LMFDB - Embedded newform 616.2.bp.c.27.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(27,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 5, 4]))

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

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

chi := DirichletCharacter("616.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bp (of order $10$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$88$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			27.9
Character	$\chi$	$=$	616.27
Dual form			616.2.bp.c.251.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36072 + 0.385294i) q^{2} +(-1.25998 + 1.73421i) q^{3} +(1.70310 - 1.04855i) q^{4} +(0.0436016 - 0.134192i) q^{5} +(1.04629 - 2.84523i) q^{6} +(-2.64209 - 0.139117i) q^{7} +(-1.91343 + 2.08298i) q^{8} +(-0.492894 - 1.51697i) q^{9} +(-0.00762601 + 0.199397i) q^{10} +(0.254747 - 3.30683i) q^{11} +(-0.327453 + 4.27468i) q^{12} +(-0.421782 - 1.29811i) q^{13} +(3.64874 - 0.828684i) q^{14} +(0.177780 + 0.244693i) q^{15} +(1.80108 - 3.57157i) q^{16} +(3.34327 + 1.08630i) q^{17} +(1.25517 + 1.87426i) q^{18} +(-0.501973 + 0.690906i) q^{19} +(-0.0664495 - 0.274260i) q^{20} +(3.57024 - 4.40666i) q^{21} +(0.927463 + 4.59781i) q^{22} -5.99703i q^{23} +(-1.20144 - 5.94280i) q^{24} +(4.02898 + 2.92722i) q^{25} +(1.07408 + 1.60385i) q^{26} +(-2.86428 - 0.930660i) q^{27} +(-4.64561 + 2.53344i) q^{28} +(-2.96338 - 4.07874i) q^{29} +(-0.336187 - 0.264461i) q^{30} +(-0.650400 - 2.00172i) q^{31} +(-1.07465 + 5.55384i) q^{32} +(5.41376 + 4.60832i) q^{33} +(-4.96779 - 0.189995i) q^{34} +(-0.133868 + 0.348482i) q^{35} +(-2.43007 - 2.06673i) q^{36} +(2.51997 + 3.46845i) q^{37} +(0.416840 - 1.13353i) q^{38} +(2.78264 + 0.904133i) q^{39} +(0.196090 + 0.347588i) q^{40} +(5.80419 - 7.98879i) q^{41} +(-3.16022 + 7.37181i) q^{42} -2.50021 q^{43} +(-3.03352 - 5.89896i) q^{44} -0.225056 q^{45} +(2.31062 + 8.16026i) q^{46} +(10.3644 + 7.53019i) q^{47} +(3.92455 + 7.62355i) q^{48} +(6.96129 + 0.735119i) q^{49} +(-6.61014 - 2.43078i) q^{50} +(-6.09632 + 4.42924i) q^{51} +(-2.07947 - 1.76855i) q^{52} +(8.62641 - 2.80289i) q^{53} +(4.25605 + 0.162774i) q^{54} +(-0.432642 - 0.178368i) q^{55} +(5.34523 - 5.23722i) q^{56} +(-0.565703 - 1.74105i) q^{57} +(5.60383 + 4.40823i) q^{58} +(-0.120231 - 0.165483i) q^{59} +(0.559351 + 0.230325i) q^{60} +(-1.71961 + 5.29241i) q^{61} +(1.65626 + 2.47318i) q^{62} +(1.09124 + 4.07655i) q^{63} +(-0.677574 - 7.97125i) q^{64} -0.192586 q^{65} +(-9.14215 - 4.18472i) q^{66} +5.75153 q^{67} +(6.83296 - 1.65553i) q^{68} +(10.4001 + 7.55613i) q^{69} +(0.0478881 - 0.525763i) q^{70} +(3.19083 + 1.03676i) q^{71} +(4.10294 + 1.87593i) q^{72} +(5.79485 + 7.97593i) q^{73} +(-4.76534 - 3.74864i) q^{74} +(-10.1529 + 3.29886i) q^{75} +(-0.130457 + 1.70302i) q^{76} +(-1.13310 + 8.70150i) q^{77} +(-4.13474 - 0.158135i) q^{78} +(7.95082 - 2.58338i) q^{79} +(-0.400746 - 0.397416i) q^{80} +(9.09413 - 6.60727i) q^{81} +(-4.81982 + 13.1068i) q^{82} +(-11.4687 - 3.72642i) q^{83} +(1.45984 - 11.2486i) q^{84} +(0.291544 - 0.401276i) q^{85} +(3.40208 - 0.963318i) q^{86} +10.8072 q^{87} +(6.40060 + 6.85801i) q^{88} -11.6165i q^{89} +(0.306238 - 0.0867130i) q^{90} +(0.933797 + 3.48840i) q^{91} +(-6.28820 - 10.2135i) q^{92} +(4.29091 + 1.39420i) q^{93} +(-17.0044 - 6.25310i) q^{94} +(0.0708272 + 0.0974852i) q^{95} +(-8.27751 - 8.86139i) q^{96} +(-12.2437 + 3.97821i) q^{97} +(-9.75558 + 1.68186i) q^{98} +(-5.14193 + 1.24347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 2 q^{2} - 10 q^{4} - 14 q^{8} + 84 q^{9} - 28 q^{11} - 32 q^{14} + 14 q^{16} - 4 q^{18} - 62 q^{22} - 108 q^{25} - 44 q^{28} + 24 q^{30} - 112 q^{32} + 14 q^{35} + 20 q^{36} - 2 q^{42} + 8 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) $ 352 * q - 2 * q^2 - 10 * q^4 - 14 * q^8 + 84 * q^9 - 28 * q^11 - 32 * q^14 + 14 * q^16 - 4 * q^18 - 62 * q^22 - 108 * q^25 - 44 * q^28 + 24 * q^30 - 112 * q^32 + 14 * q^35 + 20 * q^36 - 2 * q^42 + 8 * q^43 + 22 * q^44 - 38 * q^46 - 34 * q^49 - 24 * q^50 - 36 * q^51 - 120 * q^56 - 36 * q^57 + 30 * q^58 - 136 * q^60 + 86 * q^64 + 8 * q^65 + 24 * q^67 + 52 * q^70 + 30 * q^72 + 94 * q^74 - 68 * q^78 - 60 * q^81 - 128 * q^84 + 34 * q^86 - 38 * q^88 + 78 * q^91 - 8 * q^92 - 100 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.36072	+	0.385294i	−0.962172	+	0.272444i
$2$	−1.36072	+	0.385294i	−0.962172	+	0.272444i
$3$	−1.25998	+	1.73421i	−0.727449	+	1.00125i	0.271794	+	0.962355i	$0.412383\pi$
$3$	−1.25998	+	1.73421i	−0.727449	+	1.00125i	−0.999243	+	0.0388925i	$0.987617\pi$
$4$	1.70310	−	1.04855i	0.851548	−	0.524276i
$5$	0.0436016	−	0.134192i	0.0194992	−	0.0600124i	−0.940833	−	0.338869i	$-0.889956\pi$
$5$	0.0436016	−	0.134192i	0.0194992	−	0.0600124i	0.960333	+	0.278857i	$0.0899555\pi$
$6$	1.04629	−	2.84523i	0.427147	−	1.16156i
$7$	−2.64209	−	0.139117i	−0.998617	−	0.0525813i
$7$	−2.64209	−	0.139117i	−0.998617	−	0.0525813i
$8$	−1.91343	+	2.08298i	−0.676500	+	0.736443i
$9$	−0.492894	−	1.51697i	−0.164298	−	0.505658i
$10$	−0.00762601	+	0.199397i	−0.00241156	+	0.0630547i
$11$	0.254747	−	3.30683i	0.0768092	−	0.997046i
$11$	0.254747	−	3.30683i	0.0768092	−	0.997046i
$12$	−0.327453	+	4.27468i	−0.0945277	+	1.23400i
$13$	−0.421782	−	1.29811i	−0.116981	−	0.360031i	0.875374	−	0.483447i	$-0.160615\pi$
$13$	−0.421782	−	1.29811i	−0.116981	−	0.360031i	−0.992355	+	0.123415i	$0.960615\pi$
$14$	3.64874	−	0.828684i	0.975166	−	0.221475i
$15$	0.177780	+	0.244693i	0.0459026	+	0.0631796i
$16$	1.80108	−	3.57157i	0.450269	−	0.892893i
$17$	3.34327	+	1.08630i	0.810863	+	0.263465i	0.684963	−	0.728578i	$-0.259818\pi$
$17$	3.34327	+	1.08630i	0.810863	+	0.263465i	0.125900	+	0.992043i	$0.459818\pi$
$18$	1.25517	+	1.87426i	0.295846	+	0.441767i
$19$	−0.501973	+	0.690906i	−0.115160	+	0.158505i	−0.862706	−	0.505706i	$-0.831232\pi$
$19$	−0.501973	+	0.690906i	−0.115160	+	0.158505i	0.747546	+	0.664210i	$0.231232\pi$
$20$	−0.0664495	−	0.274260i	−0.0148586	−	0.0613265i
$21$	3.57024	−	4.40666i	0.779090	−	0.961613i
$22$	0.927463	+	4.59781i	0.197736	+	0.980255i
$23$		−	5.99703i		−	1.25047i	−0.780438	−	0.625234i	$-0.785004\pi$
$23$		−	5.99703i		−	1.25047i	0.780438	−	0.625234i	$-0.214996\pi$
$24$	−1.20144	−	5.94280i	−0.245243	−	1.21307i
$25$	4.02898	+	2.92722i	0.805796	+	0.585445i
$26$	1.07408	+	1.60385i	0.210644	+	0.314541i
$27$	−2.86428	−	0.930660i	−0.551230	−	0.179106i
$28$	−4.64561	+	2.53344i	−0.877937	+	0.478775i
$29$	−2.96338	−	4.07874i	−0.550285	−	0.757402i	0.439766	−	0.898113i	$-0.355061\pi$
$29$	−2.96338	−	4.07874i	−0.550285	−	0.757402i	−0.990051	+	0.140710i	$0.955061\pi$
$30$	−0.336187	−	0.264461i	−0.0613791	−	0.0482837i
$31$	−0.650400	−	2.00172i	−0.116815	−	0.359520i	0.875506	−	0.483207i	$-0.160528\pi$
$31$	−0.650400	−	2.00172i	−0.116815	−	0.359520i	−0.992321	+	0.123687i	$0.960528\pi$
$32$	−1.07465	+	5.55384i	−0.189972	+	0.981789i
$33$	5.41376	+	4.60832i	0.942415	+	0.802205i
$34$	−4.96779	−	0.189995i	−0.851969	−	0.0325839i
$35$	−0.133868	+	0.348482i	−0.0226278	+	0.0589041i
$36$	−2.43007	−	2.06673i	−0.405012	−	0.344454i
$37$	2.51997	+	3.46845i	0.414281	+	0.570209i	0.964256	−	0.264972i	$-0.0853628\pi$
$37$	2.51997	+	3.46845i	0.414281	+	0.570209i	−0.549975	+	0.835181i	$0.685363\pi$
$38$	0.416840	−	1.13353i	0.0676204	−	0.183884i
$39$	2.78264	+	0.904133i	0.445578	+	0.144777i
$40$	0.196090	+	0.347588i	0.0310045	+	0.0549585i
$41$	5.80419	−	7.98879i	0.906463	−	1.24764i	−0.0618977	−	0.998082i	$-0.519715\pi$
$41$	5.80419	−	7.98879i	0.906463	−	1.24764i	0.968360	−	0.249556i	$-0.0802847\pi$
$42$	−3.16022	+	7.37181i	−0.487632	+	1.13749i
$43$	−2.50021			−0.381279			−0.190639	−	0.981660i	$-0.561056\pi$
$43$	−2.50021			−0.381279			−0.190639	+	0.981660i	$0.561056\pi$
$44$	−3.03352	−	5.89896i	−0.457321	−	0.889302i
$45$	−0.225056			−0.0335494
$46$	2.31062	+	8.16026i	0.340683	+	1.20316i
$47$	10.3644	+	7.53019i	1.51180	+	1.09839i	0.965369	+	0.260890i	$0.0840159\pi$
$47$	10.3644	+	7.53019i	1.51180	+	1.09839i	0.546436	+	0.837501i	$0.315984\pi$
$48$	3.92455	+	7.62355i	0.566459	+	1.10037i
$49$	6.96129	+	0.735119i	0.994470	+	0.105017i
$50$	−6.61014	−	2.43078i	−0.934815	−	0.343764i
$51$	−6.09632	+	4.42924i	−0.853656	+	0.620217i
$52$	−2.07947	−	1.76855i	−0.288371	−	0.245253i
$53$	8.62641	−	2.80289i	1.18493	−	0.385007i	0.350733	−	0.936475i	$-0.385932\pi$
$53$	8.62641	−	2.80289i	1.18493	−	0.385007i	0.834196	+	0.551469i	$0.185932\pi$
$54$	4.25605	+	0.162774i	0.579175	+	0.0221508i
$55$	−0.432642	−	0.178368i	−0.0583374	−	0.0240511i
$56$	5.34523	−	5.23722i	0.714287	−	0.699853i
$57$	−0.565703	−	1.74105i	−0.0749292	−	0.230608i
$58$	5.60383	+	4.40823i	0.735819	+	0.578829i
$59$	−0.120231	−	0.165483i	−0.0156527	−	0.0215441i	0.801119	−	0.598505i	$-0.204238\pi$
$59$	−0.120231	−	0.165483i	−0.0156527	−	0.0215441i	−0.816772	+	0.576961i	$0.804238\pi$
$60$	0.559351	+	0.230325i	0.0722119	+	0.0297348i
$61$	−1.71961	+	5.29241i	−0.220173	+	0.677624i	0.778572	+	0.627555i	$0.215944\pi$
$61$	−1.71961	+	5.29241i	−0.220173	+	0.677624i	−0.998746	+	0.0500690i	$0.984056\pi$
$62$	1.65626	+	2.47318i	0.210346	+	0.314095i
$63$	1.09124	+	4.07655i	0.137483	+	0.513597i
$64$	−0.677574	−	7.97125i	−0.0846968	−	0.996407i
$65$	−0.192586			−0.0238874
$66$	−9.14215	−	4.18472i	−1.12532	−	0.515103i
$67$	5.75153			0.702662			0.351331	−	0.936251i	$-0.385729\pi$
$67$	5.75153			0.702662			0.351331	+	0.936251i	$0.385729\pi$
$68$	6.83296	−	1.65553i	0.828618	−	0.200763i
$69$	10.4001	+	7.55613i	1.25203	+	0.909652i
$70$	0.0478881	−	0.525763i	0.00572372	−	0.0628407i
$71$	3.19083	+	1.03676i	0.378682	+	0.123041i	0.492172	−	0.870498i	$-0.336203\pi$
$71$	3.19083	+	1.03676i	0.378682	+	0.123041i	−0.113490	+	0.993539i	$0.536203\pi$
$72$	4.10294	+	1.87593i	0.483536	+	0.221081i
$73$	5.79485	+	7.97593i	0.678236	+	0.933512i	0.999911	−	0.0133381i	$-0.00424576\pi$
$73$	5.79485	+	7.97593i	0.678236	+	0.933512i	−0.321675	+	0.946850i	$0.604246\pi$
$74$	−4.76534	−	3.74864i	−0.553959	−	0.435770i
$75$	−10.1529	+	3.29886i	−1.17235	+	0.380920i
$76$	−0.130457	+	1.70302i	−0.0149644	+	0.195350i
$77$	−1.13310	+	8.70150i	−0.129129	+	0.991628i
$78$	−4.13474	−	0.158135i	−0.468167	−	0.0179052i
$79$	7.95082	−	2.58338i	0.894537	−	0.290653i	0.174556	−	0.984647i	$-0.444151\pi$
$79$	7.95082	−	2.58338i	0.894537	−	0.290653i	0.719980	+	0.693995i	$0.244151\pi$
$80$	−0.400746	−	0.397416i	−0.0448048	−	0.0444325i
$81$	9.09413	−	6.60727i	1.01046	−	0.734142i
$82$	−4.81982	+	13.1068i	−0.532261	+	1.44740i
$83$	−11.4687	−	3.72642i	−1.25886	−	0.409027i	−0.397770	−	0.917485i	$-0.630216\pi$
$83$	−11.4687	−	3.72642i	−1.25886	−	0.409027i	−0.861087	+	0.508458i	$0.830216\pi$
$84$	1.45984	−	11.2486i	0.159282	−	1.22732i
$85$	0.291544	−	0.401276i	0.0316224	−	0.0435245i
$86$	3.40208	−	0.963318i	0.366856	−	0.103877i
$87$	10.8072			1.15865
$88$	6.40060	+	6.85801i	0.682306	+	0.731067i
$89$		−	11.6165i		−	1.23134i	−0.788003	−	0.615671i	$-0.788885\pi$
$89$		−	11.6165i		−	1.23134i	0.788003	−	0.615671i	$-0.211115\pi$
$90$	0.306238	−	0.0867130i	0.0322803	−	0.00914035i
$91$	0.933797	+	3.48840i	0.0978885	+	0.365684i
$92$	−6.28820	−	10.2135i	−0.655590	−	1.06483i
$93$	4.29091	+	1.39420i	0.444946	+	0.144572i
$94$	−17.0044	−	6.25310i	−1.75387	−	0.644958i
$95$	0.0708272	+	0.0974852i	0.00726672	+	0.0100018i
$96$	−8.27751	−	8.86139i	−0.844819	−	0.904411i
$97$	−12.2437	+	3.97821i	−1.24316	+	0.403926i	−0.855464	−	0.517863i	$-0.826728\pi$
$97$	−12.2437	+	3.97821i	−1.24316	+	0.403926i	−0.387693	+	0.921789i	$0.626728\pi$
$98$	−9.75558	+	1.68186i	−0.985462	+	0.169893i
$99$	−5.14193	+	1.24347i	−0.516783	+	0.124974i
$100$	9.93109	+	0.760751i	0.993109	+	0.0760751i
$101$	−3.94861	−	12.1526i	−0.392901	−	1.20923i	−0.930584	−	0.366079i	$-0.880700\pi$
$101$	−3.94861	−	12.1526i	−0.392901	−	1.20923i	0.537683	−	0.843147i	$-0.319300\pi$
$102$	6.58880	−	8.37581i	0.652389	−	0.829329i
$103$	8.54420	−	6.20772i	0.841885	−	0.611665i	−0.0810115	−	0.996713i	$-0.525815\pi$
$103$	8.54420	−	6.20772i	0.841885	−	0.611665i	0.922897	+	0.385048i	$0.125815\pi$
$104$	3.51098	+	1.60528i	0.344280	+	0.157411i
$105$	−0.435670	−	0.671234i	−0.0425171	−	0.0655058i
$106$	−10.6582	+	7.13765i	−1.03521	+	0.693270i
$107$	−2.67649	−	1.94458i	−0.258746	−	0.187990i	0.450848	−	0.892601i	$-0.351122\pi$
$107$	−2.67649	−	1.94458i	−0.258746	−	0.187990i	−0.709594	+	0.704611i	$0.751122\pi$
$108$	−5.85399	+	1.41834i	−0.563300	+	0.136480i
$109$		−	3.50333i		−	0.335558i	−0.985825	−	0.167779i	$-0.946341\pi$
$109$		−	3.50333i		−	0.335558i	0.985825	−	0.167779i	$-0.0536595\pi$
$110$	0.657427	+	0.0760136i	0.0626832	+	0.00724762i
$111$	−9.19013			−0.872289
$112$	−5.25547	+	9.18586i	−0.496596	+	0.867982i
$113$	−11.6306	−	8.45015i	−1.09412	−	0.794924i	−0.114029	−	0.993477i	$-0.536376\pi$
$113$	−11.6306	−	8.45015i	−1.09412	−	0.794924i	−0.980090	+	0.198554i	$0.936376\pi$
$114$	1.44058	+	2.15112i	0.134923	+	0.201471i
$115$	−0.804753	−	0.261480i	−0.0750436	−	0.0243831i
$116$	−9.32368	−	3.83923i	−0.865682	−	0.356463i
$117$	−1.76130	+	1.27966i	−0.162833	+	0.118305i
$118$	0.227360	+	0.178852i	0.0209302	+	0.0164646i
$119$	−8.68211	−	3.33520i	−0.795888	−	0.305737i
$120$	−0.849860	−	0.0978919i	−0.0775813	−	0.00893626i
$121$	−10.8702	−	1.68481i	−0.988201	−	0.153165i
$122$	0.300763	−	7.86402i	0.0272298	−	0.711975i
$123$	6.54109	+	20.1314i	0.589790	+	1.81519i
$124$	−3.20661	−	2.72715i	−0.287962	−	0.244905i
$125$	1.13923	−	0.827700i	0.101896	−	0.0740318i
$126$	−3.05553	−	5.12658i	−0.272208	−	0.456712i
$127$	1.85675	+	0.603294i	0.164760	+	0.0535337i	0.390235	−	0.920715i	$-0.372394\pi$
$127$	1.85675	+	0.603294i	0.164760	+	0.0535337i	−0.225476	+	0.974249i	$0.572394\pi$
$128$	3.99327	+	10.5855i	0.352958	+	0.935639i
$129$	3.15022	−	4.33590i	0.277361	−	0.381755i
$130$	0.262055	−	0.0742024i	0.0229838	−	0.00650798i
$131$		−	15.3199i		−	1.33851i	−0.743033	−	0.669255i	$-0.766613\pi$
$131$		−	15.3199i		−	1.33851i	0.743033	−	0.669255i	$-0.233387\pi$
$132$	14.0522	+	2.17180i	1.22309	+	0.189031i
$133$	1.42237	−	1.75560i	0.123335	−	0.152230i
$134$	−7.82620	+	2.21603i	−0.676081	+	0.191436i
$135$	−0.249774	+	0.343785i	−0.0214971	+	0.0295883i
$136$	−8.65985	+	4.88541i	−0.742576	+	0.418920i
$137$	3.32943	−	10.2469i	0.284453	−	0.875455i	−0.702110	−	0.712069i	$-0.747758\pi$
$137$	3.32943	−	10.2469i	0.284453	−	0.875455i	0.986562	−	0.163386i	$-0.0522416\pi$
$138$	−17.0630	−	6.27464i	−1.45250	−	0.534133i
$139$	−6.11328	−	8.41420i	−0.518521	−	0.713683i	0.466806	−	0.884360i	$-0.345405\pi$
$139$	−6.11328	−	8.41420i	−0.518521	−	0.713683i	−0.985327	+	0.170677i	$0.945405\pi$
$140$	0.137411	+	0.733865i	0.0116134	+	0.0620229i
$141$	−26.1179	+	8.48621i	−2.19952	+	0.714668i
$142$	−4.74128	−	0.181332i	−0.397879	−	0.0152171i
$143$	−4.40008	+	1.06407i	−0.367953	+	0.0889819i
$144$	−6.30572	−	0.971775i	−0.525476	−	0.0809813i
$145$	−0.676541	+	0.219822i	−0.0561837	+	0.0182552i
$146$	−10.9582	−	8.62025i	−0.906910	−	0.713417i
$147$	−10.0459	+	11.1461i	−0.828575	+	0.919317i
$148$	7.92860	+	3.26477i	0.651727	+	0.268363i
$149$	14.6704	+	4.76669i	1.20184	+	0.390503i	0.840439	−	0.541906i	$-0.182297\pi$
$149$	14.6704	+	4.76669i	1.20184	+	0.390503i	0.361405	+	0.932409i	$0.382297\pi$
$150$	12.5441	−	8.40065i	1.02422	−	0.685911i
$151$	−5.59892	+	7.70625i	−0.455634	+	0.627126i	−0.973596	−	0.228277i	$-0.926691\pi$
$151$	−5.59892	+	7.70625i	−0.455634	+	0.627126i	0.517962	+	0.855403i	$0.326691\pi$
$152$	−0.478651	−	2.36760i	−0.0388237	−	0.192037i
$153$		−	5.60708i		−	0.453306i
$154$	−1.81081	−	12.2768i	−0.145919	−	0.989297i
$155$	−0.296974			−0.0238535
$156$	5.68713	−	1.37791i	0.455335	−	0.110321i
$157$	3.91815	+	2.84670i	0.312702	+	0.227192i	0.733055	−	0.680169i	$-0.238094\pi$
$157$	3.91815	+	2.84670i	0.312702	+	0.227192i	−0.420353	+	0.907361i	$0.638094\pi$
$158$	−9.82344	+	6.57865i	−0.781511	+	0.523369i
$159$	−6.00829	+	18.4916i	−0.476488	+	1.46648i
$160$	0.698424	+	0.386365i	0.0552153	+	0.0305448i
$161$	−0.834289	+	15.8447i	−0.0657512	+	1.24874i
$162$	−9.82879	+	12.4945i	−0.772223	+	0.981664i
$163$	2.15311	+	6.62660i	0.168645	+	0.519035i	0.999286	−	0.0377722i	$-0.0120261\pi$
$163$	2.15311	+	6.62660i	0.168645	+	0.519035i	−0.830642	+	0.556807i	$0.812026\pi$
$164$	1.50844	−	19.6917i	0.117789	−	1.53766i
$165$	0.854448	−	0.525553i	0.0665187	−	0.0409143i
$166$	17.0415	+	0.651758i	1.32267	+	0.0505862i
$167$	−2.17727	−	6.70095i	−0.168482	−	0.518535i	0.830794	−	0.556580i	$-0.187887\pi$
$167$	−2.17727	−	6.70095i	−0.168482	−	0.518535i	−0.999276	+	0.0380455i	$0.987887\pi$
$168$	2.34757	+	15.8686i	0.181119	+	1.22429i
$169$	9.01003	−	6.54617i	0.693079	−	0.503551i
$170$	−0.242099	+	0.658353i	−0.0185682	+	0.0504934i
$171$	1.29550	+	0.420935i	0.0990697	+	0.0321897i
$172$	−4.25810	+	2.62160i	−0.324677	+	0.199895i
$173$	−18.6753	−	13.5684i	−1.41986	−	1.03159i	−0.991795	−	0.127839i	$-0.959196\pi$
$173$	−18.6753	−	13.5684i	−1.41986	−	1.03159i	−0.428064	−	0.903749i	$-0.640804\pi$
$174$	−14.7055	+	4.16395i	−1.11482	+	0.315668i
$175$	−10.2377	−	8.29449i	−0.773898	−	0.627005i
$176$	−11.3518	−	6.86569i	−0.855670	−	0.517521i
$177$	0.438472			0.0329576
$178$	4.47576	+	15.8067i	0.335472	+	1.18476i
$179$	14.9097	+	10.8325i	1.11440	+	0.809659i	0.983351	−	0.181717i	$-0.0581654\pi$
$179$	14.9097	+	10.8325i	1.11440	+	0.809659i	0.131049	+	0.991376i	$0.458165\pi$
$180$	−0.383293	+	0.235983i	−0.0285690	+	0.0175892i
$181$	3.75918	−	11.5696i	0.279417	−	0.859959i	−0.708599	−	0.705611i	$-0.750673\pi$
$181$	3.75918	−	11.5696i	0.279417	−	0.859959i	0.988017	−	0.154347i	$-0.0493275\pi$
$182$	−2.61469	−	4.38694i	−0.193814	−	0.325182i
$183$	−7.01149	−	9.65049i	−0.518304	−	0.713385i
$184$	12.4917	+	11.4749i	0.920898	+	0.845941i
$185$	0.575312	−	0.186930i	0.0422978	−	0.0137434i
$186$	−6.37588	−	0.243848i	−0.467502	−	0.0178798i
$187$	4.44388	−	10.7789i	0.324969	−	0.788231i
$188$	25.5474	+	1.95701i	1.86323	+	0.142729i
$189$	7.43821	+	2.85736i	0.541050	+	0.207842i
$190$	−0.133936	−	0.105360i	−0.00971675	−	0.00764365i
$191$	11.0474	+	15.2054i	0.799359	+	1.10022i	0.992879	+	0.119127i	$0.0380095\pi$
$191$	11.0474	+	15.2054i	0.799359	+	1.10022i	−0.193520	+	0.981096i	$0.561991\pi$
$192$	14.6776	+	8.86856i	1.05926	+	0.640033i
$193$	−3.27430	+	10.0773i	−0.235689	+	0.725377i	0.761340	+	0.648353i	$0.224542\pi$
$193$	−3.27430	+	10.0773i	−0.235689	+	0.725377i	−0.997029	+	0.0770239i	$0.975458\pi$
$194$	15.1274	−	10.1306i	1.08608	−	0.727337i
$195$	0.242655	−	0.333986i	0.0173769	−	0.0239172i
$196$	12.6266	−	6.04730i	0.901898	−	0.431950i
$197$		−	1.00811i		−	0.0718246i	−0.999355	−	0.0359123i	$-0.988566\pi$
$197$		−	1.00811i		−	0.0718246i	0.999355	−	0.0359123i	$-0.0114337\pi$
$198$	6.51760	−	3.67317i	0.463186	−	0.261041i
$199$	−14.0018			−0.992563			−0.496281	−	0.868162i	$-0.665302\pi$
$199$	−14.0018			−0.992563			−0.496281	+	0.868162i	$0.665302\pi$
$200$	−13.8065	+	2.79123i	−0.976267	+	0.197370i
$201$	−7.24681	+	9.97438i	−0.511151	+	0.703538i
$202$	10.0553	+	15.0148i	0.707485	+	1.05644i
$203$	7.26209	+	11.1887i	0.509699	+	0.785289i
$204$	−5.73834	+	13.9357i	−0.401764	+	0.975696i
$205$	−0.818958	−	1.12720i	−0.0571985	−	0.0787270i
$206$	−9.23443	+	11.7390i	−0.643393	+	0.817894i
$207$	−9.09733	+	2.95590i	−0.632308	+	0.205449i
$208$	−5.39596	−	0.831572i	−0.374142	−	0.0576592i
$209$	2.15683	+	1.83594i	0.149191	+	0.126995i
$210$	0.851447	+	0.745498i	0.0587554	+	0.0514443i
$211$	−0.378511	−	1.16494i	−0.0260578	−	0.0801975i	0.937182	−	0.348841i	$-0.113425\pi$
$211$	−0.378511	−	1.16494i	−0.0260578	−	0.0801975i	−0.963240	+	0.268643i	$0.913425\pi$
$212$	11.7526	−	13.8188i	0.807174	−	0.949082i
$213$	−5.81835	+	4.22728i	−0.398667	+	0.289649i
$214$	4.39118	+	1.61479i	0.300175	+	0.110385i
$215$	−0.109013	+	0.335508i	−0.00743464	+	0.0228815i
$216$	7.41914	−	4.18547i	0.504808	−	0.284785i
$217$	1.43994	+	5.37922i	0.0977496	+	0.365165i
$218$	1.34981	+	4.76703i	0.0914208	+	0.322864i
$219$	−21.1334			−1.42806
$220$	−0.923859	+	0.149870i	−0.0622866	+	0.0101042i
$221$		−	4.79812i		−	0.322757i
$222$	12.5052	−	3.54091i	0.839292	−	0.237650i
$223$	−10.0803	−	7.32379i	−0.675029	−	0.490437i	0.196676	−	0.980469i	$-0.436985\pi$
$223$	−10.0803	−	7.32379i	−0.675029	−	0.490437i	−0.871705	+	0.490031i	$0.836985\pi$
$224$	3.61195	−	14.5242i	0.241333	−	0.970442i
$225$	2.45466	−	7.55466i	0.163644	−	0.503644i
$226$	19.0818	+	7.01704i	1.26930	+	0.466767i
$227$	3.20900	+	4.41681i	0.212989	+	0.293154i	0.902122	−	0.431480i	$-0.142009\pi$
$227$	3.20900	+	4.41681i	0.212989	+	0.293154i	−0.689133	+	0.724635i	$0.742009\pi$
$228$	−2.78903	−	2.37201i	−0.184708	−	0.157090i
$229$	−8.32309	−	25.6159i	−0.550006	−	1.69274i	−0.708781	−	0.705428i	$-0.750755\pi$
$229$	−8.32309	−	25.6159i	−0.550006	−	1.69274i	0.158776	−	0.987315i	$-0.449245\pi$
$230$	1.19579	+	0.0457334i	0.0788479	+	0.00301557i
$231$	−13.6626	−	12.9287i	−0.898931	−	0.850649i
$232$	14.1661	+	1.63174i	0.930051	+	0.107129i
$233$	−5.91402	−	18.2015i	−0.387440	−	1.19242i	−0.934695	−	0.355452i	$-0.884327\pi$
$233$	−5.91402	−	18.2015i	−0.387440	−	1.19242i	0.547255	−	0.836966i	$-0.315673\pi$
$234$	1.90359	−	2.41988i	0.124442	−	0.158192i
$235$	1.46239	−	1.06249i	0.0953961	−	0.0693093i
$236$	−0.378283	−	0.155766i	−0.0246241	−	0.0101395i
$237$	−5.53774	+	17.0434i	−0.359715	+	1.10709i
$238$	13.0989	+	1.19309i	0.849077	+	0.0773365i
$239$	8.68777	−	11.9577i	0.561965	−	0.773479i	−0.429609	−	0.903015i	$-0.641349\pi$
$239$	8.68777	−	11.9577i	0.561965	−	0.773479i	0.991575	+	0.129536i	$0.0413487\pi$
$240$	1.19414	−	0.194243i	0.0770811	−	0.0125383i
$241$			5.01779i			0.323224i	0.986854	+	0.161612i	$0.0516694\pi$
$241$			5.01779i			0.323224i	−0.986854	+	0.161612i	$0.948331\pi$
$242$	15.4404	−	1.89568i	0.992547	−	0.121859i
$243$			15.0611i			0.966173i
$244$	2.62071	+	10.8166i	0.167774	+	0.692461i
$245$	0.402171	−	0.902097i	0.0256937	−	0.0576328i
$246$	−16.6571	−	24.8729i	−1.06202	−	1.58584i
$247$	1.10860	+	0.360205i	0.0705382	+	0.0229193i
$248$	5.41404	+	2.47539i	0.343792	+	0.157188i
$249$	20.9128	−	15.1940i	1.32529	−	0.962881i
$250$	−1.23126	+	1.56520i	−0.0778719	+	0.0989922i
$251$	4.84544	−	1.57438i	0.305841	−	0.0993739i	−0.152076	−	0.988369i	$-0.548596\pi$
$251$	4.84544	−	1.57438i	0.305841	−	0.0993739i	0.457917	+	0.888995i	$0.348596\pi$
$252$	6.13295	+	5.79854i	0.386340	+	0.365274i
$253$	−19.8311	−	1.52773i	−1.24677	−	0.0960474i
$254$	−2.75895	−	0.105517i	−0.173112	−	0.00662075i
$255$	0.328558	+	1.01120i	0.0205751	+	0.0633237i
$256$	−9.51225	−	12.8653i	−0.594516	−	0.804084i
$257$	−2.32725	−	3.20319i	−0.145170	−	0.199809i	0.730240	−	0.683191i	$-0.239408\pi$
$257$	−2.32725	−	3.20319i	−0.145170	−	0.199809i	−0.875410	+	0.483382i	$0.839408\pi$
$258$	−2.61595	+	7.11369i	−0.162862	+	0.442879i
$259$	−6.17548	−	9.51452i	−0.383726	−	0.591203i
$260$	−0.327993	+	0.201937i	−0.0203413	+	0.0125236i
$261$	−4.72670	+	6.50575i	−0.292575	+	0.402696i
$262$	5.90269	+	20.8461i	0.364669	+	1.28788i
$263$		−	14.7982i		−	0.912494i	−0.889853	−	0.456247i	$-0.849193\pi$
$263$		−	14.7982i		−	0.912494i	0.889853	−	0.456247i	$-0.150807\pi$
$264$	−19.9579	+	2.45904i	−1.22832	+	0.151344i
$265$		−	1.27981i		−	0.0786178i
$266$	−1.25902	+	2.93691i	−0.0771957	+	0.180074i
$267$	20.1454	+	14.6365i	1.23288	+	0.895739i
$268$	9.79542	−	6.03078i	0.598350	−	0.368389i
$269$	−4.45779	+	13.7197i	−0.271796	+	0.836503i	0.718253	+	0.695782i	$0.244942\pi$
$269$	−4.45779	+	13.7197i	−0.271796	+	0.836503i	−0.990049	+	0.140721i	$0.955058\pi$
$270$	0.207413	−	0.564030i	0.0126228	−	0.0343258i
$271$	7.38846	−	5.36803i	0.448817	−	0.326085i	−0.340312	−	0.940313i	$-0.610533\pi$
$271$	7.38846	−	5.36803i	0.448817	−	0.326085i	0.789128	+	0.614228i	$0.210533\pi$
$272$	9.90127	−	9.98424i	0.600353	−	0.605384i
$273$	−7.22620	−	2.77591i	−0.437349	−	0.168006i
$274$	−0.582324	+	15.2260i	−0.0351795	+	0.919835i
$275$	10.7062	−	12.5774i	0.645608	−	0.758448i
$276$	25.6354	+	1.96375i	1.54307	+	0.118204i
$277$	10.5129	−	3.41585i	0.631660	−	0.205239i	0.0243495	−	0.999704i	$-0.492249\pi$
$277$	10.5129	−	3.41585i	0.631660	−	0.205239i	0.607310	+	0.794465i	$0.292249\pi$
$278$	11.5604	+	9.09393i	0.693345	+	0.545418i
$279$	−2.71598	+	1.97328i	−0.162602	+	0.118137i
$280$	−0.469732	−	0.945638i	−0.0280719	−	0.0565127i
$281$	−9.20473	+	28.3292i	−0.549108	+	1.68998i	0.161909	+	0.986806i	$0.448235\pi$
$281$	−9.20473	+	28.3292i	−0.549108	+	1.68998i	−0.711017	+	0.703175i	$0.751765\pi$
$282$	32.2693	−	21.6104i	1.92161	−	1.28688i
$283$	−10.0363	+	13.8138i	−0.596597	+	0.821145i	−0.995391	−	0.0958951i	$-0.969429\pi$
$283$	−10.0363	+	13.8138i	−0.596597	+	0.821145i	0.398795	+	0.917040i	$0.369429\pi$
$284$	6.52140	−	1.58005i	0.386974	−	0.0937585i
$285$	−0.258301			−0.0153004
$286$	5.57727	−	3.14322i	0.329791	−	0.185863i
$287$	−16.4466	+	20.2996i	−0.970811	+	1.19825i
$288$	8.95471	−	1.10725i	0.527661	−	0.0652451i
$289$	−3.75584	−	2.72878i	−0.220932	−	0.160516i
$290$	0.835885	−	0.559782i	0.0490848	−	0.0328716i
$291$	8.52771	−	26.2456i	0.499903	−	1.53854i
$292$	18.2324	+	7.50757i	1.06697	+	0.439348i
$293$	−9.06325	+	6.58484i	−0.529481	+	0.384690i	−0.820164	−	0.572129i	$-0.806118\pi$
$293$	−9.06325	+	6.58484i	−0.529481	+	0.384690i	0.290683	+	0.956820i	$0.406118\pi$
$294$	9.37513	−	19.0374i	0.546769	−	1.11028i
$295$	−0.0274488	+	0.00891865i	−0.00159813	+	0.000519264i
$296$	−12.0465	−	1.38758i	−0.700187	−	0.0806517i
$297$	−3.80720	+	9.23459i	−0.220916	+	0.535845i
$298$	−21.7988	−	0.833704i	−1.26277	−	0.0482952i
$299$	−7.78481	+	2.52944i	−0.450207	+	0.146281i
$300$	−13.8323	+	16.2641i	−0.798606	+	0.939007i
$301$	6.60579	+	0.347822i	0.380752	+	0.0200481i
$302$	4.64937	−	12.6433i	0.267541	−	0.727538i
$303$	26.0503	+	8.46426i	1.49655	+	0.486259i
$304$	1.56353	+	3.03721i	0.0896746	+	0.174196i
$305$	0.635221	+	0.461515i	0.0363726	+	0.0264263i
$306$	2.16038	+	7.62965i	0.123501	+	0.436158i
$307$			7.36491i			0.420338i	0.977665	+	0.210169i	$0.0674014\pi$
$307$			7.36491i			0.420338i	−0.977665	+	0.210169i	$0.932599\pi$
$308$	7.19420	+	16.0076i	0.409927	+	0.912118i
$309$			22.6391i			1.28789i
$310$	0.404097	−	0.114422i	0.0229512	−	0.00649875i
$311$	22.4146	+	16.2852i	1.27102	+	0.923448i	0.999243	−	0.0389127i	$-0.0123894\pi$
$311$	22.4146	+	16.2852i	1.27102	+	0.923448i	0.271775	+	0.962361i	$0.412389\pi$
$312$	−7.20767	+	4.06617i	−0.408054	+	0.230201i
$313$	18.3031	+	5.94704i	1.03455	+	0.336146i	0.776589	−	0.630008i	$-0.216948\pi$
$313$	18.3031	+	5.94704i	1.03455	+	0.336146i	0.257964	+	0.966155i	$0.416948\pi$
$314$	−6.42831	−	2.36391i	−0.362770	−	0.133403i
$315$	0.594620	+	0.0313092i	0.0335030	+	0.00176407i
$316$	10.8322	−	12.7366i	0.609359	−	0.716489i
$317$	−12.2152	+	3.96896i	−0.686074	+	0.222919i	−0.631253	−	0.775577i	$-0.717459\pi$
$317$	−12.2152	+	3.96896i	−0.686074	+	0.222919i	−0.0548213	+	0.998496i	$0.517459\pi$
$318$	1.05086	−	27.4768i	0.0589294	−	1.54082i
$319$	−14.2426	+	8.76032i	−0.797432	+	0.490484i
$320$	−1.09922	−	0.256634i	−0.0614483	−	0.0143463i
$321$	6.74464	−	2.19147i	0.376449	−	0.122316i
$322$	−4.96964	−	21.8816i	−0.276947	−	1.21941i
$323$	−2.42876	+	1.76460i	−0.135140	+	0.0981848i
$324$	8.56011	−	20.7885i	0.475562	−	1.15492i
$325$	2.10051	−	6.46471i	0.116515	−	0.358598i
$326$	−5.48297	−	8.18734i	−0.303673	−	0.453455i
$327$	6.07551	+	4.41412i	0.335976	+	0.244101i
$328$	5.53453	+	27.3760i	0.305593	+	1.51159i
$329$	−26.3361	−	21.3373i	−1.45196	−	1.17636i
$330$	−0.960168	+	1.04434i	−0.0528555	+	0.0574892i
$331$	−10.6088			−0.583112			−0.291556	−	0.956554i	$-0.594173\pi$
$331$	−10.6088			−0.583112			−0.291556	+	0.956554i	$0.594173\pi$
$332$	−23.4397	+	5.67912i	−1.28642	+	0.311682i
$333$	4.01946	−	5.53231i	0.220265	−	0.303169i
$334$	5.54448	+	8.27920i	0.303381	+	0.453017i
$335$	0.250776	−	0.771809i	0.0137014	−	0.0421684i
$336$	−9.30844	−	20.6881i	−0.507817	−	1.12863i
$337$	17.0498	−	12.3874i	0.928762	−	0.674785i	−0.0169277	−	0.999857i	$-0.505389\pi$
$337$	17.0498	−	12.3874i	0.928762	−	0.674785i	0.945689	+	0.325072i	$0.105389\pi$
$338$	−9.73789	+	12.3790i	−0.529671	+	0.673328i
$339$	29.3087	−	9.52298i	1.59183	−	0.517217i
$340$	0.0757688	−	0.989111i	0.00410914	−	0.0536421i
$341$	−6.78504	+	1.64083i	−0.367431	+	0.0888557i
$342$	−1.92500	−	0.0736224i	−0.104092	−	0.00398104i
$343$	−18.2901	−	2.91069i	−0.987573	−	0.157162i
$344$	4.78398	−	5.20788i	0.257935	−	0.280790i
$345$	1.46743	−	1.06615i	0.0790040	−	0.0573998i
$346$	30.6396	+	11.2673i	1.64720	+	0.605732i
$347$	9.36286	−	28.8159i	0.502625	−	1.54692i	−0.302103	−	0.953275i	$-0.597689\pi$
$347$	9.36286	−	28.8159i	0.502625	−	1.54692i	0.804727	−	0.593645i	$-0.202311\pi$
$348$	18.4057	−	11.3319i	0.986648	−	0.607454i
$349$	17.8819	+	12.9920i	0.957196	+	0.695444i	0.952498	−	0.304545i	$-0.0985045\pi$
$349$	17.8819	+	12.9920i	0.957196	+	0.695444i	0.00469812	+	0.999989i	$0.498505\pi$
$350$	17.1264	+	7.34192i	0.915446	+	0.392442i
$351$			4.11069i			0.219412i
$352$	18.0918	+	4.96850i	0.964297	+	0.264822i
$353$		−	13.8845i		−	0.738998i	−0.929231	−	0.369499i	$-0.879529\pi$
$353$		−	13.8845i		−	0.738998i	0.929231	−	0.369499i	$-0.120471\pi$
$354$	−0.596635	+	0.168941i	−0.0317108	+	0.00897909i
$355$	0.278251	−	0.382979i	0.0147680	−	0.0203264i
$356$	−12.1805	−	19.7840i	−0.645563	−	1.04855i
$357$	16.7232	−	10.8543i	0.885087	−	0.574473i
$358$	−24.4615	−	8.99535i	−1.29283	−	0.475419i
$359$	4.06610	+	5.59650i	0.214600	+	0.295372i	0.902723	−	0.430222i	$-0.141565\pi$
$359$	4.06610	+	5.59650i	0.214600	+	0.295372i	−0.688123	+	0.725594i	$0.741565\pi$
$360$	0.430630	−	0.468787i	0.0226962	−	0.0247072i
$361$	5.64595	+	17.3764i	0.297155	+	0.914550i
$362$	−0.657488	+	17.1913i	−0.0345568	+	0.903553i
$363$	16.6181	−	16.7284i	0.872222	−	0.878014i
$364$	5.24812	+	4.96196i	0.275076	+	0.260077i
$365$	1.32297	−	0.429859i	0.0692474	−	0.0224999i
$366$	13.2589	+	10.4301i	0.693055	+	0.545190i
$367$	3.90880	−	2.83991i	0.204038	−	0.148242i	−0.481074	−	0.876680i	$-0.659753\pi$
$367$	3.90880	−	2.83991i	0.204038	−	0.148242i	0.685112	+	0.728438i	$0.259753\pi$
$368$	−21.4188	−	10.8011i	−1.11653	−	0.563047i
$369$	−14.9796	−	4.86717i	−0.779808	−	0.253375i
$370$	−0.710813	+	0.476023i	−0.0369534	+	0.0247473i
$371$	−23.1817	+	6.20542i	−1.20353	+	0.322169i
$372$	8.76972	−	2.12478i	0.454689	−	0.110165i
$373$		−	8.45390i		−	0.437726i	−0.975756	−	0.218863i	$-0.929765\pi$
$373$		−	8.45390i		−	0.437726i	0.975756	−	0.218863i	$-0.0702348\pi$
$374$	−1.89381	+	16.3792i	−0.0979268	+	0.846949i
$375$			3.01856i			0.155878i
$376$	−35.5168	+	7.18034i	−1.83164	+	0.370298i
$377$	−4.04476	+	5.56713i	−0.208315	+	0.286722i
$378$	−11.2222	−	1.02215i	−0.577209	−	0.0525739i
$379$	4.26684	−	13.1320i	0.219173	−	0.674544i	−0.779658	−	0.626205i	$-0.784607\pi$
$379$	4.26684	−	13.1320i	0.219173	−	0.674544i	0.998831	−	0.0483389i	$-0.0153927\pi$
$380$	0.222844	+	0.0917608i	0.0114317	+	0.00470723i
$381$	−3.38570	+	2.45986i	−0.173455	+	0.126022i
$382$	−20.8909	−	16.4337i	−1.06887	−	0.840823i
$383$	−4.95446	−	15.2483i	−0.253161	−	0.779150i	−0.994186	−	0.107673i	$-0.965660\pi$
$383$	−4.95446	−	15.2483i	−0.253161	−	0.779150i	0.741025	−	0.671477i	$-0.234340\pi$
$384$	−23.3890	−	6.41240i	−1.19357	−	0.327231i
$385$	1.11827	+	0.531452i	0.0569921	+	0.0270853i
$386$	0.572682	−	14.9738i	0.0291487	−	0.762149i
$387$	1.23234	+	3.79276i	0.0626434	+	0.192797i
$388$	−16.6808	+	19.6134i	−0.846839	+	0.995720i
$389$	7.96222	+	10.9591i	0.403701	+	0.555646i	0.961668	−	0.274217i	$-0.0884186\pi$
$389$	7.96222	+	10.9591i	0.403701	+	0.555646i	−0.557967	+	0.829863i	$0.688419\pi$
$390$	−0.201501	+	0.547953i	−0.0102034	+	0.0277467i
$391$	6.51455	−	20.0497i	0.329455	−	1.01396i
$392$	−14.8512	+	13.0936i	−0.750098	+	0.661327i
$393$	26.5680	+	19.3028i	1.34018	+	0.973698i
$394$	0.388418	+	1.37175i	0.0195682	+	0.0691076i
$395$		−	1.17957i		−	0.0593508i
$396$	−7.45336	+	7.50933i	−0.374545	+	0.377358i
$397$	−23.0467			−1.15668			−0.578340	−	0.815796i	$-0.696299\pi$
$397$	−23.0467			−1.15668			−0.578340	+	0.815796i	$0.696299\pi$
$398$	19.0525	−	5.39482i	0.955016	−	0.270418i
$399$	1.25243	+	4.67872i	0.0626998	+	0.234229i
$400$	17.7113	−	9.11763i	0.885564	−	0.455882i
$401$	−10.2340	+	31.4969i	−0.511060	+	1.57288i	0.279278	+	0.960210i	$0.409905\pi$
$401$	−10.2340	+	31.4969i	−0.511060	+	1.57288i	−0.790338	+	0.612671i	$0.790095\pi$
$402$	6.01778	−	16.3645i	0.300140	−	0.816185i
$403$	−2.32413	+	1.68858i	−0.115773	+	0.0841143i
$404$	−19.4675	−	16.5567i	−0.968543	−	0.823725i
$405$	−0.490124	−	1.50845i	−0.0243545	−	0.0749553i
$406$	−14.1926	−	12.4265i	−0.704365	−	0.616719i
$407$	12.1115	−	7.44954i	0.600345	−	0.369260i
$408$	2.43889	−	21.1735i	0.120743	−	1.04825i
$409$	−0.318284	+	0.103417i	−0.0157381	+	0.00511362i	−0.316875	−	0.948467i	$-0.602634\pi$
$409$	−0.318284	+	0.103417i	−0.0157381	+	0.00511362i	0.301137	+	0.953581i	$0.402634\pi$
$410$	1.54867	+	1.21826i	0.0764835	+	0.0601655i
$411$	13.5753	+	18.6849i	0.669623	+	0.921656i
$412$	8.04247	−	19.5314i	0.396224	−	0.962243i
$413$	0.294639	+	0.453949i	0.0144982	+	0.0223373i
$414$	11.2400	−	7.52729i	0.552416	−	0.369946i
$415$	−1.00011	+	1.37653i	−0.0490935	+	0.0675714i
$416$	7.66277	−	0.947498i	0.375698	−	0.0464549i
$417$	22.2946			1.09177
$418$	−3.64221	−	1.66718i	−0.178146	−	0.0815446i
$419$			24.3604i			1.19008i	0.803695	+	0.595042i	$0.202865\pi$
$419$			24.3604i			1.19008i	−0.803695	+	0.595042i	$0.797135\pi$
$420$	−1.44581	−	0.686354i	−0.0705485	−	0.0334906i
$421$	−14.7772	+	20.3390i	−0.720196	+	0.991264i	0.279322	+	0.960198i	$0.409890\pi$
$421$	−14.7772	+	20.3390i	−0.720196	+	0.991264i	−0.999517	+	0.0310668i	$0.990110\pi$
$422$	0.963889	+	1.43931i	0.0469214	+	0.0700645i
$423$	6.31453	−	19.4341i	0.307023	−	0.944919i
$424$	−10.6677	+	23.3317i	−0.518068	+	1.13309i
$425$	10.2901	+	14.1632i	0.499146	+	0.687015i
$426$	6.28838	−	7.99391i	0.304673	−	0.387306i
$427$	5.27963	−	13.7438i	0.255499	−	0.665109i
$428$	−6.59732	−	0.505374i	−0.318893	−	0.0244282i
$429$	3.69868	−	8.97137i	0.178574	−	0.433142i
$430$	0.0190666	−	0.498534i	0.000919476	−	0.0240414i
$431$	−17.0823	+	5.55037i	−0.822824	+	0.267352i	−0.690020	−	0.723791i	$-0.742398\pi$
$431$	−17.0823	+	5.55037i	−0.822824	+	0.267352i	−0.132804	+	0.991142i	$0.542398\pi$
$432$	−8.48270	+	8.55378i	−0.408124	+	0.411544i
$433$	6.96480	+	9.58622i	0.334707	+	0.460684i	0.942886	−	0.333115i	$-0.108100\pi$
$433$	6.96480	+	9.58622i	0.334707	+	0.460684i	−0.608179	+	0.793800i	$0.708100\pi$
$434$	−4.03194	−	6.76479i	−0.193539	−	0.324720i
$435$	0.471211	−	1.45024i	0.0225928	−	0.0695335i
$436$	−3.67342	−	5.96650i	−0.175925	−	0.285744i
$437$	4.14338	+	3.01035i	0.198205	+	0.144004i
$438$	28.7565	−	8.14256i	1.37404	−	0.389067i
$439$	23.9070			1.14102			0.570509	−	0.821291i	$-0.306746\pi$
$439$	23.9070			1.14102			0.570509	+	0.821291i	$0.306746\pi$
$440$	1.19937	−	0.559888i	0.0571775	−	0.0266916i
$441$	−2.31603	−	10.9224i	−0.110287	−	0.520116i
$442$	1.84869	+	6.52888i	0.0879332	+	0.310547i
$443$	−4.60521	−	3.34588i	−0.218800	−	0.158968i	0.472986	−	0.881070i	$-0.343176\pi$
$443$	−4.60521	−	3.34588i	−0.218800	−	0.158968i	−0.691786	+	0.722102i	$0.743176\pi$
$444$	−15.6517	+	9.63634i	−0.742796	+	0.457320i
$445$	−1.55883	−	0.506496i	−0.0738959	−	0.0240102i
$446$	16.5383	+	6.08170i	0.783111	+	0.287977i
$447$	−26.7508	+	19.4356i	−1.26527	+	0.919273i
$448$	0.681276	+	21.1550i	0.0321873	+	0.999482i
$449$	5.37460	+	16.5413i	0.253643	+	0.780632i	0.994094	+	0.108522i	$0.0346119\pi$
$449$	5.37460	+	16.5413i	0.253643	+	0.780632i	−0.740451	+	0.672110i	$0.765388\pi$
$450$	−0.429325	+	11.2255i	−0.0202386	+	0.529176i
$451$	−24.9389	−	21.2286i	−1.17433	−	0.999615i
$452$	−28.6685	−	2.19609i	−1.34845	−	0.103296i
$453$	−6.30976	−	19.4194i	−0.296458	−	0.912405i
$454$	−6.06832	−	4.77362i	−0.284800	−	0.224037i
$455$	0.508831	+	0.0267920i	0.0238543	+	0.00125603i
$456$	4.70901	+	2.15304i	0.220519	+	0.100825i
$457$	−10.6856	+	32.8869i	−0.499851	+	1.53838i	0.309407	+	0.950930i	$0.399869\pi$
$457$	−10.6856	+	32.8869i	−0.499851	+	1.53838i	−0.809258	+	0.587453i	$0.800131\pi$
$458$	21.1950	+	31.6491i	0.990378	+	1.47886i
$459$	−8.56509	−	6.22290i	−0.399784	−	0.290460i
$460$	−1.64475	+	0.398500i	−0.0766868	+	0.0185802i
$461$	22.5588			1.05067			0.525334	−	0.850896i	$-0.323940\pi$
$461$	22.5588			1.05067			0.525334	+	0.850896i	$0.323940\pi$
$462$	23.5722	+	12.3282i	1.09668	+	0.573562i
$463$			1.13655i			0.0528201i	0.999651	+	0.0264100i	$0.00840755\pi$
$463$			1.13655i			0.0528201i	−0.999651	+	0.0264100i	$0.991592\pi$
$464$	−19.9048	+	3.23780i	−0.924056	+	0.150311i
$465$	0.374181	−	0.515015i	0.0173522	−	0.0238833i
$466$	15.0602	+	22.4884i	0.697651	+	1.04175i
$467$	36.3592	+	11.8138i	1.68250	+	0.546678i	0.985394	−	0.170289i	$-0.0544702\pi$
$467$	36.3592	+	11.8138i	1.68250	+	0.546678i	0.697107	+	0.716967i	$0.254470\pi$
$468$	−1.65788	+	4.02621i	−0.0766355	+	0.186112i
$469$	−15.1961	−	0.800136i	−0.701690	−	0.0369468i
$470$	−1.58053	+	2.00920i	−0.0729045	+	0.0926776i
$471$	−9.87357	+	3.20812i	−0.454950	+	0.147822i
$472$	0.574751	+	0.0662032i	0.0264551	+	0.00304725i
$473$	−0.636923	+	8.26777i	−0.0292857	+	0.380153i
$474$	0.968562	−	25.3249i	0.0444875	−	1.16321i
$475$	−4.04487	+	1.31426i	−0.185592	+	0.0603023i
$476$	−18.2836	+	3.42349i	−0.838028	+	0.156915i
$477$	−8.50382	−	11.7045i	−0.389363	−	0.535912i
$478$	−7.21436	+	19.6184i	−0.329977	+	0.897324i
$479$	−12.9489	+	39.8527i	−0.591652	+	1.82092i	−0.0209192	+	0.999781i	$0.506659\pi$
$479$	−12.9489	+	39.8527i	−0.591652	+	1.82092i	−0.570733	+	0.821136i	$0.693341\pi$
$480$	−1.55004	+	0.724404i	−0.0707493	+	0.0330643i
$481$	3.43955	−	4.73413i	0.156830	−	0.215858i
$482$	−1.93333	−	6.82779i	−0.0880606	−	0.310997i
$483$	−26.4269	−	21.4108i	−1.20247	−	0.974226i
$484$	−20.2796	+	8.52859i	−0.921801	+	0.387663i
$485$			1.81646i			0.0824811i
$486$	−5.80297	−	20.4939i	−0.263228	−	0.929624i
$487$	0.925284	−	1.27354i	0.0419286	−	0.0577098i	−0.787538	−	0.616266i	$-0.788645\pi$
$487$	0.925284	−	1.27354i	0.0419286	−	0.0577098i	0.829467	+	0.558556i	$0.188645\pi$
$488$	−7.73361	−	13.7086i	−0.350084	−	0.620557i
$489$	−14.2048	−	4.61542i	−0.642364	−	0.208717i
$490$	−0.199667	+	1.38245i	−0.00902004	+	0.0624528i
$491$	20.4949	−	14.8904i	0.924924	−	0.671997i	−0.0198208	−	0.999804i	$-0.506310\pi$
$491$	20.4949	−	14.8904i	0.924924	−	0.671997i	0.944745	+	0.327807i	$0.106310\pi$
$492$	32.2489	+	27.4270i	1.45389	+	1.23651i
$493$	−5.47666	−	16.8554i	−0.246657	−	0.759131i
$494$	−1.64727	−	0.0630005i	−0.0741141	−	0.00283453i
$495$	−0.0573325	+	0.744223i	−0.00257691	+	0.0334503i
$496$	−8.32072	−	1.28231i	−0.373611	−	0.0575773i
$497$	−8.28624	−	3.18313i	−0.371689	−	0.142783i
$498$	−22.6022	+	28.7323i	−1.01283	+	1.28753i
$499$	−4.43635	+	3.22320i	−0.198598	+	0.144290i	−0.682640	−	0.730755i	$-0.739168\pi$
$499$	−4.43635	+	3.22320i	−0.198598	+	0.144290i	0.484042	+	0.875045i	$0.339168\pi$
$500$	1.07233	−	2.60420i	0.0479563	−	0.116463i
$501$	14.3642	+	4.66720i	0.641744	+	0.208515i
$502$	−5.98667	+	4.00920i	−0.267198	+	0.178939i
$503$	2.40582	+	1.74793i	0.107270	+	0.0779364i	0.640127	−	0.768269i	$-0.278882\pi$
$503$	2.40582	+	1.74793i	0.107270	+	0.0779364i	−0.532857	+	0.846205i	$0.678882\pi$
$504$	−10.5794	−	5.52718i	−0.471242	−	0.246200i
$505$	−1.80294			−0.0802299
$506$	27.5732	−	5.56202i	1.22578	−	0.247262i
$507$			23.8733i			1.06025i
$508$	3.79481	−	0.919429i	0.168367	−	0.0407931i
$509$	30.0657	+	21.8440i	1.33264	+	0.968218i	0.999681	+	0.0252757i	$0.00804635\pi$
$509$	30.0657	+	21.8440i	1.33264	+	0.968218i	0.332957	+	0.942942i	$0.391954\pi$
$510$	−0.836684	−	1.24936i	−0.0370490	−	0.0553227i
$511$	−14.2009	−	21.8793i	−0.628213	−	0.967883i
$512$	17.9004	+	13.8411i	0.791094	+	0.611694i
$513$	2.08079	−	1.51178i	0.0918690	−	0.0667467i
$514$	4.40090	+	3.46195i	0.194115	+	0.152700i
$515$	−0.460486	−	1.41723i	−0.0202914	−	0.0624506i
$516$	0.818703	−	10.6876i	0.0360414	−	0.470496i
$517$	27.5413	−	32.3550i	1.21127	−	1.42297i
$518$	12.0690	+	10.5672i	0.530280	+	0.464295i
$519$	47.0610	−	15.2911i	2.06575	−	0.671203i
$520$	0.368500	−	0.401153i	0.0161598	−	0.0175917i
$521$	−16.1704	−	22.2567i	−0.708439	−	0.975082i	−0.999829	−	0.0184782i	$-0.994118\pi$
$521$	−16.1704	−	22.2567i	−0.708439	−	0.975082i	0.291390	−	0.956604i	$-0.405882\pi$
$522$	3.92507	−	10.6736i	0.171796	−	0.467173i
$523$	−27.7905	−	9.02968i	−1.21519	−	0.394840i	−0.369865	−	0.929086i	$-0.620596\pi$
$523$	−27.7905	−	9.02968i	−1.21519	−	0.394840i	−0.845330	+	0.534245i	$0.820596\pi$
$524$	−16.0638	−	26.0913i	−0.701749	−	1.13981i
$525$	27.2837	−	7.30346i	1.19076	−	0.318749i
$526$	5.70165	+	20.1361i	0.248604	+	0.877975i
$527$		−	7.39884i		−	0.322299i
$528$	26.2095	−	11.0357i	1.14062	−	0.480268i
$529$	−12.9644			−0.563669
$530$	0.493102	+	1.74145i	0.0214190	+	0.0756438i
$531$	−0.191773	+	0.263953i	−0.00832223	+	0.0114546i
$532$	0.581598	−	4.48140i	0.0252155	−	0.194293i
$533$	−12.8184	−	4.16496i	−0.555228	−	0.180405i
$534$	−33.0515	−	12.1542i	−1.43028	−	0.525964i
$535$	−0.377646	+	0.274376i	−0.0163271	+	0.0118623i
$536$	−11.0052	+	11.9803i	−0.475350	+	0.517470i
$537$	−37.5717	+	12.2078i	−1.62134	+	0.526805i
$538$	0.779677	−	20.3861i	0.0336143	−	0.878909i
$539$	4.20428	−	22.8325i	0.181091	−	0.983466i
$540$	−0.0649133	+	0.847400i	−0.00279342	+	0.0364663i
$541$	−27.1456	+	8.82014i	−1.16708	+	0.379207i	−0.827552	−	0.561389i	$-0.810267\pi$
$541$	−27.1456	+	8.82014i	−1.16708	+	0.379207i	−0.339528	+	0.940596i	$0.610267\pi$
$542$	−7.98532	+	10.1511i	−0.342999	+	0.436027i
$543$	15.3276	+	21.0966i	0.657770	+	0.905342i
$544$	−9.62595	+	17.4006i	−0.412709	+	0.746046i
$545$	−0.470118	−	0.152751i	−0.0201376	−	0.00654311i
$546$	10.9023	+	0.993018i	0.466577	+	0.0424973i
$547$	−7.23699	−	5.25798i	−0.309431	−	0.224815i	0.422221	−	0.906493i	$-0.361251\pi$
$547$	−7.23699	−	5.25798i	−0.309431	−	0.224815i	−0.731652	+	0.681678i	$0.761251\pi$
$548$	−5.07411	−	20.9426i	−0.216755	−	0.894624i
$549$	8.87603			0.378820
$550$	−9.72208	+	21.2394i	−0.414551	+	0.905649i
$551$	4.30556			0.183423
$552$	−35.6392	+	7.20508i	−1.51690	+	0.306668i
$553$	−21.3662	+	5.71942i	−0.908582	+	0.243215i
$554$	−12.9890	+	8.69857i	−0.551849	+	0.369567i
$555$	−0.400704	+	1.23324i	−0.0170090	+	0.0523482i
$556$	−19.2342	−	7.92011i	−0.815713	−	0.335887i
$557$	8.72054	+	12.0028i	0.369501	+	0.508575i	0.952765	−	0.303708i	$-0.0982247\pi$
$557$	8.72054	+	12.0028i	0.369501	+	0.508575i	−0.583264	+	0.812283i	$0.698225\pi$
$558$	2.93539	−	3.73152i	0.124265	−	0.157968i
$559$	1.05454	+	3.24555i	0.0446025	+	0.137272i
$560$	1.00352	+	1.10576i	0.0424065	+	0.0467269i
$561$	13.0937	+	21.2878i	0.552816	+	0.898772i
$562$	1.60993	−	42.0946i	0.0679106	−	1.77565i
$563$	−4.11247	+	1.33622i	−0.173320	+	0.0563151i	−0.394391	−	0.918943i	$-0.629045\pi$
$563$	−4.11247	+	1.33622i	−0.173320	+	0.0563151i	0.221071	+	0.975258i	$0.429045\pi$
$564$	−35.5830	+	41.8388i	−1.49832	+	1.76173i
$565$	−1.64106	+	1.19230i	−0.0690398	+	0.0501603i
$566$	8.33419	−	22.6636i	0.350312	−	0.952622i
$567$	−24.9467	+	16.1919i	−1.04766	+	0.679995i
$568$	−8.26499	+	4.66265i	−0.346791	+	0.195641i
$569$	−14.7304	−	10.7023i	−0.617532	−	0.448664i	0.234526	−	0.972110i	$-0.424646\pi$
$569$	−14.7304	−	10.7023i	−0.617532	−	0.448664i	−0.852059	+	0.523446i	$0.824646\pi$
$570$	0.351474	−	0.0995219i	0.0147216	−	0.00416851i
$571$	26.6679			1.11602			0.558009	−	0.829835i	$-0.311565\pi$
$571$	26.6679			1.11602			0.558009	+	0.829835i	$0.311565\pi$
$572$	−6.37802	+	6.42592i	−0.266678	+	0.268681i
$573$	−40.2888			−1.68309
$574$	14.5578	−	33.9588i	0.607631	−	1.41741i
$575$	17.5547	−	24.1619i	0.732080	−	1.00762i
$576$	−11.7582	+	4.95685i	−0.489925	+	0.206535i
$577$	−29.1631	−	9.47567i	−1.21408	−	0.394477i	−0.369155	−	0.929368i	$-0.620353\pi$
$577$	−29.1631	−	9.47567i	−1.21408	−	0.394477i	−0.844921	+	0.534891i	$0.820353\pi$
$578$	6.16202	+	2.26599i	0.256306	+	0.0942528i
$579$	−13.3505	−	18.3755i	−0.554830	−	0.763658i
$580$	−0.921721	+	1.08377i	−0.0382724	+	0.0450010i
$581$	29.7830	+	11.4410i	1.23561	+	0.474654i
$582$	−1.49151	+	38.9985i	−0.0618252	+	1.61654i
$583$	−7.07112	−	29.2401i	−0.292856	−	1.21100i
$584$	−27.7017	−	3.19085i	−1.14631	−	0.132038i
$585$	0.0949247	+	0.292148i	0.00392465	+	0.0120788i
$586$	9.79541	−	12.4521i	0.404645	−	0.514392i
$587$	20.0438	+	27.5879i	0.827295	+	1.13867i	0.988420	+	0.151740i	$0.0484877\pi$
$587$	20.0438	+	27.5879i	0.827295	+	1.13867i	−0.161125	+	0.986934i	$0.551512\pi$
$588$	−5.42190	+	29.5166i	−0.223596	+	1.21724i
$589$	1.70949	+	0.555446i	0.0704382	+	0.0228867i
$590$	0.0339137	−	0.0227116i	0.00139621	−	0.000935023i
$591$	1.74827	+	1.27019i	0.0719142	+	0.0522487i
$592$	16.9265	−	2.75333i	0.695673	−	0.113161i
$593$		−	40.9118i		−	1.68005i	−0.542549	−	0.840024i	$-0.682541\pi$
$593$		−	40.9118i		−	1.68005i	0.542549	−	0.840024i	$-0.317459\pi$
$594$	1.62248	−	14.0325i	0.0665713	−	0.575762i
$595$	−0.826111	+	1.01965i	−0.0338672	+	0.0418015i
$596$	29.9832	−	7.26451i	1.22816	−	0.297566i
$597$	17.6420	−	24.2821i	0.722039	−	0.993801i
$598$	9.61834	−	6.44129i	0.393323	−	0.263404i
$599$	−24.2048	−	7.86462i	−0.988982	−	0.321340i	−0.230527	−	0.973066i	$-0.574045\pi$
$599$	−24.2048	−	7.86462i	−0.988982	−	0.321340i	−0.758454	+	0.651726i	$0.774045\pi$
$600$	12.5553	−	27.4603i	0.512569	−	1.12106i
$601$	6.23866	+	8.58677i	0.254480	+	0.350262i	0.917074	−	0.398717i	$-0.130544\pi$
$601$	6.23866	+	8.58677i	0.254480	+	0.350262i	−0.662594	+	0.748979i	$0.730544\pi$
$602$	−9.12262	+	2.07189i	−0.371810	+	0.0844438i
$603$	−2.83490	−	8.72492i	−0.115446	−	0.355306i
$604$	−1.45509	+	18.9953i	−0.0592069	+	0.772906i
$605$	−0.700046	+	1.38523i	−0.0284609	+	0.0563177i
$606$	−38.7083	−	1.48042i	−1.57242	−	0.0601378i
$607$	4.32238	+	13.3029i	0.175440	+	0.539949i	0.999653	−	0.0263308i	$-0.00838233\pi$
$607$	4.32238	+	13.3029i	0.175440	+	0.539949i	−0.824213	+	0.566279i	$0.808382\pi$
$608$	−3.29774	−	3.53035i	−0.133741	−	0.143175i
$609$	−28.5536	−	1.50346i	−1.15705	−	0.0609234i
$610$	−1.04217	−	0.383244i	−0.0421964	−	0.0155171i
$611$	5.40350	−	16.6303i	0.218602	−	0.672788i
$612$	−5.87932	−	9.54941i	−0.237657	−	0.386012i
$613$	17.4971	−	24.0827i	0.706702	−	0.972691i	−0.293160	−	0.956063i	$-0.594707\pi$
$613$	17.4971	−	24.0827i	0.706702	−	0.972691i	0.999862	−	0.0166281i	$-0.00529313\pi$
$614$	−2.83766	−	10.0216i	−0.114519	−	0.404437i
$615$	2.98667			0.120434
$616$	−15.9569	−	19.0099i	−0.642922	−	0.765932i
$617$	−24.4303			−0.983527			−0.491763	−	0.870729i	$-0.663647\pi$
$617$	−24.4303			−0.983527			−0.491763	+	0.870729i	$0.663647\pi$
$618$	−8.72270	−	30.8053i	−0.350879	−	1.23917i
$619$	18.1081	−	24.9236i	0.727825	−	1.00177i	−0.271403	−	0.962466i	$-0.587487\pi$
$619$	18.1081	−	24.9236i	0.727825	−	1.00177i	0.999227	−	0.0392992i	$-0.0125125\pi$
$620$	−0.505775	+	0.311392i	−0.0203124	+	0.0125058i
$621$	−5.58120	+	17.1772i	−0.223966	+	0.689296i
$622$	−36.7745	−	13.5233i	−1.47452	−	0.542234i
$623$	−1.61605	+	30.6917i	−0.0647455	+	1.22964i
$624$	8.24092	−	8.30997i	0.329901	−	0.332665i
$625$	7.63327	+	23.4928i	0.305331	+	0.939711i
$626$	−27.1967	−	1.04015i	−1.08700	−	0.0415727i
$627$	−5.90148	+	1.42715i	−0.235682	+	0.0569950i
$628$	9.65791	+	0.739824i	0.385392	+	0.0295222i
$629$	4.65720	+	14.3334i	0.185695	+	0.571510i
$630$	−0.821172	+	0.186501i	−0.0327163	+	0.00743036i
$631$	−26.6437	−	36.6719i	−1.06067	−	1.45989i	−0.879178	−	0.476494i	$-0.841907\pi$
$631$	−26.6437	−	36.6719i	−1.06067	−	1.45989i	−0.181492	−	0.983392i	$-0.558093\pi$
$632$	−9.83222	+	21.5045i	−0.391105	+	0.855402i
$633$	2.49716	+	0.811377i	0.0992533	+	0.0322494i
$634$	15.0922	−	10.1071i	0.599388	−	0.401403i
$635$	0.161914	−	0.222856i	0.00642537	−	0.00884377i
$636$	9.15673	+	37.7930i	0.363088	+	1.49859i
$637$	−1.98188	−	9.34659i	−0.0785249	−	0.370325i
$638$	16.0048	−	17.4079i	0.633637	−	0.689185i
$639$		−	5.35142i		−	0.211699i
$640$	1.59461	−	0.0743171i	0.0630324	−	0.00293764i
$641$	−12.8054	−	9.30363i	−0.505781	−	0.367471i	0.305440	−	0.952211i	$-0.401197\pi$
$641$	−12.8054	−	9.30363i	−0.505781	−	0.367471i	−0.811221	+	0.584740i	$0.801197\pi$
$642$	−8.33318	+	5.58063i	−0.328884	+	0.220250i
$643$	9.31721	+	3.02735i	0.367435	+	0.119387i	0.486914	−	0.873450i	$-0.338122\pi$
$643$	9.31721	+	3.02735i	0.367435	+	0.119387i	−0.119479	+	0.992837i	$0.538122\pi$
$644$	15.1931	+	27.8599i	0.598693	+	1.09783i
$645$	−0.444488	−	0.611786i	−0.0175017	−	0.0240890i
$646$	2.62496	−	3.33690i	0.103278	−	0.131289i
$647$	−11.6820	−	35.9534i	−0.459265	−	1.41347i	−0.866054	−	0.499951i	$-0.833351\pi$
$647$	−11.6820	−	35.9534i	−0.459265	−	1.41347i	0.406789	−	0.913522i	$-0.366649\pi$
$648$	−3.63819	+	31.5854i	−0.142922	+	1.24079i
$649$	−0.577854	+	0.355426i	−0.0226827	+	0.0139517i
$650$	−0.367384	+	9.60595i	−0.0144100	+	0.376776i
$651$	−11.1430	−	4.28054i	−0.436729	−	0.167768i
$652$	10.6153	+	9.02809i	0.415727	+	0.353567i
$653$	−5.61292	−	7.72552i	−0.219651	−	0.302323i	0.684944	−	0.728595i	$-0.259827\pi$
$653$	−5.61292	−	7.72552i	−0.219651	−	0.302323i	−0.904595	+	0.426272i	$0.859827\pi$
$654$	−9.96778	−	3.66550i	−0.389771	−	0.143332i
$655$	−2.05581	−	0.667974i	−0.0803272	−	0.0260999i
$656$	−18.0787	−	35.1185i	−0.705856	−	1.37115i
$657$	9.24302	−	12.7219i	0.360605	−	0.496330i
$658$	44.0572	+	18.8868i	1.71753	+	0.736286i
$659$	15.0483			0.586197			0.293098	−	0.956082i	$-0.405314\pi$
$659$	15.0483			0.586197			0.293098	+	0.956082i	$0.405314\pi$
$660$	0.904137	−	1.79100i	0.0351935	−	0.0697146i
$661$	−4.49634			−0.174887			−0.0874437	−	0.996169i	$-0.527870\pi$
$661$	−4.49634			−0.174887			−0.0874437	+	0.996169i	$0.527870\pi$
$662$	14.4356	−	4.08751i	0.561054	−	0.158866i
$663$	8.32096	+	6.04553i	0.323159	+	0.234789i
$664$	29.7066	−	16.7589i	1.15284	−	0.650370i
$665$	−0.173570	−	0.267418i	−0.00673076	−	0.0103700i
$666$	−3.33777	+	9.07657i	−0.129336	+	0.351710i
$667$	−24.4603	+	17.7715i	−0.947107	+	0.688114i
$668$	−10.7344	−	9.12938i	−0.415326	−	0.353226i
$669$	25.4020	−	8.25362i	0.982099	−	0.319103i
$670$	−0.0438612	+	1.14684i	−0.00169451	+	0.0443061i
$671$	17.0630	+	7.03467i	0.658711	+	0.271571i
$672$	20.6372	+	24.5641i	0.796096	+	0.947582i
$673$	−10.7714	−	33.1508i	−0.415205	−	1.27787i	−0.912067	−	0.410041i	$-0.865514\pi$
$673$	−10.7714	−	33.1508i	−0.415205	−	1.27787i	0.496862	−	0.867830i	$-0.334486\pi$
$674$	−18.4271	+	23.4249i	−0.709787	+	0.902294i
$675$	−8.81586	−	12.1340i	−0.339323	−	0.467038i
$676$	8.48095	−	20.5962i	0.326190	−	0.792163i
$677$	−9.86232	+	30.3531i	−0.379040	+	1.16656i	0.561673	+	0.827360i	$0.310158\pi$
$677$	−9.86232	+	30.3531i	−0.379040	+	1.16656i	−0.940712	+	0.339205i	$0.889842\pi$
$678$	−36.2117	+	24.2506i	−1.39070	+	0.931337i
$679$	32.9023	−	8.80749i	1.26268	−	0.338001i
$680$	0.277999	+	1.37509i	0.0106608	+	0.0527324i
$681$	−11.7030			−0.448459
$682$	8.60032	−	4.84694i	0.329323	−	0.185599i
$683$	5.98464			0.228996			0.114498	−	0.993423i	$-0.463474\pi$
$683$	5.98464			0.228996			0.114498	+	0.993423i	$0.463474\pi$
$684$	2.64774	−	0.641512i	0.101239	−	0.0245288i
$685$	−1.22989	−	0.893565i	−0.0469916	−	0.0341414i
$686$	26.0091	−	3.08645i	0.993032	−	0.117841i
$687$	54.9102	+	17.8414i	2.09496	+	0.680693i
$688$	−4.50307	+	8.92969i	−0.171678	+	0.340441i
$689$	−7.27693	−	10.0158i	−0.277229	−	0.381573i
$690$	−1.58598	+	2.01613i	−0.0603772	+	0.0767526i
$691$	38.2553	−	12.4299i	1.45530	−	0.472856i	0.528669	−	0.848828i	$-0.322691\pi$
$691$	38.2553	−	12.4299i	1.45530	−	0.472856i	0.926631	+	0.375973i	$0.122691\pi$
$692$	−46.0331	−	3.52627i	−1.74991	−	0.134049i
$693$	13.7584	−	2.57003i	0.522640	−	0.0976276i
$694$	−1.63758	+	42.8178i	−0.0621618	+	1.62534i
$695$	−1.39567	+	0.453479i	−0.0529406	+	0.0172015i
$696$	−20.6788	+	22.5111i	−0.783828	+	0.853281i
$697$	28.0832	−	20.4036i	1.06373	−	0.772843i
$698$	−29.3379	−	10.7886i	−1.11046	−	0.408354i
$699$	39.0167	+	12.6773i	1.47575	+	0.479500i
$700$	−26.1330	−	3.39156i	−0.987735	−	0.128189i
$701$	−8.94378	+	12.3101i	−0.337802	+	0.464944i	−0.943798	−	0.330523i	$-0.892775\pi$
$701$	−8.94378	+	12.3101i	−0.337802	+	0.464944i	0.605996	+	0.795468i	$0.292775\pi$
$702$	−1.58382	−	5.59348i	−0.0597776	−	0.211112i
$703$	−3.66133			−0.138090
$704$	−26.5322	+	0.209965i	−0.999969	+	0.00791334i
$705$			3.87482i			0.145934i
$706$	5.34962	+	18.8929i	0.201336	+	0.711043i
$707$	8.74196	+	32.6575i	0.328775	+	1.22821i
$708$	0.746760	−	0.459761i	0.0280649	−	0.0172789i
$709$	−32.2247	−	10.4704i	−1.21022	−	0.393226i	−0.366712	−	0.930335i	$-0.619516\pi$
$709$	−32.2247	−	10.4704i	−1.21022	−	0.393226i	−0.843513	+	0.537109i	$0.819516\pi$
$710$	−0.231061	+	0.628335i	−0.00867155	+	0.0235810i
$711$	−7.83782	−	10.7878i	−0.293941	−	0.404576i
$712$	24.1968	+	22.2273i	0.906813	+	0.833002i
$713$	−12.0044	+	3.90047i	−0.449569	+	0.146074i
$714$	−18.5734	+	21.2131i	−0.695094	+	0.793878i
$715$	−0.0490609	+	0.636850i	−0.00183477	+	0.0238168i
$716$	36.7510	+	2.81524i	1.37345	+	0.105210i
$717$	9.79077	+	30.1329i	0.365643	+	1.12533i
$718$	−7.68910	−	6.04861i	−0.286955	−	0.225732i
$719$	−23.2815	+	16.9150i	−0.868253	+	0.630822i	−0.930118	−	0.367262i	$-0.880295\pi$
$719$	−23.2815	+	16.9150i	−0.868253	+	0.630822i	0.0618648	+	0.998085i	$0.480295\pi$
$720$	−0.405344	+	0.803805i	−0.0151063	+	0.0299560i
$721$	−23.4382	+	15.2127i	−0.872883	+	0.566552i
$722$	−14.3776	−	21.4691i	−0.535078	−	0.798995i
$723$	−8.70192	−	6.32231i	−0.323628	−	0.235129i
$724$	−5.72905	−	23.6458i	−0.212918	−	0.878788i
$725$		−	25.1076i		−	0.932473i
$726$	−16.1671	+	29.1655i	−0.600017	+	1.08243i
$727$	34.8987			1.29432			0.647161	−	0.762354i	$-0.275956\pi$
$727$	34.8987			1.29432			0.647161	+	0.762354i	$0.275956\pi$
$728$	−9.05302	−	4.72974i	−0.335527	−	0.175296i
$729$	1.16317	+	0.845096i	0.0430805	+	0.0312998i
$730$	−1.63456	+	1.09465i	−0.0604979	+	0.0405148i
$731$	−8.35890	−	2.71597i	−0.309165	−	0.100454i
$732$	−22.0603	−	9.08380i	−0.815372	−	0.335747i
$733$	22.2770	−	16.1852i	0.822820	−	0.597814i	−0.0946987	−	0.995506i	$-0.530189\pi$
$733$	22.2770	−	16.1852i	0.822820	−	0.597814i	0.917519	+	0.397692i	$0.130189\pi$
$734$	−4.22457	+	5.37035i	−0.155932	+	0.198223i
$735$	1.05770	+	1.83407i	0.0390139	+	0.0676508i
$736$	33.3066	+	6.44469i	1.22770	+	0.237554i
$737$	1.46519	−	19.0193i	0.0539709	−	0.700586i
$738$	22.2583	+	0.851279i	0.819340	+	0.0313360i
$739$	12.7262	+	39.1671i	0.468139	+	1.44079i	0.854991	+	0.518643i	$0.173563\pi$
$739$	12.7262	+	39.1671i	0.468139	+	1.44079i	−0.386851	+	0.922142i	$0.626437\pi$
$740$	0.783806	−	0.921605i	0.0288133	−	0.0338789i
$741$	−2.02148	+	1.46869i	−0.0742609	+	0.0539537i
$742$	29.1528	−	17.3756i	1.07023	−	0.637878i
$743$	23.4411	+	7.61647i	0.859969	+	0.279421i	0.705616	−	0.708595i	$-0.250670\pi$
$743$	23.4411	+	7.61647i	0.859969	+	0.279421i	0.154354	+	0.988016i	$0.450670\pi$
$744$	−11.1144	+	6.27015i	−0.407475	+	0.229875i
$745$	1.27930	−	1.76081i	0.0468700	−	0.0645111i
$746$	3.25724	+	11.5034i	0.119256	+	0.421168i
$747$			19.2345i			0.703753i
$748$	−3.73388	−	23.0171i	−0.136524	−	0.841590i
$749$	6.80100	+	5.51011i	0.248503	+	0.201335i
$750$	−1.16303	−	4.10740i	−0.0424679	−	0.149981i
$751$	−2.94522	+	4.05374i	−0.107472	+	0.147923i	−0.859365	−	0.511362i	$-0.829141\pi$
$751$	−2.94522	+	4.05374i	−0.107472	+	0.147923i	0.751893	+	0.659285i	$0.229141\pi$
$752$	45.5617	−	23.4548i	1.66146	−	0.855309i
$753$	−3.37484	+	10.3867i	−0.122986	+	0.378512i
$754$	3.35878	−	9.13370i	0.122320	−	0.332630i
$755$	0.789995	+	1.08733i	0.0287509	+	0.0395722i
$756$	15.6641	−	2.93300i	0.569697	−	0.106672i
$757$	−21.4189	+	6.95944i	−0.778485	+	0.252945i	−0.671193	−	0.741283i	$-0.734218\pi$
$757$	−21.4189	+	6.95944i	−0.778485	+	0.252945i	−0.107292	+	0.994228i	$0.534218\pi$
$758$	−0.746278	+	19.5129i	−0.0271061	+	0.708739i
$759$	27.6362	−	32.4665i	1.00313	−	1.17846i
$760$	−0.338582	−	0.0389999i	−0.0122817	−	0.00141467i
$761$	4.46071	−	1.44937i	0.161700	−	0.0525397i	−0.227048	−	0.973884i	$-0.572907\pi$
$761$	4.46071	−	1.44937i	0.161700	−	0.0525397i	0.388749	+	0.921344i	$0.372907\pi$
$762$	3.65921	−	4.65166i	0.132559	−	0.168512i
$763$	−0.487372	+	9.25611i	−0.0176441	+	0.335094i
$764$	34.7584	+	14.3125i	1.25751	+	0.517808i
$765$	−0.752425	−	0.244478i	−0.0272040	−	0.00883911i
$766$	12.6167	+	18.8396i	0.455859	+	0.680703i
$767$	−0.164105	+	0.225871i	−0.00592548	+	0.00815572i
$768$	34.2965	−	0.286202i	1.23757	−	0.0103274i
$769$			38.9931i			1.40613i	0.711127	+	0.703064i	$0.248185\pi$
$769$			38.9931i			1.40613i	−0.711127	+	0.703064i	$0.751815\pi$
$770$	−1.72641	−	0.292294i	−0.0622154	−	0.0105336i
$771$	8.48730			0.305663
$772$	4.99008	+	20.5958i	0.179597	+	0.741259i
$773$	−23.4017	−	17.0023i	−0.841700	−	0.611531i	0.0811453	−	0.996702i	$-0.474142\pi$
$773$	−23.4017	−	17.0023i	−0.841700	−	0.611531i	−0.922845	+	0.385172i	$0.874142\pi$
$774$	−3.13819	−	4.68605i	−0.112800	−	0.168437i
$775$	3.23905	−	9.96877i	0.116350	−	0.358089i
$776$	15.1409	−	33.1153i	0.543526	−	1.18877i
$777$	24.2812	+	1.27850i	0.871082	+	0.0458661i
$778$	−15.0568	−	11.8444i	−0.539812	−	0.424641i
$779$	2.60595	+	8.02030i	0.0933680	+	0.287357i
$780$	0.0630631	−	0.823246i	0.00225802	−	0.0294769i
$781$	4.24126	−	10.2874i	0.151764	−	0.368113i
$782$	−1.13941	+	29.7920i	−0.0407452	+	1.06536i
$783$	4.69201	+	14.4405i	0.167679	+	0.516062i
$784$	15.1633	−	23.5388i	0.541548	−	0.840670i
$785$	0.552842	−	0.401663i	0.0197318	−	0.0143360i
$786$	−43.5888	−	16.0291i	−1.55476	−	0.571740i
$787$	40.7375	+	13.2364i	1.45214	+	0.471828i	0.925658	−	0.378361i	$-0.123512\pi$
$787$	40.7375	+	13.2364i	1.45214	+	0.471828i	0.526478	+	0.850189i	$0.323512\pi$
$788$	−1.05705	−	1.71690i	−0.0376559	−	0.0611621i
$789$	25.6631	+	18.6454i	0.913632	+	0.663793i
$790$	0.454483	+	1.60507i	0.0161698	+	0.0571057i
$791$	29.5537	+	23.9441i	1.05081	+	0.851354i
$792$	7.24860	−	13.0898i	0.257568	−	0.465126i
$793$	7.59544			0.269722
$794$	31.3600	−	8.87975i	1.11292	−	0.315131i
$795$	2.21945	+	1.61253i	0.0787159	+	0.0571905i
$796$	−23.8465	+	14.6816i	−0.845215	+	0.520377i
$797$	8.16232	−	25.1210i	0.289124	−	0.889833i	−0.696008	−	0.718034i	$-0.745042\pi$
$797$	8.16232	−	25.1210i	0.289124	−	0.889833i	0.985132	−	0.171799i	$-0.0549578\pi$
$798$	−3.50688	−	5.88386i	−0.124142	−	0.208286i
$799$	26.4711	+	36.4343i	0.936479	+	1.28895i
$800$	−20.5871	+	19.2306i	−0.727863	+	0.679903i
$801$	−17.6219	+	5.72569i	−0.622637	+	0.202307i
$802$	1.78994	−	46.8015i	0.0632051	−	1.65262i
$803$	27.8512	−	17.1307i	0.982849	−	0.604530i
$804$	−1.88336	+	24.5860i	−0.0664210	+	0.867081i
$805$	2.08985	+	0.802809i	0.0736577	+	0.0282953i
$806$	2.51189	−	3.19316i	0.0884774	−	0.112474i
$807$	−18.1761	−	25.0172i	−0.639829	−	0.880649i
$808$	32.8689	+	15.0282i	1.15632	+	0.528691i
$809$	−2.91376	+	8.96763i	−0.102442	+	0.315285i	−0.989122	−	0.147100i	$-0.953006\pi$
$809$	−2.91376	+	8.96763i	−0.102442	+	0.315285i	0.886679	+	0.462385i	$0.153006\pi$
$810$	1.24812	+	1.86373i	0.0438543	+	0.0654846i
$811$	3.37680	−	4.64776i	0.118575	−	0.163205i	−0.745603	−	0.666390i	$-0.767839\pi$
$811$	3.37680	−	4.64776i	0.118575	−	0.163205i	0.864179	+	0.503185i	$0.167839\pi$
$812$	24.0999	+	11.4407i	0.845742	+	0.401489i
$813$			19.5768i			0.686587i
$814$	−13.6101	+	14.8032i	−0.477032	+	0.518852i
$815$	0.983115			0.0344370
$816$	4.83940	+	29.7508i	0.169413	+	1.04149i
$817$	1.25504	−	1.72741i	0.0439082	−	0.0604345i
$818$	0.393248	−	0.263354i	0.0137496	−	0.00920794i
$819$	4.83155	−	3.13596i	0.168828	−	0.109579i
$820$	−2.57669	−	1.06101i	−0.0899820	−	0.0370520i
$821$	30.4879	+	41.9629i	1.06403	+	1.46452i	0.875974	+	0.482359i	$0.160220\pi$
$821$	30.4879	+	41.9629i	1.06403	+	1.46452i	0.188060	+	0.982158i	$0.439780\pi$
$822$	−25.6714	−	20.1943i	−0.895392	−	0.704357i
$823$	−43.6045	+	14.1680i	−1.51996	+	0.493865i	−0.945764	−	0.324854i	$-0.894685\pi$
$823$	−43.6045	+	14.1680i	−1.51996	+	0.493865i	−0.574195	+	0.818719i	$0.694685\pi$
$824$	−3.41819	+	29.6754i	−0.119078	+	1.03379i
$825$	8.32236	+	34.4141i	0.289747	+	1.19815i
$826$	−0.575824	−	0.504172i	−0.0200355	−	0.0175424i
$827$	10.7855	+	33.1943i	0.375048	+	1.15428i	0.943447	+	0.331525i	$0.107563\pi$
$827$	10.7855	+	33.1943i	0.375048	+	1.15428i	−0.568399	+	0.822753i	$0.692437\pi$
$828$	−12.3942	+	14.5732i	−0.430729	+	0.506454i
$829$	17.1124	−	12.4329i	0.594339	−	0.431812i	−0.249526	−	0.968368i	$-0.580275\pi$
$829$	17.1124	−	12.4329i	0.594339	−	0.431812i	0.843865	+	0.536556i	$0.180275\pi$
$830$	0.830495	−	2.25841i	0.0288269	−	0.0783905i
$831$	−7.32224	+	22.5355i	−0.254006	+	0.781749i
$832$	−10.0618	+	4.24170i	−0.348830	+	0.147054i
$833$	22.4750	+	10.0197i	0.778711	+	0.347163i
$834$	−30.3366	+	8.58999i	−1.05047	+	0.297447i
$835$	−0.994145			−0.0344038
$836$	5.59837	+	0.865238i	0.193624	+	0.0299249i
$837$			6.33880i			0.219101i
$838$	−9.38593	−	33.1476i	−0.324232	−	1.14507i
$839$	−25.8787	−	18.8020i	−0.893434	−	0.649118i	0.0433374	−	0.999060i	$-0.486201\pi$
$839$	−25.8787	−	18.8020i	−0.893434	−	0.649118i	−0.936771	+	0.349943i	$0.886201\pi$
$840$	2.23179	+	0.376869i	0.0770041	+	0.0130032i
$841$	1.10699	−	3.40698i	0.0381722	−	0.117482i
$842$	12.2710	−	33.3692i	0.422888	−	1.14998i
$843$	−37.5311	−	51.6572i	−1.29264	−	1.77917i
$844$	−1.86614	−	1.58711i	−0.0642351	−	0.0546306i
$845$	−0.485591	−	1.49450i	−0.0167048	−	0.0514122i
$846$	−1.10442	+	28.8773i	−0.0379709	+	0.992821i
$847$	28.4857	+	5.96365i	0.978780	+	0.204914i
$848$	5.52610	−	35.8581i	0.189767	−	1.23137i
$849$	−11.3105	−	34.8102i	−0.388176	−	1.19468i
$850$	−19.4590	−	15.3073i	−0.667437	−	0.525037i
$851$	20.8004	−	15.1124i	0.713028	−	0.518045i
$852$	−5.47669	+	13.3003i	−0.187628	+	0.455661i
$853$	−11.3795	+	35.0226i	−0.389628	+	1.19915i	0.543438	+	0.839449i	$0.317122\pi$
$853$	−11.3795	+	35.0226i	−0.389628	+	1.19915i	−0.933067	+	0.359703i	$0.882878\pi$
$854$	−1.88866	+	20.7356i	−0.0646287	+	0.709558i
$855$	0.112972	−	0.155493i	0.00386357	−	0.00531774i
$856$	9.17179	−	1.85424i	0.313485	−	0.0633766i
$857$			32.4119i			1.10717i	0.832792	+	0.553585i	$0.186741\pi$
$857$			32.4119i			1.10717i	−0.832792	+	0.553585i	$0.813259\pi$
$858$	−1.57624	+	13.6326i	−0.0538119	+	0.465408i
$859$			2.41272i			0.0823209i	0.999153	+	0.0411604i	$0.0131055\pi$
$859$			2.41272i			0.0823209i	−0.999153	+	0.0411604i	$0.986895\pi$
$860$	0.166138	+	0.685709i	0.00566526	+	0.0233825i
$861$	−14.4815	−	54.0990i	−0.493529	−	1.84369i
$862$	21.1056	−	14.1342i	0.718860	−	0.481412i
$863$	−37.5729	−	12.2082i	−1.27900	−	0.415571i	−0.410769	−	0.911739i	$-0.634740\pi$
$863$	−37.5729	−	12.2082i	−1.27900	−	0.415571i	−0.868226	+	0.496168i	$0.834740\pi$
$864$	8.24682	−	14.9076i	0.280563	−	0.507167i
$865$	−2.63505	+	1.91447i	−0.0895942	+	0.0650940i
$866$	−13.1706	−	10.3606i	−0.447556	−	0.352068i
$867$	9.46457	−	3.07522i	0.321434	−	0.104440i
$868$	8.09275	+	7.65148i	0.274686	+	0.259708i
$869$	−6.51733	−	26.9501i	−0.221085	−	0.914219i
$870$	−0.0824157	+	2.15492i	−0.00279415	+	0.0730585i
$871$	−2.42589	−	7.46613i	−0.0821982	−	0.252980i
$872$	7.29734	+	6.70337i	0.247119	+	0.227005i
$873$	12.0697	+	16.6125i	0.408496	+	0.562247i
$874$	−6.79784	−	2.49980i	−0.229940	−	0.0845571i
$875$	−3.12510	+	2.02837i	−0.105648	+	0.0685715i
$876$	−35.9921	+	22.1594i	−1.21606	+	0.748698i
$877$	−14.9064	+	20.5168i	−0.503352	+	0.692805i	−0.982781	−	0.184776i	$-0.940844\pi$
$877$	−14.9064	+	20.5168i	−0.503352	+	0.692805i	0.479429	+	0.877581i	$0.340844\pi$
$878$	−32.5306	+	9.21122i	−1.09786	+	0.310864i
$879$		−	24.0144i		−	0.809984i
$880$	−1.41627	+	1.22396i	−0.0477426	+	0.0412596i
$881$		−	29.0692i		−	0.979365i	−0.871901	−	0.489682i	$-0.837113\pi$
$881$		−	29.0692i		−	0.979365i	0.871901	−	0.489682i	$-0.162887\pi$
$882$	7.35980	+	13.9700i	0.247817	+	0.470393i
$883$	−25.4220	−	18.4701i	−0.855517	−	0.621569i	0.0711447	−	0.997466i	$-0.477335\pi$
$883$	−25.4220	−	18.4701i	−0.855517	−	0.621569i	−0.926662	+	0.375897i	$0.877335\pi$
$884$	−5.03108	−	8.17166i	−0.169214	−	0.274843i
$885$	0.0191181	−	0.0588393i	0.000642647	−	0.00197786i
$886$	7.55554	+	2.77843i	0.253833	+	0.0933433i
$887$	12.8422	−	9.33039i	0.431198	−	0.313284i	−0.350930	−	0.936402i	$-0.614134\pi$
$887$	12.8422	−	9.33039i	0.431198	−	0.313284i	0.782128	+	0.623118i	$0.214134\pi$
$888$	17.5847	−	19.1428i	0.590103	−	0.642391i
$889$	−4.82177	−	1.85226i	−0.161717	−	0.0621229i
$890$	2.31628	+	0.0885872i	0.0776419	+	0.00296945i
$891$	−19.5324	−	31.7559i	−0.654360	−	1.06386i
$892$	−24.8472	−	1.90337i	−0.831944	−	0.0637294i
$893$	−10.4053	+	3.38089i	−0.348200	+	0.113137i
$894$	28.9118	−	36.7533i	0.966956	−	1.22921i
$895$	2.10372	−	1.52844i	0.0703195	−	0.0510901i
$896$	−9.07794	−	28.5235i	−0.303273	−	0.952904i
$897$	5.42212	−	16.6876i	0.181039	−	0.557181i
$898$	−13.6866	−	20.4372i	−0.456727	−	0.681999i
$899$	−6.23713	+	8.58467i	−0.208020	+	0.286315i
$900$	−3.74094	−	15.4402i	−0.124698	−	0.514672i
$901$	31.8852			1.06225
$902$	42.1141	+	19.2772i	1.40224	+	0.641862i
$903$	−8.92636	+	11.0176i	−0.297051	+	0.366643i
$904$	39.8559	−	8.05756i	1.32559	−	0.267991i
$905$	−1.38864	−	1.00890i	−0.0461598	−	0.0335371i
$906$	16.0680	+	23.9932i	0.533823	+	0.797122i
$907$	3.49839	−	10.7669i	0.116162	−	0.357510i	−0.876026	−	0.482265i	$-0.839814\pi$
$907$	3.49839	−	10.7669i	0.116162	−	0.357510i	0.992188	+	0.124754i	$0.0398143\pi$
$908$	10.0965	+	4.15745i	0.335064	+	0.137970i
$909$	−16.4889	+	11.9799i	−0.546901	+	0.397347i
$910$	−0.702697	+	0.159593i	−0.0232942	+	0.00529046i
$911$	21.3390	−	6.93347i	0.706994	−	0.229716i	0.0666187	−	0.997779i	$-0.478779\pi$
$911$	21.3390	−	6.93347i	0.706994	−	0.229716i	0.640375	+	0.768062i	$0.278779\pi$
$912$	−7.23717	−	1.11532i	−0.239647	−	0.0369320i
$913$	−15.2442	+	36.9758i	−0.504511	+	1.22372i
$914$	1.86893	−	48.8668i	0.0618188	−	1.61637i
$915$	−1.60073	+	0.520109i	−0.0529185	+	0.0171943i
$916$	−41.0346	−	34.8991i	−1.35582	−	1.15310i
$917$	−2.13126	+	40.4767i	−0.0703805	+	1.33666i
$918$	14.0523	+	5.16752i	0.463795	+	0.170554i
$919$	−1.44851	−	0.470648i	−0.0477818	−	0.0155253i	0.285029	−	0.958519i	$-0.407997\pi$
$919$	−1.44851	−	0.470648i	−0.0477818	−	0.0155253i	−0.332810	+	0.942994i	$0.607997\pi$
$920$	2.08449	−	1.17596i	0.0687238	−	0.0387702i
$921$	−12.7723	−	9.27963i	−0.420862	−	0.305774i
$922$	−30.6961	+	8.69178i	−1.01092	+	0.286248i
$923$		−	4.57934i		−	0.150731i
$924$	−36.8251	−	7.69299i	−1.21146	−	0.253081i
$925$			21.3508i			0.702011i
$926$	−0.437907	−	1.54653i	−0.0143905	−	0.0508220i
$927$	−13.6283	−	9.90157i	−0.447613	−	0.325210i
$928$	25.8372	−	12.0749i	0.848149	−	0.396378i
$929$	−13.2049	−	4.29053i	−0.433238	−	0.140768i	0.0842756	−	0.996442i	$-0.473142\pi$
$929$	−13.2049	−	4.29053i	−0.433238	−	0.140768i	−0.517514	+	0.855675i	$0.673142\pi$
$930$	−0.310721	+	0.844959i	−0.0101889	+	0.0277073i
$931$	−4.00228	+	4.44059i	−0.131169	+	0.145534i
$932$	−29.1573	−	24.7977i	−0.955080	−	0.812276i
$933$	−56.4839	+	18.3527i	−1.84920	+	0.600842i
$934$	−54.0263	−	2.06626i	−1.76779	−	0.0676101i
$935$	−1.25268	−	1.06631i	−0.0409670	−	0.0348721i
$936$	0.704626	−	6.11730i	0.0230314	−	0.199950i
$937$	14.7024	−	4.77711i	0.480307	−	0.156061i	−0.0588494	−	0.998267i	$-0.518743\pi$
$937$	14.7024	−	4.77711i	0.480307	−	0.156061i	0.539156	+	0.842206i	$0.318743\pi$
$938$	20.9858	−	4.76620i	0.685212	−	0.155622i
$939$	−33.3749	+	24.2483i	−1.08915	+	0.791314i
$940$	1.37652	−	3.34292i	0.0448972	−	0.109034i
$941$	6.74560	−	20.7608i	0.219900	−	0.676784i	−0.778869	−	0.627187i	$-0.784206\pi$
$941$	6.74560	−	20.7608i	0.219900	−	0.676784i	0.998769	−	0.0495970i	$-0.0157937\pi$
$942$	12.1991	−	8.16957i	0.397467	−	0.266179i
$943$	−47.9090	−	34.8079i	−1.56013	−	1.13350i
$944$	−0.807581	+	0.131365i	−0.0262845	+	0.00427555i
$945$	0.707752	−	0.873562i	0.0230232	−	0.0284170i
$946$	−2.31885	−	11.4955i	−0.0753925	−	0.373751i
$947$	55.6446			1.80821			0.904103	−	0.427315i	$-0.140541\pi$
$947$	55.6446			1.80821			0.904103	+	0.427315i	$0.140541\pi$
$948$	8.43960	+	34.8332i	0.274105	+	1.13133i
$949$	7.90948	−	10.8865i	0.256753	−	0.353390i
$950$	4.99755	−	3.34680i	0.162142	−	0.108585i
$951$	8.50788	−	26.1846i	0.275887	−	0.849092i
$952$	23.5598	−	11.7030i	0.763576	−	0.379295i
$953$	8.73487	−	6.34625i	0.282950	−	0.205575i	−0.437253	−	0.899339i	$-0.644049\pi$
$953$	8.73487	−	6.34625i	0.282950	−	0.205575i	0.720203	+	0.693763i	$0.244049\pi$
$954$	16.0810	+	12.6500i	0.520640	+	0.409560i
$955$	2.52212	−	0.819487i	0.0816139	−	0.0265180i
$956$	2.25785	−	29.4747i	0.0730240	−	0.953280i
$957$	2.75310	−	35.7375i	0.0889952	−	1.15523i
$958$	2.26480	−	59.2174i	0.0731722	−	1.91323i
$959$	−10.2222	+	26.6102i	−0.330092	+	0.859287i
$960$	1.83005	−	1.58293i	0.0590647	−	0.0510888i
$961$	21.4956	−	15.6175i	0.693408	−	0.503790i
$962$	−2.85621	+	7.76705i	−0.0920880	+	0.250420i
$963$	−1.63065	+	5.01863i	−0.0525471	+	0.161723i
$964$	5.26142	+	8.54578i	0.169459	+	0.275241i
$965$	1.20952	+	0.878769i	0.0389359	+	0.0282886i
$966$	44.2090	+	18.9519i	1.42240	+	0.609768i
$967$			1.96681i			0.0632485i	0.999500	+	0.0316243i	$0.0100680\pi$
$967$			1.96681i			0.0632485i	−0.999500	+	0.0316243i	$0.989932\pi$
$968$	24.3088	−	19.4186i	0.781314	−	0.624138i
$969$		−	6.43534i		−	0.206733i
$970$	−0.699871	−	2.47168i	−0.0224715	−	0.0793610i
$971$	−34.8828	+	48.0121i	−1.11944	+	1.54078i	−0.312726	+	0.949843i	$0.601242\pi$
$971$	−34.8828	+	48.0121i	−1.11944	+	1.54078i	−0.806717	+	0.590938i	$0.798758\pi$
$972$	15.7924	+	25.6506i	0.506542	+	0.822743i
$973$	14.9813	+	23.0816i	0.480278	+	0.739961i
$974$	−0.768359	+	2.08944i	−0.0246198	+	0.0669499i
$975$	8.56458	+	11.7881i	0.274286	+	0.377522i
$976$	15.8051	+	15.6737i	0.505908	+	0.501704i
$977$	−4.63032	−	14.2507i	−0.148137	−	0.455919i	0.849264	−	0.527969i	$-0.177046\pi$
$977$	−4.63032	−	14.2507i	−0.148137	−	0.455919i	−0.997401	+	0.0720492i	$0.977046\pi$
$978$	21.1070	+	0.807247i	0.674928	+	0.0258129i
$979$	−38.4136	−	2.95926i	−1.22770	−	0.0945784i
$980$	−0.260960	−	1.95805i	−0.00833608	−	0.0625478i
$981$	−5.31445	+	1.72677i	−0.169677	+	0.0551315i
$982$	−22.1506	+	28.1583i	−0.706854	+	0.898566i
$983$	−28.9809	+	21.0559i	−0.924348	+	0.671578i	−0.944602	−	0.328217i	$-0.893552\pi$
$983$	−28.9809	+	21.0559i	−0.924348	+	0.671578i	0.0202544	+	0.999795i	$0.493552\pi$
$984$	−54.4491	−	24.8951i	−1.73578	−	0.793627i
$985$	−0.135280	−	0.0439550i	−0.00431037	−	0.00140052i
$986$	13.9465	+	20.8253i	0.444147	+	0.663214i
$987$	70.1864	−	18.7879i	2.23406	−	0.598026i
$988$	2.26574	−	0.548957i	0.0720827	−	0.0174647i
$989$			14.9939i			0.476777i
$990$	−0.208731	−	1.03477i	−0.00663392	−	0.0328870i
$991$			55.4425i			1.76119i	0.473870	+	0.880595i	$0.342857\pi$
$991$			55.4425i			1.76119i	−0.473870	+	0.880595i	$0.657143\pi$
$992$	11.8162	−	1.46107i	0.375165	−	0.0463890i
$993$	13.3669	−	18.3979i	0.424184	−	0.583840i
$994$	12.5017	+	1.13869i	0.396529	+	0.0361170i
$995$	−0.610502	+	1.87893i	−0.0193542	+	0.0595661i
$996$	19.6847	−	47.8050i	0.623735	−	1.51476i
$997$	8.44861	−	6.13827i	0.267570	−	0.194401i	−0.445908	−	0.895079i	$-0.647119\pi$
$997$	8.44861	−	6.13827i	0.267570	−	0.194401i	0.713478	+	0.700678i	$0.247119\pi$
$998$	4.79474	−	6.09516i	0.151775	−	0.192939i
$999$	−3.98996	−	12.2798i	−0.126237	−	0.388517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bp.c.27.9	✓	352
7.6	odd	2	inner	616.2.bp.c.27.10	yes	352
8.3	odd	2	inner	616.2.bp.c.27.79	yes	352
11.9	even	5	inner	616.2.bp.c.251.80	yes	352
56.27	even	2	inner	616.2.bp.c.27.80	yes	352
77.20	odd	10	inner	616.2.bp.c.251.79	yes	352
88.75	odd	10	inner	616.2.bp.c.251.10	yes	352
616.251	even	10	inner	616.2.bp.c.251.9	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bp.c.27.9	✓	352	1.1	even	1	trivial
616.2.bp.c.27.10	yes	352	7.6	odd	2	inner
616.2.bp.c.27.79	yes	352	8.3	odd	2	inner
616.2.bp.c.27.80	yes	352	56.27	even	2	inner
616.2.bp.c.251.9	yes	352	616.251	even	10	inner
616.2.bp.c.251.10	yes	352	88.75	odd	10	inner
616.2.bp.c.251.79	yes	352	77.20	odd	10	inner
616.2.bp.c.251.80	yes	352	11.9	even	5	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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bp (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36072 + 0.385294i) q^{2} +(-1.25998 + 1.73421i) q^{3} +(1.70310 - 1.04855i) q^{4} +(0.0436016 - 0.134192i) q^{5} +(1.04629 - 2.84523i) q^{6} +(-2.64209 - 0.139117i) q^{7} +(-1.91343 + 2.08298i) q^{8} +(-0.492894 - 1.51697i) q^{9} +(-0.00762601 + 0.199397i) q^{10} +(0.254747 - 3.30683i) q^{11} +(-0.327453 + 4.27468i) q^{12} +(-0.421782 - 1.29811i) q^{13} +(3.64874 - 0.828684i) q^{14} +(0.177780 + 0.244693i) q^{15} +(1.80108 - 3.57157i) q^{16} +(3.34327 + 1.08630i) q^{17} +(1.25517 + 1.87426i) q^{18} +(-0.501973 + 0.690906i) q^{19} +(-0.0664495 - 0.274260i) q^{20} +(3.57024 - 4.40666i) q^{21} +(0.927463 + 4.59781i) q^{22} -5.99703i q^{23} +(-1.20144 - 5.94280i) q^{24} +(4.02898 + 2.92722i) q^{25} +(1.07408 + 1.60385i) q^{26} +(-2.86428 - 0.930660i) q^{27} +(-4.64561 + 2.53344i) q^{28} +(-2.96338 - 4.07874i) q^{29} +(-0.336187 - 0.264461i) q^{30} +(-0.650400 - 2.00172i) q^{31} +(-1.07465 + 5.55384i) q^{32} +(5.41376 + 4.60832i) q^{33} +(-4.96779 - 0.189995i) q^{34} +(-0.133868 + 0.348482i) q^{35} +(-2.43007 - 2.06673i) q^{36} +(2.51997 + 3.46845i) q^{37} +(0.416840 - 1.13353i) q^{38} +(2.78264 + 0.904133i) q^{39} +(0.196090 + 0.347588i) q^{40} +(5.80419 - 7.98879i) q^{41} +(-3.16022 + 7.37181i) q^{42} -2.50021 q^{43} +(-3.03352 - 5.89896i) q^{44} -0.225056 q^{45} +(2.31062 + 8.16026i) q^{46} +(10.3644 + 7.53019i) q^{47} +(3.92455 + 7.62355i) q^{48} +(6.96129 + 0.735119i) q^{49} +(-6.61014 - 2.43078i) q^{50} +(-6.09632 + 4.42924i) q^{51} +(-2.07947 - 1.76855i) q^{52} +(8.62641 - 2.80289i) q^{53} +(4.25605 + 0.162774i) q^{54} +(-0.432642 - 0.178368i) q^{55} +(5.34523 - 5.23722i) q^{56} +(-0.565703 - 1.74105i) q^{57} +(5.60383 + 4.40823i) q^{58} +(-0.120231 - 0.165483i) q^{59} +(0.559351 + 0.230325i) q^{60} +(-1.71961 + 5.29241i) q^{61} +(1.65626 + 2.47318i) q^{62} +(1.09124 + 4.07655i) q^{63} +(-0.677574 - 7.97125i) q^{64} -0.192586 q^{65} +(-9.14215 - 4.18472i) q^{66} +5.75153 q^{67} +(6.83296 - 1.65553i) q^{68} +(10.4001 + 7.55613i) q^{69} +(0.0478881 - 0.525763i) q^{70} +(3.19083 + 1.03676i) q^{71} +(4.10294 + 1.87593i) q^{72} +(5.79485 + 7.97593i) q^{73} +(-4.76534 - 3.74864i) q^{74} +(-10.1529 + 3.29886i) q^{75} +(-0.130457 + 1.70302i) q^{76} +(-1.13310 + 8.70150i) q^{77} +(-4.13474 - 0.158135i) q^{78} +(7.95082 - 2.58338i) q^{79} +(-0.400746 - 0.397416i) q^{80} +(9.09413 - 6.60727i) q^{81} +(-4.81982 + 13.1068i) q^{82} +(-11.4687 - 3.72642i) q^{83} +(1.45984 - 11.2486i) q^{84} +(0.291544 - 0.401276i) q^{85} +(3.40208 - 0.963318i) q^{86} +10.8072 q^{87} +(6.40060 + 6.85801i) q^{88} -11.6165i q^{89} +(0.306238 - 0.0867130i) q^{90} +(0.933797 + 3.48840i) q^{91} +(-6.28820 - 10.2135i) q^{92} +(4.29091 + 1.39420i) q^{93} +(-17.0044 - 6.25310i) q^{94} +(0.0708272 + 0.0974852i) q^{95} +(-8.27751 - 8.86139i) q^{96} +(-12.2437 + 3.97821i) q^{97} +(-9.75558 + 1.68186i) q^{98} +(-5.14193 + 1.24347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 2 q^{2} - 10 q^{4} - 14 q^{8} + 84 q^{9} - 28 q^{11} - 32 q^{14} + 14 q^{16} - 4 q^{18} - 62 q^{22} - 108 q^{25} - 44 q^{28} + 24 q^{30} - 112 q^{32} + 14 q^{35} + 20 q^{36} - 2 q^{42} + 8 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) 352 * q - 2 * q^2 - 10 * q^4 - 14 * q^8 + 84 * q^9 - 28 * q^11 - 32 * q^14 + 14 * q^16 - 4 * q^18 - 62 * q^22 - 108 * q^25 - 44 * q^28 + 24 * q^30 - 112 * q^32 + 14 * q^35 + 20 * q^36 - 2 * q^42 + 8 * q^43 + 22 * q^44 - 38 * q^46 - 34 * q^49 - 24 * q^50 - 36 * q^51 - 120 * q^56 - 36 * q^57 + 30 * q^58 - 136 * q^60 + 86 * q^64 + 8 * q^65 + 24 * q^67 + 52 * q^70 + 30 * q^72 + 94 * q^74 - 68 * q^78 - 60 * q^81 - 128 * q^84 + 34 * q^86 - 38 * q^88 + 78 * q^91 - 8 * q^92 - 100 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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