LMFDB - Embedded newform 600.2.m.e.299.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(299,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("600.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.m (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.11
Character	$\chi$	$=$	600.299
Dual form			600.2.m.e.299.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.244153 + 1.39298i) q^{2} +(-1.12950 - 1.31310i) q^{3} +(-1.88078 - 0.680200i) q^{4} +(2.10489 - 1.25277i) q^{6} -4.34495 q^{7} +(1.40670 - 2.45381i) q^{8} +(-0.448458 + 2.96629i) q^{9} +O(q^{10})$	\(q+(-0.244153 + 1.39298i) q^{2} +(-1.12950 - 1.31310i) q^{3} +(-1.88078 - 0.680200i) q^{4} +(2.10489 - 1.25277i) q^{6} -4.34495 q^{7} +(1.40670 - 2.45381i) q^{8} +(-0.448458 + 2.96629i) q^{9} +1.83679i q^{11} +(1.23117 + 3.23793i) q^{12} -0.588129 q^{13} +(1.06083 - 6.05242i) q^{14} +(3.07466 + 2.55861i) q^{16} +5.37818 q^{17} +(-4.02249 - 1.34892i) q^{18} +5.38776 q^{19} +(4.90762 + 5.70535i) q^{21} +(-2.55861 - 0.448458i) q^{22} -2.40885i q^{23} +(-4.81097 + 0.924442i) q^{24} +(0.143593 - 0.819251i) q^{26} +(4.40157 - 2.76156i) q^{27} +(8.17189 + 2.95543i) q^{28} +7.98077 q^{29} -7.06575i q^{31} +(-4.31478 + 3.65824i) q^{32} +(2.41189 - 2.07466i) q^{33} +(-1.31310 + 7.49169i) q^{34} +(2.86112 - 5.27390i) q^{36} +2.72080 q^{37} +(-1.31544 + 7.50503i) q^{38} +(0.664291 + 0.772271i) q^{39} -3.42496i q^{41} +(-9.14564 + 5.44323i) q^{42} -2.96772i q^{43} +(1.24939 - 3.45460i) q^{44} +(3.35548 + 0.588129i) q^{46} +9.81525i q^{47} +(-0.113116 - 6.92728i) q^{48} +11.8786 q^{49} +(-6.07466 - 7.06208i) q^{51} +(1.10614 + 0.400045i) q^{52} +6.65218i q^{53} +(2.77213 + 6.80553i) q^{54} +(-6.11205 + 10.6617i) q^{56} +(-6.08547 - 7.07466i) q^{57} +(-1.94853 + 11.1170i) q^{58} +10.7564i q^{59} +9.27803i q^{61} +(9.84244 + 1.72512i) q^{62} +(1.94853 - 12.8884i) q^{63} +(-4.04238 - 6.90356i) q^{64} +(2.30108 + 3.86624i) q^{66} +4.13536i q^{67} +(-10.1152 - 3.65824i) q^{68} +(-3.16306 + 2.72080i) q^{69} -12.2241 q^{71} +(6.64787 + 5.27312i) q^{72} -4.42003i q^{73} +(-0.664291 + 3.79002i) q^{74} +(-10.1332 - 3.66475i) q^{76} -7.98077i q^{77} +(-1.23795 + 0.736791i) q^{78} -12.5870i q^{79} +(-8.59777 - 2.66052i) q^{81} +(4.77089 + 0.836213i) q^{82} +11.5594 q^{83} +(-5.34937 - 14.0687i) q^{84} +(4.13398 + 0.724579i) q^{86} +(-9.01428 - 10.4795i) q^{87} +(4.50714 + 2.58382i) q^{88} -4.21222i q^{89} +2.55539 q^{91} +(-1.63850 + 4.53052i) q^{92} +(-9.27803 + 7.98077i) q^{93} +(-13.6724 - 2.39642i) q^{94} +(9.67717 + 1.53375i) q^{96} +2.16763i q^{97} +(-2.90019 + 16.5466i) q^{98} +(-5.44846 - 0.823724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) $ 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9	$ 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9} - 12 q^{16} + 8 q^{19} - 10 q^{24} + 4 q^{34} + 38 q^{36} - 32 q^{46} + 72 q^{49} - 60 q^{51} + 60 q^{54} - 20 q^{64} + 14 q^{66} - 76 q^{76} - 20 q^{81} + 68 q^{84} - 48 q^{91} - 56 q^{94} - 62 q^{96} - 116 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9 - 12 * q^16 + 8 * q^19 - 10 * q^24 + 4 * q^34 + 38 * q^36 - 32 * q^46 + 72 * q^49 - 60 * q^51 + 60 * q^54 - 20 * q^64 + 14 * q^66 - 76 * q^76 - 20 * q^81 + 68 * q^84 - 48 * q^91 - 56 * q^94 - 62 * q^96 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.244153	+	1.39298i	−0.172642	+	0.984985i
$2$	−0.244153	+	1.39298i	−0.172642	+	0.984985i
$3$	−1.12950	−	1.31310i	−0.652117	−	0.758118i
$3$	−1.12950	−	1.31310i	−0.652117	−	0.758118i
$4$	−1.88078	−	0.680200i	−0.940389	−	0.340100i
$5$		0			0
$5$		0			0
$6$	2.10489	−	1.25277i	0.859318	−	0.511442i
$7$	−4.34495			−1.64224			−0.821118	−	0.570758i	$-0.806650\pi$
$7$	−4.34495			−1.64224			−0.821118	+	0.570758i	$0.806650\pi$
$8$	1.40670	−	2.45381i	0.497344	−	0.867553i
$9$	−0.448458	+	2.96629i	−0.149486	+	0.988764i
$10$		0			0
$11$			1.83679i			0.553813i	0.960897	+	0.276907i	$0.0893093\pi$
$11$			1.83679i			0.553813i	−0.960897	+	0.276907i	$0.910691\pi$
$12$	1.23117	+	3.23793i	0.355408	+	0.934711i
$13$	−0.588129			−0.163118			−0.0815588	−	0.996669i	$-0.525990\pi$
$13$	−0.588129			−0.163118			−0.0815588	+	0.996669i	$0.525990\pi$
$14$	1.06083	−	6.05242i	0.283520	−	1.61758i
$15$		0			0
$16$	3.07466	+	2.55861i	0.768664	+	0.639653i
$17$	5.37818			1.30440			0.652200	−	0.758047i	$-0.273846\pi$
$17$	5.37818			1.30440			0.652200	+	0.758047i	$0.273846\pi$
$18$	−4.02249	−	1.34892i	−0.948110	−	0.317944i
$19$	5.38776			1.23604			0.618018	−	0.786164i	$-0.287936\pi$
$19$	5.38776			1.23604			0.618018	+	0.786164i	$0.287936\pi$
$20$		0			0
$21$	4.90762	+	5.70535i	1.07093	+	1.24501i
$22$	−2.55861	−	0.448458i	−0.545498	−	0.0956116i
$23$		−	2.40885i		−	0.502280i	−0.967951	−	0.251140i	$-0.919194\pi$
$23$		−	2.40885i		−	0.502280i	0.967951	−	0.251140i	$-0.0808055\pi$
$24$	−4.81097	+	0.924442i	−0.982035	+	0.188701i
$25$		0			0
$26$	0.143593	−	0.819251i	0.0281610	−	0.160668i
$27$	4.40157	−	2.76156i	0.847082	−	0.531462i
$28$	8.17189	+	2.95543i	1.54434	+	0.558525i
$29$	7.98077			1.48199			0.740996	−	0.671510i	$-0.234354\pi$
$29$	7.98077			1.48199			0.740996	+	0.671510i	$0.234354\pi$
$30$		0			0
$31$		−	7.06575i		−	1.26905i	−0.772904	−	0.634523i	$-0.781197\pi$
$31$		−	7.06575i		−	1.26905i	0.772904	−	0.634523i	$-0.218803\pi$
$32$	−4.31478	+	3.65824i	−0.762752	+	0.646691i
$33$	2.41189	−	2.07466i	0.419856	−	0.361151i
$34$	−1.31310	+	7.49169i	−0.225195	+	1.28481i
$35$		0			0
$36$	2.86112	−	5.27390i	0.476854	−	0.878983i
$37$	2.72080			0.447297			0.223648	−	0.974670i	$-0.428203\pi$
$37$	2.72080			0.447297			0.223648	+	0.974670i	$0.428203\pi$
$38$	−1.31544	+	7.50503i	−0.213392	+	1.21748i
$39$	0.664291	+	0.772271i	0.106372	+	0.123662i
$40$		0			0
$41$		−	3.42496i		−	0.534888i	−0.963573	−	0.267444i	$-0.913821\pi$
$41$		−	3.42496i		−	0.534888i	0.963573	−	0.267444i	$-0.0861791\pi$
$42$	−9.14564	+	5.44323i	−1.41120	+	0.839909i
$43$		−	2.96772i		−	0.452574i	−0.974061	−	0.226287i	$-0.927341\pi$
$43$		−	2.96772i		−	0.452574i	0.974061	−	0.226287i	$-0.0726587\pi$
$44$	1.24939	−	3.45460i	0.188352	−	0.520800i
$45$		0			0
$46$	3.35548	+	0.588129i	0.494739	+	0.0867148i
$47$			9.81525i			1.43170i	0.698254	+	0.715850i	$0.253961\pi$
$47$			9.81525i			1.43170i	−0.698254	+	0.715850i	$0.746039\pi$
$48$	−0.113116	−	6.92728i	−0.0163269	−	0.999867i
$49$	11.8786			1.69694
$50$		0			0
$51$	−6.07466	−	7.06208i	−0.850622	−	0.988889i
$52$	1.10614	+	0.400045i	0.153394	+	0.0554763i
$53$			6.65218i			0.913748i	0.889531	+	0.456874i	$0.151031\pi$
$53$			6.65218i			0.913748i	−0.889531	+	0.456874i	$0.848969\pi$
$54$	2.77213	+	6.80553i	0.377240	+	0.926116i
$55$		0			0
$56$	−6.11205	+	10.6617i	−0.816757	+	1.42473i
$57$	−6.08547	−	7.07466i	−0.806040	−	0.937061i
$58$	−1.94853	+	11.1170i	−0.255854	+	1.45974i
$59$			10.7564i			1.40036i	0.713967	+	0.700179i	$0.246897\pi$
$59$			10.7564i			1.40036i	−0.713967	+	0.700179i	$0.753103\pi$
$60$		0			0
$61$			9.27803i			1.18793i	0.804491	+	0.593965i	$0.202438\pi$
$61$			9.27803i			1.18793i	−0.804491	+	0.593965i	$0.797562\pi$
$62$	9.84244	+	1.72512i	1.24999	+	0.219091i
$63$	1.94853	−	12.8884i	0.245492	−	1.62378i
$64$	−4.04238	−	6.90356i	−0.505298	−	0.862945i
$65$		0			0
$66$	2.30108	+	3.86624i	0.283244	+	0.475902i
$67$			4.13536i			0.505215i	0.967569	+	0.252607i	$0.0812881\pi$
$67$			4.13536i			0.505215i	−0.967569	+	0.252607i	$0.918712\pi$
$68$	−10.1152	−	3.65824i	−1.22664	−	0.443626i
$69$	−3.16306	+	2.72080i	−0.380788	+	0.327546i
$70$		0			0
$71$	−12.2241			−1.45073			−0.725367	−	0.688363i	$-0.758330\pi$
$71$	−12.2241			−1.45073			−0.725367	+	0.688363i	$0.758330\pi$
$72$	6.64787	+	5.27312i	0.783459	+	0.621443i
$73$		−	4.42003i		−	0.517325i	−0.965968	−	0.258663i	$-0.916718\pi$
$73$		−	4.42003i		−	0.517325i	0.965968	−	0.258663i	$-0.0832818\pi$
$74$	−0.664291	+	3.79002i	−0.0772223	+	0.440580i
$75$		0			0
$76$	−10.1332	−	3.66475i	−1.16235	−	0.420376i
$77$		−	7.98077i		−	0.909493i
$78$	−1.23795	+	0.736791i	−0.140170	+	0.0834252i
$79$		−	12.5870i		−	1.41614i	−0.706141	−	0.708072i	$-0.749565\pi$
$79$		−	12.5870i		−	1.41614i	0.706141	−	0.708072i	$-0.250435\pi$
$80$		0			0
$81$	−8.59777	−	2.66052i	−0.955308	−	0.295613i
$82$	4.77089	+	0.836213i	0.526857	+	0.0923443i
$83$	11.5594			1.26881			0.634404	−	0.773002i	$-0.281246\pi$
$83$	11.5594			1.26881			0.634404	+	0.773002i	$0.281246\pi$
$84$	−5.34937	−	14.0687i	−0.583664	−	1.53502i
$85$		0			0
$86$	4.13398	+	0.724579i	0.445778	+	0.0781334i
$87$	−9.01428	−	10.4795i	−0.966432	−	1.12352i
$88$	4.50714	+	2.58382i	0.480463	+	0.275436i
$89$		−	4.21222i		−	0.446495i	−0.974762	−	0.223247i	$-0.928334\pi$
$89$		−	4.21222i		−	0.446495i	0.974762	−	0.223247i	$-0.0716658\pi$
$90$		0			0
$91$	2.55539			0.267878
$92$	−1.63850	+	4.53052i	−0.170826	+	0.472339i
$93$	−9.27803	+	7.98077i	−0.962087	+	0.827567i
$94$	−13.6724	−	2.39642i	−1.41020	−	0.247172i
$95$		0			0
$96$	9.67717	+	1.53375i	0.987672	+	0.156538i
$97$			2.16763i			0.220090i	0.993927	+	0.110045i	$0.0350995\pi$
$97$			2.16763i			0.220090i	−0.993927	+	0.110045i	$0.964901\pi$
$98$	−2.90019	+	16.5466i	−0.292964	+	1.67146i
$99$	−5.44846	−	0.823724i	−0.547591	−	0.0827874i
$100$		0			0
$101$	−3.16306			−0.314736			−0.157368	−	0.987540i	$-0.550301\pi$
$101$	−3.16306			−0.314736			−0.157368	+	0.987540i	$0.550301\pi$
$102$	11.3205	−	6.73764i	1.12089	−	0.667125i
$103$	12.5870			1.24023			0.620115	−	0.784511i	$-0.287086\pi$
$103$	12.5870			1.24023			0.620115	+	0.784511i	$0.287086\pi$
$104$	−0.827322	+	1.44316i	−0.0811256	+	0.141513i
$105$		0			0
$106$	−9.26635	−	1.62415i	−0.900027	−	0.157751i
$107$	3.79002			0.366395			0.183197	−	0.983076i	$-0.441355\pi$
$107$	3.79002			0.366395			0.183197	+	0.983076i	$0.441355\pi$
$108$	−10.1568	+	2.19993i	−0.977337	+	0.211689i
$109$			0.588129i			0.0563325i	0.999603	+	0.0281663i	$0.00896678\pi$
$109$			0.588129i			0.0563325i	−0.999603	+	0.0281663i	$0.991033\pi$
$110$		0			0
$111$	−3.07314	−	3.57268i	−0.291690	−	0.339104i
$112$	−13.3592	−	11.1170i	−1.26233	−	1.05046i
$113$	11.0621			1.04064			0.520319	−	0.853972i	$-0.325813\pi$
$113$	11.0621			1.04064			0.520319	+	0.853972i	$0.325813\pi$
$114$	11.3406	−	6.74963i	1.06215	−	0.632161i
$115$		0			0
$116$	−15.0101	−	5.42852i	−1.39365	−	0.504025i
$117$	0.263751	−	1.74456i	0.0243838	−	0.161285i
$118$	−14.9834	−	2.62620i	−1.37933	−	0.241761i
$119$	−23.3679			−2.14213
$120$		0			0
$121$	7.62620			0.693291
$122$	−12.9241	−	2.26526i	−1.17009	−	0.205087i
$123$	−4.49731	+	3.86849i	−0.405508	+	0.348810i
$124$	−4.80612	+	13.2891i	−0.431603	+	1.19340i
$125$		0			0
$126$	17.4775	+	5.86100i	1.55702	+	0.522139i
$127$	12.9552			1.14959			0.574796	−	0.818297i	$-0.305081\pi$
$127$	12.9552			1.14959			0.574796	+	0.818297i	$0.305081\pi$
$128$	10.6035	−	3.94542i	0.937223	−	0.348730i
$129$	−3.89692	+	3.35205i	−0.343104	+	0.295131i
$130$		0			0
$131$			2.98699i			0.260974i	0.991450	+	0.130487i	$0.0416541\pi$
$131$			2.98699i			0.260974i	−0.991450	+	0.130487i	$0.958346\pi$
$132$	−5.94741	+	2.26140i	−0.517656	+	0.196830i
$133$	−23.4095			−2.02986
$134$	−5.76047	−	1.00966i	−0.497629	−	0.0872214i
$135$		0			0
$136$	7.56550	−	13.1970i	0.648736	−	1.13164i
$137$	−5.66820			−0.484267			−0.242133	−	0.970243i	$-0.577847\pi$
$137$	−5.66820			−0.484267			−0.242133	+	0.970243i	$0.577847\pi$
$138$	−3.01774	−	5.07037i	−0.256887	−	0.431618i
$139$	2.69075			0.228226			0.114113	−	0.993468i	$-0.463597\pi$
$139$	2.69075			0.228226			0.114113	+	0.993468i	$0.463597\pi$
$140$		0			0
$141$	12.8884	−	11.0863i	1.08540	−	0.933637i
$142$	2.98455	−	17.0279i	0.250458	−	1.42895i
$143$		−	1.08027i		−	0.0903367i
$144$	−8.96844	+	7.97290i	−0.747370	+	0.664408i
$145$		0			0
$146$	6.15701	+	1.07916i	0.509558	+	0.0893122i
$147$	−13.4169	−	15.5978i	−1.10661	−	1.28648i
$148$	−5.11722	−	1.85069i	−0.420633	−	0.152126i
$149$	20.9591			1.71703			0.858517	−	0.512785i	$-0.171386\pi$
$149$	20.9591			1.71703			0.858517	+	0.512785i	$0.171386\pi$
$150$		0			0
$151$			3.16869i			0.257865i	0.991653	+	0.128932i	$0.0411550\pi$
$151$			3.16869i			0.257865i	−0.991653	+	0.128932i	$0.958845\pi$
$152$	7.57896	−	13.2205i	0.614735	−	1.07233i
$153$	−2.41189	+	15.9533i	−0.194990	+	1.28974i
$154$	11.1170	+	1.94853i	0.895836	+	0.157017i
$155$		0			0
$156$	−0.724086	−	1.90432i	−0.0579733	−	0.152468i
$157$	11.9988			0.957611			0.478805	−	0.877921i	$-0.341070\pi$
$157$	11.9988			0.957611			0.478805	+	0.877921i	$0.341070\pi$
$158$	17.5334	+	3.07314i	1.39488	+	0.244486i
$159$	8.73498	−	7.51364i	0.692729	−	0.595871i
$160$		0			0
$161$			10.4663i			0.824864i
$162$	5.80521	−	11.3269i	0.456101	−	0.889928i
$163$		−	13.1816i		−	1.03246i	−0.856449	−	0.516231i	$-0.827335\pi$
$163$		−	13.1816i		−	1.03246i	0.856449	−	0.516231i	$-0.172665\pi$
$164$	−2.32965	+	6.44158i	−0.181915	+	0.503003i
$165$		0			0
$166$	−2.82226	+	16.1020i	−0.219050	+	1.24976i
$167$			3.73744i			0.289211i	0.989489	+	0.144606i	$0.0461914\pi$
$167$			3.73744i			0.289211i	−0.989489	+	0.144606i	$0.953809\pi$
$168$	20.9034	−	4.01666i	1.61273	−	0.309892i
$169$	−12.6541			−0.973393
$170$		0			0
$171$	−2.41618	+	15.9817i	−0.184770	+	1.22215i
$172$	−2.01865	+	5.58163i	−0.153920	+	0.425596i
$173$			6.65218i			0.505756i	0.967498	+	0.252878i	$0.0813772\pi$
$173$			6.65218i			0.505756i	−0.967498	+	0.252878i	$0.918623\pi$
$174$	16.7986	−	9.99809i	1.27350	−	0.757953i
$175$		0			0
$176$	−4.69963	+	5.64750i	−0.354248	+	0.425696i
$177$	14.1242	−	12.1493i	1.06164	−	0.913198i
$178$	5.86754	+	1.02843i	0.439791	+	0.0770839i
$179$		−	18.4093i		−	1.37598i	−0.725722	−	0.687988i	$-0.758494\pi$
$179$		−	18.4093i		−	1.37598i	0.725722	−	0.687988i	$-0.241506\pi$
$180$		0			0
$181$		−	19.5125i		−	1.45035i	−0.688564	−	0.725175i	$-0.741759\pi$
$181$		−	19.5125i		−	1.45035i	0.688564	−	0.725175i	$-0.258241\pi$
$182$	−0.623906	+	3.55960i	−0.0462470	+	0.263855i
$183$	12.1830	−	10.4795i	0.900591	−	0.774670i
$184$	−5.91087	−	3.38854i	−0.435755	−	0.249806i
$185$		0			0
$186$	−8.85178	−	14.8726i	−0.649044	−	1.09051i
$187$			9.87859i			0.722394i
$188$	6.67633	−	18.4603i	0.486921	−	1.34636i
$189$	−19.1246	+	11.9988i	−1.39111	+	0.872786i
$190$		0			0
$191$	8.73498			0.632041			0.316020	−	0.948752i	$-0.397653\pi$
$191$	8.73498			0.632041			0.316020	+	0.948752i	$0.397653\pi$
$192$	−4.49919	+	13.1056i	−0.324701	+	0.945817i
$193$			1.47689i			0.106309i	0.998586	+	0.0531543i	$0.0169275\pi$
$193$			1.47689i			0.106309i	−0.998586	+	0.0531543i	$0.983072\pi$
$194$	−3.01947	−	0.529235i	−0.216785	−	0.0379968i
$195$		0			0
$196$	−22.3410	−	8.07982i	−1.59579	−	0.577130i
$197$		−	11.1438i		−	0.793965i	−0.917826	−	0.396982i	$-0.870057\pi$
$197$		−	11.1438i		−	0.793965i	0.917826	−	0.396982i	$-0.129943\pi$
$198$	2.47769	−	7.38847i	0.176082	−	0.525076i
$199$			2.80041i			0.198516i	0.995062	+	0.0992578i	$0.0316469\pi$
$199$			2.80041i			0.198516i	−0.995062	+	0.0992578i	$0.968353\pi$
$200$		0			0
$201$	5.43014	−	4.67089i	0.383012	−	0.329459i
$202$	0.772271	−	4.40608i	0.0543368	−	0.310011i
$203$	−34.6760			−2.43378
$204$	6.62146	+	17.4142i	0.463595	+	1.21924i
$205$		0			0
$206$	−3.07314	+	17.5334i	−0.214116	+	1.22161i
$207$	7.14536	+	1.08027i	0.496637	+	0.0750839i
$208$	−1.80829	−	1.50479i	−0.125383	−	0.104339i
$209$			9.89618i			0.684533i
$210$		0			0
$211$	9.86464			0.679110			0.339555	−	0.940586i	$-0.389724\pi$
$211$	9.86464			0.679110			0.339555	+	0.940586i	$0.389724\pi$
$212$	4.52481	−	12.5113i	0.310766	−	0.859279i
$213$	13.8071	+	16.0515i	0.946048	+	1.09983i
$214$	−0.925344	+	5.27941i	−0.0632552	+	0.360893i
$215$		0			0
$216$	−0.584647	−	14.6853i	−0.0397802	−	0.999208i
$217$			30.7003i			2.08407i
$218$	−0.819251	−	0.143593i	−0.0554867	−	0.00972537i
$219$	−5.80394	+	4.99243i	−0.392194	+	0.337357i
$220$		0			0
$221$	−3.16306			−0.212771
$222$	5.72698	−	3.40854i	0.384370	−	0.228766i
$223$	1.62415			0.108761			0.0543806	−	0.998520i	$-0.482682\pi$
$223$	1.62415			0.108761			0.0543806	+	0.998520i	$0.482682\pi$
$224$	18.7475	−	15.8949i	1.25262	−	1.06202i
$225$		0			0
$226$	−2.70085	+	15.4093i	−0.179658	+	1.02501i
$227$	4.94021			0.327893			0.163947	−	0.986469i	$-0.447578\pi$
$227$	4.94021			0.327893			0.163947	+	0.986469i	$0.447578\pi$
$228$	6.63324	+	17.4452i	0.439297	+	1.15534i
$229$			15.2471i			1.00756i	0.863832	+	0.503779i	$0.168058\pi$
$229$			15.2471i			1.00756i	−0.863832	+	0.503779i	$0.831942\pi$
$230$		0			0
$231$	−10.4795	+	9.01428i	−0.689503	+	0.593096i
$232$	11.2266	−	19.5833i	0.737060	−	1.28571i
$233$	−22.3000			−1.46092			−0.730460	−	0.682955i	$-0.760694\pi$
$233$	−22.3000			−1.46092			−0.730460	+	0.682955i	$0.760694\pi$
$234$	2.36574	+	0.793339i	0.154653	+	0.0518622i
$235$		0			0
$236$	7.31648	−	20.2303i	0.476262	−	1.31688i
$237$	−16.5279	+	14.2170i	−1.07360	+	0.923492i
$238$	5.70535	−	32.5510i	0.369823	−	2.10997i
$239$	−14.8813			−0.962589			−0.481294	−	0.876559i	$-0.659833\pi$
$239$	−14.8813			−0.962589			−0.481294	+	0.876559i	$0.659833\pi$
$240$		0			0
$241$	−0.523114			−0.0336968			−0.0168484	−	0.999858i	$-0.505363\pi$
$241$	−0.523114			−0.0336968			−0.0168484	+	0.999858i	$0.505363\pi$
$242$	−1.86196	+	10.6231i	−0.119691	+	0.682881i
$243$	6.21766	+	14.2948i	0.398863	+	0.917010i
$244$	6.31091	−	17.4499i	0.404015	−	1.11712i
$245$		0			0
$246$	−4.29069	−	7.20915i	−0.273564	−	0.459639i
$247$	−3.16869			−0.201619
$248$	−17.3380	−	9.93940i	−1.10097	−	0.631153i
$249$	−13.0563	−	15.1786i	−0.827412	−	0.961906i
$250$		0			0
$251$		−	4.82378i		−	0.304474i	−0.988344	−	0.152237i	$-0.951352\pi$
$251$		−	4.82378i		−	0.304474i	0.988344	−	0.152237i	$-0.0486477\pi$
$252$	−12.4314	+	22.9148i	−0.783107	+	1.44350i
$253$	4.42456			0.278170
$254$	−3.16306	+	18.0464i	−0.198468	+	1.13233i
$255$		0			0
$256$	2.90702	+	15.7337i	0.181689	+	0.983356i
$257$	−22.8859			−1.42758			−0.713792	−	0.700358i	$-0.753024\pi$
$257$	−22.8859			−1.42758			−0.713792	+	0.700358i	$0.753024\pi$
$258$	−3.71788	−	6.24673i	−0.231465	−	0.388905i
$259$	−11.8217			−0.734567
$260$		0			0
$261$	−3.57904	+	23.6733i	−0.221537	+	1.46534i
$262$	−4.16081	−	0.729282i	−0.257056	−	0.0450552i
$263$			13.5527i			0.835694i	0.908517	+	0.417847i	$0.137215\pi$
$263$			13.5527i			0.835694i	−0.908517	+	0.417847i	$0.862785\pi$
$264$	−1.69801	−	8.83674i	−0.104505	−	0.543864i
$265$		0			0
$266$	5.71551	−	32.6090i	0.350440	−	1.99938i
$267$	−5.53107	+	4.75771i	−0.338496	+	0.291167i
$268$	2.81287	−	7.77769i	0.171823	−	0.475098i
$269$	12.9783			0.791301			0.395651	−	0.918401i	$-0.370519\pi$
$269$	12.9783			0.791301			0.395651	+	0.918401i	$0.370519\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	16.5361	+	13.7607i	1.00265	+	0.834363i
$273$	−2.88631	−	3.35548i	−0.174688	−	0.203083i
$274$	1.38391	−	7.89568i	0.0836049	−	0.476995i
$275$		0			0
$276$	7.79971	−	2.96571i	0.469487	−	0.178515i
$277$	−16.7917			−1.00891			−0.504457	−	0.863437i	$-0.668307\pi$
$277$	−16.7917			−1.00891			−0.504457	+	0.863437i	$0.668307\pi$
$278$	−0.656955	+	3.74816i	−0.0394015	+	0.224799i
$279$	20.9591	+	3.16869i	1.25479	+	0.189705i
$280$		0			0
$281$			11.0464i			0.658972i	0.944161	+	0.329486i	$0.106875\pi$
$281$			11.0464i			0.658972i	−0.944161	+	0.329486i	$0.893125\pi$
$282$	12.2963	+	20.6600i	0.732232	+	1.23029i
$283$			18.7047i			1.11188i	0.831223	+	0.555940i	$0.187641\pi$
$283$			18.7047i			1.11188i	−0.831223	+	0.555940i	$0.812359\pi$
$284$	22.9908	+	8.31483i	1.36425	+	0.493394i
$285$		0			0
$286$	1.50479	+	0.263751i	0.0889802	+	0.0155959i
$287$			14.8813i			0.878413i
$288$	−8.91640	−	14.4395i	−0.525404	−	0.850853i
$289$	11.9248			0.701460
$290$		0			0
$291$	2.84632	−	2.44834i	0.166854	−	0.143524i
$292$	−3.00650	+	8.31310i	−0.175942	+	0.486487i
$293$		−	29.4457i		−	1.72024i	−0.510093	−	0.860119i	$-0.670389\pi$
$293$		−	29.4457i		−	1.72024i	0.510093	−	0.860119i	$-0.329611\pi$
$294$	25.0031	−	14.8812i	1.45821	−	0.867888i
$295$		0			0
$296$	3.82735	−	6.67633i	0.222460	−	0.388054i
$297$	5.07240	+	8.08476i	0.294331	+	0.469125i
$298$	−5.11722	+	29.1955i	−0.296433	+	1.69125i
$299$			1.41672i			0.0819308i
$300$		0			0
$301$			12.8946i			0.743233i
$302$	−4.41392	−	0.773646i	−0.253993	−	0.0445183i
$303$	3.57268	+	4.15341i	0.205245	+	0.238607i
$304$	16.5655	+	13.7852i	0.950096	+	0.790634i
$305$		0			0
$306$	−21.6337	−	7.25474i	−1.23671	−	0.414726i
$307$			33.2095i			1.89537i	0.319213	+	0.947683i	$0.396581\pi$
$307$			33.2095i			1.89537i	−0.319213	+	0.947683i	$0.603419\pi$
$308$	−5.42852	+	15.0101i	−0.309318	+	0.855277i
$309$	−14.2170	−	16.5279i	−0.808775	−	0.940241i
$310$		0			0
$311$	25.7768			1.46167			0.730834	−	0.682556i	$-0.239132\pi$
$311$	25.7768			1.46167			0.730834	+	0.682556i	$0.239132\pi$
$312$	2.82947	−	0.543691i	0.160187	−	0.0307804i
$313$			9.65410i			0.545682i	0.962059	+	0.272841i	$0.0879633\pi$
$313$			9.65410i			0.545682i	−0.962059	+	0.272841i	$0.912037\pi$
$314$	−2.92955	+	16.7141i	−0.165324	+	0.943232i
$315$		0			0
$316$	−8.56165	+	23.6733i	−0.481630	+	1.33173i
$317$			4.81770i			0.270589i	0.990805	+	0.135295i	$0.0431981\pi$
$317$			4.81770i			0.270589i	−0.990805	+	0.135295i	$0.956802\pi$
$318$	8.33367	+	14.0021i	0.467329	+	0.785200i
$319$			14.6590i			0.820747i
$320$		0			0
$321$	−4.28082	−	4.97667i	−0.238932	−	0.277770i
$322$	−14.5794	−	2.55539i	−0.812478	−	0.142406i
$323$	28.9763			1.61229
$324$	14.3608	+	10.8520i	0.797823	+	0.602891i
$325$		0			0
$326$	18.3617	+	3.21832i	1.01696	+	0.178247i
$327$	0.772271	−	0.664291i	0.0427067	−	0.0367354i
$328$	−8.40420	−	4.81789i	−0.464044	−	0.266024i
$329$		−	42.6468i		−	2.35119i
$330$		0			0
$331$	−1.37380			−0.0755110			−0.0377555	−	0.999287i	$-0.512021\pi$
$331$	−1.37380			−0.0755110			−0.0377555	+	0.999287i	$0.512021\pi$
$332$	−21.7407	−	7.86270i	−1.19317	−	0.431521i
$333$	−1.22016	+	8.07068i	−0.0668646	+	0.442271i
$334$	−5.20617	−	0.912506i	−0.284869	−	0.0499301i
$335$		0			0
$336$	0.491482	+	30.0987i	0.0268126	+	1.64202i
$337$		−	13.0925i		−	0.713192i	−0.934259	−	0.356596i	$-0.883937\pi$
$337$		−	13.0925i		−	0.713192i	0.934259	−	0.356596i	$-0.116063\pi$
$338$	3.08954	−	17.6269i	0.168049	−	0.958777i
$339$	−12.4947	−	14.5257i	−0.678618	−	0.788927i
$340$		0			0
$341$	12.9783			0.702815
$342$	−21.6722	−	7.26766i	−1.17190	−	0.392990i
$343$	−21.1972			−1.14454
$344$	−7.28224	−	4.17470i	−0.392632	−	0.225085i
$345$		0			0
$346$	−9.26635	−	1.62415i	−0.498162	−	0.0873149i
$347$	3.97936			0.213623			0.106812	−	0.994279i	$-0.465936\pi$
$347$	3.97936			0.213623			0.106812	+	0.994279i	$0.465936\pi$
$348$	9.82568	+	25.8412i	0.526712	+	1.38523i
$349$		−	12.5870i		−	0.673764i	−0.941547	−	0.336882i	$-0.890628\pi$
$349$		−	12.5870i		−	0.673764i	0.941547	−	0.336882i	$-0.109372\pi$
$350$		0			0
$351$	−2.58869	+	1.62415i	−0.138174	+	0.0866908i
$352$	−6.71942	−	7.92534i	−0.358146	−	0.422422i
$353$	0.787269			0.0419021			0.0209510	−	0.999781i	$-0.493331\pi$
$353$	0.787269			0.0419021			0.0209510	+	0.999781i	$0.493331\pi$
$354$	13.4753	+	22.6410i	0.716203	+	1.20335i
$355$		0			0
$356$	−2.86515	+	7.92226i	−0.151853	+	0.419879i
$357$	26.3941	+	30.6844i	1.39692	+	1.62399i
$358$	25.6438	+	4.49469i	1.35531	+	0.237552i
$359$	1.08027			0.0570144			0.0285072	−	0.999594i	$-0.490925\pi$
$359$	1.08027			0.0570144			0.0285072	+	0.999594i	$0.490925\pi$
$360$		0			0
$361$	10.0279			0.527785
$362$	27.1805	+	4.76403i	1.42857	+	0.250392i
$363$	−8.61379	−	10.0140i	−0.452107	−	0.525596i
$364$	−4.80612	−	1.73818i	−0.251909	−	0.0911052i
$365$		0			0
$366$	11.6233	+	19.5292i	0.607558	+	1.02081i
$367$	−14.5794			−0.761038			−0.380519	−	0.924773i	$-0.624255\pi$
$367$	−14.5794			−0.761038			−0.380519	+	0.924773i	$0.624255\pi$
$368$	6.16332	−	7.40639i	0.321285	−	0.386085i
$369$	10.1594	+	1.53595i	0.528878	+	0.0799583i
$370$		0			0
$371$		−	28.9034i		−	1.50059i
$372$	22.8784	−	8.69914i	1.18619	−	0.451029i
$373$	31.5719			1.63473			0.817366	−	0.576118i	$-0.195433\pi$
$373$	31.5719			1.63473			0.817366	+	0.576118i	$0.195433\pi$
$374$	−13.7607	−	2.41189i	−0.711547	−	0.124716i
$375$		0			0
$376$	24.0848	+	13.8071i	1.24208	+	0.712048i
$377$	−4.69372			−0.241739
$378$	−12.0448	−	29.5697i	−0.619517	−	1.52090i
$379$	−4.61224			−0.236915			−0.118458	−	0.992959i	$-0.537795\pi$
$379$	−4.61224			−0.236915			−0.118458	+	0.992959i	$0.537795\pi$
$380$		0			0
$381$	−14.6330	−	17.0115i	−0.749669	−	0.871526i
$382$	−2.13267	+	12.1676i	−0.109117	+	0.622550i
$383$			14.6330i			0.747709i	0.927487	+	0.373854i	$0.121964\pi$
$383$			14.6330i			0.747709i	−0.927487	+	0.373854i	$0.878036\pi$
$384$	−17.1574	−	9.46705i	−0.875558	−	0.483113i
$385$		0			0
$386$	−2.05727	−	0.360586i	−0.104712	−	0.0183533i
$387$	8.80314	+	1.33090i	0.447489	+	0.0676535i
$388$	1.47442	−	4.07684i	0.0748526	−	0.206970i
$389$	−15.1388			−0.767570			−0.383785	−	0.923422i	$-0.625380\pi$
$389$	−15.1388			−0.767570			−0.383785	+	0.923422i	$0.625380\pi$
$390$		0			0
$391$		−	12.9552i		−	0.655175i
$392$	16.7096	−	29.1478i	0.843964	−	1.47219i
$393$	3.92221	−	3.37380i	0.197849	−	0.170186i
$394$	15.5231	+	2.72080i	0.782043	+	0.137072i
$395$		0			0
$396$	9.68705	+	5.25528i	0.486792	+	0.264088i
$397$	18.3362			0.920268			0.460134	−	0.887849i	$-0.347801\pi$
$397$	18.3362			0.920268			0.460134	+	0.887849i	$0.347801\pi$
$398$	−3.90091	−	0.683728i	−0.195535	−	0.0342722i
$399$	26.4411	+	30.7390i	1.32371	+	1.53888i
$400$		0			0
$401$		−	34.2381i		−	1.70977i	−0.518820	−	0.854884i	$-0.673628\pi$
$401$		−	34.2381i		−	1.70977i	0.518820	−	0.854884i	$-0.326372\pi$
$402$	5.18066	+	8.70447i	0.258388	+	0.434140i
$403$			4.15557i			0.207004i
$404$	5.94902	+	2.15151i	0.295975	+	0.107042i
$405$		0			0
$406$	8.46626	−	48.3030i	0.420173	−	2.39724i
$407$			4.99754i			0.247719i
$408$	−25.8742	+	4.97182i	−1.28097	+	0.246142i
$409$	−18.6926			−0.924291			−0.462146	−	0.886804i	$-0.652920\pi$
$409$	−18.6926			−0.924291			−0.462146	+	0.886804i	$0.652920\pi$
$410$		0			0
$411$	6.40223	+	7.44290i	0.315799	+	0.367131i
$412$	−23.6733	−	8.56165i	−1.16630	−	0.421802i
$413$		−	46.7359i		−	2.29972i
$414$	−3.24935	+	9.68958i	−0.159697	+	0.476217i
$415$		0			0
$416$	2.53764	−	2.15151i	0.124418	−	0.105487i
$417$	−3.03920	−	3.53322i	−0.148830	−	0.173023i
$418$	−13.7852	−	2.41618i	−0.674255	−	0.118179i
$419$			5.24599i			0.256283i	0.991756	+	0.128142i	$0.0409012\pi$
$419$			5.24599i			0.256283i	−0.991756	+	0.128142i	$0.959099\pi$
$420$		0			0
$421$		−	4.42456i		−	0.215640i	−0.994170	−	0.107820i	$-0.965613\pi$
$421$		−	4.42456i		−	0.215640i	0.994170	−	0.107820i	$-0.0343870\pi$
$422$	−2.40848	+	13.7412i	−0.117243	+	0.668913i
$423$	−29.1149	−	4.40173i	−1.41561	−	0.214019i
$424$	16.3232	+	9.35764i	0.792725	+	0.454447i
$425$		0			0
$426$	−25.7304	+	15.3140i	−1.24664	+	0.741966i
$427$		−	40.3126i		−	1.95086i
$428$	−7.12818	−	2.57797i	−0.344554	−	0.124611i
$429$	−1.41850	+	1.22016i	−0.0684859	+	0.0589101i
$430$		0			0
$431$	5.89797			0.284095			0.142048	−	0.989860i	$-0.454631\pi$
$431$	5.89797			0.284095			0.142048	+	0.989860i	$0.454631\pi$
$432$	20.5991	+	2.77106i	0.991073	+	0.133323i
$433$		−	32.2158i		−	1.54819i	−0.633069	−	0.774095i	$-0.718205\pi$
$433$		−	32.2158i		−	1.54819i	0.633069	−	0.774095i	$-0.281795\pi$
$434$	−42.7649	−	7.49558i	−2.05278	−	0.359799i
$435$		0			0
$436$	0.400045	−	1.10614i	0.0191587	−	0.0529745i
$437$		−	12.9783i		−	0.620837i
$438$	−5.53729	−	9.30368i	−0.264582	−	0.444547i
$439$			2.27291i			0.108480i	0.998528	+	0.0542399i	$0.0172736\pi$
$439$			2.27291i			0.108480i	−0.998528	+	0.0542399i	$0.982726\pi$
$440$		0			0
$441$	−5.32705	+	35.2354i	−0.253669	+	1.67787i
$442$	0.772271	−	4.40608i	0.0367332	−	0.209576i
$443$	4.59091			0.218121			0.109060	−	0.994035i	$-0.465216\pi$
$443$	4.59091			0.218121			0.109060	+	0.994035i	$0.465216\pi$
$444$	3.34977	+	8.80977i	0.158973	+	0.418093i
$445$		0			0
$446$	−0.396541	+	2.26241i	−0.0187768	+	0.107128i
$447$	−23.6733	−	27.5213i	−1.11971	−	1.30171i
$448$	17.5639	+	29.9956i	0.829818	+	1.41716i
$449$			39.0461i			1.84270i	0.388736	+	0.921349i	$0.372912\pi$
$449$			39.0461i			1.84270i	−0.388736	+	0.921349i	$0.627088\pi$
$450$		0			0
$451$	6.29093			0.296228
$452$	−20.8054	−	7.52446i	−0.978605	−	0.353921i
$453$	4.16081	−	3.57904i	0.195492	−	0.168158i
$454$	−1.20617	+	6.88161i	−0.0566082	+	0.322970i
$455$		0			0
$456$	−25.9203	+	4.98067i	−1.21383	+	0.233241i
$457$		−	4.96147i		−	0.232088i	−0.993244	−	0.116044i	$-0.962979\pi$
$457$		−	4.96147i		−	0.232088i	0.993244	−	0.116044i	$-0.0370213\pi$
$458$	−21.2389	−	3.72263i	−0.992430	−	0.173947i
$459$	23.6724	−	14.8522i	1.10493	−	0.693239i
$460$		0			0
$461$	−14.1271			−0.657963			−0.328981	−	0.944336i	$-0.606705\pi$
$461$	−14.1271			−0.657963			−0.328981	+	0.944336i	$0.606705\pi$
$462$	−9.99809	−	16.7986i	−0.465153	−	0.781543i
$463$	−14.2907			−0.664146			−0.332073	−	0.943254i	$-0.607748\pi$
$463$	−14.2907			−0.664146			−0.332073	+	0.943254i	$0.607748\pi$
$464$	24.5381	+	20.4197i	1.13915	+	0.947960i
$465$		0			0
$466$	5.44461	−	31.0634i	0.252217	−	1.43898i
$467$	−31.8469			−1.47370			−0.736849	−	0.676058i	$-0.763687\pi$
$467$	−31.8469			−1.47370			−0.736849	+	0.676058i	$0.763687\pi$
$468$	−1.68271	+	3.10173i	−0.0777832	+	0.143377i
$469$		−	17.9679i		−	0.829682i
$470$		0			0
$471$	−13.5527	−	15.7557i	−0.624475	−	0.725982i
$472$	26.3941	+	15.1310i	1.21489	+	0.696460i
$473$	5.45109			0.250641
$474$	−15.7686	−	26.4942i	−0.724276	−	1.21692i
$475$		0			0
$476$	43.9499	+	15.8949i	2.01444	+	0.728540i
$477$	−19.7323	−	2.98323i	−0.903481	−	0.136593i
$478$	3.63331	−	20.7293i	0.166184	−	0.948135i
$479$	−25.9566			−1.18599			−0.592994	−	0.805207i	$-0.702054\pi$
$479$	−25.9566			−1.18599			−0.592994	+	0.805207i	$0.702054\pi$
$480$		0			0
$481$	−1.60018			−0.0729619
$482$	0.127720	−	0.728687i	0.00581748	−	0.0331908i
$483$	13.7433	−	11.8217i	0.625344	−	0.537908i
$484$	−14.3432	−	5.18734i	−0.651963	−	0.235788i
$485$		0			0
$486$	−21.4304	+	5.17096i	−0.972102	+	0.234560i
$487$	24.4456			1.10773			0.553867	−	0.832605i	$-0.313152\pi$
$487$	24.4456			1.10773			0.553867	+	0.832605i	$0.313152\pi$
$488$	22.7665	+	13.0514i	1.03059	+	0.590810i
$489$	−17.3087	+	14.8886i	−0.782728	+	0.673286i
$490$		0			0
$491$			37.6630i			1.69971i	0.527018	+	0.849854i	$0.323310\pi$
$491$			37.6630i			1.69971i	−0.527018	+	0.849854i	$0.676690\pi$
$492$	11.0898	−	4.21670i	0.499966	−	0.190104i
$493$	42.9220			1.93311
$494$	0.773646	−	4.41392i	0.0348080	−	0.198592i
$495$		0			0
$496$	18.0785	−	21.7248i	0.811749	−	0.975470i
$497$	53.1131			2.38245
$498$	24.3312	−	14.4813i	1.09031	−	0.648922i
$499$	36.7249			1.64403			0.822016	−	0.569464i	$-0.192849\pi$
$499$	36.7249			1.64403			0.822016	+	0.569464i	$0.192849\pi$
$500$		0			0
$501$	4.90762	−	4.22143i	0.219256	−	0.188600i
$502$	6.71942	+	1.17774i	0.299902	+	0.0525651i
$503$			29.5142i			1.31597i	0.753029	+	0.657987i	$0.228592\pi$
$503$			29.5142i			1.31597i	−0.753029	+	0.657987i	$0.771408\pi$
$504$	−28.8847	−	22.9114i	−1.28663	−	1.02056i
$505$		0			0
$506$	−1.08027	+	6.16332i	−0.0480238	+	0.273993i
$507$	14.2928	+	16.6161i	0.634766	+	0.737947i
$508$	−24.3659	−	8.81215i	−1.08106	−	0.390976i
$509$	−2.16054			−0.0957642			−0.0478821	−	0.998853i	$-0.515247\pi$
$509$	−2.16054			−0.0957642			−0.0478821	+	0.998853i	$0.515247\pi$
$510$		0			0
$511$			19.2048i			0.849571i
$512$	−22.6265	+	0.207989i	−0.999958	+	0.00919190i
$513$	23.7146	−	14.8786i	1.04702	−	0.656906i
$514$	5.58767	−	31.8796i	0.246461	−	1.40615i
$515$		0			0
$516$	9.60930	−	3.65377i	0.423026	−	0.160848i
$517$	−18.0286			−0.792895
$518$	2.88631	−	16.4674i	0.126817	−	0.723537i
$519$	8.73498	−	7.51364i	0.383423	−	0.329812i
$520$		0			0
$521$			9.39893i			0.411775i	0.978576	+	0.205887i	$0.0660080\pi$
$521$			9.39893i			0.411775i	−0.978576	+	0.205887i	$0.933992\pi$
$522$	−32.1025	−	10.7654i	−1.40509	−	0.471190i
$523$		−	9.68638i		−	0.423556i	−0.977318	−	0.211778i	$-0.932075\pi$
$523$		−	9.68638i		−	0.423556i	0.977318	−	0.211778i	$-0.0679253\pi$
$524$	2.03175	−	5.61786i	0.0887573	−	0.245417i
$525$		0			0
$526$	−18.8786	−	3.30893i	−0.823146	−	0.144276i
$527$		−	38.0009i		−	1.65534i
$528$	12.7240	−	0.207770i	0.553740	−	0.00904203i
$529$	17.1974			0.747714
$530$		0			0
$531$	−31.9065	−	4.82378i	−1.38462	−	0.209334i
$532$	44.0281	+	15.9232i	1.90886	+	0.690357i
$533$			2.01431i			0.0872497i
$534$	−5.27696	−	8.86627i	−0.228356	−	0.383681i
$535$		0			0
$536$	10.1474	+	5.81722i	0.438301	+	0.251265i
$537$	−24.1732	+	20.7933i	−1.04315	+	0.897298i
$538$	−3.16869	+	18.0785i	−0.136612	+	0.779420i
$539$			21.8185i			0.939789i
$540$		0			0
$541$			13.1751i			0.566441i	0.959055	+	0.283221i	$0.0914029\pi$
$541$			13.1751i			0.566441i	−0.959055	+	0.283221i	$0.908597\pi$
$542$		0			0
$543$	−25.6218	+	22.0393i	−1.09954	+	0.945799i
$544$	−23.2056	+	19.6747i	−0.994934	+	0.843544i
$545$		0			0
$546$	5.37881	−	3.20132i	0.230192	−	0.137004i
$547$		−	28.4113i		−	1.21478i	−0.794404	−	0.607390i	$-0.792217\pi$
$547$		−	28.4113i		−	1.21478i	0.794404	−	0.607390i	$-0.207783\pi$
$548$	10.6606	+	3.85551i	0.455399	+	0.164699i
$549$	−27.5213	−	4.16081i	−1.17458	−	0.177579i
$550$		0			0
$551$	42.9984			1.83179
$552$	2.22684	+	11.5889i	0.0947808	+	0.493257i
$553$			54.6897i			2.32564i
$554$	4.09974	−	23.3904i	0.174181	−	0.993765i
$555$		0			0
$556$	−5.06070	−	1.83025i	−0.214622	−	0.0776198i
$557$		−	32.1029i		−	1.36024i	−0.733099	−	0.680122i	$-0.761927\pi$
$557$		−	32.1029i		−	1.36024i	0.733099	−	0.680122i	$-0.238073\pi$
$558$	−9.53114	+	28.4219i	−0.403485	+	1.20319i
$559$			1.74540i			0.0738227i
$560$		0			0
$561$	12.9716	−	11.1579i	0.547660	−	0.471086i
$562$	−15.3874	−	2.69701i	−0.649077	−	0.113766i
$563$	−14.2406			−0.600170			−0.300085	−	0.953913i	$-0.597015\pi$
$563$	−14.2406			−0.600170			−0.300085	+	0.953913i	$0.597015\pi$
$564$	−31.7811	+	12.0842i	−1.33823	+	0.508838i
$565$		0			0
$566$	−26.0552	−	4.56681i	−1.09518	−	0.191957i
$567$	37.3569	+	11.5598i	1.56884	+	0.485466i
$568$	−17.1957	+	29.9956i	−0.721514	+	1.25859i
$569$			9.08328i			0.380791i	0.981707	+	0.190396i	$0.0609770\pi$
$569$			9.08328i			0.380791i	−0.981707	+	0.190396i	$0.939023\pi$
$570$		0			0
$571$	−15.7432			−0.658834			−0.329417	−	0.944185i	$-0.606852\pi$
$571$	−15.7432			−0.658834			−0.329417	+	0.944185i	$0.606852\pi$
$572$	−0.734799	+	2.03175i	−0.0307235	+	0.0849516i
$573$	−9.86616	−	11.4699i	−0.412165	−	0.479161i
$574$	−20.7293	−	3.63331i	−0.865224	−	0.151651i
$575$		0			0
$576$	22.2908	−	8.89492i	0.928784	−	0.370622i
$577$		−	33.1974i		−	1.38203i	−0.722842	−	0.691014i	$-0.757164\pi$
$577$		−	33.1974i		−	1.38203i	0.722842	−	0.691014i	$-0.242836\pi$
$578$	−2.91148	+	16.6110i	−0.121102	+	0.690927i
$579$	1.93930	−	1.66814i	0.0805944	−	0.0693256i
$580$		0			0
$581$	−50.2250			−2.08368
$582$	2.71555	+	4.56263i	0.112563	+	0.189127i
$583$	−12.2187			−0.506046
$584$	−10.8459	−	6.21766i	−0.448807	−	0.257289i
$585$		0			0
$586$	41.0173	+	7.18927i	1.69441	+	0.296986i
$587$	0.613686			0.0253295			0.0126648	−	0.999920i	$-0.495969\pi$
$587$	0.613686			0.0253295			0.0126648	+	0.999920i	$0.495969\pi$
$588$	14.6246	+	38.4621i	0.603107	+	1.58615i
$589$		−	38.0685i		−	1.56859i
$590$		0			0
$591$	−14.6330	+	12.5870i	−0.601919	+	0.517758i
$592$	8.36552	+	6.96147i	0.343821	+	0.286115i
$593$	−15.5545			−0.638747			−0.319374	−	0.947629i	$-0.603472\pi$
$593$	−15.5545			−0.638747			−0.319374	+	0.947629i	$0.603472\pi$
$594$	−12.5003	+	5.09183i	−0.512895	+	0.208920i
$595$		0			0
$596$	−39.4194	−	14.2564i	−1.61468	−	0.583963i
$597$	3.67721	−	3.16306i	0.150498	−	0.129456i
$598$	−1.97345	−	0.345895i	−0.0807005	−	0.0141447i
$599$	39.0811			1.59681			0.798406	−	0.602119i	$-0.205677\pi$
$599$	39.0811			1.59681			0.798406	+	0.602119i	$0.205677\pi$
$600$		0			0
$601$	−20.5231			−0.837155			−0.418578	−	0.908181i	$-0.637471\pi$
$601$	−20.5231			−0.837155			−0.418578	+	0.908181i	$0.637471\pi$
$602$	−17.9619	−	3.14826i	−0.732073	−	0.128313i
$603$	−12.2667	−	1.85454i	−0.499538	−	0.0755225i
$604$	2.15534	−	5.95961i	0.0876997	−	0.242493i
$605$		0			0
$606$	−6.65790	+	3.96260i	−0.270459	+	0.160970i
$607$	−10.8832			−0.441735			−0.220868	−	0.975304i	$-0.570889\pi$
$607$	−10.8832			−0.441735			−0.220868	+	0.975304i	$0.570889\pi$
$608$	−23.2470	+	19.7097i	−0.942789	+	0.799333i
$609$	39.1666	+	45.5331i	1.58711	+	1.84509i
$610$		0			0
$611$		−	5.77263i		−	0.233535i
$612$	15.3876	−	28.3640i	0.622008	−	1.14655i
$613$	−30.3350			−1.22522			−0.612610	−	0.790385i	$-0.709881\pi$
$613$	−30.3350			−1.22522			−0.612610	+	0.790385i	$0.709881\pi$
$614$	−46.2601	−	8.10820i	−1.86691	−	0.327220i
$615$		0			0
$616$	−19.5833	−	11.2266i	−0.789033	−	0.452331i
$617$	−8.71447			−0.350831			−0.175416	−	0.984494i	$-0.556127\pi$
$617$	−8.71447			−0.350831			−0.175416	+	0.984494i	$0.556127\pi$
$618$	26.4942	−	15.7686i	1.06575	−	0.634306i
$619$	−13.0323			−0.523811			−0.261906	−	0.965093i	$-0.584351\pi$
$619$	−13.0323			−0.523811			−0.261906	+	0.965093i	$0.584351\pi$
$620$		0			0
$621$	−6.65218	−	10.6027i	−0.266943	−	0.425473i
$622$	−6.29348	+	35.9065i	−0.252346	+	1.43972i
$623$			18.3019i			0.733250i
$624$	0.0665266	+	4.07413i	0.00266320	+	0.163096i
$625$		0			0
$626$	−13.4480	−	2.35708i	−0.537489	−	0.0942078i
$627$	12.9947	−	11.1777i	0.518957	−	0.446396i
$628$	−22.5671	−	8.16160i	−0.900527	−	0.325683i
$629$	14.6330			0.583454
$630$		0			0
$631$			14.8599i			0.591562i	0.955256	+	0.295781i	$0.0955798\pi$
$631$			14.8599i			0.591562i	−0.955256	+	0.295781i	$0.904420\pi$
$632$	−30.8860	−	17.7061i	−1.22858	−	0.704311i
$633$	−11.1421	−	12.9533i	−0.442859	−	0.514845i
$634$	−6.71096	−	1.17626i	−0.266526	−	0.0467151i
$635$		0			0
$636$	−21.5393	+	8.18997i	−0.854090	+	0.324753i
$637$	−6.98614			−0.276801
$638$	−20.4197	−	3.57904i	−0.808423	−	0.141696i
$639$	5.48200	−	36.2602i	0.216864	−	1.43443i
$640$		0			0
$641$		−	5.97397i		−	0.235958i	−0.993016	−	0.117979i	$-0.962358\pi$
$641$		−	5.97397i		−	0.235958i	0.993016	−	0.117979i	$-0.0376415\pi$
$642$	7.97756	−	4.74803i	0.314849	−	0.187390i
$643$			15.7938i			0.622848i	0.950271	+	0.311424i	$0.100806\pi$
$643$			15.7938i			0.622848i	−0.950271	+	0.311424i	$0.899194\pi$
$644$	7.11921	−	19.6849i	0.280536	−	0.775693i
$645$		0			0
$646$	−7.07466	+	40.3634i	−0.278349	+	1.58808i
$647$			14.8128i			0.582351i	0.956670	+	0.291175i	$0.0940463\pi$
$647$			14.8128i			0.582351i	−0.956670	+	0.291175i	$0.905954\pi$
$648$	−18.6229	+	17.3548i	−0.731577	+	0.681759i
$649$	−19.7572			−0.775537
$650$		0			0
$651$	40.3126	−	34.6760i	1.57997	−	1.35906i
$652$	−8.96611	+	24.7916i	−0.351140	+	0.970916i
$653$		−	3.48912i		−	0.136540i	−0.997667	−	0.0682699i	$-0.978252\pi$
$653$		−	3.48912i		−	0.136540i	0.997667	−	0.0682699i	$-0.0217479\pi$
$654$	0.736791	+	1.23795i	0.0288108	+	0.0484075i
$655$		0			0
$656$	8.76313	−	10.5306i	0.342143	−	0.411149i
$657$	13.1111	+	1.98220i	0.511513	+	0.0773329i
$658$	59.4060	+	10.4123i	2.31589	+	0.405915i
$659$			36.5563i			1.42403i	0.702163	+	0.712017i	$0.252218\pi$
$659$			36.5563i			1.42403i	−0.702163	+	0.712017i	$0.747782\pi$
$660$		0			0
$661$		−	42.9220i		−	1.66947i	−0.550650	−	0.834736i	$-0.685620\pi$
$661$		−	42.9220i		−	1.66947i	0.550650	−	0.834736i	$-0.314380\pi$
$662$	0.335418	−	1.91368i	0.0130364	−	0.0743772i
$663$	3.57268	+	4.15341i	0.138751	+	0.161305i
$664$	16.2606	−	28.3646i	0.631034	−	1.10076i
$665$		0			0
$666$	−10.9444	−	3.67015i	−0.424086	−	0.142215i
$667$		−	19.2245i		−	0.744375i
$668$	2.54220	−	7.02929i	0.0983608	−	0.271971i
$669$	−1.83448	−	2.13267i	−0.0709251	−	0.0824538i
$670$		0			0
$671$	−17.0418			−0.657892
$672$	−42.0468	−	6.66406i	−1.62199	−	0.257072i
$673$		−	46.2899i		−	1.78434i	−0.451696	−	0.892172i	$-0.649181\pi$
$673$		−	46.2899i		−	1.78434i	0.451696	−	0.892172i	$-0.350819\pi$
$674$	18.2375	+	3.19656i	0.702483	+	0.123127i
$675$		0			0
$676$	23.7996	+	8.60732i	0.915368	+	0.331051i
$677$			27.7911i			1.06810i	0.845453	+	0.534049i	$0.179330\pi$
$677$			27.7911i			1.06810i	−0.845453	+	0.534049i	$0.820670\pi$
$678$	23.2846	−	13.8583i	0.894239	−	0.532226i
$679$		−	9.41826i		−	0.361440i
$680$		0			0
$681$	−5.57997	−	6.48699i	−0.213825	−	0.248582i
$682$	−3.16869	+	18.0785i	−0.121336	+	0.692262i
$683$	33.6521			1.28766			0.643832	−	0.765167i	$-0.277344\pi$
$683$	33.6521			1.28766			0.643832	+	0.765167i	$0.277344\pi$
$684$	15.4150	−	28.4145i	0.589408	−	1.08645i
$685$		0			0
$686$	5.17537	−	29.5273i	0.197597	−	1.12736i
$687$	20.0210	−	17.2216i	0.763849	−	0.657047i
$688$	7.59325	−	9.12473i	0.289490	−	0.347877i
$689$		−	3.91234i		−	0.149048i
$690$		0			0
$691$	−22.6820			−0.862864			−0.431432	−	0.902145i	$-0.641992\pi$
$691$	−22.6820			−0.862864			−0.431432	+	0.902145i	$0.641992\pi$
$692$	4.52481	−	12.5113i	0.172008	−	0.475608i
$693$	23.6733	+	3.57904i	0.899274	+	0.135956i
$694$	−0.971573	+	5.54316i	−0.0368804	+	0.210416i
$695$		0			0
$696$	−38.3952	+	7.37776i	−1.45537	+	0.279653i
$697$		−	18.4200i		−	0.697708i
$698$	17.5334	+	3.07314i	0.663648	+	0.116320i
$699$	25.1878	+	29.2821i	0.952692	+	1.10755i
$700$		0			0
$701$	10.6379			0.401789			0.200895	−	0.979613i	$-0.435615\pi$
$701$	10.6379			0.401789			0.200895	+	0.979613i	$0.435615\pi$
$702$	−1.63037	−	4.00253i	−0.0615344	−	0.151066i
$703$	14.6590			0.552875
$704$	12.6804	−	7.42501i	0.477911	−	0.279841i
$705$		0			0
$706$	−0.192214	+	1.09665i	−0.00723407	+	0.0412729i
$707$	13.7433			0.516872
$708$	−34.8284	+	13.2429i	−1.30893	+	0.497699i
$709$			20.5295i			0.771002i	0.922707	+	0.385501i	$0.125971\pi$
$709$			20.5295i			0.771002i	−0.922707	+	0.385501i	$0.874029\pi$
$710$		0			0
$711$	37.3366	+	5.64472i	1.40023	+	0.211694i
$712$	−10.3360	−	5.92534i	−0.387358	−	0.222062i
$713$	−17.0203			−0.637417
$714$	−49.1869	+	29.2747i	−1.84077	+	1.09558i
$715$		0			0
$716$	−12.5220	+	34.6238i	−0.467969	+	1.29395i
$717$	16.8084	+	19.5406i	0.627721	+	0.729756i
$718$	−0.263751	+	1.50479i	−0.00984310	+	0.0561583i
$719$	14.8813			0.554977			0.277489	−	0.960729i	$-0.410498\pi$
$719$	14.8813			0.554977			0.277489	+	0.960729i	$0.410498\pi$
$720$		0			0
$721$	−54.6897			−2.03675
$722$	−2.44834	+	13.9687i	−0.0911179	+	0.519860i
$723$	0.590858	+	0.686901i	0.0219742	+	0.0255461i
$724$	−13.2724	+	36.6986i	−0.493264	+	1.36389i
$725$		0			0
$726$	16.0523	−	9.55389i	0.595757	−	0.354578i
$727$	16.1239			0.598004			0.299002	−	0.954253i	$-0.403346\pi$
$727$	16.1239			0.598004			0.299002	+	0.954253i	$0.403346\pi$
$728$	3.59467	−	6.27044i	0.133227	−	0.232398i
$729$	11.7476	−	24.3104i	0.435096	−	0.900384i
$730$		0			0
$731$		−	15.9610i		−	0.590337i
$732$	−30.0417	+	11.4228i	−1.11037	+	0.422200i
$733$	−16.7310			−0.617975			−0.308988	−	0.951066i	$-0.599990\pi$
$733$	−16.7310			−0.617975			−0.308988	+	0.951066i	$0.599990\pi$
$734$	3.55960	−	20.3088i	0.131387	−	0.749611i
$735$		0			0
$736$	8.81215	+	10.3937i	0.324820	+	0.383115i
$737$	−7.59579			−0.279795
$738$	−4.62000	+	13.7768i	−0.170064	+	0.507133i
$739$	−12.5693			−0.462371			−0.231185	−	0.972910i	$-0.574260\pi$
$739$	−12.5693			−0.462371			−0.231185	+	0.972910i	$0.574260\pi$
$740$		0			0
$741$	3.57904	+	4.16081i	0.131479	+	0.152851i
$742$	40.2618	+	7.05685i	1.47806	+	0.259065i
$743$		−	22.2877i		−	0.817655i	−0.912612	−	0.408827i	$-0.865938\pi$
$743$		−	22.2877i		−	0.817655i	0.912612	−	0.408827i	$-0.134062\pi$
$744$	6.53188	+	33.9931i	0.239470	+	1.24625i
$745$		0			0
$746$	−7.70838	+	43.9790i	−0.282224	+	1.61019i
$747$	−5.18390	+	34.2885i	−0.189669	+	1.25455i
$748$	6.71942	−	18.5794i	0.245686	−	0.679332i
$749$	−16.4674			−0.601707
$750$		0			0
$751$			35.1279i			1.28183i	0.767610	+	0.640917i	$0.221446\pi$
$751$			35.1279i			1.28183i	−0.767610	+	0.640917i	$0.778554\pi$
$752$	−25.1134	+	30.1785i	−0.915791	+	1.10050i
$753$	−6.33410	+	5.44846i	−0.230827	+	0.198553i
$754$	1.14599	−	6.53825i	0.0417343	−	0.238109i
$755$		0			0
$756$	44.1307	−	9.55859i	1.60502	−	0.347643i
$757$	−20.6887			−0.751945			−0.375972	−	0.926631i	$-0.622691\pi$
$757$	−20.6887			−0.751945			−0.375972	+	0.926631i	$0.622691\pi$
$758$	1.12609	−	6.42476i	0.0409016	−	0.233358i
$759$	−4.99754	−	5.80988i	−0.181399	−	0.210885i
$760$		0			0
$761$			22.8130i			0.826971i	0.910511	+	0.413485i	$0.135689\pi$
$761$			22.8130i			0.826971i	−0.910511	+	0.413485i	$0.864311\pi$
$762$	27.2694	−	16.2300i	0.987865	−	0.587950i
$763$		−	2.55539i		−	0.0925113i
$764$	−16.4286	−	5.94153i	−0.594364	−	0.214957i
$765$		0			0
$766$	−20.3834	−	3.57268i	−0.736482	−	0.129086i
$767$		−	6.32612i		−	0.228423i
$768$	17.3764	−	21.5884i	0.627018	−	0.779005i
$769$	46.3082			1.66992			0.834958	−	0.550313i	$-0.185492\pi$
$769$	46.3082			1.66992			0.834958	+	0.550313i	$0.185492\pi$
$770$		0			0
$771$	25.8496	+	30.0515i	0.930952	+	1.08228i
$772$	1.00458	−	2.77769i	0.0361555	−	0.0999714i
$773$		−	30.2684i		−	1.08868i	−0.838865	−	0.544340i	$-0.816780\pi$
$773$		−	30.2684i		−	1.08868i	0.838865	−	0.544340i	$-0.183220\pi$
$774$	−4.00323	+	11.9376i	−0.143893	+	0.429089i
$775$		0			0
$776$	5.31897	+	3.04922i	0.190940	+	0.109460i
$777$	13.3527	+	15.5231i	0.479024	+	0.556889i
$778$	3.69620	−	21.0881i	0.132515	−	0.756045i
$779$		−	18.4528i		−	0.661141i
$780$		0			0
$781$		−	22.4531i		−	0.803436i
$782$	18.0464	+	3.16306i	0.645337	+	0.113111i
$783$	35.1279	−	22.0393i	1.25537	−	0.787622i
$784$	36.5226	+	30.3927i	1.30438	+	1.08545i
$785$		0			0
$786$	3.74201	+	6.28728i	0.133473	+	0.224260i
$787$			19.4080i			0.691819i	0.938268	+	0.345910i	$0.112430\pi$
$787$			19.4080i			0.691819i	−0.938268	+	0.345910i	$0.887570\pi$
$788$	−7.58003	+	20.9591i	−0.270027	+	0.746636i
$789$	17.7960	−	15.3078i	0.633555	−	0.544971i
$790$		0			0
$791$	−48.0644			−1.70897
$792$	−9.68562	+	12.2108i	−0.344163	+	0.433890i
$793$		−	5.45667i		−	0.193772i
$794$	−4.47684	+	25.5420i	−0.158877	+	0.906450i
$795$		0			0
$796$	1.90484	−	5.26695i	0.0675152	−	0.186682i
$797$			30.7743i			1.09008i	0.838409	+	0.545041i	$0.183486\pi$
$797$			30.7743i			1.09008i	−0.838409	+	0.545041i	$0.816514\pi$
$798$	−49.2745	+	29.3268i	−1.74430	+	1.03816i
$799$			52.7882i			1.86751i
$800$		0			0
$801$	12.4947	+	1.88901i	0.441478	+	0.0667448i
$802$	47.6929	+	8.35933i	1.68409	+	0.295178i
$803$	8.11867			0.286502
$804$	−13.3900	+	5.09133i	−0.472230	+	0.179557i
$805$		0			0
$806$	−5.78862	−	1.01460i	−0.203895	−	0.0357376i
$807$	−14.6590	−	17.0418i	−0.516021	−	0.599900i
$808$	−4.44948	+	7.76156i	−0.156532	+	0.273051i
$809$		−	37.5744i		−	1.32104i	−0.750807	−	0.660522i	$-0.770335\pi$
$809$		−	37.5744i		−	1.32104i	0.750807	−	0.660522i	$-0.229665\pi$
$810$		0			0
$811$	−30.3492			−1.06571			−0.532853	−	0.846208i	$-0.678880\pi$
$811$	−30.3492			−1.06571			−0.532853	+	0.846208i	$0.678880\pi$
$812$	65.2179	+	23.5866i	2.28870	+	0.827729i
$813$		0			0
$814$	−6.96147	−	1.22016i	−0.243999	−	0.0427668i
$815$		0			0
$816$	−0.608357	−	37.2562i	−0.0212968	−	1.30423i
$817$		−	15.9894i		−	0.559397i
$818$	4.56386	−	26.0384i	0.159572	−	0.910413i
$819$	−1.14599	+	7.58003i	−0.0400440	+	0.264868i
$820$		0			0
$821$	6.97824			0.243542			0.121771	−	0.992558i	$-0.461143\pi$
$821$	6.97824			0.243542			0.121771	+	0.992558i	$0.461143\pi$
$822$	−11.9309	+	7.10096i	−0.416139	+	0.247674i
$823$	0.569147			0.0198392			0.00991960	−	0.999951i	$-0.496842\pi$
$823$	0.569147			0.0198392			0.00991960	+	0.999951i	$0.496842\pi$
$824$	17.7061	−	30.8860i	0.616821	−	1.07597i
$825$		0			0
$826$	65.1020	+	11.4107i	2.26519	+	0.397029i
$827$	23.0851			0.802748			0.401374	−	0.915914i	$-0.368533\pi$
$827$	23.0851			0.802748			0.401374	+	0.915914i	$0.368533\pi$
$828$	−12.7040	−	6.89202i	−0.441496	−	0.239514i
$829$			48.3636i			1.67974i	0.542790	+	0.839869i	$0.317368\pi$
$829$			48.3636i			1.67974i	−0.542790	+	0.839869i	$0.682632\pi$
$830$		0			0
$831$	18.9662	+	22.0491i	0.657930	+	0.764876i
$832$	2.37744	+	4.06018i	0.0824229	+	0.140761i
$833$	63.8852			2.21349
$834$	5.66373	−	3.37090i	0.196119	−	0.116725i
$835$		0			0
$836$	6.73138	−	18.6125i	0.232810	−	0.643728i
$837$	−19.5125	−	31.1004i	−0.674450	−	1.07499i
$838$	−7.30755	−	1.28082i	−0.252435	−	0.0442453i
$839$	−22.0393			−0.760883			−0.380441	−	0.924805i	$-0.624228\pi$
$839$	−22.0393			−0.760883			−0.380441	+	0.924805i	$0.624228\pi$
$840$		0			0
$841$	34.6926			1.19630
$842$	6.16332	+	1.08027i	0.212402	+	0.0372285i
$843$	14.5050	−	12.4769i	0.499578	−	0.429727i
$844$	−18.5532	−	6.70993i	−0.638628	−	0.230965i
$845$		0			0
$846$	13.2400	−	39.4817i	0.455200	−	1.35741i
$847$	−33.1355			−1.13855
$848$	−17.0203	+	20.4532i	−0.584481	+	0.702365i
$849$	24.5611	−	21.1270i	0.842936	−	0.725076i
$850$		0			0
$851$		−	6.55400i		−	0.224668i
$852$	−15.0499	−	39.5808i	−0.515603	−	1.35602i
$853$	−6.39801			−0.219064			−0.109532	−	0.993983i	$-0.534935\pi$
$853$	−6.39801			−0.219064			−0.109532	+	0.993983i	$0.534935\pi$
$854$	56.1546	+	9.84244i	1.92157	+	0.336801i
$855$		0			0
$856$	5.33142	−	9.29998i	0.182224	−	0.317867i
$857$	−27.2124			−0.929559			−0.464780	−	0.885426i	$-0.653866\pi$
$857$	−27.2124			−0.929559			−0.464780	+	0.885426i	$0.653866\pi$
$858$	−1.35333	−	2.27385i	−0.0462020	−	0.0776279i
$859$	−23.4663			−0.800658			−0.400329	−	0.916371i	$-0.631104\pi$
$859$	−23.4663			−0.800658			−0.400329	+	0.916371i	$0.631104\pi$
$860$		0			0
$861$	19.5406	−	16.8084i	0.665941	−	0.572828i
$862$	−1.44001	+	8.21575i	−0.0490469	+	0.279830i
$863$			12.4724i			0.424566i	0.977208	+	0.212283i	$0.0680898\pi$
$863$			12.4724i			0.424566i	−0.977208	+	0.212283i	$0.931910\pi$
$864$	−8.88935	+	28.0175i	−0.302422	+	0.953174i
$865$		0			0
$866$	44.8759	+	7.86557i	1.52494	+	0.267283i
$867$	−13.4691	−	15.6585i	−0.457434	−	0.531790i
$868$	20.8824	−	57.7405i	0.708794	−	1.95984i
$869$	23.1196			0.784279
$870$		0			0
$871$		−	2.43212i		−	0.0824093i
$872$	1.44316	+	0.827322i	0.0488715	+	0.0280166i
$873$	−6.42984	−	0.972093i	−0.217617	−	0.0329004i
$874$	18.0785	+	3.16869i	0.611515	+	0.107183i
$875$		0			0
$876$	14.3118	−	5.44181i	0.483550	−	0.183862i
$877$	−48.9517			−1.65298			−0.826491	−	0.562950i	$-0.809667\pi$
$877$	−48.9517			−1.65298			−0.826491	+	0.562950i	$0.809667\pi$
$878$	−3.16611	−	0.554937i	−0.106851	−	0.0187282i
$879$	−38.6652	+	33.2590i	−1.30414	+	1.12180i
$880$		0			0
$881$		−	9.76612i		−	0.329029i	−0.986375	−	0.164514i	$-0.947394\pi$
$881$		−	9.76612i		−	0.329029i	0.986375	−	0.164514i	$-0.0526057\pi$
$882$	−47.7815	−	16.0233i	−1.60889	−	0.539532i
$883$		−	37.1170i		−	1.24909i	−0.780990	−	0.624544i	$-0.785285\pi$
$883$		−	37.1170i		−	1.24909i	0.780990	−	0.624544i	$-0.214715\pi$
$884$	5.94902	+	2.15151i	0.200087	+	0.0723633i
$885$		0			0
$886$	−1.12088	+	6.39504i	−0.0376569	+	0.214846i
$887$			20.7792i			0.697699i	0.937179	+	0.348849i	$0.113427\pi$
$887$			20.7792i			0.697699i	−0.937179	+	0.348849i	$0.886573\pi$
$888$	−13.0897	+	2.51522i	−0.439261	+	0.0844053i
$889$	−56.2899			−1.88790
$890$		0			0
$891$	4.88681	−	15.7923i	0.163714	−	0.529062i
$892$	−3.05467	−	1.10475i	−0.102278	−	0.0369897i
$893$			52.8821i			1.76963i
$894$	44.1165	−	26.2570i	1.47548	−	0.878164i
$895$		0			0
$896$	−46.0716	+	17.1427i	−1.53914	+	0.572697i
$897$	1.86029	−	1.60018i	0.0621132	−	0.0534285i
$898$	−54.3904	−	9.53322i	−1.81503	−	0.318128i
$899$		−	56.3901i		−	1.88072i
$900$		0			0
$901$			35.7766i			1.19189i
$902$	−1.53595	+	8.76313i	−0.0511415	+	0.291780i
$903$	16.9319	−	14.5645i	0.563459	−	0.484675i
$904$	15.5611	−	27.1444i	0.517555	−	0.902809i
$905$		0			0
$906$	3.96965	+	6.66975i	0.131883	+	0.221588i
$907$		−	25.5231i		−	0.847481i	−0.905784	−	0.423741i	$-0.860717\pi$
$907$		−	25.5231i		−	0.847481i	0.905784	−	0.423741i	$-0.139283\pi$
$908$	−9.29144	−	3.36033i	−0.308347	−	0.111516i
$909$	1.41850	−	9.38256i	0.0470487	−	0.311200i
$910$		0			0
$911$	18.6187			0.616865			0.308433	−	0.951246i	$-0.400196\pi$
$911$	18.6187			0.616865			0.308433	+	0.951246i	$0.400196\pi$
$912$	−0.609440	−	37.3225i	−0.0201806	−	1.23587i
$913$			21.2322i			0.702683i
$914$	6.91122	+	1.21136i	0.228603	+	0.0400681i
$915$		0			0
$916$	10.3711	−	28.6765i	0.342671	−	0.947497i
$917$		−	12.9783i		−	0.428581i
$918$	14.9090	+	36.6014i	0.492071	+	1.20803i
$919$		−	27.9743i		−	0.922788i	−0.887195	−	0.461394i	$-0.847350\pi$
$919$		−	27.9743i		−	0.922788i	0.887195	−	0.461394i	$-0.152650\pi$
$920$		0			0
$921$	43.6074	−	37.5101i	1.43691	−	1.23600i
$922$	3.44916	−	19.6787i	0.113592	−	0.648083i
$923$	7.18934			0.236640
$924$	25.8412	−	9.82568i	0.850113	−	0.323241i
$925$		0			0
$926$	3.48912	−	19.9067i	0.114660	−	0.654174i
$927$	−5.64472	+	37.3366i	−0.185397	+	1.22629i
$928$	−34.4352	+	29.1955i	−1.13039	+	0.958391i
$929$			46.7604i			1.53416i	0.641551	+	0.767080i	$0.278291\pi$
$929$			46.7604i			1.53416i	−0.641551	+	0.767080i	$0.721709\pi$
$930$		0			0
$931$	63.9990			2.09748
$932$	41.9413	+	15.1685i	1.37383	+	0.496859i
$933$	−29.1149	−	33.8475i	−0.953178	−	1.10812i
$934$	7.77551	−	44.3620i	0.254422	−	1.45157i
$935$		0			0
$936$	−3.90980	−	3.10127i	−0.127796	−	0.101368i
$937$			41.2253i			1.34677i	0.739291	+	0.673387i	$0.235161\pi$
$937$			41.2253i			1.34677i	−0.739291	+	0.673387i	$0.764839\pi$
$938$	25.0289	+	4.38692i	0.817224	+	0.143238i
$939$	12.6768	−	10.9043i	0.413692	−	0.355849i
$940$		0			0
$941$	−0.179836			−0.00586248			−0.00293124	−	0.999996i	$-0.500933\pi$
$941$	−0.179836			−0.00586248			−0.00293124	+	0.999996i	$0.500933\pi$
$942$	25.2562	−	15.0318i	0.822892	−	0.489763i
$943$	−8.25021			−0.268664
$944$	−27.5213	+	33.0721i	−0.895743	+	1.07641i
$945$		0			0
$946$	−1.33090	+	7.59325i	−0.0432713	+	0.246878i
$947$	21.3864			0.694965			0.347483	−	0.937686i	$-0.387037\pi$
$947$	21.3864			0.694965			0.347483	+	0.937686i	$0.387037\pi$
$948$	40.7557	−	15.4967i	1.32369	−	0.503309i
$949$			2.59955i			0.0843849i
$950$		0			0
$951$	6.32612	−	5.44160i	0.205139	−	0.176456i
$952$	−32.8717	+	57.3405i	−1.06538	+	1.85842i
$953$	−11.0306			−0.357317			−0.178658	−	0.983911i	$-0.557176\pi$
$953$	−11.0306			−0.357317			−0.178658	+	0.983911i	$0.557176\pi$
$954$	8.97327	−	26.7583i	0.290520	−	0.866333i
$955$		0			0
$956$	27.9884	+	10.1222i	0.905208	+	0.327376i
$957$	19.2487	−	16.5573i	0.622223	−	0.535223i
$958$	6.33739	−	36.1570i	0.204752	−	1.16818i
$959$	24.6280			0.795281
$960$		0			0
$961$	−18.9248			−0.610478
$962$	0.390689	−	2.22902i	0.0125963	−	0.0718664i
$963$	−1.69966	+	11.2423i	−0.0547709	+	0.362278i
$964$	0.983862	+	0.355822i	0.0316881	+	0.0114603i
$965$		0			0
$966$	13.1119	+	22.0305i	0.421870	+	0.708820i
$967$	−10.8832			−0.349980			−0.174990	−	0.984570i	$-0.555989\pi$
$967$	−10.8832			−0.349980			−0.174990	+	0.984570i	$0.555989\pi$
$968$	10.7278	−	18.7133i	0.344804	−	0.601467i
$969$	−32.7288	−	38.0488i	−1.05140	−	1.22230i
$970$		0			0
$971$		−	2.40482i		−	0.0771744i	−0.999255	−	0.0385872i	$-0.987714\pi$
$971$		−	2.40482i		−	0.0771744i	0.999255	−	0.0385872i	$-0.0122857\pi$
$972$	−1.97074	−	31.1146i	−0.0632117	−	0.998000i
$973$	−11.6912			−0.374802
$974$	−5.96846	+	34.0521i	−0.191242	+	1.09110i
$975$		0			0
$976$	−23.7389	+	28.5268i	−0.759863	+	0.913119i
$977$	41.7609			1.33605			0.668026	−	0.744138i	$-0.267140\pi$
$977$	41.7609			1.33605			0.668026	+	0.744138i	$0.267140\pi$
$978$	−16.5135	−	27.7458i	−0.528045	−	0.887213i
$979$	7.73698			0.247275
$980$		0			0
$981$	−1.74456	−	0.263751i	−0.0556995	−	0.00842092i
$982$	−52.4638	−	9.19554i	−1.67419	−	0.293442i
$983$		−	33.2516i		−	1.06056i	−0.847822	−	0.530281i	$-0.822086\pi$
$983$		−	33.2516i		−	1.06056i	0.847822	−	0.530281i	$-0.177914\pi$
$984$	3.16617	+	16.4774i	0.100934	+	0.525279i
$985$		0			0
$986$	−10.4795	+	59.7894i	−0.333736	+	1.90408i
$987$	−55.9994	+	48.1695i	−1.78248	+	1.53325i
$988$	5.95961	+	2.15534i	0.189600	+	0.0685707i
$989$	−7.14881			−0.227319
$990$		0			0
$991$		−	33.9434i		−	1.07825i	−0.842226	−	0.539124i	$-0.818755\pi$
$991$		−	33.9434i		−	1.07825i	0.842226	−	0.539124i	$-0.181245\pi$
$992$	25.8482	+	30.4871i	0.820681	+	0.967967i
$993$	1.55171	+	1.80394i	0.0492420	+	0.0572462i
$994$	−12.9677	+	73.9854i	−0.411311	+	2.34667i
$995$		0			0
$996$	14.2316	+	37.4285i	0.450945	+	1.18597i
$997$	45.6428			1.44552			0.722761	−	0.691098i	$-0.242873\pi$
$997$	45.6428			1.44552			0.722761	+	0.691098i	$0.242873\pi$
$998$	−8.96650	+	51.1570i	−0.283830	+	1.61935i
$999$	11.9758	−	7.51364i	0.378897	−	0.237721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.m.e.299.11		24
3.2	odd	2	inner	600.2.m.e.299.13		24
4.3	odd	2		2400.2.m.e.1199.20		24
5.2	odd	4		600.2.b.h.251.1	yes	12
5.3	odd	4		600.2.b.g.251.12	yes	12
5.4	even	2	inner	600.2.m.e.299.14		24
8.3	odd	2	inner	600.2.m.e.299.9		24
8.5	even	2		2400.2.m.e.1199.19		24
12.11	even	2		2400.2.m.e.1199.8		24
15.2	even	4		600.2.b.h.251.12	yes	12
15.8	even	4		600.2.b.g.251.1	✓	12
15.14	odd	2	inner	600.2.m.e.299.12		24
20.3	even	4		2400.2.b.h.2351.3		12
20.7	even	4		2400.2.b.g.2351.10		12
20.19	odd	2		2400.2.m.e.1199.5		24
24.5	odd	2		2400.2.m.e.1199.7		24
24.11	even	2	inner	600.2.m.e.299.15		24
40.3	even	4		600.2.b.g.251.2	yes	12
40.13	odd	4		2400.2.b.h.2351.4		12
40.19	odd	2	inner	600.2.m.e.299.16		24
40.27	even	4		600.2.b.h.251.11	yes	12
40.29	even	2		2400.2.m.e.1199.6		24
40.37	odd	4		2400.2.b.g.2351.9		12
60.23	odd	4		2400.2.b.h.2351.1		12
60.47	odd	4		2400.2.b.g.2351.12		12
60.59	even	2		2400.2.m.e.1199.17		24
120.29	odd	2		2400.2.m.e.1199.18		24
120.53	even	4		2400.2.b.h.2351.2		12
120.59	even	2	inner	600.2.m.e.299.10		24
120.77	even	4		2400.2.b.g.2351.11		12
120.83	odd	4		600.2.b.g.251.11	yes	12
120.107	odd	4		600.2.b.h.251.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.b.g.251.1	✓	12	15.8	even	4
600.2.b.g.251.2	yes	12	40.3	even	4
600.2.b.g.251.11	yes	12	120.83	odd	4
600.2.b.g.251.12	yes	12	5.3	odd	4
600.2.b.h.251.1	yes	12	5.2	odd	4
600.2.b.h.251.2	yes	12	120.107	odd	4
600.2.b.h.251.11	yes	12	40.27	even	4
600.2.b.h.251.12	yes	12	15.2	even	4
600.2.m.e.299.9		24	8.3	odd	2	inner
600.2.m.e.299.10		24	120.59	even	2	inner
600.2.m.e.299.11		24	1.1	even	1	trivial
600.2.m.e.299.12		24	15.14	odd	2	inner
600.2.m.e.299.13		24	3.2	odd	2	inner
600.2.m.e.299.14		24	5.4	even	2	inner
600.2.m.e.299.15		24	24.11	even	2	inner
600.2.m.e.299.16		24	40.19	odd	2	inner
2400.2.b.g.2351.9		12	40.37	odd	4
2400.2.b.g.2351.10		12	20.7	even	4
2400.2.b.g.2351.11		12	120.77	even	4
2400.2.b.g.2351.12		12	60.47	odd	4
2400.2.b.h.2351.1		12	60.23	odd	4
2400.2.b.h.2351.2		12	120.53	even	4
2400.2.b.h.2351.3		12	20.3	even	4
2400.2.b.h.2351.4		12	40.13	odd	4
2400.2.m.e.1199.5		24	20.19	odd	2
2400.2.m.e.1199.6		24	40.29	even	2
2400.2.m.e.1199.7		24	24.5	odd	2
2400.2.m.e.1199.8		24	12.11	even	2
2400.2.m.e.1199.17		24	60.59	even	2
2400.2.m.e.1199.18		24	120.29	odd	2
2400.2.m.e.1199.19		24	8.5	even	2
2400.2.m.e.1199.20		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.244153 + 1.39298i) q^{2} +(-1.12950 - 1.31310i) q^{3} +(-1.88078 - 0.680200i) q^{4} +(2.10489 - 1.25277i) q^{6} -4.34495 q^{7} +(1.40670 - 2.45381i) q^{8} +(-0.448458 + 2.96629i) q^{9} +O(q^{10})\)	\(q+(-0.244153 + 1.39298i) q^{2} +(-1.12950 - 1.31310i) q^{3} +(-1.88078 - 0.680200i) q^{4} +(2.10489 - 1.25277i) q^{6} -4.34495 q^{7} +(1.40670 - 2.45381i) q^{8} +(-0.448458 + 2.96629i) q^{9} +1.83679i q^{11} +(1.23117 + 3.23793i) q^{12} -0.588129 q^{13} +(1.06083 - 6.05242i) q^{14} +(3.07466 + 2.55861i) q^{16} +5.37818 q^{17} +(-4.02249 - 1.34892i) q^{18} +5.38776 q^{19} +(4.90762 + 5.70535i) q^{21} +(-2.55861 - 0.448458i) q^{22} -2.40885i q^{23} +(-4.81097 + 0.924442i) q^{24} +(0.143593 - 0.819251i) q^{26} +(4.40157 - 2.76156i) q^{27} +(8.17189 + 2.95543i) q^{28} +7.98077 q^{29} -7.06575i q^{31} +(-4.31478 + 3.65824i) q^{32} +(2.41189 - 2.07466i) q^{33} +(-1.31310 + 7.49169i) q^{34} +(2.86112 - 5.27390i) q^{36} +2.72080 q^{37} +(-1.31544 + 7.50503i) q^{38} +(0.664291 + 0.772271i) q^{39} -3.42496i q^{41} +(-9.14564 + 5.44323i) q^{42} -2.96772i q^{43} +(1.24939 - 3.45460i) q^{44} +(3.35548 + 0.588129i) q^{46} +9.81525i q^{47} +(-0.113116 - 6.92728i) q^{48} +11.8786 q^{49} +(-6.07466 - 7.06208i) q^{51} +(1.10614 + 0.400045i) q^{52} +6.65218i q^{53} +(2.77213 + 6.80553i) q^{54} +(-6.11205 + 10.6617i) q^{56} +(-6.08547 - 7.07466i) q^{57} +(-1.94853 + 11.1170i) q^{58} +10.7564i q^{59} +9.27803i q^{61} +(9.84244 + 1.72512i) q^{62} +(1.94853 - 12.8884i) q^{63} +(-4.04238 - 6.90356i) q^{64} +(2.30108 + 3.86624i) q^{66} +4.13536i q^{67} +(-10.1152 - 3.65824i) q^{68} +(-3.16306 + 2.72080i) q^{69} -12.2241 q^{71} +(6.64787 + 5.27312i) q^{72} -4.42003i q^{73} +(-0.664291 + 3.79002i) q^{74} +(-10.1332 - 3.66475i) q^{76} -7.98077i q^{77} +(-1.23795 + 0.736791i) q^{78} -12.5870i q^{79} +(-8.59777 - 2.66052i) q^{81} +(4.77089 + 0.836213i) q^{82} +11.5594 q^{83} +(-5.34937 - 14.0687i) q^{84} +(4.13398 + 0.724579i) q^{86} +(-9.01428 - 10.4795i) q^{87} +(4.50714 + 2.58382i) q^{88} -4.21222i q^{89} +2.55539 q^{91} +(-1.63850 + 4.53052i) q^{92} +(-9.27803 + 7.98077i) q^{93} +(-13.6724 - 2.39642i) q^{94} +(9.67717 + 1.53375i) q^{96} +2.16763i q^{97} +(-2.90019 + 16.5466i) q^{98} +(-5.44846 - 0.823724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9	\( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9} - 12 q^{16} + 8 q^{19} - 10 q^{24} + 4 q^{34} + 38 q^{36} - 32 q^{46} + 72 q^{49} - 60 q^{51} + 60 q^{54} - 20 q^{64} + 14 q^{66} - 76 q^{76} - 20 q^{81} + 68 q^{84} - 48 q^{91} - 56 q^{94} - 62 q^{96} - 116 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9 - 12 * q^16 + 8 * q^19 - 10 * q^24 + 4 * q^34 + 38 * q^36 - 32 * q^46 + 72 * q^49 - 60 * q^51 + 60 * q^54 - 20 * q^64 + 14 * q^66 - 76 * q^76 - 20 * q^81 + 68 * q^84 - 48 * q^91 - 56 * q^94 - 62 * q^96 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more