LMFDB - Embedded newform 300.2.x.a.113.8

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			113.8
Character	$\chi$	$=$	300.113
Dual form			300.2.x.a.77.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.983962 + 1.42542i) q^{3} +(-2.12124 + 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(-1.06364 + 2.80512i) q^{9} +O(q^{10})$	\(q+(0.983962 + 1.42542i) q^{3} +(-2.12124 + 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(-1.06364 + 2.80512i) q^{9} +(-1.16772 + 1.60723i) q^{11} +(1.08607 + 0.172017i) q^{13} +(-3.09547 - 2.32767i) q^{15} +(-3.88627 + 1.98015i) q^{17} +(7.34866 + 2.38772i) q^{19} +(-3.39415 - 0.621890i) q^{21} +(0.596200 - 0.0944288i) q^{23} +(3.99936 - 3.00085i) q^{25} +(-5.04504 + 1.24400i) q^{27} +(-1.20411 - 3.70588i) q^{29} +(2.08371 - 6.41301i) q^{31} +(-3.43996 - 0.0830386i) q^{33} +(1.99181 - 3.98468i) q^{35} +(-1.00762 + 6.36188i) q^{37} +(0.823455 + 1.71736i) q^{39} +(4.90769 + 6.75485i) q^{41} +(2.08869 + 2.08869i) q^{43} +(0.272086 - 6.70268i) q^{45} +(1.27659 - 2.50545i) q^{47} +3.03101i q^{49} +(-6.64648 - 3.59117i) q^{51} +(9.48136 + 4.83099i) q^{53} +(1.34017 - 4.23529i) q^{55} +(3.82729 + 12.8243i) q^{57} +(11.0153 - 8.00310i) q^{59} +(-7.73999 - 5.62344i) q^{61} +(-2.45326 - 5.44999i) q^{63} +(-2.42549 + 0.403324i) q^{65} +(-5.76904 - 11.3224i) q^{67} +(0.721238 + 0.756920i) q^{69} +(-2.90043 + 0.942408i) q^{71} +(1.52706 + 9.64150i) q^{73} +(8.21269 + 2.74804i) q^{75} +(-0.619145 - 3.90913i) q^{77} +(8.77277 - 2.85044i) q^{79} +(-6.73735 - 5.96726i) q^{81} +(-1.61164 - 3.16301i) q^{83} +(6.84310 - 6.94927i) q^{85} +(4.09763 - 5.36281i) q^{87} +(-2.65779 - 1.93100i) q^{89} +(-1.77229 + 1.28765i) q^{91} +(11.1915 - 3.33999i) q^{93} +(-17.2772 + 0.133005i) q^{95} +(1.19966 + 0.611256i) q^{97} +(-3.26643 - 4.98510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.983962	+	1.42542i	0.568091	+	0.822966i
$3$	0.983962	+	1.42542i	0.568091	+	0.822966i
$4$		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
$9$	−1.06364	+	2.80512i	−0.354546	+	0.935039i
$10$		0			0
$11$	−1.16772	+	1.60723i	−0.352081	+	0.484597i	−0.947921	−	0.318506i	$-0.896819\pi$
$11$	−1.16772	+	1.60723i	−0.352081	+	0.484597i	0.595840	+	0.803103i	$0.296819\pi$
$12$		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
$15$	−3.09547	−	2.32767i	−0.799247	−	0.601003i
$16$		0			0
$17$	−3.88627	+	1.98015i	−0.942558	+	0.480257i	−0.856565	−	0.516038i	$-0.827406\pi$
$17$	−3.88627	+	1.98015i	−0.942558	+	0.480257i	−0.0859928	+	0.996296i	$0.527406\pi$
$18$		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
$21$	−3.39415	−	0.621890i	−0.740663	−	0.135708i
$22$		0			0
$23$	0.596200	−	0.0944288i	0.124316	−	0.0196898i	−0.0939663	−	0.995575i	$-0.529955\pi$
$23$	0.596200	−	0.0944288i	0.124316	−	0.0196898i	0.218282	+	0.975886i	$0.429955\pi$
$24$		0			0
$25$	3.99936	−	3.00085i	0.799872	−	0.600171i
$26$		0			0
$27$	−5.04504	+	1.24400i	−0.970919	+	0.239407i
$28$		0			0
$29$	−1.20411	−	3.70588i	−0.223598	−	0.688164i	−0.998431	−	0.0559981i	$-0.982166\pi$
$29$	−1.20411	−	3.70588i	−0.223598	−	0.688164i	0.774833	−	0.632166i	$-0.217834\pi$
$30$		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
$33$	−3.43996	−	0.0830386i	−0.598821	−	0.0144552i
$34$		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
$39$	0.823455	+	1.71736i	0.131858	+	0.274998i
$40$		0			0
$41$	4.90769	+	6.75485i	0.766452	+	1.05493i	0.996650	+	0.0817869i	$0.0260627\pi$
$41$	4.90769	+	6.75485i	0.766452	+	1.05493i	−0.230198	+	0.973144i	$0.573937\pi$
$42$		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
$45$	0.272086	−	6.70268i	0.0405602	−	0.999177i
$46$		0			0
$47$	1.27659	−	2.50545i	0.186210	−	0.365458i	−0.778963	−	0.627070i	$-0.784254\pi$
$47$	1.27659	−	2.50545i	0.186210	−	0.365458i	0.965173	+	0.261612i	$0.0842541\pi$
$48$		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	0.961053	−	0.276362i	$-0.0891290\pi$
$53$	9.48136	+	4.83099i	1.30236	+	0.663588i	0.341311	+	0.939950i	$0.389129\pi$
$54$		0			0
$55$	1.34017	−	4.23529i	0.180709	−	0.571086i
$56$		0			0
$57$	3.82729	+	12.8243i	0.506937	+	1.69863i
$58$		0			0
$59$	11.0153	−	8.00310i	1.43407	−	1.04192i	0.444834	−	0.895613i	$-0.353263\pi$
$59$	11.0153	−	8.00310i	1.43407	−	1.04192i	0.989240	−	0.146302i	$-0.0467372\pi$
$60$		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
$63$	−2.45326	−	5.44999i	−0.309081	−	0.686635i
$64$		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
$69$	0.721238	+	0.756920i	0.0868269	+	0.0911225i
$70$		0			0
$71$	−2.90043	+	0.942408i	−0.344218	+	0.111843i	−0.476024	−	0.879432i	$-0.657922\pi$
$71$	−2.90043	+	0.942408i	−0.344218	+	0.111843i	0.131806	+	0.991276i	$0.457922\pi$
$72$		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
$75$	8.21269	+	2.74804i	0.948320	+	0.317316i
$76$		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
$81$	−6.73735	−	5.96726i	−0.748594	−	0.663029i
$82$		0			0
$83$	−1.61164	−	3.16301i	−0.176900	−	0.347186i	0.785483	−	0.618884i	$-0.212415\pi$
$83$	−1.61164	−	3.16301i	−0.176900	−	0.347186i	−0.962383	+	0.271698i	$0.912415\pi$
$84$		0			0
$85$	6.84310	−	6.94927i	0.742238	−	0.753755i
$86$		0			0
$87$	4.09763	−	5.36281i	0.439312	−	0.574953i
$88$		0			0
$89$	−2.65779	−	1.93100i	−0.281725	−	0.204685i	0.437944	−	0.899002i	$-0.355707\pi$
$89$	−2.65779	−	1.93100i	−0.281725	−	0.204685i	−0.719670	+	0.694317i	$0.755707\pi$
$90$		0			0
$91$	−1.77229	+	1.28765i	−0.185787	+	0.134982i
$92$		0			0
$93$	11.1915	−	3.33999i	1.16051	−	0.346341i
$94$		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	$-0.703813\pi$
$101$		−	16.1183i		−	1.60383i	0.597435	−	0.801917i	$-0.296187\pi$
$102$		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
$105$	7.63970	−	1.08161i	0.745558	−	0.105554i
$106$		0			0
$107$	5.18489	+	5.18489i	0.501242	+	0.501242i	0.911824	−	0.410582i	$-0.134674\pi$
$107$	5.18489	+	5.18489i	0.501242	+	0.501242i	−0.410582	+	0.911824i	$0.634674\pi$
$108$		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
$111$	−10.0598	+	4.82356i	−0.954835	+	0.457832i
$112$		0			0
$113$	−2.96892	+	18.7450i	−0.279292	+	1.76338i	0.305493	+	0.952194i	$0.401179\pi$
$113$	−2.96892	+	18.7450i	−0.279292	+	1.76338i	−0.584786	+	0.811188i	$0.698821\pi$
$114$		0			0
$115$	−1.19789	+	0.622019i	−0.111704	+	0.0580035i
$116$		0			0
$117$	−1.63771	+	2.86359i	−0.151407	+	0.264739i
$118$		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
$123$	−4.79952	+	13.6420i	−0.432758	+	1.23006i
$124$		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
$129$	−0.922067	+	5.03245i	−0.0811835	+	0.443082i
$130$		0			0
$131$	9.46918	+	3.07672i	0.827326	+	0.268814i	0.691918	−	0.721976i	$-0.256766\pi$
$131$	9.46918	+	3.07672i	0.827326	+	0.268814i	0.135407	+	0.990790i	$0.456766\pi$
$132$		0			0
$133$	−13.7158	+	6.98857i	−1.18931	+	0.605986i
$134$		0			0
$135$	9.82185	−	6.20735i	0.845331	−	0.534243i
$136$		0			0
$137$	−6.36073	−	1.00744i	−0.543434	−	0.0860715i	−0.121319	−	0.992614i	$-0.538712\pi$
$137$	−6.36073	−	1.00744i	−0.543434	−	0.0860715i	−0.422115	+	0.906542i	$0.638712\pi$
$138$		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
$141$	4.82744	−	0.645591i	0.406544	−	0.0543686i
$142$		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
$147$	−4.32046	+	2.98240i	−0.356346	+	0.245984i
$148$		0			0
$149$	6.16481			0.505041			0.252520	−	0.967592i	$-0.418741\pi$
$149$	6.16481			0.505041			0.252520	+	0.967592i	$0.418741\pi$
$150$		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
$153$	−1.42097	−	13.0076i	−0.114879	−	1.05160i
$154$		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
$159$	2.44310	+	18.2684i	0.193751	+	1.44878i
$160$		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
$165$	7.35574	−	2.25706i	0.572644	−	0.175712i
$166$		0			0
$167$	−12.8596	+	6.55227i	−0.995102	+	0.507030i	−0.874164	−	0.485630i	$-0.838590\pi$
$167$	−12.8596	+	6.55227i	−0.995102	+	0.507030i	−0.120938	+	0.992660i	$0.538590\pi$
$168$		0			0
$169$	−11.2138	−	3.64358i	−0.862598	−	0.280275i
$170$		0			0
$171$	−14.5142	+	18.0742i	−1.10993	+	1.38217i
$172$		0			0
$173$	−5.05212	+	0.800177i	−0.384106	+	0.0608364i	−0.345501	−	0.938418i	$-0.612291\pi$
$173$	−5.05212	+	0.800177i	−0.384106	+	0.0608364i	−0.0386042	+	0.999255i	$0.512291\pi$
$174$		0			0
$175$	−1.40661	+	9.86135i	−0.106330	+	0.745448i
$176$		0			0
$177$	22.2464	+	7.82671i	1.67214	+	0.588291i
$178$		0			0
$179$	−2.20404	−	6.78334i	−0.164738	−	0.507011i	0.834279	−	0.551342i	$-0.185884\pi$
$179$	−2.20404	−	6.78334i	−0.164738	−	0.507011i	−0.999017	+	0.0443316i	$0.985884\pi$
$180$		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
$183$	0.399893	−	16.5660i	0.0295609	−	1.22459i
$184$		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
$189$	5.35462	−	8.85950i	0.389491	−	0.644434i
$190$		0			0
$191$	15.1190	+	20.8095i	1.09397	+	1.50572i	0.843142	+	0.537691i	$0.180703\pi$
$191$	15.1190	+	20.8095i	1.09397	+	1.50572i	0.250829	+	0.968031i	$0.419297\pi$
$192$		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
$195$	−2.96150	−	3.06049i	−0.212077	−	0.219166i
$196$		0			0
$197$	9.07122	−	17.8033i	0.646298	−	1.26843i	−0.302681	−	0.953092i	$-0.597882\pi$
$197$	9.07122	−	17.8033i	0.646298	−	1.26843i	0.948979	−	0.315339i	$-0.102118\pi$
$198$		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
$207$	−0.369257	+	1.77285i	−0.0256652	+	0.123221i
$208$		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
$213$	−4.19724	−	3.20704i	−0.287590	−	0.219743i
$214$		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
$219$	−12.2406	+	11.6636i	−0.827143	+	0.788151i
$220$		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
$225$	4.16387	+	14.4105i	0.277591	+	0.960699i
$226$		0			0
$227$	−3.09802	−	19.5601i	−0.205623	−	1.29825i	−0.847233	−	0.531221i	$-0.821733\pi$
$227$	−3.09802	−	19.5601i	−0.205623	−	1.29825i	0.641610	−	0.767031i	$-0.278267\pi$
$228$		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
$231$	4.96293	−	4.72897i	0.326537	−	0.311143i
$232$		0			0
$233$	5.12583	+	10.0600i	0.335804	+	0.659053i	0.995734	−	0.0922745i	$-0.0294137\pi$
$233$	5.12583	+	10.0600i	0.335804	+	0.659053i	−0.659929	+	0.751328i	$0.729414\pi$
$234$		0			0
$235$	−0.935774	+	6.21765i	−0.0610431	+	0.405595i
$236$		0			0
$237$	12.6951	+	9.70014i	0.824638	+	0.630092i
$238$		0			0
$239$	6.41867	+	4.66343i	0.415189	+	0.301652i	0.775699	−	0.631103i	$-0.217397\pi$
$239$	6.41867	+	4.66343i	0.415189	+	0.301652i	−0.360510	+	0.932755i	$0.617397\pi$
$240$		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
$243$	1.87655	−	15.4751i	0.120381	−	0.992728i
$244$		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	$-0.822949\pi$
$251$		−	16.7296i		−	1.05596i	0.849255	−	0.527982i	$-0.177051\pi$
$252$		0			0
$253$	−0.544425	+	1.06849i	−0.0342277	+	0.0671757i
$254$		0			0
$255$	16.6390	+	2.91646i	1.04197	+	0.182636i
$256$		0			0
$257$	−14.2215	−	14.2215i	−0.887111	−	0.887111i	0.107134	−	0.994245i	$-0.465833\pi$
$257$	−14.2215	−	14.2215i	−0.887111	−	0.887111i	−0.994245	+	0.107134i	$0.965833\pi$
$258$		0			0
$259$	−7.54266	−	10.3816i	−0.468678	−	0.645080i
$260$		0			0
$261$	11.6762	+	0.564039i	0.722736	+	0.0349132i
$262$		0			0
$263$	−2.01269	+	12.7077i	−0.124108	+	0.783587i	0.844602	+	0.535394i	$0.179837\pi$
$263$	−2.01269	+	12.7077i	−0.124108	+	0.783587i	−0.968710	+	0.248193i	$0.920163\pi$
$264$		0			0
$265$	−23.5294	−	3.54124i	−1.44540	−	0.217537i
$266$		0			0
$267$	0.137317	−	5.68849i	0.00840365	−	0.348130i
$268$		0			0
$269$	3.43765	−	10.5800i	0.209597	−	0.645074i	−0.789896	−	0.613241i	$-0.789865\pi$
$269$	3.43765	−	10.5800i	0.209597	−	0.645074i	0.999493	−	0.0318333i	$-0.0101346\pi$
$270$		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
$273$	−3.57930	−	1.25927i	−0.216629	−	0.0762142i
$274$		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
$279$	15.7729	+	12.6662i	0.944300	+	0.758305i
$280$		0			0
$281$	29.8705	+	9.70552i	1.78193	+	0.578983i	0.999066	−	0.0432145i	$-0.0137599\pi$
$281$	29.8705	+	9.70552i	1.78193	+	0.578983i	0.782860	+	0.622197i	$0.213760\pi$
$282$		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
$285$	−17.1897	−	24.4964i	−1.01823	−	1.45104i
$286$		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
$291$	0.309121	+	2.31147i	0.0181210	+	0.135501i
$292$		0			0
$293$	19.7002	−	19.7002i	1.15090	−	1.15090i	0.164528	−	0.986372i	$-0.447390\pi$
$293$	19.7002	−	19.7002i	1.15090	−	1.15090i	0.986372	−	0.164528i	$-0.0526102\pi$
$294$		0			0
$295$	−17.7053	+	24.7681i	−1.03085	+	1.44205i
$296$		0			0
$297$	3.89181	−	9.56117i	0.225826	−	0.554795i
$298$		0			0
$299$	0.663758			0.0383861
$300$		0			0
$301$	−5.88476			−0.339192
$302$		0			0
$303$	22.9754	−	15.8598i	1.31990	−	0.911123i
$304$		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
$309$	−10.3199	+	1.38011i	−0.587077	+	0.0785119i
$310$		0			0
$311$	15.0505	−	20.7152i	0.853433	−	1.17465i	−0.129663	−	0.991558i	$-0.541389\pi$
$311$	15.0505	−	20.7152i	0.853433	−	1.17465i	0.983096	−	0.183092i	$-0.0586106\pi$
$312$		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
$315$	9.05892	+	9.82550i	0.510412	+	0.553604i
$316$		0			0
$317$	13.7216	−	6.99151i	0.770682	−	0.392682i	−0.0239969	−	0.999712i	$-0.507639\pi$
$317$	13.7216	−	6.99151i	0.770682	−	0.392682i	0.794679	+	0.607030i	$0.207639\pi$
$318$		0			0
$319$	7.36226	+	2.39214i	0.412207	+	0.133934i
$320$		0			0
$321$	−2.28891	+	12.4924i	−0.127754	+	0.697256i
$322$		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
$327$	2.19776	−	6.24685i	0.121536	−	0.345452i
$328$		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
$333$	−16.7741	−	9.59324i	−0.919213	−	0.525706i
$334$		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
$339$	−29.6408	+	14.2124i	−1.60987	+	0.771913i
$340$		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
$345$	−2.06532	−	1.09546i	−0.111193	−	0.0589774i
$346$		0			0
$347$	−14.2252	+	27.9185i	−0.763647	+	1.49874i	0.100189	+	0.994968i	$0.468055\pi$
$347$	−14.2252	+	27.9185i	−0.763647	+	1.49874i	−0.863836	+	0.503773i	$0.831945\pi$
$348$		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	0.447833	−	0.894117i	$-0.352196\pi$
$353$	−0.230966	−	0.117683i	−0.0122931	−	0.00626364i	−0.460126	+	0.887854i	$0.652196\pi$
$354$		0			0
$355$	5.48593	−	4.05065i	0.291163	−	0.214986i
$356$		0			0
$357$	14.4220	−	4.30409i	0.763293	−	0.227797i
$358$		0			0
$359$	17.7312	−	12.8824i	0.935815	−	0.679909i	−0.0115948	−	0.999933i	$-0.503691\pi$
$359$	17.7312	−	12.8824i	0.935815	−	0.679909i	0.947410	+	0.320024i	$0.103691\pi$
$360$		0			0
$361$	32.9302	+	23.9252i	1.73317	+	1.25922i
$362$		0			0
$363$	−7.41715	+	9.70726i	−0.389299	+	0.509499i
$364$		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
$369$	−24.1681	+	6.58191i	−1.25814	+	0.342641i
$370$		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
$375$	−19.3649	−	0.0201467i	−0.999999	−	0.00104037i
$376$		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
$381$	−1.83778	−	1.92870i	−0.0941525	−	0.0988105i
$382$		0			0
$383$	−14.1048	−	27.6823i	−0.720723	−	1.41450i	−0.902294	−	0.431121i	$-0.858118\pi$
$383$	−14.1048	−	27.6823i	−0.720723	−	1.41450i	0.181571	−	0.983378i	$-0.441882\pi$
$384$		0			0
$385$	4.07841	+	7.85427i	0.207855	+	0.400291i
$386$		0			0
$387$	−8.08062	+	3.63740i	−0.410761	+	0.184900i
$388$		0			0
$389$	−3.47117	−	2.52196i	−0.175996	−	0.127868i	0.496300	−	0.868151i	$-0.334692\pi$
$389$	−3.47117	−	2.52196i	−0.175996	−	0.127868i	−0.672296	+	0.740283i	$0.734692\pi$
$390$		0			0
$391$	−2.13001	+	1.54754i	−0.107719	+	0.0782625i
$392$		0			0
$393$	4.93169	+	16.5249i	0.248771	+	0.833572i
$394$		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	$-0.926242\pi$
$401$		−	9.19743i		−	0.459297i	0.973274	−	0.229649i	$-0.0737577\pi$
$402$		0			0
$403$	3.36620	−	6.60655i	0.167683	−	0.329096i
$404$		0			0
$405$	18.5124	+	7.89246i	0.919889	+	0.392180i
$406$		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
$411$	−4.82269	−	10.0580i	−0.237886	−	0.496124i
$412$		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
$417$	3.58995	+	0.0866593i	0.175801	+	0.00424372i
$418$		0			0
$419$	−1.79122	+	5.51280i	−0.0875066	+	0.269318i	−0.985228	−	0.171245i	$-0.945221\pi$
$419$	−1.79122	+	5.51280i	−0.0875066	+	0.269318i	0.897722	+	0.440563i	$0.145221\pi$
$420$		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
$423$	5.67025	+	6.24588i	0.275697	+	0.303685i
$424$		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
$429$	−3.72176	−	0.681916i	−0.179688	−	0.0329232i
$430$		0			0
$431$	7.18994	+	2.33615i	0.346327	+	0.112528i	0.477015	−	0.878895i	$-0.341719\pi$
$431$	7.18994	+	2.33615i	0.346327	+	0.112528i	−0.130688	+	0.991424i	$0.541719\pi$
$432$		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
$435$	−4.89878	+	14.2742i	−0.234879	+	0.684396i
$436$		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
$441$	−8.50233	−	3.22390i	−0.404873	−	0.153519i
$442$		0			0
$443$	−13.2529	+	13.2529i	−0.629663	+	0.629663i	−0.947983	−	0.318320i	$-0.896881\pi$
$443$	−13.2529	+	13.2529i	−0.629663	+	0.629663i	0.318320	+	0.947983i	$0.396881\pi$
$444$		0			0
$445$	7.00368	+	2.21618i	0.332006	+	0.105057i
$446$		0			0
$447$	6.06594	+	8.78744i	0.286909	+	0.415631i
$448$		0			0
$449$	0.687206			0.0324313			0.0162156	−	0.999869i	$-0.494838\pi$
$449$	0.687206			0.0324313			0.0162156	+	0.999869i	$0.494838\pi$
$450$		0			0
$451$	−16.5874			−0.781070
$452$		0			0
$453$	−11.6176	−	16.8298i	−0.545840	−	0.790733i
$454$		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
$459$	17.1431	−	14.8245i	0.800171	−	0.691946i
$460$		0			0
$461$	−2.51720	+	3.46463i	−0.117238	+	0.161364i	−0.863603	−	0.504173i	$-0.831797\pi$
$461$	−2.51720	+	3.46463i	−0.117238	+	0.161364i	0.746365	+	0.665537i	$0.231797\pi$
$462$		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
$465$	−21.3775	+	15.0011i	−0.991357	+	0.695659i
$466$		0			0
$467$	22.7856	−	11.6099i	1.05439	−	0.537241i	0.161205	−	0.986921i	$-0.448462\pi$
$467$	22.7856	−	11.6099i	1.05439	−	0.537241i	0.893190	+	0.449680i	$0.148462\pi$
$468$		0			0
$469$	24.0770	+	7.82310i	1.11177	+	0.361237i
$470$		0			0
$471$	−19.8270	−	3.63278i	−0.913578	−	0.167390i
$472$		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
$477$	−23.6362	+	21.4579i	−1.08223	+	0.982489i
$478$		0			0
$479$	2.06837	+	6.36579i	0.0945063	+	0.290860i	0.987125	−	0.159953i	$-0.0511341\pi$
$479$	2.06837	+	6.36579i	0.0945063	+	0.290860i	−0.892618	+	0.450813i	$0.851134\pi$
$480$		0			0
$481$	−2.18870	+	6.73612i	−0.0997960	+	0.307141i
$482$		0			0
$483$	−2.08231	−	0.0502658i	−0.0947485	−	0.00228717i
$484$		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
$489$	16.3440	+	34.0864i	0.739102	+	1.54144i
$490$		0			0
$491$	−0.878303	−	1.20888i	−0.0396373	−	0.0545560i	0.788738	−	0.614729i	$-0.210735\pi$
$491$	−0.878303	−	1.20888i	−0.0396373	−	0.0545560i	−0.828376	+	0.560173i	$0.810735\pi$
$492$		0			0
$493$	12.0177	+	12.0177i	0.541250	+	0.541250i
$494$		0			0
$495$	10.4550	+	8.26416i	0.469918	+	0.371446i
$496$		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	0.817444	−	0.576008i	$-0.195390\pi$
$503$	18.6581	+	9.50679i	0.831925	+	0.423887i	0.0144808	+	0.999895i	$0.495390\pi$
$504$		0			0
$505$	11.4010	+	34.1909i	0.507340	+	1.52148i
$506$		0			0
$507$	−5.84030	−	19.5695i	−0.259377	−	0.869111i
$508$		0			0
$509$	−29.0463	+	21.1033i	−1.28745	+	0.935389i	−0.999751	−	0.0223311i	$-0.992891\pi$
$509$	−29.0463	+	21.1033i	−1.28745	+	0.935389i	−0.287702	+	0.957720i	$0.592891\pi$
$510$		0			0
$511$	−15.7334	−	11.4310i	−0.696004	−	0.505676i
$512$		0			0
$513$	−40.0446	−	2.90447i	−1.76801	−	0.128236i
$514$		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
$519$	−6.11168	−	6.41404i	−0.268273	−	0.281545i
$520$		0			0
$521$	−39.1289	+	12.7138i	−1.71427	+	0.557000i	−0.991035	−	0.133602i	$-0.957345\pi$
$521$	−39.1289	+	12.7138i	−1.71427	+	0.557000i	−0.723235	+	0.690602i	$0.757345\pi$
$522$		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
$525$	−15.4406	+	7.69817i	−0.673883	+	0.335976i
$526$		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
$531$	10.7333	+	39.4117i	0.465786	+	1.71032i
$532$		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
$537$	7.50041	−	9.81623i	0.323667	−	0.423602i
$538$		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
$543$	−0.764860	+	0.228265i	−0.0328233	+	0.00979577i
$544$		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
$555$	17.9275	−	17.3476i	0.760978	−	0.736365i
$556$		0			0
$557$	−12.3449	−	12.3449i	−0.523071	−	0.523071i	0.395427	−	0.918498i	$-0.370597\pi$
$557$	−12.3449	−	12.3449i	−0.523071	−	0.523071i	−0.918498	+	0.395427i	$0.870597\pi$
$558$		0			0
$559$	1.90917	+	2.62775i	0.0807494	+	0.111142i
$560$		0			0
$561$	13.5330	−	6.48894i	0.571366	−	0.273963i
$562$		0			0
$563$	6.59138	−	41.6164i	0.277794	−	1.75392i	−0.315491	−	0.948928i	$-0.602169\pi$
$563$	6.59138	−	41.6164i	0.277794	−	1.75392i	0.593285	−	0.804992i	$-0.297831\pi$
$564$		0			0
$565$	−6.96117	−	41.8628i	−0.292859	−	1.76118i
$566$		0			0
$567$	17.8972	−	1.08484i	0.751614	−	0.0455590i
$568$		0			0
$569$	−2.68424	+	8.26124i	−0.112529	+	0.346329i	−0.991424	−	0.130687i	$-0.958282\pi$
$569$	−2.68424	+	8.26124i	−0.112529	+	0.346329i	0.878894	+	0.477016i	$0.158282\pi$
$570$		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
$573$	−14.7857	+	42.0266i	−0.617683	+	1.75569i
$574$		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
$579$	7.42598	−	40.5294i	0.308613	−	1.68435i
$580$		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
$585$	1.44848	−	7.23278i	0.0598871	−	0.299039i
$586$		0			0
$587$	22.9124	+	3.62898i	0.945698	+	0.149784i	0.610191	−	0.792254i	$-0.291093\pi$
$587$	22.9124	+	3.62898i	0.945698	+	0.149784i	0.335507	+	0.942038i	$0.391093\pi$
$588$		0			0
$589$	30.6250	−	42.1517i	1.26188	−	1.73683i
$590$		0			0
$591$	34.3029	−	4.58745i	1.41103	−	0.188703i
$592$		0			0
$593$	6.63871	−	6.63871i	0.272619	−	0.272619i	−0.557535	−	0.830154i	$-0.688253\pi$
$593$	6.63871	−	6.63871i	0.272619	−	0.272619i	0.830154	+	0.557535i	$0.188253\pi$
$594$		0			0
$595$	0.149574	+	19.4296i	0.00613194	+	0.796536i
$596$		0			0
$597$	−21.2956	+	14.7003i	−0.871570	+	0.601642i
$598$		0			0
$599$	3.40483			0.139118			0.0695588	−	0.997578i	$-0.477841\pi$
$599$	3.40483			0.139118			0.0695588	+	0.997578i	$0.477841\pi$
$600$		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
$603$	37.8967	−	4.13991i	1.54327	−	0.168590i
$604$		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
$609$	1.78229	+	13.3271i	0.0722218	+	0.540042i
$610$		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
$615$	0.531491	−	32.3329i	0.0214318	−	1.30379i
$616$		0			0
$617$	−8.90536	+	4.53751i	−0.358516	+	0.182673i	−0.623966	−	0.781451i	$-0.714480\pi$
$617$	−8.90536	+	4.53751i	−0.358516	+	0.182673i	0.265450	+	0.964125i	$0.414480\pi$
$618$		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
$621$	−2.89039	+	1.21807i	−0.115987	+	0.0488794i
$622$		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
$627$	−25.0808	−	8.82390i	−1.00163	−	0.352393i
$628$		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
$633$	−0.0418716	+	1.73458i	−0.00166425	+	0.0689432i
$634$		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
$639$	0.441450	−	9.13843i	0.0174635	−	0.361511i
$640$		0			0
$641$	−10.1942	−	14.0312i	−0.402648	−	0.554198i	0.558758	−	0.829331i	$-0.311278\pi$
$641$	−10.1942	−	14.0312i	−0.402648	−	0.554198i	−0.961406	+	0.275133i	$0.911278\pi$
$642$		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
$645$	−1.60369	−	11.3273i	−0.0631452	−	0.446010i
$646$		0			0
$647$	0.917006	−	1.79973i	0.0360512	−	0.0707546i	−0.872278	−	0.489010i	$-0.837358\pi$
$647$	0.917006	−	1.79973i	0.0360512	−	0.0707546i	0.908330	+	0.418255i	$0.137358\pi$
$648$		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	0.756934	−	0.653492i	$-0.226697\pi$
$653$	17.2019	+	8.76480i	0.673162	+	0.342993i	−0.0837716	+	0.996485i	$0.526697\pi$
$654$		0			0
$655$	−22.2627	+	0.171384i	−0.869876	+	0.00669653i
$656$		0			0
$657$	−28.6698	−	5.97148i	−1.11851	−	0.232970i
$658$		0			0
$659$	31.9956	−	23.2462i	1.24637	−	0.905543i	0.248367	−	0.968666i	$-0.420106\pi$
$659$	31.9956	−	23.2462i	1.24637	−	0.905543i	0.998006	+	0.0631231i	$0.0201061\pi$
$660$		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
$663$	−6.60081	−	5.04356i	−0.256354	−	0.195876i
$664$		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
$669$	31.7319	−	30.2360i	1.22683	−	1.16899i
$670$		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
$675$	−16.4439	+	20.1146i	−0.632926	+	0.774212i
$676$		0			0
$677$	4.63953	+	29.2929i	0.178312	+	1.12582i	0.900736	+	0.434366i	$0.143028\pi$
$677$	4.63953	+	29.2929i	0.178312	+	1.12582i	−0.722425	+	0.691450i	$0.756972\pi$
$678$		0			0
$679$	−2.55107	+	0.828893i	−0.0979011	+	0.0318100i
$680$		0			0
$681$	24.8331	−	23.6624i	0.951605	−	0.906745i
$682$		0			0
$683$	−4.38498	−	8.60601i	−0.167787	−	0.329300i	0.791768	−	0.610822i	$-0.209161\pi$
$683$	−4.38498	−	8.60601i	−0.167787	−	0.329300i	−0.959555	+	0.281522i	$0.909161\pi$
$684$		0			0
$685$	14.2053	−	2.36213i	0.542755	−	0.0902523i
$686$		0			0
$687$	−26.3787	−	20.1555i	−1.00641	−	0.768980i
$688$		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
$693$	11.6241	+	2.42112i	0.441563	+	0.0919709i
$694$		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	$0.354072\pi$
$701$			47.4850i			1.79348i	−0.442556	+	0.896741i	$0.645928\pi$
$702$		0			0
$703$	−22.5951	+	44.3454i	−0.852190	+	1.67252i
$704$		0			0
$705$	−9.78353	+	4.78406i	−0.368469	+	0.180178i
$706$		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
$711$	−1.33523	+	27.6405i	−0.0500749	+	1.03660i
$712$		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
$717$	−0.331625	+	13.7379i	−0.0123848	+	0.513052i
$718$		0			0
$719$	−3.07429	+	9.46170i	−0.114652	+	0.352862i	−0.991874	−	0.127222i	$-0.959394\pi$
$719$	−3.07429	+	9.46170i	−0.114652	+	0.352862i	0.877222	+	0.480084i	$0.159394\pi$
$720$		0			0
$721$	−3.70071	−	11.3896i	−0.137822	−	0.424171i
$722$		0			0
$723$	31.3911	+	11.0440i	1.16745	+	0.410730i
$724$		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
$729$	23.9049	−	12.5520i	0.885368	−	0.464890i
$730$		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
$735$	7.05520	−	9.38240i	0.260235	−	0.346075i
$736$		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
$741$	1.95071	+	14.5865i	0.0716610	+	0.535848i
$742$		0			0
$743$	17.0201	−	17.0201i	0.624409	−	0.624409i	−0.322247	−	0.946656i	$-0.604438\pi$
$743$	17.0201	−	17.0201i	0.624409	−	0.624409i	0.946656	+	0.322247i	$0.104438\pi$
$744$		0			0
$745$	−13.0771	+	4.36057i	−0.479107	+	0.159759i
$746$		0			0
$747$	10.5868	−	1.15652i	0.387351	−	0.0423149i
$748$		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
$753$	23.8467	−	16.4613i	0.869023	−	0.599884i
$754$		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
$759$	−2.05875	+	0.275324i	−0.0747278	+	0.00999363i
$760$		0			0
$761$	−2.00068	+	2.75371i	−0.0725248	+	0.0998218i	−0.843738	−	0.536755i	$-0.819650\pi$
$761$	−2.00068	+	2.75371i	−0.0725248	+	0.0998218i	0.771214	+	0.636577i	$0.219650\pi$
$762$		0			0
$763$	7.52316	+	1.19155i	0.272357	+	0.0431371i
$764$		0			0
$765$	12.2149	+	26.5872i	0.441632	+	0.961262i
$766$		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
$771$	6.27817	−	34.2649i	0.226103	−	1.23402i
$772$		0			0
$773$	24.1237	−	3.82081i	0.867668	−	0.137425i	0.293298	−	0.956021i	$-0.405247\pi$
$773$	24.1237	−	3.82081i	0.867668	−	0.137425i	0.574370	+	0.818596i	$0.305247\pi$
$774$		0			0
$775$	−10.9110	−	31.9009i	−0.391935	−	1.14591i
$776$		0			0
$777$	7.37641	−	20.9665i	0.264627	−	0.752170i
$778$		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
$783$	10.6849	+	17.1984i	0.381847	+	0.614621i
$784$		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
$789$	−20.0941	+	9.63491i	−0.715370	+	0.343012i
$790$		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
$795$	−18.1043	−	37.0237i	−0.642093	−	1.31310i
$796$		0			0
$797$	−10.8215	+	21.2383i	−0.383316	+	0.752301i	−0.999373	−	0.0354009i	$-0.988729\pi$
$797$	−10.8215	+	21.2383i	−0.383316	+	0.752301i	0.616057	+	0.787702i	$0.288729\pi$
$798$		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
$807$	18.4635	−	5.51023i	0.649944	−	0.193969i
$808$		0			0
$809$	−19.9458	+	14.4915i	−0.701257	+	0.509493i	−0.880341	−	0.474341i	$-0.842687\pi$
$809$	−19.9458	+	14.4915i	−0.701257	+	0.509493i	0.179084	+	0.983834i	$0.442687\pi$
$810$		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
$813$	−20.1395	+	26.3577i	−0.706322	+	0.924406i
$814$		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
$819$	−1.72692	−	6.34108i	−0.0603434	−	0.221575i
$820$		0			0
$821$	−47.9307	+	15.5736i	−1.67279	+	0.543524i	−0.983492	−	0.180951i	$-0.942083\pi$
$821$	−47.9307	+	15.5736i	−1.67279	+	0.543524i	−0.689302	+	0.724474i	$0.742083\pi$
$822$		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
$825$	−14.0068	+	9.99073i	−0.487655	+	0.347833i
$826$		0			0
$827$	0.379131	+	2.39374i	0.0131837	+	0.0832386i	0.993403	−	0.114676i	$-0.0365831\pi$
$827$	0.379131	+	2.39374i	0.0131837	+	0.0832386i	−0.980219	+	0.197915i	$0.936583\pi$
$828$		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
$831$	−8.39635	−	8.81174i	−0.291266	−	0.305676i
$832$		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
$837$	−2.53467	+	34.9461i	−0.0876110	+	1.20791i
$838$		0			0
$839$	−25.1246	−	18.2541i	−0.867399	−	0.630202i	0.0624889	−	0.998046i	$-0.480096\pi$
$839$	−25.1246	−	18.2541i	−0.867399	−	0.630202i	−0.929888	+	0.367844i	$0.880096\pi$
$840$		0			0
$841$	11.1778	−	8.12118i	0.385443	−	0.280041i
$842$		0			0
$843$	15.5570	+	52.1279i	0.535812	+	1.79538i
$844$		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
$855$	18.0036	−	48.6061i	0.615711	−	1.66229i
$856$		0			0
$857$	−9.19391	−	9.19391i	−0.314058	−	0.314058i	0.532421	−	0.846479i	$-0.321282\pi$
$857$	−9.19391	−	9.19391i	−0.314058	−	0.314058i	−0.846479	+	0.532421i	$0.821282\pi$
$858$		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
$861$	−12.4566	−	25.9790i	−0.424521	−	0.885362i
$862$		0			0
$863$	−2.71860	+	17.1646i	−0.0925423	+	0.584289i	0.897222	+	0.441579i	$0.145582\pi$
$863$	−2.71860	+	17.1646i	−0.0925423	+	0.584289i	−0.989765	+	0.142710i	$0.954418\pi$
$864$		0			0
$865$	10.1508	−	5.27091i	0.345137	−	0.179216i
$866$		0			0
$867$	3.50478	+	0.0846033i	0.119029	+	0.00287328i
$868$		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
$873$	−2.99064	+	2.71502i	−0.101218	+	0.0918895i
$874$		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
$879$	47.4654	+	8.69682i	1.60097	+	0.293336i
$880$		0			0
$881$	−35.5675	−	11.5566i	−1.19830	−	0.389351i	−0.359163	−	0.933275i	$-0.616938\pi$
$881$	−35.5675	−	11.5566i	−1.19830	−	0.389351i	−0.839134	+	0.543924i	$0.816938\pi$
$882$		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
$885$	−52.7262	−	0.866718i	−1.77237	−	0.0291344i
$886$		0			0
$887$	−38.2644	−	6.06049i	−1.28479	−	0.203491i	−0.523571	−	0.851982i	$-0.675400\pi$
$887$	−38.2644	−	6.06049i	−1.28479	−	0.203491i	−0.761222	+	0.648491i	$0.775400\pi$
$888$		0			0
$889$	1.80113	−	2.47905i	0.0604081	−	0.0831446i
$890$		0			0
$891$	17.4581	−	3.86037i	0.584867	−	0.129327i
$892$		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
$897$	0.653112	+	0.946133i	0.0218068	+	0.0315905i
$898$		0			0
$899$	−26.2749			−0.876316
$900$		0			0
$901$	−46.4132			−1.54625
$902$		0			0
$903$	−5.79038	−	8.38825i	−0.192692	−	0.279143i
$904$		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
$909$	45.2138	+	17.1441i	1.49965	+	0.568633i
$910$		0			0
$911$	−20.9000	+	28.7663i	−0.692446	+	0.953071i	0.307553	+	0.951531i	$0.400490\pi$
$911$	−20.9000	+	28.7663i	−0.692446	+	0.953071i	−0.999999	+	0.00153941i	$0.999510\pi$
$912$		0			0
$913$	6.96562	+	1.10325i	0.230528	+	0.0365121i
$914$		0			0
$915$	10.8694	+	35.4234i	0.359331	+	1.17106i
$916$		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
$921$	38.6472	+	7.08111i	1.27347	+	0.233330i
$922$		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
$927$	−12.1216	−	13.3522i	−0.398125	−	0.438542i
$928$		0			0
$929$	−9.97663	−	30.7049i	−0.327323	−	1.00740i	−0.970381	−	0.241578i	$-0.922335\pi$
$929$	−9.97663	−	30.7049i	−0.327323	−	1.00740i	0.643059	−	0.765817i	$-0.277665\pi$
$930$		0			0
$931$	−7.23722	+	22.2739i	−0.237190	+	0.729996i
$932$		0			0
$933$	44.3369	+	1.07027i	1.45152	+	0.0350389i
$934$		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
$939$	−0.0913609	−	0.190538i	−0.00298145	−	0.00621798i
$940$		0			0
$941$	25.1318	+	34.5909i	0.819273	+	1.12763i	0.989826	+	0.142284i	$0.0454446\pi$
$941$	25.1318	+	34.5909i	0.819273	+	1.12763i	−0.170553	+	0.985348i	$0.554555\pi$
$942$		0			0
$943$	3.56381	+	3.56381i	0.116054	+	0.116054i
$944$		0			0
$945$	−5.09183	+	22.5807i	−0.165637	+	0.734549i
$946$		0			0
$947$	−9.40618	+	18.4607i	−0.305660	+	0.599891i	−0.991832	−	0.127548i	$-0.959289\pi$
$947$	−9.40618	+	18.4607i	−0.305660	+	0.599891i	0.686173	+	0.727439i	$0.259289\pi$
$948$		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	−0.222537	−	0.974924i	$-0.571434\pi$
$953$	−35.2565	−	17.9641i	−1.14207	−	0.581914i	−0.919534	+	0.393010i	$0.871434\pi$
$954$		0			0
$955$	−46.7903	−	33.4479i	−1.51410	−	1.08235i
$956$		0			0
$957$	3.83437	+	12.8481i	0.123948	+	0.415319i
$958$		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
$963$	−20.0591	+	9.02936i	−0.646394	+	0.290967i
$964$		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
$969$	−40.2680	−	42.2602i	−1.29360	−	1.35759i
$970$		0			0
$971$	−22.9417	+	7.45420i	−0.736233	+	0.239217i	−0.653047	−	0.757317i	$-0.726510\pi$
$971$	−22.9417	+	7.45420i	−0.736233	+	0.239217i	−0.0831861	+	0.996534i	$0.526510\pi$
$972$		0			0
$973$	0.646141	+	4.07957i	0.0207143	+	0.130785i
$974$		0			0
$975$	8.44685	+	4.39728i	0.270516	+	0.140826i
$976$		0			0
$977$	1.23479	+	7.79613i	0.0395043	+	0.249420i	0.999536	−	0.0304724i	$-0.00970115\pi$
$977$	1.23479	+	7.79613i	0.0395043	+	0.249420i	−0.960031	+	0.279893i	$0.909701\pi$
$978$		0			0
$979$	6.20711	−	2.01681i	0.198380	−	0.0644576i
$980$		0			0
$981$	11.0669	−	3.01394i	0.353339	−	0.0962276i
$982$		0			0
$983$	1.78637	+	3.50596i	0.0569765	+	0.111823i	0.917739	−	0.397184i	$-0.130013\pi$
$983$	1.78637	+	3.50596i	0.0569765	+	0.111823i	−0.860762	+	0.509007i	$0.830013\pi$
$984$		0			0
$985$	−6.64943	+	44.1815i	−0.211869	+	1.40774i
$986$		0			0
$987$	−5.89105	+	7.70997i	−0.187514	+	0.245411i
$988$		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
$993$	2.91511	−	0.869985i	0.0925083	−	0.0276081i
$994$		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.113.8	yes	80
3.2	odd	2	inner	300.2.x.a.113.1	yes	80
25.2	odd	20	inner	300.2.x.a.77.1	✓	80
75.2	even	20	inner	300.2.x.a.77.8	yes	80

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

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)

\(f(q)\)	\(=\)	\(q+(0.983962 + 1.42542i) q^{3} +(-2.12124 + 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(-1.06364 + 2.80512i) q^{9} +O(q^{10})\)	\(q+(0.983962 + 1.42542i) q^{3} +(-2.12124 + 0.707333i) q^{5} +(-1.40872 + 1.40872i) q^{7} +(-1.06364 + 2.80512i) q^{9} +(-1.16772 + 1.60723i) q^{11} +(1.08607 + 0.172017i) q^{13} +(-3.09547 - 2.32767i) q^{15} +(-3.88627 + 1.98015i) q^{17} +(7.34866 + 2.38772i) q^{19} +(-3.39415 - 0.621890i) q^{21} +(0.596200 - 0.0944288i) q^{23} +(3.99936 - 3.00085i) q^{25} +(-5.04504 + 1.24400i) q^{27} +(-1.20411 - 3.70588i) q^{29} +(2.08371 - 6.41301i) q^{31} +(-3.43996 - 0.0830386i) q^{33} +(1.99181 - 3.98468i) q^{35} +(-1.00762 + 6.36188i) q^{37} +(0.823455 + 1.71736i) q^{39} +(4.90769 + 6.75485i) q^{41} +(2.08869 + 2.08869i) q^{43} +(0.272086 - 6.70268i) q^{45} +(1.27659 - 2.50545i) q^{47} +3.03101i q^{49} +(-6.64648 - 3.59117i) q^{51} +(9.48136 + 4.83099i) q^{53} +(1.34017 - 4.23529i) q^{55} +(3.82729 + 12.8243i) q^{57} +(11.0153 - 8.00310i) q^{59} +(-7.73999 - 5.62344i) q^{61} +(-2.45326 - 5.44999i) q^{63} +(-2.42549 + 0.403324i) q^{65} +(-5.76904 - 11.3224i) q^{67} +(0.721238 + 0.756920i) q^{69} +(-2.90043 + 0.942408i) q^{71} +(1.52706 + 9.64150i) q^{73} +(8.21269 + 2.74804i) q^{75} +(-0.619145 - 3.90913i) q^{77} +(8.77277 - 2.85044i) q^{79} +(-6.73735 - 5.96726i) q^{81} +(-1.61164 - 3.16301i) q^{83} +(6.84310 - 6.94927i) q^{85} +(4.09763 - 5.36281i) q^{87} +(-2.65779 - 1.93100i) q^{89} +(-1.77229 + 1.28765i) q^{91} +(11.1915 - 3.33999i) q^{93} +(-17.2772 + 0.133005i) q^{95} +(1.19966 + 0.611256i) q^{97} +(-3.26643 - 4.98510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 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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