LMFDB - Embedded newform 462.2.c.a.197.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(197,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("462.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.c (of order $2$, degree $1$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 94x^{8} + 246x^{6} + 277x^{4} + 114x^{2} + 9 $ x^12 + 16x^10 + 94x^8 + 246x^6 + 277x^4 + 114*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.5
Root			$1.18147i$ of defining polynomial
Character	$\chi$	$=$	462.197
Dual form			462.2.c.a.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.482127 - 1.66360i) q^{3} +1.00000 q^{4} -0.885172i q^{5} +(-0.482127 + 1.66360i) q^{6} +1.00000i q^{7} -1.00000 q^{8} +(-2.53511 - 1.60413i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.482127 - 1.66360i) q^{3} +1.00000 q^{4} -0.885172i q^{5} +(-0.482127 + 1.66360i) q^{6} +1.00000i q^{7} -1.00000 q^{8} +(-2.53511 - 1.60413i) q^{9} +0.885172i q^{10} +(1.14572 - 3.11245i) q^{11} +(0.482127 - 1.66360i) q^{12} -1.32719i q^{13} -1.00000i q^{14} +(-1.47257 - 0.426766i) q^{15} +1.00000 q^{16} -1.35883 q^{17} +(2.53511 + 1.60413i) q^{18} -4.67563i q^{19} -0.885172i q^{20} +(1.66360 + 0.482127i) q^{21} +(-1.14572 + 3.11245i) q^{22} -1.08319i q^{23} +(-0.482127 + 1.66360i) q^{24} +4.21647 q^{25} +1.32719i q^{26} +(-3.89087 + 3.44400i) q^{27} +1.00000i q^{28} -7.92374 q^{29} +(1.47257 + 0.426766i) q^{30} -3.05769 q^{31} -1.00000 q^{32} +(-4.62547 - 3.40662i) q^{33} +1.35883 q^{34} +0.885172 q^{35} +(-2.53511 - 1.60413i) q^{36} +0.592594 q^{37} +4.67563i q^{38} +(-2.20791 - 0.639876i) q^{39} +0.885172i q^{40} +1.73475 q^{41} +(-1.66360 - 0.482127i) q^{42} -0.991579i q^{43} +(1.14572 - 3.11245i) q^{44} +(-1.41993 + 2.24401i) q^{45} +1.08319i q^{46} -0.204156i q^{47} +(0.482127 - 1.66360i) q^{48} -1.00000 q^{49} -4.21647 q^{50} +(-0.655131 + 2.26055i) q^{51} -1.32719i q^{52} -1.07021i q^{53} +(3.89087 - 3.44400i) q^{54} +(-2.75505 - 1.01416i) q^{55} -1.00000i q^{56} +(-7.77837 - 2.25425i) q^{57} +7.92374 q^{58} -5.25570i q^{59} +(-1.47257 - 0.426766i) q^{60} -11.6057i q^{61} +3.05769 q^{62} +(1.60413 - 2.53511i) q^{63} +1.00000 q^{64} -1.17479 q^{65} +(4.62547 + 3.40662i) q^{66} +12.6414 q^{67} -1.35883 q^{68} +(-1.80199 - 0.522234i) q^{69} -0.885172 q^{70} +14.0689i q^{71} +(2.53511 + 1.60413i) q^{72} -6.28386i q^{73} -0.592594 q^{74} +(2.03288 - 7.01450i) q^{75} -4.67563i q^{76} +(3.11245 + 1.14572i) q^{77} +(2.20791 + 0.639876i) q^{78} +5.69885i q^{79} -0.885172i q^{80} +(3.85353 + 8.13328i) q^{81} -1.73475 q^{82} +9.95539 q^{83} +(1.66360 + 0.482127i) q^{84} +1.20280i q^{85} +0.991579i q^{86} +(-3.82025 + 13.1819i) q^{87} +(-1.14572 + 3.11245i) q^{88} +6.72588i q^{89} +(1.41993 - 2.24401i) q^{90} +1.32719 q^{91} -1.08319i q^{92} +(-1.47419 + 5.08676i) q^{93} +0.204156i q^{94} -4.13874 q^{95} +(-0.482127 + 1.66360i) q^{96} -3.90839 q^{97} +1.00000 q^{98} +(-7.89730 + 6.05249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8	$ 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8} - 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} - 4 q^{17} + 8 q^{22} - 4 q^{24} - 28 q^{25} - 8 q^{27} + 8 q^{29} - 4 q^{30} + 12 q^{31} - 12 q^{32} + 16 q^{33} + 4 q^{34} - 4 q^{35} - 36 q^{39} + 20 q^{41} - 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} + 28 q^{50} + 8 q^{51} + 8 q^{54} + 4 q^{55} + 28 q^{57} - 8 q^{58} + 4 q^{60} - 12 q^{62} + 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} + 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} + 44 q^{83} + 8 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{91} - 24 q^{93} - 4 q^{96} - 48 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8 - 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 - 4 * q^17 + 8 * q^22 - 4 * q^24 - 28 * q^25 - 8 * q^27 + 8 * q^29 - 4 * q^30 + 12 * q^31 - 12 * q^32 + 16 * q^33 + 4 * q^34 - 4 * q^35 - 36 * q^39 + 20 * q^41 - 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 + 28 * q^50 + 8 * q^51 + 8 * q^54 + 4 * q^55 + 28 * q^57 - 8 * q^58 + 4 * q^60 - 12 * q^62 + 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 + 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 + 44 * q^83 + 8 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^91 - 24 * q^93 - 4 * q^96 - 48 * q^97 + 12 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.482127	−	1.66360i	0.278356	−	0.960478i
$3$	0.482127	−	1.66360i	0.278356	−	0.960478i
$4$	1.00000			0.500000
$5$		−	0.885172i		−	0.395861i	−0.980216	−	0.197931i	$-0.936578\pi$
$5$		−	0.885172i		−	0.395861i	0.980216	−	0.197931i	$-0.0634221\pi$
$6$	−0.482127	+	1.66360i	−0.196828	+	0.679160i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−1.00000			−0.353553
$9$	−2.53511	−	1.60413i	−0.845036	−	0.534710i
$10$			0.885172i			0.279916i
$11$	1.14572	−	3.11245i	0.345449	−	0.938438i
$11$	1.14572	−	3.11245i	0.345449	−	0.938438i
$12$	0.482127	−	1.66360i	0.139178	−	0.480239i
$13$		−	1.32719i		−	0.368097i	−0.982917	−	0.184049i	$-0.941080\pi$
$13$		−	1.32719i		−	0.368097i	0.982917	−	0.184049i	$-0.0589204\pi$
$14$		−	1.00000i		−	0.267261i
$15$	−1.47257	−	0.426766i	−0.380216	−	0.110190i
$16$	1.00000			0.250000
$17$	−1.35883			−0.329566			−0.164783	−	0.986330i	$-0.552692\pi$
$17$	−1.35883			−0.329566			−0.164783	+	0.986330i	$0.552692\pi$
$18$	2.53511	+	1.60413i	0.597530	+	0.378097i
$19$		−	4.67563i		−	1.07266i	−0.844007	−	0.536332i	$-0.819810\pi$
$19$		−	4.67563i		−	1.07266i	0.844007	−	0.536332i	$-0.180190\pi$
$20$		−	0.885172i		−	0.197931i
$21$	1.66360	+	0.482127i	0.363027	+	0.105209i
$22$	−1.14572	+	3.11245i	−0.244269	+	0.663576i
$23$		−	1.08319i		−	0.225860i	−0.993603	−	0.112930i	$-0.963976\pi$
$23$		−	1.08319i		−	0.225860i	0.993603	−	0.112930i	$-0.0360236\pi$
$24$	−0.482127	+	1.66360i	−0.0984138	+	0.339580i
$25$	4.21647			0.843294
$26$			1.32719i			0.260284i
$27$	−3.89087	+	3.44400i	−0.748798	+	0.662798i
$28$			1.00000i			0.188982i
$29$	−7.92374			−1.47140			−0.735701	−	0.677306i	$-0.763147\pi$
$29$	−7.92374			−1.47140			−0.735701	+	0.677306i	$0.763147\pi$
$30$	1.47257	+	0.426766i	0.268853	+	0.0779164i
$31$	−3.05769			−0.549177			−0.274588	−	0.961562i	$-0.588542\pi$
$31$	−3.05769			−0.549177			−0.274588	+	0.961562i	$0.588542\pi$
$32$	−1.00000			−0.176777
$33$	−4.62547	−	3.40662i	−0.805191	−	0.593016i
$34$	1.35883			0.233038
$35$	0.885172			0.149621
$36$	−2.53511	−	1.60413i	−0.422518	−	0.267355i
$37$	0.592594			0.0974218			0.0487109	−	0.998813i	$-0.484489\pi$
$37$	0.592594			0.0974218			0.0487109	+	0.998813i	$0.484489\pi$
$38$			4.67563i			0.758488i
$39$	−2.20791	−	0.639876i	−0.353549	−	0.102462i
$40$			0.885172i			0.139958i
$41$	1.73475			0.270922			0.135461	−	0.990783i	$-0.456748\pi$
$41$	1.73475			0.270922			0.135461	+	0.990783i	$0.456748\pi$
$42$	−1.66360	−	0.482127i	−0.256699	−	0.0743938i
$43$		−	0.991579i		−	0.151214i	−0.997138	−	0.0756072i	$-0.975910\pi$
$43$		−	0.991579i		−	0.151214i	0.997138	−	0.0756072i	$-0.0240895\pi$
$44$	1.14572	−	3.11245i	0.172724	−	0.469219i
$45$	−1.41993	+	2.24401i	−0.211671	+	0.334517i
$46$			1.08319i			0.159707i
$47$		−	0.204156i		−	0.0297792i	−0.999889	−	0.0148896i	$-0.995260\pi$
$47$		−	0.204156i		−	0.0297792i	0.999889	−	0.0148896i	$-0.00473969\pi$
$48$	0.482127	−	1.66360i	0.0695891	−	0.240119i
$49$	−1.00000			−0.142857
$50$	−4.21647			−0.596299
$51$	−0.655131	+	2.26055i	−0.0917367	+	0.316541i
$52$		−	1.32719i		−	0.184049i
$53$		−	1.07021i		−	0.147005i	−0.997295	−	0.0735026i	$-0.976582\pi$
$53$		−	1.07021i		−	0.147005i	0.997295	−	0.0735026i	$-0.0234177\pi$
$54$	3.89087	−	3.44400i	0.529480	−	0.468669i
$55$	−2.75505	−	1.01416i	−0.371491	−	0.136750i
$56$		−	1.00000i		−	0.133631i
$57$	−7.77837	−	2.25425i	−1.03027	−	0.298583i
$58$	7.92374			1.04044
$59$		−	5.25570i		−	0.684234i	−0.939657	−	0.342117i	$-0.888856\pi$
$59$		−	5.25570i		−	0.684234i	0.939657	−	0.342117i	$-0.111144\pi$
$60$	−1.47257	−	0.426766i	−0.190108	−	0.0550952i
$61$		−	11.6057i		−	1.48595i	−0.669317	−	0.742977i	$-0.733413\pi$
$61$		−	11.6057i		−	1.48595i	0.669317	−	0.742977i	$-0.266587\pi$
$62$	3.05769			0.388327
$63$	1.60413	−	2.53511i	0.202101	−	0.319393i
$64$	1.00000			0.125000
$65$	−1.17479			−0.145715
$66$	4.62547	+	3.40662i	0.569356	+	0.419326i
$67$	12.6414			1.54439			0.772197	−	0.635383i	$-0.219158\pi$
$67$	12.6414			1.54439			0.772197	+	0.635383i	$0.219158\pi$
$68$	−1.35883			−0.164783
$69$	−1.80199	−	0.522234i	−0.216934	−	0.0628696i
$70$	−0.885172			−0.105798
$71$			14.0689i			1.66968i	0.550496	+	0.834838i	$0.314439\pi$
$71$			14.0689i			1.66968i	−0.550496	+	0.834838i	$0.685561\pi$
$72$	2.53511	+	1.60413i	0.298765	+	0.189049i
$73$		−	6.28386i		−	0.735470i	−0.929931	−	0.367735i	$-0.880133\pi$
$73$		−	6.28386i		−	0.735470i	0.929931	−	0.367735i	$-0.119867\pi$
$74$	−0.592594			−0.0688876
$75$	2.03288	−	7.01450i	0.234736	−	0.809965i
$76$		−	4.67563i		−	0.536332i
$77$	3.11245	+	1.14572i	0.354696	+	0.130567i
$78$	2.20791	+	0.639876i	0.249997	+	0.0724517i
$79$			5.69885i			0.641171i	0.947220	+	0.320586i	$0.103880\pi$
$79$			5.69885i			0.641171i	−0.947220	+	0.320586i	$0.896120\pi$
$80$		−	0.885172i		−	0.0989653i
$81$	3.85353	+	8.13328i	0.428170	+	0.903698i
$82$	−1.73475			−0.191571
$83$	9.95539			1.09275			0.546373	−	0.837542i	$-0.316008\pi$
$83$	9.95539			1.09275			0.546373	+	0.837542i	$0.316008\pi$
$84$	1.66360	+	0.482127i	0.181513	+	0.0526044i
$85$			1.20280i			0.130462i
$86$			0.991579i			0.106925i
$87$	−3.82025	+	13.1819i	−0.409574	+	1.41325i
$88$	−1.14572	+	3.11245i	−0.122135	+	0.331788i
$89$			6.72588i			0.712942i	0.934306	+	0.356471i	$0.116020\pi$
$89$			6.72588i			0.712942i	−0.934306	+	0.356471i	$0.883980\pi$
$90$	1.41993	−	2.24401i	0.149674	−	0.236539i
$91$	1.32719			0.139128
$92$		−	1.08319i		−	0.112930i
$93$	−1.47419	+	5.08676i	−0.152867	+	0.527472i
$94$			0.204156i			0.0210571i
$95$	−4.13874			−0.424626
$96$	−0.482127	+	1.66360i	−0.0492069	+	0.169790i
$97$	−3.90839			−0.396837			−0.198419	−	0.980117i	$-0.563581\pi$
$97$	−3.90839			−0.396837			−0.198419	+	0.980117i	$0.563581\pi$
$98$	1.00000			0.101015
$99$	−7.89730	+	6.05249i	−0.793709	+	0.608298i
$100$	4.21647			0.421647
$101$	−7.62685			−0.758900			−0.379450	−	0.925212i	$-0.623887\pi$
$101$	−7.62685			−0.758900			−0.379450	+	0.925212i	$0.623887\pi$
$102$	0.655131	−	2.26055i	0.0648676	−	0.223828i
$103$	20.0904			1.97956			0.989781	−	0.142594i	$-0.0455444\pi$
$103$	20.0904			1.97956			0.989781	+	0.142594i	$0.0455444\pi$
$104$			1.32719i			0.130142i
$105$	0.426766	−	1.47257i	0.0416481	−	0.143708i
$106$			1.07021i			0.103948i
$107$	19.3874			1.87425			0.937126	−	0.348992i	$-0.113476\pi$
$107$	19.3874			1.87425			0.937126	+	0.348992i	$0.113476\pi$
$108$	−3.89087	+	3.44400i	−0.374399	+	0.331399i
$109$			1.56081i			0.149498i	0.997202	+	0.0747491i	$0.0238156\pi$
$109$			1.56081i			0.149498i	−0.997202	+	0.0747491i	$0.976184\pi$
$110$	2.75505	+	1.01416i	0.262684	+	0.0966966i
$111$	0.285706	−	0.985837i	0.0271180	−	0.0935715i
$112$			1.00000i			0.0944911i
$113$			5.35124i			0.503403i	0.967805	+	0.251701i	$0.0809900\pi$
$113$			5.35124i			0.503403i	−0.967805	+	0.251701i	$0.919010\pi$
$114$	7.77837	+	2.25425i	0.728511	+	0.211130i
$115$	−0.958807			−0.0894092
$116$	−7.92374			−0.735701
$117$	−2.12899	+	3.36458i	−0.196825	+	0.311055i
$118$			5.25570i			0.483827i
$119$		−	1.35883i		−	0.124564i
$120$	1.47257	+	0.426766i	0.134427	+	0.0389582i
$121$	−8.37463	−	7.13201i	−0.761330	−	0.648364i
$122$			11.6057i			1.05073i
$123$	0.836368	−	2.88592i	0.0754128	−	0.260214i
$124$	−3.05769			−0.274588
$125$		−	8.15816i		−	0.729688i
$126$	−1.60413	+	2.53511i	−0.142907	+	0.225845i
$127$			16.0113i			1.42077i	0.703812	+	0.710386i	$0.251480\pi$
$127$			16.0113i			1.42077i	−0.703812	+	0.710386i	$0.748520\pi$
$128$	−1.00000			−0.0883883
$129$	−1.64959	−	0.478067i	−0.145238	−	0.0420915i
$130$	1.17479			0.103036
$131$	18.5001			1.61636			0.808178	−	0.588938i	$-0.200454\pi$
$131$	18.5001			1.61636			0.808178	+	0.588938i	$0.200454\pi$
$132$	−4.62547	−	3.40662i	−0.402595	−	0.296508i
$133$	4.67563			0.405429
$134$	−12.6414			−1.09205
$135$	3.04853	+	3.44409i	0.262376	+	0.296420i
$136$	1.35883			0.116519
$137$			5.39771i			0.461157i	0.973054	+	0.230579i	$0.0740619\pi$
$137$			5.39771i			0.461157i	−0.973054	+	0.230579i	$0.925938\pi$
$138$	1.80199	+	0.522234i	0.153395	+	0.0444555i
$139$		−	1.22693i		−	0.104067i	−0.998645	−	0.0520333i	$-0.983430\pi$
$139$		−	1.22693i		−	0.104067i	0.998645	−	0.0520333i	$-0.0165702\pi$
$140$	0.885172			0.0748107
$141$	−0.339634	−	0.0984293i	−0.0286023	−	0.00828924i
$142$		−	14.0689i		−	1.18064i
$143$	−4.13082	−	1.52060i	−0.345436	−	0.127159i
$144$	−2.53511	−	1.60413i	−0.211259	−	0.133678i
$145$			7.01388i			0.582471i
$146$			6.28386i			0.520056i
$147$	−0.482127	+	1.66360i	−0.0397652	+	0.137211i
$148$	0.592594			0.0487109
$149$	6.96374			0.570492			0.285246	−	0.958454i	$-0.407925\pi$
$149$	6.96374			0.570492			0.285246	+	0.958454i	$0.407925\pi$
$150$	−2.03288	+	7.01450i	−0.165984	+	0.572732i
$151$			6.00563i			0.488731i	0.969683	+	0.244366i	$0.0785797\pi$
$151$			6.00563i			0.488731i	−0.969683	+	0.244366i	$0.921420\pi$
$152$			4.67563i			0.379244i
$153$	3.44479	+	2.17975i	0.278495	+	0.176222i
$154$	−3.11245	−	1.14572i	−0.250808	−	0.0923251i
$155$			2.70658i			0.217398i
$156$	−2.20791	−	0.639876i	−0.176775	−	0.0512311i
$157$	8.23642			0.657337			0.328669	−	0.944445i	$-0.393400\pi$
$157$	8.23642			0.657337			0.328669	+	0.944445i	$0.393400\pi$
$158$		−	5.69885i		−	0.453376i
$159$	−1.78040	−	0.515979i	−0.141195	−	0.0409198i
$160$			0.885172i			0.0699790i
$161$	1.08319			0.0853671
$162$	−3.85353	−	8.13328i	−0.302762	−	0.639011i
$163$	−11.3803			−0.891371			−0.445685	−	0.895190i	$-0.647040\pi$
$163$	−11.3803			−0.891371			−0.445685	+	0.895190i	$0.647040\pi$
$164$	1.73475			0.135461
$165$	−3.01544	+	4.09434i	−0.234752	+	0.318744i
$166$	−9.95539			−0.772688
$167$	16.4986			1.27670			0.638350	−	0.769746i	$-0.279617\pi$
$167$	16.4986			1.27670			0.638350	+	0.769746i	$0.279617\pi$
$168$	−1.66360	−	0.482127i	−0.128349	−	0.0371969i
$169$	11.2386			0.864505
$170$		−	1.20280i		−	0.0922507i
$171$	−7.50033	+	11.8532i	−0.573564	+	0.906439i
$172$		−	0.991579i		−	0.0756072i
$173$	16.8783			1.28323			0.641617	−	0.767025i	$-0.278264\pi$
$173$	16.8783			1.28323			0.641617	+	0.767025i	$0.278264\pi$
$174$	3.82025	−	13.1819i	0.289613	−	0.999318i
$175$			4.21647i			0.318735i
$176$	1.14572	−	3.11245i	0.0863622	−	0.234609i
$177$	−8.74337	−	2.53392i	−0.657192	−	0.190461i
$178$		−	6.72588i		−	0.504126i
$179$		−	14.1519i		−	1.05776i	−0.848696	−	0.528882i	$-0.822612\pi$
$179$		−	14.1519i		−	1.05776i	0.848696	−	0.528882i	$-0.177388\pi$
$180$	−1.41993	+	2.24401i	−0.105835	+	0.167258i
$181$	−18.7096			−1.39067			−0.695336	−	0.718684i	$-0.744745\pi$
$181$	−18.7096			−1.39067			−0.695336	+	0.718684i	$0.744745\pi$
$182$	−1.32719			−0.0983781
$183$	−19.3071	−	5.59541i	−1.42723	−	0.413624i
$184$			1.08319i			0.0798536i
$185$		−	0.524548i		−	0.0385655i
$186$	1.47419	−	5.08676i	0.108093	−	0.372979i
$187$	−1.55685	+	4.22930i	−0.113848	+	0.309277i
$188$		−	0.204156i		−	0.0148896i
$189$	−3.44400	−	3.89087i	−0.250514	−	0.283019i
$190$	4.13874			0.300256
$191$		−	15.6274i		−	1.13076i	−0.824832	−	0.565378i	$-0.808730\pi$
$191$		−	15.6274i		−	1.13076i	0.824832	−	0.565378i	$-0.191270\pi$
$192$	0.482127	−	1.66360i	0.0347945	−	0.120060i
$193$		−	20.0908i		−	1.44617i	−0.690760	−	0.723084i	$-0.742724\pi$
$193$		−	20.0908i		−	1.44617i	0.690760	−	0.723084i	$-0.257276\pi$
$194$	3.90839			0.280606
$195$	−0.566400	+	1.95438i	−0.0405608	+	0.139956i
$196$	−1.00000			−0.0714286
$197$	−10.9972			−0.783519			−0.391759	−	0.920068i	$-0.628133\pi$
$197$	−10.9972			−0.783519			−0.391759	+	0.920068i	$0.628133\pi$
$198$	7.89730	−	6.05249i	0.561237	−	0.430132i
$199$	−11.5909			−0.821655			−0.410827	−	0.911713i	$-0.634760\pi$
$199$	−11.5909			−0.821655			−0.410827	+	0.911713i	$0.634760\pi$
$200$	−4.21647			−0.298149
$201$	6.09477	−	21.0302i	0.429892	−	1.48336i
$202$	7.62685			0.536623
$203$		−	7.92374i		−	0.556138i
$204$	−0.655131	+	2.26055i	−0.0458683	+	0.158270i
$205$		−	1.53555i		−	0.107247i
$206$	−20.0904			−1.39976
$207$	−1.73757	+	2.74599i	−0.120770	+	0.190860i
$208$		−	1.32719i		−	0.0920243i
$209$	−14.5527	−	5.35698i	−1.00663	−	0.370550i
$210$	−0.426766	+	1.47257i	−0.0294496	+	0.101617i
$211$			25.2106i			1.73557i	0.496938	+	0.867786i	$0.334458\pi$
$211$			25.2106i			1.73557i	−0.496938	+	0.867786i	$0.665542\pi$
$212$		−	1.07021i		−	0.0735026i
$213$	23.4050	+	6.78302i	1.60369	+	0.464765i
$214$	−19.3874			−1.32530
$215$	−0.877718			−0.0598599
$216$	3.89087	−	3.44400i	0.264740	−	0.234334i
$217$		−	3.05769i		−	0.207569i
$218$		−	1.56081i		−	0.105711i
$219$	−10.4538	−	3.02962i	−0.706402	−	0.204723i
$220$	−2.75505	−	1.01416i	−0.185745	−	0.0683749i
$221$			1.80343i			0.121312i
$222$	−0.285706	+	0.985837i	−0.0191753	+	0.0661650i
$223$	20.3866			1.36519			0.682593	−	0.730799i	$-0.260852\pi$
$223$	20.3866			1.36519			0.682593	+	0.730799i	$0.260852\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−10.6892	−	6.76377i	−0.712613	−	0.450918i
$226$		−	5.35124i		−	0.355959i
$227$	−10.2315			−0.679087			−0.339544	−	0.940590i	$-0.610273\pi$
$227$	−10.2315			−0.679087			−0.339544	+	0.940590i	$0.610273\pi$
$228$	−7.77837	−	2.25425i	−0.515135	−	0.149291i
$229$	−12.2421			−0.808979			−0.404489	−	0.914543i	$-0.632551\pi$
$229$	−12.2421			−0.808979			−0.404489	+	0.914543i	$0.632551\pi$
$230$	0.958807			0.0632219
$231$	3.40662	−	4.62547i	0.224139	−	0.304334i
$232$	7.92374			0.520219
$233$	−9.73995			−0.638085			−0.319043	−	0.947740i	$-0.603361\pi$
$233$	−9.73995			−0.638085			−0.319043	+	0.947740i	$0.603361\pi$
$234$	2.12899	−	3.36458i	0.139176	−	0.219949i
$235$	−0.180713			−0.0117884
$236$		−	5.25570i		−	0.342117i
$237$	9.48059	+	2.74757i	0.615831	+	0.178474i
$238$			1.35883i			0.0880801i
$239$	6.32689			0.409253			0.204626	−	0.978840i	$-0.434402\pi$
$239$	6.32689			0.409253			0.204626	+	0.978840i	$0.434402\pi$
$240$	−1.47257	−	0.426766i	−0.0950540	−	0.0275476i
$241$		−	9.56291i		−	0.616001i	−0.951386	−	0.308001i	$-0.900340\pi$
$241$		−	9.56291i		−	0.616001i	0.951386	−	0.308001i	$-0.0996599\pi$
$242$	8.37463	+	7.13201i	0.538342	+	0.458463i
$243$	15.3884	−	2.48944i	0.987166	−	0.159698i
$244$		−	11.6057i		−	0.742977i
$245$			0.885172i			0.0565516i
$246$	−0.836368	+	2.88592i	−0.0533249	+	0.183999i
$247$	−6.20547			−0.394845
$248$	3.05769			0.194163
$249$	4.79976	−	16.5617i	0.304173	−	1.04956i
$250$			8.15816i			0.515968i
$251$			11.0462i			0.697228i	0.937266	+	0.348614i	$0.113348\pi$
$251$			11.0462i			0.697228i	−0.937266	+	0.348614i	$0.886652\pi$
$252$	1.60413	−	2.53511i	0.101051	−	0.159697i
$253$	−3.37136	−	1.24103i	−0.211956	−	0.0780231i
$254$		−	16.0113i		−	1.00464i
$255$	2.00098	+	0.579904i	0.125306	+	0.0363150i
$256$	1.00000			0.0625000
$257$		−	15.9724i		−	0.996331i	−0.867082	−	0.498165i	$-0.834007\pi$
$257$		−	15.9724i		−	0.996331i	0.867082	−	0.498165i	$-0.165993\pi$
$258$	1.64959	+	0.478067i	0.102699	+	0.0297632i
$259$			0.592594i			0.0368220i
$260$	−1.17479			−0.0728577
$261$	20.0875	+	12.7107i	1.24339	+	0.786774i
$262$	−18.5001			−1.14294
$263$	−23.7328			−1.46343			−0.731715	−	0.681611i	$-0.761280\pi$
$263$	−23.7328			−1.46343			−0.731715	+	0.681611i	$0.761280\pi$
$264$	4.62547	+	3.40662i	0.284678	+	0.209663i
$265$	−0.947323			−0.0581936
$266$	−4.67563			−0.286682
$267$	11.1891	+	3.24273i	0.684765	+	0.198452i
$268$	12.6414			0.772197
$269$		−	22.2477i		−	1.35647i	−0.734847	−	0.678233i	$-0.762746\pi$
$269$		−	22.2477i		−	1.35647i	0.734847	−	0.678233i	$-0.237254\pi$
$270$	−3.04853	−	3.44409i	−0.185528	−	0.209601i
$271$			10.1269i			0.615163i	0.951522	+	0.307581i	$0.0995196\pi$
$271$			10.1269i			0.615163i	−0.951522	+	0.307581i	$0.900480\pi$
$272$	−1.35883			−0.0823914
$273$	0.639876	−	2.20791i	0.0387271	−	0.133629i
$274$		−	5.39771i		−	0.326087i
$275$	4.83091	−	13.1235i	0.291315	−	0.791379i
$276$	−1.80199	−	0.522234i	−0.108467	−	0.0314348i
$277$			23.2504i			1.39698i	0.715619	+	0.698491i	$0.246145\pi$
$277$			23.2504i			1.39698i	−0.715619	+	0.698491i	$0.753855\pi$
$278$			1.22693i			0.0735863i
$279$	7.75156	+	4.90493i	0.464074	+	0.293650i
$280$	−0.885172			−0.0528992
$281$	−0.993239			−0.0592517			−0.0296258	−	0.999561i	$-0.509432\pi$
$281$	−0.993239			−0.0592517			−0.0296258	+	0.999561i	$0.509432\pi$
$282$	0.339634	+	0.0984293i	0.0202249	+	0.00586138i
$283$		−	24.2391i		−	1.44087i	−0.693525	−	0.720433i	$-0.743943\pi$
$283$		−	24.2391i		−	1.44087i	0.693525	−	0.720433i	$-0.256057\pi$
$284$			14.0689i			0.834838i
$285$	−1.99540	+	6.88520i	−0.118197	+	0.407844i
$286$	4.13082	+	1.52060i	0.244260	+	0.0899148i
$287$			1.73475i			0.102399i
$288$	2.53511	+	1.60413i	0.149383	+	0.0945243i
$289$	−15.1536			−0.891386
$290$		−	7.01388i		−	0.411869i
$291$	−1.88434	+	6.50199i	−0.110462	+	0.381153i
$292$		−	6.28386i		−	0.367735i
$293$	16.8668			0.985370			0.492685	−	0.870208i	$-0.336015\pi$
$293$	16.8668			0.985370			0.492685	+	0.870208i	$0.336015\pi$
$294$	0.482127	−	1.66360i	0.0281182	−	0.0970229i
$295$	−4.65220			−0.270862
$296$	−0.592594			−0.0344438
$297$	6.26140	+	16.0560i	0.363323	+	0.931663i
$298$	−6.96374			−0.403399
$299$	−1.43760			−0.0831384
$300$	2.03288	−	7.01450i	0.117368	−	0.404983i
$301$	0.991579			0.0571537
$302$		−	6.00563i		−	0.345585i
$303$	−3.67711	+	12.6880i	−0.211245	+	0.728907i
$304$		−	4.67563i		−	0.268166i
$305$	−10.2730			−0.588231
$306$	−3.44479	−	2.17975i	−0.196925	−	0.124608i
$307$			24.4009i			1.39263i	0.717734	+	0.696317i	$0.245179\pi$
$307$			24.4009i			1.39263i	−0.717734	+	0.696317i	$0.754821\pi$
$308$	3.11245	+	1.14572i	0.177348	+	0.0652837i
$309$	9.68611	−	33.4223i	0.551024	−	1.90133i
$310$		−	2.70658i		−	0.153723i
$311$		−	2.69179i		−	0.152638i	−0.997083	−	0.0763188i	$-0.975683\pi$
$311$		−	2.69179i		−	0.152638i	0.997083	−	0.0763188i	$-0.0243167\pi$
$312$	2.20791	+	0.639876i	0.124998	+	0.0362258i
$313$	−16.7616			−0.947419			−0.473709	−	0.880681i	$-0.657085\pi$
$313$	−16.7616			−0.947419			−0.473709	+	0.880681i	$0.657085\pi$
$314$	−8.23642			−0.464808
$315$	−2.24401	−	1.41993i	−0.126435	−	0.0800041i
$316$			5.69885i			0.320586i
$317$			26.9690i			1.51473i	0.652991	+	0.757366i	$0.273514\pi$
$317$			26.9690i			1.51473i	−0.652991	+	0.757366i	$0.726486\pi$
$318$	1.78040	+	0.515979i	0.0998400	+	0.0289347i
$319$	−9.07842	+	24.6622i	−0.508294	+	1.38082i
$320$		−	0.885172i		−	0.0494826i
$321$	9.34720	−	32.2528i	0.521710	−	1.80018i
$322$	−1.08319			−0.0603636
$323$			6.35341i			0.353513i
$324$	3.85353	+	8.13328i	0.214085	+	0.451849i
$325$		−	5.59607i		−	0.310414i
$326$	11.3803			0.630294
$327$	2.59655	+	0.752507i	0.143590	+	0.0416137i
$328$	−1.73475			−0.0957853
$329$	0.204156			0.0112555
$330$	3.01544	−	4.09434i	0.165995	−	0.225386i
$331$	−20.1340			−1.10666			−0.553332	−	0.832961i	$-0.686644\pi$
$331$	−20.1340			−1.10666			−0.553332	+	0.832961i	$0.686644\pi$
$332$	9.95539			0.546373
$333$	−1.50229	−	0.950598i	−0.0823249	−	0.0520924i
$334$	−16.4986			−0.902763
$335$		−	11.1898i		−	0.611366i
$336$	1.66360	+	0.482127i	0.0907566	+	0.0263022i
$337$			4.64072i			0.252796i	0.991980	+	0.126398i	$0.0403416\pi$
$337$			4.64072i			0.252796i	−0.991980	+	0.126398i	$0.959658\pi$
$338$	−11.2386			−0.611297
$339$	8.90231	+	2.57998i	0.483507	+	0.140125i
$340$			1.20280i			0.0652311i
$341$	−3.50327	+	9.51689i	−0.189712	+	0.515368i
$342$	7.50033	−	11.8532i	0.405571	−	0.640949i
$343$		−	1.00000i		−	0.0539949i
$344$			0.991579i			0.0534624i
$345$	−0.462267	+	1.59507i	−0.0248876	+	0.0858756i
$346$	−16.8783			−0.907383
$347$	5.05434			0.271331			0.135666	−	0.990755i	$-0.456683\pi$
$347$	5.05434			0.271331			0.135666	+	0.990755i	$0.456683\pi$
$348$	−3.82025	+	13.1819i	−0.204787	+	0.706625i
$349$			20.4149i			1.09279i	0.837529	+	0.546393i	$0.184000\pi$
$349$			20.4149i			1.09279i	−0.837529	+	0.546393i	$0.816000\pi$
$350$		−	4.21647i		−	0.225380i
$351$	4.57085	+	5.16394i	0.243974	+	0.275630i
$352$	−1.14572	+	3.11245i	−0.0610673	+	0.165894i
$353$			23.2837i			1.23927i	0.784891	+	0.619634i	$0.212719\pi$
$353$			23.2837i			1.23927i	−0.784891	+	0.619634i	$0.787281\pi$
$354$	8.74337	+	2.53392i	0.464705	+	0.134676i
$355$	12.4534			0.660960
$356$			6.72588i			0.356471i
$357$	−2.26055	−	0.655131i	−0.119641	−	0.0346732i
$358$			14.1519i			0.747952i
$359$	−23.8367			−1.25805			−0.629026	−	0.777384i	$-0.716546\pi$
$359$	−23.8367			−1.25805			−0.629026	+	0.777384i	$0.716546\pi$
$360$	1.41993	−	2.24401i	0.0748370	−	0.118270i
$361$	−2.86155			−0.150608
$362$	18.7096			0.983354
$363$	−15.9024	+	10.4935i	−0.834661	+	0.550765i
$364$	1.32719			0.0695638
$365$	−5.56230			−0.291144
$366$	19.3071	+	5.59541i	1.00920	+	0.292477i
$367$	21.5358			1.12416			0.562080	−	0.827083i	$-0.310001\pi$
$367$	21.5358			1.12416			0.562080	+	0.827083i	$0.310001\pi$
$368$		−	1.08319i		−	0.0564650i
$369$	−4.39777	−	2.78276i	−0.228939	−	0.144865i
$370$			0.524548i			0.0272699i
$371$	1.07021			0.0555627
$372$	−1.47419	+	5.08676i	−0.0764334	+	0.263736i
$373$		−	5.82916i		−	0.301822i	−0.988547	−	0.150911i	$-0.951779\pi$
$373$		−	5.82916i		−	0.301822i	0.988547	−	0.150911i	$-0.0482207\pi$
$374$	1.55685	−	4.22930i	0.0805027	−	0.218692i
$375$	−13.5719	−	3.93327i	−0.700850	−	0.203113i
$376$			0.204156i			0.0105286i
$377$			10.5163i			0.541619i
$378$	3.44400	+	3.89087i	0.177140	+	0.200125i
$379$	−22.1230			−1.13638			−0.568191	−	0.822897i	$-0.692356\pi$
$379$	−22.1230			−1.13638			−0.568191	+	0.822897i	$0.692356\pi$
$380$	−4.13874			−0.212313
$381$	26.6363	+	7.71948i	1.36462	+	0.395481i
$382$			15.6274i			0.799565i
$383$			33.6351i			1.71867i	0.511409	+	0.859337i	$0.329124\pi$
$383$			33.6351i			1.71867i	−0.511409	+	0.859337i	$0.670876\pi$
$384$	−0.482127	+	1.66360i	−0.0246035	+	0.0848951i
$385$	1.01416	−	2.75505i	0.0516865	−	0.140410i
$386$			20.0908i			1.02260i
$387$	−1.59062	+	2.51376i	−0.0808559	+	0.127782i
$388$	−3.90839			−0.198419
$389$		−	7.41492i		−	0.375951i	−0.982174	−	0.187976i	$-0.939807\pi$
$389$		−	7.41492i		−	0.375951i	0.982174	−	0.187976i	$-0.0601926\pi$
$390$	0.566400	−	1.95438i	0.0286808	−	0.0989641i
$391$			1.47187i			0.0744357i
$392$	1.00000			0.0505076
$393$	8.91938	−	30.7766i	0.449923	−	1.55248i
$394$	10.9972			0.554031
$395$	5.04447			0.253815
$396$	−7.89730	+	6.05249i	−0.396854	+	0.304149i
$397$	−1.75661			−0.0881618			−0.0440809	−	0.999028i	$-0.514036\pi$
$397$	−1.75661			−0.0881618			−0.0440809	+	0.999028i	$0.514036\pi$
$398$	11.5909			0.580998
$399$	2.25425	−	7.77837i	0.112854	−	0.389405i
$400$	4.21647			0.210823
$401$			15.9480i			0.796405i	0.917298	+	0.398203i	$0.130366\pi$
$401$			15.9480i			0.796405i	−0.917298	+	0.398203i	$0.869634\pi$
$402$	−6.09477	+	21.0302i	−0.303979	+	1.04889i
$403$			4.05814i			0.202150i
$404$	−7.62685			−0.379450
$405$	7.19936	−	3.41104i	0.357739	−	0.169496i
$406$			7.92374i			0.393249i
$407$	0.678949	−	1.84442i	0.0336542	−	0.0914243i
$408$	0.655131	−	2.26055i	0.0324338	−	0.111914i
$409$		−	30.1031i		−	1.48850i	−0.667899	−	0.744252i	$-0.732806\pi$
$409$		−	30.1031i		−	1.48850i	0.667899	−	0.744252i	$-0.267194\pi$
$410$			1.53555i			0.0758354i
$411$	8.97961	+	2.60238i	0.442931	+	0.128366i
$412$	20.0904			0.989781
$413$	5.25570			0.258616
$414$	1.73757	−	2.74599i	0.0853970	−	0.134958i
$415$		−	8.81223i		−	0.432575i
$416$			1.32719i			0.0650710i
$417$	−2.04111	−	0.591536i	−0.0999538	−	0.0289676i
$418$	14.5527	+	5.35698i	0.711794	+	0.262019i
$419$		−	16.0788i		−	0.785503i	−0.919645	−	0.392751i	$-0.871523\pi$
$419$		−	16.0788i		−	0.785503i	0.919645	−	0.392751i	$-0.128477\pi$
$420$	0.426766	−	1.47257i	0.0208240	−	0.0718540i
$421$	22.9765			1.11981			0.559904	−	0.828557i	$-0.310838\pi$
$421$	22.9765			1.11981			0.559904	+	0.828557i	$0.310838\pi$
$422$		−	25.2106i		−	1.22723i
$423$	−0.327493	+	0.517558i	−0.0159233	+	0.0251645i
$424$			1.07021i			0.0519742i
$425$	−5.72948			−0.277921
$426$	−23.4050	−	6.78302i	−1.13398	−	0.328638i
$427$	11.6057			0.561638
$428$	19.3874			0.937126
$429$	−4.52124	+	6.13889i	−0.218287	+	0.296388i
$430$	0.877718			0.0423273
$431$	33.2578			1.60197			0.800986	−	0.598683i	$-0.204309\pi$
$431$	33.2578			1.60197			0.800986	+	0.598683i	$0.204309\pi$
$432$	−3.89087	+	3.44400i	−0.187200	+	0.165700i
$433$	−12.9146			−0.620637			−0.310319	−	0.950633i	$-0.600436\pi$
$433$	−12.9146			−0.620637			−0.310319	+	0.950633i	$0.600436\pi$
$434$			3.05769i			0.146774i
$435$	11.6683	+	3.38158i	0.559451	+	0.162134i
$436$			1.56081i			0.0747491i
$437$	−5.06458			−0.242272
$438$	10.4538	+	3.02962i	0.499502	+	0.144761i
$439$		−	32.9061i		−	1.57052i	−0.619164	−	0.785262i	$-0.712528\pi$
$439$		−	32.9061i		−	1.57052i	0.619164	−	0.785262i	$-0.287472\pi$
$440$	2.75505	+	1.01416i	0.131342	+	0.0483483i
$441$	2.53511	+	1.60413i	0.120719	+	0.0763872i
$442$		−	1.80343i		−	0.0857807i
$443$			40.0370i			1.90222i	0.308858	+	0.951108i	$0.400053\pi$
$443$			40.0370i			1.90222i	−0.308858	+	0.951108i	$0.599947\pi$
$444$	0.285706	−	0.985837i	0.0135590	−	0.0467858i
$445$	5.95356			0.282226
$446$	−20.3866			−0.965332
$447$	3.35741	−	11.5849i	0.158800	−	0.547945i
$448$			1.00000i			0.0472456i
$449$			8.30936i			0.392143i	0.980590	+	0.196071i	$0.0628184\pi$
$449$			8.30936i			0.392143i	−0.980590	+	0.196071i	$0.937182\pi$
$450$	10.6892	+	6.76377i	0.503894	+	0.318847i
$451$	1.98754	−	5.39930i	0.0935896	−	0.254243i
$452$			5.35124i			0.251701i
$453$	9.99094	+	2.89548i	0.469415	+	0.136041i
$454$	10.2315			0.480187
$455$		−	1.17479i		−	0.0550752i
$456$	7.77837	+	2.25425i	0.364255	+	0.105565i
$457$		−	30.7070i		−	1.43641i	−0.695831	−	0.718206i	$-0.744964\pi$
$457$		−	30.7070i		−	1.43641i	0.695831	−	0.718206i	$-0.255036\pi$
$458$	12.2421			0.572034
$459$	5.28705	−	4.67982i	0.246778	−	0.218435i
$460$	−0.958807			−0.0447046
$461$	−38.3614			−1.78667			−0.893335	−	0.449391i	$-0.851641\pi$
$461$	−38.3614			−1.78667			−0.893335	+	0.449391i	$0.851641\pi$
$462$	−3.40662	+	4.62547i	−0.158490	+	0.215196i
$463$	−10.0360			−0.466415			−0.233207	−	0.972427i	$-0.574922\pi$
$463$	−10.0360			−0.466415			−0.233207	+	0.972427i	$0.574922\pi$
$464$	−7.92374			−0.367851
$465$	4.50266	+	1.30492i	0.208806	+	0.0605140i
$466$	9.73995			0.451195
$467$		−	1.71995i		−	0.0795897i	−0.999208	−	0.0397948i	$-0.987330\pi$
$467$		−	1.71995i		−	0.0795897i	0.999208	−	0.0397948i	$-0.0126704\pi$
$468$	−2.12899	+	3.36458i	−0.0984126	+	0.155528i
$469$			12.6414i			0.583726i
$470$	0.180713			0.00833569
$471$	3.97100	−	13.7021i	0.182974	−	0.631358i
$472$			5.25570i			0.241913i
$473$	−3.08624	−	1.13608i	−0.141905	−	0.0522368i
$474$	−9.48059	−	2.74757i	−0.435458	−	0.126200i
$475$		−	19.7147i		−	0.904571i
$476$		−	1.35883i		−	0.0622821i
$477$	−1.71676	+	2.71310i	−0.0786051	+	0.124225i
$478$	−6.32689			−0.289385
$479$	22.7932			1.04145			0.520723	−	0.853726i	$-0.325662\pi$
$479$	22.7932			1.04145			0.520723	+	0.853726i	$0.325662\pi$
$480$	1.47257	+	0.426766i	0.0672133	+	0.0194791i
$481$		−	0.786486i		−	0.0358607i
$482$			9.56291i			0.435579i
$483$	0.522234	−	1.80199i	0.0237625	−	0.0819932i
$484$	−8.37463	−	7.13201i	−0.380665	−	0.324182i
$485$			3.45960i			0.157092i
$486$	−15.3884	+	2.48944i	−0.698032	+	0.112923i
$487$	−12.6749			−0.574354			−0.287177	−	0.957878i	$-0.592717\pi$
$487$	−12.6749			−0.574354			−0.287177	+	0.957878i	$0.592717\pi$
$488$			11.6057i			0.525364i
$489$	−5.48673	+	18.9322i	−0.248119	+	0.856142i
$490$		−	0.885172i		−	0.0399880i
$491$	5.54324			0.250163			0.125082	−	0.992146i	$-0.460081\pi$
$491$	5.54324			0.250163			0.125082	+	0.992146i	$0.460081\pi$
$492$	0.836368	−	2.88592i	0.0377064	−	0.130107i
$493$	10.7671			0.484924
$494$	6.20547			0.279197
$495$	5.35750	+	6.99047i	0.240802	+	0.314198i
$496$	−3.05769			−0.137294
$497$	−14.0689			−0.631078
$498$	−4.79976	+	16.5617i	−0.215083	+	0.742150i
$499$	−1.41705			−0.0634359			−0.0317180	−	0.999497i	$-0.510098\pi$
$499$	−1.41705			−0.0634359			−0.0317180	+	0.999497i	$0.510098\pi$
$500$		−	8.15816i		−	0.364844i
$501$	7.95442	−	27.4470i	0.355377	−	1.22624i
$502$		−	11.0462i		−	0.493014i
$503$	−33.8599			−1.50974			−0.754869	−	0.655876i	$-0.772300\pi$
$503$	−33.8599			−1.50974			−0.754869	+	0.655876i	$0.772300\pi$
$504$	−1.60413	+	2.53511i	−0.0714536	+	0.112923i
$505$			6.75108i			0.300419i
$506$	3.37136	+	1.24103i	0.149875	+	0.0551706i
$507$	5.41842	−	18.6964i	0.240640	−	0.830337i
$508$			16.0113i			0.710386i
$509$		−	11.3563i		−	0.503361i	−0.967810	−	0.251681i	$-0.919017\pi$
$509$		−	11.3563i		−	0.503361i	0.967810	−	0.251681i	$-0.0809832\pi$
$510$	−2.00098	−	0.579904i	−0.0886048	−	0.0256786i
$511$	6.28386			0.277981
$512$	−1.00000			−0.0441942
$513$	16.1029	+	18.1923i	0.710960	+	0.803209i
$514$			15.9724i			0.704512i
$515$		−	17.7834i		−	0.783632i
$516$	−1.64959	−	0.478067i	−0.0726190	−	0.0210457i
$517$	−0.635425	−	0.233907i	−0.0279460	−	0.0102872i
$518$		−	0.592594i		−	0.0260371i
$519$	8.13749	−	28.0787i	0.357196	−	1.23252i
$520$	1.17479			0.0515181
$521$		−	6.77331i		−	0.296744i	−0.988932	−	0.148372i	$-0.952597\pi$
$521$		−	6.77331i		−	0.296744i	0.988932	−	0.148372i	$-0.0474033\pi$
$522$	−20.0875	−	12.7107i	−0.879208	−	0.556333i
$523$		−	28.8077i		−	1.25967i	−0.776727	−	0.629837i	$-0.783122\pi$
$523$		−	28.8077i		−	1.25967i	0.776727	−	0.629837i	$-0.216878\pi$
$524$	18.5001			0.808178
$525$	7.01450	+	2.03288i	0.306138	+	0.0887219i
$526$	23.7328			1.03480
$527$	4.15489			0.180990
$528$	−4.62547	−	3.40662i	−0.201298	−	0.148254i
$529$	21.8267			0.948987
$530$	0.947323			0.0411491
$531$	−8.43083	+	13.3238i	−0.365867	+	0.578202i
$532$	4.67563			0.202714
$533$		−	2.30234i		−	0.0997255i
$534$	−11.1891	−	3.24273i	−0.484202	−	0.140327i
$535$		−	17.1612i		−	0.741943i
$536$	−12.6414			−0.546026
$537$	−23.5431	−	6.82302i	−1.01596	−	0.294435i
$538$			22.2477i			0.959166i
$539$	−1.14572	+	3.11245i	−0.0493498	+	0.134063i
$540$	3.04853	+	3.44409i	0.131188	+	0.148210i
$541$			36.4556i			1.56735i	0.621171	+	0.783675i	$0.286657\pi$
$541$			36.4556i			1.56735i	−0.621171	+	0.783675i	$0.713343\pi$
$542$		−	10.1269i		−	0.434986i
$543$	−9.02040	+	31.1252i	−0.387103	+	1.33571i
$544$	1.35883			0.0582595
$545$	1.38158			0.0591805
$546$	−0.639876	+	2.20791i	−0.0273842	+	0.0944900i
$547$		−	29.6483i		−	1.26767i	−0.773469	−	0.633835i	$-0.781480\pi$
$547$		−	29.6483i		−	1.26767i	0.773469	−	0.633835i	$-0.218520\pi$
$548$			5.39771i			0.230579i
$549$	−18.6170	+	29.4216i	−0.794554	+	1.25568i
$550$	−4.83091	+	13.1235i	−0.205991	+	0.559589i
$551$			37.0485i			1.57832i
$552$	1.80199	+	0.522234i	0.0766976	+	0.0222277i
$553$	−5.69885			−0.242340
$554$		−	23.2504i		−	0.987816i
$555$	−0.872636	−	0.252899i	−0.0370413	−	0.0107350i
$556$		−	1.22693i		−	0.0520333i
$557$	16.5964			0.703210			0.351605	−	0.936148i	$-0.385636\pi$
$557$	16.5964			0.703210			0.351605	+	0.936148i	$0.385636\pi$
$558$	−7.75156	−	4.90493i	−0.328150	−	0.207642i
$559$	−1.31602			−0.0556616
$560$	0.885172			0.0374054
$561$	6.28524	+	4.62903i	0.265363	+	0.195438i
$562$	0.993239			0.0418973
$563$	23.3646			0.984702			0.492351	−	0.870397i	$-0.336138\pi$
$563$	23.3646			0.984702			0.492351	+	0.870397i	$0.336138\pi$
$564$	−0.339634	−	0.0984293i	−0.0143012	−	0.00414462i
$565$	4.73677			0.199278
$566$			24.2391i			1.01885i
$567$	−8.13328	+	3.85353i	−0.341566	+	0.161833i
$568$		−	14.0689i		−	0.590319i
$569$	−7.32817			−0.307213			−0.153606	−	0.988132i	$-0.549089\pi$
$569$	−7.32817			−0.307213			−0.153606	+	0.988132i	$0.549089\pi$
$570$	1.99540	−	6.88520i	0.0835781	−	0.288389i
$571$		−	40.8727i		−	1.71047i	−0.518243	−	0.855234i	$-0.673414\pi$
$571$		−	40.8727i		−	1.71047i	0.518243	−	0.855234i	$-0.326586\pi$
$572$	−4.13082	−	1.52060i	−0.172718	−	0.0635793i
$573$	−25.9976	−	7.53438i	−1.08607	−	0.314753i
$574$		−	1.73475i		−	0.0724069i
$575$		−	4.56722i		−	0.190466i
$576$	−2.53511	−	1.60413i	−0.105629	−	0.0668388i
$577$	8.27478			0.344483			0.172242	−	0.985055i	$-0.444899\pi$
$577$	8.27478			0.344483			0.172242	+	0.985055i	$0.444899\pi$
$578$	15.1536			0.630305
$579$	−33.4230	−	9.68633i	−1.38901	−	0.402550i
$580$			7.01388i			0.291236i
$581$			9.95539i			0.413019i
$582$	1.88434	−	6.50199i	0.0781085	−	0.269516i
$583$	−3.33098	−	1.22617i	−0.137955	−	0.0507827i
$584$			6.28386i			0.260028i
$585$	2.97823	+	1.88452i	0.123135	+	0.0779155i
$586$	−16.8668			−0.696762
$587$		−	37.0857i		−	1.53069i	−0.643619	−	0.765346i	$-0.722568\pi$
$587$		−	37.0857i		−	1.53069i	0.643619	−	0.765346i	$-0.277432\pi$
$588$	−0.482127	+	1.66360i	−0.0198826	+	0.0686056i
$589$			14.2966i			0.589082i
$590$	4.65220			0.191528
$591$	−5.30205	+	18.2949i	−0.218097	+	0.752552i
$592$	0.592594			0.0243555
$593$	−40.5672			−1.66589			−0.832947	−	0.553352i	$-0.813348\pi$
$593$	−40.5672			−1.66589			−0.832947	+	0.553352i	$0.813348\pi$
$594$	−6.26140	−	16.0560i	−0.256908	−	0.658785i
$595$	−1.20280			−0.0493101
$596$	6.96374			0.285246
$597$	−5.58827	+	19.2825i	−0.228713	+	0.789181i
$598$	1.43760			0.0587877
$599$		−	36.3797i		−	1.48643i	−0.669051	−	0.743217i	$-0.733299\pi$
$599$		−	36.3797i		−	1.48643i	0.669051	−	0.743217i	$-0.266701\pi$
$600$	−2.03288	+	7.01450i	−0.0829918	+	0.286366i
$601$			20.1330i			0.821242i	0.911806	+	0.410621i	$0.134688\pi$
$601$			20.1330i			0.821242i	−0.911806	+	0.410621i	$0.865312\pi$
$602$	−0.991579			−0.0404137
$603$	−32.0473	−	20.2785i	−1.30507	−	0.825803i
$604$			6.00563i			0.244366i
$605$	−6.31305	+	7.41299i	−0.256662	+	0.301381i
$606$	3.67711	−	12.6880i	0.149372	−	0.515415i
$607$			9.17001i			0.372199i	0.982531	+	0.186100i	$0.0595847\pi$
$607$			9.17001i			0.372199i	−0.982531	+	0.186100i	$0.940415\pi$
$608$			4.67563i			0.189622i
$609$	−13.1819	−	3.82025i	−0.534158	−	0.154804i
$610$	10.2730			0.415942
$611$	−0.270955			−0.0109617
$612$	3.44479	+	2.17975i	0.139247	+	0.0881110i
$613$			39.8926i			1.61125i	0.592429	+	0.805623i	$0.298169\pi$
$613$			39.8926i			1.61125i	−0.592429	+	0.805623i	$0.701831\pi$
$614$		−	24.4009i		−	0.984741i
$615$	−2.55453	−	0.740330i	−0.103009	−	0.0298530i
$616$	−3.11245	−	1.14572i	−0.125404	−	0.0461625i
$617$		−	16.0980i		−	0.648079i	−0.946044	−	0.324040i	$-0.894959\pi$
$617$		−	16.0980i		−	0.648079i	0.946044	−	0.324040i	$-0.105041\pi$
$618$	−9.68611	+	33.4223i	−0.389633	+	1.34444i
$619$	−33.8820			−1.36183			−0.680916	−	0.732362i	$-0.738418\pi$
$619$	−33.8820			−1.36183			−0.680916	+	0.732362i	$0.738418\pi$
$620$			2.70658i			0.108699i
$621$	3.73049	+	4.21454i	0.149700	+	0.169124i
$622$			2.69179i			0.107931i
$623$	−6.72588			−0.269467
$624$	−2.20791	−	0.639876i	−0.0883873	−	0.0256155i
$625$	13.8610			0.554439
$626$	16.7616			0.669926
$627$	−15.9281	+	21.6270i	−0.636107	+	0.863699i
$628$	8.23642			0.328669
$629$	−0.805237			−0.0321069
$630$	2.24401	+	1.41993i	0.0894034	+	0.0565714i
$631$	−12.5148			−0.498207			−0.249104	−	0.968477i	$-0.580136\pi$
$631$	−12.5148			−0.498207			−0.249104	+	0.968477i	$0.580136\pi$
$632$		−	5.69885i		−	0.226688i
$633$	41.9403	+	12.1547i	1.66698	+	0.483107i
$634$		−	26.9690i		−	1.07108i
$635$	14.1727			0.562428
$636$	−1.78040	−	0.515979i	−0.0705976	−	0.0204599i
$637$			1.32719i			0.0525853i
$638$	9.07842	−	24.6622i	0.359418	−	0.976387i
$639$	22.5684	−	35.6663i	0.892792	−	1.41094i
$640$			0.885172i			0.0349895i
$641$		−	3.07515i		−	0.121461i	−0.998154	−	0.0607305i	$-0.980657\pi$
$641$		−	3.07515i		−	0.121461i	0.998154	−	0.0607305i	$-0.0193430\pi$
$642$	−9.34720	+	32.2528i	−0.368904	+	1.27292i
$643$	5.08419			0.200501			0.100250	−	0.994962i	$-0.468036\pi$
$643$	5.08419			0.200501			0.100250	+	0.994962i	$0.468036\pi$
$644$	1.08319			0.0426835
$645$	−0.423172	+	1.46017i	−0.0166624	+	0.0574941i
$646$		−	6.35341i		−	0.249972i
$647$		−	2.79526i		−	0.109893i	−0.998489	−	0.0549465i	$-0.982501\pi$
$647$		−	2.79526i		−	0.109893i	0.998489	−	0.0549465i	$-0.0174988\pi$
$648$	−3.85353	−	8.13328i	−0.151381	−	0.319506i
$649$	−16.3581	−	6.02158i	−0.642111	−	0.236368i
$650$			5.59607i			0.219496i
$651$	−5.08676	−	1.47419i	−0.199366	−	0.0577782i
$652$	−11.3803			−0.445685
$653$			13.2434i			0.518256i	0.965843	+	0.259128i	$0.0834351\pi$
$653$			13.2434i			0.518256i	−0.965843	+	0.259128i	$0.916565\pi$
$654$	−2.59655	−	0.752507i	−0.101533	−	0.0294254i
$655$		−	16.3757i		−	0.639853i
$656$	1.73475			0.0677304
$657$	−10.0801	+	15.9302i	−0.393263	+	0.621498i
$658$	−0.204156			−0.00795884
$659$	30.2171			1.17709			0.588546	−	0.808463i	$-0.299700\pi$
$659$	30.2171			1.17709			0.588546	+	0.808463i	$0.299700\pi$
$660$	−3.01544	+	4.09434i	−0.117376	+	0.159372i
$661$	9.22623			0.358859			0.179429	−	0.983771i	$-0.442575\pi$
$661$	9.22623			0.358859			0.179429	+	0.983771i	$0.442575\pi$
$662$	20.1340			0.782530
$663$	3.00019	+	0.869485i	0.116518	+	0.0337680i
$664$	−9.95539			−0.386344
$665$		−	4.13874i		−	0.160494i
$666$	1.50229	+	0.950598i	0.0582125	+	0.0368349i
$667$			8.58289i			0.332331i
$668$	16.4986			0.638350
$669$	9.82892	−	33.9150i	0.380008	−	1.31123i
$670$			11.1898i			0.432301i
$671$	−36.1220	−	13.2969i	−1.39447	−	0.513321i
$672$	−1.66360	−	0.482127i	−0.0641746	−	0.0185985i
$673$		−	19.4535i		−	0.749876i	−0.927050	−	0.374938i	$-0.877664\pi$
$673$		−	19.4535i		−	0.749876i	0.927050	−	0.374938i	$-0.122336\pi$
$674$		−	4.64072i		−	0.178754i
$675$	−16.4057	+	14.5215i	−0.631457	+	0.558934i
$676$	11.2386			0.432252
$677$	−38.9937			−1.49865			−0.749324	−	0.662203i	$-0.769622\pi$
$677$	−38.9937			−1.49865			−0.749324	+	0.662203i	$0.769622\pi$
$678$	−8.90231	−	2.57998i	−0.341891	−	0.0990835i
$679$		−	3.90839i		−	0.149990i
$680$		−	1.20280i		−	0.0461254i
$681$	−4.93288	+	17.0211i	−0.189028	+	0.652248i
$682$	3.50327	−	9.51689i	0.134147	−	0.364420i
$683$			27.2804i			1.04386i	0.852989	+	0.521929i	$0.174787\pi$
$683$			27.2804i			1.04386i	−0.852989	+	0.521929i	$0.825213\pi$
$684$	−7.50033	+	11.8532i	−0.286782	+	0.453220i
$685$	4.77790			0.182554
$686$			1.00000i			0.0381802i
$687$	−5.90223	+	20.3659i	−0.225184	+	0.777006i
$688$		−	0.991579i		−	0.0378036i
$689$	−1.42038			−0.0541122
$690$	0.462267	−	1.59507i	0.0175982	−	0.0607232i
$691$	38.5237			1.46551			0.732756	−	0.680491i	$-0.238234\pi$
$691$	38.5237			1.46551			0.732756	+	0.680491i	$0.238234\pi$
$692$	16.8783			0.641617
$693$	−6.05249	−	7.89730i	−0.229915	−	0.299994i
$694$	−5.05434			−0.191860
$695$	−1.08604			−0.0411960
$696$	3.82025	−	13.1819i	0.144806	−	0.499659i
$697$	−2.35723			−0.0892865
$698$		−	20.4149i		−	0.772717i
$699$	−4.69590	+	16.2033i	−0.177615	+	0.612867i
$700$			4.21647i			0.159368i
$701$	36.3616			1.37336			0.686680	−	0.726960i	$-0.259067\pi$
$701$	36.3616			1.37336			0.686680	+	0.726960i	$0.259067\pi$
$702$	−4.57085	−	5.16394i	−0.172516	−	0.194900i
$703$		−	2.77075i		−	0.104501i
$704$	1.14572	−	3.11245i	0.0431811	−	0.117305i
$705$	−0.0871269	+	0.300634i	−0.00328139	+	0.0113225i
$706$		−	23.2837i		−	0.876294i
$707$		−	7.62685i		−	0.286837i
$708$	−8.74337	−	2.53392i	−0.328596	−	0.0952304i
$709$	34.7438			1.30483			0.652416	−	0.757861i	$-0.273756\pi$
$709$	34.7438			1.30483			0.652416	+	0.757861i	$0.273756\pi$
$710$	−12.4534			−0.467369
$711$	9.14170	−	14.4472i	0.342841	−	0.541812i
$712$		−	6.72588i		−	0.252063i
$713$			3.31205i			0.124037i
$714$	2.26055	+	0.655131i	0.0845990	+	0.0245177i
$715$	−1.34599	+	3.65648i	−0.0503372	+	0.136745i
$716$		−	14.1519i		−	0.528882i
$717$	3.05037	−	10.5254i	0.113918	−	0.393078i
$718$	23.8367			0.889578
$719$		−	17.4143i		−	0.649446i	−0.945809	−	0.324723i	$-0.894729\pi$
$719$		−	17.4143i		−	0.649446i	0.945809	−	0.324723i	$-0.105271\pi$
$720$	−1.41993	+	2.24401i	−0.0529177	+	0.0836292i
$721$			20.0904i			0.748204i
$722$	2.86155			0.106496
$723$	−15.9088	−	4.61054i	−0.591656	−	0.171468i
$724$	−18.7096			−0.695336
$725$	−33.4102			−1.24082
$726$	15.9024	−	10.4935i	0.590194	−	0.389449i
$727$	34.6067			1.28349			0.641746	−	0.766917i	$-0.278210\pi$
$727$	34.6067			1.28349			0.641746	+	0.766917i	$0.278210\pi$
$728$	−1.32719			−0.0491890
$729$	3.27773	−	26.8003i	0.121398	−	0.992604i
$730$	5.56230			0.205870
$731$			1.34739i			0.0498351i
$732$	−19.3071	−	5.59541i	−0.713613	−	0.206812i
$733$			23.5214i			0.868782i	0.900724	+	0.434391i	$0.143036\pi$
$733$			23.5214i			0.868782i	−0.900724	+	0.434391i	$0.856964\pi$
$734$	−21.5358			−0.794901
$735$	1.47257	+	0.426766i	0.0543165	+	0.0157415i
$736$			1.08319i			0.0399268i
$737$	14.4836	−	39.3457i	0.533509	−	1.44932i
$738$	4.39777	+	2.78276i	0.161884	+	0.102435i
$739$			41.3951i			1.52274i	0.648315	+	0.761372i	$0.275474\pi$
$739$			41.3951i			1.52274i	−0.648315	+	0.761372i	$0.724526\pi$
$740$		−	0.524548i		−	0.0192828i
$741$	−2.99183	+	10.3234i	−0.109907	+	0.379239i
$742$	−1.07021			−0.0392888
$743$	23.1055			0.847657			0.423829	−	0.905742i	$-0.360686\pi$
$743$	23.1055			0.847657			0.423829	+	0.905742i	$0.360686\pi$
$744$	1.47419	−	5.08676i	0.0540466	−	0.186490i
$745$		−	6.16411i		−	0.225836i
$746$			5.82916i			0.213421i
$747$	−25.2380	−	15.9697i	−0.923409	−	0.584302i
$748$	−1.55685	+	4.22930i	−0.0569240	+	0.154638i
$749$			19.3874i			0.708400i
$750$	13.5719	+	3.93327i	0.495575	+	0.143623i
$751$	13.4462			0.490657			0.245328	−	0.969440i	$-0.421104\pi$
$751$	13.4462			0.490657			0.245328	+	0.969440i	$0.421104\pi$
$752$		−	0.204156i		−	0.00744481i
$753$	18.3764	+	5.32566i	0.669672	+	0.194078i
$754$		−	10.5163i		−	0.382982i
$755$	5.31602			0.193470
$756$	−3.44400	−	3.89087i	−0.125257	−	0.141510i
$757$	22.9292			0.833375			0.416687	−	0.909050i	$-0.363191\pi$
$757$	22.9292			0.833375			0.416687	+	0.909050i	$0.363191\pi$
$758$	22.1230			0.803543
$759$	−3.69000	+	5.01025i	−0.133939	+	0.181860i
$760$	4.13874			0.150128
$761$	−7.87219			−0.285367			−0.142683	−	0.989768i	$-0.545573\pi$
$761$	−7.87219			−0.285367			−0.142683	+	0.989768i	$0.545573\pi$
$762$	−26.6363	−	7.71948i	−0.964932	−	0.279647i
$763$	−1.56081			−0.0565050
$764$		−	15.6274i		−	0.565378i
$765$	1.92945	−	3.04923i	0.0697595	−	0.110245i
$766$		−	33.6351i		−	1.21529i
$767$	−6.97533			−0.251865
$768$	0.482127	−	1.66360i	0.0173973	−	0.0600299i
$769$			23.8659i			0.860625i	0.902680	+	0.430313i	$0.141597\pi$
$769$			23.8659i			0.860625i	−0.902680	+	0.430313i	$0.858403\pi$
$770$	−1.01416	+	2.75505i	−0.0365479	+	0.0992851i
$771$	−26.5716	−	7.70073i	−0.956953	−	0.277335i
$772$		−	20.0908i		−	0.723084i
$773$		−	25.1142i		−	0.903296i	−0.892196	−	0.451648i	$-0.850836\pi$
$773$		−	25.1142i		−	0.903296i	0.892196	−	0.451648i	$-0.149164\pi$
$774$	1.59062	−	2.51376i	0.0571737	−	0.0903552i
$775$	−12.8926			−0.463118
$776$	3.90839			0.140303
$777$	0.985837	+	0.285706i	0.0353667	+	0.0102496i
$778$			7.41492i			0.265838i
$779$		−	8.11104i		−	0.290608i
$780$	−0.566400	+	1.95438i	−0.0202804	+	0.0699782i
$781$	43.7888	+	16.1191i	1.56689	+	0.576787i
$782$		−	1.47187i		−	0.0526340i
$783$	30.8303	−	27.2894i	1.10178	−	0.975243i
$784$	−1.00000			−0.0357143
$785$		−	7.29065i		−	0.260214i
$786$	−8.91938	+	30.7766i	−0.318144	+	1.09777i
$787$			34.5163i			1.23037i	0.788381	+	0.615187i	$0.210919\pi$
$787$			34.5163i			1.23037i	−0.788381	+	0.615187i	$0.789081\pi$
$788$	−10.9972			−0.391759
$789$	−11.4422	+	39.4819i	−0.407355	+	1.40559i
$790$	−5.04447			−0.179474
$791$	−5.35124			−0.190268
$792$	7.89730	−	6.05249i	0.280618	−	0.215066i
$793$	−15.4030			−0.546975
$794$	1.75661			0.0623398
$795$	−0.456730	+	1.57596i	−0.0161986	+	0.0558937i
$796$	−11.5909			−0.410827
$797$		−	2.66918i		−	0.0945472i	−0.998882	−	0.0472736i	$-0.984947\pi$
$797$		−	2.66918i		−	0.0945472i	0.998882	−	0.0472736i	$-0.0150533\pi$
$798$	−2.25425	+	7.77837i	−0.0797996	+	0.275351i
$799$			0.277414i			0.00981422i
$800$	−4.21647			−0.149075
$801$	10.7892	−	17.0508i	0.381217	−	0.602461i
$802$		−	15.9480i		−	0.563143i
$803$	−19.5582	−	7.19956i	−0.690193	−	0.254067i
$804$	6.09477	−	21.0302i	0.214946	−	0.741678i
$805$		−	0.958807i		−	0.0337935i
$806$		−	4.05814i		−	0.142942i
$807$	−37.0112	−	10.7262i	−1.30286	−	0.377581i
$808$	7.62685			0.268312
$809$	13.3476			0.469278			0.234639	−	0.972083i	$-0.424609\pi$
$809$	13.3476			0.469278			0.234639	+	0.972083i	$0.424609\pi$
$810$	−7.19936	+	3.41104i	−0.252960	+	0.119852i
$811$		−	35.4413i		−	1.24451i	−0.782813	−	0.622257i	$-0.786216\pi$
$811$		−	35.4413i		−	1.24451i	0.782813	−	0.622257i	$-0.213784\pi$
$812$		−	7.92374i		−	0.278069i
$813$	16.8470	+	4.88243i	0.590850	+	0.171234i
$814$	−0.678949	+	1.84442i	−0.0237971	+	0.0646467i
$815$			10.0735i			0.352859i
$816$	−0.655131	+	2.26055i	−0.0229342	+	0.0791351i
$817$	−4.63626			−0.162202
$818$			30.1031i			1.05253i
$819$	−3.36458	−	2.12899i	−0.117568	−	0.0743930i
$820$		−	1.53555i		−	0.0536237i
$821$	−6.77914			−0.236594			−0.118297	−	0.992978i	$-0.537743\pi$
$821$	−6.77914			−0.236594			−0.118297	+	0.992978i	$0.537743\pi$
$822$	−8.97961	−	2.60238i	−0.313200	−	0.0907685i
$823$	−22.6082			−0.788072			−0.394036	−	0.919095i	$-0.628921\pi$
$823$	−22.6082			−0.788072			−0.394036	+	0.919095i	$0.628921\pi$
$824$	−20.0904			−0.699881
$825$	−19.5032	−	14.3639i	−0.679013	−	0.500087i
$826$	−5.25570			−0.182869
$827$	−5.79344			−0.201458			−0.100729	−	0.994914i	$-0.532117\pi$
$827$	−5.79344			−0.201458			−0.100729	+	0.994914i	$0.532117\pi$
$828$	−1.73757	+	2.74599i	−0.0603848	+	0.0954299i
$829$	−41.8632			−1.45397			−0.726985	−	0.686653i	$-0.759079\pi$
$829$	−41.8632			−1.45397			−0.726985	+	0.686653i	$0.759079\pi$
$830$			8.81223i			0.305877i
$831$	38.6793	+	11.2097i	1.34177	+	0.388859i
$832$		−	1.32719i		−	0.0460121i
$833$	1.35883			0.0470808
$834$	2.04111	+	0.591536i	0.0706780	+	0.0204832i
$835$		−	14.6041i		−	0.505396i
$836$	−14.5527	−	5.35698i	−0.503314	−	0.185275i
$837$	11.8971	−	10.5307i	0.411223	−	0.363993i
$838$			16.0788i			0.555434i
$839$			1.43639i			0.0495895i	0.999693	+	0.0247948i	$0.00789323\pi$
$839$			1.43639i			0.0495895i	−0.999693	+	0.0247948i	$0.992107\pi$
$840$	−0.426766	+	1.47257i	−0.0147248	+	0.0508085i
$841$	33.7857			1.16503
$842$	−22.9765			−0.791824
$843$	−0.478868	+	1.65235i	−0.0164931	+	0.0569099i
$844$			25.2106i			0.867786i
$845$		−	9.94806i		−	0.342224i
$846$	0.327493	−	0.517558i	0.0112594	−	0.0177940i
$847$	7.13201	−	8.37463i	0.245059	−	0.287756i
$848$		−	1.07021i		−	0.0367513i
$849$	−40.3241	−	11.6863i	−1.38392	−	0.401074i
$850$	5.72948			0.196520
$851$		−	0.641890i		−	0.0220037i
$852$	23.4050	+	6.78302i	0.801843	+	0.232382i
$853$			43.6024i			1.49292i	0.665432	+	0.746459i	$0.268247\pi$
$853$			43.6024i			1.49292i	−0.665432	+	0.746459i	$0.731753\pi$
$854$	−11.6057			−0.397138
$855$	10.4922	+	6.63908i	0.358824	+	0.227052i
$856$	−19.3874			−0.662648
$857$	−15.9862			−0.546080			−0.273040	−	0.962003i	$-0.588029\pi$
$857$	−15.9862			−0.546080			−0.273040	+	0.962003i	$0.588029\pi$
$858$	4.52124	−	6.13889i	0.154353	−	0.209578i
$859$	28.5623			0.974534			0.487267	−	0.873253i	$-0.337994\pi$
$859$	28.5623			0.974534			0.487267	+	0.873253i	$0.337994\pi$
$860$	−0.877718			−0.0299299
$861$	2.88592	+	0.836368i	0.0983518	+	0.0285034i
$862$	−33.2578			−1.13277
$863$			19.3223i			0.657738i	0.944375	+	0.328869i	$0.106668\pi$
$863$			19.3223i			0.657738i	−0.944375	+	0.328869i	$0.893332\pi$
$864$	3.89087	−	3.44400i	0.132370	−	0.117167i
$865$		−	14.9402i		−	0.507982i
$866$	12.9146			0.438857
$867$	−7.30595	+	25.2094i	−0.248123	+	0.856157i
$868$		−	3.05769i		−	0.103785i
$869$	17.7374	+	6.52931i	0.601699	+	0.221492i
$870$	−11.6683	−	3.38158i	−0.395591	−	0.114646i
$871$		−	16.7776i		−	0.568487i
$872$		−	1.56081i		−	0.0528556i
$873$	9.90819	+	6.26957i	0.335341	+	0.212193i
$874$	5.06458			0.171312
$875$	8.15816			0.275796
$876$	−10.4538	−	3.02962i	−0.353201	−	0.102361i
$877$		−	21.5414i		−	0.727402i	−0.931516	−	0.363701i	$-0.881513\pi$
$877$		−	21.5414i		−	0.727402i	0.931516	−	0.363701i	$-0.118487\pi$
$878$			32.9061i			1.11053i
$879$	8.13195	−	28.0596i	0.274284	−	0.946426i
$880$	−2.75505	−	1.01416i	−0.0928727	−	0.0341874i
$881$			38.4341i			1.29488i	0.762118	+	0.647439i	$0.224160\pi$
$881$			38.4341i			1.29488i	−0.762118	+	0.647439i	$0.775840\pi$
$882$	−2.53511	−	1.60413i	−0.0853615	−	0.0540139i
$883$	−38.6995			−1.30234			−0.651171	−	0.758931i	$-0.725722\pi$
$883$	−38.6995			−1.30234			−0.651171	+	0.758931i	$0.725722\pi$
$884$			1.80343i			0.0606561i
$885$	−2.24295	+	7.73939i	−0.0753961	+	0.260157i
$886$		−	40.0370i		−	1.34507i
$887$	−2.29700			−0.0771257			−0.0385628	−	0.999256i	$-0.512278\pi$
$887$	−2.29700			−0.0771257			−0.0385628	+	0.999256i	$0.512278\pi$
$888$	−0.285706	+	0.985837i	−0.00958765	+	0.0330825i
$889$	−16.0113			−0.537001
$890$	−5.95356			−0.199564
$891$	29.7295	−	2.67541i	0.995975	−	0.0896296i
$892$	20.3866			0.682593
$893$	−0.954560			−0.0319431
$894$	−3.35741	+	11.5849i	−0.112289	+	0.387456i
$895$	−12.5269			−0.418727
$896$		−	1.00000i		−	0.0334077i
$897$	−0.693105	+	2.39158i	−0.0231421	+	0.0798526i
$898$		−	8.30936i		−	0.277287i
$899$	24.2283			0.808060
$900$	−10.6892	−	6.76377i	−0.356307	−	0.225459i
$901$			1.45424i			0.0484478i
$902$	−1.98754	+	5.39930i	−0.0661778	+	0.179777i
$903$	0.478067	−	1.64959i	0.0159091	−	0.0548948i
$904$		−	5.35124i		−	0.177980i
$905$			16.5612i			0.550513i
$906$	−9.99094	−	2.89548i	−0.331927	−	0.0961958i
$907$	48.6640			1.61586			0.807930	−	0.589278i	$-0.200588\pi$
$907$	48.6640			1.61586			0.807930	+	0.589278i	$0.200588\pi$
$908$	−10.2315			−0.339544
$909$	19.3349	+	12.2345i	0.641297	+	0.405791i
$910$			1.17479i			0.0389441i
$911$		−	10.6875i		−	0.354091i	−0.984203	−	0.177046i	$-0.943346\pi$
$911$		−	10.6875i		−	0.354091i	0.984203	−	0.177046i	$-0.0566540\pi$
$912$	−7.77837	−	2.25425i	−0.257568	−	0.0746457i
$913$	11.4061	−	30.9856i	0.377488	−	1.02547i
$914$			30.7070i			1.01570i
$915$	−4.95290	+	17.0902i	−0.163738	+	0.564983i
$916$	−12.2421			−0.404489
$917$			18.5001i			0.610925i
$918$	−5.28705	+	4.67982i	−0.174499	+	0.154457i
$919$		−	28.8956i		−	0.953178i	−0.879126	−	0.476589i	$-0.841873\pi$
$919$		−	28.8956i		−	0.953178i	0.879126	−	0.476589i	$-0.158127\pi$
$920$	0.958807			0.0316109
$921$	40.5933	+	11.7644i	1.33759	+	0.387649i
$922$	38.3614			1.26337
$923$	18.6722			0.614603
$924$	3.40662	−	4.62547i	0.112069	−	0.152167i
$925$	2.49865			0.0821552
$926$	10.0360			0.329805
$927$	−50.9312	−	32.2276i	−1.67280	−	1.05849i
$928$	7.92374			0.260110
$929$		−	4.97285i		−	0.163154i	−0.996667	−	0.0815769i	$-0.974004\pi$
$929$		−	4.97285i		−	0.163154i	0.996667	−	0.0815769i	$-0.0259956\pi$
$930$	−4.50266	−	1.30492i	−0.147648	−	0.0427899i
$931$			4.67563i			0.153238i
$932$	−9.73995			−0.319043
$933$	−4.47806	−	1.29779i	−0.146605	−	0.0424876i
$934$			1.71995i			0.0562784i
$935$	3.74366	+	1.37808i	0.122431	+	0.0450680i
$936$	2.12899	−	3.36458i	0.0695882	−	0.109975i
$937$		−	21.5525i		−	0.704090i	−0.935983	−	0.352045i	$-0.885486\pi$
$937$		−	21.5525i		−	0.704090i	0.935983	−	0.352045i	$-0.114514\pi$
$938$		−	12.6414i		−	0.412757i
$939$	−8.08120	+	27.8845i	−0.263720	+	0.909975i
$940$	−0.180713			−0.00589422
$941$	8.71525			0.284109			0.142055	−	0.989859i	$-0.454629\pi$
$941$	8.71525			0.284109			0.142055	+	0.989859i	$0.454629\pi$
$942$	−3.97100	+	13.7021i	−0.129382	+	0.446438i
$943$		−	1.87905i		−	0.0611904i
$944$		−	5.25570i		−	0.171059i
$945$	−3.44409	+	3.04853i	−0.112036	+	0.0991688i
$946$	3.08624	+	1.13608i	0.100342	+	0.0369370i
$947$			36.1777i			1.17562i	0.809000	+	0.587809i	$0.200009\pi$
$947$			36.1777i			1.17562i	−0.809000	+	0.587809i	$0.799991\pi$
$948$	9.48059	+	2.74757i	0.307915	+	0.0892370i
$949$	−8.33989			−0.270724
$950$			19.7147i			0.639628i
$951$	44.8656	+	13.0025i	1.45487	+	0.421635i
$952$			1.35883i			0.0440401i
$953$	44.5878			1.44434			0.722170	−	0.691716i	$-0.243145\pi$
$953$	44.5878			1.44434			0.722170	+	0.691716i	$0.243145\pi$
$954$	1.71676	−	2.71310i	0.0555822	−	0.0878400i
$955$	−13.8329			−0.447622
$956$	6.32689			0.204626
$957$	36.6510	+	26.9932i	1.18476	+	0.872565i
$958$	−22.7932			−0.736413
$959$	−5.39771			−0.174301
$960$	−1.47257	−	0.426766i	−0.0475270	−	0.0137738i
$961$	−21.6505			−0.698405
$962$			0.786486i			0.0253573i
$963$	−49.1491	−	31.0999i	−1.58381	−	1.00218i
$964$		−	9.56291i		−	0.308001i
$965$	−17.7838			−0.572482
$966$	−0.522234	+	1.80199i	−0.0168026	+	0.0579779i
$967$			3.65013i			0.117380i	0.998276	+	0.0586901i	$0.0186924\pi$
$967$			3.65013i			0.117380i	−0.998276	+	0.0586901i	$0.981308\pi$
$968$	8.37463	+	7.13201i	0.269171	+	0.229231i
$969$	10.5695	+	3.06315i	0.339542	+	0.0984026i
$970$		−	3.45960i		−	0.111081i
$971$		−	32.1772i		−	1.03262i	−0.856403	−	0.516308i	$-0.827306\pi$
$971$		−	32.1772i		−	1.03262i	0.856403	−	0.516308i	$-0.172694\pi$
$972$	15.3884	−	2.48944i	0.493583	−	0.0798490i
$973$	1.22693			0.0393335
$974$	12.6749			0.406129
$975$	−9.30960	−	2.69802i	−0.298146	−	0.0864057i
$976$		−	11.6057i		−	0.371488i
$977$			17.5791i			0.562406i	0.959648	+	0.281203i	$0.0907334\pi$
$977$			17.5791i			0.562406i	−0.959648	+	0.281203i	$0.909267\pi$
$978$	5.48673	−	18.9322i	0.175446	−	0.605384i
$979$	20.9339	+	7.70600i	0.669051	+	0.246285i
$980$			0.885172i			0.0282758i
$981$	2.50374	−	3.95681i	0.0799382	−	0.126331i
$982$	−5.54324			−0.176892
$983$			42.0172i			1.34014i	0.742298	+	0.670070i	$0.233736\pi$
$983$			42.0172i			1.34014i	−0.742298	+	0.670070i	$0.766264\pi$
$984$	−0.836368	+	2.88592i	−0.0266624	+	0.0919997i
$985$			9.73442i			0.310165i
$986$	−10.7671			−0.342893
$987$	0.0984293	−	0.339634i	0.00313304	−	0.0108107i
$988$	−6.20547			−0.197422
$989$	−1.07407			−0.0341533
$990$	−5.35750	−	6.99047i	−0.170272	−	0.222172i
$991$	−23.8928			−0.758981			−0.379490	−	0.925196i	$-0.623901\pi$
$991$	−23.8928			−0.758981			−0.379490	+	0.925196i	$0.623901\pi$
$992$	3.05769			0.0970817
$993$	−9.70715	+	33.4949i	−0.308047	+	1.06293i
$994$	14.0689			0.446240
$995$			10.2599i			0.325261i
$996$	4.79976	−	16.5617i	0.152086	−	0.524779i
$997$			22.1120i			0.700294i	0.936695	+	0.350147i	$0.113868\pi$
$997$			22.1120i			0.700294i	−0.936695	+	0.350147i	$0.886132\pi$
$998$	1.41705			0.0448560
$999$	−2.30571	+	2.04089i	−0.0729493	+	0.0645710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.c.a.197.5	✓	12
3.2	odd	2		462.2.c.b.197.6	yes	12
11.10	odd	2		462.2.c.b.197.5	yes	12
33.32	even	2	inner	462.2.c.a.197.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.c.a.197.5	✓	12	1.1	even	1	trivial
462.2.c.a.197.6	yes	12	33.32	even	2	inner
462.2.c.b.197.5	yes	12	11.10	odd	2
462.2.c.b.197.6	yes	12	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.482127 - 1.66360i) q^{3} +1.00000 q^{4} -0.885172i q^{5} +(-0.482127 + 1.66360i) q^{6} +1.00000i q^{7} -1.00000 q^{8} +(-2.53511 - 1.60413i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.482127 - 1.66360i) q^{3} +1.00000 q^{4} -0.885172i q^{5} +(-0.482127 + 1.66360i) q^{6} +1.00000i q^{7} -1.00000 q^{8} +(-2.53511 - 1.60413i) q^{9} +0.885172i q^{10} +(1.14572 - 3.11245i) q^{11} +(0.482127 - 1.66360i) q^{12} -1.32719i q^{13} -1.00000i q^{14} +(-1.47257 - 0.426766i) q^{15} +1.00000 q^{16} -1.35883 q^{17} +(2.53511 + 1.60413i) q^{18} -4.67563i q^{19} -0.885172i q^{20} +(1.66360 + 0.482127i) q^{21} +(-1.14572 + 3.11245i) q^{22} -1.08319i q^{23} +(-0.482127 + 1.66360i) q^{24} +4.21647 q^{25} +1.32719i q^{26} +(-3.89087 + 3.44400i) q^{27} +1.00000i q^{28} -7.92374 q^{29} +(1.47257 + 0.426766i) q^{30} -3.05769 q^{31} -1.00000 q^{32} +(-4.62547 - 3.40662i) q^{33} +1.35883 q^{34} +0.885172 q^{35} +(-2.53511 - 1.60413i) q^{36} +0.592594 q^{37} +4.67563i q^{38} +(-2.20791 - 0.639876i) q^{39} +0.885172i q^{40} +1.73475 q^{41} +(-1.66360 - 0.482127i) q^{42} -0.991579i q^{43} +(1.14572 - 3.11245i) q^{44} +(-1.41993 + 2.24401i) q^{45} +1.08319i q^{46} -0.204156i q^{47} +(0.482127 - 1.66360i) q^{48} -1.00000 q^{49} -4.21647 q^{50} +(-0.655131 + 2.26055i) q^{51} -1.32719i q^{52} -1.07021i q^{53} +(3.89087 - 3.44400i) q^{54} +(-2.75505 - 1.01416i) q^{55} -1.00000i q^{56} +(-7.77837 - 2.25425i) q^{57} +7.92374 q^{58} -5.25570i q^{59} +(-1.47257 - 0.426766i) q^{60} -11.6057i q^{61} +3.05769 q^{62} +(1.60413 - 2.53511i) q^{63} +1.00000 q^{64} -1.17479 q^{65} +(4.62547 + 3.40662i) q^{66} +12.6414 q^{67} -1.35883 q^{68} +(-1.80199 - 0.522234i) q^{69} -0.885172 q^{70} +14.0689i q^{71} +(2.53511 + 1.60413i) q^{72} -6.28386i q^{73} -0.592594 q^{74} +(2.03288 - 7.01450i) q^{75} -4.67563i q^{76} +(3.11245 + 1.14572i) q^{77} +(2.20791 + 0.639876i) q^{78} +5.69885i q^{79} -0.885172i q^{80} +(3.85353 + 8.13328i) q^{81} -1.73475 q^{82} +9.95539 q^{83} +(1.66360 + 0.482127i) q^{84} +1.20280i q^{85} +0.991579i q^{86} +(-3.82025 + 13.1819i) q^{87} +(-1.14572 + 3.11245i) q^{88} +6.72588i q^{89} +(1.41993 - 2.24401i) q^{90} +1.32719 q^{91} -1.08319i q^{92} +(-1.47419 + 5.08676i) q^{93} +0.204156i q^{94} -4.13874 q^{95} +(-0.482127 + 1.66360i) q^{96} -3.90839 q^{97} +1.00000 q^{98} +(-7.89730 + 6.05249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8	\( 12 q - 12 q^{2} + 4 q^{3} + 12 q^{4} - 4 q^{6} - 12 q^{8} - 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} - 4 q^{17} + 8 q^{22} - 4 q^{24} - 28 q^{25} - 8 q^{27} + 8 q^{29} - 4 q^{30} + 12 q^{31} - 12 q^{32} + 16 q^{33} + 4 q^{34} - 4 q^{35} - 36 q^{39} + 20 q^{41} - 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} + 28 q^{50} + 8 q^{51} + 8 q^{54} + 4 q^{55} + 28 q^{57} - 8 q^{58} + 4 q^{60} - 12 q^{62} + 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} + 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} + 44 q^{83} + 8 q^{87} + 8 q^{88} + 12 q^{90} - 24 q^{91} - 24 q^{93} - 4 q^{96} - 48 q^{97} + 12 q^{98} + 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 4 * q^3 + 12 * q^4 - 4 * q^6 - 12 * q^8 - 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 - 4 * q^17 + 8 * q^22 - 4 * q^24 - 28 * q^25 - 8 * q^27 + 8 * q^29 - 4 * q^30 + 12 * q^31 - 12 * q^32 + 16 * q^33 + 4 * q^34 - 4 * q^35 - 36 * q^39 + 20 * q^41 - 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 + 28 * q^50 + 8 * q^51 + 8 * q^54 + 4 * q^55 + 28 * q^57 - 8 * q^58 + 4 * q^60 - 12 * q^62 + 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 - 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 + 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 + 44 * q^83 + 8 * q^87 + 8 * q^88 + 12 * q^90 - 24 * q^91 - 24 * q^93 - 4 * q^96 - 48 * q^97 + 12 * q^98 + 36 * q^99

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