LMFDB - Embedded newform 945.2.cc.b.82.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(82,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("945.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cc (of order $12$, degree $4$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.5
Character	$\chi$	$=$	945.82
Dual form			945.2.cc.b.703.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30162 + 0.616717i) q^{2} +(3.18506 - 1.83889i) q^{4} +(-2.21935 - 0.272932i) q^{5} +(1.10114 - 2.40572i) q^{7} +(-2.82691 + 2.82691i) q^{8} +O(q^{10})$	\(q+(-2.30162 + 0.616717i) q^{2} +(3.18506 - 1.83889i) q^{4} +(-2.21935 - 0.272932i) q^{5} +(1.10114 - 2.40572i) q^{7} +(-2.82691 + 2.82691i) q^{8} +(5.27642 - 0.740523i) q^{10} +(0.674840 + 1.16886i) q^{11} +(-0.170165 - 0.170165i) q^{13} +(-1.05075 + 6.21614i) q^{14} +(1.08527 - 1.87974i) q^{16} +(5.52917 + 1.48154i) q^{17} +(-2.23890 + 3.87789i) q^{19} +(-7.57064 + 3.21184i) q^{20} +(-2.27408 - 2.27408i) q^{22} +(-1.83056 - 6.83174i) q^{23} +(4.85102 + 1.21146i) q^{25} +(0.496598 + 0.286711i) q^{26} +(-0.916677 - 9.68723i) q^{28} +5.48973i q^{29} +(-0.0965807 + 0.0557609i) q^{31} +(0.730829 - 2.72749i) q^{32} -13.6397 q^{34} +(-3.10041 + 5.03860i) q^{35} +(-0.745840 + 0.199847i) q^{37} +(2.76153 - 10.3062i) q^{38} +(7.04544 - 5.50233i) q^{40} -10.3867i q^{41} +(3.12017 - 3.12017i) q^{43} +(4.29881 + 2.48192i) q^{44} +(8.42650 + 14.5951i) q^{46} +(-0.370937 - 1.38436i) q^{47} +(-4.57499 - 5.29806i) q^{49} +(-11.9123 + 0.203374i) q^{50} +(-0.854900 - 0.229070i) q^{52} +(-4.64236 - 1.24392i) q^{53} +(-1.17869 - 2.77829i) q^{55} +(3.68793 + 9.91356i) q^{56} +(-3.38561 - 12.6353i) q^{58} +(3.76242 + 6.51670i) q^{59} +(3.71727 + 2.14617i) q^{61} +(0.187903 - 0.187903i) q^{62} +11.0694i q^{64} +(0.331212 + 0.424099i) q^{65} +(3.88993 - 14.5174i) q^{67} +(20.3351 - 5.44877i) q^{68} +(4.02857 - 13.5090i) q^{70} -2.69063 q^{71} +(-2.11608 + 7.89733i) q^{73} +(1.59339 - 0.919945i) q^{74} +16.4684i q^{76} +(3.55504 - 0.336404i) q^{77} +(-9.42775 - 5.44311i) q^{79} +(-2.92164 + 3.87560i) q^{80} +(6.40567 + 23.9063i) q^{82} +(-5.01986 - 5.01986i) q^{83} +(-11.8668 - 4.79713i) q^{85} +(-5.25717 + 9.10569i) q^{86} +(-5.21196 - 1.39654i) q^{88} +(8.82970 - 15.2935i) q^{89} +(-0.596744 + 0.221994i) q^{91} +(-18.3933 - 18.3933i) q^{92} +(1.70751 + 2.95750i) q^{94} +(6.02730 - 7.99532i) q^{95} +(11.0460 - 11.0460i) q^{97} +(13.7973 + 9.37265i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{7}+O(q^{10}) $ 128 * q + 4 * q^7	$ 128 q + 4 q^{7} - 12 q^{10} + 64 q^{16} + 40 q^{22} - 16 q^{25} + 52 q^{28} + 16 q^{37} - 60 q^{40} - 32 q^{43} - 24 q^{58} + 48 q^{61} - 32 q^{67} + 40 q^{70} + 156 q^{82} - 8 q^{85} + 84 q^{88} + 96 q^{91}+O(q^{100}) $ 128 * q + 4 * q^7 - 12 * q^10 + 64 * q^16 + 40 * q^22 - 16 * q^25 + 52 * q^28 + 16 * q^37 - 60 * q^40 - 32 * q^43 - 24 * q^58 + 48 * q^61 - 32 * q^67 + 40 * q^70 + 156 * q^82 - 8 * q^85 + 84 * q^88 + 96 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−2.30162	+	0.616717i	−1.62749	+	0.436085i	−0.953190	−	0.302373i	$-0.902221\pi$
$2$	−2.30162	+	0.616717i	−1.62749	+	0.436085i	−0.674300	+	0.738457i	$0.735555\pi$
$3$		0			0
$3$		0			0
$4$	3.18506	−	1.83889i	1.59253	−	0.919447i
$5$	−2.21935	−	0.272932i	−0.992523	−	0.122059i
$5$	−2.21935	−	0.272932i	−0.992523	−	0.122059i
$6$		0			0
$7$	1.10114	−	2.40572i	0.416191	−	0.909277i
$7$	1.10114	−	2.40572i	0.416191	−	0.909277i
$8$	−2.82691	+	2.82691i	−0.999462	+	0.999462i
$9$		0			0
$10$	5.27642	−	0.740523i	1.66855	−	0.234174i
$11$	0.674840	+	1.16886i	0.203472	+	0.352424i	0.949645	−	0.313328i	$-0.101444\pi$
$11$	0.674840	+	1.16886i	0.203472	+	0.352424i	−0.746173	+	0.665752i	$0.768111\pi$
$12$		0			0
$13$	−0.170165	−	0.170165i	−0.0471952	−	0.0471952i	0.683115	−	0.730311i	$-0.260625\pi$
$13$	−0.170165	−	0.170165i	−0.0471952	−	0.0471952i	−0.730311	+	0.683115i	$0.760625\pi$
$14$	−1.05075	+	6.21614i	−0.280825	+	1.66133i
$15$		0			0
$16$	1.08527	−	1.87974i	0.271318	−	0.469936i
$17$	5.52917	+	1.48154i	1.34102	+	0.359325i	0.856813	−	0.515628i	$-0.172441\pi$
$17$	5.52917	+	1.48154i	1.34102	+	0.359325i	0.484208	+	0.874953i	$0.339108\pi$
$18$		0			0
$19$	−2.23890	+	3.87789i	−0.513639	+	0.889649i	0.486236	+	0.873828i	$0.338370\pi$
$19$	−2.23890	+	3.87789i	−0.513639	+	0.889649i	−0.999875	+	0.0158211i	$0.994964\pi$
$20$	−7.57064	+	3.21184i	−1.69285	+	0.718189i
$21$		0			0
$22$	−2.27408	−	2.27408i	−0.484835	−	0.484835i
$23$	−1.83056	−	6.83174i	−0.381698	−	1.42452i	−0.843307	−	0.537433i	$-0.819394\pi$
$23$	−1.83056	−	6.83174i	−0.381698	−	1.42452i	0.461609	−	0.887084i	$-0.347272\pi$
$24$		0			0
$25$	4.85102	+	1.21146i	0.970203	+	0.242293i
$26$	0.496598	+	0.286711i	0.0973909	+	0.0562287i
$27$		0			0
$28$	−0.916677	−	9.68723i	−0.173236	−	1.83072i
$29$			5.48973i			1.01942i	0.860347	+	0.509709i	$0.170247\pi$
$29$			5.48973i			1.01942i	−0.860347	+	0.509709i	$0.829753\pi$
$30$		0			0
$31$	−0.0965807	+	0.0557609i	−0.0173464	+	0.0100150i	−0.508648	−	0.860974i	$-0.669855\pi$
$31$	−0.0965807	+	0.0557609i	−0.0173464	+	0.0100150i	0.491302	+	0.870989i	$0.336521\pi$
$32$	0.730829	−	2.72749i	0.129193	−	0.482157i
$33$		0			0
$34$	−13.6397			−2.33919
$35$	−3.10041	+	5.03860i	−0.524065	+	0.851678i
$36$		0			0
$37$	−0.745840	+	0.199847i	−0.122615	+	0.0328547i	−0.319605	−	0.947551i	$-0.603550\pi$
$37$	−0.745840	+	0.199847i	−0.122615	+	0.0328547i	0.196989	+	0.980406i	$0.436884\pi$
$38$	2.76153	−	10.3062i	0.447980	−	1.67188i
$39$		0			0
$40$	7.04544	−	5.50233i	1.11398	−	0.869996i
$41$		−	10.3867i		−	1.62214i	−0.584952	−	0.811068i	$-0.698887\pi$
$41$		−	10.3867i		−	1.62214i	0.584952	−	0.811068i	$-0.301113\pi$
$42$		0			0
$43$	3.12017	−	3.12017i	0.475821	−	0.475821i	−0.427971	−	0.903792i	$-0.640772\pi$
$43$	3.12017	−	3.12017i	0.475821	−	0.475821i	0.903792	+	0.427971i	$0.140772\pi$
$44$	4.29881	+	2.48192i	0.648070	+	0.374163i
$45$		0			0
$46$	8.42650	+	14.5951i	1.24242	+	2.15193i
$47$	−0.370937	−	1.38436i	−0.0541068	−	0.201929i	0.933581	−	0.358366i	$-0.116666\pi$
$47$	−0.370937	−	1.38436i	−0.0541068	−	0.201929i	−0.987688	+	0.156437i	$0.949999\pi$
$48$		0			0
$49$	−4.57499	−	5.29806i	−0.653570	−	0.756866i
$50$	−11.9123	+	0.203374i	−1.68466	+	0.0287614i
$51$		0			0
$52$	−0.854900	−	0.229070i	−0.118553	−	0.0317662i
$53$	−4.64236	−	1.24392i	−0.637677	−	0.170865i	−0.0745258	−	0.997219i	$-0.523744\pi$
$53$	−4.64236	−	1.24392i	−0.637677	−	0.170865i	−0.563151	+	0.826354i	$0.690411\pi$
$54$		0			0
$55$	−1.17869	−	2.77829i	−0.158934	−	0.374624i
$56$	3.68793	+	9.91356i	0.492821	+	1.32476i
$57$		0			0
$58$	−3.38561	−	12.6353i	−0.444552	−	1.65909i
$59$	3.76242	+	6.51670i	0.489825	+	0.848402i	0.999931	−	0.0117094i	$-0.00372730\pi$
$59$	3.76242	+	6.51670i	0.489825	+	0.848402i	−0.510106	+	0.860111i	$0.670394\pi$
$60$		0			0
$61$	3.71727	+	2.14617i	0.475947	+	0.274788i	0.718726	−	0.695293i	$-0.244726\pi$
$61$	3.71727	+	2.14617i	0.475947	+	0.274788i	−0.242779	+	0.970082i	$0.578059\pi$
$62$	0.187903	−	0.187903i	0.0238637	−	0.0238637i
$63$		0			0
$64$			11.0694i			1.38368i
$65$	0.331212	+	0.424099i	0.0410817	+	0.0526030i
$66$		0			0
$67$	3.88993	−	14.5174i	0.475230	−	1.77358i	−0.145286	−	0.989390i	$-0.546410\pi$
$67$	3.88993	−	14.5174i	0.475230	−	1.77358i	0.620516	−	0.784194i	$-0.286923\pi$
$68$	20.3351	−	5.44877i	2.46599	−	0.660761i
$69$		0			0
$70$	4.02857	−	13.5090i	0.481506	−	1.61463i
$71$	−2.69063			−0.319319			−0.159660	−	0.987172i	$-0.551040\pi$
$71$	−2.69063			−0.319319			−0.159660	+	0.987172i	$0.551040\pi$
$72$		0			0
$73$	−2.11608	+	7.89733i	−0.247669	+	0.924313i	0.724354	+	0.689428i	$0.242138\pi$
$73$	−2.11608	+	7.89733i	−0.247669	+	0.924313i	−0.972023	+	0.234885i	$0.924529\pi$
$74$	1.59339	−	0.919945i	0.185228	−	0.106941i
$75$		0			0
$76$			16.4684i			1.88905i
$77$	3.55504	−	0.336404i	0.405134	−	0.0383368i
$78$		0			0
$79$	−9.42775	−	5.44311i	−1.06070	−	0.612398i	−0.135077	−	0.990835i	$-0.543128\pi$
$79$	−9.42775	−	5.44311i	−1.06070	−	0.612398i	−0.925627	+	0.378437i	$0.876462\pi$
$80$	−2.92164	+	3.87560i	−0.326649	+	0.433306i
$81$		0			0
$82$	6.40567	+	23.9063i	0.707388	+	2.64001i
$83$	−5.01986	−	5.01986i	−0.551002	−	0.551002i	0.375728	−	0.926730i	$-0.377393\pi$
$83$	−5.01986	−	5.01986i	−0.551002	−	0.551002i	−0.926730	+	0.375728i	$0.877393\pi$
$84$		0			0
$85$	−11.8668	−	4.79713i	−1.28713	−	0.520322i
$86$	−5.25717	+	9.10569i	−0.566895	+	0.981892i
$87$		0			0
$88$	−5.21196	−	1.39654i	−0.555597	−	0.148872i
$89$	8.82970	−	15.2935i	0.935947	−	1.62111i	0.163009	−	0.986625i	$-0.447880\pi$
$89$	8.82970	−	15.2935i	0.935947	−	1.62111i	0.772937	−	0.634482i	$-0.218787\pi$
$90$		0			0
$91$	−0.596744	+	0.221994i	−0.0625558	+	0.0232713i
$92$	−18.3933	−	18.3933i	−1.91763	−	1.91763i
$93$		0			0
$94$	1.70751	+	2.95750i	0.176116	+	0.305043i
$95$	6.02730	−	7.99532i	0.618388	−	0.820302i
$96$		0			0
$97$	11.0460	−	11.0460i	1.12156	−	1.12156i	0.130048	−	0.991508i	$-0.458487\pi$
$97$	11.0460	−	11.0460i	1.12156	−	1.12156i	0.991508	−	0.130048i	$-0.0415132\pi$
$98$	13.7973	+	9.37265i	1.39374	+	0.946780i
$99$		0			0
$100$	17.6785	−	5.06192i	1.76785	−	0.506192i
$101$	6.15937	−	3.55611i	0.612880	−	0.353847i	−0.161212	−	0.986920i	$-0.551540\pi$
$101$	6.15937	−	3.55611i	0.612880	−	0.353847i	0.774092	+	0.633073i	$0.218207\pi$
$102$		0			0
$103$	−8.23991	+	2.20788i	−0.811903	+	0.217549i	−0.640803	−	0.767705i	$-0.721399\pi$
$103$	−8.23991	+	2.20788i	−0.811903	+	0.217549i	−0.171099	+	0.985254i	$0.554732\pi$
$104$	0.962080			0.0943397
$105$		0			0
$106$	11.4521			1.11232
$107$	18.0099	−	4.82575i	1.74109	−	0.466523i	0.758398	−	0.651791i	$-0.225982\pi$
$107$	18.0099	−	4.82575i	1.74109	−	0.466523i	0.982688	+	0.185269i	$0.0593155\pi$
$108$		0			0
$109$	14.9911	−	8.65514i	1.43589	−	0.829012i	0.438330	−	0.898814i	$-0.355570\pi$
$109$	14.9911	−	8.65514i	1.43589	−	0.829012i	0.997561	+	0.0698020i	$0.0222367\pi$
$110$	4.42630	+	5.66764i	0.422031	+	0.540389i
$111$		0			0
$112$	−3.32711	−	4.68072i	−0.314382	−	0.442286i
$113$	0.142477	−	0.142477i	0.0134031	−	0.0134031i	−0.700373	−	0.713777i	$-0.746983\pi$
$113$	0.142477	−	0.142477i	0.0134031	−	0.0134031i	0.713777	+	0.700373i	$0.246983\pi$
$114$		0			0
$115$	2.19805	+	15.6616i	0.204969	+	1.46045i
$116$	10.0950	+	17.4851i	0.937300	+	1.62345i
$117$		0			0
$118$	−12.6786	−	12.6786i	−1.16716	−	1.16716i
$119$	9.65254	−	11.6703i	0.884847	−	1.06981i
$120$		0			0
$121$	4.58918	−	7.94870i	0.417198	−	0.722609i
$122$	−9.87931	−	2.64715i	−0.894431	−	0.239662i
$123$		0			0
$124$	−0.205077	+	0.355203i	−0.0184164	+	0.0318982i
$125$	−10.4354	−	4.01266i	−0.933375	−	0.358903i
$126$		0			0
$127$	0.925975	+	0.925975i	0.0821670	+	0.0821670i	0.746996	−	0.664829i	$-0.231496\pi$
$127$	0.925975	+	0.925975i	0.0821670	+	0.0821670i	−0.664829	+	0.746996i	$0.731496\pi$
$128$	−5.36505	−	20.0226i	−0.474208	−	1.76977i
$129$		0			0
$130$	−1.02387	−	0.771849i	−0.0897995	−	0.0676957i
$131$	19.3103	+	11.1488i	1.68715	+	0.974077i	0.956683	+	0.291131i	$0.0940314\pi$
$131$	19.3103	+	11.1488i	1.68715	+	0.974077i	0.730468	+	0.682947i	$0.239302\pi$
$132$		0			0
$133$	6.86378	+	9.65626i	0.595165	+	0.837304i
$134$			35.8125i			3.09373i
$135$		0			0
$136$	−19.8186	+	11.4423i	−1.69943	+	0.981167i
$137$	3.09562	−	11.5530i	0.264476	−	0.987039i	−0.698094	−	0.716006i	$-0.745968\pi$
$137$	3.09562	−	11.5530i	0.264476	−	0.987039i	0.962570	−	0.271033i	$-0.0873652\pi$
$138$		0			0
$139$	−6.45568			−0.547563			−0.273782	−	0.961792i	$-0.588275\pi$
$139$	−6.45568			−0.547563			−0.273782	+	0.961792i	$0.588275\pi$
$140$	−0.609535	+	21.7495i	−0.0515151	+	1.83817i
$141$		0			0
$142$	6.19281	−	1.65936i	0.519689	−	0.139250i
$143$	0.0840644	−	0.313733i	0.00702982	−	0.0262356i
$144$		0			0
$145$	1.49833	−	12.1836i	0.124429	−	1.01180i
$146$		−	19.4817i		−	1.61231i
$147$		0			0
$148$	−2.00805	+	2.00805i	−0.165060	+	0.165060i
$149$	−12.3309	−	7.11925i	−1.01019	−	0.583232i	−0.0989406	−	0.995093i	$-0.531545\pi$
$149$	−12.3309	−	7.11925i	−1.01019	−	0.583232i	−0.911246	+	0.411862i	$0.864879\pi$
$150$		0			0
$151$	1.25966	+	2.18179i	0.102510	+	0.177552i	0.912718	−	0.408590i	$-0.133979\pi$
$151$	1.25966	+	2.18179i	0.102510	+	0.177552i	−0.810208	+	0.586142i	$0.800646\pi$
$152$	−4.63327	−	17.2916i	−0.375808	−	1.40253i
$153$		0			0
$154$	−7.97488	+	2.96672i	−0.642634	+	0.239065i
$155$	0.229565	−	0.0973929i	0.0184391	−	0.00782278i
$156$		0			0
$157$	−2.09907	−	0.562444i	−0.167524	−	0.0448880i	0.174082	−	0.984731i	$-0.444304\pi$
$157$	−2.09907	−	0.562444i	−0.167524	−	0.0448880i	−0.341606	+	0.939843i	$0.610971\pi$
$158$	25.0559	+	6.71372i	1.99334	+	0.534115i
$159$		0			0
$160$	−2.36638	+	5.85378i	−0.187079	+	0.462782i
$161$	−18.4510	−	3.11888i	−1.45414	−	0.245802i
$162$		0			0
$163$	−2.29638	−	8.57021i	−0.179866	−	0.671271i	−0.995671	−	0.0929436i	$-0.970372\pi$
$163$	−2.29638	−	8.57021i	−0.179866	−	0.671271i	0.815805	−	0.578327i	$-0.196294\pi$
$164$	−19.1001	−	33.0823i	−1.49147	−	2.58330i
$165$		0			0
$166$	14.6496	+	8.45798i	1.13703	+	0.656466i
$167$	−8.79435	+	8.79435i	−0.680527	+	0.680527i	−0.960119	−	0.279592i	$-0.909801\pi$
$167$	−8.79435	+	8.79435i	−0.680527	+	0.680527i	0.279592	+	0.960119i	$0.409801\pi$
$168$		0			0
$169$		−	12.9421i		−	0.995545i
$170$	30.2713	+	3.72272i	2.32170	+	0.285520i
$171$		0			0
$172$	4.20025	−	15.6756i	0.320266	−	1.19525i
$173$	−4.90837	+	1.31519i	−0.373176	+	0.0999923i	−0.440532	−	0.897737i	$-0.645210\pi$
$173$	−4.90837	+	1.31519i	−0.373176	+	0.0999923i	0.0673561	+	0.997729i	$0.478544\pi$
$174$		0			0
$175$	8.25608	−	10.3362i	0.624101	−	0.781343i
$176$	2.92954			0.220822
$177$		0			0
$178$	−10.8909	+	40.6452i	−0.816304	+	3.04649i
$179$	−1.79629	+	1.03709i	−0.134261	+	0.0775155i	−0.565626	−	0.824662i	$-0.691365\pi$
$179$	−1.79629	+	1.03709i	−0.134261	+	0.0775155i	0.431365	+	0.902177i	$0.358032\pi$
$180$		0			0
$181$			19.8907i			1.47846i	0.673452	+	0.739231i	$0.264811\pi$
$181$			19.8907i			1.47846i	−0.673452	+	0.739231i	$0.735189\pi$
$182$	1.23657	−	0.878968i	0.0916606	−	0.0651534i
$183$		0			0
$184$	24.4875	+	14.1379i	1.80524	+	1.04226i
$185$	1.70982	−	0.239967i	0.125709	−	0.0176427i
$186$		0			0
$187$	1.99960	+	7.46261i	0.146225	+	0.545720i
$188$	−3.72714	−	3.72714i	−0.271830	−	0.271830i
$189$		0			0
$190$	−8.94170	+	22.1193i	−0.648699	+	1.60470i
$191$	−1.93130	+	3.34510i	−0.139744	+	0.242043i	−0.927400	−	0.374072i	$-0.877961\pi$
$191$	−1.93130	+	3.34510i	−0.139744	+	0.242043i	0.787656	+	0.616115i	$0.211295\pi$
$192$		0			0
$193$	−19.3784	−	5.19244i	−1.39489	−	0.373760i	−0.518383	−	0.855148i	$-0.673466\pi$
$193$	−19.3784	−	5.19244i	−1.39489	−	0.373760i	−0.876507	+	0.481388i	$0.840133\pi$
$194$	−18.6115	+	32.2361i	−1.33623	+	2.31441i
$195$		0			0
$196$	−24.3142	−	8.46172i	−1.73673	−	0.604408i
$197$	−10.8555	−	10.8555i	−0.773424	−	0.773424i	0.205279	−	0.978703i	$-0.434190\pi$
$197$	−10.8555	−	10.8555i	−0.773424	−	0.773424i	−0.978703	+	0.205279i	$0.934190\pi$
$198$		0			0
$199$	−11.8298	−	20.4898i	−0.838591	−	1.45248i	−0.891073	−	0.453861i	$-0.850046\pi$
$199$	−11.8298	−	20.4898i	−0.838591	−	1.45248i	0.0524812	−	0.998622i	$-0.483287\pi$
$200$	−17.1381	+	10.2887i	−1.21184	+	0.727519i
$201$		0			0
$202$	−11.9834	+	11.9834i	−0.843149	+	0.843149i
$203$	13.2068	+	6.04495i	0.926933	+	0.424272i
$204$		0			0
$205$	−2.83488	+	23.0518i	−0.197996	+	1.61001i
$206$	17.6035	−	10.1634i	1.22649	−	0.708117i
$207$		0			0
$208$	−0.504541	+	0.135191i	−0.0349837	+	0.00937384i
$209$	−6.04360			−0.418045
$210$		0			0
$211$	−4.86134			−0.334668			−0.167334	−	0.985900i	$-0.553516\pi$
$211$	−4.86134			−0.334668			−0.167334	+	0.985900i	$0.553516\pi$
$212$	−17.0736	+	4.57486i	−1.17262	+	0.314202i
$213$		0			0
$214$	−38.4759	+	22.2141i	−2.63016	+	1.51852i
$215$	−7.77633	+	6.07314i	−0.530341	+	0.414185i
$216$		0			0
$217$	0.0277965	+	0.293747i	0.00188695	+	0.0199408i
$218$	−29.1661	+	29.1661i	−1.97538	+	1.97538i
$219$		0			0
$220$	−8.86316	−	6.68153i	−0.597554	−	0.450468i
$221$	−0.688765	−	1.19298i	−0.0463313	−	0.0802482i
$222$		0			0
$223$	8.12660	+	8.12660i	0.544198	+	0.544198i	0.924757	−	0.380559i	$-0.124268\pi$
$223$	8.12660	+	8.12660i	0.544198	+	0.544198i	−0.380559	+	0.924757i	$0.624268\pi$
$224$	−5.75684	−	4.76151i	−0.384645	−	0.318142i
$225$		0			0
$226$	−0.240059	+	0.415795i	−0.0159685	+	0.0276583i
$227$	0.0592118	+	0.0158658i	0.00393002	+	0.00105305i	0.260784	−	0.965397i	$-0.416019\pi$
$227$	0.0592118	+	0.0158658i	0.00393002	+	0.00105305i	−0.256853	+	0.966450i	$0.582686\pi$
$228$		0			0
$229$	−6.00335	+	10.3981i	−0.396712	+	0.687126i	−0.993318	−	0.115409i	$-0.963182\pi$
$229$	−6.00335	+	10.3981i	−0.396712	+	0.687126i	0.596606	+	0.802534i	$0.296516\pi$
$230$	−14.7179	−	34.6915i	−0.970466	−	2.28749i
$231$		0			0
$232$	−15.5190	−	15.5190i	−1.01887	−	1.01887i
$233$	0.520290	+	1.94175i	0.0340853	+	0.127208i	0.980872	−	0.194653i	$-0.0623582\pi$
$233$	0.520290	+	1.94175i	0.0340853	+	0.127208i	−0.946787	+	0.321861i	$0.895691\pi$
$234$		0			0
$235$	0.445403	+	3.17361i	0.0290549	+	0.207024i
$236$	23.9670	+	13.8374i	1.56012	+	0.900736i
$237$		0			0
$238$	−15.0192	+	32.8134i	−0.973552	+	2.12698i
$239$			8.02048i			0.518802i	0.965770	+	0.259401i	$0.0835251\pi$
$239$			8.02048i			0.518802i	−0.965770	+	0.259401i	$0.916475\pi$
$240$		0			0
$241$	8.20013	−	4.73435i	0.528217	−	0.304966i	−0.212073	−	0.977254i	$-0.568022\pi$
$241$	8.20013	−	4.73435i	0.528217	−	0.304966i	0.740290	+	0.672288i	$0.234688\pi$
$242$	−5.66045	+	21.1251i	−0.363868	+	1.35797i
$243$		0			0
$244$	15.7863			1.01061
$245$	8.70748	+	13.0069i	0.556301	+	0.830981i
$246$		0			0
$247$	1.04086	−	0.278898i	0.0662285	−	0.0177459i
$248$	0.115394	−	0.430655i	0.00732751	−	0.0273466i
$249$		0			0
$250$	26.4931	+	2.79990i	1.67557	+	0.177081i
$251$		−	0.232481i		−	0.0146740i	−0.999973	−	0.00733702i	$-0.997665\pi$
$251$		−	0.232481i		−	0.0146740i	0.999973	−	0.00733702i	$-0.00233547\pi$
$252$		0			0
$253$	6.75000	−	6.75000i	0.424369	−	0.424369i
$254$	−2.70230	−	1.56018i	−0.169558	−	0.0978941i
$255$		0			0
$256$	13.6272	+	23.6029i	0.851698	+	1.47518i
$257$	5.42921	+	20.2621i	0.338665	+	1.26391i	0.899841	+	0.436218i	$0.143682\pi$
$257$	5.42921	+	20.2621i	0.338665	+	1.26391i	−0.561176	+	0.827696i	$0.689651\pi$
$258$		0			0
$259$	−0.340496	+	2.01434i	−0.0211574	+	0.125165i
$260$	1.83480	+	0.741715i	0.113789	+	0.0459992i
$261$		0			0
$262$	−51.3207	−	13.7513i	−3.17060	−	0.849560i
$263$	−17.1027	−	4.58266i	−1.05460	−	0.282579i	−0.310448	−	0.950590i	$-0.600479\pi$
$263$	−17.1027	−	4.58266i	−1.05460	−	0.282579i	−0.744151	+	0.668011i	$0.767146\pi$
$264$		0			0
$265$	9.96350	+	4.02773i	0.612053	+	0.247422i
$266$	−21.7530	−	17.9920i	−1.33376	−	1.10316i
$267$		0			0
$268$	−14.3063	−	53.3919i	−0.873898	−	3.26143i
$269$	7.03021	+	12.1767i	0.428640	+	0.742426i	0.996753	−	0.0805250i	$-0.0256597\pi$
$269$	7.03021	+	12.1767i	0.428640	+	0.742426i	−0.568113	+	0.822951i	$0.692326\pi$
$270$		0			0
$271$	−22.2566	−	12.8499i	−1.35199	−	0.780574i	−0.363465	−	0.931608i	$-0.618406\pi$
$271$	−22.2566	−	12.8499i	−1.35199	−	0.780574i	−0.988529	+	0.151034i	$0.951740\pi$
$272$	8.78556	−	8.78556i	0.532703	−	0.532703i
$273$		0			0
$274$			28.4997i			1.72173i
$275$	1.85763	+	6.48769i	0.112019	+	0.391223i
$276$		0			0
$277$	−1.15517	+	4.31113i	−0.0694071	+	0.259031i	−0.991907	−	0.126966i	$-0.959476\pi$
$277$	−1.15517	+	4.31113i	−0.0694071	+	0.259031i	0.922500	+	0.385997i	$0.126143\pi$
$278$	14.8585	−	3.98132i	0.891154	−	0.238784i
$279$		0			0
$280$	−5.47908	−	23.0082i	−0.327437	−	1.37500i
$281$	25.1927			1.50287			0.751434	−	0.659808i	$-0.229363\pi$
$281$	25.1927			1.50287			0.751434	+	0.659808i	$0.229363\pi$
$282$		0			0
$283$	4.98582	−	18.6073i	0.296376	−	1.10609i	−0.643742	−	0.765243i	$-0.722619\pi$
$283$	4.98582	−	18.6073i	0.296376	−	1.10609i	0.940118	−	0.340849i	$-0.110714\pi$
$284$	−8.56981	+	4.94778i	−0.508525	+	0.293597i
$285$		0			0
$286$			0.773936i			0.0457638i
$287$	−24.9876	−	11.4372i	−1.47497	−	0.675118i
$288$		0			0
$289$	13.6543	+	7.88333i	0.803195	+	0.463725i
$290$	4.06527	+	28.9661i	0.238721	+	1.70095i
$291$		0			0
$292$	7.78250	+	29.0447i	0.455437	+	1.69971i
$293$	5.29552	+	5.29552i	0.309368	+	0.309368i	0.844664	−	0.535296i	$-0.179800\pi$
$293$	5.29552	+	5.29552i	0.309368	+	0.309368i	−0.535296	+	0.844664i	$0.679800\pi$
$294$		0			0
$295$	−6.57150	−	15.4897i	−0.382607	−	0.901846i
$296$	1.54347	−	2.67337i	0.0897124	−	0.155386i
$297$		0			0
$298$	32.7716	+	8.78112i	1.89841	+	0.508677i
$299$	−0.851025	+	1.47402i	−0.0492160	+	0.0852447i
$300$		0			0
$301$	−4.07051	−	10.9420i	−0.234621	−	0.630685i
$302$	−4.24480	−	4.24480i	−0.244261	−	0.244261i
$303$		0			0
$304$	4.85963	+	8.41712i	0.278719	+	0.482755i
$305$	−7.66416	−	5.77765i	−0.438848	−	0.330827i
$306$		0			0
$307$	16.4255	−	16.4255i	0.937450	−	0.937450i	−0.0607054	−	0.998156i	$-0.519335\pi$
$307$	16.4255	−	16.4255i	0.937450	−	0.937450i	0.998156	+	0.0607054i	$0.0193350\pi$
$308$	10.7044	−	7.60880i	0.609939	−	0.433552i
$309$		0			0
$310$	−0.468308	+	0.365738i	−0.0265981	+	0.0207725i
$311$	2.79738	−	1.61507i	0.158625	−	0.0915821i	−0.418586	−	0.908177i	$-0.637474\pi$
$311$	2.79738	−	1.61507i	0.158625	−	0.0915821i	0.577211	+	0.816595i	$0.304141\pi$
$312$		0			0
$313$	8.52948	−	2.28547i	0.482115	−	0.129182i	−0.00957242	−	0.999954i	$-0.503047\pi$
$313$	8.52948	−	2.28547i	0.482115	−	0.129182i	0.491687	+	0.870772i	$0.336380\pi$
$314$	5.17813			0.292219
$315$		0			0
$316$	−40.0372			−2.25227
$317$	−22.6860	+	6.07871i	−1.27418	+	0.341414i	−0.831629	−	0.555332i	$-0.812591\pi$
$317$	−22.6860	+	6.07871i	−1.27418	+	0.341414i	−0.442546	+	0.896746i	$0.645925\pi$
$318$		0			0
$319$	−6.41671	+	3.70469i	−0.359267	+	0.207423i
$320$	3.02121	−	24.5669i	0.168891	−	1.37333i
$321$		0			0
$322$	44.3905	−	4.20056i	2.47379	−	0.234088i
$323$	−18.1245	+	18.1245i	−1.00847	+	1.00847i
$324$		0			0
$325$	−0.619324	−	1.03162i	−0.0343539	−	0.0572240i
$326$	10.5708	+	18.3091i	0.585462	+	1.01405i
$327$		0			0
$328$	29.3623	+	29.3623i	1.62126	+	1.62126i
$329$	−3.73883	−	0.631997i	−0.206128	−	0.0348431i
$330$		0			0
$331$	13.7448	−	23.8066i	0.755481	−	1.30853i	−0.189655	−	0.981851i	$-0.560737\pi$
$331$	13.7448	−	23.8066i	0.755481	−	1.30853i	0.945135	−	0.326680i	$-0.105930\pi$
$332$	−25.2195	−	6.75756i	−1.38410	−	0.370869i
$333$		0			0
$334$	14.8176	−	25.6649i	0.810784	−	1.40432i
$335$	−12.5954	+	31.1575i	−0.688159	+	1.70232i
$336$		0			0
$337$	8.19407	+	8.19407i	0.446359	+	0.446359i	0.894142	−	0.447783i	$-0.147786\pi$
$337$	8.19407	+	8.19407i	0.446359	+	0.446359i	−0.447783	+	0.894142i	$0.647786\pi$
$338$	7.98160	+	29.7877i	0.434142	+	1.62024i
$339$		0			0
$340$	−46.6178	+	6.54262i	−2.52821	+	0.354823i
$341$	−0.130353	−	0.0752594i	−0.00705902	−	0.00407552i
$342$		0			0
$343$	−17.7834	+	5.17225i	−0.960211	+	0.279275i
$344$			17.6408i			0.951130i
$345$		0			0
$346$	10.4861	−	6.05415i	0.563736	−	0.325473i
$347$	3.44897	−	12.8717i	0.185151	−	0.690991i	−0.809448	−	0.587192i	$-0.800233\pi$
$347$	3.44897	−	12.8717i	0.185151	−	0.690991i	0.994598	−	0.103799i	$-0.0330999\pi$
$348$		0			0
$349$	12.8419			0.687410			0.343705	−	0.939078i	$-0.388318\pi$
$349$	12.8419			0.687410			0.343705	+	0.939078i	$0.388318\pi$
$350$	−12.6278	+	28.8817i	−0.674987	+	1.54379i
$351$		0			0
$352$	3.68124	−	0.986385i	0.196211	−	0.0525745i
$353$	−2.49256	+	9.30236i	−0.132666	+	0.495115i	−0.999997	−	0.00261707i	$-0.999167\pi$
$353$	−2.49256	+	9.30236i	−0.132666	+	0.495115i	0.867331	+	0.497732i	$0.165834\pi$
$354$		0			0
$355$	5.97145	+	0.734361i	0.316932	+	0.0389758i
$356$		−	64.9475i		−	3.44221i
$357$		0			0
$358$	3.49478	−	3.49478i	0.184705	−	0.184705i
$359$	−17.9700	−	10.3750i	−0.948421	−	0.547571i	−0.0558308	−	0.998440i	$-0.517781\pi$
$359$	−17.9700	−	10.3750i	−0.948421	−	0.547571i	−0.892590	+	0.450869i	$0.851114\pi$
$360$		0			0
$361$	−0.525348	−	0.909930i	−0.0276499	−	0.0478910i
$362$	−12.2669	−	45.7807i	−0.644734	−	2.40618i
$363$		0			0
$364$	−1.49244	+	1.80441i	−0.0782251	+	0.0945769i
$365$	6.85176	−	16.9494i	0.358638	−	0.887171i
$366$		0			0
$367$	2.07408	+	0.555747i	0.108266	+	0.0290098i	0.312545	−	0.949903i	$-0.398818\pi$
$367$	2.07408	+	0.555747i	0.108266	+	0.0290098i	−0.204279	+	0.978913i	$0.565485\pi$
$368$	−14.8286	−	3.97331i	−0.772993	−	0.207123i
$369$		0			0
$370$	−3.78737	+	1.60679i	−0.196896	+	0.0835330i
$371$	−8.10439	+	9.79849i	−0.420759	+	0.508712i
$372$		0			0
$373$	8.54958	+	31.9075i	0.442681	+	1.65211i	0.721989	+	0.691905i	$0.243228\pi$
$373$	8.54958	+	31.9075i	0.442681	+	1.65211i	−0.279308	+	0.960202i	$0.590105\pi$
$374$	−9.20463	−	15.9429i	−0.475960	−	0.824387i
$375$		0			0
$376$	4.96205	+	2.86484i	0.255898	+	0.147743i
$377$	0.934159	−	0.934159i	0.0481116	−	0.0481116i
$378$		0			0
$379$		−	2.52285i		−	0.129590i	−0.997899	−	0.0647951i	$-0.979361\pi$
$379$		−	2.52285i		−	0.129590i	0.997899	−	0.0647951i	$-0.0206394\pi$
$380$	4.49476	−	36.5491i	0.230576	−	1.87493i
$381$		0			0
$382$	2.38212	−	8.89021i	0.121880	−	0.454863i
$383$	−4.24063	+	1.13627i	−0.216686	+	0.0580609i	−0.365529	−	0.930800i	$-0.619112\pi$
$383$	−4.24063	+	1.13627i	−0.216686	+	0.0580609i	0.148843	+	0.988861i	$0.452445\pi$
$384$		0			0
$385$	−7.98168	−	0.223688i	−0.406784	−	0.0114002i
$386$	47.8040			2.43316
$387$		0			0
$388$	14.8698	−	55.4948i	0.754899	−	2.81732i
$389$	26.9719	−	15.5722i	1.36753	−	0.789542i	0.376916	−	0.926248i	$-0.376985\pi$
$389$	26.9719	−	15.5722i	1.36753	−	0.789542i	0.990612	+	0.136705i	$0.0436514\pi$
$390$		0			0
$391$		−	40.4859i		−	2.04746i
$392$	27.9102	+	2.04406i	1.40968	+	0.103241i
$393$		0			0
$394$	31.6801	+	18.2905i	1.59602	+	0.921462i
$395$	19.4379	+	14.6533i	0.978025	+	0.737288i
$396$		0			0
$397$	3.05333	+	11.3952i	0.153242	+	0.571908i	0.999249	+	0.0387367i	$0.0123334\pi$
$397$	3.05333	+	11.3952i	0.153242	+	0.571908i	−0.846007	+	0.533172i	$0.821000\pi$
$398$	39.8641	+	39.8641i	1.99820	+	1.99820i
$399$		0			0
$400$	7.54191	−	7.80390i	0.377096	−	0.390195i
$401$	−15.0277	+	26.0288i	−0.750448	+	1.29981i	0.197158	+	0.980372i	$0.436829\pi$
$401$	−15.0277	+	26.0288i	−0.750448	+	1.29981i	−0.947606	+	0.319442i	$0.896504\pi$
$402$		0			0
$403$	0.0259232	+	0.00694610i	0.00129133	+	0.000346010i
$404$	13.0786	−	22.6529i	0.650686	−	1.12702i
$405$		0			0
$406$	−34.1249	−	5.76834i	−1.69359	−	0.286278i
$407$	−0.736916	−	0.736916i	−0.0365276	−	0.0365276i
$408$		0			0
$409$	0.267004	+	0.462464i	0.0132025	+	0.0228674i	0.872551	−	0.488523i	$-0.162464\pi$
$409$	0.267004	+	0.462464i	0.0132025	+	0.0228674i	−0.859349	+	0.511390i	$0.829131\pi$
$410$	−7.69162	−	54.8047i	−0.379862	−	2.70661i
$411$		0			0
$412$	−22.1845	+	22.1845i	−1.09295	+	1.09295i
$413$	19.8203	−	1.87554i	0.975293	−	0.0922894i
$414$		0			0
$415$	9.77074	+	12.5109i	0.479627	+	0.614136i
$416$	−0.588484	+	0.339762i	−0.0288528	+	0.0166582i
$417$		0			0
$418$	13.9101	−	3.72719i	0.680363	−	0.182303i
$419$	11.4198			0.557893			0.278947	−	0.960307i	$-0.410015\pi$
$419$	11.4198			0.557893			0.278947	+	0.960307i	$0.410015\pi$
$420$		0			0
$421$	−1.92138			−0.0936422			−0.0468211	−	0.998903i	$-0.514909\pi$
$421$	−1.92138			−0.0936422			−0.0468211	+	0.998903i	$0.514909\pi$
$422$	11.1890	−	2.99807i	0.544670	−	0.145944i
$423$		0			0
$424$	16.6399	−	9.60707i	0.808107	−	0.466561i
$425$	25.0273	+	13.8853i	1.21400	+	0.673538i
$426$		0			0
$427$	9.25630	−	6.57949i	0.447944	−	0.318404i
$428$	48.4886	−	48.4886i	2.34379	−	2.34379i
$429$		0			0
$430$	14.1527	−	18.7738i	0.682505	−	0.905355i
$431$	13.5480	+	23.4658i	0.652584	+	1.13031i	0.982494	+	0.186296i	$0.0596482\pi$
$431$	13.5480	+	23.4658i	0.652584	+	1.13031i	−0.329910	+	0.944012i	$0.607018\pi$
$432$		0			0
$433$	21.1352	+	21.1352i	1.01569	+	1.01569i	0.999875	+	0.0158158i	$0.00503454\pi$
$433$	21.1352	+	21.1352i	1.01569	+	1.01569i	0.0158158	+	0.999875i	$0.494965\pi$
$434$	−0.245135	−	0.658950i	−0.0117669	−	0.0316306i
$435$		0			0
$436$	31.8318	−	55.1342i	1.52446	−	2.64045i
$437$	30.5912	+	8.19688i	1.46337	+	0.392110i
$438$		0			0
$439$	19.5969	−	33.9429i	0.935311	−	1.62001i	0.161233	−	0.986916i	$-0.448453\pi$
$439$	19.5969	−	33.9429i	0.935311	−	1.62001i	0.774078	−	0.633090i	$-0.218214\pi$
$440$	11.1860	+	4.52192i	0.533271	+	0.215574i
$441$		0			0
$442$	2.32100	+	2.32100i	0.110399	+	0.110399i
$443$	−7.60820	−	28.3942i	−0.361476	−	1.34905i	−0.872135	−	0.489265i	$-0.837265\pi$
$443$	−7.60820	−	28.3942i	−0.361476	−	1.34905i	0.510659	−	0.859783i	$-0.329401\pi$
$444$		0			0
$445$	−23.7703	+	31.5317i	−1.12682	+	1.49474i
$446$	−23.7162	−	13.6925i	−1.12299	−	0.648360i
$447$		0			0
$448$	26.6300	+	12.1890i	1.25815	+	0.575875i
$449$			1.12844i			0.0532543i	0.999645	+	0.0266272i	$0.00847669\pi$
$449$			1.12844i			0.0532543i	−0.999645	+	0.0266272i	$0.991523\pi$
$450$		0			0
$451$	12.1406	−	7.00939i	0.571679	−	0.330059i
$452$	0.191797	−	0.715796i	0.00902137	−	0.0336682i
$453$		0			0
$454$	−0.146068			−0.00685529
$455$	1.38497	−	0.329811i	0.0649285	−	0.0154618i
$456$		0			0
$457$	−28.5224	+	7.64255i	−1.33422	+	0.357503i	−0.854287	−	0.519802i	$-0.826006\pi$
$457$	−28.5224	+	7.64255i	−1.33422	+	0.357503i	−0.479933	+	0.877305i	$0.659339\pi$
$458$	7.40473	−	27.6348i	0.346000	−	1.29129i
$459$		0			0
$460$	35.8010	+	45.8412i	1.66923	+	2.13736i
$461$			9.74526i			0.453882i	0.973909	+	0.226941i	$0.0728724\pi$
$461$			9.74526i			0.453882i	−0.973909	+	0.226941i	$0.927128\pi$
$462$		0			0
$463$	15.4201	−	15.4201i	0.716631	−	0.716631i	−0.251283	−	0.967914i	$-0.580852\pi$
$463$	15.4201	−	15.4201i	0.716631	−	0.716631i	0.967914	+	0.251283i	$0.0808523\pi$
$464$	10.3193	+	5.95785i	0.479061	+	0.276586i
$465$		0			0
$466$	−2.39502	−	4.14829i	−0.110947	−	0.192166i
$467$	−2.86810	−	10.7039i	−0.132720	−	0.495317i	0.867277	−	0.497826i	$-0.165868\pi$
$467$	−2.86810	−	10.7039i	−0.132720	−	0.495317i	−0.999997	+	0.00250867i	$0.999201\pi$
$468$		0			0
$469$	−30.6415	−	25.3438i	−1.41489	−	1.17027i
$470$	−2.98237	−	7.02975i	−0.137566	−	0.324258i
$471$		0			0
$472$	−29.0581	−	7.78609i	−1.33751	−	0.358384i
$473$	5.75264	+	1.54142i	0.264507	+	0.0708744i
$474$		0			0
$475$	−15.5589	+	16.0994i	−0.713890	+	0.738689i
$476$	9.28353	−	54.9204i	0.425510	−	2.51727i
$477$		0			0
$478$	−4.94637	−	18.4601i	−0.226242	−	0.844345i
$479$	1.08797	+	1.88443i	0.0497108	+	0.0861016i	0.889810	−	0.456331i	$-0.150837\pi$
$479$	1.08797	+	1.88443i	0.0497108	+	0.0861016i	−0.840099	+	0.542433i	$0.817503\pi$
$480$		0			0
$481$	0.160923	+	0.0929088i	0.00733745	+	0.00423628i
$482$	−15.9538	+	15.9538i	−0.726676	+	0.726676i
$483$		0			0
$484$		−	33.7561i		−	1.53437i
$485$	−27.5298	+	21.5002i	−1.25007	+	0.976274i
$486$		0			0
$487$	−5.00951	+	18.6958i	−0.227003	+	0.847186i	0.754590	+	0.656197i	$0.227836\pi$
$487$	−5.00951	+	18.6958i	−0.227003	+	0.847186i	−0.981592	+	0.190989i	$0.938831\pi$
$488$	−16.5754	+	4.44136i	−0.750332	+	0.201051i
$489$		0			0
$490$	−28.0629	−	24.5669i	−1.26775	−	1.10982i
$491$	7.07743			0.319400			0.159700	−	0.987166i	$-0.448947\pi$
$491$	7.07743			0.319400			0.159700	+	0.987166i	$0.448947\pi$
$492$		0			0
$493$	−8.13323	+	30.3536i	−0.366302	+	1.36706i
$494$	−2.22367	+	1.28383i	−0.100047	+	0.0577624i
$495$		0			0
$496$			0.242063i			0.0108689i
$497$	−2.96276	+	6.47291i	−0.132898	+	0.290350i
$498$		0			0
$499$	−22.2550	−	12.8489i	−0.996270	−	0.575197i	−0.0891276	−	0.996020i	$-0.528408\pi$
$499$	−22.2550	−	12.8489i	−0.996270	−	0.575197i	−0.907143	+	0.420823i	$0.861741\pi$
$500$	−40.6163	+	6.40912i	−1.81642	+	0.286625i
$501$		0			0
$502$	0.143375	+	0.535082i	0.00639913	+	0.0238819i
$503$	0.515716	+	0.515716i	0.0229946	+	0.0229946i	0.718511	−	0.695516i	$-0.244824\pi$
$503$	0.515716	+	0.515716i	0.0229946	+	0.0229946i	−0.695516	+	0.718511i	$0.744824\pi$
$504$		0			0
$505$	−14.6404	+	6.21116i	−0.651488	+	0.276393i
$506$	−11.3731	+	19.6988i	−0.505595	+	0.875716i
$507$		0			0
$508$	4.65205	+	1.24651i	0.206401	+	0.0553051i
$509$	−9.29825	+	16.1050i	−0.412138	+	0.713844i	−0.995123	−	0.0986388i	$-0.968551\pi$
$509$	−9.29825	+	16.1050i	−0.412138	+	0.713844i	0.582985	+	0.812483i	$0.301884\pi$
$510$		0			0
$511$	16.6687	+	13.7868i	0.737379	+	0.609890i
$512$	−16.6057	−	16.6057i	−0.733874	−	0.733874i
$513$		0			0
$514$	−24.9919	−	43.2873i	−1.10235	−	1.90932i
$515$	18.8898	−	2.65111i	0.832386	−	0.116822i
$516$		0			0
$517$	1.36779	−	1.36779i	0.0601555	−	0.0601555i
$518$	−0.458587	−	4.84624i	−0.0201491	−	0.212932i
$519$		0			0
$520$	−2.13519	−	0.262583i	−0.0936343	−	0.0115150i
$521$	−32.1688	+	18.5727i	−1.40934	+	0.813684i	−0.995325	−	0.0965845i	$-0.969208\pi$
$521$	−32.1688	+	18.5727i	−1.40934	+	0.813684i	−0.414018	+	0.910269i	$0.635875\pi$
$522$		0			0
$523$	−15.9477	+	4.27317i	−0.697344	+	0.186853i	−0.590041	−	0.807374i	$-0.700888\pi$
$523$	−15.9477	+	4.27317i	−0.697344	+	0.186853i	−0.107303	+	0.994226i	$0.534222\pi$
$524$	82.0060			3.58245
$525$		0			0
$526$	42.1901			1.83958
$527$	−0.616623	+	0.165224i	−0.0268605	+	0.00719725i
$528$		0			0
$529$	−23.4031	+	13.5118i	−1.01753	+	0.587470i
$530$	−25.4161	−	3.12564i	−1.10401	−	0.135769i
$531$		0			0
$532$	39.6184	+	18.1340i	1.71767	+	0.786208i
$533$	−1.76746	+	1.76746i	−0.0765570	+	0.0765570i
$534$		0			0
$535$	−41.2874	+	5.79452i	−1.78501	+	0.250519i
$536$	30.0429	+	52.0358i	1.29765	+	2.24760i
$537$		0			0
$538$	−23.6904	−	23.6904i	−1.02137	−	1.02137i
$539$	3.10530	−	8.92286i	0.133755	−	0.384335i
$540$		0			0
$541$	15.5609	−	26.9523i	0.669017	−	1.15877i	−0.309162	−	0.951009i	$-0.600049\pi$
$541$	15.5609	−	26.9523i	0.669017	−	1.15877i	0.978179	−	0.207763i	$-0.0666181\pi$
$542$	59.1510	+	15.8495i	2.54075	+	0.680793i
$543$		0			0
$544$	8.08175	−	13.9980i	0.346502	−	0.600159i
$545$	−35.6328	+	15.1172i	−1.52634	+	0.647550i
$546$		0			0
$547$	−4.64702	−	4.64702i	−0.198692	−	0.198692i	0.600747	−	0.799439i	$-0.294870\pi$
$547$	−4.64702	−	4.64702i	−0.198692	−	0.198692i	−0.799439	+	0.600747i	$0.794870\pi$
$548$	−11.3850	−	42.4895i	−0.486344	−	1.81506i
$549$		0			0
$550$	−8.27663	−	13.7866i	−0.352917	−	0.587861i
$551$	−21.2886	−	12.2910i	−0.906923	−	0.523612i
$552$		0			0
$553$	−23.4759	+	16.6869i	−0.998295	+	0.709600i
$554$		−	10.6350i		−	0.451838i
$555$		0			0
$556$	−20.5617	+	11.8713i	−0.872010	+	0.503455i
$557$	7.24050	−	27.0219i	0.306790	−	1.14495i	−0.624604	−	0.780942i	$-0.714740\pi$
$557$	7.24050	−	27.0219i	0.306790	−	1.14495i	0.931394	−	0.364013i	$-0.118594\pi$
$558$		0			0
$559$	−1.06188			−0.0449129
$560$	6.10649	+	11.2962i	0.258046	+	0.477353i
$561$		0			0
$562$	−57.9839	+	15.5367i	−2.44590	+	0.655378i
$563$	2.81334	−	10.4995i	0.118568	−	0.442503i	−0.880961	−	0.473189i	$-0.843103\pi$
$563$	2.81334	−	10.4995i	0.118568	−	0.442503i	0.999529	+	0.0306863i	$0.00976930\pi$
$564$		0			0
$565$	−0.355092	+	0.277319i	−0.0149388	+	0.0116669i
$566$			45.9018i			1.92940i
$567$		0			0
$568$	7.60616	−	7.60616i	0.319147	−	0.319147i
$569$	33.7434	+	19.4818i	1.41460	+	0.816718i	0.995817	−	0.0913694i	$-0.0291244\pi$
$569$	33.7434	+	19.4818i	1.41460	+	0.816718i	0.418780	+	0.908088i	$0.362458\pi$
$570$		0			0
$571$	−0.321858	−	0.557475i	−0.0134694	−	0.0233296i	0.859212	−	0.511619i	$-0.170954\pi$
$571$	−0.321858	−	0.557475i	−0.0134694	−	0.0233296i	−0.872682	+	0.488290i	$0.837621\pi$
$572$	−0.309171	−	1.15384i	−0.0129271	−	0.0482445i
$573$		0			0
$574$	64.5654	+	10.9139i	2.69491	+	0.455536i
$575$	−0.603661	−	35.3585i	−0.0251744	−	1.47455i
$576$		0			0
$577$	20.6712	+	5.53883i	0.860552	+	0.230584i	0.661998	−	0.749506i	$-0.269709\pi$
$577$	20.6712	+	5.53883i	0.860552	+	0.230584i	0.198554	+	0.980090i	$0.436375\pi$
$578$	−36.2888	−	9.72356i	−1.50942	−	0.404447i
$579$		0			0
$580$	−17.6321	−	41.5608i	−0.732135	−	1.72572i
$581$	−17.6040	+	6.54883i	−0.730335	+	0.271691i
$582$		0			0
$583$	−1.67889	−	6.26570i	−0.0695325	−	0.259499i
$584$	−16.3430	−	28.3070i	−0.676280	−	1.17135i
$585$		0			0
$586$	−15.4541	−	8.92244i	−0.638403	−	0.368582i
$587$	−13.3186	+	13.3186i	−0.549716	+	0.549716i	−0.926359	−	0.376643i	$-0.877079\pi$
$587$	−13.3186	+	13.3186i	−0.549716	+	0.549716i	0.376643	+	0.926359i	$0.377079\pi$
$588$		0			0
$589$		−	0.499372i		−	0.0205763i
$590$	24.6778	+	31.5987i	1.01597	+	1.30090i
$591$		0			0
$592$	−0.433777	+	1.61888i	−0.0178281	+	0.0665355i
$593$	−12.0904	+	3.23962i	−0.496494	+	0.133035i	−0.498372	−	0.866963i	$-0.666069\pi$
$593$	−12.0904	+	3.23962i	−0.496494	+	0.133035i	0.00187848	+	0.999998i	$0.499402\pi$
$594$		0			0
$595$	−24.6075	+	23.2659i	−1.00881	+	0.953808i
$596$	−52.3662			−2.14500
$597$		0			0
$598$	1.04968	−	3.91747i	0.0429247	−	0.160197i
$599$	2.15581	−	1.24466i	0.0880838	−	0.0508552i	−0.455311	−	0.890332i	$-0.650472\pi$
$599$	2.15581	−	1.24466i	0.0880838	−	0.0508552i	0.543395	+	0.839477i	$0.317139\pi$
$600$		0			0
$601$			28.8612i			1.17727i	0.808398	+	0.588636i	$0.200335\pi$
$601$			28.8612i			1.17727i	−0.808398	+	0.588636i	$0.799665\pi$
$602$	16.1169	+	22.6739i	0.656875	+	0.924120i
$603$		0			0
$604$	8.02417	+	4.63276i	0.326499	+	0.188504i
$605$	−12.3544	+	16.3884i	−0.502280	+	0.666283i
$606$		0			0
$607$	12.2147	+	45.5860i	0.495781	+	1.85028i	0.525611	+	0.850725i	$0.323837\pi$
$607$	12.2147	+	45.5860i	0.495781	+	1.85028i	−0.0298299	+	0.999555i	$0.509497\pi$
$608$	8.94065	+	8.94065i	0.362591	+	0.362591i
$609$		0			0
$610$	21.2031	+	8.57134i	0.858490	+	0.347043i
$611$	−0.172448	+	0.298689i	−0.00697651	+	0.0120837i
$612$		0			0
$613$	45.4315	+	12.1733i	1.83496	+	0.491676i	0.998418	−	0.0562243i	$-0.0179062\pi$
$613$	45.4315	+	12.1733i	1.83496	+	0.491676i	0.836543	+	0.547901i	$0.184573\pi$
$614$	−27.6753	+	47.9350i	−1.11688	+	1.93450i
$615$		0			0
$616$	−9.09878	+	11.0007i	−0.366600	+	0.443232i
$617$	9.17731	+	9.17731i	0.369465	+	0.369465i	0.867282	−	0.497817i	$-0.165865\pi$
$617$	9.17731	+	9.17731i	0.369465	+	0.369465i	−0.497817	+	0.867282i	$0.665865\pi$
$618$		0			0
$619$	10.0838	+	17.4656i	0.405302	+	0.702003i	0.994357	−	0.106090i	$-0.0338332\pi$
$619$	10.0838	+	17.4656i	0.405302	+	0.702003i	−0.589055	+	0.808093i	$0.700500\pi$
$620$	0.552083	−	0.732348i	0.0221722	−	0.0294118i
$621$		0			0
$622$	−5.44246	+	5.44246i	−0.218223	+	0.218223i
$623$	−27.0692	−	38.0821i	−1.08450	−	1.52573i
$624$		0			0
$625$	22.0647	+	11.7537i	0.882588	+	0.470147i
$626$	−18.2221	+	10.5205i	−0.728302	+	0.420486i
$627$		0			0
$628$	−7.71994	+	2.06855i	−0.308059	+	0.0825442i
$629$	−4.41996			−0.176235
$630$		0			0
$631$	32.4057			1.29005			0.645026	−	0.764161i	$-0.276847\pi$
$631$	32.4057			1.29005			0.645026	+	0.764161i	$0.276847\pi$
$632$	42.0385	−	11.2642i	1.67220	−	0.448065i
$633$		0			0
$634$	48.4658	−	27.9817i	1.92482	−	1.11130i
$635$	−1.80233	−	2.30779i	−0.0715234	−	0.0915818i
$636$		0			0
$637$	−0.123042	+	1.68005i	−0.00487510	+	0.0665659i
$638$	12.4841	−	12.4841i	0.494249	−	0.494249i
$639$		0			0
$640$	6.44209	+	45.9015i	0.254646	+	1.81442i
$641$	−18.1688	−	31.4692i	−0.717623	−	1.24296i	−0.961939	−	0.273263i	$-0.911897\pi$
$641$	−18.1688	−	31.4692i	−0.717623	−	1.24296i	0.244317	−	0.969696i	$-0.421436\pi$
$642$		0			0
$643$	4.38100	+	4.38100i	0.172770	+	0.172770i	0.788195	−	0.615425i	$-0.211016\pi$
$643$	4.38100	+	4.38100i	0.172770	+	0.172770i	−0.615425	+	0.788195i	$0.711016\pi$
$644$	−64.5026	+	23.9956i	−2.54176	+	0.945557i
$645$		0			0
$646$	30.5380	−	52.8933i	1.20150	−	2.08106i
$647$	26.9896	+	7.23185i	1.06107	+	0.284313i	0.746820	−	0.665026i	$-0.231580\pi$
$647$	26.9896	+	7.23185i	1.06107	+	0.284313i	0.314252	+	0.949340i	$0.398246\pi$
$648$		0			0
$649$	−5.07806	+	8.79546i	−0.199331	+	0.345252i
$650$	2.06166	+	1.99245i	0.0808651	+	0.0781503i
$651$		0			0
$652$	−23.0738	−	23.0738i	−0.903640	−	0.903640i
$653$	−2.63888	−	9.84844i	−0.103267	−	0.385399i	0.894875	−	0.446316i	$-0.147264\pi$
$653$	−2.63888	−	9.84844i	−0.103267	−	0.385399i	−0.998143	+	0.0609168i	$0.980598\pi$
$654$		0			0
$655$	−39.8135	−	30.0135i	−1.55564	−	1.17273i
$656$	−19.5244	−	11.2724i	−0.762300	−	0.440114i
$657$		0			0
$658$	8.99512	−	0.851184i	0.350666	−	0.0331826i
$659$			34.2801i			1.33536i	0.744448	+	0.667681i	$0.232713\pi$
$659$			34.2801i			1.33536i	−0.744448	+	0.667681i	$0.767287\pi$
$660$		0			0
$661$	−12.4580	+	7.19262i	−0.484559	+	0.279761i	−0.722315	−	0.691565i	$-0.756922\pi$
$661$	−12.4580	+	7.19262i	−0.484559	+	0.279761i	0.237755	+	0.971325i	$0.423588\pi$
$662$	−16.9533	+	63.2704i	−0.658907	+	2.45907i
$663$		0			0
$664$	28.3814			1.10141
$665$	−12.5976	−	23.3040i	−0.488515	−	0.903689i
$666$		0			0
$667$	37.5044	−	10.0493i	1.45218	−	0.389110i
$668$	−11.8386	+	44.1824i	−0.458050	+	1.70947i
$669$		0			0
$670$	9.77440	−	79.4805i	0.377618	−	3.07060i
$671$			5.79328i			0.223647i
$672$		0			0
$673$	5.06944	−	5.06944i	0.195413	−	0.195413i	−0.602618	−	0.798030i	$-0.705876\pi$
$673$	5.06944	−	5.06944i	0.195413	−	0.195413i	0.798030	+	0.602618i	$0.205876\pi$
$674$	−23.9130	−	13.8062i	−0.921096	−	0.531795i
$675$		0			0
$676$	−23.7991	−	41.2213i	−0.915351	−	1.58543i
$677$	−0.286844	−	1.07052i	−0.0110243	−	0.0411433i	0.960195	−	0.279332i	$-0.0901130\pi$
$677$	−0.286844	−	1.07052i	−0.0110243	−	0.0411433i	−0.971219	+	0.238189i	$0.923446\pi$
$678$		0			0
$679$	−14.4105	−	38.7369i	−0.553024	−	1.48659i
$680$	47.1074	−	19.9853i	1.80648	−	0.766400i
$681$		0			0
$682$	0.346437	+	0.0928275i	0.0132658	+	0.00355455i
$683$	−31.8589	−	8.53657i	−1.21905	−	0.326643i	−0.408742	−	0.912650i	$-0.634032\pi$
$683$	−31.8589	−	8.53657i	−1.21905	−	0.326643i	−0.810306	+	0.586007i	$0.800699\pi$
$684$		0			0
$685$	−10.0234	+	24.7952i	−0.382976	+	0.947377i
$686$	37.7407	−	22.8718i	1.44095	−	0.873251i
$687$		0			0
$688$	−2.47889	−	9.25134i	−0.0945068	−	0.352704i
$689$	0.578295	+	1.00164i	0.0220313	+	0.0381593i
$690$		0			0
$691$	−6.07081	−	3.50499i	−0.230945	−	0.133336i	0.380063	−	0.924961i	$-0.375902\pi$
$691$	−6.07081	−	3.50499i	−0.230945	−	0.133336i	−0.611008	+	0.791625i	$0.709236\pi$
$692$	−13.2149	+	13.2149i	−0.502356	+	0.502356i
$693$		0			0
$694$			31.7529i			1.20532i
$695$	14.3274	+	1.76196i	0.543469	+	0.0668351i
$696$		0			0
$697$	15.3883	−	57.4300i	0.582874	−	2.17532i
$698$	−29.5571	+	7.91980i	−1.11875	+	0.299769i
$699$		0			0
$700$	7.28893	−	48.1034i	0.275496	−	1.81814i
$701$	11.6433			0.439763			0.219882	−	0.975527i	$-0.429433\pi$
$701$	11.6433			0.439763			0.219882	+	0.975527i	$0.429433\pi$
$702$		0			0
$703$	0.894876	−	3.33972i	0.0337509	−	0.125960i
$704$	−12.9386	+	7.47010i	−0.487642	+	0.281540i
$705$		0			0
$706$		−	22.9477i		−	0.863648i
$707$	−1.77270	−	18.7335i	−0.0666693	−	0.704546i
$708$		0			0
$709$	7.45661	+	4.30508i	0.280039	+	0.161681i	0.633441	−	0.773791i	$-0.281642\pi$
$709$	7.45661	+	4.30508i	0.280039	+	0.161681i	−0.353402	+	0.935471i	$0.614975\pi$
$710$	−14.1969	+	1.99248i	−0.532800	+	0.0747763i
$711$		0			0
$712$	18.2725	+	68.1940i	0.684792	+	2.55568i
$713$	0.557741	+	0.557741i	0.0208876	+	0.0208876i
$714$		0			0
$715$	−0.272196	+	0.673338i	−0.0101796	+	0.0251814i
$716$	−3.81418	+	6.60636i	−0.142543	+	0.246891i
$717$		0			0
$718$	47.7585	+	12.7969i	1.78233	+	0.477575i
$719$	−11.6151	+	20.1179i	−0.433169	+	0.750271i	−0.997144	−	0.0755207i	$-0.975938\pi$
$719$	−11.6151	+	20.1179i	−0.433169	+	0.750271i	0.563975	+	0.825792i	$0.309271\pi$
$720$		0			0
$721$	−3.76174	+	22.2541i	−0.140095	+	0.828786i
$722$	1.77032	+	1.77032i	0.0658845	+	0.0658845i
$723$		0			0
$724$	36.5768	+	63.3529i	1.35937	+	2.35449i
$725$	−6.65061	+	26.6308i	−0.246998	+	0.989042i
$726$		0			0
$727$	10.6764	−	10.6764i	0.395966	−	0.395966i	−0.480841	−	0.876808i	$-0.659669\pi$
$727$	10.6764	−	10.6764i	0.395966	−	0.395966i	0.876808	+	0.480841i	$0.159669\pi$
$728$	1.05938	−	2.31450i	0.0392633	−	0.0857809i
$729$		0			0
$730$	−5.31718	+	43.2366i	−0.196798	+	1.60026i
$731$	21.8746	−	12.6293i	0.809060	−	0.467111i
$732$		0			0
$733$	13.9476	−	3.73726i	0.515168	−	0.138039i	0.00813740	−	0.999967i	$-0.497410\pi$
$733$	13.9476	−	3.73726i	0.515168	−	0.138039i	0.507031	+	0.861928i	$0.330743\pi$
$734$	−5.11647			−0.188852
$735$		0			0
$736$	−19.9713			−0.736153
$737$	19.5939	−	5.25016i	0.721749	−	0.193392i
$738$		0			0
$739$	−38.6034	+	22.2877i	−1.42005	+	0.819867i	−0.996303	−	0.0859135i	$-0.972619\pi$
$739$	−38.6034	+	22.2877i	−1.42005	+	0.819867i	−0.423748	+	0.905780i	$0.639286\pi$
$740$	5.00461	−	3.90849i	0.183973	−	0.143679i
$741$		0			0
$742$	12.6103	−	27.5505i	0.462939	−	1.01141i
$743$	26.7177	−	26.7177i	0.980178	−	0.980178i	−0.0196294	−	0.999807i	$-0.506249\pi$
$743$	26.7177	−	26.7177i	0.980178	−	0.980178i	0.999807	+	0.0196294i	$0.00624864\pi$
$744$		0			0
$745$	25.4235	+	19.1656i	0.931445	+	0.702173i
$746$	−39.3558	−	68.1662i	−1.44092	−	2.49574i
$747$		0			0
$748$	20.0918	+	20.0918i	0.734628	+	0.734628i
$749$	8.22203	−	48.6407i	0.300426	−	1.77729i
$750$		0			0
$751$	−1.98808	+	3.44345i	−0.0725460	+	0.125653i	−0.900017	−	0.435856i	$-0.856446\pi$
$751$	−1.98808	+	3.44345i	−0.0725460	+	0.125653i	0.827470	+	0.561509i	$0.189779\pi$
$752$	−3.00481	−	0.805135i	−0.109574	−	0.0293603i
$753$		0			0
$754$	−1.57397	+	2.72619i	−0.0573205	+	0.0992820i
$755$	−2.20014	−	5.18596i	−0.0800713	−	0.188736i
$756$		0			0
$757$	13.2786	+	13.2786i	0.482619	+	0.482619i	0.905967	−	0.423348i	$-0.139145\pi$
$757$	13.2786	+	13.2786i	0.482619	+	0.482619i	−0.423348	+	0.905967i	$0.639145\pi$
$758$	1.55588	+	5.80664i	0.0565123	+	0.210907i
$759$		0			0
$760$	5.56340	+	39.6406i	0.201806	+	1.43792i
$761$	17.7528	+	10.2496i	0.643540	+	0.371548i	0.785977	−	0.618256i	$-0.212160\pi$
$761$	17.7528	+	10.2496i	0.643540	+	0.371548i	−0.142437	+	0.989804i	$0.545494\pi$
$762$		0			0
$763$	−4.31453	−	45.5950i	−0.156197	−	1.65065i
$764$			14.2058i			0.513947i
$765$		0			0
$766$	9.05956	−	5.23054i	0.327335	−	0.188987i
$767$	0.468682	−	1.74914i	0.0169231	−	0.0631579i
$768$		0			0
$769$	1.00195			0.0361311			0.0180655	−	0.999837i	$-0.494249\pi$
$769$	1.00195			0.0361311			0.0180655	+	0.999837i	$0.494249\pi$
$770$	18.5087	−	4.40759i	0.667009	−	0.158839i
$771$		0			0
$772$	−71.2698	+	19.0967i	−2.56506	+	0.687305i
$773$	0.0814009	−	0.303792i	0.00292779	−	0.0109266i	−0.964446	−	0.264278i	$-0.914866\pi$
$773$	0.0814009	−	0.303792i	0.00292779	−	0.0109266i	0.967374	+	0.253352i	$0.0815329\pi$
$774$		0			0
$775$	−0.536067	+	0.153493i	−0.0192561	+	0.00551363i
$776$			62.4523i			2.24191i
$777$		0			0
$778$	−52.4753	+	52.4753i	−1.88133	+	1.88133i
$779$	40.2786	+	23.2549i	1.44313	+	0.833192i
$780$		0			0
$781$	−1.81575	−	3.14497i	−0.0649725	−	0.112536i
$782$	24.9683	+	93.1830i	0.892865	+	3.33222i
$783$		0			0
$784$	−14.9241	+	2.84998i	−0.533004	+	0.101785i
$785$	4.50506	+	1.82116i	0.160793	+	0.0650002i
$786$		0			0
$787$	21.7344	+	5.82372i	0.774749	+	0.207593i	0.624468	−	0.781050i	$-0.285316\pi$
$787$	21.7344	+	5.82372i	0.774749	+	0.207593i	0.150281	+	0.988643i	$0.451982\pi$
$788$	−54.5376	−	14.6133i	−1.94282	−	0.520578i
$789$		0			0
$790$	−53.7755	−	21.7387i	−1.91324	−	0.773427i
$791$	−0.185873	−	0.499646i	−0.00660887	−	0.0177654i
$792$		0			0
$793$	−0.267346	−	0.997750i	−0.00949375	−	0.0354311i
$794$	−14.0552	−	24.3443i	−0.498801	−	0.863949i
$795$		0			0
$796$	−75.3571	−	43.5074i	−2.67096	−	1.54208i
$797$	−6.43090	+	6.43090i	−0.227794	+	0.227794i	−0.811771	−	0.583976i	$-0.801496\pi$
$797$	−6.43090	+	6.43090i	−0.227794	+	0.227794i	0.583976	+	0.811771i	$0.301496\pi$
$798$		0			0
$799$		−	8.20390i		−	0.290233i
$800$	6.84952	−	12.3457i	0.242167	−	0.436487i
$801$		0			0
$802$	18.5357	−	69.1761i	0.654518	−	2.44269i
$803$	−10.6589	+	2.85604i	−0.376143	+	0.100787i
$804$		0			0
$805$	40.0979	+	11.9577i	1.41326	+	0.421455i
$806$	−0.0639490			−0.00225251
$807$		0			0
$808$	−7.35916	+	27.4648i	−0.258894	+	0.966207i
$809$	33.5720	−	19.3828i	1.18033	−	0.681462i	0.224237	−	0.974535i	$-0.428011\pi$
$809$	33.5720	−	19.3828i	1.18033	−	0.681462i	0.956090	+	0.293072i	$0.0946777\pi$
$810$		0			0
$811$		−	16.1078i		−	0.565620i	−0.959176	−	0.282810i	$-0.908733\pi$
$811$		−	16.1078i		−	0.565620i	0.959176	−	0.282810i	$-0.0912666\pi$
$812$	53.1803	−	5.03231i	1.86626	−	0.176599i
$813$		0			0
$814$	2.15057	+	1.24163i	0.0753774	+	0.0435192i
$815$	2.75738	+	19.6470i	0.0965869	+	0.688206i
$816$		0			0
$817$	5.11392	+	19.0854i	0.178913	+	0.667713i
$818$	−0.899750	−	0.899750i	−0.0314590	−	0.0314590i
$819$		0			0
$820$	33.3605	+	78.6343i	1.16500	+	2.74603i
$821$	3.32871	−	5.76549i	0.116173	−	0.201217i	−0.802075	−	0.597223i	$-0.796271\pi$
$821$	3.32871	−	5.76549i	0.116173	−	0.201217i	0.918248	+	0.396006i	$0.129604\pi$
$822$		0			0
$823$	27.0685	+	7.25299i	0.943550	+	0.252823i	0.697623	−	0.716465i	$-0.254241\pi$
$823$	27.0685	+	7.25299i	0.943550	+	0.252823i	0.245927	+	0.969288i	$0.420908\pi$
$824$	17.0520	−	29.5349i	0.594034	−	1.02890i
$825$		0			0
$826$	−44.4621	+	16.5403i	−1.54703	+	0.575510i
$827$	−22.5323	−	22.5323i	−0.783526	−	0.783526i	0.196898	−	0.980424i	$-0.436913\pi$
$827$	−22.5323	−	22.5323i	−0.783526	−	0.783526i	−0.980424	+	0.196898i	$0.936913\pi$
$828$		0			0
$829$	9.07352	+	15.7158i	0.315136	+	0.545832i	0.979466	−	0.201607i	$-0.0646164\pi$
$829$	9.07352	+	15.7158i	0.315136	+	0.545832i	−0.664330	+	0.747439i	$0.731283\pi$
$830$	−30.2042	−	22.7696i	−1.04840	−	0.790343i
$831$		0			0
$832$	1.88363	−	1.88363i	0.0653031	−	0.0653031i
$833$	−17.4466	−	36.0719i	−0.604489	−	1.24982i
$834$		0			0
$835$	21.9180	−	17.1175i	0.758503	−	0.592374i
$836$	−19.2492	+	11.1135i	−0.665748	+	0.384370i
$837$		0			0
$838$	−26.2840	+	7.04278i	−0.907966	+	0.243289i
$839$	3.45141			0.119156			0.0595780	−	0.998224i	$-0.481025\pi$
$839$	3.45141			0.119156			0.0595780	+	0.998224i	$0.481025\pi$
$840$		0			0
$841$	−1.13714			−0.0392118
$842$	4.42228	−	1.18495i	0.152402	−	0.0408359i
$843$		0			0
$844$	−15.4836	+	8.93949i	−0.532969	+	0.307710i
$845$	−3.53232	+	28.7230i	−0.121515	+	0.988101i
$846$		0			0
$847$	−14.0690	−	19.7929i	−0.483417	−	0.680092i
$848$	−7.37646	+	7.37646i	−0.253309	+	0.253309i
$849$		0			0
$850$	−66.1665	−	16.5240i	−2.26949	−	0.566770i
$851$	2.73061	+	4.72955i	0.0936041	+	0.162127i
$852$		0			0
$853$	−24.0073	−	24.0073i	−0.821994	−	0.821994i	0.164400	−	0.986394i	$-0.447431\pi$
$853$	−24.0073	−	24.0073i	−0.821994	−	0.821994i	−0.986394	+	0.164400i	$0.947431\pi$
$854$	−17.2468	+	20.8520i	−0.590173	+	0.713540i
$855$		0			0
$856$	−37.2705	+	64.5543i	−1.27388	+	2.20642i
$857$	−17.7563	−	4.75778i	−0.606543	−	0.162523i	−0.0575402	−	0.998343i	$-0.518326\pi$
$857$	−17.7563	−	4.75778i	−0.606543	−	0.162523i	−0.549003	+	0.835820i	$0.684992\pi$
$858$		0			0
$859$	−26.7201	+	46.2805i	−0.911677	+	1.57907i	−0.0999818	+	0.994989i	$0.531878\pi$
$859$	−26.7201	+	46.2805i	−0.911677	+	1.57907i	−0.811695	+	0.584081i	$0.801455\pi$
$860$	−13.6002	+	33.6431i	−0.463763	+	1.14722i
$861$		0			0
$862$	−45.6541	−	45.6541i	−1.55498	−	1.55498i
$863$	4.20456	+	15.6916i	0.143125	+	0.534150i	0.999832	+	0.0183460i	$0.00584003\pi$
$863$	4.20456	+	15.6916i	0.143125	+	0.534150i	−0.856707	+	0.515804i	$0.827493\pi$
$864$		0			0
$865$	11.2523	−	1.57922i	0.382591	−	0.0536951i
$866$	−61.6795	−	35.6107i	−2.09595	−	1.21010i
$867$		0			0
$868$	0.628702	+	0.884485i	0.0213395	+	0.0300214i
$869$		−	14.6929i		−	0.498423i
$870$		0			0
$871$	−3.13228	+	1.80842i	−0.106133	+	0.0612761i
$872$	−17.9113	+	66.8458i	−0.606553	+	2.26368i
$873$		0			0
$874$	−75.4643			−2.55262
$875$	−21.1442	+	20.6863i	−0.714805	+	0.699324i
$876$		0			0
$877$	−38.6892	+	10.3667i	−1.30644	+	0.350060i	−0.843883	−	0.536528i	$-0.819736\pi$
$877$	−38.6892	+	10.3667i	−1.30644	+	0.350060i	−0.462560	+	0.886588i	$0.653069\pi$
$878$	−24.1715	+	90.2094i	−0.815750	+	3.04442i
$879$		0			0
$880$	−6.50167	−	0.799566i	−0.219171	−	0.0269534i
$881$			41.3164i			1.39199i	0.718049	+	0.695993i	$0.245035\pi$
$881$			41.3164i			1.39199i	−0.718049	+	0.695993i	$0.754965\pi$
$882$		0			0
$883$	−12.7996	+	12.7996i	−0.430740	+	0.430740i	−0.888880	−	0.458140i	$-0.848516\pi$
$883$	−12.7996	+	12.7996i	−0.430740	+	0.430740i	0.458140	+	0.888880i	$0.348516\pi$
$884$	−4.38751	−	2.53313i	−0.147568	−	0.0851984i
$885$		0			0
$886$	35.0223	+	60.6605i	1.17660	+	2.03793i
$887$	−9.01326	−	33.6379i	−0.302636	−	1.12945i	−0.934962	−	0.354749i	$-0.884566\pi$
$887$	−9.01326	−	33.6379i	−0.302636	−	1.12945i	0.632326	−	0.774702i	$-0.282100\pi$
$888$		0			0
$889$	3.24726	−	1.20801i	0.108910	−	0.0405154i
$890$	35.2640	−	87.2334i	1.18205	−	2.92407i
$891$		0			0
$892$	40.8277	+	10.9397i	1.36701	+	0.366289i
$893$	6.19887	+	1.66098i	0.207437	+	0.0555827i
$894$		0			0
$895$	4.26964	−	1.81139i	0.142718	−	0.0605482i
$896$	−54.0766	−	9.14088i	−1.80657	−	0.305375i
$897$		0			0
$898$	−0.695927	−	2.59723i	−0.0232234	−	0.0866709i
$899$	−0.306112	−	0.530202i	−0.0102094	−	0.0176832i
$900$		0			0
$901$	−23.8255	−	13.7556i	−0.793741	−	0.458267i
$902$	−23.6203	+	23.6203i	−0.786468	+	0.786468i
$903$		0			0
$904$			0.805537i			0.0267918i
$905$	5.42881	−	44.1443i	0.180460	−	1.46741i
$906$		0			0
$907$	−11.8142	+	44.0913i	−0.392285	+	1.46403i	0.434070	+	0.900879i	$0.357077\pi$
$907$	−11.8142	+	44.0913i	−0.392285	+	1.46403i	−0.826355	+	0.563149i	$0.809590\pi$
$908$	0.217768	−	0.0583509i	0.00722690	−	0.00193644i
$909$		0			0
$910$	−2.98428	+	1.61324i	−0.0989279	+	0.0534783i
$911$	38.9288			1.28977			0.644884	−	0.764281i	$-0.276906\pi$
$911$	38.9288			1.28977			0.644884	+	0.764281i	$0.276906\pi$
$912$		0			0
$913$	2.47990	−	9.25511i	0.0820727	−	0.306299i
$914$	60.9343	−	35.1804i	2.01553	−	1.16367i
$915$		0			0
$916$			44.1581i			1.45902i
$917$	48.0843	−	34.1789i	1.58788	−	1.12869i
$918$		0			0
$919$	−27.0483	−	15.6164i	−0.892242	−	0.515136i	−0.0175667	−	0.999846i	$-0.505592\pi$
$919$	−27.0483	−	15.6164i	−0.892242	−	0.515136i	−0.874675	+	0.484710i	$0.838925\pi$
$920$	−50.4876	−	38.0603i	−1.66453	−	1.25481i
$921$		0			0
$922$	−6.01006	−	22.4299i	−0.197931	−	0.738688i
$923$	0.457851	+	0.457851i	0.0150703	+	0.0150703i
$924$		0			0
$925$	−3.86019	+	0.0659034i	−0.126922	+	0.00216689i
$926$	−25.9813	+	45.0009i	−0.853798	+	1.47882i
$927$		0			0
$928$	14.9732	+	4.01205i	0.491519	+	0.131702i
$929$	−8.25525	+	14.2985i	−0.270846	+	0.469119i	−0.969079	−	0.246752i	$-0.920637\pi$
$929$	−8.25525	+	14.2985i	−0.270846	+	0.469119i	0.698233	+	0.715871i	$0.253970\pi$
$930$		0			0
$931$	30.7882	−	5.87946i	1.00904	−	0.192692i
$932$	5.22782	+	5.22782i	0.171243	+	0.171243i
$933$		0			0
$934$	13.2025	+	22.8675i	0.432000	+	0.748247i
$935$	−2.40102	−	17.1079i	−0.0785218	−	0.559488i
$936$		0			0
$937$	−15.7177	+	15.7177i	−0.513476	+	0.513476i	−0.915590	−	0.402114i	$-0.868276\pi$
$937$	−15.7177	+	15.7177i	−0.513476	+	0.513476i	0.402114	+	0.915590i	$0.368276\pi$
$938$	86.1549	+	39.4345i	2.81306	+	1.28758i
$939$		0			0
$940$	7.25457	+	9.28908i	0.236618	+	0.302976i
$941$	43.7881	−	25.2811i	1.42745	−	0.824139i	0.430532	−	0.902575i	$-0.358326\pi$
$941$	43.7881	−	25.2811i	1.42745	−	0.824139i	0.996919	+	0.0784363i	$0.0249927\pi$
$942$		0			0
$943$	−70.9595	+	19.0135i	−2.31076	+	0.619166i
$944$	16.3330			0.531593
$945$		0			0
$946$	−14.1910			−0.461389
$947$	−20.5111	+	5.49593i	−0.666521	+	0.178594i	−0.576187	−	0.817318i	$-0.695460\pi$
$947$	−20.5111	+	5.49593i	−0.666521	+	0.178594i	−0.0903339	+	0.995912i	$0.528793\pi$
$948$		0			0
$949$	1.70393	−	0.983765i	0.0553119	−	0.0319344i
$950$	25.8818	−	46.6500i	0.839717	−	1.51353i
$951$		0			0
$952$	5.70390	+	60.2776i	0.184865	+	1.95361i
$953$	−17.8597	+	17.8597i	−0.578533	+	0.578533i	−0.934499	−	0.355966i	$-0.884152\pi$
$953$	−17.8597	+	17.8597i	−0.578533	+	0.578533i	0.355966	+	0.934499i	$0.384152\pi$
$954$		0			0
$955$	5.19920	−	6.89683i	0.168242	−	0.223176i
$956$	14.7488	+	25.5457i	0.477011	+	0.826207i
$957$		0			0
$958$	−3.66626	−	3.66626i	−0.118451	−	0.118451i
$959$	−24.3846	−	20.1686i	−0.787420	−	0.651279i
$960$		0			0
$961$	−15.4938	+	26.8360i	−0.499799	+	0.865678i
$962$	−0.427681	−	0.114597i	−0.0137890	−	0.00369475i
$963$		0			0
$964$	17.4119	−	30.1583i	0.560800	−	0.971334i
$965$	41.5903	+	16.8128i	1.33884	+	0.541224i
$966$		0			0
$967$	−40.6275	−	40.6275i	−1.30649	−	1.30649i	−0.923929	−	0.382564i	$-0.875041\pi$
$967$	−40.6275	−	40.6275i	−1.30649	−	1.30649i	−0.382564	−	0.923929i	$-0.624959\pi$
$968$	9.49703	+	35.4434i	0.305246	+	1.13919i
$969$		0			0
$970$	50.1037	−	66.4634i	1.60873	−	2.13401i
$971$	−41.4744	−	23.9452i	−1.33098	−	0.768439i	−0.345526	−	0.938409i	$-0.612300\pi$
$971$	−41.4744	−	23.9452i	−1.33098	−	0.768439i	−0.985449	+	0.169970i	$0.945633\pi$
$972$		0			0
$973$	−7.10859	+	15.5306i	−0.227891	+	0.497887i
$974$		−	46.1200i		−	1.47778i
$975$		0			0
$976$	8.06849	−	4.65834i	0.258266	−	0.149110i
$977$	10.6269	−	39.6600i	0.339983	−	1.26883i	−0.558381	−	0.829584i	$-0.688577\pi$
$977$	10.6269	−	39.6600i	0.339983	−	1.26883i	0.898365	−	0.439251i	$-0.144756\pi$
$978$		0			0
$979$	23.8346			0.761756
$980$	51.6521	+	25.4156i	1.64997	+	0.811872i
$981$		0			0
$982$	−16.2895	+	4.36477i	−0.519820	+	0.139285i
$983$	2.33114	−	8.69992i	0.0743517	−	0.277484i	−0.918734	−	0.394877i	$-0.870787\pi$
$983$	2.33114	−	8.69992i	0.0743517	−	0.277484i	0.993086	+	0.117393i	$0.0374537\pi$
$984$		0			0
$985$	21.1294	+	27.0550i	0.673238	+	0.862045i
$986$		−	74.8784i		−	2.38461i
$987$		0			0
$988$	2.80234	−	2.80234i	0.0891544	−	0.0891544i
$989$	−27.0278	−	15.6045i	−0.859434	−	0.496195i
$990$		0			0
$991$	15.0297	+	26.0323i	0.477436	+	0.826943i	0.999666	−	0.0258619i	$-0.00823302\pi$
$991$	15.0297	+	26.0323i	0.477436	+	0.826943i	−0.522230	+	0.852805i	$0.674900\pi$
$992$	0.0815033	+	0.304175i	0.00258773	+	0.00965755i
$993$		0			0
$994$	2.82719	−	16.7254i	0.0896729	−	0.530496i
$995$	20.6621	+	48.7027i	0.655032	+	1.54398i
$996$		0			0
$997$	14.2514	+	3.81865i	0.451346	+	0.120938i	0.477329	−	0.878725i	$-0.341605\pi$
$997$	14.2514	+	3.81865i	0.451346	+	0.120938i	−0.0259830	+	0.999662i	$0.508272\pi$
$998$	59.1466	+	15.8483i	1.87225	+	0.501669i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cc.b.82.5	✓	128
3.2	odd	2	inner	945.2.cc.b.82.28	yes	128
5.3	odd	4	inner	945.2.cc.b.838.28	yes	128
7.3	odd	6	inner	945.2.cc.b.892.28	yes	128
15.8	even	4	inner	945.2.cc.b.838.5	yes	128
21.17	even	6	inner	945.2.cc.b.892.5	yes	128
35.3	even	12	inner	945.2.cc.b.703.5	yes	128
105.38	odd	12	inner	945.2.cc.b.703.28	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cc.b.82.5	✓	128	1.1	even	1	trivial
945.2.cc.b.82.28	yes	128	3.2	odd	2	inner
945.2.cc.b.703.5	yes	128	35.3	even	12	inner
945.2.cc.b.703.28	yes	128	105.38	odd	12	inner
945.2.cc.b.838.5	yes	128	15.8	even	4	inner
945.2.cc.b.838.28	yes	128	5.3	odd	4	inner
945.2.cc.b.892.5	yes	128	21.17	even	6	inner
945.2.cc.b.892.28	yes	128	7.3	odd	6	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30162 + 0.616717i) q^{2} +(3.18506 - 1.83889i) q^{4} +(-2.21935 - 0.272932i) q^{5} +(1.10114 - 2.40572i) q^{7} +(-2.82691 + 2.82691i) q^{8} +O(q^{10})\)	\(q+(-2.30162 + 0.616717i) q^{2} +(3.18506 - 1.83889i) q^{4} +(-2.21935 - 0.272932i) q^{5} +(1.10114 - 2.40572i) q^{7} +(-2.82691 + 2.82691i) q^{8} +(5.27642 - 0.740523i) q^{10} +(0.674840 + 1.16886i) q^{11} +(-0.170165 - 0.170165i) q^{13} +(-1.05075 + 6.21614i) q^{14} +(1.08527 - 1.87974i) q^{16} +(5.52917 + 1.48154i) q^{17} +(-2.23890 + 3.87789i) q^{19} +(-7.57064 + 3.21184i) q^{20} +(-2.27408 - 2.27408i) q^{22} +(-1.83056 - 6.83174i) q^{23} +(4.85102 + 1.21146i) q^{25} +(0.496598 + 0.286711i) q^{26} +(-0.916677 - 9.68723i) q^{28} +5.48973i q^{29} +(-0.0965807 + 0.0557609i) q^{31} +(0.730829 - 2.72749i) q^{32} -13.6397 q^{34} +(-3.10041 + 5.03860i) q^{35} +(-0.745840 + 0.199847i) q^{37} +(2.76153 - 10.3062i) q^{38} +(7.04544 - 5.50233i) q^{40} -10.3867i q^{41} +(3.12017 - 3.12017i) q^{43} +(4.29881 + 2.48192i) q^{44} +(8.42650 + 14.5951i) q^{46} +(-0.370937 - 1.38436i) q^{47} +(-4.57499 - 5.29806i) q^{49} +(-11.9123 + 0.203374i) q^{50} +(-0.854900 - 0.229070i) q^{52} +(-4.64236 - 1.24392i) q^{53} +(-1.17869 - 2.77829i) q^{55} +(3.68793 + 9.91356i) q^{56} +(-3.38561 - 12.6353i) q^{58} +(3.76242 + 6.51670i) q^{59} +(3.71727 + 2.14617i) q^{61} +(0.187903 - 0.187903i) q^{62} +11.0694i q^{64} +(0.331212 + 0.424099i) q^{65} +(3.88993 - 14.5174i) q^{67} +(20.3351 - 5.44877i) q^{68} +(4.02857 - 13.5090i) q^{70} -2.69063 q^{71} +(-2.11608 + 7.89733i) q^{73} +(1.59339 - 0.919945i) q^{74} +16.4684i q^{76} +(3.55504 - 0.336404i) q^{77} +(-9.42775 - 5.44311i) q^{79} +(-2.92164 + 3.87560i) q^{80} +(6.40567 + 23.9063i) q^{82} +(-5.01986 - 5.01986i) q^{83} +(-11.8668 - 4.79713i) q^{85} +(-5.25717 + 9.10569i) q^{86} +(-5.21196 - 1.39654i) q^{88} +(8.82970 - 15.2935i) q^{89} +(-0.596744 + 0.221994i) q^{91} +(-18.3933 - 18.3933i) q^{92} +(1.70751 + 2.95750i) q^{94} +(6.02730 - 7.99532i) q^{95} +(11.0460 - 11.0460i) q^{97} +(13.7973 + 9.37265i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{7}+O(q^{10}) \) 128 * q + 4 * q^7	\( 128 q + 4 q^{7} - 12 q^{10} + 64 q^{16} + 40 q^{22} - 16 q^{25} + 52 q^{28} + 16 q^{37} - 60 q^{40} - 32 q^{43} - 24 q^{58} + 48 q^{61} - 32 q^{67} + 40 q^{70} + 156 q^{82} - 8 q^{85} + 84 q^{88} + 96 q^{91}+O(q^{100}) \) 128 * q + 4 * q^7 - 12 * q^10 + 64 * q^16 + 40 * q^22 - 16 * q^25 + 52 * q^28 + 16 * q^37 - 60 * q^40 - 32 * q^43 - 24 * q^58 + 48 * q^61 - 32 * q^67 + 40 * q^70 + 156 * q^82 - 8 * q^85 + 84 * q^88 + 96 * q^91

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