LMFDB - Embedded newform 804.2.o.d.365.13

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			365.13
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.870385 + 1.49747i) q^{3} +2.31311 q^{5} +(-0.381576 - 0.220303i) q^{7} +(-1.48486 + 2.60676i) q^{9} +O(q^{10})$	\(q+(0.870385 + 1.49747i) q^{3} +2.31311 q^{5} +(-0.381576 - 0.220303i) q^{7} +(-1.48486 + 2.60676i) q^{9} +(-1.81175 + 3.13804i) q^{11} +(1.86390 - 1.07613i) q^{13} +(2.01330 + 3.46383i) q^{15} +(-3.58556 + 2.07012i) q^{17} +(2.79409 + 4.83951i) q^{19} +(-0.00221981 - 0.763149i) q^{21} +(3.74237 - 2.16066i) q^{23} +0.350499 q^{25} +(-5.19595 + 0.0453423i) q^{27} +(-1.35626 - 0.783038i) q^{29} +(9.56644 + 5.52319i) q^{31} +(-6.27606 + 0.0182555i) q^{33} +(-0.882629 - 0.509586i) q^{35} +(2.08197 + 3.60607i) q^{37} +(3.23378 + 1.85450i) q^{39} +(3.96041 - 6.85963i) q^{41} -10.1204i q^{43} +(-3.43465 + 6.02973i) q^{45} +(-1.58438 - 0.914742i) q^{47} +(-3.40293 - 5.89405i) q^{49} +(-6.22078 - 3.56748i) q^{51} -5.10476 q^{53} +(-4.19079 + 7.25866i) q^{55} +(-4.81511 + 8.39632i) q^{57} +11.2026i q^{59} +(4.53420 - 2.61782i) q^{61} +(1.14086 - 0.667557i) q^{63} +(4.31142 - 2.48920i) q^{65} +(7.39142 + 3.51666i) q^{67} +(6.49283 + 3.72350i) q^{69} +(-8.03707 - 4.64021i) q^{71} +(-3.45723 - 5.98809i) q^{73} +(0.305069 + 0.524864i) q^{75} +(1.38264 - 0.798268i) q^{77} +(9.57594 + 5.52867i) q^{79} +(-4.59038 - 7.74134i) q^{81} +(-15.2893 + 8.82729i) q^{83} +(-8.29381 + 4.78843i) q^{85} +(-0.00789003 - 2.71251i) q^{87} -1.87067i q^{89} -0.948294 q^{91} +(0.0556526 + 19.1328i) q^{93} +(6.46305 + 11.1943i) q^{95} +(3.26636 - 1.88583i) q^{97} +(-5.48993 - 9.38236i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.870385	+	1.49747i	0.502517	+	0.864567i
$3$	0.870385	+	1.49747i	0.502517	+	0.864567i
$4$		0			0
$5$	2.31311			1.03446			0.517228	−	0.855848i	$-0.326964\pi$
$5$	2.31311			1.03446			0.517228	+	0.855848i	$0.326964\pi$
$6$		0			0
$7$	−0.381576	−	0.220303i	−0.144222	−	0.0832667i	0.426153	−	0.904651i	$-0.359869\pi$
$7$	−0.381576	−	0.220303i	−0.144222	−	0.0832667i	−0.570375	+	0.821385i	$0.693202\pi$
$8$		0			0
$9$	−1.48486	+	2.60676i	−0.494953	+	0.868919i
$10$		0			0
$11$	−1.81175	+	3.13804i	−0.546263	+	0.946156i	0.452263	+	0.891885i	$0.350617\pi$
$11$	−1.81175	+	3.13804i	−0.546263	+	0.946156i	−0.998526	+	0.0542713i	$0.982716\pi$
$12$		0			0
$13$	1.86390	−	1.07613i	0.516954	−	0.298463i	−0.218734	−	0.975785i	$-0.570193\pi$
$13$	1.86390	−	1.07613i	0.516954	−	0.298463i	0.735687	+	0.677321i	$0.236859\pi$
$14$		0			0
$15$	2.01330	+	3.46383i	0.519832	+	0.894357i
$16$		0			0
$17$	−3.58556	+	2.07012i	−0.869626	+	0.502079i	−0.867224	−	0.497918i	$-0.834098\pi$
$17$	−3.58556	+	2.07012i	−0.869626	+	0.502079i	−0.00240210	+	0.999997i	$0.500765\pi$
$18$		0			0
$19$	2.79409	+	4.83951i	0.641009	+	1.11026i	0.985208	+	0.171363i	$0.0548170\pi$
$19$	2.79409	+	4.83951i	0.641009	+	1.11026i	−0.344199	+	0.938897i	$0.611850\pi$
$20$		0			0
$21$	−0.00221981	−	0.763149i	−0.000484403	−	0.166533i
$22$		0			0
$23$	3.74237	−	2.16066i	0.780338	−	0.450528i	−0.0562120	−	0.998419i	$-0.517902\pi$
$23$	3.74237	−	2.16066i	0.780338	−	0.450528i	0.836550	+	0.547890i	$0.184569\pi$
$24$		0			0
$25$	0.350499			0.0700998
$26$		0			0
$27$	−5.19595	+	0.0453423i	−0.999962	+	0.00872613i
$28$		0			0
$29$	−1.35626	−	0.783038i	−0.251851	−	0.145406i	0.368760	−	0.929525i	$-0.379782\pi$
$29$	−1.35626	−	0.783038i	−0.251851	−	0.145406i	−0.620612	+	0.784118i	$0.713116\pi$
$30$		0			0
$31$	9.56644	+	5.52319i	1.71818	+	0.991993i	0.922236	+	0.386626i	$0.126360\pi$
$31$	9.56644	+	5.52319i	1.71818	+	0.991993i	0.795946	+	0.605367i	$0.206974\pi$
$32$		0			0
$33$	−6.27606	+	0.0182555i	−1.09252	+	0.00317788i
$34$		0			0
$35$	−0.882629	−	0.509586i	−0.149192	−	0.0861358i
$36$		0			0
$37$	2.08197	+	3.60607i	0.342273	+	0.592834i	0.984854	−	0.173383i	$-0.0554699\pi$
$37$	2.08197	+	3.60607i	0.342273	+	0.592834i	−0.642581	+	0.766217i	$0.722137\pi$
$38$		0			0
$39$	3.23378	+	1.85450i	0.517820	+	0.296958i
$40$		0			0
$41$	3.96041	−	6.85963i	0.618512	−	1.07129i	−0.371246	−	0.928535i	$-0.621069\pi$
$41$	3.96041	−	6.85963i	0.618512	−	1.07129i	0.989757	−	0.142759i	$-0.0455974\pi$
$42$		0			0
$43$		−	10.1204i		−	1.54334i	−0.636021	−	0.771672i	$-0.719421\pi$
$43$		−	10.1204i		−	1.54334i	0.636021	−	0.771672i	$-0.280579\pi$
$44$		0			0
$45$	−3.43465	+	6.02973i	−0.512008	+	0.898859i
$46$		0			0
$47$	−1.58438	−	0.914742i	−0.231105	−	0.133429i	0.379976	−	0.924996i	$-0.375932\pi$
$47$	−1.58438	−	0.914742i	−0.231105	−	0.133429i	−0.611082	+	0.791567i	$0.709265\pi$
$48$		0			0
$49$	−3.40293	−	5.89405i	−0.486133	−	0.842008i
$50$		0			0
$51$	−6.22078	−	3.56748i	−0.871083	−	0.499547i
$52$		0			0
$53$	−5.10476			−0.701193			−0.350596	−	0.936527i	$-0.614021\pi$
$53$	−5.10476			−0.701193			−0.350596	+	0.936527i	$0.614021\pi$
$54$		0			0
$55$	−4.19079	+	7.25866i	−0.565086	+	0.978757i
$56$		0			0
$57$	−4.81511	+	8.39632i	−0.637776	+	1.11212i
$58$		0			0
$59$			11.2026i			1.45845i	0.684274	+	0.729225i	$0.260119\pi$
$59$			11.2026i			1.45845i	−0.684274	+	0.729225i	$0.739881\pi$
$60$		0			0
$61$	4.53420	−	2.61782i	0.580544	−	0.335177i	−0.180805	−	0.983519i	$-0.557870\pi$
$61$	4.53420	−	2.61782i	0.580544	−	0.335177i	0.761350	+	0.648341i	$0.224537\pi$
$62$		0			0
$63$	1.14086	−	0.667557i	0.143735	−	0.0841043i
$64$		0			0
$65$	4.31142	−	2.48920i	0.534766	−	0.308747i
$66$		0			0
$67$	7.39142	+	3.51666i	0.903006	+	0.429628i
$67$	7.39142	+	3.51666i	0.903006	+	0.429628i
$68$		0			0
$69$	6.49283	+	3.72350i	0.781645	+	0.448257i
$70$		0			0
$71$	−8.03707	−	4.64021i	−0.953825	−	0.550691i	−0.0595580	−	0.998225i	$-0.518969\pi$
$71$	−8.03707	−	4.64021i	−0.953825	−	0.550691i	−0.894267	+	0.447534i	$0.852302\pi$
$72$		0			0
$73$	−3.45723	−	5.98809i	−0.404638	−	0.700853i	0.589642	−	0.807665i	$-0.299269\pi$
$73$	−3.45723	−	5.98809i	−0.404638	−	0.700853i	−0.994279	+	0.106812i	$0.965936\pi$
$74$		0			0
$75$	0.305069	+	0.524864i	0.0352263	+	0.0606060i
$76$		0			0
$77$	1.38264	−	0.798268i	0.157567	−	0.0909711i
$78$		0			0
$79$	9.57594	+	5.52867i	1.07738	+	0.622024i	0.930188	−	0.367084i	$-0.119644\pi$
$79$	9.57594	+	5.52867i	1.07738	+	0.622024i	0.147190	+	0.989108i	$0.452977\pi$
$80$		0			0
$81$	−4.59038	−	7.74134i	−0.510042	−	0.860149i
$82$		0			0
$83$	−15.2893	+	8.82729i	−1.67822	+	0.968921i	−0.715424	+	0.698690i	$0.753767\pi$
$83$	−15.2893	+	8.82729i	−1.67822	+	0.968921i	−0.962796	+	0.270230i	$0.912900\pi$
$84$		0			0
$85$	−8.29381	+	4.78843i	−0.899590	+	0.519379i
$86$		0			0
$87$	−0.00789003	−	2.71251i	−0.000845900	−	0.290812i
$88$		0			0
$89$		−	1.87067i		−	0.198291i	−0.995073	−	0.0991455i	$-0.968389\pi$
$89$		−	1.87067i		−	0.198291i	0.995073	−	0.0991455i	$-0.0316109\pi$
$90$		0			0
$91$	−0.948294			−0.0994082
$92$		0			0
$93$	0.0556526	+	19.1328i	0.00577090	+	1.98398i
$94$		0			0
$95$	6.46305	+	11.1943i	0.663095	+	1.14851i
$96$		0			0
$97$	3.26636	−	1.88583i	0.331648	−	0.191477i	−0.324924	−	0.945740i	$-0.605339\pi$
$97$	3.26636	−	1.88583i	0.331648	−	0.191477i	0.656573	+	0.754263i	$0.272006\pi$
$98$		0			0
$99$	−5.48993	−	9.38236i	−0.551758	−	0.942962i
$100$		0			0
$101$	1.10682	−	1.91708i	0.110133	−	0.190756i	−0.805691	−	0.592337i	$-0.798206\pi$
$101$	1.10682	−	1.91708i	0.110133	−	0.190756i	0.915824	+	0.401580i	$0.131539\pi$
$102$		0			0
$103$	4.55602	−	7.89126i	0.448918	−	0.777549i	−0.549398	−	0.835561i	$-0.685143\pi$
$103$	4.55602	−	7.89126i	0.448918	−	0.777549i	0.998316	+	0.0580118i	$0.0184761\pi$
$104$		0			0
$105$	−0.00513468	−	1.76525i	−0.000501093	−	0.172271i
$106$		0			0
$107$			8.18738i			0.791504i	0.918357	+	0.395752i	$0.129516\pi$
$107$			8.18738i			0.791504i	−0.918357	+	0.395752i	$0.870484\pi$
$108$		0			0
$109$		−	11.6045i		−	1.11151i	−0.831345	−	0.555757i	$-0.812429\pi$
$109$		−	11.6045i		−	1.11151i	0.831345	−	0.555757i	$-0.187571\pi$
$110$		0			0
$111$	−3.58789	+	6.25636i	−0.340547	+	0.593827i
$112$		0			0
$113$	5.92757	−	10.2669i	0.557619	−	0.965825i	−0.440075	−	0.897961i	$-0.645048\pi$
$113$	5.92757	−	10.2669i	0.557619	−	0.965825i	0.997695	−	0.0678640i	$-0.0216184\pi$
$114$		0			0
$115$	8.65653	−	4.99785i	0.807226	−	0.466052i
$116$		0			0
$117$	0.0375619	+	6.45664i	0.00347260	+	0.596917i
$118$		0			0
$119$	1.82422			0.167226
$120$		0			0
$121$	−1.06488	−	1.84443i	−0.0968075	−	0.167676i
$122$		0			0
$123$	13.7192	−	0.0399058i	1.23702	−	0.00359818i
$124$		0			0
$125$	−10.7548			−0.961941
$126$		0			0
$127$	8.05059	−	13.9440i	0.714375	−	1.23733i	−0.248825	−	0.968548i	$-0.580045\pi$
$127$	8.05059	−	13.9440i	0.714375	−	1.23733i	0.963200	−	0.268785i	$-0.0866221\pi$
$128$		0			0
$129$	15.1550	−	8.80863i	1.33432	−	0.775556i
$130$		0			0
$131$		−	14.8964i		−	1.30151i	−0.759289	−	0.650753i	$-0.774453\pi$
$131$		−	14.8964i		−	1.30151i	0.759289	−	0.650753i	$-0.225547\pi$
$132$		0			0
$133$		−	2.46219i		−	0.213499i
$134$		0			0
$135$	−12.0188	+	0.104882i	−1.03442	+	0.00902680i
$136$		0			0
$137$	10.4677			0.894317			0.447159	−	0.894455i	$-0.352436\pi$
$137$	10.4677			0.894317			0.447159	+	0.894455i	$0.352436\pi$
$138$		0			0
$139$			4.76990i			0.404578i	0.979326	+	0.202289i	$0.0648380\pi$
$139$			4.76990i			0.404578i	−0.979326	+	0.202289i	$0.935162\pi$
$140$		0			0
$141$	−0.00921710	−	3.16874i	−0.000776220	−	0.266856i
$142$		0			0
$143$			7.79868i			0.652159i
$144$		0			0
$145$	−3.13719	−	1.81126i	−0.260529	−	0.150417i
$146$		0			0
$147$	5.86433	−	10.2259i	0.483682	−	0.843418i
$148$		0			0
$149$		−	11.3415i		−	0.929135i	−0.885538	−	0.464568i	$-0.846210\pi$
$149$		−	11.3415i		−	0.929135i	0.885538	−	0.464568i	$-0.153790\pi$
$150$		0			0
$151$	−1.91659	−	3.31962i	−0.155970	−	0.270147i	0.777442	−	0.628954i	$-0.216517\pi$
$151$	−1.91659	−	3.31962i	−0.155970	−	0.270147i	−0.933412	+	0.358807i	$0.883183\pi$
$152$		0			0
$153$	−0.0722572	−	12.4205i	−0.00584165	−	1.00414i
$154$		0			0
$155$	22.1283	+	12.7758i	1.77739	+	1.02617i
$156$		0			0
$157$	−4.61585	−	7.99488i	−0.368385	−	0.638061i	0.620928	−	0.783867i	$-0.286756\pi$
$157$	−4.61585	−	7.99488i	−0.368385	−	0.638061i	−0.989313	+	0.145806i	$0.953422\pi$
$158$		0			0
$159$	−4.44310	−	7.64425i	−0.352361	−	0.606228i
$160$		0			0
$161$	−1.90400			−0.150056
$162$		0			0
$163$	1.92321	−	3.33111i	0.150638	−	0.260912i	−0.780824	−	0.624751i	$-0.785201\pi$
$163$	1.92321	−	3.33111i	0.150638	−	0.260912i	0.931462	+	0.363838i	$0.118534\pi$
$164$		0			0
$165$	−14.5173	+	0.0422271i	−1.13017	+	0.00328738i
$166$		0			0
$167$	−10.4061	−	6.00794i	−0.805245	−	0.464909i	0.0400566	−	0.999197i	$-0.487246\pi$
$167$	−10.4061	−	6.00794i	−0.805245	−	0.464909i	−0.845302	+	0.534289i	$0.820580\pi$
$168$		0			0
$169$	−4.18391	+	7.24674i	−0.321839	+	0.557442i
$170$		0			0
$171$	−16.7643	+	0.0975271i	−1.28200	+	0.00745808i
$172$		0			0
$173$	−0.261450	+	0.150948i	−0.0198776	+	0.0114764i	−0.509906	−	0.860230i	$-0.670320\pi$
$173$	−0.261450	+	0.150948i	−0.0198776	+	0.0114764i	0.490028	+	0.871707i	$0.336986\pi$
$174$		0			0
$175$	−0.133742	−	0.0772160i	−0.0101099	−	0.00583698i
$176$		0			0
$177$	−16.7756	+	9.75054i	−1.26093	+	0.732896i
$178$		0			0
$179$	20.6912			1.54654			0.773268	−	0.634080i	$-0.218621\pi$
$179$	20.6912			1.54654			0.773268	+	0.634080i	$0.218621\pi$
$180$		0			0
$181$	−1.05358	+	1.82485i	−0.0783119	+	0.135640i	−0.902522	−	0.430644i	$-0.858286\pi$
$181$	−1.05358	+	1.82485i	−0.0783119	+	0.135640i	0.824210	+	0.566285i	$0.191620\pi$
$182$		0			0
$183$	7.86661	+	4.51133i	0.581517	+	0.333487i
$184$		0			0
$185$	4.81582	+	8.34125i	0.354066	+	0.613261i
$186$		0			0
$187$		−	15.0022i		−	1.09707i
$188$		0			0
$189$	1.99264	+	1.12738i	0.144943	+	0.0820050i
$190$		0			0
$191$	−3.98030	−	6.89409i	−0.288005	−	0.498839i	0.685329	−	0.728234i	$-0.259659\pi$
$191$	−3.98030	−	6.89409i	−0.288005	−	0.498839i	−0.973333	+	0.229395i	$0.926325\pi$
$192$		0			0
$193$	−13.4163			−0.965729			−0.482864	−	0.875695i	$-0.660404\pi$
$193$	−13.4163			−0.965729			−0.482864	+	0.875695i	$0.660404\pi$
$194$		0			0
$195$	7.48011	+	4.28968i	0.535662	+	0.307191i
$196$		0			0
$197$	−2.21576	+	3.83781i	−0.157866	+	0.273432i	−0.934099	−	0.357014i	$-0.883795\pi$
$197$	−2.21576	+	3.83781i	−0.157866	+	0.273432i	0.776233	+	0.630446i	$0.217128\pi$
$198$		0			0
$199$	−3.61332	−	6.25845i	−0.256141	−	0.443650i	0.709064	−	0.705145i	$-0.249118\pi$
$199$	−3.61332	−	6.25845i	−0.256141	−	0.443650i	−0.965205	+	0.261495i	$0.915785\pi$
$200$		0			0
$201$	1.16727	+	14.1293i	0.0823330	+	0.996605i
$202$		0			0
$203$	0.345011	+	0.597577i	0.0242150	+	0.0419417i
$204$		0			0
$205$	9.16088	−	15.8671i	0.639823	−	1.10821i
$206$		0			0
$207$	0.0754172	+	12.9637i	0.00524186	+	0.901042i
$208$		0			0
$209$	−20.2488			−1.40064
$210$		0			0
$211$	−0.203275	−	0.352083i	−0.0139940	−	0.0242384i	0.858944	−	0.512070i	$-0.171121\pi$
$211$	−0.203275	−	0.352083i	−0.0139940	−	0.0242384i	−0.872938	+	0.487832i	$0.837788\pi$
$212$		0			0
$213$	−0.0467555	−	16.0741i	−0.00320364	−	1.10138i
$214$		0			0
$215$		−	23.4096i		−	1.59652i
$216$		0			0
$217$	−2.43355	−	4.21503i	−0.165200	−	0.286135i
$218$		0			0
$219$	5.95790	−	10.3891i	0.402597	−	0.702027i
$220$		0			0
$221$	−4.45542	+	7.71702i	−0.299704	+	0.519103i
$222$		0			0
$223$	−6.88204			−0.460856			−0.230428	−	0.973089i	$-0.574013\pi$
$223$	−6.88204			−0.460856			−0.230428	+	0.973089i	$0.574013\pi$
$224$		0			0
$225$	−0.520442	+	0.913666i	−0.0346961	+	0.0609111i
$226$		0			0
$227$	15.3026	+	8.83498i	1.01567	+	0.586398i	0.912847	−	0.408301i	$-0.133879\pi$
$227$	15.3026	+	8.83498i	1.01567	+	0.586398i	0.102824	+	0.994700i	$0.467212\pi$
$228$		0			0
$229$	−3.53670	+	2.04192i	−0.233712	+	0.134934i	−0.612283	−	0.790638i	$-0.709749\pi$
$229$	−3.53670	+	2.04192i	−0.233712	+	0.134934i	0.378571	+	0.925572i	$0.376415\pi$
$230$		0			0
$231$	2.39882	+	1.37567i	0.157831	+	0.0905124i
$232$		0			0
$233$	5.24918	−	9.09185i	0.343885	−	0.595627i	−0.641265	−	0.767319i	$-0.721590\pi$
$233$	5.24918	−	9.09185i	0.343885	−	0.595627i	0.985151	+	0.171692i	$0.0549235\pi$
$234$		0			0
$235$	−3.66485	−	2.11590i	−0.239068	−	0.138026i
$236$		0			0
$237$	0.0557079	+	19.1518i	0.00361862	+	1.24404i
$238$		0			0
$239$	10.1328	−	17.5505i	0.655435	−	1.13525i	−0.326349	−	0.945249i	$-0.605818\pi$
$239$	10.1328	−	17.5505i	0.655435	−	1.13525i	0.981784	−	0.189998i	$-0.0608482\pi$
$240$		0			0
$241$	−2.49142			−0.160486			−0.0802432	−	0.996775i	$-0.525570\pi$
$241$	−2.49142			−0.160486			−0.0802432	+	0.996775i	$0.525570\pi$
$242$		0			0
$243$	7.59707	−	13.6119i	0.487352	−	0.873205i
$244$		0			0
$245$	−7.87137	−	13.6336i	−0.502884	−	0.871020i
$246$		0			0
$247$	10.4158	+	6.01358i	0.662744	+	0.382635i
$248$		0			0
$249$	−26.5262	−	15.2122i	−1.68103	−	0.964035i
$250$		0			0
$251$	0.150552	+	0.260763i	0.00950274	+	0.0164592i	0.870738	−	0.491748i	$-0.163642\pi$
$251$	0.150552	+	0.260763i	0.00950274	+	0.0164592i	−0.861235	+	0.508207i	$0.830308\pi$
$252$		0			0
$253$			15.6583i			0.984429i
$254$		0			0
$255$	−14.3894	−	8.25199i	−0.901097	−	0.516760i
$256$		0			0
$257$	21.2815	+	12.2869i	1.32750	+	0.766435i	0.984913	−	0.173049i	$-0.0553620\pi$
$257$	21.2815	+	12.2869i	1.32750	+	0.766435i	0.342592	+	0.939484i	$0.388695\pi$
$258$		0			0
$259$		−	1.83465i		−	0.114000i
$260$		0			0
$261$	4.05505	−	2.37274i	0.251001	−	0.146869i
$262$		0			0
$263$		−	7.20954i		−	0.444560i	−0.974983	−	0.222280i	$-0.928650\pi$
$263$		−	7.20954i		−	0.444560i	0.974983	−	0.222280i	$-0.0713498\pi$
$264$		0			0
$265$	−11.8079			−0.725353
$266$		0			0
$267$	2.80129	−	1.62821i	0.171436	−	0.0996446i
$268$		0			0
$269$			26.7016i			1.62802i	0.580848	+	0.814012i	$0.302721\pi$
$269$			26.7016i			1.62802i	−0.580848	+	0.814012i	$0.697279\pi$
$270$		0			0
$271$			30.0921i			1.82796i	0.405754	+	0.913982i	$0.367009\pi$
$271$			30.0921i			1.82796i	−0.405754	+	0.913982i	$0.632991\pi$
$272$		0			0
$273$	−0.825381	−	1.42005i	−0.0499543	−	0.0859451i
$274$		0			0
$275$	−0.635017	+	1.09988i	−0.0382930	+	0.0663254i
$276$		0			0
$277$	19.0347			1.14368			0.571841	−	0.820365i	$-0.306230\pi$
$277$	19.0347			1.14368			0.571841	+	0.820365i	$0.306230\pi$
$278$		0			0
$279$	−28.6024	+	16.7362i	−1.71238	+	1.00197i
$280$		0			0
$281$	−2.09343	−	3.62592i	−0.124883	−	0.216304i	0.796804	−	0.604238i	$-0.206522\pi$
$281$	−2.09343	−	3.62592i	−0.124883	−	0.216304i	−0.921687	+	0.387934i	$0.873189\pi$
$282$		0			0
$283$	−16.3499			−0.971898			−0.485949	−	0.873987i	$-0.661526\pi$
$283$	−16.3499			−0.971898			−0.485949	+	0.873987i	$0.661526\pi$
$284$		0			0
$285$	−11.1379	+	19.4216i	−0.659752	+	1.15044i
$286$		0			0
$287$	−3.02239	+	1.74498i	−0.178406	+	0.103003i
$288$		0			0
$289$	0.0708273	−	0.122676i	0.00416631	−	0.00721626i
$290$		0			0
$291$	5.66697	+	3.24989i	0.332204	+	0.190512i
$292$		0			0
$293$		−	17.2107i		−	1.00546i	−0.864444	−	0.502729i	$-0.832329\pi$
$293$		−	17.2107i		−	1.00546i	0.864444	−	0.502729i	$-0.167671\pi$
$294$		0			0
$295$			25.9128i			1.50870i
$296$		0			0
$297$	9.27149	−	16.3873i	0.537986	−	0.950887i
$298$		0			0
$299$	4.65028	−	8.05452i	0.268932	−	0.465805i
$300$		0			0
$301$	−2.22955	+	3.86170i	−0.128509	+	0.222584i
$302$		0			0
$303$	3.83414	−	0.0111526i	0.220265	−	0.000640698i
$304$		0			0
$305$	10.4881	−	6.05532i	0.600548	−	0.346726i
$306$		0			0
$307$	−1.62191	−	2.80923i	−0.0925674	−	0.160331i	0.816023	−	0.578019i	$-0.196174\pi$
$307$	−1.62191	−	2.80923i	−0.0925674	−	0.160331i	−0.908591	+	0.417688i	$0.862841\pi$
$308$		0			0
$309$	15.7825	−	0.0459073i	0.897833	−	0.00261157i
$310$		0			0
$311$	−14.0809			−0.798452			−0.399226	−	0.916853i	$-0.630721\pi$
$311$	−14.0809			−0.798452			−0.399226	+	0.916853i	$0.630721\pi$
$312$		0			0
$313$		−	32.5424i		−	1.83941i	−0.392615	−	0.919703i	$-0.628430\pi$
$313$		−	32.5424i		−	1.83941i	0.392615	−	0.919703i	$-0.371570\pi$
$314$		0			0
$315$	2.63895	−	1.54414i	0.148688	−	0.0870022i
$316$		0			0
$317$	−8.38182	+	4.83925i	−0.470770	+	0.271799i	−0.716562	−	0.697523i	$-0.754285\pi$
$317$	−8.38182	+	4.83925i	−0.470770	+	0.271799i	0.245792	+	0.969323i	$0.420952\pi$
$318$		0			0
$319$	4.91442	−	2.83734i	0.275154	−	0.158860i
$320$		0			0
$321$	−12.2604	+	7.12617i	−0.684308	+	0.397744i
$322$		0			0
$323$	−20.0368	−	11.5682i	−1.11488	−	0.643674i
$324$		0			0
$325$	0.653296	−	0.377181i	0.0362384	−	0.0209222i
$326$		0			0
$327$	17.3775	−	10.1004i	0.960978	−	0.558554i
$328$		0			0
$329$	0.403041	+	0.698087i	0.0222203	+	0.0384868i
$330$		0			0
$331$	21.2059	+	12.2432i	1.16558	+	0.672949i	0.952635	−	0.304114i	$-0.0983605\pi$
$331$	21.2059	+	12.2432i	1.16558	+	0.672949i	0.212947	+	0.977064i	$0.431694\pi$
$332$		0			0
$333$	−12.4916	+	0.0726705i	−0.684534	+	0.00398232i
$334$		0			0
$335$	17.0972	+	8.13444i	0.934120	+	0.444432i
$336$		0			0
$337$	−0.976505	+	0.563785i	−0.0531936	+	0.0307113i	−0.526361	−	0.850261i	$-0.676444\pi$
$337$	−0.976505	+	0.563785i	−0.0531936	+	0.0307113i	0.473167	+	0.880973i	$0.343111\pi$
$338$		0			0
$339$	20.5336	−	0.0597273i	1.11523	−	0.00324394i
$340$		0			0
$341$	−34.6640	+	20.0133i	−1.87716	+	1.08378i
$342$		0			0
$343$			6.08295i			0.328448i
$344$		0			0
$345$	15.0187	+	8.61288i	0.808578	+	0.463702i
$346$		0			0
$347$	0.271102	−	0.469562i	0.0145535	−	0.0252074i	−0.858657	−	0.512551i	$-0.828701\pi$
$347$	0.271102	−	0.469562i	0.0145535	−	0.0252074i	0.873210	+	0.487343i	$0.162034\pi$
$348$		0			0
$349$	−7.61912			−0.407842			−0.203921	−	0.978987i	$-0.565369\pi$
$349$	−7.61912			−0.407842			−0.203921	+	0.978987i	$0.565369\pi$
$350$		0			0
$351$	−9.63596	+	5.67601i	−0.514330	+	0.302963i
$352$		0			0
$353$	−7.82386	−	13.5513i	−0.416422	−	0.721264i	0.579154	−	0.815218i	$-0.303383\pi$
$353$	−7.82386	−	13.5513i	−0.416422	−	0.721264i	−0.995577	+	0.0939535i	$0.970049\pi$
$354$		0			0
$355$	−18.5907	−	10.7333i	−0.986690	−	0.569666i
$356$		0			0
$357$	1.58777	+	2.73172i	0.0840338	+	0.144578i
$358$		0			0
$359$			16.8211i			0.887786i	0.896080	+	0.443893i	$0.146403\pi$
$359$			16.8211i			0.887786i	−0.896080	+	0.443893i	$0.853597\pi$
$360$		0			0
$361$	−6.11389	+	10.5896i	−0.321784	+	0.557346i
$362$		0			0
$363$	1.83513	−	3.20000i	0.0963194	−	0.167956i
$364$		0			0
$365$	−7.99696	−	13.8511i	−0.418580	−	0.725002i
$366$		0			0
$367$	10.3592	+	5.98091i	0.540748	+	0.312201i	0.745382	−	0.666638i	$-0.232267\pi$
$367$	10.3592	+	5.98091i	0.540748	+	0.312201i	−0.204634	+	0.978839i	$0.565600\pi$
$368$		0			0
$369$	12.0007	+	20.5094i	0.624733	+	1.06768i
$370$		0			0
$371$	1.94785	+	1.12459i	0.101128	+	0.0583860i
$372$		0			0
$373$	10.8082	+	6.24014i	0.559630	+	0.323102i	0.752997	−	0.658024i	$-0.228608\pi$
$373$	10.8082	+	6.24014i	0.559630	+	0.323102i	−0.193367	+	0.981126i	$0.561941\pi$
$374$		0			0
$375$	−9.36084	−	16.1051i	−0.483392	−	0.831663i
$376$		0			0
$377$	−3.37059			−0.173594
$378$		0			0
$379$	22.3180	−	12.8853i	1.14640	−	0.661874i	0.198393	−	0.980123i	$-0.436428\pi$
$379$	22.3180	−	12.8853i	1.14640	−	0.661874i	0.948007	+	0.318248i	$0.103095\pi$
$380$		0			0
$381$	27.8880	−	0.0811192i	1.42874	−	0.00415586i
$382$		0			0
$383$	13.8244	+	23.9445i	0.706391	+	1.22351i	0.966187	+	0.257842i	$0.0830115\pi$
$383$	13.8244	+	23.9445i	0.706391	+	1.22351i	−0.259796	+	0.965664i	$0.583655\pi$
$384$		0			0
$385$	3.19821	−	1.84649i	0.162996	−	0.0941056i
$386$		0			0
$387$	26.3814	+	15.0274i	1.34104	+	0.763883i
$388$		0			0
$389$	4.39472	−	2.53730i	0.222821	−	0.128646i	−0.384435	−	0.923152i	$-0.625604\pi$
$389$	4.39472	−	2.53730i	0.222821	−	0.128646i	0.607256	+	0.794506i	$0.292270\pi$
$390$		0			0
$391$	−8.94566	+	15.4943i	−0.452402	+	0.783583i
$392$		0			0
$393$	22.3070	−	12.9656i	1.12524	−	0.654029i
$394$		0			0
$395$	22.1503	+	12.7885i	1.11450	+	0.643457i
$396$		0			0
$397$	3.75138			0.188277			0.0941383	−	0.995559i	$-0.469990\pi$
$397$	3.75138			0.188277			0.0941383	+	0.995559i	$0.469990\pi$
$398$		0			0
$399$	3.68706	−	2.14305i	0.184584	−	0.107287i
$400$		0			0
$401$	−27.7301			−1.38478			−0.692388	−	0.721525i	$-0.743441\pi$
$401$	−27.7301			−1.38478			−0.692388	+	0.721525i	$0.743441\pi$
$402$		0			0
$403$	23.7746			1.18429
$404$		0			0
$405$	−10.6181	−	17.9066i	−0.527616	−	0.889787i
$406$		0			0
$407$	−15.0880			−0.747885
$408$		0			0
$409$	4.97208	+	2.87063i	0.245854	+	0.141944i	0.617864	−	0.786285i	$-0.287998\pi$
$409$	4.97208	+	2.87063i	0.245854	+	0.141944i	−0.372010	+	0.928229i	$0.621331\pi$
$410$		0			0
$411$	9.11094	+	15.6751i	0.449410	+	0.773198i
$412$		0			0
$413$	2.46796	−	4.27463i	0.121440	−	0.210341i
$414$		0			0
$415$	−35.3659	+	20.4185i	−1.73605	+	1.00231i
$416$		0			0
$417$	−7.14281	+	4.15165i	−0.349785	+	0.203307i
$418$		0			0
$419$	−18.7793	+	10.8422i	−0.917429	+	0.529678i	−0.882814	−	0.469723i	$-0.844354\pi$
$419$	−18.7793	+	10.8422i	−0.917429	+	0.529678i	−0.0346149	+	0.999401i	$0.511020\pi$
$420$		0			0
$421$	0.429347	+	0.743650i	0.0209251	+	0.0362433i	0.876298	−	0.481769i	$-0.160006\pi$
$421$	0.429347	+	0.743650i	0.0209251	+	0.0362433i	−0.855373	+	0.518012i	$0.826672\pi$
$422$		0			0
$423$	4.73709	−	2.77183i	0.230325	−	0.134771i
$424$		0			0
$425$	−1.25674	+	0.725577i	−0.0609606	+	0.0351956i
$426$		0			0
$427$	−2.30685			−0.111636
$428$		0			0
$429$	−11.6783	+	6.78785i	−0.563835	+	0.327721i
$430$		0			0
$431$	−16.0309	−	9.25544i	−0.772181	−	0.445819i	0.0614712	−	0.998109i	$-0.480421\pi$
$431$	−16.0309	−	9.25544i	−0.772181	−	0.445819i	−0.833652	+	0.552290i	$0.813754\pi$
$432$		0			0
$433$	−8.86886	−	5.12044i	−0.426210	−	0.246073i	0.271521	−	0.962433i	$-0.412474\pi$
$433$	−8.86886	−	5.12044i	−0.426210	−	0.246073i	−0.697731	+	0.716360i	$0.745807\pi$
$434$		0			0
$435$	−0.0182505	−	6.27435i	−0.000875046	−	0.300832i
$436$		0			0
$437$	20.9131	+	12.0742i	1.00041	+	0.577585i
$438$		0			0
$439$	11.5378	+	19.9840i	0.550668	+	0.953784i	0.998227	+	0.0595298i	$0.0189601\pi$
$439$	11.5378	+	19.9840i	0.550668	+	0.953784i	−0.447559	+	0.894254i	$0.647707\pi$
$440$		0			0
$441$	20.4173	−	0.118779i	0.972250	−	0.00565612i
$442$		0			0
$443$	−7.45517	+	12.9127i	−0.354206	+	0.613502i	−0.986982	−	0.160833i	$-0.948582\pi$
$443$	−7.45517	+	12.9127i	−0.354206	+	0.613502i	0.632776	+	0.774335i	$0.281915\pi$
$444$		0			0
$445$		−	4.32708i		−	0.205123i
$446$		0			0
$447$	16.9837	−	9.87150i	0.803300	−	0.466906i
$448$		0			0
$449$	33.8450	+	19.5404i	1.59724	+	0.922170i	0.992015	+	0.126119i	$0.0402520\pi$
$449$	33.8450	+	19.5404i	1.59724	+	0.922170i	0.605229	+	0.796051i	$0.293081\pi$
$450$		0			0
$451$	14.3505	+	24.8559i	0.675741	+	1.17042i
$452$		0			0
$453$	3.30288	−	5.75939i	0.155183	−	0.270600i
$454$		0			0
$455$	−2.19351			−0.102833
$456$		0			0
$457$	−6.09848	+	10.5629i	−0.285275	+	0.494111i	−0.972676	−	0.232168i	$-0.925418\pi$
$457$	−6.09848	+	10.5629i	−0.285275	+	0.494111i	0.687401	+	0.726278i	$0.258752\pi$
$458$		0			0
$459$	18.5365	−	10.9188i	0.865212	−	0.509648i
$460$		0			0
$461$			42.6980i			1.98864i	0.106414	+	0.994322i	$0.466063\pi$
$461$			42.6980i			1.98864i	−0.106414	+	0.994322i	$0.533937\pi$
$462$		0			0
$463$	−20.8070	+	12.0129i	−0.966984	+	0.558288i	−0.898315	−	0.439351i	$-0.855208\pi$
$463$	−20.8070	+	12.0129i	−0.966984	+	0.558288i	−0.0686685	+	0.997640i	$0.521875\pi$
$464$		0			0
$465$	0.128731	+	44.2563i	0.00596975	+	2.05234i
$466$		0			0
$467$	−9.78868	+	5.65150i	−0.452966	+	0.261520i	−0.709082	−	0.705126i	$-0.750890\pi$
$467$	−9.78868	+	5.65150i	−0.452966	+	0.261520i	0.256116	+	0.966646i	$0.417557\pi$
$468$		0			0
$469$	−2.04566	−	2.97023i	−0.0944597	−	0.137152i
$470$		0			0
$471$	7.95457	−	13.8707i	0.366527	−	0.639130i
$472$		0			0
$473$	31.7582	+	18.3356i	1.46024	+	0.843072i
$474$		0			0
$475$	0.979327	+	1.69624i	0.0449346	+	0.0778290i
$476$		0			0
$477$	7.57985	−	13.3069i	0.347058	−	0.609280i
$478$		0			0
$479$	−35.3077	+	20.3849i	−1.61325	+	0.931409i	−0.624637	+	0.780915i	$0.714753\pi$
$479$	−35.3077	+	20.3849i	−1.61325	+	0.931409i	−0.988611	+	0.150494i	$0.951914\pi$
$480$		0			0
$481$	7.76116	+	4.48091i	0.353879	+	0.204312i
$482$		0			0
$483$	−1.65721	−	2.85119i	−0.0754057	−	0.129734i
$484$		0			0
$485$	7.55546	−	4.36214i	0.343076	−	0.198075i
$486$		0			0
$487$	−29.9957	+	17.3180i	−1.35923	+	0.784754i	−0.989521	−	0.144392i	$-0.953878\pi$
$487$	−29.9957	+	17.3180i	−1.35923	+	0.784754i	−0.369714	+	0.929146i	$0.620544\pi$
$488$		0			0
$489$	6.66218	−	0.0193787i	0.301274	−	0.000876333i
$490$		0			0
$491$		−	35.3506i		−	1.59535i	−0.603087	−	0.797675i	$-0.706063\pi$
$491$		−	35.3506i		−	1.59535i	0.603087	−	0.797675i	$-0.293937\pi$
$492$		0			0
$493$	6.48394			0.292022
$494$		0			0
$495$	−12.6988	−	21.7025i	−0.570770	−	0.975453i
$496$		0			0
$497$	2.04450	+	3.54118i	0.0917085	+	0.158844i
$498$		0			0
$499$	−37.7587	+	21.8000i	−1.69031	+	0.975902i	−0.736052	+	0.676925i	$0.763312\pi$
$499$	−37.7587	+	21.8000i	−1.69031	+	0.975902i	−0.954260	+	0.298977i	$0.903355\pi$
$500$		0			0
$501$	−0.0605371	−	20.8120i	−0.00270460	−	0.929813i
$502$		0			0
$503$	11.8182	−	20.4697i	0.526947	−	0.912698i	−0.472560	−	0.881298i	$-0.656670\pi$
$503$	11.8182	−	20.4697i	0.526947	−	0.912698i	0.999507	−	0.0313999i	$-0.00999655\pi$
$504$		0			0
$505$	2.56021	−	4.43442i	0.113928	−	0.197329i
$506$		0			0
$507$	−14.4934	+	0.0421578i	−0.643676	+	0.00187229i
$508$		0			0
$509$			10.8076i			0.479039i	0.970892	+	0.239520i	$0.0769900\pi$
$509$			10.8076i			0.479039i	−0.970892	+	0.239520i	$0.923010\pi$
$510$		0			0
$511$			3.04655i			0.134771i
$512$		0			0
$513$	−14.7374	−	25.0192i	−0.650672	−	1.10462i
$514$		0			0
$515$	10.5386	−	18.2534i	0.464386	−	0.804341i
$516$		0			0
$517$	5.74100	−	3.31457i	0.252489	−	0.145775i
$518$		0			0
$519$	−0.453602	−	0.260131i	−0.0199109	−	0.0114185i
$520$		0			0
$521$	−20.9458			−0.917652			−0.458826	−	0.888526i	$-0.651730\pi$
$521$	−20.9458			−0.917652			−0.458826	+	0.888526i	$0.651730\pi$
$522$		0			0
$523$	3.61494	+	6.26126i	0.158070	+	0.273786i	0.934173	−	0.356821i	$-0.116139\pi$
$523$	3.61494	+	6.26126i	0.158070	+	0.273786i	−0.776102	+	0.630607i	$0.782806\pi$
$524$		0			0
$525$	−0.000778042	−	0.267483i	−3.39565e−5	−	0.0116739i
$526$		0			0
$527$	−45.7347			−1.99224
$528$		0			0
$529$	−2.16311	+	3.74662i	−0.0940482	+	0.162896i
$530$		0			0
$531$	−29.2024	−	16.6342i	−1.26728	−	0.721865i
$532$		0			0
$533$		−	17.0476i		−	0.738412i
$534$		0			0
$535$			18.9383i			0.818776i
$536$		0			0
$537$	18.0093	+	30.9846i	0.777160	+	1.33708i
$538$		0			0
$539$	24.6611			1.06223
$540$		0			0
$541$			3.95272i			0.169941i	0.996383	+	0.0849703i	$0.0270795\pi$
$541$			3.95272i			0.169941i	−0.996383	+	0.0849703i	$0.972920\pi$
$542$		0			0
$543$	−3.64969	+	0.0106160i	−0.156623	+	0.000455578i
$544$		0			0
$545$		−	26.8426i		−	1.14981i
$546$		0			0
$547$	−4.71498	−	2.72219i	−0.201598	−	0.116393i	0.395803	−	0.918336i	$-0.370466\pi$
$547$	−4.71498	−	2.72219i	−0.201598	−	0.116393i	−0.597401	+	0.801943i	$0.703800\pi$
$548$		0			0
$549$	0.0913743	+	15.7067i	0.00389976	+	0.670344i
$550$		0			0
$551$		−	8.75152i		−	0.372827i
$552$		0			0
$553$	−2.43597	−	4.21922i	−0.103588	−	0.179419i
$554$		0			0
$555$	−8.29919	+	14.4717i	−0.352281	+	0.614288i
$556$		0			0
$557$	34.1788	+	19.7331i	1.44820	+	0.836119i	0.998374	−	0.0569964i	$-0.0181524\pi$
$557$	34.1788	+	19.7331i	1.44820	+	0.836119i	0.449827	+	0.893116i	$0.351486\pi$
$558$		0			0
$559$	−10.8908	−	18.8634i	−0.460632	−	0.797837i
$560$		0			0
$561$	22.4654	−	13.0577i	0.948490	−	0.551296i
$562$		0			0
$563$	−8.23489			−0.347059			−0.173530	−	0.984829i	$-0.555517\pi$
$563$	−8.23489			−0.347059			−0.173530	+	0.984829i	$0.555517\pi$
$564$		0			0
$565$	13.7112	−	23.7484i	0.576833	−	0.999104i
$566$		0			0
$567$	0.0461369	+	3.96519i	0.00193757	+	0.166522i
$568$		0			0
$569$	−14.1899	−	8.19252i	−0.594870	−	0.343448i	0.172151	−	0.985071i	$-0.444928\pi$
$569$	−14.1899	−	8.19252i	−0.594870	−	0.343448i	−0.767021	+	0.641622i	$0.778262\pi$
$570$		0			0
$571$	6.74464	−	11.6821i	0.282254	−	0.488879i	−0.689685	−	0.724109i	$-0.742251\pi$
$571$	6.74464	−	11.6821i	0.282254	−	0.488879i	0.971940	+	0.235230i	$0.0755845\pi$
$572$		0			0
$573$	6.85933	−	11.9609i	0.286552	−	0.499674i
$574$		0			0
$575$	1.31170	−	0.757309i	0.0547016	−	0.0315820i
$576$		0			0
$577$	35.0939	+	20.2615i	1.46098	+	0.843497i	0.999057	−	0.0434231i	$-0.0138263\pi$
$577$	35.0939	+	20.2615i	1.46098	+	0.843497i	0.461923	+	0.886920i	$0.347160\pi$
$578$		0			0
$579$	−11.6774	−	20.0906i	−0.485295	−	0.834938i
$580$		0			0
$581$	7.77871			0.322715
$582$		0			0
$583$	9.24855	−	16.0190i	0.383036	−	0.663438i
$584$		0			0
$585$	0.0868849	+	14.9350i	0.00359225	+	0.617484i
$586$		0			0
$587$	−17.8679	−	30.9482i	−0.737489	−	1.27737i	−0.953623	−	0.301004i	$-0.902678\pi$
$587$	−17.8679	−	30.9482i	−0.737489	−	1.27737i	0.216134	−	0.976364i	$-0.430655\pi$
$588$		0			0
$589$			61.7291i			2.54350i
$590$		0			0
$591$	−7.67558	+	0.0223264i	−0.315731	+	0.000918384i
$592$		0			0
$593$	7.81383	+	13.5339i	0.320875	+	0.555773i	0.980669	−	0.195674i	$-0.0626896\pi$
$593$	7.81383	+	13.5339i	0.320875	+	0.555773i	−0.659793	+	0.751447i	$0.729356\pi$
$594$		0			0
$595$	4.21963			0.172988
$596$		0			0
$597$	6.22689	−	10.8581i	0.254850	−	0.444393i
$598$		0			0
$599$	−8.20698	+	14.2149i	−0.335328	+	0.580805i	−0.983548	−	0.180648i	$-0.942181\pi$
$599$	−8.20698	+	14.2149i	−0.335328	+	0.580805i	0.648220	+	0.761453i	$0.275514\pi$
$600$		0			0
$601$	−13.3502	−	23.1232i	−0.544565	−	0.943215i	−0.998634	−	0.0522481i	$-0.983361\pi$
$601$	−13.3502	−	23.1232i	−0.544565	−	0.943215i	0.454069	−	0.890967i	$-0.349972\pi$
$602$		0			0
$603$	−20.1423	+	14.0459i	−0.820258	+	0.571993i
$604$		0			0
$605$	−2.46320	−	4.26638i	−0.100143	−	0.173453i
$606$		0			0
$607$	−17.6213	+	30.5209i	−0.715225	+	1.23881i	0.247647	+	0.968850i	$0.420343\pi$
$607$	−17.6213	+	30.5209i	−0.715225	+	1.23881i	−0.962873	+	0.269957i	$0.912991\pi$
$608$		0			0
$609$	−0.594564	+	1.03677i	−0.0240929	+	0.0420119i
$610$		0			0
$611$	−3.93751			−0.159294
$612$		0			0
$613$	−20.1296	−	34.8654i	−0.813026	−	1.40820i	−0.910737	−	0.412987i	$-0.864485\pi$
$613$	−20.1296	−	34.8654i	−0.813026	−	1.40820i	0.0977108	−	0.995215i	$-0.468848\pi$
$614$		0			0
$615$	31.7341	−	0.0923066i	1.27964	−	0.00372216i
$616$		0			0
$617$		−	5.57627i		−	0.224492i	−0.993680	−	0.112246i	$-0.964196\pi$
$617$		−	5.57627i		−	0.224492i	0.993680	−	0.112246i	$-0.0358045\pi$
$618$		0			0
$619$	−12.2126	−	21.1528i	−0.490865	−	0.850203i	0.509080	−	0.860719i	$-0.329986\pi$
$619$	−12.2126	−	21.1528i	−0.490865	−	0.850203i	−0.999945	+	0.0105161i	$0.996653\pi$
$620$		0			0
$621$	−19.3472	+	11.3964i	−0.776377	+	0.457321i
$622$		0			0
$623$	−0.412115	+	0.713804i	−0.0165110	+	0.0285980i
$624$		0			0
$625$	−26.6296			−1.06519
$626$		0			0
$627$	−17.6242	−	30.3221i	−0.703844	−	1.21095i
$628$		0			0
$629$	−14.9300	−	8.61985i	−0.595299	−	0.343696i
$630$		0			0
$631$	−24.1134	+	13.9219i	−0.959940	+	0.554222i	−0.896155	−	0.443742i	$-0.853651\pi$
$631$	−24.1134	+	13.9219i	−0.959940	+	0.554222i	−0.0637856	+	0.997964i	$0.520317\pi$
$632$		0			0
$633$	0.350307	−	0.610846i	0.0139235	−	0.0242790i
$634$		0			0
$635$	18.6219	−	32.2542i	0.738989	−	1.27997i
$636$		0			0
$637$	−12.6855	−	7.32396i	−0.502617	−	0.290186i
$638$		0			0
$639$	24.0298	−	14.0606i	0.950605	−	0.556231i
$640$		0			0
$641$	−12.8046	+	22.1782i	−0.505751	+	0.875986i	0.494227	+	0.869333i	$0.335451\pi$
$641$	−12.8046	+	22.1782i	−0.505751	+	0.875986i	−0.999978	+	0.00665332i	$0.997882\pi$
$642$		0			0
$643$	3.32180			0.130999			0.0654995	−	0.997853i	$-0.479136\pi$
$643$	3.32180			0.130999			0.0654995	+	0.997853i	$0.479136\pi$
$644$		0			0
$645$	35.0553	−	20.3754i	1.38030	−	0.802279i
$646$		0			0
$647$	−6.53059	−	11.3113i	−0.256744	−	0.444694i	0.708624	−	0.705586i	$-0.249316\pi$
$647$	−6.53059	−	11.3113i	−0.256744	−	0.444694i	−0.965368	+	0.260893i	$0.915983\pi$
$648$		0			0
$649$	−35.1541	−	20.2963i	−1.37992	−	0.796698i
$650$		0			0
$651$	4.19378	−	7.31287i	0.164367	−	0.286614i
$652$		0			0
$653$	−3.55162	−	6.15158i	−0.138986	−	0.240730i	0.788127	−	0.615512i	$-0.211051\pi$
$653$	−3.55162	−	6.15158i	−0.138986	−	0.240730i	−0.927113	+	0.374782i	$0.877717\pi$
$654$		0			0
$655$		−	34.4571i		−	1.34635i
$656$		0			0
$657$	20.7430	−	0.120674i	0.809262	−	0.00470792i
$658$		0			0
$659$	−27.3348	−	15.7817i	−1.06481	−	0.614769i	−0.138052	−	0.990425i	$-0.544084\pi$
$659$	−27.3348	−	15.7817i	−1.06481	−	0.614769i	−0.926759	+	0.375656i	$0.877417\pi$
$660$		0			0
$661$		−	8.56732i		−	0.333230i	−0.986022	−	0.166615i	$-0.946716\pi$
$661$		−	8.56732i		−	0.333230i	0.986022	−	0.166615i	$-0.0532837\pi$
$662$		0			0
$663$	−15.4340	+	0.0448936i	−0.599406	+	0.00174352i
$664$		0			0
$665$		−	5.69532i		−	0.220855i
$666$		0			0
$667$	−6.76751			−0.262039
$668$		0			0
$669$	−5.99003	−	10.3057i	−0.231588	−	0.398441i
$670$		0			0
$671$			18.9713i			0.732381i
$672$		0			0
$673$		−	22.5204i		−	0.868098i	−0.900889	−	0.434049i	$-0.857085\pi$
$673$		−	22.5204i		−	0.868098i	0.900889	−	0.434049i	$-0.142915\pi$
$674$		0			0
$675$	−1.82118	+	0.0158924i	−0.0700972	+	0.000611700i
$676$		0			0
$677$	20.6650	−	35.7928i	0.794220	−	1.37563i	−0.129114	−	0.991630i	$-0.541213\pi$
$677$	20.6650	−	35.7928i	0.794220	−	1.37563i	0.923333	−	0.383999i	$-0.125453\pi$
$678$		0			0
$679$	−1.66182			−0.0637747
$680$		0			0
$681$	0.0890228	+	30.6051i	0.00341136	+	1.17279i
$682$		0			0
$683$	−8.45498	−	14.6445i	−0.323521	−	0.560354i	0.657691	−	0.753288i	$-0.271533\pi$
$683$	−8.45498	−	14.6445i	−0.323521	−	0.560354i	−0.981212	+	0.192933i	$0.938200\pi$
$684$		0			0
$685$	24.2130			0.925132
$686$		0			0
$687$	−6.13601	−	3.51887i	−0.234103	−	0.134253i
$688$		0			0
$689$	−9.51478	+	5.49336i	−0.362484	+	0.209280i
$690$		0			0
$691$	22.0876	−	38.2569i	0.840253	−	1.45536i	−0.0494277	−	0.998778i	$-0.515740\pi$
$691$	22.0876	−	38.2569i	0.840253	−	1.45536i	0.889681	−	0.456583i	$-0.150927\pi$
$692$		0			0
$693$	0.0278634	+	4.78953i	0.00105844	+	0.181939i
$694$		0			0
$695$			11.0333i			0.418518i
$696$		0			0
$697$			32.7941i			1.24217i
$698$		0			0
$699$	18.1836	−	0.0528917i	0.687768	−	0.00200055i
$700$		0			0
$701$	24.6020	−	42.6120i	0.929206	−	1.60943i	0.144553	−	0.989497i	$-0.453825\pi$
$701$	24.6020	−	42.6120i	0.929206	−	1.60943i	0.784653	−	0.619935i	$-0.212841\pi$
$702$		0			0
$703$	−11.6344	+	20.1514i	−0.438800	+	0.760024i
$704$		0			0
$705$	−0.0213202	−	7.32967i	−0.000802965	−	0.276051i
$706$		0			0
$707$	−0.844675	+	0.487673i	−0.0317673	+	0.0183408i
$708$		0			0
$709$	17.1061	+	29.6286i	0.642431	+	1.11272i	0.984888	+	0.173190i	$0.0554076\pi$
$709$	17.1061	+	29.6286i	0.642431	+	1.11272i	−0.342457	+	0.939533i	$0.611259\pi$
$710$		0			0
$711$	−28.6309	+	16.7529i	−1.07374	+	0.628281i
$712$		0			0
$713$	47.7349			1.78768
$714$		0			0
$715$			18.0392i			0.674630i
$716$		0			0
$717$	35.1009	−	0.102100i	1.31087	−	0.00381298i
$718$		0			0
$719$	33.8505	−	19.5436i	1.26241	−	0.728853i	0.288870	−	0.957368i	$-0.406720\pi$
$719$	33.8505	−	19.5436i	1.26241	−	0.728853i	0.973540	+	0.228515i	$0.0733871\pi$
$720$		0			0
$721$	−3.47694	+	2.00741i	−0.129488	+	0.0747599i
$722$		0			0
$723$	−2.16849	−	3.73083i	−0.0806471	−	0.138751i
$724$		0			0
$725$	−0.475368	−	0.274454i	−0.0176547	−	0.0101930i
$726$		0			0
$727$	−26.8478	+	15.5006i	−0.995729	+	0.574884i	−0.906982	−	0.421170i	$-0.861620\pi$
$727$	−26.8478	+	15.5006i	−0.995729	+	0.574884i	−0.0887470	+	0.996054i	$0.528286\pi$
$728$		0			0
$729$	26.9959	−	0.471193i	0.999848	−	0.0174516i
$730$		0			0
$731$	20.9504	+	36.2872i	0.774880	+	1.34213i
$732$		0			0
$733$	3.27085	+	1.88843i	0.120812	+	0.0697506i	0.559188	−	0.829041i	$-0.311113\pi$
$733$	3.27085	+	1.88843i	0.120812	+	0.0697506i	−0.438376	+	0.898791i	$0.644446\pi$
$734$		0			0
$735$	13.5649	−	23.6537i	0.500348	−	0.872479i
$736$		0			0
$737$	−24.4269	+	16.8233i	−0.899775	+	0.619694i
$738$		0			0
$739$	18.1653	−	10.4877i	0.668220	−	0.385797i	−0.127182	−	0.991879i	$-0.540593\pi$
$739$	18.1653	−	10.4877i	0.668220	−	0.385797i	0.795402	+	0.606083i	$0.207260\pi$
$740$		0			0
$741$	0.0605939	+	20.8316i	0.00222597	+	0.765267i
$742$		0			0
$743$	−0.547587	+	0.316149i	−0.0200890	+	0.0115984i	−0.510011	−	0.860168i	$-0.670359\pi$
$743$	−0.547587	+	0.316149i	−0.0200890	+	0.0115984i	0.489922	+	0.871766i	$0.337025\pi$
$744$		0			0
$745$		−	26.2343i		−	0.961150i
$746$		0			0
$747$	−0.308114	−	52.9628i	−0.0112733	−	1.93781i
$748$		0			0
$749$	1.80370	−	3.12411i	0.0659059	−	0.114152i
$750$		0			0
$751$	−40.6582			−1.48364			−0.741819	−	0.670600i	$-0.766037\pi$
$751$	−40.6582			−1.48364			−0.741819	+	0.670600i	$0.766037\pi$
$752$		0			0
$753$	−0.259448	+	0.452412i	−0.00945482	+	0.0164868i
$754$		0			0
$755$	−4.43328	−	7.67867i	−0.161344	−	0.279455i
$756$		0			0
$757$	−22.9340	−	13.2410i	−0.833552	−	0.481252i	0.0215152	−	0.999769i	$-0.493151\pi$
$757$	−22.9340	−	13.2410i	−0.833552	−	0.481252i	−0.855067	+	0.518517i	$0.826484\pi$
$758$		0			0
$759$	−23.4479	+	13.6287i	−0.851105	+	0.494692i
$760$		0			0
$761$			53.7385i			1.94802i	0.226510	+	0.974009i	$0.427268\pi$
$761$			53.7385i			1.94802i	−0.226510	+	0.974009i	$0.572732\pi$
$762$		0			0
$763$	−2.55652	+	4.42801i	−0.0925521	+	0.160305i
$764$		0			0
$765$	−0.167139	−	28.7301i	−0.00604293	−	1.03874i
$766$		0			0
$767$	12.0554	+	20.8805i	0.435294	+	0.753951i
$768$		0			0
$769$	−18.9784	−	10.9572i	−0.684378	−	0.395126i	0.117124	−	0.993117i	$-0.462632\pi$
$769$	−18.9784	−	10.9572i	−0.684378	−	0.395126i	−0.801503	+	0.597991i	$0.795966\pi$
$770$		0			0
$771$	0.123805	+	42.5629i	0.00445872	+	1.53286i
$772$		0			0
$773$	10.5528	+	6.09265i	0.379557	+	0.219137i	0.677626	−	0.735407i	$-0.263009\pi$
$773$	10.5528	+	6.09265i	0.379557	+	0.219137i	−0.298068	+	0.954545i	$0.596342\pi$
$774$		0			0
$775$	3.35303	+	1.93587i	0.120444	+	0.0695386i
$776$		0			0
$777$	2.74735	−	1.59685i	0.0985605	−	0.0572868i
$778$		0			0
$779$	44.2630			1.58589
$780$		0			0
$781$	29.1223	−	16.8138i	1.04208	−	0.601645i
$782$		0			0
$783$	7.08258	+	4.00713i	0.253111	+	0.143203i
$784$		0			0
$785$	−10.6770	−	18.4931i	−0.381078	−	0.660046i
$786$		0			0
$787$	−1.29526	+	0.747820i	−0.0461711	+	0.0266569i	−0.522908	−	0.852389i	$-0.675153\pi$
$787$	−1.29526	+	0.747820i	−0.0461711	+	0.0266569i	0.476737	+	0.879046i	$0.341819\pi$
$788$		0			0
$789$	10.7961	−	6.27508i	0.384352	−	0.223399i
$790$		0			0
$791$	−4.52364	+	2.61172i	−0.160842	+	0.0928622i
$792$		0			0
$793$	5.63420	−	9.75873i	0.200076	−	0.346542i
$794$		0			0
$795$	−10.2774	−	17.6820i	−0.364502	−	0.627117i
$796$		0			0
$797$	16.2100	+	9.35886i	0.574189	+	0.331508i	0.758820	−	0.651300i	$-0.225776\pi$
$797$	16.2100	+	9.35886i	0.574189	+	0.331508i	−0.184632	+	0.982808i	$0.559109\pi$
$798$		0			0
$799$	7.57451			0.267967
$800$		0			0
$801$	4.87639	+	2.77769i	0.172299	+	0.0981448i
$802$		0			0
$803$	25.0545			0.884155
$804$		0			0
$805$	−4.40417			−0.155226
$806$		0			0
$807$	−39.9850	+	23.2407i	−1.40754	+	0.818110i
$808$		0			0
$809$	−19.5039			−0.685721			−0.342860	−	0.939386i	$-0.611396\pi$
$809$	−19.5039			−0.685721			−0.342860	+	0.939386i	$0.611396\pi$
$810$		0			0
$811$	24.7802	+	14.3068i	0.870149	+	0.502381i	0.867398	−	0.497616i	$-0.165791\pi$
$811$	24.7802	+	14.3068i	0.870149	+	0.502381i	0.00275117	+	0.999996i	$0.499124\pi$
$812$		0			0
$813$	−45.0621	+	26.1917i	−1.58040	+	0.918583i
$814$		0			0
$815$	4.44862	−	7.70523i	0.155828	−	0.269902i
$816$		0			0
$817$	48.9777	−	28.2773i	1.71351	−	0.989297i
$818$		0			0
$819$	1.40808	−	2.47197i	0.0492025	−	0.0863778i
$820$		0			0
$821$	41.1840	−	23.7776i	1.43733	−	0.829843i	0.439667	−	0.898161i	$-0.355096\pi$
$821$	41.1840	−	23.7776i	1.43733	−	0.829843i	0.997664	+	0.0683172i	$0.0217630\pi$
$822$		0			0
$823$	−25.9842	−	45.0060i	−0.905754	−	1.56881i	−0.819902	−	0.572504i	$-0.805972\pi$
$823$	−25.9842	−	45.0060i	−0.905754	−	1.56881i	−0.0858516	−	0.996308i	$-0.527361\pi$
$824$		0			0
$825$	−2.19975	+	0.00639854i	−0.0765856	+	0.000222769i
$826$		0			0
$827$	19.4051	−	11.2036i	0.674782	−	0.389586i	−0.123104	−	0.992394i	$-0.539285\pi$
$827$	19.4051	−	11.2036i	0.674782	−	0.389586i	0.797886	+	0.602808i	$0.205952\pi$
$828$		0			0
$829$	−12.6926			−0.440831			−0.220416	−	0.975406i	$-0.570741\pi$
$829$	−12.6926			−0.440831			−0.220416	+	0.975406i	$0.570741\pi$
$830$		0			0
$831$	16.5675	+	28.5039i	0.574719	+	0.988790i
$832$		0			0
$833$	24.4028	+	14.0890i	0.845508	+	0.488154i
$834$		0			0
$835$	−24.0704	−	13.8971i	−0.832991	−	0.480928i
$836$		0			0
$837$	−49.9572	−	28.2645i	−1.72677	−	0.976963i
$838$		0			0
$839$	12.1166	+	6.99553i	0.418312	+	0.241513i	0.694355	−	0.719633i	$-0.255690\pi$
$839$	12.1166	+	6.99553i	0.418312	+	0.241513i	−0.276043	+	0.961145i	$0.589023\pi$
$840$		0			0
$841$	−13.2737	−	22.9907i	−0.457714	−	0.792784i
$842$		0			0
$843$	3.60764	−	6.29080i	0.124254	−	0.216667i
$844$		0			0
$845$	−9.67786	+	16.7626i	−0.332929	+	0.576649i
$846$		0			0
$847$			0.938387i			0.0322434i
$848$		0			0
$849$	−14.2307	−	24.4835i	−0.488395	−	0.840272i
$850$		0			0
$851$	15.5830	+	8.99683i	0.534177	+	0.308407i
$852$		0			0
$853$	1.83754	+	3.18271i	0.0629161	+	0.108974i	0.895768	−	0.444522i	$-0.146627\pi$
$853$	1.83754	+	3.18271i	0.0629161	+	0.108974i	−0.832852	+	0.553496i	$0.813293\pi$
$854$		0			0
$855$	−38.7777	+	0.225591i	−1.32617	+	0.00771506i
$856$		0			0
$857$	−48.3981			−1.65325			−0.826624	−	0.562754i	$-0.809742\pi$
$857$	−48.3981			−1.65325			−0.826624	+	0.562754i	$0.809742\pi$
$858$		0			0
$859$	−25.4651	+	44.1069i	−0.868858	+	1.50491i	−0.00569385	+	0.999984i	$0.501812\pi$
$859$	−25.4651	+	44.1069i	−0.868858	+	1.50491i	−0.863164	+	0.504923i	$0.831521\pi$
$860$		0			0
$861$	−5.24371	−	3.00715i	−0.178705	−	0.102483i
$862$		0			0
$863$			23.3381i			0.794438i	0.917724	+	0.397219i	$0.130025\pi$
$863$			23.3381i			0.794438i	−0.917724	+	0.397219i	$0.869975\pi$
$864$		0			0
$865$	−0.604763	+	0.349160i	−0.0205625	+	0.0118718i
$866$		0			0
$867$	0.245352		0.000713668i	0.00833258		2.42374e-5i
$868$		0			0
$869$	−34.6984	+	20.0332i	−1.17706	+	0.679578i
$870$		0			0
$871$	17.5613	−	1.39938i	0.595041	−	0.0474161i
$872$		0			0
$873$	0.0658245	+	11.3148i	0.00222782	+	0.382948i
$874$		0			0
$875$	4.10378	+	2.36932i	0.138733	+	0.0800977i
$876$		0			0
$877$	17.3736	+	30.0920i	0.586666	+	1.01614i	0.994665	+	0.103153i	$0.0328932\pi$
$877$	17.3736	+	30.0920i	0.586666	+	1.01614i	−0.408000	+	0.912982i	$0.633773\pi$
$878$		0			0
$879$	25.7725	−	14.9799i	0.869286	−	0.505259i
$880$		0			0
$881$	24.4950	−	14.1422i	0.825257	−	0.476462i	−0.0269688	−	0.999636i	$-0.508585\pi$
$881$	24.4950	−	14.1422i	0.825257	−	0.476462i	0.852226	+	0.523174i	$0.175252\pi$
$882$		0			0
$883$	−26.3727	−	15.2263i	−0.887513	−	0.512406i	−0.0143851	−	0.999897i	$-0.504579\pi$
$883$	−26.3727	−	15.2263i	−0.887513	−	0.512406i	−0.873128	+	0.487490i	$0.837912\pi$
$884$		0			0
$885$	−38.8038	+	22.5541i	−1.30437	+	0.758148i
$886$		0			0
$887$	18.4516	−	10.6530i	0.619545	−	0.357694i	−0.157147	−	0.987575i	$-0.550230\pi$
$887$	18.4516	−	10.6530i	0.619545	−	0.357694i	0.776692	+	0.629881i	$0.216896\pi$
$888$		0			0
$889$	−6.14383	+	3.54714i	−0.206057	+	0.118967i
$890$		0			0
$891$	32.6093	−	0.379426i	1.09245	−	0.0127112i
$892$		0			0
$893$		−	10.2235i		−	0.342116i
$894$		0			0
$895$	47.8612			1.59982
$896$		0			0
$897$	16.1090	−	0.0468570i	0.537863	−	0.00156451i
$898$		0			0
$899$	−8.64973	−	14.9818i	−0.288485	−	0.499670i
$900$		0			0
$901$	18.3034	−	10.5675i	0.609775	−	0.352054i
$902$		0			0
$903$	−7.72336	+	0.0224653i	−0.257017	+	0.000747600i
$904$		0			0
$905$	−2.43705	+	4.22109i	−0.0810103	+	0.140314i
$906$		0			0
$907$	−7.88879	+	13.6638i	−0.261943	+	0.453699i	−0.966758	−	0.255692i	$-0.917697\pi$
$907$	−7.88879	+	13.6638i	−0.261943	+	0.453699i	0.704815	+	0.709391i	$0.251030\pi$
$908$		0			0
$909$	3.35387	+	5.73181i	0.111241	+	0.190112i
$910$		0			0
$911$		−	12.7155i		−	0.421283i	−0.977563	−	0.210642i	$-0.932445\pi$
$911$		−	12.7155i		−	0.421283i	0.977563	−	0.210642i	$-0.0675553\pi$
$912$		0			0
$913$		−	63.9714i		−	2.11714i
$914$		0			0
$915$	18.1964	+	10.4352i	0.601554	+	0.344978i
$916$		0			0
$917$	−3.28173	+	5.68412i	−0.108372	+	0.187706i
$918$		0			0
$919$	−49.7814	+	28.7413i	−1.64214	+	0.948089i	−0.662066	+	0.749445i	$0.730320\pi$
$919$	−49.7814	+	28.7413i	−1.64214	+	0.948089i	−0.980072	+	0.198644i	$0.936346\pi$
$920$		0			0
$921$	2.79507	−	4.87389i	0.0921006	−	0.160600i
$922$		0			0
$923$	−19.9738			−0.657445
$924$		0			0
$925$	0.729727	+	1.26392i	0.0239933	+	0.0415576i
$926$		0			0
$927$	13.8056	+	23.5939i	0.453434	+	0.774925i
$928$		0			0
$929$	19.5567			0.641636			0.320818	−	0.947141i	$-0.396042\pi$
$929$	19.5567			0.641636			0.320818	+	0.947141i	$0.396042\pi$
$930$		0			0
$931$	19.0162	−	32.9370i	0.623231	−	1.07947i
$932$		0			0
$933$	−12.2558	−	21.0857i	−0.401236	−	0.690315i
$934$		0			0
$935$		−	34.7018i		−	1.13487i
$936$		0			0
$937$			16.5301i			0.540014i	0.962858	+	0.270007i	$0.0870260\pi$
$937$			16.5301i			0.540014i	−0.962858	+	0.270007i	$0.912974\pi$
$938$		0			0
$939$	48.7314	−	28.3244i	1.59029	−	0.924332i
$940$		0			0
$941$	−32.6952			−1.06583			−0.532917	−	0.846168i	$-0.678904\pi$
$941$	−32.6952			−1.06583			−0.532917	+	0.846168i	$0.678904\pi$
$942$		0			0
$943$		−	34.2284i		−	1.11463i
$944$		0			0
$945$	4.60921	+	2.60777i	0.149937	+	0.0848306i
$946$		0			0
$947$			44.9979i			1.46223i	0.682252	+	0.731117i	$0.261001\pi$
$947$			44.9979i			1.46223i	−0.682252	+	0.731117i	$0.738999\pi$
$948$		0			0
$949$	−12.8879	−	7.44081i	−0.418358	−	0.241539i
$950$		0			0
$951$	−14.5421	−	8.33956i	−0.471559	−	0.270429i
$952$		0			0
$953$		−	20.7420i		−	0.671900i	−0.941880	−	0.335950i	$-0.890943\pi$
$953$		−	20.7420i		−	0.671900i	0.941880	−	0.335950i	$-0.109057\pi$
$954$		0			0
$955$	−9.20690	−	15.9468i	−0.297928	−	0.516027i
$956$		0			0
$957$	8.52628	+	4.88964i	0.275615	+	0.158059i
$958$		0			0
$959$	−3.99423	−	2.30607i	−0.128980	−	0.0744669i
$960$		0			0
$961$	45.5112	+	78.8276i	1.46810	+	2.54283i
$962$		0			0
$963$	−21.3425	−	12.1571i	−0.687753	−	0.391758i
$964$		0			0
$965$	−31.0335			−0.999004
$966$		0			0
$967$	24.3740	−	42.2171i	0.783816	−	1.35761i	−0.145888	−	0.989301i	$-0.546604\pi$
$967$	24.3740	−	42.2171i	0.783816	−	1.35761i	0.929704	−	0.368308i	$-0.120063\pi$
$968$		0			0
$969$	−0.116564	−	40.0734i	−0.00374456	−	1.28734i
$970$		0			0
$971$	23.4936	+	13.5640i	0.753946	+	0.435291i	0.827118	−	0.562028i	$-0.189979\pi$
$971$	23.4936	+	13.5640i	0.753946	+	0.435291i	−0.0731719	+	0.997319i	$0.523312\pi$
$972$		0			0
$973$	1.05082	−	1.82008i	0.0336879	−	0.0583491i
$974$		0			0
$975$	1.13344	+	0.650002i	0.0362991	+	0.0208167i
$976$		0			0
$977$	−50.7595	+	29.3060i	−1.62394	+	0.937583i	−0.638089	+	0.769962i	$0.720275\pi$
$977$	−50.7595	+	29.3060i	−1.62394	+	0.937583i	−0.985852	+	0.167620i	$0.946392\pi$
$978$		0			0
$979$	5.87026	+	3.38919i	0.187614	+	0.108319i
$980$		0			0
$981$	30.2502	+	17.2311i	0.965816	+	0.550147i
$982$		0			0
$983$	46.5471			1.48462			0.742311	−	0.670055i	$-0.233730\pi$
$983$	46.5471			1.48462			0.742311	+	0.670055i	$0.233730\pi$
$984$		0			0
$985$	−5.12530	+	8.87728i	−0.163306	+	0.282854i
$986$		0			0
$987$	−0.694567	+	1.21115i	−0.0221083	+	0.0385512i
$988$		0			0
$989$	−21.8667	−	37.8742i	−0.695320	−	1.20433i
$990$		0			0
$991$			40.7607i			1.29481i	0.762148	+	0.647403i	$0.224145\pi$
$991$			40.7607i			1.29481i	−0.762148	+	0.647403i	$0.775855\pi$
$992$		0			0
$993$	0.123365	+	42.4116i	0.00391487	+	1.34589i
$994$		0			0
$995$	−8.35802	−	14.4765i	−0.264967	−	0.458936i
$996$		0			0
$997$	56.9915			1.80494			0.902469	−	0.430755i	$-0.141753\pi$
$997$	56.9915			1.80494			0.902469	+	0.430755i	$0.141753\pi$
$998$		0			0
$999$	−10.9813	−	18.6426i	−0.347433	−	0.589825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.365.13	yes	36
3.2	odd	2	inner	804.2.o.d.365.6	✓	36
67.38	odd	6	inner	804.2.o.d.641.6	yes	36
201.38	even	6	inner	804.2.o.d.641.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.6	✓	36	3.2	odd	2	inner
804.2.o.d.365.13	yes	36	1.1	even	1	trivial
804.2.o.d.641.6	yes	36	67.38	odd	6	inner
804.2.o.d.641.13	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)

\(f(q)\)	\(=\)	\(q+(0.870385 + 1.49747i) q^{3} +2.31311 q^{5} +(-0.381576 - 0.220303i) q^{7} +(-1.48486 + 2.60676i) q^{9} +O(q^{10})\)	\(q+(0.870385 + 1.49747i) q^{3} +2.31311 q^{5} +(-0.381576 - 0.220303i) q^{7} +(-1.48486 + 2.60676i) q^{9} +(-1.81175 + 3.13804i) q^{11} +(1.86390 - 1.07613i) q^{13} +(2.01330 + 3.46383i) q^{15} +(-3.58556 + 2.07012i) q^{17} +(2.79409 + 4.83951i) q^{19} +(-0.00221981 - 0.763149i) q^{21} +(3.74237 - 2.16066i) q^{23} +0.350499 q^{25} +(-5.19595 + 0.0453423i) q^{27} +(-1.35626 - 0.783038i) q^{29} +(9.56644 + 5.52319i) q^{31} +(-6.27606 + 0.0182555i) q^{33} +(-0.882629 - 0.509586i) q^{35} +(2.08197 + 3.60607i) q^{37} +(3.23378 + 1.85450i) q^{39} +(3.96041 - 6.85963i) q^{41} -10.1204i q^{43} +(-3.43465 + 6.02973i) q^{45} +(-1.58438 - 0.914742i) q^{47} +(-3.40293 - 5.89405i) q^{49} +(-6.22078 - 3.56748i) q^{51} -5.10476 q^{53} +(-4.19079 + 7.25866i) q^{55} +(-4.81511 + 8.39632i) q^{57} +11.2026i q^{59} +(4.53420 - 2.61782i) q^{61} +(1.14086 - 0.667557i) q^{63} +(4.31142 - 2.48920i) q^{65} +(7.39142 + 3.51666i) q^{67} +(6.49283 + 3.72350i) q^{69} +(-8.03707 - 4.64021i) q^{71} +(-3.45723 - 5.98809i) q^{73} +(0.305069 + 0.524864i) q^{75} +(1.38264 - 0.798268i) q^{77} +(9.57594 + 5.52867i) q^{79} +(-4.59038 - 7.74134i) q^{81} +(-15.2893 + 8.82729i) q^{83} +(-8.29381 + 4.78843i) q^{85} +(-0.00789003 - 2.71251i) q^{87} -1.87067i q^{89} -0.948294 q^{91} +(0.0556526 + 19.1328i) q^{93} +(6.46305 + 11.1943i) q^{95} +(3.26636 - 1.88583i) q^{97} +(-5.48993 - 9.38236i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 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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