LMFDB - Embedded newform 804.2.o.d.365.5

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			365.5
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34511 - 1.09118i) q^{3} -3.88149 q^{5} +(-3.35972 - 1.93974i) q^{7} +(0.618641 + 2.93552i) q^{9} +O(q^{10})$	\(q+(-1.34511 - 1.09118i) q^{3} -3.88149 q^{5} +(-3.35972 - 1.93974i) q^{7} +(0.618641 + 2.93552i) q^{9} +(0.627217 - 1.08637i) q^{11} +(0.212374 - 0.122614i) q^{13} +(5.22103 + 4.23541i) q^{15} +(-2.38011 + 1.37416i) q^{17} +(-2.25380 - 3.90370i) q^{19} +(2.40259 + 6.27523i) q^{21} +(-2.10776 + 1.21692i) q^{23} +10.0660 q^{25} +(2.37105 - 4.62365i) q^{27} +(3.32333 + 1.91873i) q^{29} +(4.36024 + 2.51738i) q^{31} +(-2.02910 + 0.776880i) q^{33} +(13.0407 + 7.52906i) q^{35} +(4.49590 + 7.78713i) q^{37} +(-0.419461 - 0.0668093i) q^{39} +(3.59904 - 6.23373i) q^{41} +4.98044i q^{43} +(-2.40125 - 11.3942i) q^{45} +(4.99134 + 2.88175i) q^{47} +(4.02515 + 6.97176i) q^{49} +(4.70096 + 0.748742i) q^{51} -11.4657 q^{53} +(-2.43453 + 4.21674i) q^{55} +(-1.22804 + 7.71022i) q^{57} -13.5856i q^{59} +(-6.26687 + 3.61818i) q^{61} +(3.61567 - 11.0625i) q^{63} +(-0.824327 + 0.475926i) q^{65} +(0.688397 - 8.15635i) q^{67} +(4.16305 + 0.663067i) q^{69} +(4.57430 + 2.64097i) q^{71} +(-1.33884 - 2.31895i) q^{73} +(-13.5398 - 10.9838i) q^{75} +(-4.21454 + 2.43327i) q^{77} +(10.3366 + 5.96787i) q^{79} +(-8.23457 + 3.63207i) q^{81} +(-4.48936 + 2.59193i) q^{83} +(9.23837 - 5.33377i) q^{85} +(-2.37657 - 6.20726i) q^{87} +14.5188i q^{89} -0.951357 q^{91} +(-3.11807 - 8.14397i) q^{93} +(8.74811 + 15.1522i) q^{95} +(-7.87275 + 4.54534i) q^{97} +(3.57709 + 1.16913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.834548\pi$
$5$	−3.88149			−1.73585			−0.867927	+	0.496692i	$0.834548\pi$
$6$		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	−0.755842	−	0.654754i	$-0.772772\pi$
$11$	0.627217	−	1.08637i	0.189113	−	0.327553i	0.944955	+	0.327201i	$0.106105\pi$
$12$		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	−0.760044	−	0.649871i	$-0.774823\pi$
$17$	−2.38011	+	1.37416i	−0.577261	+	0.333282i	0.182783	+	0.983153i	$0.441489\pi$
$18$		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
$21$	2.40259	+	6.27523i	0.524287	+	1.36937i
$22$		0			0
$23$	−2.10776	+	1.21692i	−0.439499	+	0.253745i	−0.703385	−	0.710809i	$-0.748329\pi$
$23$	−2.10776	+	1.21692i	−0.439499	+	0.253745i	0.263886	+	0.964554i	$0.414996\pi$
$24$		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	0.775750	−	0.631041i	$-0.217372\pi$
$29$	3.32333	+	1.91873i	0.617127	+	0.356299i	−0.158622	+	0.987339i	$0.550705\pi$
$30$		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
$33$	−2.02910	+	0.776880i	−0.353222	+	0.135238i
$34$		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
$39$	−0.419461	−	0.0668093i	−0.0671675	−	0.0106981i
$40$		0			0
$41$	3.59904	−	6.23373i	0.562076	−	0.973544i	−0.435239	−	0.900315i	$-0.643336\pi$
$41$	3.59904	−	6.23373i	0.562076	−	0.973544i	0.997315	−	0.0732295i	$-0.0233306\pi$
$42$		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	0.817713	−	0.575627i	$-0.195242\pi$
$47$	4.99134	+	2.88175i	0.728062	+	0.420347i	−0.0896509	+	0.995973i	$0.528575\pi$
$48$		0			0
$49$	4.02515	+	6.97176i	0.575021	+	0.995965i
$50$		0			0
$51$	4.70096	+	0.748742i	0.658267	+	0.104845i
$52$		0			0
$53$	−11.4657			−1.57493			−0.787464	−	0.616361i	$-0.788606\pi$
$53$	−11.4657			−1.57493			−0.787464	+	0.616361i	$0.788606\pi$
$54$		0			0
$55$	−2.43453	+	4.21674i	−0.328272	+	0.568585i
$56$		0			0
$57$	−1.22804	+	7.71022i	−0.162658	+	1.02124i
$58$		0			0
$59$		−	13.5856i		−	1.76869i	−0.466832	−	0.884346i	$-0.654605\pi$
$59$		−	13.5856i		−	1.76869i	0.466832	−	0.884346i	$-0.345395\pi$
$60$		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
$63$	3.61567	−	11.0625i	0.455532	−	1.39375i
$64$		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
$69$	4.16305	+	0.663067i	0.501172	+	0.0798239i
$70$		0			0
$71$	4.57430	+	2.64097i	0.542869	+	0.313426i	0.746241	−	0.665676i	$-0.231857\pi$
$71$	4.57430	+	2.64097i	0.542869	+	0.313426i	−0.203372	+	0.979102i	$0.565190\pi$
$72$		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	−0.725723	−	0.687987i	$-0.758495\pi$
$83$	−4.48936	+	2.59193i	−0.492771	+	0.284501i	0.232952	+	0.972488i	$0.425161\pi$
$84$		0			0
$85$	9.23837	−	5.33377i	1.00204	−	0.578529i
$86$		0			0
$87$	−2.37657	−	6.20726i	−0.254795	−	0.665488i
$88$		0			0
$89$			14.5188i			1.53899i	0.638654	+	0.769494i	$0.279492\pi$
$89$			14.5188i			1.53899i	−0.638654	+	0.769494i	$0.720508\pi$
$90$		0			0
$91$	−0.951357			−0.0997293
$92$		0			0
$93$	−3.11807	−	8.14397i	−0.323329	−	0.844491i
$94$		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
$99$	3.57709	+	1.16913i	0.359511	+	0.117502i
$100$		0			0
$101$	−2.52450	+	4.37257i	−0.251197	+	0.435087i	−0.963856	−	0.266425i	$-0.914158\pi$
$101$	−2.52450	+	4.37257i	−0.251197	+	0.435087i	0.712658	+	0.701511i	$0.247491\pi$
$102$		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
$105$	−9.32561	−	24.3572i	−0.910087	−	2.37702i
$106$		0			0
$107$			3.79092i			0.366482i	0.983068	+	0.183241i	$0.0586589\pi$
$107$			3.79092i			0.366482i	−0.983068	+	0.183241i	$0.941341\pi$
$108$		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
$111$	2.44970	−	15.3804i	0.232515	−	1.45984i
$112$		0			0
$113$	5.21599	−	9.03436i	0.490679	−	0.849881i	−0.509263	−	0.860611i	$-0.670082\pi$
$113$	5.21599	−	9.03436i	0.490679	−	0.849881i	0.999942	+	0.0107295i	$0.00341538\pi$
$114$		0			0
$115$	8.18126	−	4.72345i	0.762906	−	0.440464i
$116$		0			0
$117$	0.491320	+	0.547574i	0.0454225	+	0.0506233i
$118$		0			0
$119$	10.6620			0.977384
$120$		0			0
$121$	4.71320	+	8.16350i	0.428473	+	0.742136i
$122$		0			0
$123$	−11.6432	+	4.45783i	−1.04984	+	0.401949i
$124$		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	$-0.758557\pi$
$131$		−	15.7455i		−	1.37569i	0.725858	−	0.687845i	$-0.241443\pi$
$132$		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	$-0.614419\pi$
$137$	−8.23468			−0.703536			−0.351768	+	0.936087i	$0.614419\pi$
$138$		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
$141$	−3.56938	−	9.32274i	−0.300596	−	0.785116i
$142$		0			0
$143$		−	0.307623i		−	0.0257247i
$144$		0			0
$145$	−12.8995	−	7.44752i	−1.07124	−	0.618483i
$146$		0			0
$147$	2.19320	−	13.7700i	0.180892	−	1.13573i
$148$		0			0
$149$			2.73894i			0.224382i	0.993687	+	0.112191i	$0.0357869\pi$
$149$			2.73894i			0.224382i	−0.993687	+	0.112191i	$0.964213\pi$
$150$		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
$153$	−5.50630	−	6.13675i	−0.445158	−	0.496127i
$154$		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
$165$	7.87594	−	3.01545i	0.613141	−	0.234753i
$166$		0			0
$167$	−7.20297	−	4.15864i	−0.557382	−	0.321805i	0.194712	−	0.980861i	$-0.437623\pi$
$167$	−7.20297	−	4.15864i	−0.557382	−	0.321805i	−0.752094	+	0.659056i	$0.770956\pi$
$168$		0			0
$169$	−6.46993	+	11.2063i	−0.497687	+	0.862019i
$170$		0			0
$171$	10.0651	−	9.03108i	0.769698	−	0.690624i
$172$		0			0
$173$	8.59974	−	4.96506i	0.653826	−	0.377487i	−0.136094	−	0.990696i	$-0.543455\pi$
$173$	8.59974	−	4.96506i	0.653826	−	0.377487i	0.789921	+	0.613209i	$0.210122\pi$
$174$		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	$-0.296064\pi$
$179$	15.9946			1.19549			0.597745	+	0.801686i	$0.296064\pi$
$180$		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
$183$	12.3777	+	1.97145i	0.914988	+	0.145734i
$184$		0			0
$185$	−17.4508	−	30.2256i	−1.28301	−	2.22223i
$186$		0			0
$187$			3.44758i			0.252112i
$188$		0			0
$189$	−16.9347	+	10.9350i	−1.23182	+	0.795401i
$190$		0			0
$191$	4.47978	+	7.75920i	0.324145	+	0.561436i	0.981339	−	0.192286i	$-0.0615900\pi$
$191$	4.47978	+	7.75920i	0.324145	+	0.561436i	−0.657194	+	0.753722i	$0.728257\pi$
$192$		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
$195$	1.62813	+	0.259320i	0.116593	+	0.0185703i
$196$		0			0
$197$	−2.18338	+	3.78172i	−0.155559	+	0.269437i	−0.933263	−	0.359195i	$-0.883051\pi$
$197$	−2.18338	+	3.78172i	−0.155559	+	0.269437i	0.777703	+	0.628632i	$0.216385\pi$
$198$		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
$201$	−9.82604	+	10.2200i	−0.693076	+	0.720865i
$202$		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
$207$	−4.87623	−	5.43455i	−0.338922	−	0.377727i
$208$		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
$213$	−3.27115	−	8.54379i	−0.224135	−	0.585411i
$214$		0			0
$215$		−	19.3315i		−	1.31840i
$216$		0			0
$217$	−9.76612	−	16.9154i	−0.662967	−	1.14829i
$218$		0			0
$219$	−0.729501	+	4.58016i	−0.0492951	+	0.309498i
$220$		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	0.985199	−	0.171417i	$-0.0548344\pi$
$227$	20.0286	+	11.5635i	1.32935	+	0.767499i	0.344148	+	0.938915i	$0.388168\pi$
$228$		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
$231$	8.32416	+	1.32582i	0.547690	+	0.0872329i
$232$		0			0
$233$	4.25690	−	7.37317i	0.278879	−	0.483033i	−0.692227	−	0.721679i	$-0.743370\pi$
$233$	4.25690	−	7.37317i	0.278879	−	0.483033i	0.971106	+	0.238647i	$0.0767038\pi$
$234$		0			0
$235$	−19.3738	−	11.1855i	−1.26381	−	0.729661i
$236$		0			0
$237$	−7.39189	−	19.3066i	−0.480155	−	1.25410i
$238$		0			0
$239$	−8.16585	+	14.1437i	−0.528205	+	0.914877i	0.471255	+	0.881997i	$0.343801\pi$
$239$	−8.16585	+	14.1437i	−0.528205	+	0.914877i	−0.999459	+	0.0328801i	$0.989532\pi$
$240$		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
$249$	8.86695	+	1.41228i	0.561920	+	0.0894994i
$250$		0			0
$251$	9.68800	+	16.7801i	0.611501	+	1.05915i	0.990988	+	0.133954i	$0.0427673\pi$
$251$	9.68800	+	16.7801i	0.611501	+	1.05915i	−0.379487	+	0.925197i	$0.623899\pi$
$252$		0			0
$253$			3.05308i			0.191946i
$254$		0			0
$255$	−18.2467	−	2.90623i	−1.14266	−	0.181995i
$256$		0			0
$257$	13.7082	+	7.91441i	0.855091	+	0.493687i	0.862365	−	0.506286i	$-0.168982\pi$
$257$	13.7082	+	7.91441i	0.855091	+	0.493687i	−0.00727411	+	0.999974i	$0.502315\pi$
$258$		0			0
$259$		−	34.8834i		−	2.16755i
$260$		0			0
$261$	−3.57651	+	10.9427i	−0.221381	+	0.677337i
$262$		0			0
$263$		−	24.3793i		−	1.50329i	−0.659566	−	0.751646i	$-0.729260\pi$
$263$		−	24.3793i		−	1.50329i	0.659566	−	0.751646i	$-0.270740\pi$
$264$		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	$-0.966489\pi$
$269$		−	3.44695i		−	0.210165i	0.994464	−	0.105082i	$-0.0335106\pi$
$270$		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
$279$	−4.69241	+	14.3569i	−0.280927	+	0.859526i
$280$		0			0
$281$	12.1324	+	21.0139i	0.723758	+	1.25359i	0.959483	+	0.281766i	$0.0909203\pi$
$281$	12.1324	+	21.0139i	0.723758	+	1.25359i	−0.235725	+	0.971820i	$0.575746\pi$
$282$		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
$285$	4.76662	−	29.9271i	0.282350	−	1.77273i
$286$		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
$291$	15.5495	+	2.47664i	0.911528	+	0.145183i
$292$		0			0
$293$		−	22.7737i		−	1.33045i	−0.746642	−	0.665227i	$-0.768335\pi$
$293$		−	22.7737i		−	1.33045i	0.746642	−	0.665227i	$-0.231665\pi$
$294$		0			0
$295$			52.7323i			3.07019i
$296$		0			0
$297$	−3.53583	−	5.47587i	−0.205170	−	0.317742i
$298$		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
$303$	8.16700	−	3.12689i	0.469182	−	0.179635i
$304$		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
$309$	22.1549	−	8.48242i	1.26035	−	0.482548i
$310$		0			0
$311$	−24.2830			−1.37696			−0.688481	−	0.725254i	$-0.741722\pi$
$311$	−24.2830			−1.37696			−0.688481	+	0.725254i	$0.741722\pi$
$312$		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
$315$	−14.0342	+	42.9391i	−0.790737	+	2.41934i
$316$		0			0
$317$	−18.2390	+	10.5303i	−1.02440	+	0.591439i	−0.915376	−	0.402600i	$-0.868107\pi$
$317$	−18.2390	+	10.5303i	−1.02440	+	0.591439i	−0.109026	+	0.994039i	$0.534773\pi$
$318$		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
$333$	−20.0779	+	18.0152i	−1.10026	+	0.987229i
$334$		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
$339$	−16.8742	+	6.46061i	−0.916482	+	0.350892i
$340$		0			0
$341$	5.46963	−	3.15789i	0.296197	−	0.171009i
$342$		0			0
$343$		−	4.07458i		−	0.220007i
$344$		0			0
$345$	−16.1588	−	2.57369i	−0.869962	−	0.138563i
$346$		0			0
$347$	1.92761	−	3.33871i	0.103479	−	0.179231i	−0.809637	−	0.586932i	$-0.800336\pi$
$347$	1.92761	−	3.33871i	0.103479	−	0.179231i	0.913116	+	0.407700i	$0.133669\pi$
$348$		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
$351$	−0.0633754	−	1.27267i	−0.00338273	−	0.0679300i
$352$		0			0
$353$	13.8891	+	24.0566i	0.739241	+	1.28040i	0.952837	+	0.303482i	$0.0981491\pi$
$353$	13.8891	+	24.0566i	0.739241	+	1.28040i	−0.213596	+	0.976922i	$0.568518\pi$
$354$		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	$0.113537\pi$
$359$			13.2317i			0.698345i	−0.937059	+	0.349172i	$0.886463\pi$
$360$		0			0
$361$	−0.659258	+	1.14187i	−0.0346978	+	0.0600984i
$362$		0			0
$363$	2.56810	−	16.1238i	0.134790	−	0.846278i
$364$		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
$369$	20.5257	+	6.70863i	1.06853	+	0.349237i
$370$		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
$381$	25.8442	−	9.89494i	1.32404	−	0.506933i
$382$		0			0
$383$	−1.74713	−	3.02611i	−0.0892740	−	0.154627i	0.817930	−	0.575317i	$-0.195121\pi$
$383$	−1.74713	−	3.02611i	−0.0892740	−	0.154627i	−0.907204	+	0.420690i	$0.861788\pi$
$384$		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	−0.473418	−	0.880838i	$-0.656980\pi$
$389$	1.03941	−	0.600102i	0.0527001	−	0.0304264i	0.526119	+	0.850411i	$0.323647\pi$
$390$		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	$-0.244501\pi$
$401$	28.8046			1.43843			0.719216	+	0.694786i	$0.244501\pi$
$402$		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	−0.792359	−	0.610055i	$-0.791147\pi$
$419$	−13.5143	+	7.80247i	−0.660216	+	0.381176i	0.132143	+	0.991231i	$0.457814\pi$
$420$		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
$423$	−5.37160	+	16.4350i	−0.261176	+	0.799095i
$424$		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	0.207770	−	0.978178i	$-0.433380\pi$
$431$	−11.1167	−	6.41823i	−0.535472	−	0.309155i	−0.743242	+	0.669023i	$0.766713\pi$
$432$		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
$435$	9.22461	+	24.0934i	0.442286	+	1.15519i
$436$		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
$441$	−17.9756	+	16.1289i	−0.855982	+	0.768044i
$442$		0			0
$443$	−8.21846	+	14.2348i	−0.390471	+	0.676316i	−0.992512	−	0.122150i	$-0.961021\pi$
$443$	−8.21846	+	14.2348i	−0.390471	+	0.676316i	0.602041	+	0.798465i	$0.294355\pi$
$444$		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	$0.0121634\pi$
$449$	32.4623	+	18.7421i	1.53199	+	0.884495i	0.532720	+	0.846292i	$0.321170\pi$
$450$		0			0
$451$	−4.51476	−	7.81979i	−0.212592	−	0.368220i
$452$		0			0
$453$	4.26110	−	26.7532i	0.200204	−	1.25698i
$454$		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
$459$	0.710259	+	14.2630i	0.0331520	+	0.665739i
$460$		0			0
$461$			22.7880i			1.06134i	0.847578	+	0.530671i	$0.178060\pi$
$461$			22.7880i			1.06134i	−0.847578	+	0.530671i	$0.821940\pi$
$462$		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
$465$	12.1028	+	31.6107i	0.561252	+	1.46591i
$466$		0			0
$467$	−17.7284	+	10.2355i	−0.820373	+	0.473643i	−0.850545	−	0.525902i	$-0.823728\pi$
$467$	−17.7284	+	10.2355i	−0.820373	+	0.473643i	0.0301719	+	0.999545i	$0.490395\pi$
$468$		0			0
$469$	−18.1340	+	26.0678i	−0.837350	+	1.20370i
$470$		0			0
$471$	6.22166	−	39.0625i	0.286679	−	1.79991i
$472$		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	−0.971547	−	0.236848i	$-0.923886\pi$
$479$	−27.4058	+	15.8228i	−1.25220	+	0.722960i	−0.280657	+	0.959808i	$0.590552\pi$
$480$		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
$489$	−23.7585	+	9.09637i	−1.07440	+	0.411352i
$490$		0			0
$491$			17.0343i			0.768747i	0.923178	+	0.384373i	$0.125582\pi$
$491$			17.0343i			0.768747i	−0.923178	+	0.384373i	$0.874418\pi$
$492$		0			0
$493$	−10.5465			−0.474992
$494$		0			0
$495$	−13.8844	−	4.53798i	−0.624058	−	0.203967i
$496$		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
$501$	5.15095	+	13.4536i	0.230128	+	0.601062i
$502$		0			0
$503$	−1.14936	+	1.99076i	−0.0512476	+	0.0887634i	−0.890511	−	0.454961i	$-0.849653\pi$
$503$	−1.14936	+	1.99076i	−0.0512476	+	0.0887634i	0.839264	+	0.543725i	$0.182986\pi$
$504$		0			0
$505$	9.79883	−	16.9721i	0.436042	−	0.755247i
$506$		0			0
$507$	20.9308	−	8.01376i	0.929571	−	0.355904i
$508$		0			0
$509$			2.69083i			0.119269i	0.998220	+	0.0596344i	$0.0189935\pi$
$509$			2.69083i			0.119269i	−0.998220	+	0.0596344i	$0.981006\pi$
$510$		0			0
$511$			10.3880i			0.459538i
$512$		0			0
$513$	−23.3932	+	1.16492i	−1.03284	+	0.0514325i
$514$		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
$519$	−16.9854	−	2.70533i	−0.745576	−	0.118751i
$520$		0			0
$521$	40.4214			1.77089			0.885447	−	0.464740i	$-0.153852\pi$
$521$	40.4214			1.77089			0.885447	+	0.464740i	$0.153852\pi$
$522$		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
$525$	24.1843	+	63.1661i	1.05549	+	2.75680i
$526$		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
$543$	3.05028	−	1.16786i	0.130900	−	0.0501176i
$544$		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
$549$	−14.4982	−	16.1582i	−0.618768	−	0.689615i
$550$		0			0
$551$		−	17.2977i		−	0.736908i
$552$		0			0
$553$	−23.1522	−	40.1007i	−0.984530	−	1.70526i
$554$		0			0
$555$	−9.50848	+	59.6988i	−0.403613	+	2.53407i
$556$		0			0
$557$	39.0857	+	22.5661i	1.65611	+	0.956158i	0.974483	+	0.224463i	$0.0720628\pi$
$557$	39.0857	+	22.5661i	1.65611	+	0.956158i	0.681632	+	0.731695i	$0.261271\pi$
$558$		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	$-0.582384\pi$
$563$	−12.1456			−0.511876			−0.255938	+	0.966693i	$0.582384\pi$
$564$		0			0
$565$	−20.2458	+	35.0668i	−0.851748	+	1.47527i
$566$		0			0
$567$	34.7111	+	3.77016i	1.45773	+	0.158332i
$568$		0			0
$569$	−24.6397	−	14.2258i	−1.03295	−	0.596375i	−0.115123	−	0.993351i	$-0.536726\pi$
$569$	−24.6397	−	14.2258i	−1.03295	−	0.596375i	−0.917829	+	0.396977i	$0.870059\pi$
$570$		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
$573$	2.44092	−	15.3252i	0.101971	−	0.640221i
$574$		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
$585$	−1.90705	−	2.12540i	−0.0788469	−	0.0878746i
$586$		0			0
$587$	−9.85635	−	17.0717i	−0.406815	−	0.704624i	0.587716	−	0.809067i	$-0.300027\pi$
$587$	−9.85635	−	17.0717i	−0.406815	−	0.704624i	−0.994531	+	0.104443i	$0.966694\pi$
$588$		0			0
$589$		−	22.6948i		−	0.935121i
$590$		0			0
$591$	7.06344	−	2.70437i	0.290551	−	0.111243i
$592$		0			0
$593$	−4.13414	−	7.16054i	−0.169769	−	0.294048i	0.768570	−	0.639766i	$-0.220969\pi$
$593$	−4.13414	−	7.16054i	−0.169769	−	0.294048i	−0.938338	+	0.345718i	$0.887635\pi$
$594$		0			0
$595$	−41.3844			−1.69660
$596$		0			0
$597$	−5.36582	+	33.6892i	−0.219609	+	1.37881i
$598$		0			0
$599$	−0.712722	+	1.23447i	−0.0291210	+	0.0504391i	−0.880219	−	0.474568i	$-0.842604\pi$
$599$	−0.712722	+	1.23447i	−0.0291210	+	0.0504391i	0.851098	+	0.525008i	$0.175937\pi$
$600$		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
$603$	24.3690	−	3.02505i	0.992383	−	0.123189i
$604$		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
$609$	−4.05585	+	25.4646i	−0.164351	+	1.03188i
$610$		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
$615$	45.1931	−	17.3030i	1.82236	−	0.697725i
$616$		0			0
$617$			33.1197i			1.33335i	0.745349	+	0.666675i	$0.232283\pi$
$617$			33.1197i			1.33335i	−0.745349	+	0.666675i	$0.767717\pi$
$618$		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
$621$	0.628986	+	12.6309i	0.0252404	+	0.506862i
$622$		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
$633$	1.82606	−	11.4649i	0.0725792	−	0.455687i
$634$		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
$639$	−4.92278	+	15.0618i	−0.194742	+	0.595834i
$640$		0			0
$641$	8.75082	−	15.1569i	0.345637	−	0.598660i	−0.639833	−	0.768514i	$-0.720996\pi$
$641$	8.75082	−	15.1569i	0.345637	−	0.598660i	0.985469	+	0.169854i	$0.0543297\pi$
$642$		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	$-0.879352\pi$
$647$	−19.9663	−	34.5826i	−0.784956	−	1.35958i	0.144070	−	0.989568i	$-0.453981\pi$
$648$		0			0
$649$	−14.7590	−	8.52110i	−0.579341	−	0.334483i
$650$		0			0
$651$	−5.32130	+	33.4097i	−0.208558	+	1.30943i
$652$		0			0
$653$	14.3876	+	24.9200i	0.563029	+	0.975194i	0.997230	+	0.0743785i	$0.0236973\pi$
$653$	14.3876	+	24.9200i	0.563029	+	0.975194i	−0.434201	+	0.900816i	$0.642969\pi$
$654$		0			0
$655$			61.1159i			2.38800i
$656$		0			0
$657$	5.97905	−	5.36480i	0.233265	−	0.209301i
$658$		0			0
$659$	6.42882	+	3.71168i	0.250431	+	0.144586i	0.619962	−	0.784632i	$-0.287148\pi$
$659$	6.42882	+	3.71168i	0.250431	+	0.144586i	−0.369531	+	0.929219i	$0.620481\pi$
$660$		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
$663$	1.09017	−	0.417392i	0.0423387	−	0.0162101i
$664$		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	−0.975839	−	0.218489i	$-0.929887\pi$
$677$	−7.77200	+	13.4615i	−0.298702	+	0.517368i	0.677137	+	0.735857i	$0.263220\pi$
$678$		0			0
$679$	35.2670			1.35342
$680$		0			0
$681$	−14.3228	−	37.4091i	−0.548850	−	1.43352i
$682$		0			0
$683$	−4.82618	−	8.35919i	−0.184669	−	0.319856i	0.758796	−	0.651328i	$-0.225788\pi$
$683$	−4.82618	−	8.35919i	−0.184669	−	0.319856i	−0.943465	+	0.331473i	$0.892455\pi$
$684$		0			0
$685$	31.9628			1.22124
$686$		0			0
$687$	−12.3206	−	1.96235i	−0.470059	−	0.0748683i
$688$		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
$693$	−9.75020	−	10.8666i	−0.370379	−	0.412787i
$694$		0			0
$695$			26.9892i			1.02376i
$696$		0			0
$697$			19.7826i			0.749319i
$698$		0			0
$699$	−13.7715	+	5.27267i	−0.520885	+	0.199431i
$700$		0			0
$701$	−20.0498	+	34.7272i	−0.757270	+	1.31163i	0.186968	+	0.982366i	$0.440134\pi$
$701$	−20.0498	+	34.7272i	−0.757270	+	1.31163i	−0.944238	+	0.329264i	$0.893200\pi$
$702$		0			0
$703$	20.2658	−	35.1013i	0.764337	−	1.32387i
$704$		0			0
$705$	13.8545	+	36.1861i	0.521791	+	1.36285i
$706$		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
$711$	−11.1241	+	34.0354i	−0.417187	+	1.27643i
$712$		0			0
$713$	−12.2538			−0.458908
$714$		0			0
$715$			1.19403i			0.0446543i
$716$		0			0
$717$	26.4173	−	10.1143i	0.986571	−	0.377727i
$718$		0			0
$719$	15.4668	−	8.92978i	0.576815	−	0.333024i	−0.183051	−	0.983103i	$-0.558598\pi$
$719$	15.4668	−	8.92978i	0.576815	−	0.333024i	0.759867	+	0.650079i	$0.225264\pi$
$720$		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
$735$	−8.51287	+	53.4479i	−0.314002	+	1.97146i
$736$		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
$741$	0.684579	+	1.78803i	0.0251486	+	0.0656848i
$742$		0			0
$743$	−5.47183	+	3.15917i	−0.200742	+	0.115899i	−0.597002	−	0.802240i	$-0.703641\pi$
$743$	−5.47183	+	3.15917i	−0.200742	+	0.115899i	0.396259	+	0.918139i	$0.370308\pi$
$744$		0			0
$745$		−	10.6312i		−	0.389495i
$746$		0			0
$747$	−10.3860	−	11.5751i	−0.380003	−	0.423512i
$748$		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
$753$	5.27874	−	33.1425i	0.192368	−	1.20778i
$754$		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	$0.150525\pi$
$761$			25.1289i			0.910920i	−0.890256	+	0.455460i	$0.849475\pi$
$762$		0			0
$763$	−25.6954	+	44.5058i	−0.930237	+	1.61122i
$764$		0			0
$765$	21.3726	+	23.8197i	0.772729	+	0.861204i
$766$		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
$771$	−9.80291	−	25.6039i	−0.353043	−	0.922100i
$772$		0			0
$773$	−6.48734	−	3.74547i	−0.233334	−	0.134715i	0.378775	−	0.925489i	$-0.376345\pi$
$773$	−6.48734	−	3.74547i	−0.233334	−	0.134715i	−0.612109	+	0.790773i	$0.709679\pi$
$774$		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
$783$	16.7513	−	10.8165i	0.598643	−	0.386551i
$784$		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	−0.309209	−	0.950994i	$-0.600064\pi$
$797$	−36.3448	−	20.9837i	−1.28740	−	0.743280i	−0.978190	+	0.207714i	$0.933398\pi$
$798$		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	$-0.613647\pi$
$809$	−19.8814			−0.698994			−0.349497	+	0.936938i	$0.613647\pi$
$810$		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	−0.912228	−	0.409682i	$-0.865640\pi$
$821$	−29.0413	+	16.7670i	−1.01355	+	0.585172i	−0.101319	+	0.994854i	$0.532306\pi$
$822$		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
$825$	−20.4249	+	7.82004i	−0.711102	+	0.272259i
$826$		0			0
$827$	24.1337	−	13.9336i	0.839213	−	0.484520i	−0.0177839	−	0.999842i	$-0.505661\pi$
$827$	24.1337	−	13.9336i	0.839213	−	0.484520i	0.856996	+	0.515322i	$0.172328\pi$
$828$		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
$837$	21.9778	−	14.1914i	0.759665	−	0.490525i
$838$		0			0
$839$	−0.738306	−	0.426261i	−0.0254891	−	0.0147162i	0.487201	−	0.873290i	$-0.338018\pi$
$839$	−0.738306	−	0.426261i	−0.0254891	−	0.0147162i	−0.512690	+	0.858574i	$0.671351\pi$
$840$		0			0
$841$	−7.13697	−	12.3616i	−0.246103	−	0.426262i
$842$		0			0
$843$	6.61063	−	41.5047i	0.227682	−	1.42950i
$844$		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
$855$	−39.0676	+	35.0540i	−1.33608	+	1.19882i
$856$		0			0
$857$	42.4487			1.45002			0.725010	−	0.688738i	$-0.241835\pi$
$857$	42.4487			1.45002			0.725010	+	0.688738i	$0.241835\pi$
$858$		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
$861$	47.7651	+	7.60774i	1.62783	+	0.259271i
$862$		0			0
$863$		−	50.7101i		−	1.72619i	−0.505040	−	0.863096i	$-0.668522\pi$
$863$		−	50.7101i		−	1.72619i	0.505040	−	0.863096i	$-0.331478\pi$
$864$		0			0
$865$	−33.3798	+	19.2718i	−1.13495	+	0.655262i
$866$		0			0
$867$	15.2806	−	5.85046i	0.518956	−	0.198692i
$868$		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
$873$	−18.2133	−	20.2987i	−0.616428	−	0.687007i
$874$		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	−0.834503	−	0.551004i	$-0.814245\pi$
$881$	−22.9905	+	13.2736i	−0.774571	+	0.447199i	0.0599319	+	0.998202i	$0.480912\pi$
$882$		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	−0.663239	−	0.748408i	$-0.730819\pi$
$887$	−10.3261	+	5.96180i	−0.346718	+	0.200178i	0.316521	+	0.948586i	$0.397485\pi$
$888$		0			0
$889$	53.6797	−	30.9920i	1.80036	−	1.03944i
$890$		0			0
$891$	−1.21909	+	11.2239i	−0.0408409	+	0.376014i
$892$		0			0
$893$		−	25.9796i		−	0.869374i
$894$		0			0
$895$	−62.0827			−2.07520
$896$		0			0
$897$	0.965425	−	0.369631i	0.0322346	−	0.0123416i
$898$		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
$903$	−31.2534	+	11.9659i	−1.04005	+	0.398202i
$904$		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
$909$	−14.3975	−	4.70568i	−0.477536	−	0.156078i
$910$		0			0
$911$			36.7016i			1.21598i	0.793946	+	0.607989i	$0.208023\pi$
$911$			36.7016i			1.21598i	−0.793946	+	0.607989i	$0.791977\pi$
$912$		0			0
$913$			6.50281i			0.215212i
$914$		0			0
$915$	−48.0440	−	7.65217i	−1.58829	−	0.252973i
$916$		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
$921$	4.75121	−	29.8304i	0.156558	−	0.982944i
$922$		0			0
$923$	1.29528			0.0426347
$924$		0			0
$925$	45.2555	+	78.3849i	1.48799	+	2.57728i
$926$		0			0
$927$	−39.0567	−	12.7653i	−1.28279	−	0.419267i
$928$		0			0
$929$	−19.4690			−0.638756			−0.319378	−	0.947627i	$-0.603474\pi$
$929$	−19.4690			−0.638756			−0.319378	+	0.947627i	$0.603474\pi$
$930$		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	$-0.597910\pi$
$941$	−18.5751			−0.605530			−0.302765	+	0.953065i	$0.597910\pi$
$942$		0			0
$943$			17.5190i			0.570496i
$944$		0			0
$945$	65.7319	−	42.4439i	2.13826	−	1.38070i
$946$		0			0
$947$			43.0781i			1.39985i	0.714216	+	0.699926i	$0.246784\pi$
$947$			43.0781i			1.39985i	−0.714216	+	0.699926i	$0.753216\pi$
$948$		0			0
$949$	−0.568671	−	0.328323i	−0.0184599	−	0.0106578i
$950$		0			0
$951$	36.0239	+	5.73767i	1.16815	+	0.186057i
$952$		0			0
$953$		−	28.8010i		−	0.932955i	−0.884533	−	0.466478i	$-0.845523\pi$
$953$		−	28.8010i		−	0.932955i	0.884533	−	0.466478i	$-0.154477\pi$
$954$		0			0
$955$	−17.3882	−	30.1173i	−0.562669	−	0.974572i
$956$		0			0
$957$	−8.23401	−	1.31147i	−0.266168	−	0.0423937i
$958$		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
$969$	−7.67218	−	20.0387i	−0.246466	−	0.643735i
$970$		0			0
$971$	10.7975	+	6.23395i	0.346509	+	0.200057i	0.663147	−	0.748490i	$-0.269221\pi$
$971$	10.7975	+	6.23395i	0.346509	+	0.200057i	−0.316638	+	0.948547i	$0.602554\pi$
$972$		0			0
$973$	−13.4876	+	23.3611i	−0.432391	+	0.748924i
$974$		0			0
$975$	−4.22227	−	0.672499i	−0.135221	−	0.0215372i
$976$		0			0
$977$	48.4893	−	27.9953i	1.55131	−	0.895650i	0.553276	−	0.832998i	$-0.313378\pi$
$977$	48.4893	−	27.9953i	1.55131	−	0.895650i	0.998035	−	0.0626520i	$-0.0199558\pi$
$978$		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	$-0.572843\pi$
$983$	−14.2248			−0.453700			−0.226850	+	0.973930i	$0.572843\pi$
$984$		0			0
$985$	8.47476	−	14.6787i	0.270028	−	0.467703i
$986$		0			0
$987$	−6.09151	+	38.2454i	−0.193895	+	1.21737i
$988$		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
$993$	−0.788112	−	2.05844i	−0.0250100	−	0.0653227i
$994$		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
$999$	46.6649	−	2.32379i	1.47641	−	0.0735215i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.34511 - 1.09118i) q^{3} -3.88149 q^{5} +(-3.35972 - 1.93974i) q^{7} +(0.618641 + 2.93552i) q^{9} +O(q^{10})\)	\(q+(-1.34511 - 1.09118i) q^{3} -3.88149 q^{5} +(-3.35972 - 1.93974i) q^{7} +(0.618641 + 2.93552i) q^{9} +(0.627217 - 1.08637i) q^{11} +(0.212374 - 0.122614i) q^{13} +(5.22103 + 4.23541i) q^{15} +(-2.38011 + 1.37416i) q^{17} +(-2.25380 - 3.90370i) q^{19} +(2.40259 + 6.27523i) q^{21} +(-2.10776 + 1.21692i) q^{23} +10.0660 q^{25} +(2.37105 - 4.62365i) q^{27} +(3.32333 + 1.91873i) q^{29} +(4.36024 + 2.51738i) q^{31} +(-2.02910 + 0.776880i) q^{33} +(13.0407 + 7.52906i) q^{35} +(4.49590 + 7.78713i) q^{37} +(-0.419461 - 0.0668093i) q^{39} +(3.59904 - 6.23373i) q^{41} +4.98044i q^{43} +(-2.40125 - 11.3942i) q^{45} +(4.99134 + 2.88175i) q^{47} +(4.02515 + 6.97176i) q^{49} +(4.70096 + 0.748742i) q^{51} -11.4657 q^{53} +(-2.43453 + 4.21674i) q^{55} +(-1.22804 + 7.71022i) q^{57} -13.5856i q^{59} +(-6.26687 + 3.61818i) q^{61} +(3.61567 - 11.0625i) q^{63} +(-0.824327 + 0.475926i) q^{65} +(0.688397 - 8.15635i) q^{67} +(4.16305 + 0.663067i) q^{69} +(4.57430 + 2.64097i) q^{71} +(-1.33884 - 2.31895i) q^{73} +(-13.5398 - 10.9838i) q^{75} +(-4.21454 + 2.43327i) q^{77} +(10.3366 + 5.96787i) q^{79} +(-8.23457 + 3.63207i) q^{81} +(-4.48936 + 2.59193i) q^{83} +(9.23837 - 5.33377i) q^{85} +(-2.37657 - 6.20726i) q^{87} +14.5188i q^{89} -0.951357 q^{91} +(-3.11807 - 8.14397i) q^{93} +(8.74811 + 15.1522i) q^{95} +(-7.87275 + 4.54534i) q^{97} +(3.57709 + 1.16913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 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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