LMFDB - Embedded newform 675.2.u.c.274.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, 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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			274.6
Character	$\chi$	$=$	675.274
Dual form			675.2.u.c.574.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.102900 - 0.282715i) q^{2} +(1.50075 + 0.864728i) q^{3} +(1.46275 + 1.22739i) q^{4} +(0.398898 - 0.335304i) q^{6} +(-2.75715 - 3.28585i) q^{7} +(1.01862 - 0.588102i) q^{8} +(1.50449 + 2.59548i) q^{9} +O(q^{10})$	\(q+(0.102900 - 0.282715i) q^{2} +(1.50075 + 0.864728i) q^{3} +(1.46275 + 1.22739i) q^{4} +(0.398898 - 0.335304i) q^{6} +(-2.75715 - 3.28585i) q^{7} +(1.01862 - 0.588102i) q^{8} +(1.50449 + 2.59548i) q^{9} +(0.307813 + 1.74570i) q^{11} +(1.13386 + 3.10689i) q^{12} +(1.38340 + 3.80087i) q^{13} +(-1.21267 + 0.441375i) q^{14} +(0.601708 + 3.41245i) q^{16} +(3.38121 + 1.95214i) q^{17} +(0.888593 - 0.158267i) q^{18} +(0.556845 + 0.964484i) q^{19} +(-1.29643 - 7.31542i) q^{21} +(0.525208 + 0.0926084i) q^{22} +(5.54440 - 6.60755i) q^{23} +(2.03724 - 0.00176120i) q^{24} +1.21692 q^{26} +(0.0134762 + 5.19613i) q^{27} -8.19048i q^{28} +(0.562260 + 0.204646i) q^{29} +(1.24781 + 1.04704i) q^{31} +(3.34334 + 0.589520i) q^{32} +(-1.04760 + 2.88602i) q^{33} +(0.899826 - 0.755043i) q^{34} +(-0.984980 + 5.64313i) q^{36} +(-4.51818 - 2.60857i) q^{37} +(0.329973 - 0.0581832i) q^{38} +(-1.21058 + 6.90042i) q^{39} +(-0.711333 + 0.258904i) q^{41} +(-2.20158 - 0.386236i) q^{42} +(-7.10010 + 1.25194i) q^{43} +(-1.69240 + 2.93132i) q^{44} +(-1.29754 - 2.24740i) q^{46} +(-7.55208 - 9.00022i) q^{47} +(-2.04783 + 5.64155i) q^{48} +(-1.97936 + 11.2255i) q^{49} +(3.38627 + 5.85350i) q^{51} +(-2.64159 + 7.25771i) q^{52} -3.97724i q^{53} +(1.47041 + 0.530872i) q^{54} +(-4.74091 - 1.72555i) q^{56} +(0.00166759 + 1.92897i) q^{57} +(0.115713 - 0.137901i) q^{58} +(2.39974 - 13.6096i) q^{59} +(-6.49619 + 5.45095i) q^{61} +(0.424413 - 0.245035i) q^{62} +(4.38024 - 12.0997i) q^{63} +(-2.95440 + 5.11717i) q^{64} +(0.708124 + 0.593144i) q^{66} +(-2.67961 - 7.36217i) q^{67} +(2.54982 + 7.00557i) q^{68} +(14.0345 - 5.12188i) q^{69} +(2.59176 - 4.48907i) q^{71} +(3.05891 + 1.75902i) q^{72} +(3.78911 - 2.18764i) q^{73} +(-1.20240 + 1.00894i) q^{74} +(-0.369276 + 2.09427i) q^{76} +(4.88740 - 5.82458i) q^{77} +(1.82628 + 1.05230i) q^{78} +(-12.1133 - 4.40888i) q^{79} +(-4.47302 + 7.80974i) q^{81} +0.227746i q^{82} +(-2.70443 + 7.43037i) q^{83} +(7.08254 - 12.2918i) q^{84} +(-0.376657 + 2.13613i) q^{86} +(0.666848 + 0.793324i) q^{87} +(1.34019 + 1.59718i) q^{88} +(-1.62783 - 2.81949i) q^{89} +(8.67483 - 15.0252i) q^{91} +(16.2201 - 2.86005i) q^{92} +(0.967248 + 2.65036i) q^{93} +(-3.32160 + 1.20896i) q^{94} +(4.50773 + 3.77580i) q^{96} +(1.96145 - 0.345856i) q^{97} +(2.96995 + 1.71470i) q^{98} +(-4.06782 + 3.42530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^9	$ 60 q + 6 q^{9} - 12 q^{11} + 18 q^{14} + 24 q^{16} - 48 q^{19} - 72 q^{21} - 90 q^{24} - 36 q^{26} - 36 q^{29} + 24 q^{31} + 138 q^{34} - 84 q^{36} - 12 q^{39} - 150 q^{41} - 24 q^{44} + 60 q^{46} + 72 q^{49} + 42 q^{51} - 36 q^{54} + 60 q^{56} + 54 q^{59} - 24 q^{61} - 54 q^{64} + 156 q^{66} + 234 q^{69} + 24 q^{71} - 60 q^{76} - 108 q^{79} - 54 q^{81} - 90 q^{84} + 36 q^{86} - 18 q^{89} + 102 q^{91} - 30 q^{94} - 30 q^{96} - 246 q^{99}+O(q^{100}) $ 60 * q + 6 * q^9 - 12 * q^11 + 18 * q^14 + 24 * q^16 - 48 * q^19 - 72 * q^21 - 90 * q^24 - 36 * q^26 - 36 * q^29 + 24 * q^31 + 138 * q^34 - 84 * q^36 - 12 * q^39 - 150 * q^41 - 24 * q^44 + 60 * q^46 + 72 * q^49 + 42 * q^51 - 36 * q^54 + 60 * q^56 + 54 * q^59 - 24 * q^61 - 54 * q^64 + 156 * q^66 + 234 * q^69 + 24 * q^71 - 60 * q^76 - 108 * q^79 - 54 * q^81 - 90 * q^84 + 36 * q^86 - 18 * q^89 + 102 * q^91 - 30 * q^94 - 30 * q^96 - 246 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$

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 $

$2$	0.102900	−	0.282715i	0.0727612	−	0.199910i	−0.897981	−	0.440035i	$-0.854966\pi$
$2$	0.102900	−	0.282715i	0.0727612	−	0.199910i	0.970742	+	0.240125i	$0.0771884\pi$
$3$	1.50075	+	0.864728i	0.866457	+	0.499251i
$3$	1.50075	+	0.864728i	0.866457	+	0.499251i
$4$	1.46275	+	1.22739i	0.731375	+	0.613696i
$5$		0			0
$5$		0			0
$6$	0.398898	−	0.335304i	0.162850	−	0.136887i
$7$	−2.75715	−	3.28585i	−1.04211	−	1.24193i	−0.969633	−	0.244563i	$-0.921355\pi$
$7$	−2.75715	−	3.28585i	−1.04211	−	1.24193i	−0.0724727	−	0.997370i	$-0.523089\pi$
$8$	1.01862	−	0.588102i	0.360137	−	0.207925i
$9$	1.50449	+	2.59548i	0.501497	+	0.865160i
$10$		0			0
$11$	0.307813	+	1.74570i	0.0928092	+	0.526347i	0.995397	+	0.0958407i	$0.0305539\pi$
$11$	0.307813	+	1.74570i	0.0928092	+	0.526347i	−0.902587	+	0.430506i	$0.858335\pi$
$12$	1.13386	+	3.10689i	0.327316	+	0.896881i
$13$	1.38340	+	3.80087i	0.383687	+	1.05417i	0.969791	+	0.243937i	$0.0784389\pi$
$13$	1.38340	+	3.80087i	0.383687	+	1.05417i	−0.586104	+	0.810236i	$0.699339\pi$
$14$	−1.21267	+	0.441375i	−0.324099	+	0.117963i
$15$		0			0
$16$	0.601708	+	3.41245i	0.150427	+	0.853113i
$17$	3.38121	+	1.95214i	0.820064	+	0.473464i	0.850438	−	0.526075i	$-0.176337\pi$
$17$	3.38121	+	1.95214i	0.820064	+	0.473464i	−0.0303747	+	0.999539i	$0.509670\pi$
$18$	0.888593	−	0.158267i	0.209443	−	0.0373040i
$19$	0.556845	+	0.964484i	0.127749	+	0.221268i	0.922804	−	0.385269i	$-0.125891\pi$
$19$	0.556845	+	0.964484i	0.127749	+	0.221268i	−0.795055	+	0.606537i	$0.792558\pi$
$20$		0			0
$21$	−1.29643	−	7.31542i	−0.282904	−	1.59636i
$22$	0.525208	+	0.0926084i	0.111975	+	0.0197442i
$23$	5.54440	−	6.60755i	1.15609	−	1.37777i	0.242989	−	0.970029i	$-0.421872\pi$
$23$	5.54440	−	6.60755i	1.15609	−	1.37777i	0.913098	−	0.407741i	$-0.133683\pi$
$24$	2.03724	−	0.00176120i	0.415851	−	0.000359503i
$25$		0			0
$26$	1.21692			0.238657
$27$	0.0134762	+	5.19613i	0.00259350	+	0.999997i
$28$		−	8.19048i		−	1.54786i
$29$	0.562260	+	0.204646i	0.104409	+	0.0380018i	0.393696	−	0.919240i	$-0.371196\pi$
$29$	0.562260	+	0.204646i	0.104409	+	0.0380018i	−0.289287	+	0.957242i	$0.593418\pi$
$30$		0			0
$31$	1.24781	+	1.04704i	0.224114	+	0.188054i	0.747930	−	0.663777i	$-0.231048\pi$
$31$	1.24781	+	1.04704i	0.224114	+	0.188054i	−0.523816	+	0.851831i	$0.675492\pi$
$32$	3.34334	+	0.589520i	0.591024	+	0.104213i
$33$	−1.04760	+	2.88602i	−0.182364	+	0.502392i
$34$	0.899826	−	0.755043i	0.154319	−	0.129489i
$35$		0			0
$36$	−0.984980	+	5.64313i	−0.164163	+	0.940522i
$37$	−4.51818	−	2.60857i	−0.742785	−	0.428847i	0.0802963	−	0.996771i	$-0.474413\pi$
$37$	−4.51818	−	2.60857i	−0.742785	−	0.428847i	−0.823081	+	0.567924i	$0.807747\pi$
$38$	0.329973	−	0.0581832i	0.0535287	−	0.00943856i
$39$	−1.21058	+	6.90042i	−0.193848	+	1.10495i
$40$		0			0
$41$	−0.711333	+	0.258904i	−0.111092	+	0.0404340i	−0.396968	−	0.917833i	$-0.629938\pi$
$41$	−0.711333	+	0.258904i	−0.111092	+	0.0404340i	0.285876	+	0.958267i	$0.407715\pi$
$42$	−2.20158	−	0.386236i	−0.339711	−	0.0595975i
$43$	−7.10010	+	1.25194i	−1.08276	+	0.190919i	−0.686434	−	0.727193i	$-0.740825\pi$
$43$	−7.10010	+	1.25194i	−1.08276	+	0.190919i	−0.396322	+	0.918112i	$0.629714\pi$
$44$	−1.69240	+	2.93132i	−0.255139	+	0.441914i
$45$		0			0
$46$	−1.29754	−	2.24740i	−0.191311	−	0.331361i
$47$	−7.55208	−	9.00022i	−1.10158	−	1.31282i	−0.945700	−	0.325041i	$-0.894622\pi$
$47$	−7.55208	−	9.00022i	−1.10158	−	1.31282i	−0.155884	−	0.987775i	$-0.549823\pi$
$48$	−2.04783	+	5.64155i	−0.295579	+	0.814287i
$49$	−1.97936	+	11.2255i	−0.282766	+	1.60365i
$50$		0			0
$51$	3.38627	+	5.85350i	0.474173	+	0.819654i
$52$	−2.64159	+	7.25771i	−0.366323	+	1.00646i
$53$		−	3.97724i		−	0.546316i	−0.961969	−	0.273158i	$-0.911932\pi$
$53$		−	3.97724i		−	0.546316i	0.961969	−	0.273158i	$-0.0880681\pi$
$54$	1.47041	+	0.530872i	0.200098	+	0.0722425i
$55$		0			0
$56$	−4.74091	−	1.72555i	−0.633531	−	0.230586i
$57$	0.00166759	+	1.92897i	0.000220878	+	0.255498i
$58$	0.115713	−	0.137901i	0.0151939	−	0.0181073i
$59$	2.39974	−	13.6096i	0.312419	−	1.77182i	−0.273919	−	0.961753i	$-0.588320\pi$
$59$	2.39974	−	13.6096i	0.312419	−	1.77182i	0.586339	−	0.810066i	$-0.300569\pi$
$60$		0			0
$61$	−6.49619	+	5.45095i	−0.831752	+	0.697923i	−0.955693	−	0.294366i	$-0.904891\pi$
$61$	−6.49619	+	5.45095i	−0.831752	+	0.697923i	0.123940	+	0.992290i	$0.460447\pi$
$62$	0.424413	−	0.245035i	0.0539006	−	0.0311195i
$63$	4.38024	−	12.0997i	0.551858	−	1.52441i
$64$	−2.95440	+	5.11717i	−0.369300	+	0.639647i
$65$		0			0
$66$	0.708124	+	0.593144i	0.0871641	+	0.0730110i
$67$	−2.67961	−	7.36217i	−0.327367	−	0.899432i	−0.988776	−	0.149407i	$-0.952264\pi$
$67$	−2.67961	−	7.36217i	−0.327367	−	0.899432i	0.661409	−	0.750025i	$-0.269959\pi$
$68$	2.54982	+	7.00557i	0.309211	+	0.849550i
$69$	14.0345	−	5.12188i	1.68955	−	0.616602i
$70$		0			0
$71$	2.59176	−	4.48907i	0.307586	−	0.532754i	−0.670248	−	0.742137i	$-0.733812\pi$
$71$	2.59176	−	4.48907i	0.307586	−	0.532754i	0.977834	+	0.209383i	$0.0671456\pi$
$72$	3.05891	+	1.75902i	0.360496	+	0.207302i
$73$	3.78911	−	2.18764i	0.443481	−	0.256044i	−0.261592	−	0.965179i	$-0.584247\pi$
$73$	3.78911	−	2.18764i	0.443481	−	0.256044i	0.705073	+	0.709135i	$0.250914\pi$
$74$	−1.20240	+	1.00894i	−0.139777	+	0.117286i
$75$		0			0
$76$	−0.369276	+	2.09427i	−0.0423588	+	0.240229i
$77$	4.88740	−	5.82458i	0.556971	−	0.663772i
$78$	1.82628	+	1.05230i	0.206786	+	0.119150i
$79$	−12.1133	−	4.40888i	−1.36285	−	0.496038i	−0.445917	−	0.895074i	$-0.647123\pi$
$79$	−12.1133	−	4.40888i	−1.36285	−	0.496038i	−0.916935	+	0.399036i	$0.869345\pi$
$80$		0			0
$81$	−4.47302	+	7.80974i	−0.497002	+	0.867749i
$82$			0.227746i			0.0251503i
$83$	−2.70443	+	7.43037i	−0.296850	+	0.815589i	0.698172	+	0.715930i	$0.253997\pi$
$83$	−2.70443	+	7.43037i	−0.296850	+	0.815589i	−0.995022	+	0.0996585i	$0.968225\pi$
$84$	7.08254	−	12.2918i	0.772769	−	1.34115i
$85$		0			0
$86$	−0.376657	+	2.13613i	−0.0406160	+	0.230345i
$87$	0.666848	+	0.793324i	0.0714936	+	0.0850533i
$88$	1.34019	+	1.59718i	0.142865	+	0.170260i
$89$	−1.62783	−	2.81949i	−0.172550	−	0.298865i	0.766761	−	0.641933i	$-0.221867\pi$
$89$	−1.62783	−	2.81949i	−0.172550	−	0.298865i	−0.939311	+	0.343068i	$0.888534\pi$
$90$		0			0
$91$	8.67483	−	15.0252i	0.909369	−	1.57507i
$92$	16.2201	−	2.86005i	1.69106	−	0.298180i
$93$	0.967248	+	2.65036i	0.100299	+	0.274830i
$94$	−3.32160	+	1.20896i	−0.342597	+	0.124695i
$95$		0			0
$96$	4.50773	+	3.77580i	0.460068	+	0.385366i
$97$	1.96145	−	0.345856i	0.199155	−	0.0351164i	−0.0731807	−	0.997319i	$-0.523315\pi$
$97$	1.96145	−	0.345856i	0.199155	−	0.0351164i	0.272336	+	0.962202i	$0.412204\pi$
$98$	2.96995	+	1.71470i	0.300010	+	0.173211i
$99$	−4.06782	+	3.42530i	−0.408831	+	0.344256i
$100$		0			0
$101$	7.02258	−	5.89264i	0.698773	−	0.586340i	−0.222652	−	0.974898i	$-0.571471\pi$
$101$	7.02258	−	5.89264i	0.698773	−	0.586340i	0.921424	+	0.388558i	$0.127027\pi$
$102$	2.00332	−	0.355025i	0.198358	−	0.0351527i
$103$	−1.78539	−	0.314812i	−0.175919	−	0.0310193i	0.0849945	−	0.996381i	$-0.472913\pi$
$103$	−1.78539	−	0.314812i	−0.175919	−	0.0310193i	−0.260914	+	0.965362i	$0.584024\pi$
$104$	3.64447	+	3.05807i	0.357369	+	0.299869i
$105$		0			0
$106$	−1.12442	−	0.409257i	−0.109214	−	0.0397506i
$107$			3.71297i			0.358946i	0.983763	+	0.179473i	$0.0574392\pi$
$107$			3.71297i			0.358946i	−0.983763	+	0.179473i	$0.942561\pi$
$108$	−6.35799	+	7.61718i	−0.611797	+	0.732964i
$109$	3.24138			0.310468			0.155234	−	0.987878i	$-0.450387\pi$
$109$	3.24138			0.310468			0.155234	+	0.987878i	$0.450387\pi$
$110$		0			0
$111$	−4.52495	−	7.82181i	−0.429489	−	0.742414i
$112$	9.55380	−	11.3858i	0.902749	−	1.07585i
$113$	−12.1124	−	2.13575i	−1.13944	−	0.200914i	−0.428080	−	0.903741i	$-0.640810\pi$
$113$	−12.1124	−	2.13575i	−1.13944	−	0.200914i	−0.711361	+	0.702827i	$0.751921\pi$
$114$	0.545520	+	0.198019i	0.0510926	+	0.0185462i
$115$		0			0
$116$	0.571265	+	0.989460i	0.0530406	+	0.0918690i
$117$	−7.78377	+	9.30897i	−0.719610	+	0.860615i
$118$	−3.60070	−	2.07887i	−0.331472	−	0.191375i
$119$	−2.90807	−	16.4925i	−0.266583	−	1.51186i
$120$		0			0
$121$	7.38391	−	2.68752i	0.671265	−	0.244320i
$122$	0.872609	+	2.39747i	0.0790023	+	0.217057i
$123$	−1.29141	−	0.226560i	−0.116443	−	0.0204282i
$124$	0.540109	+	3.06311i	0.0485033	+	0.275076i
$125$		0			0
$126$	−2.97003	−	2.48341i	−0.264591	−	0.221240i
$127$	−9.53655	+	5.50593i	−0.846232	+	0.488572i	−0.859378	−	0.511341i	$-0.829149\pi$
$127$	−9.53655	+	5.50593i	−0.846232	+	0.488572i	0.0131457	+	0.999914i	$0.495815\pi$
$128$	5.50711	+	6.56312i	0.486764	+	0.580103i
$129$	−11.7381	−	4.26081i	−1.03348	−	0.375144i
$130$		0			0
$131$	13.4406	+	11.2780i	1.17431	+	0.985361i	1.00000		0.000669520i	$0.000213115\pi$
$131$	13.4406	+	11.2780i	1.17431	+	0.985361i	0.174307	+	0.984691i	$0.444231\pi$
$132$	−5.07467	+	2.93571i	−0.441693	+	0.255521i
$133$	1.63384	−	4.48894i	0.141672	−	0.389240i
$134$	−2.35713			−0.203625
$135$		0			0
$136$	4.59223			0.393781
$137$	0.122007	−	0.335210i	0.0104237	−	0.0286389i	−0.934372	−	0.356300i	$-0.884038\pi$
$137$	0.122007	−	0.335210i	0.0104237	−	0.0286389i	0.944795	+	0.327661i	$0.106260\pi$
$138$	−0.00388575	−	4.49480i	−0.000330777	−	0.382623i
$139$	1.14234	+	0.958535i	0.0968918	+	0.0813019i	0.689947	−	0.723860i	$-0.257634\pi$
$139$	1.14234	+	0.958535i	0.0968918	+	0.0813019i	−0.593055	+	0.805162i	$0.702078\pi$
$140$		0			0
$141$	−3.55102	−	20.0376i	−0.299050	−	1.68747i
$142$	−1.00243	−	1.19465i	−0.0841224	−	0.100253i
$143$	−6.20934	+	3.58496i	−0.519251	+	0.299790i
$144$	−7.95169	+	6.69572i	−0.662641	+	0.557977i
$145$		0			0
$146$	−0.228581	−	1.29635i	−0.0189175	−	0.107286i
$147$	−12.6775	+	15.1351i	−1.04563	+	1.24832i
$148$	−3.40722	−	9.36127i	−0.280072	−	0.769492i
$149$	−17.0077	+	6.19029i	−1.39332	+	0.507128i	−0.926190	−	0.377058i	$-0.876936\pi$
$149$	−17.0077	+	6.19029i	−1.39332	+	0.507128i	−0.467134	+	0.884186i	$0.654714\pi$
$150$		0			0
$151$	−3.68305	−	20.8876i	−0.299723	−	1.69981i	−0.647361	−	0.762183i	$-0.724127\pi$
$151$	−3.68305	−	20.8876i	−0.299723	−	1.69981i	0.347638	−	0.937629i	$-0.386984\pi$
$152$	1.13443	+	0.654963i	0.0920144	+	0.0531245i
$153$	0.0202515	+	11.7128i	0.00163724	+	0.946927i
$154$	−1.14378	−	1.98109i	−0.0921687	−	0.159641i
$155$		0			0
$156$	−10.2403	+	8.60773i	−0.819881	+	0.689170i
$157$	−5.39259	−	0.950859i	−0.430375	−	0.0758868i	−0.0457357	−	0.998954i	$-0.514563\pi$
$157$	−5.39259	−	0.950859i	−0.430375	−	0.0758868i	−0.384640	+	0.923067i	$0.625674\pi$
$158$	−2.49291	+	2.97094i	−0.198326	+	0.236355i
$159$	3.43923	−	5.96883i	0.272749	−	0.473359i
$160$		0			0
$161$	−36.9982			−2.91586
$162$	1.74766	+	2.06821i	0.137309	+	0.162494i
$163$			17.9869i			1.40884i	0.709783	+	0.704420i	$0.248793\pi$
$163$			17.9869i			1.40884i	−0.709783	+	0.704420i	$0.751207\pi$
$164$	−1.35828	−	0.494373i	−0.106064	−	0.0386040i
$165$		0			0
$166$	1.82239	+	1.52917i	0.141445	+	0.118686i
$167$	19.6348	+	3.46215i	1.51939	+	0.267909i	0.870193	−	0.492711i	$-0.163994\pi$
$167$	19.6348	+	3.46215i	1.51939	+	0.267909i	0.649197	+	0.760620i	$0.275105\pi$
$168$	−5.62278	−	6.68922i	−0.433807	−	0.516084i
$169$	−2.57425	+	2.16006i	−0.198019	+	0.166158i
$170$		0			0
$171$	−1.66553	+	2.89634i	−0.127366	+	0.221488i
$172$	−11.9223	−	6.88334i	−0.909066	−	0.524850i
$173$	6.66294	−	1.17486i	0.506574	−	0.0893226i	0.0854803	−	0.996340i	$-0.472758\pi$
$173$	6.66294	−	1.17486i	0.506574	−	0.0893226i	0.421094	+	0.907017i	$0.361646\pi$
$174$	0.292903	−	0.106895i	0.0222049	−	0.00810368i
$175$		0			0
$176$	−5.77189	+	2.10080i	−0.435073	+	0.158354i
$177$	15.3700	−	18.3495i	1.15528	−	1.37923i
$178$	−0.964615	+	0.170088i	−0.0723009	+	0.0127486i
$179$	4.71985	−	8.17503i	0.352778	−	0.611030i	−0.633957	−	0.773369i	$-0.718570\pi$
$179$	4.71985	−	8.17503i	0.352778	−	0.611030i	0.986735	+	0.162338i	$0.0519036\pi$
$180$		0			0
$181$	−0.566202	−	0.980691i	−0.0420855	−	0.0728942i	0.844215	−	0.536004i	$-0.180067\pi$
$181$	−0.566202	−	0.980691i	−0.0420855	−	0.0728942i	−0.886301	+	0.463110i	$0.846734\pi$
$182$	−3.35522	−	3.99860i	−0.248706	−	0.296396i
$183$	−14.4627	+	2.56307i	−1.06912	+	0.189467i
$184$	1.76173	−	9.99127i	0.129876	−	0.736566i
$185$		0			0
$186$	0.848827		0.000733811i	0.0622390		5.38056e-5i
$187$	−2.36707	+	6.50346i	−0.173097	+	0.475580i
$188$		−	22.4344i		−	1.63620i
$189$	17.0366	−	14.3708i	1.23923	−	1.04532i
$190$		0			0
$191$	22.1994	+	8.07991i	1.60629	+	0.584642i	0.980701	−	0.195512i	$-0.0626368\pi$
$191$	22.1994	+	8.07991i	1.60629	+	0.584642i	0.625588	+	0.780153i	$0.284859\pi$
$192$	−8.85878	+	5.12483i	−0.639327	+	0.369853i
$193$	−1.74579	+	2.08055i	−0.125665	+	0.149761i	−0.825208	−	0.564829i	$-0.808942\pi$
$193$	−1.74579	+	2.08055i	−0.125665	+	0.149761i	0.699544	+	0.714590i	$0.253387\pi$
$194$	0.104054	−	0.590120i	0.00747064	−	0.0423681i
$195$		0			0
$196$	−16.6734	+	13.9907i	−1.19096	+	0.999333i
$197$	−12.3619	+	7.13716i	−0.880750	+	0.508501i	−0.870906	−	0.491450i	$-0.836467\pi$
$197$	−12.3619	+	7.13716i	−0.880750	+	0.508501i	−0.00984437	+	0.999952i	$0.503134\pi$
$198$	0.549807	+	1.50250i	0.0390731	+	0.106778i
$199$	10.6351	−	18.4206i	0.753905	−	1.30580i	−0.192012	−	0.981393i	$-0.561501\pi$
$199$	10.6351	−	18.4206i	0.753905	−	1.30580i	0.945917	−	0.324409i	$-0.105165\pi$
$200$		0			0
$201$	2.34486	−	13.3659i	0.165393	−	0.942758i
$202$	−0.943316	−	2.59174i	−0.0663715	−	0.182354i
$203$	−0.877802	−	2.41174i	−0.0616096	−	0.169271i
$204$	−2.23128	+	12.7185i	−0.156221	+	0.890472i
$205$		0			0
$206$	−0.272718	+	0.472361i	−0.0190012	+	0.0329110i
$207$	25.4913	+	4.44936i	1.77176	+	0.309252i
$208$	−12.1379	+	7.00782i	−0.841612	+	0.485905i
$209$	−1.51229	+	1.26896i	−0.104607	+	0.0877760i
$210$		0			0
$211$	−3.49805	+	19.8384i	−0.240815	+	1.36573i	0.589198	+	0.807989i	$0.299444\pi$
$211$	−3.49805	+	19.8384i	−0.240815	+	1.36573i	−0.830013	+	0.557743i	$0.811667\pi$
$212$	4.88163	−	5.81770i	0.335272	−	0.399562i
$213$	7.77141	−	4.49579i	0.532488	−	0.308046i
$214$	1.04971	+	0.382064i	0.0717568	+	0.0261173i
$215$		0			0
$216$	3.06958	+	5.28497i	0.208859	+	0.359597i
$217$		−	6.98697i		−	0.474306i
$218$	0.333537	−	0.916386i	0.0225900	−	0.0620655i
$219$	7.57821	−	0.00655137i	0.512088	−	0.000442700i
$220$		0			0
$221$	−2.74226	+	15.5522i	−0.184465	+	1.04615i
$222$	−2.67696	+	0.474407i	−0.179666	+	0.0318401i
$223$	3.71723	+	4.43003i	0.248924	+	0.296657i	0.876009	−	0.482294i	$-0.160196\pi$
$223$	3.71723	+	4.43003i	0.248924	+	0.296657i	−0.627085	+	0.778951i	$0.715752\pi$
$224$	−7.28102	−	12.6111i	−0.486483	−	0.842614i
$225$		0			0
$226$	−1.85017	+	3.20460i	−0.123072	+	0.213167i
$227$	−15.0765	+	2.65839i	−1.00066	+	0.176443i	−0.649898	−	0.760021i	$-0.725188\pi$
$227$	−15.0765	+	2.65839i	−1.00066	+	0.176443i	−0.350762	+	0.936465i	$0.614077\pi$
$228$	−2.36516	+	2.82364i	−0.156637	+	0.187000i
$229$	2.31831	−	0.843797i	0.153198	−	0.0557596i	−0.264283	−	0.964445i	$-0.585135\pi$
$229$	2.31831	−	0.843797i	0.153198	−	0.0557596i	0.417481	+	0.908686i	$0.362913\pi$
$230$		0			0
$231$	12.3714	−	4.51495i	0.813981	−	0.297062i
$232$	0.693083	−	0.122209i	0.0455031	−	0.00802343i
$233$	7.29932	+	4.21427i	0.478195	+	0.276086i	0.719664	−	0.694323i	$-0.244296\pi$
$233$	7.29932	+	4.21427i	0.478195	+	0.276086i	−0.241469	+	0.970408i	$0.577629\pi$
$234$	1.83084	+	3.15848i	0.119686	+	0.206476i
$235$		0			0
$236$	20.2145	−	16.9620i	1.31585	−	1.10413i
$237$	−14.3665	−	17.0913i	−0.933206	−	1.11020i
$238$	−4.96192	−	0.874920i	−0.321633	−	0.0567126i
$239$	11.6818	+	9.80219i	0.755633	+	0.634051i	0.936986	−	0.349367i	$-0.113603\pi$
$239$	11.6818	+	9.80219i	0.755633	+	0.634051i	−0.181353	+	0.983418i	$0.558048\pi$
$240$		0			0
$241$	0.611555	+	0.222588i	0.0393937	+	0.0143381i	0.361642	−	0.932317i	$-0.382216\pi$
$241$	0.611555	+	0.222588i	0.0393937	+	0.0143381i	−0.322248	+	0.946655i	$0.604439\pi$
$242$		−	2.36409i		−	0.151969i
$243$	−13.4662	+	7.85251i	−0.863856	+	0.503739i
$244$	−16.1928			−1.03664
$245$		0			0
$246$	−0.196938	+	0.341789i	−0.0125563	+	0.0217917i
$247$	−2.89554	+	3.45077i	−0.184239	+	0.219567i
$248$	1.88682	+	0.332696i	0.119813	+	0.0211262i
$249$	−10.4839	+	8.81251i	−0.664392	+	0.558470i
$250$		0			0
$251$	−3.07930	−	5.33350i	−0.194364	−	0.336648i	0.752328	−	0.658789i	$-0.228931\pi$
$251$	−3.07930	−	5.33350i	−0.194364	−	0.336648i	−0.946692	+	0.322141i	$0.895597\pi$
$252$	21.2582	−	12.3225i	1.33914	−	0.776244i
$253$	13.2414	+	7.64494i	0.832481	+	0.480633i
$254$	0.575299	+	3.26268i	0.0360975	+	0.204719i
$255$		0			0
$256$	−8.68274	+	3.16026i	−0.542672	+	0.197516i
$257$	−2.39832	−	6.58933i	−0.149603	−	0.411031i	0.842142	−	0.539256i	$-0.181294\pi$
$257$	−2.39832	−	6.58933i	−0.149603	−	0.411031i	−0.991745	+	0.128225i	$0.959072\pi$
$258$	−2.41244	+	2.88009i	−0.150192	+	0.179306i
$259$	3.88595	+	22.0383i	0.241461	+	1.36939i
$260$		0			0
$261$	0.314760	+	1.76722i	0.0194832	+	0.109388i
$262$	4.57148	−	2.63935i	0.282427	−	0.163059i
$263$	−12.5040	−	14.9017i	−0.771032	−	0.918880i	0.227459	−	0.973788i	$-0.426958\pi$
$263$	−12.5040	−	14.9017i	−0.771032	−	0.918880i	−0.998491	+	0.0549074i	$0.982514\pi$
$264$	0.630165	+	3.55587i	0.0387840	+	0.218848i
$265$		0			0
$266$	−1.10097	−	0.923822i	−0.0675047	−	0.0566432i
$267$	−0.00487489	−	5.63897i	−0.000298339	−	0.345099i
$268$	5.11667	−	14.0579i	0.312551	−	0.858726i
$269$	−10.1856			−0.621026			−0.310513	−	0.950569i	$-0.600501\pi$
$269$	−10.1856			−0.621026			−0.310513	+	0.950569i	$0.600501\pi$
$270$		0			0
$271$	−6.87083			−0.417373			−0.208687	−	0.977983i	$-0.566919\pi$
$271$	−6.87083			−0.417373			−0.208687	+	0.977983i	$0.566919\pi$
$272$	−4.62710	+	12.7128i	−0.280559	+	0.770829i
$273$	26.0115	−	15.0477i	1.57429	−	0.910731i
$274$	−0.0822145	−	0.0689862i	−0.00496676	−	0.00416761i
$275$		0			0
$276$	26.8155	+	9.73379i	1.61410	+	0.585905i
$277$	17.0747	+	20.3488i	1.02592	+	1.22264i	0.974599	+	0.223959i	$0.0718981\pi$
$277$	17.0747	+	20.3488i	1.02592	+	1.22264i	0.0513192	+	0.998682i	$0.483657\pi$
$278$	0.388539	−	0.224323i	0.0233030	−	0.0134540i
$279$	−0.840247	+	4.81393i	−0.0503042	+	0.288203i
$280$		0			0
$281$	−4.15446	−	23.5611i	−0.247834	−	1.40554i	−0.813817	−	0.581121i	$-0.802614\pi$
$281$	−4.15446	−	23.5611i	−0.247834	−	1.40554i	0.565983	−	0.824417i	$-0.308497\pi$
$282$	−6.03032	−	1.05793i	−0.359100	−	0.0629990i
$283$	−4.61782	−	12.6874i	−0.274501	−	0.754186i	−0.997961	−	0.0638197i	$-0.979672\pi$
$283$	−4.61782	−	12.6874i	−0.274501	−	0.754186i	0.723460	−	0.690366i	$-0.242550\pi$
$284$	9.30095	−	3.38527i	0.551910	−	0.200879i
$285$		0			0
$286$	0.374583	+	2.12437i	0.0221496	+	0.125616i
$287$	2.81197	+	1.62349i	0.165985	+	0.0958318i
$288$	3.49993	+	9.56448i	0.206235	+	0.563593i
$289$	−0.878281	−	1.52123i	−0.0516636	−	0.0894840i
$290$		0			0
$291$	3.24271	+	1.17708i	0.190091	+	0.0690015i
$292$	8.22761	+	1.45075i	0.481484	+	0.0848987i
$293$	−3.54442	+	4.22408i	−0.207067	+	0.246773i	−0.859576	−	0.511008i	$-0.829272\pi$
$293$	−3.54442	+	4.22408i	−0.207067	+	0.246773i	0.652508	+	0.757781i	$0.273717\pi$
$294$	2.97439	+	5.14153i	0.173470	+	0.299860i
$295$		0			0
$296$	−6.13643			−0.356673
$297$	−9.06672	+	1.62296i	−0.526105	+	0.0941740i
$298$			5.44531i			0.315438i
$299$	32.7846	+	11.9326i	1.89598	+	0.690082i
$300$		0			0
$301$	23.6898	+	19.8781i	1.36545	+	1.14575i
$302$	−6.28424	−	1.10808i	−0.361617	−	0.0637628i
$303$	15.6347	−	2.77075i	0.898187	−	0.159175i
$304$	−2.95620	+	2.48055i	−0.169550	+	0.142269i
$305$		0			0
$306$	3.31348	+	1.19952i	0.189419	+	0.0685722i
$307$	−4.12852	−	2.38360i	−0.235627	−	0.136039i	0.377538	−	0.925994i	$-0.376771\pi$
$307$	−4.12852	−	2.38360i	−0.235627	−	0.136039i	−0.613165	+	0.789955i	$0.710104\pi$
$308$	14.2981	−	2.52114i	0.814709	−	0.143655i
$309$	−2.40719	−	2.01633i	−0.136940	−	0.114705i
$310$		0			0
$311$	−10.2196	+	3.71963i	−0.579500	+	0.210921i	−0.615105	−	0.788445i	$-0.710886\pi$
$311$	−10.2196	+	3.71963i	−0.579500	+	0.210921i	0.0356051	+	0.999366i	$0.488664\pi$
$312$	2.82503	+	7.74087i	0.159936	+	0.438240i
$313$	−12.2295	+	2.15639i	−0.691253	+	0.121887i	−0.508229	−	0.861222i	$-0.669700\pi$
$313$	−12.2295	+	2.15639i	−0.691253	+	0.121887i	−0.183024	+	0.983108i	$0.558589\pi$
$314$	−0.823719	+	1.42672i	−0.0464851	+	0.0805146i
$315$		0			0
$316$	−12.3073	−	21.3169i	−0.692339	−	1.19917i
$317$	−7.09191	−	8.45181i	−0.398321	−	0.474701i	0.529186	−	0.848506i	$-0.322497\pi$
$317$	−7.09191	−	8.45181i	−0.398321	−	0.474701i	−0.927507	+	0.373805i	$0.878053\pi$
$318$	−1.33358	−	1.58651i	−0.0747836	−	0.0889673i
$319$	−0.184178	+	1.04453i	−0.0103120	+	0.0584823i
$320$		0			0
$321$	−3.21071	+	5.57223i	−0.179204	+	0.311011i
$322$	−3.80710	+	10.4599i	−0.212162	+	0.582909i
$323$			4.34816i			0.241938i
$324$	−16.1285	+	5.93355i	−0.896029	+	0.329641i
$325$		0			0
$326$	5.08516	+	1.85085i	0.281641	+	0.102509i
$327$	4.86449	+	2.80291i	0.269007	+	0.155001i
$328$	−0.572317	+	0.682061i	−0.0316009	+	0.0376605i
$329$	−8.75110	+	49.6300i	−0.482464	+	2.73619i
$330$		0			0
$331$	1.55201	−	1.30229i	0.0853061	−	0.0715803i	−0.599137	−	0.800646i	$-0.704490\pi$
$331$	1.55201	−	1.30229i	0.0853061	−	0.0715803i	0.684443	+	0.729066i	$0.260045\pi$
$332$	−13.0759	+	7.54937i	−0.717633	+	0.414325i
$333$	−0.0270613	−	15.6514i	−0.00148295	−	0.857693i
$334$	2.99923	−	5.19481i	0.164110	−	0.284247i
$335$		0			0
$336$	24.1835	−	8.82574i	1.31932	−	0.481484i
$337$	5.26029	+	14.4525i	0.286546	+	0.787280i	0.996543	+	0.0830749i	$0.0264741\pi$
$337$	5.26029	+	14.4525i	0.286546	+	0.787280i	−0.709997	+	0.704205i	$0.751304\pi$
$338$	0.345790	+	0.950049i	0.0188085	+	0.0516759i
$339$	−16.3309	−	13.6792i	−0.886970	−	0.742951i
$340$		0			0
$341$	−1.44372	+	2.50059i	−0.0781818	+	0.135415i
$342$	0.647455	+	0.768903i	0.0350103	+	0.0415775i
$343$	16.3398	−	9.43380i	0.882267	−	0.509377i
$344$	−6.49605	+	5.45084i	−0.350244	+	0.293889i
$345$		0			0
$346$	0.353466	−	2.00461i	0.0190024	−	0.107768i
$347$	−0.745107	+	0.887983i	−0.0399994	+	0.0476695i	−0.785673	−	0.618642i	$-0.787683\pi$
$347$	−0.745107	+	0.887983i	−0.0399994	+	0.0476695i	0.745674	+	0.666311i	$0.232128\pi$
$348$	0.00171078	+	1.97892i	9.17072e−5	+	0.106081i
$349$	−4.85238	−	1.76612i	−0.259742	−	0.0945383i	0.208867	−	0.977944i	$-0.433022\pi$
$349$	−4.85238	−	1.76612i	−0.259742	−	0.0945383i	−0.468609	+	0.883406i	$0.655245\pi$
$350$		0			0
$351$	−19.7312	+	7.23958i	−1.05317	+	0.386420i
$352$			6.01791i			0.320756i
$353$	4.15296	−	11.4102i	0.221040	−	0.607301i	−0.778760	−	0.627322i	$-0.784151\pi$
$353$	4.15296	−	11.4102i	0.221040	−	0.607301i	0.999800	+	0.0200207i	$0.00637322\pi$
$354$	−3.60609	−	6.23349i	−0.191662	−	0.331306i
$355$		0			0
$356$	1.07951	−	6.12219i	0.0572138	−	0.324475i
$357$	9.89724	−	27.2658i	0.523818	−	1.44306i
$358$	−1.82553	−	2.17558i	−0.0964823	−	0.114983i
$359$	4.44707	+	7.70256i	0.234708	+	0.406525i	0.959188	−	0.282770i	$-0.0912534\pi$
$359$	4.44707	+	7.70256i	0.234708	+	0.406525i	−0.724480	+	0.689296i	$0.757920\pi$
$360$		0			0
$361$	8.87985	−	15.3803i	0.467360	−	0.809492i
$362$	−0.335518	+	0.0591609i	−0.0176344	+	0.00310943i
$363$	13.4054	+	2.35178i	0.703600	+	0.123437i
$364$	31.1310	−	11.3308i	1.63171	−	0.593893i
$365$		0			0
$366$	−0.763597	+	4.35257i	−0.0399139	+	0.227513i
$367$	27.2079	−	4.79749i	1.42024	−	0.250427i	0.589807	−	0.807544i	$-0.299204\pi$
$367$	27.2079	−	4.79749i	1.42024	−	0.250427i	0.830434	+	0.557117i	$0.188093\pi$
$368$	25.8841	+	14.9442i	1.34930	+	0.779019i
$369$	−1.74217	−	1.45673i	−0.0906939	−	0.0758344i
$370$		0			0
$371$	−13.0686	+	10.9659i	−0.678488	+	0.569319i
$372$	−1.83819	+	5.06401i	−0.0953058	+	0.262557i
$373$	30.3780	+	5.35646i	1.57291	+	0.277347i	0.890971	−	0.454060i	$-0.150025\pi$
$373$	30.3780	+	5.35646i	1.57291	+	0.277347i	0.681942	+	0.731407i	$0.261136\pi$
$374$	1.59505	+	1.33841i	0.0824783	+	0.0692075i
$375$		0			0
$376$	−12.9858	−	4.72643i	−0.669689	−	0.243747i
$377$			2.42019i			0.124646i
$378$	−2.30979	−	6.29524i	−0.118803	−	0.323792i
$379$	21.0219			1.07982			0.539911	−	0.841722i	$-0.318458\pi$
$379$	21.0219			1.07982			0.539911	+	0.841722i	$0.318458\pi$
$380$		0			0
$381$	−19.0731	+	0.0164887i	−0.977144	+	0.000844742i
$382$	4.56862	−	5.44467i	0.233751	−	0.278574i
$383$	21.1982	+	3.73782i	1.08318	+	0.190994i	0.686621	−	0.727016i	$-0.259093\pi$
$383$	21.1982	+	3.73782i	1.08318	+	0.190994i	0.396559	+	0.918009i	$0.370204\pi$
$384$	2.58947	+	14.6117i	0.132143	+	0.745652i
$385$		0			0
$386$	0.408561	+	0.707648i	0.0207952	+	0.0360184i
$387$	−13.9314	−	16.5446i	−0.708174	−	0.841011i
$388$	3.29361	+	1.90157i	0.167208	+	0.0965374i
$389$	−2.32909	−	13.2089i	−0.118089	−	0.669718i	−0.985174	−	0.171558i	$-0.945120\pi$
$389$	−2.32909	−	13.2089i	−0.118089	−	0.669718i	0.867085	−	0.498161i	$-0.165991\pi$
$390$		0			0
$391$	31.6456	−	11.5181i	1.60039	−	0.582494i
$392$	4.58552	+	12.5986i	0.231604	+	0.636327i
$393$	10.4185	+	28.5478i	0.525545	+	1.44005i
$394$	0.745742	+	4.22931i	0.0375699	+	0.213070i
$395$		0			0
$396$	−10.1544	+	0.0175570i	−0.510277	+	0.000882270i
$397$	−14.7276	+	8.50299i	−0.739158	+	0.426753i	−0.821763	−	0.569829i	$-0.807009\pi$
$397$	−14.7276	+	8.50299i	−0.739158	+	0.426753i	0.0826052	+	0.996582i	$0.473676\pi$
$398$	−4.11343	−	4.90219i	−0.206187	−	0.245725i
$399$	6.33369	−	5.32394i	0.317081	−	0.266530i
$400$		0			0
$401$	4.77991	+	4.01082i	0.238697	+	0.200291i	0.754287	−	0.656545i	$-0.227983\pi$
$401$	4.77991	+	4.01082i	0.238697	+	0.200291i	−0.515590	+	0.856836i	$0.672427\pi$
$402$	−3.53745	−	2.03827i	−0.176432	−	0.101660i
$403$	−2.25343	+	6.19126i	−0.112252	+	0.308409i
$404$	17.5049			0.870899
$405$		0			0
$406$	−0.772161			−0.0383217
$407$	3.16302	−	8.69033i	0.156785	−	0.430764i
$408$	6.89178	+	3.97103i	0.341194	+	0.196595i
$409$	−7.35423	−	6.17093i	−0.363643	−	0.305133i	0.442598	−	0.896720i	$-0.354057\pi$
$409$	−7.35423	−	6.17093i	−0.363643	−	0.305133i	−0.806241	+	0.591587i	$0.798501\pi$
$410$		0			0
$411$	0.472967	−	0.397564i	0.0233297	−	0.0196104i
$412$	−2.22517	−	2.65186i	−0.109626	−	0.130648i
$413$	−51.3355	+	29.6386i	−2.52606	+	1.45842i
$414$	3.88095	−	6.74892i	0.190738	−	0.331691i
$415$		0			0
$416$	2.38449	+	13.5231i	0.116909	+	0.663027i
$417$	0.885489	+	2.42633i	0.0433626	+	0.118818i
$418$	0.203140	+	0.558124i	0.00993592	+	0.0272987i
$419$	14.1004	−	5.13212i	0.688849	−	0.250721i	0.0262069	−	0.999657i	$-0.491657\pi$
$419$	14.1004	−	5.13212i	0.688849	−	0.250721i	0.662642	+	0.748936i	$0.269435\pi$
$420$		0			0
$421$	6.43175	+	36.4763i	0.313464	+	1.77774i	0.580705	+	0.814114i	$0.302777\pi$
$421$	6.43175	+	36.4763i	0.313464	+	1.77774i	−0.267240	+	0.963630i	$0.586112\pi$
$422$	5.24867	+	3.03032i	0.255501	+	0.147514i
$423$	11.9978	−	33.1420i	0.583355	−	1.61142i
$424$	−2.33902	−	4.05130i	−0.113593	−	0.196749i
$425$		0			0
$426$	−0.471350	−	2.65971i	−0.0228370	−	0.128863i
$427$	35.8220	+	6.31639i	1.73355	+	0.305671i
$428$	−4.55727	+	5.43114i	−0.220284	+	0.262524i
$429$	−12.4187	+	0.0107359i	−0.599579	+	0.000518337i
$430$		0			0
$431$	−14.3326			−0.690378			−0.345189	−	0.938533i	$-0.612185\pi$
$431$	−14.3326			−0.690378			−0.345189	+	0.938533i	$0.612185\pi$
$432$	−17.7235	+	3.17254i	−0.852720	+	0.152639i
$433$		−	14.4669i		−	0.695233i	−0.937637	−	0.347616i	$-0.886991\pi$
$433$		−	14.4669i		−	0.695233i	0.937637	−	0.347616i	$-0.113009\pi$
$434$	−1.97532	−	0.718958i	−0.0948185	−	0.0345111i
$435$		0			0
$436$	4.74132	+	3.97844i	0.227068	+	0.190533i
$437$	9.46025	+	1.66810i	0.452545	+	0.0797959i
$438$	0.777944	−	2.14315i	0.0371716	−	0.102404i
$439$	11.4536	−	9.61070i	0.546650	−	0.458694i	−0.327155	−	0.944971i	$-0.606090\pi$
$439$	11.4536	−	9.61070i	0.546650	−	0.458694i	0.873805	+	0.486277i	$0.161645\pi$
$440$		0			0
$441$	−32.1135	+	11.7513i	−1.52922	+	0.559585i
$442$	4.11465	+	2.37559i	0.195714	+	0.112995i
$443$	−34.1219	+	6.01661i	−1.62118	+	0.285858i	−0.909205	−	0.416348i	$-0.863310\pi$
$443$	−34.1219	+	6.01661i	−1.62118	+	0.285858i	−0.711974	+	0.702206i	$0.752199\pi$
$444$	2.98157	−	16.9952i	0.141499	−	0.806558i
$445$		0			0
$446$	1.63494	−	0.595069i	0.0774166	−	0.0281773i
$447$	−30.8772	−	5.41696i	−1.46044	−	0.256213i
$448$	24.9600	−	4.40112i	1.17925	−	0.207933i
$449$	−12.7777	+	22.1315i	−0.603015	+	1.04445i	0.389347	+	0.921091i	$0.372701\pi$
$449$	−12.7777	+	22.1315i	−0.603015	+	1.04445i	−0.992362	+	0.123361i	$0.960633\pi$
$450$		0			0
$451$	−0.670925	−	1.16208i	−0.0315926	−	0.0547201i
$452$	−15.0960	−	17.9908i	−0.710058	−	0.846214i
$453$	12.5348	−	34.5319i	0.588936	−	1.62245i
$454$	−0.799800	+	4.53589i	−0.0375365	+	0.212880i
$455$		0			0
$456$	1.13613	+	1.96391i	0.0532041	+	0.0919684i
$457$	−6.57250	+	18.0578i	−0.307448	+	0.844707i	0.685704	+	0.727881i	$0.259494\pi$
$457$	−6.57250	+	18.0578i	−0.307448	+	0.844707i	−0.993152	+	0.116827i	$0.962728\pi$
$458$		−	0.742248i		−	0.0346830i
$459$	−10.0980	+	17.5955i	−0.471336	+	0.821289i
$460$		0			0
$461$	10.5314	+	3.83312i	0.490497	+	0.178526i	0.575415	−	0.817862i	$-0.304841\pi$
$461$	10.5314	+	3.83312i	0.490497	+	0.178526i	−0.0849181	+	0.996388i	$0.527063\pi$
$462$	−0.00342531	−	3.96218i	−0.000159360	−	0.184337i
$463$	−8.18393	+	9.75323i	−0.380340	+	0.453271i	−0.921921	−	0.387377i	$-0.873381\pi$
$463$	−8.18393	+	9.75323i	−0.380340	+	0.453271i	0.541582	+	0.840648i	$0.317826\pi$
$464$	−0.360029	+	2.04182i	−0.0167139	+	0.0947893i
$465$		0			0
$466$	1.94254	−	1.62998i	0.0899862	−	0.0755074i
$467$	−28.5249	+	16.4688i	−1.31997	+	0.762087i	−0.983724	−	0.179687i	$-0.942492\pi$
$467$	−28.5249	+	16.4688i	−1.31997	+	0.762087i	−0.336249	+	0.941773i	$0.609158\pi$
$468$	−22.8115	+	4.06296i	−1.05446	+	0.187810i
$469$	−16.8029	+	29.1034i	−0.775884	+	1.34387i
$470$		0			0
$471$	−7.27068	−	6.09012i	−0.335015	−	0.280618i
$472$	−5.55940	−	15.2743i	−0.255892	−	0.703058i
$473$	−4.37101	−	12.0093i	−0.200979	−	0.552186i
$474$	−6.31029	+	2.30294i	−0.289841	+	0.105777i
$475$		0			0
$476$	15.9890	−	27.6937i	0.732854	−	1.26934i
$477$	10.3228	−	5.98371i	0.472650	−	0.273975i
$478$	3.97328	−	2.29398i	0.181734	−	0.104924i
$479$	16.9755	−	14.2441i	0.775628	−	0.650829i	−0.166515	−	0.986039i	$-0.553252\pi$
$479$	16.9755	−	14.2441i	0.775628	−	0.650829i	0.942144	+	0.335209i	$0.108807\pi$
$480$		0			0
$481$	3.66438	−	20.7818i	0.167082	−	0.947566i
$482$	0.125858	−	0.149992i	0.00573267	−	0.00683193i
$483$	−55.5249	−	31.9934i	−2.52647	−	1.45575i
$484$	14.0995	+	5.13178i	0.640885	+	0.233263i
$485$		0			0
$486$	0.834354	+	4.61511i	0.0378471	+	0.209346i
$487$		−	15.7072i		−	0.711761i	−0.934531	−	0.355881i	$-0.884181\pi$
$487$		−	15.7072i		−	0.711761i	0.934531	−	0.355881i	$-0.115819\pi$
$488$	−3.41145	+	9.37289i	−0.154429	+	0.424291i
$489$	−15.5538	+	26.9938i	−0.703365	+	1.22070i
$490$		0			0
$491$	−4.61638	+	26.1808i	−0.208334	+	1.18152i	0.683772	+	0.729696i	$0.260338\pi$
$491$	−4.61638	+	26.1808i	−0.208334	+	1.18152i	−0.892106	+	0.451826i	$0.850773\pi$
$492$	−1.61094	−	1.91647i	−0.0726266	−	0.0864012i
$493$	1.50162	+	1.78956i	0.0676296	+	0.0805978i
$494$	0.677634	+	1.17370i	0.0304882	+	0.0528071i
$495$		0			0
$496$	−2.82215	+	4.88811i	−0.126718	+	0.219483i
$497$	−21.8963	+	3.86090i	−0.982182	+	0.173185i
$498$	1.41264	+	3.87077i	0.0633017	+	0.173453i
$499$	−1.98733	+	0.723329i	−0.0889652	+	0.0323807i	−0.386119	−	0.922449i	$-0.626185\pi$
$499$	−1.98733	+	0.723329i	−0.0889652	+	0.0323807i	0.297154	+	0.954830i	$0.403962\pi$
$500$		0			0
$501$	26.4731	+	22.1746i	1.18273	+	0.990689i
$502$	−1.82472	+	0.321747i	−0.0814412	+	0.0143603i
$503$	8.31430	+	4.80026i	0.370716	+	0.214033i	0.673771	−	0.738940i	$-0.264673\pi$
$503$	8.31430	+	4.80026i	0.370716	+	0.214033i	−0.303055	+	0.952973i	$0.598007\pi$
$504$	−2.65402	−	14.9010i	−0.118220	−	0.663743i
$505$		0			0
$506$	3.52388	−	2.95688i	0.156655	−	0.131450i
$507$	−5.73117	+	1.01567i	−0.254530	+	0.0451074i
$508$	−20.7075	−	3.65129i	−0.918748	−	0.162000i
$509$	3.02405	+	2.53748i	0.134039	+	0.112472i	0.707342	−	0.706871i	$-0.249894\pi$
$509$	3.02405	+	2.53748i	0.134039	+	0.112472i	−0.573304	+	0.819343i	$0.694338\pi$
$510$		0			0
$511$	−17.6354	−	6.41876i	−0.780144	−	0.283949i
$512$			19.9150i			0.880128i
$513$	−5.00408	+	2.90644i	−0.220936	+	0.128322i
$514$	−2.10969			−0.0930544
$515$		0			0
$516$	−11.9401	−	20.6397i	−0.525635	−	0.908612i
$517$	13.3870	−	15.9540i	0.588760	−	0.701657i
$518$	6.63042	+	1.16912i	0.291324	+	0.0513683i
$519$	11.0153	+	3.99847i	0.483519	+	0.175513i
$520$		0			0
$521$	12.6619	+	21.9311i	0.554729	+	0.960818i	0.997925	+	0.0643933i	$0.0205112\pi$
$521$	12.6619	+	21.9311i	0.554729	+	0.960818i	−0.443196	+	0.896425i	$0.646155\pi$
$522$	0.532009	+	0.0928594i	0.0232854	+	0.00406434i
$523$	−13.4416	−	7.76052i	−0.587761	−	0.339344i	0.176451	−	0.984309i	$-0.443538\pi$
$523$	−13.4416	−	7.76052i	−0.587761	−	0.339344i	−0.764211	+	0.644966i	$0.776872\pi$
$524$	5.81768	+	32.9937i	0.254146	+	1.44134i
$525$		0			0
$526$	−5.49961	+	2.00169i	−0.239794	+	0.0872780i
$527$	2.17515	+	5.97617i	0.0947509	+	0.260326i
$528$	−10.4788	−	1.83835i	−0.456030	−	0.0800040i
$529$	−8.92553	−	50.6192i	−0.388066	−	2.20083i
$530$		0			0
$531$	38.9338	−	14.2470i	1.68958	−	0.618268i
$532$	7.89959	−	4.56083i	0.342491	−	0.197737i
$533$	−1.96812	−	2.34552i	−0.0852488	−	0.101596i
$534$	−1.59472	−	0.578871i	−0.0690104	−	0.0250502i
$535$		0			0
$536$	−7.05922	−	5.92338i	−0.304912	−	0.255851i
$537$	14.1525	−	8.18727i	0.610725	−	0.353307i
$538$	−1.04810	+	2.87962i	−0.0451866	+	0.124149i
$539$	−20.2056			−0.870317
$540$		0			0
$541$	11.7630			0.505730			0.252865	−	0.967502i	$-0.418627\pi$
$541$	11.7630			0.505730			0.252865	+	0.967502i	$0.418627\pi$
$542$	−0.707008	+	1.94249i	−0.0303686	+	0.0834370i
$543$	−0.00169561	−	1.96138i	−7.27658e−5	−	0.0841709i
$544$	10.1537	+	8.51996i	0.435336	+	0.365290i
$545$		0			0
$546$	−1.57764	−	8.90225i	−0.0675169	−	0.380981i
$547$	11.5917	+	13.8145i	0.495627	+	0.590665i	0.954639	−	0.297765i	$-0.0962411\pi$
$547$	11.5917	+	13.8145i	0.495627	+	0.590665i	−0.459012	+	0.888430i	$0.651797\pi$
$548$	0.589900	−	0.340579i	0.0251993	−	0.0145488i
$549$	−23.9213	−	8.65983i	−1.02094	−	0.369593i
$550$		0			0
$551$	0.115714	+	0.656247i	0.00492958	+	0.0279571i
$552$	11.2836	−	13.4710i	0.480264	−	0.573362i
$553$	18.9113	+	51.9584i	0.804191	+	2.20950i
$554$	7.50989	−	2.73338i	0.319065	−	0.116130i
$555$		0			0
$556$	0.494455	+	2.80419i	0.0209696	+	0.118924i
$557$	−8.58137	−	4.95446i	−0.363604	−	0.209927i	0.307056	−	0.951691i	$-0.400656\pi$
$557$	−8.58137	−	4.95446i	−0.363604	−	0.209927i	−0.670661	+	0.741764i	$0.733989\pi$
$558$	1.27451	+	0.732903i	0.0539543	+	0.0310263i
$559$	−14.5808	−	25.2547i	−0.616701	−	1.06816i
$560$		0			0
$561$	−9.17609	+	7.71319i	−0.387415	+	0.325651i
$562$	−7.08857	−	1.24991i	−0.299013	−	0.0527241i
$563$	−0.748251	+	0.891731i	−0.0315350	+	0.0375820i	−0.781581	−	0.623803i	$-0.785587\pi$
$563$	−0.748251	+	0.891731i	−0.0315350	+	0.0375820i	0.750046	+	0.661385i	$0.230031\pi$
$564$	19.3997	−	33.6684i	0.816874	−	1.41770i
$565$		0			0
$566$	−4.06208			−0.170742
$567$	37.9944	−	6.83500i	1.59562	−	0.287043i
$568$		−	6.09688i		−	0.255820i
$569$	−4.81240	−	1.75157i	−0.201746	−	0.0734296i	0.239171	−	0.970978i	$-0.423124\pi$
$569$	−4.81240	−	1.75157i	−0.201746	−	0.0734296i	−0.440917	+	0.897548i	$0.645347\pi$
$570$		0			0
$571$	−11.3635	−	9.53515i	−0.475550	−	0.399033i	0.373264	−	0.927725i	$-0.378238\pi$
$571$	−11.3635	−	9.53515i	−0.475550	−	0.399033i	−0.848814	+	0.528691i	$0.822683\pi$
$572$	−13.4829	−	2.37739i	−0.563747	−	0.0994038i
$573$	26.3287	+	31.3223i	1.09990	+	1.30851i
$574$	0.748337	−	0.627930i	0.0312350	−	0.0262093i
$575$		0			0
$576$	−17.7264	+	0.0306490i	−0.738599	+	0.00127704i
$577$	27.3347	+	15.7817i	1.13796	+	0.657001i	0.945924	−	0.324387i	$-0.105158\pi$
$577$	27.3347	+	15.7817i	1.13796	+	0.657001i	0.192035	+	0.981388i	$0.438491\pi$
$578$	−0.520449	+	0.0917692i	−0.0216478	+	0.00381710i
$579$	−4.41910	+	1.61275i	−0.183651	+	0.0670235i
$580$		0			0
$581$	31.8716	−	11.6003i	1.32226	−	0.481262i
$582$	0.666452	−	0.795643i	0.0276253	−	0.0329804i
$583$	6.94305	−	1.22425i	0.287552	−	0.0507031i
$584$	2.57311	−	4.45676i	0.106476	−	0.184422i
$585$		0			0
$586$	0.829490	+	1.43672i	0.0342659	+	0.0593503i
$587$	10.9316	+	13.0278i	0.451195	+	0.537713i	0.942912	−	0.333042i	$-0.108075\pi$
$587$	10.9316	+	13.0278i	0.451195	+	0.537713i	−0.491717	+	0.870755i	$0.663631\pi$
$588$	−37.1207	+	6.57848i	−1.53083	+	0.271292i
$589$	−0.315014	+	1.78653i	−0.0129799	+	0.0736129i
$590$		0			0
$591$	−24.7238	+	0.0213738i	−1.01700	+	0.000879199i
$592$	6.18301	−	16.9877i	0.254120	−	0.698190i
$593$		−	42.7865i		−	1.75703i	−0.477712	−	0.878517i	$-0.658534\pi$
$593$		−	42.7865i		−	1.75703i	0.477712	−	0.878517i	$-0.341466\pi$
$594$	−0.474128	+	2.73030i	−0.0194537	+	0.112026i
$595$		0			0
$596$	−32.4759	−	11.8203i	−1.33026	−	0.484177i
$597$	31.8895	−	18.4482i	1.30515	−	0.755034i
$598$	6.74706	−	8.04084i	0.275908	−	0.328814i
$599$	0.336622	−	1.90908i	0.0137540	−	0.0780029i	−0.977158	−	0.212513i	$-0.931835\pi$
$599$	0.336622	−	1.90908i	0.0137540	−	0.0780029i	0.990912	+	0.134511i	$0.0429462\pi$
$600$		0			0
$601$	−15.1011	+	12.6713i	−0.615986	+	0.516874i	−0.896539	−	0.442965i	$-0.853927\pi$
$601$	−15.1011	+	12.6713i	−0.615986	+	0.516874i	0.280553	+	0.959839i	$0.409482\pi$
$602$	8.05750	−	4.65200i	0.328399	−	0.189601i
$603$	15.0769	−	18.0312i	0.613979	−	0.734287i
$604$	20.2499	−	35.0739i	0.823959	−	1.42714i
$605$		0			0
$606$	0.825471	−	4.70526i	0.0335325	−	0.191138i
$607$	3.94987	+	10.8522i	0.160320	+	0.440477i	0.993679	−	0.112255i	$-0.0358075\pi$
$607$	3.94987	+	10.8522i	0.160320	+	0.440477i	−0.833359	+	0.552732i	$0.813585\pi$
$608$	1.29314	+	3.55287i	0.0524436	+	0.144088i
$609$	0.768141	−	4.37848i	0.0311267	−	0.177425i
$610$		0			0
$611$	23.7611	−	41.1554i	0.961271	−	1.66497i
$612$	−14.3466	+	17.1578i	−0.579928	+	0.693563i
$613$	−10.3081	+	5.95138i	−0.416340	+	0.240374i	−0.693510	−	0.720447i	$-0.743937\pi$
$613$	−10.3081	+	5.95138i	−0.416340	+	0.240374i	0.277170	+	0.960821i	$0.410603\pi$
$614$	−1.09870	+	0.921923i	−0.0443401	+	0.0372058i
$615$		0			0
$616$	1.55297	−	8.80733i	0.0625710	−	0.354858i
$617$	−18.6018	+	22.1687i	−0.748879	+	0.892480i	−0.997091	−	0.0762262i	$-0.975713\pi$
$617$	−18.6018	+	22.1687i	−0.748879	+	0.892480i	0.248211	+	0.968706i	$0.420157\pi$
$618$	−0.817745	+	0.473068i	−0.0328945	+	0.0190296i
$619$	−5.52194	−	2.00982i	−0.221946	−	0.0807816i	0.228654	−	0.973508i	$-0.426568\pi$
$619$	−5.52194	−	2.00982i	−0.221946	−	0.0807816i	−0.450600	+	0.892726i	$0.648790\pi$
$620$		0			0
$621$	34.4085	+	28.7204i	1.38076	+	1.15251i
$622$			3.27198i			0.131194i
$623$	−4.77622	+	13.1226i	−0.191355	+	0.525744i
$624$	−24.2758	+	0.0209864i	−0.971809	+	0.000840130i
$625$		0			0
$626$	−0.648770	+	3.67936i	−0.0259301	+	0.147057i
$627$	−3.36688	+	0.596673i	−0.134460	+	0.0238288i
$628$	−6.72093	−	8.00969i	−0.268194	−	0.319621i
$629$	−10.1846	−	17.6403i	−0.406087	−	0.703364i
$630$		0			0
$631$	−10.1424	+	17.5671i	−0.403761	+	0.699335i	−0.994176	−	0.107765i	$-0.965631\pi$
$631$	−10.1424	+	17.5671i	−0.403761	+	0.699335i	0.590415	+	0.807100i	$0.298964\pi$
$632$	−14.9317	+	2.63287i	−0.593953	+	0.104730i
$633$	−22.4045	+	26.7476i	−0.890499	+	1.06312i
$634$	−3.11921	+	1.13530i	−0.123880	+	0.0450885i
$635$		0			0
$636$	12.3568	−	4.50962i	0.489980	−	0.178818i
$637$	−45.4050	+	8.00613i	−1.79901	+	0.317214i
$638$	0.276352	+	0.159552i	0.0109409	+	0.00631671i
$639$	15.5506	−	0.0268870i	0.615171	−	0.00106363i
$640$		0			0
$641$	7.37134	−	6.18529i	0.291151	−	0.244304i	−0.485499	−	0.874237i	$-0.661362\pi$
$641$	7.37134	−	6.18529i	0.291151	−	0.244304i	0.776650	+	0.629933i	$0.216918\pi$
$642$	1.24497	+	1.48110i	0.0491351	+	0.0584542i
$643$	6.43500	+	1.13466i	0.253772	+	0.0447468i	0.299087	−	0.954226i	$-0.403318\pi$
$643$	6.43500	+	1.13466i	0.253772	+	0.0447468i	−0.0453151	+	0.998973i	$0.514429\pi$
$644$	−54.1190	−	45.4113i	−2.13259	−	1.78945i
$645$		0			0
$646$	1.22929	+	0.447425i	0.0483658	+	0.0176037i
$647$		−	4.88147i		−	0.191910i	−0.995386	−	0.0959551i	$-0.969409\pi$
$647$		−	4.88147i		−	0.191910i	0.995386	−	0.0959551i	$-0.0305905\pi$
$648$	0.0366057	+	10.5858i	0.00143801	+	0.415848i
$649$	24.4969			0.961587
$650$		0			0
$651$	6.04183	−	10.4857i	0.236798	−	0.410966i
$652$	−22.0769	+	26.3103i	−0.864600	+	1.03039i
$653$	−6.18430	−	1.09046i	−0.242010	−	0.0426730i	0.0513272	−	0.998682i	$-0.483655\pi$
$653$	−6.18430	−	1.09046i	−0.242010	−	0.0426730i	−0.293338	+	0.956009i	$0.594766\pi$
$654$	1.29298	−	1.08685i	0.0505595	−	0.0424990i
$655$		0			0
$656$	−1.31151	−	2.27161i	−0.0512059	−	0.0886913i
$657$	11.3786	+	6.54326i	0.443923	+	0.255277i
$658$	13.1306	+	7.58098i	0.511886	+	0.295537i
$659$	−1.25353	−	7.10913i	−0.0488307	−	0.276933i	0.950609	−	0.310389i	$-0.100459\pi$
$659$	−1.25353	−	7.10913i	−0.0488307	−	0.276933i	−0.999440	+	0.0334569i	$0.989348\pi$
$660$		0			0
$661$	−41.0593	+	14.9444i	−1.59702	+	0.581268i	−0.978815	−	0.204748i	$-0.934363\pi$
$661$	−41.0593	+	14.9444i	−1.59702	+	0.581268i	−0.618206	+	0.786016i	$0.712140\pi$
$662$	−0.208475	−	0.572781i	−0.00810263	−	0.0222618i
$663$	−17.5638	+	20.9686i	−0.682123	+	0.814351i
$664$	1.61502	+	9.15922i	0.0626748	+	0.355447i
$665$		0			0
$666$	−4.42768	−	1.60288i	−0.171569	−	0.0621103i
$667$	4.46960	−	2.58053i	0.173064	−	0.0999183i
$668$	24.4714	+	29.1639i	0.946828	+	1.12839i
$669$	1.74786	+	9.86275i	0.0675763	+	0.381316i
$670$		0			0
$671$	−11.5153	−	9.66250i	−0.444544	−	0.373017i
$672$	−0.0218046	−	25.2222i	−0.000841130	−	0.972966i
$673$	−12.1373	+	33.3471i	−0.467860	+	1.28543i	0.451589	+	0.892226i	$0.350857\pi$
$673$	−12.1373	+	33.3471i	−0.467860	+	1.28543i	−0.919449	+	0.393209i	$0.871365\pi$
$674$	4.62723			0.178234
$675$		0			0
$676$	−6.41672			−0.246797
$677$	4.90907	−	13.4876i	0.188671	−	0.518369i	−0.808906	−	0.587937i	$-0.799940\pi$
$677$	4.90907	−	13.4876i	0.188671	−	0.518369i	0.997577	+	0.0695687i	$0.0221623\pi$
$678$	−5.54775	+	3.20939i	−0.213060	+	0.123256i
$679$	−6.54445	−	5.49144i	−0.251153	−	0.210742i
$680$		0			0
$681$	−24.9248	−	9.04747i	−0.955119	−	0.346700i
$682$	0.558397	+	0.665472i	0.0213821	+	0.0254822i
$683$	−12.6212	+	7.28683i	−0.482935	+	0.278823i	−0.721639	−	0.692270i	$-0.756611\pi$
$683$	−12.6212	+	7.28683i	−0.482935	+	0.278823i	0.238704	+	0.971092i	$0.423278\pi$
$684$	−5.99119	+	2.19235i	−0.229079	+	0.0838268i
$685$		0			0
$686$	−0.985712	−	5.59025i	−0.0376346	−	0.213437i
$687$	4.20886	+	0.738384i	0.160578	+	0.0281711i
$688$	−8.54437	−	23.4755i	−0.325751	−	0.894994i
$689$	15.1170	−	5.50213i	0.575911	−	0.209614i
$690$		0			0
$691$	−4.75235	−	26.9519i	−0.180788	−	1.02530i	−0.931249	−	0.364384i	$-0.881280\pi$
$691$	−4.75235	−	26.9519i	−0.180788	−	1.02530i	0.750461	−	0.660915i	$-0.229832\pi$
$692$	11.1882	+	6.45952i	0.425312	+	0.245554i
$693$	22.4706	+	3.92213i	0.853588	+	0.148989i
$694$	0.174375	+	0.302026i	0.00661918	+	0.0114648i
$695$		0			0
$696$	1.14582	+	0.415923i	0.0434322	+	0.0157655i
$697$	−2.91058	−	0.513214i	−0.110246	−	0.0194394i
$698$	−0.998618	+	1.19011i	−0.0377983	+	0.0450462i
$699$	7.31025	+	12.6365i	0.276499	+	0.477956i
$700$		0			0
$701$	−30.5667			−1.15449			−0.577243	−	0.816572i	$-0.695872\pi$
$701$	−30.5667			−1.15449			−0.577243	+	0.816572i	$0.695872\pi$
$702$	0.0163994	+	6.32326i	0.000618956	+	0.238656i
$703$		−	5.81029i		−	0.219139i
$704$	−9.84243	−	3.58235i	−0.370951	−	0.135015i
$705$		0			0
$706$	−2.79848	−	2.34821i	−0.105322	−	0.0883759i
$707$	−38.7246	−	6.82820i	−1.45639	−	0.256801i
$708$	45.0045	−	7.97562i	1.69137	−	0.299742i
$709$	−11.3456	+	9.52012i	−0.426094	+	0.357536i	−0.830476	−	0.557055i	$-0.811931\pi$
$709$	−11.3456	+	9.52012i	−0.426094	+	0.357536i	0.404381	+	0.914590i	$0.367487\pi$
$710$		0			0
$711$	−6.78118	−	38.0729i	−0.254314	−	1.42785i
$712$	−3.31629	−	1.91466i	−0.124283	−	0.0717549i
$713$	13.8367	−	2.43979i	0.518190	−	0.0913708i
$714$	−6.69002	−	5.60374i	−0.250368	−	0.209715i
$715$		0			0
$716$	16.9379	−	6.16490i	0.633000	−	0.230393i
$717$	9.05520	+	24.8122i	0.338173	+	0.926629i
$718$	2.63523	−	0.464662i	0.0983460	−	0.0173410i
$719$	2.62426	−	4.54535i	0.0978684	−	0.169513i	−0.812934	−	0.582356i	$-0.802131\pi$
$719$	2.62426	−	4.54535i	0.0978684	−	0.169513i	0.910802	+	0.412843i	$0.135464\pi$
$720$		0			0
$721$	3.88816	+	6.73449i	0.144803	+	0.250805i
$722$	−3.43452	−	4.09310i	−0.127820	−	0.152329i
$723$	0.725312	+	0.862878i	0.0269747	+	0.0320908i
$724$	0.375481	−	2.12946i	0.0139546	−	0.0791407i
$725$		0			0
$726$	2.04429	−	3.54790i	0.0758709	−	0.131675i
$727$	16.2347	−	44.6043i	0.602110	−	1.65428i	−0.144881	−	0.989449i	$-0.546280\pi$
$727$	16.2347	−	44.6043i	0.602110	−	1.65428i	0.746991	−	0.664834i	$-0.231498\pi$
$728$		−	20.4067i		−	0.756324i
$729$	−26.9996	+	0.140048i	−0.999987	+	0.00518698i
$730$		0			0
$731$	−26.4509	−	9.62734i	−0.978322	−	0.356080i
$732$	−24.3013	−	14.0023i	−0.898201	−	0.517542i
$733$	−24.9355	+	29.7170i	−0.921014	+	1.09762i	0.0739377	+	0.997263i	$0.476443\pi$
$733$	−24.9355	+	29.7170i	−0.921014	+	1.09762i	−0.994951	+	0.100358i	$0.968001\pi$
$734$	1.44337	−	8.18574i	0.0532757	−	0.302141i
$735$		0			0
$736$	22.4321	−	18.8227i	0.826857	−	0.693815i
$737$	12.0273	−	6.94396i	0.443031	−	0.255784i
$738$	−0.591109	+	0.342641i	−0.0217590	+	0.0126128i
$739$	−7.71235	+	13.3582i	−0.283704	+	0.491389i	−0.972294	−	0.233762i	$-0.924896\pi$
$739$	−7.71235	+	13.3582i	−0.283704	+	0.491389i	0.688590	+	0.725150i	$0.258230\pi$
$740$		0			0
$741$	−7.32945	+	2.67488i	−0.269254	+	0.0982642i
$742$	1.75546	+	4.82307i	0.0644448	+	0.177061i
$743$	−14.0656	−	38.6448i	−0.516015	−	1.41774i	−0.874875	−	0.484349i	$-0.839057\pi$
$743$	−14.0656	−	38.6448i	−0.516015	−	1.41774i	0.358860	−	0.933391i	$-0.383166\pi$
$744$	2.54394	+	2.13088i	0.0932654	+	0.0781217i
$745$		0			0
$746$	4.64024	−	8.03714i	0.169891	−	0.294260i
$747$	−23.3542	+	4.15962i	−0.854484	+	0.152192i
$748$	−11.4447	+	6.60761i	−0.418460	+	0.241598i
$749$	12.2002	−	10.2372i	0.445787	−	0.374060i
$750$		0			0
$751$	−8.93875	+	50.6942i	−0.326180	+	1.84986i	0.175074	+	0.984555i	$0.443984\pi$
$751$	−8.93875	+	50.6942i	−0.326180	+	1.84986i	−0.501253	+	0.865301i	$0.667128\pi$
$752$	26.1687	−	31.1866i	0.954273	−	1.13726i
$753$	−0.00922162	−	10.6670i	−0.000336055	−	0.388727i
$754$	0.684223	+	0.249037i	0.0249179	+	0.00906939i
$755$		0			0
$756$	42.5588	−	0.110377i	1.54785	−	0.00401436i
$757$			36.7855i			1.33699i	0.743715	+	0.668497i	$0.233062\pi$
$757$			36.7855i			1.33699i	−0.743715	+	0.668497i	$0.766938\pi$
$758$	2.16315	−	5.94321i	0.0785691	−	0.215867i
$759$	13.2612	+	22.9234i	0.481353	+	0.832065i
$760$		0			0
$761$	−4.11655	+	23.3461i	−0.149225	+	0.846295i	0.814653	+	0.579949i	$0.196928\pi$
$761$	−4.11655	+	23.3461i	−0.149225	+	0.846295i	−0.963877	+	0.266346i	$0.914184\pi$
$762$	−1.95796	+	5.39395i	−0.0709293	+	0.195402i
$763$	−8.93697	−	10.6507i	−0.323540	−	0.385580i
$764$	22.5549	+	39.0662i	0.816007	+	1.41337i
$765$		0			0
$766$	3.23803	−	5.60844i	0.116995	−	0.202641i
$767$	55.0482	−	9.70648i	1.98767	−	0.350481i
$768$	−15.7634	−	2.76546i	−0.568812	−	0.0997899i
$769$	−10.3649	+	3.77252i	−0.373768	+	0.136040i	−0.522072	−	0.852901i	$-0.674841\pi$
$769$	−10.3649	+	3.77252i	−0.373768	+	0.136040i	0.148304	+	0.988942i	$0.452619\pi$
$770$		0			0
$771$	2.09871	−	11.9628i	0.0755830	−	0.430830i
$772$	−5.10730	+	0.900555i	−0.183816	+	0.0324117i
$773$	38.3301	+	22.1299i	1.37864	+	0.795958i	0.991996	−	0.126272i	$-0.0403011\pi$
$773$	38.3301	+	22.1299i	1.37864	+	0.795958i	0.386644	+	0.922229i	$0.373634\pi$
$774$	−6.11096	+	2.23618i	−0.219654	+	0.0803778i
$775$		0			0
$776$	1.79458	−	1.50583i	0.0644216	−	0.0540561i
$777$	−13.2253	+	36.4342i	−0.474455	+	1.30707i
$778$	−3.97402	−	0.700727i	−0.142475	−	0.0251223i
$779$	−0.645811	−	0.541900i	−0.0231386	−	0.0194156i
$780$		0			0
$781$	8.63433	+	3.14264i	0.308960	+	0.112452i
$782$		−	10.1319i		−	0.362316i
$783$	−1.05579	+	2.92434i	−0.0377309	+	0.104507i
$784$	−39.4976			−1.41063
$785$		0			0
$786$	9.14296	−	0.00790409i	0.326119	−	0.000281930i
$787$	26.4467	−	31.5179i	0.942722	−	1.12349i	−0.0494704	−	0.998776i	$-0.515753\pi$
$787$	26.4467	−	31.5179i	0.942722	−	1.12349i	0.992192	−	0.124717i	$-0.0398022\pi$
$788$	−26.8425	−	4.73305i	−0.956224	−	0.168608i
$789$	−5.87946	−	33.1763i	−0.209314	−	1.18111i
$790$		0			0
$791$	26.3781	+	45.6882i	0.937896	+	1.62448i
$792$	−2.12914	+	5.88138i	−0.0756556	+	0.208986i
$793$	−29.7053	−	17.1503i	−1.05486	−	0.609026i
$794$	0.888454	+	5.03867i	0.0315301	+	0.178816i
$795$		0			0
$796$	38.1659	−	13.8912i	1.35275	−	0.492362i
$797$	−7.99243	−	21.9590i	−0.283106	−	0.777828i	−0.996988	−	0.0775615i	$-0.975287\pi$
$797$	−7.99243	−	21.9590i	−0.283106	−	0.777828i	0.713881	−	0.700267i	$-0.246936\pi$
$798$	−0.853421	−	2.33846i	−0.0302108	−	0.0827807i
$799$	−7.96546	−	45.1743i	−0.281798	−	1.59815i
$800$		0			0
$801$	4.86886	−	8.46689i	0.172033	−	0.299163i
$802$	1.62577	−	0.938639i	0.0574080	−	0.0331445i
$803$	4.98529	+	5.94124i	0.175927	+	0.209662i
$804$	19.8351	−	16.6729i	0.699531	−	0.588008i
$805$		0			0
$806$	1.51848	+	1.27416i	0.0534863	+	0.0448803i
$807$	−15.2860	−	8.80777i	−0.538093	−	0.310048i
$808$	3.68788	−	10.1324i	0.129739	−	0.356455i
$809$	16.4420			0.578070			0.289035	−	0.957319i	$-0.406666\pi$
$809$	16.4420			0.578070			0.289035	+	0.957319i	$0.406666\pi$
$810$		0			0
$811$	49.2346			1.72886			0.864430	−	0.502753i	$-0.167679\pi$
$811$	49.2346			1.72886			0.864430	+	0.502753i	$0.167679\pi$
$812$	1.67615	−	4.60518i	0.0588213	−	0.161610i
$813$	−10.3114	−	5.94140i	−0.361636	−	0.208374i
$814$	−2.13141	−	1.78847i	−0.0747059	−	0.0626857i
$815$		0			0
$816$	−17.9373	+	15.0776i	−0.627930	+	0.527821i
$817$	−5.16113	−	6.15080i	−0.180565	−	0.215189i
$818$	−2.50136	+	1.44416i	−0.0874582	+	0.0504940i
$819$	52.0489	−	0.0899927i	1.81874	−	0.00314460i
$820$		0			0
$821$	−0.479682	−	2.72041i	−0.0167410	−	0.0949431i	0.975292	−	0.220918i	$-0.0709053\pi$
$821$	−0.479682	−	2.72041i	−0.0167410	−	0.0949431i	−0.992033	+	0.125975i	$0.959794\pi$
$822$	−0.0637290	−	0.174624i	−0.00222280	−	0.00609071i
$823$	−11.2842	−	31.0031i	−0.393343	−	1.08070i	−0.965465	−	0.260533i	$-0.916102\pi$
$823$	−11.2842	−	31.0031i	−0.393343	−	1.08070i	0.572122	−	0.820169i	$-0.306120\pi$
$824$	−2.00377	+	0.729314i	−0.0698048	+	0.0254069i
$825$		0			0
$826$	3.09685	+	17.5631i	0.107753	+	0.611099i
$827$	47.4431	+	27.3913i	1.64976	+	0.952489i	0.977166	+	0.212475i	$0.0681525\pi$
$827$	47.4431	+	27.3913i	1.64976	+	0.952489i	0.672592	+	0.740013i	$0.265181\pi$
$828$	31.8262	+	37.7961i	1.10604	+	1.31350i
$829$	25.5346	+	44.2272i	0.886852	+	1.53607i	0.843576	+	0.537010i	$0.180446\pi$
$829$	25.5346	+	44.2272i	0.886852	+	1.53607i	0.0432768	+	0.999063i	$0.486220\pi$
$830$		0			0
$831$	8.02860	+	45.3034i	0.278509	+	1.57156i
$832$	−23.5369	−	4.15018i	−0.815994	−	0.143882i
$833$	−28.6064	+	34.0918i	−0.991154	+	1.18121i
$834$	0.777077		0.000671783i	0.0269080		2.32620e-5i
$835$		0			0
$836$	−3.76962			−0.130375
$837$	−5.42374	+	6.49791i	−0.187472	+	0.224601i
$838$		−	4.51449i		−	0.155950i
$839$	−38.7316	−	14.0971i	−1.33716	−	0.486688i	−0.428245	−	0.903663i	$-0.640868\pi$
$839$	−38.7316	−	14.0971i	−1.33716	−	0.486688i	−0.908918	+	0.416975i	$0.863090\pi$
$840$		0			0
$841$	−21.9410	−	18.4107i	−0.756587	−	0.634852i
$842$	10.9742	+	1.93505i	0.378196	+	0.0666862i
$843$	14.1392	−	38.9518i	0.486979	−	1.34157i
$844$	−29.4663	+	24.7251i	−1.01427	+	0.851074i
$845$		0			0
$846$	−8.13516	−	6.80228i	−0.279693	−	0.233867i
$847$	−29.1894	−	16.8525i	−1.00296	−	0.579059i
$848$	13.5721	−	2.39313i	0.466069	−	0.0821806i
$849$	4.04094	−	23.0337i	0.138685	−	0.790515i
$850$		0			0
$851$	−42.2869	+	15.3912i	−1.44958	+	0.527602i
$852$	16.8857	+	2.96236i	0.578495	+	0.101489i
$853$	20.3286	−	3.58449i	0.696039	−	0.122730i	0.185576	−	0.982630i	$-0.440585\pi$
$853$	20.3286	−	3.58449i	0.696039	−	0.122730i	0.510463	+	0.859900i	$0.329474\pi$
$854$	5.47182	−	9.47746i	0.187242	−	0.324312i
$855$		0			0
$856$	2.18360	+	3.78211i	0.0746339	+	0.129270i
$857$	23.7446	+	28.2977i	0.811099	+	0.966630i	0.999882	−	0.0153887i	$-0.00489858\pi$
$857$	23.7446	+	28.2977i	0.811099	+	0.966630i	−0.188783	+	0.982019i	$0.560454\pi$
$858$	−1.27484	+	3.51205i	−0.0435225	+	0.119899i
$859$	−4.11514	+	23.3381i	−0.140407	+	0.796286i	0.830535	+	0.556967i	$0.188035\pi$
$859$	−4.11514	+	23.3381i	−0.140407	+	0.796286i	−0.970941	+	0.239318i	$0.923076\pi$
$860$		0			0
$861$	2.81618	+	4.86805i	0.0959752	+	0.165903i
$862$	−1.47482	+	4.05205i	−0.0502327	+	0.138013i
$863$		−	36.6147i		−	1.24638i	−0.782072	−	0.623189i	$-0.785837\pi$
$863$		−	36.6147i		−	1.24638i	0.782072	−	0.623189i	$-0.214163\pi$
$864$	−3.01817	+	17.3804i	−0.102680	+	0.591292i
$865$		0			0
$866$	−4.09000	−	1.48864i	−0.138984	−	0.0505859i
$867$	−0.00263020	−	3.04245i	−8.93264e−5	−	0.103327i
$868$	8.57576	−	10.2202i	0.291080	−	0.346896i
$869$	3.96793	−	22.5032i	0.134603	−	0.763370i
$870$		0			0
$871$	24.2757	−	20.3697i	0.822550	−	0.690202i
$872$	3.30174	−	1.90626i	0.111811	−	0.0645541i
$873$	3.84864	+	4.57056i	0.130257	+	0.154690i
$874$	1.44505	−	2.50291i	0.0488797	−	0.0846621i
$875$		0			0
$876$	11.0931	+	9.29185i	0.374800	+	0.313943i
$877$	−8.28105	−	22.7520i	−0.279631	−	0.768280i	−0.997404	−	0.0720034i	$-0.977061\pi$
$877$	−8.28105	−	22.7520i	−0.279631	−	0.768280i	0.717773	−	0.696277i	$-0.245161\pi$
$878$	−1.53852	−	4.22704i	−0.0519224	−	0.142656i
$879$	−8.97197	+	3.27432i	−0.302617	+	0.110440i
$880$		0			0
$881$	−13.4734	+	23.3367i	−0.453931	+	0.786232i	−0.998626	−	0.0524023i	$-0.983312\pi$
$881$	−13.4734	+	23.3367i	−0.453931	+	0.786232i	0.544695	+	0.838634i	$0.316646\pi$
$882$	0.0177883	+	10.2882i	0.000598963	+	0.346421i
$883$	−0.856656	+	0.494590i	−0.0288288	+	0.0166443i	−0.514345	−	0.857583i	$-0.671965\pi$
$883$	−0.856656	+	0.494590i	−0.0288288	+	0.0166443i	0.485516	+	0.874228i	$0.338632\pi$
$884$	−23.0998	+	19.3831i	−0.776932	+	0.651923i
$885$		0			0
$886$	−1.81015	+	10.2659i	−0.0608132	+	0.344889i
$887$	−15.9532	+	19.0122i	−0.535655	+	0.638368i	−0.964208	−	0.265148i	$-0.914579\pi$
$887$	−15.9532	+	19.0122i	−0.535655	+	0.638368i	0.428553	+	0.903517i	$0.359024\pi$
$888$	−9.20923	−	5.30634i	−0.309042	−	0.178069i
$889$	44.3854	+	16.1550i	1.48864	+	0.541820i
$890$		0			0
$891$	−15.0103	−	5.40459i	−0.502864	−	0.181061i
$892$			11.0425i			0.369731i
$893$	4.47523	−	12.2956i	0.149758	−	0.411456i
$894$	−4.70871	+	8.17203i	−0.157483	+	0.273314i
$895$		0			0
$896$	6.38146	−	36.1910i	0.213190	−	1.20906i
$897$	38.8830	+	46.2577i	1.29826	+	1.54450i
$898$	4.94210	+	5.88977i	0.164920	+	0.196544i
$899$	0.487323	+	0.844068i	0.0162531	+	0.0281512i
$900$		0			0
$901$	7.76414	−	13.4479i	0.258661	−	0.448014i
$902$	−0.397575	+	0.0701031i	−0.0132378	+	0.00233418i
$903$	18.3632	+	50.3172i	0.611090	+	1.67445i
$904$	−13.5940	+	4.94782i	−0.452130	+	0.164562i
$905$		0			0
$906$	−8.47287	−	7.09711i	−0.281492	−	0.235786i
$907$	−3.22968	+	0.569479i	−0.107240	+	0.0189092i	−0.227010	−	0.973892i	$-0.572895\pi$
$907$	−3.22968	+	0.569479i	−0.107240	+	0.0189092i	0.119771	+	0.992802i	$0.461784\pi$
$908$	−25.3160	−	14.6162i	−0.840140	−	0.485055i
$909$	25.8596	+	9.36153i	0.857710	+	0.310502i
$910$		0			0
$911$	−30.1923	+	25.3344i	−1.00032	+	0.839365i	−0.987028	−	0.160546i	$-0.948674\pi$
$911$	−30.1923	+	25.3344i	−1.00032	+	0.839365i	−0.0132884	+	0.999912i	$0.504230\pi$
$912$	−6.58151	+	1.16637i	−0.217936	+	0.0386222i
$913$	−13.8036	−	2.43395i	−0.456833	−	0.0805521i
$914$	4.42890	+	3.71629i	0.146495	+	0.122924i
$915$		0			0
$916$	4.42678	+	1.61122i	0.146265	+	0.0532361i
$917$		−	75.2587i		−	2.48526i
$918$	3.93543	+	4.66544i	0.129889	+	0.153983i
$919$	9.02247			0.297624			0.148812	−	0.988866i	$-0.452455\pi$
$919$	9.02247			0.297624			0.148812	+	0.988866i	$0.452455\pi$
$920$		0			0
$921$	−4.13470	−	7.14724i	−0.136243	−	0.235509i
$922$	2.16736	−	2.58296i	0.0713782	−	0.0850653i
$923$	20.6478	+	3.64077i	0.679632	+	0.119837i
$924$	23.6379	+	8.58037i	0.777631	+	0.282273i
$925$		0			0
$926$	1.91526	+	3.31733i	0.0629393	+	0.109014i
$927$	−1.86901	−	5.10756i	−0.0613862	−	0.167754i
$928$	1.75918	+	1.01566i	0.0577480	+	0.0333408i
$929$	4.32579	+	24.5328i	0.141925	+	0.804894i	0.969785	+	0.243960i	$0.0784467\pi$
$929$	4.32579	+	24.5328i	0.141925	+	0.804894i	−0.827861	+	0.560934i	$0.810442\pi$
$930$		0			0
$931$	−11.9290	+	4.34181i	−0.390958	+	0.142297i
$932$	5.50452	+	15.1235i	0.180307	+	0.495388i
$933$	−18.5535	−	3.25495i	−0.607414	−	0.106562i
$934$	1.72078	+	9.75904i	0.0563057	+	0.319326i
$935$		0			0
$936$	−2.45409	+	14.0600i	−0.0802146	+	0.459565i
$937$	−21.9995	+	12.7014i	−0.718694	+	0.414938i	−0.814272	−	0.580484i	$-0.802863\pi$
$937$	−21.9995	+	12.7014i	−0.718694	+	0.414938i	0.0955779	+	0.995422i	$0.469530\pi$
$938$	6.49896	+	7.74516i	0.212199	+	0.252888i
$939$	−20.2181	−	7.33900i	−0.659793	−	0.239499i
$940$		0			0
$941$	18.5701	+	15.5822i	0.605368	+	0.507964i	0.893166	−	0.449727i	$-0.148479\pi$
$941$	18.5701	+	15.5822i	0.605368	+	0.507964i	−0.287798	+	0.957691i	$0.592923\pi$
$942$	−2.46992	+	1.42886i	−0.0804744	+	0.0465547i
$943$	−2.23319	+	6.13563i	−0.0727226	+	0.199804i
$944$	47.8861			1.55856
$945$		0			0
$946$	−3.84497			−0.125011
$947$	3.73369	−	10.2582i	0.121329	−	0.333348i	−0.864129	−	0.503271i	$-0.832130\pi$
$947$	3.73369	−	10.2582i	0.121329	−	0.333348i	0.985457	+	0.169923i	$0.0543519\pi$
$948$	−0.0368569	−	42.6337i	−0.00119706	−	1.38468i
$949$	13.5568	+	11.3755i	0.440073	+	0.369265i
$950$		0			0
$951$	−3.33465	−	18.8166i	−0.108134	−	0.610171i
$952$	−12.6615	−	15.0894i	−0.410361	−	0.489050i
$953$	12.6210	−	7.28673i	0.408834	−	0.236040i	−0.281455	−	0.959575i	$-0.590817\pi$
$953$	12.6210	−	7.28673i	0.408834	−	0.236040i	0.690289	+	0.723534i	$0.257484\pi$
$954$	−0.629467	−	3.53414i	−0.0203798	−	0.114422i
$955$		0			0
$956$	5.05641	+	28.6763i	0.163536	+	0.927458i
$957$	−1.17964	+	1.40831i	−0.0381323	+	0.0455242i
$958$	−2.28025	−	6.26493i	−0.0736715	−	0.202411i
$959$	−1.43784	+	0.523331i	−0.0464303	+	0.0168992i
$960$		0			0
$961$	−4.92235	−	27.9160i	−0.158785	−	0.900517i
$962$	−5.49825	−	3.17442i	−0.177271	−	0.102347i
$963$	−9.63692	+	5.58612i	−0.310545	+	0.180010i
$964$	0.621349	+	1.07621i	0.0200123	+	0.0346623i
$965$		0			0
$966$	−14.7585	+	12.4056i	−0.474847	+	0.399144i
$967$	−47.1914	−	8.32112i	−1.51757	−	0.267589i	−0.648095	−	0.761560i	$-0.724434\pi$
$967$	−47.1914	−	8.32112i	−1.51757	−	0.267589i	−0.869478	+	0.493971i	$0.835545\pi$
$968$	5.94088	−	7.08006i	0.190947	−	0.227562i
$969$	−3.75998	+	6.52550i	−0.120788	+	0.209629i
$970$		0			0
$971$	10.0839			0.323608			0.161804	−	0.986823i	$-0.448269\pi$
$971$	10.0839			0.323608			0.161804	+	0.986823i	$0.448269\pi$
$972$	−29.3358	−	5.04204i	−0.940945	−	0.161723i
$973$		−	6.39638i		−	0.205058i
$974$	−4.44066	−	1.61627i	−0.142288	−	0.0517886i
$975$		0			0
$976$	−22.5099	−	18.8881i	−0.720526	−	0.604593i
$977$	31.7363	+	5.59597i	1.01534	+	0.179031i	0.656465	−	0.754356i	$-0.272051\pi$
$977$	31.7363	+	5.59597i	1.01534	+	0.179031i	0.358870	+	0.933387i	$0.383162\pi$
$978$	6.03106	+	7.17493i	0.192852	+	0.229429i
$979$	4.42090	−	3.70957i	0.141293	−	0.118558i
$980$		0			0
$981$	4.87662	+	8.41293i	0.155698	+	0.268604i
$982$	6.92667	+	3.99912i	0.221039	+	0.127617i
$983$	2.49182	−	0.439376i	0.0794768	−	0.0140139i	−0.133768	−	0.991013i	$-0.542708\pi$
$983$	2.49182	−	0.439376i	0.0794768	−	0.0140139i	0.213245	+	0.976999i	$0.431597\pi$
$984$	−1.44870	+	0.528703i	−0.0461829	+	0.0168544i
$985$		0			0
$986$	0.660453	−	0.240385i	0.0210331	−	0.00765542i
$987$	−56.0496	+	66.9147i	−1.78408	+	2.12992i
$988$	−8.47090	+	1.49365i	−0.269495	+	0.0475193i
$989$	−31.0935	+	53.8556i	−0.988716	+	1.71251i
$990$		0			0
$991$	25.3489	+	43.9056i	0.805234	+	1.39471i	0.916133	+	0.400875i	$0.131294\pi$
$991$	25.3489	+	43.9056i	0.805234	+	1.39471i	−0.110899	+	0.993832i	$0.535373\pi$
$992$	3.55461	+	4.23621i	0.112859	+	0.134500i
$993$	3.45530	−	0.612343i	0.109651	−	0.0194321i
$994$	−1.16159	+	6.58769i	−0.0368433	+	0.208949i
$995$		0			0
$996$	−26.1518	+	0.0226082i	−0.828650	+	0.000716369i
$997$	4.77883	−	13.1297i	0.151347	−	0.415822i	−0.840730	−	0.541455i	$-0.817874\pi$
$997$	4.77883	−	13.1297i	0.151347	−	0.415822i	0.992077	+	0.125632i	$0.0400960\pi$
$998$			0.636279i			0.0201411i
$999$	13.4936	−	23.5122i	0.426919	−	0.743894i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.c.274.6		60
5.2	odd	4		675.2.l.d.301.3		30
5.3	odd	4		135.2.k.a.31.3	✓	30
5.4	even	2	inner	675.2.u.c.274.5		60
15.8	even	4		405.2.k.a.226.3		30
27.7	even	9	inner	675.2.u.c.574.5		60
135.7	odd	36		675.2.l.d.601.3		30
135.13	odd	36		3645.2.a.h.1.9		15
135.34	even	18	inner	675.2.u.c.574.6		60
135.68	even	36		3645.2.a.g.1.7		15
135.88	odd	36		135.2.k.a.61.3	yes	30
135.128	even	36		405.2.k.a.181.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.a.31.3	✓	30	5.3	odd	4
135.2.k.a.61.3	yes	30	135.88	odd	36
405.2.k.a.181.3		30	135.128	even	36
405.2.k.a.226.3		30	15.8	even	4
675.2.l.d.301.3		30	5.2	odd	4
675.2.l.d.601.3		30	135.7	odd	36
675.2.u.c.274.5		60	5.4	even	2	inner
675.2.u.c.274.6		60	1.1	even	1	trivial
675.2.u.c.574.5		60	27.7	even	9	inner
675.2.u.c.574.6		60	135.34	even	18	inner
3645.2.a.g.1.7		15	135.68	even	36
3645.2.a.h.1.9		15	135.13	odd	36

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.102900 - 0.282715i) q^{2} +(1.50075 + 0.864728i) q^{3} +(1.46275 + 1.22739i) q^{4} +(0.398898 - 0.335304i) q^{6} +(-2.75715 - 3.28585i) q^{7} +(1.01862 - 0.588102i) q^{8} +(1.50449 + 2.59548i) q^{9} +O(q^{10})\)	\(q+(0.102900 - 0.282715i) q^{2} +(1.50075 + 0.864728i) q^{3} +(1.46275 + 1.22739i) q^{4} +(0.398898 - 0.335304i) q^{6} +(-2.75715 - 3.28585i) q^{7} +(1.01862 - 0.588102i) q^{8} +(1.50449 + 2.59548i) q^{9} +(0.307813 + 1.74570i) q^{11} +(1.13386 + 3.10689i) q^{12} +(1.38340 + 3.80087i) q^{13} +(-1.21267 + 0.441375i) q^{14} +(0.601708 + 3.41245i) q^{16} +(3.38121 + 1.95214i) q^{17} +(0.888593 - 0.158267i) q^{18} +(0.556845 + 0.964484i) q^{19} +(-1.29643 - 7.31542i) q^{21} +(0.525208 + 0.0926084i) q^{22} +(5.54440 - 6.60755i) q^{23} +(2.03724 - 0.00176120i) q^{24} +1.21692 q^{26} +(0.0134762 + 5.19613i) q^{27} -8.19048i q^{28} +(0.562260 + 0.204646i) q^{29} +(1.24781 + 1.04704i) q^{31} +(3.34334 + 0.589520i) q^{32} +(-1.04760 + 2.88602i) q^{33} +(0.899826 - 0.755043i) q^{34} +(-0.984980 + 5.64313i) q^{36} +(-4.51818 - 2.60857i) q^{37} +(0.329973 - 0.0581832i) q^{38} +(-1.21058 + 6.90042i) q^{39} +(-0.711333 + 0.258904i) q^{41} +(-2.20158 - 0.386236i) q^{42} +(-7.10010 + 1.25194i) q^{43} +(-1.69240 + 2.93132i) q^{44} +(-1.29754 - 2.24740i) q^{46} +(-7.55208 - 9.00022i) q^{47} +(-2.04783 + 5.64155i) q^{48} +(-1.97936 + 11.2255i) q^{49} +(3.38627 + 5.85350i) q^{51} +(-2.64159 + 7.25771i) q^{52} -3.97724i q^{53} +(1.47041 + 0.530872i) q^{54} +(-4.74091 - 1.72555i) q^{56} +(0.00166759 + 1.92897i) q^{57} +(0.115713 - 0.137901i) q^{58} +(2.39974 - 13.6096i) q^{59} +(-6.49619 + 5.45095i) q^{61} +(0.424413 - 0.245035i) q^{62} +(4.38024 - 12.0997i) q^{63} +(-2.95440 + 5.11717i) q^{64} +(0.708124 + 0.593144i) q^{66} +(-2.67961 - 7.36217i) q^{67} +(2.54982 + 7.00557i) q^{68} +(14.0345 - 5.12188i) q^{69} +(2.59176 - 4.48907i) q^{71} +(3.05891 + 1.75902i) q^{72} +(3.78911 - 2.18764i) q^{73} +(-1.20240 + 1.00894i) q^{74} +(-0.369276 + 2.09427i) q^{76} +(4.88740 - 5.82458i) q^{77} +(1.82628 + 1.05230i) q^{78} +(-12.1133 - 4.40888i) q^{79} +(-4.47302 + 7.80974i) q^{81} +0.227746i q^{82} +(-2.70443 + 7.43037i) q^{83} +(7.08254 - 12.2918i) q^{84} +(-0.376657 + 2.13613i) q^{86} +(0.666848 + 0.793324i) q^{87} +(1.34019 + 1.59718i) q^{88} +(-1.62783 - 2.81949i) q^{89} +(8.67483 - 15.0252i) q^{91} +(16.2201 - 2.86005i) q^{92} +(0.967248 + 2.65036i) q^{93} +(-3.32160 + 1.20896i) q^{94} +(4.50773 + 3.77580i) q^{96} +(1.96145 - 0.345856i) q^{97} +(2.96995 + 1.71470i) q^{98} +(-4.06782 + 3.42530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^9	\( 60 q + 6 q^{9} - 12 q^{11} + 18 q^{14} + 24 q^{16} - 48 q^{19} - 72 q^{21} - 90 q^{24} - 36 q^{26} - 36 q^{29} + 24 q^{31} + 138 q^{34} - 84 q^{36} - 12 q^{39} - 150 q^{41} - 24 q^{44} + 60 q^{46} + 72 q^{49} + 42 q^{51} - 36 q^{54} + 60 q^{56} + 54 q^{59} - 24 q^{61} - 54 q^{64} + 156 q^{66} + 234 q^{69} + 24 q^{71} - 60 q^{76} - 108 q^{79} - 54 q^{81} - 90 q^{84} + 36 q^{86} - 18 q^{89} + 102 q^{91} - 30 q^{94} - 30 q^{96} - 246 q^{99}+O(q^{100}) \) 60 * q + 6 * q^9 - 12 * q^11 + 18 * q^14 + 24 * q^16 - 48 * q^19 - 72 * q^21 - 90 * q^24 - 36 * q^26 - 36 * q^29 + 24 * q^31 + 138 * q^34 - 84 * q^36 - 12 * q^39 - 150 * q^41 - 24 * q^44 + 60 * q^46 + 72 * q^49 + 42 * q^51 - 36 * q^54 + 60 * q^56 + 54 * q^59 - 24 * q^61 - 54 * q^64 + 156 * q^66 + 234 * q^69 + 24 * q^71 - 60 * q^76 - 108 * q^79 - 54 * q^81 - 90 * q^84 + 36 * q^86 - 18 * q^89 + 102 * q^91 - 30 * q^94 - 30 * q^96 - 246 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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