LMFDB - Embedded newform 828.2.q.c.685.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [828,2,Mod(73,828)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(828, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("828.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.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:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 276)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			685.1
Root			$1.02355 - 2.24127i$ of defining polynomial
Character	$\chi$	$=$	828.685
Dual form			828.2.q.c.469.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.217172 + 1.51046i) q^{5} +(-1.55685 - 3.40903i) q^{7} +O(q^{10})$	$q+(-0.217172 + 1.51046i) q^{5} +(-1.55685 - 3.40903i) q^{7} +(-1.04445 + 0.306679i) q^{11} +(1.25796 - 2.75455i) q^{13} +(-2.61063 + 1.67775i) q^{17} +(-3.49220 - 2.24430i) q^{19} +(-2.35317 - 4.17883i) q^{23} +(2.56313 + 0.752602i) q^{25} +(-2.24106 + 1.44024i) q^{29} +(-4.45761 - 5.14435i) q^{31} +(5.48731 - 1.61122i) q^{35} +(-0.973540 - 6.77112i) q^{37} +(1.41678 - 9.85394i) q^{41} +(-2.62449 + 3.02882i) q^{43} +1.56940 q^{47} +(-4.61365 + 5.32444i) q^{49} +(1.19196 + 2.61003i) q^{53} +(-0.236402 - 1.64421i) q^{55} +(6.11707 - 13.3945i) q^{59} +(3.42833 + 3.95650i) q^{61} +(3.88745 + 2.49831i) q^{65} +(4.44565 + 1.30536i) q^{67} +(-14.6278 - 4.29512i) q^{71} +(2.70682 + 1.73957i) q^{73} +(2.67153 + 3.08311i) q^{77} +(-1.28701 + 2.81816i) q^{79} +(0.773779 + 5.38175i) q^{83} +(-1.96723 - 4.30763i) q^{85} +(-9.86433 + 11.3840i) q^{89} -11.3488 q^{91} +(4.14834 - 4.78744i) q^{95} +(0.546130 - 3.79842i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{5}+O(q^{10}) $ 20 * q + 4 * q^5	$ 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) $ 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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			0
$3$		0			0
$4$		0			0
$5$	−0.217172	+	1.51046i	−0.0971222	+	0.675500i	0.881854	+	0.471523i	$0.156296\pi$
$5$	−0.217172	+	1.51046i	−0.0971222	+	0.675500i	−0.978976	+	0.203977i	$0.934613\pi$
$6$		0			0
$7$	−1.55685	−	3.40903i	−0.588434	−	1.28849i	−0.936384	−	0.350977i	$-0.885849\pi$
$7$	−1.55685	−	3.40903i	−0.588434	−	1.28849i	0.347950	−	0.937513i	$-0.386878\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.04445	+	0.306679i	−0.314914	+	0.0924671i	−0.435370	−	0.900252i	$-0.643383\pi$
$11$	−1.04445	+	0.306679i	−0.314914	+	0.0924671i	0.120456	+	0.992719i	$0.461564\pi$
$12$		0			0
$13$	1.25796	−	2.75455i	0.348895	−	0.763974i	−0.651092	−	0.758999i	$-0.725689\pi$
$13$	1.25796	−	2.75455i	0.348895	−	0.763974i	0.999988	−	0.00497557i	$-0.00158378\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.61063	+	1.67775i	−0.633171	+	0.406915i	−0.817483	−	0.575953i	$-0.804631\pi$
$17$	−2.61063	+	1.67775i	−0.633171	+	0.406915i	0.184311	+	0.982868i	$0.440995\pi$
$18$		0			0
$19$	−3.49220	−	2.24430i	−0.801166	−	0.514878i	0.0748303	−	0.997196i	$-0.476158\pi$
$19$	−3.49220	−	2.24430i	−0.801166	−	0.514878i	−0.875996	+	0.482318i	$0.839795\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.35317	−	4.17883i	−0.490669	−	0.871346i
$23$	−2.35317	−	4.17883i	−0.490669	−	0.871346i
$24$		0			0
$25$	2.56313	+	0.752602i	0.512626	+	0.150520i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.24106	+	1.44024i	−0.416154	+	0.267446i	−0.731919	−	0.681391i	$-0.761375\pi$
$29$	−2.24106	+	1.44024i	−0.416154	+	0.267446i	0.315765	+	0.948837i	$0.397739\pi$
$30$		0			0
$31$	−4.45761	−	5.14435i	−0.800610	−	0.923953i	0.197804	−	0.980241i	$-0.436619\pi$
$31$	−4.45761	−	5.14435i	−0.800610	−	0.923953i	−0.998415	+	0.0562882i	$0.982073\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.48731	−	1.61122i	0.927525	−	0.272346i
$36$		0			0
$37$	−0.973540	−	6.77112i	−0.160049	−	1.11317i	−0.898537	−	0.438898i	$-0.855369\pi$
$37$	−0.973540	−	6.77112i	−0.160049	−	1.11317i	0.738488	−	0.674267i	$-0.235540\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.41678	−	9.85394i	0.221264	−	1.53893i	−0.512001	−	0.858985i	$-0.671096\pi$
$41$	1.41678	−	9.85394i	0.221264	−	1.53893i	0.733265	−	0.679943i	$-0.237995\pi$
$42$		0			0
$43$	−2.62449	+	3.02882i	−0.400231	+	0.461891i	−0.919714	−	0.392590i	$-0.871579\pi$
$43$	−2.62449	+	3.02882i	−0.400231	+	0.461891i	0.519483	+	0.854481i	$0.326125\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.56940			0.228921			0.114461	−	0.993428i	$-0.463486\pi$
$47$	1.56940			0.228921			0.114461	+	0.993428i	$0.463486\pi$
$48$		0			0
$49$	−4.61365	+	5.32444i	−0.659093	+	0.760634i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.19196	+	2.61003i	0.163728	+	0.358515i	0.973658	−	0.228011i	$-0.0732223\pi$
$53$	1.19196	+	2.61003i	0.163728	+	0.358515i	−0.809930	+	0.586526i	$0.800495\pi$
$54$		0			0
$55$	−0.236402	−	1.64421i	−0.0318764	−	0.221705i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.11707	−	13.3945i	0.796374	−	1.74382i	0.138946	−	0.990300i	$-0.455629\pi$
$59$	6.11707	−	13.3945i	0.796374	−	1.74382i	0.657429	−	0.753517i	$-0.271644\pi$
$60$		0			0
$61$	3.42833	+	3.95650i	0.438952	+	0.506578i	0.931517	−	0.363698i	$-0.118486\pi$
$61$	3.42833	+	3.95650i	0.438952	+	0.506578i	−0.492565	+	0.870276i	$0.663940\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.88745	+	2.49831i	0.482179	+	0.309878i
$66$		0			0
$67$	4.44565	+	1.30536i	0.543123	+	0.159475i	0.541775	−	0.840524i	$-0.317753\pi$
$67$	4.44565	+	1.30536i	0.543123	+	0.159475i	0.00134834	+	0.999999i	$0.499571\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.6278	−	4.29512i	−1.73600	−	0.509736i	−0.747937	−	0.663770i	$-0.768956\pi$
$71$	−14.6278	−	4.29512i	−1.73600	−	0.509736i	−0.988066	+	0.154033i	$0.950774\pi$
$72$		0			0
$73$	2.70682	+	1.73957i	0.316809	+	0.203601i	0.689375	−	0.724405i	$-0.257885\pi$
$73$	2.70682	+	1.73957i	0.316809	+	0.203601i	−0.372566	+	0.928006i	$0.621522\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.67153	+	3.08311i	0.304449	+	0.351353i
$78$		0			0
$79$	−1.28701	+	2.81816i	−0.144800	+	0.317068i	−0.968111	−	0.250523i	$-0.919397\pi$
$79$	−1.28701	+	2.81816i	−0.144800	+	0.317068i	0.823311	+	0.567591i	$0.192125\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.773779	+	5.38175i	0.0849333	+	0.590724i	0.987193	+	0.159531i	$0.0509982\pi$
$83$	0.773779	+	5.38175i	0.0849333	+	0.590724i	−0.902260	+	0.431193i	$0.858093\pi$
$84$		0			0
$85$	−1.96723	−	4.30763i	−0.213376	−	0.467228i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.86433	+	11.3840i	−1.04562	+	1.20671i	−0.0677018	+	0.997706i	$0.521567\pi$
$89$	−9.86433	+	11.3840i	−1.04562	+	1.20671i	−0.977915	+	0.209001i	$0.932979\pi$
$90$		0			0
$91$	−11.3488			−1.18968
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.14834	−	4.78744i	0.425611	−	0.491181i
$96$		0			0
$97$	0.546130	−	3.79842i	0.0554511	−	0.385671i	−0.943130	−	0.332423i	$-0.892134\pi$
$97$	0.546130	−	3.79842i	0.0554511	−	0.385671i	0.998581	−	0.0532474i	$-0.0169572\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.05517	−	7.33887i	−0.104993	−	0.730245i	−0.972514	−	0.232844i	$-0.925197\pi$
$101$	−1.05517	−	7.33887i	−0.104993	−	0.730245i	0.867521	−	0.497401i	$-0.165712\pi$
$102$		0			0
$103$	12.7260	−	3.73670i	1.25393	−	0.368188i	0.413700	−	0.910413i	$-0.364236\pi$
$103$	12.7260	−	3.73670i	1.25393	−	0.368188i	0.840233	+	0.542225i	$0.182418\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.152798	−	0.176338i	−0.0147716	−	0.0170473i	0.748316	−	0.663343i	$-0.230863\pi$
$107$	−0.152798	−	0.176338i	−0.0147716	−	0.0170473i	−0.763087	+	0.646295i	$0.776317\pi$
$108$		0			0
$109$	−9.97148	+	6.40828i	−0.955095	+	0.613802i	−0.922636	−	0.385671i	$-0.873970\pi$
$109$	−9.97148	+	6.40828i	−0.955095	+	0.613802i	−0.0324583	+	0.999473i	$0.510334\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.65402	−	2.24742i	−0.720030	−	0.211420i	−0.0988662	−	0.995101i	$-0.531522\pi$
$113$	−7.65402	−	2.24742i	−0.720030	−	0.211420i	−0.621164	+	0.783681i	$0.713340\pi$
$114$		0			0
$115$	6.82301	−	2.64685i	0.636249	−	0.246820i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.78386	+	6.28771i	0.896885	+	0.576393i
$120$		0			0
$121$	−8.25696	+	5.30643i	−0.750633	+	0.482402i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.86303	+	10.6485i	−0.434962	+	0.952435i
$126$		0			0
$127$	9.85281	−	2.89305i	0.874296	−	0.256716i	0.186354	−	0.982483i	$-0.440333\pi$
$127$	9.85281	−	2.89305i	0.874296	−	0.256716i	0.687941	+	0.725766i	$0.258515\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.47190	+	18.5509i	0.740193	+	1.62080i	0.783237	+	0.621724i	$0.213567\pi$
$131$	8.47190	+	18.5509i	0.740193	+	1.62080i	−0.0430434	+	0.999073i	$0.513705\pi$
$132$		0			0
$133$	−2.21405	+	15.3990i	−0.191982	+	1.33527i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.77788			−0.835380			−0.417690	−	0.908590i	$-0.637160\pi$
$137$	−9.77788			−0.835380			−0.417690	+	0.908590i	$0.637160\pi$
$138$		0			0
$139$	−3.43414			−0.291280			−0.145640	−	0.989338i	$-0.546524\pi$
$139$	−3.43414			−0.291280			−0.145640	+	0.989338i	$0.546524\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.469117	+	3.26278i	−0.0392296	+	0.272848i
$144$		0			0
$145$	−1.68874	−	3.69782i	−0.140242	−	0.307087i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	19.5536	−	5.74146i	1.60189	−	0.470359i	0.645822	−	0.763488i	$-0.276515\pi$
$149$	19.5536	−	5.74146i	1.60189	−	0.470359i	0.956073	+	0.293130i	$0.0946968\pi$
$150$		0			0
$151$	5.81632	−	12.7360i	0.473325	−	1.03644i	−0.510920	−	0.859629i	$-0.670695\pi$
$151$	5.81632	−	12.7360i	0.473325	−	1.03644i	0.984245	−	0.176810i	$-0.0565777\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.73843	−	5.61585i	0.701887	−	0.451076i
$156$		0			0
$157$	15.1481	+	9.73511i	1.20895	+	0.776946i	0.980483	−	0.196605i	$-0.0629916\pi$
$157$	15.1481	+	9.73511i	1.20895	+	0.776946i	0.228469	+	0.973551i	$0.426628\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−10.5822	+	14.5278i	−0.833995	+	1.14495i
$162$		0			0
$163$	10.8066	+	3.17311i	0.846439	+	0.248537i	0.676065	−	0.736842i	$-0.263684\pi$
$163$	10.8066	+	3.17311i	0.846439	+	0.248537i	0.170375	+	0.985379i	$0.445502\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−15.6618	+	10.0652i	−1.21194	+	0.778870i	−0.980983	−	0.194093i	$-0.937824\pi$
$167$	−15.6618	+	10.0652i	−1.21194	+	0.778870i	−0.230962	+	0.972963i	$0.574187\pi$
$168$		0			0
$169$	2.50812	+	2.89452i	0.192932	+	0.222656i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.1330	−	3.26895i	0.846427	−	0.248533i	0.170368	−	0.985381i	$-0.445504\pi$
$173$	11.1330	−	3.26895i	0.846427	−	0.248533i	0.676059	+	0.736847i	$0.263686\pi$
$174$		0			0
$175$	−1.42476	−	9.90946i	−0.107702	−	0.749085i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.66482	−	11.5791i	0.124434	−	0.865461i	−0.828002	−	0.560725i	$-0.810523\pi$
$179$	1.66482	−	11.5791i	0.124434	−	0.865461i	0.952437	−	0.304736i	$-0.0985682\pi$
$180$		0			0
$181$	9.76420	−	11.2685i	0.725767	−	0.837580i	−0.266221	−	0.963912i	$-0.585775\pi$
$181$	9.76420	−	11.2685i	0.725767	−	0.837580i	0.991988	+	0.126332i	$0.0403205\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.4390			0.767487
$186$		0			0
$187$	2.21215	−	2.55296i	0.161768	−	0.186691i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.72672	−	8.16038i	−0.269656	−	0.590465i	0.725560	−	0.688159i	$-0.241581\pi$
$191$	−3.72672	−	8.16038i	−0.269656	−	0.590465i	−0.995217	+	0.0976939i	$0.968853\pi$
$192$		0			0
$193$	3.17993	+	22.1169i	0.228897	+	1.59201i	0.702769	+	0.711418i	$0.251947\pi$
$193$	3.17993	+	22.1169i	0.228897	+	1.59201i	−0.473873	+	0.880593i	$0.657144\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.12840	+	4.66054i	−0.151642	+	0.332050i	−0.970173	−	0.242412i	$-0.922061\pi$
$197$	−2.12840	+	4.66054i	−0.151642	+	0.332050i	0.818531	+	0.574462i	$0.194789\pi$
$198$		0			0
$199$	17.4100	+	20.0922i	1.23416	+	1.42430i	0.870065	+	0.492937i	$0.164077\pi$
$199$	17.4100	+	20.0922i	1.23416	+	1.42430i	0.364097	+	0.931361i	$0.381378\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.39881	+	5.39759i	0.589481	+	0.378836i
$204$		0			0
$205$	14.5763	+	4.28000i	1.01806	+	0.298928i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.33572	+	1.27308i	0.299908	+	0.0880609i
$210$		0			0
$211$	−10.3560	−	6.65540i	−0.712937	−	0.458177i	0.133237	−	0.991084i	$-0.457463\pi$
$211$	−10.3560	−	6.65540i	−0.712937	−	0.458177i	−0.846173	+	0.532908i	$0.821099\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.00496	−	4.62197i	−0.273136	−	0.315216i
$216$		0			0
$217$	−10.5974	+	23.2051i	−0.719399	+	1.57526i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.33738	+	9.30166i	0.0899617	+	0.625697i
$222$		0			0
$223$	−4.00684	−	8.77376i	−0.268318	−	0.587535i	0.726731	−	0.686922i	$-0.241039\pi$
$223$	−4.00684	−	8.77376i	−0.268318	−	0.587535i	−0.995049	+	0.0993879i	$0.968312\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.1922	+	14.0705i	−0.809223	+	0.933893i	−0.998849	−	0.0479634i	$-0.984727\pi$
$227$	−12.1922	+	14.0705i	−0.809223	+	0.933893i	0.189626	+	0.981856i	$0.439272\pi$
$228$		0			0
$229$	−6.22102			−0.411097			−0.205548	−	0.978647i	$-0.565898\pi$
$229$	−6.22102			−0.411097			−0.205548	+	0.978647i	$0.565898\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.42419	+	2.79767i	−0.158814	+	0.183281i	−0.829580	−	0.558388i	$-0.811420\pi$
$233$	−2.42419	+	2.79767i	−0.158814	+	0.183281i	0.670766	+	0.741669i	$0.265966\pi$
$234$		0			0
$235$	−0.340831	+	2.37053i	−0.0222333	+	0.154636i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.28878	−	15.9188i	−0.148049	−	1.02970i	−0.919408	−	0.393304i	$-0.871332\pi$
$239$	−2.28878	−	15.9188i	−0.148049	−	1.02970i	0.771359	−	0.636400i	$-0.219577\pi$
$240$		0			0
$241$	−27.6789	+	8.12724i	−1.78295	+	0.523522i	−0.995661	−	0.0930597i	$-0.970335\pi$
$241$	−27.6789	+	8.12724i	−1.78295	+	0.523522i	−0.787291	+	0.616581i	$0.788517\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.04041	−	8.12507i	−0.449795	−	0.519092i
$246$		0			0
$247$	−10.5751	+	6.79619i	−0.672876	+	0.432431i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.175438	+	0.0515133i	0.0110736	+	0.00325149i	0.287265	−	0.957851i	$-0.407254\pi$
$251$	0.175438	+	0.0515133i	0.0110736	+	0.00325149i	−0.276191	+	0.961103i	$0.589072\pi$
$252$		0			0
$253$	3.73933	+	3.64292i	0.235089	+	0.229028i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	20.6833	+	13.2923i	1.29019	+	0.829152i	0.992108	−	0.125389i	$-0.0400180\pi$
$257$	20.6833	+	13.2923i	1.29019	+	0.829152i	0.298078	+	0.954541i	$0.403654\pi$
$258$		0			0
$259$	−21.5673	+	13.8604i	−1.34012	+	0.861246i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.88909	−	10.7056i	0.301474	−	0.660136i	−0.696898	−	0.717170i	$-0.745437\pi$
$263$	4.88909	−	10.7056i	0.301474	−	0.660136i	0.998372	+	0.0570340i	$0.0181643\pi$
$264$		0			0
$265$	−4.20122	+	1.23359i	−0.258079	+	0.0757787i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.90568	−	4.17285i	−0.116191	−	0.254423i	0.842597	−	0.538544i	$-0.181025\pi$
$269$	−1.90568	−	4.17285i	−0.116191	−	0.254423i	−0.958788	+	0.284121i	$0.908298\pi$
$270$		0			0
$271$	1.13617	−	7.90226i	0.0690176	−	0.480028i	−0.925772	−	0.378082i	$-0.876584\pi$
$271$	1.13617	−	7.90226i	0.0690176	−	0.480028i	0.994790	−	0.101946i	$-0.0325070\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.90787			−0.175351
$276$		0			0
$277$	5.12957			0.308206			0.154103	−	0.988055i	$-0.450751\pi$
$277$	5.12957			0.308206			0.154103	+	0.988055i	$0.450751\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.79046	−	26.3632i	0.226120	−	1.57270i	−0.488108	−	0.872783i	$-0.662313\pi$
$281$	3.79046	−	26.3632i	0.226120	−	1.57270i	0.714228	−	0.699913i	$-0.246778\pi$
$282$		0			0
$283$	1.47222	+	3.22371i	0.0875143	+	0.191630i	0.948329	−	0.317289i	$-0.102773\pi$
$283$	1.47222	+	3.22371i	0.0875143	+	0.191630i	−0.860815	+	0.508919i	$0.830045\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−35.7981	+	10.5113i	−2.11309	+	0.620460i
$288$		0			0
$289$	−3.06150	+	6.70376i	−0.180088	+	0.394339i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	24.1167	−	15.4989i	1.40891	−	0.905454i	0.408940	−	0.912561i	$-0.365899\pi$
$293$	24.1167	−	15.4989i	1.40891	−	0.905454i	0.999975	+	0.00710728i	$0.00226234\pi$
$294$		0			0
$295$	18.9035	+	12.1485i	1.10060	+	0.707314i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−14.4710	+	1.22511i	−0.836878	+	0.0708497i
$300$		0			0
$301$	14.4113	+	4.23153i	0.830651	+	0.243901i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.72069	+	4.31912i	−0.384826	+	0.247312i
$306$		0			0
$307$	−14.2345	−	16.4275i	−0.812406	−	0.937566i	0.186587	−	0.982438i	$-0.440257\pi$
$307$	−14.2345	−	16.4275i	−0.812406	−	0.937566i	−0.998993	+	0.0448722i	$0.985712\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	22.2553	−	6.53475i	1.26198	−	0.370552i	0.418751	−	0.908101i	$-0.362468\pi$
$311$	22.2553	−	6.53475i	1.26198	−	0.370552i	0.843232	+	0.537550i	$0.180650\pi$
$312$		0			0
$313$	−1.45243	−	10.1019i	−0.0820964	−	0.570993i	−0.988802	−	0.149230i	$-0.952320\pi$
$313$	−1.45243	−	10.1019i	−0.0820964	−	0.570993i	0.906706	−	0.421763i	$-0.138589\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.15164	−	14.9650i	0.120848	−	0.840518i	−0.835750	−	0.549109i	$-0.814967\pi$
$317$	2.15164	−	14.9650i	0.120848	−	0.840518i	0.956599	−	0.291408i	$-0.0941239\pi$
$318$		0			0
$319$	1.89899	−	2.19155i	0.106323	−	0.122703i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12.8822			0.716787
$324$		0			0
$325$	5.29739	−	6.11351i	0.293846	−	0.339117i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.44333	−	5.35014i	−0.134705	−	0.294963i
$330$		0			0
$331$	−4.22495	−	29.3852i	−0.232224	−	1.61515i	−0.688446	−	0.725288i	$-0.741707\pi$
$331$	−4.22495	−	29.3852i	−0.232224	−	1.61515i	0.456222	−	0.889866i	$-0.349202\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.93717	+	6.43151i	−0.160475	+	0.351391i
$336$		0			0
$337$	5.04882	+	5.82664i	0.275027	+	0.317398i	0.876413	−	0.481561i	$-0.159930\pi$
$337$	5.04882	+	5.82664i	0.275027	+	0.317398i	−0.601386	+	0.798959i	$0.705385\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.23342	+	4.00598i	0.337559	+	0.216936i
$342$		0			0
$343$	0.162669	+	0.0477638i	0.00878329	+	0.00257901i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.73729	−	2.27187i	−0.415359	−	0.121961i	0.0673742	−	0.997728i	$-0.478538\pi$
$347$	−7.73729	−	2.27187i	−0.415359	−	0.121961i	−0.482734	+	0.875767i	$0.660356\pi$
$348$		0			0
$349$	−13.0709	−	8.40018i	−0.699671	−	0.449651i	0.141841	−	0.989889i	$-0.454698\pi$
$349$	−13.0709	−	8.40018i	−0.699671	−	0.449651i	−0.841512	+	0.540238i	$0.818334\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.62082	+	6.48678i	0.299166	+	0.345256i	0.885353	−	0.464920i	$-0.153917\pi$
$353$	5.62082	+	6.48678i	0.299166	+	0.345256i	−0.586187	+	0.810176i	$0.699371\pi$
$354$		0			0
$355$	9.66437	−	21.1620i	0.512931	−	1.12316i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.80972	+	33.4524i	0.253847	+	1.76555i	0.574648	+	0.818401i	$0.305139\pi$
$359$	4.80972	+	33.4524i	0.253847	+	1.76555i	−0.320800	+	0.947147i	$0.603952\pi$
$360$		0			0
$361$	−0.734308	−	1.60791i	−0.0386478	−	0.0846268i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.21540	+	3.71076i	−0.168302	+	0.194230i
$366$		0			0
$367$	13.4110			0.700047			0.350023	−	0.936741i	$-0.386174\pi$
$367$	13.4110			0.700047			0.350023	+	0.936741i	$0.386174\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.04195	−	8.12685i	0.365600	−	0.421925i
$372$		0			0
$373$	4.27644	−	29.7433i	0.221426	−	1.54005i	−0.511227	−	0.859446i	$-0.670809\pi$
$373$	4.27644	−	29.7433i	0.221426	−	1.54005i	0.732652	−	0.680603i	$-0.238282\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.14805	+	7.98487i	0.0591276	+	0.411242i
$378$		0			0
$379$	18.1461	−	5.32818i	0.932103	−	0.273690i	0.219786	−	0.975548i	$-0.429464\pi$
$379$	18.1461	−	5.32818i	0.932103	−	0.273690i	0.712317	+	0.701858i	$0.247646\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.12902	−	5.91920i	−0.262081	−	0.302457i	0.609424	−	0.792845i	$-0.291401\pi$
$383$	−5.12902	−	5.91920i	−0.262081	−	0.302457i	−0.871505	+	0.490387i	$0.836855\pi$
$384$		0			0
$385$	−5.23711	+	3.36569i	−0.266908	+	0.171531i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.10650	−	2.08666i	−0.360314	−	0.105798i	0.0965649	−	0.995327i	$-0.469214\pi$
$389$	−7.10650	−	2.08666i	−0.360314	−	0.105798i	−0.456879	+	0.889529i	$0.651033\pi$
$390$		0			0
$391$	13.1543	+	6.96136i	0.665241	+	0.352051i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.97723	−	2.55601i	−0.200116	−	0.128607i
$396$		0			0
$397$	−1.57016	+	1.00908i	−0.0788042	+	0.0506444i	−0.579450	−	0.815008i	$-0.696732\pi$
$397$	−1.57016	+	1.00908i	−0.0788042	+	0.0506444i	0.500645	+	0.865652i	$0.333096\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.49667	−	9.84632i	0.224553	−	0.491702i	−0.763502	−	0.645806i	$-0.776522\pi$
$401$	4.49667	−	9.84632i	0.224553	−	0.491702i	0.988055	+	0.154104i	$0.0492489\pi$
$402$		0			0
$403$	−19.7779	+	5.80730i	−0.985205	+	0.289282i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.09338	+	6.77355i	0.153333	+	0.335752i
$408$		0			0
$409$	0.974102	−	6.77503i	0.0481663	−	0.335004i	−0.951463	−	0.307764i	$-0.900419\pi$
$409$	0.974102	−	6.77503i	0.0481663	−	0.335004i	0.999629	−	0.0272395i	$-0.00867169\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−55.1856			−2.71551
$414$		0			0
$415$	−8.29699			−0.407283
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.08920	−	28.4410i	0.199771	−	1.38944i	−0.605177	−	0.796091i	$-0.706898\pi$
$419$	4.08920	−	28.4410i	0.199771	−	1.38944i	0.804948	−	0.593345i	$-0.202193\pi$
$420$		0			0
$421$	−11.4884	−	25.1561i	−0.559911	−	1.22603i	−0.951997	−	0.306106i	$-0.900974\pi$
$421$	−11.4884	−	25.1561i	−0.559911	−	1.22603i	0.392086	−	0.919928i	$-0.371753\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.95406	+	2.33552i	−0.385829	+	0.113290i
$426$		0			0
$427$	8.15042	−	17.8469i	0.394427	−	0.863674i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−24.0681	+	15.4677i	−1.15932	+	0.745050i	−0.971474	−	0.237148i	$-0.923787\pi$
$431$	−24.0681	+	15.4677i	−1.15932	+	0.745050i	−0.187848	+	0.982198i	$0.560151\pi$
$432$		0			0
$433$	−22.9578	−	14.7541i	−1.10328	−	0.709035i	−0.143461	−	0.989656i	$-0.545823\pi$
$433$	−22.9578	−	14.7541i	−1.10328	−	0.709035i	−0.959819	+	0.280621i	$0.909460\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.16083	+	19.8745i	−0.0555298	+	0.950727i
$438$		0			0
$439$	0.908894	+	0.266875i	0.0433791	+	0.0127373i	0.303350	−	0.952879i	$-0.401895\pi$
$439$	0.908894	+	0.266875i	0.0433791	+	0.0127373i	−0.259971	+	0.965616i	$0.583713\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.3853	−	11.8155i	0.873510	−	0.561371i	−0.0253144	−	0.999680i	$-0.508059\pi$
$443$	18.3853	−	11.8155i	0.873510	−	0.561371i	0.898825	+	0.438309i	$0.144422\pi$
$444$		0			0
$445$	−15.0529	−	17.3720i	−0.713578	−	0.823512i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	5.12412	−	1.50458i	0.241822	−	0.0710054i	−0.158576	−	0.987347i	$-0.550690\pi$
$449$	5.12412	−	1.50458i	0.241822	−	0.0710054i	0.400398	+	0.916341i	$0.368872\pi$
$450$		0			0
$451$	1.54223	+	10.7265i	0.0726209	+	0.505090i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.46464	−	17.1419i	0.115544	−	0.803626i
$456$		0			0
$457$	19.5938	−	22.6125i	0.916561	−	1.05777i	−0.0815702	−	0.996668i	$-0.525993\pi$
$457$	19.5938	−	22.6125i	0.916561	−	1.05777i	0.998132	−	0.0611006i	$-0.0194611\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.50571			0.116702			0.0583512	−	0.998296i	$-0.481416\pi$
$461$	2.50571			0.116702			0.0583512	+	0.998296i	$0.481416\pi$
$462$		0			0
$463$	−27.7850	+	32.0656i	−1.29128	+	1.49021i	−0.519257	+	0.854618i	$0.673791\pi$
$463$	−27.7850	+	32.0656i	−1.29128	+	1.49021i	−0.772021	+	0.635597i	$0.780754\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.75868	+	12.6097i	0.266480	+	0.583509i	0.994814	−	0.101713i	$-0.0324323\pi$
$467$	5.75868	+	12.6097i	0.266480	+	0.583509i	−0.728334	+	0.685222i	$0.759705\pi$
$468$		0			0
$469$	−2.47120	−	17.1876i	−0.114110	−	0.793649i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.81228	−	3.96833i	0.0833286	−	0.182464i
$474$		0			0
$475$	−7.26189	−	8.38067i	−0.333198	−	0.384531i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.6280	+	6.83019i	0.485605	+	0.312079i	0.760436	−	0.649413i	$-0.224985\pi$
$479$	10.6280	+	6.83019i	0.485605	+	0.312079i	−0.274831	+	0.961493i	$0.588622\pi$
$480$		0			0
$481$	−19.8761	−	5.83614i	−0.906270	−	0.266105i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.61877	+	1.64982i	0.255135	+	0.0749144i
$486$		0			0
$487$	−13.1238	−	8.43416i	−0.594697	−	0.382188i	0.208394	−	0.978045i	$-0.433176\pi$
$487$	−13.1238	−	8.43416i	−0.594697	−	0.382188i	−0.803091	+	0.595857i	$0.796813\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−28.5515	−	32.9501i	−1.28851	−	1.48702i	−0.779720	−	0.626129i	$-0.784639\pi$
$491$	−28.5515	−	32.9501i	−1.28851	−	1.48702i	−0.508790	−	0.860891i	$-0.669907\pi$
$492$		0			0
$493$	3.43421	−	7.51988i	0.154669	−	0.338678i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.13116	+	56.5535i	0.364732	+	2.53677i
$498$		0			0
$499$	4.18252	+	9.15843i	0.187235	+	0.409988i	0.979850	−	0.199735i	$-0.0640081\pi$
$499$	4.18252	+	9.15843i	0.187235	+	0.409988i	−0.792615	+	0.609723i	$0.791281\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.51425	+	5.20973i	−0.201281	+	0.232290i	−0.847412	−	0.530936i	$-0.821840\pi$
$503$	−4.51425	+	5.20973i	−0.201281	+	0.232290i	0.646131	+	0.763226i	$0.276386\pi$
$504$		0			0
$505$	11.3143			0.503478
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.7523	−	14.7170i	0.565236	−	0.652318i	−0.399128	−	0.916895i	$-0.630687\pi$
$509$	12.7523	−	14.7170i	0.565236	−	0.652318i	0.964364	+	0.264578i	$0.0852325\pi$
$510$		0			0
$511$	1.71612	−	11.9359i	0.0759165	−	0.528011i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.88041	+	20.0337i	0.126926	+	0.882791i
$516$		0			0
$517$	−1.63917	+	0.481303i	−0.0720905	+	0.0211677i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−21.9203	−	25.2973i	−0.960344	−	1.10830i	−0.994057	−	0.108865i	$-0.965278\pi$
$521$	−21.9203	−	25.2973i	−0.960344	−	1.10830i	0.0337122	−	0.999432i	$-0.489267\pi$
$522$		0			0
$523$	−26.8575	+	17.2602i	−1.17439	+	0.754738i	−0.974348	−	0.225049i	$-0.927746\pi$
$523$	−26.8575	+	17.2602i	−1.17439	+	0.754738i	−0.200047	+	0.979786i	$0.564110\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.2681	+	5.95126i	0.882893	+	0.259241i
$528$		0			0
$529$	−11.9252	+	19.6670i	−0.518488	+	0.855085i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−25.3609	−	16.2985i	−1.09850	−	0.705965i
$534$		0			0
$535$	0.299536	−	0.192500i	0.0129501	−	0.00832251i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.18584	−	6.97603i	0.137224	−	0.300479i
$540$		0			0
$541$	30.5324	−	8.96512i	1.31269	−	0.385441i	0.450841	−	0.892604i	$-0.351124\pi$
$541$	30.5324	−	8.96512i	1.31269	−	0.385441i	0.861850	+	0.507163i	$0.169306\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.51395	−	16.4533i	−0.321862	−	0.704780i
$546$		0			0
$547$	−5.24592	+	36.4862i	−0.224299	+	1.56004i	0.497209	+	0.867631i	$0.334358\pi$
$547$	−5.24592	+	36.4862i	−0.224299	+	1.56004i	−0.721508	+	0.692406i	$0.756551\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	11.0586			0.471111
$552$		0			0
$553$	11.6109			0.493744
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.83552	−	33.6318i	0.204888	−	1.42503i	−0.584631	−	0.811299i	$-0.698761\pi$
$557$	4.83552	−	33.6318i	0.204888	−	1.42503i	0.789519	−	0.613726i	$-0.210330\pi$
$558$		0			0
$559$	5.04153	+	11.0394i	0.213234	+	0.466917i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.9632	+	5.27448i	−0.757059	+	0.222293i	−0.637411	−	0.770524i	$-0.719995\pi$
$563$	−17.9632	+	5.27448i	−0.757059	+	0.222293i	−0.119648	+	0.992816i	$0.538177\pi$
$564$		0			0
$565$	5.05689	−	11.0730i	0.212745	−	0.465846i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−26.3796	+	16.9531i	−1.10589	+	0.710712i	−0.960394	−	0.278647i	$-0.910114\pi$
$569$	−26.3796	+	16.9531i	−1.10589	+	0.710712i	−0.145495	+	0.989359i	$0.546478\pi$
$570$		0			0
$571$	6.29897	+	4.04810i	0.263604	+	0.169408i	0.665766	−	0.746161i	$-0.268105\pi$
$571$	6.29897	+	4.04810i	0.263604	+	0.169408i	−0.402162	+	0.915568i	$0.631741\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.88647	−	12.4819i	−0.120374	−	0.520530i
$576$		0			0
$577$	39.5545	+	11.6142i	1.64668	+	0.483508i	0.968004	−	0.250935i	$-0.0807379\pi$
$577$	39.5545	+	11.6142i	1.64668	+	0.483508i	0.678671	+	0.734442i	$0.262556\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	17.1419	−	11.0164i	0.711165	−	0.457038i
$582$		0			0
$583$	−2.04539	−	2.36050i	−0.0847113	−	0.0977620i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.3002	−	3.90530i	0.548959	−	0.161189i	0.00452086	−	0.999990i	$-0.498561\pi$
$587$	13.3002	−	3.90530i	0.548959	−	0.161189i	0.544438	+	0.838801i	$0.316743\pi$
$588$		0			0
$589$	4.02138	+	27.9693i	0.165698	+	1.15246i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.08436	+	14.4970i	−0.0855943	+	0.595321i	0.901207	+	0.433388i	$0.142682\pi$
$593$	−2.08436	+	14.4970i	−0.0855943	+	0.595321i	−0.986802	+	0.161933i	$0.948227\pi$
$594$		0			0
$595$	−11.6221	+	13.4127i	−0.476461	+	0.549865i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	25.6306			1.04724			0.523618	−	0.851953i	$-0.324582\pi$
$599$	25.6306			1.04724			0.523618	+	0.851953i	$0.324582\pi$
$600$		0			0
$601$	10.9786	−	12.6700i	0.447826	−	0.516819i	−0.486286	−	0.873800i	$-0.661649\pi$
$601$	10.9786	−	12.6700i	0.447826	−	0.516819i	0.934112	+	0.356981i	$0.116194\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.22198	−	13.6242i	−0.252960	−	0.553904i
$606$		0			0
$607$	−1.47889	−	10.2859i	−0.0600263	−	0.417492i	−0.997573	−	0.0696320i	$-0.977818\pi$
$607$	−1.47889	−	10.2859i	−0.0600263	−	0.417492i	0.937546	−	0.347860i	$-0.113092\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.97425	−	4.32300i	0.0798695	−	0.174890i
$612$		0			0
$613$	−14.6036	−	16.8534i	−0.589833	−	0.680704i	0.379856	−	0.925046i	$-0.375974\pi$
$613$	−14.6036	−	16.8534i	−0.589833	−	0.680704i	−0.969689	+	0.244342i	$0.921428\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.96316	+	6.40294i	0.401102	+	0.257773i	0.725604	−	0.688112i	$-0.241560\pi$
$617$	9.96316	+	6.40294i	0.401102	+	0.257773i	−0.324502	+	0.945885i	$0.605197\pi$
$618$		0			0
$619$	36.4170	+	10.6930i	1.46372	+	0.429788i	0.914054	−	0.405593i	$-0.132935\pi$
$619$	36.4170	+	10.6930i	1.46372	+	0.429788i	0.549671	+	0.835381i	$0.314753\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	54.1658	+	15.9045i	2.17011	+	0.637201i
$624$		0			0
$625$	−3.79177	−	2.43682i	−0.151671	−	0.0974729i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	13.9018	+	16.0435i	0.554302	+	0.639698i
$630$		0			0
$631$	−3.01905	+	6.61079i	−0.120186	+	0.263171i	−0.960157	−	0.279460i	$-0.909845\pi$
$631$	−3.01905	+	6.61079i	−0.120186	+	0.263171i	0.839971	+	0.542631i	$0.182572\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.23009	+	15.5106i	0.0884984	+	0.615520i
$636$		0			0
$637$	8.86263	+	19.4064i	0.351150	+	0.768911i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.1302	−	19.7693i	0.676601	−	0.780840i	−0.308793	−	0.951129i	$-0.599925\pi$
$641$	17.1302	−	19.7693i	0.676601	−	0.780840i	0.985394	+	0.170290i	$0.0544703\pi$
$642$		0			0
$643$	−33.0605			−1.30378			−0.651889	−	0.758314i	$-0.726023\pi$
$643$	−33.0605			−1.30378			−0.651889	+	0.758314i	$0.726023\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.6327	−	18.0411i	0.614586	−	0.709271i	−0.360083	−	0.932920i	$-0.617252\pi$
$647$	15.6327	−	18.0411i	0.614586	−	0.709271i	0.974670	+	0.223650i	$0.0717971\pi$
$648$		0			0
$649$	−2.28117	+	15.8659i	−0.0895438	+	0.622791i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.83034	−	40.5509i	−0.228159	−	1.58688i	−0.705857	−	0.708354i	$-0.749438\pi$
$653$	−5.83034	−	40.5509i	−0.228159	−	1.58688i	0.477698	−	0.878524i	$-0.341471\pi$
$654$		0			0
$655$	−29.8603	+	8.76777i	−1.16674	+	0.342585i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.59931	−	4.15383i	−0.140209	−	0.161810i	0.681302	−	0.732003i	$-0.261414\pi$
$659$	−3.59931	−	4.15383i	−0.140209	−	0.161810i	−0.821511	+	0.570192i	$0.806869\pi$
$660$		0			0
$661$	17.4827	−	11.2354i	0.679997	−	0.437007i	−0.154520	−	0.987990i	$-0.549383\pi$
$661$	17.4827	−	11.2354i	0.679997	−	0.437007i	0.834517	+	0.550982i	$0.185747\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−22.7789	−	6.68848i	−0.883326	−	0.259368i
$666$		0			0
$667$	11.2921	+	5.97588i	0.437232	+	0.231387i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.79410	−	3.08098i	−0.185074	−	0.118940i
$672$		0			0
$673$	−9.76169	+	6.27346i	−0.376285	+	0.241824i	−0.715089	−	0.699033i	$-0.753614\pi$
$673$	−9.76169	+	6.27346i	−0.376285	+	0.241824i	0.338804	+	0.940857i	$0.389978\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.65441	+	8.00205i	−0.140450	+	0.307544i	−0.966766	−	0.255664i	$-0.917706\pi$
$677$	−3.65441	+	8.00205i	−0.140450	+	0.307544i	0.826315	+	0.563208i	$0.190433\pi$
$678$		0			0
$679$	−13.7991	+	4.05179i	−0.529562	+	0.155494i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	11.9782	+	26.2287i	0.458334	+	1.00361i	0.987864	+	0.155320i	$0.0496410\pi$
$683$	11.9782	+	26.2287i	0.458334	+	1.00361i	−0.529530	+	0.848291i	$0.677632\pi$
$684$		0			0
$685$	2.12348	−	14.7691i	0.0811340	−	0.564299i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	8.68889			0.331020
$690$		0			0
$691$	9.54501			0.363109			0.181555	−	0.983381i	$-0.441887\pi$
$691$	9.54501			0.363109			0.181555	+	0.983381i	$0.441887\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.745798	−	5.18714i	0.0282897	−	0.196759i
$696$		0			0
$697$	12.8338	+	28.1020i	0.486114	+	1.06444i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.3490	−	3.03875i	0.390878	−	0.114772i	−0.0803874	−	0.996764i	$-0.525616\pi$
$701$	10.3490	−	3.03875i	0.390878	−	0.114772i	0.471265	+	0.881992i	$0.343798\pi$
$702$		0			0
$703$	−11.7966	+	25.8310i	−0.444919	+	0.974236i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−23.3757	+	15.0226i	−0.879132	+	0.564984i
$708$		0			0
$709$	5.71727	+	3.67427i	0.214717	+	0.137990i	0.643579	−	0.765380i	$-0.277449\pi$
$709$	5.71727	+	3.67427i	0.214717	+	0.137990i	−0.428862	+	0.903370i	$0.641085\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−11.0079	+	30.7331i	−0.412249	+	1.15096i
$714$		0			0
$715$	−4.82644	−	1.41717i	−0.180498	−	0.0529991i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−31.3385	+	20.1400i	−1.16873	+	0.751097i	−0.973281	−	0.229617i	$-0.926253\pi$
$719$	−31.3385	+	20.1400i	−1.16873	+	0.751097i	−0.195448	+	0.980714i	$0.562616\pi$
$720$		0			0
$721$	−32.5510	−	37.5659i	−1.21226	−	1.39903i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.82805	+	2.00490i	−0.253587	+	0.0744600i
$726$		0			0
$727$	6.56541	+	45.6634i	0.243498	+	1.69356i	0.634299	+	0.773088i	$0.281289\pi$
$727$	6.56541	+	45.6634i	0.243498	+	1.69356i	−0.390801	+	0.920475i	$0.627802\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.76996	−	12.3104i	0.0654645	−	0.455316i
$732$		0			0
$733$	22.8021	−	26.3150i	0.842214	−	0.971967i	−0.157665	−	0.987493i	$-0.550397\pi$
$733$	22.8021	−	26.3150i	0.842214	−	0.971967i	0.999879	+	0.0155256i	$0.00494217\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.04360			−0.185783
$738$		0			0
$739$	13.8178	−	15.9466i	0.508295	−	0.586604i	−0.442366	−	0.896834i	$-0.645861\pi$
$739$	13.8178	−	15.9466i	0.508295	−	0.586604i	0.950661	+	0.310231i	$0.100406\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.7483	−	25.7253i	−0.431005	−	0.943769i	−0.993163	−	0.116739i	$-0.962756\pi$
$743$	−11.7483	−	25.7253i	−0.431005	−	0.943769i	0.562158	−	0.827030i	$-0.309971\pi$
$744$		0			0
$745$	4.42577	+	30.7819i	0.162148	+	1.12776i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.363258	+	0.795425i	−0.0132732	+	0.0290642i
$750$		0			0
$751$	2.79296	+	3.22325i	0.101917	+	0.117618i	0.804416	−	0.594066i	$-0.202478\pi$
$751$	2.79296	+	3.22325i	0.101917	+	0.117618i	−0.702500	+	0.711684i	$0.747933\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	17.9741	+	11.5512i	0.654143	+	0.420392i
$756$		0			0
$757$	−35.9380	−	10.5523i	−1.30619	−	0.383531i	−0.446698	−	0.894685i	$-0.647400\pi$
$757$	−35.9380	−	10.5523i	−1.30619	−	0.383531i	−0.859489	+	0.511154i	$0.829218\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	40.8916	+	12.0068i	1.48232	+	0.435248i	0.920081	−	0.391728i	$-0.128123\pi$
$761$	40.8916	+	12.0068i	1.48232	+	0.435248i	0.562237	+	0.826976i	$0.309941\pi$
$762$		0			0
$763$	37.3701	+	24.0163i	1.35289	+	0.869449i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−29.2008	−	33.6995i	−1.05438	−	1.21682i
$768$		0			0
$769$	−7.88108	+	17.2572i	−0.284199	+	0.622309i	−0.996859	−	0.0792007i	$-0.974763\pi$
$769$	−7.88108	+	17.2572i	−0.284199	+	0.622309i	0.712660	+	0.701510i	$0.247490\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.52233	+	52.3190i	0.270559	+	1.88178i	0.442640	+	0.896699i	$0.354042\pi$
$773$	7.52233	+	52.3190i	0.270559	+	1.88178i	−0.172081	+	0.985083i	$0.555049\pi$
$774$		0			0
$775$	−7.55377	−	16.5404i	−0.271339	−	0.594150i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−27.0629	+	31.2323i	−0.969629	+	1.11901i
$780$		0			0
$781$	16.5953			0.593826
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−17.9943	+	20.7665i	−0.642243	+	0.741188i
$786$		0			0
$787$	−3.90826	+	27.1825i	−0.139314	+	0.968952i	0.793494	+	0.608578i	$0.208260\pi$
$787$	−3.90826	+	27.1825i	−0.139314	+	0.968952i	−0.932808	+	0.360374i	$0.882649\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.25464	+	29.5917i	0.151278	+	1.05216i
$792$		0			0
$793$	15.2111	−	4.46637i	0.540161	−	0.158606i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	25.1457	+	29.0197i	0.890706	+	1.02793i	0.999427	+	0.0338575i	$0.0107792\pi$
$797$	25.1457	+	29.0197i	0.890706	+	1.02793i	−0.108720	+	0.994072i	$0.534675\pi$
$798$		0			0
$799$	−4.09714	+	2.63307i	−0.144946	+	0.0931514i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.36063	−	0.986770i	−0.118594	−	0.0348223i
$804$		0			0
$805$	−19.6456	−	19.1391i	−0.692415	−	0.674564i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−10.5055	−	6.75147i	−0.369354	−	0.237369i	0.342776	−	0.939417i	$-0.388633\pi$
$809$	−10.5055	−	6.75147i	−0.369354	−	0.237369i	−0.712130	+	0.702048i	$0.752269\pi$
$810$		0			0
$811$	14.8611	−	9.55067i	0.521845	−	0.335369i	−0.253057	−	0.967451i	$-0.581436\pi$
$811$	14.8611	−	9.55067i	0.521845	−	0.335369i	0.774901	+	0.632082i	$0.217800\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.13976	+	15.6339i	−0.250095	+	0.547631i
$816$		0			0
$817$	15.9628	−	4.68711i	0.558468	−	0.163981i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.49865	+	12.0404i	0.191904	+	0.420211i	0.980987	−	0.194076i	$-0.0621708\pi$
$821$	5.49865	+	12.0404i	0.191904	+	0.420211i	−0.789082	+	0.614287i	$0.789444\pi$
$822$		0			0
$823$	5.67981	−	39.5039i	0.197986	−	1.37702i	−0.612133	−	0.790755i	$-0.709688\pi$
$823$	5.67981	−	39.5039i	0.197986	−	1.37702i	0.810119	−	0.586266i	$-0.199402\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.108053			0.00375736			0.00187868	−	0.999998i	$-0.499402\pi$
$827$	0.108053			0.00375736			0.00187868	+	0.999998i	$0.499402\pi$
$828$		0			0
$829$	50.3641			1.74922			0.874608	−	0.484830i	$-0.161119\pi$
$829$	50.3641			1.74922			0.874608	+	0.484830i	$0.161119\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.11146	−	21.6407i	0.107806	−	0.749806i
$834$		0			0
$835$	−11.8018	−	25.8424i	−0.408420	−	0.894314i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.69755	−	1.08570i	0.127653	−	0.0374824i	−0.217282	−	0.976109i	$-0.569719\pi$
$839$	3.69755	−	1.08570i	0.127653	−	0.0374824i	0.344935	+	0.938626i	$0.387901\pi$
$840$		0			0
$841$	−9.09898	+	19.9240i	−0.313758	+	0.687034i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.91677	+	3.15981i	−0.169142	+	0.108701i
$846$		0			0
$847$	30.9446	+	19.8869i	1.06327	+	0.683321i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−26.0045	+	20.0018i	−0.891421	+	0.685654i
$852$		0			0
$853$	0.492793	+	0.144697i	0.0168729	+	0.00495433i	0.290158	−	0.956979i	$-0.406292\pi$
$853$	0.492793	+	0.144697i	0.0168729	+	0.00495433i	−0.273285	+	0.961933i	$0.588110\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−32.7260	+	21.0317i	−1.11790	+	0.718431i	−0.963001	−	0.269500i	$-0.913142\pi$
$857$	−32.7260	+	21.0317i	−1.11790	+	0.718431i	−0.154899	+	0.987930i	$0.549505\pi$
$858$		0			0
$859$	31.2989	+	36.1208i	1.06790	+	1.23243i	0.971489	+	0.237085i	$0.0761921\pi$
$859$	31.2989	+	36.1208i	1.06790	+	1.23243i	0.0964148	+	0.995341i	$0.469262\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.32726	−	2.15148i	0.249423	−	0.0732371i	−0.154631	−	0.987972i	$-0.549419\pi$
$863$	7.32726	−	2.15148i	0.249423	−	0.0732371i	0.404054	+	0.914735i	$0.367601\pi$
$864$		0			0
$865$	2.51985	+	17.5259i	0.0856774	+	0.595900i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.479951	−	3.33813i	0.0162812	−	0.113238i
$870$		0			0
$871$	9.18813	−	10.6037i	0.311328	−	0.359292i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	43.8722			1.48315
$876$		0			0
$877$	1.60997	−	1.85800i	0.0543648	−	0.0627403i	−0.727916	−	0.685667i	$-0.759511\pi$
$877$	1.60997	−	1.85800i	0.0543648	−	0.0627403i	0.782281	+	0.622926i	$0.214056\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.71552	−	5.94616i	−0.0914881	−	0.200331i	0.858356	−	0.513054i	$-0.171486\pi$
$881$	−2.71552	−	5.94616i	−0.0914881	−	0.200331i	−0.949844	+	0.312723i	$0.898759\pi$
$882$		0			0
$883$	4.62567	+	32.1722i	0.155666	+	1.08268i	0.906505	+	0.422196i	$0.138741\pi$
$883$	4.62567	+	32.1722i	0.155666	+	1.08268i	−0.750839	+	0.660486i	$0.770350\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.92245	+	12.9684i	−0.198856	+	0.435435i	−0.982621	−	0.185623i	$-0.940570\pi$
$887$	−5.92245	+	12.9684i	−0.198856	+	0.435435i	0.783765	+	0.621058i	$0.213297\pi$
$888$		0			0
$889$	−25.2018	−	29.0845i	−0.845242	−	0.975461i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.48068	−	3.52222i	−0.183404	−	0.117866i
$894$		0			0
$895$	17.1282	+	5.02930i	0.572533	+	0.168111i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	17.3989	+	5.10877i	0.580285	+	0.170387i
$900$		0			0
$901$	−7.49075	−	4.81401i	−0.249553	−	0.160378i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.9001	+	17.1957i	0.495297	+	0.571603i
$906$		0			0
$907$	11.5242	−	25.2345i	0.382655	−	0.837897i	−0.616084	−	0.787681i	$-0.711282\pi$
$907$	11.5242	−	25.2345i	0.382655	−	0.837897i	0.998738	−	0.0502161i	$-0.0159910\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.42768	−	16.8849i	−0.0804325	−	0.559421i	−0.989694	−	0.143196i	$-0.954262\pi$
$911$	−2.42768	−	16.8849i	−0.0804325	−	0.559421i	0.909262	−	0.416225i	$-0.136647\pi$
$912$		0			0
$913$	−2.45865	−	5.38368i	−0.0813693	−	0.178174i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	50.0509	−	57.7618i	1.65283	−	1.90746i
$918$		0			0
$919$	−32.9304			−1.08627			−0.543137	−	0.839644i	$-0.682764\pi$
$919$	−32.9304			−1.08627			−0.543137	+	0.839644i	$0.682764\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−30.2323	+	34.8899i	−0.995109	+	1.14842i
$924$		0			0
$925$	2.60065	−	18.0879i	0.0855089	−	0.594728i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.97550	−	55.4708i	−0.261668	−	1.81994i	−0.520323	−	0.853970i	$-0.674188\pi$
$929$	−7.97550	−	55.4708i	−0.261668	−	1.81994i	0.258655	−	0.965970i	$-0.416721\pi$
$930$		0			0
$931$	28.0614	−	8.23958i	0.919676	−	0.270041i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.37573	+	3.89580i	0.110398	+	0.127406i
$936$		0			0
$937$	−14.4897	+	9.31194i	−0.473357	+	0.304208i	−0.755482	−	0.655170i	$-0.772597\pi$
$937$	−14.4897	+	9.31194i	−0.473357	+	0.304208i	0.282125	+	0.959378i	$0.408961\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	16.9149	+	4.96666i	0.551410	+	0.161909i	0.545556	−	0.838074i	$-0.316318\pi$
$941$	16.9149	+	4.96666i	0.551410	+	0.161909i	0.00585385	+	0.999983i	$0.498137\pi$
$942$		0			0
$943$	−44.5119	+	17.2675i	−1.44951	+	0.562306i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−17.4410	−	11.2087i	−0.566758	−	0.364233i	0.225665	−	0.974205i	$-0.427544\pi$
$947$	−17.4410	−	11.2087i	−0.566758	−	0.364233i	−0.792423	+	0.609972i	$0.791181\pi$
$948$		0			0
$949$	8.19678	−	5.26775i	0.266079	−	0.170999i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	5.80162	−	12.7038i	0.187933	−	0.411515i	−0.792089	−	0.610406i	$-0.791006\pi$
$953$	5.80162	−	12.7038i	0.187933	−	0.411515i	0.980022	+	0.198890i	$0.0637337\pi$
$954$		0			0
$955$	13.1353	−	3.85687i	0.425048	−	0.124805i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	15.2227	+	33.3330i	0.491566	+	1.07638i
$960$		0			0
$961$	−2.18235	+	15.1786i	−0.0703983	+	0.489631i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−34.0974			−1.09763
$966$		0			0
$967$	18.2603			0.587212			0.293606	−	0.955926i	$-0.405145\pi$
$967$	18.2603			0.587212			0.293606	+	0.955926i	$0.405145\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.49342	+	10.3869i	−0.0479260	+	0.333332i	0.951726	+	0.306949i	$0.0993081\pi$
$971$	−1.49342	+	10.3869i	−0.0479260	+	0.333332i	−0.999652	+	0.0263833i	$0.991601\pi$
$972$		0			0
$973$	5.34644	+	11.7071i	0.171399	+	0.375311i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	28.2385	−	8.29157i	0.903429	−	0.265271i	0.203157	−	0.979146i	$-0.434880\pi$
$977$	28.2385	−	8.29157i	0.903429	−	0.265271i	0.700273	+	0.713875i	$0.253062\pi$
$978$		0			0
$979$	6.81158	−	14.9153i	0.217699	−	0.476694i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	16.1940	−	10.4073i	0.516509	−	0.331940i	−0.256281	−	0.966602i	$-0.582497\pi$
$983$	16.1940	−	10.4073i	0.516509	−	0.331940i	0.772789	+	0.634662i	$0.218861\pi$
$984$		0			0
$985$	−6.57735	−	4.22700i	−0.209572	−	0.134684i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	18.8328	+	3.83997i	0.598847	+	0.122104i
$990$		0			0
$991$	−48.0664	−	14.1136i	−1.52688	−	0.448332i	−0.592786	−	0.805360i	$-0.701972\pi$
$991$	−48.0664	−	14.1136i	−1.52688	−	0.448332i	−0.934094	+	0.357027i	$0.883790\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−34.1295	+	21.9337i	−1.08198	+	0.695345i
$996$		0			0
$997$	23.8904	+	27.5710i	0.756618	+	0.873184i	0.995192	−	0.0979406i	$-0.0312255\pi$
$997$	23.8904	+	27.5710i	0.756618	+	0.873184i	−0.238574	+	0.971124i	$0.576680\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.q.c.685.1		20
3.2	odd	2		276.2.i.a.133.2	✓	20
23.9	even	11	inner	828.2.q.c.469.1		20
69.20	even	22		6348.2.a.t.1.7		10
69.26	odd	22		6348.2.a.s.1.4		10
69.32	odd	22		276.2.i.a.193.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.133.2	✓	20	3.2	odd	2
276.2.i.a.193.2	yes	20	69.32	odd	22
828.2.q.c.469.1		20	23.9	even	11	inner
828.2.q.c.685.1		20	1.1	even	1	trivial
6348.2.a.s.1.4		10	69.26	odd	22
6348.2.a.t.1.7		10	69.20	even	22

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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:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.217172 + 1.51046i) q^{5} +(-1.55685 - 3.40903i) q^{7} +O(q^{10})\)	\(q+(-0.217172 + 1.51046i) q^{5} +(-1.55685 - 3.40903i) q^{7} +(-1.04445 + 0.306679i) q^{11} +(1.25796 - 2.75455i) q^{13} +(-2.61063 + 1.67775i) q^{17} +(-3.49220 - 2.24430i) q^{19} +(-2.35317 - 4.17883i) q^{23} +(2.56313 + 0.752602i) q^{25} +(-2.24106 + 1.44024i) q^{29} +(-4.45761 - 5.14435i) q^{31} +(5.48731 - 1.61122i) q^{35} +(-0.973540 - 6.77112i) q^{37} +(1.41678 - 9.85394i) q^{41} +(-2.62449 + 3.02882i) q^{43} +1.56940 q^{47} +(-4.61365 + 5.32444i) q^{49} +(1.19196 + 2.61003i) q^{53} +(-0.236402 - 1.64421i) q^{55} +(6.11707 - 13.3945i) q^{59} +(3.42833 + 3.95650i) q^{61} +(3.88745 + 2.49831i) q^{65} +(4.44565 + 1.30536i) q^{67} +(-14.6278 - 4.29512i) q^{71} +(2.70682 + 1.73957i) q^{73} +(2.67153 + 3.08311i) q^{77} +(-1.28701 + 2.81816i) q^{79} +(0.773779 + 5.38175i) q^{83} +(-1.96723 - 4.30763i) q^{85} +(-9.86433 + 11.3840i) q^{89} -11.3488 q^{91} +(4.14834 - 4.78744i) q^{95} +(0.546130 - 3.79842i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{5}+O(q^{10}) \) 20 * q + 4 * q^5	\( 20 q + 4 q^{5} - 22 q^{13} - 7 q^{17} + 19 q^{19} - 20 q^{23} + 20 q^{25} - 32 q^{29} - 3 q^{31} + 26 q^{35} - 10 q^{37} + 40 q^{41} + 8 q^{43} + 18 q^{47} - 34 q^{49} + 34 q^{53} - 17 q^{55} + 32 q^{59} + 32 q^{61} - 49 q^{65} + 35 q^{67} - 33 q^{71} - q^{73} + 50 q^{77} + 22 q^{79} + 14 q^{83} - 9 q^{85} - 10 q^{89} - 72 q^{91} + 51 q^{95} - 4 q^{97}+O(q^{100}) \) 20 * q + 4 * q^5 - 22 * q^13 - 7 * q^17 + 19 * q^19 - 20 * q^23 + 20 * q^25 - 32 * q^29 - 3 * q^31 + 26 * q^35 - 10 * q^37 + 40 * q^41 + 8 * q^43 + 18 * q^47 - 34 * q^49 + 34 * q^53 - 17 * q^55 + 32 * q^59 + 32 * q^61 - 49 * q^65 + 35 * q^67 - 33 * q^71 - q^73 + 50 * q^77 + 22 * q^79 + 14 * q^83 - 9 * q^85 - 10 * q^89 - 72 * q^91 + 51 * q^95 - 4 * q^97

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