LMFDB - Embedded newform 360.2.x.a.53.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(53,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("360.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.x (of order $4$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.10
Character	$\chi$	$=$	360.53
Dual form			360.2.x.a.197.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.473189 + 1.33270i) q^{2} +(-1.55218 - 1.26124i) q^{4} +(1.45381 + 1.69895i) q^{5} +(1.53029 - 1.53029i) q^{7} +(2.41533 - 1.47179i) q^{8} +O(q^{10})$	\(q+(-0.473189 + 1.33270i) q^{2} +(-1.55218 - 1.26124i) q^{4} +(1.45381 + 1.69895i) q^{5} +(1.53029 - 1.53029i) q^{7} +(2.41533 - 1.47179i) q^{8} +(-2.95212 + 1.13358i) q^{10} +2.72480 q^{11} +(0.857617 - 0.857617i) q^{13} +(1.31530 + 2.76353i) q^{14} +(0.818554 + 3.91535i) q^{16} +(2.55531 + 2.55531i) q^{17} -3.54160 q^{19} +(-0.113809 - 4.47069i) q^{20} +(-1.28935 + 3.63135i) q^{22} +(-0.626051 + 0.626051i) q^{23} +(-0.772849 + 4.93991i) q^{25} +(0.737133 + 1.54876i) q^{26} +(-4.30535 + 0.445231i) q^{28} +5.12260i q^{29} +7.89544 q^{31} +(-5.60532 - 0.761813i) q^{32} +(-4.61460 + 2.19632i) q^{34} +(4.82463 + 0.375125i) q^{35} +(-4.21539 - 4.21539i) q^{37} +(1.67585 - 4.71990i) q^{38} +(6.01194 + 1.96381i) q^{40} +12.4074i q^{41} +(5.67823 - 5.67823i) q^{43} +(-4.22940 - 3.43663i) q^{44} +(-0.538098 - 1.13058i) q^{46} +(-9.45505 - 9.45505i) q^{47} +2.31644i q^{49} +(-6.21772 - 3.36749i) q^{50} +(-2.41284 + 0.249520i) q^{52} +(-6.46657 - 6.46657i) q^{53} +(3.96136 + 4.62930i) q^{55} +(1.44388 - 5.94842i) q^{56} +(-6.82690 - 2.42396i) q^{58} -2.51407i q^{59} -9.49179i q^{61} +(-3.73603 + 10.5223i) q^{62} +(3.66765 - 7.10974i) q^{64} +(2.70386 + 0.210231i) q^{65} +(9.91318 + 9.91318i) q^{67} +(-0.743456 - 7.18916i) q^{68} +(-2.78289 + 6.25229i) q^{70} +2.19671i q^{71} +(-5.71276 - 5.71276i) q^{73} +(7.61252 - 3.62318i) q^{74} +(5.49722 + 4.46681i) q^{76} +(4.16973 - 4.16973i) q^{77} -12.7576i q^{79} +(-5.46195 + 7.08287i) q^{80} +(-16.5353 - 5.87103i) q^{82} +(-3.58072 - 3.58072i) q^{83} +(-0.626392 + 8.05627i) q^{85} +(4.88051 + 10.2543i) q^{86} +(6.58130 - 4.01035i) q^{88} +10.2214 q^{89} -2.62480i q^{91} +(1.76135 - 0.182147i) q^{92} +(17.0748 - 8.12673i) q^{94} +(-5.14884 - 6.01700i) q^{95} +(-1.29731 + 1.29731i) q^{97} +(-3.08712 - 1.09611i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) $ 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.473189	+	1.33270i	−0.334595	+	0.942362i
$2$	−0.473189	+	1.33270i	−0.334595	+	0.942362i
$3$		0			0
$3$		0			0
$4$	−1.55218	−	1.26124i	−0.776092	−	0.630619i
$5$	1.45381	+	1.69895i	0.650165	+	0.759793i
$5$	1.45381	+	1.69895i	0.650165	+	0.759793i
$6$		0			0
$7$	1.53029	−	1.53029i	0.578394	−	0.578394i	−0.356066	−	0.934461i	$-0.615882\pi$
$7$	1.53029	−	1.53029i	0.578394	−	0.578394i	0.934461	+	0.356066i	$0.115882\pi$
$8$	2.41533	−	1.47179i	0.853948	−	0.520358i
$9$		0			0
$10$	−2.95212	+	1.13358i	−0.933542	+	0.358468i
$11$	2.72480			0.821559			0.410779	−	0.911735i	$-0.365257\pi$
$11$	2.72480			0.821559			0.410779	+	0.911735i	$0.365257\pi$
$12$		0			0
$13$	0.857617	−	0.857617i	0.237860	−	0.237860i	−0.578103	−	0.815964i	$-0.696207\pi$
$13$	0.857617	−	0.857617i	0.237860	−	0.237860i	0.815964	+	0.578103i	$0.196207\pi$
$14$	1.31530	+	2.76353i	0.351529	+	0.738585i
$15$		0			0
$16$	0.818554	+	3.91535i	0.204638	+	0.978838i
$17$	2.55531	+	2.55531i	0.619753	+	0.619753i	0.945468	−	0.325715i	$-0.105605\pi$
$17$	2.55531	+	2.55531i	0.619753	+	0.619753i	−0.325715	+	0.945468i	$0.605605\pi$
$18$		0			0
$19$	−3.54160			−0.812500			−0.406250	−	0.913762i	$-0.633164\pi$
$19$	−3.54160			−0.812500			−0.406250	+	0.913762i	$0.633164\pi$
$20$	−0.113809	−	4.47069i	−0.0254484	−	0.999676i
$21$		0			0
$22$	−1.28935	+	3.63135i	−0.274889	+	0.774206i
$23$	−0.626051	+	0.626051i	−0.130541	+	0.130541i	−0.769358	−	0.638818i	$-0.779424\pi$
$23$	−0.626051	+	0.626051i	−0.130541	+	0.130541i	0.638818	+	0.769358i	$0.279424\pi$
$24$		0			0
$25$	−0.772849	+	4.93991i	−0.154570	+	0.987982i
$26$	0.737133	+	1.54876i	0.144564	+	0.303737i
$27$		0			0
$28$	−4.30535	+	0.445231i	−0.813634	+	0.0841407i
$29$			5.12260i			0.951243i	0.879650	+	0.475622i	$0.157777\pi$
$29$			5.12260i			0.951243i	−0.879650	+	0.475622i	$0.842223\pi$
$30$		0			0
$31$	7.89544			1.41806			0.709031	−	0.705177i	$-0.249132\pi$
$31$	7.89544			1.41806			0.709031	+	0.705177i	$0.249132\pi$
$32$	−5.60532	−	0.761813i	−0.990890	−	0.134671i
$33$		0			0
$34$	−4.61460	+	2.19632i	−0.791398	+	0.376665i
$35$	4.82463	+	0.375125i	0.815512	+	0.0634078i
$36$		0			0
$37$	−4.21539	−	4.21539i	−0.693005	−	0.693005i	0.269887	−	0.962892i	$-0.413014\pi$
$37$	−4.21539	−	4.21539i	−0.693005	−	0.693005i	−0.962892	+	0.269887i	$0.913014\pi$
$38$	1.67585	−	4.71990i	0.271858	−	0.765669i
$39$		0			0
$40$	6.01194	+	1.96381i	0.950572	+	0.310505i
$41$			12.4074i			1.93771i	0.247638	+	0.968853i	$0.420346\pi$
$41$			12.4074i			1.93771i	−0.247638	+	0.968853i	$0.579654\pi$
$42$		0			0
$43$	5.67823	−	5.67823i	0.865922	−	0.865922i	−0.126096	−	0.992018i	$-0.540245\pi$
$43$	5.67823	−	5.67823i	0.865922	−	0.865922i	0.992018	+	0.126096i	$0.0402447\pi$
$44$	−4.22940	−	3.43663i	−0.637605	−	0.518091i
$45$		0			0
$46$	−0.538098	−	1.13058i	−0.0793383	−	0.166695i
$47$	−9.45505	−	9.45505i	−1.37916	−	1.37916i	−0.846037	−	0.533124i	$-0.821018\pi$
$47$	−9.45505	−	9.45505i	−1.37916	−	1.37916i	−0.533124	−	0.846037i	$-0.678982\pi$
$48$		0			0
$49$			2.31644i			0.330920i
$50$	−6.21772	−	3.36749i	−0.879318	−	0.476235i
$51$		0			0
$52$	−2.41284	+	0.249520i	−0.334601	+	0.0346022i
$53$	−6.46657	−	6.46657i	−0.888252	−	0.888252i	0.106103	−	0.994355i	$-0.466163\pi$
$53$	−6.46657	−	6.46657i	−0.888252	−	0.888252i	−0.994355	+	0.106103i	$0.966163\pi$
$54$		0			0
$55$	3.96136	+	4.62930i	0.534149	+	0.624214i
$56$	1.44388	−	5.94842i	0.192947	−	0.794891i
$57$		0			0
$58$	−6.82690	−	2.42396i	−0.896416	−	0.318281i
$59$		−	2.51407i		−	0.327304i	−0.986518	−	0.163652i	$-0.947673\pi$
$59$		−	2.51407i		−	0.327304i	0.986518	−	0.163652i	$-0.0523274\pi$
$60$		0			0
$61$		−	9.49179i		−	1.21530i	−0.794205	−	0.607649i	$-0.792113\pi$
$61$		−	9.49179i		−	1.21530i	0.794205	−	0.607649i	$-0.207887\pi$
$62$	−3.73603	+	10.5223i	−0.474477	+	1.33633i
$63$		0			0
$64$	3.66765	−	7.10974i	0.458456	−	0.888717i
$65$	2.70386	+	0.210231i	0.335373	+	0.0260760i
$66$		0			0
$67$	9.91318	+	9.91318i	1.21109	+	1.21109i	0.970669	+	0.240418i	$0.0772846\pi$
$67$	9.91318	+	9.91318i	1.21109	+	1.21109i	0.240418	+	0.970669i	$0.422715\pi$
$68$	−0.743456	−	7.18916i	−0.0901573	−	0.871814i
$69$		0			0
$70$	−2.78289	+	6.25229i	−0.332619	+	0.747292i
$71$			2.19671i			0.260702i	0.991468	+	0.130351i	$0.0416104\pi$
$71$			2.19671i			0.260702i	−0.991468	+	0.130351i	$0.958390\pi$
$72$		0			0
$73$	−5.71276	−	5.71276i	−0.668628	−	0.668628i	0.288771	−	0.957398i	$-0.406754\pi$
$73$	−5.71276	−	5.71276i	−0.668628	−	0.668628i	−0.957398	+	0.288771i	$0.906754\pi$
$74$	7.61252	−	3.62318i	0.884938	−	0.421186i
$75$		0			0
$76$	5.49722	+	4.46681i	0.630575	+	0.512378i
$77$	4.16973	−	4.16973i	0.475185	−	0.475185i
$78$		0			0
$79$		−	12.7576i		−	1.43534i	−0.696384	−	0.717670i	$-0.745209\pi$
$79$		−	12.7576i		−	1.43534i	0.696384	−	0.717670i	$-0.254791\pi$
$80$	−5.46195	+	7.08287i	−0.610665	+	0.791889i
$81$		0			0
$82$	−16.5353	−	5.87103i	−1.82602	−	0.648347i
$83$	−3.58072	−	3.58072i	−0.393035	−	0.393035i	0.482733	−	0.875768i	$-0.339644\pi$
$83$	−3.58072	−	3.58072i	−0.393035	−	0.393035i	−0.875768	+	0.482733i	$0.839644\pi$
$84$		0			0
$85$	−0.626392	+	8.05627i	−0.0679418	+	0.873826i
$86$	4.88051	+	10.2543i	0.526279	+	1.10575i
$87$		0			0
$88$	6.58130	−	4.01035i	0.701569	−	0.427504i
$89$	10.2214			1.08347			0.541734	−	0.840550i	$-0.317768\pi$
$89$	10.2214			1.08347			0.541734	+	0.840550i	$0.317768\pi$
$90$		0			0
$91$		−	2.62480i		−	0.275154i
$92$	1.76135	−	0.182147i	0.183633	−	0.0189901i
$93$		0			0
$94$	17.0748	−	8.12673i	1.76113	−	0.838208i
$95$	−5.14884	−	6.01700i	−0.528259	−	0.617331i
$96$		0			0
$97$	−1.29731	+	1.29731i	−0.131722	+	0.131722i	−0.769894	−	0.638172i	$-0.779691\pi$
$97$	−1.29731	+	1.29731i	−0.131722	+	0.131722i	0.638172	+	0.769894i	$0.279691\pi$
$98$	−3.08712	−	1.09611i	−0.311846	−	0.110724i
$99$		0			0
$100$	7.43001	−	6.69290i	0.743001	−	0.669290i
$101$	−5.82360			−0.579470			−0.289735	−	0.957107i	$-0.593567\pi$
$101$	−5.82360			−0.579470			−0.289735	+	0.957107i	$0.593567\pi$
$102$		0			0
$103$	−3.08360	−	3.08360i	−0.303836	−	0.303836i	0.538677	−	0.842513i	$-0.318924\pi$
$103$	−3.08360	−	3.08360i	−0.303836	−	0.303836i	−0.842513	+	0.538677i	$0.818924\pi$
$104$	0.809193	−	3.33367i	0.0793479	−	0.326893i
$105$		0			0
$106$	11.6779	−	5.55810i	1.13426	−	0.539850i
$107$	6.49670	−	6.49670i	0.628060	−	0.628060i	−0.319520	−	0.947580i	$-0.603522\pi$
$107$	6.49670	−	6.49670i	0.628060	−	0.628060i	0.947580	+	0.319520i	$0.103522\pi$
$108$		0			0
$109$	5.41031			0.518213			0.259107	−	0.965849i	$-0.416572\pi$
$109$	5.41031			0.518213			0.259107	+	0.965849i	$0.416572\pi$
$110$	−8.04394	+	3.08877i	−0.766959	+	0.294503i
$111$		0			0
$112$	7.24424	+	4.73899i	0.684516	+	0.447793i
$113$	−0.358788	+	0.358788i	−0.0337519	+	0.0337519i	−0.723781	−	0.690029i	$-0.757598\pi$
$113$	−0.358788	+	0.358788i	−0.0337519	+	0.0337519i	0.690029	+	0.723781i	$0.257598\pi$
$114$		0			0
$115$	−1.97379	−	0.153466i	−0.184057	−	0.0143108i
$116$	6.46082	−	7.95122i	0.599873	−	0.738253i
$117$		0			0
$118$	3.35050	+	1.18963i	0.308439	+	0.109514i
$119$	7.82071			0.716923
$120$		0			0
$121$	−3.57545			−0.325041
$122$	12.6497	+	4.49141i	1.14525	+	0.406633i
$123$		0			0
$124$	−12.2552	−	9.95803i	−1.10055	−	0.894258i
$125$	−9.51623	+	5.86868i	−0.851157	+	0.524911i
$126$		0			0
$127$	−0.916401	+	0.916401i	−0.0813174	+	0.0813174i	−0.746596	−	0.665278i	$-0.768313\pi$
$127$	−0.916401	+	0.916401i	−0.0813174	+	0.0813174i	0.665278	+	0.746596i	$0.268313\pi$
$128$	7.73967	+	8.25212i	0.684096	+	0.729392i
$129$		0			0
$130$	−1.55961	+	3.50396i	−0.136787	+	0.307318i
$131$	−19.5355			−1.70683			−0.853413	−	0.521235i	$-0.825471\pi$
$131$	−19.5355			−1.70683			−0.853413	+	0.521235i	$0.825471\pi$
$132$		0			0
$133$	−5.41968	+	5.41968i	−0.469945	+	0.469945i
$134$	−17.9021	+	8.52050i	−1.54651	+	0.736059i
$135$		0			0
$136$	9.93280	+	2.41103i	0.851730	+	0.206744i
$137$	−7.66611	−	7.66611i	−0.654960	−	0.654960i	0.299223	−	0.954183i	$-0.403273\pi$
$137$	−7.66611	−	7.66611i	−0.654960	−	0.654960i	−0.954183	+	0.299223i	$0.903273\pi$
$138$		0			0
$139$	−14.7210			−1.24862			−0.624308	−	0.781178i	$-0.714619\pi$
$139$	−14.7210			−1.24862			−0.624308	+	0.781178i	$0.714619\pi$
$140$	−7.01560	−	6.66728i	−0.592926	−	0.563488i
$141$		0			0
$142$	−2.92756	−	1.03946i	−0.245676	−	0.0872296i
$143$	2.33684	−	2.33684i	0.195416	−	0.195416i
$144$		0			0
$145$	−8.70304	+	7.44731i	−0.722748	+	0.618466i
$146$	10.3166	−	4.91019i	0.853809	−	0.406370i
$147$		0			0
$148$	1.22645	+	11.8597i	0.100813	+	0.974859i
$149$			15.6300i			1.28046i	0.768182	+	0.640231i	$0.221162\pi$
$149$			15.6300i			1.28046i	−0.768182	+	0.640231i	$0.778838\pi$
$150$		0			0
$151$	−17.5889			−1.43136			−0.715682	−	0.698426i	$-0.753884\pi$
$151$	−17.5889			−1.43136			−0.715682	+	0.698426i	$0.753884\pi$
$152$	−8.55415	+	5.21251i	−0.693833	+	0.422791i
$153$		0			0
$154$	3.58394	+	7.53008i	0.288802	+	0.606791i
$155$	11.4785	+	13.4139i	0.921975	+	1.07743i
$156$		0			0
$157$	7.60352	+	7.60352i	0.606827	+	0.606827i	0.942116	−	0.335288i	$-0.108834\pi$
$157$	7.60352	+	7.60352i	0.606827	+	0.606827i	−0.335288	+	0.942116i	$0.608834\pi$
$158$	17.0020	+	6.03674i	1.35261	+	0.480257i
$159$		0			0
$160$	−6.85482	−	10.6307i	−0.541921	−	0.840430i
$161$			1.91608i			0.151008i
$162$		0			0
$163$	−8.53586	+	8.53586i	−0.668580	+	0.668580i	−0.957387	−	0.288807i	$-0.906741\pi$
$163$	−8.53586	+	8.53586i	−0.668580	+	0.668580i	0.288807	+	0.957387i	$0.406741\pi$
$164$	15.6487	−	19.2585i	1.22195	−	1.50384i
$165$		0			0
$166$	6.46639	−	3.07767i	0.501889	−	0.238874i
$167$	−6.11022	−	6.11022i	−0.472823	−	0.472823i	0.430004	−	0.902827i	$-0.358512\pi$
$167$	−6.11022	−	6.11022i	−0.472823	−	0.472823i	−0.902827	+	0.430004i	$0.858512\pi$
$168$		0			0
$169$			11.5290i			0.886845i
$170$	−10.4402	−	4.64693i	−0.800727	−	0.356403i
$171$		0			0
$172$	−15.9753	+	1.65206i	−1.21810	+	0.125968i
$173$	0.593720	+	0.593720i	0.0451397	+	0.0451397i	0.729316	−	0.684177i	$-0.239838\pi$
$173$	0.593720	+	0.593720i	0.0451397	+	0.0451397i	−0.684177	+	0.729316i	$0.739838\pi$
$174$		0			0
$175$	6.37680	+	8.74217i	0.482041	+	0.660846i
$176$	2.23040	+	10.6686i	0.168123	+	0.804173i
$177$		0			0
$178$	−4.83666	+	13.6221i	−0.362523	+	1.02102i
$179$		−	11.3935i		−	0.851593i	−0.904819	−	0.425796i	$-0.859994\pi$
$179$		−	11.3935i		−	0.851593i	0.904819	−	0.425796i	$-0.140006\pi$
$180$		0			0
$181$		−	7.31410i		−	0.543653i	−0.962346	−	0.271827i	$-0.912372\pi$
$181$		−	7.31410i		−	0.543653i	0.962346	−	0.271827i	$-0.0876277\pi$
$182$	3.49808	+	1.24203i	0.259295	+	0.0920652i
$183$		0			0
$184$	−0.590702	+	2.43354i	−0.0435471	+	0.179403i
$185$	1.03333	−	13.2901i	0.0759722	−	0.977108i
$186$		0			0
$187$	6.96270	+	6.96270i	0.509163	+	0.509163i
$188$	2.75091	+	26.6011i	0.200631	+	1.94008i
$189$		0			0
$190$	10.4552	−	4.01468i	0.758503	−	0.291255i
$191$		−	1.32855i		−	0.0961302i	−0.998844	−	0.0480651i	$-0.984695\pi$
$191$		−	1.32855i		−	0.0961302i	0.998844	−	0.0480651i	$-0.0153055\pi$
$192$		0			0
$193$	−11.5366	−	11.5366i	−0.830423	−	0.830423i	0.157152	−	0.987574i	$-0.449769\pi$
$193$	−11.5366	−	11.5366i	−0.830423	−	0.830423i	−0.987574	+	0.157152i	$0.949769\pi$
$194$	−1.11506	−	2.34280i	−0.0800563	−	0.168203i
$195$		0			0
$196$	2.92158	−	3.59554i	0.208684	−	0.256824i
$197$	16.1999	−	16.1999i	1.15420	−	1.15420i	0.168494	−	0.985703i	$-0.446110\pi$
$197$	16.1999	−	16.1999i	1.15420	−	1.15420i	0.985703	−	0.168494i	$-0.0538905\pi$
$198$		0			0
$199$			6.09388i			0.431984i	0.976395	+	0.215992i	$0.0692985\pi$
$199$			6.09388i			0.431984i	−0.976395	+	0.215992i	$0.930702\pi$
$200$	5.40384	+	13.0690i	0.382109	+	0.924117i
$201$		0			0
$202$	2.75566	−	7.76112i	0.193888	−	0.546071i
$203$	7.83906	+	7.83906i	0.550194	+	0.550194i
$204$		0			0
$205$	−21.0795	+	18.0380i	−1.47225	+	1.25983i
$206$	5.56864	−	2.65039i	0.387986	−	0.184662i
$207$		0			0
$208$	4.05988	+	2.65587i	0.281502	+	0.184151i
$209$	−9.65017			−0.667516
$210$		0			0
$211$			24.9318i			1.71637i	0.513338	+	0.858186i	$0.328409\pi$
$211$			24.9318i			1.71637i	−0.513338	+	0.858186i	$0.671591\pi$
$212$	1.88142	+	18.1932i	0.129217	+	1.24951i
$213$		0			0
$214$	5.58399	+	11.7323i	0.381714	+	0.802005i
$215$	17.9021	+	1.39193i	1.22091	+	0.0949286i
$216$		0			0
$217$	12.0823	−	12.0823i	0.820200	−	0.820200i
$218$	−2.56010	+	7.21032i	−0.173392	+	0.488345i
$219$		0			0
$220$	−0.310106	−	12.1817i	−0.0209074	−	0.821293i
$221$	4.38295			0.294829
$222$		0			0
$223$	−5.42573	−	5.42573i	−0.363334	−	0.363334i	0.501705	−	0.865039i	$-0.332706\pi$
$223$	−5.42573	−	5.42573i	−0.363334	−	0.363334i	−0.865039	+	0.501705i	$0.832706\pi$
$224$	−9.74355	+	7.41196i	−0.651018	+	0.495233i
$225$		0			0
$226$	−0.308383	−	0.647931i	−0.0205133	−	0.0430998i
$227$	−8.15485	+	8.15485i	−0.541256	+	0.541256i	−0.923897	−	0.382641i	$-0.875015\pi$
$227$	−8.15485	+	8.15485i	−0.541256	+	0.541256i	0.382641	+	0.923897i	$0.375015\pi$
$228$		0			0
$229$	14.5344			0.960462			0.480231	−	0.877142i	$-0.340553\pi$
$229$	14.5344			0.960462			0.480231	+	0.877142i	$0.340553\pi$
$230$	1.13850	−	2.55785i	0.0750705	−	0.168660i
$231$		0			0
$232$	7.53942	+	12.3728i	0.494987	+	0.812313i
$233$	2.40471	−	2.40471i	0.157538	−	0.157538i	−0.623937	−	0.781475i	$-0.714468\pi$
$233$	2.40471	−	2.40471i	0.157538	−	0.157538i	0.781475	+	0.623937i	$0.214468\pi$
$234$		0			0
$235$	2.31775	−	29.8095i	0.151194	−	1.94456i
$236$	−3.17084	+	3.90230i	−0.206404	+	0.254018i
$237$		0			0
$238$	−3.70067	+	10.4227i	−0.239879	+	0.675601i
$239$	6.79965			0.439833			0.219917	−	0.975519i	$-0.429422\pi$
$239$	6.79965			0.439833			0.219917	+	0.975519i	$0.429422\pi$
$240$		0			0
$241$	16.2108			1.04423			0.522114	−	0.852876i	$-0.325143\pi$
$241$	16.2108			1.04423			0.522114	+	0.852876i	$0.325143\pi$
$242$	1.69187	−	4.76501i	0.108757	−	0.306307i
$243$		0			0
$244$	−11.9714	+	14.7330i	−0.766391	+	0.943184i
$245$	−3.93551	+	3.36767i	−0.251430	+	0.215153i
$246$		0			0
$247$	−3.03734	+	3.03734i	−0.193261	+	0.193261i
$248$	19.0701	−	11.6205i	1.21095	−	0.737900i
$249$		0			0
$250$	−3.31822	−	15.4593i	−0.209863	−	0.977731i
$251$	−9.56946			−0.604019			−0.302009	−	0.953305i	$-0.597657\pi$
$251$	−9.56946			−0.604019			−0.302009	+	0.953305i	$0.597657\pi$
$252$		0			0
$253$	−1.70587	+	1.70587i	−0.107247	+	0.107247i
$254$	−0.787658	−	1.65492i	−0.0494220	−	0.103839i
$255$		0			0
$256$	−14.6599	+	6.40985i	−0.916246	+	0.400616i
$257$	−5.61999	−	5.61999i	−0.350566	−	0.350566i	0.509754	−	0.860320i	$-0.329736\pi$
$257$	−5.61999	−	5.61999i	−0.350566	−	0.350566i	−0.860320	+	0.509754i	$0.829736\pi$
$258$		0			0
$259$	−12.9015			−0.801661
$260$	−3.93174	−	3.73653i	−0.243836	−	0.231730i
$261$		0			0
$262$	9.24399	−	26.0350i	0.571096	−	1.60845i
$263$	−16.0240	+	16.0240i	−0.988080	+	0.988080i	−0.999930	−	0.0118502i	$-0.996228\pi$
$263$	−16.0240	+	16.0240i	−0.988080	+	0.988080i	0.0118502	+	0.999930i	$0.496228\pi$
$264$		0			0
$265$	1.58518	−	20.3876i	0.0973766	−	1.25240i
$266$	−4.65828	−	9.78734i	−0.285617	−	0.600100i
$267$		0			0
$268$	−2.88420	−	27.8900i	−0.176180	−	1.70365i
$269$		−	8.90392i		−	0.542882i	−0.962455	−	0.271441i	$-0.912500\pi$
$269$		−	8.90392i		−	0.542882i	0.962455	−	0.271441i	$-0.0875001\pi$
$270$		0			0
$271$	−14.0162			−0.851422			−0.425711	−	0.904859i	$-0.639976\pi$
$271$	−14.0162			−0.851422			−0.425711	+	0.904859i	$0.639976\pi$
$272$	−7.91326	+	12.0966i	−0.479812	+	0.733463i
$273$		0			0
$274$	13.8442	−	6.58912i	0.836356	−	0.398063i
$275$	−2.10586	+	13.4603i	−0.126988	+	0.811685i
$276$		0			0
$277$	−2.00404	−	2.00404i	−0.120411	−	0.120411i	0.644333	−	0.764745i	$-0.277135\pi$
$277$	−2.00404	−	2.00404i	−0.120411	−	0.120411i	−0.764745	+	0.644333i	$0.777135\pi$
$278$	6.96580	−	19.6186i	0.417781	−	1.17665i
$279$		0			0
$280$	12.2052	−	6.19482i	0.729400	−	0.370211i
$281$		−	9.33618i		−	0.556950i	−0.960444	−	0.278475i	$-0.910171\pi$
$281$		−	9.33618i		−	0.556950i	0.960444	−	0.278475i	$-0.0898289\pi$
$282$		0			0
$283$	22.3583	−	22.3583i	1.32906	−	1.32906i	0.422877	−	0.906187i	$-0.361020\pi$
$283$	22.3583	−	22.3583i	1.32906	−	1.32906i	0.906187	−	0.422877i	$-0.138980\pi$
$284$	2.77058	−	3.40971i	0.164404	−	0.202329i
$285$		0			0
$286$	2.00854	+	4.22007i	0.118767	+	0.249538i
$287$	18.9868	+	18.9868i	1.12076	+	1.12076i
$288$		0			0
$289$		−	3.94082i		−	0.231813i
$290$	−5.80686	−	15.1225i	−0.340991	−	0.888026i
$291$		0			0
$292$	1.66210	+	16.0724i	0.0972672	+	0.940566i
$293$	−5.84966	−	5.84966i	−0.341741	−	0.341741i	0.515281	−	0.857021i	$-0.327688\pi$
$293$	−5.84966	−	5.84966i	−0.341741	−	0.341741i	−0.857021	+	0.515281i	$0.827688\pi$
$294$		0			0
$295$	4.27127	−	3.65499i	0.248683	−	0.212802i
$296$	−16.3857	−	3.97737i	−0.952401	−	0.231180i
$297$		0			0
$298$	−20.8302	−	7.39596i	−1.20666	−	0.428437i
$299$			1.07382i			0.0621009i
$300$		0			0
$301$		−	17.3787i		−	1.00169i
$302$	8.32287	−	23.4407i	0.478927	−	1.34886i
$303$		0			0
$304$	−2.89899	−	13.8666i	−0.166269	−	0.795305i
$305$	16.1261	−	13.7993i	0.923375	−	0.790145i
$306$		0			0
$307$	6.13875	+	6.13875i	0.350357	+	0.350357i	0.860242	−	0.509886i	$-0.170312\pi$
$307$	6.13875	+	6.13875i	0.350357	+	0.350357i	−0.509886	+	0.860242i	$0.670312\pi$
$308$	−11.7312	+	1.21317i	−0.668448	+	0.0691266i
$309$		0			0
$310$	−23.3083	+	8.95008i	−1.32382	+	0.508331i
$311$			13.0614i			0.740642i	0.928904	+	0.370321i	$0.120752\pi$
$311$			13.0614i			0.740642i	−0.928904	+	0.370321i	$0.879248\pi$
$312$		0			0
$313$	22.0110	+	22.0110i	1.24414	+	1.24414i	0.958269	+	0.285869i	$0.0922822\pi$
$313$	22.0110	+	22.0110i	1.24414	+	1.24414i	0.285869	+	0.958269i	$0.407718\pi$
$314$	−13.7311	+	6.53532i	−0.774892	+	0.368810i
$315$		0			0
$316$	−16.0903	+	19.8021i	−0.905153	+	1.11396i
$317$	6.28577	−	6.28577i	0.353044	−	0.353044i	−0.508197	−	0.861241i	$-0.669688\pi$
$317$	6.28577	−	6.28577i	0.353044	−	0.353044i	0.861241	+	0.508197i	$0.169688\pi$
$318$		0			0
$319$			13.9581i			0.781502i
$320$	17.4112	−	4.10510i	0.973313	−	0.229482i
$321$		0			0
$322$	−2.55356	−	0.906666i	−0.142304	−	0.0505265i
$323$	−9.04989	−	9.04989i	−0.503549	−	0.503549i
$324$		0			0
$325$	3.57374	+	4.89936i	0.198236	+	0.271768i
$326$	−7.33668	−	15.4148i	−0.406341	−	0.853748i
$327$		0			0
$328$	18.2611	+	29.9679i	1.00830	+	1.65470i
$329$	−28.9379			−1.59540
$330$		0			0
$331$		−	26.2733i		−	1.44411i	−0.691836	−	0.722055i	$-0.743198\pi$
$331$		−	26.2733i		−	1.44411i	0.691836	−	0.722055i	$-0.256802\pi$
$332$	1.04180	+	10.0741i	0.0571760	+	0.552887i
$333$		0			0
$334$	11.0344	−	5.25181i	0.603775	−	0.287366i
$335$	−2.43006	+	31.2539i	−0.132768	+	1.70758i
$336$		0			0
$337$	16.4860	−	16.4860i	0.898047	−	0.898047i	−0.0972161	−	0.995263i	$-0.530994\pi$
$337$	16.4860	−	16.4860i	0.898047	−	0.898047i	0.995263	+	0.0972161i	$0.0309938\pi$
$338$	−15.3647	−	5.45539i	−0.835729	−	0.296734i
$339$		0			0
$340$	11.1332	−	11.7148i	0.603780	−	0.635324i
$341$	21.5135			1.16502
$342$		0			0
$343$	14.2568	+	14.2568i	0.769797	+	0.769797i
$344$	5.35762	−	22.0720i	0.288863	−	1.19004i
$345$		0			0
$346$	−1.07219	+	0.510310i	−0.0576415	+	0.0274344i
$347$	2.85611	−	2.85611i	0.153324	−	0.153324i	−0.626277	−	0.779601i	$-0.715422\pi$
$347$	2.85611	−	2.85611i	0.153324	−	0.153324i	0.779601	+	0.626277i	$0.215422\pi$
$348$		0			0
$349$	19.3216			1.03426			0.517130	−	0.855907i	$-0.327000\pi$
$349$	19.3216			1.03426			0.517130	+	0.855907i	$0.327000\pi$
$350$	−14.6681	+	4.36168i	−0.784044	+	0.233141i
$351$		0			0
$352$	−15.2734	−	2.07579i	−0.814075	−	0.110640i
$353$	−17.0194	+	17.0194i	−0.905850	+	0.905850i	−0.995934	−	0.0900845i	$-0.971286\pi$
$353$	−17.0194	+	17.0194i	−0.905850	+	0.905850i	0.0900845	+	0.995934i	$0.471286\pi$
$354$		0			0
$355$	−3.73210	+	3.19361i	−0.198079	+	0.169499i
$356$	−15.8655	−	12.8917i	−0.840872	−	0.683256i
$357$		0			0
$358$	15.1842	+	5.39129i	0.802509	+	0.284939i
$359$	14.6210			0.771665			0.385832	−	0.922569i	$-0.373914\pi$
$359$	14.6210			0.771665			0.385832	+	0.922569i	$0.373914\pi$
$360$		0			0
$361$	−6.45703			−0.339844
$362$	9.74751	+	3.46095i	0.512318	+	0.181904i
$363$		0			0
$364$	−3.31050	+	4.07418i	−0.173517	+	0.213545i
$365$	1.40039	−	18.0110i	0.0732998	−	0.942737i
$366$		0			0
$367$	−8.21722	+	8.21722i	−0.428935	+	0.428935i	−0.888266	−	0.459330i	$-0.848089\pi$
$367$	−8.21722	+	8.21722i	−0.428935	+	0.428935i	0.459330	+	0.888266i	$0.348089\pi$
$368$	−2.96367	−	1.93875i	−0.154492	−	0.101064i
$369$		0			0
$370$	17.2228	+	7.66586i	0.895370	+	0.398529i
$371$	−19.7914			−1.02752
$372$		0			0
$373$	9.54965	−	9.54965i	0.494462	−	0.494462i	−0.415247	−	0.909709i	$-0.636305\pi$
$373$	9.54965	−	9.54965i	0.494462	−	0.494462i	0.909709	+	0.415247i	$0.136305\pi$
$374$	−12.5739	+	5.98453i	−0.650180	+	0.309453i
$375$		0			0
$376$	−36.7530	−	8.92119i	−1.89539	−	0.460075i
$377$	4.39323	+	4.39323i	0.226263	+	0.226263i
$378$		0			0
$379$	−9.71237			−0.498891			−0.249445	−	0.968389i	$-0.580248\pi$
$379$	−9.71237			−0.498891			−0.249445	+	0.968389i	$0.580248\pi$
$380$	0.403066	+	15.8334i	0.0206768	+	0.812237i
$381$		0			0
$382$	1.77056	+	0.628653i	0.0905895	+	0.0321647i
$383$	−3.97088	+	3.97088i	−0.202903	+	0.202903i	−0.801242	−	0.598340i	$-0.795827\pi$
$383$	−3.97088	+	3.97088i	−0.202903	+	0.202903i	0.598340	+	0.801242i	$0.295827\pi$
$384$		0			0
$385$	13.1462	+	1.02214i	0.669991	+	0.0520932i
$386$	20.8338	−	9.91585i	1.06041	−	0.504703i
$387$		0			0
$388$	3.64989	−	0.377447i	0.185295	−	0.0191620i
$389$			15.9006i			0.806194i	0.915157	+	0.403097i	$0.132066\pi$
$389$			15.9006i			0.806194i	−0.915157	+	0.403097i	$0.867934\pi$
$390$		0			0
$391$	−3.19950			−0.161806
$392$	3.40932	+	5.59496i	0.172197	+	0.282588i
$393$		0			0
$394$	13.9240	+	29.2553i	0.701483	+	1.47386i
$395$	21.6745	−	18.5471i	1.09056	−	0.933208i
$396$		0			0
$397$	−17.2354	−	17.2354i	−0.865019	−	0.865019i	0.126897	−	0.991916i	$-0.459498\pi$
$397$	−17.2354	−	17.2354i	−0.865019	−	0.865019i	−0.991916	+	0.126897i	$0.959498\pi$
$398$	−8.12132	−	2.88356i	−0.407085	−	0.144540i
$399$		0			0
$400$	−19.9741	+	1.01761i	−0.998705	+	0.0508804i
$401$		−	13.1249i		−	0.655428i	−0.944777	−	0.327714i	$-0.893722\pi$
$401$		−	13.1249i		−	0.655428i	0.944777	−	0.327714i	$-0.106278\pi$
$402$		0			0
$403$	6.77127	−	6.77127i	0.337301	−	0.337301i
$404$	9.03931	+	7.34495i	0.449722	+	0.365425i
$405$		0			0
$406$	−14.1565	+	6.73777i	−0.702574	+	0.334390i
$407$	−11.4861	−	11.4861i	−0.569345	−	0.569345i
$408$		0			0
$409$			11.2852i			0.558017i	0.960289	+	0.279008i	$0.0900058\pi$
$409$			11.2852i			0.558017i	−0.960289	+	0.279008i	$0.909994\pi$
$410$	−14.0647	−	36.6280i	−0.694606	−	1.80893i
$411$		0			0
$412$	0.897160	+	8.67547i	0.0441999	+	0.427410i
$413$	−3.84725	−	3.84725i	−0.189311	−	0.189311i
$414$		0			0
$415$	0.877757	−	11.2892i	0.0430874	−	0.554163i
$416$	−5.46057	+	4.15388i	−0.267726	+	0.203661i
$417$		0			0
$418$	4.56635	−	12.8608i	0.223348	−	0.629042i
$419$		−	4.75266i		−	0.232183i	−0.993239	−	0.116091i	$-0.962963\pi$
$419$		−	4.75266i		−	0.232183i	0.993239	−	0.116091i	$-0.0370365\pi$
$420$		0			0
$421$			0.283341i			0.0138092i	0.999976	+	0.00690460i	$0.00219782\pi$
$421$			0.283341i			0.0138092i	−0.999976	+	0.00690460i	$0.997802\pi$
$422$	−33.2266	−	11.7974i	−1.61744	−	0.574290i
$423$		0			0
$424$	−25.1364	−	6.10145i	−1.22073	−	0.296313i
$425$	−14.5978	+	10.6481i	−0.708100	+	0.516510i
$426$		0			0
$427$	−14.5252	−	14.5252i	−0.702922	−	0.702922i
$428$	−18.2780	+	1.89019i	−0.883499	+	0.0913657i
$429$		0			0
$430$	−10.3261	+	23.1995i	−0.497969	+	1.11878i
$431$		−	10.1002i		−	0.486508i	−0.969963	−	0.243254i	$-0.921785\pi$
$431$		−	10.1002i		−	0.486508i	0.969963	−	0.243254i	$-0.0782149\pi$
$432$		0			0
$433$	5.65232	+	5.65232i	0.271633	+	0.271633i	0.829757	−	0.558124i	$-0.188479\pi$
$433$	5.65232	+	5.65232i	0.271633	+	0.271633i	−0.558124	+	0.829757i	$0.688479\pi$
$434$	10.3849	+	21.8193i	0.498490	+	1.04736i
$435$		0			0
$436$	−8.39779	−	6.82369i	−0.402181	−	0.326795i
$437$	2.21723	−	2.21723i	0.106064	−	0.106064i
$438$		0			0
$439$		−	17.0307i		−	0.812831i	−0.913688	−	0.406415i	$-0.866779\pi$
$439$		−	17.0307i		−	0.812831i	0.913688	−	0.406415i	$-0.133221\pi$
$440$	16.3814	+	5.35098i	0.780950	+	0.255098i
$441$		0			0
$442$	−2.07396	+	5.84116i	−0.0986484	+	0.277836i
$443$	10.8863	+	10.8863i	0.517226	+	0.517226i	0.916731	−	0.399505i	$-0.130818\pi$
$443$	10.8863	+	10.8863i	0.517226	+	0.517226i	−0.399505	+	0.916731i	$0.630818\pi$
$444$		0			0
$445$	14.8600	+	17.3657i	0.704434	+	0.823211i
$446$	9.79827	−	4.66348i	0.463961	−	0.220822i
$447$		0			0
$448$	−5.26739	−	16.4925i	−0.248861	−	0.779197i
$449$	−10.3509			−0.488488			−0.244244	−	0.969714i	$-0.578540\pi$
$449$	−10.3509			−0.488488			−0.244244	+	0.969714i	$0.578540\pi$
$450$		0			0
$451$			33.8076i			1.59194i
$452$	1.00942	−	0.104388i	0.0474792	−	0.00490999i
$453$		0			0
$454$	−7.00919	−	14.7268i	−0.328958	−	0.691161i
$455$	4.45940	−	3.81598i	0.209060	−	0.178896i
$456$		0			0
$457$	6.38449	−	6.38449i	0.298654	−	0.298654i	−0.541833	−	0.840486i	$-0.682269\pi$
$457$	6.38449	−	6.38449i	0.298654	−	0.298654i	0.840486	+	0.541833i	$0.182269\pi$
$458$	−6.87753	+	19.3700i	−0.321366	+	0.905103i
$459$		0			0
$460$	2.87013	+	2.72763i	0.133820	+	0.127176i
$461$	6.07751			0.283058			0.141529	−	0.989934i	$-0.454798\pi$
$461$	6.07751			0.283058			0.141529	+	0.989934i	$0.454798\pi$
$462$		0			0
$463$	22.2374	+	22.2374i	1.03346	+	1.03346i	0.999421	+	0.0340371i	$0.0108364\pi$
$463$	22.2374	+	22.2374i	1.03346	+	1.03346i	0.0340371	+	0.999421i	$0.489164\pi$
$464$	−20.0568	+	4.19313i	−0.931113	+	0.194661i
$465$		0			0
$466$	2.06688	+	4.34265i	0.0957464	+	0.201169i
$467$	−17.6001	+	17.6001i	−0.814434	+	0.814434i	−0.985295	−	0.170861i	$-0.945345\pi$
$467$	−17.6001	+	17.6001i	−0.814434	+	0.814434i	0.170861	+	0.985295i	$0.445345\pi$
$468$		0			0
$469$	30.3400			1.40097
$470$	38.6305	+	17.1944i	1.78189	+	0.793119i
$471$		0			0
$472$	−3.70019	−	6.07231i	−0.170315	−	0.279501i
$473$	15.4721	−	15.4721i	0.711406	−	0.711406i
$474$		0			0
$475$	2.73713	−	17.4952i	0.125588	−	0.802735i
$476$	−12.1392	−	9.86378i	−0.556399	−	0.452106i
$477$		0			0
$478$	−3.21752	+	9.06191i	−0.147166	+	0.414482i
$479$	2.47636			0.113148			0.0565740	−	0.998398i	$-0.481982\pi$
$479$	2.47636			0.113148			0.0565740	+	0.998398i	$0.481982\pi$
$480$		0			0
$481$	−7.23038			−0.329677
$482$	−7.67076	+	21.6041i	−0.349394	+	0.984041i
$483$		0			0
$484$	5.54976	+	4.50950i	0.252262	+	0.204977i
$485$	−4.09012	−	0.318015i	−0.185723	−	0.0144403i
$486$		0			0
$487$	12.3734	−	12.3734i	0.560694	−	0.560694i	−0.368811	−	0.929505i	$-0.620235\pi$
$487$	12.3734	−	12.3734i	0.560694	−	0.560694i	0.929505	+	0.368811i	$0.120235\pi$
$488$	−13.9700	−	22.9258i	−0.632390	−	1.03780i
$489$		0			0
$490$	−2.62586	−	6.83840i	−0.118624	−	0.308927i
$491$	37.1551			1.67679			0.838394	−	0.545064i	$-0.183495\pi$
$491$	37.1551			1.67679			0.838394	+	0.545064i	$0.183495\pi$
$492$		0			0
$493$	−13.0898	+	13.0898i	−0.589536	+	0.589536i
$494$	−2.61063	−	5.48510i	−0.117458	−	0.246787i
$495$		0			0
$496$	6.46284	+	30.9134i	0.290190	+	1.38805i
$497$	3.36160	+	3.36160i	0.150789	+	0.150789i
$498$		0			0
$499$	−34.8644			−1.56075			−0.780373	−	0.625315i	$-0.784971\pi$
$499$	−34.8644			−1.56075			−0.780373	+	0.625315i	$0.784971\pi$
$500$	22.1727	+	2.89296i	0.991595	+	0.129377i
$501$		0			0
$502$	4.52816	−	12.7532i	0.202102	−	0.569204i
$503$	1.25041	−	1.25041i	0.0557529	−	0.0557529i	−0.678681	−	0.734434i	$-0.737448\pi$
$503$	1.25041	−	1.25041i	0.0557529	−	0.0557529i	0.734434	+	0.678681i	$0.237448\pi$
$504$		0			0
$505$	−8.46644	−	9.89400i	−0.376752	−	0.440277i
$506$	−1.46621	−	3.08060i	−0.0651811	−	0.136950i
$507$		0			0
$508$	2.57822	−	0.266623i	0.114390	−	0.0118295i
$509$			38.4393i			1.70379i	0.523711	+	0.851896i	$0.324547\pi$
$509$			38.4393i			1.70379i	−0.523711	+	0.851896i	$0.675453\pi$
$510$		0			0
$511$	−17.4843			−0.773461
$512$	−1.60549	−	22.5704i	−0.0709535	−	0.997480i
$513$		0			0
$514$	10.1491	−	4.83045i	0.447657	−	0.213062i
$515$	0.755895	−	9.72185i	0.0333087	−	0.428396i
$516$		0			0
$517$	−25.7631	−	25.7631i	−1.13306	−	1.13306i
$518$	6.10485	−	17.1939i	0.268232	−	0.755455i
$519$		0			0
$520$	6.84014	−	3.47175i	0.299960	−	0.152246i
$521$			19.1329i			0.838226i	0.907934	+	0.419113i	$0.137659\pi$
$521$			19.1329i			0.838226i	−0.907934	+	0.419113i	$0.862341\pi$
$522$		0			0
$523$	0.870444	−	0.870444i	0.0380619	−	0.0380619i	−0.687820	−	0.725882i	$-0.741432\pi$
$523$	0.870444	−	0.870444i	0.0380619	−	0.0380619i	0.725882	+	0.687820i	$0.241432\pi$
$524$	30.3227	+	24.6389i	1.32465	+	1.07636i
$525$		0			0
$526$	−13.7728	−	28.9375i	−0.600522	−	1.26174i
$527$	20.1753	+	20.1753i	0.878849	+	0.878849i
$528$		0			0
$529$			22.2161i			0.965918i
$530$	26.4204	+	11.7597i	1.14763	+	0.510810i
$531$		0			0
$532$	15.2478	−	1.57683i	0.661078	−	0.0683643i
$533$	10.6408	+	10.6408i	0.460903	+	0.460903i
$534$		0			0
$535$	20.4825	+	1.59256i	0.885538	+	0.0688524i
$536$	38.5338	+	9.35345i	1.66441	+	0.404007i
$537$		0			0
$538$	11.8663	+	4.21324i	0.511591	+	0.181646i
$539$			6.31183i			0.271870i
$540$		0			0
$541$			18.7259i			0.805089i	0.915400	+	0.402544i	$0.131874\pi$
$541$			18.7259i			0.805089i	−0.915400	+	0.402544i	$0.868126\pi$
$542$	6.63230	−	18.6794i	0.284881	−	0.802347i
$543$		0			0
$544$	−12.3767	−	16.2700i	−0.530645	−	0.697570i
$545$	7.86558	+	9.19183i	0.336924	+	0.393735i
$546$		0			0
$547$	25.7085	+	25.7085i	1.09922	+	1.09922i	0.994502	+	0.104713i	$0.0333924\pi$
$547$	25.7085	+	25.7085i	1.09922	+	1.09922i	0.104713	+	0.994502i	$0.466608\pi$
$548$	2.23042	+	21.5680i	0.0952790	+	0.921340i
$549$		0			0
$550$	−16.9421	−	9.17574i	−0.722412	−	0.391255i
$551$		−	18.1422i		−	0.772885i
$552$		0			0
$553$	−19.5228	−	19.5228i	−0.830192	−	0.830192i
$554$	3.61908	−	1.72250i	0.153760	−	0.0731819i
$555$		0			0
$556$	22.8497	+	18.5667i	0.969041	+	0.787401i
$557$	−4.85098	+	4.85098i	−0.205543	+	0.205543i	−0.802370	−	0.596827i	$-0.796428\pi$
$557$	−4.85098	+	4.85098i	−0.205543	+	0.205543i	0.596827	+	0.802370i	$0.296428\pi$
$558$		0			0
$559$		−	9.73950i		−	0.411937i
$560$	2.48047	+	19.1972i	0.104819	+	0.811229i
$561$		0			0
$562$	12.4423	+	4.41778i	0.524848	+	0.186353i
$563$	5.13320	+	5.13320i	0.216339	+	0.216339i	0.806954	−	0.590615i	$-0.201115\pi$
$563$	5.13320	+	5.13320i	0.216339	+	0.216339i	−0.590615	+	0.806954i	$0.701115\pi$
$564$		0			0
$565$	−1.13117	−	0.0879511i	−0.0475888	−	0.00370013i
$566$	19.2172	+	40.3767i	0.807761	+	1.69716i
$567$		0			0
$568$	3.23311	+	5.30579i	0.135658	+	0.222626i
$569$	27.4425			1.15045			0.575224	−	0.817996i	$-0.304915\pi$
$569$	27.4425			1.15045			0.575224	+	0.817996i	$0.304915\pi$
$570$		0			0
$571$		−	7.73020i		−	0.323499i	−0.986832	−	0.161749i	$-0.948286\pi$
$571$		−	7.73020i		−	0.323499i	0.986832	−	0.161749i	$-0.0517136\pi$
$572$	−6.57451	+	0.679893i	−0.274894	+	0.0284278i
$573$		0			0
$574$	−34.2882	+	16.3194i	−1.43116	+	0.681160i
$575$	−2.60879	−	3.57648i	−0.108794	−	0.149149i
$576$		0			0
$577$	−9.33858	+	9.33858i	−0.388770	+	0.388770i	−0.874249	−	0.485478i	$-0.838645\pi$
$577$	−9.33858	+	9.33858i	−0.388770	+	0.388770i	0.485478	+	0.874249i	$0.338645\pi$
$578$	5.25193	+	1.86475i	0.218452	+	0.0775634i
$579$		0			0
$580$	22.9016	−	0.582997i	0.950935	−	0.0242076i
$581$	−10.9591			−0.454659
$582$		0			0
$583$	−17.6201	−	17.6201i	−0.729751	−	0.729751i
$584$	−22.2062	−	5.39020i	−0.918899	−	0.223048i
$585$		0			0
$586$	10.5638	−	5.02785i	0.436388	−	0.207699i
$587$	−20.5419	+	20.5419i	−0.847856	+	0.847856i	−0.989865	−	0.142010i	$-0.954644\pi$
$587$	−20.5419	+	20.5419i	−0.847856	+	0.847856i	0.142010	+	0.989865i	$0.454644\pi$
$588$		0			0
$589$	−27.9625			−1.15218
$590$	2.84989	+	7.42183i	0.117328	+	0.305552i
$591$		0			0
$592$	13.0542	−	19.9552i	0.536524	−	0.820155i
$593$	15.8708	−	15.8708i	0.651734	−	0.651734i	−0.301676	−	0.953410i	$-0.597546\pi$
$593$	15.8708	−	15.8708i	0.651734	−	0.651734i	0.953410	+	0.301676i	$0.0975462\pi$
$594$		0			0
$595$	11.3699	+	13.2870i	0.466119	+	0.544713i
$596$	19.7132	−	24.2607i	0.807485	−	0.993757i
$597$		0			0
$598$	−1.43109	−	0.508122i	−0.0585215	−	0.0207786i
$599$	−31.5111			−1.28751			−0.643754	−	0.765232i	$-0.722624\pi$
$599$	−31.5111			−1.28751			−0.643754	+	0.765232i	$0.722624\pi$
$600$		0			0
$601$	7.28520			0.297169			0.148585	−	0.988900i	$-0.452528\pi$
$601$	7.28520			0.297169			0.148585	+	0.988900i	$0.452528\pi$
$602$	23.1606	+	8.22339i	0.943954	+	0.335160i
$603$		0			0
$604$	27.3012	+	22.1838i	1.11087	+	0.902646i
$605$	−5.19805	−	6.07451i	−0.211331	−	0.246964i
$606$		0			0
$607$	−28.1836	+	28.1836i	−1.14394	+	1.14394i	−0.156213	+	0.987723i	$0.549929\pi$
$607$	−28.1836	+	28.1836i	−1.14394	+	1.14394i	−0.987723	+	0.156213i	$0.950071\pi$
$608$	19.8518	+	2.69804i	0.805098	+	0.109420i
$609$		0			0
$610$	10.7597	+	28.0209i	0.435646	+	1.13453i
$611$	−16.2176			−0.656095
$612$		0			0
$613$	−24.9782	+	24.9782i	−1.00886	+	1.00886i	−0.00890069	+	0.999960i	$0.502833\pi$
$613$	−24.9782	+	24.9782i	−1.00886	+	1.00886i	−0.999960	+	0.00890069i	$0.997167\pi$
$614$	−11.0859	+	5.27633i	−0.447391	+	0.212935i
$615$		0			0
$616$	3.93430	−	16.2083i	0.158517	−	0.653050i
$617$	19.7928	+	19.7928i	0.796830	+	0.796830i	0.982594	−	0.185764i	$-0.0594761\pi$
$617$	19.7928	+	19.7928i	0.796830	+	0.796830i	−0.185764	+	0.982594i	$0.559476\pi$
$618$		0			0
$619$	25.0717			1.00772			0.503859	−	0.863786i	$-0.331913\pi$
$619$	25.0717			1.00772			0.503859	+	0.863786i	$0.331913\pi$
$620$	−0.898570	−	35.2980i	−0.0360875	−	1.41760i
$621$		0			0
$622$	−17.4069	−	6.18049i	−0.697953	−	0.247815i
$623$	15.6417	−	15.6417i	0.626672	−	0.626672i
$624$		0			0
$625$	−23.8054	−	7.63561i	−0.952216	−	0.305424i
$626$	−39.7495	+	18.9188i	−1.58871	+	0.756146i
$627$		0			0
$628$	−2.21221	−	21.3919i	−0.0882769	−	0.853631i
$629$		−	21.5432i		−	0.858984i
$630$		0			0
$631$	6.42730			0.255867			0.127933	−	0.991783i	$-0.459166\pi$
$631$	6.42730			0.255867			0.127933	+	0.991783i	$0.459166\pi$
$632$	−18.7765	−	30.8138i	−0.746890	−	1.22571i
$633$		0			0
$634$	5.40270	+	11.3514i	0.214569	+	0.450822i
$635$	−2.88919	−	0.224641i	−0.114654	−	0.00891460i
$636$		0			0
$637$	1.98662	+	1.98662i	0.0787126	+	0.0787126i
$638$	−18.6019	−	6.60481i	−0.736458	−	0.261487i
$639$		0			0
$640$	−2.76789	+	25.1463i	−0.109411	+	0.993997i
$641$		−	28.9552i		−	1.14366i	−0.820372	−	0.571830i	$-0.806234\pi$
$641$		−	28.9552i		−	1.14366i	0.820372	−	0.571830i	$-0.193766\pi$
$642$		0			0
$643$	−20.0962	+	20.0962i	−0.792517	+	0.792517i	−0.981903	−	0.189385i	$-0.939350\pi$
$643$	−20.0962	+	20.0962i	−0.792517	+	0.792517i	0.189385	+	0.981903i	$0.439350\pi$
$644$	2.41663	−	2.97410i	0.0952286	−	0.117196i
$645$		0			0
$646$	16.3431	−	7.77849i	0.643011	−	0.306041i
$647$	−27.5740	−	27.5740i	−1.08405	−	1.08405i	−0.996128	−	0.0879193i	$-0.971978\pi$
$647$	−27.5740	−	27.5740i	−1.08405	−	1.08405i	−0.0879193	−	0.996128i	$-0.528022\pi$
$648$		0			0
$649$		−	6.85034i		−	0.268899i
$650$	−8.22044	+	2.44441i	−0.322432	+	0.0958776i
$651$		0			0
$652$	24.0150	−	2.48347i	0.940500	−	0.0972603i
$653$	−17.8261	−	17.8261i	−0.697590	−	0.697590i	0.266300	−	0.963890i	$-0.414199\pi$
$653$	−17.8261	−	17.8261i	−0.697590	−	0.697590i	−0.963890	+	0.266300i	$0.914199\pi$
$654$		0			0
$655$	−28.4010	−	33.1898i	−1.10972	−	1.29683i
$656$	−48.5792	+	10.1561i	−1.89670	+	0.396529i
$657$		0			0
$658$	13.6931	−	38.5656i	0.533812	−	1.50344i
$659$		−	37.7533i		−	1.47066i	−0.677709	−	0.735331i	$-0.737027\pi$
$659$		−	37.7533i		−	1.47066i	0.677709	−	0.735331i	$-0.262973\pi$
$660$		0			0
$661$			6.03049i			0.234559i	0.993099	+	0.117279i	$0.0374173\pi$
$661$			6.03049i			0.234559i	−0.993099	+	0.117279i	$0.962583\pi$
$662$	35.0144	+	12.4322i	1.36087	+	0.483192i
$663$		0			0
$664$	−13.9187	−	3.37854i	−0.540151	−	0.131113i
$665$	−17.0869	−	1.32855i	−0.662603	−	0.0515188i
$666$		0			0
$667$	−3.20701	−	3.20701i	−0.124176	−	0.124176i
$668$	1.77774	+	17.1906i	0.0687830	+	0.665126i
$669$		0			0
$670$	−40.5022	−	18.0275i	−1.56474	−	0.696464i
$671$		−	25.8632i		−	0.998439i
$672$		0			0
$673$	3.75403	+	3.75403i	0.144707	+	0.144707i	0.775749	−	0.631042i	$-0.217372\pi$
$673$	3.75403	+	3.75403i	0.144707	+	0.144707i	−0.631042	+	0.775749i	$0.717372\pi$
$674$	14.1699	+	29.7718i	0.545803	+	1.14677i
$675$		0			0
$676$	14.5408	−	17.8951i	0.559262	−	0.688274i
$677$	−12.0579	+	12.0579i	−0.463421	+	0.463421i	−0.899775	−	0.436354i	$-0.856270\pi$
$677$	−12.0579	+	12.0579i	−0.463421	+	0.463421i	0.436354	+	0.899775i	$0.356270\pi$
$678$		0			0
$679$			3.97052i			0.152375i
$680$	10.3442	+	20.3805i	0.396683	+	0.781556i
$681$		0			0
$682$	−10.1800	+	28.6711i	−0.389811	+	1.09787i
$683$	18.0083	+	18.0083i	0.689068	+	0.689068i	0.962026	−	0.272958i	$-0.0880020\pi$
$683$	18.0083	+	18.0083i	0.689068	+	0.689068i	−0.272958	+	0.962026i	$0.588002\pi$
$684$		0			0
$685$	1.87922	−	24.1694i	0.0718015	−	0.923467i
$686$	−25.7463	+	12.2539i	−0.982997	+	0.467857i
$687$		0			0
$688$	26.8802	+	17.5843i	1.02480	+	0.670396i
$689$	−11.0917			−0.422560
$690$		0			0
$691$			37.0052i			1.40774i	0.710327	+	0.703872i	$0.248547\pi$
$691$			37.0052i			1.40774i	−0.710327	+	0.703872i	$0.751453\pi$
$692$	−0.172740	−	1.67039i	−0.00656660	−	0.0634985i
$693$		0			0
$694$	2.45486	+	5.15782i	0.0931853	+	0.195788i
$695$	−21.4015	−	25.0102i	−0.811807	−	0.948689i
$696$		0			0
$697$	−31.7046	+	31.7046i	−1.20090	+	1.20090i
$698$	−9.14276	+	25.7499i	−0.346058	+	0.974648i
$699$		0			0
$700$	1.12798	−	21.6121i	0.0426338	−	0.816862i
$701$	10.8810			0.410968			0.205484	−	0.978660i	$-0.434123\pi$
$701$	10.8810			0.410968			0.205484	+	0.978660i	$0.434123\pi$
$702$		0			0
$703$	14.9292	+	14.9292i	0.563067	+	0.563067i
$704$	9.99361	−	19.3726i	0.376648	−	0.730133i
$705$		0			0
$706$	−14.6284	−	30.7351i	−0.550545	−	1.15673i
$707$	−8.91179	+	8.91179i	−0.335162	+	0.335162i
$708$		0			0
$709$	−17.9836			−0.675389			−0.337695	−	0.941256i	$-0.609647\pi$
$709$	−17.9836			−0.675389			−0.337695	+	0.941256i	$0.609647\pi$
$710$	−2.49014	−	6.48496i	−0.0934534	−	0.243376i
$711$		0			0
$712$	24.6881	−	15.0438i	0.925226	−	0.563791i
$713$	−4.94295	+	4.94295i	−0.185115	+	0.185115i
$714$		0			0
$715$	7.36749	+	0.572838i	0.275529	+	0.0214229i
$716$	−14.3700	+	17.6849i	−0.537031	+	0.660915i
$717$		0			0
$718$	−6.91848	+	19.4854i	−0.258195	+	0.727188i
$719$	−32.0959			−1.19698			−0.598488	−	0.801132i	$-0.704231\pi$
$719$	−32.0959			−1.19698			−0.598488	+	0.801132i	$0.704231\pi$
$720$		0			0
$721$	−9.43759			−0.351474
$722$	3.05540	−	8.60530i	0.113710	−	0.320256i
$723$		0			0
$724$	−9.22483	+	11.3528i	−0.342838	+	0.421925i
$725$	−25.3052	−	3.95900i	−0.939811	−	0.147033i
$726$		0			0
$727$	15.2813	−	15.2813i	0.566754	−	0.566754i	−0.364464	−	0.931218i	$-0.618748\pi$
$727$	15.2813	−	15.2813i	0.566754	−	0.566754i	0.931218	+	0.364464i	$0.118748\pi$
$728$	−3.86317	−	6.33977i	−0.143179	−	0.234967i
$729$		0			0
$730$	23.3406	+	10.3889i	0.863874	+	0.384510i
$731$	29.0192			1.07332
$732$		0			0
$733$	25.4494	−	25.4494i	0.939996	−	0.939996i	−0.0583028	−	0.998299i	$-0.518569\pi$
$733$	25.4494	−	25.4494i	0.939996	−	0.939996i	0.998299	+	0.0583028i	$0.0185689\pi$
$734$	−7.06280	−	14.8394i	−0.260693	−	0.547732i
$735$		0			0
$736$	3.98615	−	3.03228i	0.146931	−	0.111771i
$737$	27.0115	+	27.0115i	0.994980	+	0.994980i
$738$		0			0
$739$	23.6936			0.871584			0.435792	−	0.900047i	$-0.356468\pi$
$739$	23.6936			0.871584			0.435792	+	0.900047i	$0.356468\pi$
$740$	−18.3659	+	19.3254i	−0.675145	+	0.710417i
$741$		0			0
$742$	9.36509	−	26.3761i	0.343803	−	0.968296i
$743$	10.4630	−	10.4630i	0.383852	−	0.383852i	−0.488636	−	0.872488i	$-0.662505\pi$
$743$	10.4630	−	10.4630i	0.383852	−	0.383852i	0.872488	+	0.488636i	$0.162505\pi$
$744$		0			0
$745$	−26.5546	+	22.7232i	−0.972886	+	0.832513i
$746$	8.20804	+	17.2456i	0.300518	+	0.631407i
$747$		0			0
$748$	−2.02577	−	19.5890i	−0.0740695	−	0.716246i
$749$		−	19.8836i		−	0.726532i
$750$		0			0
$751$	51.4858			1.87874			0.939372	−	0.342899i	$-0.111409\pi$
$751$	51.4858			1.87874			0.939372	+	0.342899i	$0.111409\pi$
$752$	29.2804	−	44.7593i	1.06775	−	1.63220i
$753$		0			0
$754$	−7.93369	+	3.77604i	−0.288928	+	0.137515i
$755$	−25.5710	−	29.8826i	−0.930623	−	1.08754i
$756$		0			0
$757$	20.4014	+	20.4014i	0.741501	+	0.741501i	0.972867	−	0.231366i	$-0.0743195\pi$
$757$	20.4014	+	20.4014i	0.741501	+	0.741501i	−0.231366	+	0.972867i	$0.574319\pi$
$758$	4.59579	−	12.9437i	0.166926	−	0.470136i
$759$		0			0
$760$	−21.2919	−	6.95503i	−0.772339	−	0.252285i
$761$			13.3989i			0.485709i	0.970063	+	0.242855i	$0.0780838\pi$
$761$			13.3989i			0.485709i	−0.970063	+	0.242855i	$0.921916\pi$
$762$		0			0
$763$	8.27933	−	8.27933i	0.299732	−	0.299732i
$764$	−1.67561	+	2.06215i	−0.0606216	+	0.0746059i
$765$		0			0
$766$	−3.41302	−	7.17097i	−0.123317	−	0.259098i
$767$	−2.15611	−	2.15611i	−0.0778526	−	0.0778526i
$768$		0			0
$769$		−	15.5493i		−	0.560721i	−0.959895	−	0.280361i	$-0.909546\pi$
$769$		−	15.5493i		−	0.560721i	0.959895	−	0.280361i	$-0.0904540\pi$
$770$	−7.58283	+	17.0363i	−0.273266	+	0.613944i
$771$		0			0
$772$	3.35653	+	32.4573i	0.120804	+	1.16817i
$773$	4.70360	+	4.70360i	0.169177	+	0.169177i	0.786617	−	0.617441i	$-0.211830\pi$
$773$	4.70360	+	4.70360i	0.169177	+	0.169177i	−0.617441	+	0.786617i	$0.711830\pi$
$774$		0			0
$775$	−6.10198	+	39.0028i	−0.219190	+	1.40102i
$776$	−1.22406	+	5.04281i	−0.0439412	+	0.181026i
$777$		0			0
$778$	−21.1908	−	7.52401i	−0.759727	−	0.269749i
$779$		−	43.9420i		−	1.57439i
$780$		0			0
$781$			5.98561i			0.214182i
$782$	1.51397	−	4.26398i	0.0541395	−	0.152480i
$783$		0			0
$784$	−9.06966	+	1.89613i	−0.323917	+	0.0677189i
$785$	−1.86388	+	23.9721i	−0.0665248	+	0.855601i
$786$		0			0
$787$	−7.45088	−	7.45088i	−0.265595	−	0.265595i	0.561727	−	0.827322i	$-0.310137\pi$
$787$	−7.45088	−	7.45088i	−0.265595	−	0.265595i	−0.827322	+	0.561727i	$0.810137\pi$
$788$	−45.5772	+	4.71330i	−1.62362	+	0.167904i
$789$		0			0
$790$	14.4617	+	37.6619i	0.514524	+	1.33995i
$791$			1.09810i			0.0390439i
$792$		0			0
$793$	−8.14032	−	8.14032i	−0.289071	−	0.289071i
$794$	31.1252	−	14.8140i	1.10459	−	0.525730i
$795$		0			0
$796$	7.68584	−	9.45883i	0.272417	−	0.335259i
$797$	−27.5898	+	27.5898i	−0.977280	+	0.977280i	−0.999748	−	0.0224677i	$-0.992848\pi$
$797$	−27.5898	+	27.5898i	−0.977280	+	0.977280i	0.0224677	+	0.999748i	$0.492848\pi$
$798$		0			0
$799$		−	48.3211i		−	1.70948i
$800$	8.09535	−	27.1010i	0.286214	−	0.958166i
$801$		0			0
$802$	17.4916	+	6.21058i	0.617651	+	0.219303i
$803$	−15.5661	−	15.5661i	−0.549317	−	0.549317i
$804$		0			0
$805$	−3.25531	+	2.78562i	−0.114735	+	0.0981802i
$806$	5.81999	+	12.2282i	0.205000	+	0.430719i
$807$		0			0
$808$	−14.0659	+	8.57115i	−0.494838	+	0.301532i
$809$	9.93002			0.349121			0.174560	−	0.984646i	$-0.444150\pi$
$809$	9.93002			0.349121			0.174560	+	0.984646i	$0.444150\pi$
$810$		0			0
$811$		−	0.144213i		−	0.00506400i	−0.999997	−	0.00253200i	$-0.999194\pi$
$811$		−	0.144213i		−	0.00506400i	0.999997	−	0.00253200i	$-0.000805962\pi$
$812$	−2.28074	−	22.0546i	−0.0800383	−	0.773964i
$813$		0			0
$814$	20.7426	−	9.87244i	0.727028	−	0.346029i
$815$	−26.9115	−	2.09243i	−0.942670	−	0.0732946i
$816$		0			0
$817$	−20.1100	+	20.1100i	−0.703562	+	0.703562i
$818$	−15.0398	−	5.34003i	−0.525854	−	0.186710i
$819$		0			0
$820$	55.4695	−	1.41207i	1.93708	−	0.0493115i
$821$	−20.3654			−0.710757			−0.355379	−	0.934722i	$-0.615648\pi$
$821$	−20.3654			−0.710757			−0.355379	+	0.934722i	$0.615648\pi$
$822$		0			0
$823$	−31.7594	−	31.7594i	−1.10706	−	1.10706i	−0.993535	−	0.113529i	$-0.963784\pi$
$823$	−31.7594	−	31.7594i	−1.10706	−	1.10706i	−0.113529	−	0.993535i	$-0.536216\pi$
$824$	−11.9863	−	2.90949i	−0.417564	−	0.101357i
$825$		0			0
$826$	6.94771	−	3.30676i	0.241742	−	0.115057i
$827$	28.5251	−	28.5251i	0.991916	−	0.991916i	−0.00805118	−	0.999968i	$-0.502563\pi$
$827$	28.5251	−	28.5251i	0.991916	−	0.991916i	0.999968	+	0.00805118i	$0.00256280\pi$
$828$		0			0
$829$	54.4189			1.89005			0.945024	−	0.327002i	$-0.106038\pi$
$829$	54.4189			1.89005			0.945024	+	0.327002i	$0.106038\pi$
$830$	14.6297	+	6.51169i	0.507806	+	0.226024i
$831$		0			0
$832$	−2.95200	−	9.24287i	−0.102342	−	0.320439i
$833$	−5.91921	+	5.91921i	−0.205088	+	0.205088i
$834$		0			0
$835$	1.49782	−	19.2641i	0.0518343	−	0.666661i
$836$	14.9788	+	12.1712i	0.518054	+	0.420949i
$837$		0			0
$838$	6.33388	+	2.24891i	0.218800	+	0.0776872i
$839$	47.3060			1.63318			0.816592	−	0.577215i	$-0.195861\pi$
$839$	47.3060			1.63318			0.816592	+	0.577215i	$0.195861\pi$
$840$		0			0
$841$	2.75894			0.0951360
$842$	−0.377609	−	0.134074i	−0.0130133	−	0.00462049i
$843$		0			0
$844$	31.4449	−	38.6987i	1.08238	−	1.33206i
$845$	−19.5871	+	16.7610i	−0.673818	+	0.576596i
$846$		0			0
$847$	−5.47147	+	5.47147i	−0.188002	+	0.188002i
$848$	20.0257	−	30.6121i	0.687684	−	1.05123i
$849$		0			0
$850$	−7.28322	−	24.4931i	−0.249812	−	0.840108i
$851$	5.27809			0.180931
$852$		0			0
$853$	−14.9083	+	14.9083i	−0.510449	+	0.510449i	−0.914664	−	0.404215i	$-0.867545\pi$
$853$	−14.9083	+	14.9083i	−0.510449	+	0.510449i	0.404215	+	0.914664i	$0.367545\pi$
$854$	26.2309	−	12.4846i	0.897601	−	0.427213i
$855$		0			0
$856$	6.12987	−	25.2535i	0.209515	−	0.863146i
$857$	−6.64085	−	6.64085i	−0.226847	−	0.226847i	0.584527	−	0.811374i	$-0.301280\pi$
$857$	−6.64085	−	6.64085i	−0.226847	−	0.226847i	−0.811374	+	0.584527i	$0.801280\pi$
$858$		0			0
$859$	−3.27984			−0.111907			−0.0559534	−	0.998433i	$-0.517820\pi$
$859$	−3.27984			−0.111907			−0.0559534	+	0.998433i	$0.517820\pi$
$860$	−26.0318	−	24.7394i	−0.887678	−	0.843605i
$861$		0			0
$862$	13.4605	+	4.77929i	0.458467	+	0.162783i
$863$	11.7285	−	11.7285i	0.399243	−	0.399243i	−0.478723	−	0.877966i	$-0.658900\pi$
$863$	11.7285	−	11.7285i	0.399243	−	0.399243i	0.877966	+	0.478723i	$0.158900\pi$
$864$		0			0
$865$	−0.145541	+	1.87186i	−0.00494854	+	0.0636451i
$866$	−10.2075	+	4.85824i	−0.346864	+	0.165090i
$867$		0			0
$868$	−33.9926	+	3.51529i	−1.15378	+	0.119317i
$869$		−	34.7619i		−	1.17922i
$870$		0			0
$871$	17.0034			0.576139
$872$	13.0677	−	7.96286i	0.442527	−	0.269656i
$873$		0			0
$874$	1.90573	+	4.00406i	0.0644624	+	0.135440i
$875$	−5.58180	+	23.5433i	−0.188699	+	0.795910i
$876$		0			0
$877$	−27.6401	−	27.6401i	−0.933339	−	0.933339i	0.0645744	−	0.997913i	$-0.479431\pi$
$877$	−27.6401	−	27.6401i	−0.933339	−	0.933339i	−0.997913	+	0.0645744i	$0.979431\pi$
$878$	22.6968	+	8.05874i	0.765981	+	0.271969i
$879$		0			0
$880$	−14.8827	+	19.2994i	−0.501697	+	0.650583i
$881$			37.9900i			1.27991i	0.768410	+	0.639957i	$0.221048\pi$
$881$			37.9900i			1.27991i	−0.768410	+	0.639957i	$0.778952\pi$
$882$		0			0
$883$	−33.6777	+	33.6777i	−1.13335	+	1.13335i	−0.143729	+	0.989617i	$0.545909\pi$
$883$	−33.6777	+	33.6777i	−1.13335	+	1.13335i	−0.989617	+	0.143729i	$0.954091\pi$
$884$	−6.80315	−	5.52795i	−0.228815	−	0.185925i
$885$		0			0
$886$	−19.6595	+	9.35694i	−0.660475	+	0.314353i
$887$	1.17366	+	1.17366i	0.0394078	+	0.0394078i	0.726536	−	0.687128i	$-0.241129\pi$
$887$	1.17366	+	1.17366i	0.0394078	+	0.0394078i	−0.687128	+	0.726536i	$0.741129\pi$
$888$		0			0
$889$			2.80471i			0.0940671i
$890$	−30.1748	+	11.5868i	−1.01146	+	0.388389i
$891$		0			0
$892$	1.57859	+	15.2649i	0.0528552	+	0.511106i
$893$	33.4861	+	33.4861i	1.12057	+	1.12057i
$894$		0			0
$895$	19.3570	−	16.5641i	0.647034	−	0.553676i
$896$	24.4720	+	0.784206i	0.817554	+	0.0261985i
$897$		0			0
$898$	4.89792	−	13.7946i	0.163446	−	0.460332i
$899$			40.4452i			1.34892i
$900$		0			0
$901$		−	33.0482i		−	1.10099i
$902$	−45.0555	−	15.9974i	−1.50018	−	0.532655i
$903$		0			0
$904$	−0.338530	+	1.39465i	−0.0112593	+	0.0463855i
$905$	12.4263	−	10.6333i	0.413064	−	0.353464i
$906$		0			0
$907$	−16.4248	−	16.4248i	−0.545377	−	0.545377i	0.379723	−	0.925100i	$-0.376019\pi$
$907$	−16.4248	−	16.4248i	−0.545377	−	0.545377i	−0.925100	+	0.379723i	$0.876019\pi$
$908$	22.9430	−	2.37262i	0.761391	−	0.0787381i
$909$		0			0
$910$	2.97541	+	7.74873i	0.0986340	+	0.256868i
$911$		−	32.3497i		−	1.07179i	−0.844284	−	0.535897i	$-0.819974\pi$
$911$		−	32.3497i		−	1.07179i	0.844284	−	0.535897i	$-0.180026\pi$
$912$		0			0
$913$	−9.75676	−	9.75676i	−0.322902	−	0.322902i
$914$	5.48755	+	11.5297i	0.181512	+	0.381368i
$915$		0			0
$916$	−22.5601	−	18.3314i	−0.745407	−	0.605686i
$917$	−29.8950	+	29.8950i	−0.987219	+	0.987219i
$918$		0			0
$919$		−	5.60588i		−	0.184921i	−0.995716	−	0.0924605i	$-0.970527\pi$
$919$		−	5.60588i		−	0.184921i	0.995716	−	0.0924605i	$-0.0294732\pi$
$920$	−4.99323	+	2.53434i	−0.164622	+	0.0835547i
$921$		0			0
$922$	−2.87581	+	8.09950i	−0.0947097	+	0.266743i
$923$	1.88394	+	1.88394i	0.0620106	+	0.0620106i
$924$		0			0
$925$	24.0815	−	17.5658i	0.791794	−	0.577559i
$926$	−40.1582	+	19.1133i	−1.31968	+	0.628101i
$927$		0			0
$928$	3.90246	−	28.7138i	0.128105	−	0.942578i
$929$	34.7413			1.13983			0.569913	−	0.821705i	$-0.306977\pi$
$929$	34.7413			1.13983			0.569913	+	0.821705i	$0.306977\pi$
$930$		0			0
$931$		−	8.20391i		−	0.268872i
$932$	−6.76548	+	0.699642i	−0.221611	+	0.0229175i
$933$		0			0
$934$	−15.1275	−	31.7838i	−0.494986	−	1.04000i
$935$	−1.70680	+	21.9518i	−0.0558182	+	0.717899i
$936$		0			0
$937$	5.80471	−	5.80471i	0.189632	−	0.189632i	−0.605905	−	0.795537i	$-0.707189\pi$
$937$	5.80471	−	5.80471i	0.189632	−	0.189632i	0.795537	+	0.605905i	$0.207189\pi$
$938$	−14.3566	+	40.4342i	−0.468759	+	1.32022i
$939$		0			0
$940$	−41.1945	+	43.3467i	−1.34362	+	1.41381i
$941$	23.7893			0.775510			0.387755	−	0.921762i	$-0.373251\pi$
$941$	23.7893			0.775510			0.387755	+	0.921762i	$0.373251\pi$
$942$		0			0
$943$	−7.76765	−	7.76765i	−0.252949	−	0.252949i
$944$	9.84346	−	2.05790i	0.320377	−	0.0669789i
$945$		0			0
$946$	13.2984	+	27.9408i	0.432369	+	0.908435i
$947$	12.4008	−	12.4008i	0.402972	−	0.402972i	−0.476307	−	0.879279i	$-0.658025\pi$
$947$	12.4008	−	12.4008i	0.402972	−	0.402972i	0.879279	+	0.476307i	$0.158025\pi$
$948$		0			0
$949$	−9.79872			−0.318080
$950$	22.0207	+	11.9263i	0.714446	+	0.386941i
$951$		0			0
$952$	18.8896	−	11.5105i	0.612215	−	0.373057i
$953$	4.46081	−	4.46081i	0.144500	−	0.144500i	−0.631156	−	0.775656i	$-0.717419\pi$
$953$	4.46081	−	4.46081i	0.144500	−	0.144500i	0.775656	+	0.631156i	$0.217419\pi$
$954$		0			0
$955$	2.25713	−	1.93146i	0.0730390	−	0.0625006i
$956$	−10.5543	−	8.57599i	−0.341351	−	0.277367i
$957$		0			0
$958$	−1.17179	+	3.30025i	−0.0378587	+	0.106626i
$959$	−23.4627			−0.757651
$960$		0			0
$961$	31.3380			1.01090
$962$	3.42133	−	9.63593i	0.110308	−	0.310675i
$963$		0			0
$964$	−25.1621	−	20.4457i	−0.810418	−	0.658511i
$965$	2.82801	−	36.3722i	0.0910369	−	1.17086i
$966$		0			0
$967$	2.74162	−	2.74162i	0.0881645	−	0.0881645i	−0.661649	−	0.749814i	$-0.730143\pi$
$967$	2.74162	−	2.74162i	0.0881645	−	0.0881645i	0.749814	+	0.661649i	$0.230143\pi$
$968$	−8.63590	+	5.26233i	−0.277568	+	0.169138i
$969$		0			0
$970$	2.35922	−	5.30042i	0.0757499	−	0.170186i
$971$	−10.5455			−0.338421			−0.169210	−	0.985580i	$-0.554122\pi$
$971$	−10.5455			−0.338421			−0.169210	+	0.985580i	$0.554122\pi$
$972$		0			0
$973$	−22.5273	+	22.5273i	−0.722193	+	0.722193i
$974$	10.6351	+	22.3451i	0.340771	+	0.715982i
$975$		0			0
$976$	37.1637	−	7.76954i	1.18958	−	0.248697i
$977$	13.3372	+	13.3372i	0.426695	+	0.426695i	0.887501	−	0.460806i	$-0.152440\pi$
$977$	13.3372	+	13.3372i	0.426695	+	0.426695i	−0.460806	+	0.887501i	$0.652440\pi$
$978$		0			0
$979$	27.8513			0.890133
$980$	10.3561	−	0.263631i	0.330812	−	0.00842138i
$981$		0			0
$982$	−17.5814	+	49.5167i	−0.561045	+	1.58014i
$983$	−3.84412	+	3.84412i	−0.122608	+	0.122608i	−0.765749	−	0.643140i	$-0.777631\pi$
$983$	−3.84412	+	3.84412i	−0.122608	+	0.122608i	0.643140	+	0.765749i	$0.277631\pi$
$984$		0			0
$985$	51.0745	+	3.97115i	1.62737	+	0.126531i
$986$	−11.2509	−	23.6388i	−0.358300	−	0.752812i
$987$		0			0
$988$	8.54533	−	0.883702i	0.271863	−	0.0281143i
$989$			7.10972i			0.226076i
$990$		0			0
$991$	34.9248			1.10942			0.554711	−	0.832043i	$-0.312829\pi$
$991$	34.9248			1.10942			0.554711	+	0.832043i	$0.312829\pi$
$992$	−44.2565	−	6.01485i	−1.40514	−	0.190972i
$993$		0			0
$994$	−6.07069	+	2.88934i	−0.192551	+	0.0916443i
$995$	−10.3532	+	8.85937i	−0.328218	+	0.280861i
$996$		0			0
$997$	11.0217	+	11.0217i	0.349062	+	0.349062i	0.859760	−	0.510698i	$-0.170613\pi$
$997$	11.0217	+	11.0217i	0.349062	+	0.349062i	−0.510698	+	0.859760i	$0.670613\pi$
$998$	16.4975	−	46.4638i	0.522218	−	1.47079i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.x.a.53.10	yes	48
3.2	odd	2	inner	360.2.x.a.53.15	yes	48
4.3	odd	2		1440.2.bj.a.593.19		48
5.2	odd	4	inner	360.2.x.a.197.3	yes	48
8.3	odd	2		1440.2.bj.a.593.5		48
8.5	even	2	inner	360.2.x.a.53.22	yes	48
12.11	even	2		1440.2.bj.a.593.6		48
15.2	even	4	inner	360.2.x.a.197.22	yes	48
20.7	even	4		1440.2.bj.a.17.20		48
24.5	odd	2	inner	360.2.x.a.53.3	✓	48
24.11	even	2		1440.2.bj.a.593.20		48
40.27	even	4		1440.2.bj.a.17.6		48
40.37	odd	4	inner	360.2.x.a.197.15	yes	48
60.47	odd	4		1440.2.bj.a.17.5		48
120.77	even	4	inner	360.2.x.a.197.10	yes	48
120.107	odd	4		1440.2.bj.a.17.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.x.a.53.3	✓	48	24.5	odd	2	inner
360.2.x.a.53.10	yes	48	1.1	even	1	trivial
360.2.x.a.53.15	yes	48	3.2	odd	2	inner
360.2.x.a.53.22	yes	48	8.5	even	2	inner
360.2.x.a.197.3	yes	48	5.2	odd	4	inner
360.2.x.a.197.10	yes	48	120.77	even	4	inner
360.2.x.a.197.15	yes	48	40.37	odd	4	inner
360.2.x.a.197.22	yes	48	15.2	even	4	inner
1440.2.bj.a.17.5		48	60.47	odd	4
1440.2.bj.a.17.6		48	40.27	even	4
1440.2.bj.a.17.19		48	120.107	odd	4
1440.2.bj.a.17.20		48	20.7	even	4
1440.2.bj.a.593.5		48	8.3	odd	2
1440.2.bj.a.593.6		48	12.11	even	2
1440.2.bj.a.593.19		48	4.3	odd	2
1440.2.bj.a.593.20		48	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.473189 + 1.33270i) q^{2} +(-1.55218 - 1.26124i) q^{4} +(1.45381 + 1.69895i) q^{5} +(1.53029 - 1.53029i) q^{7} +(2.41533 - 1.47179i) q^{8} +O(q^{10})\)	\(q+(-0.473189 + 1.33270i) q^{2} +(-1.55218 - 1.26124i) q^{4} +(1.45381 + 1.69895i) q^{5} +(1.53029 - 1.53029i) q^{7} +(2.41533 - 1.47179i) q^{8} +(-2.95212 + 1.13358i) q^{10} +2.72480 q^{11} +(0.857617 - 0.857617i) q^{13} +(1.31530 + 2.76353i) q^{14} +(0.818554 + 3.91535i) q^{16} +(2.55531 + 2.55531i) q^{17} -3.54160 q^{19} +(-0.113809 - 4.47069i) q^{20} +(-1.28935 + 3.63135i) q^{22} +(-0.626051 + 0.626051i) q^{23} +(-0.772849 + 4.93991i) q^{25} +(0.737133 + 1.54876i) q^{26} +(-4.30535 + 0.445231i) q^{28} +5.12260i q^{29} +7.89544 q^{31} +(-5.60532 - 0.761813i) q^{32} +(-4.61460 + 2.19632i) q^{34} +(4.82463 + 0.375125i) q^{35} +(-4.21539 - 4.21539i) q^{37} +(1.67585 - 4.71990i) q^{38} +(6.01194 + 1.96381i) q^{40} +12.4074i q^{41} +(5.67823 - 5.67823i) q^{43} +(-4.22940 - 3.43663i) q^{44} +(-0.538098 - 1.13058i) q^{46} +(-9.45505 - 9.45505i) q^{47} +2.31644i q^{49} +(-6.21772 - 3.36749i) q^{50} +(-2.41284 + 0.249520i) q^{52} +(-6.46657 - 6.46657i) q^{53} +(3.96136 + 4.62930i) q^{55} +(1.44388 - 5.94842i) q^{56} +(-6.82690 - 2.42396i) q^{58} -2.51407i q^{59} -9.49179i q^{61} +(-3.73603 + 10.5223i) q^{62} +(3.66765 - 7.10974i) q^{64} +(2.70386 + 0.210231i) q^{65} +(9.91318 + 9.91318i) q^{67} +(-0.743456 - 7.18916i) q^{68} +(-2.78289 + 6.25229i) q^{70} +2.19671i q^{71} +(-5.71276 - 5.71276i) q^{73} +(7.61252 - 3.62318i) q^{74} +(5.49722 + 4.46681i) q^{76} +(4.16973 - 4.16973i) q^{77} -12.7576i q^{79} +(-5.46195 + 7.08287i) q^{80} +(-16.5353 - 5.87103i) q^{82} +(-3.58072 - 3.58072i) q^{83} +(-0.626392 + 8.05627i) q^{85} +(4.88051 + 10.2543i) q^{86} +(6.58130 - 4.01035i) q^{88} +10.2214 q^{89} -2.62480i q^{91} +(1.76135 - 0.182147i) q^{92} +(17.0748 - 8.12673i) q^{94} +(-5.14884 - 6.01700i) q^{95} +(-1.29731 + 1.29731i) q^{97} +(-3.08712 - 1.09611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Introduction

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