LMFDB - Embedded newform 429.2.n.c.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	429.235
Dual form			429.2.n.c.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05353 - 1.49197i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.37295 + 4.22550i) q^{4} +(-3.43019 + 2.49218i) q^{5} +(2.05353 - 1.49197i) q^{6} +(0.899200 + 2.76745i) q^{7} +(1.91620 - 5.89746i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-2.05353 - 1.49197i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.37295 + 4.22550i) q^{4} +(-3.43019 + 2.49218i) q^{5} +(2.05353 - 1.49197i) q^{6} +(0.899200 + 2.76745i) q^{7} +(1.91620 - 5.89746i) q^{8} +(-0.809017 - 0.587785i) q^{9} +10.7623 q^{10} +(3.13933 + 1.06986i) q^{11} -4.44296 q^{12} +(-0.809017 - 0.587785i) q^{13} +(2.28244 - 7.02462i) q^{14} +(-1.31022 - 4.03243i) q^{15} +(-5.54497 + 4.02866i) q^{16} +(-0.626709 + 0.455331i) q^{17} +(0.784377 + 2.41407i) q^{18} +(-2.41669 + 7.43781i) q^{19} +(-15.2402 - 11.0726i) q^{20} -2.90987 q^{21} +(-4.85049 - 6.88079i) q^{22} -3.36268 q^{23} +(5.01668 + 3.64483i) q^{24} +(4.01016 - 12.3420i) q^{25} +(0.784377 + 2.41407i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-10.4593 + 7.59915i) q^{28} +(-0.289444 - 0.890816i) q^{29} +(-3.32572 + 10.2355i) q^{30} +(-3.28474 - 2.38651i) q^{31} +4.99548 q^{32} +(-1.98761 + 2.65507i) q^{33} +1.96631 q^{34} +(-9.98142 - 7.25192i) q^{35} +(1.37295 - 4.22550i) q^{36} +(-1.44029 - 4.43274i) q^{37} +(16.0598 - 11.6681i) q^{38} +(0.809017 - 0.587785i) q^{39} +(8.12459 + 25.0049i) q^{40} +(-0.615421 + 1.89407i) q^{41} +(5.97550 + 4.34145i) q^{42} +3.54317 q^{43} +(-0.210571 + 14.7341i) q^{44} +4.23995 q^{45} +(6.90536 + 5.01703i) q^{46} +(-1.43367 + 4.41239i) q^{47} +(-2.11799 - 6.51850i) q^{48} +(-1.18712 + 0.862491i) q^{49} +(-26.6490 + 19.3616i) q^{50} +(-0.239382 - 0.736741i) q^{51} +(1.37295 - 4.22550i) q^{52} +(-6.46262 - 4.69537i) q^{53} -2.53830 q^{54} +(-13.4348 + 4.15394i) q^{55} +18.0440 q^{56} +(-6.32698 - 4.59682i) q^{57} +(-0.734694 + 2.26116i) q^{58} +(2.90367 + 8.93657i) q^{59} +(15.2402 - 11.0726i) q^{60} +(4.52572 - 3.28813i) q^{61} +(3.18470 + 9.80150i) q^{62} +(0.899200 - 2.76745i) q^{63} +(0.831591 + 0.604186i) q^{64} +4.23995 q^{65} +(8.04291 - 2.48681i) q^{66} -13.2680 q^{67} +(-2.78444 - 2.02302i) q^{68} +(1.03913 - 3.19810i) q^{69} +(9.67742 + 29.7840i) q^{70} +(8.27322 - 6.01084i) q^{71} +(-5.01668 + 3.64483i) q^{72} +(-0.616317 - 1.89683i) q^{73} +(-3.65587 + 11.2516i) q^{74} +(10.4987 + 7.62779i) q^{75} -34.7465 q^{76} +(-0.137912 + 9.64997i) q^{77} -2.53830 q^{78} +(-5.01552 - 3.64399i) q^{79} +(8.98017 - 27.6381i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.08969 - 2.97133i) q^{82} +(13.9807 - 10.1576i) q^{83} +(-3.99511 - 12.2957i) q^{84} +(1.01497 - 3.12374i) q^{85} +(-7.27598 - 5.28631i) q^{86} +0.936659 q^{87} +(12.3251 - 16.4640i) q^{88} +1.56195 q^{89} +(-8.70685 - 6.32589i) q^{90} +(0.899200 - 2.76745i) q^{91} +(-4.61679 - 14.2090i) q^{92} +(3.28474 - 2.38651i) q^{93} +(9.52725 - 6.92195i) q^{94} +(-10.2466 - 31.5359i) q^{95} +(-1.54369 + 4.75098i) q^{96} +(-7.32906 - 5.32487i) q^{97} +3.72459 q^{98} +(-1.91092 - 2.71079i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) $ 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.05353	−	1.49197i	−1.45206	−	1.05499i	−0.985344	−	0.170579i	$-0.945436\pi$
$2$	−2.05353	−	1.49197i	−1.45206	−	1.05499i	−0.466718	−	0.884406i	$-0.654564\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	1.37295	+	4.22550i	0.686475	+	2.11275i
$5$	−3.43019	+	2.49218i	−1.53403	+	1.11454i	−0.580082	+	0.814558i	$0.696979\pi$
$5$	−3.43019	+	2.49218i	−1.53403	+	1.11454i	−0.953946	+	0.299978i	$0.903021\pi$
$6$	2.05353	−	1.49197i	0.838349	−	0.609096i
$7$	0.899200	+	2.76745i	0.339866	+	1.04600i	0.964275	+	0.264902i	$0.0853396\pi$
$7$	0.899200	+	2.76745i	0.339866	+	1.04600i	−0.624410	+	0.781097i	$0.714660\pi$
$8$	1.91620	−	5.89746i	0.677479	−	2.08507i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	10.7623			3.40332
$11$	3.13933	+	1.06986i	0.946544	+	0.322576i
$11$	3.13933	+	1.06986i	0.946544	+	0.322576i
$12$	−4.44296			−1.28257
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$13$	−0.809017	−	0.587785i	−0.224381	−	0.163022i
$14$	2.28244	−	7.02462i	0.610007	−	1.87741i
$15$	−1.31022	−	4.03243i	−0.338296	−	1.04117i
$16$	−5.54497	+	4.02866i	−1.38624	+	1.00716i
$17$	−0.626709	+	0.455331i	−0.151999	+	0.110434i	−0.661186	−	0.750222i	$-0.729946\pi$
$17$	−0.626709	+	0.455331i	−0.151999	+	0.110434i	0.509186	+	0.860656i	$0.329946\pi$
$18$	0.784377	+	2.41407i	0.184879	+	0.569001i
$19$	−2.41669	+	7.43781i	−0.554427	+	1.70635i	0.143025	+	0.989719i	$0.454317\pi$
$19$	−2.41669	+	7.43781i	−0.554427	+	1.70635i	−0.697452	+	0.716632i	$0.745683\pi$
$20$	−15.2402	−	11.0726i	−3.40781	−	2.47592i
$21$	−2.90987			−0.634986
$22$	−4.85049	−	6.88079i	−1.03413	−	1.46699i
$23$	−3.36268			−0.701168			−0.350584	−	0.936531i	$-0.614017\pi$
$23$	−3.36268			−0.701168			−0.350584	+	0.936531i	$0.614017\pi$
$24$	5.01668	+	3.64483i	1.02403	+	0.743998i
$25$	4.01016	−	12.3420i	0.802033	−	2.46840i
$26$	0.784377	+	2.41407i	0.153829	+	0.473437i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−10.4593	+	7.59915i	−1.97663	+	1.43610i
$29$	−0.289444	−	0.890816i	−0.0537483	−	0.165420i	0.920579	−	0.390556i	$-0.127717\pi$
$29$	−0.289444	−	0.890816i	−0.0537483	−	0.165420i	−0.974327	+	0.225136i	$0.927717\pi$
$30$	−3.32572	+	10.2355i	−0.607191	+	1.86874i
$31$	−3.28474	−	2.38651i	−0.589957	−	0.428629i	0.252343	−	0.967638i	$-0.418799\pi$
$31$	−3.28474	−	2.38651i	−0.589957	−	0.428629i	−0.842300	+	0.539009i	$0.818799\pi$
$32$	4.99548			0.883084
$33$	−1.98761	+	2.65507i	−0.345998	+	0.462189i
$34$	1.96631			0.337219
$35$	−9.98142	−	7.25192i	−1.68717	−	1.22580i
$36$	1.37295	−	4.22550i	0.228825	−	0.704251i
$37$	−1.44029	−	4.43274i	−0.236781	−	0.728738i	−0.996880	−	0.0789307i	$-0.974849\pi$
$37$	−1.44029	−	4.43274i	−0.236781	−	0.728738i	0.760099	−	0.649808i	$-0.225151\pi$
$38$	16.0598	−	11.6681i	2.60524	−	1.89282i
$39$	0.809017	−	0.587785i	0.129546	−	0.0941210i
$40$	8.12459	+	25.0049i	1.28461	+	3.95363i
$41$	−0.615421	+	1.89407i	−0.0961126	+	0.295804i	−0.987542	−	0.157355i	$-0.949703\pi$
$41$	−0.615421	+	1.89407i	−0.0961126	+	0.295804i	0.891429	+	0.453160i	$0.149703\pi$
$42$	5.97550	+	4.34145i	0.922040	+	0.669901i
$43$	3.54317			0.540328			0.270164	−	0.962814i	$-0.412922\pi$
$43$	3.54317			0.540328			0.270164	+	0.962814i	$0.412922\pi$
$44$	−0.210571	+	14.7341i	−0.0317448	+	2.22125i
$45$	4.23995			0.632054
$46$	6.90536	+	5.01703i	1.01814	+	0.739721i
$47$	−1.43367	+	4.41239i	−0.209123	+	0.643613i	0.790396	+	0.612596i	$0.209875\pi$
$47$	−1.43367	+	4.41239i	−0.209123	+	0.643613i	−0.999519	+	0.0310171i	$0.990125\pi$
$48$	−2.11799	−	6.51850i	−0.305705	−	0.940865i
$49$	−1.18712	+	0.862491i	−0.169588	+	0.123213i
$50$	−26.6490	+	19.3616i	−3.76873	+	2.73814i
$51$	−0.239382	−	0.736741i	−0.0335201	−	0.103164i
$52$	1.37295	−	4.22550i	0.190394	−	0.585972i
$53$	−6.46262	−	4.69537i	−0.887710	−	0.644959i	0.0475702	−	0.998868i	$-0.484852\pi$
$53$	−6.46262	−	4.69537i	−0.887710	−	0.644959i	−0.935280	+	0.353909i	$0.884852\pi$
$54$	−2.53830			−0.345419
$55$	−13.4348	+	4.15394i	−1.81155	+	0.560117i
$56$	18.0440			2.41123
$57$	−6.32698	−	4.59682i	−0.838029	−	0.608864i
$58$	−0.734694	+	2.26116i	−0.0964700	+	0.296904i
$59$	2.90367	+	8.93657i	0.378025	+	1.16344i	0.941415	+	0.337251i	$0.109497\pi$
$59$	2.90367	+	8.93657i	0.378025	+	1.16344i	−0.563389	+	0.826192i	$0.690503\pi$
$60$	15.2402	−	11.0726i	1.96750	−	1.42947i
$61$	4.52572	−	3.28813i	0.579459	−	0.421001i	−0.259070	−	0.965858i	$-0.583416\pi$
$61$	4.52572	−	3.28813i	0.579459	−	0.421001i	0.838529	+	0.544857i	$0.183416\pi$
$62$	3.18470	+	9.80150i	0.404458	+	1.24479i
$63$	0.899200	−	2.76745i	0.113289	−	0.348666i
$64$	0.831591	+	0.604186i	0.103949	+	0.0755233i
$65$	4.23995			0.525901
$66$	8.04291	−	2.48681i	0.990013	−	0.306105i
$67$	−13.2680			−1.62095			−0.810474	−	0.585775i	$-0.800790\pi$
$67$	−13.2680			−1.62095			−0.810474	+	0.585775i	$0.800790\pi$
$68$	−2.78444	−	2.02302i	−0.337663	−	0.245327i
$69$	1.03913	−	3.19810i	0.125096	−	0.385006i
$70$	9.67742	+	29.7840i	1.15667	+	3.55987i
$71$	8.27322	−	6.01084i	0.981850	−	0.713356i	0.0237289	−	0.999718i	$-0.492446\pi$
$71$	8.27322	−	6.01084i	0.981850	−	0.713356i	0.958121	+	0.286362i	$0.0924461\pi$
$72$	−5.01668	+	3.64483i	−0.591221	+	0.429547i
$73$	−0.616317	−	1.89683i	−0.0721345	−	0.222007i	0.908489	−	0.417908i	$-0.137237\pi$
$73$	−0.616317	−	1.89683i	−0.0721345	−	0.222007i	−0.980624	+	0.195901i	$0.937237\pi$
$74$	−3.65587	+	11.2516i	−0.424987	+	1.30797i
$75$	10.4987	+	7.62779i	1.21229	+	0.880781i
$76$	−34.7465			−3.98570
$77$	−0.137912	+	9.64997i	−0.0157165	+	1.09972i
$78$	−2.53830			−0.287406
$79$	−5.01552	−	3.64399i	−0.564290	−	0.409981i	0.268736	−	0.963214i	$-0.413394\pi$
$79$	−5.01552	−	3.64399i	−0.564290	−	0.409981i	−0.833027	+	0.553233i	$0.813394\pi$
$80$	8.98017	−	27.6381i	1.00401	−	3.09003i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	4.08969	−	2.97133i	0.451631	−	0.328129i
$83$	13.9807	−	10.1576i	1.53459	−	1.11494i	0.580965	−	0.813929i	$-0.302675\pi$
$83$	13.9807	−	10.1576i	1.53459	−	1.11494i	0.953620	−	0.301013i	$-0.0973247\pi$
$84$	−3.99511	−	12.2957i	−0.435902	−	1.34157i
$85$	1.01497	−	3.12374i	0.110089	−	0.338818i
$86$	−7.27598	−	5.28631i	−0.784589	−	0.570038i
$87$	0.936659			0.100420
$88$	12.3251	−	16.4640i	1.31386	−	1.75507i
$89$	1.56195			0.165566			0.0827831	−	0.996568i	$-0.473619\pi$
$89$	1.56195			0.165566			0.0827831	+	0.996568i	$0.473619\pi$
$90$	−8.70685	−	6.32589i	−0.917782	−	0.666808i
$91$	0.899200	−	2.76745i	0.0942618	−	0.290108i
$92$	−4.61679	−	14.2090i	−0.481334	−	1.48139i
$93$	3.28474	−	2.38651i	0.340612	−	0.247469i
$94$	9.52725	−	6.92195i	0.982661	−	0.713945i
$95$	−10.2466	−	31.5359i	−1.05128	−	3.23552i
$96$	−1.54369	+	4.75098i	−0.157552	+	0.484895i
$97$	−7.32906	−	5.32487i	−0.744153	−	0.540659i	0.149856	−	0.988708i	$-0.452119\pi$
$97$	−7.32906	−	5.32487i	−0.744153	−	0.540659i	−0.894009	+	0.448049i	$0.852119\pi$
$98$	3.72459			0.376241
$99$	−1.91092	−	2.71079i	−0.192055	−	0.272445i
$100$	57.6570			5.76570
$101$	2.49382	+	1.81187i	0.248144	+	0.180287i	0.704904	−	0.709303i	$-0.250990\pi$
$101$	2.49382	+	1.81187i	0.248144	+	0.180287i	−0.456760	+	0.889590i	$0.650990\pi$
$102$	−0.607622	+	1.87007i	−0.0601635	+	0.185164i
$103$	−2.54026	−	7.81813i	−0.250300	−	0.770343i	−0.994719	−	0.102631i	$-0.967274\pi$
$103$	−2.54026	−	7.81813i	−0.250300	−	0.770343i	0.744420	−	0.667712i	$-0.232726\pi$
$104$	−5.01668	+	3.64483i	−0.491926	+	0.357405i
$105$	9.98142	−	7.25192i	0.974087	−	0.707715i
$106$	6.26580	+	19.2841i	0.608588	+	1.87304i
$107$	−5.82809	+	17.9370i	−0.563423	+	1.73404i	0.109169	+	0.994023i	$0.465181\pi$
$107$	−5.82809	+	17.9370i	−0.563423	+	1.73404i	−0.672592	+	0.740013i	$0.734819\pi$
$108$	3.59443	+	2.61150i	0.345874	+	0.251292i
$109$	−10.7130			−1.02612			−0.513061	−	0.858352i	$-0.671488\pi$
$109$	−10.7130			−1.02612			−0.513061	+	0.858352i	$0.671488\pi$
$110$	33.7863	+	11.5141i	3.22139	+	1.09783i
$111$	4.66086			0.442389
$112$	−16.1351	−	11.7229i	−1.52463	−	1.10771i
$113$	1.34981	−	4.15430i	0.126980	−	0.390804i	−0.867277	−	0.497826i	$-0.834132\pi$
$113$	1.34981	−	4.15430i	0.126980	−	0.390804i	0.994257	+	0.107023i	$0.0341317\pi$
$114$	6.13428	+	18.8794i	0.574528	+	1.76822i
$115$	11.5346	−	8.38041i	1.07561	−	0.781477i
$116$	3.36675	−	2.44609i	0.312595	−	0.227114i
$117$	0.309017	+	0.951057i	0.0285686	+	0.0879252i
$118$	7.37038	−	22.6837i	0.678498	−	2.08820i
$119$	−1.82364	−	1.32495i	−0.167173	−	0.121458i
$120$	−26.2917			−2.40010
$121$	8.71078	+	6.71731i	0.791889	+	0.610664i
$122$	−14.1995			−1.28556
$123$	−1.61119	−	1.17060i	−0.145276	−	0.105550i
$124$	5.57440	−	17.1562i	0.500596	−	1.54068i
$125$	10.4518	+	32.1674i	0.934838	+	2.87714i
$126$	−5.97550	+	4.34145i	−0.532340	+	0.386768i
$127$	0.116965	−	0.0849802i	0.0103790	−	0.00754078i	−0.582584	−	0.812771i	$-0.697958\pi$
$127$	0.116965	−	0.0849802i	0.0103790	−	0.00754078i	0.592963	+	0.805230i	$0.297958\pi$
$128$	−3.89364	−	11.9834i	−0.344152	−	1.05919i
$129$	−1.09490	+	3.36975i	−0.0964004	+	0.296690i
$130$	−8.70685	−	6.32589i	−0.763641	−	0.554818i
$131$	4.28002			0.373947			0.186974	−	0.982365i	$-0.440132\pi$
$131$	4.28002			0.373947			0.186974	+	0.982365i	$0.440132\pi$
$132$	−13.9479	−	4.75336i	−1.21401	−	0.413727i
$133$	−22.7569			−1.97327
$134$	27.2462	+	19.7956i	2.35372	+	1.71008i
$135$	−1.31022	+	4.03243i	−0.112765	+	0.347056i
$136$	1.48439	+	4.56850i	0.127286	+	0.391745i
$137$	−9.44724	+	6.86382i	−0.807132	+	0.586416i	−0.912998	−	0.407965i	$-0.866239\pi$
$137$	−9.44724	+	6.86382i	−0.807132	+	0.586416i	0.105866	+	0.994380i	$0.466239\pi$
$138$	−6.90536	+	5.01703i	−0.587823	+	0.427078i
$139$	7.07374	+	21.7707i	0.599987	+	1.84657i	0.528146	+	0.849154i	$0.322887\pi$
$139$	7.07374	+	21.7707i	0.599987	+	1.84657i	0.0718412	+	0.997416i	$0.477113\pi$
$140$	16.9391	−	52.1330i	1.43161	−	4.40605i
$141$	−3.75340	−	2.72701i	−0.316093	−	0.229655i
$142$	−25.9573			−2.17829
$143$	−1.91092	−	2.71079i	−0.159799	−	0.226688i
$144$	6.85396			0.571163
$145$	3.21292	+	2.33432i	0.266818	+	0.193855i
$146$	−1.56440	+	4.81472i	−0.129470	+	0.398469i
$147$	−0.453438	−	1.39554i	−0.0373990	−	0.115102i
$148$	16.7531	−	12.1719i	1.37710	−	1.00052i
$149$	−7.61950	+	5.53589i	−0.624214	+	0.453518i	−0.854391	−	0.519631i	$-0.826070\pi$
$149$	−7.61950	+	5.53589i	−0.624214	+	0.453518i	0.230177	+	0.973149i	$0.426070\pi$
$150$	−10.1790	−	31.3277i	−0.831111	−	2.55790i
$151$	−0.881867	+	2.71411i	−0.0717653	+	0.220871i	−0.980506	−	0.196491i	$-0.937045\pi$
$151$	−0.881867	+	2.71411i	−0.0717653	+	0.220871i	0.908740	+	0.417362i	$0.137045\pi$
$152$	39.2333	+	28.5047i	3.18224	+	2.31203i
$153$	0.774655			0.0626272
$154$	14.6807	−	19.6107i	1.18301	−	1.58028i
$155$	17.2149			1.38273
$156$	3.59443	+	2.61150i	0.287785	+	0.209088i
$157$	1.20738	−	3.71595i	0.0963597	−	0.296565i	−0.891246	−	0.453520i	$-0.850168\pi$
$157$	1.20738	−	3.71595i	0.0963597	−	0.296565i	0.987606	+	0.156956i	$0.0501680\pi$
$158$	4.86277	+	14.9661i	0.386861	+	1.19064i
$159$	6.46262	−	4.69537i	0.512519	−	0.372367i
$160$	−17.1354	+	12.4496i	−1.35468	+	0.984229i
$161$	−3.02372	−	9.30606i	−0.238303	−	0.733421i
$162$	0.784377	−	2.41407i	0.0616265	−	0.189667i
$163$	3.63845	+	2.64349i	0.284985	+	0.207054i	0.721089	−	0.692842i	$-0.243642\pi$
$163$	3.63845	+	2.64349i	0.284985	+	0.207054i	−0.436104	+	0.899896i	$0.643642\pi$
$164$	−8.84835			−0.690940
$165$	0.200950	−	14.0609i	0.0156439	−	1.09464i
$166$	−43.8647			−3.40456
$167$	−11.4583	−	8.32495i	−0.886670	−	0.644204i	0.0483375	−	0.998831i	$-0.484608\pi$
$167$	−11.4583	−	8.32495i	−0.886670	−	0.644204i	−0.935008	+	0.354627i	$0.884608\pi$
$168$	−5.57590	+	17.1609i	−0.430190	+	1.32399i
$169$	0.309017	+	0.951057i	0.0237705	+	0.0731582i
$170$	−6.74480	+	4.90039i	−0.517303	+	0.375843i
$171$	6.32698	−	4.59682i	0.483836	−	0.351528i
$172$	4.86459	+	14.9717i	0.370921	+	1.14158i
$173$	−5.76564	+	17.7448i	−0.438353	+	1.34911i	0.451258	+	0.892394i	$0.350975\pi$
$173$	−5.76564	+	17.7448i	−0.438353	+	1.34911i	−0.889611	+	0.456719i	$0.849025\pi$
$174$	−1.92345	−	1.39747i	−0.145817	−	0.105942i
$175$	37.7619			2.85453
$176$	−21.7176	+	6.71492i	−1.63703	+	0.506156i
$177$	−9.39647			−0.706282
$178$	−3.20750	−	2.33039i	−0.240413	−	0.174670i
$179$	4.58270	−	14.1041i	0.342527	−	1.05419i	−0.620368	−	0.784311i	$-0.713017\pi$
$179$	4.58270	−	14.1041i	0.342527	−	1.05419i	0.962895	−	0.269878i	$-0.0869834\pi$
$180$	5.82124	+	17.9159i	0.433889	+	1.33537i
$181$	−10.3293	+	7.50464i	−0.767767	+	0.557816i	−0.901283	−	0.433231i	$-0.857373\pi$
$181$	−10.3293	+	7.50464i	−0.767767	+	0.557816i	0.133515	+	0.991047i	$0.457373\pi$
$182$	−5.97550	+	4.34145i	−0.442934	+	0.321810i
$183$	1.72867	+	5.32030i	0.127787	+	0.393288i
$184$	−6.44357	+	19.8313i	−0.475026	+	1.46198i
$185$	15.9876	+	11.6157i	1.17543	+	0.854003i
$186$	−10.3059			−0.755666
$187$	−2.45459	+	0.758941i	−0.179497	+	0.0554992i
$188$	−20.6129			−1.50335
$189$	2.35414	+	1.71038i	0.171238	+	0.124412i
$190$	−26.0090	+	80.0476i	−1.88689	+	5.80726i
$191$	−1.03127	−	3.17391i	−0.0746199	−	0.229656i	0.906789	−	0.421585i	$-0.138526\pi$
$191$	−1.03127	−	3.17391i	−0.0746199	−	0.229656i	−0.981409	+	0.191928i	$0.938526\pi$
$192$	−0.831591	+	0.604186i	−0.0600149	+	0.0436034i
$193$	−15.2261	+	11.0624i	−1.09600	+	0.796291i	−0.980403	−	0.197005i	$-0.936879\pi$
$193$	−15.2261	+	11.0624i	−1.09600	+	0.796291i	−0.115598	+	0.993296i	$0.536879\pi$
$194$	7.10584	+	21.8695i	0.510170	+	1.57014i
$195$	−1.31022	+	4.03243i	−0.0938265	+	0.288768i
$196$	−5.27431	−	3.83201i	−0.376737	−	0.273715i
$197$	7.88673			0.561907			0.280953	−	0.959721i	$-0.409349\pi$
$197$	7.88673			0.561907			0.280953	+	0.959721i	$0.409349\pi$
$198$	−0.120301	+	8.41772i	−0.00854942	+	0.598222i
$199$	6.64393			0.470976			0.235488	−	0.971877i	$-0.424331\pi$
$199$	6.64393			0.470976			0.235488	+	0.971877i	$0.424331\pi$
$200$	−65.1023	−	47.2996i	−4.60342	−	3.34458i
$201$	4.10005	−	12.6186i	0.289195	−	0.890050i
$202$	−2.41787	−	7.44143i	−0.170121	−	0.523577i
$203$	2.20502	−	1.60204i	0.154762	−	0.112441i
$204$	2.78444	−	2.02302i	0.194950	−	0.141639i
$205$	−2.60935	−	8.03077i	−0.182245	−	0.560893i
$206$	−6.44794	+	19.8447i	−0.449250	+	1.38265i
$207$	2.72047	+	1.97653i	0.189085	+	0.137379i
$208$	6.85396			0.475236
$209$	−15.5442	+	20.7642i	−1.07522	+	1.43629i
$210$	−31.3168			−2.16106
$211$	7.65263	+	5.55996i	0.526829	+	0.382764i	0.819170	−	0.573550i	$-0.194434\pi$
$211$	7.65263	+	5.55996i	0.526829	+	0.382764i	−0.292341	+	0.956314i	$0.594434\pi$
$212$	10.9675	−	33.7543i	0.753248	−	2.31826i
$213$	3.16009	+	9.72575i	0.216526	+	0.666397i
$214$	38.7297	−	28.1388i	2.64751	−	1.92353i
$215$	−12.1537	+	8.83020i	−0.828878	+	0.602215i
$216$	−1.91620	−	5.89746i	−0.130381	−	0.401271i
$217$	3.65090	−	11.2363i	0.247839	−	0.762771i
$218$	21.9995	+	15.9836i	1.48999	+	1.08254i
$219$	1.99444			0.134772
$220$	−35.9978	−	51.0656i	−2.42697	−	3.44284i
$221$	0.774655			0.0521089
$222$	−9.57120	−	6.95388i	−0.642377	−	0.466714i
$223$	4.18676	−	12.8855i	0.280366	−	0.862878i	−0.707383	−	0.706830i	$-0.750125\pi$
$223$	4.18676	−	12.8855i	0.280366	−	0.862878i	0.987749	−	0.156048i	$-0.0498755\pi$
$224$	4.49193	+	13.8248i	0.300130	+	0.923705i
$225$	−10.4987	+	7.62779i	−0.699916	+	0.508519i
$226$	−8.96998	+	6.51707i	−0.596674	+	0.433509i
$227$	8.05283	+	24.7840i	0.534485	+	1.64498i	0.744760	+	0.667333i	$0.232564\pi$
$227$	8.05283	+	24.7840i	0.534485	+	1.64498i	−0.210275	+	0.977642i	$0.567436\pi$
$228$	10.7373	−	33.0459i	0.711092	−	2.18852i
$229$	22.2301	+	16.1511i	1.46901	+	1.06730i	0.980899	+	0.194515i	$0.0623134\pi$
$229$	22.2301	+	16.1511i	1.46901	+	1.06730i	0.488110	+	0.872782i	$0.337687\pi$
$230$	−36.1900			−2.38630
$231$	−9.13505	−	3.11317i	−0.601042	−	0.204831i
$232$	−5.80818			−0.381326
$233$	4.19683	+	3.04918i	0.274944	+	0.199758i	0.716709	−	0.697372i	$-0.245648\pi$
$233$	4.19683	+	3.04918i	0.274944	+	0.199758i	−0.441765	+	0.897131i	$0.645648\pi$
$234$	0.784377	−	2.41407i	0.0512763	−	0.157812i
$235$	−6.07870	−	18.7083i	−0.396530	−	1.22039i
$236$	−33.7749	+	24.5389i	−2.19856	+	1.59735i
$237$	5.01552	−	3.64399i	0.325793	−	0.236702i
$238$	1.76810	+	5.44166i	0.114609	+	0.352730i
$239$	−0.644556	+	1.98374i	−0.0416929	+	0.128317i	−0.969736	−	0.244154i	$-0.921490\pi$
$239$	−0.644556	+	1.98374i	−0.0416929	+	0.128317i	0.928044	+	0.372472i	$0.121490\pi$
$240$	23.5104	+	17.0813i	1.51759	+	1.10259i
$241$	−7.72932			−0.497889			−0.248945	−	0.968518i	$-0.580084\pi$
$241$	−7.72932			−0.497889			−0.248945	+	0.968518i	$0.580084\pi$
$242$	−7.86577	−	26.7904i	−0.505631	−	1.72215i
$243$	−1.00000			−0.0641500
$244$	20.1076	+	14.6090i	1.28726	+	0.935246i
$245$	1.92256	−	5.91702i	0.122828	−	0.378024i
$246$	1.56212	+	4.80772i	0.0995973	+	0.306529i
$247$	6.32698	−	4.59682i	0.402576	−	0.292489i
$248$	−20.3685	+	14.7986i	−1.29340	+	0.939713i
$249$	5.34017	+	16.4353i	0.338419	+	1.04155i
$250$	26.5298	−	81.6504i	1.67789	−	5.16402i
$251$	−16.5162	−	11.9997i	−1.04249	−	0.757415i	−0.0717218	−	0.997425i	$-0.522849\pi$
$251$	−16.5162	−	11.9997i	−1.04249	−	0.757415i	−0.970770	+	0.240010i	$0.922849\pi$
$252$	12.9284			0.814415
$253$	−10.5566	−	3.59761i	−0.663686	−	0.226180i
$254$	−0.366980			−0.0230263
$255$	2.65722	+	1.93058i	0.166401	+	0.120898i
$256$	−9.24794	+	28.4622i	−0.577996	+	1.77889i
$257$	3.06767	+	9.44131i	0.191356	+	0.588932i	1.00000		0.000634216i	$0.000201877\pi$
$257$	3.06767	+	9.44131i	0.191356	+	0.588932i	−0.808644	+	0.588298i	$0.799798\pi$
$258$	7.27598	−	5.28631i	0.452983	−	0.329111i
$259$	10.9723	−	7.97184i	0.681786	−	0.495346i
$260$	5.82124	+	17.9159i	0.361018	+	1.11110i
$261$	−0.289444	+	0.890816i	−0.0179161	+	0.0551401i
$262$	−8.78914	−	6.38568i	−0.542995	−	0.394509i
$263$	−11.0697			−0.682588			−0.341294	−	0.939957i	$-0.610865\pi$
$263$	−11.0697			−0.682588			−0.341294	+	0.939957i	$0.610865\pi$
$264$	11.8495	+	16.8095i	0.729289	+	1.03455i
$265$	33.8697			2.08060
$266$	46.7319	+	33.9527i	2.86531	+	2.08177i
$267$	−0.482669	+	1.48550i	−0.0295388	+	0.0909112i
$268$	−18.2163	−	56.0641i	−1.11274	−	3.42466i
$269$	1.26350	−	0.917984i	0.0770367	−	0.0559705i	−0.548600	−	0.836085i	$-0.684839\pi$
$269$	1.26350	−	0.917984i	0.0770367	−	0.0559705i	0.625637	+	0.780114i	$0.284839\pi$
$270$	8.70685	−	6.32589i	0.529882	−	0.384982i
$271$	−0.622397	−	1.91554i	−0.0378079	−	0.116361i	0.930371	−	0.366619i	$-0.119485\pi$
$271$	−0.622397	−	1.91554i	−0.0378079	−	0.116361i	−0.968179	+	0.250258i	$0.919485\pi$
$272$	1.64071	−	5.04959i	0.0994827	−	0.306176i
$273$	2.35414	+	1.71038i	0.142479	+	0.103517i
$274$	29.6408			1.79067
$275$	25.7935	−	34.4553i	1.55541	−	2.07773i
$276$	14.9403			0.899297
$277$	7.73303	+	5.61837i	0.464633	+	0.337575i	0.795346	−	0.606156i	$-0.207289\pi$
$277$	7.73303	+	5.61837i	0.464633	+	0.337575i	−0.330713	+	0.943731i	$0.607289\pi$
$278$	17.9553	−	55.2606i	1.07689	−	3.31431i
$279$	1.25466	+	3.86145i	0.0751145	+	0.231179i
$280$	−61.8943	+	44.9689i	−3.69889	+	2.68740i
$281$	−3.18700	+	2.31549i	−0.190120	+	0.138130i	−0.678774	−	0.734348i	$-0.737488\pi$
$281$	−3.18700	+	2.31549i	−0.190120	+	0.138130i	0.488653	+	0.872478i	$0.337488\pi$
$282$	3.63909	+	11.2000i	0.216704	+	0.666948i
$283$	−2.65674	+	8.17662i	−0.157927	+	0.486050i	−0.998446	−	0.0557331i	$-0.982250\pi$
$283$	−2.65674	+	8.17662i	−0.157927	+	0.486050i	0.840519	+	0.541783i	$0.182250\pi$
$284$	36.7576	+	26.7059i	2.18116	+	1.58471i
$285$	33.1588			1.96416
$286$	−0.120301	+	8.41772i	−0.00711355	+	0.497750i
$287$	−5.79514			−0.342076
$288$	−4.04143	−	2.93627i	−0.238143	−	0.173021i
$289$	−5.06785	+	15.5972i	−0.298109	+	0.917485i
$290$	−3.11506	−	9.58718i	−0.182923	−	0.562979i
$291$	7.32906	−	5.32487i	0.429637	−	0.312150i
$292$	7.16889	−	5.20850i	0.419527	−	0.304804i
$293$	−8.27637	−	25.4721i	−0.483511	−	1.48809i	−0.834126	−	0.551574i	$-0.814027\pi$
$293$	−8.27637	−	25.4721i	−0.483511	−	1.48809i	0.350615	−	0.936520i	$-0.385973\pi$
$294$	−1.15096	+	3.54230i	−0.0671255	+	0.206591i
$295$	−32.2317	−	23.4177i	−1.87660	−	1.36343i
$296$	−28.9018			−1.67988
$297$	3.16862	−	0.979714i	0.183862	−	0.0568488i
$298$	23.9063			1.38485
$299$	2.72047	+	1.97653i	0.157329	+	0.114306i
$300$	−17.8170	+	54.8351i	−1.02866	+	3.16590i
$301$	3.18601	+	9.80554i	0.183639	+	0.565182i
$302$	5.86032	−	4.25777i	0.337223	−	0.245007i
$303$	−2.49382	+	1.81187i	−0.143266	+	0.104089i
$304$	−16.5639	−	50.9784i	−0.950005	−	2.92381i
$305$	−7.32947	+	22.5578i	−0.419684	+	1.29166i
$306$	−1.59077	−	1.15577i	−0.0909385	−	0.0660707i
$307$	17.0080			0.970700			0.485350	−	0.874320i	$-0.338692\pi$
$307$	17.0080			0.970700			0.485350	+	0.874320i	$0.338692\pi$
$308$	−40.9653	+	12.6662i	−2.33422	+	0.721722i
$309$	8.22046			0.467646
$310$	−35.3512	−	25.6842i	−2.00782	−	1.45876i
$311$	−7.58929	+	23.3574i	−0.430349	+	1.32448i	0.467429	+	0.884031i	$0.345180\pi$
$311$	−7.58929	+	23.3574i	−0.430349	+	1.32448i	−0.897778	+	0.440448i	$0.854820\pi$
$312$	−1.91620	−	5.89746i	−0.108483	−	0.333878i
$313$	−18.9782	+	13.7885i	−1.07271	+	0.779372i	−0.976398	−	0.215978i	$-0.930706\pi$
$313$	−18.9782	+	13.7885i	−1.07271	+	0.779372i	−0.0963159	+	0.995351i	$0.530706\pi$
$314$	−8.02349	+	5.82941i	−0.452792	+	0.328972i
$315$	3.81256	+	11.7339i	0.214814	+	0.661128i
$316$	8.51163	−	26.1961i	0.478817	−	1.47365i
$317$	−24.3500	−	17.6913i	−1.36763	−	0.993643i	−0.997918	−	0.0644969i	$-0.979456\pi$
$317$	−24.3500	−	17.6913i	−1.36763	−	0.993643i	−0.369714	−	0.929146i	$-0.620544\pi$
$318$	−20.2765			−1.13705
$319$	0.0443924	−	3.10623i	0.00248550	−	0.173915i
$320$	−4.35826			−0.243634
$321$	−15.2581	−	11.0857i	−0.851626	−	0.618743i
$322$	−7.67511	+	23.6216i	−0.427717	+	1.31638i
$323$	−1.87210	−	5.76174i	−0.104167	−	0.320592i
$324$	−3.59443	+	2.61150i	−0.199690	+	0.145084i
$325$	−10.4987	+	7.62779i	−0.582366	+	0.423113i
$326$	−3.52764	−	10.8569i	−0.195378	−	0.601311i
$327$	3.31051	−	10.1887i	0.183071	−	0.563436i
$328$	9.99094	+	7.25884i	0.551657	+	0.400802i
$329$	−13.5002			−0.744292
$330$	−21.3911	+	28.5746i	−1.17754	+	1.57298i
$331$	11.2054			0.615907			0.307953	−	0.951401i	$-0.400356\pi$
$331$	11.2054			0.615907			0.307953	+	0.951401i	$0.400356\pi$
$332$	62.1158	+	45.1298i	3.40905	+	2.47682i
$333$	−1.44029	+	4.43274i	−0.0789271	+	0.242913i
$334$	11.1093	+	34.1910i	0.607875	+	1.87085i
$335$	45.5119	−	33.0663i	2.48658	−	1.80660i
$336$	16.1351	−	11.7229i	0.880245	−	0.639535i
$337$	7.73245	+	23.7980i	0.421213	+	1.29636i	0.906574	+	0.422047i	$0.138688\pi$
$337$	7.73245	+	23.7980i	0.421213	+	1.29636i	−0.485360	+	0.874314i	$0.661312\pi$
$338$	0.784377	−	2.41407i	0.0426645	−	0.131308i
$339$	3.53386	+	2.56750i	0.191933	+	0.139447i
$340$	14.5929			0.791410
$341$	−7.75866	−	11.0063i	−0.420155	−	0.596022i
$342$	−19.8510			−1.07342
$343$	13.0246	+	9.46292i	0.703262	+	0.510950i
$344$	6.78941	−	20.8957i	0.366061	−	1.12662i
$345$	4.40584	+	13.5598i	0.237202	+	0.730034i
$346$	38.3147	−	27.8372i	2.05981	−	1.49654i
$347$	18.9220	−	13.7476i	1.01579	−	0.738011i	0.0503706	−	0.998731i	$-0.483960\pi$
$347$	18.9220	−	13.7476i	1.01579	−	0.738011i	0.965415	+	0.260719i	$0.0839597\pi$
$348$	1.28599	+	3.95786i	0.0689360	+	0.212163i
$349$	3.33327	−	10.2587i	0.178426	−	0.549138i	−0.821348	−	0.570428i	$-0.806777\pi$
$349$	3.33327	−	10.2587i	0.178426	−	0.549138i	0.999773	+	0.0212900i	$0.00677732\pi$
$350$	−77.5450	−	56.3398i	−4.14496	−	3.01149i
$351$	−1.00000			−0.0533761
$352$	15.6825	+	5.34448i	0.835877	+	0.284862i
$353$	1.10779			0.0589615			0.0294807	−	0.999565i	$-0.490615\pi$
$353$	1.10779			0.0589615			0.0294807	+	0.999565i	$0.490615\pi$
$354$	19.2959	+	14.0193i	1.02557	+	0.745117i
$355$	−13.3986	+	41.2367i	−0.711124	+	2.18862i
$356$	2.14448	+	6.60002i	0.113657	+	0.349800i
$357$	1.82364	−	1.32495i	0.0965175	−	0.0701240i
$358$	−30.4536	+	22.1259i	−1.60952	+	1.16939i
$359$	1.70698	+	5.25353i	0.0900907	+	0.277271i	0.985943	−	0.167081i	$-0.0534341\pi$
$359$	1.70698	+	5.25353i	0.0900907	+	0.277271i	−0.895852	+	0.444352i	$0.853434\pi$
$360$	8.12459	−	25.0049i	0.428204	−	1.31788i
$361$	−34.1093	−	24.7819i	−1.79523	−	1.30431i
$362$	32.4081			1.70333
$363$	−9.08032	+	6.20869i	−0.476593	+	0.325871i
$364$	12.9284			0.677634
$365$	6.84132	+	4.97051i	0.358091	+	0.260168i
$366$	4.38788	−	13.5045i	0.229358	−	0.705892i
$367$	−5.87475	−	18.0806i	−0.306659	−	0.943801i	−0.979053	−	0.203607i	$-0.934734\pi$
$367$	−5.87475	−	18.0806i	−0.306659	−	0.943801i	0.672393	−	0.740194i	$-0.265266\pi$
$368$	18.6460	−	13.5471i	0.971988	−	0.706191i
$369$	1.61119	−	1.17060i	0.0838754	−	0.0609390i
$370$	−15.5007	−	47.7063i	−0.805844	−	2.48013i
$371$	7.18303	−	22.1071i	0.372924	−	1.14774i
$372$	14.5940	+	10.6031i	0.756662	+	0.549747i
$373$	8.71301			0.451143			0.225571	−	0.974227i	$-0.427575\pi$
$373$	8.71301			0.451143			0.225571	+	0.974227i	$0.427575\pi$
$374$	6.17288	+	2.10368i	0.319192	+	0.108779i
$375$	−33.8228			−1.74660
$376$	23.2747	+	16.9100i	1.20030	+	0.872069i
$377$	−0.289444	+	0.890816i	−0.0149071	+	0.0458793i
$378$	−2.28244	−	7.02462i	−0.117396	−	0.361308i
$379$	−26.4936	+	19.2487i	−1.36088	+	0.988740i	−0.362496	+	0.931985i	$0.618075\pi$
$379$	−26.4936	+	19.2487i	−1.36088	+	0.988740i	−0.998388	+	0.0567553i	$0.981925\pi$
$380$	119.187	−	86.5945i	6.11417	−	4.44220i
$381$	0.0446768	+	0.137501i	0.00228886	+	0.00704438i
$382$	−2.61766	+	8.05634i	−0.133931	+	0.412198i
$383$	−9.13555	−	6.63737i	−0.466805	−	0.339154i	0.329390	−	0.944194i	$-0.393157\pi$
$383$	−9.13555	−	6.63737i	−0.466805	−	0.339154i	−0.796195	+	0.605040i	$0.793157\pi$
$384$	12.6001			0.642995
$385$	−23.5764	−	33.4449i	−1.20156	−	1.70451i
$386$	47.7721			2.43154
$387$	−2.86648	−	2.08262i	−0.145711	−	0.105866i
$388$	12.4378	−	38.2797i	0.631436	−	1.94336i
$389$	2.58841	+	7.96630i	0.131238	+	0.403908i	0.994986	−	0.100016i	$-0.0318893\pi$
$389$	2.58841	+	7.96630i	0.131238	+	0.403908i	−0.863748	+	0.503924i	$0.831889\pi$
$390$	8.70685	−	6.32589i	0.440888	−	0.320324i
$391$	2.10742	−	1.53113i	0.106577	−	0.0774327i
$392$	2.81175	+	8.65368i	0.142015	+	0.437077i
$393$	−1.32260	+	4.07054i	−0.0667163	+	0.205332i
$394$	−16.1956	−	11.7668i	−0.815923	−	0.592803i
$395$	26.2857			1.32258
$396$	8.83085	−	11.7964i	0.443767	−	0.592790i
$397$	−9.15050			−0.459250			−0.229625	−	0.973279i	$-0.573750\pi$
$397$	−9.15050			−0.459250			−0.229625	+	0.973279i	$0.573750\pi$
$398$	−13.6435	−	9.91258i	−0.683886	−	0.496873i
$399$	7.03226	−	21.6431i	0.352054	−	1.08351i
$400$	27.4855	+	84.5917i	1.37427	+	4.22958i
$401$	8.53273	−	6.19939i	0.426104	−	0.309583i	−0.353985	−	0.935251i	$-0.615174\pi$
$401$	8.53273	−	6.19939i	0.426104	−	0.309583i	0.780089	+	0.625668i	$0.215174\pi$
$402$	−27.2462	+	19.7956i	−1.35892	+	0.987312i
$403$	1.25466	+	3.86145i	0.0624991	+	0.192352i
$404$	−4.23216	+	13.0252i	−0.210558	+	0.648030i
$405$	−3.43019	−	2.49218i	−0.170448	−	0.123837i
$406$	−6.91828			−0.343348
$407$	0.220899	−	15.4567i	0.0109495	−	0.766163i
$408$	−4.80360			−0.237814
$409$	−18.0486	−	13.1131i	−0.892447	−	0.648401i	0.0440681	−	0.999029i	$-0.485968\pi$
$409$	−18.0486	−	13.1131i	−0.892447	−	0.648401i	−0.936515	+	0.350628i	$0.885968\pi$
$410$	−6.62332	+	20.3845i	−0.327102	+	1.00672i
$411$	−3.60852	−	11.1059i	−0.177995	−	0.547813i
$412$	29.5479	−	21.4678i	1.45572	−	1.05764i
$413$	−22.1206	+	16.0715i	−1.08848	+	0.790828i
$414$	−2.63761	−	8.11773i	−0.129632	−	0.398965i
$415$	−22.6420	+	69.6850i	−1.11145	+	3.42070i
$416$	−4.04143	−	2.93627i	−0.198147	−	0.143962i
$417$	−22.8911			−1.12098
$418$	62.9002	−	19.4483i	3.07655	−	0.951246i
$419$	−14.9132			−0.728556			−0.364278	−	0.931290i	$-0.618684\pi$
$419$	−14.9132			−0.728556			−0.364278	+	0.931290i	$0.618684\pi$
$420$	44.3470	+	32.2200i	2.16391	+	1.57217i
$421$	−3.79331	+	11.6746i	−0.184875	+	0.568986i	−0.999946	−	0.0103746i	$-0.996698\pi$
$421$	−3.79331	+	11.6746i	−0.184875	+	0.568986i	0.815072	+	0.579360i	$0.196698\pi$
$422$	−7.41956	−	22.8351i	−0.361179	−	1.11159i
$423$	3.75340	−	2.72701i	0.182497	−	0.132592i
$424$	−40.0744	+	29.1158i	−1.94619	+	1.41399i
$425$	3.10649	+	9.56081i	0.150687	+	0.463767i
$426$	8.02125	−	24.6869i	0.388631	−	1.19608i
$427$	13.1693	+	9.56803i	0.637305	+	0.463029i
$428$	−83.7946			−4.05036
$429$	3.16862	−	0.979714i	0.152982	−	0.0473010i
$430$	38.1324			1.83891
$431$	4.68595	+	3.40455i	0.225714	+	0.163991i	0.694895	−	0.719111i	$-0.255451\pi$
$431$	4.68595	+	3.40455i	0.225714	+	0.163991i	−0.469181	+	0.883102i	$0.655451\pi$
$432$	−2.11799	+	6.51850i	−0.101902	+	0.313622i
$433$	4.77298	+	14.6897i	0.229375	+	0.705943i	0.997818	+	0.0660250i	$0.0210317\pi$
$433$	4.77298	+	14.6897i	0.229375	+	0.705943i	−0.768443	+	0.639918i	$0.778968\pi$
$434$	−24.2615	+	17.6270i	−1.16459	+	0.846124i
$435$	−3.21292	+	2.33432i	−0.154048	+	0.111922i
$436$	−14.7084	−	45.2679i	−0.704407	−	2.16794i
$437$	8.12656	−	25.0110i	0.388746	−	1.19644i
$438$	−4.09564	−	2.97566i	−0.195697	−	0.142182i
$439$	−25.9386			−1.23798			−0.618990	−	0.785399i	$-0.712458\pi$
$439$	−25.9386			−1.23798			−0.618990	+	0.785399i	$0.712458\pi$
$440$	−1.24608	+	87.1909i	−0.0594045	+	4.15666i
$441$	1.46736			0.0698742
$442$	−1.59077	−	1.15577i	−0.0756654	−	0.0549742i
$443$	2.00121	−	6.15911i	0.0950806	−	0.292628i	−0.892194	−	0.451652i	$-0.850835\pi$
$443$	2.00121	−	6.15911i	0.0950806	−	0.292628i	0.987275	+	0.159024i	$0.0508348\pi$
$444$	6.39913	+	19.6945i	0.303689	+	0.934659i
$445$	−5.35778	+	3.89266i	−0.253983	+	0.184530i
$446$	−27.8225	+	20.2142i	−1.31743	+	0.957171i
$447$	−2.91039	−	8.95726i	−0.137657	−	0.423664i
$448$	−0.924291	+	2.84467i	−0.0436686	+	0.134398i
$449$	−20.3046	−	14.7522i	−0.958235	−	0.696199i	−0.00549499	−	0.999985i	$-0.501749\pi$
$449$	−20.3046	−	14.7522i	−0.958235	−	0.696199i	−0.952740	+	0.303786i	$0.901749\pi$
$450$	32.9399			1.55280
$451$	−3.95841	+	5.28770i	−0.186394	+	0.248988i
$452$	19.4072			0.912839
$453$	−2.30876	−	1.67741i	−0.108475	−	0.0788117i
$454$	20.4405	−	62.9093i	0.959319	−	2.95248i
$455$	3.81256	+	11.7339i	0.178736	+	0.550092i
$456$	−39.2333	+	28.5047i	−1.83727	+	1.33485i
$457$	−4.61687	+	3.35435i	−0.215968	+	0.156910i	−0.690510	−	0.723323i	$-0.742614\pi$
$457$	−4.61687	+	3.35435i	−0.215968	+	0.156910i	0.474542	+	0.880233i	$0.342614\pi$
$458$	−21.5531	−	66.3336i	−1.00711	−	3.09957i
$459$	−0.239382	+	0.736741i	−0.0111734	+	0.0343881i
$460$	51.2479	+	37.2338i	2.38945	+	1.73603i
$461$	−10.0596			−0.468520			−0.234260	−	0.972174i	$-0.575267\pi$
$461$	−10.0596			−0.468520			−0.234260	+	0.972174i	$0.575267\pi$
$462$	14.1143	+	20.0222i	0.656657	+	0.931518i
$463$	19.6675			0.914024			0.457012	−	0.889461i	$-0.348920\pi$
$463$	19.6675			0.914024			0.457012	+	0.889461i	$0.348920\pi$
$464$	5.19374	+	3.77348i	0.241113	+	0.175179i
$465$	−5.31970	+	16.3723i	−0.246695	+	0.759249i
$466$	−4.06901	−	12.5231i	−0.188493	−	0.580123i
$467$	−18.8337	+	13.6835i	−0.871522	+	0.633198i	−0.930995	−	0.365032i	$-0.881058\pi$
$467$	−18.8337	+	13.6835i	−0.871522	+	0.633198i	0.0594731	+	0.998230i	$0.481058\pi$
$468$	−3.59443	+	2.61150i	−0.166153	+	0.120717i
$469$	−11.9306	−	36.7186i	−0.550904	−	1.69551i
$470$	−15.4295	+	47.4872i	−0.711712	+	2.19042i
$471$	3.16097	+	2.29658i	0.145650	+	0.105821i
$472$	58.2671			2.68196
$473$	11.1232	+	3.79070i	0.511444	+	0.174297i
$474$	−15.7362			−0.722789
$475$	82.1063	+	59.6537i	3.76729	+	2.73710i
$476$	3.09483	−	9.52491i	0.141851	−	0.436574i
$477$	2.46850	+	7.59727i	0.113025	+	0.347855i
$478$	4.28330	−	3.11200i	0.195914	−	0.142340i
$479$	−1.58621	+	1.15245i	−0.0724759	+	0.0526568i	−0.623433	−	0.781877i	$-0.714263\pi$
$479$	−1.58621	+	1.15245i	−0.0724759	+	0.0526568i	0.550957	+	0.834533i	$0.314263\pi$
$480$	−6.54516	−	20.1439i	−0.298744	−	0.919440i
$481$	−1.44029	+	4.43274i	−0.0656714	+	0.202116i
$482$	15.8724	+	11.5319i	0.722966	+	0.525266i
$483$	9.78497			0.445232
$484$	−16.4245	+	46.0300i	−0.746570	+	2.09227i
$485$	38.4106			1.74414
$486$	2.05353	+	1.49197i	0.0931498	+	0.0676773i
$487$	0.511393	−	1.57391i	0.0231734	−	0.0713205i	−0.938801	−	0.344460i	$-0.888062\pi$
$487$	0.511393	−	1.57391i	0.0231734	−	0.0713205i	0.961974	+	0.273139i	$0.0880620\pi$
$488$	−10.7194	−	32.9909i	−0.485245	−	1.49343i
$489$	−3.63845	+	2.64349i	−0.164536	+	0.119543i
$490$	−12.7761	+	9.28235i	−0.577163	+	0.419334i
$491$	−6.40416	−	19.7100i	−0.289016	−	0.889499i	−0.985166	−	0.171603i	$-0.945105\pi$
$491$	−6.40416	−	19.7100i	−0.289016	−	0.889499i	0.696150	−	0.717896i	$-0.254895\pi$
$492$	2.73429	−	8.41528i	0.123271	−	0.379390i
$493$	0.587013	+	0.426490i	0.0264377	+	0.0192081i
$494$	−19.8510			−0.893137
$495$	13.3106	+	4.53617i	0.598267	+	0.203886i
$496$	27.8282			1.24952
$497$	24.0740	+	17.4908i	1.07987	+	0.784569i
$498$	13.5549	−	41.7178i	0.607411	−	1.86942i
$499$	−4.11783	−	12.6734i	−0.184339	−	0.567338i	0.815597	−	0.578620i	$-0.196409\pi$
$499$	−4.11783	−	12.6734i	−0.184339	−	0.567338i	−0.999936	+	0.0112821i	$0.996409\pi$
$500$	−121.574	+	88.3283i	−5.43693	+	3.95016i
$501$	11.4583	−	8.32495i	0.511919	−	0.371931i
$502$	16.0132	+	49.2834i	0.714702	+	2.19963i
$503$	−3.09643	+	9.52983i	−0.138063	+	0.424914i	−0.996054	−	0.0887508i	$-0.971713\pi$
$503$	−3.09643	+	9.52983i	−0.138063	+	0.424914i	0.857991	+	0.513665i	$0.171713\pi$
$504$	−14.5979	−	10.6060i	−0.650242	−	0.472428i
$505$	−13.0698			−0.581597
$506$	16.3106	+	23.1379i	0.725097	+	1.02861i
$507$	−1.00000			−0.0444116
$508$	0.519672	+	0.377564i	0.0230567	+	0.0167517i
$509$	−9.48804	+	29.2012i	−0.420550	+	1.29432i	0.486642	+	0.873602i	$0.338222\pi$
$509$	−9.48804	+	29.2012i	−0.420550	+	1.29432i	−0.907192	+	0.420718i	$0.861778\pi$
$510$	−2.57629	−	7.92899i	−0.114080	−	0.351102i
$511$	4.69519	−	3.41126i	0.207703	−	0.150905i
$512$	41.0684	−	29.8380i	1.81499	−	1.31866i
$513$	2.41669	+	7.43781i	0.106700	+	0.328387i
$514$	7.78665	−	23.9648i	0.343454	−	1.05704i
$515$	28.1978	+	20.4869i	1.24254	+	0.902759i
$516$	−15.7421			−0.693009
$517$	−9.22142	+	12.3181i	−0.405558	+	0.541750i
$518$	−34.4257			−1.51258
$519$	−15.0946	−	10.9669i	−0.662581	−	0.481393i
$520$	8.12459	−	25.0049i	0.356287	−	1.09654i
$521$	−4.81093	−	14.8065i	−0.210771	−	0.648686i	−0.999427	−	0.0338512i	$-0.989223\pi$
$521$	−4.81093	−	14.8065i	−0.210771	−	0.648686i	0.788656	−	0.614835i	$-0.210777\pi$
$522$	1.92345	−	1.39747i	0.0841873	−	0.0611656i
$523$	−5.04532	+	3.66564i	−0.220616	+	0.160287i	−0.692604	−	0.721318i	$-0.743537\pi$
$523$	−5.04532	+	3.66564i	−0.220616	+	0.160287i	0.471988	+	0.881605i	$0.343537\pi$
$524$	5.87625	+	18.0853i	0.256705	+	0.790058i
$525$	−11.6691	+	35.9137i	−0.509280	+	1.56740i
$526$	22.7320	+	16.5157i	0.991160	+	0.720120i
$527$	3.14523			0.137008
$528$	0.324839	−	22.7297i	0.0141368	−	0.989183i
$529$	−11.6924			−0.508364
$530$	−69.5524	−	50.5328i	−3.02116	−	2.19500i
$531$	2.90367	−	8.93657i	0.126008	−	0.387814i
$532$	−31.2440	−	96.1593i	−1.35460	−	4.16903i
$533$	1.61119	−	1.17060i	0.0697885	−	0.0507043i
$534$	3.20750	−	2.33039i	0.138802	−	0.100846i
$535$	−24.7108	−	76.0520i	−1.06834	−	3.28802i
$536$	−25.4242	+	78.2476i	−1.09816	+	3.37978i
$537$	11.9977	+	8.71681i	0.517737	+	0.376158i
$538$	−3.96423			−0.170910
$539$	−4.64950	+	1.43759i	−0.200268	+	0.0619214i
$540$	−18.8379			−0.810655
$541$	11.0803	+	8.05029i	0.476378	+	0.346109i	0.799922	−	0.600104i	$-0.204874\pi$
$541$	11.0803	+	8.05029i	0.476378	+	0.346109i	−0.323544	+	0.946213i	$0.604874\pi$
$542$	−1.57983	+	4.86222i	−0.0678595	+	0.208850i
$543$	−3.94542	−	12.1428i	−0.169314	−	0.521096i
$544$	−3.13071	+	2.27460i	−0.134228	+	0.0975225i
$545$	36.7477	−	26.6988i	1.57410	−	1.14365i
$546$	−2.28244	−	7.02462i	−0.0976793	−	0.300626i
$547$	−10.8993	+	33.5447i	−0.466022	+	1.43427i	0.391670	+	0.920106i	$0.371898\pi$
$547$	−10.8993	+	33.5447i	−0.466022	+	1.43427i	−0.857692	+	0.514164i	$0.828102\pi$
$548$	−41.9737	−	30.4957i	−1.79303	−	1.30271i
$549$	−5.59409			−0.238750
$550$	−104.374	+	32.2717i	−4.45053	+	1.37607i
$551$	7.32521			0.312065
$552$	−16.8695	−	12.2564i	−0.718013	−	0.521667i
$553$	5.57461	−	17.1569i	0.237057	−	0.729585i
$554$	−7.49751	−	23.0750i	−0.318539	−	0.980361i
$555$	−15.9876	+	11.6157i	−0.678638	+	0.493059i
$556$	−82.2804	+	59.7802i	−3.48947	+	2.53525i
$557$	0.118885	+	0.365889i	0.00503730	+	0.0155032i	0.953544	−	0.301255i	$-0.0974056\pi$
$557$	0.118885	+	0.365889i	0.00503730	+	0.0155032i	−0.948506	+	0.316758i	$0.897406\pi$
$558$	3.18470	−	9.80150i	0.134819	−	0.414931i
$559$	−2.86648	−	2.08262i	−0.121239	−	0.0880854i
$560$	84.5621			3.57340
$561$	0.0367143	−	2.56898i	0.00155008	−	0.108462i
$562$	9.99923			0.421792
$563$	7.47112	+	5.42809i	0.314870	+	0.228767i	0.733983	−	0.679167i	$-0.237659\pi$
$563$	7.47112	+	5.42809i	0.314870	+	0.228767i	−0.419113	+	0.907934i	$0.637659\pi$
$564$	6.36974	−	19.6041i	0.268215	−	0.825480i
$565$	5.72314	+	17.6140i	0.240774	+	0.741027i
$566$	17.6550	−	12.8271i	0.742095	−	0.539164i
$567$	−2.35414	+	1.71038i	−0.0988644	+	0.0718292i
$568$	−19.5956	−	60.3089i	−0.822212	−	2.53051i
$569$	−2.91295	+	8.96514i	−0.122117	+	0.375838i	−0.993365	−	0.115005i	$-0.963311\pi$
$569$	−2.91295	+	8.96514i	−0.122117	+	0.375838i	0.871248	+	0.490844i	$0.163311\pi$
$570$	−68.0926	−	49.4721i	−2.85208	−	2.07216i
$571$	9.23726			0.386567			0.193284	−	0.981143i	$-0.438086\pi$
$571$	9.23726			0.386567			0.193284	+	0.981143i	$0.438086\pi$
$572$	8.83085	−	11.7964i	0.369237	−	0.493232i
$573$	3.33725			0.139416
$574$	11.9005	+	8.64620i	0.496716	+	0.360885i
$575$	−13.4849	+	41.5023i	−0.562359	+	1.73076i
$576$	−0.317640	−	0.977594i	−0.0132350	−	0.0407331i
$577$	−6.16974	+	4.48258i	−0.256850	+	0.186612i	−0.708757	−	0.705453i	$-0.750744\pi$
$577$	−6.16974	+	4.48258i	−0.256850	+	0.186612i	0.451907	+	0.892065i	$0.350744\pi$
$578$	33.6776	−	24.4682i	1.40081	−	1.01774i
$579$	−5.81586	−	17.8994i	−0.241699	−	0.743873i
$580$	−5.45251	+	16.7811i	−0.226403	+	0.696797i
$581$	40.6822	+	29.5573i	1.68778	+	1.22624i
$582$	−22.9950			−0.953173
$583$	−15.2649	−	21.6544i	−0.632208	−	0.896835i
$584$	−12.3675			−0.511769
$585$	−3.43019	−	2.49218i	−0.141821	−	0.103039i
$586$	−21.0079	+	64.6557i	−0.867828	+	2.67090i
$587$	−7.96326	−	24.5084i	−0.328679	−	1.01157i	−0.969753	−	0.244090i	$-0.921511\pi$
$587$	−7.96326	−	24.5084i	−0.328679	−	1.01157i	0.641074	−	0.767479i	$-0.278489\pi$
$588$	5.27431	−	3.83201i	0.217509	−	0.158030i
$589$	25.6886	−	18.6639i	1.05848	−	0.769031i
$590$	31.2500	+	96.1777i	1.28654	+	3.95957i
$591$	−2.43714	+	7.50073i	−0.100250	+	0.308539i
$592$	25.8443	+	18.7770i	1.06220	+	0.771730i
$593$	23.7206			0.974088			0.487044	−	0.873377i	$-0.338075\pi$
$593$	23.7206			0.974088			0.487044	+	0.873377i	$0.338075\pi$
$594$	−7.96856	−	2.71563i	−0.326954	−	0.111424i
$595$	9.55747			0.391818
$596$	−33.8531	−	24.5957i	−1.38668	−	1.00748i
$597$	−2.05309	+	6.31876i	−0.0840273	+	0.258609i
$598$	−2.63761	−	8.11773i	−0.107860	−	0.331959i
$599$	5.28929	−	3.84289i	0.216114	−	0.157016i	−0.474461	−	0.880276i	$-0.657357\pi$
$599$	5.28929	−	3.84289i	0.216114	−	0.157016i	0.690576	+	0.723260i	$0.257357\pi$
$600$	65.1023	−	47.2996i	2.65779	−	1.93100i
$601$	−1.92550	−	5.92609i	−0.0785430	−	0.241730i	0.904074	−	0.427377i	$-0.140562\pi$
$601$	−1.92550	−	5.92609i	−0.0785430	−	0.241730i	−0.982617	+	0.185646i	$0.940562\pi$
$602$	8.08705	−	24.8894i	0.329604	−	1.01442i
$603$	10.7341	+	7.79875i	0.437125	+	0.317590i
$604$	−12.6792			−0.515911
$605$	−46.6204	−	1.33281i	−1.89539	−	0.0541866i
$606$	7.82438			0.317844
$607$	−23.4618	−	17.0460i	−0.952287	−	0.691877i	−0.000940390	−	1.00000i	$-0.500299\pi$
$607$	−23.4618	−	17.0460i	−0.952287	−	0.691877i	−0.951347	+	0.308122i	$0.900299\pi$
$608$	−12.0725	+	37.1554i	−0.489606	+	1.50685i
$609$	0.842244	+	2.59216i	0.0341294	+	0.105040i
$610$	48.7069	−	35.3876i	1.97209	−	1.43280i
$611$	3.75340	−	2.72701i	0.151846	−	0.110323i
$612$	1.06356	+	3.27331i	0.0429920	+	0.132316i
$613$	−3.60379	+	11.0913i	−0.145556	+	0.447975i	−0.997082	−	0.0763372i	$-0.975677\pi$
$613$	−3.60379	+	11.0913i	−0.145556	+	0.447975i	0.851526	+	0.524312i	$0.175677\pi$
$614$	−34.9265	−	25.3756i	−1.40952	−	1.02407i
$615$	8.44405			0.340497
$616$	56.6460	+	19.3046i	2.28233	+	0.777805i
$617$	35.3625			1.42364			0.711820	−	0.702362i	$-0.247871\pi$
$617$	35.3625			1.42364			0.711820	+	0.702362i	$0.247871\pi$
$618$	−16.8809	−	12.2647i	−0.679051	−	0.493359i
$619$	7.03025	−	21.6369i	0.282570	−	0.869660i	−0.704547	−	0.709657i	$-0.748850\pi$
$619$	7.03025	−	21.6369i	0.282570	−	0.869660i	0.987117	−	0.160003i	$-0.0511503\pi$
$620$	23.6352	+	72.7416i	0.949212	+	2.92137i
$621$	−2.72047	+	1.97653i	−0.109169	+	0.0793156i
$622$	50.4335	−	36.6421i	2.02220	−	1.46921i
$623$	1.40450	+	4.32262i	0.0562703	+	0.173182i
$624$	−2.11799	+	6.51850i	−0.0847874	+	0.260949i
$625$	−63.5248	−	46.1535i	−2.54099	−	1.84614i
$626$	59.5444			2.37987
$627$	−14.9445	−	21.1999i	−0.596826	−	0.846644i
$628$	17.3594			0.692716
$629$	2.92100	+	2.12223i	0.116468	+	0.0846190i
$630$	9.67742	−	29.7840i	0.385558	−	1.18662i
$631$	−10.3091	−	31.7283i	−0.410400	−	1.26308i	−0.916301	−	0.400491i	$-0.868840\pi$
$631$	−10.3091	−	31.7283i	−0.410400	−	1.26308i	0.505901	−	0.862592i	$-0.331160\pi$
$632$	−31.1010	+	22.5962i	−1.23713	+	0.898829i
$633$	−7.65263	+	5.55996i	−0.304165	+	0.220989i
$634$	23.6084	+	72.6591i	0.937608	+	2.88566i
$635$	−0.189427	+	0.582997i	−0.00751719	+	0.0231355i
$636$	28.7132	+	20.8613i	1.13855	+	0.827206i
$637$	1.46736			0.0581388
$638$	−4.72557	+	6.31249i	−0.187087	+	0.249914i
$639$	−10.2263			−0.404545
$640$	43.2207	+	31.4017i	1.70845	+	1.24126i
$641$	14.3083	−	44.0364i	0.565144	−	1.73933i	−0.102379	−	0.994745i	$-0.532645\pi$
$641$	14.3083	−	44.0364i	0.565144	−	1.73933i	0.667523	−	0.744589i	$-0.267355\pi$
$642$	14.7934	+	45.5295i	0.583850	+	1.79691i
$643$	−32.1592	+	23.3650i	−1.26824	+	0.921427i	−0.999131	−	0.0416837i	$-0.986728\pi$
$643$	−32.1592	+	23.3650i	−1.26824	+	0.921427i	−0.269105	+	0.963111i	$0.586728\pi$
$644$	35.1714	−	25.5535i	1.38595	−	1.00695i
$645$	−4.64231	−	14.2876i	−0.182791	−	0.562572i
$646$	−4.75195	+	14.6250i	−0.186963	+	0.575413i
$647$	13.5189	+	9.82207i	0.531484	+	0.386146i	0.820913	−	0.571054i	$-0.193465\pi$
$647$	13.5189	+	9.82207i	0.531484	+	0.386146i	−0.289429	+	0.957200i	$0.593465\pi$
$648$	6.20095			0.243597
$649$	−0.445340	+	31.1614i	−0.0174811	+	1.22319i
$650$	32.9399			1.29201
$651$	9.55818	+	6.94443i	0.374615	+	0.272174i
$652$	−6.17466	+	19.0037i	−0.241818	+	0.744241i
$653$	9.29381	+	28.6034i	0.363695	+	1.11934i	0.950794	+	0.309823i	$0.100270\pi$
$653$	9.29381	+	28.6034i	0.363695	+	1.11934i	−0.587099	+	0.809515i	$0.699730\pi$
$654$	−21.9995	+	15.9836i	−0.860248	+	0.625007i
$655$	−14.6813	+	10.6666i	−0.573646	+	0.416778i
$656$	−4.21807	−	12.9819i	−0.164688	−	0.506858i
$657$	−0.616317	+	1.89683i	−0.0240448	+	0.0740023i
$658$	27.7231	+	20.1420i	1.08076	+	0.785217i
$659$	−8.53745			−0.332572			−0.166286	−	0.986078i	$-0.553177\pi$
$659$	−8.53745			−0.332572			−0.166286	+	0.986078i	$0.553177\pi$
$660$	59.6902	−	18.4558i	2.32344	−	0.718390i
$661$	−7.46076			−0.290190			−0.145095	−	0.989418i	$-0.546349\pi$
$661$	−7.46076			−0.290190			−0.145095	+	0.989418i	$0.546349\pi$
$662$	−23.0107	−	16.7182i	−0.894335	−	0.649772i
$663$	−0.239382	+	0.736741i	−0.00929681	+	0.0286126i
$664$	−33.1141	−	101.915i	−1.28508	−	3.95506i
$665$	78.0604	−	56.7142i	3.02705	−	2.19928i
$666$	9.57120	−	6.95388i	0.370876	−	0.269458i
$667$	0.973306	+	2.99553i	0.0376866	+	0.115987i
$668$	19.4454	−	59.8468i	0.752366	−	2.31554i
$669$	10.9611	+	7.96369i	0.423780	+	0.307894i
$670$	−142.794			−5.51661
$671$	17.7256	−	5.48061i	0.684288	−	0.211577i
$672$	−14.5362			−0.560746
$673$	18.8649	+	13.7062i	0.727190	+	0.528334i	0.888673	−	0.458541i	$-0.151628\pi$
$673$	18.8649	+	13.7062i	0.727190	+	0.528334i	−0.161483	+	0.986875i	$0.551628\pi$
$674$	19.6273	−	60.4065i	0.756014	−	2.32677i
$675$	−4.01016	−	12.3420i	−0.154351	−	0.475044i
$676$	−3.59443	+	2.61150i	−0.138247	+	0.100442i
$677$	22.9295	−	16.6592i	0.881251	−	0.640266i	−0.0523313	−	0.998630i	$-0.516665\pi$
$677$	22.9295	−	16.6592i	0.881251	−	0.640266i	0.933582	+	0.358364i	$0.116665\pi$
$678$	−3.42623	−	10.5448i	−0.131584	−	0.404972i
$679$	8.14604	−	25.0709i	0.312617	−	0.962135i
$680$	−16.4773	−	11.9714i	−0.631874	−	0.459084i
$681$	−26.0595			−0.998602
$682$	−0.488442	+	34.1774i	−0.0187034	+	1.30872i
$683$	7.36889			0.281963			0.140981	−	0.990012i	$-0.454974\pi$
$683$	7.36889			0.281963			0.140981	+	0.990012i	$0.454974\pi$
$684$	28.1105	+	20.4235i	1.07483	+	0.780911i
$685$	15.3000	−	47.0884i	0.584581	−	1.79916i
$686$	−12.6279	−	38.8647i	−0.482136	−	1.48386i
$687$	−22.2301	+	16.1511i	−0.848133	+	0.616205i
$688$	−19.6467	+	14.2742i	−0.749025	+	0.544198i
$689$	2.46850	+	7.59727i	0.0940425	+	0.289433i
$690$	11.1833	−	34.4188i	0.425742	−	1.31030i
$691$	11.2321	+	8.16063i	0.427291	+	0.310445i	0.780565	−	0.625075i	$-0.214932\pi$
$691$	11.2321	+	8.16063i	0.427291	+	0.310445i	−0.353274	+	0.935520i	$0.614932\pi$
$692$	−82.8967			−3.15126
$693$	5.78368	−	7.72593i	0.219704	−	0.293484i
$694$	−59.3679			−2.25357
$695$	−78.5209	−	57.0487i	−2.97847	−	2.16398i
$696$	1.79483	−	5.52391i	0.0680327	−	0.209383i
$697$	−0.476739	−	1.46725i	−0.0180578	−	0.0555762i
$698$	−22.1507	+	16.0935i	−0.838418	+	0.609146i
$699$	−4.19683	+	3.04918i	−0.158739	+	0.115330i
$700$	51.8452	+	159.563i	1.95956	+	6.03092i
$701$	−5.29491	+	16.2961i	−0.199986	+	0.615494i	0.799896	+	0.600139i	$0.204888\pi$
$701$	−5.29491	+	16.2961i	−0.199986	+	0.615494i	−0.999882	+	0.0153553i	$0.995112\pi$
$702$	2.05353	+	1.49197i	0.0775054	+	0.0563109i
$703$	36.4506			1.37476
$704$	1.96424	+	2.78643i	0.0740302	+	0.105018i
$705$	19.6711			0.740855
$706$	−2.27487	−	1.65279i	−0.0856157	−	0.0622035i
$707$	−2.77181	+	8.53076i	−0.104245	+	0.320832i
$708$	−12.9009	−	39.7048i	−0.484845	−	1.49220i
$709$	−8.06019	+	5.85607i	−0.302707	+	0.219929i	−0.728761	−	0.684768i	$-0.759903\pi$
$709$	−8.06019	+	5.85607i	−0.302707	+	0.219929i	0.426054	+	0.904698i	$0.359903\pi$
$710$	89.0385	−	64.6902i	3.34155	−	2.42778i
$711$	1.91576	+	5.89610i	0.0718465	+	0.221121i
$712$	2.99301	−	9.21153i	0.112168	−	0.345217i
$713$	11.0455	+	8.02506i	0.413659	+	0.300541i
$714$	−5.72170			−0.214129
$715$	13.3106	+	4.53617i	0.497788	+	0.169643i
$716$	65.8887			2.46238
$717$	−1.68747	−	1.22602i	−0.0630197	−	0.0457865i
$718$	4.33281	−	13.3350i	0.161699	−	0.497659i
$719$	−8.97751	−	27.6299i	−0.334805	−	1.03042i	−0.966818	−	0.255466i	$-0.917771\pi$
$719$	−8.97751	−	27.6299i	−0.334805	−	1.03042i	0.632013	−	0.774957i	$-0.282229\pi$
$720$	−23.5104	+	17.0813i	−0.876180	+	0.636582i
$721$	19.3521	−	14.0601i	0.720710	−	0.523626i
$722$	33.0705	+	101.780i	1.23076	+	3.78788i
$723$	2.38849	−	7.35102i	0.0888290	−	0.273387i
$724$	−45.8924	−	33.3428i	−1.70558	−	1.23918i
$725$	−12.1552			−0.451432
$726$	27.9099	+	0.797906i	1.03583	+	0.0296131i
$727$	−8.86626			−0.328831			−0.164416	−	0.986391i	$-0.552574\pi$
$727$	−8.86626			−0.328831			−0.164416	+	0.986391i	$0.552574\pi$
$728$	−14.5979	−	10.6060i	−0.541034	−	0.393084i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−6.63296	−	20.4142i	−0.245497	−	0.755562i
$731$	−2.22053	+	1.61331i	−0.0821294	+	0.0596705i
$732$	−20.1076	+	14.6090i	−0.743197	+	0.539964i
$733$	7.21724	+	22.2124i	0.266575	+	0.820433i	0.991326	+	0.131423i	$0.0419545\pi$
$733$	7.21724	+	22.2124i	0.266575	+	0.820433i	−0.724752	+	0.689010i	$0.758045\pi$
$734$	−14.9119	+	45.8940i	−0.550407	+	1.69398i
$735$	5.03332	+	3.65692i	0.185657	+	0.134887i
$736$	−16.7982			−0.619190
$737$	−41.6527	−	14.1950i	−1.53430	−	0.522879i
$738$	−5.05513			−0.186082
$739$	−6.32918	−	4.59842i	−0.232823	−	0.169156i	0.465257	−	0.885176i	$-0.345962\pi$
$739$	−6.32918	−	4.59842i	−0.232823	−	0.169156i	−0.698080	+	0.716020i	$0.745962\pi$
$740$	−27.1320	+	83.5036i	−0.997391	+	3.06965i
$741$	2.41669	+	7.43781i	0.0887794	+	0.273235i
$742$	−47.7337	+	34.6806i	−1.75236	+	1.27316i
$743$	−28.7485	+	20.8870i	−1.05468	+	0.766269i	−0.973097	−	0.230398i	$-0.925997\pi$
$743$	−28.7485	+	20.8870i	−1.05468	+	0.766269i	−0.0815823	+	0.996667i	$0.525997\pi$
$744$	−7.78009	−	23.9447i	−0.285232	−	0.877854i
$745$	12.3399	−	37.9783i	0.452099	−	1.39142i
$746$	−17.8924	−	12.9996i	−0.655087	−	0.475949i
$747$	−17.2811			−0.632284
$748$	−6.57693	−	9.32989i	−0.240476	−	0.341134i
$749$	−54.8805			−2.00529
$750$	69.4560	+	50.4627i	2.53617	+	1.84264i
$751$	10.7353	−	33.0399i	0.391738	−	1.20564i	−0.539735	−	0.841835i	$-0.681476\pi$
$751$	10.7353	−	33.0399i	0.391738	−	1.20564i	0.931473	−	0.363810i	$-0.118524\pi$
$752$	−9.82633	−	30.2423i	−0.358329	−	1.10282i
$753$	16.5162	−	11.9997i	0.601883	−	0.437294i
$754$	1.92345	−	1.39747i	0.0700481	−	0.0508929i
$755$	−3.73907	−	11.5077i	−0.136079	−	0.418807i
$756$	−3.99511	+	12.2957i	−0.145301	+	0.447189i
$757$	26.0420	+	18.9206i	0.946514	+	0.687683i	0.949980	−	0.312311i	$-0.101103\pi$
$757$	26.0420	+	18.9206i	0.946514	+	0.687683i	−0.00346582	+	0.999994i	$0.501103\pi$
$758$	83.1239			3.01920
$759$	6.68369	−	8.92817i	0.242603	−	0.324072i
$760$	−205.617			−7.45849
$761$	−19.4476	−	14.1295i	−0.704974	−	0.512194i	0.176574	−	0.984287i	$-0.443498\pi$
$761$	−19.4476	−	14.1295i	−0.704974	−	0.512194i	−0.881548	+	0.472094i	$0.843498\pi$
$762$	0.113403	−	0.349018i	0.00410815	−	0.0126436i
$763$	−9.63315	−	29.6478i	−0.348744	−	1.07332i
$764$	11.9955	−	8.71525i	0.433982	−	0.315307i
$765$	−2.65722	+	1.93058i	−0.0960718	+	0.0698003i
$766$	8.85732	+	27.2600i	0.320028	+	0.984944i
$767$	2.90367	−	8.93657i	0.104845	−	0.322681i
$768$	−24.2114	−	17.5906i	−0.873654	−	0.634747i
$769$	17.7925			0.641613			0.320807	−	0.947145i	$-0.396046\pi$
$769$	17.7925			0.641613			0.320807	+	0.947145i	$0.396046\pi$
$770$	−1.48424	+	103.855i	−0.0534883	+	3.74269i
$771$	−9.92718			−0.357519
$772$	−67.6491	−	49.1499i	−2.43474	−	1.76894i
$773$	−4.33107	+	13.3297i	−0.155778	+	0.479435i	−0.998239	−	0.0593223i	$-0.981106\pi$
$773$	−4.33107	+	13.3297i	−0.155778	+	0.479435i	0.842461	+	0.538757i	$0.181106\pi$
$774$	2.77918	+	8.55343i	0.0998955	+	0.307447i
$775$	−42.6267	+	30.9701i	−1.53119	+	1.11248i
$776$	−45.4472	+	33.0193i	−1.63146	+	1.18532i
$777$	4.19105	+	12.8987i	0.150353	+	0.462739i
$778$	6.57015	−	20.2209i	0.235551	−	0.724953i
$779$	−12.6005	−	9.15477i	−0.451458	−	0.328004i
$780$	−18.8379			−0.674505
$781$	32.4031	−	10.0188i	1.15948	−	0.358501i
$782$	−6.61206			−0.236447
$783$	−0.757773	−	0.550554i	−0.0270806	−	0.0196752i
$784$	3.10785	−	9.56497i	0.110995	−	0.341606i
$785$	5.11925	+	15.7554i	0.182714	+	0.562335i
$786$	8.78914	−	6.38568i	0.313498	−	0.227770i
$787$	28.7442	−	20.8839i	1.02462	−	0.744431i	0.0573965	−	0.998351i	$-0.481720\pi$
$787$	28.7442	−	20.8839i	1.02462	−	0.744431i	0.967225	+	0.253920i	$0.0817201\pi$
$788$	10.8281	+	33.3254i	0.385735	+	1.18717i
$789$	3.42073	−	10.5279i	0.121781	−	0.374804i
$790$	−53.9783	−	39.2175i	−1.92046	−	1.39530i
$791$	12.7106			0.451936
$792$	−19.6485	+	6.07516i	−0.698178	+	0.215872i
$793$	−5.59409			−0.198652
$794$	18.7908	+	13.6523i	0.666860	+	0.484502i
$795$	−10.4663	+	32.2120i	−0.371202	+	1.14244i
$796$	9.12178	+	28.0740i	0.323313	+	0.995055i
$797$	−30.5386	+	22.1876i	−1.08173	+	0.785926i	−0.977984	−	0.208678i	$-0.933084\pi$
$797$	−30.5386	+	22.1876i	−1.08173	+	0.785926i	−0.103750	+	0.994603i	$0.533084\pi$
$798$	−46.7319	+	33.9527i	−1.65429	+	1.20191i
$799$	−1.11060	−	3.41808i	−0.0392903	−	0.120923i
$800$	20.0327	−	61.6543i	0.708262	−	2.17981i
$801$	−1.26364	−	0.918091i	−0.0446486	−	0.0324391i
$802$	−26.7715			−0.945335
$803$	0.0945254	−	6.61415i	0.00333573	−	0.233408i
$804$	58.9493			2.07898
$805$	33.5643	+	24.3859i	1.18299	+	0.859490i
$806$	3.18470	−	9.80150i	0.112176	−	0.345243i
$807$	0.482613	+	1.48533i	0.0169888	+	0.0522861i
$808$	15.4641	−	11.2353i	0.544024	−	0.395256i
$809$	8.96242	−	6.51158i	0.315102	−	0.228935i	−0.418981	−	0.907995i	$-0.637612\pi$
$809$	8.96242	−	6.51158i	0.315102	−	0.228935i	0.734083	+	0.679060i	$0.237612\pi$
$810$	3.32572	+	10.2355i	0.116854	+	0.359639i
$811$	−3.48859	+	10.7368i	−0.122501	+	0.377019i	−0.993437	−	0.114376i	$-0.963513\pi$
$811$	−3.48859	+	10.7368i	−0.122501	+	0.377019i	0.870937	+	0.491395i	$0.163513\pi$
$812$	9.79682	+	7.11781i	0.343801	+	0.249786i
$813$	2.01412			0.0706383
$814$	−23.5147	+	31.4113i	−0.824190	+	1.10096i
$815$	−19.0686			−0.667945
$816$	4.29544	+	3.12082i	0.150370	+	0.109251i
$817$	−8.56274	+	26.3534i	−0.299572	+	0.921988i
$818$	17.4989	+	53.8561i	0.611836	+	1.88304i
$819$	−2.35414	+	1.71038i	−0.0822602	+	0.0597655i
$820$	30.3515	−	22.0517i	1.05992	−	0.770078i
$821$	−7.03946	−	21.6652i	−0.245679	−	0.756121i	−0.995524	−	0.0945082i	$-0.969872\pi$
$821$	−7.03946	−	21.6652i	−0.245679	−	0.756121i	0.749845	−	0.661613i	$-0.230128\pi$
$822$	−9.15951	+	28.1901i	−0.319475	+	0.983242i
$823$	37.1408	+	26.9844i	1.29465	+	0.940616i	0.999888	−	0.0149563i	$-0.00476092\pi$
$823$	37.1408	+	26.9844i	1.29465	+	0.940616i	0.294758	+	0.955572i	$0.404761\pi$
$824$	−50.9747			−1.77579
$825$	24.7983	+	35.1784i	0.863367	+	1.22475i
$826$	69.4035			2.41486
$827$	31.2959	+	22.7378i	1.08826	+	0.790671i	0.979105	−	0.203353i	$-0.0651841\pi$
$827$	31.2959	+	22.7378i	1.08826	+	0.790671i	0.109160	+	0.994024i	$0.465184\pi$
$828$	−4.61679	+	14.2090i	−0.160445	+	0.493798i
$829$	15.3511	+	47.2458i	0.533166	+	1.64092i	0.747579	+	0.664173i	$0.231216\pi$
$829$	15.3511	+	47.2458i	0.533166	+	1.64092i	−0.214413	+	0.976743i	$0.568784\pi$
$830$	150.464	−	109.319i	5.22269	−	3.79451i
$831$	−7.73303	+	5.61837i	−0.268256	+	0.194899i
$832$	−0.317640	−	0.977594i	−0.0110122	−	0.0338920i
$833$	0.351258	−	1.08106i	0.0121704	−	0.0374566i
$834$	47.0075	+	34.1529i	1.62774	+	1.18262i
$835$	60.0514			2.07817
$836$	−109.081	−	37.1740i	−3.77264	−	1.28569i
$837$	−4.06017			−0.140340
$838$	30.6246	+	22.2501i	1.05791	+	0.768616i
$839$	−16.3528	+	50.3288i	−0.564561	+	1.73754i	0.104689	+	0.994505i	$0.466615\pi$
$839$	−16.3528	+	50.3288i	−0.564561	+	1.73754i	−0.669251	+	0.743037i	$0.733385\pi$
$840$	−23.6415	−	72.7611i	−0.815710	−	2.51050i
$841$	22.7517	−	16.5301i	0.784542	−	0.570003i
$842$	25.2079	−	18.3146i	0.868721	−	0.631163i
$843$	−1.21732	−	3.74654i	−0.0419269	−	0.129038i
$844$	−12.9870	+	39.9698i	−0.447030	+	1.37582i
$845$	−3.43019	−	2.49218i	−0.118002	−	0.0857336i
$846$	−11.7763			−0.404879
$847$	−10.7571	+	30.1469i	−0.369618	+	1.03586i
$848$	54.7511			1.88016
$849$	−6.95545	−	5.05343i	−0.238710	−	0.173433i
$850$	7.88521	−	24.2682i	0.270460	−	0.832392i
$851$	4.84322	+	14.9059i	0.166023	+	0.510968i
$852$	−36.7576	+	26.7059i	−1.25929	+	0.914930i
$853$	−21.5047	+	15.6241i	−0.736306	+	0.534958i	−0.891552	−	0.452918i	$-0.850383\pi$
$853$	−21.5047	+	15.6241i	−0.736306	+	0.534958i	0.155246	+	0.987876i	$0.450383\pi$
$854$	−12.7682	−	39.2964i	−0.436918	−	1.34469i
$855$	−10.2466	+	31.5359i	−0.350428	+	1.07851i
$856$	94.6150	+	68.7418i	3.23387	+	2.34955i
$857$	0.463785			0.0158426			0.00792130	−	0.999969i	$-0.497479\pi$
$857$	0.463785			0.0158426			0.00792130	+	0.999969i	$0.497479\pi$
$858$	−7.96856	−	2.71563i	−0.272042	−	0.0927102i
$859$	35.7585			1.22006			0.610032	−	0.792376i	$-0.291156\pi$
$859$	35.7585			1.22006			0.610032	+	0.792376i	$0.291156\pi$
$860$	−53.9985	−	39.2322i	−1.84133	−	1.33781i
$861$	1.79080	−	5.51151i	0.0610302	−	0.187832i
$862$	−4.54324	−	13.9826i	−0.154743	−	0.476251i
$863$	−3.78032	+	2.74656i	−0.128684	+	0.0934941i	−0.650265	−	0.759707i	$-0.725342\pi$
$863$	−3.78032	+	2.74656i	−0.128684	+	0.0934941i	0.521582	+	0.853201i	$0.325342\pi$
$864$	4.04143	−	2.93627i	0.137492	−	0.0998939i
$865$	−24.4460	−	75.2371i	−0.831189	−	2.55814i
$866$	12.1152	−	37.2869i	0.411693	−	1.26706i
$867$	−13.2678	−	9.63962i	−0.450598	−	0.327379i
$868$	52.4916			1.78168
$869$	−11.8468	−	16.8056i	−0.401875	−	0.570091i
$870$	10.0806			0.341763
$871$	10.7341	+	7.79875i	0.363710	+	0.264251i
$872$	−20.5283	+	63.1796i	−0.695176	+	2.13953i
$873$	2.79945	+	8.61582i	0.0947471	+	0.291601i
$874$	−54.0039	+	39.2361i	−1.82671	+	1.32718i
$875$	−79.6234	+	57.8498i	−2.69176	+	1.95568i
$876$	2.73827	+	8.42753i	0.0925176	+	0.284740i
$877$	−14.7163	+	45.2921i	−0.496934	+	1.52941i	0.316986	+	0.948430i	$0.397329\pi$
$877$	−14.7163	+	45.2921i	−0.496934	+	1.52941i	−0.813920	+	0.580976i	$0.802671\pi$
$878$	53.2655	+	38.6997i	1.79763	+	1.30605i
$879$	26.7829			0.903365
$880$	57.7607	−	77.1576i	1.94711	−	2.60098i
$881$	33.2974			1.12182			0.560909	−	0.827877i	$-0.310452\pi$
$881$	33.2974			1.12182			0.560909	+	0.827877i	$0.310452\pi$
$882$	−3.01326	−	2.18926i	−0.101462	−	0.0737162i
$883$	7.72739	−	23.7825i	0.260047	−	0.800344i	−0.732746	−	0.680503i	$-0.761762\pi$
$883$	7.72739	−	23.7825i	0.260047	−	0.800344i	0.992793	−	0.119841i	$-0.0382385\pi$
$884$	1.06356	+	3.27331i	0.0357715	+	0.110093i
$885$	32.2317	−	23.4177i	1.08346	−	0.787177i
$886$	−13.2988	+	9.66212i	−0.446781	+	0.324605i
$887$	9.68079	+	29.7944i	0.325049	+	1.00040i	0.971418	+	0.237374i	$0.0762865\pi$
$887$	9.68079	+	29.7944i	0.325049	+	1.00040i	−0.646369	+	0.763025i	$0.723713\pi$
$888$	8.93114	−	27.4872i	0.299710	−	0.922411i
$889$	0.340354	+	0.247282i	0.0114151	+	0.00829356i
$890$	16.8101			0.563476
$891$	−0.0473944	+	3.31629i	−0.00158777	+	0.111100i
$892$	60.1960			2.01551
$893$	−29.3538	−	21.3268i	−0.982286	−	0.713673i
$894$	−7.38744	+	22.7362i	−0.247073	+	0.760413i
$895$	19.4304	+	59.8006i	0.649487	+	1.99891i
$896$	29.6623	−	21.5509i	0.990948	−	0.719966i
$897$	−2.72047	+	1.97653i	−0.0908337	+	0.0659946i
$898$	19.6862	+	60.5880i	0.656938	+	2.02185i
$899$	−1.17519	+	3.61686i	−0.0391947	+	0.120629i
$900$	−46.6455	−	33.8899i	−1.55485	−	1.12966i
$901$	6.18813			0.206157
$902$	16.0178	−	4.95259i	0.533335	−	0.164903i
$903$	−10.3102			−0.343101
$904$	−21.9133	−	15.9209i	−0.728825	−	0.529522i
$905$	16.7284	−	51.4847i	0.556071	−	1.71141i
$906$	2.23844	+	6.88922i	0.0743673	+	0.228879i
$907$	39.9052	−	28.9928i	1.32503	−	0.962692i	0.325177	−	0.945653i	$-0.394576\pi$
$907$	39.9052	−	28.9928i	1.32503	−	0.962692i	0.999855	−	0.0170385i	$-0.00542379\pi$
$908$	−93.6690	+	68.0545i	−3.10851	+	2.25847i
$909$	−0.952554	−	2.93166i	−0.0315942	−	0.0972370i
$910$	9.67742	−	29.7840i	0.320803	−	0.987331i
$911$	5.09260	+	3.69999i	0.168726	+	0.122586i	0.668944	−	0.743313i	$-0.266747\pi$
$911$	5.09260	+	3.69999i	0.168726	+	0.122586i	−0.500218	+	0.865900i	$0.666747\pi$
$912$	53.6019			1.77494
$913$	54.7574	−	16.9306i	1.81220	−	0.560320i
$914$	14.4855			0.479137
$915$	−19.1888	−	13.9415i	−0.634362	−	0.460891i
$916$	−37.7259	+	116.108i	−1.24650	+	3.83632i
$917$	3.84860	+	11.8448i	0.127092	+	0.391149i
$918$	1.59077	−	1.15577i	0.0525034	−	0.0381459i
$919$	−5.87612	+	4.26925i	−0.193835	+	0.140830i	−0.680470	−	0.732776i	$-0.738224\pi$
$919$	−5.87612	+	4.26925i	−0.193835	+	0.140830i	0.486635	+	0.873606i	$0.338224\pi$
$920$	−27.3204	−	84.0836i	−0.900727	−	2.77215i
$921$	−5.25577	+	16.1756i	−0.173184	+	0.533004i
$922$	20.6576	+	15.0086i	0.680320	+	0.494282i
$923$	−10.2263			−0.336601
$924$	0.612735	−	42.8744i	0.0201575	−	1.41046i
$925$	−60.4848			−1.98873
$926$	−40.3876	−	29.3433i	−1.32722	−	0.964282i
$927$	−2.54026	+	7.81813i	−0.0834332	+	0.256781i
$928$	−1.44591	−	4.45005i	−0.0474643	−	0.146080i
$929$	8.07166	−	5.86440i	0.264822	−	0.192405i	−0.447448	−	0.894310i	$-0.647667\pi$
$929$	8.07166	−	5.86440i	0.264822	−	0.192405i	0.712270	+	0.701905i	$0.247667\pi$
$930$	35.3512	−	25.6842i	1.15921	−	0.842217i
$931$	−3.54615	−	10.9139i	−0.116220	−	0.357690i
$932$	−7.12227	+	21.9201i	−0.233298	+	0.718017i
$933$	−19.8690	−	14.4357i	−0.650483	−	0.472603i
$934$	59.0910			1.93352
$935$	6.52829	−	8.72059i	0.213498	−	0.285194i
$936$	6.20095			0.202685
$937$	24.2072	+	17.5876i	0.790815	+	0.574561i	0.908205	−	0.418525i	$-0.137453\pi$
$937$	24.2072	+	17.5876i	0.790815	+	0.574561i	−0.117390	+	0.993086i	$0.537453\pi$
$938$	−30.2834	+	93.2029i	−0.988790	+	3.04318i
$939$	−7.24905	−	22.3103i	−0.236564	−	0.728068i
$940$	70.7063	−	51.3711i	2.30618	−	1.67554i
$941$	−5.50383	+	3.99877i	−0.179420	+	0.130356i	−0.673870	−	0.738850i	$-0.735369\pi$
$941$	−5.50383	+	3.99877i	−0.179420	+	0.130356i	0.494450	+	0.869206i	$0.335369\pi$
$942$	−3.06470	−	9.43218i	−0.0998533	−	0.307317i
$943$	2.06947	−	6.36916i	0.0673911	−	0.207408i
$944$	−52.1031	−	37.8551i	−1.69581	−	1.23208i
$945$	−12.3377			−0.401346
$946$	−17.1861	−	24.3798i	−0.558768	−	0.792655i
$947$	−25.6645			−0.833985			−0.416993	−	0.908910i	$-0.636916\pi$
$947$	−25.6645			−0.833985			−0.416993	+	0.908910i	$0.636916\pi$
$948$	22.2837	+	16.1901i	0.723742	+	0.525830i
$949$	−0.616317	+	1.89683i	−0.0200065	+	0.0615737i
$950$	−79.6056	−	245.001i	−2.58275	−	7.94888i
$951$	24.3500	−	17.6913i	0.789603	−	0.573680i
$952$	−11.3083	+	8.21599i	−0.366505	+	0.266282i
$953$	1.19456	+	3.67647i	0.0386955	+	0.119093i	0.968538	−	0.248864i	$-0.0800574\pi$
$953$	1.19456	+	3.67647i	0.0386955	+	0.119093i	−0.929843	+	0.367957i	$0.880057\pi$
$954$	6.26580	−	19.2841i	0.202863	−	0.624347i
$955$	11.4474	+	8.31703i	0.370429	+	0.269133i
$956$	−9.26725			−0.299724
$957$	2.94048	+	1.00210i	0.0950523	+	0.0323932i
$958$	4.97675			0.160792
$959$	−27.4903	−	19.9728i	−0.887707	−	0.644957i
$960$	1.34678	−	4.14495i	0.0434670	−	0.133778i
$961$	−4.48540	−	13.8046i	−0.144690	−	0.445311i
$962$	9.57120	−	6.95388i	0.308588	−	0.224202i
$963$	15.2581	−	11.0857i	0.491687	−	0.357231i
$964$	−10.6120	−	32.6603i	−0.341788	−	1.05192i
$965$	24.6590	−	75.8925i	0.793800	−	2.44307i
$966$	−20.0937	−	14.5989i	−0.646504	−	0.469713i
$967$	−12.4272			−0.399632			−0.199816	−	0.979833i	$-0.564034\pi$
$967$	−12.4272			−0.399632			−0.199816	+	0.979833i	$0.564034\pi$
$968$	56.3067	−	38.4998i	1.80976	−	1.23743i
$969$	6.05825			0.194619
$970$	−78.8772	−	57.3076i	−2.53259	−	1.84004i
$971$	12.8549	−	39.5632i	0.412532	−	1.26964i	−0.501908	−	0.864921i	$-0.667368\pi$
$971$	12.8549	−	39.5632i	0.412532	−	1.26964i	0.914440	−	0.404722i	$-0.132632\pi$
$972$	−1.37295	−	4.22550i	−0.0440374	−	0.135533i
$973$	−53.8888	+	39.1525i	−1.72760	+	1.25517i
$974$	−3.39839	+	2.46907i	−0.108891	+	0.0791142i
$975$	−4.01016	−	12.3420i	−0.128428	−	0.395261i
$976$	−11.8482	+	36.4651i	−0.379253	+	1.16722i
$977$	22.4162	+	16.2863i	0.717157	+	0.521045i	0.885475	−	0.464688i	$-0.153833\pi$
$977$	22.4162	+	16.2863i	0.717157	+	0.521045i	−0.168317	+	0.985733i	$0.553833\pi$
$978$	11.4157			0.365033
$979$	4.90347	+	1.67107i	0.156716	+	0.0534077i
$980$	27.6420			0.882990
$981$	8.66702	+	6.29696i	0.276717	+	0.201046i
$982$	−16.2557	+	50.0298i	−0.518739	+	1.59652i
$983$	13.8777	+	42.7113i	0.442631	+	1.36228i	0.885061	+	0.465476i	$0.154117\pi$
$983$	13.8777	+	42.7113i	0.442631	+	1.36228i	−0.442429	+	0.896803i	$0.645883\pi$
$984$	−9.99094	+	7.25884i	−0.318499	+	0.231403i
$985$	−27.0530	+	19.6552i	−0.861980	+	0.626265i
$986$	−0.569135	−	1.75162i	−0.0181249	−	0.0557828i
$987$	4.17180	−	12.8395i	0.132790	−	0.408685i
$988$	28.1105	+	20.4235i	0.894314	+	0.649757i
$989$	−11.9145			−0.378860
$990$	−20.5658	−	29.1742i	−0.653625	−	0.927217i
$991$	−27.2762			−0.866456			−0.433228	−	0.901284i	$-0.642626\pi$
$991$	−27.2762			−0.866456			−0.433228	+	0.901284i	$0.642626\pi$
$992$	−16.4089	−	11.9217i	−0.520982	−	0.378515i
$993$	−3.46267	+	10.6570i	−0.109885	+	0.338190i
$994$	−23.3408	−	71.8356i	−0.740325	−	2.27849i
$995$	−22.7900	+	16.5579i	−0.722490	+	0.524920i
$996$	−62.1158	+	45.1298i	−1.96821	+	1.42999i
$997$	−12.0855	−	37.1952i	−0.382750	−	1.17798i	−0.938099	−	0.346367i	$-0.887415\pi$
$997$	−12.0855	−	37.1952i	−0.382750	−	1.17798i	0.555349	−	0.831618i	$-0.312585\pi$
$998$	−10.4523	+	32.1688i	−0.330861	+	1.01829i
$999$	−3.77072	−	2.73959i	−0.119300	−	0.0866766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.c.235.1	yes	28
11.3	even	5	inner	429.2.n.c.157.1	✓	28
11.5	even	5		4719.2.a.bp.1.13		14
11.6	odd	10		4719.2.a.bo.1.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.c.157.1	✓	28	11.3	even	5	inner
429.2.n.c.235.1	yes	28	1.1	even	1	trivial
4719.2.a.bo.1.2		14	11.6	odd	10
4719.2.a.bp.1.13		14	11.5	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.05353 - 1.49197i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.37295 + 4.22550i) q^{4} +(-3.43019 + 2.49218i) q^{5} +(2.05353 - 1.49197i) q^{6} +(0.899200 + 2.76745i) q^{7} +(1.91620 - 5.89746i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-2.05353 - 1.49197i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.37295 + 4.22550i) q^{4} +(-3.43019 + 2.49218i) q^{5} +(2.05353 - 1.49197i) q^{6} +(0.899200 + 2.76745i) q^{7} +(1.91620 - 5.89746i) q^{8} +(-0.809017 - 0.587785i) q^{9} +10.7623 q^{10} +(3.13933 + 1.06986i) q^{11} -4.44296 q^{12} +(-0.809017 - 0.587785i) q^{13} +(2.28244 - 7.02462i) q^{14} +(-1.31022 - 4.03243i) q^{15} +(-5.54497 + 4.02866i) q^{16} +(-0.626709 + 0.455331i) q^{17} +(0.784377 + 2.41407i) q^{18} +(-2.41669 + 7.43781i) q^{19} +(-15.2402 - 11.0726i) q^{20} -2.90987 q^{21} +(-4.85049 - 6.88079i) q^{22} -3.36268 q^{23} +(5.01668 + 3.64483i) q^{24} +(4.01016 - 12.3420i) q^{25} +(0.784377 + 2.41407i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-10.4593 + 7.59915i) q^{28} +(-0.289444 - 0.890816i) q^{29} +(-3.32572 + 10.2355i) q^{30} +(-3.28474 - 2.38651i) q^{31} +4.99548 q^{32} +(-1.98761 + 2.65507i) q^{33} +1.96631 q^{34} +(-9.98142 - 7.25192i) q^{35} +(1.37295 - 4.22550i) q^{36} +(-1.44029 - 4.43274i) q^{37} +(16.0598 - 11.6681i) q^{38} +(0.809017 - 0.587785i) q^{39} +(8.12459 + 25.0049i) q^{40} +(-0.615421 + 1.89407i) q^{41} +(5.97550 + 4.34145i) q^{42} +3.54317 q^{43} +(-0.210571 + 14.7341i) q^{44} +4.23995 q^{45} +(6.90536 + 5.01703i) q^{46} +(-1.43367 + 4.41239i) q^{47} +(-2.11799 - 6.51850i) q^{48} +(-1.18712 + 0.862491i) q^{49} +(-26.6490 + 19.3616i) q^{50} +(-0.239382 - 0.736741i) q^{51} +(1.37295 - 4.22550i) q^{52} +(-6.46262 - 4.69537i) q^{53} -2.53830 q^{54} +(-13.4348 + 4.15394i) q^{55} +18.0440 q^{56} +(-6.32698 - 4.59682i) q^{57} +(-0.734694 + 2.26116i) q^{58} +(2.90367 + 8.93657i) q^{59} +(15.2402 - 11.0726i) q^{60} +(4.52572 - 3.28813i) q^{61} +(3.18470 + 9.80150i) q^{62} +(0.899200 - 2.76745i) q^{63} +(0.831591 + 0.604186i) q^{64} +4.23995 q^{65} +(8.04291 - 2.48681i) q^{66} -13.2680 q^{67} +(-2.78444 - 2.02302i) q^{68} +(1.03913 - 3.19810i) q^{69} +(9.67742 + 29.7840i) q^{70} +(8.27322 - 6.01084i) q^{71} +(-5.01668 + 3.64483i) q^{72} +(-0.616317 - 1.89683i) q^{73} +(-3.65587 + 11.2516i) q^{74} +(10.4987 + 7.62779i) q^{75} -34.7465 q^{76} +(-0.137912 + 9.64997i) q^{77} -2.53830 q^{78} +(-5.01552 - 3.64399i) q^{79} +(8.98017 - 27.6381i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.08969 - 2.97133i) q^{82} +(13.9807 - 10.1576i) q^{83} +(-3.99511 - 12.2957i) q^{84} +(1.01497 - 3.12374i) q^{85} +(-7.27598 - 5.28631i) q^{86} +0.936659 q^{87} +(12.3251 - 16.4640i) q^{88} +1.56195 q^{89} +(-8.70685 - 6.32589i) q^{90} +(0.899200 - 2.76745i) q^{91} +(-4.61679 - 14.2090i) q^{92} +(3.28474 - 2.38651i) q^{93} +(9.52725 - 6.92195i) q^{94} +(-10.2466 - 31.5359i) q^{95} +(-1.54369 + 4.75098i) q^{96} +(-7.32906 - 5.32487i) q^{97} +3.72459 q^{98} +(-1.91092 - 2.71079i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9}+O(q^{10}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9	\( 28 q + q^{2} + 7 q^{3} - 5 q^{4} - 4 q^{5} - q^{6} + q^{7} - 7 q^{8} - 7 q^{9} - 2 q^{10} + 14 q^{11} - 30 q^{12} - 7 q^{13} - 9 q^{14} + 4 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} - 41 q^{20} - 6 q^{21} + 5 q^{22} + 30 q^{23} + 2 q^{24} + 3 q^{25} - 4 q^{26} + 7 q^{27} - 12 q^{28} - 4 q^{29} + 7 q^{30} - 4 q^{31} + 22 q^{32} + q^{33} - 24 q^{34} - 6 q^{35} - 5 q^{36} - 8 q^{37} + 73 q^{38} + 7 q^{39} - 28 q^{40} + 10 q^{41} + 9 q^{42} - 12 q^{43} - 22 q^{44} + 16 q^{45} + 35 q^{46} + 12 q^{47} + 14 q^{48} + 16 q^{49} - 57 q^{50} - 13 q^{51} - 5 q^{52} + q^{53} - 6 q^{54} - 28 q^{55} + 48 q^{56} - 30 q^{58} - 15 q^{59} + 41 q^{60} - 22 q^{61} - 40 q^{62} + q^{63} - 19 q^{64} + 16 q^{65} + 20 q^{66} - 88 q^{67} + 39 q^{68} + 14 q^{70} + 34 q^{71} - 2 q^{72} - 59 q^{73} + 79 q^{74} + 27 q^{75} - 124 q^{76} - 42 q^{77} - 6 q^{78} - 3 q^{79} + 37 q^{80} - 7 q^{81} + 82 q^{82} - 8 q^{83} - 8 q^{84} + 70 q^{85} - 35 q^{86} - 36 q^{87} + 59 q^{88} + 126 q^{89} + 8 q^{90} + q^{91} - 82 q^{92} + 4 q^{93} + 23 q^{94} - 77 q^{95} + 73 q^{96} - 18 q^{97} - 66 q^{98} - 6 q^{99}+O(q^{100}) \) 28 * q + q^2 + 7 * q^3 - 5 * q^4 - 4 * q^5 - q^6 + q^7 - 7 * q^8 - 7 * q^9 - 2 * q^10 + 14 * q^11 - 30 * q^12 - 7 * q^13 - 9 * q^14 + 4 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 - 41 * q^20 - 6 * q^21 + 5 * q^22 + 30 * q^23 + 2 * q^24 + 3 * q^25 - 4 * q^26 + 7 * q^27 - 12 * q^28 - 4 * q^29 + 7 * q^30 - 4 * q^31 + 22 * q^32 + q^33 - 24 * q^34 - 6 * q^35 - 5 * q^36 - 8 * q^37 + 73 * q^38 + 7 * q^39 - 28 * q^40 + 10 * q^41 + 9 * q^42 - 12 * q^43 - 22 * q^44 + 16 * q^45 + 35 * q^46 + 12 * q^47 + 14 * q^48 + 16 * q^49 - 57 * q^50 - 13 * q^51 - 5 * q^52 + q^53 - 6 * q^54 - 28 * q^55 + 48 * q^56 - 30 * q^58 - 15 * q^59 + 41 * q^60 - 22 * q^61 - 40 * q^62 + q^63 - 19 * q^64 + 16 * q^65 + 20 * q^66 - 88 * q^67 + 39 * q^68 + 14 * q^70 + 34 * q^71 - 2 * q^72 - 59 * q^73 + 79 * q^74 + 27 * q^75 - 124 * q^76 - 42 * q^77 - 6 * q^78 - 3 * q^79 + 37 * q^80 - 7 * q^81 + 82 * q^82 - 8 * q^83 - 8 * q^84 + 70 * q^85 - 35 * q^86 - 36 * q^87 + 59 * q^88 + 126 * q^89 + 8 * q^90 + q^91 - 82 * q^92 + 4 * q^93 + 23 * q^94 - 77 * q^95 + 73 * q^96 - 18 * q^97 - 66 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more