0.757293	+	0.491792i	0.864617	−	0.502432i	$-0.167561\pi$
$103$	7.68569	+	4.99114i	0.757293	+	0.491792i	−0.107323	+	0.994224i	$0.534228\pi$
$104$	−0.414820	+	1.27669i	−0.0406765	+	0.125189i
$105$	0.287790	−	0.0460676i	0.0280855	−	0.00449574i
$106$	0.978982	+	3.01300i	0.0950871	+	0.292648i
$107$	−4.48536	+	16.7396i	−0.433617	+	1.61828i	0.310739	+	0.950495i	$0.399424\pi$
$107$	−4.48536	+	16.7396i	−0.433617	+	1.61828i	−0.744355	+	0.667784i	$0.767243\pi$
$108$	0.256185	+	0.394491i	0.0246514	+	0.0379599i
$109$	−1.10392	−	2.47944i	−0.105736	−	0.237487i	0.852927	−	0.522030i	$-0.174825\pi$
$109$	−1.10392	−	2.47944i	−0.105736	−	0.237487i	−0.958663	+	0.284542i	$0.908158\pi$
$110$	−4.98628	−	0.634921i	−0.475423	−	0.0605373i
$111$	−0.0352408	−	0.0485048i	−0.00334491	−	0.00460387i
$112$	3.46459	−	2.94349i	0.327373	−	0.278134i
$113$	13.6793	−	2.16659i	1.28684	−	0.203815i	0.524733	−	0.851267i	$-0.324165\pi$
$113$	13.6793	−	2.16659i	1.28684	−	0.203815i	0.762107	+	0.647451i	$0.224165\pi$
$114$	0.0843764	−	0.189513i	0.00790258	−	0.0177495i
$115$	9.70267	+	2.28586i	0.904779	+	0.213158i
$116$	−11.7629	+	5.23717i	−1.09216	+	0.486259i
$117$	0.0917840	+	1.75134i	0.00848543	+	0.161912i
$118$	0.460317	+	0.460317i	0.0423757	+	0.0423757i
$119$	0.00808377	+	0.00151999i	0.000741038	+	0.000139337i
$120$	0.227670	−	0.109782i	0.0207833	−	0.0100217i
$121$	−1.35404	+	0.287810i	−0.123094	+	0.0261645i
$122$	5.35073	+	0.280420i	0.484432	+	0.0253880i
$123$	−0.130579	−	0.105741i	−0.0117739	−	0.00953434i
$124$	−3.50880	−	6.07742i	−0.315099	−	0.545768i
$125$	2.47126	−	10.9038i	0.221036	−	0.975266i
$126$	−2.42887	+	4.44581i	−0.216381	+	0.396064i
$127$	−5.96983	−	0.945529i	−0.529737	−	0.0839021i	−0.114164	−	0.993462i	$-0.536419\pi$
$127$	−5.96983	−	0.945529i	−0.529737	−	0.0839021i	−0.415573	+	0.909560i	$0.636419\pi$
$128$	6.12607	−	9.43332i	0.541473	−	0.833795i
$129$	−0.303731	−	0.337328i	−0.0267420	−	0.0297000i
$130$	0.833357	+	0.0620261i	0.0730902	+	0.00544005i
$131$	10.8977	+	9.81230i	0.952133	+	0.857304i	0.989869	−	0.141983i	$-0.0453480\pi$
$131$	10.8977	+	9.81230i	0.952133	+	0.857304i	−0.0377361	+	0.999288i	$0.512015\pi$
$132$	0.195160	−	0.195160i	0.0169865	−	0.0169865i
$133$	−17.3908	+	1.32319i	−1.50797	+	0.114735i
$134$	0.740372	−	1.01903i	0.0639584	−	0.0880312i
$135$	0.452748	−	0.481174i	0.0389663	−	0.0414128i
$136$	0.00709422		0.000745632i	0.000608324		6.39375e-5i
$137$	−9.24006	−	3.54693i	−0.789432	−	0.303034i	−0.0699541	−	0.997550i	$-0.522285\pi$
$137$	−9.24006	−	3.54693i	−0.789432	−	0.303034i	−0.719477	+	0.694516i	$0.755619\pi$
$138$	0.109024	−	0.0882861i	0.00928076	−	0.00751541i
$139$	14.6696	−	10.6581i	1.24426	−	0.904005i	0.246382	−	0.969173i	$-0.420758\pi$
$139$	14.6696	−	10.6581i	1.24426	−	0.904005i	0.997874	+	0.0651678i	$0.0207583\pi$
$140$	−7.62859	−	5.52332i	−0.644733	−	0.466805i
$141$	0.00299027	+	0.00217256i	0.000251826	+	0.000182962i
$142$	5.30058	−	0.277792i	0.444815	−	0.0233118i
$143$	1.98873	−	0.532879i	0.166306	−	0.0445616i
$144$	1.07089	−	5.03813i	0.0892406	−	0.419844i
$145$	11.0707	+	14.3014i	0.919372	+	1.18767i
$146$	4.43813	+	1.44204i	0.367302	+	0.119344i
$147$	−0.344848	−	0.00179341i	−0.0284426	−	0.000147918i
$148$	−0.303080	+	1.91357i	−0.0249130	+	0.157295i
$149$	−5.99122	+	3.45903i	−0.490820	+	0.283375i	−0.724914	−	0.688839i	$-0.758121\pi$
$149$	−5.99122	+	3.45903i	−0.490820	+	0.283375i	0.234095	+	0.972214i	$0.424787\pi$
$150$	−0.100056	−	0.121435i	−0.00816954	−	0.00991512i
$151$	−3.27178	+	5.66690i	−0.266254	+	0.461166i	−0.967891	−	0.251369i	$-0.919119\pi$
$151$	−3.27178	+	5.66690i	−0.266254	+	0.461166i	0.701637	+	0.712534i	$0.252453\pi$
$152$	−14.1207	+	5.42042i	−1.14534	+	0.439654i
$153$	0.00830348	−	0.00423084i	0.000671297	−	0.000342043i
$154$	5.69815	+	1.70400i	0.459170	+	0.137312i
$155$	−7.12105	+	6.81534i	−0.571976	+	0.547421i
$156$	−0.0307028	+	0.0340989i	−0.00245819	+	0.00273010i
$157$	−6.17486	−	23.0449i	−0.492807	−	1.83918i	−0.541979	−	0.840392i	$-0.682325\pi$
$157$	−6.17486	−	23.0449i	−0.492807	−	1.83918i	0.0491717	−	0.998790i	$-0.484342\pi$
$158$	−6.06887	+	3.94117i	−0.482813	+	0.313542i
$159$	−0.0255396	+	0.242993i	−0.00202542	+	0.0192706i
$160$	−12.0040	−	4.19355i	−0.949002	−	0.331529i
$161$	−10.8851	−	4.54194i	−0.857863	−	0.357955i
$162$	0.897157	+	5.66443i	0.0704873	+	0.445039i
$163$	−8.62952	−	10.6566i	−0.675916	−	0.834687i	0.317618	−	0.948219i	$-0.397117\pi$
$163$	−8.62952	−	10.6566i	−0.675916	−	0.834687i	−0.993534	+	0.113532i	$0.963784\pi$
$164$	0.567549	+	5.39987i	0.0443181	+	0.421659i
$165$	−0.331396	−	0.201149i	−0.0257992	−	0.0156594i
$166$	−9.60050	−	1.00905i	−0.745144	−	0.0783178i
$167$	−4.26144	−	2.17131i	−0.329760	−	0.168021i	0.281270	−	0.959629i	$-0.409244\pi$
$167$	−4.26144	−	2.17131i	−0.329760	−	0.168021i	−0.611030	+	0.791608i	$0.709244\pi$
$168$	−0.286969	+	0.0841932i	−0.0221402	+	0.00649564i
$169$	12.0382	−	3.91145i	0.926015	−	0.300881i
$170$	−0.00150007	−	0.00417957i	−0.000115050	−	0.000320559i
$171$	−14.6848	+	13.2222i	−1.12297	+	1.01113i
$172$	−0.767673	+	14.6481i	−0.0585345	+	1.11691i
$173$	−6.36138	−	16.5720i	−0.483647	−	1.25994i	−0.930814	−	0.365493i	$-0.880900\pi$
$173$	−6.36138	−	16.5720i	−0.483647	−	1.25994i	0.447167	−	0.894451i	$-0.352433\pi$
$174$	0.254527			0.0192957
$175$	−4.99029	+	12.2514i	−0.377231	+	0.926119i
$176$	−6.04687			−0.455800
$177$	0.0179924	+	0.0468718i	0.00135239	+	0.00352310i
$178$	−0.0421712	+	0.804675i	−0.00316087	+	0.0603130i
$179$	3.49351	−	3.14557i	0.261117	−	0.235111i	−0.528165	−	0.849142i	$-0.677120\pi$
$179$	3.49351	−	3.14557i	0.261117	−	0.235111i	0.789282	+	0.614031i	$0.210453\pi$
$180$	−10.6657	+	0.324630i	−0.794971	+	0.0241965i
$181$	23.4101	−	7.60642i	1.74006	−	0.565380i	0.745220	−	0.666818i	$-0.232344\pi$
$181$	23.4101	−	7.60642i	1.74006	−	0.565380i	0.994842	+	0.101438i	$0.0323444\pi$
$182$	−0.960845	−	0.233323i	−0.0712226	−	0.0172950i
$183$	0.368194	+	0.187604i	0.0272177	+	0.0138681i
$184$	−10.1726	−	1.06918i	−0.749933	−	0.0788211i
$185$	2.71198	−	0.225032i	0.199388	−	0.0165447i
$186$	0.0145002	+	0.137960i	0.00106321	+	0.0101157i
$187$	−0.00688521	−	0.00850252i	−0.000503496	−	0.000621766i
$188$	−0.0186846	−	0.117970i	−0.00136271	−	0.00860382i
$189$	−0.621429	+	0.474277i	−0.0452023	+	0.0344986i
$190$	5.36608	+	7.73708i	0.389296	+	0.561307i
$191$	0.283233	−	2.69478i	0.0204940	−	0.194988i	−0.979485	−	0.201519i	$-0.935412\pi$
$191$	0.283233	−	2.69478i	0.0204940	−	0.194988i	0.999979	+	0.00653111i	$0.00207893\pi$
$192$	−0.00809154	+	0.00525471i	−0.000583957	+	0.000379226i
$193$	−1.94899	−	7.27372i	−0.140291	−	0.523574i	−0.999920	−	0.0126547i	$-0.995972\pi$
$193$	−1.94899	−	7.27372i	−0.140291	−	0.523574i	0.859629	−	0.510919i	$-0.170695\pi$
$194$	6.04663	−	6.71546i	0.434123	−	0.482142i
$195$	0.0567692	+	0.0305117i	0.00406533	+	0.00218499i
$196$	7.83874	+	7.92070i	0.559910	+	0.565764i
$197$	−17.4980	+	8.91567i	−1.24668	+	0.635215i	−0.947736	−	0.319056i	$-0.896634\pi$
$197$	−17.4980	+	8.91567i	−1.24668	+	0.635215i	−0.298944	+	0.954271i	$0.596634\pi$
$198$	6.29079	−	2.41481i	0.447067	−	0.171613i
$199$	−6.20257	+	10.7432i	−0.439689	+	0.761563i	−0.997665	−	0.0682937i	$-0.978245\pi$
$199$	−6.20257	+	10.7432i	−0.439689	+	0.761563i	0.557977	+	0.829857i	$0.311578\pi$
$200$	−1.10221	+	11.4192i	−0.0779383	+	0.807462i
$201$	0.0841298	−	0.0485723i	0.00593406	−	0.00342603i
$202$	1.10667	−	6.98725i	0.0778652	−	0.491621i
$203$	−10.1619	−	18.8325i	−0.713226	−	1.32178i
$204$	0.000231892	0	7.53463e-5i	1.62357e−5	0	5.27529e-6i
$205$	7.17809	−	2.57626i	0.501340	−	0.179934i
$206$	−1.21708	+	5.72590i	−0.0847979	+	0.398943i
$207$	−12.9077	+	3.45861i	−0.897149	+	0.240390i
$208$	1.00391	−	0.0526129i	0.0696089	−	0.00364805i
$209$	18.7679	+	13.6357i	1.29821	+	0.943202i
$210$	0.0933524	+	0.161078i	0.00644193	+	0.0111154i
$211$	18.7799	−	13.6444i	1.29286	−	0.939319i	0.293003	−	0.956112i	$-0.405346\pi$
$211$	18.7799	−	13.6444i	1.29286	−	0.939319i	0.999859	+	0.0167927i	$0.00534553\pi$
$212$	6.13593	−	4.96877i	0.421417	−	0.341257i
$213$	0.382172	+	0.146702i	0.0261860	+	0.0100519i
$214$	−11.0094	+	1.15714i	−0.752588	+	0.0791002i
$215$	20.2417	−	3.84059i	1.38047	−	0.261926i
$216$	−0.398484	+	0.548466i	−0.0271134	+	0.0373184i
$217$	9.62878	−	6.58088i	0.653644	−	0.446739i
$218$	1.22591	−	1.22591i	0.0830288	−	0.0830288i
$219$	0.267458	+	0.240820i	0.0180731	+	0.0162731i
$220$	2.97613	+	12.1685i	0.200651	+	0.820403i
$221$	0.00121708	+	0.00135170i	8.18694e−5	+	9.09251e-5i
$222$	0.0208585	−	0.0321194i	0.00139993	−	0.00215571i
$223$	−26.2337	−	4.15501i	−1.75674	−	0.278240i	−0.806833	−	0.590779i	$-0.798820\pi$
$223$	−26.2337	−	4.15501i	−1.75674	−	0.278240i	−0.949905	+	0.312539i	$0.898820\pi$
$224$	13.2032	+	7.21327i	0.882176	+	0.481957i
$225$	4.00199	+	14.4437i	0.266799	+	0.962913i
$226$	4.42346	+	7.66166i	0.294244	+	0.509646i
$227$	14.5040	+	11.7451i	0.962665	+	0.779551i	0.975417	−	0.220368i	$-0.0707258\pi$
$227$	14.5040	+	11.7451i	0.962665	+	0.779551i	−0.0127517	+	0.999919i	$0.504059\pi$
$228$	−0.516295	−	0.0270578i	−0.0341924	−	0.00179195i
$229$	8.83466	−	1.87787i	0.583811	−	0.124093i	0.0934678	−	0.995622i	$-0.470205\pi$
$229$	8.83466	−	1.87787i	0.583811	−	0.124093i	0.490343	+	0.871529i	$0.336871\pi$
$230$	0.857934	+	6.30945i	0.0565705	+	0.416033i
$231$	0.348016	+	0.298802i	0.0228978	+	0.0196597i
$232$	−13.1225	−	13.1225i	−0.861532	−	0.861532i
$233$	0.00666441	+	0.127164i	0.000436600	+	0.00833082i	0.998839	−	0.0481701i	$-0.0153390\pi$
$233$	0.00666441	+	0.127164i	0.000436600	+	0.00833082i	−0.998403	+	0.0565009i	$0.982006\pi$
$234$	−1.02340	+	0.455647i	−0.0669017	+	0.0297866i
$235$	−0.154721	+	0.0648587i	−0.0100929	+	0.00423092i
$236$	0.659889	−	1.48214i	0.0429551	−	0.0964788i
$237$	−0.551218	+	0.0873044i	−0.0358055	+	0.00567103i
$238$	0.000944066		0.00516870i	6.11947e−5		0.000335037i
$239$	−10.3096	−	14.1899i	−0.666871	−	0.917870i	0.332813	−	0.942993i	$-0.392002\pi$
$239$	−10.3096	−	14.1899i	−0.666871	−	0.917870i	−0.999684	+	0.0251232i	$0.992002\pi$
$240$	−0.137855	−	0.129711i	−0.00889848	−	0.00837280i
$241$	0.647399	+	1.45408i	0.0417026	+	0.0936657i	0.933196	−	0.359369i	$-0.117008\pi$
$241$	0.647399	+	1.45408i	0.0417026	+	0.0936657i	−0.891493	+	0.453035i	$0.850341\pi$
$242$	−0.481597	−	0.741595i	−0.0309582	−	0.0476715i
$243$	−0.343896	+	1.28344i	−0.0220610	+	0.0823326i
$244$	−4.12644	−	12.6999i	−0.264168	−	0.813027i
$245$	8.19111	−	13.3381i	0.523311	−	0.852142i
$246$	0.0331667	−	0.102077i	0.00211463	−	0.00650816i
$247$	−3.23453	−	2.10053i	−0.205809	−	0.133654i
$248$	6.36513	−	7.86028i	0.404186	−	0.499128i
$249$	−0.644760	−	0.372252i	−0.0408600	−	0.0235905i
$250$	7.06818	−	1.02233i	0.447031	−	0.0646579i
$251$			16.8292i			1.06225i	0.847294	+	0.531124i	$0.178230\pi$
$251$			16.8292i			1.06225i	−0.847294	+	0.531124i	$0.821770\pi$
$252$	12.5133	+	1.68052i	0.788262	+	0.105863i
$253$	7.12227	+	13.9782i	0.447773	+	0.878805i
$254$	−0.802730	−	3.77655i	−0.0503678	−	0.236962i
$255$	2.54199e−5	0	0.000341532i	1.59186e−6	0	2.13875e-5i
$256$	7.41103	+	1.57526i	0.463189	+	0.0984539i
$257$	18.6352	+	4.99329i	1.16243	+	0.311473i	0.787937	−	0.615756i	$-0.211149\pi$
$257$	18.6352	+	4.99329i	1.16243	+	0.311473i	0.374496	+	0.927229i	$0.377816\pi$
$258$	0.131636	−	0.258350i	0.00819528	−	0.0160841i
$259$	−3.20929	−	0.260975i	−0.199415	−	0.0162162i
$260$	−0.599980	−	1.99435i	−0.0372092	−	0.123685i
$261$	−22.1488	−	9.86127i	−1.37097	−	0.610397i
$262$	−3.35689	+	8.74500i	−0.207389	+	0.540268i
$263$	6.03286	−	15.7161i	0.372002	−	0.969098i	−0.611987	−	0.790868i	$-0.709629\pi$
$263$	6.03286	−	15.7161i	0.372002	−	0.969098i	0.983989	−	0.178230i	$-0.0570372\pi$
$264$	0.363398	+	0.161795i	0.0223656	+	0.00995780i
$265$	−8.82683	−	6.71369i	−0.542228	−	0.412419i
$266$	−4.77012	−	10.0681i	−0.292475	−	0.617313i
$267$	−0.0282131	+	0.0553713i	−0.00172661	+	0.00338867i
$268$	−3.03222	−	0.812480i	−0.185222	−	0.0496301i
$269$	23.4861	+	4.99213i	1.43197	+	0.304376i	0.857642	−	0.514247i	$-0.171928\pi$
$269$	23.4861	+	4.99213i	1.43197	+	0.304376i	0.574332	+	0.818622i	$0.305262\pi$
$270$	0.390589	+	0.159847i	0.0237705	+	0.00972797i
$271$	−0.519589	−	2.44447i	−0.0315628	−	0.148491i	0.959544	−	0.281558i	$-0.0908510\pi$
$271$	−0.519589	−	2.44447i	−0.0315628	−	0.148491i	−0.991107	+	0.133066i	$0.957518\pi$
$272$	−0.00242522	−	0.00475977i	−0.000147051	−	0.000288603i
$273$	−0.0603782	−	0.0465797i	−0.00365425	−	0.00281913i
$274$		−	6.32225i		−	0.381941i
$275$	15.6094	−	8.12116i	0.941283	−	0.489724i
$276$	−0.302787	−	0.174814i	−0.0182256	−	0.0105226i
$277$	−17.3370	+	21.4095i	−1.04168	+	1.28637i	−0.0846428	+	0.996411i	$0.526975\pi$
$277$	−17.3370	+	21.4095i	−1.04168	+	1.28637i	−0.957039	+	0.289959i	$0.906358\pi$
$278$	9.71403	+	6.30836i	0.582609	+	0.378351i
$279$	4.08326	−	12.5670i	0.244458	−	0.752365i
$280$	3.49166	−	13.1175i	0.208667	−	0.783918i
$281$	2.24129	+	6.89798i	0.133704	+	0.411499i	0.995386	−	0.0959494i	$-0.0305887\pi$
$281$	2.24129	+	6.89798i	0.133704	+	0.411499i	−0.861682	+	0.507449i	$0.830589\pi$
$282$	−0.000611079		0.00228058i	−3.63892e−5		0.000135806i
$283$	4.41837	+	6.80370i	0.262645	+	0.404438i	0.945249	−	0.326351i	$-0.105819\pi$
$283$	4.41837	+	6.80370i	0.262645	+	0.404438i	−0.682604	+	0.730789i	$0.739152\pi$
$284$	−5.38044	−	12.0847i	−0.319270	−	0.717093i
$285$	0.135368	+	0.713452i	0.00801848	+	0.0422612i
$286$	0.773036	+	1.06399i	0.0457106	+	0.0629152i
$287$	−8.87683	+	1.62136i	−0.523983	+	0.0957059i
$288$	16.8359	−	2.66654i	0.992065	−	0.157128i
$289$	−6.91452	+	15.5303i	−0.406736	+	0.913545i
$290$	−5.99437	+	9.87584i	−0.352002	+	0.579929i
$291$	0.636679	−	0.283468i	0.0373228	−	0.0166172i
$292$	−0.608666	−	11.6140i	−0.0356195	−	0.679661i
$293$	22.2968	+	22.2968i	1.30259	+	1.30259i	0.926638	+	0.375956i	$0.122686\pi$
$293$	22.2968	+	22.2968i	1.30259	+	1.30259i	0.375956	+	0.926638i	$0.377314\pi$
$294$	−0.0778721	−	0.206060i	−0.00454159	−	0.0120177i
$295$	−2.24240	−	0.405760i	−0.130558	−	0.0236243i
$296$	−2.73134	+	0.580564i	−0.158756	+	0.0337446i
$297$	1.03837	+	0.0544186i	0.0602523	+	0.00315769i
$298$	−3.43428	−	2.78102i	−0.198942	−	0.161100i
$299$	−1.30408	−	2.25873i	−0.0754167	−	0.130626i
$300$	−0.193177	+	0.341255i	−0.0111531	+	0.0197024i
$301$	−24.3709	+	0.574763i	−1.40471	+	0.0331288i
$302$	−4.12841	−	0.653876i	−0.237563	−	0.0376264i
$303$	0.297155	−	0.457578i	0.0170711	−	0.0262872i
$304$	7.57931	+	8.41767i	0.434703	+	0.482787i
$305$	−15.9505	+	9.86793i	−0.913324	+	0.565036i
$306$	0.00442386	+	0.00398326i	0.000252895	+	0.000227708i
$307$	15.2811	−	15.2811i	0.872140	−	0.872140i	−0.120566	−	0.992705i	$-0.538471\pi$
$307$	15.2811	−	15.2811i	0.872140	−	0.872140i	0.992705	+	0.120566i	$0.0384708\pi$
$308$	−1.12452	−	14.7797i	−0.0640757	−	0.842150i
$309$	−0.265366	+	0.365246i	−0.0150962	+	0.0207781i
$310$	−5.69445	−	2.68648i	−0.323423	−	0.152582i
$311$	9.75391	−	1.02518i	0.553093	−	0.0581325i	0.176141	−	0.984365i	$-0.443639\pi$
$311$	9.75391	−	1.02518i	0.553093	−	0.0581325i	0.376953	+	0.926233i	$0.376972\pi$
$312$	−0.0617398	−	0.0236997i	−0.00349533	−	0.00134173i
$313$	−13.7509	+	11.1352i	−0.777245	+	0.629400i	−0.933607	−	0.358299i	$-0.883357\pi$
$313$	−13.7509	+	11.1352i	−0.777245	+	0.629400i	0.156362	+	0.987700i	$0.450023\pi$
$314$	12.3293	−	8.95773i	0.695780	−	0.505514i
$315$	−1.88275	−	17.6337i	−0.106081	−	0.993544i
$316$	14.5901	+	10.6003i	0.820759	+	0.596316i
$317$	21.3171	−	1.11718i	1.19729	−	0.0627473i	0.556755	−	0.830676i	$-0.312046\pi$
$317$	21.3171	−	1.11718i	1.19729	−	0.0627473i	0.640535	+	0.767929i	$0.278713\pi$
$318$	−0.150755	+	0.0403947i	−0.00845393	+	0.00226522i
$319$	−5.91785	+	27.8413i	−0.331336	+	1.55881i
$320$	−0.0133226	−	0.437711i	−0.000744755	−	0.0244688i
$321$	−0.811977	−	0.263827i	−0.0453201	−	0.0147254i
$322$	0.216804	−	7.53102i	0.0120820	−	0.419687i
$323$	−0.00320601	+	0.0202420i	−0.000178387	+	0.00112629i
$324$	12.3780	−	7.14646i	0.687669	−	0.397026i
$325$	−2.52085	+	1.48411i	−0.139831	+	0.0823234i
$326$	4.37959	−	7.58567i	0.242563	−	0.420131i
$327$	0.124828	−	0.0479169i	0.00690300	−	0.00264981i
$328$	−6.97263	+	3.55273i	−0.384999	+	0.196167i
$329$	0.193138	−	0.0458374i	0.0106480	−	0.00252710i
$330$	0.0440925	−	0.243674i	0.00242721	−	0.0134138i
$331$	−6.39481	+	7.10215i	−0.351490	+	0.390370i	−0.892800	−	0.450454i	$-0.851262\pi$
$331$	−6.39481	+	7.10215i	−0.351490	+	0.390370i	0.541309	+	0.840824i	$0.317929\pi$
$332$	6.22675	+	23.2385i	0.341737	+	1.27538i
$333$	−3.05951	+	1.98687i	−0.167660	+	0.108880i
$334$	0.319344	−	3.03835i	0.0174737	−	0.166251i
$335$	−0.0966982	+	4.40822i	−0.00528318	+	0.240847i
$336$	0.135879	+	0.178037i	0.00741280	+	0.00971273i
$337$	−1.18291	−	7.46859i	−0.0644372	−	0.406840i	−0.998732	−	0.0503394i	$-0.983970\pi$
$337$	−1.18291	−	7.46859i	−0.0644372	−	0.406840i	0.934295	−	0.356501i	$-0.116030\pi$
$338$	5.08833	+	6.28357i	0.276769	+	0.341781i
$339$	0.0713205	+	0.678569i	0.00387360	+	0.0368548i
$340$	−0.00838478	+	0.00722310i	−0.000454728	+	0.000391727i
$341$	−15.4278	−	1.62153i	−0.835463	−	0.0878107i
$342$	−11.2466	−	5.73045i	−0.608148	−	0.309867i
$343$	−12.1374	+	13.9887i	−0.655360	+	0.755317i
$344$	−20.1062	+	6.53289i	−1.08405	+	0.352230i
$345$	−0.137475	+	0.471451i	−0.00740138	+	0.0253821i
$346$	8.42645	−	7.58721i	0.453009	−	0.407891i
$347$	0.180528	−	3.44467i	0.00969123	−	0.184920i	−0.989494	−	0.144571i	$-0.953820\pi$
$347$	0.180528	−	3.44467i	0.00969123	−	0.184920i	0.999186	−	0.0403487i	$-0.0128469\pi$
$348$	−0.227326	−	0.592204i	−0.0121859	−	0.0317455i
$349$	−5.03213			−0.269364			−0.134682	−	0.990889i	$-0.543001\pi$
$349$	−5.03213			−0.269364			−0.134682	+	0.990889i	$0.543001\pi$
$350$	−8.44847	−	0.171401i	−0.451590	−	0.00916176i
$351$	−0.172866			−0.00922688
$352$	−7.17152	−	18.6825i	−0.382243	−	0.995778i
$353$	−0.349494	+	6.66875i	−0.0186017	+	0.354942i	0.973433	+	0.228974i	$0.0735370\pi$
$353$	−0.349494	+	6.66875i	−0.0186017	+	0.354942i	−0.992034	+	0.125968i	$0.959796\pi$
$354$	−0.0238332	+	0.0214595i	−0.00126672	+	0.00114056i
$355$	−14.6927	+	11.3736i	−0.779806	+	0.603646i
$356$	1.90989	−	0.620560i	0.101224	−	0.0328896i
$357$	−9.56218e−5	0	0.000393780i	−5.06084e−6	0	2.08410e-5i
$358$	2.67558	+	1.36327i	0.141409	+	0.0720513i
$359$	−3.98990	−	0.419355i	−0.210579	−	0.0221327i	−0.00134837	−	0.999999i	$-0.500429\pi$
$359$	−3.98990	−	0.419355i	−0.210579	−	0.0221327i	−0.209230	+	0.977866i	$0.567096\pi$
$360$	−5.94569	−	14.1835i	−0.313365	−	0.747534i
$361$	−2.55632	−	24.3217i	−0.134543	−	1.28009i
$362$	9.89505	+	12.2194i	0.520072	+	0.642236i
$363$	−0.0106683	−	0.0673570i	−0.000559940	−	0.00353532i
$364$	0.315292	+	2.44397i	0.0165258	+	0.128099i
$365$	−15.6429	+	4.70600i	−0.818786	+	0.246323i
$366$	−0.0275917	+	0.262518i	−0.00144224	+	0.0137220i
$367$	−18.2531	+	11.8537i	−0.952803	+	0.618758i	−0.924639	−	0.380845i	$-0.875633\pi$
$367$	−18.2531	+	11.8537i	−0.952803	+	0.618758i	−0.0281648	+	0.999603i	$0.508966\pi$
$368$	1.98257	+	7.39904i	0.103348	+	0.385701i
$369$	−6.84094	+	7.59764i	−0.356125	+	0.395517i
$370$	0.755014	+	1.56577i	0.0392513	+	0.0814005i
$371$	9.00766	+	9.54166i	0.467654	+	0.495378i
$372$	0.308039	−	0.156954i	0.0159711	−	0.00813766i
$373$	3.44356	−	1.32186i	0.178301	−	0.0684432i	−0.267580	−	0.963536i	$-0.586224\pi$
$373$	3.44356	−	1.32186i	0.178301	−	0.0684432i	0.445881	+	0.895092i	$0.352891\pi$
$374$	0.00349433	−	0.00605235i	0.000180687	−	0.000312960i
$375$	0.530065	+	0.149692i	0.0273724	+	0.00773008i
$376$	0.149083	−	0.0860731i	0.00768837	−	0.00443888i
$377$	0.740251	−	4.67376i	0.0381249	−	0.240711i
$378$	−0.425090	−	0.262018i	−0.0218643	−	0.0134768i
$379$	−4.03502	−	1.31106i	−0.207265	−	0.0673446i	0.203544	−	0.979066i	$-0.434754\pi$
$379$	−4.03502	−	1.31106i	−0.207265	−	0.0673446i	−0.410810	+	0.911721i	$0.634754\pi$
$380$	13.2091	−	19.3954i	0.677613	−	0.994961i
$381$	0.0619095	−	0.291261i	0.00317172	−	0.0149218i
$382$	1.67187	−	0.447976i	0.0855402	−	0.0229204i
$383$	0.909095	−	0.0476437i	0.0464526	−	0.00243448i	−0.0290955	−	0.999577i	$-0.509263\pi$
$383$	0.909095	−	0.0476437i	0.0464526	−	0.00243448i	0.0755481	+	0.997142i	$0.475929\pi$
$384$	0.448298	+	0.325708i	0.0228771	+	0.0166212i
$385$	−19.7899	+	6.46618i	−1.00858	+	0.329547i
$386$	3.89152	−	2.82735i	0.198073	−	0.143908i
$387$	−21.4642	+	17.3814i	−1.09109	+	0.883545i
$388$	−21.0252	−	8.07081i	−1.06739	−	0.409733i
$389$	−9.71731	+	1.02133i	−0.492687	+	0.0517835i	−0.347615	−	0.937638i	$-0.613008\pi$
$389$	−9.71731	+	1.02133i	−0.492687	+	0.0517835i	−0.145073	+	0.989421i	$0.546342\pi$
$390$	−0.00520017	+	0.0408389i	−0.000263321	+	0.00206796i
$391$	−0.00814638	+	0.0112125i	−0.000411980	+	0.000567042i
$392$	−6.60891	+	14.6385i	−0.333800	+	0.739355i
$393$	−0.510835	+	0.510835i	−0.0257682	+	0.0257682i
$394$	−9.32243	−	8.39395i	−0.469657	−	0.422881i
$395$	9.59427	−	23.4438i	0.482740	−	1.17958i
$396$	−11.2370	−	12.4799i	−0.564680	−	0.627140i
$397$	3.44084	−	5.29843i	0.172691	−	0.265921i	−0.741718	−	0.670711i	$-0.765989\pi$
$397$	3.44084	−	5.29843i	0.172691	−	0.265921i	0.914409	+	0.404791i	$0.132656\pi$
$398$	−7.82654	−	1.23960i	−0.392309	−	0.0621357i
$399$	−0.0202584	−	0.858989i	−0.00101419	−	0.0430033i
$400$	8.27949	−	2.29404i	0.413975	−	0.114702i
$401$	−1.84234	−	3.19103i	−0.0920023	−	0.159353i	0.816351	−	0.577556i	$-0.195993\pi$
$401$	−1.84234	−	3.19103i	−0.0920023	−	0.159353i	−0.908354	+	0.418203i	$0.862660\pi$
$402$	0.0482248	+	0.0390516i	0.00240523	+	0.00194772i
$403$	2.57547	+	0.134975i	0.128293	+	0.00672356i
$404$	−17.2455	+	3.66565i	−0.857996	+	0.182373i
$405$	−13.8810	−	14.5036i	−0.689752	−	0.720691i
$406$	8.90452	−	10.3711i	0.441924	−	0.514710i
$407$	3.02839	+	3.02839i	0.150112	+	0.150112i
$408$	1.83919e−5	0	0.000350938i	9.10534e−7	0	1.73740e-5i
$409$	−28.0200	+	12.4753i	−1.38550	+	0.616864i	−0.957899	−	0.287104i	$-0.907308\pi$
$409$	−28.0200	+	12.4753i	−1.38550	+	0.616864i	−0.427600	+	0.903968i	$0.640641\pi$
$410$	3.17954	+	3.69090i	0.157026	+	0.182280i
$411$	0.198323	−	0.445440i	0.00978254	−	0.0219719i
$412$	14.4094	−	2.28222i	0.709898	−	0.112437i
$413$	2.53932	+	0.906659i	0.124952	+	0.0446138i
$414$	−5.01733	−	6.90577i	−0.246589	−	0.339400i
$415$	29.6284	−	16.2502i	1.45440	−	0.797693i
$416$	1.35318	+	3.03930i	0.0663453	+	0.149014i
$417$	0.486524	+	0.749181i	0.0238252	+	0.0366876i
$418$	−3.83534	+	14.3137i	−0.187593	+	0.700105i
$419$	1.92150	+	5.91378i	0.0938716	+	0.288907i	0.986958	−	0.160978i	$-0.0514649\pi$
$419$	1.92150	+	5.91378i	0.0938716	+	0.288907i	−0.893086	+	0.449885i	$0.851465\pi$
$420$	0.291401	−	0.361064i	0.0142189	−	0.0176181i
$421$	8.85803	−	27.2622i	0.431714	−	1.32868i	−0.464703	−	0.885467i	$-0.653839\pi$
$421$	8.85803	−	27.2622i	0.431714	−	1.32868i	0.896417	−	0.443212i	$-0.146161\pi$
$422$	12.4358	+	8.07594i	0.605368	+	0.393130i
$423$	0.141533	−	0.174779i	0.00688158	−	0.00849804i
$424$	9.85496	+	5.68977i	0.478599	+	0.276319i
$425$	0.0126530	+	0.00902973i	0.000613761	+	0.000438006i
$426$			0.261490i			0.0126692i
$427$	20.5253	−	8.43941i	0.993291	−	0.408412i
$428$	12.5251	+	24.5819i	0.605425	+	1.18821i
$429$	0.0210886	+	0.0992140i	0.00101817	+	0.00479010i
$430$	6.92400	+	11.1920i	0.333905	+	0.539724i
$431$	−6.49460	−	1.38047i	−0.312834	−	0.0664949i	0.0488191	−	0.998808i	$-0.484454\pi$
$431$	−6.49460	−	1.38047i	−0.312834	−	0.0664949i	−0.361653	+	0.932313i	$0.617788\pi$
$432$	0.490400	+	0.131402i	0.0235944	+	0.00632210i
$433$	9.17080	−	17.9987i	0.440721	−	0.864963i	−0.558647	−	0.829406i	$-0.688679\pi$
$433$	9.17080	−	17.9987i	0.440721	−	0.864963i	0.999368	−	0.0355575i	$-0.0113207\pi$
$434$	6.12869	+	4.23564i	0.294186	+	0.203317i
$435$	−0.732134	+	0.507774i	−0.0351032	+	0.0243459i
$436$	−3.94719	−	1.75740i	−0.189036	−	0.0841642i
$437$	10.5315	−	27.4354i	0.503788	−	1.31241i
$438$	−0.0823871	+	0.214626i	−0.00393661	+	0.0102552i
$439$	−9.03790	−	4.02393i	−0.431356	−	0.192052i	0.179561	−	0.983747i	$-0.442532\pi$
$439$	−9.03790	−	4.02393i	−0.431356	−	0.192052i	−0.610917	+	0.791695i	$0.709199\pi$
$440$	−14.8362	+	10.2897i	−0.707286	+	0.490540i
$441$	−1.20712	+	20.9483i	−0.0574821	+	0.997536i
$442$	−0.000527475		0.00103523i	−2.50894e−5		4.92408e-5i
$443$	7.74261	+	2.07463i	0.367863	+	0.0985685i	0.438015	−	0.898968i	$-0.355682\pi$
$443$	7.74261	+	2.07463i	0.367863	+	0.0985685i	−0.0701521	+	0.997536i	$0.522348\pi$
$444$	−0.0933609	−	0.0198445i	−0.00443071	−	0.000941777i
$445$	−1.48400	−	2.39874i	−0.0703483	−	0.113711i
$446$	−3.52750	−	16.5956i	−0.167032	−	0.785823i
$447$	−0.154727	−	0.303670i	−0.00731835	−	0.0143631i
$448$	−0.0689673	+	0.513536i	−0.00325840	+	0.0242623i
$449$			3.52087i			0.166160i	0.996543	+	0.0830800i	$0.0264757\pi$
$449$			3.52087i			0.166160i	−0.996543	+	0.0830800i	$0.973524\pi$
$450$	−7.69735	+	5.69298i	−0.362857	+	0.268370i
$451$	10.3944	+	6.00124i	0.489455	+	0.282587i
$452$	13.8755	−	17.1348i	0.652650	−	0.805955i
$453$	−0.270360	−	0.175574i	−0.0127026	−	0.00824917i
$454$	−3.68397	+	11.3381i	−0.172897	+	0.532123i
$455$	3.22929	−	1.24572i	0.151392	−	0.0584001i
$456$	−0.230262	−	0.708674i	−0.0107830	−	0.0331867i
$457$	−0.802653	+	2.99554i	−0.0375465	+	0.140125i	−0.982155	−	0.188075i	$-0.939775\pi$
$457$	−0.802653	+	2.99554i	−0.0375465	+	0.140125i	0.944608	+	0.328200i	$0.106442\pi$
$458$	3.14226	+	4.83866i	0.146828	+	0.226096i
$459$	0.000373624	0	0.000839173i	1.74393e−5	0	3.91692e-5i
$460$	13.9138	−	7.63129i	0.648736	−	0.355811i
$461$	14.6393	+	20.1493i	0.681821	+	0.938446i	0.999954	−	0.00960024i	$-0.00305590\pi$
$461$	14.6393	+	20.1493i	0.681821	+	0.938446i	−0.318133	+	0.948046i	$0.603056\pi$
$462$	−0.0985236	+	0.275940i	−0.00458373	+	0.0128379i
$463$	−10.3501	+	1.63929i	−0.481008	+	0.0761842i	−0.392230	−	0.919867i	$-0.628296\pi$
$463$	−10.3501	+	1.63929i	−0.481008	+	0.0761842i	−0.0887782	+	0.996051i	$0.528296\pi$
$464$	−5.65273	+	12.6962i	−0.262421	+	0.589408i
$465$	−0.316935	−	0.367908i	−0.0146975	−	0.0170613i
$466$	−0.0743087	+	0.0330844i	−0.00344229	+	0.00153260i
$467$	−0.984172	−	18.7791i	−0.0455421	−	0.868994i	−0.921922	−	0.387375i	$-0.873382\pi$
$467$	−0.984172	−	18.7791i	−0.0455421	−	0.868994i	0.876380	−	0.481620i	$-0.159951\pi$
$468$	1.97417	+	1.97417i	0.0912562	+	0.0912562i
$469$	0.964083	−	5.12728i	0.0445172	−	0.236756i
$470$	−0.0740966	−	0.0774202i	−0.00341782	−	0.00357113i
$471$	1.14966	−	0.244369i	0.0529738	−	0.0112599i
$472$	2.33512	+	0.122378i	0.107483	+	0.00563292i
$473$	25.1988	+	20.4056i	1.15864	+	0.938252i
$474$	−0.178247	−	0.308733i	−0.00818715	−	0.0141806i
$475$	−30.8705	−	11.5501i	−1.41644	−	0.529957i
$476$	0.0111827	−	0.00681286i	0.000512560	−	0.000312267i
$477$	14.6836	+	2.32566i	0.672317	+	0.106485i
$478$	6.10210	−	9.39641i	0.279104	−	0.429782i
$479$	−25.9607	−	28.8323i	−1.18618	−	1.31738i	−0.937167	−	0.348881i	$-0.886562\pi$
$479$	−25.9607	−	28.8323i	−1.18618	−	1.31738i	−0.249010	−	0.968501i	$-0.580105\pi$
$480$	0.237261	−	0.579752i	0.0108294	−	0.0264620i
$481$	−0.529129	−	0.476430i	−0.0241262	−	0.0217233i
$482$	−0.718939	+	0.718939i	−0.0327468	+	0.0327468i
$483$	0.251516	−	0.523804i	0.0114444	−	0.0238339i
$484$	−1.29533	+	1.78286i	−0.0588784	+	0.0810392i
$485$	−3.99567	+	31.3795i	−0.181434	+	1.42487i
$486$	−0.844100	+	0.0887185i	−0.0382892	+	0.00402435i
$487$	31.3690	+	12.0414i	1.42146	+	0.545649i	0.943099	−	0.332512i	$-0.107896\pi$
$487$	31.3690	+	12.0414i	1.42146	+	0.545649i	0.478366	+	0.878161i	$0.341229\pi$
$488$	14.9570	−	12.1119i	0.677069	−	0.548280i
$489$	0.546523	−	0.397072i	0.0247146	−	0.0179562i
$490$	9.82926	+	1.83144i	0.444041	+	0.0827358i
$491$	−2.90556	−	2.11101i	−0.131126	−	0.0952686i	0.520289	−	0.853990i	$-0.325824\pi$
$491$	−2.90556	−	2.11101i	−0.131126	−	0.0952686i	−0.651415	+	0.758722i	$0.725824\pi$
$492$	−0.267122	+	0.0139993i	−0.0120428	+	0.000631135i
$493$	−0.0242886	+	0.00650812i	−0.00109391	+	0.000293111i
$494$	0.512210	−	2.40976i	0.0230454	−	0.108420i
$495$	−13.2777	+	19.4960i	−0.596787	+	0.876281i
$496$	−7.20371	−	2.34063i	−0.323456	−	0.105097i
$497$	19.3477	−	10.4399i	0.867864	−	0.468294i
$498$	0.0743958	−	0.469716i	0.00333375	−	0.0210485i
$499$	−29.9009	+	17.2633i	−1.33855	+	0.772812i	−0.986592	−	0.163204i	$-0.947817\pi$
$499$	−29.9009	+	17.2633i	−1.33855	+	0.772812i	−0.351958	+	0.936016i	$0.614484\pi$
$500$	−8.69144	−	15.5323i	−0.388693	−	0.694627i
$501$	0.117810	−	0.204053i	0.00526335	−	0.00911640i
$502$	−10.0360	+	3.85248i	−0.447931	+	0.171944i
$503$	4.14229	−	2.11060i	0.184696	−	0.0941072i	−0.359198	−	0.933262i	$-0.616950\pi$
$503$	4.14229	−	2.11060i	0.184696	−	0.0941072i	0.543893	+	0.839154i	$0.316950\pi$
$504$	4.20198	+	17.7052i	0.187171	+	0.788652i
$505$	10.7561	+	22.3062i	0.478639	+	0.992615i
$506$	−6.70550	+	7.44721i	−0.298096	+	0.331069i
$507$	0.161394	+	0.602331i	0.00716776	+	0.0267504i
$508$	−8.06988	+	5.24064i	−0.358043	+	0.232516i
$509$	0.986814	−	9.38891i	0.0437398	−	0.416156i	−0.950641	−	0.310293i	$-0.899573\pi$
$509$	0.986814	−	9.38891i	0.0437398	−	0.416156i	0.994381	−	0.105863i	$-0.0337605\pi$
$510$	0.000209491	0	6.30232e-5i	9.27642e−6	0	2.79071e-6i
$511$	19.1695	−	2.47302i	0.848008	−	0.109400i
$512$	−2.76203	−	17.4388i	−0.122066	−	0.770692i
$513$	−1.22576	−	1.51369i	−0.0541188	−	0.0668311i
$514$	1.28817	+	12.2561i	0.0568188	+	0.540595i
$515$	−7.92215	−	18.8983i	−0.349091	−	0.832759i
$516$	−0.718665	−	0.0755347i	−0.0316375	−	0.00332523i
$517$	−0.235252	−	0.119867i	−0.0103464	−	0.00527174i
$518$	−0.579028	−	1.97360i	−0.0254410	−	0.0867148i
$519$	0.831697	−	0.270235i	0.0365074	−	0.0118620i
$520$	2.37360	−	1.83740i	0.104089	−	0.0805752i
$521$	−13.5338	+	12.1859i	−0.592926	+	0.533873i	−0.910043	−	0.414514i	$-0.863952\pi$
$521$	−13.5338	+	12.1859i	−0.592926	+	0.533873i	0.317117	+	0.948386i	$0.397285\pi$
$522$	0.810528	−	15.4658i	0.0354759	−	0.676920i
$523$	14.6872	+	38.2614i	0.642226	+	1.67306i	0.735592	+	0.677424i	$0.236904\pi$
$523$	14.6872	+	38.2614i	0.642226	+	1.67306i	−0.0933662	+	0.995632i	$0.529763\pi$
$524$	23.3450			1.01983
$525$	−0.589868	−	0.277096i	−0.0257440	−	0.0120935i
$526$	10.7533			0.468867
$527$	−0.00491127	−	0.0127943i	−0.000213938	−	0.000557328i
$528$	0.0155907	−	0.297489i	0.000678500	−	0.0129466i
$529$	−2.32351	+	2.09210i	−0.101022	+	0.0909608i
$530$	1.98309	−	6.80074i	0.0861399	−	0.295405i
$531$	2.90536	−	0.944009i	0.126082	−	0.0409665i
$532$	−19.1648	+	20.0906i	−0.830901	+	0.871040i
$533$	−1.77792	−	0.905897i	−0.0770104	−	0.0392388i
$534$	−0.0394790	−	0.00414941i	−0.00170843	−	0.000179563i
$535$	29.3596	−	25.2919i	1.26932	−	1.09346i
$536$	−0.472931	−	4.49964i	−0.0204275	−	0.194355i
$537$	0.145746	+	0.179981i	0.00628939	+	0.00776675i
$538$	2.39932	+	15.1487i	0.103442	+	0.653107i
$539$	24.3503	−	3.72701i	1.04884	−	0.160534i
$540$	0.0230664	−	1.05154i	0.000992621	−	0.0452511i
$541$	2.36398	−	22.4918i	0.101635	−	0.966996i	−0.818264	−	0.574842i	$-0.805063\pi$
$541$	2.36398	−	22.4918i	0.101635	−	0.966996i	0.919900	−	0.392154i	$-0.128270\pi$
$542$	1.33882	−	0.869437i	0.0575071	−	0.0373455i
$543$	0.313856	+	1.17133i	0.0134688	+	0.0502664i
$544$	0.0118295	−	0.0131380i	0.000507186	−	0.000563288i
$545$	−1.08061	+	5.97190i	−0.0462882	+	0.255808i
$546$	0.0139562	−	0.0466693i	0.000597269	−	0.00199726i
$547$	−1.71779	+	0.875256i	−0.0734473	+	0.0374232i	−0.490328	−	0.871538i	$-0.663123\pi$
$547$	−1.71779	+	0.875256i	−0.0734473	+	0.0374232i	0.416881	+	0.908961i	$0.363123\pi$
$548$	−14.7099	+	5.64658i	−0.628374	+	0.241210i
$549$	12.5719	−	21.7751i	0.536554	−	0.929339i
$550$	8.41630	+	7.44959i	0.358872	+	0.317651i
$551$	46.1747	−	26.6590i	1.96711	−	1.13571i
$552$	0.0788289	−	0.497706i	0.00335518	−	0.0211838i
$553$	−15.7268	+	25.5146i	−0.668770	+	1.08499i
$554$	−16.7362	−	5.43794i	−0.711055	−	0.231036i
$555$	0.00407860	+	0.134002i	0.000173127	+	0.00568806i
$556$	6.00167	−	28.2356i	0.254528	−	1.19746i
$557$	5.68596	−	1.52355i	0.240922	−	0.0645548i	−0.136338	−	0.990662i	$-0.543533\pi$
$557$	5.68596	−	1.52355i	0.240922	−	0.0645548i	0.377259	+	0.926108i	$0.376867\pi$
$558$	8.42902	−	0.441746i	0.356829	−	0.0187006i
$559$	−4.36111	−	3.16853i	−0.184455	−	0.134015i
$560$	−10.1081	+	1.07924i	−0.427143	+	0.0456061i
$561$	0.000436053	0	0.000316811i	1.84102e−5	0	1.33758e-5i
$562$	−3.60053	+	2.91566i	−0.151879	+	0.122989i
$563$	−14.8493	−	5.70009i	−0.625821	−	0.240230i	0.0247281	−	0.999694i	$-0.492128\pi$
$563$	−14.8493	−	5.70009i	−0.625821	−	0.240230i	−0.650549	+	0.759464i	$0.725461\pi$
$564$	0.00585195		0.000615065i	0.000246412		2.58989e-5i
$565$	−28.0086	−	13.2137i	−1.17833	−	0.555905i
$566$	−3.04594	+	4.19237i	−0.128030	+	0.176219i
$567$	13.4035	+	19.6112i	0.562892	+	0.823593i
$568$	13.4814	−	13.4814i	0.565669	−	0.565669i
$569$	18.8462	+	16.9692i	0.790072	+	0.711384i	0.961798	−	0.273761i	$-0.0882677\pi$
$569$	18.8462	+	16.9692i	0.790072	+	0.711384i	−0.171726	+	0.985145i	$0.554934\pi$
$570$	−0.394478	+	0.244047i	−0.0165229	+	0.0102220i
$571$	18.0577	+	20.0552i	0.755693	+	0.839282i	0.991170	−	0.132598i	$-0.0423319\pi$
$571$	18.0577	+	20.0552i	0.755693	+	0.839282i	−0.235477	+	0.971880i	$0.575665\pi$
$572$	1.78515	−	2.74889i	0.0746409	−	0.114937i
$573$	0.131846	+	0.0208823i	0.00550793	+	0.000872370i
$574$	−2.99895	−	4.92253i	−0.125174	−	0.205462i
$575$	−15.0550	−	16.4373i	−0.627836	−	0.685481i
$576$	0.293524	+	0.508398i	0.0122302	+	0.0211833i
$577$	13.7154	+	11.1065i	0.570979	+	0.462370i	0.870808	−	0.491623i	$-0.163596\pi$
$577$	13.7154	+	11.1065i	0.570979	+	0.462370i	−0.299829	+	0.953993i	$0.596930\pi$
$578$	−10.8443	−	0.568326i	−0.451063	−	0.0236392i
$579$	0.362872	−	0.0771308i	0.0150804	−	0.00320545i
$580$	28.3317	+	5.12659i	1.17641	+	0.212870i
$581$	−37.7246	+	13.2487i	−1.56508	+	0.549649i
$582$	0.314792	+	0.314792i	0.0130485	+	0.0130485i
$583$	−0.913439	−	17.4295i	−0.0378308	−	0.721854i
$584$	15.3129	−	6.81772i	0.633651	−	0.282119i
$585$	2.03476	−	3.35230i	0.0841268	−	0.138600i
$586$	−8.19256	+	18.4008i	−0.338431	+	0.760129i
$587$	−22.2860	+	3.52976i	−0.919842	+	0.145689i	−0.598360	−	0.801227i	$-0.704181\pi$
$587$	−22.2860	+	3.52976i	−0.919842	+	0.145689i	−0.321482	+	0.946916i	$0.604181\pi$
$588$	−0.409887	+	0.365222i	−0.0169035	+	0.0150615i
$589$	17.0803	+	23.5091i	0.703784	+	0.968675i
$590$	−0.271349	−	1.43014i	−0.0111712	−	0.0588778i
$591$	−0.393511	−	0.883839i	−0.0161869	−	0.0363563i
$592$	1.13892	+	1.75379i	0.0468095	+	0.0720803i
$593$	7.76827	−	28.9916i	0.319005	−	1.19054i	−0.601199	−	0.799100i	$-0.705310\pi$
$593$	7.76827	−	28.9916i	0.319005	−	1.19054i	0.920203	−	0.391441i	$-0.128023\pi$
$594$	0.205248	+	0.631687i	0.00842141	+	0.0259184i
$595$	−0.0130270	−	0.0129841i	−0.000534053	−	0.000532296i
$596$	−3.40330	+	10.4743i	−0.139405	+	0.429043i
$597$	−0.512542	−	0.332848i	−0.0209769	−	0.0136226i
$598$	1.04846	−	1.29475i	0.0428749	−	0.0529461i
$599$	0.212550	+	0.122716i	0.00868454	+	0.00501402i	0.504336	−	0.863508i	$-0.331737\pi$
$599$	0.212550	+	0.122716i	0.00868454	+	0.00501402i	−0.495651	+	0.868522i	$0.665071\pi$
$600$	−0.558952	−	0.0836683i	−0.0228191	−	0.00341574i
$601$		−	0.0516122i		−	0.00210530i	−0.999999	−	0.00105265i	$-0.999665\pi$
$601$		−	0.0516122i		−	0.00210530i	0.999999	−	0.00105265i	$-0.000335070\pi$
$602$	−5.92166	−	14.4020i	−0.241349	−	0.586980i
$603$	−2.68349	−	5.26664i	−0.109280	−	0.214474i
$604$	2.16584	+	10.1895i	0.0881270	+	0.414605i
$605$	2.86475	+	1.17239i	0.116469	+	0.0476643i
$606$	0.340900	+	0.0724605i	0.0138481	+	0.00294351i
$607$	15.7457	+	4.21905i	0.639099	+	0.171246i	0.563795	−	0.825915i	$-0.309341\pi$
$607$	15.7457	+	4.21905i	0.639099	+	0.171246i	0.0753037	+	0.997161i	$0.476007\pi$
$608$	−17.0183	+	33.4003i	−0.690184	+	1.35456i
$609$	0.952708	−	0.451381i	0.0386057	−	0.0182909i
$610$	−9.53607	−	7.25313i	−0.386104	−	0.293671i
$611$	0.0401000	+	0.0178537i	0.00162227	+	0.000722282i
$612$	0.00531670	−	0.0138505i	0.000214915	−	0.000559872i
$613$	8.43988	−	21.9866i	0.340883	−	0.888032i	−0.650791	−	0.759257i	$-0.725562\pi$
$613$	8.43988	−	21.9866i	0.340883	−	0.888032i	0.991674	−	0.128774i	$-0.0411043\pi$
$614$	12.6110	+	5.61477i	0.508938	+	0.226594i
$615$	0.108237	+	0.359785i	0.00436456	+	0.0145079i
$616$	19.3059	−	9.14690i	0.777857	−	0.368539i
$617$	−18.8430	+	36.9814i	−0.758590	+	1.48882i	0.110347	+	0.993893i	$0.464804\pi$
$617$	−18.8430	+	36.9814i	−0.758590	+	1.48882i	−0.868937	+	0.494924i	$0.835196\pi$
$618$	−0.278560	−	0.0746401i	−0.0112053	−	0.00300246i
$619$	−32.6605	−	6.94219i	−1.31273	−	0.279030i	−0.502216	−	0.864742i	$-0.667482\pi$
$619$	−32.6605	−	6.94219i	−1.31273	−	0.279030i	−0.810519	+	0.585712i	$0.800815\pi$
$620$	−1.16471	+	15.6485i	−0.0467758	+	0.628460i
$621$	−0.273859	−	1.28840i	−0.0109896	−	0.0517019i
$622$	2.84420	+	5.58205i	0.114042	+	0.223820i
$623$	1.26917	+	3.08673i	0.0508482	+	0.123667i
$624$			0.0495254i			0.00198260i
$625$	−18.2917	+	17.0415i	−0.731669	+	0.681660i
$626$	−9.78828	−	5.65127i	−0.391218	−	0.225870i
$627$	−0.719228	+	0.888173i	−0.0287232	+	0.0354702i
$628$	−31.8534	−	20.6858i	−1.27109	−	0.825455i
$629$	−0.00116918	+	0.00359838i	−4.66184e−5	+	0.000143477i
$630$	10.0848	−	5.15941i	0.401789	−	0.205556i
$631$	−7.10523	−	21.8676i	−0.282855	−	0.870537i	−0.987034	−	0.160514i	$-0.948685\pi$
$631$	−7.10523	−	21.8676i	−0.282855	−	0.870537i	0.704179	−	0.710023i	$-0.251315\pi$
$632$	−6.72736	+	25.1068i	−0.267600	+	0.998696i
$633$	0.622846	+	0.959098i	0.0247559	+	0.0381207i
$634$	5.54608	+	12.4567i	0.220263	+	0.494719i
$635$	9.84312	+	9.26163i	0.390612	+	0.367536i
$636$	0.228629	+	0.314681i	0.00906575	+	0.0124779i
$637$	−4.01027	+	0.830635i	−0.158893	+	0.0329110i
$638$	−17.9578	+	2.84424i	−0.710957	+	0.112605i
$639$	10.1310	−	22.7547i	0.400778	−	0.900161i
$640$	−23.1956	+	9.72355i	−0.916885	+	0.384357i
$641$	24.0230	−	10.6957i	0.948853	−	0.422456i	0.126839	−	0.991923i	$-0.459517\pi$
$641$	24.0230	−	10.6957i	0.948853	−	0.422456i	0.822014	+	0.569467i	$0.192850\pi$
$642$	−0.0285421	−	0.544616i	−0.00112647	−	0.0214943i
$643$	−18.6442	−	18.6442i	−0.735254	−	0.735254i	0.236402	−	0.971655i	$-0.424032\pi$
$643$	−18.6442	−	18.6442i	−0.735254	−	0.735254i	−0.971655	+	0.236402i	$0.924032\pi$
$644$	−17.7159	+	6.22174i	−0.698105	+	0.245171i
$645$	0.136757	+	1.00574i	0.00538478	+	0.0396009i
$646$	−0.0128052	+	0.00272183i	−0.000503813	+	0.000107089i
$647$	−14.8219	−	0.776781i	−0.582707	−	0.0305384i	−0.241295	−	0.970452i	$-0.577572\pi$
$647$	−14.8219	−	0.776781i	−0.582707	−	0.0305384i	−0.341413	+	0.939913i	$0.610905\pi$
$648$	16.0092	+	12.9640i	0.628902	+	0.509275i
$649$	−1.79320	−	3.10592i	−0.0703894	−	0.121918i
$650$	−1.46211	−	1.16357i	−0.0573486	−	0.0456389i
$651$	0.298935	+	0.490677i	0.0117162	+	0.0192311i
$652$	−21.5610	−	3.41492i	−0.844393	−	0.133739i
$653$	−1.34699	+	2.07418i	−0.0527117	+	0.0811689i	−0.864044	−	0.503416i	$-0.832076\pi$
$653$	−1.34699	+	2.07418i	−0.0527117	+	0.0811689i	0.811332	+	0.584585i	$0.198743\pi$
$654$	0.0571504	+	0.0634719i	0.00223476	+	0.00248195i
$655$	−7.79009	−	31.8515i	−0.304384	−	1.24454i
$656$	4.35516	+	3.92140i	0.170040	+	0.153105i
$657$	15.4846	−	15.4846i	0.604112	−	0.604112i
$658$	0.0715475	+	0.104684i	0.00278921	+	0.00408102i
$659$	20.7720	−	28.5901i	0.809161	−	1.11371i	−0.182292	−	0.983245i	$-0.558352\pi$
$659$	20.7720	−	28.5901i	0.809161	−	1.11371i	0.991452	−	0.130470i	$-0.0416485\pi$
$660$	−0.606332	+	0.115043i	−0.0236014	+	0.00447804i
$661$	−12.7496	+	1.34004i	−0.495903	+	0.0521215i	−0.349179	−	0.937056i	$-0.613539\pi$
$661$	−12.7496	+	1.34004i	−0.495903	+	0.0521215i	−0.146724	+	0.989178i	$0.546873\pi$
$662$	−5.69924	−	2.18773i	−0.221507	−	0.0850286i
$663$	−6.96378e−5	0	5.63916e-5i	−2.70451e−6	0	2.19007e-6i
$664$	−28.0524	+	20.3812i	−1.08864	+	0.790945i
$665$	33.8065	+	19.4440i	1.31096	+	0.754007i
$666$	−1.88524	−	1.36971i	−0.0730516	−	0.0530751i
$667$	36.0073	−	1.88706i	1.39421	−	0.0730673i
$668$	−7.35449	+	1.97063i	−0.284554	+	0.0762460i
$669$	0.272054	−	1.27991i	0.0105182	−	0.0494842i
$670$	−2.65097	+	0.951450i	−0.102416	+	0.0367577i
$671$	−28.0738	−	9.12174i	−1.08378	−	0.352141i
$672$	−0.388915	+	0.630962i	−0.0150027	+	0.0243399i
$673$	4.67041	−	29.4878i	0.180031	−	1.13667i	−0.717773	−	0.696277i	$-0.754839\pi$
$673$	4.67041	−	29.4878i	0.180031	−	1.13667i	0.897804	−	0.440394i	$-0.145161\pi$
$674$	4.18310	−	2.41511i	0.161127	−	0.0930267i
$675$	−1.44240	+	0.319422i	−0.0555180	+	0.0122946i
$676$	10.0753	−	17.4510i	0.387512	−	0.671191i
$677$	−42.5152	+	16.3200i	−1.63399	+	0.627230i	−0.990411	−	0.138149i	$-0.955885\pi$
$677$	−42.5152	+	16.3200i	−1.63399	+	0.627230i	−0.643579	+	0.765379i	$0.722551\pi$
$678$	−0.388337	+	0.197868i	−0.0149140	+	0.00759907i
$679$	10.7236	−	35.8595i	0.411533	−	1.37616i
$680$	−0.0140498	−	0.00755133i	−0.000538785	−	0.000289580i
$681$	−0.615223	+	0.683274i	−0.0235754	+	0.0261831i
$682$	−2.56469	−	9.57155i	−0.0982071	−	0.366514i
$683$	28.8396	−	18.7286i	1.10352	−	0.716631i	0.141585	−	0.989926i	$-0.454780\pi$
$683$	28.8396	−	18.7286i	1.10352	−	0.716631i	0.961930	+	0.273295i	$0.0881135\pi$
$684$	−3.28822	+	31.2854i	−0.125728	+	1.19623i
$685$	12.6127	+	18.1856i	0.481906	+	0.694837i
$686$	−11.1206	−	4.03590i	−0.424586	−	0.154092i
$687$	0.0696072	+	0.439482i	0.00265568	+	0.0167673i
$688$	9.96345	+	12.3038i	0.379853	+	0.469079i
$689$	0.303302	+	2.88573i	0.0115549	+	0.109937i
$690$	−0.312619	+	0.0259402i	−0.0119012	+	0.000987528i
$691$	−29.6140	−	3.11256i	−1.12657	−	0.118407i	−0.477140	−	0.878827i	$-0.658326\pi$
$691$	−29.6140	−	3.11256i	−1.12657	−	0.118407i	−0.649432	+	0.760420i	$0.724993\pi$
$692$	−25.1789	−	12.8293i	−0.957159	−	0.487697i
$693$	19.2643	−	20.1949i	0.731791	−	0.767141i
$694$	2.09555	−	0.680886i	0.0795460	−	0.0258461i
$695$	−40.5269	+	1.23351i	−1.53727	+	0.0467899i
$696$	0.679422	−	0.611755i	0.0257534	−	0.0231885i
$697$	−0.000554939		0.0105889i	−2.10198e−5		0.000401082i
$698$	−1.15194	−	3.00090i	−0.0436015	−	0.113586i
$699$	−0.00627332			−0.000237279
$700$	7.14678	+	19.8100i	0.270123	+	0.748747i
$701$	−45.8591			−1.73208			−0.866038	−	0.499979i	$-0.833341\pi$
$701$	−45.8591			−1.73208			−0.866038	+	0.499979i	$0.833341\pi$
$702$	−0.0395718	−	0.103088i	−0.00149354	−	0.00389081i
$703$	0.419870	−	8.01159i	0.0158357	−	0.302163i
$704$	0.512168	−	0.461159i	0.0193031	−	0.0173806i
$705$	−0.00279195	−	0.00777905i	−0.000105151	−	0.000292976i
$706$	−4.05690	+	1.31817i	−0.152684	+	0.0496099i
$707$	−8.24894	−	28.1162i	−0.310233	−	1.05742i
$708$	0.0712155	+	0.0362861i	0.00267644	+	0.00136372i
$709$	23.4280	+	2.46238i	0.879856	+	0.0924766i	0.533673	−	0.845691i	$-0.320811\pi$
$709$	23.4280	+	2.46238i	0.879856	+	0.0924766i	0.346182	+	0.938167i	$0.387478\pi$
$710$	−10.1460	−	6.15835i	−0.380773	−	0.231119i
$711$	3.54954	+	33.7716i	0.133118	+	1.26653i
$712$	1.82146	+	2.24932i	0.0682622	+	0.0842968i
$713$	3.07414	+	19.4093i	0.115127	+	0.726885i
$714$	−0.000256720	0	3.31189e-5i	−9.60749e−6	0	1.23944e-6i
$715$	−4.34623	−	1.51834i	−0.162540	−	0.0567826i
$716$	0.782269	−	7.44279i	0.0292348	−	0.278150i
$717$	0.724686	−	0.470616i	0.0270639	−	0.0175755i
$718$	−0.663273	−	2.47537i	−0.0247531	−	0.0923799i
$719$	23.8551	−	26.4938i	0.889645	−	0.988051i	−0.110338	−	0.993894i	$-0.535193\pi$
$719$	23.8551	−	26.4938i	0.889645	−	0.988051i	0.999983	+	0.00584290i	$0.00185986\pi$
$720$	−8.32059	+	7.96339i	−0.310090	+	0.296778i
$721$	5.59880	+	23.5907i	0.208510	+	0.878565i
$722$	13.9191	−	7.09211i	0.518013	−	0.263941i
$723$	−0.0732060	+	0.0281011i	−0.00272256	+	0.00104509i
$724$	19.5930	−	33.9361i	0.728169	−	1.26123i
$725$	−2.45951	−	40.3659i	−0.0913439	−	1.49915i
$726$	0.0377261	−	0.0217812i	0.00140015	−	0.000808375i
$727$	−5.37689	+	33.9484i	−0.199418	+	1.25907i	0.661350	+	0.750077i	$0.269984\pi$
$727$	−5.37689	+	33.9484i	−0.199418	+	1.25907i	−0.860768	+	0.508998i	$0.830016\pi$
$728$	−3.12562	+	1.68657i	−0.115843	+	0.0625083i
$729$	25.5540	+	8.30299i	0.946443	+	0.307518i
$730$	−6.38733	−	8.25133i	−0.236406	−	0.305395i
$731$	−0.00595568	+	0.0280193i	−0.000220279	+	0.00103633i
$732$	0.635438	−	0.170265i	0.0234865	−	0.00629318i
$733$	4.40918	−	0.231075i	0.162857	−	0.00853496i	0.0292667	−	0.999572i	$-0.490683\pi$
$733$	4.40918	−	0.231075i	0.162857	−	0.00853496i	0.133590	+	0.991037i	$0.457349\pi$
$734$	−11.2474	−	8.17169i	−0.415148	−	0.301623i
$735$	0.635079	+	0.437370i	0.0234253	+	0.0161326i
$736$	−20.5088	+	14.9005i	−0.755965	+	0.549240i
$737$	−5.39288	+	4.36707i	−0.198649	+	0.160863i
$738$	−6.09685	−	2.34036i	−0.224428	−	0.0861498i
$739$	9.96776	−	1.04765i	0.366670	−	0.0385386i	0.0805980	−	0.996747i	$-0.474317\pi$
$739$	9.96776	−	1.04765i	0.366670	−	0.0385386i	0.286072	+	0.958208i	$0.407650\pi$
$740$	2.96872	−	3.15511i	0.109132	−	0.115984i
$741$	0.111680	−	0.153714i	0.00410267	−	0.00564683i
$742$	−3.62815	+	7.55595i	−0.133194	+	0.277388i
$743$	−6.77097	+	6.77097i	−0.248403	+	0.248403i	−0.820315	−	0.571912i	$-0.806202\pi$
$743$	−6.77097	+	6.77097i	−0.248403	+	0.248403i	0.571912	+	0.820315i	$0.306202\pi$
$744$	0.370292	+	0.333413i	0.0135756	+	0.0122235i
$745$	15.4266	+	1.14819i	0.565186	+	0.0420664i
$746$	1.57658	+	1.75096i	0.0577225	+	0.0641074i
$747$	−24.6723	+	37.9920i	−0.902713	+	1.39006i
$748$	−0.0172028	−	0.00272465i	−0.000628996	−	9.96232e-5i
$749$	−39.1567	+	23.8554i	−1.43076	+	0.871659i
$750$	0.0320719	+	0.350371i	0.00117110	+	0.0127937i
$751$	15.4883	+	26.8266i	0.565177	+	0.978916i	0.997033	+	0.0769731i	$0.0245255\pi$
$751$	15.4883	+	26.8266i	0.565177	+	0.978916i	−0.431856	+	0.901943i	$0.642141\pi$
$752$	−0.100188	−	0.0811304i	−0.00365347	−	0.00295852i
$753$	−0.827948	−	0.0433909i	−0.0301721	−	0.00158125i
$754$	2.95665	−	0.628455i	0.107675	−	0.0228870i
$755$	13.1796	−	6.35522i	0.479656	−	0.231290i
$756$	−0.229973	+	1.22307i	−0.00836403	+	0.0444824i
$757$	−4.48925	−	4.48925i	−0.163164	−	0.163164i	0.620803	−	0.783967i	$-0.286807\pi$
$757$	−4.48925	−	4.48925i	−0.163164	−	0.163164i	−0.783967	+	0.620803i	$0.786807\pi$
$758$	−0.141837	−	2.70640i	−0.00515174	−	0.0983010i
$759$	−0.706054	+	0.314355i	−0.0256281	+	0.0114104i
$760$	32.9200	+	7.75564i	1.19413	+	0.281327i
$761$	−18.9521	+	42.5670i	−0.687012	+	1.54305i	0.145688	+	0.989331i	$0.453460\pi$
$761$	−18.9521	+	42.5670i	−0.687012	+	1.54305i	−0.832700	+	0.553724i	$0.813206\pi$
$762$	0.187865	−	0.0297549i	0.00680564	−	0.00107791i
$763$	2.41459	−	6.76266i	0.0874141	−	0.244825i
$764$	−2.53549	−	3.48980i	−0.0917308	−	0.126257i
$765$	−0.0206715	−	0.00263218i	−0.000747379	−	9.51666e-5i
$766$	0.236519	+	0.531231i	0.00854579	+	0.0191942i
$767$	0.324736	+	0.500049i	0.0117255	+	0.0180557i
$768$	−0.0966065	+	0.360540i	−0.00348599	+	0.0130099i
$769$	3.45276	+	10.6265i	0.124510	+	0.383201i	0.993811	−	0.111081i	$-0.0354312\pi$
$769$	3.45276	+	10.6265i	0.124510	+	0.383201i	−0.869302	+	0.494282i	$0.835431\pi$
$770$	−8.38633	−	10.3214i	−0.302222	−	0.371959i
$771$	−0.293704	+	0.903926i	−0.0105775	+	0.0325541i
$772$	−10.0540	−	6.52913i	−0.361851	−	0.234989i
$773$	−6.04651	+	7.46682i	−0.217478	+	0.268563i	−0.874196	−	0.485573i	$-0.838611\pi$
$773$	−6.04651	+	7.46682i	−0.217478	+	0.268563i	0.656718	+	0.754136i	$0.271944\pi$
$774$	−15.2789	−	8.82126i	−0.549188	−	0.317074i
$775$	21.7392	−	3.63273i	0.780896	−	0.130491i
$776$		−	32.4590i		−	1.16521i
$777$	0.0211138	−	0.157215i	0.000757453	−	0.00564006i
$778$	−2.83352	−	5.56110i	−0.101587	−	0.199375i
$779$	−4.67453	−	21.9919i	−0.167482	−	0.787942i
$780$	0.0996635	−	0.0243753i	0.00356853	−	0.000872775i
$781$	−28.6029	−	6.07974i	−1.02349	−	0.217550i
$782$	−0.00855142	−	0.00229135i	−0.000305798	−	8.19383e-5i
$783$	1.08495	−	2.12933i	0.0387728	−	0.0760959i
$784$	12.0081	+	0.691954i	0.428860	+	0.0247126i
$785$	−17.5941	+	50.3630i	−0.627959	+	1.79753i
$786$	−0.421575	−	0.187697i	−0.0150371	−	0.00669493i
$787$	6.62709	−	17.2641i	0.236230	−	0.615400i	−0.763300	−	0.646044i	$-0.776422\pi$
$787$	6.62709	−	17.2641i	0.236230	−	0.615400i	0.999530	+	0.0306434i	$0.00975563\pi$
$788$	−11.2039	+	29.1872i	−0.399123	+	1.03975i
$789$	0.757635	+	0.337321i	0.0269725	+	0.0120089i
$790$	16.1769	+	0.354855i	0.575550	+	0.0126252i
$791$	30.1445	+	20.8334i	1.07182	+	0.740749i
$792$	10.9884	−	21.5659i	0.390454	−	0.766309i
$793$	4.74024	+	1.27014i	0.168331	+	0.0451042i
$794$	3.94738	+	0.839041i	0.140087	+	0.0297765i
$795$	0.353053	−	0.416945i	0.0125215	−	0.0147875i
$796$	4.10596	+	19.3170i	0.145532	+	0.684673i
$797$	10.6238	+	20.8503i	0.376313	+	0.738556i	0.999037	−	0.0438861i	$-0.0139739\pi$
$797$	10.6238	+	20.8503i	0.376313	+	0.738556i	−0.622724	+	0.782442i	$0.713974\pi$
$798$	0.507620	−	0.208718i	0.0179695	−	0.00738854i
$799$		0	0.000233253i		0	8.25188e-6i
$800$	16.9071	+	22.8597i	0.597755	+	0.808211i
$801$	3.27467	+	1.89063i	0.115705	+	0.0668023i
$802$	1.48122	−	1.82916i	0.0523039	−	0.0645899i
$803$	−21.5612	−	14.0020i	−0.760877	−	0.494119i
$804$	0.0477898	−	0.147082i	0.00168542	−	0.00518718i
$805$	14.4005	+	22.0951i	0.507552	+	0.778750i
$806$	0.509076	+	1.56677i	0.0179314	+	0.0551873i
$807$	−0.306154	+	1.14258i	−0.0107771	+	0.0402207i
$808$	−13.8397	−	21.3113i	−0.486880	−	0.749729i
$809$	−8.98201	−	20.1739i	−0.315791	−	0.709277i	0.684005	−	0.729477i	$-0.260236\pi$
$809$	−8.98201	−	20.1739i	−0.315791	−	0.709277i	−0.999796	+	0.0201997i	$0.993570\pi$
$810$	5.47163	−	11.5980i	0.192253	−	0.407513i
$811$	11.7193	+	16.1302i	0.411519	+	0.566408i	0.963588	−	0.267391i	$-0.0861614\pi$
$811$	11.7193	+	16.1302i	0.411519	+	0.566408i	−0.552069	+	0.833799i	$0.686161\pi$
$812$	−32.0832	−	11.4552i	−1.12590	−	0.401999i
$813$	0.121601	−	0.0192597i	0.00426473	−	0.000675467i
$814$	−1.11273	+	2.49922i	−0.0390010	+	0.0875977i
$815$	2.53552	+	30.5569i	0.0888156	+	1.07036i
$816$	0.000240420	0	0.000107042i	8.41639e−6	0	3.74722e-6i
$817$	−3.17882	−	60.6555i	−0.111213	−	2.12207i
$818$	−13.8539	−	13.8539i	−0.484389	−	0.484389i
$819$	−3.02259	+	3.52042i	−0.105618	+	0.123013i
$820$	5.74780	−	10.6942i	0.200722	−	0.373458i
$821$	39.4208	−	8.37915i	1.37580	−	0.292434i	0.540088	−	0.841609i	$-0.318391\pi$
$821$	39.4208	−	8.37915i	1.37580	−	0.292434i	0.835708	+	0.549174i	$0.185058\pi$
$822$	0.311037	+	0.0163008i	0.0108487	+	0.000568554i
$823$	−1.42474	−	1.15373i	−0.0496633	−	0.0402165i	0.604167	−	0.796857i	$-0.293506\pi$
$823$	−1.42474	−	1.15373i	−0.0496633	−	0.0402165i	−0.653831	+	0.756641i	$0.726839\pi$
$824$	10.5134	+	18.2097i	0.366251	+	0.634365i
$825$	0.359292	+	0.788879i	0.0125090	+	0.0274652i
$826$	0.0406087	+	1.72187i	0.00141296	+	0.0599116i
$827$	19.8131	+	3.13808i	0.688968	+	0.109122i	0.491095	−	0.871106i	$-0.336597\pi$
$827$	19.8131	+	3.13808i	0.688968	+	0.109122i	0.197873	+	0.980228i	$0.436597\pi$
$828$	−11.5864	+	17.8415i	−0.402655	+	0.620034i
$829$	7.42726	+	8.24881i	0.257959	+	0.286493i	0.858188	−	0.513336i	$-0.171590\pi$
$829$	7.42726	+	8.24881i	0.257959	+	0.286493i	−0.600229	+	0.799829i	$0.704924\pi$
$830$	16.4732	+	13.9489i	0.571794	+	0.484173i
$831$	−1.00859	−	0.908134i	−0.0349874	−	0.0315028i
$832$	−0.0810188	+	0.0810188i	−0.00280882	+	0.00280882i
$833$	0.0126999	+	0.0176725i	0.000440026	+	0.000612315i
$834$	−0.335400	+	0.461638i	−0.0116139	+	0.0159852i
$835$	5.14285	+	9.37675i	0.177976	+	0.324496i
$836$	36.7288	−	3.86035i	1.27029	−	0.133513i
$837$	1.21596	+	0.466762i	0.0420296	+	0.0161337i
$838$	−3.08681	+	2.49965i	−0.106632	+	0.0863490i
$839$	−14.2530	+	10.3554i	−0.492069	+	0.357509i	−0.805980	−	0.591943i	$-0.798361\pi$
$839$	−14.2530	+	10.3554i	−0.492069	+	0.357509i	0.313910	+	0.949453i	$0.398361\pi$
$840$	0.636339	+	0.205601i	0.0219558	+	0.00709390i
$841$	29.4630	+	21.4062i	1.01597	+	0.738143i
$842$	18.2855	−	0.958304i	0.630161	−	0.0330253i
$843$	−0.345140	+	0.0924801i	−0.0118873	+	0.00318518i
$844$	7.68331	−	36.1471i	0.264470	−	1.24424i
$845$	−27.1719	−	7.92329i	−0.934740	−	0.272569i
$846$	0.136629	+	0.0443933i	0.00469739	+	0.00152627i
$847$	−3.11779	−	1.92176i	−0.107129	−	0.0660323i
$848$	1.33313	−	8.41703i	0.0457798	−	0.289042i
$849$	−0.346115	+	0.199830i	−0.0118786	+	0.00685813i
$850$	−0.00248838	+	0.00961266i	−8.53506e−5	+	0.000329712i
$851$	2.71267	−	4.69848i	0.0929891	−	0.161062i
$852$	0.608404	−	0.233545i	0.0208436	−	0.00800110i
$853$	27.1996	−	13.8589i	0.931297	−	0.474519i	0.0785886	−	0.996907i	$-0.474959\pi$
$853$	27.1996	−	13.8589i	0.931297	−	0.474519i	0.852708	+	0.522388i	$0.174959\pi$
$854$	9.73142	+	10.3083i	0.333002	+	0.352744i
$855$	43.7824	−	5.95337i	1.49733	−	0.203601i
$856$	−26.6068	+	29.5499i	−0.909402	+	1.00999i
$857$	−7.00877	−	26.1571i	−0.239415	−	0.893509i	−0.976109	−	0.217283i	$-0.930281\pi$
$857$	−7.00877	−	26.1571i	−0.239415	−	0.893509i	0.736694	−	0.676227i	$-0.236386\pi$
$858$	−0.0543386	+	0.0352879i	−0.00185509	+	0.00120471i
$859$	0.100406	−	0.955297i	0.00342580	−	0.0325943i	−0.992675	−	0.120812i	$-0.961450\pi$
$859$	0.100406	−	0.955297i	0.00342580	−	0.0325943i	0.996101	+	0.0882173i	$0.0281170\pi$
$860$	19.8561	−	26.1058i	0.677087	−	0.890201i
$861$	−0.0568791	−	0.440896i	−0.00193844	−	0.0150257i
$862$	−0.663482	−	4.18906i	−0.0225983	−	0.142680i
$863$	−12.6776	−	15.6555i	−0.431551	−	0.532921i	0.514262	−	0.857633i	$-0.328066\pi$
$863$	−12.6776	−	15.6555i	−0.431551	−	0.532921i	−0.945813	+	0.324712i	$0.894732\pi$
$864$	0.175628	+	1.67098i	0.00597497	+	0.0568481i
$865$	−9.10199	+	38.6347i	−0.309477	+	1.31362i
$866$	12.8329	+	1.34879i	0.436078	+	0.0458337i
$867$	−0.746218	−	0.380217i	−0.0253429	−	0.0129128i
$868$	4.38127	−	18.0425i	0.148710	−	0.612402i
$869$	37.9149	−	12.3193i	1.28617	−	0.417903i
$870$	−0.470408	−	0.320369i	−0.0159483	−	0.0108615i
$871$	0.857341	−	0.771953i	0.0290499	−	0.0261566i
$872$	0.325915	−	6.21883i	0.0110369	−	0.210596i
$873$	−15.1968	−	39.5891i	−0.514335	−	1.33989i
$874$	18.7719			0.634969
$875$	24.6435	−	16.3614i	0.833104	−	0.553117i
$876$	0.572948			0.0193581
$877$	−18.6776	−	48.6569i	−0.630699	−	1.64303i	−0.758845	−	0.651271i	$-0.774236\pi$
$877$	−18.6776	−	48.6569i	−0.630699	−	1.64303i	0.128146	−	0.991755i	$-0.459097\pi$
$878$	0.330740	−	6.31089i	0.0111619	−	0.212982i
$879$	−1.15443	+	1.03945i	−0.0389379	+	0.0350599i
$880$	11.1756	+	7.61110i	0.376730	+	0.256570i
$881$	−1.59813	+	0.519265i	−0.0538425	+	0.0174945i	−0.335814	−	0.941928i	$-0.609012\pi$
$881$	−1.59813	+	0.519265i	−0.0538425	+	0.0174945i	0.281972	+	0.959423i	$0.409012\pi$
$882$	−12.7688	+	4.07554i	−0.429948	+	0.137231i
$883$	10.8356	+	5.52102i	0.364647	+	0.185797i	0.626708	−	0.779254i	$-0.284402\pi$
$883$	10.8356	+	5.52102i	0.364647	+	0.185797i	−0.262061	+	0.965051i	$0.584402\pi$
$884$	0.00287975		0.000302674i	9.68564e−5		1.01800e-5i
$885$	0.0257439	−	0.109274i	0.000865371	−	0.00367319i
$886$	0.535213	+	5.09221i	0.0179808	+	0.171076i
$887$	10.4114	+	12.8570i	0.349580	+	0.431696i	0.921359	−	0.388712i	$-0.127080\pi$
$887$	10.4114	+	12.8570i	0.349580	+	0.431696i	−0.571779	+	0.820408i	$0.693747\pi$
$888$	−0.0215199	−	0.135871i	−0.000722160	−	0.00455954i
$889$	−9.70203	−	12.7122i	−0.325396	−	0.426355i
$890$	1.09077	−	1.43409i	0.0365627	−	0.0480709i
$891$	3.30261	−	31.4223i	0.110642	−	1.05269i
$892$	−35.4621	+	23.0294i	−1.18736	+	0.771080i
$893$	0.128008	+	0.477732i	0.00428362	+	0.0159867i
$894$	0.145673	−	0.161787i	0.00487204	−	0.00541095i
$895$	−10.4158	+	1.41631i	−0.348163	+	0.0473419i
$896$	28.9550	−	6.87189i	0.967318	−	0.229574i
$897$	0.114485	−	0.0583332i	0.00382256	−	0.00194769i
$898$	−2.09966	+	0.805985i	−0.0700667	+	0.0268961i
$899$	−17.8268	+	30.8770i	−0.594558	+	1.02981i
$900$	20.1205	+	12.8247i	0.670683	+	0.427490i
$901$	0.0133532	−	0.00770945i	0.000444858	−	0.000256839i
$902$	−1.19937	+	7.57250i	−0.0399345	+	0.252137i
$903$	0.0345590	−	1.20046i	0.00115005	−	0.0399488i
$904$	30.2225	+	9.81989i	1.00519	+	0.326605i
$905$	−52.8399	−	15.4081i	−1.75646	−	0.512181i
$906$	0.0428132	−	0.201420i	0.00142237	−	0.00669175i
$907$	1.23627	−	0.331257i	0.0410496	−	0.0109992i	−0.238236	−	0.971207i	$-0.576569\pi$
$907$	1.23627	−	0.331257i	0.0410496	−	0.0109992i	0.279285	+	0.960208i	$0.409902\pi$
$908$	29.6704	−	1.55496i	0.984647	−	0.0516032i
$909$	−26.8575	−	19.5131i	−0.890807	−	0.647209i
$910$	1.48212	+	1.64062i	0.0491318	+	0.0543860i
$911$	−31.4927	+	22.8808i	−1.04340	+	0.758075i	−0.970946	−	0.239297i	$-0.923083\pi$
$911$	−31.4927	+	22.8808i	−1.04340	+	0.758075i	−0.0724537	+	0.997372i	$0.523083\pi$
$912$	−0.433668	+	0.351177i	−0.0143602	+	0.0116286i
$913$	49.6499	+	19.0588i	1.64317	+	0.630755i
$914$	−1.97013	+	0.207069i	−0.0651660	+	0.00684922i
$915$	−0.444349	−	0.810164i	−0.0146897	−	0.0267832i
$916$	8.45158	−	11.6326i	0.279248	−	0.384352i
$917$	2.94347	+	38.6861i	0.0972019	+	1.27753i
$918$	−0.000414911	0	0.000414911i	−1.36941e−5	0	1.36941e-5i
$919$	11.4703	+	10.3279i	0.378372	+	0.340687i	0.836271	−	0.548317i	$-0.184731\pi$
$919$	11.4703	+	10.3279i	0.378372	+	0.340687i	−0.457899	+	0.889004i	$0.651398\pi$
$920$	17.4548	+	14.7801i	0.575469	+	0.487285i
$921$	0.712389	+	0.791188i	0.0234740	+	0.0260705i
$922$	−8.66481	+	13.3426i	−0.285360	+	0.439417i
$923$	4.80162	+	0.760502i	0.158047	+	0.0250322i
$924$	0.730018	−	0.0172168i	0.0240158	−	0.000566390i
$925$	−5.29542	−	2.99763i	−0.174112	−	0.0985613i
$926$	−3.34689	−	5.79698i	−0.109986	−	0.190501i
$927$	21.3483	+	17.2875i	0.701171	+	0.567797i
$928$	−45.9305	−	2.40711i	−1.50774	−	0.0790174i
$929$	−11.5873	+	2.46296i	−0.380168	+	0.0808072i	−0.394032	−	0.919097i	$-0.628920\pi$
$929$	−11.5873	+	2.46296i	−0.380168	+	0.0808072i	0.0138641	+	0.999904i	$0.495587\pi$
$930$	0.146849	−	0.273224i	0.00481538	−	0.00895937i
$931$	−35.7096	−	29.2259i	−1.17034	−	0.957840i
$932$	0.143344	+	0.143344i	0.00469539	+	0.00469539i
$933$	0.0252872	+	0.482508i	0.000827865	+	0.0157966i
$934$	10.9736	−	4.88577i	0.359067	−	0.159867i
$935$	0.00202301	+	0.0243804i	6.61595e−5	+	0.000797323i
$936$	−1.63667	+	3.67602i	−0.0534962	+	0.120154i
$937$	17.7357	−	2.80906i	0.579401	−	0.0917681i	0.140146	−	0.990131i	$-0.455243\pi$
$937$	17.7357	−	2.80906i	0.579401	−	0.0917681i	0.439254	+	0.898363i	$0.355243\pi$
$938$	3.27834	−	0.598792i	0.107042	−	0.0195512i
$939$	−0.512368	−	0.705214i	−0.0167205	−	0.0230138i
$940$	−0.113954	+	0.241545i	−0.00371678	+	0.00787834i
$941$	13.8674	+	31.1468i	0.452065	+	1.01536i	0.985525	+	0.169530i	$0.0542249\pi$
$941$	13.8674	+	31.1468i	0.452065	+	1.01536i	−0.533460	+	0.845825i	$0.679108\pi$
$942$	0.408907	+	0.629661i	0.0133229	+	0.0205155i
$943$	3.93521	−	14.6864i	0.128148	−	0.478255i
$944$	−0.541130	−	1.66543i	−0.0176123	−	0.0542050i
$945$	1.74547	−	0.0943596i	0.0567801	−	0.00306952i
$946$	−6.40043	+	19.6985i	−0.208096	+	0.640453i
$947$	−23.5407	−	15.2875i	−0.764970	−	0.496777i	0.102216	−	0.994762i	$-0.467407\pi$
$947$	−23.5407	−	15.2875i	−0.764970	−	0.496777i	−0.867186	+	0.497985i	$0.834073\pi$
$948$	−0.559125	+	0.690462i	−0.0181595	+	0.0224252i
$949$	3.70146	+	2.13704i	0.120154	+	0.0693712i
$950$	−0.178859	−	21.0536i	−0.00580294	−	0.683069i
$951$			1.05162i			0.0341013i
$952$	0.0149430	+	0.0115280i	0.000484305	+	0.000373625i
$953$	−13.8074	−	27.0986i	−0.447266	−	0.877809i	−0.999040	−	0.0438152i	$-0.986049\pi$
$953$	−13.8074	−	27.0986i	−0.447266	−	0.877809i	0.551774	−	0.833994i	$-0.313951\pi$
$954$	1.97443	+	9.28895i	0.0639244	+	0.300741i
$955$	−3.91534	+	4.62391i	−0.126698	+	0.149626i
$956$	−27.3124	−	5.80544i	−0.883347	−	0.187761i
$957$	−1.35446	−	0.362926i	−0.0437834	−	0.0117317i
$958$	11.2513	−	22.0819i	0.363512	−	0.713432i
$959$	−11.2119	−	23.6645i	−0.362053	−	0.764166i
$960$	0.0215685		0.000473124i	0.000696121		1.52700e-5i
$961$	10.5682	+	4.70528i	0.340911	+	0.151783i
$962$	0.162992	−	0.424608i	0.00525506	−	0.0136899i
$963$	−18.6166	+	48.4979i	−0.599912	+	1.56282i
$964$	2.31485	+	1.03064i	0.0745563	+	0.0331946i
$965$	−5.55327	+	15.8962i	−0.178766	+	0.511717i
$966$	0.369946	+	0.0300835i	0.0119028	+	0.000967921i
$967$	9.03721	−	17.7365i	0.290617	−	0.570368i	−0.698826	−	0.715292i	$-0.746294\pi$
$967$	9.03721	−	17.7365i	0.290617	−	0.570368i	0.989443	+	0.144924i	$0.0462937\pi$
$968$	−3.06797	−	0.822060i	−0.0986083	−	0.0264220i
$969$	−0.000987583	0	0.000209917i	−3.17257e−5	0	6.74351e-6i
$970$	−19.6278	+	4.80049i	−0.630211	+	0.154134i
$971$	0.137281	+	0.645855i	0.00440555	+	0.0207265i	0.980295	−	0.197537i	$-0.0632942\pi$
$971$	0.137281	+	0.645855i	0.00440555	+	0.0207265i	−0.975890	+	0.218263i	$0.929961\pi$
$972$	0.960310	+	1.88472i	0.0308020	+	0.0604523i
$973$	47.5474	+	6.38556i	1.52430	+	0.204712i
$974$			21.4633i			0.687730i
$975$	−0.0665144	−	0.127845i	−0.00213016	−	0.00409432i
$976$	−12.4820	−	7.20651i	−0.399540	−	0.230675i
$977$	−12.3854	+	15.2947i	−0.396244	+	0.489321i	−0.935751	−	0.352660i	$-0.885277\pi$
$977$	−12.3854	+	15.2947i	−0.396244	+	0.489321i	0.539507	+	0.841981i	$0.318611\pi$
$978$	0.361902	+	0.235022i	0.0115723	+	0.00751517i
$979$	1.37178	−	4.22192i	0.0438424	−	0.134933i
$980$	−4.51763	−	24.5053i	−0.144310	−	0.782792i
$981$	−2.51406	−	7.73748i	−0.0802678	−	0.247039i
$982$	0.593768	−	2.21597i	0.0189479	−	0.0707145i
$983$	8.54122	+	13.1523i	0.272423	+	0.419494i	0.948230	−	0.317584i	$-0.102872\pi$
$983$	8.54122	+	13.1523i	0.272423	+	0.419494i	−0.675807	+	0.737078i	$0.736205\pi$
$984$	−0.156807	−	0.352194i	−0.00499882	−	0.0112275i
$985$	43.5612	+	5.54681i	1.38797	+	0.176736i
$986$	−0.00944118	−	0.0129947i	−0.000300669	−	0.000413835i
$987$	0.00175710	+	0.00962002i	5.59292e−5	+	0.000306208i
$988$	−6.06421	+	0.960476i	−0.192928	+	0.0305568i
$989$	16.7068	−	37.5240i	0.531244	−	1.19319i
$990$	−14.6659	−	3.45515i	−0.466113	−	0.109812i
$991$	−19.2192	+	8.55695i	−0.610519	+	0.271821i	−0.688617	−	0.725125i	$-0.741782\pi$
$991$	−19.2192	+	8.55695i	−0.610519	+	0.271821i	0.0780982	+	0.996946i	$0.475115\pi$
$992$	−1.31190	−	25.0326i	−0.0416529	−	0.794785i
$993$	−0.332918	−	0.332918i	−0.0105648	−	0.0105648i
$994$	10.6548	+	9.14811i	0.337951	+	0.290160i
$995$	24.9856	−	12.0481i	0.792098	−	0.381950i
$996$	−1.15933	+	0.246422i	−0.0367346	+	0.00780819i
$997$	−12.9964	−	0.681112i	−0.411600	−	0.0215710i	−0.154587	−	0.987979i	$-0.549405\pi$
$997$	−12.9964	−	0.681112i	−0.411600	−	0.0215710i	−0.257012	+	0.966408i	$0.582738\pi$
$998$	−17.1398	−	13.8795i	−0.542550	−	0.439349i
$999$	−0.179793	−	0.311410i	−0.00568839	−	0.00985259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.52.12	yes	288
5.2	odd	4		875.2.bb.a.843.7		288
5.3	odd	4		875.2.bb.b.843.12		288
5.4	even	2		875.2.bb.c.157.7		288
7.5	odd	6	inner	175.2.x.a.152.12	yes	288
25.9	even	10		875.2.bb.a.332.12		288
25.12	odd	20		875.2.bb.c.668.7		288
25.13	odd	20	inner	175.2.x.a.38.12	✓	288
25.16	even	5		875.2.bb.b.332.7		288
35.12	even	12		875.2.bb.a.593.12		288
35.19	odd	6		875.2.bb.c.782.7		288
35.33	even	12		875.2.bb.b.593.7		288
175.12	even	60		875.2.bb.c.418.7		288
175.138	even	60	inner	175.2.x.a.138.12	yes	288
175.159	odd	30		875.2.bb.a.82.7		288
175.166	odd	30		875.2.bb.b.82.12		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.38.12	✓	288	25.13	odd	20	inner
175.2.x.a.52.12	yes	288	1.1	even	1	trivial
175.2.x.a.138.12	yes	288	175.138	even	60	inner
175.2.x.a.152.12	yes	288	7.5	odd	6	inner
875.2.bb.a.82.7		288	175.159	odd	30
875.2.bb.a.332.12		288	25.9	even	10
875.2.bb.a.593.12		288	35.12	even	12
875.2.bb.a.843.7		288	5.2	odd	4
875.2.bb.b.82.12		288	175.166	odd	30
875.2.bb.b.332.7		288	25.16	even	5
875.2.bb.b.593.7		288	35.33	even	12
875.2.bb.b.843.12		288	5.3	odd	4
875.2.bb.c.157.7		288	5.4	even	2
875.2.bb.c.418.7		288	175.12	even	60
875.2.bb.c.668.7		288	25.12	odd	20
875.2.bb.c.782.7		288	35.19	odd	6

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+(0.228917 + 0.596349i) q^{2} +(-0.00257832 + 0.0491972i) q^{3} +(1.18306 - 1.06523i) q^{4} +(-1.84817 - 1.25868i) q^{5} +(-0.0299289 + 0.00972449i) q^{6} +(1.91442 + 1.82620i) q^{7} +(2.04438 + 1.04166i) q^{8} +(2.98115 + 0.313332i) q^{9} +(0.327538 - 1.39028i) q^{10} +(-0.367849 - 3.49985i) q^{11} +(0.0493562 + 0.0609498i) q^{12} +(0.0915228 + 0.577852i) q^{13} +(-0.650809 + 1.55971i) q^{14} +(0.0666889 - 0.0876793i) q^{15} +(0.179610 - 1.70887i) q^{16} +(0.00260736 - 0.00169324i) q^{17} +(0.495581 + 1.84953i) q^{18} +(-4.41097 + 4.89888i) q^{19} +(-3.52728 + 0.479626i) q^{20} +(-0.0947799 + 0.0894755i) q^{21} +(2.00293 - 1.02054i) q^{22} +(-4.16186 + 1.59759i) q^{23} +(-0.0565180 + 0.0978920i) q^{24} +(1.83143 + 4.65251i) q^{25} +(-0.323650 + 0.186860i) q^{26} +(-0.0462215 + 0.291831i) q^{27} +(4.21020 + 0.121204i) q^{28} +(-7.69230 - 2.49938i) q^{29} +(0.0675536 + 0.0196986i) q^{30} +(0.916502 - 4.31180i) q^{31} +(5.49276 - 1.47178i) q^{32} +(0.173131 - 0.00907344i) q^{33} +(0.00160663 + 0.00116728i) q^{34} +(-1.23955 - 5.78477i) q^{35} +(3.86066 - 2.80493i) q^{36} +(-0.945787 + 0.765883i) q^{37} +(-3.93119 - 1.50904i) q^{38} +(-0.0286647 + 0.00301278i) q^{39} +(-2.46723 - 4.49839i) q^{40} +(-2.00472 + 2.75926i) q^{41} +(-0.0750553 - 0.0360394i) q^{42} +(-6.51520 + 6.51520i) q^{43} +(-4.16335 - 3.74869i) q^{44} +(-5.11528 - 4.33142i) q^{45} +(-1.90544 - 2.11621i) q^{46} +(0.0408626 - 0.0629228i) q^{47} +(0.0836086 + 0.0132423i) q^{48} +(0.329993 + 6.99222i) q^{49} +(-2.35527 + 2.15721i) q^{50} +(7.65801e-5 + 0.000132641i) q^{51} +(0.723824 + 0.586142i) q^{52} +(4.95277 + 0.259564i) q^{53} +(-0.184614 + 0.0392409i) q^{54} +(-3.72536 + 6.93131i) q^{55} +(2.01151 + 5.72762i) q^{56} +(-0.229638 - 0.229638i) q^{57} +(-0.270395 - 5.15944i) q^{58} +(0.931010 - 0.414512i) q^{59} +(-0.0145018 - 0.174769i) q^{60} +(3.41172 - 7.66284i) q^{61} +(2.78114 - 0.440489i) q^{62} +(5.13497 + 6.04403i) q^{63} +(0.115113 + 0.158439i) q^{64} +(0.558184 - 1.18317i) q^{65} +(0.0450436 + 0.101170i) q^{66} +(-1.07397 - 1.65377i) q^{67} +(0.00128097 - 0.00478065i) q^{68} +(-0.0678664 - 0.208871i) q^{69} +(3.16598 - 2.06344i) q^{70} +(2.56775 - 7.90273i) q^{71} +(5.76822 + 3.74593i) q^{72} +(4.59745 - 5.67738i) q^{73} +(-0.673240 - 0.388695i) q^{74} +(-0.233613 + 0.0781056i) q^{75} +10.4944i q^{76} +(5.68721 - 7.37195i) q^{77} +(-0.00835850 - 0.0164045i) q^{78} +(2.35530 + 11.0808i) q^{79} +(-2.48288 + 2.93221i) q^{80} +(8.78197 + 1.86667i) q^{81} +(-2.10440 - 0.563871i) q^{82} +(-6.86085 + 13.4652i) q^{83} +(-0.0168181 + 0.206818i) q^{84} +(-0.00695009 - 0.000152456i) q^{85} +(-5.37677 - 2.39389i) q^{86} +(0.142796 - 0.371995i) q^{87} +(2.89365 - 7.53820i) q^{88} +(1.15239 + 0.513075i) q^{89} +(1.41206 - 4.04202i) q^{90} +(-0.880061 + 1.27339i) q^{91} +(-3.22193 + 6.32340i) q^{92} +(0.209766 + 0.0562065i) q^{93} +(0.0468781 + 0.00996424i) q^{94} +(14.3183 - 3.50192i) q^{95} +(0.0582454 + 0.274023i) q^{96} +(-6.42245 - 12.6048i) q^{97} +(-4.09426 + 1.79743i) q^{98} -10.5489i 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

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