LMFDB - Embedded newform 429.2.i.e.133.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.i (of order $3$, degree $2$, 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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 6x^{7} + 46x^{6} - 31x^{5} + 111x^{4} - 36x^{3} + 145x^{2} - 72x + 81 $ x^10 - 2x^9 + 10x^8 - 6x^7 + 46x^6 - 31x^5 + 111x^4 - 36x^3 + 145x^2 - 72*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.3
Root			$0.423911 + 0.734236i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.e.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.423911 + 0.734236i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.640598 - 1.10955i) q^{4} -2.90954 q^{5} +(-0.423911 + 0.734236i) q^{6} +(2.22113 - 3.84711i) q^{7} +2.78187 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.423911 + 0.734236i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.640598 - 1.10955i) q^{4} -2.90954 q^{5} +(-0.423911 + 0.734236i) q^{6} +(2.22113 - 3.84711i) q^{7} +2.78187 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.23339 - 2.13629i) q^{10} +(0.500000 + 0.866025i) q^{11} +1.28120 q^{12} +(3.53598 + 0.704876i) q^{13} +3.76625 q^{14} +(-1.45477 - 2.51974i) q^{15} +(-0.101929 - 0.176546i) q^{16} +(1.01670 - 1.76098i) q^{17} -0.847823 q^{18} +(1.49287 - 2.58572i) q^{19} +(-1.86385 + 3.22828i) q^{20} +4.44226 q^{21} +(-0.423911 + 0.734236i) q^{22} +(3.31929 + 5.74918i) q^{23} +(1.39094 + 2.40917i) q^{24} +3.46542 q^{25} +(0.981397 + 2.89505i) q^{26} -1.00000 q^{27} +(-2.84571 - 4.92891i) q^{28} +(-2.25034 - 3.89770i) q^{29} +(1.23339 - 2.13629i) q^{30} -3.24594 q^{31} +(2.86829 - 4.96803i) q^{32} +(-0.500000 + 0.866025i) q^{33} +1.72396 q^{34} +(-6.46247 + 11.1933i) q^{35} +(0.640598 + 1.10955i) q^{36} +(3.33155 + 5.77041i) q^{37} +2.53137 q^{38} +(1.15755 + 3.41469i) q^{39} -8.09397 q^{40} +(-3.03365 - 5.25444i) q^{41} +(1.88313 + 3.26167i) q^{42} +(-5.57573 + 9.65744i) q^{43} +1.28120 q^{44} +(1.45477 - 2.51974i) q^{45} +(-2.81417 + 4.87429i) q^{46} -4.68676 q^{47} +(0.101929 - 0.176546i) q^{48} +(-6.36685 - 11.0277i) q^{49} +(1.46903 + 2.54444i) q^{50} +2.03340 q^{51} +(3.04724 - 3.47180i) q^{52} -1.52519 q^{53} +(-0.423911 - 0.734236i) q^{54} +(-1.45477 - 2.51974i) q^{55} +(6.17891 - 10.7022i) q^{56} +2.98573 q^{57} +(1.90789 - 3.30456i) q^{58} +(1.22919 - 2.12903i) q^{59} -3.72769 q^{60} +(-4.58756 + 7.94588i) q^{61} +(-1.37599 - 2.38329i) q^{62} +(2.22113 + 3.84711i) q^{63} +4.45589 q^{64} +(-10.2881 - 2.05086i) q^{65} -0.847823 q^{66} +(-1.64737 - 2.85333i) q^{67} +(-1.30259 - 2.25616i) q^{68} +(-3.31929 + 5.74918i) q^{69} -10.9581 q^{70} +(-4.81381 + 8.33776i) q^{71} +(-1.39094 + 2.40917i) q^{72} +9.88080 q^{73} +(-2.82456 + 4.89228i) q^{74} +(1.73271 + 3.00114i) q^{75} +(-1.91265 - 3.31281i) q^{76} +4.44226 q^{77} +(-2.01649 + 2.29744i) q^{78} +9.34642 q^{79} +(0.296567 + 0.513669i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.57200 - 4.45483i) q^{82} +8.98708 q^{83} +(2.84571 - 4.92891i) q^{84} +(-2.95813 + 5.12363i) q^{85} -9.45446 q^{86} +(2.25034 - 3.89770i) q^{87} +(1.39094 + 2.40917i) q^{88} +(-3.77339 - 6.53570i) q^{89} +2.46677 q^{90} +(10.5656 - 12.0377i) q^{91} +8.50533 q^{92} +(-1.62297 - 2.81107i) q^{93} +(-1.98677 - 3.44119i) q^{94} +(-4.34355 + 7.52325i) q^{95} +5.73658 q^{96} +(0.512507 - 0.887688i) q^{97} +(5.39796 - 9.34954i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.423911	+	0.734236i	0.299751	+	0.519183i	0.976079	−	0.217417i	$-0.0697632\pi$
$2$	0.423911	+	0.734236i	0.299751	+	0.519183i	−0.676328	+	0.736600i	$0.736430\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.640598	−	1.10955i	0.320299	−	0.554774i
$5$	−2.90954			−1.30119			−0.650593	−	0.759427i	$-0.725480\pi$
$5$	−2.90954			−1.30119			−0.650593	+	0.759427i	$0.725480\pi$
$6$	−0.423911	+	0.734236i	−0.173061	+	0.299751i
$7$	2.22113	−	3.84711i	0.839509	−	1.45407i	−0.0507971	−	0.998709i	$-0.516176\pi$
$7$	2.22113	−	3.84711i	0.839509	−	1.45407i	0.890306	−	0.455363i	$-0.150490\pi$
$8$	2.78187			0.983541
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.23339	−	2.13629i	−0.390031	−	0.675554i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.28120			0.369850
$13$	3.53598	+	0.704876i	0.980704	+	0.195497i
$13$	3.53598	+	0.704876i	0.980704	+	0.195497i
$14$	3.76625			1.00657
$15$	−1.45477	−	2.51974i	−0.375620	−	0.650593i
$16$	−0.101929	−	0.176546i	−0.0254823	−	0.0441366i
$17$	1.01670	−	1.76098i	0.246586	−	0.427099i	−0.715990	−	0.698110i	$-0.754025\pi$
$17$	1.01670	−	1.76098i	0.246586	−	0.427099i	0.962576	+	0.271011i	$0.0873579\pi$
$18$	−0.847823			−0.199834
$19$	1.49287	−	2.58572i	0.342487	−	0.593205i	−0.642407	−	0.766364i	$-0.722064\pi$
$19$	1.49287	−	2.58572i	0.342487	−	0.593205i	0.984894	+	0.173159i	$0.0553974\pi$
$20$	−1.86385	+	3.22828i	−0.416769	+	0.721865i
$21$	4.44226			0.969381
$22$	−0.423911	+	0.734236i	−0.0903782	+	0.156540i
$23$	3.31929	+	5.74918i	0.692120	+	1.19879i	0.971142	+	0.238503i	$0.0766566\pi$
$23$	3.31929	+	5.74918i	0.692120	+	1.19879i	−0.279022	+	0.960285i	$0.590010\pi$
$24$	1.39094	+	2.40917i	0.283924	+	0.491770i
$25$	3.46542			0.693084
$26$	0.981397	+	2.89505i	0.192468	+	0.567766i
$27$	−1.00000			−0.192450
$28$	−2.84571	−	4.92891i	−0.537788	−	0.931476i
$29$	−2.25034	−	3.89770i	−0.417877	−	0.723785i	0.577848	−	0.816144i	$-0.303892\pi$
$29$	−2.25034	−	3.89770i	−0.417877	−	0.723785i	−0.995726	+	0.0923594i	$0.970559\pi$
$30$	1.23339	−	2.13629i	0.225185	−	0.390031i
$31$	−3.24594			−0.582988			−0.291494	−	0.956573i	$-0.594152\pi$
$31$	−3.24594			−0.582988			−0.291494	+	0.956573i	$0.594152\pi$
$32$	2.86829	−	4.96803i	0.507047	−	0.878231i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	1.72396			0.295657
$35$	−6.46247	+	11.1933i	−1.09236	+	1.89202i
$36$	0.640598	+	1.10955i	0.106766	+	0.184925i
$37$	3.33155	+	5.77041i	0.547703	+	0.948650i	0.998431	+	0.0559884i	$0.0178310\pi$
$37$	3.33155	+	5.77041i	0.547703	+	0.948650i	−0.450728	+	0.892661i	$0.648836\pi$
$38$	2.53137			0.410643
$39$	1.15755	+	3.41469i	0.185356	+	0.546787i
$40$	−8.09397			−1.27977
$41$	−3.03365	−	5.25444i	−0.473777	−	0.820605i	0.525773	−	0.850625i	$-0.323776\pi$
$41$	−3.03365	−	5.25444i	−0.473777	−	0.820605i	−0.999549	+	0.0300198i	$0.990443\pi$
$42$	1.88313	+	3.26167i	0.290573	+	0.503287i
$43$	−5.57573	+	9.65744i	−0.850290	+	1.47275i	0.0306559	+	0.999530i	$0.490240\pi$
$43$	−5.57573	+	9.65744i	−0.850290	+	1.47275i	−0.880946	+	0.473216i	$0.843093\pi$
$44$	1.28120			0.193148
$45$	1.45477	−	2.51974i	0.216864	−	0.375620i
$46$	−2.81417	+	4.87429i	−0.414927	+	0.718675i
$47$	−4.68676			−0.683634			−0.341817	−	0.939767i	$-0.611042\pi$
$47$	−4.68676			−0.683634			−0.341817	+	0.939767i	$0.611042\pi$
$48$	0.101929	−	0.176546i	0.0147122	−	0.0254823i
$49$	−6.36685	−	11.0277i	−0.909550	−	1.57539i
$50$	1.46903	+	2.54444i	0.207752	+	0.359838i
$51$	2.03340			0.284733
$52$	3.04724	−	3.47180i	0.422576	−	0.481452i
$53$	−1.52519			−0.209501			−0.104750	−	0.994499i	$-0.533404\pi$
$53$	−1.52519			−0.209501			−0.104750	+	0.994499i	$0.533404\pi$
$54$	−0.423911	−	0.734236i	−0.0576870	−	0.0999169i
$55$	−1.45477	−	2.51974i	−0.196161	−	0.339761i
$56$	6.17891	−	10.7022i	0.825691	−	1.43014i
$57$	2.98573			0.395470
$58$	1.90789	−	3.30456i	0.250518	−	0.433910i
$59$	1.22919	−	2.12903i	0.160027	−	0.277176i	−0.774851	−	0.632144i	$-0.782175\pi$
$59$	1.22919	−	2.12903i	0.160027	−	0.277176i	0.934878	+	0.354969i	$0.115508\pi$
$60$	−3.72769			−0.481243
$61$	−4.58756	+	7.94588i	−0.587377	+	1.01737i	0.407198	+	0.913340i	$0.366506\pi$
$61$	−4.58756	+	7.94588i	−0.587377	+	1.01737i	−0.994575	+	0.104026i	$0.966827\pi$
$62$	−1.37599	−	2.38329i	−0.174751	−	0.302678i
$63$	2.22113	+	3.84711i	0.279836	+	0.484691i
$64$	4.45589			0.556986
$65$	−10.2881	−	2.05086i	−1.27608	−	0.254378i
$66$	−0.847823			−0.104360
$67$	−1.64737	−	2.85333i	−0.201258	−	0.348590i	0.747676	−	0.664064i	$-0.231170\pi$
$67$	−1.64737	−	2.85333i	−0.201258	−	0.348590i	−0.948934	+	0.315474i	$0.897836\pi$
$68$	−1.30259	−	2.25616i	−0.157963	−	0.273599i
$69$	−3.31929	+	5.74918i	−0.399596	+	0.692120i
$70$	−10.9581			−1.30974
$71$	−4.81381	+	8.33776i	−0.571294	+	0.989510i	0.425139	+	0.905128i	$0.360225\pi$
$71$	−4.81381	+	8.33776i	−0.571294	+	0.989510i	−0.996433	+	0.0843825i	$0.973108\pi$
$72$	−1.39094	+	2.40917i	−0.163923	+	0.283924i
$73$	9.88080			1.15646			0.578230	−	0.815874i	$-0.303744\pi$
$73$	9.88080			1.15646			0.578230	+	0.815874i	$0.303744\pi$
$74$	−2.82456	+	4.89228i	−0.328349	+	0.568717i
$75$	1.73271	+	3.00114i	0.200076	+	0.346542i
$76$	−1.91265	−	3.31281i	−0.219397	−	0.380006i
$77$	4.44226			0.506243
$78$	−2.01649	+	2.29744i	−0.228322	+	0.260134i
$79$	9.34642			1.05155			0.525777	−	0.850622i	$-0.323774\pi$
$79$	9.34642			1.05155			0.525777	+	0.850622i	$0.323774\pi$
$80$	0.296567	+	0.513669i	0.0331572	+	0.0574299i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.57200	−	4.45483i	0.284030	−	0.491954i
$83$	8.98708			0.986461			0.493230	−	0.869899i	$-0.335816\pi$
$83$	8.98708			0.986461			0.493230	+	0.869899i	$0.335816\pi$
$84$	2.84571	−	4.92891i	0.310492	−	0.537788i
$85$	−2.95813	+	5.12363i	−0.320854	+	0.555736i
$86$	−9.45446			−1.01950
$87$	2.25034	−	3.89770i	0.241262	−	0.417877i
$88$	1.39094	+	2.40917i	0.148274	+	0.256819i
$89$	−3.77339	−	6.53570i	−0.399978	−	0.692782i	0.593745	−	0.804654i	$-0.297649\pi$
$89$	−3.77339	−	6.53570i	−0.399978	−	0.692782i	−0.993723	+	0.111871i	$0.964316\pi$
$90$	2.46677			0.260021
$91$	10.5656	−	12.0377i	1.10758	−	1.26189i
$92$	8.50533			0.886742
$93$	−1.62297	−	2.81107i	−0.168294	−	0.291494i
$94$	−1.98677	−	3.44119i	−0.204920	−	0.354931i
$95$	−4.34355	+	7.52325i	−0.445639	+	0.771869i
$96$	5.73658			0.585487
$97$	0.512507	−	0.887688i	0.0520372	−	0.0901310i	−0.838833	−	0.544388i	$-0.816762\pi$
$97$	0.512507	−	0.887688i	0.0520372	−	0.0901310i	0.890871	+	0.454257i	$0.150095\pi$
$98$	5.39796	−	9.34954i	0.545276	−	0.944446i
$99$	−1.00000			−0.100504
$100$	2.21994	−	3.84505i	0.221994	−	0.384505i
$101$	3.92434	+	6.79715i	0.390486	+	0.676342i	0.992514	−	0.122134i	$-0.0389736\pi$
$101$	3.92434	+	6.79715i	0.390486	+	0.676342i	−0.602028	+	0.798475i	$0.705640\pi$
$102$	0.861981	+	1.49300i	0.0853489	+	0.147829i
$103$	−17.6610			−1.74019			−0.870096	−	0.492882i	$-0.835943\pi$
$103$	−17.6610			−1.74019			−0.870096	+	0.492882i	$0.835943\pi$
$104$	9.83665	+	1.96087i	0.964562	+	0.192280i
$105$	−12.9249			−1.26135
$106$	−0.646544	−	1.11985i	−0.0627979	−	0.108769i
$107$	0.194718	+	0.337261i	0.0188241	+	0.0326042i	0.875284	−	0.483609i	$-0.160674\pi$
$107$	0.194718	+	0.337261i	0.0188241	+	0.0326042i	−0.856460	+	0.516214i	$0.827341\pi$
$108$	−0.640598	+	1.10955i	−0.0616416	+	0.106766i
$109$	−13.3890			−1.28243			−0.641217	−	0.767359i	$-0.721570\pi$
$109$	−13.3890			−1.28243			−0.641217	+	0.767359i	$0.721570\pi$
$110$	1.23339	−	2.13629i	0.117599	−	0.203687i
$111$	−3.33155	+	5.77041i	−0.316217	+	0.547703i
$112$	−0.905592			−0.0855704
$113$	−9.42257	+	16.3204i	−0.886401	+	1.53529i	−0.0423021	+	0.999105i	$0.513469\pi$
$113$	−9.42257	+	16.3204i	−0.886401	+	1.53529i	−0.844099	+	0.536187i	$0.819864\pi$
$114$	1.26569	+	2.19223i	0.118542	+	0.205321i
$115$	−9.65761	−	16.7275i	−0.900577	−	1.55985i
$116$	−5.76625			−0.535383
$117$	−2.37843	+	2.70981i	−0.219886	+	0.250522i
$118$	2.08428			0.191873
$119$	−4.51645	−	7.82272i	−0.414022	−	0.717107i
$120$	−4.04698	−	7.00958i	−0.369437	−	0.639885i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−7.77887			−0.704266
$123$	3.03365	−	5.25444i	0.273535	−	0.473777i
$124$	−2.07934	+	3.60153i	−0.186731	+	0.323427i
$125$	4.46492			0.399354
$126$	−1.88313	+	3.26167i	−0.167762	+	0.290573i
$127$	0.208986	+	0.361975i	0.0185445	+	0.0321201i	0.875149	−	0.483854i	$-0.160763\pi$
$127$	0.208986	+	0.361975i	0.0185445	+	0.0321201i	−0.856604	+	0.515974i	$0.827430\pi$
$128$	−3.84768	−	6.66438i	−0.340090	−	0.589053i
$129$	−11.1515			−0.981831
$130$	−2.85541	−	8.42326i	−0.250436	−	0.738769i
$131$	−0.828189			−0.0723592			−0.0361796	−	0.999345i	$-0.511519\pi$
$131$	−0.828189			−0.0723592			−0.0361796	+	0.999345i	$0.511519\pi$
$132$	0.640598	+	1.10955i	0.0557569	+	0.0965738i
$133$	−6.63170	−	11.4864i	−0.575041	−	0.996001i
$134$	1.39668	−	2.41912i	0.120655	−	0.208980i
$135$	2.90954			0.250413
$136$	2.82833	−	4.89881i	0.242527	−	0.420070i
$137$	4.70174	−	8.14366i	0.401697	−	0.695759i	−0.592234	−	0.805766i	$-0.701754\pi$
$137$	4.70174	−	8.14366i	0.401697	−	0.695759i	0.993931	+	0.110007i	$0.0350872\pi$
$138$	−5.62834			−0.479116
$139$	−10.2941	+	17.8300i	−0.873137	+	1.51232i	−0.0144020	+	0.999896i	$0.504584\pi$
$139$	−10.2941	+	17.8300i	−0.873137	+	1.51232i	−0.858735	+	0.512421i	$0.828749\pi$
$140$	8.27970	+	14.3409i	0.699762	+	1.21202i
$141$	−2.34338	−	4.05885i	−0.197348	−	0.341817i
$142$	−8.16251			−0.684983
$143$	1.15755	+	3.41469i	0.0967992	+	0.285550i
$144$	0.203858			0.0169882
$145$	6.54745	+	11.3405i	0.543736	+	0.941778i
$146$	4.18858	+	7.25484i	0.346649	+	0.600415i
$147$	6.36685	−	11.0277i	0.525129	−	0.909550i
$148$	8.53674			0.701715
$149$	−5.63311	+	9.75683i	−0.461482	+	0.799311i	−0.999035	−	0.0439193i	$-0.986016\pi$
$149$	−5.63311	+	9.75683i	−0.461482	+	0.799311i	0.537553	+	0.843230i	$0.319349\pi$
$150$	−1.46903	+	2.54444i	−0.119946	+	0.207752i
$151$	−0.644391			−0.0524398			−0.0262199	−	0.999656i	$-0.508347\pi$
$151$	−0.644391			−0.0524398			−0.0262199	+	0.999656i	$0.508347\pi$
$152$	4.15296	−	7.19314i	0.336850	−	0.583441i
$153$	1.01670	+	1.76098i	0.0821953	+	0.142366i
$154$	1.88313	+	3.26167i	0.151747	+	0.262833i
$155$	9.44420			0.758576
$156$	4.53029	+	0.903084i	0.362713	+	0.0723046i
$157$	−12.4461			−0.993304			−0.496652	−	0.867950i	$-0.665438\pi$
$157$	−12.4461			−0.993304			−0.496652	+	0.867950i	$0.665438\pi$
$158$	3.96205	+	6.86248i	0.315204	+	0.545950i
$159$	−0.762594	−	1.32085i	−0.0604776	−	0.104750i
$160$	−8.34541	+	14.4547i	−0.659762	+	1.14274i
$161$	29.4903			2.32416
$162$	0.423911	−	0.734236i	0.0333056	−	0.0576870i
$163$	8.53587	−	14.7846i	0.668581	−	1.15802i	−0.309720	−	0.950828i	$-0.600235\pi$
$163$	8.53587	−	14.7846i	0.668581	−	1.15802i	0.978301	−	0.207188i	$-0.0664313\pi$
$164$	−7.77341			−0.607001
$165$	1.45477	−	2.51974i	0.113254	−	0.196161i
$166$	3.80973	+	6.59864i	0.295692	+	0.512154i
$167$	−5.43161	−	9.40783i	−0.420311	−	0.728000i	0.575659	−	0.817690i	$-0.304746\pi$
$167$	−5.43161	−	9.40783i	−0.420311	−	0.728000i	−0.995970	+	0.0896903i	$0.971412\pi$
$168$	12.3578			0.953426
$169$	12.0063	+	4.98485i	0.923562	+	0.383450i
$170$	−5.01594			−0.384705
$171$	1.49287	+	2.58572i	0.114162	+	0.197735i
$172$	7.14360	+	12.3731i	0.544695	+	0.943439i
$173$	−5.02161	+	8.69768i	−0.381786	+	0.661272i	−0.991318	−	0.131489i	$-0.958024\pi$
$173$	−5.02161	+	8.69768i	−0.381786	+	0.661272i	0.609532	+	0.792762i	$0.291357\pi$
$174$	3.81578			0.289273
$175$	7.69716	−	13.3319i	0.581850	−	1.00779i
$176$	0.101929	−	0.176546i	0.00768320	−	0.0133077i
$177$	2.45839			0.184784
$178$	3.19916	−	5.54111i	0.239787	−	0.415324i
$179$	7.44649	+	12.8977i	0.556577	+	0.964020i	0.997779	+	0.0666120i	$0.0212190\pi$
$179$	7.44649	+	12.8977i	0.556577	+	0.964020i	−0.441202	+	0.897408i	$0.645448\pi$
$180$	−1.86385	−	3.22828i	−0.138923	−	0.240622i
$181$	23.5518			1.75059			0.875295	−	0.483590i	$-0.160667\pi$
$181$	23.5518			1.75059			0.875295	+	0.483590i	$0.160667\pi$
$182$	13.3174	+	2.65474i	0.987150	+	0.196782i
$183$	−9.17511			−0.678244
$184$	9.23385	+	15.9935i	0.680728	+	1.17906i
$185$	−9.69327	−	16.7892i	−0.712663	−	1.23437i
$186$	1.37599	−	2.38329i	0.100893	−	0.174751i
$187$	2.03340			0.148697
$188$	−3.00233	+	5.20019i	−0.218967	+	0.379262i
$189$	−2.22113	+	3.84711i	−0.161564	+	0.279836i
$190$	−7.36512			−0.534322
$191$	−5.72743	+	9.92020i	−0.414422	+	0.717801i	−0.995368	−	0.0961420i	$-0.969350\pi$
$191$	−5.72743	+	9.92020i	−0.414422	+	0.717801i	0.580945	+	0.813943i	$0.302683\pi$
$192$	2.22794	+	3.85891i	0.160788	+	0.278493i
$193$	4.34581	+	7.52716i	0.312818	+	0.541817i	0.978971	−	0.203998i	$-0.0653936\pi$
$193$	4.34581	+	7.52716i	0.312818	+	0.541817i	−0.666153	+	0.745815i	$0.732060\pi$
$194$	0.869030			0.0623927
$195$	−3.36794	−	9.93516i	−0.241183	−	0.711472i
$196$	−16.3144			−1.16531
$197$	12.3497	+	21.3903i	0.879879	+	1.52399i	0.851473	+	0.524398i	$0.175710\pi$
$197$	12.3497	+	21.3903i	0.879879	+	1.52399i	0.0284056	+	0.999596i	$0.490957\pi$
$198$	−0.423911	−	0.734236i	−0.0301261	−	0.0521799i
$199$	10.9694	−	18.9995i	0.777597	−	1.34684i	−0.155726	−	0.987800i	$-0.549772\pi$
$199$	10.9694	−	18.9995i	0.777597	−	1.34684i	0.933323	−	0.359037i	$-0.116895\pi$
$200$	9.64036			0.681676
$201$	1.64737	−	2.85333i	0.116197	−	0.201258i
$202$	−3.32714	+	5.76278i	−0.234097	+	0.405468i
$203$	−19.9932			−1.40325
$204$	1.30259	−	2.25616i	0.0911997	−	0.157963i
$205$	8.82653	+	15.2880i	0.616471	+	1.06776i
$206$	−7.48671	−	12.9674i	−0.521624	−	0.903479i
$207$	−6.63858			−0.461414
$208$	−0.235976	−	0.696112i	−0.0163620	−	0.0482667i
$209$	2.98573			0.206527
$210$	−5.47903	−	9.48996i	−0.378089	−	0.654869i
$211$	11.4598	+	19.8489i	0.788924	+	1.36646i	0.926627	+	0.375983i	$0.122695\pi$
$211$	11.4598	+	19.8489i	0.788924	+	1.36646i	−0.137703	+	0.990474i	$0.543972\pi$
$212$	−0.977032	+	1.69227i	−0.0671029	+	0.116226i
$213$	−9.62762			−0.659674
$214$	−0.165086	+	0.285937i	−0.0112851	+	0.0195463i
$215$	16.2228	−	28.0987i	1.10639	−	1.91632i
$216$	−2.78187			−0.189282
$217$	−7.20966	+	12.4875i	−0.489424	+	0.847707i
$218$	−5.67575	−	9.83069i	−0.384410	−	0.665819i
$219$	4.94040	+	8.55702i	0.333841	+	0.578230i
$220$	−3.72769			−0.251321
$221$	4.83630	−	5.51013i	0.325325	−	0.370651i
$222$	−5.64912			−0.379144
$223$	6.58472	+	11.4051i	0.440945	+	0.763740i	0.997760	−	0.0668972i	$-0.0213100\pi$
$223$	6.58472	+	11.4051i	0.440945	+	0.763740i	−0.556815	+	0.830637i	$0.687977\pi$
$224$	−12.7417	−	22.0693i	−0.851341	−	1.47457i
$225$	−1.73271	+	3.00114i	−0.115514	+	0.200076i
$226$	−15.9773			−1.06280
$227$	13.8980	−	24.0721i	0.922444	−	1.59772i	0.126824	−	0.991925i	$-0.459522\pi$
$227$	13.8980	−	24.0721i	0.922444	−	1.59772i	0.795621	−	0.605795i	$-0.207145\pi$
$228$	1.91265	−	3.31281i	0.126669	−	0.219397i
$229$	3.32163			0.219500			0.109750	−	0.993959i	$-0.464995\pi$
$229$	3.32163			0.219500			0.109750	+	0.993959i	$0.464995\pi$
$230$	8.18794	−	14.1819i	0.539897	−	0.935129i
$231$	2.22113	+	3.84711i	0.146140	+	0.253121i
$232$	−6.26016	−	10.8429i	−0.410999	−	0.711872i
$233$	−5.13087			−0.336135			−0.168067	−	0.985776i	$-0.553753\pi$
$233$	−5.13087			−0.336135			−0.168067	+	0.985776i	$0.553753\pi$
$234$	−2.99788	−	0.597609i	−0.195978	−	0.0390670i
$235$	13.6363			0.889534
$236$	−1.57484	−	2.72770i	−0.102513	−	0.177558i
$237$	4.67321	+	8.09424i	0.303558	+	0.525777i
$238$	3.82915	−	6.63228i	0.248207	−	0.429907i
$239$	−28.6247			−1.85158			−0.925790	−	0.378038i	$-0.876599\pi$
$239$	−28.6247			−1.85158			−0.925790	+	0.378038i	$0.876599\pi$
$240$	−0.296567	+	0.513669i	−0.0191433	+	0.0331572i
$241$	0.188669	−	0.326784i	0.0121532	−	0.0210500i	−0.859885	−	0.510488i	$-0.829465\pi$
$241$	0.188669	−	0.326784i	0.0121532	−	0.0210500i	0.872038	+	0.489438i	$0.162798\pi$
$242$	−0.847823			−0.0545001
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	5.87756	+	10.1802i	0.376272	+	0.651723i
$245$	18.5246	+	32.0856i	1.18349	+	2.04987i
$246$	5.14400			0.327969
$247$	7.10135	−	8.09077i	0.451848	−	0.514803i
$248$	−9.02980			−0.573393
$249$	4.49354	+	7.78304i	0.284767	+	0.493230i
$250$	1.89273	+	3.27830i	0.119707	+	0.207338i
$251$	8.66325	−	15.0052i	0.546819	−	0.947119i	−0.451671	−	0.892185i	$-0.649172\pi$
$251$	8.66325	−	15.0052i	0.546819	−	0.947119i	0.998490	−	0.0549340i	$-0.0174948\pi$
$252$	5.69141			0.358525
$253$	−3.31929	+	5.74918i	−0.208682	+	0.361448i
$254$	−0.177183	+	0.306891i	−0.0111175	+	0.0192560i
$255$	−5.91626			−0.370490
$256$	7.71804	−	13.3680i	0.482377	−	0.835502i
$257$	−11.0176	−	19.0831i	−0.687261	−	1.19037i	−0.972720	−	0.231981i	$-0.925479\pi$
$257$	−11.0176	−	19.0831i	−0.687261	−	1.19037i	0.285459	−	0.958391i	$-0.407854\pi$
$258$	−4.72723	−	8.18780i	−0.294304	−	0.509750i
$259$	29.5992			1.83921
$260$	−8.86605	+	10.1013i	−0.549849	+	0.626458i
$261$	4.50068			0.278585
$262$	−0.351079	−	0.608086i	−0.0216897	−	0.0375677i
$263$	−13.2526	−	22.9541i	−0.817188	−	1.41541i	−0.907746	−	0.419519i	$-0.862199\pi$
$263$	−13.2526	−	22.9541i	−0.817188	−	1.41541i	0.0905588	−	0.995891i	$-0.471135\pi$
$264$	−1.39094	+	2.40917i	−0.0856062	+	0.148274i
$265$	4.43759			0.272599
$266$	5.62251	−	9.73847i	0.344738	−	0.597104i
$267$	3.77339	−	6.53570i	0.230927	−	0.399978i
$268$	−4.22121			−0.257852
$269$	−7.69679	+	13.3312i	−0.469282	+	0.812820i	−0.999383	−	0.0351142i	$-0.988820\pi$
$269$	−7.69679	+	13.3312i	−0.469282	+	0.812820i	0.530101	+	0.847934i	$0.322154\pi$
$270$	1.23339	+	2.13629i	0.0750615	+	0.130010i
$271$	−6.65436	−	11.5257i	−0.404223	−	0.700135i	0.590007	−	0.807398i	$-0.299125\pi$
$271$	−6.65436	−	11.5257i	−0.404223	−	0.700135i	−0.994231	+	0.107262i	$0.965792\pi$
$272$	−0.414525			−0.0251343
$273$	15.7078	+	3.13124i	0.950676	+	0.189511i
$274$	7.97249			0.481636
$275$	1.73271	+	3.00114i	0.104486	+	0.180976i
$276$	4.25267	+	7.36583i	0.255980	+	0.443371i
$277$	−1.84244	+	3.19120i	−0.110702	+	0.191741i	−0.916053	−	0.401056i	$-0.868643\pi$
$277$	−1.84244	+	3.19120i	−0.110702	+	0.191741i	0.805352	+	0.592797i	$0.201976\pi$
$278$	−17.4552			−1.04689
$279$	1.62297	−	2.81107i	0.0971647	−	0.168294i
$280$	−17.9778	+	31.1384i	−1.07438	+	1.86088i
$281$	17.2145			1.02693			0.513466	−	0.858110i	$-0.328361\pi$
$281$	17.2145			1.02693			0.513466	+	0.858110i	$0.328361\pi$
$282$	1.98677	−	3.44119i	0.118310	−	0.204920i
$283$	−9.69941	−	16.7999i	−0.576570	−	0.998649i	−0.995869	−	0.0908007i	$-0.971057\pi$
$283$	−9.69941	−	16.7999i	−0.576570	−	0.998649i	0.419299	−	0.907848i	$-0.362276\pi$
$284$	6.16744	+	10.6823i	0.365970	+	0.633879i
$285$	−8.68710			−0.514580
$286$	−2.01649	+	2.29744i	−0.119237	+	0.135850i
$287$	−26.9526			−1.59096
$288$	2.86829	+	4.96803i	0.169016	+	0.292744i
$289$	6.43264	+	11.1417i	0.378391	+	0.655392i
$290$	−5.55108	+	9.61474i	−0.325970	+	0.564597i
$291$	1.02501			0.0600874
$292$	6.32962	−	10.9632i	0.370413	−	0.641574i
$293$	−1.26387	+	2.18908i	−0.0738360	+	0.127888i	−0.900579	−	0.434691i	$-0.856857\pi$
$293$	−1.26387	+	2.18908i	−0.0738360	+	0.127888i	0.826744	+	0.562579i	$0.190191\pi$
$294$	10.7959			0.629631
$295$	−3.57639	+	6.19449i	−0.208225	+	0.360657i
$296$	9.26794	+	16.0525i	0.538688	+	0.933035i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	−9.55176			−0.553318
$299$	7.68449	+	22.6687i	0.444406	+	1.31096i
$300$	4.43989			0.256337
$301$	24.7688	+	42.9009i	1.42765	+	2.47277i
$302$	−0.273165	−	0.473135i	−0.0157189	−	0.0272259i
$303$	−3.92434	+	6.79715i	−0.225447	+	0.390486i
$304$	−0.608666			−0.0349094
$305$	13.3477	−	23.1189i	0.764286	−	1.32378i
$306$	−0.861981	+	1.49300i	−0.0492762	+	0.0853489i
$307$	−10.7343			−0.612639			−0.306319	−	0.951929i	$-0.599098\pi$
$307$	−10.7343			−0.612639			−0.306319	+	0.951929i	$0.599098\pi$
$308$	2.84571	−	4.92891i	0.162149	−	0.280851i
$309$	−8.83051	−	15.2949i	−0.502350	−	0.870096i
$310$	4.00350	+	6.93427i	0.227384	+	0.393840i
$311$	5.19269			0.294450			0.147225	−	0.989103i	$-0.452966\pi$
$311$	5.19269			0.294450			0.147225	+	0.989103i	$0.452966\pi$
$312$	3.22016	+	9.49922i	0.182305	+	0.537788i
$313$	−6.49580			−0.367164			−0.183582	−	0.983004i	$-0.558769\pi$
$313$	−6.49580			−0.367164			−0.183582	+	0.983004i	$0.558769\pi$
$314$	−5.27603	−	9.13835i	−0.297744	−	0.515707i
$315$	−6.46247	−	11.1933i	−0.364119	−	0.630673i
$316$	5.98730	−	10.3703i	0.336812	−	0.583376i
$317$	15.5260			0.872025			0.436013	−	0.899940i	$-0.356390\pi$
$317$	15.5260			0.872025			0.436013	+	0.899940i	$0.356390\pi$
$318$	0.646544	−	1.11985i	0.0362564	−	0.0627979i
$319$	2.25034	−	3.89770i	0.125995	−	0.218229i
$320$	−12.9646			−0.724742
$321$	−0.194718	+	0.337261i	−0.0108681	+	0.0188241i
$322$	12.5013	+	21.6529i	0.696670	+	1.20667i
$323$	−3.03559	−	5.25780i	−0.168905	−	0.292552i
$324$	−1.28120			−0.0711776
$325$	12.2537	+	2.44269i	0.679711	+	0.135496i
$326$	14.4738			0.801630
$327$	−6.69450	−	11.5952i	−0.370207	−	0.641217i
$328$	−8.43923	−	14.6172i	−0.465979	−	0.807099i
$329$	−10.4099	+	18.0305i	−0.573916	+	0.994053i
$330$	2.46677			0.135791
$331$	−1.53717	+	2.66245i	−0.0844904	+	0.146342i	−0.905174	−	0.425041i	$-0.860260\pi$
$331$	−1.53717	+	2.66245i	−0.0844904	+	0.146342i	0.820684	+	0.571383i	$0.193593\pi$
$332$	5.75711	−	9.97161i	0.315963	−	0.547263i
$333$	−6.66310			−0.365135
$334$	4.60504	−	7.97617i	0.251977	−	0.436437i
$335$	4.79309	+	8.30188i	0.261875	+	0.453580i
$336$	−0.452796	−	0.784266i	−0.0247020	−	0.0427852i
$337$	−5.39560			−0.293917			−0.146959	−	0.989143i	$-0.546948\pi$
$337$	−5.39560			−0.293917			−0.146959	+	0.989143i	$0.546948\pi$
$338$	1.42955	+	10.9286i	0.0777573	+	0.594437i
$339$	−18.8451			−1.02353
$340$	3.78994	+	6.56438i	0.205539	+	0.356003i
$341$	−1.62297	−	2.81107i	−0.0878888	−	0.152228i
$342$	−1.26569	+	2.19223i	−0.0684404	+	0.118542i
$343$	−25.4706			−1.37528
$344$	−15.5110	+	26.8658i	−0.836295	+	1.44851i
$345$	9.65761	−	16.7275i	0.519948	−	0.900577i
$346$	−8.51487			−0.457762
$347$	5.38499	−	9.32708i	0.289081	−	0.500704i	−0.684509	−	0.729004i	$-0.739984\pi$
$347$	5.38499	−	9.32708i	0.289081	−	0.500704i	0.973591	+	0.228300i	$0.0733168\pi$
$348$	−2.88313	−	4.99372i	−0.154552	−	0.267692i
$349$	8.75504	+	15.1642i	0.468647	+	0.811720i	0.999358	−	0.0358329i	$-0.0114084\pi$
$349$	8.75504	+	15.1642i	0.468647	+	0.811720i	−0.530711	+	0.847553i	$0.678075\pi$
$350$	13.0516			0.697640
$351$	−3.53598	−	0.704876i	−0.188737	−	0.0376235i
$352$	5.73658			0.305761
$353$	−15.1377	−	26.2193i	−0.805699	−	1.39551i	−0.915818	−	0.401593i	$-0.868457\pi$
$353$	−15.1377	−	26.2193i	−0.805699	−	1.39551i	0.110119	−	0.993918i	$-0.464877\pi$
$354$	1.04214	+	1.80504i	0.0553890	+	0.0959366i
$355$	14.0060	−	24.2591i	0.743360	−	1.28754i
$356$	−9.66890			−0.512451
$357$	4.51645	−	7.82272i	0.239036	−	0.414022i
$358$	−6.31331	+	10.9350i	−0.333669	+	0.577931i
$359$	4.95491			0.261510			0.130755	−	0.991415i	$-0.458260\pi$
$359$	4.95491			0.261510			0.130755	+	0.991415i	$0.458260\pi$
$360$	4.04698	−	7.00958i	0.213295	−	0.369437i
$361$	5.04270	+	8.73422i	0.265405	+	0.459696i
$362$	9.98387	+	17.2926i	0.524740	+	0.908877i
$363$	−1.00000			−0.0524864
$364$	−6.58809	−	19.4344i	−0.345310	−	1.01864i
$365$	−28.7486			−1.50477
$366$	−3.88944	−	6.73670i	−0.203304	−	0.352133i
$367$	−4.88241	−	8.45658i	−0.254860	−	0.441430i	0.709998	−	0.704204i	$-0.248696\pi$
$367$	−4.88241	−	8.45658i	−0.254860	−	0.441430i	−0.964857	+	0.262774i	$0.915363\pi$
$368$	0.676665	−	1.17202i	0.0352736	−	0.0610957i
$369$	6.06730			0.315851
$370$	8.21817	−	14.2343i	0.427243	−	0.740006i
$371$	−3.38764	+	5.86757i	−0.175878	+	0.304629i
$372$	−4.15869			−0.215618
$373$	19.0771	−	33.0424i	0.987772	−	1.71087i	0.358871	−	0.933387i	$-0.383162\pi$
$373$	19.0771	−	33.0424i	0.987772	−	1.71087i	0.628902	−	0.777485i	$-0.283505\pi$
$374$	0.861981	+	1.49300i	0.0445720	+	0.0772010i
$375$	2.23246	+	3.86673i	0.115284	+	0.199677i
$376$	−13.0380			−0.672381
$377$	−5.20976	−	15.3684i	−0.268316	−	0.791513i
$378$	−3.76625			−0.193715
$379$	−0.993338	−	1.72051i	−0.0510244	−	0.0883768i	0.839385	−	0.543537i	$-0.182915\pi$
$379$	−0.993338	−	1.72051i	−0.0510244	−	0.0883768i	−0.890410	+	0.455160i	$0.849582\pi$
$380$	5.56494	+	9.63877i	0.285476	+	0.494458i
$381$	−0.208986	+	0.361975i	−0.0107067	+	0.0185445i
$382$	−9.71169			−0.496893
$383$	−1.45239	+	2.51562i	−0.0742139	+	0.128542i	−0.900744	−	0.434350i	$-0.856978\pi$
$383$	−1.45239	+	2.51562i	−0.0742139	+	0.128542i	0.826530	+	0.562892i	$0.190311\pi$
$384$	3.84768	−	6.66438i	0.196351	−	0.340090i
$385$	−12.9249			−0.658716
$386$	−3.68448	+	6.38170i	−0.187535	+	0.324820i
$387$	−5.57573	−	9.65744i	−0.283430	−	0.490915i
$388$	−0.656622	−	1.13730i	−0.0333349	−	0.0577378i
$389$	5.23243			0.265295			0.132647	−	0.991163i	$-0.457652\pi$
$389$	5.23243			0.265295			0.132647	+	0.991163i	$0.457652\pi$
$390$	5.86705	−	6.68449i	0.297090	−	0.338482i
$391$	13.4989			0.682669
$392$	−17.7118	−	30.6777i	−0.894580	−	1.54946i
$393$	−0.414094	−	0.717233i	−0.0208883	−	0.0361796i
$394$	−10.4703	+	18.1352i	−0.527488	+	0.913637i
$395$	−27.1938			−1.36827
$396$	−0.640598	+	1.10955i	−0.0321913	+	0.0557569i
$397$	−11.2185	+	19.4311i	−0.563043	+	0.975218i	0.434186	+	0.900823i	$0.357036\pi$
$397$	−11.2185	+	19.4311i	−0.563043	+	0.975218i	−0.997229	+	0.0743952i	$0.976297\pi$
$398$	18.6001			0.932340
$399$	6.63170	−	11.4864i	0.332000	−	0.575041i
$400$	−0.353227	−	0.611808i	−0.0176614	−	0.0305904i
$401$	−5.28306	−	9.15053i	−0.263824	−	0.456956i	0.703431	−	0.710763i	$-0.251650\pi$
$401$	−5.28306	−	9.15053i	−0.263824	−	0.456956i	−0.967255	+	0.253808i	$0.918317\pi$
$402$	2.79336			0.139320
$403$	−11.4776	−	2.28798i	−0.571739	−	0.113973i
$404$	10.0557			0.500289
$405$	1.45477	+	2.51974i	0.0722881	+	0.125207i
$406$	−8.47534	−	14.6797i	−0.420624	−	0.728542i
$407$	−3.33155	+	5.77041i	−0.165139	+	0.286029i
$408$	5.65666			0.280046
$409$	−12.4034	+	21.4833i	−0.613309	+	1.06228i	0.377370	+	0.926063i	$0.376829\pi$
$409$	−12.4034	+	21.4833i	−0.613309	+	1.06228i	−0.990679	+	0.136220i	$0.956505\pi$
$410$	−7.48333	+	12.9615i	−0.369575	+	0.640123i
$411$	9.40348			0.463840
$412$	−11.3136	+	19.5958i	−0.557382	+	0.965414i
$413$	−5.46040	−	9.45769i	−0.268689	−	0.465383i
$414$	−2.81417	−	4.87429i	−0.138309	−	0.239558i
$415$	−26.1483			−1.28357
$416$	13.6441	−	15.5450i	0.668955	−	0.762159i
$417$	−20.5883			−1.00821
$418$	1.26569	+	2.19223i	0.0619067	+	0.107226i
$419$	−15.9716	−	27.6637i	−0.780265	−	1.35146i	−0.931787	−	0.363005i	$-0.881751\pi$
$419$	−15.9716	−	27.6637i	−0.780265	−	1.35146i	0.151522	−	0.988454i	$-0.451583\pi$
$420$	−8.27970	+	14.3409i	−0.404008	+	0.699762i
$421$	−32.5599			−1.58687			−0.793436	−	0.608654i	$-0.791710\pi$
$421$	−32.5599			−1.58687			−0.793436	+	0.608654i	$0.791710\pi$
$422$	−9.71586	+	16.8284i	−0.472961	+	0.819192i
$423$	2.34338	−	4.05885i	0.113939	−	0.197348i
$424$	−4.24288			−0.206052
$425$	3.52329	−	6.10252i	0.170905	−	0.296016i
$426$	−4.08126	−	7.06895i	−0.197738	−	0.342492i
$427$	20.3791	+	35.2977i	0.986216	+	1.70818i
$428$	0.498943			0.0241173
$429$	−2.37843	+	2.70981i	−0.114832	+	0.130831i
$430$	27.5081			1.32656
$431$	−1.55944	−	2.70104i	−0.0751158	−	0.130104i	0.826021	−	0.563640i	$-0.190599\pi$
$431$	−1.55944	−	2.70104i	−0.0751158	−	0.130104i	−0.901137	+	0.433535i	$0.857266\pi$
$432$	0.101929	+	0.176546i	0.00490407	+	0.00849409i
$433$	15.3847	−	26.6471i	0.739341	−	1.28058i	−0.213451	−	0.976954i	$-0.568470\pi$
$433$	15.3847	−	26.6471i	0.739341	−	1.28058i	0.952792	−	0.303623i	$-0.0981962\pi$
$434$	−12.2250			−0.586820
$435$	−6.54745	+	11.3405i	−0.313926	+	0.543736i
$436$	−8.57698	+	14.8558i	−0.410763	+	0.711462i
$437$	19.8210			0.948168
$438$	−4.18858	+	7.25484i	−0.200138	+	0.346649i
$439$	4.22278	+	7.31408i	0.201542	+	0.349082i	0.949026	−	0.315199i	$-0.102071\pi$
$439$	4.22278	+	7.31408i	0.201542	+	0.349082i	−0.747483	+	0.664281i	$0.768738\pi$
$440$	−4.04698	−	7.00958i	−0.192932	−	0.334169i
$441$	12.7337			0.606367
$442$	6.09590	+	1.21518i	0.289952	+	0.0578002i
$443$	20.8631			0.991234			0.495617	−	0.868541i	$-0.334942\pi$
$443$	20.8631			0.991234			0.495617	+	0.868541i	$0.334942\pi$
$444$	4.26837	+	7.39303i	0.202568	+	0.350858i
$445$	10.9788	+	19.0159i	0.520446	+	0.901439i
$446$	−5.58267	+	9.66947i	−0.264347	+	0.457863i
$447$	−11.2662			−0.532874
$448$	9.89711	−	17.1423i	0.467595	−	0.809898i
$449$	−0.0911750	+	0.157920i	−0.00430281	+	0.00745269i	−0.868169	−	0.496269i	$-0.834703\pi$
$449$	−0.0911750	+	0.157920i	−0.00430281	+	0.00745269i	0.863866	+	0.503722i	$0.168036\pi$
$450$	−2.93806			−0.138502
$451$	3.03365	−	5.25444i	0.142849	−	0.247422i
$452$	12.0722	+	20.9096i	0.567827	+	0.983505i
$453$	−0.322195	−	0.558059i	−0.0151381	−	0.0262199i
$454$	23.5661			1.10601
$455$	−30.7411	+	35.0241i	−1.44116	+	1.64196i
$456$	8.30593			0.388961
$457$	−10.2576	−	17.7666i	−0.479829	−	0.831088i	0.519903	−	0.854225i	$-0.325968\pi$
$457$	−10.2576	−	17.7666i	−0.479829	−	0.831088i	−0.999732	+	0.0231368i	$0.992635\pi$
$458$	1.40808	+	2.43886i	0.0657951	+	0.113960i
$459$	−1.01670	+	1.76098i	−0.0474555	+	0.0821953i
$460$	−24.7466			−1.15382
$461$	9.89105	−	17.1318i	0.460672	−	0.797907i	−0.538323	−	0.842739i	$-0.680942\pi$
$461$	9.89105	−	17.1318i	0.460672	−	0.797907i	0.998995	+	0.0448316i	$0.0142751\pi$
$462$	−1.88313	+	3.26167i	−0.0876109	+	0.151747i
$463$	−33.5816			−1.56067			−0.780335	−	0.625362i	$-0.784951\pi$
$463$	−33.5816			−1.56067			−0.780335	+	0.625362i	$0.784951\pi$
$464$	−0.458750	+	0.794578i	−0.0212969	+	0.0368874i
$465$	4.72210	+	8.17891i	0.218982	+	0.379288i
$466$	−2.17504	−	3.76727i	−0.100757	−	0.174516i
$467$	3.46778			0.160470			0.0802348	−	0.996776i	$-0.474433\pi$
$467$	3.46778			0.160470			0.0802348	+	0.996776i	$0.474433\pi$
$468$	1.48305	+	4.37488i	0.0685540	+	0.202229i
$469$	−14.6361			−0.675833
$470$	5.78058	+	10.0123i	0.266638	+	0.461831i
$471$	−6.22303	−	10.7786i	−0.286742	−	0.496652i
$472$	3.41946	−	5.92268i	0.157393	−	0.272613i
$473$	−11.1515			−0.512744
$474$	−3.96205	+	6.86248i	−0.181983	+	0.315204i
$475$	5.17341	−	8.96061i	0.237372	−	0.411141i
$476$	−11.5729			−0.530444
$477$	0.762594	−	1.32085i	0.0349168	−	0.0604776i
$478$	−12.1344	−	21.0173i	−0.555012	−	0.961310i
$479$	−21.2997	−	36.8921i	−0.973207	−	1.68564i	−0.685729	−	0.727857i	$-0.740517\pi$
$479$	−21.2997	−	36.8921i	−0.973207	−	1.68564i	−0.287478	−	0.957787i	$-0.592817\pi$
$480$	−16.6908			−0.761828
$481$	7.71286	+	22.7524i	0.351676	+	1.03742i
$482$	0.319916			0.0145718
$483$	14.7452	+	25.5394i	0.670928	+	1.16208i
$484$	0.640598	+	1.10955i	0.0291181	+	0.0504340i
$485$	−1.49116	+	2.58276i	−0.0677100	+	0.117277i
$486$	0.847823			0.0384580
$487$	10.6351	−	18.4205i	0.481921	−	0.834712i	−0.517863	−	0.855463i	$-0.673272\pi$
$487$	10.6351	−	18.4205i	0.481921	−	0.834712i	0.999785	+	0.0207511i	$0.00660575\pi$
$488$	−12.7620	+	22.1044i	−0.577709	+	1.00062i
$489$	17.0717			0.772011
$490$	−15.7056	+	27.2029i	−0.709506	+	1.22890i
$491$	−8.29672	−	14.3703i	−0.374426	−	0.648524i	0.615815	−	0.787891i	$-0.288827\pi$
$491$	−8.29672	−	14.3703i	−0.374426	−	0.648524i	−0.990241	+	0.139366i	$0.955493\pi$
$492$	−3.88670	−	6.73197i	−0.175226	−	0.303501i
$493$	−9.15167			−0.412171
$494$	8.95087	+	1.78430i	0.402719	+	0.0802795i
$495$	2.90954			0.130774
$496$	0.330856	+	0.573059i	0.0148559	+	0.0257311i
$497$	21.3842	+	37.0385i	0.959213	+	1.66141i
$498$	−3.80973	+	6.59864i	−0.170718	+	0.295692i
$499$	30.0700			1.34612			0.673059	−	0.739589i	$-0.264980\pi$
$499$	30.0700			1.34612			0.673059	+	0.739589i	$0.264980\pi$
$500$	2.86022	−	4.95405i	0.127913	−	0.221552i
$501$	5.43161	−	9.40783i	0.242667	−	0.420311i
$502$	14.6898			0.655638
$503$	−19.7373	+	34.1860i	−0.880044	+	1.52428i	−0.0287525	+	0.999587i	$0.509153\pi$
$503$	−19.7373	+	34.1860i	−0.880044	+	1.52428i	−0.851291	+	0.524694i	$0.824180\pi$
$504$	6.17891	+	10.7022i	0.275230	+	0.476713i
$505$	−11.4180	−	19.7766i	−0.508095	−	0.880046i
$506$	−5.62834			−0.250210
$507$	1.68614	+	12.8902i	0.0748843	+	0.572473i
$508$	0.535505			0.0237592
$509$	−11.1988	−	19.3969i	−0.496378	−	0.859752i	0.503613	−	0.863929i	$-0.332004\pi$
$509$	−11.1988	−	19.3969i	−0.496378	−	0.859752i	−0.999991	+	0.00417727i	$0.998670\pi$
$510$	−2.50797	−	4.34393i	−0.111055	−	0.192352i
$511$	21.9465	−	38.0125i	0.970858	−	1.68158i
$512$	−2.30366			−0.101809
$513$	−1.49287	+	2.58572i	−0.0659116	+	0.114162i
$514$	9.34100	−	16.1791i	0.412014	−	0.713629i
$515$	51.3854			2.26431
$516$	−7.14360	+	12.3731i	−0.314480	+	0.544695i
$517$	−2.34338	−	4.05885i	−0.103062	−	0.178508i
$518$	12.5474	+	21.7328i	0.551303	+	0.954885i
$519$	−10.0432			−0.440848
$520$	−28.6201	−	5.70524i	−1.25507	−	0.250191i
$521$	1.76174			0.0771831			0.0385915	−	0.999255i	$-0.487713\pi$
$521$	1.76174			0.0771831			0.0385915	+	0.999255i	$0.487713\pi$
$522$	1.90789	+	3.30456i	0.0835060	+	0.144637i
$523$	−8.96685	−	15.5310i	−0.392093	−	0.679125i	0.600632	−	0.799525i	$-0.294916\pi$
$523$	−8.96685	−	15.5310i	−0.392093	−	0.679125i	−0.992725	+	0.120400i	$0.961582\pi$
$524$	−0.530536	+	0.918916i	−0.0231766	+	0.0401430i
$525$	15.3943			0.671863
$526$	11.2358	−	19.4610i	0.489905	−	0.848540i
$527$	−3.30015	+	5.71602i	−0.143757	+	0.248994i
$528$	0.203858			0.00887179
$529$	−10.5354	+	18.2479i	−0.458061	+	0.793385i
$530$	1.88115	+	3.25824i	0.0817117	+	0.141529i
$531$	1.22919	+	2.12903i	0.0533425	+	0.0923919i
$532$	−16.9930			−0.736741
$533$	−7.02320	−	20.7179i	−0.304209	−	0.897393i
$534$	6.39832			0.276883
$535$	−0.566539	−	0.981274i	−0.0244936	−	0.0424242i
$536$	−4.58278	−	7.93760i	−0.197946	−	0.342852i
$537$	−7.44649	+	12.8977i	−0.321340	+	0.556577i
$538$	−13.0510			−0.562670
$539$	6.36685	−	11.0277i	0.274240	−	0.474997i
$540$	1.86385	−	3.22828i	0.0802072	−	0.138923i
$541$	24.9206			1.07142			0.535710	−	0.844402i	$-0.320044\pi$
$541$	24.9206			1.07142			0.535710	+	0.844402i	$0.320044\pi$
$542$	5.64172	−	9.77174i	0.242332	−	0.419732i
$543$	11.7759	+	20.3964i	0.505352	+	0.875295i
$544$	−5.83238	−	10.1020i	−0.250061	−	0.433119i
$545$	38.9559			1.66869
$546$	4.35962	+	12.8606i	0.186575	+	0.550381i
$547$	29.3952			1.25685			0.628425	−	0.777870i	$-0.283700\pi$
$547$	29.3952			1.25685			0.628425	+	0.777870i	$0.283700\pi$
$548$	−6.02386	−	10.4336i	−0.257326	−	0.445702i
$549$	−4.58756	−	7.94588i	−0.195792	−	0.339122i
$550$	−1.46903	+	2.54444i	−0.0626397	+	0.108495i
$551$	−13.4378			−0.572470
$552$	−9.23385	+	15.9935i	−0.393019	+	0.680728i
$553$	20.7596	−	35.9567i	0.882790	−	1.52904i
$554$	−3.12413			−0.132731
$555$	9.69327	−	16.7892i	0.411456	−	0.712663i
$556$	13.1888	+	22.8437i	0.559330	+	0.968788i
$557$	8.60003	+	14.8957i	0.364395	+	0.631150i	0.988679	−	0.150047i	$-0.0479425\pi$
$557$	8.60003	+	14.8957i	0.364395	+	0.631150i	−0.624284	+	0.781197i	$0.714609\pi$
$558$	2.75198			0.116501
$559$	−26.5230	+	30.2183i	−1.12180	+	1.27810i
$560$	2.63486			0.111343
$561$	1.01670	+	1.76098i	0.0429251	+	0.0743485i
$562$	7.29743	+	12.6395i	0.307824	+	0.533166i
$563$	1.07216	−	1.85703i	0.0451860	−	0.0782645i	−0.842548	−	0.538622i	$-0.818945\pi$
$563$	1.07216	−	1.85703i	0.0451860	−	0.0782645i	0.887734	+	0.460357i	$0.152279\pi$
$564$	−6.00466			−0.252842
$565$	27.4154	−	47.4848i	1.15337	−	1.99770i
$566$	8.22338	−	14.2433i	0.345655	−	0.598691i
$567$	−4.44226			−0.186558
$568$	−13.3914	+	23.1946i	−0.561891	+	0.973224i
$569$	2.88524	+	4.99739i	0.120956	+	0.209501i	0.920145	−	0.391578i	$-0.128071\pi$
$569$	2.88524	+	4.99739i	0.120956	+	0.209501i	−0.799189	+	0.601080i	$0.794737\pi$
$570$	−3.68256	−	6.37838i	−0.154246	−	0.267161i
$571$	9.94966			0.416380			0.208190	−	0.978088i	$-0.433243\pi$
$571$	9.94966			0.416380			0.208190	+	0.978088i	$0.433243\pi$
$572$	4.53029	+	0.903084i	0.189421	+	0.0377598i
$573$	−11.4549			−0.478534
$574$	−11.4255	−	19.7895i	−0.476891	−	0.825999i
$575$	11.5027	+	19.9233i	0.479698	+	0.830861i
$576$	−2.22794	+	3.85891i	−0.0928310	+	0.160788i
$577$	6.50263			0.270708			0.135354	−	0.990797i	$-0.456783\pi$
$577$	6.50263			0.270708			0.135354	+	0.990797i	$0.456783\pi$
$578$	−5.45374	+	9.44616i	−0.226846	+	0.392908i
$579$	−4.34581	+	7.52716i	−0.180606	+	0.312818i
$580$	16.7771			0.696633
$581$	19.9615	−	34.5743i	0.828142	−	1.43438i
$582$	0.434515	+	0.752602i	0.0180112	+	0.0311963i
$583$	−0.762594	−	1.32085i	−0.0315834	−	0.0547040i
$584$	27.4871			1.13743
$585$	6.92014	−	7.88430i	0.286112	−	0.325976i
$586$	−2.14307			−0.0885295
$587$	2.98878	+	5.17672i	0.123360	+	0.213666i	0.921091	−	0.389348i	$-0.127300\pi$
$587$	2.98878	+	5.17672i	0.123360	+	0.213666i	−0.797731	+	0.603014i	$0.793966\pi$
$588$	−8.15719	−	14.1287i	−0.336397	−	0.582656i
$589$	−4.84575	+	8.39309i	−0.199666	+	0.345831i
$590$	−6.06429			−0.249663
$591$	−12.3497	+	21.3903i	−0.507998	+	0.879879i
$592$	0.679163	−	1.17635i	0.0279134	−	0.0483475i
$593$	20.6424			0.847683			0.423841	−	0.905736i	$-0.360681\pi$
$593$	20.6424			0.847683			0.423841	+	0.905736i	$0.360681\pi$
$594$	0.423911	−	0.734236i	0.0173933	−	0.0301261i
$595$	13.1408	+	22.7605i	0.538720	+	0.933090i
$596$	7.21712	+	12.5004i	0.295625	+	0.512037i
$597$	21.9387			0.897891
$598$	−13.3866	+	15.2517i	−0.547420	+	0.623690i
$599$	−19.5894			−0.800401			−0.400200	−	0.916428i	$-0.631059\pi$
$599$	−19.5894			−0.800401			−0.400200	+	0.916428i	$0.631059\pi$
$600$	4.82018	+	8.34880i	0.196783	+	0.340838i
$601$	12.2891	+	21.2854i	0.501283	+	0.868248i	0.999999	+	0.00148236i	$0.000471851\pi$
$601$	12.2891	+	21.2854i	0.501283	+	0.868248i	−0.498716	+	0.866766i	$0.666195\pi$
$602$	−20.9996	+	36.3724i	−0.855879	+	1.48243i
$603$	3.29474			0.134172
$604$	−0.412796	+	0.714983i	−0.0167964	+	0.0290922i
$605$	1.45477	−	2.51974i	0.0591448	−	0.102442i
$606$	−6.65428			−0.270312
$607$	14.3766	−	24.9010i	0.583527	−	1.01070i	−0.411530	−	0.911396i	$-0.635005\pi$
$607$	14.3766	−	24.9010i	0.583527	−	1.01070i	0.995057	−	0.0993028i	$-0.0316613\pi$
$608$	−8.56395	−	14.8332i	−0.347314	−	0.601565i
$609$	−9.99659	−	17.3146i	−0.405082	−	0.701623i
$610$	22.6329			0.916381
$611$	−16.5723	−	3.30358i	−0.670442	−	0.133649i
$612$	2.60519			0.105308
$613$	−4.25669	−	7.37280i	−0.171926	−	0.297784i	0.767167	−	0.641447i	$-0.221666\pi$
$613$	−4.25669	−	7.37280i	−0.171926	−	0.297784i	−0.939093	+	0.343663i	$0.888332\pi$
$614$	−4.55039	−	7.88151i	−0.183639	−	0.318072i
$615$	−8.82653	+	15.2880i	−0.355920	+	0.616471i
$616$	12.3578			0.497910
$617$	7.43403	−	12.8761i	0.299283	−	0.518373i	−0.676689	−	0.736269i	$-0.736586\pi$
$617$	7.43403	−	12.8761i	0.299283	−	0.518373i	0.975972	+	0.217896i	$0.0699193\pi$
$618$	7.48671	−	12.9674i	0.301160	−	0.521624i
$619$	−46.1341			−1.85429			−0.927143	−	0.374708i	$-0.877743\pi$
$619$	−46.1341			−1.85429			−0.927143	+	0.374708i	$0.877743\pi$
$620$	6.04994	−	10.4788i	0.242971	−	0.420839i
$621$	−3.31929	−	5.74918i	−0.133199	−	0.230707i
$622$	2.20124	+	3.81266i	0.0882616	+	0.152874i
$623$	−33.5247			−1.34314
$624$	0.484862	−	0.552417i	0.0194100	−	0.0221144i
$625$	−30.3180			−1.21272
$626$	−2.75364	−	4.76945i	−0.110058	−	0.190626i
$627$	1.49287	+	2.58572i	0.0596193	+	0.103264i
$628$	−7.97293	+	13.8095i	−0.318155	+	0.551060i
$629$	13.5487			0.540224
$630$	5.47903	−	9.48996i	0.218290	−	0.378089i
$631$	11.7794	−	20.4026i	0.468932	−	0.812214i	−0.530437	−	0.847724i	$-0.677972\pi$
$631$	11.7794	−	20.4026i	0.468932	−	0.812214i	0.999369	+	0.0355102i	$0.0113056\pi$
$632$	26.0006			1.03425
$633$	−11.4598	+	19.8489i	−0.455485	+	0.788924i
$634$	6.58164	+	11.3997i	0.261390	+	0.452741i
$635$	−0.608054	−	1.05318i	−0.0241299	−	0.0417942i
$636$	−1.95406			−0.0774837
$637$	−14.7399	−	43.4816i	−0.584016	−	1.72280i
$638$	3.81578			0.151068
$639$	−4.81381	−	8.33776i	−0.190431	−	0.329837i
$640$	11.1950	+	19.3903i	0.442520	+	0.766468i
$641$	−16.3349	+	28.2929i	−0.645190	+	1.11750i	0.339067	+	0.940762i	$0.389889\pi$
$641$	−16.3349	+	28.2929i	−0.645190	+	1.11750i	−0.984258	+	0.176740i	$0.943445\pi$
$642$	−0.330172			−0.0130309
$643$	−14.3250	+	24.8116i	−0.564922	+	0.978474i	0.432135	+	0.901809i	$0.357760\pi$
$643$	−14.3250	+	24.8116i	−0.564922	+	0.978474i	−0.997057	+	0.0766647i	$0.975573\pi$
$644$	18.8915	−	32.7210i	0.744428	−	1.28939i
$645$	32.4456			1.27754
$646$	2.57364	−	4.45768i	0.101259	−	0.175385i
$647$	24.3734	+	42.2159i	0.958215	+	1.65968i	0.726832	+	0.686815i	$0.240992\pi$
$647$	24.3734	+	42.2159i	0.958215	+	1.65968i	0.231383	+	0.972863i	$0.425675\pi$
$648$	−1.39094	−	2.40917i	−0.0546411	−	0.0946412i
$649$	2.45839			0.0965001
$650$	3.40095	+	10.0326i	0.133396	+	0.393509i
$651$	−14.4193			−0.565138
$652$	−10.9361	−	18.9419i	−0.428292	−	0.741823i
$653$	19.9255	+	34.5120i	0.779745	+	1.35056i	0.932088	+	0.362231i	$0.117985\pi$
$653$	19.9255	+	34.5120i	0.779745	+	1.35056i	−0.152343	+	0.988328i	$0.548682\pi$
$654$	5.67575	−	9.83069i	0.221940	−	0.384410i
$655$	2.40965			0.0941528
$656$	−0.618435	+	1.07116i	−0.0241458	+	0.0418218i
$657$	−4.94040	+	8.55702i	−0.192743	+	0.333841i
$658$	−17.6515			−0.688127
$659$	7.32245	−	12.6829i	0.285242	−	0.494054i	−0.687426	−	0.726255i	$-0.741259\pi$
$659$	7.32245	−	12.6829i	0.285242	−	0.494054i	0.972668	+	0.232201i	$0.0745926\pi$
$660$	−1.86385	−	3.22828i	−0.0725501	−	0.125660i
$661$	−22.2183	−	38.4833i	−0.864194	−	1.49683i	−0.867846	−	0.496834i	$-0.834496\pi$
$661$	−22.2183	−	38.4833i	−0.864194	−	1.49683i	0.00365216	−	0.999993i	$-0.498837\pi$
$662$	−2.60649			−0.101304
$663$	7.19006	+	1.43329i	0.279239	+	0.0556645i
$664$	25.0009			0.970224
$665$	19.2952	+	33.4203i	0.748236	+	1.29598i
$666$	−2.82456	−	4.89228i	−0.109450	−	0.189572i
$667$	14.9391	−	25.8752i	0.578443	−	1.00189i
$668$	−13.9179			−0.538501
$669$	−6.58472	+	11.4051i	−0.254580	+	0.440945i
$670$	−4.06369	+	7.03852i	−0.156994	+	0.271922i
$671$	−9.17511			−0.354201
$672$	12.7417	−	22.0693i	0.491522	−	0.851341i
$673$	−12.0182	−	20.8161i	−0.463266	−	0.802400i	0.535855	−	0.844310i	$-0.319989\pi$
$673$	−12.0182	−	20.8161i	−0.463266	−	0.802400i	−0.999121	+	0.0419094i	$0.986656\pi$
$674$	−2.28726	−	3.96164i	−0.0881018	−	0.152597i
$675$	−3.46542			−0.133384
$676$	13.2222	−	10.1283i	0.508544	−	0.389550i
$677$	17.5297			0.673722			0.336861	−	0.941554i	$-0.390635\pi$
$677$	17.5297			0.673722			0.336861	+	0.941554i	$0.390635\pi$
$678$	−7.98867	−	13.8368i	−0.306803	−	0.531399i
$679$	−2.27669	−	3.94334i	−0.0873713	−	0.151332i
$680$	−8.22914	+	14.2533i	−0.315573	+	0.546589i
$681$	27.7960			1.06515
$682$	1.37599	−	2.38329i	0.0526894	−	0.0912608i
$683$	10.4840	−	18.1588i	0.401159	−	0.694827i	−0.592707	−	0.805418i	$-0.701941\pi$
$683$	10.4840	−	18.1588i	0.401159	−	0.694827i	0.993866	+	0.110591i	$0.0352743\pi$
$684$	3.82531			0.146264
$685$	−13.6799	+	23.6943i	−0.522682	+	0.905312i
$686$	−10.7973	−	18.7014i	−0.412242	−	0.714024i
$687$	1.66082	+	2.87662i	0.0633640	+	0.109750i
$688$	2.27332			0.0866693
$689$	−5.39303	−	1.07507i	−0.205458	−	0.0409568i
$690$	16.3759			0.623419
$691$	19.4827	+	33.7450i	0.741157	+	1.28372i	0.951969	+	0.306194i	$0.0990557\pi$
$691$	19.4827	+	33.7450i	0.741157	+	1.28372i	−0.210812	+	0.977527i	$0.567611\pi$
$692$	6.43367	+	11.1434i	0.244571	+	0.423610i
$693$	−2.22113	+	3.84711i	−0.0843738	+	0.146140i
$694$	9.13103			0.346609
$695$	29.9512	−	51.8770i	1.13611	−	1.96781i
$696$	6.26016	−	10.8429i	0.237291	−	0.410999i
$697$	−12.3373			−0.467307
$698$	−7.42272	+	12.8565i	−0.280954	+	0.486627i
$699$	−2.56544	−	4.44347i	−0.0970338	−	0.168067i
$700$	−9.86157	−	17.0807i	−0.372732	−	0.645591i
$701$	−21.9718			−0.829862			−0.414931	−	0.909853i	$-0.636194\pi$
$701$	−21.9718			−0.829862			−0.414931	+	0.909853i	$0.636194\pi$
$702$	−0.981397	−	2.89505i	−0.0370404	−	0.109267i
$703$	19.8942			0.750324
$704$	2.22794	+	3.85891i	0.0839688	+	0.145438i
$705$	6.81815	+	11.8094i	0.256786	+	0.444767i
$706$	12.8341	−	22.2293i	0.483018	−	0.836611i
$707$	34.8659			1.31127
$708$	1.57484	−	2.72770i	0.0591861	−	0.102513i
$709$	1.93945	−	3.35922i	0.0728375	−	0.126158i	−0.827306	−	0.561751i	$-0.810128\pi$
$709$	1.93945	−	3.35922i	0.0728375	−	0.126158i	0.900144	+	0.435593i	$0.143461\pi$
$710$	23.7492			0.891290
$711$	−4.67321	+	8.09424i	−0.175259	+	0.303558i
$712$	−10.4971	−	18.1815i	−0.393395	−	0.681380i
$713$	−10.7742	−	18.6615i	−0.403498	−	0.698879i
$714$	7.65830			0.286604
$715$	−3.36794	−	9.93516i	−0.125954	−	0.371554i
$716$	19.0808			0.713085
$717$	−14.3124	−	24.7898i	−0.534505	−	0.925790i
$718$	2.10044	+	3.63807i	0.0783878	+	0.135772i
$719$	10.9581	−	18.9800i	0.408669	−	0.707836i	−0.586072	−	0.810259i	$-0.699326\pi$
$719$	10.9581	−	18.9800i	0.408669	−	0.707836i	0.994741	+	0.102423i	$0.0326596\pi$
$720$	−0.593134			−0.0221048
$721$	−39.2274	+	67.9439i	−1.46091	+	2.53036i
$722$	−4.27532	+	7.40507i	−0.159111	+	0.275588i
$723$	0.377338			0.0140333
$724$	15.0872	−	26.1318i	0.560712	−	0.971182i
$725$	−7.79837	−	13.5072i	−0.289624	−	0.501644i
$726$	−0.423911	−	0.734236i	−0.0157328	−	0.0272501i
$727$	4.35802			0.161630			0.0808150	−	0.996729i	$-0.474248\pi$
$727$	4.35802			0.161630			0.0808150	+	0.996729i	$0.474248\pi$
$728$	29.3922	−	33.4873i	1.08935	−	1.24112i
$729$	1.00000			0.0370370
$730$	−12.1868	−	21.1082i	−0.451055	−	0.781251i
$731$	11.3377	+	19.6374i	0.419339	+	0.726317i
$732$	−5.87756	+	10.1802i	−0.217241	+	0.376272i
$733$	−34.9092			−1.28940			−0.644701	−	0.764435i	$-0.723018\pi$
$733$	−34.9092			−1.28940			−0.644701	+	0.764435i	$0.723018\pi$
$734$	4.13942	−	7.16968i	0.152789	−	0.264638i
$735$	−18.5246	+	32.0856i	−0.683290	+	1.18349i
$736$	38.0828			1.40375
$737$	1.64737	−	2.85333i	0.0606817	−	0.105104i
$738$	2.57200	+	4.45483i	0.0946766	+	0.163985i
$739$	−8.89195	−	15.4013i	−0.327096	−	0.566546i	0.654839	−	0.755769i	$-0.272737\pi$
$739$	−8.89195	−	15.4013i	−0.327096	−	0.566546i	−0.981934	+	0.189222i	$0.939403\pi$
$740$	−24.8380			−0.913062
$741$	10.5575	+	2.10457i	0.387839	+	0.0773133i
$742$	−5.74424			−0.210878
$743$	−1.53018	−	2.65035i	−0.0561369	−	0.0972320i	0.836591	−	0.547828i	$-0.184545\pi$
$743$	−1.53018	−	2.65035i	−0.0561369	−	0.0972320i	−0.892728	+	0.450596i	$0.851212\pi$
$744$	−4.51490	−	7.82003i	−0.165524	−	0.286696i
$745$	16.3898	−	28.3879i	0.600474	−	1.04005i
$746$	32.3479			1.18434
$747$	−4.49354	+	7.78304i	−0.164410	+	0.284767i
$748$	1.30259	−	2.25616i	0.0476275	−	0.0824932i
$749$	1.72997			0.0632119
$750$	−1.89273	+	3.27830i	−0.0691127	+	0.119707i
$751$	−21.4319	−	37.1212i	−0.782063	−	1.35457i	−0.930738	−	0.365686i	$-0.880834\pi$
$751$	−21.4319	−	37.1212i	−0.782063	−	1.35457i	0.148675	−	0.988886i	$-0.452499\pi$
$752$	0.477717	+	0.827430i	0.0174205	+	0.0301733i
$753$	17.3265			0.631412
$754$	9.07555	−	10.3400i	0.330512	−	0.376562i
$755$	1.87488			0.0682339
$756$	2.84571	+	4.92891i	0.103497	+	0.179263i
$757$	8.57433	+	14.8512i	0.311640	+	0.539775i	0.978717	−	0.205212i	$-0.0657885\pi$
$757$	8.57433	+	14.8512i	0.311640	+	0.539775i	−0.667078	+	0.744988i	$0.732455\pi$
$758$	0.842175	−	1.45869i	0.0305892	−	0.0529820i
$759$	−6.63858			−0.240965
$760$	−12.0832	+	20.9287i	−0.438304	+	0.759165i
$761$	−8.43543	+	14.6106i	−0.305784	+	0.529633i	−0.977436	−	0.211234i	$-0.932252\pi$
$761$	−8.43543	+	14.6106i	−0.305784	+	0.529633i	0.671652	+	0.740867i	$0.265585\pi$
$762$	−0.354367			−0.0128374
$763$	−29.7388	+	51.5090i	−1.07662	+	1.86475i
$764$	7.33797	+	12.7097i	0.265478	+	0.459822i
$765$	−2.95813	−	5.12363i	−0.106951	−	0.185245i
$766$	−2.46275			−0.0889827
$767$	5.84710	−	6.66176i	0.211127	−	0.240542i
$768$	15.4361			0.557001
$769$	18.3888	+	31.8503i	0.663115	+	1.14855i	0.979793	+	0.200016i	$0.0640994\pi$
$769$	18.3888	+	31.8503i	0.663115	+	1.14855i	−0.316677	+	0.948533i	$0.602567\pi$
$770$	−5.47903	−	9.48996i	−0.197451	−	0.341994i
$771$	11.0176	−	19.0831i	0.396790	−	0.687261i
$772$	11.1357			0.400782
$773$	−13.8552	+	23.9979i	−0.498336	+	0.863143i	−0.999998	−	0.00192051i	$-0.999389\pi$
$773$	−13.8552	+	23.9979i	−0.498336	+	0.863143i	0.501662	+	0.865064i	$0.332722\pi$
$774$	4.72723	−	8.18780i	0.169917	−	0.294304i
$775$	−11.2486			−0.404060
$776$	1.42573	−	2.46943i	0.0511807	−	0.0886475i
$777$	14.7996	+	25.6337i	0.530933	+	0.919603i
$778$	2.21809	+	3.84184i	0.0795222	+	0.137737i
$779$	−18.1153			−0.649049
$780$	−13.1810	−	2.62756i	−0.471957	−	0.0940817i
$781$	−9.62762			−0.344503
$782$	5.72234	+	9.91138i	0.204630	+	0.354430i
$783$	2.25034	+	3.89770i	0.0804205	+	0.139292i
$784$	−1.29793	+	2.24809i	−0.0463548	+	0.0802889i
$785$	36.2123			1.29247
$786$	0.351079	−	0.608086i	0.0125226	−	0.0216897i
$787$	−10.4353	+	18.0745i	−0.371979	+	0.644286i	−0.989870	−	0.141977i	$-0.954654\pi$
$787$	−10.4353	+	18.0745i	−0.371979	+	0.644286i	0.617891	+	0.786264i	$0.287987\pi$
$788$	31.6448			1.12730
$789$	13.2526	−	22.9541i	0.471803	−	0.817188i
$790$	−11.5278	−	19.9667i	−0.410139	−	0.710382i
$791$	41.8576	+	72.4994i	1.48828	+	2.57778i
$792$	−2.78187			−0.0988496
$793$	−21.8224	+	24.8628i	−0.774935	+	0.882905i
$794$	−19.0227			−0.675089
$795$	2.21880	+	3.84307i	0.0786926	+	0.136300i
$796$	−14.0539	−	24.3421i	−0.498127	−	0.862782i
$797$	−15.5511	+	26.9353i	−0.550848	+	0.954097i	0.447365	+	0.894351i	$0.352362\pi$
$797$	−15.5511	+	26.9353i	−0.550848	+	0.954097i	−0.998214	+	0.0597460i	$0.980971\pi$
$798$	11.2450			0.398069
$799$	−4.76502	+	8.25326i	−0.168574	+	0.291980i
$800$	9.93984	−	17.2163i	0.351426	−	0.608688i
$801$	7.54677			0.266652
$802$	4.47910	−	7.75803i	0.158163	−	0.273945i
$803$	4.94040	+	8.55702i	0.174343	+	0.301971i
$804$	−2.11061	−	3.65568i	−0.0744353	−	0.128926i
$805$	−85.8033			−3.02417
$806$	−3.18556	−	9.39716i	−0.112206	−	0.331001i
$807$	−15.3936			−0.541880
$808$	10.9170	+	18.9088i	0.384059	+	0.665210i
$809$	−6.53132	−	11.3126i	−0.229629	−	0.397729i	0.728069	−	0.685504i	$-0.240418\pi$
$809$	−6.53132	−	11.3126i	−0.229629	−	0.397729i	−0.957698	+	0.287774i	$0.907085\pi$
$810$	−1.23339	+	2.13629i	−0.0433368	+	0.0750615i
$811$	4.78878			0.168157			0.0840784	−	0.996459i	$-0.473205\pi$
$811$	4.78878			0.168157			0.0840784	+	0.996459i	$0.473205\pi$
$812$	−12.8076	+	22.1834i	−0.449459	+	0.778485i
$813$	6.65436	−	11.5257i	0.233378	−	0.404223i
$814$	−5.64912			−0.198002
$815$	−24.8355	+	43.0163i	−0.869948	+	1.50679i
$816$	−0.207263	−	0.358989i	−0.00725564	−	0.0125671i
$817$	16.6476	+	28.8345i	0.582427	+	1.00879i
$818$	−21.0318			−0.735359
$819$	5.14214	+	15.1689i	0.179681	+	0.530045i
$820$	22.6170			0.789821
$821$	3.64990	+	6.32182i	0.127382	+	0.220633i	0.922662	−	0.385610i	$-0.126009\pi$
$821$	3.64990	+	6.32182i	0.127382	+	0.220633i	−0.795279	+	0.606243i	$0.792676\pi$
$822$	3.98624	+	6.90438i	0.139036	+	0.240818i
$823$	19.8524	−	34.3854i	0.692011	−	1.19860i	−0.279166	−	0.960243i	$-0.590058\pi$
$823$	19.8524	−	34.3854i	0.692011	−	1.19860i	0.971178	−	0.238356i	$-0.0766086\pi$
$824$	−49.1307			−1.71155
$825$	−1.73271	+	3.00114i	−0.0603252	+	0.104486i
$826$	4.62945	−	8.01845i	0.161079	−	0.278997i
$827$	−23.3190			−0.810883			−0.405441	−	0.914121i	$-0.632882\pi$
$827$	−23.3190			−0.810883			−0.405441	+	0.914121i	$0.632882\pi$
$828$	−4.25267	+	7.36583i	−0.147790	+	0.255980i
$829$	−7.61123	−	13.1830i	−0.264349	−	0.457866i	0.703044	−	0.711147i	$-0.251824\pi$
$829$	−7.61123	−	13.1830i	−0.264349	−	0.457866i	−0.967393	+	0.253281i	$0.918490\pi$
$830$	−11.0846	−	19.1990i	−0.384750	−	0.666407i
$831$	−3.68488			−0.127827
$832$	15.7559	+	3.14085i	0.546239	+	0.108889i
$833$	−25.8927			−0.897129
$834$	−8.72760	−	15.1166i	−0.302212	−	0.523446i
$835$	15.8035	+	27.3724i	0.546902	+	0.947263i
$836$	1.91265	−	3.31281i	0.0661505	−	0.114576i
$837$	3.24594			0.112196
$838$	13.5411	−	23.4539i	0.467770	−	0.810201i
$839$	8.99495	−	15.5797i	0.310540	−	0.537871i	−0.667939	−	0.744216i	$-0.732823\pi$
$839$	8.99495	−	15.5797i	0.310540	−	0.537871i	0.978479	+	0.206344i	$0.0661567\pi$
$840$	−35.9555			−1.24058
$841$	4.37196	−	7.57245i	0.150757	−	0.261119i
$842$	−13.8025	−	23.9066i	−0.475666	−	0.823877i
$843$	8.60726	+	14.9082i	0.296450	+	0.513466i
$844$	29.3645			1.01077
$845$	−34.9328	−	14.5036i	−1.20173	−	0.498940i
$846$	3.97354			0.136613
$847$	2.22113	+	3.84711i	0.0763190	+	0.132188i
$848$	0.155461	+	0.269266i	0.00533855	+	0.00924664i
$849$	9.69941	−	16.7999i	0.332883	−	0.576570i
$850$	5.97426			0.204915
$851$	−22.1168	+	38.3074i	−0.758153	+	1.31316i
$852$	−6.16744	+	10.6823i	−0.211293	+	0.365970i
$853$	−54.8726			−1.87880			−0.939400	−	0.342822i	$-0.888617\pi$
$853$	−54.8726			−1.87880			−0.939400	+	0.342822i	$0.888617\pi$
$854$	−17.2779	+	29.9262i	−0.591237	+	1.02405i
$855$	−4.34355	−	7.52325i	−0.148546	−	0.257290i
$856$	0.541680	+	0.938217i	0.0185142	+	0.0320676i
$857$	20.0447			0.684713			0.342356	−	0.939570i	$-0.388775\pi$
$857$	20.0447			0.684713			0.342356	+	0.939570i	$0.388775\pi$
$858$	−2.99788	−	0.597609i	−0.102346	−	0.0204021i
$859$	9.89952			0.337767			0.168884	−	0.985636i	$-0.445984\pi$
$859$	9.89952			0.337767			0.168884	+	0.985636i	$0.445984\pi$
$860$	−20.7846	−	36.0000i	−0.708749	−	1.22759i
$861$	−13.4763	−	23.3416i	−0.459270	−	0.795479i
$862$	1.32213	−	2.29000i	0.0450320	−	0.0779977i
$863$	34.2277			1.16512			0.582562	−	0.812786i	$-0.302050\pi$
$863$	34.2277			1.16512			0.582562	+	0.812786i	$0.302050\pi$
$864$	−2.86829	+	4.96803i	−0.0975812	+	0.169016i
$865$	14.6106	−	25.3062i	0.496774	−	0.860438i
$866$	26.0870			0.886472
$867$	−6.43264	+	11.1417i	−0.218464	+	0.378391i
$868$	9.23700	+	15.9989i	0.313524	+	0.543040i
$869$	4.67321	+	8.09424i	0.158528	+	0.274578i
$870$	−11.1022			−0.376398
$871$	−3.81383	−	11.2505i	−0.129227	−	0.381209i
$872$	−37.2465			−1.26133
$873$	0.512507	+	0.887688i	0.0173457	+	0.0300437i
$874$	8.40236	+	14.5533i	0.284214	+	0.492273i
$875$	9.91717	−	17.1770i	0.335262	−	0.580690i
$876$	12.6592			0.427716
$877$	−10.7882	+	18.6857i	−0.364292	+	0.630973i	−0.988662	−	0.150156i	$-0.952022\pi$
$877$	−10.7882	+	18.6857i	−0.364292	+	0.630973i	0.624370	+	0.781129i	$0.285356\pi$
$878$	−3.58017	+	6.20104i	−0.120825	+	0.209275i
$879$	−2.52774			−0.0852584
$880$	−0.296567	+	0.513669i	−0.00999726	+	0.0173158i
$881$	24.8200	+	42.9895i	0.836208	+	1.44835i	0.893043	+	0.449971i	$0.148566\pi$
$881$	24.8200	+	42.9895i	0.836208	+	1.44835i	−0.0568354	+	0.998384i	$0.518101\pi$
$882$	5.39796	+	9.34954i	0.181759	+	0.314815i
$883$	12.1133			0.407644			0.203822	−	0.979008i	$-0.434664\pi$
$883$	12.1133			0.407644			0.203822	+	0.979008i	$0.434664\pi$
$884$	−3.01563	−	8.89589i	−0.101427	−	0.299201i
$885$	−7.15278			−0.240438
$886$	8.84409	+	15.3184i	0.297123	+	0.514632i
$887$	9.11543	+	15.7884i	0.306066	+	0.530122i	0.977498	−	0.210944i	$-0.0676537\pi$
$887$	9.11543	+	15.7884i	0.306066	+	0.530122i	−0.671432	+	0.741066i	$0.734320\pi$
$888$	−9.26794	+	16.0525i	−0.311012	+	0.538688i
$889$	1.85675			0.0622732
$890$	−9.30809	+	16.1221i	−0.312008	+	0.540413i
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	16.8726			0.564938
$893$	−6.99670	+	12.1186i	−0.234136	+	0.405535i
$894$	−4.77588	−	8.27206i	−0.159729	−	0.276659i
$895$	−21.6659	−	37.5264i	−0.724210	−	1.25437i
$896$	−34.1848			−1.14203
$897$	−15.7894	+	17.9893i	−0.527193	+	0.600645i
$898$	−0.154600			−0.00515908
$899$	7.30447	+	12.6517i	0.243618	+	0.421958i
$900$	2.21994	+	3.84505i	0.0739981	+	0.128168i
$901$	−1.55066	+	2.68582i	−0.0516599	+	0.0894776i
$902$	5.14400			0.171276
$903$	−24.7688	+	42.9009i	−0.824256	+	1.42765i
$904$	−26.2124	+	45.4012i	−0.871812	+	1.51002i
$905$	−68.5248			−2.27784
$906$	0.273165	−	0.473135i	0.00907528	−	0.0157189i
$907$	−12.4647	−	21.5895i	−0.413884	−	0.716868i	0.581427	−	0.813599i	$-0.302495\pi$
$907$	−12.4647	−	21.5895i	−0.413884	−	0.716868i	−0.995311	+	0.0967310i	$0.969161\pi$
$908$	−17.8061	−	30.8411i	−0.590916	−	1.02350i
$909$	−7.84867			−0.260324
$910$	−38.7475	−	7.72407i	−1.28447	−	0.256050i
$911$	−0.835534			−0.0276825			−0.0138412	−	0.999904i	$-0.504406\pi$
$911$	−0.835534			−0.0276825			−0.0138412	+	0.999904i	$0.504406\pi$
$912$	−0.304333	−	0.527120i	−0.0100775	−	0.0174547i
$913$	4.49354	+	7.78304i	0.148715	+	0.257581i
$914$	8.69660	−	15.0630i	0.287658	−	0.498238i
$915$	26.6954			0.882521
$916$	2.12783	−	3.68551i	0.0703055	−	0.121773i
$917$	−1.83952	+	3.18614i	−0.0607462	+	0.105215i
$918$	−1.72396			−0.0568992
$919$	11.8486	−	20.5223i	0.390848	−	0.676968i	−0.601714	−	0.798712i	$-0.705515\pi$
$919$	11.8486	−	20.5223i	0.390848	−	0.676968i	0.992562	+	0.121744i	$0.0388486\pi$
$920$	−26.8663	−	46.5337i	−0.885754	−	1.53417i
$921$	−5.36715	−	9.29618i	−0.176854	−	0.306319i
$922$	16.7717			0.552347
$923$	−22.8986	+	26.0890i	−0.753717	+	0.858731i
$924$	5.69141			0.187234
$925$	11.5452	+	19.9969i	0.379604	+	0.657494i
$926$	−14.2356	−	24.6568i	−0.467812	−	0.810274i
$927$	8.83051	−	15.2949i	0.290032	−	0.502350i
$928$	−25.8185			−0.847534
$929$	−24.2769	+	42.0489i	−0.796500	+	1.37958i	0.125383	+	0.992108i	$0.459984\pi$
$929$	−24.2769	+	42.0489i	−0.796500	+	1.37958i	−0.921882	+	0.387470i	$0.873349\pi$
$930$	−4.00350	+	6.93427i	−0.131280	+	0.227384i
$931$	−38.0194			−1.24604
$932$	−3.28683	+	5.69296i	−0.107664	+	0.186479i
$933$	2.59634	+	4.49700i	0.0850005	+	0.147225i
$934$	1.47003	+	2.54617i	0.0481009	+	0.0833132i
$935$	−5.91626			−0.193482
$936$	−6.61649	+	7.53835i	−0.216267	+	0.246399i
$937$	−14.3113			−0.467530			−0.233765	−	0.972293i	$-0.575105\pi$
$937$	−14.3113			−0.467530			−0.233765	+	0.972293i	$0.575105\pi$
$938$	−6.20441	−	10.7464i	−0.202581	−	0.350881i
$939$	−3.24790	−	5.62553i	−0.105991	−	0.183582i
$940$	8.73539	−	15.1301i	0.284917	−	0.493491i
$941$	26.3874			0.860206			0.430103	−	0.902780i	$-0.358477\pi$
$941$	26.3874			0.860206			0.430103	+	0.902780i	$0.358477\pi$
$942$	5.27603	−	9.13835i	0.171902	−	0.297744i
$943$	20.1392	−	34.8820i	0.655821	−	1.13592i
$944$	−0.501162			−0.0163114
$945$	6.46247	−	11.1933i	0.210224	−	0.364119i
$946$	−4.72723	−	8.18780i	−0.153695	−	0.266208i
$947$	−24.5156	−	42.4622i	−0.796649	−	1.37984i	−0.921787	−	0.387697i	$-0.873271\pi$
$947$	−24.5156	−	42.4622i	−0.796649	−	1.37984i	0.125138	−	0.992139i	$-0.460063\pi$
$948$	11.9746			0.388917
$949$	34.9383	+	6.96473i	1.13414	+	0.226085i
$950$	8.77227			0.284610
$951$	7.76299	+	13.4459i	0.251732	+	0.436013i
$952$	−12.5642	−	21.7618i	−0.407208	−	0.705304i
$953$	5.19743	−	9.00222i	0.168361	−	0.291610i	−0.769483	−	0.638668i	$-0.779486\pi$
$953$	5.19743	−	9.00222i	0.168361	−	0.291610i	0.937844	+	0.347057i	$0.112819\pi$
$954$	1.29309			0.0418653
$955$	16.6642	−	28.8632i	0.539241	−	0.933992i
$956$	−18.3370	+	31.7605i	−0.593060	+	1.02721i
$957$	4.50068			0.145486
$958$	18.0583	−	31.2780i	0.583439	−	1.01055i
$959$	−20.8864	−	36.1763i	−0.674456	−	1.16819i
$960$	−6.48229	−	11.2277i	−0.209215	−	0.362371i
$961$	−20.4639			−0.660125
$962$	−13.4360	+	15.3081i	−0.433195	+	0.493551i
$963$	−0.389435			−0.0125494
$964$	−0.241722	−	0.418675i	−0.00778534	−	0.0134846i
$965$	−12.6443	−	21.9006i	−0.407035	−	0.705005i
$966$	−12.5013	+	21.6529i	−0.402222	+	0.696670i
$967$	−0.678023			−0.0218037			−0.0109019	−	0.999941i	$-0.503470\pi$
$967$	−0.678023			−0.0218037			−0.0109019	+	0.999941i	$0.503470\pi$
$968$	−1.39094	+	2.40917i	−0.0447064	+	0.0774337i
$969$	3.03559	−	5.25780i	0.0975173	−	0.168905i
$970$	−2.52848			−0.0811845
$971$	28.3531	−	49.1090i	0.909894	−	1.57598i	0.0956832	−	0.995412i	$-0.469496\pi$
$971$	28.3531	−	49.1090i	0.909894	−	1.57598i	0.814210	−	0.580570i	$-0.197170\pi$
$972$	−0.640598	−	1.10955i	−0.0205472	−	0.0355888i
$973$	45.7292	+	79.2053i	1.46601	+	2.53921i
$974$	18.0333			0.577825
$975$	4.01140	+	11.8333i	0.128468	+	0.378970i
$976$	1.87042			0.0598708
$977$	−25.7138	−	44.5375i	−0.822656	−	1.42488i	−0.903698	−	0.428171i	$-0.859158\pi$
$977$	−25.7138	−	44.5375i	−0.822656	−	1.42488i	0.0810415	−	0.996711i	$-0.474175\pi$
$978$	7.23690	+	12.5347i	0.231411	+	0.400815i
$979$	3.77339	−	6.53570i	0.120598	−	0.208882i
$980$	47.4673			1.51629
$981$	6.69450	−	11.5952i	0.213739	−	0.370207i
$982$	7.03415	−	12.1835i	0.224469	−	0.388791i
$983$	0.743742			0.0237217			0.0118608	−	0.999930i	$-0.496224\pi$
$983$	0.743742			0.0237217			0.0118608	+	0.999930i	$0.496224\pi$
$984$	8.43923	−	14.6172i	0.269033	−	0.465979i
$985$	−35.9319	−	62.2359i	−1.14489	−	1.98300i
$986$	−3.87950	−	6.71949i	−0.123548	−	0.213992i
$987$	−20.8198			−0.662702
$988$	−4.42798	−	13.0622i	−0.140873	−	0.415565i
$989$	−74.0299			−2.35401
$990$	1.23339	+	2.13629i	0.0391996	+	0.0678957i
$991$	19.9154	+	34.4945i	0.632635	+	1.09576i	0.987011	+	0.160652i	$0.0513598\pi$
$991$	19.9154	+	34.4945i	0.632635	+	1.09576i	−0.354376	+	0.935103i	$0.615307\pi$
$992$	−9.31030	+	16.1259i	−0.295602	+	0.511998i
$993$	−3.07434			−0.0975611
$994$	−18.1300	+	31.4021i	−0.575049	+	0.996015i
$995$	−31.9158	+	55.2797i	−1.01180	+	1.75249i
$996$	11.5142			0.364842
$997$	11.0410	−	19.1235i	0.349671	−	0.605647i	−0.636520	−	0.771260i	$-0.719627\pi$
$997$	11.0410	−	19.1235i	0.349671	−	0.605647i	0.986191	+	0.165613i	$0.0529601\pi$
$998$	12.7470	+	22.0785i	0.403500	+	0.698882i
$999$	−3.33155	−	5.77041i	−0.105406	−	0.182568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.e.133.3	yes	10
13.3	even	3		5577.2.a.o.1.3		5
13.9	even	3	inner	429.2.i.e.100.3	✓	10
13.10	even	6		5577.2.a.u.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.e.100.3	✓	10	13.9	even	3	inner
429.2.i.e.133.3	yes	10	1.1	even	1	trivial
5577.2.a.o.1.3		5	13.3	even	3
5577.2.a.u.1.3		5	13.10	even	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.423911 + 0.734236i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.640598 - 1.10955i) q^{4} -2.90954 q^{5} +(-0.423911 + 0.734236i) q^{6} +(2.22113 - 3.84711i) q^{7} +2.78187 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.423911 + 0.734236i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.640598 - 1.10955i) q^{4} -2.90954 q^{5} +(-0.423911 + 0.734236i) q^{6} +(2.22113 - 3.84711i) q^{7} +2.78187 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.23339 - 2.13629i) q^{10} +(0.500000 + 0.866025i) q^{11} +1.28120 q^{12} +(3.53598 + 0.704876i) q^{13} +3.76625 q^{14} +(-1.45477 - 2.51974i) q^{15} +(-0.101929 - 0.176546i) q^{16} +(1.01670 - 1.76098i) q^{17} -0.847823 q^{18} +(1.49287 - 2.58572i) q^{19} +(-1.86385 + 3.22828i) q^{20} +4.44226 q^{21} +(-0.423911 + 0.734236i) q^{22} +(3.31929 + 5.74918i) q^{23} +(1.39094 + 2.40917i) q^{24} +3.46542 q^{25} +(0.981397 + 2.89505i) q^{26} -1.00000 q^{27} +(-2.84571 - 4.92891i) q^{28} +(-2.25034 - 3.89770i) q^{29} +(1.23339 - 2.13629i) q^{30} -3.24594 q^{31} +(2.86829 - 4.96803i) q^{32} +(-0.500000 + 0.866025i) q^{33} +1.72396 q^{34} +(-6.46247 + 11.1933i) q^{35} +(0.640598 + 1.10955i) q^{36} +(3.33155 + 5.77041i) q^{37} +2.53137 q^{38} +(1.15755 + 3.41469i) q^{39} -8.09397 q^{40} +(-3.03365 - 5.25444i) q^{41} +(1.88313 + 3.26167i) q^{42} +(-5.57573 + 9.65744i) q^{43} +1.28120 q^{44} +(1.45477 - 2.51974i) q^{45} +(-2.81417 + 4.87429i) q^{46} -4.68676 q^{47} +(0.101929 - 0.176546i) q^{48} +(-6.36685 - 11.0277i) q^{49} +(1.46903 + 2.54444i) q^{50} +2.03340 q^{51} +(3.04724 - 3.47180i) q^{52} -1.52519 q^{53} +(-0.423911 - 0.734236i) q^{54} +(-1.45477 - 2.51974i) q^{55} +(6.17891 - 10.7022i) q^{56} +2.98573 q^{57} +(1.90789 - 3.30456i) q^{58} +(1.22919 - 2.12903i) q^{59} -3.72769 q^{60} +(-4.58756 + 7.94588i) q^{61} +(-1.37599 - 2.38329i) q^{62} +(2.22113 + 3.84711i) q^{63} +4.45589 q^{64} +(-10.2881 - 2.05086i) q^{65} -0.847823 q^{66} +(-1.64737 - 2.85333i) q^{67} +(-1.30259 - 2.25616i) q^{68} +(-3.31929 + 5.74918i) q^{69} -10.9581 q^{70} +(-4.81381 + 8.33776i) q^{71} +(-1.39094 + 2.40917i) q^{72} +9.88080 q^{73} +(-2.82456 + 4.89228i) q^{74} +(1.73271 + 3.00114i) q^{75} +(-1.91265 - 3.31281i) q^{76} +4.44226 q^{77} +(-2.01649 + 2.29744i) q^{78} +9.34642 q^{79} +(0.296567 + 0.513669i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.57200 - 4.45483i) q^{82} +8.98708 q^{83} +(2.84571 - 4.92891i) q^{84} +(-2.95813 + 5.12363i) q^{85} -9.45446 q^{86} +(2.25034 - 3.89770i) q^{87} +(1.39094 + 2.40917i) q^{88} +(-3.77339 - 6.53570i) q^{89} +2.46677 q^{90} +(10.5656 - 12.0377i) q^{91} +8.50533 q^{92} +(-1.62297 - 2.81107i) q^{93} +(-1.98677 - 3.44119i) q^{94} +(-4.34355 + 7.52325i) q^{95} +5.73658 q^{96} +(0.512507 - 0.887688i) q^{97} +(5.39796 - 9.34954i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

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