LMFDB - Embedded newform 429.2.n.a.157.3

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 9 x^{10} - 15 x^{9} + 29 x^{8} - 26 x^{7} + 43 x^{6} + 24 x^{5} + 16 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 9x^10 - 15x^9 + 29x^8 - 26x^7 + 43x^6 + 24x^5 + 16x^4 - 17x^3 + 14x^2 - 5*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.3
Root			$1.72363 + 1.25229i$ of defining polynomial
Character	$\chi$	$=$	429.157
Dual form			429.2.n.a.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72363 - 1.25229i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.784639 - 2.41487i) q^{4} +(1.18874 + 0.863672i) q^{5} +(1.72363 + 1.25229i) q^{6} +(0.349352 - 1.07520i) q^{7} +(-0.354958 - 1.09245i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.72363 - 1.25229i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.784639 - 2.41487i) q^{4} +(1.18874 + 0.863672i) q^{5} +(1.72363 + 1.25229i) q^{6} +(0.349352 - 1.07520i) q^{7} +(-0.354958 - 1.09245i) q^{8} +(-0.809017 + 0.587785i) q^{9} +3.13053 q^{10} +(2.88626 + 1.63386i) q^{11} +2.53915 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.744304 - 2.29073i) q^{14} +(-0.454059 + 1.39745i) q^{15} +(2.12855 + 1.54648i) q^{16} +(-5.36749 - 3.89971i) q^{17} +(-0.658369 + 2.02625i) q^{18} +(-0.893053 - 2.74853i) q^{19} +(3.01839 - 2.19299i) q^{20} +1.13053 q^{21} +(7.02093 - 0.798260i) q^{22} -2.09991 q^{23} +(0.929291 - 0.675169i) q^{24} +(-0.877905 - 2.70191i) q^{25} +(-0.658369 + 2.02625i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.32234 - 1.68728i) q^{28} +(-0.199461 + 0.613878i) q^{29} +(0.967386 + 2.97731i) q^{30} +(2.03928 - 1.48162i) q^{31} +7.90281 q^{32} +(-0.661993 + 3.24989i) q^{33} -14.1352 q^{34} +(1.34391 - 0.976405i) q^{35} +(0.784639 + 2.41487i) q^{36} +(-1.44945 + 4.46094i) q^{37} +(-4.98126 - 3.61910i) q^{38} +(-0.809017 - 0.587785i) q^{39} +(0.521563 - 1.60521i) q^{40} +(0.218861 + 0.673584i) q^{41} +(1.94861 - 1.41575i) q^{42} -10.6900 q^{43} +(6.21024 - 5.68795i) q^{44} -1.46937 q^{45} +(-3.61948 + 2.62970i) q^{46} +(0.553502 + 1.70350i) q^{47} +(-0.813032 + 2.50226i) q^{48} +(4.62912 + 3.36325i) q^{49} +(-4.89677 - 3.55771i) q^{50} +(2.05020 - 6.30986i) q^{51} +(0.784639 + 2.41487i) q^{52} +(0.217613 - 0.158105i) q^{53} -2.13053 q^{54} +(2.01990 + 4.43503i) q^{55} -1.29860 q^{56} +(2.33804 - 1.69869i) q^{57} +(0.424957 + 1.30788i) q^{58} +(0.821752 - 2.52909i) q^{59} +(3.01839 + 2.19299i) q^{60} +(-6.42542 - 4.66834i) q^{61} +(1.65954 - 5.10755i) q^{62} +(0.349352 + 1.07520i) q^{63} +(9.36445 - 6.80367i) q^{64} -1.46937 q^{65} +(2.92878 + 6.43062i) q^{66} -15.6561 q^{67} +(-13.6288 + 9.90193i) q^{68} +(-0.648908 - 1.99713i) q^{69} +(1.09366 - 3.36593i) q^{70} +(7.04867 + 5.12116i) q^{71} +(0.929291 + 0.675169i) q^{72} +(-2.19287 + 6.74895i) q^{73} +(3.08809 + 9.50415i) q^{74} +(2.29838 - 1.66987i) q^{75} -7.33808 q^{76} +(2.76504 - 2.53250i) q^{77} -2.13053 q^{78} +(-13.0247 + 9.46298i) q^{79} +(1.19464 + 3.67673i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.22076 + 0.886934i) q^{82} +(-3.69812 - 2.68685i) q^{83} +(0.887056 - 2.73008i) q^{84} +(-3.01249 - 9.27150i) q^{85} +(-18.4256 + 13.3870i) q^{86} -0.645470 q^{87} +(0.760410 - 3.73304i) q^{88} +4.35301 q^{89} +(-2.53265 + 1.84008i) q^{90} +(0.349352 + 1.07520i) q^{91} +(-1.64767 + 5.07102i) q^{92} +(2.03928 + 1.48162i) q^{93} +(3.08732 + 2.24307i) q^{94} +(1.31222 - 4.03861i) q^{95} +(2.44210 + 7.51602i) q^{96} +(8.14570 - 5.91819i) q^{97} +12.1907 q^{98} +(-3.29539 + 0.374677i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9 + 14 * q^10 - 6 * q^11 + 2 * q^12 - 3 * q^13 + 11 * q^14 - 2 * q^15 - 5 * q^16 - 14 * q^17 - 2 * q^18 - 2 * q^19 - 9 * q^20 - 10 * q^21 + 21 * q^22 - 6 * q^23 + 4 * q^24 + 19 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 - 12 * q^29 - q^30 - 12 * q^31 + 26 * q^32 + 9 * q^33 - 24 * q^34 - 2 * q^35 - 3 * q^36 + 4 * q^37 - 13 * q^38 - 3 * q^39 + 4 * q^40 - 10 * q^41 + q^42 + 28 * q^43 - 12 * q^45 - 5 * q^46 + 28 * q^47 + 10 * q^48 + 20 * q^49 - q^50 + 11 * q^51 - 3 * q^52 - 29 * q^53 - 2 * q^54 + 4 * q^55 + 12 * q^56 + 8 * q^57 + 22 * q^58 - 11 * q^59 - 9 * q^60 - 18 * q^61 + 40 * q^62 + 5 * q^63 + 11 * q^64 - 12 * q^65 + 16 * q^66 - 72 * q^67 - 35 * q^68 + 4 * q^69 - 6 * q^70 + 10 * q^71 + 4 * q^72 - 11 * q^73 - 15 * q^74 - 11 * q^75 + 4 * q^76 + 20 * q^77 - 2 * q^78 - 7 * q^79 - 27 * q^80 - 3 * q^81 - 10 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^85 - 35 * q^86 + 28 * q^87 + 25 * q^88 - 62 * q^89 - 6 * q^90 + 5 * q^91 - 34 * q^92 - 12 * q^93 - q^94 + 15 * q^95 + q^96 + 54 * q^97 + 50 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.72363	−	1.25229i	1.21879	−	0.885505i	0.222793	−	0.974866i	$-0.428483\pi$
$2$	1.72363	−	1.25229i	1.21879	−	0.885505i	0.995999	+	0.0893612i	$0.0284825\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.784639	−	2.41487i	0.392320	−	1.20744i
$5$	1.18874	+	0.863672i	0.531622	+	0.386246i	0.820964	−	0.570980i	$-0.193437\pi$
$5$	1.18874	+	0.863672i	0.531622	+	0.386246i	−0.289342	+	0.957226i	$0.593437\pi$
$6$	1.72363	+	1.25229i	0.703670	+	0.511246i
$7$	0.349352	−	1.07520i	0.132043	−	0.406386i	−0.863076	−	0.505075i	$-0.831465\pi$
$7$	0.349352	−	1.07520i	0.132043	−	0.406386i	0.995118	+	0.0986891i	$0.0314649\pi$
$8$	−0.354958	−	1.09245i	−0.125496	−	0.386238i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	3.13053			0.989960
$11$	2.88626	+	1.63386i	0.870240	+	0.492628i
$11$	2.88626	+	1.63386i	0.870240	+	0.492628i
$12$	2.53915			0.732988
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$	−0.744304	−	2.29073i	−0.198924	−	0.612224i
$15$	−0.454059	+	1.39745i	−0.117238	+	0.360820i
$16$	2.12855	+	1.54648i	0.532137	+	0.386620i
$17$	−5.36749	−	3.89971i	−1.30181	−	0.945818i	−0.301835	−	0.953360i	$-0.597599\pi$
$17$	−5.36749	−	3.89971i	−1.30181	−	0.945818i	−0.999972	+	0.00754214i	$0.997599\pi$
$18$	−0.658369	+	2.02625i	−0.155179	+	0.477592i
$19$	−0.893053	−	2.74853i	−0.204880	−	0.630557i	−0.999718	−	0.0237351i	$-0.992444\pi$
$19$	−0.893053	−	2.74853i	−0.204880	−	0.630557i	0.794838	−	0.606822i	$-0.207556\pi$
$20$	3.01839	−	2.19299i	0.674933	−	0.490368i
$21$	1.13053			0.246701
$22$	7.02093	−	0.798260i	1.49687	−	0.170190i
$23$	−2.09991			−0.437862			−0.218931	−	0.975740i	$-0.570257\pi$
$23$	−2.09991			−0.437862			−0.218931	+	0.975740i	$0.570257\pi$
$24$	0.929291	−	0.675169i	0.189691	−	0.137818i
$25$	−0.877905	−	2.70191i	−0.175581	−	0.540383i
$26$	−0.658369	+	2.02625i	−0.129117	+	0.397381i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−2.32234	−	1.68728i	−0.438882	−	0.318866i
$29$	−0.199461	+	0.613878i	−0.0370390	+	0.113994i	−0.967867	−	0.251464i	$-0.919088\pi$
$29$	−0.199461	+	0.613878i	−0.0370390	+	0.113994i	0.930828	+	0.365459i	$0.119088\pi$
$30$	0.967386	+	2.97731i	0.176620	+	0.543580i
$31$	2.03928	−	1.48162i	0.366265	−	0.266107i	−0.389395	−	0.921071i	$-0.627316\pi$
$31$	2.03928	−	1.48162i	0.366265	−	0.266107i	0.755661	+	0.654963i	$0.227316\pi$
$32$	7.90281			1.39703
$33$	−0.661993	+	3.24989i	−0.115238	+	0.565733i
$34$	−14.1352			−2.42416
$35$	1.34391	−	0.976405i	0.227162	−	0.165043i
$36$	0.784639	+	2.41487i	0.130773	+	0.402479i
$37$	−1.44945	+	4.46094i	−0.238288	+	0.733374i	0.758381	+	0.651812i	$0.225991\pi$
$37$	−1.44945	+	4.46094i	−0.238288	+	0.733374i	−0.996668	+	0.0815620i	$0.974009\pi$
$38$	−4.98126	−	3.61910i	−0.808068	−	0.587096i
$39$	−0.809017	−	0.587785i	−0.129546	−	0.0941210i
$40$	0.521563	−	1.60521i	0.0824663	−	0.253805i
$41$	0.218861	+	0.673584i	0.0341803	+	0.105196i	0.966691	−	0.255946i	$-0.0823869\pi$
$41$	0.218861	+	0.673584i	0.0341803	+	0.105196i	−0.932511	+	0.361142i	$0.882387\pi$
$42$	1.94861	−	1.41575i	0.300678	−	0.218455i
$43$	−10.6900			−1.63021			−0.815104	−	0.579315i	$-0.803320\pi$
$43$	−10.6900			−1.63021			−0.815104	+	0.579315i	$0.803320\pi$
$44$	6.21024	−	5.68795i	0.936229	−	0.857491i
$45$	−1.46937			−0.219040
$46$	−3.61948	+	2.62970i	−0.533663	+	0.387729i
$47$	0.553502	+	1.70350i	0.0807366	+	0.248482i	0.983275	−	0.182128i	$-0.0582986\pi$
$47$	0.553502	+	1.70350i	0.0807366	+	0.248482i	−0.902538	+	0.430610i	$0.858299\pi$
$48$	−0.813032	+	2.50226i	−0.117351	+	0.361170i
$49$	4.62912	+	3.36325i	0.661303	+	0.480465i
$50$	−4.89677	−	3.55771i	−0.692508	−	0.503137i
$51$	2.05020	−	6.30986i	0.287085	−	0.883557i
$52$	0.784639	+	2.41487i	0.108810	+	0.334882i
$53$	0.217613	−	0.158105i	0.0298914	−	0.0217174i	−0.572739	−	0.819738i	$-0.694119\pi$
$53$	0.217613	−	0.158105i	0.0298914	−	0.0217174i	0.602631	+	0.798020i	$0.294119\pi$
$54$	−2.13053			−0.289928
$55$	2.01990	+	4.43503i	0.272363	+	0.598019i
$56$	−1.29860			−0.173533
$57$	2.33804	−	1.69869i	0.309681	−	0.224997i
$58$	0.424957	+	1.30788i	0.0557996	+	0.171734i
$59$	0.821752	−	2.52909i	0.106983	−	0.329260i	−0.883208	−	0.468982i	$-0.844621\pi$
$59$	0.821752	−	2.52909i	0.106983	−	0.329260i	0.990191	+	0.139722i	$0.0446209\pi$
$60$	3.01839	+	2.19299i	0.389673	+	0.283114i
$61$	−6.42542	−	4.66834i	−0.822691	−	0.597720i	0.0947912	−	0.995497i	$-0.469782\pi$
$61$	−6.42542	−	4.66834i	−0.822691	−	0.597720i	−0.917482	+	0.397777i	$0.869782\pi$
$62$	1.65954	−	5.10755i	0.210762	−	0.648659i
$63$	0.349352	+	1.07520i	0.0440142	+	0.135462i
$64$	9.36445	−	6.80367i	1.17056	−	0.850459i
$65$	−1.46937			−0.182253
$66$	2.92878	+	6.43062i	0.360507	+	0.791555i
$67$	−15.6561			−1.91270			−0.956348	−	0.292231i	$-0.905602\pi$
$67$	−15.6561			−1.91270			−0.956348	+	0.292231i	$0.905602\pi$
$68$	−13.6288	+	9.90193i	−1.65274	+	1.20079i
$69$	−0.648908	−	1.99713i	−0.0781194	−	0.240427i
$70$	1.09366	−	3.36593i	0.130717	−	0.402305i
$71$	7.04867	+	5.12116i	0.836523	+	0.607770i	0.921397	−	0.388622i	$-0.127049\pi$
$71$	7.04867	+	5.12116i	0.836523	+	0.607770i	−0.0848740	+	0.996392i	$0.527049\pi$
$72$	0.929291	+	0.675169i	0.109518	+	0.0795695i
$73$	−2.19287	+	6.74895i	−0.256656	+	0.789905i	0.736843	+	0.676064i	$0.236316\pi$
$73$	−2.19287	+	6.74895i	−0.256656	+	0.789905i	−0.993499	+	0.113841i	$0.963684\pi$
$74$	3.08809	+	9.50415i	0.358983	+	1.10484i
$75$	2.29838	−	1.66987i	0.265395	−	0.192820i
$76$	−7.33808			−0.841736
$77$	2.76504	−	2.53250i	0.315106	−	0.288605i
$78$	−2.13053			−0.241235
$79$	−13.0247	+	9.46298i	−1.46539	+	1.06467i	−0.483474	+	0.875359i	$0.660625\pi$
$79$	−13.0247	+	9.46298i	−1.46539	+	1.06467i	−0.981917	+	0.189310i	$0.939375\pi$
$80$	1.19464	+	3.67673i	0.133565	+	0.411071i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	1.22076	+	0.886934i	0.134810	+	0.0979455i
$83$	−3.69812	−	2.68685i	−0.405922	−	0.294920i	0.366027	−	0.930604i	$-0.380718\pi$
$83$	−3.69812	−	2.68685i	−0.405922	−	0.294920i	−0.771949	+	0.635685i	$0.780718\pi$
$84$	0.887056	−	2.73008i	0.0967858	−	0.297876i
$85$	−3.01249	−	9.27150i	−0.326751	−	1.00564i
$86$	−18.4256	+	13.3870i	−1.98689	+	1.44356i
$87$	−0.645470			−0.0692016
$88$	0.760410	−	3.73304i	0.0810599	−	0.397943i
$89$	4.35301			0.461418			0.230709	−	0.973023i	$-0.425895\pi$
$89$	4.35301			0.461418			0.230709	+	0.973023i	$0.425895\pi$
$90$	−2.53265	+	1.84008i	−0.266965	+	0.193961i
$91$	0.349352	+	1.07520i	0.0366221	+	0.112711i
$92$	−1.64767	+	5.07102i	−0.171782	+	0.528690i
$93$	2.03928	+	1.48162i	0.211463	+	0.153637i
$94$	3.08732	+	2.24307i	0.318433	+	0.231355i
$95$	1.31222	−	4.03861i	0.134631	−	0.414352i
$96$	2.44210	+	7.51602i	0.249246	+	0.767100i
$97$	8.14570	−	5.91819i	0.827070	−	0.600902i	−0.0916588	−	0.995790i	$-0.529217\pi$
$97$	8.14570	−	5.91819i	0.827070	−	0.600902i	0.918729	+	0.394889i	$0.129217\pi$
$98$	12.1907			1.23144
$99$	−3.29539	+	0.374677i	−0.331199	+	0.0376565i
$100$	−7.21361			−0.721361
$101$	15.6953	−	11.4033i	1.56174	−	1.13467i	0.627181	−	0.778873i	$-0.284209\pi$
$101$	15.6953	−	11.4033i	1.56174	−	1.13467i	0.934562	−	0.355800i	$-0.115791\pi$
$102$	−4.36800	−	13.4433i	−0.432497	−	1.33109i
$103$	2.27512	−	7.00211i	0.224175	−	0.689938i	−0.774200	−	0.632941i	$-0.781847\pi$
$103$	2.27512	−	7.00211i	0.224175	−	0.689938i	0.998374	−	0.0569971i	$-0.0181526\pi$
$104$	0.929291	+	0.675169i	0.0911245	+	0.0662058i
$105$	1.34391	+	0.976405i	0.131152	+	0.0952874i
$106$	0.177091	−	0.545029i	0.0172006	−	0.0529379i
$107$	−1.27776	−	3.93253i	−0.123525	−	0.380172i	0.870104	−	0.492868i	$-0.164051\pi$
$107$	−1.27776	−	3.93253i	−0.123525	−	0.380172i	−0.993630	+	0.112696i	$0.964051\pi$
$108$	−2.05421	+	1.49247i	−0.197667	+	0.143613i
$109$	2.25649			0.216133			0.108066	−	0.994144i	$-0.465534\pi$
$109$	2.25649			0.216133			0.108066	+	0.994144i	$0.465534\pi$
$110$	9.03551	+	5.11485i	0.861502	+	0.487682i
$111$	−4.69051			−0.445204
$112$	2.40638	−	1.74834i	0.227381	−	0.165202i
$113$	4.85891	+	14.9542i	0.457088	+	1.40677i	0.868666	+	0.495398i	$0.164978\pi$
$113$	4.85891	+	14.9542i	0.457088	+	1.40677i	−0.411578	+	0.911375i	$0.635022\pi$
$114$	1.90267	−	5.85583i	0.178202	−	0.548448i
$115$	−2.49626	−	1.81364i	−0.232777	−	0.169122i
$116$	1.32593	+	0.963346i	0.123110	+	0.0894444i
$117$	0.309017	−	0.951057i	0.0285686	−	0.0879252i
$118$	−1.75077	−	5.38830i	−0.161171	−	0.496033i
$119$	−6.06809	+	4.40873i	−0.556261	+	0.404147i
$120$	1.68781			0.154076
$121$	5.66098	+	9.43151i	0.514635	+	0.857410i
$122$	−16.9212			−1.53197
$123$	−0.572985	+	0.416298i	−0.0516643	+	0.0375363i
$124$	−1.97783	−	6.08714i	−0.177614	−	0.546641i
$125$	3.56026	−	10.9574i	0.318440	−	0.980056i
$126$	1.94861	+	1.41575i	0.173596	+	0.126125i
$127$	7.52163	+	5.46478i	0.667436	+	0.484921i	0.869166	−	0.494520i	$-0.164656\pi$
$127$	7.52163	+	5.46478i	0.667436	+	0.484921i	−0.201730	+	0.979441i	$0.564656\pi$
$128$	2.73648	−	8.42202i	0.241873	−	0.744409i
$129$	−3.30339	−	10.1668i	−0.290847	−	0.895135i
$130$	−2.53265	+	1.84008i	−0.222128	+	0.161385i
$131$	15.7890			1.37949			0.689744	−	0.724054i	$-0.257723\pi$
$131$	15.7890			1.37949			0.689744	+	0.724054i	$0.257723\pi$
$132$	7.32863	+	4.14862i	0.637876	+	0.361091i
$133$	−3.26720			−0.283302
$134$	−26.9853	+	19.6060i	−2.33118	+	1.69370i
$135$	−0.454059	−	1.39745i	−0.0390792	−	0.120273i
$136$	−2.35499	+	7.24792i	−0.201939	+	0.621504i
$137$	10.7817	+	7.83335i	0.921141	+	0.669248i	0.943808	−	0.330495i	$-0.107216\pi$
$137$	10.7817	+	7.83335i	0.921141	+	0.669248i	−0.0226667	+	0.999743i	$0.507216\pi$
$138$	−3.61948	−	2.62970i	−0.308110	−	0.223855i
$139$	4.48605	−	13.8066i	0.380502	−	1.17106i	−0.559189	−	0.829040i	$-0.688887\pi$
$139$	4.48605	−	13.8066i	0.380502	−	1.17106i	0.939691	−	0.342024i	$-0.111113\pi$
$140$	−1.30341	−	4.01149i	−0.110158	−	0.339033i
$141$	−1.44909	+	1.05282i	−0.122035	+	0.0886637i
$142$	18.5625			1.55773
$143$	−3.29539	+	0.374677i	−0.275575	+	0.0313321i
$144$	−2.63103			−0.219252
$145$	−0.767298	+	0.557474i	−0.0637206	+	0.0462957i
$146$	4.67196	+	14.3788i	0.386655	+	1.19000i
$147$	−1.76817	+	5.44186i	−0.145836	+	0.448837i
$148$	9.63531	+	7.00046i	0.792017	+	0.575434i
$149$	7.47669	+	5.43213i	0.612514	+	0.445018i	0.850299	−	0.526300i	$-0.176421\pi$
$149$	7.47669	+	5.43213i	0.612514	+	0.445018i	−0.237784	+	0.971318i	$0.576421\pi$
$150$	1.87040	−	5.75650i	0.152718	−	0.470016i
$151$	−5.52381	−	17.0005i	−0.449522	−	1.38348i	−0.877448	−	0.479671i	$-0.840756\pi$
$151$	−5.52381	−	17.0005i	−0.449522	−	1.38348i	0.427927	−	0.903813i	$-0.359244\pi$
$152$	−2.68563	+	1.95123i	−0.217833	+	0.158265i
$153$	6.63458			0.536374
$154$	1.59449	−	7.82774i	0.128488	−	0.630777i
$155$	3.70382			0.297498
$156$	−2.05421	+	1.49247i	−0.164469	+	0.119493i
$157$	0.667097	+	2.05311i	0.0532401	+	0.163856i	0.974141	−	0.225940i	$-0.0725454\pi$
$157$	0.667097	+	2.05311i	0.0532401	+	0.163856i	−0.920901	+	0.389796i	$0.872545\pi$
$158$	−10.5993	+	32.6214i	−0.843238	+	2.59522i
$159$	0.217613	+	0.158105i	0.0172578	+	0.0125385i
$160$	9.39441	+	6.82544i	0.742693	+	0.539598i
$161$	−0.733609	+	2.25782i	−0.0578165	+	0.177941i
$162$	−0.658369	−	2.02625i	−0.0517264	−	0.159197i
$163$	−0.988160	+	0.717940i	−0.0773987	+	0.0562334i	−0.625812	−	0.779974i	$-0.715232\pi$
$163$	−0.988160	+	0.717940i	−0.0773987	+	0.0562334i	0.548413	+	0.836208i	$0.315232\pi$
$164$	1.79835			0.140427
$165$	−3.59378	+	3.29154i	−0.279775	+	0.256246i
$166$	−9.73893			−0.755887
$167$	−2.84474	+	2.06683i	−0.220133	+	0.159936i	−0.692386	−	0.721527i	$-0.743441\pi$
$167$	−2.84474	+	2.06683i	−0.220133	+	0.159936i	0.472254	+	0.881463i	$0.343441\pi$
$168$	−0.401289	−	1.23504i	−0.0309601	−	0.0952855i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−16.8031	−	12.2081i	−1.28874	−	0.936322i
$171$	2.33804	+	1.69869i	0.178795	+	0.129902i
$172$	−8.38779	+	25.8150i	−0.639563	+	1.96837i
$173$	−2.97304	−	9.15007i	−0.226036	−	0.695667i	−0.998185	−	0.0602251i	$-0.980818\pi$
$173$	−2.97304	−	9.15007i	−0.226036	−	0.695667i	0.772149	−	0.635441i	$-0.219182\pi$
$174$	−1.11255	+	0.808317i	−0.0843424	+	0.0612783i
$175$	−3.21178			−0.242788
$176$	3.61680	+	7.94129i	0.272627	+	0.598597i
$177$	2.65925			0.199881
$178$	7.50299	−	5.45124i	0.562373	−	0.408588i
$179$	−1.78423	−	5.49128i	−0.133359	−	0.410438i	0.861972	−	0.506956i	$-0.169229\pi$
$179$	−1.78423	−	5.49128i	−0.133359	−	0.410438i	−0.995331	+	0.0965183i	$0.969229\pi$
$180$	−1.15292	+	3.54833i	−0.0859339	+	0.264477i
$181$	2.93883	+	2.13518i	0.218441	+	0.158707i	0.691625	−	0.722257i	$-0.256895\pi$
$181$	2.93883	+	2.13518i	0.218441	+	0.158707i	−0.473183	+	0.880964i	$0.656895\pi$
$182$	1.94861	+	1.41575i	0.144441	+	0.104942i
$183$	2.45429	−	7.55353i	0.181426	−	0.558373i
$184$	0.745379	+	2.29404i	0.0549501	+	0.169119i
$185$	−5.57581	+	4.05106i	−0.409942	+	0.297840i
$186$	5.37039			0.393776
$187$	−9.12037	−	20.0253i	−0.666947	−	1.46440i
$188$	4.54804			0.331700
$189$	−0.914616	+	0.664507i	−0.0665285	+	0.0483358i
$190$	−2.79573	−	8.60436i	−0.202823	−	0.624226i
$191$	−1.47163	+	4.52922i	−0.106484	+	0.327723i	−0.990076	−	0.140534i	$-0.955118\pi$
$191$	−1.47163	+	4.52922i	−0.106484	+	0.327723i	0.883592	+	0.468257i	$0.155118\pi$
$192$	9.36445	+	6.80367i	0.675821	+	0.491013i
$193$	11.6349	+	8.45323i	0.837496	+	0.608477i	0.921670	−	0.387974i	$-0.126825\pi$
$193$	11.6349	+	8.45323i	0.837496	+	0.608477i	−0.0841739	+	0.996451i	$0.526825\pi$
$194$	6.62888	−	20.4016i	0.475926	−	1.46475i
$195$	−0.454059	−	1.39745i	−0.0325159	−	0.100074i
$196$	11.7540	−	8.53979i	0.839573	−	0.609985i
$197$	−2.05882			−0.146685			−0.0733424	−	0.997307i	$-0.523367\pi$
$197$	−2.05882			−0.146685			−0.0733424	+	0.997307i	$0.523367\pi$
$198$	−5.21084	+	4.77260i	−0.370318	+	0.339174i
$199$	6.72463			0.476696			0.238348	−	0.971180i	$-0.423394\pi$
$199$	6.72463			0.476696			0.238348	+	0.971180i	$0.423394\pi$
$200$	−2.64008	+	1.91813i	−0.186682	+	0.135632i
$201$	−4.83800	−	14.8898i	−0.341246	−	1.05025i
$202$	12.7727	−	39.3103i	0.898683	−	2.76586i
$203$	0.590357	+	0.428919i	0.0414349	+	0.0301042i
$204$	−13.6288	−	9.90193i	−0.954209	−	0.693274i
$205$	−0.321587	+	0.989743i	−0.0224606	+	0.0691266i
$206$	−4.84721	−	14.9182i	−0.337721	−	1.03940i
$207$	1.69886	−	1.23430i	0.118079	−	0.0857896i
$208$	−2.63103			−0.182429
$209$	1.91315	−	9.39211i	0.132335	−	0.649666i
$210$	3.53915			0.244224
$211$	−22.3575	+	16.2437i	−1.53915	+	1.11826i	−0.588289	+	0.808651i	$0.700198\pi$
$211$	−22.3575	+	16.2437i	−1.53915	+	1.11826i	−0.950864	+	0.309609i	$0.899802\pi$
$212$	−0.211055	−	0.649562i	−0.0144953	−	0.0446121i
$213$	−2.69235	+	8.28621i	−0.184477	+	0.567762i
$214$	−7.12706	−	5.17811i	−0.487196	−	0.353969i
$215$	−12.7076	−	9.23265i	−0.866655	−	0.629661i
$216$	−0.354958	+	1.09245i	−0.0241518	+	0.0743316i
$217$	−0.880608	−	2.71023i	−0.0597795	−	0.183983i
$218$	3.88936	−	2.82579i	0.263421	−	0.191387i
$219$	−7.09627			−0.479521
$220$	12.2949	−	1.39790i	0.828923	−	0.0942463i
$221$	6.63458			0.446290
$222$	−8.08472	+	5.87389i	−0.542611	+	0.394230i
$223$	−5.60357	−	17.2460i	−0.375243	−	1.15488i	−0.943315	−	0.331900i	$-0.892310\pi$
$223$	−5.60357	−	17.2460i	−0.375243	−	1.15488i	0.568072	−	0.822979i	$-0.307690\pi$
$224$	2.76086	−	8.49706i	0.184468	−	0.567734i
$225$	2.29838	+	1.66987i	0.153226	+	0.111325i
$226$	27.1020	+	19.6908i	1.80280	+	1.30981i
$227$	0.452790	−	1.39354i	0.0300527	−	0.0924928i	−0.934905	−	0.354898i	$-0.884516\pi$
$227$	0.452790	−	1.39354i	0.0300527	−	0.0924928i	0.964958	+	0.262405i	$0.0845157\pi$
$228$	−2.26759	−	6.97893i	−0.150175	−	0.462191i
$229$	−7.82057	+	5.68197i	−0.516798	+	0.375475i	−0.815396	−	0.578903i	$-0.803481\pi$
$229$	−7.82057	+	5.68197i	−0.516798	+	0.375475i	0.298599	+	0.954379i	$0.403481\pi$
$230$	−6.57383			−0.433466
$231$	3.26299	+	1.84713i	0.214689	+	0.121532i
$232$	0.741429			0.0486772
$233$	11.9021	−	8.64737i	0.779731	−	0.566508i	−0.125167	−	0.992136i	$-0.539947\pi$
$233$	11.9021	−	8.64737i	0.779731	−	0.566508i	0.904898	+	0.425628i	$0.139947\pi$
$234$	−0.658369	−	2.02625i	−0.0430389	−	0.132460i
$235$	−0.813298	+	2.50307i	−0.0530537	+	0.163282i
$236$	−5.46266	−	3.96885i	−0.355589	−	0.258350i
$237$	−13.0247	−	9.46298i	−0.846044	−	0.614687i
$238$	−4.93815	+	15.1980i	−0.320092	+	0.985143i
$239$	−8.80115	−	27.0871i	−0.569299	−	1.75212i	−0.654819	−	0.755785i	$-0.727255\pi$
$239$	−8.80115	−	27.0871i	−0.569299	−	1.75212i	0.0855205	−	0.996336i	$-0.472745\pi$
$240$	−3.12762	+	2.27235i	−0.201887	+	0.146679i
$241$	−17.5509			−1.13056			−0.565278	−	0.824901i	$-0.691231\pi$
$241$	−17.5509			−1.13056			−0.565278	+	0.824901i	$0.691231\pi$
$242$	21.5685	+	9.16725i	1.38647	+	0.589293i
$243$	1.00000			0.0641500
$244$	−16.3151	+	11.8536i	−1.04447	+	0.758849i
$245$	2.59809	+	7.99609i	0.165986	+	0.510851i
$246$	−0.466289	+	1.43509i	−0.0297295	+	0.0914980i
$247$	2.33804	+	1.69869i	0.148766	+	0.108085i
$248$	−2.34245	−	1.70189i	−0.148746	−	0.108070i
$249$	1.41256	−	4.34741i	0.0895172	−	0.275506i
$250$	−7.58524	−	23.3450i	−0.479732	−	1.47646i
$251$	−5.37527	+	3.90537i	−0.339284	+	0.246505i	−0.744360	−	0.667779i	$-0.767245\pi$
$251$	−5.37527	+	3.90537i	−0.339284	+	0.246505i	0.405075	+	0.914283i	$0.367245\pi$
$252$	2.87057			0.180829
$253$	−6.06089	−	3.43097i	−0.381045	−	0.215703i
$254$	19.8080			1.24287
$255$	7.88681	−	5.73010i	0.493891	−	0.358833i
$256$	1.32365	+	4.07379i	0.0827284	+	0.254612i
$257$	−4.72422	+	14.5396i	−0.294688	+	0.906958i	0.688637	+	0.725106i	$0.258209\pi$
$257$	−4.72422	+	14.5396i	−0.294688	+	0.906958i	−0.983326	+	0.181852i	$0.941791\pi$
$258$	−18.4256	−	13.3870i	−1.14713	−	0.833438i
$259$	4.29001	+	3.11688i	0.266569	+	0.193673i
$260$	−1.15292	+	3.54833i	−0.0715013	+	0.220058i
$261$	−0.199461	−	0.613878i	−0.0123463	−	0.0379981i
$262$	27.2144	−	19.7724i	1.68131	−	1.22154i
$263$	7.95406			0.490468			0.245234	−	0.969464i	$-0.421135\pi$
$263$	7.95406			0.490468			0.245234	+	0.969464i	$0.421135\pi$
$264$	3.78531	−	0.430379i	0.232970	−	0.0264880i
$265$	0.395236			0.0242792
$266$	−5.63145	+	4.09149i	−0.345287	+	0.250865i
$267$	1.34515	+	4.13996i	0.0823220	+	0.253361i
$268$	−12.2844	+	37.8074i	−0.750388	+	2.30946i
$269$	16.2550	+	11.8099i	0.991084	+	0.720064i	0.960158	−	0.279457i	$-0.0901545\pi$
$269$	16.2550	+	11.8099i	0.991084	+	0.720064i	0.0309255	+	0.999522i	$0.490155\pi$
$270$	−2.53265	−	1.84008i	−0.154132	−	0.111984i
$271$	−3.89825	+	11.9976i	−0.236802	+	0.728801i	0.760075	+	0.649835i	$0.225162\pi$
$271$	−3.89825	+	11.9976i	−0.236802	+	0.728801i	−0.996877	+	0.0789663i	$0.974838\pi$
$272$	−5.39413	−	16.6014i	−0.327067	−	1.00661i
$273$	−0.914616	+	0.664507i	−0.0553551	+	0.0402178i
$274$	28.3933			1.71530
$275$	1.88070	−	9.23280i	0.113410	−	0.556759i
$276$	−5.33198			−0.320948
$277$	4.44760	−	3.23137i	0.267231	−	0.194154i	−0.446098	−	0.894984i	$-0.647187\pi$
$277$	4.44760	−	3.23137i	0.267231	−	0.194154i	0.713329	+	0.700830i	$0.247187\pi$
$278$	−9.55765	−	29.4154i	−0.573230	−	1.76422i
$279$	−0.778935	+	2.39732i	−0.0466336	+	0.143524i
$280$	−1.54370	−	1.12156i	−0.0922538	−	0.0670263i
$281$	3.00779	+	2.18529i	0.179430	+	0.130363i	0.673875	−	0.738846i	$-0.264629\pi$
$281$	3.00779	+	2.18529i	0.179430	+	0.130363i	−0.494445	+	0.869209i	$0.664629\pi$
$282$	−1.17925	+	3.62936i	−0.0702234	+	0.216125i
$283$	8.24272	+	25.3685i	0.489979	+	1.50800i	0.824638	+	0.565661i	$0.191379\pi$
$283$	8.24272	+	25.3685i	0.489979	+	1.50800i	−0.334659	+	0.942339i	$0.608621\pi$
$284$	17.8976	−	13.0034i	1.06203	−	0.771608i
$285$	4.24644			0.251538
$286$	−5.21084	+	4.77260i	−0.308124	+	0.282210i
$287$	0.800694			0.0472635
$288$	−6.39351	+	4.64515i	−0.376741	+	0.273718i
$289$	8.34891	+	25.6953i	0.491112	+	1.51149i
$290$	−0.624418	+	1.92176i	−0.0366671	+	0.112850i
$291$	8.14570	+	5.91819i	0.477509	+	0.346931i
$292$	14.5772	+	10.5910i	0.853069	+	0.619791i
$293$	6.49511	−	19.9899i	0.379448	−	1.16782i	−0.560980	−	0.827829i	$-0.689576\pi$
$293$	6.49511	−	19.9899i	0.379448	−	1.16782i	0.940428	−	0.339992i	$-0.110424\pi$
$294$	3.76713	+	11.5940i	0.219703	+	0.676177i
$295$	3.16116	−	2.29672i	0.184050	−	0.133720i
$296$	5.38783			0.313161
$297$	−1.37467	−	3.01832i	−0.0797665	−	0.175141i
$298$	19.6897			1.14059
$299$	1.69886	−	1.23430i	0.0982478	−	0.0713812i
$300$	−2.22913	−	6.86055i	−0.128699	−	0.396094i
$301$	−3.73457	+	11.4938i	−0.215257	+	0.662493i
$302$	−30.8107	−	22.3853i	−1.77296	−	1.28813i
$303$	15.6953	+	11.4033i	0.901673	+	0.655104i
$304$	2.34965	−	7.23147i	0.134761	−	0.414753i
$305$	−3.60626	−	11.0989i	−0.206494	−	0.635522i
$306$	11.4356	−	8.30843i	0.653728	−	0.474962i
$307$	28.3699			1.61915			0.809577	−	0.587014i	$-0.199696\pi$
$307$	28.3699			1.61915			0.809577	+	0.587014i	$0.199696\pi$
$308$	−3.94610	−	8.66432i	−0.224850	−	0.493696i
$309$	7.36245			0.418835
$310$	6.38402	−	4.63826i	0.362588	−	0.263436i
$311$	2.89897	+	8.92212i	0.164386	+	0.505927i	0.998990	−	0.0449221i	$-0.0143040\pi$
$311$	2.89897	+	8.92212i	0.164386	+	0.505927i	−0.834605	+	0.550849i	$0.814304\pi$
$312$	−0.354958	+	1.09245i	−0.0200955	+	0.0618476i
$313$	24.0710	+	17.4886i	1.36057	+	0.988514i	0.998408	+	0.0563996i	$0.0179621\pi$
$313$	24.0710	+	17.4886i	1.36057	+	0.988514i	0.362164	+	0.932114i	$0.382038\pi$
$314$	3.72093	+	2.70341i	0.209984	+	0.152562i
$315$	−0.513327	+	1.57986i	−0.0289227	+	0.0890149i
$316$	12.6322	+	38.8780i	0.710618	+	2.18706i
$317$	−22.6732	+	16.4730i	−1.27345	+	0.925216i	−0.999334	−	0.0364801i	$-0.988385\pi$
$317$	−22.6732	+	16.4730i	−1.27345	+	0.925216i	−0.274117	+	0.961696i	$0.588385\pi$
$318$	0.573078			0.0321366
$319$	−1.57869	+	1.44592i	−0.0883896	+	0.0809559i
$320$	17.0081			0.950780
$321$	3.34521	−	2.43044i	0.186711	−	0.135654i
$322$	1.56297	+	4.81034i	0.0871011	+	0.268070i
$323$	−5.92503	+	18.2354i	−0.329677	+	1.01464i
$324$	−2.05421	−	1.49247i	−0.114123	−	0.0829152i
$325$	2.29838	+	1.66987i	0.127491	+	0.0926280i
$326$	−0.804154	+	2.47493i	−0.0445380	+	0.137074i
$327$	0.697294	+	2.14605i	0.0385605	+	0.118677i
$328$	0.658169	−	0.478188i	0.0363413	−	0.0264035i
$329$	2.02497			0.111640
$330$	−2.07239	+	10.1739i	−0.114081	+	0.560053i
$331$	−22.6985			−1.24762			−0.623811	−	0.781576i	$-0.714416\pi$
$331$	−22.6985			−1.24762			−0.623811	+	0.781576i	$0.714416\pi$
$332$	−9.39008	+	6.82229i	−0.515348	+	0.374422i
$333$	−1.44945	−	4.46094i	−0.0794292	−	0.244458i
$334$	−2.31502	+	7.12490i	−0.126672	+	0.389857i
$335$	−18.6111	−	13.5217i	−1.01683	−	0.738771i
$336$	2.40638	+	1.74834i	0.131279	+	0.0953796i
$337$	−0.403925	+	1.24315i	−0.0220032	+	0.0677190i	−0.961455	−	0.274962i	$-0.911335\pi$
$337$	−0.403925	+	1.24315i	−0.0220032	+	0.0677190i	0.939452	+	0.342681i	$0.111335\pi$
$338$	−0.658369	−	2.02625i	−0.0358106	−	0.110214i
$339$	−12.7208	+	9.24220i	−0.690899	+	0.501968i
$340$	−24.7532			−1.34243
$341$	8.30666	−	0.944444i	0.449831	−	0.0511445i
$342$	6.15718			0.332942
$343$	11.6357	−	8.45380i	0.628266	−	0.456462i
$344$	3.79449	+	11.6782i	0.204585	+	0.629649i
$345$	0.953485	−	2.93452i	0.0513339	−	0.157989i
$346$	−16.5830	−	12.0482i	−0.891507	−	0.647717i
$347$	9.50602	+	6.90653i	0.510310	+	0.370762i	0.812941	−	0.582346i	$-0.197865\pi$
$347$	9.50602	+	6.90653i	0.510310	+	0.370762i	−0.302631	+	0.953108i	$0.597865\pi$
$348$	−0.506461	+	1.55873i	−0.0271492	+	0.0835565i
$349$	1.81263	+	5.57869i	0.0970277	+	0.298621i	0.987777	−	0.155875i	$-0.0498196\pi$
$349$	1.81263	+	5.57869i	0.0970277	+	0.298621i	−0.890749	+	0.454495i	$0.849820\pi$
$350$	−5.53593	+	4.02209i	−0.295908	+	0.214990i
$351$	1.00000			0.0533761
$352$	22.8096	+	12.9121i	1.21575	+	0.688218i
$353$	5.35236			0.284878			0.142439	−	0.989804i	$-0.454506\pi$
$353$	5.35236			0.284878			0.142439	+	0.989804i	$0.454506\pi$
$354$	4.58356	−	3.33015i	0.243614	−	0.176996i
$355$	3.95606	+	12.1755i	0.209966	+	0.646208i
$356$	3.41554	−	10.5120i	0.181023	−	0.557133i
$357$	−6.06809	−	4.40873i	−0.321157	−	0.233335i
$358$	−9.95204	−	7.23058i	−0.525982	−	0.382148i
$359$	4.96474	−	15.2799i	0.262029	−	0.806442i	−0.730334	−	0.683090i	$-0.760636\pi$
$359$	4.96474	−	15.2799i	0.262029	−	0.806442i	0.992363	−	0.123352i	$-0.0393644\pi$
$360$	0.521563	+	1.60521i	0.0274888	+	0.0846018i
$361$	8.61443	−	6.25875i	0.453391	−	0.329408i
$362$	7.73934			0.406771
$363$	−7.22055	+	8.29841i	−0.378981	+	0.435553i
$364$	2.87057			0.150459
$365$	−8.43564	+	6.12885i	−0.441542	+	0.320799i
$366$	−5.22894	−	16.0930i	−0.273321	−	0.841195i
$367$	0.406985	−	1.25257i	0.0212445	−	0.0653838i	−0.939872	−	0.341526i	$-0.889056\pi$
$367$	0.406985	−	1.25257i	0.0212445	−	0.0653838i	0.961117	+	0.276142i	$0.0890562\pi$
$368$	−4.46976	−	3.24747i	−0.233002	−	0.169286i
$369$	−0.572985	−	0.416298i	−0.0298284	−	0.0216716i
$370$	−4.53753	+	13.9651i	−0.235895	+	0.726011i
$371$	−0.0939701	−	0.289210i	−0.00487868	−	0.0150150i
$372$	5.17803	−	3.76206i	0.268468	−	0.195054i
$373$	−18.7843			−0.972615			−0.486307	−	0.873788i	$-0.661656\pi$
$373$	−18.7843			−0.972615			−0.486307	+	0.873788i	$0.661656\pi$
$374$	−40.7977	−	23.0949i	−2.10960	−	1.19421i
$375$	11.5213			0.594955
$376$	1.66452	−	1.20934i	0.0858410	−	0.0623671i
$377$	−0.199461	−	0.613878i	−0.0102728	−	0.0316163i
$378$	−0.744304	+	2.29073i	−0.0382829	+	0.117823i
$379$	−0.175946	−	0.127832i	−0.00903771	−	0.00656628i	0.583257	−	0.812288i	$-0.301778\pi$
$379$	−0.175946	−	0.127832i	−0.00903771	−	0.00656628i	−0.592295	+	0.805721i	$0.701778\pi$
$380$	−8.72310	−	6.33770i	−0.447485	−	0.325117i
$381$	−2.87301	+	8.84220i	−0.147189	+	0.453000i
$382$	3.13535	+	9.64963i	0.160419	+	0.493718i
$383$	−20.0164	+	14.5428i	−1.02279	+	0.743101i	−0.966853	−	0.255333i	$-0.917815\pi$
$383$	−20.0164	+	14.5428i	−1.02279	+	0.743101i	−0.0559379	+	0.998434i	$0.517815\pi$
$384$	8.85544			0.451902
$385$	5.47418	−	0.622399i	0.278990	−	0.0317204i
$386$	30.6402			1.55954
$387$	8.64838	−	6.28342i	0.439622	−	0.319404i
$388$	−7.90025	−	24.3145i	−0.401074	−	1.23438i
$389$	2.95339	−	9.08958i	0.149743	−	0.460860i	−0.847848	−	0.530240i	$-0.822102\pi$
$389$	2.95339	−	9.08958i	0.149743	−	0.460860i	0.997590	+	0.0693795i	$0.0221019\pi$
$390$	−2.53265	−	1.84008i	−0.128246	−	0.0931760i
$391$	11.2712	+	8.18904i	0.570011	+	0.414138i
$392$	2.03103	−	6.25088i	0.102583	−	0.315717i
$393$	4.87906	+	15.0162i	0.246116	+	0.757467i
$394$	−3.54865	+	2.57824i	−0.178778	+	0.129890i
$395$	−23.6559			−1.19026
$396$	−1.68090	+	8.25194i	−0.0844683	+	0.414676i
$397$	−26.6594			−1.33800			−0.668999	−	0.743263i	$-0.733277\pi$
$397$	−26.6594			−1.33800			−0.668999	+	0.743263i	$0.733277\pi$
$398$	11.5908	−	8.42120i	0.580994	−	0.422117i
$399$	−1.00962	−	3.10729i	−0.0505443	−	0.155559i
$400$	2.30979	−	7.10881i	0.115490	−	0.355440i
$401$	3.21159	+	2.33336i	0.160379	+	0.116522i	0.665080	−	0.746772i	$-0.268397\pi$
$401$	3.21159	+	2.33336i	0.160379	+	0.116522i	−0.504701	+	0.863294i	$0.668397\pi$
$402$	−26.9853	−	19.6060i	−1.34591	−	0.977858i
$403$	−0.778935	+	2.39732i	−0.0388015	+	0.119419i
$404$	−15.2224	−	46.8497i	−0.757342	−	2.33086i
$405$	1.18874	−	0.863672i	0.0590691	−	0.0429162i
$406$	1.55469			0.0771580
$407$	−11.4720	+	10.5072i	−0.568648	+	0.520824i
$408$	−7.62092			−0.377292
$409$	−13.2595	+	9.63360i	−0.655641	+	0.476351i	−0.865188	−	0.501448i	$-0.832801\pi$
$409$	−13.2595	+	9.63360i	−0.655641	+	0.476351i	0.209547	+	0.977798i	$0.432801\pi$
$410$	0.685150	+	2.10867i	0.0338371	+	0.104140i
$411$	−4.11824	+	12.6746i	−0.203138	+	0.625193i
$412$	−15.1240	−	10.9883i	−0.745108	−	0.541353i
$413$	−2.43219	−	1.76709i	−0.119680	−	0.0869527i
$414$	1.38252	−	4.25495i	0.0679470	−	0.209119i
$415$	−2.07557	−	6.38794i	−0.101886	−	0.313572i
$416$	−6.39351	+	4.64515i	−0.313467	+	0.227747i
$417$	14.5172			0.710909
$418$	−8.46410	−	18.5844i	−0.413993	−	0.908991i
$419$	−13.8400			−0.676126			−0.338063	−	0.941123i	$-0.609772\pi$
$419$	−13.8400			−0.676126			−0.338063	+	0.941123i	$0.609772\pi$
$420$	3.41238	−	2.47924i	0.166507	−	0.120974i
$421$	3.87115	+	11.9142i	0.188668	+	0.580662i	0.999992	−	0.00393534i	$-0.00125266\pi$
$421$	3.87115	+	11.9142i	0.188668	+	0.580662i	−0.811324	+	0.584597i	$0.801253\pi$
$422$	−18.1943	+	55.9962i	−0.885684	+	2.72585i
$423$	−1.44909	−	1.05282i	−0.0704570	−	0.0511900i
$424$	−0.249964	−	0.181610i	−0.0121393	−	0.00881975i
$425$	−5.82453	+	17.9261i	−0.282531	+	0.869541i
$426$	5.73613	+	17.6540i	0.277916	+	0.855339i
$427$	−7.26411	+	5.27769i	−0.351535	+	0.255405i
$428$	−10.4991			−0.507495
$429$	−1.37467	−	3.01832i	−0.0663698	−	0.145726i
$430$	−33.4653			−1.61384
$431$	10.7760	−	7.82920i	0.519060	−	0.377119i	−0.297189	−	0.954819i	$-0.596049\pi$
$431$	10.7760	−	7.82920i	0.519060	−	0.377119i	0.816250	+	0.577699i	$0.196049\pi$
$432$	−0.813032	−	2.50226i	−0.0391170	−	0.120390i
$433$	8.06475	−	24.8208i	0.387567	−	1.19281i	−0.547034	−	0.837111i	$-0.684243\pi$
$433$	8.06475	−	24.8208i	0.387567	−	1.19281i	0.934601	−	0.355699i	$-0.115757\pi$
$434$	−4.91185	−	3.56867i	−0.235776	−	0.171301i
$435$	−0.767298	−	0.557474i	−0.0367891	−	0.0267288i
$436$	1.77053	−	5.44914i	0.0847932	−	0.260966i
$437$	1.87533	+	5.77168i	0.0897093	+	0.276097i
$438$	−12.2314	+	8.88660i	−0.584437	+	0.424618i
$439$	−34.1519			−1.62998			−0.814991	−	0.579474i	$-0.803258\pi$
$439$	−34.1519			−1.62998			−0.814991	+	0.579474i	$0.803258\pi$
$440$	4.12805	−	3.78088i	0.196797	−	0.180246i
$441$	−5.72191			−0.272472
$442$	11.4356	−	8.30843i	0.543935	−	0.395192i
$443$	−0.104471	−	0.321528i	−0.00496356	−	0.0152763i	0.948544	−	0.316645i	$-0.102556\pi$
$443$	−0.104471	−	0.321528i	−0.00496356	−	0.0152763i	−0.953508	+	0.301369i	$0.902556\pi$
$444$	−3.68036	+	11.3270i	−0.174662	+	0.537555i
$445$	5.17461	+	3.75957i	0.245300	+	0.178221i
$446$	−31.2556	−	22.7085i	−1.47999	−	1.07528i
$447$	−2.85584	+	8.78938i	−0.135077	+	0.415723i
$448$	−4.04378	−	12.4455i	−0.191051	−	0.587994i
$449$	19.8901	−	14.4510i	0.938672	−	0.681985i	−0.00942836	−	0.999956i	$-0.503001\pi$
$449$	19.8901	−	14.4510i	0.938672	−	0.681985i	0.948101	+	0.317970i	$0.103001\pi$
$450$	6.05274			0.285329
$451$	−0.468856	+	2.30173i	−0.0220776	+	0.108384i
$452$	39.9250			1.87791
$453$	14.4615	−	10.5069i	0.679462	−	0.493658i
$454$	−0.964681	−	2.96898i	−0.0452747	−	0.139341i
$455$	−0.513327	+	1.57986i	−0.0240651	+	0.0740648i
$456$	−2.68563	−	1.95123i	−0.125766	−	0.0913745i
$457$	17.5020	+	12.7160i	0.818710	+	0.594828i	0.916343	−	0.400395i	$-0.131127\pi$
$457$	17.5020	+	12.7160i	0.818710	+	0.594828i	−0.0976327	+	0.995223i	$0.531127\pi$
$458$	−6.36429	+	19.5873i	−0.297384	+	0.915253i
$459$	2.05020	+	6.30986i	0.0956950	+	0.294519i
$460$	−6.33836	+	4.60509i	−0.295528	+	0.214713i
$461$	24.8452			1.15716			0.578579	−	0.815626i	$-0.303607\pi$
$461$	24.8452			1.15716			0.578579	+	0.815626i	$0.303607\pi$
$462$	7.93735	−	0.902455i	0.369279	−	0.0419860i
$463$	−37.9227			−1.76242			−0.881208	−	0.472729i	$-0.843269\pi$
$463$	−37.9227			−1.76242			−0.881208	+	0.472729i	$0.843269\pi$
$464$	−1.37391	+	0.998205i	−0.0637823	+	0.0463405i
$465$	1.14454	+	3.52254i	0.0530769	+	0.163354i
$466$	9.68578	−	29.8098i	0.448685	−	1.38091i
$467$	−21.9082	−	15.9172i	−1.01379	−	0.736562i	−0.0487897	−	0.998809i	$-0.515536\pi$
$467$	−21.9082	−	15.9172i	−1.01379	−	0.736562i	−0.965001	+	0.262247i	$0.915536\pi$
$468$	−2.05421	−	1.49247i	−0.0949560	−	0.0689896i
$469$	−5.46949	+	16.8334i	−0.252557	+	0.777292i
$470$	1.73275	+	5.33287i	0.0799259	+	0.245987i
$471$	−1.74648	+	1.26889i	−0.0804736	+	0.0584675i
$472$	−3.05459			−0.140599
$473$	−30.8541	−	17.4660i	−1.41867	−	0.803087i
$474$	−34.3002			−1.57546
$475$	−6.64228	+	4.82590i	−0.304769	+	0.221428i
$476$	5.88524	+	18.1129i	0.269750	+	0.830204i
$477$	−0.0831206	+	0.255819i	−0.00380583	+	0.0117131i
$478$	−49.0910	−	35.6667i	−2.24537	−	1.63136i
$479$	23.9616	+	17.4092i	1.09484	+	0.795445i	0.980209	−	0.197964i	$-0.0634329\pi$
$479$	23.9616	+	17.4092i	1.09484	+	0.795445i	0.114626	+	0.993409i	$0.463433\pi$
$480$	−3.58835	+	11.0438i	−0.163785	+	0.504078i
$481$	−1.44945	−	4.46094i	−0.0660891	−	0.203401i
$482$	−30.2514	+	21.9789i	−1.37791	+	1.00111i
$483$	−2.37401			−0.108021
$484$	27.2177	−	6.27021i	1.23717	−	0.285010i
$485$	14.7945			0.671785
$486$	1.72363	−	1.25229i	0.0781856	−	0.0568051i
$487$	0.441043	+	1.35739i	0.0199856	+	0.0615093i	0.960552	−	0.278101i	$-0.0897049\pi$
$487$	0.441043	+	1.35739i	0.0199856	+	0.0615093i	−0.940566	+	0.339610i	$0.889705\pi$
$488$	−2.81916	+	8.67649i	−0.127618	+	0.392766i
$489$	−0.988160	−	0.717940i	−0.0446861	−	0.0324664i
$490$	14.4916	+	10.5288i	0.654663	+	0.475641i
$491$	−13.2293	+	40.7157i	−0.597032	+	1.83748i	−0.0526922	+	0.998611i	$0.516780\pi$
$491$	−13.2293	+	40.7157i	−0.597032	+	1.83748i	−0.544340	+	0.838865i	$0.683220\pi$
$492$	0.555720	+	1.71033i	0.0250538	+	0.0771076i
$493$	3.46455	−	2.51714i	0.156035	−	0.113366i
$494$	6.15718			0.277025
$495$	−4.24097	−	2.40075i	−0.190618	−	0.107905i
$496$	6.63200			0.297786
$497$	7.96871	−	5.78961i	0.357446	−	0.259700i
$498$	−3.00949	−	9.26227i	−0.134859	−	0.415052i
$499$	1.48163	−	4.55998i	0.0663267	−	0.204133i	−0.912400	−	0.409299i	$-0.865773\pi$
$499$	1.48163	−	4.55998i	0.0663267	−	0.204133i	0.978727	+	0.205166i	$0.0657734\pi$
$500$	−23.6671	−	17.1952i	−1.05842	−	0.768991i
$501$	−2.84474	−	2.06683i	−0.127094	−	0.0923390i
$502$	−4.37434	+	13.4628i	−0.195236	+	0.600876i
$503$	3.92058	+	12.0663i	0.174810	+	0.538009i	0.999625	−	0.0273935i	$-0.00872071\pi$
$503$	3.92058	+	12.0663i	0.174810	+	0.538009i	−0.824815	+	0.565403i	$0.808721\pi$
$504$	1.05059	−	0.763297i	0.0467969	−	0.0340000i
$505$	28.5064			1.26852
$506$	−14.7433	+	1.67628i	−0.655421	+	0.0745195i
$507$	1.00000			0.0444116
$508$	19.0985	−	13.8759i	0.847359	−	0.615643i
$509$	−12.9142	−	39.7460i	−0.572414	−	1.76171i	−0.644821	−	0.764333i	$-0.723068\pi$
$509$	−12.9142	−	39.7460i	−0.572414	−	1.76171i	0.0724075	−	0.997375i	$-0.476932\pi$
$510$	6.41820	−	19.7532i	0.284203	−	0.874686i
$511$	6.49036	+	4.71552i	0.287117	+	0.208602i
$512$	21.7115	+	15.7743i	0.959521	+	0.697133i
$513$	−0.893053	+	2.74853i	−0.0394292	+	0.121351i
$514$	10.0651	+	30.9771i	0.443951	+	1.36634i
$515$	8.75207	−	6.35875i	0.385662	−	0.280200i
$516$	−27.1434			−1.19492
$517$	−1.18574	+	5.82110i	−0.0521489	+	0.256012i
$518$	11.2977			0.496390
$519$	7.78351	−	5.65505i	0.341658	−	0.248229i
$520$	0.521563	+	1.60521i	0.0228720	+	0.0703929i
$521$	−11.9840	+	36.8830i	−0.525029	+	1.61587i	0.239229	+	0.970963i	$0.423105\pi$
$521$	−11.9840	+	36.8830i	−0.525029	+	1.61587i	−0.764258	+	0.644910i	$0.776895\pi$
$522$	−1.11255	−	0.808317i	−0.0486951	−	0.0353791i
$523$	5.14102	+	3.73517i	0.224801	+	0.163327i	0.694485	−	0.719507i	$-0.255632\pi$
$523$	5.14102	+	3.73517i	0.224801	+	0.163327i	−0.469684	+	0.882835i	$0.655632\pi$
$524$	12.3886	−	38.1283i	0.541200	−	1.66564i
$525$	−0.992495	−	3.05459i	−0.0433160	−	0.133313i
$526$	13.7099	−	9.96081i	0.597779	−	0.434312i
$527$	−16.7237			−0.728496
$528$	−6.43497	+	5.89378i	−0.280046	+	0.256494i
$529$	−18.5904			−0.808277
$530$	0.681242	−	0.494951i	0.0295913	−	0.0214993i
$531$	0.821752	+	2.52909i	0.0356610	+	0.109753i
$532$	−2.56357	+	7.88987i	−0.111145	+	0.342069i
$533$	−0.572985	−	0.416298i	−0.0248187	−	0.0180319i
$534$	7.50299	+	5.45124i	0.324686	+	0.235898i
$535$	1.87749	−	5.77833i	0.0811712	−	0.249819i
$536$	5.55725	+	17.1034i	0.240036	+	0.738756i
$537$	4.67116	−	3.39380i	0.201576	−	0.146453i
$538$	42.8071			1.84555
$539$	7.86575	+	17.2706i	0.338802	+	0.743896i
$540$	−3.73094			−0.160554
$541$	20.8656	−	15.1597i	0.897082	−	0.651768i	−0.0406328	−	0.999174i	$-0.512937\pi$
$541$	20.8656	−	15.1597i	0.897082	−	0.651768i	0.937715	+	0.347406i	$0.112937\pi$
$542$	8.30533	+	25.5612i	0.356744	+	1.09795i
$543$	−1.12253	+	3.45480i	−0.0481725	+	0.148260i
$544$	−42.4182	−	30.8186i	−1.81867	−	1.32134i
$545$	2.68239	+	1.94887i	0.114901	+	0.0834804i
$546$	−0.744304	+	2.29073i	−0.0318533	+	0.0980343i
$547$	−2.11413	−	6.50662i	−0.0903936	−	0.278203i	0.895632	−	0.444795i	$-0.146724\pi$
$547$	−2.11413	−	6.50662i	−0.0903936	−	0.278203i	−0.986026	+	0.166592i	$0.946724\pi$
$548$	27.3763	−	19.8900i	1.16946	−	0.849660i
$549$	7.94226			0.338967
$550$	−8.32053	−	18.2691i	−0.354789	−	0.778998i
$551$	1.86539			0.0794685
$552$	−1.95143	+	1.41780i	−0.0830583	+	0.0603454i
$553$	5.62436	+	17.3100i	0.239172	+	0.736096i
$554$	3.61941	−	11.1394i	0.153774	−	0.473268i
$555$	−5.57581	−	4.05106i	−0.236680	−	0.171958i
$556$	−29.8213	−	21.6665i	−1.26471	−	0.918863i
$557$	−9.12900	+	28.0962i	−0.386808	+	1.19047i	0.548352	+	0.836248i	$0.315255\pi$
$557$	−9.12900	+	28.0962i	−0.386808	+	1.19047i	−0.935160	+	0.354225i	$0.884745\pi$
$558$	1.65954	+	5.10755i	0.0702541	+	0.216220i
$559$	8.64838	−	6.28342i	0.365788	−	0.265760i
$560$	4.37056			0.184690
$561$	16.2268	−	14.8621i	0.685098	−	0.627480i
$562$	7.92094			0.334125
$563$	−10.0221	+	7.28151i	−0.422383	+	0.306879i	−0.778596	−	0.627526i	$-0.784068\pi$
$563$	−10.0221	+	7.28151i	−0.422383	+	0.306879i	0.356213	+	0.934405i	$0.384068\pi$
$564$	1.40542	+	4.32545i	0.0591790	+	0.182134i
$565$	−7.13953	+	21.9732i	−0.300362	+	0.924420i
$566$	45.9762	+	33.4037i	1.93252	+	1.40406i
$567$	−0.914616	−	0.664507i	−0.0384103	−	0.0279067i
$568$	3.09262	−	9.51809i	0.129763	−	0.399370i
$569$	3.91249	+	12.0414i	0.164020	+	0.504801i	0.998963	−	0.0455353i	$-0.0144994\pi$
$569$	3.91249	+	12.0414i	0.164020	+	0.504801i	−0.834943	+	0.550337i	$0.814499\pi$
$570$	7.31931	−	5.31779i	0.306572	−	0.222738i
$571$	13.4042			0.560947			0.280474	−	0.959862i	$-0.409509\pi$
$571$	13.4042			0.560947			0.280474	+	0.959862i	$0.409509\pi$
$572$	−1.68090	+	8.25194i	−0.0702819	+	0.345031i
$573$	−4.76230			−0.198948
$574$	1.38010	−	1.00270i	0.0576044	−	0.0418520i
$575$	1.84352	+	5.67378i	0.0768802	+	0.236613i
$576$	−3.57690	+	11.0086i	−0.149038	+	0.458690i
$577$	4.70693	+	3.41978i	0.195952	+	0.142367i	0.681435	−	0.731879i	$-0.261356\pi$
$577$	4.70693	+	3.41978i	0.195952	+	0.142367i	−0.485483	+	0.874246i	$0.661356\pi$
$578$	46.5685	+	33.8340i	1.93699	+	1.40731i
$579$	−4.44412	+	13.6776i	−0.184692	+	0.568422i
$580$	0.744177	+	2.29034i	0.0309003	+	0.0951013i
$581$	−4.18083	+	3.03755i	−0.173450	+	0.126019i
$582$	21.4515			0.889193
$583$	0.886408	−	0.100782i	0.0367113	−	0.00417397i
$584$	8.15125			0.337301
$585$	1.18874	−	0.863672i	0.0491485	−	0.0357085i
$586$	−13.8380	−	42.5890i	−0.571643	−	1.75934i
$587$	−8.33245	+	25.6447i	−0.343917	+	1.05847i	0.618244	+	0.785986i	$0.287844\pi$
$587$	−8.33245	+	25.6447i	−0.343917	+	1.05847i	−0.962161	+	0.272482i	$0.912156\pi$
$588$	11.7540	+	8.53979i	0.484727	+	0.352175i
$589$	−5.89348	−	4.28186i	−0.242836	−	0.176431i
$590$	2.57252	−	7.91739i	0.105909	−	0.325954i
$591$	−0.636210	−	1.95805i	−0.0261702	−	0.0805436i
$592$	−9.98397	+	7.25378i	−0.410338	+	0.298128i
$593$	−9.69441			−0.398102			−0.199051	−	0.979989i	$-0.563786\pi$
$593$	−9.69441			−0.398102			−0.199051	+	0.979989i	$0.563786\pi$
$594$	−6.14925	−	3.48099i	−0.252307	−	0.142827i
$595$	−11.0211			−0.451821
$596$	18.9844	−	13.7930i	0.777632	−	0.564983i
$597$	2.07802	+	6.39550i	0.0850479	+	0.261750i
$598$	1.38252	−	4.25495i	0.0565353	−	0.173998i
$599$	31.3480	+	22.7757i	1.28084	+	0.930588i	0.999578	−	0.0290416i	$-0.00924554\pi$
$599$	31.3480	+	22.7757i	1.28084	+	0.930588i	0.281266	+	0.959630i	$0.409246\pi$
$600$	−2.64008	−	1.91813i	−0.107781	−	0.0783073i
$601$	11.3454	−	34.9176i	0.462790	−	1.42432i	−0.398952	−	0.916972i	$-0.630626\pi$
$601$	11.3454	−	34.9176i	0.462790	−	1.42432i	0.861741	−	0.507348i	$-0.169374\pi$
$602$	7.95660	+	24.4879i	0.324287	+	0.998053i
$603$	12.6660	−	9.20242i	0.515801	−	0.374751i
$604$	−45.3883			−1.84683
$605$	−1.41628	+	16.1009i	−0.0575799	+	0.654593i
$606$	41.3333			1.67905
$607$	12.6296	−	9.17597i	0.512621	−	0.372441i	−0.301196	−	0.953562i	$-0.597386\pi$
$607$	12.6296	−	9.17597i	0.512621	−	0.372441i	0.813817	+	0.581121i	$0.197386\pi$
$608$	−7.05763	−	21.7211i	−0.286225	−	0.880909i
$609$	−0.225496	+	0.694006i	−0.00913757	+	0.0281225i
$610$	−20.1150	−	14.6144i	−0.814431	−	0.591719i
$611$	−1.44909	−	1.05282i	−0.0586238	−	0.0425927i
$612$	5.20575	−	16.0217i	0.210430	−	0.647637i
$613$	−5.88711	−	18.1187i	−0.237778	−	0.731806i	−0.996741	−	0.0806719i	$-0.974293\pi$
$613$	−5.88711	−	18.1187i	−0.237778	−	0.731806i	0.758962	−	0.651134i	$-0.225707\pi$
$614$	48.8992	−	35.5274i	1.97341	−	1.43377i
$615$	−1.04068			−0.0419641
$616$	−3.74809	−	2.12173i	−0.151015	−	0.0854871i
$617$	−22.0472			−0.887585			−0.443793	−	0.896130i	$-0.646367\pi$
$617$	−22.0472			−0.887585			−0.443793	+	0.896130i	$0.646367\pi$
$618$	12.6902	−	9.21995i	0.510473	−	0.370881i
$619$	−12.9584	−	39.8817i	−0.520841	−	1.60298i	−0.772397	−	0.635140i	$-0.780943\pi$
$619$	−12.9584	−	39.8817i	−0.520841	−	1.60298i	0.251557	−	0.967843i	$-0.419057\pi$
$620$	2.90616	−	8.94424i	0.116714	−	0.359209i
$621$	1.69886	+	1.23430i	0.0681731	+	0.0495306i
$622$	16.1699	+	11.7481i	0.648353	+	0.471056i
$623$	1.52073	−	4.68033i	0.0609269	−	0.187514i
$624$	−0.813032	−	2.50226i	−0.0325473	−	0.100170i
$625$	2.20388	−	1.60122i	0.0881554	−	0.0640486i
$626$	63.3904			2.53359
$627$	9.52362	−	1.08281i	0.380337	−	0.0432433i
$628$	5.48143			0.218733
$629$	25.1763	−	18.2916i	1.00384	−	0.729335i
$630$	1.09366	+	3.36593i	0.0435723	+	0.134102i
$631$	14.8341	−	45.6548i	0.590537	−	1.81749i	0.0147452	−	0.999891i	$-0.495306\pi$
$631$	14.8341	−	45.6548i	0.590537	−	1.81749i	0.575792	−	0.817596i	$-0.304694\pi$
$632$	14.9610	+	10.8698i	0.595117	+	0.432378i
$633$	−22.3575	−	16.2437i	−0.888630	−	0.645628i
$634$	−18.4512	+	56.7868i	−0.732789	+	2.25529i
$635$	4.22150	+	12.9924i	0.167525	+	0.515589i
$636$	0.552550	−	0.401451i	0.0219100	−	0.0159186i
$637$	−5.72191			−0.226710
$638$	−0.910367	+	4.46921i	−0.0360418	+	0.176938i
$639$	−8.71264			−0.344667
$640$	10.5268	−	7.64820i	0.416110	−	0.302322i
$641$	−7.47453	−	23.0042i	−0.295226	−	0.908613i	−0.983145	−	0.182826i	$-0.941476\pi$
$641$	−7.47453	−	23.0042i	−0.295226	−	0.908613i	0.687919	−	0.725787i	$-0.258524\pi$
$642$	2.72230	−	8.37837i	0.107440	−	0.330668i
$643$	−0.125042	−	0.0908485i	−0.00493118	−	0.00358271i	0.585317	−	0.810805i	$-0.300970\pi$
$643$	−0.125042	−	0.0908485i	−0.00493118	−	0.00358271i	−0.590248	+	0.807222i	$0.700970\pi$
$644$	4.87672	+	3.54314i	0.192170	+	0.139619i
$645$	4.85389	−	14.9387i	0.191122	−	0.588212i
$646$	12.6234	+	38.8509i	0.496662	+	1.52857i
$647$	−24.4473	+	17.7620i	−0.961121	+	0.698296i	−0.953411	−	0.301675i	$-0.902454\pi$
$647$	−24.4473	+	17.7620i	−0.961121	+	0.698296i	−0.00771044	+	0.999970i	$0.502454\pi$
$648$	−1.14867			−0.0451239
$649$	6.50398	−	5.95699i	0.255304	−	0.233832i
$650$	6.05274			0.237408
$651$	2.30546	−	1.67502i	0.0903581	−	0.0656490i
$652$	0.958384	+	2.94960i	0.0375332	+	0.115515i
$653$	13.9955	−	43.0738i	0.547688	−	1.68561i	−0.166825	−	0.985986i	$-0.553352\pi$
$653$	13.9955	−	43.0738i	0.547688	−	1.68561i	0.714513	−	0.699622i	$-0.246648\pi$
$654$	3.88936	+	2.82579i	0.152086	+	0.110497i
$655$	18.7690	+	13.6365i	0.733366	+	0.532822i
$656$	−0.575829	+	1.77222i	−0.0224823	+	0.0691935i
$657$	−2.19287	−	6.74895i	−0.0855519	−	0.263302i
$658$	3.49030	−	2.53585i	0.136066	−	0.0988577i
$659$	−42.0369			−1.63753			−0.818763	−	0.574132i	$-0.805340\pi$
$659$	−42.0369			−1.63753			−0.818763	+	0.574132i	$0.805340\pi$
$660$	5.12882	+	11.2612i	0.199639	+	0.438341i
$661$	21.5042			0.836416			0.418208	−	0.908351i	$-0.362658\pi$
$661$	21.5042			0.836416			0.418208	+	0.908351i	$0.362658\pi$
$662$	−39.1238	+	28.4251i	−1.52059	+	1.10477i
$663$	2.05020	+	6.30986i	0.0796231	+	0.245055i
$664$	−1.62256	+	4.99372i	−0.0629675	+	0.193794i
$665$	−3.88386	−	2.82179i	−0.150610	−	0.109424i
$666$	−8.08472	−	5.87389i	−0.313276	−	0.227609i
$667$	0.418851	−	1.28909i	0.0162180	−	0.0499137i
$668$	2.75902	+	8.49140i	0.106750	+	0.328542i
$669$	14.6703	−	10.6586i	0.567188	−	0.412086i
$670$	−49.0118			−1.89349
$671$	−10.9180	−	23.9723i	−0.421485	−	0.925440i
$672$	8.93434			0.344650
$673$	23.5584	−	17.1162i	0.908108	−	0.659779i	−0.0324276	−	0.999474i	$-0.510324\pi$
$673$	23.5584	−	17.1162i	0.908108	−	0.659779i	0.940536	+	0.339695i	$0.110324\pi$
$674$	0.860574	+	2.64858i	0.0331481	+	0.102019i
$675$	−0.877905	+	2.70191i	−0.0337906	+	0.103997i
$676$	−2.05421	−	1.49247i	−0.0790082	−	0.0574028i
$677$	−37.5010	−	27.2461i	−1.44128	−	1.04715i	−0.987773	−	0.155898i	$-0.950173\pi$
$677$	−37.5010	−	27.2461i	−1.44128	−	1.04715i	−0.453507	−	0.891253i	$-0.649827\pi$
$678$	−10.3520	+	31.8603i	−0.397568	+	1.22359i
$679$	−3.51750	−	10.8257i	−0.134989	−	0.415454i
$680$	−9.05932	+	6.58198i	−0.347409	+	0.252407i
$681$	1.46526			0.0561489
$682$	13.1349	−	12.0302i	0.502962	−	0.460662i
$683$	27.1270			1.03798			0.518992	−	0.854779i	$-0.326307\pi$
$683$	27.1270			1.03798			0.518992	+	0.854779i	$0.326307\pi$
$684$	5.93663	−	4.31322i	0.226993	−	0.164920i
$685$	6.05120	+	18.6237i	0.231204	+	0.711574i
$686$	9.46897	−	29.1425i	0.361527	−	1.11267i
$687$	−7.82057	−	5.68197i	−0.298373	−	0.216781i
$688$	−22.7541	−	16.5318i	−0.867493	−	0.630271i
$689$	−0.0831206	+	0.255819i	−0.00316664	+	0.00974592i
$690$	−2.03143	−	6.25208i	−0.0773350	−	0.238013i
$691$	−23.4285	+	17.0218i	−0.891261	+	0.647539i	−0.936207	−	0.351450i	$-0.885689\pi$
$691$	−23.4285	+	17.0218i	−0.891261	+	0.647539i	0.0449452	+	0.998989i	$0.485689\pi$
$692$	−24.4290			−0.928651
$693$	−0.748401	+	3.67409i	−0.0284294	+	0.139567i
$694$	25.0339			0.950273
$695$	17.2572	−	12.5381i	0.654602	−	0.475596i
$696$	0.229114	+	0.705141i	0.00868455	+	0.0267283i
$697$	1.45205	−	4.46895i	0.0550003	−	0.169273i
$698$	10.1105	+	7.34568i	0.382687	+	0.278038i
$699$	11.9021	+	8.64737i	0.450178	+	0.327074i
$700$	−2.52009	+	7.75604i	−0.0952505	+	0.293151i
$701$	13.6384	+	41.9748i	0.515116	+	1.58537i	0.783070	+	0.621933i	$0.213653\pi$
$701$	13.6384	+	41.9748i	0.515116	+	1.58537i	−0.267954	+	0.963432i	$0.586347\pi$
$702$	1.72363	−	1.25229i	0.0650543	−	0.0472647i
$703$	13.5555			0.511255
$704$	38.1445	−	4.33693i	1.43762	−	0.163454i
$705$	−2.63189			−0.0991226
$706$	9.22551	−	6.70272i	0.347207	−	0.252260i
$707$	−6.77760	−	20.8593i	−0.254898	−	0.784495i
$708$	2.08655	−	6.42174i	0.0784173	−	0.241344i
$709$	35.7181	+	25.9507i	1.34142	+	0.974598i	0.999390	+	0.0349091i	$0.0111142\pi$
$709$	35.7181	+	25.9507i	1.34142	+	0.974598i	0.342029	+	0.939689i	$0.388886\pi$
$710$	22.0661	+	16.0319i	0.828124	+	0.601668i
$711$	4.97498	−	15.3114i	0.186577	−	0.574223i
$712$	−1.54513	−	4.75543i	−0.0579063	−	0.178217i
$713$	−4.28231	+	3.11128i	−0.160374	+	0.116518i
$714$	−15.9802			−0.598043
$715$	−4.24097	−	2.40075i	−0.158603	−	0.0897828i
$716$	−14.6607			−0.547897
$717$	23.0417	−	16.7408i	0.860508	−	0.625196i
$718$	−10.5775	−	32.5542i	−0.394749	−	1.21491i
$719$	3.87427	−	11.9238i	0.144486	−	0.444682i	−0.852459	−	0.522795i	$-0.824890\pi$
$719$	3.87427	−	11.9238i	0.144486	−	0.444682i	0.996945	+	0.0781130i	$0.0248895\pi$
$720$	−3.12762	−	2.27235i	−0.116559	−	0.0846853i
$721$	−6.73382	−	4.89240i	−0.250780	−	0.182203i
$722$	7.01033	−	21.5756i	0.260897	−	0.802959i
$723$	−5.42354	−	16.6919i	−0.201704	−	0.620780i
$724$	7.46212	−	5.42155i	0.277327	−	0.201490i
$725$	1.83375			0.0681039
$726$	−2.05355	+	23.3457i	−0.0762144	+	0.866439i
$727$	−16.7027			−0.619467			−0.309734	−	0.950823i	$-0.600240\pi$
$727$	−16.7027			−0.619467			−0.309734	+	0.950823i	$0.600240\pi$
$728$	1.05059	−	0.763297i	0.0389374	−	0.0282897i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−6.86483	+	21.1278i	−0.254079	+	0.781974i
$731$	57.3784	+	41.6878i	2.12222	+	1.54188i
$732$	−16.3151	−	11.8536i	−0.603023	−	0.438122i
$733$	−4.53691	+	13.9632i	−0.167575	+	0.515742i	−0.999217	−	0.0395703i	$-0.987401\pi$
$733$	−4.53691	+	13.9632i	−0.167575	+	0.515742i	0.831642	+	0.555312i	$0.187401\pi$
$734$	−0.867094	−	2.66864i	−0.0320050	−	0.0985013i
$735$	−6.80188	+	4.94185i	−0.250891	+	0.182283i
$736$	−16.5952			−0.611707
$737$	−45.1875	−	25.5799i	−1.66450	−	0.942248i
$738$	−1.50894			−0.0555449
$739$	25.9253	−	18.8358i	0.953677	−	0.692887i	0.00200370	−	0.999998i	$-0.499362\pi$
$739$	25.9253	−	18.8358i	0.953677	−	0.692887i	0.951674	+	0.307111i	$0.0993622\pi$
$740$	5.40780	+	16.6435i	0.198795	+	0.611827i
$741$	−0.893053	+	2.74853i	−0.0328071	+	0.100970i
$742$	−0.524146	−	0.380814i	−0.0192420	−	0.0139801i
$743$	−3.70427	−	2.69131i	−0.135897	−	0.0987347i	0.517760	−	0.855526i	$-0.326766\pi$
$743$	−3.70427	−	2.69131i	−0.135897	−	0.0987347i	−0.653657	+	0.756791i	$0.726766\pi$
$744$	0.894737	−	2.75372i	0.0328027	−	0.100956i
$745$	4.19628	+	12.9148i	0.153740	+	0.473162i
$746$	−32.3772	+	23.5234i	−1.18542	+	0.861255i
$747$	4.57113			0.167249
$748$	−55.5147	+	6.31188i	−2.02982	+	0.230785i
$749$	−4.67463			−0.170807
$750$	19.8584	−	14.4280i	0.725126	−	0.526835i
$751$	−13.3726	−	41.1566i	−0.487973	−	1.50183i	−0.827629	−	0.561276i	$-0.810311\pi$
$751$	−13.3726	−	41.1566i	−0.487973	−	1.50183i	0.339656	−	0.940550i	$-0.389689\pi$
$752$	−1.45628	+	4.48197i	−0.0531050	+	0.163440i
$753$	−5.37527	−	3.90537i	−0.195886	−	0.142319i
$754$	−1.11255	−	0.808317i	−0.0405168	−	0.0294372i
$755$	8.11651	−	24.9801i	0.295390	−	0.909117i
$756$	0.887056	+	2.73008i	0.0322619	+	0.0992920i
$757$	−3.93974	+	2.86239i	−0.143192	+	0.104035i	−0.657075	−	0.753825i	$-0.728207\pi$
$757$	−3.93974	+	2.86239i	−0.143192	+	0.104035i	0.513883	+	0.857860i	$0.328207\pi$
$758$	−0.463348			−0.0168296
$759$	1.39013	−	6.82448i	0.0504584	−	0.247713i
$760$	−4.87775			−0.176934
$761$	27.1534	−	19.7281i	0.984311	−	0.715144i	0.0256432	−	0.999671i	$-0.491837\pi$
$761$	27.1534	−	19.7281i	0.984311	−	0.715144i	0.958668	+	0.284527i	$0.0918366\pi$
$762$	6.12102	+	18.8386i	0.221741	+	0.682449i
$763$	0.788310	−	2.42617i	0.0285388	−	0.0878333i
$764$	9.78279	+	7.10761i	0.353929	+	0.257144i
$765$	7.88681	+	5.73010i	0.285148	+	0.207172i
$766$	−16.2891	+	50.1328i	−0.588550	+	1.81137i
$767$	0.821752	+	2.52909i	0.0296717	+	0.0913202i
$768$	−3.46537	+	2.51774i	−0.125046	+	0.0908511i
$769$	−6.93094			−0.249936			−0.124968	−	0.992161i	$-0.539883\pi$
$769$	−6.93094			−0.249936			−0.124968	+	0.992161i	$0.539883\pi$
$770$	8.65604	−	7.92806i	0.311942	−	0.285707i
$771$	−15.2879			−0.550580
$772$	29.5426	−	21.4640i	1.06326	−	0.772506i
$773$	−6.06315	−	18.6605i	−0.218076	−	0.671170i	−0.998921	−	0.0464447i	$-0.985211\pi$
$773$	−6.06315	−	18.6605i	−0.218076	−	0.671170i	0.780844	−	0.624726i	$-0.214789\pi$
$774$	7.03796	−	21.6606i	0.252974	−	0.778574i
$775$	−5.79351	−	4.20923i	−0.208109	−	0.151200i
$776$	−9.35669	−	6.79803i	−0.335886	−	0.244035i
$777$	−1.63864	+	5.04321i	−0.0587859	+	0.180924i
$778$	−6.29227	−	19.3656i	−0.225589	−	0.694291i
$779$	1.65591	−	1.20309i	0.0593293	−	0.0431053i
$780$	−3.73094			−0.133589
$781$	11.9770	+	26.2976i	0.428571	+	0.941001i
$782$	29.6826			1.06145
$783$	0.522196	−	0.379397i	0.0186618	−	0.0135586i
$784$	4.65210	+	14.3177i	0.166146	+	0.511346i
$785$	−0.980210	+	3.01678i	−0.0349852	+	0.107673i
$786$	27.2144	+	19.7724i	0.970704	+	0.705258i
$787$	−21.4436	−	15.5797i	−0.764381	−	0.555355i	0.135870	−	0.990727i	$-0.456617\pi$
$787$	−21.4436	−	15.5797i	−0.764381	−	0.555355i	−0.900251	+	0.435371i	$0.856617\pi$
$788$	−1.61543	+	4.97179i	−0.0575473	+	0.177113i
$789$	2.45794	+	7.56476i	0.0875050	+	0.269313i
$790$	−40.7741	+	29.6241i	−1.45068	+	1.05398i
$791$	17.7762			0.632047
$792$	1.57904	+	3.46705i	0.0561087	+	0.123196i
$793$	7.94226			0.282038
$794$	−45.9510	+	33.3854i	−1.63074	+	1.18480i
$795$	0.122135	+	0.375892i	0.00433167	+	0.0133315i
$796$	5.27641	−	16.2391i	0.187017	−	0.575580i
$797$	4.71797	+	3.42781i	0.167119	+	0.121419i	0.668201	−	0.743981i	$-0.267065\pi$
$797$	4.71797	+	3.42781i	0.167119	+	0.121419i	−0.501082	+	0.865400i	$0.667065\pi$
$798$	−5.63145	−	4.09149i	−0.199351	−	0.144837i
$799$	3.67225	−	11.3020i	0.129915	−	0.399837i
$800$	−6.93791	−	21.3527i	−0.245292	−	0.754932i
$801$	−3.52166	+	2.55863i	−0.124432	+	0.0904049i
$802$	8.45764			0.298650
$803$	−17.3560	+	15.8964i	−0.612482	+	0.560971i
$804$	−39.7531			−1.40198
$805$	−2.82209	+	2.05036i	−0.0994654	+	0.0722659i
$806$	1.65954	+	5.10755i	0.0584549	+	0.179906i
$807$	−6.20885	+	19.1089i	−0.218562	+	0.672664i
$808$	−18.0287	−	13.0986i	−0.634247	−	0.460808i
$809$	29.0062	+	21.0743i	1.01980	+	0.740931i	0.966243	−	0.257633i	$-0.0829426\pi$
$809$	29.0062	+	21.0743i	1.01980	+	0.740931i	0.0535617	+	0.998565i	$0.482943\pi$
$810$	0.967386	−	2.97731i	0.0339905	−	0.104612i
$811$	−3.21955	−	9.90875i	−0.113054	−	0.347943i	0.878482	−	0.477775i	$-0.158556\pi$
$811$	−3.21955	−	9.90875i	−0.113054	−	0.347943i	−0.991536	+	0.129831i	$0.958556\pi$
$812$	1.49900	−	1.08909i	0.0526047	−	0.0382195i
$813$	−12.6150			−0.442428
$814$	−6.61547	+	32.4770i	−0.231872	+	1.13832i
$815$	−1.79473			−0.0628668
$816$	14.1220	−	10.2602i	0.494369	−	0.359180i
$817$	9.54672	+	29.3818i	0.333998	+	1.02794i
$818$	−10.7904	+	33.2096i	−0.377279	+	1.16115i
$819$	−0.914616	−	0.664507i	−0.0319593	−	0.0232198i
$820$	2.13777	+	1.55318i	0.0746542	+	0.0542395i
$821$	13.7227	−	42.2340i	0.478924	−	1.47398i	−0.361667	−	0.932307i	$-0.617792\pi$
$821$	13.7227	−	42.2340i	0.478924	−	1.47398i	0.840591	−	0.541670i	$-0.182208\pi$
$822$	8.77401	+	27.0036i	0.306029	+	0.941860i
$823$	−3.57282	+	2.59581i	−0.124541	+	0.0904841i	−0.648312	−	0.761375i	$-0.724525\pi$
$823$	−3.57282	+	2.59581i	−0.124541	+	0.0904841i	0.523771	+	0.851859i	$0.324525\pi$
$824$	−8.45700			−0.294614
$825$	9.36208	−	1.06444i	0.325946	−	0.0370591i
$826$	−6.40511			−0.222862
$827$	−42.8109	+	31.1039i	−1.48868	+	1.08159i	−0.514054	+	0.857758i	$0.671857\pi$
$827$	−42.8109	+	31.1039i	−1.48868	+	1.08159i	−0.974628	+	0.223832i	$0.928143\pi$
$828$	−1.64767	−	5.07102i	−0.0572606	−	0.176230i
$829$	−0.905776	+	2.78769i	−0.0314589	+	0.0968206i	−0.965553	−	0.260206i	$-0.916209\pi$
$829$	−0.905776	+	2.78769i	−0.0314589	+	0.0968206i	0.934094	+	0.357027i	$0.116209\pi$
$830$	−11.5771	−	8.41124i	−0.401846	−	0.291958i
$831$	4.44760	+	3.23137i	0.154286	+	0.112095i
$832$	−3.57690	+	11.0086i	−0.124007	+	0.381654i
$833$	−11.7310	−	36.1044i	−0.406456	−	1.25094i
$834$	25.0223	−	18.1797i	0.866450	−	0.629513i
$835$	−5.16673			−0.178802
$836$	−21.1796	−	11.9894i	−0.732512	−	0.414663i
$837$	−2.52069			−0.0871277
$838$	−23.8550	+	17.3317i	−0.824058	+	0.598713i
$839$	7.63759	+	23.5061i	0.263679	+	0.811521i	0.991995	+	0.126279i	$0.0403034\pi$
$839$	7.63759	+	23.5061i	0.263679	+	0.811521i	−0.728316	+	0.685242i	$0.759697\pi$
$840$	0.589641	−	1.81473i	0.0203446	−	0.0626141i
$841$	23.1244	+	16.8009i	0.797394	+	0.579341i
$842$	21.5925	+	15.6879i	0.744126	+	0.540639i
$843$	−1.14887	+	3.53587i	−0.0395693	+	0.121782i
$844$	21.6838	+	66.7359i	0.746387	+	2.29714i
$845$	1.18874	−	0.863672i	0.0408940	−	0.0297112i
$846$	−3.81614			−0.131201
$847$	12.1184	−	2.79174i	0.416393	−	0.0959255i
$848$	0.707704			0.0243027
$849$	−21.5797	+	15.6786i	−0.740614	+	0.538088i
$850$	12.4093	+	38.1919i	0.425636	+	1.30997i
$851$	3.04371	−	9.36758i	0.104337	−	0.321116i
$852$	17.8976	+	13.0034i	0.613162	+	0.445488i
$853$	−23.8846	−	17.3532i	−0.817792	−	0.594161i	0.0982869	−	0.995158i	$-0.468664\pi$
$853$	−23.8846	−	17.3532i	−0.817792	−	0.594161i	−0.916079	+	0.400997i	$0.868664\pi$
$854$	−5.91146	+	18.1936i	−0.202286	+	0.622572i
$855$	1.31222	+	4.03861i	0.0448771	+	0.138117i
$856$	−3.84253	+	2.79176i	−0.131335	+	0.0954205i
$857$	−36.7845			−1.25653			−0.628267	−	0.777997i	$-0.716236\pi$
$857$	−36.7845			−1.25653			−0.628267	+	0.777997i	$0.716236\pi$
$858$	−6.14925	−	3.48099i	−0.209932	−	0.118839i
$859$	−44.5780			−1.52098			−0.760491	−	0.649348i	$-0.775042\pi$
$859$	−44.5780			−1.52098			−0.760491	+	0.649348i	$0.775042\pi$
$860$	−32.2666	+	23.4430i	−1.10028	+	0.799401i
$861$	0.247428	+	0.761505i	0.00843233	+	0.0259520i
$862$	8.76937	−	26.9893i	0.298686	−	0.919261i
$863$	−18.8124	−	13.6680i	−0.640381	−	0.465264i	0.219600	−	0.975590i	$-0.429525\pi$
$863$	−18.8124	−	13.6680i	−0.640381	−	0.465264i	−0.859981	+	0.510326i	$0.829525\pi$
$864$	−6.39351	−	4.64515i	−0.217512	−	0.158031i
$865$	4.36848	−	13.4448i	0.148533	−	0.457137i
$866$	−17.1822	−	52.8813i	−0.583874	−	1.79698i
$867$	−21.8577	+	15.8806i	−0.742327	+	0.539332i
$868$	−7.23582			−0.245600
$869$	−53.0538	+	6.03208i	−1.79973	+	0.204624i
$870$	−2.02066			−0.0685068
$871$	12.6660	−	9.20242i	0.429172	−	0.311812i
$872$	−0.800959	−	2.46510i	−0.0271239	−	0.0834788i
$873$	−3.11138	+	9.57584i	−0.105304	+	0.324093i
$874$	10.4602	+	7.59979i	0.353822	+	0.257067i
$875$	−10.5375	−	7.65595i	−0.356233	−	0.258819i
$876$	−5.56801	+	17.1366i	−0.188126	+	0.578991i
$877$	−6.41899	−	19.7556i	−0.216754	−	0.667100i	−0.999024	−	0.0441613i	$-0.985938\pi$
$877$	−6.41899	−	19.7556i	−0.216754	−	0.667100i	0.782270	−	0.622939i	$-0.214062\pi$
$878$	−58.8654	+	42.7682i	−1.98661	+	1.44336i
$879$	21.0186			0.708940
$880$	−2.55923	+	12.5639i	−0.0862716	+	0.423529i
$881$	−7.94227			−0.267582			−0.133791	−	0.991010i	$-0.542715\pi$
$881$	−7.94227			−0.267582			−0.133791	+	0.991010i	$0.542715\pi$
$882$	−9.86247	+	7.16550i	−0.332087	+	0.241275i
$883$	−12.9346	−	39.8087i	−0.435285	−	1.33967i	−0.892795	−	0.450464i	$-0.851259\pi$
$883$	−12.9346	−	39.8087i	−0.435285	−	1.33967i	0.457510	−	0.889204i	$-0.348741\pi$
$884$	5.20575	−	16.0217i	0.175088	−	0.538867i
$885$	3.16116	+	2.29672i	0.106261	+	0.0772033i
$886$	−0.582717	−	0.423368i	−0.0195767	−	0.0142233i
$887$	8.94698	−	27.5360i	0.300410	−	0.924567i	−0.680940	−	0.732339i	$-0.738429\pi$
$887$	8.94698	−	27.5360i	0.300410	−	0.924567i	0.981350	−	0.192228i	$-0.0615714\pi$
$888$	1.66493	+	5.12413i	0.0558715	+	0.171955i
$889$	8.50340	−	6.17808i	0.285195	−	0.207206i
$890$	13.6272			0.456785
$891$	2.44580	−	2.24010i	0.0819374	−	0.0750463i
$892$	−46.0437			−1.54166
$893$	4.18783	−	3.04264i	0.140140	−	0.101818i
$894$	6.08445	+	18.7260i	0.203494	+	0.626291i
$895$	2.62168	−	8.06871i	0.0876332	−	0.269707i
$896$	−8.09933	−	5.88450i	−0.270579	−	0.196587i
$897$	1.69886	+	1.23430i	0.0567234	+	0.0412120i
$898$	16.1864	−	49.8165i	0.540146	−	1.66240i
$899$	0.502779	+	1.54739i	0.0167686	+	0.0516085i
$900$	5.83594	−	4.24006i	0.194531	−	0.141335i
$901$	−1.78459			−0.0594535
$902$	2.07430	+	4.55448i	0.0690667	+	0.151647i
$903$	−12.0853			−0.402174
$904$	14.6120	−	10.6162i	0.485986	−	0.353090i
$905$	1.64941	+	5.07637i	0.0548283	+	0.168744i
$906$	11.7686	−	36.2201i	0.390987	−	1.20333i
$907$	38.8906	+	28.2557i	1.29134	+	0.938215i	0.999832	−	0.0183519i	$-0.00584193\pi$
$907$	38.8906	+	28.2557i	1.29134	+	0.938215i	0.291511	+	0.956567i	$0.405842\pi$
$908$	−3.00995	−	2.18686i	−0.0998888	−	0.0725735i
$909$	−5.99508	+	18.4510i	−0.198844	+	0.611980i
$910$	1.09366	+	3.36593i	0.0362544	+	0.111579i
$911$	30.9180	−	22.4633i	1.02436	−	0.744241i	0.0571879	−	0.998363i	$-0.481787\pi$
$911$	30.9180	−	22.4633i	1.02436	−	0.744241i	0.967172	+	0.254122i	$0.0817866\pi$
$912$	7.60362			0.251781
$913$	−6.28381	−	13.7972i	−0.207964	−	0.456619i
$914$	46.0912			1.52456
$915$	9.44130	−	6.85951i	0.312120	−	0.226768i
$916$	7.58491	+	23.3440i	0.250613	+	0.771306i
$917$	5.51591	−	16.9762i	0.182151	−	0.560604i
$918$	11.4356	+	8.30843i	0.377430	+	0.274219i
$919$	−22.5579	−	16.3892i	−0.744115	−	0.540631i	0.149882	−	0.988704i	$-0.452111\pi$
$919$	−22.5579	−	16.3892i	−0.744115	−	0.540631i	−0.893997	+	0.448073i	$0.852111\pi$
$920$	−1.09524	+	3.37079i	−0.0361089	+	0.111132i
$921$	8.76677	+	26.9814i	0.288875	+	0.889066i
$922$	42.8241	−	31.1135i	1.41034	−	1.02467i
$923$	−8.71264			−0.286780
$924$	7.02085	−	6.43039i	0.230969	−	0.211544i
$925$	13.3255			0.438141
$926$	−65.3648	+	47.4903i	−2.14802	+	1.56063i
$927$	2.27512	+	7.00211i	0.0747249	+	0.229979i
$928$	−1.57630	+	4.85136i	−0.0517447	+	0.159254i
$929$	−22.8513	−	16.6024i	−0.749727	−	0.544709i	0.146015	−	0.989282i	$-0.453355\pi$
$929$	−22.8513	−	16.6024i	−0.749727	−	0.544709i	−0.895742	+	0.444574i	$0.853355\pi$
$930$	6.38402	+	4.63826i	0.209340	+	0.152095i
$931$	5.10997	−	15.7269i	0.167472	−	0.515427i
$932$	−11.5434	−	35.5271i	−0.378118	−	1.16373i
$933$	−7.58961	+	5.51417i	−0.248473	+	0.180526i
$934$	−57.6947			−1.88783
$935$	6.45353	−	31.6820i	0.211053	−	1.03611i
$936$	−1.14867			−0.0375453
$937$	−18.6705	+	13.5649i	−0.609937	+	0.443145i	−0.849392	−	0.527762i	$-0.823031\pi$
$937$	−18.6705	+	13.5649i	−0.609937	+	0.443145i	0.239455	+	0.970907i	$0.423031\pi$
$938$	11.6529	+	35.8639i	0.380480	+	1.17100i
$939$	−9.19430	+	28.2971i	−0.300045	+	0.923442i
$940$	5.40646	+	3.92802i	0.176339	+	0.128118i
$941$	−35.8669	−	26.0588i	−1.16923	−	0.849494i	−0.178311	−	0.983974i	$-0.557063\pi$
$941$	−35.8669	−	26.0588i	−1.16923	−	0.849494i	−0.990916	+	0.134480i	$0.957063\pi$
$942$	−1.42127	+	4.37421i	−0.0463074	+	0.142520i
$943$	−0.459588	−	1.41447i	−0.0149663	−	0.0460614i
$944$	5.66033	−	4.11247i	0.184228	−	0.133849i
$945$	−1.66116			−0.0540375
$946$	−75.0536	+	8.53339i	−2.44020	+	0.277444i
$947$	21.8127			0.708818			0.354409	−	0.935090i	$-0.384682\pi$
$947$	21.8127			0.708818			0.354409	+	0.935090i	$0.384682\pi$
$948$	−33.0716	+	24.0279i	−1.07411	+	0.780390i
$949$	−2.19287	−	6.74895i	−0.0711835	−	0.219080i
$950$	−5.40542	+	16.6362i	−0.175375	+	0.539749i
$951$	−22.6732	−	16.4730i	−0.735227	−	0.534174i
$952$	6.97021	+	5.06416i	0.225906	+	0.164130i
$953$	11.0618	−	34.0447i	0.358326	−	1.10282i	−0.595729	−	0.803185i	$-0.703137\pi$
$953$	11.0618	−	34.0447i	0.358326	−	1.10282i	0.954056	−	0.299630i	$-0.0968632\pi$
$954$	0.177091	+	0.545029i	0.00573352	+	0.0176460i
$955$	−5.66116	+	4.11307i	−0.183191	+	0.133096i
$956$	−72.3177			−2.33892
$957$	−1.86299	−	1.05461i	−0.0602220	−	0.0340907i
$958$	63.1024			2.03875
$959$	12.1890	−	8.85581i	0.393603	−	0.285969i
$960$	5.25578	+	16.1756i	0.169630	+	0.522066i
$961$	−7.61607	+	23.4399i	−0.245680	+	0.756125i
$962$	−8.08472	−	5.87389i	−0.260662	−	0.189382i
$963$	3.34521	+	2.43044i	0.107798	+	0.0783198i
$964$	−13.7712	+	42.3833i	−0.443539	+	1.36507i
$965$	6.53005	+	20.0974i	0.210210	+	0.646959i
$966$	−4.09192	+	2.97295i	−0.131655	+	0.0956532i
$967$	1.46519			0.0471175			0.0235587	−	0.999722i	$-0.492500\pi$
$967$	1.46519			0.0471175			0.0235587	+	0.999722i	$0.492500\pi$
$968$	8.29401	−	9.53211i	0.266580	−	0.306373i
$969$	−19.1738			−0.615951
$970$	25.5003	−	18.5271i	0.818766	−	0.594868i
$971$	−1.24760	−	3.83973i	−0.0400375	−	0.123223i	0.929040	−	0.369979i	$-0.120635\pi$
$971$	−1.24760	−	3.83973i	−0.0400375	−	0.123223i	−0.969078	+	0.246756i	$0.920635\pi$
$972$	0.784639	−	2.41487i	0.0251673	−	0.0774571i
$973$	−13.2776	−	9.64676i	−0.425661	−	0.309261i
$974$	2.46005	+	1.78733i	0.0788250	+	0.0572698i
$975$	−0.877905	+	2.70191i	−0.0281155	+	0.0865305i
$976$	−6.45731	−	19.8736i	−0.206693	−	0.636137i
$977$	−22.7235	+	16.5096i	−0.726989	+	0.528188i	−0.888609	−	0.458665i	$-0.848328\pi$
$977$	−22.7235	+	16.5096i	−0.726989	+	0.528188i	0.161621	+	0.986853i	$0.448328\pi$
$978$	−2.60230			−0.0832123
$979$	12.5639	+	7.11222i	0.401544	+	0.227308i
$980$	21.3481			0.681940
$981$	−1.82554	+	1.32633i	−0.0582850	+	0.0423466i
$982$	28.1855	+	86.7460i	0.899435	+	2.76818i
$983$	0.0987293	−	0.303858i	0.00314898	−	0.00969155i	−0.949470	−	0.313859i	$-0.898378\pi$
$983$	0.0987293	−	0.303858i	0.00314898	−	0.00969155i	0.952619	+	0.304167i	$0.0983782\pi$
$984$	0.658169	+	0.478188i	0.0209817	+	0.0152441i
$985$	−2.44741	−	1.77815i	−0.0779809	−	0.0566564i
$986$	2.81941	−	8.67726i	0.0897884	−	0.276340i
$987$	0.625749	+	1.92586i	0.0199178	+	0.0613007i
$988$	5.93663	−	4.31322i	0.188869	−	0.137222i
$989$	22.4480			0.713806
$990$	−10.3163	+	1.17294i	−0.327874	+	0.0372784i
$991$	55.2270			1.75434			0.877172	−	0.480177i	$-0.159428\pi$
$991$	55.2270			1.75434			0.877172	+	0.480177i	$0.159428\pi$
$992$	16.1160	−	11.7090i	0.511685	−	0.371761i
$993$	−7.01421	−	21.5875i	−0.222589	−	0.685060i
$994$	6.48485	−	19.9583i	0.205687	−	0.633040i
$995$	7.99386	+	5.80788i	0.253422	+	0.184122i
$996$	−9.39008	−	6.82229i	−0.297536	−	0.216173i
$997$	13.8373	−	42.5867i	0.438231	−	1.34873i	−0.451509	−	0.892267i	$-0.649114\pi$
$997$	13.8373	−	42.5867i	0.438231	−	1.34873i	0.889740	−	0.456468i	$-0.150886\pi$
$998$	−3.15665	−	9.71516i	−0.0999219	−	0.307528i
$999$	3.79470	−	2.75701i	0.120059	−	0.0872280i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.a.157.3	✓	12
11.2	odd	10		4719.2.a.bh.1.6		6
11.4	even	5	inner	429.2.n.a.235.3	yes	12
11.9	even	5		4719.2.a.bg.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.a.157.3	✓	12	1.1	even	1	trivial
429.2.n.a.235.3	yes	12	11.4	even	5	inner
4719.2.a.bg.1.1		6	11.9	even	5
4719.2.a.bh.1.6		6	11.2	odd	10

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)

\(f(q)\)	\(=\)	\(q+(1.72363 - 1.25229i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.784639 - 2.41487i) q^{4} +(1.18874 + 0.863672i) q^{5} +(1.72363 + 1.25229i) q^{6} +(0.349352 - 1.07520i) q^{7} +(-0.354958 - 1.09245i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.72363 - 1.25229i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.784639 - 2.41487i) q^{4} +(1.18874 + 0.863672i) q^{5} +(1.72363 + 1.25229i) q^{6} +(0.349352 - 1.07520i) q^{7} +(-0.354958 - 1.09245i) q^{8} +(-0.809017 + 0.587785i) q^{9} +3.13053 q^{10} +(2.88626 + 1.63386i) q^{11} +2.53915 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.744304 - 2.29073i) q^{14} +(-0.454059 + 1.39745i) q^{15} +(2.12855 + 1.54648i) q^{16} +(-5.36749 - 3.89971i) q^{17} +(-0.658369 + 2.02625i) q^{18} +(-0.893053 - 2.74853i) q^{19} +(3.01839 - 2.19299i) q^{20} +1.13053 q^{21} +(7.02093 - 0.798260i) q^{22} -2.09991 q^{23} +(0.929291 - 0.675169i) q^{24} +(-0.877905 - 2.70191i) q^{25} +(-0.658369 + 2.02625i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.32234 - 1.68728i) q^{28} +(-0.199461 + 0.613878i) q^{29} +(0.967386 + 2.97731i) q^{30} +(2.03928 - 1.48162i) q^{31} +7.90281 q^{32} +(-0.661993 + 3.24989i) q^{33} -14.1352 q^{34} +(1.34391 - 0.976405i) q^{35} +(0.784639 + 2.41487i) q^{36} +(-1.44945 + 4.46094i) q^{37} +(-4.98126 - 3.61910i) q^{38} +(-0.809017 - 0.587785i) q^{39} +(0.521563 - 1.60521i) q^{40} +(0.218861 + 0.673584i) q^{41} +(1.94861 - 1.41575i) q^{42} -10.6900 q^{43} +(6.21024 - 5.68795i) q^{44} -1.46937 q^{45} +(-3.61948 + 2.62970i) q^{46} +(0.553502 + 1.70350i) q^{47} +(-0.813032 + 2.50226i) q^{48} +(4.62912 + 3.36325i) q^{49} +(-4.89677 - 3.55771i) q^{50} +(2.05020 - 6.30986i) q^{51} +(0.784639 + 2.41487i) q^{52} +(0.217613 - 0.158105i) q^{53} -2.13053 q^{54} +(2.01990 + 4.43503i) q^{55} -1.29860 q^{56} +(2.33804 - 1.69869i) q^{57} +(0.424957 + 1.30788i) q^{58} +(0.821752 - 2.52909i) q^{59} +(3.01839 + 2.19299i) q^{60} +(-6.42542 - 4.66834i) q^{61} +(1.65954 - 5.10755i) q^{62} +(0.349352 + 1.07520i) q^{63} +(9.36445 - 6.80367i) q^{64} -1.46937 q^{65} +(2.92878 + 6.43062i) q^{66} -15.6561 q^{67} +(-13.6288 + 9.90193i) q^{68} +(-0.648908 - 1.99713i) q^{69} +(1.09366 - 3.36593i) q^{70} +(7.04867 + 5.12116i) q^{71} +(0.929291 + 0.675169i) q^{72} +(-2.19287 + 6.74895i) q^{73} +(3.08809 + 9.50415i) q^{74} +(2.29838 - 1.66987i) q^{75} -7.33808 q^{76} +(2.76504 - 2.53250i) q^{77} -2.13053 q^{78} +(-13.0247 + 9.46298i) q^{79} +(1.19464 + 3.67673i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.22076 + 0.886934i) q^{82} +(-3.69812 - 2.68685i) q^{83} +(0.887056 - 2.73008i) q^{84} +(-3.01249 - 9.27150i) q^{85} +(-18.4256 + 13.3870i) q^{86} -0.645470 q^{87} +(0.760410 - 3.73304i) q^{88} +4.35301 q^{89} +(-2.53265 + 1.84008i) q^{90} +(0.349352 + 1.07520i) q^{91} +(-1.64767 + 5.07102i) q^{92} +(2.03928 + 1.48162i) q^{93} +(3.08732 + 2.24307i) q^{94} +(1.31222 - 4.03861i) q^{95} +(2.44210 + 7.51602i) q^{96} +(8.14570 - 5.91819i) q^{97} +12.1907 q^{98} +(-3.29539 + 0.374677i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 8 q^{5} + 3 q^{6} + 5 q^{7} - q^{8} - 3 q^{9} + 14 q^{10} - 6 q^{11} + 2 q^{12} - 3 q^{13} + 11 q^{14} - 2 q^{15} - 5 q^{16} - 14 q^{17} - 2 q^{18} - 2 q^{19} - 9 q^{20} - 10 q^{21} + 21 q^{22} - 6 q^{23} + 4 q^{24} + 19 q^{25} - 2 q^{26} - 3 q^{27} - 12 q^{28} - 12 q^{29} - q^{30} - 12 q^{31} + 26 q^{32} + 9 q^{33} - 24 q^{34} - 2 q^{35} - 3 q^{36} + 4 q^{37} - 13 q^{38} - 3 q^{39} + 4 q^{40} - 10 q^{41} + q^{42} + 28 q^{43} - 12 q^{45} - 5 q^{46} + 28 q^{47} + 10 q^{48} + 20 q^{49} - q^{50} + 11 q^{51} - 3 q^{52} - 29 q^{53} - 2 q^{54} + 4 q^{55} + 12 q^{56} + 8 q^{57} + 22 q^{58} - 11 q^{59} - 9 q^{60} - 18 q^{61} + 40 q^{62} + 5 q^{63} + 11 q^{64} - 12 q^{65} + 16 q^{66} - 72 q^{67} - 35 q^{68} + 4 q^{69} - 6 q^{70} + 10 q^{71} + 4 q^{72} - 11 q^{73} - 15 q^{74} - 11 q^{75} + 4 q^{76} + 20 q^{77} - 2 q^{78} - 7 q^{79} - 27 q^{80} - 3 q^{81} - 10 q^{82} + 16 q^{83} + 8 q^{84} - 26 q^{85} - 35 q^{86} + 28 q^{87} + 25 q^{88} - 62 q^{89} - 6 q^{90} + 5 q^{91} - 34 q^{92} - 12 q^{93} - q^{94} + 15 q^{95} + q^{96} + 54 q^{97} + 50 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 8 * q^5 + 3 * q^6 + 5 * q^7 - q^8 - 3 * q^9 + 14 * q^10 - 6 * q^11 + 2 * q^12 - 3 * q^13 + 11 * q^14 - 2 * q^15 - 5 * q^16 - 14 * q^17 - 2 * q^18 - 2 * q^19 - 9 * q^20 - 10 * q^21 + 21 * q^22 - 6 * q^23 + 4 * q^24 + 19 * q^25 - 2 * q^26 - 3 * q^27 - 12 * q^28 - 12 * q^29 - q^30 - 12 * q^31 + 26 * q^32 + 9 * q^33 - 24 * q^34 - 2 * q^35 - 3 * q^36 + 4 * q^37 - 13 * q^38 - 3 * q^39 + 4 * q^40 - 10 * q^41 + q^42 + 28 * q^43 - 12 * q^45 - 5 * q^46 + 28 * q^47 + 10 * q^48 + 20 * q^49 - q^50 + 11 * q^51 - 3 * q^52 - 29 * q^53 - 2 * q^54 + 4 * q^55 + 12 * q^56 + 8 * q^57 + 22 * q^58 - 11 * q^59 - 9 * q^60 - 18 * q^61 + 40 * q^62 + 5 * q^63 + 11 * q^64 - 12 * q^65 + 16 * q^66 - 72 * q^67 - 35 * q^68 + 4 * q^69 - 6 * q^70 + 10 * q^71 + 4 * q^72 - 11 * q^73 - 15 * q^74 - 11 * q^75 + 4 * q^76 + 20 * q^77 - 2 * q^78 - 7 * q^79 - 27 * q^80 - 3 * q^81 - 10 * q^82 + 16 * q^83 + 8 * q^84 - 26 * q^85 - 35 * q^86 + 28 * q^87 + 25 * q^88 - 62 * q^89 - 6 * q^90 + 5 * q^91 - 34 * q^92 - 12 * q^93 - q^94 + 15 * q^95 + q^96 + 54 * q^97 + 50 * q^98 - 6 * q^99

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