LMFDB - Embedded newform 775.2.ck.a.599.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			599.3
Character	$\chi$	$=$	775.599
Dual form			775.2.ck.a.524.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.206567 - 0.284315i) q^{2} +(2.87744 - 0.302431i) q^{3} +(0.579869 + 1.78465i) q^{4} +(0.508398 - 0.880572i) q^{6} +(-0.224987 + 1.05848i) q^{7} +(1.29565 + 0.420982i) q^{8} +(5.25377 - 1.11672i) q^{9} +(-1.62690 + 1.80686i) q^{11} +(2.20827 + 4.95987i) q^{12} +(1.16882 - 2.62521i) q^{13} +(0.254466 + 0.282614i) q^{14} +(-2.64890 + 1.92454i) q^{16} +(1.35606 - 1.22101i) q^{17} +(0.767753 - 1.72440i) q^{18} +(-1.93514 + 0.861580i) q^{19} +(-0.327269 + 3.11375i) q^{21} +(0.177653 + 0.835790i) q^{22} +(0.420572 + 0.136652i) q^{23} +(3.85547 + 0.819506i) q^{24} +(-0.504947 - 0.874594i) q^{26} +(6.52462 - 2.11998i) q^{27} +(-2.01948 + 0.212256i) q^{28} +(-2.55579 - 1.85689i) q^{29} +(1.15354 - 5.44696i) q^{31} +3.87532i q^{32} +(-4.13487 + 5.69116i) q^{33} +(-0.0670322 - 0.637769i) q^{34} +(5.03946 + 8.72860i) q^{36} +(-2.72517 - 1.57338i) q^{37} +(-0.154776 + 0.728163i) q^{38} +(2.56926 - 7.90738i) q^{39} +(0.726079 - 6.90818i) q^{41} +(0.817684 + 0.736246i) q^{42} +(3.42162 + 7.68509i) q^{43} +(-4.16801 - 1.85572i) q^{44} +(0.125728 - 0.0913471i) q^{46} +(4.67998 + 6.44144i) q^{47} +(-7.04003 + 6.33887i) q^{48} +(5.32506 + 2.37087i) q^{49} +(3.53273 - 3.92349i) q^{51} +(5.36285 + 0.563659i) q^{52} +(-1.03478 - 4.86824i) q^{53} +(0.745029 - 2.29296i) q^{54} +(-0.737104 + 1.27670i) q^{56} +(-5.30768 + 3.06439i) q^{57} +(-1.05588 + 0.343078i) q^{58} +(-1.25580 - 11.9481i) q^{59} -14.4351 q^{61} +(-1.31037 - 1.45313i) q^{62} +5.81225i q^{63} +(-4.19600 - 3.04857i) q^{64} +(0.763955 + 2.35121i) q^{66} +(-5.57511 + 3.21879i) q^{67} +(2.96541 + 1.71208i) q^{68} +(1.25150 + 0.266015i) q^{69} +(-1.64121 + 0.348850i) q^{71} +(7.27716 + 0.764860i) q^{72} +(-10.6717 - 9.60883i) q^{73} +(-1.01026 + 0.449798i) q^{74} +(-2.65975 - 2.95395i) q^{76} +(-1.54649 - 2.12856i) q^{77} +(-1.71746 - 2.36388i) q^{78} +(2.30692 + 2.56210i) q^{79} +(3.41274 - 1.51945i) q^{81} +(-1.81412 - 1.63344i) q^{82} +(12.7832 + 1.34357i) q^{83} +(-5.74674 + 1.22151i) q^{84} +(2.89178 + 0.614667i) q^{86} +(-7.91573 - 4.57015i) q^{87} +(-2.86855 + 1.65616i) q^{88} +(-0.698188 - 2.14880i) q^{89} +(2.51576 + 1.82781i) q^{91} +0.829816i q^{92} +(1.67190 - 16.0222i) q^{93} +2.79812 q^{94} +(1.17202 + 11.1510i) q^{96} +(-3.24582 + 1.05463i) q^{97} +(1.77405 - 1.02425i) q^{98} +(-6.52961 + 11.3096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) $ 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{7}{15}\right)$	$-1$

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 $

$2$	0.206567	−	0.284315i	0.146065	−	0.201041i	−0.729715	−	0.683751i	$-0.760347\pi$
$2$	0.206567	−	0.284315i	0.146065	−	0.201041i	0.875780	+	0.482710i	$0.160347\pi$
$3$	2.87744	−	0.302431i	1.66129	−	0.174609i	0.773164	−	0.634206i	$-0.218673\pi$
$3$	2.87744	−	0.302431i	1.66129	−	0.174609i	0.888128	+	0.459597i	$0.152006\pi$
$4$	0.579869	+	1.78465i	0.289934	+	0.892327i
$5$		0			0
$5$		0			0
$6$	0.508398	−	0.880572i	0.207553	−	0.359492i
$7$	−0.224987	+	1.05848i	−0.0850369	+	0.400067i	−0.999994	−	0.00348400i	$-0.998891\pi$
$7$	−0.224987	+	1.05848i	−0.0850369	+	0.400067i	0.914957	+	0.403551i	$0.132224\pi$
$8$	1.29565	+	0.420982i	0.458081	+	0.148840i
$9$	5.25377	−	1.11672i	1.75126	−	0.372241i
$10$		0			0
$11$	−1.62690	+	1.80686i	−0.490530	+	0.544789i	−0.936688	−	0.350165i	$-0.886125\pi$
$11$	−1.62690	+	1.80686i	−0.490530	+	0.544789i	0.446158	+	0.894954i	$0.352792\pi$
$12$	2.20827	+	4.95987i	0.637474	+	1.43179i
$13$	1.16882	−	2.62521i	0.324172	−	0.728103i	−0.675787	−	0.737097i	$-0.736196\pi$
$13$	1.16882	−	2.62521i	0.324172	−	0.728103i	0.999960	+	0.00899389i	$0.00286288\pi$
$14$	0.254466	+	0.282614i	0.0680090	+	0.0755317i
$15$		0			0
$16$	−2.64890	+	1.92454i	−0.662226	+	0.481135i
$17$	1.35606	−	1.22101i	0.328894	−	0.296137i	−0.488095	−	0.872790i	$-0.662308\pi$
$17$	1.35606	−	1.22101i	0.328894	−	0.296137i	0.816989	+	0.576653i	$0.195641\pi$
$18$	0.767753	−	1.72440i	0.180961	−	0.406445i
$19$	−1.93514	+	0.861580i	−0.443951	+	0.197660i	−0.616523	−	0.787337i	$-0.711459\pi$
$19$	−1.93514	+	0.861580i	−0.443951	+	0.197660i	0.172571	+	0.984997i	$0.444792\pi$
$20$		0			0
$21$	−0.327269	+	3.11375i	−0.0714159	+	0.679477i
$22$	0.177653	+	0.835790i	0.0378757	+	0.178191i
$23$	0.420572	+	0.136652i	0.0876953	+	0.0284939i	0.352536	−	0.935798i	$-0.385319\pi$
$23$	0.420572	+	0.136652i	0.0876953	+	0.0284939i	−0.264841	+	0.964292i	$0.585319\pi$
$24$	3.85547	+	0.819506i	0.786995	+	0.167281i
$25$		0			0
$26$	−0.504947	−	0.874594i	−0.0990283	−	0.171522i
$27$	6.52462	−	2.11998i	1.25566	−	0.407990i
$28$	−2.01948	+	0.212256i	−0.381646	+	0.0401126i
$29$	−2.55579	−	1.85689i	−0.474599	−	0.344816i	0.324632	−	0.945840i	$-0.394760\pi$
$29$	−2.55579	−	1.85689i	−0.474599	−	0.344816i	−0.799231	+	0.601024i	$0.794760\pi$
$30$		0			0
$31$	1.15354	−	5.44696i	0.207181	−	0.978303i
$31$	1.15354	−	5.44696i	0.207181	−	0.978303i
$32$			3.87532i			0.685067i
$33$	−4.13487	+	5.69116i	−0.719789	+	0.990704i
$34$	−0.0670322	−	0.637769i	−0.0114959	−	0.109376i
$35$		0			0
$36$	5.03946	+	8.72860i	0.839910	+	1.45477i
$37$	−2.72517	−	1.57338i	−0.448015	−	0.258661i	0.258977	−	0.965884i	$-0.416615\pi$
$37$	−2.72517	−	1.57338i	−0.448015	−	0.258661i	−0.706991	+	0.707222i	$0.749948\pi$
$38$	−0.154776	+	0.728163i	−0.0251079	+	0.118124i
$39$	2.56926	−	7.90738i	0.411412	−	1.26619i
$40$		0			0
$41$	0.726079	−	6.90818i	0.113395	−	1.07888i	−0.778814	−	0.627254i	$-0.784179\pi$
$41$	0.726079	−	6.90818i	0.113395	−	1.07888i	0.892209	−	0.451623i	$-0.149155\pi$
$42$	0.817684	+	0.736246i	0.126171	+	0.113605i
$43$	3.42162	+	7.68509i	0.521793	+	1.17197i	0.961746	+	0.273944i	$0.0883285\pi$
$43$	3.42162	+	7.68509i	0.521793	+	1.17197i	−0.439953	+	0.898021i	$0.645005\pi$
$44$	−4.16801	−	1.85572i	−0.628351	−	0.279760i
$45$		0			0
$46$	0.125728	−	0.0913471i	0.0185377	−	0.0134684i
$47$	4.67998	+	6.44144i	0.682645	+	0.939580i	0.999962	−	0.00873953i	$-0.00278191\pi$
$47$	4.67998	+	6.44144i	0.682645	+	0.939580i	−0.317317	+	0.948320i	$0.602782\pi$
$48$	−7.04003	+	6.33887i	−1.01614	+	0.914937i
$49$	5.32506	+	2.37087i	0.760723	+	0.338696i
$50$		0			0
$51$	3.53273	−	3.92349i	0.494681	−	0.549399i
$52$	5.36285	+	0.563659i	0.743694	+	0.0781654i
$53$	−1.03478	−	4.86824i	−0.142137	−	0.668704i	−0.990297	−	0.138964i	$-0.955623\pi$
$53$	−1.03478	−	4.86824i	−0.142137	−	0.668704i	0.848160	−	0.529740i	$-0.177711\pi$
$54$	0.745029	−	2.29296i	0.101386	−	0.312033i
$55$		0			0
$56$	−0.737104	+	1.27670i	−0.0984997	+	0.170606i
$57$	−5.30768	+	3.06439i	−0.703020	+	0.405889i
$58$	−1.05588	+	0.343078i	−0.138644	+	0.0450483i
$59$	−1.25580	−	11.9481i	−0.163491	−	1.55551i	−0.701559	−	0.712612i	$-0.747512\pi$
$59$	−1.25580	−	11.9481i	−0.163491	−	1.55551i	0.538068	−	0.842902i	$-0.319154\pi$
$60$		0			0
$61$	−14.4351			−1.84823			−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351			−1.84823			−0.924115	+	0.382115i	$0.875196\pi$
$62$	−1.31037	−	1.45313i	−0.166417	−	0.184548i
$63$			5.81225i			0.732274i
$64$	−4.19600	−	3.04857i	−0.524499	−	0.381071i
$65$		0			0
$66$	0.763955	+	2.35121i	0.0940363	+	0.289414i
$67$	−5.57511	+	3.21879i	−0.681108	+	0.393238i	−0.800273	−	0.599636i	$-0.795312\pi$
$67$	−5.57511	+	3.21879i	−0.681108	+	0.393238i	0.119164	+	0.992875i	$0.461979\pi$
$68$	2.96541	+	1.71208i	0.359609	+	0.207620i
$69$	1.25150	+	0.266015i	0.150663	+	0.0320244i
$70$		0			0
$71$	−1.64121	+	0.348850i	−0.194776	+	0.0414009i	−0.304266	−	0.952587i	$-0.598411\pi$
$71$	−1.64121	+	0.348850i	−0.194776	+	0.0414009i	0.109491	+	0.993988i	$0.465078\pi$
$72$	7.27716	+	0.764860i	0.857621	+	0.0901396i
$73$	−10.6717	−	9.60883i	−1.24903	−	1.12463i	−0.987196	−	0.159514i	$-0.949007\pi$
$73$	−10.6717	−	9.60883i	−1.24903	−	1.12463i	−0.261830	−	0.965114i	$-0.584326\pi$
$74$	−1.01026	+	0.449798i	−0.117441	+	0.0522880i
$75$		0			0
$76$	−2.65975	−	2.95395i	−0.305094	−	0.338841i
$77$	−1.54649	−	2.12856i	−0.176239	−	0.242572i
$78$	−1.71746	−	2.36388i	−0.194464	−	0.267657i
$79$	2.30692	+	2.56210i	0.259549	+	0.288259i	0.858809	−	0.512296i	$-0.171205\pi$
$79$	2.30692	+	2.56210i	0.259549	+	0.288259i	−0.599260	+	0.800555i	$0.704538\pi$
$80$		0			0
$81$	3.41274	−	1.51945i	0.379194	−	0.168828i
$82$	−1.81412	−	1.63344i	−0.200336	−	0.180383i
$83$	12.7832	+	1.34357i	1.40314	+	0.147476i	0.775657	−	0.631155i	$-0.217419\pi$
$83$	12.7832	+	1.34357i	1.40314	+	0.147476i	0.627482	+	0.778631i	$0.284086\pi$
$84$	−5.74674	+	1.22151i	−0.627021	+	0.133277i
$85$		0			0
$86$	2.89178	+	0.614667i	0.311829	+	0.0662812i
$87$	−7.91573	−	4.57015i	−0.848656	−	0.489972i
$88$	−2.86855	+	1.65616i	−0.305789	+	0.176547i
$89$	−0.698188	−	2.14880i	−0.0740078	−	0.227773i	0.907209	−	0.420680i	$-0.138208\pi$
$89$	−0.698188	−	2.14880i	−0.0740078	−	0.227773i	−0.981217	+	0.192907i	$0.938208\pi$
$90$		0			0
$91$	2.51576	+	1.82781i	0.263724	+	0.191606i
$92$			0.829816i			0.0865143i
$93$	1.67190	−	16.0222i	0.173368	−	1.66142i
$94$	2.79812			0.288604
$95$		0			0
$96$	1.17202	+	11.1510i	0.119619	+	1.13810i
$97$	−3.24582	+	1.05463i	−0.329563	+	0.107082i	−0.469125	−	0.883132i	$-0.655431\pi$
$97$	−3.24582	+	1.05463i	−0.329563	+	0.107082i	0.139562	+	0.990213i	$0.455431\pi$
$98$	1.77405	−	1.02425i	0.179207	−	0.103465i
$99$	−6.52961	+	11.3096i	−0.656251	+	1.13666i
$100$		0			0
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	−0.176741	−	0.984257i	$-0.556555\pi$
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	0.721518	−	0.692395i	$-0.243445\pi$
$102$	−0.385763	−	1.81487i	−0.0381962	−	0.179699i
$103$	8.02962	+	0.843947i	0.791182	+	0.0831566i	0.491494	−	0.870881i	$-0.336451\pi$
$103$	8.02962	+	0.843947i	0.791182	+	0.0831566i	0.299688	+	0.954037i	$0.403118\pi$
$104$	2.61955	−	2.90930i	0.256868	−	0.285281i
$105$		0			0
$106$	−1.59786	−	0.711414i	−0.155198	−	0.0690987i
$107$	9.03010	−	8.13074i	0.872972	−	0.786028i	−0.105063	−	0.994466i	$-0.533505\pi$
$107$	9.03010	−	8.13074i	0.872972	−	0.786028i	0.978036	+	0.208438i	$0.0668378\pi$
$108$	7.56685	+	10.4149i	0.728121	+	1.00217i
$109$	−0.511381	+	0.371540i	−0.0489815	+	0.0355871i	−0.612007	−	0.790853i	$-0.709637\pi$
$109$	−0.511381	+	0.371540i	−0.0489815	+	0.0355871i	0.563025	+	0.826440i	$0.309637\pi$
$110$		0			0
$111$	−8.31735	−	3.70312i	−0.789448	−	0.351485i
$112$	−1.44112	−	3.23680i	−0.136173	−	0.305849i
$113$	8.39779	+	7.56140i	0.789998	+	0.711317i	0.961782	−	0.273818i	$-0.0882864\pi$
$113$	8.39779	+	7.56140i	0.789998	+	0.711317i	−0.171784	+	0.985135i	$0.554953\pi$
$114$	−0.225139	+	2.14205i	−0.0210862	+	0.200622i
$115$		0			0
$116$	1.83188	−	5.63796i	0.170086	−	0.523472i
$117$	3.20907	−	15.0975i	0.296679	−	1.39576i
$118$	−3.65643	−	2.11104i	−0.336602	−	0.194337i
$119$	0.987313	+	1.71008i	0.0905068	+	0.156762i
$120$		0			0
$121$	0.531887	+	5.06056i	0.0483533	+	0.460051i
$122$	−2.98182	+	4.10412i	−0.269961	+	0.371570i
$123$		−	20.0975i		−	1.81213i
$124$	10.3898	−	1.09986i	0.933034	−	0.0987702i
$125$		0			0
$126$	1.65251	+	1.20062i	0.147217	+	0.106960i
$127$	0.117161	−	0.0123141i	0.0103963	−	0.00109270i	−0.0993289	−	0.995055i	$-0.531670\pi$
$127$	0.117161	−	0.0123141i	0.0103963	−	0.00109270i	0.109725	+	0.993962i	$0.465003\pi$
$128$	−9.10481	+	2.95833i	−0.804759	+	0.261482i
$129$	12.1697	+	21.0786i	1.07149	+	1.85587i
$130$		0			0
$131$	−5.65756	−	1.20255i	−0.494303	−	0.105067i	−0.0459863	−	0.998942i	$-0.514643\pi$
$131$	−5.65756	−	1.20255i	−0.494303	−	0.105067i	−0.448317	+	0.893875i	$0.647976\pi$
$132$	−12.5544	−	4.07918i	−1.09272	−	0.355047i
$133$	−0.476583	−	2.24215i	−0.0413250	−	0.194419i
$134$	−0.236483	+	2.24998i	−0.0204290	+	0.194369i
$135$		0			0
$136$	2.27101	−	1.01112i	0.194737	−	0.0867026i
$137$	−4.80170	+	10.7848i	−0.410237	+	0.921407i	0.583753	+	0.811931i	$0.301584\pi$
$137$	−4.80170	+	10.7848i	−0.410237	+	0.921407i	−0.993990	+	0.109475i	$0.965083\pi$
$138$	0.334150	−	0.300870i	0.0284448	−	0.0256118i
$139$	−12.4767	+	9.06482i	−1.05826	+	0.768868i	−0.973765	−	0.227556i	$-0.926927\pi$
$139$	−12.4767	+	9.06482i	−1.05826	+	0.768868i	−0.0844915	+	0.996424i	$0.526927\pi$
$140$		0			0
$141$	15.4145	+	17.1195i	1.29813	+	1.44172i
$142$	−0.239836	+	0.538681i	−0.0201266	+	0.0452051i
$143$	2.84183	+	6.38286i	0.237646	+	0.533762i
$144$	−11.7675	+	13.0692i	−0.980628	+	1.08910i
$145$		0			0
$146$	−4.93635	+	1.04925i	−0.408535	+	0.0868368i
$147$	16.0396	+	5.21157i	1.32292	+	0.429843i
$148$	1.22769	−	5.77583i	0.100916	−	0.474770i
$149$	−5.97511	+	10.3492i	−0.489500	+	0.847840i	−0.999927	−	0.0120817i	$-0.996154\pi$
$149$	−5.97511	+	10.3492i	−0.489500	+	0.847840i	0.510427	+	0.859921i	$0.329488\pi$
$150$		0			0
$151$	−1.33561	−	4.11059i	−0.108691	−	0.334515i	0.881888	−	0.471458i	$-0.156272\pi$
$151$	−1.33561	−	4.11059i	−0.108691	−	0.334515i	−0.990579	+	0.136943i	$0.956272\pi$
$152$	−2.86997	+	0.301646i	−0.232785	+	0.0244667i
$153$	5.76092	−	7.92923i	0.465743	−	0.641040i
$154$	−0.924636			−0.0745093
$155$		0			0
$156$	15.6018			1.24914
$157$	−5.11634	+	7.04204i	−0.408328	+	0.562016i	−0.962810	−	0.270180i	$-0.912917\pi$
$157$	−5.11634	+	7.04204i	−0.408328	+	0.562016i	0.554481	+	0.832196i	$0.312917\pi$
$158$	1.20498	−	0.126648i	0.0958628	−	0.0100756i
$159$	−4.44982	−	13.6951i	−0.352893	−	1.08609i
$160$		0			0
$161$	−0.239267	+	0.414422i	−0.0188568	+	0.0326610i
$162$	0.272957	−	1.28416i	0.0214455	−	0.100893i
$163$	−2.97481	−	0.966575i	−0.233005	−	0.0757080i	0.190187	−	0.981748i	$-0.439091\pi$
$163$	−2.97481	−	0.966575i	−0.233005	−	0.0757080i	−0.423192	+	0.906040i	$0.639091\pi$
$164$	12.7497	−	2.71004i	0.995588	−	0.211619i
$165$		0			0
$166$	3.02258	−	3.35692i	0.234598	−	0.260547i
$167$	−5.43194	−	12.2003i	−0.420336	−	0.944090i	−0.992305	−	0.123815i	$-0.960487\pi$
$167$	−5.43194	−	12.2003i	−0.420336	−	0.944090i	0.571969	−	0.820275i	$-0.306180\pi$
$168$	−1.73486	+	3.89656i	−0.133847	+	0.300626i
$169$	3.17310	+	3.52408i	0.244085	+	0.271083i
$170$		0			0
$171$	−9.20462	+	6.68755i	−0.703895	+	0.511410i
$172$	−11.7311	+	10.5628i	−0.894490	+	0.805402i
$173$	7.74619	−	17.3982i	0.588932	−	1.32276i	−0.335724	−	0.941960i	$-0.608981\pi$
$173$	7.74619	−	17.3982i	0.588932	−	1.32276i	0.924656	−	0.380803i	$-0.124352\pi$
$174$	−2.93449	+	1.30652i	−0.222463	+	0.0990469i
$175$		0			0
$176$	0.832136	−	7.91724i	0.0627246	−	0.596785i
$177$	−7.22697	−	34.0002i	−0.543213	−	2.55561i
$178$	−0.755159	−	0.245366i	−0.0566016	−	0.0183910i
$179$	−0.0775964	−	0.0164936i	−0.00579983	−	0.00123279i	0.205011	−	0.978760i	$-0.434277\pi$
$179$	−0.0775964	−	0.0164936i	−0.00579983	−	0.00123279i	−0.210811	+	0.977527i	$0.567610\pi$
$180$		0			0
$181$	−1.08143	−	1.87308i	−0.0803817	−	0.139225i	0.823032	−	0.567995i	$-0.192281\pi$
$181$	−1.08143	−	1.87308i	−0.0803817	−	0.139225i	−0.903414	+	0.428769i	$0.858947\pi$
$182$	1.03935	−	0.337704i	0.0770415	−	0.0250323i
$183$	−41.5363	+	4.36564i	−3.07045	+	0.322717i
$184$	0.487386	+	0.354107i	0.0359306	+	0.0261051i
$185$		0			0
$186$	−4.20998	−	3.78500i	−0.308691	−	0.277529i
$187$			4.43668i			0.324442i
$188$	−8.78195	+	12.0873i	−0.640490	+	0.881559i
$189$	0.776000	+	7.38314i	0.0564457	+	0.537045i
$190$		0			0
$191$	2.67085	+	4.62604i	0.193256	+	0.334729i	0.946327	−	0.323210i	$-0.104762\pi$
$191$	2.67085	+	4.62604i	0.193256	+	0.334729i	−0.753072	+	0.657939i	$0.771429\pi$
$192$	−12.9957	−	7.50308i	−0.937885	−	0.541488i
$193$	0.443616	−	2.08705i	0.0319322	−	0.150229i	−0.959293	−	0.282412i	$-0.908865\pi$
$193$	0.443616	−	2.08705i	0.0319322	−	0.150229i	0.991225	+	0.132183i	$0.0421987\pi$
$194$	−0.370632	+	1.14069i	−0.0266098	+	0.0818966i
$195$		0			0
$196$	−1.14334	+	10.8782i	−0.0816673	+	0.777013i
$197$	−4.36652	−	3.93163i	−0.311102	−	0.280117i	0.498758	−	0.866742i	$-0.333790\pi$
$197$	−4.36652	−	3.93163i	−0.311102	−	0.280117i	−0.809859	+	0.586624i	$0.800456\pi$
$198$	1.86669	+	4.19266i	0.132660	+	0.297959i
$199$	−6.32901	−	2.81786i	−0.448652	−	0.199753i	0.169958	−	0.985451i	$-0.445637\pi$
$199$	−6.32901	−	2.81786i	−0.448652	−	0.199753i	−0.618609	+	0.785699i	$0.712304\pi$
$200$		0			0
$201$	−15.0686	+	10.9480i	−1.06286	+	0.772211i
$202$	−3.65981	−	5.03729i	−0.257503	−	0.354423i
$203$	2.54050	−	2.28748i	0.178308	−	0.160549i
$204$	9.05059	+	4.02958i	0.633668	+	0.282127i
$205$		0			0
$206$	1.89860	−	2.10861i	0.132282	−	0.146914i
$207$	2.36219	+	0.248276i	0.164184	+	0.0172564i
$208$	1.95624	+	9.20337i	0.135641	+	0.638139i
$209$	1.59153	−	4.89823i	0.110089	−	0.338818i
$210$		0			0
$211$	−8.35437	+	14.4702i	−0.575139	+	0.996170i	0.420888	+	0.907113i	$0.361719\pi$
$211$	−8.35437	+	14.4702i	−0.575139	+	0.996170i	−0.996027	+	0.0890568i	$0.971615\pi$
$212$	8.08808	−	4.66966i	0.555492	−	0.320713i
$213$	−4.61698	+	1.50015i	−0.316350	+	0.102788i
$214$	−0.446370	−	4.24693i	−0.0305133	−	0.290314i
$215$		0			0
$216$	9.34610			0.635921
$217$	5.50596	+	2.44649i	0.373769	+	0.166078i
$218$			0.222141i			0.0150453i
$219$	−33.6132	−	24.4214i	−2.27137	−	1.65024i
$220$		0			0
$221$	−1.62040	−	4.98709i	−0.109000	−	0.335468i
$222$	−2.77094	+	1.59980i	−0.185973	+	0.107372i
$223$	−5.42267	−	3.13078i	−0.363129	−	0.209653i	0.307323	−	0.951605i	$-0.400567\pi$
$223$	−5.42267	−	3.13078i	−0.363129	−	0.209653i	−0.670453	+	0.741952i	$0.733900\pi$
$224$	−4.10195	−	0.871895i	−0.274073	−	0.0582560i
$225$		0			0
$226$	3.88452	−	0.825681i	0.258395	−	0.0549235i
$227$	7.80452	+	0.820289i	0.518004	+	0.0544445i	0.359924	−	0.932982i	$-0.382803\pi$
$227$	7.80452	+	0.820289i	0.518004	+	0.0544445i	0.158081	+	0.987426i	$0.449469\pi$
$228$	−8.54664	−	7.69543i	−0.566015	−	0.509642i
$229$	−11.6687	+	5.19524i	−0.771089	+	0.343311i	−0.754285	−	0.656548i	$-0.772016\pi$
$229$	−11.6687	+	5.19524i	−0.771089	+	0.343311i	−0.0168049	+	0.999859i	$0.505349\pi$
$230$		0			0
$231$	−5.09368	−	5.65711i	−0.335140	−	0.372210i
$232$	−2.52969	−	3.48183i	−0.166083	−	0.228593i
$233$	7.47514	+	10.2887i	0.489713	+	0.674032i	0.980335	−	0.197340i	$-0.0632304\pi$
$233$	7.47514	+	10.2887i	0.489713	+	0.674032i	−0.490622	+	0.871373i	$0.663230\pi$
$234$	−3.62955	−	4.03103i	−0.237271	−	0.263517i
$235$		0			0
$236$	20.5951	−	9.16951i	1.34062	−	0.596884i
$237$	7.41290	+	6.67460i	0.481520	+	0.433562i
$238$	0.690146	+	0.0725373i	0.0447355	+	0.00470189i
$239$	−24.8690	+	5.28607i	−1.60864	+	0.341928i	−0.922638	−	0.385668i	$-0.873971\pi$
$239$	−24.8690	+	5.28607i	−1.60864	+	0.341928i	−0.686006	+	0.727596i	$0.740638\pi$
$240$		0			0
$241$	−2.30939	−	0.490876i	−0.148761	−	0.0316201i	0.132929	−	0.991126i	$-0.457562\pi$
$241$	−2.30939	−	0.490876i	−0.148761	−	0.0316201i	−0.281690	+	0.959505i	$0.590895\pi$
$242$	1.54866	+	0.894121i	0.0995519	+	0.0574763i
$243$	−8.46339	+	4.88634i	−0.542927	+	0.313459i
$244$	−8.37048	−	25.7617i	−0.535865	−	1.64922i
$245$		0			0
$246$	−5.71401	−	4.15147i	−0.364312	−	0.264688i
$247$			6.08718i			0.387318i
$248$	3.78765	−	6.57173i	0.240516	−	0.417305i
$249$	37.1893			2.35677
$250$		0			0
$251$	−0.246336	−	2.34373i	−0.0155486	−	0.147935i	0.983993	−	0.178206i	$-0.0570294\pi$
$251$	−0.246336	−	2.34373i	−0.0155486	−	0.147935i	−0.999542	+	0.0302716i	$0.990363\pi$
$252$	−10.3728	+	3.37034i	−0.653428	+	0.212312i
$253$	−0.931142	+	0.537595i	−0.0585404	+	0.0337983i
$254$	0.0207005	−	0.0358542i	0.00129886	−	0.00224970i
$255$		0			0
$256$	2.16580	−	6.66565i	0.135363	−	0.416603i
$257$	5.40862	+	25.4455i	0.337380	+	1.58725i	0.740470	+	0.672089i	$0.234603\pi$
$257$	5.40862	+	25.4455i	0.337380	+	1.58725i	−0.403090	+	0.915160i	$0.632064\pi$
$258$	8.50682	+	0.894103i	0.529612	+	0.0556644i
$259$	2.27851	−	2.53054i	0.141580	−	0.157240i
$260$		0			0
$261$	−15.5012	−	6.90157i	−0.959499	−	0.427196i
$262$	−1.51057	+	1.36012i	−0.0933232	+	0.0840285i
$263$	13.4812	+	18.5552i	0.831285	+	1.14417i	0.987683	+	0.156471i	$0.0500119\pi$
$263$	13.4812	+	18.5552i	0.831285	+	1.14417i	−0.156398	+	0.987694i	$0.549988\pi$
$264$	−7.75322	+	5.63304i	−0.477178	+	0.346690i
$265$		0			0
$266$	−0.735922	−	0.327654i	−0.0451223	−	0.0200897i
$267$	−2.65886	−	5.97190i	−0.162720	−	0.365474i
$268$	−8.97726	−	8.08316i	−0.548374	−	0.493758i
$269$	−1.78193	+	16.9539i	−0.108646	+	1.03370i	0.795347	+	0.606154i	$0.207288\pi$
$269$	−1.78193	+	16.9539i	−0.108646	+	1.03370i	−0.903994	+	0.427546i	$0.859378\pi$
$270$		0			0
$271$	2.23929	−	6.89184i	0.136027	−	0.418649i	−0.859721	−	0.510764i	$-0.829363\pi$
$271$	2.23929	−	6.89184i	0.136027	−	0.418649i	0.995748	+	0.0921146i	$0.0293626\pi$
$272$	−1.24221	+	5.84413i	−0.0753199	+	0.354352i
$273$	7.79175	+	4.49857i	0.471578	+	0.272266i
$274$	2.07440	+	3.59297i	0.125319	+	0.217059i
$275$		0			0
$276$	0.250962	+	2.38775i	0.0151062	+	0.143725i
$277$	8.87748	−	12.2188i	0.533396	−	0.734157i	−0.454247	−	0.890876i	$-0.650092\pi$
$277$	8.87748	−	12.2188i	0.533396	−	0.734157i	0.987643	+	0.156719i	$0.0500917\pi$
$278$			5.41979i			0.325058i
$279$	−0.0223278	−	29.9052i	−0.00133673	−	1.79038i
$280$		0			0
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	0.646181	−	0.763184i	$-0.276365\pi$
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	−0.526150	+	0.850392i	$0.676365\pi$
$282$	8.05144	−	0.846240i	0.479456	−	0.0503929i
$283$	−4.49503	+	1.46052i	−0.267202	+	0.0868192i	−0.439554	−	0.898216i	$-0.644863\pi$
$283$	−4.49503	+	1.46052i	−0.267202	+	0.0868192i	0.172352	+	0.985035i	$0.444863\pi$
$284$	−1.57426	−	2.72670i	−0.0934153	−	0.161800i
$285$		0			0
$286$	2.40177	+	0.510512i	0.142020	+	0.0301872i
$287$	7.14881	+	2.32279i	0.421981	+	0.137110i
$288$	4.32766	+	20.3600i	0.255010	+	1.19973i
$289$	−1.42893	+	13.5953i	−0.0840546	+	0.799726i
$290$		0			0
$291$	−9.02071	+	4.01628i	−0.528804	+	0.235439i
$292$	10.9602	−	24.6171i	0.641400	−	1.44061i
$293$	−7.83935	+	7.05858i	−0.457980	+	0.412367i	−0.865562	−	0.500802i	$-0.833039\pi$
$293$	−7.83935	+	7.05858i	−0.457980	+	0.412367i	0.407582	+	0.913169i	$0.366372\pi$
$294$	4.79497	−	3.48375i	0.279648	−	0.203177i
$295$		0			0
$296$	−2.86850	−	3.18579i	−0.166728	−	0.185170i
$297$	−6.78443	+	15.2381i	−0.393673	+	0.884203i
$298$	1.70817	+	3.83662i	0.0989517	+	0.222249i
$299$	0.850314	−	0.944369i	0.0491749	−	0.0546143i
$300$		0			0
$301$	−8.90432	+	1.89267i	−0.513237	+	0.109092i
$302$	−1.44459	−	0.469377i	−0.0831271	−	0.0270096i
$303$	10.6578	−	50.1411i	0.612276	−	2.88053i
$304$	3.46785	−	6.00650i	0.198895	−	0.344496i
$305$		0			0
$306$	−1.06438	−	3.27583i	−0.0608467	−	0.187267i
$307$	2.63399	−	0.276844i	0.150330	−	0.0158003i	−0.0290645	−	0.999578i	$-0.509253\pi$
$307$	2.63399	−	0.276844i	0.150330	−	0.0158003i	0.179394	+	0.983777i	$0.442586\pi$
$308$	2.90198	−	3.99424i	0.165356	−	0.227593i
$309$	23.3600			1.32890
$310$		0			0
$311$	5.51283			0.312604			0.156302	−	0.987709i	$-0.450043\pi$
$311$	5.51283			0.312604			0.156302	+	0.987709i	$0.450043\pi$
$312$	6.65773	−	9.16358i	0.376920	−	0.518786i
$313$	26.5293	−	2.78834i	1.49953	−	0.157607i	0.681088	−	0.732201i	$-0.261507\pi$
$313$	26.5293	−	2.78834i	1.49953	−	0.157607i	0.818438	+	0.574595i	$0.194840\pi$
$314$	0.945290	+	2.90930i	0.0533458	+	0.164181i
$315$		0			0
$316$	−3.23474	+	5.60274i	−0.181969	+	0.315179i
$317$	2.23302	−	10.5055i	0.125419	−	0.590050i	−0.869885	−	0.493254i	$-0.835807\pi$
$317$	2.23302	−	10.5055i	0.125419	−	0.590050i	0.995304	−	0.0967957i	$-0.0308593\pi$
$318$	−4.81291	−	1.56381i	−0.269895	−	0.0876941i
$319$	7.51318	−	1.59698i	0.420657	−	0.0894135i
$320$		0			0
$321$	23.5246	−	26.1267i	1.31301	−	1.45825i
$322$	0.0684017	+	0.153633i	0.00381188	+	0.00856162i
$323$	−1.57218	+	3.53117i	−0.0874784	+	0.196480i
$324$	4.69064	+	5.20948i	0.260591	+	0.289416i
$325$		0			0
$326$	−0.889309	+	0.646121i	−0.0492543	+	0.0357853i
$327$	−1.35911	+	1.22374i	−0.0751587	+	0.0676732i
$328$	3.84897	−	8.64492i	0.212524	−	0.477336i
$329$	−7.87106	+	3.50442i	−0.433945	+	0.193205i
$330$		0			0
$331$	−2.05373	+	19.5400i	−0.112883	+	1.07401i	0.780635	+	0.624987i	$0.214896\pi$
$331$	−2.05373	+	19.5400i	−0.112883	+	1.07401i	−0.893518	+	0.449027i	$0.851771\pi$
$332$	5.01478	+	23.5927i	0.275222	+	1.29482i
$333$	−16.0744	−	5.22289i	−0.880872	−	0.286213i
$334$	−4.59080	−	0.975804i	−0.251197	−	0.0533936i
$335$		0			0
$336$	−5.12565	−	8.87788i	−0.279627	−	0.484328i
$337$	−18.2401	+	5.92655i	−0.993599	+	0.322840i	−0.760305	−	0.649566i	$-0.774950\pi$
$337$	−18.2401	+	5.92655i	−0.993599	+	0.322840i	−0.233294	+	0.972406i	$0.574950\pi$
$338$	1.65741	−	0.174200i	0.0901510	−	0.00947525i
$339$	26.4510	+	19.2178i	1.43662	+	1.04376i
$340$		0			0
$341$	7.96520	+	10.9460i	0.431340	+	0.592757i
$342$			3.99844i			0.216211i
$343$	−8.15999	+	11.2313i	−0.440598	+	0.606431i
$344$	1.19794	+	11.3976i	0.0645885	+	0.614519i
$345$		0			0
$346$	−3.34647	−	5.79626i	−0.179907	−	0.311609i
$347$	−9.23180	−	5.32998i	−0.495589	−	0.286128i	0.231301	−	0.972882i	$-0.425702\pi$
$347$	−9.23180	−	5.32998i	−0.495589	−	0.286128i	−0.726890	+	0.686754i	$0.759035\pi$
$348$	3.56605	−	16.7769i	0.191160	−	0.899338i
$349$	5.77910	−	17.7862i	0.309348	−	0.952075i	−0.668671	−	0.743559i	$-0.733136\pi$
$349$	5.77910	−	17.7862i	0.309348	−	0.952075i	0.978019	−	0.208517i	$-0.0668636\pi$
$350$		0			0
$351$	2.06072	−	19.6064i	0.109993	−	1.04651i
$352$	−7.00216	−	6.30478i	−0.373217	−	0.336046i
$353$	5.15020	+	11.5675i	0.274117	+	0.615678i	0.997175	−	0.0751097i	$-0.0239307\pi$
$353$	5.15020	+	11.5675i	0.274117	+	0.615678i	−0.723058	+	0.690787i	$0.757264\pi$
$354$	−11.1596	−	4.96859i	−0.593127	−	0.264077i
$355$		0			0
$356$	3.43001	−	2.49205i	0.181790	−	0.132078i
$357$	3.35812	+	4.62205i	0.177730	+	0.244625i
$358$	−0.0207182	+	0.0186548i	−0.00109499	+	0.000985936i
$359$	20.7175	+	9.22402i	1.09343	+	0.486825i	0.872574	−	0.488482i	$-0.162449\pi$
$359$	20.7175	+	9.22402i	1.09343	+	0.486825i	0.220853	+	0.975307i	$0.429116\pi$
$360$		0			0
$361$	−9.71104	+	10.7852i	−0.511107	+	0.567642i
$362$	−0.755932	−	0.0794517i	−0.0397309	−	0.00417589i
$363$	3.06095	+	14.4006i	0.160658	+	0.755837i
$364$	−1.80319	+	5.54965i	−0.0945129	+	0.290881i
$365$		0			0
$366$	−7.33880	+	12.7112i	−0.383605	+	0.664424i
$367$	7.55147	−	4.35984i	0.394183	−	0.227582i	−0.289788	−	0.957091i	$-0.593585\pi$
$367$	7.55147	−	4.35984i	0.394183	−	0.227582i	0.683971	+	0.729509i	$0.260251\pi$
$368$	−1.37705	+	0.447430i	−0.0717836	+	0.0233239i
$369$	−3.89987	−	37.1048i	−0.203019	−	1.93160i
$370$		0			0
$371$	5.38574			0.279614
$372$	29.5635	−	6.30699i	1.53280	−	0.327002i
$373$		−	25.4134i		−	1.31586i	−0.753081	−	0.657928i	$-0.771433\pi$
$373$		−	25.4134i		−	1.31586i	0.753081	−	0.657928i	$-0.228567\pi$
$374$	1.26141	+	0.916471i	0.0652262	+	0.0473896i
$375$		0			0
$376$	3.35188	+	10.3160i	0.172860	+	0.532009i
$377$	−7.86200	+	4.53913i	−0.404914	+	0.233777i
$378$	2.25943	+	1.30448i	0.116213	+	0.0670954i
$379$	21.6150	+	4.59441i	1.11029	+	0.235999i	0.726326	−	0.687350i	$-0.241226\pi$
$379$	21.6150	+	4.59441i	1.11029	+	0.235999i	0.383961	+	0.923349i	$0.374560\pi$
$380$		0			0
$381$	0.333399	−	0.0708662i	0.0170806	−	0.00363059i
$382$	1.86696	+	0.196226i	0.0955220	+	0.0100398i
$383$	19.7993	+	17.8274i	1.01170	+	0.910938i	0.996037	−	0.0889398i	$-0.0283479\pi$
$383$	19.7993	+	17.8274i	1.01170	+	0.910938i	0.0156617	+	0.999877i	$0.495015\pi$
$384$	−25.3039	+	11.2660i	−1.29128	+	0.574916i
$385$		0			0
$386$	−0.501743	−	0.557242i	−0.0255380	−	0.0283629i
$387$	26.5585	+	36.5547i	1.35005	+	1.85818i
$388$	−3.76430	−	5.18112i	−0.191104	−	0.263032i
$389$	8.66862	+	9.62748i	0.439517	+	0.488133i	0.921681	−	0.387948i	$-0.126816\pi$
$389$	8.66862	+	9.62748i	0.439517	+	0.488133i	−0.482165	+	0.876081i	$0.660149\pi$
$390$		0			0
$391$	0.737176	−	0.328212i	0.0372806	−	0.0165984i
$392$	5.90132	+	5.31357i	0.298062	+	0.268376i
$393$	−16.6430	−	1.74925i	−0.839528	−	0.0882379i
$394$	−2.01980	+	0.429321i	−0.101756	+	0.0216289i
$395$		0			0
$396$	−23.9701	−	5.09500i	−1.20454	−	0.256033i
$397$	2.53508	+	1.46363i	0.127232	+	0.0734574i	0.562265	−	0.826957i	$-0.309930\pi$
$397$	2.53508	+	1.46363i	0.127232	+	0.0734574i	−0.435033	+	0.900414i	$0.643263\pi$
$398$	−2.10852	+	1.21736i	−0.105691	+	0.0610205i
$399$	−2.04944	−	6.30752i	−0.102600	−	0.315771i
$400$		0			0
$401$	9.93025	+	7.21475i	0.495893	+	0.360287i	0.807446	−	0.589942i	$-0.200849\pi$
$401$	9.93025	+	7.21475i	0.495893	+	0.360287i	−0.311553	+	0.950229i	$0.600849\pi$
$402$			6.54572i			0.326471i
$403$	−12.9511	−	9.39479i	−0.645142	−	0.467988i
$404$	33.2464			1.65407
$405$		0			0
$406$	−0.125581	−	1.19482i	−0.00623246	−	0.0592979i
$407$	7.27645	−	2.36426i	0.360680	−	0.117192i
$408$	6.22889	−	3.59625i	0.308376	−	0.178041i
$409$	−8.59861	+	14.8932i	−0.425174	+	0.736423i	−0.996437	−	0.0843442i	$-0.973120\pi$
$409$	−8.59861	+	14.8932i	−0.425174	+	0.736423i	0.571263	+	0.820767i	$0.306454\pi$
$410$		0			0
$411$	−10.5549	+	32.4848i	−0.520637	+	1.60236i
$412$	3.14997	+	14.8195i	0.155188	+	0.730102i
$413$	12.9294	+	1.35893i	0.636213	+	0.0668687i
$414$	0.558539	−	0.620320i	0.0274507	−	0.0304871i
$415$		0			0
$416$	10.1735	+	4.52955i	0.498799	+	0.222080i
$417$	−33.1594	+	29.8568i	−1.62382	+	1.46210i
$418$	−1.06388	−	1.46431i	−0.0520362	−	0.0716217i
$419$	18.7251	−	13.6046i	0.914782	−	0.664628i	−0.0274378	−	0.999624i	$-0.508735\pi$
$419$	18.7251	−	13.6046i	0.914782	−	0.664628i	0.942220	+	0.334996i	$0.108735\pi$
$420$		0			0
$421$	26.6593	+	11.8695i	1.29929	+	0.578483i	0.935609	−	0.353038i	$-0.114851\pi$
$421$	26.6593	+	11.8695i	1.29929	+	0.578483i	0.363686	+	0.931522i	$0.381518\pi$
$422$	2.38836	+	5.36434i	0.116263	+	0.261132i
$423$	31.7808	+	28.6156i	1.54524	+	1.39134i
$424$	0.708734	−	6.74315i	0.0344192	−	0.327476i
$425$		0			0
$426$	−0.527201	+	1.62256i	−0.0255430	+	0.0786132i
$427$	3.24771	−	15.2793i	0.157168	−	0.739416i
$428$	19.7468	+	11.4008i	0.954498	+	0.551080i
$429$	10.1076	+	17.5069i	0.487999	+	0.845239i
$430$		0			0
$431$	−3.17267	−	30.1859i	−0.152822	−	1.45401i	−0.755042	−	0.655676i	$-0.772384\pi$
$431$	−3.17267	−	30.1859i	−0.152822	−	1.45401i	0.602220	−	0.798330i	$-0.294283\pi$
$432$	−13.2031	+	18.1725i	−0.635235	+	0.874326i
$433$			13.8400i			0.665107i	0.943084	+	0.332553i	$0.107910\pi$
$433$			13.8400i			0.665107i	−0.943084	+	0.332553i	$0.892090\pi$
$434$	1.83292	−	1.06006i	0.0879830	−	0.0508846i
$435$		0			0
$436$	−0.959605	−	0.697194i	−0.0459567	−	0.0333895i
$437$	−0.931602	+	0.0979154i	−0.0445646	+	0.00468393i
$438$	−13.8867	+	4.51207i	−0.663534	+	0.215595i
$439$	6.46006	+	11.1892i	0.308322	+	0.534029i	0.977995	−	0.208626i	$-0.0668993\pi$
$439$	6.46006	+	11.1892i	0.308322	+	0.534029i	−0.669674	+	0.742656i	$0.733566\pi$
$440$		0			0
$441$	30.6242	+	6.50938i	1.45830	+	0.309970i
$442$	−1.75263	−	0.569463i	−0.0833639	−	0.0270866i
$443$	4.93962	+	23.2391i	0.234688	+	1.10412i	0.924810	+	0.380429i	$0.124224\pi$
$443$	4.93962	+	23.2391i	0.234688	+	1.10412i	−0.690122	+	0.723693i	$0.742443\pi$
$444$	1.78582	−	16.9909i	0.0847511	−	0.806353i
$445$		0			0
$446$	−2.01027	+	0.895031i	−0.0951892	+	0.0423809i
$447$	−14.0631	+	31.5863i	−0.665163	+	1.49398i
$448$	4.17089	−	3.75549i	0.197056	−	0.177430i
$449$	−15.7054	+	11.4106i	−0.741181	+	0.538500i	−0.893081	−	0.449896i	$-0.851461\pi$
$449$	−15.7054	+	11.4106i	−0.741181	+	0.538500i	0.151900	+	0.988396i	$0.451461\pi$
$450$		0			0
$451$	11.3009	+	12.5509i	0.532137	+	0.590998i
$452$	−8.62487	+	19.3718i	−0.405680	+	0.911171i
$453$	−5.08632	−	11.4241i	−0.238976	−	0.536749i
$454$	1.84538	−	2.04950i	0.0866078	−	0.0961877i
$455$		0			0
$456$	−8.16695	+	1.73594i	−0.382452	+	0.0812928i
$457$	23.1506	+	7.52208i	1.08294	+	0.351868i	0.795514	−	0.605935i	$-0.207201\pi$
$457$	23.1506	+	7.52208i	1.08294	+	0.351868i	0.287424	+	0.957803i	$0.407201\pi$
$458$	−0.933283	+	4.39075i	−0.0436094	+	0.205166i
$459$	6.25931	−	10.8414i	0.292159	−	0.506035i
$460$		0			0
$461$	−11.8487	−	36.4665i	−0.551848	−	1.69841i	−0.704126	−	0.710075i	$-0.748661\pi$
$461$	−11.8487	−	36.4665i	−0.551848	−	1.69841i	0.152279	−	0.988338i	$-0.451339\pi$
$462$	−2.66059	+	0.279639i	−0.123782	+	0.0130100i
$463$	3.87603	−	5.33489i	0.180134	−	0.247934i	−0.709396	−	0.704810i	$-0.751032\pi$
$463$	3.87603	−	5.33489i	0.180134	−	0.247934i	0.889530	+	0.456877i	$0.151032\pi$
$464$	10.3437			0.480195
$465$		0			0
$466$	4.46933			0.207038
$467$	22.5718	−	31.0674i	1.04450	−	1.43763i	0.151014	−	0.988532i	$-0.451746\pi$
$467$	22.5718	−	31.0674i	1.04450	−	1.43763i	0.893484	−	0.449096i	$-0.148254\pi$
$468$	28.8046	−	3.02749i	1.33149	−	0.139946i
$469$	−2.15270	−	6.62532i	−0.0994024	−	0.305929i
$470$		0			0
$471$	−12.5922	+	21.8104i	−0.580220	+	1.00497i
$472$	3.40287	−	16.0092i	0.156630	−	0.736885i
$473$	−19.4525	−	6.32051i	−0.894429	−	0.290617i
$474$	3.42895	−	0.728845i	0.157497	−	0.0334770i
$475$		0			0
$476$	−2.47938	+	2.75363i	−0.113642	+	0.126212i
$477$	−10.8729	−	24.4210i	−0.497838	−	1.11816i
$478$	−3.63421	+	8.16256i	−0.166225	+	0.373347i
$479$	−5.03531	−	5.59228i	−0.230069	−	0.255518i	0.617046	−	0.786927i	$-0.288329\pi$
$479$	−5.03531	−	5.59228i	−0.230069	−	0.255518i	−0.847115	+	0.531409i	$0.821663\pi$
$480$		0			0
$481$	−7.31567	+	5.31515i	−0.333566	+	0.242350i
$482$	−0.616606	+	0.555195i	−0.0280856	+	0.0252884i
$483$	−0.563141	+	1.26484i	−0.0256238	+	0.0575520i
$484$	−8.72293	+	3.88370i	−0.396497	+	0.176532i
$485$		0			0
$486$	−0.358996	+	3.41562i	−0.0162844	+	0.154936i
$487$	−5.20450	−	24.4852i	−0.235838	−	1.10953i	−0.923529	−	0.383528i	$-0.874709\pi$
$487$	−5.20450	−	24.4852i	−0.235838	−	1.10953i	0.687691	−	0.726004i	$-0.258625\pi$
$488$	−18.7029	−	6.07693i	−0.846639	−	0.275090i
$489$	−8.85217	−	1.88159i	−0.400309	−	0.0850883i
$490$		0			0
$491$	19.8550	+	34.3899i	0.896044	+	1.55199i	0.832507	+	0.554015i	$0.186905\pi$
$491$	19.8550	+	34.3899i	0.896044	+	1.55199i	0.0635377	+	0.997979i	$0.479762\pi$
$492$	35.8670	−	11.6539i	1.61701	−	0.525399i
$493$	−5.73310	+	0.602573i	−0.258206	+	0.0271385i
$494$	1.73068	+	1.25741i	0.0778668	+	0.0565735i
$495$		0			0
$496$	7.42729	+	16.6485i	0.333495	+	0.747539i
$497$		−	1.81567i		−	0.0814440i
$498$	7.68207	−	10.5735i	0.344242	−	0.473808i
$499$	−2.47252	−	23.5245i	−0.110685	−	1.05310i	−0.899036	−	0.437875i	$-0.855731\pi$
$499$	−2.47252	−	23.5245i	−0.110685	−	1.05310i	0.788351	−	0.615226i	$-0.210935\pi$
$500$		0			0
$501$	−19.3199	−	33.4630i	−0.863148	−	1.49502i
$502$	−0.717241	−	0.414099i	−0.0320120	−	0.0184822i
$503$	4.19699	−	19.7453i	0.187135	−	0.880400i	−0.779930	−	0.625867i	$-0.784745\pi$
$503$	4.19699	−	19.7453i	0.187135	−	0.880400i	0.967064	−	0.254532i	$-0.0819215\pi$
$504$	−2.44685	+	7.53063i	−0.108991	+	0.335441i
$505$		0			0
$506$	−0.0394968	+	0.375787i	−0.00175585	+	0.0167058i
$507$	10.1962	+	9.18070i	0.452829	+	0.407729i
$508$	0.0899143	+	0.201951i	0.00398930	+	0.00896012i
$509$	−10.8155	−	4.81536i	−0.479387	−	0.213437i	0.152793	−	0.988258i	$-0.451173\pi$
$509$	−10.8155	−	4.81536i	−0.479387	−	0.213437i	−0.632180	+	0.774821i	$0.717840\pi$
$510$		0			0
$511$	12.5717	−	9.13389i	0.556140	−	0.404060i
$512$	−12.7019	−	17.4827i	−0.561351	−	0.772633i
$513$	−10.7995	+	9.72394i	−0.476811	+	0.429322i
$514$	8.35179	+	3.71845i	0.368381	+	0.164014i
$515$		0			0
$516$	−30.5611	+	33.9416i	−1.34538	+	1.49419i
$517$	−19.2526	−	2.02354i	−0.846731	−	0.0889950i
$518$	−0.248806	−	1.17054i	−0.0109319	−	0.0514306i
$519$	17.0275	−	52.4051i	0.747422	−	2.30033i
$520$		0			0
$521$	16.3742	−	28.3610i	0.717368	−	1.24252i	−0.244672	−	0.969606i	$-0.578680\pi$
$521$	16.3742	−	28.3610i	0.717368	−	1.24252i	0.962039	−	0.272911i	$-0.0879865\pi$
$522$	−5.16425	+	2.98158i	−0.226033	+	0.130500i
$523$	−28.0587	+	9.11682i	−1.22692	+	0.398651i	−0.849598	−	0.527431i	$-0.823155\pi$
$523$	−28.0587	+	9.11682i	−1.22692	+	0.398651i	−0.377323	+	0.926082i	$0.623155\pi$
$524$	−1.13451	−	10.7941i	−0.0495611	−	0.471543i
$525$		0			0
$526$	8.06030			0.351446
$527$	−5.08650	−	8.79490i	−0.221571	−	0.383112i
$528$		−	23.0331i		−	1.00239i
$529$	−18.4492	−	13.4041i	−0.802138	−	0.582788i
$530$		0			0
$531$	−19.9404	−	61.3703i	−0.865340	−	2.66324i
$532$	3.72510	−	2.15069i	0.161504	−	0.0932441i
$533$	−17.2868	−	9.98053i	−0.748774	−	0.432305i
$534$	−2.24713	−	0.477643i	−0.0972430	−	0.0206696i
$535$		0			0
$536$	−8.57845	+	1.82340i	−0.370532	+	0.0787591i
$537$	−0.228267	−	0.0239919i	−0.00985047	−	0.00103533i
$538$	4.45217	+	4.00875i	0.191947	+	0.172830i
$539$	−12.9472	+	5.76446i	−0.557675	+	0.248293i
$540$		0			0
$541$	8.87657	+	9.85843i	0.381634	+	0.423847i	0.903104	−	0.429423i	$-0.141283\pi$
$541$	8.87657	+	9.85843i	0.381634	+	0.423847i	−0.521470	+	0.853270i	$0.674616\pi$
$542$	−1.49689	−	2.06029i	−0.0642968	−	0.0884970i
$543$	−3.67822	−	5.06264i	−0.157848	−	0.217258i
$544$	4.73179	+	5.25519i	0.202874	+	0.225314i
$545$		0			0
$546$	2.88853	−	1.28605i	0.123618	−	0.0550381i
$547$	28.0640	+	25.2689i	1.19993	+	1.08042i	0.994817	+	0.101684i	$0.0324231\pi$
$547$	28.0640	+	25.2689i	1.19993	+	1.08042i	0.205114	+	0.978738i	$0.434244\pi$
$548$	−22.0315	−	2.31560i	−0.941137	−	0.0989175i
$549$	−75.8388	+	16.1200i	−3.23672	+	0.687986i
$550$		0			0
$551$	6.54568	+	1.39133i	0.278855	+	0.0592725i
$552$	1.50952	+	0.871520i	0.0642493	+	0.0370944i
$553$	−3.23095	+	1.86539i	−0.137394	+	0.0793245i
$554$	−1.64019	−	5.04800i	−0.0696852	−	0.214469i
$555$		0			0
$556$	−23.4124	−	17.0101i	−0.992907	−	0.721389i
$557$		−	11.3637i		−	0.481496i	−0.970588	−	0.240748i	$-0.922607\pi$
$557$		−	11.3637i		−	0.481496i	0.970588	−	0.240748i	$-0.0773928\pi$
$558$	−8.50711	−	6.17108i	−0.360135	−	0.261243i
$559$	24.1743			1.02246
$560$		0			0
$561$	1.34179	+	12.7663i	0.0566505	+	0.538993i
$562$	0.831262	−	0.270094i	0.0350647	−	0.0113932i
$563$	17.4821	−	10.0933i	0.736781	−	0.425381i	−0.0841167	−	0.996456i	$-0.526807\pi$
$563$	17.4821	−	10.0933i	0.736781	−	0.425381i	0.820898	+	0.571075i	$0.193474\pi$
$564$	−21.6140	+	37.4365i	−0.910113	+	1.57636i
$565$		0			0
$566$	−0.513276	+	1.57970i	−0.0215746	+	0.0663998i
$567$	0.840485	+	3.95417i	0.0352971	+	0.166060i
$568$	−2.27329	−	0.238933i	−0.0953852	−	0.0100254i
$569$	20.7361	−	23.0298i	0.869304	−	0.965460i	−0.130358	−	0.991467i	$-0.541613\pi$
$569$	20.7361	−	23.0298i	0.869304	−	0.965460i	0.999662	+	0.0260074i	$0.00827935\pi$
$570$		0			0
$571$	−9.50060	−	4.22994i	−0.397588	−	0.177017i	0.198196	−	0.980162i	$-0.436492\pi$
$571$	−9.50060	−	4.22994i	−0.397588	−	0.177017i	−0.595784	+	0.803145i	$0.703158\pi$
$572$	−9.74330	+	8.77291i	−0.407388	+	0.366814i
$573$	9.08427	+	12.5034i	0.379501	+	0.522338i
$574$	2.13711	−	1.55270i	0.0892012	−	0.0648085i
$575$		0			0
$576$	−25.4492	−	11.3307i	−1.06038	−	0.472113i
$577$	2.20201	+	4.94581i	0.0916711	+	0.205897i	0.953562	−	0.301197i	$-0.0973863\pi$
$577$	2.20201	+	4.94581i	0.0916711	+	0.205897i	−0.861891	+	0.507094i	$0.830720\pi$
$578$	3.57019	+	3.21461i	0.148500	+	0.133710i
$579$	0.645291	−	6.13953i	0.0268174	−	0.255150i
$580$		0			0
$581$	−4.29819	+	13.2285i	−0.178319	+	0.548809i
$582$	−0.721492	+	3.39435i	−0.0299068	+	0.140700i
$583$	10.4797	+	6.05046i	0.434025	+	0.250585i
$584$	−9.78162	−	16.9423i	−0.404766	−	0.701076i
$585$		0			0
$586$	0.387510	+	3.68691i	0.0160079	+	0.152305i
$587$	−7.38424	+	10.1635i	−0.304780	+	0.419494i	−0.933744	−	0.357940i	$-0.883479\pi$
$587$	−7.38424	+	10.1635i	−0.304780	+	0.419494i	0.628964	+	0.777434i	$0.283479\pi$
$588$			31.6471i			1.30510i
$589$	2.46073	+	11.5345i	0.101393	+	0.475270i
$590$		0			0
$591$	−13.7535	−	9.99247i	−0.565741	−	0.411035i
$592$	10.2467	−	1.07697i	0.421138	−	0.0442634i
$593$	25.7451	−	8.36510i	1.05723	−	0.343513i	0.271726	−	0.962375i	$-0.412406\pi$
$593$	25.7451	−	8.36510i	1.05723	−	0.343513i	0.785500	+	0.618861i	$0.212406\pi$
$594$	2.93098	+	5.07660i	0.120259	+	0.208295i
$595$		0			0
$596$	−21.9345	−	4.66233i	−0.898473	−	0.190976i
$597$	−19.0636	−	6.19413i	−0.780220	−	0.253509i
$598$	−0.0928516	−	0.436832i	−0.00379698	−	0.0178634i
$599$	−1.50051	+	14.2764i	−0.0613094	+	0.583320i	0.920139	+	0.391592i	$0.128076\pi$
$599$	−1.50051	+	14.2764i	−0.0613094	+	0.583320i	−0.981448	+	0.191727i	$0.938591\pi$
$600$		0			0
$601$	0.584684	−	0.260318i	0.0238498	−	0.0106186i	−0.394777	−	0.918777i	$-0.629178\pi$
$601$	0.584684	−	0.260318i	0.0238498	−	0.0106186i	0.418627	+	0.908158i	$0.362512\pi$
$602$	−1.30122	+	2.92260i	−0.0530339	+	0.119116i
$603$	−25.6958	+	23.1366i	−1.04642	+	0.942197i
$604$	6.56150	−	4.76721i	0.266984	−	0.193975i
$605$		0			0
$606$	−12.0543	−	13.3877i	−0.489673	−	0.543837i
$607$	2.65104	−	5.95432i	0.107602	−	0.241679i	−0.851717	−	0.524002i	$-0.824438\pi$
$607$	2.65104	−	5.95432i	0.107602	−	0.241679i	0.959319	+	0.282323i	$0.0911051\pi$
$608$	−3.33890	−	7.49929i	−0.135410	−	0.304136i
$609$	6.61834	−	7.35041i	0.268189	−	0.297854i
$610$		0			0
$611$	22.3802	−	4.75706i	0.905405	−	0.192450i
$612$	17.4915	+	5.68333i	0.707052	+	0.229735i
$613$	−2.17170	+	10.2171i	−0.0877143	+	0.412663i	0.912281	+	0.409565i	$0.134320\pi$
$613$	−2.17170	+	10.2171i	−0.0877143	+	0.412663i	−0.999995	+	0.00309833i	$0.999014\pi$
$614$	0.465385	−	0.806070i	0.0187814	−	0.0325303i
$615$		0			0
$616$	−1.10762	−	3.40892i	−0.0446274	−	0.137349i
$617$	21.5845	−	2.26862i	0.868958	−	0.0913311i	0.340453	−	0.940262i	$-0.389420\pi$
$617$	21.5845	−	2.26862i	0.868958	−	0.0913311i	0.528505	+	0.848930i	$0.322753\pi$
$618$	4.82540	−	6.64159i	0.194106	−	0.267164i
$619$	−28.5478			−1.14743			−0.573716	−	0.819054i	$-0.694499\pi$
$619$	−28.5478			−1.14743			−0.573716	+	0.819054i	$0.694499\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$	1.13877	−	1.56738i	0.0456604	−	0.0628462i
$623$	2.43155	−	0.255566i	0.0974178	−	0.0102390i
$624$	8.41235	+	25.8906i	0.336764	+	1.03645i
$625$		0			0
$626$	4.68731	−	8.11866i	0.187343	−	0.324487i
$627$	3.09816	−	14.5757i	0.123729	−	0.582098i
$628$	−15.5344	−	5.04743i	−0.619890	−	0.201414i
$629$	−5.61660	+	1.19385i	−0.223949	+	0.0476018i
$630$		0			0
$631$	18.2275	−	20.2436i	0.725624	−	0.805887i	−0.261609	−	0.965174i	$-0.584253\pi$
$631$	18.2275	−	20.2436i	0.725624	−	0.805887i	0.987232	+	0.159287i	$0.0509196\pi$
$632$	1.91037	+	4.29075i	0.0759903	+	0.170677i
$633$	−19.6630	+	44.1638i	−0.781533	+	1.75535i
$634$	−2.52561	−	2.80498i	−0.100305	−	0.111400i
$635$		0			0
$636$	21.8607	−	15.8828i	0.866835	−	0.629792i
$637$	12.4481	−	11.2083i	0.493210	−	0.444089i
$638$	1.09793	−	2.46599i	0.0434675	−	0.0976295i
$639$	−8.23296	+	3.66555i	−0.325691	+	0.145007i
$640$		0			0
$641$	−4.30742	+	40.9824i	−0.170133	+	1.61871i	0.492880	+	0.870097i	$0.335944\pi$
$641$	−4.30742	+	40.9824i	−0.170133	+	1.61871i	−0.663013	+	0.748608i	$0.730722\pi$
$642$	−2.56881	−	12.0853i	−0.101383	−	0.476969i
$643$	29.3044	+	9.52156i	1.15565	+	0.375494i	0.823269	−	0.567651i	$-0.192148\pi$
$643$	29.3044	+	9.52156i	1.15565	+	0.375494i	0.332382	+	0.943145i	$0.392148\pi$
$644$	−0.878342	−	0.186697i	−0.0346115	−	0.00735691i
$645$		0			0
$646$	0.679205	+	1.17642i	0.0267230	+	0.0462855i
$647$	−8.47978	+	2.75525i	−0.333375	+	0.108320i	−0.470921	−	0.882175i	$-0.656078\pi$
$647$	−8.47978	+	2.75525i	−0.333375	+	0.108320i	0.137547	+	0.990495i	$0.456078\pi$
$648$	5.06138	−	0.531973i	0.198830	−	0.0208979i
$649$	23.6317	+	17.1694i	0.927623	+	0.673958i
$650$		0			0
$651$	16.5830	+	5.37445i	0.649938	+	0.210641i
$652$		−	5.86949i		−	0.229867i
$653$	−23.0655	+	31.7469i	−0.902623	+	1.24235i	0.0670010	+	0.997753i	$0.478657\pi$
$653$	−23.0655	+	31.7469i	−0.902623	+	1.24235i	−0.969624	+	0.244601i	$0.921343\pi$
$654$	0.0671825	+	0.639199i	0.00262704	+	0.0249946i
$655$		0			0
$656$	11.3718	+	19.6965i	0.443993	+	0.769018i
$657$	−66.7969	−	38.5652i	−2.60600	−	1.50457i
$658$	−0.629540	+	2.96175i	−0.0245420	+	0.115461i
$659$	−10.1832	+	31.3407i	−0.396681	+	1.22086i	0.530963	+	0.847395i	$0.321830\pi$
$659$	−10.1832	+	31.3407i	−0.396681	+	1.22086i	−0.927644	+	0.373465i	$0.878170\pi$
$660$		0			0
$661$	0.0177359	−	0.168746i	0.000689846	−	0.00656345i	−0.994172	−	0.107810i	$-0.965616\pi$
$661$	0.0177359	−	0.168746i	0.000689846	−	0.00656345i	0.994861	+	0.101246i	$0.0322830\pi$
$662$	5.13127	+	4.62022i	0.199433	+	0.179570i
$663$	−6.17087	−	13.8600i	−0.239657	−	0.538278i
$664$	15.9969	+	7.12229i	0.620801	+	0.276398i
$665$		0			0
$666$	−4.80539	+	3.49132i	−0.186205	+	0.135286i
$667$	−0.821147	−	1.13021i	−0.0317950	−	0.0437620i
$668$	18.6236	−	16.7687i	0.720567	−	0.648801i
$669$	−16.5503	−	7.36866i	−0.639871	−	0.284889i
$670$		0			0
$671$	23.4846	−	26.0823i	0.906612	−	1.00689i
$672$	−12.0668	−	1.26827i	−0.465487	−	0.0489246i
$673$	−3.03267	−	14.2676i	−0.116901	−	0.549976i	−0.997149	−	0.0754613i	$-0.975957\pi$
$673$	−3.03267	−	14.2676i	−0.116901	−	0.549976i	0.880248	−	0.474514i	$-0.157376\pi$
$674$	−2.08278	+	6.41015i	−0.0802258	+	0.246910i
$675$		0			0
$676$	−4.44929	+	7.70639i	−0.171126	+	0.296400i
$677$	13.6545	−	7.88341i	0.524784	−	0.302984i	−0.214106	−	0.976810i	$-0.568684\pi$
$677$	13.6545	−	7.88341i	0.524784	−	0.302984i	0.738890	+	0.673826i	$0.235350\pi$
$678$	10.9278	−	3.55065i	0.419679	−	0.136362i
$679$	−0.386039	−	3.67291i	−0.0148148	−	0.140953i
$680$		0			0
$681$	22.7051			0.870063
$682$	4.75744	−	0.00355200i	0.182172	−	0.000136013i
$683$		−	20.5935i		−	0.787988i	−0.919113	−	0.393994i	$-0.871093\pi$
$683$		−	20.5935i		−	0.787988i	0.919113	−	0.393994i	$-0.128907\pi$
$684$	−17.2724	−	12.5492i	−0.660428	−	0.479829i
$685$		0			0
$686$	1.50763	+	4.64001i	0.0575616	+	0.177156i
$687$	−32.0048	+	18.4780i	−1.22106	+	0.704979i
$688$	−23.8538	−	13.7720i	−0.909418	−	0.525053i
$689$	−13.9896	−	2.97359i	−0.532962	−	0.113285i
$690$		0			0
$691$	5.82165	−	1.23743i	0.221466	−	0.0470741i	−0.0958421	−	0.995397i	$-0.530554\pi$
$691$	5.82165	−	1.23743i	0.221466	−	0.0470741i	0.317308	+	0.948322i	$0.397221\pi$
$692$	35.5416	+	3.73557i	1.35109	+	0.142005i
$693$	−10.5019	−	9.45597i	−0.398935	−	0.359203i
$694$	−3.42238	+	1.52374i	−0.129912	+	0.0578404i
$695$		0			0
$696$	−8.33206	−	9.25369i	−0.315826	−	0.350760i
$697$	−7.45032	−	10.2545i	−0.282201	−	0.388417i
$698$	−3.86312	−	5.31713i	−0.146221	−	0.201256i
$699$	24.6209	+	27.3443i	0.931248	+	1.03426i
$700$		0			0
$701$	−24.3281	+	10.8316i	−0.918859	+	0.409103i	−0.810988	−	0.585062i	$-0.801070\pi$
$701$	−24.3281	+	10.8316i	−0.918859	+	0.409103i	−0.107871	+	0.994165i	$0.534403\pi$
$702$	−5.14871	−	4.63592i	−0.194326	−	0.174972i
$703$	6.62916	+	0.696753i	0.250024	+	0.0262785i
$704$	12.3348	−	2.62185i	0.464886	−	0.0988146i
$705$		0			0
$706$	4.35268	+	0.925191i	0.163815	+	0.0348200i
$707$	16.6037	+	9.58617i	0.624448	+	0.360525i
$708$	56.4879	−	32.6133i	2.12295	−	1.22568i
$709$	0.816662	+	2.51343i	0.0306704	+	0.0943938i	0.965220	−	0.261439i	$-0.0841971\pi$
$709$	0.816662	+	2.51343i	0.0306704	+	0.0943938i	−0.934550	+	0.355833i	$0.884197\pi$
$710$		0			0
$711$	14.9812	+	10.8845i	0.561839	+	0.408200i
$712$		−	3.07802i		−	0.115354i
$713$	1.22948	−	2.13321i	0.0460445	−	0.0798892i
$714$	2.00779			0.0751398
$715$		0			0
$716$	−0.0155603	−	0.148047i	−0.000581518	−	0.00553277i
$717$	−69.9605	+	22.7315i	−2.61272	+	0.848925i
$718$	6.90207	−	3.98491i	0.257583	−	0.148716i
$719$	2.59912	−	4.50181i	0.0969308	−	0.167889i	−0.813482	−	0.581590i	$-0.802431\pi$
$719$	2.59912	−	4.50181i	0.0969308	−	0.167889i	0.910413	+	0.413701i	$0.135764\pi$
$720$		0			0
$721$	−2.69986	+	8.30930i	−0.100548	+	0.309455i
$722$	1.06041	+	4.98886i	0.0394645	+	0.185666i
$723$	−6.79359	−	0.714035i	−0.252656	−	0.0265552i
$724$	2.71572	−	3.01611i	0.100929	−	0.112093i
$725$		0			0
$726$	4.72660	+	2.10442i	0.175421	+	0.0781023i
$727$	−17.9889	+	16.1973i	−0.667171	+	0.600723i	−0.931514	−	0.363705i	$-0.881512\pi$
$727$	−17.9889	+	16.1973i	−0.667171	+	0.600723i	0.264343	+	0.964429i	$0.414845\pi$
$728$	2.49007	+	3.42729i	0.0922882	+	0.127024i
$729$	−31.9419	+	23.2071i	−1.18303	+	0.859524i
$730$		0			0
$731$	14.0235	+	6.24366i	0.518677	+	0.230930i
$732$	−31.8767	−	71.5963i	−1.17820	−	2.64628i
$733$	−29.9954	−	27.0080i	−1.10790	−	0.997562i	−0.999994	−	0.00340093i	$-0.998917\pi$
$733$	−29.9954	−	27.0080i	−1.10790	−	0.997562i	−0.107910	−	0.994161i	$-0.534416\pi$
$734$	0.320315	−	3.04759i	0.0118230	−	0.112489i
$735$		0			0
$736$	−0.529571	+	1.62985i	−0.0195202	+	0.0600771i
$737$	3.25427	−	15.3101i	0.119872	−	0.563955i
$738$	−11.3550	−	6.55583i	−0.417985	−	0.241324i
$739$	3.04893	+	5.28089i	0.112157	+	0.194261i	0.916640	−	0.399715i	$-0.130891\pi$
$739$	3.04893	+	5.28089i	0.112157	+	0.194261i	−0.804483	+	0.593976i	$0.797558\pi$
$740$		0			0
$741$	1.84095	+	17.5155i	0.0676292	+	0.643449i
$742$	1.11251	−	1.53125i	0.0408417	−	0.0562138i
$743$		−	16.2263i		−	0.595284i	−0.954678	−	0.297642i	$-0.903800\pi$
$743$		−	16.2263i		−	0.595284i	0.954678	−	0.297642i	$-0.0962001\pi$
$744$	8.91125	−	20.0553i	0.326702	−	0.735262i
$745$		0			0
$746$	−7.22540	−	5.24956i	−0.264541	−	0.192200i
$747$	68.6603	−	7.21649i	2.51215	−	0.264038i
$748$	−7.91793	+	2.57269i	−0.289508	+	0.0940670i
$749$	6.57456	+	11.3875i	0.240229	+	0.416089i
$750$		0			0
$751$	−35.6481	−	7.57723i	−1.30082	−	0.276497i	−0.495119	−	0.868825i	$-0.664876\pi$
$751$	−35.6481	−	7.57723i	−1.30082	−	0.276497i	−0.805697	+	0.592328i	$0.798209\pi$
$752$	−24.7936	−	8.05593i	−0.904130	−	0.293770i
$753$	−1.41763	−	6.66944i	−0.0516614	−	0.243048i
$754$	−0.333487	+	3.17292i	−0.0121449	+	0.115551i
$755$		0			0
$756$	−12.7264	+	5.66615i	−0.462854	+	0.206076i
$757$	−17.7183	+	39.7960i	−0.643984	+	1.44641i	0.236164	+	0.971713i	$0.424110\pi$
$757$	−17.7183	+	39.7960i	−0.643984	+	1.44641i	−0.880148	+	0.474699i	$0.842557\pi$
$758$	5.77120	−	5.19641i	0.209619	−	0.188742i
$759$	−2.51672	+	1.82851i	−0.0913512	+	0.0663705i
$760$		0			0
$761$	2.20765	+	2.45184i	0.0800272	+	0.0888792i	0.781828	−	0.623494i	$-0.214287\pi$
$761$	2.20765	+	2.45184i	0.0800272	+	0.0888792i	−0.701801	+	0.712373i	$0.747621\pi$
$762$	0.0487209	−	0.109429i	0.00176497	−	0.00396419i
$763$	−0.278214	−	0.624878i	−0.0100720	−	0.0226221i
$764$	−6.70714	+	7.44903i	−0.242656	+	0.269497i
$765$		0			0
$766$	9.15848	−	1.94669i	0.330909	−	0.0703369i
$767$	−32.8342	−	10.6685i	−1.18557	−	0.385216i
$768$	4.21607	−	19.8350i	0.152134	−	0.715735i
$769$	−22.8568	+	39.5891i	−0.824237	+	1.42762i	0.0782634	+	0.996933i	$0.475062\pi$
$769$	−22.8568	+	39.5891i	−0.824237	+	1.42762i	−0.902501	+	0.430688i	$0.858271\pi$
$770$		0			0
$771$	23.2585	+	71.5823i	0.837635	+	2.57798i
$772$	3.98190	−	0.418515i	0.143312	−	0.0150627i
$773$	−17.6339	+	24.2710i	−0.634249	+	0.872969i	−0.998292	−	0.0584131i	$-0.981396\pi$
$773$	−17.6339	+	24.2710i	−0.634249	+	0.872969i	0.364044	+	0.931382i	$0.381396\pi$
$774$	15.8791			0.570764
$775$		0			0
$776$	−4.64943			−0.166905
$777$	5.79097	−	7.97058i	0.207750	−	0.285943i
$778$	4.52789	−	0.475900i	0.162333	−	0.0170618i
$779$	4.54689	+	13.9939i	0.162909	+	0.501383i
$780$		0			0
$781$	2.03977	−	3.53298i	0.0729886	−	0.126420i
$782$	0.0589606	−	0.277388i	0.00210843	−	0.00991937i
$783$	−20.6122	−	6.69730i	−0.736619	−	0.239342i
$784$	−18.6684	+	3.96809i	−0.666729	+	0.141718i
$785$		0			0
$786$	−3.93523	+	4.37051i	−0.140365	+	0.155891i
$787$	−17.5840	−	39.4944i	−0.626803	−	1.40782i	−0.895702	−	0.444654i	$-0.853327\pi$
$787$	−17.5840	−	39.4944i	−0.626803	−	1.40782i	0.268899	−	0.963168i	$-0.413340\pi$
$788$	4.48459	−	10.0725i	0.159757	−	0.358820i
$789$	44.4030	+	49.3145i	1.58079	+	1.75564i
$790$		0			0
$791$	−9.89298	+	7.18767i	−0.351754	+	0.255564i
$792$	−13.2212	+	11.9045i	−0.469796	+	0.423006i
$793$	−16.8721	+	37.8953i	−0.599145	+	1.34570i
$794$	0.939794	−	0.418423i	0.0333520	−	0.0148493i
$795$		0			0
$796$	1.35890	−	12.9291i	0.0481649	−	0.458259i
$797$	−4.74532	−	22.3250i	−0.168088	−	0.790792i	−0.978714	−	0.205228i	$-0.934206\pi$
$797$	−4.74532	−	22.3250i	−0.168088	−	0.790792i	0.810626	−	0.585564i	$-0.199127\pi$
$798$	−2.21667	−	0.720239i	−0.0784691	−	0.0254962i
$799$	14.2114	+	3.02072i	0.502763	+	0.106865i
$800$		0			0
$801$	−6.06773	−	10.5096i	−0.214393	−	0.371339i
$802$	4.10252	−	1.33299i	0.144865	−	0.0470695i
$803$	34.7236	−	3.64960i	1.22537	−	0.128792i
$804$	−28.2762	−	20.5438i	−0.997223	−	0.724525i
$805$		0			0
$806$	−5.34635	+	1.74155i	−0.188317	+	0.0613435i
$807$			49.3229i			1.73625i
$808$	14.1872	−	19.5270i	0.499105	−	0.686959i
$809$	−2.22002	−	21.1221i	−0.0780517	−	0.742613i	−0.961634	−	0.274336i	$-0.911542\pi$
$809$	−2.22002	−	21.1221i	−0.0780517	−	0.742613i	0.883582	−	0.468276i	$-0.155125\pi$
$810$		0			0
$811$	−1.06157	−	1.83869i	−0.0372767	−	0.0645652i	0.846785	−	0.531935i	$-0.178535\pi$
$811$	−1.06157	−	1.83869i	−0.0372767	−	0.0645652i	−0.884062	+	0.467370i	$0.845202\pi$
$812$	5.55551	+	3.20748i	0.194960	+	0.112560i
$813$	4.35913	−	20.5081i	0.152881	−	0.719250i
$814$	0.830879	−	2.55718i	0.0291223	−	0.0896292i
$815$		0			0
$816$	−1.80693	+	17.1918i	−0.0632553	+	0.601834i
$817$	−13.2426	−	11.9237i	−0.463301	−	0.417158i
$818$	2.45818	+	5.52116i	0.0859482	+	0.193043i
$819$	15.2584	+	6.79347i	0.533171	+	0.237383i
$820$		0			0
$821$	−33.8104	+	24.5647i	−1.17999	+	0.857313i	−0.992171	−	0.124891i	$-0.960142\pi$
$821$	−33.8104	+	24.5647i	−1.17999	+	0.857313i	−0.187819	+	0.982204i	$0.560142\pi$
$822$	7.05561	+	9.71121i	0.246093	+	0.338717i
$823$	12.1121	−	10.9058i	0.422203	−	0.380153i	−0.430464	−	0.902608i	$-0.641650\pi$
$823$	12.1121	−	10.9058i	0.422203	−	0.380153i	0.852667	+	0.522454i	$0.174984\pi$
$824$	10.0483	+	4.47378i	0.350049	+	0.155852i
$825$		0			0
$826$	3.05714	−	3.39530i	0.106372	−	0.118138i
$827$	30.9192	+	3.24974i	1.07517	+	0.113005i	0.625524	−	0.780205i	$-0.284885\pi$
$827$	30.9192	+	3.24974i	1.07517	+	0.113005i	0.449642	+	0.893209i	$0.351552\pi$
$828$	0.926674	+	4.35966i	0.0322041	+	0.151509i
$829$	8.66756	−	26.6760i	0.301037	−	0.926496i	−0.680090	−	0.733129i	$-0.738059\pi$
$829$	8.66756	−	26.6760i	0.301037	−	0.926496i	0.981126	−	0.193367i	$-0.0619409\pi$
$830$		0			0
$831$	21.8491	−	37.8437i	0.757936	−	1.31278i
$832$	−12.9075	+	7.45215i	−0.447487	+	0.258357i
$833$	10.1160	−	3.28688i	0.350498	−	0.113884i
$834$	1.63912	+	15.5951i	0.0567579	+	0.540015i
$835$		0			0
$836$	9.66453			0.334255
$837$	−4.02104	−	37.9848i	−0.138988	−	1.31295i
$838$		−	8.13409i		−	0.280987i
$839$	−18.6621	−	13.5588i	−0.644287	−	0.468102i	0.217034	−	0.976164i	$-0.430362\pi$
$839$	−18.6621	−	13.5588i	−0.644287	−	0.468102i	−0.861320	+	0.508062i	$0.830362\pi$
$840$		0			0
$841$	−5.87746	−	18.0890i	−0.202671	−	0.623757i
$842$	8.88160	−	5.12779i	0.306080	−	0.176715i
$843$	6.23179	+	3.59793i	0.214634	+	0.123919i
$844$	−30.6687	−	6.51884i	−1.05566	−	0.224388i
$845$		0			0
$846$	14.7007	−	3.12473i	0.505420	−	0.107430i
$847$	−5.47617	−	0.575568i	−0.188163	−	0.0197768i
$848$	12.1101	+	10.9040i	0.415864	+	0.374446i
$849$	−12.4925	+	5.56202i	−0.428741	+	0.190888i
$850$		0			0
$851$	−0.931124	−	1.03412i	−0.0319185	−	0.0354491i
$852$	−5.35449	−	7.36982i	−0.183442	−	0.252486i
$853$	17.6458	+	24.2874i	0.604182	+	0.831585i	0.996083	−	0.0884221i	$-0.0281824\pi$
$853$	17.6458	+	24.2874i	0.604182	+	0.831585i	−0.391901	+	0.920007i	$0.628182\pi$
$854$	−3.67326	−	4.07957i	−0.125696	−	0.139600i
$855$		0			0
$856$	15.1227	−	6.73307i	0.516884	−	0.230132i
$857$	−40.5663	−	36.5261i	−1.38572	−	1.24771i	−0.934815	−	0.355135i	$-0.884435\pi$
$857$	−40.5663	−	36.5261i	−1.38572	−	1.24771i	−0.450904	−	0.892572i	$-0.648898\pi$
$858$	7.06535	+	0.742598i	0.241207	+	0.0253519i
$859$	9.13238	−	1.94115i	0.311593	−	0.0662311i	−0.0494610	−	0.998776i	$-0.515750\pi$
$859$	9.13238	−	1.94115i	0.311593	−	0.0662311i	0.361054	+	0.932545i	$0.382417\pi$
$860$		0			0
$861$	21.2728	+	4.52167i	0.724974	+	0.154098i
$862$	−9.23768	−	5.33338i	−0.314637	−	0.181656i
$863$	−11.5326	+	6.65836i	−0.392575	+	0.226653i	−0.683275	−	0.730161i	$-0.739445\pi$
$863$	−11.5326	+	6.65836i	−0.392575	+	0.226653i	0.290700	+	0.956814i	$0.406112\pi$
$864$	8.21560	+	25.2850i	0.279500	+	0.860214i
$865$		0			0
$866$	3.93491	+	2.85888i	0.133714	+	0.0971487i
$867$			39.5520i			1.34326i
$868$	−1.17340	+	11.2449i	−0.0398276	+	0.381676i
$869$	−8.38250			−0.284357
$870$		0			0
$871$	1.93371	+	18.3980i	0.0655213	+	0.623394i
$872$	−0.818983	+	0.266104i	−0.0277343	+	0.00901141i
$873$	−15.8751	+	9.16547i	−0.537290	+	0.310204i
$874$	−0.164599	+	0.285094i	−0.00556766	+	0.00964346i
$875$		0			0
$876$	24.0925	−	74.1490i	0.814010	−	2.50526i
$877$	8.84998	+	41.6359i	0.298843	+	1.40594i	0.829571	+	0.558402i	$0.188585\pi$
$877$	8.84998	+	41.6359i	0.298843	+	1.40594i	−0.530728	+	0.847542i	$0.678081\pi$
$878$	4.51568	+	0.474617i	0.152397	+	0.0160175i
$879$	−20.4225	+	22.6815i	−0.688835	+	0.765029i
$880$		0			0
$881$	−5.27402	−	2.34814i	−0.177686	−	0.0791110i	0.315966	−	0.948771i	$-0.397672\pi$
$881$	−5.27402	−	2.34814i	−0.177686	−	0.0791110i	−0.493652	+	0.869660i	$0.664338\pi$
$882$	8.17666	−	7.36230i	0.275323	−	0.247902i
$883$	15.9860	+	22.0029i	0.537973	+	0.740457i	0.988319	−	0.152397i	$-0.0486994\pi$
$883$	15.9860	+	22.0029i	0.537973	+	0.740457i	−0.450346	+	0.892854i	$0.648699\pi$
$884$	7.96061	−	5.78372i	0.267744	−	0.194528i
$885$		0			0
$886$	7.62758	+	3.39602i	0.256254	+	0.114091i
$887$	−2.99834	−	6.73437i	−0.100674	−	0.226118i	0.856185	−	0.516669i	$-0.172828\pi$
$887$	−2.99834	−	6.73437i	−0.100674	−	0.226118i	−0.956860	+	0.290551i	$0.906161\pi$
$888$	−9.21742	−	8.29940i	−0.309316	−	0.278510i
$889$	−0.0133254	+	0.126783i	−0.000446920	+	0.00425216i
$890$		0			0
$891$	−2.80677	+	8.63835i	−0.0940304	+	0.289396i
$892$	2.44292	−	11.4930i	0.0817950	−	0.384815i
$893$	−14.6062	−	8.43290i	−0.488778	−	0.282196i
$894$	6.07548	+	10.5230i	0.203194	+	0.351943i
$895$		0			0
$896$	−1.08287	−	10.3028i	−0.0361762	−	0.344193i
$897$	2.16112	−	2.97453i	0.0721578	−	0.0993166i
$898$			6.82232i			0.227664i
$899$	−13.0626	+	11.7793i	−0.435663	+	0.392862i
$900$		0			0
$901$	−7.34737	−	5.33818i	−0.244776	−	0.177841i
$902$	5.90278	−	0.620408i	0.196541	−	0.0206573i
$903$	−25.0493	+	8.13900i	−0.833588	+	0.270849i
$904$	7.69738	+	13.3322i	0.256011	+	0.443424i
$905$		0			0
$906$	−4.29869	−	0.913715i	−0.142814	−	0.0303562i
$907$	15.6763	+	5.09354i	0.520523	+	0.169128i	0.557482	−	0.830189i	$-0.311767\pi$
$907$	15.6763	+	5.09354i	0.520523	+	0.169128i	−0.0369599	+	0.999317i	$0.511767\pi$
$908$	3.06167	+	14.4040i	0.101605	+	0.478014i
$909$	9.94714	−	94.6408i	0.329926	−	3.13904i
$910$		0			0
$911$	40.9333	−	18.2247i	1.35618	−	0.603810i	0.405531	−	0.914081i	$-0.367087\pi$
$911$	40.9333	−	18.2247i	1.35618	−	0.603810i	0.950648	+	0.310271i	$0.100420\pi$
$912$	8.16199	−	18.3321i	0.270271	−	0.607038i
$913$	−23.2247	+	20.9116i	−0.768625	+	0.692073i
$914$	6.92078	−	5.02824i	0.228919	−	0.166319i
$915$		0			0
$916$	−16.0380	−	17.8120i	−0.529911	−	0.588526i
$917$	2.54575	−	5.71785i	0.0840681	−	0.188820i
$918$	−1.78942	−	4.01909i	−0.0590595	−	0.132650i
$919$	6.93006	−	7.69662i	0.228602	−	0.253888i	−0.617921	−	0.786240i	$-0.712025\pi$
$919$	6.93006	−	7.69662i	0.228602	−	0.253888i	0.846523	+	0.532352i	$0.178692\pi$
$920$		0			0
$921$	7.49544	−	1.59320i	0.246983	−	0.0524979i
$922$	−12.8155	−	4.16401i	−0.422056	−	0.137134i
$923$	−1.00247	+	4.71626i	−0.0329968	+	0.155238i
$924$	7.14231	−	12.3708i	0.234965	−	0.406971i
$925$		0			0
$926$	−0.716131	−	2.20402i	−0.0235335	−	0.0724287i
$927$	43.1282	−	4.53296i	1.41652	−	0.148882i
$928$	7.19606	−	9.90452i	0.236222	−	0.325132i
$929$	−44.0624			−1.44564			−0.722820	−	0.691037i	$-0.757154\pi$
$929$	−44.0624			−1.44564			−0.722820	+	0.691037i	$0.757154\pi$
$930$		0			0
$931$	−12.3474			−0.404671
$932$	−14.0271	+	19.3066i	−0.459472	+	0.632409i
$933$	15.8629	−	1.66725i	0.519327	−	0.0545834i
$934$	−4.17034	−	12.8350i	−0.136458	−	0.419974i
$935$		0			0
$936$	10.5136	−	18.2101i	0.343648	−	0.595216i
$937$	−7.18687	+	33.8116i	−0.234785	+	1.10458i	0.689918	+	0.723887i	$0.257646\pi$
$937$	−7.18687	+	33.8116i	−0.234785	+	1.10458i	−0.924703	+	0.380689i	$0.875687\pi$
$938$	−2.32835	−	0.756528i	−0.0760235	−	0.0247015i
$939$	75.4933	−	16.0466i	2.46363	−	0.523661i
$940$		0			0
$941$	−14.8206	+	16.4600i	−0.483138	+	0.536580i	−0.934595	−	0.355713i	$-0.884238\pi$
$941$	−14.8206	+	16.4600i	−0.483138	+	0.536580i	0.451457	+	0.892293i	$0.350905\pi$
$942$	3.59988	+	8.08546i	0.117290	+	0.263439i
$943$	1.24939	−	2.80617i	0.0406856	−	0.0913814i
$944$	26.3211	+	29.2326i	0.856680	+	0.951440i
$945$		0			0
$946$	−5.81526	+	4.22504i	−0.189071	+	0.137368i
$947$	20.8694	−	18.7909i	0.678165	−	0.610622i	−0.256334	−	0.966588i	$-0.582515\pi$
$947$	20.8694	−	18.7909i	0.678165	−	0.610622i	0.934499	+	0.355966i	$0.115848\pi$
$948$	−7.61334	+	17.0998i	−0.247270	+	0.555377i
$949$	−37.6985	+	16.7844i	−1.22374	+	0.544846i
$950$		0			0
$951$	3.24818	−	30.9044i	0.105330	−	1.00214i
$952$	0.559300	+	2.63130i	0.0181270	+	0.0852809i
$953$	−7.29152	−	2.36916i	−0.236196	−	0.0767446i	0.188527	−	0.982068i	$-0.439629\pi$
$953$	−7.29152	−	2.36916i	−0.236196	−	0.0767446i	−0.424723	+	0.905323i	$0.639629\pi$
$954$	−9.18925	−	1.95324i	−0.297513	−	0.0632383i
$955$		0			0
$956$	−23.8546	−	41.3173i	−0.771512	−	1.33630i
$957$	21.1358	−	6.86743i	0.683222	−	0.221992i
$958$	−2.63009	+	0.276434i	−0.0849745	+	0.00893118i
$959$	−10.3352	−	7.50893i	−0.333740	−	0.242476i
$960$		0			0
$961$	−28.3387	−	12.5665i	−0.914152	−	0.405372i
$962$			3.17789i			0.102459i
$963$	38.3622	−	52.8011i	1.23621	−	1.70149i
$964$	−0.463100	−	4.40610i	−0.0149154	−	0.141911i
$965$		0			0
$966$	0.243285	+	0.421383i	0.00782758	+	0.0135578i
$967$	1.60246	+	0.925182i	0.0515317	+	0.0297518i	0.525545	−	0.850766i	$-0.323862\pi$
$967$	1.60246	+	0.925182i	0.0515317	+	0.0297518i	−0.474013	+	0.880518i	$0.657195\pi$
$968$	−1.44127	+	6.78063i	−0.0463241	+	0.217938i
$969$	−3.45592	+	10.6362i	−0.111020	+	0.341685i
$970$		0			0
$971$	−5.16072	+	49.1010i	−0.165615	+	1.57573i	0.524107	+	0.851652i	$0.324399\pi$
$971$	−5.16072	+	49.1010i	−0.165615	+	1.57573i	−0.689723	+	0.724074i	$0.742268\pi$
$972$	−13.6281	−	12.2708i	−0.437121	−	0.393585i
$973$	−6.78784	−	15.2457i	−0.217608	−	0.488756i
$974$	−8.03659	−	3.57812i	−0.257509	−	0.114650i
$975$		0			0
$976$	38.2373	−	27.7810i	1.22395	−	0.889248i
$977$	20.9383	+	28.8192i	0.669877	+	0.922007i	0.999758	−	0.0220160i	$-0.00700848\pi$
$977$	20.9383	+	28.8192i	0.669877	+	0.922007i	−0.329881	+	0.944023i	$0.607008\pi$
$978$	−2.36353	+	2.12813i	−0.0755773	+	0.0680501i
$979$	5.01847	+	2.23437i	0.160391	+	0.0714107i
$980$		0			0
$981$	−2.27177	+	2.52306i	−0.0725321	+	0.0805550i
$982$	13.8789	+	1.45874i	0.442895	+	0.0465501i
$983$	−1.32722	−	6.24409i	−0.0423318	−	0.199156i	0.951900	−	0.306409i	$-0.0991276\pi$
$983$	−1.32722	−	6.24409i	−0.0423318	−	0.199156i	−0.994232	+	0.107254i	$0.965794\pi$
$984$	8.46068	−	26.0393i	0.269717	−	0.830103i
$985$		0			0
$986$	−1.01295	+	1.75448i	−0.0322588	+	0.0558739i
$987$	−21.5887	+	12.4642i	−0.687175	+	0.396740i
$988$	−10.8635	+	3.52977i	−0.345614	+	0.112297i
$989$	0.388855	+	3.69971i	0.0123649	+	0.117644i
$990$		0			0
$991$	−44.2919			−1.40698			−0.703489	−	0.710706i	$-0.748376\pi$
$991$	−44.2919			−1.40698			−0.703489	+	0.710706i	$0.748376\pi$
$992$	21.1087	+	4.47033i	0.670202	+	0.141933i
$993$			56.8463i			1.80396i
$994$	−0.516222	−	0.375058i	−0.0163736	−	0.0118961i
$995$		0			0
$996$	21.5649	+	66.3699i	0.683310	+	2.10301i
$997$	4.60999	−	2.66158i	0.146000	−	0.0842931i	−0.425221	−	0.905090i	$-0.639803\pi$
$997$	4.60999	−	2.66158i	0.146000	−	0.0842931i	0.571220	+	0.820797i	$0.306470\pi$
$998$	−7.19911	−	4.15641i	−0.227884	−	0.131569i
$999$	−21.1162	−	4.48839i	−0.668087	−	0.142006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.a.599.3		32
5.2	odd	4		775.2.bl.a.351.1		16
5.3	odd	4		31.2.g.a.10.2	✓	16
5.4	even	2	inner	775.2.ck.a.599.2		32
15.8	even	4		279.2.y.c.10.1		16
20.3	even	4		496.2.bg.c.289.1		16
31.28	even	15	inner	775.2.ck.a.524.2		32
155.3	even	60		961.2.g.l.338.2		16
155.8	odd	20		961.2.g.s.547.1		16
155.13	even	60		961.2.d.n.388.3		16
155.18	odd	60		961.2.d.o.388.3		16
155.23	even	20		961.2.g.m.547.1		16
155.28	odd	60		31.2.g.a.28.2	yes	16
155.33	odd	20		961.2.g.t.846.1		16
155.38	odd	60		961.2.c.j.521.4		16
155.43	even	60		961.2.g.m.448.1		16
155.48	even	60		961.2.g.n.844.1		16
155.53	even	60		961.2.d.q.531.2		16
155.58	even	20		961.2.c.i.439.4		16
155.59	even	30	inner	775.2.ck.a.524.3		32
155.68	even	12		961.2.g.j.732.2		16
155.73	even	60		961.2.a.j.1.4		8
155.78	odd	20		961.2.g.k.235.2		16
155.83	even	60		961.2.d.q.628.2		16
155.88	even	12		961.2.d.n.374.3		16
155.98	odd	12		961.2.d.o.374.3		16
155.103	odd	60		961.2.d.p.628.2		16
155.108	even	20		961.2.g.j.235.2		16
155.113	odd	60		961.2.a.i.1.4		8
155.118	odd	12		961.2.g.k.732.2		16
155.123	even	4		961.2.g.l.816.2		16
155.128	odd	20		961.2.c.j.439.4		16
155.133	odd	60		961.2.d.p.531.2		16
155.138	odd	60		961.2.g.t.844.1		16
155.143	odd	60		961.2.g.s.448.1		16
155.148	even	60		961.2.c.i.521.4		16
155.152	odd	60		775.2.bl.a.276.1		16
155.153	even	20		961.2.g.n.846.1		16
465.113	even	60		8649.2.a.bf.1.5		8
465.338	even	60		279.2.y.c.28.1		16
465.383	odd	60		8649.2.a.be.1.5		8
620.183	even	60		496.2.bg.c.369.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	5.3	odd	4
31.2.g.a.28.2	yes	16	155.28	odd	60
279.2.y.c.10.1		16	15.8	even	4
279.2.y.c.28.1		16	465.338	even	60
496.2.bg.c.289.1		16	20.3	even	4
496.2.bg.c.369.1		16	620.183	even	60
775.2.bl.a.276.1		16	155.152	odd	60
775.2.bl.a.351.1		16	5.2	odd	4
775.2.ck.a.524.2		32	31.28	even	15	inner
775.2.ck.a.524.3		32	155.59	even	30	inner
775.2.ck.a.599.2		32	5.4	even	2	inner
775.2.ck.a.599.3		32	1.1	even	1	trivial
961.2.a.i.1.4		8	155.113	odd	60
961.2.a.j.1.4		8	155.73	even	60
961.2.c.i.439.4		16	155.58	even	20
961.2.c.i.521.4		16	155.148	even	60
961.2.c.j.439.4		16	155.128	odd	20
961.2.c.j.521.4		16	155.38	odd	60
961.2.d.n.374.3		16	155.88	even	12
961.2.d.n.388.3		16	155.13	even	60
961.2.d.o.374.3		16	155.98	odd	12
961.2.d.o.388.3		16	155.18	odd	60
961.2.d.p.531.2		16	155.133	odd	60
961.2.d.p.628.2		16	155.103	odd	60
961.2.d.q.531.2		16	155.53	even	60
961.2.d.q.628.2		16	155.83	even	60
961.2.g.j.235.2		16	155.108	even	20
961.2.g.j.732.2		16	155.68	even	12
961.2.g.k.235.2		16	155.78	odd	20
961.2.g.k.732.2		16	155.118	odd	12
961.2.g.l.338.2		16	155.3	even	60
961.2.g.l.816.2		16	155.123	even	4
961.2.g.m.448.1		16	155.43	even	60
961.2.g.m.547.1		16	155.23	even	20
961.2.g.n.844.1		16	155.48	even	60
961.2.g.n.846.1		16	155.153	even	20
961.2.g.s.448.1		16	155.143	odd	60
961.2.g.s.547.1		16	155.8	odd	20
961.2.g.t.844.1		16	155.138	odd	60
961.2.g.t.846.1		16	155.33	odd	20
8649.2.a.be.1.5		8	465.383	odd	60
8649.2.a.bf.1.5		8	465.113	even	60

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.206567 - 0.284315i) q^{2} +(2.87744 - 0.302431i) q^{3} +(0.579869 + 1.78465i) q^{4} +(0.508398 - 0.880572i) q^{6} +(-0.224987 + 1.05848i) q^{7} +(1.29565 + 0.420982i) q^{8} +(5.25377 - 1.11672i) q^{9} +(-1.62690 + 1.80686i) q^{11} +(2.20827 + 4.95987i) q^{12} +(1.16882 - 2.62521i) q^{13} +(0.254466 + 0.282614i) q^{14} +(-2.64890 + 1.92454i) q^{16} +(1.35606 - 1.22101i) q^{17} +(0.767753 - 1.72440i) q^{18} +(-1.93514 + 0.861580i) q^{19} +(-0.327269 + 3.11375i) q^{21} +(0.177653 + 0.835790i) q^{22} +(0.420572 + 0.136652i) q^{23} +(3.85547 + 0.819506i) q^{24} +(-0.504947 - 0.874594i) q^{26} +(6.52462 - 2.11998i) q^{27} +(-2.01948 + 0.212256i) q^{28} +(-2.55579 - 1.85689i) q^{29} +(1.15354 - 5.44696i) q^{31} +3.87532i q^{32} +(-4.13487 + 5.69116i) q^{33} +(-0.0670322 - 0.637769i) q^{34} +(5.03946 + 8.72860i) q^{36} +(-2.72517 - 1.57338i) q^{37} +(-0.154776 + 0.728163i) q^{38} +(2.56926 - 7.90738i) q^{39} +(0.726079 - 6.90818i) q^{41} +(0.817684 + 0.736246i) q^{42} +(3.42162 + 7.68509i) q^{43} +(-4.16801 - 1.85572i) q^{44} +(0.125728 - 0.0913471i) q^{46} +(4.67998 + 6.44144i) q^{47} +(-7.04003 + 6.33887i) q^{48} +(5.32506 + 2.37087i) q^{49} +(3.53273 - 3.92349i) q^{51} +(5.36285 + 0.563659i) q^{52} +(-1.03478 - 4.86824i) q^{53} +(0.745029 - 2.29296i) q^{54} +(-0.737104 + 1.27670i) q^{56} +(-5.30768 + 3.06439i) q^{57} +(-1.05588 + 0.343078i) q^{58} +(-1.25580 - 11.9481i) q^{59} -14.4351 q^{61} +(-1.31037 - 1.45313i) q^{62} +5.81225i q^{63} +(-4.19600 - 3.04857i) q^{64} +(0.763955 + 2.35121i) q^{66} +(-5.57511 + 3.21879i) q^{67} +(2.96541 + 1.71208i) q^{68} +(1.25150 + 0.266015i) q^{69} +(-1.64121 + 0.348850i) q^{71} +(7.27716 + 0.764860i) q^{72} +(-10.6717 - 9.60883i) q^{73} +(-1.01026 + 0.449798i) q^{74} +(-2.65975 - 2.95395i) q^{76} +(-1.54649 - 2.12856i) q^{77} +(-1.71746 - 2.36388i) q^{78} +(2.30692 + 2.56210i) q^{79} +(3.41274 - 1.51945i) q^{81} +(-1.81412 - 1.63344i) q^{82} +(12.7832 + 1.34357i) q^{83} +(-5.74674 + 1.22151i) q^{84} +(2.89178 + 0.614667i) q^{86} +(-7.91573 - 4.57015i) q^{87} +(-2.86855 + 1.65616i) q^{88} +(-0.698188 - 2.14880i) q^{89} +(2.51576 + 1.82781i) q^{91} +0.829816i q^{92} +(1.67190 - 16.0222i) q^{93} +2.79812 q^{94} +(1.17202 + 11.1510i) q^{96} +(-3.24582 + 1.05463i) q^{97} +(1.77405 - 1.02425i) q^{98} +(-6.52961 + 11.3096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) \) 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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