LMFDB - Embedded newform 804.2.q.b.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (of order $11$, degree $10$, 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:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	804.25
Dual form			804.2.q.b.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{3} +(1.69814 - 1.09133i) q^{5} +(-0.693468 - 4.82317i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{3} +(1.69814 - 1.09133i) q^{5} +(-0.693468 - 4.82317i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.656414 - 0.421852i) q^{11} +(0.749561 - 1.64131i) q^{13} +(0.287274 - 1.99804i) q^{15} +(-4.81748 - 1.41454i) q^{17} +(-0.841566 + 5.85322i) q^{19} +(-4.09924 - 2.63442i) q^{21} +(-4.58797 + 5.29480i) q^{23} +(-0.384395 + 0.841709i) q^{25} +(-0.841254 - 0.540641i) q^{27} +4.90421 q^{29} +(-4.31097 - 9.43970i) q^{31} +(0.111046 - 0.772339i) q^{33} +(-6.44127 - 7.43362i) q^{35} +8.86088 q^{37} +(-0.749561 - 1.64131i) q^{39} +(9.14557 + 2.68538i) q^{41} +(-0.967308 - 0.284027i) q^{43} +(-1.32189 - 1.52554i) q^{45} +(-2.68948 + 3.10382i) q^{47} +(-16.0657 + 4.71730i) q^{49} +(-4.22381 + 2.71448i) q^{51} +(12.5726 - 3.69164i) q^{53} +(0.654304 - 1.43273i) q^{55} +(3.87246 + 4.46906i) q^{57} +(-0.517190 - 1.13249i) q^{59} +(-0.873249 - 0.561203i) q^{61} +(-4.67539 + 1.37282i) q^{63} +(-0.518348 - 3.60519i) q^{65} +(3.64682 - 7.32808i) q^{67} +(0.997061 + 6.93471i) q^{69} +(15.7387 - 4.62130i) q^{71} +(-0.241827 - 0.155413i) q^{73} +(0.384395 + 0.841709i) q^{75} +(-2.48987 - 2.87346i) q^{77} +(-1.73759 + 3.80479i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(12.5737 - 8.08062i) q^{83} +(-9.72447 + 2.85536i) q^{85} +(3.21157 - 3.70635i) q^{87} +(-2.07902 - 2.39932i) q^{89} +(-8.43612 - 2.47707i) q^{91} +(-9.95713 - 2.92368i) q^{93} +(4.95869 + 10.8580i) q^{95} -0.952015 q^{97} +(-0.510975 - 0.589697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$	$1$

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
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$		0			0
$5$	1.69814	−	1.09133i	0.759431	−	0.488057i	−0.102719	−	0.994710i	$-0.532754\pi$
$5$	1.69814	−	1.09133i	0.759431	−	0.488057i	0.862150	+	0.506654i	$0.169118\pi$
$6$		0			0
$7$	−0.693468	−	4.82317i	−0.262106	−	1.82299i	−0.516961	−	0.856009i	$-0.672937\pi$
$7$	−0.693468	−	4.82317i	−0.262106	−	1.82299i	0.254855	−	0.966979i	$-0.417972\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	0.656414	−	0.421852i	0.197916	−	0.127193i	−0.437929	−	0.899009i	$-0.644288\pi$
$11$	0.656414	−	0.421852i	0.197916	−	0.127193i	0.635845	+	0.771816i	$0.280652\pi$
$12$		0			0
$13$	0.749561	−	1.64131i	0.207891	−	0.455217i	−0.776750	−	0.629809i	$-0.783133\pi$
$13$	0.749561	−	1.64131i	0.207891	−	0.455217i	0.984641	+	0.174591i	$0.0558605\pi$
$14$		0			0
$15$	0.287274	−	1.99804i	0.0741739	−	0.515890i
$16$		0			0
$17$	−4.81748	−	1.41454i	−1.16841	−	0.343076i	−0.360714	−	0.932676i	$-0.617467\pi$
$17$	−4.81748	−	1.41454i	−1.16841	−	0.343076i	−0.807695	+	0.589600i	$0.799285\pi$
$18$		0			0
$19$	−0.841566	+	5.85322i	−0.193069	+	1.34282i	0.630758	+	0.775980i	$0.282744\pi$
$19$	−0.841566	+	5.85322i	−0.193069	+	1.34282i	−0.823827	+	0.566842i	$0.808165\pi$
$20$		0			0
$21$	−4.09924	−	2.63442i	−0.894527	−	0.574877i
$22$		0			0
$23$	−4.58797	+	5.29480i	−0.956658	+	1.10404i	0.0378397	+	0.999284i	$0.487952\pi$
$23$	−4.58797	+	5.29480i	−0.956658	+	1.10404i	−0.994498	+	0.104758i	$0.966593\pi$
$24$		0			0
$25$	−0.384395	+	0.841709i	−0.0768791	+	0.168342i
$26$		0			0
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$		0			0
$29$	4.90421			0.910689			0.455344	−	0.890315i	$-0.349516\pi$
$29$	4.90421			0.910689			0.455344	+	0.890315i	$0.349516\pi$
$30$		0			0
$31$	−4.31097	−	9.43970i	−0.774272	−	1.69542i	−0.717012	−	0.697061i	$-0.754491\pi$
$31$	−4.31097	−	9.43970i	−0.774272	−	1.69542i	−0.0572601	−	0.998359i	$-0.518236\pi$
$32$		0			0
$33$	0.111046	−	0.772339i	0.0193305	−	0.134447i
$34$		0			0
$35$	−6.44127	−	7.43362i	−1.08877	−	1.25651i
$36$		0			0
$37$	8.86088			1.45672			0.728360	−	0.685195i	$-0.240283\pi$
$37$	8.86088			1.45672			0.728360	+	0.685195i	$0.240283\pi$
$38$		0			0
$39$	−0.749561	−	1.64131i	−0.120026	−	0.262820i
$40$		0			0
$41$	9.14557	+	2.68538i	1.42830	+	0.419386i	0.902303	−	0.431102i	$-0.141875\pi$
$41$	9.14557	+	2.68538i	1.42830	+	0.419386i	0.525995	+	0.850488i	$0.323693\pi$
$42$		0			0
$43$	−0.967308	−	0.284027i	−0.147513	−	0.0433138i	0.207142	−	0.978311i	$-0.433584\pi$
$43$	−0.967308	−	0.284027i	−0.147513	−	0.0433138i	−0.354655	+	0.934997i	$0.615402\pi$
$44$		0			0
$45$	−1.32189	−	1.52554i	−0.197056	−	0.227414i
$46$		0			0
$47$	−2.68948	+	3.10382i	−0.392300	+	0.452739i	−0.917201	−	0.398425i	$-0.869557\pi$
$47$	−2.68948	+	3.10382i	−0.392300	+	0.452739i	0.524901	+	0.851164i	$0.324102\pi$
$48$		0			0
$49$	−16.0657	+	4.71730i	−2.29509	+	0.673900i
$50$		0			0
$51$	−4.22381	+	2.71448i	−0.591452	+	0.380103i
$52$		0			0
$53$	12.5726	−	3.69164i	1.72698	−	0.507086i	0.740650	−	0.671891i	$-0.234518\pi$
$53$	12.5726	−	3.69164i	1.72698	−	0.507086i	0.986326	+	0.164805i	$0.0526996\pi$
$54$		0			0
$55$	0.654304	−	1.43273i	0.0882263	−	0.193189i
$56$		0			0
$57$	3.87246	+	4.46906i	0.512920	+	0.591941i
$58$		0			0
$59$	−0.517190	−	1.13249i	−0.0673324	−	0.147437i	0.872974	−	0.487767i	$-0.162189\pi$
$59$	−0.517190	−	1.13249i	−0.0673324	−	0.147437i	−0.940306	+	0.340330i	$0.889461\pi$
$60$		0			0
$61$	−0.873249	−	0.561203i	−0.111808	−	0.0718547i	0.483542	−	0.875321i	$-0.339350\pi$
$61$	−0.873249	−	0.561203i	−0.111808	−	0.0718547i	−0.595350	+	0.803467i	$0.702987\pi$
$62$		0			0
$63$	−4.67539	+	1.37282i	−0.589044	+	0.172959i
$64$		0			0
$65$	−0.518348	−	3.60519i	−0.0642931	−	0.447169i
$66$		0			0
$67$	3.64682	−	7.32808i	0.445530	−	0.895267i
$67$	3.64682	−	7.32808i	0.445530	−	0.895267i
$68$		0			0
$69$	0.997061	+	6.93471i	0.120032	+	0.834841i
$70$		0			0
$71$	15.7387	−	4.62130i	1.86784	−	0.548448i	0.869310	−	0.494268i	$-0.164564\pi$
$71$	15.7387	−	4.62130i	1.86784	−	0.548448i	0.998531	−	0.0541797i	$-0.0172544\pi$
$72$		0			0
$73$	−0.241827	−	0.155413i	−0.0283037	−	0.0181897i	0.526412	−	0.850229i	$-0.323537\pi$
$73$	−0.241827	−	0.155413i	−0.0283037	−	0.0181897i	−0.554716	+	0.832040i	$0.687173\pi$
$74$		0			0
$75$	0.384395	+	0.841709i	0.0443862	+	0.0971921i
$76$		0			0
$77$	−2.48987	−	2.87346i	−0.283746	−	0.327461i
$78$		0			0
$79$	−1.73759	+	3.80479i	−0.195494	+	0.428072i	−0.981839	−	0.189715i	$-0.939244\pi$
$79$	−1.73759	+	3.80479i	−0.195494	+	0.428072i	0.786345	+	0.617787i	$0.211971\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	12.5737	−	8.08062i	1.38014	−	0.886964i	0.380852	−	0.924636i	$-0.375631\pi$
$83$	12.5737	−	8.08062i	1.38014	−	0.886964i	0.999290	+	0.0376723i	$0.0119943\pi$
$84$		0			0
$85$	−9.72447	+	2.85536i	−1.05477	+	0.309707i
$86$		0			0
$87$	3.21157	−	3.70635i	0.344317	−	0.397363i
$88$		0			0
$89$	−2.07902	−	2.39932i	−0.220376	−	0.254327i	0.634787	−	0.772687i	$-0.281088\pi$
$89$	−2.07902	−	2.39932i	−0.220376	−	0.254327i	−0.855162	+	0.518361i	$0.826543\pi$
$90$		0			0
$91$	−8.43612	−	2.47707i	−0.884346	−	0.259667i
$92$		0			0
$93$	−9.95713	−	2.92368i	−1.03251	−	0.303171i
$94$		0			0
$95$	4.95869	+	10.8580i	0.508751	+	1.11401i
$96$		0			0
$97$	−0.952015			−0.0966625			−0.0483312	−	0.998831i	$-0.515390\pi$
$97$	−0.952015			−0.0966625			−0.0483312	+	0.998831i	$0.515390\pi$
$98$		0			0
$99$	−0.510975	−	0.589697i	−0.0513549	−	0.0592668i
$100$		0			0
$101$	−0.562569	+	3.91275i	−0.0559777	+	0.389334i	0.942501	+	0.334202i	$0.108467\pi$
$101$	−0.562569	+	3.91275i	−0.0559777	+	0.389334i	−0.998479	+	0.0551314i	$0.982442\pi$
$102$		0			0
$103$	−7.06490	−	15.4700i	−0.696126	−	1.52430i	−0.844607	−	0.535387i	$-0.820166\pi$
$103$	−7.06490	−	15.4700i	−0.696126	−	1.52430i	0.148481	−	0.988915i	$-0.452562\pi$
$104$		0			0
$105$	−9.83608			−0.959904
$106$		0			0
$107$	−0.540581	−	0.347410i	−0.0522599	−	0.0335854i	0.514250	−	0.857640i	$-0.328070\pi$
$107$	−0.540581	−	0.347410i	−0.0522599	−	0.0335854i	−0.566510	+	0.824055i	$0.691707\pi$
$108$		0			0
$109$	0.199094	−	0.435955i	0.0190697	−	0.0417569i	−0.899857	−	0.436184i	$-0.856330\pi$
$109$	0.199094	−	0.435955i	0.0190697	−	0.0417569i	0.918927	+	0.394427i	$0.129057\pi$
$110$		0			0
$111$	5.80264	−	6.69660i	0.550762	−	0.635613i
$112$		0			0
$113$	5.27425	+	3.38956i	0.496160	+	0.318863i	0.764679	−	0.644412i	$-0.222898\pi$
$113$	5.27425	+	3.38956i	0.496160	+	0.318863i	−0.268519	+	0.963274i	$0.586534\pi$
$114$		0			0
$115$	−2.01265	+	13.9983i	−0.187681	+	1.30535i
$116$		0			0
$117$	−1.73128	−	0.508349i	−0.160057	−	0.0469969i
$118$		0			0
$119$	−3.48180	+	24.2165i	−0.319176	+	2.21992i
$120$		0			0
$121$	−4.31664	+	9.45213i	−0.392422	+	0.859285i
$122$		0			0
$123$	8.01855	−	5.15321i	0.723008	−	0.464649i
$124$		0			0
$125$	1.70219	+	11.8390i	0.152249	+	1.05891i
$126$		0			0
$127$	−1.22297	−	8.50596i	−0.108521	−	0.754782i	−0.969314	−	0.245826i	$-0.920941\pi$
$127$	−1.22297	−	8.50596i	−0.108521	−	0.754782i	0.860793	−	0.508956i	$-0.169968\pi$
$128$		0			0
$129$	−0.848106	+	0.545044i	−0.0746715	+	0.0479885i
$130$		0			0
$131$	−5.57733	+	6.43659i	−0.487294	+	0.562367i	−0.945141	−	0.326664i	$-0.894075\pi$
$131$	−5.57733	+	6.43659i	−0.487294	+	0.562367i	0.457847	+	0.889031i	$0.348621\pi$
$132$		0			0
$133$	28.8147			2.49855
$134$		0			0
$135$	−2.01858			−0.173732
$136$		0			0
$137$	1.82918	−	2.11099i	0.156278	−	0.180354i	−0.672211	−	0.740359i	$-0.734655\pi$
$137$	1.82918	−	2.11099i	0.156278	−	0.180354i	0.828489	+	0.560005i	$0.189201\pi$
$138$		0			0
$139$	−2.73377	+	1.75689i	−0.231875	+	0.149017i	−0.651420	−	0.758718i	$-0.725826\pi$
$139$	−2.73377	+	1.75689i	−0.231875	+	0.149017i	0.419544	+	0.907735i	$0.362190\pi$
$140$		0			0
$141$	0.584479	+	4.06514i	0.0492220	+	0.342347i
$142$		0			0
$143$	−0.200367	−	1.39358i	−0.0167555	−	0.116537i
$144$		0			0
$145$	8.32803	−	5.35210i	0.691605	−	0.444468i
$146$		0			0
$147$	−6.95567	+	15.2308i	−0.573694	+	1.25621i
$148$		0			0
$149$	1.48716	−	10.3434i	0.121833	−	0.847367i	−0.833644	−	0.552302i	$-0.813750\pi$
$149$	1.48716	−	10.3434i	0.121833	−	0.847367i	0.955477	−	0.295065i	$-0.0953414\pi$
$150$		0			0
$151$	−8.69841	−	2.55408i	−0.707867	−	0.207848i	−0.0920688	−	0.995753i	$-0.529348\pi$
$151$	−8.69841	−	2.55408i	−0.707867	−	0.207848i	−0.615798	+	0.787904i	$0.711166\pi$
$152$		0			0
$153$	−0.714542	+	4.96975i	−0.0577673	+	0.401780i
$154$		0			0
$155$	−17.6224	−	11.3252i	−1.41547	−	0.909665i
$156$		0			0
$157$	1.03551	−	1.19505i	0.0826430	−	0.0953751i	−0.712922	−	0.701243i	$-0.752629\pi$
$157$	1.03551	−	1.19505i	0.0826430	−	0.0953751i	0.795565	+	0.605868i	$0.207174\pi$
$158$		0			0
$159$	5.44333	−	11.9192i	0.431684	−	0.945256i
$160$		0			0
$161$	28.7193	+	18.4568i	2.26340	+	1.45460i
$162$		0			0
$163$	14.2474			1.11594			0.557971	−	0.829860i	$-0.311580\pi$
$163$	14.2474			1.11594			0.557971	+	0.829860i	$0.311580\pi$
$164$		0			0
$165$	−0.654304	−	1.43273i	−0.0509375	−	0.111538i
$166$		0			0
$167$	−0.641035	+	4.45850i	−0.0496048	+	0.345009i	0.949871	+	0.312641i	$0.101214\pi$
$167$	−0.641035	+	4.45850i	−0.0496048	+	0.345009i	−0.999476	+	0.0323675i	$0.989695\pi$
$168$		0			0
$169$	6.38113	+	7.36422i	0.490856	+	0.566478i
$170$		0			0
$171$	5.91341			0.452210
$172$		0			0
$173$	10.2562	+	22.4578i	0.779761	+	1.70744i	0.703878	+	0.710321i	$0.251450\pi$
$173$	10.2562	+	22.4578i	0.779761	+	1.70744i	0.0758829	+	0.997117i	$0.475822\pi$
$174$		0			0
$175$	4.32627	+	1.27031i	0.327035	+	0.0960263i
$176$		0			0
$177$	−1.19456	−	0.350756i	−0.0897889	−	0.0263644i
$178$		0			0
$179$	13.7752	+	15.8974i	1.02961	+	1.18823i	0.981906	+	0.189368i	$0.0606440\pi$
$179$	13.7752	+	15.8974i	1.02961	+	1.18823i	0.0477008	+	0.998862i	$0.484811\pi$
$180$		0			0
$181$	−14.8676	+	17.1581i	−1.10510	+	1.27535i	−0.146932	+	0.989147i	$0.546940\pi$
$181$	−14.8676	+	17.1581i	−1.10510	+	1.27535i	−0.958168	+	0.286207i	$0.907605\pi$
$182$		0			0
$183$	−0.995986	+	0.292448i	−0.0736254	+	0.0216184i
$184$		0			0
$185$	15.0470	−	9.67012i	1.10628	−	0.710961i
$186$		0			0
$187$	−3.75898	+	1.10374i	−0.274884	+	0.0807132i
$188$		0			0
$189$	−2.02422	+	4.43243i	−0.147240	+	0.322412i
$190$		0			0
$191$	5.24895	+	6.05761i	0.379800	+	0.438313i	0.913176	−	0.407565i	$-0.133622\pi$
$191$	5.24895	+	6.05761i	0.379800	+	0.438313i	−0.533376	+	0.845879i	$0.679077\pi$
$192$		0			0
$193$	−9.74788	−	21.3449i	−0.701668	−	1.53644i	−0.837937	−	0.545767i	$-0.816239\pi$
$193$	−9.74788	−	21.3449i	−0.701668	−	1.53644i	0.136269	−	0.990672i	$-0.456489\pi$
$194$		0			0
$195$	−3.06407	−	1.96916i	−0.219422	−	0.141014i
$196$		0			0
$197$	−10.3475	+	3.03831i	−0.737232	+	0.216471i	−0.628728	−	0.777625i	$-0.716424\pi$
$197$	−10.3475	+	3.03831i	−0.737232	+	0.216471i	−0.108504	+	0.994096i	$0.534606\pi$
$198$		0			0
$199$	0.502079	+	3.49204i	0.0355914	+	0.247544i	0.999848	−	0.0174259i	$-0.00554712\pi$
$199$	0.502079	+	3.49204i	0.0355914	+	0.247544i	−0.964257	+	0.264970i	$0.914638\pi$
$200$		0			0
$201$	−3.15003	−	7.55495i	−0.222186	−	0.532885i
$202$		0			0
$203$	−3.40091	−	23.6538i	−0.238697	−	1.66017i
$204$		0			0
$205$	18.4611	−	5.42066i	1.28938	−	0.378595i
$206$		0			0
$207$	5.89384	+	3.78774i	0.409650	+	0.263266i
$208$		0			0
$209$	1.91678	+	4.19715i	0.132586	+	0.290323i
$210$		0			0
$211$	−8.17700	−	9.43676i	−0.562928	−	0.649653i	0.400918	−	0.916114i	$-0.368691\pi$
$211$	−8.17700	−	9.43676i	−0.562928	−	0.649653i	−0.963846	+	0.266461i	$0.914146\pi$
$212$		0			0
$213$	6.81411	−	14.9208i	0.466895	−	1.02236i
$214$		0			0
$215$	−1.95259	+	0.573332i	−0.133166	+	0.0391009i
$216$		0			0
$217$	−42.5398	+	27.3387i	−2.88779	+	1.85587i
$218$		0			0
$219$	−0.275816	+	0.0809868i	−0.0186379	+	0.00547258i
$220$		0			0
$221$	−5.93269	+	6.84669i	−0.399076	+	0.460558i
$222$		0			0
$223$	15.5541	+	17.9504i	1.04158	+	1.20205i	0.978969	+	0.204007i	$0.0653966\pi$
$223$	15.5541	+	17.9504i	1.04158	+	1.20205i	0.0626089	+	0.998038i	$0.480058\pi$
$224$		0			0
$225$	0.887847	+	0.260695i	0.0591898	+	0.0173797i
$226$		0			0
$227$	−26.4985	−	7.78065i	−1.75877	−	0.516420i	−0.766685	−	0.642023i	$-0.778095\pi$
$227$	−26.4985	−	7.78065i	−1.75877	−	0.516420i	−0.992081	+	0.125603i	$0.959913\pi$
$228$		0			0
$229$	3.05444	+	6.68830i	0.201843	+	0.441975i	0.983302	−	0.181982i	$-0.0582512\pi$
$229$	3.05444	+	6.68830i	0.201843	+	0.441975i	−0.781459	+	0.623957i	$0.785524\pi$
$230$		0			0
$231$	−3.80213			−0.250162
$232$		0			0
$233$	0.809277	+	0.933956i	0.0530175	+	0.0611855i	0.781639	−	0.623731i	$-0.214384\pi$
$233$	0.809277	+	0.933956i	0.0530175	+	0.0611855i	−0.728621	+	0.684917i	$0.759839\pi$
$234$		0			0
$235$	−1.17982	+	8.20582i	−0.0769629	+	0.535289i
$236$		0			0
$237$	1.73759	+	3.80479i	0.112869	+	0.247148i
$238$		0			0
$239$	8.34297			0.539662			0.269831	−	0.962908i	$-0.413032\pi$
$239$	8.34297			0.539662			0.269831	+	0.962908i	$0.413032\pi$
$240$		0			0
$241$	20.3678	+	13.0896i	1.31201	+	0.843176i	0.994465	−	0.105068i	$-0.0335061\pi$
$241$	20.3678	+	13.0896i	1.31201	+	0.843176i	0.317542	+	0.948244i	$0.397142\pi$
$242$		0			0
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$		0			0
$245$	−22.1336	+	25.5435i	−1.41406	+	1.63192i
$246$		0			0
$247$	8.97615	+	5.76862i	0.571139	+	0.367048i
$248$		0			0
$249$	2.12709	−	14.7942i	0.134799	−	0.937547i
$250$		0			0
$251$	−11.4967	−	3.37573i	−0.725664	−	0.213074i	−0.102020	−	0.994782i	$-0.532531\pi$
$251$	−11.4967	−	3.37573i	−0.725664	−	0.213074i	−0.623645	+	0.781708i	$0.714349\pi$
$252$		0			0
$253$	−0.777988	+	5.41102i	−0.0489117	+	0.340188i
$254$		0			0
$255$	−4.21023	+	9.21913i	−0.263655	+	0.577324i
$256$		0			0
$257$	12.3112	−	7.91193i	0.767952	−	0.493533i	−0.0970634	−	0.995278i	$-0.530945\pi$
$257$	12.3112	−	7.91193i	0.767952	−	0.493533i	0.865015	+	0.501745i	$0.167309\pi$
$258$		0			0
$259$	−6.14473	−	42.7375i	−0.381815	−	2.65558i
$260$		0			0
$261$	−0.697942	−	4.85429i	−0.0432015	−	0.300473i
$262$		0			0
$263$	−9.11311	+	5.85664i	−0.561939	+	0.361136i	−0.790565	−	0.612378i	$-0.790213\pi$
$263$	−9.11311	+	5.85664i	−0.561939	+	0.361136i	0.228626	+	0.973514i	$0.426577\pi$
$264$		0			0
$265$	17.3212	−	19.9897i	1.06403	−	1.22796i
$266$		0			0
$267$	−3.17475			−0.194292
$268$		0			0
$269$	−1.15339			−0.0703235			−0.0351617	−	0.999382i	$-0.511195\pi$
$269$	−1.15339			−0.0703235			−0.0351617	+	0.999382i	$0.511195\pi$
$270$		0			0
$271$	−4.00442	+	4.62134i	−0.243251	+	0.280727i	−0.864226	−	0.503104i	$-0.832191\pi$
$271$	−4.00442	+	4.62134i	−0.243251	+	0.280727i	0.620975	+	0.783830i	$0.286737\pi$
$272$		0			0
$273$	−7.39653	+	4.75346i	−0.447658	+	0.287692i
$274$		0			0
$275$	0.102754	+	0.714667i	0.00619628	+	0.0430961i
$276$		0			0
$277$	0.484910	+	3.37262i	0.0291354	+	0.202641i	0.999190	−	0.0402467i	$-0.0128144\pi$
$277$	0.484910	+	3.37262i	0.0291354	+	0.202641i	−0.970054	+	0.242888i	$0.921905\pi$
$278$		0			0
$279$	−8.73010	+	5.61050i	−0.522658	+	0.335892i
$280$		0			0
$281$	−2.02477	+	4.43362i	−0.120787	+	0.264488i	−0.960361	−	0.278758i	$-0.910077\pi$
$281$	−2.02477	+	4.43362i	−0.120787	+	0.264488i	0.839574	+	0.543245i	$0.182805\pi$
$282$		0			0
$283$	−3.06644	+	21.3276i	−0.182281	+	1.26779i	0.669071	+	0.743198i	$0.266692\pi$
$283$	−3.06644	+	21.3276i	−0.182281	+	1.26779i	−0.851352	+	0.524594i	$0.824217\pi$
$284$		0			0
$285$	11.4532	+	3.36296i	0.678428	+	0.199204i
$286$		0			0
$287$	6.60990	−	45.9729i	0.390170	−	2.71369i
$288$		0			0
$289$	6.90584	+	4.43811i	0.406226	+	0.261066i
$290$		0			0
$291$	−0.623437	+	0.719485i	−0.0365465	+	0.0421770i
$292$		0			0
$293$	−0.249125	+	0.545507i	−0.0145540	+	0.0318688i	−0.916769	−	0.399417i	$-0.869213\pi$
$293$	−0.249125	+	0.545507i	−0.0145540	+	0.0318688i	0.902215	+	0.431286i	$0.141940\pi$
$294$		0			0
$295$	−2.11417	−	1.35870i	−0.123092	−	0.0791064i
$296$		0			0
$297$	−0.780281			−0.0452765
$298$		0			0
$299$	5.25144	+	11.4991i	0.303699	+	0.665008i
$300$		0			0
$301$	−0.699116	+	4.86246i	−0.0402964	+	0.280267i
$302$		0			0
$303$	2.58866	+	2.98747i	0.148715	+	0.171626i
$304$		0			0
$305$	−2.09535			−0.119980
$306$		0			0
$307$	2.89730	+	6.34419i	0.165357	+	0.362082i	0.974113	−	0.226063i	$-0.0725856\pi$
$307$	2.89730	+	6.34419i	0.165357	+	0.362082i	−0.808755	+	0.588145i	$0.799858\pi$
$308$		0			0
$309$	−16.3180	−	4.79139i	−0.928296	−	0.272572i
$310$		0			0
$311$	−13.4896	−	3.96090i	−0.764924	−	0.224602i	−0.124079	−	0.992272i	$-0.539598\pi$
$311$	−13.4896	−	3.96090i	−0.764924	−	0.224602i	−0.640845	+	0.767670i	$0.721416\pi$
$312$		0			0
$313$	−19.9896	−	23.0692i	−1.12988	−	1.30395i	−0.947151	−	0.320787i	$-0.896053\pi$
$313$	−19.9896	−	23.0692i	−1.12988	−	1.30395i	−0.182728	−	0.983163i	$-0.558493\pi$
$314$		0			0
$315$	−6.44127	+	7.43362i	−0.362924	+	0.418837i
$316$		0			0
$317$	26.4579	−	7.76875i	1.48603	−	0.436336i	0.564755	−	0.825259i	$-0.308971\pi$
$317$	26.4579	−	7.76875i	1.48603	−	0.436336i	0.921271	+	0.388922i	$0.127152\pi$
$318$		0			0
$319$	3.21919	−	2.06885i	0.180240	−	0.115833i
$320$		0			0
$321$	−0.616560	+	0.181038i	−0.0344130	+	0.0101046i
$322$		0			0
$323$	12.3338	−	27.0073i	0.686273	−	1.50273i
$324$		0			0
$325$	1.09338	+	1.26182i	0.0606496	+	0.0699934i
$326$		0			0
$327$	−0.199094	−	0.435955i	−0.0110099	−	0.0241084i
$328$		0			0
$329$	16.8353	+	10.8194i	0.928162	+	0.596493i
$330$		0			0
$331$	−15.0585	+	4.42157i	−0.827690	+	0.243032i	−0.668024	−	0.744140i	$-0.732860\pi$
$331$	−15.0585	+	4.42157i	−0.827690	+	0.243032i	−0.159665	+	0.987171i	$0.551042\pi$
$332$		0			0
$333$	−1.26103	−	8.77069i	−0.0691042	−	0.480631i
$334$		0			0
$335$	−1.80453	−	16.4240i	−0.0985920	−	0.897337i
$336$		0			0
$337$	−2.18286	−	15.1821i	−0.118908	−	0.827024i	−0.958762	−	0.284211i	$-0.908268\pi$
$337$	−2.18286	−	15.1821i	−0.118908	−	0.827024i	0.839854	−	0.542813i	$-0.182641\pi$
$338$		0			0
$339$	6.01556	−	1.76633i	0.326720	−	0.0959337i
$340$		0			0
$341$	−6.81193	−	4.37776i	−0.368887	−	0.237069i
$342$		0			0
$343$	19.7238	+	43.1891i	1.06499	+	2.33199i
$344$		0			0
$345$	9.26119	+	10.6880i	0.498606	+	0.575422i
$346$		0			0
$347$	−8.78288	+	19.2318i	−0.471490	+	1.03242i	0.513227	+	0.858253i	$0.328450\pi$
$347$	−8.78288	+	19.2318i	−0.471490	+	1.03242i	−0.984716	+	0.174165i	$0.944277\pi$
$348$		0			0
$349$	0.531914	−	0.156184i	0.0284727	−	0.00836034i	−0.267465	−	0.963568i	$-0.586186\pi$
$349$	0.531914	−	0.156184i	0.0284727	−	0.00836034i	0.295938	+	0.955207i	$0.404368\pi$
$350$		0			0
$351$	−1.51793	+	0.975514i	−0.0810211	+	0.0520691i
$352$		0			0
$353$	5.65818	−	1.66139i	0.301154	−	0.0884269i	−0.127664	−	0.991817i	$-0.540748\pi$
$353$	5.65818	−	1.66139i	0.301154	−	0.0884269i	0.428819	+	0.903391i	$0.358930\pi$
$354$		0			0
$355$	21.6832	−	25.0237i	1.15082	−	1.32812i
$356$		0			0
$357$	16.0215	+	18.4898i	0.847947	+	0.978583i
$358$		0			0
$359$	−17.5469	−	5.15225i	−0.926092	−	0.271925i	−0.216292	−	0.976329i	$-0.569396\pi$
$359$	−17.5469	−	5.15225i	−0.926092	−	0.271925i	−0.709800	+	0.704403i	$0.751215\pi$
$360$		0			0
$361$	−15.3216	−	4.49883i	−0.806401	−	0.236781i
$362$		0			0
$363$	4.31664	+	9.45213i	0.226565	+	0.496108i
$364$		0			0
$365$	−0.580261			−0.0303723
$366$		0			0
$367$	17.5323	+	20.2334i	0.915180	+	1.05617i	0.998221	+	0.0596282i	$0.0189915\pi$
$367$	17.5323	+	20.2334i	0.915180	+	1.05617i	−0.0830404	+	0.996546i	$0.526463\pi$
$368$		0			0
$369$	1.35650	−	9.43465i	0.0706165	−	0.491148i
$370$		0			0
$371$	−26.5241	−	58.0797i	−1.37706	−	3.01535i
$372$		0			0
$373$	−18.1521			−0.939882			−0.469941	−	0.882698i	$-0.655725\pi$
$373$	−18.1521			−0.939882			−0.469941	+	0.882698i	$0.655725\pi$
$374$		0			0
$375$	10.0620	+	6.46647i	0.519601	+	0.333927i
$376$		0			0
$377$	3.67600	−	8.04933i	0.189324	−	0.414561i
$378$		0			0
$379$	0.595678	−	0.687449i	0.0305979	−	0.0353119i	−0.740244	−	0.672338i	$-0.765290\pi$
$379$	0.595678	−	0.687449i	0.0305979	−	0.0353119i	0.770842	+	0.637026i	$0.219836\pi$
$380$		0			0
$381$	−7.22925	−	4.64596i	−0.370366	−	0.238020i
$382$		0			0
$383$	2.30968	−	16.0642i	0.118019	−	0.820843i	−0.841713	−	0.539926i	$-0.818452\pi$
$383$	2.30968	−	16.0642i	0.118019	−	0.820843i	0.959732	−	0.280917i	$-0.0906386\pi$
$384$		0			0
$385$	−7.36402	−	2.16227i	−0.375305	−	0.110200i
$386$		0			0
$387$	−0.143474	+	0.997884i	−0.00729319	+	0.0507253i
$388$		0			0
$389$	−1.82491	+	3.99599i	−0.0925264	+	0.202605i	−0.950237	−	0.311529i	$-0.899159\pi$
$389$	−1.82491	+	3.99599i	−0.0925264	+	0.202605i	0.857710	+	0.514133i	$0.171886\pi$
$390$		0			0
$391$	29.5921	−	19.0177i	1.49654	−	0.961767i
$392$		0			0
$393$	1.21207	+	8.43014i	0.0611409	+	0.425244i
$394$		0			0
$395$	1.20160	+	8.35734i	0.0604593	+	0.420503i
$396$		0			0
$397$	−9.37733	+	6.02645i	−0.470635	+	0.302459i	−0.754376	−	0.656442i	$-0.772061\pi$
$397$	−9.37733	+	6.02645i	−0.470635	+	0.302459i	0.283741	+	0.958901i	$0.408424\pi$
$398$		0			0
$399$	18.8696	−	21.7767i	0.944663	−	1.09020i
$400$		0			0
$401$	1.76059			0.0879196			0.0439598	−	0.999033i	$-0.486003\pi$
$401$	1.76059			0.0879196			0.0439598	+	0.999033i	$0.486003\pi$
$402$		0			0
$403$	−18.7248			−0.932749
$404$		0			0
$405$	−1.32189	+	1.52554i	−0.0656852	+	0.0758048i
$406$		0			0
$407$	5.81640	−	3.73797i	0.288308	−	0.185285i
$408$		0			0
$409$	−2.41312	−	16.7837i	−0.119321	−	0.829898i	−0.958306	−	0.285743i	$-0.907760\pi$
$409$	−2.41312	−	16.7837i	−0.119321	−	0.829898i	0.838985	−	0.544155i	$-0.183150\pi$
$410$		0			0
$411$	−0.397519	−	2.76481i	−0.0196082	−	0.136378i
$412$		0			0
$413$	−5.10353	+	3.27984i	−0.251128	+	0.161390i
$414$		0			0
$415$	12.5333	−	27.4440i	0.615234	−	1.34717i
$416$		0			0
$417$	−0.462471	+	3.21656i	−0.0226473	+	0.157516i
$418$		0			0
$419$	−38.2174	−	11.2217i	−1.86704	−	0.548214i	−0.998627	−	0.0523795i	$-0.983319\pi$
$419$	−38.2174	−	11.2217i	−1.86704	−	0.548214i	−0.868417	−	0.495834i	$-0.834862\pi$
$420$		0			0
$421$	2.42240	−	16.8482i	0.118061	−	0.821130i	−0.841627	−	0.540060i	$-0.818402\pi$
$421$	2.42240	−	16.8482i	0.118061	−	0.821130i	0.959687	−	0.281070i	$-0.0906894\pi$
$422$		0			0
$423$	3.45498	+	2.22038i	0.167987	+	0.107959i
$424$		0			0
$425$	3.04245	−	3.51117i	0.147580	−	0.170317i
$426$		0			0
$427$	−2.10121	+	4.60101i	−0.101685	+	0.222658i
$428$		0			0
$429$	−1.18441	−	0.761175i	−0.0571839	−	0.0367499i
$430$		0			0
$431$	−16.7065			−0.804725			−0.402363	−	0.915480i	$-0.631811\pi$
$431$	−16.7065			−0.804725			−0.402363	+	0.915480i	$0.631811\pi$
$432$		0			0
$433$	1.75990	+	3.85364i	0.0845754	+	0.185194i	0.947194	−	0.320660i	$-0.103905\pi$
$433$	1.75990	+	3.85364i	0.0845754	+	0.185194i	−0.862619	+	0.505854i	$0.831177\pi$
$434$		0			0
$435$	1.40885	−	9.79878i	0.0675493	−	0.469816i
$436$		0			0
$437$	−27.1306	−	31.3103i	−1.29783	−	1.49778i
$438$		0			0
$439$	−22.0099			−1.05048			−0.525239	−	0.850955i	$-0.676024\pi$
$439$	−22.0099			−1.05048			−0.525239	+	0.850955i	$0.676024\pi$
$440$		0			0
$441$	6.95567	+	15.2308i	0.331222	+	0.725275i
$442$		0			0
$443$	17.8577	+	5.24351i	0.848447	+	0.249127i	0.676923	−	0.736053i	$-0.263313\pi$
$443$	17.8577	+	5.24351i	0.848447	+	0.249127i	0.171524	+	0.985180i	$0.445131\pi$
$444$		0			0
$445$	−6.14890	−	1.80548i	−0.291486	−	0.0855880i
$446$		0			0
$447$	−6.84316	−	7.89743i	−0.323671	−	0.373536i
$448$		0			0
$449$	−15.1683	+	17.5051i	−0.715835	+	0.826117i	−0.990800	−	0.135337i	$-0.956788\pi$
$449$	−15.1683	+	17.5051i	−0.715835	+	0.826117i	0.274965	+	0.961454i	$0.411334\pi$
$450$		0			0
$451$	7.13611	−	2.09535i	0.336026	−	0.0986663i
$452$		0			0
$453$	−7.62649	+	4.90125i	−0.358324	+	0.230281i
$454$		0			0
$455$	−17.0290	+	5.00016i	−0.798331	+	0.234411i
$456$		0			0
$457$	8.50451	−	18.6223i	0.397824	−	0.871114i	−0.599662	−	0.800253i	$-0.704698\pi$
$457$	8.50451	−	18.6223i	0.397824	−	0.871114i	0.997486	−	0.0708603i	$-0.0225744\pi$
$458$		0			0
$459$	3.28796	+	3.79451i	0.153469	+	0.177113i
$460$		0			0
$461$	5.85350	+	12.8174i	0.272624	+	0.596964i	0.995579	−	0.0939317i	$-0.0299435\pi$
$461$	5.85350	+	12.8174i	0.272624	+	0.596964i	−0.722954	+	0.690896i	$0.757216\pi$
$462$		0			0
$463$	11.2181	+	7.20943i	0.521349	+	0.335051i	0.774705	−	0.632322i	$-0.217898\pi$
$463$	11.2181	+	7.20943i	0.521349	+	0.335051i	−0.253356	+	0.967373i	$0.581535\pi$
$464$		0			0
$465$	−20.0993	+	5.90168i	−0.932082	+	0.273684i
$466$		0			0
$467$	−1.11098	−	7.72707i	−0.0514102	−	0.357566i	−0.999247	−	0.0388089i	$-0.987644\pi$
$467$	−1.11098	−	7.72707i	−0.0514102	−	0.357566i	0.947836	−	0.318757i	$-0.103265\pi$
$468$		0			0
$469$	−37.8735	−	12.5074i	−1.74884	−	0.577540i
$470$		0			0
$471$	−0.225039	−	1.56518i	−0.0103692	−	0.0721196i
$472$		0			0
$473$	−0.754772	+	0.221621i	−0.0347044	+	0.0101901i
$474$		0			0
$475$	−4.60321	−	2.95831i	−0.211210	−	0.135736i
$476$		0			0
$477$	−5.44333	−	11.9192i	−0.249233	−	0.545744i
$478$		0			0
$479$	19.6750	+	22.7062i	0.898975	+	1.03747i	0.999097	+	0.0424974i	$0.0135314\pi$
$479$	19.6750	+	22.7062i	0.898975	+	1.03747i	−0.100121	+	0.994975i	$0.531923\pi$
$480$		0			0
$481$	6.64177	−	14.5434i	0.302839	−	0.663124i
$482$		0			0
$483$	32.7559	−	9.61800i	1.49044	−	0.437634i
$484$		0			0
$485$	−1.61665	+	1.03896i	−0.0734085	+	0.0471768i
$486$		0			0
$487$	26.5014	−	7.78152i	1.20089	−	0.352614i	0.380700	−	0.924699i	$-0.375683\pi$
$487$	26.5014	−	7.78152i	1.20089	−	0.352614i	0.820195	+	0.572084i	$0.193865\pi$
$488$		0			0
$489$	9.33006	−	10.7675i	0.421920	−	0.486922i
$490$		0			0
$491$	3.91167	+	4.51430i	0.176531	+	0.203728i	0.837119	−	0.547021i	$-0.184238\pi$
$491$	3.91167	+	4.51430i	0.176531	+	0.203728i	−0.660588	+	0.750749i	$0.729693\pi$
$492$		0			0
$493$	−23.6259	−	6.93719i	−1.06406	−	0.312435i
$494$		0			0
$495$	−1.51126	−	0.443746i	−0.0679260	−	0.0199449i
$496$		0			0
$497$	−33.2036	−	72.7058i	−1.48939	−	3.26130i
$498$		0			0
$499$	3.47258			0.155454			0.0777269	−	0.996975i	$-0.475234\pi$
$499$	3.47258			0.155454			0.0777269	+	0.996975i	$0.475234\pi$
$500$		0			0
$501$	2.94972	+	3.40416i	0.131784	+	0.152086i
$502$		0			0
$503$	−5.95885	+	41.4447i	−0.265692	+	1.84793i	0.222171	+	0.975008i	$0.428686\pi$
$503$	−5.95885	+	41.4447i	−0.265692	+	1.84793i	−0.487863	+	0.872920i	$0.662223\pi$
$504$		0			0
$505$	3.31478	+	7.25835i	0.147506	+	0.322992i
$506$		0			0
$507$	9.74426			0.432758
$508$		0			0
$509$	17.8823	+	11.4923i	0.792621	+	0.509387i	0.873200	−	0.487362i	$-0.162041\pi$
$509$	17.8823	+	11.4923i	0.792621	+	0.509387i	−0.0805792	+	0.996748i	$0.525677\pi$
$510$		0			0
$511$	−0.581883	+	1.27415i	−0.0257410	+	0.0563649i
$512$		0			0
$513$	3.87246	−	4.46906i	0.170973	−	0.197314i
$514$		0			0
$515$	−28.8800	−	18.5601i	−1.27261	−	0.817854i
$516$		0			0
$517$	−0.456058	+	3.17195i	−0.0200574	+	0.139502i
$518$		0			0
$519$	23.6889	+	6.95567i	1.03983	+	0.305320i
$520$		0			0
$521$	−2.96176	+	20.5995i	−0.129757	+	0.902479i	0.816103	+	0.577906i	$0.196130\pi$
$521$	−2.96176	+	20.5995i	−0.129757	+	0.902479i	−0.945860	+	0.324574i	$0.894779\pi$
$522$		0			0
$523$	6.04314	−	13.2326i	0.264248	−	0.578623i	−0.730273	−	0.683155i	$-0.760607\pi$
$523$	6.04314	−	13.2326i	0.264248	−	0.578623i	0.994521	+	0.104532i	$0.0333346\pi$
$524$		0			0
$525$	3.79314	−	2.43770i	0.165546	−	0.106390i
$526$		0			0
$527$	7.41516	+	51.5735i	0.323009	+	2.24658i
$528$		0			0
$529$	−3.71220	−	25.8189i	−0.161400	−	1.12256i
$530$		0			0
$531$	−1.04736	+	0.673095i	−0.0454514	+	0.0292098i
$532$		0			0
$533$	11.2627	−	12.9979i	0.487842	−	0.563000i
$534$		0			0
$535$	−1.29712			−0.0560794
$536$		0			0
$537$	21.0353			0.907741
$538$		0			0
$539$	−8.55572	+	9.87382i	−0.368521	+	0.425296i
$540$		0			0
$541$	1.32937	−	0.854337i	0.0571543	−	0.0367308i	−0.511752	−	0.859133i	$-0.671003\pi$
$541$	1.32937	−	0.854337i	0.0571543	−	0.0367308i	0.568906	+	0.822403i	$0.307367\pi$
$542$		0			0
$543$	3.23104	+	22.4724i	0.138657	+	0.964382i
$544$		0			0
$545$	−0.137680	−	0.957589i	−0.00589758	−	0.0410186i
$546$		0			0
$547$	10.7454	−	6.90563i	0.459439	−	0.295264i	−0.290374	−	0.956913i	$-0.593780\pi$
$547$	10.7454	−	6.90563i	0.459439	−	0.295264i	0.749813	+	0.661650i	$0.230143\pi$
$548$		0			0
$549$	−0.431215	+	0.944228i	−0.0184038	+	0.0402987i
$550$		0			0
$551$	−4.12722	+	28.7054i	−0.175825	+	1.22289i
$552$		0			0
$553$	19.5561	+	5.74219i	0.831611	+	0.244183i
$554$		0			0
$555$	2.54550	−	17.7043i	0.108050	−	0.751507i
$556$		0			0
$557$	−17.6492	−	11.3425i	−0.747821	−	0.480595i	0.110393	−	0.993888i	$-0.464789\pi$
$557$	−17.6492	−	11.3425i	−0.747821	−	0.480595i	−0.858214	+	0.513293i	$0.828426\pi$
$558$		0			0
$559$	−1.19123	+	1.37476i	−0.0503838	+	0.0581460i
$560$		0			0
$561$	−1.62746	+	3.56364i	−0.0687115	+	0.150457i
$562$		0			0
$563$	12.7710	+	8.20746i	0.538236	+	0.345903i	0.781348	−	0.624095i	$-0.214532\pi$
$563$	12.7710	+	8.20746i	0.538236	+	0.345903i	−0.243113	+	0.969998i	$0.578169\pi$
$564$		0			0
$565$	12.6555			0.532422
$566$		0			0
$567$	2.02422	+	4.43243i	0.0850093	+	0.186144i
$568$		0			0
$569$	−0.609586	+	4.23976i	−0.0255552	+	0.177740i	−0.998601	−	0.0528700i	$-0.983163\pi$
$569$	−0.609586	+	4.23976i	−0.0255552	+	0.177740i	0.973046	+	0.230610i	$0.0740722\pi$
$570$		0			0
$571$	−7.58639	−	8.75516i	−0.317481	−	0.366392i	0.574470	−	0.818526i	$-0.305208\pi$
$571$	−7.58639	−	8.75516i	−0.317481	−	0.366392i	−0.891950	+	0.452134i	$0.850663\pi$
$572$		0			0
$573$	8.01536			0.334847
$574$		0			0
$575$	−2.69308	−	5.89703i	−0.112309	−	0.245923i
$576$		0			0
$577$	−2.75241	−	0.808181i	−0.114584	−	0.0336450i	0.223938	−	0.974603i	$-0.428109\pi$
$577$	−2.75241	−	0.808181i	−0.114584	−	0.0336450i	−0.338522	+	0.940958i	$0.609927\pi$
$578$		0			0
$579$	−22.5149	−	6.61097i	−0.935687	−	0.274743i
$580$		0			0
$581$	−47.6937	−	55.0415i	−1.97867	−	2.28350i
$582$		0			0
$583$	6.69549	−	7.72700i	0.277299	−	0.320020i
$584$		0			0
$585$	−3.49472	+	1.02614i	−0.144489	+	0.0424258i
$586$		0			0
$587$	−29.7151	+	19.0967i	−1.22647	+	0.788207i	−0.983338	−	0.181786i	$-0.941812\pi$
$587$	−29.7151	+	19.0967i	−1.22647	+	0.788207i	−0.243135	+	0.969992i	$0.578176\pi$
$588$		0			0
$589$	58.8806	−	17.2889i	2.42613	−	0.712377i
$590$		0			0
$591$	−4.48000	+	9.80983i	−0.184283	+	0.403522i
$592$		0			0
$593$	8.67864	+	10.0157i	0.356389	+	0.411295i	0.905427	−	0.424503i	$-0.139551\pi$
$593$	8.67864	+	10.0157i	0.356389	+	0.411295i	−0.549038	+	0.835798i	$0.685006\pi$
$594$		0			0
$595$	20.5155	+	44.9227i	0.841054	+	1.84165i
$596$		0			0
$597$	2.96790	+	1.90735i	0.121468	+	0.0780627i
$598$		0			0
$599$	28.1855	−	8.27600i	1.15163	−	0.338148i	0.350454	−	0.936580i	$-0.386027\pi$
$599$	28.1855	−	8.27600i	1.15163	−	0.338148i	0.801174	+	0.598432i	$0.204209\pi$
$600$		0			0
$601$	4.67780	+	32.5348i	0.190811	+	1.32712i	0.829867	+	0.557961i	$0.188416\pi$
$601$	4.67780	+	32.5348i	0.190811	+	1.32712i	−0.639056	+	0.769160i	$0.720675\pi$
$602$		0			0
$603$	−7.77248	−	2.56680i	−0.316520	−	0.104528i
$604$		0			0
$605$	2.98511	+	20.7619i	0.121362	+	0.844092i
$606$		0			0
$607$	−16.0373	+	4.70898i	−0.650935	+	0.191132i	−0.590496	−	0.807040i	$-0.701068\pi$
$607$	−16.0373	+	4.70898i	−0.650935	+	0.191132i	−0.0604384	+	0.998172i	$0.519250\pi$
$608$		0			0
$609$	−20.1035	−	12.9197i	−0.814635	−	0.523534i
$610$		0			0
$611$	3.07841	+	6.74077i	0.124539	+	0.272702i
$612$		0			0
$613$	6.11279	+	7.05454i	0.246893	+	0.284930i	0.865647	−	0.500655i	$-0.166907\pi$
$613$	6.11279	+	7.05454i	0.246893	+	0.284930i	−0.618754	+	0.785585i	$0.712362\pi$
$614$		0			0
$615$	7.99277	−	17.5017i	0.322300	−	0.705738i
$616$		0			0
$617$	−25.5246	+	7.49469i	−1.02758	+	0.301725i	−0.751727	−	0.659474i	$-0.770779\pi$
$617$	−25.5246	+	7.49469i	−1.02758	+	0.301725i	−0.275854	+	0.961200i	$0.588961\pi$
$618$		0			0
$619$	−13.6915	+	8.79900i	−0.550308	+	0.353662i	−0.786059	−	0.618152i	$-0.787882\pi$
$619$	−13.6915	+	8.79900i	−0.550308	+	0.353662i	0.235750	+	0.971814i	$0.424245\pi$
$620$		0			0
$621$	6.72223	−	1.97383i	0.269754	−	0.0792069i
$622$		0			0
$623$	−10.1306	+	11.6913i	−0.405873	+	0.468403i
$624$		0			0
$625$	12.7810	+	14.7501i	0.511240	+	0.590002i
$626$		0			0
$627$	4.42722	+	1.29995i	0.176806	+	0.0519149i
$628$		0			0
$629$	−42.6871	−	12.5340i	−1.70204	−	0.499765i
$630$		0			0
$631$	18.1424	+	39.7262i	0.722236	+	1.58148i	0.810744	+	0.585401i	$0.199063\pi$
$631$	18.1424	+	39.7262i	0.722236	+	1.58148i	−0.0885083	+	0.996075i	$0.528210\pi$
$632$		0			0
$633$	−12.4866			−0.496299
$634$		0			0
$635$	−11.3596	−	13.1096i	−0.450791	−	0.520240i
$636$		0			0
$637$	−4.29963	+	29.9046i	−0.170358	+	1.18486i
$638$		0			0
$639$	−6.81411	−	14.9208i	−0.269562	−	0.590259i
$640$		0			0
$641$	25.9495			1.02495			0.512473	−	0.858704i	$-0.328730\pi$
$641$	25.9495			1.02495			0.512473	+	0.858704i	$0.328730\pi$
$642$		0			0
$643$	19.6379	+	12.6205i	0.774442	+	0.497704i	0.867185	−	0.497986i	$-0.165927\pi$
$643$	19.6379	+	12.6205i	0.774442	+	0.497704i	−0.0927426	+	0.995690i	$0.529563\pi$
$644$		0			0
$645$	−0.845379	+	1.85112i	−0.0332868	+	0.0728879i
$646$		0			0
$647$	−20.8555	+	24.0685i	−0.819915	+	0.946232i	−0.999295	−	0.0375477i	$-0.988045\pi$
$647$	−20.8555	+	24.0685i	−0.819915	+	0.946232i	0.179380	+	0.983780i	$0.442591\pi$
$648$		0			0
$649$	−0.817232	−	0.525203i	−0.0320792	−	0.0206160i
$650$		0			0
$651$	−7.19645	+	50.0524i	−0.282051	+	1.96171i
$652$		0			0
$653$	29.8833	+	8.77452i	1.16942	+	0.343374i	0.808088	−	0.589062i	$-0.200503\pi$
$653$	29.8833	+	8.77452i	1.16942	+	0.343374i	0.361335	+	0.932436i	$0.382321\pi$
$654$		0			0
$655$	−2.44666	+	17.0169i	−0.0955990	+	0.664906i
$656$		0			0
$657$	−0.119415	+	0.261483i	−0.00465883	+	0.0102014i
$658$		0			0
$659$	−8.45305	+	5.43244i	−0.329284	+	0.211618i	−0.694828	−	0.719176i	$-0.744519\pi$
$659$	−8.45305	+	5.43244i	−0.329284	+	0.211618i	0.365544	+	0.930794i	$0.380883\pi$
$660$		0			0
$661$	3.67476	+	25.5585i	0.142932	+	0.994112i	0.927434	+	0.373986i	$0.122009\pi$
$661$	3.67476	+	25.5585i	0.142932	+	0.994112i	−0.784502	+	0.620126i	$0.787082\pi$
$662$		0			0
$663$	1.28930	+	8.96725i	0.0500721	+	0.348259i
$664$		0			0
$665$	48.9314	−	31.4463i	1.89748	−	1.21943i
$666$		0			0
$667$	−22.5004	+	25.9668i	−0.871218	+	1.00544i
$668$		0			0
$669$	23.7517			0.918295
$670$		0			0
$671$	−0.809957			−0.0312681
$672$		0			0
$673$	13.3837	−	15.4457i	0.515905	−	0.595386i	−0.436696	−	0.899609i	$-0.643851\pi$
$673$	13.3837	−	15.4457i	0.515905	−	0.595386i	0.952601	+	0.304223i	$0.0983968\pi$
$674$		0			0
$675$	0.778436	−	0.500271i	0.0299620	−	0.0192554i
$676$		0			0
$677$	−6.53198	−	45.4309i	−0.251044	−	1.74605i	−0.591969	−	0.805960i	$-0.701649\pi$
$677$	−6.53198	−	45.4309i	−0.251044	−	1.74605i	0.340925	−	0.940090i	$-0.389260\pi$
$678$		0			0
$679$	0.660192	+	4.59173i	0.0253358	+	0.176215i
$680$		0			0
$681$	−23.2330	+	14.9310i	−0.890292	+	0.572156i
$682$		0			0
$683$	10.4938	−	22.9783i	0.401535	−	0.879240i	−0.595577	−	0.803298i	$-0.703076\pi$
$683$	10.4938	−	22.9783i	0.401535	−	0.879240i	0.997112	−	0.0759416i	$-0.0241963\pi$
$684$		0			0
$685$	0.802425	−	5.58099i	0.0306591	−	0.213239i
$686$		0			0
$687$	7.05491	+	2.07151i	0.269162	+	0.0790330i
$688$		0			0
$689$	3.36479	−	23.4026i	0.128188	−	0.891568i
$690$		0			0
$691$	−9.26787	−	5.95610i	−0.352566	−	0.226581i	0.352355	−	0.935867i	$-0.385381\pi$
$691$	−9.26787	−	5.95610i	−0.352566	−	0.226581i	−0.704921	+	0.709286i	$0.749017\pi$
$692$		0			0
$693$	−2.48987	+	2.87346i	−0.0945822	+	0.109154i
$694$		0			0
$695$	−2.72498	+	5.96687i	−0.103364	+	0.226336i
$696$		0			0
$697$	−40.2600	−	25.8735i	−1.52496	−	0.980029i
$698$		0			0
$699$	1.23580			0.0467423
$700$		0			0
$701$	−1.94442	−	4.25768i	−0.0734395	−	0.160810i	0.869352	−	0.494194i	$-0.164537\pi$
$701$	−1.94442	−	4.25768i	−0.0734395	−	0.160810i	−0.942791	+	0.333384i	$0.891809\pi$
$702$		0			0
$703$	−7.45702	+	51.8647i	−0.281247	+	1.95611i
$704$		0			0
$705$	5.42893	+	6.26532i	0.204465	+	0.235965i
$706$		0			0
$707$	19.2620			0.724423
$708$		0			0
$709$	−0.854364	−	1.87080i	−0.0320863	−	0.0702592i	0.892910	−	0.450235i	$-0.148660\pi$
$709$	−0.854364	−	1.87080i	−0.0320863	−	0.0702592i	−0.924997	+	0.379976i	$0.875932\pi$
$710$		0			0
$711$	4.01335	+	1.17842i	0.150512	+	0.0441944i
$712$		0			0
$713$	69.7599	+	20.4834i	2.61253	+	0.767108i
$714$		0			0
$715$	−1.86111	−	2.14783i	−0.0696014	−	0.0803243i
$716$		0			0
$717$	5.46348	−	6.30519i	0.204037	−	0.235472i
$718$		0			0
$719$	−9.58930	+	2.81567i	−0.357621	+	0.105007i	−0.455607	−	0.890181i	$-0.650578\pi$
$719$	−9.58930	+	2.81567i	−0.357621	+	0.105007i	0.0979867	+	0.995188i	$0.468760\pi$
$720$		0			0
$721$	−69.7151	+	44.8032i	−2.59633	+	1.66856i
$722$		0			0
$723$	23.2306	−	6.82111i	0.863954	−	0.253680i
$724$		0			0
$725$	−1.88516	+	4.12791i	−0.0700129	+	0.153307i
$726$		0			0
$727$	1.47923	+	1.70712i	0.0548615	+	0.0633136i	0.782517	−	0.622629i	$-0.213935\pi$
$727$	1.47923	+	1.70712i	0.0548615	+	0.0633136i	−0.727655	+	0.685943i	$0.759390\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	4.25822	+	2.73659i	0.157496	+	0.101216i
$732$		0			0
$733$	−18.6844	+	5.48623i	−0.690124	+	0.202639i	−0.607945	−	0.793979i	$-0.708006\pi$
$733$	−18.6844	+	5.48623i	−0.690124	+	0.202639i	−0.0821785	+	0.996618i	$0.526188\pi$
$734$		0			0
$735$	4.81009	+	33.4549i	0.177423	+	1.23400i
$736$		0			0
$737$	−0.697539	−	6.34867i	−0.0256942	−	0.233856i
$738$		0			0
$739$	−5.93100	−	41.2510i	−0.218175	−	1.51744i	−0.744767	−	0.667325i	$-0.767439\pi$
$739$	−5.93100	−	41.2510i	−0.218175	−	1.51744i	0.526592	−	0.850118i	$-0.323470\pi$
$740$		0			0
$741$	10.2378	−	3.00608i	0.376093	−	0.110431i
$742$		0			0
$743$	−23.3711	−	15.0197i	−0.857404	−	0.551020i	0.0364716	−	0.999335i	$-0.488388\pi$
$743$	−23.3711	−	15.0197i	−0.857404	−	0.551020i	−0.893876	+	0.448314i	$0.852025\pi$
$744$		0			0
$745$	−8.76267	−	19.1876i	−0.321039	−	0.702978i
$746$		0			0
$747$	−9.78780	−	11.2957i	−0.358117	−	0.413289i
$748$		0			0
$749$	−1.30074	+	2.84823i	−0.0475282	+	0.104072i
$750$		0			0
$751$	37.2009	−	10.9232i	1.35748	−	0.398592i	0.479605	−	0.877484i	$-0.340780\pi$
$751$	37.2009	−	10.9232i	1.35748	−	0.398592i	0.877873	+	0.478893i	$0.158962\pi$
$752$		0			0
$753$	−10.0799	+	6.47798i	−0.367333	+	0.236071i
$754$		0			0
$755$	−17.5584	+	5.15563i	−0.639017	+	0.187632i
$756$		0			0
$757$	−2.57616	+	2.97305i	−0.0936322	+	0.108057i	−0.800632	−	0.599156i	$-0.795503\pi$
$757$	−2.57616	+	2.97305i	−0.0936322	+	0.108057i	0.707000	+	0.707214i	$0.250048\pi$
$758$		0			0
$759$	3.57991	+	4.13143i	0.129942	+	0.149961i
$760$		0			0
$761$	−34.3144	−	10.0756i	−1.24390	−	0.365241i	−0.407419	−	0.913241i	$-0.633571\pi$
$761$	−34.3144	−	10.0756i	−1.24390	−	0.365241i	−0.836478	+	0.548000i	$0.815389\pi$
$762$		0			0
$763$	−2.24075	−	0.657944i	−0.0811206	−	0.0238192i
$764$		0			0
$765$	4.21023	+	9.21913i	0.152221	+	0.333318i
$766$		0			0
$767$	−2.24643			−0.0811138
$768$		0			0
$769$	20.8718	+	24.0873i	0.752656	+	0.868612i	0.994823	−	0.101623i	$-0.0324036\pi$
$769$	20.8718	+	24.0873i	0.752656	+	0.868612i	−0.242167	+	0.970235i	$0.577858\pi$
$770$		0			0
$771$	2.08269	−	14.4854i	0.0750061	−	0.521679i
$772$		0			0
$773$	−5.44363	−	11.9199i	−0.195794	−	0.428729i	0.786116	−	0.618079i	$-0.212089\pi$
$773$	−5.44363	−	11.9199i	−0.195794	−	0.428729i	−0.981910	+	0.189351i	$0.939362\pi$
$774$		0			0
$775$	9.60259			0.344935
$776$		0			0
$777$	−36.3228	−	23.3433i	−1.30307	−	0.837435i
$778$		0			0
$779$	−23.4147	+	51.2711i	−0.838920	+	1.83698i
$780$		0			0
$781$	8.38160	−	9.67289i	0.299917	−	0.346123i
$782$		0			0
$783$	−4.12568	−	2.65142i	−0.147440	−	0.0947538i
$784$		0			0
$785$	0.454259	−	3.15944i	0.0162132	−	0.112765i
$786$		0			0
$787$	−13.0532	−	3.83278i	−0.465298	−	0.136624i	0.0406763	−	0.999172i	$-0.487049\pi$
$787$	−13.0532	−	3.83278i	−0.465298	−	0.136624i	−0.505974	+	0.862549i	$0.668867\pi$
$788$		0			0
$789$	−1.54167	+	10.7225i	−0.0548847	+	0.381732i
$790$		0			0
$791$	12.6909	−	27.7892i	0.451236	−	0.988069i
$792$		0			0
$793$	−1.57566	+	1.01262i	−0.0559534	+	0.0359591i
$794$		0			0
$795$	−3.76425	−	26.1810i	−0.133504	−	0.928543i
$796$		0			0
$797$	5.38841	+	37.4772i	0.190867	+	1.32751i	0.829719	+	0.558182i	$0.188501\pi$
$797$	5.38841	+	37.4772i	0.190867	+	1.32751i	−0.638851	+	0.769330i	$0.720590\pi$
$798$		0			0
$799$	17.3470	−	11.1482i	0.613691	−	0.394396i
$800$		0			0
$801$	−2.07902	+	2.39932i	−0.0734585	+	0.0847757i
$802$		0			0
$803$	−0.224300			−0.00791536
$804$		0			0
$805$	68.9119			2.42882
$806$		0			0
$807$	−0.755310	+	0.871674i	−0.0265882	+	0.0306844i
$808$		0			0
$809$	9.99157	−	6.42119i	0.351285	−	0.225757i	−0.353083	−	0.935592i	$-0.614867\pi$
$809$	9.99157	−	6.42119i	0.351285	−	0.225757i	0.704368	+	0.709835i	$0.251230\pi$
$810$		0			0
$811$	5.95152	+	41.3938i	0.208986	+	1.45353i	0.776474	+	0.630149i	$0.217006\pi$
$811$	5.95152	+	41.3938i	0.208986	+	1.45353i	−0.567488	+	0.823382i	$0.692085\pi$
$812$		0			0
$813$	0.870243	+	6.05267i	0.0305208	+	0.212277i
$814$		0			0
$815$	24.1941	−	15.5486i	0.847481	−	0.544643i
$816$		0			0
$817$	2.47653	−	5.42284i	0.0866428	−	0.189721i
$818$		0			0
$819$	−1.25127	+	8.70277i	−0.0437229	+	0.304100i
$820$		0			0
$821$	−17.2893	−	5.07660i	−0.603401	−	0.177175i	−0.0342579	−	0.999413i	$-0.510907\pi$
$821$	−17.2893	−	5.07660i	−0.603401	−	0.177175i	−0.569143	+	0.822239i	$0.692725\pi$
$822$		0			0
$823$	2.67887	−	18.6319i	0.0933794	−	0.649468i	−0.888347	−	0.459172i	$-0.848146\pi$
$823$	2.67887	−	18.6319i	0.0933794	−	0.649468i	0.981727	−	0.190296i	$-0.0609448\pi$
$824$		0			0
$825$	0.607399	+	0.390351i	0.0211469	+	0.0135903i
$826$		0			0
$827$	18.2745	−	21.0899i	0.635468	−	0.733369i	−0.343099	−	0.939299i	$-0.611477\pi$
$827$	18.2745	−	21.0899i	0.635468	−	0.733369i	0.978567	+	0.205930i	$0.0660220\pi$
$828$		0			0
$829$	15.0681	−	32.9944i	0.523335	−	1.14594i	−0.444826	−	0.895617i	$-0.646734\pi$
$829$	15.0681	−	32.9944i	0.523335	−	1.14594i	0.968161	−	0.250328i	$-0.0805383\pi$
$830$		0			0
$831$	2.86641	+	1.84213i	0.0994345	+	0.0639027i
$832$		0			0
$833$	84.0687			2.91281
$834$		0			0
$835$	3.77711	+	8.27072i	0.130712	+	0.286220i
$836$		0			0
$837$	−1.47687	+	10.2719i	−0.0510481	+	0.355048i
$838$		0			0
$839$	3.56027	+	4.10877i	0.122914	+	0.141851i	0.813871	−	0.581045i	$-0.197356\pi$
$839$	3.56027	+	4.10877i	0.122914	+	0.141851i	−0.690957	+	0.722896i	$0.742811\pi$
$840$		0			0
$841$	−4.94874			−0.170646
$842$		0			0
$843$	2.02477	+	4.43362i	0.0697367	+	0.152702i
$844$		0			0
$845$	18.8728	+	5.54156i	0.649245	+	0.190636i
$846$		0			0
$847$	48.5827	+	14.2652i	1.66932	+	0.490157i
$848$		0			0
$849$	14.1102	+	16.2840i	0.484261	+	0.558867i
$850$		0			0
$851$	−40.6534	+	46.9166i	−1.39358	+	1.60828i
$852$		0			0
$853$	25.2506	−	7.41424i	0.864564	−	0.253859i	0.180762	−	0.983527i	$-0.442144\pi$
$853$	25.2506	−	7.41424i	0.864564	−	0.253859i	0.683802	+	0.729668i	$0.260325\pi$
$854$		0			0
$855$	10.0418	−	6.45347i	0.343422	−	0.220704i
$856$		0			0
$857$	−46.5540	+	13.6695i	−1.59025	+	0.466940i	−0.952813	−	0.303559i	$-0.901825\pi$
$857$	−46.5540	+	13.6695i	−1.59025	+	0.466940i	−0.637440	+	0.770500i	$0.720007\pi$
$858$		0			0
$859$	8.14732	−	17.8401i	0.277983	−	0.608698i	−0.718214	−	0.695822i	$-0.755040\pi$
$859$	8.14732	−	17.8401i	0.277983	−	0.608698i	0.996197	+	0.0871239i	$0.0277676\pi$
$860$		0			0
$861$	−30.4154	−	35.1013i	−1.03656	−	1.19625i
$862$		0			0
$863$	16.7708	+	36.7229i	0.570884	+	1.25006i	0.946326	+	0.323215i	$0.104764\pi$
$863$	16.7708	+	36.7229i	0.570884	+	1.25006i	−0.375442	+	0.926846i	$0.622509\pi$
$864$		0			0
$865$	41.9252	+	26.9437i	1.42550	+	0.916113i
$866$		0			0
$867$	7.87647	−	2.31274i	0.267499	−	0.0785447i
$868$		0			0
$869$	0.464479	+	3.23052i	0.0157564	+	0.109588i
$870$		0			0
$871$	−9.29413	−	11.4784i	−0.314920	−	0.388931i
$872$		0			0
$873$	0.135486	+	0.942325i	0.00458550	+	0.0318929i
$874$		0			0
$875$	55.9212	−	16.4199i	1.89048	−	0.555096i
$876$		0			0
$877$	6.69531	+	4.30281i	0.226085	+	0.145296i	0.648780	−	0.760976i	$-0.275280\pi$
$877$	6.69531	+	4.30281i	0.226085	+	0.145296i	−0.422695	+	0.906272i	$0.638916\pi$
$878$		0			0
$879$	0.249125	+	0.545507i	0.00840276	+	0.0183995i
$880$		0			0
$881$	−23.6606	−	27.3058i	−0.797145	−	0.919955i	0.201076	−	0.979576i	$-0.435556\pi$
$881$	−23.6606	−	27.3058i	−0.797145	−	0.919955i	−0.998221	+	0.0596210i	$0.981011\pi$
$882$		0			0
$883$	3.73309	−	8.17432i	0.125628	−	0.275088i	−0.836359	−	0.548182i	$-0.815320\pi$
$883$	3.73309	−	8.17432i	0.125628	−	0.275088i	0.961987	+	0.273095i	$0.0880472\pi$
$884$		0			0
$885$	−2.41132	+	0.708029i	−0.0810558	+	0.0238001i
$886$		0			0
$887$	39.5249	−	25.4011i	1.32711	−	0.852885i	0.331233	−	0.943549i	$-0.392535\pi$
$887$	39.5249	−	25.4011i	1.32711	−	0.852885i	0.995882	+	0.0906640i	$0.0288989\pi$
$888$		0			0
$889$	−40.1776	+	11.7972i	−1.34751	+	0.395666i
$890$		0			0
$891$	−0.510975	+	0.589697i	−0.0171183	+	0.0197556i
$892$		0			0
$893$	−15.9040	−	18.3542i	−0.532207	−	0.614199i
$894$		0			0
$895$	40.7415	+	11.9628i	1.36184	+	0.399872i
$896$		0			0
$897$	12.1294	+	3.56151i	0.404988	+	0.118915i
$898$		0			0
$899$	−21.1419	−	46.2942i	−0.705121	−	1.54400i
$900$		0			0
$901$	−65.7900			−2.19178
$902$		0			0
$903$	3.21698	+	3.71259i	0.107054	+	0.123547i
$904$		0			0
$905$	−6.52212	+	45.3623i	−0.216802	+	1.50789i
$906$		0			0
$907$	−1.90208	−	4.16497i	−0.0631575	−	0.138296i	0.875421	−	0.483361i	$-0.160584\pi$
$907$	−1.90208	−	4.16497i	−0.0631575	−	0.138296i	−0.938579	+	0.345065i	$0.887857\pi$
$908$		0			0
$909$	3.95299			0.131112
$910$		0			0
$911$	17.8834	+	11.4929i	0.592502	+	0.380778i	0.802259	−	0.596976i	$-0.203631\pi$
$911$	17.8834	+	11.4929i	0.592502	+	0.380778i	−0.209757	+	0.977753i	$0.567267\pi$
$912$		0			0
$913$	4.84472	−	10.6085i	0.160337	−	0.351089i
$914$		0			0
$915$	−1.37217	+	1.58356i	−0.0453624	+	0.0523510i
$916$		0			0
$917$	34.9125	+	22.4369i	1.15291	+	0.740931i
$918$		0			0
$919$	−4.99134	+	34.7155i	−0.164649	+	1.14516i	0.725078	+	0.688667i	$0.241804\pi$
$919$	−4.99134	+	34.7155i	−0.164649	+	1.14516i	−0.889727	+	0.456493i	$0.849105\pi$
$920$		0			0
$921$	6.69195	+	1.96493i	0.220507	+	0.0647467i
$922$		0			0
$923$	4.21214	−	29.2960i	0.138644	−	0.964291i
$924$		0			0
$925$	−3.40608	+	7.45828i	−0.111991	+	0.245227i
$926$		0			0
$927$	−14.3071	+	9.19460i	−0.469906	+	0.301990i
$928$		0			0
$929$	−1.63633	−	11.3809i	−0.0536862	−	0.373396i	−0.998898	−	0.0469374i	$-0.985054\pi$
$929$	−1.63633	−	11.3809i	−0.0536862	−	0.373396i	0.945212	−	0.326458i	$-0.105855\pi$
$930$		0			0
$931$	−14.0911	−	98.0058i	−0.461817	−	3.21201i
$932$		0			0
$933$	−11.8272	+	7.60091i	−0.387207	+	0.248843i
$934$		0			0
$935$	−5.17874	+	5.97658i	−0.169363	+	0.195455i
$936$		0			0
$937$	−46.0106			−1.50310			−0.751550	−	0.659676i	$-0.770694\pi$
$937$	−46.0106			−1.50310			−0.751550	+	0.659676i	$0.770694\pi$
$938$		0			0
$939$	−30.5250			−0.996145
$940$		0			0
$941$	−4.37215	+	5.04573i	−0.142528	+	0.164486i	−0.822525	−	0.568729i	$-0.807435\pi$
$941$	−4.37215	+	5.04573i	−0.142528	+	0.164486i	0.679997	+	0.733215i	$0.261981\pi$
$942$		0			0
$943$	−56.1782	+	36.1035i	−1.82941	+	1.17569i
$944$		0			0
$945$	1.39982	+	9.73597i	0.0455362	+	0.316711i
$946$		0			0
$947$	5.87317	+	40.8488i	0.190852	+	1.32741i	0.829758	+	0.558123i	$0.188478\pi$
$947$	5.87317	+	40.8488i	0.190852	+	1.32741i	−0.638906	+	0.769285i	$0.720613\pi$
$948$		0			0
$949$	−0.436344	+	0.280421i	−0.0141643	+	0.00910286i
$950$		0			0
$951$	11.4550	−	25.0830i	0.371455	−	0.813373i
$952$		0			0
$953$	−5.66141	+	39.3760i	−0.183391	+	1.27551i	0.665281	+	0.746593i	$0.268312\pi$
$953$	−5.66141	+	39.3760i	−0.183391	+	1.27551i	−0.848672	+	0.528920i	$0.822597\pi$
$954$		0			0
$955$	15.5243	+	4.55834i	0.502354	+	0.147504i
$956$		0			0
$957$	0.544590	−	3.78771i	0.0176041	−	0.122439i
$958$		0			0
$959$	−11.4501	−	7.35856i	−0.369744	−	0.237620i
$960$		0			0
$961$	−50.2228	+	57.9602i	−1.62009	+	1.86968i
$962$		0			0
$963$	−0.266941	+	0.584520i	−0.00860207	+	0.0188359i
$964$		0			0
$965$	−39.8475	−	25.6084i	−1.28274	−	0.824365i
$966$		0			0
$967$	−9.45684			−0.304111			−0.152056	−	0.988372i	$-0.548589\pi$
$967$	−9.45684			−0.304111			−0.152056	+	0.988372i	$0.548589\pi$
$968$		0			0
$969$	−12.3338	−	27.0073i	−0.396220	−	0.867600i
$970$		0			0
$971$	−2.68907	+	18.7029i	−0.0862962	+	0.600204i	0.900083	+	0.435718i	$0.143505\pi$
$971$	−2.68907	+	18.7029i	−0.0862962	+	0.600204i	−0.986379	+	0.164486i	$0.947404\pi$
$972$		0			0
$973$	10.3695	+	11.9671i	0.332432	+	0.383647i
$974$		0			0
$975$	1.66963			0.0534710
$976$		0			0
$977$	2.87055	+	6.28562i	0.0918369	+	0.201095i	0.949976	−	0.312322i	$-0.101107\pi$
$977$	2.87055	+	6.28562i	0.0918369	+	0.201095i	−0.858139	+	0.513417i	$0.828380\pi$
$978$		0			0
$979$	−2.37685	−	0.697907i	−0.0759645	−	0.0223052i
$980$		0			0
$981$	−0.459852	−	0.135025i	−0.0146819	−	0.00431100i
$982$		0			0
$983$	31.0968	+	35.8877i	0.991835	+	1.14464i	0.989484	+	0.144641i	$0.0462028\pi$
$983$	31.0968	+	35.8877i	0.991835	+	1.14464i	0.00235066	+	0.999997i	$0.499252\pi$
$984$		0			0
$985$	−14.2558	+	16.4520i	−0.454227	+	0.524206i
$986$		0			0
$987$	19.2016	−	5.63809i	0.611193	−	0.179462i
$988$		0			0
$989$	5.94185	−	3.81859i	0.188940	−	0.121424i
$990$		0			0
$991$	−21.4473	+	6.29749i	−0.681295	+	0.200046i	−0.604027	−	0.796964i	$-0.706438\pi$
$991$	−21.4473	+	6.29749i	−0.681295	+	0.200046i	−0.0772685	+	0.997010i	$0.524620\pi$
$992$		0			0
$993$	−6.51961	+	14.2760i	−0.206894	+	0.453034i
$994$		0			0
$995$	4.66355	+	5.38203i	0.147845	+	0.170622i
$996$		0			0
$997$	−22.2215	−	48.6582i	−0.703760	−	1.54102i	−0.835351	−	0.549716i	$-0.814736\pi$
$997$	−22.2215	−	48.6582i	−0.703760	−	1.54102i	0.131591	−	0.991304i	$-0.457991\pi$
$998$		0			0
$999$	−7.45424	−	4.79055i	−0.235842	−	0.151566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.25.5	✓	60
67.59	even	11	inner	804.2.q.b.193.5	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.25.5	✓	60	1.1	even	1	trivial
804.2.q.b.193.5	yes	60	67.59	even	11	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.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{3} +(1.69814 - 1.09133i) q^{5} +(-0.693468 - 4.82317i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{3} +(1.69814 - 1.09133i) q^{5} +(-0.693468 - 4.82317i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(0.656414 - 0.421852i) q^{11} +(0.749561 - 1.64131i) q^{13} +(0.287274 - 1.99804i) q^{15} +(-4.81748 - 1.41454i) q^{17} +(-0.841566 + 5.85322i) q^{19} +(-4.09924 - 2.63442i) q^{21} +(-4.58797 + 5.29480i) q^{23} +(-0.384395 + 0.841709i) q^{25} +(-0.841254 - 0.540641i) q^{27} +4.90421 q^{29} +(-4.31097 - 9.43970i) q^{31} +(0.111046 - 0.772339i) q^{33} +(-6.44127 - 7.43362i) q^{35} +8.86088 q^{37} +(-0.749561 - 1.64131i) q^{39} +(9.14557 + 2.68538i) q^{41} +(-0.967308 - 0.284027i) q^{43} +(-1.32189 - 1.52554i) q^{45} +(-2.68948 + 3.10382i) q^{47} +(-16.0657 + 4.71730i) q^{49} +(-4.22381 + 2.71448i) q^{51} +(12.5726 - 3.69164i) q^{53} +(0.654304 - 1.43273i) q^{55} +(3.87246 + 4.46906i) q^{57} +(-0.517190 - 1.13249i) q^{59} +(-0.873249 - 0.561203i) q^{61} +(-4.67539 + 1.37282i) q^{63} +(-0.518348 - 3.60519i) q^{65} +(3.64682 - 7.32808i) q^{67} +(0.997061 + 6.93471i) q^{69} +(15.7387 - 4.62130i) q^{71} +(-0.241827 - 0.155413i) q^{73} +(0.384395 + 0.841709i) q^{75} +(-2.48987 - 2.87346i) q^{77} +(-1.73759 + 3.80479i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(12.5737 - 8.08062i) q^{83} +(-9.72447 + 2.85536i) q^{85} +(3.21157 - 3.70635i) q^{87} +(-2.07902 - 2.39932i) q^{89} +(-8.43612 - 2.47707i) q^{91} +(-9.95713 - 2.92368i) q^{93} +(4.95869 + 10.8580i) q^{95} -0.952015 q^{97} +(-0.510975 - 0.589697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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