LMFDB - Embedded newform 300.2.x.a.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.1
Character	$\chi$	$=$	300.113
Dual form			300.2.x.a.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73155 + 0.0417985i) q^{3} +(2.12124 - 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(2.99651 - 0.144752i) q^{9} +O(q^{10})$	\(q+(-1.73155 + 0.0417985i) q^{3} +(2.12124 - 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(2.99651 - 0.144752i) q^{9} +(1.16772 - 1.60723i) q^{11} +(1.08607 + 0.172017i) q^{13} +(-3.64347 + 1.31345i) q^{15} +(3.88627 - 1.98015i) q^{17} +(7.34866 + 2.38772i) q^{19} +(2.38038 - 2.49815i) q^{21} +(-0.596200 + 0.0944288i) q^{23} +(3.99936 - 3.00085i) q^{25} +(-5.18254 + 0.375894i) q^{27} +(1.20411 + 3.70588i) q^{29} +(2.08371 - 6.41301i) q^{31} +(-1.95478 + 2.83180i) q^{33} +(-1.99181 + 3.98468i) q^{35} +(-1.00762 + 6.36188i) q^{37} +(-1.88777 - 0.252459i) q^{39} +(-4.90769 - 6.75485i) q^{41} +(2.08869 + 2.08869i) q^{43} +(6.25393 - 2.42658i) q^{45} +(-1.27659 + 2.50545i) q^{47} +3.03101i q^{49} +(-6.64648 + 3.59117i) q^{51} +(-9.48136 - 4.83099i) q^{53} +(1.34017 - 4.23529i) q^{55} +(-12.8243 - 3.82729i) q^{57} +(-11.0153 + 8.00310i) q^{59} +(-7.73999 - 5.62344i) q^{61} +(-4.01733 + 4.42516i) q^{63} +(2.42549 - 0.403324i) q^{65} +(-5.76904 - 11.3224i) q^{67} +(1.02840 - 0.188428i) q^{69} +(2.90043 - 0.942408i) q^{71} +(1.52706 + 9.64150i) q^{73} +(-6.79964 + 5.36329i) q^{75} +(0.619145 + 3.90913i) q^{77} +(8.77277 - 2.85044i) q^{79} +(8.95809 - 0.867500i) q^{81} +(1.61164 + 3.16301i) q^{83} +(6.84310 - 6.94927i) q^{85} +(-2.23988 - 6.36657i) q^{87} +(2.65779 + 1.93100i) q^{89} +(-1.77229 + 1.28765i) q^{91} +(-3.33999 + 11.1915i) q^{93} +(17.2772 - 0.133005i) q^{95} +(1.19966 + 0.611256i) q^{97} +(3.26643 - 4.98510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.73155	+	0.0417985i	−0.999709	+	0.0241324i
$3$	−1.73155	+	0.0417985i	−0.999709	+	0.0241324i
$4$		0			0
$5$	2.12124	−	0.707333i	0.948650	−	0.316329i
$5$	2.12124	−	0.707333i	0.948650	−	0.316329i
$6$		0			0
$7$	−1.40872	+	1.40872i	−0.532446	+	0.532446i	−0.921300	−	0.388853i	$-0.872871\pi$
$7$	−1.40872	+	1.40872i	−0.532446	+	0.532446i	0.388853	+	0.921300i	$0.372871\pi$
$8$		0			0
$9$	2.99651	−	0.144752i	0.998835	−	0.0482507i
$10$		0			0
$11$	1.16772	−	1.60723i	0.352081	−	0.484597i	−0.595840	−	0.803103i	$-0.703181\pi$
$11$	1.16772	−	1.60723i	0.352081	−	0.484597i	0.947921	+	0.318506i	$0.103181\pi$
$12$		0			0
$13$	1.08607	+	0.172017i	0.301222	+	0.0477088i	0.305216	−	0.952283i	$-0.401271\pi$
$13$	1.08607	+	0.172017i	0.301222	+	0.0477088i	−0.00399423	+	0.999992i	$0.501271\pi$
$14$		0			0
$15$	−3.64347	+	1.31345i	−0.940739	+	0.339130i
$16$		0			0
$17$	3.88627	−	1.98015i	0.942558	−	0.480257i	0.0859928	−	0.996296i	$-0.472594\pi$
$17$	3.88627	−	1.98015i	0.942558	−	0.480257i	0.856565	+	0.516038i	$0.172594\pi$
$18$		0			0
$19$	7.34866	+	2.38772i	1.68590	+	0.547781i	0.986041	−	0.166502i	$-0.0532472\pi$
$19$	7.34866	+	2.38772i	1.68590	+	0.547781i	0.699857	+	0.714283i	$0.253247\pi$
$20$		0			0
$21$	2.38038	−	2.49815i	0.519442	−	0.545141i
$22$		0			0
$23$	−0.596200	+	0.0944288i	−0.124316	+	0.0196898i	−0.218282	−	0.975886i	$-0.570045\pi$
$23$	−0.596200	+	0.0944288i	−0.124316	+	0.0196898i	0.0939663	+	0.995575i	$0.470045\pi$
$24$		0			0
$25$	3.99936	−	3.00085i	0.799872	−	0.600171i
$26$		0			0
$27$	−5.18254	+	0.375894i	−0.997380	+	0.0723409i
$28$		0			0
$29$	1.20411	+	3.70588i	0.223598	+	0.688164i	0.998431	+	0.0559981i	$0.0178341\pi$
$29$	1.20411	+	3.70588i	0.223598	+	0.688164i	−0.774833	+	0.632166i	$0.782166\pi$
$30$		0			0
$31$	2.08371	−	6.41301i	0.374246	−	1.15181i	−0.569740	−	0.821825i	$-0.692956\pi$
$31$	2.08371	−	6.41301i	0.374246	−	1.15181i	0.943986	−	0.329986i	$-0.107044\pi$
$32$		0			0
$33$	−1.95478	+	2.83180i	−0.340284	+	0.492953i
$34$		0			0
$35$	−1.99181	+	3.98468i	−0.336677	+	0.673533i
$36$		0			0
$37$	−1.00762	+	6.36188i	−0.165652	+	1.04589i	0.755063	+	0.655652i	$0.227606\pi$
$37$	−1.00762	+	6.36188i	−0.165652	+	1.04589i	−0.920715	+	0.390235i	$0.872394\pi$
$38$		0			0
$39$	−1.88777	−	0.252459i	−0.302285	−	0.0404257i
$40$		0			0
$41$	−4.90769	−	6.75485i	−0.766452	−	1.05493i	−0.996650	−	0.0817869i	$-0.973937\pi$
$41$	−4.90769	−	6.75485i	−0.766452	−	1.05493i	0.230198	−	0.973144i	$-0.426063\pi$
$42$		0			0
$43$	2.08869	+	2.08869i	0.318522	+	0.318522i	0.848199	−	0.529677i	$-0.177687\pi$
$43$	2.08869	+	2.08869i	0.318522	+	0.318522i	−0.529677	+	0.848199i	$0.677687\pi$
$44$		0			0
$45$	6.25393	−	2.42658i	0.932281	−	0.361734i
$46$		0			0
$47$	−1.27659	+	2.50545i	−0.186210	+	0.365458i	−0.965173	−	0.261612i	$-0.915746\pi$
$47$	−1.27659	+	2.50545i	−0.186210	+	0.365458i	0.778963	+	0.627070i	$0.215746\pi$
$48$		0			0
$49$			3.03101i			0.433001i
$50$		0			0
$51$	−6.64648	+	3.59117i	−0.930694	+	0.502864i
$52$		0			0
$53$	−9.48136	−	4.83099i	−1.30236	−	0.663588i	−0.341311	−	0.939950i	$-0.610871\pi$
$53$	−9.48136	−	4.83099i	−1.30236	−	0.663588i	−0.961053	+	0.276362i	$0.910871\pi$
$54$		0			0
$55$	1.34017	−	4.23529i	0.180709	−	0.571086i
$56$		0			0
$57$	−12.8243	−	3.82729i	−1.69863	−	0.506937i
$58$		0			0
$59$	−11.0153	+	8.00310i	−1.43407	+	1.04192i	−0.444834	+	0.895613i	$0.646737\pi$
$59$	−11.0153	+	8.00310i	−1.43407	+	1.04192i	−0.989240	+	0.146302i	$0.953263\pi$
$60$		0			0
$61$	−7.73999	−	5.62344i	−0.991005	−	0.720007i	−0.0308639	−	0.999524i	$-0.509826\pi$
$61$	−7.73999	−	5.62344i	−0.991005	−	0.720007i	−0.960141	+	0.279516i	$0.909826\pi$
$62$		0			0
$63$	−4.01733	+	4.42516i	−0.506135	+	0.557517i
$64$		0			0
$65$	2.42549	−	0.403324i	0.300845	−	0.0500262i
$66$		0			0
$67$	−5.76904	−	11.3224i	−0.704800	−	1.38325i	−0.914137	−	0.405405i	$-0.867131\pi$
$67$	−5.76904	−	11.3224i	−0.704800	−	1.38325i	0.209337	−	0.977844i	$-0.432869\pi$
$68$		0			0
$69$	1.02840	−	0.188428i	0.123805	−	0.0226841i
$70$		0			0
$71$	2.90043	−	0.942408i	0.344218	−	0.111843i	−0.131806	−	0.991276i	$-0.542078\pi$
$71$	2.90043	−	0.942408i	0.344218	−	0.111843i	0.476024	+	0.879432i	$0.342078\pi$
$72$		0			0
$73$	1.52706	+	9.64150i	0.178729	+	1.12845i	0.900029	+	0.435829i	$0.143545\pi$
$73$	1.52706	+	9.64150i	0.178729	+	1.12845i	−0.721300	+	0.692623i	$0.756455\pi$
$74$		0			0
$75$	−6.79964	+	5.36329i	−0.785155	+	0.619299i
$76$		0			0
$77$	0.619145	+	3.90913i	0.0705581	+	0.445486i
$78$		0			0
$79$	8.77277	−	2.85044i	0.987013	−	0.320700i	0.229349	−	0.973344i	$-0.426340\pi$
$79$	8.77277	−	2.85044i	0.987013	−	0.320700i	0.757665	+	0.652644i	$0.226340\pi$
$80$		0			0
$81$	8.95809	−	0.867500i	0.995344	−	0.0963889i
$82$		0			0
$83$	1.61164	+	3.16301i	0.176900	+	0.347186i	0.962383	−	0.271698i	$-0.0875852\pi$
$83$	1.61164	+	3.16301i	0.176900	+	0.347186i	−0.785483	+	0.618884i	$0.787585\pi$
$84$		0			0
$85$	6.84310	−	6.94927i	0.742238	−	0.753755i
$86$		0			0
$87$	−2.23988	−	6.36657i	−0.240140	−	0.682568i
$88$		0			0
$89$	2.65779	+	1.93100i	0.281725	+	0.204685i	0.719670	−	0.694317i	$-0.244293\pi$
$89$	2.65779	+	1.93100i	0.281725	+	0.204685i	−0.437944	+	0.899002i	$0.644293\pi$
$90$		0			0
$91$	−1.77229	+	1.28765i	−0.185787	+	0.134982i
$92$		0			0
$93$	−3.33999	+	11.1915i	−0.346341	+	1.16051i
$94$		0			0
$95$	17.2772	−	0.133005i	1.77261	−	0.0136460i
$96$		0			0
$97$	1.19966	+	0.611256i	0.121807	+	0.0620636i	0.513832	−	0.857891i	$-0.328225\pi$
$97$	1.19966	+	0.611256i	0.121807	+	0.0620636i	−0.392025	+	0.919954i	$0.628225\pi$
$98$		0			0
$99$	3.26643	−	4.98510i	0.328288	−	0.501021i
$100$		0			0
$101$			16.1183i			1.60383i	0.597435	+	0.801917i	$0.296187\pi$
$101$			16.1183i			1.60383i	−0.597435	+	0.801917i	$0.703813\pi$
$102$		0			0
$103$	−2.72904	+	5.35604i	−0.268900	+	0.527746i	−0.985487	−	0.169752i	$-0.945703\pi$
$103$	−2.72904	+	5.35604i	−0.268900	+	0.527746i	0.716587	+	0.697498i	$0.245703\pi$
$104$		0			0
$105$	3.28235	−	6.98291i	0.320325	−	0.681462i
$106$		0			0
$107$	−5.18489	−	5.18489i	−0.501242	−	0.501242i	0.410582	−	0.911824i	$-0.365326\pi$
$107$	−5.18489	−	5.18489i	−0.501242	−	0.501242i	−0.911824	+	0.410582i	$0.865326\pi$
$108$		0			0
$109$	−2.24729	−	3.09313i	−0.215251	−	0.296268i	0.687714	−	0.725982i	$-0.258614\pi$
$109$	−2.24729	−	3.09313i	−0.215251	−	0.296268i	−0.902965	+	0.429714i	$0.858614\pi$
$110$		0			0
$111$	1.47883	−	11.0580i	0.140364	−	1.04958i
$112$		0			0
$113$	2.96892	−	18.7450i	0.279292	−	1.76338i	−0.305493	−	0.952194i	$-0.598821\pi$
$113$	2.96892	−	18.7450i	0.279292	−	1.76338i	0.584786	−	0.811188i	$-0.301179\pi$
$114$		0			0
$115$	−1.19789	+	0.622019i	−0.111704	+	0.0580035i
$116$		0			0
$117$	3.27931	+	0.358238i	0.303173	+	0.0331191i
$118$		0			0
$119$	−2.68518	+	8.26415i	−0.246150	+	0.757573i
$120$		0			0
$121$	2.17957	+	6.70804i	0.198143	+	0.609822i
$122$		0			0
$123$	8.78023	+	11.4912i	0.791687	+	1.03613i
$124$		0			0
$125$	6.36101	−	9.19443i	0.568946	−	0.822375i
$126$		0			0
$127$	−1.51917	+	0.240614i	−0.134805	+	0.0213510i	−0.223472	−	0.974710i	$-0.571739\pi$
$127$	−1.51917	+	0.240614i	−0.134805	+	0.0213510i	0.0886673	+	0.996061i	$0.471739\pi$
$128$		0			0
$129$	−3.70397	−	3.52936i	−0.326116	−	0.310743i
$130$		0			0
$131$	−9.46918	−	3.07672i	−0.827326	−	0.268814i	−0.135407	−	0.990790i	$-0.543234\pi$
$131$	−9.46918	−	3.07672i	−0.827326	−	0.268814i	−0.691918	+	0.721976i	$0.743234\pi$
$132$		0			0
$133$	−13.7158	+	6.98857i	−1.18931	+	0.605986i
$134$		0			0
$135$	−10.7276	+	4.46315i	−0.923281	+	0.384126i
$136$		0			0
$137$	6.36073	+	1.00744i	0.543434	+	0.0860715i	0.422115	−	0.906542i	$-0.361288\pi$
$137$	6.36073	+	1.00744i	0.543434	+	0.0860715i	0.121319	+	0.992614i	$0.461288\pi$
$138$		0			0
$139$	1.21863	−	1.67731i	0.103363	−	0.142267i	−0.754202	−	0.656642i	$-0.771976\pi$
$139$	1.21863	−	1.67731i	0.103363	−	0.142267i	0.857565	+	0.514375i	$0.171976\pi$
$140$		0			0
$141$	2.10575	−	4.39167i	0.177336	−	0.369845i
$142$		0			0
$143$	1.54469	−	1.54469i	0.129174	−	0.129174i
$144$		0			0
$145$	5.17551	+	7.00937i	0.429803	+	0.582096i
$146$		0			0
$147$	−0.126692	−	5.24834i	−0.0104493	−	0.432875i
$148$		0			0
$149$	−6.16481			−0.505041			−0.252520	−	0.967592i	$-0.581259\pi$
$149$	−6.16481			−0.505041			−0.252520	+	0.967592i	$0.581259\pi$
$150$		0			0
$151$	−11.8069			−0.960833			−0.480417	−	0.877040i	$-0.659515\pi$
$151$	−11.8069			−0.960833			−0.480417	+	0.877040i	$0.659515\pi$
$152$		0			0
$153$	11.3586	−	6.49608i	0.918288	−	0.525177i
$154$		0			0
$155$	−0.116070	−	15.0775i	−0.00932298	−	1.21105i
$156$		0			0
$157$	−8.22907	+	8.22907i	−0.656751	+	0.656751i	−0.954610	−	0.297859i	$-0.903728\pi$
$157$	−8.22907	+	8.22907i	−0.656751	+	0.656751i	0.297859	+	0.954610i	$0.403728\pi$
$158$		0			0
$159$	16.6193	+	7.96878i	1.31800	+	0.631966i
$160$		0			0
$161$	0.706855	−	0.972903i	0.0557080	−	0.0766755i
$162$		0			0
$163$	21.5564	+	3.41420i	1.68843	+	0.267421i	0.925413	−	0.378959i	$-0.123718\pi$
$163$	21.5564	+	3.41420i	1.68843	+	0.267421i	0.763016	+	0.646380i	$0.223718\pi$
$164$		0			0
$165$	−2.14354	+	7.38962i	−0.166875	+	0.575281i
$166$		0			0
$167$	12.8596	−	6.55227i	0.995102	−	0.507030i	0.120938	−	0.992660i	$-0.461410\pi$
$167$	12.8596	−	6.55227i	0.995102	−	0.507030i	0.874164	+	0.485630i	$0.161410\pi$
$168$		0			0
$169$	−11.2138	−	3.64358i	−0.862598	−	0.280275i
$170$		0			0
$171$	22.3659	+	6.09109i	1.71036	+	0.465798i
$172$		0			0
$173$	5.05212	−	0.800177i	0.384106	−	0.0608364i	0.0386042	−	0.999255i	$-0.487709\pi$
$173$	5.05212	−	0.800177i	0.384106	−	0.0608364i	0.345501	+	0.938418i	$0.387709\pi$
$174$		0			0
$175$	−1.40661	+	9.86135i	−0.106330	+	0.745448i
$176$		0			0
$177$	18.7390	−	14.3182i	1.40851	−	1.07622i
$178$		0			0
$179$	2.20404	+	6.78334i	0.164738	+	0.507011i	0.999017	−	0.0443316i	$-0.0141158\pi$
$179$	2.20404	+	6.78334i	0.164738	+	0.507011i	−0.834279	+	0.551342i	$0.814116\pi$
$180$		0			0
$181$	−0.142407	+	0.438283i	−0.0105850	+	0.0325773i	−0.956210	−	0.292683i	$-0.905452\pi$
$181$	−0.142407	+	0.438283i	−0.0105850	+	0.0325773i	0.945625	+	0.325260i	$0.105452\pi$
$182$		0			0
$183$	13.6372	+	9.41372i	1.00809	+	0.695882i
$184$		0			0
$185$	2.36256	+	14.2078i	0.173699	+	1.04458i
$186$		0			0
$187$	1.35551	−	8.55838i	0.0991250	−	0.625851i
$188$		0			0
$189$	6.77122	−	7.83028i	0.492534	−	0.569569i
$190$		0			0
$191$	−15.1190	−	20.8095i	−1.09397	−	1.50572i	−0.843142	−	0.537691i	$-0.819297\pi$
$191$	−15.1190	−	20.8095i	−1.09397	−	1.50572i	−0.250829	−	0.968031i	$-0.580703\pi$
$192$		0			0
$193$	−16.8215	−	16.8215i	−1.21084	−	1.21084i	−0.970751	−	0.240087i	$-0.922824\pi$
$193$	−16.8215	−	16.8215i	−1.21084	−	1.21084i	−0.240087	−	0.970751i	$-0.577176\pi$
$194$		0			0
$195$	−4.18300	+	0.799756i	−0.299551	+	0.0572717i
$196$		0			0
$197$	−9.07122	+	17.8033i	−0.646298	+	1.26843i	0.302681	+	0.953092i	$0.402118\pi$
$197$	−9.07122	+	17.8033i	−0.646298	+	1.26843i	−0.948979	+	0.315339i	$0.897882\pi$
$198$		0			0
$199$			14.9399i			1.05906i	0.848291	+	0.529530i	$0.177632\pi$
$199$			14.9399i			1.05906i	−0.848291	+	0.529530i	$0.822368\pi$
$200$		0			0
$201$	10.4626	+	19.3641i	0.737976	+	1.36584i
$202$		0			0
$203$	−6.91681	−	3.52429i	−0.485465	−	0.247357i
$204$		0			0
$205$	−15.1883	−	10.8573i	−1.06080	−	0.758308i
$206$		0			0
$207$	−1.77285	+	0.369257i	−0.123221	+	0.0256652i
$208$		0			0
$209$	12.4188	−	9.02277i	0.859025	−	0.624118i
$210$		0			0
$211$	0.810432	+	0.588813i	0.0557925	+	0.0405356i	0.615332	−	0.788268i	$-0.289022\pi$
$211$	0.810432	+	0.588813i	0.0557925	+	0.0405356i	−0.559539	+	0.828804i	$0.689022\pi$
$212$		0			0
$213$	−4.98285	+	1.75306i	−0.341419	+	0.120118i
$214$		0			0
$215$	5.90802	+	2.95322i	0.402924	+	0.201408i
$216$		0			0
$217$	6.09877	+	11.9695i	0.414012	+	0.812544i
$218$		0			0
$219$	−3.04718	−	16.6309i	−0.205909	−	1.12381i
$220$		0			0
$221$	4.56138	−	1.48208i	0.306831	−	0.0996956i
$222$		0			0
$223$	−3.95868	−	24.9941i	−0.265093	−	1.67373i	−0.657127	−	0.753780i	$-0.728228\pi$
$223$	−3.95868	−	24.9941i	−0.265093	−	1.67373i	0.392034	−	0.919951i	$-0.371772\pi$
$224$		0			0
$225$	11.5497	−	9.57099i	0.769982	−	0.638066i
$226$		0			0
$227$	3.09802	+	19.5601i	0.205623	+	1.29825i	0.847233	+	0.531221i	$0.178267\pi$
$227$	3.09802	+	19.5601i	0.205623	+	1.29825i	−0.641610	+	0.767031i	$0.721733\pi$
$228$		0			0
$229$	−18.2285	+	5.92281i	−1.20458	+	0.391390i	−0.841442	−	0.540347i	$-0.818293\pi$
$229$	−18.2285	+	5.92281i	−1.20458	+	0.391390i	−0.363133	+	0.931737i	$0.618293\pi$
$230$		0			0
$231$	−1.23547	−	6.74295i	−0.0812882	−	0.443654i
$232$		0			0
$233$	−5.12583	−	10.0600i	−0.335804	−	0.659053i	0.659929	−	0.751328i	$-0.270586\pi$
$233$	−5.12583	−	10.0600i	−0.335804	−	0.659053i	−0.995734	+	0.0922745i	$0.970586\pi$
$234$		0			0
$235$	−0.935774	+	6.21765i	−0.0610431	+	0.405595i
$236$		0			0
$237$	−15.0713	+	5.30237i	−0.978987	+	0.344426i
$238$		0			0
$239$	−6.41867	−	4.66343i	−0.415189	−	0.301652i	0.360510	−	0.932755i	$-0.382603\pi$
$239$	−6.41867	−	4.66343i	−0.415189	−	0.301652i	−0.775699	+	0.631103i	$0.782603\pi$
$240$		0			0
$241$	15.5433	−	11.2929i	1.00123	−	0.727439i	0.0388814	−	0.999244i	$-0.487621\pi$
$241$	15.5433	−	11.2929i	1.00123	−	0.727439i	0.962352	+	0.271805i	$0.0876205\pi$
$242$		0			0
$243$	−15.4751	+	1.87655i	−0.992728	+	0.120381i
$244$		0			0
$245$	2.14393	+	6.42952i	0.136971	+	0.410767i
$246$		0			0
$247$	7.57043	+	3.85733i	0.481695	+	0.245436i
$248$		0			0
$249$	−2.92283	−	5.40954i	−0.185227	−	0.342816i
$250$		0			0
$251$			16.7296i			1.05596i	0.849255	+	0.527982i	$0.177051\pi$
$251$			16.7296i			1.05596i	−0.849255	+	0.527982i	$0.822949\pi$
$252$		0			0
$253$	−0.544425	+	1.06849i	−0.0342277	+	0.0671757i
$254$		0			0
$255$	−11.5587	+	12.3190i	−0.723832	+	0.771447i
$256$		0			0
$257$	14.2215	+	14.2215i	0.887111	+	0.887111i	0.994245	−	0.107134i	$-0.0341673\pi$
$257$	14.2215	+	14.2215i	0.887111	+	0.887111i	−0.107134	+	0.994245i	$0.534167\pi$
$258$		0			0
$259$	−7.54266	−	10.3816i	−0.468678	−	0.645080i
$260$		0			0
$261$	4.14456	+	10.9304i	0.256542	+	0.676574i
$262$		0			0
$263$	2.01269	−	12.7077i	0.124108	−	0.783587i	−0.844602	−	0.535394i	$-0.820163\pi$
$263$	2.01269	−	12.7077i	0.124108	−	0.783587i	0.968710	−	0.248193i	$-0.0798369\pi$
$264$		0			0
$265$	−23.5294	−	3.54124i	−1.44540	−	0.217537i
$266$		0			0
$267$	−4.68280	−	3.23252i	−0.286583	−	0.197827i
$268$		0			0
$269$	−3.43765	+	10.5800i	−0.209597	+	0.645074i	0.789896	+	0.613241i	$0.210135\pi$
$269$	−3.43765	+	10.5800i	−0.209597	+	0.645074i	−0.999493	+	0.0318333i	$0.989865\pi$
$270$		0			0
$271$	5.91811	+	18.2141i	0.359499	+	1.10643i	0.953354	+	0.301853i	$0.0976053\pi$
$271$	5.91811	+	18.2141i	0.359499	+	1.10643i	−0.593855	+	0.804572i	$0.702395\pi$
$272$		0			0
$273$	3.01499	−	2.30370i	0.182475	−	0.139426i
$274$		0			0
$275$	−0.152928	−	9.93204i	−0.00922190	−	0.598924i
$276$		0			0
$277$	−6.94071	+	1.09930i	−0.417027	+	0.0660505i	−0.361422	−	0.932402i	$-0.617709\pi$
$277$	−6.94071	+	1.09930i	−0.417027	+	0.0660505i	−0.0556046	+	0.998453i	$0.517709\pi$
$278$		0			0
$279$	5.31557	−	19.5183i	0.318235	−	1.16853i
$280$		0			0
$281$	−29.8705	−	9.70552i	−1.78193	−	0.578983i	−0.782860	−	0.622197i	$-0.786240\pi$
$281$	−29.8705	−	9.70552i	−1.78193	−	0.578983i	−0.999066	+	0.0432145i	$0.986240\pi$
$282$		0			0
$283$	13.6669	−	6.96363i	0.812412	−	0.413945i	0.00213954	−	0.999998i	$-0.499319\pi$
$283$	13.6669	−	6.96363i	0.812412	−	0.413945i	0.810273	+	0.586053i	$0.199319\pi$
$284$		0			0
$285$	−29.9107	+	0.952465i	−1.77176	+	0.0564191i
$286$		0			0
$287$	16.4293	+	2.60214i	0.969789	+	0.153599i
$288$		0			0
$289$	1.18972	−	1.63751i	0.0699837	−	0.0963243i
$290$		0			0
$291$	−2.10281	−	1.00827i	−0.123269	−	0.0591060i
$292$		0			0
$293$	−19.7002	+	19.7002i	−1.15090	+	1.15090i	−0.164528	+	0.986372i	$0.552610\pi$
$293$	−19.7002	+	19.7002i	−1.15090	+	1.15090i	−0.986372	+	0.164528i	$0.947390\pi$
$294$		0			0
$295$	−17.7053	+	24.7681i	−1.03085	+	1.44205i
$296$		0			0
$297$	−5.44760	+	8.76846i	−0.316102	+	0.508797i
$298$		0			0
$299$	−0.663758			−0.0383861
$300$		0			0
$301$	−5.88476			−0.339192
$302$		0			0
$303$	−0.673722	−	27.9096i	−0.0387043	−	1.60337i
$304$		0			0
$305$	−20.3961	−	6.45393i	−1.16788	−	0.369551i
$306$		0			0
$307$	16.0403	−	16.0403i	0.915468	−	0.915468i	−0.0812272	−	0.996696i	$-0.525884\pi$
$307$	16.0403	−	16.0403i	0.915468	−	0.915468i	0.996696	+	0.0812272i	$0.0258839\pi$
$308$		0			0
$309$	4.50158	−	9.38830i	0.256086	−	0.534081i
$310$		0			0
$311$	−15.0505	+	20.7152i	−0.853433	+	1.17465i	0.129663	+	0.991558i	$0.458611\pi$
$311$	−15.0505	+	20.7152i	−0.853433	+	1.17465i	−0.983096	+	0.183092i	$0.941389\pi$
$312$		0			0
$313$	−0.120497	−	0.0190849i	−0.00681092	−	0.00107874i	0.153028	−	0.988222i	$-0.451098\pi$
$313$	−0.120497	−	0.0190849i	−0.00681092	−	0.00107874i	−0.159839	+	0.987143i	$0.551098\pi$
$314$		0			0
$315$	−5.39167	+	12.2284i	−0.303786	+	0.688994i
$316$		0			0
$317$	−13.7216	+	6.99151i	−0.770682	+	0.392682i	−0.794679	−	0.607030i	$-0.792361\pi$
$317$	−13.7216	+	6.99151i	−0.770682	+	0.392682i	0.0239969	+	0.999712i	$0.492361\pi$
$318$		0			0
$319$	7.36226	+	2.39214i	0.412207	+	0.133934i
$320$		0			0
$321$	9.19459	+	8.76115i	0.513192	+	0.489000i
$322$		0			0
$323$	33.2869	−	5.27213i	1.85213	−	0.293349i
$324$		0			0
$325$	4.85978	−	2.57118i	0.269572	−	0.142623i
$326$		0			0
$327$	4.02057	+	5.26196i	0.222338	+	0.290987i
$328$		0			0
$329$	−1.73112	−	5.32784i	−0.0954398	−	0.293734i
$330$		0			0
$331$	0.542755	−	1.67043i	0.0298325	−	0.0918151i	−0.935032	−	0.354564i	$-0.884629\pi$
$331$	0.542755	−	1.67043i	0.0298325	−	0.0918151i	0.964864	+	0.262749i	$0.0846292\pi$
$332$		0			0
$333$	−2.09845	+	19.2093i	−0.114995	+	1.05266i
$334$		0			0
$335$	−20.2462	−	19.9369i	−1.10617	−	1.08927i
$336$		0			0
$337$	1.61810	−	10.2163i	0.0881434	−	0.556516i	−0.903610	−	0.428356i	$-0.859093\pi$
$337$	1.61810	−	10.2163i	0.0881434	−	0.556516i	0.991754	−	0.128160i	$-0.0409070\pi$
$338$		0			0
$339$	−4.35731	+	32.5819i	−0.236656	+	1.76961i
$340$		0			0
$341$	−7.87398	−	10.8376i	−0.426400	−	0.586889i
$342$		0			0
$343$	−14.1309	−	14.1309i	−0.762997	−	0.762997i
$344$		0			0
$345$	2.04821	−	1.12712i	0.110272	−	0.0606823i
$346$		0			0
$347$	14.2252	−	27.9185i	0.763647	−	1.49874i	−0.100189	−	0.994968i	$-0.531945\pi$
$347$	14.2252	−	27.9185i	0.763647	−	1.49874i	0.863836	−	0.503773i	$-0.168055\pi$
$348$		0			0
$349$		−	16.4381i		−	0.879913i	−0.898019	−	0.439956i	$-0.854994\pi$
$349$		−	16.4381i		−	0.879913i	0.898019	−	0.439956i	$-0.145006\pi$
$350$		0			0
$351$	−5.69326	−	0.483235i	−0.303884	−	0.0257932i
$352$		0			0
$353$	0.230966	+	0.117683i	0.0122931	+	0.00626364i	0.460126	−	0.887854i	$-0.347804\pi$
$353$	0.230966	+	0.117683i	0.0122931	+	0.00626364i	−0.447833	+	0.894117i	$0.647804\pi$
$354$		0			0
$355$	5.48593	−	4.05065i	0.291163	−	0.214986i
$356$		0			0
$357$	4.30409	−	14.4220i	0.227797	−	0.763293i
$358$		0			0
$359$	−17.7312	+	12.8824i	−0.935815	+	0.679909i	−0.947410	−	0.320024i	$-0.896309\pi$
$359$	−17.7312	+	12.8824i	−0.935815	+	0.679909i	0.0115948	+	0.999933i	$0.496309\pi$
$360$		0			0
$361$	32.9302	+	23.9252i	1.73317	+	1.25922i
$362$		0			0
$363$	−4.05442	−	11.5242i	−0.212802	−	0.604863i
$364$		0			0
$365$	10.0590	+	19.3718i	0.526514	+	1.01397i
$366$		0			0
$367$	0.897351	+	1.76115i	0.0468413	+	0.0919313i	0.913241	−	0.407420i	$-0.133572\pi$
$367$	0.897351	+	1.76115i	0.0468413	+	0.0919313i	−0.866399	+	0.499352i	$0.833572\pi$
$368$		0			0
$369$	−15.6837	−	19.5306i	−0.816460	−	1.01672i
$370$		0			0
$371$	20.1621	−	6.55107i	1.04676	−	0.340114i
$372$		0			0
$373$	0.199978	+	1.26261i	0.0103545	+	0.0653755i	0.992325	−	0.123661i	$-0.0394635\pi$
$373$	0.199978	+	1.26261i	0.0103545	+	0.0653755i	−0.981970	+	0.189037i	$0.939464\pi$
$374$		0			0
$375$	−10.6301	+	16.1865i	−0.548935	+	0.835865i
$376$		0			0
$377$	0.670278	+	4.23197i	0.0345211	+	0.217958i
$378$		0			0
$379$	−5.76610	+	1.87352i	−0.296185	+	0.0962362i	−0.453340	−	0.891338i	$-0.649768\pi$
$379$	−5.76610	+	1.87352i	−0.296185	+	0.0962362i	0.157155	+	0.987574i	$0.449768\pi$
$380$		0			0
$381$	2.62046	−	0.480133i	0.134250	−	0.0245979i
$382$		0			0
$383$	14.1048	+	27.6823i	0.720723	+	1.41450i	0.902294	+	0.431121i	$0.141882\pi$
$383$	14.1048	+	27.6823i	0.720723	+	1.41450i	−0.181571	+	0.983378i	$0.558118\pi$
$384$		0			0
$385$	4.07841	+	7.85427i	0.207855	+	0.400291i
$386$		0			0
$387$	6.56111	+	5.95643i	0.333520	+	0.302782i
$388$		0			0
$389$	3.47117	+	2.52196i	0.175996	+	0.127868i	0.672296	−	0.740283i	$-0.265308\pi$
$389$	3.47117	+	2.52196i	0.175996	+	0.127868i	−0.496300	+	0.868151i	$0.665308\pi$
$390$		0			0
$391$	−2.13001	+	1.54754i	−0.107719	+	0.0782625i
$392$		0			0
$393$	16.5249	+	4.93169i	0.833572	+	0.248771i
$394$		0			0
$395$	16.5930	−	12.2518i	0.834883	−	0.616453i
$396$		0			0
$397$	13.0514	+	6.65001i	0.655030	+	0.333754i	0.749723	−	0.661752i	$-0.230187\pi$
$397$	13.0514	+	6.65001i	0.655030	+	0.333754i	−0.0946927	+	0.995507i	$0.530187\pi$
$398$		0			0
$399$	23.4575	−	12.6743i	1.17434	−	0.634511i
$400$		0			0
$401$			9.19743i			0.459297i	0.973274	+	0.229649i	$0.0737577\pi$
$401$			9.19743i			0.459297i	−0.973274	+	0.229649i	$0.926242\pi$
$402$		0			0
$403$	3.36620	−	6.60655i	0.167683	−	0.329096i
$404$		0			0
$405$	18.3887	−	8.17654i	0.913742	−	0.406295i
$406$		0			0
$407$	9.04837	+	9.04837i	0.448511	+	0.448511i
$408$		0			0
$409$	−14.8606	−	20.4539i	−0.734809	−	1.01138i	−0.998901	−	0.0468802i	$-0.985072\pi$
$409$	−14.8606	−	20.4539i	−0.734809	−	1.01138i	0.264091	−	0.964498i	$-0.414928\pi$
$410$		0			0
$411$	−11.0560	−	1.47856i	−0.545353	−	0.0729321i
$412$		0			0
$413$	4.24338	−	26.7917i	0.208803	−	1.31833i
$414$		0			0
$415$	5.65598	+	5.56956i	0.277641	+	0.273399i
$416$		0			0
$417$	−2.04001	+	2.95527i	−0.0998999	+	0.144720i
$418$		0			0
$419$	1.79122	−	5.51280i	0.0875066	−	0.269318i	−0.897722	−	0.440563i	$-0.854779\pi$
$419$	1.79122	−	5.51280i	0.0875066	−	0.269318i	0.985228	+	0.171245i	$0.0547789\pi$
$420$		0			0
$421$	5.27994	+	16.2500i	0.257328	+	0.791975i	0.993362	+	0.115030i	$0.0366965\pi$
$421$	5.27994	+	16.2500i	0.257328	+	0.791975i	−0.736034	+	0.676945i	$0.763304\pi$
$422$		0			0
$423$	−3.46265	+	7.69239i	−0.168360	+	0.374017i
$424$		0			0
$425$	9.60043	−	19.5815i	0.465689	−	0.949840i
$426$		0			0
$427$	18.8253	−	2.98164i	0.911022	−	0.144292i
$428$		0			0
$429$	−2.61014	+	2.73928i	−0.126019	+	0.132253i
$430$		0			0
$431$	−7.18994	−	2.33615i	−0.346327	−	0.112528i	0.130688	−	0.991424i	$-0.458281\pi$
$431$	−7.18994	−	2.33615i	−0.346327	−	0.112528i	−0.477015	+	0.878895i	$0.658281\pi$
$432$		0			0
$433$	−4.16519	+	2.12227i	−0.200166	+	0.101990i	−0.551200	−	0.834373i	$-0.685830\pi$
$433$	−4.16519	+	2.12227i	−0.200166	+	0.101990i	0.351034	+	0.936363i	$0.385830\pi$
$434$		0			0
$435$	−9.25462	−	11.9207i	−0.443725	−	0.571555i
$436$		0			0
$437$	−4.60674	−	0.729636i	−0.220370	−	0.0349032i
$438$		0			0
$439$	−3.13091	+	4.30933i	−0.149430	+	0.205673i	−0.877170	−	0.480181i	$-0.840571\pi$
$439$	−3.13091	+	4.30933i	−0.149430	+	0.205673i	0.727739	+	0.685854i	$0.240571\pi$
$440$		0			0
$441$	0.438745	+	9.08244i	0.0208926	+	0.432497i
$442$		0			0
$443$	13.2529	−	13.2529i	0.629663	−	0.629663i	−0.318320	−	0.947983i	$-0.603119\pi$
$443$	13.2529	−	13.2529i	0.629663	−	0.629663i	0.947983	+	0.318320i	$0.103119\pi$
$444$		0			0
$445$	7.00368	+	2.21618i	0.332006	+	0.105057i
$446$		0			0
$447$	10.6747	−	0.257680i	0.504894	−	0.0121878i
$448$		0			0
$449$	−0.687206			−0.0324313			−0.0162156	−	0.999869i	$-0.505162\pi$
$449$	−0.687206			−0.0324313			−0.0162156	+	0.999869i	$0.505162\pi$
$450$		0			0
$451$	−16.5874			−0.781070
$452$		0			0
$453$	20.4442	−	0.493511i	0.960553	−	0.0231872i
$454$		0			0
$455$	−2.84867	+	3.98501i	−0.133548	+	0.186820i
$456$		0			0
$457$	20.4930	−	20.4930i	0.958623	−	0.958623i	−0.0405546	−	0.999177i	$-0.512912\pi$
$457$	20.4930	−	20.4930i	0.958623	−	0.958623i	0.999177	+	0.0405546i	$0.0129125\pi$
$458$		0			0
$459$	−19.3964	+	11.7230i	−0.905347	+	0.547185i
$460$		0			0
$461$	2.51720	−	3.46463i	0.117238	−	0.161364i	−0.746365	−	0.665537i	$-0.768203\pi$
$461$	2.51720	−	3.46463i	0.117238	−	0.161364i	0.863603	+	0.504173i	$0.168203\pi$
$462$		0			0
$463$	29.9000	+	4.73569i	1.38957	+	0.220086i	0.805971	−	0.591955i	$-0.201644\pi$
$463$	29.9000	+	4.73569i	1.38957	+	0.220086i	0.583599	+	0.812042i	$0.301644\pi$
$464$		0			0
$465$	0.831195	+	26.1025i	0.0385458	+	1.21047i
$466$		0			0
$467$	−22.7856	+	11.6099i	−1.05439	+	0.537241i	−0.893190	−	0.449680i	$-0.851538\pi$
$467$	−22.7856	+	11.6099i	−1.05439	+	0.537241i	−0.161205	+	0.986921i	$0.551538\pi$
$468$		0			0
$469$	24.0770	+	7.82310i	1.11177	+	0.361237i
$470$		0			0
$471$	13.9050	−	14.5930i	0.640711	−	0.672409i
$472$		0			0
$473$	5.79600	−	0.917996i	0.266500	−	0.0422095i
$474$		0			0
$475$	36.5551	−	12.5029i	1.67726	−	0.573672i
$476$		0			0
$477$	−29.1102	−	13.1037i	−1.33287	−	0.599975i
$478$		0			0
$479$	−2.06837	−	6.36579i	−0.0945063	−	0.290860i	0.892618	−	0.450813i	$-0.148866\pi$
$479$	−2.06837	−	6.36579i	−0.0945063	−	0.290860i	−0.987125	+	0.159953i	$0.948866\pi$
$480$		0			0
$481$	−2.18870	+	6.73612i	−0.0997960	+	0.307141i
$482$		0			0
$483$	−1.18329	+	1.71417i	−0.0538414	+	0.0779975i
$484$		0			0
$485$	2.97713	+	0.448066i	0.135184	+	0.0203456i
$486$		0			0
$487$	−2.38639	+	15.0671i	−0.108138	+	0.682755i	0.872748	+	0.488171i	$0.162336\pi$
$487$	−2.38639	+	15.0671i	−0.108138	+	0.682755i	−0.980886	+	0.194584i	$0.937664\pi$
$488$		0			0
$489$	−37.4687	−	5.01082i	−1.69439	−	0.226597i
$490$		0			0
$491$	0.878303	+	1.20888i	0.0396373	+	0.0545560i	0.828376	−	0.560173i	$-0.189265\pi$
$491$	0.878303	+	1.20888i	0.0396373	+	0.0545560i	−0.788738	+	0.614729i	$0.789265\pi$
$492$		0			0
$493$	12.0177	+	12.0177i	0.541250	+	0.541250i
$494$		0			0
$495$	3.40277	−	12.8851i	0.152943	−	0.579141i
$496$		0			0
$497$	−2.75831	+	5.41349i	−0.123727	+	0.242828i
$498$		0			0
$499$			11.6309i			0.520672i	0.965518	+	0.260336i	$0.0838333\pi$
$499$			11.6309i			0.520672i	−0.965518	+	0.260336i	$0.916167\pi$
$500$		0			0
$501$	−21.9930	+	11.8831i	−0.982576	+	0.530896i
$502$		0			0
$503$	−18.6581	−	9.50679i	−0.831925	−	0.423887i	−0.0144808	−	0.999895i	$-0.504610\pi$
$503$	−18.6581	−	9.50679i	−0.831925	−	0.423887i	−0.817444	+	0.576008i	$0.804610\pi$
$504$		0			0
$505$	11.4010	+	34.1909i	0.507340	+	1.52148i
$506$		0			0
$507$	19.5695	+	5.84030i	0.869111	+	0.259377i
$508$		0			0
$509$	29.0463	−	21.1033i	1.28745	−	0.935389i	0.287702	−	0.957720i	$-0.407109\pi$
$509$	29.0463	−	21.1033i	1.28745	−	0.935389i	0.999751	+	0.0223311i	$0.00710880\pi$
$510$		0			0
$511$	−15.7334	−	11.4310i	−0.696004	−	0.505676i
$512$		0			0
$513$	−38.9822	−	9.61215i	−1.72111	−	0.424387i
$514$		0			0
$515$	−2.00045	+	13.2918i	−0.0881504	+	0.585707i
$516$		0			0
$517$	2.53613	+	4.97744i	0.111539	+	0.218907i
$518$		0			0
$519$	−8.71453	+	1.59671i	−0.382526	+	0.0700880i
$520$		0			0
$521$	39.1289	−	12.7138i	1.71427	−	0.557000i	0.723235	−	0.690602i	$-0.242655\pi$
$521$	39.1289	−	12.7138i	1.71427	−	0.557000i	0.991035	+	0.133602i	$0.0426545\pi$
$522$		0			0
$523$	0.431314	+	2.72321i	0.0188601	+	0.119078i	0.995322	−	0.0966111i	$-0.0308003\pi$
$523$	0.431314	+	2.72321i	0.0188601	+	0.119078i	−0.976462	+	0.215689i	$0.930800\pi$
$524$		0			0
$525$	2.02343	−	17.1342i	0.0883097	−	0.747797i
$526$		0			0
$527$	−4.60087	−	29.0488i	−0.200417	−	1.26538i
$528$		0			0
$529$	−21.5278	+	6.99479i	−0.935990	+	0.304121i
$530$		0			0
$531$	−31.8490	+	25.5758i	−1.38213	+	1.10990i
$532$		0			0
$533$	−4.16815	−	8.18045i	−0.180542	−	0.354334i
$534$		0			0
$535$	−14.6659	−	7.33097i	−0.634060	−	0.316946i
$536$		0			0
$537$	−4.09993	−	11.6535i	−0.176925	−	0.502888i
$538$		0			0
$539$	4.87152	+	3.53937i	0.209831	+	0.152451i
$540$		0			0
$541$	17.6370	−	12.8140i	0.758273	−	0.550918i	−0.140107	−	0.990136i	$-0.544745\pi$
$541$	17.6370	−	12.8140i	0.758273	−	0.550918i	0.898380	+	0.439219i	$0.144745\pi$
$542$		0			0
$543$	0.228265	−	0.764860i	0.00979577	−	0.0328233i
$544$		0			0
$545$	−6.95492	−	4.97170i	−0.297916	−	0.212964i
$546$		0			0
$547$	−26.1267	−	13.3122i	−1.11710	−	0.569189i	−0.204834	−	0.978797i	$-0.565665\pi$
$547$	−26.1267	−	13.3122i	−1.11710	−	0.569189i	−0.912262	+	0.409608i	$0.865665\pi$
$548$		0			0
$549$	−24.0069	−	15.7303i	−1.02459	−	0.671352i
$550$		0			0
$551$			30.1083i			1.28266i
$552$		0			0
$553$	−8.34290	+	16.3739i	−0.354776	+	0.696287i
$554$		0			0
$555$	−4.68474	−	24.5028i	−0.198856	−	1.04008i
$556$		0			0
$557$	12.3449	+	12.3449i	0.523071	+	0.523071i	0.918498	−	0.395427i	$-0.129403\pi$
$557$	12.3449	+	12.3449i	0.523071	+	0.523071i	−0.395427	+	0.918498i	$0.629403\pi$
$558$		0			0
$559$	1.90917	+	2.62775i	0.0807494	+	0.111142i
$560$		0			0
$561$	−1.98941	+	14.8759i	−0.0839929	+	0.628060i
$562$		0			0
$563$	−6.59138	+	41.6164i	−0.277794	+	1.75392i	0.315491	+	0.948928i	$0.397831\pi$
$563$	−6.59138	+	41.6164i	−0.277794	+	1.75392i	−0.593285	+	0.804992i	$0.702169\pi$
$564$		0			0
$565$	−6.96117	−	41.8628i	−0.292859	−	1.76118i
$566$		0			0
$567$	−11.3974	+	13.8415i	−0.478645	+	0.581289i
$568$		0			0
$569$	2.68424	−	8.26124i	0.112529	−	0.346329i	−0.878894	−	0.477016i	$-0.841718\pi$
$569$	2.68424	−	8.26124i	0.112529	−	0.346329i	0.991424	+	0.130687i	$0.0417183\pi$
$570$		0			0
$571$	−3.08502	−	9.49470i	−0.129104	−	0.397341i	0.865523	−	0.500870i	$-0.166987\pi$
$571$	−3.08502	−	9.49470i	−0.129104	−	0.397341i	−0.994626	+	0.103529i	$0.966987\pi$
$572$		0			0
$573$	27.0490	+	35.4007i	1.12999	+	1.47888i
$574$		0			0
$575$	−2.10105	+	2.16676i	−0.0876198	+	0.0903603i
$576$		0			0
$577$	10.6032	−	1.67937i	0.441415	−	0.0699133i	0.0682288	−	0.997670i	$-0.478265\pi$
$577$	10.6032	−	1.67937i	0.441415	−	0.0699133i	0.373186	+	0.927756i	$0.378265\pi$
$578$		0			0
$579$	29.8303	+	28.4241i	1.23971	+	1.18127i
$580$		0			0
$581$	−6.72615	−	2.18546i	−0.279048	−	0.0906681i
$582$		0			0
$583$	−18.8361	+	9.59746i	−0.780110	+	0.397486i
$584$		0			0
$585$	7.20962	−	1.55966i	0.298081	−	0.0644839i
$586$		0			0
$587$	−22.9124	−	3.62898i	−0.945698	−	0.149784i	−0.335507	−	0.942038i	$-0.608907\pi$
$587$	−22.9124	−	3.62898i	−0.945698	−	0.149784i	−0.610191	+	0.792254i	$0.708907\pi$
$588$		0			0
$589$	30.6250	−	42.1517i	1.26188	−	1.73683i
$590$		0			0
$591$	14.9631	−	31.2064i	0.615500	−	1.28366i
$592$		0			0
$593$	−6.63871	+	6.63871i	−0.272619	+	0.272619i	−0.830154	−	0.557535i	$-0.811747\pi$
$593$	−6.63871	+	6.63871i	−0.272619	+	0.272619i	0.557535	+	0.830154i	$0.311747\pi$
$594$		0			0
$595$	0.149574	+	19.4296i	0.00613194	+	0.796536i
$596$		0			0
$597$	−0.624464	−	25.8691i	−0.0255576	−	1.05875i
$598$		0			0
$599$	−3.40483			−0.139118			−0.0695588	−	0.997578i	$-0.522159\pi$
$599$	−3.40483			−0.139118			−0.0695588	+	0.997578i	$0.522159\pi$
$600$		0			0
$601$	2.96693			0.121024			0.0605118	−	0.998167i	$-0.480727\pi$
$601$	2.96693			0.121024			0.0605118	+	0.998167i	$0.480727\pi$
$602$		0			0
$603$	−18.9259	−	33.0925i	−0.770722	−	1.34763i
$604$		0			0
$605$	9.36823	+	12.6877i	0.380873	+	0.515829i
$606$		0			0
$607$	−11.7030	+	11.7030i	−0.475010	+	0.475010i	−0.903532	−	0.428521i	$-0.859035\pi$
$607$	−11.7030	+	11.7030i	−0.475010	+	0.475010i	0.428521	+	0.903532i	$0.359035\pi$
$608$		0			0
$609$	12.1241	+	5.81336i	0.491293	+	0.235569i
$610$		0			0
$611$	−1.81745	+	2.50150i	−0.0735260	+	0.101200i
$612$		0			0
$613$	41.1420	+	6.51626i	1.66171	+	0.263189i	0.915440	−	0.402454i	$-0.131843\pi$
$613$	41.1420	+	6.51626i	1.66171	+	0.263189i	0.746271	+	0.665643i	$0.231843\pi$
$614$		0			0
$615$	26.7531	+	18.1651i	1.07879	+	0.732488i
$616$		0			0
$617$	8.90536	−	4.53751i	0.358516	−	0.182673i	−0.265450	−	0.964125i	$-0.585520\pi$
$617$	8.90536	−	4.53751i	0.358516	−	0.182673i	0.623966	+	0.781451i	$0.285520\pi$
$618$		0			0
$619$	−0.701573	−	0.227955i	−0.0281986	−	0.00916228i	0.294884	−	0.955533i	$-0.404719\pi$
$619$	−0.701573	−	0.227955i	−0.0281986	−	0.00916228i	−0.323082	+	0.946371i	$0.604719\pi$
$620$		0			0
$621$	3.05433	−	0.713489i	0.122566	−	0.0286313i
$622$		0			0
$623$	−6.46432	+	1.02385i	−0.258988	+	0.0410196i
$624$		0			0
$625$	6.98974	−	24.0030i	0.279590	−	0.960120i
$626$		0			0
$627$	−21.1266	+	16.1424i	−0.843714	+	0.644667i
$628$		0			0
$629$	8.68160	+	26.7192i	0.346158	+	1.06537i
$630$		0			0
$631$	7.30043	−	22.4684i	0.290626	−	0.894454i	−0.694030	−	0.719946i	$-0.744167\pi$
$631$	7.30043	−	22.4684i	0.290626	−	0.894454i	0.984656	−	0.174508i	$-0.0558334\pi$
$632$		0			0
$633$	−1.42791	−	0.985683i	−0.0567544	−	0.0391774i
$634$		0			0
$635$	−3.05235	+	1.58496i	−0.121129	+	0.0628973i
$636$		0			0
$637$	−0.521384	+	3.29189i	−0.0206580	+	0.130429i
$638$		0			0
$639$	8.55475	−	3.24378i	0.338421	−	0.128322i
$640$		0			0
$641$	10.1942	+	14.0312i	0.402648	+	0.554198i	0.961406	−	0.275133i	$-0.0887220\pi$
$641$	10.1942	+	14.0312i	0.402648	+	0.554198i	−0.558758	+	0.829331i	$0.688722\pi$
$642$		0			0
$643$	−19.4481	−	19.4481i	−0.766958	−	0.766958i	0.210612	−	0.977570i	$-0.432454\pi$
$643$	−19.4481	−	19.4481i	−0.766958	−	0.766958i	−0.977570	+	0.210612i	$0.932454\pi$
$644$		0			0
$645$	−10.3535	−	4.86669i	−0.407667	−	0.191626i
$646$		0			0
$647$	−0.917006	+	1.79973i	−0.0360512	+	0.0707546i	−0.908330	−	0.418255i	$-0.862642\pi$
$647$	−0.917006	+	1.79973i	−0.0360512	+	0.0707546i	0.872278	+	0.489010i	$0.162642\pi$
$648$		0			0
$649$			27.0495i			1.06179i
$650$		0			0
$651$	−11.0606	−	20.4709i	−0.433500	−	0.802316i
$652$		0			0
$653$	−17.2019	−	8.76480i	−0.673162	−	0.342993i	0.0837716	−	0.996485i	$-0.473303\pi$
$653$	−17.2019	−	8.76480i	−0.673162	−	0.342993i	−0.756934	+	0.653492i	$0.773303\pi$
$654$		0			0
$655$	−22.2627	+	0.171384i	−0.869876	+	0.00669653i
$656$		0			0
$657$	5.97148	+	28.6698i	0.232970	+	1.11851i
$658$		0			0
$659$	−31.9956	+	23.2462i	−1.24637	+	0.905543i	−0.998006	−	0.0631231i	$-0.979894\pi$
$659$	−31.9956	+	23.2462i	−1.24637	+	0.905543i	−0.248367	+	0.968666i	$0.579894\pi$
$660$		0			0
$661$	−29.5919	−	21.4997i	−1.15099	−	0.836243i	−0.162378	−	0.986729i	$-0.551916\pi$
$661$	−29.5919	−	21.4997i	−1.15099	−	0.836243i	−0.988612	+	0.150486i	$0.951916\pi$
$662$		0			0
$663$	−7.83629	+	2.75695i	−0.304336	+	0.107071i
$664$		0			0
$665$	−24.1514	+	24.5261i	−0.936552	+	0.951083i
$666$		0			0
$667$	−1.06783	−	2.09574i	−0.0413467	−	0.0811474i
$668$		0			0
$669$	7.89936	+	43.1130i	0.305407	+	1.66685i
$670$		0			0
$671$	−18.0763	+	5.87334i	−0.697827	+	0.226738i
$672$		0			0
$673$	−4.75453	−	30.0189i	−0.183274	−	1.15714i	−0.892126	−	0.451787i	$-0.850787\pi$
$673$	−4.75453	−	30.0189i	−0.183274	−	1.15714i	0.708852	−	0.705357i	$-0.249213\pi$
$674$		0			0
$675$	−19.5988	+	17.0554i	−0.754359	+	0.656462i
$676$		0			0
$677$	−4.63953	−	29.2929i	−0.178312	−	1.12582i	−0.900736	−	0.434366i	$-0.856972\pi$
$677$	−4.63953	−	29.2929i	−0.178312	−	1.12582i	0.722425	−	0.691450i	$-0.243028\pi$
$678$		0			0
$679$	−2.55107	+	0.828893i	−0.0979011	+	0.0318100i
$680$		0			0
$681$	−6.18195	−	33.7398i	−0.236893	−	1.29291i
$682$		0			0
$683$	4.38498	+	8.60601i	0.167787	+	0.329300i	0.959555	−	0.281522i	$-0.0908392\pi$
$683$	4.38498	+	8.60601i	0.167787	+	0.329300i	−0.791768	+	0.610822i	$0.790839\pi$
$684$		0			0
$685$	14.2053	−	2.36213i	0.542755	−	0.0902523i
$686$		0			0
$687$	31.3160	−	11.0175i	1.19478	−	0.420346i
$688$		0			0
$689$	−9.46640	−	6.87775i	−0.360641	−	0.262021i
$690$		0			0
$691$	−9.38046	+	6.81530i	−0.356849	+	0.259266i	−0.751737	−	0.659463i	$-0.770784\pi$
$691$	−9.38046	+	6.81530i	−0.356849	+	0.259266i	0.394887	+	0.918730i	$0.370784\pi$
$692$		0			0
$693$	2.42112	+	11.6241i	0.0919709	+	0.441563i
$694$		0			0
$695$	1.39861	−	4.41996i	0.0530522	−	0.167659i
$696$		0			0
$697$	−32.4482	−	16.5332i	−1.22906	−	0.626239i
$698$		0			0
$699$	9.29611	+	17.2051i	0.351611	+	0.650758i
$700$		0			0
$701$		−	47.4850i		−	1.79348i	−0.442556	−	0.896741i	$-0.645928\pi$
$701$		−	47.4850i		−	1.79348i	0.442556	−	0.896741i	$-0.354072\pi$
$702$		0			0
$703$	−22.5951	+	44.3454i	−0.852190	+	1.67252i
$704$		0			0
$705$	1.36045	−	10.8053i	0.0512374	−	0.406950i
$706$		0			0
$707$	−22.7062	−	22.7062i	−0.853956	−	0.853956i
$708$		0			0
$709$	24.5873	+	33.8414i	0.923394	+	1.27094i	0.962381	+	0.271703i	$0.0875867\pi$
$709$	24.5873	+	33.8414i	0.923394	+	1.27094i	−0.0389877	+	0.999240i	$0.512413\pi$
$710$		0			0
$711$	25.8750	−	9.81125i	0.970390	−	0.367951i
$712$		0			0
$713$	−0.636737	+	4.02020i	−0.0238460	+	0.150558i
$714$		0			0
$715$	2.18406	−	4.36929i	0.0816792	−	0.163402i
$716$		0			0
$717$	11.3091	+	7.80666i	0.422348	+	0.291545i
$718$		0			0
$719$	3.07429	−	9.46170i	0.114652	−	0.352862i	−0.877222	−	0.480084i	$-0.840606\pi$
$719$	3.07429	−	9.46170i	0.114652	−	0.352862i	0.991874	+	0.127222i	$0.0406062\pi$
$720$		0			0
$721$	−3.70071	−	11.3896i	−0.137822	−	0.424171i
$722$		0			0
$723$	−26.4420	+	20.2038i	−0.983387	+	0.751389i
$724$		0			0
$725$	15.9365	+	11.2078i	0.591866	+	0.416246i
$726$		0			0
$727$	−34.3889	+	5.44666i	−1.27541	+	0.202005i	−0.757164	−	0.653225i	$-0.773416\pi$
$727$	−34.3889	+	5.44666i	−1.27541	+	0.202005i	−0.518248	+	0.855230i	$0.673416\pi$
$728$		0			0
$729$	26.7174	−	3.89617i	0.989534	−	0.144303i
$730$		0			0
$731$	12.2531	+	3.98128i	0.453198	+	0.147253i
$732$		0			0
$733$	−11.5143	+	5.86682i	−0.425290	+	0.216696i	−0.653517	−	0.756912i	$-0.726707\pi$
$733$	−11.5143	+	5.86682i	−0.425290	+	0.216696i	0.228227	+	0.973608i	$0.426707\pi$
$734$		0			0
$735$	−3.98107	−	11.0434i	−0.146844	−	0.407342i
$736$		0			0
$737$	−24.9343	−	3.94920i	−0.918465	−	0.145471i
$738$		0			0
$739$	7.98551	−	10.9911i	0.293752	−	0.404315i	−0.636476	−	0.771296i	$-0.719609\pi$
$739$	7.98551	−	10.9911i	0.293752	−	0.404315i	0.930228	+	0.366981i	$0.119609\pi$
$740$		0			0
$741$	−13.2698	−	6.36271i	−0.487477	−	0.233740i
$742$		0			0
$743$	−17.0201	+	17.0201i	−0.624409	+	0.624409i	−0.946656	−	0.322247i	$-0.895562\pi$
$743$	−17.0201	+	17.0201i	−0.624409	+	0.624409i	0.322247	+	0.946656i	$0.395562\pi$
$744$		0			0
$745$	−13.0771	+	4.36057i	−0.479107	+	0.159759i
$746$		0			0
$747$	5.28713	+	9.24470i	0.193446	+	0.338246i
$748$		0			0
$749$	14.6081			0.533769
$750$		0			0
$751$	4.62541			0.168784			0.0843918	−	0.996433i	$-0.473105\pi$
$751$	4.62541			0.168784			0.0843918	+	0.996433i	$0.473105\pi$
$752$		0			0
$753$	−0.699273	−	28.9681i	−0.0254829	−	1.05566i
$754$		0			0
$755$	−25.0454	+	8.35142i	−0.911494	+	0.303939i
$756$		0			0
$757$	−37.1450	+	37.1450i	−1.35006	+	1.35006i	−0.464471	+	0.885588i	$0.653756\pi$
$757$	−37.1450	+	37.1450i	−1.35006	+	1.35006i	−0.885588	+	0.464471i	$0.846244\pi$
$758$		0			0
$759$	0.898036	−	1.87290i	0.0325967	−	0.0679821i
$760$		0			0
$761$	2.00068	−	2.75371i	0.0725248	−	0.0998218i	−0.771214	−	0.636577i	$-0.780350\pi$
$761$	2.00068	−	2.75371i	0.0725248	−	0.0998218i	0.843738	+	0.536755i	$0.180350\pi$
$762$		0			0
$763$	7.52316	+	1.19155i	0.272357	+	0.0431371i
$764$		0			0
$765$	19.4995	−	21.8141i	0.705004	−	0.788690i
$766$		0			0
$767$	−13.3401	+	6.79711i	−0.481682	+	0.245429i
$768$		0			0
$769$	25.5702	+	8.30827i	0.922086	+	0.299604i	0.731322	−	0.682032i	$-0.238904\pi$
$769$	25.5702	+	8.30827i	0.922086	+	0.299604i	0.190764	+	0.981636i	$0.438904\pi$
$770$		0			0
$771$	−25.2196	−	24.0307i	−0.908261	−	0.865444i
$772$		0			0
$773$	−24.1237	+	3.82081i	−0.867668	+	0.137425i	−0.574370	−	0.818596i	$-0.694753\pi$
$773$	−24.1237	+	3.82081i	−0.867668	+	0.137425i	−0.293298	+	0.956021i	$0.594753\pi$
$774$		0			0
$775$	−10.9110	−	31.9009i	−0.391935	−	1.14591i
$776$		0			0
$777$	13.4944	+	17.6609i	0.484109	+	0.633582i
$778$		0			0
$779$	−19.9362	−	61.3573i	−0.714288	−	2.19835i
$780$		0			0
$781$	1.87223	−	5.76213i	0.0669936	−	0.206185i
$782$		0			0
$783$	−7.63338	−	18.7532i	−0.272795	−	0.670186i
$784$		0			0
$785$	−11.6352	+	23.2766i	−0.415277	+	0.830776i
$786$		0			0
$787$	−4.41590	+	27.8809i	−0.157410	+	0.993846i	0.774873	+	0.632117i	$0.217814\pi$
$787$	−4.41590	+	27.8809i	−0.157410	+	0.993846i	−0.932283	+	0.361730i	$0.882186\pi$
$788$		0			0
$789$	−2.95391	+	22.0880i	−0.105162	+	0.786354i
$790$		0			0
$791$	22.2241	+	30.5889i	0.790198	+	1.08761i
$792$		0			0
$793$	−7.43885	−	7.43885i	−0.264161	−	0.264161i
$794$		0			0
$795$	40.8903	+	5.14832i	1.45023	+	0.182592i
$796$		0			0
$797$	10.8215	−	21.2383i	0.383316	−	0.752301i	−0.616057	−	0.787702i	$-0.711271\pi$
$797$	10.8215	−	21.2383i	0.383316	−	0.752301i	0.999373	+	0.0354009i	$0.0112708\pi$
$798$		0			0
$799$			12.2647i			0.433894i
$800$		0			0
$801$	8.24360	+	5.40153i	0.291273	+	0.190854i
$802$		0			0
$803$	17.2793	+	8.80422i	0.609772	+	0.310694i
$804$		0			0
$805$	0.811246	−	2.56375i	0.0285927	−	0.0903602i
$806$		0			0
$807$	5.51023	−	18.4635i	0.193969	−	0.649944i
$808$		0			0
$809$	19.9458	−	14.4915i	0.701257	−	0.509493i	−0.179084	−	0.983834i	$-0.557313\pi$
$809$	19.9458	−	14.4915i	0.701257	−	0.509493i	0.880341	+	0.474341i	$0.157313\pi$
$810$		0			0
$811$	5.81250	+	4.22303i	0.204105	+	0.148291i	0.685142	−	0.728409i	$-0.259740\pi$
$811$	5.81250	+	4.22303i	0.204105	+	0.148291i	−0.481038	+	0.876700i	$0.659740\pi$
$812$		0			0
$813$	−11.0088	−	31.2911i	−0.386095	−	1.09743i
$814$		0			0
$815$	48.1414	−	8.00522i	1.68632	−	0.280411i
$816$		0			0
$817$	10.3618	+	20.3363i	0.362515	+	0.711476i
$818$		0			0
$819$	−5.12430	+	4.11498i	−0.179057	+	0.143789i
$820$		0			0
$821$	47.9307	−	15.5736i	1.67279	−	0.543524i	0.689302	−	0.724474i	$-0.257917\pi$
$821$	47.9307	−	15.5736i	1.67279	−	0.543524i	0.983492	+	0.180951i	$0.0579174\pi$
$822$		0			0
$823$	1.19622	+	7.55262i	0.0416975	+	0.263268i	0.999726	−	0.0234051i	$-0.00745076\pi$
$823$	1.19622	+	7.55262i	0.0416975	+	0.263268i	−0.958029	+	0.286673i	$0.907451\pi$
$824$		0			0
$825$	0.679946	+	17.1914i	0.0236727	+	0.598527i
$826$		0			0
$827$	−0.379131	−	2.39374i	−0.0131837	−	0.0832386i	0.980219	−	0.197915i	$-0.0634169\pi$
$827$	−0.379131	−	2.39374i	−0.0131837	−	0.0832386i	−0.993403	+	0.114676i	$0.963417\pi$
$828$		0			0
$829$	−4.29112	+	1.39427i	−0.149037	+	0.0484250i	−0.382585	−	0.923920i	$-0.624966\pi$
$829$	−4.29112	+	1.39427i	−0.149037	+	0.0484250i	0.233549	+	0.972345i	$0.424966\pi$
$830$		0			0
$831$	11.9722	−	2.19360i	0.415311	−	0.0760951i
$832$		0			0
$833$	6.00186	+	11.7793i	0.207952	+	0.408129i
$834$		0			0
$835$	22.6436	−	22.9950i	0.783615	−	0.795773i
$836$		0			0
$837$	−8.38832	+	34.0189i	−0.289943	+	1.17587i
$838$		0			0
$839$	25.1246	+	18.2541i	0.867399	+	0.630202i	0.929888	−	0.367844i	$-0.119904\pi$
$839$	25.1246	+	18.2541i	0.867399	+	0.630202i	−0.0624889	+	0.998046i	$0.519904\pi$
$840$		0			0
$841$	11.1778	−	8.12118i	0.385443	−	0.280041i
$842$		0			0
$843$	52.1279	+	15.5570i	1.79538	+	0.535812i
$844$		0			0
$845$	−26.3644	+	0.202960i	−0.906963	+	0.00698204i
$846$		0			0
$847$	−12.5202	−	6.37935i	−0.430198	−	0.219197i
$848$		0			0
$849$	−23.3738	+	12.6291i	−0.802186	+	0.433430i
$850$		0			0
$851$		−	3.88810i		−	0.133282i
$852$		0			0
$853$	−8.57106	+	16.8217i	−0.293468	+	0.575963i	−0.989918	−	0.141642i	$-0.954762\pi$
$853$	−8.57106	+	16.8217i	−0.293468	+	0.575963i	0.696450	+	0.717605i	$0.254762\pi$
$854$		0			0
$855$	51.7520	−	2.89946i	1.76988	−	0.0991595i
$856$		0			0
$857$	9.19391	+	9.19391i	0.314058	+	0.314058i	0.846479	−	0.532421i	$-0.178718\pi$
$857$	9.19391	+	9.19391i	0.314058	+	0.314058i	−0.532421	+	0.846479i	$0.678718\pi$
$858$		0			0
$859$	0.706094	+	0.971854i	0.0240916	+	0.0331592i	0.820893	−	0.571082i	$-0.193476\pi$
$859$	0.706094	+	0.971854i	0.0240916	+	0.0331592i	−0.796801	+	0.604241i	$0.793476\pi$
$860$		0			0
$861$	−28.5568	−	3.81901i	−0.973213	−	0.130151i
$862$		0			0
$863$	2.71860	−	17.1646i	0.0925423	−	0.584289i	−0.897222	−	0.441579i	$-0.854418\pi$
$863$	2.71860	−	17.1646i	0.0925423	−	0.584289i	0.989765	−	0.142710i	$-0.0455815\pi$
$864$		0			0
$865$	10.1508	−	5.27091i	0.345137	−	0.179216i
$866$		0			0
$867$	−1.99161	+	2.88516i	−0.0676388	+	0.0979851i
$868$		0			0
$869$	5.66281	−	17.4284i	0.192098	−	0.591216i
$870$		0			0
$871$	−4.31794	−	13.2893i	−0.146308	−	0.450289i
$872$		0			0
$873$	3.68326	+	1.65798i	0.124659	+	0.0561141i
$874$		0			0
$875$	3.99149	+	21.9133i	0.134937	+	0.740804i
$876$		0			0
$877$	−6.09174	+	0.964837i	−0.205704	+	0.0325802i	−0.258436	−	0.966028i	$-0.583207\pi$
$877$	−6.09174	+	0.964837i	−0.205704	+	0.0325802i	0.0527322	+	0.998609i	$0.483207\pi$
$878$		0			0
$879$	33.2885	−	34.9353i	1.12279	−	1.17834i
$880$		0			0
$881$	35.5675	+	11.5566i	1.19830	+	0.389351i	0.839134	−	0.543924i	$-0.183062\pi$
$881$	35.5675	+	11.5566i	1.19830	+	0.389351i	0.359163	+	0.933275i	$0.383062\pi$
$882$		0			0
$883$	−6.51192	+	3.31799i	−0.219144	+	0.111659i	−0.560116	−	0.828414i	$-0.689244\pi$
$883$	−6.51192	+	3.31799i	−0.219144	+	0.111659i	0.340973	+	0.940073i	$0.389244\pi$
$884$		0			0
$885$	29.6224	−	43.6271i	0.995745	−	1.46651i
$886$		0			0
$887$	38.2644	+	6.06049i	1.28479	+	0.203491i	0.761222	−	0.648491i	$-0.224600\pi$
$887$	38.2644	+	6.06049i	1.28479	+	0.203491i	0.523571	+	0.851982i	$0.324600\pi$
$888$		0			0
$889$	1.80113	−	2.47905i	0.0604081	−	0.0831446i
$890$		0			0
$891$	9.06627	−	15.4107i	0.303731	−	0.516278i
$892$		0			0
$893$	−15.3636	+	15.3636i	−0.514122	+	0.514122i
$894$		0			0
$895$	9.47340	+	12.8301i	0.316661	+	0.428864i
$896$		0			0
$897$	1.14933	−	0.0277441i	0.0383749	−	0.000926347i
$898$		0			0
$899$	26.2749			0.876316
$900$		0			0
$901$	−46.4132			−1.54625
$902$		0			0
$903$	10.1897	−	0.245974i	0.339093	−	0.00818550i
$904$		0			0
$905$	0.00793256	+	1.03044i	0.000263687	+	0.0342528i
$906$		0			0
$907$	−6.92591	+	6.92591i	−0.229971	+	0.229971i	−0.812681	−	0.582710i	$-0.801993\pi$
$907$	−6.92591	+	6.92591i	−0.229971	+	0.229971i	0.582710	+	0.812681i	$0.301993\pi$
$908$		0			0
$909$	2.33316	+	48.2987i	0.0773861	+	1.60197i
$910$		0			0
$911$	20.9000	−	28.7663i	0.692446	−	0.953071i	−0.307553	−	0.951531i	$-0.599510\pi$
$911$	20.9000	−	28.7663i	0.692446	−	0.953071i	0.999999	−	0.00153941i	$-0.000490009\pi$
$912$		0			0
$913$	6.96562	+	1.10325i	0.230528	+	0.0365121i
$914$		0			0
$915$	35.5865	+	10.3227i	1.17645	+	0.341260i
$916$		0			0
$917$	17.6737	−	9.00518i	0.583636	−	0.297377i
$918$		0			0
$919$	−4.22169	−	1.37171i	−0.139261	−	0.0452485i	0.238557	−	0.971128i	$-0.423326\pi$
$919$	−4.22169	−	1.37171i	−0.139261	−	0.0452485i	−0.377818	+	0.925880i	$0.623326\pi$
$920$		0			0
$921$	−27.1041	+	28.4450i	−0.893109	+	0.937294i
$922$		0			0
$923$	3.31218	−	0.524598i	0.109022	−	0.0172674i
$924$		0			0
$925$	15.0612	+	28.4672i	0.495210	+	0.935995i
$926$		0			0
$927$	−7.40228	+	16.4444i	−0.243123	+	0.540106i
$928$		0			0
$929$	9.97663	+	30.7049i	0.327323	+	1.00740i	0.970381	+	0.241578i	$0.0776651\pi$
$929$	9.97663	+	30.7049i	0.327323	+	1.00740i	−0.643059	+	0.765817i	$0.722335\pi$
$930$		0			0
$931$	−7.23722	+	22.2739i	−0.237190	+	0.729996i
$932$		0			0
$933$	25.1947	−	36.4984i	0.824838	−	1.19490i
$934$		0			0
$935$	−3.17825	−	19.1132i	−0.103940	−	0.625069i
$936$		0			0
$937$	7.99879	−	50.5024i	0.261309	−	1.64984i	−0.412516	−	0.910950i	$-0.635350\pi$
$937$	7.99879	−	50.5024i	0.261309	−	1.64984i	0.673825	−	0.738891i	$-0.264650\pi$
$938$		0			0
$939$	0.209445	+	0.0280098i	0.00683497	+	0.000914066i
$940$		0			0
$941$	−25.1318	−	34.5909i	−0.819273	−	1.12763i	−0.989826	−	0.142284i	$-0.954555\pi$
$941$	−25.1318	−	34.5909i	−0.819273	−	1.12763i	0.170553	−	0.985348i	$-0.445445\pi$
$942$		0			0
$943$	3.56381	+	3.56381i	0.116054	+	0.116054i
$944$		0			0
$945$	8.82480	−	21.3995i	0.287071	−	0.696124i
$946$		0			0
$947$	9.40618	−	18.4607i	0.305660	−	0.599891i	−0.686173	−	0.727439i	$-0.740711\pi$
$947$	9.40618	−	18.4607i	0.305660	−	0.599891i	0.991832	+	0.127548i	$0.0407106\pi$
$948$		0			0
$949$			10.7340i			0.348441i
$950$		0			0
$951$	23.4674	−	12.6797i	0.760981	−	0.411166i
$952$		0			0
$953$	35.2565	+	17.9641i	1.14207	+	0.581914i	0.919534	−	0.393010i	$-0.128566\pi$
$953$	35.2565	+	17.9641i	1.14207	+	0.581914i	0.222537	+	0.974924i	$0.428566\pi$
$954$		0			0
$955$	−46.7903	−	33.4479i	−1.51410	−	1.08235i
$956$		0			0
$957$	−12.8481	−	3.83437i	−0.415319	−	0.123948i
$958$		0			0
$959$	−10.3797	+	7.54129i	−0.335178	+	0.243521i
$960$		0			0
$961$	−11.7054	−	8.50444i	−0.377592	−	0.274337i
$962$		0			0
$963$	−16.2871	−	14.7860i	−0.524843	−	0.476473i
$964$		0			0
$965$	−47.5810	−	23.7841i	−1.53168	−	0.765638i
$966$		0			0
$967$	−3.50332	−	6.87564i	−0.112659	−	0.221106i	0.827792	−	0.561035i	$-0.189597\pi$
$967$	−3.50332	−	6.87564i	−0.112659	−	0.221106i	−0.940451	+	0.339929i	$0.889597\pi$
$968$		0			0
$969$	−57.4175	+	10.5203i	−1.84451	+	0.337960i
$970$		0			0
$971$	22.9417	−	7.45420i	0.736233	−	0.239217i	0.0831861	−	0.996534i	$-0.473490\pi$
$971$	22.9417	−	7.45420i	0.736233	−	0.239217i	0.653047	+	0.757317i	$0.273490\pi$
$972$		0			0
$973$	0.646141	+	4.07957i	0.0207143	+	0.130785i
$974$		0			0
$975$	−8.30746	+	4.65525i	−0.266052	+	0.149087i
$976$		0			0
$977$	−1.23479	−	7.79613i	−0.0395043	−	0.249420i	0.960031	−	0.279893i	$-0.0902988\pi$
$977$	−1.23479	−	7.79613i	−0.0395043	−	0.249420i	−0.999536	+	0.0304724i	$0.990299\pi$
$978$		0			0
$979$	6.20711	−	2.01681i	0.198380	−	0.0644576i
$980$		0			0
$981$	−7.18175	−	8.94328i	−0.229296	−	0.285537i
$982$		0			0
$983$	−1.78637	−	3.50596i	−0.0569765	−	0.111823i	0.860762	−	0.509007i	$-0.169987\pi$
$983$	−1.78637	−	3.50596i	−0.0569765	−	0.111823i	−0.917739	+	0.397184i	$0.869987\pi$
$984$		0			0
$985$	−6.64943	+	44.1815i	−0.211869	+	1.40774i
$986$		0			0
$987$	3.22021	+	9.15305i	0.102501	+	0.291345i
$988$		0			0
$989$	−1.44251	−	1.04804i	−0.0458691	−	0.0333258i
$990$		0			0
$991$	−28.1998	+	20.4884i	−0.895797	+	0.650834i	−0.937383	−	0.348301i	$-0.886759\pi$
$991$	−28.1998	+	20.4884i	−0.895797	+	0.650834i	0.0415863	+	0.999135i	$0.486759\pi$
$992$		0			0
$993$	−0.869985	+	2.91511i	−0.0276081	+	0.0925083i
$994$		0			0
$995$	10.5675	+	31.6911i	0.335011	+	1.00468i
$996$		0			0
$997$	9.54686	+	4.86437i	0.302352	+	0.154056i	0.598584	−	0.801060i	$-0.295730\pi$
$997$	9.54686	+	4.86437i	0.302352	+	0.154056i	−0.296232	+	0.955116i	$0.595730\pi$
$998$		0			0
$999$	2.83065	−	33.3495i	0.0895579	−	1.05513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.113.1	yes	80
3.2	odd	2	inner	300.2.x.a.113.8	yes	80
25.2	odd	20	inner	300.2.x.a.77.8	yes	80
75.2	even	20	inner	300.2.x.a.77.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.77.1	✓	80	75.2	even	20	inner
300.2.x.a.77.8	yes	80	25.2	odd	20	inner
300.2.x.a.113.1	yes	80	1.1	even	1	trivial
300.2.x.a.113.8	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73155 + 0.0417985i) q^{3} +(2.12124 - 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(2.99651 - 0.144752i) q^{9} +O(q^{10})\)	\(q+(-1.73155 + 0.0417985i) q^{3} +(2.12124 - 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(2.99651 - 0.144752i) q^{9} +(1.16772 - 1.60723i) q^{11} +(1.08607 + 0.172017i) q^{13} +(-3.64347 + 1.31345i) q^{15} +(3.88627 - 1.98015i) q^{17} +(7.34866 + 2.38772i) q^{19} +(2.38038 - 2.49815i) q^{21} +(-0.596200 + 0.0944288i) q^{23} +(3.99936 - 3.00085i) q^{25} +(-5.18254 + 0.375894i) q^{27} +(1.20411 + 3.70588i) q^{29} +(2.08371 - 6.41301i) q^{31} +(-1.95478 + 2.83180i) q^{33} +(-1.99181 + 3.98468i) q^{35} +(-1.00762 + 6.36188i) q^{37} +(-1.88777 - 0.252459i) q^{39} +(-4.90769 - 6.75485i) q^{41} +(2.08869 + 2.08869i) q^{43} +(6.25393 - 2.42658i) q^{45} +(-1.27659 + 2.50545i) q^{47} +3.03101i q^{49} +(-6.64648 + 3.59117i) q^{51} +(-9.48136 - 4.83099i) q^{53} +(1.34017 - 4.23529i) q^{55} +(-12.8243 - 3.82729i) q^{57} +(-11.0153 + 8.00310i) q^{59} +(-7.73999 - 5.62344i) q^{61} +(-4.01733 + 4.42516i) q^{63} +(2.42549 - 0.403324i) q^{65} +(-5.76904 - 11.3224i) q^{67} +(1.02840 - 0.188428i) q^{69} +(2.90043 - 0.942408i) q^{71} +(1.52706 + 9.64150i) q^{73} +(-6.79964 + 5.36329i) q^{75} +(0.619145 + 3.90913i) q^{77} +(8.77277 - 2.85044i) q^{79} +(8.95809 - 0.867500i) q^{81} +(1.61164 + 3.16301i) q^{83} +(6.84310 - 6.94927i) q^{85} +(-2.23988 - 6.36657i) q^{87} +(2.65779 + 1.93100i) q^{89} +(-1.77229 + 1.28765i) q^{91} +(-3.33999 + 11.1915i) q^{93} +(17.2772 - 0.133005i) q^{95} +(1.19966 + 0.611256i) q^{97} +(3.26643 - 4.98510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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