LMFDB - Embedded newform 605.2.j.f.9.3

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			9.3
Root			$0.304260 + 0.418778i$ of defining polynomial
Character	$\chi$	$=$	605.9
Dual form			605.2.j.f.269.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.492303 + 0.159959i) q^{2} +(-1.13551 - 1.56290i) q^{3} +(-1.40126 - 1.01807i) q^{4} +(1.88023 + 1.21026i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.96677 + 2.70702i) q^{7} +(-1.13551 - 1.56290i) q^{8} +(-0.226216 + 0.696222i) q^{9} +O(q^{10})$	\(q+(0.492303 + 0.159959i) q^{2} +(-1.13551 - 1.56290i) q^{3} +(-1.40126 - 1.01807i) q^{4} +(1.88023 + 1.21026i) 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} +(-0.243508 - 4.31288i) 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} +(-1.40255 - 3.61010i) q^{20} +6.46410 q^{21} -3.48477i q^{23} +(-1.15327 + 3.54939i) q^{24} +(2.07053 + 4.55114i) 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} +(0.570005 - 2.16220i) q^{30} +(-2.69835 + 8.30467i) q^{31} +5.13922i q^{32} -2.00000 q^{34} +(-6.97418 + 2.70952i) 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} +(-0.243508 - 4.31288i) 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} +(0.291333 + 2.57174i) 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} +(-4.04962 + 6.29137i) 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} +(-3.86682 + 0.218323i) 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} +(4.76187 - 8.40392i) q^{75} +7.26795 q^{76} +4.24264i q^{78} +(-0.452432 + 1.39244i) q^{79} +(-1.40455 + 5.32787i) 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} +(-8.35409 - 2.20233i) q^{85} +(-1.03204 + 3.17629i) q^{86} -13.3843i q^{87} -0.464102 q^{89} +(-0.789817 + 0.306850i) 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} +(-9.36796 + 0.528920i) 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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	0.477853	−	0.878440i	$-0.341415\pi$
$2$	0.492303	+	0.159959i	0.348111	+	0.113108i	−0.129742	+	0.991548i	$0.541415\pi$
$3$	−1.13551	−	1.56290i	−0.655589	−	0.902341i	0.343736	−	0.939066i	$-0.388307\pi$
$3$	−1.13551	−	1.56290i	−0.655589	−	0.902341i	−0.999325	+	0.0367251i	$0.988307\pi$
$4$	−1.40126	−	1.01807i	−0.700629	−	0.509037i
$5$	1.88023	+	1.21026i	0.840864	+	0.541246i
$5$	1.88023	+	1.21026i	0.840864	+	0.541246i
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−1.96677	+	2.70702i	−0.743368	+	1.02316i	0.255049	+	0.966928i	$0.417908\pi$
$7$	−1.96677	+	2.70702i	−0.743368	+	1.02316i	−0.998418	+	0.0562307i	$0.982092\pi$
$8$	−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	−0.309679	−	0.950841i	$-0.600222\pi$
$13$	−4.03499	−	1.31105i	−1.11911	−	0.363619i	−0.809426	+	0.587222i	$0.800222\pi$
$14$	−1.40126	+	1.01807i	−0.374502	+	0.272092i
$15$	−0.243508	−	4.31288i	−0.0628734	−	1.11358i
$16$	0.761449	+	2.34350i	0.190362	+	0.585875i
$17$	−3.67460	+	1.19395i	−0.891221	+	0.289575i	−0.718609	−	0.695414i	$-0.755221\pi$
$17$	−3.67460	+	1.19395i	−0.891221	+	0.289575i	−0.172613	+	0.984990i	$0.555221\pi$
$18$	−0.222734	+	0.306567i	−0.0524989	+	0.0722585i
$19$	−3.39476	+	2.46644i	−0.778811	+	0.565839i	−0.904622	−	0.426215i	$-0.859847\pi$
$19$	−3.39476	+	2.46644i	−0.778811	+	0.565839i	0.125811	+	0.992054i	$0.459847\pi$
$20$	−1.40255	−	3.61010i	−0.313620	−	0.807244i
$21$	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
$25$	2.07053	+	4.55114i	0.414106	+	0.910229i
$26$	−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	$-0.0775783\pi$
$29$	5.60503	+	4.07230i	1.04083	+	0.756206i	0.0703816	+	0.997520i	$0.477578\pi$
$30$	0.570005	−	2.16220i	0.104068	−	0.394761i
$31$	−2.69835	+	8.30467i	−0.484638	+	1.49156i	0.347866	+	0.937544i	$0.386907\pi$
$31$	−2.69835	+	8.30467i	−0.484638	+	1.49156i	−0.832504	+	0.554019i	$0.813093\pi$
$32$			5.13922i			0.908494i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	−6.97418	+	2.70952i	−1.17885	+	0.457993i
$36$	1.02579	−	0.745282i	0.170965	−	0.124214i
$37$	1.05399	−	1.45069i	0.173275	−	0.238492i	−0.713543	−	0.700611i	$-0.752911\pi$
$37$	1.05399	−	1.45069i	0.173275	−	0.238492i	0.886818	+	0.462119i	$0.152911\pi$
$38$	−2.06578	+	0.671212i	−0.335114	+	0.108885i
$39$	2.53275	+	7.79500i	0.405565	+	1.24820i
$40$	−0.243508	−	4.31288i	−0.0385020	−	0.681927i
$41$	−1.40126	+	1.01807i	−0.218840	+	0.158996i	−0.691804	−	0.722085i	$-0.743184\pi$
$41$	−1.40126	+	1.01807i	−0.218840	+	0.158996i	0.472964	+	0.881082i	$0.343184\pi$
$42$	3.18230	+	1.03399i	0.491039	+	0.159548i
$43$			6.45189i			0.983905i	0.870622	+	0.491952i	$0.163717\pi$
$43$			6.45189i			0.983905i	−0.870622	+	0.491952i	$0.836283\pi$
$44$		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	−0.935800	−	0.352530i	$-0.885321\pi$
$47$	−6.73156	−	9.26519i	−0.981899	−	1.35147i	−0.0460982	−	0.998937i	$-0.514679\pi$
$48$	2.79802	−	3.85115i	0.403860	−	0.555865i
$49$	−1.29668	−	3.99078i	−0.185240	−	0.570111i
$50$	0.291333	+	2.57174i	0.0412007	+	0.363699i
$51$	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	$-0.447663\pi$
$53$	−2.06578	−	0.671212i	−0.283757	−	0.0921981i	−0.447437	+	0.894315i	$0.647663\pi$
$54$	−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	0.519006	−	0.854770i	$-0.326302\pi$
$59$	−1.02579	−	0.745282i	−0.133547	−	0.0970274i	−0.652553	+	0.757743i	$0.726302\pi$
$60$	−4.04962	+	6.29137i	−0.522803	+	0.812213i
$61$	−3.62540	−	11.1578i	−0.464185	−	1.42862i	−0.860004	−	0.510287i	$-0.829539\pi$
$61$	−3.62540	−	11.1578i	−0.464185	−	1.42862i	0.395819	−	0.918329i	$-0.370461\pi$
$62$	−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
$70$	−3.86682	+	0.218323i	−0.462174	+	0.0260946i
$71$	−2.53275	−	7.79500i	−0.300582	−	0.925097i	−0.981289	−	0.192541i	$-0.938327\pi$
$71$	−2.53275	−	7.79500i	−0.300582	−	0.925097i	0.680707	−	0.732556i	$-0.261673\pi$
$72$	1.34500	−	0.437016i	0.158509	−	0.0515028i
$73$	2.87955	−	3.96336i	0.337026	−	0.463876i	−0.606544	−	0.795050i	$-0.707445\pi$
$73$	2.87955	−	3.96336i	0.337026	−	0.463876i	0.943570	+	0.331174i	$0.107445\pi$
$74$	0.750932	−	0.545584i	0.0872941	−	0.0634229i
$75$	4.76187	−	8.40392i	0.549853	−	0.970401i
$76$	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	$-0.926246\pi$
$79$	−0.452432	+	1.39244i	−0.0509026	+	0.156662i	0.922374	+	0.386298i	$0.126246\pi$
$80$	−1.40455	+	5.32787i	−0.157033	+	0.595674i
$81$	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	−0.776145	−	0.630555i	$-0.782827\pi$
$83$	−9.41498	+	3.05911i	−1.03343	+	0.335781i	−0.257283	+	0.966336i	$0.582827\pi$
$84$	−9.05788	−	6.58093i	−0.988295	−	0.718039i
$85$	−8.35409	−	2.20233i	−0.906128	−	0.238876i
$86$	−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	$0.507830\pi$
$90$	−0.789817	+	0.306850i	−0.0832540	+	0.0323448i
$91$	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
$95$	−9.36796	+	0.528920i	−0.961133	+	0.0542661i
$96$	8.03209	−	5.83565i	0.819771	−	0.595599i
$97$	−8.69420	−	2.82492i	−0.882762	−	0.286827i	−0.167658	−	0.985845i	$-0.553621\pi$
$97$	−8.69420	−	2.82492i	−0.882762	−	0.286827i	−0.715104	+	0.699018i	$0.753621\pi$
$98$		−	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	0.0480385	−	0.998845i	$-0.484703\pi$
$101$	5.99255	−	18.4432i	0.596281	−	1.83516i	0.548243	−	0.836319i	$-0.315297\pi$
$102$	2.27103	+	3.12580i	0.224865	+	0.309500i
$103$	−2.49376	+	3.43237i	−0.245718	+	0.338201i	−0.914006	−	0.405701i	$-0.867027\pi$
$103$	−2.49376	+	3.43237i	−0.245718	+	0.338201i	0.668288	+	0.743903i	$0.267027\pi$
$104$	2.53275	+	7.79500i	0.248357	+	0.764363i
$105$	12.1540	+	7.82326i	1.18611	+	0.763472i
$106$	−0.909623	−	0.660880i	−0.0883504	−	0.0641903i
$107$	−1.74403	−	2.40046i	−0.168602	−	0.232061i	0.716352	−	0.697739i	$-0.245810\pi$
$107$	−1.74403	−	2.40046i	−0.168602	−	0.232061i	−0.884954	+	0.465678i	$0.845810\pi$
$108$	7.21729	+	2.34504i	0.694484	+	0.225651i
$109$	−9.19615			−0.880832			−0.440416	−	0.897794i	$-0.645169\pi$
$109$	−9.19615			−0.880832			−0.440416	+	0.897794i	$0.645169\pi$
$110$		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	$-0.157527\pi$
$113$	1.66251	+	2.28825i	0.156396	+	0.215260i	−0.723628	+	0.690190i	$0.757527\pi$
$114$	3.39476	+	2.46644i	0.317948	+	0.231003i
$115$	4.21748	−	6.55216i	0.393282	−	0.610992i
$116$	−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
$125$	−1.61500	+	11.0631i	−0.144450	+	0.989512i
$126$	−0.391818	−	1.20589i	−0.0349059	−	0.107429i
$127$	0.852694	−	0.277057i	0.0756644	−	0.0245848i	−0.270940	−	0.962596i	$-0.587335\pi$
$127$	0.852694	−	0.277057i	0.0756644	−	0.0245848i	0.346605	+	0.938011i	$0.387335\pi$
$128$	6.73156	−	9.26519i	0.594991	−	0.818935i
$129$	10.0837	−	7.32622i	0.887818	−	0.645037i
$130$	−1.77836	−	4.57743i	−0.155973	−	0.401467i
$131$	−3.12436			−0.272976			−0.136488	−	0.990642i	$-0.543582\pi$
$131$	−3.12436			−0.272976			−0.136488	+	0.990642i	$0.543582\pi$
$132$		0			0
$133$		−	14.0406i		−	1.21747i
$134$	−0.353390	+	1.08762i	−0.0305282	+	0.0939562i
$135$	−9.47332	−	2.49739i	−0.815334	−	0.214941i
$136$	6.03859	+	4.38729i	0.517804	+	0.376207i
$137$	8.43037	−	2.73919i	0.720255	−	0.234025i	0.0741215	−	0.997249i	$-0.476385\pi$
$137$	8.43037	−	2.73919i	0.720255	−	0.234025i	0.646134	+	0.763224i	$0.276385\pi$
$138$	−3.31421	+	1.07685i	−0.282124	+	0.0916677i
$139$	−11.8023	−	8.57488i	−1.00106	−	0.727312i	−0.0387439	−	0.999249i	$-0.512336\pi$
$139$	−11.8023	−	8.57488i	−1.00106	−	0.727312i	−0.962315	+	0.271937i	$0.912336\pi$
$140$	12.5311	+	3.30349i	1.05907	+	0.279196i
$141$	−6.83680	+	21.0415i	−0.575763	+	1.77202i
$142$		−	4.24264i		−	0.356034i
$143$		0			0
$144$	−1.80385			−0.150321
$145$	5.61021	+	14.4404i	0.465902	+	1.19921i
$146$	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	0.992816	+	0.119651i	$0.0381775\pi$
$149$	3.17297	+	9.76540i	0.259940	+	0.800013i	−0.732876	+	0.680362i	$0.761823\pi$
$150$	3.68856	−	3.37557i	0.301170	−	0.275614i
$151$	−3.39476	+	2.46644i	−0.276262	+	0.200716i	−0.717285	−	0.696780i	$-0.754616\pi$
$151$	−3.39476	+	2.46644i	−0.276262	+	0.200716i	0.441024	+	0.897495i	$0.354616\pi$
$152$	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	0.907977	+	0.419020i	$0.137626\pi$
$157$	12.8546	+	17.6928i	1.02591	+	1.41204i	0.117931	+	0.993022i	$0.462374\pi$
$158$	−0.445468	+	0.613134i	−0.0354395	+	0.0487783i
$159$	1.29668	+	3.99078i	0.102834	+	0.316489i
$160$	−6.21980	+	9.66291i	−0.491718	+	0.763920i
$161$	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	$-0.335494\pi$
$163$	4.88769	+	1.58811i	0.382833	+	0.124390i	−0.111277	+	0.993789i	$0.535494\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	−5.12436			−0.397727
$167$	0.492303	+	0.159959i	0.0380956	+	0.0123780i	0.328003	−	0.944677i	$-0.393624\pi$
$167$	0.492303	+	0.159959i	0.0380956	+	0.0123780i	−0.289907	+	0.957055i	$0.593624\pi$
$168$	−7.34008	−	10.1027i	−0.566299	−	0.779444i
$169$	4.04508	+	2.93893i	0.311160	+	0.226071i
$170$	−3.76046	−	2.42052i	−0.288414	−	0.185646i
$171$	−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	0.940630	+	0.339433i	$0.110235\pi$
$173$	12.7949	+	17.6107i	0.972779	+	1.33892i	0.0321489	+	0.999483i	$0.489765\pi$
$174$	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	−0.947235	−	0.320540i	$-0.896136\pi$
$179$	−12.5107	+	9.08957i	−0.935095	+	0.679386i	0.0121398	+	0.999926i	$0.496136\pi$
$180$	2.83071	−	0.159824i	0.210989	−	0.0119125i
$181$	−5.37452	−	16.5411i	−0.399485	−	1.22949i	−0.925413	−	0.378959i	$-0.876282\pi$
$181$	−5.37452	−	16.5411i	−0.399485	−	1.22949i	0.525929	−	0.850529i	$-0.323718\pi$
$182$	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
$185$	3.73745	−	1.45203i	0.274783	−	0.106755i
$186$	8.73205			0.640265
$187$		0			0
$188$			19.8362i			1.44670i
$189$	4.53027	−	13.9427i	0.329528	−	1.01418i
$190$	−4.69648	−	1.23810i	−0.340719	−	0.0898212i
$191$	5.87989	+	4.27199i	0.425454	+	0.309111i	0.779829	−	0.625993i	$-0.215306\pi$
$191$	5.87989	+	4.27199i	0.425454	+	0.309111i	−0.354374	+	0.935104i	$0.615306\pi$
$192$	−4.16690	+	1.35391i	−0.300720	+	0.0977100i
$193$	14.4346	−	4.69008i	1.03902	−	0.337599i	0.260672	−	0.965428i	$-0.416056\pi$
$193$	14.4346	−	4.69008i	1.03902	−	0.337599i	0.778352	+	0.627828i	$0.216056\pi$
$194$	−3.82831	−	2.78143i	−0.274857	−	0.199695i
$195$	−4.67185	+	17.7217i	−0.334558	+	1.26908i
$196$	−2.24592	+	6.91223i	−0.160423	+	0.493731i
$197$			17.2480i			1.22887i	0.788969	+	0.614433i	$0.210615\pi$
$197$			17.2480i			1.22887i	−0.788969	+	0.614433i	$0.789385\pi$
$198$		0			0
$199$	2.00000			0.141776			0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000			0.141776			0.0708881	+	0.997484i	$0.477417\pi$
$200$	4.76187	−	8.40392i	0.336715	−	0.594247i
$201$	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
$205$	−3.86682	+	0.218323i	−0.270071	+	0.0152483i
$206$	−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	0.708874	+	0.705335i	$0.249203\pi$
$211$	−4.05565	+	12.4820i	−0.279202	+	0.859297i	−0.988077	+	0.153962i	$0.950797\pi$
$212$	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
$215$	−7.80848	+	12.1310i	−0.532534	+	0.827330i
$216$	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	$-0.183442\pi$
$223$	0.912780	+	1.25633i	0.0611243	+	0.0841303i	−0.777361	+	0.629055i	$0.783442\pi$
$224$	−13.9120	−	10.1076i	−0.929533	−	0.675345i
$225$	−3.63699	+	0.412007i	−0.242466	+	0.0274671i
$226$	0.452432	+	1.39244i	0.0300953	+	0.0926240i
$227$	11.8225	−	16.2722i	0.784684	−	1.08002i	−0.210066	−	0.977687i	$-0.567368\pi$
$227$	11.8225	−	16.2722i	0.784684	−	1.08002i	0.994750	−	0.102337i	$-0.0326321\pi$
$228$	−8.25286	−	11.3591i	−0.546559	−	0.752274i
$229$	1.25825	−	3.87251i	0.0831478	−	0.255903i	−0.900836	−	0.434159i	$-0.857046\pi$
$229$	1.25825	−	3.87251i	0.0831478	−	0.255903i	0.983984	+	0.178256i	$0.0570456\pi$
$230$	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	0.255844	−	0.966718i	$-0.417647\pi$
$233$	−1.60882	−	0.522738i	−0.105397	−	0.0342457i	−0.361241	+	0.932473i	$0.617647\pi$
$234$	1.30065	−	0.944980i	0.0850263	−	0.0617752i
$235$	−1.44356	−	25.5676i	−0.0941677	−	1.66785i
$236$	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	$-0.641398\pi$
$239$	4.57924	−	3.32701i	0.296207	−	0.215207i	0.725955	+	0.687742i	$0.241398\pi$
$240$	9.92182	−	3.85470i	0.640451	−	0.248820i
$241$	14.1244			0.909830			0.454915	−	0.890535i	$-0.349670\pi$
$241$	14.1244			0.909830			0.454915	+	0.890535i	$0.349670\pi$
$242$		0			0
$243$		−	7.45001i		−	0.477918i
$244$	−6.27938	+	19.3260i	−0.401996	+	1.23722i
$245$	2.39183	−	9.07291i	0.152808	−	0.579647i
$246$	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
$250$	−2.56471	+	5.18806i	−0.162206	+	0.328121i
$251$	−1.17545	+	3.61767i	−0.0741940	+	0.228346i	−0.981276	−	0.192609i	$-0.938305\pi$
$251$	−1.17545	+	3.61767i	−0.0741940	+	0.228346i	0.907082	+	0.420955i	$0.138305\pi$
$252$			4.24264i			0.267261i
$253$		0			0
$254$	0.464102			0.0291203
$255$	6.04416	+	15.5574i	0.378500	+	0.974241i
$256$	1.12640	−	0.818376i	0.0703999	−	0.0511485i
$257$	8.69833	−	11.9722i	0.542587	−	0.746806i	−0.446396	−	0.894835i	$-0.647293\pi$
$257$	8.69833	−	11.9722i	0.542587	−	0.746806i	0.988983	+	0.148029i	$0.0472929\pi$
$258$	6.13612	−	1.99374i	0.382018	−	0.124125i
$259$	1.85410	+	5.70634i	0.115208	+	0.354575i
$260$	0.926266	+	16.4055i	0.0574446	+	1.01743i
$261$	−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	$0.0671699\pi$
$263$			6.79367i			0.418915i	−0.977818	+	0.209458i	$0.932830\pi$
$264$		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	0.979111	+	0.203327i	$0.0651754\pi$
$269$	5.02707	+	15.4717i	0.306506	+	0.943329i	−0.672605	+	0.740002i	$0.734825\pi$
$270$	−4.26427	−	2.74481i	−0.259515	−	0.167044i
$271$	−9.27465	−	6.73843i	−0.563395	−	0.409330i	0.269305	−	0.963055i	$-0.413206\pi$
$271$	−9.27465	−	6.73843i	−0.563395	−	0.409330i	−0.832700	+	0.553725i	$0.813206\pi$
$272$	−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	−0.783055	−	0.621952i	$-0.786340\pi$
$277$	−29.6606	−	9.63732i	−1.78213	−	0.579051i	−0.999079	+	0.0429019i	$0.986340\pi$
$278$	−4.43868	−	6.10933i	−0.266215	−	0.366413i
$279$	−5.17148	−	3.75730i	−0.309609	−	0.224944i
$280$	12.1540	+	7.82326i	0.726340	+	0.467529i
$281$	−5.35233	−	16.4728i	−0.319293	−	0.982684i	−0.973951	−	0.226758i	$-0.927187\pi$
$281$	−5.35233	−	16.4728i	−0.319293	−	0.982684i	0.654658	−	0.755925i	$-0.272813\pi$
$282$	−6.73156	+	9.26519i	−0.400858	+	0.551734i
$283$	−4.74294	−	6.52810i	−0.281939	−	0.388055i	0.644436	−	0.764658i	$-0.277092\pi$
$283$	−4.74294	−	6.52810i	−0.281939	−	0.388055i	−0.926375	+	0.376603i	$0.877092\pi$
$284$	−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
$290$	0.452049	+	8.00646i	0.0265453	+	0.470156i
$291$	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	−0.985192	−	0.171455i	$-0.945153\pi$
$293$	−8.86138	+	12.1966i	−0.517687	+	0.712535i	0.467505	+	0.883991i	$0.345153\pi$
$294$	−3.39476	+	2.46644i	−0.197986	+	0.143845i
$295$	−1.02674	−	2.64278i	−0.0597791	−	0.153869i
$296$	−3.46410			−0.201347
$297$		0			0
$298$			5.31508i			0.307894i
$299$	−4.56870	+	14.0610i	−0.264214	+	0.813169i
$300$	−15.2284	+	6.92813i	−0.879213	+	0.399996i
$301$	−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
$305$	6.68732	−	25.3670i	0.382915	−	1.45251i
$306$	0.452432	−	1.39244i	0.0258638	−	0.0796007i
$307$		−	7.82894i		−	0.446821i	−0.974724	−	0.223411i	$-0.928281\pi$
$307$		−	7.82894i		−	0.446821i	0.974724	−	0.223411i	$-0.0717191\pi$
$308$		0			0
$309$	8.19615			0.466263
$310$	−9.42110	+	3.66017i	−0.535082	+	0.207884i
$311$	−8.13269	+	5.90875i	−0.461163	+	0.335054i	−0.793987	−	0.607935i	$-0.791998\pi$
$311$	−8.13269	+	5.90875i	−0.461163	+	0.335054i	0.332825	+	0.942989i	$0.391998\pi$
$312$	9.30685	−	12.8098i	0.526896	−	0.725211i
$313$	−16.3072	+	5.29854i	−0.921739	+	0.299491i	−0.731180	−	0.682185i	$-0.761030\pi$
$313$	−16.3072	+	5.29854i	−0.921739	+	0.299491i	−0.190559	+	0.981676i	$0.561030\pi$
$314$	3.49823	+	10.7664i	0.197417	+	0.607586i
$315$	−0.308755	−	5.46852i	−0.0173964	−	0.308116i
$316$	2.05158	−	1.49056i	0.115411	−	0.0838508i
$317$	−12.0084	−	3.90177i	−0.674459	−	0.219145i	−0.0482913	−	0.998833i	$-0.515378\pi$
$317$	−12.0084	−	3.90177i	−0.674459	−	0.219145i	−0.626168	+	0.779688i	$0.715378\pi$
$318$			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
$325$	−2.38781	−	21.0784i	−0.132452	−	1.16922i
$326$	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
$335$	−2.67378	+	4.15390i	−0.146084	+	0.226952i
$336$	4.92209	+	15.1486i	0.268522	+	0.826425i
$337$	−10.3608	+	14.2605i	−0.564391	+	0.776817i	−0.991876	−	0.127205i	$-0.959399\pi$
$337$	−10.3608	+	14.2605i	−0.564391	+	0.776817i	0.427486	+	0.904022i	$0.359399\pi$
$338$	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
$345$	−15.0294	+	0.848567i	−0.809155	+	0.0456853i
$346$	3.48199	+	10.7165i	0.187193	+	0.576120i
$347$	4.16690	−	1.35391i	0.223691	−	0.0726816i	−0.195027	−	0.980798i	$-0.562479\pi$
$347$	4.16690	−	1.35391i	0.223691	−	0.0726816i	0.418718	+	0.908116i	$0.362479\pi$
$348$	−13.6262	+	18.7548i	−0.730439	+	1.00536i
$349$	−5.92242	+	4.30289i	−0.317020	+	0.230328i	−0.734903	−	0.678173i	$-0.762772\pi$
$349$	−5.92242	+	4.30289i	−0.317020	+	0.230328i	0.417883	+	0.908501i	$0.362772\pi$
$350$	−7.53475	−	4.26937i	−0.402749	−	0.228208i
$351$	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
$355$	4.67185	−	17.7217i	0.247956	−	0.940570i
$356$	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	0.960164	+	0.279437i	$0.0901479\pi$
$359$	28.8498	+	20.9606i	1.52263	+	1.10626i	0.562468	+	0.826819i	$0.309852\pi$
$360$	3.05781	+	0.806108i	0.161161	+	0.0424856i
$361$	−0.430246	+	1.32416i	−0.0226445	+	0.0696927i
$362$		−	9.00292i		−	0.473183i
$363$		0			0
$364$	−24.5885			−1.28879
$365$	10.2109	−	3.96702i	0.534464	−	0.207643i
$366$	−9.49143	+	6.89593i	−0.496125	+	0.360456i
$367$	−9.93721	+	13.6774i	−0.518718	+	0.713954i	−0.985359	−	0.170493i	$-0.945464\pi$
$367$	−9.93721	+	13.6774i	−0.518718	+	0.713954i	0.466641	+	0.884447i	$0.345464\pi$
$368$	8.16655	−	2.65347i	0.425711	−	0.138322i
$369$	−0.391818	−	1.20589i	−0.0203972	−	0.0627762i
$370$	2.07223	−	0.116999i	0.107730	−	0.00608249i
$371$	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	$-0.998551\pi$
$373$		−	0.175865i		−	0.00910597i	0.999990	−	0.00455298i	$-0.00144926\pi$
$374$		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	0.938764	−	0.344561i	$-0.111972\pi$
$379$	−0.452432	−	1.39244i	−0.0232399	−	0.0715250i	−0.962004	+	0.273036i	$0.911972\pi$
$380$	13.6654	+	8.79612i	0.701021	+	0.451232i
$381$	−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	0.991878	+	0.127194i	$0.0405969\pi$
$383$	36.5787	+	11.8852i	1.86909	+	0.607303i	0.877209	+	0.480109i	$0.159403\pi$
$384$	−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	0.706265	−	0.707948i	$-0.250379\pi$
$389$	4.95471	+	3.59981i	0.251214	+	0.182517i	−0.455051	+	0.890465i	$0.650379\pi$
$390$	−5.13471	+	7.97714i	−0.260006	+	0.403938i
$391$	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
$400$	−9.08900	+	8.31775i	−0.454450	+	0.415888i
$401$	0.717076	+	2.20693i	0.0358091	+	0.110209i	0.967363	−	0.253393i	$-0.0815467\pi$
$401$	0.717076	+	2.20693i	0.0358091	+	0.110209i	−0.931554	+	0.363602i	$0.881547\pi$
$402$	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
$405$	8.63229	+	22.2191i	0.428942	+	1.10408i
$406$	−12.0000			−0.595550
$407$		0			0
$408$		−	14.4195i		−	0.713873i
$409$	8.07287	−	24.8457i	0.399178	−	1.22854i	−0.526482	−	0.850186i	$-0.676489\pi$
$409$	8.07287	−	24.8457i	0.399178	−	1.22854i	0.925660	−	0.378357i	$-0.123511\pi$
$410$	−1.93857	−	0.511052i	−0.0957393	−	0.0252391i
$411$	−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
$415$	−21.4047	−	5.64276i	−1.05071	−	0.276992i
$416$	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	$0.402540\pi$
$420$	−9.06624	−	23.3361i	−0.442387	−	1.13868i
$421$	13.7958	−	10.0232i	0.672367	−	0.488503i	−0.198450	−	0.980111i	$-0.563591\pi$
$421$	13.7958	−	10.0232i	0.672367	−	0.488503i	0.870817	+	0.491608i	$0.163591\pi$
$422$	−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
$425$	−13.0422	−	14.2515i	−0.632640	−	0.691300i
$426$	−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	$-0.938979\pi$
$431$	−1.56727	+	4.82357i	−0.0754928	+	0.232343i	0.906188	+	0.422874i	$0.138979\pi$
$432$	−6.34577	−	8.73420i	−0.305311	−	0.420225i
$433$	16.8915	−	23.2492i	0.811754	−	1.11728i	−0.179297	−	0.983795i	$-0.557382\pi$
$433$	16.8915	−	23.2492i	0.811754	−	1.11728i	0.991050	−	0.133488i	$-0.0426178\pi$
$434$	−4.67368	−	14.3841i	−0.224344	−	0.690460i
$435$	16.1985	−	25.1655i	0.776657	−	1.20659i
$436$	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	$-0.735476\pi$
$439$	−28.2487			−1.34824			−0.674119	+	0.738623i	$0.735476\pi$
$440$		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	0.996339	+	0.0854846i	$0.0272438\pi$
$443$	16.2015	+	22.2994i	0.769754	+	1.05948i	−0.226585	+	0.973991i	$0.572756\pi$
$444$	4.85410	+	3.52671i	0.230365	+	0.167370i
$445$	−0.872618	−	0.561685i	−0.0413661	−	0.0266264i
$446$	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	0.300122	+	0.953901i	$0.402973\pi$
$449$	−10.6662	+	32.8273i	−0.503371	+	1.54922i	−0.803492	+	0.595315i	$0.797027\pi$
$450$	−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
$455$	31.6931	−	1.78941i	1.48579	−	0.0838888i
$456$	−4.83928	−	14.8938i	−0.226620	−	0.697465i
$457$	20.1750	−	6.55524i	0.943745	−	0.306641i	0.203573	−	0.979060i	$-0.434744\pi$
$457$	20.1750	−	6.55524i	0.943745	−	0.306641i	0.740171	+	0.672418i	$0.234744\pi$
$458$	1.23889	−	1.70518i	0.0578893	−	0.0796778i
$459$	13.6952	−	9.95015i	0.639237	−	0.464433i
$460$	−12.5804	+	4.88757i	−0.586563	+	0.227884i
$461$	−33.0000			−1.53696			−0.768482	−	0.639872i	$-0.778987\pi$
$461$	−33.0000			−1.53696			−0.768482	+	0.639872i	$0.778987\pi$
$462$		0			0
$463$			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
$465$	36.4742	+	9.61542i	1.69145	+	0.445905i
$466$	−0.708411	−	0.514691i	−0.0328165	−	0.0238426i
$467$	0.588870	−	0.191335i	0.0272496	−	0.00885394i	−0.295360	−	0.955386i	$-0.595440\pi$
$467$	0.588870	−	0.191335i	0.0272496	−	0.00885394i	0.322610	+	0.946532i	$0.395440\pi$
$468$	−5.11616	+	1.66234i	−0.236495	+	0.0768418i
$469$	−5.98050	−	4.34509i	−0.276154	−	0.200638i
$470$	3.37910	−	12.8179i	0.155866	−	0.591248i
$471$	13.0556	−	40.1809i	0.601569	−	1.85144i
$472$			2.44949i			0.112747i
$473$		0			0
$474$	1.46410			0.0672484
$475$	−18.2541	−	10.3432i	−0.837554	−	0.474579i
$476$	−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	$-0.118451\pi$
$479$	−0.783636	−	2.41178i	−0.0358052	−	0.110197i	−0.967362	+	0.253399i	$0.918451\pi$
$480$	22.1648	−	1.25144i	1.01168	−	0.0571201i
$481$	−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	$-0.293116\pi$
$487$	−7.48128	−	10.2971i	−0.339009	−	0.466606i	−0.944152	+	0.329511i	$0.893116\pi$
$488$	−13.3219	+	18.3360i	−0.603054	+	0.830033i
$489$	−3.06798	−	9.44228i	−0.138739	−	0.426995i
$490$	2.62880	−	4.08403i	0.118757	−	0.184497i
$491$	−32.1283	−	23.3426i	−1.44993	−	1.05344i	−0.985847	−	0.167646i	$-0.946383\pi$
$491$	−32.1283	−	23.3426i	−1.44993	−	1.05344i	−0.464084	−	0.885791i	$-0.653617\pi$
$492$	−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	0.859056	−	0.511882i	$-0.171051\pi$
$499$	14.2449	+	10.3495i	0.637690	+	0.463309i	−0.221366	+	0.975191i	$0.571051\pi$
$500$	13.5261	−	13.8580i	0.604904	−	0.619751i
$501$	−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	0.701193	−	0.712971i	$-0.252651\pi$
$503$	−4.34117	−	5.97510i	−0.193563	−	0.266417i	−0.894756	+	0.446554i	$0.852651\pi$
$504$	−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	−0.723027	−	0.690819i	$-0.757250\pi$
$509$	−6.53022	+	4.74448i	−0.289447	+	0.210296i	0.433580	+	0.901115i	$0.357250\pi$
$510$	0.487015	+	8.62577i	0.0215654	+	0.381955i
$511$	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
$515$	−8.84291	+	3.43554i	−0.389665	+	0.151388i
$516$	−21.5885			−0.950379
$517$		0			0
$518$			3.10583i			0.136462i
$519$	12.9950	−	39.9944i	0.570415	−	1.75556i
$520$	−4.67185	+	17.7217i	−0.204874	+	0.777148i
$521$	7.48236	+	5.43626i	0.327808	+	0.238167i	0.739500	−	0.673156i	$-0.235062\pi$
$521$	7.48236	+	5.43626i	0.327808	+	0.238167i	−0.411692	+	0.911323i	$0.635062\pi$
$522$	−2.49686	+	0.811279i	−0.109285	+	0.0355087i
$523$	24.3772	−	7.92063i	1.06594	−	0.346345i	0.277035	−	0.960860i	$-0.410648\pi$
$523$	24.3772	−	7.92063i	1.06594	−	0.346345i	0.788905	+	0.614515i	$0.210648\pi$
$524$	4.37803	+	3.18083i	0.191255	+	0.138955i
$525$	13.3841	+	29.4191i	0.584131	+	1.28395i
$526$	−1.08671	+	3.34454i	−0.0473827	+	0.145829i
$527$		−	33.7381i		−	1.46965i
$528$		0			0
$529$	10.8564			0.472018
$530$	−0.910463	−	2.34349i	−0.0395480	−	0.101795i
$531$	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
$535$	−0.374003	−	6.62415i	−0.0161696	−	0.286387i
$536$	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	$-0.917853\pi$
$541$	−0.805822	+	2.48007i	−0.0346450	+	0.106626i	0.932239	+	0.361844i	$0.117853\pi$
$542$	−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
$545$	−17.2909	−	11.1298i	−0.740660	−	0.476746i
$546$	−11.4849	−	8.34429i	−0.491510	−	0.357103i
$547$	16.8915	+	23.2492i	0.722228	+	0.994062i	0.999447	+	0.0332552i	$0.0105874\pi$
$547$	16.8915	+	23.2492i	0.722228	+	0.994062i	−0.277218	+	0.960807i	$0.589413\pi$
$548$	−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
$555$	−6.51331	−	4.19247i	−0.276475	−	0.177960i
$556$	7.80823	+	24.0312i	0.331143	+	1.01915i
$557$	−22.1018	+	30.4205i	−0.936482	+	1.28896i	0.0207955	+	0.999784i	$0.493380\pi$
$557$	−22.1018	+	30.4205i	−0.936482	+	1.28896i	−0.957277	+	0.289173i	$0.906620\pi$
$558$	−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	−0.0291185	−	0.999576i	$-0.509270\pi$
$563$	−15.1907	−	4.93576i	−0.640212	−	0.208017i	−0.611093	+	0.791559i	$0.709270\pi$
$564$	31.0019	−	22.5242i	1.30542	−	0.948441i
$565$	0.356520	+	6.31450i	0.0149989	+	0.265653i
$566$	−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	$-0.482464\pi$
$569$	24.3711	−	17.7067i	1.02169	−	0.742301i	0.966629	+	0.256181i	$0.0824645\pi$
$570$	3.39789	+	8.74602i	0.142322	+	0.366330i
$571$	−19.7128			−0.824956			−0.412478	−	0.910968i	$-0.635337\pi$
$571$	−19.7128			−0.824956			−0.412478	+	0.910968i	$0.635337\pi$
$572$		0			0
$573$		−	14.0406i		−	0.586554i
$574$	0.927051	−	2.85317i	0.0386944	−	0.119089i
$575$	15.8597	−	7.21532i	0.661394	−	0.300899i
$576$	1.34317	+	0.975873i	0.0559656	+	0.0406614i
$577$	3.57803	−	1.16257i	0.148955	−	0.0483986i	−0.233590	−	0.972335i	$-0.575047\pi$
$577$	3.57803	−	1.16257i	0.148955	−	0.0483986i	0.382546	+	0.923937i	$0.375047\pi$
$578$	−1.01995	+	0.331402i	−0.0424244	+	0.0137845i
$579$	−23.7208	−	17.2342i	−0.985802	−	0.716227i
$580$	6.84006	−	25.9464i	0.284018	−	1.07736i
$581$	10.2360	−	31.5031i	0.424660	−	1.30697i
$582$			9.14162i			0.378932i
$583$		0			0
$584$	−9.46410			−0.391627
$585$	6.47346	−	2.51499i	0.267645	−	0.103982i
$586$	−6.31345	+	4.58699i	−0.260806	+	0.189487i
$587$	−11.9855	+	16.4966i	−0.494695	+	0.680889i	−0.981245	−	0.192764i	$-0.938255\pi$
$587$	−11.9855	+	16.4966i	−0.494695	+	0.680889i	0.486551	+	0.873652i	$0.338255\pi$
$588$	13.3534	−	4.33878i	0.550685	−	0.178928i
$589$	−11.3227	−	34.8477i	−0.466544	−	1.43587i
$590$	−0.0827308	−	1.46528i	−0.00340597	−	0.0603248i
$591$	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	$-0.994383\pi$
$593$		−	0.859411i		−	0.0352918i	0.999844	−	0.0176459i	$-0.00561715\pi$
$594$		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	0.831389	+	0.555692i	$0.187546\pi$
$599$	11.8801	+	36.5632i	0.485408	+	1.49393i	−0.345980	+	0.938242i	$0.612454\pi$
$600$	−18.5417	+	2.10044i	−0.756960	+	0.0857501i
$601$	−16.1803	−	11.7557i	−0.660010	−	0.479525i	0.206656	−	0.978414i	$-0.433742\pi$
$601$	−16.1803	−	11.7557i	−0.660010	−	0.479525i	−0.866666	+	0.498888i	$0.833742\pi$
$602$	−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	0.910726	−	0.413011i	$-0.135523\pi$
$607$	34.6095	+	11.2453i	1.40476	+	0.456433i	0.494031	+	0.869444i	$0.335523\pi$
$608$	−12.6756	−	17.4464i	−0.514061	−	0.707545i
$609$	36.2315	+	26.3237i	1.46817	+	1.06669i
$610$	7.34987	−	11.4186i	0.297588	−	0.462324i
$611$	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	0.829771	−	0.558103i	$-0.188471\pi$
$613$	1.05399	+	1.45069i	0.0425702	+	0.0585928i	−0.787201	+	0.616696i	$0.788471\pi$
$614$	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	−0.360194	−	0.932877i	$-0.617290\pi$
$619$	10.3430	−	7.51461i	0.415719	−	0.302037i	0.775913	+	0.630840i	$0.217290\pi$
$620$	33.7653	−	1.90641i	1.35605	−	0.0765632i
$621$	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
$625$	−16.4258	+	18.8466i	−0.657032	+	0.753863i
$626$	−8.87564			−0.354742
$627$		0			0
$628$		−	37.8792i		−	1.51154i
$629$	−2.14093	+	6.58911i	−0.0853646	+	0.262725i
$630$	0.722737	−	2.74156i	0.0287945	−	0.109226i
$631$	12.3946	+	9.00517i	0.493419	+	0.358490i	0.806498	−	0.591237i	$-0.201360\pi$
$631$	12.3946	+	9.00517i	0.493419	+	0.358490i	−0.313078	+	0.949727i	$0.601360\pi$
$632$	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
$635$	1.93857	+	0.511052i	0.0769299	+	0.0202805i
$636$	2.24592	−	6.91223i	0.0890565	−	0.274088i
$637$			17.8028i			0.705371i
$638$		0			0
$639$	6.00000			0.237356
$640$	23.8702	−	9.27375i	0.943552	−	0.366577i
$641$	6.35597	−	4.61788i	0.251046	−	0.182395i	−0.455144	−	0.890418i	$-0.650412\pi$
$641$	6.35597	−	4.61788i	0.251046	−	0.182395i	0.706190	+	0.708022i	$0.250412\pi$
$642$	−1.74403	+	2.40046i	−0.0688315	+	0.0947385i
$643$	−10.0038	+	3.25045i	−0.394513	+	0.128185i	−0.499554	−	0.866283i	$-0.666503\pi$
$643$	−10.0038	+	3.25045i	−0.394513	+	0.128185i	0.105041	+	0.994468i	$0.466503\pi$
$644$	−6.24095	−	19.2077i	−0.245928	−	0.756889i
$645$	27.8263	−	1.57109i	1.09566	−	0.0618615i
$646$	6.78952	−	4.93287i	0.267130	−	0.194081i
$647$	−35.5329	−	11.5453i	−1.39694	−	0.453894i	−0.488742	−	0.872428i	$-0.662544\pi$
$647$	−35.5329	−	11.5453i	−1.39694	−	0.453894i	−0.908201	+	0.418534i	$0.862544\pi$
$648$		−	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	$-0.876378\pi$
$653$	−7.13919	+	9.82625i	−0.279378	+	0.384531i	0.646150	+	0.763211i	$0.276378\pi$
$654$	2.84177	+	8.74606i	0.111122	+	0.341998i
$655$	−5.87451	−	3.78129i	−0.229536	−	0.147747i
$656$	−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	$-0.349918\pi$
$659$	23.3205			0.908438			0.454219	+	0.890890i	$0.349918\pi$
$660$		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
$665$	16.9928	−	26.3996i	0.658953	−	1.02373i
$666$	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	0.938873	−	0.344264i	$-0.111871\pi$
$673$	38.8118	+	12.6107i	1.49608	+	0.486107i	0.557211	+	0.830371i	$0.311871\pi$
$674$	−7.38176	+	5.36316i	−0.284335	+	0.206581i
$675$	−14.7895	−	16.1609i	−0.569249	−	0.622032i
$676$	−2.67617	−	8.23639i	−0.102929	−	0.316784i
$677$	−19.3576	+	6.28967i	−0.743973	+	0.241732i	−0.656386	−	0.754425i	$-0.727916\pi$
$677$	−19.3576	+	6.28967i	−0.743973	+	0.241732i	−0.0875873	+	0.996157i	$0.527916\pi$
$678$	1.66251	−	2.28825i	0.0638482	−	0.0878795i
$679$	24.7466	−	17.9794i	0.949687	−	0.689988i
$680$	6.04416	+	15.5574i	0.231783	+	0.596598i
$681$	−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
$685$	19.1662	+	5.05265i	0.732302	+	0.193052i
$686$	−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
$690$	−7.53475	−	1.98633i	−0.286843	−	0.0756184i
$691$	11.7145	−	36.0536i	0.445641	−	1.37154i	−0.436138	−	0.899880i	$-0.643654\pi$
$691$	11.7145	−	36.0536i	0.445641	−	1.37154i	0.881779	−	0.471663i	$-0.156346\pi$
$692$		−	37.7033i		−	1.43326i
$693$		0			0
$694$	2.26795			0.0860902
$695$	−11.8132	−	30.4066i	−0.448100	−	1.15339i
$696$	−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
$700$	19.5633	+	21.3773i	0.739424	+	0.807985i
$701$	−30.6265	+	22.2514i	−1.15675	+	0.840425i	−0.989363	−	0.145467i	$-0.953532\pi$
$701$	−30.6265	+	22.2514i	−1.15675	+	0.840425i	−0.167383	+	0.985892i	$0.553532\pi$
$702$	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	0.934784	−	0.355217i	$-0.115593\pi$
$709$	−0.805822	−	2.48007i	−0.0302633	−	0.0931408i	−0.965047	+	0.262076i	$0.915593\pi$
$710$	5.13471	−	7.97714i	0.192702	−	0.299377i
$711$	−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	−0.964140	−	0.265394i	$-0.914498\pi$
$719$	−40.6095	−	29.5046i	−1.51448	−	1.10033i	−0.550340	−	0.834941i	$-0.685502\pi$
$720$	−3.39165	−	2.18313i	−0.126399	−	0.0813604i
$721$	−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
$730$	5.66142	−	0.319647i	0.209539	−	0.0118307i
$731$	−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	−0.695807	−	0.718229i	$-0.744953\pi$
$733$	5.47668	−	7.53800i	0.202286	−	0.278423i	0.898093	+	0.439807i	$0.144953\pi$
$734$	−7.07994	+	5.14388i	−0.261325	+	0.189864i
$735$	−16.8960	+	6.56422i	−0.623219	+	0.242125i
$736$	17.9090			0.660133
$737$		0			0
$738$		−	0.656339i		−	0.0241602i
$739$	12.0295	−	37.0229i	0.442511	−	1.36191i	−0.442679	−	0.896680i	$-0.645972\pi$
$739$	12.0295	−	37.0229i	0.442511	−	1.36191i	0.885190	−	0.465230i	$-0.154028\pi$
$740$	−6.71541	−	1.77034i	−0.246863	−	0.0650789i
$741$	−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	0.570057	−	0.821605i	$-0.306921\pi$
$743$	41.2733	−	13.4105i	1.51417	−	0.491984i	0.944113	+	0.329621i	$0.106921\pi$
$744$	−26.3646	−	19.1550i	−0.966574	−	0.702257i
$745$	−5.85278	+	22.2013i	−0.214429	+	0.813394i
$746$	0.0281313	−	0.0865791i	0.00102996	−	0.00316989i
$747$		−	7.24693i		−	0.265151i
$748$		0			0
$749$	9.92820			0.362769
$750$	11.0207	−	1.88272i	0.402418	−	0.0687473i
$751$	−39.3514	+	28.5905i	−1.43595	+	1.04328i	−0.447084	+	0.894492i	$0.647538\pi$
$751$	−39.3514	+	28.5905i	−1.43595	+	1.04328i	−0.988869	+	0.148789i	$0.952462\pi$
$752$	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
$755$	−9.36796	+	0.528920i	−0.340935	+	0.0192494i
$756$	−20.5428	+	14.9252i	−0.747135	+	0.542825i
$757$	−47.3387	−	15.3813i	−1.72056	−	0.559042i	−0.728522	−	0.685022i	$-0.759793\pi$
$757$	−47.3387	−	15.3813i	−1.72056	−	0.559042i	−0.992033	+	0.125980i	$0.959793\pi$
$758$		−	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	0.776114	+	0.630593i	$0.217188\pi$
$761$	−6.13597	+	18.8846i	−0.222429	+	0.684565i	−0.998542	+	0.0539721i	$0.982812\pi$
$762$	−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
$765$	3.42314	−	5.31809i	0.123764	−	0.192276i
$766$	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	$-0.443129\pi$
$769$	9.85641			0.355431			0.177716	+	0.984082i	$0.443129\pi$
$770$		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	$-0.269498\pi$
$773$	−7.07951	−	9.74411i	−0.254632	−	0.350471i	−0.917127	+	0.398596i	$0.869498\pi$
$774$	−1.97794	−	1.43705i	−0.0710955	−	0.0516539i
$775$	−43.3828	+	4.91450i	−1.55836	+	0.176534i
$776$	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
$785$	2.75663	+	48.8240i	0.0983884	+	1.74260i
$786$	0.965479	+	2.97144i	0.0344375	+	0.105988i
$787$	16.5357	−	5.37277i	0.589434	−	0.191519i	0.000911585	−	1.00000i	$-0.499710\pi$
$787$	16.5357	−	5.37277i	0.589434	−	0.191519i	0.588522	+	0.808481i	$0.299710\pi$
$788$	17.5597	−	24.1689i	0.625539	−	0.860980i
$789$	10.6178	−	7.71430i	0.378005	−	0.274636i
$790$	−1.57963	+	0.613700i	−0.0562009	+	0.0218345i
$791$	−9.46410			−0.336505
$792$		0			0
$793$			49.7749i			1.76756i
$794$	−5.27548	+	16.2362i	−0.187220	+	0.576203i
$795$	−2.39183	+	9.07291i	−0.0848293	+	0.321783i
$796$	−2.80252	−	2.03615i	−0.0993326	−	0.0721693i
$797$	−34.4164	+	11.1826i	−1.21909	+	0.396107i	−0.846751	−	0.531989i	$-0.821445\pi$
$797$	−34.4164	+	11.1826i	−1.21909	+	0.396107i	−0.372340	+	0.928096i	$0.621445\pi$
$798$	−13.3534	+	4.33878i	−0.472705	+	0.153591i
$799$	35.7980	+	26.0087i	1.26644	+	0.920123i
$800$	−23.3893	+	10.6409i	−0.826937	+	0.376213i
$801$	0.104987	−	0.323118i	0.00370954	−	0.0114168i
$802$			1.20118i			0.0424153i
$803$		0			0
$804$	−7.39230			−0.260706
$805$	9.44205	+	24.3034i	0.332789	+	0.856582i
$806$	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	$-0.0177509\pi$
$809$	4.49184	+	13.8245i	0.157925	+	0.486042i	−0.840521	+	0.541779i	$0.817751\pi$
$810$	0.695557	+	12.3193i	0.0244394	+	0.432858i
$811$	−15.3558	+	11.1566i	−0.539214	+	0.391762i	−0.823793	−	0.566891i	$-0.808146\pi$
$811$	−15.3558	+	11.1566i	−0.539214	+	0.391762i	0.284579	+	0.958653i	$0.408146\pi$
$812$	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
$820$	5.64069	+	3.63079i	0.196981	+	0.126793i
$821$	−23.6202	−	17.1611i	−0.824350	−	0.598925i	0.0936051	−	0.995609i	$-0.470161\pi$
$821$	−23.6202	−	17.1611i	−0.824350	−	0.598925i	−0.917955	+	0.396684i	$0.870161\pi$
$822$	−5.21026	−	7.17130i	−0.181729	−	0.250128i
$823$	6.42581	+	2.08787i	0.223990	+	0.0727787i	0.418862	−	0.908050i	$-0.362429\pi$
$823$	6.42581	+	2.08787i	0.223990	+	0.0727787i	−0.194872	+	0.980829i	$0.562429\pi$
$824$	8.19615			0.285526
$825$		0			0
$826$	2.19615			0.0764139
$827$	−32.4118	−	10.5312i	−1.12707	−	0.366207i	−0.314608	−	0.949222i	$-0.601873\pi$
$827$	−32.4118	−	10.5312i	−1.12707	−	0.366207i	−0.812462	+	0.583014i	$0.801873\pi$
$828$	−2.59713	−	3.57465i	−0.0902566	−	0.124228i
$829$	−8.07461	−	5.86654i	−0.280443	−	0.203754i	0.438668	−	0.898649i	$-0.355450\pi$
$829$	−8.07461	−	5.86654i	−0.280443	−	0.203754i	−0.719110	+	0.694896i	$0.755450\pi$
$830$	−9.63497	−	6.20181i	−0.334435	−	0.215268i
$831$	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	−0.978250	−	0.207430i	$-0.933490\pi$
$839$	−31.3774	+	22.7970i	−1.08327	+	0.787041i	−0.105019	+	0.994470i	$0.533490\pi$
$840$	−1.57406	−	27.8789i	−0.0543102	−	0.961914i
$841$	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
$845$	4.04882	+	10.4215i	0.139284	+	0.358510i
$846$	4.33975			0.149204
$847$		0			0
$848$		−	5.35225i		−	0.183797i
$849$	−4.81710	+	14.8255i	−0.165322	+	0.508810i
$850$	−4.14106	−	9.10229i	−0.142037	−	0.312206i
$851$	−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	−0.942856	−	0.333201i	$-0.891871\pi$
$853$	−44.0952	+	14.3274i	−1.50979	+	0.490561i	−0.566935	+	0.823762i	$0.691871\pi$
$854$	16.4396	+	11.9441i	0.562553	+	0.408719i
$855$	1.75094	−	6.64183i	0.0598808	−	0.227146i
$856$	−1.77130	+	5.45150i	−0.0605418	+	0.186329i
$857$			29.3195i			1.00154i	0.865581	+	0.500768i	$0.166949\pi$
$857$			29.3195i			1.00154i	−0.865581	+	0.500768i	$0.833051\pi$
$858$		0			0
$859$	22.1962			0.757323			0.378661	−	0.925535i	$-0.376384\pi$
$859$	22.1962			0.757323			0.378661	+	0.925535i	$0.376384\pi$
$860$	23.2920	−	9.04912i	0.794251	−	0.308572i
$861$	−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	$-0.505944\pi$
$863$	16.2719	−	5.28705i	0.553901	−	0.179973i	0.572575	+	0.819852i	$0.305944\pi$
$864$	−6.95803	−	21.4146i	−0.236717	−	0.728540i
$865$	2.74383	+	48.5973i	0.0932931	+	1.65236i
$866$	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
$875$	−26.7717	−	26.1304i	−0.905048	−	0.883367i
$876$	13.2617	+	9.63516i	0.448070	+	0.325542i
$877$	−6.99213	−	9.62384i	−0.236107	−	0.324974i	0.674478	−	0.738295i	$-0.264369\pi$
$877$	−6.99213	−	9.62384i	−0.236107	−	0.324974i	−0.910585	+	0.413321i	$0.864369\pi$
$878$	−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	$-0.318199\pi$
$883$	−12.6756	−	17.4464i	−0.426566	−	0.587118i	−0.967161	+	0.254165i	$0.918199\pi$
$884$	−22.9699	−	16.6886i	−0.772560	−	0.561298i
$885$	−2.96452	+	4.60560i	−0.0996514	+	0.154816i
$886$	4.40904	+	13.5696i	0.148125	+	0.455881i
$887$	9.22532	−	12.6976i	0.309756	−	0.426342i	−0.625549	−	0.780185i	$-0.715125\pi$
$887$	9.22532	−	12.6976i	0.309756	−	0.426342i	0.935305	+	0.353842i	$0.115125\pi$
$888$	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
$895$	−34.5238	+	1.94923i	−1.15400	+	0.0651557i
$896$	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
$900$	5.51582	+	3.12540i	0.183861	+	0.104180i
$901$	8.39230			0.279588
$902$		0			0
$903$			41.7057i			1.38788i
$904$	1.68850	−	5.19667i	0.0561587	−	0.172839i
$905$	9.91369	−	37.6056i	0.329542	−	1.25005i
$906$	3.39476	+	2.46644i	0.112783	+	0.0819419i
$907$	28.6407	−	9.30592i	0.950998	−	0.308998i	0.207877	−	0.978155i	$-0.433345\pi$
$907$	28.6407	−	9.30592i	0.950998	−	0.308998i	0.743121	+	0.669157i	$0.233345\pi$
$908$	−33.1326	+	10.7654i	−1.09954	+	0.357264i
$909$	11.4849	+	8.34429i	0.380931	+	0.276763i
$910$	15.8888	+	4.18866i	0.526710	+	0.138853i
$911$	−9.34737	+	28.7682i	−0.309692	+	0.953134i	0.668192	+	0.743988i	$0.267068\pi$
$911$	−9.34737	+	28.7682i	−0.309692	+	0.953134i	−0.977885	+	0.209146i	$0.932932\pi$
$912$			19.9749i			0.661434i
$913$		0			0
$914$	10.9808			0.363211
$915$	−47.2397	+	18.3530i	−1.56169	+	0.606730i
$916$	−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	0.999991	+	0.00425273i	$0.00135369\pi$
$919$	5.86538	+	18.0518i	0.193481	+	0.595473i	−0.806510	+	0.591220i	$0.798646\pi$
$920$	−15.0294	+	0.848567i	−0.495504	+	0.0279764i
$921$	−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	0.882879	+	0.469600i	$0.155602\pi$
$929$	13.5524	+	41.7099i	0.444639	+	1.36846i	−0.438240	+	0.898858i	$0.644398\pi$
$930$	16.4183	+	10.5681i	0.538376	+	0.346541i
$931$	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	−0.218570	−	0.975821i	$-0.570139\pi$
$937$	−29.6606	−	9.63732i	−0.968970	−	0.314838i	−0.750400	+	0.660984i	$0.770139\pi$
$938$	−2.24918	−	3.09573i	−0.0734384	−	0.101079i
$939$	26.7982	+	19.4700i	0.874525	+	0.635380i
$940$	−24.0069	+	37.2965i	−0.783020	+	1.21648i
$941$	−8.34346	−	25.6785i	−0.271989	−	0.837096i	−0.990000	−	0.141065i	$-0.954947\pi$
$941$	−8.34346	−	25.6785i	−0.271989	−	0.837096i	0.718011	−	0.696031i	$-0.245053\pi$
$942$	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
$950$	−7.33204	−	8.01189i	−0.237883	−	0.259940i
$951$	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	−0.937807	−	0.347158i	$-0.887147\pi$
$953$	−9.81199	+	13.5051i	−0.317842	+	0.437472i	0.619965	+	0.784629i	$0.287147\pi$
$954$	0.665890	−	0.483797i	0.0215590	−	0.0156635i
$955$	5.88532	+	15.1485i	0.190445	+	0.490195i
$956$	−9.80385			−0.317079
$957$		0			0
$958$		−	1.31268i		−	0.0424107i
$959$	−9.16552	+	28.2086i	−0.295970	+	0.910902i
$960$	−9.47332	−	2.49739i	−0.305750	−	0.0806028i
$961$	−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
$965$	32.8166	+	8.65120i	1.05640	+	0.278492i
$966$	3.60322	−	11.0896i	0.115932	−	0.356801i
$967$			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
$969$	−31.3205			−1.00616
$970$	−3.83184	−	9.86299i	−0.123033	−	0.316681i
$971$	20.1673	−	14.6524i	0.647201	−	0.470219i	−0.215116	−	0.976589i	$-0.569013\pi$
$971$	20.1673	−	14.6524i	0.647201	−	0.470219i	0.862316	+	0.506370i	$0.169013\pi$
$972$	−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
$975$	−30.2320	+	27.6667i	−0.968200	+	0.886044i
$976$	23.3878	−	16.9923i	0.748627	−	0.543909i
$977$	−27.6914	−	8.99749i	−0.885927	−	0.287855i	−0.169511	−	0.985528i	$-0.554219\pi$
$977$	−27.6914	−	8.99749i	−0.885927	−	0.287855i	−0.716416	+	0.697673i	$0.754219\pi$
$978$		−	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	0.161753	−	0.986831i	$-0.448285\pi$
$983$	32.9299	−	45.3241i	1.05030	−	1.44562i	0.888548	−	0.458784i	$-0.151715\pi$
$984$	−1.99752	−	6.14773i	−0.0636785	−	0.195982i
$985$	−20.8746	+	32.4301i	−0.665119	+	1.03331i
$986$	−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
$995$	3.76046	+	2.42052i	0.119215	+	0.0767358i
$996$	−10.2360	−	31.5031i	−0.324340	−	0.998215i
$997$	−20.0535	+	27.6012i	−0.635100	+	0.874140i	−0.998342	−	0.0575549i	$-0.981670\pi$
$997$	−20.0535	+	27.6012i	−0.635100	+	0.874140i	0.363243	+	0.931695i	$0.381670\pi$
$998$	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.f.9.3		16
5.4	even	2	inner	605.2.j.f.9.2		16
11.2	odd	10		605.2.j.e.124.3		16
11.3	even	5	inner	605.2.j.f.444.3		16
11.4	even	5		605.2.b.d.364.3	yes	4
11.5	even	5	inner	605.2.j.f.269.2		16
11.6	odd	10		605.2.j.e.269.3		16
11.7	odd	10		605.2.b.e.364.2	yes	4
11.8	odd	10		605.2.j.e.444.2		16
11.9	even	5	inner	605.2.j.f.124.2		16
11.10	odd	2		605.2.j.e.9.2		16
55.4	even	10		605.2.b.d.364.2	✓	4
55.7	even	20		3025.2.a.z.1.3		4
55.9	even	10	inner	605.2.j.f.124.3		16
55.14	even	10	inner	605.2.j.f.444.2		16
55.18	even	20		3025.2.a.z.1.2		4
55.19	odd	10		605.2.j.e.444.3		16
55.24	odd	10		605.2.j.e.124.2		16
55.29	odd	10		605.2.b.e.364.3	yes	4
55.37	odd	20		3025.2.a.y.1.2		4
55.39	odd	10		605.2.j.e.269.2		16
55.48	odd	20		3025.2.a.y.1.3		4
55.49	even	10	inner	605.2.j.f.269.3		16
55.54	odd	2		605.2.j.e.9.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.d.364.2	✓	4	55.4	even	10
605.2.b.d.364.3	yes	4	11.4	even	5
605.2.b.e.364.2	yes	4	11.7	odd	10
605.2.b.e.364.3	yes	4	55.29	odd	10
605.2.j.e.9.2		16	11.10	odd	2
605.2.j.e.9.3		16	55.54	odd	2
605.2.j.e.124.2		16	55.24	odd	10
605.2.j.e.124.3		16	11.2	odd	10
605.2.j.e.269.2		16	55.39	odd	10
605.2.j.e.269.3		16	11.6	odd	10
605.2.j.e.444.2		16	11.8	odd	10
605.2.j.e.444.3		16	55.19	odd	10
605.2.j.f.9.2		16	5.4	even	2	inner
605.2.j.f.9.3		16	1.1	even	1	trivial
605.2.j.f.124.2		16	11.9	even	5	inner
605.2.j.f.124.3		16	55.9	even	10	inner
605.2.j.f.269.2		16	11.5	even	5	inner
605.2.j.f.269.3		16	55.49	even	10	inner
605.2.j.f.444.2		16	55.14	even	10	inner
605.2.j.f.444.3		16	11.3	even	5	inner
3025.2.a.y.1.2		4	55.37	odd	20
3025.2.a.y.1.3		4	55.48	odd	20
3025.2.a.z.1.2		4	55.18	even	20
3025.2.a.z.1.3		4	55.7	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.492303 + 0.159959i) q^{2} +(-1.13551 - 1.56290i) q^{3} +(-1.40126 - 1.01807i) q^{4} +(1.88023 + 1.21026i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-1.96677 + 2.70702i) q^{7} +(-1.13551 - 1.56290i) q^{8} +(-0.226216 + 0.696222i) q^{9} +O(q^{10})\)	\(q+(0.492303 + 0.159959i) q^{2} +(-1.13551 - 1.56290i) q^{3} +(-1.40126 - 1.01807i) q^{4} +(1.88023 + 1.21026i) 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} +(-0.243508 - 4.31288i) 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} +(-1.40255 - 3.61010i) q^{20} +6.46410 q^{21} -3.48477i q^{23} +(-1.15327 + 3.54939i) q^{24} +(2.07053 + 4.55114i) 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} +(0.570005 - 2.16220i) q^{30} +(-2.69835 + 8.30467i) q^{31} +5.13922i q^{32} -2.00000 q^{34} +(-6.97418 + 2.70952i) 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} +(-0.243508 - 4.31288i) 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} +(0.291333 + 2.57174i) 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} +(-4.04962 + 6.29137i) 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} +(-3.86682 + 0.218323i) 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} +(4.76187 - 8.40392i) q^{75} +7.26795 q^{76} +4.24264i q^{78} +(-0.452432 + 1.39244i) q^{79} +(-1.40455 + 5.32787i) 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} +(-8.35409 - 2.20233i) q^{85} +(-1.03204 + 3.17629i) q^{86} -13.3843i q^{87} -0.464102 q^{89} +(-0.789817 + 0.306850i) 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} +(-9.36796 + 0.528920i) 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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