LMFDB - Embedded newform 600.2.k.c.301.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(301,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.301"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.k (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			301.1
Root			$1.40680 + 0.144584i$ of defining polynomial
Character	$\chi$	$=$	600.301
Dual form			600.2.k.c.301.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40680 - 0.144584i) q^{2} +1.00000i q^{3} +(1.95819 + 0.406803i) q^{4} +(0.144584 - 1.40680i) q^{6} +3.62721 q^{7} +(-2.69597 - 0.855416i) q^{8} -1.00000 q^{9} +6.20555i q^{11} +(-0.406803 + 1.95819i) q^{12} +0.578337i q^{13} +(-5.10278 - 0.524438i) q^{14} +(3.66902 + 1.59320i) q^{16} -1.42166 q^{17} +(1.40680 + 0.144584i) q^{18} -5.62721i q^{19} +3.62721i q^{21} +(0.897225 - 8.72999i) q^{22} +5.62721 q^{23} +(0.855416 - 2.69597i) q^{24} +(0.0836184 - 0.813607i) q^{26} -1.00000i q^{27} +(7.10278 + 1.47556i) q^{28} +2.00000i q^{29} -2.57834 q^{31} +(-4.93124 - 2.77180i) q^{32} -6.20555 q^{33} +(2.00000 + 0.205550i) q^{34} +(-1.95819 - 0.406803i) q^{36} +7.83276i q^{37} +(-0.813607 + 7.91638i) q^{38} -0.578337 q^{39} +5.25443 q^{41} +(0.524438 - 5.10278i) q^{42} +7.25443i q^{43} +(-2.52444 + 12.1517i) q^{44} +(-7.91638 - 0.813607i) q^{46} -6.78389 q^{47} +(-1.59320 + 3.66902i) q^{48} +6.15667 q^{49} -1.42166i q^{51} +(-0.235269 + 1.13249i) q^{52} +2.00000i q^{53} +(-0.144584 + 1.40680i) q^{54} +(-9.77886 - 3.10278i) q^{56} +5.62721 q^{57} +(0.289169 - 2.81361i) q^{58} -2.20555i q^{59} +12.4111i q^{61} +(3.62721 + 0.372787i) q^{62} -3.62721 q^{63} +(6.53653 + 4.61235i) q^{64} +(8.72999 + 0.897225i) q^{66} -4.00000i q^{67} +(-2.78389 - 0.578337i) q^{68} +5.62721i q^{69} +8.41110 q^{71} +(2.69597 + 0.855416i) q^{72} +6.00000 q^{73} +(1.13249 - 11.0192i) q^{74} +(2.28917 - 11.0192i) q^{76} +22.5089i q^{77} +(0.813607 + 0.0836184i) q^{78} +5.42166 q^{79} +1.00000 q^{81} +(-7.39194 - 0.759707i) q^{82} -3.25443i q^{83} +(-1.47556 + 7.10278i) q^{84} +(1.04888 - 10.2056i) q^{86} -2.00000 q^{87} +(5.30833 - 16.7300i) q^{88} -13.2544 q^{89} +2.09775i q^{91} +(11.0192 + 2.28917i) q^{92} -2.57834i q^{93} +(9.54359 + 0.980843i) q^{94} +(2.77180 - 4.93124i) q^{96} -4.84333 q^{97} +(-8.66123 - 0.890158i) q^{98} -6.20555i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 8 q^{8} - 6 q^{9} + 4 q^{12} - 16 q^{14} + 10 q^{16} - 12 q^{17} + 2 q^{18} + 20 q^{22} + 8 q^{23} + 6 q^{24} + 28 q^{26} + 28 q^{28} - 12 q^{31} - 12 q^{32} - 8 q^{33}+ \cdots + 6 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 8 * q^8 - 6 * q^9 + 4 * q^12 - 16 * q^14 + 10 * q^16 - 12 * q^17 + 2 * q^18 + 20 * q^22 + 8 * q^23 + 6 * q^24 + 28 * q^26 + 28 * q^28 - 12 * q^31 - 12 * q^32 - 8 * q^33 + 12 * q^34 + 2 * q^36 + 8 * q^38 - 20 * q^41 - 8 * q^42 - 4 * q^44 - 20 * q^46 - 8 * q^47 - 16 * q^48 + 30 * q^49 + 8 * q^52 + 4 * q^56 + 8 * q^57 - 4 * q^62 + 4 * q^63 + 22 * q^64 + 12 * q^66 + 16 * q^68 - 8 * q^71 + 8 * q^72 + 36 * q^73 + 12 * q^74 + 12 * q^76 - 8 * q^78 + 36 * q^79 + 6 * q^81 - 28 * q^82 - 20 * q^84 - 16 * q^86 - 12 * q^87 - 12 * q^88 - 28 * q^89 + 24 * q^92 + 4 * q^94 - 10 * q^96 - 36 * q^97 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.40680	−	0.144584i	−0.994760	−	0.102237i
$2$	−1.40680	−	0.144584i	−0.994760	−	0.102237i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.95819	+	0.406803i	0.979095	+	0.203402i
$5$		0			0
$5$		0			0
$6$	0.144584	−	1.40680i	0.0590263	−	0.574325i
$7$	3.62721			1.37096			0.685479	−	0.728093i	$-0.259593\pi$
$7$	3.62721			1.37096			0.685479	+	0.728093i	$0.259593\pi$
$8$	−2.69597	−	0.855416i	−0.953170	−	0.302435i
$9$	−1.00000			−0.333333
$10$		0			0
$11$			6.20555i			1.87104i	0.353269	+	0.935522i	$0.385070\pi$
$11$			6.20555i			1.87104i	−0.353269	+	0.935522i	$0.614930\pi$
$12$	−0.406803	+	1.95819i	−0.117434	+	0.565281i
$13$			0.578337i			0.160402i	0.996779	+	0.0802009i	$0.0255562\pi$
$13$			0.578337i			0.160402i	−0.996779	+	0.0802009i	$0.974444\pi$
$14$	−5.10278	−	0.524438i	−1.36377	−	0.140162i
$15$		0			0
$16$	3.66902	+	1.59320i	0.917256	+	0.398299i
$17$	−1.42166			−0.344804			−0.172402	−	0.985027i	$-0.555153\pi$
$17$	−1.42166			−0.344804			−0.172402	+	0.985027i	$0.555153\pi$
$18$	1.40680	+	0.144584i	0.331587	+	0.0340788i
$19$		−	5.62721i		−	1.29097i	−0.763772	−	0.645486i	$-0.776655\pi$
$19$		−	5.62721i		−	1.29097i	0.763772	−	0.645486i	$-0.223345\pi$
$20$		0			0
$21$			3.62721i			0.791523i
$22$	0.897225	−	8.72999i	0.191289	−	1.86124i
$23$	5.62721			1.17336			0.586678	−	0.809821i	$-0.300436\pi$
$23$	5.62721			1.17336			0.586678	+	0.809821i	$0.300436\pi$
$24$	0.855416	−	2.69597i	0.174611	−	0.550313i
$25$		0			0
$26$	0.0836184	−	0.813607i	0.0163989	−	0.159561i
$27$		−	1.00000i		−	0.192450i
$28$	7.10278	+	1.47556i	1.34230	+	0.278855i
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$		0			0
$31$	−2.57834			−0.463083			−0.231542	−	0.972825i	$-0.574377\pi$
$31$	−2.57834			−0.463083			−0.231542	+	0.972825i	$0.574377\pi$
$32$	−4.93124	−	2.77180i	−0.871729	−	0.489989i
$33$	−6.20555			−1.08025
$34$	2.00000	+	0.205550i	0.342997	+	0.0352516i
$35$		0			0
$36$	−1.95819	−	0.406803i	−0.326365	−	0.0678005i
$37$			7.83276i			1.28770i	0.765152	+	0.643849i	$0.222664\pi$
$37$			7.83276i			1.28770i	−0.765152	+	0.643849i	$0.777336\pi$
$38$	−0.813607	+	7.91638i	−0.131984	+	1.28421i
$39$	−0.578337			−0.0926081
$40$		0			0
$41$	5.25443			0.820603			0.410302	−	0.911950i	$-0.365423\pi$
$41$	5.25443			0.820603			0.410302	+	0.911950i	$0.365423\pi$
$42$	0.524438	−	5.10278i	0.0809225	−	0.787375i
$43$			7.25443i			1.10629i	0.833085	+	0.553145i	$0.186572\pi$
$43$			7.25443i			1.10629i	−0.833085	+	0.553145i	$0.813428\pi$
$44$	−2.52444	+	12.1517i	−0.380573	+	1.83193i
$45$		0			0
$46$	−7.91638	−	0.813607i	−1.16721	−	0.119960i
$47$	−6.78389			−0.989532			−0.494766	−	0.869026i	$-0.664746\pi$
$47$	−6.78389			−0.989532			−0.494766	+	0.869026i	$0.664746\pi$
$48$	−1.59320	+	3.66902i	−0.229958	+	0.529578i
$49$	6.15667			0.879525
$50$		0			0
$51$		−	1.42166i		−	0.199073i
$52$	−0.235269	+	1.13249i	−0.0326260	+	0.157049i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−0.144584	+	1.40680i	−0.0196754	+	0.191442i
$55$		0			0
$56$	−9.77886	−	3.10278i	−1.30676	−	0.414626i
$57$	5.62721			0.745343
$58$	0.289169	−	2.81361i	0.0379697	−	0.369445i
$59$		−	2.20555i		−	0.287138i	−0.989640	−	0.143569i	$-0.954142\pi$
$59$		−	2.20555i		−	0.287138i	0.989640	−	0.143569i	$-0.0458579\pi$
$60$		0			0
$61$			12.4111i			1.58908i	0.607213	+	0.794539i	$0.292288\pi$
$61$			12.4111i			1.58908i	−0.607213	+	0.794539i	$0.707712\pi$
$62$	3.62721	+	0.372787i	0.460657	+	0.0473440i
$63$	−3.62721			−0.456986
$64$	6.53653	+	4.61235i	0.817066	+	0.576544i
$65$		0			0
$66$	8.72999	+	0.897225i	1.07459	+	0.110441i
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	−2.78389	−	0.578337i	−0.337596	−	0.0701337i
$69$			5.62721i			0.677437i
$70$		0			0
$71$	8.41110			0.998214			0.499107	−	0.866540i	$-0.333661\pi$
$71$	8.41110			0.998214			0.499107	+	0.866540i	$0.333661\pi$
$72$	2.69597	+	0.855416i	0.317723	+	0.100812i
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$	1.13249	−	11.0192i	0.131650	−	1.28095i
$75$		0			0
$76$	2.28917	−	11.0192i	0.262586	−	1.26398i
$77$			22.5089i			2.56512i
$78$	0.813607	+	0.0836184i	0.0921228	+	0.00946792i
$79$	5.42166			0.609985			0.304992	−	0.952355i	$-0.401346\pi$
$79$	5.42166			0.609985			0.304992	+	0.952355i	$0.401346\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−7.39194	−	0.759707i	−0.816304	−	0.0838956i
$83$		−	3.25443i		−	0.357220i	−0.983920	−	0.178610i	$-0.942840\pi$
$83$		−	3.25443i		−	0.357220i	0.983920	−	0.178610i	$-0.0571600\pi$
$84$	−1.47556	+	7.10278i	−0.160997	+	0.774976i
$85$		0			0
$86$	1.04888	−	10.2056i	0.113103	−	1.10049i
$87$	−2.00000			−0.214423
$88$	5.30833	−	16.7300i	0.565869	−	1.78342i
$89$	−13.2544			−1.40497			−0.702483	−	0.711700i	$-0.747925\pi$
$89$	−13.2544			−1.40497			−0.702483	+	0.711700i	$0.747925\pi$
$90$		0			0
$91$			2.09775i			0.219904i
$92$	11.0192	+	2.28917i	1.14883	+	0.238662i
$93$		−	2.57834i		−	0.267361i
$94$	9.54359	+	0.980843i	0.984347	+	0.101166i
$95$		0			0
$96$	2.77180	−	4.93124i	0.282895	−	0.503293i
$97$	−4.84333			−0.491765			−0.245883	−	0.969300i	$-0.579078\pi$
$97$	−4.84333			−0.491765			−0.245883	+	0.969300i	$0.579078\pi$
$98$	−8.66123	−	0.890158i	−0.874916	−	0.0899196i
$99$		−	6.20555i		−	0.623681i
$100$		0			0
$101$		−	2.00000i		−	0.199007i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$		−	2.00000i		−	0.199007i	0.995037	−	0.0995037i	$-0.0317255\pi$
$102$	−0.205550	+	2.00000i	−0.0203525	+	0.198030i
$103$	−2.47054			−0.243429			−0.121715	−	0.992565i	$-0.538839\pi$
$103$	−2.47054			−0.243429			−0.121715	+	0.992565i	$0.538839\pi$
$104$	0.494719	−	1.55918i	0.0485112	−	0.152890i
$105$		0			0
$106$	0.289169	−	2.81361i	0.0280865	−	0.273282i
$107$		−	14.0978i		−	1.36288i	−0.731873	−	0.681441i	$-0.761354\pi$
$107$		−	14.0978i		−	1.36288i	0.731873	−	0.681441i	$-0.238646\pi$
$108$	0.406803	−	1.95819i	0.0391447	−	0.188427i
$109$			7.25443i			0.694848i	0.937708	+	0.347424i	$0.112944\pi$
$109$			7.25443i			0.694848i	−0.937708	+	0.347424i	$0.887056\pi$
$110$		0			0
$111$	−7.83276			−0.743453
$112$	13.3083	+	5.77886i	1.25752	+	0.546051i
$113$	9.08719			0.854851			0.427425	−	0.904051i	$-0.359421\pi$
$113$	9.08719			0.854851			0.427425	+	0.904051i	$0.359421\pi$
$114$	−7.91638	−	0.813607i	−0.741437	−	0.0762012i
$115$		0			0
$116$	−0.813607	+	3.91638i	−0.0755415	+	0.363627i
$117$		−	0.578337i		−	0.0534673i
$118$	−0.318888	+	3.10278i	−0.0293560	+	0.285634i
$119$	−5.15667			−0.472712
$120$		0			0
$121$	−27.5089			−2.50080
$122$	1.79445	−	17.4600i	0.162462	−	1.58075i
$123$			5.25443i			0.473776i
$124$	−5.04888	−	1.04888i	−0.453402	−	0.0941918i
$125$		0			0
$126$	5.10278	+	0.524438i	0.454591	+	0.0467206i
$127$	10.4705			0.929110			0.464555	−	0.885544i	$-0.346214\pi$
$127$	10.4705			0.929110			0.464555	+	0.885544i	$0.346214\pi$
$128$	−8.52873	−	7.43375i	−0.753841	−	0.657057i
$129$	−7.25443			−0.638717
$130$		0			0
$131$		−	13.4600i		−	1.17600i	−0.808860	−	0.588002i	$-0.799915\pi$
$131$		−	13.4600i		−	1.17600i	0.808860	−	0.588002i	$-0.200085\pi$
$132$	−12.1517	−	2.52444i	−1.05767	−	0.219724i
$133$		−	20.4111i		−	1.76987i
$134$	−0.578337	+	5.62721i	−0.0499607	+	0.486117i
$135$		0			0
$136$	3.83276	+	1.21611i	0.328657	+	0.104281i
$137$	10.5783			0.903768			0.451884	−	0.892077i	$-0.350752\pi$
$137$	10.5783			0.903768			0.451884	+	0.892077i	$0.350752\pi$
$138$	0.813607	−	7.91638i	0.0692588	−	0.673887i
$139$		−	12.4705i		−	1.05774i	−0.848704	−	0.528869i	$-0.822616\pi$
$139$		−	12.4705i		−	1.05774i	0.848704	−	0.528869i	$-0.177384\pi$
$140$		0			0
$141$		−	6.78389i		−	0.571306i
$142$	−11.8328	−	1.21611i	−0.992983	−	0.102054i
$143$	−3.58890			−0.300119
$144$	−3.66902	−	1.59320i	−0.305752	−	0.132766i
$145$		0			0
$146$	−8.44082	−	0.867506i	−0.698567	−	0.0717953i
$147$			6.15667i			0.507794i
$148$	−3.18639	+	15.3380i	−0.261920	+	1.26078i
$149$			2.00000i			0.163846i	0.996639	+	0.0819232i	$0.0261062\pi$
$149$			2.00000i			0.163846i	−0.996639	+	0.0819232i	$0.973894\pi$
$150$		0			0
$151$	12.6761			1.03157			0.515783	−	0.856719i	$-0.327501\pi$
$151$	12.6761			1.03157			0.515783	+	0.856719i	$0.327501\pi$
$152$	−4.81361	+	15.1708i	−0.390435	+	1.23051i
$153$	1.42166			0.114935
$154$	3.25443	−	31.6655i	0.262249	−	2.55168i
$155$		0			0
$156$	−1.13249	−	0.235269i	−0.0906721	−	0.0188366i
$157$			1.32391i			0.105660i	0.998604	+	0.0528298i	$0.0168241\pi$
$157$			1.32391i			0.105660i	−0.998604	+	0.0528298i	$0.983176\pi$
$158$	−7.62721	−	0.783887i	−0.606788	−	0.0623627i
$159$	−2.00000			−0.158610
$160$		0			0
$161$	20.4111			1.60862
$162$	−1.40680	−	0.144584i	−0.110529	−	0.0113596i
$163$		−	15.2544i		−	1.19482i	−0.801936	−	0.597409i	$-0.796197\pi$
$163$		−	15.2544i		−	1.19482i	0.801936	−	0.597409i	$-0.203803\pi$
$164$	10.2892	+	2.13752i	0.803449	+	0.166912i
$165$		0			0
$166$	−0.470539	+	4.57834i	−0.0365209	+	0.355348i
$167$	−10.7839			−0.834482			−0.417241	−	0.908796i	$-0.637003\pi$
$167$	−10.7839			−0.834482			−0.417241	+	0.908796i	$0.637003\pi$
$168$	3.10278	−	9.77886i	0.239384	−	0.754456i
$169$	12.6655			0.974271
$170$		0			0
$171$			5.62721i			0.430324i
$172$	−2.95112	+	14.2056i	−0.225021	+	1.08316i
$173$		−	13.6655i		−	1.03897i	−0.854479	−	0.519485i	$-0.826124\pi$
$173$		−	13.6655i		−	1.03897i	0.854479	−	0.519485i	$-0.173876\pi$
$174$	2.81361	+	0.289169i	0.213299	+	0.0219218i
$175$		0			0
$176$	−9.88666	+	22.7683i	−0.745235	+	1.71623i
$177$	2.20555			0.165779
$178$	18.6464	+	1.91638i	1.39760	+	0.143639i
$179$		−	9.04888i		−	0.676345i	−0.941084	−	0.338172i	$-0.890191\pi$
$179$		−	9.04888i		−	0.676345i	0.941084	−	0.338172i	$-0.109809\pi$
$180$		0			0
$181$		−	23.2544i		−	1.72849i	−0.503073	−	0.864244i	$-0.667797\pi$
$181$		−	23.2544i		−	1.72849i	0.503073	−	0.864244i	$-0.332203\pi$
$182$	0.303302	−	2.95112i	0.0224822	−	0.218752i
$183$	−12.4111			−0.917455
$184$	−15.1708	−	4.81361i	−1.11841	−	0.354864i
$185$		0			0
$186$	−0.372787	+	3.62721i	−0.0273341	+	0.265960i
$187$		−	8.82220i		−	0.645143i
$188$	−13.2841	−	2.75971i	−0.968846	−	0.201272i
$189$		−	3.62721i		−	0.263841i
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$	−4.61235	+	6.53653i	−0.332868	+	0.471733i
$193$	−25.6655			−1.84745			−0.923723	−	0.383062i	$-0.874869\pi$
$193$	−25.6655			−1.84745			−0.923723	+	0.383062i	$0.874869\pi$
$194$	6.81361	+	0.700269i	0.489188	+	0.0502764i
$195$		0			0
$196$	12.0559	+	2.50456i	0.861139	+	0.178897i
$197$		−	15.1567i		−	1.07987i	−0.841707	−	0.539934i	$-0.818449\pi$
$197$		−	15.1567i		−	1.07987i	0.841707	−	0.539934i	$-0.181551\pi$
$198$	−0.897225	+	8.72999i	−0.0637630	+	0.620413i
$199$	−20.6761			−1.46569			−0.732845	−	0.680396i	$-0.761808\pi$
$199$	−20.6761			−1.46569			−0.732845	+	0.680396i	$0.761808\pi$
$200$		0			0
$201$	4.00000			0.282138
$202$	−0.289169	+	2.81361i	−0.0203458	+	0.197965i
$203$			7.25443i			0.509161i
$204$	0.578337	−	2.78389i	0.0404917	−	0.194911i
$205$		0			0
$206$	3.47556	+	0.357201i	0.242154	+	0.0248874i
$207$	−5.62721			−0.391118
$208$	−0.921405	+	2.12193i	−0.0638879	+	0.147129i
$209$	34.9200			2.41546
$210$		0			0
$211$		−	2.03831i		−	0.140323i	−0.997536	−	0.0701616i	$-0.977648\pi$
$211$		−	2.03831i		−	0.140323i	0.997536	−	0.0701616i	$-0.0223515\pi$
$212$	−0.813607	+	3.91638i	−0.0558787	+	0.268978i
$213$			8.41110i			0.576319i
$214$	−2.03831	+	19.8328i	−0.139336	+	1.35574i
$215$		0			0
$216$	−0.855416	+	2.69597i	−0.0582037	+	0.183438i
$217$	−9.35218			−0.634867
$218$	1.04888	−	10.2056i	0.0710388	−	0.691207i
$219$			6.00000i			0.405442i
$220$		0			0
$221$		−	0.822200i		−	0.0553072i
$222$	11.0192	+	1.13249i	0.739557	+	0.0760080i
$223$	7.21611			0.483227			0.241613	−	0.970373i	$-0.422323\pi$
$223$	7.21611			0.483227			0.241613	+	0.970373i	$0.422323\pi$
$224$	−17.8867	−	10.0539i	−1.19510	−	0.671754i
$225$		0			0
$226$	−12.7839	−	1.31386i	−0.850372	−	0.0873970i
$227$		−	1.15667i		−	0.0767712i	−0.999263	−	0.0383856i	$-0.987778\pi$
$227$		−	1.15667i		−	0.0767712i	0.999263	−	0.0383856i	$-0.0122215\pi$
$228$	11.0192	+	2.28917i	0.729761	+	0.151604i
$229$			14.0978i			0.931606i	0.884889	+	0.465803i	$0.154234\pi$
$229$			14.0978i			0.931606i	−0.884889	+	0.465803i	$0.845766\pi$
$230$		0			0
$231$	−22.5089			−1.48097
$232$	1.71083	−	5.39194i	0.112322	−	0.353998i
$233$	14.5783			0.955059			0.477529	−	0.878616i	$-0.341532\pi$
$233$	14.5783			0.955059			0.477529	+	0.878616i	$0.341532\pi$
$234$	−0.0836184	+	0.813607i	−0.00546631	+	0.0531871i
$235$		0			0
$236$	0.897225	−	4.31889i	0.0584044	−	0.281136i
$237$			5.42166i			0.352175i
$238$	7.25443	+	0.745574i	0.470235	+	0.0483284i
$239$	19.2544			1.24547			0.622733	−	0.782435i	$-0.286022\pi$
$239$	19.2544			1.24547			0.622733	+	0.782435i	$0.286022\pi$
$240$		0			0
$241$	−13.6655			−0.880274			−0.440137	−	0.897931i	$-0.645070\pi$
$241$	−13.6655			−0.880274			−0.440137	+	0.897931i	$0.645070\pi$
$242$	38.6995	+	3.97735i	2.48770	+	0.255674i
$243$			1.00000i			0.0641500i
$244$	−5.04888	+	24.3033i	−0.323221	+	1.55586i
$245$		0			0
$246$	0.759707	−	7.39194i	0.0484372	−	0.471293i
$247$	3.25443			0.207074
$248$	6.95112	+	2.20555i	0.441397	+	0.140053i
$249$	3.25443			0.206241
$250$		0			0
$251$		−	7.14663i		−	0.451091i	−0.974233	−	0.225546i	$-0.927584\pi$
$251$		−	7.14663i		−	0.451091i	0.974233	−	0.225546i	$-0.0724165\pi$
$252$	−7.10278	−	1.47556i	−0.447433	−	0.0929517i
$253$			34.9200i			2.19540i
$254$	−14.7300	−	1.51388i	−0.924242	−	0.0949890i
$255$		0			0
$256$	10.9234	+	11.6909i	0.682716	+	0.730684i
$257$	−7.73501			−0.482497			−0.241248	−	0.970463i	$-0.577557\pi$
$257$	−7.73501			−0.482497			−0.241248	+	0.970463i	$0.577557\pi$
$258$	10.2056	+	1.04888i	0.635370	+	0.0653002i
$259$			28.4111i			1.76538i
$260$		0			0
$261$		−	2.00000i		−	0.123797i
$262$	−1.94610	+	18.9355i	−0.120231	+	1.16984i
$263$	18.7839			1.15826			0.579132	−	0.815234i	$-0.303392\pi$
$263$	18.7839			1.15826			0.579132	+	0.815234i	$0.303392\pi$
$264$	16.7300	+	5.30833i	1.02966	+	0.326705i
$265$		0			0
$266$	−2.95112	+	28.7144i	−0.180945	+	1.76059i
$267$		−	13.2544i		−	0.811158i
$268$	1.62721	−	7.83276i	0.0993979	−	0.478462i
$269$			8.50885i			0.518794i	0.965771	+	0.259397i	$0.0835238\pi$
$269$			8.50885i			0.518794i	−0.965771	+	0.259397i	$0.916476\pi$
$270$		0			0
$271$	30.9894			1.88247			0.941237	−	0.337746i	$-0.109665\pi$
$271$	30.9894			1.88247			0.941237	+	0.337746i	$0.109665\pi$
$272$	−5.21611	−	2.26499i	−0.316273	−	0.137335i
$273$	−2.09775			−0.126962
$274$	−14.8816	−	1.52946i	−0.899033	−	0.0923981i
$275$		0			0
$276$	−2.28917	+	11.0192i	−0.137792	+	0.663275i
$277$		−	9.51941i		−	0.571966i	−0.958235	−	0.285983i	$-0.907680\pi$
$277$		−	9.51941i		−	0.571966i	0.958235	−	0.285983i	$-0.0923201\pi$
$278$	−1.80304	+	17.5436i	−0.108139	+	1.05219i
$279$	2.57834			0.154361
$280$		0			0
$281$	13.6655			0.815217			0.407608	−	0.913157i	$-0.366363\pi$
$281$	13.6655			0.815217			0.407608	+	0.913157i	$0.366363\pi$
$282$	−0.980843	+	9.54359i	−0.0584084	+	0.568313i
$283$			20.0000i			1.18888i	0.804141	+	0.594438i	$0.202626\pi$
$283$			20.0000i			1.18888i	−0.804141	+	0.594438i	$0.797374\pi$
$284$	16.4705	+	3.42166i	0.977347	+	0.203038i
$285$		0			0
$286$	5.04888	+	0.518898i	0.298546	+	0.0306831i
$287$	19.0589			1.12501
$288$	4.93124	+	2.77180i	0.290576	+	0.163330i
$289$	−14.9789			−0.881110
$290$		0			0
$291$		−	4.84333i		−	0.283921i
$292$	11.7491	+	2.44082i	0.687567	+	0.142838i
$293$			4.31335i			0.251989i	0.992031	+	0.125994i	$0.0402121\pi$
$293$			4.31335i			0.251989i	−0.992031	+	0.125994i	$0.959788\pi$
$294$	0.890158	−	8.66123i	0.0519151	−	0.505133i
$295$		0			0
$296$	6.70027	−	21.1169i	0.389445	−	1.22740i
$297$	6.20555			0.360083
$298$	0.289169	−	2.81361i	0.0167511	−	0.162988i
$299$			3.25443i			0.188208i
$300$		0			0
$301$			26.3133i			1.51668i
$302$	−17.8328	−	1.83276i	−1.02616	−	0.105464i
$303$	2.00000			0.114897
$304$	8.96526	−	20.6464i	0.514193	−	1.18415i
$305$		0			0
$306$	−2.00000	−	0.205550i	−0.114332	−	0.0117505i
$307$		−	25.5678i		−	1.45923i	−0.683858	−	0.729615i	$-0.739699\pi$
$307$		−	25.5678i		−	1.45923i	0.683858	−	0.729615i	$-0.260301\pi$
$308$	−9.15667	+	44.0766i	−0.521750	+	2.51150i
$309$		−	2.47054i		−	0.140544i
$310$		0			0
$311$	−20.0766			−1.13844			−0.569221	−	0.822185i	$-0.692755\pi$
$311$	−20.0766			−1.13844			−0.569221	+	0.822185i	$0.692755\pi$
$312$	1.55918	+	0.494719i	0.0882712	+	0.0280079i
$313$	−7.15667			−0.404519			−0.202260	−	0.979332i	$-0.564828\pi$
$313$	−7.15667			−0.404519			−0.202260	+	0.979332i	$0.564828\pi$
$314$	0.191417	−	1.86248i	0.0108023	−	0.105106i
$315$		0			0
$316$	10.6167	+	2.20555i	0.597233	+	0.124072i
$317$		−	24.1744i		−	1.35777i	−0.734245	−	0.678884i	$-0.762464\pi$
$317$		−	24.1744i		−	1.35777i	0.734245	−	0.678884i	$-0.237536\pi$
$318$	2.81361	+	0.289169i	0.157779	+	0.0162158i
$319$	−12.4111			−0.694888
$320$		0			0
$321$	14.0978			0.786860
$322$	−28.7144	−	2.95112i	−1.60019	−	0.164460i
$323$			8.00000i			0.445132i
$324$	1.95819	+	0.406803i	0.108788	+	0.0226002i
$325$		0			0
$326$	−2.20555	+	21.4600i	−0.122154	+	1.18856i
$327$	−7.25443			−0.401171
$328$	−14.1658	−	4.49472i	−0.782175	−	0.248179i
$329$	−24.6066			−1.35661
$330$		0			0
$331$		−	27.1950i		−	1.49477i	−0.664390	−	0.747386i	$-0.731309\pi$
$331$		−	27.1950i		−	1.49477i	0.664390	−	0.747386i	$-0.268691\pi$
$332$	1.32391	−	6.37279i	0.0726591	−	0.349752i
$333$		−	7.83276i		−	0.429233i
$334$	15.1708	+	1.55918i	0.830110	+	0.0853146i
$335$		0			0
$336$	−5.77886	+	13.3083i	−0.315263	+	0.726029i
$337$	−22.8222			−1.24320			−0.621602	−	0.783333i	$-0.713518\pi$
$337$	−22.8222			−1.24320			−0.621602	+	0.783333i	$0.713518\pi$
$338$	−17.8179	−	1.83124i	−0.969166	−	0.0996061i
$339$			9.08719i			0.493548i
$340$		0			0
$341$		−	16.0000i		−	0.866449i
$342$	0.813607	−	7.91638i	0.0439948	−	0.428069i
$343$	−3.05892			−0.165166
$344$	6.20555	−	19.5577i	0.334581	−	1.05448i
$345$		0			0
$346$	−1.97582	+	19.2247i	−0.106221	+	1.03353i
$347$			23.6655i			1.27043i	0.772335	+	0.635216i	$0.219089\pi$
$347$			23.6655i			1.27043i	−0.772335	+	0.635216i	$0.780911\pi$
$348$	−3.91638	−	0.813607i	−0.209940	−	0.0436139i
$349$		−	34.9200i		−	1.86922i	−0.355671	−	0.934611i	$-0.615748\pi$
$349$		−	34.9200i		−	1.86922i	0.355671	−	0.934611i	$-0.384252\pi$
$350$		0			0
$351$	0.578337			0.0308694
$352$	17.2005	−	30.6011i	0.916791	−	1.63104i
$353$	15.9305			0.847896			0.423948	−	0.905687i	$-0.360644\pi$
$353$	15.9305			0.847896			0.423948	+	0.905687i	$0.360644\pi$
$354$	−3.10278	−	0.318888i	−0.164911	−	0.0169487i
$355$		0			0
$356$	−25.9547	−	5.39194i	−1.37560	−	0.285772i
$357$		−	5.15667i		−	0.272920i
$358$	−1.30833	+	12.7300i	−0.0691471	+	0.672801i
$359$	8.41110			0.443921			0.221960	−	0.975056i	$-0.428754\pi$
$359$	8.41110			0.443921			0.221960	+	0.975056i	$0.428754\pi$
$360$		0			0
$361$	−12.6655			−0.666607
$362$	−3.36222	+	32.7144i	−0.176715	+	1.71943i
$363$		−	27.5089i		−	1.44384i
$364$	−0.853372	+	4.10780i	−0.0447289	+	0.215307i
$365$		0			0
$366$	17.4600	+	1.79445i	0.912648	+	0.0937974i
$367$	24.4494			1.27625			0.638124	−	0.769933i	$-0.279711\pi$
$367$	24.4494			1.27625			0.638124	+	0.769933i	$0.279711\pi$
$368$	20.6464	+	8.96526i	1.07627	+	0.467346i
$369$	−5.25443			−0.273534
$370$		0			0
$371$			7.25443i			0.376631i
$372$	1.04888	−	5.04888i	0.0543817	−	0.261772i
$373$			0.167237i			0.00865920i	0.999991	+	0.00432960i	$0.00137816\pi$
$373$			0.167237i			0.00865920i	−0.999991	+	0.00432960i	$0.998622\pi$
$374$	−1.27555	+	12.4111i	−0.0659572	+	0.641763i
$375$		0			0
$376$	18.2892	+	5.80304i	0.943192	+	0.299269i
$377$	−1.15667			−0.0595718
$378$	−0.524438	+	5.10278i	−0.0269742	+	0.262458i
$379$			7.72496i			0.396805i	0.980121	+	0.198402i	$0.0635753\pi$
$379$			7.72496i			0.396805i	−0.980121	+	0.198402i	$0.936425\pi$
$380$		0			0
$381$			10.4705i			0.536422i
$382$	11.2544	+	1.15667i	0.575827	+	0.0591806i
$383$	1.62721			0.0831467			0.0415734	−	0.999135i	$-0.486763\pi$
$383$	1.62721			0.0831467			0.0415734	+	0.999135i	$0.486763\pi$
$384$	7.43375	−	8.52873i	0.379352	−	0.435230i
$385$		0			0
$386$	36.1063	+	3.71083i	1.83776	+	0.188876i
$387$		−	7.25443i		−	0.368763i
$388$	−9.48416	−	1.97028i	−0.481485	−	0.100026i
$389$			12.3133i			0.624312i	0.950031	+	0.312156i	$0.101051\pi$
$389$			12.3133i			0.624312i	−0.950031	+	0.312156i	$0.898949\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$	−16.5982	−	5.26652i	−0.838337	−	0.265999i
$393$	13.4600			0.678966
$394$	−2.19142	+	21.3225i	−0.110402	+	1.07421i
$395$		0			0
$396$	2.52444	−	12.1517i	0.126858	−	0.610643i
$397$			19.0872i			0.957959i	0.877826	+	0.478979i	$0.158993\pi$
$397$			19.0872i			0.957959i	−0.877826	+	0.478979i	$0.841007\pi$
$398$	29.0872	+	2.98944i	1.45801	+	0.149847i
$399$	20.4111			1.02183
$400$		0			0
$401$	−14.4111			−0.719656			−0.359828	−	0.933019i	$-0.617165\pi$
$401$	−14.4111			−0.719656			−0.359828	+	0.933019i	$0.617165\pi$
$402$	−5.62721	−	0.578337i	−0.280660	−	0.0288448i
$403$		−	1.49115i		−	0.0742794i
$404$	0.813607	−	3.91638i	0.0404784	−	0.194847i
$405$		0			0
$406$	1.04888	−	10.2056i	0.0520548	−	0.506493i
$407$	−48.6066			−2.40934
$408$	−1.21611	+	3.83276i	−0.0602066	+	0.189750i
$409$	−8.31335			−0.411069			−0.205534	−	0.978650i	$-0.565893\pi$
$409$	−8.31335			−0.411069			−0.205534	+	0.978650i	$0.565893\pi$
$410$		0			0
$411$			10.5783i			0.521791i
$412$	−4.83779	−	1.00502i	−0.238341	−	0.0495139i
$413$		−	8.00000i		−	0.393654i
$414$	7.91638	+	0.813607i	0.389069	+	0.0399866i
$415$		0			0
$416$	1.60303	−	2.85192i	0.0785952	−	0.139827i
$417$	12.4705			0.610685
$418$	−49.1255	−	5.04888i	−2.40281	−	0.246949i
$419$		−	7.36222i		−	0.359668i	−0.983697	−	0.179834i	$-0.942444\pi$
$419$		−	7.36222i		−	0.359668i	0.983697	−	0.179834i	$-0.0575561\pi$
$420$		0			0
$421$		−	30.0978i		−	1.46687i	−0.679757	−	0.733437i	$-0.737915\pi$
$421$		−	30.0978i		−	1.46687i	0.679757	−	0.733437i	$-0.262085\pi$
$422$	−0.294708	+	2.86751i	−0.0143462	+	0.139588i
$423$	6.78389			0.329844
$424$	1.71083	−	5.39194i	0.0830853	−	0.261856i
$425$		0			0
$426$	1.21611	−	11.8328i	0.0589209	−	0.573299i
$427$			45.0177i			2.17856i
$428$	5.73501	−	27.6061i	0.277212	−	1.33439i
$429$		−	3.58890i		−	0.173274i
$430$		0			0
$431$	8.41110			0.405148			0.202574	−	0.979267i	$-0.435069\pi$
$431$	8.41110			0.405148			0.202574	+	0.979267i	$0.435069\pi$
$432$	1.59320	−	3.66902i	0.0766527	−	0.176526i
$433$	4.31335			0.207286			0.103643	−	0.994615i	$-0.466950\pi$
$433$	4.31335			0.207286			0.103643	+	0.994615i	$0.466950\pi$
$434$	13.1567	+	1.35218i	0.631541	+	0.0649066i
$435$		0			0
$436$	−2.95112	+	14.2056i	−0.141333	+	0.680322i
$437$		−	31.6655i		−	1.51477i
$438$	0.867506	−	8.44082i	0.0414510	−	0.403318i
$439$	9.83276			0.469292			0.234646	−	0.972081i	$-0.424607\pi$
$439$	9.83276			0.469292			0.234646	+	0.972081i	$0.424607\pi$
$440$		0			0
$441$	−6.15667			−0.293175
$442$	−0.118877	+	1.15667i	−0.00565441	+	0.0550174i
$443$		−	21.3522i		−	1.01447i	−0.861807	−	0.507236i	$-0.830667\pi$
$443$		−	21.3522i		−	1.01447i	0.861807	−	0.507236i	$-0.169333\pi$
$444$	−15.3380	−	3.18639i	−0.727911	−	0.151220i
$445$		0			0
$446$	−10.1517	−	1.04334i	−0.480695	−	0.0494034i
$447$	−2.00000			−0.0945968
$448$	23.7094	+	16.7300i	1.12016	+	0.790418i
$449$	−20.3133			−0.958646			−0.479323	−	0.877639i	$-0.659118\pi$
$449$	−20.3133			−0.958646			−0.479323	+	0.877639i	$0.659118\pi$
$450$		0			0
$451$			32.6066i			1.53539i
$452$	17.7944	+	3.69670i	0.836981	+	0.173878i
$453$			12.6761i			0.595575i
$454$	−0.167237	+	1.62721i	−0.00784882	+	0.0763689i
$455$		0			0
$456$	−15.1708	−	4.81361i	−0.710438	−	0.225418i
$457$	3.35218			0.156808			0.0784041	−	0.996922i	$-0.475018\pi$
$457$	3.35218			0.156808			0.0784041	+	0.996922i	$0.475018\pi$
$458$	2.03831	−	19.8328i	0.0952441	−	0.926724i
$459$			1.42166i			0.0663575i
$460$		0			0
$461$			28.5089i			1.32779i	0.747826	+	0.663895i	$0.231098\pi$
$461$			28.5089i			1.32779i	−0.747826	+	0.663895i	$0.768902\pi$
$462$	31.6655	+	3.25443i	1.47321	+	0.151410i
$463$	−23.6272			−1.09805			−0.549025	−	0.835806i	$-0.685001\pi$
$463$	−23.6272			−1.09805			−0.549025	+	0.835806i	$0.685001\pi$
$464$	−3.18639	+	7.33804i	−0.147925	+	0.340660i
$465$		0			0
$466$	−20.5089	−	2.10780i	−0.950054	−	0.0976419i
$467$			29.5678i			1.36823i	0.729373	+	0.684117i	$0.239812\pi$
$467$			29.5678i			1.36823i	−0.729373	+	0.684117i	$0.760188\pi$
$468$	0.235269	−	1.13249i	0.0108753	−	0.0523496i
$469$		−	14.5089i		−	0.669957i
$470$		0			0
$471$	−1.32391			−0.0610026
$472$	−1.88666	+	5.94610i	−0.0868407	+	0.273691i
$473$	−45.0177			−2.06992
$474$	0.783887	−	7.62721i	0.0360051	−	0.350329i
$475$		0			0
$476$	−10.0978	−	2.09775i	−0.462830	−	0.0961503i
$477$		−	2.00000i		−	0.0915737i
$478$	−27.0872	−	2.78389i	−1.23894	−	0.127332i
$479$	−22.0978			−1.00967			−0.504836	−	0.863215i	$-0.668447\pi$
$479$	−22.0978			−1.00967			−0.504836	+	0.863215i	$0.668447\pi$
$480$		0			0
$481$	−4.52998			−0.206549
$482$	19.2247	+	1.97582i	0.875661	+	0.0899961i
$483$			20.4111i			0.928737i
$484$	−53.8676	−	11.1907i	−2.44853	−	0.508668i
$485$		0			0
$486$	0.144584	−	1.40680i	0.00655848	−	0.0638139i
$487$	−4.03831			−0.182993			−0.0914967	−	0.995805i	$-0.529165\pi$
$487$	−4.03831			−0.182993			−0.0914967	+	0.995805i	$0.529165\pi$
$488$	10.6167	−	33.4600i	0.480593	−	1.51466i
$489$	15.2544			0.689829
$490$		0			0
$491$			18.2056i			0.821605i	0.911724	+	0.410802i	$0.134751\pi$
$491$			18.2056i			0.821605i	−0.911724	+	0.410802i	$0.865249\pi$
$492$	−2.13752	+	10.2892i	−0.0963667	+	0.463872i
$493$		−	2.84333i		−	0.128057i
$494$	−4.57834	−	0.470539i	−0.205989	−	0.0211705i
$495$		0			0
$496$	−9.45998	−	4.10780i	−0.424765	−	0.184446i
$497$	30.5089			1.36851
$498$	−4.57834	−	0.470539i	−0.205160	−	0.0210853i
$499$			0.0594386i			0.00266084i	0.999999	+	0.00133042i	$0.000423486\pi$
$499$			0.0594386i			0.00266084i	−0.999999	+	0.00133042i	$0.999577\pi$
$500$		0			0
$501$		−	10.7839i		−	0.481789i
$502$	−1.03329	+	10.0539i	−0.0461180	+	0.448727i
$503$	−2.03831			−0.0908839			−0.0454419	−	0.998967i	$-0.514470\pi$
$503$	−2.03831			−0.0908839			−0.0454419	+	0.998967i	$0.514470\pi$
$504$	9.77886	+	3.10278i	0.435585	+	0.138209i
$505$		0			0
$506$	5.04888	−	49.1255i	0.224450	−	2.18389i
$507$			12.6655i			0.562496i
$508$	20.5033	+	4.25945i	0.909687	+	0.188983i
$509$		−	40.7044i		−	1.80419i	−0.431539	−	0.902094i	$-0.642029\pi$
$509$		−	40.7044i		−	1.80419i	0.431539	−	0.902094i	$-0.357971\pi$
$510$		0			0
$511$	21.7633			0.962751
$512$	−13.6768	−	18.0262i	−0.604436	−	0.796654i
$513$	−5.62721			−0.248448
$514$	10.8816	+	1.11836i	0.479969	+	0.0493288i
$515$		0			0
$516$	−14.2056	−	2.95112i	−0.625364	−	0.129916i
$517$		−	42.0978i		−	1.85146i
$518$	4.10780	−	39.9688i	0.180486	−	1.75613i
$519$	13.6655			0.599850
$520$		0			0
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$	−0.289169	+	2.81361i	−0.0126566	+	0.123148i
$523$		−	35.3311i		−	1.54492i	−0.635064	−	0.772460i	$-0.719026\pi$
$523$		−	35.3311i		−	1.54492i	0.635064	−	0.772460i	$-0.280974\pi$
$524$	5.47556	−	26.3572i	0.239201	−	1.15142i
$525$		0			0
$526$	−26.4252	−	2.71585i	−1.15219	−	0.118417i
$527$	3.66553			0.159673
$528$	−22.7683	−	9.88666i	−0.990863	−	0.430262i
$529$	8.66553			0.376762
$530$		0			0
$531$			2.20555i			0.0957127i
$532$	8.30330	−	39.9688i	0.359994	−	1.73287i
$533$			3.03883i			0.131626i
$534$	−1.91638	+	18.6464i	−0.0829299	+	0.806907i
$535$		0			0
$536$	−3.42166	+	10.7839i	−0.147793	+	0.465793i
$537$	9.04888			0.390488
$538$	1.23025	−	11.9703i	0.0530397	−	0.516075i
$539$			38.2056i			1.64563i
$540$		0			0
$541$			3.05892i			0.131513i	0.997836	+	0.0657567i	$0.0209461\pi$
$541$			3.05892i			0.131513i	−0.997836	+	0.0657567i	$0.979054\pi$
$542$	−43.5960	−	4.48059i	−1.87261	−	0.192458i
$543$	23.2544			0.997943
$544$	7.01056	+	3.94056i	0.300575	+	0.168950i
$545$		0			0
$546$	2.95112	+	0.303302i	0.126296	+	0.0129801i
$547$			32.0766i			1.37150i	0.727838	+	0.685749i	$0.240525\pi$
$547$			32.0766i			1.37150i	−0.727838	+	0.685749i	$0.759475\pi$
$548$	20.7144	+	4.30330i	0.884875	+	0.183828i
$549$		−	12.4111i		−	0.529693i
$550$		0			0
$551$	11.2544			0.479455
$552$	4.81361	−	15.1708i	0.204881	−	0.645712i
$553$	19.6655			0.836263
$554$	−1.37636	+	13.3919i	−0.0584758	+	0.568969i
$555$		0			0
$556$	5.07306	−	24.4197i	0.215145	−	1.03563i
$557$			33.6655i			1.42645i	0.700933	+	0.713227i	$0.252767\pi$
$557$			33.6655i			1.42645i	−0.700933	+	0.713227i	$0.747233\pi$
$558$	−3.62721	−	0.372787i	−0.153552	−	0.0157813i
$559$	−4.19550			−0.177451
$560$		0			0
$561$	8.82220			0.372474
$562$	−19.2247	−	1.97582i	−0.810945	−	0.0833449i
$563$			5.35218i			0.225567i	0.993620	+	0.112784i	$0.0359767\pi$
$563$			5.35218i			0.225567i	−0.993620	+	0.112784i	$0.964023\pi$
$564$	2.75971	−	13.2841i	0.116205	−	0.559363i
$565$		0			0
$566$	2.89169	−	28.1361i	0.121547	−	1.18265i
$567$	3.62721			0.152329
$568$	−22.6761	−	7.19499i	−0.951468	−	0.301895i
$569$	5.58890			0.234299			0.117149	−	0.993114i	$-0.462624\pi$
$569$	5.58890			0.234299			0.117149	+	0.993114i	$0.462624\pi$
$570$		0			0
$571$		−	10.3728i		−	0.434088i	−0.976162	−	0.217044i	$-0.930359\pi$
$571$		−	10.3728i		−	0.434088i	0.976162	−	0.217044i	$-0.0696414\pi$
$572$	−7.02775	−	1.45998i	−0.293845	−	0.0610447i
$573$		−	8.00000i		−	0.334205i
$574$	−26.8122	−	2.75562i	−1.11912	−	0.115017i
$575$		0			0
$576$	−6.53653	−	4.61235i	−0.272355	−	0.192181i
$577$	−21.6655			−0.901948			−0.450974	−	0.892537i	$-0.648923\pi$
$577$	−21.6655			−0.901948			−0.450974	+	0.892537i	$0.648923\pi$
$578$	21.0723	+	2.16571i	0.876493	+	0.0900816i
$579$		−	25.6655i		−	1.06662i
$580$		0			0
$581$		−	11.8045i		−	0.489733i
$582$	−0.700269	+	6.81361i	−0.0290271	+	0.282433i
$583$	−12.4111			−0.514015
$584$	−16.1758	−	5.13249i	−0.669361	−	0.212384i
$585$		0			0
$586$	0.623642	−	6.06803i	0.0257624	−	0.250668i
$587$		−	1.90225i		−	0.0785142i	−0.999229	−	0.0392571i	$-0.987501\pi$
$587$		−	1.90225i		−	0.0785142i	0.999229	−	0.0392571i	$-0.0124991\pi$
$588$	−2.50456	+	12.0559i	−0.103286	+	0.497179i
$589$			14.5089i			0.597827i
$590$		0			0
$591$	15.1567			0.623462
$592$	−12.4791	+	28.7386i	−0.512889	+	1.18115i
$593$	2.57834			0.105880			0.0529398	−	0.998598i	$-0.483141\pi$
$593$	2.57834			0.105880			0.0529398	+	0.998598i	$0.483141\pi$
$594$	−8.72999	−	0.897225i	−0.358196	−	0.0368136i
$595$		0			0
$596$	−0.813607	+	3.91638i	−0.0333266	+	0.160421i
$597$		−	20.6761i		−	0.846216i
$598$	0.470539	−	4.57834i	0.0192418	−	0.187222i
$599$	26.7244			1.09193			0.545966	−	0.837808i	$-0.316163\pi$
$599$	26.7244			1.09193			0.545966	+	0.837808i	$0.316163\pi$
$600$		0			0
$601$	33.3311			1.35960			0.679801	−	0.733397i	$-0.262066\pi$
$601$	33.3311			1.35960			0.679801	+	0.733397i	$0.262066\pi$
$602$	3.80450	−	37.0177i	0.155060	−	1.50873i
$603$			4.00000i			0.162893i
$604$	24.8222	+	5.15667i	1.01000	+	0.209822i
$605$		0			0
$606$	−2.81361	−	0.289169i	−0.114295	−	0.0117467i
$607$	21.9406			0.890540			0.445270	−	0.895396i	$-0.353108\pi$
$607$	21.9406			0.890540			0.445270	+	0.895396i	$0.353108\pi$
$608$	−15.5975	+	27.7491i	−0.632562	+	1.12538i
$609$	−7.25443			−0.293964
$610$		0			0
$611$		−	3.92337i		−	0.158723i
$612$	2.78389	+	0.578337i	0.112532	+	0.0233779i
$613$			3.42166i			0.138200i	0.997610	+	0.0690998i	$0.0220127\pi$
$613$			3.42166i			0.138200i	−0.997610	+	0.0690998i	$0.977987\pi$
$614$	−3.69670	+	35.9688i	−0.149187	+	1.45158i
$615$		0			0
$616$	19.2544	−	60.6832i	0.775783	−	2.44500i
$617$	−19.7350			−0.794502			−0.397251	−	0.917710i	$-0.630036\pi$
$617$	−19.7350			−0.794502			−0.397251	+	0.917710i	$0.630036\pi$
$618$	−0.357201	+	3.47556i	−0.0143687	+	0.139808i
$619$		−	20.4705i		−	0.822780i	−0.911459	−	0.411390i	$-0.865043\pi$
$619$		−	20.4705i		−	0.822780i	0.911459	−	0.411390i	$-0.134957\pi$
$620$		0			0
$621$		−	5.62721i		−	0.225812i
$622$	28.2439	+	2.90276i	1.13248	+	0.116390i
$623$	−48.0766			−1.92615
$624$	−2.12193	−	0.921405i	−0.0849452	−	0.0368857i
$625$		0			0
$626$	10.0680	+	1.03474i	0.402400	+	0.0413566i
$627$			34.9200i			1.39457i
$628$	−0.538571	+	2.59247i	−0.0214913	+	0.103451i
$629$		−	11.1355i		−	0.444003i
$630$		0			0
$631$	1.08719			0.0432803			0.0216402	−	0.999766i	$-0.493111\pi$
$631$	1.08719			0.0432803			0.0216402	+	0.999766i	$0.493111\pi$
$632$	−14.6167	−	4.63778i	−0.581419	−	0.184481i
$633$	2.03831			0.0810157
$634$	−3.49523	+	34.0086i	−0.138814	+	1.35065i
$635$		0			0
$636$	−3.91638	−	0.813607i	−0.155295	−	0.0322616i
$637$			3.56063i			0.141077i
$638$	17.4600	+	1.79445i	0.691247	+	0.0710430i
$639$	−8.41110			−0.332738
$640$		0			0
$641$	−27.9789			−1.10510			−0.552550	−	0.833480i	$-0.686345\pi$
$641$	−27.9789			−1.10510			−0.552550	+	0.833480i	$0.686345\pi$
$642$	−19.8328	−	2.03831i	−0.782737	−	0.0804458i
$643$			4.94108i			0.194857i	0.995243	+	0.0974285i	$0.0310617\pi$
$643$			4.94108i			0.194857i	−0.995243	+	0.0974285i	$0.968938\pi$
$644$	39.9688	+	8.30330i	1.57499	+	0.327196i
$645$		0			0
$646$	1.15667	−	11.2544i	0.0455087	−	0.442799i
$647$	49.3694			1.94091			0.970455	−	0.241282i	$-0.0775679\pi$
$647$	49.3694			1.94091			0.970455	+	0.241282i	$0.0775679\pi$
$648$	−2.69597	−	0.855416i	−0.105908	−	0.0336039i
$649$	13.6867			0.537248
$650$		0			0
$651$		−	9.35218i		−	0.366541i
$652$	6.20555	−	29.8711i	0.243028	−	1.16984i
$653$			40.1744i			1.57214i	0.618134	+	0.786072i	$0.287889\pi$
$653$			40.1744i			1.57214i	−0.618134	+	0.786072i	$0.712111\pi$
$654$	10.2056	+	1.04888i	0.399069	+	0.0410143i
$655$		0			0
$656$	19.2786	+	8.37133i	0.752703	+	0.326846i
$657$	−6.00000			−0.234082
$658$	34.6167	+	3.55773i	1.34950	+	0.138695i
$659$			21.1255i			0.822933i	0.911425	+	0.411466i	$0.134983\pi$
$659$			21.1255i			0.822933i	−0.911425	+	0.411466i	$0.865017\pi$
$660$		0			0
$661$			10.9200i			0.424737i	0.977190	+	0.212368i	$0.0681177\pi$
$661$			10.9200i			0.424737i	−0.977190	+	0.212368i	$0.931882\pi$
$662$	−3.93197	+	38.2580i	−0.152820	+	1.48694i
$663$	0.822200			0.0319316
$664$	−2.78389	+	8.77384i	−0.108036	+	0.340491i
$665$		0			0
$666$	−1.13249	+	11.0192i	−0.0438833	+	0.426984i
$667$			11.2544i			0.435773i
$668$	−21.1169	−	4.38692i	−0.817038	−	0.169735i
$669$			7.21611i			0.278991i
$670$		0			0
$671$	−77.0177			−2.97324
$672$	10.0539	−	17.8867i	0.387838	−	0.689993i
$673$	18.0000			0.693849			0.346925	−	0.937893i	$-0.387226\pi$
$673$	18.0000			0.693849			0.346925	+	0.937893i	$0.387226\pi$
$674$	32.1063	+	3.29973i	1.23669	+	0.127101i
$675$		0			0
$676$	24.8015	+	5.15238i	0.953904	+	0.198168i
$677$			30.4877i			1.17174i	0.810406	+	0.585869i	$0.199247\pi$
$677$			30.4877i			1.17174i	−0.810406	+	0.585869i	$0.800753\pi$
$678$	1.31386	−	12.7839i	0.0504587	−	0.490962i
$679$	−17.5678			−0.674189
$680$		0			0
$681$	1.15667			0.0443239
$682$	−2.31335	+	22.5089i	−0.0885827	+	0.861908i
$683$		−	35.2544i		−	1.34897i	−0.738287	−	0.674487i	$-0.764365\pi$
$683$		−	35.2544i		−	1.34897i	0.738287	−	0.674487i	$-0.235635\pi$
$684$	−2.28917	+	11.0192i	−0.0875285	+	0.421328i
$685$		0			0
$686$	4.30330	+	0.442272i	0.164301	+	0.0168860i
$687$	−14.0978			−0.537863
$688$	−11.5577	+	26.6167i	−0.440634	+	1.01475i
$689$	−1.15667			−0.0440658
$690$		0			0
$691$			28.1361i			1.07035i	0.844742	+	0.535173i	$0.179754\pi$
$691$			28.1361i			1.07035i	−0.844742	+	0.535173i	$0.820246\pi$
$692$	5.55918	−	26.7597i	0.211328	−	1.01725i
$693$		−	22.5089i		−	0.855041i
$694$	3.42166	−	33.2927i	0.129885	−	1.26378i
$695$		0			0
$696$	5.39194	+	1.71083i	0.204381	+	0.0648489i
$697$	−7.47002			−0.282947
$698$	−5.04888	+	49.1255i	−0.191103	+	1.85943i
$699$			14.5783i			0.551403i
$700$		0			0
$701$			34.8222i			1.31522i	0.753360	+	0.657608i	$0.228432\pi$
$701$			34.8222i			1.31522i	−0.753360	+	0.657608i	$0.771568\pi$
$702$	−0.813607	−	0.0836184i	−0.0307076	−	0.00315597i
$703$	44.0766			1.66238
$704$	−28.6222	+	40.5628i	−1.07874	+	1.52877i
$705$		0			0
$706$	−22.4111	−	2.30330i	−0.843453	−	0.0866859i
$707$		−	7.25443i		−	0.272831i
$708$	4.31889	+	0.897225i	0.162314	+	0.0337198i
$709$			7.58890i			0.285007i	0.989794	+	0.142504i	$0.0455152\pi$
$709$			7.58890i			0.285007i	−0.989794	+	0.142504i	$0.954485\pi$
$710$		0			0
$711$	−5.42166			−0.203328
$712$	35.7336	+	11.3380i	1.33917	+	0.424911i
$713$	−14.5089			−0.543361
$714$	−0.745574	+	7.25443i	−0.0279024	+	0.271490i
$715$		0			0
$716$	3.68111	−	17.7194i	0.137570	−	0.662206i
$717$			19.2544i			0.719070i
$718$	−11.8328	−	1.21611i	−0.441595	−	0.0453849i
$719$	−3.66553			−0.136701			−0.0683505	−	0.997661i	$-0.521774\pi$
$719$	−3.66553			−0.136701			−0.0683505	+	0.997661i	$0.521774\pi$
$720$		0			0
$721$	−8.96117			−0.333731
$722$	17.8179	+	1.83124i	0.663114	+	0.0681515i
$723$		−	13.6655i		−	0.508226i
$724$	9.45998	−	45.5366i	0.351577	−	1.69235i
$725$		0			0
$726$	−3.97735	+	38.6995i	−0.147613	+	1.43627i
$727$	36.1149			1.33943			0.669714	−	0.742619i	$-0.266416\pi$
$727$	36.1149			1.33943			0.669714	+	0.742619i	$0.266416\pi$
$728$	1.79445	−	5.65548i	0.0665067	−	0.209606i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$		−	10.3133i		−	0.381453i
$732$	−24.3033	−	5.04888i	−0.898276	−	0.186612i
$733$		−	34.0071i		−	1.25608i	−0.778180	−	0.628041i	$-0.783857\pi$
$733$		−	34.0071i		−	1.25608i	0.778180	−	0.628041i	$-0.216143\pi$
$734$	−34.3955	−	3.53500i	−1.26956	−	0.130479i
$735$		0			0
$736$	−27.7491	−	15.5975i	−1.02285	−	0.574931i
$737$	24.8222			0.914338
$738$	7.39194	+	0.759707i	0.272101	+	0.0279652i
$739$			52.0172i			1.91348i	0.290939	+	0.956742i	$0.406032\pi$
$739$			52.0172i			1.91348i	−0.290939	+	0.956742i	$0.593968\pi$
$740$		0			0
$741$			3.25443i			0.119554i
$742$	1.04888	−	10.2056i	0.0385054	−	0.374658i
$743$	23.3139			0.855303			0.427651	−	0.903944i	$-0.359341\pi$
$743$	23.3139			0.855303			0.427651	+	0.903944i	$0.359341\pi$
$744$	−2.20555	+	6.95112i	−0.0808594	+	0.254841i
$745$		0			0
$746$	0.0241798	−	0.235269i	0.000885286	−	0.00861383i
$747$			3.25443i			0.119073i
$748$	3.58890	−	17.2756i	0.131223	−	0.631657i
$749$		−	51.1355i		−	1.86845i
$750$		0			0
$751$	11.1083			0.405348			0.202674	−	0.979246i	$-0.435037\pi$
$751$	11.1083			0.405348			0.202674	+	0.979246i	$0.435037\pi$
$752$	−24.8902	−	10.8081i	−0.907653	−	0.394130i
$753$	7.14663			0.260438
$754$	1.62721	+	0.167237i	0.0592596	+	0.00609041i
$755$		0			0
$756$	1.47556	−	7.10278i	0.0536657	−	0.258325i
$757$		−	13.3239i		−	0.484266i	−0.970243	−	0.242133i	$-0.922153\pi$
$757$		−	13.3239i		−	0.484266i	0.970243	−	0.242133i	$-0.0778470\pi$
$758$	1.11691	−	10.8675i	0.0405679	−	0.394726i
$759$	−34.9200			−1.26751
$760$		0			0
$761$	−17.1355			−0.621163			−0.310582	−	0.950547i	$-0.600524\pi$
$761$	−17.1355			−0.621163			−0.310582	+	0.950547i	$0.600524\pi$
$762$	1.51388	−	14.7300i	0.0548419	−	0.533611i
$763$			26.3133i			0.952607i
$764$	−15.6655	−	3.25443i	−0.566759	−	0.117741i
$765$		0			0
$766$	−2.28917	−	0.235269i	−0.0827110	−	0.00850063i
$767$	1.27555			0.0460575
$768$	−11.6909	+	10.9234i	−0.421861	+	0.394166i
$769$	5.47002			0.197254			0.0986270	−	0.995124i	$-0.468555\pi$
$769$	5.47002			0.197254			0.0986270	+	0.995124i	$0.468555\pi$
$770$		0			0
$771$		−	7.73501i		−	0.278570i
$772$	−50.2580	−	10.4408i	−1.80882	−	0.375773i
$773$			3.15667i			0.113538i	0.998387	+	0.0567688i	$0.0180798\pi$
$773$			3.15667i			0.113538i	−0.998387	+	0.0567688i	$0.981920\pi$
$774$	−1.04888	+	10.2056i	−0.0377011	+	0.366831i
$775$		0			0
$776$	13.0575	+	4.14306i	0.468736	+	0.148727i
$777$	−28.4111			−1.01924
$778$	1.78032	−	17.3225i	0.0638274	−	0.621040i
$779$		−	29.5678i		−	1.05938i
$780$		0			0
$781$			52.1955i			1.86770i
$782$	11.2544	+	1.15667i	0.402457	+	0.0413626i
$783$	2.00000			0.0714742
$784$	22.5890	+	9.80879i	0.806749	+	0.350314i
$785$		0			0
$786$	−18.9355	−	1.94610i	−0.675408	−	0.0694151i
$787$		−	31.1355i		−	1.10986i	−0.831896	−	0.554931i	$-0.812745\pi$
$787$		−	31.1355i		−	1.10986i	0.831896	−	0.554931i	$-0.187255\pi$
$788$	6.16578	−	29.6797i	0.219647	−	1.05729i
$789$			18.7839i			0.668724i
$790$		0			0
$791$	32.9612			1.17196
$792$	−5.30833	+	16.7300i	−0.188623	+	0.594474i
$793$	−7.17780			−0.254891
$794$	2.75971	−	26.8519i	0.0979383	−	0.952939i
$795$		0			0
$796$	−40.4877	−	8.41110i	−1.43505	−	0.298124i
$797$			10.0000i			0.354218i	0.984191	+	0.177109i	$0.0566745\pi$
$797$			10.0000i			0.354218i	−0.984191	+	0.177109i	$0.943325\pi$
$798$	−28.7144	−	2.95112i	−1.01648	−	0.104469i
$799$	9.64440			0.341194
$800$		0			0
$801$	13.2544			0.468322
$802$	20.2736	+	2.08362i	0.715885	+	0.0735751i
$803$			37.2333i			1.31393i
$804$	7.83276	+	1.62721i	0.276240	+	0.0573874i
$805$		0			0
$806$	−0.215597	+	2.09775i	−0.00759406	+	0.0738902i
$807$	−8.50885			−0.299526
$808$	−1.71083	+	5.39194i	−0.0601868	+	0.189688i
$809$	29.0388			1.02095			0.510475	−	0.859892i	$-0.329469\pi$
$809$	29.0388			1.02095			0.510475	+	0.859892i	$0.329469\pi$
$810$		0			0
$811$			2.58838i			0.0908904i	0.998967	+	0.0454452i	$0.0144706\pi$
$811$			2.58838i			0.0908904i	−0.998967	+	0.0454452i	$0.985529\pi$
$812$	−2.95112	+	14.2056i	−0.103564	+	0.498517i
$813$			30.9894i			1.08685i
$814$	68.3799	+	7.02775i	2.39672	+	0.246323i
$815$		0			0
$816$	2.26499	−	5.21611i	0.0792905	−	0.182600i
$817$	40.8222			1.42819
$818$	11.6952	+	1.20198i	0.408915	+	0.0420262i
$819$		−	2.09775i		−	0.0733014i
$820$		0			0
$821$		−	38.1955i		−	1.33303i	−0.745491	−	0.666516i	$-0.767785\pi$
$821$		−	38.1955i		−	1.33303i	0.745491	−	0.666516i	$-0.232215\pi$
$822$	1.52946	−	14.8816i	0.0533461	−	0.519057i
$823$	18.3517			0.639699			0.319849	−	0.947468i	$-0.396368\pi$
$823$	18.3517			0.639699			0.319849	+	0.947468i	$0.396368\pi$
$824$	6.66050	+	2.11334i	0.232030	+	0.0736216i
$825$		0			0
$826$	−1.15667	+	11.2544i	−0.0402458	+	0.391592i
$827$		−	20.0000i		−	0.695468i	−0.937593	−	0.347734i	$-0.886951\pi$
$827$		−	20.0000i		−	0.695468i	0.937593	−	0.347734i	$-0.113049\pi$
$828$	−11.0192	−	2.28917i	−0.382942	−	0.0795541i
$829$		−	24.7456i		−	0.859449i	−0.902960	−	0.429725i	$-0.858611\pi$
$829$		−	24.7456i		−	0.859449i	0.902960	−	0.429725i	$-0.141389\pi$
$830$		0			0
$831$	9.51941			0.330225
$832$	−2.66750	+	3.78032i	−0.0924788	+	0.131059i
$833$	−8.75272			−0.303264
$834$	−17.5436	−	1.80304i	−0.607485	−	0.0624343i
$835$		0			0
$836$	68.3799	+	14.2056i	2.36497	+	0.491309i
$837$			2.57834i			0.0891204i
$838$	−1.06446	+	10.3572i	−0.0367712	+	0.357784i
$839$	−53.4288			−1.84457			−0.922284	−	0.386514i	$-0.873679\pi$
$839$	−53.4288			−1.84457			−0.922284	+	0.386514i	$0.873679\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	−4.35166	+	42.3416i	−0.149968	+	1.45919i
$843$			13.6655i			0.470666i
$844$	0.829192	−	3.99141i	0.0285420	−	0.137390i
$845$		0			0
$846$	−9.54359	−	0.980843i	−0.328116	−	0.0337221i
$847$	−99.7805			−3.42850
$848$	−3.18639	+	7.33804i	−0.109421	+	0.251989i
$849$	−20.0000			−0.686398
$850$		0			0
$851$			44.0766i			1.51093i
$852$	−3.42166	+	16.4705i	−0.117224	+	0.564271i
$853$			29.0661i			0.995203i	0.867406	+	0.497602i	$0.165786\pi$
$853$			29.0661i			0.995203i	−0.867406	+	0.497602i	$0.834214\pi$
$854$	6.50885	−	63.3311i	0.222728	−	2.16714i
$855$		0			0
$856$	−12.0594	+	38.0071i	−0.412183	+	1.29906i
$857$	10.2439			0.349924			0.174962	−	0.984575i	$-0.444020\pi$
$857$	10.2439			0.349924			0.174962	+	0.984575i	$0.444020\pi$
$858$	−0.518898	+	5.04888i	−0.0177149	+	0.172366i
$859$		−	10.9794i		−	0.374612i	−0.982302	−	0.187306i	$-0.940024\pi$
$859$		−	10.9794i		−	0.374612i	0.982302	−	0.187306i	$-0.0599756\pi$
$860$		0			0
$861$			19.0589i			0.649526i
$862$	−11.8328	−	1.21611i	−0.403026	−	0.0414210i
$863$	−38.8605			−1.32283			−0.661414	−	0.750021i	$-0.730043\pi$
$863$	−38.8605			−1.32283			−0.661414	+	0.750021i	$0.730043\pi$
$864$	−2.77180	+	4.93124i	−0.0942985	+	0.167764i
$865$		0			0
$866$	−6.06803	−	0.623642i	−0.206200	−	0.0211922i
$867$		−	14.9789i		−	0.508709i
$868$	−18.3133	−	3.80450i	−0.621596	−	0.129133i
$869$			33.6444i			1.14131i
$870$		0			0
$871$	2.31335			0.0783848
$872$	6.20555	−	19.5577i	0.210146	−	0.662308i
$873$	4.84333			0.163922
$874$	−4.57834	+	44.5472i	−0.154865	+	1.50683i
$875$		0			0
$876$	−2.44082	+	11.7491i	−0.0824676	+	0.396967i
$877$			22.3416i			0.754423i	0.926127	+	0.377211i	$0.123117\pi$
$877$			22.3416i			0.754423i	−0.926127	+	0.377211i	$0.876883\pi$
$878$	−13.8328	−	1.42166i	−0.466833	−	0.0479788i
$879$	−4.31335			−0.145486
$880$		0			0
$881$	9.88112			0.332903			0.166452	−	0.986050i	$-0.446769\pi$
$881$	9.88112			0.332903			0.166452	+	0.986050i	$0.446769\pi$
$882$	8.66123	+	0.890158i	0.291639	+	0.0299732i
$883$		−	10.6277i		−	0.357652i	−0.983881	−	0.178826i	$-0.942770\pi$
$883$		−	10.6277i		−	0.357652i	0.983881	−	0.178826i	$-0.0572298\pi$
$884$	0.334474	−	1.61003i	0.0112496	−	0.0541510i
$885$		0			0
$886$	−3.08719	+	30.0383i	−0.103716	+	1.00916i
$887$	−11.6061			−0.389694			−0.194847	−	0.980834i	$-0.562421\pi$
$887$	−11.6061			−0.389694			−0.194847	+	0.980834i	$0.562421\pi$
$888$	21.1169	+	6.70027i	0.708637	+	0.224846i
$889$	37.9789			1.27377
$890$		0			0
$891$			6.20555i			0.207894i
$892$	14.1305	+	2.93554i	0.473125	+	0.0982891i
$893$			38.1744i			1.27746i
$894$	2.81361	+	0.289169i	0.0941011	+	0.00967124i
$895$		0			0
$896$	−30.9355	−	26.9638i	−1.03348	−	0.900797i
$897$	−3.25443			−0.108662
$898$	28.5769	+	2.93699i	0.953623	+	0.0980086i
$899$		−	5.15667i		−	0.171985i
$900$		0			0
$901$		−	2.84333i		−	0.0947249i
$902$	4.71440	−	45.8711i	0.156972	−	1.52734i
$903$	−26.3133			−0.875653
$904$	−24.4988	−	7.77332i	−0.814818	−	0.258537i
$905$		0			0
$906$	1.83276	−	17.8328i	0.0608895	−	0.592454i
$907$		−	0.195504i		−	0.00649159i	−0.999995	−	0.00324580i	$-0.998967\pi$
$907$		−	0.195504i		−	0.00649159i	0.999995	−	0.00324580i	$-0.00103317\pi$
$908$	0.470539	−	2.26499i	0.0156154	−	0.0751663i
$909$			2.00000i			0.0663358i
$910$		0			0
$911$	−7.88112			−0.261113			−0.130557	−	0.991441i	$-0.541676\pi$
$911$	−7.88112			−0.261113			−0.130557	+	0.991441i	$0.541676\pi$
$912$	20.6464	+	8.96526i	0.683670	+	0.296869i
$913$	20.1955			0.668374
$914$	−4.71585	−	0.484672i	−0.155987	−	0.0160315i
$915$		0			0
$916$	−5.73501	+	27.6061i	−0.189490	+	0.912131i
$917$		−	48.8222i		−	1.61225i
$918$	0.205550	−	2.00000i	0.00678416	−	0.0660098i
$919$	9.75614			0.321825			0.160913	−	0.986969i	$-0.448556\pi$
$919$	9.75614			0.321825			0.160913	+	0.986969i	$0.448556\pi$
$920$		0			0
$921$	25.5678			0.842487
$922$	4.12193	−	40.1063i	0.135749	−	1.32083i
$923$			4.86445i			0.160115i
$924$	−44.0766	−	9.15667i	−1.45001	−	0.301232i
$925$		0			0
$926$	33.2388	+	3.41612i	1.09230	+	0.112261i
$927$	2.47054			0.0811431
$928$	5.54359	−	9.86248i	0.181977	−	0.323752i
$929$	6.82220			0.223829			0.111915	−	0.993718i	$-0.464302\pi$
$929$	6.82220			0.223829			0.111915	+	0.993718i	$0.464302\pi$
$930$		0			0
$931$		−	34.6449i		−	1.13544i
$932$	28.5472	+	5.93051i	0.935093	+	0.194260i
$933$		−	20.0766i		−	0.657279i
$934$	4.27504	−	41.5960i	0.139883	−	1.36106i
$935$		0			0
$936$	−0.494719	+	1.55918i	−0.0161704	+	0.0509634i
$937$	−57.5266			−1.87931			−0.939655	−	0.342123i	$-0.888854\pi$
$937$	−57.5266			−1.87931			−0.939655	+	0.342123i	$0.888854\pi$
$938$	−2.09775	+	20.4111i	−0.0684940	+	0.666446i
$939$		−	7.15667i		−	0.233549i
$940$		0			0
$941$		−	0.508852i		−	0.0165881i	−0.999966	−	0.00829405i	$-0.997360\pi$
$941$		−	0.508852i		−	0.0165881i	0.999966	−	0.00829405i	$-0.00264011\pi$
$942$	1.86248	+	0.191417i	0.0606830	+	0.00623669i
$943$	29.5678			0.962859
$944$	3.51388	−	8.09221i	0.114367	−	0.263379i
$945$		0			0
$946$	63.3311	+	6.50885i	2.05907	+	0.211621i
$947$		−	1.68665i		−	0.0548088i	−0.999624	−	0.0274044i	$-0.991276\pi$
$947$		−	1.68665i		−	0.0548088i	0.999624	−	0.0274044i	$-0.00872419\pi$
$948$	−2.20555	+	10.6167i	−0.0716329	+	0.344813i
$949$			3.47002i			0.112642i
$950$		0			0
$951$	24.1744			0.783908
$952$	13.9022	+	4.41110i	0.450574	+	0.142965i
$953$	−9.22616			−0.298865			−0.149432	−	0.988772i	$-0.547745\pi$
$953$	−9.22616			−0.298865			−0.149432	+	0.988772i	$0.547745\pi$
$954$	−0.289169	+	2.81361i	−0.00936218	+	0.0910939i
$955$		0			0
$956$	37.7038	+	7.83276i	1.21943	+	0.253330i
$957$		−	12.4111i		−	0.401194i
$958$	31.0872	+	3.19499i	1.00438	+	0.103225i
$959$	38.3699			1.23903
$960$		0			0
$961$	−24.3522			−0.785554
$962$	6.37279	+	0.654963i	0.205467	+	0.0211169i
$963$			14.0978i			0.454294i
$964$	−26.7597	−	5.55918i	−0.861872	−	0.179049i
$965$		0			0
$966$	2.95112	−	28.7144i	0.0949509	−	0.923871i
$967$	−12.2338			−0.393413			−0.196707	−	0.980462i	$-0.563025\pi$
$967$	−12.2338			−0.393413			−0.196707	+	0.980462i	$0.563025\pi$
$968$	74.1631	+	23.5315i	2.38369	+	0.756331i
$969$	−8.00000			−0.256997
$970$		0			0
$971$			33.2444i			1.06686i	0.845843	+	0.533431i	$0.179098\pi$
$971$			33.2444i			1.06686i	−0.845843	+	0.533431i	$0.820902\pi$
$972$	−0.406803	+	1.95819i	−0.0130482	+	0.0628090i
$973$		−	45.2333i		−	1.45011i
$974$	5.68111	+	0.583877i	0.182035	+	0.0187086i
$975$		0			0
$976$	−19.7733	+	45.5366i	−0.632929	+	1.45759i
$977$	−7.93051			−0.253720			−0.126860	−	0.991921i	$-0.540490\pi$
$977$	−7.93051			−0.253720			−0.126860	+	0.991921i	$0.540490\pi$
$978$	−21.4600	−	2.20555i	−0.686214	−	0.0705257i
$979$		−	82.2510i		−	2.62875i
$980$		0			0
$981$		−	7.25443i		−	0.231616i
$982$	2.63224	−	25.6116i	0.0839980	−	0.817300i
$983$	−41.8993			−1.33638			−0.668191	−	0.743990i	$-0.732931\pi$
$983$	−41.8993			−1.33638			−0.668191	+	0.743990i	$0.732931\pi$
$984$	4.49472	−	14.1658i	0.143286	−	0.451589i
$985$		0			0
$986$	−0.411100	+	4.00000i	−0.0130921	+	0.127386i
$987$		−	24.6066i		−	0.783237i
$988$	6.37279	+	1.32391i	0.202745	+	0.0421192i
$989$			40.8222i			1.29807i
$990$		0			0
$991$	−35.1849			−1.11769			−0.558843	−	0.829273i	$-0.688755\pi$
$991$	−35.1849			−1.11769			−0.558843	+	0.829273i	$0.688755\pi$
$992$	12.7144	+	7.14663i	0.403683	+	0.226906i
$993$	27.1950			0.863007
$994$	−42.9200	−	4.41110i	−1.36134	−	0.139912i
$995$		0			0
$996$	6.37279	+	1.32391i	0.201929	+	0.0419497i
$997$		−	8.04836i		−	0.254894i	−0.991845	−	0.127447i	$-0.959322\pi$
$997$		−	8.04836i		−	0.254894i	0.991845	−	0.127447i	$-0.0406783\pi$
$998$	0.00859389	−	0.0836184i	0.000272035	−	0.00264690i
$999$	7.83276			0.247818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.k.c.301.1		6
3.2	odd	2		1800.2.k.p.901.6		6
4.3	odd	2		2400.2.k.c.1201.1		6
5.2	odd	4		600.2.d.f.349.3		6
5.3	odd	4		600.2.d.e.349.4		6
5.4	even	2		120.2.k.b.61.6	yes	6
8.3	odd	2		2400.2.k.c.1201.4		6
8.5	even	2	inner	600.2.k.c.301.2		6
12.11	even	2		7200.2.k.p.3601.2		6
15.2	even	4		1800.2.d.r.1549.4		6
15.8	even	4		1800.2.d.q.1549.3		6
15.14	odd	2		360.2.k.f.181.1		6
20.3	even	4		2400.2.d.f.49.5		6
20.7	even	4		2400.2.d.e.49.2		6
20.19	odd	2		480.2.k.b.241.6		6
24.5	odd	2		1800.2.k.p.901.5		6
24.11	even	2		7200.2.k.p.3601.1		6
40.3	even	4		2400.2.d.e.49.5		6
40.13	odd	4		600.2.d.f.349.4		6
40.19	odd	2		480.2.k.b.241.3		6
40.27	even	4		2400.2.d.f.49.2		6
40.29	even	2		120.2.k.b.61.5	✓	6
40.37	odd	4		600.2.d.e.349.3		6
60.23	odd	4		7200.2.d.q.2449.5		6
60.47	odd	4		7200.2.d.r.2449.2		6
60.59	even	2		1440.2.k.f.721.6		6
80.19	odd	4		3840.2.a.bo.1.1		3
80.29	even	4		3840.2.a.bq.1.3		3
80.59	odd	4		3840.2.a.br.1.1		3
80.69	even	4		3840.2.a.bp.1.3		3
120.29	odd	2		360.2.k.f.181.2		6
120.53	even	4		1800.2.d.r.1549.3		6
120.59	even	2		1440.2.k.f.721.3		6
120.77	even	4		1800.2.d.q.1549.4		6
120.83	odd	4		7200.2.d.r.2449.5		6
120.107	odd	4		7200.2.d.q.2449.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.k.b.61.5	✓	6	40.29	even	2
120.2.k.b.61.6	yes	6	5.4	even	2
360.2.k.f.181.1		6	15.14	odd	2
360.2.k.f.181.2		6	120.29	odd	2
480.2.k.b.241.3		6	40.19	odd	2
480.2.k.b.241.6		6	20.19	odd	2
600.2.d.e.349.3		6	40.37	odd	4
600.2.d.e.349.4		6	5.3	odd	4
600.2.d.f.349.3		6	5.2	odd	4
600.2.d.f.349.4		6	40.13	odd	4
600.2.k.c.301.1		6	1.1	even	1	trivial
600.2.k.c.301.2		6	8.5	even	2	inner
1440.2.k.f.721.3		6	120.59	even	2
1440.2.k.f.721.6		6	60.59	even	2
1800.2.d.q.1549.3		6	15.8	even	4
1800.2.d.q.1549.4		6	120.77	even	4
1800.2.d.r.1549.3		6	120.53	even	4
1800.2.d.r.1549.4		6	15.2	even	4
1800.2.k.p.901.5		6	24.5	odd	2
1800.2.k.p.901.6		6	3.2	odd	2
2400.2.d.e.49.2		6	20.7	even	4
2400.2.d.e.49.5		6	40.3	even	4
2400.2.d.f.49.2		6	40.27	even	4
2400.2.d.f.49.5		6	20.3	even	4
2400.2.k.c.1201.1		6	4.3	odd	2
2400.2.k.c.1201.4		6	8.3	odd	2
3840.2.a.bo.1.1		3	80.19	odd	4
3840.2.a.bp.1.3		3	80.69	even	4
3840.2.a.bq.1.3		3	80.29	even	4
3840.2.a.br.1.1		3	80.59	odd	4
7200.2.d.q.2449.2		6	120.107	odd	4
7200.2.d.q.2449.5		6	60.23	odd	4
7200.2.d.r.2449.2		6	60.47	odd	4
7200.2.d.r.2449.5		6	120.83	odd	4
7200.2.k.p.3601.1		6	24.11	even	2
7200.2.k.p.3601.2		6	12.11	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40680 - 0.144584i) q^{2} +1.00000i q^{3} +(1.95819 + 0.406803i) q^{4} +(0.144584 - 1.40680i) q^{6} +3.62721 q^{7} +(-2.69597 - 0.855416i) q^{8} -1.00000 q^{9} +6.20555i q^{11} +(-0.406803 + 1.95819i) q^{12} +0.578337i q^{13} +(-5.10278 - 0.524438i) q^{14} +(3.66902 + 1.59320i) q^{16} -1.42166 q^{17} +(1.40680 + 0.144584i) q^{18} -5.62721i q^{19} +3.62721i q^{21} +(0.897225 - 8.72999i) q^{22} +5.62721 q^{23} +(0.855416 - 2.69597i) q^{24} +(0.0836184 - 0.813607i) q^{26} -1.00000i q^{27} +(7.10278 + 1.47556i) q^{28} +2.00000i q^{29} -2.57834 q^{31} +(-4.93124 - 2.77180i) q^{32} -6.20555 q^{33} +(2.00000 + 0.205550i) q^{34} +(-1.95819 - 0.406803i) q^{36} +7.83276i q^{37} +(-0.813607 + 7.91638i) q^{38} -0.578337 q^{39} +5.25443 q^{41} +(0.524438 - 5.10278i) q^{42} +7.25443i q^{43} +(-2.52444 + 12.1517i) q^{44} +(-7.91638 - 0.813607i) q^{46} -6.78389 q^{47} +(-1.59320 + 3.66902i) q^{48} +6.15667 q^{49} -1.42166i q^{51} +(-0.235269 + 1.13249i) q^{52} +2.00000i q^{53} +(-0.144584 + 1.40680i) q^{54} +(-9.77886 - 3.10278i) q^{56} +5.62721 q^{57} +(0.289169 - 2.81361i) q^{58} -2.20555i q^{59} +12.4111i q^{61} +(3.62721 + 0.372787i) q^{62} -3.62721 q^{63} +(6.53653 + 4.61235i) q^{64} +(8.72999 + 0.897225i) q^{66} -4.00000i q^{67} +(-2.78389 - 0.578337i) q^{68} +5.62721i q^{69} +8.41110 q^{71} +(2.69597 + 0.855416i) q^{72} +6.00000 q^{73} +(1.13249 - 11.0192i) q^{74} +(2.28917 - 11.0192i) q^{76} +22.5089i q^{77} +(0.813607 + 0.0836184i) q^{78} +5.42166 q^{79} +1.00000 q^{81} +(-7.39194 - 0.759707i) q^{82} -3.25443i q^{83} +(-1.47556 + 7.10278i) q^{84} +(1.04888 - 10.2056i) q^{86} -2.00000 q^{87} +(5.30833 - 16.7300i) q^{88} -13.2544 q^{89} +2.09775i q^{91} +(11.0192 + 2.28917i) q^{92} -2.57834i q^{93} +(9.54359 + 0.980843i) q^{94} +(2.77180 - 4.93124i) q^{96} -4.84333 q^{97} +(-8.66123 - 0.890158i) q^{98} -6.20555i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 2 q^{4} - 4 q^{7} - 8 q^{8} - 6 q^{9} + 4 q^{12} - 16 q^{14} + 10 q^{16} - 12 q^{17} + 2 q^{18} + 20 q^{22} + 8 q^{23} + 6 q^{24} + 28 q^{26} + 28 q^{28} - 12 q^{31} - 12 q^{32} - 8 q^{33}+ \cdots + 6 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 2 * q^4 - 4 * q^7 - 8 * q^8 - 6 * q^9 + 4 * q^12 - 16 * q^14 + 10 * q^16 - 12 * q^17 + 2 * q^18 + 20 * q^22 + 8 * q^23 + 6 * q^24 + 28 * q^26 + 28 * q^28 - 12 * q^31 - 12 * q^32 - 8 * q^33 + 12 * q^34 + 2 * q^36 + 8 * q^38 - 20 * q^41 - 8 * q^42 - 4 * q^44 - 20 * q^46 - 8 * q^47 - 16 * q^48 + 30 * q^49 + 8 * q^52 + 4 * q^56 + 8 * q^57 - 4 * q^62 + 4 * q^63 + 22 * q^64 + 12 * q^66 + 16 * q^68 - 8 * q^71 + 8 * q^72 + 36 * q^73 + 12 * q^74 + 12 * q^76 - 8 * q^78 + 36 * q^79 + 6 * q^81 - 28 * q^82 - 20 * q^84 - 16 * q^86 - 12 * q^87 - 12 * q^88 - 28 * q^89 + 24 * q^92 + 4 * q^94 - 10 * q^96 - 36 * q^97 + 6 * q^98

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