LMFDB - Embedded newform 605.2.j.f.124.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.6879707136000000000000.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 $ x^16 - 4x^14 + 15x^12 - 56x^10 + 209x^8 - 56x^6 + 15x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.4
Root			$-1.83730 + 0.596975i$ of defining polynomial
Character	$\chi$	$=$	605.124
Dual form			605.2.j.f.444.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13551 + 1.56290i) q^{2} +(0.492303 - 0.159959i) q^{3} +(-0.535233 + 1.64728i) q^{4} +(0.570005 + 2.16220i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.852694 - 0.277057i) q^{7} +(0.492303 - 0.159959i) q^{8} +(-2.21028 + 1.60586i) q^{9} +O(q^{10})$	\(q+(1.13551 + 1.56290i) q^{2} +(0.492303 - 0.159959i) q^{3} +(-0.535233 + 1.64728i) q^{4} +(0.570005 + 2.16220i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.852694 - 0.277057i) q^{7} +(0.492303 - 0.159959i) q^{8} +(-2.21028 + 1.60586i) q^{9} +(-2.73205 + 3.34607i) q^{10} +0.896575i q^{12} +(2.49376 + 3.43237i) q^{13} +(-0.535233 - 1.64728i) q^{14} +(0.626478 + 0.973279i) q^{15} +(3.61153 + 2.62393i) q^{16} +(-0.608520 + 0.837556i) q^{17} +(-5.01960 - 1.63097i) q^{18} +(-1.91472 - 5.89289i) q^{19} +(-3.86682 - 0.218323i) q^{20} -0.464102 q^{21} +6.31319i q^{23} +(0.216775 - 0.157497i) q^{24} +(-4.35019 + 2.46492i) q^{25} +(-2.53275 + 7.79500i) q^{26} +(-1.74403 + 2.40046i) q^{27} +(0.912780 - 1.25633i) q^{28} +(2.14093 - 6.58911i) q^{29} +(-0.809764 + 2.08429i) q^{30} +(4.26186 - 3.09642i) q^{31} +7.58871i q^{32} -2.00000 q^{34} +(0.113012 - 2.00162i) q^{35} +(-1.46228 - 4.50045i) q^{36} +(6.36459 + 2.06798i) q^{37} +(7.03582 - 9.68397i) q^{38} +(1.77672 + 1.29087i) q^{39} +(0.626478 + 0.973279i) q^{40} +(-0.535233 - 1.64728i) q^{41} +(-0.526994 - 0.725345i) q^{42} -10.6945i q^{43} +(-4.73205 - 3.86370i) q^{45} +(-9.86689 + 7.16872i) q^{46} +(-3.90308 + 1.26819i) q^{47} +(2.19769 + 0.714073i) q^{48} +(-5.01279 - 3.64201i) q^{49} +(-8.79213 - 3.99996i) q^{50} +(-0.165602 + 0.509670i) q^{51} +(-6.98881 + 2.27080i) q^{52} +(7.03582 + 9.68397i) q^{53} -5.73205 q^{54} -0.464102 q^{56} +(-1.88524 - 2.59481i) q^{57} +(12.7292 - 4.13596i) q^{58} +(1.46228 - 4.50045i) q^{59} +(-1.93857 + 0.511052i) q^{60} +(6.68891 + 4.85978i) q^{61} +(9.67880 + 3.14483i) q^{62} +(2.32960 - 0.756934i) q^{63} +(-4.63733 + 3.36921i) q^{64} +(-6.00000 + 7.34847i) q^{65} -14.9372i q^{67} +(-1.05399 - 1.45069i) q^{68} +(1.00985 + 3.10800i) q^{69} +(3.25665 - 2.09624i) q^{70} +(-1.77672 - 1.29087i) q^{71} +(-0.831254 + 1.14412i) q^{72} +(-4.65921 - 1.51387i) q^{73} +(3.99503 + 12.2955i) q^{74} +(-1.74732 + 1.90934i) q^{75} +10.7321 q^{76} +4.24264i q^{78} +(-4.42055 + 3.21172i) q^{79} +(-3.61487 + 9.30450i) q^{80} +(2.05813 - 6.33428i) q^{81} +(1.96677 - 2.70702i) q^{82} +(5.81878 - 8.00886i) q^{83} +(0.248403 - 0.764504i) q^{84} +(-2.15782 - 0.838329i) q^{85} +(16.7145 - 12.1438i) q^{86} -3.58630i q^{87} +6.46410 q^{89} +(0.665276 - 11.7830i) q^{90} +(-1.17545 - 3.61767i) q^{91} +(-10.3996 - 3.37903i) q^{92} +(1.60283 - 2.20610i) q^{93} +(-6.41405 - 4.66008i) q^{94} +(11.6502 - 7.49897i) q^{95} +(1.21388 + 3.73594i) q^{96} +(-0.385786 - 0.530989i) q^{97} -11.9700i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^6 - 4 * q^9	$ 16 q + 4 q^{6} - 4 q^{9} - 16 q^{10} - 4 q^{15} + 4 q^{16} + 4 q^{19} - 12 q^{20} + 48 q^{21} + 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} + 12 q^{35} + 12 q^{36} - 12 q^{39} - 4 q^{40} - 48 q^{45} - 28 q^{46} - 4 q^{49} - 24 q^{50} + 16 q^{51} - 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} + 40 q^{61} - 16 q^{64} - 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} - 24 q^{74} - 24 q^{75} + 144 q^{76} - 8 q^{79} - 24 q^{80} + 8 q^{81} - 24 q^{84} - 8 q^{85} + 48 q^{86} + 48 q^{89} + 16 q^{90} + 36 q^{91} - 4 q^{94} - 36 q^{95} + 12 q^{96}+O(q^{100}) $ 16 * q + 4 * q^6 - 4 * q^9 - 16 * q^10 - 4 * q^15 + 4 * q^16 + 4 * q^19 - 12 * q^20 + 48 * q^21 + 8 * q^24 - 4 * q^25 + 12 * q^26 + 28 * q^31 - 32 * q^34 + 12 * q^35 + 12 * q^36 - 12 * q^39 - 4 * q^40 - 48 * q^45 - 28 * q^46 - 4 * q^49 - 24 * q^50 + 16 * q^51 - 64 * q^54 + 48 * q^56 - 12 * q^59 - 12 * q^60 + 40 * q^61 - 16 * q^64 - 96 * q^65 - 20 * q^69 - 12 * q^70 + 12 * q^71 - 24 * q^74 - 24 * q^75 + 144 * q^76 - 8 * q^79 - 24 * q^80 + 8 * q^81 - 24 * q^84 - 8 * q^85 + 48 * q^86 + 48 * q^89 + 16 * q^90 + 36 * q^91 - 4 * q^94 - 36 * q^95 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.13551	+	1.56290i	0.802930	+	1.10514i	0.992376	+	0.123247i	$0.0393307\pi$
$2$	1.13551	+	1.56290i	0.802930	+	1.10514i	−0.189446	+	0.981891i	$0.560669\pi$
$3$	0.492303	−	0.159959i	0.284231	−	0.0923524i	−0.163432	−	0.986555i	$-0.552256\pi$
$3$	0.492303	−	0.159959i	0.284231	−	0.0923524i	0.447663	+	0.894202i	$0.352256\pi$
$4$	−0.535233	+	1.64728i	−0.267617	+	0.823639i
$5$	0.570005	+	2.16220i	0.254914	+	0.966964i
$5$	0.570005	+	2.16220i	0.254914	+	0.966964i
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	−0.852694	−	0.277057i	−0.322288	−	0.104718i	0.143405	−	0.989664i	$-0.454195\pi$
$7$	−0.852694	−	0.277057i	−0.322288	−	0.104718i	−0.465693	+	0.884946i	$0.654195\pi$
$8$	0.492303	−	0.159959i	0.174055	−	0.0565540i
$9$	−2.21028	+	1.60586i	−0.736759	+	0.535286i
$10$	−2.73205	+	3.34607i	−0.863950	+	1.05812i
$11$		0			0
$11$		0			0
$12$			0.896575i			0.258819i
$13$	2.49376	+	3.43237i	0.691645	+	0.951968i	1.00000		0.000696272i	$0.000221630\pi$
$13$	2.49376	+	3.43237i	0.691645	+	0.951968i	−0.308355	+	0.951271i	$0.599778\pi$
$14$	−0.535233	−	1.64728i	−0.143047	−	0.440254i
$15$	0.626478	+	0.973279i	0.161756	+	0.251299i
$16$	3.61153	+	2.62393i	0.902884	+	0.655983i
$17$	−0.608520	+	0.837556i	−0.147588	+	0.203137i	−0.876410	−	0.481566i	$-0.840068\pi$
$17$	−0.608520	+	0.837556i	−0.147588	+	0.203137i	0.728822	+	0.684703i	$0.240068\pi$
$18$	−5.01960	−	1.63097i	−1.18313	−	0.384422i
$19$	−1.91472	−	5.89289i	−0.439266	−	1.35192i	−0.888651	−	0.458584i	$-0.848357\pi$
$19$	−1.91472	−	5.89289i	−0.439266	−	1.35192i	0.449385	−	0.893338i	$-0.351643\pi$
$20$	−3.86682	−	0.218323i	−0.864648	−	0.0488185i
$21$	−0.464102			−0.101275
$22$		0			0
$23$			6.31319i			1.31639i	0.752847	+	0.658196i	$0.228680\pi$
$23$			6.31319i			1.31639i	−0.752847	+	0.658196i	$0.771320\pi$
$24$	0.216775	−	0.157497i	0.0442491	−	0.0321489i
$25$	−4.35019	+	2.46492i	−0.870038	+	0.492985i
$26$	−2.53275	+	7.79500i	−0.496713	+	1.52873i
$27$	−1.74403	+	2.40046i	−0.335639	+	0.461968i
$28$	0.912780	−	1.25633i	0.172499	−	0.237425i
$29$	2.14093	−	6.58911i	0.397561	−	1.22357i	−0.529388	−	0.848380i	$-0.677578\pi$
$29$	2.14093	−	6.58911i	0.397561	−	1.22357i	0.926949	−	0.375188i	$-0.122422\pi$
$30$	−0.809764	+	2.08429i	−0.147842	+	0.380538i
$31$	4.26186	−	3.09642i	0.765453	−	0.556134i	−0.135125	−	0.990829i	$-0.543144\pi$
$31$	4.26186	−	3.09642i	0.765453	−	0.556134i	0.900578	+	0.434695i	$0.143144\pi$
$32$			7.58871i			1.34151i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	0.113012	−	2.00162i	0.0191026	−	0.338335i
$36$	−1.46228	−	4.50045i	−0.243714	−	0.750075i
$37$	6.36459	+	2.06798i	1.04633	+	0.339974i	0.781228	−	0.624246i	$-0.214594\pi$
$37$	6.36459	+	2.06798i	1.04633	+	0.339974i	0.265105	+	0.964220i	$0.414594\pi$
$38$	7.03582	−	9.68397i	1.14136	−	1.57095i
$39$	1.77672	+	1.29087i	0.284504	+	0.206704i
$40$	0.626478	+	0.973279i	0.0990548	+	0.153889i
$41$	−0.535233	−	1.64728i	−0.0835894	−	0.257262i	0.900523	−	0.434808i	$-0.143184\pi$
$41$	−0.535233	−	1.64728i	−0.0835894	−	0.257262i	−0.984112	+	0.177547i	$0.943184\pi$
$42$	−0.526994	−	0.725345i	−0.0813169	−	0.111923i
$43$		−	10.6945i		−	1.63090i	−0.578827	−	0.815451i	$-0.696489\pi$
$43$		−	10.6945i		−	1.63090i	0.578827	−	0.815451i	$-0.303511\pi$
$44$		0			0
$45$	−4.73205	−	3.86370i	−0.705412	−	0.575967i
$46$	−9.86689	+	7.16872i	−1.45479	+	1.05697i
$47$	−3.90308	+	1.26819i	−0.569323	+	0.184984i	−0.579512	−	0.814964i	$-0.696757\pi$
$47$	−3.90308	+	1.26819i	−0.569323	+	0.184984i	0.0101891	+	0.999948i	$0.496757\pi$
$48$	2.19769	+	0.714073i	0.317209	+	0.103068i
$49$	−5.01279	−	3.64201i	−0.716113	−	0.520287i
$50$	−8.79213	−	3.99996i	−1.24340	−	0.565680i
$51$	−0.165602	+	0.509670i	−0.0231889	+	0.0713680i
$52$	−6.98881	+	2.27080i	−0.969174	+	0.314904i
$53$	7.03582	+	9.68397i	0.966444	+	1.33020i	0.943823	+	0.330452i	$0.107201\pi$
$53$	7.03582	+	9.68397i	0.966444	+	1.33020i	0.0226209	+	0.999744i	$0.492799\pi$
$54$	−5.73205			−0.780033
$55$		0			0
$56$	−0.464102			−0.0620182
$57$	−1.88524	−	2.59481i	−0.249706	−	0.343691i
$58$	12.7292	−	4.13596i	1.67142	−	0.543079i
$59$	1.46228	−	4.50045i	0.190373	−	0.585908i	−0.809626	−	0.586946i	$-0.800330\pi$
$59$	1.46228	−	4.50045i	0.190373	−	0.585908i	0.999999	+	0.00103733i	$0.000330192\pi$
$60$	−1.93857	+	0.511052i	−0.250269	+	0.0659766i
$61$	6.68891	+	4.85978i	0.856427	+	0.622231i	0.926911	−	0.375282i	$-0.122454\pi$
$61$	6.68891	+	4.85978i	0.856427	+	0.622231i	−0.0704833	+	0.997513i	$0.522454\pi$
$62$	9.67880	+	3.14483i	1.22921	+	0.399394i
$63$	2.32960	−	0.756934i	0.293502	−	0.0953647i
$64$	−4.63733	+	3.36921i	−0.579666	+	0.421152i
$65$	−6.00000	+	7.34847i	−0.744208	+	0.911465i
$66$		0			0
$67$		−	14.9372i		−	1.82487i	−0.409226	−	0.912433i	$-0.634201\pi$
$67$		−	14.9372i		−	1.82487i	0.409226	−	0.912433i	$-0.365799\pi$
$68$	−1.05399	−	1.45069i	−0.127815	−	0.175922i
$69$	1.00985	+	3.10800i	0.121572	+	0.374160i
$70$	3.25665	−	2.09624i	0.389245	−	0.250548i
$71$	−1.77672	−	1.29087i	−0.210858	−	0.153198i	0.477344	−	0.878717i	$-0.341600\pi$
$71$	−1.77672	−	1.29087i	−0.210858	−	0.153198i	−0.688202	+	0.725519i	$0.741600\pi$
$72$	−0.831254	+	1.14412i	−0.0979642	+	0.134836i
$73$	−4.65921	−	1.51387i	−0.545319	−	0.177185i	0.0233860	−	0.999727i	$-0.492555\pi$
$73$	−4.65921	−	1.51387i	−0.545319	−	0.177185i	−0.568705	+	0.822542i	$0.692555\pi$
$74$	3.99503	+	12.2955i	0.464413	+	1.42932i
$75$	−1.74732	+	1.90934i	−0.201764	+	0.220472i
$76$	10.7321			1.23105
$77$		0			0
$78$			4.24264i			0.480384i
$79$	−4.42055	+	3.21172i	−0.497351	+	0.361347i	−0.808004	−	0.589177i	$-0.799452\pi$
$79$	−4.42055	+	3.21172i	−0.497351	+	0.361347i	0.310653	+	0.950523i	$0.399452\pi$
$80$	−3.61487	+	9.30450i	−0.404155	+	1.04027i
$81$	2.05813	−	6.33428i	0.228681	−	0.703809i
$82$	1.96677	−	2.70702i	0.217193	−	0.298941i
$83$	5.81878	−	8.00886i	0.638694	−	0.879087i	−0.359851	−	0.933010i	$-0.617173\pi$
$83$	5.81878	−	8.00886i	0.638694	−	0.879087i	0.998545	+	0.0539231i	$0.0171726\pi$
$84$	0.248403	−	0.764504i	0.0271029	−	0.0834143i
$85$	−2.15782	−	0.838329i	−0.234048	−	0.0909296i
$86$	16.7145	−	12.1438i	1.80237	−	1.30950i
$87$		−	3.58630i		−	0.384492i
$88$		0			0
$89$	6.46410			0.685193			0.342597	−	0.939483i	$-0.388694\pi$
$89$	6.46410			0.685193			0.342597	+	0.939483i	$0.388694\pi$
$90$	0.665276	−	11.7830i	0.0701262	−	1.24204i
$91$	−1.17545	−	3.61767i	−0.123221	−	0.379235i
$92$	−10.3996	−	3.37903i	−1.08423	−	0.352288i
$93$	1.60283	−	2.20610i	0.166205	−	0.228762i
$94$	−6.41405	−	4.66008i	−0.661559	−	0.480651i
$95$	11.6502	−	7.49897i	1.19528	−	0.769378i
$96$	1.21388	+	3.73594i	0.123891	+	0.381298i
$97$	−0.385786	−	0.530989i	−0.0391707	−	0.0539138i	0.788982	−	0.614416i	$-0.210608\pi$
$97$	−0.385786	−	0.530989i	−0.0391707	−	0.0539138i	−0.828153	+	0.560502i	$0.810608\pi$
$98$		−	11.9700i		−	1.20916i
$99$		0			0
$100$	−1.73205	−	8.48528i	−0.173205	−	0.848528i
$101$	1.12640	−	0.818376i	0.112081	−	0.0814315i	−0.530333	−	0.847789i	$-0.677933\pi$
$101$	1.12640	−	0.818376i	0.112081	−	0.0814315i	0.642414	+	0.766358i	$0.277933\pi$
$102$	−0.984606	+	0.319918i	−0.0974905	+	0.0316766i
$103$	−4.03499	−	1.31105i	−0.397579	−	0.129181i	0.103401	−	0.994640i	$-0.467027\pi$
$103$	−4.03499	−	1.31105i	−0.397579	−	0.129181i	−0.500981	+	0.865458i	$0.667027\pi$
$104$	1.77672	+	1.29087i	0.174222	+	0.126580i
$105$	−0.264540	−	1.00348i	−0.0258165	−	0.0979295i
$106$	−7.14582	+	21.9926i	−0.694063	+	2.13611i
$107$	4.16690	−	1.35391i	0.402830	−	0.130887i	−0.100593	−	0.994928i	$-0.532074\pi$
$107$	4.16690	−	1.35391i	0.402830	−	0.130887i	0.503423	+	0.864040i	$0.332074\pi$
$108$	−3.02076	−	4.15771i	−0.290672	−	0.400076i
$109$	1.19615			0.114571			0.0572853	−	0.998358i	$-0.481756\pi$
$109$	1.19615			0.114571			0.0572853	+	0.998358i	$0.481756\pi$
$110$		0			0
$111$	3.46410			0.328798
$112$	−2.35255	−	3.23801i	−0.222295	−	0.305963i
$113$	2.68999	−	0.874032i	0.253053	−	0.0822220i	−0.179743	−	0.983714i	$-0.557527\pi$
$113$	2.68999	−	0.874032i	0.253053	−	0.0822220i	0.432797	+	0.901492i	$0.357527\pi$
$114$	1.91472	−	5.89289i	0.179330	−	0.551920i
$115$	−13.6504	+	3.59855i	−1.27290	+	0.335566i
$116$	9.70820	+	7.05342i	0.901384	+	0.654894i
$117$	−11.0238	−	3.58185i	−1.01915	−	0.331142i
$118$	8.69420	−	2.82492i	0.800366	−	0.260055i
$119$	0.750932	−	0.545584i	0.0688378	−	0.0500136i
$120$	0.464102	+	0.378937i	0.0423665	+	0.0345921i
$121$		0			0
$122$			15.9725i			1.44608i
$123$	−0.526994	−	0.725345i	−0.0475174	−	0.0654021i
$124$	2.81958	+	8.67778i	0.253206	+	0.779287i
$125$	−7.80928	−	8.00095i	−0.698483	−	0.715626i
$126$	3.82831	+	2.78143i	0.341053	+	0.247789i
$127$	−1.96677	+	2.70702i	−0.174522	+	0.240210i	−0.887313	−	0.461167i	$-0.847431\pi$
$127$	−1.96677	+	2.70702i	−0.174522	+	0.240210i	0.712791	+	0.701377i	$0.247431\pi$
$128$	3.90308	+	1.26819i	0.344987	+	0.112093i
$129$	−1.71069	−	5.26495i	−0.150618	−	0.463553i
$130$	−18.2980	−	1.03312i	−1.60484	−	0.0906103i
$131$	21.1244			1.84564			0.922822	−	0.385227i	$-0.125877\pi$
$131$	21.1244			1.84564			0.922822	+	0.385227i	$0.125877\pi$
$132$		0			0
$133$			5.55532i			0.481707i
$134$	23.3453	−	16.9614i	2.01673	−	1.46524i
$135$	−6.18437	−	2.40267i	−0.532266	−	0.206789i
$136$	−0.165602	+	0.509670i	−0.0142002	+	0.0437038i
$137$	−8.08980	+	11.1347i	−0.691159	+	0.951298i	0.308841	+	0.951114i	$0.400059\pi$
$137$	−8.08980	+	11.1347i	−0.691159	+	0.951298i	−1.00000		0.000184728i	$0.999941\pi$
$138$	−3.71080	+	5.10748i	−0.315884	+	0.434778i
$139$	−5.12612	+	15.7766i	−0.434791	+	1.33815i	0.458509	+	0.888690i	$0.348384\pi$
$139$	−5.12612	+	15.7766i	−0.434791	+	1.33815i	−0.893300	+	0.449461i	$0.851616\pi$
$140$	3.23673	+	1.25749i	0.273554	+	0.106278i
$141$	−1.71864	+	1.24866i	−0.144736	+	0.105157i
$142$		−	4.24264i		−	0.356034i
$143$		0			0
$144$	−12.1962			−1.01635
$145$	15.4673	+	0.873292i	1.28449	+	0.0725230i
$146$	−2.92457	−	9.00090i	−0.242039	−	0.744919i
$147$	−3.05038	−	0.991130i	−0.251592	−	0.0817470i
$148$	−6.81308	+	9.37740i	−0.560032	+	0.770818i
$149$	−11.1095	−	8.07150i	−0.910123	−	0.661243i	0.0309232	−	0.999522i	$-0.490155\pi$
$149$	−11.1095	−	8.07150i	−0.910123	−	0.661243i	−0.941046	+	0.338279i	$0.890155\pi$
$150$	−4.96822	−	0.562811i	−0.405654	−	0.0459534i
$151$	−1.91472	−	5.89289i	−0.155817	−	0.479557i	0.842425	−	0.538813i	$-0.181127\pi$
$151$	−1.91472	−	5.89289i	−0.155817	−	0.479557i	−0.998243	+	0.0592563i	$0.981127\pi$
$152$	−1.88524	−	2.59481i	−0.152913	−	0.210467i
$153$		−	2.82843i		−	0.228665i
$154$		0			0
$155$	9.12436	+	7.45001i	0.732886	+	0.598399i
$156$	−3.07738	+	2.23585i	−0.246387	+	0.179011i
$157$	11.4808	−	3.73032i	0.916264	−	0.297712i	0.187331	−	0.982297i	$-0.440016\pi$
$157$	11.4808	−	3.73032i	0.916264	−	0.297712i	0.728933	+	0.684585i	$0.240016\pi$
$158$	−10.0392	−	3.26193i	−0.798675	−	0.259505i
$159$	5.01279	+	3.64201i	0.397540	+	0.288830i
$160$	−16.4083	+	4.32560i	−1.29719	+	0.341969i
$161$	1.74911	−	5.38322i	0.137850	−	0.424257i
$162$	12.2369	−	3.97601i	0.961421	−	0.312384i
$163$	−4.46053	−	6.13939i	−0.349376	−	0.480874i	0.597775	−	0.801664i	$-0.296052\pi$
$163$	−4.46053	−	6.13939i	−0.349376	−	0.480874i	−0.947150	+	0.320790i	$0.896052\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	19.1244			1.48434
$167$	1.13551	+	1.56290i	0.0878687	+	0.120941i	0.850688	−	0.525671i	$-0.176186\pi$
$167$	1.13551	+	1.56290i	0.0878687	+	0.120941i	−0.762820	+	0.646611i	$0.776186\pi$
$168$	−0.228479	+	0.0742372i	−0.0176275	+	0.00572753i
$169$	−1.54508	+	4.75528i	−0.118853	+	0.365791i
$170$	−1.14001	−	4.32439i	−0.0874347	−	0.331666i
$171$	13.6952	+	9.95015i	1.04730	+	0.760907i
$172$	17.6169	+	5.72407i	1.34327	+	0.436456i
$173$	−7.25263	+	2.35652i	−0.551408	+	0.179163i	−0.571451	−	0.820636i	$-0.693619\pi$
$173$	−7.25263	+	2.35652i	−0.551408	+	0.179163i	0.0200438	+	0.999799i	$0.493619\pi$
$174$	5.60503	−	4.07230i	0.424917	−	0.308720i
$175$	4.39230	−	0.896575i	0.332027	−	0.0677747i
$176$		0			0
$177$		−	2.44949i		−	0.184115i
$178$	7.34008	+	10.1027i	0.550162	+	0.757233i
$179$	2.63774	+	8.11812i	0.197154	+	0.606777i	0.999945	+	0.0105163i	$0.00334750\pi$
$179$	2.63774	+	8.11812i	0.197154	+	0.606777i	−0.802791	+	0.596261i	$0.796652\pi$
$180$	8.89734	−	5.72702i	0.663169	−	0.426867i
$181$	−2.74443	−	1.99395i	−0.203992	−	0.148209i	0.481099	−	0.876666i	$-0.340238\pi$
$181$	−2.74443	−	1.99395i	−0.203992	−	0.148209i	−0.685091	+	0.728457i	$0.740238\pi$
$182$	4.31932	−	5.94504i	0.320169	−	0.440675i
$183$	4.07034	+	1.32253i	0.300888	+	0.0977644i
$184$	1.00985	+	3.10800i	0.0744473	+	0.229125i
$185$	−0.843536	+	14.9403i	−0.0620180	+	1.09843i
$186$	5.26795			0.386265
$187$		0			0
$188$		−	7.10823i		−	0.518421i
$189$	2.15219	−	1.56366i	0.156549	−	0.113739i
$190$	24.9491	+	9.69291i	1.81000	+	0.703198i
$191$	−3.31639	+	10.2068i	−0.239965	+	0.738537i	0.756459	+	0.654042i	$0.226928\pi$
$191$	−3.31639	+	10.2068i	−0.239965	+	0.738537i	−0.996424	+	0.0844956i	$0.973072\pi$
$192$	−1.74403	+	2.40046i	−0.125865	+	0.173238i
$193$	−6.04151	+	8.31543i	−0.434877	+	0.598557i	−0.969064	−	0.246809i	$-0.920618\pi$
$193$	−6.04151	+	8.31543i	−0.434877	+	0.598557i	0.534187	+	0.845367i	$0.320618\pi$
$194$	0.391818	−	1.20589i	0.0281309	−	0.0865780i
$195$	−1.77836	+	4.57743i	−0.127351	+	0.327796i
$196$	8.68241	−	6.30814i	0.620172	−	0.450582i
$197$			2.55103i			0.181753i	0.995862	+	0.0908765i	$0.0289669\pi$
$197$			2.55103i			0.181753i	−0.995862	+	0.0908765i	$0.971033\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	−1.74732	+	1.90934i	−0.123555	+	0.135011i
$201$	−2.38934	−	7.35362i	−0.168531	−	0.518684i
$202$	2.55808	+	0.831171i	0.179986	+	0.0584810i
$203$	−3.65112	+	5.02534i	−0.256258	+	0.352709i
$204$	−0.750932	−	0.545584i	−0.0525758	−	0.0381985i
$205$	3.25665	−	2.09624i	0.227455	−	0.146407i
$206$	−2.53275	−	7.79500i	−0.176465	−	0.543104i
$207$	−10.1381	−	13.9539i	−0.704647	−	0.969863i
$208$			18.9396i			1.31322i
$209$		0			0
$210$	1.26795	−	1.55291i	0.0874968	−	0.107161i
$211$	−8.99979	+	6.53873i	−0.619571	+	0.450145i	−0.852772	−	0.522284i	$-0.825080\pi$
$211$	−8.99979	+	6.53873i	−0.619571	+	0.450145i	0.233200	+	0.972429i	$0.425080\pi$
$212$	−19.7180	+	6.40677i	−1.35424	+	0.440018i
$213$	−1.08117	−	0.351294i	−0.0740807	−	0.0240703i
$214$	6.84760	+	4.97507i	0.468092	+	0.340089i
$215$	23.1237	−	6.09593i	1.57702	−	0.415739i
$216$	−0.474619	+	1.46073i	−0.0322937	+	0.0993898i
$217$	−4.49195	+	1.45952i	−0.304933	+	0.0990788i
$218$	1.35825	+	1.86947i	0.0919921	+	0.126616i
$219$	−2.53590			−0.171360
$220$		0			0
$221$	−4.39230			−0.295458
$222$	3.93354	+	5.41405i	0.264002	+	0.363367i
$223$	−5.51190	+	1.79092i	−0.369104	+	0.119929i	−0.487695	−	0.873014i	$-0.662162\pi$
$223$	−5.51190	+	1.79092i	−0.369104	+	0.119929i	0.118591	+	0.992943i	$0.462162\pi$
$224$	2.10250	−	6.47084i	0.140479	−	0.432351i
$225$	5.65680	−	12.4340i	0.377120	−	0.828930i
$226$	4.42055	+	3.21172i	0.294051	+	0.213640i
$227$	−20.4741	−	6.65245i	−1.35892	−	0.441538i	−0.463235	−	0.886236i	$-0.653311\pi$
$227$	−20.4741	−	6.65245i	−1.35892	−	0.441538i	−0.895681	+	0.444697i	$0.853311\pi$
$228$	5.28342	−	1.71669i	0.349903	−	0.113690i
$229$	−14.5042	+	10.5379i	−0.958466	+	0.696366i	−0.952794	−	0.303618i	$-0.901805\pi$
$229$	−14.5042	+	10.5379i	−0.958466	+	0.696366i	−0.00567196	+	0.999984i	$0.501805\pi$
$230$	−21.1244	−	17.2480i	−1.39290	−	1.13730i
$231$		0			0
$232$		−	3.58630i		−	0.235452i
$233$	−7.64434	−	10.5215i	−0.500797	−	0.689288i	0.481536	−	0.876426i	$-0.340079\pi$
$233$	−7.64434	−	10.5215i	−0.500797	−	0.689288i	−0.982334	+	0.187138i	$0.940079\pi$
$234$	−6.91960	−	21.2963i	−0.452349	−	1.39219i
$235$	−4.96684	−	7.71635i	−0.324001	−	0.503359i
$236$	6.63083	+	4.81758i	0.431630	+	0.313598i
$237$	−1.66251	+	2.28825i	−0.107991	+	0.148638i
$238$	1.70539	+	0.554114i	0.110544	+	0.0359179i
$239$	3.60322	+	11.0896i	0.233073	+	0.717324i	0.997371	+	0.0724614i	$0.0230854\pi$
$239$	3.60322	+	11.0896i	0.233073	+	0.717324i	−0.764299	+	0.644863i	$0.776915\pi$
$240$	−0.291272	+	5.15887i	−0.0188016	+	0.333003i
$241$	−10.1244			−0.652167			−0.326084	−	0.945341i	$-0.605729\pi$
$241$	−10.1244			−0.652167			−0.326084	+	0.945341i	$0.605729\pi$
$242$		0			0
$243$		−	12.3490i		−	0.792188i
$244$	−11.5855	+	8.41738i	−0.741688	+	0.538868i
$245$	5.01742	−	12.9146i	0.320551	−	0.825084i
$246$	0.535233	−	1.64728i	0.0341252	−	0.105027i
$247$	15.4517	−	21.2675i	0.983170	−	1.35322i
$248$	1.60283	−	2.20610i	0.101780	−	0.140088i
$249$	1.58351	−	4.87355i	0.100351	−	0.308849i
$250$	3.63714	−	21.2903i	0.230033	−	1.34652i
$251$	11.4849	−	8.34429i	0.724922	−	0.526687i	−0.163031	−	0.986621i	$-0.552127\pi$
$251$	11.4849	−	8.34429i	0.724922	−	0.526687i	0.887953	+	0.459934i	$0.152127\pi$
$252$			4.24264i			0.267261i
$253$		0			0
$254$	−6.46410			−0.405594
$255$	−1.19640	−	0.0675494i	−0.0749215	−	0.00423011i
$256$	5.99255	+	18.4432i	0.374534	+	1.15270i
$257$	4.75577	+	1.54524i	0.296657	+	0.0963897i	0.453564	−	0.891224i	$-0.350152\pi$
$257$	4.75577	+	1.54524i	0.296657	+	0.0963897i	−0.156907	+	0.987613i	$0.550152\pi$
$258$	6.28609	−	8.65206i	0.391355	−	0.538654i
$259$	−4.85410	−	3.52671i	−0.301619	−	0.219139i
$260$	−8.89357	−	13.8168i	−0.551556	−	0.856882i
$261$	5.84914	+	18.0018i	0.362052	+	1.11428i
$262$	23.9870	+	33.0153i	1.48192	+	2.03969i
$263$			21.4906i			1.32517i	0.748988	+	0.662584i	$0.230540\pi$
$263$			21.4906i			1.32517i	−0.748988	+	0.662584i	$0.769460\pi$
$264$		0			0
$265$	−16.9282	+	20.7327i	−1.03989	+	1.27360i
$266$	−8.68241	+	6.30814i	−0.532353	+	0.386777i
$267$	3.18230	−	1.03399i	0.194753	−	0.0632792i
$268$	24.6057	+	7.99487i	1.50303	+	0.488364i
$269$	−15.9636	−	11.5982i	−0.973316	−	0.707155i	−0.0171109	−	0.999854i	$-0.505447\pi$
$269$	−15.9636	−	11.5982i	−0.973316	−	0.707155i	−0.956205	+	0.292698i	$0.905447\pi$
$270$	−3.26730	−	12.3938i	−0.198841	−	0.754264i
$271$	1.40167	−	4.31390i	0.0851454	−	0.262051i	−0.899415	−	0.437096i	$-0.856007\pi$
$271$	1.40167	−	4.31390i	0.0851454	−	0.262051i	0.984560	+	0.175045i	$0.0560071\pi$
$272$	−4.39538	+	1.42815i	−0.266509	+	0.0865941i
$273$	−1.15736	−	1.59297i	−0.0700465	−	0.0964108i
$274$	−26.5885			−1.60627
$275$		0			0
$276$	−5.66025			−0.340707
$277$	−13.3438	−	18.3661i	−0.801748	−	1.10351i	−0.992545	−	0.121882i	$-0.961107\pi$
$277$	−13.3438	−	18.3661i	−0.801748	−	1.10351i	0.190796	−	0.981630i	$-0.438893\pi$
$278$	−30.4780	+	9.90289i	−1.82795	+	0.593936i
$279$	−4.44747	+	13.6879i	−0.266263	+	0.819473i
$280$	−0.264540	−	1.00348i	−0.0158093	−	0.0599693i
$281$	−14.0126	−	10.1807i	−0.835921	−	0.607332i	0.0853074	−	0.996355i	$-0.472813\pi$
$281$	−14.0126	−	10.1807i	−0.835921	−	0.607332i	−0.921228	+	0.389023i	$0.872813\pi$
$282$	−3.90308	−	1.26819i	−0.232425	−	0.0755194i
$283$	−28.6407	+	9.30592i	−1.70251	+	0.553179i	−0.989059	−	0.147524i	$-0.952870\pi$
$283$	−28.6407	+	9.30592i	−1.70251	+	0.553179i	−0.713453	+	0.700703i	$0.752870\pi$
$284$	3.07738	−	2.23585i	0.182609	−	0.132673i
$285$	4.53590	−	5.55532i	0.268683	−	0.329069i
$286$		0			0
$287$			1.55291i			0.0916656i
$288$	−12.1864	−	16.7731i	−0.718090	−	0.988366i
$289$	4.92209	+	15.1486i	0.289534	+	0.891095i
$290$	16.1985	+	25.1655i	0.951207	+	1.47777i
$291$	−0.274860	−	0.199698i	−0.0161126	−	0.0117065i
$292$	4.98752	−	6.86474i	0.291873	−	0.401728i
$293$	8.95802	+	2.91064i	0.523333	+	0.170041i	0.558757	−	0.829331i	$-0.311278\pi$
$293$	8.95802	+	2.91064i	0.523333	+	0.170041i	−0.0354243	+	0.999372i	$0.511278\pi$
$294$	−1.91472	−	5.89289i	−0.111669	−	0.343680i
$295$	10.5644	+	0.596470i	0.615081	+	0.0347278i
$296$	3.46410			0.201347
$297$		0			0
$298$		−	26.5283i		−	1.53674i
$299$	−21.6692	+	15.7436i	−1.25316	+	0.910476i
$300$	−2.20999	−	3.90027i	−0.127594	−	0.225182i
$301$	−2.96300	+	9.11916i	−0.170784	+	0.525620i
$302$	7.03582	−	9.68397i	0.404866	−	0.557250i
$303$	0.423623	−	0.583067i	0.0243365	−	0.0334963i
$304$	8.54749	−	26.3065i	0.490232	−	1.50878i
$305$	−6.69509	+	17.2328i	−0.383360	+	0.986749i
$306$	4.42055	−	3.21172i	0.252706	−	0.183602i
$307$		−	17.6269i		−	1.00602i	−0.864280	−	0.503010i	$-0.832226\pi$
$307$		−	17.6269i		−	1.00602i	0.864280	−	0.503010i	$-0.167774\pi$
$308$		0			0
$309$	−2.19615			−0.124935
$310$	−1.28279	+	22.7200i	−0.0728574	+	1.29041i
$311$	−8.66872	−	26.6796i	−0.491558	−	1.51286i	−0.822253	−	0.569122i	$-0.807283\pi$
$311$	−8.66872	−	26.6796i	−0.491558	−	1.51286i	0.330695	−	0.943738i	$-0.392717\pi$
$312$	1.08117	+	0.351294i	0.0612093	+	0.0198881i
$313$	−10.0784	+	13.8718i	−0.569666	+	0.784078i	−0.992515	−	0.122122i	$-0.961030\pi$
$313$	−10.0784	+	13.8718i	−0.569666	+	0.784078i	0.422849	+	0.906200i	$0.361030\pi$
$314$	18.8667	+	13.7075i	1.06471	+	0.773556i
$315$	2.96452	+	4.60560i	0.167032	+	0.259496i
$316$	−2.92457	−	9.00090i	−0.164520	−	0.506340i
$317$	−4.09659	−	5.63847i	−0.230087	−	0.316688i	0.678326	−	0.734761i	$-0.262706\pi$
$317$	−4.09659	−	5.63847i	−0.230087	−	0.316688i	−0.908413	+	0.418073i	$0.862706\pi$
$318$			11.9700i			0.671247i
$319$		0			0
$320$	−9.92820	−	8.10634i	−0.555003	−	0.453158i
$321$	1.83481	−	1.33307i	0.102409	−	0.0744045i
$322$	10.3996	−	3.37903i	0.579546	−	0.188306i
$323$	6.10077	+	1.98226i	0.339456	+	0.110296i
$324$	9.33274	+	6.78063i	0.518485	+	0.376702i
$325$	−19.3089	−	8.78452i	−1.07106	−	0.487277i
$326$	4.53027	−	13.9427i	0.250908	−	0.772216i
$327$	0.588870	−	0.191335i	0.0325646	−	0.0105809i
$328$	−0.526994	−	0.725345i	−0.0290984	−	0.0400505i
$329$	3.67949			0.202857
$330$		0			0
$331$	−7.80385			−0.428938			−0.214469	−	0.976731i	$-0.568802\pi$
$331$	−7.80385			−0.428938			−0.214469	+	0.976731i	$0.568802\pi$
$332$	10.0784	+	13.8718i	0.553125	+	0.761311i
$333$	−17.3884	+	5.64983i	−0.952878	+	0.309609i
$334$	−1.15327	+	3.54939i	−0.0631040	+	0.194214i
$335$	32.2971	−	8.51426i	1.76458	−	0.465184i
$336$	−1.67612	−	1.21777i	−0.0914398	−	0.0664349i
$337$	−7.44577	−	2.41928i	−0.405597	−	0.131786i	0.0991115	−	0.995076i	$-0.468400\pi$
$337$	−7.44577	−	2.41928i	−0.405597	−	0.131786i	−0.504708	+	0.863290i	$0.668400\pi$
$338$	−9.18650	+	2.98487i	−0.499680	+	0.162356i
$339$	1.18448	−	0.860577i	0.0643323	−	0.0467401i
$340$	2.53590	−	3.10583i	0.137528	−	0.168437i
$341$		0			0
$342$			32.7028i			1.76836i
$343$	6.95429	+	9.57176i	0.375496	+	0.516826i
$344$	−1.71069	−	5.26495i	−0.0922340	−	0.283867i
$345$	−6.14450	+	3.95508i	−0.330809	+	0.212934i
$346$	−11.9185	−	8.65928i	−0.640741	−	0.465526i
$347$	1.74403	−	2.40046i	0.0936246	−	0.128863i	−0.759635	−	0.650350i	$-0.774622\pi$
$347$	1.74403	−	2.40046i	0.0936246	−	0.128863i	0.853260	+	0.521487i	$0.174622\pi$
$348$	5.90764	+	1.91951i	0.316683	+	0.102896i
$349$	−8.44250	−	25.9833i	−0.451917	−	1.39086i	−0.874717	−	0.484634i	$-0.838953\pi$
$349$	−8.44250	−	25.9833i	−0.451917	−	1.39086i	0.422800	−	0.906223i	$-0.361047\pi$
$350$	6.38878	+	5.84666i	0.341495	+	0.312517i
$351$	−12.5885			−0.671922
$352$		0			0
$353$		−	1.69161i		−	0.0900356i	−0.998986	−	0.0450178i	$-0.985666\pi$
$353$		−	1.69161i		−	0.0900356i	0.998986	−	0.0450178i	$-0.0143345\pi$
$354$	3.82831	−	2.78143i	0.203472	−	0.147831i
$355$	1.77836	−	4.57743i	0.0943858	−	0.242945i
$356$	−3.45980	+	10.6482i	−0.183369	+	0.564352i
$357$	0.282415	−	0.388711i	0.0149470	−	0.0205728i
$358$	−9.69263	+	13.3408i	−0.512271	+	0.705081i
$359$	−5.66729	+	17.4421i	−0.299108	+	0.920561i	0.682702	+	0.730697i	$0.260805\pi$
$359$	−5.66729	+	17.4421i	−0.299108	+	0.920561i	−0.981810	+	0.189864i	$0.939195\pi$
$360$	−2.94764	−	1.14518i	−0.155354	−	0.0603562i
$361$	−15.6887	+	11.3985i	−0.825721	+	0.599922i
$362$		−	6.55343i		−	0.344441i
$363$		0			0
$364$	6.58846			0.345329
$365$	0.617511	−	10.9370i	0.0323220	−	0.572470i
$366$	2.55494	+	7.86329i	0.133549	+	0.411021i
$367$	28.1837	+	9.15744i	1.47118	+	0.478015i	0.931464	−	0.363834i	$-0.118532\pi$
$367$	28.1837	+	9.15744i	1.47118	+	0.478015i	0.539714	+	0.841848i	$0.318532\pi$
$368$	−16.5654	+	22.8003i	−0.863531	+	1.18855i
$369$	3.82831	+	2.78143i	0.199294	+	0.144795i
$370$	−24.3080	+	15.6465i	−1.26371	+	0.813424i
$371$	−3.31639	−	10.2068i	−0.172178	−	0.529910i
$372$	2.77618	+	3.82108i	0.143938	+	0.198114i
$373$			34.1170i			1.76651i	0.468892	+	0.883255i	$0.344653\pi$
$373$			34.1170i			1.76651i	−0.468892	+	0.883255i	$0.655347\pi$
$374$		0			0
$375$	−5.12436	−	2.68973i	−0.264621	−	0.138897i
$376$	−1.71864	+	1.24866i	−0.0886321	+	0.0643950i
$377$	27.9552	−	9.08321i	1.43977	−	0.467809i
$378$	4.88769	+	1.58811i	0.251395	+	0.0816833i
$379$	−4.42055	−	3.21172i	−0.227068	−	0.164975i	0.468434	−	0.883498i	$-0.344818\pi$
$379$	−4.42055	−	3.21172i	−0.227068	−	0.164975i	−0.695503	+	0.718523i	$0.744818\pi$
$380$	6.11732	+	23.2048i	0.313812	+	1.19038i
$381$	−0.535233	+	1.64728i	−0.0274208	+	0.0843926i
$382$	−19.7180	+	6.40677i	−1.00886	+	0.327799i
$383$	−13.9683	−	19.2257i	−0.713745	−	0.982386i	−0.999708	−	0.0241451i	$-0.992314\pi$
$383$	−13.9683	−	19.2257i	−0.713745	−	0.982386i	0.285964	−	0.958240i	$-0.407686\pi$
$384$	2.12436			0.108408
$385$		0			0
$386$	−19.8564			−1.01066
$387$	17.1739	+	23.6379i	0.872999	+	1.20158i
$388$	1.08117	−	0.351294i	0.0548882	−	0.0178343i
$389$	5.60073	−	17.2373i	0.283968	−	0.873965i	−0.702737	−	0.711449i	$-0.748039\pi$
$389$	5.60073	−	17.2373i	0.283968	−	0.873965i	0.986706	−	0.162516i	$-0.0519609\pi$
$390$	−9.17342	+	2.41832i	−0.464514	+	0.122457i
$391$	−5.28765	−	3.84170i	−0.267408	−	0.194283i
$392$	−3.05038	−	0.991130i	−0.154068	−	0.0500596i
$393$	10.3996	−	3.37903i	0.524590	−	0.170450i
$394$	−3.98700	+	2.89673i	−0.200862	+	0.145935i
$395$	−9.46410	−	7.72741i	−0.476191	−	0.388808i
$396$		0			0
$397$		−	16.0096i		−	0.803500i	−0.915749	−	0.401750i	$-0.868402\pi$
$397$		−	16.0096i		−	0.803500i	0.915749	−	0.401750i	$-0.131598\pi$
$398$	2.27103	+	3.12580i	0.113836	+	0.156682i
$399$	0.888623	+	2.73490i	0.0444868	+	0.136916i
$400$	−22.1787	−	2.51245i	−1.10893	−	0.125622i
$401$	26.1478	+	18.9975i	1.30576	+	0.948691i	0.999994	−	0.00341570i	$-0.00108725\pi$
$401$	26.1478	+	18.9975i	1.30576	+	0.948691i	0.305767	+	0.952106i	$0.401087\pi$
$402$	8.77985	−	12.0844i	0.437899	−	0.602717i
$403$	21.2561	+	6.90653i	1.05884	+	0.344039i
$404$	0.745208	+	2.29351i	0.0370755	+	0.114107i
$405$	14.8691	+	0.839518i	0.738852	+	0.0417160i
$406$	−12.0000			−0.595550
$407$		0			0
$408$			0.277401i			0.0137334i
$409$	−1.51743	+	1.10248i	−0.0750320	+	0.0545139i	−0.624669	−	0.780890i	$-0.714766\pi$
$409$	−1.51743	+	1.10248i	−0.0750320	+	0.0545139i	0.549637	+	0.835404i	$0.314766\pi$
$410$	6.97418	+	2.70952i	0.344430	+	0.133814i
$411$	−2.20155	+	6.77566i	−0.108594	+	0.334219i
$412$	4.31932	−	5.94504i	0.212798	−	0.292891i
$413$	−2.49376	+	3.43237i	−0.122710	+	0.168896i
$414$	10.2966	−	31.6897i	0.506050	−	1.55746i
$415$	20.6335	+	8.01625i	1.01286	+	0.393502i
$416$	−26.0472	+	18.9244i	−1.27707	+	0.927846i
$417$			8.58682i			0.420498i
$418$		0			0
$419$	29.6603			1.44900			0.724499	−	0.689276i	$-0.242071\pi$
$419$	29.6603			1.44900			0.724499	+	0.689276i	$0.242071\pi$
$420$	1.79460	+	0.101324i	0.0875675	+	0.00494411i
$421$	6.50560	+	20.0222i	0.317063	+	0.975821i	0.974897	+	0.222657i	$0.0714731\pi$
$421$	6.50560	+	20.0222i	0.317063	+	0.975821i	−0.657833	+	0.753164i	$0.728527\pi$
$422$	−20.4388	−	6.64096i	−0.994944	−	0.323277i
$423$	6.59035	−	9.07084i	0.320434	−	0.441039i
$424$	5.01279	+	3.64201i	0.243443	+	0.176871i
$425$	0.582665	−	5.14348i	0.0282634	−	0.249496i
$426$	−0.678648	−	2.08867i	−0.0328806	−	0.101196i
$427$	−4.35716	−	5.99711i	−0.210858	−	0.290221i
$428$			7.58871i			0.366814i
$429$		0			0
$430$	35.7846	+	29.2180i	1.72569	+	1.40902i
$431$	15.3132	−	11.1257i	0.737613	−	0.535907i	−0.154350	−	0.988016i	$-0.549328\pi$
$431$	15.3132	−	11.1257i	0.737613	−	0.535907i	0.891963	+	0.452109i	$0.149328\pi$
$432$	−12.5973	+	4.09310i	−0.606087	+	0.196930i
$433$	−19.2610	−	6.25829i	−0.925627	−	0.300754i	−0.192854	−	0.981228i	$-0.561774\pi$
$433$	−19.2610	−	6.25829i	−0.925627	−	0.300754i	−0.732773	+	0.680473i	$0.761774\pi$
$434$	−7.38176	−	5.36316i	−0.354336	−	0.257440i
$435$	7.75429	−	2.04421i	0.371790	−	0.0980123i
$436$	−0.640220	+	1.97040i	−0.0306610	+	0.0943648i
$437$	37.2030	−	12.0880i	1.77966	−	0.578246i
$438$	−2.87955	−	3.96336i	−0.137590	−	0.189377i
$439$	20.2487			0.966418			0.483209	−	0.875505i	$-0.339471\pi$
$439$	20.2487			0.966418			0.483209	+	0.875505i	$0.339471\pi$
$440$		0			0
$441$	16.9282			0.806105
$442$	−4.98752	−	6.86474i	−0.237232	−	0.326522i
$443$	−8.72954	+	2.83640i	−0.414753	+	0.134761i	−0.508958	−	0.860791i	$-0.669969\pi$
$443$	−8.72954	+	2.83640i	−0.414753	+	0.134761i	0.0942048	+	0.995553i	$0.469969\pi$
$444$	−1.85410	+	5.70634i	−0.0879918	+	0.270811i
$445$	3.68457	+	13.9767i	0.174665	+	0.662557i
$446$	−9.05788	−	6.58093i	−0.428903	−	0.311616i
$447$	−6.76033	−	2.19656i	−0.319753	−	0.103894i
$448$	4.88769	−	1.58811i	0.230921	−	0.0750309i
$449$	−8.50816	+	6.18154i	−0.401525	+	0.291725i	−0.770162	−	0.637849i	$-0.779825\pi$
$449$	−8.50816	+	6.18154i	−0.401525	+	0.291725i	0.368637	+	0.929573i	$0.379825\pi$
$450$	25.8564	−	5.27792i	1.21888	−	0.248803i
$451$		0			0
$452$			4.89898i			0.230429i
$453$	−1.88524	−	2.59481i	−0.0885764	−	0.121915i
$454$	−12.8515	−	39.5530i	−0.603153	−	1.85631i
$455$	7.15211	−	4.60365i	0.335296	−	0.215823i
$456$	−1.34317	−	0.975873i	−0.0628999	−	0.0456994i
$457$	−12.4688	+	17.1618i	−0.583266	+	0.802797i	−0.994049	−	0.108936i	$-0.965256\pi$
$457$	−12.4688	+	17.1618i	−0.583266	+	0.802797i	0.410782	+	0.911733i	$0.365256\pi$
$458$	−32.9395	−	10.7027i	−1.53916	−	0.500104i
$459$	−0.949237	−	2.92145i	−0.0443066	−	0.136362i
$460$	1.37832	−	24.4120i	0.0642643	−	1.13822i
$461$	−33.0000			−1.53696			−0.768482	−	0.639872i	$-0.778987\pi$
$461$	−33.0000			−1.53696			−0.768482	+	0.639872i	$0.778987\pi$
$462$		0			0
$463$			17.8671i			0.830356i	0.909740	+	0.415178i	$0.136281\pi$
$463$			17.8671i			0.830356i	−0.909740	+	0.415178i	$0.863719\pi$
$464$	25.0214	−	18.1791i	1.16159	−	0.843945i
$465$	5.68364	+	2.20814i	0.263573	+	0.102400i
$466$	7.76385	−	23.8947i	0.359654	−	1.10690i
$467$	−10.4424	+	14.3727i	−0.483215	+	0.665088i	−0.979119	−	0.203289i	$-0.934837\pi$
$467$	−10.4424	+	14.3727i	−0.483215	+	0.665088i	0.495904	+	0.868377i	$0.334837\pi$
$468$	11.8006	−	16.2421i	0.545483	−	0.750793i
$469$	−4.13845	+	12.7368i	−0.191096	+	0.588133i
$470$	6.41997	−	16.5247i	0.296131	−	0.762228i
$471$	5.05531	−	3.67290i	0.232937	−	0.169238i
$472$		−	2.44949i		−	0.112747i
$473$		0			0
$474$	−5.46410			−0.250974
$475$	22.8549	+	20.9156i	1.04866	+	0.959672i
$476$	0.496805	+	1.52901i	0.0227710	+	0.0700820i
$477$	−31.1022	−	10.1057i	−1.42407	−	0.462709i
$478$	−13.2404	+	18.2238i	−0.605601	+	0.833538i
$479$	7.65662	+	5.56286i	0.349840	+	0.254174i	0.748802	−	0.662794i	$-0.230629\pi$
$479$	7.65662	+	5.56286i	0.349840	+	0.254174i	−0.398962	+	0.916967i	$0.630629\pi$
$480$	−7.38593	+	4.75416i	−0.337120	+	0.216997i
$481$	8.77370	+	27.0027i	0.400047	+	1.23122i
$482$	−11.4963	−	15.8234i	−0.523644	−	0.720734i
$483$		−	2.92996i		−	0.133318i
$484$		0			0
$485$	0.928203	−	1.13681i	0.0421475	−	0.0516200i
$486$	19.3002	−	14.0224i	0.875477	−	0.636071i
$487$	−12.1050	+	3.93314i	−0.548529	+	0.178228i	−0.570153	−	0.821538i	$-0.693116\pi$
$487$	−12.1050	+	3.93314i	−0.548529	+	0.178228i	0.0216245	+	0.999766i	$0.493116\pi$
$488$	4.07034	+	1.32253i	0.184255	+	0.0598682i
$489$	−3.17798	−	2.30894i	−0.143713	−	0.104414i
$490$	25.8816	−	6.82298i	1.16921	−	0.308231i
$491$	−4.85553	+	14.9438i	−0.219127	+	0.674403i	0.779708	+	0.626143i	$0.215368\pi$
$491$	−4.85553	+	14.9438i	−0.219127	+	0.674403i	−0.998835	+	0.0482597i	$0.984632\pi$
$492$	1.47691	−	0.479877i	0.0665842	−	0.0216345i
$493$	4.21595	+	5.80276i	0.189877	+	0.261343i
$494$	50.7846			2.28491
$495$		0			0
$496$	23.5167			1.05593
$497$	1.15736	+	1.59297i	0.0519146	+	0.0714544i
$498$	9.41498	−	3.05911i	0.421895	−	0.137082i
$499$	−11.8639	+	36.5133i	−0.531100	+	1.63456i	0.220828	+	0.975313i	$0.429124\pi$
$499$	−11.8639	+	36.5133i	−0.531100	+	1.63456i	−0.751928	+	0.659245i	$0.770876\pi$
$500$	17.3596	−	8.58168i	0.776344	−	0.383785i
$501$	0.809017	+	0.587785i	0.0361442	+	0.0262603i
$502$	26.0826	+	8.47475i	1.16412	+	0.378247i
$503$	32.5791	−	10.5856i	1.45263	−	0.471988i	0.526820	−	0.849977i	$-0.323384\pi$
$503$	32.5791	−	10.5856i	1.45263	−	0.471988i	0.925810	+	0.377989i	$0.123384\pi$
$504$	1.02579	−	0.745282i	0.0456924	−	0.0331975i
$505$	2.41154	+	1.96902i	0.107312	+	0.0876201i
$506$		0			0
$507$			2.58819i			0.114946i
$508$	−3.40654	−	4.68870i	−0.151141	−	0.208028i
$509$	6.77619	+	20.8550i	0.300349	+	0.924380i	0.981372	+	0.192118i	$0.0615355\pi$
$509$	6.77619	+	20.8550i	0.300349	+	0.924380i	−0.681023	+	0.732262i	$0.738465\pi$
$510$	−1.25296	−	1.94656i	−0.0554818	−	0.0861950i
$511$	3.55345	+	2.58173i	0.157195	+	0.114209i
$512$	−17.1958	+	23.6679i	−0.759952	+	1.04598i
$513$	17.4850	+	5.68121i	0.771980	+	0.250831i
$514$	2.98518	+	9.18745i	0.131671	+	0.405241i
$515$	0.534780	−	9.47175i	0.0235652	−	0.417375i
$516$	9.58846			0.422108
$517$		0			0
$518$		−	11.5911i		−	0.509284i
$519$	−3.19355	+	2.32025i	−0.140181	+	0.101848i
$520$	−1.77836	+	4.57743i	−0.0779865	+	0.200733i
$521$	12.1285	−	37.3277i	0.531360	−	1.63536i	−0.220025	−	0.975494i	$-0.570614\pi$
$521$	12.1285	−	37.3277i	0.531360	−	1.63536i	0.751385	−	0.659864i	$-0.229386\pi$
$522$	−21.4932	+	29.5829i	−0.940733	+	1.29481i
$523$	5.09089	−	7.00701i	0.222609	−	0.306395i	−0.683075	−	0.730348i	$-0.739358\pi$
$523$	5.09089	−	7.00701i	0.222609	−	0.306395i	0.905684	+	0.423953i	$0.139358\pi$
$524$	−11.3065	+	34.7977i	−0.493925	+	1.52014i
$525$	2.01893	−	1.14398i	0.0881133	−	0.0499272i
$526$	−33.5877	+	24.4029i	−1.46449	+	1.06402i
$527$			5.45378i			0.237570i
$528$		0			0
$529$	−16.8564			−0.732887
$530$	−51.6254	−	2.91480i	−2.24246	−	0.126611i
$531$	3.99503	+	12.2955i	0.173370	+	0.533577i
$532$	−9.15115	−	2.97339i	−0.396753	−	0.128913i
$533$	4.31932	−	5.94504i	0.187091	−	0.257508i
$534$	5.22957	+	3.79950i	0.226306	+	0.164421i
$535$	5.30257	+	8.23793i	0.229250	+	0.356157i
$536$	−2.38934	−	7.35362i	−0.103204	−	0.317628i
$537$	2.59713	+	3.57465i	0.112075	+	0.154257i
$538$		−	38.1194i		−	1.64344i
$539$		0			0
$540$	7.26795	−	8.90138i	0.312763	−	0.383055i
$541$	18.9248	−	13.7497i	0.813640	−	0.591144i	−0.101244	−	0.994862i	$-0.532282\pi$
$541$	18.9248	−	13.7497i	0.813640	−	0.591144i	0.914884	+	0.403718i	$0.132282\pi$
$542$	8.33381	−	2.70782i	0.357968	−	0.116311i
$543$	−1.67004	−	0.542630i	−0.0716684	−	0.0232865i
$544$	−6.35597	−	4.61788i	−0.272510	−	0.197990i
$545$	0.681812	+	2.58632i	0.0292056	+	0.110786i
$546$	1.17545	−	3.61767i	0.0503048	−	0.154822i
$547$	−19.2610	+	6.25829i	−0.823543	+	0.267585i	−0.690323	−	0.723501i	$-0.742532\pi$
$547$	−19.2610	+	6.25829i	−0.823543	+	0.267585i	−0.133220	+	0.991087i	$0.542532\pi$
$548$	−14.0120	−	19.2858i	−0.598561	−	0.823849i
$549$	−22.5885			−0.964052
$550$		0			0
$551$	−42.9282			−1.82880
$552$	0.994306	+	1.36855i	0.0423205	+	0.0582492i
$553$	4.65921	−	1.51387i	0.198130	−	0.0643762i
$554$	13.5524	−	41.7099i	0.575785	−	1.77208i
$555$	1.97455	+	7.49007i	0.0838152	+	0.317936i
$556$	−23.2447	−	16.8883i	−0.985796	−	0.716222i
$557$	6.17146	+	2.00523i	0.261493	+	0.0849643i	0.436830	−	0.899544i	$-0.356101\pi$
$557$	6.17146	+	2.00523i	0.261493	+	0.0849643i	−0.175336	+	0.984509i	$0.556101\pi$
$558$	−26.4430	+	8.59185i	−1.11942	+	0.363722i
$559$	36.7076	−	26.6696i	1.55257	−	1.12800i
$560$	5.66025	−	6.93237i	0.239189	−	0.292946i
$561$		0			0
$562$		−	33.4607i		−	1.41145i
$563$	−3.56959	−	4.91312i	−0.150440	−	0.207064i	0.727145	−	0.686484i	$-0.240847\pi$
$563$	−3.56959	−	4.91312i	−0.150440	−	0.207064i	−0.877585	+	0.479421i	$0.840847\pi$
$564$	−1.13703	−	3.49940i	−0.0478774	−	0.147352i
$565$	3.42314	+	5.31809i	0.144013	+	0.223734i
$566$	−47.0661	−	34.1955i	−1.97834	−	1.43735i
$567$	−3.50991	+	4.83098i	−0.147402	+	0.202882i
$568$	−1.08117	−	0.351294i	−0.0453650	−	0.0147400i
$569$	−1.81567	−	5.58807i	−0.0761170	−	0.234264i	0.905757	−	0.423796i	$-0.139303\pi$
$569$	−1.81567	−	5.58807i	−0.0761170	−	0.234264i	−0.981874	+	0.189532i	$0.939303\pi$
$570$	13.8330	+	0.781018i	0.579400	+	0.0327132i
$571$	35.7128			1.49453			0.747267	−	0.664524i	$-0.231365\pi$
$571$	35.7128			1.49453			0.747267	+	0.664524i	$0.231365\pi$
$572$		0			0
$573$			5.55532i			0.232077i
$574$	−2.42705	+	1.76336i	−0.101303	+	0.0736010i
$575$	−15.5615	−	27.4636i	−0.648961	−	1.14531i
$576$	4.83928	−	14.8938i	0.201637	−	0.620574i
$577$	12.1864	−	16.7731i	0.507326	−	0.698275i	−0.476139	−	0.879370i	$-0.657964\pi$
$577$	12.1864	−	16.7731i	0.507326	−	0.698275i	0.983466	+	0.181095i	$0.0579642\pi$
$578$	−18.0867	+	24.8942i	−0.752307	+	1.03546i
$579$	−1.64413	+	5.06010i	−0.0683276	+	0.210291i
$580$	−9.71717	+	25.0115i	−0.403483	+	1.03855i
$581$	−7.18055	+	5.21697i	−0.297899	+	0.216437i
$582$		−	0.656339i		−	0.0272061i
$583$		0			0
$584$	−2.53590			−0.104936
$585$	1.46105	−	25.8773i	0.0604068	−	1.06989i
$586$	5.62292	+	17.3056i	0.232281	+	0.714886i
$587$	34.1879	+	11.1083i	1.41109	+	0.458490i	0.912759	−	0.408499i	$-0.133948\pi$
$587$	34.1879	+	11.1083i	1.41109	+	0.458490i	0.498328	+	0.866989i	$0.333948\pi$
$588$	3.26533	−	4.49435i	0.134660	−	0.185344i
$589$	−26.4071	−	19.1859i	−1.08809	−	0.790542i
$590$	11.0638	+	17.1883i	0.455488	+	0.707633i
$591$	0.408059	+	1.25588i	0.0167853	+	0.0516599i
$592$	17.5597	+	24.1689i	0.721699	+	0.993334i
$593$		−	30.2533i		−	1.24235i	−0.783670	−	0.621177i	$-0.786655\pi$
$593$		−	30.2533i		−	1.24235i	0.783670	−	0.621177i	$-0.213345\pi$
$594$		0			0
$595$	1.60770	+	1.31268i	0.0659091	+	0.0538145i
$596$	19.2422	−	13.9802i	0.788189	−	0.572653i
$597$	0.984606	−	0.319918i	0.0402972	−	0.0130934i
$598$	−49.2114	−	15.9897i	−2.01240	−	0.653869i
$599$	16.5402	+	12.0172i	0.675816	+	0.491009i	0.871967	−	0.489565i	$-0.162844\pi$
$599$	16.5402	+	12.0172i	0.675816	+	0.491009i	−0.196151	+	0.980574i	$0.562844\pi$
$600$	−0.554797	+	1.21948i	−0.0226495	+	0.0497849i
$601$	6.18034	−	19.0211i	0.252101	−	0.775888i	−0.742286	−	0.670084i	$-0.766258\pi$
$601$	6.18034	−	19.0211i	0.252101	−	0.775888i	0.994387	−	0.105804i	$-0.0337418\pi$
$602$	−17.6169	+	5.72407i	−0.718010	+	0.233296i
$603$	23.9870	+	33.0153i	0.976826	+	1.34449i
$604$	10.7321			0.436681
$605$		0			0
$606$	1.39230			0.0565585
$607$	−18.5103	−	25.4773i	−0.751311	−	1.03409i	−0.997887	−	0.0649672i	$-0.979306\pi$
$607$	−18.5103	−	25.4773i	−0.751311	−	1.03409i	0.246577	−	0.969123i	$-0.420694\pi$
$608$	44.7194	−	14.5302i	1.81361	−	0.589278i
$609$	−0.993610	+	3.05802i	−0.0402631	+	0.123917i
$610$	−34.5356	+	9.10437i	−1.39830	+	0.368625i
$611$	−14.0862	−	10.2342i	−0.569868	−	0.414033i
$612$	4.65921	+	1.51387i	0.188337	+	0.0611945i
$613$	6.36459	−	2.06798i	0.257064	−	0.0835250i	−0.177650	−	0.984094i	$-0.556850\pi$
$613$	6.36459	−	2.06798i	0.257064	−	0.0835250i	0.434714	+	0.900569i	$0.356850\pi$
$614$	27.5491	−	20.0156i	1.11179	−	0.807764i
$615$	1.26795	−	1.55291i	0.0511286	−	0.0626195i
$616$		0			0
$617$		−	1.69161i		−	0.0681019i	−0.999420	−	0.0340509i	$-0.989159\pi$
$617$		−	1.69161i		−	0.0681019i	0.999420	−	0.0340509i	$-0.0108408\pi$
$618$	−2.49376	−	3.43237i	−0.100314	−	0.138070i
$619$	8.89493	+	27.3758i	0.357518	+	1.10033i	0.954535	+	0.298098i	$0.0963522\pi$
$619$	8.89493	+	27.3758i	0.357518	+	1.10033i	−0.597018	+	0.802228i	$0.703648\pi$
$620$	−17.1559	+	11.0429i	−0.688997	+	0.443492i
$621$	−15.1545	−	11.0104i	−0.608131	−	0.441833i
$622$	31.8541	−	43.8434i	1.27723	−	1.75796i
$623$	−5.51190	−	1.79092i	−0.220830	−	0.0717519i
$624$	3.02956	+	9.32401i	0.121279	+	0.373259i
$625$	12.8483	−	21.4458i	0.513932	−	0.857831i
$626$	−33.1244			−1.32392
$627$		0			0
$628$			20.9086i			0.834344i
$629$	−5.60503	+	4.07230i	−0.223487	+	0.162373i
$630$	−3.83184	+	9.86299i	−0.152664	+	0.392951i
$631$	5.97037	−	18.3749i	0.237676	−	0.731493i	−0.759079	−	0.650999i	$-0.774350\pi$
$631$	5.97037	−	18.3749i	0.237676	−	0.731493i	0.996755	−	0.0804940i	$-0.0256498\pi$
$632$	−1.66251	+	2.28825i	−0.0661310	+	0.0910215i
$633$	−3.38470	+	4.65864i	−0.134530	+	0.185164i
$634$	4.16064	−	12.8051i	0.165240	−	0.508556i
$635$	−6.97418	−	2.70952i	−0.276762	−	0.107524i
$636$	−8.68241	+	6.30814i	−0.344280	+	0.250134i
$637$		−	26.2880i		−	1.04157i
$638$		0			0
$639$	6.00000			0.237356
$640$	−0.517297	+	9.16210i	−0.0204480	+	0.362164i
$641$	6.13597	+	18.8846i	0.242356	+	0.745895i	0.996060	+	0.0886813i	$0.0282653\pi$
$641$	6.13597	+	18.8846i	0.242356	+	0.745895i	−0.753704	+	0.657214i	$0.771735\pi$
$642$	4.16690	+	1.35391i	0.164455	+	0.0534345i
$643$	16.2611	−	22.3815i	0.641277	−	0.882642i	−0.357406	−	0.933949i	$-0.616339\pi$
$643$	16.2611	−	22.3815i	0.641277	−	0.882642i	0.998683	+	0.0513075i	$0.0163388\pi$
$644$	7.93148	+	5.76256i	0.312544	+	0.227077i
$645$	10.4088	−	6.69989i	0.409845	−	0.263808i
$646$	3.82943	+	11.7858i	0.150667	+	0.463705i
$647$	−11.1543	−	15.3525i	−0.438519	−	0.603569i	0.531363	−	0.847144i	$-0.321680\pi$
$647$	−11.1543	−	15.3525i	−0.438519	−	0.603569i	−0.969882	+	0.243575i	$0.921680\pi$
$648$		−	3.44760i		−	0.135435i
$649$		0			0
$650$	−8.19615	−	40.1528i	−0.321480	−	1.57492i
$651$	−1.97794	+	1.43705i	−0.0775214	+	0.0563226i
$652$	12.5007	−	4.06173i	0.489566	−	0.159069i
$653$	30.3814	+	9.87152i	1.18892	+	0.386302i	0.835672	−	0.549229i	$-0.185078\pi$
$653$	30.3814	+	9.87152i	1.18892	+	0.386302i	0.353244	+	0.935531i	$0.385078\pi$
$654$	0.967708	+	0.703081i	0.0378404	+	0.0274926i
$655$	12.0410	+	45.6750i	0.470480	+	1.78467i
$656$	2.38934	−	7.35362i	0.0932879	−	0.287111i
$657$	12.7292	−	4.13596i	0.496613	−	0.161359i
$658$	4.17811	+	5.75068i	0.162880	+	0.224185i
$659$	−11.3205			−0.440984			−0.220492	−	0.975389i	$-0.570766\pi$
$659$	−11.3205			−0.440984			−0.220492	+	0.975389i	$0.570766\pi$
$660$		0			0
$661$	−1.58846			−0.0617838			−0.0308919	−	0.999523i	$-0.509835\pi$
$661$	−1.58846			−0.0617838			−0.0308919	+	0.999523i	$0.509835\pi$
$662$	−8.86138	−	12.1966i	−0.344407	−	0.474036i
$663$	−2.16235	+	0.702589i	−0.0839785	+	0.0272863i
$664$	1.58351	−	4.87355i	0.0614522	−	0.189130i
$665$	−12.0117	+	3.16656i	−0.465793	+	0.122794i
$666$	−28.5749	−	20.7609i	−1.10725	−	0.804468i
$667$	41.5983	+	13.5161i	1.61069	+	0.523346i
$668$	−3.18230	+	1.03399i	−0.123127	+	0.0400063i
$669$	−2.42705	+	1.76336i	−0.0938352	+	0.0681753i
$670$	49.9808	+	40.8091i	1.93093	+	1.57659i
$671$		0			0
$672$		−	3.52193i		−	0.135861i
$673$	−0.950617	−	1.30841i	−0.0366436	−	0.0504356i	0.790302	−	0.612717i	$-0.209924\pi$
$673$	−0.950617	−	1.30841i	−0.0366436	−	0.0504356i	−0.826946	+	0.562282i	$0.809924\pi$
$674$	−4.67368	−	14.3841i	−0.180024	−	0.554055i
$675$	1.66993	−	14.7414i	0.0642758	−	0.567395i
$676$	−7.00629	−	5.09037i	−0.269473	−	0.195783i
$677$	−5.31363	+	7.31358i	−0.204219	+	0.281084i	−0.898826	−	0.438306i	$-0.855579\pi$
$677$	−5.31363	+	7.31358i	−0.204219	+	0.281084i	0.694606	+	0.719390i	$0.255579\pi$
$678$	2.68999	+	0.874032i	0.103309	+	0.0335670i
$679$	0.181843	+	0.559656i	0.00697851	+	0.0214776i
$680$	−1.19640	−	0.0675494i	−0.0458798	−	0.00259040i
$681$	−11.1436			−0.427023
$682$		0			0
$683$		−	22.4887i		−	0.860507i	−0.902708	−	0.430253i	$-0.858424\pi$
$683$		−	22.4887i		−	0.860507i	0.902708	−	0.430253i	$-0.141576\pi$
$684$	−23.7208	+	17.2342i	−0.906987	+	0.658965i
$685$	−28.6866	−	11.1449i	−1.09606	−	0.425826i
$686$	−7.06302	+	21.7377i	−0.269667	+	0.829951i
$687$	−5.45484	+	7.50794i	−0.208115	+	0.286446i
$688$	28.0617	−	38.6237i	1.06984	−	1.47251i
$689$	−15.6933	+	48.2990i	−0.597867	+	1.84005i
$690$	−13.1586	−	5.11220i	−0.500938	−	0.194618i
$691$	22.5788	−	16.4045i	0.858939	−	0.624056i	−0.0686571	−	0.997640i	$-0.521871\pi$
$691$	22.5788	−	16.4045i	0.858939	−	0.624056i	0.927596	+	0.373585i	$0.121871\pi$
$692$		−	13.2084i		−	0.502108i
$693$		0			0
$694$	5.73205			0.217586
$695$	−37.0339	−	2.09096i	−1.40478	−	0.0793145i
$696$	−0.573661	−	1.76555i	−0.0217446	−	0.0669229i
$697$	1.70539	+	0.554114i	0.0645962	+	0.0209886i
$698$	31.0228	−	42.6992i	1.17423	−	1.61619i
$699$	−5.44634	−	3.95700i	−0.206000	−	0.149667i
$700$	−0.873998	+	7.71522i	−0.0330340	+	0.291608i
$701$	3.13454	+	9.64713i	0.118390	+	0.364367i	0.992639	−	0.121111i	$-0.0386456\pi$
$701$	3.13454	+	9.64713i	0.118390	+	0.364367i	−0.874249	+	0.485478i	$0.838646\pi$
$702$	−14.2944	−	19.6745i	−0.539506	−	0.742567i
$703$		−	41.4655i		−	1.56390i
$704$		0			0
$705$	−3.67949	−	3.00429i	−0.138578	−	0.113148i
$706$	2.64383	−	1.92085i	0.0995017	−	0.0722922i
$707$	−1.18721	+	0.385748i	−0.0446496	+	0.0145075i
$708$	4.03499	+	1.31105i	0.151644	+	0.0492722i
$709$	18.9248	+	13.7497i	0.710735	+	0.516379i	0.883411	−	0.468600i	$-0.155241\pi$
$709$	18.9248	+	13.7497i	0.710735	+	0.516379i	−0.172676	+	0.984979i	$0.555241\pi$
$710$	9.17342	−	2.41832i	0.344272	−	0.0907581i
$711$	4.61307	−	14.1976i	0.173004	−	0.532450i
$712$	3.18230	−	1.03399i	0.119262	−	0.0387505i
$713$	19.5483	+	26.9059i	0.732090	+	1.00764i
$714$	0.928203			0.0347371
$715$		0			0
$716$	−14.7846			−0.552527
$717$	3.54775	+	4.88306i	0.132493	+	0.182361i
$718$	−33.6956	+	10.9484i	−1.25751	+	0.408590i
$719$	12.3001	−	37.8557i	0.458715	−	1.41178i	−0.408003	−	0.912981i	$-0.633775\pi$
$719$	12.3001	−	37.8557i	0.458715	−	1.41178i	0.866718	−	0.498799i	$-0.166225\pi$
$720$	−6.95186	−	26.3705i	−0.259081	−	0.982770i
$721$	3.07738	+	2.23585i	0.114608	+	0.0832672i
$722$	−35.6295	−	11.5767i	−1.32599	−	0.430841i
$723$	−4.98425	+	1.61948i	−0.185366	+	0.0602292i
$724$	4.75350	−	3.45362i	0.176662	−	0.128353i
$725$	6.92820	+	33.9411i	0.257307	+	1.26054i
$726$		0			0
$727$			4.00240i			0.148441i	0.997242	+	0.0742205i	$0.0236469\pi$
$727$			4.00240i			0.148441i	−0.997242	+	0.0742205i	$0.976353\pi$
$728$	−1.15736	−	1.59297i	−0.0428946	−	0.0590393i
$729$	4.19906	+	12.9234i	0.155521	+	0.478644i
$730$	17.7947	−	11.4540i	0.658611	−	0.423933i
$731$	8.95727	+	6.50784i	0.331297	+	0.240701i
$732$	−4.35716	+	5.99711i	−0.161045	+	0.221660i
$733$	−33.0714	−	10.7455i	−1.22152	−	0.396896i	−0.373885	−	0.927475i	$-0.621974\pi$
$733$	−33.0714	−	10.7455i	−1.22152	−	0.396896i	−0.847635	+	0.530579i	$0.821974\pi$
$734$	17.6908	+	54.4468i	0.652980	+	2.00967i
$735$	0.404285	−	7.16048i	0.0149123	−	0.264118i
$736$	−47.9090			−1.76595
$737$		0			0
$738$			9.14162i			0.336508i
$739$	−20.2835	+	14.7368i	−0.746141	+	0.542103i	−0.894628	−	0.446811i	$-0.852560\pi$
$739$	−20.2835	+	14.7368i	−0.746141	+	0.542103i	0.148487	+	0.988914i	$0.452560\pi$
$740$	−24.1593	−	9.38606i	−0.888113	−	0.345039i
$741$	4.20501	−	12.9417i	0.154475	−	0.475425i
$742$	12.1864	−	16.7731i	0.447377	−	0.615761i
$743$	4.72695	−	6.50609i	0.173415	−	0.238685i	−0.713459	−	0.700697i	$-0.752872\pi$
$743$	4.72695	−	6.50609i	0.173415	−	0.238685i	0.886874	+	0.462012i	$0.152872\pi$
$744$	0.436191	−	1.34246i	0.0159915	−	0.0492169i
$745$	11.1197	−	28.6216i	0.407395	−	1.04862i
$746$	−53.3215	+	38.7403i	−1.95224	+	1.41838i
$747$			27.0459i			0.989559i
$748$		0			0
$749$	−3.92820			−0.143533
$750$	−1.61500	−	11.0631i	−0.0589715	−	0.403967i
$751$	−6.37842	−	19.6308i	−0.232752	−	0.716337i	−0.997412	−	0.0719027i	$-0.977093\pi$
$751$	−6.37842	−	19.6308i	−0.232752	−	0.716337i	0.764660	−	0.644434i	$-0.222907\pi$
$752$	−17.4237	−	5.66132i	−0.635378	−	0.206447i
$753$	4.31932	−	5.94504i	0.157405	−	0.216649i
$754$	45.9397	+	33.3772i	1.67303	+	1.21552i
$755$	11.6502	−	7.49897i	0.423994	−	0.272915i
$756$	1.42386	+	4.38218i	0.0517851	+	0.159378i
$757$	20.6183	+	28.3786i	0.749385	+	1.03144i	0.998023	+	0.0628432i	$0.0200168\pi$
$757$	20.6183	+	28.3786i	0.749385	+	1.03144i	−0.248639	+	0.968596i	$0.579983\pi$
$758$		−	10.5558i		−	0.383405i
$759$		0			0
$760$	4.53590	−	5.55532i	0.164534	−	0.201513i
$761$	−6.35597	+	4.61788i	−0.230404	+	0.167398i	−0.696997	−	0.717074i	$-0.745481\pi$
$761$	−6.35597	+	4.61788i	−0.230404	+	0.167398i	0.466594	+	0.884472i	$0.345481\pi$
$762$	−3.18230	+	1.03399i	−0.115282	+	0.0374575i
$763$	−1.01995	−	0.331402i	−0.0369247	−	0.0119976i
$764$	−15.0384	−	10.9260i	−0.544069	−	0.395290i
$765$	6.11562	−	1.61222i	0.221111	−	0.0582898i
$766$	14.1867	−	43.6620i	0.512585	−	1.57757i
$767$	19.0938	−	6.20395i	0.689437	−	0.224012i
$768$	5.90030	+	8.12107i	0.212909	+	0.293044i
$769$	−17.8564			−0.643918			−0.321959	−	0.946754i	$-0.604341\pi$
$769$	−17.8564			−0.643918			−0.321959	+	0.946754i	$0.604341\pi$
$770$		0			0
$771$	2.58846			0.0932210
$772$	−10.4642	−	14.4027i	−0.376615	−	0.518366i
$773$	49.1148	−	15.9584i	1.76654	−	0.573983i	0.768693	−	0.639618i	$-0.220907\pi$
$773$	49.1148	−	15.9584i	1.76654	−	0.573983i	0.997844	+	0.0656355i	$0.0209075\pi$
$774$	−17.4424	+	53.6823i	−0.626955	+	1.92957i
$775$	−10.9075	+	23.9752i	−0.391807	+	0.861214i
$776$	−0.274860	−	0.199698i	−0.00986691	−	0.00716873i
$777$	−2.95382	−	0.959754i	−0.105968	−	0.0344310i
$778$	33.2999	−	10.8198i	1.19386	−	0.387908i
$779$	−8.68241	+	6.30814i	−0.311080	+	0.226013i
$780$	−6.58846	−	5.37945i	−0.235905	−	0.192615i
$781$		0			0
$782$		−	12.6264i		−	0.451519i
$783$	12.0830	+	16.6309i	0.431812	+	0.594338i
$784$	−8.54749	−	26.3065i	−0.305267	−	0.939517i
$785$	14.6098	+	22.6974i	0.521445	+	0.810103i
$786$	17.0900	+	12.4166i	0.609579	+	0.442885i
$787$	2.73834	−	3.76900i	0.0976113	−	0.134350i	−0.757418	−	0.652931i	$-0.773539\pi$
$787$	2.73834	−	3.76900i	0.0976113	−	0.134350i	0.855029	+	0.518580i	$0.173539\pi$
$788$	−4.20225	−	1.36539i	−0.149699	−	0.0486401i
$789$	3.43761	+	10.5799i	0.122382	+	0.376654i
$790$	1.33055	−	23.5660i	0.0473389	−	0.838442i
$791$	−2.53590			−0.0901662
$792$		0			0
$793$			35.0779i			1.24565i
$794$	25.0214	−	18.1791i	0.887978	−	0.645154i
$795$	−5.01742	+	12.9146i	−0.177950	+	0.458034i
$796$	−1.07047	+	3.29456i	−0.0379417	+	0.116772i
$797$	−4.64543	+	6.39388i	−0.164549	+	0.226483i	−0.883327	−	0.468757i	$-0.844702\pi$
$797$	−4.64543	+	6.39388i	−0.164549	+	0.226483i	0.718778	+	0.695240i	$0.244702\pi$
$798$	−3.26533	+	4.49435i	−0.115592	+	0.159098i
$799$	1.31292	−	4.04076i	0.0464479	−	0.142952i
$800$	−18.7056	−	33.0123i	−0.661342	−	1.16716i
$801$	−14.2874	+	10.3804i	−0.504822	+	0.366775i
$802$			62.4384i			2.20478i
$803$		0			0
$804$	13.3923			0.472310
$805$	12.6366	+	0.713469i	0.445381	+	0.0251465i
$806$	13.3424	+	41.0637i	0.469966	+	1.44641i
$807$	−9.71415	−	3.15632i	−0.341954	−	0.111108i
$808$	0.423623	−	0.583067i	0.0149030	−	0.0205122i
$809$	−17.3648	−	12.6163i	−0.610515	−	0.443565i	0.239081	−	0.971000i	$-0.423154\pi$
$809$	−17.3648	−	12.6163i	−0.610515	−	0.443565i	−0.849596	+	0.527435i	$0.823154\pi$
$810$	15.5720	+	24.1922i	0.547144	+	0.850028i
$811$	−10.1916	−	31.3666i	−0.357876	−	1.10143i	−0.954323	−	0.298777i	$-0.903421\pi$
$811$	−10.1916	−	31.3666i	−0.357876	−	1.10143i	0.596447	−	0.802652i	$-0.296579\pi$
$812$	−6.32393	−	8.70414i	−0.221926	−	0.305455i
$813$		−	2.34795i		−	0.0823463i
$814$		0			0
$815$	10.7321	−	13.1440i	0.375927	−	0.460415i
$816$	−1.93542	+	1.40616i	−0.0677531	+	0.0492255i
$817$	−63.0217	+	20.4770i	−2.20485	+	0.716400i
$818$	−3.44612	−	1.11971i	−0.120491	−	0.0391498i
$819$	8.40755	+	6.10844i	0.293784	+	0.213446i
$820$	1.71001	+	6.48659i	0.0597163	+	0.226522i
$821$	5.81071	−	17.8835i	0.202795	−	0.624139i	−0.797002	−	0.603977i	$-0.793582\pi$
$821$	5.81071	−	17.8835i	0.202795	−	0.624139i	0.999797	−	0.0201620i	$-0.00641821\pi$
$822$	−13.0896	+	4.25306i	−0.456552	+	0.148343i
$823$	−28.4475	−	39.1547i	−0.991619	−	1.36485i	−0.930329	−	0.366726i	$-0.880479\pi$
$823$	−28.4475	−	39.1547i	−0.991619	−	1.36485i	−0.0612894	−	0.998120i	$-0.519521\pi$
$824$	−2.19615			−0.0765066
$825$		0			0
$826$	−8.19615			−0.285181
$827$	15.7123	+	21.6261i	0.546370	+	0.752014i	0.989514	−	0.144437i	$-0.0461369\pi$
$827$	15.7123	+	21.6261i	0.546370	+	0.752014i	−0.443144	+	0.896450i	$0.646137\pi$
$828$	28.4122	−	9.23168i	0.987392	−	0.320823i
$829$	−12.9728	+	39.9261i	−0.450563	+	1.38669i	0.425703	+	0.904863i	$0.360027\pi$
$829$	−12.9728	+	39.9261i	−0.450563	+	1.38669i	−0.876266	+	0.481827i	$0.839973\pi$
$830$	10.9010	+	41.3506i	0.378378	+	1.43530i
$831$	−9.50699	−	6.90723i	−0.329794	−	0.239609i
$832$	−23.1288	−	7.51499i	−0.801846	−	0.260536i
$833$	6.10077	−	1.98226i	0.211379	−	0.0686812i
$834$	−13.4203	+	9.75045i	−0.464709	+	0.337630i
$835$	−2.73205	+	3.34607i	−0.0945465	+	0.115795i
$836$		0			0
$837$			15.6307i			0.540275i
$838$	33.6796	+	46.3560i	1.16344	+	1.60134i
$839$	−0.860492	−	2.64832i	−0.0297075	−	0.0914302i	0.935103	−	0.354375i	$-0.115306\pi$
$839$	−0.860492	−	2.64832i	−0.0297075	−	0.0914302i	−0.964811	+	0.262945i	$0.915306\pi$
$840$	−0.290749	−	0.451700i	−0.0100318	−	0.0155851i
$841$	−15.3713	−	11.1679i	−0.530046	−	0.385101i
$842$	−23.9055	+	32.9031i	−0.823837	+	1.13391i
$843$	−8.52694	−	2.77057i	−0.293683	−	0.0954235i
$844$	−5.95412	−	18.3249i	−0.204949	−	0.630769i
$845$	−11.1626	−	0.630244i	−0.384004	−	0.0216811i
$846$	21.6603			0.744695
$847$		0			0
$848$			53.4355i			1.83498i
$849$	−12.6113	+	9.16267i	−0.432820	+	0.314462i
$850$	8.70038	−	4.92985i	0.298421	−	0.169092i
$851$	−13.0556	+	40.1809i	−0.447539	+	1.37738i
$852$	1.15736	−	1.59297i	0.0396505	−	0.0545742i
$853$	−7.30224	+	10.0507i	−0.250024	+	0.344128i	−0.915520	−	0.402273i	$-0.868220\pi$
$853$	−7.30224	+	10.0507i	−0.250024	+	0.344128i	0.665496	+	0.746402i	$0.268220\pi$
$854$	4.42528	−	13.6196i	0.151430	−	0.466054i
$855$	−13.7078	+	35.2834i	−0.468798	+	1.20667i
$856$	1.83481	−	1.33307i	0.0627125	−	0.0455633i
$857$			24.4206i			0.834191i	0.908863	+	0.417095i	$0.136952\pi$
$857$			24.4206i			0.834191i	−0.908863	+	0.417095i	$0.863048\pi$
$858$		0			0
$859$	11.8038			0.402742			0.201371	−	0.979515i	$-0.435460\pi$
$859$	11.8038			0.402742			0.201371	+	0.979515i	$0.435460\pi$
$860$	−2.33486	+	41.3539i	−0.0796182	+	1.41016i
$861$	0.248403	+	0.764504i	0.00846554	+	0.0260542i
$862$	34.7768	+	11.2997i	1.18450	+	0.384868i
$863$	−5.73725	+	7.89665i	−0.195298	+	0.268805i	−0.895424	−	0.445215i	$-0.853127\pi$
$863$	−5.73725	+	7.89665i	−0.195298	+	0.268805i	0.700126	+	0.714020i	$0.253127\pi$
$864$	−18.2164	−	13.2350i	−0.619733	−	0.450263i
$865$	−9.22930	−	14.3384i	−0.313806	−	0.487520i
$866$	−12.0901	−	37.2095i	−0.410838	−	1.26443i
$867$	4.84632	+	6.67038i	0.164590	+	0.226538i
$868$		−	8.18067i		−	0.277670i
$869$		0			0
$870$	12.0000	+	9.79796i	0.406838	+	0.332182i
$871$	51.2699	−	37.2498i	1.73721	−	1.26216i
$872$	0.588870	−	0.191335i	0.0199416	−	0.00647943i
$873$	1.70539	+	0.554114i	0.0577186	+	0.0187539i
$874$	61.1368	+	44.4185i	2.06798	+	1.50248i
$875$	4.44221	+	8.98597i	0.150174	+	0.303781i
$876$	1.35730	−	4.17733i	0.0458588	−	0.141139i
$877$	−53.2464	+	17.3008i	−1.79800	+	0.584206i	−0.999834	−	0.0182289i	$-0.994197\pi$
$877$	−53.2464	+	17.3008i	−1.79800	+	0.584206i	−0.798168	+	0.602435i	$0.794197\pi$
$878$	22.9927	+	31.6467i	0.775966	+	1.06803i
$879$	4.87564			0.164451
$880$		0			0
$881$	38.9090			1.31088			0.655438	−	0.755249i	$-0.272484\pi$
$881$	38.9090			1.31088			0.655438	+	0.755249i	$0.272484\pi$
$882$	19.2222	+	26.4571i	0.647245	+	0.890857i
$883$	44.7194	−	14.5302i	1.50493	−	0.488981i	0.563477	−	0.826131i	$-0.309463\pi$
$883$	44.7194	−	14.5302i	1.50493	−	0.488981i	0.941451	+	0.337151i	$0.109463\pi$
$884$	2.35091	−	7.23535i	0.0790696	−	0.243351i
$885$	5.29628	−	1.39622i	0.178032	−	0.0469334i
$886$	−14.3455	−	10.4226i	−0.481948	−	0.350155i
$887$	7.93807	+	2.57924i	0.266534	+	0.0866022i	0.439235	−	0.898372i	$-0.355249\pi$
$887$	7.93807	+	2.57924i	0.266534	+	0.0866022i	−0.172701	+	0.984974i	$0.555249\pi$
$888$	1.70539	−	0.554114i	0.0572291	−	0.0185949i
$889$	2.42705	−	1.76336i	0.0814007	−	0.0591411i
$890$	−17.6603	+	21.6293i	−0.591973	+	0.725016i
$891$		0			0
$892$		−	10.0382i		−	0.336104i
$893$	14.9466	+	20.5722i	0.500168	+	0.688422i
$894$	−4.24344	−	13.0600i	−0.141922	−	0.436790i
$895$	−16.0495	+	10.3307i	−0.536474	+	0.345316i
$896$	−2.97677	−	2.16275i	−0.0994470	−	0.0722524i
$897$	−8.14949	+	11.2168i	−0.272103	+	0.374518i
$898$	−19.3223	−	6.27818i	−0.644792	−	0.209506i
$899$	−11.2783	−	34.7111i	−0.376153	−	1.15768i
$900$	17.4545	+	15.9734i	0.581816	+	0.532446i
$901$	−12.3923			−0.412848
$902$		0			0
$903$			4.96335i			0.165170i
$904$	1.18448	−	0.860577i	0.0393953	−	0.0286224i
$905$	2.74697	−	7.07056i	0.0913122	−	0.235033i
$906$	1.91472	−	5.89289i	0.0636122	−	0.195778i
$907$	−4.74294	+	6.52810i	−0.157487	+	0.216762i	−0.880468	−	0.474106i	$-0.842771\pi$
$907$	−4.74294	+	6.52810i	−0.157487	+	0.216762i	0.722981	+	0.690868i	$0.242771\pi$
$908$	21.9169	−	30.1660i	0.727337	−	1.00109i
$909$	−1.17545	+	3.61767i	−0.0389873	+	0.119991i
$910$	15.3164	+	5.95053i	0.507733	+	0.197258i
$911$	−14.7635	+	10.7263i	−0.489137	+	0.355379i	−0.804852	−	0.593475i	$-0.797756\pi$
$911$	−14.7635	+	10.7263i	−0.489137	+	0.355379i	0.315715	+	0.948854i	$0.397756\pi$
$912$		−	14.3180i		−	0.474116i
$913$		0			0
$914$	−40.9808			−1.35552
$915$	−0.539465	+	9.55472i	−0.0178342	+	0.315869i
$916$	−9.59577	−	29.5327i	−0.317053	−	0.975789i
$917$	−18.0126	−	5.85265i	−0.594829	−	0.193272i
$918$	3.48807	−	4.80091i	0.115123	−	0.158454i
$919$	26.6820	+	19.3856i	0.880158	+	0.639472i	0.933293	−	0.359115i	$-0.116921\pi$
$919$	26.6820	+	19.3856i	0.880158	+	0.639472i	−0.0531354	+	0.998587i	$0.516921\pi$
$920$	−6.14450	+	3.95508i	−0.202578	+	0.130395i
$921$	−2.81958	−	8.67778i	−0.0929084	−	0.285943i
$922$	−37.4720	−	51.5757i	−1.23407	−	1.69856i
$923$		−	9.31749i		−	0.306689i
$924$		0			0
$925$	−32.7846	+	6.69213i	−1.07795	+	0.220036i
$926$	−27.9246	+	20.2884i	−0.917658	+	0.666718i
$927$	11.0238	−	3.58185i	0.362069	−	0.117643i
$928$	50.0028	+	16.2469i	1.64142	+	0.533331i
$929$	−13.0604	−	9.48897i	−0.428499	−	0.311323i	0.352549	−	0.935793i	$-0.385315\pi$
$929$	−13.0604	−	9.48897i	−0.428499	−	0.311323i	−0.781049	+	0.624470i	$0.785315\pi$
$930$	3.00276	+	11.3903i	0.0984642	+	0.373504i
$931$	−11.8639	+	36.5133i	−0.388823	+	1.19667i
$932$	21.4234	−	6.96088i	0.701746	−	0.228011i
$933$	−8.53527	−	11.7478i	−0.279432	−	0.384606i
$934$	−34.3205			−1.12300
$935$		0			0
$936$	−6.00000			−0.196116
$937$	−13.3438	−	18.3661i	−0.435921	−	0.599994i	0.533378	−	0.845877i	$-0.320922\pi$
$937$	−13.3438	−	18.3661i	−0.435921	−	0.599994i	−0.969300	+	0.245883i	$0.920922\pi$
$938$	−24.6057	+	7.99487i	−0.803404	+	0.261042i
$939$	−2.74272	+	8.44124i	−0.0895054	+	0.275469i
$940$	15.3694	−	4.05173i	0.501294	−	0.132153i
$941$	21.8435	+	15.8702i	0.712076	+	0.517354i	0.883843	−	0.467784i	$-0.154947\pi$
$941$	21.8435	+	15.8702i	0.712076	+	0.517354i	−0.171766	+	0.985138i	$0.554947\pi$
$942$	11.4808	+	3.73032i	0.374063	+	0.121541i
$943$	10.3996	−	3.37903i	0.338657	−	0.110036i
$944$	17.0900	−	12.4166i	0.556231	−	0.404125i
$945$	4.60770	+	3.76217i	0.149888	+	0.122383i
$946$		0			0
$947$			14.3180i			0.465273i	0.972564	+	0.232636i	$0.0747352\pi$
$947$			14.3180i			0.465273i	−0.972564	+	0.232636i	$0.925265\pi$
$948$	−2.87955	−	3.96336i	−0.0935234	−	0.128724i
$949$	−6.42280	−	19.7673i	−0.208493	−	0.641675i
$950$	−6.73688	+	59.4699i	−0.218573	+	1.92946i
$951$	−2.91869	−	2.12055i	−0.0946449	−	0.0687635i
$952$	0.282415	−	0.388711i	0.00915313	−	0.0125982i
$953$	−29.8538	−	9.70007i	−0.967058	−	0.314216i	−0.217430	−	0.976076i	$-0.569767\pi$
$953$	−29.8538	−	9.70007i	−0.967058	−	0.314216i	−0.749628	+	0.661860i	$0.769767\pi$
$954$	−19.5227	−	60.0848i	−0.632072	−	1.94532i
$955$	−23.9594	−	1.35276i	−0.775309	−	0.0437744i
$956$	−20.1962			−0.653190
$957$		0			0
$958$			18.2832i			0.590705i
$959$	9.98306	−	7.25312i	0.322370	−	0.234215i
$960$	−6.18437	−	2.40267i	−0.199600	−	0.0775459i
$961$	−1.00391	+	3.08971i	−0.0323841	+	0.0996680i
$962$	−32.2399	+	44.3744i	−1.03945	+	1.43069i
$963$	−7.03582	+	9.68397i	−0.226726	+	0.312062i
$964$	5.41889	−	16.6776i	0.174531	−	0.537150i
$965$	−21.4233	−	8.32310i	−0.689640	−	0.267930i
$966$	4.57924	−	3.32701i	0.147335	−	0.107045i
$967$			4.24264i			0.136434i	0.997671	+	0.0682171i	$0.0217310\pi$
$967$			4.24264i			0.136434i	−0.997671	+	0.0682171i	$0.978269\pi$
$968$		0			0
$969$	3.32051			0.106670
$970$	2.83071	+	0.159824i	0.0908887	+	0.00513163i
$971$	−3.42137	−	10.5299i	−0.109797	−	0.337921i	0.881029	−	0.473062i	$-0.156851\pi$
$971$	−3.42137	−	10.5299i	−0.109797	−	0.337921i	−0.990826	+	0.135141i	$0.956851\pi$
$972$	20.3422	+	6.60959i	0.652477	+	0.212003i
$973$	8.74201	−	12.0324i	0.280256	−	0.385739i
$974$	−19.8925	−	14.4527i	−0.637396	−	0.463095i
$975$	−10.9110	−	1.23602i	−0.349431	−	0.0395843i
$976$	11.4055	+	35.1025i	0.365081	+	1.12360i
$977$	−8.80170	−	12.1145i	−0.281591	−	0.387577i	0.644669	−	0.764462i	$-0.276995\pi$
$977$	−8.80170	−	12.1145i	−0.281591	−	0.387577i	−0.926260	+	0.376885i	$0.876995\pi$
$978$		−	7.58871i		−	0.242660i
$979$		0			0
$980$	18.5885	+	15.1774i	0.593786	+	0.484825i
$981$	−2.64383	+	1.92085i	−0.0844109	+	0.0613281i
$982$	−28.8692	+	9.38016i	−0.921252	+	0.299333i
$983$	−14.2768	−	4.63881i	−0.455359	−	0.147955i	0.0723519	−	0.997379i	$-0.476950\pi$
$983$	−14.2768	−	4.63881i	−0.455359	−	0.147955i	−0.527711	+	0.849424i	$0.676950\pi$
$984$	−0.375466	−	0.272792i	−0.0119694	−	0.00869629i
$985$	−5.51582	+	1.45410i	−0.175749	+	0.0463314i
$986$	−4.28187	+	13.1782i	−0.136362	+	0.419680i
$987$	1.81143	−	0.588568i	0.0576583	−	0.0187343i
$988$	26.7632	+	36.8364i	0.851450	+	1.17192i
$989$	67.5167			2.14690
$990$		0			0
$991$	−45.9090			−1.45835			−0.729173	−	0.684329i	$-0.760095\pi$
$991$	−45.9090			−1.45835			−0.729173	+	0.684329i	$0.760095\pi$
$992$	23.4978	+	32.3420i	0.746057	+	1.02686i
$993$	−3.84186	+	1.24830i	−0.121918	+	0.0396135i
$994$	−1.17545	+	3.61767i	−0.0372831	+	0.114746i
$995$	1.14001	+	4.32439i	0.0361407	+	0.137092i
$996$	7.18055	+	5.21697i	0.227524	+	0.165306i
$997$	0.167258	+	0.0543454i	0.00529711	+	0.00172114i	0.311664	−	0.950192i	$-0.399114\pi$
$997$	0.167258	+	0.0543454i	0.00529711	+	0.00172114i	−0.306367	+	0.951913i	$0.599114\pi$
$998$	−70.5382	+	22.9192i	−2.23285	+	0.725496i
$999$	−16.0642	+	11.6713i	−0.508248	+	0.369264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.f.124.4		16
5.4	even	2	inner	605.2.j.f.124.1		16
11.2	odd	10		605.2.b.e.364.4	yes	4
11.3	even	5	inner	605.2.j.f.269.4		16
11.4	even	5	inner	605.2.j.f.444.1		16
11.5	even	5	inner	605.2.j.f.9.1		16
11.6	odd	10		605.2.j.e.9.4		16
11.7	odd	10		605.2.j.e.444.4		16
11.8	odd	10		605.2.j.e.269.1		16
11.9	even	5		605.2.b.d.364.1	✓	4
11.10	odd	2		605.2.j.e.124.1		16
55.2	even	20		3025.2.a.z.1.1		4
55.4	even	10	inner	605.2.j.f.444.4		16
55.9	even	10		605.2.b.d.364.4	yes	4
55.13	even	20		3025.2.a.z.1.4		4
55.14	even	10	inner	605.2.j.f.269.1		16
55.19	odd	10		605.2.j.e.269.4		16
55.24	odd	10		605.2.b.e.364.1	yes	4
55.29	odd	10		605.2.j.e.444.1		16
55.39	odd	10		605.2.j.e.9.1		16
55.42	odd	20		3025.2.a.y.1.4		4
55.49	even	10	inner	605.2.j.f.9.4		16
55.53	odd	20		3025.2.a.y.1.1		4
55.54	odd	2		605.2.j.e.124.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.d.364.1	✓	4	11.9	even	5
605.2.b.d.364.4	yes	4	55.9	even	10
605.2.b.e.364.1	yes	4	55.24	odd	10
605.2.b.e.364.4	yes	4	11.2	odd	10
605.2.j.e.9.1		16	55.39	odd	10
605.2.j.e.9.4		16	11.6	odd	10
605.2.j.e.124.1		16	11.10	odd	2
605.2.j.e.124.4		16	55.54	odd	2
605.2.j.e.269.1		16	11.8	odd	10
605.2.j.e.269.4		16	55.19	odd	10
605.2.j.e.444.1		16	55.29	odd	10
605.2.j.e.444.4		16	11.7	odd	10
605.2.j.f.9.1		16	11.5	even	5	inner
605.2.j.f.9.4		16	55.49	even	10	inner
605.2.j.f.124.1		16	5.4	even	2	inner
605.2.j.f.124.4		16	1.1	even	1	trivial
605.2.j.f.269.1		16	55.14	even	10	inner
605.2.j.f.269.4		16	11.3	even	5	inner
605.2.j.f.444.1		16	11.4	even	5	inner
605.2.j.f.444.4		16	55.4	even	10	inner
3025.2.a.y.1.1		4	55.53	odd	20
3025.2.a.y.1.4		4	55.42	odd	20
3025.2.a.z.1.1		4	55.2	even	20
3025.2.a.z.1.4		4	55.13	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.13551 + 1.56290i) q^{2} +(0.492303 - 0.159959i) q^{3} +(-0.535233 + 1.64728i) q^{4} +(0.570005 + 2.16220i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.852694 - 0.277057i) q^{7} +(0.492303 - 0.159959i) q^{8} +(-2.21028 + 1.60586i) q^{9} +O(q^{10})\)	\(q+(1.13551 + 1.56290i) q^{2} +(0.492303 - 0.159959i) q^{3} +(-0.535233 + 1.64728i) q^{4} +(0.570005 + 2.16220i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-0.852694 - 0.277057i) q^{7} +(0.492303 - 0.159959i) q^{8} +(-2.21028 + 1.60586i) q^{9} +(-2.73205 + 3.34607i) q^{10} +0.896575i q^{12} +(2.49376 + 3.43237i) q^{13} +(-0.535233 - 1.64728i) q^{14} +(0.626478 + 0.973279i) q^{15} +(3.61153 + 2.62393i) q^{16} +(-0.608520 + 0.837556i) q^{17} +(-5.01960 - 1.63097i) q^{18} +(-1.91472 - 5.89289i) q^{19} +(-3.86682 - 0.218323i) q^{20} -0.464102 q^{21} +6.31319i q^{23} +(0.216775 - 0.157497i) q^{24} +(-4.35019 + 2.46492i) q^{25} +(-2.53275 + 7.79500i) q^{26} +(-1.74403 + 2.40046i) q^{27} +(0.912780 - 1.25633i) q^{28} +(2.14093 - 6.58911i) q^{29} +(-0.809764 + 2.08429i) q^{30} +(4.26186 - 3.09642i) q^{31} +7.58871i q^{32} -2.00000 q^{34} +(0.113012 - 2.00162i) q^{35} +(-1.46228 - 4.50045i) q^{36} +(6.36459 + 2.06798i) q^{37} +(7.03582 - 9.68397i) q^{38} +(1.77672 + 1.29087i) q^{39} +(0.626478 + 0.973279i) q^{40} +(-0.535233 - 1.64728i) q^{41} +(-0.526994 - 0.725345i) q^{42} -10.6945i q^{43} +(-4.73205 - 3.86370i) q^{45} +(-9.86689 + 7.16872i) q^{46} +(-3.90308 + 1.26819i) q^{47} +(2.19769 + 0.714073i) q^{48} +(-5.01279 - 3.64201i) q^{49} +(-8.79213 - 3.99996i) q^{50} +(-0.165602 + 0.509670i) q^{51} +(-6.98881 + 2.27080i) q^{52} +(7.03582 + 9.68397i) q^{53} -5.73205 q^{54} -0.464102 q^{56} +(-1.88524 - 2.59481i) q^{57} +(12.7292 - 4.13596i) q^{58} +(1.46228 - 4.50045i) q^{59} +(-1.93857 + 0.511052i) q^{60} +(6.68891 + 4.85978i) q^{61} +(9.67880 + 3.14483i) q^{62} +(2.32960 - 0.756934i) q^{63} +(-4.63733 + 3.36921i) q^{64} +(-6.00000 + 7.34847i) q^{65} -14.9372i q^{67} +(-1.05399 - 1.45069i) q^{68} +(1.00985 + 3.10800i) q^{69} +(3.25665 - 2.09624i) q^{70} +(-1.77672 - 1.29087i) q^{71} +(-0.831254 + 1.14412i) q^{72} +(-4.65921 - 1.51387i) q^{73} +(3.99503 + 12.2955i) q^{74} +(-1.74732 + 1.90934i) q^{75} +10.7321 q^{76} +4.24264i q^{78} +(-4.42055 + 3.21172i) q^{79} +(-3.61487 + 9.30450i) q^{80} +(2.05813 - 6.33428i) q^{81} +(1.96677 - 2.70702i) q^{82} +(5.81878 - 8.00886i) q^{83} +(0.248403 - 0.764504i) q^{84} +(-2.15782 - 0.838329i) q^{85} +(16.7145 - 12.1438i) q^{86} -3.58630i q^{87} +6.46410 q^{89} +(0.665276 - 11.7830i) q^{90} +(-1.17545 - 3.61767i) q^{91} +(-10.3996 - 3.37903i) q^{92} +(1.60283 - 2.20610i) q^{93} +(-6.41405 - 4.66008i) q^{94} +(11.6502 - 7.49897i) q^{95} +(1.21388 + 3.73594i) q^{96} +(-0.385786 - 0.530989i) q^{97} -11.9700i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^6 - 4 * q^9	\( 16 q + 4 q^{6} - 4 q^{9} - 16 q^{10} - 4 q^{15} + 4 q^{16} + 4 q^{19} - 12 q^{20} + 48 q^{21} + 8 q^{24} - 4 q^{25} + 12 q^{26} + 28 q^{31} - 32 q^{34} + 12 q^{35} + 12 q^{36} - 12 q^{39} - 4 q^{40} - 48 q^{45} - 28 q^{46} - 4 q^{49} - 24 q^{50} + 16 q^{51} - 64 q^{54} + 48 q^{56} - 12 q^{59} - 12 q^{60} + 40 q^{61} - 16 q^{64} - 96 q^{65} - 20 q^{69} - 12 q^{70} + 12 q^{71} - 24 q^{74} - 24 q^{75} + 144 q^{76} - 8 q^{79} - 24 q^{80} + 8 q^{81} - 24 q^{84} - 8 q^{85} + 48 q^{86} + 48 q^{89} + 16 q^{90} + 36 q^{91} - 4 q^{94} - 36 q^{95} + 12 q^{96}+O(q^{100}) \) 16 * q + 4 * q^6 - 4 * q^9 - 16 * q^10 - 4 * q^15 + 4 * q^16 + 4 * q^19 - 12 * q^20 + 48 * q^21 + 8 * q^24 - 4 * q^25 + 12 * q^26 + 28 * q^31 - 32 * q^34 + 12 * q^35 + 12 * q^36 - 12 * q^39 - 4 * q^40 - 48 * q^45 - 28 * q^46 - 4 * q^49 - 24 * q^50 + 16 * q^51 - 64 * q^54 + 48 * q^56 - 12 * q^59 - 12 * q^60 + 40 * q^61 - 16 * q^64 - 96 * q^65 - 20 * q^69 - 12 * q^70 + 12 * q^71 - 24 * q^74 - 24 * q^75 + 144 * q^76 - 8 * q^79 - 24 * q^80 + 8 * q^81 - 24 * q^84 - 8 * q^85 + 48 * q^86 + 48 * q^89 + 16 * q^90 + 36 * q^91 - 4 * q^94 - 36 * q^95 + 12 * q^96

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