LMFDB - Embedded newform 833.2.k.c.120.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(120,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([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("833.120");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.k (of order $7$, degree $6$, 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$234$
Relative dimension:	$39$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			120.10
Character	$\chi$	$=$	833.120
Dual form			833.2.k.c.715.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.52554 + 0.734659i) q^{2} +(-0.245038 + 1.07358i) q^{3} +(0.540556 - 0.677835i) q^{4} +(0.390090 - 1.70910i) q^{5} +(-0.414902 - 1.81780i) q^{6} +(-2.19439 - 1.47806i) q^{7} +(0.426894 - 1.87034i) q^{8} +(1.61038 + 0.775517i) q^{9} +(0.660507 + 2.89387i) q^{10} +(-1.27782 + 0.615366i) q^{11} +(0.595254 + 0.746425i) q^{12} +(3.24409 - 1.56227i) q^{13} +(4.43349 + 0.642713i) q^{14} +(1.73926 + 0.837585i) q^{15} +(1.10867 + 4.85739i) q^{16} +(0.623490 + 0.781831i) q^{17} -3.02643 q^{18} -6.10089 q^{19} +(-0.947620 - 1.18828i) q^{20} +(2.12453 - 1.99367i) q^{21} +(1.49728 - 1.87753i) q^{22} +(-4.91583 + 6.16426i) q^{23} +(1.90336 + 0.916608i) q^{24} +(1.73601 + 0.836017i) q^{25} +(-3.80124 + 4.76661i) q^{26} +(-3.28692 + 4.12167i) q^{27} +(-2.18807 + 0.688456i) q^{28} +(-5.74407 - 7.20283i) q^{29} -3.26865 q^{30} -6.33306 q^{31} +(-2.86758 - 3.59583i) q^{32} +(-0.347530 - 1.52263i) q^{33} +(-1.52554 - 0.734659i) q^{34} +(-3.38216 + 3.17384i) q^{35} +(1.39617 - 0.672360i) q^{36} +(0.398986 + 0.500313i) q^{37} +(9.30712 - 4.48207i) q^{38} +(0.882300 + 3.86561i) q^{39} +(-3.03007 - 1.45920i) q^{40} +(0.0473267 - 0.207352i) q^{41} +(-1.77637 + 4.60221i) q^{42} +(1.59775 + 7.00022i) q^{43} +(-0.273616 + 1.19879i) q^{44} +(1.95362 - 2.44977i) q^{45} +(2.97065 - 13.0153i) q^{46} +(-0.0734786 + 0.0353854i) q^{47} -5.48646 q^{48} +(2.63066 + 6.48688i) q^{49} -3.26253 q^{50} +(-0.992137 + 0.477788i) q^{51} +(0.694649 - 3.04346i) q^{52} +(-3.98091 + 4.99191i) q^{53} +(1.98629 - 8.70252i) q^{54} +(0.553254 + 2.42397i) q^{55} +(-3.70125 + 3.47328i) q^{56} +(1.49495 - 6.54979i) q^{57} +(14.0544 + 6.76825i) q^{58} +(-1.06121 - 4.64944i) q^{59} +(1.50791 - 0.726173i) q^{60} +(-3.84681 - 4.82375i) q^{61} +(9.66130 - 4.65264i) q^{62} +(-2.38752 - 4.08202i) q^{63} +(-1.96150 - 0.944607i) q^{64} +(-1.40459 - 6.15389i) q^{65} +(1.64878 + 2.06751i) q^{66} -9.13844 q^{67} +0.866984 q^{68} +(-5.41326 - 6.78801i) q^{69} +(2.82792 - 7.32654i) q^{70} +(5.89354 - 7.39026i) q^{71} +(2.13794 - 2.68089i) q^{72} +(4.79769 + 2.31044i) q^{73} +(-0.976228 - 0.470127i) q^{74} +(-1.32292 + 1.65889i) q^{75} +(-3.29787 + 4.13540i) q^{76} +(3.71358 + 0.538350i) q^{77} +(-4.18588 - 5.24893i) q^{78} +9.99391 q^{79} +8.73422 q^{80} +(-0.276275 - 0.346437i) q^{81} +(0.0801344 + 0.351092i) q^{82} +(-7.48275 - 3.60350i) q^{83} +(-0.202953 - 2.51777i) q^{84} +(1.57944 - 0.760619i) q^{85} +(-7.58021 - 9.50528i) q^{86} +(9.14033 - 4.40175i) q^{87} +(0.605452 + 2.65266i) q^{88} +(-6.81817 - 3.28346i) q^{89} +(-1.18058 + 5.17245i) q^{90} +(-9.42793 - 1.36675i) q^{91} +(1.52107 + 6.66425i) q^{92} +(1.55184 - 6.79904i) q^{93} +(0.0860979 - 0.107963i) q^{94} +(-2.37989 + 10.4270i) q^{95} +(4.56308 - 2.19746i) q^{96} -12.1737 q^{97} +(-8.77881 - 7.96334i) q^{98} -2.53500 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q + q^{2} - 7 q^{3} - 39 q^{4} + 2 q^{5} + 7 q^{6} - 13 q^{7} - 23 q^{8} - 42 q^{9} + 21 q^{10} - 7 q^{11} + q^{12} - 15 q^{13} - 22 q^{14} + 36 q^{15} - 55 q^{16} - 39 q^{17} + 62 q^{18} - 4 q^{19}+ \cdots + 72 q^{99}+O(q^{100}) $ 234 * q + q^2 - 7 * q^3 - 39 * q^4 + 2 * q^5 + 7 * q^6 - 13 * q^7 - 23 * q^8 - 42 * q^9 + 21 * q^10 - 7 * q^11 + q^12 - 15 * q^13 - 22 * q^14 + 36 * q^15 - 55 * q^16 - 39 * q^17 + 62 * q^18 - 4 * q^19 - 26 * q^20 - 30 * q^21 - 47 * q^22 - 32 * q^23 - 43 * q^24 - 69 * q^25 + 7 * q^26 - 19 * q^27 - 21 * q^28 + 8 * q^29 + 40 * q^30 - 8 * q^31 + 55 * q^32 - 59 * q^33 + q^34 - 20 * q^35 - 109 * q^36 + 22 * q^37 - 71 * q^38 - 41 * q^39 - 32 * q^40 - 9 * q^41 + 104 * q^42 - 15 * q^43 + 40 * q^44 + 102 * q^45 - 2 * q^46 - 21 * q^47 + 32 * q^48 + 35 * q^49 + 102 * q^50 - 21 * q^52 - 42 * q^53 - 59 * q^54 + 39 * q^55 + q^56 - 87 * q^57 - 27 * q^58 + 42 * q^59 + 162 * q^60 + 27 * q^61 - 77 * q^62 - 12 * q^63 - 53 * q^64 - 26 * q^65 - 66 * q^66 + 154 * q^67 + 276 * q^68 - 6 * q^69 - 32 * q^70 - 70 * q^71 + 106 * q^72 - 70 * q^73 - 44 * q^74 - 90 * q^75 - 20 * q^76 + 26 * q^77 - 93 * q^78 + 130 * q^79 - 4 * q^80 + 120 * q^81 - 30 * q^82 - 10 * q^83 - 148 * q^84 - 12 * q^85 - 4 * q^86 - 2 * q^87 - 68 * q^88 - 53 * q^89 + 195 * q^90 + 80 * q^91 + 153 * q^92 - 85 * q^93 + 130 * q^94 - 92 * q^95 - 89 * q^96 - 4 * q^97 + 42 * q^98 + 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.52554	+	0.734659i	−1.07872	+	0.519483i	−0.886906	−	0.461949i	$-0.847150\pi$
$2$	−1.52554	+	0.734659i	−1.07872	+	0.519483i	−0.191810	+	0.981432i	$0.561436\pi$
$3$	−0.245038	+	1.07358i	−0.141472	+	0.619831i	0.853621	+	0.520894i	$0.174401\pi$
$3$	−0.245038	+	1.07358i	−0.141472	+	0.619831i	−0.995094	+	0.0989372i	$0.968456\pi$
$4$	0.540556	−	0.677835i	0.270278	−	0.338918i
$5$	0.390090	−	1.70910i	0.174454	−	0.764331i	−0.809676	−	0.586878i	$-0.800357\pi$
$5$	0.390090	−	1.70910i	0.174454	−	0.764331i	0.984129	−	0.177453i	$-0.0567859\pi$
$6$	−0.414902	−	1.81780i	−0.169383	−	0.742115i
$7$	−2.19439	−	1.47806i	−0.829400	−	0.558656i
$7$	−2.19439	−	1.47806i	−0.829400	−	0.558656i
$8$	0.426894	−	1.87034i	0.150930	−	0.661266i
$9$	1.61038	+	0.775517i	0.536792	+	0.258506i
$10$	0.660507	+	2.89387i	0.208871	+	0.915122i
$11$	−1.27782	+	0.615366i	−0.385277	+	0.185540i	−0.616489	−	0.787364i	$-0.711445\pi$
$11$	−1.27782	+	0.615366i	−0.385277	+	0.185540i	0.231211	+	0.972904i	$0.425731\pi$
$12$	0.595254	+	0.746425i	0.171835	+	0.215474i
$13$	3.24409	−	1.56227i	0.899750	−	0.433297i	0.0739511	−	0.997262i	$-0.476439\pi$
$13$	3.24409	−	1.56227i	0.899750	−	0.433297i	0.825798	+	0.563965i	$0.190725\pi$
$14$	4.43349	+	0.642713i	1.18490	+	0.171772i
$15$	1.73926	+	0.837585i	0.449076	+	0.216264i
$16$	1.10867	+	4.85739i	0.277167	+	1.21435i
$17$	0.623490	+	0.781831i	0.151218	+	0.189622i
$17$	0.623490	+	0.781831i	0.151218	+	0.189622i
$18$	−3.02643			−0.713336
$19$	−6.10089			−1.39964			−0.699820	−	0.714319i	$-0.746736\pi$
$19$	−6.10089			−1.39964			−0.699820	+	0.714319i	$0.746736\pi$
$20$	−0.947620	−	1.18828i	−0.211894	−	0.265707i
$21$	2.12453	−	1.99367i	0.463610	−	0.435054i
$22$	1.49728	−	1.87753i	0.319220	−	0.400290i
$23$	−4.91583	+	6.16426i	−1.02502	+	1.28534i	−0.0672714	+	0.997735i	$0.521429\pi$
$23$	−4.91583	+	6.16426i	−1.02502	+	1.28534i	−0.957750	+	0.287602i	$0.907142\pi$
$24$	1.90336	+	0.916608i	0.388521	+	0.187102i
$25$	1.73601	+	0.836017i	0.347201	+	0.167203i
$26$	−3.80124	+	4.76661i	−0.745485	+	0.934808i
$27$	−3.28692	+	4.12167i	−0.632568	+	0.793216i
$28$	−2.18807	+	0.688456i	−0.413507	+	0.130106i
$29$	−5.74407	−	7.20283i	−1.06665	−	1.33753i	−0.938307	−	0.345803i	$-0.887607\pi$
$29$	−5.74407	−	7.20283i	−1.06665	−	1.33753i	−0.128340	−	0.991730i	$-0.540965\pi$
$30$	−3.26865			−0.596771
$31$	−6.33306			−1.13745			−0.568725	−	0.822528i	$-0.692563\pi$
$31$	−6.33306			−1.13745			−0.568725	+	0.822528i	$0.692563\pi$
$32$	−2.86758	−	3.59583i	−0.506921	−	0.635659i
$33$	−0.347530	−	1.52263i	−0.0604973	−	0.265056i
$34$	−1.52554	−	0.734659i	−0.261627	−	0.125993i
$35$	−3.38216	+	3.17384i	−0.571689	+	0.536476i
$36$	1.39617	−	0.672360i	0.232695	−	0.112060i
$37$	0.398986	+	0.500313i	0.0655930	+	0.0822510i	0.813546	−	0.581501i	$-0.197534\pi$
$37$	0.398986	+	0.500313i	0.0655930	+	0.0822510i	−0.747953	+	0.663752i	$0.768963\pi$
$38$	9.30712	−	4.48207i	1.50981	−	0.727088i
$39$	0.882300	+	3.86561i	0.141281	+	0.618993i
$40$	−3.03007	−	1.45920i	−0.479096	−	0.230720i
$41$	0.0473267	−	0.207352i	0.00739119	−	0.0323829i	−0.971098	−	0.238682i	$-0.923285\pi$
$41$	0.0473267	−	0.207352i	0.00739119	−	0.0323829i	0.978489	+	0.206299i	$0.0661419\pi$
$42$	−1.77637	+	4.60221i	−0.274101	+	0.710137i
$43$	1.59775	+	7.00022i	0.243655	+	1.06752i	0.937660	+	0.347553i	$0.112987\pi$
$43$	1.59775	+	7.00022i	0.243655	+	1.06752i	−0.694005	+	0.719970i	$0.744155\pi$
$44$	−0.273616	+	1.19879i	−0.0412492	+	0.180725i
$45$	1.95362	−	2.44977i	0.291229	−	0.365190i
$46$	2.97065	−	13.0153i	0.437998	−	1.91899i
$47$	−0.0734786	+	0.0353854i	−0.0107179	+	0.00516149i	−0.439235	−	0.898372i	$-0.644750\pi$
$47$	−0.0734786	+	0.0353854i	−0.0107179	+	0.00516149i	0.428517	+	0.903534i	$0.359036\pi$
$48$	−5.48646			−0.791902
$49$	2.63066	+	6.48688i	0.375808	+	0.926698i
$50$	−3.26253			−0.461391
$51$	−0.992137	+	0.477788i	−0.138927	+	0.0669037i
$52$	0.694649	−	3.04346i	0.0963305	−	0.422051i
$53$	−3.98091	+	4.99191i	−0.546821	+	0.685691i	−0.976060	−	0.217499i	$-0.930210\pi$
$53$	−3.98091	+	4.99191i	−0.546821	+	0.685691i	0.429240	+	0.903190i	$0.358781\pi$
$54$	1.98629	−	8.70252i	0.270300	−	1.18426i
$55$	0.553254	+	2.42397i	0.0746008	+	0.326847i
$56$	−3.70125	+	3.47328i	−0.494601	+	0.464136i
$57$	1.49495	−	6.54979i	0.198011	−	0.867541i
$58$	14.0544	+	6.76825i	1.84543	+	0.888715i
$59$	−1.06121	−	4.64944i	−0.138157	−	0.605306i	−0.995839	−	0.0911260i	$-0.970953\pi$
$59$	−1.06121	−	4.64944i	−0.138157	−	0.605306i	0.857682	−	0.514180i	$-0.171904\pi$
$60$	1.50791	−	0.726173i	0.194671	−	0.0937485i
$61$	−3.84681	−	4.82375i	−0.492534	−	0.617618i	0.471993	−	0.881602i	$-0.343535\pi$
$61$	−3.84681	−	4.82375i	−0.492534	−	0.617618i	−0.964527	+	0.263984i	$0.914963\pi$
$62$	9.66130	−	4.65264i	1.22699	−	0.590886i
$63$	−2.38752	−	4.08202i	−0.300800	−	0.514286i
$64$	−1.96150	−	0.944607i	−0.245187	−	0.118076i
$65$	−1.40459	−	6.15389i	−0.174217	−	0.763296i
$66$	1.64878	+	2.06751i	0.202951	+	0.254493i
$67$	−9.13844			−1.11644			−0.558219	−	0.829694i	$-0.688515\pi$
$67$	−9.13844			−1.11644			−0.558219	+	0.829694i	$0.688515\pi$
$68$	0.866984			0.105137
$69$	−5.41326	−	6.78801i	−0.651680	−	0.817180i
$70$	2.82792	−	7.32654i	0.338001	−	0.875689i
$71$	5.89354	−	7.39026i	0.699434	−	0.877063i	−0.297547	−	0.954707i	$-0.596169\pi$
$71$	5.89354	−	7.39026i	0.699434	−	0.877063i	0.996981	+	0.0776446i	$0.0247399\pi$
$72$	2.13794	−	2.68089i	0.251959	−	0.315946i
$73$	4.79769	+	2.31044i	0.561527	+	0.270417i	0.693042	−	0.720897i	$-0.256270\pi$
$73$	4.79769	+	2.31044i	0.561527	+	0.270417i	−0.131515	+	0.991314i	$0.541984\pi$
$74$	−0.976228	−	0.470127i	−0.113484	−	0.0546511i
$75$	−1.32292	+	1.65889i	−0.152757	+	0.191552i
$76$	−3.29787	+	4.13540i	−0.378292	+	0.474363i
$77$	3.71358	+	0.538350i	0.423202	+	0.0613507i
$78$	−4.18588	−	5.24893i	−0.473958	−	0.594325i
$79$	9.99391			1.12440			0.562201	−	0.827000i	$-0.309955\pi$
$79$	9.99391			1.12440			0.562201	+	0.827000i	$0.309955\pi$
$80$	8.73422			0.976516
$81$	−0.276275	−	0.346437i	−0.0306972	−	0.0384930i
$82$	0.0801344	+	0.351092i	0.00884936	+	0.0387716i
$83$	−7.48275	−	3.60350i	−0.821339	−	0.395536i	−0.0244792	−	0.999700i	$-0.507793\pi$
$83$	−7.48275	−	3.60350i	−0.821339	−	0.395536i	−0.796860	+	0.604164i	$0.793507\pi$
$84$	−0.202953	−	2.51777i	−0.0221440	−	0.274711i
$85$	1.57944	−	0.760619i	0.171315	−	0.0825007i
$86$	−7.58021	−	9.50528i	−0.817395	−	1.02498i
$87$	9.14033	−	4.40175i	0.979946	−	0.471917i
$88$	0.605452	+	2.65266i	0.0645414	+	0.282774i
$89$	−6.81817	−	3.28346i	−0.722725	−	0.348046i	0.0360935	−	0.999348i	$-0.488509\pi$
$89$	−6.81817	−	3.28346i	−0.722725	−	0.348046i	−0.758818	+	0.651303i	$0.774223\pi$
$90$	−1.18058	+	5.17245i	−0.124444	+	0.545225i
$91$	−9.42793	−	1.36675i	−0.988316	−	0.143274i
$92$	1.52107	+	6.66425i	0.158583	+	0.694796i
$93$	1.55184	−	6.79904i	0.160918	−	0.705028i
$94$	0.0860979	−	0.107963i	0.00888033	−	0.0111356i
$95$	−2.37989	+	10.4270i	−0.244172	+	1.06979i
$96$	4.56308	−	2.19746i	0.465717	−	0.224278i
$97$	−12.1737			−1.23605			−0.618027	−	0.786157i	$-0.712068\pi$
$97$	−12.1737			−1.23605			−0.618027	+	0.786157i	$0.712068\pi$
$98$	−8.77881	−	7.96334i	−0.886794	−	0.804418i
$99$	−2.53500			−0.254777
$100$	1.50509	−	0.724813i	0.150509	−	0.0724813i
$101$	−1.08680	+	4.76158i	−0.108141	+	0.473795i	0.891638	+	0.452749i	$0.149557\pi$
$101$	−1.08680	+	4.76158i	−0.108141	+	0.473795i	−0.999779	+	0.0210459i	$0.993300\pi$
$102$	1.16253	−	1.45777i	0.115108	−	0.144340i
$103$	−2.43511	+	10.6689i	−0.239938	+	1.05124i	0.701134	+	0.713030i	$0.252678\pi$
$103$	−2.43511	+	10.6689i	−0.239938	+	1.05124i	−0.941072	+	0.338207i	$0.890179\pi$
$104$	−1.53710	−	6.73449i	−0.150725	−	0.660371i
$105$	−2.57861	−	4.40873i	−0.251647	−	0.430248i
$106$	2.40567	−	10.5400i	0.233660	−	1.02373i
$107$	−12.5641	−	6.05056i	−1.21462	−	0.584930i	−0.286811	−	0.957987i	$-0.592595\pi$
$107$	−12.5641	−	6.05056i	−1.21462	−	0.584930i	−0.927808	+	0.373058i	$0.878309\pi$
$108$	1.01705	+	4.45598i	0.0978656	+	0.428777i
$109$	−17.5276	+	8.44085i	−1.67884	+	0.808486i	−0.681804	+	0.731534i	$0.738804\pi$
$109$	−17.5276	+	8.44085i	−1.67884	+	0.808486i	−0.997035	+	0.0769519i	$0.975481\pi$
$110$	−2.62480	−	3.29139i	−0.250265	−	0.313822i
$111$	−0.634893	+	0.305748i	−0.0602614	+	0.0290203i
$112$	4.74669	−	12.2977i	0.448520	−	1.16202i
$113$	−6.61344	−	3.18487i	−0.622140	−	0.299607i	0.0961326	−	0.995369i	$-0.469353\pi$
$113$	−6.61344	−	3.18487i	−0.622140	−	0.299607i	−0.718273	+	0.695762i	$0.755067\pi$
$114$	2.53127	+	11.0902i	0.237075	+	1.03869i
$115$	8.61769	+	10.8062i	0.803604	+	1.00769i
$116$	−7.98732			−0.741605
$117$	6.43578			0.594988
$118$	5.03466	+	6.31327i	0.463478	+	0.581184i
$119$	−0.212580	−	2.63720i	−0.0194872	−	0.241751i
$120$	2.30905	−	2.89546i	0.210787	−	0.264318i
$121$	−5.60424	+	7.02749i	−0.509476	+	0.638863i
$122$	9.41226	+	4.53271i	0.852146	+	0.410372i
$123$	0.211012	+	0.101618i	0.0190263	+	0.00916259i
$124$	−3.42337	+	4.29277i	−0.307428	+	0.385502i
$125$	7.57107	−	9.49382i	0.677177	−	0.849153i
$126$	6.64115	+	4.47325i	0.591641	+	0.398509i
$127$	1.12104	+	1.40574i	0.0994761	+	0.124739i	0.829078	−	0.559133i	$-0.188866\pi$
$127$	1.12104	+	1.40574i	0.0994761	+	0.124739i	−0.729602	+	0.683872i	$0.760295\pi$
$128$	12.8848			1.13886
$129$	−7.90680			−0.696155
$130$	6.66376	+	8.35609i	0.584450	+	0.732878i
$131$	1.21275	+	5.31341i	0.105959	+	0.464235i	0.999872	+	0.0159953i	$0.00509167\pi$
$131$	1.21275	+	5.31341i	0.105959	+	0.464235i	−0.893914	+	0.448239i	$0.852051\pi$
$132$	−1.21995	−	0.587498i	−0.106183	−	0.0511351i
$133$	13.3877	+	9.01750i	1.16086	+	0.781916i
$134$	13.9410	−	6.71364i	1.20432	−	0.579970i
$135$	5.76213	+	7.22548i	0.495925	+	0.621871i
$136$	1.72846	−	0.832381i	0.148214	−	0.0713761i
$137$	−1.33199	−	5.83581i	−0.113799	−	0.498587i	−0.999416	−	0.0341702i	$-0.989121\pi$
$137$	−1.33199	−	5.83581i	−0.113799	−	0.498587i	0.885617	−	0.464417i	$-0.153736\pi$
$138$	13.2450	+	6.37845i	1.12749	+	0.542970i
$139$	4.16275	−	18.2382i	0.353080	−	1.54694i	−0.416945	−	0.908932i	$-0.636899\pi$
$139$	4.16275	−	18.2382i	0.353080	−	1.54694i	0.770025	−	0.638013i	$-0.220244\pi$
$140$	0.323093	+	4.00818i	0.0273064	+	0.338753i
$141$	−0.0199840	−	0.0875558i	−0.00168296	−	0.00737353i
$142$	−3.56148	+	15.6038i	−0.298872	+	1.30945i
$143$	−3.18400	+	3.99261i	−0.266259	+	0.333879i
$144$	−1.98161	+	8.68202i	−0.165135	+	0.723502i
$145$	−14.5510	+	7.00741i	−1.20840	+	0.581934i
$146$	−9.01643			−0.746205
$147$	−7.60879	+	1.23469i	−0.627563	+	0.101835i
$148$	0.554804			0.0456046
$149$	0.750469	−	0.361407i	0.0614808	−	0.0296076i	−0.402891	−	0.915248i	$-0.631995\pi$
$149$	0.750469	−	0.361407i	0.0614808	−	0.0296076i	0.464372	+	0.885640i	$0.346280\pi$
$150$	0.799442	−	3.50258i	0.0652742	−	0.285985i
$151$	4.81396	−	6.03652i	0.391755	−	0.491245i	−0.546369	−	0.837544i	$-0.683990\pi$
$151$	4.81396	−	6.03652i	0.391755	−	0.491245i	0.938124	+	0.346299i	$0.112562\pi$
$152$	−2.60443	+	11.4108i	−0.211247	+	0.925534i
$153$	0.397730	+	1.74257i	0.0321546	+	0.140878i
$154$	−6.06070	+	1.90694i	−0.488385	+	0.153666i
$155$	−2.47046	+	10.8238i	−0.198432	+	0.869388i
$156$	3.09718	+	1.49152i	0.247973	+	0.119417i
$157$	4.53662	+	19.8762i	0.362062	+	1.58630i	0.747953	+	0.663752i	$0.231037\pi$
$157$	4.53662	+	19.8762i	0.362062	+	1.58630i	−0.385891	+	0.922544i	$0.626106\pi$
$158$	−15.2461	+	7.34212i	−1.21291	+	0.584108i
$159$	−4.38374	−	5.49703i	−0.347653	−	0.435943i
$160$	−7.26424	+	3.49827i	−0.574288	+	0.276563i
$161$	19.8984	−	6.26085i	1.56821	−	0.493424i
$162$	0.675980	+	0.325535i	0.0531100	+	0.0255764i
$163$	3.70701	+	16.2415i	0.290355	+	1.27213i	0.884032	+	0.467426i	$0.154819\pi$
$163$	3.70701	+	16.2415i	0.290355	+	1.27213i	−0.593677	+	0.804703i	$0.702324\pi$
$164$	−0.114968	−	0.144165i	−0.00897747	−	0.0112574i
$165$	−2.73789			−0.213144
$166$	14.0626			1.09147
$167$	−9.36337	−	11.7413i	−0.724559	−	0.908569i	0.274027	−	0.961722i	$-0.411644\pi$
$167$	−9.36337	−	11.7413i	−0.724559	−	0.908569i	−0.998586	+	0.0531533i	$0.983073\pi$
$168$	−2.82189	−	4.82467i	−0.217714	−	0.372232i
$169$	−0.0219243	+	0.0274922i	−0.00168648	+	0.00211478i
$170$	−1.85070	+	2.32070i	−0.141942	+	0.177990i
$171$	−9.82473	−	4.73134i	−0.751316	−	0.361815i
$172$	5.60867	+	2.70099i	0.427657	+	0.205949i
$173$	8.04454	−	10.0875i	0.611615	−	0.766941i	−0.375523	−	0.926813i	$-0.622537\pi$
$173$	8.04454	−	10.0875i	0.611615	−	0.766941i	0.987138	+	0.159872i	$0.0511082\pi$
$174$	−10.7101	+	13.4301i	−0.811932	+	1.01813i
$175$	−2.57378	−	4.40047i	−0.194560	−	0.332644i
$176$	−4.40575	−	5.52464i	−0.332096	−	0.416435i
$177$	5.25158			0.394733
$178$	12.8136			0.960419
$179$	0.0137353	+	0.0172235i	0.00102662	+	0.00128735i	0.782345	−	0.622846i	$-0.214024\pi$
$179$	0.0137353	+	0.0172235i	0.00102662	+	0.00128735i	−0.781318	+	0.624133i	$0.785452\pi$
$180$	−0.604496	−	2.64847i	−0.0450565	−	0.197405i
$181$	−2.56005	−	1.23286i	−0.190287	−	0.0916376i	0.336314	−	0.941750i	$-0.390820\pi$
$181$	−2.56005	−	1.23286i	−0.190287	−	0.0916376i	−0.526601	+	0.850112i	$0.676534\pi$
$182$	15.3867	−	4.84130i	1.14054	−	0.358861i
$183$	6.12129	−	2.94786i	0.452499	−	0.217912i
$184$	9.43074	+	11.8258i	0.695243	+	0.871807i
$185$	1.01072	−	0.486739i	0.0743099	−	0.0357858i
$186$	2.62760	+	11.5122i	0.192665	+	0.844119i
$187$	−1.27782	−	0.615366i	−0.0934435	−	0.0450000i
$188$	−0.0157338	+	0.0689341i	−0.00114750	+	0.00502754i
$189$	13.3049	−	4.18625i	0.967786	−	0.304505i
$190$	−4.02968	−	17.6552i	−0.292344	−	1.28084i
$191$	2.60176	−	11.3990i	0.188257	−	0.824806i	−0.789279	−	0.614035i	$-0.789545\pi$
$191$	2.60176	−	11.3990i	0.188257	−	0.824806i	0.977535	−	0.210771i	$-0.0675975\pi$
$192$	1.49475	−	1.87436i	0.107874	−	0.135270i
$193$	−5.98502	+	26.2221i	−0.430811	+	1.88751i	0.0291644	+	0.999575i	$0.490715\pi$
$193$	−5.98502	+	26.2221i	−0.430811	+	1.88751i	−0.459975	+	0.887932i	$0.652142\pi$
$194$	18.5714	−	8.94353i	1.33335	−	0.642108i
$195$	6.95087			0.497762
$196$	5.81905	+	1.72337i	0.415647	+	0.123098i
$197$	−7.06254			−0.503185			−0.251593	−	0.967833i	$-0.580954\pi$
$197$	−7.06254			−0.503185			−0.251593	+	0.967833i	$0.580954\pi$
$198$	3.86723	−	1.86236i	0.274832	−	0.132352i
$199$	0.572937	−	2.51020i	0.0406144	−	0.177943i	−0.950552	−	0.310564i	$-0.899482\pi$
$199$	0.572937	−	2.51020i	0.0406144	−	0.177943i	0.991167	+	0.132621i	$0.0423392\pi$
$200$	2.30473	−	2.89004i	0.162969	−	0.204356i
$201$	2.23926	−	9.81084i	0.157945	−	0.692003i
$202$	−1.84019	−	8.06239i	−0.129475	−	0.567268i
$203$	1.95845	+	24.2959i	0.137457	+	1.70524i
$204$	−0.212444	+	0.930776i	−0.0148740	+	0.0651674i
$205$	−0.335923	−	0.161772i	−0.0234618	−	0.0112986i
$206$	−4.12316	−	18.0648i	−0.287274	−	1.25863i
$207$	−12.6968	+	6.11447i	−0.882490	+	0.424985i
$208$	11.1852	+	14.0258i	0.775553	+	0.972513i
$209$	7.79584	−	3.75428i	0.539249	−	0.259689i
$210$	7.17268	+	4.83127i	0.494962	+	0.333389i
$211$	13.8307	+	6.66053i	0.952148	+	0.458530i	0.844439	−	0.535652i	$-0.179934\pi$
$211$	13.8307	+	6.66053i	0.952148	+	0.458530i	0.107709	+	0.994182i	$0.465649\pi$
$212$	1.23179	+	5.39681i	0.0845994	+	0.370654i
$213$	6.48990	+	8.13807i	0.444680	+	0.557611i
$214$	23.6121			1.61409
$215$	12.5873			0.858448
$216$	6.30577	+	7.90718i	0.429053	+	0.538016i
$217$	13.8972	+	9.36066i	0.943401	+	0.635443i
$218$	20.5378	−	25.7536i	1.39100	−	1.74426i
$219$	−3.65606	+	4.58455i	−0.247054	+	0.309795i
$220$	1.94211	+	0.935273i	0.130937	+	0.0630561i
$221$	3.24409	+	1.56227i	0.218221	+	0.105090i
$222$	0.743931	−	0.932860i	0.0499294	−	0.0626094i
$223$	−4.45746	+	5.58948i	−0.298494	+	0.374299i	−0.908349	−	0.418214i	$-0.862656\pi$
$223$	−4.45746	+	5.58948i	−0.298494	+	0.374299i	0.609855	+	0.792513i	$0.291228\pi$
$224$	0.977709	+	12.1291i	0.0653259	+	0.810410i
$225$	2.14728	+	2.69260i	0.143152	+	0.179507i
$226$	12.4288			0.826754
$227$	−4.35842			−0.289279			−0.144639	−	0.989484i	$-0.546202\pi$
$227$	−4.35842			−0.289279			−0.144639	+	0.989484i	$0.546202\pi$
$228$	−3.63158	−	4.55385i	−0.240507	−	0.301586i
$229$	4.35873	+	19.0968i	0.288033	+	1.26195i	0.887220	+	0.461346i	$0.152633\pi$
$229$	4.35873	+	19.0968i	0.288033	+	1.26195i	−0.599187	+	0.800609i	$0.704510\pi$
$230$	−21.0855	−	10.1542i	−1.39034	−	0.669551i
$231$	−1.48793	+	3.85491i	−0.0978985	+	0.253634i
$232$	−15.9239	+	7.66853i	−1.04545	+	0.503464i
$233$	4.06102	+	5.09236i	0.266046	+	0.333612i	0.896853	−	0.442328i	$-0.145847\pi$
$233$	4.06102	+	5.09236i	0.266046	+	0.333612i	−0.630807	+	0.775940i	$0.717276\pi$
$234$	−9.81801	+	4.72811i	−0.641824	+	0.309086i
$235$	0.0318138	+	0.139385i	0.00207530	+	0.00909250i
$236$	−3.72520	−	1.79396i	−0.242490	−	0.116777i
$237$	−2.44888	+	10.7293i	−0.159072	+	0.696940i
$238$	2.26174	+	3.86696i	0.146607	+	0.250658i
$239$	0.174413	+	0.764152i	0.0112818	+	0.0494289i	0.980256	−	0.197735i	$-0.0633585\pi$
$239$	0.174413	+	0.764152i	0.0112818	+	0.0494289i	−0.968974	+	0.247164i	$0.920501\pi$
$240$	−2.14021	+	9.37688i	−0.138150	+	0.605275i
$241$	8.13369	−	10.1993i	0.523937	−	0.656997i	−0.447503	−	0.894283i	$-0.647686\pi$
$241$	8.13369	−	10.1993i	0.523937	−	0.656997i	0.971440	+	0.237286i	$0.0762579\pi$
$242$	3.38665	−	14.8379i	0.217702	−	0.953816i
$243$	−13.8096	+	6.65035i	−0.885886	+	0.426620i
$244$	−5.34913			−0.342443
$245$	12.1129	−	1.96557i	0.773865	−	0.125576i
$246$	−0.396561			−0.0252838
$247$	−19.7918	+	9.53125i	−1.25933	+	0.606459i
$248$	−2.70354	+	11.8450i	−0.171675	+	0.752157i
$249$	5.70220	−	7.15034i	0.361363	−	0.453134i
$250$	−4.57521	+	20.0453i	−0.289362	+	1.26778i
$251$	−0.346720	−	1.51908i	−0.0218848	−	0.0958834i	0.962806	−	0.270193i	$-0.0870877\pi$
$251$	−0.346720	−	1.51908i	−0.0218848	−	0.0958834i	−0.984691	+	0.174310i	$0.944231\pi$
$252$	−4.05753	−	0.588211i	−0.255600	−	0.0370538i
$253$	2.48828	−	10.9018i	0.156437	−	0.685393i
$254$	−2.74292	−	1.32092i	−0.172106	−	0.0828820i
$255$	0.429563	+	1.88204i	0.0269003	+	0.117858i
$256$	−15.7332	+	7.57671i	−0.983325	+	0.473545i
$257$	−0.681442	−	0.854502i	−0.0425072	−	0.0533024i	0.760124	−	0.649779i	$-0.225138\pi$
$257$	−0.681442	−	0.854502i	−0.0425072	−	0.0533024i	−0.802631	+	0.596476i	$0.796567\pi$
$258$	12.0621	−	5.80881i	0.750954	−	0.361641i
$259$	−0.136035	−	1.68761i	−0.00845283	−	0.104863i
$260$	−4.93058	−	2.37444i	−0.305782	−	0.147257i
$261$	−3.66420	−	16.0539i	−0.226808	−	0.993711i
$262$	−5.75364	−	7.21484i	−0.355461	−	0.445734i
$263$	9.40825			0.580138			0.290069	−	0.957006i	$-0.406322\pi$
$263$	9.40825			0.580138			0.290069	+	0.957006i	$0.406322\pi$
$264$	−2.99620			−0.184403
$265$	6.97873	+	8.75106i	0.428700	+	0.537573i
$266$	−27.0482	−	3.92112i	−1.65843	−	0.240419i
$267$	5.19576	−	6.51528i	0.317975	−	0.398729i
$268$	−4.93983	+	6.19436i	−0.301748	+	0.378380i
$269$	−2.03100	−	0.978079i	−0.123832	−	0.0596345i	0.370942	−	0.928656i	$-0.379035\pi$
$269$	−2.03100	−	0.978079i	−0.123832	−	0.0596345i	−0.494774	+	0.869022i	$0.664749\pi$
$270$	−14.0986	−	6.78953i	−0.858014	−	0.413198i
$271$	8.98358	−	11.2651i	0.545713	−	0.684303i	−0.430132	−	0.902766i	$-0.641533\pi$
$271$	8.98358	−	11.2651i	0.545713	−	0.684303i	0.975845	+	0.218463i	$0.0701043\pi$
$272$	−3.10642	+	3.89532i	−0.188354	+	0.236189i
$273$	3.77751	−	9.78673i	0.228625	−	0.592320i
$274$	6.31932	+	7.92418i	0.381764	+	0.478717i
$275$	−2.73276			−0.164792
$276$	−7.52732			−0.453091
$277$	−9.62689	−	12.0717i	−0.578424	−	0.725320i	0.403419	−	0.915015i	$-0.367822\pi$
$277$	−9.62689	−	12.0717i	−0.578424	−	0.725320i	−0.981843	+	0.189695i	$0.939250\pi$
$278$	7.04844	+	30.8813i	0.422738	+	1.85213i
$279$	−10.1986	−	4.91139i	−0.610575	−	0.294037i
$280$	4.49234	+	7.68069i	0.268469	+	0.459009i
$281$	4.31583	−	2.07839i	0.257461	−	0.123987i	−0.300702	−	0.953718i	$-0.597221\pi$
$281$	4.31583	−	2.07839i	0.257461	−	0.123987i	0.558162	+	0.829732i	$0.311507\pi$
$282$	0.0948101	+	0.118888i	0.00564586	+	0.00707968i
$283$	−5.58189	+	2.68810i	−0.331809	+	0.159791i	−0.592369	−	0.805667i	$-0.701807\pi$
$283$	−5.58189	+	2.68810i	−0.331809	+	0.159791i	0.260560	+	0.965458i	$0.416093\pi$
$284$	−1.82360	−	7.98969i	−0.108210	−	0.474101i
$285$	−10.6111	−	5.11001i	−0.628544	−	0.302691i
$286$	1.92410	−	8.43002i	0.113774	−	0.498478i
$287$	−0.410332	+	0.385058i	−0.0242212	+	0.0227293i
$288$	−1.82926	−	8.01450i	−0.107790	−	0.472259i
$289$	−0.222521	+	0.974928i	−0.0130895	+	0.0573487i
$290$	17.0501	−	21.3801i	1.00121	−	1.25548i
$291$	2.98302	−	13.0695i	0.174868	−	0.766145i
$292$	4.15952	−	2.00312i	0.243417	−	0.117224i
$293$	−8.40417			−0.490977			−0.245488	−	0.969400i	$-0.578948\pi$
$293$	−8.40417			−0.490977			−0.245488	+	0.969400i	$0.578948\pi$
$294$	10.7004	−	7.47343i	0.624061	−	0.435860i
$295$	−8.36031			−0.486756
$296$	1.10608	−	0.532661i	0.0642897	−	0.0309603i
$297$	1.66376	−	7.28941i	0.0965412	−	0.422975i
$298$	−0.879357	+	1.10268i	−0.0509398	+	0.0638765i
$299$	−6.31716	+	27.6773i	−0.365331	+	1.60062i
$300$	0.409341	+	1.79344i	0.0236333	+	0.103544i
$301$	6.84068	−	17.7228i	0.394290	−	1.02152i
$302$	−2.90909	+	12.7455i	−0.167399	+	0.733424i
$303$	−4.84563	−	2.33353i	−0.278374	−	0.134058i
$304$	−6.76386	−	29.6344i	−0.387934	−	1.69965i
$305$	−9.74485	+	4.69287i	−0.557989	+	0.268713i
$306$	−1.88695	−	2.36616i	−0.107870	−	0.135264i
$307$	25.0077	−	12.0431i	1.42726	−	0.687334i	0.448777	−	0.893644i	$-0.351860\pi$
$307$	25.0077	−	12.0431i	1.42726	−	0.687334i	0.978487	+	0.206310i	$0.0661456\pi$
$308$	2.37231	−	2.22619i	0.135175	−	0.126849i
$309$	−10.8572	−	5.22856i	−0.617645	−	0.297442i
$310$	−4.18303	−	18.3270i	−0.237580	−	1.04091i
$311$	4.31805	+	5.41466i	0.244854	+	0.307037i	0.889038	−	0.457833i	$-0.151374\pi$
$311$	4.31805	+	5.41466i	0.244854	+	0.307037i	−0.644184	+	0.764871i	$0.722803\pi$
$312$	7.60666			0.430642
$313$	1.86966			0.105679			0.0528396	−	0.998603i	$-0.483173\pi$
$313$	1.86966			0.105679			0.0528396	+	0.998603i	$0.483173\pi$
$314$	−21.5230	−	26.9890i	−1.21462	−	1.52308i
$315$	−7.90791	+	2.48815i	−0.445561	+	0.140192i
$316$	5.40227	−	6.77423i	0.303901	−	0.381080i
$317$	7.36648	−	9.23728i	0.413743	−	0.518817i	−0.530670	−	0.847578i	$-0.678060\pi$
$317$	7.36648	−	9.23728i	0.413743	−	0.518817i	0.944413	+	0.328761i	$0.106631\pi$
$318$	10.7260	+	5.16537i	0.601484	+	0.289659i
$319$	11.7723	+	5.66922i	0.659120	+	0.317416i
$320$	−2.37958	+	2.98390i	−0.133023	+	0.166805i
$321$	9.57444	−	12.0060i	0.534393	−	0.670108i
$322$	−25.7561	+	24.1697i	−1.43533	+	1.34692i
$323$	−3.80384	−	4.76987i	−0.211651	−	0.265402i
$324$	−0.384169			−0.0213427
$325$	6.93785			0.384843
$326$	−17.5871	−	22.0535i	−0.974060	−	1.22143i
$327$	−4.76700	−	20.8856i	−0.263616	−	1.15498i
$328$	−0.367616	−	0.177034i	−0.0202982	−	0.00977509i
$329$	0.213542	+	0.0309568i	0.0117730	+	0.00170670i
$330$	4.17675	−	2.01141i	0.229922	−	0.110725i
$331$	−17.7908	−	22.3089i	−0.977868	−	1.22621i	−0.974077	−	0.226215i	$-0.927365\pi$
$331$	−17.7908	−	22.3089i	−0.977868	−	1.22621i	−0.00379121	−	0.999993i	$-0.501207\pi$
$332$	−6.48743	+	3.12418i	−0.356044	+	0.171462i
$333$	0.254517	+	1.11511i	0.0139475	+	0.0611078i
$334$	22.9100	+	11.0329i	1.25358	+	0.603692i
$335$	−3.56481	+	15.6185i	−0.194766	+	0.853328i
$336$	12.0394	+	8.10934i	0.656804	+	0.442401i
$337$	4.77781	+	20.9330i	0.260264	+	1.14029i	0.920966	+	0.389643i	$0.127402\pi$
$337$	4.77781	+	20.9330i	0.260264	+	1.14029i	−0.660702	+	0.750649i	$0.729741\pi$
$338$	0.0132489	−	0.0580471i	0.000720644	−	0.00315735i
$339$	5.03975	−	6.31964i	0.273722	−	0.343236i
$340$	0.338202	−	1.48176i	0.0183416	−	0.0803596i
$341$	8.09251	−	3.89715i	0.438234	−	0.211042i
$342$	18.4639			0.998413
$343$	3.81535	−	18.1230i	0.206010	−	0.978550i
$344$	13.7749			0.742692
$345$	−13.7130	+	6.60384i	−0.738284	+	0.355539i
$346$	−4.86133	+	21.2989i	−0.261347	+	1.14504i
$347$	−21.7264	+	27.2440i	−1.16633	+	1.46253i	−0.306565	+	0.951850i	$0.599180\pi$
$347$	−21.7264	+	27.2440i	−1.16633	+	1.46253i	−0.859768	+	0.510685i	$0.829392\pi$
$348$	1.95719	−	8.57503i	0.104917	−	0.459670i
$349$	5.27700	+	23.1200i	0.282471	+	1.23759i	0.894614	+	0.446840i	$0.147451\pi$
$349$	5.27700	+	23.1200i	0.282471	+	1.23759i	−0.612143	+	0.790747i	$0.709692\pi$
$350$	7.15924	+	4.82222i	0.382678	+	0.257759i
$351$	−4.22391	+	18.5061i	−0.225455	+	0.987785i
$352$	5.87701	+	2.83022i	0.313245	+	0.150851i
$353$	3.60045	+	15.7746i	0.191633	+	0.839597i	0.975733	+	0.218963i	$0.0702675\pi$
$353$	3.60045	+	15.7746i	0.191633	+	0.839597i	−0.784101	+	0.620634i	$0.786875\pi$
$354$	−8.01148	+	3.85813i	−0.425805	+	0.205057i
$355$	−10.3317	−	12.9555i	−0.548347	−	0.687606i
$356$	−5.91125	+	2.84671i	−0.313295	+	0.150875i
$357$	2.88333	+	0.417990i	0.152602	+	0.0221224i
$358$	−0.0336071	−	0.0161843i	−0.00177619	−	0.000855369i
$359$	−3.28401	−	14.3882i	−0.173323	−	0.759379i	−0.984615	−	0.174738i	$-0.944092\pi$
$359$	−3.28401	−	14.3882i	−0.173323	−	0.759379i	0.811292	−	0.584642i	$-0.198765\pi$
$360$	−3.74791	−	4.69974i	−0.197532	−	0.247698i
$361$	18.2208			0.958991
$362$	4.81118			0.252870
$363$	−6.17132	−	7.73860i	−0.323910	−	0.406171i
$364$	−6.02275	+	5.65178i	−0.315678	+	0.296234i
$365$	5.82030	−	7.29842i	0.304648	−	0.382017i
$366$	−7.17258	+	8.99413i	−0.374917	+	0.470131i
$367$	8.34792	+	4.02014i	0.435758	+	0.209850i	0.638885	−	0.769303i	$-0.279396\pi$
$367$	8.34792	+	4.02014i	0.435758	+	0.209850i	−0.203127	+	0.979152i	$0.565110\pi$
$368$	−35.3922	−	17.0440i	−1.84495	−	0.888480i
$369$	0.237019	−	0.297212i	0.0123387	−	0.0154722i
$370$	−1.18431	+	1.48508i	−0.0615692	+	0.0772054i
$371$	16.1140	−	5.07013i	0.836598	−	0.263228i
$372$	−3.76978	−	4.72715i	−0.195454	−	0.245091i
$373$	−15.4391			−0.799405			−0.399702	−	0.916645i	$-0.630887\pi$
$373$	−15.4391			−0.799405			−0.399702	+	0.916645i	$0.630887\pi$
$374$	2.40145			0.124176
$375$	8.33718	+	10.4545i	0.430530	+	0.539867i
$376$	0.0348153	+	0.152536i	0.00179546	+	0.00786644i
$377$	−29.8871	−	14.3929i	−1.53926	−	0.741270i
$378$	−17.2216	+	16.1608i	−0.885782	+	0.831223i
$379$	11.5042	−	5.54011i	0.590929	−	0.284576i	−0.114425	−	0.993432i	$-0.536503\pi$
$379$	11.5042	−	5.54011i	0.590929	−	0.284576i	0.705354	+	0.708856i	$0.250788\pi$
$380$	5.78132	+	7.24955i	0.296576	+	0.371894i
$381$	−1.78387	+	0.859066i	−0.0913903	+	0.0440113i
$382$	4.40534	+	19.3011i	0.225397	+	0.987528i
$383$	14.6860	+	7.07241i	0.750420	+	0.361383i	0.769679	−	0.638431i	$-0.220416\pi$
$383$	14.6860	+	7.07241i	0.750420	+	0.361383i	−0.0192590	+	0.999815i	$0.506131\pi$
$384$	−3.15726	+	13.8328i	−0.161118	+	0.705904i
$385$	2.36872	−	6.13686i	0.120721	−	0.312763i
$386$	−10.1339	−	44.3997i	−0.515804	−	2.25988i
$387$	−2.85580	+	12.5121i	−0.145168	+	0.636025i
$388$	−6.58057	+	8.25177i	−0.334078	+	0.418920i
$389$	6.84807	−	30.0034i	0.347211	−	1.52123i	−0.436270	−	0.899816i	$-0.643701\pi$
$389$	6.84807	−	30.0034i	0.347211	−	1.52123i	0.783481	−	0.621415i	$-0.213442\pi$
$390$	−10.6038	+	5.10652i	−0.536944	+	0.258579i
$391$	−7.88438			−0.398730
$392$	13.2557	−	2.15102i	0.669514	−	0.108643i
$393$	−6.00154			−0.302738
$394$	10.7742	−	5.18856i	0.542794	−	0.261396i
$395$	3.89852	−	17.0806i	0.196156	−	0.859416i
$396$	−1.37031	+	1.71831i	−0.0688606	+	0.0863484i
$397$	6.35519	−	27.8439i	0.318958	−	1.39745i	−0.520426	−	0.853907i	$-0.674227\pi$
$397$	6.35519	−	27.8439i	0.318958	−	1.39745i	0.839384	−	0.543539i	$-0.182916\pi$
$398$	0.970106	+	4.25031i	0.0486270	+	0.213049i
$399$	−12.9615	+	12.1631i	−0.648886	+	0.608918i
$400$	−2.13621	+	9.35933i	−0.106810	+	0.467966i
$401$	−29.8493	−	14.3747i	−1.49060	−	0.717837i	−0.501515	−	0.865149i	$-0.667224\pi$
$401$	−29.8493	−	14.3747i	−1.49060	−	0.717837i	−0.989090	+	0.147312i	$0.952938\pi$
$402$	3.79155	+	16.6119i	0.189105	+	0.828525i
$403$	−20.5450	+	9.89396i	−1.02342	+	0.492853i
$404$	2.64009	+	3.31057i	0.131350	+	0.164707i
$405$	−0.699867	+	0.337038i	−0.0347767	+	0.0167476i
$406$	−20.8369	−	35.6255i	−1.03412	−	1.76806i
$407$	−0.817709	−	0.393788i	−0.0405323	−	0.0195193i
$408$	0.470090	+	2.05960i	0.0232729	+	0.101965i
$409$	−13.9376	−	17.4772i	−0.689171	−	0.864193i	0.306992	−	0.951712i	$-0.400678\pi$
$409$	−13.9376	−	17.4772i	−0.689171	−	0.864193i	−0.996163	+	0.0875191i	$0.972106\pi$
$410$	0.631309			0.0311781
$411$	6.59159			0.325139
$412$	5.91544	+	7.41773i	0.291433	+	0.365445i
$413$	−4.54348	+	11.7712i	−0.223570	+	0.579223i
$414$	14.8774	−	18.6557i	0.731185	−	0.916877i
$415$	−9.07768	+	11.3831i	−0.445606	+	0.558772i
$416$	−14.9204	−	7.18527i	−0.731531	−	0.352287i
$417$	18.5601	+	8.93809i	0.908894	+	0.437700i
$418$	−9.13472	+	11.4546i	−0.446794	+	0.560261i
$419$	6.23576	−	7.81940i	0.304637	−	0.382003i	−0.605823	−	0.795599i	$-0.707156\pi$
$419$	6.23576	−	7.81940i	0.304637	−	0.382003i	0.910460	+	0.413597i	$0.135728\pi$
$420$	−4.38227	−	0.635289i	−0.213833	−	0.0309989i
$421$	5.64696	+	7.08106i	0.275216	+	0.345110i	0.900160	−	0.435560i	$-0.143450\pi$
$421$	5.64696	+	7.08106i	0.275216	+	0.345110i	−0.624944	+	0.780670i	$0.714878\pi$
$422$	−25.9925			−1.26530
$423$	−0.145770			−0.00708759
$424$	7.63715	+	9.57669i	0.370893	+	0.465085i
$425$	0.428758	+	1.87851i	0.0207978	+	0.0911212i
$426$	−15.8793	−	7.64706i	−0.769354	−	0.370501i
$427$	1.31158	+	16.2710i	0.0634718	+	0.787409i
$428$	−10.8929	+	5.24574i	−0.526528	+	0.253562i
$429$	−3.50618	−	4.39662i	−0.169280	−	0.212271i
$430$	−19.2024	+	9.24739i	−0.926022	+	0.445949i
$431$	5.39621	+	23.6423i	0.259926	+	1.13881i	0.921330	+	0.388781i	$0.127104\pi$
$431$	5.39621	+	23.6423i	0.259926	+	1.13881i	−0.661404	+	0.750030i	$0.730039\pi$
$432$	−23.6647	−	11.3963i	−1.13857	−	0.548305i
$433$	5.95484	−	26.0899i	0.286171	−	1.25380i	−0.603561	−	0.797317i	$-0.706252\pi$
$433$	5.95484	−	26.0899i	0.286171	−	1.25380i	0.889733	−	0.456482i	$-0.150891\pi$
$434$	−28.0775	−	4.07034i	−1.34776	−	0.195382i
$435$	−3.95746	−	17.3388i	−0.189746	−	0.831331i
$436$	−3.75314	+	16.4436i	−0.179743	+	0.787504i
$437$	29.9909	−	37.6074i	1.43466	−	1.79901i
$438$	2.20936	−	9.67986i	0.105568	−	0.462521i
$439$	29.3255	−	14.1224i	1.39963	−	0.674026i	0.426543	−	0.904467i	$-0.359731\pi$
$439$	29.3255	−	14.1224i	1.39963	−	0.674026i	0.973086	+	0.230442i	$0.0740171\pi$
$440$	4.76983			0.227393
$441$	−0.794338	+	12.4864i	−0.0378256	+	0.594593i
$442$	−6.09672			−0.289991
$443$	−16.7791	+	8.08038i	−0.797198	+	0.383910i	−0.787711	−	0.616045i	$-0.788734\pi$
$443$	−16.7791	+	8.08038i	−0.797198	+	0.383910i	−0.00948700	+	0.999955i	$0.503020\pi$
$444$	−0.135948	+	0.595627i	−0.00645180	+	0.0282672i
$445$	−8.27144	+	10.3721i	−0.392104	+	0.491683i
$446$	2.69365	−	11.8017i	0.127548	−	0.558825i
$447$	0.204106	+	0.894247i	0.00965388	+	0.0422964i
$448$	2.90809	+	4.97205i	0.137394	+	0.234907i
$449$	−9.03838	+	39.5997i	−0.426547	+	1.86883i	0.0648574	+	0.997895i	$0.479341\pi$
$449$	−9.03838	+	39.5997i	−0.426547	+	1.86883i	−0.491405	+	0.870931i	$0.663516\pi$
$450$	−5.25390	−	2.53014i	−0.247671	−	0.119272i
$451$	0.0671222	+	0.294082i	0.00316066	+	0.0138478i
$452$	−5.73375	+	2.76123i	−0.269693	+	0.129877i
$453$	5.30108	+	6.64735i	0.249067	+	0.312320i
$454$	6.64893	−	3.20196i	0.312050	−	0.150275i
$455$	−6.01364	+	15.5801i	−0.281924	+	0.730405i
$456$	−11.6122	−	5.59212i	−0.543790	−	0.261875i
$457$	7.18594	+	31.4837i	0.336144	+	1.47274i	0.807010	+	0.590538i	$0.201084\pi$
$457$	7.18594	+	31.4837i	0.336144	+	1.47274i	−0.470866	+	0.882205i	$0.656058\pi$
$458$	−20.6791	−	25.9307i	−0.966269	−	1.21166i
$459$	−5.27181			−0.246067
$460$	11.9832			0.558719
$461$	−16.0861	−	20.1713i	−0.749204	−	0.939472i	0.250385	−	0.968146i	$-0.419443\pi$
$461$	−16.0861	−	20.1713i	−0.749204	−	0.939472i	−0.999589	+	0.0286744i	$0.990871\pi$
$462$	−0.562157	−	6.97392i	−0.0261539	−	0.324456i
$463$	6.95917	−	8.72652i	0.323420	−	0.405556i	−0.593367	−	0.804932i	$-0.702202\pi$
$463$	6.95917	−	8.72652i	0.323420	−	0.405556i	0.916787	+	0.399376i	$0.130773\pi$
$464$	28.6187	−	35.8867i	1.32859	−	1.66600i
$465$	−11.0149	−	5.30447i	−0.510802	−	0.245989i
$466$	−9.93638	−	4.78511i	−0.460294	−	0.221666i
$467$	20.4791	−	25.6800i	0.947661	−	1.18833i	−0.0343319	−	0.999410i	$-0.510930\pi$
$467$	20.4791	−	25.6800i	0.947661	−	1.18833i	0.981993	−	0.188919i	$-0.0604982\pi$
$468$	3.47890	−	4.36240i	0.160812	−	0.201652i
$469$	20.0533	+	13.5072i	0.925973	+	0.623704i
$470$	−0.150934	−	0.189265i	−0.00696206	−	0.00873015i
$471$	−22.4504			−1.03446
$472$	−9.14908			−0.421120
$473$	−6.34934	−	7.96182i	−0.291943	−	0.366085i
$474$	−4.14649	−	18.1670i	−0.190455	−	0.834436i
$475$	−10.5912	−	5.10044i	−0.485957	−	0.234024i
$476$	−1.90250	−	1.28146i	−0.0872008	−	0.0587355i
$477$	−10.2821	+	4.95159i	−0.470784	+	0.226718i
$478$	−0.827464	−	1.03761i	−0.0378473	−	0.0474591i
$479$	14.2414	−	6.85830i	0.650706	−	0.313364i	−0.0792527	−	0.996855i	$-0.525253\pi$
$479$	14.2414	−	6.85830i	0.650706	−	0.313364i	0.729959	+	0.683491i	$0.239539\pi$
$480$	−1.97566	−	8.65594i	−0.0901763	−	0.395088i
$481$	2.07598	+	0.999737i	0.0946563	+	0.0455841i
$482$	−4.91521	+	21.5349i	−0.223882	+	0.980889i
$483$	1.84566	+	22.8966i	0.0839806	+	1.04183i
$484$	1.73408	+	7.59750i	0.0788218	+	0.345341i
$485$	−4.74884	+	20.8060i	−0.215634	+	0.944754i
$486$	16.1813	−	20.2907i	0.733998	−	0.920404i
$487$	2.73083	−	11.9646i	0.123746	−	0.542166i	−0.874609	−	0.484829i	$-0.838882\pi$
$487$	2.73083	−	11.9646i	0.123746	−	0.542166i	0.998355	−	0.0573371i	$-0.0182610\pi$
$488$	−10.6642	+	5.13563i	−0.482748	+	0.232479i
$489$	−18.3449			−0.829583
$490$	−17.0346	+	11.8974i	−0.769546	+	0.537470i
$491$	−2.86586			−0.129335			−0.0646673	−	0.997907i	$-0.520599\pi$
$491$	−2.86586			−0.129335			−0.0646673	+	0.997907i	$0.520599\pi$
$492$	0.182944	−	0.0881012i	0.00824775	−	0.00397191i
$493$	2.05003	−	8.98179i	0.0923289	−	0.404519i
$494$	23.1909	−	29.0805i	1.04341	−	1.30839i
$495$	−0.988877	+	4.33256i	−0.0444467	+	0.194734i
$496$	−7.02125	−	30.7621i	−0.315264	−	1.38126i
$497$	−23.8560	+	7.50606i	−1.07009	+	0.336693i
$498$	−3.44585	+	15.0973i	−0.154412	+	0.676525i
$499$	11.4072	+	5.49339i	0.510654	+	0.245918i	0.671423	−	0.741074i	$-0.265683\pi$
$499$	11.4072	+	5.49339i	0.510654	+	0.245918i	−0.160769	+	0.986992i	$0.551397\pi$
$500$	−2.34266	−	10.2639i	−0.104767	−	0.459015i
$501$	14.8996	−	7.17527i	0.665665	−	0.320567i
$502$	1.64494	+	2.06269i	0.0734172	+	0.0920623i
$503$	29.4580	−	14.1862i	1.31347	−	0.632532i	0.359696	−	0.933070i	$-0.382881\pi$
$503$	29.4580	−	14.1862i	1.31347	−	0.632532i	0.953770	+	0.300538i	$0.0971663\pi$
$504$	−8.65400	+	2.72290i	−0.385480	+	0.121288i
$505$	7.71405	+	3.71489i	0.343271	+	0.165310i
$506$	4.21319	+	18.4592i	0.187299	+	0.820611i
$507$	−0.0241428	−	0.0302741i	−0.00107222	−	0.00134452i
$508$	1.55884			0.0691625
$509$	33.1931			1.47126			0.735629	−	0.677385i	$-0.236887\pi$
$509$	33.1931			1.47126			0.735629	+	0.677385i	$0.236887\pi$
$510$	−2.03797	−	2.55553i	−0.0902428	−	0.113161i
$511$	−7.11299	−	12.1613i	−0.314660	−	0.537984i
$512$	2.36820	−	2.96963i	0.104661	−	0.131241i
$513$	20.0531	−	25.1458i	0.885368	−	1.11022i
$514$	1.66733	+	0.802945i	0.0735429	+	0.0354164i
$515$	17.2843	+	8.32366i	0.761635	+	0.366784i
$516$	−4.27407	+	5.35951i	−0.188155	+	0.235939i
$517$	0.0721174	−	0.0904324i	0.00317172	−	0.00397721i
$518$	1.44734	+	2.47457i	0.0635926	+	0.108726i
$519$	8.85856	+	11.1083i	0.388848	+	0.487599i
$520$	−12.1095			−0.531037
$521$	−35.4300			−1.55222			−0.776108	−	0.630600i	$-0.782809\pi$
$521$	−35.4300			−1.55222			−0.776108	+	0.630600i	$0.782809\pi$
$522$	17.3840	+	21.7989i	0.760878	+	0.954110i
$523$	−7.53766	−	33.0247i	−0.329599	−	1.44407i	−0.819896	−	0.572512i	$-0.805969\pi$
$523$	−7.53766	−	33.0247i	−0.329599	−	1.44407i	0.490297	−	0.871555i	$-0.336888\pi$
$524$	4.25718	+	2.05015i	0.185976	+	0.0895611i
$525$	5.35493	−	1.68488i	0.233708	−	0.0735342i
$526$	−14.3526	+	6.91186i	−0.625804	+	0.301371i
$527$	−3.94860	−	4.95138i	−0.172004	−	0.215686i
$528$	7.01071	−	3.37618i	0.305102	−	0.146929i
$529$	−8.71469	−	38.1815i	−0.378899	−	1.66007i
$530$	−17.0754	−	8.22306i	−0.741706	−	0.357187i
$531$	1.89678	−	8.31034i	0.0823133	−	0.360638i
$532$	13.3492	−	4.20020i	0.578760	−	0.182102i
$533$	−0.170408	−	0.746606i	−0.00738119	−	0.0323391i
$534$	−3.13981	+	13.7564i	−0.135873	+	0.595298i
$535$	−15.2421	+	19.1130i	−0.658974	+	0.826328i
$536$	−3.90114	+	17.0920i	−0.168504	+	0.738262i
$537$	−0.0218565	+	0.0105255i	−0.000943177	+	0.000454210i
$538$	3.81692			0.164559
$539$	−7.35331	−	6.67026i	−0.316730	−	0.287308i
$540$	8.01244			0.344801
$541$	0.165419	−	0.0796618i	0.00711193	−	0.00342493i	−0.430324	−	0.902674i	$-0.641601\pi$
$541$	0.165419	−	0.0796618i	0.00711193	−	0.00342493i	0.437436	+	0.899249i	$0.355887\pi$
$542$	−5.42880	+	23.7851i	−0.233187	+	1.02166i
$543$	1.95088	−	2.44633i	0.0837203	−	0.104982i
$544$	1.02343	−	4.48393i	0.0438791	−	0.192247i
$545$	7.58887	+	33.2490i	0.325072	+	1.42423i
$546$	1.42719	+	17.7052i	0.0610780	+	0.757712i
$547$	−7.47653	+	32.7568i	−0.319673	+	1.40058i	0.518454	+	0.855105i	$0.326508\pi$
$547$	−7.47653	+	32.7568i	−0.319673	+	1.40058i	−0.838127	+	0.545474i	$0.816349\pi$
$548$	−4.67573	−	2.25171i	−0.199737	−	0.0961884i
$549$	−2.45392	−	10.7513i	−0.104731	−	0.458855i
$550$	4.16892	−	2.00765i	0.177764	−	0.0856064i
$551$	35.0439	+	43.9437i	1.49292	+	1.87206i
$552$	−15.0068	+	7.22689i	−0.638731	+	0.307597i
$553$	−21.9305	−	14.7716i	−0.932580	−	0.628154i
$554$	23.5548	+	11.3434i	1.00075	+	0.481934i
$555$	0.274888	+	1.20436i	0.0116683	+	0.0511223i
$556$	−10.1123	−	12.6804i	−0.428857	−	0.537770i
$557$	−9.61272			−0.407304			−0.203652	−	0.979043i	$-0.565281\pi$
$557$	−9.61272			−0.407304			−0.203652	+	0.979043i	$0.565281\pi$
$558$	19.1665			0.811384
$559$	16.1195	+	20.2132i	0.681783	+	0.854929i
$560$	−19.1663	−	12.9097i	−0.809922	−	0.545536i
$561$	0.973758	−	1.22105i	0.0411121	−	0.0515529i
$562$	−5.05704	+	6.34133i	−0.213318	+	0.267493i
$563$	33.4184	+	16.0934i	1.40842	+	0.678258i	0.974850	−	0.222863i	$-0.0715404\pi$
$563$	33.4184	+	16.0934i	1.40842	+	0.678258i	0.433567	+	0.901121i	$0.357255\pi$
$564$	−0.0701509	−	0.0337829i	−0.00295389	−	0.00142252i
$565$	−8.02308	+	10.0606i	−0.337533	+	0.423253i
$566$	6.54054	−	8.20158i	0.274920	−	0.344738i
$567$	0.0941965	+	1.16857i	0.00395588	+	0.0490753i
$568$	−11.3064	−	14.1778i	−0.474406	−	0.594887i
$569$	26.9229			1.12867			0.564333	−	0.825547i	$-0.309133\pi$
$569$	26.9229			1.12867			0.564333	+	0.825547i	$0.309133\pi$
$570$	19.9417			0.835264
$571$	−27.7637	−	34.8145i	−1.16187	−	1.45694i	−0.864820	−	0.502082i	$-0.832568\pi$
$571$	−27.7637	−	34.8145i	−1.16187	−	1.45694i	−0.297053	−	0.954861i	$-0.596004\pi$
$572$	0.985202	+	4.31645i	0.0411934	+	0.180480i
$573$	11.6003	+	5.58639i	0.484608	+	0.233375i
$574$	0.343090	−	0.888874i	0.0143203	−	0.0371009i
$575$	−13.6873	+	6.59147i	−0.570801	+	0.274883i
$576$	−2.42619	−	3.04235i	−0.101091	−	0.126764i
$577$	5.44171	−	2.62059i	0.226541	−	0.109097i	−0.317170	−	0.948369i	$-0.602733\pi$
$577$	5.44171	−	2.62059i	0.226541	−	0.109097i	0.543712	+	0.839272i	$0.317018\pi$
$578$	−0.376776	−	1.65076i	−0.0156718	−	0.0686628i
$579$	−26.6849	−	12.8508i	−1.10899	−	0.534060i
$580$	−3.11577	+	13.6511i	−0.129376	+	0.566831i
$581$	11.0938	+	18.9675i	0.460250	+	0.786903i
$582$	5.05090	+	22.1294i	0.209366	+	0.917294i
$583$	2.01504	−	8.82848i	0.0834546	−	0.365638i
$584$	6.36942	−	7.98700i	0.263569	−	0.330505i
$585$	2.51053	−	10.9994i	0.103798	−	0.454768i
$586$	12.8209	−	6.17420i	0.529625	−	0.255054i
$587$	36.2592			1.49658			0.748289	−	0.663373i	$-0.230876\pi$
$587$	36.2592			1.49658			0.748289	+	0.663373i	$0.230876\pi$
$588$	−3.27606	+	5.82493i	−0.135102	+	0.240216i
$589$	38.6373			1.59202
$590$	12.7540	−	6.14198i	0.525072	−	0.252861i
$591$	1.73059	−	7.58220i	0.0711868	−	0.311890i
$592$	−1.98787	+	2.49271i	−0.0817011	+	0.102450i
$593$	2.35309	−	10.3096i	0.0966299	−	0.423363i	−0.903355	−	0.428894i	$-0.858903\pi$
$593$	2.35309	−	10.3096i	0.0966299	−	0.423363i	0.999985	+	0.00553090i	$0.00176055\pi$
$594$	2.81711	+	12.3426i	0.115587	+	0.506421i
$595$	−4.59015	−	0.665424i	−0.188178	−	0.0272797i
$596$	0.160696	−	0.704055i	0.00658237	−	0.0288392i
$597$	2.55451	+	1.23019i	0.104549	+	0.0503482i
$598$	−10.6963	−	46.8637i	−0.437405	−	1.91640i
$599$	−38.5935	+	18.5856i	−1.57689	+	0.759389i	−0.998413	−	0.0563124i	$-0.982066\pi$
$599$	−38.5935	+	18.5856i	−1.57689	+	0.759389i	−0.578474	+	0.815701i	$0.696351\pi$
$600$	2.53794	+	3.18248i	0.103611	+	0.129924i
$601$	19.7961	−	9.53330i	0.807500	−	0.388872i	0.0158715	−	0.999874i	$-0.494948\pi$
$601$	19.7961	−	9.53330i	0.807500	−	0.388872i	0.791629	+	0.611002i	$0.209233\pi$
$602$	2.58449	+	32.0623i	0.105336	+	1.30676i
$603$	−14.7163	−	7.08701i	−0.599295	−	0.288605i
$604$	−1.48955	−	6.52615i	−0.0606090	−	0.265545i
$605$	9.82450	+	12.3195i	0.399423	+	0.500860i
$606$	9.10654			0.369928
$607$	21.3828			0.867901			0.433951	−	0.900937i	$-0.357119\pi$
$607$	21.3828			0.867901			0.433951	+	0.900937i	$0.357119\pi$
$608$	17.4948	+	21.9378i	0.709507	+	0.889694i
$609$	−26.5635	−	3.85085i	−1.07641	−	0.156044i
$610$	11.4185	−	14.3183i	0.462320	−	0.579731i
$611$	−0.183090	+	0.229587i	−0.00740701	+	0.00928810i
$612$	1.39617	+	0.672360i	0.0564369	+	0.0271786i
$613$	10.6482	+	5.12793i	0.430079	+	0.207115i	0.636384	−	0.771373i	$-0.280430\pi$
$613$	10.6482	+	5.12793i	0.430079	+	0.207115i	−0.206305	+	0.978488i	$0.566144\pi$
$614$	−29.3026	+	36.7442i	−1.18255	+	1.48288i
$615$	0.255989	−	0.320999i	0.0103225	−	0.0129439i
$616$	2.59220	−	6.71585i	0.104443	−	0.270589i
$617$	−8.51835	−	10.6817i	−0.342936	−	0.430028i	0.580216	−	0.814462i	$-0.302968\pi$
$617$	−8.51835	−	10.6817i	−0.342936	−	0.430028i	−0.923152	+	0.384434i	$0.874397\pi$
$618$	20.4043			0.820781
$619$	9.75370			0.392034			0.196017	−	0.980600i	$-0.437199\pi$
$619$	9.75370			0.392034			0.196017	+	0.980600i	$0.437199\pi$
$620$	6.00133	+	7.52543i	0.241019	+	0.302229i
$621$	−9.24908	−	40.5229i	−0.371153	−	1.62613i
$622$	−10.5653	−	5.08797i	−0.423629	−	0.204009i
$623$	10.1085	+	17.2829i	0.404990	+	0.692423i
$624$	−17.7986	+	8.57135i	−0.712514	+	0.343129i
$625$	−7.26568	−	9.11087i	−0.290627	−	0.364435i
$626$	−2.85223	+	1.37356i	−0.113998	+	0.0548985i
$627$	2.12024	+	9.28939i	0.0846744	+	0.370983i
$628$	15.9251	+	7.66913i	0.635481	+	0.306032i
$629$	−0.142397	+	0.623880i	−0.00567773	+	0.0248757i
$630$	10.2359	−	9.60539i	0.407807	−	0.382688i
$631$	−4.98395	−	21.8361i	−0.198408	−	0.869281i	−0.971885	−	0.235457i	$-0.924341\pi$
$631$	−4.98395	−	21.8361i	−0.198408	−	0.869281i	0.773477	−	0.633824i	$-0.218516\pi$
$632$	4.26634	−	18.6920i	0.169706	−	0.743529i
$633$	−10.5397	+	13.2163i	−0.418914	+	0.525302i
$634$	−4.45158	+	19.5037i	−0.176795	+	0.774589i
$635$	2.83985	−	1.36760i	0.112696	−	0.0542715i
$636$	−6.09574			−0.241712
$637$	18.6684	+	16.9342i	0.739668	+	0.670959i
$638$	−22.1240			−0.875896
$639$	15.2221	−	7.33057i	0.602176	−	0.289993i
$640$	5.02622	−	22.0213i	0.198679	−	0.870469i
$641$	0.976102	−	1.22399i	0.0385537	−	0.0483448i	−0.762181	−	0.647364i	$-0.775871\pi$
$641$	0.976102	−	1.22399i	0.0385537	−	0.0483448i	0.800735	+	0.599019i	$0.204443\pi$
$642$	−5.78585	+	25.3495i	−0.228349	+	1.00046i
$643$	7.11421	+	31.1694i	0.280557	+	1.22920i	0.897082	+	0.441865i	$0.145683\pi$
$643$	7.11421	+	31.1694i	0.280557	+	1.22920i	−0.616525	+	0.787336i	$0.711460\pi$
$644$	6.51237	−	16.8722i	0.256623	−	0.664857i
$645$	−3.08436	+	13.5135i	−0.121447	+	0.532093i
$646$	9.30712	+	4.48207i	0.366184	+	0.176345i
$647$	−2.31164	−	10.1280i	−0.0908800	−	0.398171i	0.908944	−	0.416918i	$-0.136890\pi$
$647$	−2.31164	−	10.1280i	−0.0908800	−	0.398171i	−0.999824	+	0.0187462i	$0.994033\pi$
$648$	−0.765897	+	0.368836i	−0.0300873	+	0.0144893i
$649$	4.21714	+	5.28813i	0.165537	+	0.207577i
$650$	−10.5839	+	5.09696i	−0.415136	+	0.199919i
$651$	−13.4547	+	12.6260i	−0.527333	+	0.494852i
$652$	13.0129	+	6.26667i	0.509624	+	0.245422i
$653$	9.15642	+	40.1169i	0.358318	+	1.56990i	0.757382	+	0.652972i	$0.226478\pi$
$653$	9.15642	+	40.1169i	0.358318	+	1.56990i	−0.399064	+	0.916923i	$0.630665\pi$
$654$	22.6160	+	28.3596i	0.884357	+	1.10895i
$655$	9.55421			0.373314
$656$	1.05966			0.0413727
$657$	5.93430	+	7.44137i	0.231519	+	0.290316i
$658$	−0.348509	+	0.109655i	−0.0135863	+	0.00427480i
$659$	−22.9176	+	28.7378i	−0.892745	+	1.11947i	0.0994840	+	0.995039i	$0.468281\pi$
$659$	−22.9176	+	28.7378i	−0.892745	+	1.11947i	−0.992229	+	0.124427i	$0.960291\pi$
$660$	−1.47998	+	1.85584i	−0.0576082	+	0.0722384i
$661$	−25.7562	−	12.4035i	−1.00180	−	0.482441i	−0.140251	−	0.990116i	$-0.544791\pi$
$661$	−25.7562	−	12.4035i	−1.00180	−	0.482441i	−0.861549	+	0.507675i	$0.830505\pi$
$662$	43.5299	+	20.9629i	1.69184	+	0.814746i
$663$	−2.47215	+	3.09998i	−0.0960103	+	0.120393i
$664$	−9.93413	+	12.4570i	−0.385519	+	0.483425i
$665$	20.6342	−	19.3632i	0.800159	−	0.750874i
$666$	−1.20750	−	1.51416i	−0.0467898	−	0.0586726i
$667$	72.6370			2.81252
$668$	−13.0201			−0.503762
$669$	−4.90851	−	6.15507i	−0.189774	−	0.237969i
$670$	−6.03600	−	26.4454i	−0.233191	−	1.02168i
$671$	7.88391	+	3.79669i	0.304355	+	0.146570i
$672$	−13.2611	−	1.92244i	−0.511560	−	0.0741597i
$673$	−27.3827	+	13.1868i	−1.05553	+	0.508314i	−0.879415	−	0.476056i	$-0.842066\pi$
$673$	−27.3827	+	13.1868i	−1.05553	+	0.508314i	−0.176110	+	0.984370i	$0.556352\pi$
$674$	−22.6673	−	28.4239i	−0.873113	−	1.09485i
$675$	−9.15190	+	4.40732i	−0.352257	+	0.169638i
$676$	0.00678387	+	0.0297221i	0.000260918	+	0.00114316i
$677$	24.3582	+	11.7303i	0.936163	+	0.450832i	0.838814	−	0.544418i	$-0.183249\pi$
$677$	24.3582	+	11.7303i	0.936163	+	0.450832i	0.0973491	+	0.995250i	$0.468964\pi$
$678$	−3.04553	+	13.3433i	−0.116963	+	0.512448i
$679$	26.7138	+	17.9935i	1.02518	+	0.690528i
$680$	−0.748365	−	3.27880i	−0.0286985	−	0.125736i
$681$	1.06798	−	4.67912i	0.0409250	−	0.179304i
$682$	−9.48234	+	11.8905i	−0.363097	+	0.455310i
$683$	0.755776	−	3.31127i	0.0289190	−	0.126702i	−0.958408	−	0.285402i	$-0.907873\pi$
$683$	0.755776	−	3.31127i	0.0289190	−	0.126702i	0.987327	+	0.158699i	$0.0507301\pi$
$684$	−8.51788	+	4.10200i	−0.325689	+	0.156844i
$685$	−10.4936			−0.400938
$686$	7.49377	+	30.4503i	0.286114	+	1.16260i
$687$	−21.5700			−0.822948
$688$	−32.2314	+	15.5218i	−1.22881	+	0.591764i
$689$	−5.11573	+	22.4135i	−0.194894	+	0.853886i
$690$	16.0681	−	20.1488i	0.611703	−	0.767051i
$691$	9.34969	−	40.9637i	0.355679	−	1.55833i	−0.408152	−	0.912914i	$-0.633827\pi$
$691$	9.34969	−	40.9637i	0.355679	−	1.55833i	0.763831	−	0.645417i	$-0.223316\pi$
$692$	−2.48917	−	10.9057i	−0.0946239	−	0.414574i
$693$	5.56276	+	3.74689i	0.211312	+	0.142333i
$694$	13.1293	−	57.5232i	0.498381	−	2.18355i
$695$	−29.5470	−	14.2291i	−1.12078	−	0.539740i
$696$	−4.33083	−	18.9746i	−0.164160	−	0.719231i
$697$	0.191622	−	0.0922803i	0.00725820	−	0.00349536i
$698$	−25.0356	−	31.3936i	−0.947611	−	1.18827i
$699$	−6.46216	+	3.11201i	−0.244421	+	0.117707i
$700$	−4.37407	−	0.634099i	−0.165324	−	0.0239667i
$701$	15.2804	+	7.35864i	0.577132	+	0.277932i	0.699593	−	0.714541i	$-0.253365\pi$
$701$	15.2804	+	7.35864i	0.577132	+	0.277932i	−0.122462	+	0.992473i	$0.539079\pi$
$702$	−7.15199	−	31.3349i	−0.269935	−	1.18266i
$703$	−2.43417	−	3.05235i	−0.0918065	−	0.115122i
$704$	3.08772			0.116373
$705$	−0.157437			−0.00592942
$706$	−17.0816	−	21.4196i	−0.642873	−	0.806137i
$707$	9.42278	−	8.84239i	0.354380	−	0.332552i
$708$	2.83877	−	3.55971i	0.106688	−	0.133782i
$709$	6.16721	−	7.73343i	0.231614	−	0.290435i	−0.652420	−	0.757858i	$-0.726246\pi$
$709$	6.16721	−	7.73343i	0.231614	−	0.290435i	0.884034	+	0.467423i	$0.154817\pi$
$710$	25.2792	+	12.1738i	0.948711	+	0.456875i
$711$	16.0940	+	7.75044i	0.603571	+	0.290664i
$712$	−9.05182	+	11.3506i	−0.339231	+	0.425383i
$713$	31.1322	−	39.0386i	1.16591	−	1.46201i
$714$	−4.70571	+	1.48061i	−0.176107	+	0.0554103i
$715$	5.58170	+	6.99923i	0.208744	+	0.261757i
$716$	0.0190994			0.000713779
$717$	−0.863116			−0.0322337
$718$	15.5803	+	19.5371i	0.581451	+	0.729117i
$719$	2.88274	+	12.6301i	0.107508	+	0.471023i	0.999808	+	0.0195807i	$0.00623314\pi$
$719$	2.88274	+	12.6301i	0.107508	+	0.471023i	−0.892300	+	0.451442i	$0.850910\pi$
$720$	14.0654	+	6.77354i	0.524186	+	0.252435i
$721$	21.1129	−	19.8124i	0.786284	−	0.737853i
$722$	−27.7965	+	13.3861i	−1.03448	+	0.498179i
$723$	8.95673	+	11.2314i	0.333104	+	0.417700i
$724$	−2.21953	+	1.06887i	−0.0824880	+	0.0397241i
$725$	−3.95005	−	17.3063i	−0.146701	−	0.642740i
$726$	15.0998	+	7.27168i	0.560406	+	0.269877i
$727$	−5.15693	+	22.5940i	−0.191260	+	0.837965i	0.784676	+	0.619906i	$0.212829\pi$
$727$	−5.15693	+	22.5940i	−0.191260	+	0.837965i	−0.975936	+	0.218058i	$0.930028\pi$
$728$	−6.58101	+	17.0500i	−0.243908	+	0.631915i
$729$	−4.05161	−	17.7513i	−0.150060	−	0.657455i
$730$	−3.51722	+	15.4099i	−0.130178	+	0.570348i
$731$	−4.47681	+	5.61374i	−0.165581	+	0.207632i
$732$	1.31074	−	5.74271i	0.0484462	−	0.212257i
$733$	−33.8266	+	16.2900i	−1.24941	+	0.601685i	−0.937354	−	0.348378i	$-0.886733\pi$
$733$	−33.8266	+	16.2900i	−1.24941	+	0.601685i	−0.312058	+	0.950063i	$0.601018\pi$
$734$	−15.6885			−0.579072
$735$	−0.857913	+	13.4858i	−0.0316446	+	0.497431i
$736$	36.2622			1.33664
$737$	11.6773	−	5.62348i	0.430138	−	0.207144i
$738$	−0.143231	+	0.627536i	−0.00527240	+	0.0230999i
$739$	−11.6919	+	14.6612i	−0.430095	+	0.539322i	−0.948903	−	0.315569i	$-0.897805\pi$
$739$	−11.6919	+	14.6612i	−0.430095	+	0.539322i	0.518808	+	0.854891i	$0.326376\pi$
$740$	0.216424	−	0.948214i	0.00795589	−	0.0348570i
$741$	−5.38281	−	23.5836i	−0.197743	−	0.866367i
$742$	−20.8577	+	19.5730i	−0.765710	+	0.718546i
$743$	−10.1449	+	44.4479i	−0.372182	+	1.63064i	0.348456	+	0.937325i	$0.386706\pi$
$743$	−10.1449	+	44.4479i	−0.372182	+	1.63064i	−0.720638	+	0.693311i	$0.756151\pi$
$744$	−12.0541	−	5.80493i	−0.441923	−	0.212819i
$745$	−0.324929	−	1.42361i	−0.0119045	−	0.0521569i
$746$	23.5529	−	11.3425i	0.862331	−	0.415277i
$747$	−9.25548	−	11.6060i	−0.338640	−	0.424641i
$748$	−1.10785	+	0.533512i	−0.0405070	+	0.0195071i
$749$	18.6274	+	31.8478i	0.680631	+	1.16369i
$750$	−20.3991	−	9.82371i	−0.744872	−	0.358711i
$751$	−1.42473	−	6.24215i	−0.0519892	−	0.227779i	0.942258	−	0.334887i	$-0.108698\pi$
$751$	−1.42473	−	6.24215i	−0.0519892	−	0.227779i	−0.994247	+	0.107108i	$0.965841\pi$
$752$	−0.253344	−	0.317683i	−0.00923851	−	0.0115847i
$753$	1.71581			0.0625277
$754$	56.1677			2.04551
$755$	−8.43911	−	10.5823i	−0.307131	−	0.385130i
$756$	4.35443	−	11.2814i	0.158369	−	0.410301i
$757$	0.893607	−	1.12055i	0.0324787	−	0.0407270i	−0.765327	−	0.643642i	$-0.777423\pi$
$757$	0.893607	−	1.12055i	0.0324787	−	0.0407270i	0.797806	+	0.602915i	$0.205994\pi$
$758$	−13.4799	+	16.9033i	−0.489612	+	0.613954i
$759$	11.0943	+	5.34272i	0.402697	+	0.193929i
$760$	18.4861	+	8.90244i	0.670561	+	0.322925i
$761$	−27.8687	+	34.9463i	−1.01024	+	1.26680i	−0.0467920	+	0.998905i	$0.514900\pi$
$761$	−27.8687	+	34.9463i	−1.01024	+	1.26680i	−0.963448	+	0.267896i	$0.913672\pi$
$762$	2.09023	−	2.62107i	0.0757212	−	0.0949514i
$763$	50.9384	+	7.38443i	1.84409	+	0.267334i
$764$	−6.32028	−	7.92538i	−0.228660	−	0.286730i
$765$	3.13337			0.113287
$766$	−27.5998			−0.997222
$767$	−10.7064	−	13.4253i	−0.386584	−	0.484761i
$768$	−4.27898	−	18.7474i	−0.154404	−	0.676490i
$769$	−8.08098	−	3.89159i	−0.291407	−	0.140334i	0.282469	−	0.959277i	$-0.408847\pi$
$769$	−8.08098	−	3.89159i	−0.291407	−	0.140334i	−0.573876	+	0.818942i	$0.694561\pi$
$770$	0.894931	+	11.1022i	0.0322511	+	0.400096i
$771$	1.08435	−	0.522198i	0.0390521	−	0.0188065i
$772$	14.5390	+	18.2313i	0.523271	+	0.656161i
$773$	−6.98592	+	3.36424i	−0.251266	+	0.121003i	−0.555278	−	0.831665i	$-0.687388\pi$
$773$	−6.98592	+	3.36424i	−0.251266	+	0.121003i	0.304012	+	0.952668i	$0.401674\pi$
$774$	−4.83549	−	21.1857i	−0.173808	−	0.761503i
$775$	−10.9942	−	5.29454i	−0.394924	−	0.190186i
$776$	−5.19688	+	22.7690i	−0.186557	+	0.817360i
$777$	1.84511	+	0.267482i	0.0661931	+	0.00959588i
$778$	11.5953	+	50.8022i	0.415711	+	1.82135i
$779$	−0.288735	+	1.26503i	−0.0103450	+	0.0453244i
$780$	3.75733	−	4.71154i	0.134534	−	0.168700i
$781$	−2.98317	+	13.0701i	−0.106746	+	0.467685i
$782$	12.0279	−	5.79233i	0.430117	−	0.207133i
$783$	48.5680			1.73568
$784$	−28.5928	+	19.9699i	−1.02117	+	0.713211i
$785$	35.7401			1.27562
$786$	9.15556	−	4.40909i	0.326568	−	0.157267i
$787$	9.14285	−	40.0575i	0.325908	−	1.42789i	−0.500947	−	0.865478i	$-0.667015\pi$
$787$	9.14285	−	40.0575i	0.325908	−	1.42789i	0.826854	−	0.562416i	$-0.190128\pi$
$788$	−3.81770	+	4.78724i	−0.136000	+	0.170538i
$789$	−2.30538	+	10.1005i	−0.0820735	+	0.359588i
$790$	6.60105	+	28.9211i	0.234855	+	1.02897i
$791$	9.80501	+	16.7639i	0.348626	+	0.596056i
$792$	−1.08217	+	4.74132i	−0.0384534	+	0.168475i
$793$	−20.0154	−	9.63892i	−0.710769	−	0.342288i
$794$	10.7607	+	47.1458i	0.381884	+	1.67314i
$795$	−11.1050	+	5.34789i	−0.393854	+	0.189670i
$796$	−1.39180	−	1.74526i	−0.0493310	−	0.0618591i
$797$	30.4956	−	14.6859i	1.08021	−	0.520201i	0.192825	−	0.981233i	$-0.438235\pi$
$797$	30.4956	−	14.6859i	1.08021	−	0.520201i	0.887384	+	0.461032i	$0.152521\pi$
$798$	10.8375	−	28.0776i	0.383642	−	0.993936i
$799$	−0.0734786	−	0.0353854i	−0.00259948	−	0.00125185i
$800$	−1.97196	−	8.63974i	−0.0697194	−	0.305461i
$801$	−8.43345	−	10.5752i	−0.297981	−	0.373657i
$802$	56.0967			1.98084
$803$	−7.55235			−0.266517
$804$	−5.43969	−	6.82115i	−0.191843	−	0.240564i
$805$	−2.93822	−	36.4505i	−0.103559	−	1.28471i
$806$	24.0735	−	30.1872i	0.847952	−	1.06330i
$807$	1.54772	−	1.94078i	0.0544823	−	0.0683186i
$808$	8.44184	+	4.06538i	0.296983	+	0.143019i
$809$	−22.1315	−	10.6580i	−0.778101	−	0.374714i	0.00229647	−	0.999997i	$-0.499269\pi$
$809$	−22.1315	−	10.6580i	−0.778101	−	0.374714i	−0.780398	+	0.625284i	$0.784983\pi$
$810$	0.820064	−	1.02833i	0.0288141	−	0.0361317i
$811$	−29.6400	+	37.1674i	−1.04080	+	1.30512i	−0.0897920	+	0.995961i	$0.528620\pi$
$811$	−29.6400	+	37.1674i	−1.04080	+	1.30512i	−0.951009	+	0.309163i	$0.899951\pi$
$812$	17.5273	+	11.8058i	0.615087	+	0.414301i
$813$	9.89261	+	12.4049i	0.346949	+	0.435060i
$814$	1.53674			0.0538628
$815$	29.2043			1.02298
$816$	−3.42075	−	4.28949i	−0.119750	−	0.150162i
$817$	−9.74772	−	42.7076i	−0.341030	−	1.49415i
$818$	34.1021	+	16.4227i	1.19235	+	0.574207i
$819$	−14.1226	−	9.51249i	−0.493483	−	0.332393i
$820$	−0.291239	+	0.140254i	−0.0101705	+	0.00489787i
$821$	−4.48671	−	5.62616i	−0.156587	−	0.196354i	0.697349	−	0.716732i	$-0.254363\pi$
$821$	−4.48671	−	5.62616i	−0.156587	−	0.196354i	−0.853936	+	0.520377i	$0.825791\pi$
$822$	−10.0557	+	4.84257i	−0.350733	+	0.168904i
$823$	−3.70882	−	16.2494i	−0.129281	−	0.566418i	−0.997527	−	0.0702839i	$-0.977609\pi$
$823$	−3.70882	−	16.2494i	−0.129281	−	0.566418i	0.868246	−	0.496134i	$-0.165248\pi$
$824$	18.9150	+	9.10896i	0.658934	+	0.317326i
$825$	0.669629	−	2.93384i	0.0233135	−	0.102143i
$826$	−1.71658	−	21.2953i	−0.0597275	−	0.740958i
$827$	−1.04186	−	4.56467i	−0.0362289	−	0.158729i	0.953578	−	0.301147i	$-0.0973695\pi$
$827$	−1.04186	−	4.56467i	−0.0362289	−	0.158729i	−0.989807	+	0.142418i	$0.954512\pi$
$828$	−2.71874	+	11.9116i	−0.0944826	+	0.413956i
$829$	25.8576	−	32.4244i	0.898072	−	1.12615i	−0.0933744	−	0.995631i	$-0.529765\pi$
$829$	25.8576	−	32.4244i	0.898072	−	1.12615i	0.991446	−	0.130515i	$-0.0416632\pi$
$830$	5.48566	−	24.0343i	0.190410	−	0.834241i
$831$	15.3189	−	7.37720i	0.531407	−	0.255912i
$832$	−7.83901			−0.271769
$833$	−3.43146	+	6.10123i	−0.118893	+	0.211395i
$834$	−34.8806			−1.20782
$835$	−23.7196	+	11.4227i	−0.820849	+	0.395300i
$836$	1.66930	−	7.31369i	0.0577340	−	0.252949i
$837$	20.8163	−	26.1028i	0.719515	−	0.902243i
$838$	−3.76828	+	16.5099i	−0.130173	+	0.570326i
$839$	7.99072	+	35.0097i	0.275870	+	1.20867i	0.902962	+	0.429721i	$0.141388\pi$
$839$	7.99072	+	35.0097i	0.275870	+	1.20867i	−0.627091	+	0.778946i	$0.715755\pi$
$840$	−9.34662	+	2.94083i	−0.322489	+	0.101468i
$841$	−12.4334	+	54.4742i	−0.428738	+	1.87842i
$842$	−13.8168	−	6.65382i	−0.476158	−	0.229306i
$843$	1.17378	+	5.14267i	0.0404272	+	0.177123i
$844$	11.9910	−	5.77458i	0.412748	−	0.198769i
$845$	0.0384343	+	0.0481951i	0.00132218	+	0.00165796i
$846$	0.222378	−	0.107091i	0.00764550	−	0.00368188i
$847$	22.6849	−	7.13761i	0.779464	−	0.245251i
$848$	−28.6612	−	13.8025i	−0.984228	−	0.473979i
$849$	−1.51811	−	6.65129i	−0.0521015	−	0.228272i
$850$	−2.03415	−	2.55075i	−0.0697709	−	0.0874899i
$851$	−5.04541			−0.172954
$852$	9.02442			0.309172
$853$	−23.0541	−	28.9089i	−0.789357	−	0.989823i	−0.999925	−	0.0122436i	$-0.996103\pi$
$853$	−23.0541	−	28.9089i	−0.789357	−	0.989823i	0.210568	−	0.977579i	$-0.432469\pi$
$854$	−13.9545	−	23.8584i	−0.477513	−	0.816419i
$855$	−11.9188	+	14.9458i	−0.407616	+	0.511134i
$856$	−16.6802	+	20.9163i	−0.570116	+	0.714903i
$857$	−7.82285	−	3.76728i	−0.267223	−	0.128688i	0.295475	−	0.955351i	$-0.404522\pi$
$857$	−7.82285	−	3.76728i	−0.267223	−	0.128688i	−0.562698	+	0.826663i	$0.690237\pi$
$858$	8.57882	+	4.13134i	0.292876	+	0.141042i
$859$	−27.4552	+	34.4277i	−0.936759	+	1.17466i	0.0476675	+	0.998863i	$0.484821\pi$
$859$	−27.4552	+	34.4277i	−0.936759	+	1.17466i	−0.984427	+	0.175796i	$0.943750\pi$
$860$	6.80414	−	8.53213i	0.232019	−	0.290943i
$861$	−0.312844	−	0.534878i	−0.0106617	−	0.0182286i
$862$	−25.6012	−	32.1028i	−0.871979	−	1.09343i
$863$	2.34311			0.0797603			0.0398801	−	0.999204i	$-0.487302\pi$
$863$	2.34311			0.0797603			0.0398801	+	0.999204i	$0.487302\pi$
$864$	24.2463			0.824877
$865$	−14.1025	−	17.6839i	−0.479498	−	0.601272i
$866$	10.0828	+	44.1758i	0.342629	+	1.50115i
$867$	−0.992137	−	0.477788i	−0.0336947	−	0.0162265i
$868$	13.8572	−	4.36003i	0.470343	−	0.147989i
$869$	−12.7704	+	6.14991i	−0.433207	+	0.208621i
$870$	18.7753	+	23.5435i	0.636544	+	0.798201i
$871$	−29.6459	+	14.2767i	−1.00451	+	0.483749i
$872$	8.30486	+	36.3860i	0.281238	+	1.23218i
$873$	−19.6043	−	9.44092i	−0.663504	−	0.319527i
$874$	−18.1236	+	79.4046i	−0.613039	+	2.68590i
$875$	−30.6463	+	9.64258i	−1.03603	+	0.325979i
$876$	1.13127	+	4.95641i	0.0382220	+	0.167462i
$877$	6.16320	−	27.0028i	0.208117	−	0.911818i	−0.757702	−	0.652600i	$-0.773678\pi$
$877$	6.16320	−	27.0028i	0.208117	−	0.911818i	0.965819	−	0.259218i	$-0.0834648\pi$
$878$	−34.3619	+	43.0885i	−1.15966	+	1.45417i
$879$	2.05934	−	9.02255i	0.0694597	−	0.304323i
$880$	−11.1608	+	5.37474i	−0.376229	+	0.181183i
$881$	−5.98603			−0.201674			−0.100837	−	0.994903i	$-0.532152\pi$
$881$	−5.98603			−0.201674			−0.100837	+	0.994903i	$0.532152\pi$
$882$	−7.96149	−	19.6321i	−0.268077	−	0.661047i
$883$	57.4659			1.93388			0.966940	−	0.255003i	$-0.0820763\pi$
$883$	57.4659			1.93388			0.966940	+	0.255003i	$0.0820763\pi$
$884$	2.81258	−	1.35447i	0.0945972	−	0.0455556i
$885$	2.04859	−	8.97546i	0.0688626	−	0.301707i
$886$	19.6608	−	24.6538i	0.660516	−	0.828261i
$887$	12.9709	−	56.8290i	0.435519	−	1.90813i	0.0171531	−	0.999853i	$-0.494540\pi$
$887$	12.9709	−	56.8290i	0.435519	−	1.90813i	0.418365	−	0.908279i	$-0.362603\pi$
$888$	0.300822	+	1.31799i	0.0100949	+	0.0442288i
$889$	−0.382221	−	4.74170i	−0.0128193	−	0.159031i
$890$	4.99845	−	21.8996i	0.167548	−	0.734078i
$891$	0.566215	+	0.272675i	0.0189689	+	0.00913495i
$892$	1.37924	+	6.04285i	0.0461804	+	0.202330i
$893$	0.448284	−	0.215882i	0.0150013	−	0.00722423i
$894$	−0.968338	−	1.21426i	−0.0323861	−	0.0406108i
$895$	0.0347947	−	0.0167562i	0.00116306	−	0.000560099i
$896$	−28.2742	−	19.0445i	−0.944574	−	0.636233i
$897$	−28.1658	−	13.5640i	−0.940430	−	0.452887i
$898$	−15.3039	−	67.0509i	−0.510699	−	2.23752i
$899$	36.3775	+	45.6160i	1.21326	+	1.52138i
$900$	2.98587			0.0995289
$901$	−6.38489			−0.212712
$902$	−0.318447	−	0.399320i	−0.0106031	−	0.0132959i
$903$	17.3506	+	11.6868i	0.577391	+	0.388911i
$904$	−8.78003	+	11.0098i	−0.292019	+	0.366181i
$905$	−3.10572	+	3.89445i	−0.103238	+	0.129456i
$906$	−12.9705	−	6.24628i	−0.430917	−	0.207519i
$907$	−43.3406	−	20.8717i	−1.43910	−	0.693034i	−0.458436	−	0.888728i	$-0.651590\pi$
$907$	−43.3406	−	20.8717i	−1.43910	−	0.693034i	−0.980665	+	0.195693i	$0.937304\pi$
$908$	−2.35597	+	2.95429i	−0.0781857	+	0.0980417i
$909$	−5.44284	+	6.82511i	−0.180528	+	0.226375i
$910$	−2.27203	−	28.1859i	−0.0753169	−	0.934355i
$911$	−20.4455	−	25.6379i	−0.677390	−	0.849420i	0.317721	−	0.948184i	$-0.397082\pi$
$911$	−20.4455	−	25.6379i	−0.677390	−	0.849420i	−0.995111	+	0.0987642i	$0.968511\pi$
$912$	33.4723			1.10838
$913$	11.7791			0.389831
$914$	−34.0922	−	42.7502i	−1.12767	−	1.41405i
$915$	−2.65032	−	11.6118i	−0.0876168	−	0.383874i
$916$	15.3006	+	7.36840i	0.505548	+	0.243459i
$917$	5.19231	−	13.4522i	0.171465	−	0.444231i
$918$	8.04234	−	3.87299i	0.265437	−	0.127828i
$919$	25.8469	+	32.4110i	0.852610	+	1.06914i	0.996827	+	0.0795935i	$0.0253622\pi$
$919$	25.8469	+	32.4110i	0.852610	+	1.06914i	−0.144217	+	0.989546i	$0.546066\pi$
$920$	23.8902	−	11.5049i	0.787637	−	0.379306i
$921$	6.80137	+	29.7987i	0.224113	+	0.981901i
$922$	39.3590	+	18.9543i	1.29622	+	0.624226i
$923$	7.57358	−	33.1820i	0.249287	−	1.09220i
$924$	1.80869	+	3.09236i	0.0595014	+	0.101731i
$925$	0.274373	+	1.20211i	0.00902133	+	0.0395250i
$926$	−4.20544	+	18.4252i	−0.138199	+	0.605491i
$927$	−12.1953	+	15.2925i	−0.400548	+	0.502271i
$928$	−9.42861	+	41.3094i	−0.309509	+	1.35605i
$929$	−27.5500	+	13.2674i	−0.903886	+	0.435289i	−0.827291	−	0.561774i	$-0.810119\pi$
$929$	−27.5500	+	13.2674i	−0.903886	+	0.435289i	−0.0765952	+	0.997062i	$0.524405\pi$
$930$	20.7005			0.678797
$931$	−16.0493	−	39.5757i	−0.525996	−	1.29704i
$932$	5.64699			0.184973
$933$	−6.87116	+	3.30898i	−0.224952	+	0.108331i
$934$	−12.3756	+	54.2210i	−0.404941	+	1.77416i
$935$	−1.55018	+	1.94387i	−0.0506964	+	0.0635713i
$936$	2.74739	−	12.0371i	0.0898014	−	0.393445i
$937$	11.6160	+	50.8929i	0.379477	+	1.66260i	0.699078	+	0.715045i	$0.253594\pi$
$937$	11.6160	+	50.8929i	0.379477	+	1.66260i	−0.319602	+	0.947552i	$0.603549\pi$
$938$	−40.5151	−	5.87339i	−1.32287	−	0.191773i
$939$	−0.458136	+	2.00722i	−0.0149507	+	0.0655033i
$940$	0.111677	+	0.0537810i	0.00364252	+	0.00175414i
$941$	−10.9780	−	48.0977i	−0.357872	−	1.56794i	−0.758483	−	0.651693i	$-0.774059\pi$
$941$	−10.9780	−	48.0977i	−0.357872	−	1.56794i	0.400610	−	0.916248i	$-0.368798\pi$
$942$	34.2488	−	16.4934i	1.11589	−	0.537383i
$943$	1.04552	+	1.31104i	0.0340468	+	0.0426934i
$944$	21.4076	−	10.3094i	0.696759	−	0.335542i
$945$	−1.96461	−	24.3723i	−0.0639089	−	0.792831i
$946$	15.5354	+	7.48144i	0.505099	+	0.243243i
$947$	1.17558	+	5.15056i	0.0382013	+	0.167371i	0.990430	−	0.138014i	$-0.0440720\pi$
$947$	1.17558	+	5.15056i	0.0382013	+	0.167371i	−0.952229	+	0.305385i	$0.901215\pi$
$948$	5.94891	+	7.45970i	0.193212	+	0.242280i
$949$	19.1737			0.622404
$950$	19.9043			0.645781
$951$	8.11189	+	10.1720i	0.263046	+	0.329849i
$952$	−5.02321	−	0.728204i	−0.162803	−	0.0236012i
$953$	25.9613	−	32.5545i	0.840970	−	1.05454i	−0.156789	−	0.987632i	$-0.550114\pi$
$953$	25.9613	−	32.5545i	0.840970	−	1.05454i	0.997759	−	0.0669110i	$-0.0213144\pi$
$954$	12.0479	−	15.1077i	0.390067	−	0.489128i
$955$	−18.4671	−	8.89331i	−0.597583	−	0.287781i
$956$	0.612249	+	0.294844i	0.0198016	+	0.00953593i
$957$	−8.97101	+	11.2493i	−0.289992	+	0.363638i
$958$	−16.6873	+	20.9252i	−0.539141	+	0.676061i
$959$	−5.70281	+	14.7748i	−0.184153	+	0.477102i
$960$	−2.62037	−	3.28584i	−0.0845721	−	0.106050i
$961$	9.10760			0.293793
$962$	−3.90144			−0.125787
$963$	−15.5407	−	19.4874i	−0.500791	−	0.627971i
$964$	−2.51675	−	11.0266i	−0.0810591	−	0.355143i
$965$	42.4813	+	20.4579i	1.36752	+	0.658564i
$966$	−19.6369	−	33.5737i	−0.631806	−	1.08022i
$967$	−37.0115	+	17.8238i	−1.19021	+	0.573175i	−0.920870	−	0.389869i	$-0.872520\pi$
$967$	−37.0115	+	17.8238i	−1.19021	+	0.573175i	−0.269341	+	0.963045i	$0.586806\pi$
$968$	10.7514	+	13.4818i	0.345563	+	0.433323i
$969$	6.05291	−	2.91493i	0.194448	−	0.0936410i
$970$	−8.04082	−	35.2291i	−0.258175	−	1.13114i
$971$	−49.8353	−	23.9994i	−1.59929	−	0.770178i	−0.599742	−	0.800194i	$-0.704730\pi$
$971$	−49.8353	−	23.9994i	−1.59929	−	0.770178i	−0.999549	+	0.0300158i	$0.990444\pi$
$972$	−2.95701	+	12.9555i	−0.0948462	+	0.415548i
$973$	−36.0919	+	33.8689i	−1.15705	+	1.08579i
$974$	4.62389	+	20.2586i	0.148159	+	0.649127i
$975$	−1.70003	+	7.44834i	−0.0544447	+	0.238538i
$976$	19.1660	−	24.0334i	0.613489	−	0.769291i
$977$	3.80663	−	16.6779i	0.121785	−	0.533574i	−0.876823	−	0.480814i	$-0.840341\pi$
$977$	3.80663	−	16.6779i	0.121785	−	0.533574i	0.998607	−	0.0527596i	$-0.0168017\pi$
$978$	27.9857	−	13.4772i	0.894885	−	0.430954i
$979$	10.7329			0.343026
$980$	5.21536	−	9.27305i	0.166599	−	0.296217i
$981$	−34.7721			−1.11019
$982$	4.37198	−	2.10543i	0.139515	−	0.0671871i
$983$	−9.70426	+	42.5171i	−0.309518	+	1.35609i	0.545771	+	0.837934i	$0.316237\pi$
$983$	−9.70426	+	42.5171i	−0.309518	+	1.35609i	−0.855289	+	0.518151i	$0.826620\pi$
$984$	0.280140	−	0.351285i	0.00893054	−	0.0111985i
$985$	−2.75503	+	12.0706i	−0.0877824	+	0.384600i
$986$	3.47115	+	15.2081i	0.110544	+	0.484325i
$987$	−0.0855604	+	0.221669i	−0.00272342	+	0.00705580i
$988$	−4.23798	+	18.5678i	−0.134828	+	0.590720i
$989$	−51.0054	−	24.5629i	−1.62188	−	0.781056i
$990$	−1.67438	−	7.33596i	−0.0532154	−	0.233152i
$991$	42.6265	−	20.5279i	1.35408	−	0.652089i	0.390769	−	0.920489i	$-0.372209\pi$
$991$	42.6265	−	20.5279i	1.35408	−	0.652089i	0.963308	+	0.268400i	$0.0864948\pi$
$992$	18.1605	+	22.7726i	0.576598	+	0.723031i
$993$	28.3098	−	13.6333i	0.898384	−	0.432639i
$994$	30.8787	−	28.9768i	0.979414	−	0.919087i
$995$	−4.06668	−	1.95841i	−0.128922	−	0.0620857i
$996$	−1.76439	−	7.73031i	−0.0559069	−	0.244944i
$997$	−14.9491	−	18.7456i	−0.473442	−	0.593678i	0.486568	−	0.873643i	$-0.338249\pi$
$997$	−14.9491	−	18.7456i	−0.473442	−	0.593678i	−0.960010	+	0.279965i	$0.909677\pi$
$998$	−21.4378			−0.678601
$999$	−3.37356			−0.106735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.k.c.120.10	✓	234
49.29	even	7	inner	833.2.k.c.715.10	yes	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.k.c.120.10	✓	234	1.1	even	1	trivial
833.2.k.c.715.10	yes	234	49.29	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52554 + 0.734659i) q^{2} +(-0.245038 + 1.07358i) q^{3} +(0.540556 - 0.677835i) q^{4} +(0.390090 - 1.70910i) q^{5} +(-0.414902 - 1.81780i) q^{6} +(-2.19439 - 1.47806i) q^{7} +(0.426894 - 1.87034i) q^{8} +(1.61038 + 0.775517i) q^{9} +(0.660507 + 2.89387i) q^{10} +(-1.27782 + 0.615366i) q^{11} +(0.595254 + 0.746425i) q^{12} +(3.24409 - 1.56227i) q^{13} +(4.43349 + 0.642713i) q^{14} +(1.73926 + 0.837585i) q^{15} +(1.10867 + 4.85739i) q^{16} +(0.623490 + 0.781831i) q^{17} -3.02643 q^{18} -6.10089 q^{19} +(-0.947620 - 1.18828i) q^{20} +(2.12453 - 1.99367i) q^{21} +(1.49728 - 1.87753i) q^{22} +(-4.91583 + 6.16426i) q^{23} +(1.90336 + 0.916608i) q^{24} +(1.73601 + 0.836017i) q^{25} +(-3.80124 + 4.76661i) q^{26} +(-3.28692 + 4.12167i) q^{27} +(-2.18807 + 0.688456i) q^{28} +(-5.74407 - 7.20283i) q^{29} -3.26865 q^{30} -6.33306 q^{31} +(-2.86758 - 3.59583i) q^{32} +(-0.347530 - 1.52263i) q^{33} +(-1.52554 - 0.734659i) q^{34} +(-3.38216 + 3.17384i) q^{35} +(1.39617 - 0.672360i) q^{36} +(0.398986 + 0.500313i) q^{37} +(9.30712 - 4.48207i) q^{38} +(0.882300 + 3.86561i) q^{39} +(-3.03007 - 1.45920i) q^{40} +(0.0473267 - 0.207352i) q^{41} +(-1.77637 + 4.60221i) q^{42} +(1.59775 + 7.00022i) q^{43} +(-0.273616 + 1.19879i) q^{44} +(1.95362 - 2.44977i) q^{45} +(2.97065 - 13.0153i) q^{46} +(-0.0734786 + 0.0353854i) q^{47} -5.48646 q^{48} +(2.63066 + 6.48688i) q^{49} -3.26253 q^{50} +(-0.992137 + 0.477788i) q^{51} +(0.694649 - 3.04346i) q^{52} +(-3.98091 + 4.99191i) q^{53} +(1.98629 - 8.70252i) q^{54} +(0.553254 + 2.42397i) q^{55} +(-3.70125 + 3.47328i) q^{56} +(1.49495 - 6.54979i) q^{57} +(14.0544 + 6.76825i) q^{58} +(-1.06121 - 4.64944i) q^{59} +(1.50791 - 0.726173i) q^{60} +(-3.84681 - 4.82375i) q^{61} +(9.66130 - 4.65264i) q^{62} +(-2.38752 - 4.08202i) q^{63} +(-1.96150 - 0.944607i) q^{64} +(-1.40459 - 6.15389i) q^{65} +(1.64878 + 2.06751i) q^{66} -9.13844 q^{67} +0.866984 q^{68} +(-5.41326 - 6.78801i) q^{69} +(2.82792 - 7.32654i) q^{70} +(5.89354 - 7.39026i) q^{71} +(2.13794 - 2.68089i) q^{72} +(4.79769 + 2.31044i) q^{73} +(-0.976228 - 0.470127i) q^{74} +(-1.32292 + 1.65889i) q^{75} +(-3.29787 + 4.13540i) q^{76} +(3.71358 + 0.538350i) q^{77} +(-4.18588 - 5.24893i) q^{78} +9.99391 q^{79} +8.73422 q^{80} +(-0.276275 - 0.346437i) q^{81} +(0.0801344 + 0.351092i) q^{82} +(-7.48275 - 3.60350i) q^{83} +(-0.202953 - 2.51777i) q^{84} +(1.57944 - 0.760619i) q^{85} +(-7.58021 - 9.50528i) q^{86} +(9.14033 - 4.40175i) q^{87} +(0.605452 + 2.65266i) q^{88} +(-6.81817 - 3.28346i) q^{89} +(-1.18058 + 5.17245i) q^{90} +(-9.42793 - 1.36675i) q^{91} +(1.52107 + 6.66425i) q^{92} +(1.55184 - 6.79904i) q^{93} +(0.0860979 - 0.107963i) q^{94} +(-2.37989 + 10.4270i) q^{95} +(4.56308 - 2.19746i) q^{96} -12.1737 q^{97} +(-8.77881 - 7.96334i) q^{98} -2.53500 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q + q^{2} - 7 q^{3} - 39 q^{4} + 2 q^{5} + 7 q^{6} - 13 q^{7} - 23 q^{8} - 42 q^{9} + 21 q^{10} - 7 q^{11} + q^{12} - 15 q^{13} - 22 q^{14} + 36 q^{15} - 55 q^{16} - 39 q^{17} + 62 q^{18} - 4 q^{19}+ \cdots + 72 q^{99}+O(q^{100}) \) 234 * q + q^2 - 7 * q^3 - 39 * q^4 + 2 * q^5 + 7 * q^6 - 13 * q^7 - 23 * q^8 - 42 * q^9 + 21 * q^10 - 7 * q^11 + q^12 - 15 * q^13 - 22 * q^14 + 36 * q^15 - 55 * q^16 - 39 * q^17 + 62 * q^18 - 4 * q^19 - 26 * q^20 - 30 * q^21 - 47 * q^22 - 32 * q^23 - 43 * q^24 - 69 * q^25 + 7 * q^26 - 19 * q^27 - 21 * q^28 + 8 * q^29 + 40 * q^30 - 8 * q^31 + 55 * q^32 - 59 * q^33 + q^34 - 20 * q^35 - 109 * q^36 + 22 * q^37 - 71 * q^38 - 41 * q^39 - 32 * q^40 - 9 * q^41 + 104 * q^42 - 15 * q^43 + 40 * q^44 + 102 * q^45 - 2 * q^46 - 21 * q^47 + 32 * q^48 + 35 * q^49 + 102 * q^50 - 21 * q^52 - 42 * q^53 - 59 * q^54 + 39 * q^55 + q^56 - 87 * q^57 - 27 * q^58 + 42 * q^59 + 162 * q^60 + 27 * q^61 - 77 * q^62 - 12 * q^63 - 53 * q^64 - 26 * q^65 - 66 * q^66 + 154 * q^67 + 276 * q^68 - 6 * q^69 - 32 * q^70 - 70 * q^71 + 106 * q^72 - 70 * q^73 - 44 * q^74 - 90 * q^75 - 20 * q^76 + 26 * q^77 - 93 * q^78 + 130 * q^79 - 4 * q^80 + 120 * q^81 - 30 * q^82 - 10 * q^83 - 148 * q^84 - 12 * q^85 - 4 * q^86 - 2 * q^87 - 68 * q^88 - 53 * q^89 + 195 * q^90 + 80 * q^91 + 153 * q^92 - 85 * q^93 + 130 * q^94 - 92 * q^95 - 89 * q^96 - 4 * q^97 + 42 * q^98 + 72 * q^99

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