LMFDB - Embedded newform 403.2.f.c.94.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.11
Character	$\chi$	$=$	403.94
Dual form			403.2.f.c.373.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.105154 + 0.182132i) q^{2} +(0.0693408 + 0.120102i) q^{3} +(0.977885 - 1.69375i) q^{4} +1.89472 q^{5} +(-0.0145830 + 0.0252584i) q^{6} +(-2.28636 + 3.96010i) q^{7} +0.831932 q^{8} +(1.49038 - 2.58142i) q^{9} +O(q^{10})$	\(q+(0.105154 + 0.182132i) q^{2} +(0.0693408 + 0.120102i) q^{3} +(0.977885 - 1.69375i) q^{4} +1.89472 q^{5} +(-0.0145830 + 0.0252584i) q^{6} +(-2.28636 + 3.96010i) q^{7} +0.831932 q^{8} +(1.49038 - 2.58142i) q^{9} +(0.199238 + 0.345090i) q^{10} +(1.94290 + 3.36520i) q^{11} +0.271229 q^{12} +(1.30434 + 3.36136i) q^{13} -0.961683 q^{14} +(0.131381 + 0.227559i) q^{15} +(-1.86829 - 3.23597i) q^{16} +(1.13616 - 1.96788i) q^{17} +0.626880 q^{18} +(2.95994 - 5.12676i) q^{19} +(1.85282 - 3.20917i) q^{20} -0.634153 q^{21} +(-0.408607 + 0.707729i) q^{22} +(-0.137590 - 0.238313i) q^{23} +(0.0576868 + 0.0999165i) q^{24} -1.41004 q^{25} +(-0.475056 + 0.591022i) q^{26} +0.829422 q^{27} +(4.47160 + 7.74505i) q^{28} +(-2.91234 - 5.04432i) q^{29} +(-0.0276306 + 0.0478576i) q^{30} +1.00000 q^{31} +(1.22485 - 2.12150i) q^{32} +(-0.269444 + 0.466691i) q^{33} +0.477887 q^{34} +(-4.33202 + 7.50327i) q^{35} +(-2.91485 - 5.04867i) q^{36} +(1.27443 + 2.20737i) q^{37} +1.24500 q^{38} +(-0.313261 + 0.389732i) q^{39} +1.57628 q^{40} +(0.712581 + 1.23423i) q^{41} +(-0.0666839 - 0.115500i) q^{42} +(-3.51642 + 6.09061i) q^{43} +7.59972 q^{44} +(2.82386 - 4.89106i) q^{45} +(0.0289363 - 0.0501192i) q^{46} -3.28567 q^{47} +(0.259097 - 0.448770i) q^{48} +(-6.95493 - 12.0463i) q^{49} +(-0.148272 - 0.256814i) q^{50} +0.315128 q^{51} +(6.96877 + 1.07781i) q^{52} +2.00557 q^{53} +(0.0872172 + 0.151065i) q^{54} +(3.68124 + 6.37610i) q^{55} +(-1.90210 + 3.29453i) q^{56} +0.820978 q^{57} +(0.612489 - 1.06086i) q^{58} +(-6.77261 + 11.7305i) q^{59} +0.513903 q^{60} +(-1.46369 + 2.53518i) q^{61} +(0.105154 + 0.182132i) q^{62} +(6.81512 + 11.8041i) q^{63} -6.95796 q^{64} +(2.47135 + 6.36882i) q^{65} -0.113333 q^{66} +(-6.79081 - 11.7620i) q^{67} +(-2.22206 - 3.84873i) q^{68} +(0.0190812 - 0.0330496i) q^{69} -1.82212 q^{70} +(-4.60485 + 7.97583i) q^{71} +(1.23990 - 2.14757i) q^{72} +9.73133 q^{73} +(-0.268023 + 0.464229i) q^{74} +(-0.0977734 - 0.169349i) q^{75} +(-5.78896 - 10.0268i) q^{76} -17.7687 q^{77} +(-0.103924 - 0.0160731i) q^{78} +5.84564 q^{79} +(-3.53988 - 6.13126i) q^{80} +(-4.41364 - 7.64465i) q^{81} +(-0.149862 + 0.259568i) q^{82} -18.1775 q^{83} +(-0.620129 + 1.07410i) q^{84} +(2.15270 - 3.72858i) q^{85} -1.47906 q^{86} +(0.403888 - 0.699554i) q^{87} +(1.61636 + 2.79961i) q^{88} +(-8.03965 - 13.9251i) q^{89} +1.18776 q^{90} +(-16.2935 - 2.51999i) q^{91} -0.538189 q^{92} +(0.0693408 + 0.120102i) q^{93} +(-0.345502 - 0.598426i) q^{94} +(5.60825 - 9.71377i) q^{95} +0.339728 q^{96} +(5.24516 - 9.08488i) q^{97} +(1.46268 - 2.53344i) q^{98} +11.5826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.105154	+	0.182132i	0.0743553	+	0.128787i	0.900806	−	0.434222i	$-0.142977\pi$
$2$	0.105154	+	0.182132i	0.0743553	+	0.128787i	−0.826450	+	0.563009i	$0.809643\pi$
$3$	0.0693408	+	0.120102i	0.0400339	+	0.0693408i	0.885348	−	0.464929i	$-0.153920\pi$
$3$	0.0693408	+	0.120102i	0.0400339	+	0.0693408i	−0.845314	+	0.534270i	$0.820587\pi$
$4$	0.977885	−	1.69375i	0.488943	−	0.846873i
$5$	1.89472			0.847344			0.423672	−	0.905816i	$-0.360741\pi$
$5$	1.89472			0.847344			0.423672	+	0.905816i	$0.360741\pi$
$6$	−0.0145830	+	0.0252584i	−0.00595347	+	0.0103117i
$7$	−2.28636	+	3.96010i	−0.864165	+	1.49678i	0.00370968	+	0.999993i	$0.498819\pi$
$7$	−2.28636	+	3.96010i	−0.864165	+	1.49678i	−0.867874	+	0.496784i	$0.834514\pi$
$8$	0.831932			0.294132
$9$	1.49038	−	2.58142i	0.496795	−	0.860473i
$10$	0.199238	+	0.345090i	0.0630045	+	0.109127i
$11$	1.94290	+	3.36520i	0.585805	+	1.01464i	0.994775	+	0.102096i	$0.0325550\pi$
$11$	1.94290	+	3.36520i	0.585805	+	1.01464i	−0.408969	+	0.912548i	$0.634112\pi$
$12$	0.271229			0.0782972
$13$	1.30434	+	3.36136i	0.361757	+	0.932272i
$13$	1.30434	+	3.36136i	0.361757	+	0.932272i
$14$	−0.961683			−0.257021
$15$	0.131381	+	0.227559i	0.0339225	+	0.0587555i
$16$	−1.86829	−	3.23597i	−0.467072	−	0.808993i
$17$	1.13616	−	1.96788i	0.275559	−	0.477282i	−0.694717	−	0.719283i	$-0.744470\pi$
$17$	1.13616	−	1.96788i	0.275559	−	0.477282i	0.970276	+	0.242001i	$0.0778038\pi$
$18$	0.626880			0.147757
$19$	2.95994	−	5.12676i	0.679056	−	1.17616i	−0.296209	−	0.955123i	$-0.595722\pi$
$19$	2.95994	−	5.12676i	0.679056	−	1.17616i	0.975265	−	0.221037i	$-0.0709442\pi$
$20$	1.85282	−	3.20917i	0.414303	−	0.717593i
$21$	−0.634153			−0.138384
$22$	−0.408607	+	0.707729i	−0.0871154	+	0.150888i
$23$	−0.137590	−	0.238313i	−0.0286895	−	0.0496917i	0.851324	−	0.524640i	$-0.175800\pi$
$23$	−0.137590	−	0.238313i	−0.0286895	−	0.0496917i	−0.880014	+	0.474948i	$0.842467\pi$
$24$	0.0576868	+	0.0999165i	0.0117753	+	0.0203954i
$25$	−1.41004			−0.282008
$26$	−0.475056	+	0.591022i	−0.0931661	+	0.115909i
$27$	0.829422			0.159622
$28$	4.47160	+	7.74505i	0.845054	+	1.46368i
$29$	−2.91234	−	5.04432i	−0.540808	−	0.936707i	−0.998858	−	0.0477802i	$-0.984785\pi$
$29$	−2.91234	−	5.04432i	−0.540808	−	0.936707i	0.458050	−	0.888926i	$-0.348548\pi$
$30$	−0.0276306	+	0.0478576i	−0.00504463	+	0.00873756i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	1.22485	−	2.12150i	0.216525	−	0.375032i
$33$	−0.269444	+	0.466691i	−0.0469042	+	0.0812404i
$34$	0.477887			0.0819570
$35$	−4.33202	+	7.50327i	−0.732245	+	1.26828i
$36$	−2.91485	−	5.04867i	−0.485808	−	0.841444i
$37$	1.27443	+	2.20737i	0.209515	+	0.362890i	0.951562	−	0.307458i	$-0.0994783\pi$
$37$	1.27443	+	2.20737i	0.209515	+	0.362890i	−0.742047	+	0.670348i	$0.766145\pi$
$38$	1.24500			0.201966
$39$	−0.313261	+	0.389732i	−0.0501619	+	0.0624071i
$40$	1.57628			0.249231
$41$	0.712581	+	1.23423i	0.111286	+	0.192754i	0.916289	−	0.400517i	$-0.131170\pi$
$41$	0.712581	+	1.23423i	0.111286	+	0.192754i	−0.805003	+	0.593271i	$0.797836\pi$
$42$	−0.0666839	−	0.115500i	−0.0102895	−	0.0178220i
$43$	−3.51642	+	6.09061i	−0.536248	+	0.928809i	0.462853	+	0.886435i	$0.346826\pi$
$43$	−3.51642	+	6.09061i	−0.536248	+	0.928809i	−0.999102	+	0.0423746i	$0.986508\pi$
$44$	7.59972			1.14570
$45$	2.82386	−	4.89106i	0.420956	−	0.729117i
$46$	0.0289363	−	0.0501192i	0.00426643	−	0.00738967i
$47$	−3.28567			−0.479264			−0.239632	−	0.970864i	$-0.577027\pi$
$47$	−3.28567			−0.479264			−0.239632	+	0.970864i	$0.577027\pi$
$48$	0.259097	−	0.448770i	0.0373975	−	0.0647743i
$49$	−6.95493	−	12.0463i	−0.993561	−	1.72090i
$50$	−0.148272	−	0.256814i	−0.0209688	−	0.0363190i
$51$	0.315128			0.0441268
$52$	6.96877	+	1.07781i	0.966395	+	0.149465i
$53$	2.00557			0.275487			0.137743	−	0.990468i	$-0.456015\pi$
$53$	2.00557			0.275487			0.137743	+	0.990468i	$0.456015\pi$
$54$	0.0872172	+	0.151065i	0.0118688	+	0.0205573i
$55$	3.68124	+	6.37610i	0.496379	+	0.859753i
$56$	−1.90210	+	3.29453i	−0.254179	+	0.440250i
$57$	0.820978			0.108741
$58$	0.612489	−	1.06086i	0.0804238	−	0.139298i
$59$	−6.77261	+	11.7305i	−0.881718	+	1.52718i	−0.0322887	+	0.999479i	$0.510280\pi$
$59$	−6.77261	+	11.7305i	−0.881718	+	1.52718i	−0.849429	+	0.527702i	$0.823054\pi$
$60$	0.513903			0.0663446
$61$	−1.46369	+	2.53518i	−0.187406	+	0.324597i	−0.944385	−	0.328843i	$-0.893341\pi$
$61$	−1.46369	+	2.53518i	−0.187406	+	0.324597i	0.756979	+	0.653440i	$0.226675\pi$
$62$	0.105154	+	0.182132i	0.0133546	+	0.0231308i
$63$	6.81512	+	11.8041i	0.858625	+	1.48718i
$64$	−6.95796			−0.869746
$65$	2.47135	+	6.36882i	0.306533	+	0.789955i
$66$	−0.113333			−0.0139503
$67$	−6.79081	−	11.7620i	−0.829630	−	1.43696i	−0.898329	−	0.439324i	$-0.855218\pi$
$67$	−6.79081	−	11.7620i	−0.829630	−	1.43696i	0.0686988	−	0.997637i	$-0.478115\pi$
$68$	−2.22206	−	3.84873i	−0.269465	−	0.466727i
$69$	0.0190812	−	0.0330496i	0.00229711	−	0.00397870i
$70$	−1.82212			−0.217785
$71$	−4.60485	+	7.97583i	−0.546495	+	0.946557i	0.452016	+	0.892010i	$0.350705\pi$
$71$	−4.60485	+	7.97583i	−0.546495	+	0.946557i	−0.998511	+	0.0545474i	$0.982628\pi$
$72$	1.23990	−	2.14757i	0.146123	−	0.253093i
$73$	9.73133			1.13897			0.569483	−	0.822003i	$-0.307143\pi$
$73$	9.73133			1.13897			0.569483	+	0.822003i	$0.307143\pi$
$74$	−0.268023	+	0.464229i	−0.0311570	+	0.0539655i
$75$	−0.0977734	−	0.169349i	−0.0112899	−	0.0195547i
$76$	−5.78896	−	10.0268i	−0.664039	−	1.15015i
$77$	−17.7687			−2.02493
$78$	−0.103924	−	0.0160731i	−0.0117670	−	0.00181991i
$79$	5.84564			0.657686			0.328843	−	0.944385i	$-0.393341\pi$
$79$	5.84564			0.657686			0.328843	+	0.944385i	$0.393341\pi$
$80$	−3.53988	−	6.13126i	−0.395771	−	0.685495i
$81$	−4.41364	−	7.64465i	−0.490404	−	0.849405i
$82$	−0.149862	+	0.259568i	−0.0165495	+	0.0286645i
$83$	−18.1775			−1.99524			−0.997622	−	0.0689264i	$-0.978043\pi$
$83$	−18.1775			−1.99524			−0.997622	+	0.0689264i	$0.978043\pi$
$84$	−0.620129	+	1.07410i	−0.0676616	+	0.117193i
$85$	2.15270	−	3.72858i	0.233493	−	0.404422i
$86$	−1.47906			−0.159492
$87$	0.403888	−	0.699554i	0.0433013	−	0.0750001i
$88$	1.61636	+	2.79961i	0.172304	+	0.298440i
$89$	−8.03965	−	13.9251i	−0.852201	−	1.47606i	−0.879217	−	0.476421i	$-0.841934\pi$
$89$	−8.03965	−	13.9251i	−0.852201	−	1.47606i	0.0270158	−	0.999635i	$-0.491400\pi$
$90$	1.18776			0.125201
$91$	−16.2935	−	2.51999i	−1.70802	−	0.264166i
$92$	−0.538189			−0.0561101
$93$	0.0693408	+	0.120102i	0.00719030	+	0.0124540i
$94$	−0.345502	−	0.598426i	−0.0356358	−	0.0617230i
$95$	5.60825	−	9.71377i	0.575394	−	0.996612i
$96$	0.339728			0.0346733
$97$	5.24516	−	9.08488i	0.532565	−	0.922429i	−0.466712	−	0.884409i	$-0.654562\pi$
$97$	5.24516	−	9.08488i	0.532565	−	0.922429i	0.999277	−	0.0380200i	$-0.0121051\pi$
$98$	1.46268	−	2.53344i	0.147753	−	0.255916i
$99$	11.5826			1.16410
$100$	−1.37886	+	2.38825i	−0.137886	+	0.238825i
$101$	−0.823992	−	1.42720i	−0.0819903	−	0.142011i	0.822114	−	0.569322i	$-0.192794\pi$
$101$	−0.823992	−	1.42720i	−0.0819903	−	0.142011i	−0.904105	+	0.427311i	$0.859461\pi$
$102$	0.0331371	+	0.0573951i	0.00328106	+	0.00568296i
$103$	1.51131			0.148914			0.0744570	−	0.997224i	$-0.476278\pi$
$103$	1.51131			0.148914			0.0744570	+	0.997224i	$0.476278\pi$
$104$	1.08512	+	2.79642i	0.106405	+	0.274211i
$105$	−1.20154			−0.117258
$106$	0.210895	+	0.365280i	0.0204839	+	0.0354791i
$107$	1.31791	+	2.28268i	0.127407	+	0.220675i	0.922671	−	0.385588i	$-0.126001\pi$
$107$	1.31791	+	2.28268i	0.127407	+	0.220675i	−0.795264	+	0.606263i	$0.792668\pi$
$108$	0.811080	−	1.40483i	0.0780462	−	0.135180i
$109$	−8.90020			−0.852484			−0.426242	−	0.904609i	$-0.640163\pi$
$109$	−8.90020			−0.852484			−0.426242	+	0.904609i	$0.640163\pi$
$110$	−0.774196	+	1.34095i	−0.0738167	+	0.127854i
$111$	−0.176740	+	0.306122i	−0.0167754	+	0.0290558i
$112$	17.0864			1.61451
$113$	−5.62307	+	9.73945i	−0.528974	+	0.916210i	0.470455	+	0.882424i	$0.344090\pi$
$113$	−5.62307	+	9.73945i	−0.528974	+	0.916210i	−0.999429	+	0.0337861i	$0.989244\pi$
$114$	0.0863293	+	0.149527i	0.00808548	+	0.0140045i
$115$	−0.260694	−	0.451536i	−0.0243099	−	0.0421059i
$116$	−11.3917			−1.05770
$117$	10.6210	+	1.64267i	0.981915	+	0.151865i
$118$	−2.84867			−0.262242
$119$	5.19534	+	8.99860i	0.476256	+	0.824900i
$120$	0.109300	+	0.189314i	0.00997770	+	0.0172819i
$121$	−2.04969	+	3.55017i	−0.186336	+	0.322743i
$122$	−0.615652			−0.0557385
$123$	−0.0988218	+	0.171164i	−0.00891046	+	0.0154334i
$124$	0.977885	−	1.69375i	0.0878167	−	0.152103i
$125$	−12.1452			−1.08630
$126$	−1.43328	+	2.48251i	−0.127686	+	0.221159i
$127$	1.85566	+	3.21409i	0.164663	+	0.285204i	0.936536	−	0.350573i	$-0.114013\pi$
$127$	1.85566	+	3.21409i	0.164663	+	0.285204i	−0.771873	+	0.635777i	$0.780680\pi$
$128$	−3.18136	−	5.51027i	−0.281195	−	0.487044i
$129$	−0.975324			−0.0858725
$130$	−0.900096	+	1.11982i	−0.0789437	+	0.0982148i
$131$	14.6432			1.27939			0.639693	−	0.768630i	$-0.279061\pi$
$131$	14.6432			1.27939			0.639693	+	0.768630i	$0.279061\pi$
$132$	0.526970	+	0.912740i	0.0458669	+	0.0794438i
$133$	13.5350	+	23.4433i	1.17363	+	2.03279i
$134$	1.42817	−	2.47365i	0.123375	−	0.213691i
$135$	1.57152			0.135255
$136$	0.945206	−	1.63714i	0.0810507	−	0.140384i
$137$	−5.54974	+	9.61244i	−0.474146	+	0.821246i	−0.999562	−	0.0296001i	$-0.990577\pi$
$137$	−5.54974	+	9.61244i	−0.474146	+	0.821246i	0.525415	+	0.850846i	$0.323910\pi$
$138$	0.00802587			0.000683208
$139$	6.05408	−	10.4860i	0.513500	−	0.889409i	−0.486377	−	0.873749i	$-0.661682\pi$
$139$	6.05408	−	10.4860i	0.513500	−	0.889409i	0.999877	−	0.0156597i	$-0.00498483\pi$
$140$	8.47243	+	14.6747i	0.716051	+	1.24024i
$141$	−0.227831	−	0.394614i	−0.0191868	−	0.0332325i
$142$	−1.93688			−0.162539
$143$	−8.77743	+	10.9201i	−0.734006	+	0.913185i
$144$	−11.1379			−0.928156
$145$	−5.51806	−	9.55757i	−0.458250	−	0.793713i
$146$	1.02329	+	1.77239i	0.0846882	+	0.146684i
$147$	0.964520	−	1.67060i	0.0795523	−	0.137789i
$148$	4.98498			0.409762
$149$	−2.79381	+	4.83902i	−0.228878	+	0.396428i	−0.957476	−	0.288513i	$-0.906839\pi$
$149$	−2.79381	+	4.83902i	−0.228878	+	0.396428i	0.728598	+	0.684942i	$0.240172\pi$
$150$	0.0205626	−	0.0356154i	0.00167893	−	0.00290799i
$151$	17.6485			1.43621			0.718107	−	0.695933i	$-0.245009\pi$
$151$	17.6485			1.43621			0.718107	+	0.695933i	$0.245009\pi$
$152$	2.46247	−	4.26512i	0.199732	−	0.345947i
$153$	−3.38662	−	5.86580i	−0.273792	−	0.474222i
$154$	−1.86845	−	3.23625i	−0.150564	−	0.260785i
$155$	1.89472			0.152187
$156$	0.353774	+	0.911698i	0.0283246	+	0.0729943i
$157$	2.77104			0.221153			0.110577	−	0.993868i	$-0.464730\pi$
$157$	2.77104			0.221153			0.110577	+	0.993868i	$0.464730\pi$
$158$	0.614694	+	1.06468i	0.0489024	+	0.0847014i
$159$	0.139068	+	0.240873i	0.0110288	+	0.0191025i
$160$	2.32074	−	4.01965i	0.183471	−	0.317781i
$161$	1.25832			0.0991698
$162$	0.928225	−	1.60773i	0.0729283	−	0.126315i
$163$	4.36285	−	7.55668i	0.341725	−	0.591885i	−0.643028	−	0.765842i	$-0.722322\pi$
$163$	4.36285	−	7.55668i	0.341725	−	0.591885i	0.984753	+	0.173958i	$0.0556555\pi$
$164$	2.78729			0.217651
$165$	−0.510520	+	0.884247i	−0.0397440	+	0.0688386i
$166$	−1.91144	−	3.31072i	−0.148357	−	0.256962i
$167$	−2.00549	−	3.47362i	−0.155190	−	0.268796i	0.777938	−	0.628341i	$-0.216266\pi$
$167$	−2.00549	−	3.47362i	−0.155190	−	0.268796i	−0.933128	+	0.359544i	$0.882932\pi$
$168$	−0.527572			−0.0407031
$169$	−9.59742	+	8.76867i	−0.738263	+	0.674513i
$170$	0.905462			0.0694457
$171$	−8.82289	−	15.2817i	−0.674703	−	1.16862i
$172$	6.87730	+	11.9118i	0.524389	+	0.908269i
$173$	0.432621	−	0.749322i	0.0328916	−	0.0569699i	−0.849111	−	0.528214i	$-0.822862\pi$
$173$	0.432621	−	0.749322i	0.0328916	−	0.0569699i	0.882003	+	0.471245i	$0.156195\pi$
$174$	0.169882			0.0128787
$175$	3.22387	−	5.58391i	0.243702	−	0.422104i
$176$	7.25979	−	12.5743i	0.547227	−	0.947825i
$177$	−1.87847			−0.141195
$178$	1.69081	−	2.92856i	0.126731	−	0.219505i
$179$	2.82723	+	4.89690i	0.211317	+	0.366012i	0.952127	−	0.305703i	$-0.0988914\pi$
$179$	2.82723	+	4.89690i	0.211317	+	0.366012i	−0.740810	+	0.671715i	$0.765558\pi$
$180$	−5.52282	−	9.56580i	−0.411646	−	0.712993i
$181$	−2.46913			−0.183529			−0.0917647	−	0.995781i	$-0.529251\pi$
$181$	−2.46913			−0.183529			−0.0917647	+	0.995781i	$0.529251\pi$
$182$	−1.25436	−	3.23256i	−0.0929792	−	0.239613i
$183$	−0.405973			−0.0300104
$184$	−0.114465	−	0.198260i	−0.00843851	−	0.0146159i
$185$	2.41468	+	4.18235i	0.177531	+	0.307493i
$186$	−0.0145830	+	0.0252584i	−0.00106927	+	0.00185204i
$187$	8.82975			0.645695
$188$	−3.21300	+	5.56509i	−0.234332	+	0.405876i
$189$	−1.89636	+	3.28459i	−0.137940	+	0.238919i
$190$	2.35892			0.171134
$191$	−8.08721	+	14.0075i	−0.585170	+	1.01354i	0.409684	+	0.912227i	$0.365639\pi$
$191$	−8.08721	+	14.0075i	−0.585170	+	1.01354i	−0.994854	+	0.101317i	$0.967694\pi$
$192$	−0.482471	−	0.835664i	−0.0348193	−	0.0603088i
$193$	−9.34236	−	16.1814i	−0.672478	−	1.16477i	−0.977199	−	0.212324i	$-0.931897\pi$
$193$	−9.34236	−	16.1814i	−0.672478	−	1.16477i	0.304721	−	0.952442i	$-0.401437\pi$
$194$	2.20620			0.158396
$195$	−0.593542	+	0.738432i	−0.0425044	+	0.0528802i
$196$	−27.2045			−1.94318
$197$	6.82179	+	11.8157i	0.486032	+	0.841832i	0.999871	−	0.0160542i	$-0.00511044\pi$
$197$	6.82179	+	11.8157i	0.486032	+	0.841832i	−0.513839	+	0.857887i	$0.671777\pi$
$198$	1.21796	+	2.10958i	0.0865569	+	0.149921i
$199$	7.51354	−	13.0138i	0.532620	−	0.922526i	−0.466654	−	0.884440i	$-0.654541\pi$
$199$	7.51354	−	13.0138i	0.532620	−	0.922526i	0.999274	−	0.0380857i	$-0.0121260\pi$
$200$	−1.17306			−0.0829478
$201$	0.941761	−	1.63118i	0.0664267	−	0.115054i
$202$	0.173293	−	0.300152i	0.0121928	−	0.0211186i
$203$	26.6347			1.86939
$204$	0.308159	−	0.533748i	0.0215755	−	0.0373698i
$205$	1.35014	+	2.33851i	0.0942978	+	0.163329i
$206$	0.158921	+	0.275259i	0.0110725	+	0.0191782i
$207$	−0.820247			−0.0570111
$208$	8.44038	−	10.5008i	0.585235	−	0.728098i
$209$	23.0034			1.59118
$210$	−0.126347	−	0.218840i	−0.00871878	−	0.0151014i
$211$	2.91492	+	5.04878i	0.200671	+	0.347573i	0.948745	−	0.316043i	$-0.102354\pi$
$211$	2.91492	+	5.04878i	0.200671	+	0.347573i	−0.748074	+	0.663616i	$0.769021\pi$
$212$	1.96122	−	3.39694i	0.134697	−	0.233302i
$213$	−1.27722			−0.0875134
$214$	−0.277167	+	0.480067i	−0.0189467	+	0.0328167i
$215$	−6.66262	+	11.5400i	−0.454387	+	0.787021i
$216$	0.690023			0.0469501
$217$	−2.28636	+	3.96010i	−0.155209	+	0.268829i
$218$	−0.935893	−	1.62101i	−0.0633867	−	0.109789i
$219$	0.674778	+	1.16875i	0.0455973	+	0.0789768i
$220$	14.3993			0.970802
$221$	8.09668	+	1.25225i	0.544642	+	0.0842355i
$222$	−0.0743397			−0.00498935
$223$	3.96770	+	6.87225i	0.265697	+	0.460200i	0.967746	−	0.251928i	$-0.0810647\pi$
$223$	3.96770	+	6.87225i	0.265697	+	0.460200i	−0.702049	+	0.712128i	$0.747731\pi$
$224$	5.60090	+	9.70105i	0.374226	+	0.648178i
$225$	−2.10150	+	3.63991i	−0.140100	+	0.242661i
$226$	−2.36516			−0.157328
$227$	−9.98404	+	17.2929i	−0.662664	+	1.14777i	0.317249	+	0.948342i	$0.397241\pi$
$227$	−9.98404	+	17.2929i	−0.662664	+	1.14777i	−0.979913	+	0.199426i	$0.936092\pi$
$228$	0.802822	−	1.39053i	0.0531682	−	0.0920900i
$229$	1.24718			0.0824157			0.0412078	−	0.999151i	$-0.486879\pi$
$229$	1.24718			0.0824157			0.0412078	+	0.999151i	$0.486879\pi$
$230$	0.0548262	−	0.0949618i	0.00361513	−	0.00626159i
$231$	−1.23209	−	2.13405i	−0.0810658	−	0.140410i
$232$	−2.42287	−	4.19653i	−0.159069	−	0.275516i
$233$	−1.09514			−0.0717453			−0.0358726	−	0.999356i	$-0.511421\pi$
$233$	−1.09514			−0.0717453			−0.0358726	+	0.999356i	$0.511421\pi$
$234$	0.817662	+	2.10717i	0.0534522	+	0.137750i
$235$	−6.22541			−0.406101
$236$	13.2457	+	22.9422i	0.862219	+	1.49341i
$237$	0.405341	+	0.702072i	0.0263297	+	0.0456045i
$238$	−1.09262	+	1.89248i	−0.0708243	+	0.122671i
$239$	19.1710			1.24007			0.620036	−	0.784574i	$-0.287118\pi$
$239$	19.1710			1.24007			0.620036	+	0.784574i	$0.287118\pi$
$240$	0.490916	−	0.850292i	0.0316885	−	0.0548861i
$241$	1.16342	−	2.01510i	0.0749425	−	0.129804i	−0.826119	−	0.563496i	$-0.809456\pi$
$241$	1.16342	−	2.01510i	0.0749425	−	0.129804i	0.901061	+	0.433692i	$0.142789\pi$
$242$	−0.862135			−0.0554202
$243$	1.85622	−	3.21507i	0.119077	−	0.206247i
$244$	2.86264	+	4.95824i	0.183262	+	0.317419i
$245$	−13.1776	−	22.8243i	−0.841888	−	1.45819i
$246$	−0.0415661			−0.00265016
$247$	21.0936	+	3.26239i	1.34216	+	0.207581i
$248$	0.831932			0.0528277
$249$	−1.26044	−	2.18315i	−0.0798774	−	0.138352i
$250$	−1.27712	−	2.21204i	−0.0807723	−	0.139902i
$251$	14.0799	−	24.3870i	0.888713	−	1.53930i	0.0473154	−	0.998880i	$-0.484933\pi$
$251$	14.0799	−	24.3870i	0.888713	−	1.53930i	0.841398	−	0.540416i	$-0.181733\pi$
$252$	26.6576			1.67927
$253$	0.534646	−	0.926034i	0.0336129	−	0.0582193i
$254$	−0.390260	+	0.675950i	−0.0244871	+	0.0424129i
$255$	0.597079			0.0373906
$256$	−6.28890	+	10.8927i	−0.393056	+	0.680793i
$257$	−9.45896	−	16.3834i	−0.590034	−	1.02197i	−0.994227	−	0.107295i	$-0.965781\pi$
$257$	−9.45896	−	16.3834i	−0.590034	−	1.02197i	0.404193	−	0.914674i	$-0.367552\pi$
$258$	−0.102559	−	0.177638i	−0.00638507	−	0.0110593i
$259$	−11.6552			−0.724220
$260$	13.2039	+	2.04214i	0.818869	+	0.126648i
$261$	−17.3620			−1.07468
$262$	1.53980	+	2.66701i	0.0951291	+	0.164768i
$263$	−14.6297	−	25.3393i	−0.902103	−	1.56249i	−0.824759	−	0.565484i	$-0.808689\pi$
$263$	−14.6297	−	25.3393i	−0.902103	−	1.56249i	−0.0773441	−	0.997004i	$-0.524644\pi$
$264$	−0.224159	+	0.388255i	−0.0137960	+	0.0238954i
$265$	3.80000			0.233432
$266$	−2.84652	+	4.93032i	−0.174532	+	0.302298i
$267$	1.11495	−	1.93115i	0.0682339	−	0.118185i
$268$	−26.5625			−1.62257
$269$	0.414877	−	0.718589i	0.0252955	−	0.0438131i	−0.853101	−	0.521747i	$-0.825281\pi$
$269$	0.414877	−	0.718589i	0.0252955	−	0.0438131i	0.878396	+	0.477933i	$0.158614\pi$
$270$	0.165252	+	0.286225i	0.0100569	+	0.0174191i
$271$	11.0137	+	19.0763i	0.669035	+	1.15880i	0.978174	+	0.207786i	$0.0666257\pi$
$271$	11.0137	+	19.0763i	0.669035	+	1.15880i	−0.309139	+	0.951017i	$0.600041\pi$
$272$	−8.49069			−0.514823
$273$	−0.827148	−	2.13161i	−0.0500613	−	0.129011i
$274$	−2.33432			−0.141021
$275$	−2.73957	−	4.74507i	−0.165202	−	0.286138i
$276$	−0.0373184	−	0.0646374i	−0.00224631	−	0.00389072i
$277$	−0.953972	+	1.65233i	−0.0573186	+	0.0992788i	−0.893261	−	0.449539i	$-0.851588\pi$
$277$	−0.953972	+	1.65233i	−0.0573186	+	0.0992788i	0.835942	+	0.548817i	$0.184922\pi$
$278$	2.54645			0.152726
$279$	1.49038	−	2.58142i	0.0892269	−	0.154546i
$280$	−3.60394	+	6.24221i	−0.215377	+	0.373044i
$281$	18.4723			1.10197			0.550983	−	0.834516i	$-0.314253\pi$
$281$	18.4723			1.10197			0.550983	+	0.834516i	$0.314253\pi$
$282$	0.0479147	−	0.0829907i	0.00285328	−	0.00494203i
$283$	−8.79341	−	15.2306i	−0.522714	−	0.905368i	−0.999651	−	0.0264298i	$-0.991586\pi$
$283$	−8.79341	−	15.2306i	−0.522714	−	0.905368i	0.476936	−	0.878938i	$-0.341747\pi$
$284$	9.00603	+	15.5989i	0.534409	+	0.925624i
$285$	1.55552			0.0921412
$286$	−2.91189	−	0.450359i	−0.172184	−	0.0266303i
$287$	−6.51688			−0.384679
$288$	−3.65099	−	6.32370i	−0.215137	−	0.372628i
$289$	5.91829	+	10.2508i	0.348135	+	0.602987i
$290$	1.16050	−	2.01004i	0.0681466	−	0.118033i
$291$	1.45481			0.0852826
$292$	9.51613	−	16.4824i	0.556889	−	0.964561i
$293$	8.91786	−	15.4462i	0.520987	−	0.902376i	−0.478715	−	0.877970i	$-0.658897\pi$
$293$	8.91786	−	15.4462i	0.520987	−	0.902376i	0.999702	−	0.0244057i	$-0.00776933\pi$
$294$	0.405693			0.0236605
$295$	−12.8322	+	22.2260i	−0.747119	+	1.29405i
$296$	1.06024	+	1.83638i	0.0616250	+	0.106738i
$297$	1.61148	+	2.79117i	0.0935076	+	0.161960i
$298$	−1.17512			−0.0680731
$299$	0.621591	−	0.773329i	0.0359475	−	0.0447227i
$300$	−0.382445			−0.0220805
$301$	−16.0796	−	27.8507i	−0.926814	−	1.60529i
$302$	1.85581	+	3.21436i	0.106790	+	0.184966i
$303$	0.114273	−	0.197926i	0.00656479	−	0.0113705i
$304$	−22.1201			−1.26867
$305$	−2.77328	+	4.80346i	−0.158797	+	0.275045i
$306$	0.712235	−	1.23363i	0.0407158	−	0.0705218i
$307$	12.4905			0.712873			0.356437	−	0.934320i	$-0.383992\pi$
$307$	12.4905			0.712873			0.356437	+	0.934320i	$0.383992\pi$
$308$	−17.3757	+	30.0956i	−0.990074	+	1.71486i
$309$	0.104796	+	0.181511i	0.00596161	+	0.0103258i
$310$	0.199238	+	0.345090i	0.0113159	+	0.0195998i
$311$	−18.3133			−1.03845			−0.519226	−	0.854637i	$-0.673780\pi$
$311$	−18.3133			−1.03845			−0.519226	+	0.854637i	$0.673780\pi$
$312$	−0.260612	+	0.324230i	−0.0147542	+	0.0183559i
$313$	−22.9177			−1.29539			−0.647694	−	0.761901i	$-0.724266\pi$
$313$	−22.9177			−1.29539			−0.647694	+	0.761901i	$0.724266\pi$
$314$	0.291387	+	0.504697i	0.0164439	+	0.0284817i
$315$	12.9127	+	22.3655i	0.727550	+	1.26015i
$316$	5.71636	−	9.90103i	0.321571	−	0.556977i
$317$	14.7152			0.826486			0.413243	−	0.910621i	$-0.364396\pi$
$317$	14.7152			0.826486			0.413243	+	0.910621i	$0.364396\pi$
$318$	−0.0292472	+	0.0506576i	−0.00164010	+	0.00284074i
$319$	11.3167	−	19.6012i	0.633616	−	1.09746i
$320$	−13.1834			−0.736974
$321$	−0.182769	+	0.316565i	−0.0102012	+	0.0176690i
$322$	0.132318	+	0.229182i	0.00737379	+	0.0127718i
$323$	−6.72591	−	11.6496i	−0.374240	−	0.648203i
$324$	−17.2641			−0.959118
$325$	−1.83917	−	4.73965i	−0.102019	−	0.262909i
$326$	1.83509			0.101636
$327$	−0.617147	−	1.06893i	−0.0341283	−	0.0591119i
$328$	0.592819	+	1.02679i	0.0327329	+	0.0566951i
$329$	7.51223	−	13.0116i	0.414163	−	0.717351i
$330$	−0.214733			−0.0118207
$331$	−14.6548	+	25.3828i	−0.805498	+	1.39516i	0.110456	+	0.993881i	$0.464769\pi$
$331$	−14.6548	+	25.3828i	−0.805498	+	1.39516i	−0.915954	+	0.401283i	$0.868565\pi$
$332$	−17.7755	+	30.7881i	−0.975560	+	1.68972i
$333$	7.59754			0.416343
$334$	0.421772	−	0.730531i	0.0230783	−	0.0399729i
$335$	−12.8667	−	22.2857i	−0.702982	−	1.21760i
$336$	1.18478	+	2.05210i	0.0646351	+	0.111951i
$337$	33.2342			1.81038			0.905192	−	0.425003i	$-0.139727\pi$
$337$	33.2342			1.81038			0.905192	+	0.425003i	$0.139727\pi$
$338$	−2.60627	−	0.825939i	−0.141762	−	0.0449252i
$339$	−1.55963			−0.0847076
$340$	−4.21019	−	7.29225i	−0.228329	−	0.395478i
$341$	1.94290	+	3.36520i	0.105214	+	0.182236i
$342$	1.85553	−	3.21387i	0.100335	−	0.173786i
$343$	31.5969			1.70607
$344$	−2.92542	+	5.06697i	−0.157728	+	0.273193i
$345$	0.0361535	−	0.0626197i	0.00194644	−	0.00337133i
$346$	0.181968			0.00978265
$347$	−17.0505	+	29.5323i	−0.915319	+	1.58538i	−0.108886	+	0.994054i	$0.534728\pi$
$347$	−17.0505	+	29.5323i	−0.915319	+	1.58538i	−0.806433	+	0.591325i	$0.798605\pi$
$348$	−0.789912	−	1.36817i	−0.0423437	−	0.0733415i
$349$	0.0225981	+	0.0391411i	0.00120965	+	0.00209517i	0.866630	−	0.498952i	$-0.166282\pi$
$349$	0.0225981	+	0.0391411i	0.00120965	+	0.00209517i	−0.865420	+	0.501047i	$0.832948\pi$
$350$	1.35601			0.0724820
$351$	1.08184	+	2.78798i	0.0577446	+	0.148812i
$352$	9.51902			0.507365
$353$	14.4199	+	24.9760i	0.767494	+	1.32934i	0.938918	+	0.344142i	$0.111830\pi$
$353$	14.4199	+	24.9760i	0.767494	+	1.32934i	−0.171423	+	0.985197i	$0.554837\pi$
$354$	−0.197529	−	0.342131i	−0.0104986	−	0.0181840i
$355$	−8.72489	+	15.1120i	−0.463069	+	0.802059i
$356$	−31.4474			−1.66671
$357$	−0.720498	+	1.24794i	−0.0381328	+	0.0660480i
$358$	−0.594590	+	1.02986i	−0.0314251	+	0.0544298i
$359$	−15.4449			−0.815152			−0.407576	−	0.913171i	$-0.633626\pi$
$359$	−15.4449			−0.815152			−0.407576	+	0.913171i	$0.633626\pi$
$360$	2.34926	−	4.06903i	0.123817	−	0.214457i
$361$	−8.02247	−	13.8953i	−0.422235	−	0.731333i
$362$	−0.259640	−	0.449709i	−0.0136464	−	0.0236362i
$363$	−0.568509			−0.0298390
$364$	−20.2014	+	25.1328i	−1.05884	+	1.31732i
$365$	18.4381			0.965096
$366$	−0.0426898	−	0.0739409i	−0.00223143	−	0.00386495i
$367$	−8.10986	−	14.0467i	−0.423331	−	0.733231i	0.572932	−	0.819603i	$-0.305806\pi$
$367$	−8.10986	−	14.0467i	−0.423331	−	0.733231i	−0.996263	+	0.0863718i	$0.972473\pi$
$368$	−0.514116	+	0.890475i	−0.0268001	+	0.0464192i
$369$	4.24807			0.221146
$370$	−0.507828	+	0.879584i	−0.0264007	+	0.0457274i
$371$	−4.58547	+	7.94227i	−0.238066	+	0.412342i
$372$	0.271229			0.0140626
$373$	−0.655967	+	1.13617i	−0.0339647	+	0.0588285i	−0.882508	−	0.470297i	$-0.844147\pi$
$373$	−0.655967	+	1.13617i	−0.0339647	+	0.0588285i	0.848543	+	0.529126i	$0.177480\pi$
$374$	0.928485	+	1.60818i	0.0480108	+	0.0831572i
$375$	−0.842159	−	1.45866i	−0.0434889	−	0.0753250i
$376$	−2.73345			−0.140967
$377$	13.1571	−	16.3689i	0.677624	−	0.843041i
$378$	−0.797642			−0.0410263
$379$	−9.36880	−	16.2272i	−0.481243	−	0.833537i	0.518525	−	0.855062i	$-0.326481\pi$
$379$	−9.36880	−	16.2272i	−0.481243	−	0.833537i	−0.999768	+	0.0215251i	$0.993148\pi$
$380$	−10.9684	−	18.9979i	−0.562670	−	0.974572i
$381$	−0.257345	+	0.445735i	−0.0131842	+	0.0228357i
$382$	−3.40162			−0.174042
$383$	15.3995	−	26.6728i	0.786879	−	1.36291i	−0.140992	−	0.990011i	$-0.545029\pi$
$383$	15.3995	−	26.6728i	0.786879	−	1.36291i	0.927870	−	0.372903i	$-0.121638\pi$
$384$	0.441196	−	0.764173i	0.0225147	−	0.0389965i
$385$	−33.6666			−1.71581
$386$	1.96478	−	3.40309i	0.100005	−	0.173213i
$387$	10.4816	+	18.1547i	0.532811	+	0.922855i
$388$	−10.2583	−	17.7679i	−0.520787	−	0.902030i
$389$	26.3957			1.33831			0.669157	−	0.743121i	$-0.266655\pi$
$389$	26.3957			1.33831			0.669157	+	0.743121i	$0.266655\pi$
$390$	−0.196906	−	0.0304539i	−0.00997072	−	0.00154209i
$391$	−0.625296			−0.0316226
$392$	−5.78602	−	10.0217i	−0.292238	−	0.506172i
$393$	1.01537	+	1.75868i	0.0512188	+	0.0887136i
$394$	−1.43468	+	2.48494i	−0.0722781	+	0.125189i
$395$	11.0758			0.557286
$396$	11.3265	−	19.6181i	0.569178	−	0.985845i
$397$	2.11377	−	3.66115i	0.106087	−	0.183748i	−0.808095	−	0.589052i	$-0.799501\pi$
$397$	2.11377	−	3.66115i	0.106087	−	0.183748i	0.914182	+	0.405304i	$0.132834\pi$
$398$	3.16032			0.158413
$399$	−1.87705	+	3.25115i	−0.0939703	+	0.162761i
$400$	2.63437	+	4.56286i	0.131718	+	0.228143i
$401$	−2.63540	−	4.56465i	−0.131606	−	0.227948i	0.792690	−	0.609625i	$-0.208680\pi$
$401$	−2.63540	−	4.56465i	−0.131606	−	0.227948i	−0.924296	+	0.381677i	$0.875347\pi$
$402$	0.396120			0.0197567
$403$	1.30434	+	3.36136i	0.0649736	+	0.167441i
$404$	−3.22308			−0.160354
$405$	−8.36260	−	14.4845i	−0.415541	−	0.719738i
$406$	2.80075	+	4.85104i	0.138999	+	0.240753i
$407$	−4.95216	+	8.57739i	−0.245470	+	0.425166i
$408$	0.262165			0.0129791
$409$	10.6297	−	18.4111i	0.525604	−	0.910373i	−0.473951	−	0.880551i	$-0.657173\pi$
$409$	10.6297	−	18.4111i	0.525604	−	0.910373i	0.999555	−	0.0298216i	$-0.00949391\pi$
$410$	−0.283946	+	0.491808i	−0.0140231	+	0.0242887i
$411$	−1.53929			−0.0759278
$412$	1.47789	−	2.55978i	0.0728104	−	0.126111i
$413$	−30.9693	−	53.6404i	−1.52390	−	2.63947i
$414$	−0.0862525	−	0.149394i	−0.00423908	−	0.00734230i
$415$	−34.4413			−1.69066
$416$	8.72873	+	1.35000i	0.427961	+	0.0661894i
$417$	1.67918			0.0822297
$418$	2.41891	+	4.18967i	0.118313	+	0.204923i
$419$	2.18337	+	3.78170i	0.106664	+	0.184748i	0.914417	−	0.404773i	$-0.132650\pi$
$419$	2.18337	+	3.78170i	0.106664	+	0.184748i	−0.807753	+	0.589522i	$0.799316\pi$
$420$	−1.17497	+	2.03511i	−0.0573327	+	0.0993031i
$421$	21.6061			1.05301			0.526507	−	0.850171i	$-0.323501\pi$
$421$	21.6061			1.05301			0.526507	+	0.850171i	$0.323501\pi$
$422$	−0.613031	+	1.06180i	−0.0298419	+	0.0516877i
$423$	−4.89690	+	8.48169i	−0.238096	+	0.412394i
$424$	1.66850			0.0810296
$425$	−1.60203	+	2.77480i	−0.0777099	+	0.134597i
$426$	−0.134305	−	0.232622i	−0.00650708	−	0.0112706i
$427$	−6.69305	−	11.5927i	−0.323900	−	0.561011i
$428$	5.15504			0.249178
$429$	−1.92016	−	0.296976i	−0.0927061	−	0.0143381i
$430$	−2.80241			−0.135144
$431$	−16.0102	−	27.7304i	−0.771183	−	1.33573i	−0.936915	−	0.349557i	$-0.886332\pi$
$431$	−16.0102	−	27.7304i	−0.771183	−	1.33573i	0.165732	−	0.986171i	$-0.447001\pi$
$432$	−1.54960	−	2.68399i	−0.0745552	−	0.129133i
$433$	−6.75646	+	11.7025i	−0.324695	+	0.562388i	−0.981451	−	0.191715i	$-0.938595\pi$
$433$	−6.75646	+	11.7025i	−0.324695	+	0.562388i	0.656756	+	0.754103i	$0.271928\pi$
$434$	−0.961683			−0.0461623
$435$	0.765254	−	1.32546i	0.0366911	−	0.0635509i
$436$	−8.70337	+	15.0747i	−0.416816	+	0.721946i
$437$	−1.62903			−0.0779271
$438$	−0.141912	+	0.245798i	−0.00678080	+	0.0117447i
$439$	19.8127	+	34.3166i	0.945607	+	1.63784i	0.754531	+	0.656265i	$0.227865\pi$
$439$	19.8127	+	34.3166i	0.945607	+	1.63784i	0.191077	+	0.981575i	$0.438802\pi$
$440$	3.06254	+	5.30448i	0.146001	+	0.252881i
$441$	−41.4620			−1.97438
$442$	0.623325	+	1.60635i	0.0296485	+	0.0764062i
$443$	−10.9350			−0.519537			−0.259768	−	0.965671i	$-0.583646\pi$
$443$	−10.9350			−0.519537			−0.259768	+	0.965671i	$0.583646\pi$
$444$	0.345662	+	0.598704i	0.0164044	+	0.0284132i
$445$	−15.2329	−	26.3841i	−0.722108	−	1.25073i
$446$	−0.834440	+	1.44529i	−0.0395119	+	0.0684366i
$447$	−0.774901			−0.0366515
$448$	15.9084	−	27.5542i	0.751603	−	1.30182i
$449$	−9.33021	+	16.1604i	−0.440320	+	0.762656i	−0.997713	−	0.0675925i	$-0.978468\pi$
$449$	−9.33021	+	16.1604i	−0.440320	+	0.762656i	0.557393	+	0.830249i	$0.311802\pi$
$450$	−0.883928			−0.0416688
$451$	−2.76894	+	4.79595i	−0.130384	+	0.225832i
$452$	10.9974	+	19.0481i	0.517276	+	0.895948i
$453$	1.22376	+	2.11961i	0.0574973	+	0.0995882i
$454$	−4.19946			−0.197090
$455$	−30.8716	−	4.77467i	−1.44728	−	0.223840i
$456$	0.682998			0.0319843
$457$	13.5527	+	23.4740i	0.633969	+	1.09807i	0.986733	+	0.162354i	$0.0519087\pi$
$457$	13.5527	+	23.4740i	0.633969	+	1.09807i	−0.352763	+	0.935713i	$0.614758\pi$
$458$	0.131146	+	0.227151i	0.00612804	+	0.0106141i
$459$	0.942355	−	1.63221i	0.0439853	−	0.0761849i
$460$	−1.01972			−0.0475445
$461$	−21.1110	+	36.5654i	−0.983239	+	1.70302i	−0.333722	+	0.942671i	$0.608305\pi$
$461$	−21.1110	+	36.5654i	−0.983239	+	1.70302i	−0.649516	+	0.760348i	$0.725029\pi$
$462$	0.259120	−	0.448809i	0.0120553	−	0.0208805i
$463$	12.3794			0.575321			0.287661	−	0.957732i	$-0.407122\pi$
$463$	12.3794			0.575321			0.287661	+	0.957732i	$0.407122\pi$
$464$	−10.8822	+	18.8485i	−0.505193	+	0.875019i
$465$	0.131381	+	0.227559i	0.00609266	+	0.0105528i
$466$	−0.115159	−	0.199461i	−0.00533464	−	0.00923986i
$467$	28.3221			1.31059			0.655296	−	0.755373i	$-0.272544\pi$
$467$	28.3221			1.31059			0.655296	+	0.755373i	$0.272544\pi$
$468$	13.1684	−	16.3830i	0.608710	−	0.757304i
$469$	62.1051			2.86775
$470$	−0.654628	−	1.13385i	−0.0301958	−	0.0523006i
$471$	0.192146	+	0.332807i	0.00885364	+	0.0153350i
$472$	−5.63435	+	9.75897i	−0.259342	+	0.449193i
$473$	−27.3281			−1.25655
$474$	−0.0852467	+	0.147652i	−0.00391551	+	0.00678186i
$475$	−4.17364	+	7.22895i	−0.191500	+	0.331687i
$476$	20.3218			0.931448
$477$	2.98908	−	5.17723i	0.136860	−	0.237049i
$478$	2.01592	+	3.49167i	0.0922058	+	0.159705i
$479$	14.3481	+	24.8517i	0.655583	+	1.13550i	0.981747	+	0.190190i	$0.0609103\pi$
$479$	14.3481	+	24.8517i	0.655583	+	1.13550i	−0.326165	+	0.945313i	$0.605756\pi$
$480$	0.643689			0.0293802
$481$	−5.75749	+	7.16296i	−0.262519	+	0.326603i
$482$	0.489354			0.0222895
$483$	0.0872531	+	0.151127i	0.00397016	+	0.00687651i
$484$	4.00873	+	6.94332i	0.182215	+	0.315606i
$485$	9.93809	−	17.2133i	0.451266	−	0.781615i
$486$	0.780759			0.0354159
$487$	−9.88032	+	17.1132i	−0.447720	+	0.775474i	−0.998237	−	0.0593500i	$-0.981097\pi$
$487$	−9.88032	+	17.1132i	−0.447720	+	0.775474i	0.550517	+	0.834824i	$0.314431\pi$
$488$	−1.21769	+	2.10910i	−0.0551222	+	0.0954745i
$489$	1.21009			0.0547224
$490$	2.77137	−	4.80015i	0.125198	−	0.216849i
$491$	−2.19675	−	3.80488i	−0.0991380	−	0.171712i	0.812190	−	0.583393i	$-0.198275\pi$
$491$	−2.19675	−	3.80488i	−0.0991380	−	0.171712i	−0.911328	+	0.411681i	$0.864942\pi$
$492$	0.193273	+	0.334758i	0.00871341	+	0.0150921i
$493$	−13.2355			−0.596097
$494$	1.62390	+	4.18489i	0.0730626	+	0.188287i
$495$	21.9459			0.986393
$496$	−1.86829	−	3.23597i	−0.0838887	−	0.145299i
$497$	−21.0567	−	36.4713i	−0.944523	−	1.63596i
$498$	0.265082	−	0.459136i	0.0118786	−	0.0205744i
$499$	25.4308			1.13844			0.569220	−	0.822186i	$-0.307245\pi$
$499$	25.4308			1.13844			0.569220	+	0.822186i	$0.307245\pi$
$500$	−11.8766	+	20.5709i	−0.531139	+	0.919960i
$501$	0.278125	−	0.481727i	0.0124257	−	0.0215220i
$502$	5.92223			0.264322
$503$	−2.21882	+	3.84311i	−0.0989322	+	0.171356i	−0.911243	−	0.411869i	$-0.864876\pi$
$503$	−2.21882	+	3.84311i	−0.0989322	+	0.171356i	0.812311	+	0.583225i	$0.198209\pi$
$504$	5.66972	+	9.82024i	0.252549	+	0.437428i
$505$	−1.56123	−	2.70414i	−0.0694740	−	0.120332i
$506$	0.224881			0.00999719
$507$	−1.71863	−	0.544641i	−0.0763268	−	0.0241883i
$508$	7.25848			0.322043
$509$	1.81066	+	3.13615i	0.0802561	+	0.139008i	0.903360	−	0.428883i	$-0.141093\pi$
$509$	1.81066	+	3.13615i	0.0802561	+	0.139008i	−0.823104	+	0.567891i	$0.807760\pi$
$510$	0.0627854	+	0.108748i	0.00278018	+	0.00481542i
$511$	−22.2494	+	38.5371i	−0.984255	+	1.70478i
$512$	−15.3706			−0.679293
$513$	2.45504	−	4.25225i	0.108393	−	0.187742i
$514$	1.98930	−	3.44557i	0.0877442	−	0.151977i
$515$	2.86351			0.126181
$516$	−0.953755	+	1.65195i	−0.0419867	+	0.0727231i
$517$	−6.38371	−	11.0569i	−0.280755	−	0.486282i
$518$	−1.22560	−	2.12279i	−0.0538496	−	0.0932702i
$519$	0.119993			0.00526712
$520$	2.05599	+	5.29843i	0.0901612	+	0.232351i
$521$	−29.6654			−1.29966			−0.649832	−	0.760078i	$-0.725161\pi$
$521$	−29.6654			−1.29966			−0.649832	+	0.760078i	$0.725161\pi$
$522$	−1.82569	−	3.16219i	−0.0799082	−	0.138405i
$523$	11.0654	+	19.1658i	0.483855	+	0.838061i	0.999828	−	0.0185435i	$-0.00590292\pi$
$523$	11.0654	+	19.1658i	0.483855	+	0.838061i	−0.515973	+	0.856605i	$0.672570\pi$
$524$	14.3194	−	24.8019i	0.625546	−	1.08348i
$525$	0.894183			0.0390253
$526$	3.07674	−	5.32907i	0.134152	−	0.232358i
$527$	1.13616	−	1.96788i	0.0494918	−	0.0857223i
$528$	2.01360			0.0876306
$529$	11.4621	−	19.8530i	0.498354	−	0.863174i
$530$	0.399586	+	0.692103i	0.0173569	+	0.0300630i
$531$	20.1876	+	34.9659i	0.876066	+	1.51739i
$532$	52.9427			2.29536
$533$	−3.21923	+	4.00508i	−0.139440	+	0.173479i
$534$	0.468967			0.0202942
$535$	2.49706	+	4.32503i	0.107957	+	0.186988i
$536$	−5.64949	−	9.78521i	−0.244021	−	0.422657i
$537$	−0.392084	+	0.679110i	−0.0169197	+	0.0293058i
$538$	0.174504			0.00752342
$539$	27.0254	−	46.8094i	1.16407	−	2.01622i
$540$	1.53677	−	2.66176i	0.0661320	−	0.114544i
$541$	25.2288			1.08467			0.542336	−	0.840162i	$-0.317540\pi$
$541$	25.2288			1.08467			0.542336	+	0.840162i	$0.317540\pi$
$542$	−2.31628	+	4.01191i	−0.0994925	+	0.172326i
$543$	−0.171212	−	0.296547i	−0.00734740	−	0.0127261i
$544$	−2.78324	−	4.82072i	−0.119331	−	0.206687i
$545$	−16.8634			−0.722347
$546$	0.301258	−	0.374799i	0.0128927	−	0.0160399i
$547$	1.69988			0.0726814			0.0363407	−	0.999339i	$-0.488430\pi$
$547$	1.69988			0.0726814			0.0363407	+	0.999339i	$0.488430\pi$
$548$	10.8540	+	18.7997i	0.463661	+	0.803084i
$549$	4.36292	+	7.55679i	0.186205	+	0.322516i
$550$	0.576154	−	0.997927i	0.0245673	−	0.0425518i
$551$	−34.4814			−1.46896
$552$	0.0158743	−	0.0274950i	0.000675653	−	0.00117027i
$553$	−13.3653	+	23.1493i	−0.568349	+	0.984409i
$554$	−0.401257			−0.0170478
$555$	−0.334872	+	0.580015i	−0.0142145	+	0.0246203i
$556$	−11.8404	−	20.5082i	−0.502144	−	0.869740i
$557$	−9.24415	−	16.0113i	−0.391687	−	0.678422i	0.600985	−	0.799260i	$-0.294775\pi$
$557$	−9.24415	−	16.0113i	−0.391687	−	0.678422i	−0.992672	+	0.120838i	$0.961442\pi$
$558$	0.626880			0.0265380
$559$	−25.0593	−	3.87573i	−1.05990	−	0.163926i
$560$	32.3738			1.36804
$561$	0.612262	+	1.06047i	0.0258497	+	0.0447730i
$562$	1.94244	+	3.36441i	0.0819370	+	0.141919i
$563$	7.04578	−	12.2037i	0.296944	−	0.514323i	−0.678491	−	0.734609i	$-0.737366\pi$
$563$	7.04578	−	12.2037i	0.296944	−	0.514323i	0.975435	+	0.220286i	$0.0706991\pi$
$564$	−0.891169			−0.0375250
$565$	−10.6541	+	18.4535i	−0.448223	+	0.776345i
$566$	1.84933	−	3.20313i	0.0777331	−	0.134638i
$567$	40.3647			1.69516
$568$	−3.83092	+	6.63535i	−0.160742	+	0.278413i
$569$	6.01153	+	10.4123i	0.252017	+	0.436506i	0.964081	−	0.265609i	$-0.0855729\pi$
$569$	6.01153	+	10.4123i	0.252017	+	0.436506i	−0.712064	+	0.702114i	$0.752240\pi$
$570$	0.163570	+	0.283311i	0.00685118	+	0.0118666i
$571$	−2.14551			−0.0897868			−0.0448934	−	0.998992i	$-0.514295\pi$
$571$	−2.14551			−0.0897868			−0.0448934	+	0.998992i	$0.514295\pi$
$572$	9.91258	+	25.5454i	0.414466	+	1.06810i
$573$	−2.24309			−0.0937066
$574$	−0.685277	−	1.18693i	−0.0286029	−	0.0495417i
$575$	0.194008	+	0.336031i	0.00809068	+	0.0140135i
$576$	−10.3700	+	17.9614i	−0.432085	+	0.748393i
$577$	26.7175			1.11226			0.556131	−	0.831094i	$-0.312285\pi$
$577$	26.7175			1.11226			0.556131	+	0.831094i	$0.312285\pi$
$578$	−1.24467	+	2.15583i	−0.0517713	+	0.0896705i
$579$	1.29561	−	2.24407i	0.0538439	−	0.0932603i
$580$	−21.5841			−0.896232
$581$	41.5605	−	71.9848i	1.72422	−	2.98643i
$582$	0.152980	+	0.264969i	0.00634121	+	0.0109833i
$583$	3.89662	+	6.74915i	0.161382	+	0.279521i
$584$	8.09581			0.335007
$585$	20.1239	+	3.11240i	0.832019	+	0.128682i
$586$	3.75100			0.154952
$587$	−17.4269	−	30.1843i	−0.719286	−	1.24584i	−0.961283	−	0.275563i	$-0.911136\pi$
$587$	−17.4269	−	30.1843i	−0.719286	−	1.24584i	0.241997	−	0.970277i	$-0.422198\pi$
$588$	−1.88638	−	3.26731i	−0.0777930	−	0.134741i
$589$	2.95994	−	5.12676i	0.121962	−	0.211245i
$590$	−5.39743			−0.222209
$591$	−0.946056	+	1.63862i	−0.0389156	+	0.0674037i
$592$	4.76200	−	8.24802i	0.195717	−	0.338992i
$593$	14.3711			0.590148			0.295074	−	0.955474i	$-0.404656\pi$
$593$	14.3711			0.590148			0.295074	+	0.955474i	$0.404656\pi$
$594$	−0.338908	+	0.587006i	−0.0139056	+	0.0240852i
$595$	9.84371	+	17.0498i	0.403553	+	0.698974i
$596$	5.46405	+	9.46402i	0.223816	+	0.387661i
$597$	2.08398			0.0852915
$598$	0.206211	+	0.0318931i	0.00843260	+	0.00130420i
$599$	−22.7638			−0.930102			−0.465051	−	0.885284i	$-0.653964\pi$
$599$	−22.7638			−0.930102			−0.465051	+	0.885284i	$0.653964\pi$
$600$	−0.0813408	−	0.140886i	−0.00332072	−	0.00575166i
$601$	−14.7747	−	25.5905i	−0.602673	−	1.04386i	−0.992415	−	0.122935i	$-0.960769\pi$
$601$	−14.7747	−	25.5905i	−0.602673	−	1.04386i	0.389742	−	0.920924i	$-0.372564\pi$
$602$	3.38168	−	5.85724i	0.137827	−	0.238723i
$603$	−40.4837			−1.64862
$604$	17.2582	−	29.8921i	0.702226	−	1.21629i
$605$	−3.88359	+	6.72658i	−0.157890	+	0.273474i
$606$	0.0480650			0.00195251
$607$	2.48600	−	4.30587i	0.100904	−	0.174770i	−0.811154	−	0.584833i	$-0.801160\pi$
$607$	2.48600	−	4.30587i	0.100904	−	0.174770i	0.912057	+	0.410063i	$0.134493\pi$
$608$	−7.25095	−	12.5590i	−0.294065	−	0.509336i
$609$	1.84687	+	3.19887i	0.0748389	+	0.129625i
$610$	−1.16649			−0.0472297
$611$	−4.28561	−	11.0443i	−0.173377	−	0.446804i
$612$	−13.2469			−0.535475
$613$	20.6822	+	35.8226i	0.835346	+	1.44686i	0.893749	+	0.448568i	$0.148066\pi$
$613$	20.6822	+	35.8226i	0.835346	+	1.44686i	−0.0584029	+	0.998293i	$0.518601\pi$
$614$	1.31343	+	2.27493i	0.0530059	+	0.0918088i
$615$	−0.187240	+	0.324308i	−0.00755023	+	0.0130774i
$616$	−14.7823			−0.595597
$617$	−9.74216	+	16.8739i	−0.392204	+	0.679318i	−0.992740	−	0.120280i	$-0.961621\pi$
$617$	−9.74216	+	16.8739i	−0.392204	+	0.679318i	0.600536	+	0.799598i	$0.294954\pi$
$618$	−0.0220394	+	0.0381733i	−0.000886554	+	0.00153556i
$619$	−8.29399			−0.333364			−0.166682	−	0.986011i	$-0.553305\pi$
$619$	−8.29399			−0.333364			−0.166682	+	0.986011i	$0.553305\pi$
$620$	1.85282	−	3.20917i	0.0744109	−	0.128884i
$621$	−0.114120	−	0.197662i	−0.00457949	−	0.00793190i
$622$	−1.92572	−	3.33545i	−0.0772144	−	0.133739i
$623$	73.5263			2.94577
$624$	1.84642	+	0.285572i	0.0739161	+	0.0114320i
$625$	−15.9616			−0.638463
$626$	−2.40990	−	4.17406i	−0.0963189	−	0.166829i
$627$	1.59508	+	2.76275i	0.0637012	+	0.110334i
$628$	2.70976	−	4.69345i	0.108131	−	0.187289i
$629$	5.79180			0.230934
$630$	−2.71566	+	4.70366i	−0.108194	+	0.187398i
$631$	−0.538983	+	0.933546i	−0.0214566	+	0.0371639i	−0.876554	−	0.481303i	$-0.840164\pi$
$631$	−0.538983	+	0.933546i	−0.0214566	+	0.0371639i	0.855098	+	0.518467i	$0.173497\pi$
$632$	4.86317			0.193447
$633$	−0.404245	+	0.700173i	−0.0160673	+	0.0278294i
$634$	1.54736	+	2.68011i	0.0614536	+	0.106441i
$635$	3.51595	+	6.08980i	0.139526	+	0.241666i
$636$	0.543971			0.0215698
$637$	31.4203	−	39.0904i	1.24492	−	1.54882i
$638$	4.76001			0.188451
$639$	13.7260	+	23.7741i	0.542991	+	0.940489i
$640$	−6.02778	−	10.4404i	−0.238269	−	0.412694i
$641$	−6.83941	+	11.8462i	−0.270140	+	0.467897i	−0.968898	−	0.247462i	$-0.920403\pi$
$641$	−6.83941	+	11.8462i	−0.270140	+	0.467897i	0.698757	+	0.715359i	$0.253737\pi$
$642$	−0.0768758			−0.00303405
$643$	9.28612	−	16.0840i	0.366209	−	0.634293i	−0.622760	−	0.782413i	$-0.713989\pi$
$643$	9.28612	−	16.0840i	0.366209	−	0.634293i	0.988969	+	0.148120i	$0.0473222\pi$
$644$	1.23050	−	2.13128i	0.0484883	−	0.0839842i
$645$	−1.84796			−0.0727635
$646$	1.41452	−	2.45001i	0.0556534	−	0.0963945i
$647$	−1.48391	−	2.57021i	−0.0583386	−	0.101045i	0.835381	−	0.549671i	$-0.185247\pi$
$647$	−1.48391	−	2.57021i	−0.0583386	−	0.101045i	−0.893720	+	0.448626i	$0.851914\pi$
$648$	−3.67185	−	6.35982i	−0.144244	−	0.249837i
$649$	−52.6339			−2.06606
$650$	0.669848	−	0.833366i	0.0262736	−	0.0326873i
$651$	−0.634153			−0.0248544
$652$	−8.53274	−	14.7791i	−0.334168	−	0.578796i
$653$	23.5939	+	40.8657i	0.923299	+	1.59920i	0.794275	+	0.607559i	$0.207851\pi$
$653$	23.5939	+	40.8657i	0.923299	+	1.59920i	0.129024	+	0.991641i	$0.458816\pi$
$654$	0.129791	−	0.224805i	0.00507523	−	0.00879056i
$655$	27.7448			1.08408
$656$	2.66261	−	4.61178i	0.103958	−	0.180060i
$657$	14.5034	−	25.1207i	0.565832	−	0.980051i
$658$	3.15977			0.123181
$659$	17.5596	−	30.4141i	0.684024	−	1.18476i	−0.289718	−	0.957112i	$-0.593562\pi$
$659$	17.5596	−	30.4141i	0.684024	−	1.18476i	0.973742	−	0.227653i	$-0.0731050\pi$
$660$	0.998461	+	1.72938i	0.0388650	+	0.0673162i
$661$	−23.1051	−	40.0192i	−0.898684	−	1.55657i	−0.829178	−	0.558984i	$-0.811191\pi$
$661$	−23.1051	−	40.0192i	−0.898684	−	1.55657i	−0.0695050	−	0.997582i	$-0.522142\pi$
$662$	−6.16404			−0.239572
$663$	0.411033	+	1.05926i	0.0159632	+	0.0411382i
$664$	−15.1225			−0.586866
$665$	25.6450	+	44.4185i	0.994471	+	1.72247i
$666$	0.798914	+	1.38376i	0.0309573	+	0.0536196i
$667$	−0.801417	+	1.38810i	−0.0310310	+	0.0537473i
$668$	−7.84457			−0.303515
$669$	−0.550246	+	0.953055i	−0.0212738	+	0.0368472i
$670$	2.70597	−	4.68688i	0.104541	−	0.181070i
$671$	−11.3752			−0.439134
$672$	−0.776742	+	1.34536i	−0.0299635	+	0.0518983i
$673$	6.99876	+	12.1222i	0.269782	+	0.467277i	0.968806	−	0.247822i	$-0.0797149\pi$
$673$	6.99876	+	12.1222i	0.269782	+	0.467277i	−0.699023	+	0.715099i	$0.746382\pi$
$674$	3.49472	+	6.05303i	0.134612	+	0.233154i
$675$	−1.16952			−0.0450149
$676$	5.46673	+	24.8303i	0.210259	+	0.955013i
$677$	31.4820			1.20995			0.604976	−	0.796244i	$-0.293183\pi$
$677$	31.4820			1.20995			0.604976	+	0.796244i	$0.293183\pi$
$678$	−0.164002	−	0.284060i	−0.00629846	−	0.0109092i
$679$	23.9847	+	41.5427i	0.920447	+	1.59426i
$680$	1.79090	−	3.10193i	0.0686778	−	0.118954i
$681$	−2.76921			−0.106116
$682$	−0.408607	+	0.707729i	−0.0156464	+	0.0271003i
$683$	5.48485	−	9.50005i	0.209872	−	0.363509i	−0.741802	−	0.670619i	$-0.766029\pi$
$683$	5.48485	−	9.50005i	0.209872	−	0.363509i	0.951674	+	0.307110i	$0.0993619\pi$
$684$	−34.5111			−1.31956
$685$	−10.5152	+	18.2129i	−0.401765	+	0.695878i
$686$	3.32255	+	5.75482i	0.126855	+	0.219720i
$687$	0.0864801	+	0.149788i	0.00329942	+	0.00571477i
$688$	26.2787			1.00187
$689$	2.61594	+	6.74145i	0.0996594	+	0.256829i
$690$	0.0152068			0.000578912
$691$	6.40820	+	11.0993i	0.243780	+	0.422239i	0.961788	−	0.273796i	$-0.0882793\pi$
$691$	6.40820	+	11.0993i	0.243780	+	0.422239i	−0.718008	+	0.696035i	$0.754946\pi$
$692$	−0.846108	−	1.46550i	−0.0321642	−	0.0557100i
$693$	−26.4821	+	45.8684i	−1.00597	+	1.74240i
$694$	−7.17173			−0.272235
$695$	11.4708	−	19.8680i	0.435111	−	0.753635i
$696$	0.336007	−	0.581981i	0.0127363	−	0.0220599i
$697$	3.23842			0.122664
$698$	−0.00475258	+	0.00823170i	−0.000179888	+	0.000311574i
$699$	−0.0759381	−	0.131529i	−0.00287224	−	0.00497487i
$700$	−6.30515	−	10.9208i	−0.238312	−	0.412769i
$701$	−21.8737			−0.826160			−0.413080	−	0.910695i	$-0.635547\pi$
$701$	−21.8737			−0.826160			−0.413080	+	0.910695i	$0.635547\pi$
$702$	−0.394022	+	0.490207i	−0.0148714	+	0.0185017i
$703$	15.0889			0.569089
$704$	−13.5186	−	23.4149i	−0.509502	−	0.882483i
$705$	−0.431675	−	0.747683i	−0.0162578	−	0.0281594i
$706$	−3.03263	+	5.25267i	−0.114134	+	0.197687i
$707$	7.53579			0.283413
$708$	−1.83693	+	3.18165i	−0.0690360	+	0.119574i
$709$	7.52739	−	13.0378i	0.282697	−	0.489646i	−0.689351	−	0.724427i	$-0.742104\pi$
$709$	7.52739	−	13.0378i	0.282697	−	0.489646i	0.972048	+	0.234782i	$0.0754375\pi$
$710$	−3.66984			−0.137727
$711$	8.71225	−	15.0901i	0.326735	−	0.565921i
$712$	−6.68844	−	11.5847i	−0.250660	−	0.434156i
$713$	−0.137590	−	0.238313i	−0.00515279	−	0.00892489i
$714$	−0.303054			−0.0113415
$715$	−16.6308	+	20.6905i	−0.621955	+	0.773782i
$716$	11.0588			0.413287
$717$	1.32934	+	2.30248i	0.0496449	+	0.0859875i
$718$	−1.62410	−	2.81302i	−0.0606108	−	0.104981i
$719$	−0.969688	+	1.67955i	−0.0361633	+	0.0626366i	−0.883541	−	0.468355i	$-0.844847\pi$
$719$	−0.969688	+	1.67955i	−0.0361633	+	0.0626366i	0.847377	+	0.530991i	$0.178180\pi$
$720$	−21.1031			−0.786467
$721$	−3.45541	+	5.98494i	−0.128686	+	0.222891i
$722$	1.68719	−	2.92231i	0.0627908	−	0.108757i
$723$	0.322690			0.0120010
$724$	−2.41453	+	4.18209i	−0.0897353	+	0.155426i
$725$	4.10652	+	7.11270i	0.152512	+	0.264159i
$726$	−0.0597812	−	0.103544i	−0.00221869	−	0.00384288i
$727$	−45.5464			−1.68922			−0.844611	−	0.535381i	$-0.820168\pi$
$727$	−45.5464			−1.68922			−0.844611	+	0.535381i	$0.820168\pi$
$728$	−13.5551	−	2.09646i	−0.502384	−	0.0776999i
$729$	−25.9670			−0.961740
$730$	1.93885	+	3.35818i	0.0717600	+	0.124292i
$731$	7.99041	+	13.8398i	0.295536	+	0.511883i
$732$	−0.396995	+	0.687616i	−0.0146734	+	0.0254150i
$733$	−16.9392			−0.625663			−0.312831	−	0.949809i	$-0.601278\pi$
$733$	−16.9392			−0.625663			−0.312831	+	0.949809i	$0.601278\pi$
$734$	1.70557	−	2.95414i	0.0629538	−	0.109039i
$735$	1.82749	−	3.16531i	0.0674081	−	0.116754i
$736$	−0.674108			−0.0248479
$737$	26.3877	−	45.7048i	0.972003	−	1.68356i
$738$	0.446703	+	0.773712i	0.0164434	+	0.0284807i
$739$	9.88209	+	17.1163i	0.363519	+	0.629633i	0.988537	−	0.150977i	$-0.0482420\pi$
$739$	9.88209	+	17.1163i	0.363519	+	0.629633i	−0.625019	+	0.780610i	$0.714909\pi$
$740$	9.44512			0.347210
$741$	1.07083	+	2.75960i	0.0393379	+	0.101376i
$742$	−1.92873			−0.0708058
$743$	11.6443	+	20.1684i	0.427186	+	0.739909i	0.996622	−	0.0821275i	$-0.0261715\pi$
$743$	11.6443	+	20.1684i	0.427186	+	0.739909i	−0.569435	+	0.822036i	$0.692838\pi$
$744$	0.0576868	+	0.0999165i	0.00211490	+	0.00366312i
$745$	−5.29349	+	9.16859i	−0.193938	+	0.335911i
$746$	−0.275911			−0.0101018
$747$	−27.0915	+	46.9239i	−0.991226	+	1.71685i
$748$	8.63448	−	14.9554i	0.315708	−	0.546822i
$749$	−12.0528			−0.440401
$750$	0.177113	−	0.306769i	0.00646726	−	0.0112016i
$751$	−14.4688	−	25.0606i	−0.527973	−	0.914475i	−0.999468	−	0.0326069i	$-0.989619\pi$
$751$	−14.4688	−	25.0606i	−0.527973	−	0.914475i	0.471496	−	0.881868i	$-0.343714\pi$
$752$	6.13858	+	10.6323i	0.223851	+	0.387721i
$753$	3.90524			0.142315
$754$	4.36483	+	0.675074i	0.158958	+	0.0245848i
$755$	33.4389			1.21697
$756$	3.70885	+	6.42391i	0.134889	+	0.233635i
$757$	26.0937	+	45.1956i	0.948392	+	1.64266i	0.748813	+	0.662781i	$0.230624\pi$
$757$	26.0937	+	45.1956i	0.948392	+	1.64266i	0.199579	+	0.979882i	$0.436042\pi$
$758$	1.97034	−	3.41272i	0.0715659	−	0.123956i
$759$	0.148291			0.00538263
$760$	4.66568	−	8.08120i	0.169242	−	0.293136i
$761$	−0.546146	+	0.945952i	−0.0197978	+	0.0342907i	−0.875755	−	0.482757i	$-0.839636\pi$
$761$	−0.546146	+	0.945952i	−0.0197978	+	0.0342907i	0.855957	+	0.517047i	$0.172969\pi$
$762$	−0.108244			−0.00392126
$763$	20.3491	−	35.2457i	0.736687	−	1.27598i
$764$	15.8167	+	27.3954i	0.572229	+	0.991130i
$765$	−6.41670	−	11.1140i	−0.231996	−	0.401829i
$766$	6.47730			0.234034
$767$	−48.2641	−	7.46464i	−1.74272	−	0.269532i
$768$	−1.74431			−0.0629423
$769$	−12.2746	−	21.2602i	−0.442633	−	0.766663i	0.555251	−	0.831683i	$-0.312622\pi$
$769$	−12.2746	−	21.2602i	−0.442633	−	0.766663i	−0.997884	+	0.0650201i	$0.979289\pi$
$770$	−3.54019	−	6.13179i	−0.127580	−	0.220974i
$771$	1.31178	−	2.27208i	0.0472427	−	0.0818268i
$772$	−36.5430			−1.31521
$773$	−5.87331	+	10.1729i	−0.211248	+	0.365893i	−0.952105	−	0.305770i	$-0.901086\pi$
$773$	−5.87331	+	10.1729i	−0.211248	+	0.365893i	0.740857	+	0.671663i	$0.234420\pi$
$774$	−2.20437	+	3.81808i	−0.0792345	+	0.137238i
$775$	−1.41004			−0.0506502
$776$	4.36361	−	7.55800i	0.156645	−	0.271316i
$777$	−0.808182	−	1.39981i	−0.0289934	−	0.0502180i
$778$	2.77562	+	4.80751i	0.0995107	+	0.172358i
$779$	8.43678			0.302279
$780$	0.670302	+	1.72741i	0.0240007	+	0.0618512i
$781$	−35.7870			−1.28056
$782$	−0.0657525	−	0.113887i	−0.00235130	−	0.00407258i
$783$	−2.41556	−	4.18387i	−0.0863250	−	0.149519i
$784$	−25.9876	+	45.0119i	−0.928130	+	1.60757i
$785$	5.25035			0.187393
$786$	−0.213542	+	0.369865i	−0.00761678	+	0.0131927i
$787$	−4.14909	+	7.18644i	−0.147899	+	0.256169i	−0.930451	−	0.366417i	$-0.880584\pi$
$787$	−4.14909	+	7.18644i	−0.147899	+	0.256169i	0.782552	+	0.622586i	$0.213918\pi$
$788$	26.6837			0.950567
$789$	2.02886	−	3.51410i	0.0722295	−	0.125105i
$790$	1.16467	+	2.01727i	0.0414371	+	0.0717712i
$791$	−25.7128	−	44.5359i	−0.914241	−	1.58351i
$792$	9.63597			0.342399
$793$	−10.4308	−	1.61325i	−0.370408	−	0.0572882i
$794$	0.889087			0.0315525
$795$	0.263495	+	0.456387i	0.00934520	+	0.0161864i
$796$	−14.6947	−	25.4521i	−0.520842	−	0.902124i
$797$	9.92741	−	17.1948i	0.351647	−	0.609070i	−0.634891	−	0.772601i	$-0.718955\pi$
$797$	9.92741	−	17.1948i	0.351647	−	0.609070i	0.986538	+	0.163531i	$0.0522885\pi$
$798$	−0.789521			−0.0279487
$799$	−3.73304	+	6.46581i	−0.132065	+	0.228744i
$800$	−1.72709	+	2.99140i	−0.0610618	+	0.105762i
$801$	−47.9287			−1.69348
$802$	0.554248	−	0.959985i	0.0195712	−	0.0338982i
$803$	18.9070	+	32.7478i	0.667213	+	1.15565i
$804$	−1.84187	−	3.19021i	−0.0649577	−	0.112510i
$805$	2.38417			0.0840309
$806$	−0.475056	+	0.591022i	−0.0167331	+	0.0208179i
$807$	0.115072			0.00405072
$808$	−0.685506	−	1.18733i	−0.0241160	−	0.0417701i
$809$	−0.628555	−	1.08869i	−0.0220988	−	0.0382763i	0.854764	−	0.519016i	$-0.173702\pi$
$809$	−0.628555	−	1.08869i	−0.0220988	−	0.0382763i	−0.876863	+	0.480740i	$0.840368\pi$
$810$	1.75873	−	3.04620i	0.0617953	−	0.107033i
$811$	15.0280			0.527705			0.263853	−	0.964563i	$-0.415007\pi$
$811$	15.0280			0.527705			0.263853	+	0.964563i	$0.415007\pi$
$812$	26.0457	−	45.1124i	0.914023	−	1.58313i
$813$	−1.52740	+	2.64553i	−0.0535682	+	0.0927828i
$814$	−2.08296			−0.0730078
$815$	8.26638	−	14.3178i	0.289559	−	0.501530i
$816$	−0.588751	−	1.01975i	−0.0206104	−	0.0356983i
$817$	20.8167	+	36.0557i	0.728286	+	1.26143i
$818$	4.47102			0.156326
$819$	−30.7887	+	38.3046i	−1.07584	+	1.33847i
$820$	5.28113			0.184425
$821$	20.0740	+	34.7692i	0.700588	+	1.21345i	0.968260	+	0.249943i	$0.0804120\pi$
$821$	20.0740	+	34.7692i	0.700588	+	1.21345i	−0.267673	+	0.963510i	$0.586255\pi$
$822$	−0.161863	−	0.280355i	−0.00564563	−	0.00977852i
$823$	−7.37645	+	12.7764i	−0.257127	+	0.445357i	−0.965471	−	0.260511i	$-0.916109\pi$
$823$	−7.37645	+	12.7764i	−0.257127	+	0.445357i	0.708344	+	0.705867i	$0.249442\pi$
$824$	1.25731			0.0438004
$825$	0.379927	−	0.658053i	0.0132274	−	0.0229105i
$826$	6.51310	−	11.2810i	0.226620	−	0.392517i
$827$	−31.0626			−1.08015			−0.540077	−	0.841616i	$-0.681605\pi$
$827$	−31.0626			−1.08015			−0.540077	+	0.841616i	$0.681605\pi$
$828$	−0.802108	+	1.38929i	−0.0278752	+	0.0482812i
$829$	−0.580377	−	1.00524i	−0.0201573	−	0.0349135i	0.855771	−	0.517355i	$-0.173083\pi$
$829$	−0.580377	−	1.00524i	−0.0201573	−	0.0349135i	−0.875928	+	0.482442i	$0.839750\pi$
$830$	−3.62165	−	6.27288i	−0.125709	−	0.217735i
$831$	−0.264597			−0.00917876
$832$	−9.07552	−	23.3882i	−0.314637	−	0.810840i
$833$	−31.6076			−1.09514
$834$	0.176573	+	0.305833i	0.00611421	+	0.0105901i
$835$	−3.79984	−	6.58152i	−0.131499	−	0.227763i
$836$	22.4947	−	38.9620i	0.777995	−	1.34753i
$837$	0.829422			0.0286690
$838$	−0.459181	+	0.795324i	−0.0158621	+	0.0274740i
$839$	15.2845	−	26.4735i	0.527680	−	0.913968i	−0.471800	−	0.881706i	$-0.656395\pi$
$839$	15.2845	−	26.4735i	0.527680	−	0.913968i	0.999479	−	0.0322623i	$-0.0102712\pi$
$840$	−0.999601			−0.0344895
$841$	−2.46344	+	4.26680i	−0.0849462	+	0.147131i
$842$	2.27197	+	3.93516i	0.0782972	+	0.135615i
$843$	1.28089	+	2.21856i	0.0441161	+	0.0764112i
$844$	11.4018			0.392467
$845$	−18.1844	+	16.6142i	−0.625563	+	0.571544i
$846$	−2.05972			−0.0708146
$847$	−9.37269	−	16.2340i	−0.322050	−	0.557806i
$848$	−3.74699	−	6.48998i	−0.128672	−	0.222867i
$849$	1.21948	−	2.11221i	0.0418526	−	0.0724908i
$850$	−0.673841			−0.0231125
$851$	0.350697	−	0.607425i	0.0120217	−	0.0208223i
$852$	−1.24897	+	2.16328i	−0.0427890	+	0.0741127i
$853$	−34.7534			−1.18994			−0.594968	−	0.803750i	$-0.702835\pi$
$853$	−34.7534			−1.18994			−0.594968	+	0.803750i	$0.702835\pi$
$854$	1.40761	−	2.43804i	0.0481673	−	0.0834282i
$855$	−16.7169	−	28.9545i	−0.571706	−	0.990223i
$856$	1.09641	+	1.89903i	0.0374744	+	0.0649076i
$857$	−3.00468			−0.102638			−0.0513190	−	0.998682i	$-0.516343\pi$
$857$	−3.00468			−0.102638			−0.0513190	+	0.998682i	$0.516343\pi$
$858$	−0.147824	−	0.380951i	−0.00504662	−	0.0130055i
$859$	−36.3811			−1.24131			−0.620654	−	0.784085i	$-0.713133\pi$
$859$	−36.3811			−1.24131			−0.620654	+	0.784085i	$0.713133\pi$
$860$	13.0305	+	22.5696i	0.444338	+	0.769616i
$861$	−0.451885	−	0.782688i	−0.0154002	−	0.0266740i
$862$	3.36707	−	5.83194i	0.114683	−	0.198637i
$863$	2.53283			0.0862186			0.0431093	−	0.999070i	$-0.486274\pi$
$863$	2.53283			0.0862186			0.0431093	+	0.999070i	$0.486274\pi$
$864$	1.01592	−	1.75962i	0.0345622	−	0.0598635i
$865$	0.819695	−	1.41975i	0.0278705	−	0.0482731i
$866$	−2.84188			−0.0965711
$867$	−0.820758	+	1.42159i	−0.0278744	+	0.0482799i
$868$	4.47160	+	7.74505i	0.151776	+	0.262884i
$869$	11.3575	+	19.6717i	0.385276	+	0.667317i
$870$	0.321879			0.0109127
$871$	30.6789	−	38.1680i	1.03951	−	1.29327i
$872$	−7.40436			−0.250743
$873$	−15.6346	−	27.0799i	−0.529151	−	0.916516i
$874$	−0.171300	−	0.296699i	−0.00579429	−	0.0100360i
$875$	27.7684	−	48.0963i	0.938744	−	1.62595i
$876$	2.63942			0.0891779
$877$	−12.8508	+	22.2582i	−0.433941	+	0.751608i	−0.997209	−	0.0746669i	$-0.976211\pi$
$877$	−12.8508	+	22.2582i	−0.433941	+	0.751608i	0.563268	+	0.826274i	$0.309544\pi$
$878$	−4.16677	+	7.21706i	−0.140622	+	0.243564i
$879$	2.47349			0.0834286
$880$	13.7552	−	23.8248i	0.463689	−	0.803134i
$881$	22.0065	+	38.1164i	0.741419	+	1.28418i	0.951849	+	0.306566i	$0.0991801\pi$
$881$	22.0065	+	38.1164i	0.741419	+	1.28418i	−0.210431	+	0.977609i	$0.567487\pi$
$882$	−4.35991	−	7.55158i	−0.146806	−	0.254275i
$883$	−45.3633			−1.52660			−0.763298	−	0.646047i	$-0.776421\pi$
$883$	−45.3633			−1.52660			−0.763298	+	0.646047i	$0.776421\pi$
$884$	10.0386	−	12.4892i	0.337635	−	0.420056i
$885$	−3.55917			−0.119640
$886$	−1.14986	−	1.99162i	−0.0386303	−	0.0669097i
$887$	−10.5363	−	18.2494i	−0.353774	−	0.612754i	0.633134	−	0.774042i	$-0.281768\pi$
$887$	−10.5363	−	18.2494i	−0.353774	−	0.612754i	−0.986907	+	0.161289i	$0.948435\pi$
$888$	−0.147035	+	0.254673i	−0.00493418	+	0.00854625i
$889$	−16.9708			−0.569183
$890$	3.20360	−	5.54880i	0.107385	−	0.185996i
$891$	17.1505	−	29.7055i	0.574563	−	0.995172i
$892$	15.5198			0.519642
$893$	−9.72537	+	16.8448i	−0.325447	+	0.563691i
$894$	−0.0814841	−	0.141135i	−0.00272523	−	0.00472024i
$895$	5.35680	+	9.27825i	0.179058	+	0.310138i
$896$	29.0950			0.971995
$897$	0.135980	+	0.0210309i	0.00454023	+	0.000702202i
$898$	−3.92444			−0.130960
$899$	−2.91234	−	5.04432i	−0.0971320	−	0.168237i
$900$	4.11006	+	7.11883i	0.137002	+	0.237294i
$901$	2.27865	−	3.94674i	0.0759128	−	0.131485i
$902$	−1.16466			−0.0387790
$903$	2.22995	−	3.86238i	0.0742080	−	0.128532i
$904$	−4.67801	+	8.10256i	−0.155588	+	0.269487i
$905$	−4.67831			−0.155512
$906$	−0.257367	+	0.445773i	−0.00855045	+	0.0148098i
$907$	17.1483	+	29.7018i	0.569401	+	0.986231i	0.996625	+	0.0820856i	$0.0261581\pi$
$907$	17.1483	+	29.7018i	0.569401	+	0.986231i	−0.427224	+	0.904146i	$0.640509\pi$
$908$	19.5265	+	33.8209i	0.648009	+	1.12239i
$909$	−4.91226			−0.162929
$910$	−2.37665	−	6.12479i	−0.0787853	−	0.203035i
$911$	−28.1732			−0.933421			−0.466710	−	0.884410i	$-0.654561\pi$
$911$	−28.1732			−0.933421			−0.466710	+	0.884410i	$0.654561\pi$
$912$	−1.53382	−	2.65666i	−0.0507900	−	0.0879709i
$913$	−35.3171	−	61.1710i	−1.16882	−	2.02446i
$914$	−2.85025	+	4.93678i	−0.0942779	+	0.163294i
$915$	−0.769205			−0.0254291
$916$	1.21959	−	2.11240i	0.0402965	−	0.0697957i
$917$	−33.4798	+	57.9887i	−1.10560	+	1.91496i
$918$	0.396370			0.0130822
$919$	−29.8034	+	51.6210i	−0.983124	+	1.70282i	−0.333131	+	0.942881i	$0.608105\pi$
$919$	−29.8034	+	51.6210i	−0.983124	+	1.70282i	−0.649993	+	0.759940i	$0.725228\pi$
$920$	−0.216880	−	0.375647i	−0.00715032	−	0.0123847i
$921$	0.866104	+	1.50014i	0.0285391	+	0.0494312i
$922$	−8.87965			−0.292436
$923$	−32.8159	−	5.07538i	−1.08015	−	0.167058i
$924$	−4.81939			−0.158546
$925$	−1.79700	−	3.11249i	−0.0590849	−	0.102338i
$926$	1.30175	+	2.25470i	0.0427782	+	0.0740940i
$927$	2.25243	−	3.90133i	0.0739796	−	0.128137i
$928$	−14.2687			−0.468393
$929$	−5.50270	+	9.53095i	−0.180538	+	0.312700i	−0.942064	−	0.335434i	$-0.891117\pi$
$929$	−5.50270	+	9.53095i	−0.180538	+	0.312700i	0.761526	+	0.648134i	$0.224450\pi$
$930$	−0.0276306	+	0.0478576i	−0.000906043	+	0.00156931i
$931$	−82.3446			−2.69874
$932$	−1.07092	+	1.85490i	−0.0350793	+	0.0607591i
$933$	−1.26986	−	2.19946i	−0.0415733	−	0.0720071i
$934$	2.97819	+	5.15838i	0.0974493	+	0.168787i
$935$	16.7299			0.547126
$936$	8.83597	+	1.36659i	0.288813	+	0.0446684i
$937$	9.94667			0.324944			0.162472	−	0.986713i	$-0.448053\pi$
$937$	9.94667			0.324944			0.162472	+	0.986713i	$0.448053\pi$
$938$	6.53061	+	11.3114i	0.213232	+	0.369329i
$939$	−1.58913	−	2.75246i	−0.0518594	−	0.0898232i
$940$	−6.08774	+	10.5443i	−0.198560	+	0.343916i
$941$	44.5767			1.45316			0.726579	−	0.687083i	$-0.241109\pi$
$941$	44.5767			1.45316			0.726579	+	0.687083i	$0.241109\pi$
$942$	−0.0404100	+	0.0699922i	−0.00131663	+	0.00228047i
$943$	0.196088	−	0.339634i	0.00638550	−	0.0110600i
$944$	50.6127			1.64730
$945$	−3.59307	+	6.22338i	−0.116883	+	0.202447i
$946$	−2.87367	−	4.97734i	−0.0934310	−	0.161827i
$947$	12.9544	+	22.4377i	0.420963	+	0.729129i	0.996034	−	0.0889747i	$-0.0283590\pi$
$947$	12.9544	+	22.4377i	0.420963	+	0.729129i	−0.575071	+	0.818103i	$0.695026\pi$
$948$	1.58551			0.0514949
$949$	12.6929	+	32.7105i	0.412030	+	1.06183i
$950$	−1.75550			−0.0569560
$951$	1.02036	+	1.76732i	0.0330875	+	0.0573092i
$952$	4.32217	+	7.48622i	0.140082	+	0.242630i
$953$	−7.20268	+	12.4754i	−0.233318	+	0.404118i	−0.958782	−	0.284141i	$-0.908291\pi$
$953$	−7.20268	+	12.4754i	−0.233318	+	0.404118i	0.725465	+	0.688259i	$0.241625\pi$
$954$	1.25726			0.0407051
$955$	−15.3230	+	26.5402i	−0.495840	+	0.858820i
$956$	18.7471	−	32.4709i	0.606324	−	1.05018i
$957$	3.13885			0.101465
$958$	−3.01753	+	5.22652i	−0.0974920	+	0.168861i
$959$	−25.3775	−	43.9551i	−0.819481	−	1.41938i
$960$	−0.914146	−	1.58335i	−0.0295039	−	0.0511023i
$961$	1.00000			0.0322581
$962$	−1.91003	−	0.295410i	−0.0615819	−	0.00952439i
$963$	7.85674			0.253180
$964$	−2.27538	−	3.94108i	−0.0732851	−	0.126934i
$965$	−17.7011	−	30.6593i	−0.569820	−	0.986957i
$966$	−0.0183501	+	0.0317833i	−0.000590404	+	0.00102261i
$967$	−19.3103			−0.620977			−0.310489	−	0.950577i	$-0.600493\pi$
$967$	−19.3103			−0.620977			−0.310489	+	0.950577i	$0.600493\pi$
$968$	−1.70520	+	2.95350i	−0.0548074	+	0.0949291i
$969$	0.932760	−	1.61559i	0.0299646	−	0.0519002i
$970$	4.18013			0.134216
$971$	−25.5990	+	44.3388i	−0.821513	+	1.42290i	0.0830432	+	0.996546i	$0.473536\pi$
$971$	−25.5990	+	44.3388i	−0.821513	+	1.42290i	−0.904556	+	0.426355i	$0.859797\pi$
$972$	−3.63035	−	6.28795i	−0.116443	−	0.201686i
$973$	27.6837	+	47.9495i	0.887498	+	1.53719i
$974$	−4.15583			−0.133161
$975$	0.441711	−	0.549538i	0.0141461	−	0.0175993i
$976$	10.9384			0.350129
$977$	−20.4273	−	35.3811i	−0.653526	−	1.13194i	−0.982261	−	0.187518i	$-0.939956\pi$
$977$	−20.4273	−	35.3811i	−0.653526	−	1.13194i	0.328735	−	0.944422i	$-0.393378\pi$
$978$	0.127247	+	0.220397i	0.00406890	+	0.00704753i
$979$	31.2404	−	54.1100i	0.998448	−	1.72936i
$980$	−51.5448			−1.64654
$981$	−13.2647	+	22.9751i	−0.423509	+	0.733540i
$982$	0.461995	−	0.800199i	0.0147429	−	0.0255354i
$983$	−21.8227			−0.696037			−0.348018	−	0.937488i	$-0.613145\pi$
$983$	−21.8227			−0.696037			−0.348018	+	0.937488i	$0.613145\pi$
$984$	−0.0822130	+	0.142397i	−0.00262085	+	0.00453945i
$985$	12.9254	+	22.3874i	0.411836	+	0.713322i
$986$	−1.39177	−	2.41062i	−0.0443230	−	0.0767696i
$987$	2.08362			0.0663222
$988$	26.1528	−	32.5370i	0.832032	−	1.03514i
$989$	1.93529			0.0615388
$990$	2.30770	+	3.99705i	0.0733435	+	0.127035i
$991$	−21.9209	−	37.9681i	−0.696340	−	1.20610i	−0.969727	−	0.244192i	$-0.921477\pi$
$991$	−21.9209	−	37.9681i	−0.696340	−	1.20610i	0.273387	−	0.961904i	$-0.411856\pi$
$992$	1.22485	−	2.12150i	0.0388890	−	0.0673577i
$993$	−4.06469			−0.128989
$994$	4.42841	−	7.67023i	0.140461	−	0.243285i
$995$	14.2360	−	24.6575i	0.451313	−	0.781696i
$996$	−4.93028			−0.156222
$997$	14.3584	−	24.8695i	0.454735	−	0.787625i	−0.543938	−	0.839126i	$-0.683067\pi$
$997$	14.3584	−	24.8695i	0.454735	−	0.787625i	0.998673	+	0.0515010i	$0.0164005\pi$
$998$	2.67416	+	4.63177i	0.0846489	+	0.146616i
$999$	1.05704	+	1.83084i	0.0334432	+	0.0579254i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.94.11	✓	36
13.3	even	3		5239.2.a.p.1.8		18
13.9	even	3	inner	403.2.f.c.373.11	yes	36
13.10	even	6		5239.2.a.o.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.11	✓	36	1.1	even	1	trivial
403.2.f.c.373.11	yes	36	13.9	even	3	inner
5239.2.a.o.1.11		18	13.10	even	6
5239.2.a.p.1.8		18	13.3	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.105154 + 0.182132i) q^{2} +(0.0693408 + 0.120102i) q^{3} +(0.977885 - 1.69375i) q^{4} +1.89472 q^{5} +(-0.0145830 + 0.0252584i) q^{6} +(-2.28636 + 3.96010i) q^{7} +0.831932 q^{8} +(1.49038 - 2.58142i) q^{9} +O(q^{10})\)	\(q+(0.105154 + 0.182132i) q^{2} +(0.0693408 + 0.120102i) q^{3} +(0.977885 - 1.69375i) q^{4} +1.89472 q^{5} +(-0.0145830 + 0.0252584i) q^{6} +(-2.28636 + 3.96010i) q^{7} +0.831932 q^{8} +(1.49038 - 2.58142i) q^{9} +(0.199238 + 0.345090i) q^{10} +(1.94290 + 3.36520i) q^{11} +0.271229 q^{12} +(1.30434 + 3.36136i) q^{13} -0.961683 q^{14} +(0.131381 + 0.227559i) q^{15} +(-1.86829 - 3.23597i) q^{16} +(1.13616 - 1.96788i) q^{17} +0.626880 q^{18} +(2.95994 - 5.12676i) q^{19} +(1.85282 - 3.20917i) q^{20} -0.634153 q^{21} +(-0.408607 + 0.707729i) q^{22} +(-0.137590 - 0.238313i) q^{23} +(0.0576868 + 0.0999165i) q^{24} -1.41004 q^{25} +(-0.475056 + 0.591022i) q^{26} +0.829422 q^{27} +(4.47160 + 7.74505i) q^{28} +(-2.91234 - 5.04432i) q^{29} +(-0.0276306 + 0.0478576i) q^{30} +1.00000 q^{31} +(1.22485 - 2.12150i) q^{32} +(-0.269444 + 0.466691i) q^{33} +0.477887 q^{34} +(-4.33202 + 7.50327i) q^{35} +(-2.91485 - 5.04867i) q^{36} +(1.27443 + 2.20737i) q^{37} +1.24500 q^{38} +(-0.313261 + 0.389732i) q^{39} +1.57628 q^{40} +(0.712581 + 1.23423i) q^{41} +(-0.0666839 - 0.115500i) q^{42} +(-3.51642 + 6.09061i) q^{43} +7.59972 q^{44} +(2.82386 - 4.89106i) q^{45} +(0.0289363 - 0.0501192i) q^{46} -3.28567 q^{47} +(0.259097 - 0.448770i) q^{48} +(-6.95493 - 12.0463i) q^{49} +(-0.148272 - 0.256814i) q^{50} +0.315128 q^{51} +(6.96877 + 1.07781i) q^{52} +2.00557 q^{53} +(0.0872172 + 0.151065i) q^{54} +(3.68124 + 6.37610i) q^{55} +(-1.90210 + 3.29453i) q^{56} +0.820978 q^{57} +(0.612489 - 1.06086i) q^{58} +(-6.77261 + 11.7305i) q^{59} +0.513903 q^{60} +(-1.46369 + 2.53518i) q^{61} +(0.105154 + 0.182132i) q^{62} +(6.81512 + 11.8041i) q^{63} -6.95796 q^{64} +(2.47135 + 6.36882i) q^{65} -0.113333 q^{66} +(-6.79081 - 11.7620i) q^{67} +(-2.22206 - 3.84873i) q^{68} +(0.0190812 - 0.0330496i) q^{69} -1.82212 q^{70} +(-4.60485 + 7.97583i) q^{71} +(1.23990 - 2.14757i) q^{72} +9.73133 q^{73} +(-0.268023 + 0.464229i) q^{74} +(-0.0977734 - 0.169349i) q^{75} +(-5.78896 - 10.0268i) q^{76} -17.7687 q^{77} +(-0.103924 - 0.0160731i) q^{78} +5.84564 q^{79} +(-3.53988 - 6.13126i) q^{80} +(-4.41364 - 7.64465i) q^{81} +(-0.149862 + 0.259568i) q^{82} -18.1775 q^{83} +(-0.620129 + 1.07410i) q^{84} +(2.15270 - 3.72858i) q^{85} -1.47906 q^{86} +(0.403888 - 0.699554i) q^{87} +(1.61636 + 2.79961i) q^{88} +(-8.03965 - 13.9251i) q^{89} +1.18776 q^{90} +(-16.2935 - 2.51999i) q^{91} -0.538189 q^{92} +(0.0693408 + 0.120102i) q^{93} +(-0.345502 - 0.598426i) q^{94} +(5.60825 - 9.71377i) q^{95} +0.339728 q^{96} +(5.24516 - 9.08488i) q^{97} +(1.46268 - 2.53344i) q^{98} +11.5826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

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