LMFDB - Embedded newform 605.2.j.e.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.e.444.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13551 + 1.56290i) q^{2} +(-0.492303 + 0.159959i) q^{3} +(-0.535233 + 1.64728i) q^{4} +(2.23251 - 0.126049i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.852694 - 0.277057i) q^{7} +(0.492303 - 0.159959i) q^{8} +(-2.21028 + 1.60586i) q^{9} +O(q^{10})$	\(q+(1.13551 + 1.56290i) q^{2} +(-0.492303 + 0.159959i) q^{3} +(-0.535233 + 1.64728i) q^{4} +(2.23251 - 0.126049i) 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} +(-1.07891 + 0.419165i) 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} +(-0.987277 + 3.74503i) q^{20} +0.464102 q^{21} -6.31319i q^{23} +(-0.216775 + 0.157497i) q^{24} +(4.96822 - 0.562811i) 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} +(-1.88023 - 1.21026i) q^{30} +(4.26186 - 3.09642i) q^{31} +7.58871i q^{32} -2.00000 q^{34} +(-1.93857 - 0.511052i) 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} +(1.07891 - 0.419165i) 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} +(6.52111 + 7.12576i) 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} +(-0.113012 - 2.00162i) 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} +(-1.40255 - 3.61010i) 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} +(-2.35584 + 1.07179i) q^{75} -10.7321 q^{76} -4.24264i q^{78} +(4.42055 - 3.21172i) q^{79} +(8.39354 + 5.40273i) 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} +(-1.25296 + 1.94656i) q^{85} +(16.7145 - 12.1438i) q^{86} -3.58630i q^{87} +6.46410 q^{89} +(-11.4119 - 3.00844i) 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} +(5.01742 + 12.9146i) 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	−0.447663	−	0.894202i	$-0.647744\pi$
$3$	−0.492303	+	0.159959i	−0.284231	+	0.0923524i	0.163432	+	0.986555i	$0.447744\pi$
$4$	−0.535233	+	1.64728i	−0.267617	+	0.823639i
$5$	2.23251	−	0.126049i	0.998410	−	0.0563708i
$5$	2.23251	−	0.126049i	0.998410	−	0.0563708i
$6$	−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
$15$	−1.07891	+	0.419165i	−0.278573	+	0.108228i
$16$	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	$0.151643\pi$
$19$	1.91472	+	5.89289i	0.439266	+	1.35192i	−0.449385	+	0.893338i	$0.648357\pi$
$20$	−0.987277	+	3.74503i	−0.220762	+	0.837415i
$21$	0.464102			0.101275
$22$		0			0
$23$		−	6.31319i		−	1.31639i	−0.752847	−	0.658196i	$-0.771320\pi$
$23$		−	6.31319i		−	1.31639i	0.752847	−	0.658196i	$-0.228680\pi$
$24$	−0.216775	+	0.157497i	−0.0442491	+	0.0321489i
$25$	4.96822	−	0.562811i	0.993645	−	0.112562i
$26$	−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	$0.322422\pi$
$29$	−2.14093	+	6.58911i	−0.397561	+	1.22357i	−0.926949	+	0.375188i	$0.877578\pi$
$30$	−1.88023	−	1.21026i	−0.343281	−	0.220963i
$31$	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
$35$	−1.93857	−	0.511052i	−0.327679	−	0.0863836i
$36$	−1.46228	−	4.50045i	−0.243714	−	0.750075i
$37$	−6.36459	−	2.06798i	−1.04633	−	0.339974i	−0.265105	−	0.964220i	$-0.585406\pi$
$37$	−6.36459	−	2.06798i	−1.04633	−	0.339974i	−0.781228	+	0.624246i	$0.785406\pi$
$38$	−7.03582	+	9.68397i	−1.14136	+	1.57095i
$39$	−1.77672	−	1.29087i	−0.284504	−	0.206704i
$40$	1.07891	−	0.419165i	0.170591	−	0.0662757i
$41$	0.535233	+	1.64728i	0.0835894	+	0.257262i	0.984112	−	0.177547i	$-0.0568161\pi$
$41$	0.535233	+	1.64728i	0.0835894	+	0.257262i	−0.900523	+	0.434808i	$0.856816\pi$
$42$	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	−0.0101891	−	0.999948i	$-0.503243\pi$
$47$	3.90308	−	1.26819i	0.569323	−	0.184984i	0.579512	+	0.814964i	$0.303243\pi$
$48$	−2.19769	−	0.714073i	−0.317209	−	0.103068i
$49$	−5.01279	−	3.64201i	−0.716113	−	0.520287i
$50$	6.52111	+	7.12576i	0.922224	+	1.00773i
$51$	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	$-0.892799\pi$
$53$	−7.03582	−	9.68397i	−0.966444	−	1.33020i	−0.0226209	−	0.999744i	$-0.507201\pi$
$54$	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	$0.000330192\pi$
$60$	−0.113012	−	2.00162i	−0.0145898	−	0.258407i
$61$	−6.68891	−	4.85978i	−0.856427	−	0.622231i	0.0704833	−	0.997513i	$-0.477546\pi$
$61$	−6.68891	−	4.85978i	−0.856427	−	0.622231i	−0.926911	+	0.375282i	$0.877546\pi$
$62$	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	$0.365799\pi$
$67$			14.9372i			1.82487i	−0.409226	+	0.912433i	$0.634201\pi$
$68$	−1.05399	−	1.45069i	−0.127815	−	0.175922i
$69$	1.00985	+	3.10800i	0.121572	+	0.374160i
$70$	−1.40255	−	3.61010i	−0.167637	−	0.431490i
$71$	−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
$75$	−2.35584	+	1.07179i	−0.272030	+	0.123759i
$76$	−10.7321			−1.23105
$77$		0			0
$78$		−	4.24264i		−	0.480384i
$79$	4.42055	−	3.21172i	0.497351	−	0.361347i	−0.310653	−	0.950523i	$-0.600548\pi$
$79$	4.42055	−	3.21172i	0.497351	−	0.361347i	0.808004	+	0.589177i	$0.200548\pi$
$80$	8.39354	+	5.40273i	0.938426	+	0.604044i
$81$	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
$85$	−1.25296	+	1.94656i	−0.135902	+	0.211134i
$86$	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	$0.388694\pi$
$90$	−11.4119	−	3.00844i	−1.20292	−	0.317117i
$91$	−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
$95$	5.01742	+	12.9146i	0.514776	+	1.32501i
$96$	−1.21388	−	3.73594i	−0.123891	−	0.381298i
$97$	0.385786	+	0.530989i	0.0391707	+	0.0539138i	0.828153	−	0.560502i	$-0.189392\pi$
$97$	0.385786	+	0.530989i	0.0391707	+	0.0539138i	−0.788982	+	0.614416i	$0.789392\pi$
$98$		−	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	−0.642414	−	0.766358i	$-0.722067\pi$
$101$	−1.12640	+	0.818376i	−0.112081	+	0.0814315i	0.530333	+	0.847789i	$0.322067\pi$
$102$	0.984606	−	0.319918i	0.0974905	−	0.0316766i
$103$	4.03499	+	1.31105i	0.397579	+	0.129181i	0.500981	−	0.865458i	$-0.332973\pi$
$103$	4.03499	+	1.31105i	0.397579	+	0.129181i	−0.103401	+	0.994640i	$0.532973\pi$
$104$	1.77672	+	1.29087i	0.174222	+	0.126580i
$105$	1.03611	−	0.0584995i	0.101114	−	0.00570897i
$106$	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	$-0.518244\pi$
$109$	−1.19615			−0.114571			−0.0572853	+	0.998358i	$0.518244\pi$
$110$		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	−0.432797	−	0.901492i	$-0.642473\pi$
$113$	−2.68999	+	0.874032i	−0.253053	+	0.0822220i	0.179743	+	0.983714i	$0.442473\pi$
$114$	1.91472	−	5.89289i	0.179330	−	0.551920i
$115$	−0.795771	−	14.0943i	−0.0742060	−	1.31430i
$116$	−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
$125$	11.0207	−	1.88272i	0.985719	−	0.168396i
$126$	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
$130$	−4.67185	+	17.7217i	−0.409748	+	1.55430i
$131$	−21.1244			−1.84564			−0.922822	−	0.385227i	$-0.874123\pi$
$131$	−21.1244			−1.84564			−0.922822	+	0.385227i	$0.874123\pi$
$132$		0			0
$133$		−	5.55532i		−	0.481707i
$134$	−23.3453	+	16.9614i	−2.01673	+	1.46524i
$135$	3.59100	−	5.57888i	0.309064	−	0.480154i
$136$	−0.165602	+	0.509670i	−0.0142002	+	0.0437038i
$137$	8.08980	−	11.1347i	0.691159	−	0.951298i	−0.308841	−	0.951114i	$-0.599941\pi$
$137$	8.08980	−	11.1347i	0.691159	−	0.951298i	1.00000		0.000184728i	$-5.88009e-5\pi$
$138$	−3.71080	+	5.10748i	−0.315884	+	0.434778i
$139$	5.12612	−	15.7766i	0.434791	−	1.33815i	−0.458509	−	0.888690i	$-0.651616\pi$
$139$	5.12612	−	15.7766i	0.434791	−	1.33815i	0.893300	−	0.449461i	$-0.148384\pi$
$140$	1.87943	−	2.91984i	0.158841	−	0.246771i
$141$	−1.71864	+	1.24866i	−0.144736	+	0.105157i
$142$		−	4.24264i		−	0.356034i
$143$		0			0
$144$	−12.1962			−1.01635
$145$	−3.94911	+	14.9801i	−0.327956	+	1.24403i
$146$	−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	0.941046	−	0.338279i	$-0.109845\pi$
$149$	11.1095	+	8.07150i	0.910123	+	0.661243i	−0.0309232	+	0.999522i	$0.509845\pi$
$150$	−4.35019	−	2.46492i	−0.355191	−	0.201260i
$151$	1.91472	+	5.89289i	0.155817	+	0.479557i	0.998243	−	0.0592563i	$-0.0188729\pi$
$151$	1.91472	+	5.89289i	0.155817	+	0.479557i	−0.842425	+	0.538813i	$0.818873\pi$
$152$	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	−0.728933	−	0.684585i	$-0.759984\pi$
$157$	−11.4808	+	3.73032i	−0.916264	+	0.297712i	−0.187331	+	0.982297i	$0.559984\pi$
$158$	10.0392	+	3.26193i	0.798675	+	0.259505i
$159$	5.01279	+	3.64201i	0.397540	+	0.288830i
$160$	0.956548	+	16.9419i	0.0756218	+	1.33937i
$161$	−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	0.947150	−	0.320790i	$-0.103948\pi$
$163$	4.46053	+	6.13939i	0.349376	+	0.480874i	−0.597775	+	0.801664i	$0.703948\pi$
$164$	−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
$170$	−4.46502	+	0.252098i	−0.342452	+	0.0193350i
$171$	−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	$0.796652\pi$
$180$	−3.83184	−	9.86299i	−0.285609	−	0.735144i
$181$	−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
$185$	−14.4697	−	3.81455i	−1.06383	−	0.280451i
$186$	−5.26795			−0.386265
$187$		0			0
$188$			7.10823i			0.518421i
$189$	−2.15219	+	1.56366i	−0.156549	+	0.113739i
$190$	−14.4869	+	22.5064i	−1.05099	+	1.63279i
$191$	−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
$195$	−4.12927	−	2.65792i	−0.295703	−	0.190338i
$196$	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	$0.477417\pi$
$200$	2.35584	−	1.07179i	0.166583	−	0.0757867i
$201$	−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
$205$	1.40255	+	3.61010i	0.0979585	+	0.252141i
$206$	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	−0.233200	−	0.972429i	$-0.574920\pi$
$211$	8.99979	−	6.53873i	0.619571	−	0.450145i	0.852772	+	0.522284i	$0.174920\pi$
$212$	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
$215$	−1.34803	−	23.8757i	−0.0919352	−	1.62831i
$216$	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	−0.118591	−	0.992943i	$-0.537838\pi$
$223$	5.51190	−	1.79092i	0.369104	−	0.119929i	0.487695	+	0.873014i	$0.337838\pi$
$224$	2.10250	−	6.47084i	0.140479	−	0.432351i
$225$	−10.0773	+	9.22224i	−0.671823	+	0.614816i
$226$	−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
$235$	8.55382	−	3.32322i	0.557990	−	0.216783i
$236$	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	$-0.976915\pi$
$239$	−3.60322	−	11.0896i	−0.233073	−	0.717324i	0.764299	−	0.644863i	$-0.223085\pi$
$240$	−4.99638	−	1.31716i	−0.322515	−	0.0850223i
$241$	10.1244			0.652167			0.326084	−	0.945341i	$-0.394271\pi$
$241$	10.1244			0.652167			0.326084	+	0.945341i	$0.394271\pi$
$242$		0			0
$243$			12.3490i			0.792188i
$244$	11.5855	−	8.41738i	0.741688	−	0.538868i
$245$	−11.6502	−	7.49897i	−0.744304	−	0.479092i
$246$	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
$250$	15.4566	+	15.0864i	0.977564	+	0.954146i
$251$	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
$255$	0.305465	−	1.15872i	0.0191289	−	0.0725617i
$256$	5.99255	+	18.4432i	0.374534	+	1.15270i
$257$	−4.75577	−	1.54524i	−0.296657	−	0.0963897i	0.156907	−	0.987613i	$-0.449848\pi$
$257$	−4.75577	−	1.54524i	−0.296657	−	0.0963897i	−0.453564	+	0.891224i	$0.649848\pi$
$258$	−6.28609	+	8.65206i	−0.391355	+	0.538654i
$259$	4.85410	+	3.52671i	0.301619	+	0.219139i
$260$	−15.3164	+	5.95053i	−0.949881	+	0.369036i
$261$	−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	$0.905447\pi$
$270$	12.7969	−	0.722519i	0.778793	−	0.0439711i
$271$	−1.40167	+	4.31390i	−0.0851454	+	0.262051i	−0.984560	−	0.175045i	$-0.943993\pi$
$271$	−1.40167	+	4.31390i	−0.0851454	+	0.262051i	0.899415	+	0.437096i	$0.143993\pi$
$272$	−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
$280$	−1.03611	+	0.0584995i	−0.0619196	+	0.00349601i
$281$	14.0126	+	10.1807i	0.835921	+	0.607332i	0.921228	−	0.389023i	$-0.127187\pi$
$281$	14.0126	+	10.1807i	0.835921	+	0.607332i	−0.0853074	+	0.996355i	$0.527187\pi$
$282$	−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
$290$	−27.8967	+	10.8381i	−1.63815	+	0.636435i
$291$	−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
$295$	2.69729	−	10.2316i	0.157042	−	0.595708i
$296$	−3.46410			−0.201347
$297$		0			0
$298$			26.5283i			1.53674i
$299$	21.6692	−	15.7436i	1.25316	−	0.910476i
$300$	−0.504603	−	4.45439i	−0.0291333	−	0.257174i
$301$	−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
$305$	−15.5456	−	10.0064i	−0.890141	−	0.572964i
$306$	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
$310$	22.0045	+	5.80088i	1.24977	+	0.329468i
$311$	−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	−0.422849	−	0.906200i	$-0.638970\pi$
$313$	10.0784	−	13.8718i	0.569666	−	0.784078i	0.992515	+	0.122122i	$0.0389700\pi$
$314$	−18.8667	−	13.7075i	−1.06471	−	0.773556i
$315$	5.10546	−	1.98351i	0.287660	−	0.111758i
$316$	2.92457	+	9.00090i	0.164520	+	0.506340i
$317$	4.09659	+	5.63847i	0.230087	+	0.316688i	0.908413	−	0.418073i	$-0.137294\pi$
$317$	4.09659	+	5.63847i	0.230087	+	0.316688i	−0.678326	+	0.734761i	$0.737294\pi$
$318$			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
$325$	14.3213	+	15.6493i	0.794405	+	0.868065i
$326$	−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
$335$	1.88281	+	33.3474i	0.102869	+	1.82196i
$336$	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
$345$	2.64627	+	6.81137i	0.142470	+	0.366712i
$346$	−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	$0.161047\pi$
$349$	8.44250	+	25.9833i	0.451917	+	1.39086i	−0.422800	+	0.906223i	$0.638953\pi$
$350$	−3.58626	−	7.88281i	−0.191694	−	0.421354i
$351$	12.5885			0.671922
$352$		0			0
$353$			1.69161i			0.0900356i	0.998986	+	0.0450178i	$0.0143345\pi$
$353$			1.69161i			0.0900356i	−0.998986	+	0.0450178i	$0.985666\pi$
$354$	−3.82831	+	2.78143i	−0.203472	+	0.147831i
$355$	−4.12927	−	2.65792i	−0.219159	−	0.141068i
$356$	−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	$-0.739195\pi$
$359$	5.66729	−	17.4421i	0.299108	−	0.920561i	0.981810	−	0.189864i	$-0.0608047\pi$
$360$	−1.71157	+	2.65905i	−0.0902076	+	0.140144i
$361$	−15.6887	+	11.3985i	−0.825721	+	0.599922i
$362$		−	6.55343i		−	0.344441i
$363$		0			0
$364$	6.58846			0.345329
$365$	−10.5926	−	2.79244i	−0.554440	−	0.146163i
$366$	2.55494	+	7.86329i	0.133549	+	0.411021i
$367$	−28.1837	−	9.15744i	−1.47118	−	0.478015i	−0.539714	−	0.841848i	$-0.681468\pi$
$367$	−28.1837	−	9.15744i	−1.47118	−	0.478015i	−0.931464	+	0.363834i	$0.881468\pi$
$368$	16.5654	−	22.8003i	0.863531	−	1.18855i
$369$	−3.82831	−	2.78143i	−0.199294	−	0.144795i
$370$	−10.4688	−	26.9462i	−0.544247	−	1.40087i
$371$	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	$0.744818\pi$
$380$	−23.9594	+	1.35276i	−1.22909	+	0.0693953i
$381$	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	$0.00768637\pi$
$383$	13.9683	+	19.2257i	0.713745	+	0.982386i	−0.285964	+	0.958240i	$0.592314\pi$
$384$	−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	$-0.0519609\pi$
$390$	−0.534780	−	9.47175i	−0.0270796	−	0.479621i
$391$	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	$0.131598\pi$
$397$			16.0096i			0.803500i	−0.915749	+	0.401750i	$0.868402\pi$
$398$	2.27103	+	3.12580i	0.113836	+	0.156682i
$399$	0.888623	+	2.73490i	0.0444868	+	0.136916i
$400$	19.4197	+	11.0037i	0.970984	+	0.550184i
$401$	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
$405$	3.79638	−	14.4008i	0.188643	−	0.715580i
$406$	12.0000			0.595550
$407$		0			0
$408$		−	0.277401i		−	0.0137334i
$409$	1.51743	−	1.10248i	0.0750320	−	0.0545139i	−0.549637	−	0.835404i	$-0.685234\pi$
$409$	1.51743	−	1.10248i	0.0750320	−	0.0545139i	0.624669	+	0.780890i	$0.285234\pi$
$410$	−4.04962	+	6.29137i	−0.199996	+	0.310709i
$411$	−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
$415$	11.9810	−	18.6133i	0.588123	−	0.913692i
$416$	−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	$0.242071\pi$
$420$	−0.458197	+	1.73808i	−0.0223577	+	0.0848095i
$421$	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
$425$	−2.55188	+	4.50365i	−0.123784	+	0.218459i
$426$	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	−0.891963	−	0.452109i	$-0.850672\pi$
$431$	−15.3132	+	11.1257i	−0.737613	+	0.535907i	0.154350	+	0.988016i	$0.450672\pi$
$432$	12.5973	−	4.09310i	0.606087	−	0.196930i
$433$	19.2610	+	6.25829i	0.925627	+	0.300754i	0.732773	−	0.680473i	$-0.238226\pi$
$433$	19.2610	+	6.25829i	0.925627	+	0.300754i	0.192854	+	0.981228i	$0.438226\pi$
$434$	−7.38176	−	5.36316i	−0.354336	−	0.257440i
$435$	−0.452049	−	8.00646i	−0.0216741	−	0.383881i
$436$	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	$-0.660529\pi$
$439$	−20.2487			−0.966418			−0.483209	+	0.875505i	$0.660529\pi$
$440$		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	−0.0942048	−	0.995553i	$-0.530031\pi$
$443$	8.72954	−	2.83640i	0.414753	−	0.134761i	0.508958	+	0.860791i	$0.330031\pi$
$444$	−1.85410	+	5.70634i	−0.0879918	+	0.270811i
$445$	14.4312	−	0.814793i	0.684104	−	0.0386249i
$446$	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
$455$	−3.08022	−	7.92834i	−0.144403	−	0.371686i
$456$	−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
$460$	23.6431	+	6.23287i	1.10237	+	0.290609i
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$		−	17.8671i		−	0.830356i	−0.909740	−	0.415178i	$-0.863719\pi$
$463$		−	17.8671i		−	0.830356i	0.909740	−	0.415178i	$-0.136281\pi$
$464$	−25.0214	+	18.1791i	−1.16159	+	0.843945i
$465$	−3.30025	+	5.12718i	−0.153046	+	0.237767i
$466$	7.76385	−	23.8947i	0.359654	−	1.10690i
$467$	10.4424	−	14.3727i	0.483215	−	0.665088i	−0.495904	−	0.868377i	$-0.665163\pi$
$467$	10.4424	−	14.3727i	0.483215	−	0.665088i	0.979119	+	0.203289i	$0.0651632\pi$
$468$	11.8006	−	16.2421i	0.545483	−	0.750793i
$469$	4.13845	−	12.7368i	0.191096	−	0.588133i
$470$	14.9068	+	9.59520i	0.687602	+	0.442594i
$471$	5.05531	−	3.67290i	0.232937	−	0.169238i
$472$		−	2.44949i		−	0.112747i
$473$		0			0
$474$	−5.46410			−0.250974
$475$	12.8293	+	28.1996i	0.588650	+	1.29389i
$476$	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	0.398962	−	0.916967i	$-0.369371\pi$
$479$	−7.65662	−	5.56286i	−0.349840	−	0.254174i	−0.748802	+	0.662794i	$0.769371\pi$
$480$	−3.18092	−	8.18753i	−0.145188	−	0.373708i
$481$	−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	−0.0216245	−	0.999766i	$-0.506884\pi$
$487$	12.1050	−	3.93314i	0.548529	−	0.178228i	0.570153	+	0.821538i	$0.306884\pi$
$488$	−4.07034	−	1.32253i	−0.184255	−	0.0598682i
$489$	−3.17798	−	2.30894i	−0.143713	−	0.104414i
$490$	−1.50881	−	26.7233i	−0.0681611	−	1.20723i
$491$	4.85553	−	14.9438i	0.219127	−	0.674403i	−0.779708	−	0.626143i	$-0.784632\pi$
$491$	4.85553	−	14.9438i	0.219127	−	0.674403i	0.998835	−	0.0482597i	$-0.0153675\pi$
$492$	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	$0.770876\pi$
$500$	−2.79726	+	19.1618i	−0.125097	+	0.856943i
$501$	−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	$0.738465\pi$
$510$	2.15782	−	0.838329i	0.0955499	−	0.0371218i
$511$	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
$515$	9.17342	+	2.41832i	0.404229	+	0.106564i
$516$	−9.58846			−0.422108
$517$		0			0
$518$			11.5911i			0.509284i
$519$	3.19355	−	2.32025i	0.140181	−	0.101848i
$520$	4.12927	+	2.65792i	0.181081	+	0.116558i
$521$	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
$525$	2.30576	−	0.261202i	0.100632	−	0.0113998i
$526$	−33.5877	+	24.4029i	−1.46449	+	1.06402i
$527$			5.45378i			0.237570i
$528$		0			0
$529$	−16.8564			−0.732887
$530$	13.1810	−	49.9994i	0.572546	−	2.17184i
$531$	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
$535$	9.13200	−	3.54785i	0.394811	−	0.153387i
$536$	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	−0.914884	−	0.403718i	$-0.867718\pi$
$541$	−18.9248	+	13.7497i	−0.813640	+	0.591144i	0.101244	+	0.994862i	$0.467718\pi$
$542$	−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
$545$	−2.67043	+	0.150774i	−0.114388	+	0.00645843i
$546$	−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
$555$	7.73365	−	0.436646i	0.328275	−	0.0185346i
$556$	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
$565$	−5.89527	+	2.29036i	−0.248016	+	0.0963561i
$566$	−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	0.981874	−	0.189532i	$-0.0606972\pi$
$569$	1.81567	+	5.58807i	0.0761170	+	0.234264i	−0.905757	+	0.423796i	$0.860697\pi$
$570$	3.53184	−	13.3973i	0.147932	−	0.561151i
$571$	−35.7128			−1.49453			−0.747267	−	0.664524i	$-0.768635\pi$
$571$	−35.7128			−1.49453			−0.747267	+	0.664524i	$0.768635\pi$
$572$		0			0
$573$		−	5.55532i		−	0.232077i
$574$	2.42705	−	1.76336i	0.101303	−	0.0736010i
$575$	−3.55314	−	31.3654i	−0.148176	−	1.30803i
$576$	4.83928	−	14.8938i	0.201637	−	0.620574i
$577$	−12.1864	+	16.7731i	−0.507326	+	0.698275i	−0.983466	−	0.181095i	$-0.942036\pi$
$577$	−12.1864	+	16.7731i	−0.507326	+	0.698275i	0.476139	+	0.879370i	$0.342036\pi$
$578$	−18.0867	+	24.8942i	−0.752307	+	1.03546i
$579$	1.64413	−	5.06010i	0.0683276	−	0.210291i
$580$	−22.5628	−	14.5231i	−0.936868	−	0.603041i
$581$	−7.18055	+	5.21697i	−0.297899	+	0.216437i
$582$		−	0.656339i		−	0.0272061i
$583$		0			0
$584$	−2.53590			−0.104936
$585$	−25.0623	−	6.60699i	−1.03620	−	0.273165i
$586$	5.62292	+	17.3056i	0.232281	+	0.714886i
$587$	−34.1879	−	11.1083i	−1.41109	−	0.458490i	−0.498328	−	0.866989i	$-0.666052\pi$
$587$	−34.1879	−	11.1083i	−1.41109	−	0.458490i	−0.912759	+	0.408499i	$0.866052\pi$
$588$	−3.26533	+	4.49435i	−0.134660	+	0.185344i
$589$	26.4071	+	19.1859i	1.08809	+	0.790542i
$590$	19.0538	−	7.40255i	0.784434	−	0.304758i
$591$	−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	$0.562844\pi$
$600$	−0.988348	+	0.904482i	−0.0403491	+	0.0369253i
$601$	−6.18034	+	19.0211i	−0.252101	+	0.775888i	0.742286	+	0.670084i	$0.233742\pi$
$601$	−6.18034	+	19.0211i	−0.252101	+	0.775888i	−0.994387	+	0.105804i	$0.966258\pi$
$602$	−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
$610$	−2.01331	−	35.6587i	−0.0815165	−	1.44378i
$611$	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	$0.0108408\pi$
$617$			1.69161i			0.0681019i	−0.999420	+	0.0340509i	$0.989159\pi$
$618$	−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	$0.703648\pi$
$620$	7.38857	+	19.0178i	0.296732	+	0.763775i
$621$	−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
$625$	24.3665	−	5.59235i	0.974659	−	0.223694i
$626$	33.1244			1.32392
$627$		0			0
$628$		−	20.9086i		−	0.834344i
$629$	5.60503	−	4.07230i	0.223487	−	0.162373i
$630$	8.89734	+	5.72702i	0.354479	+	0.228170i
$631$	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
$635$	−4.04962	+	6.29137i	−0.160704	+	0.249666i
$636$	−8.68241	+	6.30814i	−0.344280	+	0.250134i
$637$		−	26.2880i		−	1.04157i
$638$		0			0
$639$	6.00000			0.237356
$640$	8.87353	+	2.33926i	0.350757	+	0.0924676i
$641$	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	−0.998683	−	0.0513075i	$-0.983661\pi$
$643$	−16.2611	+	22.3815i	−0.641277	+	0.882642i	0.357406	+	0.933949i	$0.383661\pi$
$644$	−7.93148	−	5.76256i	−0.312544	−	0.227077i
$645$	4.48277	+	11.5384i	0.176509	+	0.454326i
$646$	−3.82943	−	11.7858i	−0.150667	−	0.463705i
$647$	11.1543	+	15.3525i	0.438519	+	0.603569i	0.969882	−	0.243575i	$-0.0783201\pi$
$647$	11.1543	+	15.3525i	0.438519	+	0.603569i	−0.531363	+	0.847144i	$0.678320\pi$
$648$		−	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	−0.353244	−	0.935531i	$-0.614922\pi$
$653$	−30.3814	−	9.87152i	−1.18892	−	0.386302i	−0.835672	+	0.549229i	$0.814922\pi$
$654$	0.967708	+	0.703081i	0.0378404	+	0.0274926i
$655$	−47.1604	+	2.66270i	−1.84271	+	0.104040i
$656$	−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	$-0.429234\pi$
$659$	11.3205			0.440984			0.220492	+	0.975389i	$0.429234\pi$
$660$		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
$665$	−0.700242	−	12.4023i	−0.0271542	−	0.480941i
$666$	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
$675$	7.31375	−	12.9076i	0.281506	−	0.496813i
$676$	−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
$680$	−0.305465	+	1.15872i	−0.0117140	+	0.0444348i
$681$	11.1436			0.427023
$682$		0			0
$683$			22.4887i			0.860507i	0.902708	+	0.430253i	$0.141576\pi$
$683$			22.4887i			0.860507i	−0.902708	+	0.430253i	$0.858424\pi$
$684$	23.7208	−	17.2342i	0.906987	−	0.658965i
$685$	16.6571	−	25.8780i	0.636434	−	0.988747i
$686$	−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
$690$	−7.64062	+	11.8703i	−0.290873	+	0.451893i
$691$	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
$695$	9.45550	−	35.8675i	0.358667	−	1.36053i
$696$	−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
$700$	3.82782	−	6.75547i	0.144678	−	0.255333i
$701$	−3.13454	−	9.64713i	−0.118390	−	0.364367i	0.874249	−	0.485478i	$-0.161354\pi$
$701$	−3.13454	−	9.64713i	−0.118390	−	0.364367i	−0.992639	+	0.121111i	$0.961354\pi$
$702$	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	$0.555241\pi$
$710$	−0.534780	−	9.47175i	−0.0200699	−	0.355468i
$711$	−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	$-0.166225\pi$
$720$	−27.2281	+	1.53731i	−1.01473	+	0.0572922i
$721$	−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	$-0.976353\pi$
$727$		−	4.00240i		−	0.148441i	0.997242	−	0.0742205i	$-0.0236469\pi$
$728$	−1.15736	−	1.59297i	−0.0428946	−	0.0590393i
$729$	4.19906	+	12.9234i	0.155521	+	0.478644i
$730$	−7.66369	−	19.7260i	−0.283646	−	0.730091i
$731$	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
$735$	6.93495	+	1.82821i	0.255800	+	0.0674346i
$736$	47.9090			1.76595
$737$		0			0
$738$		−	9.14162i		−	0.336508i
$739$	20.2835	−	14.7368i	0.746141	−	0.542103i	−0.148487	−	0.988914i	$-0.547440\pi$
$739$	20.2835	−	14.7368i	0.746141	−	0.542103i	0.894628	+	0.446811i	$0.147440\pi$
$740$	14.0283	−	21.7940i	0.515690	−	0.801162i
$741$	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
$745$	25.8194	+	16.6194i	0.945950	+	0.608887i
$746$	−53.3215	+	38.7403i	−1.95224	+	1.41838i
$747$			27.0459i			0.989559i
$748$		0			0
$749$	−3.92820			−0.143533
$750$	−10.0226	−	4.95464i	−0.365972	−	0.180918i
$751$	−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
$755$	5.01742	+	12.9146i	0.182603	+	0.470011i
$756$	−1.42386	−	4.38218i	−0.0517851	−	0.159378i
$757$	−20.6183	−	28.3786i	−0.749385	−	1.03144i	−0.998023	−	0.0628432i	$-0.979983\pi$
$757$	−20.6183	−	28.3786i	−0.749385	−	1.03144i	0.248639	−	0.968596i	$-0.420017\pi$
$758$		−	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	−0.466594	−	0.884472i	$-0.654519\pi$
$761$	6.35597	−	4.61788i	0.230404	−	0.167398i	0.696997	+	0.717074i	$0.254519\pi$
$762$	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
$765$	−0.356520	−	6.31450i	−0.0128900	−	0.228301i
$766$	−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	$-0.395659\pi$
$769$	17.8564			0.643918			0.321959	+	0.946754i	$0.395659\pi$
$770$		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	−0.997844	−	0.0656355i	$-0.979093\pi$
$773$	−49.1148	+	15.9584i	−1.76654	+	0.573983i	−0.768693	+	0.639618i	$0.779093\pi$
$774$	−17.4424	+	53.6823i	−0.626955	+	1.92957i
$775$	19.4312	−	17.7823i	0.697988	−	0.638761i
$776$	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
$785$	−25.1607	+	9.77513i	−0.898025	+	0.348889i
$786$	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
$790$	22.8238	+	6.01687i	0.812034	+	0.214071i
$791$	2.53590			0.0901662
$792$		0			0
$793$		−	35.0779i		−	1.24565i
$794$	−25.0214	+	18.1791i	−0.887978	+	0.645154i
$795$	11.6502	+	7.49897i	0.413190	+	0.265961i
$796$	−1.07047	+	3.29456i	−0.0379417	+	0.116772i
$797$	4.64543	−	6.39388i	0.164549	−	0.226483i	−0.718778	−	0.695240i	$-0.755298\pi$
$797$	4.64543	−	6.39388i	0.164549	−	0.226483i	0.883327	+	0.468757i	$0.155298\pi$
$798$	−3.26533	+	4.49435i	−0.115592	+	0.159098i
$799$	−1.31292	+	4.04076i	−0.0464479	+	0.142952i
$800$	4.27101	+	37.7024i	0.151003	+	1.33298i
$801$	−14.2874	+	10.3804i	−0.504822	+	0.366775i
$802$			62.4384i			2.20478i
$803$		0			0
$804$	13.3923			0.472310
$805$	−3.22637	+	12.2386i	−0.113715	+	0.431353i
$806$	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	0.849596	−	0.527435i	$-0.176846\pi$
$809$	17.3648	+	12.6163i	0.610515	+	0.443565i	−0.239081	+	0.971000i	$0.576846\pi$
$810$	26.8178	−	10.4189i	0.942282	−	0.366084i
$811$	10.1916	+	31.3666i	0.357876	+	1.10143i	0.954323	+	0.298777i	$0.0965786\pi$
$811$	10.1916	+	31.3666i	0.357876	+	1.10143i	−0.596447	+	0.802652i	$0.703421\pi$
$812$	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
$820$	−6.69754	+	0.378147i	−0.233888	+	0.0132055i
$821$	−5.81071	+	17.8835i	−0.202795	+	0.624139i	0.797002	+	0.603977i	$0.206418\pi$
$821$	−5.81071	+	17.8835i	−0.202795	+	0.624139i	−0.999797	+	0.0201620i	$0.993582\pi$
$822$	−13.0896	+	4.25306i	−0.456552	+	0.148343i
$823$	28.4475	+	39.1547i	0.991619	+	1.36485i	0.930329	+	0.366726i	$0.119521\pi$
$823$	28.4475	+	39.1547i	0.991619	+	1.36485i	0.0612894	+	0.998120i	$0.480479\pi$
$824$	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	$0.839973\pi$
$830$	42.6954	−	2.41060i	1.48198	−	0.0836733i
$831$	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	$0.915306\pi$
$840$	0.500724	−	0.194535i	0.0172766	−	0.00671209i
$841$	−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
$845$	−2.85002	+	10.8110i	−0.0980438	+	0.371909i
$846$	−21.6603			−0.744695
$847$		0			0
$848$		−	53.4355i		−	1.83498i
$849$	12.6113	−	9.16267i	0.432820	−	0.314462i
$850$	−9.93645	+	1.12562i	−0.340817	+	0.0386085i
$851$	−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
$855$	−31.8289	−	20.4876i	−1.08853	−	0.700660i
$856$	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	$0.435460\pi$
$860$	40.0514	+	10.5585i	1.36574	+	0.360041i
$861$	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	−0.700126	−	0.714020i	$-0.746873\pi$
$863$	5.73725	−	7.89665i	0.195298	−	0.268805i	0.895424	+	0.445215i	$0.146873\pi$
$864$	18.2164	+	13.2350i	0.619733	+	0.450263i
$865$	−15.8946	+	6.17515i	−0.540431	+	0.209962i
$866$	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
$875$	−9.91889	−	1.44797i	−0.335320	−	0.0489503i
$876$	−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	−0.941451	−	0.337151i	$-0.890537\pi$
$883$	−44.7194	+	14.5302i	−1.50493	+	0.488981i	−0.563477	+	0.826131i	$0.690537\pi$
$884$	2.35091	−	7.23535i	0.0790696	−	0.243351i
$885$	0.308755	+	5.46852i	0.0103787	+	0.183822i
$886$	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
$895$	6.91206	+	17.7913i	0.231045	+	0.594698i
$896$	−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
$900$	−9.79786	−	21.5362i	−0.326595	−	0.717875i
$901$	12.3923			0.412848
$902$		0			0
$903$		−	4.96335i		−	0.165170i
$904$	−1.18448	+	0.860577i	−0.0393953	+	0.0286224i
$905$	−6.37831	−	4.10558i	−0.212022	−	0.136474i
$906$	1.91472	−	5.89289i	0.0636122	−	0.195778i
$907$	4.74294	−	6.52810i	0.157487	−	0.216762i	−0.722981	−	0.690868i	$-0.757229\pi$
$907$	4.74294	−	6.52810i	0.157487	−	0.216762i	0.880468	+	0.474106i	$0.157229\pi$
$908$	21.9169	−	30.1660i	0.727337	−	1.00109i
$909$	1.17545	−	3.61767i	0.0389873	−	0.119991i
$910$	8.89357	−	13.8168i	0.294819	−	0.458023i
$911$	−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
$915$	9.25378	+	2.43951i	0.305921	+	0.0806477i
$916$	−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	0.0531354	−	0.998587i	$-0.483079\pi$
$919$	−26.6820	−	19.3856i	−0.880158	−	0.639472i	−0.933293	+	0.359115i	$0.883079\pi$
$920$	−2.64627	−	6.81137i	−0.0872448	−	0.224564i
$921$	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	$0.785315\pi$
$930$	−11.7608	+	0.664019i	−0.385651	+	0.0217740i
$931$	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
$940$	0.895985	+	15.8692i	0.0292238	+	0.517597i
$941$	−21.8435	−	15.8702i	−0.712076	−	0.517354i	0.171766	−	0.985138i	$-0.445053\pi$
$941$	−21.8435	−	15.8702i	−0.712076	−	0.517354i	−0.883843	+	0.467784i	$0.845053\pi$
$942$	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	$-0.925265\pi$
$947$		−	14.3180i		−	0.465273i	0.972564	−	0.232636i	$-0.0747352\pi$
$948$	−2.87955	−	3.96336i	−0.0935234	−	0.128724i
$949$	−6.42280	−	19.7673i	−0.208493	−	0.641675i
$950$	−29.5053	+	52.0720i	−0.957277	+	1.68944i
$951$	−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
$955$	−6.11732	+	23.2048i	−0.197952	+	0.750890i
$956$	20.1962			0.653190
$957$		0			0
$958$		−	18.2832i		−	0.590705i
$959$	−9.98306	+	7.25312i	−0.322370	+	0.234215i
$960$	3.59100	−	5.57888i	0.115899	−	0.180058i
$961$	−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
$965$	−12.4396	+	19.3258i	−0.400445	+	0.622120i
$966$	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
$970$	−0.722737	+	2.74156i	−0.0232057	+	0.0880260i
$971$	−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
$975$	−9.55368	−	5.41335i	−0.305963	−	0.173366i
$976$	−11.4055	−	35.1025i	−0.365081	−	1.12360i
$977$	8.80170	+	12.1145i	0.281591	+	0.387577i	0.926260	−	0.376885i	$-0.123005\pi$
$977$	8.80170	+	12.1145i	0.281591	+	0.387577i	−0.644669	+	0.764462i	$0.723005\pi$
$978$		−	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	0.527711	−	0.849424i	$-0.323050\pi$
$983$	14.2768	+	4.63881i	0.455359	+	0.147955i	−0.0723519	+	0.997379i	$0.523050\pi$
$984$	−0.375466	−	0.272792i	−0.0119694	−	0.00869629i
$985$	0.321554	+	5.69520i	0.0102456	+	0.181464i
$986$	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
$995$	4.46502	−	0.252098i	0.141551	−	0.00799204i
$996$	−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.e.124.4		16
5.4	even	2	inner	605.2.j.e.124.1		16
11.2	odd	10		605.2.b.d.364.4	yes	4
11.3	even	5	inner	605.2.j.e.269.4		16
11.4	even	5	inner	605.2.j.e.444.1		16
11.5	even	5	inner	605.2.j.e.9.1		16
11.6	odd	10		605.2.j.f.9.4		16
11.7	odd	10		605.2.j.f.444.4		16
11.8	odd	10		605.2.j.f.269.1		16
11.9	even	5		605.2.b.e.364.1	yes	4
11.10	odd	2		605.2.j.f.124.1		16
55.2	even	20		3025.2.a.y.1.1		4
55.4	even	10	inner	605.2.j.e.444.4		16
55.9	even	10		605.2.b.e.364.4	yes	4
55.13	even	20		3025.2.a.y.1.4		4
55.14	even	10	inner	605.2.j.e.269.1		16
55.19	odd	10		605.2.j.f.269.4		16
55.24	odd	10		605.2.b.d.364.1	✓	4
55.29	odd	10		605.2.j.f.444.1		16
55.39	odd	10		605.2.j.f.9.1		16
55.42	odd	20		3025.2.a.z.1.4		4
55.49	even	10	inner	605.2.j.e.9.4		16
55.53	odd	20		3025.2.a.z.1.1		4
55.54	odd	2		605.2.j.f.124.4		16

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

\(f(q)\)	\(=\)	\(q+(1.13551 + 1.56290i) q^{2} +(-0.492303 + 0.159959i) q^{3} +(-0.535233 + 1.64728i) q^{4} +(2.23251 - 0.126049i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(-0.852694 - 0.277057i) q^{7} +(0.492303 - 0.159959i) q^{8} +(-2.21028 + 1.60586i) q^{9} +O(q^{10})\)	\(q+(1.13551 + 1.56290i) q^{2} +(-0.492303 + 0.159959i) q^{3} +(-0.535233 + 1.64728i) q^{4} +(2.23251 - 0.126049i) 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} +(-1.07891 + 0.419165i) 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} +(-0.987277 + 3.74503i) q^{20} +0.464102 q^{21} -6.31319i q^{23} +(-0.216775 + 0.157497i) q^{24} +(4.96822 - 0.562811i) 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} +(-1.88023 - 1.21026i) q^{30} +(4.26186 - 3.09642i) q^{31} +7.58871i q^{32} -2.00000 q^{34} +(-1.93857 - 0.511052i) 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} +(1.07891 - 0.419165i) 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} +(6.52111 + 7.12576i) 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} +(-0.113012 - 2.00162i) 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} +(-1.40255 - 3.61010i) 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} +(-2.35584 + 1.07179i) q^{75} -10.7321 q^{76} -4.24264i q^{78} +(4.42055 - 3.21172i) q^{79} +(8.39354 + 5.40273i) 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} +(-1.25296 + 1.94656i) q^{85} +(16.7145 - 12.1438i) q^{86} -3.58630i q^{87} +6.46410 q^{89} +(-11.4119 - 3.00844i) 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} +(5.01742 + 12.9146i) 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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