LMFDB - Embedded newform 152.2.t.a.149.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(5,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 16])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, 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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.6
Character	$\chi$	$=$	152.149
Dual form			152.2.t.a.101.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.759711 - 1.19283i) q^{2} +(0.467226 + 1.28369i) q^{3} +(-0.845679 + 1.81241i) q^{4} +(-1.73333 - 0.305632i) q^{5} +(1.17627 - 1.53255i) q^{6} +(1.91364 + 3.31452i) q^{7} +(2.80436 - 0.368156i) q^{8} +(0.868569 - 0.728816i) q^{9} +(0.952259 + 2.29975i) q^{10} +(2.26499 + 1.30769i) q^{11} +(-2.72170 - 0.238788i) q^{12} +(-2.03996 + 5.60474i) q^{13} +(2.49984 - 4.80072i) q^{14} +(-0.417517 - 2.36785i) q^{15} +(-2.56965 - 3.06543i) q^{16} +(2.13151 + 1.78855i) q^{17} +(-1.52921 - 0.482364i) q^{18} +(-0.713969 - 4.30003i) q^{19} +(2.01977 - 2.88303i) q^{20} +(-3.36072 + 4.00515i) q^{21} +(-0.160884 - 3.69521i) q^{22} +(-1.10686 - 6.27729i) q^{23} +(1.78287 + 3.42793i) q^{24} +(-1.78746 - 0.650581i) q^{25} +(8.23527 - 1.82466i) q^{26} +(4.89056 + 2.82357i) q^{27} +(-7.62559 + 0.665276i) q^{28} +(-2.78015 - 3.31326i) q^{29} +(-2.50725 + 2.29691i) q^{30} +(2.41499 + 4.18289i) q^{31} +(-1.70434 + 5.39400i) q^{32} +(-0.620412 + 3.51853i) q^{33} +(0.514101 - 3.90131i) q^{34} +(-2.30393 - 6.33001i) q^{35} +(0.586382 + 2.19055i) q^{36} -7.50278i q^{37} +(-4.58679 + 4.11842i) q^{38} -8.14787 q^{39} +(-4.97340 - 0.218969i) q^{40} +(-6.78504 + 2.46955i) q^{41} +(7.33063 + 0.966007i) q^{42} +(3.24204 + 0.571659i) q^{43} +(-4.28552 + 2.99919i) q^{44} +(-1.72826 + 0.997812i) q^{45} +(-6.64685 + 6.08922i) q^{46} +(3.73496 - 3.13400i) q^{47} +(2.73446 - 4.73089i) q^{48} +(-3.82402 + 6.62340i) q^{49} +(0.581919 + 2.62638i) q^{50} +(-1.30005 + 3.57186i) q^{51} +(-8.43292 - 8.43705i) q^{52} +(1.49917 - 0.264344i) q^{53} +(-0.347381 - 7.97870i) q^{54} +(-3.52629 - 2.95890i) q^{55} +(6.58680 + 8.59060i) q^{56} +(5.18633 - 2.92560i) q^{57} +(-1.84004 + 5.83336i) q^{58} +(4.81703 - 5.74071i) q^{59} +(4.64461 + 1.24573i) q^{60} +(5.64385 - 0.995163i) q^{61} +(3.15478 - 6.05846i) q^{62} +(4.07780 + 1.48420i) q^{63} +(7.72892 - 2.06489i) q^{64} +(5.24890 - 9.09135i) q^{65} +(4.66834 - 1.93302i) q^{66} +(2.11430 + 2.51972i) q^{67} +(-5.04416 + 2.35063i) q^{68} +(7.54096 - 4.35377i) q^{69} +(-5.80029 + 7.55717i) q^{70} +(0.236392 - 1.34065i) q^{71} +(2.16747 - 2.36363i) q^{72} +(10.5450 - 3.83807i) q^{73} +(-8.94953 + 5.69994i) q^{74} -2.59851i q^{75} +(8.39720 + 2.34244i) q^{76} +10.0098i q^{77} +(6.19003 + 9.71901i) q^{78} +(-6.51619 + 2.37170i) q^{79} +(3.51715 + 6.09876i) q^{80} +(-0.748928 + 4.24738i) q^{81} +(8.10042 + 6.21724i) q^{82} +(5.89196 - 3.40173i) q^{83} +(-4.41688 - 9.47807i) q^{84} +(-3.14796 - 3.75160i) q^{85} +(-1.78112 - 4.30149i) q^{86} +(2.95424 - 5.11690i) q^{87} +(6.83328 + 2.83337i) q^{88} +(-6.91135 - 2.51553i) q^{89} +(2.50320 + 1.30347i) q^{90} +(-22.4807 + 3.96396i) q^{91} +(12.3131 + 3.30250i) q^{92} +(-4.24120 + 5.05446i) q^{93} +(-6.57581 - 2.07423i) q^{94} +(-0.0766864 + 7.67156i) q^{95} +(-7.72054 + 0.332363i) q^{96} +(-9.33891 - 7.83628i) q^{97} +(10.8057 - 0.470466i) q^{98} +(2.92036 - 0.514939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26}+ \cdots + 93 q^{98}+O(q^{100}) $ 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.759711	−	1.19283i	−0.537197	−	0.843457i
$2$	−0.759711	−	1.19283i	−0.537197	−	0.843457i
$3$	0.467226	+	1.28369i	0.269753	+	0.741140i	0.998416	+	0.0562672i	$0.0179199\pi$
$3$	0.467226	+	1.28369i	0.269753	+	0.741140i	−0.728663	+	0.684872i	$0.759858\pi$
$4$	−0.845679	+	1.81241i	−0.422840	+	0.906205i
$5$	−1.73333	−	0.305632i	−0.775167	−	0.136683i	−0.227949	−	0.973673i	$-0.573202\pi$
$5$	−1.73333	−	0.305632i	−0.775167	−	0.136683i	−0.547218	+	0.836990i	$0.684313\pi$
$6$	1.17627	−	1.53255i	0.480209	−	0.625663i
$7$	1.91364	+	3.31452i	0.723287	+	1.25277i	0.959675	+	0.281112i	$0.0907031\pi$
$7$	1.91364	+	3.31452i	0.723287	+	1.25277i	−0.236388	+	0.971659i	$0.575964\pi$
$8$	2.80436	−	0.368156i	0.991493	−	0.130163i
$9$	0.868569	−	0.728816i	0.289523	−	0.242939i
$10$	0.952259	+	2.29975i	0.301131	+	0.727245i
$11$	2.26499	+	1.30769i	0.682919	+	0.394283i	0.800954	−	0.598726i	$-0.204326\pi$
$11$	2.26499	+	1.30769i	0.682919	+	0.394283i	−0.118035	+	0.993009i	$0.537659\pi$
$12$	−2.72170	−	0.238788i	−0.785686	−	0.0689320i
$13$	−2.03996	+	5.60474i	−0.565782	+	1.55447i	0.245242	+	0.969462i	$0.421133\pi$
$13$	−2.03996	+	5.60474i	−0.565782	+	1.55447i	−0.811024	+	0.585012i	$0.801090\pi$
$14$	2.49984	−	4.80072i	0.668111	−	1.28305i
$15$	−0.417517	−	2.36785i	−0.107802	−	0.611377i
$16$	−2.56965	−	3.06543i	−0.642413	−	0.766358i
$17$	2.13151	+	1.78855i	0.516967	+	0.433787i	0.863573	−	0.504224i	$-0.168221\pi$
$17$	2.13151	+	1.78855i	0.516967	+	0.433787i	−0.346606	+	0.938011i	$0.612666\pi$
$18$	−1.52921	−	0.482364i	−0.360439	−	0.113694i
$19$	−0.713969	−	4.30003i	−0.163796	−	0.986494i
$19$	−0.713969	−	4.30003i	−0.163796	−	0.986494i
$20$	2.01977	−	2.88303i	0.451634	−	0.644665i
$21$	−3.36072	+	4.00515i	−0.733369	+	0.873995i
$22$	−0.160884	−	3.69521i	−0.0343006	−	0.787821i
$23$	−1.10686	−	6.27729i	−0.230796	−	1.30891i	−0.851290	−	0.524696i	$-0.824179\pi$
$23$	−1.10686	−	6.27729i	−0.230796	−	1.30891i	0.620494	−	0.784211i	$-0.286932\pi$
$24$	1.78287	+	3.42793i	0.363927	+	0.699723i
$25$	−1.78746	−	0.650581i	−0.357492	−	0.130116i
$26$	8.23527	−	1.82466i	1.61507	−	0.357845i
$27$	4.89056	+	2.82357i	0.941189	+	0.543396i
$28$	−7.62559	+	0.665276i	−1.44110	+	0.125725i
$29$	−2.78015	−	3.31326i	−0.516261	−	0.615256i	0.443431	−	0.896308i	$-0.353761\pi$
$29$	−2.78015	−	3.31326i	−0.516261	−	0.615256i	−0.959693	+	0.281052i	$0.909317\pi$
$30$	−2.50725	+	2.29691i	−0.457759	+	0.419356i
$31$	2.41499	+	4.18289i	0.433746	+	0.751270i	0.997192	−	0.0748828i	$-0.0238583\pi$
$31$	2.41499	+	4.18289i	0.433746	+	0.751270i	−0.563447	+	0.826153i	$0.690525\pi$
$32$	−1.70434	+	5.39400i	−0.301288	+	0.953533i
$33$	−0.620412	+	3.51853i	−0.108000	+	0.612497i
$34$	0.514101	−	3.90131i	0.0881677	−	0.669068i
$35$	−2.30393	−	6.33001i	−0.389436	−	1.06997i
$36$	0.586382	+	2.19055i	0.0977303	+	0.365091i
$37$		−	7.50278i		−	1.23345i	−0.787179	−	0.616725i	$-0.788459\pi$
$37$		−	7.50278i		−	1.23345i	0.787179	−	0.616725i	$-0.211541\pi$
$38$	−4.58679	+	4.11842i	−0.744075	+	0.668096i
$39$	−8.14787			−1.30470
$40$	−4.97340	−	0.218969i	−0.786363	−	0.0346220i
$41$	−6.78504	+	2.46955i	−1.05964	+	0.385679i	−0.812295	−	0.583247i	$-0.801782\pi$
$41$	−6.78504	+	2.46955i	−1.05964	+	0.385679i	−0.247350	+	0.968926i	$0.579560\pi$
$42$	7.33063	+	0.966007i	1.13114	+	0.149058i
$43$	3.24204	+	0.571659i	0.494407	+	0.0871772i	0.415292	−	0.909688i	$-0.363679\pi$
$43$	3.24204	+	0.571659i	0.494407	+	0.0871772i	0.0791149	+	0.996866i	$0.474791\pi$
$44$	−4.28552	+	2.99919i	−0.646067	+	0.452146i
$45$	−1.72826	+	0.997812i	−0.257634	+	0.148745i
$46$	−6.64685	+	6.08922i	−0.980024	+	0.897806i
$47$	3.73496	−	3.13400i	0.544800	−	0.457141i	−0.328376	−	0.944547i	$-0.606501\pi$
$47$	3.73496	−	3.13400i	0.544800	−	0.457141i	0.873175	+	0.487406i	$0.162057\pi$
$48$	2.73446	−	4.73089i	0.394686	−	0.682845i
$49$	−3.82402	+	6.62340i	−0.546289	+	0.946200i
$50$	0.581919	+	2.62638i	0.0822958	+	0.371427i
$51$	−1.30005	+	3.57186i	−0.182043	+	0.500160i
$52$	−8.43292	−	8.43705i	−1.16944	−	1.17001i
$53$	1.49917	−	0.264344i	0.205927	−	0.0363104i	−0.0697332	−	0.997566i	$-0.522215\pi$
$53$	1.49917	−	0.264344i	0.205927	−	0.0363104i	0.275660	+	0.961255i	$0.411104\pi$
$54$	−0.347381	−	7.97870i	−0.0472726	−	1.08576i
$55$	−3.52629	−	2.95890i	−0.475484	−	0.398979i
$56$	6.58680	+	8.59060i	0.880198	+	1.14797i
$57$	5.18633	−	2.92560i	0.686946	−	0.387505i
$58$	−1.84004	+	5.83336i	−0.241609	+	0.765958i
$59$	4.81703	−	5.74071i	0.627124	−	0.747377i	−0.355154	−	0.934808i	$-0.615572\pi$
$59$	4.81703	−	5.74071i	0.627124	−	0.747377i	0.982278	+	0.187431i	$0.0600161\pi$
$60$	4.64461	+	1.24573i	0.599616	+	0.160824i
$61$	5.64385	−	0.995163i	0.722621	−	0.127418i	0.199771	−	0.979843i	$-0.435980\pi$
$61$	5.64385	−	0.995163i	0.722621	−	0.127418i	0.522850	+	0.852425i	$0.324869\pi$
$62$	3.15478	−	6.05846i	0.400657	−	0.769425i
$63$	4.07780	+	1.48420i	0.513755	+	0.186991i
$64$	7.72892	−	2.06489i	0.966115	−	0.258111i
$65$	5.24890	−	9.09135i	0.651045	−	1.12764i
$66$	4.66834	−	1.93302i	0.574632	−	0.237938i
$67$	2.11430	+	2.51972i	0.258302	+	0.307833i	0.879574	−	0.475763i	$-0.157828\pi$
$67$	2.11430	+	2.51972i	0.258302	+	0.307833i	−0.621271	+	0.783596i	$0.713383\pi$
$68$	−5.04416	+	2.35063i	−0.611694	+	0.285056i
$69$	7.54096	−	4.35377i	0.907825	−	0.524133i
$70$	−5.80029	+	7.55717i	−0.693267	+	0.903255i
$71$	0.236392	−	1.34065i	0.0280546	−	0.159106i	−0.967562	−	0.252633i	$-0.918703\pi$
$71$	0.236392	−	1.34065i	0.0280546	−	0.159106i	0.995617	+	0.0935279i	$0.0298144\pi$
$72$	2.16747	−	2.36363i	0.255438	−	0.278557i
$73$	10.5450	−	3.83807i	1.23420	−	0.449212i	0.359166	−	0.933274i	$-0.383061\pi$
$73$	10.5450	−	3.83807i	1.23420	−	0.449212i	0.875034	+	0.484062i	$0.160839\pi$
$74$	−8.94953	+	5.69994i	−1.04036	+	0.662605i
$75$		−	2.59851i		−	0.300050i
$76$	8.39720	+	2.34244i	0.963225	+	0.268697i
$77$			10.0098i			1.14072i
$78$	6.19003	+	9.71901i	0.700882	+	1.10046i
$79$	−6.51619	+	2.37170i	−0.733128	+	0.266837i	−0.681488	−	0.731829i	$-0.738667\pi$
$79$	−6.51619	+	2.37170i	−0.733128	+	0.266837i	−0.0516399	+	0.998666i	$0.516445\pi$
$80$	3.51715	+	6.09876i	0.393229	+	0.681862i
$81$	−0.748928	+	4.24738i	−0.0832143	+	0.471932i
$82$	8.10042	+	6.21724i	0.894541	+	0.686579i
$83$	5.89196	−	3.40173i	0.646727	−	0.373388i	−0.140474	−	0.990084i	$-0.544863\pi$
$83$	5.89196	−	3.40173i	0.646727	−	0.373388i	0.787201	+	0.616696i	$0.211529\pi$
$84$	−4.41688	−	9.47807i	−0.481921	−	1.03414i
$85$	−3.14796	−	3.75160i	−0.341444	−	0.406918i
$86$	−1.78112	−	4.30149i	−0.192063	−	0.463842i
$87$	2.95424	−	5.11690i	0.316728	−	0.548589i
$88$	6.83328	+	2.83337i	0.728430	+	0.302038i
$89$	−6.91135	−	2.51553i	−0.732602	−	0.266645i	−0.0513361	−	0.998681i	$-0.516348\pi$
$89$	−6.91135	−	2.51553i	−0.732602	−	0.266645i	−0.681266	+	0.732036i	$0.738570\pi$
$90$	2.50320	+	1.30347i	0.263860	+	0.137398i
$91$	−22.4807	+	3.96396i	−2.35662	+	0.415536i
$92$	12.3131	+	3.30250i	1.28373	+	0.344310i
$93$	−4.24120	+	5.05446i	−0.439792	+	0.524123i
$94$	−6.57581	−	2.07423i	−0.678243	−	0.213940i
$95$	−0.0766864	+	7.67156i	−0.00786786	+	0.787085i
$96$	−7.72054	+	0.332363i	−0.787975	+	0.0339216i
$97$	−9.33891	−	7.83628i	−0.948223	−	0.795653i	0.0307745	−	0.999526i	$-0.490203\pi$
$97$	−9.33891	−	7.83628i	−0.948223	−	0.795653i	−0.978997	+	0.203873i	$0.934647\pi$
$98$	10.8057	−	0.470466i	1.09154	−	0.0475243i
$99$	2.92036	−	0.514939i	0.293507	−	0.0517533i
$100$	2.69074	−	2.68942i	0.269074	−	0.268942i
$101$	4.36652	−	11.9969i	0.434485	−	1.19374i	−0.508546	−	0.861035i	$-0.669817\pi$
$101$	4.36652	−	11.9969i	0.434485	−	1.19374i	0.943031	−	0.332704i	$-0.107961\pi$
$102$	5.24827	−	1.16284i	0.519657	−	0.115139i
$103$	−2.02806	+	3.51270i	−0.199831	+	0.346117i	−0.948473	−	0.316857i	$-0.897373\pi$
$103$	−2.02806	+	3.51270i	−0.199831	+	0.346117i	0.748643	+	0.662974i	$0.230706\pi$
$104$	−3.65736	+	16.4687i	−0.358634	+	1.61489i
$105$	7.04932	−	5.91508i	0.687943	−	0.577253i
$106$	−1.45425	−	1.58743i	−0.141249	−	0.154184i
$107$	1.10131	−	0.635844i	0.106468	−	0.0614693i	−0.445820	−	0.895122i	$-0.647088\pi$
$107$	1.10131	−	0.635844i	0.106468	−	0.0614693i	0.552288	+	0.833653i	$0.313755\pi$
$108$	−9.25331	+	6.47587i	−0.890400	+	0.623141i
$109$	−3.33109	−	0.587360i	−0.319060	−	0.0562589i	0.0118246	−	0.999930i	$-0.496236\pi$
$109$	−3.33109	−	0.587360i	−0.319060	−	0.0562589i	−0.330885	+	0.943671i	$0.607347\pi$
$110$	−0.850509	+	6.45416i	−0.0810928	+	0.615380i
$111$	9.63126	−	3.50549i	0.914159	−	0.332727i
$112$	5.24305	−	14.3833i	0.495422	−	1.35909i
$113$	−15.3010			−1.43939			−0.719697	−	0.694288i	$-0.755719\pi$
$113$	−15.3010			−1.43939			−0.719697	+	0.694288i	$0.755719\pi$
$114$	−7.42985	−	3.96379i	−0.695869	−	0.371243i
$115$			11.2189i			1.04617i
$116$	8.35610	−	2.23682i	0.775844	−	0.207684i
$117$	2.31298	+	6.35485i	0.213835	+	0.587506i
$118$	−10.5072	−	1.38461i	−0.967269	−	0.127464i
$119$	−1.84924	+	10.4876i	−0.169520	+	0.961394i
$120$	−2.04261	−	6.48661i	−0.186464	−	0.592144i
$121$	−2.07989	−	3.60248i	−0.189081	−	0.327498i
$122$	−5.47475	−	5.97611i	−0.495661	−	0.541051i
$123$	−6.34028	−	7.55606i	−0.571684	−	0.681307i
$124$	−9.62342	+	0.839572i	−0.864209	+	0.0753958i
$125$	10.5207	+	6.07413i	0.941001	+	0.543287i
$126$	−1.32756	−	5.99168i	−0.118268	−	0.533781i
$127$	10.6056	+	3.86013i	0.941097	+	0.342531i	0.766599	−	0.642126i	$-0.221947\pi$
$127$	10.6056	+	3.86013i	0.941097	+	0.342531i	0.174498	+	0.984657i	$0.444170\pi$
$128$	−8.33480	−	7.65056i	−0.736699	−	0.676220i
$129$	0.780930	+	4.42887i	0.0687571	+	0.389941i
$130$	−14.8321	+	0.645767i	−1.30086	+	0.0566375i
$131$	−7.04562	+	8.39664i	−0.615579	+	0.733618i	−0.980303	−	0.197497i	$-0.936719\pi$
$131$	−7.04562	+	8.39664i	−0.615579	+	0.733618i	0.364725	+	0.931115i	$0.381163\pi$
$132$	−5.85235	−	4.09999i	−0.509381	−	0.356858i
$133$	12.8862	−	10.5952i	1.11738	−	0.918717i
$134$	1.39934	−	4.43625i	0.120885	−	0.383234i
$135$	−7.61396	−	6.38887i	−0.655305	−	0.549867i
$136$	6.63600	+	4.23102i	0.569032	+	0.362807i
$137$	3.48972	+	19.7912i	0.298147	+	1.69087i	0.654130	+	0.756382i	$0.273035\pi$
$137$	3.48972	+	19.7912i	0.298147	+	1.69087i	−0.355984	+	0.934492i	$0.615854\pi$
$138$	−10.9223	−	5.68746i	−0.929764	−	0.484149i
$139$	−5.65104	+	15.5261i	−0.479315	+	1.31691i	0.430761	+	0.902466i	$0.358245\pi$
$139$	−5.65104	+	15.5261i	−0.479315	+	1.31691i	−0.910076	+	0.414441i	$0.863977\pi$
$140$	13.4210	+	1.17748i	1.13428	+	0.0995156i
$141$	5.76816	+	3.33025i	0.485767	+	0.280458i
$142$	−1.77875	+	0.736529i	−0.149270	+	0.0618081i
$143$	−11.9497	+	10.0270i	−0.999287	+	0.838501i
$144$	−4.46606	−	0.789736i	−0.372171	−	0.0658114i
$145$	3.80627	+	6.59266i	0.316094	+	0.547490i
$146$	−12.5893	−	9.66256i	−1.04190	−	0.799679i
$147$	−10.2891	−	1.81424i	−0.848630	−	0.149636i
$148$	13.5981	+	6.34495i	1.11776	+	0.521552i
$149$	−6.28070	−	17.2561i	−0.514535	−	1.41367i	−0.876464	−	0.481468i	$-0.840104\pi$
$149$	−6.28070	−	17.2561i	−0.514535	−	1.41367i	0.361929	−	0.932206i	$-0.382118\pi$
$150$	−3.09958	+	1.97412i	−0.253080	+	0.161186i
$151$	13.2947			1.08191			0.540954	−	0.841052i	$-0.318063\pi$
$151$	13.2947			1.08191			0.540954	+	0.841052i	$0.318063\pi$
$152$	−3.58531	−	11.7960i	−0.290807	−	0.956782i
$153$	3.15489			0.255057
$154$	11.9400	−	7.60454i	0.962149	−	0.612791i
$155$	−2.90754	−	7.98841i	−0.233540	−	0.641645i
$156$	6.89049	−	14.7673i	0.551680	−	1.18233i
$157$	−0.992527	−	0.175009i	−0.0792123	−	0.0139673i	0.133902	−	0.990995i	$-0.457249\pi$
$157$	−0.992527	−	0.175009i	−0.0792123	−	0.0139673i	−0.213114	+	0.977027i	$0.568361\pi$
$158$	7.77945	+	5.97089i	0.618900	+	0.475018i
$159$	1.03979	+	1.80096i	0.0824604	+	0.142826i
$160$	4.60276	−	8.82865i	0.363880	−	0.697966i
$161$	18.6881	−	15.6812i	1.47283	−	1.23585i
$162$	5.63537	−	2.33344i	0.442756	−	0.183332i
$163$	12.9858	+	7.49734i	1.01712	+	0.587237i	0.913270	−	0.407356i	$-0.133549\pi$
$163$	12.9858	+	7.49734i	1.01712	+	0.587237i	0.103854	+	0.994593i	$0.466882\pi$
$164$	1.26213	−	14.3857i	0.0985556	−	1.12334i
$165$	2.15075	−	5.90914i	0.167436	−	0.460026i
$166$	−8.53387	−	4.44377i	−0.662356	−	0.344904i
$167$	−0.413879	−	2.34722i	−0.0320269	−	0.181634i	0.964598	−	0.263725i	$-0.0849512\pi$
$167$	−0.413879	−	2.34722i	−0.0320269	−	0.181634i	−0.996625	+	0.0820914i	$0.973840\pi$
$168$	−7.95016	+	12.4692i	−0.613368	+	0.962017i
$169$	−17.2931	−	14.5106i	−1.33024	−	1.11620i
$170$	−2.08347	+	6.60511i	−0.159795	+	0.506588i
$171$	−3.75406	−	3.21452i	−0.287080	−	0.245820i
$172$	−3.77781	+	5.39246i	−0.288055	+	0.411172i
$173$	−11.5139	+	13.7218i	−0.875388	+	1.04325i	0.123317	+	0.992367i	$0.460647\pi$
$173$	−11.5139	+	13.7218i	−0.875388	+	1.04325i	−0.998705	+	0.0508794i	$0.983798\pi$
$174$	−8.34795	+	0.363458i	−0.632856	+	0.0275537i
$175$	−1.26418	−	7.16954i	−0.0955633	−	0.541966i
$176$	−1.81159	−	10.3035i	−0.136554	−	0.776654i
$177$	9.61994	+	3.50137i	0.723079	+	0.263179i
$178$	2.25004	+	10.1551i	0.168647	+	0.761159i
$179$	−19.7528	−	11.4043i	−1.47639	−	0.852394i	−0.476745	−	0.879042i	$-0.658184\pi$
$179$	−19.7528	−	11.4043i	−1.47639	−	0.852394i	−0.999645	+	0.0266474i	$0.991517\pi$
$180$	−0.346889	−	3.97615i	−0.0258556	−	0.296364i
$181$	3.56113	+	4.24399i	0.264696	+	0.315453i	0.881979	−	0.471289i	$-0.156211\pi$
$181$	3.56113	+	4.24399i	0.264696	+	0.315453i	−0.617283	+	0.786741i	$0.711767\pi$
$182$	21.8072	+	23.8042i	1.61646	+	1.76448i
$183$	3.91443	+	6.78000i	0.289363	+	0.501192i
$184$	−5.41505	−	17.1963i	−0.399203	−	1.26773i
$185$	−2.29309	+	13.0048i	−0.168591	+	0.956129i
$186$	9.25119	+	1.21909i	0.678330	+	0.0893881i
$187$	2.48897	+	6.83839i	0.182012	+	0.500073i
$188$	2.52152	+	9.41963i	0.183901	+	0.686997i
$189$			21.6131i			1.57213i
$190$	9.20911	−	5.73669i	0.668099	−	0.416183i
$191$	−1.52320			−0.110215			−0.0551073	−	0.998480i	$-0.517550\pi$
$191$	−1.52320			−0.110215			−0.0551073	+	0.998480i	$0.517550\pi$
$192$	6.26183	+	8.95678i	0.451909	+	0.646400i
$193$	9.17926	−	3.34098i	0.660738	−	0.240489i	0.0101828	−	0.999948i	$-0.496759\pi$
$193$	9.17926	−	3.34098i	0.660738	−	0.240489i	0.650555	+	0.759459i	$0.274536\pi$
$194$	−2.25246	+	17.0930i	−0.161717	+	1.22721i
$195$	14.1229	+	2.49025i	1.01136	+	0.178331i
$196$	−8.77042	−	12.5320i	−0.626458	−	0.895141i
$197$	−5.18292	+	2.99236i	−0.369268	+	0.213197i	−0.673138	−	0.739517i	$-0.735054\pi$
$197$	−5.18292	+	2.99236i	−0.369268	+	0.213197i	0.303871	+	0.952713i	$0.401721\pi$
$198$	−2.83286	−	3.09229i	−0.201323	−	0.219759i
$199$	3.61157	−	3.03047i	0.256017	−	0.214824i	−0.505741	−	0.862685i	$-0.668781\pi$
$199$	3.61157	−	3.03047i	0.256017	−	0.214824i	0.761758	+	0.647861i	$0.224336\pi$
$200$	−5.25220	−	1.16640i	−0.371387	−	0.0824772i
$201$	−2.24669	+	3.89138i	−0.158469	+	0.274477i
$202$	−17.6276	+	3.90568i	−1.24027	+	0.274803i
$203$	5.66165	−	15.5552i	0.397370	−	1.09176i
$204$	−5.37424	−	5.37687i	−0.376272	−	0.376456i
$205$	12.5154	−	2.20681i	0.874117	−	0.154130i
$206$	5.73079	−	0.249511i	0.399283	−	0.0173842i
$207$	−5.53637	−	4.64557i	−0.384805	−	0.322889i
$208$	22.4229	−	8.14887i	1.55475	−	0.565023i
$209$	4.00598	−	10.6732i	0.277099	−	0.738278i
$210$	−12.4111	−	3.91488i	−0.856449	−	0.270152i
$211$	−14.2288	+	16.9573i	−0.979553	+	1.16739i	0.00633485	+	0.999980i	$0.497984\pi$
$211$	−14.2288	+	16.9573i	−0.979553	+	1.16739i	−0.985888	+	0.167406i	$0.946461\pi$
$212$	−0.788716	+	2.94066i	−0.0541693	+	0.201965i
$213$	1.83143	−	0.322930i	0.125487	−	0.0221268i
$214$	−1.59513	−	0.830621i	−0.109041	−	0.0567801i
$215$	−5.44479	−	1.98174i	−0.371332	−	0.135154i
$216$	14.7544	+	6.11782i	1.00391	+	0.416265i
$217$	−9.24285	+	16.0091i	−0.627446	+	1.08677i
$218$	1.83004	+	4.41964i	0.123946	+	0.299336i
$219$	9.85379	+	11.7433i	0.665857	+	0.793538i
$220$	8.34485	−	3.88879i	0.562610	−	0.262182i
$221$	−14.3725	+	8.29799i	−0.966801	+	0.558183i
$222$	−11.4984	−	8.82528i	−0.771724	−	0.592314i
$223$	4.15766	−	23.5792i	0.278417	−	1.57898i	−0.449476	−	0.893292i	$-0.648389\pi$
$223$	4.15766	−	23.5792i	0.278417	−	1.57898i	0.727894	−	0.685690i	$-0.240500\pi$
$224$	−21.1400	+	4.67308i	−1.41248	+	0.312234i
$225$	−2.02668	+	0.737653i	−0.135112	+	0.0491769i
$226$	11.6243	+	18.2514i	0.773238	+	1.21407i
$227$		−	1.68680i		−	0.111957i	−0.998432	−	0.0559784i	$-0.982172\pi$
$227$		−	1.68680i		−	0.111957i	0.998432	−	0.0559784i	$-0.0178278\pi$
$228$	0.916413	+	11.8739i	0.0606909	+	0.786366i
$229$		−	3.60123i		−	0.237976i	−0.992896	−	0.118988i	$-0.962035\pi$
$229$		−	3.60123i		−	0.237976i	0.992896	−	0.118988i	$-0.0379650\pi$
$230$	13.3822	−	8.52311i	0.882396	−	0.561997i
$231$	−12.8495	+	4.67683i	−0.845433	+	0.307713i
$232$	−9.01636	−	8.26805i	−0.591953	−	0.542824i
$233$	−0.677514	+	3.84237i	−0.0443854	+	0.251722i	−0.998925	−	0.0463631i	$-0.985237\pi$
$233$	−0.677514	+	3.84237i	−0.0443854	+	0.251722i	0.954539	+	0.298085i	$0.0963480\pi$
$234$	5.82306	−	7.58683i	0.380665	−	0.495967i
$235$	−7.43175	+	4.29072i	−0.484794	+	0.279896i
$236$	6.33085	+	13.5852i	0.412103	+	0.884323i
$237$	−6.08906	−	7.25666i	−0.395527	−	0.471371i
$238$	13.9148	−	5.76169i	0.901960	−	0.373475i
$239$	−1.71193	+	2.96514i	−0.110735	+	0.191799i	−0.916067	−	0.401025i	$-0.868654\pi$
$239$	−1.71193	+	2.96514i	−0.110735	+	0.191799i	0.805332	+	0.592825i	$0.201987\pi$
$240$	−6.18563	+	7.36443i	−0.399280	+	0.475372i
$241$	8.46332	+	3.08040i	0.545171	+	0.198426i	0.599900	−	0.800075i	$-0.295207\pi$
$241$	8.46332	+	3.08040i	0.545171	+	0.198426i	−0.0547288	+	0.998501i	$0.517429\pi$
$242$	−2.71702	+	5.21780i	−0.174657	+	0.335413i
$243$	10.8818	−	1.91875i	0.698066	−	0.123088i
$244$	−2.96924	+	11.0706i	−0.190086	+	0.708720i
$245$	8.65260	−	10.3118i	0.552794	−	0.658795i
$246$	−4.19630	+	13.3033i	−0.267546	+	0.848187i
$247$	25.5570	+	4.77027i	1.62615	+	0.303525i
$248$	8.31248	+	10.8413i	0.527843	+	0.688421i
$249$	7.11964	+	5.97409i	0.451189	+	0.378593i
$250$	−0.747296	−	17.1640i	−0.0472631	−	1.08555i
$251$	−5.43707	+	0.958702i	−0.343185	+	0.0605127i	−0.342584	−	0.939487i	$-0.611302\pi$
$251$	−5.43707	+	0.958702i	−0.343185	+	0.0605127i	−0.000600364		1.00000i	$0.500191\pi$
$252$	−6.13849	+	6.13549i	−0.386688	+	0.386499i
$253$	5.70174	−	15.6654i	0.358466	−	0.984876i
$254$	−3.45273	−	15.5833i	−0.216644	−	0.977782i
$255$	3.34508	−	5.79385i	0.209477	−	0.362825i
$256$	−2.79377	+	15.7542i	−0.174610	+	0.984638i
$257$	−16.0217	+	13.4438i	−0.999404	+	0.838600i	−0.986902	−	0.161322i	$-0.948424\pi$
$257$	−16.0217	+	13.4438i	−0.999404	+	0.838600i	−0.0125022	+	0.999922i	$0.503980\pi$
$258$	4.68961	−	4.29618i	0.291962	−	0.267468i
$259$	24.8681	−	14.3576i	1.54523	−	0.892139i
$260$	12.0384	+	17.2015i	0.746588	+	1.06679i
$261$	−4.82951	−	0.851573i	−0.298939	−	0.0527110i
$262$	15.3684	+	2.02520i	0.949462	+	0.125117i
$263$	−1.63905	+	0.596565i	−0.101068	+	0.0367857i	−0.392059	−	0.919940i	$-0.628237\pi$
$263$	−1.63905	+	0.596565i	−0.101068	+	0.0367857i	0.290991	+	0.956726i	$0.406015\pi$
$264$	−0.444492	+	10.0956i	−0.0273566	+	0.621344i
$265$	−2.67934			−0.164590
$266$	−22.4280	−	7.32182i	−1.37515	−	0.448930i
$267$		−	10.0474i		−	0.614889i
$268$	−6.35478	+	1.70109i	−0.388180	+	0.103911i
$269$	3.49933	+	9.61432i	0.213358	+	0.586195i	0.999492	−	0.0318599i	$-0.0101430\pi$
$269$	3.49933	+	9.61432i	0.213358	+	0.586195i	−0.786135	+	0.618055i	$0.787921\pi$
$270$	−1.83642	+	13.9358i	−0.111761	+	0.848109i
$271$	−3.72486	+	21.1247i	−0.226269	+	1.28323i	0.633976	+	0.773353i	$0.281422\pi$
$271$	−3.72486	+	21.1247i	−0.226269	+	1.28323i	−0.860244	+	0.509882i	$0.829689\pi$
$272$	0.00543739	−	11.1300i	0.000329690	−	0.674853i
$273$	−15.5921	−	27.0063i	−0.943676	−	1.63449i
$274$	20.9563	−	19.1982i	1.26602	−	1.15981i
$275$	−3.19781	−	3.81100i	−0.192835	−	0.229812i
$276$	1.51359	+	17.3492i	0.0911073	+	1.04430i
$277$	−12.5634	−	7.25348i	−0.754862	−	0.435820i	0.0725863	−	0.997362i	$-0.476875\pi$
$277$	−12.5634	−	7.25348i	−0.754862	−	0.435820i	−0.827448	+	0.561543i	$0.810208\pi$
$278$	22.8131	−	5.05463i	1.36824	−	0.303156i
$279$	5.14615	+	1.87304i	0.308092	+	0.112136i
$280$	−8.79150	−	16.9034i	−0.525393	−	1.01017i
$281$	−4.40069	−	24.9576i	−0.262523	−	1.48884i	−0.775996	−	0.630738i	$-0.782752\pi$
$281$	−4.40069	−	24.9576i	−0.262523	−	1.48884i	0.513473	−	0.858106i	$-0.328359\pi$
$282$	−0.409718	−	9.41045i	−0.0243983	−	0.560384i
$283$	7.08527	−	8.44390i	0.421176	−	0.501938i	−0.513179	−	0.858282i	$-0.671532\pi$
$283$	7.08527	−	8.44390i	0.421176	−	0.501938i	0.934355	+	0.356344i	$0.115977\pi$
$284$	2.22989	+	1.56220i	0.132320	+	0.0926994i
$285$	−9.88375	+	3.48591i	−0.585463	+	0.206487i
$286$	21.0389	+	6.63635i	1.24405	+	0.392416i
$287$	−21.1695	−	17.7633i	−1.24959	−	1.04853i
$288$	2.45089	+	5.92721i	0.144420	+	0.349264i
$289$	−1.60759	−	9.11711i	−0.0945643	−	0.536301i
$290$	4.97224	−	9.54874i	0.291980	−	0.560721i
$291$	5.69599	−	15.6496i	0.333905	−	0.917395i
$292$	−1.96154	+	22.3576i	−0.114791	+	1.30838i
$293$	−9.23806	−	5.33360i	−0.539693	−	0.311592i	0.205261	−	0.978707i	$-0.434196\pi$
$293$	−9.23806	−	5.33360i	−0.539693	−	0.311592i	−0.744955	+	0.667115i	$0.767529\pi$
$294$	5.65265	+	13.6514i	0.329669	+	0.796167i
$295$	−10.1040	+	8.47828i	−0.588279	+	0.493624i
$296$	−2.76220	−	21.0405i	−0.160549	−	1.22296i
$297$	7.38470	+	12.7907i	0.428504	+	0.742191i
$298$	−15.8120	+	20.6014i	−0.915966	+	1.19341i
$299$	37.4405	+	6.60177i	2.16524	+	0.381790i
$300$	4.70957	+	2.19751i	0.271907	+	0.126873i
$301$	4.30932	+	11.8398i	0.248385	+	0.682432i
$302$	−10.1001	−	15.8583i	−0.581197	−	0.912542i
$303$	17.4405			1.00193
$304$	−11.3468	+	13.2382i	−0.650784	+	0.759263i
$305$	−10.0868			−0.577567
$306$	−2.39680	−	3.76324i	−0.137016	−	0.215130i
$307$	1.80674	+	4.96398i	0.103116	+	0.283309i	0.980512	−	0.196457i	$-0.0629436\pi$
$307$	1.80674	+	4.96398i	0.103116	+	0.283309i	−0.877396	+	0.479766i	$0.840721\pi$
$308$	−18.1418	−	8.46507i	−1.03373	−	0.482342i
$309$	−5.45679	−	0.962179i	−0.310426	−	0.0547365i
$310$	−7.31991	+	9.53708i	−0.415743	+	0.541670i
$311$	−3.54816	−	6.14559i	−0.201197	−	0.348484i	0.747717	−	0.664017i	$-0.231150\pi$
$311$	−3.54816	−	6.14559i	−0.201197	−	0.348484i	−0.948915	+	0.315533i	$0.897817\pi$
$312$	−22.8496	+	2.99969i	−1.29360	+	0.169824i
$313$	19.4806	−	16.3462i	1.10111	−	0.923942i	0.103612	−	0.994618i	$-0.466960\pi$
$313$	19.4806	−	16.3462i	1.10111	−	0.923942i	0.997499	+	0.0706759i	$0.0225156\pi$
$314$	0.545278	+	1.31687i	0.0307718	+	0.0743154i
$315$	−6.61454	−	3.81890i	−0.372687	−	0.215171i
$316$	1.21212	−	13.8157i	0.0681869	−	0.777193i
$317$	0.393337	−	1.08068i	0.0220920	−	0.0606973i	−0.928156	−	0.372190i	$-0.878607\pi$
$317$	0.393337	−	1.08068i	0.0220920	−	0.0606973i	0.950248	+	0.311493i	$0.100829\pi$
$318$	1.35830	−	2.60850i	0.0761698	−	0.146277i
$319$	−1.96429	−	11.1401i	−0.109979	−	0.623724i
$320$	−14.0278	+	1.21692i	−0.784180	+	0.0680278i
$321$	1.33079	+	1.11666i	0.0742774	+	0.0623261i
$322$	−32.9025	−	10.3785i	−1.83358	−	0.578373i
$323$	6.16898	−	10.4425i	0.343251	−	0.581038i
$324$	−7.06464	−	4.94929i	−0.392480	−	0.274961i
$325$	7.29267	−	8.69107i	0.404525	−	0.482094i
$326$	−0.922391	−	21.1856i	−0.0510865	−	1.17336i
$327$	−0.802379	−	4.55052i	−0.0443716	−	0.251644i
$328$	−18.1185	+	9.42348i	−1.00043	+	0.520324i
$329$	17.5351	+	6.38224i	0.966740	+	0.351864i
$330$	−8.68254	+	1.92376i	−0.477958	+	0.105899i
$331$	−3.68736	−	2.12890i	−0.202676	−	0.117015i	0.395227	−	0.918583i	$-0.370666\pi$
$331$	−3.68736	−	2.12890i	−0.202676	−	0.117015i	−0.597903	+	0.801568i	$0.703999\pi$
$332$	1.18261	+	13.5554i	0.0649041	+	0.743950i
$333$	−5.46815	−	6.51668i	−0.299653	−	0.357112i
$334$	−2.48541	+	2.27690i	−0.135995	+	0.124586i
$335$	−2.89466	−	5.01369i	−0.158152	−	0.273927i
$336$	20.9134	+	0.0102170i	1.14092	+	0.000557381i
$337$	−4.68326	+	26.5601i	−0.255114	+	1.44682i	0.540667	+	0.841237i	$0.318172\pi$
$337$	−4.68326	+	26.5601i	−0.255114	+	1.44682i	−0.795781	+	0.605585i	$0.792939\pi$
$338$	−4.17093	+	31.6515i	−0.226869	+	1.72162i
$339$	−7.14900	−	19.6417i	−0.388281	−	1.06679i
$340$	9.46159	−	2.53275i	0.513127	−	0.137358i
$341$			12.6323i			0.684075i
$342$	−0.982371	+	6.92006i	−0.0531205	+	0.374194i
$343$	−2.48025			−0.133921
$344$	9.30233	+	0.409563i	0.501548	+	0.0220822i
$345$	−14.4016	+	5.24175i	−0.775355	+	0.282206i
$346$	25.1150	+	3.30957i	1.35019	+	0.177924i
$347$	17.6565	+	3.11331i	0.947849	+	0.167131i	0.626143	−	0.779708i	$-0.284633\pi$
$347$	17.6565	+	3.11331i	0.947849	+	0.167131i	0.321706	+	0.946840i	$0.395744\pi$
$348$	6.77557	+	9.68155i	0.363209	+	0.518986i
$349$	−17.4551	+	10.0777i	−0.934352	+	0.539449i	−0.888185	−	0.459485i	$-0.848034\pi$
$349$	−17.4551	+	10.0777i	−0.934352	+	0.539449i	−0.0461670	+	0.998934i	$0.514701\pi$
$350$	−7.59162	+	6.95473i	−0.405789	+	0.371746i
$351$	−25.8019	+	21.6504i	−1.37720	+	1.15561i
$352$	−10.9140	+	9.98858i	−0.581718	+	0.532393i
$353$	−5.89589	+	10.2120i	−0.313806	+	0.543529i	−0.979183	−	0.202979i	$-0.934938\pi$
$353$	−5.89589	+	10.2120i	−0.313806	+	0.543529i	0.665377	+	0.746508i	$0.268271\pi$
$354$	−3.13184	−	14.1350i	−0.166455	−	0.751265i
$355$	−0.819490	+	2.25153i	−0.0434940	+	0.119499i
$356$	10.4040	−	10.3989i	0.551408	−	0.551139i
$357$	−14.3268	+	2.52620i	−0.758255	+	0.133701i
$358$	1.40306	+	32.2256i	0.0741538	+	1.70317i
$359$	9.80756	+	8.22952i	0.517623	+	0.434338i	0.863802	−	0.503831i	$-0.168077\pi$
$359$	9.80756	+	8.22952i	0.517623	+	0.434338i	−0.346179	+	0.938169i	$0.612521\pi$
$360$	−4.47933	+	3.43450i	−0.236081	+	0.181014i
$361$	−17.9805	+	6.14017i	−0.946342	+	0.323167i
$362$	2.35692	−	7.47201i	0.123877	−	0.392720i
$363$	3.65269	−	4.35311i	0.191717	−	0.228479i
$364$	11.8272	−	44.0965i	0.619913	−	2.31129i
$365$	−19.4510	+	3.42973i	−1.01811	+	0.179520i
$366$	5.11354	−	9.82008i	0.267289	−	0.513304i
$367$	−31.4886	−	11.4609i	−1.64369	−	0.598256i	−0.656015	−	0.754748i	$-0.727759\pi$
$367$	−31.4886	−	11.4609i	−1.64369	−	0.598256i	−0.987679	+	0.156492i	$0.949981\pi$
$368$	−16.3984	+	19.5235i	−0.854825	+	1.01773i
$369$	−4.09342	+	7.09002i	−0.213095	+	0.369092i
$370$	17.2545	−	7.14459i	0.897021	−	0.371430i
$371$	3.74504	+	4.46316i	0.194433	+	0.231716i
$372$	−5.57406	−	11.9612i	−0.289002	−	0.620161i
$373$	27.8103	−	16.0563i	1.43996	−	0.831363i	0.442117	−	0.896957i	$-0.354228\pi$
$373$	27.8103	−	16.0563i	1.43996	−	0.831363i	0.997846	+	0.0655941i	$0.0208942\pi$
$374$	6.26613	−	8.16412i	0.324014	−	0.422156i
$375$	−2.88177	+	16.3433i	−0.148814	+	0.843966i
$376$	9.32038	−	10.1639i	0.480662	−	0.524165i
$377$	24.2413	−	8.82312i	1.24849	−	0.454414i
$378$	25.7808	−	16.4197i	1.32602	−	0.844540i
$379$		−	4.90569i		−	0.251989i	−0.992031	−	0.125994i	$-0.959788\pi$
$379$		−	4.90569i		−	0.251989i	0.992031	−	0.125994i	$-0.0402121\pi$
$380$	−13.8392	−	6.62667i	−0.709934	−	0.339941i
$381$			15.4179i			0.789883i
$382$	1.15719	+	1.81691i	0.0592069	+	0.0929612i
$383$	−3.08105	+	1.12141i	−0.157434	+	0.0573015i	−0.419535	−	0.907739i	$-0.637807\pi$
$383$	−3.08105	+	1.12141i	−0.157434	+	0.0573015i	0.262101	+	0.965041i	$0.415585\pi$
$384$	5.92673	−	14.2739i	0.302447	−	0.728410i
$385$	3.05931	−	17.3502i	0.155917	−	0.884249i
$386$	−10.9588	−	8.41111i	−0.557788	−	0.428114i
$387$	3.23257	−	1.86633i	0.164321	−	0.0948707i
$388$	22.1003	−	10.2990i	1.12197	−	0.522850i
$389$	−11.9048	−	14.1876i	−0.603598	−	0.719340i	0.374560	−	0.927203i	$-0.377794\pi$
$389$	−11.9048	−	14.1876i	−0.603598	−	0.719340i	−0.978158	+	0.207863i	$0.933349\pi$
$390$	−7.75889	−	18.7381i	−0.392886	−	0.948840i
$391$	8.86798	−	15.3598i	0.448473	−	0.776778i
$392$	−8.28551	+	19.9823i	−0.418481	+	1.00926i
$393$	−14.0706	−	5.12128i	−0.709768	−	0.258334i
$394$	7.50689	+	3.90900i	0.378192	+	0.196933i
$395$	12.0195	−	2.11937i	0.604769	−	0.106637i
$396$	−1.53641	+	5.72836i	−0.0772075	+	0.287861i
$397$	−8.96487	+	10.6839i	−0.449934	+	0.536210i	−0.942563	−	0.334029i	$-0.891592\pi$
$397$	−8.96487	+	10.6839i	−0.449934	+	0.536210i	0.492629	+	0.870240i	$0.336036\pi$
$398$	−6.35858	−	2.00571i	−0.318727	−	0.100537i
$399$	19.6217	+	11.5916i	0.982314	+	0.580308i
$400$	2.59883	+	7.15110i	0.129942	+	0.357555i
$401$	18.4067	+	15.4451i	0.919188	+	0.771291i	0.973845	−	0.227215i	$-0.0729619\pi$
$401$	18.4067	+	15.4451i	0.919188	+	0.771291i	−0.0546563	+	0.998505i	$0.517406\pi$
$402$	6.34859	−	0.276408i	0.316639	−	0.0137860i
$403$	−28.3705	+	5.00248i	−1.41323	+	0.249191i
$404$	18.0507	+	18.0595i	0.898054	+	0.898493i
$405$	2.59627	−	7.13320i	0.129010	−	0.354452i
$406$	−22.8560	+	5.06411i	−1.13432	+	0.251328i
$407$	9.81132	−	16.9937i	0.486329	−	0.842346i
$408$	−2.33081	+	10.4954i	−0.115392	+	0.519600i
$409$	27.4590	−	23.0409i	1.35776	−	1.13930i	0.381095	−	0.924536i	$-0.375547\pi$
$409$	27.4590	−	23.0409i	1.35776	−	1.13930i	0.976667	−	0.214762i	$-0.0688974\pi$
$410$	−12.1405	−	13.2522i	−0.599575	−	0.654482i
$411$	−23.7753	+	13.7267i	−1.17275	+	0.677086i
$412$	−4.65137	−	6.64630i	−0.229156	−	0.327439i
$413$	28.2457	+	4.98049i	1.38988	+	0.245074i
$414$	−1.33532	+	10.1332i	−0.0656276	+	0.498021i
$415$	−11.2524	+	4.09553i	−0.552357	+	0.201041i
$416$	−26.7551	−	20.5559i	−1.31178	−	1.00784i
$417$	−22.5710			−1.10531
$418$	−15.7746	+	3.33007i	−0.771562	+	0.162879i
$419$			16.1004i			0.786557i	0.919419	+	0.393279i	$0.128659\pi$
$419$			16.1004i			0.786557i	−0.919419	+	0.393279i	$0.871341\pi$
$420$	4.75908	+	17.7785i	0.232220	+	0.867503i
$421$	0.928735	+	2.55168i	0.0452638	+	0.124361i	0.960265	−	0.279090i	$-0.0900328\pi$
$421$	0.928735	+	2.55168i	0.0452638	+	0.124361i	−0.915001	+	0.403451i	$0.867811\pi$
$422$	31.0369	+	4.08994i	1.51085	+	0.199095i
$423$	0.959958	−	5.44419i	0.0466748	−	0.264706i
$424$	4.10689	−	1.29324i	0.199448	−	0.0628055i
$425$	−2.64639	−	4.58368i	−0.128369	−	0.222341i
$426$	−1.77655	−	1.93924i	−0.0860743	−	0.0939567i
$427$	14.0988	+	16.8023i	0.682288	+	0.813119i
$428$	0.221051	+	2.53375i	0.0106849	+	0.122473i
$429$	−18.4548	−	10.6549i	−0.891007	−	0.514423i
$430$	1.77259	+	8.00026i	0.0854818	+	0.385807i
$431$	27.2647	+	9.92353i	1.31329	+	0.478000i	0.901303	−	0.433189i	$-0.142612\pi$
$431$	27.2647	+	9.92353i	1.31329	+	0.478000i	0.411990	+	0.911188i	$0.364834\pi$
$432$	−3.91159	−	22.2473i	−0.188196	−	1.07037i
$433$	4.76510	+	27.0242i	0.228996	+	1.29870i	0.854897	+	0.518798i	$0.173620\pi$
$433$	4.76510	+	27.0242i	0.228996	+	1.29870i	−0.625901	+	0.779903i	$0.715269\pi$
$434$	26.1180	−	1.13714i	1.25370	−	0.0545845i
$435$	−6.68455	+	7.96634i	−0.320500	+	0.381957i
$436$	3.88157	−	5.54057i	0.185893	−	0.265345i
$437$	−26.2023	+	9.24131i	−1.25343	+	0.442072i
$438$	6.52170	−	20.6754i	0.311619	−	0.987908i
$439$	−2.72236	−	2.28433i	−0.129931	−	0.109025i	0.575506	−	0.817797i	$-0.304805\pi$
$439$	−2.72236	−	2.28433i	−0.129931	−	0.109025i	−0.705437	+	0.708772i	$0.749249\pi$
$440$	−10.9783	−	6.99962i	−0.523371	−	0.333694i
$441$	1.50581	+	8.53989i	0.0717054	+	0.406661i
$442$	20.8170	+	10.8399i	0.990166	+	0.515601i
$443$	−11.4208	+	31.3785i	−0.542620	+	1.49084i	0.300856	+	0.953670i	$0.402728\pi$
$443$	−11.4208	+	31.3785i	−0.542620	+	1.49084i	−0.843476	+	0.537167i	$0.819494\pi$
$444$	−1.79157	+	20.4203i	−0.0850242	+	0.969105i
$445$	11.2108	+	6.47256i	0.531443	+	0.306829i
$446$	−31.2846	+	12.9540i	−1.48137	+	0.613391i
$447$	19.2170	−	16.1250i	0.908932	−	0.762685i
$448$	21.6345	+	21.6662i	1.02213	+	1.02363i
$449$	−5.75115	−	9.96129i	−0.271414	−	0.470102i	0.697810	−	0.716283i	$-0.254158\pi$
$449$	−5.75115	−	9.96129i	−0.271414	−	0.470102i	−0.969224	+	0.246180i	$0.920825\pi$
$450$	2.41959	+	1.85708i	0.114060	+	0.0875438i
$451$	−18.5974	−	3.27923i	−0.875718	−	0.154413i
$452$	12.9397	−	27.7316i	0.608633	−	1.30439i
$453$	6.21162	+	17.0663i	0.291847	+	0.801844i
$454$	−2.01206	+	1.28148i	−0.0944307	+	0.0601428i
$455$	40.1779			1.88357
$456$	13.4673	−	10.1138i	0.630663	−	0.473623i
$457$	−10.9250			−0.511048			−0.255524	−	0.966803i	$-0.582248\pi$
$457$	−10.9250			−0.511048			−0.255524	+	0.966803i	$0.582248\pi$
$458$	−4.29565	+	2.73589i	−0.200723	+	0.127840i
$459$	5.37419	+	14.7655i	0.250846	+	0.689193i
$460$	−20.3332	−	9.48758i	−0.948041	−	0.442361i
$461$	40.6685	+	7.17095i	1.89412	+	0.333985i	0.994676	−	0.103050i	$-0.0328602\pi$
$461$	40.6685	+	7.17095i	1.89412	+	0.333985i	0.899445	+	0.437035i	$0.143971\pi$
$462$	15.3405	+	11.7742i	0.713706	+	0.547785i
$463$	−5.45960	−	9.45631i	−0.253729	−	0.439472i	0.710820	−	0.703374i	$-0.248324\pi$
$463$	−5.45960	−	9.45631i	−0.253729	−	0.439472i	−0.964550	+	0.263902i	$0.914991\pi$
$464$	−3.01254	+	17.0363i	−0.139854	+	0.790890i
$465$	8.89618	−	7.46478i	0.412550	−	0.346171i
$466$	5.09801	−	2.11093i	0.236161	−	0.0977871i
$467$	−18.6654	−	10.7765i	−0.863734	−	0.498677i	0.00152700	−	0.999999i	$-0.499514\pi$
$467$	−18.6654	−	10.7765i	−0.863734	−	0.498677i	−0.865261	+	0.501322i	$0.832847\pi$
$468$	−13.4736	−	1.18211i	−0.622819	−	0.0546429i
$469$	−4.30566	+	11.8297i	−0.198817	+	0.546245i
$470$	10.7641	+	5.60509i	0.496510	+	0.258544i
$471$	−0.239076	−	1.35587i	−0.0110160	−	0.0624751i
$472$	11.3952	−	17.8725i	0.524508	−	0.822647i
$473$	6.59562	+	5.53439i	0.303267	+	0.254471i
$474$	−4.03002	+	12.7762i	−0.185105	+	0.586829i
$475$	−1.52133	+	8.15062i	−0.0698034	+	0.373976i
$476$	−17.4439	−	12.2207i	−0.799540	−	0.560135i
$477$	1.10947	−	1.32222i	0.0507993	−	0.0605402i
$478$	4.83748	−	0.210617i	0.221261	−	0.00963339i
$479$	−5.48301	−	31.0957i	−0.250525	−	1.42080i	−0.807303	−	0.590137i	$-0.799074\pi$
$479$	−5.48301	−	31.0957i	−0.250525	−	1.42080i	0.556778	−	0.830661i	$-0.312037\pi$
$480$	13.4838	+	1.78355i	0.615448	+	0.0814077i
$481$	42.0511	+	15.3054i	1.91737	+	0.697864i
$482$	−2.75529	−	12.4355i	−0.125500	−	0.566422i
$483$	28.8613	+	16.6631i	1.31324	+	0.758197i
$484$	8.28809	−	0.723074i	0.376731	−	0.0328670i
$485$	13.7924	+	16.4371i	0.626279	+	0.746370i
$486$	−10.5557	−	11.5224i	−0.478818	−	0.522667i
$487$	8.73788	+	15.1345i	0.395951	+	0.685808i	0.993222	−	0.116232i	$-0.0370816\pi$
$487$	8.73788	+	15.1345i	0.395951	+	0.685808i	−0.597271	+	0.802040i	$0.703748\pi$
$488$	15.4610	−	4.86862i	0.699888	−	0.220392i
$489$	−3.55699	+	20.1727i	−0.160852	+	0.912240i
$490$	−18.8736	−	2.48711i	−0.852624	−	0.112356i
$491$	−3.77132	−	10.3616i	−0.170197	−	0.467613i	0.825042	−	0.565071i	$-0.191151\pi$
$491$	−3.77132	−	10.3616i	−0.170197	−	0.467613i	−0.995240	+	0.0974577i	$0.968929\pi$
$492$	19.0565	−	5.10119i	0.859134	−	0.229979i
$493$		−	12.0347i		−	0.542015i
$494$	−13.7258	−	34.1091i	−0.617553	−	1.53464i
$495$	−5.21932			−0.234591
$496$	6.61668	−	18.1516i	0.297098	−	0.815030i
$497$	4.89597	−	1.78199i	0.219614	−	0.0799331i
$498$	1.71720	−	13.0311i	0.0769494	−	0.583937i
$499$	−27.4017	−	4.83166i	−1.22667	−	0.216295i	−0.477474	−	0.878646i	$-0.658448\pi$
$499$	−27.4017	−	4.83166i	−1.22667	−	0.216295i	−0.749193	+	0.662351i	$0.769559\pi$
$500$	−19.9060	+	13.9311i	−0.890222	+	0.623016i
$501$	2.81974	−	1.62798i	0.125977	−	0.0727326i
$502$	5.27416	+	5.75715i	0.235397	+	0.256954i
$503$	−5.06697	+	4.25169i	−0.225925	+	0.189573i	−0.748723	−	0.662883i	$-0.769333\pi$
$503$	−5.06697	+	4.25169i	−0.225925	+	0.189573i	0.522798	+	0.852457i	$0.324888\pi$
$504$	11.9821	+	2.66096i	0.533723	+	0.118529i
$505$	−11.2352	+	19.4600i	−0.499962	+	0.865960i
$506$	−23.0178	+	5.09998i	−1.02327	+	0.226722i
$507$	10.5474	−	28.9787i	0.468425	−	1.28699i
$508$	−15.9651	+	15.9573i	−0.708337	+	0.707991i
$509$	−12.0534	+	2.12533i	−0.534256	+	0.0942038i	−0.434266	−	0.900785i	$-0.642992\pi$
$509$	−12.0534	+	2.12533i	−0.534256	+	0.0942038i	−0.0999901	+	0.994988i	$0.531881\pi$
$510$	−9.45237	+	0.411543i	−0.418558	+	0.0182234i
$511$	32.9007	+	27.6069i	1.45544	+	1.22126i
$512$	20.9145	−	8.63615i	0.924300	−	0.381668i
$513$	8.64971	−	23.0455i	0.381894	−	1.01748i
$514$	28.2079	+	8.89772i	1.24420	+	0.392462i
$515$	4.58888	−	5.46882i	0.202210	−	0.240985i
$516$	−8.68735	−	2.33004i	−0.382439	−	0.102574i
$517$	12.5579	−	2.21430i	0.552297	−	0.0973849i
$518$	−36.0187	−	18.7558i	−1.58257	−	0.824081i
$519$	−22.9941	−	8.36918i	−1.00933	−	0.367366i
$520$	11.3728	−	27.4279i	0.498729	−	1.20279i
$521$	−6.12941	+	10.6165i	−0.268534	+	0.465115i	−0.968484	−	0.249077i	$-0.919873\pi$
$521$	−6.12941	+	10.6165i	−0.268534	+	0.465115i	0.699949	+	0.714193i	$0.253206\pi$
$522$	2.65325	+	6.40773i	0.116130	+	0.280459i
$523$	−6.53118	−	7.78356i	−0.285589	−	0.340351i	0.604109	−	0.796902i	$-0.293529\pi$
$523$	−6.53118	−	7.78356i	−0.285589	−	0.340351i	−0.889697	+	0.456551i	$0.849085\pi$
$524$	−9.25982	−	19.8704i	−0.404517	−	0.868043i
$525$	8.61282	−	4.97261i	0.375894	−	0.217023i
$526$	1.95680	+	1.50189i	0.0853206	+	0.0654853i
$527$	−2.33373	+	13.2352i	−0.101659	+	0.576535i
$528$	12.3801	−	7.13957i	0.538773	−	0.310710i
$529$	−16.5664	+	6.02967i	−0.720277	+	0.262159i
$530$	2.03552	+	3.19599i	0.0884174	+	0.138825i
$531$		−	8.49693i		−	0.368735i
$532$	8.30514	+	32.3153i	0.360073	+	1.40104i
$533$		−	43.0661i		−	1.86540i
$534$	−11.9848	+	7.63309i	−0.518632	+	0.330316i
$535$	−2.10327	+	0.765527i	−0.0909322	+	0.0330966i
$536$	6.85691	+	6.28782i	0.296173	+	0.271593i
$537$	5.41056	−	30.6848i	0.233483	−	1.32415i
$538$	8.80976	−	11.4782i	0.379816	−	0.494860i
$539$	−17.3227	+	10.0013i	−0.746142	+	0.430785i
$540$	18.0182	−	8.39668i	0.775381	−	0.361335i
$541$	−14.8292	−	17.6728i	−0.637557	−	0.759811i	0.346425	−	0.938078i	$-0.387395\pi$
$541$	−14.8292	−	17.6728i	−0.637557	−	0.759811i	−0.983982	+	0.178267i	$0.942951\pi$
$542$	28.0280	−	11.6056i	1.20390	−	0.498501i
$543$	−3.78412	+	6.55429i	−0.162392	+	0.281271i
$544$	−13.2803	+	8.44906i	−0.569386	+	0.362250i
$545$	5.59434	+	2.03617i	0.239635	+	0.0872200i
$546$	−20.3684	+	39.1156i	−0.871686	+	1.67399i
$547$	13.3611	−	2.35593i	0.571281	−	0.100732i	0.119457	−	0.992839i	$-0.461885\pi$
$547$	13.3611	−	2.35593i	0.571281	−	0.100732i	0.451824	+	0.892107i	$0.350773\pi$
$548$	−38.8209	−	10.4122i	−1.65835	−	0.444787i
$549$	4.17678	−	4.97770i	0.178261	−	0.212443i
$550$	−2.11646	+	6.70969i	−0.0902461	+	0.286102i
$551$	−12.2622	+	14.3203i	−0.522386	+	0.610065i
$552$	19.5447	−	14.9858i	0.831879	−	0.637839i
$553$	−20.3307	−	17.0595i	−0.864548	−	0.725442i
$554$	0.892390	+	20.4965i	0.0379140	+	0.870814i
$555$	−17.7655	+	3.13254i	−0.754103	+	0.132969i
$556$	−23.3607	−	23.3721i	−0.990714	−	0.991198i
$557$	−12.9729	+	35.6427i	−0.549679	+	1.51023i	0.284466	+	0.958686i	$0.408184\pi$
$557$	−12.9729	+	35.6427i	−0.549679	+	1.51023i	−0.834145	+	0.551545i	$0.814039\pi$
$558$	−1.67536	−	7.56144i	−0.0709238	−	0.320101i
$559$	−9.81762	+	17.0046i	−0.415241	+	0.719219i
$560$	−13.4839	+	23.3285i	−0.569799	+	0.985808i
$561$	−7.61548	+	6.39014i	−0.321526	+	0.269792i
$562$	−26.4268	+	24.2098i	−1.11475	+	1.02123i
$563$	−24.8787	+	14.3637i	−1.04851	+	0.605360i	−0.922233	−	0.386635i	$-0.873637\pi$
$563$	−24.8787	+	14.3637i	−1.04851	+	0.605360i	−0.126281	+	0.991995i	$0.540304\pi$
$564$	−10.9138	+	7.63794i	−0.459553	+	0.321615i
$565$	26.5216	+	4.67647i	1.11577	+	0.196740i
$566$	−15.4549	−	2.03659i	−0.649617	−	0.0856044i
$567$	−15.5112	+	5.64562i	−0.651410	+	0.237094i
$568$	0.169362	−	3.84669i	0.00710629	−	0.161404i
$569$	−14.4506			−0.605800			−0.302900	−	0.953022i	$-0.597955\pi$
$569$	−14.4506			−0.605800			−0.302900	+	0.953022i	$0.597955\pi$
$570$	11.6669	+	9.14133i	0.488672	+	0.382888i
$571$		−	38.7437i		−	1.62137i	−0.585480	−	0.810687i	$-0.699094\pi$
$571$		−	38.7437i		−	1.62137i	0.585480	−	0.810687i	$-0.300906\pi$
$572$	−8.06741	−	30.1374i	−0.337316	−	1.26011i
$573$	−0.711676	−	1.95531i	−0.0297307	−	0.0816844i
$574$	−5.10589	+	38.7465i	−0.213116	+	1.61725i
$575$	−2.10543	+	11.9405i	−0.0878026	+	0.497953i
$576$	5.20818	−	7.42646i	0.217007	−	0.309436i
$577$	−15.5793	−	26.9841i	−0.648575	−	1.12336i	−0.983463	−	0.181107i	$-0.942032\pi$
$577$	−15.5793	−	26.9841i	−0.648575	−	1.12336i	0.334889	−	0.942258i	$-0.391301\pi$
$578$	−9.65384	+	8.84395i	−0.401547	+	0.367860i
$579$	8.57757	+	10.2223i	0.356472	+	0.424826i
$580$	−15.1675	+	1.32325i	−0.629795	+	0.0549449i
$581$	22.5502	+	13.0194i	0.935539	+	0.540134i
$582$	−22.9946	+	5.09483i	−0.953156	+	0.211187i
$583$	3.74127	+	1.36171i	0.154948	+	0.0563964i
$584$	28.1590	−	14.6455i	1.16523	−	0.606037i
$585$	−2.06690	−	11.7219i	−0.0854556	−	0.484643i
$586$	0.656188	+	15.0714i	0.0271069	+	0.622594i
$587$	−11.8358	+	14.1054i	−0.488517	+	0.582192i	−0.952840	−	0.303474i	$-0.901853\pi$
$587$	−11.8358	+	14.1054i	−0.488517	+	0.582192i	0.464323	+	0.885666i	$0.346298\pi$
$588$	11.9894	−	17.1138i	0.494435	−	0.705760i
$589$	16.2623	−	13.3710i	0.670078	−	0.550942i
$590$	17.7893	+	5.61132i	0.732372	+	0.231014i
$591$	−6.26286	−	5.25516i	−0.257619	−	0.216168i
$592$	−22.9993	+	19.2796i	−0.945265	+	0.792385i
$593$	1.95725	+	11.1001i	0.0803747	+	0.455828i	0.998259	+	0.0589799i	$0.0187848\pi$
$593$	1.95725	+	11.1001i	0.0803747	+	0.455828i	−0.917884	+	0.396848i	$0.870104\pi$
$594$	9.64685	−	18.5259i	0.395815	−	0.760127i
$595$	6.41067	−	17.6132i	0.262812	−	0.722070i
$596$	36.5865	+	3.20991i	1.49864	+	0.131483i
$597$	5.57760	+	3.22023i	0.228276	+	0.131795i
$598$	−20.5692	−	49.6756i	−0.841136	−	2.03138i
$599$	−23.7426	+	19.9224i	−0.970095	+	0.814007i	−0.982566	−	0.185916i	$-0.940475\pi$
$599$	−23.7426	+	19.9224i	−0.970095	+	0.814007i	0.0124703	+	0.999922i	$0.496030\pi$
$600$	−0.956659	−	7.28718i	−0.0390554	−	0.297498i
$601$	−11.2846	−	19.5455i	−0.460307	−	0.797276i	0.538669	−	0.842518i	$-0.318927\pi$
$601$	−11.2846	−	19.5455i	−0.460307	−	0.797276i	−0.998976	+	0.0452420i	$0.985594\pi$
$602$	10.8490	−	14.1351i	0.442171	−	0.576102i
$603$	3.67282	+	0.647618i	0.149569	+	0.0263730i
$604$	−11.2431	+	24.0954i	−0.457473	+	0.980429i
$605$	2.50410	+	6.87995i	0.101806	+	0.279710i
$606$	−13.2497	−	20.8035i	−0.538234	−	0.845086i
$607$	−15.7003			−0.637257			−0.318628	−	0.947880i	$-0.603222\pi$
$607$	−15.7003			−0.637257			−0.318628	+	0.947880i	$0.603222\pi$
$608$	24.4112	+	3.47758i	0.990005	+	0.141034i
$609$	22.6134			0.916341
$610$	7.66304	+	12.0318i	0.310267	+	0.487153i
$611$	9.94610	+	27.3267i	0.402376	+	1.10552i
$612$	−2.66802	+	5.71794i	−0.107848	+	0.231134i
$613$	−27.8884	−	4.91748i	−1.12640	−	0.198615i	−0.420752	−	0.907176i	$-0.638234\pi$
$613$	−27.8884	−	4.91748i	−1.12640	−	0.198615i	−0.705650	+	0.708561i	$0.749345\pi$
$614$	4.54858	−	5.92632i	0.183566	−	0.239167i
$615$	8.68040	+	15.0349i	0.350028	+	0.606266i
$616$	3.68517	+	28.0711i	0.148480	+	1.13102i
$617$	20.1984	−	16.9484i	0.813155	−	0.682318i	−0.138203	−	0.990404i	$-0.544133\pi$
$617$	20.1984	−	16.9484i	0.813155	−	0.682318i	0.951359	+	0.308086i	$0.0996883\pi$
$618$	2.99787	+	7.23999i	0.120592	+	0.291235i
$619$	−8.70164	−	5.02389i	−0.349748	−	0.201927i	0.314826	−	0.949149i	$-0.398054\pi$
$619$	−8.70164	−	5.02389i	−0.349748	−	0.201927i	−0.664574	+	0.747222i	$0.731387\pi$
$620$	16.9371	+	1.48598i	0.680211	+	0.0596782i
$621$	12.3112	−	33.8248i	0.494032	−	1.35734i
$622$	−4.63506	+	8.90121i	−0.185849	+	0.356906i
$623$	−4.88807	−	27.7216i	−0.195836	−	1.11064i
$624$	20.9372	+	24.9768i	0.838159	+	0.999871i
$625$	−9.09362	−	7.63045i	−0.363745	−	0.305218i
$626$	−34.2979	−	10.8187i	−1.37082	−	0.432401i
$627$	15.5727	+	0.155668i	0.621915	+	0.00621679i
$628$	1.15655	−	1.65086i	0.0461513	−	0.0658766i
$629$	13.4191	−	15.9923i	0.535054	−	0.637653i
$630$	0.469836	+	10.7913i	0.0187187	+	0.429934i
$631$	1.03255	+	5.85590i	0.0411053	+	0.233120i	0.998438	−	0.0558677i	$-0.0177925\pi$
$631$	1.03255	+	5.85590i	0.0411053	+	0.233120i	−0.957333	+	0.288987i	$0.906681\pi$
$632$	−17.4006	+	9.05008i	−0.692159	+	0.359993i
$633$	−28.4160	−	10.3426i	−1.12943	−	0.411080i
$634$	−1.58789	+	0.351824i	−0.0630633	+	0.0139727i
$635$	−17.2032	−	9.93228i	−0.682689	−	0.394151i
$636$	−4.14340	+	0.361481i	−0.164297	+	0.0143337i
$637$	−29.3216	−	34.9441i	−1.16176	−	1.38454i
$638$	−11.7959	+	10.8063i	−0.467004	+	0.427825i
$639$	−0.771762	−	1.33673i	−0.0305304	−	0.0528803i
$640$	12.1087	+	15.8083i	0.478637	+	0.624877i
$641$	−1.53945	+	8.73067i	−0.0608047	+	0.344841i	0.939194	+	0.343386i	$0.111574\pi$
$641$	−1.53945	+	8.73067i	−0.0608047	+	0.344841i	−0.999999	+	0.00145435i	$0.999537\pi$
$642$	0.320974	−	2.43574i	0.0126679	−	0.0961312i
$643$	11.2379	+	30.8759i	0.443180	+	1.21763i	0.937389	+	0.348284i	$0.113235\pi$
$643$	11.2379	+	30.8759i	0.443180	+	1.21763i	−0.494209	+	0.869343i	$0.664542\pi$
$644$	12.6166	+	47.1317i	0.497162	+	1.85725i
$645$		−	7.91536i		−	0.311667i
$646$	−17.1428	+	0.574759i	−0.674474	+	0.0226136i
$647$	−4.85643			−0.190926			−0.0954629	−	0.995433i	$-0.530433\pi$
$647$	−4.85643			−0.190926			−0.0954629	+	0.995433i	$0.530433\pi$
$648$	−0.536567	+	12.1869i	−0.0210783	+	0.478748i
$649$	18.4176	−	6.70345i	0.722953	−	0.263133i
$650$	−15.9073	−	2.09621i	−0.623935	−	0.0822201i
$651$	−24.8692	−	4.38512i	−0.974702	−	0.171866i
$652$	−24.5700	+	17.1952i	−0.962237	+	0.673415i
$653$	22.9690	−	13.2611i	0.898846	−	0.518949i	0.0220202	−	0.999758i	$-0.492990\pi$
$653$	22.9690	−	13.2611i	0.898846	−	0.518949i	0.876826	+	0.480809i	$0.159657\pi$
$654$	−4.81841	+	4.41418i	−0.188415	+	0.172608i
$655$	14.7786	−	12.4007i	0.577449	−	0.484537i
$656$	25.0054	+	14.4532i	0.976298	+	0.564302i
$657$	6.36182	−	11.0190i	0.248198	−	0.429892i
$658$	−5.70866	−	25.7650i	−0.222547	−	1.00442i
$659$	−1.53725	+	4.22355i	−0.0598827	+	0.164526i	−0.966026	−	0.258444i	$-0.916790\pi$
$659$	−1.53725	+	4.22355i	−0.0598827	+	0.164526i	0.906144	+	0.422970i	$0.139013\pi$
$660$	8.89093	+	8.89528i	0.346079	+	0.346248i
$661$	14.3356	−	2.52775i	0.557589	−	0.0983179i	0.112250	−	0.993680i	$-0.464194\pi$
$661$	14.3356	−	2.52775i	0.557589	−	0.0983179i	0.445339	+	0.895362i	$0.353083\pi$
$662$	0.261917	+	6.01574i	0.0101797	+	0.233808i
$663$	−17.3673	−	14.5729i	−0.674489	−	0.565963i
$664$	15.2708	−	11.7088i	0.592624	−	0.454391i
$665$	−25.5743	+	14.4264i	−0.991728	+	0.559432i
$666$	−3.61908	+	11.4734i	−0.140236	+	0.444584i
$667$	−17.7211	+	21.1191i	−0.686162	+	0.817736i
$668$	4.60414	+	1.23488i	0.178139	+	0.0477790i
$669$	32.2110	−	5.67967i	1.24535	−	0.219589i
$670$	−3.78137	+	7.26178i	−0.146087	+	0.280547i
$671$	14.0846	+	5.12638i	0.543730	+	0.197902i
$672$	−15.8759	−	24.9539i	−0.612428	−	0.962616i
$673$	−1.27655	+	2.21106i	−0.0492076	+	0.0852300i	−0.889580	−	0.456779i	$-0.849003\pi$
$673$	−1.27655	+	2.21106i	−0.0492076	+	0.0852300i	0.840372	+	0.542009i	$0.182336\pi$
$674$	35.2396	−	14.5917i	1.35738	−	0.562050i
$675$	−6.90471	−	8.22872i	−0.265763	−	0.316723i
$676$	40.9235	−	19.0708i	1.57398	−	0.733492i
$677$	−26.8658	+	15.5109i	−1.03253	+	0.596134i	−0.917710	−	0.397252i	$-0.869964\pi$
$677$	−26.8658	+	15.5109i	−1.03253	+	0.596134i	−0.114825	+	0.993386i	$0.536631\pi$
$678$	−17.9980	+	23.4496i	−0.691210	+	0.900575i
$679$	8.10219	−	45.9498i	0.310933	−	1.76339i
$680$	−10.2092	−	9.36190i	−0.391505	−	0.359012i
$681$	2.16533	−	0.788115i	0.0829756	−	0.0302006i
$682$	15.0681	−	9.59686i	0.576988	−	0.367483i
$683$		−	39.1949i		−	1.49975i	−0.661578	−	0.749876i	$-0.730113\pi$
$683$		−	39.1949i		−	1.49975i	0.661578	−	0.749876i	$-0.269887\pi$
$684$	9.00076	−	4.08544i	0.344153	−	0.156211i
$685$		−	35.3711i		−	1.35146i
$686$	1.88427	+	2.95851i	0.0719419	+	0.112957i
$687$	4.62287	−	1.68259i	0.176374	−	0.0641947i
$688$	−6.57854	−	11.4072i	−0.250804	−	0.434896i
$689$	−1.57666	+	8.94169i	−0.0600660	+	0.340651i
$690$	17.1935	+	13.1964i	0.654547	+	0.502379i
$691$	0.357391	−	0.206340i	0.0135958	−	0.00784954i	−0.493187	−	0.869923i	$-0.664168\pi$
$691$	0.357391	−	0.206340i	0.0135958	−	0.00784954i	0.506782	+	0.862074i	$0.330835\pi$
$692$	−15.1324	−	32.4722i	−0.575246	−	1.23441i
$693$	7.29529	+	8.69419i	0.277125	+	0.330265i
$694$	−9.70016	−	23.4263i	−0.368213	−	0.889252i
$695$	14.5404	−	25.1847i	0.551548	−	0.955309i
$696$	6.40095	−	15.4373i	0.242628	−	0.585148i
$697$	−18.8793	−	6.87150i	−0.715104	−	0.260277i
$698$	25.2819	+	13.1648i	0.956933	+	0.498296i
$699$	−5.24897	+	0.925536i	−0.198534	+	0.0350070i
$700$	14.0632	+	3.77191i	0.531540	+	0.142565i
$701$	0.701629	−	0.836169i	0.0265002	−	0.0315817i	−0.752632	−	0.658442i	$-0.771216\pi$
$701$	0.701629	−	0.836169i	0.0265002	−	0.0315817i	0.779132	+	0.626860i	$0.215660\pi$
$702$	45.4271	+	14.3292i	1.71454	+	0.540821i
$703$	−32.2622	+	5.35675i	−1.21679	+	0.202034i
$704$	20.2061	+	5.43009i	0.761547	+	0.204654i
$705$	−8.98027	−	7.53534i	−0.338216	−	0.283797i
$706$	16.6603	−	0.725366i	0.627019	−	0.0272995i
$707$	48.1200	−	8.48485i	1.80974	−	0.319106i
$708$	−14.4813	+	14.4742i	−0.544241	+	0.543975i
$709$	−15.5133	+	42.6225i	−0.582615	+	1.60072i	0.201080	+	0.979575i	$0.435555\pi$
$709$	−15.5133	+	42.6225i	−0.582615	+	1.60072i	−0.783695	+	0.621146i	$0.786667\pi$
$710$	3.30826	−	0.733000i	0.124157	−	0.0275090i
$711$	−3.93123	+	6.80908i	−0.147433	+	0.255361i
$712$	−20.3081	−	4.51000i	−0.761077	−	0.169019i
$713$	23.5842	−	19.7895i	0.883235	−	0.741122i
$714$	13.8976	+	15.1702i	0.520103	+	0.567732i
$715$	23.7773	−	13.7279i	0.889222	−	0.513393i
$716$	37.3737	−	26.1557i	1.39672	−	0.977485i
$717$	−4.60619	−	0.812195i	−0.172021	−	0.0303320i
$718$	2.36550	−	17.9508i	0.0882796	−	0.669918i
$719$	27.5011	−	10.0096i	1.02562	−	0.373295i	0.226207	−	0.974079i	$-0.427367\pi$
$719$	27.5011	−	10.0096i	1.02562	−	0.373295i	0.799411	+	0.600785i	$0.205145\pi$
$720$	7.49976	+	2.73384i	0.279500	+	0.101884i
$721$	−15.5239			−0.578140
$722$	20.9841	+	16.7829i	0.780949	+	0.624595i
$723$			12.3035i			0.457574i
$724$	−10.7034	+	2.86517i	−0.397789	+	0.106483i
$725$	2.81386	+	7.73102i	0.104504	+	0.287123i
$726$	−7.96750	−	1.04993i	−0.295702	−	0.0389666i
$727$	−4.42851	+	25.1153i	−0.164244	+	0.931476i	0.785596	+	0.618740i	$0.212357\pi$
$727$	−4.42851	+	25.1153i	−0.164244	+	0.931476i	−0.949840	+	0.312736i	$0.898754\pi$
$728$	−61.5848	+	19.3928i	−2.28249	+	0.718746i
$729$	14.0167	+	24.2776i	0.519137	+	0.899171i
$730$	18.8682	+	20.5960i	0.698342	+	0.762294i
$731$	5.88800	+	7.01705i	0.217776	+	0.259535i
$732$	−15.5985	+	1.36085i	−0.576537	+	0.0502985i
$733$	24.3750	+	14.0729i	0.900312	+	0.519795i	0.877301	−	0.479940i	$-0.159342\pi$
$733$	24.3750	+	14.0729i	0.900312	+	0.519795i	0.0230105	+	0.999735i	$0.492675\pi$
$734$	10.2513	+	46.2675i	0.378384	+	1.70777i
$735$	17.2798	+	6.28935i	0.637377	+	0.231986i
$736$	35.7462	+	4.72828i	1.31762	+	0.174287i
$737$	1.49384	+	8.47198i	0.0550262	+	0.312069i
$738$	11.5670	−	0.503610i	0.425787	−	0.0185382i
$739$	23.3977	−	27.8843i	0.860699	−	1.02574i	−0.138674	−	0.990338i	$-0.544284\pi$
$739$	23.3977	−	27.8843i	0.860699	−	1.02574i	0.999373	−	0.0354033i	$-0.0112716\pi$
$740$	−21.6307	−	15.1539i	−0.795161	−	0.557068i
$741$	5.81733	+	35.0361i	0.213705	+	1.28708i
$742$	2.47864	−	7.85790i	0.0909938	−	0.288473i
$743$	33.0844	+	27.7611i	1.21375	+	1.01845i	0.999128	+	0.0417571i	$0.0132956\pi$
$743$	33.0844	+	27.7611i	1.21375	+	1.01845i	0.214619	+	0.976698i	$0.431149\pi$
$744$	−10.0330	+	15.7360i	−0.367829	+	0.576909i
$745$	5.61248	+	31.8300i	0.205626	+	1.16616i
$746$	−40.2802	−	20.9748i	−1.47476	−	0.767942i
$747$	2.63834	−	7.24879i	0.0965320	−	0.265219i
$748$	−14.4988	−	1.27205i	−0.530130	−	0.0465109i
$749$	4.21503	+	2.43355i	0.154014	+	0.0889199i
$750$	21.6841	−	8.97875i	0.791792	−	0.327858i
$751$	−21.9887	+	18.4507i	−0.802379	+	0.673276i	−0.948776	−	0.315950i	$-0.897677\pi$
$751$	−21.9887	+	18.4507i	−0.802379	+	0.673276i	0.146397	+	0.989226i	$0.453232\pi$
$752$	−19.2046	−	3.39597i	−0.700321	−	0.123838i
$753$	−3.77101	−	6.53159i	−0.137423	−	0.238024i
$754$	−28.9409	−	22.2127i	−1.05396	−	0.808940i
$755$	−23.0440	−	4.06329i	−0.838658	−	0.147878i
$756$	−39.1719	−	18.2778i	−1.42467	−	0.664757i
$757$	−9.23982	−	25.3862i	−0.335827	−	0.922677i	−0.986564	−	0.163374i	$-0.947762\pi$
$757$	−9.23982	−	25.3862i	−0.335827	−	0.922677i	0.650737	−	0.759303i	$-0.274460\pi$
$758$	−5.85165	+	3.72691i	−0.212542	+	0.135367i
$759$	22.7736			0.826628
$760$	2.60928	+	21.5421i	0.0946484	+	0.781414i
$761$	42.3246			1.53427			0.767133	−	0.641488i	$-0.221682\pi$
$761$	42.3246			1.53427			0.767133	+	0.641488i	$0.221682\pi$
$762$	18.3909	−	11.7131i	0.666233	−	0.424323i
$763$	−4.42768	−	12.1649i	−0.160293	−	0.440400i
$764$	1.28813	−	2.76065i	0.0466031	−	0.0998769i
$765$	−5.46844	−	0.964234i	−0.197712	−	0.0348620i
$766$	3.67836	+	2.82322i	0.132905	+	0.102007i
$767$	22.3486	+	38.7090i	0.806962	+	1.39770i
$768$	−21.5289	+	3.77443i	−0.776856	+	0.136198i
$769$	−25.9294	+	21.7574i	−0.935038	+	0.784590i	−0.976715	−	0.214541i	$-0.931175\pi$
$769$	−25.9294	+	21.7574i	−0.935038	+	0.784590i	0.0416766	+	0.999131i	$0.486730\pi$
$770$	−23.0200	+	9.53191i	−0.829584	+	0.343506i
$771$	−24.7434	−	14.2856i	−0.891111	−	0.514483i
$772$	−1.70749	+	19.4620i	−0.0614540	+	0.700452i
$773$	−6.59542	+	18.1208i	−0.237221	+	0.651759i	0.762766	+	0.646674i	$0.223841\pi$
$773$	−6.59542	+	18.1208i	−0.237221	+	0.651759i	−0.999987	+	0.00508474i	$0.998381\pi$
$774$	−4.68202	−	2.43803i	−0.168292	−	0.0876333i
$775$	−1.59539	−	9.04790i	−0.0573080	−	0.325010i
$776$	−29.0747	−	18.5376i	−1.04372	−	0.665461i
$777$	30.0498	+	25.2147i	1.07803	+	0.904574i
$778$	−7.87916	+	24.9789i	−0.282482	+	0.895536i
$779$	15.4634	+	27.4127i	0.554035	+	0.982161i
$780$	−16.4568	+	23.4905i	−0.589248	+	0.841096i
$781$	2.28858	−	2.72742i	0.0818917	−	0.0975948i
$782$	−25.0587	+	1.09102i	−0.896097	+	0.0390148i
$783$	−4.24131	−	24.0536i	−0.151572	−	0.859607i
$784$	30.1300	−	5.29756i	1.07607	−	0.189198i
$785$	1.66688	+	0.606696i	0.0594937	+	0.0216539i
$786$	4.58078	+	20.6745i	0.163391	+	0.737435i
$787$	19.0253	+	10.9843i	0.678179	+	0.391547i	0.799169	−	0.601107i	$-0.205273\pi$
$787$	19.0253	+	10.9843i	0.678179	+	0.391547i	−0.120990	+	0.992654i	$0.538607\pi$
$788$	−1.04029	−	11.9241i	−0.0370589	−	0.424780i
$789$	−1.53161	−	1.82530i	−0.0545267	−	0.0649824i
$790$	−11.6594	−	12.7271i	−0.414823	−	0.452811i
$791$	−29.2805	−	50.7154i	−1.04110	−	1.80323i
$792$	8.00018	−	2.51923i	0.284274	−	0.0895168i
$793$	−5.93559	+	33.6624i	−0.210779	+	1.19539i
$794$	19.5548	+	2.57687i	0.693973	+	0.0914495i
$795$	−1.25186	−	3.43944i	−0.0443987	−	0.121984i
$796$	2.43822	+	9.10845i	0.0864203	+	0.322840i
$797$		−	0.710570i		−	0.0251697i	−0.999921	−	0.0125848i	$-0.995994\pi$
$797$		−	0.710570i		−	0.0251697i	0.999921	−	0.0125848i	$-0.00400599\pi$
$798$	−1.07998	−	32.2116i	−0.0382310	−	1.14028i
$799$	13.5664			0.479945
$800$	6.55568	−	8.53273i	0.231778	−	0.301678i
$801$	−7.83634	+	2.85220i	−0.276884	+	0.100777i
$802$	4.43954	−	33.6899i	0.156766	−	1.18963i
$803$	28.9033	+	5.09643i	1.01997	+	0.179849i
$804$	−5.15280	−	7.36278i	−0.181725	−	0.259665i
$805$	−37.1852	+	21.4689i	−1.31061	+	0.756679i
$806$	27.5205	+	30.0407i	0.969367	+	1.05814i
$807$	−10.7068	+	8.98411i	−0.376899	+	0.316256i
$808$	7.82858	−	35.2513i	0.275409	−	1.24014i
$809$	7.13032	−	12.3501i	0.250689	−	0.434205i	−0.713027	−	0.701137i	$-0.752676\pi$
$809$	7.13032	−	12.3501i	0.250689	−	0.434205i	0.963716	+	0.266931i	$0.0860096\pi$
$810$	−10.4811	+	2.32226i	−0.368268	+	0.0815959i
$811$	−4.63202	+	12.7264i	−0.162652	+	0.446883i	−0.994067	−	0.108769i	$-0.965309\pi$
$811$	−4.63202	+	12.7264i	−0.162652	+	0.446883i	0.831415	+	0.555652i	$0.187531\pi$
$812$	23.4045	+	23.4160i	0.821338	+	0.821739i
$813$	−28.8580	+	5.08844i	−1.01209	+	0.178459i
$814$	−27.7243	+	1.20708i	−0.971737	+	0.0423081i
$815$	−20.2171	−	16.9642i	−0.708175	−	0.594230i
$816$	14.2900	−	5.19322i	0.500249	−	0.181799i
$817$	0.143436	−	14.3490i	0.00501818	−	0.502009i
$818$	−48.3447	−	15.2495i	−1.69033	−	0.533187i
$819$	−16.6371	+	19.8273i	−0.581346	+	0.692822i
$820$	−6.58441	+	24.5494i	−0.229938	+	0.857301i
$821$	21.6215	−	3.81246i	0.754597	−	0.133056i	0.216900	−	0.976194i	$-0.430406\pi$
$821$	21.6215	−	3.81246i	0.754597	−	0.133056i	0.537697	+	0.843138i	$0.319294\pi$
$822$	34.4359	+	17.9315i	1.20109	+	0.625434i
$823$	−37.4025	−	13.6134i	−1.30377	−	0.474533i	−0.405547	−	0.914074i	$-0.632919\pi$
$823$	−37.4025	−	13.6134i	−1.30377	−	0.474533i	−0.898222	+	0.439541i	$0.855141\pi$
$824$	−4.39420	+	10.5975i	−0.153079	+	0.369183i
$825$	3.39805	−	5.88560i	0.118305	−	0.204910i
$826$	−15.5177	−	37.4760i	−0.539931	−	1.30396i
$827$	−8.15261	−	9.71590i	−0.283494	−	0.337855i	0.605439	−	0.795891i	$-0.292997\pi$
$827$	−8.15261	−	9.71590i	−0.283494	−	0.337855i	−0.888933	+	0.458036i	$0.848553\pi$
$828$	13.1017	−	6.10551i	0.455314	−	0.212181i
$829$	−38.1089	+	22.0022i	−1.32358	+	0.764168i	−0.984297	−	0.176518i	$-0.943517\pi$
$829$	−38.1089	+	22.0022i	−1.32358	+	0.764168i	−0.339280	+	0.940686i	$0.610183\pi$
$830$	13.4338	+	10.3107i	0.466294	+	0.357891i
$831$	3.44129	−	19.5165i	0.119377	−	0.677021i
$832$	−4.19351	+	47.5309i	−0.145384	+	1.64784i
$833$	−19.9972	+	7.27839i	−0.692863	+	0.252181i
$834$	17.1475	+	26.9234i	0.593768	+	0.932281i
$835$			4.19500i			0.145174i
$836$	15.9564	+	16.2865i	0.551862	+	0.563282i
$837$			27.2756i			0.942783i
$838$	19.2050	−	12.2317i	0.663427	−	0.422536i
$839$	18.6755	−	6.79733i	0.644750	−	0.234670i	0.00111150	−	0.999999i	$-0.499646\pi$
$839$	18.6755	−	6.79733i	0.644750	−	0.234670i	0.643639	+	0.765330i	$0.277424\pi$
$840$	17.5912	−	19.1833i	0.606954	−	0.661887i
$841$	1.78737	−	10.1367i	0.0616336	−	0.349541i
$842$	2.33814	−	3.04636i	0.0805777	−	0.104984i
$843$	29.9817	−	17.3099i	1.03262	−	0.596186i
$844$	−18.7005	−	40.1289i	−0.643697	−	1.38129i
$845$	25.5396	+	30.4369i	0.878589	+	1.04706i
$846$	−7.22328	+	2.99095i	−0.248341	+	0.102831i
$847$	7.96032	−	13.7877i	0.273520	−	0.473750i
$848$	−4.66267	−	3.91633i	−0.160117	−	0.134487i
$849$	14.1498	+	5.15010i	0.485619	+	0.176751i
$850$	−3.45705	+	6.63896i	−0.118576	+	0.227714i
$851$	−47.0972	+	8.30450i	−1.61447	+	0.284675i
$852$	−0.963518	+	3.59239i	−0.0330096	+	0.123073i
$853$	−11.0526	+	13.1720i	−0.378434	+	0.451000i	−0.921319	−	0.388807i	$-0.872887\pi$
$853$	−11.0526	+	13.1720i	−0.378434	+	0.451000i	0.542885	+	0.839807i	$0.317332\pi$
$854$	9.33123	−	29.5823i	0.319308	−	1.01228i
$855$	5.52455	+	6.71917i	0.188936	+	0.229791i
$856$	2.85439	−	2.18859i	0.0975612	−	0.0748046i
$857$	5.45272	+	4.57537i	0.186261	+	0.156292i	0.731150	−	0.682216i	$-0.238984\pi$
$857$	5.45272	+	4.57537i	0.186261	+	0.156292i	−0.544889	+	0.838508i	$0.683428\pi$
$858$	1.31086	+	30.1081i	0.0447521	+	1.02787i
$859$	20.8842	−	3.68245i	0.712559	−	0.125643i	0.194394	−	0.980924i	$-0.437726\pi$
$859$	20.8842	−	3.68245i	0.712559	−	0.125643i	0.518166	+	0.855280i	$0.326615\pi$
$860$	8.19628	−	8.19227i	0.279491	−	0.279354i
$861$	12.9117	−	35.4746i	0.440029	−	1.20897i
$862$	−8.87620	−	40.0611i	−0.302325	−	1.36449i
$863$	2.52232	−	4.36878i	0.0858607	−	0.148715i	−0.819897	−	0.572511i	$-0.805969\pi$
$863$	2.52232	−	4.36878i	0.0858607	−	0.148715i	0.905758	+	0.423796i	$0.139303\pi$
$864$	−23.5655	+	21.5674i	−0.801715	+	0.733736i
$865$	24.1512	−	20.2653i	0.821165	−	0.689040i
$866$	28.6151	−	26.2145i	0.972382	−	0.890806i
$867$	10.9524	−	6.32340i	0.371965	−	0.214754i
$868$	−21.1985	−	30.2904i	−0.719525	−	1.02812i
$869$	−17.8605	−	3.14929i	−0.605877	−	0.106832i
$870$	14.5808	+	1.92141i	0.494335	+	0.0651419i
$871$	−18.4354	+	6.70995i	−0.624661	+	0.227358i
$872$	−9.55782	−	0.420812i	−0.323669	−	0.0142505i
$873$	−13.8227			−0.467827
$874$	30.9295	+	24.2341i	1.04620	+	0.819731i
$875$			46.4948i			1.57181i
$876$	−29.6168	+	7.92804i	−1.00066	+	0.267864i
$877$	−18.5385	−	50.9342i	−0.626001	−	1.71992i	−0.691798	−	0.722091i	$-0.743181\pi$
$877$	−18.5385	−	50.9342i	−0.626001	−	1.71992i	0.0657963	−	0.997833i	$-0.479041\pi$
$878$	−0.656609	+	4.98273i	−0.0221595	+	0.168159i
$879$	2.53044	−	14.3508i	0.0853495	−	0.484041i
$880$	−0.00899539	+	18.4130i	−0.000303235	+	0.620700i
$881$	−21.6502	−	37.4992i	−0.729412	−	1.26338i	−0.957132	−	0.289653i	$-0.906460\pi$
$881$	−21.6502	−	37.4992i	−0.729412	−	1.26338i	0.227719	−	0.973727i	$-0.426873\pi$
$882$	9.04264	−	8.28402i	0.304482	−	0.278938i
$883$	−29.3322	−	34.9568i	−0.987108	−	1.17639i	−0.984320	−	0.176393i	$-0.943557\pi$
$883$	−29.3322	−	34.9568i	−0.987108	−	1.17639i	−0.00278783	−	0.999996i	$-0.500887\pi$
$884$	−2.88479	−	33.0663i	−0.0970261	−	1.11214i
$885$	−15.6044	−	9.00918i	−0.524535	−	0.302840i
$886$	46.1057	−	10.2155i	1.54895	−	0.343196i
$887$	−9.47441	−	3.44840i	−0.318120	−	0.115786i	0.178025	−	0.984026i	$-0.443029\pi$
$887$	−9.47441	−	3.44840i	−0.318120	−	0.115786i	−0.496145	+	0.868240i	$0.665251\pi$
$888$	25.7190	−	13.3765i	0.863073	−	0.448885i
$889$	7.50085	+	42.5394i	0.251570	+	1.42673i
$890$	−0.796313	−	18.2898i	−0.0266925	−	0.613076i
$891$	−7.25057	+	8.64090i	−0.242903	+	0.289481i
$892$	39.2192	+	27.4758i	1.31316	+	0.919959i
$893$	−16.1429	−	13.8228i	−0.540203	−	0.462564i
$894$	−33.8337	−	10.6723i	−1.13157	−	0.356934i
$895$	30.7524	+	25.8044i	1.02794	+	0.862545i
$896$	9.40812	−	42.2663i	0.314303	−	1.41202i
$897$	9.01853	+	51.1466i	0.301120	+	1.70774i
$898$	−7.51290	+	14.4278i	−0.250709	+	0.481463i
$899$	7.14495	−	19.6306i	0.238297	−	0.654717i
$900$	0.376996	−	4.29700i	0.0125665	−	0.143233i
$901$	3.66828	+	2.11788i	0.122208	+	0.0705570i
$902$	10.2171	+	24.6748i	0.340192	+	0.821581i
$903$	−13.1852	+	11.0637i	−0.438775	+	0.368176i
$904$	−42.9095	+	5.63315i	−1.42715	+	0.187356i
$905$	−4.87549	−	8.44460i	−0.162067	−	0.280708i
$906$	15.6381	−	20.3748i	0.519542	−	0.676909i
$907$	10.1146	+	1.78348i	0.335850	+	0.0592195i	0.339030	−	0.940775i	$-0.389901\pi$
$907$	10.1146	+	1.78348i	0.335850	+	0.0592195i	−0.00317994	+	0.999995i	$0.501012\pi$
$908$	3.05717	+	1.42649i	0.101456	+	0.0473397i
$909$	−4.95092	−	13.6025i	−0.164212	−	0.451168i
$910$	−30.5236	−	47.9254i	−1.01185	−	1.58871i
$911$	18.0080			0.596631			0.298316	−	0.954467i	$-0.403575\pi$
$911$	18.0080			0.596631			0.298316	+	0.954467i	$0.403575\pi$
$912$	−22.2953	−	8.38056i	−0.738271	−	0.277508i
$913$	17.7936			0.588883
$914$	8.29982	+	13.0316i	0.274534	+	0.431047i
$915$	−4.71280	−	12.9483i	−0.155800	−	0.428058i
$916$	6.52690	+	3.04549i	0.215655	+	0.100626i
$917$	−41.3136	−	7.28470i	−1.36430	−	0.240562i
$918$	13.5298	−	17.6280i	0.446551	−	0.581810i
$919$	3.23798	+	5.60834i	0.106811	+	0.185002i	0.914477	−	0.404639i	$-0.132603\pi$
$919$	3.23798	+	5.60834i	0.106811	+	0.185002i	−0.807666	+	0.589641i	$0.799269\pi$
$920$	4.13030	+	31.4618i	0.136172	+	1.03727i
$921$	−5.52806	+	4.63860i	−0.182156	+	0.152847i
$922$	−22.3426	−	53.9584i	−0.735814	−	1.77702i
$923$	7.03175	+	4.05978i	0.231453	+	0.133629i
$924$	2.39021	−	27.2436i	0.0786322	−	0.896249i
$925$	−4.88117	+	13.4109i	−0.160492	+	0.440948i
$926$	−7.13203	+	13.6964i	−0.234373	+	0.450092i
$927$	0.798604	+	4.52911i	0.0262296	+	0.148755i
$928$	22.6100	−	9.34921i	0.742211	−	0.306903i
$929$	−5.56288	−	4.66781i	−0.182512	−	0.153146i	0.546954	−	0.837162i	$-0.315787\pi$
$929$	−5.56288	−	4.66781i	−0.182512	−	0.153146i	−0.729466	+	0.684017i	$0.760232\pi$
$930$	−15.6627	−	4.94054i	−0.513601	−	0.162007i
$931$	31.2111	+	11.7145i	1.02290	+	0.383927i
$932$	−6.39099	−	4.47735i	−0.209344	−	0.146660i
$933$	6.23125	−	7.42611i	0.204002	−	0.243120i
$934$	1.32582	+	30.4517i	0.0433823	+	0.996410i
$935$	−2.22417	−	12.6139i	−0.0727380	−	0.412518i
$936$	8.82601	+	16.9698i	0.288487	+	0.554675i
$937$	−10.5825	−	3.85173i	−0.345717	−	0.125831i	0.163325	−	0.986572i	$-0.447778\pi$
$937$	−10.5825	−	3.85173i	−0.345717	−	0.125831i	−0.509042	+	0.860742i	$0.670000\pi$
$938$	17.3819	−	3.85124i	0.567538	−	0.125747i
$939$	30.0853	+	17.3698i	0.981798	+	0.566841i
$940$	−1.49167	−	17.0979i	−0.0486528	−	0.557673i
$941$	11.4013	+	13.5876i	0.371673	+	0.442942i	0.919168	−	0.393867i	$-0.128863\pi$
$941$	11.4013	+	13.5876i	0.371673	+	0.442942i	−0.547495	+	0.836809i	$0.684418\pi$
$942$	−1.43569	+	1.31524i	−0.0467773	+	0.0428530i
$943$	23.0122	+	39.8582i	0.749379	+	1.29796i
$944$	−29.9759	−	0.0146443i	−0.975631	−	0.000476631i
$945$	6.60567	−	37.4626i	0.214882	−	1.21866i
$946$	1.59081	−	12.0720i	0.0517216	−	0.392494i
$947$	19.3370	+	53.1281i	0.628370	+	1.72643i	0.685508	+	0.728065i	$0.259580\pi$
$947$	19.3370	+	53.1281i	0.628370	+	1.72643i	−0.0571383	+	0.998366i	$0.518198\pi$
$948$	18.3014	−	4.89906i	0.594403	−	0.159114i
$949$			66.9314i			2.17269i
$950$	10.8781	−	4.37742i	0.352931	−	0.142022i
$951$	1.57104			0.0509446
$952$	−1.32488	+	30.0918i	−0.0429397	+	0.975280i
$953$	−14.6290	+	5.32453i	−0.473880	+	0.172478i	−0.567909	−	0.823091i	$-0.692248\pi$
$953$	−14.6290	+	5.32453i	−0.473880	+	0.172478i	0.0940291	+	0.995569i	$0.470025\pi$
$954$	−2.42006	−	0.318907i	−0.0783523	−	0.0103250i
$955$	2.64019	+	0.465537i	0.0854346	+	0.0150644i
$956$	−3.92631	−	5.61027i	−0.126986	−	0.181449i
$957$	13.3826	−	7.72647i	0.432599	−	0.249761i
$958$	−32.9263	+	30.1640i	−1.06380	+	0.974555i
$959$	−58.9202	+	49.4399i	−1.90263	+	1.59650i
$960$	−8.11631	−	17.4388i	−0.261953	−	0.562836i
$961$	3.83561	−	6.64346i	0.123729	−	0.214305i
$962$	−13.6900	−	61.7874i	−0.441384	−	1.99211i
$963$	0.493154	−	1.35493i	0.0158917	−	0.0436620i
$964$	−12.7402	+	12.7340i	−0.410334	+	0.410134i
$965$	−16.9318	+	2.98552i	−0.545052	+	0.0961074i
$966$	−2.05005	−	47.0858i	−0.0659592	−	1.51496i
$967$	−20.7509	−	17.4121i	−0.667304	−	0.559935i	0.244962	−	0.969533i	$-0.421225\pi$
$967$	−20.7509	−	17.4121i	−0.667304	−	0.559935i	−0.912266	+	0.409598i	$0.865669\pi$
$968$	−7.15905	−	9.33694i	−0.230101	−	0.300101i
$969$	16.2873	+	3.04006i	0.523223	+	0.0976607i
$970$	9.12843	−	28.9393i	0.293096	−	0.929186i
$971$	26.6891	−	31.8069i	0.856495	−	1.02073i	−0.143024	−	0.989719i	$-0.545683\pi$
$971$	26.6891	−	31.8069i	0.856495	−	1.02073i	0.999519	−	0.0310118i	$-0.00987295\pi$
$972$	−5.72493	+	21.3449i	−0.183627	+	0.684637i
$973$	−62.2756	+	10.9809i	−1.99647	+	0.352031i
$974$	11.4145	−	21.9206i	0.365746	−	0.702382i
$975$	14.5640	+	5.30085i	0.466421	+	0.169763i
$976$	−17.5533	−	14.7436i	−0.561869	−	0.471932i
$977$	22.2421	−	38.5244i	0.711587	−	1.23251i	−0.252674	−	0.967551i	$-0.581310\pi$
$977$	22.2421	−	38.5244i	0.711587	−	1.23251i	0.964261	−	0.264954i	$-0.0853567\pi$
$978$	26.7648	−	11.0825i	0.855844	−	0.354380i
$979$	−12.3646	−	14.7355i	−0.395174	−	0.470950i
$980$	11.3718	+	24.4025i	0.363259	+	0.779509i
$981$	−3.32135	+	1.91759i	−0.106043	+	0.0612238i
$982$	−9.49452	+	12.3704i	−0.302982	+	0.394754i
$983$	−1.03224	+	5.85410i	−0.0329232	+	0.186717i	−0.996834	−	0.0795078i	$-0.974665\pi$
$983$	−1.03224	+	5.85410i	−0.0329232	+	0.186717i	0.963911	+	0.266225i	$0.0857763\pi$
$984$	−20.5623	−	18.8557i	−0.655502	−	0.601098i
$985$	9.89824	−	3.60266i	0.315384	−	0.114790i
$986$	−14.3553	+	9.14288i	−0.457166	+	0.291169i
$987$			25.4916i			0.811405i
$988$	−30.2587	+	42.2856i	−0.962657	+	1.34528i
$989$		−	20.9840i		−	0.667252i
$990$	3.96517	+	6.22575i	0.126021	+	0.197867i
$991$	8.99995	−	3.27572i	0.285893	−	0.104057i	−0.195093	−	0.980785i	$-0.562501\pi$
$991$	8.99995	−	3.27572i	0.285893	−	0.104057i	0.480986	+	0.876728i	$0.340279\pi$
$992$	−26.6785	+	5.89739i	−0.847043	+	0.187242i
$993$	1.01002	−	5.72811i	0.0320520	−	0.181776i
$994$	−5.84513	−	4.48626i	−0.185396	−	0.142295i
$995$	−7.18623	+	4.14897i	−0.227819	+	0.131531i
$996$	−16.8484	+	7.85154i	−0.533863	+	0.248786i
$997$	19.6721	+	23.4443i	0.623021	+	0.742487i	0.981587	−	0.191017i	$-0.0611787\pi$
$997$	19.6721	+	23.4443i	0.623021	+	0.742487i	−0.358566	+	0.933504i	$0.616734\pi$
$998$	15.0540	+	36.3562i	0.476526	+	1.15083i
$999$	21.1846	−	36.6928i	0.670252	−	1.16091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.t.a.149.6	yes	108
4.3	odd	2		608.2.bf.a.529.6		108
8.3	odd	2		608.2.bf.a.529.13		108
8.5	even	2	inner	152.2.t.a.149.4	yes	108
19.6	even	9	inner	152.2.t.a.101.4	✓	108
76.63	odd	18		608.2.bf.a.177.13		108
152.101	even	18	inner	152.2.t.a.101.6	yes	108
152.139	odd	18		608.2.bf.a.177.6		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.t.a.101.4	✓	108	19.6	even	9	inner
152.2.t.a.101.6	yes	108	152.101	even	18	inner
152.2.t.a.149.4	yes	108	8.5	even	2	inner
152.2.t.a.149.6	yes	108	1.1	even	1	trivial
608.2.bf.a.177.6		108	152.139	odd	18
608.2.bf.a.177.13		108	76.63	odd	18
608.2.bf.a.529.6		108	4.3	odd	2
608.2.bf.a.529.13		108	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.759711 - 1.19283i) q^{2} +(0.467226 + 1.28369i) q^{3} +(-0.845679 + 1.81241i) q^{4} +(-1.73333 - 0.305632i) q^{5} +(1.17627 - 1.53255i) q^{6} +(1.91364 + 3.31452i) q^{7} +(2.80436 - 0.368156i) q^{8} +(0.868569 - 0.728816i) q^{9} +(0.952259 + 2.29975i) q^{10} +(2.26499 + 1.30769i) q^{11} +(-2.72170 - 0.238788i) q^{12} +(-2.03996 + 5.60474i) q^{13} +(2.49984 - 4.80072i) q^{14} +(-0.417517 - 2.36785i) q^{15} +(-2.56965 - 3.06543i) q^{16} +(2.13151 + 1.78855i) q^{17} +(-1.52921 - 0.482364i) q^{18} +(-0.713969 - 4.30003i) q^{19} +(2.01977 - 2.88303i) q^{20} +(-3.36072 + 4.00515i) q^{21} +(-0.160884 - 3.69521i) q^{22} +(-1.10686 - 6.27729i) q^{23} +(1.78287 + 3.42793i) q^{24} +(-1.78746 - 0.650581i) q^{25} +(8.23527 - 1.82466i) q^{26} +(4.89056 + 2.82357i) q^{27} +(-7.62559 + 0.665276i) q^{28} +(-2.78015 - 3.31326i) q^{29} +(-2.50725 + 2.29691i) q^{30} +(2.41499 + 4.18289i) q^{31} +(-1.70434 + 5.39400i) q^{32} +(-0.620412 + 3.51853i) q^{33} +(0.514101 - 3.90131i) q^{34} +(-2.30393 - 6.33001i) q^{35} +(0.586382 + 2.19055i) q^{36} -7.50278i q^{37} +(-4.58679 + 4.11842i) q^{38} -8.14787 q^{39} +(-4.97340 - 0.218969i) q^{40} +(-6.78504 + 2.46955i) q^{41} +(7.33063 + 0.966007i) q^{42} +(3.24204 + 0.571659i) q^{43} +(-4.28552 + 2.99919i) q^{44} +(-1.72826 + 0.997812i) q^{45} +(-6.64685 + 6.08922i) q^{46} +(3.73496 - 3.13400i) q^{47} +(2.73446 - 4.73089i) q^{48} +(-3.82402 + 6.62340i) q^{49} +(0.581919 + 2.62638i) q^{50} +(-1.30005 + 3.57186i) q^{51} +(-8.43292 - 8.43705i) q^{52} +(1.49917 - 0.264344i) q^{53} +(-0.347381 - 7.97870i) q^{54} +(-3.52629 - 2.95890i) q^{55} +(6.58680 + 8.59060i) q^{56} +(5.18633 - 2.92560i) q^{57} +(-1.84004 + 5.83336i) q^{58} +(4.81703 - 5.74071i) q^{59} +(4.64461 + 1.24573i) q^{60} +(5.64385 - 0.995163i) q^{61} +(3.15478 - 6.05846i) q^{62} +(4.07780 + 1.48420i) q^{63} +(7.72892 - 2.06489i) q^{64} +(5.24890 - 9.09135i) q^{65} +(4.66834 - 1.93302i) q^{66} +(2.11430 + 2.51972i) q^{67} +(-5.04416 + 2.35063i) q^{68} +(7.54096 - 4.35377i) q^{69} +(-5.80029 + 7.55717i) q^{70} +(0.236392 - 1.34065i) q^{71} +(2.16747 - 2.36363i) q^{72} +(10.5450 - 3.83807i) q^{73} +(-8.94953 + 5.69994i) q^{74} -2.59851i q^{75} +(8.39720 + 2.34244i) q^{76} +10.0098i q^{77} +(6.19003 + 9.71901i) q^{78} +(-6.51619 + 2.37170i) q^{79} +(3.51715 + 6.09876i) q^{80} +(-0.748928 + 4.24738i) q^{81} +(8.10042 + 6.21724i) q^{82} +(5.89196 - 3.40173i) q^{83} +(-4.41688 - 9.47807i) q^{84} +(-3.14796 - 3.75160i) q^{85} +(-1.78112 - 4.30149i) q^{86} +(2.95424 - 5.11690i) q^{87} +(6.83328 + 2.83337i) q^{88} +(-6.91135 - 2.51553i) q^{89} +(2.50320 + 1.30347i) q^{90} +(-22.4807 + 3.96396i) q^{91} +(12.3131 + 3.30250i) q^{92} +(-4.24120 + 5.05446i) q^{93} +(-6.57581 - 2.07423i) q^{94} +(-0.0766864 + 7.67156i) q^{95} +(-7.72054 + 0.332363i) q^{96} +(-9.33891 - 7.83628i) q^{97} +(10.8057 - 0.470466i) q^{98} +(2.92036 - 0.514939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26}+ \cdots + 93 q^{98}+O(q^{100}) \) 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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