LMFDB - Embedded newform 605.2.j.e.269.3

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			269.3
Root			$0.304260 - 0.418778i$ of defining polynomial
Character	$\chi$	$=$	605.269
Dual form			605.2.j.e.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.492303 - 0.159959i) q^{2} +(1.13551 - 1.56290i) q^{3} +(-1.40126 + 1.01807i) q^{4} +(-0.809764 - 2.08429i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.96677 - 2.70702i) q^{7} +(-1.13551 + 1.56290i) q^{8} +(-0.226216 - 0.696222i) q^{9} +O(q^{10})$	\(q+(0.492303 - 0.159959i) q^{2} +(1.13551 - 1.56290i) q^{3} +(-1.40126 + 1.01807i) q^{4} +(-0.809764 - 2.08429i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.96677 - 2.70702i) q^{7} +(-1.13551 + 1.56290i) q^{8} +(-0.226216 - 0.696222i) q^{9} +(-0.732051 - 0.896575i) q^{10} +3.34607i q^{12} +(-4.03499 + 1.31105i) q^{13} +(-1.40126 - 1.01807i) q^{14} +(-4.17704 - 1.10116i) q^{15} +(0.761449 - 2.34350i) q^{16} +(-3.67460 - 1.19395i) q^{17} +(-0.222734 - 0.306567i) q^{18} +(3.39476 + 2.46644i) q^{19} +(3.25665 + 2.09624i) q^{20} -6.46410 q^{21} -3.48477i q^{23} +(1.15327 + 3.54939i) q^{24} +(-3.68856 + 3.37557i) q^{25} +(-1.77672 + 1.29087i) q^{26} +(4.16690 + 1.35391i) q^{27} +(5.51190 + 1.79092i) q^{28} +(-5.60503 + 4.07230i) q^{29} +(-2.23251 + 0.126049i) q^{30} +(-2.69835 - 8.30467i) q^{31} -5.13922i q^{32} -2.00000 q^{34} +(-4.04962 + 6.29137i) q^{35} +(1.02579 + 0.745282i) q^{36} +(-1.05399 - 1.45069i) q^{37} +(2.06578 + 0.671212i) q^{38} +(-2.53275 + 7.79500i) q^{39} +(4.17704 + 1.10116i) q^{40} +(1.40126 + 1.01807i) q^{41} +(-3.18230 + 1.03399i) q^{42} -6.45189i q^{43} +(-1.26795 + 1.03528i) q^{45} +(-0.557420 - 1.71556i) q^{46} +(6.73156 - 9.26519i) q^{47} +(-2.79802 - 3.85115i) q^{48} +(-1.29668 + 3.99078i) q^{49} +(-1.27594 + 2.25182i) q^{50} +(-6.03859 + 4.38729i) q^{51} +(4.31932 - 5.94504i) q^{52} +(2.06578 - 0.671212i) q^{53} +2.26795 q^{54} +6.46410 q^{56} +(7.70959 - 2.50500i) q^{57} +(-2.10798 + 2.90138i) q^{58} +(-1.02579 + 0.745282i) q^{59} +(6.97418 - 2.70952i) q^{60} +(3.62540 - 11.1578i) q^{61} +(-2.65681 - 3.65679i) q^{62} +(-1.43977 + 1.98168i) q^{63} +(0.700835 + 2.15695i) q^{64} +(6.00000 + 7.34847i) q^{65} +2.20925i q^{67} +(6.36459 - 2.06798i) q^{68} +(-5.44634 - 3.95700i) q^{69} +(-0.987277 + 3.74503i) q^{70} +(-2.53275 + 7.79500i) q^{71} +(1.34500 + 0.437016i) q^{72} +(2.87955 + 3.96336i) q^{73} +(-0.750932 - 0.545584i) q^{74} +(1.08727 + 9.59787i) q^{75} -7.26795 q^{76} +4.24264i q^{78} +(0.452432 + 1.39244i) q^{79} +(-5.50114 + 0.310597i) q^{80} +(8.62433 - 6.26594i) q^{81} +(0.852694 + 0.277057i) q^{82} +(-9.41498 - 3.05911i) q^{83} +(9.05788 - 6.58093i) q^{84} +(0.487015 + 8.62577i) q^{85} +(-1.03204 - 3.17629i) q^{86} +13.3843i q^{87} -0.464102 q^{89} +(-0.458614 + 0.712489i) q^{90} +(11.4849 + 8.34429i) q^{91} +(3.54775 + 4.88306i) q^{92} +(-16.0434 - 5.21282i) q^{93} +(1.83192 - 5.63806i) q^{94} +(2.39183 - 9.07291i) q^{95} +(-8.03209 - 5.83565i) q^{96} +(8.69420 - 2.82492i) q^{97} +2.17209i 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.492303	−	0.159959i	0.348111	−	0.113108i	−0.129742	−	0.991548i	$-0.541415\pi$
$2$	0.492303	−	0.159959i	0.348111	−	0.113108i	0.477853	+	0.878440i	$0.341415\pi$
$3$	1.13551	−	1.56290i	0.655589	−	0.902341i	−0.343736	−	0.939066i	$-0.611693\pi$
$3$	1.13551	−	1.56290i	0.655589	−	0.902341i	0.999325	+	0.0367251i	$0.0116926\pi$
$4$	−1.40126	+	1.01807i	−0.700629	+	0.509037i
$5$	−0.809764	−	2.08429i	−0.362137	−	0.932125i
$5$	−0.809764	−	2.08429i	−0.362137	−	0.932125i
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−1.96677	−	2.70702i	−0.743368	−	1.02316i	−0.998418	−	0.0562307i	$-0.982092\pi$
$7$	−1.96677	−	2.70702i	−0.743368	−	1.02316i	0.255049	−	0.966928i	$-0.417908\pi$
$8$	−1.13551	+	1.56290i	−0.401465	+	0.552569i
$9$	−0.226216	−	0.696222i	−0.0754054	−	0.232074i
$10$	−0.732051	−	0.896575i	−0.231495	−	0.283522i
$11$		0			0
$11$		0			0
$12$			3.34607i			0.965926i
$13$	−4.03499	+	1.31105i	−1.11911	+	0.363619i	−0.809426	−	0.587222i	$-0.800222\pi$
$13$	−4.03499	+	1.31105i	−1.11911	+	0.363619i	−0.309679	+	0.950841i	$0.600222\pi$
$14$	−1.40126	−	1.01807i	−0.374502	−	0.272092i
$15$	−4.17704	−	1.10116i	−1.07851	−	0.284319i
$16$	0.761449	−	2.34350i	0.190362	−	0.585875i
$17$	−3.67460	−	1.19395i	−0.891221	−	0.289575i	−0.172613	−	0.984990i	$-0.555221\pi$
$17$	−3.67460	−	1.19395i	−0.891221	−	0.289575i	−0.718609	+	0.695414i	$0.755221\pi$
$18$	−0.222734	−	0.306567i	−0.0524989	−	0.0722585i
$19$	3.39476	+	2.46644i	0.778811	+	0.565839i	0.904622	−	0.426215i	$-0.140153\pi$
$19$	3.39476	+	2.46644i	0.778811	+	0.565839i	−0.125811	+	0.992054i	$0.540153\pi$
$20$	3.25665	+	2.09624i	0.728210	+	0.468733i
$21$	−6.46410			−1.41058
$22$		0			0
$23$		−	3.48477i		−	0.726624i	−0.931668	−	0.363312i	$-0.881646\pi$
$23$		−	3.48477i		−	0.726624i	0.931668	−	0.363312i	$-0.118354\pi$
$24$	1.15327	+	3.54939i	0.235410	+	0.724516i
$25$	−3.68856	+	3.37557i	−0.737713	+	0.675114i
$26$	−1.77672	+	1.29087i	−0.348444	+	0.253160i
$27$	4.16690	+	1.35391i	0.801921	+	0.260560i
$28$	5.51190	+	1.79092i	1.04165	+	0.338453i
$29$	−5.60503	+	4.07230i	−1.04083	+	0.756206i	−0.970447	−	0.241314i	$-0.922422\pi$
$29$	−5.60503	+	4.07230i	−1.04083	+	0.756206i	−0.0703816	+	0.997520i	$0.522422\pi$
$30$	−2.23251	+	0.126049i	−0.407599	+	0.0230133i
$31$	−2.69835	−	8.30467i	−0.484638	−	1.49156i	−0.832504	−	0.554019i	$-0.813093\pi$
$31$	−2.69835	−	8.30467i	−0.484638	−	1.49156i	0.347866	−	0.937544i	$-0.386907\pi$
$32$		−	5.13922i		−	0.908494i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	−4.04962	+	6.29137i	−0.684510	+	1.06344i
$36$	1.02579	+	0.745282i	0.170965	+	0.124214i
$37$	−1.05399	−	1.45069i	−0.173275	−	0.238492i	0.713543	−	0.700611i	$-0.247089\pi$
$37$	−1.05399	−	1.45069i	−0.173275	−	0.238492i	−0.886818	+	0.462119i	$0.847089\pi$
$38$	2.06578	+	0.671212i	0.335114	+	0.108885i
$39$	−2.53275	+	7.79500i	−0.405565	+	1.24820i
$40$	4.17704	+	1.10116i	0.660449	+	0.174109i
$41$	1.40126	+	1.01807i	0.218840	+	0.158996i	0.691804	−	0.722085i	$-0.256816\pi$
$41$	1.40126	+	1.01807i	0.218840	+	0.158996i	−0.472964	+	0.881082i	$0.656816\pi$
$42$	−3.18230	+	1.03399i	−0.491039	+	0.159548i
$43$		−	6.45189i		−	0.983905i	−0.870622	−	0.491952i	$-0.836283\pi$
$43$		−	6.45189i		−	0.983905i	0.870622	−	0.491952i	$-0.163717\pi$
$44$		0			0
$45$	−1.26795	+	1.03528i	−0.189015	+	0.154330i
$46$	−0.557420	−	1.71556i	−0.0821870	−	0.252946i
$47$	6.73156	−	9.26519i	0.981899	−	1.35147i	0.0460982	−	0.998937i	$-0.485321\pi$
$47$	6.73156	−	9.26519i	0.981899	−	1.35147i	0.935800	−	0.352530i	$-0.114679\pi$
$48$	−2.79802	−	3.85115i	−0.403860	−	0.555865i
$49$	−1.29668	+	3.99078i	−0.185240	+	0.570111i
$50$	−1.27594	+	2.25182i	−0.180445	+	0.318456i
$51$	−6.03859	+	4.38729i	−0.845571	+	0.614343i
$52$	4.31932	−	5.94504i	0.598982	−	0.824428i
$53$	2.06578	−	0.671212i	0.283757	−	0.0921981i	−0.163681	−	0.986513i	$-0.552337\pi$
$53$	2.06578	−	0.671212i	0.283757	−	0.0921981i	0.447437	+	0.894315i	$0.352337\pi$
$54$	2.26795			0.308629
$55$		0			0
$56$	6.46410			0.863802
$57$	7.70959	−	2.50500i	1.02116	−	0.331795i
$58$	−2.10798	+	2.90138i	−0.276791	+	0.380970i
$59$	−1.02579	+	0.745282i	−0.133547	+	0.0970274i	−0.652553	−	0.757743i	$-0.726302\pi$
$59$	−1.02579	+	0.745282i	−0.133547	+	0.0970274i	0.519006	+	0.854770i	$0.326302\pi$
$60$	6.97418	−	2.70952i	0.900363	−	0.349798i
$61$	3.62540	−	11.1578i	0.464185	−	1.42862i	−0.395819	−	0.918329i	$-0.629539\pi$
$61$	3.62540	−	11.1578i	0.464185	−	1.42862i	0.860004	−	0.510287i	$-0.170461\pi$
$62$	−2.65681	−	3.65679i	−0.337416	−	0.464413i
$63$	−1.43977	+	1.98168i	−0.181394	+	0.249668i
$64$	0.700835	+	2.15695i	0.0876044	+	0.269618i
$65$	6.00000	+	7.34847i	0.744208	+	0.911465i
$66$		0			0
$67$			2.20925i			0.269903i	0.990852	+	0.134952i	$0.0430879\pi$
$67$			2.20925i			0.269903i	−0.990852	+	0.134952i	$0.956912\pi$
$68$	6.36459	−	2.06798i	0.771820	−	0.250780i
$69$	−5.44634	−	3.95700i	−0.655663	−	0.476367i
$70$	−0.987277	+	3.74503i	−0.118002	+	0.447617i
$71$	−2.53275	+	7.79500i	−0.300582	+	0.925097i	0.680707	+	0.732556i	$0.261673\pi$
$71$	−2.53275	+	7.79500i	−0.300582	+	0.925097i	−0.981289	+	0.192541i	$0.938327\pi$
$72$	1.34500	+	0.437016i	0.158509	+	0.0515028i
$73$	2.87955	+	3.96336i	0.337026	+	0.463876i	0.943570	−	0.331174i	$-0.107445\pi$
$73$	2.87955	+	3.96336i	0.337026	+	0.463876i	−0.606544	+	0.795050i	$0.707445\pi$
$74$	−0.750932	−	0.545584i	−0.0872941	−	0.0634229i
$75$	1.08727	+	9.59787i	0.125547	+	1.10827i
$76$	−7.26795			−0.833691
$77$		0			0
$78$			4.24264i			0.480384i
$79$	0.452432	+	1.39244i	0.0509026	+	0.156662i	0.973277	−	0.229636i	$-0.0737536\pi$
$79$	0.452432	+	1.39244i	0.0509026	+	0.156662i	−0.922374	+	0.386298i	$0.873754\pi$
$80$	−5.50114	+	0.310597i	−0.615046	+	0.0347258i
$81$	8.62433	−	6.26594i	0.958259	−	0.696216i
$82$	0.852694	+	0.277057i	0.0941643	+	0.0305958i
$83$	−9.41498	−	3.05911i	−1.03343	−	0.335781i	−0.257283	−	0.966336i	$-0.582827\pi$
$83$	−9.41498	−	3.05911i	−1.03343	−	0.335781i	−0.776145	+	0.630555i	$0.782827\pi$
$84$	9.05788	−	6.58093i	0.988295	−	0.718039i
$85$	0.487015	+	8.62577i	0.0528242	+	0.935596i
$86$	−1.03204	−	3.17629i	−0.111288	−	0.342508i
$87$			13.3843i			1.43494i
$88$		0			0
$89$	−0.464102			−0.0491947			−0.0245973	−	0.999697i	$-0.507830\pi$
$89$	−0.464102			−0.0491947			−0.0245973	+	0.999697i	$0.507830\pi$
$90$	−0.458614	+	0.712489i	−0.0483421	+	0.0751030i
$91$	11.4849	+	8.34429i	1.20395	+	0.874719i
$92$	3.54775	+	4.88306i	0.369878	+	0.509094i
$93$	−16.0434	−	5.21282i	−1.66362	−	0.540544i
$94$	1.83192	−	5.63806i	0.188948	−	0.581521i
$95$	2.39183	−	9.07291i	0.245396	−	0.930861i
$96$	−8.03209	−	5.83565i	−0.819771	−	0.595599i
$97$	8.69420	−	2.82492i	0.882762	−	0.286827i	0.167658	−	0.985845i	$-0.446379\pi$
$97$	8.69420	−	2.82492i	0.882762	−	0.286827i	0.715104	+	0.699018i	$0.246379\pi$
$98$			2.17209i			0.219414i
$99$		0			0
$100$	1.73205	−	8.48528i	0.173205	−	0.848528i
$101$	−5.99255	−	18.4432i	−0.596281	−	1.83516i	−0.548243	−	0.836319i	$-0.684703\pi$
$101$	−5.99255	−	18.4432i	−0.596281	−	1.83516i	−0.0480385	−	0.998845i	$-0.515297\pi$
$102$	−2.27103	+	3.12580i	−0.224865	+	0.309500i
$103$	2.49376	+	3.43237i	0.245718	+	0.338201i	0.914006	−	0.405701i	$-0.132973\pi$
$103$	2.49376	+	3.43237i	0.245718	+	0.338201i	−0.668288	+	0.743903i	$0.732973\pi$
$104$	2.53275	−	7.79500i	0.248357	−	0.764363i
$105$	5.23440	+	13.4731i	0.510825	+	1.31484i
$106$	0.909623	−	0.660880i	0.0883504	−	0.0641903i
$107$	−1.74403	+	2.40046i	−0.168602	+	0.232061i	−0.884954	−	0.465678i	$-0.845810\pi$
$107$	−1.74403	+	2.40046i	−0.168602	+	0.232061i	0.716352	+	0.697739i	$0.245810\pi$
$108$	−7.21729	+	2.34504i	−0.694484	+	0.225651i
$109$	9.19615			0.880832			0.440416	−	0.897794i	$-0.354831\pi$
$109$	9.19615			0.880832			0.440416	+	0.897794i	$0.354831\pi$
$110$		0			0
$111$	−3.46410			−0.328798
$112$	−7.84150	+	2.54786i	−0.740952	+	0.240750i
$113$	−1.66251	+	2.28825i	−0.156396	+	0.215260i	−0.880023	−	0.474930i	$-0.842473\pi$
$113$	−1.66251	+	2.28825i	−0.156396	+	0.215260i	0.723628	+	0.690190i	$0.242473\pi$
$114$	3.39476	−	2.46644i	0.317948	−	0.231003i
$115$	−7.26328	+	2.82184i	−0.677304	+	0.263138i
$116$	3.70820	−	11.4127i	0.344298	−	1.05964i
$117$	1.82556	+	2.51267i	0.168773	+	0.232296i
$118$	−0.385786	+	0.530989i	−0.0355145	+	0.0488815i
$119$	3.99503	+	12.2955i	0.366224	+	1.12712i
$120$	6.46410	−	5.27792i	0.590089	−	0.481806i
$121$		0			0
$122$		−	6.07296i		−	0.549820i
$123$	3.18230	−	1.03399i	0.286938	−	0.0932318i
$124$	12.2359	+	8.88987i	1.09881	+	0.798334i
$125$	10.0226	+	4.95464i	0.896444	+	0.443156i
$126$	−0.391818	+	1.20589i	−0.0349059	+	0.107429i
$127$	0.852694	+	0.277057i	0.0756644	+	0.0245848i	0.346605	−	0.938011i	$-0.387335\pi$
$127$	0.852694	+	0.277057i	0.0756644	+	0.0245848i	−0.270940	+	0.962596i	$0.587335\pi$
$128$	6.73156	+	9.26519i	0.594991	+	0.818935i
$129$	−10.0837	−	7.32622i	−0.887818	−	0.645037i
$130$	4.12927	+	2.65792i	0.362161	+	0.233115i
$131$	3.12436			0.272976			0.136488	−	0.990642i	$-0.456418\pi$
$131$	3.12436			0.272976			0.136488	+	0.990642i	$0.456418\pi$
$132$		0			0
$133$		−	14.0406i		−	1.21747i
$134$	0.353390	+	1.08762i	0.0305282	+	0.0939562i
$135$	−0.552263	−	9.78140i	−0.0475312	−	0.841849i
$136$	6.03859	−	4.38729i	0.517804	−	0.376207i
$137$	−8.43037	−	2.73919i	−0.720255	−	0.234025i	−0.0741215	−	0.997249i	$-0.523615\pi$
$137$	−8.43037	−	2.73919i	−0.720255	−	0.234025i	−0.646134	+	0.763224i	$0.723615\pi$
$138$	−3.31421	−	1.07685i	−0.282124	−	0.0916677i
$139$	11.8023	−	8.57488i	1.00106	−	0.727312i	0.0387439	−	0.999249i	$-0.487664\pi$
$139$	11.8023	−	8.57488i	1.00106	−	0.727312i	0.962315	+	0.271937i	$0.0876643\pi$
$140$	−0.730523	−	12.9386i	−0.0617405	−	1.09352i
$141$	−6.83680	−	21.0415i	−0.575763	−	1.77202i
$142$			4.24264i			0.356034i
$143$		0			0
$144$	−1.80385			−0.150321
$145$	13.0266	+	8.38494i	1.08180	+	0.696332i
$146$	2.05158	+	1.49056i	0.169790	+	0.123360i
$147$	4.76479	+	6.55817i	0.392993	+	0.540909i
$148$	2.95382	+	0.959754i	0.242802	+	0.0788913i
$149$	−3.17297	+	9.76540i	−0.259940	+	0.800013i	0.732876	+	0.680362i	$0.238177\pi$
$149$	−3.17297	+	9.76540i	−0.259940	+	0.800013i	−0.992816	+	0.119651i	$0.961823\pi$
$150$	2.07053	+	4.55114i	0.169058	+	0.371599i
$151$	3.39476	+	2.46644i	0.276262	+	0.200716i	0.717285	−	0.696780i	$-0.245384\pi$
$151$	3.39476	+	2.46644i	0.276262	+	0.200716i	−0.441024	+	0.897495i	$0.645384\pi$
$152$	−7.70959	+	2.50500i	−0.625330	+	0.203182i
$153$			2.82843i			0.228665i
$154$		0			0
$155$	−15.1244	+	12.3490i	−1.21482	+	0.991894i
$156$	−4.38685	−	13.5013i	−0.351229	−	1.08097i
$157$	−12.8546	+	17.6928i	−1.02591	+	1.41204i	−0.117931	+	0.993022i	$0.537626\pi$
$157$	−12.8546	+	17.6928i	−1.02591	+	1.41204i	−0.907977	+	0.419020i	$0.862374\pi$
$158$	0.445468	+	0.613134i	0.0354395	+	0.0487783i
$159$	1.29668	−	3.99078i	0.102834	−	0.316489i
$160$	−10.7116	+	4.16155i	−0.846829	+	0.329000i
$161$	−9.43334	+	6.85373i	−0.743452	+	0.540149i
$162$	3.24349	−	4.46428i	0.254833	−	0.350747i
$163$	−4.88769	+	1.58811i	−0.382833	+	0.124390i	−0.494110	−	0.869399i	$-0.664506\pi$
$163$	−4.88769	+	1.58811i	−0.382833	+	0.124390i	0.111277	+	0.993789i	$0.464506\pi$
$164$	−3.00000			−0.234261
$165$		0			0
$166$	−5.12436			−0.397727
$167$	0.492303	−	0.159959i	0.0380956	−	0.0123780i	−0.289907	−	0.957055i	$-0.593624\pi$
$167$	0.492303	−	0.159959i	0.0380956	−	0.0123780i	0.328003	+	0.944677i	$0.393624\pi$
$168$	7.34008	−	10.1027i	0.566299	−	0.779444i
$169$	4.04508	−	2.93893i	0.311160	−	0.226071i
$170$	1.61953	+	4.16859i	0.124212	+	0.319716i
$171$	0.949237	−	2.92145i	0.0725900	−	0.223409i
$172$	6.56850	+	9.04077i	0.500844	+	0.689352i
$173$	12.7949	−	17.6107i	0.972779	−	1.33892i	0.0321489	−	0.999483i	$-0.489765\pi$
$173$	12.7949	−	17.6107i	0.972779	−	1.33892i	0.940630	−	0.339433i	$-0.110235\pi$
$174$	2.14093	+	6.58911i	0.162304	+	0.499519i
$175$	16.3923	+	3.34607i	1.23914	+	0.252939i
$176$		0			0
$177$			2.44949i			0.184115i
$178$	−0.228479	+	0.0742372i	−0.0171252	+	0.00556431i
$179$	−12.5107	−	9.08957i	−0.935095	−	0.679386i	0.0121398	−	0.999926i	$-0.496136\pi$
$179$	−12.5107	−	9.08957i	−0.935095	−	0.679386i	−0.947235	+	0.320540i	$0.896136\pi$
$180$	0.722737	−	2.74156i	0.0538696	−	0.204343i
$181$	−5.37452	+	16.5411i	−0.399485	+	1.22949i	0.525929	+	0.850529i	$0.323718\pi$
$181$	−5.37452	+	16.5411i	−0.399485	+	1.22949i	−0.925413	+	0.378959i	$0.876282\pi$
$182$	6.98881	+	2.27080i	0.518045	+	0.168323i
$183$	−13.3219	−	18.3360i	−0.984784	−	1.35544i
$184$	5.44634	+	3.95700i	0.401510	+	0.291714i
$185$	−2.17018	+	3.37154i	−0.159555	+	0.247880i
$186$	−8.73205			−0.640265
$187$		0			0
$188$			19.8362i			1.44670i
$189$	−4.53027	−	13.9427i	−0.329528	−	1.01418i
$190$	−0.273789	−	4.84921i	−0.0198628	−	0.351799i
$191$	5.87989	−	4.27199i	0.425454	−	0.309111i	−0.354374	−	0.935104i	$-0.615306\pi$
$191$	5.87989	−	4.27199i	0.425454	−	0.309111i	0.779829	+	0.625993i	$0.215306\pi$
$192$	4.16690	+	1.35391i	0.300720	+	0.0977100i
$193$	14.4346	+	4.69008i	1.03902	+	0.337599i	0.778352	−	0.627828i	$-0.216056\pi$
$193$	14.4346	+	4.69008i	1.03902	+	0.337599i	0.260672	+	0.965428i	$0.416056\pi$
$194$	3.82831	−	2.78143i	0.274857	−	0.199695i
$195$	18.2980	−	1.03312i	1.31035	−	0.0739830i
$196$	−2.24592	−	6.91223i	−0.160423	−	0.493731i
$197$		−	17.2480i		−	1.22887i	−0.788969	−	0.614433i	$-0.789385\pi$
$197$		−	17.2480i		−	1.22887i	0.788969	−	0.614433i	$-0.210615\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	−1.08727	−	9.59787i	−0.0768815	−	0.678672i
$201$	3.45284	+	2.50864i	0.243545	+	0.176946i
$202$	−5.90030	−	8.12107i	−0.415144	−	0.571397i
$203$	22.0476	+	7.16370i	1.54744	+	0.502793i
$204$	3.99503	−	12.2955i	0.279708	−	0.860854i
$205$	0.987277	−	3.74503i	0.0689544	−	0.261565i
$206$	1.77672	+	1.29087i	0.123790	+	0.0899389i
$207$	−2.42617	+	0.788310i	−0.168630	+	0.0547914i
$208$			10.4543i			0.724875i
$209$		0			0
$210$	4.73205	+	5.79555i	0.326543	+	0.399931i
$211$	4.05565	+	12.4820i	0.279202	+	0.859297i	0.988077	+	0.153962i	$0.0492033\pi$
$211$	4.05565	+	12.4820i	0.279202	+	0.859297i	−0.708874	+	0.705335i	$0.750797\pi$
$212$	−2.21135	+	3.04366i	−0.151876	+	0.209039i
$213$	9.30685	+	12.8098i	0.637695	+	0.877711i
$214$	−0.474619	+	1.46073i	−0.0324443	+	0.0998532i
$215$	−13.4476	+	5.22451i	−0.917122	+	0.356309i
$216$	−6.84760	+	4.97507i	−0.465920	+	0.338511i
$217$	−17.1739	+	23.6379i	−1.16584	+	1.60464i
$218$	4.52729	−	1.47101i	0.306627	−	0.0996292i
$219$	9.46410			0.639525
$220$		0			0
$221$	16.3923			1.10267
$222$	−1.70539	+	0.554114i	−0.114458	+	0.0371897i
$223$	−0.912780	+	1.25633i	−0.0611243	+	0.0841303i	−0.838485	−	0.544925i	$-0.816558\pi$
$223$	−0.912780	+	1.25633i	−0.0611243	+	0.0841303i	0.777361	+	0.629055i	$0.216558\pi$
$224$	−13.9120	+	10.1076i	−0.929533	+	0.675345i
$225$	3.18456	+	1.80445i	0.212304	+	0.120297i
$226$	−0.452432	+	1.39244i	−0.0300953	+	0.0926240i
$227$	11.8225	+	16.2722i	0.784684	+	1.08002i	0.994750	+	0.102337i	$0.0326321\pi$
$227$	11.8225	+	16.2722i	0.784684	+	1.08002i	−0.210066	+	0.977687i	$0.567368\pi$
$228$	−8.25286	+	11.3591i	−0.546559	+	0.752274i
$229$	1.25825	+	3.87251i	0.0831478	+	0.255903i	0.983984	−	0.178256i	$-0.0570456\pi$
$229$	1.25825	+	3.87251i	0.0831478	+	0.255903i	−0.900836	+	0.434159i	$0.857046\pi$
$230$	−3.12436	+	2.55103i	−0.206014	+	0.168210i
$231$		0			0
$232$		−	13.3843i		−	0.878720i
$233$	−1.60882	+	0.522738i	−0.105397	+	0.0342457i	−0.361241	−	0.932473i	$-0.617647\pi$
$233$	−1.60882	+	0.522738i	−0.105397	+	0.0342457i	0.255844	+	0.966718i	$0.417647\pi$
$234$	1.30065	+	0.944980i	0.0850263	+	0.0617752i
$235$	−24.7624	−	6.52793i	−1.61532	−	0.425835i
$236$	0.678648	−	2.08867i	0.0441762	−	0.135961i
$237$	2.68999	+	0.874032i	0.174734	+	0.0567745i
$238$	3.93354	+	5.41405i	0.254973	+	0.350941i
$239$	−4.57924	−	3.32701i	−0.296207	−	0.215207i	0.429749	−	0.902948i	$-0.358602\pi$
$239$	−4.57924	−	3.32701i	−0.296207	−	0.215207i	−0.725955	+	0.687742i	$0.758602\pi$
$240$	−5.76119	+	8.95042i	−0.371883	+	0.577747i
$241$	−14.1244			−0.909830			−0.454915	−	0.890535i	$-0.650330\pi$
$241$	−14.1244			−0.909830			−0.454915	+	0.890535i	$0.650330\pi$
$242$		0			0
$243$		−	7.45001i		−	0.477918i
$244$	6.27938	+	19.3260i	0.401996	+	1.23722i
$245$	9.36796	−	0.528920i	0.598497	−	0.0337915i
$246$	1.40126	−	1.01807i	0.0893410	−	0.0649100i
$247$	−16.9314	−	5.50136i	−1.07732	−	0.350043i
$248$	16.0434	+	5.21282i	1.01876	+	0.331014i
$249$	−15.4719	+	11.2410i	−0.980494	+	0.712370i
$250$	5.72667	+	0.835986i	0.362187	+	0.0528724i
$251$	−1.17545	−	3.61767i	−0.0741940	−	0.228346i	0.907082	−	0.420955i	$-0.138305\pi$
$251$	−1.17545	−	3.61767i	−0.0741940	−	0.228346i	−0.981276	+	0.192609i	$0.938305\pi$
$252$		−	4.24264i		−	0.267261i
$253$		0			0
$254$	0.464102			0.0291203
$255$	14.0342	+	9.03352i	0.878858	+	0.565701i
$256$	1.12640	+	0.818376i	0.0703999	+	0.0511485i
$257$	−8.69833	−	11.9722i	−0.542587	−	0.746806i	0.446396	−	0.894835i	$-0.352707\pi$
$257$	−8.69833	−	11.9722i	−0.542587	−	0.746806i	−0.988983	+	0.148029i	$0.952707\pi$
$258$	−6.13612	−	1.99374i	−0.382018	−	0.124125i
$259$	−1.85410	+	5.70634i	−0.115208	+	0.354575i
$260$	−15.8888	−	4.18866i	−0.985384	−	0.259770i
$261$	4.10317	+	2.98113i	0.253980	+	0.184527i
$262$	1.53813	−	0.499769i	0.0950260	−	0.0308758i
$263$		−	6.79367i		−	0.418915i	−0.977818	−	0.209458i	$-0.932830\pi$
$263$		−	6.79367i		−	0.418915i	0.977818	−	0.209458i	$-0.0671699\pi$
$264$		0			0
$265$	−3.07180	−	3.76217i	−0.188699	−	0.231108i
$266$	−2.24592	−	6.91223i	−0.137706	−	0.423816i
$267$	−0.526994	+	0.725345i	−0.0322515	+	0.0443904i
$268$	−2.24918	−	3.09573i	−0.137391	−	0.189102i
$269$	5.02707	−	15.4717i	0.306506	−	0.943329i	−0.672605	−	0.740002i	$-0.734825\pi$
$269$	5.02707	−	15.4717i	0.306506	−	0.943329i	0.979111	−	0.203327i	$-0.0651754\pi$
$270$	−1.83650	−	4.72707i	−0.111766	−	0.287681i
$271$	9.27465	−	6.73843i	0.563395	−	0.409330i	−0.269305	−	0.963055i	$-0.586794\pi$
$271$	9.27465	−	6.73843i	0.563395	−	0.409330i	0.832700	+	0.553725i	$0.186794\pi$
$272$	−5.59604	+	7.70229i	−0.339310	+	0.467020i
$273$	26.0826	−	8.47475i	1.57859	−	0.512915i
$274$	−4.58846			−0.277199
$275$		0			0
$276$	11.6603			0.701865
$277$	−29.6606	+	9.63732i	−1.78213	+	0.579051i	−0.999079	−	0.0429019i	$-0.986340\pi$
$277$	−29.6606	+	9.63732i	−1.78213	+	0.579051i	−0.783055	+	0.621952i	$0.786340\pi$
$278$	4.43868	−	6.10933i	0.266215	−	0.366413i
$279$	−5.17148	+	3.75730i	−0.309609	+	0.224944i
$280$	−5.23440	−	13.4731i	−0.312815	−	0.805171i
$281$	5.35233	−	16.4728i	0.319293	−	0.982684i	−0.654658	−	0.755925i	$-0.727187\pi$
$281$	5.35233	−	16.4728i	0.319293	−	0.982684i	0.973951	−	0.226758i	$-0.0728128\pi$
$282$	−6.73156	−	9.26519i	−0.400858	−	0.551734i
$283$	−4.74294	+	6.52810i	−0.281939	+	0.388055i	−0.926375	−	0.376603i	$-0.877092\pi$
$283$	−4.74294	+	6.52810i	−0.281939	+	0.388055i	0.644436	+	0.764658i	$0.277092\pi$
$284$	−4.38685	−	13.5013i	−0.260312	−	0.801157i
$285$	−11.4641	−	14.0406i	−0.679075	−	0.831693i
$286$		0			0
$287$		−	5.79555i		−	0.342101i
$288$	−3.57803	+	1.16257i	−0.210838	+	0.0685053i
$289$	−1.67612	−	1.21777i	−0.0985952	−	0.0716336i
$290$	7.75429	+	2.04421i	0.455348	+	0.120040i
$291$	5.45732	−	16.7959i	0.319914	−	0.984593i
$292$	−8.06998	−	2.62210i	−0.472260	−	0.153447i
$293$	−8.86138	−	12.1966i	−0.517687	−	0.712535i	0.467505	−	0.883991i	$-0.345153\pi$
$293$	−8.86138	−	12.1966i	−0.517687	−	0.712535i	−0.985192	+	0.171455i	$0.945153\pi$
$294$	3.39476	+	2.46644i	0.197986	+	0.143845i
$295$	2.38404	+	1.53455i	0.138804	+	0.0893450i
$296$	3.46410			0.201347
$297$		0			0
$298$			5.31508i			0.307894i
$299$	4.56870	+	14.0610i	0.264214	+	0.813169i
$300$	−11.2949	−	12.3422i	−0.652111	−	0.712576i
$301$	−17.4654	+	12.6894i	−1.00669	+	0.731404i
$302$	2.06578	+	0.671212i	0.118872	+	0.0386239i
$303$	−35.6295	−	11.5767i	−2.04686	−	0.665065i
$304$	8.36503	−	6.07755i	0.479767	−	0.348571i
$305$	−26.1919	+	1.47881i	−1.49975	+	0.0846765i
$306$	0.452432	+	1.39244i	0.0258638	+	0.0796007i
$307$			7.82894i			0.446821i	0.974724	+	0.223411i	$0.0717191\pi$
$307$			7.82894i			0.446821i	−0.974724	+	0.223411i	$0.928281\pi$
$308$		0			0
$309$	8.19615			0.466263
$310$	−5.47044	+	8.49872i	−0.310700	+	0.482695i
$311$	−8.13269	−	5.90875i	−0.461163	−	0.335054i	0.332825	−	0.942989i	$-0.391998\pi$
$311$	−8.13269	−	5.90875i	−0.461163	−	0.335054i	−0.793987	+	0.607935i	$0.791998\pi$
$312$	−9.30685	−	12.8098i	−0.526896	−	0.725211i
$313$	16.3072	+	5.29854i	0.921739	+	0.299491i	0.731180	−	0.682185i	$-0.238970\pi$
$313$	16.3072	+	5.29854i	0.921739	+	0.299491i	0.190559	+	0.981676i	$0.438970\pi$
$314$	−3.49823	+	10.7664i	−0.197417	+	0.607586i
$315$	5.29628	+	1.39622i	0.298411	+	0.0786681i
$316$	−2.05158	−	1.49056i	−0.115411	−	0.0838508i
$317$	12.0084	−	3.90177i	0.674459	−	0.219145i	0.0482913	−	0.998833i	$-0.484622\pi$
$317$	12.0084	−	3.90177i	0.674459	−	0.219145i	0.626168	+	0.779688i	$0.284622\pi$
$318$		−	2.17209i		−	0.121805i
$319$		0			0
$320$	3.92820	−	3.20736i	0.219593	−	0.179297i
$321$	1.77130	+	5.45150i	0.0988644	+	0.304273i
$322$	−3.54775	+	4.88306i	−0.197708	+	0.272122i
$323$	−9.52958	−	13.1163i	−0.530240	−	0.729813i
$324$	−5.70572	+	17.5604i	−0.316985	+	0.975578i
$325$	10.4578	−	18.4563i	0.580094	−	1.02377i
$326$	−2.15219	+	1.56366i	−0.119199	+	0.0866030i
$327$	10.4424	−	14.3727i	0.577464	−	0.794811i
$328$	−3.18230	+	1.03399i	−0.175713	+	0.0570926i
$329$	−38.3205			−2.11268
$330$		0			0
$331$	−18.1962			−1.00015			−0.500075	−	0.865982i	$-0.666694\pi$
$331$	−18.1962			−1.00015			−0.500075	+	0.865982i	$0.666694\pi$
$332$	16.3072	−	5.29854i	0.894975	−	0.290795i
$333$	−0.771573	+	1.06198i	−0.0422819	+	0.0581961i
$334$	0.216775	−	0.157497i	0.0118614	−	0.00861783i
$335$	4.60473	−	1.78897i	0.251583	−	0.0977421i
$336$	−4.92209	+	15.1486i	−0.268522	+	0.826425i
$337$	−10.3608	−	14.2605i	−0.564391	−	0.776817i	0.427486	−	0.904022i	$-0.359399\pi$
$337$	−10.3608	−	14.2605i	−0.564391	−	0.776817i	−0.991876	+	0.127205i	$0.959399\pi$
$338$	1.52130	−	2.09389i	0.0827478	−	0.113893i
$339$	1.68850	+	5.19667i	0.0917067	+	0.282244i
$340$	−9.46410	−	11.5911i	−0.513263	−	0.628616i
$341$		0			0
$342$		−	1.59008i		−	0.0859816i
$343$	−8.92268	+	2.89915i	−0.481779	+	0.156540i
$344$	10.0837	+	7.32622i	0.543675	+	0.395003i
$345$	−3.83730	+	14.5560i	−0.206593	+	0.783670i
$346$	3.48199	−	10.7165i	0.187193	−	0.576120i
$347$	4.16690	+	1.35391i	0.223691	+	0.0726816i	0.418718	−	0.908116i	$-0.362479\pi$
$347$	4.16690	+	1.35391i	0.223691	+	0.0726816i	−0.195027	+	0.980798i	$0.562479\pi$
$348$	−13.6262	−	18.7548i	−0.730439	−	1.00536i
$349$	5.92242	+	4.30289i	0.317020	+	0.230328i	0.734903	−	0.678173i	$-0.237228\pi$
$349$	5.92242	+	4.30289i	0.317020	+	0.230328i	−0.417883	+	0.908501i	$0.637228\pi$
$350$	8.60522	−	0.974818i	0.459968	−	0.0521062i
$351$	−18.5885			−0.992178
$352$		0			0
$353$			13.0053i			0.692204i	0.938197	+	0.346102i	$0.112495\pi$
$353$			13.0053i			0.692204i	−0.938197	+	0.346102i	$0.887505\pi$
$354$	0.391818	+	1.20589i	0.0208249	+	0.0640924i
$355$	18.2980	−	1.03312i	0.971158	−	0.0548321i
$356$	0.650326	−	0.472490i	0.0344672	−	0.0250419i
$357$	23.7530	+	7.71781i	1.25714	+	0.408470i
$358$	−7.61302	−	2.47362i	−0.402361	−	0.130735i
$359$	−28.8498	+	20.9606i	−1.52263	+	1.10626i	−0.562468	+	0.826819i	$0.690148\pi$
$359$	−28.8498	+	20.9606i	−1.52263	+	1.10626i	−0.960164	+	0.279437i	$0.909852\pi$
$360$	−0.178260	−	3.15725i	−0.00939513	−	0.166402i
$361$	−0.430246	−	1.32416i	−0.0226445	−	0.0696927i
$362$			9.00292i			0.473183i
$363$		0			0
$364$	−24.5885			−1.28879
$365$	5.92905	−	9.21121i	0.310341	−	0.482137i
$366$	−9.49143	−	6.89593i	−0.496125	−	0.360456i
$367$	9.93721	+	13.6774i	0.518718	+	0.713954i	0.985359	−	0.170493i	$-0.0545359\pi$
$367$	9.93721	+	13.6774i	0.518718	+	0.713954i	−0.466641	+	0.884447i	$0.654536\pi$
$368$	−8.16655	−	2.65347i	−0.425711	−	0.138322i
$369$	0.391818	−	1.20589i	0.0203972	−	0.0627762i
$370$	−0.529080	+	2.00696i	−0.0275056	+	0.104337i
$371$	−5.87989	−	4.27199i	−0.305269	−	0.221791i
$372$	27.7880	−	9.02886i	1.44074	−	0.468125i
$373$			0.175865i			0.00910597i	0.999990	+	0.00455298i	$0.00144926\pi$
$373$			0.175865i			0.00910597i	−0.999990	+	0.00455298i	$0.998551\pi$
$374$		0			0
$375$	19.1244	−	10.0382i	0.987577	−	0.518370i
$376$	6.83680	+	21.0415i	0.352581	+	1.08513i
$377$	17.2773	−	23.7801i	0.889826	−	1.22474i
$378$	−4.46053	−	6.13939i	−0.229425	−	0.315776i
$379$	−0.452432	+	1.39244i	−0.0232399	+	0.0715250i	−0.962004	−	0.273036i	$-0.911972\pi$
$379$	−0.452432	+	1.39244i	−0.0232399	+	0.0715250i	0.938764	+	0.344561i	$0.111972\pi$
$380$	5.88532	+	15.1485i	0.301911	+	0.777104i
$381$	1.40126	−	1.01807i	0.0717886	−	0.0521575i
$382$	2.21135	−	3.04366i	0.113142	−	0.155727i
$383$	−36.5787	+	11.8852i	−1.86909	+	0.607303i	−0.877209	+	0.480109i	$0.840597\pi$
$383$	−36.5787	+	11.8852i	−1.86909	+	0.607303i	−0.991878	+	0.127194i	$0.959403\pi$
$384$	22.1244			1.12903
$385$		0			0
$386$	7.85641			0.399881
$387$	−4.49195	+	1.45952i	−0.228339	+	0.0741917i
$388$	−9.30685	+	12.8098i	−0.472483	+	0.650318i
$389$	4.95471	−	3.59981i	0.251214	−	0.182517i	−0.455051	−	0.890465i	$-0.650379\pi$
$389$	4.95471	−	3.59981i	0.251214	−	0.182517i	0.706265	+	0.707948i	$0.250379\pi$
$390$	8.84291	−	3.43554i	0.447778	−	0.173965i
$391$	−4.16064	+	12.8051i	−0.210412	+	0.647583i
$392$	−4.76479	−	6.55817i	−0.240658	−	0.331238i
$393$	3.54775	−	4.88306i	0.178960	−	0.246318i
$394$	−2.75897	−	8.49123i	−0.138995	−	0.427782i
$395$	2.53590	−	2.07055i	0.127595	−	0.104181i
$396$		0			0
$397$			32.9802i			1.65523i	0.561298	+	0.827614i	$0.310302\pi$
$397$			32.9802i			1.65523i	−0.561298	+	0.827614i	$0.689698\pi$
$398$	0.984606	−	0.319918i	0.0493538	−	0.0160360i
$399$	−21.9441	−	15.9433i	−1.09858	−	0.798163i
$400$	5.10200	+	11.2145i	0.255100	+	0.560724i
$401$	0.717076	−	2.20693i	0.0358091	−	0.110209i	−0.931554	−	0.363602i	$-0.881547\pi$
$401$	0.717076	−	2.20693i	0.0358091	−	0.110209i	0.967363	+	0.253393i	$0.0815467\pi$
$402$	2.10112	+	0.682697i	0.104795	+	0.0340498i
$403$	21.7757	+	29.9716i	1.08472	+	1.49299i
$404$	27.1736	+	19.7428i	1.35194	+	0.982241i
$405$	−20.0437	−	12.9017i	−0.995981	−	0.641091i
$406$	12.0000			0.595550
$407$		0			0
$408$		−	14.4195i		−	0.713873i
$409$	−8.07287	−	24.8457i	−0.399178	−	1.22854i	−0.925660	−	0.378357i	$-0.876489\pi$
$409$	−8.07287	−	24.8457i	−0.399178	−	1.22854i	0.526482	−	0.850186i	$-0.323511\pi$
$410$	−0.113012	−	2.00162i	−0.00558128	−	0.0988528i
$411$	−13.8539	+	10.0654i	−0.683362	+	0.496492i
$412$	−6.98881	−	2.27080i	−0.344314	−	0.111874i
$413$	4.03499	+	1.31105i	0.198549	+	0.0645125i
$414$	−1.06831	+	0.776175i	−0.0525047	+	0.0381469i
$415$	1.24782	+	22.1007i	0.0612531	+	1.08488i
$416$	6.73776	+	20.7367i	0.330346	+	1.01670i
$417$		−	28.1827i		−	1.38011i
$418$		0			0
$419$	12.3397			0.602836			0.301418	−	0.953492i	$-0.402540\pi$
$419$	12.3397			0.602836			0.301418	+	0.953492i	$0.402540\pi$
$420$	−21.0513	−	13.5503i	−1.02720	−	0.661186i
$421$	13.7958	+	10.0232i	0.672367	+	0.488503i	0.870817	−	0.491608i	$-0.163591\pi$
$421$	13.7958	+	10.0232i	0.672367	+	0.488503i	−0.198450	+	0.980111i	$0.563591\pi$
$422$	3.99322	+	5.49619i	0.194387	+	0.267550i
$423$	−7.97342	−	2.59072i	−0.387681	−	0.125965i
$424$	−1.29668	+	3.99078i	−0.0629725	+	0.193809i
$425$	17.5843	−	7.99992i	0.852962	−	0.388053i
$426$	6.63083	+	4.81758i	0.321265	+	0.233412i
$427$	−37.3349	+	12.1308i	−1.80676	+	0.587052i
$428$		−	5.13922i		−	0.248413i
$429$		0			0
$430$	−5.78461	+	4.72311i	−0.278959	+	0.227769i
$431$	1.56727	+	4.82357i	0.0754928	+	0.232343i	0.981681	−	0.190531i	$-0.0610211\pi$
$431$	1.56727	+	4.82357i	0.0754928	+	0.232343i	−0.906188	+	0.422874i	$0.861021\pi$
$432$	6.34577	−	8.73420i	0.305311	−	0.420225i
$433$	−16.8915	−	23.2492i	−0.811754	−	1.11728i	−0.991050	−	0.133488i	$-0.957382\pi$
$433$	−16.8915	−	23.2492i	−0.811754	−	1.11728i	0.179297	−	0.983795i	$-0.442618\pi$
$434$	−4.67368	+	14.3841i	−0.224344	+	0.690460i
$435$	27.8967	−	10.8381i	1.33755	−	0.519647i
$436$	−12.8862	+	9.36236i	−0.617136	+	0.448376i
$437$	8.59495	−	11.8299i	0.411152	−	0.565903i
$438$	4.65921	−	1.51387i	0.222625	−	0.0723354i
$439$	28.2487			1.34824			0.674119	−	0.738623i	$-0.264524\pi$
$439$	28.2487			1.34824			0.674119	+	0.738623i	$0.264524\pi$
$440$		0			0
$441$	3.07180			0.146276
$442$	8.06998	−	2.62210i	0.383850	−	0.124720i
$443$	−16.2015	+	22.2994i	−0.769754	+	1.05948i	0.226585	+	0.973991i	$0.427244\pi$
$443$	−16.2015	+	22.2994i	−0.769754	+	1.05948i	−0.996339	+	0.0854846i	$0.972756\pi$
$444$	4.85410	−	3.52671i	0.230365	−	0.167370i
$445$	0.375813	+	0.967324i	0.0178152	+	0.0458556i
$446$	−0.248403	+	0.764504i	−0.0117622	+	0.0362003i
$447$	11.6594	+	16.0478i	0.551471	+	0.759034i
$448$	4.46053	−	6.13939i	0.210740	−	0.290059i
$449$	−10.6662	−	32.8273i	−0.503371	−	1.54922i	−0.803492	−	0.595315i	$-0.797027\pi$
$449$	−10.6662	−	32.8273i	−0.503371	−	1.54922i	0.300122	−	0.953901i	$-0.402973\pi$
$450$	1.85641	+	0.378937i	0.0875118	+	0.0178633i
$451$		0			0
$452$		−	4.89898i		−	0.230429i
$453$	7.70959	−	2.50500i	0.362228	−	0.117695i
$454$	8.42312	+	6.11975i	0.395316	+	0.287214i
$455$	8.09187	−	30.6949i	0.379353	−	1.43900i
$456$	−4.83928	+	14.8938i	−0.226620	+	0.697465i
$457$	20.1750	+	6.55524i	0.943745	+	0.306641i	0.740171	−	0.672418i	$-0.234744\pi$
$457$	20.1750	+	6.55524i	0.943745	+	0.306641i	0.203573	+	0.979060i	$0.434744\pi$
$458$	1.23889	+	1.70518i	0.0578893	+	0.0796778i
$459$	−13.6952	−	9.95015i	−0.639237	−	0.464433i
$460$	7.30489	−	11.3487i	0.340592	−	0.529135i
$461$	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
$463$			20.3166i			0.944194i	0.881547	+	0.472097i	$0.156503\pi$
$463$			20.3166i			0.944194i	−0.881547	+	0.472097i	$0.843497\pi$
$464$	5.27548	+	16.2362i	0.244908	+	0.753749i
$465$	2.12632	+	37.6603i	0.0986058	+	1.74646i
$466$	−0.708411	+	0.514691i	−0.0328165	+	0.0238426i
$467$	−0.588870	−	0.191335i	−0.0272496	−	0.00885394i	0.295360	−	0.955386i	$-0.404560\pi$
$467$	−0.588870	−	0.191335i	−0.0272496	−	0.00885394i	−0.322610	+	0.946532i	$0.604560\pi$
$468$	−5.11616	−	1.66234i	−0.236495	−	0.0768418i
$469$	5.98050	−	4.34509i	0.276154	−	0.200638i
$470$	−13.2348	+	0.747243i	−0.610475	+	0.0344678i
$471$	13.0556	+	40.1809i	0.601569	+	1.85144i
$472$		−	2.44949i		−	0.112747i
$473$		0			0
$474$	1.46410			0.0672484
$475$	−20.8474	+	2.36164i	−0.956545	+	0.108360i
$476$	−18.1158	−	13.1619i	−0.830334	−	0.603273i
$477$	−0.934625	−	1.28640i	−0.0427935	−	0.0589003i
$478$	−2.78656	−	0.905408i	−0.127454	−	0.0414124i
$479$	0.783636	−	2.41178i	0.0358052	−	0.110197i	−0.931557	−	0.363597i	$-0.881549\pi$
$479$	0.783636	−	2.41178i	0.0358052	−	0.110197i	0.967362	+	0.253399i	$0.0815487\pi$
$480$	−5.65912	+	21.4667i	−0.258302	+	0.979818i
$481$	6.15475	+	4.47169i	0.280633	+	0.203892i
$482$	−6.95346	+	2.25932i	−0.316722	+	0.102909i
$483$			22.5259i			1.02496i
$484$		0			0
$485$	−12.9282	−	15.8338i	−0.587039	−	0.718974i
$486$	−1.19170	−	3.66766i	−0.0540564	−	0.166368i
$487$	7.48128	−	10.2971i	0.339009	−	0.466606i	−0.605142	−	0.796117i	$-0.706884\pi$
$487$	7.48128	−	10.2971i	0.339009	−	0.466606i	0.944152	+	0.329511i	$0.106884\pi$
$488$	13.3219	+	18.3360i	0.603054	+	0.830033i
$489$	−3.06798	+	9.44228i	−0.138739	+	0.426995i
$490$	4.52727	−	1.75888i	0.204521	−	0.0794580i
$491$	32.1283	−	23.3426i	1.44993	−	1.05344i	0.464084	−	0.885791i	$-0.346383\pi$
$491$	32.1283	−	23.3426i	1.44993	−	1.05344i	0.985847	−	0.167646i	$-0.0536166\pi$
$492$	−3.40654	+	4.68870i	−0.153579	+	0.211383i
$493$	25.4584	−	8.27193i	1.14659	−	0.372549i
$494$	−9.21539			−0.414620
$495$		0			0
$496$	−21.5167			−0.966127
$497$	26.0826	−	8.47475i	1.16996	−	0.380144i
$498$	−5.81878	+	8.00886i	−0.260746	+	0.358886i
$499$	14.2449	−	10.3495i	0.637690	−	0.463309i	−0.221366	−	0.975191i	$-0.571051\pi$
$499$	14.2449	−	10.3495i	0.637690	−	0.463309i	0.859056	+	0.511882i	$0.171051\pi$
$500$	−19.0884	+	3.26097i	−0.853658	+	0.145835i
$501$	0.309017	−	0.951057i	0.0138059	−	0.0424901i
$502$	−1.15736	−	1.59297i	−0.0516555	−	0.0710976i
$503$	−4.34117	+	5.97510i	−0.193563	+	0.266417i	−0.894756	−	0.446554i	$-0.852651\pi$
$503$	−4.34117	+	5.97510i	−0.193563	+	0.266417i	0.701193	+	0.712971i	$0.252651\pi$
$504$	−1.46228	−	4.50045i	−0.0651353	−	0.200466i
$505$	−33.5885	+	27.4249i	−1.49467	+	1.22039i
$506$		0			0
$507$		−	9.65926i		−	0.428983i
$508$	−1.47691	+	0.479877i	−0.0655273	+	0.0212911i
$509$	−6.53022	−	4.74448i	−0.289447	−	0.210296i	0.433580	−	0.901115i	$-0.357250\pi$
$509$	−6.53022	−	4.74448i	−0.289447	−	0.210296i	−0.723027	+	0.690819i	$0.757250\pi$
$510$	8.35409	+	2.20233i	0.369925	+	0.0975208i
$511$	5.06550	−	15.5900i	0.224085	−	0.689661i
$512$	−21.0983	−	6.85527i	−0.932424	−	0.302963i
$513$	10.8063	+	14.8736i	0.477110	+	0.656685i
$514$	−6.19728	−	4.50258i	−0.273350	−	0.198600i
$515$	5.13471	−	7.97714i	0.226262	−	0.351515i
$516$	21.5885			0.950379
$517$		0			0
$518$			3.10583i			0.136462i
$519$	−12.9950	−	39.9944i	−0.570415	−	1.75556i
$520$	−18.2980	+	1.03312i	−0.802421	+	0.0453051i
$521$	7.48236	−	5.43626i	0.327808	−	0.238167i	−0.411692	−	0.911323i	$-0.635062\pi$
$521$	7.48236	−	5.43626i	0.327808	−	0.238167i	0.739500	+	0.673156i	$0.235062\pi$
$522$	2.49686	+	0.811279i	0.109285	+	0.0355087i
$523$	24.3772	+	7.92063i	1.06594	+	0.346345i	0.788905	−	0.614515i	$-0.210648\pi$
$523$	24.3772	+	7.92063i	1.06594	+	0.346345i	0.277035	+	0.960860i	$0.410648\pi$
$524$	−4.37803	+	3.18083i	−0.191255	+	0.138955i
$525$	23.8433	−	21.8200i	1.04061	−	0.952305i
$526$	−1.08671	−	3.34454i	−0.0473827	−	0.145829i
$527$			33.7381i			1.46965i
$528$		0			0
$529$	10.8564			0.472018
$530$	−2.11405	−	1.36077i	−0.0918284	−	0.0591079i
$531$	0.750932	+	0.545584i	0.0325877	+	0.0236763i
$532$	14.2944	+	19.6745i	0.619739	+	0.852998i
$533$	−6.98881	−	2.27080i	−0.302719	−	0.0983593i
$534$	−0.143415	+	0.441387i	−0.00620619	+	0.0191007i
$535$	6.41551	+	1.69128i	0.277367	+	0.0731203i
$536$	−3.45284	−	2.50864i	−0.149140	−	0.108357i
$537$	−28.4122	+	9.23168i	−1.22608	+	0.398376i
$538$		−	8.42091i		−	0.363051i
$539$		0			0
$540$	10.7321	+	13.1440i	0.461834	+	0.565629i
$541$	0.805822	+	2.48007i	0.0346450	+	0.106626i	0.966884	−	0.255218i	$-0.0821472\pi$
$541$	0.805822	+	2.48007i	0.0346450	+	0.106626i	−0.932239	+	0.361844i	$0.882147\pi$
$542$	3.48807	−	4.80091i	0.149825	−	0.206217i
$543$	19.7492	+	27.1824i	0.847519	+	1.16651i
$544$	−6.13597	+	18.8846i	−0.263077	+	0.809669i
$545$	−7.44671	−	19.1675i	−0.318982	−	0.821045i
$546$	11.4849	−	8.34429i	0.491510	−	0.357103i
$547$	16.8915	−	23.2492i	0.722228	−	0.994062i	−0.277218	−	0.960807i	$-0.589413\pi$
$547$	16.8915	−	23.2492i	0.722228	−	0.994062i	0.999447	−	0.0332552i	$-0.0105874\pi$
$548$	14.6018	−	4.74442i	0.623759	−	0.202672i
$549$	−8.58846			−0.366546
$550$		0			0
$551$	−29.0718			−1.23850
$552$	12.3688	−	4.01887i	0.526451	−	0.171054i
$553$	2.87955	−	3.96336i	0.122451	−	0.168539i
$554$	−13.0604	+	9.48897i	−0.554885	+	0.403148i
$555$	2.80510	+	7.22021i	0.119070	+	0.306481i
$556$	−7.80823	+	24.0312i	−0.331143	+	1.01915i
$557$	−22.1018	−	30.4205i	−0.936482	−	1.28896i	−0.957277	−	0.289173i	$-0.906620\pi$
$557$	−22.1018	−	30.4205i	−0.936482	−	1.28896i	0.0207955	−	0.999784i	$-0.493380\pi$
$558$	−1.94492	+	2.67696i	−0.0823352	+	0.113325i
$559$	8.45874	+	26.0333i	0.357767	+	1.10109i
$560$	11.6603	+	14.2808i	0.492736	+	0.603475i
$561$		0			0
$562$		−	8.96575i		−	0.378198i
$563$	−15.1907	+	4.93576i	−0.640212	+	0.208017i	−0.611093	−	0.791559i	$-0.709270\pi$
$563$	−15.1907	+	4.93576i	−0.640212	+	0.208017i	−0.0291185	+	0.999576i	$0.509270\pi$
$564$	31.0019	+	22.5242i	1.30542	+	0.948441i
$565$	6.11562	+	1.61222i	0.257286	+	0.0678265i
$566$	−1.29074	+	3.97248i	−0.0542537	+	0.166976i
$567$	−33.9241	−	11.0226i	−1.42468	−	0.462906i
$568$	−9.30685	−	12.8098i	−0.390507	−	0.537486i
$569$	−24.3711	−	17.7067i	−1.02169	−	0.742301i	−0.0550616	−	0.998483i	$-0.517536\pi$
$569$	−24.3711	−	17.7067i	−1.02169	−	0.742301i	−0.966629	+	0.256181i	$0.917536\pi$
$570$	−7.88973	−	5.07844i	−0.330465	−	0.212713i
$571$	19.7128			0.824956			0.412478	−	0.910968i	$-0.364663\pi$
$571$	19.7128			0.824956			0.412478	+	0.910968i	$0.364663\pi$
$572$		0			0
$573$		−	14.0406i		−	0.586554i
$574$	−0.927051	−	2.85317i	−0.0386944	−	0.119089i
$575$	11.7631	+	12.8538i	0.490554	+	0.536040i
$576$	1.34317	−	0.975873i	0.0559656	−	0.0406614i
$577$	−3.57803	−	1.16257i	−0.148955	−	0.0483986i	0.233590	−	0.972335i	$-0.424953\pi$
$577$	−3.57803	−	1.16257i	−0.148955	−	0.0483986i	−0.382546	+	0.923937i	$0.624953\pi$
$578$	−1.01995	−	0.331402i	−0.0424244	−	0.0137845i
$579$	23.7208	−	17.2342i	0.985802	−	0.716227i
$580$	−26.7901	+	1.51259i	−1.11240	+	0.0628067i
$581$	10.2360	+	31.5031i	0.424660	+	1.30697i
$582$		−	9.14162i		−	0.378932i
$583$		0			0
$584$	−9.46410			−0.391627
$585$	3.75887	−	5.83967i	0.155410	−	0.241441i
$586$	−6.31345	−	4.58699i	−0.260806	−	0.189487i
$587$	11.9855	+	16.4966i	0.494695	+	0.680889i	0.981245	−	0.192764i	$-0.0617451\pi$
$587$	11.9855	+	16.4966i	0.494695	+	0.680889i	−0.486551	+	0.873652i	$0.661745\pi$
$588$	−13.3534	−	4.33878i	−0.550685	−	0.178928i
$589$	11.3227	−	34.8477i	0.466544	−	1.43587i
$590$	1.41913	+	0.374116i	0.0584248	+	0.0154021i
$591$	−26.9569	−	19.5853i	−1.10886	−	0.805632i
$592$	−4.20225	+	1.36539i	−0.172711	+	0.0561173i
$593$			0.859411i			0.0352918i	0.999844	+	0.0176459i	$0.00561715\pi$
$593$			0.859411i			0.0352918i	−0.999844	+	0.0176459i	$0.994383\pi$
$594$		0			0
$595$	22.3923	−	18.2832i	0.917995	−	0.749540i
$596$	−5.49575	−	16.9142i	−0.225115	−	0.692831i
$597$	2.27103	−	3.12580i	0.0929470	−	0.127931i
$598$	4.49837	+	6.19147i	0.183952	+	0.253188i
$599$	11.8801	−	36.5632i	0.485408	−	1.49393i	−0.345980	−	0.938242i	$-0.612454\pi$
$599$	11.8801	−	36.5632i	0.485408	−	1.49393i	0.831389	−	0.555692i	$-0.187546\pi$
$600$	−16.2351	−	9.19922i	−0.662796	−	0.375557i
$601$	16.1803	−	11.7557i	0.660010	−	0.479525i	−0.206656	−	0.978414i	$-0.566258\pi$
$601$	16.1803	−	11.7557i	0.660010	−	0.479525i	0.866666	+	0.498888i	$0.166258\pi$
$602$	−6.56850	+	9.04077i	−0.267712	+	0.368474i
$603$	1.53813	−	0.499769i	0.0626375	−	0.0203522i
$604$	−7.26795			−0.295729
$605$		0			0
$606$	−19.3923			−0.787759
$607$	34.6095	−	11.2453i	1.40476	−	0.456433i	0.494031	−	0.869444i	$-0.335523\pi$
$607$	34.6095	−	11.2453i	1.40476	−	0.456433i	0.910726	+	0.413011i	$0.135523\pi$
$608$	12.6756	−	17.4464i	0.514061	−	0.707545i
$609$	36.2315	−	26.3237i	1.46817	−	1.06669i
$610$	−12.6578	+	4.91766i	−0.512500	+	0.199110i
$611$	−15.0147	+	46.2104i	−0.607428	+	1.86947i
$612$	−2.87955	−	3.96336i	−0.116399	−	0.160209i
$613$	1.05399	−	1.45069i	0.0425702	−	0.0585928i	−0.787201	−	0.616696i	$-0.788471\pi$
$613$	1.05399	−	1.45069i	0.0425702	−	0.0585928i	0.829771	+	0.558103i	$0.188471\pi$
$614$	1.25231	+	3.85421i	0.0505391	+	0.155543i
$615$	−4.73205	−	5.79555i	−0.190815	−	0.233699i
$616$		0			0
$617$			13.0053i			0.523575i	0.965126	+	0.261787i	$0.0843119\pi$
$617$			13.0053i			0.523575i	−0.965126	+	0.261787i	$0.915688\pi$
$618$	4.03499	−	1.31105i	0.162311	−	0.0527381i
$619$	10.3430	+	7.51461i	0.415719	+	0.302037i	0.775913	−	0.630840i	$-0.217290\pi$
$619$	10.3430	+	7.51461i	0.415719	+	0.302037i	−0.360194	+	0.932877i	$0.617290\pi$
$620$	8.62095	−	32.7018i	0.346226	−	1.31334i
$621$	4.71806	−	14.5207i	0.189329	−	0.582695i
$622$	−4.94891	−	1.60800i	−0.198433	−	0.0644748i
$623$	0.912780	+	1.25633i	0.0365698	+	0.0503340i
$624$	16.3390	+	11.8710i	0.654085	+	0.475220i
$625$	2.21102	−	24.9020i	0.0884409	−	0.996081i
$626$	8.87564			0.354742
$627$		0			0
$628$		−	37.8792i		−	1.51154i
$629$	2.14093	+	6.58911i	0.0853646	+	0.262725i
$630$	2.83071	−	0.159824i	0.112778	−	0.00636752i
$631$	12.3946	−	9.00517i	0.493419	−	0.358490i	−0.313078	−	0.949727i	$-0.601360\pi$
$631$	12.3946	−	9.00517i	0.493419	−	0.358490i	0.806498	+	0.591237i	$0.201360\pi$
$632$	−2.68999	−	0.874032i	−0.107002	−	0.0347671i
$633$	24.1134	+	7.83491i	0.958421	+	0.311410i
$634$	5.28765	−	3.84170i	0.210000	−	0.152574i
$635$	−0.113012	−	2.00162i	−0.00448476	−	0.0794317i
$636$	2.24592	+	6.91223i	0.0890565	+	0.274088i
$637$		−	17.8028i		−	0.705371i
$638$		0			0
$639$	6.00000			0.237356
$640$	13.8604	−	21.5332i	0.547881	−	0.851173i
$641$	6.35597	+	4.61788i	0.251046	+	0.182395i	0.706190	−	0.708022i	$-0.250412\pi$
$641$	6.35597	+	4.61788i	0.251046	+	0.182395i	−0.455144	+	0.890418i	$0.650412\pi$
$642$	1.74403	+	2.40046i	0.0688315	+	0.0947385i
$643$	10.0038	+	3.25045i	0.394513	+	0.128185i	0.499554	−	0.866283i	$-0.333497\pi$
$643$	10.0038	+	3.25045i	0.394513	+	0.128185i	−0.105041	+	0.994468i	$0.533497\pi$
$644$	6.24095	−	19.2077i	0.245928	−	0.756889i
$645$	−7.10460	+	26.9498i	−0.279743	+	1.06115i
$646$	−6.78952	−	4.93287i	−0.267130	−	0.194081i
$647$	35.5329	−	11.5453i	1.39694	−	0.453894i	0.488742	−	0.872428i	$-0.337456\pi$
$647$	35.5329	−	11.5453i	1.39694	−	0.453894i	0.908201	+	0.418534i	$0.137456\pi$
$648$			20.5940i			0.809010i
$649$		0			0
$650$	2.19615	−	10.7589i	0.0861402	−	0.421999i
$651$	17.4424	+	53.6823i	0.683622	+	2.10397i
$652$	5.23210	−	7.20137i	0.204905	−	0.282027i
$653$	7.13919	+	9.82625i	0.279378	+	0.384531i	0.925528	−	0.378680i	$-0.123622\pi$
$653$	7.13919	+	9.82625i	0.279378	+	0.384531i	−0.646150	+	0.763211i	$0.723622\pi$
$654$	2.84177	−	8.74606i	0.111122	−	0.341998i
$655$	−2.52999	−	6.51208i	−0.0988549	−	0.254448i
$656$	3.45284	−	2.50864i	0.134811	−	0.0979458i
$657$	2.10798	−	2.90138i	0.0822400	−	0.113194i
$658$	−18.8653	+	6.12971i	−0.735446	+	0.238961i
$659$	−23.3205			−0.908438			−0.454219	−	0.890890i	$-0.650082\pi$
$659$	−23.3205			−0.908438			−0.454219	+	0.890890i	$0.650082\pi$
$660$		0			0
$661$	29.5885			1.15086			0.575429	−	0.817852i	$-0.304835\pi$
$661$	29.5885			1.15086			0.575429	+	0.817852i	$0.304835\pi$
$662$	−8.95802	+	2.91064i	−0.348163	+	0.113125i
$663$	18.6137	−	25.6195i	0.722896	−	0.994981i
$664$	15.4719	−	11.2410i	0.600427	−	0.436236i
$665$	−29.2647	+	11.3696i	−1.13484	+	0.440893i
$666$	−0.209975	+	0.646235i	−0.00813635	+	0.0250411i
$667$	14.1910	+	19.5322i	0.549478	+	0.756291i
$668$	−0.526994	+	0.725345i	−0.0203900	+	0.0280644i
$669$	0.927051	+	2.85317i	0.0358419	+	0.110310i
$670$	1.98076	−	1.61729i	0.0765235	−	0.0624812i
$671$		0			0
$672$			33.2204i			1.28151i
$673$	38.8118	−	12.6107i	1.49608	−	0.486107i	0.557211	−	0.830371i	$-0.311871\pi$
$673$	38.8118	−	12.6107i	1.49608	−	0.486107i	0.938873	+	0.344264i	$0.111871\pi$
$674$	−7.38176	−	5.36316i	−0.284335	−	0.206581i
$675$	−19.9401	+	9.07170i	−0.767495	+	0.349170i
$676$	−2.67617	+	8.23639i	−0.102929	+	0.316784i
$677$	−19.3576	−	6.28967i	−0.743973	−	0.241732i	−0.0875873	−	0.996157i	$-0.527916\pi$
$677$	−19.3576	−	6.28967i	−0.743973	−	0.241732i	−0.656386	+	0.754425i	$0.727916\pi$
$678$	1.66251	+	2.28825i	0.0638482	+	0.0878795i
$679$	−24.7466	−	17.9794i	−0.949687	−	0.689988i
$680$	−14.0342	−	9.03352i	−0.538188	−	0.346420i
$681$	38.8564			1.48898
$682$		0			0
$683$		−	29.8372i		−	1.14169i	−0.821058	−	0.570844i	$-0.806616\pi$
$683$		−	29.8372i		−	1.14169i	0.821058	−	0.570844i	$-0.193384\pi$
$684$	1.64413	+	5.06010i	0.0628648	+	0.193478i
$685$	1.11732	+	19.7895i	0.0426908	+	0.756117i
$686$	−3.92892	+	2.85452i	−0.150007	+	0.108986i
$687$	7.48111	+	2.43076i	0.285422	+	0.0927393i
$688$	−15.1200	−	4.91279i	−0.576445	−	0.187298i
$689$	−7.45541	+	5.41667i	−0.284028	+	0.206359i
$690$	0.439251	+	7.77978i	0.0167220	+	0.296171i
$691$	11.7145	+	36.0536i	0.445641	+	1.37154i	0.881779	+	0.471663i	$0.156346\pi$
$691$	11.7145	+	36.0536i	0.445641	+	1.37154i	−0.436138	+	0.899880i	$0.643654\pi$
$692$			37.7033i			1.43326i
$693$		0			0
$694$	2.26795			0.0860902
$695$	−27.4297	−	17.6559i	−1.04047	−	0.669725i
$696$	−20.9183	−	15.1980i	−0.792905	−	0.576079i
$697$	−3.93354	−	5.41405i	−0.148993	−	0.205072i
$698$	3.60391	+	1.17098i	0.136410	+	0.0443223i
$699$	−1.00985	+	3.10800i	−0.0381961	+	0.117556i
$700$	−26.3764	+	11.9999i	−0.996934	+	0.453553i
$701$	30.6265	+	22.2514i	1.15675	+	0.840425i	0.989363	−	0.145467i	$-0.0464684\pi$
$701$	30.6265	+	22.2514i	1.15675	+	0.840425i	0.167383	+	0.985892i	$0.446468\pi$
$702$	−9.15115	+	2.97339i	−0.345388	+	0.112223i
$703$		−	7.52433i		−	0.283786i
$704$		0			0
$705$	−38.3205	+	31.2886i	−1.44323	+	1.17840i
$706$	2.08032	+	6.40256i	0.0782938	+	0.240964i
$707$	−38.1402	+	52.4954i	−1.43441	+	1.97429i
$708$	−2.49376	−	3.43237i	−0.0937213	−	0.128996i
$709$	−0.805822	+	2.48007i	−0.0302633	+	0.0931408i	−0.965047	−	0.262076i	$-0.915593\pi$
$709$	−0.805822	+	2.48007i	−0.0302633	+	0.0931408i	0.934784	+	0.355217i	$0.115593\pi$
$710$	8.84291	−	3.43554i	0.331869	−	0.128933i
$711$	0.867102	−	0.629986i	0.0325189	−	0.0236263i
$712$	0.526994	−	0.725345i	0.0197499	−	0.0271834i
$713$	−28.9398	+	9.40313i	−1.08381	+	0.352150i
$714$	12.9282			0.483826
$715$		0			0
$716$	26.7846			1.00099
$717$	−10.3996	+	3.37903i	−0.388380	+	0.126192i
$718$	−10.8500	+	14.9337i	−0.404918	+	0.557322i
$719$	−40.6095	+	29.5046i	−1.51448	+	1.10033i	−0.550340	+	0.834941i	$0.685502\pi$
$719$	−40.6095	+	29.5046i	−1.51448	+	1.10033i	−0.964140	+	0.265394i	$0.914498\pi$
$720$	1.46069	+	3.75975i	0.0544367	+	0.140118i
$721$	4.38685	−	13.5013i	0.163375	−	0.502816i
$722$	−0.423623	−	0.583067i	−0.0157656	−	0.0216995i
$723$	−16.0384	+	22.0750i	−0.596475	+	0.820977i
$724$	−9.30894	−	28.6500i	−0.345964	−	1.06477i
$725$	6.92820	−	33.9411i	0.257307	−	1.26054i
$726$		0			0
$727$		−	8.24504i		−	0.305792i	−0.988242	−	0.152896i	$-0.951140\pi$
$727$		−	8.24504i		−	0.305792i	0.988242	−	0.152896i	$-0.0488599\pi$
$728$	−26.0826	+	8.47475i	−0.966685	+	0.314095i
$729$	14.2294	+	10.3382i	0.527013	+	0.382898i
$730$	1.44547	−	5.48311i	0.0534994	−	0.202939i
$731$	−7.70324	+	23.7081i	−0.284915	+	0.876877i
$732$	37.3349	+	12.1308i	1.37994	+	0.448369i
$733$	5.47668	+	7.53800i	0.202286	+	0.278423i	0.898093	−	0.439807i	$-0.144953\pi$
$733$	5.47668	+	7.53800i	0.202286	+	0.278423i	−0.695807	+	0.718229i	$0.744953\pi$
$734$	7.07994	+	5.14388i	0.261325	+	0.189864i
$735$	9.81080	−	15.2418i	0.361877	−	0.562202i
$736$	−17.9090			−0.660133
$737$		0			0
$738$		−	0.656339i		−	0.0241602i
$739$	−12.0295	−	37.0229i	−0.442511	−	1.36191i	−0.885190	−	0.465230i	$-0.845972\pi$
$739$	−12.0295	−	37.0229i	−0.442511	−	1.36191i	0.442679	−	0.896680i	$-0.354028\pi$
$740$	−0.391486	−	6.93380i	−0.0143913	−	0.254892i
$741$	−27.8240	+	20.2153i	−1.02214	+	0.742627i
$742$	−3.57803	−	1.16257i	−0.131354	−	0.0426794i
$743$	41.2733	+	13.4105i	1.51417	+	0.491984i	0.944113	−	0.329621i	$-0.106921\pi$
$743$	41.2733	+	13.4105i	1.51417	+	0.491984i	0.570057	+	0.821605i	$0.306921\pi$
$744$	26.3646	−	19.1550i	0.966574	−	0.702257i
$745$	22.9233	−	1.29426i	0.839846	−	0.0474181i
$746$	0.0281313	+	0.0865791i	0.00102996	+	0.00316989i
$747$			7.24693i			0.265151i
$748$		0			0
$749$	9.92820			0.362769
$750$	7.80928	−	8.00095i	0.285155	−	0.292153i
$751$	−39.3514	−	28.5905i	−1.43595	−	1.04328i	−0.988869	−	0.148789i	$-0.952462\pi$
$751$	−39.3514	−	28.5905i	−1.43595	−	1.04328i	−0.447084	−	0.894492i	$-0.647538\pi$
$752$	−16.5872	−	22.8304i	−0.604874	−	0.832538i
$753$	−6.98881	−	2.27080i	−0.254686	−	0.0827526i
$754$	4.70181	−	14.4707i	0.171230	−	0.526992i
$755$	2.39183	−	9.07291i	0.0870475	−	0.330197i
$756$	20.5428	+	14.9252i	0.747135	+	0.542825i
$757$	47.3387	−	15.3813i	1.72056	−	0.559042i	0.728522	−	0.685022i	$-0.240207\pi$
$757$	47.3387	−	15.3813i	1.72056	−	0.559042i	0.992033	+	0.125980i	$0.0402075\pi$
$758$			0.757875i			0.0275273i
$759$		0			0
$760$	11.4641	+	14.0406i	0.415847	+	0.509306i
$761$	6.13597	+	18.8846i	0.222429	+	0.684565i	0.998542	+	0.0539721i	$0.0171882\pi$
$761$	6.13597	+	18.8846i	0.222429	+	0.684565i	−0.776114	+	0.630593i	$0.782812\pi$
$762$	0.526994	−	0.725345i	0.0190910	−	0.0262765i
$763$	−18.0867	−	24.8942i	−0.654782	−	0.901231i
$764$	−3.89005	+	11.9723i	−0.140737	+	0.433144i
$765$	5.89527	−	2.29036i	0.213144	−	0.0828081i
$766$	−16.1067	+	11.7022i	−0.581958	+	0.422818i
$767$	3.16196	−	4.35207i	0.114172	−	0.157144i
$768$	2.55808	−	0.831171i	0.0923068	−	0.0299923i
$769$	−9.85641			−0.355431			−0.177716	−	0.984082i	$-0.556871\pi$
$769$	−9.85641			−0.355431			−0.177716	+	0.984082i	$0.556871\pi$
$770$		0			0
$771$	−28.5885			−1.02959
$772$	−25.0014	+	8.12345i	−0.899821	+	0.292369i
$773$	7.07951	−	9.74411i	0.254632	−	0.350471i	−0.662495	−	0.749067i	$-0.730502\pi$
$773$	7.07951	−	9.74411i	0.254632	−	0.350471i	0.917127	+	0.398596i	$0.130502\pi$
$774$	−1.97794	+	1.43705i	−0.0710955	+	0.0516539i
$775$	37.9861	+	21.5238i	1.36450	+	0.773159i
$776$	−5.45732	+	16.7959i	−0.195906	+	0.602938i
$777$	6.81308	+	9.37740i	0.244418	+	0.336413i
$778$	1.86340	−	2.56475i	0.0668060	−	0.0919506i
$779$	2.24592	+	6.91223i	0.0804684	+	0.247656i
$780$	−24.5885	+	20.0764i	−0.880408	+	0.718850i
$781$		0			0
$782$			6.96953i			0.249230i
$783$	−28.8692	+	9.38016i	−1.03170	+	0.335219i
$784$	8.36503	+	6.07755i	0.298751	+	0.217055i
$785$	47.2863	+	12.4657i	1.68772	+	0.444921i
$786$	0.965479	−	2.97144i	0.0344375	−	0.105988i
$787$	16.5357	+	5.37277i	0.589434	+	0.191519i	0.588522	−	0.808481i	$-0.299710\pi$
$787$	16.5357	+	5.37277i	0.589434	+	0.191519i	0.000911585		1.00000i	$0.499710\pi$
$788$	17.5597	+	24.1689i	0.625539	+	0.860980i
$789$	−10.6178	−	7.71430i	−0.378005	−	0.274636i
$790$	0.917227	−	1.42498i	0.0326335	−	0.0506985i
$791$	9.46410			0.336505
$792$		0			0
$793$			49.7749i			1.76756i
$794$	5.27548	+	16.2362i	0.187220	+	0.576203i
$795$	−9.36796	+	0.528920i	−0.332247	+	0.0187589i
$796$	−2.80252	+	2.03615i	−0.0993326	+	0.0721693i
$797$	34.4164	+	11.1826i	1.21909	+	0.396107i	0.846751	−	0.531989i	$-0.178555\pi$
$797$	34.4164	+	11.1826i	1.21909	+	0.396107i	0.372340	+	0.928096i	$0.378555\pi$
$798$	−13.3534	−	4.33878i	−0.472705	−	0.153591i
$799$	−35.7980	+	26.0087i	−1.26644	+	0.920123i
$800$	17.3478	+	18.9563i	0.613337	+	0.670208i
$801$	0.104987	+	0.323118i	0.00370954	+	0.0114168i
$802$		−	1.20118i		−	0.0424153i
$803$		0			0
$804$	−7.39230			−0.260706
$805$	21.9240	+	14.1120i	0.772718	+	0.497381i
$806$	15.5144	+	11.2719i	0.546473	+	0.397036i
$807$	−18.4725	−	25.4252i	−0.650262	−	0.895009i
$808$	35.6295	+	11.5767i	1.25344	+	0.407268i
$809$	−4.49184	+	13.8245i	−0.157925	+	0.486042i	−0.998445	−	0.0557371i	$-0.982249\pi$
$809$	−4.49184	+	13.8245i	−0.157925	+	0.486042i	0.840521	+	0.541779i	$0.182249\pi$
$810$	−11.9313	−	3.14537i	−0.419224	−	0.110517i
$811$	15.3558	+	11.1566i	0.539214	+	0.391762i	0.823793	−	0.566891i	$-0.191854\pi$
$811$	15.3558	+	11.1566i	0.539214	+	0.391762i	−0.284579	+	0.958653i	$0.591854\pi$
$812$	−38.1876	+	12.4079i	−1.34012	+	0.435432i
$813$		−	22.1469i		−	0.776727i
$814$		0			0
$815$	7.26795	+	8.90138i	0.254585	+	0.311802i
$816$	5.68353	+	17.4921i	0.198964	+	0.612347i
$817$	15.9132	−	21.9026i	0.556732	−	0.766276i
$818$	−7.94860	−	10.9403i	−0.277916	−	0.382519i
$819$	3.21140	−	9.88367i	0.112215	−	0.345363i
$820$	2.42929	+	6.25288i	0.0848345	+	0.218360i
$821$	23.6202	−	17.1611i	0.824350	−	0.598925i	−0.0936051	−	0.995609i	$-0.529839\pi$
$821$	23.6202	−	17.1611i	0.824350	−	0.598925i	0.917955	+	0.396684i	$0.129839\pi$
$822$	−5.21026	+	7.17130i	−0.181729	+	0.250128i
$823$	−6.42581	+	2.08787i	−0.223990	+	0.0727787i	−0.418862	−	0.908050i	$-0.637571\pi$
$823$	−6.42581	+	2.08787i	−0.223990	+	0.0727787i	0.194872	+	0.980829i	$0.437571\pi$
$824$	−8.19615			−0.285526
$825$		0			0
$826$	2.19615			0.0764139
$827$	−32.4118	+	10.5312i	−1.12707	+	0.366207i	−0.812462	−	0.583014i	$-0.801873\pi$
$827$	−32.4118	+	10.5312i	−1.12707	+	0.366207i	−0.314608	+	0.949222i	$0.601873\pi$
$828$	2.59713	−	3.57465i	0.0902566	−	0.124228i
$829$	−8.07461	+	5.86654i	−0.280443	+	0.203754i	−0.719110	−	0.694896i	$-0.755450\pi$
$829$	−8.07461	+	5.86654i	−0.280443	+	0.203754i	0.438668	+	0.898649i	$0.355450\pi$
$830$	4.14952	+	10.6807i	0.144032	+	0.370731i
$831$	−18.6179	+	57.2999i	−0.645847	+	1.98771i
$832$	−5.65572	−	7.78444i	−0.196077	−	0.269877i
$833$	9.52958	−	13.1163i	0.330180	−	0.454454i
$834$	−4.50808	−	13.8744i	−0.156102	−	0.480433i
$835$	−0.732051	−	0.896575i	−0.0253337	−	0.0310273i
$836$		0			0
$837$		−	38.2581i		−	1.32239i
$838$	6.07489	−	1.97385i	0.209854	−	0.0681856i
$839$	−31.3774	−	22.7970i	−1.08327	−	0.787041i	−0.105019	−	0.994470i	$-0.533490\pi$
$839$	−31.3774	−	22.7970i	−1.08327	−	0.787041i	−0.978250	+	0.207430i	$0.933490\pi$
$840$	−27.0008	−	7.11804i	−0.931617	−	0.245596i
$841$	5.87132	−	18.0701i	0.202459	−	0.623106i
$842$	8.39503	+	2.72771i	0.289312	+	0.0940031i
$843$	−19.6677	−	27.0702i	−0.677391	−	0.932348i
$844$	−18.3906	−	13.3616i	−0.633031	−	0.459924i
$845$	−9.40115	−	6.05131i	−0.323409	−	0.208171i
$846$	−4.33975			−0.149204
$847$		0			0
$848$		−	5.35225i		−	0.183797i
$849$	4.81710	+	14.8255i	0.165322	+	0.508810i
$850$	7.37713	−	6.75114i	0.253033	−	0.231562i
$851$	−5.05531	+	3.67290i	−0.173294	+	0.125905i
$852$	−26.0826	−	8.47475i	−0.893575	−	0.290340i
$853$	−44.0952	−	14.3274i	−1.50979	−	0.490561i	−0.566935	−	0.823762i	$-0.691871\pi$
$853$	−44.0952	−	14.3274i	−1.50979	−	0.490561i	−0.942856	+	0.333201i	$0.891871\pi$
$854$	−16.4396	+	11.9441i	−0.562553	+	0.408719i
$855$	−6.85782	+	0.387197i	−0.234533	+	0.0132418i
$856$	−1.77130	−	5.45150i	−0.0605418	−	0.186329i
$857$		−	29.3195i		−	1.00154i	−0.865581	−	0.500768i	$-0.833051\pi$
$857$		−	29.3195i		−	1.00154i	0.865581	−	0.500768i	$-0.166949\pi$
$858$		0			0
$859$	22.1962			0.757323			0.378661	−	0.925535i	$-0.376384\pi$
$859$	22.1962			0.757323			0.378661	+	0.925535i	$0.376384\pi$
$860$	13.5247	−	21.0116i	0.461188	−	0.716489i
$861$	−9.05788	−	6.58093i	−0.308692	−	0.224278i
$862$	1.54315	+	2.12396i	0.0525597	+	0.0723423i
$863$	−16.2719	−	5.28705i	−0.553901	−	0.179973i	0.0186740	−	0.999826i	$-0.494056\pi$
$863$	−16.2719	−	5.28705i	−0.553901	−	0.179973i	−0.572575	+	0.819852i	$0.694056\pi$
$864$	6.95803	−	21.4146i	0.236717	−	0.728540i
$865$	−47.0667	−	12.4079i	−1.60032	−	0.421880i
$866$	−12.0346	−	8.74368i	−0.408954	−	0.297122i
$867$	−3.80651	+	1.23681i	−0.129276	+	0.0420043i
$868$		−	50.6071i		−	1.71772i
$869$		0			0
$870$	12.0000	−	9.79796i	0.406838	−	0.332182i
$871$	−2.89644	−	8.91432i	−0.0981420	−	0.302050i
$872$	−10.4424	+	14.3727i	−0.353623	+	0.486720i
$873$	−3.93354	−	5.41405i	−0.133130	−	0.183238i
$874$	2.33902	−	7.19876i	0.0791184	−	0.243502i
$875$	−6.29971	−	36.8759i	−0.212969	−	1.24663i
$876$	−13.2617	+	9.63516i	−0.448070	+	0.325542i
$877$	−6.99213	+	9.62384i	−0.236107	+	0.324974i	−0.910585	−	0.413321i	$-0.864369\pi$
$877$	−6.99213	+	9.62384i	−0.236107	+	0.324974i	0.674478	+	0.738295i	$0.264369\pi$
$878$	13.9069	−	4.51863i	0.469336	−	0.152497i
$879$	−29.1244			−0.982340
$880$		0			0
$881$	−26.9090			−0.906586			−0.453293	−	0.891362i	$-0.649751\pi$
$881$	−26.9090			−0.906586			−0.453293	+	0.891362i	$0.649751\pi$
$882$	1.51226	−	0.491361i	0.0509203	−	0.0165450i
$883$	12.6756	−	17.4464i	0.426566	−	0.587118i	−0.540595	−	0.841283i	$-0.681801\pi$
$883$	12.6756	−	17.4464i	0.426566	−	0.587118i	0.967161	+	0.254165i	$0.0818007\pi$
$884$	−22.9699	+	16.6886i	−0.772560	+	0.561298i
$885$	5.10546	−	1.98351i	0.171618	−	0.0666749i
$886$	−4.40904	+	13.5696i	−0.148125	+	0.455881i
$887$	9.22532	+	12.6976i	0.309756	+	0.426342i	0.935305	−	0.353842i	$-0.115125\pi$
$887$	9.22532	+	12.6976i	0.309756	+	0.426342i	−0.625549	+	0.780185i	$0.715125\pi$
$888$	3.93354	−	5.41405i	0.132001	−	0.181684i
$889$	−0.927051	−	2.85317i	−0.0310923	−	0.0956922i
$890$	0.339746	+	0.416102i	0.0113883	+	0.0139478i
$891$		0			0
$892$		−	2.68973i		−	0.0900587i
$893$	45.7040	−	14.8501i	1.52943	−	0.496941i
$894$	8.30695	+	6.03535i	0.277826	+	0.201852i
$895$	−8.81461	+	33.4364i	−0.294640	+	1.11766i
$896$	11.8417	−	36.4450i	0.395603	−	1.21754i
$897$	27.1638	+	8.82604i	0.906972	+	0.294693i
$898$	−10.5020	−	14.4548i	−0.350458	−	0.482364i
$899$	48.9434	+	35.5595i	1.63236	+	1.18598i
$900$	−6.29945	+	0.713616i	−0.209982	+	0.0237872i
$901$	−8.39230			−0.279588
$902$		0			0
$903$			41.7057i			1.38788i
$904$	−1.68850	−	5.19667i	−0.0561587	−	0.172839i
$905$	38.8285	−	2.19228i	1.29070	−	0.0728739i
$906$	3.39476	−	2.46644i	0.112783	−	0.0819419i
$907$	−28.6407	−	9.30592i	−0.950998	−	0.308998i	−0.207877	−	0.978155i	$-0.566655\pi$
$907$	−28.6407	−	9.30592i	−0.950998	−	0.308998i	−0.743121	+	0.669157i	$0.766655\pi$
$908$	−33.1326	−	10.7654i	−1.09954	−	0.357264i
$909$	−11.4849	+	8.34429i	−0.380931	+	0.276763i
$910$	−0.926266	−	16.4055i	−0.0307054	−	0.543839i
$911$	−9.34737	−	28.7682i	−0.309692	−	0.953134i	−0.977885	−	0.209146i	$-0.932932\pi$
$911$	−9.34737	−	28.7682i	−0.309692	−	0.953134i	0.668192	−	0.743988i	$-0.267068\pi$
$912$		−	19.9749i		−	0.661434i
$913$		0			0
$914$	10.9808			0.363211
$915$	−27.4301	+	42.6146i	−0.906811	+	1.40880i
$916$	−5.70564	−	4.14539i	−0.188520	−	0.136968i
$917$	−6.14488	−	8.45770i	−0.202922	−	0.279298i
$918$	−8.33381	−	2.70782i	−0.275057	−	0.0893713i
$919$	−5.86538	+	18.0518i	−0.193481	+	0.595473i	0.806510	+	0.591220i	$0.201354\pi$
$919$	−5.86538	+	18.0518i	−0.193481	+	0.595473i	−0.999991	+	0.00425273i	$0.998646\pi$
$920$	3.83730	−	14.5560i	0.126512	−	0.479898i
$921$	12.2359	+	8.88987i	0.403185	+	0.292931i
$922$	16.2460	−	5.27865i	0.535034	−	0.173843i
$923$		−	34.7733i		−	1.14458i
$924$		0			0
$925$	8.78461	+	1.79315i	0.288836	+	0.0589584i
$926$	3.24983	+	10.0019i	0.106796	+	0.328684i
$927$	1.82556	−	2.51267i	0.0599593	−	0.0825268i
$928$	20.9284	+	28.8055i	0.687009	+	0.945586i
$929$	13.5524	−	41.7099i	0.444639	−	1.36846i	−0.438240	−	0.898858i	$-0.644398\pi$
$929$	13.5524	−	41.7099i	0.444639	−	1.36846i	0.882879	−	0.469600i	$-0.155602\pi$
$930$	7.07090	+	18.2002i	0.231864	+	0.596807i
$931$	−14.2449	+	10.3495i	−0.466859	+	0.339193i
$932$	1.72219	−	2.37039i	0.0564122	−	0.0776447i
$933$	−18.4696	+	6.00113i	−0.604666	+	0.196468i
$934$	−0.320508			−0.0104873
$935$		0			0
$936$	−6.00000			−0.196116
$937$	−29.6606	+	9.63732i	−0.968970	+	0.314838i	−0.750400	−	0.660984i	$-0.770139\pi$
$937$	−29.6606	+	9.63732i	−0.968970	+	0.314838i	−0.218570	+	0.975821i	$0.570139\pi$
$938$	2.24918	−	3.09573i	0.0734384	−	0.101079i
$939$	26.7982	−	19.4700i	0.874525	−	0.635380i
$940$	41.3444	−	16.0626i	1.34851	−	0.523904i
$941$	8.34346	−	25.6785i	0.271989	−	0.837096i	−0.718011	−	0.696031i	$-0.754947\pi$
$941$	8.34346	−	25.6785i	0.271989	−	0.837096i	0.990000	−	0.141065i	$-0.0450526\pi$
$942$	12.8546	+	17.6928i	0.418825	+	0.576464i
$943$	3.54775	−	4.88306i	0.115531	−	0.159014i
$944$	0.965479	+	2.97144i	0.0314237	+	0.0967121i
$945$	−25.3923	+	20.7327i	−0.826012	+	0.674436i
$946$		0			0
$947$		−	19.9749i		−	0.649096i	−0.945869	−	0.324548i	$-0.894788\pi$
$947$		−	19.9749i		−	0.649096i	0.945869	−	0.324548i	$-0.105212\pi$
$948$	−4.65921	+	1.51387i	−0.151324	+	0.0491681i
$949$	−16.8151	−	12.2169i	−0.545841	−	0.396577i
$950$	−9.88548	+	4.49738i	−0.320727	+	0.145914i
$951$	7.53764	−	23.1985i	0.244425	−	0.752262i
$952$	−23.7530	−	7.71781i	−0.769839	−	0.250136i
$953$	−9.81199	−	13.5051i	−0.317842	−	0.437472i	0.619965	−	0.784629i	$-0.287147\pi$
$953$	−9.81199	−	13.5051i	−0.317842	−	0.437472i	−0.937807	+	0.347158i	$0.887147\pi$
$954$	−0.665890	−	0.483797i	−0.0215590	−	0.0156635i
$955$	−13.6654	−	8.79612i	−0.442203	−	0.284636i
$956$	9.80385			0.317079
$957$		0			0
$958$		−	1.31268i		−	0.0424107i
$959$	9.16552	+	28.2086i	0.295970	+	0.910902i
$960$	−0.552263	−	9.78140i	−0.0178242	−	0.315693i
$961$	−36.6070	+	26.5965i	−1.18087	+	0.857952i
$962$	3.74529	+	1.21692i	0.120753	+	0.0392350i
$963$	2.06578	+	0.671212i	0.0665688	+	0.0216295i
$964$	19.7919	−	14.3796i	0.637453	−	0.463137i
$965$	−1.91310	−	33.8838i	−0.0615847	−	1.09076i
$966$	3.60322	+	11.0896i	0.115932	+	0.356801i
$967$		−	4.24264i		−	0.136434i	−0.997671	−	0.0682171i	$-0.978269\pi$
$967$		−	4.24264i		−	0.136434i	0.997671	−	0.0682171i	$-0.0217310\pi$
$968$		0			0
$969$	−31.3205			−1.00616
$970$	−8.89734	−	5.72702i	−0.285677	−	0.183884i
$971$	20.1673	+	14.6524i	0.647201	+	0.470219i	0.862316	−	0.506370i	$-0.169013\pi$
$971$	20.1673	+	14.6524i	0.647201	+	0.470219i	−0.215116	+	0.976589i	$0.569013\pi$
$972$	7.58466	+	10.4394i	0.243278	+	0.334843i
$973$	−46.4248	−	15.0843i	−1.48831	−	0.483582i
$974$	2.03595	−	6.26600i	0.0652359	−	0.200775i
$975$	−16.9704	−	37.3019i	−0.543487	−	1.19462i
$976$	−23.3878	−	16.9923i	−0.748627	−	0.543909i
$977$	27.6914	−	8.99749i	0.885927	−	0.287855i	0.169511	−	0.985528i	$-0.445781\pi$
$977$	27.6914	−	8.99749i	0.885927	−	0.287855i	0.716416	+	0.697673i	$0.245781\pi$
$978$			5.13922i			0.164334i
$979$		0			0
$980$	−12.5885	+	10.2784i	−0.402124	+	0.328332i
$981$	−2.08032	−	6.40256i	−0.0664194	−	0.204418i
$982$	12.0830	−	16.6309i	0.385585	−	0.530712i
$983$	−32.9299	−	45.3241i	−1.05030	−	1.44562i	−0.888548	−	0.458784i	$-0.848285\pi$
$983$	−32.9299	−	45.3241i	−1.05030	−	1.44562i	−0.161753	−	0.986831i	$-0.551715\pi$
$984$	−1.99752	+	6.14773i	−0.0636785	+	0.195982i
$985$	−35.9498	+	13.9668i	−1.14546	+	0.445019i
$986$	11.2101	−	8.14459i	0.357001	−	0.259377i
$987$	−43.5135	+	59.8912i	−1.38505	+	1.90636i
$988$	29.3261	−	9.52863i	0.932988	−	0.303146i
$989$	−22.4833			−0.714929
$990$		0			0
$991$	19.9090			0.632429			0.316215	−	0.948688i	$-0.397588\pi$
$991$	19.9090			0.632429			0.316215	+	0.948688i	$0.397588\pi$
$992$	−42.6795	+	13.8674i	−1.35508	+	0.440291i
$993$	−20.6620	+	28.4388i	−0.655688	+	0.902477i
$994$	11.4849	−	8.34429i	0.364280	−	0.264665i
$995$	−1.61953	−	4.16859i	−0.0513425	−	0.132153i
$996$	10.2360	−	31.5031i	0.324340	−	0.998215i
$997$	−20.0535	−	27.6012i	−0.635100	−	0.874140i	0.363243	−	0.931695i	$-0.381670\pi$
$997$	−20.0535	−	27.6012i	−0.635100	−	0.874140i	−0.998342	+	0.0575549i	$0.981670\pi$
$998$	5.35732	−	7.37372i	0.169583	−	0.233411i
$999$	−2.42776	−	7.47189i	−0.0768110	−	0.236400i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.e.269.3		16
5.4	even	2	inner	605.2.j.e.269.2		16
11.2	odd	10		605.2.j.f.9.3		16
11.3	even	5		605.2.b.e.364.2	yes	4
11.4	even	5	inner	605.2.j.e.124.3		16
11.5	even	5	inner	605.2.j.e.444.2		16
11.6	odd	10		605.2.j.f.444.3		16
11.7	odd	10		605.2.j.f.124.2		16
11.8	odd	10		605.2.b.d.364.3	yes	4
11.9	even	5	inner	605.2.j.e.9.2		16
11.10	odd	2		605.2.j.f.269.2		16
55.3	odd	20		3025.2.a.z.1.2		4
55.4	even	10	inner	605.2.j.e.124.2		16
55.8	even	20		3025.2.a.y.1.3		4
55.9	even	10	inner	605.2.j.e.9.3		16
55.14	even	10		605.2.b.e.364.3	yes	4
55.19	odd	10		605.2.b.d.364.2	✓	4
55.24	odd	10		605.2.j.f.9.2		16
55.29	odd	10		605.2.j.f.124.3		16
55.39	odd	10		605.2.j.f.444.2		16
55.47	odd	20		3025.2.a.z.1.3		4
55.49	even	10	inner	605.2.j.e.444.3		16
55.52	even	20		3025.2.a.y.1.2		4
55.54	odd	2		605.2.j.f.269.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.d.364.2	✓	4	55.19	odd	10
605.2.b.d.364.3	yes	4	11.8	odd	10
605.2.b.e.364.2	yes	4	11.3	even	5
605.2.b.e.364.3	yes	4	55.14	even	10
605.2.j.e.9.2		16	11.9	even	5	inner
605.2.j.e.9.3		16	55.9	even	10	inner
605.2.j.e.124.2		16	55.4	even	10	inner
605.2.j.e.124.3		16	11.4	even	5	inner
605.2.j.e.269.2		16	5.4	even	2	inner
605.2.j.e.269.3		16	1.1	even	1	trivial
605.2.j.e.444.2		16	11.5	even	5	inner
605.2.j.e.444.3		16	55.49	even	10	inner
605.2.j.f.9.2		16	55.24	odd	10
605.2.j.f.9.3		16	11.2	odd	10
605.2.j.f.124.2		16	11.7	odd	10
605.2.j.f.124.3		16	55.29	odd	10
605.2.j.f.269.2		16	11.10	odd	2
605.2.j.f.269.3		16	55.54	odd	2
605.2.j.f.444.2		16	55.39	odd	10
605.2.j.f.444.3		16	11.6	odd	10
3025.2.a.y.1.2		4	55.52	even	20
3025.2.a.y.1.3		4	55.8	even	20
3025.2.a.z.1.2		4	55.3	odd	20
3025.2.a.z.1.3		4	55.47	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)

\(f(q)\)	\(=\)	\(q+(0.492303 - 0.159959i) q^{2} +(1.13551 - 1.56290i) q^{3} +(-1.40126 + 1.01807i) q^{4} +(-0.809764 - 2.08429i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.96677 - 2.70702i) q^{7} +(-1.13551 + 1.56290i) q^{8} +(-0.226216 - 0.696222i) q^{9} +O(q^{10})\)	\(q+(0.492303 - 0.159959i) q^{2} +(1.13551 - 1.56290i) q^{3} +(-1.40126 + 1.01807i) q^{4} +(-0.809764 - 2.08429i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-1.96677 - 2.70702i) q^{7} +(-1.13551 + 1.56290i) q^{8} +(-0.226216 - 0.696222i) q^{9} +(-0.732051 - 0.896575i) q^{10} +3.34607i q^{12} +(-4.03499 + 1.31105i) q^{13} +(-1.40126 - 1.01807i) q^{14} +(-4.17704 - 1.10116i) q^{15} +(0.761449 - 2.34350i) q^{16} +(-3.67460 - 1.19395i) q^{17} +(-0.222734 - 0.306567i) q^{18} +(3.39476 + 2.46644i) q^{19} +(3.25665 + 2.09624i) q^{20} -6.46410 q^{21} -3.48477i q^{23} +(1.15327 + 3.54939i) q^{24} +(-3.68856 + 3.37557i) q^{25} +(-1.77672 + 1.29087i) q^{26} +(4.16690 + 1.35391i) q^{27} +(5.51190 + 1.79092i) q^{28} +(-5.60503 + 4.07230i) q^{29} +(-2.23251 + 0.126049i) q^{30} +(-2.69835 - 8.30467i) q^{31} -5.13922i q^{32} -2.00000 q^{34} +(-4.04962 + 6.29137i) q^{35} +(1.02579 + 0.745282i) q^{36} +(-1.05399 - 1.45069i) q^{37} +(2.06578 + 0.671212i) q^{38} +(-2.53275 + 7.79500i) q^{39} +(4.17704 + 1.10116i) q^{40} +(1.40126 + 1.01807i) q^{41} +(-3.18230 + 1.03399i) q^{42} -6.45189i q^{43} +(-1.26795 + 1.03528i) q^{45} +(-0.557420 - 1.71556i) q^{46} +(6.73156 - 9.26519i) q^{47} +(-2.79802 - 3.85115i) q^{48} +(-1.29668 + 3.99078i) q^{49} +(-1.27594 + 2.25182i) q^{50} +(-6.03859 + 4.38729i) q^{51} +(4.31932 - 5.94504i) q^{52} +(2.06578 - 0.671212i) q^{53} +2.26795 q^{54} +6.46410 q^{56} +(7.70959 - 2.50500i) q^{57} +(-2.10798 + 2.90138i) q^{58} +(-1.02579 + 0.745282i) q^{59} +(6.97418 - 2.70952i) q^{60} +(3.62540 - 11.1578i) q^{61} +(-2.65681 - 3.65679i) q^{62} +(-1.43977 + 1.98168i) q^{63} +(0.700835 + 2.15695i) q^{64} +(6.00000 + 7.34847i) q^{65} +2.20925i q^{67} +(6.36459 - 2.06798i) q^{68} +(-5.44634 - 3.95700i) q^{69} +(-0.987277 + 3.74503i) q^{70} +(-2.53275 + 7.79500i) q^{71} +(1.34500 + 0.437016i) q^{72} +(2.87955 + 3.96336i) q^{73} +(-0.750932 - 0.545584i) q^{74} +(1.08727 + 9.59787i) q^{75} -7.26795 q^{76} +4.24264i q^{78} +(0.452432 + 1.39244i) q^{79} +(-5.50114 + 0.310597i) q^{80} +(8.62433 - 6.26594i) q^{81} +(0.852694 + 0.277057i) q^{82} +(-9.41498 - 3.05911i) q^{83} +(9.05788 - 6.58093i) q^{84} +(0.487015 + 8.62577i) q^{85} +(-1.03204 - 3.17629i) q^{86} +13.3843i q^{87} -0.464102 q^{89} +(-0.458614 + 0.712489i) q^{90} +(11.4849 + 8.34429i) q^{91} +(3.54775 + 4.88306i) q^{92} +(-16.0434 - 5.21282i) q^{93} +(1.83192 - 5.63806i) q^{94} +(2.39183 - 9.07291i) q^{95} +(-8.03209 - 5.83565i) q^{96} +(8.69420 - 2.82492i) q^{97} +2.17209i 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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