LMFDB - Embedded newform 804.2.o.d.365.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(365,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("804.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			365.14
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34511 - 1.09118i) q^{3} +3.88149 q^{5} +(-3.35972 - 1.93974i) q^{7} +(0.618641 - 2.93552i) q^{9} +O(q^{10})$	\(q+(1.34511 - 1.09118i) q^{3} +3.88149 q^{5} +(-3.35972 - 1.93974i) q^{7} +(0.618641 - 2.93552i) q^{9} +(-0.627217 + 1.08637i) q^{11} +(0.212374 - 0.122614i) q^{13} +(5.22103 - 4.23541i) q^{15} +(2.38011 - 1.37416i) q^{17} +(-2.25380 - 3.90370i) q^{19} +(-6.63580 + 1.05691i) q^{21} +(2.10776 - 1.21692i) q^{23} +10.0660 q^{25} +(-2.37105 - 4.62365i) q^{27} +(-3.32333 - 1.91873i) q^{29} +(4.36024 + 2.51738i) q^{31} +(0.341754 + 2.14570i) q^{33} +(-13.0407 - 7.52906i) q^{35} +(4.49590 + 7.78713i) q^{37} +(0.151872 - 0.396668i) q^{39} +(-3.59904 + 6.23373i) q^{41} +4.98044i q^{43} +(2.40125 - 11.3942i) q^{45} +(-4.99134 - 2.88175i) q^{47} +(4.02515 + 6.97176i) q^{49} +(1.70205 - 4.44553i) q^{51} +11.4657 q^{53} +(-2.43453 + 4.21674i) q^{55} +(-7.29126 - 2.79160i) q^{57} +13.5856i q^{59} +(-6.26687 + 3.61818i) q^{61} +(-7.77259 + 8.66253i) q^{63} +(0.824327 - 0.475926i) q^{65} +(0.688397 - 8.15635i) q^{67} +(1.50729 - 3.93684i) q^{69} +(-4.57430 - 2.64097i) q^{71} +(-1.33884 - 2.31895i) q^{73} +(13.5398 - 10.9838i) q^{75} +(4.21454 - 2.43327i) q^{77} +(10.3366 + 5.96787i) q^{79} +(-8.23457 - 3.63207i) q^{81} +(4.48936 - 2.59193i) q^{83} +(9.23837 - 5.33377i) q^{85} +(-6.56393 + 1.04546i) q^{87} -14.5188i q^{89} -0.951357 q^{91} +(8.61192 - 1.37166i) q^{93} +(-8.74811 - 15.1522i) q^{95} +(-7.87275 + 4.54534i) q^{97} +(2.80104 + 2.51328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{9}+O(q^{10}) $ 36 * q + 4 * q^9	$ 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) $ 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.34511	−	1.09118i	0.776599	−	0.629995i
$3$	1.34511	−	1.09118i	0.776599	−	0.629995i
$4$		0			0
$5$	3.88149			1.73585			0.867927	−	0.496692i	$-0.165452\pi$
$5$	3.88149			1.73585			0.867927	+	0.496692i	$0.165452\pi$
$6$		0			0
$7$	−3.35972	−	1.93974i	−1.26985	−	0.733151i	−0.294895	−	0.955530i	$-0.595285\pi$
$7$	−3.35972	−	1.93974i	−1.26985	−	0.733151i	−0.974960	+	0.222379i	$0.928618\pi$
$8$		0			0
$9$	0.618641	−	2.93552i	0.206214	−	0.978507i
$10$		0			0
$11$	−0.627217	+	1.08637i	−0.189113	+	0.327553i	−0.944955	−	0.327201i	$-0.893895\pi$
$11$	−0.627217	+	1.08637i	−0.189113	+	0.327553i	0.755842	+	0.654754i	$0.227228\pi$
$12$		0			0
$13$	0.212374	−	0.122614i	0.0589020	−	0.0340071i	−0.470260	−	0.882528i	$-0.655840\pi$
$13$	0.212374	−	0.122614i	0.0589020	−	0.0340071i	0.529162	+	0.848521i	$0.322506\pi$
$14$		0			0
$15$	5.22103	−	4.23541i	1.34806	−	1.09358i
$16$		0			0
$17$	2.38011	−	1.37416i	0.577261	−	0.333282i	−0.182783	−	0.983153i	$-0.558511\pi$
$17$	2.38011	−	1.37416i	0.577261	−	0.333282i	0.760044	+	0.649871i	$0.225177\pi$
$18$		0			0
$19$	−2.25380	−	3.90370i	−0.517058	−	0.895571i	−0.999804	−	0.0198101i	$-0.993694\pi$
$19$	−2.25380	−	3.90370i	−0.517058	−	0.895571i	0.482746	−	0.875761i	$-0.339639\pi$
$20$		0			0
$21$	−6.63580	+	1.05691i	−1.44805	+	0.230637i
$22$		0			0
$23$	2.10776	−	1.21692i	0.439499	−	0.253745i	−0.263886	−	0.964554i	$-0.585004\pi$
$23$	2.10776	−	1.21692i	0.439499	−	0.253745i	0.703385	+	0.710809i	$0.251671\pi$
$24$		0			0
$25$	10.0660			2.01319
$26$		0			0
$27$	−2.37105	−	4.62365i	−0.456309	−	0.889821i
$28$		0			0
$29$	−3.32333	−	1.91873i	−0.617127	−	0.356299i	0.158622	−	0.987339i	$-0.449295\pi$
$29$	−3.32333	−	1.91873i	−0.617127	−	0.356299i	−0.775750	+	0.631041i	$0.782628\pi$
$30$		0			0
$31$	4.36024	+	2.51738i	0.783122	+	0.452135i	0.837535	−	0.546383i	$-0.183996\pi$
$31$	4.36024	+	2.51738i	0.783122	+	0.452135i	−0.0544138	+	0.998518i	$0.517329\pi$
$32$		0			0
$33$	0.341754	+	2.14570i	0.0594917	+	0.373518i
$34$		0			0
$35$	−13.0407	−	7.52906i	−2.20428	−	1.27264i
$36$		0			0
$37$	4.49590	+	7.78713i	0.739122	+	1.28020i	0.952891	+	0.303312i	$0.0980924\pi$
$37$	4.49590	+	7.78713i	0.739122	+	1.28020i	−0.213770	+	0.976884i	$0.568574\pi$
$38$		0			0
$39$	0.151872	−	0.396668i	0.0243190	−	0.0635178i
$40$		0			0
$41$	−3.59904	+	6.23373i	−0.562076	+	0.973544i	0.435239	+	0.900315i	$0.356664\pi$
$41$	−3.59904	+	6.23373i	−0.562076	+	0.973544i	−0.997315	+	0.0732295i	$0.976669\pi$
$42$		0			0
$43$			4.98044i			0.759510i	0.925087	+	0.379755i	$0.123992\pi$
$43$			4.98044i			0.759510i	−0.925087	+	0.379755i	$0.876008\pi$
$44$		0			0
$45$	2.40125	−	11.3942i	0.357957	−	1.69855i
$46$		0			0
$47$	−4.99134	−	2.88175i	−0.728062	−	0.420347i	0.0896509	−	0.995973i	$-0.471425\pi$
$47$	−4.99134	−	2.88175i	−0.728062	−	0.420347i	−0.817713	+	0.575627i	$0.804758\pi$
$48$		0			0
$49$	4.02515	+	6.97176i	0.575021	+	0.995965i
$50$		0			0
$51$	1.70205	−	4.44553i	0.238335	−	0.622498i
$52$		0			0
$53$	11.4657			1.57493			0.787464	−	0.616361i	$-0.211394\pi$
$53$	11.4657			1.57493			0.787464	+	0.616361i	$0.211394\pi$
$54$		0			0
$55$	−2.43453	+	4.21674i	−0.328272	+	0.568585i
$56$		0			0
$57$	−7.29126	−	2.79160i	−0.965752	−	0.369756i
$58$		0			0
$59$			13.5856i			1.76869i	0.466832	+	0.884346i	$0.345395\pi$
$59$			13.5856i			1.76869i	−0.466832	+	0.884346i	$0.654605\pi$
$60$		0			0
$61$	−6.26687	+	3.61818i	−0.802391	+	0.463261i	−0.844307	−	0.535860i	$-0.819987\pi$
$61$	−6.26687	+	3.61818i	−0.802391	+	0.463261i	0.0419155	+	0.999121i	$0.486654\pi$
$62$		0			0
$63$	−7.77259	+	8.66253i	−0.979255	+	1.09138i
$64$		0			0
$65$	0.824327	−	0.475926i	0.102245	−	0.0590313i
$66$		0			0
$67$	0.688397	−	8.15635i	0.0841011	−	0.996457i
$67$	0.688397	−	8.15635i	0.0841011	−	0.996457i
$68$		0			0
$69$	1.50729	−	3.93684i	0.181457	−	0.473940i
$70$		0			0
$71$	−4.57430	−	2.64097i	−0.542869	−	0.313426i	0.203372	−	0.979102i	$-0.434810\pi$
$71$	−4.57430	−	2.64097i	−0.542869	−	0.313426i	−0.746241	+	0.665676i	$0.768143\pi$
$72$		0			0
$73$	−1.33884	−	2.31895i	−0.156700	−	0.271412i	0.776977	−	0.629529i	$-0.216752\pi$
$73$	−1.33884	−	2.31895i	−0.156700	−	0.271412i	−0.933677	+	0.358117i	$0.883419\pi$
$74$		0			0
$75$	13.5398	−	10.9838i	1.56344	−	1.26830i
$76$		0			0
$77$	4.21454	−	2.43327i	0.480292	−	0.277297i
$78$		0			0
$79$	10.3366	+	5.96787i	1.16296	+	0.671437i	0.952012	−	0.306059i	$-0.0990106\pi$
$79$	10.3366	+	5.96787i	1.16296	+	0.671437i	0.210951	+	0.977497i	$0.432344\pi$
$80$		0			0
$81$	−8.23457	−	3.63207i	−0.914952	−	0.403563i
$82$		0			0
$83$	4.48936	−	2.59193i	0.492771	−	0.284501i	−0.232952	−	0.972488i	$-0.574839\pi$
$83$	4.48936	−	2.59193i	0.492771	−	0.284501i	0.725723	+	0.687987i	$0.241505\pi$
$84$		0			0
$85$	9.23837	−	5.33377i	1.00204	−	0.578529i
$86$		0			0
$87$	−6.56393	+	1.04546i	−0.703727	+	0.112086i
$88$		0			0
$89$		−	14.5188i		−	1.53899i	−0.638654	−	0.769494i	$-0.720508\pi$
$89$		−	14.5188i		−	1.53899i	0.638654	−	0.769494i	$-0.279492\pi$
$90$		0			0
$91$	−0.951357			−0.0997293
$92$		0			0
$93$	8.61192	−	1.37166i	0.893015	−	0.142234i
$94$		0			0
$95$	−8.74811	−	15.1522i	−0.897537	−	1.55458i
$96$		0			0
$97$	−7.87275	+	4.54534i	−0.799357	+	0.461509i	−0.843246	−	0.537527i	$-0.819358\pi$
$97$	−7.87275	+	4.54534i	−0.799357	+	0.461509i	0.0438893	+	0.999036i	$0.486025\pi$
$98$		0			0
$99$	2.80104	+	2.51328i	0.281515	+	0.252594i
$100$		0			0
$101$	2.52450	−	4.37257i	0.251197	−	0.435087i	−0.712658	−	0.701511i	$-0.752509\pi$
$101$	2.52450	−	4.37257i	0.251197	−	0.435087i	0.963856	+	0.266425i	$0.0858424\pi$
$102$		0			0
$103$	−6.84831	+	11.8616i	−0.674784	+	1.16876i	0.301748	+	0.953388i	$0.402430\pi$
$103$	−6.84831	+	11.8616i	−0.674784	+	1.16876i	−0.976532	+	0.215372i	$0.930904\pi$
$104$		0			0
$105$	−25.7568	+	4.10239i	−2.51360	+	0.400352i
$106$		0			0
$107$		−	3.79092i		−	0.366482i	−0.983068	−	0.183241i	$-0.941341\pi$
$107$		−	3.79092i		−	0.366482i	0.983068	−	0.183241i	$-0.0586589\pi$
$108$		0			0
$109$		−	13.2469i		−	1.26882i	−0.772996	−	0.634410i	$-0.781243\pi$
$109$		−	13.2469i		−	1.26882i	0.772996	−	0.634410i	$-0.218757\pi$
$110$		0			0
$111$	14.5447	+	5.56869i	1.38052	+	0.528557i
$112$		0			0
$113$	−5.21599	+	9.03436i	−0.490679	+	0.849881i	−0.999942	−	0.0107295i	$-0.996585\pi$
$113$	−5.21599	+	9.03436i	−0.490679	+	0.849881i	0.509263	+	0.860611i	$0.329918\pi$
$114$		0			0
$115$	8.18126	−	4.72345i	0.762906	−	0.440464i
$116$		0			0
$117$	−0.228553	−	0.699283i	−0.0211298	−	0.0646487i
$118$		0			0
$119$	−10.6620			−0.977384
$120$		0			0
$121$	4.71320	+	8.16350i	0.428473	+	0.742136i
$122$		0			0
$123$	1.96103	+	12.3123i	0.176820	+	1.11016i
$124$		0			0
$125$	19.6634			1.75875
$126$		0			0
$127$	−7.98871	+	13.8369i	−0.708883	+	1.22782i	0.256388	+	0.966574i	$0.417467\pi$
$127$	−7.98871	+	13.8369i	−0.708883	+	1.22782i	−0.965272	+	0.261248i	$0.915866\pi$
$128$		0			0
$129$	5.43457	+	6.69924i	0.478487	+	0.589835i
$130$		0			0
$131$			15.7455i			1.37569i	0.725858	+	0.687845i	$0.241443\pi$
$131$			15.7455i			1.37569i	−0.725858	+	0.687845i	$0.758557\pi$
$132$		0			0
$133$			17.4871i			1.51633i
$134$		0			0
$135$	−9.20320	−	17.9466i	−0.792086	−	1.54460i
$136$		0			0
$137$	8.23468			0.703536			0.351768	−	0.936087i	$-0.385581\pi$
$137$	8.23468			0.703536			0.351768	+	0.936087i	$0.385581\pi$
$138$		0			0
$139$		−	6.95330i		−	0.589771i	−0.955533	−	0.294886i	$-0.904718\pi$
$139$		−	6.95330i		−	0.589771i	0.955533	−	0.294886i	$-0.0952815\pi$
$140$		0			0
$141$	−9.85842	+	1.57019i	−0.830228	+	0.132234i
$142$		0			0
$143$			0.307623i			0.0257247i
$144$		0			0
$145$	−12.8995	−	7.44752i	−1.07124	−	0.618483i
$146$		0			0
$147$	13.0217	+	4.98561i	1.07401	+	0.411206i
$148$		0			0
$149$		−	2.73894i		−	0.224382i	−0.993687	−	0.112191i	$-0.964213\pi$
$149$		−	2.73894i		−	0.224382i	0.993687	−	0.112191i	$-0.0357869\pi$
$150$		0			0
$151$	7.82034	+	13.5452i	0.636410	+	1.10230i	0.986214	+	0.165472i	$0.0529148\pi$
$151$	7.82034	+	13.5452i	0.636410	+	1.10230i	−0.349804	+	0.936823i	$0.613752\pi$
$152$		0			0
$153$	−2.56143	−	7.83697i	−0.207080	−	0.633581i
$154$		0			0
$155$	16.9242	+	9.77120i	1.35939	+	0.784841i
$156$		0			0
$157$	11.4185	+	19.7775i	0.911297	+	1.57841i	0.812234	+	0.583332i	$0.198251\pi$
$157$	11.4185	+	19.7775i	0.911297	+	1.57841i	0.0990631	+	0.995081i	$0.468415\pi$
$158$		0			0
$159$	15.4226	−	12.5111i	1.22309	−	0.992196i
$160$		0			0
$161$	−9.44199			−0.744133
$162$		0			0
$163$	7.34398	−	12.7202i	0.575225	−	0.996319i	−0.420792	−	0.907157i	$-0.638248\pi$
$163$	7.34398	−	12.7202i	0.575225	−	0.996319i	0.996017	−	0.0891620i	$-0.0284189\pi$
$164$		0			0
$165$	1.32651	+	8.32849i	0.103269	+	0.648372i
$166$		0			0
$167$	7.20297	+	4.15864i	0.557382	+	0.321805i	0.752094	−	0.659056i	$-0.229044\pi$
$167$	7.20297	+	4.15864i	0.557382	+	0.321805i	−0.194712	+	0.980861i	$0.562377\pi$
$168$		0			0
$169$	−6.46993	+	11.2063i	−0.497687	+	0.862019i
$170$		0			0
$171$	−12.8537	+	4.20110i	−0.982946	+	0.321266i
$172$		0			0
$173$	−8.59974	+	4.96506i	−0.653826	+	0.377487i	−0.789921	−	0.613209i	$-0.789878\pi$
$173$	−8.59974	+	4.96506i	−0.653826	+	0.377487i	0.136094	+	0.990696i	$0.456545\pi$
$174$		0			0
$175$	−33.8188	−	19.5253i	−2.55646	−	1.47597i
$176$		0			0
$177$	14.8244	+	18.2741i	1.11427	+	1.37357i
$178$		0			0
$179$	−15.9946			−1.19549			−0.597745	−	0.801686i	$-0.703936\pi$
$179$	−15.9946			−1.19549			−0.597745	+	0.801686i	$0.703936\pi$
$180$		0			0
$181$	−0.942874	+	1.63310i	−0.0700832	+	0.121388i	−0.898938	−	0.438077i	$-0.855660\pi$
$181$	−0.942874	+	1.63310i	−0.0700832	+	0.121388i	0.828854	+	0.559464i	$0.188993\pi$
$182$		0			0
$183$	−4.48154	+	11.7052i	−0.331285	+	0.865270i
$184$		0			0
$185$	17.4508	+	30.2256i	1.28301	+	2.22223i
$186$		0			0
$187$			3.44758i			0.252112i
$188$		0			0
$189$	−1.00259	+	20.1334i	−0.0729276	+	1.46449i
$190$		0			0
$191$	−4.47978	−	7.75920i	−0.324145	−	0.561436i	0.657194	−	0.753722i	$-0.271743\pi$
$191$	−4.47978	−	7.75920i	−0.324145	−	0.561436i	−0.981339	+	0.192286i	$0.938410\pi$
$192$		0			0
$193$	−23.0959			−1.66248			−0.831240	−	0.555913i	$-0.812369\pi$
$193$	−23.0959			−1.66248			−0.831240	+	0.555913i	$0.812369\pi$
$194$		0			0
$195$	0.589489	−	1.53966i	0.0422142	−	0.110258i
$196$		0			0
$197$	2.18338	−	3.78172i	0.155559	−	0.269437i	−0.777703	−	0.628632i	$-0.783615\pi$
$197$	2.18338	−	3.78172i	0.155559	−	0.269437i	0.933263	+	0.359195i	$0.116949\pi$
$198$		0			0
$199$	−9.84782	−	17.0569i	−0.698094	−	1.20913i	−0.969127	−	0.246563i	$-0.920699\pi$
$199$	−9.84782	−	17.0569i	−0.698094	−	1.20913i	0.271033	−	0.962570i	$-0.412635\pi$
$200$		0			0
$201$	−7.97410	−	11.7224i	−0.562450	−	0.826831i
$202$		0			0
$203$	7.44365	+	12.8928i	0.522441	+	0.904895i
$204$		0			0
$205$	−13.9696	+	24.1961i	−0.975682	+	1.68993i
$206$		0			0
$207$	−2.26834	−	6.94022i	−0.157660	−	0.482378i
$208$		0			0
$209$	5.65449			0.391129
$210$		0			0
$211$	3.35134	+	5.80468i	0.230715	+	0.399611i	0.958019	−	0.286705i	$-0.0925600\pi$
$211$	3.35134	+	5.80468i	0.230715	+	0.399611i	−0.727303	+	0.686316i	$0.759227\pi$
$212$		0			0
$213$	−9.03471	+	1.43900i	−0.619048	+	0.0985984i
$214$		0			0
$215$			19.3315i			1.31840i
$216$		0			0
$217$	−9.76612	−	16.9154i	−0.662967	−	1.14829i
$218$		0			0
$219$	−4.33128	−	1.65831i	−0.292681	−	0.112058i
$220$		0			0
$221$	0.336982	−	0.583670i	0.0226679	−	0.0392619i
$222$		0			0
$223$	21.8757			1.46491			0.732453	−	0.680818i	$-0.238375\pi$
$223$	21.8757			1.46491			0.732453	+	0.680818i	$0.238375\pi$
$224$		0			0
$225$	6.22721	−	29.5488i	0.415147	−	1.96992i
$226$		0			0
$227$	−20.0286	−	11.5635i	−1.32935	−	0.767499i	−0.344148	−	0.938915i	$-0.611832\pi$
$227$	−20.0286	−	11.5635i	−1.32935	−	0.767499i	−0.985199	+	0.171417i	$0.945166\pi$
$228$		0			0
$229$	6.23794	−	3.60148i	0.412215	−	0.237992i	−0.279526	−	0.960138i	$-0.590177\pi$
$229$	6.23794	−	3.60148i	0.412215	−	0.237992i	0.691741	+	0.722146i	$0.256844\pi$
$230$		0			0
$231$	3.01388	−	7.87185i	0.198299	−	0.517930i
$232$		0			0
$233$	−4.25690	+	7.37317i	−0.278879	+	0.483033i	−0.971106	−	0.238647i	$-0.923296\pi$
$233$	−4.25690	+	7.37317i	−0.278879	+	0.483033i	0.692227	+	0.721679i	$0.256630\pi$
$234$		0			0
$235$	−19.3738	−	11.1855i	−1.26381	−	0.729661i
$236$		0			0
$237$	20.4160	−	3.25174i	1.32616	−	0.211223i
$238$		0			0
$239$	8.16585	−	14.1437i	0.528205	−	0.914877i	−0.471255	−	0.881997i	$-0.656199\pi$
$239$	8.16585	−	14.1437i	0.528205	−	0.914877i	0.999459	−	0.0328801i	$-0.0104679\pi$
$240$		0			0
$241$	23.8540			1.53657			0.768285	−	0.640107i	$-0.221110\pi$
$241$	23.8540			1.53657			0.768285	+	0.640107i	$0.221110\pi$
$242$		0			0
$243$	−15.0396	+	4.09989i	−0.964794	+	0.263008i
$244$		0			0
$245$	15.6236	+	27.0608i	0.998153	+	1.72885i
$246$		0			0
$247$	−0.957299	−	0.552697i	−0.0609115	−	0.0351672i
$248$		0			0
$249$	3.21041	−	8.38514i	0.203451	−	0.531387i
$250$		0			0
$251$	−9.68800	−	16.7801i	−0.611501	−	1.05915i	−0.990988	−	0.133954i	$-0.957233\pi$
$251$	−9.68800	−	16.7801i	−0.611501	−	1.05915i	0.379487	−	0.925197i	$-0.376101\pi$
$252$		0			0
$253$			3.05308i			0.191946i
$254$		0			0
$255$	6.60650	−	17.2553i	0.413715	−	1.08057i
$256$		0			0
$257$	−13.7082	−	7.91441i	−0.855091	−	0.493687i	0.00727411	−	0.999974i	$-0.497685\pi$
$257$	−13.7082	−	7.91441i	−0.855091	−	0.493687i	−0.862365	+	0.506286i	$0.831018\pi$
$258$		0			0
$259$		−	34.8834i		−	2.16755i
$260$		0			0
$261$	−7.68841	+	8.56871i	−0.475901	+	0.530390i
$262$		0			0
$263$			24.3793i			1.50329i	0.659566	+	0.751646i	$0.270740\pi$
$263$			24.3793i			1.50329i	−0.659566	+	0.751646i	$0.729260\pi$
$264$		0			0
$265$	44.5038			2.73385
$266$		0			0
$267$	−15.8427	−	19.5294i	−0.969555	−	1.19518i
$268$		0			0
$269$			3.44695i			0.210165i	0.994464	+	0.105082i	$0.0335106\pi$
$269$			3.44695i			0.210165i	−0.994464	+	0.105082i	$0.966489\pi$
$270$		0			0
$271$		−	2.75984i		−	0.167648i	−0.996481	−	0.0838242i	$-0.973287\pi$
$271$		−	2.75984i		−	0.167648i	0.996481	−	0.0838242i	$-0.0267134\pi$
$272$		0			0
$273$	−1.27968	+	1.03810i	−0.0774497	+	0.0628289i
$274$		0			0
$275$	−6.31353	+	10.9354i	−0.380720	+	0.659427i
$276$		0			0
$277$	13.6723			0.821486			0.410743	−	0.911751i	$-0.365269\pi$
$277$	13.6723			0.821486			0.410743	+	0.911751i	$0.365269\pi$
$278$		0			0
$279$	10.0873	−	11.2422i	0.603908	−	0.673054i
$280$		0			0
$281$	−12.1324	−	21.0139i	−0.723758	−	1.25359i	−0.959483	−	0.281766i	$-0.909080\pi$
$281$	−12.1324	−	21.0139i	−0.723758	−	1.25359i	0.235725	−	0.971820i	$-0.424254\pi$
$282$		0			0
$283$	−27.4244			−1.63021			−0.815105	−	0.579314i	$-0.803321\pi$
$283$	−27.4244			−1.63021			−0.815105	+	0.579314i	$0.803321\pi$
$284$		0			0
$285$	−28.3010	−	10.8355i	−1.67640	−	0.641842i
$286$		0			0
$287$	24.1836	−	13.9624i	1.42751	−	0.824173i
$288$		0			0
$289$	−4.72339	+	8.18115i	−0.277846	+	0.481244i
$290$		0			0
$291$	−5.62992	+	14.7046i	−0.330032	+	0.861998i
$292$		0			0
$293$			22.7737i			1.33045i	0.746642	+	0.665227i	$0.231665\pi$
$293$			22.7737i			1.33045i	−0.746642	+	0.665227i	$0.768335\pi$
$294$		0			0
$295$			52.7323i			3.07019i
$296$		0			0
$297$	6.51016	+	0.324189i	0.377758	+	0.0188113i
$298$		0			0
$299$	0.298423	−	0.516883i	0.0172582	−	0.0298921i
$300$		0			0
$301$	9.66074	−	16.7329i	0.556836	−	0.964468i
$302$		0			0
$303$	−1.37554	−	8.63627i	−0.0790225	−	0.496141i
$304$		0			0
$305$	−24.3248	+	14.0439i	−1.39283	+	0.804153i
$306$		0			0
$307$	8.71982	+	15.1032i	0.497667	+	0.861984i	0.999996	−	0.00269227i	$-0.000856979\pi$
$307$	8.71982	+	15.1032i	0.497667	+	0.861984i	−0.502330	+	0.864676i	$0.667524\pi$
$308$		0			0
$309$	3.73147	+	23.4279i	0.212276	+	1.33277i
$310$		0			0
$311$	24.2830			1.37696			0.688481	−	0.725254i	$-0.258278\pi$
$311$	24.2830			1.37696			0.688481	+	0.725254i	$0.258278\pi$
$312$		0			0
$313$			16.0128i			0.905096i	0.891740	+	0.452548i	$0.149485\pi$
$313$			16.0128i			0.905096i	−0.891740	+	0.452548i	$0.850515\pi$
$314$		0			0
$315$	−30.1692	+	33.6235i	−1.69984	+	1.89447i
$316$		0			0
$317$	18.2390	−	10.5303i	1.02440	−	0.591439i	0.109026	−	0.994039i	$-0.465227\pi$
$317$	18.2390	−	10.5303i	1.02440	−	0.591439i	0.915376	+	0.402600i	$0.131893\pi$
$318$		0			0
$319$	4.16890	−	2.40691i	0.233414	−	0.134761i
$320$		0			0
$321$	−4.13659	−	5.09921i	−0.230882	−	0.284610i
$322$		0			0
$323$	−10.7286	−	6.19416i	−0.596955	−	0.344652i
$324$		0			0
$325$	2.13775	−	1.23423i	0.118581	−	0.0684627i
$326$		0			0
$327$	−14.4548	−	17.8185i	−0.799350	−	0.985366i
$328$		0			0
$329$	11.1797	+	19.3638i	0.616355	+	1.06756i
$330$		0			0
$331$	1.10208	+	0.636285i	0.0605757	+	0.0349734i	0.529982	−	0.848009i	$-0.322199\pi$
$331$	1.10208	+	0.636285i	0.0605757	+	0.0349734i	−0.469406	+	0.882982i	$0.655532\pi$
$332$		0			0
$333$	25.6406	−	8.38038i	1.40510	−	0.459242i
$334$		0			0
$335$	2.67201	−	31.6588i	0.145987	−	1.72970i
$336$		0			0
$337$	6.06739	−	3.50301i	0.330512	−	0.190821i	−0.325556	−	0.945523i	$-0.605552\pi$
$337$	6.06739	−	3.50301i	0.330512	−	0.190821i	0.656068	+	0.754701i	$0.272218\pi$
$338$		0			0
$339$	2.84206	+	17.8438i	0.154359	+	0.969143i
$340$		0			0
$341$	−5.46963	+	3.15789i	−0.296197	+	0.171009i
$342$		0			0
$343$		−	4.07458i		−	0.220007i
$344$		0			0
$345$	5.85054	−	15.2808i	0.314982	−	0.822691i
$346$		0			0
$347$	−1.92761	+	3.33871i	−0.103479	+	0.179231i	−0.913116	−	0.407700i	$-0.866331\pi$
$347$	−1.92761	+	3.33871i	−0.103479	+	0.179231i	0.809637	+	0.586932i	$0.199664\pi$
$348$		0			0
$349$	−9.82588			−0.525967			−0.262984	−	0.964800i	$-0.584707\pi$
$349$	−9.82588			−0.525967			−0.262984	+	0.964800i	$0.584707\pi$
$350$		0			0
$351$	−1.07047	−	0.691218i	−0.0571377	−	0.0368945i
$352$		0			0
$353$	−13.8891	−	24.0566i	−0.739241	−	1.28040i	−0.952837	−	0.303482i	$-0.901851\pi$
$353$	−13.8891	−	24.0566i	−0.739241	−	1.28040i	0.213596	−	0.976922i	$-0.431482\pi$
$354$		0			0
$355$	−17.7551	−	10.2509i	−0.942342	−	0.544061i
$356$		0			0
$357$	−14.3416	+	11.6342i	−0.759036	+	0.615747i
$358$		0			0
$359$		−	13.2317i		−	0.698345i	−0.937059	−	0.349172i	$-0.886463\pi$
$359$		−	13.2317i		−	0.698345i	0.937059	−	0.349172i	$-0.113537\pi$
$360$		0			0
$361$	−0.659258	+	1.14187i	−0.0346978	+	0.0600984i
$362$		0			0
$363$	15.2476	+	5.83784i	0.800294	+	0.306407i
$364$		0			0
$365$	−5.19671	−	9.00096i	−0.272008	−	0.471132i
$366$		0			0
$367$	11.1785	+	6.45394i	0.583515	+	0.336893i	0.762529	−	0.646954i	$-0.223957\pi$
$367$	11.1785	+	6.45394i	0.583515	+	0.336893i	−0.179014	+	0.983847i	$0.557291\pi$
$368$		0			0
$369$	16.0727	+	14.4215i	0.836712	+	0.750754i
$370$		0			0
$371$	−38.5214	−	22.2403i	−1.99993	−	1.15466i
$372$		0			0
$373$	−26.7907	−	15.4676i	−1.38717	−	0.800884i	−0.394176	−	0.919035i	$-0.628970\pi$
$373$	−26.7907	−	15.4676i	−1.38717	−	0.800884i	−0.992996	+	0.118151i	$0.962303\pi$
$374$		0			0
$375$	26.4495	−	21.4564i	1.36584	−	1.10800i
$376$		0			0
$377$	−0.941053			−0.0484667
$378$		0			0
$379$	3.14215	−	1.81412i	0.161402	−	0.0931853i	−0.417124	−	0.908850i	$-0.636962\pi$
$379$	3.14215	−	1.81412i	0.161402	−	0.0931853i	0.578525	+	0.815665i	$0.303628\pi$
$380$		0			0
$381$	4.35284	+	27.3292i	0.223003	+	1.40012i
$382$		0			0
$383$	1.74713	+	3.02611i	0.0892740	+	0.154627i	0.907204	−	0.420690i	$-0.138212\pi$
$383$	1.74713	+	3.02611i	0.0892740	+	0.154627i	−0.817930	+	0.575317i	$0.804879\pi$
$384$		0			0
$385$	16.3587	−	9.44470i	0.833717	−	0.481347i
$386$		0			0
$387$	14.6202	+	3.08110i	0.743186	+	0.156621i
$388$		0			0
$389$	−1.03941	+	0.600102i	−0.0527001	+	0.0304264i	−0.526119	−	0.850411i	$-0.676353\pi$
$389$	−1.03941	+	0.600102i	−0.0527001	+	0.0304264i	0.473418	+	0.880838i	$0.343020\pi$
$390$		0			0
$391$	3.34447	−	5.79279i	0.169137	−	0.292954i
$392$		0			0
$393$	17.1812	+	21.1794i	0.866677	+	1.06836i
$394$		0			0
$395$	40.1216	+	23.1642i	2.01874	+	1.16552i
$396$		0			0
$397$	17.9116			0.898957			0.449479	−	0.893291i	$-0.351610\pi$
$397$	17.9116			0.898957			0.449479	+	0.893291i	$0.351610\pi$
$398$		0			0
$399$	19.0817	+	23.5221i	0.955277	+	1.17758i
$400$		0			0
$401$	−28.8046			−1.43843			−0.719216	−	0.694786i	$-0.755499\pi$
$401$	−28.8046			−1.43843			−0.719216	+	0.694786i	$0.755499\pi$
$402$		0			0
$403$	1.23467			0.0615032
$404$		0			0
$405$	−31.9624	−	14.0978i	−1.58822	−	0.700526i
$406$		0			0
$407$	−11.2796			−0.559110
$408$		0			0
$409$	0.151315	+	0.0873619i	0.00748206	+	0.00431977i	0.503736	−	0.863857i	$-0.331958\pi$
$409$	0.151315	+	0.0873619i	0.00748206	+	0.00431977i	−0.496254	+	0.868177i	$0.665292\pi$
$410$		0			0
$411$	11.0765	−	8.98554i	0.546366	−	0.443224i
$412$		0			0
$413$	26.3524	−	45.6438i	1.29672	−	2.24598i
$414$		0			0
$415$	17.4254	−	10.0605i	0.855378	−	0.493853i
$416$		0			0
$417$	−7.58732	−	9.35295i	−0.371553	−	0.458016i
$418$		0			0
$419$	13.5143	−	7.80247i	0.660216	−	0.381176i	−0.132143	−	0.991231i	$-0.542186\pi$
$419$	13.5143	−	7.80247i	0.660216	−	0.381176i	0.792359	+	0.610055i	$0.208853\pi$
$420$		0			0
$421$	−6.45391	−	11.1785i	−0.314544	−	0.544807i	0.664796	−	0.747025i	$-0.268518\pi$
$421$	−6.45391	−	11.1785i	−0.314544	−	0.544807i	−0.979341	+	0.202218i	$0.935185\pi$
$422$		0			0
$423$	−11.5473	+	12.8694i	−0.561448	+	0.625732i
$424$		0			0
$425$	23.9581	−	13.8322i	1.16214	−	0.670960i
$426$		0			0
$427$	28.0733			1.35856
$428$		0			0
$429$	0.335673	+	0.413786i	0.0162064	+	0.0199778i
$430$		0			0
$431$	11.1167	+	6.41823i	0.535472	+	0.309155i	0.743242	−	0.669023i	$-0.233287\pi$
$431$	11.1167	+	6.41823i	0.535472	+	0.309155i	−0.207770	+	0.978178i	$0.566620\pi$
$432$		0			0
$433$	16.1828	+	9.34314i	0.777695	+	0.449003i	0.835613	−	0.549319i	$-0.185113\pi$
$433$	16.1828	+	9.34314i	0.777695	+	0.449003i	−0.0579175	+	0.998321i	$0.518446\pi$
$434$		0			0
$435$	−25.4778	+	4.05796i	−1.22157	+	0.194564i
$436$		0			0
$437$	−9.50096	−	5.48538i	−0.454493	−	0.262402i
$438$		0			0
$439$	−17.0816	−	29.5861i	−0.815258	−	1.41207i	−0.909142	−	0.416486i	$-0.863262\pi$
$439$	−17.0816	−	29.5861i	−0.815258	−	1.41207i	0.0938839	−	0.995583i	$-0.470072\pi$
$440$		0			0
$441$	22.9559	−	7.50289i	1.09314	−	0.357280i
$442$		0			0
$443$	8.21846	−	14.2348i	0.390471	−	0.676316i	−0.602041	−	0.798465i	$-0.705645\pi$
$443$	8.21846	−	14.2348i	0.390471	−	0.676316i	0.992512	+	0.122150i	$0.0389788\pi$
$444$		0			0
$445$		−	56.3545i		−	2.67146i
$446$		0			0
$447$	−2.98868	−	3.68417i	−0.141360	−	0.174255i
$448$		0			0
$449$	−32.4623	−	18.7421i	−1.53199	−	0.884495i	−0.999270	−	0.0382032i	$-0.987837\pi$
$449$	−32.4623	−	18.7421i	−1.53199	−	0.884495i	−0.532720	−	0.846292i	$-0.678830\pi$
$450$		0			0
$451$	−4.51476	−	7.81979i	−0.212592	−	0.368220i
$452$		0			0
$453$	25.2995	+	9.68640i	1.18868	+	0.455107i
$454$		0			0
$455$	−3.69268			−0.173115
$456$		0			0
$457$	12.0175	−	20.8150i	0.562157	−	0.973684i	−0.435151	−	0.900357i	$-0.643305\pi$
$457$	12.0175	−	20.8150i	0.562157	−	0.973684i	0.997308	−	0.0733264i	$-0.0233615\pi$
$458$		0			0
$459$	−11.9970	−	7.74659i	−0.559971	−	0.361580i
$460$		0			0
$461$		−	22.7880i		−	1.06134i	−0.847578	−	0.530671i	$-0.821940\pi$
$461$		−	22.7880i		−	1.06134i	0.847578	−	0.530671i	$-0.178060\pi$
$462$		0			0
$463$	−9.57563	+	5.52849i	−0.445017	+	0.256931i	−0.705724	−	0.708487i	$-0.749378\pi$
$463$	−9.57563	+	5.52849i	−0.445017	+	0.256931i	0.260706	+	0.965418i	$0.416045\pi$
$464$		0			0
$465$	33.4271	−	5.32407i	1.55014	−	0.246898i
$466$		0			0
$467$	17.7284	−	10.2355i	0.820373	−	0.473643i	−0.0301719	−	0.999545i	$-0.509605\pi$
$467$	17.7284	−	10.2355i	0.820373	−	0.473643i	0.850545	+	0.525902i	$0.176272\pi$
$468$		0			0
$469$	−18.1340	+	26.0678i	−0.837350	+	1.20370i
$470$		0			0
$471$	36.9400	+	14.1432i	1.70210	+	0.651682i
$472$		0			0
$473$	−5.41061	−	3.12382i	−0.248780	−	0.143633i
$474$		0			0
$475$	−22.6867	−	39.2945i	−1.04094	−	1.80295i
$476$		0			0
$477$	7.09312	−	33.6577i	0.324772	−	1.54108i
$478$		0			0
$479$	27.4058	−	15.8228i	1.25220	−	0.722960i	0.280657	−	0.959808i	$-0.409448\pi$
$479$	27.4058	−	15.8228i	1.25220	−	0.722960i	0.971547	+	0.236848i	$0.0761142\pi$
$480$		0			0
$481$	1.90963	+	1.10252i	0.0870714	+	0.0502707i
$482$		0			0
$483$	−12.7005	+	10.3029i	−0.577893	+	0.468800i
$484$		0			0
$485$	−30.5580	+	17.6427i	−1.38757	+	0.801112i
$486$		0			0
$487$	29.3373	−	16.9379i	1.32940	−	0.767529i	0.344193	−	0.938899i	$-0.388153\pi$
$487$	29.3373	−	16.9379i	1.32940	−	0.767529i	0.985207	+	0.171369i	$0.0548192\pi$
$488$		0			0
$489$	−4.00155	−	25.1236i	−0.180956	−	1.13613i
$490$		0			0
$491$		−	17.0343i		−	0.768747i	−0.923178	−	0.384373i	$-0.874418\pi$
$491$		−	17.0343i		−	0.768747i	0.923178	−	0.384373i	$-0.125582\pi$
$492$		0			0
$493$	−10.5465			−0.474992
$494$		0			0
$495$	10.8722	+	9.75527i	0.488670	+	0.438467i
$496$		0			0
$497$	10.2456	+	17.7458i	0.459577	+	0.796010i
$498$		0			0
$499$	−27.8520	+	16.0803i	−1.24682	+	0.719855i	−0.970475	−	0.241203i	$-0.922458\pi$
$499$	−27.8520	+	16.0803i	−1.24682	+	0.719855i	−0.276350	+	0.961057i	$0.589125\pi$
$500$		0			0
$501$	14.2266	−	2.26593i	0.635598	−	0.101234i
$502$		0			0
$503$	1.14936	−	1.99076i	0.0512476	−	0.0887634i	−0.839264	−	0.543725i	$-0.817014\pi$
$503$	1.14936	−	1.99076i	0.0512476	−	0.0887634i	0.890511	+	0.454961i	$0.150347\pi$
$504$		0			0
$505$	9.79883	−	16.9721i	0.436042	−	0.755247i
$506$		0			0
$507$	3.52530	+	22.1335i	0.156564	+	0.982984i
$508$		0			0
$509$		−	2.69083i		−	0.119269i	−0.998220	−	0.0596344i	$-0.981006\pi$
$509$		−	2.69083i		−	0.119269i	0.998220	−	0.0596344i	$-0.0189935\pi$
$510$		0			0
$511$			10.3880i			0.459538i
$512$		0			0
$513$	−12.7055	+	19.6767i	−0.560960	+	0.868746i
$514$		0			0
$515$	−26.5816	+	46.0407i	−1.17133	+	2.02880i
$516$		0			0
$517$	6.26130	−	3.61496i	0.275372	−	0.158986i
$518$		0			0
$519$	−6.14980	+	16.0624i	−0.269946	+	0.705063i
$520$		0			0
$521$	−40.4214			−1.77089			−0.885447	−	0.464740i	$-0.846148\pi$
$521$	−40.4214			−1.77089			−0.885447	+	0.464740i	$0.846148\pi$
$522$		0			0
$523$	5.99149	+	10.3776i	0.261989	+	0.453779i	0.966770	−	0.255646i	$-0.0822881\pi$
$523$	5.99149	+	10.3776i	0.261989	+	0.453779i	−0.704781	+	0.709425i	$0.748955\pi$
$524$		0			0
$525$	−66.7956	+	10.6388i	−2.91520	+	0.464316i
$526$		0			0
$527$	13.8371			0.602754
$528$		0			0
$529$	−8.53822	+	14.7886i	−0.371227	+	0.642984i
$530$		0			0
$531$	39.8808	+	8.40459i	1.73068	+	0.364728i
$532$		0			0
$533$			1.76518i			0.0764582i
$534$		0			0
$535$		−	14.7144i		−	0.636160i
$536$		0			0
$537$	−21.5144	+	17.4530i	−0.928417	+	0.753152i
$538$		0			0
$539$	−10.0986			−0.434976
$540$		0			0
$541$		−	3.07859i		−	0.132359i	−0.997808	−	0.0661794i	$-0.978919\pi$
$541$		−	3.07859i		−	0.132359i	0.997808	−	0.0661794i	$-0.0210810\pi$
$542$		0			0
$543$	0.513747	+	3.22555i	0.0220470	+	0.138422i
$544$		0			0
$545$		−	51.4176i		−	2.20249i
$546$		0			0
$547$	−7.65174	−	4.41774i	−0.327165	−	0.188889i	0.327417	−	0.944880i	$-0.393822\pi$
$547$	−7.65174	−	4.41774i	−0.327165	−	0.188889i	−0.654582	+	0.755991i	$0.727155\pi$
$548$		0			0
$549$	6.74431	+	20.6349i	0.287840	+	0.880676i
$550$		0			0
$551$			17.2977i			0.736908i
$552$		0			0
$553$	−23.1522	−	40.1007i	−0.984530	−	1.70526i
$554$		0			0
$555$	56.4549	+	21.6148i	2.39638	+	0.917498i
$556$		0			0
$557$	−39.0857	−	22.5661i	−1.65611	−	0.956158i	−0.974483	−	0.224463i	$-0.927937\pi$
$557$	−39.0857	−	22.5661i	−1.65611	−	0.956158i	−0.681632	−	0.731695i	$-0.738729\pi$
$558$		0			0
$559$	0.610673	+	1.05772i	0.0258287	+	0.0447367i
$560$		0			0
$561$	3.76193	+	4.63737i	0.158829	+	0.195790i
$562$		0			0
$563$	12.1456			0.511876			0.255938	−	0.966693i	$-0.417616\pi$
$563$	12.1456			0.511876			0.255938	+	0.966693i	$0.417616\pi$
$564$		0			0
$565$	−20.2458	+	35.0668i	−0.851748	+	1.47527i
$566$		0			0
$567$	20.6206	+	28.1756i	0.865984	+	1.18326i
$568$		0			0
$569$	24.6397	+	14.2258i	1.03295	+	0.596375i	0.917829	−	0.396977i	$-0.129941\pi$
$569$	24.6397	+	14.2258i	1.03295	+	0.596375i	0.115123	+	0.993351i	$0.463274\pi$
$570$		0			0
$571$	4.58436	−	7.94035i	0.191850	−	0.332293i	−0.754014	−	0.656859i	$-0.771885\pi$
$571$	4.58436	−	7.94035i	0.191850	−	0.332293i	0.945863	+	0.324566i	$0.105218\pi$
$572$		0			0
$573$	−14.4925	−	5.54872i	−0.605433	−	0.231801i
$574$		0			0
$575$	21.2166	−	12.2494i	0.884795	−	0.510837i
$576$		0			0
$577$	15.6479	+	9.03430i	0.651429	+	0.376103i	0.789004	−	0.614389i	$-0.210597\pi$
$577$	15.6479	+	9.03430i	0.651429	+	0.376103i	−0.137574	+	0.990491i	$0.543931\pi$
$578$		0			0
$579$	−31.0665	+	25.2019i	−1.29108	+	1.04735i
$580$		0			0
$581$	−20.1106			−0.834330
$582$		0			0
$583$	−7.19145	+	12.4559i	−0.297839	+	0.515873i
$584$		0			0
$585$	−0.887127	−	2.71426i	−0.0366782	−	0.112221i
$586$		0			0
$587$	9.85635	+	17.0717i	0.406815	+	0.704624i	0.994531	−	0.104443i	$-0.0333060\pi$
$587$	9.85635	+	17.0717i	0.406815	+	0.704624i	−0.587716	+	0.809067i	$0.699973\pi$
$588$		0			0
$589$		−	22.6948i		−	0.935121i
$590$		0			0
$591$	−1.18967	−	7.46930i	−0.0489364	−	0.307246i
$592$		0			0
$593$	4.13414	+	7.16054i	0.169769	+	0.294048i	0.938338	−	0.345718i	$-0.112365\pi$
$593$	4.13414	+	7.16054i	0.169769	+	0.294048i	−0.768570	+	0.639766i	$0.779031\pi$
$594$		0			0
$595$	−41.3844			−1.69660
$596$		0			0
$597$	−31.8586	−	12.1977i	−1.30389	−	0.499217i
$598$		0			0
$599$	0.712722	−	1.23447i	0.0291210	−	0.0504391i	−0.851098	−	0.525008i	$-0.824063\pi$
$599$	0.712722	−	1.23447i	0.0291210	−	0.0504391i	0.880219	+	0.474568i	$0.157396\pi$
$600$		0			0
$601$	−1.39290	−	2.41258i	−0.0568177	−	0.0984111i	0.836218	−	0.548398i	$-0.184762\pi$
$601$	−1.39290	−	2.41258i	−0.0568177	−	0.0984111i	−0.893035	+	0.449987i	$0.851429\pi$
$602$		0			0
$603$	−23.5173	−	7.06666i	−0.957698	−	0.287777i
$604$		0			0
$605$	18.2942	+	31.6865i	0.743766	+	1.28824i
$606$		0			0
$607$	8.90480	−	15.4236i	0.361435	−	0.626024i	−0.626762	−	0.779210i	$-0.715620\pi$
$607$	8.90480	−	15.4236i	0.361435	−	0.626024i	0.988197	+	0.153187i	$0.0489537\pi$
$608$		0			0
$609$	24.0809	+	9.21982i	0.975807	+	0.373606i
$610$		0			0
$611$	−1.41337			−0.0571790
$612$		0			0
$613$	10.5256	+	18.2308i	0.425124	+	0.736336i	0.996432	−	0.0843993i	$-0.0268971\pi$
$613$	10.5256	+	18.2308i	0.425124	+	0.736336i	−0.571308	+	0.820736i	$0.693564\pi$
$614$		0			0
$615$	7.61170	+	47.7899i	0.306933	+	1.92707i
$616$		0			0
$617$		−	33.1197i		−	1.33335i	−0.745349	−	0.666675i	$-0.767717\pi$
$617$		−	33.1197i		−	1.33335i	0.745349	−	0.666675i	$-0.232283\pi$
$618$		0			0
$619$	−1.99266	−	3.45138i	−0.0800916	−	0.138723i	0.823197	−	0.567755i	$-0.192188\pi$
$619$	−1.99266	−	3.45138i	−0.0800916	−	0.138723i	−0.903289	+	0.429032i	$0.858855\pi$
$620$		0			0
$621$	−10.6242	−	6.86018i	−0.426335	−	0.275290i
$622$		0			0
$623$	−28.1626	+	48.7791i	−1.12831	+	1.95429i
$624$		0			0
$625$	25.9936			1.03974
$626$		0			0
$627$	7.60591	−	6.17008i	0.303751	−	0.246409i
$628$		0			0
$629$	21.4015	+	12.3561i	0.853333	+	0.492672i
$630$		0			0
$631$	−27.8864	+	16.1002i	−1.11014	+	0.640939i	−0.938865	−	0.344285i	$-0.888121\pi$
$631$	−27.8864	+	16.1002i	−1.11014	+	0.640939i	−0.171273	+	0.985224i	$0.554788\pi$
$632$		0			0
$633$	10.8419	+	4.15102i	0.430926	+	0.164988i
$634$		0			0
$635$	−31.0081	+	53.7076i	−1.23052	+	2.13132i
$636$		0			0
$637$	1.70967	+	0.987080i	0.0677397	+	0.0391095i
$638$		0			0
$639$	−10.5825	+	11.7941i	−0.418636	+	0.466569i
$640$		0			0
$641$	−8.75082	+	15.1569i	−0.345637	+	0.598660i	−0.985469	−	0.169854i	$-0.945670\pi$
$641$	−8.75082	+	15.1569i	−0.345637	+	0.598660i	0.639833	+	0.768514i	$0.279004\pi$
$642$		0			0
$643$	−25.4591			−1.00401			−0.502005	−	0.864864i	$-0.667404\pi$
$643$	−25.4591			−1.00401			−0.502005	+	0.864864i	$0.667404\pi$
$644$		0			0
$645$	21.0942	+	26.0030i	0.830584	+	1.02387i
$646$		0			0
$647$	19.9663	+	34.5826i	0.784956	+	1.35958i	0.929026	+	0.370016i	$0.120648\pi$
$647$	19.9663	+	34.5826i	0.784956	+	1.35958i	−0.144070	+	0.989568i	$0.546019\pi$
$648$		0			0
$649$	−14.7590	−	8.52110i	−0.579341	−	0.334483i
$650$		0			0
$651$	−31.5943	−	12.0965i	−1.23828	−	0.474098i
$652$		0			0
$653$	−14.3876	−	24.9200i	−0.563029	−	0.975194i	−0.997230	−	0.0743785i	$-0.976303\pi$
$653$	−14.3876	−	24.9200i	−0.563029	−	0.975194i	0.434201	−	0.900816i	$-0.357031\pi$
$654$		0			0
$655$			61.1159i			2.38800i
$656$		0			0
$657$	−7.63558	+	2.49561i	−0.297892	+	0.0973630i
$658$		0			0
$659$	−6.42882	−	3.71168i	−0.250431	−	0.144586i	0.369531	−	0.929219i	$-0.379519\pi$
$659$	−6.42882	−	3.71168i	−0.250431	−	0.144586i	−0.619962	+	0.784632i	$0.712852\pi$
$660$		0			0
$661$		−	0.557131i		−	0.0216699i	−0.999941	−	0.0108350i	$-0.996551\pi$
$661$		−	0.557131i		−	0.0216699i	0.999941	−	0.0108350i	$-0.00344894\pi$
$662$		0			0
$663$	−0.183613	−	1.15281i	−0.00713094	−	0.0447714i
$664$		0			0
$665$			67.8761i			2.63212i
$666$		0			0
$667$	−9.33973			−0.361636
$668$		0			0
$669$	29.4252	−	23.8704i	1.13765	−	0.922883i
$670$		0			0
$671$		−	9.07753i		−	0.350434i
$672$		0			0
$673$		−	31.2558i		−	1.20482i	−0.798186	−	0.602411i	$-0.794207\pi$
$673$		−	31.2558i		−	1.20482i	0.798186	−	0.602411i	$-0.205793\pi$
$674$		0			0
$675$	−23.8669	−	46.5414i	−0.918636	−	1.79138i
$676$		0			0
$677$	7.77200	−	13.4615i	0.298702	−	0.517368i	−0.677137	−	0.735857i	$-0.736780\pi$
$677$	7.77200	−	13.4615i	0.298702	−	0.517368i	0.975839	+	0.218489i	$0.0701129\pi$
$678$		0			0
$679$	35.2670			1.35342
$680$		0			0
$681$	−39.5586	+	6.30067i	−1.51589	+	0.241442i
$682$		0			0
$683$	4.82618	+	8.35919i	0.184669	+	0.319856i	0.943465	−	0.331473i	$-0.107545\pi$
$683$	4.82618	+	8.35919i	0.184669	+	0.319856i	−0.758796	+	0.651328i	$0.774212\pi$
$684$		0			0
$685$	31.9628			1.22124
$686$		0			0
$687$	4.46084	−	11.6511i	0.170192	−	0.444518i
$688$		0			0
$689$	2.43501	−	1.40585i	0.0927664	−	0.0535587i
$690$		0			0
$691$	−6.61337	+	11.4547i	−0.251584	+	0.435757i	−0.963962	−	0.266039i	$-0.914285\pi$
$691$	−6.61337	+	11.4547i	−0.251584	+	0.435757i	0.712378	+	0.701796i	$0.247618\pi$
$692$		0			0
$693$	−4.53562	−	13.8772i	−0.172294	−	0.527151i
$694$		0			0
$695$		−	26.9892i		−	1.02376i
$696$		0			0
$697$			19.7826i			0.749319i
$698$		0			0
$699$	2.31948	+	14.5628i	0.0877306	+	0.550815i
$700$		0			0
$701$	20.0498	−	34.7272i	0.757270	−	1.31163i	−0.186968	−	0.982366i	$-0.559866\pi$
$701$	20.0498	−	34.7272i	0.757270	−	1.31163i	0.944238	−	0.329264i	$-0.106800\pi$
$702$		0			0
$703$	20.2658	−	35.1013i	0.764337	−	1.32387i
$704$		0			0
$705$	−38.2653	+	6.09468i	−1.44116	+	0.229539i
$706$		0			0
$707$	−16.9632	+	9.79373i	−0.637968	+	0.368331i
$708$		0			0
$709$	−1.94242	−	3.36436i	−0.0729490	−	0.126351i	0.827244	−	0.561844i	$-0.189908\pi$
$709$	−1.94242	−	3.36436i	−0.0729490	−	0.126351i	−0.900193	+	0.435492i	$0.856574\pi$
$710$		0			0
$711$	23.9135	−	26.6515i	0.896825	−	0.999508i
$712$		0			0
$713$	12.2538			0.458908
$714$		0			0
$715$			1.19403i			0.0446543i
$716$		0			0
$717$	−4.44936	−	27.9352i	−0.166164	−	1.04326i
$718$		0			0
$719$	−15.4668	+	8.92978i	−0.576815	+	0.333024i	−0.759867	−	0.650079i	$-0.774736\pi$
$719$	−15.4668	+	8.92978i	−0.576815	+	0.333024i	0.183051	+	0.983103i	$0.441402\pi$
$720$		0			0
$721$	46.0168	−	26.5678i	1.71376	−	0.989437i
$722$		0			0
$723$	32.0862	−	26.0291i	1.19330	−	0.968031i
$724$		0			0
$725$	−33.4525	−	19.3138i	−1.24239	−	0.717297i
$726$		0			0
$727$	−17.9418	+	10.3587i	−0.665424	+	0.384182i	−0.794340	−	0.607473i	$-0.792183\pi$
$727$	−17.9418	+	10.3587i	−0.665424	+	0.384182i	0.128917	+	0.991655i	$0.458850\pi$
$728$		0			0
$729$	−15.7562	+	21.9258i	−0.583565	+	0.812067i
$730$		0			0
$731$	6.84391	+	11.8540i	0.253131	+	0.438436i
$732$		0			0
$733$	−10.4427	−	6.02908i	−0.385709	−	0.222689i	0.294590	−	0.955624i	$-0.404817\pi$
$733$	−10.4427	−	6.02908i	−0.385709	−	0.222689i	−0.680299	+	0.732935i	$0.738150\pi$
$734$		0			0
$735$	50.5437	+	19.3516i	1.86433	+	0.713794i
$736$		0			0
$737$	8.42905	+	5.86366i	0.310488	+	0.215991i
$738$		0			0
$739$	−11.6383	+	6.71938i	−0.428122	+	0.247177i	−0.698546	−	0.715565i	$-0.746169\pi$
$739$	−11.6383	+	6.71938i	−0.428122	+	0.247177i	0.270424	+	0.962741i	$0.412836\pi$
$740$		0			0
$741$	−1.89076	+	0.301150i	−0.0694590	+	0.0110630i
$742$		0			0
$743$	5.47183	−	3.15917i	0.200742	−	0.115899i	−0.396259	−	0.918139i	$-0.629692\pi$
$743$	5.47183	−	3.15917i	0.200742	−	0.115899i	0.597002	+	0.802240i	$0.296359\pi$
$744$		0			0
$745$		−	10.6312i		−	0.389495i
$746$		0			0
$747$	−4.83137	−	14.7821i	−0.176771	−	0.540848i
$748$		0			0
$749$	−7.35339	+	12.7364i	−0.268687	+	0.465380i
$750$		0			0
$751$	15.8746			0.579271			0.289635	−	0.957137i	$-0.406466\pi$
$751$	15.8746			0.579271			0.289635	+	0.957137i	$0.406466\pi$
$752$		0			0
$753$	−31.3416	−	11.9997i	−1.14215	−	0.437294i
$754$		0			0
$755$	30.3546	+	52.5756i	1.10472	+	1.91342i
$756$		0			0
$757$	−11.0269	−	6.36636i	−0.400778	−	0.231389i	0.286042	−	0.958217i	$-0.407660\pi$
$757$	−11.0269	−	6.36636i	−0.400778	−	0.231389i	−0.686820	+	0.726828i	$0.740994\pi$
$758$		0			0
$759$	3.33147	+	4.10673i	0.120925	+	0.149065i
$760$		0			0
$761$		−	25.1289i		−	0.910920i	−0.890256	−	0.455460i	$-0.849475\pi$
$761$		−	25.1289i		−	0.910920i	0.890256	−	0.455460i	$-0.150525\pi$
$762$		0			0
$763$	−25.6954	+	44.5058i	−0.930237	+	1.61122i
$764$		0			0
$765$	−9.94217	−	30.4191i	−0.359460	−	1.09981i
$766$		0			0
$767$	1.66579	+	2.88523i	0.0601480	+	0.104179i
$768$		0			0
$769$	−26.0315	−	15.0293i	−0.938719	−	0.541970i	−0.0491603	−	0.998791i	$-0.515655\pi$
$769$	−26.0315	−	15.0293i	−0.938719	−	0.541970i	−0.889558	+	0.456821i	$0.848988\pi$
$770$		0			0
$771$	−27.0750	+	4.31236i	−0.975084	+	0.155306i
$772$		0			0
$773$	6.48734	+	3.74547i	0.233334	+	0.134715i	0.612109	−	0.790773i	$-0.290321\pi$
$773$	6.48734	+	3.74547i	0.233334	+	0.134715i	−0.378775	+	0.925489i	$0.623655\pi$
$774$		0			0
$775$	43.8899	+	25.3399i	1.57657	+	0.910235i
$776$		0			0
$777$	−38.0642	−	46.9220i	−1.36555	−	1.68332i
$778$		0			0
$779$	32.4461			1.16250
$780$		0			0
$781$	5.73815	−	3.31292i	0.205327	−	0.118546i
$782$		0			0
$783$	−0.991730	+	19.9153i	−0.0354415	+	0.711715i
$784$		0			0
$785$	44.3209	+	76.7660i	1.58188	+	2.73989i
$786$		0			0
$787$	−41.3368	+	23.8658i	−1.47350	+	0.850725i	−0.999555	−	0.0298303i	$-0.990503\pi$
$787$	−41.3368	+	23.8658i	−1.47350	+	0.850725i	−0.473944	+	0.880555i	$0.657170\pi$
$788$		0			0
$789$	26.6023	+	32.7929i	0.947066	+	1.16746i
$790$		0			0
$791$	35.0485	−	20.2353i	1.24618	−	0.719484i
$792$		0			0
$793$	−0.887281	+	1.53682i	−0.0315083	+	0.0545739i
$794$		0			0
$795$	59.8625	−	48.5618i	2.12310	−	1.72231i
$796$		0			0
$797$	36.3448	+	20.9837i	1.28740	+	0.743280i	0.978190	−	0.207714i	$-0.0666024\pi$
$797$	36.3448	+	20.9837i	1.28740	+	0.743280i	0.309209	+	0.950994i	$0.399936\pi$
$798$		0			0
$799$	−15.8399			−0.560376
$800$		0			0
$801$	−42.6202	−	8.98191i	−1.50591	−	0.317360i
$802$		0			0
$803$	3.35898			0.118536
$804$		0			0
$805$	−36.6490			−1.29171
$806$		0			0
$807$	3.76126	+	4.63653i	0.132403	+	0.163214i
$808$		0			0
$809$	19.8814			0.698994			0.349497	−	0.936938i	$-0.386353\pi$
$809$	19.8814			0.698994			0.349497	+	0.936938i	$0.386353\pi$
$810$		0			0
$811$	−32.6504	−	18.8507i	−1.14651	−	0.661938i	−0.198475	−	0.980106i	$-0.563599\pi$
$811$	−32.6504	−	18.8507i	−1.14651	−	0.661938i	−0.948034	+	0.318168i	$0.896932\pi$
$812$		0			0
$813$	−3.01149	−	3.71229i	−0.105618	−	0.130196i
$814$		0			0
$815$	28.5056	−	49.3731i	0.998507	−	1.72946i
$816$		0			0
$817$	19.4422	−	11.2249i	0.680195	−	0.392711i
$818$		0			0
$819$	−0.588548	+	2.79273i	−0.0205655	+	0.0975858i
$820$		0			0
$821$	29.0413	−	16.7670i	1.01355	−	0.585172i	0.101319	−	0.994854i	$-0.467694\pi$
$821$	29.0413	−	16.7670i	1.01355	−	0.585172i	0.912228	+	0.409682i	$0.134360\pi$
$822$		0			0
$823$	−20.7643	−	35.9649i	−0.723799	−	1.25366i	−0.959466	−	0.281823i	$-0.909061\pi$
$823$	−20.7643	−	35.9649i	−0.723799	−	1.25366i	0.235667	−	0.971834i	$-0.424273\pi$
$824$		0			0
$825$	3.44008	+	21.5985i	0.119768	+	0.751962i
$826$		0			0
$827$	−24.1337	+	13.9336i	−0.839213	+	0.484520i	−0.856996	−	0.515322i	$-0.827672\pi$
$827$	−24.1337	+	13.9336i	−0.839213	+	0.484520i	0.0177839	+	0.999842i	$0.494339\pi$
$828$		0			0
$829$	−20.5976			−0.715384			−0.357692	−	0.933840i	$-0.616436\pi$
$829$	−20.5976			−0.715384			−0.357692	+	0.933840i	$0.616436\pi$
$830$		0			0
$831$	18.3907	−	14.9189i	0.637966	−	0.517532i
$832$		0			0
$833$	19.1606	+	11.0624i	0.663875	+	0.383288i
$834$		0			0
$835$	27.9582	+	16.1417i	0.967535	+	0.558606i
$836$		0			0
$837$	1.30116	−	26.1290i	0.0449746	−	0.903152i
$838$		0			0
$839$	0.738306	+	0.426261i	0.0254891	+	0.0147162i	0.512690	−	0.858574i	$-0.328649\pi$
$839$	0.738306	+	0.426261i	0.0254891	+	0.0147162i	−0.487201	+	0.873290i	$0.661982\pi$
$840$		0			0
$841$	−7.13697	−	12.3616i	−0.246103	−	0.426262i
$842$		0			0
$843$	−39.2494	−	15.0274i	−1.35182	−	0.517571i
$844$		0			0
$845$	−25.1130	+	43.4969i	−0.863912	+	1.49634i
$846$		0			0
$847$		−	36.5694i		−	1.25654i
$848$		0			0
$849$	−36.8888	+	29.9250i	−1.26602	+	1.02702i
$850$		0			0
$851$	18.9526	+	10.9423i	0.649686	+	0.375096i
$852$		0			0
$853$	13.5911	+	23.5405i	0.465350	+	0.806010i	0.999217	−	0.0395585i	$-0.0125951\pi$
$853$	13.5911	+	23.5405i	0.465350	+	0.806010i	−0.533867	+	0.845568i	$0.679262\pi$
$854$		0			0
$855$	−49.8915	+	16.3065i	−1.70625	+	0.557671i
$856$		0			0
$857$	−42.4487			−1.45002			−0.725010	−	0.688738i	$-0.758165\pi$
$857$	−42.4487			−1.45002			−0.725010	+	0.688738i	$0.758165\pi$
$858$		0			0
$859$	3.96448	−	6.86668i	0.135266	−	0.234288i	−0.790433	−	0.612549i	$-0.790144\pi$
$859$	3.96448	−	6.86668i	0.135266	−	0.234288i	0.925699	+	0.378261i	$0.123478\pi$
$860$		0			0
$861$	17.2940	−	45.1696i	0.589379	−	1.53938i
$862$		0			0
$863$			50.7101i			1.72619i	0.505040	+	0.863096i	$0.331478\pi$
$863$			50.7101i			1.72619i	−0.505040	+	0.863096i	$0.668522\pi$
$864$		0			0
$865$	−33.3798	+	19.2718i	−1.13495	+	0.655262i
$866$		0			0
$867$	2.57365	+	16.1586i	0.0874058	+	0.548775i
$868$		0			0
$869$	−12.9666	+	7.48629i	−0.439863	+	0.253955i
$870$		0			0
$871$	−0.853887	−	1.81661i	−0.0289329	−	0.0615533i
$872$		0			0
$873$	8.47252	+	25.9226i	0.286752	+	0.877346i
$874$		0			0
$875$	−66.0636	−	38.1418i	−2.23336	−	1.28943i
$876$		0			0
$877$	11.0822	+	19.1949i	0.374219	+	0.648166i	0.990210	−	0.139587i	$-0.0445776\pi$
$877$	11.0822	+	19.1949i	0.374219	+	0.648166i	−0.615991	+	0.787753i	$0.711244\pi$
$878$		0			0
$879$	24.8503	+	30.6331i	0.838178	+	1.03323i
$880$		0			0
$881$	22.9905	−	13.2736i	0.774571	−	0.447199i	−0.0599319	−	0.998202i	$-0.519088\pi$
$881$	22.9905	−	13.2736i	0.774571	−	0.447199i	0.834503	+	0.551004i	$0.185755\pi$
$882$		0			0
$883$	13.3390	+	7.70128i	0.448893	+	0.259169i	0.707363	−	0.706851i	$-0.249885\pi$
$883$	13.3390	+	7.70128i	0.448893	+	0.259169i	−0.258469	+	0.966019i	$0.583218\pi$
$884$		0			0
$885$	57.5405	+	70.9307i	1.93420	+	2.38431i
$886$		0			0
$887$	10.3261	−	5.96180i	0.346718	−	0.200178i	−0.316521	−	0.948586i	$-0.602515\pi$
$887$	10.3261	−	5.96180i	0.346718	−	0.200178i	0.663239	+	0.748408i	$0.269181\pi$
$888$		0			0
$889$	53.6797	−	30.9920i	1.80036	−	1.03944i
$890$		0			0
$891$	9.11063	−	6.66770i	0.305217	−	0.223376i
$892$		0			0
$893$			25.9796i			0.869374i
$894$		0			0
$895$	−62.0827			−2.07520
$896$		0			0
$897$	−0.162603	−	1.02090i	−0.00542915	−	0.0340868i
$898$		0			0
$899$	−9.66035	−	16.7322i	−0.322191	−	0.558050i
$900$		0			0
$901$	27.2895	−	15.7556i	0.909145	−	0.524895i
$902$		0			0
$903$	−5.26389	−	33.0492i	−0.175171	−	1.09981i
$904$		0			0
$905$	−3.65975	+	6.33888i	−0.121654	+	0.210711i
$906$		0			0
$907$	−12.4082	+	21.4917i	−0.412009	+	0.713620i	−0.995109	−	0.0987800i	$-0.968506\pi$
$907$	−12.4082	+	21.4917i	−0.412009	+	0.713620i	0.583101	+	0.812400i	$0.301839\pi$
$908$		0			0
$909$	−11.2740	−	10.1158i	−0.373935	−	0.335519i
$910$		0			0
$911$		−	36.7016i		−	1.21598i	−0.793946	−	0.607989i	$-0.791977\pi$
$911$		−	36.7016i		−	1.21598i	0.793946	−	0.607989i	$-0.208023\pi$
$912$		0			0
$913$			6.50281i			0.215212i
$914$		0			0
$915$	−17.3950	+	45.4334i	−0.575062	+	1.50198i
$916$		0			0
$917$	30.5421	−	52.9004i	1.00859	−	1.74693i
$918$		0			0
$919$	−16.9165	+	9.76677i	−0.558025	+	0.322176i	−0.752353	−	0.658761i	$-0.771081\pi$
$919$	−16.9165	+	9.76677i	−0.558025	+	0.322176i	0.194327	+	0.980937i	$0.437748\pi$
$920$		0			0
$921$	28.2094	+	10.8005i	0.929533	+	0.355889i
$922$		0			0
$923$	−1.29528			−0.0426347
$924$		0			0
$925$	45.2555	+	78.3849i	1.48799	+	2.57728i
$926$		0			0
$927$	30.5834	+	27.4414i	1.00449	+	0.901295i
$928$		0			0
$929$	19.4690			0.638756			0.319378	−	0.947627i	$-0.396526\pi$
$929$	19.4690			0.638756			0.319378	+	0.947627i	$0.396526\pi$
$930$		0			0
$931$	18.1438	−	31.4259i	0.594638	−	1.02994i
$932$		0			0
$933$	32.6633	−	26.4972i	1.06935	−	0.867479i
$934$		0			0
$935$			13.3817i			0.437629i
$936$		0			0
$937$			24.0802i			0.786666i	0.919396	+	0.393333i	$0.128678\pi$
$937$			24.0802i			0.786666i	−0.919396	+	0.393333i	$0.871322\pi$
$938$		0			0
$939$	17.4729	+	21.5390i	0.570206	+	0.702897i
$940$		0			0
$941$	18.5751			0.605530			0.302765	−	0.953065i	$-0.402090\pi$
$941$	18.5751			0.605530			0.302765	+	0.953065i	$0.402090\pi$
$942$		0			0
$943$			17.5190i			0.570496i
$944$		0			0
$945$	−3.89154	+	78.1475i	−0.126592	+	2.54214i
$946$		0			0
$947$		−	43.0781i		−	1.39985i	−0.714216	−	0.699926i	$-0.753216\pi$
$947$		−	43.0781i		−	1.39985i	0.714216	−	0.699926i	$-0.246784\pi$
$948$		0			0
$949$	−0.568671	−	0.328323i	−0.0184599	−	0.0106578i
$950$		0			0
$951$	13.0430	−	34.0664i	0.422947	−	1.10468i
$952$		0			0
$953$			28.8010i			0.932955i	0.884533	+	0.466478i	$0.154477\pi$
$953$			28.8010i			0.932955i	−0.884533	+	0.466478i	$0.845523\pi$
$954$		0			0
$955$	−17.3882	−	30.1173i	−0.562669	−	0.974572i
$956$		0			0
$957$	2.98124	−	7.78659i	0.0963699	−	0.251705i
$958$		0			0
$959$	−27.6662	−	15.9731i	−0.893389	−	0.515798i
$960$		0			0
$961$	−2.82556	−	4.89401i	−0.0911470	−	0.157871i
$962$		0			0
$963$	−11.1283	−	2.34522i	−0.358606	−	0.0755737i
$964$		0			0
$965$	−89.6465			−2.88582
$966$		0			0
$967$	14.3674	−	24.8851i	0.462025	−	0.800251i	−0.537036	−	0.843559i	$-0.680456\pi$
$967$	14.3674	−	24.8851i	0.462025	−	0.800251i	0.999062	+	0.0433076i	$0.0137896\pi$
$968$		0			0
$969$	−21.1901	+	3.37504i	−0.680724	+	0.108422i
$970$		0			0
$971$	−10.7975	−	6.23395i	−0.346509	−	0.200057i	0.316638	−	0.948547i	$-0.397446\pi$
$971$	−10.7975	−	6.23395i	−0.346509	−	0.200057i	−0.663147	+	0.748490i	$0.730779\pi$
$972$		0			0
$973$	−13.4876	+	23.3611i	−0.432391	+	0.748924i
$974$		0			0
$975$	1.52874	−	3.99285i	0.0489587	−	0.127873i
$976$		0			0
$977$	−48.4893	+	27.9953i	−1.55131	+	0.895650i	−0.553276	+	0.832998i	$0.686622\pi$
$977$	−48.4893	+	27.9953i	−1.55131	+	0.895650i	−0.998035	+	0.0626520i	$0.980044\pi$
$978$		0			0
$979$	15.7728	+	9.10642i	0.504101	+	0.291043i
$980$		0			0
$981$	−38.8865	−	8.19506i	−1.24155	−	0.261648i
$982$		0			0
$983$	14.2248			0.453700			0.226850	−	0.973930i	$-0.427157\pi$
$983$	14.2248			0.453700			0.226850	+	0.973930i	$0.427157\pi$
$984$		0			0
$985$	8.47476	−	14.6787i	0.270028	−	0.467703i
$986$		0			0
$987$	36.1673	+	13.8473i	1.15122	+	0.440765i
$988$		0			0
$989$	6.06079	+	10.4976i	0.192722	+	0.333804i
$990$		0			0
$991$			6.31569i			0.200624i	0.994956	+	0.100312i	$0.0319842\pi$
$991$			6.31569i			0.200624i	−0.994956	+	0.100312i	$0.968016\pi$
$992$		0			0
$993$	2.17672	−	0.346695i	0.0690761	−	0.0110020i
$994$		0			0
$995$	−38.2242	−	66.2063i	−1.21179	−	2.09888i
$996$		0			0
$997$	−55.5807			−1.76026			−0.880130	−	0.474733i	$-0.842545\pi$
$997$	−55.5807			−1.76026			−0.880130	+	0.474733i	$0.842545\pi$
$998$		0			0
$999$	25.3449	−	39.2511i	0.801878	−	1.24185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.365.14	yes	36
3.2	odd	2	inner	804.2.o.d.365.5	✓	36
67.38	odd	6	inner	804.2.o.d.641.5	yes	36
201.38	even	6	inner	804.2.o.d.641.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.5	✓	36	3.2	odd	2	inner
804.2.o.d.365.14	yes	36	1.1	even	1	trivial
804.2.o.d.641.5	yes	36	67.38	odd	6	inner
804.2.o.d.641.14	yes	36	201.38	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34511 - 1.09118i) q^{3} +3.88149 q^{5} +(-3.35972 - 1.93974i) q^{7} +(0.618641 - 2.93552i) q^{9} +O(q^{10})\)	\(q+(1.34511 - 1.09118i) q^{3} +3.88149 q^{5} +(-3.35972 - 1.93974i) q^{7} +(0.618641 - 2.93552i) q^{9} +(-0.627217 + 1.08637i) q^{11} +(0.212374 - 0.122614i) q^{13} +(5.22103 - 4.23541i) q^{15} +(2.38011 - 1.37416i) q^{17} +(-2.25380 - 3.90370i) q^{19} +(-6.63580 + 1.05691i) q^{21} +(2.10776 - 1.21692i) q^{23} +10.0660 q^{25} +(-2.37105 - 4.62365i) q^{27} +(-3.32333 - 1.91873i) q^{29} +(4.36024 + 2.51738i) q^{31} +(0.341754 + 2.14570i) q^{33} +(-13.0407 - 7.52906i) q^{35} +(4.49590 + 7.78713i) q^{37} +(0.151872 - 0.396668i) q^{39} +(-3.59904 + 6.23373i) q^{41} +4.98044i q^{43} +(2.40125 - 11.3942i) q^{45} +(-4.99134 - 2.88175i) q^{47} +(4.02515 + 6.97176i) q^{49} +(1.70205 - 4.44553i) q^{51} +11.4657 q^{53} +(-2.43453 + 4.21674i) q^{55} +(-7.29126 - 2.79160i) q^{57} +13.5856i q^{59} +(-6.26687 + 3.61818i) q^{61} +(-7.77259 + 8.66253i) q^{63} +(0.824327 - 0.475926i) q^{65} +(0.688397 - 8.15635i) q^{67} +(1.50729 - 3.93684i) q^{69} +(-4.57430 - 2.64097i) q^{71} +(-1.33884 - 2.31895i) q^{73} +(13.5398 - 10.9838i) q^{75} +(4.21454 - 2.43327i) q^{77} +(10.3366 + 5.96787i) q^{79} +(-8.23457 - 3.63207i) q^{81} +(4.48936 - 2.59193i) q^{83} +(9.23837 - 5.33377i) q^{85} +(-6.56393 + 1.04546i) q^{87} -14.5188i q^{89} -0.951357 q^{91} +(8.61192 - 1.37166i) q^{93} +(-8.74811 - 15.1522i) q^{95} +(-7.87275 + 4.54534i) q^{97} +(2.80104 + 2.51328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 36 * q + 4 * q^9	\( 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) \) 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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