LMFDB - Embedded newform 624.2.q.j.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(289,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("624.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.q (of order $3$, degree $2$, not 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2101707.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} - 4x^{3} - 12x^{2} - 18x + 31 $ x^6 + 6x^4 - 4x^3 - 12x^2 - 18x + 31
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$-1.18073 + 1.01456i$ of defining polynomial
Character	$\chi$	$=$	624.529
Dual form			624.2.q.j.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} -3.93800 q^{5} +(0.892467 + 1.54580i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} -3.93800 q^{5} +(0.892467 + 1.54580i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.36147 - 4.09018i) q^{11} +(-2.86147 - 2.19363i) q^{13} +(1.96900 - 3.41041i) q^{15} +(-0.392467 - 0.679773i) q^{17} +(2.57653 + 4.46269i) q^{19} -1.78493 q^{21} +(2.36147 - 4.09018i) q^{23} +10.5079 q^{25} +1.00000 q^{27} +(3.96900 - 6.87451i) q^{29} +2.93800 q^{31} +(2.36147 + 4.09018i) q^{33} +(-3.51454 - 6.08736i) q^{35} +(-0.607533 + 1.05228i) q^{37} +(3.33047 - 1.38129i) q^{39} +(4.33047 - 7.50059i) q^{41} +(-3.10753 - 5.38241i) q^{43} +(1.96900 + 3.41041i) q^{45} -0.722938 q^{47} +(1.90701 - 3.30303i) q^{49} +0.784934 q^{51} -13.8140 q^{53} +(-9.29947 + 16.1072i) q^{55} -5.15307 q^{57} +(0.215066 + 0.372505i) q^{59} +(-2.07653 - 3.59666i) q^{61} +(0.892467 - 1.54580i) q^{63} +(11.2685 + 8.63851i) q^{65} +(4.89247 - 8.47400i) q^{67} +(2.36147 + 4.09018i) q^{69} +(4.36147 + 7.55429i) q^{71} +4.87601 q^{73} +(-5.25394 + 9.10008i) q^{75} +8.43013 q^{77} -16.3839 q^{79} +(-0.500000 + 0.866025i) q^{81} -6.59894 q^{83} +(1.54554 + 2.67695i) q^{85} +(3.96900 + 6.87451i) q^{87} +(-7.93800 + 13.7490i) q^{89} +(0.837137 - 6.38099i) q^{91} +(-1.46900 + 2.54439i) q^{93} +(-10.1464 - 17.5741i) q^{95} +(-1.53100 - 2.65177i) q^{97} -4.72294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	$ 6 q - 3 q^{3} + 3 q^{7} - 3 q^{9} - 3 q^{13} + 6 q^{19} - 6 q^{21} + 30 q^{25} + 6 q^{27} + 12 q^{29} - 6 q^{31} + 12 q^{35} - 6 q^{37} - 6 q^{39} - 21 q^{43} + 24 q^{47} - 24 q^{49} - 12 q^{53} - 18 q^{55} - 12 q^{57} + 6 q^{59} - 3 q^{61} + 3 q^{63} + 18 q^{65} + 27 q^{67} + 12 q^{71} - 18 q^{73} - 15 q^{75} + 60 q^{77} - 18 q^{79} - 3 q^{81} + 36 q^{83} - 12 q^{85} + 12 q^{87} - 24 q^{89} - 21 q^{91} + 3 q^{93} - 42 q^{95} - 21 q^{97}+O(q^{100}) $ 6 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 - 3 * q^13 + 6 * q^19 - 6 * q^21 + 30 * q^25 + 6 * q^27 + 12 * q^29 - 6 * q^31 + 12 * q^35 - 6 * q^37 - 6 * q^39 - 21 * q^43 + 24 * q^47 - 24 * q^49 - 12 * q^53 - 18 * q^55 - 12 * q^57 + 6 * q^59 - 3 * q^61 + 3 * q^63 + 18 * q^65 + 27 * q^67 + 12 * q^71 - 18 * q^73 - 15 * q^75 + 60 * q^77 - 18 * q^79 - 3 * q^81 + 36 * q^83 - 12 * q^85 + 12 * q^87 - 24 * q^89 - 21 * q^91 + 3 * q^93 - 42 * q^95 - 21 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−3.93800			−1.76113			−0.880564	−	0.473927i	$-0.842836\pi$
$5$	−3.93800			−1.76113			−0.880564	+	0.473927i	$0.842836\pi$
$6$		0			0
$7$	0.892467	+	1.54580i	0.337321	+	0.584257i	0.983928	−	0.178566i	$-0.0571460\pi$
$7$	0.892467	+	1.54580i	0.337321	+	0.584257i	−0.646607	+	0.762823i	$0.723813\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	2.36147	−	4.09018i	0.712010	−	1.23324i	−0.252092	−	0.967703i	$-0.581119\pi$
$11$	2.36147	−	4.09018i	0.712010	−	1.23324i	0.964102	−	0.265534i	$-0.0855481\pi$
$12$		0			0
$13$	−2.86147	−	2.19363i	−0.793629	−	0.608402i
$13$	−2.86147	−	2.19363i	−0.793629	−	0.608402i
$14$		0			0
$15$	1.96900	−	3.41041i	0.508394	−	0.880564i
$16$		0			0
$17$	−0.392467	−	0.679773i	−0.0951872	−	0.164869i	0.814500	−	0.580164i	$-0.197012\pi$
$17$	−0.392467	−	0.679773i	−0.0951872	−	0.164869i	−0.909687	+	0.415295i	$0.863678\pi$
$18$		0			0
$19$	2.57653	+	4.46269i	0.591098	+	1.02381i	0.994085	+	0.108606i	$0.0346385\pi$
$19$	2.57653	+	4.46269i	0.591098	+	1.02381i	−0.402987	+	0.915206i	$0.632028\pi$
$20$		0			0
$21$	−1.78493			−0.389505
$22$		0			0
$23$	2.36147	−	4.09018i	0.492400	−	0.852862i	−0.507561	−	0.861616i	$-0.669453\pi$
$23$	2.36147	−	4.09018i	0.492400	−	0.852862i	0.999962	+	0.00875329i	$0.00278629\pi$
$24$		0			0
$25$	10.5079			2.10157
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.96900	−	6.87451i	0.737025	−	1.27656i	−0.216804	−	0.976215i	$-0.569563\pi$
$29$	3.96900	−	6.87451i	0.737025	−	1.27656i	0.953829	−	0.300350i	$-0.0971034\pi$
$30$		0			0
$31$	2.93800			0.527681			0.263841	−	0.964566i	$-0.415011\pi$
$31$	2.93800			0.527681			0.263841	+	0.964566i	$0.415011\pi$
$32$		0			0
$33$	2.36147	+	4.09018i	0.411079	+	0.712010i
$34$		0			0
$35$	−3.51454	−	6.08736i	−0.594065	−	1.02895i
$36$		0			0
$37$	−0.607533	+	1.05228i	−0.0998778	+	0.172993i	−0.911634	−	0.411003i	$-0.865179\pi$
$37$	−0.607533	+	1.05228i	−0.0998778	+	0.172993i	0.811756	+	0.583997i	$0.198512\pi$
$38$		0			0
$39$	3.33047	−	1.38129i	0.533302	−	0.221184i
$40$		0			0
$41$	4.33047	−	7.50059i	0.676306	−	1.17140i	−0.299779	−	0.954009i	$-0.596913\pi$
$41$	4.33047	−	7.50059i	0.676306	−	1.17140i	0.976085	−	0.217388i	$-0.0697536\pi$
$42$		0			0
$43$	−3.10753	−	5.38241i	−0.473894	−	0.820809i	0.525659	−	0.850695i	$-0.323819\pi$
$43$	−3.10753	−	5.38241i	−0.473894	−	0.820809i	−0.999553	+	0.0298863i	$0.990485\pi$
$44$		0			0
$45$	1.96900	+	3.41041i	0.293521	+	0.508394i
$46$		0			0
$47$	−0.722938			−0.105451			−0.0527256	−	0.998609i	$-0.516791\pi$
$47$	−0.722938			−0.105451			−0.0527256	+	0.998609i	$0.516791\pi$
$48$		0			0
$49$	1.90701	−	3.30303i	0.272429	−	0.471861i
$50$		0			0
$51$	0.784934			0.109913
$52$		0			0
$53$	−13.8140			−1.89750			−0.948750	−	0.316027i	$-0.897651\pi$
$53$	−13.8140			−1.89750			−0.948750	+	0.316027i	$0.897651\pi$
$54$		0			0
$55$	−9.29947	+	16.1072i	−1.25394	+	2.17189i
$56$		0			0
$57$	−5.15307			−0.682541
$58$		0			0
$59$	0.215066	+	0.372505i	0.0279992	+	0.0484960i	0.879685	−	0.475556i	$-0.157753\pi$
$59$	0.215066	+	0.372505i	0.0279992	+	0.0484960i	−0.851686	+	0.524052i	$0.824420\pi$
$60$		0			0
$61$	−2.07653	−	3.59666i	−0.265873	−	0.460506i	0.701919	−	0.712257i	$-0.252327\pi$
$61$	−2.07653	−	3.59666i	−0.265873	−	0.460506i	−0.967792	+	0.251751i	$0.918994\pi$
$62$		0			0
$63$	0.892467	−	1.54580i	0.112440	−	0.194752i
$64$		0			0
$65$	11.2685	+	8.63851i	1.39768	+	1.07148i
$66$		0			0
$67$	4.89247	−	8.47400i	0.597710	−	1.03526i	−0.395448	−	0.918488i	$-0.629411\pi$
$67$	4.89247	−	8.47400i	0.597710	−	1.03526i	0.993158	−	0.116776i	$-0.0372559\pi$
$68$		0			0
$69$	2.36147	+	4.09018i	0.284287	+	0.492400i
$70$		0			0
$71$	4.36147	+	7.55429i	0.517611	+	0.896529i	0.999791	+	0.0204564i	$0.00651192\pi$
$71$	4.36147	+	7.55429i	0.517611	+	0.896529i	−0.482180	+	0.876072i	$0.660155\pi$
$72$		0			0
$73$	4.87601			0.570693			0.285347	−	0.958424i	$-0.407891\pi$
$73$	4.87601			0.570693			0.285347	+	0.958424i	$0.407891\pi$
$74$		0			0
$75$	−5.25394	+	9.10008i	−0.606672	+	1.05079i
$76$		0			0
$77$	8.43013			0.960703
$78$		0			0
$79$	−16.3839			−1.84333			−0.921665	−	0.387986i	$-0.873171\pi$
$79$	−16.3839			−1.84333			−0.921665	+	0.387986i	$0.873171\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−6.59894			−0.724328			−0.362164	−	0.932114i	$-0.617962\pi$
$83$	−6.59894			−0.724328			−0.362164	+	0.932114i	$0.617962\pi$
$84$		0			0
$85$	1.54554	+	2.67695i	0.167637	+	0.290356i
$86$		0			0
$87$	3.96900	+	6.87451i	0.425522	+	0.737025i
$88$		0			0
$89$	−7.93800	+	13.7490i	−0.841427	+	1.45739i	0.0472619	+	0.998883i	$0.484950\pi$
$89$	−7.93800	+	13.7490i	−0.841427	+	1.45739i	−0.888689	+	0.458511i	$0.848383\pi$
$90$		0			0
$91$	0.837137	−	6.38099i	0.0877558	−	0.668910i
$92$		0			0
$93$	−1.46900	+	2.54439i	−0.152328	+	0.263841i
$94$		0			0
$95$	−10.1464	−	17.5741i	−1.04100	−	1.80306i
$96$		0			0
$97$	−1.53100	−	2.65177i	−0.155449	−	0.269246i	0.777773	−	0.628545i	$-0.216349\pi$
$97$	−1.53100	−	2.65177i	−0.155449	−	0.269246i	−0.933223	+	0.359299i	$0.883016\pi$
$98$		0			0
$99$	−4.72294			−0.474673
$100$		0			0
$101$	0.815932	−	1.41324i	0.0811883	−	0.140622i	−0.822572	−	0.568661i	$-0.807462\pi$
$101$	0.815932	−	1.41324i	0.0811883	−	0.140622i	0.903761	+	0.428038i	$0.140795\pi$
$102$		0			0
$103$	7.66094			0.754855			0.377427	−	0.926039i	$-0.376809\pi$
$103$	7.66094			0.754855			0.377427	+	0.926039i	$0.376809\pi$
$104$		0			0
$105$	7.02908			0.685968
$106$		0			0
$107$	0.361469	−	0.626082i	0.0349445	−	0.0605257i	−0.848024	−	0.529957i	$-0.822208\pi$
$107$	0.361469	−	0.626082i	0.0349445	−	0.0605257i	0.882969	+	0.469432i	$0.155541\pi$
$108$		0			0
$109$	5.36814			0.514174			0.257087	−	0.966388i	$-0.417237\pi$
$109$	5.36814			0.514174			0.257087	+	0.966388i	$0.417237\pi$
$110$		0			0
$111$	−0.607533	−	1.05228i	−0.0576645	−	0.0998778i
$112$		0			0
$113$	−6.60753	−	11.4446i	−0.621584	−	1.07662i	−0.989191	−	0.146634i	$-0.953156\pi$
$113$	−6.60753	−	11.4446i	−0.621584	−	1.07662i	0.367606	−	0.929981i	$-0.380177\pi$
$114$		0			0
$115$	−9.29947	+	16.1072i	−0.867180	+	1.50200i
$116$		0			0
$117$	−0.469002	+	3.57492i	−0.0433592	+	0.330501i
$118$		0			0
$119$	0.700528	−	1.21335i	0.0642173	−	0.111228i
$120$		0			0
$121$	−5.65307	−	9.79140i	−0.513915	−	0.890128i
$122$		0			0
$123$	4.33047	+	7.50059i	0.390465	+	0.676306i
$124$		0			0
$125$	−21.6900			−1.94001
$126$		0			0
$127$	8.19194	−	14.1889i	0.726917	−	1.25906i	−0.231263	−	0.972891i	$-0.574286\pi$
$127$	8.19194	−	14.1889i	0.726917	−	1.25906i	0.958180	−	0.286166i	$-0.0923809\pi$
$128$		0			0
$129$	6.21507			0.547206
$130$		0			0
$131$	21.0157			1.83615			0.918077	−	0.396402i	$-0.129741\pi$
$131$	21.0157			1.83615			0.918077	+	0.396402i	$0.129741\pi$
$132$		0			0
$133$	−4.59894	+	7.96561i	−0.398779	+	0.690706i
$134$		0			0
$135$	−3.93800			−0.338929
$136$		0			0
$137$	−6.26847	−	10.8573i	−0.535552	−	0.927603i	−0.999136	−	0.0415504i	$-0.986770\pi$
$137$	−6.26847	−	10.8573i	−0.535552	−	0.927603i	0.463585	−	0.886053i	$-0.346563\pi$
$138$		0			0
$139$	4.40701	+	7.63316i	0.373797	+	0.647436i	0.990146	−	0.140037i	$-0.0447222\pi$
$139$	4.40701	+	7.63316i	0.373797	+	0.647436i	−0.616349	+	0.787473i	$0.711389\pi$
$140$		0			0
$141$	0.361469	−	0.626082i	0.0304412	−	0.0527256i
$142$		0			0
$143$	−15.7296	+	6.52375i	−1.31538	+	0.545544i
$144$		0			0
$145$	−15.6299	+	27.0719i	−1.29800	+	2.24820i
$146$		0			0
$147$	1.90701	+	3.30303i	0.157287	+	0.272429i
$148$		0			0
$149$	−1.81593	−	3.14529i	−0.148767	−	0.257672i	0.782005	−	0.623272i	$-0.214197\pi$
$149$	−1.81593	−	3.14529i	−0.148767	−	0.257672i	−0.930772	+	0.365600i	$0.880864\pi$
$150$		0			0
$151$	14.5989			1.18805			0.594023	−	0.804448i	$-0.297539\pi$
$151$	14.5989			1.18805			0.594023	+	0.804448i	$0.297539\pi$
$152$		0			0
$153$	−0.392467	+	0.679773i	−0.0317291	+	0.0549564i
$154$		0			0
$155$	−11.5699			−0.929314
$156$		0			0
$157$	−15.5989			−1.24493			−0.622466	−	0.782647i	$-0.713869\pi$
$157$	−15.5989			−1.24493			−0.622466	+	0.782647i	$0.713869\pi$
$158$		0			0
$159$	6.90701	−	11.9633i	0.547761	−	0.948750i
$160$		0			0
$161$	8.43013			0.664387
$162$		0			0
$163$	5.46900	+	9.47259i	0.428365	+	0.741950i	0.996728	−	0.0808276i	$-0.0257563\pi$
$163$	5.46900	+	9.47259i	0.428365	+	0.741950i	−0.568363	+	0.822778i	$0.692423\pi$
$164$		0			0
$165$	−9.29947	−	16.1072i	−0.723963	−	1.25394i
$166$		0			0
$167$	−10.2928	+	17.8277i	−0.796481	+	1.37955i	0.125413	+	0.992105i	$0.459974\pi$
$167$	−10.2928	+	17.8277i	−0.796481	+	1.37955i	−0.921894	+	0.387441i	$0.873359\pi$
$168$		0			0
$169$	3.37601	+	12.5540i	0.259693	+	0.965691i
$170$		0			0
$171$	2.57653	−	4.46269i	0.197033	−	0.341270i
$172$		0			0
$173$	0.153069	+	0.265124i	0.0116377	+	0.0201570i	0.871786	−	0.489888i	$-0.162962\pi$
$173$	0.153069	+	0.265124i	0.0116377	+	0.0201570i	−0.860148	+	0.510045i	$0.829629\pi$
$174$		0			0
$175$	9.37793	+	16.2430i	0.708905	+	1.22786i
$176$		0			0
$177$	−0.430132			−0.0323307
$178$		0			0
$179$	−1.42347	+	2.46551i	−0.106395	+	0.184281i	−0.914307	−	0.405021i	$-0.867264\pi$
$179$	−1.42347	+	2.46551i	−0.106395	+	0.184281i	0.807912	+	0.589303i	$0.200597\pi$
$180$		0			0
$181$	13.2151			0.982268			0.491134	−	0.871084i	$-0.336583\pi$
$181$	13.2151			0.982268			0.491134	+	0.871084i	$0.336583\pi$
$182$		0			0
$183$	4.15307			0.307004
$184$		0			0
$185$	2.39247	−	4.14387i	0.175898	−	0.304664i
$186$		0			0
$187$	−3.70719			−0.271097
$188$		0			0
$189$	0.892467	+	1.54580i	0.0649174	+	0.112440i
$190$		0			0
$191$	−1.78493	−	3.09160i	−0.129153	−	0.223700i	0.794195	−	0.607662i	$-0.207893\pi$
$191$	−1.78493	−	3.09160i	−0.129153	−	0.223700i	−0.923349	+	0.383962i	$0.874559\pi$
$192$		0			0
$193$	−6.22294	+	10.7784i	−0.447937	+	0.775849i	−0.998252	−	0.0591079i	$-0.981174\pi$
$193$	−6.22294	+	10.7784i	−0.447937	+	0.775849i	0.550315	+	0.834957i	$0.314508\pi$
$194$		0			0
$195$	−13.1154	+	5.43953i	−0.939214	+	0.389533i
$196$		0			0
$197$	4.36814	−	7.56583i	0.311217	−	0.539043i	−0.667409	−	0.744691i	$-0.732597\pi$
$197$	4.36814	−	7.56583i	0.311217	−	0.539043i	0.978626	+	0.205648i	$0.0659301\pi$
$198$		0			0
$199$	−8.04554	−	13.9353i	−0.570333	−	0.987846i	−0.996532	−	0.0832160i	$-0.973481\pi$
$199$	−8.04554	−	13.9353i	−0.570333	−	0.987846i	0.426199	−	0.904630i	$-0.359852\pi$
$200$		0			0
$201$	4.89247	+	8.47400i	0.345088	+	0.597710i
$202$		0			0
$203$	14.1688			0.994456
$204$		0			0
$205$	−17.0534	+	29.5374i	−1.19106	+	2.06298i
$206$		0			0
$207$	−4.72294			−0.328267
$208$		0			0
$209$	24.3376			1.68347
$210$		0			0
$211$	2.19194	−	3.79655i	0.150899	−	0.261365i	−0.780659	−	0.624957i	$-0.785116\pi$
$211$	2.19194	−	3.79655i	0.150899	−	0.261365i	0.931558	+	0.363592i	$0.118450\pi$
$212$		0			0
$213$	−8.72294			−0.597686
$214$		0			0
$215$	12.2375	+	21.1959i	0.834589	+	1.44555i
$216$		0			0
$217$	2.62207	+	4.54156i	0.177998	+	0.308301i
$218$		0			0
$219$	−2.43800	+	4.22275i	−0.164745	+	0.285347i
$220$		0			0
$221$	−0.368135	+	2.80607i	−0.0247635	+	0.188757i
$222$		0			0
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$		0			0
$225$	−5.25394	−	9.10008i	−0.350262	−	0.606672i
$226$		0			0
$227$	−8.86934	−	15.3621i	−0.588679	−	1.01962i	−0.994406	−	0.105627i	$-0.966315\pi$
$227$	−8.86934	−	15.3621i	−0.588679	−	1.01962i	0.405727	−	0.913994i	$-0.367018\pi$
$228$		0			0
$229$	11.4459			0.756365			0.378182	−	0.925731i	$-0.376549\pi$
$229$	11.4459			0.756365			0.378182	+	0.925731i	$0.376549\pi$
$230$		0			0
$231$	−4.21507	+	7.30071i	−0.277331	+	0.480351i
$232$		0			0
$233$	−9.75201			−0.638876			−0.319438	−	0.947607i	$-0.603494\pi$
$233$	−9.75201			−0.638876			−0.319438	+	0.947607i	$0.603494\pi$
$234$		0			0
$235$	2.84693			0.185713
$236$		0			0
$237$	8.19194	−	14.1889i	0.532124	−	0.921665i
$238$		0			0
$239$	−6.59894			−0.426850			−0.213425	−	0.976959i	$-0.568462\pi$
$239$	−6.59894			−0.426850			−0.213425	+	0.976959i	$0.568462\pi$
$240$		0			0
$241$	−11.9070	−	20.6235i	−0.766998	−	1.32848i	−0.939184	−	0.343414i	$-0.888416\pi$
$241$	−11.9070	−	20.6235i	−0.766998	−	1.32848i	0.172186	−	0.985064i	$-0.444917\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−7.50979	+	13.0073i	−0.479783	+	0.831009i
$246$		0			0
$247$	2.41680	−	18.4218i	0.153777	−	1.17215i
$248$		0			0
$249$	3.29947	−	5.71485i	0.209096	−	0.362164i
$250$		0			0
$251$	4.72294	+	8.18037i	0.298109	+	0.516340i	0.975703	−	0.219096i	$-0.0703107\pi$
$251$	4.72294	+	8.18037i	0.298109	+	0.516340i	−0.677594	+	0.735436i	$0.736977\pi$
$252$		0			0
$253$	−11.1531	−	19.3177i	−0.701187	−	1.21449i
$254$		0			0
$255$	−3.09107			−0.193570
$256$		0			0
$257$	6.33047	−	10.9647i	0.394884	−	0.683959i	−0.598202	−	0.801345i	$-0.704118\pi$
$257$	6.33047	−	10.9647i	0.394884	−	0.683959i	0.993086	+	0.117386i	$0.0374515\pi$
$258$		0			0
$259$	−2.16881			−0.134763
$260$		0			0
$261$	−7.93800			−0.491350
$262$		0			0
$263$	−0.146403	+	0.253577i	−0.00902758	+	0.0156362i	−0.870504	−	0.492162i	$-0.836207\pi$
$263$	−0.146403	+	0.253577i	−0.00902758	+	0.0156362i	0.861476	+	0.507798i	$0.169540\pi$
$264$		0			0
$265$	54.3996			3.34174
$266$		0			0
$267$	−7.93800	−	13.7490i	−0.485798	−	0.841427i
$268$		0			0
$269$	−2.78493	−	4.82365i	−0.169800	−	0.294103i	0.768549	−	0.639791i	$-0.220979\pi$
$269$	−2.78493	−	4.82365i	−0.169800	−	0.294103i	−0.938350	+	0.345688i	$0.887646\pi$
$270$		0			0
$271$	5.97687	−	10.3522i	0.363069	−	0.628854i	−0.625395	−	0.780308i	$-0.715062\pi$
$271$	5.97687	−	10.3522i	0.363069	−	0.628854i	0.988464	+	0.151454i	$0.0483955\pi$
$272$		0			0
$273$	5.10753	+	3.91548i	0.309122	+	0.236976i
$274$		0			0
$275$	24.8140	−	42.9791i	1.49634	−	2.59174i
$276$		0			0
$277$	−9.33047	−	16.1608i	−0.560614	−	0.971011i	−0.997443	−	0.0714669i	$-0.977232\pi$
$277$	−9.33047	−	16.1608i	−0.560614	−	0.971011i	0.436829	−	0.899544i	$-0.356101\pi$
$278$		0			0
$279$	−1.46900	−	2.54439i	−0.0879468	−	0.152328i
$280$		0			0
$281$	4.96708			0.296311			0.148156	−	0.988964i	$-0.452666\pi$
$281$	4.96708			0.296311			0.148156	+	0.988964i	$0.452666\pi$
$282$		0			0
$283$	−5.40034	+	9.35366i	−0.321017	+	0.556017i	−0.980698	−	0.195528i	$-0.937358\pi$
$283$	−5.40034	+	9.35366i	−0.321017	+	0.556017i	0.659681	+	0.751545i	$0.270691\pi$
$284$		0			0
$285$	20.2928			1.20204
$286$		0			0
$287$	15.4592			0.912528
$288$		0			0
$289$	8.19194	−	14.1889i	0.481879	−	0.834639i
$290$		0			0
$291$	3.06200			0.179497
$292$		0			0
$293$	13.1221	+	22.7281i	0.766600	+	1.32779i	0.939397	+	0.342832i	$0.111386\pi$
$293$	13.1221	+	22.7281i	0.766600	+	1.32779i	−0.172797	+	0.984957i	$0.555281\pi$
$294$		0			0
$295$	−0.846931	−	1.46693i	−0.0493102	−	0.0854078i
$296$		0			0
$297$	2.36147	−	4.09018i	0.137026	−	0.237337i
$298$		0			0
$299$	−15.7296	+	6.52375i	−0.909666	+	0.377278i
$300$		0			0
$301$	5.54674	−	9.60724i	0.319709	−	0.553752i
$302$		0			0
$303$	0.815932	+	1.41324i	0.0468741	+	0.0811883i
$304$		0			0
$305$	8.17740	+	14.1637i	0.468237	+	0.811010i
$306$		0			0
$307$	−21.5369			−1.22918			−0.614589	−	0.788847i	$-0.710678\pi$
$307$	−21.5369			−1.22918			−0.614589	+	0.788847i	$0.710678\pi$
$308$		0			0
$309$	−3.83047	+	6.63457i	−0.217908	+	0.377427i
$310$		0			0
$311$	−21.1531			−1.19948			−0.599740	−	0.800195i	$-0.704729\pi$
$311$	−21.1531			−1.19948			−0.599740	+	0.800195i	$0.704729\pi$
$312$		0			0
$313$	9.79827			0.553831			0.276915	−	0.960894i	$-0.410688\pi$
$313$	9.79827			0.553831			0.276915	+	0.960894i	$0.410688\pi$
$314$		0			0
$315$	−3.51454	+	6.08736i	−0.198022	+	0.342984i
$316$		0			0
$317$	22.5236			1.26505			0.632526	−	0.774539i	$-0.282018\pi$
$317$	22.5236			1.26505			0.632526	+	0.774539i	$0.282018\pi$
$318$		0			0
$319$	−18.7453	−	32.4679i	−1.04954	−	1.81785i
$320$		0			0
$321$	0.361469	+	0.626082i	0.0201752	+	0.0349445i
$322$		0			0
$323$	2.02241	−	3.50292i	0.112530	−	0.194907i
$324$		0			0
$325$	−30.0679	−	23.0503i	−1.66787	−	1.27860i
$326$		0			0
$327$	−2.68407	+	4.64894i	−0.148429	+	0.257087i
$328$		0			0
$329$	−0.645198	−	1.11752i	−0.0355709	−	0.0616106i
$330$		0			0
$331$	10.5310	+	18.2402i	0.578836	+	1.00257i	0.995613	+	0.0935647i	$0.0298262\pi$
$331$	10.5310	+	18.2402i	0.578836	+	1.00257i	−0.416777	+	0.909009i	$0.636840\pi$
$332$		0			0
$333$	1.21507			0.0665852
$334$		0			0
$335$	−19.2666	+	33.3706i	−1.05264	+	1.82323i
$336$		0			0
$337$	−2.01574			−0.109805			−0.0549023	−	0.998492i	$-0.517485\pi$
$337$	−2.01574			−0.109805			−0.0549023	+	0.998492i	$0.517485\pi$
$338$		0			0
$339$	13.2151			0.717744
$340$		0			0
$341$	6.93800	−	12.0170i	0.375714	−	0.650756i
$342$		0			0
$343$	19.3023			1.04223
$344$		0			0
$345$	−9.29947	−	16.1072i	−0.500667	−	0.867180i
$346$		0			0
$347$	11.2995	+	19.5713i	0.606587	+	1.05064i	0.991798	+	0.127812i	$0.0407953\pi$
$347$	11.2995	+	19.5713i	0.606587	+	1.05064i	−0.385211	+	0.922829i	$0.625871\pi$
$348$		0			0
$349$	2.12994	−	3.68917i	0.114013	−	0.197477i	−0.803372	−	0.595478i	$-0.796963\pi$
$349$	2.12994	−	3.68917i	0.114013	−	0.197477i	0.917385	+	0.398001i	$0.130296\pi$
$350$		0			0
$351$	−2.86147	−	2.19363i	−0.152734	−	0.117087i
$352$		0			0
$353$	−1.76060	+	3.04945i	−0.0937074	+	0.162306i	−0.909068	−	0.416647i	$-0.863205\pi$
$353$	−1.76060	+	3.04945i	−0.0937074	+	0.162306i	0.815361	+	0.578953i	$0.196538\pi$
$354$		0			0
$355$	−17.1755	−	29.7488i	−0.911580	−	1.57890i
$356$		0			0
$357$	0.700528	+	1.21335i	0.0370759	+	0.0642173i
$358$		0			0
$359$	−9.15307			−0.483081			−0.241540	−	0.970391i	$-0.577653\pi$
$359$	−9.15307			−0.483081			−0.241540	+	0.970391i	$0.577653\pi$
$360$		0			0
$361$	−3.77706	+	6.54206i	−0.198793	+	0.344319i
$362$		0			0
$363$	11.3061			0.593418
$364$		0			0
$365$	−19.2017			−1.00506
$366$		0			0
$367$	1.10753	−	1.91830i	0.0578128	−	0.100135i	−0.835671	−	0.549231i	$-0.814921\pi$
$367$	1.10753	−	1.91830i	0.0578128	−	0.100135i	0.893483	+	0.449096i	$0.148254\pi$
$368$		0			0
$369$	−8.66094			−0.450871
$370$		0			0
$371$	−12.3285	−	21.3537i	−0.640066	−	1.10863i
$372$		0			0
$373$	14.2296	+	24.6464i	0.736781	+	1.27614i	0.953938	+	0.300005i	$0.0969885\pi$
$373$	14.2296	+	24.6464i	0.736781	+	1.27614i	−0.217157	+	0.976137i	$0.569678\pi$
$374$		0			0
$375$	10.8450	−	18.7841i	0.560034	−	0.970007i
$376$		0			0
$377$	−26.4373	+	10.9647i	−1.36159	+	0.564711i
$378$		0			0
$379$	−17.0059	+	29.4552i	−0.873537	+	1.51301i	−0.0152238	+	0.999884i	$0.504846\pi$
$379$	−17.0059	+	29.4552i	−0.873537	+	1.51301i	−0.858313	+	0.513126i	$0.828487\pi$
$380$		0			0
$381$	8.19194	+	14.1889i	0.419686	+	0.726917i
$382$		0			0
$383$	13.4459	+	23.2889i	0.687052	+	1.19001i	0.972787	+	0.231701i	$0.0744289\pi$
$383$	13.4459	+	23.2889i	0.687052	+	1.19001i	−0.285735	+	0.958309i	$0.592238\pi$
$384$		0			0
$385$	−33.1979			−1.69192
$386$		0			0
$387$	−3.10753	+	5.38241i	−0.157965	+	0.273603i
$388$		0			0
$389$	34.2756			1.73784			0.868922	−	0.494950i	$-0.164813\pi$
$389$	34.2756			1.73784			0.868922	+	0.494950i	$0.164813\pi$
$390$		0			0
$391$	−3.70719			−0.187481
$392$		0			0
$393$	−10.5079	+	18.2002i	−0.530052	+	0.918077i
$394$		0			0
$395$	64.5198			3.24634
$396$		0			0
$397$	13.6998	+	23.7288i	0.687574	+	1.19091i	0.972621	+	0.232399i	$0.0746576\pi$
$397$	13.6998	+	23.7288i	0.687574	+	1.19091i	−0.285047	+	0.958514i	$0.592009\pi$
$398$		0			0
$399$	−4.59894	−	7.96561i	−0.230235	−	0.398779i
$400$		0			0
$401$	−8.69861	+	15.0664i	−0.434388	+	0.752381i	−0.997245	−	0.0741723i	$-0.976369\pi$
$401$	−8.69861	+	15.0664i	−0.434388	+	0.752381i	0.562858	+	0.826554i	$0.309702\pi$
$402$		0			0
$403$	−8.40701	−	6.44488i	−0.418783	−	0.321042i
$404$		0			0
$405$	1.96900	−	3.41041i	0.0978405	−	0.169465i
$406$		0			0
$407$	2.86934	+	4.96984i	0.142228	+	0.246346i
$408$		0			0
$409$	−17.7599	−	30.7610i	−0.878170	−	1.52103i	−0.853347	−	0.521343i	$-0.825431\pi$
$409$	−17.7599	−	30.7610i	−0.878170	−	1.52103i	−0.0248225	−	0.999692i	$-0.507902\pi$
$410$		0			0
$411$	12.5369			0.618402
$412$		0			0
$413$	−0.383879	+	0.664897i	−0.0188894	+	0.0327175i
$414$		0			0
$415$	25.9867			1.27564
$416$		0			0
$417$	−8.81401			−0.431624
$418$		0			0
$419$	3.56987	−	6.18319i	0.174399	−	0.302069i	−0.765554	−	0.643372i	$-0.777535\pi$
$419$	3.56987	−	6.18319i	0.174399	−	0.302069i	0.939953	+	0.341303i	$0.110868\pi$
$420$		0			0
$421$	18.0291			0.878683			0.439342	−	0.898320i	$-0.355212\pi$
$421$	18.0291			0.878683			0.439342	+	0.898320i	$0.355212\pi$
$422$		0			0
$423$	0.361469	+	0.626082i	0.0175752	+	0.0304412i
$424$		0			0
$425$	−4.12399	−	7.14297i	−0.200043	−	0.346485i
$426$		0			0
$427$	3.70648	−	6.41981i	0.179369	−	0.310676i
$428$		0			0
$429$	2.21507	−	16.8841i	0.106944	−	0.815173i
$430$		0			0
$431$	−2.70053	+	4.67745i	−0.130080	+	0.225305i	−0.923707	−	0.383099i	$-0.874857\pi$
$431$	−2.70053	+	4.67745i	−0.130080	+	0.225305i	0.793627	+	0.608404i	$0.208190\pi$
$432$		0			0
$433$	−16.9459	−	29.3511i	−0.814367	−	1.41052i	−0.909782	−	0.415087i	$-0.863751\pi$
$433$	−16.9459	−	29.3511i	−0.814367	−	1.41052i	0.0954149	−	0.995438i	$-0.469582\pi$
$434$		0			0
$435$	−15.6299	−	27.0719i	−0.749398	−	1.29800i
$436$		0			0
$437$	24.3376			1.16423
$438$		0			0
$439$	3.32260	−	5.75491i	0.158579	−	0.274667i	−0.775777	−	0.631007i	$-0.782642\pi$
$439$	3.32260	−	5.75491i	0.158579	−	0.274667i	0.934356	+	0.356340i	$0.115975\pi$
$440$		0			0
$441$	−3.81401			−0.181620
$442$		0			0
$443$	−9.44588			−0.448787			−0.224394	−	0.974499i	$-0.572040\pi$
$443$	−9.44588			−0.448787			−0.224394	+	0.974499i	$0.572040\pi$
$444$		0			0
$445$	31.2599	−	54.1437i	1.48186	−	2.56666i
$446$		0			0
$447$	3.63186			0.171781
$448$		0			0
$449$	4.87601	+	8.44549i	0.230113	+	0.398567i	0.957841	−	0.287298i	$-0.0927571\pi$
$449$	4.87601	+	8.44549i	0.230113	+	0.398567i	−0.727728	+	0.685866i	$0.759424\pi$
$450$		0			0
$451$	−20.4525	−	35.4248i	−0.963073	−	1.66809i
$452$		0			0
$453$	−7.29947	+	12.6431i	−0.342959	+	0.594023i
$454$		0			0
$455$	−3.29665	+	25.1284i	−0.154549	+	1.17804i
$456$		0			0
$457$	−8.73081	+	15.1222i	−0.408410	+	0.707387i	−0.994712	−	0.102706i	$-0.967250\pi$
$457$	−8.73081	+	15.1222i	−0.408410	+	0.707387i	0.586302	+	0.810093i	$0.300583\pi$
$458$		0			0
$459$	−0.392467	−	0.679773i	−0.0183188	−	0.0317291i
$460$		0			0
$461$	−0.122071	−	0.211434i	−0.00568542	−	0.00984744i	0.863169	−	0.504916i	$-0.168476\pi$
$461$	−0.122071	−	0.211434i	−0.00568542	−	0.00984744i	−0.868854	+	0.495068i	$0.835143\pi$
$462$		0			0
$463$	0.0910730			0.00423252			0.00211626	−	0.999998i	$-0.499326\pi$
$463$	0.0910730			0.00423252			0.00211626	+	0.999998i	$0.499326\pi$
$464$		0			0
$465$	5.78493	−	10.0198i	0.268270	−	0.464657i
$466$		0			0
$467$	14.1688			0.655654			0.327827	−	0.944738i	$-0.393684\pi$
$467$	14.1688			0.655654			0.327827	+	0.944738i	$0.393684\pi$
$468$		0			0
$469$	17.4655			0.806480
$470$		0			0
$471$	7.79947	−	13.5091i	0.359381	−	0.622466i
$472$		0			0
$473$	−29.3534			−1.34967
$474$		0			0
$475$	27.0739	+	46.8934i	1.24224	+	2.15162i
$476$		0			0
$477$	6.90701	+	11.9633i	0.316250	+	0.547761i
$478$		0			0
$479$	0.846931	−	1.46693i	0.0386972	−	0.0670256i	−0.846028	−	0.533138i	$-0.821013\pi$
$479$	0.846931	−	1.46693i	0.0386972	−	0.0670256i	0.884725	+	0.466113i	$0.154346\pi$
$480$		0			0
$481$	4.04674	−	1.67836i	0.184516	−	0.0765266i
$482$		0			0
$483$	−4.21507	+	7.30071i	−0.191792	+	0.332194i
$484$		0			0
$485$	6.02908	+	10.4427i	0.273766	+	0.474177i
$486$		0			0
$487$	9.42347	+	16.3219i	0.427018	+	0.739617i	0.996607	−	0.0823132i	$-0.0262308\pi$
$487$	9.42347	+	16.3219i	0.427018	+	0.739617i	−0.569589	+	0.821930i	$0.692897\pi$
$488$		0			0
$489$	−10.9380			−0.494634
$490$		0			0
$491$	10.9604	−	18.9840i	0.494637	−	0.856736i	−0.505344	−	0.862918i	$-0.668635\pi$
$491$	10.9604	−	18.9840i	0.494637	−	0.856736i	0.999981	+	0.00618217i	$0.00196786\pi$
$492$		0			0
$493$	−6.23081			−0.280622
$494$		0			0
$495$	18.5989			0.835960
$496$		0			0
$497$	−7.78493	+	13.4839i	−0.349202	+	0.604836i
$498$		0			0
$499$	−13.4459			−0.601920			−0.300960	−	0.953637i	$-0.597307\pi$
$499$	−13.4459			−0.601920			−0.300960	+	0.953637i	$0.597307\pi$
$500$		0			0
$501$	−10.2928	−	17.8277i	−0.459849	−	0.796481i
$502$		0			0
$503$	4.96041	+	8.59169i	0.221174	+	0.383084i	0.955165	−	0.296075i	$-0.0956778\pi$
$503$	4.96041	+	8.59169i	0.221174	+	0.383084i	−0.733991	+	0.679159i	$0.762344\pi$
$504$		0			0
$505$	−3.21314	+	5.56533i	−0.142983	+	0.247654i
$506$		0			0
$507$	−12.5601	−	3.35329i	−0.557813	−	0.148925i
$508$		0			0
$509$	−10.1998	+	17.6666i	−0.452099	+	0.783058i	−0.998516	−	0.0544550i	$-0.982658\pi$
$509$	−10.1998	+	17.6666i	−0.452099	+	0.783058i	0.546418	+	0.837513i	$0.315991\pi$
$510$		0			0
$511$	4.35168	+	7.53732i	0.192507	+	0.333432i
$512$		0			0
$513$	2.57653	+	4.46269i	0.113757	+	0.197033i
$514$		0			0
$515$	−30.1688			−1.32940
$516$		0			0
$517$	−1.70719	+	2.95695i	−0.0750823	+	0.130046i
$518$		0			0
$519$	−0.306139			−0.0134380
$520$		0			0
$521$	−1.49454			−0.0654769			−0.0327385	−	0.999464i	$-0.510423\pi$
$521$	−1.49454			−0.0654769			−0.0327385	+	0.999464i	$0.510423\pi$
$522$		0			0
$523$	−16.0224	+	27.7516i	−0.700611	+	1.21349i	0.267641	+	0.963519i	$0.413756\pi$
$523$	−16.0224	+	27.7516i	−0.700611	+	1.21349i	−0.968252	+	0.249975i	$0.919577\pi$
$524$		0			0
$525$	−18.7559			−0.818573
$526$		0			0
$527$	−1.15307	−	1.99717i	−0.0502285	−	0.0869983i
$528$		0			0
$529$	0.346931	+	0.600901i	0.0150839	+	0.0261261i
$530$		0			0
$531$	0.215066	−	0.372505i	0.00933307	−	0.0161653i
$532$		0			0
$533$	−28.8450	+	11.9633i	−1.24942	+	0.518187i
$534$		0			0
$535$	−1.42347	+	2.46551i	−0.0615418	+	0.106593i
$536$		0			0
$537$	−1.42347	−	2.46551i	−0.0614271	−	0.106395i
$538$		0			0
$539$	−9.00667	−	15.6000i	−0.387945	−	0.671940i
$540$		0			0
$541$	1.44347			0.0620594			0.0310297	−	0.999518i	$-0.490121\pi$
$541$	1.44347			0.0620594			0.0310297	+	0.999518i	$0.490121\pi$
$542$		0			0
$543$	−6.60753	+	11.4446i	−0.283556	+	0.491134i
$544$		0			0
$545$	−21.1397			−0.905527
$546$		0			0
$547$	18.3972			0.786608			0.393304	−	0.919408i	$-0.371332\pi$
$547$	18.3972			0.786608			0.393304	+	0.919408i	$0.371332\pi$
$548$		0			0
$549$	−2.07653	+	3.59666i	−0.0886243	+	0.153502i
$550$		0			0
$551$	40.9051			1.74262
$552$		0			0
$553$	−14.6221	−	25.3262i	−0.621794	−	1.07698i
$554$		0			0
$555$	2.39247	+	4.14387i	0.101555	+	0.175898i
$556$		0			0
$557$	8.04674	−	13.9374i	0.340951	−	0.590545i	−0.643658	−	0.765313i	$-0.722584\pi$
$557$	8.04674	−	13.9374i	0.340951	−	0.590545i	0.984610	+	0.174768i	$0.0559175\pi$
$558$		0			0
$559$	−2.91488	+	22.2184i	−0.123286	+	0.939736i
$560$		0			0
$561$	1.85360	−	3.21052i	0.0782589	−	0.135548i
$562$		0			0
$563$	6.52120	+	11.2951i	0.274836	+	0.476030i	0.970094	−	0.242731i	$-0.0780431\pi$
$563$	6.52120	+	11.2951i	0.274836	+	0.476030i	−0.695258	+	0.718761i	$0.744710\pi$
$564$		0			0
$565$	26.0205	+	45.0688i	1.09469	+	1.89606i
$566$		0			0
$567$	−1.78493			−0.0749602
$568$		0			0
$569$	−3.29281	+	5.70331i	−0.138042	+	0.239095i	−0.926755	−	0.375666i	$-0.877414\pi$
$569$	−3.29281	+	5.70331i	−0.138042	+	0.239095i	0.788714	+	0.614761i	$0.210747\pi$
$570$		0			0
$571$	26.8469			1.12351			0.561755	−	0.827304i	$-0.310127\pi$
$571$	26.8469			1.12351			0.561755	+	0.827304i	$0.310127\pi$
$572$		0			0
$573$	3.56987			0.149133
$574$		0			0
$575$	24.8140	−	42.9791i	1.03482	−	1.79235i
$576$		0			0
$577$	−22.5818			−0.940091			−0.470046	−	0.882642i	$-0.655763\pi$
$577$	−22.5818			−0.940091			−0.470046	+	0.882642i	$0.655763\pi$
$578$		0			0
$579$	−6.22294	−	10.7784i	−0.258616	−	0.447937i
$580$		0			0
$581$	−5.88934	−	10.2006i	−0.244331	−	0.423194i
$582$		0			0
$583$	−32.6214	+	56.5018i	−1.35104	+	2.34007i
$584$		0			0
$585$	1.84693	−	14.0780i	0.0763612	−	0.582055i
$586$		0			0
$587$	−2.93800	+	5.08877i	−0.121264	+	0.210036i	−0.920267	−	0.391292i	$-0.872028\pi$
$587$	−2.93800	+	5.08877i	−0.121264	+	0.210036i	0.799002	+	0.601328i	$0.205362\pi$
$588$		0			0
$589$	7.56987	+	13.1114i	0.311911	+	0.540246i
$590$		0			0
$591$	4.36814	+	7.56583i	0.179681	+	0.311217i
$592$		0			0
$593$	−12.4788			−0.512443			−0.256221	−	0.966618i	$-0.582478\pi$
$593$	−12.4788			−0.512443			−0.256221	+	0.966618i	$0.582478\pi$
$594$		0			0
$595$	−2.75868	+	4.77818i	−0.113095	+	0.195886i
$596$		0			0
$597$	16.0911			0.658564
$598$		0			0
$599$	−41.6280			−1.70087			−0.850437	−	0.526076i	$-0.823663\pi$
$599$	−41.6280			−1.70087			−0.850437	+	0.526076i	$0.823663\pi$
$600$		0			0
$601$	−14.6299	+	25.3398i	−0.596768	+	1.03363i	0.396527	+	0.918023i	$0.370215\pi$
$601$	−14.6299	+	25.3398i	−0.596768	+	1.03363i	−0.993295	+	0.115609i	$0.963118\pi$
$602$		0			0
$603$	−9.78493			−0.398473
$604$		0			0
$605$	22.2618	+	38.5586i	0.905071	+	1.56763i
$606$		0			0
$607$	−9.02908	−	15.6388i	−0.366479	−	0.634760i	0.622533	−	0.782593i	$-0.286103\pi$
$607$	−9.02908	−	15.6388i	−0.366479	−	0.634760i	−0.989012	+	0.147833i	$0.952770\pi$
$608$		0			0
$609$	−7.08441	+	12.2706i	−0.287075	+	0.497228i
$610$		0			0
$611$	2.06866	+	1.58585i	0.0836892	+	0.0641568i
$612$		0			0
$613$	8.95254	−	15.5063i	0.361590	−	0.626292i	−0.626633	−	0.779315i	$-0.715567\pi$
$613$	8.95254	−	15.5063i	0.361590	−	0.626292i	0.988223	+	0.153023i	$0.0489008\pi$
$614$		0			0
$615$	−17.0534	−	29.5374i	−0.687660	−	1.19106i
$616$		0			0
$617$	11.6986	+	20.2626i	0.470968	+	0.815741i	0.999449	−	0.0332047i	$-0.0105713\pi$
$617$	11.6986	+	20.2626i	0.470968	+	0.815741i	−0.528480	+	0.848945i	$0.677238\pi$
$618$		0			0
$619$	−43.9537			−1.76665			−0.883325	−	0.468761i	$-0.844701\pi$
$619$	−43.9537			−1.76665			−0.883325	+	0.468761i	$0.844701\pi$
$620$		0			0
$621$	2.36147	−	4.09018i	0.0947625	−	0.164133i
$622$		0			0
$623$	−28.3376			−1.13532
$624$		0			0
$625$	32.8760			1.31504
$626$		0			0
$627$	−12.1688	+	21.0770i	−0.485976	+	0.841734i
$628$		0			0
$629$	0.953747			0.0380284
$630$		0			0
$631$	−4.83714	−	8.37817i	−0.192563	−	0.333530i	0.753536	−	0.657407i	$-0.228347\pi$
$631$	−4.83714	−	8.37817i	−0.192563	−	0.333530i	−0.946099	+	0.323877i	$0.895013\pi$
$632$		0			0
$633$	2.19194	+	3.79655i	0.0871218	+	0.150899i
$634$		0			0
$635$	−32.2599	+	55.8758i	−1.28019	+	2.21736i
$636$		0			0
$637$	−12.7024	+	5.26826i	−0.503289	+	0.208736i
$638$		0			0
$639$	4.36147	−	7.55429i	0.172537	−	0.298843i
$640$		0			0
$641$	−7.20648	−	12.4820i	−0.284639	−	0.493009i	0.687883	−	0.725822i	$-0.258540\pi$
$641$	−7.20648	−	12.4820i	−0.284639	−	0.493009i	−0.972522	+	0.232813i	$0.925207\pi$
$642$		0			0
$643$	9.34501	+	16.1860i	0.368531	+	0.638315i	0.989336	−	0.145650i	$-0.0465274\pi$
$643$	9.34501	+	16.1860i	0.368531	+	0.638315i	−0.620805	+	0.783965i	$0.713194\pi$
$644$		0			0
$645$	−24.4750			−0.963700
$646$		0			0
$647$	11.3681	−	19.6902i	0.446928	−	0.774101i	−0.551257	−	0.834336i	$-0.685852\pi$
$647$	11.3681	−	19.6902i	0.446928	−	0.774101i	0.998184	+	0.0602345i	$0.0191848\pi$
$648$		0			0
$649$	2.03149			0.0797428
$650$		0			0
$651$	−5.24414			−0.205534
$652$		0			0
$653$	−10.1068	+	17.5055i	−0.395510	+	0.685044i	−0.993166	−	0.116709i	$-0.962766\pi$
$653$	−10.1068	+	17.5055i	−0.395510	+	0.685044i	0.597656	+	0.801753i	$0.296099\pi$
$654$		0			0
$655$	−82.7601			−3.23370
$656$		0			0
$657$	−2.43800	−	4.22275i	−0.0951156	−	0.164745i
$658$		0			0
$659$	9.87601	+	17.1057i	0.384715	+	0.666345i	0.991730	−	0.128345i	$-0.0409665\pi$
$659$	9.87601	+	17.1057i	0.384715	+	0.666345i	−0.607015	+	0.794690i	$0.707633\pi$
$660$		0			0
$661$	5.38267	−	9.32306i	0.209362	−	0.362625i	−0.742152	−	0.670232i	$-0.766195\pi$
$661$	5.38267	−	9.32306i	0.209362	−	0.362625i	0.951514	+	0.307607i	$0.0995280\pi$
$662$		0			0
$663$	−2.24606	−	1.72185i	−0.0872299	−	0.0668712i
$664$		0			0
$665$	18.1107	−	31.3686i	0.702301	−	1.21642i
$666$		0			0
$667$	−18.7453	−	32.4679i	−0.725823	−	1.25716i
$668$		0			0
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$		0			0
$671$	−19.6147			−0.757217
$672$		0			0
$673$	−23.2520	+	40.2737i	−0.896299	+	1.55244i	−0.0641110	+	0.997943i	$0.520421\pi$
$673$	−23.2520	+	40.2737i	−0.896299	+	1.55244i	−0.832188	+	0.554493i	$0.812912\pi$
$674$		0			0
$675$	10.5079			0.404448
$676$		0			0
$677$	2.18215			0.0838667			0.0419333	−	0.999120i	$-0.486648\pi$
$677$	2.18215			0.0838667			0.0419333	+	0.999120i	$0.486648\pi$
$678$		0			0
$679$	2.73273	−	4.73323i	0.104873	−	0.181645i
$680$		0			0
$681$	17.7387			0.679748
$682$		0			0
$683$	−2.93800	−	5.08877i	−0.112420	−	0.194716i	0.804326	−	0.594189i	$-0.202527\pi$
$683$	−2.93800	−	5.08877i	−0.112420	−	0.194716i	−0.916745	+	0.399472i	$0.869193\pi$
$684$		0			0
$685$	24.6853	+	42.7561i	0.943176	+	1.63363i
$686$		0			0
$687$	−5.72294	+	9.91242i	−0.218344	+	0.378182i
$688$		0			0
$689$	39.5284	+	30.3028i	1.50591	+	1.15444i
$690$		0			0
$691$	−5.73940	+	9.94093i	−0.218337	+	0.378171i	−0.954300	−	0.298851i	$-0.903397\pi$
$691$	−5.73940	+	9.94093i	−0.218337	+	0.378171i	0.735963	+	0.677022i	$0.236730\pi$
$692$		0			0
$693$	−4.21507	−	7.30071i	−0.160117	−	0.277331i
$694$		0			0
$695$	−17.3548	−	30.0594i	−0.658305	−	1.14022i
$696$		0			0
$697$	−6.79827			−0.257503
$698$		0			0
$699$	4.87601	−	8.44549i	0.184428	−	0.319438i
$700$		0			0
$701$	−26.4301			−0.998252			−0.499126	−	0.866529i	$-0.666346\pi$
$701$	−26.4301			−0.998252			−0.499126	+	0.866529i	$0.666346\pi$
$702$		0			0
$703$	−6.26132			−0.236150
$704$		0			0
$705$	−1.42347	+	2.46551i	−0.0536108	+	0.0928566i
$706$		0			0
$707$	2.91277			0.109546
$708$		0			0
$709$	−26.0303	−	45.0858i	−0.977588	−	1.69323i	−0.671117	−	0.741352i	$-0.734185\pi$
$709$	−26.0303	−	45.0858i	−0.977588	−	1.69323i	−0.306471	−	0.951880i	$-0.599148\pi$
$710$		0			0
$711$	8.19194	+	14.1889i	0.307222	+	0.532124i
$712$		0			0
$713$	6.93800	−	12.0170i	0.259830	−	0.450039i
$714$		0			0
$715$	61.9432	−	25.6906i	2.31655	−	0.960773i
$716$		0			0
$717$	3.29947	−	5.71485i	0.123221	−	0.213425i
$718$		0			0
$719$	17.2308	+	29.8446i	0.642601	+	1.11302i	0.984850	+	0.173408i	$0.0554779\pi$
$719$	17.2308	+	29.8446i	0.642601	+	1.11302i	−0.342249	+	0.939609i	$0.611189\pi$
$720$		0			0
$721$	6.83714	+	11.8423i	0.254628	+	0.441029i
$722$		0			0
$723$	23.8140			0.885653
$724$		0			0
$725$	41.7058	−	72.2365i	1.54891	−	2.68280i
$726$		0			0
$727$	29.1335			1.08050			0.540251	−	0.841504i	$-0.318329\pi$
$727$	29.1335			1.08050			0.540251	+	0.841504i	$0.318329\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.43921	+	4.22483i	−0.0902174	+	0.156261i
$732$		0			0
$733$	−37.7229			−1.39333			−0.696664	−	0.717397i	$-0.745333\pi$
$733$	−37.7229			−1.39333			−0.696664	+	0.717397i	$0.745333\pi$
$734$		0			0
$735$	−7.50979	−	13.0073i	−0.277003	−	0.479783i
$736$		0			0
$737$	−23.1068	−	40.0222i	−0.851151	−	1.47424i
$738$		0			0
$739$	13.8760	−	24.0339i	0.510437	−	0.884103i	−0.489490	−	0.872009i	$-0.662817\pi$
$739$	13.8760	−	24.0339i	0.510437	−	0.884103i	0.999927	−	0.0120940i	$-0.00384974\pi$
$740$		0			0
$741$	14.7453	+	11.3039i	0.541684	+	0.415259i
$742$		0			0
$743$	−12.0911	+	20.9424i	−0.443578	+	0.768300i	−0.997952	−	0.0639676i	$-0.979625\pi$
$743$	−12.0911	+	20.9424i	−0.443578	+	0.768300i	0.554374	+	0.832268i	$0.312958\pi$
$744$		0			0
$745$	7.15115	+	12.3862i	0.261998	+	0.453793i
$746$		0			0
$747$	3.29947	+	5.71485i	0.120721	+	0.209096i
$748$		0			0
$749$	1.29040			0.0471500
$750$		0			0
$751$	21.8984	−	37.9292i	0.799085	−	1.38406i	−0.121128	−	0.992637i	$-0.538651\pi$
$751$	21.8984	−	37.9292i	0.799085	−	1.38406i	0.920213	−	0.391418i	$-0.128015\pi$
$752$		0			0
$753$	−9.44588			−0.344227
$754$		0			0
$755$	−57.4907			−2.09230
$756$		0			0
$757$	−8.44588	+	14.6287i	−0.306971	+	0.531689i	−0.977698	−	0.210015i	$-0.932649\pi$
$757$	−8.44588	+	14.6287i	−0.306971	+	0.531689i	0.670728	+	0.741704i	$0.265982\pi$
$758$		0			0
$759$	22.3061			0.809662
$760$		0			0
$761$	0.0619965	+	0.107381i	0.00224737	+	0.00389256i	0.867147	−	0.498052i	$-0.165951\pi$
$761$	0.0619965	+	0.107381i	0.00224737	+	0.00389256i	−0.864900	+	0.501945i	$0.832618\pi$
$762$		0			0
$763$	4.79088	+	8.29805i	0.173442	+	0.300410i
$764$		0			0
$765$	1.54554	−	2.67695i	0.0558790	−	0.0967852i
$766$		0			0
$767$	0.201733	−	1.53769i	0.00728414	−	0.0555226i
$768$		0			0
$769$	21.9051	−	37.9407i	0.789918	−	1.36818i	−0.136099	−	0.990695i	$-0.543457\pi$
$769$	21.9051	−	37.9407i	0.789918	−	1.36818i	0.926017	−	0.377482i	$-0.123210\pi$
$770$		0			0
$771$	6.33047	+	10.9647i	0.227986	+	0.394884i
$772$		0			0
$773$	2.27706	+	3.94399i	0.0819002	+	0.141855i	0.904066	−	0.427393i	$-0.140568\pi$
$773$	2.27706	+	3.94399i	0.0819002	+	0.141855i	−0.822166	+	0.569248i	$0.807234\pi$
$774$		0			0
$775$	30.8722			1.10896
$776$		0			0
$777$	1.08441	−	1.87825i	0.0389029	−	0.0673817i
$778$		0			0
$779$	44.6304			1.59905
$780$		0			0
$781$	41.1979			1.47418
$782$		0			0
$783$	3.96900	−	6.87451i	0.141841	−	0.245675i
$784$		0			0
$785$	61.4287			2.19248
$786$		0			0
$787$	0.0231267	+	0.0400566i	0.000824377	+	0.00142786i	0.866437	−	0.499286i	$-0.166404\pi$
$787$	0.0231267	+	0.0400566i	0.000824377	+	0.00142786i	−0.865613	+	0.500714i	$0.833071\pi$
$788$		0			0
$789$	−0.146403	−	0.253577i	−0.00521208	−	0.00902758i
$790$		0			0
$791$	11.7940	−	20.4278i	0.419347	−	0.726330i
$792$		0			0
$793$	−1.94780	+	14.8469i	−0.0691683	+	0.527228i
$794$		0			0
$795$	−27.1998	+	47.1115i	−0.964678	+	1.67087i
$796$		0			0
$797$	−9.25989	−	16.0386i	−0.328002	−	0.568116i	0.654113	−	0.756397i	$-0.273042\pi$
$797$	−9.25989	−	16.0386i	−0.328002	−	0.568116i	−0.982115	+	0.188280i	$0.939709\pi$
$798$		0			0
$799$	0.283729	+	0.491433i	0.0100376	+	0.0173857i
$800$		0			0
$801$	15.8760			0.560951
$802$		0			0
$803$	11.5145	−	19.9438i	0.406339	−	0.703800i
$804$		0			0
$805$	−33.1979			−1.17007
$806$		0			0
$807$	5.56987			0.196069
$808$		0			0
$809$	−21.8517	+	37.8482i	−0.768264	+	1.33067i	0.170240	+	0.985403i	$0.445546\pi$
$809$	−21.8517	+	37.8482i	−0.768264	+	1.33067i	−0.938504	+	0.345270i	$0.887787\pi$
$810$		0			0
$811$	−12.2017			−0.428461			−0.214230	−	0.976783i	$-0.568724\pi$
$811$	−12.2017			−0.428461			−0.214230	+	0.976783i	$0.568724\pi$
$812$		0			0
$813$	5.97687	+	10.3522i	0.209618	+	0.363069i
$814$		0			0
$815$	−21.5369	−	37.3031i	−0.754406	−	1.30667i
$816$		0			0
$817$	16.0133	−	27.7359i	0.560236	−	0.970357i
$818$		0			0
$819$	−5.94467	+	2.46551i	−0.207724	+	0.0861520i
$820$		0			0
$821$	19.2928	−	33.4161i	0.673324	−	1.16623i	−0.303632	−	0.952789i	$-0.598199\pi$
$821$	19.2928	−	33.4161i	0.673324	−	1.16623i	0.976956	−	0.213441i	$-0.0684672\pi$
$822$		0			0
$823$	24.1688	+	41.8616i	0.842472	+	1.45920i	0.887799	+	0.460232i	$0.152234\pi$
$823$	24.1688	+	41.8616i	0.842472	+	1.45920i	−0.0453269	+	0.998972i	$0.514433\pi$
$824$		0			0
$825$	24.8140	+	42.9791i	0.863913	+	1.49634i
$826$		0			0
$827$	1.19789			0.0416547			0.0208273	−	0.999783i	$-0.493370\pi$
$827$	1.19789			0.0416547			0.0208273	+	0.999783i	$0.493370\pi$
$828$		0			0
$829$	9.16761	−	15.8788i	0.318404	−	0.551492i	−0.661751	−	0.749724i	$-0.730186\pi$
$829$	9.16761	−	15.8788i	0.318404	−	0.551492i	0.980155	+	0.198231i	$0.0635198\pi$
$830$		0			0
$831$	18.6609			0.647341
$832$		0			0
$833$	−2.99375			−0.103727
$834$		0			0
$835$	40.5331	−	70.2054i	1.40271	−	2.42956i
$836$		0			0
$837$	2.93800			0.101552
$838$		0			0
$839$	23.2441	+	40.2600i	0.802477	+	1.38993i	0.917981	+	0.396624i	$0.129818\pi$
$839$	23.2441	+	40.2600i	0.802477	+	1.38993i	−0.115504	+	0.993307i	$0.536848\pi$
$840$		0			0
$841$	−17.0059	−	29.4552i	−0.586412	−	1.01570i
$842$		0			0
$843$	−2.48354	+	4.30162i	−0.0855377	+	0.148156i
$844$		0			0
$845$	−13.2947	−	49.4376i	−0.457353	−	1.70071i
$846$		0			0
$847$	10.0904	−	17.4770i	0.346709	−	0.600517i
$848$		0			0
$849$	−5.40034	−	9.35366i	−0.185339	−	0.321017i
$850$		0			0
$851$	2.86934	+	4.96984i	0.0983597	+	0.170364i
$852$		0			0
$853$	−10.7653			−0.368598			−0.184299	−	0.982870i	$-0.559002\pi$
$853$	−10.7653			−0.368598			−0.184299	+	0.982870i	$0.559002\pi$
$854$		0			0
$855$	−10.1464	+	17.5741i	−0.347000	+	0.601021i
$856$		0			0
$857$	−23.3972			−0.799234			−0.399617	−	0.916682i	$-0.630857\pi$
$857$	−23.3972			−0.799234			−0.399617	+	0.916682i	$0.630857\pi$
$858$		0			0
$859$	−0.339059			−0.0115685			−0.00578427	−	0.999983i	$-0.501841\pi$
$859$	−0.339059			−0.0115685			−0.00578427	+	0.999983i	$0.501841\pi$
$860$		0			0
$861$	−7.72960	+	13.3881i	−0.263424	+	0.456264i
$862$		0			0
$863$	−13.9208			−0.473870			−0.236935	−	0.971525i	$-0.576143\pi$
$863$	−13.9208			−0.473870			−0.236935	+	0.971525i	$0.576143\pi$
$864$		0			0
$865$	−0.602788	−	1.04406i	−0.0204954	−	0.0354991i
$866$		0			0
$867$	8.19194	+	14.1889i	0.278213	+	0.481879i
$868$		0			0
$869$	−38.6900	+	67.0131i	−1.31247	+	2.27326i
$870$		0			0
$871$	−32.5884	+	13.5158i	−1.10422	+	0.457967i
$872$		0			0
$873$	−1.53100	+	2.65177i	−0.0518164	+	0.0897487i
$874$		0			0
$875$	−19.3576	−	33.5284i	−0.654407	−	1.13347i
$876$		0			0
$877$	3.68527	+	6.38308i	0.124443	+	0.215541i	0.921515	−	0.388343i	$-0.126952\pi$
$877$	3.68527	+	6.38308i	0.124443	+	0.215541i	−0.797072	+	0.603884i	$0.793619\pi$
$878$		0			0
$879$	−26.2441			−0.885193
$880$		0			0
$881$	15.4835	−	26.8183i	0.521654	−	0.903531i	−0.478029	−	0.878344i	$-0.658649\pi$
$881$	15.4835	−	26.8183i	0.521654	−	0.903531i	0.999683	−	0.0251867i	$-0.00801803\pi$
$882$		0			0
$883$	−24.5660			−0.826713			−0.413356	−	0.910569i	$-0.635644\pi$
$883$	−24.5660			−0.826713			−0.413356	+	0.910569i	$0.635644\pi$
$884$		0			0
$885$	1.69386			0.0569385
$886$		0			0
$887$	−10.0911	+	17.4783i	−0.338825	+	0.586862i	−0.984212	−	0.176994i	$-0.943363\pi$
$887$	−10.0911	+	17.4783i	−0.338825	+	0.586862i	0.645387	+	0.763856i	$0.276696\pi$
$888$		0			0
$889$	29.2441			0.980817
$890$		0			0
$891$	2.36147	+	4.09018i	0.0791122	+	0.137026i
$892$		0			0
$893$	−1.86267	−	3.22625i	−0.0623320	−	0.107962i
$894$		0			0
$895$	5.60561	−	9.70920i	0.187375	−	0.324543i
$896$		0			0
$897$	2.21507	−	16.8841i	0.0739589	−	0.563744i
$898$		0			0
$899$	11.6609	−	20.1973i	0.388914	−	0.673619i
$900$		0			0
$901$	5.42154	+	9.39039i	0.180618	+	0.312839i
$902$		0			0
$903$	5.54674	+	9.60724i	0.184584	+	0.319709i
$904$		0			0
$905$	−52.0410			−1.72990
$906$		0			0
$907$	23.6147	−	40.9018i	0.784113	−	1.35812i	−0.145415	−	0.989371i	$-0.546452\pi$
$907$	23.6147	−	40.9018i	0.784113	−	1.35812i	0.929528	−	0.368752i	$-0.120215\pi$
$908$		0			0
$909$	−1.63186			−0.0541255
$910$		0			0
$911$	48.3376			1.60150			0.800748	−	0.599001i	$-0.204435\pi$
$911$	48.3376			1.60150			0.800748	+	0.599001i	$0.204435\pi$
$912$		0			0
$913$	−15.5832	+	26.9909i	−0.515729	+	0.893268i
$914$		0			0
$915$	−16.3548			−0.540673
$916$		0			0
$917$	18.7559	+	32.4861i	0.619373	+	1.07279i
$918$		0			0
$919$	−5.02908	−	8.71062i	−0.165894	−	0.287337i	0.771078	−	0.636740i	$-0.219718\pi$
$919$	−5.02908	−	8.71062i	−0.165894	−	0.287337i	−0.936972	+	0.349403i	$0.886384\pi$
$920$		0			0
$921$	10.7685	−	18.6515i	0.354833	−	0.614589i
$922$		0			0
$923$	4.09107	−	31.1838i	0.134659	−	1.02643i
$924$		0			0
$925$	−6.38388	+	11.0572i	−0.209901	+	0.363559i
$926$		0			0
$927$	−3.83047	−	6.63457i	−0.125809	−	0.217908i
$928$		0			0
$929$	6.02433	+	10.4344i	0.197652	+	0.342343i	0.947767	−	0.318965i	$-0.103335\pi$
$929$	6.02433	+	10.4344i	0.197652	+	0.342343i	−0.750115	+	0.661308i	$0.770002\pi$
$930$		0			0
$931$	19.6539			0.644129
$932$		0			0
$933$	10.5765	−	18.3191i	0.346260	−	0.599740i
$934$		0			0
$935$	14.5989			0.477437
$936$		0			0
$937$	−22.8298			−0.745816			−0.372908	−	0.927868i	$-0.621639\pi$
$937$	−22.8298			−0.745816			−0.372908	+	0.927868i	$0.621639\pi$
$938$		0			0
$939$	−4.89913	+	8.48555i	−0.159877	+	0.276915i
$940$		0			0
$941$	−39.8102			−1.29777			−0.648887	−	0.760885i	$-0.724765\pi$
$941$	−39.8102			−1.29777			−0.648887	+	0.760885i	$0.724765\pi$
$942$		0			0
$943$	−20.4525	−	35.4248i	−0.666026	−	1.15359i
$944$		0			0
$945$	−3.51454	−	6.08736i	−0.114328	−	0.198022i
$946$		0			0
$947$	−15.1531	+	26.2459i	−0.492409	+	0.852877i	−0.999962	−	0.00874373i	$-0.997217\pi$
$947$	−15.1531	+	26.2459i	−0.492409	+	0.852877i	0.507553	+	0.861620i	$0.330550\pi$
$948$		0			0
$949$	−13.9525	−	10.6961i	−0.452919	−	0.347211i
$950$		0			0
$951$	−11.2618	+	19.5060i	−0.365189	+	0.632526i
$952$		0			0
$953$	−5.01333	−	8.68335i	−0.162398	−	0.281281i	0.773330	−	0.634003i	$-0.218589\pi$
$953$	−5.01333	−	8.68335i	−0.162398	−	0.281281i	−0.935728	+	0.352722i	$0.885256\pi$
$954$		0			0
$955$	7.02908	+	12.1747i	0.227456	+	0.393965i
$956$		0			0
$957$	37.4907			1.21190
$958$		0			0
$959$	11.1888	−	19.3796i	0.361306	−	0.625800i
$960$		0			0
$961$	−22.3681			−0.721553
$962$		0			0
$963$	−0.722938			−0.0232963
$964$		0			0
$965$	24.5059	−	42.4456i	0.788874	−	1.36637i
$966$		0			0
$967$	43.7702			1.40755			0.703777	−	0.710421i	$-0.251495\pi$
$967$	43.7702			1.40755			0.703777	+	0.710421i	$0.251495\pi$
$968$		0			0
$969$	2.02241	+	3.50292i	0.0649692	+	0.112530i
$970$		0			0
$971$	−24.4616	−	42.3688i	−0.785011	−	1.35968i	−0.928993	−	0.370098i	$-0.879324\pi$
$971$	−24.4616	−	42.3688i	−0.785011	−	1.35968i	0.143982	−	0.989580i	$-0.454009\pi$
$972$		0			0
$973$	−7.86621	+	13.6247i	−0.252179	+	0.436787i
$974$		0			0
$975$	34.9962	−	14.5144i	1.12077	−	0.464834i
$976$		0			0
$977$	13.7897	−	23.8844i	0.441171	−	0.764130i	−0.556606	−	0.830777i	$-0.687897\pi$
$977$	13.7897	−	23.8844i	0.441171	−	0.764130i	0.997777	+	0.0666463i	$0.0212299\pi$
$978$		0			0
$979$	37.4907	+	64.9358i	1.19821	+	2.07536i
$980$		0			0
$981$	−2.68407	−	4.64894i	−0.0856957	−	0.148429i
$982$		0			0
$983$	34.7096			1.10706			0.553532	−	0.832828i	$-0.313280\pi$
$983$	34.7096			1.10706			0.553532	+	0.832828i	$0.313280\pi$
$984$		0			0
$985$	−17.2017	+	29.7943i	−0.548093	+	0.949325i
$986$		0			0
$987$	1.29040			0.0410738
$988$		0			0
$989$	−29.3534			−0.933383
$990$		0			0
$991$	−16.3285	+	28.2819i	−0.518693	+	0.898403i	0.481071	+	0.876682i	$0.340248\pi$
$991$	−16.3285	+	28.2819i	−0.518693	+	0.898403i	−0.999764	+	0.0217216i	$0.993085\pi$
$992$		0			0
$993$	−21.0620			−0.668382
$994$		0			0
$995$	31.6834	+	54.8772i	1.00443	+	1.73972i
$996$		0			0
$997$	−2.79947	−	4.84883i	−0.0886602	−	0.153564i	0.818285	−	0.574813i	$-0.194925\pi$
$997$	−2.79947	−	4.84883i	−0.0886602	−	0.153564i	−0.906945	+	0.421249i	$0.861592\pi$
$998$		0			0
$999$	−0.607533	+	1.05228i	−0.0192215	+	0.0332926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.q.j.529.1		6
3.2	odd	2		1872.2.t.u.1153.3		6
4.3	odd	2		312.2.q.e.217.1	✓	6
12.11	even	2		936.2.t.h.217.3		6
13.3	even	3	inner	624.2.q.j.289.1		6
13.4	even	6		8112.2.a.cl.1.3		3
13.9	even	3		8112.2.a.ck.1.1		3
39.29	odd	6		1872.2.t.u.289.3		6
52.3	odd	6		312.2.q.e.289.1	yes	6
52.7	even	12		4056.2.c.m.337.1		6
52.19	even	12		4056.2.c.m.337.6		6
52.35	odd	6		4056.2.a.z.1.1		3
52.43	odd	6		4056.2.a.y.1.3		3
156.107	even	6		936.2.t.h.289.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.q.e.217.1	✓	6	4.3	odd	2
312.2.q.e.289.1	yes	6	52.3	odd	6
624.2.q.j.289.1		6	13.3	even	3	inner
624.2.q.j.529.1		6	1.1	even	1	trivial
936.2.t.h.217.3		6	12.11	even	2
936.2.t.h.289.3		6	156.107	even	6
1872.2.t.u.289.3		6	39.29	odd	6
1872.2.t.u.1153.3		6	3.2	odd	2
4056.2.a.y.1.3		3	52.43	odd	6
4056.2.a.z.1.1		3	52.35	odd	6
4056.2.c.m.337.1		6	52.7	even	12
4056.2.c.m.337.6		6	52.19	even	12
8112.2.a.ck.1.1		3	13.9	even	3
8112.2.a.cl.1.3		3	13.4	even	6

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} -3.93800 q^{5} +(0.892467 + 1.54580i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} -3.93800 q^{5} +(0.892467 + 1.54580i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.36147 - 4.09018i) q^{11} +(-2.86147 - 2.19363i) q^{13} +(1.96900 - 3.41041i) q^{15} +(-0.392467 - 0.679773i) q^{17} +(2.57653 + 4.46269i) q^{19} -1.78493 q^{21} +(2.36147 - 4.09018i) q^{23} +10.5079 q^{25} +1.00000 q^{27} +(3.96900 - 6.87451i) q^{29} +2.93800 q^{31} +(2.36147 + 4.09018i) q^{33} +(-3.51454 - 6.08736i) q^{35} +(-0.607533 + 1.05228i) q^{37} +(3.33047 - 1.38129i) q^{39} +(4.33047 - 7.50059i) q^{41} +(-3.10753 - 5.38241i) q^{43} +(1.96900 + 3.41041i) q^{45} -0.722938 q^{47} +(1.90701 - 3.30303i) q^{49} +0.784934 q^{51} -13.8140 q^{53} +(-9.29947 + 16.1072i) q^{55} -5.15307 q^{57} +(0.215066 + 0.372505i) q^{59} +(-2.07653 - 3.59666i) q^{61} +(0.892467 - 1.54580i) q^{63} +(11.2685 + 8.63851i) q^{65} +(4.89247 - 8.47400i) q^{67} +(2.36147 + 4.09018i) q^{69} +(4.36147 + 7.55429i) q^{71} +4.87601 q^{73} +(-5.25394 + 9.10008i) q^{75} +8.43013 q^{77} -16.3839 q^{79} +(-0.500000 + 0.866025i) q^{81} -6.59894 q^{83} +(1.54554 + 2.67695i) q^{85} +(3.96900 + 6.87451i) q^{87} +(-7.93800 + 13.7490i) q^{89} +(0.837137 - 6.38099i) q^{91} +(-1.46900 + 2.54439i) q^{93} +(-10.1464 - 17.5741i) q^{95} +(-1.53100 - 2.65177i) q^{97} -4.72294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 + 3 * q^7 - 3 * q^9	\( 6 q - 3 q^{3} + 3 q^{7} - 3 q^{9} - 3 q^{13} + 6 q^{19} - 6 q^{21} + 30 q^{25} + 6 q^{27} + 12 q^{29} - 6 q^{31} + 12 q^{35} - 6 q^{37} - 6 q^{39} - 21 q^{43} + 24 q^{47} - 24 q^{49} - 12 q^{53} - 18 q^{55} - 12 q^{57} + 6 q^{59} - 3 q^{61} + 3 q^{63} + 18 q^{65} + 27 q^{67} + 12 q^{71} - 18 q^{73} - 15 q^{75} + 60 q^{77} - 18 q^{79} - 3 q^{81} + 36 q^{83} - 12 q^{85} + 12 q^{87} - 24 q^{89} - 21 q^{91} + 3 q^{93} - 42 q^{95} - 21 q^{97}+O(q^{100}) \) 6 * q - 3 * q^3 + 3 * q^7 - 3 * q^9 - 3 * q^13 + 6 * q^19 - 6 * q^21 + 30 * q^25 + 6 * q^27 + 12 * q^29 - 6 * q^31 + 12 * q^35 - 6 * q^37 - 6 * q^39 - 21 * q^43 + 24 * q^47 - 24 * q^49 - 12 * q^53 - 18 * q^55 - 12 * q^57 + 6 * q^59 - 3 * q^61 + 3 * q^63 + 18 * q^65 + 27 * q^67 + 12 * q^71 - 18 * q^73 - 15 * q^75 + 60 * q^77 - 18 * q^79 - 3 * q^81 + 36 * q^83 - 12 * q^85 + 12 * q^87 - 24 * q^89 - 21 * q^91 + 3 * q^93 - 42 * q^95 - 21 * q^97

Introduction

L-functions

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