LMFDB - Embedded newform 675.2.e.d.451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(226,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("675.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.e (of order $3$, degree $2$, not 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	675.451
Dual form			675.2.e.d.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.448288i) q^{2} +(0.866025 + 1.50000i) q^{4} +(-1.67303 + 2.89778i) q^{7} -1.93185 q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.448288i) q^{2} +(0.866025 + 1.50000i) q^{4} +(-1.67303 + 2.89778i) q^{7} -1.93185 q^{8} +(0.633975 - 1.09808i) q^{11} +(1.22474 + 2.12132i) q^{13} +(-0.866025 - 1.50000i) q^{14} +(-1.23205 + 2.13397i) q^{16} -5.27792 q^{17} -0.732051 q^{19} +(0.328169 + 0.568406i) q^{22} +(0.258819 + 0.448288i) q^{23} -1.26795 q^{26} -5.79555 q^{28} +(-0.232051 + 0.401924i) q^{29} +(-0.366025 - 0.633975i) q^{31} +(-2.56961 - 4.45069i) q^{32} +(1.36603 - 2.36603i) q^{34} -4.24264 q^{37} +(0.189469 - 0.328169i) q^{38} +(3.86603 + 6.69615i) q^{41} +(0.328169 - 0.568406i) q^{43} +2.19615 q^{44} -0.267949 q^{46} +(-1.48356 + 2.56961i) q^{47} +(-2.09808 - 3.63397i) q^{49} +(-2.12132 + 3.67423i) q^{52} +1.03528 q^{53} +(3.23205 - 5.59808i) q^{56} +(-0.120118 - 0.208051i) q^{58} +(4.73205 + 8.19615i) q^{59} +(3.33013 - 5.76795i) q^{61} +0.378937 q^{62} -2.26795 q^{64} +(3.79435 + 6.57201i) q^{67} +(-4.57081 - 7.91688i) q^{68} -14.1962 q^{71} +8.48528 q^{73} +(1.09808 - 1.90192i) q^{74} +(-0.633975 - 1.09808i) q^{76} +(2.12132 + 3.67423i) q^{77} +(-3.73205 + 6.46410i) q^{79} -4.00240 q^{82} +(-3.98382 + 6.90018i) q^{83} +(0.169873 + 0.294229i) q^{86} +(-1.22474 + 2.12132i) q^{88} -13.3923 q^{89} -8.19615 q^{91} +(-0.448288 + 0.776457i) q^{92} +(-0.767949 - 1.33013i) q^{94} +(7.58871 - 13.1440i) q^{97} +2.17209 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 12 q^{11} + 4 q^{16} + 8 q^{19} - 24 q^{26} + 12 q^{29} + 4 q^{31} + 4 q^{34} + 24 q^{41} - 24 q^{44} - 16 q^{46} + 4 q^{49} + 12 q^{56} + 24 q^{59} - 8 q^{61} - 32 q^{64} - 72 q^{71} - 12 q^{74} - 12 q^{76} - 16 q^{79} + 36 q^{86} - 24 q^{89} - 24 q^{91} - 20 q^{94}+O(q^{100}) $ 8 * q + 12 * q^11 + 4 * q^16 + 8 * q^19 - 24 * q^26 + 12 * q^29 + 4 * q^31 + 4 * q^34 + 24 * q^41 - 24 * q^44 - 16 * q^46 + 4 * q^49 + 12 * q^56 + 24 * q^59 - 8 * q^61 - 32 * q^64 - 72 * q^71 - 12 * q^74 - 12 * q^76 - 16 * q^79 + 36 * q^86 - 24 * q^89 - 24 * q^91 - 20 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.258819	+	0.448288i	−0.183013	+	0.316987i	−0.942905	−	0.333062i	$-0.891918\pi$
$2$	−0.258819	+	0.448288i	−0.183013	+	0.316987i	0.759892	+	0.650049i	$0.225252\pi$
$3$		0			0
$3$		0			0
$4$	0.866025	+	1.50000i	0.433013	+	0.750000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.67303	+	2.89778i	−0.632347	+	1.09526i	0.354724	+	0.934971i	$0.384575\pi$
$7$	−1.67303	+	2.89778i	−0.632347	+	1.09526i	−0.987071	+	0.160286i	$0.948758\pi$
$8$	−1.93185			−0.683013
$9$		0			0
$10$		0			0
$11$	0.633975	−	1.09808i	0.191151	−	0.331082i	−0.754481	−	0.656322i	$-0.772111\pi$
$11$	0.633975	−	1.09808i	0.191151	−	0.331082i	0.945632	+	0.325239i	$0.105445\pi$
$12$		0			0
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	0.984373	−	0.176096i	$-0.0563468\pi$
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	−0.644690	+	0.764444i	$0.723014\pi$
$14$	−0.866025	−	1.50000i	−0.231455	−	0.400892i
$15$		0			0
$16$	−1.23205	+	2.13397i	−0.308013	+	0.533494i
$17$	−5.27792			−1.28008			−0.640041	−	0.768340i	$-0.721083\pi$
$17$	−5.27792			−1.28008			−0.640041	+	0.768340i	$0.721083\pi$
$18$		0			0
$19$	−0.732051			−0.167944			−0.0839720	−	0.996468i	$-0.526761\pi$
$19$	−0.732051			−0.167944			−0.0839720	+	0.996468i	$0.526761\pi$
$20$		0			0
$21$		0			0
$22$	0.328169	+	0.568406i	0.0699660	+	0.121185i
$23$	0.258819	+	0.448288i	0.0539675	+	0.0934745i	0.891747	−	0.452534i	$-0.149480\pi$
$23$	0.258819	+	0.448288i	0.0539675	+	0.0934745i	−0.837780	+	0.546009i	$0.816147\pi$
$24$		0			0
$25$		0			0
$26$	−1.26795			−0.248665
$27$		0			0
$28$	−5.79555			−1.09526
$29$	−0.232051	+	0.401924i	−0.0430908	+	0.0746354i	−0.886766	−	0.462218i	$-0.847054\pi$
$29$	−0.232051	+	0.401924i	−0.0430908	+	0.0746354i	0.843676	+	0.536853i	$0.180387\pi$
$30$		0			0
$31$	−0.366025	−	0.633975i	−0.0657401	−	0.113865i	0.831282	−	0.555851i	$-0.187607\pi$
$31$	−0.366025	−	0.633975i	−0.0657401	−	0.113865i	−0.897022	+	0.441986i	$0.854274\pi$
$32$	−2.56961	−	4.45069i	−0.454247	−	0.786779i
$33$		0			0
$34$	1.36603	−	2.36603i	0.234271	−	0.405770i
$35$		0			0
$36$		0			0
$37$	−4.24264			−0.697486			−0.348743	−	0.937218i	$-0.613391\pi$
$37$	−4.24264			−0.697486			−0.348743	+	0.937218i	$0.613391\pi$
$38$	0.189469	−	0.328169i	0.0307359	−	0.0532361i
$39$		0			0
$40$		0			0
$41$	3.86603	+	6.69615i	0.603772	+	1.04576i	0.992244	+	0.124303i	$0.0396695\pi$
$41$	3.86603	+	6.69615i	0.603772	+	1.04576i	−0.388473	+	0.921460i	$0.626997\pi$
$42$		0			0
$43$	0.328169	−	0.568406i	0.0500454	−	0.0866811i	−0.839918	−	0.542714i	$-0.817397\pi$
$43$	0.328169	−	0.568406i	0.0500454	−	0.0866811i	0.889963	+	0.456033i	$0.150730\pi$
$44$	2.19615			0.331082
$45$		0			0
$46$	−0.267949			−0.0395070
$47$	−1.48356	+	2.56961i	−0.216400	+	0.374816i	−0.953705	−	0.300744i	$-0.902765\pi$
$47$	−1.48356	+	2.56961i	−0.216400	+	0.374816i	0.737305	+	0.675560i	$0.236098\pi$
$48$		0			0
$49$	−2.09808	−	3.63397i	−0.299725	−	0.519139i
$50$		0			0
$51$		0			0
$52$	−2.12132	+	3.67423i	−0.294174	+	0.509525i
$53$	1.03528			0.142206			0.0711031	−	0.997469i	$-0.477348\pi$
$53$	1.03528			0.142206			0.0711031	+	0.997469i	$0.477348\pi$
$54$		0			0
$55$		0			0
$56$	3.23205	−	5.59808i	0.431901	−	0.748074i
$57$		0			0
$58$	−0.120118	−	0.208051i	−0.0157723	−	0.0273184i
$59$	4.73205	+	8.19615i	0.616061	+	1.06705i	0.990197	+	0.139675i	$0.0446057\pi$
$59$	4.73205	+	8.19615i	0.616061	+	1.06705i	−0.374137	+	0.927373i	$0.622061\pi$
$60$		0			0
$61$	3.33013	−	5.76795i	0.426379	−	0.738510i	−0.570169	−	0.821527i	$-0.693122\pi$
$61$	3.33013	−	5.76795i	0.426379	−	0.738510i	0.996548	+	0.0830172i	$0.0264556\pi$
$62$	0.378937			0.0481251
$63$		0			0
$64$	−2.26795			−0.283494
$65$		0			0
$66$		0			0
$67$	3.79435	+	6.57201i	0.463554	+	0.802899i	0.999135	−	0.0415848i	$-0.0132407\pi$
$67$	3.79435	+	6.57201i	0.463554	+	0.802899i	−0.535581	+	0.844484i	$0.679907\pi$
$68$	−4.57081	−	7.91688i	−0.554292	−	0.960062i
$69$		0			0
$70$		0			0
$71$	−14.1962			−1.68477			−0.842387	−	0.538874i	$-0.818850\pi$
$71$	−14.1962			−1.68477			−0.842387	+	0.538874i	$0.818850\pi$
$72$		0			0
$73$	8.48528			0.993127			0.496564	−	0.868000i	$-0.334595\pi$
$73$	8.48528			0.993127			0.496564	+	0.868000i	$0.334595\pi$
$74$	1.09808	−	1.90192i	0.127649	−	0.221094i
$75$		0			0
$76$	−0.633975	−	1.09808i	−0.0727219	−	0.125958i
$77$	2.12132	+	3.67423i	0.241747	+	0.418718i
$78$		0			0
$79$	−3.73205	+	6.46410i	−0.419889	+	0.727268i	−0.995928	−	0.0901537i	$-0.971264\pi$
$79$	−3.73205	+	6.46410i	−0.419889	+	0.727268i	0.576039	+	0.817422i	$0.304597\pi$
$80$		0			0
$81$		0			0
$82$	−4.00240			−0.441992
$83$	−3.98382	+	6.90018i	−0.437281	+	0.757393i	−0.997479	−	0.0709657i	$-0.977392\pi$
$83$	−3.98382	+	6.90018i	−0.437281	+	0.757393i	0.560198	+	0.828359i	$0.310725\pi$
$84$		0			0
$85$		0			0
$86$	0.169873	+	0.294229i	0.0183179	+	0.0317275i
$87$		0			0
$88$	−1.22474	+	2.12132i	−0.130558	+	0.226134i
$89$	−13.3923			−1.41958			−0.709791	−	0.704413i	$-0.751211\pi$
$89$	−13.3923			−1.41958			−0.709791	+	0.704413i	$0.751211\pi$
$90$		0			0
$91$	−8.19615			−0.859190
$92$	−0.448288	+	0.776457i	−0.0467372	+	0.0809513i
$93$		0			0
$94$	−0.767949	−	1.33013i	−0.0792079	−	0.137192i
$95$		0			0
$96$		0			0
$97$	7.58871	−	13.1440i	0.770516	−	1.33457i	−0.166764	−	0.985997i	$-0.553332\pi$
$97$	7.58871	−	13.1440i	0.770516	−	1.33457i	0.937280	−	0.348577i	$-0.113335\pi$
$98$	2.17209			0.219414
$99$		0			0
$100$		0			0
$101$	4.73205	−	8.19615i	0.470857	−	0.815548i	−0.528588	−	0.848879i	$-0.677278\pi$
$101$	4.73205	−	8.19615i	0.470857	−	0.815548i	0.999444	+	0.0333310i	$0.0106116\pi$
$102$		0			0
$103$	−0.328169	−	0.568406i	−0.0323355	−	0.0560067i	0.849405	−	0.527742i	$-0.176961\pi$
$103$	−0.328169	−	0.568406i	−0.0323355	−	0.0560067i	−0.881740	+	0.471735i	$0.843628\pi$
$104$	−2.36603	−	4.09808i	−0.232008	−	0.401849i
$105$		0			0
$106$	−0.267949	+	0.464102i	−0.0260255	+	0.0450775i
$107$	10.3156			0.997246			0.498623	−	0.866819i	$-0.333839\pi$
$107$	10.3156			0.997246			0.498623	+	0.866819i	$0.333839\pi$
$108$		0			0
$109$	12.6603			1.21263			0.606316	−	0.795224i	$-0.292647\pi$
$109$	12.6603			1.21263			0.606316	+	0.795224i	$0.292647\pi$
$110$		0			0
$111$		0			0
$112$	−4.12252	−	7.14042i	−0.389542	−	0.674706i
$113$	8.62398	+	14.9372i	0.811276	+	1.40517i	0.911971	+	0.410254i	$0.134560\pi$
$113$	8.62398	+	14.9372i	0.811276	+	1.40517i	−0.100695	+	0.994917i	$0.532107\pi$
$114$		0			0
$115$		0			0
$116$	−0.803848			−0.0746354
$117$		0			0
$118$	−4.89898			−0.450988
$119$	8.83013	−	15.2942i	0.809456	−	1.40202i
$120$		0			0
$121$	4.69615	+	8.13397i	0.426923	+	0.739452i
$122$	1.72380	+	2.98571i	0.156066	+	0.270314i
$123$		0			0
$124$	0.633975	−	1.09808i	0.0569326	−	0.0986102i
$125$		0			0
$126$		0			0
$127$	17.3867			1.54282			0.771409	−	0.636340i	$-0.219553\pi$
$127$	17.3867			1.54282			0.771409	+	0.636340i	$0.219553\pi$
$128$	5.72620	−	9.91808i	0.506130	−	0.876642i
$129$		0			0
$130$		0			0
$131$	6.46410	+	11.1962i	0.564771	+	0.978212i	0.997071	+	0.0764824i	$0.0243689\pi$
$131$	6.46410	+	11.1962i	0.564771	+	0.978212i	−0.432300	+	0.901730i	$0.642298\pi$
$132$		0			0
$133$	1.22474	−	2.12132i	0.106199	−	0.183942i
$134$	−3.92820			−0.339345
$135$		0			0
$136$	10.1962			0.874313
$137$	7.86611	−	13.6245i	0.672047	−	1.16402i	−0.305276	−	0.952264i	$-0.598749\pi$
$137$	7.86611	−	13.6245i	0.672047	−	1.16402i	0.977323	−	0.211755i	$-0.0679180\pi$
$138$		0			0
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$		0			0
$142$	3.67423	−	6.36396i	0.308335	−	0.534052i
$143$	3.10583			0.259722
$144$		0			0
$145$		0			0
$146$	−2.19615	+	3.80385i	−0.181755	+	0.314809i
$147$		0			0
$148$	−3.67423	−	6.36396i	−0.302020	−	0.523114i
$149$	2.13397	+	3.69615i	0.174822	+	0.302801i	0.940100	−	0.340900i	$-0.110732\pi$
$149$	2.13397	+	3.69615i	0.174822	+	0.302801i	−0.765278	+	0.643700i	$0.777398\pi$
$150$		0			0
$151$	−4.29423	+	7.43782i	−0.349459	+	0.605281i	−0.986154	−	0.165835i	$-0.946968\pi$
$151$	−4.29423	+	7.43782i	−0.349459	+	0.605281i	0.636694	+	0.771116i	$0.280301\pi$
$152$	1.41421			0.114708
$153$		0			0
$154$	−2.19615			−0.176971
$155$		0			0
$156$		0			0
$157$	−6.45189	−	11.1750i	−0.514917	−	0.891863i	−0.999850	−	0.0173114i	$-0.994489\pi$
$157$	−6.45189	−	11.1750i	−0.514917	−	0.891863i	0.484933	−	0.874551i	$-0.338844\pi$
$158$	−1.93185	−	3.34607i	−0.153690	−	0.266199i
$159$		0			0
$160$		0			0
$161$	−1.73205			−0.136505
$162$		0			0
$163$	10.4543			0.818844			0.409422	−	0.912345i	$-0.365730\pi$
$163$	10.4543			0.818844			0.409422	+	0.912345i	$0.365730\pi$
$164$	−6.69615	+	11.5981i	−0.522882	+	0.905658i
$165$		0			0
$166$	−2.06218	−	3.57180i	−0.160056	−	0.277225i
$167$	4.96833	+	8.60540i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$167$	4.96833	+	8.60540i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$168$		0			0
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$		0			0
$171$		0			0
$172$	1.13681			0.0866811
$173$	5.27792	−	9.14162i	0.401273	−	0.695025i	−0.592607	−	0.805492i	$-0.701901\pi$
$173$	5.27792	−	9.14162i	0.401273	−	0.695025i	0.993880	+	0.110467i	$0.0352347\pi$
$174$		0			0
$175$		0			0
$176$	1.56218	+	2.70577i	0.117754	+	0.203955i
$177$		0			0
$178$	3.46618	−	6.00361i	0.259801	−	0.449989i
$179$	6.58846			0.492444			0.246222	−	0.969213i	$-0.420811\pi$
$179$	6.58846			0.492444			0.246222	+	0.969213i	$0.420811\pi$
$180$		0			0
$181$	1.53590			0.114162			0.0570812	−	0.998370i	$-0.481821\pi$
$181$	1.53590			0.114162			0.0570812	+	0.998370i	$0.481821\pi$
$182$	2.12132	−	3.67423i	0.157243	−	0.272352i
$183$		0			0
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$		0			0
$186$		0			0
$187$	−3.34607	+	5.79555i	−0.244689	+	0.423813i
$188$	−5.13922			−0.374816
$189$		0			0
$190$		0			0
$191$	8.83013	−	15.2942i	0.638926	−	1.10665i	−0.346743	−	0.937960i	$-0.612713\pi$
$191$	8.83013	−	15.2942i	0.638926	−	1.10665i	0.985669	−	0.168691i	$-0.0539542\pi$
$192$		0			0
$193$	−1.88108	−	3.25813i	−0.135403	−	0.234526i	0.790348	−	0.612658i	$-0.209900\pi$
$193$	−1.88108	−	3.25813i	−0.135403	−	0.234526i	−0.925751	+	0.378133i	$0.876566\pi$
$194$	3.92820	+	6.80385i	0.282029	+	0.488488i
$195$		0			0
$196$	3.63397	−	6.29423i	0.259570	−	0.449588i
$197$	15.9353			1.13534			0.567671	−	0.823255i	$-0.307845\pi$
$197$	15.9353			1.13534			0.567671	+	0.823255i	$0.307845\pi$
$198$		0			0
$199$	−26.5885			−1.88481			−0.942403	−	0.334480i	$-0.891439\pi$
$199$	−26.5885			−1.88481			−0.942403	+	0.334480i	$0.891439\pi$
$200$		0			0
$201$		0			0
$202$	2.44949	+	4.24264i	0.172345	+	0.298511i
$203$	−0.776457	−	1.34486i	−0.0544966	−	0.0943909i
$204$		0			0
$205$		0			0
$206$	0.339746			0.0236712
$207$		0			0
$208$	−6.03579			−0.418507
$209$	−0.464102	+	0.803848i	−0.0321026	+	0.0556033i
$210$		0			0
$211$	−5.56218	−	9.63397i	−0.382916	−	0.663230i	0.608562	−	0.793507i	$-0.291747\pi$
$211$	−5.56218	−	9.63397i	−0.382916	−	0.663230i	−0.991478	+	0.130276i	$0.958414\pi$
$212$	0.896575	+	1.55291i	0.0615771	+	0.106655i
$213$		0			0
$214$	−2.66987	+	4.62436i	−0.182509	+	0.316114i
$215$		0			0
$216$		0			0
$217$	2.44949			0.166282
$218$	−3.27671	+	5.67544i	−0.221927	+	0.384389i
$219$		0			0
$220$		0			0
$221$	−6.46410	−	11.1962i	−0.434823	−	0.753135i
$222$		0			0
$223$	2.24144	−	3.88229i	0.150098	−	0.259977i	−0.781165	−	0.624324i	$-0.785374\pi$
$223$	2.24144	−	3.88229i	0.150098	−	0.259977i	0.931263	+	0.364347i	$0.118708\pi$
$224$	17.1962			1.14897
$225$		0			0
$226$	−8.92820			−0.593895
$227$	−13.1948	+	22.8541i	−0.875769	+	1.51688i	−0.0198279	+	0.999803i	$0.506312\pi$
$227$	−13.1948	+	22.8541i	−0.875769	+	1.51688i	−0.855941	+	0.517073i	$0.827021\pi$
$228$		0			0
$229$	−3.03590	−	5.25833i	−0.200618	−	0.347480i	0.748110	−	0.663575i	$-0.230962\pi$
$229$	−3.03590	−	5.25833i	−0.200618	−	0.347480i	−0.948728	+	0.316095i	$0.897628\pi$
$230$		0			0
$231$		0			0
$232$	0.448288	−	0.776457i	0.0294315	−	0.0509769i
$233$	7.07107			0.463241			0.231621	−	0.972806i	$-0.425597\pi$
$233$	7.07107			0.463241			0.231621	+	0.972806i	$0.425597\pi$
$234$		0			0
$235$		0			0
$236$	−8.19615	+	14.1962i	−0.533524	+	0.924091i
$237$		0			0
$238$	4.57081	+	7.91688i	0.296282	+	0.513175i
$239$	−0.464102	−	0.803848i	−0.0300202	−	0.0519966i	0.850625	−	0.525773i	$-0.176224\pi$
$239$	−0.464102	−	0.803848i	−0.0300202	−	0.0519966i	−0.880645	+	0.473776i	$0.842891\pi$
$240$		0			0
$241$	−4.86603	+	8.42820i	−0.313448	+	0.542908i	−0.979106	−	0.203348i	$-0.934818\pi$
$241$	−4.86603	+	8.42820i	−0.313448	+	0.542908i	0.665658	+	0.746257i	$0.268151\pi$
$242$	−4.86181			−0.312529
$243$		0			0
$244$	11.5359			0.738510
$245$		0			0
$246$		0			0
$247$	−0.896575	−	1.55291i	−0.0570477	−	0.0988096i
$248$	0.707107	+	1.22474i	0.0449013	+	0.0777714i
$249$		0			0
$250$		0			0
$251$	12.5885			0.794576			0.397288	−	0.917694i	$-0.369951\pi$
$251$	12.5885			0.794576			0.397288	+	0.917694i	$0.369951\pi$
$252$		0			0
$253$	0.656339			0.0412637
$254$	−4.50000	+	7.79423i	−0.282355	+	0.489053i
$255$		0			0
$256$	0.696152	+	1.20577i	0.0435095	+	0.0753607i
$257$	−8.38375	−	14.5211i	−0.522964	−	0.905800i	−0.999643	−	0.0267223i	$-0.991493\pi$
$257$	−8.38375	−	14.5211i	−0.522964	−	0.905800i	0.476679	−	0.879077i	$-0.341840\pi$
$258$		0			0
$259$	7.09808	−	12.2942i	0.441053	−	0.763926i
$260$		0			0
$261$		0			0
$262$	−6.69213			−0.413441
$263$	−10.8840	+	18.8516i	−0.671136	+	1.16244i	0.306446	+	0.951888i	$0.400860\pi$
$263$	−10.8840	+	18.8516i	−0.671136	+	1.16244i	−0.977582	+	0.210554i	$0.932473\pi$
$264$		0			0
$265$		0			0
$266$	0.633975	+	1.09808i	0.0388715	+	0.0673274i
$267$		0			0
$268$	−6.57201	+	11.3831i	−0.401450	+	0.695331i
$269$	−6.80385			−0.414838			−0.207419	−	0.978252i	$-0.566506\pi$
$269$	−6.80385			−0.414838			−0.207419	+	0.978252i	$0.566506\pi$
$270$		0			0
$271$	21.5167			1.30704			0.653522	−	0.756908i	$-0.273291\pi$
$271$	21.5167			1.30704			0.653522	+	0.756908i	$0.273291\pi$
$272$	6.50266	−	11.2629i	0.394282	−	0.682916i
$273$		0			0
$274$	4.07180	+	7.05256i	0.245986	+	0.426061i
$275$		0			0
$276$		0			0
$277$	−6.12372	+	10.6066i	−0.367939	+	0.637289i	−0.989243	−	0.146281i	$-0.953270\pi$
$277$	−6.12372	+	10.6066i	−0.367939	+	0.637289i	0.621304	+	0.783569i	$0.286603\pi$
$278$	−4.14110			−0.248367
$279$		0			0
$280$		0			0
$281$	−9.86603	+	17.0885i	−0.588558	+	1.01941i	0.405864	+	0.913934i	$0.366971\pi$
$281$	−9.86603	+	17.0885i	−0.588558	+	1.01941i	−0.994422	+	0.105478i	$0.966363\pi$
$282$		0			0
$283$	8.36516	+	14.4889i	0.497257	+	0.861275i	0.999995	−	0.00316407i	$-0.00100716\pi$
$283$	8.36516	+	14.4889i	0.497257	+	0.861275i	−0.502738	+	0.864439i	$0.667674\pi$
$284$	−12.2942	−	21.2942i	−0.729528	−	1.26358i
$285$		0			0
$286$	−0.803848	+	1.39230i	−0.0475325	+	0.0823287i
$287$	−25.8719			−1.52717
$288$		0			0
$289$	10.8564			0.638612
$290$		0			0
$291$		0			0
$292$	7.34847	+	12.7279i	0.430037	+	0.744845i
$293$	−6.88160	−	11.9193i	−0.402027	−	0.696332i	0.591943	−	0.805980i	$-0.298361\pi$
$293$	−6.88160	−	11.9193i	−0.402027	−	0.696332i	−0.993970	+	0.109648i	$0.965028\pi$
$294$		0			0
$295$		0			0
$296$	8.19615			0.476392
$297$		0			0
$298$	−2.20925			−0.127979
$299$	−0.633975	+	1.09808i	−0.0366637	+	0.0635034i
$300$		0			0
$301$	1.09808	+	1.90192i	0.0632921	+	0.109625i
$302$	−2.22286	−	3.85010i	−0.127911	−	0.221548i
$303$		0			0
$304$	0.901924	−	1.56218i	0.0517289	−	0.0895970i
$305$		0			0
$306$		0			0
$307$	−3.82654			−0.218392			−0.109196	−	0.994020i	$-0.534828\pi$
$307$	−3.82654			−0.218392			−0.109196	+	0.994020i	$0.534828\pi$
$308$	−3.67423	+	6.36396i	−0.209359	+	0.362620i
$309$		0			0
$310$		0			0
$311$	−5.02628	−	8.70577i	−0.285014	−	0.493659i	0.687598	−	0.726091i	$-0.258665\pi$
$311$	−5.02628	−	8.70577i	−0.285014	−	0.493659i	−0.972613	+	0.232432i	$0.925332\pi$
$312$		0			0
$313$	−7.02030	+	12.1595i	−0.396811	+	0.687296i	−0.993330	−	0.115302i	$-0.963216\pi$
$313$	−7.02030	+	12.1595i	−0.396811	+	0.687296i	0.596520	+	0.802598i	$0.296550\pi$
$314$	6.67949			0.376946
$315$		0			0
$316$	−12.9282			−0.727268
$317$	−2.01978	+	3.49837i	−0.113442	+	0.196488i	−0.917156	−	0.398528i	$-0.869521\pi$
$317$	−2.01978	+	3.49837i	−0.113442	+	0.196488i	0.803714	+	0.595016i	$0.202854\pi$
$318$		0			0
$319$	0.294229	+	0.509619i	0.0164736	+	0.0285332i
$320$		0			0
$321$		0			0
$322$	0.448288	−	0.776457i	0.0249821	−	0.0432703i
$323$	3.86370			0.214982
$324$		0			0
$325$		0			0
$326$	−2.70577	+	4.68653i	−0.149859	+	0.259563i
$327$		0			0
$328$	−7.46859	−	12.9360i	−0.412384	−	0.714270i
$329$	−4.96410	−	8.59808i	−0.273680	−	0.474027i
$330$		0			0
$331$	4.19615	−	7.26795i	0.230641	−	0.399483i	−0.727356	−	0.686261i	$-0.759251\pi$
$331$	4.19615	−	7.26795i	0.230641	−	0.399483i	0.957997	+	0.286778i	$0.0925842\pi$
$332$	−13.8004			−0.757393
$333$		0			0
$334$	−5.14359			−0.281445
$335$		0			0
$336$		0			0
$337$	−3.34607	−	5.79555i	−0.182272	−	0.315704i	0.760382	−	0.649476i	$-0.225012\pi$
$337$	−3.34607	−	5.79555i	−0.182272	−	0.315704i	−0.942654	+	0.333772i	$0.891678\pi$
$338$	1.81173	+	3.13801i	0.0985453	+	0.170685i
$339$		0			0
$340$		0			0
$341$	−0.928203			−0.0502650
$342$		0			0
$343$	−9.38186			−0.506573
$344$	−0.633975	+	1.09808i	−0.0341816	+	0.0592043i
$345$		0			0
$346$	2.73205	+	4.73205i	0.146876	+	0.254397i
$347$	−4.94975	−	8.57321i	−0.265716	−	0.460234i	0.702035	−	0.712143i	$-0.252275\pi$
$347$	−4.94975	−	8.57321i	−0.265716	−	0.460234i	−0.967751	+	0.251909i	$0.918942\pi$
$348$		0			0
$349$	−14.2321	+	24.6506i	−0.761824	+	1.31952i	0.180085	+	0.983651i	$0.442363\pi$
$349$	−14.2321	+	24.6506i	−0.761824	+	1.31952i	−0.941909	+	0.335867i	$0.890971\pi$
$350$		0			0
$351$		0			0
$352$	−6.51626			−0.347318
$353$	10.1769	−	17.6269i	0.541662	−	0.938185i	−0.457147	−	0.889391i	$-0.651129\pi$
$353$	10.1769	−	17.6269i	0.541662	−	0.938185i	0.998809	−	0.0487943i	$-0.0155379\pi$
$354$		0			0
$355$		0			0
$356$	−11.5981	−	20.0885i	−0.614697	−	1.06469i
$357$		0			0
$358$	−1.70522	+	2.95352i	−0.0901236	+	0.156099i
$359$	−20.1962			−1.06591			−0.532956	−	0.846143i	$-0.678919\pi$
$359$	−20.1962			−1.06591			−0.532956	+	0.846143i	$0.678919\pi$
$360$		0			0
$361$	−18.4641			−0.971795
$362$	−0.397520	+	0.688524i	−0.0208932	+	0.0361880i
$363$		0			0
$364$	−7.09808	−	12.2942i	−0.372040	−	0.644393i
$365$		0			0
$366$		0			0
$367$	−17.2987	+	29.9623i	−0.902986	+	1.56402i	−0.0793890	+	0.996844i	$0.525297\pi$
$367$	−17.2987	+	29.9623i	−0.902986	+	1.56402i	−0.823597	+	0.567175i	$0.808036\pi$
$368$	−1.27551			−0.0664907
$369$		0			0
$370$		0			0
$371$	−1.73205	+	3.00000i	−0.0899236	+	0.155752i
$372$		0			0
$373$	−13.6245	−	23.5983i	−0.705450	−	1.22187i	−0.966529	−	0.256557i	$-0.917412\pi$
$373$	−13.6245	−	23.5983i	−0.705450	−	1.22187i	0.261079	−	0.965317i	$-0.415922\pi$
$374$	−1.73205	−	3.00000i	−0.0895622	−	0.155126i
$375$		0			0
$376$	2.86603	−	4.96410i	0.147804	−	0.256004i
$377$	−1.13681			−0.0585488
$378$		0			0
$379$	19.4641			0.999804			0.499902	−	0.866082i	$-0.333369\pi$
$379$	19.4641			0.999804			0.499902	+	0.866082i	$0.333369\pi$
$380$		0			0
$381$		0			0
$382$	4.57081	+	7.91688i	0.233863	+	0.405063i
$383$	−5.32868	−	9.22955i	−0.272283	−	0.471608i	0.697163	−	0.716913i	$-0.254445\pi$
$383$	−5.32868	−	9.22955i	−0.272283	−	0.471608i	−0.969446	+	0.245305i	$0.921112\pi$
$384$		0			0
$385$		0			0
$386$	1.94744			0.0991221
$387$		0			0
$388$	26.2880			1.33457
$389$	0.0621778	−	0.107695i	0.00315254	−	0.00546036i	−0.864445	−	0.502728i	$-0.832330\pi$
$389$	0.0621778	−	0.107695i	0.00315254	−	0.00546036i	0.867597	+	0.497267i	$0.165663\pi$
$390$		0			0
$391$	−1.36603	−	2.36603i	−0.0690829	−	0.119655i
$392$	4.05317	+	7.02030i	0.204716	+	0.354579i
$393$		0			0
$394$	−4.12436	+	7.14359i	−0.207782	+	0.359889i
$395$		0			0
$396$		0			0
$397$	−29.3939			−1.47524			−0.737618	−	0.675218i	$-0.764050\pi$
$397$	−29.3939			−1.47524			−0.737618	+	0.675218i	$0.764050\pi$
$398$	6.88160	−	11.9193i	0.344943	−	0.597459i
$399$		0			0
$400$		0			0
$401$	−8.53590	−	14.7846i	−0.426262	−	0.738308i	0.570275	−	0.821454i	$-0.306837\pi$
$401$	−8.53590	−	14.7846i	−0.426262	−	0.738308i	−0.996537	+	0.0831457i	$0.973503\pi$
$402$		0			0
$403$	0.896575	−	1.55291i	0.0446616	−	0.0773562i
$404$	16.3923			0.815548
$405$		0			0
$406$	0.803848			0.0398943
$407$	−2.68973	+	4.65874i	−0.133325	+	0.230925i
$408$		0			0
$409$	8.26795	+	14.3205i	0.408824	+	0.708104i	0.994758	−	0.102255i	$-0.0326057\pi$
$409$	8.26795	+	14.3205i	0.408824	+	0.708104i	−0.585934	+	0.810358i	$0.699272\pi$
$410$		0			0
$411$		0			0
$412$	0.568406	−	0.984508i	0.0280034	−	0.0485032i
$413$	−31.6675			−1.55826
$414$		0			0
$415$		0			0
$416$	6.29423	−	10.9019i	0.308600	−	0.534511i
$417$		0			0
$418$	−0.240237	−	0.416102i	−0.0117504	−	0.0203522i
$419$	11.0263	+	19.0981i	0.538669	+	0.933002i	0.998976	+	0.0452423i	$0.0144060\pi$
$419$	11.0263	+	19.0981i	0.538669	+	0.933002i	−0.460307	+	0.887760i	$0.652261\pi$
$420$		0			0
$421$	9.73205	−	16.8564i	0.474311	−	0.821531i	−0.525256	−	0.850944i	$-0.676031\pi$
$421$	9.73205	−	16.8564i	0.474311	−	0.821531i	0.999567	+	0.0294132i	$0.00936385\pi$
$422$	5.75839			0.280314
$423$		0			0
$424$	−2.00000			−0.0971286
$425$		0			0
$426$		0			0
$427$	11.1428	+	19.2999i	0.539239	+	0.933989i
$428$	8.93357	+	15.4734i	0.431820	+	0.747935i
$429$		0			0
$430$		0			0
$431$	6.00000			0.289010			0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000			0.289010			0.144505	+	0.989504i	$0.453841\pi$
$432$		0			0
$433$	−13.5601			−0.651658			−0.325829	−	0.945429i	$-0.605643\pi$
$433$	−13.5601			−0.651658			−0.325829	+	0.945429i	$0.605643\pi$
$434$	−0.633975	+	1.09808i	−0.0304318	+	0.0527093i
$435$		0			0
$436$	10.9641	+	18.9904i	0.525085	+	0.909474i
$437$	−0.189469	−	0.328169i	−0.00906352	−	0.0156985i
$438$		0			0
$439$	12.6603	−	21.9282i	0.604241	−	1.04658i	−0.387930	−	0.921689i	$-0.626810\pi$
$439$	12.6603	−	21.9282i	0.604241	−	1.04658i	0.992171	−	0.124887i	$-0.0398569\pi$
$440$		0			0
$441$		0			0
$442$	6.69213			0.318312
$443$	0.827225	−	1.43280i	0.0393027	−	0.0680742i	−0.845705	−	0.533651i	$-0.820820\pi$
$443$	0.827225	−	1.43280i	0.0393027	−	0.0680742i	0.885008	+	0.465577i	$0.154153\pi$
$444$		0			0
$445$		0			0
$446$	1.16025	+	2.00962i	0.0549396	+	0.0951582i
$447$		0			0
$448$	3.79435	−	6.57201i	0.179266	−	0.310498i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$	9.80385			0.461645
$452$	−14.9372	+	25.8719i	−0.702586	+	1.21691i
$453$		0			0
$454$	−6.83013	−	11.8301i	−0.320554	−	0.555215i
$455$		0			0
$456$		0			0
$457$	12.3998	−	21.4770i	0.580036	−	1.00465i	−0.415438	−	0.909621i	$-0.636372\pi$
$457$	12.3998	−	21.4770i	0.580036	−	1.00465i	0.995474	−	0.0950304i	$-0.0302948\pi$
$458$	3.14299			0.146862
$459$		0			0
$460$		0			0
$461$	−18.3564	+	31.7942i	−0.854943	+	1.48080i	0.0217547	+	0.999763i	$0.493075\pi$
$461$	−18.3564	+	31.7942i	−0.854943	+	1.48080i	−0.876698	+	0.481042i	$0.840259\pi$
$462$		0			0
$463$	17.0585	+	29.5462i	0.792776	+	1.37313i	0.924242	+	0.381807i	$0.124698\pi$
$463$	17.0585	+	29.5462i	0.792776	+	1.37313i	−0.131467	+	0.991321i	$0.541969\pi$
$464$	−0.571797	−	0.990381i	−0.0265450	−	0.0459773i
$465$		0			0
$466$	−1.83013	+	3.16987i	−0.0847790	+	0.146842i
$467$	−25.3543			−1.17326			−0.586629	−	0.809856i	$-0.699545\pi$
$467$	−25.3543			−1.17326			−0.586629	+	0.809856i	$0.699545\pi$
$468$		0			0
$469$	−25.3923			−1.17251
$470$		0			0
$471$		0			0
$472$	−9.14162	−	15.8338i	−0.420777	−	0.728807i
$473$	−0.416102	−	0.720710i	−0.0191324	−	0.0331383i
$474$		0			0
$475$		0			0
$476$	30.5885			1.40202
$477$		0			0
$478$	0.480473			0.0219763
$479$	2.07180	−	3.58846i	0.0946628	−	0.163961i	−0.814805	−	0.579735i	$-0.803156\pi$
$479$	2.07180	−	3.58846i	0.0946628	−	0.163961i	0.909468	+	0.415774i	$0.136489\pi$
$480$		0			0
$481$	−5.19615	−	9.00000i	−0.236924	−	0.410365i
$482$	−2.51884	−	4.36276i	−0.114730	−	0.198718i
$483$		0			0
$484$	−8.13397	+	14.0885i	−0.369726	+	0.640384i
$485$		0			0
$486$		0			0
$487$	15.8338			0.717496			0.358748	−	0.933435i	$-0.383204\pi$
$487$	15.8338			0.717496			0.358748	+	0.933435i	$0.383204\pi$
$488$	−6.43331	+	11.1428i	−0.291222	+	0.504412i
$489$		0			0
$490$		0			0
$491$	16.8564	+	29.1962i	0.760719	+	1.31760i	0.942480	+	0.334261i	$0.108487\pi$
$491$	16.8564	+	29.1962i	0.760719	+	1.31760i	−0.181761	+	0.983343i	$0.558180\pi$
$492$		0			0
$493$	1.22474	−	2.12132i	0.0551597	−	0.0955395i
$494$	0.928203			0.0417618
$495$		0			0
$496$	1.80385			0.0809951
$497$	23.7506	−	41.1373i	1.06536	−	1.84526i
$498$		0			0
$499$	−11.9282	−	20.6603i	−0.533980	−	0.924880i	−0.999212	−	0.0396914i	$-0.987363\pi$
$499$	−11.9282	−	20.6603i	−0.533980	−	0.924880i	0.465232	−	0.885189i	$-0.345971\pi$
$500$		0			0
$501$		0			0
$502$	−3.25813	+	5.64325i	−0.145418	+	0.251871i
$503$	−2.48665			−0.110874			−0.0554372	−	0.998462i	$-0.517655\pi$
$503$	−2.48665			−0.110874			−0.0554372	+	0.998462i	$0.517655\pi$
$504$		0			0
$505$		0			0
$506$	−0.169873	+	0.294229i	−0.00755178	+	0.0130801i
$507$		0			0
$508$	15.0573	+	26.0800i	0.668059	+	1.15711i
$509$	8.42820	+	14.5981i	0.373574	+	0.647048i	0.990112	−	0.140276i	$-0.0447990\pi$
$509$	8.42820	+	14.5981i	0.373574	+	0.647048i	−0.616539	+	0.787324i	$0.711466\pi$
$510$		0			0
$511$	−14.1962	+	24.5885i	−0.628001	+	1.08773i
$512$	22.1841			0.980408
$513$		0			0
$514$	8.67949			0.382836
$515$		0			0
$516$		0			0
$517$	1.88108	+	3.25813i	0.0827300	+	0.143293i
$518$	3.67423	+	6.36396i	0.161437	+	0.279616i
$519$		0			0
$520$		0			0
$521$	19.3923			0.849592			0.424796	−	0.905289i	$-0.360346\pi$
$521$	19.3923			0.849592			0.424796	+	0.905289i	$0.360346\pi$
$522$		0			0
$523$	−35.1894			−1.53873			−0.769363	−	0.638812i	$-0.779426\pi$
$523$	−35.1894			−1.53873			−0.769363	+	0.638812i	$0.779426\pi$
$524$	−11.1962	+	19.3923i	−0.489106	+	0.847157i
$525$		0			0
$526$	−5.63397	−	9.75833i	−0.245653	−	0.425483i
$527$	1.93185	+	3.34607i	0.0841528	+	0.145757i
$528$		0			0
$529$	11.3660	−	19.6865i	0.494175	−	0.855936i
$530$		0			0
$531$		0			0
$532$	4.24264			0.183942
$533$	−9.46979	+	16.4022i	−0.410182	+	0.710456i
$534$		0			0
$535$		0			0
$536$	−7.33013	−	12.6962i	−0.316613	−	0.548390i
$537$		0			0
$538$	1.76097	−	3.05008i	0.0759206	−	0.131498i
$539$	−5.32051			−0.229171
$540$		0			0
$541$	0.607695			0.0261269			0.0130634	−	0.999915i	$-0.495842\pi$
$541$	0.607695			0.0261269			0.0130634	+	0.999915i	$0.495842\pi$
$542$	−5.56892	+	9.64566i	−0.239206	+	0.414316i
$543$		0			0
$544$	13.5622	+	23.4904i	0.581474	+	1.00714i
$545$		0			0
$546$		0			0
$547$	13.0239	−	22.5581i	0.556862	−	0.964513i	−0.440894	−	0.897559i	$-0.645339\pi$
$547$	13.0239	−	22.5581i	0.556862	−	0.964513i	0.997756	−	0.0669541i	$-0.0213281\pi$
$548$	27.2490			1.16402
$549$		0			0
$550$		0			0
$551$	0.169873	−	0.294229i	0.00723683	−	0.0125346i
$552$		0			0
$553$	−12.4877	−	21.6293i	−0.531030	−	0.919772i
$554$	−3.16987	−	5.49038i	−0.134675	−	0.233264i
$555$		0			0
$556$	−6.92820	+	12.0000i	−0.293821	+	0.508913i
$557$	31.1127			1.31829			0.659144	−	0.752017i	$-0.270919\pi$
$557$	31.1127			1.31829			0.659144	+	0.752017i	$0.270919\pi$
$558$		0			0
$559$	1.60770			0.0679983
$560$		0			0
$561$		0			0
$562$	−5.10703	−	8.84564i	−0.215427	−	0.373131i
$563$	4.58939	+	7.94906i	0.193420	+	0.335013i	0.946381	−	0.323052i	$-0.104709\pi$
$563$	4.58939	+	7.94906i	0.193420	+	0.335013i	−0.752962	+	0.658065i	$0.771375\pi$
$564$		0			0
$565$		0			0
$566$	−8.66025			−0.364018
$567$		0			0
$568$	27.4249			1.15072
$569$	14.6603	−	25.3923i	0.614590	−	1.06450i	−0.375867	−	0.926674i	$-0.622655\pi$
$569$	14.6603	−	25.3923i	0.614590	−	1.06450i	0.990456	−	0.137827i	$-0.0440118\pi$
$570$		0			0
$571$	0.732051	+	1.26795i	0.0306354	+	0.0530620i	0.880937	−	0.473234i	$-0.156914\pi$
$571$	0.732051	+	1.26795i	0.0306354	+	0.0530620i	−0.850301	+	0.526296i	$0.823580\pi$
$572$	2.68973	+	4.65874i	0.112463	+	0.194792i
$573$		0			0
$574$	6.69615	−	11.5981i	0.279492	−	0.484094i
$575$		0			0
$576$		0			0
$577$	13.8647			0.577196			0.288598	−	0.957450i	$-0.406811\pi$
$577$	13.8647			0.577196			0.288598	+	0.957450i	$0.406811\pi$
$578$	−2.80984	+	4.86679i	−0.116874	+	0.202432i
$579$		0			0
$580$		0			0
$581$	−13.3301	−	23.0885i	−0.553027	−	0.957871i
$582$		0			0
$583$	0.656339	−	1.13681i	0.0271828	−	0.0470819i
$584$	−16.3923			−0.678318
$585$		0			0
$586$	7.12436			0.294304
$587$	2.43091	−	4.21046i	0.100334	−	0.173784i	−0.811488	−	0.584369i	$-0.801342\pi$
$587$	2.43091	−	4.21046i	0.100334	−	0.173784i	0.911822	+	0.410585i	$0.134675\pi$
$588$		0			0
$589$	0.267949	+	0.464102i	0.0110407	+	0.0191230i
$590$		0			0
$591$		0			0
$592$	5.22715	−	9.05369i	0.214834	−	0.372104i
$593$	19.1427			0.786094			0.393047	−	0.919518i	$-0.371421\pi$
$593$	19.1427			0.786094			0.393047	+	0.919518i	$0.371421\pi$
$594$		0			0
$595$		0			0
$596$	−3.69615	+	6.40192i	−0.151400	+	0.262233i
$597$		0			0
$598$	−0.328169	−	0.568406i	−0.0134198	−	0.0232439i
$599$	−10.8564	−	18.8038i	−0.443581	−	0.768304i	0.554371	−	0.832269i	$-0.312959\pi$
$599$	−10.8564	−	18.8038i	−0.443581	−	0.768304i	−0.997952	+	0.0639650i	$0.979625\pi$
$600$		0			0
$601$	1.53590	−	2.66025i	0.0626506	−	0.108514i	−0.832999	−	0.553275i	$-0.813378\pi$
$601$	1.53590	−	2.66025i	0.0626506	−	0.108514i	0.895649	+	0.444761i	$0.146711\pi$
$602$	−1.13681			−0.0463330
$603$		0			0
$604$	−14.8756			−0.605281
$605$		0			0
$606$		0			0
$607$	−10.4865	−	18.1631i	−0.425633	−	0.737218i	0.570846	−	0.821057i	$-0.306615\pi$
$607$	−10.4865	−	18.1631i	−0.425633	−	0.737218i	−0.996479	+	0.0838387i	$0.973282\pi$
$608$	1.88108	+	3.25813i	0.0762880	+	0.132135i
$609$		0			0
$610$		0			0
$611$	−7.26795			−0.294030
$612$		0			0
$613$	−9.62209			−0.388633			−0.194316	−	0.980939i	$-0.562249\pi$
$613$	−9.62209			−0.388633			−0.194316	+	0.980939i	$0.562249\pi$
$614$	0.990381	−	1.71539i	0.0399685	−	0.0692275i
$615$		0			0
$616$	−4.09808	−	7.09808i	−0.165116	−	0.285990i
$617$	9.00292	+	15.5935i	0.362444	+	0.627771i	0.988362	−	0.152117i	$-0.0486091\pi$
$617$	9.00292	+	15.5935i	0.362444	+	0.627771i	−0.625919	+	0.779888i	$0.715276\pi$
$618$		0			0
$619$	−15.0981	+	26.1506i	−0.606843	+	1.05108i	0.384914	+	0.922952i	$0.374231\pi$
$619$	−15.0981	+	26.1506i	−0.606843	+	1.05108i	−0.991757	+	0.128130i	$0.959102\pi$
$620$		0			0
$621$		0			0
$622$	5.20359			0.208645
$623$	22.4058	−	38.8079i	0.897668	−	1.55481i
$624$		0			0
$625$		0			0
$626$	−3.63397	−	6.29423i	−0.145243	−	0.251568i
$627$		0			0
$628$	11.1750	−	19.3557i	0.445931	−	0.772376i
$629$	22.3923			0.892840
$630$		0			0
$631$	1.32051			0.0525686			0.0262843	−	0.999655i	$-0.491632\pi$
$631$	1.32051			0.0525686			0.0262843	+	0.999655i	$0.491632\pi$
$632$	7.20977	−	12.4877i	0.286789	−	0.496733i
$633$		0			0
$634$	−1.04552	−	1.81089i	−0.0415228	−	0.0719196i
$635$		0			0
$636$		0			0
$637$	5.13922	−	8.90138i	0.203623	−	0.352686i
$638$	−0.304608			−0.0120595
$639$		0			0
$640$		0			0
$641$	6.52628	−	11.3038i	0.257773	−	0.446475i	−0.707872	−	0.706340i	$-0.750345\pi$
$641$	6.52628	−	11.3038i	0.257773	−	0.446475i	0.965645	+	0.259865i	$0.0836781\pi$
$642$		0			0
$643$	−6.48408	−	11.2308i	−0.255707	−	0.442898i	0.709380	−	0.704826i	$-0.248975\pi$
$643$	−6.48408	−	11.2308i	−0.255707	−	0.442898i	−0.965087	+	0.261928i	$0.915642\pi$
$644$	−1.50000	−	2.59808i	−0.0591083	−	0.102379i
$645$		0			0
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	19.4572			0.764942			0.382471	−	0.923967i	$-0.375073\pi$
$647$	19.4572			0.764942			0.382471	+	0.923967i	$0.375073\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$		0			0
$651$		0			0
$652$	9.05369	+	15.6814i	0.354570	+	0.614133i
$653$	−24.2683	−	42.0339i	−0.949691	−	1.64491i	−0.746076	−	0.665861i	$-0.768064\pi$
$653$	−24.2683	−	42.0339i	−0.949691	−	1.64491i	−0.203615	−	0.979051i	$-0.565269\pi$
$654$		0			0
$655$		0			0
$656$	−19.0526			−0.743877
$657$		0			0
$658$	5.13922			0.200348
$659$	−6.12436	+	10.6077i	−0.238571	+	0.413217i	−0.960304	−	0.278954i	$-0.910012\pi$
$659$	−6.12436	+	10.6077i	−0.238571	+	0.413217i	0.721733	+	0.692171i	$0.243346\pi$
$660$		0			0
$661$	−5.39230	−	9.33975i	−0.209736	−	0.363274i	0.741895	−	0.670516i	$-0.233927\pi$
$661$	−5.39230	−	9.33975i	−0.209736	−	0.363274i	−0.951631	+	0.307242i	$0.900594\pi$
$662$	2.17209	+	3.76217i	0.0844206	+	0.146221i
$663$		0			0
$664$	7.69615	−	13.3301i	0.298669	−	0.517309i
$665$		0			0
$666$		0			0
$667$	−0.240237			−0.00930200
$668$	−8.60540	+	14.9050i	−0.332953	+	0.576691i
$669$		0			0
$670$		0			0
$671$	−4.22243	−	7.31347i	−0.163005	−	0.282333i
$672$		0			0
$673$	20.4046	−	35.3417i	0.786538	−	1.36232i	−0.141538	−	0.989933i	$-0.545205\pi$
$673$	20.4046	−	35.3417i	0.786538	−	1.36232i	0.928076	−	0.372391i	$-0.121462\pi$
$674$	3.46410			0.133432
$675$		0			0
$676$	12.1244			0.466321
$677$	−1.84392	+	3.19376i	−0.0708676	+	0.122746i	−0.899282	−	0.437370i	$-0.855910\pi$
$677$	−1.84392	+	3.19376i	−0.0708676	+	0.122746i	0.828414	+	0.560116i	$0.189243\pi$
$678$		0			0
$679$	25.3923	+	43.9808i	0.974467	+	1.68783i
$680$		0			0
$681$		0			0
$682$	0.240237	−	0.416102i	0.00919914	−	0.0159334i
$683$	−0.101536			−0.00388517			−0.00194258	−	0.999998i	$-0.500618\pi$
$683$	−0.101536			−0.00388517			−0.00194258	+	0.999998i	$0.500618\pi$
$684$		0			0
$685$		0			0
$686$	2.42820	−	4.20577i	0.0927092	−	0.160577i
$687$		0			0
$688$	0.808643	+	1.40061i	0.0308292	+	0.0533978i
$689$	1.26795	+	2.19615i	0.0483050	+	0.0836667i
$690$		0			0
$691$	14.1244	−	24.4641i	0.537316	−	0.930658i	−0.461732	−	0.887020i	$-0.652772\pi$
$691$	14.1244	−	24.4641i	0.537316	−	0.930658i	0.999047	−	0.0436386i	$-0.0138950\pi$
$692$	18.2832			0.695025
$693$		0			0
$694$	5.12436			0.194518
$695$		0			0
$696$		0			0
$697$	−20.4046	−	35.3417i	−0.772878	−	1.33866i
$698$	−7.36705	−	12.7601i	−0.278847	−	0.482977i
$699$		0			0
$700$		0			0
$701$	12.8038			0.483595			0.241797	−	0.970327i	$-0.422263\pi$
$701$	12.8038			0.483595			0.241797	+	0.970327i	$0.422263\pi$
$702$		0			0
$703$	3.10583			0.117139
$704$	−1.43782	+	2.49038i	−0.0541900	+	0.0938598i
$705$		0			0
$706$	5.26795	+	9.12436i	0.198262	+	0.343400i
$707$	15.8338	+	27.4249i	0.595489	+	1.03142i
$708$		0			0
$709$	−4.89230	+	8.47372i	−0.183734	+	0.318237i	−0.943149	−	0.332369i	$-0.892152\pi$
$709$	−4.89230	+	8.47372i	−0.183734	+	0.318237i	0.759415	+	0.650607i	$0.225485\pi$
$710$		0			0
$711$		0			0
$712$	25.8719			0.969592
$713$	0.189469	−	0.328169i	0.00709566	−	0.0122900i
$714$		0			0
$715$		0			0
$716$	5.70577	+	9.88269i	0.213235	+	0.369333i
$717$		0			0
$718$	5.22715	−	9.05369i	0.195075	−	0.337881i
$719$	−40.3923			−1.50638			−0.753189	−	0.657804i	$-0.771486\pi$
$719$	−40.3923			−1.50638			−0.753189	+	0.657804i	$0.771486\pi$
$720$		0			0
$721$	2.19615			0.0817890
$722$	4.77886	−	8.27723i	0.177851	−	0.308047i
$723$		0			0
$724$	1.33013	+	2.30385i	0.0494338	+	0.0856218i
$725$		0			0
$726$		0			0
$727$	−0.688524	+	1.19256i	−0.0255360	+	0.0442296i	−0.878511	−	0.477722i	$-0.841463\pi$
$727$	−0.688524	+	1.19256i	−0.0255360	+	0.0442296i	0.852975	+	0.521952i	$0.174796\pi$
$728$	15.8338			0.586838
$729$		0			0
$730$		0			0
$731$	−1.73205	+	3.00000i	−0.0640622	+	0.110959i
$732$		0			0
$733$	3.76217	+	6.51626i	0.138959	+	0.240684i	0.927103	−	0.374807i	$-0.122291\pi$
$733$	3.76217	+	6.51626i	0.138959	+	0.240684i	−0.788144	+	0.615491i	$0.788958\pi$
$734$	−8.95448	−	15.5096i	−0.330516	−	0.572470i
$735$		0			0
$736$	1.33013	−	2.30385i	0.0490291	−	0.0849209i
$737$	9.62209			0.354434
$738$		0			0
$739$	−18.1436			−0.667423			−0.333711	−	0.942675i	$-0.608301\pi$
$739$	−18.1436			−0.667423			−0.333711	+	0.942675i	$0.608301\pi$
$740$		0			0
$741$		0			0
$742$	−0.896575	−	1.55291i	−0.0329143	−	0.0570093i
$743$	16.3328	+	28.2893i	0.599193	+	1.03783i	0.992941	+	0.118613i	$0.0378449\pi$
$743$	16.3328	+	28.2893i	0.599193	+	1.03783i	−0.393748	+	0.919218i	$0.628822\pi$
$744$		0			0
$745$		0			0
$746$	14.1051			0.516425
$747$		0			0
$748$	−11.5911			−0.423813
$749$	−17.2583	+	29.8923i	−0.630606	+	1.09224i
$750$		0			0
$751$	12.2224	+	21.1699i	0.446003	+	0.772500i	0.998121	−	0.0612659i	$-0.0195138\pi$
$751$	12.2224	+	21.1699i	0.446003	+	0.772500i	−0.552119	+	0.833766i	$0.686180\pi$
$752$	−3.65565	−	6.33178i	−0.133308	−	0.230896i
$753$		0			0
$754$	0.294229	−	0.509619i	0.0107152	−	0.0185592i
$755$		0			0
$756$		0			0
$757$	−7.34847			−0.267085			−0.133542	−	0.991043i	$-0.542635\pi$
$757$	−7.34847			−0.267085			−0.133542	+	0.991043i	$0.542635\pi$
$758$	−5.03768	+	8.72552i	−0.182977	+	0.316925i
$759$		0			0
$760$		0			0
$761$	7.96410	+	13.7942i	0.288698	+	0.500040i	0.973499	−	0.228690i	$-0.0734442\pi$
$761$	7.96410	+	13.7942i	0.288698	+	0.500040i	−0.684801	+	0.728730i	$0.740111\pi$
$762$		0			0
$763$	−21.1810	+	36.6866i	−0.766804	+	1.32814i
$764$	30.5885			1.10665
$765$		0			0
$766$	5.51666			0.199325
$767$	−11.5911	+	20.0764i	−0.418531	+	0.724916i
$768$		0			0
$769$	−20.8205	−	36.0622i	−0.750807	−	1.30044i	−0.947432	−	0.319957i	$-0.896332\pi$
$769$	−20.8205	−	36.0622i	−0.750807	−	1.30044i	0.196625	−	0.980479i	$-0.437002\pi$
$770$		0			0
$771$		0			0
$772$	3.25813	−	5.64325i	0.117263	−	0.203105i
$773$	−2.07055			−0.0744726			−0.0372363	−	0.999306i	$-0.511855\pi$
$773$	−2.07055			−0.0744726			−0.0372363	+	0.999306i	$0.511855\pi$
$774$		0			0
$775$		0			0
$776$	−14.6603	+	25.3923i	−0.526272	+	0.911531i
$777$		0			0
$778$	0.0321856	+	0.0557471i	0.00115391	+	0.00199863i
$779$	−2.83013	−	4.90192i	−0.101400	−	0.175630i
$780$		0			0
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$	1.41421			0.0505722
$783$		0			0
$784$	10.3397			0.369277
$785$		0			0
$786$		0			0
$787$	13.0561	+	22.6138i	0.465399	+	0.806095i	0.999219	−	0.0395027i	$-0.0125774\pi$
$787$	13.0561	+	22.6138i	0.465399	+	0.806095i	−0.533820	+	0.845598i	$0.679244\pi$
$788$	13.8004	+	23.9029i	0.491618	+	0.851507i
$789$		0			0
$790$		0			0
$791$	−57.7128			−2.05203
$792$		0			0
$793$	16.3142			0.579335
$794$	7.60770	−	13.1769i	0.269987	−	0.467631i
$795$		0			0
$796$	−23.0263	−	39.8827i	−0.816145	−	1.41360i
$797$	−26.3388	−	45.6202i	−0.932969	−	1.61595i	−0.778217	−	0.627996i	$-0.783875\pi$
$797$	−26.3388	−	45.6202i	−0.932969	−	1.61595i	−0.154752	−	0.987953i	$-0.549458\pi$
$798$		0			0
$799$	7.83013	−	13.5622i	0.277010	−	0.479795i
$800$		0			0
$801$		0			0
$802$	8.83701			0.312046
$803$	5.37945	−	9.31749i	0.189837	−	0.328807i
$804$		0			0
$805$		0			0
$806$	0.464102	+	0.803848i	0.0163473	+	0.0283143i
$807$		0			0
$808$	−9.14162	+	15.8338i	−0.321601	+	0.557029i
$809$	25.1769			0.885173			0.442587	−	0.896726i	$-0.354061\pi$
$809$	25.1769			0.885173			0.442587	+	0.896726i	$0.354061\pi$
$810$		0			0
$811$	−39.5692			−1.38946			−0.694732	−	0.719269i	$-0.744477\pi$
$811$	−39.5692			−1.38946			−0.694732	+	0.719269i	$0.744477\pi$
$812$	1.34486	−	2.32937i	0.0471954	−	0.0817449i
$813$		0			0
$814$	−1.39230	−	2.41154i	−0.0488003	−	0.0845245i
$815$		0			0
$816$		0			0
$817$	−0.240237	+	0.416102i	−0.00840482	+	0.0145576i
$818$	−8.55961			−0.299280
$819$		0			0
$820$		0			0
$821$	14.7224	−	25.5000i	0.513816	−	0.889956i	−0.486055	−	0.873928i	$-0.661565\pi$
$821$	14.7224	−	25.5000i	0.513816	−	0.889956i	0.999872	−	0.0160280i	$-0.00510208\pi$
$822$		0			0
$823$	−9.58991	−	16.6102i	−0.334283	−	0.578995i	0.649064	−	0.760734i	$-0.275161\pi$
$823$	−9.58991	−	16.6102i	−0.334283	−	0.578995i	−0.983347	+	0.181739i	$0.941828\pi$
$824$	0.633975	+	1.09808i	0.0220856	+	0.0382533i
$825$		0			0
$826$	8.19615	−	14.1962i	0.285181	−	0.493947i
$827$	−23.8014			−0.827656			−0.413828	−	0.910355i	$-0.635808\pi$
$827$	−23.8014			−0.827656			−0.413828	+	0.910355i	$0.635808\pi$
$828$		0			0
$829$	0.411543			0.0142935			0.00714673	−	0.999974i	$-0.497725\pi$
$829$	0.411543			0.0142935			0.00714673	+	0.999974i	$0.497725\pi$
$830$		0			0
$831$		0			0
$832$	−2.77766	−	4.81105i	−0.0962980	−	0.166793i
$833$	11.0735	+	19.1798i	0.383673	+	0.664541i
$834$		0			0
$835$		0			0
$836$	−1.60770			−0.0556033
$837$		0			0
$838$	−11.4152			−0.394333
$839$	2.36603	−	4.09808i	0.0816843	−	0.141481i	−0.822289	−	0.569070i	$-0.807303\pi$
$839$	2.36603	−	4.09808i	0.0816843	−	0.141481i	0.903974	+	0.427588i	$0.140637\pi$
$840$		0			0
$841$	14.3923	+	24.9282i	0.496286	+	0.859593i
$842$	5.03768	+	8.72552i	0.173610	+	0.300701i
$843$		0			0
$844$	9.63397	−	16.6865i	0.331615	−	0.574374i
$845$		0			0
$846$		0			0
$847$	−31.4273			−1.07985
$848$	−1.27551	+	2.20925i	−0.0438013	+	0.0758661i
$849$		0			0
$850$		0			0
$851$	−1.09808	−	1.90192i	−0.0376416	−	0.0651971i
$852$		0			0
$853$	−21.7172	+	37.6154i	−0.743584	+	1.28793i	0.207269	+	0.978284i	$0.433542\pi$
$853$	−21.7172	+	37.6154i	−0.743584	+	1.28793i	−0.950853	+	0.309641i	$0.899791\pi$
$854$	−11.5359			−0.394750
$855$		0			0
$856$	−19.9282			−0.681132
$857$	6.88160	−	11.9193i	0.235071	−	0.407155i	−0.724222	−	0.689567i	$-0.757801\pi$
$857$	6.88160	−	11.9193i	0.235071	−	0.407155i	0.959293	+	0.282412i	$0.0911344\pi$
$858$		0			0
$859$	−18.2224	−	31.5622i	−0.621741	−	1.07689i	−0.989161	−	0.146832i	$-0.953092\pi$
$859$	−18.2224	−	31.5622i	−0.621741	−	1.07689i	0.367420	−	0.930055i	$-0.380241\pi$
$860$		0			0
$861$		0			0
$862$	−1.55291	+	2.68973i	−0.0528925	+	0.0916124i
$863$	−44.9131			−1.52886			−0.764429	−	0.644708i	$-0.776979\pi$
$863$	−44.9131			−1.52886			−0.764429	+	0.644708i	$0.776979\pi$
$864$		0			0
$865$		0			0
$866$	3.50962	−	6.07884i	0.119262	−	0.206567i
$867$		0			0
$868$	2.12132	+	3.67423i	0.0720023	+	0.124712i
$869$	4.73205	+	8.19615i	0.160524	+	0.278035i
$870$		0			0
$871$	−9.29423	+	16.0981i	−0.314923	+	0.545463i
$872$	−24.4577			−0.828243
$873$		0			0
$874$	0.196152			0.00663495
$875$		0			0
$876$		0			0
$877$	14.6090	+	25.3035i	0.493311	+	0.854440i	0.999970	−	0.00770656i	$-0.00245310\pi$
$877$	14.6090	+	25.3035i	0.493311	+	0.854440i	−0.506659	+	0.862146i	$0.669120\pi$
$878$	6.55343	+	11.3509i	0.221168	+	0.383073i
$879$		0			0
$880$		0			0
$881$	39.5885			1.33377			0.666885	−	0.745161i	$-0.267627\pi$
$881$	39.5885			1.33377			0.666885	+	0.745161i	$0.267627\pi$
$882$		0			0
$883$	54.4336			1.83184			0.915919	−	0.401364i	$-0.131464\pi$
$883$	54.4336			1.83184			0.915919	+	0.401364i	$0.131464\pi$
$884$	11.1962	−	19.3923i	0.376567	−	0.652234i
$885$		0			0
$886$	0.428203	+	0.741670i	0.0143858	+	0.0249169i
$887$	−4.29341	−	7.43640i	−0.144159	−	0.249690i	0.784900	−	0.619622i	$-0.212714\pi$
$887$	−4.29341	−	7.43640i	−0.144159	−	0.249690i	−0.929059	+	0.369932i	$0.879381\pi$
$888$		0			0
$889$	−29.0885	+	50.3827i	−0.975596	+	1.68978i
$890$		0			0
$891$		0			0
$892$	7.76457			0.259977
$893$	1.08604	−	1.88108i	0.0363431	−	0.0629481i
$894$		0			0
$895$		0			0
$896$	19.1603	+	33.1865i	0.640099	+	1.10868i
$897$		0			0
$898$	−3.10583	+	5.37945i	−0.103643	+	0.179515i
$899$	0.339746			0.0113312
$900$		0			0
$901$	−5.46410			−0.182036
$902$	−2.53742	+	4.39494i	−0.0844869	+	0.146336i
$903$		0			0
$904$	−16.6603	−	28.8564i	−0.554112	−	0.959750i
$905$		0			0
$906$		0			0
$907$	−5.76337	+	9.98245i	−0.191370	+	0.331462i	−0.945704	−	0.325028i	$-0.894626\pi$
$907$	−5.76337	+	9.98245i	−0.191370	+	0.331462i	0.754335	+	0.656490i	$0.227960\pi$
$908$	−45.7081			−1.51688
$909$		0			0
$910$		0			0
$911$	24.9282	−	43.1769i	0.825908	−	1.43051i	−0.0753150	−	0.997160i	$-0.523996\pi$
$911$	24.9282	−	43.1769i	0.825908	−	1.43051i	0.901223	−	0.433355i	$-0.142670\pi$
$912$		0			0
$913$	5.05128	+	8.74908i	0.167173	+	0.289552i
$914$	6.41858	+	11.1173i	0.212308	+	0.367728i
$915$		0			0
$916$	5.25833	−	9.10770i	0.173740	−	0.300927i
$917$	−43.2586			−1.42853
$918$		0			0
$919$	47.1769			1.55622			0.778111	−	0.628126i	$-0.216178\pi$
$919$	47.1769			1.55622			0.778111	+	0.628126i	$0.216178\pi$
$920$		0			0
$921$		0			0
$922$	−9.50198	−	16.4579i	−0.312931	−	0.542012i
$923$	−17.3867	−	30.1146i	−0.572289	−	0.991234i
$924$		0			0
$925$		0			0
$926$	−17.6603			−0.580352
$927$		0			0
$928$	2.38512			0.0782954
$929$	−1.73205	+	3.00000i	−0.0568267	+	0.0984268i	−0.893039	−	0.449979i	$-0.851432\pi$
$929$	−1.73205	+	3.00000i	−0.0568267	+	0.0984268i	0.836213	+	0.548405i	$0.184765\pi$
$930$		0			0
$931$	1.53590	+	2.66025i	0.0503370	+	0.0871863i
$932$	6.12372	+	10.6066i	0.200589	+	0.347431i
$933$		0			0
$934$	6.56218	−	11.3660i	0.214721	−	0.371908i
$935$		0			0
$936$		0			0
$937$	−28.5617			−0.933069			−0.466535	−	0.884503i	$-0.654498\pi$
$937$	−28.5617			−0.933069			−0.466535	+	0.884503i	$0.654498\pi$
$938$	6.57201	−	11.3831i	0.214584	−	0.371670i
$939$		0			0
$940$		0			0
$941$	13.1603	+	22.7942i	0.429012	+	0.743071i	0.996786	−	0.0801141i	$-0.0255285\pi$
$941$	13.1603	+	22.7942i	0.429012	+	0.743071i	−0.567774	+	0.823185i	$0.692195\pi$
$942$		0			0
$943$	−2.00120	+	3.46618i	−0.0651681	+	0.112874i
$944$	−23.3205			−0.759018
$945$		0			0
$946$	0.430781			0.0140059
$947$	−2.38014	+	4.12252i	−0.0773441	+	0.133964i	−0.902103	−	0.431520i	$-0.857977\pi$
$947$	−2.38014	+	4.12252i	−0.0773441	+	0.133964i	0.824759	+	0.565484i	$0.191311\pi$
$948$		0			0
$949$	10.3923	+	18.0000i	0.337348	+	0.584305i
$950$		0			0
$951$		0			0
$952$	−17.0585	+	29.5462i	−0.552869	+	0.957597i
$953$	51.1619			1.65730			0.828648	−	0.559770i	$-0.189111\pi$
$953$	51.1619			1.65730			0.828648	+	0.559770i	$0.189111\pi$
$954$		0			0
$955$		0			0
$956$	0.803848	−	1.39230i	0.0259983	−	0.0450304i
$957$		0			0
$958$	1.07244	+	1.85752i	0.0346490	+	0.0600138i
$959$	26.3205	+	45.5885i	0.849934	+	1.47213i
$960$		0			0
$961$	15.2321	−	26.3827i	0.491356	−	0.851054i
$962$	5.37945			0.173441
$963$		0			0
$964$	−16.8564			−0.542908
$965$		0			0
$966$		0			0
$967$	27.9611	+	48.4300i	0.899168	+	1.55740i	0.828560	+	0.559900i	$0.189160\pi$
$967$	27.9611	+	48.4300i	0.899168	+	1.55740i	0.0706076	+	0.997504i	$0.477506\pi$
$968$	−9.07227	−	15.7136i	−0.291594	−	0.505055i
$969$		0			0
$970$		0			0
$971$	−38.1962			−1.22577			−0.612886	−	0.790171i	$-0.709992\pi$
$971$	−38.1962			−1.22577			−0.612886	+	0.790171i	$0.709992\pi$
$972$		0			0
$973$	−26.7685			−0.858159
$974$	−4.09808	+	7.09808i	−0.131311	+	0.227437i
$975$		0			0
$976$	8.20577	+	14.2128i	0.262660	+	0.454941i
$977$	7.77817	+	13.4722i	0.248846	+	0.431014i	0.963206	−	0.268765i	$-0.0866154\pi$
$977$	7.77817	+	13.4722i	0.248846	+	0.431014i	−0.714360	+	0.699778i	$0.753282\pi$
$978$		0			0
$979$	−8.49038	+	14.7058i	−0.271354	+	0.469998i
$980$		0			0
$981$		0			0
$982$	−17.4510			−0.556885
$983$	−16.7117	+	28.9456i	−0.533022	+	0.923221i	0.466234	+	0.884661i	$0.345610\pi$
$983$	−16.7117	+	28.9456i	−0.533022	+	0.923221i	−0.999256	+	0.0385597i	$0.987723\pi$
$984$		0			0
$985$		0			0
$986$	0.633975	+	1.09808i	0.0201899	+	0.0349699i
$987$		0			0
$988$	1.55291	−	2.68973i	0.0494048	−	0.0855716i
$989$	0.339746			0.0108033
$990$		0			0
$991$	38.9282			1.23660			0.618298	−	0.785944i	$-0.287823\pi$
$991$	38.9282			1.23660			0.618298	+	0.785944i	$0.287823\pi$
$992$	−1.88108	+	3.25813i	−0.0597245	+	0.103446i
$993$		0			0
$994$	12.2942	+	21.2942i	0.389949	+	0.675412i
$995$		0			0
$996$		0			0
$997$	−5.13922	+	8.90138i	−0.162761	+	0.281910i	−0.935858	−	0.352378i	$-0.885373\pi$
$997$	−5.13922	+	8.90138i	−0.162761	+	0.281910i	0.773097	+	0.634288i	$0.218706\pi$
$998$	12.3490			0.390900
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.e.d.451.2		8
3.2	odd	2		225.2.e.d.151.3		8
5.2	odd	4		135.2.j.a.19.2		8
5.3	odd	4		135.2.j.a.19.3		8
5.4	even	2	inner	675.2.e.d.451.3		8
9.2	odd	6		2025.2.a.t.1.2		4
9.4	even	3	inner	675.2.e.d.226.2		8
9.5	odd	6		225.2.e.d.76.3		8
9.7	even	3		2025.2.a.r.1.3		4
15.2	even	4		45.2.j.a.34.3	yes	8
15.8	even	4		45.2.j.a.34.2	yes	8
15.14	odd	2		225.2.e.d.151.2		8
20.3	even	4		2160.2.by.c.289.3		8
20.7	even	4		2160.2.by.c.289.1		8
45.2	even	12		405.2.b.d.244.2		4
45.4	even	6	inner	675.2.e.d.226.3		8
45.7	odd	12		405.2.b.c.244.3		4
45.13	odd	12		135.2.j.a.64.2		8
45.14	odd	6		225.2.e.d.76.2		8
45.22	odd	12		135.2.j.a.64.3		8
45.23	even	12		45.2.j.a.4.3	yes	8
45.29	odd	6		2025.2.a.t.1.3		4
45.32	even	12		45.2.j.a.4.2	✓	8
45.34	even	6		2025.2.a.r.1.2		4
45.38	even	12		405.2.b.d.244.3		4
45.43	odd	12		405.2.b.c.244.2		4
60.23	odd	4		720.2.by.d.529.2		8
60.47	odd	4		720.2.by.d.529.3		8
180.23	odd	12		720.2.by.d.49.3		8
180.67	even	12		2160.2.by.c.1009.3		8
180.103	even	12		2160.2.by.c.1009.1		8
180.167	odd	12		720.2.by.d.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.2	✓	8	45.32	even	12
45.2.j.a.4.3	yes	8	45.23	even	12
45.2.j.a.34.2	yes	8	15.8	even	4
45.2.j.a.34.3	yes	8	15.2	even	4
135.2.j.a.19.2		8	5.2	odd	4
135.2.j.a.19.3		8	5.3	odd	4
135.2.j.a.64.2		8	45.13	odd	12
135.2.j.a.64.3		8	45.22	odd	12
225.2.e.d.76.2		8	45.14	odd	6
225.2.e.d.76.3		8	9.5	odd	6
225.2.e.d.151.2		8	15.14	odd	2
225.2.e.d.151.3		8	3.2	odd	2
405.2.b.c.244.2		4	45.43	odd	12
405.2.b.c.244.3		4	45.7	odd	12
405.2.b.d.244.2		4	45.2	even	12
405.2.b.d.244.3		4	45.38	even	12
675.2.e.d.226.2		8	9.4	even	3	inner
675.2.e.d.226.3		8	45.4	even	6	inner
675.2.e.d.451.2		8	1.1	even	1	trivial
675.2.e.d.451.3		8	5.4	even	2	inner
720.2.by.d.49.2		8	180.167	odd	12
720.2.by.d.49.3		8	180.23	odd	12
720.2.by.d.529.2		8	60.23	odd	4
720.2.by.d.529.3		8	60.47	odd	4
2025.2.a.r.1.2		4	45.34	even	6
2025.2.a.r.1.3		4	9.7	even	3
2025.2.a.t.1.2		4	9.2	odd	6
2025.2.a.t.1.3		4	45.29	odd	6
2160.2.by.c.289.1		8	20.7	even	4
2160.2.by.c.289.3		8	20.3	even	4
2160.2.by.c.1009.1		8	180.103	even	12
2160.2.by.c.1009.3		8	180.67	even	12

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.448288i) q^{2} +(0.866025 + 1.50000i) q^{4} +(-1.67303 + 2.89778i) q^{7} -1.93185 q^{8} +O(q^{10})\)	\(q+(-0.258819 + 0.448288i) q^{2} +(0.866025 + 1.50000i) q^{4} +(-1.67303 + 2.89778i) q^{7} -1.93185 q^{8} +(0.633975 - 1.09808i) q^{11} +(1.22474 + 2.12132i) q^{13} +(-0.866025 - 1.50000i) q^{14} +(-1.23205 + 2.13397i) q^{16} -5.27792 q^{17} -0.732051 q^{19} +(0.328169 + 0.568406i) q^{22} +(0.258819 + 0.448288i) q^{23} -1.26795 q^{26} -5.79555 q^{28} +(-0.232051 + 0.401924i) q^{29} +(-0.366025 - 0.633975i) q^{31} +(-2.56961 - 4.45069i) q^{32} +(1.36603 - 2.36603i) q^{34} -4.24264 q^{37} +(0.189469 - 0.328169i) q^{38} +(3.86603 + 6.69615i) q^{41} +(0.328169 - 0.568406i) q^{43} +2.19615 q^{44} -0.267949 q^{46} +(-1.48356 + 2.56961i) q^{47} +(-2.09808 - 3.63397i) q^{49} +(-2.12132 + 3.67423i) q^{52} +1.03528 q^{53} +(3.23205 - 5.59808i) q^{56} +(-0.120118 - 0.208051i) q^{58} +(4.73205 + 8.19615i) q^{59} +(3.33013 - 5.76795i) q^{61} +0.378937 q^{62} -2.26795 q^{64} +(3.79435 + 6.57201i) q^{67} +(-4.57081 - 7.91688i) q^{68} -14.1962 q^{71} +8.48528 q^{73} +(1.09808 - 1.90192i) q^{74} +(-0.633975 - 1.09808i) q^{76} +(2.12132 + 3.67423i) q^{77} +(-3.73205 + 6.46410i) q^{79} -4.00240 q^{82} +(-3.98382 + 6.90018i) q^{83} +(0.169873 + 0.294229i) q^{86} +(-1.22474 + 2.12132i) q^{88} -13.3923 q^{89} -8.19615 q^{91} +(-0.448288 + 0.776457i) q^{92} +(-0.767949 - 1.33013i) q^{94} +(7.58871 - 13.1440i) q^{97} +2.17209 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 12 q^{11} + 4 q^{16} + 8 q^{19} - 24 q^{26} + 12 q^{29} + 4 q^{31} + 4 q^{34} + 24 q^{41} - 24 q^{44} - 16 q^{46} + 4 q^{49} + 12 q^{56} + 24 q^{59} - 8 q^{61} - 32 q^{64} - 72 q^{71} - 12 q^{74} - 12 q^{76} - 16 q^{79} + 36 q^{86} - 24 q^{89} - 24 q^{91} - 20 q^{94}+O(q^{100}) \) 8 * q + 12 * q^11 + 4 * q^16 + 8 * q^19 - 24 * q^26 + 12 * q^29 + 4 * q^31 + 4 * q^34 + 24 * q^41 - 24 * q^44 - 16 * q^46 + 4 * q^49 + 12 * q^56 + 24 * q^59 - 8 * q^61 - 32 * q^64 - 72 * q^71 - 12 * q^74 - 12 * q^76 - 16 * q^79 + 36 * q^86 - 24 * q^89 - 24 * q^91 - 20 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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