LMFDB - Embedded newform 210.2.x.a.107.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("210.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.15
Character	$\chi$	$=$	210.107
Dual form			210.2.x.a.53.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(1.53804 - 0.796522i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.136630 + 2.23189i) q^{5} +(1.16745 + 1.27947i) q^{6} +(2.35340 - 1.20893i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.73111 - 2.45016i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(1.53804 - 0.796522i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.136630 + 2.23189i) q^{5} +(1.16745 + 1.27947i) q^{6} +(2.35340 - 1.20893i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.73111 - 2.45016i) q^{9} +(-2.12048 + 0.709630i) q^{10} +(-3.01159 + 1.73874i) q^{11} +(-0.933717 + 1.45883i) q^{12} +(-0.354405 + 0.354405i) q^{13} +(1.77684 + 1.96031i) q^{14} +(1.98789 + 3.32390i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.12860 - 0.838307i) q^{17} +(2.81471 + 1.03797i) q^{18} +(2.42435 + 1.39970i) q^{19} +(-1.23427 - 1.86456i) q^{20} +(2.65667 - 3.73391i) q^{21} +(-2.45895 - 2.45895i) q^{22} +(5.64018 - 1.51128i) q^{23} +(-1.65078 - 0.524329i) q^{24} +(-4.96266 + 0.609888i) q^{25} +(-0.434056 - 0.250602i) q^{26} +(0.710897 - 5.14729i) q^{27} +(-1.43364 + 2.22367i) q^{28} -1.97825 q^{29} +(-2.69613 + 2.78044i) q^{30} +(-4.44221 - 7.69413i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-3.24699 + 5.07305i) q^{33} -3.23897i q^{34} +(3.01975 + 5.08735i) q^{35} +(-0.274103 + 2.98745i) q^{36} +(-8.09819 + 2.16990i) q^{37} +(-0.724539 + 2.70402i) q^{38} +(-0.262796 + 0.827379i) q^{39} +(1.48157 - 1.67480i) q^{40} -7.96768i q^{41} +(4.29428 + 1.59974i) q^{42} +(-6.03572 + 6.03572i) q^{43} +(1.73874 - 3.01159i) q^{44} +(5.70500 + 3.52887i) q^{45} +(2.91957 + 5.05684i) q^{46} +(0.617891 + 2.30600i) q^{47} +(0.0792095 - 1.73024i) q^{48} +(4.07696 - 5.69020i) q^{49} +(-1.87354 - 4.63571i) q^{50} +(-5.47963 + 1.20266i) q^{51} +(0.129721 - 0.484126i) q^{52} +(1.55389 - 5.79919i) q^{53} +(5.15590 - 0.645543i) q^{54} +(-4.29216 - 6.48398i) q^{55} +(-2.51895 - 0.809259i) q^{56} +(4.84364 + 0.221739i) q^{57} +(-0.512009 - 1.91084i) q^{58} +(-2.18403 - 3.78284i) q^{59} +(-3.38351 - 1.88463i) q^{60} +(3.79381 - 6.57108i) q^{61} +(6.28223 - 6.28223i) q^{62} +(1.11190 - 7.85899i) q^{63} +1.00000i q^{64} +(-0.839416 - 0.742571i) q^{65} +(-5.74057 - 1.82335i) q^{66} +(-3.64677 + 13.6099i) q^{67} +(3.12860 - 0.838307i) q^{68} +(7.47102 - 6.81693i) q^{69} +(-4.13243 + 4.23356i) q^{70} +3.96344i q^{71} +(-2.95660 + 0.508447i) q^{72} +(3.68750 + 0.988062i) q^{73} +(-4.19193 - 7.26063i) q^{74} +(-7.14696 + 4.89090i) q^{75} -2.79940 q^{76} +(-4.98545 + 7.73277i) q^{77} +(-0.867203 - 0.0397001i) q^{78} +(7.48605 + 4.32207i) q^{79} +(2.00119 + 0.997619i) q^{80} +(-3.00655 - 8.48296i) q^{81} +(7.69619 - 2.06219i) q^{82} +(10.4891 + 10.4891i) q^{83} +(-0.433784 + 4.56200i) q^{84} +(1.44355 - 7.09724i) q^{85} +(-7.39221 - 4.26790i) q^{86} +(-3.04262 + 1.57572i) q^{87} +(3.35899 + 0.900040i) q^{88} +(-3.59897 + 6.23359i) q^{89} +(-1.93206 + 6.42395i) q^{90} +(-0.405604 + 1.26251i) q^{91} +(-4.12890 + 4.12890i) q^{92} +(-12.9608 - 8.29553i) q^{93} +(-2.06750 + 1.19367i) q^{94} +(-2.79274 + 5.60213i) q^{95} +(1.69178 - 0.371308i) q^{96} +(11.6503 + 11.6503i) q^{97} +(6.55151 + 2.46531i) q^{98} +(-0.953188 + 10.3888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	1.53804	−	0.796522i	0.887985	−	0.459872i
$3$	1.53804	−	0.796522i	0.887985	−	0.459872i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.136630	+	2.23189i	0.0611030	+	0.998131i
$5$	0.136630	+	2.23189i	0.0611030	+	0.998131i
$6$	1.16745	+	1.27947i	0.476611	+	0.522343i
$7$	2.35340	−	1.20893i	0.889501	−	0.456934i
$7$	2.35340	−	1.20893i	0.889501	−	0.456934i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.73111	−	2.45016i	0.577035	−	0.816719i
$10$	−2.12048	+	0.709630i	−0.670554	+	0.224405i
$11$	−3.01159	+	1.73874i	−0.908029	+	0.524251i	−0.879797	−	0.475350i	$-0.842321\pi$
$11$	−3.01159	+	1.73874i	−0.908029	+	0.524251i	−0.0282327	+	0.999601i	$0.508988\pi$
$12$	−0.933717	+	1.45883i	−0.269541	+	0.421127i
$13$	−0.354405	+	0.354405i	−0.0982943	+	0.0982943i	−0.754544	−	0.656250i	$-0.772142\pi$
$13$	−0.354405	+	0.354405i	−0.0982943	+	0.0982943i	0.656250	+	0.754544i	$0.272142\pi$
$14$	1.77684	+	1.96031i	0.474881	+	0.523916i
$15$	1.98789	+	3.32390i	0.513271	+	0.858226i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.12860	−	0.838307i	−0.758798	−	0.203319i	−0.141381	−	0.989955i	$-0.545154\pi$
$17$	−3.12860	−	0.838307i	−0.758798	−	0.203319i	−0.617417	+	0.786636i	$0.711821\pi$
$18$	2.81471	+	1.03797i	0.663434	+	0.244652i
$19$	2.42435	+	1.39970i	0.556185	+	0.321114i	0.751613	−	0.659604i	$-0.229276\pi$
$19$	2.42435	+	1.39970i	0.556185	+	0.321114i	−0.195428	+	0.980718i	$0.562610\pi$
$20$	−1.23427	−	1.86456i	−0.275991	−	0.416928i
$21$	2.65667	−	3.73391i	0.579732	−	0.814807i
$22$	−2.45895	−	2.45895i	−0.524251	−	0.524251i
$23$	5.64018	−	1.51128i	1.17606	−	0.315124i	0.382696	−	0.923874i	$-0.374996\pi$
$23$	5.64018	−	1.51128i	1.17606	−	0.315124i	0.793362	+	0.608750i	$0.208329\pi$
$24$	−1.65078	−	0.524329i	−0.336964	−	0.107028i
$25$	−4.96266	+	0.609888i	−0.992533	+	0.121978i
$26$	−0.434056	−	0.250602i	−0.0851254	−	0.0491471i
$27$	0.710897	−	5.14729i	0.136812	−	0.990597i
$28$	−1.43364	+	2.22367i	−0.270932	+	0.420233i
$29$	−1.97825			−0.367352			−0.183676	−	0.982987i	$-0.558800\pi$
$29$	−1.97825			−0.367352			−0.183676	+	0.982987i	$0.558800\pi$
$30$	−2.69613	+	2.78044i	−0.492244	+	0.507637i
$31$	−4.44221	−	7.69413i	−0.797844	−	1.38191i	−0.921018	−	0.389521i	$-0.872641\pi$
$31$	−4.44221	−	7.69413i	−0.797844	−	1.38191i	0.123174	−	0.992385i	$-0.460693\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−3.24699	+	5.07305i	−0.565228	+	0.883104i
$34$		−	3.23897i		−	0.555479i
$35$	3.01975	+	5.08735i	0.510431	+	0.859919i
$36$	−0.274103	+	2.98745i	−0.0456838	+	0.497909i
$37$	−8.09819	+	2.16990i	−1.33133	+	0.356730i	−0.853212	−	0.521564i	$-0.825349\pi$
$37$	−8.09819	+	2.16990i	−1.33133	+	0.356730i	−0.478121	+	0.878294i	$0.658682\pi$
$38$	−0.724539	+	2.70402i	−0.117536	+	0.438649i
$39$	−0.262796	+	0.827379i	−0.0420811	+	0.132487i
$40$	1.48157	−	1.67480i	0.234257	−	0.264809i
$41$		−	7.96768i		−	1.24434i	−0.782881	−	0.622171i	$-0.786251\pi$
$41$		−	7.96768i		−	1.24434i	0.782881	−	0.622171i	$-0.213749\pi$
$42$	4.29428	+	1.59974i	0.662622	+	0.246845i
$43$	−6.03572	+	6.03572i	−0.920438	+	0.920438i	−0.997060	−	0.0766219i	$-0.975587\pi$
$43$	−6.03572	+	6.03572i	−0.920438	+	0.920438i	0.0766219	+	0.997060i	$0.475587\pi$
$44$	1.73874	−	3.01159i	0.262125	−	0.454015i
$45$	5.70500	+	3.52887i	0.850452	+	0.526053i
$46$	2.91957	+	5.05684i	0.430467	+	0.745591i
$47$	0.617891	+	2.30600i	0.0901286	+	0.336365i	0.996236	−	0.0866833i	$-0.0276268\pi$
$47$	0.617891	+	2.30600i	0.0901286	+	0.336365i	−0.906107	+	0.423048i	$0.860960\pi$
$48$	0.0792095	−	1.73024i	0.0114329	−	0.249738i
$49$	4.07696	−	5.69020i	0.582423	−	0.812886i
$50$	−1.87354	−	4.63571i	−0.264958	−	0.655589i
$51$	−5.47963	+	1.20266i	−0.767302	+	0.168406i
$52$	0.129721	−	0.484126i	0.0179891	−	0.0671362i
$53$	1.55389	−	5.79919i	0.213443	−	0.796580i	−0.773266	−	0.634082i	$-0.781378\pi$
$53$	1.55389	−	5.79919i	0.213443	−	0.796580i	0.986709	−	0.162498i	$-0.0519552\pi$
$54$	5.15590	−	0.645543i	0.701629	−	0.0878473i
$55$	−4.29216	−	6.48398i	−0.578755	−	0.874299i
$56$	−2.51895	−	0.809259i	−0.336609	−	0.108142i
$57$	4.84364	+	0.221739i	0.641555	+	0.0293701i
$58$	−0.512009	−	1.91084i	−0.0672301	−	0.250906i
$59$	−2.18403	−	3.78284i	−0.284336	−	0.492484i	0.688112	−	0.725604i	$-0.258440\pi$
$59$	−2.18403	−	3.78284i	−0.284336	−	0.492484i	−0.972448	+	0.233120i	$0.925106\pi$
$60$	−3.38351	−	1.88463i	−0.436810	−	0.243305i
$61$	3.79381	−	6.57108i	0.485748	−	0.841340i	−0.514118	−	0.857720i	$-0.671881\pi$
$61$	3.79381	−	6.57108i	0.485748	−	0.841340i	0.999866	+	0.0163794i	$0.00521396\pi$
$62$	6.28223	−	6.28223i	0.797844	−	0.797844i
$63$	1.11190	−	7.85899i	0.140087	−	0.990139i
$64$			1.00000i			0.125000i
$65$	−0.839416	−	0.742571i	−0.104117	−	0.0921045i
$66$	−5.74057	−	1.82335i	−0.706615	−	0.224439i
$67$	−3.64677	+	13.6099i	−0.445524	+	1.66272i	0.269026	+	0.963133i	$0.413298\pi$
$67$	−3.64677	+	13.6099i	−0.445524	+	1.66272i	−0.714550	+	0.699584i	$0.753369\pi$
$68$	3.12860	−	0.838307i	0.379399	−	0.101660i
$69$	7.47102	−	6.81693i	0.899406	−	0.820662i
$70$	−4.13243	+	4.23356i	−0.493920	+	0.506007i
$71$			3.96344i			0.470374i	0.971950	+	0.235187i	$0.0755702\pi$
$71$			3.96344i			0.470374i	−0.971950	+	0.235187i	$0.924430\pi$
$72$	−2.95660	+	0.508447i	−0.348439	+	0.0599210i
$73$	3.68750	+	0.988062i	0.431589	+	0.115644i	0.468072	−	0.883690i	$-0.344949\pi$
$73$	3.68750	+	0.988062i	0.431589	+	0.115644i	−0.0364830	+	0.999334i	$0.511615\pi$
$74$	−4.19193	−	7.26063i	−0.487302	−	0.844032i
$75$	−7.14696	+	4.89090i	−0.825260	+	0.564753i
$76$	−2.79940			−0.321114
$77$	−4.98545	+	7.73277i	−0.568145	+	0.881231i
$78$	−0.867203	−	0.0397001i	−0.0981915	−	0.00449516i
$79$	7.48605	+	4.32207i	0.842246	+	0.486271i	0.858027	−	0.513604i	$-0.171690\pi$
$79$	7.48605	+	4.32207i	0.842246	+	0.486271i	−0.0157809	+	0.999875i	$0.505023\pi$
$80$	2.00119	+	0.997619i	0.223740	+	0.111537i
$81$	−3.00655	−	8.48296i	−0.334061	−	0.942552i
$82$	7.69619	−	2.06219i	0.849901	−	0.227730i
$83$	10.4891	+	10.4891i	1.15132	+	1.15132i	0.986287	+	0.165037i	$0.0527745\pi$
$83$	10.4891	+	10.4891i	1.15132	+	1.15132i	0.165037	+	0.986287i	$0.447225\pi$
$84$	−0.433784	+	4.56200i	−0.0473298	+	0.497755i
$85$	1.44355	−	7.09724i	0.156575	−	0.769804i
$86$	−7.39221	−	4.26790i	−0.797123	−	0.460219i
$87$	−3.04262	+	1.57572i	−0.326203	+	0.168935i
$88$	3.35899	+	0.900040i	0.358070	+	0.0959446i
$89$	−3.59897	+	6.23359i	−0.381490	+	0.660760i	−0.991275	−	0.131807i	$-0.957922\pi$
$89$	−3.59897	+	6.23359i	−0.381490	+	0.660760i	0.609786	+	0.792566i	$0.291256\pi$
$90$	−1.93206	+	6.42395i	−0.203657	+	0.677144i
$91$	−0.405604	+	1.26251i	−0.0425189	+	0.132347i
$92$	−4.12890	+	4.12890i	−0.430467	+	0.430467i
$93$	−12.9608	−	8.29553i	−1.34397	−	0.860206i
$94$	−2.06750	+	1.19367i	−0.213247	+	0.123118i
$95$	−2.79274	+	5.60213i	−0.286529	+	0.574767i
$96$	1.69178	−	0.371308i	0.172667	−	0.0378965i
$97$	11.6503	+	11.6503i	1.18291	+	1.18291i	0.978988	+	0.203919i	$0.0653678\pi$
$97$	11.6503	+	11.6503i	1.18291	+	1.18291i	0.203919	+	0.978988i	$0.434632\pi$
$98$	6.55151	+	2.46531i	0.661802	+	0.249034i
$99$	−0.953188	+	10.3888i	−0.0957990	+	1.04412i
$100$	3.99285	−	3.00951i	0.399285	−	0.300951i
$101$	2.74872	−	1.58698i	0.273508	−	0.157910i	−0.356973	−	0.934115i	$-0.616191\pi$
$101$	2.74872	−	1.58698i	0.273508	−	0.157910i	0.630481	+	0.776205i	$0.282858\pi$
$102$	−2.57991	−	4.98165i	−0.255449	−	0.493257i
$103$	−1.29286	−	4.82502i	−0.127389	−	0.475423i	0.872524	−	0.488571i	$-0.162482\pi$
$103$	−1.29286	−	4.82502i	−0.127389	−	0.475423i	−0.999914	+	0.0131477i	$0.995815\pi$
$104$	0.501205			0.0491471
$105$	8.69667	+	5.41922i	0.848708	+	0.528862i
$106$	6.00376			0.583137
$107$	3.55941	+	13.2839i	0.344101	+	1.28420i	0.893659	+	0.448747i	$0.148130\pi$
$107$	3.55941	+	13.2839i	0.344101	+	1.28420i	−0.549558	+	0.835456i	$0.685204\pi$
$108$	1.95799	+	4.81314i	0.188408	+	0.463144i
$109$	−1.66115	+	0.959063i	−0.159109	+	0.0918615i	−0.577440	−	0.816433i	$-0.695948\pi$
$109$	−1.66115	+	0.959063i	−0.159109	+	0.0918615i	0.418331	+	0.908294i	$0.362615\pi$
$110$	5.15215	−	5.82408i	0.491238	−	0.555305i
$111$	−10.7269	+	9.78777i	−1.01815	+	0.929014i
$112$	0.129732	−	2.64257i	0.0122586	−	0.249699i
$113$	5.10087	+	5.10087i	0.479850	+	0.479850i	0.905084	−	0.425234i	$-0.139808\pi$
$113$	5.10087	+	5.10087i	0.479850	+	0.479850i	−0.425234	+	0.905084i	$0.639808\pi$
$114$	1.03944	+	4.73598i	0.0973526	+	0.443565i
$115$	4.14363	+	12.3818i	0.386396	+	1.15461i
$116$	1.71321	−	0.989125i	0.159068	−	0.0918380i
$117$	0.254836	+	1.48186i	0.0235596	+	0.136998i
$118$	3.08868	−	3.08868i	0.284336	−	0.284336i
$119$	−8.37631	+	1.80940i	−0.767855	+	0.165868i
$120$	0.944698	−	3.75600i	0.0862387	−	0.342874i
$121$	0.546459	−	0.946494i	0.0496781	−	0.0860449i
$122$	7.32908	+	1.96382i	0.663544	+	0.177796i
$123$	−6.34643	−	12.2546i	−0.572238	−	1.10496i
$124$	7.69413	+	4.44221i	0.690953	+	0.398922i
$125$	−2.03925	−	10.9928i	−0.182396	−	0.983225i
$126$	7.87898	−	0.960039i	0.701915	−	0.0855270i
$127$	−5.65099	−	5.65099i	−0.501444	−	0.501444i	0.410443	−	0.911886i	$-0.365374\pi$
$127$	−5.65099	−	5.65099i	−0.501444	−	0.501444i	−0.911886	+	0.410443i	$0.865374\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−4.47557	+	14.0907i	−0.394052	+	1.24062i
$130$	0.500011	−	1.00300i	0.0438539	−	0.0879693i
$131$	0.812657	+	0.469187i	0.0710021	+	0.0409931i	0.535081	−	0.844801i	$-0.320281\pi$
$131$	0.812657	+	0.469187i	0.0710021	+	0.0409931i	−0.464079	+	0.885794i	$0.653615\pi$
$132$	0.275450	−	6.01688i	0.0239748	−	0.523702i
$133$	7.39762	+	0.363173i	0.641455	+	0.0314911i
$134$	−14.0900			−1.21719
$135$	11.5853	+	0.883368i	0.997106	+	0.0760282i
$136$	1.61948	+	2.80503i	0.138870	+	0.240529i
$137$	−17.5136	−	4.69276i	−1.49629	−	0.400929i	−0.584433	−	0.811442i	$-0.698683\pi$
$137$	−17.5136	−	4.69276i	−1.49629	−	0.400929i	−0.911855	+	0.410513i	$0.865350\pi$
$138$	8.51829	+	5.45210i	0.725125	+	0.464114i
$139$		−	14.4400i		−	1.22478i	−0.790555	−	0.612391i	$-0.790208\pi$
$139$		−	14.4400i		−	1.22478i	0.790555	−	0.612391i	$-0.209792\pi$
$140$	−5.15885	−	2.89590i	−0.436003	−	0.244748i
$141$	2.78712	+	3.05455i	0.234718	+	0.257239i
$142$	−3.82839	+	1.02581i	−0.321271	+	0.0860843i
$143$	0.451104	−	1.68354i	0.0377232	−	0.140785i
$144$	−1.25635	−	2.72426i	−0.104696	−	0.227022i
$145$	−0.270289	−	4.41524i	−0.0224463	−	0.366665i
$146$			3.81758i			0.315945i
$147$	1.73814	−	11.9991i	0.143360	−	0.989671i
$148$	5.92828	−	5.92828i	0.487302	−	0.487302i
$149$	4.55062	−	7.88190i	0.372801	−	0.645711i	−0.617194	−	0.786811i	$-0.711731\pi$
$149$	4.55062	−	7.88190i	0.372801	−	0.645711i	0.989995	+	0.141100i	$0.0450640\pi$
$150$	−6.57402	−	5.63758i	−0.536766	−	0.460306i
$151$	10.0131	+	17.3431i	0.814852	+	1.41136i	0.909434	+	0.415848i	$0.136515\pi$
$151$	10.0131	+	17.3431i	0.814852	+	1.41136i	−0.0945826	+	0.995517i	$0.530152\pi$
$152$	−0.724539	−	2.70402i	−0.0587679	−	0.219325i
$153$	−7.46993	+	6.21438i	−0.603908	+	0.502403i
$154$	−8.75961	−	2.81419i	−0.705870	−	0.226774i
$155$	16.5655	−	10.9658i	1.33057	−	0.880792i
$156$	−0.186101	−	0.847929i	−0.0149000	−	0.0678887i
$157$	1.22616	−	4.57610i	0.0978584	−	0.365212i	−0.899579	−	0.436758i	$-0.856127\pi$
$157$	1.22616	−	4.57610i	0.0978584	−	0.365212i	0.997437	+	0.0715458i	$0.0227932\pi$
$158$	−2.23727	+	8.34960i	−0.177988	+	0.664259i
$159$	−2.22925	−	10.1571i	−0.176791	−	0.805508i
$160$	−0.445681	+	2.19120i	−0.0352342	+	0.173230i
$161$	11.4465	−	10.3752i	0.902114	−	0.817684i
$162$	7.41576	−	5.09965i	0.582637	−	0.400667i
$163$	−1.52298	−	5.68384i	−0.119289	−	0.445193i	0.880283	−	0.474449i	$-0.157353\pi$
$163$	−1.52298	−	5.68384i	−0.119289	−	0.445193i	−0.999572	+	0.0292565i	$0.990686\pi$
$164$	3.98384	+	6.90021i	0.311086	+	0.538816i
$165$	−11.7661	−	6.55379i	−0.915991	−	0.510212i
$166$	−7.41689	+	12.8464i	−0.575662	+	0.997076i
$167$	−6.77976	+	6.77976i	−0.524634	+	0.524634i	−0.918967	−	0.394334i	$-0.870975\pi$
$167$	−6.77976	+	6.77976i	−0.524634	+	0.524634i	0.394334	+	0.918967i	$0.370975\pi$
$168$	−4.51882	+	0.761729i	−0.348635	+	0.0587686i
$169$			12.7488i			0.980676i
$170$	7.22902	−	0.442542i	0.554441	−	0.0339414i
$171$	7.62630	−	3.51702i	0.583198	−	0.268953i
$172$	2.20923	−	8.24494i	0.168452	−	0.628671i
$173$	−12.8827	+	3.45191i	−0.979455	+	0.262444i	−0.712815	−	0.701352i	$-0.752580\pi$
$173$	−12.8827	+	3.45191i	−0.979455	+	0.262444i	−0.266640	+	0.963796i	$0.585913\pi$
$174$	−2.30952	−	2.53112i	−0.175084	−	0.191884i
$175$	−10.9418	+	7.43484i	−0.827123	+	0.562021i
$176$			3.47749i			0.262125i
$177$	−6.37223	−	4.07852i	−0.478966	−	0.306560i
$178$	−6.95267	−	1.86296i	−0.521125	−	0.139635i
$179$	11.6481	+	20.1751i	0.870619	+	1.50796i	0.861358	+	0.507999i	$0.169615\pi$
$179$	11.6481	+	20.1751i	0.870619	+	1.50796i	0.00926137	+	0.999957i	$0.497052\pi$
$180$	−6.70511	−	0.203590i	−0.499770	−	0.0151747i
$181$	0.785759			0.0584050			0.0292025	−	0.999574i	$-0.490703\pi$
$181$	0.785759			0.0584050			0.0292025	+	0.999574i	$0.490703\pi$
$182$	−1.32447	−	0.0650224i	−0.0981761	−	0.00481978i
$183$	0.601012	−	13.1284i	0.0444281	−	0.970479i
$184$	−5.05684	−	2.91957i	−0.372796	−	0.215234i
$185$	−5.94944	−	17.7778i	−0.437412	−	1.30705i
$186$	4.65836	−	14.6662i	0.341567	−	1.07538i
$187$	10.8797	−	2.91520i	0.795601	−	0.213181i
$188$	−1.68811	−	1.68811i	−0.123118	−	0.123118i
$189$	−4.54971	−	12.9731i	−0.330943	−	0.943651i
$190$	−6.13406	−	1.24764i	−0.445011	−	0.0905133i
$191$	−8.94888	−	5.16664i	−0.647518	−	0.373845i	0.139987	−	0.990153i	$-0.455294\pi$
$191$	−8.94888	−	5.16664i	−0.647518	−	0.373845i	−0.787505	+	0.616309i	$0.788627\pi$
$192$	0.796522	+	1.53804i	0.0574840	+	0.110998i
$193$	11.8723	+	3.18118i	0.854589	+	0.228986i	0.659412	−	0.751782i	$-0.270805\pi$
$193$	11.8723	+	3.18118i	0.854589	+	0.228986i	0.195177	+	0.980768i	$0.437472\pi$
$194$	−8.23799	+	14.2686i	−0.591453	+	1.02443i
$195$	−1.88252	−	0.473487i	−0.134810	−	0.0339071i
$196$	−0.685653	+	6.96634i	−0.0489752	+	0.497596i
$197$	8.78363	−	8.78363i	0.625808	−	0.625808i	−0.321203	−	0.947010i	$-0.604087\pi$
$197$	8.78363	−	8.78363i	0.625808	−	0.625808i	0.947010	+	0.321203i	$0.104087\pi$
$198$	−10.2815	+	1.76812i	−0.730677	+	0.125655i
$199$	14.0224	−	8.09584i	0.994022	−	0.573899i	0.0875478	−	0.996160i	$-0.472097\pi$
$199$	14.0224	−	8.09584i	0.994022	−	0.573899i	0.906474	+	0.422262i	$0.138764\pi$
$200$	3.94039	+	3.07788i	0.278628	+	0.217639i
$201$	5.23174	+	23.8373i	0.369019	+	1.68135i
$202$	2.24432	+	2.24432i	0.157910	+	0.157910i
$203$	−4.65561	+	2.39157i	−0.326760	+	0.167855i
$204$	4.14417	−	3.78135i	0.290150	−	0.264747i
$205$	17.7830	−	1.08863i	1.24202	−	0.0760330i
$206$	4.32599	−	2.49761i	0.301406	−	0.174017i
$207$	6.06087	−	16.4355i	0.421259	−	1.14235i
$208$	0.129721	+	0.484126i	0.00899455	+	0.0335681i
$209$	−9.73489			−0.673376
$210$	−2.98370	+	9.80293i	−0.205895	+	0.676467i
$211$	−10.8789			−0.748933			−0.374466	−	0.927240i	$-0.622174\pi$
$211$	−10.8789			−0.748933			−0.374466	+	0.927240i	$0.622174\pi$
$212$	1.55389	+	5.79919i	0.106722	+	0.398290i
$213$	3.15697	+	6.09591i	0.216312	+	0.417685i
$214$	−11.9100	+	6.87625i	−0.814152	+	0.470051i
$215$	−14.2957	−	12.6464i	−0.974960	−	0.862477i
$216$	−4.14237	+	3.13701i	−0.281852	+	0.213446i
$217$	−19.7560	−	12.7370i	−1.34112	−	0.864645i
$218$	−1.35632	−	1.35632i	−0.0918615	−	0.0918615i
$219$	6.45851	−	1.41750i	0.436426	−	0.0957856i
$220$	6.95911	+	3.46921i	0.469183	+	0.233894i
$221$	1.40589	−	0.811693i	0.0945707	−	0.0546004i
$222$	−12.2306	−	7.82815i	−0.820863	−	0.525391i
$223$	−4.82814	+	4.82814i	−0.323316	+	0.323316i	−0.850038	−	0.526722i	$-0.823421\pi$
$223$	−4.82814	+	4.82814i	−0.323316	+	0.323316i	0.526722	+	0.850038i	$0.323421\pi$
$224$	2.58610	−	0.558635i	0.172791	−	0.0373254i
$225$	−7.09657	+	13.2151i	−0.473105	+	0.881006i
$226$	−3.60686	+	6.24727i	−0.239925	+	0.415562i
$227$	11.5202	+	3.08682i	0.764620	+	0.204879i	0.619993	−	0.784607i	$-0.287135\pi$
$227$	11.5202	+	3.08682i	0.764620	+	0.204879i	0.144627	+	0.989486i	$0.453802\pi$
$228$	−4.30558	+	2.22979i	−0.285144	+	0.147671i
$229$	−11.5271	−	6.65520i	−0.761735	−	0.439788i	0.0681831	−	0.997673i	$-0.478280\pi$
$229$	−11.5271	−	6.65520i	−0.761735	−	0.439788i	−0.829918	+	0.557885i	$0.811613\pi$
$230$	−10.8874	+	7.20708i	−0.717895	+	0.475221i
$231$	−1.50848	+	15.8643i	−0.0992507	+	1.04379i
$232$	1.39883	+	1.39883i	0.0918380	+	0.0918380i
$233$	0.184410	−	0.0494125i	0.0120811	−	0.00323712i	−0.252773	−	0.967525i	$-0.581343\pi$
$233$	0.184410	−	0.0494125i	0.0120811	−	0.00323712i	0.264855	+	0.964288i	$0.414676\pi$
$234$	−1.36541	+	0.629686i	−0.0892597	+	0.0411639i
$235$	−5.06231	+	1.69413i	−0.330229	+	0.110513i
$236$	3.78284	+	2.18403i	0.246242	+	0.142168i
$237$	14.9564	+	0.684698i	0.971525	+	0.0444759i
$238$	−3.91570	−	7.62258i	−0.253817	−	0.494099i
$239$	7.37456			0.477020			0.238510	−	0.971140i	$-0.423341\pi$
$239$	7.37456			0.477020			0.238510	+	0.971140i	$0.423341\pi$
$240$	3.87252	−	0.0596165i	0.249970	−	0.00384823i
$241$	−7.27332	−	12.5978i	−0.468516	−	0.811493i	0.530837	−	0.847474i	$-0.321878\pi$
$241$	−7.27332	−	12.5978i	−0.468516	−	0.811493i	−0.999352	+	0.0359810i	$0.988544\pi$
$242$	1.05568	+	0.282868i	0.0678615	+	0.0181834i
$243$	−11.3810	−	10.6523i	−0.730094	−	0.683347i
$244$			7.58763i			0.485748i
$245$	13.2569	+	8.32188i	0.846955	+	0.531665i
$246$	10.1944	−	9.30190i	0.649973	−	0.593067i
$247$	−1.35527	+	0.363142i	−0.0862334	+	0.0231062i
$248$	−2.29946	+	8.58169i	−0.146016	+	0.544938i
$249$	24.4873	+	7.77778i	1.55182	+	0.492897i
$250$	10.0904	−	4.81491i	0.638174	−	0.304522i
$251$			2.79937i			0.176694i	0.996090	+	0.0883472i	$0.0281585\pi$
$251$			2.79937i			0.176694i	−0.996090	+	0.0883472i	$0.971842\pi$
$252$	2.96656	+	7.36203i	0.186875	+	0.463765i
$253$	−14.3582	+	14.3582i	−0.902691	+	0.902691i
$254$	3.99585	−	6.92102i	0.250722	−	0.434263i
$255$	−3.43288	−	12.0656i	−0.214975	−	0.755579i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.15470	−	26.7017i	−0.446298	−	1.66561i	−0.712487	−	0.701686i	$-0.752431\pi$
$257$	−7.15470	−	26.7017i	−0.446298	−	1.66561i	0.266189	−	0.963921i	$-0.414236\pi$
$258$	−14.7690	−	0.676116i	−0.919475	−	0.0420931i
$259$	−16.4350	+	14.8968i	−1.02122	+	0.925642i
$260$	1.09824	+	0.223377i	0.0681100	+	0.0138533i
$261$	−3.42456	+	4.84703i	−0.211975	+	0.300023i
$262$	−0.242869	+	0.906401i	−0.0150045	+	0.0559976i
$263$	2.52286	−	9.41543i	0.155566	−	0.580580i	−0.843490	−	0.537145i	$-0.819503\pi$
$263$	2.52286	−	9.41543i	0.155566	−	0.580580i	0.999056	−	0.0434357i	$-0.0138304\pi$
$264$	5.88315	−	1.29122i	0.362083	−	0.0794691i
$265$	13.1555	+	2.67576i	0.808134	+	0.164371i
$266$	1.56385	+	7.23954i	0.0958855	+	0.443885i
$267$	−0.570145	+	12.4541i	−0.0348923	+	0.762181i
$268$	−3.64677	−	13.6099i	−0.222762	−	0.831359i
$269$	−10.2899	−	17.8226i	−0.627384	−	1.08666i	−0.988075	−	0.153975i	$-0.950792\pi$
$269$	−10.2899	−	17.8226i	−0.627384	−	1.08666i	0.360691	−	0.932685i	$-0.382541\pi$
$270$	2.14523	+	11.4192i	0.130555	+	0.694950i
$271$	11.5399	−	19.9876i	0.700997	−	1.21416i	−0.267120	−	0.963663i	$-0.586072\pi$
$271$	11.5399	−	19.9876i	0.700997	−	1.21416i	0.968117	−	0.250499i	$-0.0805945\pi$
$272$	−2.29030	+	2.29030i	−0.138870	+	0.138870i
$273$	0.381782	+	2.26485i	0.0231065	+	0.137075i
$274$		−	18.1314i		−	1.09536i
$275$	13.8851	−	10.4655i	0.837302	−	0.631096i
$276$	−3.06163	+	9.63915i	−0.184289	+	0.580208i
$277$	1.89941	−	7.08871i	0.114125	−	0.425919i	−0.885095	−	0.465410i	$-0.845907\pi$
$277$	1.89941	−	7.08871i	0.114125	−	0.425919i	0.999220	+	0.0394907i	$0.0125735\pi$
$278$	13.9479	−	3.73734i	0.836542	−	0.224151i
$279$	−26.5418	−	2.43524i	−1.58901	−	0.145794i
$280$	1.46201	−	5.73258i	0.0873719	−	0.342587i
$281$			7.12223i			0.424877i	0.977174	+	0.212438i	$0.0681405\pi$
$281$			7.12223i			0.424877i	−0.977174	+	0.212438i	$0.931860\pi$
$282$	−2.22911	+	3.48272i	−0.132741	+	0.207393i
$283$	−12.0074	−	3.21738i	−0.713768	−	0.191254i	−0.116379	−	0.993205i	$-0.537129\pi$
$283$	−12.0074	−	3.21738i	−0.713768	−	0.191254i	−0.597389	+	0.801951i	$0.703795\pi$
$284$	−1.98172	−	3.43244i	−0.117593	−	0.203678i
$285$	0.166891	+	10.8408i	0.00988574	+	0.642151i
$286$	1.74293			0.103062
$287$	−9.63239	−	18.7511i	−0.568582	−	1.10684i
$288$	2.30627	−	1.91863i	0.135898	−	0.113056i
$289$	−5.63702	−	3.25454i	−0.331590	−	0.191443i
$290$	4.19484	−	1.40383i	0.246329	−	0.0824355i
$291$	27.1982	+	8.63884i	1.59439	+	0.506418i
$292$	−3.68750	+	0.988062i	−0.215794	+	0.0578219i
$293$	4.01118	+	4.01118i	0.234336	+	0.234336i	0.814500	−	0.580164i	$-0.197012\pi$
$293$	4.01118	+	4.01118i	0.234336	+	0.234336i	−0.580164	+	0.814500i	$0.697012\pi$
$294$	12.0401	−	1.42668i	0.702194	−	0.0832058i
$295$	8.14448	−	5.39136i	0.474190	−	0.313897i
$296$	7.26063	+	4.19193i	0.422016	+	0.243651i
$297$	6.80889	+	16.7376i	0.395092	+	0.971215i
$298$	8.79112	+	2.35557i	0.509256	+	0.136455i
$299$	−1.46330	+	2.53451i	−0.0846249	+	0.146575i
$300$	3.74400	−	7.80913i	0.216160	−	0.450860i
$301$	−6.90767	+	21.5012i	−0.398151	+	1.23931i
$302$	−14.1606	+	14.1606i	−0.814852	+	0.814852i
$303$	2.96357	−	4.63025i	0.170253	−	0.266001i
$304$	2.42435	−	1.39970i	0.139046	−	0.0802784i
$305$	15.1843	+	7.56956i	0.869449	+	0.433432i
$306$	−7.93599	−	5.60700i	−0.453670	−	0.320531i
$307$	17.5067	+	17.5067i	0.999159	+	0.999159i	1.00000		0.000841117i	$-0.000267736\pi$
$307$	17.5067	+	17.5067i	0.999159	+	0.999159i	−0.000841117		1.00000i	$0.500268\pi$
$308$	0.451143	−	9.18950i	0.0257062	−	0.523620i
$309$	−5.83169	−	6.39125i	−0.331753	−	0.363586i
$310$	14.8796	+	13.1629i	0.845104	+	0.747603i
$311$	−4.32483	+	2.49694i	−0.245238	+	0.141588i	−0.617582	−	0.786506i	$-0.711888\pi$
$311$	−4.32483	+	2.49694i	−0.245238	+	0.141588i	0.372344	+	0.928095i	$0.378554\pi$
$312$	0.770870	−	0.399220i	0.0436419	−	0.0226014i
$313$	2.94360	+	10.9857i	0.166382	+	0.620946i	0.997860	+	0.0653882i	$0.0208286\pi$
$313$	2.94360	+	10.9857i	0.166382	+	0.620946i	−0.831478	+	0.555558i	$0.812505\pi$
$314$	4.73752			0.267354
$315$	17.6923	+	1.40787i	0.996849	+	0.0793245i
$316$	−8.64414			−0.486271
$317$	6.95813	+	25.9681i	0.390808	+	1.45851i	0.828805	+	0.559537i	$0.189021\pi$
$317$	6.95813	+	25.9681i	0.390808	+	1.45851i	−0.437998	+	0.898976i	$0.644312\pi$
$318$	9.23400	−	4.78213i	0.517817	−	0.268169i
$319$	5.95768	−	3.43967i	0.333566	−	0.192585i
$320$	−2.23189	+	0.136630i	−0.124766	+	0.00763787i
$321$	16.0554	+	17.5960i	0.896126	+	0.982111i
$322$	12.9843	+	8.37120i	0.723587	+	0.466509i
$323$	−6.41147	−	6.41147i	−0.356744	−	0.356744i
$324$	6.84523	+	5.84319i	0.380290	+	0.324622i
$325$	1.54265	−	1.97494i	0.0855706	−	0.109550i
$326$	5.09599	−	2.94217i	0.282241	−	0.162952i
$327$	−1.79099	+	2.79821i	−0.0990417	+	0.154741i
$328$	−5.63400	+	5.63400i	−0.311086	+	0.311086i
$329$	4.24194	+	4.67995i	0.233866	+	0.258014i
$330$	3.28518	−	13.0614i	0.180843	−	0.719009i
$331$	13.4191	−	23.2426i	0.737580	−	1.27753i	−0.216002	−	0.976393i	$-0.569302\pi$
$331$	13.4191	−	23.2426i	0.737580	−	1.27753i	0.953582	−	0.301133i	$-0.0973649\pi$
$332$	−14.3283	−	3.83927i	−0.786369	−	0.210707i
$333$	−8.70221	+	23.5982i	−0.476878	+	1.29317i
$334$	−8.30348	−	4.79401i	−0.454346	−	0.262317i
$335$	−30.8741	−	6.27966i	−1.68683	−	0.343094i
$336$	−1.90533	−	4.16770i	−0.103944	−	0.227367i
$337$	−10.5014	−	10.5014i	−0.572050	−	0.572050i	0.360651	−	0.932701i	$-0.382555\pi$
$337$	−10.5014	−	10.5014i	−0.572050	−	0.572050i	−0.932701	+	0.360651i	$0.882555\pi$
$338$	−12.3144	+	3.29963i	−0.669814	+	0.179476i
$339$	11.9083	+	3.78237i	0.646769	+	0.205430i
$340$	2.29847	+	6.86816i	0.124652	+	0.372478i
$341$	26.7562	+	15.4477i	1.44893	+	0.836541i
$342$	5.37101	+	6.45617i	0.290431	+	0.349110i
$343$	2.71565	−	18.3201i	0.146631	−	0.989191i
$344$	8.53579			0.460219
$345$	16.2354	+	15.7431i	0.874085	+	0.847580i
$346$	−6.66858	−	11.5503i	−0.358505	−	0.620949i
$347$	15.0442	+	4.03107i	0.807613	+	0.216399i	0.638924	−	0.769270i	$-0.279380\pi$
$347$	15.0442	+	4.03107i	0.807613	+	0.216399i	0.168689	+	0.985669i	$0.446047\pi$
$348$	1.84713	−	2.88592i	0.0990163	−	0.154702i
$349$			26.9797i			1.44419i	0.691794	+	0.722095i	$0.256821\pi$
$349$			26.9797i			1.44419i	−0.691794	+	0.722095i	$0.743179\pi$
$350$	−10.0135	−	8.64470i	−0.535241	−	0.462079i
$351$	1.57228	+	2.07617i	0.0839222	+	0.110818i
$352$	−3.35899	+	0.900040i	−0.179035	+	0.0479723i
$353$	−6.06139	+	22.6214i	−0.322615	+	1.20402i	0.594072	+	0.804412i	$0.297519\pi$
$353$	−6.06139	+	22.6214i	−0.322615	+	1.20402i	−0.916687	+	0.399605i	$0.869147\pi$
$354$	2.29030	−	7.21070i	0.121728	−	0.383244i
$355$	−8.84596	+	0.541526i	−0.469495	+	0.0287412i
$356$		−	7.19793i		−	0.381490i
$357$	−11.4418	+	9.45484i	−0.605566	+	0.500403i
$358$	−16.4729	+	16.4729i	−0.870619	+	0.870619i
$359$	−9.51649	+	16.4830i	−0.502261	+	0.869941i	0.497736	+	0.867329i	$0.334165\pi$
$359$	−9.51649	+	16.4830i	−0.502261	+	0.869941i	−0.999997	+	0.00261263i	$0.999168\pi$
$360$	−1.53876	−	6.52934i	−0.0810997	−	0.344126i
$361$	−5.58167	−	9.66774i	−0.293772	−	0.508828i
$362$	0.203369	+	0.758985i	0.0106889	+	0.0398914i
$363$	0.0865694	−	1.89101i	0.00454372	−	0.0992522i
$364$	−0.279991	−	1.29617i	−0.0146755	−	0.0679376i
$365$	−1.70142	+	8.36509i	−0.0890564	+	0.437849i
$366$	12.8366	−	2.81735i	0.670981	−	0.147265i
$367$	2.31823	−	8.65175i	0.121011	−	0.451618i	−0.878655	−	0.477456i	$-0.841559\pi$
$367$	2.31823	−	8.65175i	0.121011	−	0.451618i	0.999666	+	0.0258384i	$0.00822554\pi$
$368$	1.51128	−	5.64018i	0.0787810	−	0.294015i
$369$	−19.5221	−	13.7929i	−1.01628	−	0.718029i
$370$	15.6322	−	10.3479i	0.812679	−	0.537964i
$371$	−3.35391	−	15.5264i	−0.174127	−	0.806088i
$372$	15.3722	+	0.703730i	0.797009	+	0.0364867i
$373$	2.50213	+	9.33806i	0.129555	+	0.483506i	0.999961	−	0.00882841i	$-0.00281021\pi$
$373$	2.50213	+	9.33806i	0.129555	+	0.483506i	−0.870406	+	0.492335i	$0.836144\pi$
$374$	5.63174	+	9.75446i	0.291210	+	0.504391i
$375$	−11.8924	−	15.2830i	−0.614123	−	0.789210i
$376$	1.19367	−	2.06750i	0.0615590	−	0.106623i
$377$	0.701102	−	0.701102i	0.0361086	−	0.0361086i
$378$	11.3535	−	7.75235i	0.583959	−	0.398738i
$379$		−	9.63664i		−	0.495001i	−0.968888	−	0.247500i	$-0.920391\pi$
$379$		−	9.63664i		−	0.495001i	0.968888	−	0.247500i	$-0.0796092\pi$
$380$	−0.382484	−	6.24796i	−0.0196210	−	0.320514i
$381$	−13.1925	−	4.19028i	−0.675875	−	0.214675i
$382$	2.67445	−	9.98118i	0.136837	−	0.510681i
$383$	18.9303	−	5.07236i	0.967293	−	0.259185i	0.259609	−	0.965714i	$-0.416406\pi$
$383$	18.9303	−	5.07236i	0.967293	−	0.259185i	0.707685	+	0.706529i	$0.249740\pi$
$384$	−1.27947	+	1.16745i	−0.0652928	+	0.0595764i
$385$	−17.9399	−	10.0704i	−0.914299	−	0.513237i
$386$			12.2911i			0.625602i
$387$	4.34000	+	25.2369i	0.220614	+	1.28286i
$388$	−15.9146	−	4.26430i	−0.807940	−	0.216487i
$389$	−5.28560	−	9.15493i	−0.267991	−	0.464174i	0.700352	−	0.713798i	$-0.253026\pi$
$389$	−5.28560	−	9.15493i	−0.267991	−	0.464174i	−0.968343	+	0.249624i	$0.919693\pi$
$390$	−0.0298800	−	1.94093i	−0.00151303	−	0.0982826i
$391$	−18.9128			−0.956462
$392$	−6.90643	+	1.14073i	−0.348827	+	0.0576156i
$393$	1.62361	+	0.0743282i	0.0819004	+	0.00374936i
$394$	10.7577	+	6.21096i	0.541965	+	0.312904i
$395$	−8.62357	+	17.2986i	−0.433899	+	0.870385i
$396$	−4.36893	−	9.47358i	−0.219547	−	0.476065i
$397$	−15.1363	+	4.05577i	−0.759671	+	0.203553i	−0.617804	−	0.786332i	$-0.711977\pi$
$397$	−15.1363	+	4.05577i	−0.759671	+	0.203553i	−0.141868	+	0.989886i	$0.545311\pi$
$398$	11.4492	+	11.4492i	0.573899	+	0.573899i
$399$	11.6671	−	5.33379i	0.584084	−	0.267023i
$400$	−1.95315	+	4.60274i	−0.0976577	+	0.230137i
$401$	−22.4638	−	12.9695i	−1.12179	−	0.647666i	−0.179932	−	0.983679i	$-0.557588\pi$
$401$	−22.4638	−	12.9695i	−1.12179	−	0.647666i	−0.941857	+	0.336013i	$0.890921\pi$
$402$	−21.6710	+	11.2230i	−1.08085	+	0.559753i
$403$	4.30118	+	1.15250i	0.214257	+	0.0574100i
$404$	−1.58698	+	2.74872i	−0.0789551	+	0.136754i
$405$	18.5223	−	7.86931i	0.920378	−	0.391029i
$406$	−3.51504	−	3.87799i	−0.174449	−	0.192461i
$407$	20.6155	−	20.6155i	1.02187	−	1.02187i
$408$	4.72509	+	3.02428i	0.233927	+	0.149724i
$409$	−5.22497	+	3.01664i	−0.258358	+	0.149163i	−0.623585	−	0.781755i	$-0.714325\pi$
$409$	−5.22497	+	3.01664i	−0.258358	+	0.149163i	0.365227	+	0.930918i	$0.380991\pi$
$410$	5.65411	+	16.8953i	0.279236	+	0.834398i
$411$	−30.6744	+	6.73234i	−1.51306	+	0.332082i
$412$	3.53216	+	3.53216i	0.174017	+	0.174017i
$413$	−9.71308	−	6.26219i	−0.477950	−	0.308142i
$414$	17.4442	+	1.60052i	0.857333	+	0.0786614i
$415$	−21.9773	+	24.8436i	−1.07882	+	1.21952i
$416$	−0.434056	+	0.250602i	−0.0212813	+	0.0122868i
$417$	−11.5018	−	22.2092i	−0.563244	−	1.08759i
$418$	−2.51957	−	9.40318i	−0.123236	−	0.459925i
$419$	3.42723			0.167431			0.0837157	−	0.996490i	$-0.473321\pi$
$419$	3.42723			0.167431			0.0837157	+	0.996490i	$0.473321\pi$
$420$	−10.2411	−	0.344851i	−0.499717	−	0.0168270i
$421$	−12.2231			−0.595718			−0.297859	−	0.954610i	$-0.596272\pi$
$421$	−12.2231			−0.595718			−0.297859	+	0.954610i	$0.596272\pi$
$422$	−2.81566	−	10.5082i	−0.137064	−	0.511531i
$423$	6.71970	+	2.47800i	0.326723	+	0.120484i
$424$	−5.19941	+	3.00188i	−0.252506	+	0.145784i
$425$	16.0375	+	2.25214i	0.777932	+	0.109245i
$426$	−5.07111	+	4.62713i	−0.245696	+	0.224185i
$427$	0.984361	−	20.0508i	0.0476365	−	0.970327i
$428$	−9.72449	−	9.72449i	−0.470051	−	0.470051i
$429$	−0.647165	−	2.94866i	−0.0312454	−	0.142363i
$430$	8.51547	−	17.0817i	0.410653	−	0.823754i
$431$	−5.13623	+	2.96540i	−0.247403	+	0.142838i	−0.618575	−	0.785726i	$-0.712290\pi$
$431$	−5.13623	+	2.96540i	−0.247403	+	0.142838i	0.371171	+	0.928564i	$0.378956\pi$
$432$	−4.10224	−	3.18930i	−0.197369	−	0.153445i
$433$	6.21844	−	6.21844i	0.298839	−	0.298839i	−0.541720	−	0.840559i	$-0.682227\pi$
$433$	6.21844	−	6.21844i	0.298839	−	0.298839i	0.840559	+	0.541720i	$0.182227\pi$
$434$	7.18979	−	22.3794i	0.345121	−	1.07424i
$435$	−3.93255	−	6.57550i	−0.188551	−	0.315271i
$436$	0.959063	−	1.66115i	0.0459308	−	0.0795544i
$437$	15.7891	+	4.23069i	0.755297	+	0.202381i
$438$	3.04078	+	5.87157i	0.145294	+	0.280554i
$439$	2.39660	+	1.38368i	0.114383	+	0.0660393i	0.556100	−	0.831115i	$-0.312297\pi$
$439$	2.39660	+	1.38368i	0.114383	+	0.0660393i	−0.441717	+	0.897155i	$0.645630\pi$
$440$	−1.54985	+	7.61988i	−0.0738862	+	0.363263i
$441$	−6.88423	−	19.8395i	−0.327821	−	0.944740i
$442$	1.14791	+	1.14791i	0.0546004	+	0.0546004i
$443$	−23.3822	+	6.26524i	−1.11092	+	0.297671i	−0.767204	−	0.641403i	$-0.778353\pi$
$443$	−23.3822	+	6.26524i	−1.11092	+	0.297671i	−0.343717	+	0.939073i	$0.611686\pi$
$444$	4.39590	−	13.8399i	0.208620	−	0.656813i
$445$	−14.4044	−	7.18080i	−0.682835	−	0.340403i
$446$	−5.91324	−	3.41401i	−0.280000	−	0.161658i
$447$	0.720904	−	15.7473i	0.0340976	−	0.744822i
$448$	1.20893	+	2.35340i	0.0571167	+	0.111188i
$449$	−6.14519			−0.290010			−0.145005	−	0.989431i	$-0.546320\pi$
$449$	−6.14519			−0.290010			−0.145005	+	0.989431i	$0.546320\pi$
$450$	−14.6015	−	3.43445i	−0.688323	−	0.161901i
$451$	13.8537	+	23.9954i	0.652348	+	1.12990i
$452$	−6.96792	−	1.86705i	−0.327743	−	0.0878186i
$453$	29.2146	+	18.6987i	1.37262	+	0.878543i
$454$			11.9266i			0.559741i
$455$	−2.87320	−	0.732767i	−0.134698	−	0.0343526i
$456$	−3.26817	−	3.58176i	−0.153046	−	0.167731i
$457$	−10.5798	+	2.83485i	−0.494903	+	0.132609i	−0.497633	−	0.867387i	$-0.665798\pi$
$457$	−10.5798	+	2.83485i	−0.494903	+	0.132609i	0.00273047	+	0.999996i	$0.499131\pi$
$458$	3.44499	−	12.8569i	0.160974	−	0.600762i
$459$	−6.53913	+	15.5079i	−0.305220	+	0.723847i
$460$	−9.77938	−	8.65111i	−0.455966	−	0.403360i
$461$			0.00387108i			0.000180294i	1.00000		9.01471e-5i	$2.86947e-5\pi$
$461$			0.00387108i			0.000180294i	−1.00000		9.01471e-5i	$0.999971\pi$
$462$	−15.7142	+	2.64890i	−0.731089	+	0.123238i
$463$	27.8340	−	27.8340i	1.29356	−	1.29356i	0.360986	−	0.932571i	$-0.382440\pi$
$463$	27.8340	−	27.8340i	1.29356	−	1.29356i	0.932571	−	0.360986i	$-0.117560\pi$
$464$	−0.989125	+	1.71321i	−0.0459190	+	0.0795340i
$465$	16.7439	−	30.0605i	0.776478	−	1.39402i
$466$	0.0954575	+	0.165337i	0.00442199	+	0.00765910i
$467$	−2.68649	−	10.0261i	−0.124316	−	0.463953i	0.875499	−	0.483221i	$-0.160533\pi$
$467$	−2.68649	−	10.0261i	−0.124316	−	0.463953i	−0.999814	+	0.0192680i	$0.993866\pi$
$468$	−0.961625	−	1.15591i	−0.0444511	−	0.0534320i
$469$	7.87119	+	36.4383i	0.363458	+	1.68256i
$470$	−2.94663	−	4.45135i	−0.135918	−	0.205325i
$471$	−1.75908	−	8.01486i	−0.0810542	−	0.369305i
$472$	−1.13053	+	4.21921i	−0.0520371	+	0.194205i
$473$	7.68255	−	28.6717i	0.353244	−	1.31833i
$474$	3.20964	+	14.6240i	0.147424	+	0.671703i
$475$	−12.8849	−	5.46766i	−0.591201	−	0.250874i
$476$	6.34939	−	5.75514i	0.291024	−	0.263787i
$477$	−11.5190	−	13.8463i	−0.527418	−	0.633978i
$478$	1.90868	+	7.12327i	0.0873008	+	0.325811i
$479$	−2.84062	−	4.92009i	−0.129791	−	0.224805i	0.793805	−	0.608173i	$-0.208097\pi$
$479$	−2.84062	−	4.92009i	−0.129791	−	0.224805i	−0.923596	+	0.383368i	$0.874764\pi$
$480$	1.05987	+	3.72514i	0.0483761	+	0.170029i
$481$	2.10101	−	3.63906i	0.0957980	−	0.165927i
$482$	10.2860	−	10.2860i	0.468516	−	0.468516i
$483$	9.34108	−	25.0749i	0.425034	−	1.14095i
$484$			1.09292i			0.0496781i
$485$	−24.4104	+	27.5939i	−1.10842	+	1.25298i
$486$	7.34372	−	13.7503i	0.333118	−	0.623725i
$487$	1.75220	−	6.53929i	0.0793997	−	0.296324i	−0.914795	−	0.403918i	$-0.867648\pi$
$487$	1.75220	−	6.53929i	0.0793997	−	0.296324i	0.994195	+	0.107594i	$0.0343148\pi$
$488$	−7.32908	+	1.96382i	−0.331772	+	0.0888980i
$489$	−6.86970	−	7.52886i	−0.310659	−	0.340467i
$490$	−4.60717	+	14.9591i	−0.208131	+	0.675782i
$491$		−	11.2931i		−	0.509652i	−0.966987	−	0.254826i	$-0.917982\pi$
$491$		−	11.2931i		−	0.509652i	0.966987	−	0.254826i	$-0.0820182\pi$
$492$	11.6235	+	7.43955i	0.524026	+	0.335401i
$493$	6.18916	+	1.65838i	0.278746	+	0.0746897i
$494$	−0.701537	−	1.21510i	−0.0315636	−	0.0546698i
$495$	−23.3169	−	0.707981i	−1.04802	−	0.0318214i
$496$	−8.88441			−0.398922
$497$	4.79153	+	9.32755i	0.214930	+	0.418398i
$498$	−1.17498	+	25.6660i	−0.0526519	+	1.15012i
$499$	−2.82144	−	1.62896i	−0.126305	−	0.0729221i	0.435516	−	0.900181i	$-0.356566\pi$
$499$	−2.82144	−	1.62896i	−0.126305	−	0.0729221i	−0.561821	+	0.827259i	$0.689899\pi$
$500$	7.26244	+	8.50041i	0.324786	+	0.380150i
$501$	−5.02728	+	15.8277i	−0.224602	+	0.707131i
$502$	−2.70398	+	0.724529i	−0.120685	+	0.0323373i
$503$	29.1072	+	29.1072i	1.29783	+	1.29783i	0.929825	+	0.368003i	$0.119958\pi$
$503$	29.1072	+	29.1072i	1.29783	+	1.29783i	0.368003	+	0.929825i	$0.380042\pi$
$504$	−6.34338	+	4.77091i	−0.282556	+	0.212513i
$505$	3.91752	+	5.91802i	0.174327	+	0.263349i
$506$	−17.5851	−	10.1528i	−0.781754	−	0.451346i
$507$	10.1547	+	19.6081i	0.450986	+	0.870826i
$508$	7.71939	+	2.06840i	0.342493	+	0.0917706i
$509$	15.2527	−	26.4185i	0.676064	−	1.17098i	−0.300092	−	0.953910i	$-0.597017\pi$
$509$	15.2527	−	26.4185i	0.676064	−	1.17098i	0.976157	−	0.217068i	$-0.0696493\pi$
$510$	10.7660	−	6.43872i	0.476727	−	0.285111i
$511$	9.87265	−	2.13263i	0.436740	−	0.0943422i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	8.92814	−	11.4838i	0.394187	−	0.507023i
$514$	23.9401	−	13.8218i	1.05595	−	0.609654i
$515$	10.5923	−	3.54476i	0.466751	−	0.156201i
$516$	−3.16941	−	14.4407i	−0.139526	−	0.635717i
$517$	−5.87038	−	5.87038i	−0.258179	−	0.258179i
$518$	−18.6429	−	12.0194i	−0.819122	−	0.528102i
$519$	−17.0645	+	15.5705i	−0.749051	+	0.683470i
$520$	0.0684798	+	1.11863i	0.00300304	+	0.0490553i
$521$	−37.2040	+	21.4798i	−1.62994	+	0.941045i	−0.645829	+	0.763482i	$0.723488\pi$
$521$	−37.2040	+	21.4798i	−1.62994	+	0.941045i	−0.984109	+	0.177563i	$0.943179\pi$
$522$	−5.56821	−	2.05337i	−0.243714	−	0.0898735i
$523$	9.14379	+	34.1251i	0.399830	+	1.49219i	0.813396	+	0.581711i	$0.197617\pi$
$523$	9.14379	+	34.1251i	0.399830	+	1.49219i	−0.413566	+	0.910474i	$0.635717\pi$
$524$	−0.938375			−0.0409931
$525$	−10.9069	+	20.1504i	−0.476015	+	0.879437i
$526$	9.74757			0.425014
$527$	7.44787	+	27.7958i	0.324434	+	1.21080i
$528$	2.76989	+	5.34850i	0.120544	+	0.232764i
$529$	9.60905	−	5.54779i	0.417785	−	0.241208i
$530$	0.820297	+	13.3997i	0.0356314	+	0.582048i
$531$	−13.0493	−	1.19729i	−0.566293	−	0.0519581i
$532$	−6.58811	+	3.38429i	−0.285631	+	0.146728i
$533$	2.82379	+	2.82379i	0.122312	+	0.122312i
$534$	−12.1773	+	2.67265i	−0.526965	+	0.115657i
$535$	−29.1619	+	9.75919i	−1.26078	+	0.421927i
$536$	12.2023	−	7.04502i	0.527060	−	0.304298i
$537$	33.9851	+	21.7520i	1.46656	+	0.938669i
$538$	14.5521	−	14.5521i	0.627384	−	0.627384i
$539$	−2.38435	+	24.2254i	−0.102701	+	1.04346i
$540$	−10.4749	+	5.02764i	−0.450766	+	0.216355i
$541$	17.0132	−	29.4677i	0.731454	−	1.26692i	−0.224807	−	0.974403i	$-0.572175\pi$
$541$	17.0132	−	29.4677i	0.731454	−	1.26692i	0.956262	−	0.292513i	$-0.0944914\pi$
$542$	22.2933	+	5.97347i	0.957579	+	0.256583i
$543$	1.20853	−	0.625875i	0.0518628	−	0.0268588i
$544$	−2.80503	−	1.61948i	−0.120265	−	0.0694348i
$545$	−2.36749	−	3.57646i	−0.101412	−	0.153199i
$546$	−2.08887	+	0.954960i	−0.0893954	+	0.0408685i
$547$	16.7941	+	16.7941i	0.718062	+	0.718062i	0.968208	−	0.250146i	$-0.0804787\pi$
$547$	16.7941	+	16.7941i	0.718062	+	0.718062i	−0.250146	+	0.968208i	$0.580479\pi$
$548$	17.5136	−	4.69276i	0.748144	−	0.200465i
$549$	−9.53268	−	20.6707i	−0.406845	−	0.882203i
$550$	13.7027	+	10.7033i	0.584283	+	0.456389i
$551$	−4.79598	−	2.76896i	−0.204316	−	0.117962i
$552$	−10.1031	−	0.462515i	−0.430017	−	0.0196860i
$553$	22.8427	+	1.12143i	0.971372	+	0.0476879i
$554$	7.33877			0.311795
$555$	−23.3108	−	22.6040i	−0.989490	−	0.959486i
$556$	7.21999	+	12.5054i	0.306196	+	0.530347i
$557$	−16.9638	−	4.54543i	−0.718778	−	0.192596i	−0.119152	−	0.992876i	$-0.538017\pi$
$557$	−16.9638	−	4.54543i	−0.718778	−	0.192596i	−0.599626	+	0.800280i	$0.704684\pi$
$558$	−4.51725	−	26.2677i	−0.191230	−	1.11200i
$559$		−	4.27818i		−	0.180948i
$560$	5.91565	−	0.0715070i	0.249982	−	0.00302172i
$561$	14.4113	−	13.1496i	0.608446	−	0.555176i
$562$	−6.87955	+	1.84337i	−0.290196	+	0.0777578i
$563$	4.96217	−	18.5191i	0.209130	−	0.780486i	−0.779020	−	0.626999i	$-0.784283\pi$
$563$	4.96217	−	18.5191i	0.209130	−	0.780486i	0.988151	−	0.153487i	$-0.0490502\pi$
$564$	−3.94099	−	1.25176i	−0.165946	−	0.0527084i
$565$	−10.6877	+	12.0815i	−0.449633	+	0.508273i
$566$		−	12.4310i		−	0.522515i
$567$	−17.3309	−	16.3291i	−0.727831	−	0.685757i
$568$	2.80257	−	2.80257i	0.117593	−	0.117593i
$569$	16.9400	−	29.3410i	0.710164	−	1.23004i	−0.254632	−	0.967038i	$-0.581954\pi$
$569$	16.9400	−	29.3410i	0.710164	−	1.23004i	0.964795	−	0.263002i	$-0.0847124\pi$
$570$	−10.4282	+	2.96700i	−0.436788	+	0.124274i
$571$	1.99106	+	3.44862i	0.0833234	+	0.144320i	0.904676	−	0.426101i	$-0.140113\pi$
$571$	1.99106	+	3.44862i	0.0833234	+	0.144320i	−0.821352	+	0.570421i	$0.806780\pi$
$572$	0.451104	+	1.68354i	0.0188616	+	0.0703925i
$573$	−17.8790	−	0.818493i	−0.746907	−	0.0341930i
$574$	15.6191	−	14.1573i	0.651930	−	0.590915i
$575$	−27.0686	+	10.9399i	−1.12884	+	0.456224i
$576$	2.45016	+	1.73111i	0.102090	+	0.0721294i
$577$	−1.26390	+	4.71693i	−0.0526168	+	0.196369i	−0.987231	−	0.159294i	$-0.949078\pi$
$577$	−1.26390	+	4.71693i	−0.0526168	+	0.196369i	0.934614	+	0.355663i	$0.115745\pi$
$578$	1.68467	−	6.28728i	0.0700731	−	0.261516i
$579$	20.7939	−	4.56380i	0.864166	−	0.189665i
$580$	2.44170	+	3.68856i	0.101386	+	0.153159i
$581$	37.3655	+	12.0044i	1.55018	+	0.498025i
$582$	−1.30505	+	28.5074i	−0.0540962	+	1.18167i
$583$	5.40363	+	20.1666i	0.223795	+	0.835216i
$584$	−1.90879	−	3.30612i	−0.0789862	−	0.136808i
$585$	−3.27253	+	0.771233i	−0.135303	+	0.0318865i
$586$	−2.83634	+	4.91268i	−0.117168	+	0.202941i
$587$	−11.5042	+	11.5042i	−0.474828	+	0.474828i	−0.903473	−	0.428645i	$-0.858991\pi$
$587$	−11.5042	+	11.5042i	−0.474828	+	0.474828i	0.428645	+	0.903473i	$0.358991\pi$
$588$	4.49428	+	11.2606i	0.185341	+	0.464380i
$589$		−	24.8711i		−	1.02479i
$590$	7.31560	+	6.47158i	0.301178	+	0.266431i
$591$	6.51318	−	20.5059i	0.267916	−	0.843499i
$592$	−2.16990	+	8.09819i	−0.0891824	+	0.332833i
$593$	−15.7426	+	4.21822i	−0.646471	+	0.173221i	−0.567133	−	0.823626i	$-0.691947\pi$
$593$	−15.7426	+	4.21822i	−0.646471	+	0.173221i	−0.0793383	+	0.996848i	$0.525281\pi$
$594$	−14.4050	+	10.9089i	−0.591045	+	0.447597i
$595$	−5.18285	−	18.4478i	−0.212476	−	0.756285i
$596$			9.10124i			0.372801i
$597$	15.1184	−	23.6208i	0.618757	−	0.966736i
$598$	−2.82688	−	0.757461i	−0.115600	−	0.0309749i
$599$	−8.39829	−	14.5463i	−0.343145	−	0.594344i	0.641870	−	0.766813i	$-0.278159\pi$
$599$	−8.39829	−	14.5463i	−0.343145	−	0.594344i	−0.985015	+	0.172469i	$0.944825\pi$
$600$	8.51206	+	1.59528i	0.347503	+	0.0651269i
$601$	10.7142			0.437041			0.218520	−	0.975832i	$-0.429877\pi$
$601$	10.7142			0.437041			0.218520	+	0.975832i	$0.429877\pi$
$602$	−22.5564	−	1.10737i	−0.919331	−	0.0451330i
$603$	27.0335	+	32.4954i	1.10089	+	1.32331i
$604$	−17.3431	−	10.0131i	−0.705682	−	0.407426i
$605$	2.18713	+	1.09032i	0.0889196	+	0.0443276i
$606$	5.23950	+	1.66420i	0.212840	+	0.0676034i
$607$	26.4205	−	7.07936i	1.07238	−	0.287342i	0.320907	−	0.947111i	$-0.396012\pi$
$607$	26.4205	−	7.07936i	1.07238	−	0.287342i	0.751469	+	0.659768i	$0.229346\pi$
$608$	1.97948	+	1.97948i	0.0802784	+	0.0802784i
$609$	−5.25555	+	7.38662i	−0.212966	+	0.299321i
$610$	−3.38166	+	16.6260i	−0.136919	+	0.673168i
$611$	−1.03624	−	0.598274i	−0.0419219	−	0.0242036i
$612$	3.36196	−	9.11677i	0.135899	−	0.368524i
$613$	4.51412	+	1.20955i	0.182323	+	0.0488534i	0.348826	−	0.937188i	$-0.386581\pi$
$613$	4.51412	+	1.20955i	0.182323	+	0.0488534i	−0.166502	+	0.986041i	$0.553247\pi$
$614$	−12.3791	+	21.4412i	−0.499579	+	0.865297i
$615$	26.4837	−	15.8389i	1.06793	−	0.638685i
$616$	8.99314	−	1.94265i	0.362344	−	0.0782715i
$617$	5.85206	−	5.85206i	0.235595	−	0.235595i	−0.579428	−	0.815023i	$-0.696724\pi$
$617$	5.85206	−	5.85206i	0.235595	−	0.235595i	0.815023	+	0.579428i	$0.196724\pi$
$618$	4.66412	−	7.28716i	0.187619	−	0.293133i
$619$	0.702396	−	0.405529i	0.0282317	−	0.0162996i	−0.485818	−	0.874060i	$-0.661478\pi$
$619$	0.702396	−	0.405529i	0.0282317	−	0.0162996i	0.514049	+	0.857761i	$0.328145\pi$
$620$	−8.86326	+	17.7794i	−0.355957	+	0.714037i
$621$	−3.76942	−	30.1060i	−0.151262	−	1.20811i
$622$	−3.53121	−	3.53121i	−0.141588	−	0.141588i
$623$	−0.933805	+	19.0210i	−0.0374121	+	0.762062i
$624$	0.585133	+	0.641278i	0.0234241	+	0.0256717i
$625$	24.2561	−	6.05334i	0.970243	−	0.242134i
$626$	−9.84947	+	5.68659i	−0.393664	+	0.227282i
$627$	−14.9726	+	7.75405i	−0.597948	+	0.309667i
$628$	1.22616	+	4.57610i	0.0489292	+	0.182606i
$629$	27.1551			1.08274
$630$	3.21921	+	17.4538i	0.128256	+	0.695378i
$631$	26.9516			1.07293			0.536463	−	0.843924i	$-0.319760\pi$
$631$	26.9516			1.07293			0.536463	+	0.843924i	$0.319760\pi$
$632$	−2.23727	−	8.34960i	−0.0889938	−	0.332129i
$633$	−16.7321	+	8.66527i	−0.665041	+	0.344413i
$634$	−23.2824	+	13.4421i	−0.924661	+	0.533853i
$635$	11.8403	−	13.3845i	0.469867	−	0.531147i
$636$	7.00912	+	7.68165i	0.277930	+	0.304597i
$637$	0.571739	+	3.46153i	0.0226531	+	0.137151i
$638$	4.86443	+	4.86443i	0.192585	+	0.192585i
$639$	9.71105	+	6.86113i	0.384163	+	0.271422i
$640$	−0.709630	−	2.12048i	−0.0280506	−	0.0838192i
$641$	−36.5634	+	21.1099i	−1.44417	+	0.833791i	−0.998124	−	0.0612207i	$-0.980501\pi$
$641$	−36.5634	+	21.1099i	−1.44417	+	0.833791i	−0.446043	+	0.895011i	$0.647167\pi$
$642$	−12.8409	+	20.0625i	−0.506792	+	0.791804i
$643$	0.470316	−	0.470316i	0.0185475	−	0.0185475i	−0.697772	−	0.716320i	$-0.745825\pi$
$643$	0.470316	−	0.470316i	0.0185475	−	0.0185475i	0.716320	+	0.697772i	$0.245825\pi$
$644$	−4.72538	+	14.7085i	−0.186206	+	0.579596i
$645$	−32.0605	−	8.06375i	−1.26238	−	0.317510i
$646$	4.53359	−	7.85241i	0.178372	−	0.308949i
$647$	−23.0768	−	6.18342i	−0.907244	−	0.243095i	−0.225119	−	0.974331i	$-0.572277\pi$
$647$	−23.0768	−	6.18342i	−0.907244	−	0.243095i	−0.682125	+	0.731236i	$0.738944\pi$
$648$	−3.87241	+	8.12431i	−0.152123	+	0.319153i
$649$	13.1548	+	7.59492i	0.516371	+	0.298127i
$650$	2.30691	+	0.978929i	0.0904846	+	0.0383968i
$651$	−40.5307	−	3.85392i	−1.58852	−	0.151047i
$652$	4.16086	+	4.16086i	0.162952	+	0.162952i
$653$	−5.86586	+	1.57175i	−0.229549	+	0.0615075i	−0.371760	−	0.928329i	$-0.621246\pi$
$653$	−5.86586	+	1.57175i	−0.229549	+	0.0615075i	0.142211	+	0.989836i	$0.454579\pi$
$654$	−3.16641	−	1.00573i	−0.123816	−	0.0393271i
$655$	−0.936141	+	1.87787i	−0.0365781	+	0.0733743i
$656$	−6.90021	−	3.98384i	−0.269408	−	0.155543i
$657$	8.80435	−	7.32451i	0.343491	−	0.285756i
$658$	−3.42259	+	5.30866i	−0.133426	+	0.206953i
$659$	6.09039			0.237248			0.118624	−	0.992939i	$-0.462152\pi$
$659$	6.09039			0.237248			0.118624	+	0.992939i	$0.462152\pi$
$660$	13.4667	−	0.207316i	0.524189	−	0.00806975i
$661$	10.6307	+	18.4129i	0.413485	+	0.716177i	0.995268	−	0.0971670i	$-0.0309781\pi$
$661$	10.6307	+	18.4129i	0.413485	+	0.716177i	−0.581783	+	0.813344i	$0.697645\pi$
$662$	25.9237	+	6.94623i	1.00755	+	0.269973i
$663$	1.51578	−	2.36824i	0.0588681	−	0.0919747i
$664$		−	14.8338i		−	0.575662i
$665$	0.200177	+	16.5603i	0.00776253	+	0.642180i
$666$	−25.0464	−	2.29804i	−0.970527	−	0.0890471i
$667$	−11.1577	+	2.98969i	−0.432027	+	0.115761i
$668$	2.48156	−	9.26132i	0.0960146	−	0.358331i
$669$	−3.58013	+	11.2716i	−0.138416	+	0.435784i
$670$	−1.92513	−	31.4474i	−0.0743742	−	1.21492i
$671$			26.3859i			1.01862i
$672$	3.53255	−	2.91909i	0.136271	−	0.112606i
$673$	2.29463	−	2.29463i	0.0884515	−	0.0884515i	−0.661497	−	0.749948i	$-0.730078\pi$
$673$	2.29463	−	2.29463i	0.0884515	−	0.0884515i	0.749948	+	0.661497i	$0.230078\pi$
$674$	7.42564	−	12.8616i	0.286025	−	0.495410i
$675$	−0.388672	+	25.9779i	−0.0149600	+	0.999888i
$676$	−6.37440	−	11.0408i	−0.245169	−	0.424645i
$677$	8.05463	+	30.0603i	0.309564	+	1.15531i	0.928944	+	0.370219i	$0.120717\pi$
$677$	8.05463	+	30.0603i	0.309564	+	1.15531i	−0.619380	+	0.785091i	$0.712616\pi$
$678$	−0.571395	+	12.4815i	−0.0219443	+	0.479348i
$679$	41.5021	+	13.3333i	1.59271	+	0.511686i
$680$	−6.03925	+	3.99776i	−0.231595	+	0.153307i
$681$	20.1771	−	4.42843i	0.773190	−	0.169698i
$682$	−7.99633	+	29.8427i	−0.306195	+	1.14274i
$683$	6.15496	−	22.9706i	0.235513	−	0.878947i	−0.742404	−	0.669953i	$-0.766314\pi$
$683$	6.15496	−	22.9706i	0.235513	−	0.878947i	0.977917	−	0.208994i	$-0.0670190\pi$
$684$	−4.84606	+	6.85898i	−0.185294	+	0.262260i
$685$	8.08082	−	39.7296i	0.308752	−	1.51799i
$686$	18.3987	−	2.11847i	0.702466	−	0.0808837i
$687$	−23.0302	−	1.05431i	−0.878656	−	0.0402244i
$688$	2.20923	+	8.24494i	0.0842259	+	0.314336i
$689$	1.50456	+	2.60597i	0.0573190	+	0.0992795i
$690$	−11.0046	+	19.7568i	−0.418939	+	0.752129i
$691$	−4.20725	+	7.28718i	−0.160051	+	0.277217i	−0.934887	−	0.354946i	$-0.884499\pi$
$691$	−4.20725	+	7.28718i	−0.160051	+	0.277217i	0.774835	+	0.632163i	$0.217833\pi$
$692$	9.43080	−	9.43080i	0.358505	−	0.358505i
$693$	10.3162	+	25.6014i	0.391879	+	0.972516i
$694$			15.5749i			0.591213i
$695$	32.2284	−	1.97294i	1.22249	−	0.0748379i
$696$	3.26566	+	1.03725i	0.123784	+	0.0393170i
$697$	−6.67936	+	24.9277i	−0.252999	+	0.944204i
$698$	−26.0604	+	6.98286i	−0.986400	+	0.264305i
$699$	0.244271	−	0.222885i	0.00923917	−	0.00843027i
$700$	5.75847	−	11.9097i	0.217650	−	0.450143i
$701$			15.9126i			0.601012i	0.953780	+	0.300506i	$0.0971556\pi$
$701$			15.9126i			0.601012i	−0.953780	+	0.300506i	$0.902844\pi$
$702$	−1.59849	+	2.05606i	−0.0603312	+	0.0776010i
$703$	−22.6701	−	6.07443i	−0.855019	−	0.229102i
$704$	−1.73874	−	3.01159i	−0.0655314	−	0.113504i
$705$	−6.43660	+	6.63788i	−0.242417	+	0.249997i
$706$	−23.4194			−0.881401
$707$	4.55029	−	7.05781i	0.171131	−	0.265436i
$708$	7.55777	+	0.345991i	0.284038	+	0.0130031i
$709$	−15.6443	−	9.03223i	−0.587533	−	0.339213i	0.176588	−	0.984285i	$-0.443494\pi$
$709$	−15.6443	−	9.03223i	−0.587533	−	0.339213i	−0.764122	+	0.645072i	$0.776827\pi$
$710$	−2.81258	−	8.40438i	−0.105554	−	0.315411i
$711$	23.5489	−	10.8600i	0.883153	−	0.407283i
$712$	6.95267	−	1.86296i	0.260562	−	0.0698175i
$713$	−36.6828	−	36.6828i	−1.37378	−	1.37378i
$714$	−12.0940	−	8.60487i	−0.452608	−	0.322029i
$715$	3.81912	+	0.776791i	0.142827	+	0.0290503i
$716$	−20.1751	−	11.6481i	−0.753978	−	0.435309i
$717$	11.3423	−	5.87400i	0.423587	−	0.219368i
$718$	−18.3844	−	4.92610i	−0.686101	−	0.183840i
$719$	5.34310	−	9.25452i	0.199264	−	0.345135i	−0.749026	−	0.662541i	$-0.769478\pi$
$719$	5.34310	−	9.25452i	0.199264	−	0.345135i	0.948290	+	0.317405i	$0.102812\pi$
$720$	5.90859	−	3.17624i	0.220200	−	0.118372i
$721$	−8.87573	−	9.79220i	−0.330550	−	0.364681i
$722$	7.89367	−	7.89367i	0.293772	−	0.293772i
$723$	−21.2210	−	13.5824i	−0.789218	−	0.505137i
$724$	−0.680488	+	0.392880i	−0.0252901	+	0.0146013i
$725$	9.81739	−	1.20651i	0.364609	−	0.0448087i
$726$	1.84898	−	0.405809i	0.0686221	−	0.0150610i
$727$	−24.1736	−	24.1736i	−0.896550	−	0.896550i	0.0985796	−	0.995129i	$-0.468570\pi$
$727$	−24.1736	−	24.1736i	−0.896550	−	0.896550i	−0.995129	+	0.0985796i	$0.968570\pi$
$728$	1.17953	−	0.605923i	0.0437164	−	0.0224570i
$729$	−25.9893	−	7.31839i	−0.962565	−	0.271052i
$730$	−8.52041	+	0.521597i	−0.315355	+	0.0193052i
$731$	23.9432	−	13.8236i	0.885570	−	0.511284i
$732$	6.04371	+	11.6700i	0.223382	+	0.431337i
$733$	−2.23406	−	8.33762i	−0.0825168	−	0.307957i	0.912316	−	0.409488i	$-0.134293\pi$
$733$	−2.23406	−	8.33762i	−0.0825168	−	0.307957i	−0.994832	+	0.101531i	$0.967626\pi$
$734$	8.95696			0.330607
$735$	27.0182	+	2.23990i	0.996581	+	0.0826200i
$736$	5.83914			0.215234
$737$	−12.6816	−	47.3283i	−0.467132	−	1.74336i
$738$	8.27023	−	22.4267i	0.304431	−	0.825539i
$739$	8.19770	−	4.73295i	0.301557	−	0.174104i	−0.341585	−	0.939851i	$-0.610964\pi$
$739$	8.19770	−	4.73295i	0.301557	−	0.174104i	0.643142	+	0.765747i	$0.277630\pi$
$740$	14.0413	+	12.4213i	0.516167	+	0.456616i
$741$	−1.79519	+	1.63802i	−0.0659481	+	0.0601743i
$742$	14.1292	−	7.25815i	0.518701	−	0.266455i
$743$	−14.3909	−	14.3909i	−0.527951	−	0.527951i	0.392010	−	0.919961i	$-0.371780\pi$
$743$	−14.3909	−	14.3909i	−0.527951	−	0.527951i	−0.919961	+	0.392010i	$0.871780\pi$
$744$	3.29886	+	15.0305i	0.120942	+	0.551045i
$745$	18.2133	+	9.07957i	0.667283	+	0.332650i
$746$	−8.37228	+	4.83374i	−0.306531	+	0.176976i
$747$	43.8576	−	7.54219i	1.60466	−	0.275954i
$748$	−7.96448	+	7.96448i	−0.291210	+	0.291210i
$749$	24.4360	+	26.9592i	0.892874	+	0.985068i
$750$	11.6842	−	15.4427i	0.426648	−	0.563889i
$751$	−6.73442	+	11.6644i	−0.245742	+	0.425638i	−0.962340	−	0.271848i	$-0.912365\pi$
$751$	−6.73442	+	11.6644i	−0.245742	+	0.425638i	0.716598	+	0.697487i	$0.245698\pi$
$752$	2.30600	+	0.617891i	0.0840912	+	0.0225322i
$753$	2.22976	+	4.30552i	0.0812568	+	0.156902i
$754$	0.858671	+	0.495754i	0.0312710	+	0.0180543i
$755$	−37.3399	+	24.7177i	−1.35894	+	0.899568i
$756$	10.4267	+	8.96014i	0.379215	+	0.325877i
$757$	18.0263	+	18.0263i	0.655177	+	0.655177i	0.954235	−	0.299058i	$-0.0966724\pi$
$757$	18.0263	+	18.0263i	0.655177	+	0.655177i	−0.299058	+	0.954235i	$0.596672\pi$
$758$	9.30828	−	2.49415i	0.338092	−	0.0905914i
$759$	−10.6468	+	33.5200i	−0.386454	+	1.21670i
$760$	5.93607	−	1.98654i	0.215324	−	0.0720594i
$761$	10.1461	+	5.85784i	0.367795	+	0.212347i	0.672495	−	0.740102i	$-0.265223\pi$
$761$	10.1461	+	5.85784i	0.367795	+	0.212347i	−0.304700	+	0.952448i	$0.598556\pi$
$762$	0.633018	−	13.8275i	0.0229318	−	0.500919i
$763$	−2.74989	+	4.26527i	−0.0995528	+	0.154413i
$764$	10.3333			0.373845
$765$	−14.8904	−	15.8230i	−0.538364	−	0.572081i
$766$	9.79904	+	16.9724i	0.354054	+	0.613239i
$767$	2.11469	+	0.566629i	0.0763570	+	0.0204598i
$768$	−1.45883	−	0.933717i	−0.0526408	−	0.0336926i
$769$		−	22.2703i		−	0.803088i	−0.915840	−	0.401544i	$-0.868474\pi$
$769$		−	22.2703i		−	0.803088i	0.915840	−	0.401544i	$-0.131526\pi$
$770$	5.08413	−	19.9350i	0.183219	−	0.718407i
$771$	−32.2727	−	35.3693i	−1.16227	−	1.27379i
$772$	−11.8723	+	3.18118i	−0.427294	+	0.114493i
$773$	5.19759	−	19.3977i	0.186944	−	0.697686i	−0.807261	−	0.590194i	$-0.799051\pi$
$773$	5.19759	−	19.3977i	0.186944	−	0.697686i	0.994206	−	0.107492i	$-0.0342821\pi$
$774$	−23.2537	+	10.7239i	−0.835838	+	0.385463i
$775$	26.7377	+	35.4741i	0.960448	+	1.27427i
$776$		−	16.4760i		−	0.591453i
$777$	−13.4120	+	36.0026i	−0.481151	+	1.29159i
$778$	7.47497	−	7.47497i	0.267991	−	0.267991i
$779$	11.1524	−	19.3165i	0.399575	−	0.692084i
$780$	1.86706	−	0.531211i	0.0668514	−	0.0190204i
$781$	−6.89140	−	11.9363i	−0.246594	−	0.427113i
$782$	−4.89499	−	18.2684i	−0.175045	−	0.653275i
$783$	−1.40633	+	10.1826i	−0.0502582	+	0.363898i
$784$	−2.88938	−	6.37585i	−0.103192	−	0.227709i
$785$	10.3809	+	2.11142i	0.370509	+	0.0753599i
$786$	0.348426	+	1.58753i	0.0124280	+	0.0566252i
$787$	−4.43996	+	16.5702i	−0.158268	+	0.590663i	0.840536	+	0.541756i	$0.182240\pi$
$787$	−4.43996	+	16.5702i	−0.158268	+	0.590663i	−0.998803	+	0.0489067i	$0.984426\pi$
$788$	−3.21503	+	11.9987i	−0.114531	+	0.427435i
$789$	−3.61935	−	16.4908i	−0.128852	−	0.587087i
$790$	−18.9411	−	3.85253i	−0.673893	−	0.137067i
$791$	18.1710	+	5.83777i	0.646086	+	0.207567i
$792$	8.02001	−	6.67200i	0.284979	−	0.237079i
$793$	0.984276	+	3.67337i	0.0349527	+	0.130445i
$794$	−7.83515	−	13.5709i	−0.278059	−	0.481612i
$795$	22.3649	−	6.36320i	0.793200	−	0.225679i
$796$	−8.09584	+	14.0224i	−0.286949	+	0.497011i
$797$	26.9706	−	26.9706i	0.955347	−	0.955347i	−0.0436979	−	0.999045i	$-0.513914\pi$
$797$	26.9706	−	26.9706i	0.955347	−	0.955347i	0.999045	+	0.0436979i	$0.0139139\pi$
$798$	8.17171	+	9.88904i	0.289275	+	0.350068i
$799$		−	7.73254i		−	0.273558i
$800$	−4.95142	−	0.695325i	−0.175059	−	0.0245835i
$801$	9.04310	+	19.6090i	0.319522	+	0.692852i
$802$	6.71350	−	25.0551i	0.237062	−	0.884728i
$803$	−12.8232	+	3.43597i	−0.452522	+	0.121253i
$804$	−16.4495	−	18.0278i	−0.580128	−	0.635792i
$805$	24.7203	+	24.1299i	0.871278	+	0.850466i
$806$			4.45291i			0.156847i
$807$	−30.0222	−	19.2156i	−1.05683	−	0.676422i
$808$	−3.06580	−	0.821480i	−0.107855	−	0.0288996i
$809$	−4.15287	−	7.19297i	−0.146007	−	0.252891i	0.783741	−	0.621088i	$-0.213309\pi$
$809$	−4.15287	−	7.19297i	−0.146007	−	0.252891i	−0.929748	+	0.368196i	$0.879976\pi$
$810$	12.3951	+	15.8544i	0.435519	+	0.557067i
$811$	−17.0386			−0.598306			−0.299153	−	0.954205i	$-0.596704\pi$
$811$	−17.0386			−0.598306			−0.299153	+	0.954205i	$0.596704\pi$
$812$	2.83609	−	4.39897i	0.0995273	−	0.154373i
$813$	1.82813	−	39.9334i	0.0641154	−	1.40053i
$814$	25.2488	+	14.5774i	0.884969	+	0.510937i
$815$	12.4776	−	4.17571i	0.437072	−	0.146269i
$816$	−1.69829	+	5.34683i	−0.0594519	+	0.187177i
$817$	−23.0809	+	6.18451i	−0.807499	+	0.216369i
$818$	−4.26617	−	4.26617i	−0.149163	−	0.149163i
$819$	2.39120	+	3.17933i	0.0835553	+	0.111095i
$820$	−14.8562	+	9.83427i	−0.518801	+	0.343428i
$821$	9.60555	+	5.54577i	0.335236	+	0.193549i	0.658163	−	0.752875i	$-0.271334\pi$
$821$	9.60555	+	5.54577i	0.335236	+	0.193549i	−0.322927	+	0.946424i	$0.604667\pi$
$822$	−14.4421	−	27.8868i	−0.503725	−	0.972662i
$823$	−37.9719	−	10.1745i	−1.32362	−	0.354662i	−0.473285	−	0.880909i	$-0.656932\pi$
$823$	−37.9719	−	10.1745i	−1.32362	−	0.354662i	−0.850332	+	0.526247i	$0.823599\pi$
$824$	−2.49761	+	4.32599i	−0.0870084	+	0.150703i
$825$	13.0197	−	27.1561i	0.453288	−	0.945455i
$826$	3.53488	−	11.0029i	0.122994	−	0.382840i
$827$	−12.4819	+	12.4819i	−0.434037	+	0.434037i	−0.889999	−	0.455962i	$-0.849295\pi$
$827$	−12.4819	+	12.4819i	−0.434037	+	0.434037i	0.455962	+	0.889999i	$0.349295\pi$
$828$	2.96889	+	17.2640i	0.103176	+	0.599966i
$829$	9.94204	−	5.74004i	0.345301	−	0.199360i	−0.317313	−	0.948321i	$-0.602780\pi$
$829$	9.94204	−	5.74004i	0.345301	−	0.199360i	0.662614	+	0.748961i	$0.269447\pi$
$830$	−29.6852	−	14.7985i	−1.03039	−	0.513662i
$831$	−2.72495	−	12.4156i	−0.0945274	−	0.430693i
$832$	−0.354405	−	0.354405i	−0.0122868	−	0.0122868i
$833$	−17.5253	+	14.3846i	−0.607217	+	0.498398i
$834$	18.4756	−	16.8580i	0.639756	−	0.583745i
$835$	−16.0580	−	14.2054i	−0.555710	−	0.491597i
$836$	8.43066	−	4.86744i	0.291581	−	0.168344i
$837$	−42.7619	+	17.3956i	−1.47807	+	0.601280i
$838$	0.887033	+	3.31045i	0.0306421	+	0.114358i
$839$	44.5591			1.53835			0.769176	−	0.639037i	$-0.220667\pi$
$839$	44.5591			1.53835			0.769176	+	0.639037i	$0.220667\pi$
$840$	−2.31750	−	9.98144i	−0.0799615	−	0.344392i
$841$	−25.0865			−0.865053
$842$	−3.16357	−	11.8066i	−0.109024	−	0.406883i
$843$	5.67301	+	10.9542i	0.195389	+	0.377284i
$844$	9.42139	−	5.43944i	0.324297	−	0.187233i
$845$	−28.4539	+	1.74187i	−0.978844	+	0.0599223i
$846$	−0.654378	+	7.13208i	−0.0224980	+	0.245206i
$847$	0.141787	−	2.88811i	0.00487185	−	0.0992366i
$848$	−4.24530	−	4.24530i	−0.145784	−	0.145784i
$849$	−21.0306	+	4.61574i	−0.721768	+	0.158412i
$850$	1.97541	+	16.0739i	0.0677560	+	0.551331i
$851$	−42.3959	+	24.4773i	−1.45331	+	0.839070i
$852$	−5.78197	−	3.70073i	−0.198087	−	0.126785i
$853$	−7.83980	+	7.83980i	−0.268430	+	0.268430i	−0.828467	−	0.560037i	$-0.810787\pi$
$853$	−7.83980	+	7.83980i	−0.268430	+	0.268430i	0.560037	+	0.828467i	$0.310787\pi$
$854$	19.6224	−	4.23872i	0.671464	−	0.145046i
$855$	8.89159	+	16.5405i	0.304086	+	0.565674i
$856$	6.87625	−	11.9100i	0.235025	−	0.407076i
$857$	24.9220	+	6.67783i	0.851319	+	0.228110i	0.657993	−	0.753024i	$-0.271406\pi$
$857$	24.9220	+	6.67783i	0.851319	+	0.228110i	0.193327	+	0.981134i	$0.438072\pi$
$858$	2.68069	−	1.38828i	0.0915173	−	0.0473952i
$859$	−26.5807	−	15.3464i	−0.906923	−	0.523612i	−0.0274833	−	0.999622i	$-0.508749\pi$
$859$	−26.5807	−	15.3464i	−0.906923	−	0.523612i	−0.879440	+	0.476010i	$0.842083\pi$
$860$	18.7037	+	3.80424i	0.637789	+	0.129723i
$861$	−29.7506	−	21.1675i	−1.01390	−	0.721385i
$862$	−4.19371	−	4.19371i	−0.142838	−	0.142838i
$863$	−17.2391	+	4.61920i	−0.586826	+	0.157240i	−0.540002	−	0.841664i	$-0.681577\pi$
$863$	−17.2391	+	4.61920i	−0.586826	+	0.157240i	−0.0468238	+	0.998903i	$0.514910\pi$
$864$	2.01889	−	4.78791i	0.0686841	−	0.162888i
$865$	−9.46446	−	28.2812i	−0.321801	−	0.961588i
$866$	7.61601	+	4.39710i	0.258802	+	0.149420i
$867$	−11.2623	−	0.515580i	−0.382486	−	0.0175100i
$868$	23.4777	+	1.15260i	0.796884	+	0.0391217i
$869$	−30.0599			−1.01971
$870$	5.33363	−	5.50041i	0.180827	−	0.186481i
$871$	−3.53099	−	6.11586i	−0.119643	−	0.207228i
$872$	1.85277	+	0.496447i	0.0627426	+	0.0168118i
$873$	48.7129	−	8.37716i	1.64868	−	0.283524i
$874$			16.3461i			0.552916i
$875$	−18.0887	−	23.4051i	−0.611510	−	0.791236i
$876$	−4.88449	+	4.45685i	−0.165032	+	0.150583i
$877$	2.17203	−	0.581994i	0.0733443	−	0.0196525i	−0.221960	−	0.975056i	$-0.571246\pi$
$877$	2.17203	−	0.581994i	0.0733443	−	0.0196525i	0.295305	+	0.955403i	$0.404579\pi$
$878$	−0.716244	+	2.67306i	−0.0241720	+	0.0902113i
$879$	9.36434	+	2.97435i	0.315851	+	0.100322i
$880$	−7.76137	+	0.475131i	−0.261636	+	0.0160166i
$881$		−	38.0258i		−	1.28112i	−0.767908	−	0.640560i	$-0.778702\pi$
$881$		−	38.0258i		−	1.28112i	0.767908	−	0.640560i	$-0.221298\pi$
$882$	17.3818	−	11.7845i	0.585274	−	0.396805i
$883$	−37.1733	+	37.1733i	−1.25098	+	1.25098i	−0.295701	+	0.955281i	$0.595553\pi$
$883$	−37.1733	+	37.1733i	−1.25098	+	1.25098i	−0.955281	+	0.295701i	$0.904447\pi$
$884$	−0.811693	+	1.40589i	−0.0273002	+	0.0472853i
$885$	8.23217	−	14.7794i	0.276721	−	0.496803i
$886$	−12.1035	−	20.9639i	−0.406626	−	0.704296i
$887$	5.08637	+	18.9826i	0.170783	+	0.637373i	0.997231	+	0.0743596i	$0.0236913\pi$
$887$	5.08637	+	18.9826i	0.170783	+	0.637373i	−0.826448	+	0.563013i	$0.809642\pi$
$888$	14.5061	+	0.664081i	0.486792	+	0.0222851i
$889$	−20.1307	−	6.46735i	−0.675161	−	0.216908i
$890$	3.20798	−	15.7721i	0.107532	−	0.528683i
$891$	23.8042	+	20.3196i	0.797470	+	0.680733i
$892$	1.76722	−	6.59536i	0.0591709	−	0.220829i
$893$	−1.72973	+	6.45542i	−0.0578831	+	0.216023i
$894$	15.3973	−	3.37936i	0.514963	−	0.113023i
$895$	−43.4371	+	28.7538i	−1.45194	+	0.961133i
$896$	−1.96031	+	1.77684i	−0.0654895	+	0.0593602i
$897$	−0.231815	+	5.06372i	−0.00774007	+	0.169073i
$898$	−1.59049	−	5.93580i	−0.0530754	−	0.198080i
$899$	8.78780	+	15.2209i	0.293089	+	0.507646i
$900$	−0.461732	−	14.9929i	−0.0153911	−	0.499763i
$901$	−9.72301	+	16.8407i	−0.323920	+	0.561046i
$902$	−19.5922	+	19.5922i	−0.652348	+	0.652348i
$903$	6.50196	+	38.5717i	0.216372	+	1.28359i
$904$		−	7.21372i		−	0.239925i
$905$	0.107359	+	1.75373i	0.00356872	+	0.0582959i
$906$	−10.5003	+	33.0588i	−0.348849	+	1.09830i
$907$	3.12499	−	11.6626i	0.103764	−	0.387251i	−0.894438	−	0.447191i	$-0.852424\pi$
$907$	3.12499	−	11.6626i	0.103764	−	0.387251i	0.998202	+	0.0599403i	$0.0190910\pi$
$908$	−11.5202	+	3.08682i	−0.382310	+	0.102440i
$909$	0.869989	−	9.48203i	0.0288557	−	0.314499i
$910$	−0.0358396	−	2.96495i	−0.00118807	−	0.0982871i
$911$		−	29.5439i		−	0.978834i	−0.872050	−	0.489417i	$-0.837210\pi$
$911$		−	29.5439i		−	0.978834i	0.872050	−	0.489417i	$-0.162790\pi$
$912$	2.61385	−	4.08384i	0.0865532	−	0.135230i
$913$	−49.8266	−	13.3510i	−1.64902	−	0.441853i
$914$	−5.47652	−	9.48561i	−0.181147	−	0.313756i
$915$	29.3833	−	0.452347i	0.971381	−	0.0149541i
$916$	13.3104			0.439788
$917$	2.47972	+	0.121738i	0.0818876	+	0.00402013i
$918$	−16.6719	−	2.30258i	−0.550256	−	0.0759963i
$919$	−38.4441	−	22.1957i	−1.26816	−	0.732170i	−0.293516	−	0.955954i	$-0.594826\pi$
$919$	−38.4441	−	22.1957i	−1.26816	−	0.732170i	−0.974639	+	0.223784i	$0.928159\pi$
$920$	5.82524	−	11.6852i	0.192053	−	0.385250i
$921$	40.8703	+	12.9814i	1.34672	+	0.427753i
$922$	−0.00373918	+	0.00100191i	−0.000123143	+	3.29961e-5i
$923$	−1.40466	−	1.40466i	−0.0462350	−	0.0462350i
$924$	−6.62576	−	14.4931i	−0.217972	−	0.476789i
$925$	38.8652	−	15.7075i	1.27788	−	0.516459i
$926$	34.0896	+	19.6816i	1.12025	+	0.646778i
$927$	−14.0601	−	5.18490i	−0.461795	−	0.170295i
$928$	−1.91084	−	0.512009i	−0.0627265	−	0.0168075i
$929$	−20.6408	+	35.7508i	−0.677201	+	1.17295i	0.298619	+	0.954372i	$0.403474\pi$
$929$	−20.6408	+	35.7508i	−0.677201	+	1.17295i	−0.975820	+	0.218575i	$0.929859\pi$
$930$	33.3699	+	8.39309i	1.09424	+	0.275220i
$931$	17.8486	−	8.08853i	0.584964	−	0.265091i
$932$	−0.134997	+	0.134997i	−0.00442199	+	0.00442199i
$933$	−4.66287	+	7.28520i	−0.152656	+	0.238507i
$934$	8.98915	−	5.18989i	0.294134	−	0.169818i
$935$	7.99291	+	23.8839i	0.261396	+	0.781089i
$936$	0.867638	−	1.22803i	0.0283596	−	0.0401394i
$937$	−6.68894	−	6.68894i	−0.218518	−	0.218518i	0.589356	−	0.807874i	$-0.299382\pi$
$937$	−6.68894	−	6.68894i	−0.218518	−	0.218518i	−0.807874	+	0.589356i	$0.799382\pi$
$938$	−33.1594	+	17.0339i	−1.08269	+	0.556177i
$939$	13.2777	+	14.5517i	0.433300	+	0.474876i
$940$	3.53703	−	3.99832i	0.115365	−	0.130411i
$941$	−11.8432	+	6.83768i	−0.386078	+	0.222902i	−0.680459	−	0.732786i	$-0.738220\pi$
$941$	−11.8432	+	6.83768i	−0.386078	+	0.222902i	0.294382	+	0.955688i	$0.404886\pi$
$942$	7.28648	−	3.77354i	0.237406	−	0.122949i
$943$	−12.0414	−	44.9391i	−0.392122	−	1.46342i
$944$	−4.36805			−0.142168
$945$	28.3328	−	11.9270i	0.921666	−	0.387984i
$946$	29.6831			0.965081
$947$	2.14815	+	8.01700i	0.0698054	+	0.260517i	0.992005	−	0.126196i	$-0.0402769\pi$
$947$	2.14815	+	8.01700i	0.0698054	+	0.260517i	−0.922200	+	0.386714i	$0.873610\pi$
$948$	−13.2950	+	6.88525i	−0.431802	+	0.223623i
$949$	−1.65704	+	0.956694i	−0.0537899	+	0.0310556i
$950$	1.94650	−	13.8610i	0.0631527	−	0.449711i
$951$	31.3860	+	34.3975i	1.01776	+	1.11542i
$952$	7.20239	+	4.64350i	0.233431	+	0.150497i
$953$	27.8231	+	27.8231i	0.901277	+	0.901277i	0.995547	−	0.0942697i	$-0.0300516\pi$
$953$	27.8231	+	27.8231i	0.901277	+	0.901277i	−0.0942697	+	0.995547i	$0.530052\pi$
$954$	10.3932	−	14.7102i	0.336491	−	0.476259i
$955$	10.3087	−	20.6788i	0.333581	−	0.669151i
$956$	−6.38655	+	3.68728i	−0.206556	+	0.119255i
$957$	6.42336	−	10.0358i	0.207638	−	0.324410i
$958$	4.01724	−	4.01724i	0.129791	−	0.129791i
$959$	−46.8897	+	10.1288i	−1.51415	+	0.327078i
$960$	−3.32390	+	1.98789i	−0.107278	+	0.0641589i
$961$	−23.9664	+	41.5110i	−0.773110	+	1.33907i
$962$	4.05885	+	1.08756i	0.130862	+	0.0350645i
$963$	38.7094	+	14.2747i	1.24739	+	0.459996i
$964$	12.5978	+	7.27332i	0.405747	+	0.234258i
$965$	−5.47792	+	26.9324i	−0.176341	+	0.866984i
$966$	26.6382	+	2.53293i	0.857069	+	0.0814956i
$967$	18.6189	+	18.6189i	0.598743	+	0.598743i	0.939978	−	0.341235i	$-0.110845\pi$
$967$	18.6189	+	18.6189i	0.598743	+	0.598743i	−0.341235	+	0.939978i	$0.610845\pi$
$968$	−1.05568	+	0.282868i	−0.0339308	+	0.00909172i
$969$	−14.9679	−	4.75419i	−0.480839	−	0.152727i
$970$	−32.9715	−	16.4368i	−1.05865	−	0.527753i
$971$	43.2885	+	24.9926i	1.38920	+	0.802052i	0.993225	−	0.116211i	$-0.0370749\pi$
$971$	43.2885	+	24.9926i	1.38920	+	0.802052i	0.395971	+	0.918263i	$0.370408\pi$
$972$	15.1824	+	3.53466i	0.486977	+	0.113374i
$973$	−17.4570	−	33.9830i	−0.559645	−	1.08945i
$974$	6.76997			0.216924
$975$	0.799560	−	4.26628i	0.0256064	−	0.136630i
$976$	−3.79381	−	6.57108i	−0.121437	−	0.210335i
$977$	−4.16509	−	1.11603i	−0.133253	−	0.0357050i	0.191576	−	0.981478i	$-0.438640\pi$
$977$	−4.16509	−	1.11603i	−0.133253	−	0.0357050i	−0.324829	+	0.945773i	$0.605307\pi$
$978$	5.49431	−	8.58423i	0.175689	−	0.274494i
$979$		−	25.0307i		−	0.799985i
$980$	−15.6418	−	0.578489i	−0.499658	−	0.0184791i
$981$	−0.525763	+	5.73031i	−0.0167863	+	0.182955i
$982$	10.9083	−	2.92288i	0.348099	−	0.0932728i
$983$	−0.632479	+	2.36044i	−0.0201730	+	0.0752865i	−0.975279	−	0.220979i	$-0.929075\pi$
$983$	−0.632479	+	2.36044i	−0.0201730	+	0.0752865i	0.955106	+	0.296266i	$0.0957414\pi$
$984$	−4.17769	+	13.1529i	−0.133180	+	0.419299i
$985$	20.8042	+	18.4040i	0.662877	+	0.586400i
$986$			6.40749i			0.204056i
$987$	10.2519	+	3.81912i	0.326323	+	0.121564i
$988$	0.992123	−	0.992123i	0.0315636	−	0.0315636i
$989$	−24.9209	+	43.1642i	−0.792437	+	1.37254i
$990$	−5.35101	−	22.7057i	−0.170066	−	0.721634i
$991$	17.2356	+	29.8529i	0.547506	+	0.948309i	0.998445	+	0.0557538i	$0.0177562\pi$
$991$	17.2356	+	29.8529i	0.547506	+	0.948309i	−0.450938	+	0.892555i	$0.648910\pi$
$992$	−2.29946	−	8.58169i	−0.0730078	−	0.272469i
$993$	2.12584	−	46.4365i	0.0674614	−	1.47362i
$994$	−7.76958	+	7.04241i	−0.246436	+	0.223372i
$995$	19.9849	+	30.1903i	0.633564	+	0.957097i
$996$	−25.0955	+	5.50791i	−0.795183	+	0.174525i
$997$	14.3099	−	53.4053i	0.453199	−	1.69136i	−0.240129	−	0.970741i	$-0.577190\pi$
$997$	14.3099	−	53.4053i	0.453199	−	1.69136i	0.693328	−	0.720622i	$-0.256144\pi$
$998$	0.843210	−	3.14690i	0.0266913	−	0.0996135i
$999$	5.41214	+	43.2263i	0.171233	+	1.36762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.107.15	yes	64
3.2	odd	2	inner	210.2.x.a.107.5	yes	64
5.3	odd	4	inner	210.2.x.a.23.14	yes	64
7.4	even	3	inner	210.2.x.a.137.2	yes	64
15.8	even	4	inner	210.2.x.a.23.2	✓	64
21.11	odd	6	inner	210.2.x.a.137.14	yes	64
35.18	odd	12	inner	210.2.x.a.53.5	yes	64
105.53	even	12	inner	210.2.x.a.53.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.2	✓	64	15.8	even	4	inner
210.2.x.a.23.14	yes	64	5.3	odd	4	inner
210.2.x.a.53.5	yes	64	35.18	odd	12	inner
210.2.x.a.53.15	yes	64	105.53	even	12	inner
210.2.x.a.107.5	yes	64	3.2	odd	2	inner
210.2.x.a.107.15	yes	64	1.1	even	1	trivial
210.2.x.a.137.2	yes	64	7.4	even	3	inner
210.2.x.a.137.14	yes	64	21.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.53804 - 0.796522i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.136630 + 2.23189i) q^{5} +(1.16745 + 1.27947i) q^{6} +(2.35340 - 1.20893i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.73111 - 2.45016i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.53804 - 0.796522i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.136630 + 2.23189i) q^{5} +(1.16745 + 1.27947i) q^{6} +(2.35340 - 1.20893i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.73111 - 2.45016i) q^{9} +(-2.12048 + 0.709630i) q^{10} +(-3.01159 + 1.73874i) q^{11} +(-0.933717 + 1.45883i) q^{12} +(-0.354405 + 0.354405i) q^{13} +(1.77684 + 1.96031i) q^{14} +(1.98789 + 3.32390i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.12860 - 0.838307i) q^{17} +(2.81471 + 1.03797i) q^{18} +(2.42435 + 1.39970i) q^{19} +(-1.23427 - 1.86456i) q^{20} +(2.65667 - 3.73391i) q^{21} +(-2.45895 - 2.45895i) q^{22} +(5.64018 - 1.51128i) q^{23} +(-1.65078 - 0.524329i) q^{24} +(-4.96266 + 0.609888i) q^{25} +(-0.434056 - 0.250602i) q^{26} +(0.710897 - 5.14729i) q^{27} +(-1.43364 + 2.22367i) q^{28} -1.97825 q^{29} +(-2.69613 + 2.78044i) q^{30} +(-4.44221 - 7.69413i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-3.24699 + 5.07305i) q^{33} -3.23897i q^{34} +(3.01975 + 5.08735i) q^{35} +(-0.274103 + 2.98745i) q^{36} +(-8.09819 + 2.16990i) q^{37} +(-0.724539 + 2.70402i) q^{38} +(-0.262796 + 0.827379i) q^{39} +(1.48157 - 1.67480i) q^{40} -7.96768i q^{41} +(4.29428 + 1.59974i) q^{42} +(-6.03572 + 6.03572i) q^{43} +(1.73874 - 3.01159i) q^{44} +(5.70500 + 3.52887i) q^{45} +(2.91957 + 5.05684i) q^{46} +(0.617891 + 2.30600i) q^{47} +(0.0792095 - 1.73024i) q^{48} +(4.07696 - 5.69020i) q^{49} +(-1.87354 - 4.63571i) q^{50} +(-5.47963 + 1.20266i) q^{51} +(0.129721 - 0.484126i) q^{52} +(1.55389 - 5.79919i) q^{53} +(5.15590 - 0.645543i) q^{54} +(-4.29216 - 6.48398i) q^{55} +(-2.51895 - 0.809259i) q^{56} +(4.84364 + 0.221739i) q^{57} +(-0.512009 - 1.91084i) q^{58} +(-2.18403 - 3.78284i) q^{59} +(-3.38351 - 1.88463i) q^{60} +(3.79381 - 6.57108i) q^{61} +(6.28223 - 6.28223i) q^{62} +(1.11190 - 7.85899i) q^{63} +1.00000i q^{64} +(-0.839416 - 0.742571i) q^{65} +(-5.74057 - 1.82335i) q^{66} +(-3.64677 + 13.6099i) q^{67} +(3.12860 - 0.838307i) q^{68} +(7.47102 - 6.81693i) q^{69} +(-4.13243 + 4.23356i) q^{70} +3.96344i q^{71} +(-2.95660 + 0.508447i) q^{72} +(3.68750 + 0.988062i) q^{73} +(-4.19193 - 7.26063i) q^{74} +(-7.14696 + 4.89090i) q^{75} -2.79940 q^{76} +(-4.98545 + 7.73277i) q^{77} +(-0.867203 - 0.0397001i) q^{78} +(7.48605 + 4.32207i) q^{79} +(2.00119 + 0.997619i) q^{80} +(-3.00655 - 8.48296i) q^{81} +(7.69619 - 2.06219i) q^{82} +(10.4891 + 10.4891i) q^{83} +(-0.433784 + 4.56200i) q^{84} +(1.44355 - 7.09724i) q^{85} +(-7.39221 - 4.26790i) q^{86} +(-3.04262 + 1.57572i) q^{87} +(3.35899 + 0.900040i) q^{88} +(-3.59897 + 6.23359i) q^{89} +(-1.93206 + 6.42395i) q^{90} +(-0.405604 + 1.26251i) q^{91} +(-4.12890 + 4.12890i) q^{92} +(-12.9608 - 8.29553i) q^{93} +(-2.06750 + 1.19367i) q^{94} +(-2.79274 + 5.60213i) q^{95} +(1.69178 - 0.371308i) q^{96} +(11.6503 + 11.6503i) q^{97} +(6.55151 + 2.46531i) q^{98} +(-0.953188 + 10.3888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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