LMFDB - Embedded newform 429.2.n.c.196.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			196.7
Character	$\chi$	$=$	429.196
Dual form			429.2.n.c.313.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.856521 - 2.63610i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-4.59737 - 3.34018i) q^{4} +(0.276429 + 0.850760i) q^{5} +(-0.856521 - 2.63610i) q^{6} +(-1.00325 - 0.728906i) q^{7} +(-8.25799 + 5.99978i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.856521 - 2.63610i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-4.59737 - 3.34018i) q^{4} +(0.276429 + 0.850760i) q^{5} +(-0.856521 - 2.63610i) q^{6} +(-1.00325 - 0.728906i) q^{7} +(-8.25799 + 5.99978i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.47946 q^{10} +(-1.75401 - 2.81486i) q^{11} -5.68266 q^{12} +(0.309017 - 0.951057i) q^{13} +(-2.78078 + 2.02035i) q^{14} +(0.723700 + 0.525799i) q^{15} +(5.23081 + 16.0988i) q^{16} +(-1.40622 - 4.32790i) q^{17} +(-2.24240 - 1.62920i) q^{18} +(-3.60822 + 2.62153i) q^{19} +(1.57085 - 4.83458i) q^{20} -1.24009 q^{21} +(-8.92261 + 2.21275i) q^{22} +7.00750 q^{23} +(-3.15427 + 9.70785i) q^{24} +(3.39771 - 2.46858i) q^{25} +(-2.24240 - 1.62920i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(2.17764 + 6.70209i) q^{28} +(4.78175 + 3.47414i) q^{29} +(2.00592 - 1.45739i) q^{30} +(2.24451 - 6.90790i) q^{31} +26.5034 q^{32} +(-3.07356 - 1.24629i) q^{33} -12.6132 q^{34} +(0.342796 - 1.05502i) q^{35} +(-4.59737 + 3.34018i) q^{36} +(3.13275 + 2.27608i) q^{37} +(3.82009 + 11.7570i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-7.38712 - 5.36706i) q^{40} +(3.63527 - 2.64118i) q^{41} +(-1.06216 + 3.26900i) q^{42} -1.53068 q^{43} +(-1.33834 + 18.7997i) q^{44} +0.894542 q^{45} +(6.00207 - 18.4725i) q^{46} +(-0.0565735 + 0.0411030i) q^{47} +(13.6944 + 9.94960i) q^{48} +(-1.68791 - 5.19484i) q^{49} +(-3.59721 - 11.0711i) q^{50} +(-3.68154 - 2.67479i) q^{51} +(-4.59737 + 3.34018i) q^{52} +(1.32733 - 4.08512i) q^{53} -2.77176 q^{54} +(1.90991 - 2.27035i) q^{55} +12.6581 q^{56} +(-1.37822 + 4.24172i) q^{57} +(13.2539 - 9.62949i) q^{58} +(2.59561 + 1.88582i) q^{59} +(-1.57085 - 4.83458i) q^{60} +(2.62186 + 8.06926i) q^{61} +(-16.2875 - 11.8335i) q^{62} +(-1.00325 + 0.728906i) q^{63} +(12.2391 - 37.6682i) q^{64} +0.894542 q^{65} +(-5.91792 + 7.03473i) q^{66} -15.9882 q^{67} +(-7.99107 + 24.5940i) q^{68} +(5.66919 - 4.11891i) q^{69} +(-2.48752 - 1.80729i) q^{70} +(1.59801 + 4.91818i) q^{71} +(3.15427 + 9.70785i) q^{72} +(-0.397635 - 0.288899i) q^{73} +(8.68323 - 6.30874i) q^{74} +(1.29781 - 3.99424i) q^{75} +25.3447 q^{76} +(-0.292057 + 4.10253i) q^{77} -2.77176 q^{78} +(-3.39990 + 10.4638i) q^{79} +(-12.2503 + 8.90033i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.84873 - 11.8452i) q^{82} +(4.44002 + 13.6650i) q^{83} +(5.70114 + 4.14212i) q^{84} +(3.29329 - 2.39271i) q^{85} +(-1.31106 + 4.03503i) q^{86} +5.91057 q^{87} +(31.3732 + 12.7215i) q^{88} +11.5824 q^{89} +(0.766194 - 2.35810i) q^{90} +(-1.00325 + 0.728906i) q^{91} +(-32.2160 - 23.4063i) q^{92} +(-2.24451 - 6.90790i) q^{93} +(0.0598954 + 0.184339i) q^{94} +(-3.22770 - 2.34506i) q^{95} +(21.4417 - 15.5783i) q^{96} +(0.837610 - 2.57790i) q^{97} -15.1399 q^{98} +(-3.21911 + 0.798320i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) $ 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.856521	−	2.63610i	0.605652	−	1.86400i	0.113406	−	0.993549i	$-0.463824\pi$
$2$	0.856521	−	2.63610i	0.605652	−	1.86400i	0.492246	−	0.870456i	$-0.336176\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−4.59737	−	3.34018i	−2.29868	−	1.67009i
$5$	0.276429	+	0.850760i	0.123623	+	0.380471i	0.993648	−	0.112536i	$-0.0358975\pi$
$5$	0.276429	+	0.850760i	0.123623	+	0.380471i	−0.870025	+	0.493008i	$0.835897\pi$
$6$	−0.856521	−	2.63610i	−0.349673	−	1.07618i
$7$	−1.00325	−	0.728906i	−0.379194	−	0.275501i	0.381819	−	0.924237i	$-0.375298\pi$
$7$	−1.00325	−	0.728906i	−0.379194	−	0.275501i	−0.761013	+	0.648737i	$0.775298\pi$
$8$	−8.25799	+	5.99978i	−2.91964	+	2.12124i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.47946			0.784073
$11$	−1.75401	−	2.81486i	−0.528853	−	0.848713i
$11$	−1.75401	−	2.81486i	−0.528853	−	0.848713i
$12$	−5.68266			−1.64044
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	−2.78078	+	2.02035i	−0.743194	+	0.539962i
$15$	0.723700	+	0.525799i	0.186858	+	0.135761i
$16$	5.23081	+	16.0988i	1.30770	+	4.02470i
$17$	−1.40622	−	4.32790i	−0.341059	−	1.04967i	−0.963660	−	0.267132i	$-0.913924\pi$
$17$	−1.40622	−	4.32790i	−0.341059	−	1.04967i	0.622601	−	0.782539i	$-0.286076\pi$
$18$	−2.24240	−	1.62920i	−0.528539	−	0.384006i
$19$	−3.60822	+	2.62153i	−0.827783	+	0.601419i	−0.918931	−	0.394418i	$-0.870946\pi$
$19$	−3.60822	+	2.62153i	−0.827783	+	0.601419i	0.0911486	+	0.995837i	$0.470946\pi$
$20$	1.57085	−	4.83458i	0.351252	−	1.08104i
$21$	−1.24009			−0.270610
$22$	−8.92261	+	2.21275i	−1.90231	+	0.471760i
$23$	7.00750			1.46117			0.730583	−	0.682824i	$-0.239249\pi$
$23$	7.00750			1.46117			0.730583	+	0.682824i	$0.239249\pi$
$24$	−3.15427	+	9.70785i	−0.643863	+	1.98161i
$25$	3.39771	−	2.46858i	0.679541	−	0.493716i
$26$	−2.24240	−	1.62920i	−0.439771	−	0.319512i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	2.17764	+	6.70209i	0.411536	+	1.26658i
$29$	4.78175	+	3.47414i	0.887948	+	0.645132i	0.935342	−	0.353744i	$-0.115092\pi$
$29$	4.78175	+	3.47414i	0.887948	+	0.645132i	−0.0473939	+	0.998876i	$0.515092\pi$
$30$	2.00592	−	1.45739i	0.366230	−	0.266081i
$31$	2.24451	−	6.90790i	0.403127	−	1.24070i	−0.519323	−	0.854578i	$-0.673816\pi$
$31$	2.24451	−	6.90790i	0.403127	−	1.24070i	0.922449	−	0.386118i	$-0.126184\pi$
$32$	26.5034			4.68519
$33$	−3.07356	−	1.24629i	−0.535038	−	0.216952i
$34$	−12.6132			−2.16315
$35$	0.342796	−	1.05502i	0.0579431	−	0.178331i
$36$	−4.59737	+	3.34018i	−0.766228	+	0.556697i
$37$	3.13275	+	2.27608i	0.515021	+	0.374185i	0.814725	−	0.579848i	$-0.196888\pi$
$37$	3.13275	+	2.27608i	0.515021	+	0.374185i	−0.299704	+	0.954032i	$0.596888\pi$
$38$	3.82009	+	11.7570i	0.619700	+	1.90724i
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$	−7.38712	−	5.36706i	−1.16801	−	0.848606i
$41$	3.63527	−	2.64118i	0.567734	−	0.412483i	−0.266547	−	0.963822i	$-0.585883\pi$
$41$	3.63527	−	2.64118i	0.567734	−	0.412483i	0.834282	+	0.551339i	$0.185883\pi$
$42$	−1.06216	+	3.26900i	−0.163895	+	0.504418i
$43$	−1.53068			−0.233427			−0.116713	−	0.993166i	$-0.537236\pi$
$43$	−1.53068			−0.233427			−0.116713	+	0.993166i	$0.537236\pi$
$44$	−1.33834	+	18.7997i	−0.201762	+	2.83416i
$45$	0.894542			0.133350
$46$	6.00207	−	18.4725i	0.884957	−	2.72362i
$47$	−0.0565735	+	0.0411030i	−0.00825209	+	0.00599550i	−0.591904	−	0.806009i	$-0.701623\pi$
$47$	−0.0565735	+	0.0411030i	−0.00825209	+	0.00599550i	0.583652	+	0.812004i	$0.301623\pi$
$48$	13.6944	+	9.94960i	1.97662	+	1.43610i
$49$	−1.68791	−	5.19484i	−0.241129	−	0.742120i
$50$	−3.59721	−	11.0711i	−0.508723	−	1.56569i
$51$	−3.68154	−	2.67479i	−0.515518	−	0.374546i
$52$	−4.59737	+	3.34018i	−0.637540	+	0.463200i
$53$	1.32733	−	4.08512i	0.182323	−	0.561134i	−0.817569	−	0.575831i	$-0.804678\pi$
$53$	1.32733	−	4.08512i	0.182323	−	0.561134i	0.999892	+	0.0146974i	$0.00467849\pi$
$54$	−2.77176			−0.377189
$55$	1.90991	−	2.27035i	0.257533	−	0.306134i
$56$	12.6581			1.69151
$57$	−1.37822	+	4.24172i	−0.182549	+	0.561829i
$58$	13.2539	−	9.62949i	1.74032	−	1.26441i
$59$	2.59561	+	1.88582i	0.337919	+	0.245513i	0.743783	−	0.668421i	$-0.233029\pi$
$59$	2.59561	+	1.88582i	0.337919	+	0.245513i	−0.405864	+	0.913933i	$0.633029\pi$
$60$	−1.57085	−	4.83458i	−0.202796	−	0.624141i
$61$	2.62186	+	8.06926i	0.335695	+	1.03316i	0.966379	+	0.257123i	$0.0827745\pi$
$61$	2.62186	+	8.06926i	0.335695	+	1.03316i	−0.630684	+	0.776040i	$0.717225\pi$
$62$	−16.2875	−	11.8335i	−2.06851	−	1.50286i
$63$	−1.00325	+	0.728906i	−0.126398	+	0.0918335i
$64$	12.2391	−	37.6682i	1.52989	−	4.70852i
$65$	0.894542			0.110954
$66$	−5.91792	+	7.03473i	−0.728445	+	0.865916i
$67$	−15.9882			−1.95326			−0.976632	−	0.214917i	$-0.931052\pi$
$67$	−15.9882			−1.95326			−0.976632	+	0.214917i	$0.931052\pi$
$68$	−7.99107	+	24.5940i	−0.969060	+	2.98246i
$69$	5.66919	−	4.11891i	0.682490	−	0.495858i
$70$	−2.48752	−	1.80729i	−0.297316	−	0.216012i
$71$	1.59801	+	4.91818i	0.189649	+	0.583680i	0.999997	−	0.00226826i	$-0.000722010\pi$
$71$	1.59801	+	4.91818i	0.189649	+	0.583680i	−0.810348	+	0.585949i	$0.800722\pi$
$72$	3.15427	+	9.70785i	0.371735	+	1.14408i
$73$	−0.397635	−	0.288899i	−0.0465397	−	0.0338130i	0.564272	−	0.825589i	$-0.309157\pi$
$73$	−0.397635	−	0.288899i	−0.0465397	−	0.0338130i	−0.610812	+	0.791776i	$0.709157\pi$
$74$	8.68323	−	6.30874i	1.00941	−	0.733376i
$75$	1.29781	−	3.99424i	0.149858	−	0.461215i
$76$	25.3447			2.90723
$77$	−0.292057	+	4.10253i	−0.0332829	+	0.467526i
$78$	−2.77176			−0.313840
$79$	−3.39990	+	10.4638i	−0.382519	+	1.17727i	0.555745	+	0.831353i	$0.312433\pi$
$79$	−3.39990	+	10.4638i	−0.382519	+	1.17727i	−0.938264	+	0.345920i	$0.887567\pi$
$80$	−12.2503	+	8.90033i	−1.36962	+	0.995087i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−3.84873	−	11.8452i	−0.425021	−	1.30808i
$83$	4.44002	+	13.6650i	0.487355	+	1.49993i	0.828540	+	0.559929i	$0.189172\pi$
$83$	4.44002	+	13.6650i	0.487355	+	1.49993i	−0.341185	+	0.939996i	$0.610828\pi$
$84$	5.70114	+	4.14212i	0.622046	+	0.451943i
$85$	3.29329	−	2.39271i	0.357207	−	0.259526i
$86$	−1.31106	+	4.03503i	−0.141375	+	0.435108i
$87$	5.91057			0.633679
$88$	31.3732	+	12.7215i	3.34439	+	1.35611i
$89$	11.5824			1.22774			0.613869	−	0.789408i	$-0.289612\pi$
$89$	11.5824			1.22774			0.613869	+	0.789408i	$0.289612\pi$
$90$	0.766194	−	2.35810i	0.0807639	−	0.248566i
$91$	−1.00325	+	0.728906i	−0.105169	+	0.0764101i
$92$	−32.2160	−	23.4063i	−3.35875	−	2.44028i
$93$	−2.24451	−	6.90790i	−0.232745	−	0.716316i
$94$	0.0598954	+	0.184339i	0.00617774	+	0.0190131i
$95$	−3.22770	−	2.34506i	−0.331155	−	0.240599i
$96$	21.4417	−	15.5783i	2.18839	−	1.58996i
$97$	0.837610	−	2.57790i	0.0850464	−	0.261746i	−0.899486	−	0.436950i	$-0.856059\pi$
$97$	0.837610	−	2.57790i	0.0850464	−	0.261746i	0.984532	+	0.175204i	$0.0560586\pi$
$98$	−15.1399			−1.52936
$99$	−3.21911	+	0.798320i	−0.323533	+	0.0802342i
$100$	−23.8660			−2.38660
$101$	−0.450597	+	1.38679i	−0.0448361	+	0.137991i	−0.970969	−	0.239207i	$-0.923112\pi$
$101$	−0.450597	+	1.38679i	−0.0448361	+	0.137991i	0.926133	+	0.377198i	$0.123112\pi$
$102$	−10.2043	+	7.41388i	−1.01038	+	0.734084i
$103$	−11.5641	−	8.40180i	−1.13944	−	0.827854i	−0.152401	−	0.988319i	$-0.548701\pi$
$103$	−11.5641	−	8.40180i	−1.13944	−	0.827854i	−0.987042	+	0.160465i	$0.948701\pi$
$104$	3.15427	+	9.70785i	0.309302	+	0.951933i
$105$	−0.342796	−	1.05502i	−0.0334535	−	0.102959i
$106$	−9.63189	−	6.99798i	−0.935532	−	0.679704i
$107$	−1.93007	+	1.40228i	−0.186587	+	0.135563i	−0.677158	−	0.735838i	$-0.736788\pi$
$107$	−1.93007	+	1.40228i	−0.186587	+	0.135563i	0.490570	+	0.871402i	$0.336788\pi$
$108$	−1.75604	+	5.40453i	−0.168975	+	0.520051i
$109$	−13.8016			−1.32196			−0.660978	−	0.750405i	$-0.729858\pi$
$109$	−13.8016			−1.32196			−0.660978	+	0.750405i	$0.729858\pi$
$110$	−4.34899	−	6.97933i	−0.414660	−	0.665453i
$111$	3.87229			0.367542
$112$	6.48667	−	19.9639i	0.612933	−	1.88641i
$113$	5.69959	−	4.14099i	0.536172	−	0.389552i	−0.286489	−	0.958083i	$-0.592488\pi$
$113$	5.69959	−	4.14099i	0.536172	−	0.389552i	0.822661	+	0.568532i	$0.192488\pi$
$114$	10.0011	+	7.26624i	0.936691	+	0.680546i
$115$	1.93707	+	5.96170i	0.180633	+	0.555931i
$116$	−10.3792	−	31.9438i	−0.963682	−	2.96591i
$117$	−0.809017	−	0.587785i	−0.0747936	−	0.0543408i
$118$	7.19440	−	5.22704i	0.662299	−	0.481188i
$119$	−1.74384	+	5.36699i	−0.159858	+	0.491991i
$120$	−9.13098			−0.833541
$121$	−4.84691	+	9.87459i	−0.440628	+	0.897690i
$122$	23.5171			2.12913
$123$	1.38855	−	4.27352i	0.125201	−	0.385330i
$124$	−33.3925	+	24.2611i	−2.99873	+	2.17871i
$125$	6.65789	+	4.83724i	0.595500	+	0.432656i
$126$	1.06216	+	3.26900i	0.0946249	+	0.291226i
$127$	−3.45495	−	10.6332i	−0.306577	−	0.943547i	−0.979084	−	0.203456i	$-0.934783\pi$
$127$	−3.45495	−	10.6332i	−0.306577	−	0.943547i	0.672507	−	0.740091i	$-0.265217\pi$
$128$	−45.9306	−	33.3705i	−4.05973	−	2.94957i
$129$	−1.23835	+	0.899712i	−0.109030	+	0.0792152i
$130$	0.766194	−	2.35810i	0.0671997	−	0.206819i
$131$	7.24495			0.632994			0.316497	−	0.948593i	$-0.397493\pi$
$131$	7.24495			0.632994			0.316497	+	0.948593i	$0.397493\pi$
$132$	9.96743	+	15.9959i	0.867553	+	1.39226i
$133$	5.53080			0.479582
$134$	−13.6942	+	42.1464i	−1.18300	+	3.64089i
$135$	0.723700	−	0.525799i	0.0622861	−	0.0452535i
$136$	37.5790	+	27.3028i	3.22238	+	2.34119i
$137$	3.97344	+	12.2290i	0.339474	+	1.04479i	0.964476	+	0.264170i	$0.0850981\pi$
$137$	3.97344	+	12.2290i	0.339474	+	1.04479i	−0.625002	+	0.780623i	$0.714902\pi$
$138$	−6.00207	−	18.4725i	−0.510930	−	1.57248i
$139$	7.68679	+	5.58478i	0.651985	+	0.473695i	0.863947	−	0.503583i	$-0.167985\pi$
$139$	7.68679	+	5.58478i	0.651985	+	0.473695i	−0.211962	+	0.977278i	$0.567985\pi$
$140$	−5.09991	+	3.70530i	−0.431021	+	0.313155i
$141$	−0.0216092	+	0.0665061i	−0.00181982	+	0.00560083i
$142$	14.3335			1.20284
$143$	−3.21911	+	0.798320i	−0.269196	+	0.0667589i
$144$	16.9273			1.41061
$145$	−1.63385	+	5.02847i	−0.135684	+	0.417592i
$146$	−1.10215	+	0.800758i	−0.0912145	+	0.0662712i
$147$	−4.41900	−	3.21059i	−0.364473	−	0.264805i
$148$	−6.79989	−	20.9279i	−0.558947	−	1.72026i
$149$	−4.69588	−	14.4524i	−0.384702	−	1.18399i	−0.936696	−	0.350142i	$-0.886133\pi$
$149$	−4.69588	−	14.4524i	−0.384702	−	1.18399i	0.551995	−	0.833848i	$-0.313867\pi$
$150$	−9.41763	−	6.84231i	−0.768946	−	0.558672i
$151$	2.45948	−	1.78692i	0.200150	−	0.145417i	−0.483196	−	0.875512i	$-0.660524\pi$
$151$	2.45948	−	1.78692i	0.200150	−	0.145417i	0.683346	+	0.730095i	$0.260524\pi$
$152$	14.0681	−	43.2971i	1.14107	−	3.51186i
$153$	−4.55063			−0.367896
$154$	10.5645	+	4.28379i	0.851313	+	0.345198i
$155$	6.49741			0.521885
$156$	−1.75604	+	5.40453i	−0.140596	+	0.432708i
$157$	18.3760	−	13.3509i	1.46656	−	1.06552i	0.484968	−	0.874532i	$-0.338831\pi$
$157$	18.3760	−	13.3509i	1.46656	−	1.06552i	0.981593	−	0.190987i	$-0.0611688\pi$
$158$	24.6716	+	17.9250i	1.96277	+	1.42604i
$159$	−1.32733	−	4.08512i	−0.105265	−	0.323971i
$160$	7.32631	+	22.5481i	0.579196	+	1.78258i
$161$	−7.03030	−	5.10781i	−0.554065	−	0.402552i
$162$	−2.24240	+	1.62920i	−0.176180	+	0.128002i
$163$	−4.54983	+	14.0029i	−0.356370	+	1.09680i	0.598840	+	0.800869i	$0.295628\pi$
$163$	−4.54983	+	14.0029i	−0.356370	+	1.09680i	−0.955211	+	0.295927i	$0.904372\pi$
$164$	−25.5347			−1.99393
$165$	0.210676	−	2.95937i	0.0164011	−	0.230387i
$166$	39.8252			3.09104
$167$	4.03826	−	12.4285i	0.312490	−	0.961745i	−0.664285	−	0.747479i	$-0.731264\pi$
$167$	4.03826	−	12.4285i	0.312490	−	0.961745i	0.976775	−	0.214266i	$-0.0687360\pi$
$168$	10.2406	−	7.44026i	0.790083	−	0.574029i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−3.48666	−	10.7308i	−0.267415	−	0.823018i
$171$	1.37822	+	4.24172i	0.105395	+	0.324372i
$172$	7.03710	+	5.11275i	0.536574	+	0.389844i
$173$	0.423925	−	0.307999i	0.0322304	−	0.0234168i	−0.571553	−	0.820565i	$-0.693659\pi$
$173$	0.423925	−	0.307999i	0.0322304	−	0.0234168i	0.603784	+	0.797148i	$0.293659\pi$
$174$	5.06252	−	15.5808i	0.383789	−	1.18118i
$175$	−5.20812			−0.393697
$176$	36.1410	−	42.9614i	2.72423	−	3.23834i
$177$	3.20835			0.241154
$178$	9.92061	−	30.5325i	0.743581	−	2.28851i
$179$	12.4419	−	9.03954i	0.929948	−	0.675647i	−0.0160320	−	0.999871i	$-0.505103\pi$
$179$	12.4419	−	9.03954i	0.929948	−	0.675647i	0.945980	+	0.324225i	$0.105103\pi$
$180$	−4.11254	−	2.98793i	−0.306530	−	0.222707i
$181$	6.42179	+	19.7642i	0.477328	+	1.46906i	0.842792	+	0.538239i	$0.180910\pi$
$181$	6.42179	+	19.7642i	0.477328	+	1.46906i	−0.365464	+	0.930825i	$0.619090\pi$
$182$	1.06216	+	3.26900i	0.0787327	+	0.242314i
$183$	6.86412	+	4.98708i	0.507411	+	0.368655i
$184$	−57.8679	+	42.0435i	−4.26608	+	3.09949i
$185$	−1.07041	+	3.29439i	−0.0786983	+	0.242208i
$186$	−20.1324			−1.47618
$187$	−9.71593	+	11.5495i	−0.710500	+	0.844583i
$188$	0.397381			0.0289820
$189$	−0.383209	+	1.17939i	−0.0278743	+	0.0857883i
$190$	−8.94642	+	6.49996i	−0.649042	+	0.471556i
$191$	1.75752	+	1.27692i	0.127170	+	0.0923944i	0.649552	−	0.760317i	$-0.274956\pi$
$191$	1.75752	+	1.27692i	0.127170	+	0.0923944i	−0.522382	+	0.852712i	$0.674956\pi$
$192$	−12.2391	−	37.6682i	−0.883284	−	2.71847i
$193$	3.89030	+	11.9731i	0.280030	+	0.861844i	0.987844	+	0.155446i	$0.0496813\pi$
$193$	3.89030	+	11.9731i	0.280030	+	0.861844i	−0.707814	+	0.706399i	$0.750319\pi$
$194$	−6.07817	−	4.41605i	−0.436387	−	0.317054i
$195$	0.723700	−	0.525799i	0.0518252	−	0.0376532i
$196$	−9.59179	+	29.5205i	−0.685128	+	2.10861i
$197$	−2.13051			−0.151793			−0.0758963	−	0.997116i	$-0.524182\pi$
$197$	−2.13051			−0.151793			−0.0758963	+	0.997116i	$0.524182\pi$
$198$	−0.652785	+	9.16968i	−0.0463914	+	0.651661i
$199$	8.95995			0.635154			0.317577	−	0.948232i	$-0.397131\pi$
$199$	8.95995			0.635154			0.317577	+	0.948232i	$0.397131\pi$
$200$	−13.2473	+	40.7710i	−0.936725	+	2.88294i
$201$	−12.9347	+	9.39761i	−0.912343	+	0.662856i
$202$	3.26978	+	2.37564i	0.230061	+	0.167149i
$203$	−2.26498	−	6.97089i	−0.158970	−	0.489261i
$204$	7.99107	+	24.5940i	0.559487	+	1.72192i
$205$	3.25191	+	2.36265i	0.227123	+	0.165014i
$206$	−32.0529	+	23.2878i	−2.23323	+	1.62254i
$207$	2.16544	−	6.66453i	0.150508	−	0.463217i
$208$	16.9273			1.17369
$209$	13.7081	+	5.55847i	0.948208	+	0.384487i
$210$	−3.07475			−0.212178
$211$	5.73148	−	17.6397i	0.394571	−	1.21437i	−0.534724	−	0.845027i	$-0.679584\pi$
$211$	5.73148	−	17.6397i	0.394571	−	1.21437i	0.929295	−	0.369339i	$-0.120416\pi$
$212$	−19.7473	+	14.3472i	−1.35625	+	0.985372i
$213$	4.18365	+	3.03960i	0.286659	+	0.208270i
$214$	2.04340	+	6.28894i	0.139684	+	0.429903i
$215$	−0.423124	−	1.30224i	−0.0288568	−	0.0888122i
$216$	8.25799	+	5.99978i	0.561885	+	0.408234i
$217$	−7.28703	+	5.29434i	−0.494676	+	0.359403i
$218$	−11.8214	+	36.3825i	−0.800645	+	2.46413i
$219$	−0.491504			−0.0332128
$220$	−16.3640	+	4.05816i	−1.10326	+	0.273601i
$221$	−4.55063			−0.306108
$222$	3.31670	−	10.2078i	0.222602	−	0.685099i
$223$	6.40987	−	4.65704i	0.429236	−	0.311858i	−0.352107	−	0.935960i	$-0.614535\pi$
$223$	6.40987	−	4.65704i	0.429236	−	0.311858i	0.781343	+	0.624101i	$0.214535\pi$
$224$	−26.5897	−	19.3185i	−1.77660	−	1.29077i
$225$	−1.29781	−	3.99424i	−0.0865205	−	0.266283i
$226$	−6.03426	−	18.5715i	−0.401393	−	1.23536i
$227$	10.3238	+	7.50067i	0.685214	+	0.497837i	0.875083	−	0.483972i	$-0.160806\pi$
$227$	10.3238	+	7.50067i	0.685214	+	0.497837i	−0.189869	+	0.981809i	$0.560806\pi$
$228$	20.5043	−	14.8972i	1.35793	−	0.986593i
$229$	−3.78636	+	11.6532i	−0.250210	+	0.770067i	0.744526	+	0.667594i	$0.232676\pi$
$229$	−3.78636	+	11.6532i	−0.250210	+	0.770067i	−0.994736	+	0.102473i	$0.967324\pi$
$230$	17.3748			1.14566
$231$	2.17513	+	3.49068i	0.143113	+	0.229670i
$232$	−60.3317			−3.96097
$233$	−3.60030	+	11.0806i	−0.235863	+	0.725913i	0.761142	+	0.648585i	$0.224639\pi$
$233$	−3.60030	+	11.0806i	−0.235863	+	0.725913i	−0.997006	+	0.0773281i	$0.975361\pi$
$234$	−2.24240	+	1.62920i	−0.146590	+	0.106504i
$235$	−0.0506074	−	0.0367684i	−0.00330126	−	0.00239851i
$236$	−5.63398	−	17.3396i	−0.366741	−	1.12871i
$237$	3.39990	+	10.4638i	0.220848	+	0.679699i
$238$	12.6543	+	9.19387i	0.820255	+	0.595950i
$239$	−14.9122	+	10.8344i	−0.964590	+	0.700816i	−0.954212	−	0.299130i	$-0.903303\pi$
$239$	−14.9122	+	10.8344i	−0.964590	+	0.700816i	−0.0103781	+	0.999946i	$0.503303\pi$
$240$	−4.67918	+	14.4010i	−0.302040	+	0.929583i
$241$	−21.3911			−1.37793			−0.688963	−	0.724797i	$-0.741934\pi$
$241$	−21.3911			−1.37793			−0.688963	+	0.724797i	$0.741934\pi$
$242$	21.8789	+	21.2347i	1.40643	+	1.36502i
$243$	−1.00000			−0.0641500
$244$	14.8991	−	45.8548i	0.953820	−	2.93555i
$245$	3.95298	−	2.87201i	0.252546	−	0.183486i
$246$	−10.0761	−	7.32072i	−0.642429	−	0.466752i
$247$	1.37822	+	4.24172i	0.0876939	+	0.269894i
$248$	22.9107	+	70.5120i	1.45483	+	4.47752i
$249$	11.6241	+	8.44542i	0.736649	+	0.535207i
$250$	18.4541	−	13.4077i	1.16714	−	0.847975i
$251$	0.350838	−	1.07977i	0.0221447	−	0.0681545i	−0.939373	−	0.342896i	$-0.888592\pi$
$251$	0.350838	−	1.07977i	0.0221447	−	0.0681545i	0.961518	+	0.274741i	$0.0885922\pi$
$252$	7.04700			0.443919
$253$	−12.2912	−	19.7252i	−0.772742	−	1.24011i
$254$	−30.9895			−1.94445
$255$	1.25792	−	3.87149i	0.0787742	−	0.242442i
$256$	−63.2236	+	45.9347i	−3.95148	+	2.87092i
$257$	21.9849	+	15.9730i	1.37138	+	0.996368i	0.997628	+	0.0688407i	$0.0219300\pi$
$257$	21.9849	+	15.9730i	1.37138	+	0.996368i	0.373755	+	0.927527i	$0.378070\pi$
$258$	1.31106	+	4.03503i	0.0816231	+	0.251210i
$259$	−1.48390	−	4.56696i	−0.0922048	−	0.283777i
$260$	−4.11254	−	2.98793i	−0.255049	−	0.185304i
$261$	4.78175	−	3.47414i	0.295983	−	0.215044i
$262$	6.20545	−	19.0984i	0.383374	−	1.17990i
$263$	−23.2995			−1.43671			−0.718355	−	0.695677i	$-0.755105\pi$
$263$	−23.2995			−1.43671			−0.718355	+	0.695677i	$0.755105\pi$
$264$	32.8589	−	8.14881i	2.02233	−	0.501524i
$265$	3.84237			0.236035
$266$	4.73725	−	14.5798i	0.290459	−	0.893942i
$267$	9.37040	−	6.80799i	0.573459	−	0.416642i
$268$	73.5034	+	53.4034i	4.48994	+	3.26213i
$269$	7.92290	+	24.3842i	0.483068	+	1.48673i	0.834760	+	0.550614i	$0.185606\pi$
$269$	7.92290	+	24.3842i	0.483068	+	1.48673i	−0.351692	+	0.936116i	$0.614394\pi$
$270$	−0.766194	−	2.35810i	−0.0466291	−	0.143510i
$271$	−0.100089	−	0.0727190i	−0.00607998	−	0.00441736i	0.584741	−	0.811220i	$-0.301196\pi$
$271$	−0.100089	−	0.0727190i	−0.00607998	−	0.00441736i	−0.590821	+	0.806803i	$0.701196\pi$
$272$	62.3183	−	45.2769i	3.77860	−	2.74532i
$273$	−0.383209	+	1.17939i	−0.0231928	+	0.0713802i
$274$	35.6402			2.15310
$275$	−12.9083	−	5.23417i	−0.778400	−	0.315632i
$276$	−39.8212			−2.39696
$277$	6.83789	−	21.0449i	0.410849	−	1.26446i	−0.505063	−	0.863083i	$-0.668531\pi$
$277$	6.83789	−	21.0449i	0.410849	−	1.26446i	0.915912	−	0.401380i	$-0.131469\pi$
$278$	21.3059	−	15.4797i	1.27785	−	0.928409i
$279$	−5.87621	−	4.26932i	−0.351800	−	0.255597i
$280$	3.49907	+	10.7690i	0.209109	+	0.643573i
$281$	−2.46308	−	7.58059i	−0.146935	−	0.452220i	0.850319	−	0.526267i	$-0.176409\pi$
$281$	−2.46308	−	7.58059i	−0.146935	−	0.452220i	−0.997255	+	0.0740464i	$0.976409\pi$
$282$	0.156808	+	0.113928i	0.00933779	+	0.00678430i
$283$	−13.2676	+	9.63949i	−0.788678	+	0.573008i	−0.907571	−	0.419899i	$-0.862066\pi$
$283$	−13.2676	+	9.63949i	−0.788678	+	0.573008i	0.118893	+	0.992907i	$0.462066\pi$
$284$	9.08096	−	27.9483i	0.538856	−	1.65843i
$285$	−3.98966			−0.236327
$286$	−0.652785	+	9.16968i	−0.0386000	+	0.542215i
$287$	−5.57227			−0.328921
$288$	8.19002	−	25.2063i	0.482601	−	1.48529i
$289$	−3.00001	+	2.17963i	−0.176471	+	0.128214i
$290$	11.8561	+	8.61398i	0.696216	+	0.505831i
$291$	−0.837610	−	2.57790i	−0.0491016	−	0.151119i
$292$	0.863099	+	2.65635i	0.0505091	+	0.155451i
$293$	−2.04802	−	1.48797i	−0.119646	−	0.0869282i	0.526353	−	0.850266i	$-0.323559\pi$
$293$	−2.04802	−	1.48797i	−0.119646	−	0.0869282i	−0.645999	+	0.763338i	$0.723559\pi$
$294$	−12.2484	+	8.89898i	−0.714341	+	0.518999i
$295$	−0.886879	+	2.72953i	−0.0516361	+	0.158920i
$296$	−39.5262			−2.29741
$297$	−2.13508	+	2.53800i	−0.123890	+	0.147270i
$298$	−42.1202			−2.43996
$299$	2.16544	−	6.66453i	0.125230	−	0.385420i
$300$	−19.3080	+	14.0281i	−1.11475	+	0.809911i
$301$	1.53566	+	1.11572i	0.0885140	+	0.0643092i
$302$	−2.60390	−	8.01398i	−0.149838	−	0.461153i
$303$	0.450597	+	1.38679i	0.0258861	+	0.0796693i
$304$	−61.0773	−	44.3753i	−3.50302	−	2.54510i
$305$	−6.14025	+	4.46115i	−0.351589	+	0.255445i
$306$	−3.89771	+	11.9959i	−0.222817	+	0.685761i
$307$	−23.2782			−1.32856			−0.664280	−	0.747484i	$-0.731262\pi$
$307$	−23.2782			−1.32856			−0.664280	+	0.747484i	$0.731262\pi$
$308$	15.0459	−	17.8853i	0.857318	−	1.01911i
$309$	−14.2940			−0.813157
$310$	5.56517	−	17.1278i	0.316081	−	0.972796i
$311$	−12.6971	+	9.22500i	−0.719987	+	0.523102i	−0.886380	−	0.462958i	$-0.846788\pi$
$311$	−12.6971	+	9.22500i	−0.719987	+	0.523102i	0.166393	+	0.986060i	$0.446788\pi$
$312$	8.25799	+	5.99978i	0.467517	+	0.339671i
$313$	3.12469	+	9.61681i	0.176618	+	0.543574i	0.999704	−	0.0243428i	$-0.00774933\pi$
$313$	3.12469	+	9.61681i	0.176618	+	0.543574i	−0.823086	+	0.567917i	$0.807749\pi$
$314$	−19.4550	−	59.8762i	−1.09791	−	3.37901i
$315$	−0.897452	−	0.652037i	−0.0505657	−	0.0367381i
$316$	50.5817	−	36.7498i	2.84544	−	2.06734i
$317$	8.83469	−	27.1904i	0.496206	−	1.52716i	−0.318864	−	0.947801i	$-0.603301\pi$
$317$	8.83469	−	27.1904i	0.496206	−	1.52716i	0.815069	−	0.579363i	$-0.196699\pi$
$318$	−11.9057			−0.667637
$319$	1.39201	−	19.5536i	0.0779378	−	1.09479i
$320$	35.4298			1.98059
$321$	−0.737222	+	2.26894i	−0.0411477	+	0.126640i
$322$	−19.4863	+	14.1576i	−1.08593	+	0.788974i
$323$	16.4197	+	11.9296i	0.913615	+	0.663780i
$324$	1.75604	+	5.40453i	0.0975576	+	0.300251i
$325$	−1.29781	−	3.99424i	−0.0719894	−	0.221561i
$326$	33.0162	+	23.9876i	1.82860	+	1.32855i
$327$	−11.1658	+	8.11240i	−0.617468	+	0.448617i
$328$	−14.1736	+	43.6217i	−0.782604	+	2.40861i
$329$	0.0867178			0.00478091
$330$	−7.62075	−	3.09013i	−0.419508	−	0.170106i
$331$	−27.3040			−1.50076			−0.750382	−	0.661004i	$-0.770130\pi$
$331$	−27.3040			−1.50076			−0.750382	+	0.661004i	$0.770130\pi$
$332$	25.2311	−	77.6533i	1.38474	−	4.26178i
$333$	3.13275	−	2.27608i	0.171674	−	0.124728i
$334$	−29.3039	−	21.2905i	−1.60344	−	1.16497i
$335$	−4.41959	−	13.6021i	−0.241468	−	0.743161i
$336$	−6.48667	−	19.9639i	−0.353877	−	1.08912i
$337$	22.4761	+	16.3299i	1.22435	+	0.889544i	0.996454	−	0.0841409i	$-0.0268146\pi$
$337$	22.4761	+	16.3299i	1.22435	+	0.889544i	0.227898	+	0.973685i	$0.426815\pi$
$338$	−2.24240	+	1.62920i	−0.121971	+	0.0886168i
$339$	2.17705	−	6.70027i	0.118241	−	0.363909i
$340$	−23.1325			−1.25454
$341$	−23.3817	+	5.79852i	−1.26619	+	0.314007i
$342$	12.3621			0.668464
$343$	−4.77561	+	14.6978i	−0.257859	+	0.793608i
$344$	12.6404	−	9.18375i	0.681522	−	0.495155i
$345$	5.07133	+	3.68453i	0.273031	+	0.198369i
$346$	−0.448817	−	1.38132i	−0.0241286	−	0.0742600i
$347$	3.01188	+	9.26963i	0.161686	+	0.497620i	0.998777	−	0.0494448i	$-0.0157452\pi$
$347$	3.01188	+	9.26963i	0.161686	+	0.497620i	−0.837090	+	0.547065i	$0.815745\pi$
$348$	−27.1730	−	19.7424i	−1.45663	−	1.05830i
$349$	23.1266	−	16.8024i	1.23794	−	0.899413i	0.240477	−	0.970655i	$-0.422696\pi$
$349$	23.1266	−	16.8024i	1.23794	−	0.899413i	0.997459	+	0.0712414i	$0.0226961\pi$
$350$	−4.46086	+	13.7291i	−0.238443	+	0.733853i
$351$	−1.00000			−0.0533761
$352$	−46.4873	−	74.6036i	−2.47778	−	3.97638i
$353$	26.7002			1.42111			0.710555	−	0.703642i	$-0.248444\pi$
$353$	26.7002			1.42111			0.710555	+	0.703642i	$0.248444\pi$
$354$	2.74802	−	8.45753i	0.146056	−	0.449513i
$355$	−3.74245	+	2.71905i	−0.198629	+	0.144312i
$356$	−53.2488	−	38.6875i	−2.82218	−	2.05043i
$357$	1.74384	+	5.36699i	0.0922938	+	0.284051i
$358$	−13.1724	−	40.5406i	−0.696184	−	2.14263i
$359$	−2.41053	−	1.75135i	−0.127223	−	0.0924329i	0.522354	−	0.852729i	$-0.325054\pi$
$359$	−2.41053	−	1.75135i	−0.127223	−	0.0924329i	−0.649577	+	0.760296i	$0.725054\pi$
$360$	−7.38712	+	5.36706i	−0.389335	+	0.282869i
$361$	0.275535	−	0.848010i	0.0145019	−	0.0446321i
$362$	57.6009			3.02744
$363$	1.88290	+	10.8377i	0.0988268	+	0.568829i
$364$	7.04700			0.369363
$365$	0.135866	−	0.418152i	0.00711154	−	0.0218871i
$366$	19.0257	−	13.8230i	0.994489	−	0.722539i
$367$	−5.11575	−	3.71681i	−0.267040	−	0.194016i	0.446205	−	0.894931i	$-0.352775\pi$
$367$	−5.11575	−	3.71681i	−0.267040	−	0.194016i	−0.713245	+	0.700915i	$0.752775\pi$
$368$	36.6549	+	112.812i	1.91077	+	5.88075i
$369$	−1.38855	−	4.27352i	−0.0722851	−	0.222471i
$370$	7.76752	+	5.64343i	0.403814	+	0.293388i
$371$	−4.30932	+	3.13090i	−0.223729	+	0.162548i
$372$	−12.7548	+	39.2552i	−0.661306	+	2.03529i
$373$	14.3080			0.740838			0.370419	−	0.928865i	$-0.379214\pi$
$373$	14.3080			0.740838			0.370419	+	0.928865i	$0.379214\pi$
$374$	22.1237	+	35.5046i	1.14399	+	1.83590i
$375$	8.22960			0.424975
$376$	0.220574	−	0.678857i	0.0113752	−	0.0350094i
$377$	4.78175	−	3.47414i	0.246273	−	0.178927i
$378$	2.78078	+	2.02035i	0.143028	+	0.103916i
$379$	2.06282	+	6.34871i	0.105960	+	0.326111i	0.989955	−	0.141386i	$-0.0451559\pi$
$379$	2.06282	+	6.34871i	0.105960	+	0.326111i	−0.883995	+	0.467497i	$0.845156\pi$
$380$	7.00599	+	21.5622i	0.359400	+	1.10612i
$381$	−9.04517	−	6.57170i	−0.463398	−	0.336678i
$382$	4.87144	−	3.53931i	0.249244	−	0.181087i
$383$	8.36061	−	25.7313i	0.427207	−	1.31481i	−0.473658	−	0.880709i	$-0.657067\pi$
$383$	8.36061	−	25.7313i	0.427207	−	1.31481i	0.900865	−	0.434099i	$-0.142933\pi$
$384$	−56.7733			−2.89720
$385$	−3.57100	+	0.885586i	−0.181995	+	0.0451336i
$386$	34.8945			1.77608
$387$	−0.473006	+	1.45576i	−0.0240443	+	0.0740007i
$388$	−12.4614	+	9.05377i	−0.632634	+	0.459636i
$389$	−23.1192	−	16.7971i	−1.17219	−	0.851648i	−0.180923	−	0.983497i	$-0.557908\pi$
$389$	−23.1192	−	16.7971i	−1.17219	−	0.851648i	−0.991270	+	0.131850i	$0.957908\pi$
$390$	−0.766194	−	2.35810i	−0.0387977	−	0.119407i
$391$	−9.85410	−	30.3278i	−0.498343	−	1.53374i
$392$	45.1066	+	32.7719i	2.27823	+	1.65523i
$393$	5.86129	−	4.25848i	0.295663	−	0.214812i
$394$	−1.82483	+	5.61624i	−0.0919334	+	0.282942i
$395$	−9.84204			−0.495207
$396$	17.4660	+	7.08225i	0.877698	+	0.355896i
$397$	15.5568			0.780773			0.390387	−	0.920651i	$-0.372341\pi$
$397$	15.5568			0.780773			0.390387	+	0.920651i	$0.372341\pi$
$398$	7.67439	−	23.6193i	0.384682	−	1.18393i
$399$	4.47451	−	3.25092i	0.224006	−	0.162750i
$400$	57.5139	+	41.7863i	2.87569	+	2.08931i
$401$	−5.92985	−	18.2502i	−0.296122	−	0.911371i	−0.982842	−	0.184449i	$-0.940950\pi$
$401$	−5.92985	−	18.2502i	−0.296122	−	0.911371i	0.686720	−	0.726922i	$-0.259050\pi$
$402$	13.6942	+	42.1464i	0.683004	+	2.10207i
$403$	−5.87621	−	4.26932i	−0.292715	−	0.212670i
$404$	6.70370	−	4.87053i	0.333522	−	0.242318i
$405$	0.276429	−	0.850760i	0.0137358	−	0.0422746i
$406$	−20.3160			−1.00826
$407$	0.911974	−	12.8105i	0.0452049	−	0.634994i
$408$	46.4503			2.29963
$409$	−5.83974	+	17.9729i	−0.288757	+	0.888701i	0.696491	+	0.717566i	$0.254744\pi$
$409$	−5.83974	+	17.9729i	−0.288757	+	0.888701i	−0.985247	+	0.171136i	$0.945256\pi$
$410$	9.01350	−	6.54869i	0.445145	−	0.323417i
$411$	10.4026	+	7.55793i	0.513123	+	0.372805i
$412$	25.1008	+	77.2523i	1.23663	+	3.80595i
$413$	−1.22947	−	3.78391i	−0.0604981	−	0.186194i
$414$	−15.7136	−	11.4166i	−0.772283	−	0.561096i
$415$	−10.3983	+	7.55478i	−0.510431	+	0.370850i
$416$	8.19002	−	25.2063i	0.401549	−	1.23584i
$417$	9.50139			0.465285
$418$	26.3939	−	31.3749i	1.29097	−	1.53460i
$419$	−12.1794			−0.595002			−0.297501	−	0.954721i	$-0.596153\pi$
$419$	−12.1794			−0.595002			−0.297501	+	0.954721i	$0.596153\pi$
$420$	−1.94799	+	5.99530i	−0.0950523	+	0.292541i
$421$	−16.6317	+	12.0836i	−0.810578	+	0.588919i	−0.913998	−	0.405718i	$-0.867021\pi$
$421$	−16.6317	+	12.0836i	−0.810578	+	0.588919i	0.103420	+	0.994638i	$0.467021\pi$
$422$	−41.5908	−	30.2175i	−2.02461	−	1.47097i
$423$	0.0216092	+	0.0665061i	0.00105067	+	0.00323364i
$424$	13.5487	+	41.6986i	0.657983	+	2.02506i
$425$	−15.4617	−	11.2336i	−0.750002	−	0.544909i
$426$	11.5961	−	8.42505i	0.561832	−	0.408195i
$427$	3.25134	−	10.0066i	0.157343	−	0.484253i
$428$	13.5571			0.655308
$429$	−2.13508	+	2.53800i	−0.103082	+	0.122536i
$430$	−3.79526			−0.183023
$431$	1.80032	−	5.54083i	0.0867185	−	0.266892i	−0.898289	−	0.439406i	$-0.855189\pi$
$431$	1.80032	−	5.54083i	0.0867185	−	0.266892i	0.985007	+	0.172514i	$0.0551890\pi$
$432$	13.6944	−	9.94960i	0.658874	−	0.478700i
$433$	−1.17976	−	0.857142i	−0.0566954	−	0.0411916i	0.559077	−	0.829116i	$-0.311156\pi$
$433$	−1.17976	−	0.857142i	−0.0566954	−	0.0411916i	−0.615772	+	0.787924i	$0.711156\pi$
$434$	7.71491	+	23.7440i	0.370327	+	1.13975i
$435$	1.63385	+	5.02847i	0.0783371	+	0.241097i
$436$	63.4511	+	46.1000i	3.03876	+	2.20779i
$437$	−25.2846	+	18.3703i	−1.20953	+	0.878773i
$438$	−0.420984	+	1.29565i	−0.0201154	+	0.0619088i
$439$	1.86582			0.0890506			0.0445253	−	0.999008i	$-0.485822\pi$
$439$	1.86582			0.0890506			0.0445253	+	0.999008i	$0.485822\pi$
$440$	−2.15046	+	30.2076i	−0.102519	+	1.44009i
$441$	−5.46218			−0.260104
$442$	−3.89771	+	11.9959i	−0.185395	+	0.570587i
$443$	9.44268	−	6.86051i	0.448635	−	0.325952i	−0.340422	−	0.940273i	$-0.610570\pi$
$443$	9.44268	−	6.86051i	0.448635	−	0.325952i	0.789057	+	0.614320i	$0.210570\pi$
$444$	−17.8023	−	12.9342i	−0.844862	−	0.613828i
$445$	3.20172	+	9.85388i	0.151776	+	0.467119i
$446$	−6.78624	−	20.8859i	−0.321338	−	0.988976i
$447$	−12.2940	−	8.93210i	−0.581485	−	0.422474i
$448$	−39.7355	+	28.8695i	−1.87733	+	1.36396i
$449$	−9.70474	+	29.8681i	−0.457995	+	1.40956i	0.409588	+	0.912271i	$0.365672\pi$
$449$	−9.70474	+	29.8681i	−0.457995	+	1.40956i	−0.867583	+	0.497292i	$0.834328\pi$
$450$	−11.6408			−0.548754
$451$	−13.8109	−	5.60015i	−0.650328	−	0.263701i
$452$	−40.0348			−1.88308
$453$	0.939439	−	2.89130i	0.0441387	−	0.135845i
$454$	28.6151	−	20.7901i	1.34297	−	0.975726i
$455$	−0.897452	−	0.652037i	−0.0420732	−	0.0305680i
$456$	−14.0681	−	43.2971i	−0.658798	−	2.02757i
$457$	−4.31821	−	13.2901i	−0.201997	−	0.621684i	−0.999823	−	0.0187963i	$-0.994017\pi$
$457$	−4.31821	−	13.2901i	−0.201997	−	0.621684i	0.797826	−	0.602888i	$-0.205983\pi$
$458$	27.4760	+	19.9625i	1.28387	+	0.932785i
$459$	−3.68154	+	2.67479i	−0.171839	+	0.124849i
$460$	11.0077	−	33.8783i	0.513238	−	1.57958i
$461$	−17.5919			−0.819338			−0.409669	−	0.912234i	$-0.634356\pi$
$461$	−17.5919			−0.819338			−0.409669	+	0.912234i	$0.634356\pi$
$462$	11.0648	−	2.74401i	0.514782	−	0.127663i
$463$	−30.3624			−1.41106			−0.705529	−	0.708681i	$-0.749291\pi$
$463$	−30.3624			−1.41106			−0.705529	+	0.708681i	$0.749291\pi$
$464$	−30.9171	+	95.1529i	−1.43529	+	4.41736i
$465$	5.25652	−	3.81908i	0.243765	−	0.177106i
$466$	26.1258	+	18.9815i	1.21025	+	0.879301i
$467$	−9.64078	−	29.6713i	−0.446122	−	1.37302i	−0.881248	−	0.472653i	$-0.843296\pi$
$467$	−9.64078	−	29.6713i	−0.446122	−	1.37302i	0.435126	−	0.900369i	$-0.356704\pi$
$468$	1.75604	+	5.40453i	0.0811729	+	0.249824i
$469$	16.0402	+	11.6539i	0.740666	+	0.538126i
$470$	−0.140271	+	0.101913i	−0.00647024	+	0.00470090i
$471$	7.01899	−	21.6022i	0.323418	−	0.995378i
$472$	−32.7490			−1.50740
$473$	2.68483	+	4.30866i	0.123448	+	0.198112i
$474$	30.4958			1.40072
$475$	−5.78823	+	17.8143i	−0.265582	+	0.817378i
$476$	25.9438	−	18.8493i	1.18913	−	0.863954i
$477$	−3.47501	−	2.52474i	−0.159110	−	0.115600i
$478$	15.7878	+	48.5899i	0.722118	+	2.22245i
$479$	−3.64486	−	11.2177i	−0.166538	−	0.512550i	0.832609	−	0.553862i	$-0.186846\pi$
$479$	−3.64486	−	11.2177i	−0.166538	−	0.512550i	−0.999146	+	0.0413115i	$0.986846\pi$
$480$	19.1805	+	13.9355i	0.875468	+	0.636064i
$481$	3.13275	−	2.27608i	0.142841	−	0.103780i
$482$	−18.3220	+	56.3892i	−0.834543	+	2.56846i
$483$	−8.68992			−0.395405
$484$	55.2659	−	29.2075i	2.51209	−	1.32761i
$485$	2.42471			0.110100
$486$	−0.856521	+	2.63610i	−0.0388526	+	0.119576i
$487$	1.50802	−	1.09564i	0.0683349	−	0.0496482i	−0.553093	−	0.833119i	$-0.686553\pi$
$487$	1.50802	−	1.09564i	0.0683349	−	0.0496482i	0.621428	+	0.783471i	$0.286553\pi$
$488$	−70.0651	−	50.9053i	−3.17170	−	2.30437i
$489$	4.54983	+	14.0029i	0.205751	+	0.633235i
$490$	−4.18509	−	12.8804i	−0.189063	−	0.581876i
$491$	−4.97920	−	3.61760i	−0.224708	−	0.163260i	0.469735	−	0.882807i	$-0.344349\pi$
$491$	−4.97920	−	3.61760i	−0.224708	−	0.163260i	−0.694443	+	0.719547i	$0.744349\pi$
$492$	−20.6580	+	15.0089i	−0.931335	+	0.676655i
$493$	8.31156	−	25.5804i	0.374334	−	1.15208i
$494$	12.3621			0.556196
$495$	−1.56903	−	2.51801i	−0.0705228	−	0.113176i
$496$	122.949			5.52060
$497$	1.98168	−	6.09898i	0.0888904	−	0.273577i
$498$	32.2193	−	23.4087i	1.44378	−	1.04897i
$499$	−8.27931	−	6.01527i	−0.370633	−	0.269280i	0.386840	−	0.922147i	$-0.373566\pi$
$499$	−8.27931	−	6.01527i	−0.370633	−	0.269280i	−0.757473	+	0.652866i	$0.773566\pi$
$500$	−14.4515	−	44.4771i	−0.646290	−	1.98908i
$501$	−4.03826	−	12.4285i	−0.180416	−	0.555264i
$502$	−2.54588	−	1.84969i	−0.113628	−	0.0825558i
$503$	33.4120	−	24.2753i	1.48977	−	1.08238i	0.515528	−	0.856873i	$-0.327596\pi$
$503$	33.4120	−	24.2753i	1.48977	−	1.08238i	0.974241	−	0.225508i	$-0.0724042\pi$
$504$	3.91158	−	12.0386i	0.174236	−	0.536242i
$505$	−1.30439			−0.0580444
$506$	−62.5252	+	15.5059i	−2.77958	+	0.689320i
$507$	−1.00000			−0.0444116
$508$	−19.6333	+	60.4250i	−0.871086	+	2.68093i
$509$	−23.3095	+	16.9354i	−1.03318	+	0.750647i	−0.968942	−	0.247288i	$-0.920461\pi$
$509$	−23.3095	+	16.9354i	−1.03318	+	0.750647i	−0.0642350	+	0.997935i	$0.520461\pi$
$510$	−9.12820	−	6.63203i	−0.404204	−	0.293671i
$511$	0.188349	+	0.579677i	0.00833205	+	0.0256434i
$512$	31.8482	+	98.0186i	1.40750	+	4.33185i
$513$	3.60822	+	2.62153i	0.159307	+	0.115743i
$514$	60.9370	−	44.2733i	2.68782	−	1.95281i
$515$	3.95127	−	12.1608i	0.174114	−	0.535867i
$516$	8.69833			0.382923
$517$	0.214930	+	0.0871516i	0.00945260	+	0.00383292i
$518$	−13.3100			−0.584806
$519$	0.161925	−	0.498354i	0.00710771	−	0.0218753i
$520$	−7.38712	+	5.36706i	−0.323947	+	0.235361i
$521$	−9.31233	−	6.76580i	−0.407980	−	0.296415i	0.364803	−	0.931085i	$-0.381136\pi$
$521$	−9.31233	−	6.76580i	−0.407980	−	0.296415i	−0.772784	+	0.634669i	$0.781136\pi$
$522$	−5.06252	−	15.5808i	−0.221581	−	0.681955i
$523$	−2.56346	−	7.88951i	−0.112092	−	0.344984i	0.879237	−	0.476384i	$-0.158053\pi$
$523$	−2.56346	−	7.88951i	−0.112092	−	0.344984i	−0.991329	+	0.131400i	$0.958053\pi$
$524$	−33.3077	−	24.1995i	−1.45505	−	1.05716i
$525$	−4.21346	+	3.06126i	−0.183890	+	0.133604i
$526$	−19.9565	+	61.4199i	−0.870146	+	2.67803i
$527$	−33.0530			−1.43981
$528$	3.98659	−	55.9997i	0.173494	−	2.43707i
$529$	26.1051			1.13500
$530$	3.29107	−	10.1289i	0.142955	−	0.439970i
$531$	2.59561	−	1.88582i	0.112640	−	0.0818376i
$532$	−25.4271	−	18.4739i	−1.10241	−	0.800945i
$533$	−1.38855	−	4.27352i	−0.0601448	−	0.185107i
$534$	−9.92061	−	30.5325i	−0.429307	−	1.32127i
$535$	−1.72653	−	1.25440i	−0.0746444	−	0.0542323i
$536$	132.030	−	95.9255i	5.70283	−	4.14335i
$537$	4.75237	−	14.6263i	0.205080	−	0.631171i
$538$	71.0653			3.06384
$539$	−11.6622	+	13.8630i	−0.502325	+	0.597123i
$540$	−5.08337			−0.218754
$541$	1.06966	−	3.29208i	0.0459883	−	0.141537i	−0.925426	−	0.378929i	$-0.876292\pi$
$541$	1.06966	−	3.29208i	0.0459883	−	0.141537i	0.971414	+	0.237392i	$0.0762925\pi$
$542$	−0.277423	+	0.201560i	−0.0119163	+	0.00865772i
$543$	16.8125	+	12.2150i	0.721492	+	0.524195i
$544$	−37.2697	−	114.704i	−1.59793	−	4.91791i
$545$	−3.81517	−	11.7419i	−0.163424	−	0.502967i
$546$	2.78078	+	2.02035i	0.119006	+	0.0864631i
$547$	26.9989	−	19.6158i	1.15439	−	0.838713i	0.165331	−	0.986238i	$-0.447131\pi$
$547$	26.9989	−	19.6158i	1.15439	−	0.838713i	0.989058	+	0.147525i	$0.0471307\pi$
$548$	22.5797	−	69.4932i	0.964557	−	2.96860i
$549$	8.48452			0.362111
$550$	−24.8540	+	29.5444i	−1.05978	+	1.25978i
$551$	−26.3612			−1.12302
$552$	−22.1036	+	68.0278i	−0.940790	+	2.89545i
$553$	11.0381	−	8.01966i	0.469388	−	0.341031i
$554$	−49.6196	−	36.0507i	−2.10813	−	1.53165i
$555$	1.07041	+	3.29439i	0.0454365	+	0.139839i
$556$	−16.6848	−	51.3505i	−0.707593	−	2.17775i
$557$	33.3537	+	24.2329i	1.41324	+	1.02678i	0.992841	+	0.119440i	$0.0381100\pi$
$557$	33.3537	+	24.2329i	1.41324	+	1.02678i	0.420399	+	0.907339i	$0.361890\pi$
$558$	−16.2875	+	11.8335i	−0.689503	+	0.500953i
$559$	−0.473006	+	1.45576i	−0.0200060	+	0.0615723i
$560$	18.7776			0.793499
$561$	−1.07173	+	15.0546i	−0.0452485	+	0.635607i
$562$	−22.0929			−0.931933
$563$	0.549515	−	1.69123i	0.0231593	−	0.0712770i	−0.938809	−	0.344438i	$-0.888069\pi$
$563$	0.549515	−	1.69123i	0.0231593	−	0.0712770i	0.961968	+	0.273161i	$0.0880693\pi$
$564$	0.321488	−	0.233574i	0.0135371	−	0.00983526i
$565$	5.09852	+	3.70429i	0.214496	+	0.155841i
$566$	14.0467	+	43.2312i	0.590426	+	1.81714i
$567$	0.383209	+	1.17939i	0.0160932	+	0.0495299i
$568$	−42.7044	−	31.0266i	−1.79184	−	1.30185i
$569$	4.38380	−	3.18502i	0.183779	−	0.133523i	−0.492092	−	0.870543i	$-0.663768\pi$
$569$	4.38380	−	3.18502i	0.183779	−	0.133523i	0.675871	+	0.737020i	$0.263768\pi$
$570$	−3.41723	+	10.5172i	−0.143132	+	0.440515i
$571$	−9.67740			−0.404987			−0.202493	−	0.979284i	$-0.564904\pi$
$571$	−9.67740			−0.404987			−0.202493	+	0.979284i	$0.564904\pi$
$572$	17.4660	+	7.08225i	0.730289	+	0.296124i
$573$	2.17242			0.0907541
$574$	−4.77277	+	14.6891i	−0.199212	+	0.613110i
$575$	23.8094	−	17.2986i	0.992922	−	0.721400i
$576$	−32.0425	−	23.2802i	−1.33510	−	0.970009i
$577$	4.08904	+	12.5848i	0.170229	+	0.523911i	0.999384	−	0.0351082i	$-0.0111776\pi$
$577$	4.08904	+	12.5848i	0.170229	+	0.523911i	−0.829154	+	0.559020i	$0.811178\pi$
$578$	3.17616	+	9.77522i	0.132111	+	0.406596i
$579$	10.1849	+	7.39980i	0.423272	+	0.307525i
$580$	24.3074	−	17.6604i	1.00931	−	0.733307i
$581$	5.50602	−	16.9458i	0.228428	−	0.703030i
$582$	−7.51303			−0.311425
$583$	−13.8272	+	3.42906i	−0.572664	+	0.142017i
$584$	5.01700			0.207605
$585$	0.276429	−	0.850760i	0.0114289	−	0.0351746i
$586$	−5.67661	+	4.12430i	−0.234499	+	0.170373i
$587$	32.9288	+	23.9241i	1.35912	+	0.987455i	0.998501	+	0.0547404i	$0.0174331\pi$
$587$	32.9288	+	23.9241i	1.35912	+	0.987455i	0.360615	+	0.932715i	$0.382567\pi$
$588$	9.59179	+	29.5205i	0.395559	+	1.21740i
$589$	10.0105	+	30.8093i	0.412477	+	1.26947i
$590$	6.43570	+	4.67581i	0.264953	+	0.192500i
$591$	−1.72362	+	1.25228i	−0.0709002	+	0.0515120i
$592$	−20.2552	+	62.3392i	−0.832485	+	2.56213i
$593$	−37.8588			−1.55467			−0.777337	−	0.629084i	$-0.783430\pi$
$593$	−37.8588			−1.55467			−0.777337	+	0.629084i	$0.783430\pi$
$594$	4.86169	+	7.80213i	0.199478	+	0.320125i
$595$	−5.04806			−0.206950
$596$	−26.6851	+	82.1282i	−1.09306	+	3.36410i
$597$	7.24876	−	5.26653i	0.296672	−	0.215545i
$598$	−15.7136	−	11.4166i	−0.642578	−	0.466860i
$599$	7.14557	+	21.9918i	0.291960	+	0.898560i	0.984226	+	0.176918i	$0.0566126\pi$
$599$	7.14557	+	21.9918i	0.291960	+	0.898560i	−0.692266	+	0.721643i	$0.743387\pi$
$600$	13.2473	+	40.7710i	0.540819	+	1.66447i
$601$	12.0927	+	8.78588i	0.493273	+	0.358384i	0.806441	−	0.591314i	$-0.201391\pi$
$601$	12.0927	+	8.78588i	0.493273	+	0.358384i	−0.313169	+	0.949697i	$0.601391\pi$
$602$	4.25648	−	3.09252i	0.173481	−	0.126042i
$603$	−4.94061	+	15.2056i	−0.201197	+	0.619222i
$604$	−17.2758			−0.702942
$605$	−9.74073	−	1.39394i	−0.396017	−	0.0566717i
$606$	4.04168			0.164182
$607$	−1.28401	+	3.95177i	−0.0521163	+	0.160397i	−0.973727	−	0.227718i	$-0.926874\pi$
$607$	−1.28401	+	3.95177i	−0.0521163	+	0.160397i	0.921611	+	0.388115i	$0.126874\pi$
$608$	−95.6303	+	69.4795i	−3.87832	+	2.81776i
$609$	−5.92979	−	4.30825i	−0.240287	−	0.174579i
$610$	6.50079	+	20.0074i	0.263209	+	0.810075i
$611$	0.0216092	+	0.0665061i	0.000874213	+	0.00269055i
$612$	20.9209	+	15.1999i	0.845677	+	0.614420i
$613$	−25.8993	+	18.8169i	−1.04606	+	0.760008i	−0.971459	−	0.237206i	$-0.923768\pi$
$613$	−25.8993	+	18.8169i	−1.04606	+	0.760008i	−0.0746015	+	0.997213i	$0.523768\pi$
$614$	−19.9383	+	61.3638i	−0.804644	+	2.47644i
$615$	4.01958			0.162085
$616$	−22.2025	−	35.6309i	−0.894563	−	1.43561i
$617$	−4.58657			−0.184649			−0.0923243	−	0.995729i	$-0.529430\pi$
$617$	−4.58657			−0.184649			−0.0923243	+	0.995729i	$0.529430\pi$
$618$	−12.2431	+	37.6804i	−0.492490	+	1.51573i
$619$	20.8265	−	15.1313i	0.837087	−	0.608180i	−0.0844682	−	0.996426i	$-0.526919\pi$
$619$	20.8265	−	15.1313i	0.837087	−	0.608180i	0.921556	+	0.388247i	$0.126919\pi$
$620$	−29.8710	−	21.7025i	−1.19965	−	0.871595i
$621$	−2.16544	−	6.66453i	−0.0868960	−	0.267438i
$622$	13.4427	+	41.3723i	0.539002	+	1.65888i
$623$	−11.6201	−	8.44252i	−0.465551	−	0.338242i
$624$	13.6944	−	9.94960i	0.548217	−	0.398303i
$625$	4.21414	−	12.9698i	0.168566	−	0.518792i
$626$	28.0273			1.12019
$627$	14.3573	−	3.56051i	0.573374	−	0.142193i
$628$	−129.075			−5.15067
$629$	5.44530	−	16.7589i	0.217118	−	0.668221i
$630$	−2.48752	+	1.80729i	−0.0991052	+	0.0720042i
$631$	−3.79391	−	2.75643i	−0.151033	−	0.109732i	0.509702	−	0.860351i	$-0.329755\pi$
$631$	−3.79391	−	2.75643i	−0.151033	−	0.109732i	−0.660735	+	0.750619i	$0.729755\pi$
$632$	−34.7043	−	106.809i	−1.38046	−	4.24863i
$633$	−5.73148	−	17.6397i	−0.227806	−	0.701114i
$634$	−64.1095	−	46.5783i	−2.54611	−	1.84986i
$635$	8.09128	−	5.87866i	0.321093	−	0.233287i
$636$	−7.54279	+	23.2143i	−0.299091	+	0.920507i
$637$	−5.46218			−0.216419
$638$	−50.3531	−	20.4176i	−1.99350	−	0.808340i
$639$	5.17128			0.204573
$640$	15.6938	−	48.3005i	0.620351	−	1.90924i
$641$	−29.5157	+	21.4444i	−1.16580	+	0.847003i	−0.990500	−	0.137512i	$-0.956089\pi$
$641$	−29.5157	+	21.4444i	−1.16580	+	0.847003i	−0.175300	+	0.984515i	$0.556089\pi$
$642$	5.34970	+	3.88678i	0.211136	+	0.153399i
$643$	−5.49114	−	16.9000i	−0.216550	−	0.666471i	−0.999040	−	0.0438083i	$-0.986051\pi$
$643$	−5.49114	−	16.9000i	−0.216550	−	0.666471i	0.782490	−	0.622663i	$-0.213949\pi$
$644$	15.2598	+	46.9649i	0.601322	+	1.85068i
$645$	−1.10775	−	0.804830i	−0.0436177	−	0.0316901i
$646$	45.5114	−	33.0660i	1.79062	−	1.30096i
$647$	8.89315	−	27.3703i	0.349626	−	1.07604i	−0.609434	−	0.792836i	$-0.708603\pi$
$647$	8.89315	−	27.3703i	0.349626	−	1.07604i	0.959060	−	0.283202i	$-0.0913966\pi$
$648$	10.2074			0.400986
$649$	0.755607	−	10.6140i	0.0296602	−	0.416637i
$650$	−11.6408			−0.456591
$651$	−2.78340	+	8.56641i	−0.109090	+	0.335744i
$652$	67.6896	−	49.1794i	2.65093	−	1.92601i
$653$	−9.42026	−	6.84422i	−0.368643	−	0.267835i	0.388005	−	0.921657i	$-0.373164\pi$
$653$	−9.42026	−	6.84422i	−0.368643	−	0.267835i	−0.756648	+	0.653822i	$0.773164\pi$
$654$	11.8214	+	36.3825i	0.462253	+	1.42267i
$655$	2.00271	+	6.16371i	0.0782524	+	0.240836i
$656$	61.5353	+	44.7080i	2.40255	+	1.74555i
$657$	−0.397635	+	0.288899i	−0.0155132	+	0.0112710i
$658$	0.0742756	−	0.228597i	0.00289556	−	0.00891163i
$659$	−41.3933			−1.61245			−0.806227	−	0.591606i	$-0.798494\pi$
$659$	−41.3933			−1.61245			−0.806227	+	0.591606i	$0.798494\pi$
$660$	−10.8534	+	12.9016i	−0.422468	+	0.502194i
$661$	29.1692			1.13455			0.567276	−	0.823528i	$-0.307997\pi$
$661$	29.1692			1.13455			0.567276	+	0.823528i	$0.307997\pi$
$662$	−23.3865	+	71.9761i	−0.908941	+	2.79743i
$663$	−3.68154	+	2.67479i	−0.142979	+	0.103880i
$664$	−118.653	−	86.2061i	−4.60461	−	3.34545i
$665$	1.52887	+	4.70539i	0.0592871	+	0.182467i
$666$	−3.31670	−	10.2078i	−0.128520	−	0.395542i
$667$	33.5081	+	24.3451i	1.29744	+	0.942645i
$668$	−60.0788	+	43.6498i	−2.32452	+	1.68886i
$669$	2.44835	−	7.53525i	0.0946587	−	0.291330i
$670$	−39.6419			−1.53150
$671$	18.1151	−	21.5337i	0.699326	−	0.831300i
$672$	−32.8666			−1.26786
$673$	−1.57392	+	4.84404i	−0.0606703	+	0.186724i	−0.976798	−	0.214162i	$-0.931298\pi$
$673$	−1.57392	+	4.84404i	−0.0606703	+	0.186724i	0.916128	+	0.400886i	$0.131298\pi$
$674$	62.2984	−	45.2625i	2.39965	−	1.74344i
$675$	−3.39771	−	2.46858i	−0.130778	−	0.0950156i
$676$	1.75604	+	5.40453i	0.0675399	+	0.207866i
$677$	10.5489	+	32.4661i	0.405426	+	1.24777i	0.920539	+	0.390651i	$0.127750\pi$
$677$	10.5489	+	32.4661i	0.405426	+	1.24777i	−0.515112	+	0.857123i	$0.672250\pi$
$678$	−15.7979	−	11.4778i	−0.606715	−	0.440804i
$679$	−2.71938	+	1.97575i	−0.104360	+	0.0758222i
$680$	−12.8402	+	39.5180i	−0.492398	+	1.51545i
$681$	12.7609			0.488999
$682$	−4.74144	+	66.6031i	−0.181559	+	2.55036i
$683$	−7.78048			−0.297712			−0.148856	−	0.988859i	$-0.547559\pi$
$683$	−7.78048			−0.297712			−0.148856	+	0.988859i	$0.547559\pi$
$684$	7.83194	−	24.1042i	0.299462	−	0.921648i
$685$	−9.30557	+	6.76089i	−0.355547	+	0.258320i
$686$	34.6545	+	25.1780i	1.32312	+	0.961300i
$687$	3.78636	+	11.6532i	0.144459	+	0.444598i
$688$	−8.00671	−	24.6421i	−0.305253	−	0.939472i
$689$	−3.47501	−	2.52474i	−0.132387	−	0.0961850i
$690$	14.0565	−	10.2126i	0.535122	−	0.388789i
$691$	−14.1844	+	43.6550i	−0.539599	+	1.66072i	0.193897	+	0.981022i	$0.437887\pi$
$691$	−14.1844	+	43.6550i	−0.539599	+	1.66072i	−0.733496	+	0.679694i	$0.762113\pi$
$692$	−2.97771			−0.113196
$693$	3.81148	+	1.54551i	0.144786	+	0.0587092i
$694$	27.0154			1.02549
$695$	−2.62646	+	8.08340i	−0.0996272	+	0.306621i
$696$	−48.8094	+	35.4621i	−1.85012	+	1.34419i
$697$	−16.5428	−	12.0190i	−0.626603	−	0.455253i
$698$	−24.4845	−	75.3556i	−0.926752	−	2.85225i
$699$	3.60030	+	11.0806i	0.136176	+	0.419106i
$700$	23.9436	+	17.3961i	0.904984	+	0.657509i
$701$	9.63254	−	6.99845i	0.363816	−	0.264328i	−0.390826	−	0.920465i	$-0.627811\pi$
$701$	9.63254	−	6.99845i	0.363816	−	0.264328i	0.754642	+	0.656137i	$0.227811\pi$
$702$	−0.856521	+	2.63610i	−0.0323273	+	0.0994932i
$703$	−17.2704			−0.651367
$704$	−127.498	+	31.6188i	−4.80527	+	1.19168i
$705$	−0.0625541			−0.00235592
$706$	22.8693	−	70.3845i	0.860698	−	2.64896i
$707$	1.46291	−	1.06286i	0.0550182	−	0.0399731i
$708$	−14.7499	−	10.7165i	−0.554337	−	0.402749i
$709$	3.99044	+	12.2813i	0.149864	+	0.461235i	0.997604	−	0.0691770i	$-0.0220373\pi$
$709$	3.99044	+	12.2813i	0.149864	+	0.461235i	−0.847740	+	0.530412i	$0.822037\pi$
$710$	3.96220	+	12.1944i	0.148699	+	0.457648i
$711$	8.90107	+	6.46700i	0.333816	+	0.242532i
$712$	−95.6478	+	69.4922i	−3.58455	+	2.60433i
$713$	15.7284	−	48.4071i	0.589034	−	1.81286i
$714$	15.6416			0.585370
$715$	−1.56903	−	2.51801i	−0.0586785	−	0.0941683i
$716$	−87.3935			−3.26605
$717$	−5.69596	+	17.5303i	−0.212719	+	0.654683i
$718$	−6.68142	+	4.85433i	−0.249348	+	0.181162i
$719$	21.3814	+	15.5345i	0.797392	+	0.579339i	0.910148	−	0.414283i	$-0.135968\pi$
$719$	21.3814	+	15.5345i	0.797392	+	0.579339i	−0.112756	+	0.993623i	$0.535968\pi$
$720$	4.67918	+	14.4010i	0.174383	+	0.536695i
$721$	5.47758	+	16.8583i	0.203996	+	0.627834i
$722$	−1.99944	−	1.45268i	−0.0744114	−	0.0540631i
$723$	−17.3058	+	12.5734i	−0.643610	+	0.467610i
$724$	36.4928	−	112.313i	1.35625	−	4.17409i
$725$	24.8232			0.921909
$726$	30.1819	+	4.31915i	1.12015	+	0.160299i
$727$	−19.7952			−0.734162			−0.367081	−	0.930189i	$-0.619643\pi$
$727$	−19.7952			−0.734162			−0.367081	+	0.930189i	$0.619643\pi$
$728$	3.91158	−	12.0386i	0.144973	−	0.446180i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−0.985919	−	0.716312i	−0.0364905	−	0.0265119i
$731$	2.15248	+	6.62464i	0.0796122	+	0.245021i
$732$	−14.8991	−	45.8548i	−0.550688	−	1.69484i
$733$	32.4925	+	23.6072i	1.20014	+	0.871951i	0.994298	−	0.106634i	$-0.0340074\pi$
$733$	32.4925	+	23.6072i	1.20014	+	0.871951i	0.205840	+	0.978586i	$0.434007\pi$
$734$	−14.1796	+	10.3021i	−0.523380	+	0.380258i
$735$	1.50990	−	4.64700i	0.0556936	−	0.171407i
$736$	185.723			6.84584
$737$	28.0434	+	45.0045i	1.03299	+	1.65776i
$738$	−12.4548			−0.458466
$739$	−2.08888	+	6.42891i	−0.0768406	+	0.236491i	−0.982097	−	0.188374i	$-0.939678\pi$
$739$	−2.08888	+	6.42891i	−0.0768406	+	0.236491i	0.905257	+	0.424865i	$0.139678\pi$
$740$	15.9249	−	11.5701i	0.585412	−	0.425327i
$741$	3.60822	+	2.62153i	0.132551	+	0.0963041i
$742$	4.56235	+	14.0415i	0.167489	+	0.515479i
$743$	−0.924660	−	2.84581i	−0.0339225	−	0.104403i	0.932662	−	0.360752i	$-0.117480\pi$
$743$	−0.924660	−	2.84581i	−0.0339225	−	0.104403i	−0.966584	+	0.256350i	$0.917480\pi$
$744$	59.9811	+	43.5788i	2.19901	+	1.59768i
$745$	10.9975	−	7.99014i	0.402916	−	0.292736i
$746$	12.2551	−	37.7172i	0.448690	−	1.38093i
$747$	14.3682			0.525705
$748$	83.2451	−	20.6443i	3.04374	−	0.754830i
$749$	2.95848			0.108100
$750$	7.04883	−	21.6941i	0.257387	−	0.792155i
$751$	16.3309	−	11.8651i	0.595922	−	0.432963i	−0.248507	−	0.968630i	$-0.579940\pi$
$751$	16.3309	−	11.8651i	0.595922	−	0.432963i	0.844429	+	0.535668i	$0.179940\pi$
$752$	−0.957635	−	0.695762i	−0.0349213	−	0.0253718i
$753$	−0.350838	−	1.07977i	−0.0127853	−	0.0393490i
$754$	−5.06252	−	15.5808i	−0.184366	−	0.567421i
$755$	2.20011	+	1.59847i	0.0800702	+	0.0581744i
$756$	5.70114	−	4.14212i	0.207349	−	0.150648i
$757$	−5.77833	+	17.7839i	−0.210017	+	0.646366i	0.789453	+	0.613811i	$0.210364\pi$
$757$	−5.77833	+	17.7839i	−0.210017	+	0.646366i	−0.999470	+	0.0325549i	$0.989636\pi$
$758$	18.5027			0.672047
$759$	−21.5380	−	8.73339i	−0.781778	−	0.317002i
$760$	40.7242			1.47722
$761$	1.71258	−	5.27079i	0.0620811	−	0.191066i	−0.915206	−	0.402987i	$-0.867972\pi$
$761$	1.71258	−	5.27079i	0.0620811	−	0.191066i	0.977287	+	0.211921i	$0.0679720\pi$
$762$	−25.0710	+	18.2152i	−0.908228	+	0.659866i
$763$	13.8465	+	10.0601i	0.501278	+	0.364200i
$764$	−3.81485	−	11.7409i	−0.138016	−	0.424771i
$765$	−1.25792	−	3.87149i	−0.0454803	−	0.139974i
$766$	−60.6693	−	44.0788i	−2.19207	−	1.59263i
$767$	2.59561	−	1.88582i	0.0937220	−	0.0680930i
$768$	−24.1493	+	74.3238i	−0.871412	+	2.68193i
$769$	21.5106			0.775692			0.387846	−	0.921724i	$-0.373219\pi$
$769$	21.5106			0.775692			0.387846	+	0.921724i	$0.373219\pi$
$770$	−0.724142	+	10.1720i	−0.0260963	+	0.366575i
$771$	27.1749			0.978679
$772$	22.1073	−	68.0391i	0.795657	−	2.44878i
$773$	−6.93275	+	5.03694i	−0.249354	+	0.181166i	−0.705440	−	0.708769i	$-0.749251\pi$
$773$	−6.93275	+	5.03694i	−0.249354	+	0.181166i	0.456087	+	0.889935i	$0.349251\pi$
$774$	3.43240	+	2.49379i	0.123375	+	0.0896373i
$775$	−9.42650	−	29.0118i	−0.338610	−	1.04213i
$776$	8.54985	+	26.3137i	0.306922	+	0.944608i
$777$	−3.88489	−	2.82254i	−0.139370	−	0.101258i
$778$	−64.0810	+	46.5576i	−2.29742	+	1.66917i
$779$	−6.19295	+	19.0599i	−0.221885	+	0.682893i
$780$	−5.08337			−0.182014
$781$	11.0411	−	13.1247i	0.395081	−	0.469639i
$782$	−88.3874			−3.16073
$783$	1.82647	−	5.62128i	0.0652725	−	0.200888i
$784$	74.8015	−	54.3465i	2.67148	−	1.94095i
$785$	16.4381	+	11.9429i	0.586699	+	0.426262i
$786$	−6.20545	−	19.0984i	−0.221341	−	0.681218i
$787$	8.42496	+	25.9294i	0.300317	+	0.924282i	0.981383	+	0.192060i	$0.0615167\pi$
$787$	8.42496	+	25.9294i	0.300317	+	0.924282i	−0.681066	+	0.732222i	$0.738483\pi$
$788$	9.79473	+	7.11629i	0.348923	+	0.253507i
$789$	−18.8497	+	13.6951i	−0.671067	+	0.487559i
$790$	−8.42991	+	25.9446i	−0.299923	+	0.923068i
$791$	−8.73653			−0.310635
$792$	21.7937	−	25.9065i	0.774404	−	0.920547i
$793$	8.48452			0.301294
$794$	13.3247	−	41.0093i	0.472877	−	1.45536i
$795$	3.10854	−	2.25849i	0.110249	−	0.0801003i
$796$	−41.1922	−	29.9279i	−1.46002	−	1.06077i
$797$	5.54602	+	17.0689i	0.196450	+	0.604611i	0.999957	+	0.00931509i	$0.00296513\pi$
$797$	5.54602	+	17.0689i	0.196450	+	0.604611i	−0.803507	+	0.595296i	$0.797035\pi$
$798$	−4.73725	−	14.5798i	−0.167697	−	0.516118i
$799$	0.257445	+	0.187045i	0.00910775	+	0.00661716i
$800$	90.0509	−	65.4258i	3.18378	−	2.31315i
$801$	3.57917	−	11.0156i	0.126464	−	0.389216i
$802$	−53.1884			−1.87815
$803$	−0.115755	+	1.62602i	−0.00408492	+	0.0573810i
$804$	90.8552			3.20422
$805$	2.40214	−	7.39304i	0.0846645	−	0.260570i
$806$	−16.2875	+	11.8335i	−0.573701	+	0.416818i
$807$	20.7424	+	15.0703i	0.730168	+	0.530498i
$808$	−4.59944	−	14.1556i	−0.161808	−	0.497993i
$809$	−6.33462	−	19.4960i	−0.222713	−	0.685441i	−0.998516	−	0.0544652i	$-0.982655\pi$
$809$	−6.33462	−	19.4960i	−0.222713	−	0.685441i	0.775802	−	0.630976i	$-0.217345\pi$
$810$	−2.00592	−	1.45739i	−0.0704809	−	0.0512074i
$811$	−1.26164	+	0.916634i	−0.0443021	+	0.0321874i	−0.609716	−	0.792620i	$-0.708716\pi$
$811$	−1.26164	+	0.916634i	−0.0443021	+	0.0321874i	0.565414	+	0.824807i	$0.308716\pi$
$812$	−12.8711	+	39.6132i	−0.451687	+	1.39015i
$813$	−0.123717			−0.00433894
$814$	−32.9887	−	13.3765i	−1.15625	−	0.468847i
$815$	−13.1708			−0.461355
$816$	23.8035	−	73.2596i	0.833289	−	2.56460i
$817$	5.52303	−	4.01272i	0.193227	−	0.140387i
$818$	42.3764	+	30.7883i	1.48166	+	1.07649i
$819$	0.383209	+	1.17939i	0.0133904	+	0.0412114i
$820$	−7.05852	−	21.7239i	−0.246494	−	0.758632i
$821$	−31.6239	−	22.9761i	−1.10368	−	0.801871i	−0.122024	−	0.992527i	$-0.538938\pi$
$821$	−31.6239	−	22.9761i	−1.10368	−	0.801871i	−0.981657	+	0.190656i	$0.938938\pi$
$822$	28.8335	−	20.9488i	1.00568	−	0.730673i
$823$	9.56522	−	29.4387i	0.333422	−	1.02617i	−0.634071	−	0.773274i	$-0.718617\pi$
$823$	9.56522	−	29.4387i	0.333422	−	1.02617i	0.967494	−	0.252894i	$-0.0813825\pi$
$824$	145.905			5.08284
$825$	−13.5196	+	3.35278i	−0.470692	+	0.116729i
$826$	−11.0278			−0.383707
$827$	−7.57488	+	23.3131i	−0.263404	+	0.810675i	0.728652	+	0.684884i	$0.240147\pi$
$827$	−7.57488	+	23.3131i	−0.263404	+	0.810675i	−0.992057	+	0.125792i	$0.959853\pi$
$828$	−32.2160	+	23.4063i	−1.11958	+	0.813426i
$829$	−13.9452	−	10.1318i	−0.484338	−	0.351892i	0.318665	−	0.947867i	$-0.396766\pi$
$829$	−13.9452	−	10.1318i	−0.484338	−	0.351892i	−0.803003	+	0.595976i	$0.796766\pi$
$830$	11.0088	+	33.8817i	0.382122	+	1.17605i
$831$	−6.83789	−	21.0449i	−0.237204	−	0.730038i
$832$	−32.0425	−	23.2802i	−1.11087	−	0.807096i
$833$	−20.1092	+	14.6102i	−0.696743	+	0.506213i
$834$	8.13814	−	25.0466i	0.281801	−	0.867294i
$835$	11.6900			0.404547
$836$	−44.4548	−	71.3418i	−1.53750	−	2.46741i
$837$	−7.26340			−0.251060
$838$	−10.4319	+	32.1061i	−0.360364	+	1.10909i
$839$	−12.0040	+	8.72144i	−0.414425	+	0.301098i	−0.775391	−	0.631482i	$-0.782447\pi$
$839$	−12.0040	+	8.72144i	−0.414425	+	0.301098i	0.360966	+	0.932579i	$0.382447\pi$
$840$	9.16069	+	6.65563i	0.316074	+	0.229641i
$841$	1.83395	+	5.64432i	0.0632397	+	0.194632i
$842$	17.6083	+	54.1926i	0.606821	+	1.86760i
$843$	−6.44844	−	4.68507i	−0.222096	−	0.161362i
$844$	−85.2694	+	61.9519i	−2.93509	+	2.13247i
$845$	0.276429	−	0.850760i	0.00950943	−	0.0292670i
$846$	0.193826			0.00666386
$847$	12.0603	−	6.37377i	0.414398	−	0.219005i
$848$	72.7085			2.49682
$849$	−5.06778	+	15.5970i	−0.173926	+	0.535289i
$850$	−42.8561	+	31.1368i	−1.46995	+	1.06798i
$851$	21.9528	+	15.9496i	0.752531	+	0.546745i
$852$	−9.08096	−	27.9483i	−0.311109	−	0.957494i
$853$	−0.803678	−	2.47347i	−0.0275174	−	0.0846898i	0.936355	−	0.351055i	$-0.114177\pi$
$853$	−0.803678	−	2.47347i	−0.0275174	−	0.0846898i	−0.963872	+	0.266366i	$0.914177\pi$
$854$	−23.5936	−	17.1417i	−0.807355	−	0.586578i
$855$	−3.22770	+	2.34506i	−0.110385	+	0.0801995i
$856$	7.52515	−	23.1600i	0.257204	−	0.791593i
$857$	14.5630			0.497463			0.248732	−	0.968572i	$-0.419986\pi$
$857$	14.5630			0.497463			0.248732	+	0.968572i	$0.419986\pi$
$858$	4.86169	+	7.80213i	0.165975	+	0.266360i
$859$	41.8340			1.42736			0.713679	−	0.700473i	$-0.247028\pi$
$859$	41.8340			1.42736			0.713679	+	0.700473i	$0.247028\pi$
$860$	−2.40447	+	7.40019i	−0.0819917	+	0.252344i
$861$	−4.50806	+	3.27530i	−0.153634	+	0.111622i
$862$	−13.0642	−	9.49167i	−0.444967	−	0.323287i
$863$	16.9758	+	52.2461i	0.577863	+	1.77848i	0.626218	+	0.779648i	$0.284602\pi$
$863$	16.9758	+	52.2461i	0.577863	+	1.77848i	−0.0483549	+	0.998830i	$0.515398\pi$
$864$	−8.19002	−	25.2063i	−0.278630	−	0.857535i
$865$	0.379219	+	0.275518i	0.0128938	+	0.00936791i
$866$	−3.27000	+	2.37579i	−0.111119	+	0.0807327i
$867$	−1.14590	+	3.52672i	−0.0389168	+	0.119774i
$868$	51.1852			1.73734
$869$	35.4177	−	8.78338i	1.20146	−	0.297956i
$870$	14.6550			0.496851
$871$	−4.94061	+	15.2056i	−0.167406	+	0.515224i
$872$	113.974	−	82.8068i	3.85964	−	2.80419i
$873$	−2.19289	−	1.59323i	−0.0742181	−	0.0539226i
$874$	26.7693	+	82.3874i	0.905484	+	2.78679i
$875$	−3.15365	−	9.70595i	−0.106613	−	0.328121i
$876$	2.25962	+	1.64171i	0.0763456	+	0.0554683i
$877$	34.3675	−	24.9695i	1.16051	−	0.843159i	0.170667	−	0.985329i	$-0.445408\pi$
$877$	34.3675	−	24.9695i	1.16051	−	0.843159i	0.989842	+	0.142170i	$0.0454078\pi$
$878$	1.59811	−	4.91848i	0.0539336	−	0.165991i
$879$	−2.53149			−0.0853849
$880$	46.5403	+	18.8715i	1.56887	+	0.636159i
$881$	−12.6664			−0.426741			−0.213370	−	0.976971i	$-0.568444\pi$
$881$	−12.6664			−0.426741			−0.213370	+	0.976971i	$0.568444\pi$
$882$	−4.67847	+	14.3989i	−0.157532	+	0.484835i
$883$	−37.4771	+	27.2287i	−1.26121	+	0.916319i	−0.998816	−	0.0486432i	$-0.984510\pi$
$883$	−37.4771	+	27.2287i	−1.26121	+	0.916319i	−0.262389	+	0.964962i	$0.584510\pi$
$884$	20.9209	+	15.1999i	0.703646	+	0.511229i
$885$	0.886879	+	2.72953i	0.0298121	+	0.0917523i
$886$	−9.99713	−	30.7680i	−0.335860	−	1.03367i
$887$	−15.3167	−	11.1282i	−0.514283	−	0.373648i	0.300163	−	0.953888i	$-0.402959\pi$
$887$	−15.3167	−	11.1282i	−0.514283	−	0.373648i	−0.814446	+	0.580239i	$0.802959\pi$
$888$	−31.9774	+	23.2329i	−1.07309	+	0.779645i
$889$	−4.28444	+	13.1862i	−0.143696	+	0.442249i
$890$	28.7182			0.962635
$891$	−0.235513	+	3.30825i	−0.00788997	+	0.110831i
$892$	−45.0239			−1.50751
$893$	0.0963769	−	0.296618i	0.00322513	−	0.00992593i
$894$	−34.0760	+	24.7576i	−1.13967	+	0.828019i
$895$	11.1298	+	8.08625i	0.372027	+	0.270293i
$896$	21.7560	+	66.9582i	0.726818	+	2.23691i
$897$	−2.16544	−	6.66453i	−0.0723018	−	0.222522i
$898$	70.4230	+	51.1653i	2.35005	+	1.70741i
$899$	34.7317	−	25.2341i	1.15837	−	0.841604i
$900$	−7.37500	+	22.6979i	−0.245833	+	0.756597i
$901$	−19.5465			−0.651189
$902$	−26.5918	+	31.6102i	−0.885412	+	1.05250i
$903$	1.89818			0.0631675
$904$	−22.2221	+	68.3926i	−0.739096	+	2.27470i
$905$	−15.0395	+	10.9268i	−0.499929	+	0.363219i
$906$	−6.81710	−	4.95291i	−0.226483	−	0.164550i
$907$	11.3359	+	34.8883i	0.376403	+	1.15845i	0.942527	+	0.334129i	$0.108442\pi$
$907$	11.3359	+	34.8883i	0.376403	+	1.15845i	−0.566125	+	0.824320i	$0.691558\pi$
$908$	−22.4086	−	68.9667i	−0.743656	−	2.28874i
$909$	1.17968	+	0.857086i	0.0391274	+	0.0284277i
$910$	−2.48752	+	1.80729i	−0.0824605	+	0.0599111i
$911$	3.02781	−	9.31865i	0.100316	−	0.308741i	−0.888287	−	0.459290i	$-0.848104\pi$
$911$	3.02781	−	9.31865i	0.100316	−	0.308741i	0.988603	+	0.150549i	$0.0481040\pi$
$912$	−75.4957			−2.49991
$913$	30.6772	−	36.4665i	1.01527	−	1.20687i
$914$	−38.7327			−1.28116
$915$	−2.34536	+	7.21829i	−0.0775354	+	0.238629i
$916$	56.3312	−	40.9270i	1.86123	−	1.35227i
$917$	−7.26852	−	5.28089i	−0.240028	−	0.174390i
$918$	3.89771	+	11.9959i	0.128644	+	0.395924i
$919$	14.9988	+	46.1614i	0.494763	+	1.52272i	0.817325	+	0.576176i	$0.195456\pi$
$919$	14.9988	+	46.1614i	0.494763	+	1.52272i	−0.322562	+	0.946548i	$0.604544\pi$
$920$	−51.7653	−	37.6097i	−1.70665	−	1.23995i
$921$	−18.8325	+	13.6826i	−0.620552	+	0.450857i
$922$	−15.0679	+	46.3741i	−0.496234	+	1.52725i
$923$	5.17128			0.170215
$924$	1.65966	−	23.3133i	0.0545987	−	0.766950i
$925$	16.2628			0.534719
$926$	−26.0060	+	80.0382i	−0.854610	+	2.63022i
$927$	−11.5641	+	8.40180i	−0.379814	+	0.275951i
$928$	126.733	+	92.0768i	4.16021	+	3.02257i
$929$	−2.25436	−	6.93820i	−0.0739631	−	0.227635i	0.907240	−	0.420614i	$-0.138185\pi$
$929$	−2.25436	−	6.93820i	−0.0739631	−	0.227635i	−0.981203	+	0.192979i	$0.938185\pi$
$930$	−5.56517	−	17.1278i	−0.182489	−	0.561644i
$931$	19.7087	+	14.3192i	0.645928	+	0.469294i
$932$	53.5630	−	38.9158i	1.75452	−	1.27473i
$933$	−4.84987	+	14.9264i	−0.158778	+	0.488667i
$934$	−86.4740			−2.82952
$935$	−12.5116	−	5.07331i	−0.409174	−	0.165915i
$936$	10.2074			0.333641
$937$	13.3213	−	40.9986i	0.435186	−	1.33937i	−0.457709	−	0.889102i	$-0.651330\pi$
$937$	13.3213	−	40.9986i	0.435186	−	1.33937i	0.892895	−	0.450264i	$-0.148670\pi$
$938$	44.4595	−	32.3017i	1.45165	−	1.05469i
$939$	8.18055	+	5.94352i	0.266962	+	0.193959i
$940$	0.109847	+	0.338076i	0.00358283	+	0.0110268i
$941$	−9.24682	−	28.4588i	−0.301438	−	0.927730i	−0.980983	−	0.194096i	$-0.937823\pi$
$941$	−9.24682	−	28.4588i	−0.301438	−	0.927730i	0.679545	−	0.733634i	$-0.262177\pi$
$942$	−50.9337	−	37.0055i	−1.65951	−	1.20571i
$943$	25.4742	−	18.5081i	0.829554	−	0.602706i
$944$	−16.7823	+	51.6505i	−0.546216	+	1.68108i
$945$	−1.10931			−0.0360859
$946$	13.6577	−	3.38702i	0.444049	−	0.110121i
$947$	58.3691			1.89674			0.948370	−	0.317165i	$-0.102731\pi$
$947$	58.3691			1.89674			0.948370	+	0.317165i	$0.102731\pi$
$948$	19.3205	−	59.4623i	0.627500	−	1.93125i
$949$	−0.397635	+	0.288899i	−0.0129078	+	0.00937805i
$950$	42.0027	+	30.5167i	1.36275	+	0.990093i
$951$	−8.83469	−	27.1904i	−0.286484	−	0.881708i
$952$	−17.8001	−	54.7832i	−0.576906	−	1.77553i
$953$	11.7803	+	8.55890i	0.381602	+	0.277250i	0.762005	−	0.647571i	$-0.224215\pi$
$953$	11.7803	+	8.55890i	0.381602	+	0.277250i	−0.380404	+	0.924821i	$0.624215\pi$
$954$	−9.63189	+	6.99798i	−0.311844	+	0.226568i
$955$	−0.600519	+	1.84821i	−0.0194323	+	0.0598066i
$956$	104.746			3.38771
$957$	−10.3672	−	16.6374i	−0.335123	−	0.537812i
$958$	−32.6929			−1.05626
$959$	4.92742	−	15.1650i	0.159115	−	0.489705i
$960$	28.6633	−	20.8251i	0.925105	−	0.672128i
$961$	−17.6018	−	12.7884i	−0.567799	−	0.412530i
$962$	−3.31670	−	10.2078i	−0.106935	−	0.329111i
$963$	0.737222	+	2.26894i	0.0237566	+	0.0731154i
$964$	98.3429	+	71.4503i	3.16741	+	2.30126i
$965$	−9.11086	+	6.61943i	−0.293289	+	0.213087i
$966$	−7.44310	+	22.9075i	−0.239478	+	0.737037i
$967$	−12.0573			−0.387738			−0.193869	−	0.981027i	$-0.562104\pi$
$967$	−12.0573			−0.387738			−0.193869	+	0.981027i	$0.562104\pi$
$968$	−19.2196	−	110.625i	−0.617742	−	3.55561i
$969$	20.2958			0.651996
$970$	2.07682	−	6.39178i	0.0666826	−	0.205228i
$971$	−43.6507	+	31.7141i	−1.40082	+	1.01775i	−0.406238	+	0.913767i	$0.633160\pi$
$971$	−43.6507	+	31.7141i	−1.40082	+	1.01775i	−0.994579	+	0.103986i	$0.966840\pi$
$972$	4.59737	+	3.34018i	0.147461	+	0.107136i
$973$	−3.64101	−	11.2059i	−0.116726	−	0.359244i
$974$	−1.59657	−	4.91373i	−0.0511574	−	0.157446i
$975$	−3.39771	−	2.46858i	−0.108814	−	0.0790578i
$976$	−116.191	+	84.4176i	−3.71918	+	2.70214i
$977$	−3.63775	+	11.1959i	−0.116382	+	0.358187i	−0.992233	−	0.124395i	$-0.960301\pi$
$977$	−3.63775	+	11.1959i	−0.116382	+	0.358187i	0.875851	+	0.482582i	$0.160301\pi$
$978$	40.8102			1.30497
$979$	−20.3157	−	32.6030i	−0.649293	−	1.04200i
$980$	−27.7663			−0.886962
$981$	−4.26494	+	13.1261i	−0.136169	+	0.419085i
$982$	−13.8012	+	10.0271i	−0.440412	+	0.319978i
$983$	11.5278	+	8.37543i	0.367679	+	0.267135i	0.756248	−	0.654285i	$-0.227030\pi$
$983$	11.5278	+	8.37543i	0.367679	+	0.267135i	−0.388569	+	0.921420i	$0.627030\pi$
$984$	14.1736	+	43.6217i	0.451836	+	1.39061i
$985$	−0.588934	−	1.81255i	−0.0187650	−	0.0577527i
$986$	−60.3134	−	43.8202i	−1.92077	−	1.39552i
$987$	0.0701562	−	0.0509714i	0.00223310	−	0.00162244i
$988$	7.83194	−	24.1042i	0.249167	−	0.766857i
$989$	−10.7262			−0.341075
$990$	−7.98165	+	1.97940i	−0.253673	+	0.0629095i
$991$	−10.4598			−0.332266			−0.166133	−	0.986103i	$-0.553128\pi$
$991$	−10.4598			−0.332266			−0.166133	+	0.986103i	$0.553128\pi$
$992$	59.4874	−	183.083i	1.88873	−	5.81290i
$993$	−22.0894	+	16.0489i	−0.700986	+	0.509296i
$994$	−14.3802	−	10.4478i	−0.456111	−	0.331384i
$995$	2.47679	+	7.62277i	0.0785195	+	0.241658i
$996$	−25.2311	−	77.6533i	−0.799478	−	2.46054i
$997$	40.5168	+	29.4372i	1.28318	+	0.932285i	0.999644	−	0.0266772i	$-0.00849261\pi$
$997$	40.5168	+	29.4372i	1.28318	+	0.932285i	0.283536	+	0.958962i	$0.408493\pi$
$998$	−22.9483	+	16.6729i	−0.726415	+	0.527771i
$999$	1.19660	−	3.68277i	0.0378589	−	0.116518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.c.196.7	✓	28
11.4	even	5		4719.2.a.bp.1.14		14
11.5	even	5	inner	429.2.n.c.313.7	yes	28
11.7	odd	10		4719.2.a.bo.1.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.196.7	✓	28	1.1	even	1	trivial
429.2.n.c.313.7	yes	28	11.5	even	5	inner
4719.2.a.bo.1.1		14	11.7	odd	10
4719.2.a.bp.1.14		14	11.4	even	5

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.856521 - 2.63610i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-4.59737 - 3.34018i) q^{4} +(0.276429 + 0.850760i) q^{5} +(-0.856521 - 2.63610i) q^{6} +(-1.00325 - 0.728906i) q^{7} +(-8.25799 + 5.99978i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.856521 - 2.63610i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-4.59737 - 3.34018i) q^{4} +(0.276429 + 0.850760i) q^{5} +(-0.856521 - 2.63610i) q^{6} +(-1.00325 - 0.728906i) q^{7} +(-8.25799 + 5.99978i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.47946 q^{10} +(-1.75401 - 2.81486i) q^{11} -5.68266 q^{12} +(0.309017 - 0.951057i) q^{13} +(-2.78078 + 2.02035i) q^{14} +(0.723700 + 0.525799i) q^{15} +(5.23081 + 16.0988i) q^{16} +(-1.40622 - 4.32790i) q^{17} +(-2.24240 - 1.62920i) q^{18} +(-3.60822 + 2.62153i) q^{19} +(1.57085 - 4.83458i) q^{20} -1.24009 q^{21} +(-8.92261 + 2.21275i) q^{22} +7.00750 q^{23} +(-3.15427 + 9.70785i) q^{24} +(3.39771 - 2.46858i) q^{25} +(-2.24240 - 1.62920i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(2.17764 + 6.70209i) q^{28} +(4.78175 + 3.47414i) q^{29} +(2.00592 - 1.45739i) q^{30} +(2.24451 - 6.90790i) q^{31} +26.5034 q^{32} +(-3.07356 - 1.24629i) q^{33} -12.6132 q^{34} +(0.342796 - 1.05502i) q^{35} +(-4.59737 + 3.34018i) q^{36} +(3.13275 + 2.27608i) q^{37} +(3.82009 + 11.7570i) q^{38} +(-0.309017 - 0.951057i) q^{39} +(-7.38712 - 5.36706i) q^{40} +(3.63527 - 2.64118i) q^{41} +(-1.06216 + 3.26900i) q^{42} -1.53068 q^{43} +(-1.33834 + 18.7997i) q^{44} +0.894542 q^{45} +(6.00207 - 18.4725i) q^{46} +(-0.0565735 + 0.0411030i) q^{47} +(13.6944 + 9.94960i) q^{48} +(-1.68791 - 5.19484i) q^{49} +(-3.59721 - 11.0711i) q^{50} +(-3.68154 - 2.67479i) q^{51} +(-4.59737 + 3.34018i) q^{52} +(1.32733 - 4.08512i) q^{53} -2.77176 q^{54} +(1.90991 - 2.27035i) q^{55} +12.6581 q^{56} +(-1.37822 + 4.24172i) q^{57} +(13.2539 - 9.62949i) q^{58} +(2.59561 + 1.88582i) q^{59} +(-1.57085 - 4.83458i) q^{60} +(2.62186 + 8.06926i) q^{61} +(-16.2875 - 11.8335i) q^{62} +(-1.00325 + 0.728906i) q^{63} +(12.2391 - 37.6682i) q^{64} +0.894542 q^{65} +(-5.91792 + 7.03473i) q^{66} -15.9882 q^{67} +(-7.99107 + 24.5940i) q^{68} +(5.66919 - 4.11891i) q^{69} +(-2.48752 - 1.80729i) q^{70} +(1.59801 + 4.91818i) q^{71} +(3.15427 + 9.70785i) q^{72} +(-0.397635 - 0.288899i) q^{73} +(8.68323 - 6.30874i) q^{74} +(1.29781 - 3.99424i) q^{75} +25.3447 q^{76} +(-0.292057 + 4.10253i) q^{77} -2.77176 q^{78} +(-3.39990 + 10.4638i) q^{79} +(-12.2503 + 8.90033i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.84873 - 11.8452i) q^{82} +(4.44002 + 13.6650i) q^{83} +(5.70114 + 4.14212i) q^{84} +(3.29329 - 2.39271i) q^{85} +(-1.31106 + 4.03503i) q^{86} +5.91057 q^{87} +(31.3732 + 12.7215i) q^{88} +11.5824 q^{89} +(0.766194 - 2.35810i) q^{90} +(-1.00325 + 0.728906i) q^{91} +(-32.2160 - 23.4063i) q^{92} +(-2.24451 - 6.90790i) q^{93} +(0.0598954 + 0.184339i) q^{94} +(-3.22770 - 2.34506i) q^{95} +(21.4417 - 15.5783i) q^{96} +(0.837610 - 2.57790i) q^{97} -15.1399 q^{98} +(-3.21911 + 0.798320i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

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