LMFDB - Embedded newform 616.2.bi.c.13.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(13,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))

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

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

chi := DirichletCharacter("616.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bi (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$88$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.13
Character	$\chi$	$=$	616.13
Dual form			616.2.bi.c.237.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26963 + 0.622922i) q^{2} +(-2.02333 + 1.47003i) q^{3} +(1.22394 - 1.58177i) q^{4} +(-0.495683 - 1.52556i) q^{5} +(1.65317 - 3.12678i) q^{6} +(-0.564533 + 2.58482i) q^{7} +(-0.568632 + 2.77068i) q^{8} +(1.00581 - 3.09555i) q^{9} +O(q^{10})$	\(q+(-1.26963 + 0.622922i) q^{2} +(-2.02333 + 1.47003i) q^{3} +(1.22394 - 1.58177i) q^{4} +(-0.495683 - 1.52556i) q^{5} +(1.65317 - 3.12678i) q^{6} +(-0.564533 + 2.58482i) q^{7} +(-0.568632 + 2.77068i) q^{8} +(1.00581 - 3.09555i) q^{9} +(1.57964 + 1.62812i) q^{10} +(1.70727 - 2.84345i) q^{11} +(-0.151174 + 4.99966i) q^{12} +(-4.34191 - 1.41077i) q^{13} +(-0.893394 - 3.63343i) q^{14} +(3.24555 + 2.35803i) q^{15} +(-1.00396 - 3.87196i) q^{16} +(-0.650077 - 2.00073i) q^{17} +(0.651284 + 4.55675i) q^{18} +(0.636161 + 0.875600i) q^{19} +(-3.01975 - 1.08313i) q^{20} +(-2.65754 - 6.05982i) q^{21} +(-0.396355 + 4.67364i) q^{22} +7.56410 q^{23} +(-2.92246 - 6.44190i) q^{24} +(1.96347 - 1.42654i) q^{25} +(6.39143 - 0.913510i) q^{26} +(0.196963 + 0.606190i) q^{27} +(3.39763 + 4.05661i) q^{28} +(2.35819 + 1.71333i) q^{29} +(-5.58952 - 0.972106i) q^{30} +(2.42778 + 0.788833i) q^{31} +(3.68659 + 4.29057i) q^{32} +(0.725607 + 8.26298i) q^{33} +(2.07166 + 2.13525i) q^{34} +(4.22312 - 0.420026i) q^{35} +(-3.66539 - 5.37970i) q^{36} +(-2.00580 + 2.76074i) q^{37} +(-1.35312 - 0.715412i) q^{38} +(10.8590 - 3.52830i) q^{39} +(4.50868 - 0.505899i) q^{40} +(-5.22121 + 3.79343i) q^{41} +(7.14890 + 6.03831i) q^{42} -5.83924 q^{43} +(-2.40809 - 6.18070i) q^{44} -5.22100 q^{45} +(-9.60363 + 4.71185i) q^{46} +(7.19745 + 9.90643i) q^{47} +(7.72326 + 6.35838i) q^{48} +(-6.36261 - 2.91843i) q^{49} +(-1.60426 + 3.03427i) q^{50} +(4.25646 + 3.09250i) q^{51} +(-7.54573 + 5.14119i) q^{52} +(10.0978 + 3.28097i) q^{53} +(-0.627680 - 0.646946i) q^{54} +(-5.18411 - 1.19508i) q^{55} +(-6.84070 - 3.03395i) q^{56} +(-2.57432 - 0.836448i) q^{57} +(-4.06131 - 0.706326i) q^{58} +(6.16326 + 4.47787i) q^{59} +(7.70219 - 2.24762i) q^{60} +(12.1031 - 3.93254i) q^{61} +(-3.57377 + 0.510789i) q^{62} +(7.43364 + 4.34737i) q^{63} +(-7.35332 - 3.15099i) q^{64} +7.32312i q^{65} +(-6.06845 - 10.0390i) q^{66} +8.54696i q^{67} +(-3.96034 - 1.42050i) q^{68} +(-15.3047 + 11.1195i) q^{69} +(-5.10017 + 3.16395i) q^{70} +(-0.165084 - 0.508077i) q^{71} +(8.00484 + 4.54699i) q^{72} +(-4.44244 - 3.22762i) q^{73} +(0.826897 - 4.75458i) q^{74} +(-1.87567 + 5.77273i) q^{75} +(2.16361 + 0.0654211i) q^{76} +(6.38601 + 6.01821i) q^{77} +(-11.5891 + 11.2440i) q^{78} +(1.17593 + 0.382081i) q^{79} +(-5.40924 + 3.45087i) q^{80} +(6.61006 + 4.80249i) q^{81} +(4.26601 - 8.06867i) q^{82} +(-0.508852 + 0.165336i) q^{83} +(-12.8379 - 3.21323i) q^{84} +(-2.73000 + 1.98346i) q^{85} +(7.41369 - 3.63739i) q^{86} -7.29005 q^{87} +(6.90749 + 6.34717i) q^{88} -16.8480i q^{89} +(6.62875 - 3.25227i) q^{90} +(6.09774 - 10.4266i) q^{91} +(9.25797 - 11.9646i) q^{92} +(-6.07181 + 1.97285i) q^{93} +(-15.3091 - 8.09408i) q^{94} +(1.02044 - 1.40452i) q^{95} +(-13.7665 - 3.26182i) q^{96} +(16.6489 + 5.40957i) q^{97} +(9.89613 - 0.258071i) q^{98} +(-7.08488 - 8.14490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.26963	+	0.622922i	−0.897766	+	0.440473i
$2$	−1.26963	+	0.622922i	−0.897766	+	0.440473i
$3$	−2.02333	+	1.47003i	−1.16817	+	0.848724i	−0.990789	−	0.135418i	$-0.956762\pi$
$3$	−2.02333	+	1.47003i	−1.16817	+	0.848724i	−0.177380	+	0.984142i	$0.556762\pi$
$4$	1.22394	−	1.58177i	0.611968	−	0.790883i
$5$	−0.495683	−	1.52556i	−0.221676	−	0.682249i	−0.998612	−	0.0526693i	$-0.983227\pi$
$5$	−0.495683	−	1.52556i	−0.221676	−	0.682249i	0.776936	−	0.629580i	$-0.216773\pi$
$6$	1.65317	−	3.12678i	0.674903	−	1.27650i
$7$	−0.564533	+	2.58482i	−0.213373	+	0.976971i
$7$	−0.564533	+	2.58482i	−0.213373	+	0.976971i
$8$	−0.568632	+	2.77068i	−0.201042	+	0.979583i
$9$	1.00581	−	3.09555i	0.335269	−	1.03185i
$10$	1.57964	+	1.62812i	0.499525	+	0.514858i
$11$	1.70727	−	2.84345i	0.514761	−	0.857334i
$11$	1.70727	−	2.84345i	0.514761	−	0.857334i
$12$	−0.151174	+	4.99966i	−0.0436403	+	1.44328i
$13$	−4.34191	−	1.41077i	−1.20423	−	0.391278i	−0.362914	−	0.931823i	$-0.618218\pi$
$13$	−4.34191	−	1.41077i	−1.20423	−	0.391278i	−0.841315	+	0.540545i	$0.818218\pi$
$14$	−0.893394	−	3.63343i	−0.238770	−	0.971076i
$15$	3.24555	+	2.35803i	0.837997	+	0.608840i
$16$	−1.00396	−	3.87196i	−0.250991	−	0.967989i
$17$	−0.650077	−	2.00073i	−0.157667	−	0.485249i	0.840754	−	0.541417i	$-0.182112\pi$
$17$	−0.650077	−	2.00073i	−0.157667	−	0.485249i	−0.998421	+	0.0561678i	$0.982112\pi$
$18$	0.651284	+	4.55675i	0.153509	+	1.07404i
$19$	0.636161	+	0.875600i	0.145945	+	0.200876i	0.875731	−	0.482800i	$-0.160380\pi$
$19$	0.636161	+	0.875600i	0.145945	+	0.200876i	−0.729786	+	0.683676i	$0.760380\pi$
$20$	−3.01975	−	1.08313i	−0.675238	−	0.242195i
$21$	−2.65754	−	6.05982i	−0.579923	−	1.32236i
$22$	−0.396355	+	4.67364i	−0.0845031	+	0.996423i
$23$	7.56410			1.57722			0.788612	−	0.614891i	$-0.210800\pi$
$23$	7.56410			1.57722			0.788612	+	0.614891i	$0.210800\pi$
$24$	−2.92246	−	6.44190i	−0.596545	−	1.31495i
$25$	1.96347	−	1.42654i	0.392693	−	0.285308i
$26$	6.39143	−	0.913510i	1.25346	−	0.179154i
$27$	0.196963	+	0.606190i	0.0379056	+	0.116661i
$28$	3.39763	+	4.05661i	0.642092	+	0.766628i
$29$	2.35819	+	1.71333i	0.437906	+	0.318157i	0.784802	−	0.619746i	$-0.212765\pi$
$29$	2.35819	+	1.71333i	0.437906	+	0.318157i	−0.346897	+	0.937903i	$0.612765\pi$
$30$	−5.58952	−	0.972106i	−1.02050	−	0.177482i
$31$	2.42778	+	0.788833i	0.436042	+	0.141679i	0.518809	−	0.854890i	$-0.326376\pi$
$31$	2.42778	+	0.788833i	0.436042	+	0.141679i	−0.0827667	+	0.996569i	$0.526376\pi$
$32$	3.68659	+	4.29057i	0.651704	+	0.758473i
$33$	0.725607	+	8.26298i	0.126312	+	1.43840i
$34$	2.07166	+	2.13525i	0.355287	+	0.366192i
$35$	4.22312	−	0.420026i	0.713837	−	0.0709974i
$36$	−3.66539	−	5.37970i	−0.610899	−	0.896617i
$37$	−2.00580	+	2.76074i	−0.329751	+	0.453863i	−0.941413	−	0.337256i	$-0.890501\pi$
$37$	−2.00580	+	2.76074i	−0.329751	+	0.453863i	0.611662	+	0.791119i	$0.290501\pi$
$38$	−1.35312	−	0.715412i	−0.219505	−	0.116055i
$39$	10.8590	−	3.52830i	1.73883	−	0.564980i
$40$	4.50868	−	0.505899i	0.712886	−	0.0799896i
$41$	−5.22121	+	3.79343i	−0.815416	+	0.592434i	−0.915396	−	0.402555i	$-0.868122\pi$
$41$	−5.22121	+	3.79343i	−0.815416	+	0.592434i	0.0999797	+	0.994989i	$0.468122\pi$
$42$	7.14890	+	6.03831i	1.10310	+	0.931732i
$43$	−5.83924			−0.890476			−0.445238	−	0.895412i	$-0.646881\pi$
$43$	−5.83924			−0.890476			−0.445238	+	0.895412i	$0.646881\pi$
$44$	−2.40809	−	6.18070i	−0.363033	−	0.931776i
$45$	−5.22100			−0.778300
$46$	−9.60363	+	4.71185i	−1.41598	+	0.694724i
$47$	7.19745	+	9.90643i	1.04986	+	1.44500i	0.888934	+	0.458035i	$0.151446\pi$
$47$	7.19745	+	9.90643i	1.04986	+	1.44500i	0.160921	+	0.986967i	$0.448554\pi$
$48$	7.72326	+	6.35838i	1.11476	+	0.917753i
$49$	−6.36261	−	2.91843i	−0.908944	−	0.416919i
$50$	−1.60426	+	3.03427i	−0.226876	+	0.429111i
$51$	4.25646	+	3.09250i	0.596024	+	0.433037i
$52$	−7.54573	+	5.14119i	−1.04640	+	0.712955i
$53$	10.0978	+	3.28097i	1.38704	+	0.450676i	0.904977	−	0.425461i	$-0.139888\pi$
$53$	10.0978	+	3.28097i	1.38704	+	0.450676i	0.482062	+	0.876137i	$0.339888\pi$
$54$	−0.627680	−	0.646946i	−0.0854165	−	0.0880382i
$55$	−5.18411	−	1.19508i	−0.699025	−	0.161145i
$56$	−6.84070	−	3.03395i	−0.914127	−	0.405429i
$57$	−2.57432	−	0.836448i	−0.340977	−	0.110790i
$58$	−4.06131	−	0.706326i	−0.533276	−	0.0927452i
$59$	6.16326	+	4.47787i	0.802388	+	0.582969i	0.911614	−	0.411048i	$-0.134837\pi$
$59$	6.16326	+	4.47787i	0.802388	+	0.582969i	−0.109226	+	0.994017i	$0.534837\pi$
$60$	7.70219	−	2.24762i	0.994348	−	0.290166i
$61$	12.1031	−	3.93254i	1.54965	−	0.503510i	0.595628	−	0.803260i	$-0.296903\pi$
$61$	12.1031	−	3.93254i	1.54965	−	0.503510i	0.954018	+	0.299750i	$0.0969032\pi$
$62$	−3.57377	+	0.510789i	−0.453869	+	0.0648703i
$63$	7.43364	+	4.34737i	0.936550	+	0.547717i
$64$	−7.35332	−	3.15099i	−0.919164	−	0.393874i
$65$			7.32312i			0.908321i
$66$	−6.06845	−	10.0390i	−0.746975	−	1.23571i
$67$			8.54696i			1.04418i	0.852891	+	0.522089i	$0.174847\pi$
$67$			8.54696i			1.04418i	−0.852891	+	0.522089i	$0.825153\pi$
$68$	−3.96034	−	1.42050i	−0.480262	−	0.172261i
$69$	−15.3047	+	11.1195i	−1.84246	+	1.33863i
$70$	−5.10017	+	3.16395i	−0.609586	+	0.378165i
$71$	−0.165084	−	0.508077i	−0.0195919	−	0.0602977i	0.940783	−	0.339011i	$-0.110092\pi$
$71$	−0.165084	−	0.508077i	−0.0195919	−	0.0602977i	−0.960374	+	0.278713i	$0.910092\pi$
$72$	8.00484	+	4.54699i	0.943380	+	0.535868i
$73$	−4.44244	−	3.22762i	−0.519948	−	0.377765i	0.296636	−	0.954991i	$-0.404135\pi$
$73$	−4.44244	−	3.22762i	−0.519948	−	0.377765i	−0.816584	+	0.577226i	$0.804135\pi$
$74$	0.826897	−	4.75458i	0.0961249	−	0.552709i
$75$	−1.87567	+	5.77273i	−0.216584	+	0.666577i
$76$	2.16361	+	0.0654211i	0.248183	+	0.00750431i
$77$	6.38601	+	6.01821i	0.727754	+	0.685839i
$78$	−11.5891	+	11.2440i	−1.31220	+	1.27313i
$79$	1.17593	+	0.382081i	0.132302	+	0.0429875i	0.374420	−	0.927259i	$-0.377842\pi$
$79$	1.17593	+	0.382081i	0.132302	+	0.0429875i	−0.242118	+	0.970247i	$0.577842\pi$
$80$	−5.40924	+	3.45087i	−0.604771	+	0.385819i
$81$	6.61006	+	4.80249i	0.734451	+	0.533610i
$82$	4.26601	−	8.06867i	0.471102	−	0.891036i
$83$	−0.508852	+	0.165336i	−0.0558538	+	0.0181480i	−0.336811	−	0.941572i	$-0.609348\pi$
$83$	−0.508852	+	0.165336i	−0.0558538	+	0.0181480i	0.280957	+	0.959720i	$0.409348\pi$
$84$	−12.8379	−	3.21323i	−1.40073	−	0.350592i
$85$	−2.73000	+	1.98346i	−0.296110	+	0.215136i
$86$	7.41369	−	3.63739i	0.799439	−	0.392230i
$87$	−7.29005			−0.781575
$88$	6.90749	+	6.34717i	0.736341	+	0.676611i
$89$		−	16.8480i		−	1.78588i	−0.450176	−	0.892940i	$-0.648639\pi$
$89$		−	16.8480i		−	1.78588i	0.450176	−	0.892940i	$-0.351361\pi$
$90$	6.62875	−	3.25227i	0.698731	−	0.342820i
$91$	6.09774	−	10.4266i	0.639217	−	1.09301i
$92$	9.25797	−	11.9646i	0.965210	−	1.24740i
$93$	−6.07181	+	1.97285i	−0.629617	+	0.204575i
$94$	−15.3091	−	8.09408i	−1.57901	−	0.834841i
$95$	1.02044	−	1.40452i	0.104695	−	0.144101i
$96$	−13.7665	−	3.26182i	−1.40504	−	0.332908i
$97$	16.6489	+	5.40957i	1.69044	+	0.549258i	0.986891	−	0.161386i	$-0.0515965\pi$
$97$	16.6489	+	5.40957i	1.69044	+	0.549258i	0.703551	+	0.710644i	$0.251596\pi$
$98$	9.89613	−	0.258071i	0.999660	−	0.0260691i
$99$	−7.08488	−	8.14490i	−0.712057	−	0.818594i
$100$	0.146702	−	4.85174i	0.0146702	−	0.485174i
$101$	18.7363	+	6.08780i	1.86433	+	0.605759i	0.993450	+	0.114268i	$0.0364524\pi$
$101$	18.7363	+	6.08780i	1.86433	+	0.605759i	0.870883	+	0.491490i	$0.163548\pi$
$102$	−7.33054	−	1.27490i	−0.725831	−	0.126234i
$103$	1.20060	−	1.65248i	0.118298	−	0.162823i	−0.745761	−	0.666213i	$-0.767914\pi$
$103$	1.20060	−	1.65248i	0.118298	−	0.162823i	0.864059	+	0.503390i	$0.167914\pi$
$104$	6.37774	−	11.2278i	0.625389	−	1.10098i
$105$	−7.92730	+	7.05798i	−0.773625	+	0.688788i
$106$	−14.8643	+	2.12451i	−1.44375	+	0.206351i
$107$	12.4539	−	9.04829i	1.20396	−	0.874731i	0.209295	−	0.977853i	$-0.432883\pi$
$107$	12.4539	−	9.04829i	1.20396	−	0.874731i	0.994669	+	0.103122i	$0.0328831\pi$
$108$	1.19992	+	0.430388i	0.115462	+	0.0414141i
$109$	−8.61501			−0.825168			−0.412584	−	0.910920i	$-0.635374\pi$
$109$	−8.61501			−0.825168			−0.412584	+	0.910920i	$0.635374\pi$
$110$	7.32636	−	1.71198i	0.698541	−	0.163231i
$111$		−	8.53447i		−	0.810056i
$112$	10.5751	−	0.409220i	0.999252	−	0.0386676i
$113$	1.69666	−	1.23270i	0.159609	−	0.115962i	−0.505114	−	0.863052i	$-0.668550\pi$
$113$	1.69666	−	1.23270i	0.159609	−	0.115962i	0.664723	+	0.747090i	$0.268550\pi$
$114$	3.78949	−	0.541621i	0.354918	−	0.0507275i
$115$	−3.74940	−	11.5395i	−0.349633	−	1.07606i
$116$	5.59636	−	1.63311i	0.519609	−	0.151630i
$117$	−8.73423	+	12.0216i	−0.807480	+	1.11140i
$118$	−10.6144	−	1.84602i	−0.977138	−	0.169940i
$119$	5.53853	−	0.550855i	0.507716	−	0.0504968i
$120$	−8.37886	+	7.65152i	−0.764882	+	0.698485i
$121$	−5.17046	−	9.70909i	−0.470042	−	0.882644i
$122$	−12.9169	+	12.5322i	−1.16944	+	1.13461i
$123$	4.98775	−	15.3507i	0.449730	−	1.38413i
$124$	4.21920	−	2.87470i	0.378895	−	0.258155i
$125$	−9.63810	−	7.00249i	−0.862058	−	0.626322i
$126$	−12.1461	−	0.888983i	−1.08206	−	0.0791969i
$127$	−0.152665	+	0.0496040i	−0.0135469	+	0.00440165i	−0.315783	−	0.948832i	$-0.602267\pi$
$127$	−0.152665	+	0.0496040i	−0.0135469	+	0.00440165i	0.302236	+	0.953233i	$0.402267\pi$
$128$	11.2988	−	0.579941i	0.998685	−	0.0512600i
$129$	11.8147	−	8.58388i	1.04023	−	0.755769i
$130$	−4.56173	−	9.29767i	−0.400091	−	0.815460i
$131$			1.43689i			0.125542i	0.998028	+	0.0627708i	$0.0199937\pi$
$131$			1.43689i			0.125542i	−0.998028	+	0.0627708i	$0.980006\pi$
$132$	13.9582	+	8.96562i	1.21491	+	0.780357i
$133$	−2.62240	+	1.15006i	−0.227391	+	0.0997226i
$134$	−5.32409	−	10.8515i	−0.459931	−	0.937427i
$135$	0.827145	−	0.600956i	0.0711893	−	0.0517221i
$136$	5.91304	−	0.663475i	0.507039	−	0.0568925i
$137$	−5.18903	−	15.9702i	−0.443329	−	1.36443i	−0.884306	−	0.466907i	$-0.845368\pi$
$137$	−5.18903	−	15.9702i	−0.443329	−	1.36443i	0.440978	−	0.897518i	$-0.354632\pi$
$138$	12.5047	−	23.6513i	1.06447	−	2.01333i
$139$	−1.14661	+	1.57817i	−0.0972538	+	0.133858i	−0.854871	−	0.518841i	$-0.826364\pi$
$139$	−1.14661	+	1.57817i	−0.0972538	+	0.133858i	0.757617	+	0.652700i	$0.226364\pi$
$140$	4.50444	−	7.19407i	0.380695	−	0.608010i
$141$	−29.1256	−	9.46348i	−2.45282	−	0.796968i
$142$	0.526089	+	0.542237i	0.0441484	+	0.0455035i
$143$	−11.4243	+	9.93745i	−0.955346	+	0.831011i
$144$	−12.9956	−	0.786616i	−1.08297	−	0.0655514i
$145$	1.44486	−	4.44682i	0.119989	−	0.369289i
$146$	7.65083	+	1.33060i	0.633187	+	0.110121i
$147$	17.1638	−	3.44830i	1.41565	−	0.284411i
$148$	1.91188	+	6.55167i	0.157156	+	0.538544i
$149$	1.93676	+	5.96073i	0.158666	+	0.488322i	0.998514	−	0.0544989i	$-0.0173561\pi$
$149$	1.93676	+	5.96073i	0.158666	+	0.488322i	−0.839848	+	0.542821i	$0.817356\pi$
$150$	−1.21454	−	8.49764i	−0.0991671	−	0.693830i
$151$	0.496700	+	0.683649i	0.0404209	+	0.0556345i	0.828749	−	0.559620i	$-0.189053\pi$
$151$	0.496700	+	0.683649i	0.0404209	+	0.0556345i	−0.788328	+	0.615255i	$0.789053\pi$
$152$	−2.78775	+	1.26470i	−0.226116	+	0.102581i
$153$	−6.84722			−0.553565
$154$	−11.8568	−	3.66293i	−0.955446	−	0.295167i
$155$		−	4.09472i		−	0.328896i
$156$	7.70976	−	21.4948i	0.617275	−	1.72096i
$157$	6.91751	−	5.02586i	0.552077	−	0.401108i	−0.276473	−	0.961022i	$-0.589166\pi$
$157$	6.91751	−	5.02586i	0.552077	−	0.401108i	0.828551	+	0.559914i	$0.189166\pi$
$158$	−1.73100	+	0.247407i	−0.137711	+	0.0196827i
$159$	−25.2543	+	8.20561i	−2.00279	+	0.650747i
$160$	4.71813	−	7.75087i	0.373001	−	0.612760i
$161$	−4.27018	+	19.5518i	−0.336537	+	1.54090i
$162$	−11.3839	−	1.97984i	−0.894406	−	0.155551i
$163$	−7.57373	−	2.46085i	−0.593220	−	0.192749i	−0.00300588	−	0.999995i	$-0.500957\pi$
$163$	−7.57373	−	2.46085i	−0.593220	−	0.192749i	−0.590214	+	0.807247i	$0.700957\pi$
$164$	−0.390107	+	12.9016i	−0.0304622	+	1.00745i
$165$	12.2460	−	5.20277i	0.953347	−	0.405035i
$166$	0.543064	−	0.526892i	0.0421499	−	0.0408947i
$167$	0.0470152	−	0.144698i	0.00363815	−	0.0111971i	−0.949221	−	0.314610i	$-0.898126\pi$
$167$	0.0470152	−	0.144698i	0.00363815	−	0.0111971i	0.952859	+	0.303413i	$0.0981262\pi$
$168$	18.3010	−	3.91738i	1.41195	−	0.302232i
$169$	6.34468	+	4.60968i	0.488052	+	0.354591i
$170$	2.23055	−	4.21884i	0.171076	−	0.323570i
$171$	3.35032	−	1.08858i	0.256205	−	0.0832461i
$172$	−7.14685	+	9.23631i	−0.544943	+	0.704262i
$173$	4.67633	+	6.43641i	0.355535	+	0.489351i	0.948898	−	0.315584i	$-0.102200\pi$
$173$	4.67633	+	6.43641i	0.355535	+	0.489351i	−0.593363	+	0.804935i	$0.702200\pi$
$174$	9.25569	−	4.54114i	0.701672	−	0.344263i
$175$	2.57892	+	5.88054i	0.194948	+	0.444527i
$176$	−12.7238	−	3.75575i	−0.959090	−	0.283100i
$177$	−19.0529			−1.43210
$178$	10.4950	+	21.3907i	0.786631	+	1.60330i
$179$	4.57691	+	6.29958i	0.342094	+	0.470852i	0.945052	−	0.326921i	$-0.106011\pi$
$179$	4.57691	+	6.29958i	0.342094	+	0.470852i	−0.602957	+	0.797773i	$0.706011\pi$
$180$	−6.39016	+	8.25839i	−0.476295	+	0.615544i
$181$	−2.22538	−	6.84902i	−0.165411	−	0.509083i	0.833655	−	0.552285i	$-0.186244\pi$
$181$	−2.22538	−	6.84902i	−0.165411	−	0.509083i	−0.999066	+	0.0432019i	$0.986244\pi$
$182$	−1.24691	+	17.0364i	−0.0924273	+	1.26282i
$183$	−18.7076	+	25.7488i	−1.38291	+	1.90341i
$184$	−4.30119	+	20.9577i	−0.317088	+	1.54502i
$185$	5.20590	+	1.69150i	0.382746	+	0.124362i
$186$	6.48003	−	6.28706i	0.475139	−	0.460989i
$187$	−6.79885	−	1.56732i	−0.497181	−	0.114614i
$188$	24.4789	+	0.740166i	1.78530	+	0.0539822i
$189$	−1.67809	+	0.166900i	−0.122063	+	0.0121402i
$190$	−0.420681	+	2.41888i	−0.0305194	+	0.175484i
$191$	−0.725384	−	0.527023i	−0.0524870	−	0.0381340i	0.561232	−	0.827658i	$-0.310327\pi$
$191$	−0.725384	−	0.527023i	−0.0524870	−	0.0381340i	−0.613719	+	0.789524i	$0.710327\pi$
$192$	19.5102	−	4.43413i	1.40803	−	0.320006i
$193$	−1.78690	+	0.580600i	−0.128624	+	0.0417925i	−0.372622	−	0.927983i	$-0.621541\pi$
$193$	−1.78690	+	0.580600i	−0.128624	+	0.0417925i	0.243998	+	0.969776i	$0.421541\pi$
$194$	−24.5078	+	3.50283i	−1.75956	+	0.251488i
$195$	−10.7652	−	14.8171i	−0.770914	−	1.06107i
$196$	−12.4037	+	6.49218i	−0.885978	+	0.463727i
$197$	−13.1956			−0.940147			−0.470074	−	0.882627i	$-0.655773\pi$
$197$	−13.1956			−0.940147			−0.470074	+	0.882627i	$0.655773\pi$
$198$	14.0688	+	5.92771i	0.999829	+	0.421264i
$199$		−	1.00783i		−	0.0714429i	−0.999362	−	0.0357215i	$-0.988627\pi$
$199$		−	1.00783i		−	0.0714429i	0.999362	−	0.0357215i	$-0.0113729\pi$
$200$	2.83600	+	6.25131i	0.200535	+	0.442035i
$201$	−12.5643	−	17.2933i	−0.886219	−	1.21978i
$202$	−27.5805	+	3.94200i	−1.94056	+	0.277358i
$203$	−5.75993	+	5.12828i	−0.404268	+	0.359935i
$204$	10.1012	−	2.94770i	0.707229	−	0.206381i
$205$	8.37516	+	6.08491i	0.584946	+	0.424988i
$206$	−0.494950	+	2.84592i	−0.0344848	+	0.198285i
$207$	7.60801	−	23.4151i	0.528794	−	1.62746i
$208$	−1.10333	+	18.2281i	−0.0765022	+	1.26389i
$209$	3.57583	−	0.314008i	0.247345	−	0.0217204i
$210$	5.66819	−	13.8991i	0.391142	−	0.959131i
$211$	−1.96950	+	6.06148i	−0.135586	+	0.417290i	−0.995681	−	0.0928441i	$-0.970404\pi$
$211$	−1.96950	+	6.06148i	−0.135586	+	0.417290i	0.860095	+	0.510134i	$0.170404\pi$
$212$	17.5488	−	11.9566i	1.20525	−	0.821185i
$213$	1.08091	+	0.785327i	0.0740628	+	0.0538098i
$214$	−10.1755	+	19.2458i	−0.695583	+	1.31562i
$215$	2.89441	+	8.90809i	0.197397	+	0.607526i
$216$	−1.79156	+	0.201022i	−0.121900	+	0.0136778i
$217$	−3.40955	+	5.83006i	−0.231456	+	0.395770i
$218$	10.9379	−	5.36648i	0.740808	−	0.363464i
$219$	13.7332			0.928006
$220$	−8.23536	+	6.73734i	−0.555228	+	0.454232i
$221$			9.60411i			0.646042i
$222$	5.31631	+	10.8356i	0.356808	+	0.727241i
$223$	4.05064	+	5.57523i	0.271251	+	0.373345i	0.922811	−	0.385252i	$-0.125885\pi$
$223$	4.05064	+	5.57523i	0.271251	+	0.373345i	−0.651561	+	0.758597i	$0.725885\pi$
$224$	−13.1716	+	7.10702i	−0.880063	+	0.474858i
$225$	−2.44107	−	7.51284i	−0.162738	−	0.500856i
$226$	−1.38626	+	2.62196i	−0.0922129	+	0.174410i
$227$	11.0346	−	15.1878i	0.732391	−	1.00805i	−0.266629	−	0.963799i	$-0.585910\pi$
$227$	11.0346	−	15.1878i	0.732391	−	1.00805i	0.999020	−	0.0442511i	$-0.0140902\pi$
$228$	−4.47387	+	3.04822i	−0.296289	+	0.201873i
$229$	7.12498	−	21.9284i	0.470832	−	1.44907i	−0.380666	−	0.924713i	$-0.624305\pi$
$229$	7.12498	−	21.9284i	0.470832	−	1.44907i	0.851498	−	0.524358i	$-0.175695\pi$
$230$	11.9485	+	12.3153i	0.787863	+	0.812046i
$231$	−21.7680	−	2.78916i	−1.43223	−	0.183513i
$232$	−6.08803	+	5.55954i	−0.399698	+	0.365002i
$233$	−10.9042	−	3.54300i	−0.714359	−	0.232109i	−0.0707833	−	0.997492i	$-0.522550\pi$
$233$	−10.9042	−	3.54300i	−0.714359	−	0.232109i	−0.643576	+	0.765382i	$0.722550\pi$
$234$	3.60072	−	20.7038i	0.235387	−	1.35345i
$235$	11.5452	−	15.8906i	0.753123	−	1.03659i
$236$	14.6264	−	4.26821i	0.952096	−	0.277836i
$237$	−2.94096	+	0.955574i	−0.191036	+	0.0620712i
$238$	−6.68876	+	4.14946i	−0.433568	+	0.268969i
$239$	−0.349753	−	0.481393i	−0.0226236	−	0.0311387i	0.797555	−	0.603246i	$-0.206126\pi$
$239$	−0.349753	−	0.481393i	−0.0226236	−	0.0311387i	−0.820179	+	0.572107i	$0.806126\pi$
$240$	5.87177	−	14.9340i	0.379021	−	0.963985i
$241$	3.75932			0.242159			0.121079	−	0.992643i	$-0.461364\pi$
$241$	3.75932			0.242159			0.121079	+	0.992643i	$0.461364\pi$
$242$	12.6126	+	9.10618i	0.810768	+	0.585367i
$243$	−22.3463			−1.43352
$244$	8.59308	−	23.9575i	0.550116	−	1.53372i
$245$	−1.29840	+	11.1531i	−0.0829514	+	0.712547i
$246$	3.22969	+	22.5967i	0.205918	+	1.44072i
$247$	−1.52688	−	4.69925i	−0.0971530	−	0.299006i
$248$	−3.56612	+	6.27804i	−0.226449	+	0.398656i
$249$	0.786525	−	1.08256i	0.0498440	−	0.0686044i
$250$	16.5989	+	2.88680i	1.04980	+	0.182578i
$251$	−1.30763	+	4.02449i	−0.0825372	+	0.254023i	−0.983806	−	0.179237i	$-0.942637\pi$
$251$	−1.30763	+	4.02449i	−0.0825372	+	0.254023i	0.901269	+	0.433261i	$0.142637\pi$
$252$	15.9748	−	6.43737i	1.00632	−	0.405516i
$253$	12.9140	−	21.5082i	0.811894	−	1.35221i
$254$	0.162930	−	0.158078i	0.0102231	−	0.00991867i
$255$	2.60793	−	8.02637i	0.163315	−	0.502631i
$256$	−13.9841	+	7.77461i	−0.874007	+	0.485913i
$257$	16.0622	−	22.1078i	1.00193	−	1.37904i	0.0778026	−	0.996969i	$-0.475210\pi$
$257$	16.0622	−	22.1078i	1.00193	−	1.37904i	0.924131	−	0.382075i	$-0.124790\pi$
$258$	−9.65324	+	18.2580i	−0.600984	+	1.13669i
$259$	−6.00369	−	6.74315i	−0.373051	−	0.418999i
$260$	11.5835	+	8.96303i	0.718375	+	0.555863i
$261$	7.67558	−	5.57664i	0.475107	−	0.345185i
$262$	−0.895070	−	1.82432i	−0.0552976	−	0.112707i
$263$		−	27.1311i		−	1.67297i	−0.547987	−	0.836487i	$-0.684606\pi$
$263$		−	27.1311i		−	1.67297i	0.547987	−	0.836487i	$-0.315394\pi$
$264$	−23.3067	−	2.68817i	−1.43443	−	0.165446i
$265$		−	17.0311i		−	1.04621i
$266$	2.61309	−	3.09370i	0.160219	−	0.189687i
$267$	24.7671	+	34.0889i	1.51572	+	2.08621i
$268$	13.5193	+	10.4609i	0.825822	+	0.639003i
$269$	1.67346	+	5.15038i	0.102033	+	0.314024i	0.989023	−	0.147765i	$-0.0472078\pi$
$269$	1.67346	+	5.15038i	0.102033	+	0.314024i	−0.886990	+	0.461789i	$0.847208\pi$
$270$	−0.675822	+	1.27824i	−0.0411292	+	0.0777913i
$271$	23.0782	+	16.7673i	1.40190	+	1.01854i	0.994439	+	0.105318i	$0.0335862\pi$
$271$	23.0782	+	16.7673i	1.40190	+	1.01854i	0.407462	+	0.913222i	$0.366414\pi$
$272$	−7.09410	+	4.52573i	−0.430143	+	0.274413i
$273$	2.98977	+	30.0604i	0.180949	+	1.81934i
$274$	16.5363	+	17.0439i	0.998997	+	1.02966i
$275$	−0.704140	−	8.01852i	−0.0424612	−	0.483535i
$276$	−1.14350	+	37.8179i	−0.0688305	+	2.27637i
$277$	−8.15861	+	25.1096i	−0.490204	+	1.50869i	0.334097	+	0.942539i	$0.391569\pi$
$277$	−8.15861	+	25.1096i	−0.490204	+	1.50869i	−0.824300	+	0.566153i	$0.808431\pi$
$278$	0.472693	−	2.71794i	0.0283502	−	0.163011i
$279$	4.88375	−	6.72190i	0.292382	−	0.402430i
$280$	−1.23764	+	11.9397i	−0.0739633	+	0.713536i
$281$	13.9539	−	4.53388i	0.832417	−	0.270469i	0.138354	−	0.990383i	$-0.455819\pi$
$281$	13.9539	−	4.53388i	0.832417	−	0.270469i	0.694063	+	0.719914i	$0.255819\pi$
$282$	42.8738	−	6.12784i	2.55310	−	0.364907i
$283$	−1.04328	−	1.43595i	−0.0620165	−	0.0853583i	0.776882	−	0.629646i	$-0.216800\pi$
$283$	−1.04328	−	1.43595i	−0.0620165	−	0.0853583i	−0.838899	+	0.544288i	$0.816800\pi$
$284$	−1.00571	−	0.360729i	−0.0596780	−	0.0214053i
$285$			4.34189i			0.257191i
$286$	8.31438	−	19.7334i	0.491639	−	1.16686i
$287$	−6.85780	−	15.6374i	−0.404803	−	0.923047i
$288$	16.9897	−	7.09656i	1.00113	−	0.418169i
$289$	10.1730	−	7.39109i	0.598409	−	0.434770i
$290$	0.935583	+	6.54587i	0.0549393	+	0.384387i
$291$	−41.6385	+	13.5292i	−2.44089	+	0.793094i
$292$	−10.5426	+	3.07650i	−0.616959	+	0.180038i
$293$	−5.43458	+	7.48006i	−0.317492	+	0.436990i	−0.937699	−	0.347448i	$-0.887048\pi$
$293$	−5.43458	+	7.48006i	−0.317492	+	0.436990i	0.620208	+	0.784438i	$0.287048\pi$
$294$	−19.6437	+	15.0698i	−1.14565	+	0.878889i
$295$	3.77622	−	11.6220i	0.219860	−	0.676659i
$296$	−6.50857	−	7.12726i	−0.378303	−	0.414264i
$297$	2.05994	+	0.474874i	0.119530	+	0.0275550i
$298$	−6.17205	−	6.36149i	−0.357537	−	0.368511i
$299$	−32.8426	−	10.6712i	−1.89934	−	0.617133i
$300$	6.83540	+	10.0323i	0.394642	+	0.579216i
$301$	3.29644	−	15.0934i	0.190004	−	0.869969i
$302$	−1.05649	−	0.558577i	−0.0607940	−	0.0321425i
$303$	−46.8590	+	15.2254i	−2.69198	+	0.874677i
$304$	2.75160	−	3.34226i	0.157815	−	0.191692i
$305$	−11.9986	−	16.5147i	−0.687039	−	0.945628i
$306$	8.69346	−	4.26529i	0.496972	−	0.243830i
$307$			24.1920i			1.38071i	0.723469	+	0.690356i	$0.242546\pi$
$307$			24.1920i			1.38071i	−0.723469	+	0.690356i	$0.757454\pi$
$308$	17.3355	−	2.73527i	0.987780	−	0.155857i
$309$			5.10842i			0.290608i
$310$	2.55069	+	5.19880i	0.144870	+	0.295272i
$311$	9.37751	+	12.9070i	0.531750	+	0.731891i	0.987396	−	0.158270i	$-0.0505916\pi$
$311$	9.37751	+	12.9070i	0.531750	+	0.731891i	−0.455646	+	0.890161i	$0.650592\pi$
$312$	3.60101	+	32.0931i	0.203867	+	1.81691i
$313$	−17.4749	+	5.67793i	−0.987738	+	0.320936i	−0.757955	−	0.652306i	$-0.773802\pi$
$313$	−17.4749	+	5.67793i	−0.987738	+	0.320936i	−0.229783	+	0.973242i	$0.573802\pi$
$314$	−5.65197	+	10.6901i	−0.318959	+	0.603276i
$315$	2.94742	−	13.4953i	0.166068	−	0.760376i
$316$	2.04362	−	1.39240i	0.114963	−	0.0783284i
$317$	21.1489	+	6.87170i	1.18784	+	0.385953i	0.835275	−	0.549833i	$-0.185309\pi$
$317$	21.1489	+	6.87170i	1.18784	+	0.385953i	0.352568	+	0.935786i	$0.385309\pi$
$318$	26.9522	−	26.1496i	1.51140	−	1.46640i
$319$	8.89784	−	3.78030i	0.498184	−	0.211656i
$320$	−1.16210	+	12.7798i	−0.0649633	+	0.714412i
$321$	−11.8970	+	36.6153i	−0.664028	+	2.04367i
$322$	−6.75772	−	27.4837i	−0.376593	−	1.53160i
$323$	1.33829	−	1.84199i	0.0744643	−	0.102491i
$324$	15.6867	−	4.57763i	0.871483	−	0.254313i
$325$	−10.5377	+	3.42391i	−0.584528	+	0.189925i
$326$	11.1488	−	1.59346i	0.617474	−	0.0882538i
$327$	17.4310	−	12.6644i	0.963936	−	0.700340i
$328$	−7.54143	−	16.6234i	−0.416406	−	0.917872i
$329$	−29.6696	+	13.0116i	−1.63574	+	0.717353i
$330$	−12.3070	+	14.2339i	−0.677476	+	0.783550i
$331$			32.1356i			1.76633i	0.469060	+	0.883166i	$0.344593\pi$
$331$			32.1356i			1.76633i	−0.469060	+	0.883166i	$0.655407\pi$
$332$	−0.361279	+	1.00725i	−0.0198278	+	0.0552798i
$333$	6.52858	+	8.98582i	0.357764	+	0.492420i
$334$	0.0304435	+	0.213000i	0.00166580	+	0.0116549i
$335$	13.0389	−	4.23658i	0.712389	−	0.231469i
$336$	−20.7953	+	16.3737i	−1.13448	+	0.893260i
$337$	9.15127	−	12.5956i	0.498502	−	0.686128i	−0.483426	−	0.875385i	$-0.660608\pi$
$337$	9.15127	−	12.5956i	0.498502	−	0.686128i	0.981928	+	0.189257i	$0.0606078\pi$
$338$	−10.9269	−	1.90036i	−0.594344	−	0.103366i
$339$	−1.62080	+	4.98830i	−0.0880296	+	0.270927i
$340$	−0.203974	+	6.74584i	−0.0110620	+	0.365844i
$341$	6.38789	−	5.55653i	0.345923	−	0.300903i
$342$	−3.57557	+	3.46909i	−0.193345	+	0.187587i
$343$	11.1355	−	14.7987i	0.601262	−	0.799052i
$344$	3.32038	−	16.1787i	0.179023	−	0.872295i
$345$	24.5496	+	17.8364i	1.32171	+	0.960277i
$346$	−9.94660	−	5.25889i	−0.534733	−	0.282720i
$347$	−6.70908	−	20.6484i	−0.360162	−	1.10847i	−0.952955	−	0.303111i	$-0.901975\pi$
$347$	−6.70908	−	20.6484i	−0.360162	−	1.10847i	0.592793	−	0.805355i	$-0.298025\pi$
$348$	−8.92255	+	11.5311i	−0.478299	+	0.618134i
$349$	8.59249	+	11.8265i	0.459945	+	0.633061i	0.974497	−	0.224399i	$-0.0720418\pi$
$349$	8.59249	+	11.8265i	0.459945	+	0.633061i	−0.514552	+	0.857459i	$0.672042\pi$
$350$	−6.93740	−	5.85967i	−0.370820	−	0.313212i
$351$		−	2.90989i		−	0.155319i
$352$	18.4941	−	3.15749i	0.985737	−	0.168295i
$353$		−	11.9327i		−	0.635113i	−0.948239	−	0.317557i	$-0.897138\pi$
$353$		−	11.9327i		−	0.635113i	0.948239	−	0.317557i	$-0.102862\pi$
$354$	24.1902	−	11.8685i	1.28569	−	0.630803i
$355$	−0.693271	+	0.503691i	−0.0367950	+	0.0267331i
$356$	−26.6495	−	20.6208i	−1.41242	−	1.09290i
$357$	−10.3965	+	9.25638i	−0.550240	+	0.489900i
$358$	−9.73514	−	5.14709i	−0.514518	−	0.272032i
$359$	−9.97792	+	13.7334i	−0.526614	+	0.724822i	−0.986610	−	0.163099i	$-0.947851\pi$
$359$	−9.97792	+	13.7334i	−0.526614	+	0.724822i	0.459995	+	0.887921i	$0.347851\pi$
$360$	2.96883	−	14.4657i	0.156471	−	0.762409i
$361$	5.50935	−	16.9560i	0.289966	−	0.892423i
$362$	7.09182	+	7.30950i	0.372738	+	0.384179i
$363$	24.7342	+	12.0439i	1.29821	+	0.632141i
$364$	−9.02924	−	22.4067i	−0.473261	−	1.17443i
$365$	−2.72187	+	8.37707i	−0.142469	+	0.438476i
$366$	7.71229	−	44.3449i	0.403128	−	2.31795i
$367$	−15.5042	+	21.3397i	−0.809313	+	1.11392i	0.182116	+	0.983277i	$0.441705\pi$
$367$	−15.5042	+	21.3397i	−0.809313	+	1.11392i	−0.991429	+	0.130647i	$0.958295\pi$
$368$	−7.59408	−	29.2879i	−0.395869	−	1.52674i
$369$	6.49124	+	19.9780i	0.337920	+	1.04001i
$370$	−7.66326	+	1.09529i	−0.398394	+	0.0569413i
$371$	−14.1813	+	24.2488i	−0.736254	+	1.25893i
$372$	−4.31091	+	12.0188i	−0.223511	+	0.623146i
$373$	−10.7832			−0.558333			−0.279167	−	0.960243i	$-0.590058\pi$
$373$	−10.7832			−0.558333			−0.279167	+	0.960243i	$0.590058\pi$
$374$	9.60836	−	2.24523i	0.496837	−	0.116098i
$375$	29.7949			1.53860
$376$	−31.5402	+	14.3087i	−1.62656	+	0.737914i
$377$	−7.82195	−	10.7660i	−0.402851	−	0.554477i
$378$	2.02659	−	1.25722i	0.104236	−	0.0646644i
$379$	9.31132	−	3.02543i	0.478290	−	0.155406i	−0.0599431	−	0.998202i	$-0.519092\pi$
$379$	9.31132	−	3.02543i	0.478290	−	0.155406i	0.538233	+	0.842796i	$0.319092\pi$
$380$	−0.972663	−	3.33314i	−0.0498966	−	0.170986i
$381$	0.235973	−	0.324789i	0.0120893	−	0.0166394i
$382$	1.24927	+	0.217267i	0.0639180	+	0.0111164i
$383$	−27.1355	−	8.81686i	−1.38656	−	0.450520i	−0.481739	−	0.876315i	$-0.659995\pi$
$383$	−27.1355	−	8.81686i	−1.38656	−	0.450520i	−0.904820	+	0.425794i	$0.859995\pi$
$384$	−22.0087	+	17.7831i	−1.12313	+	0.907489i
$385$	6.01568	−	12.7253i	0.306587	−	0.648543i
$386$	1.90704	−	1.85025i	0.0970659	−	0.0941753i
$387$	−5.87314	+	18.0757i	−0.298549	+	0.918838i
$388$	28.9339	−	19.7137i	1.46890	−	1.00081i
$389$	11.1138	−	15.2968i	0.563490	−	0.775578i	−0.428275	−	0.903649i	$-0.640879\pi$
$389$	11.1138	−	15.2968i	0.563490	−	0.775578i	0.991765	+	0.128071i	$0.0408785\pi$
$390$	22.8978	+	12.1063i	1.15947	+	0.613028i
$391$	−4.91725	−	15.1337i	−0.248676	−	0.765346i
$392$	11.7040	−	15.9692i	0.591142	−	0.806567i
$393$	−2.11228	−	2.90730i	−0.106550	−	0.146654i
$394$	16.7536	−	8.21983i	0.844032	−	0.414109i
$395$		−	1.98333i		−	0.0997922i
$396$	−21.5548	+	1.23778i	−1.08317	+	0.0622006i
$397$	17.3578			0.871165			0.435583	−	0.900149i	$-0.356542\pi$
$397$	17.3578			0.871165			0.435583	+	0.900149i	$0.356542\pi$
$398$	0.627798	+	1.27957i	0.0314686	+	0.0641390i
$399$	3.61536	−	6.18196i	0.180994	−	0.309485i
$400$	−7.49476	−	6.17027i	−0.374738	−	0.308513i
$401$	2.42194	+	7.45396i	0.120946	+	0.372233i	0.993141	−	0.116926i	$-0.0373039\pi$
$401$	2.42194	+	7.45396i	0.120946	+	0.372233i	−0.872195	+	0.489159i	$0.837304\pi$
$402$	26.7245	+	14.1295i	1.33289	+	0.704718i
$403$	−9.42834	−	6.85009i	−0.469659	−	0.341227i
$404$	32.5615	−	22.1854i	1.62000	−	1.10376i
$405$	4.04997	−	12.4645i	0.201245	−	0.619367i
$406$	4.11847	−	10.0990i	0.204396	−	0.501206i
$407$	4.42561	+	10.4167i	0.219369	+	0.516338i
$408$	−10.9887	+	10.0348i	−0.544021	+	0.496796i
$409$	−8.88724	+	27.3521i	−0.439446	+	1.35247i	0.449016	+	0.893524i	$0.351775\pi$
$409$	−8.88724	+	27.3521i	−0.439446	+	1.35247i	−0.888462	+	0.458951i	$0.848225\pi$
$410$	−14.4238	−	2.50853i	−0.712341	−	0.123887i
$411$	33.9758	+	24.6849i	1.67590	+	1.21762i
$412$	−1.14438	−	3.92159i	−0.0563796	−	0.193203i
$413$	−15.0539	+	13.4030i	−0.740752	+	0.659519i
$414$	4.92638	+	34.4677i	0.242118	+	1.69400i
$415$	0.504459	+	0.694328i	0.0247629	+	0.0340832i
$416$	−9.95384	−	23.8302i	−0.488027	−	1.16837i
$417$		−	4.87870i		−	0.238911i
$418$	−4.34438	+	2.62614i	−0.212491	+	0.128449i
$419$	32.6680			1.59594			0.797968	−	0.602699i	$-0.205908\pi$
$419$	32.6680			1.59594			0.797968	+	0.602699i	$0.205908\pi$
$420$	1.46156	+	21.1776i	0.0713168	+	1.03336i
$421$	−12.0458	−	16.5796i	−0.587075	−	0.808039i	0.407374	−	0.913262i	$-0.366445\pi$
$421$	−12.0458	−	16.5796i	−0.587075	−	0.808039i	−0.994449	+	0.105222i	$0.966445\pi$
$422$	−1.27530	−	8.92270i	−0.0620805	−	0.434350i
$423$	37.9051	−	12.3161i	1.84301	−	0.598830i
$424$	−14.8324	+	26.1121i	−0.720327	+	1.26811i
$425$	−4.13054	−	3.00101i	−0.200360	−	0.145570i
$426$	−1.86156	−	0.323754i	−0.0901928	−	0.0156859i
$427$	3.33231	+	33.5045i	0.161262	+	1.62139i
$428$	0.930502	−	30.7737i	0.0449775	−	1.48750i
$429$	8.50666	−	36.9008i	0.410706	−	1.78159i
$430$	−9.22389	−	9.50700i	−0.444815	−	0.458468i
$431$	9.62398	+	3.12702i	0.463571	+	0.150623i	0.531485	−	0.847068i	$-0.321634\pi$
$431$	9.62398	+	3.12702i	0.463571	+	0.150623i	−0.0679140	+	0.997691i	$0.521634\pi$
$432$	2.14940	−	1.37123i	0.103413	−	0.0659731i
$433$	−12.6608	+	17.4261i	−0.608439	+	0.837444i	−0.996448	−	0.0842112i	$-0.973163\pi$
$433$	−12.6608	+	17.4261i	−0.608439	+	0.837444i	0.388009	+	0.921656i	$0.373163\pi$
$434$	0.697211	−	9.52592i	0.0334672	−	0.457259i
$435$	3.61355	+	11.1214i	0.173257	+	0.533229i
$436$	−10.5442	+	13.6269i	−0.504976	+	0.652611i
$437$	4.81198	+	6.62313i	0.230188	+	0.316827i
$438$	−17.4362	+	8.55474i	−0.833132	+	0.408761i
$439$	12.5502			0.598989			0.299495	−	0.954098i	$-0.403182\pi$
$439$	12.5502			0.598989			0.299495	+	0.954098i	$0.403182\pi$
$440$	6.25904	−	13.6839i	0.298388	−	0.652356i
$441$	−15.4337	+	16.7604i	−0.734938	+	0.798114i
$442$	−5.98261	−	12.1937i	−0.284564	−	0.579995i
$443$	5.58693	+	7.68974i	0.265443	+	0.365351i	0.920845	−	0.389930i	$-0.127501\pi$
$443$	5.58693	+	7.68974i	0.265443	+	0.365351i	−0.655402	+	0.755280i	$0.727501\pi$
$444$	−13.4995	−	10.4456i	−0.640660	−	0.495728i
$445$	−25.7025	+	8.35124i	−1.21841	+	0.395887i
$446$	−8.61576	−	4.55526i	−0.407968	−	0.215698i
$447$	−12.6812	−	9.21342i	−0.599799	−	0.435780i
$448$	12.2959	−	17.2282i	0.580929	−	0.813955i
$449$	−8.59531	+	26.4536i	−0.405638	+	1.24842i	0.514724	+	0.857356i	$0.327894\pi$
$449$	−8.59531	+	26.4536i	−0.405638	+	1.24842i	−0.920362	+	0.391068i	$0.872106\pi$
$450$	7.77918	+	8.01795i	0.366714	+	0.377970i
$451$	1.87243	+	21.3227i	0.0881695	+	1.00405i
$452$	0.126767	−	4.19246i	0.00596263	−	0.197197i
$453$	−2.00997	−	0.653080i	−0.0944368	−	0.0306844i
$454$	−4.54905	+	26.1566i	−0.213498	+	1.22759i
$455$	−18.9290	−	4.13414i	−0.887403	−	0.193811i
$456$	3.78137	−	6.65699i	0.177079	−	0.311742i
$457$	17.4721	−	5.67702i	0.817309	−	0.265560i	0.129619	−	0.991564i	$-0.458625\pi$
$457$	17.4721	−	5.67702i	0.817309	−	0.265560i	0.687691	+	0.726004i	$0.258625\pi$
$458$	4.61360	+	32.2793i	0.215579	+	1.50831i
$459$	1.08478	−	0.788141i	0.0506333	−	0.0367873i
$460$	−22.8417	−	8.19288i	−1.06500	−	0.381995i
$461$		−	13.5220i		−	0.629782i	−0.949128	−	0.314891i	$-0.898032\pi$
$461$		−	13.5220i		−	0.629782i	0.949128	−	0.314891i	$-0.101968\pi$
$462$	29.3748	−	10.0185i	1.36664	−	0.466105i
$463$	−37.9391			−1.76318			−0.881590	−	0.472015i	$-0.843527\pi$
$463$	−37.9391			−1.76318			−0.881590	+	0.472015i	$0.843527\pi$
$464$	4.26639	−	10.8509i	0.198062	−	0.503743i
$465$	6.01938	+	8.28497i	0.279142	+	0.384206i
$466$	16.0514	−	2.29418i	0.743565	−	0.106276i
$467$	−7.91829	−	24.3700i	−0.366415	−	1.12771i	−0.949090	−	0.315004i	$-0.897994\pi$
$467$	−7.91829	−	24.3700i	−0.366415	−	1.12771i	0.582676	−	0.812705i	$-0.302006\pi$
$468$	8.32528	+	28.5292i	0.384836	+	1.31876i
$469$	−22.0924	−	4.82504i	−1.02013	−	0.222800i
$470$	−4.75954	+	27.3669i	−0.219541	+	1.26234i
$471$	−6.60820	+	20.3379i	−0.304490	+	0.937123i
$472$	−15.9114	+	14.5301i	−0.732380	+	0.668804i
$473$	−9.96916	+	16.6036i	−0.458382	+	0.763435i
$474$	3.13869	−	3.04522i	0.144165	−	0.139871i
$475$	2.49816	+	0.811702i	0.114623	+	0.0372434i
$476$	5.90748	−	9.43486i	0.270769	−	0.432446i
$477$	20.3128	−	27.9582i	0.930061	−	1.28012i
$478$	0.743928	+	0.393324i	0.0340265	+	0.0179902i
$479$	−4.41931	−	13.6012i	−0.201923	−	0.621457i	−0.999826	−	0.0186696i	$-0.994057\pi$
$479$	−4.41931	−	13.6012i	−0.201923	−	0.621457i	0.797902	−	0.602787i	$-0.205943\pi$
$480$	1.84772	+	22.6184i	0.0843366	+	1.03238i
$481$	12.6038	−	9.15717i	0.574682	−	0.417531i
$482$	−4.77295	+	2.34176i	−0.217402	+	0.106664i
$483$	−20.1019	−	45.8371i	−0.914668	−	2.08566i
$484$	−21.6858	−	3.70484i	−0.985718	−	0.168402i
$485$		−	28.0803i		−	1.27506i
$486$	28.3716	−	13.9200i	1.28696	−	0.631424i
$487$	7.13065	−	5.18072i	0.323120	−	0.234761i	−0.414385	−	0.910102i	$-0.636003\pi$
$487$	7.13065	−	5.18072i	0.323120	−	0.234761i	0.737506	+	0.675341i	$0.236003\pi$
$488$	4.01359	+	35.7700i	0.181687	+	1.61923i
$489$	18.9417	−	6.15452i	0.856572	−	0.278317i
$490$	−5.29905	−	14.9692i	−0.239386	−	0.676238i
$491$	21.9073	+	15.9166i	0.988661	+	0.718304i	0.959627	−	0.281274i	$-0.0907570\pi$
$491$	21.9073	+	15.9166i	0.988661	+	0.718304i	0.0290337	+	0.999578i	$0.490757\pi$
$492$	−18.1765	−	26.6777i	−0.819462	−	1.20272i
$493$	1.89490	−	5.83191i	0.0853421	−	0.262656i
$494$	4.86585	+	5.01520i	0.218925	+	0.225644i
$495$	−8.91365	+	14.8457i	−0.400639	+	0.667263i
$496$	0.616928	−	10.1922i	0.0277009	−	0.457644i
$497$	1.40648	−	0.139887i	0.0630895	−	0.00627480i
$498$	−0.324248	+	1.86440i	−0.0145299	+	0.0835456i
$499$	−9.32574	+	12.8358i	−0.417478	+	0.574609i	−0.965022	−	0.262168i	$-0.915563\pi$
$499$	−9.32574	+	12.8358i	−0.417478	+	0.574609i	0.547545	+	0.836776i	$0.315563\pi$
$500$	−22.8727	+	6.67462i	−1.02290	+	0.298498i
$501$	0.117584	+	0.361886i	0.00525325	+	0.0161679i
$502$	−0.846726	−	5.92417i	−0.0377912	−	0.264409i
$503$	−6.11620	+	4.44368i	−0.272708	+	0.198134i	−0.715731	−	0.698377i	$-0.753906\pi$
$503$	−6.11620	+	4.44368i	−0.272708	+	0.198134i	0.443023	+	0.896510i	$0.353906\pi$
$504$	−16.2722	+	18.1242i	−0.724820	+	0.807315i
$505$		−	31.6009i		−	1.40622i
$506$	−2.99807	+	35.3519i	−0.133280	+	1.57158i
$507$	−19.6138			−0.871077
$508$	−0.108391	+	0.302193i	−0.00480906	+	0.0134077i
$509$	−4.77230	+	3.46728i	−0.211529	+	0.153684i	−0.688505	−	0.725232i	$-0.741733\pi$
$509$	−4.77230	+	3.46728i	−0.211529	+	0.153684i	0.476976	+	0.878916i	$0.341733\pi$
$510$	1.68870	+	11.8151i	0.0747768	+	0.523181i
$511$	10.8507	−	9.66082i	0.480008	−	0.427370i
$512$	12.9117	−	18.5819i	0.570623	−	0.821212i
$513$	−0.405480	+	0.558095i	−0.0179024	+	0.0246405i
$514$	−6.62171	+	38.0742i	−0.292071	+	1.67938i
$515$	−3.11606	−	1.01247i	−0.137310	−	0.0446148i
$516$	0.882744	−	29.1942i	0.0388606	−	1.28520i
$517$	40.4565	−	3.55265i	1.77927	−	0.156245i
$518$	11.8229	+	4.82150i	0.519470	+	0.211845i
$519$	−18.9235	−	6.14861i	−0.830649	−	0.269894i
$520$	−20.2900	−	4.16416i	−0.889776	−	0.182610i
$521$	−14.2983	+	19.6799i	−0.626419	+	0.862192i	−0.997800	−	0.0662885i	$-0.978884\pi$
$521$	−14.2983	+	19.6799i	−0.626419	+	0.862192i	0.371381	+	0.928480i	$0.378884\pi$
$522$	−6.27136	+	11.8616i	−0.274490	+	0.519167i
$523$	−7.53213	+	2.44734i	−0.329357	+	0.107015i	−0.469028	−	0.883183i	$-0.655396\pi$
$523$	−7.53213	+	2.44734i	−0.329357	+	0.107015i	0.139671	+	0.990198i	$0.455396\pi$
$524$	2.27282	+	1.75866i	0.0992887	+	0.0768274i
$525$	−13.8626	−	8.10717i	−0.605013	−	0.353826i
$526$	16.9005	+	34.4465i	0.736899	+	1.50194i
$527$		−	5.37014i		−	0.233927i
$528$	31.2654	−	11.1053i	1.36065	−	0.483294i
$529$	34.2156			1.48763
$530$	10.6090	+	21.6232i	0.460827	+	0.939252i
$531$	20.0605	−	14.5748i	0.870552	−	0.632493i
$532$	−1.39053	+	5.55562i	−0.0602872	+	0.240867i
$533$	28.0217	−	9.10480i	1.21375	−	0.394373i
$534$	−52.6798	−	27.8525i	−2.27968	−	1.20529i
$535$	−19.9768	−	14.5140i	−0.863674	−	0.627496i
$536$	−23.6809	−	4.86007i	−1.02286	−	0.209923i
$537$	−18.5212	−	6.01790i	−0.799248	−	0.259691i
$538$	−5.33297	−	5.49666i	−0.229920	−	0.236978i
$539$	−19.1611	+	13.1092i	−0.825328	+	0.564654i
$540$	0.0618008	−	2.04388i	0.00265948	−	0.0879547i
$541$	0.701603	−	2.15931i	0.0301642	−	0.0928360i	−0.934841	−	0.355067i	$-0.884458\pi$
$541$	0.701603	−	2.15931i	0.0301642	−	0.0928360i	0.965005	+	0.262231i	$0.0844581\pi$
$542$	−39.7456	−	6.91238i	−1.70722	−	0.296912i
$543$	14.5710	+	10.5864i	0.625300	+	0.454307i
$544$	6.18772	−	10.1651i	0.265296	−	0.435825i
$545$	4.27031	+	13.1427i	0.182920	+	0.562970i
$546$	−22.5212	−	36.3033i	−0.963818	−	1.55364i
$547$	3.21498	−	2.33582i	0.137462	−	0.0998723i	−0.516929	−	0.856028i	$-0.672925\pi$
$547$	3.21498	−	2.33582i	0.137462	−	0.0998723i	0.654391	+	0.756156i	$0.272925\pi$
$548$	−31.6121	−	11.3387i	−1.35040	−	0.484363i
$549$		−	41.4212i		−	1.76781i
$550$	5.88892	+	9.74195i	0.251104	+	0.415398i
$551$			3.15479i			0.134398i
$552$	−22.1058	−	48.7272i	−0.940885	−	2.07397i
$553$	−1.65146	+	2.82386i	−0.0702273	+	0.120083i
$554$	−5.28290	−	36.9622i	−0.224449	−	1.57037i
$555$	−13.0198	+	4.23039i	−0.552660	+	0.179570i
$556$	1.09292	+	3.74524i	0.0463501	+	0.158833i
$557$	6.82168	+	4.95624i	0.289044	+	0.210003i	0.722852	−	0.691002i	$-0.242831\pi$
$557$	6.82168	+	4.95624i	0.289044	+	0.210003i	−0.433809	+	0.901005i	$0.642831\pi$
$558$	−2.01334	+	11.5765i	−0.0852317	+	0.490074i
$559$	25.3535	+	8.23784i	1.07234	+	0.348423i
$560$	−5.86618	−	15.9300i	−0.247891	−	0.673167i
$561$	16.0603	−	6.82332i	0.678067	−	0.288081i
$562$	−14.8920	+	14.4485i	−0.628182	+	0.609475i
$563$	−36.6990	−	11.9242i	−1.54668	−	0.502547i	−0.593470	−	0.804856i	$-0.702242\pi$
$563$	−36.6990	−	11.9242i	−1.54668	−	0.502547i	−0.953210	+	0.302309i	$0.902242\pi$
$564$	−50.6168	+	34.4872i	−2.13135	+	1.45217i
$565$	−2.72155	−	1.97732i	−0.114497	−	0.0831867i
$566$	2.21907	+	1.17325i	0.0932743	+	0.0493153i
$567$	−16.1452	+	14.3747i	−0.678034	+	0.603679i
$568$	1.50159	−	0.168487i	0.0630054	−	0.00706954i
$569$	0.0118865	+	0.0163603i	0.000498307	+	0.000685861i	0.809266	−	0.587442i	$-0.199865\pi$
$569$	0.0118865	+	0.0163603i	0.000498307	+	0.000685861i	−0.808768	+	0.588128i	$0.799865\pi$
$570$	−2.70466	−	5.51260i	−0.113286	−	0.230897i
$571$	15.4072			0.644769			0.322385	−	0.946609i	$-0.395516\pi$
$571$	15.4072			0.644769			0.322385	+	0.946609i	$0.395516\pi$
$572$	1.73614	+	30.2333i	0.0725917	+	1.26412i
$573$	2.24243			0.0936789
$574$	18.4478	+	15.5819i	0.769996	+	0.650376i
$575$	14.8519	−	10.7905i	0.619365	−	0.449995i
$576$	−17.1501	+	19.5933i	−0.714586	+	0.816387i
$577$	15.4617	−	5.02382i	0.643681	−	0.209145i	0.0310550	−	0.999518i	$-0.490113\pi$
$577$	15.4617	−	5.02382i	0.643681	−	0.209145i	0.612626	+	0.790373i	$0.290113\pi$
$578$	−8.31185	+	15.7209i	−0.345727	+	0.653905i
$579$	2.76199	−	3.80155i	0.114784	−	0.157987i
$580$	−5.26542	−	7.72806i	−0.218634	−	0.320890i
$581$	−0.140101	−	1.40863i	−0.00581235	−	0.0584398i
$582$	44.4380	−	43.1146i	1.84201	−	1.78716i
$583$	26.5689	−	23.1111i	1.10037	−	0.957164i
$584$	11.4688	−	10.4732i	0.474583	−	0.433386i
$585$	22.6691	+	7.36563i	0.937252	+	0.304532i
$586$	2.24043	−	12.8822i	0.0925512	−	0.532161i
$587$	−19.1516	−	13.9144i	−0.790470	−	0.574310i	0.117633	−	0.993057i	$-0.462469\pi$
$587$	−19.1516	−	13.9144i	−0.790470	−	0.574310i	−0.908103	+	0.418747i	$0.862469\pi$
$588$	15.5530	−	31.3697i	0.641396	−	1.29366i
$589$	0.853755	+	2.62759i	0.0351784	+	0.108268i
$590$	2.44519	+	17.1080i	0.100667	+	0.704323i
$591$	26.6990	−	19.3980i	1.09825	−	0.797926i
$592$	12.7032	+	4.99467i	0.522099	+	0.205280i
$593$	3.24535			0.133270			0.0666352	−	0.997777i	$-0.478774\pi$
$593$	3.24535			0.133270			0.0666352	+	0.997777i	$0.478774\pi$
$594$	−2.91118	+	0.680268i	−0.119447	+	0.0279117i
$595$	−3.58571	−	8.17628i	−0.147000	−	0.335195i
$596$	11.7990	+	4.23205i	0.483304	+	0.173352i
$597$	1.48154	+	2.03916i	0.0606353	+	0.0834574i
$598$	48.3454	−	6.90988i	1.97699	−	0.282566i
$599$	1.50425	+	4.62961i	0.0614620	+	0.189161i	0.977073	−	0.212905i	$-0.0682924\pi$
$599$	1.50425	+	4.62961i	0.0614620	+	0.189161i	−0.915611	+	0.402065i	$0.868292\pi$
$600$	−14.9278	−	8.47944i	−0.609425	−	0.346172i
$601$	−19.8624	−	14.4309i	−0.810205	−	0.588648i	0.103685	−	0.994610i	$-0.466937\pi$
$601$	−19.8624	−	14.4309i	−0.810205	−	0.588648i	−0.913890	+	0.405962i	$0.866937\pi$
$602$	5.21674	+	21.2165i	0.212619	+	0.864720i
$603$	26.4576	+	8.59658i	1.07743	+	0.350080i
$604$	1.68930	+	0.0510793i	0.0687366	+	0.00207839i
$605$	−12.2488	+	12.7005i	−0.497986	+	0.516347i
$606$	50.0095	−	48.5202i	2.03150	−	1.97100i
$607$	−3.25324	+	10.0124i	−0.132045	+	0.406392i	−0.995119	−	0.0986857i	$-0.968536\pi$
$607$	−3.25324	+	10.0124i	−0.132045	+	0.406392i	0.863074	+	0.505078i	$0.168536\pi$
$608$	−1.41156	+	5.95748i	−0.0572463	+	0.241608i
$609$	4.11547	−	18.8435i	0.166767	−	0.763576i
$610$	25.5212	+	13.4934i	1.03332	+	0.546331i
$611$	−17.2749	−	53.1668i	−0.698869	−	2.15090i
$612$	−8.38056	+	10.8307i	−0.338764	+	0.437805i
$613$	27.1937	−	19.7574i	1.09834	−	0.797993i	0.117555	−	0.993066i	$-0.462494\pi$
$613$	27.1937	−	19.7574i	1.09834	−	0.797993i	0.980789	+	0.195073i	$0.0624944\pi$
$614$	−15.0698	−	30.7150i	−0.608166	−	1.23956i
$615$	−25.8907			−1.04401
$616$	−20.3058	+	14.2714i	−0.818145	+	0.575013i
$617$	47.3796			1.90743			0.953715	−	0.300713i	$-0.0972247\pi$
$617$	47.3796			1.90743			0.953715	+	0.300713i	$0.0972247\pi$
$618$	−3.18215	−	6.48582i	−0.128005	−	0.260898i
$619$	−18.3749	+	13.3501i	−0.738550	+	0.536588i	−0.892257	−	0.451529i	$-0.850879\pi$
$619$	−18.3749	+	13.3501i	−0.738550	+	0.536588i	0.153707	+	0.988116i	$0.450879\pi$
$620$	−6.47689	−	5.01168i	−0.260118	−	0.201274i
$621$	1.48985	+	4.58528i	0.0597856	+	0.184001i
$622$	−19.9461	−	10.5457i	−0.799765	−	0.422846i
$623$	43.5490	+	9.51122i	1.74475	+	0.381059i
$624$	−24.5635	−	38.5033i	−0.983325	−	1.54136i
$625$	−2.15536	+	6.63350i	−0.0862142	+	0.265340i
$626$	18.6498	−	18.0944i	0.745394	−	0.723197i
$627$	−6.77347	+	5.89193i	−0.270506	+	0.235301i
$628$	0.516847	−	17.0932i	0.0206244	−	0.682093i
$629$	6.82743	+	2.21837i	0.272227	+	0.0884520i
$630$	4.66441	+	18.9701i	0.185834	+	0.755789i
$631$	−32.5659	−	23.6605i	−1.29643	−	0.941909i	−0.296512	−	0.955029i	$-0.595824\pi$
$631$	−32.5659	−	23.6605i	−1.29643	−	0.941909i	−0.999914	+	0.0131205i	$0.995824\pi$
$632$	−1.72729	+	3.04085i	−0.0687080	+	0.120958i
$633$	−4.92565	−	15.1596i	−0.195777	−	0.602540i
$634$	−31.1319	+	4.44960i	−1.23641	+	0.176716i
$635$	0.151347	+	0.208312i	0.00600604	+	0.00826660i
$636$	−17.9303	+	49.9895i	−0.710981	+	1.98221i
$637$	23.5086	+	21.6478i	0.931445	+	0.857715i
$638$	−8.94216	+	10.3423i	−0.354023	+	0.409454i
$639$	−1.73882			−0.0687867
$640$	−6.48537	−	16.9495i	−0.256357	−	0.669989i
$641$	−27.7468	+	20.1592i	−1.09593	+	0.796241i	−0.980391	−	0.197062i	$-0.936860\pi$
$641$	−27.7468	+	20.1592i	−1.09593	+	0.796241i	−0.115540	+	0.993303i	$0.536860\pi$
$642$	−7.70362	−	53.8989i	−0.304038	−	2.12722i
$643$	−9.86011	−	30.3463i	−0.388845	−	1.19674i	−0.933653	−	0.358180i	$-0.883397\pi$
$643$	−9.86011	−	30.3463i	−0.388845	−	1.19674i	0.544808	−	0.838561i	$-0.316603\pi$
$644$	25.7000	+	30.6846i	1.01272	+	1.20914i
$645$	−18.9515	−	13.7691i	−0.746216	−	0.542158i
$646$	−0.551714	+	3.17231i	−0.0217069	+	0.124813i
$647$	−15.4690	−	5.02619i	−0.608150	−	0.197600i	−0.0112782	−	0.999936i	$-0.503590\pi$
$647$	−15.4690	−	5.02619i	−0.608150	−	0.197600i	−0.596872	+	0.802336i	$0.703590\pi$
$648$	−17.0648	+	15.5835i	−0.670370	+	0.612178i
$649$	23.2550	−	9.88001i	0.912837	−	0.387824i
$650$	11.2462	−	10.9113i	0.441113	−	0.427976i
$651$	−1.67173	−	16.8083i	−0.0655203	−	0.658768i
$652$	−13.1623	+	8.96794i	−0.515474	+	0.351212i
$653$	−16.0040	+	22.0276i	−0.626285	+	0.862007i	−0.997792	−	0.0664230i	$-0.978841\pi$
$653$	−16.0040	+	22.0276i	−0.626285	+	0.862007i	0.371507	+	0.928430i	$0.378841\pi$
$654$	−14.2420	+	26.9372i	−0.556908	+	1.05333i
$655$	2.19205	−	0.712241i	0.0856506	−	0.0278296i
$656$	19.9299	+	16.4078i	0.778132	+	0.640619i
$657$	−14.4595	+	10.5054i	−0.564119	+	0.409856i
$658$	29.5642	−	35.0018i	1.15253	−	1.36451i
$659$	−49.1562			−1.91485			−0.957426	−	0.288678i	$-0.906784\pi$
$659$	−49.1562			−1.91485			−0.957426	+	0.288678i	$0.906784\pi$
$660$	6.75871	−	25.7381i	0.263082	−	1.00185i
$661$	−36.9367			−1.43667			−0.718336	−	0.695697i	$-0.755096\pi$
$661$	−36.9367			−1.43667			−0.718336	+	0.695697i	$0.755096\pi$
$662$	−20.0180	−	40.8004i	−0.778021	−	1.58575i
$663$	−14.1184	−	19.4323i	−0.548312	−	0.754687i
$664$	−0.168744	−	1.50388i	−0.00654852	−	0.0583619i
$665$	3.05436	+	3.43056i	0.118443	+	0.133031i
$666$	−13.8864	−	7.34189i	−0.538086	−	0.284492i
$667$	17.8376	+	12.9598i	0.690675	+	0.501805i
$668$	−0.171335	−	0.251468i	−0.00662914	−	0.00972959i
$669$	−16.3915	−	5.32593i	−0.633734	−	0.205913i
$670$	−13.9155	+	13.5011i	−0.537603	+	0.521593i
$671$	9.48129	−	41.1286i	0.366021	−	1.58775i
$672$	16.2029	−	33.7425i	0.625039	−	1.30164i
$673$	32.9309	+	10.6999i	1.26939	+	0.412451i	0.864833	−	0.502060i	$-0.167424\pi$
$673$	32.9309	+	10.6999i	1.26939	+	0.412451i	0.404561	+	0.914511i	$0.367424\pi$
$674$	−3.77265	+	21.6924i	−0.145317	+	0.835559i
$675$	1.25149	+	0.909258i	0.0481697	+	0.0349974i
$676$	15.0569	−	4.39384i	0.579112	−	0.168994i
$677$	15.2488	−	4.95462i	0.586057	−	0.190422i	−0.000954964	−	1.00000i	$-0.500304\pi$
$677$	15.2488	−	4.95462i	0.586057	−	0.190422i	0.587012	+	0.809578i	$0.300304\pi$
$678$	−1.04951	−	7.34294i	−0.0403060	−	0.282004i
$679$	−23.3816	+	39.9806i	−0.897304	+	1.53432i
$680$	−3.94316	−	8.69180i	−0.151213	−	0.333315i
$681$			46.9511i			1.79917i
$682$	−4.64898	+	11.0339i	−0.178019	+	0.422510i
$683$		−	23.9979i		−	0.918254i	−0.888371	−	0.459127i	$-0.848162\pi$
$683$		−	23.9979i		−	0.918254i	0.888371	−	0.459127i	$-0.151838\pi$
$684$	2.37869	−	6.63178i	0.0909514	−	0.253572i
$685$	−21.7913	+	15.8323i	−0.832602	+	0.604921i
$686$	−4.91962	+	25.7254i	−0.187832	+	0.982201i
$687$	17.8194	+	54.8423i	0.679851	+	2.09237i
$688$	5.86238	+	22.6093i	0.223501	+	0.861971i
$689$	−39.2150	−	28.4914i	−1.49397	−	1.08543i
$690$	−42.2797	−	7.35311i	−1.60956	−	0.279928i
$691$	10.2474	−	31.5381i	0.389828	−	1.19977i	−0.543089	−	0.839675i	$-0.682745\pi$
$691$	10.2474	−	31.5381i	0.389828	−	1.19977i	0.932917	−	0.360092i	$-0.117255\pi$
$692$	15.9044	+	0.480901i	0.604595	+	0.0182811i
$693$	25.0528	−	13.7151i	0.951676	−	0.520993i
$694$	21.3804	+	22.0367i	0.811591	+	0.836501i
$695$	2.97593	+	0.966940i	0.112884	+	0.0366781i
$696$	4.14536	−	20.1984i	0.157129	−	0.765618i
$697$	10.9838	+	7.98022i	0.416042	+	0.302272i
$698$	−18.2763	−	9.66292i	−0.691769	−	0.365747i
$699$	27.2711	−	8.86093i	1.03149	−	0.335151i
$700$	12.4581	+	3.11816i	0.470871	+	0.117856i
$701$	30.0110	−	21.8043i	1.13350	−	0.823537i	0.147301	−	0.989092i	$-0.452942\pi$
$701$	30.0110	−	21.8043i	1.13350	−	0.823537i	0.986201	+	0.165555i	$0.0529415\pi$
$702$	1.81264	+	3.69450i	0.0684136	+	0.139440i
$703$	−3.69331			−0.139296
$704$	−21.5138	+	15.5292i	−0.810832	+	0.585280i
$705$			49.1236i			1.85010i
$706$	7.43314	+	15.1501i	0.279750	+	0.570183i
$707$	−26.3131	+	44.9933i	−0.989607	+	1.69215i
$708$	−23.3195	+	30.1372i	−0.876402	+	1.13263i
$709$	−32.6517	+	10.6092i	−1.22626	+	0.398436i	−0.849358	−	0.527817i	$-0.823011\pi$
$709$	−32.6517	+	10.6092i	−1.22626	+	0.398436i	−0.376902	+	0.926253i	$0.623011\pi$
$710$	0.566439	−	1.07136i	0.0212581	−	0.0402073i
$711$	2.36551	−	3.25584i	0.0887134	−	0.122103i
$712$	46.6803	+	9.58028i	1.74942	+	0.359036i
$713$	18.3640	+	5.96681i	0.687736	+	0.223459i
$714$	7.43371	−	18.2284i	0.278199	−	0.682181i
$715$	20.8230	+	12.5025i	0.778734	+	0.467568i
$716$	15.5663	+	0.470677i	0.581740	+	0.0175900i
$717$	1.41533	+	0.459868i	0.0528564	+	0.0171741i
$718$	4.11344	−	23.6519i	0.153512	−	0.882680i
$719$	−4.78208	+	6.58197i	−0.178342	+	0.245466i	−0.888824	−	0.458249i	$-0.848477\pi$
$719$	−4.78208	+	6.58197i	−0.178342	+	0.245466i	0.710482	+	0.703715i	$0.248477\pi$
$720$	5.24169	+	20.2155i	0.195346	+	0.753386i
$721$	3.59359	+	4.03620i	0.133832	+	0.150316i
$722$	3.56744	+	24.9598i	0.132766	+	0.928909i
$723$	−7.60633	+	5.52632i	−0.282882	+	0.205526i
$724$	−13.5573	−	4.86273i	−0.503852	−	0.180722i
$725$	7.07437			0.262736
$726$	−38.9058	+	0.116153i	−1.44393	+	0.00431086i
$727$			43.8420i			1.62601i	0.582256	+	0.813005i	$0.302170\pi$
$727$			43.8420i			1.62601i	−0.582256	+	0.813005i	$0.697830\pi$
$728$	25.4215	+	22.8238i	0.942183	+	0.845906i
$729$	25.3837	−	18.4423i	0.940137	−	0.683050i
$730$	−1.76248	−	12.3313i	−0.0652324	−	0.456403i
$731$	3.79596	+	11.6828i	0.140399	+	0.432102i
$732$	17.8317	+	61.1060i	0.659078	+	2.25854i
$733$	−4.35473	+	5.99377i	−0.160846	+	0.221385i	−0.881831	−	0.471565i	$-0.843689\pi$
$733$	−4.35473	+	5.99377i	−0.160846	+	0.221385i	0.720986	+	0.692950i	$0.243689\pi$
$734$	6.39167	−	36.7515i	0.235921	−	1.35652i
$735$	−13.7684	−	24.4751i	−0.507855	−	0.902778i
$736$	27.8858	+	32.4543i	1.02788	+	1.19628i
$737$	24.3029	+	14.5920i	0.895208	+	0.537502i
$738$	−20.6862	−	21.3212i	−0.761470	−	0.784843i
$739$	5.25017	−	16.1584i	0.193131	−	0.594395i	−0.806863	−	0.590739i	$-0.798836\pi$
$739$	5.25017	−	16.1584i	0.193131	−	0.594395i	0.999993	−	0.00365589i	$-0.00116371\pi$
$740$	9.04725	−	6.16423i	0.332583	−	0.226602i
$741$	9.99744	+	7.26357i	0.367265	+	0.266834i
$742$	2.89989	−	39.6209i	0.106458	−	1.45453i
$743$	−9.51193	+	3.09061i	−0.348959	+	0.113384i	−0.478252	−	0.878223i	$-0.658729\pi$
$743$	−9.51193	+	3.09061i	−0.348959	+	0.113384i	0.129293	+	0.991606i	$0.458729\pi$
$744$	−2.01351	−	17.9448i	−0.0738188	−	0.657890i
$745$	8.13341	−	5.90927i	0.297985	−	0.216499i
$746$	13.6907	−	6.71710i	0.501253	−	0.245930i
$747$			1.74147i			0.0637172i
$748$	−10.8005	+	8.83588i	−0.394905	+	0.323072i
$749$	16.3576	+	37.2992i	0.597693	+	1.36288i
$750$	−37.8286	+	18.5599i	−1.38131	+	0.677713i
$751$	−30.6773	+	22.2883i	−1.11943	+	0.813313i	−0.984123	−	0.177491i	$-0.943202\pi$
$751$	−30.6773	+	22.2883i	−1.11943	+	0.813313i	−0.135307	+	0.990804i	$0.543202\pi$
$752$	31.1313	−	37.8139i	1.13524	−	1.37893i
$753$	−3.27036	−	10.0651i	−0.119178	−	0.366793i
$754$	16.6374	+	8.79639i	0.605898	+	0.320346i
$755$	0.796738	−	1.09662i	0.0289963	−	0.0399099i
$756$	−1.78987	+	2.85861i	−0.0650970	+	0.103967i
$757$	3.85346	+	1.25206i	0.140056	+	0.0455070i	0.378206	−	0.925721i	$-0.376541\pi$
$757$	3.85346	+	1.25206i	0.140056	+	0.0455070i	−0.238150	+	0.971228i	$0.576541\pi$
$758$	−9.93735	+	9.64141i	−0.360941	+	0.350192i
$759$	5.48857	+	62.5020i	0.199222	+	2.26868i
$760$	3.31121	+	3.62597i	0.120110	+	0.131528i
$761$	−12.1869	+	37.5075i	−0.441775	+	1.35964i	0.444206	+	0.895925i	$0.353486\pi$
$761$	−12.1869	+	37.5075i	−0.441775	+	1.35964i	−0.885982	+	0.463720i	$0.846514\pi$
$762$	−0.0972807	+	0.559355i	−0.00352411	+	0.0202633i
$763$	4.86345	−	22.2683i	0.176069	−	0.806165i
$764$	−1.72145	+	0.502346i	−0.0622799	+	0.0181742i
$765$	3.39405	+	10.4458i	0.122712	+	0.377669i
$766$	39.9443	−	5.70913i	1.44325	−	0.206279i
$767$	−20.4431	−	28.1375i	−0.738156	−	1.01598i
$768$	16.8655	−	36.2877i	0.608582	−	1.30942i
$769$	45.3274			1.63455			0.817274	−	0.576250i	$-0.195484\pi$
$769$	45.3274			1.63455			0.817274	+	0.576250i	$0.195484\pi$
$770$	0.289198	+	19.9038i	0.0104220	+	0.717283i
$771$			68.3432i			2.46132i
$772$	−1.26868	+	3.53708i	−0.0456608	+	0.127302i
$773$	−8.13594	+	5.91111i	−0.292629	+	0.212608i	−0.724407	−	0.689372i	$-0.757886\pi$
$773$	−8.13594	+	5.91111i	−0.292629	+	0.212608i	0.431778	+	0.901980i	$0.357886\pi$
$774$	−3.80301	−	26.6080i	−0.136696	−	0.956404i
$775$	5.89217	−	1.91448i	0.211653	−	0.0687702i
$776$	−24.4553	+	43.0528i	−0.877893	+	1.54550i
$777$	22.0601	+	4.81799i	0.791401	+	0.172844i
$778$	−4.58169	+	26.3443i	−0.164262	+	0.944489i
$779$	−6.64306	−	2.15846i	−0.238012	−	0.0773349i
$780$	−36.6131	−	1.10707i	−1.31096	−	0.0396394i
$781$	−1.72654	−	0.398015i	−0.0617804	−	0.0142421i
$782$	15.6702	+	16.1512i	0.560367	+	0.577567i
$783$	−0.574125	+	1.76698i	−0.0205176	+	0.0631466i
$784$	−4.91222	+	27.5657i	−0.175437	+	0.984491i
$785$	−11.0961	−	8.06181i	−0.396038	−	0.287738i
$786$	4.49283	+	2.37542i	0.160254	+	0.0847283i
$787$	13.1956	−	4.28751i	0.470372	−	0.152833i	−0.0642333	−	0.997935i	$-0.520460\pi$
$787$	13.1956	−	4.28751i	0.470372	−	0.152833i	0.534606	+	0.845102i	$0.320460\pi$
$788$	−16.1506	+	20.8723i	−0.575340	+	0.743546i
$789$	39.8836	+	54.8950i	1.41989	+	1.95432i
$790$	1.23546	+	2.51810i	0.0439557	+	0.0895901i
$791$	2.22848	+	5.08147i	0.0792356	+	0.180676i
$792$	26.5956	−	14.9985i	0.945033	−	0.532947i
$793$	−58.0986			−2.06314
$794$	−22.0381	+	10.8126i	−0.782103	+	0.383724i
$795$	25.0362	+	34.4594i	0.887944	+	1.22215i
$796$	−1.59414	−	1.23351i	−0.0565030	−	0.0437208i
$797$	4.97620	+	15.3152i	0.176266	+	0.542491i	0.999689	−	0.0249369i	$-0.00793849\pi$
$797$	4.97620	+	15.3152i	0.176266	+	0.542491i	−0.823423	+	0.567428i	$0.807938\pi$
$798$	−0.739296	+	10.1009i	−0.0261708	+	0.357568i
$799$	15.1412	−	20.8401i	0.535658	−	0.737270i
$800$	13.3592	+	3.16532i	0.472319	+	0.111911i
$801$	−52.1537	−	16.9458i	−1.84276	−	0.598749i
$802$	−7.71821	−	7.95512i	−0.272540	−	0.280905i
$803$	−16.7620	+	7.12146i	−0.591520	+	0.251311i
$804$	−42.7319	−	1.29208i	−1.50704	−	0.0455682i
$805$	31.9441	−	3.17712i	1.12588	−	0.111979i
$806$	16.2376	+	2.82398i	0.571945	+	0.0994703i
$807$	−10.9572	−	7.96086i	−0.385711	−	0.280236i
$808$	−27.5214	+	48.4506i	−0.968199	+	1.70449i
$809$	20.0605	−	6.51804i	0.705288	−	0.229162i	0.0656551	−	0.997842i	$-0.479086\pi$
$809$	20.0605	−	6.51804i	0.705288	−	0.229162i	0.639633	+	0.768680i	$0.279086\pi$
$810$	2.62246	+	18.3482i	0.0921437	+	0.644690i
$811$	2.23184	+	3.07186i	0.0783704	+	0.107868i	0.846402	−	0.532544i	$-0.178764\pi$
$811$	2.23184	+	3.07186i	0.0783704	+	0.107868i	−0.768032	+	0.640411i	$0.778764\pi$
$812$	1.06196	+	15.3875i	0.0372675	+	0.539997i
$813$	−71.3433			−2.50212
$814$	−12.1077	−	10.4686i	−0.424375	−	0.366924i
$815$			12.7739i			0.447452i
$816$	7.70070	−	19.5856i	0.269579	−	0.685633i
$817$	−3.71470	−	5.11284i	−0.129961	−	0.178876i
$818$	−5.75471	−	40.2632i	−0.201209	−	1.40777i
$819$	−26.1430	−	29.3630i	−0.913512	−	1.02603i
$820$	19.8755	−	5.80000i	0.694084	−	0.202545i
$821$	−15.1659	−	11.0187i	−0.529293	−	0.384554i	0.290800	−	0.956784i	$-0.406078\pi$
$821$	−15.1659	−	11.0187i	−0.529293	−	0.384554i	−0.820093	+	0.572230i	$0.806078\pi$
$822$	−58.5136	−	10.1764i	−2.04090	−	0.354944i
$823$	9.60567	−	29.5632i	0.334833	−	1.03051i	−0.631972	−	0.774992i	$-0.717754\pi$
$823$	9.60567	−	29.5632i	0.334833	−	1.03051i	0.966804	−	0.255518i	$-0.0822459\pi$
$824$	3.89579	+	4.26612i	0.135716	+	0.148617i
$825$	13.2122	+	15.1890i	0.459990	+	0.528813i
$826$	10.7638	−	26.3943i	0.374521	−	0.918375i
$827$	−1.04699	+	3.22229i	−0.0364072	+	0.112050i	−0.967609	−	0.252455i	$-0.918762\pi$
$827$	−1.04699	+	3.22229i	−0.0364072	+	0.112050i	0.931201	+	0.364505i	$0.118762\pi$
$828$	−27.7254	−	40.6926i	−0.963525	−	1.41417i
$829$	14.8225	+	10.7692i	0.514807	+	0.374029i	0.814644	−	0.579961i	$-0.196932\pi$
$829$	14.8225	+	10.7692i	0.514807	+	0.374029i	−0.299837	+	0.953990i	$0.596932\pi$
$830$	−1.07299	−	0.567303i	−0.0372440	−	0.0196914i
$831$	−20.4045	−	62.7984i	−0.707823	−	2.17845i
$832$	27.4821	+	24.0552i	0.952770	+	0.833963i
$833$	−1.70282	+	14.6271i	−0.0589991	+	0.506798i
$834$	3.03905	+	6.19416i	0.105234	+	0.214486i
$835$	−0.244050			−0.00844568
$836$	3.87989	−	6.04044i	0.134189	−	0.208913i
$837$			1.62707i			0.0562397i
$838$	−41.4764	+	20.3496i	−1.43278	+	0.702966i
$839$	18.7414	+	25.7953i	0.647025	+	0.890554i	0.998966	−	0.0454685i	$-0.0144781\pi$
$839$	18.7414	+	25.7953i	0.647025	+	0.890554i	−0.351940	+	0.936022i	$0.614478\pi$
$840$	−15.0477	−	25.9774i	−0.519194	−	0.896305i
$841$	−6.33591	−	19.4999i	−0.218480	−	0.672411i
$842$	25.6215	+	13.5464i	0.882975	+	0.466840i
$843$	−21.5683	+	29.6862i	−0.742850	+	1.02245i
$844$	7.17731	+	10.5341i	0.247053	+	0.362600i
$845$	3.88737	−	11.9641i	0.133730	−	0.411578i
$846$	−40.4536	+	39.2489i	−1.39082	+	1.34940i
$847$	28.0151	−	7.88362i	0.962612	−	0.270885i
$848$	2.56597	−	42.3922i	0.0881157	−	1.45575i
$849$	4.22179	+	1.37174i	0.144891	+	0.0470781i
$850$	7.11366	+	1.23718i	0.243996	+	0.0424349i
$851$	−15.1720	+	20.8825i	−0.520091	+	0.715844i
$852$	2.56517	−	0.748557i	0.0878812	−	0.0256451i
$853$	2.04013	−	0.662877i	0.0698526	−	0.0226965i	−0.273882	−	0.961763i	$-0.588308\pi$
$853$	2.04013	−	0.662877i	0.0698526	−	0.0226965i	0.343735	+	0.939067i	$0.388308\pi$
$854$	−25.1015	−	40.4626i	−0.858955	−	1.38460i
$855$	−3.32139	−	4.57150i	−0.113589	−	0.156342i
$856$	17.9882	+	39.6509i	0.614824	+	1.35524i
$857$	20.6072			0.703929			0.351964	−	0.936013i	$-0.385514\pi$
$857$	20.6072			0.703929			0.351964	+	0.936013i	$0.385514\pi$
$858$	12.1860	+	52.1495i	0.416023	+	1.78035i
$859$	20.7579			0.708251			0.354125	−	0.935198i	$-0.384779\pi$
$859$	20.7579			0.708251			0.354125	+	0.935198i	$0.384779\pi$
$860$	17.6331	+	6.32464i	0.601283	+	0.215668i
$861$	36.8631	+	21.5584i	1.25629	+	0.734709i
$862$	−14.1668	+	2.02482i	−0.482523	+	0.0689657i
$863$	6.24198	+	19.2108i	0.212479	+	0.653944i	0.999323	+	0.0367918i	$0.0117138\pi$
$863$	6.24198	+	19.2108i	0.212479	+	0.653944i	−0.786844	+	0.617152i	$0.788286\pi$
$864$	−1.87478	+	3.07986i	−0.0637813	+	0.104779i
$865$	7.50113	−	10.3244i	0.255046	−	0.351041i
$866$	5.21946	−	30.0114i	0.177365	−	1.01983i
$867$	−9.71808	+	29.9092i	−0.330043	+	1.01577i
$868$	5.04870	+	12.5287i	0.171364	+	0.425253i
$869$	3.09405	−	2.69137i	0.104959	−	0.0912986i
$870$	−11.5156	−	11.8691i	−0.390417	−	0.402400i
$871$	12.0578	−	37.1101i	0.408563	−	1.25743i
$872$	4.89877	−	23.8694i	0.165893	−	0.808320i
$873$	33.4912	−	46.0966i	1.13350	−	1.56014i
$874$	−10.2351	−	5.41145i	−0.346209	−	0.183045i
$875$	23.5412	−	20.9596i	0.795838	−	0.708565i
$876$	16.8086	−	21.7227i	0.567910	−	0.733944i
$877$	27.7276	−	20.1453i	0.936294	−	0.680258i	−0.0112315	−	0.999937i	$-0.503575\pi$
$877$	27.7276	−	20.1453i	0.936294	−	0.680258i	0.947526	+	0.319679i	$0.103575\pi$
$878$	−15.9342	+	7.81781i	−0.537752	+	0.263838i
$879$		−	23.1236i		−	0.779941i
$880$	0.577349	+	21.2725i	0.0194624	+	0.717095i
$881$		−	16.8738i		−	0.568494i	−0.958751	−	0.284247i	$-0.908256\pi$
$881$		−	16.8738i		−	0.568494i	0.958751	−	0.284247i	$-0.0917436\pi$
$882$	9.15471	−	30.8936i	0.308255	−	1.04024i
$883$	−10.5063	−	14.4607i	−0.353565	−	0.486641i	0.594777	−	0.803891i	$-0.297240\pi$
$883$	−10.5063	−	14.4607i	−0.353565	−	0.486641i	−0.948342	+	0.317250i	$0.897240\pi$
$884$	15.1914	+	11.7548i	0.510944	+	0.395357i
$885$	9.44420	+	29.0663i	0.317463	+	0.977052i
$886$	−11.8835	−	6.28293i	−0.399233	−	0.211079i
$887$	34.8248	+	25.3017i	1.16930	+	0.849548i	0.990925	−	0.134414i	$-0.0429151\pi$
$887$	34.8248	+	25.3017i	1.16930	+	0.849548i	0.178378	+	0.983962i	$0.442915\pi$
$888$	23.6463	+	4.85297i	0.793517	+	0.162855i
$889$	−0.0420329	−	0.422616i	−0.00140974	−	0.0141741i
$890$	27.4305	−	26.6137i	0.919474	−	0.892092i
$891$	24.9408	−	10.5963i	0.835549	−	0.354988i
$892$	13.7764	+	0.416557i	0.461269	+	0.0139474i
$893$	−4.09534	+	12.6042i	−0.137045	+	0.421782i
$894$	21.8397	+	3.79827i	0.730428	+	0.127033i
$895$	7.34166	−	10.1049i	0.245405	−	0.337770i
$896$	−4.87952	+	29.5329i	−0.163013	+	0.986624i
$897$	82.1385	−	26.6884i	2.74252	−	0.891100i
$898$	−5.56567	−	38.9406i	−0.185729	−	1.29947i
$899$	4.37364	+	6.01981i	0.145869	+	0.200772i
$900$	−14.8713	−	5.33403i	−0.495709	−	0.177801i
$901$		−	22.3359i		−	0.744115i
$902$	−15.6597	−	25.9056i	−0.521410	−	0.862562i
$903$	15.5180	+	35.3848i	0.516407	+	1.17753i
$904$	2.45063	+	5.40185i	0.0815068	+	0.179663i
$905$	−9.34547	+	6.78988i	−0.310654	+	0.225703i
$906$	2.95875	−	0.422885i	0.0982977	−	0.0140494i
$907$	−32.7166	+	10.6303i	−1.08634	+	0.352973i	−0.796830	−	0.604203i	$-0.793492\pi$
$907$	−32.7166	+	10.6303i	−1.08634	+	0.352973i	−0.289508	+	0.957176i	$0.593492\pi$
$908$	−10.5179	−	36.0430i	−0.349050	−	1.19613i
$909$	37.6902	−	51.8761i	1.25010	−	1.72062i
$910$	26.6081	−	6.54243i	0.882049	−	0.216879i
$911$	−0.917940	+	2.82513i	−0.0304127	+	0.0936007i	−0.965111	−	0.261842i	$-0.915670\pi$
$911$	−0.917940	+	2.82513i	−0.0304127	+	0.0936007i	0.934698	+	0.355443i	$0.115670\pi$
$912$	−0.654166	+	10.8074i	−0.0216616	+	0.357870i
$913$	−0.398622	+	1.72917i	−0.0131925	+	0.0572272i
$914$	−18.6468	+	18.0915i	−0.616781	+	0.598413i
$915$	48.5543	+	15.7762i	1.60516	+	0.521547i
$916$	−25.9651	−	38.1090i	−0.857911	−	1.25916i
$917$	−3.71410	−	0.811171i	−0.122650	−	0.0267872i
$918$	−0.886325	+	1.67639i	−0.0292531	+	0.0553290i
$919$	−34.4179	+	11.1831i	−1.13534	+	0.368895i	−0.815604	−	0.578611i	$-0.803595\pi$
$919$	−34.4179	+	11.1831i	−1.13534	+	0.368895i	−0.319739	+	0.947506i	$0.603595\pi$
$920$	34.1041	−	3.82667i	1.12438	−	0.126161i
$921$	−35.5631	−	48.9484i	−1.17184	−	1.61291i
$922$	8.42315	+	17.1680i	0.277402	+	0.565397i
$923$			2.43892i			0.0802781i
$924$	−31.0544	+	31.0181i	−1.02161	+	1.02042i
$925$			8.28198i			0.272310i
$926$	48.1688	−	23.6331i	1.58292	−	0.776633i
$927$	−3.90776	−	5.37858i	−0.128348	−	0.176656i
$928$	1.34254	+	16.4344i	0.0440711	+	0.539484i
$929$	8.47074	−	2.75231i	0.277916	−	0.0903004i	−0.166743	−	0.986000i	$-0.553325\pi$
$929$	8.47074	−	2.75231i	0.277916	−	0.0903004i	0.444659	+	0.895700i	$0.353325\pi$
$930$	−12.8033	−	6.76926i	−0.419837	−	0.221973i
$931$	−1.49226	−	7.42769i	−0.0489068	−	0.243433i
$932$	−18.9502	+	12.9115i	−0.620736	+	0.422931i
$933$	−37.9476	−	12.3299i	−1.24235	−	0.403663i
$934$	25.2339	+	26.0085i	0.825679	+	0.851023i
$935$	0.979033	+	11.1489i	0.0320178	+	0.364608i
$936$	−28.3415	−	31.0356i	−0.926372	−	1.01443i
$937$	14.2358	−	43.8133i	0.465063	−	1.43132i	−0.393840	−	0.919179i	$-0.628854\pi$
$937$	14.2358	−	43.8133i	0.465063	−	1.43132i	0.858903	−	0.512138i	$-0.171146\pi$
$938$	31.0548	−	7.63580i	1.01398	−	0.249318i
$939$	27.0106	−	37.1770i	0.881459	−	1.21322i
$940$	−11.0046	−	37.7107i	−0.358930	−	1.22999i
$941$	−17.8403	+	5.79665i	−0.581576	+	0.188965i	−0.585006	−	0.811029i	$-0.698908\pi$
$941$	−17.8403	+	5.79665i	−0.581576	+	0.188965i	0.00343056	+	0.999994i	$0.498908\pi$
$942$	−4.27897	−	29.9381i	−0.139416	−	0.975437i
$943$	−39.4938	+	28.6939i	−1.28609	+	0.934402i
$944$	11.1504	−	28.3595i	0.362916	−	0.923023i
$945$	1.08641	+	2.47728i	0.0353411	+	0.0805860i
$946$	2.31441	−	27.2905i	0.0752480	−	0.887291i
$947$			36.6874i			1.19218i	0.802917	+	0.596091i	$0.203280\pi$
$947$			36.6874i			1.19218i	−0.802917	+	0.596091i	$0.796720\pi$
$948$	−2.08805	+	5.82146i	−0.0678166	+	0.189072i
$949$	14.7352	+	20.2813i	0.478326	+	0.658359i
$950$	−3.67737	+	0.525597i	−0.119310	+	0.0170526i
$951$	−52.8929	+	17.1859i	−1.71517	+	0.557292i
$952$	−1.62314	+	15.6587i	−0.0526063	+	0.507502i
$953$	−28.9526	+	39.8499i	−0.937867	+	1.29086i	0.0188434	+	0.999822i	$0.494002\pi$
$953$	−28.9526	+	39.8499i	−0.937867	+	1.29086i	−0.956711	+	0.291041i	$0.905998\pi$
$954$	−8.37404	+	48.1500i	−0.271120	+	1.55891i
$955$	−0.444442	+	1.36785i	−0.0143818	+	0.0442626i
$956$	−1.18953	−	0.0359677i	−0.0384720	−	0.00116328i
$957$	−12.4461	+	20.7289i	−0.402325	+	0.670071i
$958$	14.0834	+	14.5157i	0.455015	+	0.468981i
$959$	44.2095	−	4.39702i	1.42760	−	0.141987i
$960$	−16.4354	−	27.5660i	−0.530450	−	0.889689i
$961$	−19.8077	−	14.3911i	−0.638957	−	0.464230i
$962$	−10.2979	+	19.4774i	−0.332019	+	0.627977i
$963$	−15.4832	−	47.6525i	−0.498940	−	1.53558i
$964$	4.60116	−	5.94636i	0.148193	−	0.191519i
$965$	1.77148	+	2.43823i	0.0570258	+	0.0784893i
$966$	54.0750	+	45.6744i	1.73983	+	1.46955i
$967$			4.35133i			0.139929i	0.997549	+	0.0699647i	$0.0222887\pi$
$967$			4.35133i			0.139929i	−0.997549	+	0.0699647i	$0.977711\pi$
$968$	29.8408	−	8.80479i	0.959121	−	0.282997i
$969$			5.69429i			0.182927i
$970$	17.4918	+	35.6517i	0.561629	+	1.14471i
$971$	38.8940	−	28.2582i	1.24817	−	0.906848i	0.250054	−	0.968232i	$-0.419551\pi$
$971$	38.8940	−	28.2582i	1.24817	−	0.906848i	0.998114	+	0.0613842i	$0.0195515\pi$
$972$	−27.3504	+	35.3466i	−0.877265	+	1.13374i
$973$	−3.43198	−	3.85470i	−0.110024	−	0.123576i
$974$	−5.82612	+	11.0194i	−0.186681	+	0.353086i
$975$	16.2880	−	22.4185i	0.521634	−	0.717967i
$976$	−27.3777	−	42.9146i	−0.876340	−	1.37366i
$977$	−15.8945	+	48.9183i	−0.508511	+	1.56504i	0.286275	+	0.958147i	$0.407583\pi$
$977$	−15.8945	+	48.9183i	−0.508511	+	1.56504i	−0.794787	+	0.606889i	$0.792417\pi$
$978$	−20.2152	+	19.6132i	−0.646410	+	0.627160i
$979$	−47.9064	−	28.7640i	−1.53109	−	0.919301i
$980$	16.0525	+	15.7045i	0.512778	+	0.501661i
$981$	−8.66502	+	26.6682i	−0.276653	+	0.851450i
$982$	−37.7290	−	6.56167i	−1.20398	−	0.209391i
$983$	2.10641	−	2.89922i	0.0671840	−	0.0924708i	−0.774103	−	0.633060i	$-0.781799\pi$
$983$	2.10641	−	2.89922i	0.0671840	−	0.0924708i	0.841287	+	0.540589i	$0.181799\pi$
$984$	39.6957	+	22.5484i	1.26545	+	0.718815i
$985$	6.54083	+	20.1306i	0.208408	+	0.641415i
$986$	1.22700	+	8.58476i	0.0390755	+	0.273395i
$987$	40.9037	−	69.9420i	1.30198	−	2.22628i
$988$	−9.30192	−	3.33642i	−0.295933	−	0.106146i
$989$	−44.1686			−1.40448
$990$	2.06937	−	24.4011i	0.0657688	−	0.775516i
$991$	25.4739			0.809206			0.404603	−	0.914492i	$-0.367410\pi$
$991$	25.4739			0.809206			0.404603	+	0.914492i	$0.367410\pi$
$992$	5.56569	+	13.3247i	0.176711	+	0.423059i
$993$	−47.2404	−	65.0209i	−1.49913	−	2.06337i
$994$	−1.69858	+	1.05374i	−0.0538757	+	0.0334225i
$995$	−1.53749	+	0.499562i	−0.0487419	+	0.0158372i
$996$	−0.749698	−	2.56908i	−0.0237551	−	0.0814044i
$997$	−7.31506	+	10.0683i	−0.231670	+	0.318867i	−0.908987	−	0.416825i	$-0.863143\pi$
$997$	−7.31506	+	10.0683i	−0.231670	+	0.318867i	0.677316	+	0.735692i	$0.263143\pi$
$998$	3.84457	−	22.1059i	0.121698	−	0.699752i
$999$	−2.06860	−	0.672130i	−0.0654477	−	0.0212652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.c.13.13	✓	352
7.6	odd	2	inner	616.2.bi.c.13.14	yes	352
8.5	even	2	inner	616.2.bi.c.13.32	yes	352
11.6	odd	10	inner	616.2.bi.c.237.31	yes	352
56.13	odd	2	inner	616.2.bi.c.13.31	yes	352
77.6	even	10	inner	616.2.bi.c.237.32	yes	352
88.61	odd	10	inner	616.2.bi.c.237.14	yes	352
616.237	even	10	inner	616.2.bi.c.237.13	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.c.13.13	✓	352	1.1	even	1	trivial
616.2.bi.c.13.14	yes	352	7.6	odd	2	inner
616.2.bi.c.13.31	yes	352	56.13	odd	2	inner
616.2.bi.c.13.32	yes	352	8.5	even	2	inner
616.2.bi.c.237.13	yes	352	616.237	even	10	inner
616.2.bi.c.237.14	yes	352	88.61	odd	10	inner
616.2.bi.c.237.31	yes	352	11.6	odd	10	inner
616.2.bi.c.237.32	yes	352	77.6	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26963 + 0.622922i) q^{2} +(-2.02333 + 1.47003i) q^{3} +(1.22394 - 1.58177i) q^{4} +(-0.495683 - 1.52556i) q^{5} +(1.65317 - 3.12678i) q^{6} +(-0.564533 + 2.58482i) q^{7} +(-0.568632 + 2.77068i) q^{8} +(1.00581 - 3.09555i) q^{9} +O(q^{10})\)	\(q+(-1.26963 + 0.622922i) q^{2} +(-2.02333 + 1.47003i) q^{3} +(1.22394 - 1.58177i) q^{4} +(-0.495683 - 1.52556i) q^{5} +(1.65317 - 3.12678i) q^{6} +(-0.564533 + 2.58482i) q^{7} +(-0.568632 + 2.77068i) q^{8} +(1.00581 - 3.09555i) q^{9} +(1.57964 + 1.62812i) q^{10} +(1.70727 - 2.84345i) q^{11} +(-0.151174 + 4.99966i) q^{12} +(-4.34191 - 1.41077i) q^{13} +(-0.893394 - 3.63343i) q^{14} +(3.24555 + 2.35803i) q^{15} +(-1.00396 - 3.87196i) q^{16} +(-0.650077 - 2.00073i) q^{17} +(0.651284 + 4.55675i) q^{18} +(0.636161 + 0.875600i) q^{19} +(-3.01975 - 1.08313i) q^{20} +(-2.65754 - 6.05982i) q^{21} +(-0.396355 + 4.67364i) q^{22} +7.56410 q^{23} +(-2.92246 - 6.44190i) q^{24} +(1.96347 - 1.42654i) q^{25} +(6.39143 - 0.913510i) q^{26} +(0.196963 + 0.606190i) q^{27} +(3.39763 + 4.05661i) q^{28} +(2.35819 + 1.71333i) q^{29} +(-5.58952 - 0.972106i) q^{30} +(2.42778 + 0.788833i) q^{31} +(3.68659 + 4.29057i) q^{32} +(0.725607 + 8.26298i) q^{33} +(2.07166 + 2.13525i) q^{34} +(4.22312 - 0.420026i) q^{35} +(-3.66539 - 5.37970i) q^{36} +(-2.00580 + 2.76074i) q^{37} +(-1.35312 - 0.715412i) q^{38} +(10.8590 - 3.52830i) q^{39} +(4.50868 - 0.505899i) q^{40} +(-5.22121 + 3.79343i) q^{41} +(7.14890 + 6.03831i) q^{42} -5.83924 q^{43} +(-2.40809 - 6.18070i) q^{44} -5.22100 q^{45} +(-9.60363 + 4.71185i) q^{46} +(7.19745 + 9.90643i) q^{47} +(7.72326 + 6.35838i) q^{48} +(-6.36261 - 2.91843i) q^{49} +(-1.60426 + 3.03427i) q^{50} +(4.25646 + 3.09250i) q^{51} +(-7.54573 + 5.14119i) q^{52} +(10.0978 + 3.28097i) q^{53} +(-0.627680 - 0.646946i) q^{54} +(-5.18411 - 1.19508i) q^{55} +(-6.84070 - 3.03395i) q^{56} +(-2.57432 - 0.836448i) q^{57} +(-4.06131 - 0.706326i) q^{58} +(6.16326 + 4.47787i) q^{59} +(7.70219 - 2.24762i) q^{60} +(12.1031 - 3.93254i) q^{61} +(-3.57377 + 0.510789i) q^{62} +(7.43364 + 4.34737i) q^{63} +(-7.35332 - 3.15099i) q^{64} +7.32312i q^{65} +(-6.06845 - 10.0390i) q^{66} +8.54696i q^{67} +(-3.96034 - 1.42050i) q^{68} +(-15.3047 + 11.1195i) q^{69} +(-5.10017 + 3.16395i) q^{70} +(-0.165084 - 0.508077i) q^{71} +(8.00484 + 4.54699i) q^{72} +(-4.44244 - 3.22762i) q^{73} +(0.826897 - 4.75458i) q^{74} +(-1.87567 + 5.77273i) q^{75} +(2.16361 + 0.0654211i) q^{76} +(6.38601 + 6.01821i) q^{77} +(-11.5891 + 11.2440i) q^{78} +(1.17593 + 0.382081i) q^{79} +(-5.40924 + 3.45087i) q^{80} +(6.61006 + 4.80249i) q^{81} +(4.26601 - 8.06867i) q^{82} +(-0.508852 + 0.165336i) q^{83} +(-12.8379 - 3.21323i) q^{84} +(-2.73000 + 1.98346i) q^{85} +(7.41369 - 3.63739i) q^{86} -7.29005 q^{87} +(6.90749 + 6.34717i) q^{88} -16.8480i q^{89} +(6.62875 - 3.25227i) q^{90} +(6.09774 - 10.4266i) q^{91} +(9.25797 - 11.9646i) q^{92} +(-6.07181 + 1.97285i) q^{93} +(-15.3091 - 8.09408i) q^{94} +(1.02044 - 1.40452i) q^{95} +(-13.7665 - 3.26182i) q^{96} +(16.6489 + 5.40957i) q^{97} +(9.89613 - 0.258071i) q^{98} +(-7.08488 - 8.14490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Introduction

L-functions

Modular forms

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