LMFDB - Embedded newform 675.2.f.g.107.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(107,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,-8,0,0,0,0,0,16,0,0,-16,0,0,0,0,0,8,0,0,0,0,0,-40, 0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(31)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.33973862400.8
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 44x^{4} + 100 $ x^8 + 44*x^4 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.1
Root			$-1.79576 + 1.79576i$ of defining polynomial
Character	$\chi$	$=$	675.107
Dual form			675.2.f.g.593.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.79576 + 1.79576i) q^{2} -4.44949i q^{4} +(-2.22474 - 2.22474i) q^{7} +(4.39869 + 4.39869i) q^{8} +0.807175i q^{11} +(0.775255 - 0.775255i) q^{13} +7.99020 q^{14} -6.89898 q^{16} +(-0.807175 + 0.807175i) q^{17} +3.00000i q^{19} +(-1.44949 - 1.44949i) q^{22} +(1.79576 + 1.79576i) q^{23} +2.78434i q^{26} +(-9.89898 + 9.89898i) q^{28} -6.37586 q^{29} -5.34847 q^{31} +(3.59151 - 3.59151i) q^{32} -2.89898i q^{34} +(5.67423 + 5.67423i) q^{37} +(-5.38727 - 5.38727i) q^{38} +11.5817i q^{41} +(-3.44949 + 3.44949i) q^{43} +3.59151 q^{44} -6.44949 q^{46} +(-7.18303 + 7.18303i) q^{47} +2.89898i q^{49} +(-3.44949 - 3.44949i) q^{52} +(-7.00162 - 7.00162i) q^{53} -19.5719i q^{56} +(11.4495 - 11.4495i) q^{58} -6.82021 q^{59} -1.00000 q^{61} +(9.60455 - 9.60455i) q^{62} -0.898979i q^{64} +(6.22474 + 6.22474i) q^{67} +(3.59151 + 3.59151i) q^{68} -9.96737i q^{71} +(2.67423 - 2.67423i) q^{73} -20.3791 q^{74} +13.3485 q^{76} +(1.79576 - 1.79576i) q^{77} -0.550510i q^{79} +(-20.7980 - 20.7980i) q^{82} +(-2.60293 - 2.60293i) q^{83} -12.3889i q^{86} +(-3.55051 + 3.55051i) q^{88} +10.7745 q^{89} -3.44949 q^{91} +(7.99020 - 7.99020i) q^{92} -25.7980i q^{94} +(2.12372 + 2.12372i) q^{97} +(-5.20586 - 5.20586i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{7} + 16 q^{13} - 16 q^{16} + 8 q^{22} - 40 q^{28} + 16 q^{31} + 16 q^{37} - 8 q^{43} - 32 q^{46} - 8 q^{52} + 72 q^{58} - 8 q^{61} + 40 q^{67} - 8 q^{73} + 48 q^{76} - 88 q^{82} - 48 q^{88} - 8 q^{91}+ \cdots - 32 q^{97}+O(q^{100}) $ 8 * q - 8 * q^7 + 16 * q^13 - 16 * q^16 + 8 * q^22 - 40 * q^28 + 16 * q^31 + 16 * q^37 - 8 * q^43 - 32 * q^46 - 8 * q^52 + 72 * q^58 - 8 * q^61 + 40 * q^67 - 8 * q^73 + 48 * q^76 - 88 * q^82 - 48 * q^88 - 8 * q^91 - 32 * q^97

Character values

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

$n$	$326$	$352$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.79576	+	1.79576i	−1.26979	+	1.26979i	−0.323597	+	0.946195i	$0.604892\pi$
$2$	−1.79576	+	1.79576i	−1.26979	+	1.26979i	−0.946195	+	0.323597i	$0.895108\pi$
$3$		0			0
$3$		0			0
$4$		−	4.44949i		−	2.22474i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.22474	−	2.22474i	−0.840875	−	0.840875i	0.148098	−	0.988973i	$-0.452685\pi$
$7$	−2.22474	−	2.22474i	−0.840875	−	0.840875i	−0.988973	+	0.148098i	$0.952685\pi$
$8$	4.39869	+	4.39869i	1.55517	+	1.55517i
$9$		0			0
$10$		0			0
$11$			0.807175i			0.243372i	0.992569	+	0.121686i	$0.0388301\pi$
$11$			0.807175i			0.243372i	−0.992569	+	0.121686i	$0.961170\pi$
$12$		0			0
$13$	0.775255	−	0.775255i	0.215017	−	0.215017i	−0.591378	−	0.806395i	$-0.701416\pi$
$13$	0.775255	−	0.775255i	0.215017	−	0.215017i	0.806395	+	0.591378i	$0.201416\pi$
$14$	7.99020			2.13547
$15$		0			0
$16$	−6.89898			−1.72474
$17$	−0.807175	+	0.807175i	−0.195769	+	0.195769i	−0.798183	−	0.602415i	$-0.794205\pi$
$17$	−0.807175	+	0.807175i	−0.195769	+	0.195769i	0.602415	+	0.798183i	$0.294205\pi$
$18$		0			0
$19$			3.00000i			0.688247i	0.938924	+	0.344124i	$0.111824\pi$
$19$			3.00000i			0.688247i	−0.938924	+	0.344124i	$0.888176\pi$
$20$		0			0
$21$		0			0
$22$	−1.44949	−	1.44949i	−0.309032	−	0.309032i
$23$	1.79576	+	1.79576i	0.374441	+	0.374441i	0.869092	−	0.494651i	$-0.164704\pi$
$23$	1.79576	+	1.79576i	0.374441	+	0.374441i	−0.494651	+	0.869092i	$0.664704\pi$
$24$		0			0
$25$		0			0
$26$			2.78434i			0.546054i
$27$		0			0
$28$	−9.89898	+	9.89898i	−1.87073	+	1.87073i
$29$	−6.37586			−1.18397			−0.591983	−	0.805950i	$-0.701655\pi$
$29$	−6.37586			−1.18397			−0.591983	+	0.805950i	$0.701655\pi$
$30$		0			0
$31$	−5.34847			−0.960613			−0.480307	−	0.877101i	$-0.659475\pi$
$31$	−5.34847			−0.960613			−0.480307	+	0.877101i	$0.659475\pi$
$32$	3.59151	−	3.59151i	0.634896	−	0.634896i
$33$		0			0
$34$		−	2.89898i		−	0.497171i
$35$		0			0
$36$		0			0
$37$	5.67423	+	5.67423i	0.932838	+	0.932838i	0.997882	−	0.0650440i	$-0.0207188\pi$
$37$	5.67423	+	5.67423i	0.932838	+	0.932838i	−0.0650440	+	0.997882i	$0.520719\pi$
$38$	−5.38727	−	5.38727i	−0.873931	−	0.873931i
$39$		0			0
$40$		0			0
$41$			11.5817i			1.80876i	0.426727	+	0.904380i	$0.359666\pi$
$41$			11.5817i			1.80876i	−0.426727	+	0.904380i	$0.640334\pi$
$42$		0			0
$43$	−3.44949	+	3.44949i	−0.526042	+	0.526042i	−0.919390	−	0.393348i	$-0.871317\pi$
$43$	−3.44949	+	3.44949i	−0.526042	+	0.526042i	0.393348	+	0.919390i	$0.371317\pi$
$44$	3.59151			0.541441
$45$		0			0
$46$	−6.44949			−0.950925
$47$	−7.18303	+	7.18303i	−1.04775	+	1.04775i	−0.0489514	+	0.998801i	$0.515588\pi$
$47$	−7.18303	+	7.18303i	−1.04775	+	1.04775i	−0.998801	+	0.0489514i	$0.984412\pi$
$48$		0			0
$49$			2.89898i			0.414140i
$50$		0			0
$51$		0			0
$52$	−3.44949	−	3.44949i	−0.478358	−	0.478358i
$53$	−7.00162	−	7.00162i	−0.961747	−	0.961747i	0.0375481	−	0.999295i	$-0.488045\pi$
$53$	−7.00162	−	7.00162i	−0.961747	−	0.961747i	−0.999295	+	0.0375481i	$0.988045\pi$
$54$		0			0
$55$		0			0
$56$		−	19.5719i		−	2.61541i
$57$		0			0
$58$	11.4495	−	11.4495i	1.50339	−	1.50339i
$59$	−6.82021			−0.887916			−0.443958	−	0.896048i	$-0.646426\pi$
$59$	−6.82021			−0.887916			−0.443958	+	0.896048i	$0.646426\pi$
$60$		0			0
$61$	−1.00000			−0.128037			−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000			−0.128037			−0.0640184	+	0.997949i	$0.520392\pi$
$62$	9.60455	−	9.60455i	1.21978	−	1.21978i
$63$		0			0
$64$		−	0.898979i		−	0.112372i
$65$		0			0
$66$		0			0
$67$	6.22474	+	6.22474i	0.760474	+	0.760474i	0.976408	−	0.215934i	$-0.0692797\pi$
$67$	6.22474	+	6.22474i	0.760474	+	0.760474i	−0.215934	+	0.976408i	$0.569280\pi$
$68$	3.59151	+	3.59151i	0.435535	+	0.435535i
$69$		0			0
$70$		0			0
$71$		−	9.96737i		−	1.18291i	−0.806338	−	0.591455i	$-0.798554\pi$
$71$		−	9.96737i		−	1.18291i	0.806338	−	0.591455i	$-0.201446\pi$
$72$		0			0
$73$	2.67423	−	2.67423i	0.312995	−	0.312995i	−0.533073	−	0.846069i	$-0.678963\pi$
$73$	2.67423	−	2.67423i	0.312995	−	0.312995i	0.846069	+	0.533073i	$0.178963\pi$
$74$	−20.3791			−2.36902
$75$		0			0
$76$	13.3485			1.53117
$77$	1.79576	−	1.79576i	0.204646	−	0.204646i
$78$		0			0
$79$		−	0.550510i		−	0.0619372i	−0.999520	−	0.0309686i	$-0.990141\pi$
$79$		−	0.550510i		−	0.0619372i	0.999520	−	0.0309686i	$-0.00985919\pi$
$80$		0			0
$81$		0			0
$82$	−20.7980	−	20.7980i	−2.29675	−	2.29675i
$83$	−2.60293	−	2.60293i	−0.285709	−	0.285709i	0.549672	−	0.835381i	$-0.314753\pi$
$83$	−2.60293	−	2.60293i	−0.285709	−	0.285709i	−0.835381	+	0.549672i	$0.814753\pi$
$84$		0			0
$85$		0			0
$86$		−	12.3889i		−	1.33593i
$87$		0			0
$88$	−3.55051	+	3.55051i	−0.378486	+	0.378486i
$89$	10.7745			1.14210			0.571050	−	0.820915i	$-0.306536\pi$
$89$	10.7745			1.14210			0.571050	+	0.820915i	$0.306536\pi$
$90$		0			0
$91$	−3.44949			−0.361605
$92$	7.99020	−	7.99020i	0.833036	−	0.833036i
$93$		0			0
$94$		−	25.7980i		−	2.66086i
$95$		0			0
$96$		0			0
$97$	2.12372	+	2.12372i	0.215632	+	0.215632i	0.806655	−	0.591023i	$-0.201276\pi$
$97$	2.12372	+	2.12372i	0.215632	+	0.215632i	−0.591023	+	0.806655i	$0.701276\pi$
$98$	−5.20586	−	5.20586i	−0.525872	−	0.525872i
$99$		0			0
$100$		0			0
$101$			9.16020i			0.911474i	0.890115	+	0.455737i	$0.150624\pi$
$101$			9.16020i			0.911474i	−0.890115	+	0.455737i	$0.849376\pi$
$102$		0			0
$103$	−9.57321	+	9.57321i	−0.943277	+	0.943277i	−0.998475	−	0.0551986i	$-0.982421\pi$
$103$	−9.57321	+	9.57321i	−0.943277	+	0.943277i	0.0551986	+	0.998475i	$0.482421\pi$
$104$	6.82021			0.668777
$105$		0			0
$106$	25.1464			2.44244
$107$	−6.19445	+	6.19445i	−0.598840	+	0.598840i	−0.940004	−	0.341164i	$-0.889179\pi$
$107$	−6.19445	+	6.19445i	−0.598840	+	0.598840i	0.341164	+	0.940004i	$0.389179\pi$
$108$		0			0
$109$			7.34847i			0.703856i	0.936027	+	0.351928i	$0.114474\pi$
$109$			7.34847i			0.703856i	−0.936027	+	0.351928i	$0.885526\pi$
$110$		0			0
$111$		0			0
$112$	15.3485	+	15.3485i	1.45029	+	1.45029i
$113$	−8.97879	−	8.97879i	−0.844653	−	0.844653i	0.144807	−	0.989460i	$-0.453744\pi$
$113$	−8.97879	−	8.97879i	−0.844653	−	0.844653i	−0.989460	+	0.144807i	$0.953744\pi$
$114$		0			0
$115$		0			0
$116$			28.3693i			2.63402i
$117$		0			0
$118$	12.2474	−	12.2474i	1.12747	−	1.12747i
$119$	3.59151			0.329234
$120$		0			0
$121$	10.3485			0.940770
$122$	1.79576	−	1.79576i	0.162580	−	0.162580i
$123$		0			0
$124$			23.7980i			2.13712i
$125$		0			0
$126$		0			0
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	0.324676	−	0.945825i	$-0.394745\pi$
$127$	−7.00000	−	7.00000i	−0.621150	−	0.621150i	−0.945825	+	0.324676i	$0.894745\pi$
$128$	8.79738	+	8.79738i	0.777586	+	0.777586i
$129$		0			0
$130$		0			0
$131$		−	1.61435i		−	0.141046i	−0.997510	−	0.0705232i	$-0.977533\pi$
$131$		−	1.61435i		−	0.141046i	0.997510	−	0.0705232i	$-0.0224669\pi$
$132$		0			0
$133$	6.67423	−	6.67423i	0.578730	−	0.578730i
$134$	−22.3563			−1.93129
$135$		0			0
$136$	−7.10102			−0.608907
$137$	−4.21728	+	4.21728i	−0.360307	+	0.360307i	−0.863926	−	0.503619i	$-0.832001\pi$
$137$	−4.21728	+	4.21728i	−0.360307	+	0.360307i	0.503619	+	0.863926i	$0.332001\pi$
$138$		0			0
$139$			15.2474i			1.29327i	0.762799	+	0.646636i	$0.223825\pi$
$139$			15.2474i			1.29327i	−0.762799	+	0.646636i	$0.776175\pi$
$140$		0			0
$141$		0			0
$142$	17.8990	+	17.8990i	1.50205	+	1.50205i
$143$	0.625766	+	0.625766i	0.0523292	+	0.0523292i
$144$		0			0
$145$		0			0
$146$			9.60455i			0.794879i
$147$		0			0
$148$	25.2474	−	25.2474i	2.07533	−	2.07533i
$149$	−1.97717			−0.161976			−0.0809879	−	0.996715i	$-0.525808\pi$
$149$	−1.97717			−0.161976			−0.0809879	+	0.996715i	$0.525808\pi$
$150$		0			0
$151$	−20.3485			−1.65593			−0.827967	−	0.560776i	$-0.810503\pi$
$151$	−20.3485			−1.65593			−0.827967	+	0.560776i	$0.810503\pi$
$152$	−13.1961	+	13.1961i	−1.07034	+	1.07034i
$153$		0			0
$154$			6.44949i			0.519715i
$155$		0			0
$156$		0			0
$157$	−0.449490	−	0.449490i	−0.0358732	−	0.0358732i	0.688943	−	0.724816i	$-0.258075\pi$
$157$	−0.449490	−	0.449490i	−0.0358732	−	0.0358732i	−0.724816	+	0.688943i	$0.758075\pi$
$158$	0.988583	+	0.988583i	0.0786474	+	0.0786474i
$159$		0			0
$160$		0			0
$161$		−	7.99020i		−	0.629716i
$162$		0			0
$163$	−10.6742	+	10.6742i	−0.836071	+	0.836071i	−0.988339	−	0.152269i	$-0.951342\pi$
$163$	−10.6742	+	10.6742i	−0.836071	+	0.836071i	0.152269	+	0.988339i	$0.451342\pi$
$164$	51.5327			4.02403
$165$		0			0
$166$	9.34847			0.725582
$167$	−2.78434	+	2.78434i	−0.215459	+	0.215459i	−0.806582	−	0.591123i	$-0.798685\pi$
$167$	−2.78434	+	2.78434i	−0.215459	+	0.215459i	0.591123	+	0.806582i	$0.298685\pi$
$168$		0			0
$169$			11.7980i			0.907535i
$170$		0			0
$171$		0			0
$172$	15.3485	+	15.3485i	1.17031	+	1.17031i
$173$	15.9804	+	15.9804i	1.21497	+	1.21497i	0.969372	+	0.245596i	$0.0789835\pi$
$173$	15.9804	+	15.9804i	1.21497	+	1.21497i	0.245596	+	0.969372i	$0.421016\pi$
$174$		0			0
$175$		0			0
$176$		−	5.56868i		−	0.419755i
$177$		0			0
$178$	−19.3485	+	19.3485i	−1.45023	+	1.45023i
$179$	13.1961			0.986320			0.493160	−	0.869938i	$-0.335842\pi$
$179$	13.1961			0.986320			0.493160	+	0.869938i	$0.335842\pi$
$180$		0			0
$181$	6.34847			0.471878			0.235939	−	0.971768i	$-0.424183\pi$
$181$	6.34847			0.471878			0.235939	+	0.971768i	$0.424183\pi$
$182$	6.19445	−	6.19445i	0.459163	−	0.459163i
$183$		0			0
$184$			15.7980i			1.16464i
$185$		0			0
$186$		0			0
$187$	−0.651531	−	0.651531i	−0.0476446	−	0.0476446i
$188$	31.9608	+	31.9608i	2.33098	+	2.33098i
$189$		0			0
$190$		0			0
$191$			14.0032i			1.01324i	0.862170	+	0.506620i	$0.169105\pi$
$191$			14.0032i			1.01324i	−0.862170	+	0.506620i	$0.830895\pi$
$192$		0			0
$193$	−0.876276	+	0.876276i	−0.0630757	+	0.0630757i	−0.737941	−	0.674865i	$-0.764202\pi$
$193$	−0.876276	+	0.876276i	−0.0630757	+	0.0630757i	0.674865	+	0.737941i	$0.264202\pi$
$194$	−7.62739			−0.547615
$195$		0			0
$196$	12.8990			0.921356
$197$	12.3889	−	12.3889i	0.882672	−	0.882672i	−0.111133	−	0.993806i	$-0.535448\pi$
$197$	12.3889	−	12.3889i	0.882672	−	0.882672i	0.993806	+	0.111133i	$0.0354481\pi$
$198$		0			0
$199$		−	10.3485i		−	0.733584i	−0.930303	−	0.366792i	$-0.880456\pi$
$199$		−	10.3485i		−	0.733584i	0.930303	−	0.366792i	$-0.119544\pi$
$200$		0			0
$201$		0			0
$202$	−16.4495	−	16.4495i	−1.15738	−	1.15738i
$203$	14.1847	+	14.1847i	0.995567	+	0.995567i
$204$		0			0
$205$		0			0
$206$		−	34.3823i		−	2.39553i
$207$		0			0
$208$	−5.34847	+	5.34847i	−0.370850	+	0.370850i
$209$	−2.42152			−0.167500
$210$		0			0
$211$	−2.34847			−0.161675			−0.0808376	−	0.996727i	$-0.525760\pi$
$211$	−2.34847			−0.161675			−0.0808376	+	0.996727i	$0.525760\pi$
$212$	−31.1536	+	31.1536i	−2.13964	+	2.13964i
$213$		0			0
$214$		−	22.2474i		−	1.52080i
$215$		0			0
$216$		0			0
$217$	11.8990	+	11.8990i	0.807755	+	0.807755i
$218$	−13.1961	−	13.1961i	−0.893751	−	0.893751i
$219$		0			0
$220$		0			0
$221$			1.25153i			0.0841872i
$222$		0			0
$223$	15.8990	−	15.8990i	1.06467	−	1.06467i	0.0669158	−	0.997759i	$-0.478684\pi$
$223$	15.8990	−	15.8990i	1.06467	−	1.06467i	0.997759	−	0.0669158i	$-0.0213159\pi$
$224$	−15.9804			−1.06774
$225$		0			0
$226$	32.2474			2.14507
$227$	11.4003	−	11.4003i	0.756665	−	0.756665i	−0.219049	−	0.975714i	$-0.570295\pi$
$227$	11.4003	−	11.4003i	0.756665	−	0.756665i	0.975714	+	0.219049i	$0.0702954\pi$
$228$		0			0
$229$		−	8.44949i		−	0.558358i	−0.960239	−	0.279179i	$-0.909938\pi$
$229$		−	8.44949i		−	0.558358i	0.960239	−	0.279179i	$-0.0900623\pi$
$230$		0			0
$231$		0			0
$232$	−28.0454	−	28.0454i	−1.84127	−	1.84127i
$233$	−9.96737	−	9.96737i	−0.652984	−	0.652984i	0.300726	−	0.953710i	$-0.402771\pi$
$233$	−9.96737	−	9.96737i	−0.652984	−	0.652984i	−0.953710	+	0.300726i	$0.902771\pi$
$234$		0			0
$235$		0			0
$236$			30.3465i			1.97539i
$237$		0			0
$238$	−6.44949	+	6.44949i	−0.418058	+	0.418058i
$239$	−10.3302			−0.668204			−0.334102	−	0.942537i	$-0.608433\pi$
$239$	−10.3302			−0.668204			−0.334102	+	0.942537i	$0.608433\pi$
$240$		0			0
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$	−18.5833	+	18.5833i	−1.19458	+	1.19458i
$243$		0			0
$244$			4.44949i			0.284849i
$245$		0			0
$246$		0			0
$247$	2.32577	+	2.32577i	0.147985	+	0.147985i
$248$	−23.5263	−	23.5263i	−1.49392	−	1.49392i
$249$		0			0
$250$		0			0
$251$		−	25.5850i		−	1.61491i	−0.589930	−	0.807454i	$-0.700845\pi$
$251$		−	25.5850i		−	1.61491i	0.589930	−	0.807454i	$-0.299155\pi$
$252$		0			0
$253$	−1.44949	+	1.44949i	−0.0911286	+	0.0911286i
$254$	25.1406			1.57746
$255$		0			0
$256$	−29.7980			−1.86237
$257$	−2.78434	+	2.78434i	−0.173682	+	0.173682i	−0.788595	−	0.614913i	$-0.789191\pi$
$257$	−2.78434	+	2.78434i	−0.173682	+	0.173682i	0.614913	+	0.788595i	$0.289191\pi$
$258$		0			0
$259$		−	25.2474i		−	1.56880i
$260$		0			0
$261$		0			0
$262$	2.89898	+	2.89898i	0.179100	+	0.179100i
$263$	0.362817	+	0.362817i	0.0223722	+	0.0223722i	0.718204	−	0.695832i	$-0.244964\pi$
$263$	0.362817	+	0.362817i	0.0223722	+	0.0223722i	−0.695832	+	0.718204i	$0.744964\pi$
$264$		0			0
$265$		0			0
$266$			23.9706i			1.46973i
$267$		0			0
$268$	27.6969	−	27.6969i	1.69186	−	1.69186i
$269$	−10.7745			−0.656936			−0.328468	−	0.944515i	$-0.606532\pi$
$269$	−10.7745			−0.656936			−0.328468	+	0.944515i	$0.606532\pi$
$270$		0			0
$271$	−9.69694			−0.589047			−0.294524	−	0.955644i	$-0.595161\pi$
$271$	−9.69694			−0.589047			−0.294524	+	0.955644i	$0.595161\pi$
$272$	5.56868	−	5.56868i	0.337651	−	0.337651i
$273$		0			0
$274$		−	15.1464i		−	0.915029i
$275$		0			0
$276$		0			0
$277$	−11.8990	−	11.8990i	−0.714940	−	0.714940i	0.252624	−	0.967564i	$-0.418706\pi$
$277$	−11.8990	−	11.8990i	−0.714940	−	0.714940i	−0.967564	+	0.252624i	$0.918706\pi$
$278$	−27.3807	−	27.3807i	−1.64219	−	1.64219i
$279$		0			0
$280$		0			0
$281$		−	17.2319i		−	1.02797i	−0.857799	−	0.513986i	$-0.828168\pi$
$281$		−	17.2319i		−	1.02797i	0.857799	−	0.513986i	$-0.171832\pi$
$282$		0			0
$283$	0.101021	−	0.101021i	0.00600505	−	0.00600505i	−0.704098	−	0.710103i	$-0.748648\pi$
$283$	0.101021	−	0.101021i	0.00600505	−	0.00600505i	0.710103	+	0.704098i	$0.248648\pi$
$284$	−44.3497			−2.63167
$285$		0			0
$286$	−2.24745			−0.132894
$287$	25.7664	−	25.7664i	1.52094	−	1.52094i
$288$		0			0
$289$			15.6969i			0.923349i
$290$		0			0
$291$		0			0
$292$	−11.8990	−	11.8990i	−0.696335	−	0.696335i
$293$	10.1488	+	10.1488i	0.592898	+	0.592898i	0.938413	−	0.345515i	$-0.112296\pi$
$293$	10.1488	+	10.1488i	0.592898	+	0.592898i	−0.345515	+	0.938413i	$0.612296\pi$
$294$		0			0
$295$		0			0
$296$			49.9184i			2.90145i
$297$		0			0
$298$	3.55051	−	3.55051i	0.205676	−	0.205676i
$299$	2.78434			0.161023
$300$		0			0
$301$	15.3485			0.884671
$302$	36.5409	−	36.5409i	2.10269	−	2.10269i
$303$		0			0
$304$		−	20.6969i		−	1.18705i
$305$		0			0
$306$		0			0
$307$	6.65153	+	6.65153i	0.379623	+	0.379623i	0.870966	−	0.491343i	$-0.163494\pi$
$307$	6.65153	+	6.65153i	0.379623	+	0.379623i	−0.491343	+	0.870966i	$0.663494\pi$
$308$	−7.99020	−	7.99020i	−0.455284	−	0.455284i
$309$		0			0
$310$		0			0
$311$		−	17.2319i		−	0.977134i	−0.872526	−	0.488567i	$-0.837520\pi$
$311$		−	17.2319i		−	0.977134i	0.872526	−	0.488567i	$-0.162480\pi$
$312$		0			0
$313$	−7.12372	+	7.12372i	−0.402657	+	0.402657i	−0.879168	−	0.476512i	$-0.841901\pi$
$313$	−7.12372	+	7.12372i	−0.402657	+	0.402657i	0.476512	+	0.879168i	$0.341901\pi$
$314$	1.61435			0.0911030
$315$		0			0
$316$	−2.44949			−0.137795
$317$	16.7876	−	16.7876i	0.942885	−	0.942885i	−0.0555702	−	0.998455i	$-0.517698\pi$
$317$	16.7876	−	16.7876i	0.942885	−	0.942885i	0.998455	+	0.0555702i	$0.0176976\pi$
$318$		0			0
$319$		−	5.14643i		−	0.288145i
$320$		0			0
$321$		0			0
$322$	14.3485	+	14.3485i	0.799609	+	0.799609i
$323$	−2.42152	−	2.42152i	−0.134737	−	0.134737i
$324$		0			0
$325$		0			0
$326$		−	38.3367i		−	2.12327i
$327$		0			0
$328$	−50.9444	+	50.9444i	−2.81293	+	2.81293i
$329$	31.9608			1.76206
$330$		0			0
$331$	9.65153			0.530496			0.265248	−	0.964180i	$-0.414546\pi$
$331$	9.65153			0.530496			0.265248	+	0.964180i	$0.414546\pi$
$332$	−11.5817	+	11.5817i	−0.635629	+	0.635629i
$333$		0			0
$334$		−	10.0000i		−	0.547176i
$335$		0			0
$336$		0			0
$337$	14.9217	+	14.9217i	0.812836	+	0.812836i	0.985058	−	0.172222i	$-0.0550947\pi$
$337$	14.9217	+	14.9217i	0.812836	+	0.812836i	−0.172222	+	0.985058i	$0.555095\pi$
$338$	−21.1863	−	21.1863i	−1.15238	−	1.15238i
$339$		0			0
$340$		0			0
$341$		−	4.31715i		−	0.233787i
$342$		0			0
$343$	−9.12372	+	9.12372i	−0.492635	+	0.492635i
$344$	−30.3465			−1.63617
$345$		0			0
$346$	−57.3939			−3.08551
$347$	0.181408	−	0.181408i	0.00973851	−	0.00973851i	−0.702221	−	0.711959i	$-0.747808\pi$
$347$	0.181408	−	0.181408i	0.00973851	−	0.00973851i	0.711959	+	0.702221i	$0.247808\pi$
$348$		0			0
$349$			18.7980i			1.00623i	0.864219	+	0.503116i	$0.167813\pi$
$349$			18.7980i			1.00623i	−0.864219	+	0.503116i	$0.832187\pi$
$350$		0			0
$351$		0			0
$352$	2.89898	+	2.89898i	0.154516	+	0.154516i
$353$	7.62739	+	7.62739i	0.405965	+	0.405965i	0.880329	−	0.474364i	$-0.157322\pi$
$353$	7.62739	+	7.62739i	0.405965	+	0.405965i	−0.474364	+	0.880329i	$0.657322\pi$
$354$		0			0
$355$		0			0
$356$		−	47.9412i		−	2.54088i
$357$		0			0
$358$	−23.6969	+	23.6969i	−1.25242	+	1.25242i
$359$	−18.0391			−0.952068			−0.476034	−	0.879427i	$-0.657926\pi$
$359$	−18.0391			−0.952068			−0.476034	+	0.879427i	$0.657926\pi$
$360$		0			0
$361$	10.0000			0.526316
$362$	−11.4003	+	11.4003i	−0.599187	+	0.599187i
$363$		0			0
$364$			15.3485i			0.804478i
$365$		0			0
$366$		0			0
$367$	−13.9217	−	13.9217i	−0.726706	−	0.726706i	0.243256	−	0.969962i	$-0.421784\pi$
$367$	−13.9217	−	13.9217i	−0.726706	−	0.726706i	−0.969962	+	0.243256i	$0.921784\pi$
$368$	−12.3889	−	12.3889i	−0.645816	−	0.645816i
$369$		0			0
$370$		0			0
$371$			31.1536i			1.61742i
$372$		0			0
$373$	3.47219	−	3.47219i	0.179783	−	0.179783i	−0.611478	−	0.791261i	$-0.709425\pi$
$373$	3.47219	−	3.47219i	0.179783	−	0.179783i	0.791261	+	0.611478i	$0.209425\pi$
$374$	2.33998			0.120998
$375$		0			0
$376$	−63.1918			−3.25887
$377$	−4.94291	+	4.94291i	−0.254573	+	0.254573i
$378$		0			0
$379$			0.303062i			0.0155672i	0.999970	+	0.00778361i	$0.00247763\pi$
$379$			0.303062i			0.0155672i	−0.999970	+	0.00778361i	$0.997522\pi$
$380$		0			0
$381$		0			0
$382$	−25.1464	−	25.1464i	−1.28660	−	1.28660i
$383$	−3.59151	−	3.59151i	−0.183518	−	0.183518i	0.609369	−	0.792887i	$-0.291423\pi$
$383$	−3.59151	−	3.59151i	−0.183518	−	0.183518i	−0.792887	+	0.609369i	$0.791423\pi$
$384$		0			0
$385$		0			0
$386$		−	3.14716i		−	0.160186i
$387$		0			0
$388$	9.44949	−	9.44949i	0.479725	−	0.479725i
$389$	−30.3465			−1.53863			−0.769314	−	0.638871i	$-0.779402\pi$
$389$	−30.3465			−1.53863			−0.769314	+	0.638871i	$0.779402\pi$
$390$		0			0
$391$	−2.89898			−0.146608
$392$	−12.7517	+	12.7517i	−0.644059	+	0.644059i
$393$		0			0
$394$			44.4949i			2.24162i
$395$		0			0
$396$		0			0
$397$	−8.34847	−	8.34847i	−0.418998	−	0.418998i	0.465861	−	0.884858i	$-0.345745\pi$
$397$	−8.34847	−	8.34847i	−0.418998	−	0.418998i	−0.884858	+	0.465861i	$0.845745\pi$
$398$	18.5833	+	18.5833i	0.931499	+	0.931499i
$399$		0			0
$400$		0			0
$401$		−	14.8104i		−	0.739597i	−0.929112	−	0.369798i	$-0.879427\pi$
$401$		−	14.8104i		−	0.739597i	0.929112	−	0.369798i	$-0.120573\pi$
$402$		0			0
$403$	−4.14643	+	4.14643i	−0.206548	+	0.206548i
$404$	40.7582			2.02780
$405$		0			0
$406$	−50.9444			−2.52833
$407$	−4.58010	+	4.58010i	−0.227027	+	0.227027i
$408$		0			0
$409$			31.8990i			1.57730i	0.614840	+	0.788652i	$0.289220\pi$
$409$			31.8990i			1.57730i	−0.614840	+	0.788652i	$0.710780\pi$
$410$		0			0
$411$		0			0
$412$	42.5959	+	42.5959i	2.09855	+	2.09855i
$413$	15.1732	+	15.1732i	0.746626	+	0.746626i
$414$		0			0
$415$		0			0
$416$		−	5.56868i		−	0.273027i
$417$		0			0
$418$	4.34847	−	4.34847i	0.212691	−	0.212691i
$419$	8.79738			0.429780			0.214890	−	0.976638i	$-0.431061\pi$
$419$	8.79738			0.429780			0.214890	+	0.976638i	$0.431061\pi$
$420$		0			0
$421$	35.7423			1.74198			0.870988	−	0.491305i	$-0.163480\pi$
$421$	35.7423			1.74198			0.870988	+	0.491305i	$0.163480\pi$
$422$	4.21728	−	4.21728i	0.205294	−	0.205294i
$423$		0			0
$424$		−	61.5959i		−	2.99136i
$425$		0			0
$426$		0			0
$427$	2.22474	+	2.22474i	0.107663	+	0.107663i
$428$	27.5621	+	27.5621i	1.33227	+	1.33227i
$429$		0			0
$430$		0			0
$431$			33.1308i			1.59585i	0.602753	+	0.797927i	$0.294070\pi$
$431$			33.1308i			1.59585i	−0.602753	+	0.797927i	$0.705930\pi$
$432$		0			0
$433$	23.0000	−	23.0000i	1.10531	−	1.10531i	0.111551	−	0.993759i	$-0.464418\pi$
$433$	23.0000	−	23.0000i	1.10531	−	1.10531i	0.993759	−	0.111551i	$-0.0355818\pi$
$434$	−42.7354			−2.05136
$435$		0			0
$436$	32.6969			1.56590
$437$	−5.38727	+	5.38727i	−0.257708	+	0.257708i
$438$		0			0
$439$		−	24.2474i		−	1.15727i	−0.815587	−	0.578634i	$-0.803586\pi$
$439$		−	24.2474i		−	1.15727i	0.815587	−	0.578634i	$-0.196414\pi$
$440$		0			0
$441$		0			0
$442$	−2.24745	−	2.24745i	−0.106900	−	0.106900i
$443$	−16.3432	−	16.3432i	−0.776490	−	0.776490i	0.202742	−	0.979232i	$-0.435015\pi$
$443$	−16.3432	−	16.3432i	−0.776490	−	0.776490i	−0.979232	+	0.202742i	$0.935015\pi$
$444$		0			0
$445$		0			0
$446$			57.1014i			2.70383i
$447$		0			0
$448$	−2.00000	+	2.00000i	−0.0944911	+	0.0944911i
$449$	32.3236			1.52545			0.762723	−	0.646725i	$-0.223862\pi$
$449$	32.3236			1.52545			0.762723	+	0.646725i	$0.223862\pi$
$450$		0			0
$451$	−9.34847			−0.440202
$452$	−39.9510	+	39.9510i	−1.87914	+	1.87914i
$453$		0			0
$454$			40.9444i			1.92162i
$455$		0			0
$456$		0			0
$457$	−10.5505	−	10.5505i	−0.493532	−	0.493532i	0.415885	−	0.909417i	$-0.363472\pi$
$457$	−10.5505	−	10.5505i	−0.493532	−	0.493532i	−0.909417	+	0.415885i	$0.863472\pi$
$458$	15.1732	+	15.1732i	0.708999	+	0.708999i
$459$		0			0
$460$		0			0
$461$		−	33.9380i		−	1.58065i	−0.612688	−	0.790325i	$-0.709912\pi$
$461$		−	33.9380i		−	1.58065i	0.612688	−	0.790325i	$-0.290088\pi$
$462$		0			0
$463$	3.47219	−	3.47219i	0.161367	−	0.161367i	−0.621805	−	0.783172i	$-0.713600\pi$
$463$	3.47219	−	3.47219i	0.161367	−	0.161367i	0.783172	+	0.621805i	$0.213600\pi$
$464$	43.9869			2.04204
$465$		0			0
$466$	35.7980			1.65831
$467$	−5.65022	+	5.65022i	−0.261461	+	0.261461i	−0.825647	−	0.564186i	$-0.809190\pi$
$467$	−5.65022	+	5.65022i	−0.261461	+	0.261461i	0.564186	+	0.825647i	$0.309190\pi$
$468$		0			0
$469$		−	27.6969i		−	1.27893i
$470$		0			0
$471$		0			0
$472$	−30.0000	−	30.0000i	−1.38086	−	1.38086i
$473$	−2.78434	−	2.78434i	−0.128024	−	0.128024i
$474$		0			0
$475$		0			0
$476$		−	15.9804i		−	0.732461i
$477$		0			0
$478$	18.5505	−	18.5505i	0.848481	−	0.848481i
$479$	35.6339			1.62815			0.814077	−	0.580757i	$-0.197244\pi$
$479$	35.6339			1.62815			0.814077	+	0.580757i	$0.197244\pi$
$480$		0			0
$481$	8.79796			0.401152
$482$	23.3448	−	23.3448i	1.06333	−	1.06333i
$483$		0			0
$484$		−	46.0454i		−	2.09297i
$485$		0			0
$486$		0			0
$487$	−16.6742	−	16.6742i	−0.755582	−	0.755582i	0.219933	−	0.975515i	$-0.429416\pi$
$487$	−16.6742	−	16.6742i	−0.755582	−	0.755582i	−0.975515	+	0.219933i	$0.929416\pi$
$488$	−4.39869	−	4.39869i	−0.199119	−	0.199119i
$489$		0			0
$490$		0			0
$491$			16.4248i			0.741239i	0.928785	+	0.370620i	$0.120855\pi$
$491$			16.4248i			0.741239i	−0.928785	+	0.370620i	$0.879145\pi$
$492$		0			0
$493$	5.14643	−	5.14643i	0.231783	−	0.231783i
$494$	−8.35302			−0.375820
$495$		0			0
$496$	36.8990			1.65681
$497$	−22.1749	+	22.1749i	−0.994678	+	0.994678i
$498$		0			0
$499$		−	36.4949i		−	1.63374i	−0.576825	−	0.816868i	$-0.695708\pi$
$499$		−	36.4949i		−	1.63374i	0.576825	−	0.816868i	$-0.304292\pi$
$500$		0			0
$501$		0			0
$502$	45.9444	+	45.9444i	2.05060	+	2.05060i
$503$	−2.15857	−	2.15857i	−0.0962461	−	0.0962461i	0.657344	−	0.753590i	$-0.271680\pi$
$503$	−2.15857	−	2.15857i	−0.0962461	−	0.0962461i	−0.753590	+	0.657344i	$0.771680\pi$
$504$		0			0
$505$		0			0
$506$		−	5.20586i		−	0.231429i
$507$		0			0
$508$	−31.1464	+	31.1464i	−1.38190	+	1.38190i
$509$	−20.0163			−0.887206			−0.443603	−	0.896223i	$-0.646300\pi$
$509$	−20.0163			−0.887206			−0.443603	+	0.896223i	$0.646300\pi$
$510$		0			0
$511$	−11.8990			−0.526380
$512$	35.9151	−	35.9151i	1.58724	−	1.58724i
$513$		0			0
$514$		−	10.0000i		−	0.441081i
$515$		0			0
$516$		0			0
$517$	−5.79796	−	5.79796i	−0.254994	−	0.254994i
$518$	45.3383	+	45.3383i	1.99205	+	1.99205i
$519$		0			0
$520$		0			0
$521$			6.73867i			0.295227i	0.989045	+	0.147613i	$0.0471591\pi$
$521$			6.73867i			0.295227i	−0.989045	+	0.147613i	$0.952841\pi$
$522$		0			0
$523$	−12.3258	+	12.3258i	−0.538968	+	0.538968i	−0.923226	−	0.384258i	$-0.874457\pi$
$523$	−12.3258	+	12.3258i	−0.538968	+	0.538968i	0.384258	+	0.923226i	$0.374457\pi$
$524$	−7.18303			−0.313792
$525$		0			0
$526$	−1.30306			−0.0568162
$527$	4.31715	−	4.31715i	0.188058	−	0.188058i
$528$		0			0
$529$		−	16.5505i		−	0.719587i
$530$		0			0
$531$		0			0
$532$	−29.6969	−	29.6969i	−1.28753	−	1.28753i
$533$	8.97879	+	8.97879i	0.388914	+	0.388914i
$534$		0			0
$535$		0			0
$536$			54.7614i			2.36533i
$537$		0			0
$538$	19.3485	−	19.3485i	0.834172	−	0.834172i
$539$	−2.33998			−0.100790
$540$		0			0
$541$	27.0454			1.16277			0.581386	−	0.813628i	$-0.302510\pi$
$541$	27.0454			1.16277			0.581386	+	0.813628i	$0.302510\pi$
$542$	17.4133	−	17.4133i	0.747967	−	0.747967i
$543$		0			0
$544$			5.79796i			0.248585i
$545$		0			0
$546$		0			0
$547$	−10.9217	−	10.9217i	−0.466977	−	0.466977i	0.433956	−	0.900934i	$-0.357117\pi$
$547$	−10.9217	−	10.9217i	−0.466977	−	0.466977i	−0.900934	+	0.433956i	$0.857117\pi$
$548$	18.7647	+	18.7647i	0.801590	+	0.801590i
$549$		0			0
$550$		0			0
$551$		−	19.1276i		−	0.814862i
$552$		0			0
$553$	−1.22474	+	1.22474i	−0.0520814	+	0.0520814i
$554$	42.7354			1.81565
$555$		0			0
$556$	67.8434			2.87720
$557$	−14.0032	+	14.0032i	−0.593336	+	0.593336i	−0.938531	−	0.345195i	$-0.887813\pi$
$557$	−14.0032	+	14.0032i	−0.593336	+	0.593336i	0.345195	+	0.938531i	$0.387813\pi$
$558$		0			0
$559$			5.34847i			0.226216i
$560$		0			0
$561$		0			0
$562$	30.9444	+	30.9444i	1.30531	+	1.30531i
$563$	−11.9445	−	11.9445i	−0.503402	−	0.503402i	0.409091	−	0.912493i	$-0.365846\pi$
$563$	−11.9445	−	11.9445i	−0.503402	−	0.503402i	−0.912493	+	0.409091i	$0.865846\pi$
$564$		0			0
$565$		0			0
$566$			0.362817i			0.0152503i
$567$		0			0
$568$	43.8434	−	43.8434i	1.83963	−	1.83963i
$569$	1.97717			0.0828871			0.0414436	−	0.999141i	$-0.486804\pi$
$569$	1.97717			0.0828871			0.0414436	+	0.999141i	$0.486804\pi$
$570$		0			0
$571$	−20.3485			−0.851557			−0.425778	−	0.904827i	$-0.640000\pi$
$571$	−20.3485			−0.851557			−0.425778	+	0.904827i	$0.640000\pi$
$572$	2.78434	−	2.78434i	0.116419	−	0.116419i
$573$		0			0
$574$			92.5403i			3.86256i
$575$		0			0
$576$		0			0
$577$	20.6742	+	20.6742i	0.860680	+	0.860680i	0.991417	−	0.130737i	$-0.0417345\pi$
$577$	20.6742	+	20.6742i	0.860680	+	0.860680i	−0.130737	+	0.991417i	$0.541734\pi$
$578$	−28.1879	−	28.1879i	−1.17246	−	1.17246i
$579$		0			0
$580$		0			0
$581$			11.5817i			0.480491i
$582$		0			0
$583$	5.65153	−	5.65153i	0.234062	−	0.234062i
$584$	23.5263			0.973523
$585$		0			0
$586$	−36.4495			−1.50571
$587$	0.625766	−	0.625766i	0.0258281	−	0.0258281i	−0.694075	−	0.719903i	$-0.744186\pi$
$587$	0.625766	−	0.625766i	0.0258281	−	0.0258281i	0.719903	+	0.694075i	$0.244186\pi$
$588$		0			0
$589$		−	16.0454i		−	0.661140i
$590$		0			0
$591$		0			0
$592$	−39.1464	−	39.1464i	−1.60891	−	1.60891i
$593$	−4.58010	−	4.58010i	−0.188082	−	0.188082i	0.606784	−	0.794866i	$-0.292459\pi$
$593$	−4.58010	−	4.58010i	−0.188082	−	0.188082i	−0.794866	+	0.606784i	$0.792459\pi$
$594$		0			0
$595$		0			0
$596$			8.79738i			0.360355i
$597$		0			0
$598$	−5.00000	+	5.00000i	−0.204465	+	0.204465i
$599$	17.1504			0.700746			0.350373	−	0.936610i	$-0.386055\pi$
$599$	17.1504			0.700746			0.350373	+	0.936610i	$0.386055\pi$
$600$		0			0
$601$	−35.3485			−1.44189			−0.720947	−	0.692990i	$-0.756293\pi$
$601$	−35.3485			−1.44189			−0.720947	+	0.692990i	$0.756293\pi$
$602$	−27.5621	+	27.5621i	−1.12335	+	1.12335i
$603$		0			0
$604$			90.5403i			3.68403i
$605$		0			0
$606$		0			0
$607$	9.22474	+	9.22474i	0.374421	+	0.374421i	0.869084	−	0.494664i	$-0.164709\pi$
$607$	9.22474	+	9.22474i	0.374421	+	0.374421i	−0.494664	+	0.869084i	$0.664709\pi$
$608$	10.7745	+	10.7745i	0.436965	+	0.436965i
$609$		0			0
$610$		0			0
$611$			11.1374i			0.450569i
$612$		0			0
$613$	26.3712	−	26.3712i	1.06512	−	1.06512i	0.0673953	−	0.997726i	$-0.478531\pi$
$613$	26.3712	−	26.3712i	1.06512	−	1.06512i	0.997726	−	0.0673953i	$-0.0214689\pi$
$614$	−23.8891			−0.964084
$615$		0			0
$616$	15.7980			0.636518
$617$	−16.5246	+	16.5246i	−0.665257	+	0.665257i	−0.956614	−	0.291358i	$-0.905893\pi$
$617$	−16.5246	+	16.5246i	−0.665257	+	0.665257i	0.291358	+	0.956614i	$0.405893\pi$
$618$		0			0
$619$		−	0.550510i		−	0.0221269i	−0.999939	−	0.0110634i	$-0.996478\pi$
$619$		−	0.550510i		−	0.0221269i	0.999939	−	0.0110634i	$-0.00352167\pi$
$620$		0			0
$621$		0			0
$622$	30.9444	+	30.9444i	1.24076	+	1.24076i
$623$	−23.9706	−	23.9706i	−0.960362	−	0.960362i
$624$		0			0
$625$		0			0
$626$		−	25.5850i		−	1.02258i
$627$		0			0
$628$	−2.00000	+	2.00000i	−0.0798087	+	0.0798087i
$629$	−9.16020			−0.365241
$630$		0			0
$631$	−13.0000			−0.517522			−0.258761	−	0.965941i	$-0.583314\pi$
$631$	−13.0000			−0.517522			−0.258761	+	0.965941i	$0.583314\pi$
$632$	2.42152	−	2.42152i	0.0963230	−	0.0963230i
$633$		0			0
$634$			60.2929i			2.39454i
$635$		0			0
$636$		0			0
$637$	2.24745	+	2.24745i	0.0890472	+	0.0890472i
$638$	9.24174	+	9.24174i	0.365884	+	0.365884i
$639$		0			0
$640$		0			0
$641$			29.6208i			1.16995i	0.811050	+	0.584976i	$0.198896\pi$
$641$			29.6208i			1.16995i	−0.811050	+	0.584976i	$0.801104\pi$
$642$		0			0
$643$	−4.55051	+	4.55051i	−0.179455	+	0.179455i	−0.791118	−	0.611663i	$-0.790501\pi$
$643$	−4.55051	+	4.55051i	−0.179455	+	0.179455i	0.611663	+	0.791118i	$0.290501\pi$
$644$	−35.5523			−1.40096
$645$		0			0
$646$	8.69694			0.342176
$647$	−14.5475	+	14.5475i	−0.571920	+	0.571920i	−0.932665	−	0.360745i	$-0.882523\pi$
$647$	−14.5475	+	14.5475i	−0.571920	+	0.571920i	0.360745	+	0.932665i	$0.382523\pi$
$648$		0			0
$649$		−	5.50510i		−	0.216094i
$650$		0			0
$651$		0			0
$652$	47.4949	+	47.4949i	1.86004	+	1.86004i
$653$	−21.6306	−	21.6306i	−0.846472	−	0.846472i	0.143219	−	0.989691i	$-0.454255\pi$
$653$	−21.6306	−	21.6306i	−0.846472	−	0.846472i	−0.989691	+	0.143219i	$0.954255\pi$
$654$		0			0
$655$		0			0
$656$		−	79.9020i		−	3.11965i
$657$		0			0
$658$	−57.3939	+	57.3939i	−2.23745	+	2.23745i
$659$	−35.1895			−1.37079			−0.685394	−	0.728172i	$-0.740370\pi$
$659$	−35.1895			−1.37079			−0.685394	+	0.728172i	$0.740370\pi$
$660$		0			0
$661$	16.3939			0.637648			0.318824	−	0.947814i	$-0.396712\pi$
$661$	16.3939			0.637648			0.318824	+	0.947814i	$0.396712\pi$
$662$	−17.3318	+	17.3318i	−0.673620	+	0.673620i
$663$		0			0
$664$		−	22.8990i		−	0.888653i
$665$		0			0
$666$		0			0
$667$	−11.4495	−	11.4495i	−0.443326	−	0.443326i
$668$	12.3889	+	12.3889i	0.479341	+	0.479341i
$669$		0			0
$670$		0			0
$671$		−	0.807175i		−	0.0311606i
$672$		0			0
$673$	−4.42679	+	4.42679i	−0.170640	+	0.170640i	−0.787261	−	0.616620i	$-0.788501\pi$
$673$	−4.42679	+	4.42679i	−0.170640	+	0.170640i	0.616620	+	0.787261i	$0.288501\pi$
$674$	−53.5914			−2.06427
$675$		0			0
$676$	52.4949			2.01903
$677$	−7.18303	+	7.18303i	−0.276066	+	0.276066i	−0.831536	−	0.555470i	$-0.812538\pi$
$677$	−7.18303	+	7.18303i	−0.276066	+	0.276066i	0.555470	+	0.831536i	$0.312538\pi$
$678$		0			0
$679$		−	9.44949i		−	0.362638i
$680$		0			0
$681$		0			0
$682$	7.75255	+	7.75255i	0.296861	+	0.296861i
$683$	12.1259	+	12.1259i	0.463986	+	0.463986i	0.899960	−	0.435973i	$-0.143596\pi$
$683$	12.1259	+	12.1259i	0.463986	+	0.463986i	−0.435973	+	0.899960i	$0.643596\pi$
$684$		0			0
$685$		0			0
$686$		−	32.7680i		−	1.25109i
$687$		0			0
$688$	23.7980	−	23.7980i	0.907289	−	0.907289i
$689$	−10.8561			−0.413584
$690$		0			0
$691$	−26.0454			−0.990814			−0.495407	−	0.868661i	$-0.664981\pi$
$691$	−26.0454			−0.990814			−0.495407	+	0.868661i	$0.664981\pi$
$692$	71.1047	−	71.1047i	2.70299	−	2.70299i
$693$		0			0
$694$			0.651531i			0.0247318i
$695$		0			0
$696$		0			0
$697$	−9.34847	−	9.34847i	−0.354099	−	0.354099i
$698$	−33.7566	−	33.7566i	−1.27771	−	1.27771i
$699$		0			0
$700$		0			0
$701$			11.5817i			0.437436i	0.975788	+	0.218718i	$0.0701874\pi$
$701$			11.5817i			0.437436i	−0.975788	+	0.218718i	$0.929813\pi$
$702$		0			0
$703$	−17.0227	+	17.0227i	−0.642023	+	0.642023i
$704$	0.725633			0.0273483
$705$		0			0
$706$	−27.3939			−1.03098
$707$	20.3791	−	20.3791i	0.766435	−	0.766435i
$708$		0			0
$709$		−	17.9444i		−	0.673916i	−0.941520	−	0.336958i	$-0.890602\pi$
$709$		−	17.9444i		−	0.673916i	0.941520	−	0.336958i	$-0.109398\pi$
$710$		0			0
$711$		0			0
$712$	47.3939	+	47.3939i	1.77616	+	1.77616i
$713$	−9.60455	−	9.60455i	−0.359693	−	0.359693i
$714$		0			0
$715$		0			0
$716$		−	58.7158i		−	2.19431i
$717$		0			0
$718$	32.3939	−	32.3939i	1.20893	−	1.20893i
$719$	−28.8137			−1.07457			−0.537284	−	0.843401i	$-0.680550\pi$
$719$	−28.8137			−1.07457			−0.537284	+	0.843401i	$0.680550\pi$
$720$		0			0
$721$	42.5959			1.58635
$722$	−17.9576	+	17.9576i	−0.668312	+	0.668312i
$723$		0			0
$724$		−	28.2474i		−	1.04981i
$725$		0			0
$726$		0			0
$727$	−3.20204	−	3.20204i	−0.118757	−	0.118757i	0.645231	−	0.763988i	$-0.276761\pi$
$727$	−3.20204	−	3.20204i	−0.118757	−	0.118757i	−0.763988	+	0.645231i	$0.776761\pi$
$728$	−15.1732	−	15.1732i	−0.562357	−	0.562357i
$729$		0			0
$730$		0			0
$731$		−	5.56868i		−	0.205965i
$732$		0			0
$733$	−4.55051	+	4.55051i	−0.168077	+	0.168077i	−0.786134	−	0.618057i	$-0.787920\pi$
$733$	−4.55051	+	4.55051i	−0.168077	+	0.168077i	0.618057	+	0.786134i	$0.287920\pi$
$734$	49.9999			1.84553
$735$		0			0
$736$	12.8990			0.475463
$737$	−5.02446	+	5.02446i	−0.185078	+	0.185078i
$738$		0			0
$739$			34.6515i			1.27468i	0.770584	+	0.637339i	$0.219965\pi$
$739$			34.6515i			1.27468i	−0.770584	+	0.637339i	$0.780035\pi$
$740$		0			0
$741$		0			0
$742$	−55.9444	−	55.9444i	−2.05378	−	2.05378i
$743$	15.5361	+	15.5361i	0.569962	+	0.569962i	0.932118	−	0.362155i	$-0.117959\pi$
$743$	15.5361	+	15.5361i	0.569962	+	0.569962i	−0.362155	+	0.932118i	$0.617959\pi$
$744$		0			0
$745$		0			0
$746$			12.4704i			0.456575i
$747$		0			0
$748$	−2.89898	+	2.89898i	−0.105997	+	0.105997i
$749$	27.5621			1.00710
$750$		0			0
$751$	37.6969			1.37558			0.687790	−	0.725909i	$-0.258581\pi$
$751$	37.6969			1.37558			0.687790	+	0.725909i	$0.258581\pi$
$752$	49.5556	−	49.5556i	1.80711	−	1.80711i
$753$		0			0
$754$		−	17.7526i		−	0.646510i
$755$		0			0
$756$		0			0
$757$	16.3258	+	16.3258i	0.593370	+	0.593370i	0.938540	−	0.345170i	$-0.112179\pi$
$757$	16.3258	+	16.3258i	0.593370	+	0.593370i	−0.345170	+	0.938540i	$0.612179\pi$
$758$	−0.544225	−	0.544225i	−0.0197671	−	0.0197671i
$759$		0			0
$760$		0			0
$761$		−	9.96737i		−	0.361317i	−0.983546	−	0.180658i	$-0.942177\pi$
$761$		−	9.96737i		−	0.361317i	0.983546	−	0.180658i	$-0.0578229\pi$
$762$		0			0
$763$	16.3485	−	16.3485i	0.591854	−	0.591854i
$764$	62.3073			2.25420
$765$		0			0
$766$	12.8990			0.466059
$767$	−5.28741	+	5.28741i	−0.190917	+	0.190917i
$768$		0			0
$769$			38.6413i			1.39344i	0.717342	+	0.696721i	$0.245358\pi$
$769$			38.6413i			1.39344i	−0.717342	+	0.696721i	$0.754642\pi$
$770$		0			0
$771$		0			0
$772$	3.89898	+	3.89898i	0.140327	+	0.140327i
$773$	12.1259	+	12.1259i	0.436140	+	0.436140i	0.890711	−	0.454571i	$-0.150207\pi$
$773$	12.1259	+	12.1259i	0.436140	+	0.436140i	−0.454571	+	0.890711i	$0.650207\pi$
$774$		0			0
$775$		0			0
$776$			18.6832i			0.670688i
$777$		0			0
$778$	54.4949	−	54.4949i	1.95374	−	1.95374i
$779$	−34.7452			−1.24487
$780$		0			0
$781$	8.04541			0.287887
$782$	5.20586	−	5.20586i	0.186161	−	0.186161i
$783$		0			0
$784$		−	20.0000i		−	0.714286i
$785$		0			0
$786$		0			0
$787$	−29.4722	−	29.4722i	−1.05057	−	1.05057i	−0.998651	−	0.0519189i	$-0.983466\pi$
$787$	−29.4722	−	29.4722i	−1.05057	−	1.05057i	−0.0519189	−	0.998651i	$-0.516534\pi$
$788$	−55.1243	−	55.1243i	−1.96372	−	1.96372i
$789$		0			0
$790$		0			0
$791$			39.9510i			1.42049i
$792$		0			0
$793$	−0.775255	+	0.775255i	−0.0275301	+	0.0275301i
$794$	29.9837			1.06408
$795$		0			0
$796$	−46.0454			−1.63204
$797$	29.5393	−	29.5393i	1.04634	−	1.04634i	0.0474625	−	0.998873i	$-0.484887\pi$
$797$	29.5393	−	29.5393i	1.04634	−	1.04634i	0.998873	−	0.0474625i	$-0.0151134\pi$
$798$		0			0
$799$		−	11.5959i		−	0.410234i
$800$		0			0
$801$		0			0
$802$	26.5959	+	26.5959i	0.939135	+	0.939135i
$803$	2.15857	+	2.15857i	0.0761744	+	0.0761744i
$804$		0			0
$805$		0			0
$806$		−	14.8920i		−	0.524547i
$807$		0			0
$808$	−40.2929	+	40.2929i	−1.41750	+	1.41750i
$809$	−53.8727			−1.89406			−0.947032	−	0.321139i	$-0.895934\pi$
$809$	−53.8727			−1.89406			−0.947032	+	0.321139i	$0.895934\pi$
$810$		0			0
$811$	12.0454			0.422971			0.211486	−	0.977381i	$-0.432170\pi$
$811$	12.0454			0.422971			0.211486	+	0.977381i	$0.432170\pi$
$812$	63.1145	−	63.1145i	2.21488	−	2.21488i
$813$		0			0
$814$		−	16.4495i		−	0.576554i
$815$		0			0
$816$		0			0
$817$	−10.3485	−	10.3485i	−0.362047	−	0.362047i
$818$	−57.2828	−	57.2828i	−2.00285	−	2.00285i
$819$		0			0
$820$		0			0
$821$		−	12.3889i		−	0.432375i	−0.976352	−	0.216188i	$-0.930638\pi$
$821$		−	12.3889i		−	0.432375i	0.976352	−	0.216188i	$-0.0693623\pi$
$822$		0			0
$823$	−7.92168	+	7.92168i	−0.276133	+	0.276133i	−0.831563	−	0.555430i	$-0.812554\pi$
$823$	−7.92168	+	7.92168i	−0.276133	+	0.276133i	0.555430	+	0.831563i	$0.312554\pi$
$824$	−84.2192			−2.93391
$825$		0			0
$826$	−54.4949			−1.89612
$827$	−30.7093	+	30.7093i	−1.06787	+	1.06787i	−0.0703437	+	0.997523i	$0.522410\pi$
$827$	−30.7093	+	30.7093i	−1.06787	+	1.06787i	−0.997523	+	0.0703437i	$0.977590\pi$
$828$		0			0
$829$		−	33.7423i		−	1.17192i	−0.810340	−	0.585960i	$-0.800718\pi$
$829$		−	33.7423i		−	1.17192i	0.810340	−	0.585960i	$-0.199282\pi$
$830$		0			0
$831$		0			0
$832$	−0.696938	−	0.696938i	−0.0241620	−	0.0241620i
$833$	−2.33998	−	2.33998i	−0.0810756	−	0.0810756i
$834$		0			0
$835$		0			0
$836$			10.7745i			0.372645i
$837$		0			0
$838$	−15.7980	+	15.7980i	−0.545731	+	0.545731i
$839$	−13.6404			−0.470920			−0.235460	−	0.971884i	$-0.575660\pi$
$839$	−13.6404			−0.470920			−0.235460	+	0.971884i	$0.575660\pi$
$840$		0			0
$841$	11.6515			0.401777
$842$	−64.1846	+	64.1846i	−2.21195	+	2.21195i
$843$		0			0
$844$			10.4495i			0.359686i
$845$		0			0
$846$		0			0
$847$	−23.0227	−	23.0227i	−0.791069	−	0.791069i
$848$	48.3040	+	48.3040i	1.65877	+	1.65877i
$849$		0			0
$850$		0			0
$851$			20.3791i			0.698586i
$852$		0			0
$853$	35.9217	−	35.9217i	1.22994	−	1.22994i	0.265947	−	0.963988i	$-0.414315\pi$
$853$	35.9217	−	35.9217i	1.22994	−	1.22994i	0.963988	−	0.265947i	$-0.0856848\pi$
$854$	−7.99020			−0.273419
$855$		0			0
$856$	−54.4949			−1.86260
$857$	17.3318	−	17.3318i	0.592043	−	0.592043i	−0.346140	−	0.938183i	$-0.612508\pi$
$857$	17.3318	−	17.3318i	0.592043	−	0.592043i	0.938183	+	0.346140i	$0.112508\pi$
$858$		0			0
$859$		−	23.4495i		−	0.800086i	−0.916496	−	0.400043i	$-0.868995\pi$
$859$		−	23.4495i		−	0.800086i	0.916496	−	0.400043i	$-0.131005\pi$
$860$		0			0
$861$		0			0
$862$	−59.4949	−	59.4949i	−2.02640	−	2.02640i
$863$	−4.03587	−	4.03587i	−0.137383	−	0.137383i	0.635071	−	0.772454i	$-0.280971\pi$
$863$	−4.03587	−	4.03587i	−0.137383	−	0.137383i	−0.772454	+	0.635071i	$0.780971\pi$
$864$		0			0
$865$		0			0
$866$			82.6048i			2.80703i
$867$		0			0
$868$	52.9444	−	52.9444i	1.79705	−	1.79705i
$869$	0.444358			0.0150738
$870$		0			0
$871$	9.65153			0.327030
$872$	−32.3236	+	32.3236i	−1.09462	+	1.09462i
$873$		0			0
$874$		−	19.3485i		−	0.654472i
$875$		0			0
$876$		0			0
$877$	−5.77526	−	5.77526i	−0.195017	−	0.195017i	0.602843	−	0.797860i	$-0.294034\pi$
$877$	−5.77526	−	5.77526i	−0.195017	−	0.195017i	−0.797860	+	0.602843i	$0.794034\pi$
$878$	43.5425	+	43.5425i	1.46949	+	1.46949i
$879$		0			0
$880$		0			0
$881$			27.1993i			0.916368i	0.888857	+	0.458184i	$0.151500\pi$
$881$			27.1993i			0.916368i	−0.888857	+	0.458184i	$0.848500\pi$
$882$		0			0
$883$	−36.0227	+	36.0227i	−1.21226	+	1.21226i	−0.241979	+	0.970281i	$0.577797\pi$
$883$	−36.0227	+	36.0227i	−1.21226	+	1.21226i	−0.970281	+	0.241979i	$0.922203\pi$
$884$	5.56868			0.187295
$885$		0			0
$886$	58.6969			1.97196
$887$	−32.6865	+	32.6865i	−1.09750	+	1.09750i	−0.102802	+	0.994702i	$0.532781\pi$
$887$	−32.6865	+	32.6865i	−1.09750	+	1.09750i	−0.994702	+	0.102802i	$0.967219\pi$
$888$		0			0
$889$			31.1464i			1.04462i
$890$		0			0
$891$		0			0
$892$	−70.7423	−	70.7423i	−2.36863	−	2.36863i
$893$	−21.5491	−	21.5491i	−0.721113	−	0.721113i
$894$		0			0
$895$		0			0
$896$		−	39.1438i		−	1.30770i
$897$		0			0
$898$	−58.0454	+	58.0454i	−1.93700	+	1.93700i
$899$	34.1011			1.13733
$900$		0			0
$901$	11.3031			0.376560
$902$	16.7876	−	16.7876i	0.558965	−	0.558965i
$903$		0			0
$904$		−	78.9898i		−	2.62716i
$905$		0			0
$906$		0			0
$907$	32.1237	+	32.1237i	1.06665	+	1.06665i	0.997614	+	0.0690366i	$0.0219925\pi$
$907$	32.1237	+	32.1237i	1.06665	+	1.06665i	0.0690366	+	0.997614i	$0.478007\pi$
$908$	−50.7256	−	50.7256i	−1.68339	−	1.68339i
$909$		0			0
$910$		0			0
$911$		−	43.6241i		−	1.44533i	−0.691198	−	0.722665i	$-0.742917\pi$
$911$		−	43.6241i		−	1.44533i	0.691198	−	0.722665i	$-0.257083\pi$
$912$		0			0
$913$	2.10102	−	2.10102i	0.0695336	−	0.0695336i
$914$	37.8923			1.25337
$915$		0			0
$916$	−37.5959			−1.24220
$917$	−3.59151	+	3.59151i	−0.118602	+	0.118602i
$918$		0			0
$919$		−	1.34847i		−	0.0444819i	−0.999753	−	0.0222409i	$-0.992920\pi$
$919$		−	1.34847i		−	0.0444819i	0.999753	−	0.0222409i	$-0.00708010\pi$
$920$		0			0
$921$		0			0
$922$	60.9444	+	60.9444i	2.00710	+	2.00710i
$923$	−7.72725	−	7.72725i	−0.254346	−	0.254346i
$924$		0			0
$925$		0			0
$926$			12.4704i			0.409804i
$927$		0			0
$928$	−22.8990	+	22.8990i	−0.751696	+	0.751696i
$929$	30.7908			1.01021			0.505107	−	0.863057i	$-0.331453\pi$
$929$	30.7908			1.01021			0.505107	+	0.863057i	$0.331453\pi$
$930$		0			0
$931$	−8.69694			−0.285031
$932$	−44.3497	+	44.3497i	−1.45272	+	1.45272i
$933$		0			0
$934$		−	20.2929i		−	0.664003i
$935$		0			0
$936$		0			0
$937$	18.7196	+	18.7196i	0.611544	+	0.611544i	0.943348	−	0.331804i	$-0.107657\pi$
$937$	18.7196	+	18.7196i	0.611544	+	0.611544i	−0.331804	+	0.943348i	$0.607657\pi$
$938$	49.7370	+	49.7370i	1.62397	+	1.62397i
$939$		0			0
$940$		0			0
$941$			16.4248i			0.535432i	0.963498	+	0.267716i	$0.0862689\pi$
$941$			16.4248i			0.535432i	−0.963498	+	0.267716i	$0.913731\pi$
$942$		0			0
$943$	−20.7980	+	20.7980i	−0.677275	+	0.677275i
$944$	47.0525			1.53143
$945$		0			0
$946$	10.0000			0.325128
$947$	16.7876	−	16.7876i	0.545523	−	0.545523i	−0.379620	−	0.925143i	$-0.623945\pi$
$947$	16.7876	−	16.7876i	0.545523	−	0.545523i	0.925143	+	0.379620i	$0.123945\pi$
$948$		0			0
$949$		−	4.14643i		−	0.134599i
$950$		0			0
$951$		0			0
$952$	15.7980	+	15.7980i	0.512015	+	0.512015i
$953$	14.0032	+	14.0032i	0.453610	+	0.453610i	0.896551	−	0.442941i	$-0.146065\pi$
$953$	14.0032	+	14.0032i	0.453610	+	0.453610i	−0.442941	+	0.896551i	$0.646065\pi$
$954$		0			0
$955$		0			0
$956$			45.9641i			1.48658i
$957$		0			0
$958$	−63.9898	+	63.9898i	−2.06742	+	2.06742i
$959$	18.7647			0.605945
$960$		0			0
$961$	−2.39388			−0.0772218
$962$	−15.7990	+	15.7990i	−0.509380	+	0.509380i
$963$		0			0
$964$			57.8434i			1.86301i
$965$		0			0
$966$		0			0
$967$	15.5278	+	15.5278i	0.499341	+	0.499341i	0.911233	−	0.411892i	$-0.135132\pi$
$967$	15.5278	+	15.5278i	0.499341	+	0.499341i	−0.411892	+	0.911233i	$0.635132\pi$
$968$	45.5197	+	45.5197i	1.46306	+	1.46306i
$969$		0			0
$970$		0			0
$971$		−	61.4186i		−	1.97102i	−0.169630	−	0.985508i	$-0.554257\pi$
$971$		−	61.4186i		−	1.97102i	0.169630	−	0.985508i	$-0.445743\pi$
$972$		0			0
$973$	33.9217	−	33.9217i	1.08748	−	1.08748i
$974$	59.8858			1.91886
$975$		0			0
$976$	6.89898			0.220831
$977$	8.53443	−	8.53443i	0.273041	−	0.273041i	−0.557282	−	0.830323i	$-0.688156\pi$
$977$	8.53443	−	8.53443i	0.273041	−	0.273041i	0.830323	+	0.557282i	$0.188156\pi$
$978$		0			0
$979$			8.69694i			0.277955i
$980$		0			0
$981$		0			0
$982$	−29.4949	−	29.4949i	−0.941220	−	0.941220i
$983$	34.5637	+	34.5637i	1.10241	+	1.10241i	0.994119	+	0.108293i	$0.0345386\pi$
$983$	34.5637	+	34.5637i	1.10241	+	1.10241i	0.108293	+	0.994119i	$0.465461\pi$
$984$		0			0
$985$		0			0
$986$			18.4835i			0.588634i
$987$		0			0
$988$	10.3485	−	10.3485i	0.329229	−	0.329229i
$989$	−12.3889			−0.393944
$990$		0			0
$991$	−59.0454			−1.87564			−0.937820	−	0.347123i	$-0.887159\pi$
$991$	−59.0454			−1.87564			−0.937820	+	0.347123i	$0.887159\pi$
$992$	−19.2091	+	19.2091i	−0.609890	+	0.609890i
$993$		0			0
$994$		−	79.6413i		−	2.52607i
$995$		0			0
$996$		0			0
$997$	0.101021	+	0.101021i	0.00319935	+	0.00319935i	0.708705	−	0.705505i	$-0.249280\pi$
$997$	0.101021	+	0.101021i	0.00319935	+	0.00319935i	−0.705505	+	0.708705i	$0.749280\pi$
$998$	65.5360	+	65.5360i	2.07451	+	2.07451i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.f.g.107.1		8
3.2	odd	2	inner	675.2.f.g.107.4		8
5.2	odd	4		135.2.f.b.53.1	✓	8
5.3	odd	4	inner	675.2.f.g.593.4		8
5.4	even	2		135.2.f.b.107.4	yes	8
15.2	even	4		135.2.f.b.53.4	yes	8
15.8	even	4	inner	675.2.f.g.593.1		8
15.14	odd	2		135.2.f.b.107.1	yes	8
20.7	even	4		2160.2.w.a.593.4		8
20.19	odd	2		2160.2.w.a.1457.1		8
45.2	even	12		405.2.m.b.53.4		16
45.4	even	6		405.2.m.b.107.4		16
45.7	odd	12		405.2.m.b.53.1		16
45.14	odd	6		405.2.m.b.107.1		16
45.22	odd	12		405.2.m.b.188.4		16
45.29	odd	6		405.2.m.b.377.4		16
45.32	even	12		405.2.m.b.188.1		16
45.34	even	6		405.2.m.b.377.1		16
60.47	odd	4		2160.2.w.a.593.1		8
60.59	even	2		2160.2.w.a.1457.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.f.b.53.1	✓	8	5.2	odd	4
135.2.f.b.53.4	yes	8	15.2	even	4
135.2.f.b.107.1	yes	8	15.14	odd	2
135.2.f.b.107.4	yes	8	5.4	even	2
405.2.m.b.53.1		16	45.7	odd	12
405.2.m.b.53.4		16	45.2	even	12
405.2.m.b.107.1		16	45.14	odd	6
405.2.m.b.107.4		16	45.4	even	6
405.2.m.b.188.1		16	45.32	even	12
405.2.m.b.188.4		16	45.22	odd	12
405.2.m.b.377.1		16	45.34	even	6
405.2.m.b.377.4		16	45.29	odd	6
675.2.f.g.107.1		8	1.1	even	1	trivial
675.2.f.g.107.4		8	3.2	odd	2	inner
675.2.f.g.593.1		8	15.8	even	4	inner
675.2.f.g.593.4		8	5.3	odd	4	inner
2160.2.w.a.593.1		8	60.47	odd	4
2160.2.w.a.593.4		8	20.7	even	4
2160.2.w.a.1457.1		8	20.19	odd	2
2160.2.w.a.1457.4		8	60.59	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79576 + 1.79576i) q^{2} -4.44949i q^{4} +(-2.22474 - 2.22474i) q^{7} +(4.39869 + 4.39869i) q^{8} +0.807175i q^{11} +(0.775255 - 0.775255i) q^{13} +7.99020 q^{14} -6.89898 q^{16} +(-0.807175 + 0.807175i) q^{17} +3.00000i q^{19} +(-1.44949 - 1.44949i) q^{22} +(1.79576 + 1.79576i) q^{23} +2.78434i q^{26} +(-9.89898 + 9.89898i) q^{28} -6.37586 q^{29} -5.34847 q^{31} +(3.59151 - 3.59151i) q^{32} -2.89898i q^{34} +(5.67423 + 5.67423i) q^{37} +(-5.38727 - 5.38727i) q^{38} +11.5817i q^{41} +(-3.44949 + 3.44949i) q^{43} +3.59151 q^{44} -6.44949 q^{46} +(-7.18303 + 7.18303i) q^{47} +2.89898i q^{49} +(-3.44949 - 3.44949i) q^{52} +(-7.00162 - 7.00162i) q^{53} -19.5719i q^{56} +(11.4495 - 11.4495i) q^{58} -6.82021 q^{59} -1.00000 q^{61} +(9.60455 - 9.60455i) q^{62} -0.898979i q^{64} +(6.22474 + 6.22474i) q^{67} +(3.59151 + 3.59151i) q^{68} -9.96737i q^{71} +(2.67423 - 2.67423i) q^{73} -20.3791 q^{74} +13.3485 q^{76} +(1.79576 - 1.79576i) q^{77} -0.550510i q^{79} +(-20.7980 - 20.7980i) q^{82} +(-2.60293 - 2.60293i) q^{83} -12.3889i q^{86} +(-3.55051 + 3.55051i) q^{88} +10.7745 q^{89} -3.44949 q^{91} +(7.99020 - 7.99020i) q^{92} -25.7980i q^{94} +(2.12372 + 2.12372i) q^{97} +(-5.20586 - 5.20586i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{7} + 16 q^{13} - 16 q^{16} + 8 q^{22} - 40 q^{28} + 16 q^{31} + 16 q^{37} - 8 q^{43} - 32 q^{46} - 8 q^{52} + 72 q^{58} - 8 q^{61} + 40 q^{67} - 8 q^{73} + 48 q^{76} - 88 q^{82} - 48 q^{88} - 8 q^{91}+ \cdots - 32 q^{97}+O(q^{100}) \) 8 * q - 8 * q^7 + 16 * q^13 - 16 * q^16 + 8 * q^22 - 40 * q^28 + 16 * q^31 + 16 * q^37 - 8 * q^43 - 32 * q^46 - 8 * q^52 + 72 * q^58 - 8 * q^61 + 40 * q^67 - 8 * q^73 + 48 * q^76 - 88 * q^82 - 48 * q^88 - 8 * q^91 - 32 * q^97

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