LMFDB - Embedded newform 675.2.ba.c.518.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(32,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("675.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, 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:	$288$
Relative dimension:	$24$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			518.13
Character	$\chi$	$=$	675.518
Dual form			675.2.ba.c.632.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.347779 + 0.0304268i) q^{2} +(-0.528165 - 1.64956i) q^{3} +(-1.84959 - 0.326133i) q^{4} +(-0.133494 - 0.589753i) q^{6} +(-0.994510 - 0.696364i) q^{7} +(-1.30775 - 0.350411i) q^{8} +(-2.44208 + 1.74248i) q^{9} +O(q^{10})$	\(q+(0.347779 + 0.0304268i) q^{2} +(-0.528165 - 1.64956i) q^{3} +(-1.84959 - 0.326133i) q^{4} +(-0.133494 - 0.589753i) q^{6} +(-0.994510 - 0.696364i) q^{7} +(-1.30775 - 0.350411i) q^{8} +(-2.44208 + 1.74248i) q^{9} +(-0.626120 + 1.72025i) q^{11} +(0.438914 + 3.22326i) q^{12} +(0.0303916 + 0.347377i) q^{13} +(-0.324682 - 0.272441i) q^{14} +(3.08557 + 1.12306i) q^{16} +(1.92212 - 0.515030i) q^{17} +(-0.902324 + 0.531693i) q^{18} +(-4.81794 + 2.78164i) q^{19} +(-0.623426 + 2.00830i) q^{21} +(-0.270093 + 0.579217i) q^{22} +(1.69206 + 2.41651i) q^{23} +(0.112685 + 2.34229i) q^{24} +0.121735i q^{26} +(4.16414 + 3.10804i) q^{27} +(1.61233 + 1.61233i) q^{28} +(-1.34520 + 1.12876i) q^{29} +(-0.372471 + 2.11239i) q^{31} +(3.49300 + 1.62881i) q^{32} +(3.16835 + 0.124245i) q^{33} +(0.684143 - 0.120633i) q^{34} +(5.08513 - 2.42643i) q^{36} +(0.433293 + 1.61707i) q^{37} +(-1.76022 + 0.820803i) q^{38} +(0.556967 - 0.233605i) q^{39} +(-7.15599 + 8.52817i) q^{41} +(-0.277921 + 0.679476i) q^{42} +(1.86279 + 3.99477i) q^{43} +(1.71910 - 2.97756i) q^{44} +(0.514936 + 0.891896i) q^{46} +(6.40776 - 9.15123i) q^{47} +(0.222855 - 5.68299i) q^{48} +(-1.89001 - 5.19277i) q^{49} +(-1.86477 - 2.89862i) q^{51} +(0.0570792 - 0.652418i) q^{52} +(-5.25853 + 5.25853i) q^{53} +(1.35364 + 1.20761i) q^{54} +(1.05656 + 1.25916i) q^{56} +(7.13315 + 6.47831i) q^{57} +(-0.502179 + 0.351629i) q^{58} +(-5.35536 + 1.94919i) q^{59} +(1.30500 + 7.40100i) q^{61} +(-0.193811 + 0.723312i) q^{62} +(3.64208 - 0.0323344i) q^{63} +(-4.52212 - 2.61085i) q^{64} +(1.09811 + 0.139612i) q^{66} +(-9.76158 + 0.854027i) q^{67} +(-3.72310 + 0.325729i) q^{68} +(3.09249 - 4.06746i) q^{69} +(-13.6425 - 7.87649i) q^{71} +(3.80422 - 1.42299i) q^{72} +(-3.10541 + 11.5895i) q^{73} +(0.101488 + 0.575568i) q^{74} +(9.81841 - 3.57361i) q^{76} +(1.82060 - 1.27480i) q^{77} +(0.200810 - 0.0642964i) q^{78} +(9.65809 + 11.5101i) q^{79} +(2.92754 - 8.51055i) q^{81} +(-2.74819 + 2.74819i) q^{82} +(1.12664 - 12.8776i) q^{83} +(1.80806 - 3.51121i) q^{84} +(0.526293 + 1.44598i) q^{86} +(2.57244 + 1.62282i) q^{87} +(1.42160 - 2.03026i) q^{88} +(-1.27248 - 2.20400i) q^{89} +(0.211676 - 0.366634i) q^{91} +(-2.34151 - 5.02139i) q^{92} +(3.68124 - 0.501277i) q^{93} +(2.50693 - 2.98764i) q^{94} +(0.841940 - 6.62218i) q^{96} +(-5.51873 + 2.57343i) q^{97} +(-0.499308 - 1.86344i) q^{98} +(-1.46846 - 5.29200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 24 q^{6}+O(q^{10}) $ 288 * q + 24 * q^6	$ 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) $ 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.347779	+	0.0304268i	0.245917	+	0.0215150i	0.209448	−	0.977820i	$-0.432833\pi$
$2$	0.347779	+	0.0304268i	0.245917	+	0.0215150i	0.0364693	+	0.999335i	$0.488389\pi$
$3$	−0.528165	−	1.64956i	−0.304936	−	0.952373i
$3$	−0.528165	−	1.64956i	−0.304936	−	0.952373i
$4$	−1.84959	−	0.326133i	−0.924795	−	0.163066i
$5$		0			0
$5$		0			0
$6$	−0.133494	−	0.589753i	−0.0544988	−	0.240765i
$7$	−0.994510	−	0.696364i	−0.375890	−	0.263201i	0.370330	−	0.928900i	$-0.379244\pi$
$7$	−0.994510	−	0.696364i	−0.375890	−	0.263201i	−0.746220	+	0.665699i	$0.768133\pi$
$8$	−1.30775	−	0.350411i	−0.462360	−	0.123889i
$9$	−2.44208	+	1.74248i	−0.814028	+	0.580826i
$10$		0			0
$11$	−0.626120	+	1.72025i	−0.188782	+	0.518675i	−0.997589	−	0.0693995i	$-0.977892\pi$
$11$	−0.626120	+	1.72025i	−0.188782	+	0.518675i	0.808807	+	0.588075i	$0.200114\pi$
$12$	0.438914	+	3.22326i	0.126704	+	0.930475i
$13$	0.0303916	+	0.347377i	0.00842911	+	0.0963452i	0.999244	−	0.0388812i	$-0.0123794\pi$
$13$	0.0303916	+	0.347377i	0.00842911	+	0.0963452i	−0.990815	+	0.135226i	$0.956824\pi$
$14$	−0.324682	−	0.272441i	−0.0867749	−	0.0728128i
$15$		0			0
$16$	3.08557	+	1.12306i	0.771393	+	0.280764i
$17$	1.92212	−	0.515030i	0.466182	−	0.124913i	−0.0180793	−	0.999837i	$-0.505755\pi$
$17$	1.92212	−	0.515030i	0.466182	−	0.124913i	0.484261	+	0.874924i	$0.339088\pi$
$18$	−0.902324	+	0.531693i	−0.212680	+	0.125321i
$19$	−4.81794	+	2.78164i	−1.10531	+	0.638152i	−0.937611	−	0.347685i	$-0.886968\pi$
$19$	−4.81794	+	2.78164i	−1.10531	+	0.638152i	−0.167701	+	0.985838i	$0.553634\pi$
$20$		0			0
$21$	−0.623426	+	2.00830i	−0.136043	+	0.438246i
$22$	−0.270093	+	0.579217i	−0.0575841	+	0.123489i
$23$	1.69206	+	2.41651i	0.352818	+	0.503877i	0.955856	−	0.293836i	$-0.0949320\pi$
$23$	1.69206	+	2.41651i	0.352818	+	0.503877i	−0.603037	+	0.797713i	$0.706043\pi$
$24$	0.112685	+	2.34229i	0.0230018	+	0.478117i
$25$		0			0
$26$			0.121735i			0.0238743i
$27$	4.16414	+	3.10804i	0.801389	+	0.598143i
$28$	1.61233	+	1.61233i	0.304702	+	0.304702i
$29$	−1.34520	+	1.12876i	−0.249798	+	0.209605i	−0.759085	−	0.650991i	$-0.774353\pi$
$29$	−1.34520	+	1.12876i	−0.249798	+	0.209605i	0.509287	+	0.860597i	$0.329909\pi$
$30$		0			0
$31$	−0.372471	+	2.11239i	−0.0668978	+	0.379396i	0.932916	+	0.360094i	$0.117256\pi$
$31$	−0.372471	+	2.11239i	−0.0668978	+	0.379396i	−0.999814	+	0.0193020i	$0.993856\pi$
$32$	3.49300	+	1.62881i	0.617481	+	0.287936i
$33$	3.16835	+	0.124245i	0.551539	+	0.0216283i
$34$	0.684143	−	0.120633i	0.117330	−	0.0206884i
$35$		0			0
$36$	5.08513	−	2.42643i	0.847522	−	0.404405i
$37$	0.433293	+	1.61707i	0.0712329	+	0.265845i	0.992353	−	0.123434i	$-0.0393908\pi$
$37$	0.433293	+	1.61707i	0.0712329	+	0.265845i	−0.921120	+	0.389279i	$0.872724\pi$
$38$	−1.76022	+	0.820803i	−0.285545	+	0.133152i
$39$	0.556967	−	0.233605i	0.0891862	−	0.0374068i
$40$		0			0
$41$	−7.15599	+	8.52817i	−1.11758	+	1.33188i	−0.180172	+	0.983635i	$0.557666\pi$
$41$	−7.15599	+	8.52817i	−1.11758	+	1.33188i	−0.937405	+	0.348242i	$0.886779\pi$
$42$	−0.277921	+	0.679476i	−0.0428841	+	0.104845i
$43$	1.86279	+	3.99477i	0.284073	+	0.609197i	0.995625	−	0.0934362i	$-0.0297851\pi$
$43$	1.86279	+	3.99477i	0.284073	+	0.609197i	−0.711552	+	0.702634i	$0.752007\pi$
$44$	1.71910	−	2.97756i	0.259163	−	0.448884i
$45$		0			0
$46$	0.514936	+	0.891896i	0.0759232	+	0.131503i
$47$	6.40776	−	9.15123i	0.934668	−	1.33484i	−0.00759474	−	0.999971i	$-0.502418\pi$
$47$	6.40776	−	9.15123i	0.934668	−	1.33484i	0.942263	−	0.334874i	$-0.108694\pi$
$48$	0.222855	−	5.68299i	0.0321664	−	0.820269i
$49$	−1.89001	−	5.19277i	−0.270002	−	0.741824i
$50$		0			0
$51$	−1.86477	−	2.89862i	−0.261119	−	0.405888i
$52$	0.0570792	−	0.652418i	0.00791545	−	0.0904741i
$53$	−5.25853	+	5.25853i	−0.722314	+	0.722314i	−0.969076	−	0.246762i	$-0.920633\pi$
$53$	−5.25853	+	5.25853i	−0.722314	+	0.722314i	0.246762	+	0.969076i	$0.420633\pi$
$54$	1.35364	+	1.20761i	0.184206	+	0.164335i
$55$		0			0
$56$	1.05656	+	1.25916i	0.141189	+	0.168262i
$57$	7.13315	+	6.47831i	0.944809	+	0.858074i
$58$	−0.502179	+	0.351629i	−0.0659393	+	0.0461712i
$59$	−5.35536	+	1.94919i	−0.697209	+	0.253763i	−0.666219	−	0.745756i	$-0.732088\pi$
$59$	−5.35536	+	1.94919i	−0.697209	+	0.253763i	−0.0309902	+	0.999520i	$0.509866\pi$
$60$		0			0
$61$	1.30500	+	7.40100i	0.167088	+	0.947602i	0.946886	+	0.321570i	$0.104211\pi$
$61$	1.30500	+	7.40100i	0.167088	+	0.947602i	−0.779798	+	0.626031i	$0.784678\pi$
$62$	−0.193811	+	0.723312i	−0.0246140	+	0.0918608i
$63$	3.64208	−	0.0323344i	0.458858	−	0.00407376i
$64$	−4.52212	−	2.61085i	−0.565265	−	0.326356i
$65$		0			0
$66$	1.09811	+	0.139612i	0.135167	+	0.0171851i
$67$	−9.76158	+	0.854027i	−1.19257	+	0.104336i	−0.666102	−	0.745861i	$-0.732038\pi$
$67$	−9.76158	+	0.854027i	−1.19257	+	0.104336i	−0.526465	+	0.850197i	$0.676483\pi$
$68$	−3.72310	+	0.325729i	−0.451492	+	0.0395004i
$69$	3.09249	−	4.06746i	0.372291	−	0.489665i
$70$		0			0
$71$	−13.6425	−	7.87649i	−1.61906	−	0.934767i	−0.987163	−	0.159718i	$-0.948942\pi$
$71$	−13.6425	−	7.87649i	−1.61906	−	0.934767i	−0.631901	−	0.775049i	$-0.717725\pi$
$72$	3.80422	−	1.42299i	0.448332	−	0.167702i
$73$	−3.10541	+	11.5895i	−0.363460	+	1.35645i	0.506036	+	0.862513i	$0.331110\pi$
$73$	−3.10541	+	11.5895i	−0.363460	+	1.35645i	−0.869496	+	0.493940i	$0.835556\pi$
$74$	0.101488	+	0.575568i	0.0117978	+	0.0669084i
$75$		0			0
$76$	9.81841	−	3.57361i	1.12625	−	0.409921i
$77$	1.82060	−	1.27480i	0.207477	−	0.145277i
$78$	0.200810	−	0.0642964i	0.0227372	−	0.00728013i
$79$	9.65809	+	11.5101i	1.08662	+	1.29498i	0.952674	+	0.303995i	$0.0983205\pi$
$79$	9.65809	+	11.5101i	1.08662	+	1.29498i	0.133946	+	0.990989i	$0.457235\pi$
$80$		0			0
$81$	2.92754	−	8.51055i	0.325282	−	0.945617i
$82$	−2.74819	+	2.74819i	−0.303487	+	0.303487i
$83$	1.12664	−	12.8776i	0.123665	−	1.41350i	−0.640241	−	0.768174i	$-0.721166\pi$
$83$	1.12664	−	12.8776i	0.123665	−	1.41350i	0.763906	−	0.645327i	$-0.223279\pi$
$84$	1.80806	−	3.51121i	0.197275	−	0.383104i
$85$		0			0
$86$	0.526293	+	1.44598i	0.0567517	+	0.155924i
$87$	2.57244	+	1.62282i	0.275795	+	0.173985i
$88$	1.42160	−	2.03026i	0.151543	−	0.216426i
$89$	−1.27248	−	2.20400i	−0.134883	−	0.233623i	0.790670	−	0.612243i	$-0.209732\pi$
$89$	−1.27248	−	2.20400i	−0.134883	−	0.233623i	−0.925553	+	0.378619i	$0.876399\pi$
$90$		0			0
$91$	0.211676	−	0.366634i	0.0221897	−	0.0384337i
$92$	−2.34151	−	5.02139i	−0.244119	−	0.523516i
$93$	3.68124	−	0.501277i	0.381726	−	0.0519801i
$94$	2.50693	−	2.98764i	0.258570	−	0.308152i
$95$		0			0
$96$	0.841940	−	6.62218i	0.0859301	−	0.675874i
$97$	−5.51873	+	2.57343i	−0.560342	+	0.261292i	−0.682089	−	0.731269i	$-0.738928\pi$
$97$	−5.51873	+	2.57343i	−0.560342	+	0.261292i	0.121746	+	0.992561i	$0.461151\pi$
$98$	−0.499308	−	1.86344i	−0.0504378	−	0.188236i
$99$	−1.46846	−	5.29200i	−0.147586	−	0.531866i
$100$		0			0
$101$	6.16986	−	1.08791i	0.613924	−	0.108251i	0.141965	−	0.989872i	$-0.454658\pi$
$101$	6.16986	−	1.08791i	0.613924	−	0.108251i	0.471959	+	0.881620i	$0.343547\pi$
$102$	−0.560332	−	1.06482i	−0.0554811	−	0.105433i
$103$	−12.9364	−	6.03233i	−1.27466	−	0.594383i	−0.336858	−	0.941556i	$-0.609364\pi$
$103$	−12.9364	−	6.03233i	−1.27466	−	0.594383i	−0.937801	+	0.347172i	$0.887142\pi$
$104$	0.0819802	−	0.464933i	0.00803882	−	0.0455904i
$105$		0			0
$106$	−1.98881	+	1.66881i	−0.193170	+	0.162089i
$107$	−12.7480	−	12.7480i	−1.23240	−	1.23240i	−0.963041	−	0.269355i	$-0.913190\pi$
$107$	−12.7480	−	12.7480i	−1.23240	−	1.23240i	−0.269355	−	0.963041i	$-0.586810\pi$
$108$	−6.68832	−	7.10667i	−0.643584	−	0.683839i
$109$			9.14545i			0.875976i	0.898981	+	0.437988i	$0.144309\pi$
$109$			9.14545i			0.875976i	−0.898981	+	0.437988i	$0.855691\pi$
$110$		0			0
$111$	2.43860	−	1.56882i	0.231462	−	0.148906i
$112$	−2.28658	−	3.26557i	−0.216061	−	0.308567i
$113$	5.16253	−	11.0711i	0.485650	−	1.04148i	−0.498946	−	0.866633i	$-0.666279\pi$
$113$	5.16253	−	11.0711i	0.485650	−	1.04148i	0.984596	−	0.174846i	$-0.0559428\pi$
$114$	2.28365	+	2.47006i	0.213883	+	0.231343i
$115$		0			0
$116$	2.85620	−	1.64903i	0.265192	−	0.153108i
$117$	−0.679516	−	0.795368i	−0.0628213	−	0.0735318i
$118$	−1.92179	+	0.514943i	−0.176915	+	0.0474043i
$119$	−2.27021	−	0.826290i	−0.208110	−	0.0757459i
$120$		0			0
$121$	5.85925	+	4.91650i	0.532659	+	0.446954i
$122$	0.228662	+	2.61362i	0.0207021	+	0.236626i
$123$	17.8473	+	7.29993i	1.60923	+	0.658213i
$124$	1.37784	−	3.78558i	0.123734	−	0.339955i
$125$		0			0
$126$	1.26762	+	0.0995713i	0.112929	+	0.00887051i
$127$	−6.64080	−	1.77940i	−0.589276	−	0.157896i	−0.0481536	−	0.998840i	$-0.515334\pi$
$127$	−6.64080	−	1.77940i	−0.589276	−	0.157896i	−0.541122	+	0.840944i	$0.682000\pi$
$128$	−7.80744	−	5.46683i	−0.690087	−	0.483204i
$129$	5.60575	−	5.18269i	0.493559	−	0.456310i
$130$		0			0
$131$	−18.1487	−	3.20011i	−1.58566	−	0.279595i	−0.689823	−	0.723978i	$-0.742312\pi$
$131$	−18.1487	−	3.20011i	−1.58566	−	0.279595i	−0.895837	+	0.444384i	$0.853423\pi$
$132$	−5.81963	−	1.26310i	−0.506534	−	0.109939i
$133$	6.72853	+	0.588670i	0.583438	+	0.0510442i
$134$	−3.42086			−0.295517
$135$		0			0
$136$	−2.69412			−0.231019
$137$	−0.496033	−	0.0433972i	−0.0423789	−	0.00370768i	0.0659466	−	0.997823i	$-0.478993\pi$
$137$	−0.496033	−	0.0433972i	−0.0423789	−	0.00370768i	−0.108325	+	0.994115i	$0.534549\pi$
$138$	1.19926	−	1.32049i	0.102088	−	0.112407i
$139$	1.39820	+	0.246540i	0.118594	+	0.0209113i	0.232630	−	0.972565i	$-0.425267\pi$
$139$	1.39820	+	0.246540i	0.118594	+	0.0209113i	−0.114036	+	0.993477i	$0.536378\pi$
$140$		0			0
$141$	−18.4798	−	5.73661i	−1.55628	−	0.483110i
$142$	−4.50492	−	3.15438i	−0.378044	−	0.264709i
$143$	−0.616605	−	0.165219i	−0.0515631	−	0.0138163i
$144$	−9.49212	+	2.63394i	−0.791010	+	0.219495i
$145$		0			0
$146$	−1.43263	+	3.93611i	−0.118565	+	0.325755i
$147$	−7.56753	+	5.86032i	−0.624159	+	0.483351i
$148$	−0.274035	−	3.13223i	−0.0225255	−	0.257468i
$149$	12.3163	+	10.3346i	1.00899	+	0.846644i	0.988204	−	0.153140i	$-0.0489386\pi$
$149$	12.3163	+	10.3346i	1.00899	+	0.846644i	0.0207862	+	0.999784i	$0.493383\pi$
$150$		0			0
$151$	−0.578102	−	0.210412i	−0.0470453	−	0.0171231i	0.318390	−	0.947960i	$-0.396858\pi$
$151$	−0.578102	−	0.210412i	−0.0470453	−	0.0171231i	−0.365436	+	0.930837i	$0.619080\pi$
$152$	7.27539	−	1.94943i	0.590112	−	0.158120i
$153$	−3.79654	+	4.60699i	−0.306932	+	0.372453i
$154$	0.671956	−	0.387954i	0.0541478	−	0.0312622i
$155$		0			0
$156$	−1.10635	+	0.250429i	−0.0885787	+	0.0200504i
$157$	−3.52308	+	7.55527i	−0.281172	+	0.602976i	−0.995278	−	0.0970614i	$-0.969056\pi$
$157$	−3.52308	+	7.55527i	−0.281172	+	0.602976i	0.714106	+	0.700038i	$0.246833\pi$
$158$	3.00867	+	4.29683i	0.239357	+	0.341837i
$159$	11.4516	+	5.89687i	0.908172	+	0.467652i
$160$		0			0
$161$		−	3.58153i		−	0.282264i
$162$	1.27709	−	2.87072i	0.100337	−	0.225545i
$163$	12.1060	+	12.1060i	0.948215	+	0.948215i	0.998724	−	0.0505083i	$-0.0160841\pi$
$163$	12.1060	+	12.1060i	0.948215	+	0.948215i	−0.0505083	+	0.998724i	$0.516084\pi$
$164$	16.0170	−	13.4398i	1.25071	−	1.04947i
$165$		0			0
$166$	0.783648	−	4.44429i	0.0608228	−	0.344943i
$167$	−16.2781	−	7.59058i	−1.25963	−	0.587377i	−0.325920	−	0.945397i	$-0.605674\pi$
$167$	−16.2781	−	7.59058i	−1.25963	−	0.587377i	−0.933714	+	0.358020i	$0.883452\pi$
$168$	1.51902	−	2.40790i	0.117195	−	0.185773i
$169$	12.6828	−	2.23631i	0.975596	−	0.172024i
$170$		0			0
$171$	6.91887	−	15.1882i	0.529099	−	1.16147i
$172$	−2.14258	−	7.99621i	−0.163370	−	0.609706i
$173$	6.74861	−	3.14693i	0.513088	−	0.239257i	−0.148790	−	0.988869i	$-0.547538\pi$
$173$	6.74861	−	3.14693i	0.513088	−	0.239257i	0.661877	+	0.749612i	$0.269760\pi$
$174$	0.845266	+	0.642654i	0.0640794	+	0.0487195i
$175$		0			0
$176$	−3.86388	+	4.60479i	−0.291251	+	0.347099i
$177$	6.04382	+	7.80449i	0.454282	+	0.586621i
$178$	−0.375482	−	0.805223i	−0.0281435	−	0.0603540i
$179$	−1.32416	+	2.29350i	−0.0989720	+	0.171425i	−0.911259	−	0.411833i	$-0.864889\pi$
$179$	−1.32416	+	2.29350i	−0.0989720	+	0.171425i	0.812287	+	0.583257i	$0.198222\pi$
$180$		0			0
$181$	−4.01126	−	6.94770i	−0.298155	−	0.516419i	0.677559	−	0.735468i	$-0.263038\pi$
$181$	−4.01126	−	6.94770i	−0.298155	−	0.516419i	−0.975714	+	0.219049i	$0.929704\pi$
$182$	0.0847721	−	0.121067i	0.00628373	−	0.00897409i
$183$	11.5191	−	6.06162i	0.851519	−	0.448088i
$184$	−1.36602	−	3.75311i	−0.100704	−	0.276683i
$185$		0			0
$186$	1.29551	−	0.0623259i	0.0949914	−	0.00456996i
$187$	−0.317496	+	3.62899i	−0.0232176	+	0.265378i
$188$	−14.8363	+	14.8363i	−1.08205	+	1.08205i
$189$	−1.97695	−	5.99074i	−0.143802	−	0.435762i
$190$		0			0
$191$	7.76324	+	9.25187i	0.561728	+	0.669442i	0.969911	−	0.243458i	$-0.0782820\pi$
$191$	7.76324	+	9.25187i	0.561728	+	0.669442i	−0.408183	+	0.912900i	$0.633838\pi$
$192$	−1.91832	+	8.83846i	−0.138443	+	0.637861i
$193$	−6.37332	+	4.46264i	−0.458761	+	0.321228i	−0.780010	−	0.625767i	$-0.784786\pi$
$193$	−6.37332	+	4.46264i	−0.458761	+	0.321228i	0.321249	+	0.946995i	$0.395897\pi$
$194$	−1.99760	+	0.727068i	−0.143420	+	0.0522004i
$195$		0			0
$196$	1.80222	+	10.2209i	0.128730	+	0.730063i
$197$	−0.144274	+	0.538437i	−0.0102791	+	0.0383620i	−0.970875	−	0.239587i	$-0.922988\pi$
$197$	−0.144274	+	0.538437i	−0.0102791	+	0.0383620i	0.960596	+	0.277949i	$0.0896546\pi$
$198$	−0.349683	−	1.88513i	−0.0248509	−	0.133970i
$199$	2.90871	+	1.67935i	0.206193	+	0.119046i	0.599541	−	0.800344i	$-0.295350\pi$
$199$	2.90871	+	1.67935i	0.206193	+	0.119046i	−0.393348	+	0.919390i	$0.628683\pi$
$200$		0			0
$201$	6.56449	+	15.6512i	0.463023	+	1.10395i
$202$	2.17885	−	0.190625i	0.153304	−	0.0134123i
$203$	2.12385	−	0.185812i	0.149065	−	0.0130415i
$204$	2.50372	+	5.96943i	0.175295	+	0.417943i
$205$		0			0
$206$	−4.31546	−	2.49153i	−0.300672	−	0.173593i
$207$	−8.34286	−	2.95294i	−0.579869	−	0.205244i
$208$	−0.296349	+	1.10599i	−0.0205481	+	0.0766865i
$209$	−1.76851	−	10.0297i	−0.122330	−	0.693770i
$210$		0			0
$211$	12.2782	−	4.46890i	0.845267	−	0.307652i	0.117158	−	0.993113i	$-0.462622\pi$
$211$	12.2782	−	4.46890i	0.845267	−	0.307652i	0.728109	+	0.685461i	$0.240399\pi$
$212$	11.4411	−	8.01114i	0.785778	−	0.550208i
$213$	−5.78724	+	26.6641i	−0.396535	+	1.82700i
$214$	−4.04561	−	4.82137i	−0.276552	−	0.329582i
$215$		0			0
$216$	−4.35657	−	5.52370i	−0.296427	−	0.375841i
$217$	1.84142	−	1.84142i	0.125004	−	0.125004i
$218$	−0.278266	+	3.18060i	−0.0188466	+	0.215417i
$219$	20.7578	−	0.998640i	1.40268	−	0.0674818i
$220$		0			0
$221$	0.237326	+	0.652047i	0.0159643	+	0.0438615i
$222$	0.895830	−	0.471406i	0.0601242	−	0.0316387i
$223$	9.16597	−	13.0904i	0.613799	−	0.876595i	−0.385131	−	0.922862i	$-0.625844\pi$
$223$	9.16597	−	13.0904i	0.613799	−	0.876595i	0.998929	+	0.0462669i	$0.0147325\pi$
$224$	−2.33958	−	4.05227i	−0.156320	−	0.270753i
$225$		0			0
$226$	2.13228	−	3.69321i	0.141837	−	0.245669i
$227$	3.92241	+	8.41164i	0.260340	+	0.558300i	0.992416	−	0.122922i	$-0.0392265\pi$
$227$	3.92241	+	8.41164i	0.260340	+	0.558300i	−0.732077	+	0.681222i	$0.761449\pi$
$228$	−11.0806	−	14.3086i	−0.733832	−	0.947609i
$229$	−4.29414	+	5.11756i	−0.283765	+	0.338178i	−0.889032	−	0.457844i	$-0.848622\pi$
$229$	−4.29414	+	5.11756i	−0.283765	+	0.338178i	0.605268	+	0.796022i	$0.293066\pi$
$230$		0			0
$231$	−3.06444	−	2.32989i	−0.201625	−	0.153295i
$232$	2.15472	−	1.00476i	0.141464	−	0.0659659i
$233$	1.43934	+	5.37169i	0.0942942	+	0.351911i	0.996911	−	0.0785332i	$-0.0250237\pi$
$233$	1.43934	+	5.37169i	0.0942942	+	0.351911i	−0.902617	+	0.430444i	$0.858357\pi$
$234$	−0.212121	−	0.297288i	−0.0138668	−	0.0194343i
$235$		0			0
$236$	10.5409	−	1.85865i	0.686156	−	0.120988i
$237$	13.8855	−	22.0108i	0.901957	−	1.42975i
$238$	−0.764392	−	0.356442i	−0.0495482	−	0.0231047i
$239$	1.28207	−	7.27098i	0.0829302	−	0.470320i	−0.914854	−	0.403785i	$-0.867694\pi$
$239$	1.28207	−	7.27098i	0.0829302	−	0.470320i	0.997784	−	0.0665354i	$-0.0211945\pi$
$240$		0			0
$241$	−11.5447	+	9.68711i	−0.743656	+	0.624002i	−0.933817	−	0.357751i	$-0.883544\pi$
$241$	−11.5447	+	9.68711i	−0.743656	+	0.624002i	0.190161	+	0.981753i	$0.439099\pi$
$242$	1.88813	+	1.88813i	0.121374	+	0.121374i
$243$	−15.5849	−	0.334171i	−0.999770	−	0.0214371i
$244$		−	14.1144i		−	0.903584i
$245$		0			0
$246$	5.98479	+	3.08180i	0.381577	+	0.196488i
$247$	−1.11270	−	1.58911i	−0.0707997	−	0.101112i
$248$	1.22730	−	2.63196i	0.0779339	−	0.167130i
$249$	−21.8374	+	4.94304i	−1.38389	+	0.313252i
$250$		0			0
$251$	24.4606	−	14.1224i	1.54394	−	0.891395i	0.545357	−	0.838204i	$-0.316394\pi$
$251$	24.4606	−	14.1224i	1.54394	−	0.891395i	0.998584	−	0.0531910i	$-0.0169392\pi$
$252$	−6.74689	−	1.12799i	−0.425014	−	0.0710570i
$253$	−5.21643	+	1.39774i	−0.327954	+	0.0878751i
$254$	−2.25539	−	0.820896i	−0.141516	−	0.0515076i
$255$		0			0
$256$	5.45117	+	4.57408i	0.340698	+	0.285880i
$257$	1.75903	+	20.1058i	0.109725	+	1.25417i	0.828924	+	0.559362i	$0.188954\pi$
$257$	1.75903	+	20.1058i	0.109725	+	1.25417i	−0.719198	+	0.694805i	$0.755491\pi$
$258$	2.10726	−	1.63187i	0.131192	−	0.101596i
$259$	0.695156	−	1.90992i	0.0431949	−	0.118677i
$260$		0			0
$261$	1.31826	−	5.10051i	0.0815982	−	0.315714i
$262$	−6.21438	−	1.66514i	−0.383925	−	0.102872i
$263$	−10.3997	−	7.28196i	−0.641274	−	0.449025i	0.207174	−	0.978304i	$-0.433573\pi$
$263$	−10.3997	−	7.28196i	−0.641274	−	0.449025i	−0.848448	+	0.529279i	$0.822462\pi$
$264$	−4.09987	−	1.27270i	−0.252330	−	0.0783296i
$265$		0			0
$266$	2.32213	+	0.409455i	0.142379	+	0.0251053i
$267$	−2.96354	+	3.26310i	−0.181366	+	0.199699i
$268$	18.3334	+	1.60397i	1.11989	+	0.0979780i
$269$	−19.2549			−1.17399			−0.586995	−	0.809591i	$-0.699689\pi$
$269$	−19.2549			−1.17399			−0.586995	+	0.809591i	$0.699689\pi$
$270$		0			0
$271$	−21.6954			−1.31790			−0.658952	−	0.752185i	$-0.729000\pi$
$271$	−21.6954			−1.31790			−0.658952	+	0.752185i	$0.729000\pi$
$272$	6.50923	+	0.569484i	0.394680	+	0.0345301i
$273$	−0.716584	−	0.155529i	−0.0433696	−	0.00941304i
$274$	−0.171189	−	0.0301853i	−0.0103419	−	0.00182356i
$275$		0			0
$276$	−7.04636	+	6.51458i	−0.424141	+	0.392132i
$277$	21.1890	+	14.8367i	1.27312	+	0.891452i	0.997559	−	0.0698305i	$-0.0222458\pi$
$277$	21.1890	+	14.8367i	1.27312	+	0.891452i	0.275566	+	0.961282i	$0.411135\pi$
$278$	0.478764	+	0.128284i	0.0287143	+	0.00769399i
$279$	−2.77119	−	5.80765i	−0.165907	−	0.347695i
$280$		0			0
$281$	1.44986	−	3.98347i	0.0864916	−	0.237634i	−0.888905	−	0.458092i	$-0.848533\pi$
$281$	1.44986	−	3.98347i	0.0864916	−	0.237634i	0.975396	+	0.220458i	$0.0707553\pi$
$282$	−6.25236	−	2.55736i	−0.372323	−	0.152288i
$283$	−1.24561	−	14.2374i	−0.0740440	−	0.846327i	−0.938874	−	0.344262i	$-0.888129\pi$
$283$	−1.24561	−	14.2374i	−0.0740440	−	0.846327i	0.864830	−	0.502065i	$-0.167426\pi$
$284$	22.6642	+	19.0175i	1.34487	+	1.12848i
$285$		0			0
$286$	−0.209415	−	0.0762210i	−0.0123830	−	0.00450704i
$287$	13.0554	−	3.49819i	0.770636	−	0.206491i
$288$	−11.3684	+	2.10878i	−0.669887	+	0.124261i
$289$	−11.2932	+	6.52011i	−0.664303	+	0.383536i
$290$		0			0
$291$	7.15982	+	7.74428i	0.419716	+	0.453977i
$292$	9.52346	−	20.4231i	0.557318	−	1.19517i
$293$	16.4573	+	23.5035i	0.961447	+	1.37309i	0.927565	+	0.373663i	$0.121898\pi$
$293$	16.4573	+	23.5035i	0.961447	+	1.37309i	0.0338821	+	0.999426i	$0.489213\pi$
$294$	−2.81014	+	1.80784i	−0.163891	+	0.105436i
$295$		0			0
$296$		−	2.26656i		−	0.131741i
$297$	−7.95386	+	5.21736i	−0.461530	+	0.302742i
$298$	3.96891	+	3.96891i	0.229913	+	0.229913i
$299$	−0.788016	+	0.661224i	−0.0455722	+	0.0382396i
$300$		0			0
$301$	0.929248	−	5.27003i	0.0535609	−	0.303759i
$302$	−0.194650	−	0.0907668i	−0.0112008	−	0.00522304i
$303$	−5.05328	−	9.60295i	−0.290303	−	0.551675i
$304$	−17.9901	+	3.17213i	−1.03180	+	0.181934i
$305$		0			0
$306$	−1.46053	+	1.48670i	−0.0834932	+	0.0849890i
$307$	0.586171	+	2.18762i	0.0334545	+	0.124854i	0.980634	−	0.195851i	$-0.0627469\pi$
$307$	0.586171	+	2.18762i	0.0334545	+	0.124854i	−0.947179	+	0.320705i	$0.896080\pi$
$308$	−3.78312	+	1.76410i	−0.215564	+	0.100519i
$309$	−3.11814	+	24.5254i	−0.177385	+	1.39520i
$310$		0			0
$311$	−7.85950	+	9.36659i	−0.445672	+	0.531131i	−0.941375	−	0.337361i	$-0.890466\pi$
$311$	−7.85950	+	9.36659i	−0.445672	+	0.531131i	0.495704	+	0.868492i	$0.334910\pi$
$312$	−0.810233	+	0.110330i	−0.0458704	+	0.00624622i
$313$	−7.14921	−	15.3315i	−0.404097	−	0.866590i	−0.998070	−	0.0621042i	$-0.980219\pi$
$313$	−7.14921	−	15.3315i	−0.404097	−	0.866590i	0.593972	−	0.804486i	$-0.297559\pi$
$314$	−1.45514	+	2.52037i	−0.0821181	+	0.142233i
$315$		0			0
$316$	−14.1097	−	24.4387i	−0.793733	−	1.37479i
$317$	−7.16210	+	10.2285i	−0.402264	+	0.574492i	−0.968269	−	0.249909i	$-0.919599\pi$
$317$	−7.16210	+	10.2285i	−0.402264	+	0.574492i	0.566006	+	0.824401i	$0.308488\pi$
$318$	3.80321	+	2.39925i	0.213274	+	0.134543i
$319$	−1.09949	−	3.02083i	−0.0615597	−	0.169134i
$320$		0			0
$321$	−14.2955	+	27.7616i	−0.797898	+	1.54950i
$322$	0.108974	−	1.24558i	0.00607290	−	0.0694136i
$323$	−7.82802	+	7.82802i	−0.435563	+	0.435563i
$324$	−8.19032	+	14.7863i	−0.455018	+	0.821460i
$325$		0			0
$326$	3.84187	+	4.57856i	0.212782	+	0.253583i
$327$	15.0860	−	4.83031i	0.834255	−	0.267117i
$328$	12.3466	−	8.64519i	0.681728	−	0.477351i
$329$	−12.7452	+	4.63886i	−0.702664	+	0.255749i
$330$		0			0
$331$	3.65344	+	20.7197i	0.200811	+	1.13886i	0.903897	+	0.427751i	$0.140694\pi$
$331$	3.65344	+	20.7197i	0.200811	+	1.13886i	−0.703086	+	0.711105i	$0.748195\pi$
$332$	−6.28364	+	23.4509i	−0.344860	+	1.28703i
$333$	−3.87585	−	3.19402i	−0.212395	−	0.175031i
$334$	−5.43022	−	3.13514i	−0.297128	−	0.171547i
$335$		0			0
$336$	−4.17906	+	5.49660i	−0.227986	+	0.299864i
$337$	31.2906	−	2.73757i	1.70451	−	0.149125i	0.807125	−	0.590380i	$-0.201022\pi$
$337$	31.2906	−	2.73757i	1.70451	−	0.149125i	0.897382	+	0.441255i	$0.145467\pi$
$338$	4.47884	−	0.391848i	0.243617	−	0.0213137i
$339$	−20.9891	−	2.66853i	−1.13997	−	0.144935i
$340$		0			0
$341$	−3.40063	−	1.96335i	−0.184154	−	0.106322i
$342$	2.86837	−	5.07161i	0.155104	−	0.274241i
$343$	−3.93599	+	14.6893i	−0.212524	+	0.793149i
$344$	−1.03626	−	5.87691i	−0.0558713	−	0.316862i
$345$		0			0
$346$	2.44278	−	0.889099i	0.131325	−	0.0477983i
$347$	−4.96853	+	3.47900i	−0.266725	+	0.186763i	−0.699286	−	0.714842i	$-0.746499\pi$
$347$	−4.96853	+	3.47900i	−0.266725	+	0.186763i	0.432562	+	0.901604i	$0.357610\pi$
$348$	−4.22871	−	3.84051i	−0.226683	−	0.205873i
$349$	6.64292	+	7.91672i	0.355587	+	0.423772i	0.913951	−	0.405824i	$-0.133015\pi$
$349$	6.64292	+	7.91672i	0.355587	+	0.423772i	−0.558364	+	0.829596i	$0.688571\pi$
$350$		0			0
$351$	−0.953109	+	1.54099i	−0.0508732	+	0.0822518i
$352$	−4.98900	+	4.98900i	−0.265915	+	0.265915i
$353$	1.17998	−	13.4872i	0.0628039	−	0.717851i	−0.897886	−	0.440228i	$-0.854898\pi$
$353$	1.17998	−	13.4872i	0.0628039	−	0.717851i	0.960690	−	0.277624i	$-0.0895468\pi$
$354$	1.86445	+	2.89813i	0.0990945	+	0.154034i
$355$		0			0
$356$	1.63477	+	4.49149i	0.0866426	+	0.238049i
$357$	−0.163966	+	4.18126i	−0.00867799	+	0.221296i
$358$	−0.530298	+	0.757344i	−0.0280271	+	0.0400269i
$359$	4.91852	+	8.51912i	0.259589	+	0.449622i	0.966132	−	0.258049i	$-0.0830795\pi$
$359$	4.91852	+	8.51912i	0.259589	+	0.449622i	−0.706543	+	0.707670i	$0.749746\pi$
$360$		0			0
$361$	5.97506	−	10.3491i	0.314477	−	0.544690i
$362$	−1.18364	−	2.53832i	−0.0622106	−	0.133411i
$363$	5.01539	−	12.2619i	0.263240	−	0.643583i
$364$	−0.511086	+	0.609088i	−0.0267882	+	0.0319249i
$365$		0			0
$366$	4.19055	−	1.75762i	0.219044	−	0.0918721i
$367$	−5.70110	+	2.65847i	−0.297595	+	0.138771i	−0.565681	−	0.824624i	$-0.691387\pi$
$367$	−5.70110	+	2.65847i	−0.297595	+	0.138771i	0.268086	+	0.963395i	$0.413609\pi$
$368$	2.50709	+	9.35658i	0.130691	+	0.487746i
$369$	2.61536	−	33.2957i	0.136150	−	1.73330i
$370$		0			0
$371$	8.89150	−	1.56781i	0.461624	−	0.0813967i
$372$	−6.97226	−	0.273413i	−0.361495	−	0.0141758i
$373$	−20.3048	−	9.46829i	−1.05134	−	0.490249i	−0.181404	−	0.983409i	$-0.558064\pi$
$373$	−20.3048	−	9.46829i	−1.05134	−	0.490249i	−0.869939	+	0.493159i	$0.835842\pi$
$374$	−0.220837	+	1.25243i	−0.0114192	+	0.0647615i
$375$		0			0
$376$	−11.5865	+	9.72219i	−0.597526	+	0.501383i
$377$	−0.432989	−	0.432989i	−0.0223000	−	0.0223000i
$378$	−0.505265	−	2.14361i	−0.0259880	−	0.110255i
$379$			19.0825i			0.980201i	0.871666	+	0.490101i	$0.163040\pi$
$379$			19.0825i			0.980201i	−0.871666	+	0.490101i	$0.836960\pi$
$380$		0			0
$381$	0.572220	+	11.8942i	0.0293157	+	0.609358i
$382$	2.41839	+	3.45382i	0.123736	+	0.176713i
$383$	15.7700	−	33.8190i	0.805811	−	1.72807i	0.129338	−	0.991601i	$-0.458715\pi$
$383$	15.7700	−	33.8190i	0.805811	−	1.72807i	0.676473	−	0.736467i	$-0.263507\pi$
$384$	−4.89423	+	15.7662i	−0.249758	+	0.804566i
$385$		0			0
$386$	−2.35229	+	1.35810i	−0.119729	+	0.0691253i
$387$	−11.5099	−	6.50969i	−0.585081	−	0.330906i
$388$	11.0467	−	2.95995i	0.560810	−	0.150269i
$389$	−15.5765	−	5.66936i	−0.789757	−	0.287448i	−0.0845222	−	0.996422i	$-0.526936\pi$
$389$	−15.5765	−	5.66936i	−0.789757	−	0.287448i	−0.705235	+	0.708973i	$0.749159\pi$
$390$		0			0
$391$	4.49691	+	3.77335i	0.227418	+	0.190827i
$392$	0.652064	+	7.45313i	0.0329342	+	0.376440i
$393$	4.30675	+	31.6275i	0.217247	+	1.59540i
$394$	−0.0665583	+	0.182867i	−0.00335316	+	0.00921273i
$395$		0			0
$396$	0.990160	+	10.2669i	0.0497574	+	0.515933i
$397$	21.8514	+	5.85505i	1.09669	+	0.293857i	0.761415	−	0.648264i	$-0.224505\pi$
$397$	21.8514	+	5.85505i	1.09669	+	0.293857i	0.335273	+	0.942121i	$0.391171\pi$
$398$	0.960494	+	0.672545i	0.0481452	+	0.0337116i
$399$	−2.58273	−	11.4100i	−0.129298	−	0.571215i
$400$		0			0
$401$	16.6110	+	2.92896i	0.829512	+	0.146265i	0.572253	−	0.820077i	$-0.306069\pi$
$401$	16.6110	+	2.92896i	0.829512	+	0.146265i	0.257259	+	0.966342i	$0.417181\pi$
$402$	1.80678	+	5.64291i	0.0901139	+	0.281443i
$403$	−0.745116	−	0.0651892i	−0.0371169	−	0.00324731i
$404$	−11.7665			−0.585406
$405$		0			0
$406$	0.744283			0.0369382
$407$	−3.05306	−	0.267108i	−0.151335	−	0.0132401i
$408$	1.42294	+	4.44411i	0.0704461	+	0.220016i
$409$	−18.0511	−	3.18290i	−0.892572	−	0.157384i	−0.291492	−	0.956573i	$-0.594152\pi$
$409$	−18.0511	−	3.18290i	−0.892572	−	0.157384i	−0.601080	+	0.799189i	$0.705263\pi$
$410$		0			0
$411$	0.190401	+	0.841156i	0.00939178	+	0.0414911i
$412$	21.9597	+	15.3763i	1.08187	+	0.757537i
$413$	6.68331	+	1.79079i	0.328864	+	0.0881189i
$414$	−2.81163	−	1.28082i	−0.138184	−	0.0629488i
$415$		0			0
$416$	−0.459655	+	1.26289i	−0.0225364	+	0.0619183i
$417$	−0.331798	−	2.43663i	−0.0162482	−	0.119322i
$418$	−0.309879	−	3.54194i	−0.0151567	−	0.173242i
$419$	15.7554	+	13.2204i	0.769702	+	0.645857i	0.940633	−	0.339426i	$-0.110233\pi$
$419$	15.7554	+	13.2204i	0.769702	+	0.645857i	−0.170930	+	0.985283i	$0.554677\pi$
$420$		0			0
$421$	−20.2545	−	7.37202i	−0.987143	−	0.359290i	−0.202529	−	0.979276i	$-0.564916\pi$
$421$	−20.2545	−	7.37202i	−0.987143	−	0.359290i	−0.784613	+	0.619986i	$0.787138\pi$
$422$	4.40608	−	1.18061i	0.214485	−	0.0574710i
$423$	0.297533	+	33.5135i	0.0144666	+	1.62948i
$424$	8.71949	−	5.03420i	0.423456	−	0.244482i
$425$		0			0
$426$	−2.82399	+	9.09715i	−0.136823	+	0.440758i
$427$	3.85596	−	8.26913i	0.186603	−	0.400171i
$428$	19.4210	+	27.7361i	0.938752	+	1.34068i
$429$	0.0531312	+	1.10439i	0.00256520	+	0.0533204i
$430$		0			0
$431$		−	12.5960i		−	0.606728i	−0.952875	−	0.303364i	$-0.901890\pi$
$431$		−	12.5960i		−	0.606728i	0.952875	−	0.303364i	$-0.0981099\pi$
$432$	9.35825	+	14.2666i	0.450249	+	0.686404i
$433$	−21.2452	−	21.2452i	−1.02098	−	1.02098i	−0.999775	−	0.0212037i	$-0.993250\pi$
$433$	−21.2452	−	21.2452i	−1.02098	−	1.02098i	−0.0212037	−	0.999775i	$-0.506750\pi$
$434$	0.696435	−	0.584379i	0.0334300	−	0.0280511i
$435$		0			0
$436$	2.98263	−	16.9153i	0.142842	−	0.810098i
$437$	−14.8741	−	6.93591i	−0.711525	−	0.331789i
$438$	7.24951	+	0.284285i	0.346395	+	0.0135837i
$439$	18.8946	−	3.33163i	0.901790	−	0.159010i	0.296517	−	0.955028i	$-0.404175\pi$
$439$	18.8946	−	3.33163i	0.901790	−	0.159010i	0.605273	+	0.796018i	$0.293064\pi$
$440$		0			0
$441$	13.6639	+	9.38786i	0.650660	+	0.447041i
$442$	0.0626973	+	0.233990i	0.00298221	+	0.0111298i
$443$	10.3607	−	4.83128i	0.492252	−	0.229541i	−0.160610	−	0.987018i	$-0.551346\pi$
$443$	10.3607	−	4.83128i	0.492252	−	0.229541i	0.652862	+	0.757477i	$0.273568\pi$
$444$	−5.02206	+	2.10637i	−0.238337	+	0.0999640i
$445$		0			0
$446$	3.58603	−	4.27367i	0.169804	−	0.202364i
$447$	10.5425	−	25.7748i	0.498643	−	1.21911i
$448$	2.67920	+	5.74556i	0.126580	+	0.271452i
$449$	−16.0515	+	27.8021i	−0.757519	+	1.31206i	0.186593	+	0.982437i	$0.440256\pi$
$449$	−16.0515	+	27.8021i	−0.757519	+	1.31206i	−0.944112	+	0.329625i	$0.893078\pi$
$450$		0			0
$451$	−10.1901	−	17.6497i	−0.479832	−	0.831094i
$452$	−13.1592	+	18.7933i	−0.618957	+	0.883962i
$453$	−0.0417534	+	1.06475i	−0.00196175	+	0.0500261i
$454$	1.10820	+	3.04474i	0.0520102	+	0.142897i
$455$		0			0
$456$	−7.05831	−	10.9716i	−0.330536	−	0.513790i
$457$	0.332479	−	3.80025i	0.0155527	−	0.177768i	−0.984445	−	0.175692i	$-0.943784\pi$
$457$	0.332479	−	3.80025i	0.0155527	−	0.177768i	0.999998	−	0.00207595i	$-0.000660797\pi$
$458$	−1.64912	+	1.64912i	−0.0770585	+	0.0770585i
$459$	9.60470	+	3.82936i	0.448309	+	0.178739i
$460$		0			0
$461$	19.3941	+	23.1130i	0.903273	+	1.07648i	0.996726	+	0.0808555i	$0.0257652\pi$
$461$	19.3941	+	23.1130i	0.903273	+	1.07648i	−0.0934525	+	0.995624i	$0.529790\pi$
$462$	−0.994857	−	0.903527i	−0.0462849	−	0.0420359i
$463$	−28.0226	+	19.6216i	−1.30232	+	0.911895i	−0.999157	−	0.0410431i	$-0.986932\pi$
$463$	−28.0226	+	19.6216i	−1.30232	+	0.911895i	−0.303164	+	0.952938i	$0.598043\pi$
$464$	−5.41838	+	1.97213i	−0.251542	+	0.0915538i
$465$		0			0
$466$	0.337129	+	1.91196i	0.0156172	+	0.0885696i
$467$	0.957293	−	3.57267i	0.0442982	−	0.165323i	−0.940233	−	0.340531i	$-0.889393\pi$
$467$	0.957293	−	3.57267i	0.0442982	−	0.165323i	0.984531	+	0.175208i	$0.0560598\pi$
$468$	0.997432	+	1.69272i	0.0461063	+	0.0782459i
$469$	10.3027	+	5.94827i	0.475734	+	0.274665i
$470$		0			0
$471$	14.3236	+	1.82110i	0.659998	+	0.0839116i
$472$	7.68650	−	0.672482i	0.353800	−	0.0309535i
$473$	−8.03835	+	0.703264i	−0.369604	+	0.0323361i
$474$	5.49879	−	7.23241i	0.252568	−	0.332196i
$475$		0			0
$476$	3.92948	+	2.26869i	0.180108	+	0.103985i
$477$	3.67889	−	22.0046i	0.168445	−	1.00752i
$478$	0.667110	−	2.48969i	0.0305129	−	0.113876i
$479$	−2.01746	−	11.4416i	−0.0921799	−	0.522778i	−0.995575	−	0.0939694i	$-0.970044\pi$
$479$	−2.01746	−	11.4416i	−0.0921799	−	0.522778i	0.903395	−	0.428809i	$-0.141067\pi$
$480$		0			0
$481$	−0.548566	+	0.199662i	−0.0250124	+	0.00910379i
$482$	−4.30974	+	3.01771i	−0.196303	+	0.137453i
$483$	−5.90794	+	1.89164i	−0.268821	+	0.0860726i
$484$	−9.23379	−	11.0044i	−0.419718	−	0.500200i
$485$		0			0
$486$	−5.40993	−	0.590415i	−0.245399	−	0.0267818i
$487$	8.89951	−	8.89951i	0.403275	−	0.403275i	−0.476110	−	0.879386i	$-0.657954\pi$
$487$	8.89951	−	8.89951i	0.403275	−	0.403275i	0.879386	+	0.476110i	$0.157954\pi$
$488$	0.886781	−	10.1360i	0.0401427	−	0.458833i
$489$	13.5756	−	26.3635i	0.613909	−	1.19220i
$490$		0			0
$491$	−9.12806	−	25.0791i	−0.411943	−	1.13181i	−0.956156	−	0.292858i	$-0.905394\pi$
$491$	−9.12806	−	25.0791i	−0.411943	−	1.13181i	0.544212	−	0.838947i	$-0.316829\pi$
$492$	−30.6294	−	19.3225i	−1.38088	−	0.871124i
$493$	−2.00429	+	2.86243i	−0.0902688	+	0.128917i
$494$	−0.338624	−	0.586515i	−0.0152354	−	0.0263885i
$495$		0			0
$496$	−3.52162	+	6.09962i	−0.158125	+	0.273881i
$497$	8.08268	+	17.3334i	0.362558	+	0.777508i
$498$	−7.74500	+	1.05464i	−0.347062	+	0.0472598i
$499$	19.0750	−	22.7327i	0.853916	−	1.01766i	−0.145683	−	0.989331i	$-0.546538\pi$
$499$	19.0750	−	22.7327i	0.853916	−	1.01766i	0.999599	−	0.0283261i	$-0.00901768\pi$
$500$		0			0
$501$	−3.92360	+	30.8607i	−0.175294	+	1.37875i
$502$	8.93660	−	4.16721i	0.398860	−	0.185991i
$503$	−0.889794	−	3.32076i	−0.0396740	−	0.148065i	0.943248	−	0.332090i	$-0.107754\pi$
$503$	−0.889794	−	3.32076i	−0.0396740	−	0.148065i	−0.982922	+	0.184025i	$0.941087\pi$
$504$	−4.77426	−	1.23394i	−0.212662	−	0.0549639i
$505$		0			0
$506$	−1.85670	+	0.327386i	−0.0825402	+	0.0145541i
$507$	−10.3875	−	19.7398i	−0.461326	−	0.876675i
$508$	11.7024	+	5.45694i	0.519212	+	0.242113i
$509$	6.07079	−	34.4292i	0.269083	−	1.52605i	−0.488068	−	0.872806i	$-0.662298\pi$
$509$	6.07079	−	34.4292i	0.269083	−	1.52605i	0.757151	−	0.653240i	$-0.226591\pi$
$510$		0			0
$511$	11.1589	−	9.36342i	0.493640	−	0.414213i
$512$	15.2357	+	15.2357i	0.673328	+	0.673328i
$513$	−28.7081	−	3.39122i	−1.26749	−	0.149726i
$514$			7.04591i			0.310782i
$515$		0			0
$516$	−12.0586	+	7.75763i	−0.530850	+	0.341511i
$517$	11.7304	+	16.7527i	0.515902	+	0.736784i
$518$	0.299874	−	0.643081i	0.0131757	−	0.0282554i
$519$	−8.75543	−	9.47013i	−0.384321	−	0.415693i
$520$		0			0
$521$	20.9011	−	12.0673i	0.915696	−	0.528677i	0.0334362	−	0.999441i	$-0.489355\pi$
$521$	20.9011	−	12.0673i	0.915696	−	0.528677i	0.882259	+	0.470764i	$0.156022\pi$
$522$	0.613656	−	1.73374i	0.0268590	−	0.0758839i
$523$	−13.0959	+	3.50904i	−0.572645	+	0.153440i	−0.533509	−	0.845794i	$-0.679127\pi$
$523$	−13.0959	+	3.50904i	−0.572645	+	0.153440i	−0.0391356	+	0.999234i	$0.512460\pi$
$524$	32.5240	+	11.8378i	1.42082	+	0.517135i
$525$		0			0
$526$	−3.39524	−	2.84894i	−0.148040	−	0.124220i
$527$	0.372010	+	4.25209i	0.0162050	+	0.185224i
$528$	9.63663	+	3.94160i	0.419380	+	0.171536i
$529$	4.89001	−	13.4352i	0.212609	−	0.584139i
$530$		0			0
$531$	9.68182	−	14.0917i	0.420155	−	0.611527i
$532$	−12.2530	−	3.28319i	−0.531237	−	0.142344i
$533$	−3.17998	−	2.22664i	−0.137740	−	0.0964466i
$534$	−1.12995	+	1.04467i	−0.0488975	+	0.0452073i
$535$		0			0
$536$	13.0650	+	2.30371i	0.564321	+	0.0995050i
$537$	4.48264	+	0.972922i	0.193440	+	0.0419847i
$538$	−6.69645	−	0.585863i	−0.288704	−	0.0252584i
$539$	10.1162			0.435737
$540$		0			0
$541$	−4.99037			−0.214553			−0.107276	−	0.994229i	$-0.534213\pi$
$541$	−4.99037			−0.214553			−0.107276	+	0.994229i	$0.534213\pi$
$542$	−7.54523	−	0.660122i	−0.324095	−	0.0283547i
$543$	−9.34203	+	10.2863i	−0.400905	+	0.441429i
$544$	7.55283	+	1.33177i	0.323825	+	0.0570991i
$545$		0			0
$546$	−0.244481	−	0.0758931i	−0.0104628	−	0.00324792i
$547$	−21.3890	−	14.9768i	−0.914528	−	0.640360i	0.0186294	−	0.999826i	$-0.494070\pi$
$547$	−21.3890	−	14.9768i	−0.914528	−	0.640360i	−0.933158	+	0.359467i	$0.882959\pi$
$548$	0.903304	+	0.242040i	0.0385872	+	0.0103394i
$549$	−16.0830	−	15.7999i	−0.686406	−	0.674325i
$550$		0			0
$551$	3.34131	−	9.18018i	0.142345	−	0.391089i
$552$	−5.46948	+	4.23559i	−0.232797	+	0.180279i
$553$	−1.58988	−	18.1724i	−0.0676086	−	0.772770i
$554$	6.91767	+	5.80462i	0.293904	+	0.246615i
$555$		0			0
$556$	−2.50569	−	0.911998i	−0.106265	−	0.0386773i
$557$	−43.1866	+	11.5718i	−1.82987	+	0.490313i	−0.997916	−	0.0645241i	$-0.979447\pi$
$557$	−43.1866	+	11.5718i	−1.82987	+	0.490313i	−0.831959	+	0.554838i	$0.812780\pi$
$558$	−0.787053	−	2.10410i	−0.0333186	−	0.0890737i
$559$	−1.33108	+	0.768500i	−0.0562987	+	0.0325041i
$560$		0			0
$561$	6.15392	−	1.39298i	0.259819	−	0.0588117i
$562$	0.625436	−	1.34125i	0.0263824	−	0.0565773i
$563$	20.8190	+	29.7327i	0.877418	+	1.25308i	0.966398	+	0.257049i	$0.0827501\pi$
$563$	20.8190	+	29.7327i	0.877418	+	1.25308i	−0.0889809	+	0.996033i	$0.528361\pi$
$564$	32.3093	+	16.6373i	1.36047	+	0.700556i
$565$		0			0
$566$		−	4.98938i		−	0.209719i
$567$	−8.83791	+	6.42520i	−0.371157	+	0.269833i
$568$	15.0810	+	15.0810i	0.632783	+	0.632783i
$569$	−15.5547	+	13.0520i	−0.652088	+	0.547167i	−0.907704	−	0.419612i	$-0.862166\pi$
$569$	−15.5547	+	13.0520i	−0.652088	+	0.547167i	0.255616	+	0.966778i	$0.417722\pi$
$570$		0			0
$571$	0.319709	−	1.81316i	0.0133794	−	0.0758784i	−0.977387	−	0.211458i	$-0.932179\pi$
$571$	0.319709	−	1.81316i	0.0133794	−	0.0758784i	0.990766	+	0.135580i	$0.0432898\pi$
$572$	1.08658	+	0.506682i	0.0454324	+	0.0211855i
$573$	11.1612	−	17.6924i	0.466267	−	0.739112i
$574$	4.64684	−	0.819363i	0.193955	−	0.0341996i
$575$		0			0
$576$	15.5927	−	1.50379i	0.649698	−	0.0626579i
$577$	2.35105	+	8.77425i	0.0978756	+	0.365277i	0.997440	−	0.0715120i	$-0.0227824\pi$
$577$	2.35105	+	8.77425i	0.0978756	+	0.365277i	−0.899564	+	0.436789i	$0.856116\pi$
$578$	−4.12591	+	1.92394i	−0.171615	+	0.0800255i
$579$	10.7276	+	8.15614i	0.445822	+	0.338958i
$580$		0			0
$581$	−10.0880	+	12.0224i	−0.418519	+	0.498771i
$582$	2.25440	+	2.91115i	0.0934481	+	0.120671i
$583$	−5.75351	−	12.3385i	−0.238286	−	0.511006i
$584$	8.12220	−	14.0681i	0.336099	−	0.582140i
$585$		0			0
$586$	5.00838	+	8.67477i	0.206894	+	0.358351i
$587$	6.25159	−	8.92820i	0.258031	−	0.368506i	−0.669145	−	0.743131i	$-0.733340\pi$
$587$	6.25159	−	8.92820i	0.258031	−	0.368506i	0.927176	+	0.374625i	$0.122229\pi$
$588$	15.9081	−	8.37118i	0.656038	−	0.345222i
$589$	−4.08136	−	11.2135i	−0.168170	−	0.462042i
$590$		0			0
$591$	0.964383	−	0.0463957i	0.0396694	−	0.00190846i
$592$	−0.479106	+	5.47620i	−0.0196911	+	0.225071i
$593$	14.2644	−	14.2644i	0.585769	−	0.585769i	−0.350714	−	0.936483i	$-0.614061\pi$
$593$	14.2644	−	14.2644i	0.585769	−	0.585769i	0.936483	+	0.350714i	$0.114061\pi$
$594$	−2.92494	+	1.57248i	−0.120012	+	0.0645196i
$595$		0			0
$596$	−19.4097	−	23.1315i	−0.795051	−	0.947505i
$597$	1.23390	−	5.68507i	0.0505001	−	0.232674i
$598$	−0.294175	+	0.205983i	−0.0120297	+	0.00842328i
$599$	−29.1082	+	10.5945i	−1.18933	+	0.432880i	−0.859488	−	0.511157i	$-0.829217\pi$
$599$	−29.1082	+	10.5945i	−1.18933	+	0.432880i	−0.329841	+	0.944037i	$0.606995\pi$
$600$		0			0
$601$	−6.41218	−	36.3653i	−0.261558	−	1.48337i	−0.778659	−	0.627447i	$-0.784100\pi$
$601$	−6.41218	−	36.3653i	−0.261558	−	1.48337i	0.517101	−	0.855925i	$-0.327011\pi$
$602$	0.483523	−	1.80453i	0.0197069	−	0.0735472i
$603$	22.3505	−	19.0949i	0.910181	−	0.777606i
$604$	1.00063	+	0.577714i	0.0407151	+	0.0235069i
$605$		0			0
$606$	−1.46524	−	3.49346i	−0.0595213	−	0.141912i
$607$	−23.5036	+	2.05629i	−0.953980	+	0.0834624i	−0.553506	−	0.832846i	$-0.686710\pi$
$607$	−23.5036	+	2.05629i	−0.953980	+	0.0834624i	−0.400474	+	0.916308i	$0.631155\pi$
$608$	−21.3598	+	1.86874i	−0.866256	+	0.0757876i
$609$	−1.42825	−	3.40527i	−0.0578756	−	0.137988i
$610$		0			0
$611$	3.37367	+	1.94779i	0.136484	+	0.0787992i
$612$	8.52454	−	7.28287i	0.344584	−	0.294393i
$613$	4.63610	−	17.3022i	0.187251	−	0.698828i	−0.806887	−	0.590706i	$-0.798849\pi$
$613$	4.63610	−	17.3022i	0.187251	−	0.698828i	0.994138	−	0.108123i	$-0.0344839\pi$
$614$	0.137296	+	0.778644i	0.00554081	+	0.0314235i
$615$		0			0
$616$	−2.82760	+	1.02916i	−0.113927	+	0.0414661i
$617$	2.87925	−	2.01607i	0.115914	−	0.0811641i	−0.514182	−	0.857681i	$-0.671904\pi$
$617$	2.87925	−	2.01607i	0.115914	−	0.0811641i	0.630096	+	0.776517i	$0.283015\pi$
$618$	−1.83065	+	8.43454i	−0.0736396	+	0.339287i
$619$	15.8282	+	18.8633i	0.636188	+	0.758180i	0.983763	−	0.179473i	$-0.0574391\pi$
$619$	15.8282	+	18.8633i	0.636188	+	0.758180i	−0.347575	+	0.937652i	$0.612995\pi$
$620$		0			0
$621$	−0.464642	+	15.3217i	−0.0186455	+	0.614837i
$622$	−3.01837	+	3.01837i	−0.121026	+	0.121026i
$623$	−0.269291	+	3.07801i	−0.0107889	+	0.123318i
$624$	1.98091	−	0.0953002i	0.0793000	−	0.00381506i
$625$		0			0
$626$	−2.01986	−	5.54952i	−0.0807299	−	0.221803i
$627$	−15.6105	+	8.21460i	−0.623425	+	0.328060i
$628$	8.98028	−	12.8252i	0.358352	−	0.511780i
$629$	1.66568	+	2.88504i	0.0664150	+	0.115034i
$630$		0			0
$631$	−3.43649	+	5.95218i	−0.136805	+	0.236953i	−0.926285	−	0.376823i	$-0.877017\pi$
$631$	−3.43649	+	5.95218i	−0.136805	+	0.236953i	0.789481	+	0.613775i	$0.210350\pi$
$632$	−8.59713	−	18.4366i	−0.341975	−	0.733368i
$633$	−13.8566	−	17.8933i	−0.550752	−	0.711195i
$634$	−2.80205	+	3.33936i	−0.111284	+	0.132623i
$635$		0			0
$636$	−19.2576	−	14.6415i	−0.763615	−	0.580575i
$637$	1.74641	−	0.814364i	0.0691953	−	0.0322663i
$638$	−0.290466	−	1.08404i	−0.0114997	−	0.0429174i
$639$	47.0407	−	4.53668i	1.86090	−	0.179468i
$640$		0			0
$641$	11.3164	−	1.99539i	0.446972	−	0.0788133i	0.0543684	−	0.998521i	$-0.482685\pi$
$641$	11.3164	−	1.99539i	0.446972	−	0.0788133i	0.392604	+	0.919708i	$0.371574\pi$
$642$	−5.81638	+	9.21995i	−0.229554	+	0.363882i
$643$	8.56819	+	3.99541i	0.337896	+	0.157564i	0.584158	−	0.811640i	$-0.301425\pi$
$643$	8.56819	+	3.99541i	0.337896	+	0.157564i	−0.246262	+	0.969203i	$0.579202\pi$
$644$	−1.16805	+	6.62436i	−0.0460278	+	0.261037i
$645$		0			0
$646$	−2.96061	+	2.48424i	−0.116484	+	0.0977413i
$647$	−19.8792	−	19.8792i	−0.781533	−	0.781533i	0.198556	−	0.980090i	$-0.436375\pi$
$647$	−19.8792	−	19.8792i	−0.781533	−	0.781533i	−0.980090	+	0.198556i	$0.936375\pi$
$648$	−6.81068	+	10.1038i	−0.267549	+	0.396916i
$649$		−	10.4330i		−	0.409531i
$650$		0			0
$651$	−4.01010	−	2.06495i	−0.157168	−	0.0809319i
$652$	−18.4430	−	26.3393i	−0.722283	−	1.03153i
$653$	15.1637	−	32.5186i	0.593400	−	1.27255i	−0.348705	−	0.937233i	$-0.613378\pi$
$653$	15.1637	−	32.5186i	0.593400	−	1.27255i	0.942105	−	0.335318i	$-0.108844\pi$
$654$	5.39356	−	1.22087i	0.210905	−	0.0477396i
$655$		0			0
$656$	−31.6579	+	18.2777i	−1.23603	+	0.713625i
$657$	−12.6109	−	33.7137i	−0.491996	−	1.31530i
$658$	−4.57365	+	1.22551i	−0.178300	+	0.0477752i
$659$	24.5585	+	8.93857i	0.956664	+	0.348197i	0.772725	−	0.634741i	$-0.218893\pi$
$659$	24.5585	+	8.93857i	0.956664	+	0.348197i	0.183939	+	0.982938i	$0.441115\pi$
$660$		0			0
$661$	−12.4073	−	10.4109i	−0.482587	−	0.404939i	0.368774	−	0.929519i	$-0.379778\pi$
$661$	−12.4073	−	10.4109i	−0.482587	−	0.404939i	−0.851361	+	0.524581i	$0.824222\pi$
$662$	0.640157	+	7.31703i	0.0248804	+	0.284385i
$663$	0.950243	−	0.735871i	0.0369044	−	0.0285789i
$664$	−5.98582	+	16.4459i	−0.232295	+	0.638225i
$665$		0			0
$666$	−1.25076	−	1.22874i	−0.0484659	−	0.0476129i
$667$	−5.00382	−	1.34077i	−0.193749	−	0.0519148i
$668$	27.6322	+	19.3483i	1.06912	+	0.748607i
$669$	−26.4345	−	8.20592i	−1.02201	−	0.317259i
$670$		0			0
$671$	−13.5487	−	2.38900i	−0.523041	−	0.0922262i
$672$	−5.44876	+	5.99953i	−0.210191	+	0.231437i
$673$	19.6853	+	1.72224i	0.758813	+	0.0663875i	0.459994	−	0.887922i	$-0.347852\pi$
$673$	19.6853	+	1.72224i	0.758813	+	0.0663875i	0.298819	+	0.954310i	$0.403407\pi$
$674$	10.9655			0.422376
$675$		0			0
$676$	−24.1872			−0.930278
$677$	11.7973	+	1.03213i	0.453407	+	0.0396679i	0.311572	−	0.950222i	$-0.399144\pi$
$677$	11.7973	+	1.03213i	0.453407	+	0.0396679i	0.141834	+	0.989890i	$0.454700\pi$
$678$	−7.21836	−	1.56669i	−0.277220	−	0.0601683i
$679$	7.28048	+	1.28374i	0.279399	+	0.0492656i
$680$		0			0
$681$	11.8038	−	10.9130i	0.452323	−	0.418187i
$682$	−1.12293	−	0.786284i	−0.0429992	−	0.0301084i
$683$	−11.3569	−	3.04307i	−0.434559	−	0.116440i	0.0349062	−	0.999391i	$-0.488887\pi$
$683$	−11.3569	−	3.04307i	−0.434559	−	0.116440i	−0.469466	+	0.882951i	$0.655553\pi$
$684$	−17.7504	+	25.8354i	−0.678705	+	0.987842i
$685$		0			0
$686$	−1.81581	+	4.98889i	−0.0693278	+	0.190477i
$687$	10.7097	+	4.38052i	0.408601	+	0.167127i
$688$	1.26143	+	14.4182i	0.0480915	+	0.549688i
$689$	−1.98651	−	1.66688i	−0.0756799	−	0.0635030i
$690$		0			0
$691$	5.29511	+	1.92726i	0.201435	+	0.0733165i	0.440768	−	0.897621i	$-0.354706\pi$
$691$	5.29511	+	1.92726i	0.201435	+	0.0733165i	−0.239332	+	0.970938i	$0.576929\pi$
$692$	−13.5085	+	3.61959i	−0.513516	+	0.137596i
$693$	−2.22475	+	6.28553i	−0.0845114	+	0.238767i
$694$	−1.83381	+	1.05875i	−0.0696104	+	0.0401896i
$695$		0			0
$696$	−2.79546	−	3.02366i	−0.105962	−	0.114611i
$697$	−9.36238	+	20.0777i	−0.354625	+	0.760497i
$698$	2.06939	+	2.95540i	0.0783276	+	0.111863i
$699$	8.10070	−	5.21141i	0.306397	−	0.197114i
$700$		0			0
$701$		−	21.8407i		−	0.824911i	−0.910978	−	0.412455i	$-0.864671\pi$
$701$		−	21.8407i		−	0.824911i	0.910978	−	0.412455i	$-0.135329\pi$
$702$	−0.378359	+	0.506924i	−0.0142802	+	0.0191326i
$703$	−6.58570	−	6.58570i	−0.248384	−	0.248384i
$704$	7.32271	−	6.14448i	0.275985	−	0.231579i
$705$		0			0
$706$	0.820744	−	4.65467i	0.0308891	−	0.175181i
$707$	−6.89357	−	3.21453i	−0.259260	−	0.120895i
$708$	−8.63330	−	16.4062i	−0.324459	−	0.616583i
$709$	−17.5327	+	3.09148i	−0.658453	+	0.116103i	−0.492884	−	0.870095i	$-0.664057\pi$
$709$	−17.5327	+	3.09148i	−0.658453	+	0.116103i	−0.165569	+	0.986198i	$0.552946\pi$
$710$		0			0
$711$	−43.6419	−	11.2795i	−1.63670	−	0.423015i
$712$	0.891781	+	3.32817i	0.0334209	+	0.124729i
$713$	−5.73485	+	2.67420i	−0.214772	+	0.100150i
$714$	−0.184246	+	1.44917i	−0.00689524	+	0.0542338i
$715$		0			0
$716$	3.19713	−	3.81019i	0.119482	−	0.142394i
$717$	−12.6710	+	1.72543i	−0.473209	+	0.0644373i
$718$	1.45135	+	3.11243i	0.0541639	+	0.116155i
$719$	12.2911	−	21.2888i	0.458381	−	0.793939i	−0.540495	−	0.841347i	$-0.681763\pi$
$719$	12.2911	−	21.2888i	0.458381	−	0.793939i	0.998876	+	0.0474084i	$0.0150962\pi$
$720$		0			0
$721$	8.66466	+	15.0076i	0.322689	+	0.558914i
$722$	2.39289	−	3.41741i	0.0890543	−	0.127183i
$723$	22.0769	+	13.9272i	0.821050	+	0.517957i
$724$	5.15331	+	14.1586i	0.191521	+	0.526201i
$725$		0			0
$726$	2.11734	−	4.11183i	0.0785819	−	0.152604i
$727$	2.85719	−	32.6578i	0.105967	−	1.21121i	−0.737994	−	0.674807i	$-0.764227\pi$
$727$	2.85719	−	32.6578i	0.105967	−	1.21121i	0.843962	−	0.536404i	$-0.180218\pi$
$728$	−0.405292	+	0.405292i	−0.0150211	+	0.0150211i
$729$	7.68015	+	25.8847i	0.284450	+	0.958691i
$730$		0			0
$731$	5.63793	+	6.71903i	0.208526	+	0.248512i
$732$	−23.2826	+	7.45475i	−0.860549	+	0.275536i
$733$	25.5313	−	17.8772i	0.943022	−	0.660311i	0.00248290	−	0.999997i	$-0.499210\pi$
$733$	25.5313	−	17.8772i	0.943022	−	0.660311i	0.940539	+	0.339686i	$0.110321\pi$
$734$	−2.06361	+	0.751094i	−0.0761694	+	0.0277234i
$735$		0			0
$736$	1.97432	+	11.1969i	0.0727742	+	0.412723i
$737$	4.64278	−	17.3271i	0.171019	−	0.638251i
$738$	1.92265	−	11.5000i	0.0707736	−	0.423320i
$739$	−9.53500	−	5.50503i	−0.350751	−	0.202506i	0.314265	−	0.949335i	$-0.398242\pi$
$739$	−9.53500	−	5.50503i	−0.350751	−	0.202506i	−0.665016	+	0.746829i	$0.731575\pi$
$740$		0			0
$741$	−2.03363	+	2.67478i	−0.0747073	+	0.0982606i
$742$	3.13998	−	0.274713i	0.115272	−	0.0100850i
$743$	−50.0244	+	4.37657i	−1.83522	+	0.160561i	−0.951538	−	0.307532i	$-0.900497\pi$
$743$	−50.0244	+	4.37657i	−1.83522	+	0.160561i	−0.883679	+	0.468092i	$0.844941\pi$
$744$	−4.98979	−	0.634398i	−0.182935	−	0.0232582i
$745$		0			0
$746$	−6.77350	−	3.91068i	−0.247996	−	0.143180i
$747$	19.6876	+	33.4113i	0.720331	+	1.22246i
$748$	1.77077	−	6.60861i	0.0647458	−	0.241635i
$749$	3.80077	+	21.5553i	0.138877	+	0.787612i
$750$		0			0
$751$	−11.3558	+	4.13319i	−0.414380	+	0.150822i	−0.540793	−	0.841156i	$-0.681876\pi$
$751$	−11.3558	+	4.13319i	−0.414380	+	0.150822i	0.126413	+	0.991978i	$0.459654\pi$
$752$	30.0490	−	21.0405i	1.09577	−	0.767268i
$753$	−36.2149	−	32.8903i	−1.31974	−	1.19859i
$754$	−0.137410	−	0.163759i	−0.00500418	−	0.00596375i
$755$		0			0
$756$	1.70278	+	11.7252i	0.0619296	+	0.426440i
$757$	14.6269	−	14.6269i	0.531625	−	0.531625i	−0.389431	−	0.921056i	$-0.627328\pi$
$757$	14.6269	−	14.6269i	0.531625	−	0.531625i	0.921056	+	0.389431i	$0.127328\pi$
$758$	−0.580618	+	6.63649i	−0.0210890	+	0.241048i
$759$	5.06079	+	7.86657i	0.183695	+	0.285538i
$760$		0			0
$761$	7.74333	+	21.2746i	0.280695	+	0.771204i	0.997280	+	0.0737041i	$0.0234820\pi$
$761$	7.74333	+	21.2746i	0.280695	+	0.771204i	−0.716585	+	0.697500i	$0.754296\pi$
$762$	−0.162895	+	4.15397i	−0.00590108	+	0.150482i
$763$	6.36856	−	9.09525i	0.230557	−	0.329270i
$764$	−11.3415	−	19.6440i	−0.410320	−	0.710696i
$765$		0			0
$766$	6.51349	−	11.2817i	0.235342	−	0.407625i
$767$	−0.839864	−	1.80109i	−0.0303257	−	0.0650337i
$768$	4.66609	−	11.4079i	0.168373	−	0.411647i
$769$	13.7049	−	16.3329i	0.494213	−	0.588980i	−0.460071	−	0.887882i	$-0.652176\pi$
$769$	13.7049	−	16.3329i	0.494213	−	0.588980i	0.954284	+	0.298902i	$0.0966204\pi$
$770$		0			0
$771$	32.2367	−	13.5208i	1.16098	−	0.486940i
$772$	13.2434	−	6.17552i	0.476642	−	0.222262i
$773$	4.23460	+	15.8037i	0.152308	+	0.568421i	0.999321	+	0.0368487i	$0.0117320\pi$
$773$	4.23460	+	15.8037i	0.152308	+	0.568421i	−0.847013	+	0.531572i	$0.821601\pi$
$774$	−3.80484	−	2.61415i	−0.136762	−	0.0939635i
$775$		0			0
$776$	8.11889	−	1.43158i	0.291451	−	0.0513907i
$777$	−3.51769	−	0.137944i	−0.126196	−	0.00494872i
$778$	−5.24467	−	2.44563i	−0.188030	−	0.0876800i
$779$	10.7548	−	60.9936i	0.385332	−	2.18532i
$780$		0			0
$781$	22.0914	−	18.5368i	0.790491	−	0.663301i
$782$	1.44912	+	1.44912i	0.0518204	+	0.0518204i
$783$	−9.10985	+	0.519367i	−0.325559	+	0.0185607i
$784$		−	18.1452i		−	0.648044i
$785$		0			0
$786$	0.535476	+	11.1304i	0.0190998	+	0.397010i
$787$	7.09564	+	10.1336i	0.252932	+	0.361225i	0.925459	−	0.378848i	$-0.123680\pi$
$787$	7.09564	+	10.1336i	0.252932	+	0.361225i	−0.672527	+	0.740073i	$0.734791\pi$
$788$	0.442449	−	0.948835i	0.0157616	−	0.0338009i
$789$	−6.51925	+	21.0010i	−0.232091	+	0.747656i
$790$		0			0
$791$	−12.8437	+	7.41530i	−0.456669	+	0.263658i
$792$	0.0660097	+	7.43518i	0.00234555	+	0.264198i
$793$	−2.53128	+	0.678255i	−0.0898884	+	0.0240855i
$794$	7.42130	+	2.70113i	0.263372	+	0.0958596i
$795$		0			0
$796$	−4.83224	−	4.05473i	−0.171274	−	0.143716i
$797$	4.48822	+	51.3006i	0.158981	+	1.81716i	0.488009	+	0.872839i	$0.337723\pi$
$797$	4.48822	+	51.3006i	0.158981	+	1.81716i	−0.329028	+	0.944320i	$0.606721\pi$
$798$	−0.551050	−	4.04675i	−0.0195070	−	0.143253i
$799$	7.60331	−	20.8899i	0.268986	−	0.739033i
$800$		0			0
$801$	6.94792	+	3.16508i	0.245493	+	0.111833i
$802$	5.68784	+	1.52405i	0.200844	+	0.0538161i
$803$	−17.9926	−	12.5985i	−0.634943	−	0.444592i
$804$	−7.03725	−	31.0892i	−0.248185	−	1.09643i
$805$		0			0
$806$	−0.257153	−	0.0453429i	−0.00905781	−	0.00159714i
$807$	10.1697	+	31.7620i	0.357992	+	1.11808i
$808$	−8.44986	−	0.739267i	−0.297265	−	0.0260073i
$809$	29.5460			1.03878			0.519391	−	0.854537i	$-0.326159\pi$
$809$	29.5460			1.03878			0.519391	+	0.854537i	$0.326159\pi$
$810$		0			0
$811$	51.8564			1.82093			0.910463	−	0.413591i	$-0.135726\pi$
$811$	51.8564			1.82093			0.910463	+	0.413591i	$0.135726\pi$
$812$	−3.98885	−	0.348979i	−0.139981	−	0.0122468i
$813$	11.4588	+	35.7879i	0.401877	+	1.25514i
$814$	−1.05367	−	0.185790i	−0.0369309	−	0.00651192i
$815$		0			0
$816$	−2.49855	−	11.0381i	−0.0874669	−	0.386412i
$817$	−20.0869	−	14.0650i	−0.702751	−	0.492071i
$818$	−6.18097	−	1.65619i	−0.216113	−	0.0579072i
$819$	0.121921	+	1.26419i	0.00426025	+	0.0441744i
$820$		0			0
$821$	9.08233	−	24.9535i	0.316976	−	0.870883i	−0.674226	−	0.738525i	$-0.735523\pi$
$821$	9.08233	−	24.9535i	0.316976	−	0.870883i	0.991202	−	0.132358i	$-0.0422550\pi$
$822$	0.0406239	+	0.298330i	0.00141692	+	0.0104054i
$823$	2.06396	+	23.5911i	0.0719450	+	0.822335i	0.943356	+	0.331782i	$0.107650\pi$
$823$	2.06396	+	23.5911i	0.0719450	+	0.822335i	−0.871411	+	0.490553i	$0.836795\pi$
$824$	14.8038	+	12.4218i	0.515714	+	0.432735i
$825$		0			0
$826$	2.26983	+	0.826151i	0.0789775	+	0.0287455i
$827$	10.7335	−	2.87604i	0.373241	−	0.100010i	−0.0673219	−	0.997731i	$-0.521445\pi$
$827$	10.7335	−	2.87604i	0.373241	−	0.100010i	0.440563	+	0.897722i	$0.354779\pi$
$828$	14.4678	+	8.18261i	0.502792	+	0.284365i
$829$	−22.4115	+	12.9393i	−0.778382	+	0.449399i	−0.835857	−	0.548948i	$-0.815029\pi$
$829$	−22.4115	+	12.9393i	−0.778382	+	0.449399i	0.0574744	+	0.998347i	$0.481695\pi$
$830$		0			0
$831$	13.2827	−	42.7888i	0.460772	−	1.48433i
$832$	0.769515	−	1.65023i	0.0266781	−	0.0572115i
$833$	−6.30725	−	9.00769i	−0.218533	−	0.312098i
$834$	−0.0412538	−	0.857504i	−0.00142850	−	0.0296929i
$835$		0			0
$836$			19.1276i			0.661543i
$837$	−8.11642	+	7.63863i	−0.280544	+	0.264030i
$838$	5.07716	+	5.07716i	0.175387	+	0.175387i
$839$	−7.70983	+	6.46931i	−0.266173	+	0.223346i	−0.766099	−	0.642722i	$-0.777805\pi$
$839$	−7.70983	+	6.46931i	−0.266173	+	0.223346i	0.499926	+	0.866068i	$0.333360\pi$
$840$		0			0
$841$	−4.50032	+	25.5226i	−0.155184	+	0.880090i
$842$	−6.81978	−	3.18012i	−0.235025	−	0.109594i
$843$	−7.33673	−	0.287705i	−0.252690	−	0.00990910i
$844$	−24.1671	+	4.26131i	−0.831866	+	0.146680i
$845$		0			0
$846$	−0.916230	+	11.6643i	−0.0315006	+	0.401028i
$847$	−2.40342	−	8.96968i	−0.0825824	−	0.308202i
$848$	−22.1312	+	10.3199i	−0.759988	+	0.354388i
$849$	−22.8276	+	9.57442i	−0.783440	+	0.328593i
$850$		0			0
$851$	−3.17451	+	3.78323i	−0.108821	+	0.129688i
$852$	19.4001	−	47.4303i	0.664636	−	1.62494i
$853$	8.70782	+	18.6740i	0.298150	+	0.639385i	0.997126	−	0.0757601i	$-0.0241383\pi$
$853$	8.70782	+	18.6740i	0.298150	+	0.639385i	−0.698976	+	0.715145i	$0.746361\pi$
$854$	1.59263	−	2.75851i	0.0544985	−	0.0943942i
$855$		0			0
$856$	12.2042	+	21.1382i	0.417130	+	0.722490i
$857$	14.8249	−	21.1722i	0.506409	−	0.723228i	−0.481809	−	0.876276i	$-0.660020\pi$
$857$	14.8249	−	21.1722i	0.506409	−	0.723228i	0.988219	+	0.153048i	$0.0489091\pi$
$858$	−0.0151250	+	0.385700i	−0.000516359	+	0.0131676i
$859$	−7.25364	−	19.9292i	−0.247491	−	0.679976i	−0.999777	−	0.0211390i	$-0.993271\pi$
$859$	−7.25364	−	19.9292i	−0.247491	−	0.679976i	0.752285	−	0.658837i	$-0.228951\pi$
$860$		0			0
$861$	−12.6659	−	19.6880i	−0.431652	−	0.670966i
$862$	0.383256	−	4.38063i	0.0130537	−	0.149205i
$863$	27.3490	−	27.3490i	0.930969	−	0.930969i	−0.0667973	−	0.997767i	$-0.521278\pi$
$863$	27.3490	−	27.3490i	0.930969	−	0.930969i	0.997767	+	0.0667973i	$0.0212781\pi$
$864$	9.48292	+	17.6390i	0.322616	+	0.600090i
$865$		0			0
$866$	−6.74222	−	8.03506i	−0.229110	−	0.273043i
$867$	16.7199	+	15.1850i	0.567839	+	0.515710i
$868$	−4.00642	+	2.80532i	−0.135987	+	0.0952188i
$869$	−25.8473	+	9.40766i	−0.876810	+	0.319133i
$870$		0			0
$871$	−0.593339	−	3.36500i	−0.0201045	−	0.114019i
$872$	3.20467	−	11.9600i	0.108524	−	0.405016i
$873$	8.99306	−	15.9008i	0.304369	−	0.538160i
$874$	−4.96187	−	2.86474i	−0.167838	−	0.0969011i
$875$		0			0
$876$	−38.7191	−	4.92272i	−1.30820	−	0.166323i
$877$	−35.0252	+	3.06431i	−1.18272	+	0.103474i	−0.661497	−	0.749948i	$-0.730079\pi$
$877$	−35.0252	+	3.06431i	−1.18272	+	0.103474i	−0.521221	+	0.853422i	$0.674523\pi$
$878$	6.67252	−	0.583770i	0.225187	−	0.0197013i
$879$	30.0782	−	39.5610i	1.01451	−	1.33436i
$880$		0			0
$881$	30.8912	+	17.8350i	1.04075	+	0.600877i	0.920046	−	0.391811i	$-0.128151\pi$
$881$	30.8912	+	17.8350i	1.04075	+	0.600877i	0.120704	+	0.992689i	$0.461485\pi$
$882$	4.46636	+	3.68065i	0.150390	+	0.123934i
$883$	−9.00780	+	33.6176i	−0.303137	+	1.13132i	0.631401	+	0.775457i	$0.282480\pi$
$883$	−9.00780	+	33.6176i	−0.303137	+	1.13132i	−0.934537	+	0.355865i	$0.884186\pi$
$884$	−0.226302	−	1.28342i	−0.00761135	−	0.0431661i
$885$		0			0
$886$	3.75024	−	1.36498i	0.125992	−	0.0458572i
$887$	40.9327	−	28.6614i	1.37439	−	0.962355i	0.375010	−	0.927021i	$-0.377639\pi$
$887$	40.9327	−	28.6614i	1.37439	−	0.962355i	0.999376	−	0.0353349i	$-0.0112498\pi$
$888$	−3.73882	+	1.19712i	−0.125467	+	0.0401726i
$889$	5.36524	+	6.39404i	0.179944	+	0.214449i
$890$		0			0
$891$	12.8073	+	10.3647i	0.429060	+	0.347232i
$892$	−21.2225	+	21.2225i	−0.710581	+	0.710581i
$893$	−5.41679	+	61.9142i	−0.181266	+	2.07188i
$894$	4.45070	−	8.64318i	0.148854	−	0.289071i
$895$		0			0
$896$	3.95768	+	10.8736i	0.132217	+	0.363263i
$897$	1.50693	+	0.950643i	0.0503149	+	0.0317410i
$898$	−6.42832	+	9.18060i	−0.214516	+	0.306361i
$899$	−1.88333	−	3.26202i	−0.0628126	−	0.108795i
$900$		0			0
$901$	−7.39920	+	12.8158i	−0.246503	+	0.426956i
$902$	−3.00688	−	6.44827i	−0.100118	−	0.214704i
$903$	−9.18401	+	1.25060i	−0.305625	+	0.0416172i
$904$	−10.6307	+	12.6692i	−0.353573	+	0.421372i
$905$		0			0
$906$	−0.0469177	+	0.369026i	−0.00155874	+	0.0122601i
$907$	−46.8450	+	21.8442i	−1.55546	+	0.725325i	−0.994716	−	0.102662i	$-0.967264\pi$
$907$	−46.8450	+	21.8442i	−1.55546	+	0.725325i	−0.560747	+	0.827987i	$0.689486\pi$
$908$	−4.51155	−	16.8373i	−0.149721	−	0.558766i
$909$	−13.1717	+	13.4076i	−0.436876	+	0.444703i
$910$		0			0
$911$	−57.8699	+	10.2040i	−1.91731	+	0.338074i	−0.998408	−	0.0564017i	$-0.982037\pi$
$911$	−57.8699	+	10.2040i	−1.91731	+	0.338074i	−0.918906	+	0.394476i	$0.870926\pi$
$912$	14.7343	+	28.0002i	0.487902	+	0.927180i
$913$	21.4473	+	10.0010i	0.709802	+	0.330986i
$914$	0.231259	−	1.31153i	0.00764935	−	0.0433816i
$915$		0			0
$916$	9.61141	−	8.06493i	0.317570	−	0.266473i
$917$	15.8206	+	15.8206i	0.522443	+	0.522443i
$918$	3.22380	+	1.62401i	0.106401	+	0.0536004i
$919$			31.9476i			1.05385i	0.849911	+	0.526927i	$0.176656\pi$
$919$			31.9476i			1.05385i	−0.849911	+	0.526927i	$0.823344\pi$
$920$		0			0
$921$	3.29901	−	2.12235i	0.108706	−	0.0699337i
$922$	6.04162	+	8.62832i	0.198970	+	0.284159i
$923$	2.32150	−	4.97847i	0.0764130	−	0.163868i
$924$	4.90810	+	5.30875i	0.161465	+	0.174645i
$925$		0			0
$926$	−10.3427	+	5.97137i	−0.339883	+	0.196231i
$927$	42.1029	−	7.80990i	1.38284	−	0.256511i
$928$	−6.53733	+	1.75167i	−0.214598	+	0.0575014i
$929$	−42.9561	−	15.6347i	−1.40934	−	0.512959i	−0.478407	−	0.878138i	$-0.658785\pi$
$929$	−42.9561	−	15.6347i	−1.40934	−	0.512959i	−0.930937	+	0.365179i	$0.881008\pi$
$930$		0			0
$931$	23.5504	+	19.7611i	0.771833	+	0.647645i
$932$	−0.910305	−	10.4048i	−0.0298180	−	0.340822i
$933$	19.6019	+	8.01760i	0.641736	+	0.262484i
$934$	0.441631	−	1.21337i	0.0144506	−	0.0397028i
$935$		0			0
$936$	0.609933	+	1.27825i	0.0199363	+	0.0417810i
$937$	42.7303	+	11.4496i	1.39594	+	0.374041i	0.876885	−	0.480701i	$-0.159618\pi$
$937$	42.7303	+	11.4496i	1.39594	+	0.374041i	0.519054	+	0.854741i	$0.326284\pi$
$938$	3.40208	+	2.38216i	0.111082	+	0.0777804i
$939$	−21.5143	+	19.8906i	−0.702093	+	0.649106i
$940$		0			0
$941$	2.76151	+	0.486928i	0.0900225	+	0.0158734i	0.218478	−	0.975842i	$-0.429891\pi$
$941$	2.76151	+	0.486928i	0.0900225	+	0.0158734i	−0.128455	+	0.991715i	$0.541002\pi$
$942$	4.92605	+	1.06916i	0.160499	+	0.0348351i
$943$	−32.7167	−	2.86234i	−1.06540	−	0.0932107i
$944$	−18.7134			−0.609070
$945$		0			0
$946$	−2.81697			−0.0915876
$947$	32.3652	+	2.83159i	1.05173	+	0.0920142i	0.599887	−	0.800085i	$-0.295212\pi$
$947$	32.3652	+	2.83159i	1.05173	+	0.0920142i	0.451840	+	0.892099i	$0.350768\pi$
$948$	−32.8608	+	36.1825i	−1.06727	+	1.17515i
$949$	−4.12032	−	0.726524i	−0.133751	−	0.0235840i
$950$		0			0
$951$	20.6553	+	6.41194i	0.669795	+	0.207921i
$952$	2.67933	+	1.87609i	0.0868376	+	0.0608044i
$953$	−8.92145	−	2.39049i	−0.288994	−	0.0774357i	0.111410	−	0.993775i	$-0.464463\pi$
$953$	−8.92145	−	2.39049i	−0.288994	−	0.0774357i	−0.400404	+	0.916339i	$0.631130\pi$
$954$	1.94897	−	7.54082i	0.0631003	−	0.244143i
$955$		0			0
$956$	−4.74261	+	13.0302i	−0.153387	+	0.421427i
$957$	−4.40232	+	3.40917i	−0.142307	+	0.110203i
$958$	−0.353500	−	4.04053i	−0.0114211	−	0.130543i
$959$	0.463089	+	0.388578i	0.0149539	+	0.0125478i
$960$		0			0
$961$	24.8070	+	9.02902i	0.800226	+	0.291259i
$962$	−0.196855	+	0.0527471i	−0.00634686	+	0.00170064i
$963$	53.3448	+	8.91857i	1.71901	+	0.287397i
$964$	24.5122	−	14.1521i	0.789484	−	0.455809i
$965$		0			0
$966$	−2.11222	+	0.478114i	−0.0679595	+	0.0153831i
$967$	−17.1014	+	36.6740i	−0.549943	+	1.17936i	0.413267	+	0.910610i	$0.364387\pi$
$967$	−17.1014	+	36.6740i	−0.549943	+	1.17936i	−0.963211	+	0.268747i	$0.913390\pi$
$968$	−5.93965	−	8.48270i	−0.190908	−	0.272644i
$969$	17.0473	+	8.77829i	0.547637	+	0.281999i
$970$		0			0
$971$			12.5885i			0.403983i	0.979387	+	0.201991i	$0.0647413\pi$
$971$			12.5885i			0.403983i	−0.979387	+	0.201991i	$0.935259\pi$
$972$	28.7167	+	5.70082i	0.921087	+	0.182854i
$973$	−1.21884	−	1.21884i	−0.0390743	−	0.0390743i
$974$	3.36585	−	2.82428i	0.107849	−	0.0904959i
$975$		0			0
$976$	−4.28508	+	24.3019i	−0.137162	+	0.777885i
$977$	−29.7224	−	13.8598i	−0.950905	−	0.443414i	−0.115658	−	0.993289i	$-0.536898\pi$
$977$	−29.7224	−	13.8598i	−0.950905	−	0.443414i	−0.835247	+	0.549875i	$0.814675\pi$
$978$	5.52347	−	8.75563i	0.176621	−	0.279974i
$979$	4.58816	−	0.809016i	0.146638	−	0.0258563i
$980$		0			0
$981$	−15.9358	−	22.3340i	−0.508789	−	0.713068i
$982$	−2.41147	−	8.99974i	−0.0769532	−	0.287193i
$983$	13.6314	−	6.35642i	0.434774	−	0.202738i	−0.192894	−	0.981220i	$-0.561787\pi$
$983$	13.6314	−	6.35642i	0.434774	−	0.202738i	0.627668	+	0.778481i	$0.284010\pi$
$984$	−20.7818	−	15.8004i	−0.662499	−	0.503697i
$985$		0			0
$986$	−0.784146	+	0.934509i	−0.0249723	+	0.0297608i
$987$	14.3836	+	18.5738i	0.457836	+	0.591211i
$988$	1.53979	+	3.30209i	0.0489872	+	0.105053i
$989$	−6.50145	+	11.2608i	−0.206734	+	0.358074i
$990$		0			0
$991$	26.1024	+	45.2106i	0.829169	+	1.43616i	0.898691	+	0.438583i	$0.144519\pi$
$991$	26.1024	+	45.2106i	0.829169	+	1.43616i	−0.0695216	+	0.997580i	$0.522147\pi$
$992$	−4.74172	+	6.77188i	−0.150550	+	0.215008i
$993$	32.2487	−	16.9700i	1.02338	−	0.538525i
$994$	2.28359	+	6.27412i	0.0724311	+	0.199003i
$995$		0			0
$996$	42.0024	−	2.02070i	1.33090	−	0.0640283i
$997$	−0.819878	+	9.37125i	−0.0259658	+	0.296791i	0.972097	+	0.234579i	$0.0753710\pi$
$997$	−0.819878	+	9.37125i	−0.0259658	+	0.296791i	−0.998063	+	0.0622119i	$0.980185\pi$
$998$	7.32559	−	7.32559i	0.231887	−	0.231887i
$999$	−3.22163	+	8.08041i	−0.101928	+	0.255653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.c.518.13	yes	288
5.2	odd	4	inner	675.2.ba.c.32.12	✓	288
5.3	odd	4	inner	675.2.ba.c.32.13	yes	288
5.4	even	2	inner	675.2.ba.c.518.12	yes	288
27.11	odd	18	inner	675.2.ba.c.443.12	yes	288
135.38	even	36	inner	675.2.ba.c.632.12	yes	288
135.92	even	36	inner	675.2.ba.c.632.13	yes	288
135.119	odd	18	inner	675.2.ba.c.443.13	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.ba.c.32.12	✓	288	5.2	odd	4	inner
675.2.ba.c.32.13	yes	288	5.3	odd	4	inner
675.2.ba.c.443.12	yes	288	27.11	odd	18	inner
675.2.ba.c.443.13	yes	288	135.119	odd	18	inner
675.2.ba.c.518.12	yes	288	5.4	even	2	inner
675.2.ba.c.518.13	yes	288	1.1	even	1	trivial
675.2.ba.c.632.12	yes	288	135.38	even	36	inner
675.2.ba.c.632.13	yes	288	135.92	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.347779 + 0.0304268i) q^{2} +(-0.528165 - 1.64956i) q^{3} +(-1.84959 - 0.326133i) q^{4} +(-0.133494 - 0.589753i) q^{6} +(-0.994510 - 0.696364i) q^{7} +(-1.30775 - 0.350411i) q^{8} +(-2.44208 + 1.74248i) q^{9} +O(q^{10})\)	\(q+(0.347779 + 0.0304268i) q^{2} +(-0.528165 - 1.64956i) q^{3} +(-1.84959 - 0.326133i) q^{4} +(-0.133494 - 0.589753i) q^{6} +(-0.994510 - 0.696364i) q^{7} +(-1.30775 - 0.350411i) q^{8} +(-2.44208 + 1.74248i) q^{9} +(-0.626120 + 1.72025i) q^{11} +(0.438914 + 3.22326i) q^{12} +(0.0303916 + 0.347377i) q^{13} +(-0.324682 - 0.272441i) q^{14} +(3.08557 + 1.12306i) q^{16} +(1.92212 - 0.515030i) q^{17} +(-0.902324 + 0.531693i) q^{18} +(-4.81794 + 2.78164i) q^{19} +(-0.623426 + 2.00830i) q^{21} +(-0.270093 + 0.579217i) q^{22} +(1.69206 + 2.41651i) q^{23} +(0.112685 + 2.34229i) q^{24} +0.121735i q^{26} +(4.16414 + 3.10804i) q^{27} +(1.61233 + 1.61233i) q^{28} +(-1.34520 + 1.12876i) q^{29} +(-0.372471 + 2.11239i) q^{31} +(3.49300 + 1.62881i) q^{32} +(3.16835 + 0.124245i) q^{33} +(0.684143 - 0.120633i) q^{34} +(5.08513 - 2.42643i) q^{36} +(0.433293 + 1.61707i) q^{37} +(-1.76022 + 0.820803i) q^{38} +(0.556967 - 0.233605i) q^{39} +(-7.15599 + 8.52817i) q^{41} +(-0.277921 + 0.679476i) q^{42} +(1.86279 + 3.99477i) q^{43} +(1.71910 - 2.97756i) q^{44} +(0.514936 + 0.891896i) q^{46} +(6.40776 - 9.15123i) q^{47} +(0.222855 - 5.68299i) q^{48} +(-1.89001 - 5.19277i) q^{49} +(-1.86477 - 2.89862i) q^{51} +(0.0570792 - 0.652418i) q^{52} +(-5.25853 + 5.25853i) q^{53} +(1.35364 + 1.20761i) q^{54} +(1.05656 + 1.25916i) q^{56} +(7.13315 + 6.47831i) q^{57} +(-0.502179 + 0.351629i) q^{58} +(-5.35536 + 1.94919i) q^{59} +(1.30500 + 7.40100i) q^{61} +(-0.193811 + 0.723312i) q^{62} +(3.64208 - 0.0323344i) q^{63} +(-4.52212 - 2.61085i) q^{64} +(1.09811 + 0.139612i) q^{66} +(-9.76158 + 0.854027i) q^{67} +(-3.72310 + 0.325729i) q^{68} +(3.09249 - 4.06746i) q^{69} +(-13.6425 - 7.87649i) q^{71} +(3.80422 - 1.42299i) q^{72} +(-3.10541 + 11.5895i) q^{73} +(0.101488 + 0.575568i) q^{74} +(9.81841 - 3.57361i) q^{76} +(1.82060 - 1.27480i) q^{77} +(0.200810 - 0.0642964i) q^{78} +(9.65809 + 11.5101i) q^{79} +(2.92754 - 8.51055i) q^{81} +(-2.74819 + 2.74819i) q^{82} +(1.12664 - 12.8776i) q^{83} +(1.80806 - 3.51121i) q^{84} +(0.526293 + 1.44598i) q^{86} +(2.57244 + 1.62282i) q^{87} +(1.42160 - 2.03026i) q^{88} +(-1.27248 - 2.20400i) q^{89} +(0.211676 - 0.366634i) q^{91} +(-2.34151 - 5.02139i) q^{92} +(3.68124 - 0.501277i) q^{93} +(2.50693 - 2.98764i) q^{94} +(0.841940 - 6.62218i) q^{96} +(-5.51873 + 2.57343i) q^{97} +(-0.499308 - 1.86344i) q^{98} +(-1.46846 - 5.29200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 24 q^{6}+O(q^{10}) \) 288 * q + 24 * q^6	\( 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) \) 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more