LMFDB - Embedded newform 315.2.ce.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(53,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("315.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$315 = 3^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$ , degree $4$ , 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			107.2
Character	$\chi$	$=$	315.107
Dual form			315.2.ce.a.53.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.604483 - 2.25596i) q^{2} +(-2.99191 + 1.72738i) q^{4} +(-0.254820 - 2.22150i) q^{5} +(-2.19240 - 1.48100i) q^{7} +(2.40251 + 2.40251i) q^{8} +(-4.85759 + 1.91772i) q^{10} +(2.61609 - 1.51040i) q^{11} +(-1.77456 + 1.77456i) q^{13} +(-2.01581 + 5.84122i) q^{14} +(0.512928 - 0.888417i) q^{16} +(-3.73962 - 1.00203i) q^{17} +(3.79826 + 2.19292i) q^{19} +(4.59978 + 6.20636i) q^{20} +(-4.98879 - 4.98879i) q^{22} +(-7.23056 + 1.93742i) q^{23} +(-4.87013 + 1.13217i) q^{25} +(5.07603 + 2.93065i) q^{26} +(9.11773 + 0.643912i) q^{28} +1.25900 q^{29} +(-2.64259 - 4.57710i) q^{31} +(4.24948 + 1.13865i) q^{32} +9.04214i q^{34} +(-2.73138 + 5.24782i) q^{35} +(7.36414 - 1.97321i) q^{37} +(2.65117 - 9.89430i) q^{38} +(4.72497 - 5.94938i) q^{40} -10.7696i q^{41} +(5.73749 - 5.73749i) q^{43} +(-5.21807 + 9.03797i) q^{44} +(8.74151 + 15.1407i) q^{46} +(-2.09056 - 7.80209i) q^{47} +(2.61327 + 6.49391i) q^{49} +(5.49803 + 10.3025i) q^{50} +(2.24398 - 8.37466i) q^{52} +(-0.472193 + 1.76225i) q^{53} +(-4.02199 - 5.42677i) q^{55} +(-1.70915 - 8.82539i) q^{56} +(-0.761042 - 2.84025i) q^{58} +(-2.97005 - 5.14428i) q^{59} +(-3.71170 + 6.42886i) q^{61} +(-8.72836 + 8.72836i) q^{62} -12.3267i q^{64} +(4.39438 + 3.48999i) q^{65} +(2.50901 - 9.36375i) q^{67} +(12.9195 - 3.46176i) q^{68} +(13.4899 + 2.98967i) q^{70} +1.07298i q^{71} +(-2.07401 - 0.555728i) q^{73} +(-8.90299 - 15.4204i) q^{74} -15.1521 q^{76} +(-7.97243 - 0.563028i) q^{77} +(-5.75001 - 3.31977i) q^{79} +(-2.10432 - 0.913083i) q^{80} +(-24.2957 + 6.51003i) q^{82} +(-1.25073 - 1.25073i) q^{83} +(-1.27308 + 8.56290i) q^{85} +(-16.4118 - 9.47534i) q^{86} +(9.91392 + 2.65643i) q^{88} +(2.44200 - 4.22966i) q^{89} +(6.51867 - 1.26242i) q^{91} +(18.2865 - 18.2865i) q^{92} +(-16.3375 + 9.43246i) q^{94} +(3.90371 - 8.99663i) q^{95} +(2.69087 + 2.69087i) q^{97} +(13.0703 - 9.82088i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100})$ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$ .

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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

)

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

$2$	−0.604483	−	2.25596i	−0.427434	−	1.59521i	−0.758550	−	0.651615i	$-0.774092\pi$
$2$	−0.604483	−	2.25596i	−0.427434	−	1.59521i	0.331115	−	0.943590i	$-0.392575\pi$
$3$		0			0
$3$		0			0
$4$	−2.99191	+	1.72738i	−1.49596	+	0.863690i
$5$	−0.254820	−	2.22150i	−0.113959	−	0.993485i
$5$	−0.254820	−	2.22150i	−0.113959	−	0.993485i
$6$		0			0
$7$	−2.19240	−	1.48100i	−0.828651	−	0.559766i
$7$	−2.19240	−	1.48100i	−0.828651	−	0.559766i
$8$	2.40251	+	2.40251i	0.849415	+	0.849415i
$9$		0			0
$10$	−4.85759	+	1.91772i	−1.53610	+	0.606437i
$11$	2.61609	−	1.51040i	0.788781	−	0.455403i	−0.0507524	−	0.998711i	$-0.516162\pi$
$11$	2.61609	−	1.51040i	0.788781	−	0.455403i	0.839533	+	0.543309i	$0.182829\pi$
$12$		0			0
$13$	−1.77456	+	1.77456i	−0.492174	+	0.492174i	−0.908991	−	0.416817i	$-0.863146\pi$
$13$	−1.77456	+	1.77456i	−0.492174	+	0.492174i	0.416817	+	0.908991i	$0.363146\pi$
$14$	−2.01581	+	5.84122i	−0.538749	+	1.56113i
$15$		0			0
$16$	0.512928	−	0.888417i	0.128232	−	0.222104i
$17$	−3.73962	−	1.00203i	−0.906990	−	0.243027i	−0.224974	−	0.974365i	$-0.572230\pi$
$17$	−3.73962	−	1.00203i	−0.906990	−	0.243027i	−0.682016	+	0.731337i	$0.738896\pi$
$18$		0			0
$19$	3.79826	+	2.19292i	0.871380	+	0.503091i	0.867806	−	0.496902i	$-0.165529\pi$
$19$	3.79826	+	2.19292i	0.871380	+	0.503091i	0.00357323	+	0.999994i	$0.498863\pi$
$20$	4.59978	+	6.20636i	1.02854	+	1.38779i
$21$		0			0
$22$	−4.98879	−	4.98879i	−1.06361	−	1.06361i
$23$	−7.23056	+	1.93742i	−1.50768	+	0.403981i	−0.915663	−	0.401947i	$-0.868334\pi$
$23$	−7.23056	+	1.93742i	−1.50768	+	0.403981i	−0.592014	+	0.805928i	$0.701667\pi$
$24$		0			0
$25$	−4.87013	+	1.13217i	−0.974027	+	0.226433i
$26$	5.07603	+	2.93065i	0.995491	+	0.574747i
$27$		0			0
$28$	9.11773	+	0.643912i	1.72309	+	0.121688i
$29$	1.25900			0.233790			0.116895	−	0.993144i	$-0.462706\pi$
$29$	1.25900			0.233790			0.116895	+	0.993144i	$0.462706\pi$
$30$		0			0
$31$	−2.64259	−	4.57710i	−0.474623	−	0.822072i	0.524954	−	0.851130i	$-0.324082\pi$
$31$	−2.64259	−	4.57710i	−0.474623	−	0.822072i	−0.999578	+	0.0290586i	$0.990749\pi$
$32$	4.24948	+	1.13865i	0.751209	+	0.201286i
$33$		0			0
$34$			9.04214i			1.55071i
$35$	−2.73138	+	5.24782i	−0.461687	+	0.887043i
$36$		0			0
$37$	7.36414	−	1.97321i	1.21066	−	0.324395i	0.403637	−	0.914919i	$-0.367746\pi$
$37$	7.36414	−	1.97321i	1.21066	−	0.324395i	0.807020	+	0.590525i	$0.201079\pi$
$38$	2.65117	−	9.89430i	0.430077	−	1.60507i
$39$		0			0
$40$	4.72497	−	5.94938i	0.747083	−	0.940680i
$41$		−	10.7696i		−	1.68193i	−0.541093	−	0.840963i	$-0.681989\pi$
$41$		−	10.7696i		−	1.68193i	0.541093	−	0.840963i	$-0.318011\pi$
$42$		0			0
$43$	5.73749	−	5.73749i	0.874959	−	0.874959i	−0.118049	−	0.993008i	$-0.537664\pi$
$43$	5.73749	−	5.73749i	0.874959	−	0.874959i	0.993008	+	0.118049i	$0.0376640\pi$
$44$	−5.21807	+	9.03797i	−0.786654	+	1.36252i
$45$		0			0
$46$	8.74151	+	15.1407i	1.28886	+	2.23238i
$47$	−2.09056	−	7.80209i	−0.304940	−	1.13805i	−0.932997	−	0.359884i	$-0.882816\pi$
$47$	−2.09056	−	7.80209i	−0.304940	−	1.13805i	0.628057	−	0.778168i	$-0.283851\pi$
$48$		0			0
$49$	2.61327	+	6.49391i	0.373324	+	0.927701i
$50$	5.49803	+	10.3025i	0.777539	+	1.45699i
$51$		0			0
$52$	2.24398	−	8.37466i	0.311185	−	1.16136i
$53$	−0.472193	+	1.76225i	−0.0648607	+	0.242064i	−0.990743	−	0.135747i	$-0.956656\pi$
$53$	−0.472193	+	1.76225i	−0.0648607	+	0.242064i	0.925883	+	0.377811i	$0.123323\pi$
$54$		0			0
$55$	−4.02199	−	5.42677i	−0.542325	−	0.731745i
$56$	−1.70915	−	8.82539i	−0.228394	−	1.17934i
$57$		0			0
$58$	−0.761042	−	2.84025i	−0.0999298	−	0.372943i
$59$	−2.97005	−	5.14428i	−0.386668	−	0.669729i	0.605331	−	0.795974i	$-0.293041\pi$
$59$	−2.97005	−	5.14428i	−0.386668	−	0.669729i	−0.991999	+	0.126245i	$0.959707\pi$
$60$		0			0
$61$	−3.71170	+	6.42886i	−0.475235	+	0.823131i	−0.999598	−	0.0283643i	$-0.990970\pi$
$61$	−3.71170	+	6.42886i	−0.475235	+	0.823131i	0.524363	+	0.851495i	$0.324303\pi$
$62$	−8.72836	+	8.72836i	−1.10850	+	1.10850i
$63$		0			0
$64$		−	12.3267i		−	1.54083i
$65$	4.39438	+	3.48999i	0.545055	+	0.432880i
$66$		0			0
$67$	2.50901	−	9.36375i	0.306524	−	1.14396i	−0.625101	−	0.780544i	$-0.714942\pi$
$67$	2.50901	−	9.36375i	0.306524	−	1.14396i	0.931625	−	0.363420i	$-0.118391\pi$
$68$	12.9195	−	3.46176i	1.56672	−	0.419801i
$69$		0			0
$70$	13.4899	+	2.98967i	1.61236	+	0.357334i
$71$			1.07298i			0.127339i	0.997971	+	0.0636696i	$0.0202804\pi$
$71$			1.07298i			0.127339i	−0.997971	+	0.0636696i	$0.979720\pi$
$72$		0			0
$73$	−2.07401	−	0.555728i	−0.242744	−	0.0650431i	0.135396	−	0.990792i	$-0.456769\pi$
$73$	−2.07401	−	0.555728i	−0.242744	−	0.0650431i	−0.378140	+	0.925749i	$0.623436\pi$
$74$	−8.90299	−	15.4204i	−1.03495	−	1.79259i
$75$		0			0
$76$	−15.1521			−1.73806
$77$	−7.97243	−	0.563028i	−0.908543	−	0.0641630i
$78$		0			0
$79$	−5.75001	−	3.31977i	−0.646927	−	0.373503i	0.140351	−	0.990102i	$-0.455177\pi$
$79$	−5.75001	−	3.31977i	−0.646927	−	0.373503i	−0.787278	+	0.616599i	$0.788510\pi$
$80$	−2.10432	−	0.913083i	−0.235271	−	0.102086i
$81$		0			0
$82$	−24.2957	+	6.51003i	−2.68302	+	0.718912i
$83$	−1.25073	−	1.25073i	−0.137285	−	0.137285i	0.635124	−	0.772410i	$-0.280949\pi$
$83$	−1.25073	−	1.25073i	−0.137285	−	0.137285i	−0.772410	+	0.635124i	$0.780949\pi$
$84$		0			0
$85$	−1.27308	+	8.56290i	−0.138084	+	0.928777i
$86$	−16.4118	−	9.47534i	−1.76973	−	1.02175i
$87$		0			0
$88$	9.91392	+	2.65643i	1.05683	+	0.283176i
$89$	2.44200	−	4.22966i	0.258851	−	0.448343i	−0.707083	−	0.707130i	$-0.749989\pi$
$89$	2.44200	−	4.22966i	0.258851	−	0.448343i	0.965934	+	0.258787i	$0.0833227\pi$
$90$		0			0
$91$	6.51867	−	1.26242i	0.683343	−	0.132338i
$92$	18.2865	−	18.2865i	1.90650	−	1.90650i
$93$		0			0
$94$	−16.3375	+	9.43246i	−1.68509	+	0.972884i
$95$	3.90371	−	8.99663i	0.400512	−	0.923035i
$96$		0			0
$97$	2.69087	+	2.69087i	0.273217	+	0.273217i	0.830394	−	0.557177i	$-0.188115\pi$
$97$	2.69087	+	2.69087i	0.273217	+	0.273217i	−0.557177	+	0.830394i	$0.688115\pi$
$98$	13.0703	−	9.82088i	1.32030	−	0.992059i
$99$		0			0
$100$	12.6153	−	11.7999i	1.26153	−	1.17999i
$101$	−10.8964	+	6.29104i	−1.08423	+	0.625982i	−0.932035	−	0.362368i	$-0.881968\pi$
$101$	−10.8964	+	6.29104i	−1.08423	+	0.625982i	−0.152197	+	0.988350i	$0.548635\pi$
$102$		0			0
$103$	−3.55530	−	13.2685i	−0.350314	−	1.30739i	−0.886280	−	0.463149i	$-0.846719\pi$
$103$	−3.55530	−	13.2685i	−0.350314	−	1.30739i	0.535966	−	0.844239i	$-0.319947\pi$
$104$	−8.52678			−0.836120
$105$		0			0
$106$	4.26100			0.413865
$107$	−0.786918	−	2.93682i	−0.0760742	−	0.283913i	0.917401	−	0.397965i	$-0.130284\pi$
$107$	−0.786918	−	2.93682i	−0.0760742	−	0.283913i	−0.993475	+	0.114052i	$0.963617\pi$
$108$		0			0
$109$	14.3581	−	8.28967i	1.37526	−	0.794006i	0.383674	−	0.923468i	$-0.374659\pi$
$109$	14.3581	−	8.28967i	1.37526	−	0.794006i	0.991584	+	0.129462i	$0.0413252\pi$
$110$	−9.81135	+	12.3538i	−0.935476	+	1.17789i
$111$		0			0
$112$	−2.44029	+	1.18812i	−0.230586	+	0.112267i
$113$	13.7810	+	13.7810i	1.29641	+	1.29641i	0.930750	+	0.365657i	$0.119156\pi$
$113$	13.7810	+	13.7810i	1.29641	+	1.29641i	0.365657	+	0.930750i	$0.380844\pi$
$114$		0			0
$115$	6.14648	+	15.5690i	0.573162	+	1.45182i
$116$	−3.76681	+	2.17477i	−0.349739	+	0.201922i
$117$		0			0
$118$	−9.80996	+	9.80996i	−0.903080	+	0.903080i
$119$	6.71474	+	7.73523i	0.615539	+	0.709087i
$120$		0			0
$121$	−0.937384	+	1.62360i	−0.0852167	+	0.147600i
$122$	16.7469	+	4.48732i	1.51619	+	0.406263i
$123$		0			0
$124$	15.8128	+	9.12952i	1.42003	+	0.819855i
$125$	3.75611	+	10.5305i	0.335957	+	0.941877i
$126$		0			0
$127$	13.1848	+	13.1848i	1.16996	+	1.16996i	0.982218	+	0.187742i	$0.0601167\pi$
$127$	13.1848	+	13.1848i	1.16996	+	1.16996i	0.187742	+	0.982218i	$0.439883\pi$
$128$	−19.3095	+	5.17397i	−1.70674	+	0.457319i
$129$		0			0
$130$	5.21696	−	12.0232i	0.457558	−	1.05450i
$131$	9.06836	+	5.23562i	0.792306	+	0.457438i	0.840774	−	0.541387i	$-0.182100\pi$
$131$	9.06836	+	5.23562i	0.792306	+	0.457438i	−0.0484676	+	0.998825i	$0.515434\pi$
$132$		0			0
$133$	−5.07958	−	10.4330i	−0.440456	−	0.904656i
$134$	−22.6409			−1.95588
$135$		0			0
$136$	−6.57708	−	11.3918i	−0.563980	−	0.976842i
$137$	16.0127	+	4.29058i	1.36806	+	0.366569i	0.866768	−	0.498712i	$-0.166193\pi$
$137$	16.0127	+	4.29058i	1.36806	+	0.366569i	0.501287	+	0.865281i	$0.332860\pi$
$138$		0			0
$139$		−	7.58102i		−	0.643014i	−0.946907	−	0.321507i	$-0.895811\pi$
$139$		−	7.58102i		−	0.643014i	0.946907	−	0.321507i	$-0.104189\pi$
$140$	−0.892929	−	20.4191i	−0.0754663	−	1.72573i
$141$		0			0
$142$	2.42060	−	0.648597i	0.203132	−	0.0544291i
$143$	−1.96211	+	7.32270i	−0.164080	+	0.612355i
$144$		0			0
$145$	−0.320818	−	2.79686i	−0.0266424	−	0.232267i
$146$			5.01481i			0.415028i
$147$		0			0
$148$	−18.6244	+	18.6244i	−1.53091	+	1.53091i
$149$	1.70147	−	2.94704i	0.139390	−	0.241431i	−0.787876	−	0.615834i	$-0.788819\pi$
$149$	1.70147	−	2.94704i	0.139390	−	0.241431i	0.927266	+	0.374403i	$0.122152\pi$
$150$		0			0
$151$	−7.87968	−	13.6480i	−0.641239	−	1.11066i	−0.985157	−	0.171659i	$-0.945087\pi$
$151$	−7.87968	−	13.6480i	−0.641239	−	1.11066i	0.343918	−	0.939000i	$-0.388246\pi$
$152$	3.85682	+	14.3939i	0.312830	+	1.16750i
$153$		0			0
$154$	3.54903	+	18.3258i	0.285989	+	1.47674i
$155$	−9.49465	+	7.03686i	−0.762629	+	0.565214i
$156$		0			0
$157$	1.60818	−	6.00182i	0.128347	−	0.478998i	−0.871590	−	0.490236i	$-0.836911\pi$
$157$	1.60818	−	6.00182i	0.128347	−	0.478998i	0.999937	+	0.0112383i	$0.00357732\pi$
$158$	−4.01349	+	14.9785i	−0.319296	+	1.19163i
$159$		0			0
$160$	1.44665	−	9.73038i	0.114368	−	0.769254i
$161$	18.7216	+	6.46087i	1.47547	+	0.509188i
$162$		0			0
$163$	−0.940977	−	3.51177i	−0.0737030	−	0.275063i	0.919233	−	0.393714i	$-0.128810\pi$
$163$	−0.940977	−	3.51177i	−0.0737030	−	0.275063i	−0.992936	+	0.118650i	$0.962143\pi$
$164$	18.6032	+	32.2216i	1.45266	+	2.51609i
$165$		0			0
$166$	−2.06555	+	3.57764i	−0.160318	+	0.277679i
$167$	−6.11816	+	6.11816i	−0.473437	+	0.473437i	−0.903025	−	0.429588i	$-0.858659\pi$
$167$	−6.11816	+	6.11816i	−0.473437	+	0.473437i	0.429588	+	0.903025i	$0.358659\pi$
$168$		0			0
$169$			6.70188i			0.515529i
$170$	20.0871	−	2.30412i	1.54061	−	0.176718i
$171$		0			0
$172$	−7.25523	+	27.0769i	−0.553206	+	2.06459i
$173$	−22.7578	+	6.09793i	−1.73024	+	0.463617i	−0.980239	−	0.197816i	$-0.936615\pi$
$173$	−22.7578	+	6.09793i	−1.73024	+	0.463617i	−0.750004	+	0.661433i	$0.769949\pi$
$174$		0			0
$175$	12.3540	+	4.73052i	0.933877	+	0.357593i
$176$		−	3.09891i		−	0.233589i
$177$		0			0
$178$	−11.0181	−	2.95229i	−0.825842	−	0.221284i
$179$	−0.228953	−	0.396558i	−0.0171127	−	0.0296401i	0.857342	−	0.514747i	$-0.172114\pi$
$179$	−0.228953	−	0.396558i	−0.0171127	−	0.0296401i	−0.874455	+	0.485107i	$0.838781\pi$
$180$		0			0
$181$	−12.9702			−0.964070			−0.482035	−	0.876152i	$-0.660102\pi$
$181$	−12.9702			−0.964070			−0.482035	+	0.876152i	$0.660102\pi$
$182$	−6.78841	−	13.9428i	−0.503190	−	1.03351i
$183$		0			0
$184$	−22.0262	−	12.7168i	−1.62379	−	0.937496i
$185$	−6.26003	−	15.8566i	−0.460246	−	1.16580i
$186$		0			0
$187$	−11.2966	+	3.02692i	−0.826091	+	0.221351i
$188$	19.7320	+	19.7320i	1.43910	+	1.43910i
$189$		0			0
$190$	−22.6558	−	3.36831i	−1.64362	−	0.244363i
$191$	5.84564	+	3.37498i	0.422975	+	0.244205i	0.696350	−	0.717703i	$-0.254806\pi$
$191$	5.84564	+	3.37498i	0.422975	+	0.244205i	−0.273374	+	0.961908i	$0.588140\pi$
$192$		0			0
$193$	4.93109	+	1.32128i	0.354948	+	0.0951079i	0.431887	−	0.901928i	$-0.357848\pi$
$193$	4.93109	+	1.32128i	0.354948	+	0.0951079i	−0.0769390	+	0.997036i	$0.524515\pi$
$194$	4.44392	−	7.69710i	0.319055	−	0.552619i
$195$		0			0
$196$	−19.0361	−	14.9151i	−1.35972	−	1.06536i
$197$	5.34774	−	5.34774i	0.381011	−	0.381011i	−0.490456	−	0.871466i	$-0.663170\pi$
$197$	5.34774	−	5.34774i	0.381011	−	0.381011i	0.871466	+	0.490456i	$0.163170\pi$
$198$		0			0
$199$	14.9596	−	8.63693i	1.06046	−	0.612256i	0.134899	−	0.990859i	$-0.456929\pi$
$199$	14.9596	−	8.63693i	1.06046	−	0.612256i	0.925559	+	0.378603i	$0.123596\pi$
$200$	−14.4206	−	8.98050i	−1.01969	−	0.635017i
$201$		0			0
$202$	20.7790	+	20.7790i	1.46201	+	1.46201i
$203$	−2.76023	−	1.86458i	−0.193730	−	0.130868i
$204$		0			0
$205$	−23.9246	+	2.74430i	−1.67097	+	0.191670i
$206$	−27.7842	+	16.0412i	−1.93582	+	1.11764i
$207$		0			0
$208$	0.666328	+	2.48677i	0.0462015	+	0.172426i
$209$	13.2488			0.916437
$210$		0			0
$211$	11.1106			0.764882			0.382441	−	0.923980i	$-0.375084\pi$
$211$	11.1106			0.764882			0.382441	+	0.923980i	$0.375084\pi$
$212$	−1.63131	−	6.08815i	−0.112039	−	0.418136i
$213$		0			0
$214$	−6.14967	+	3.55051i	−0.420383	+	0.242708i
$215$	−14.2079	−	11.2838i	−0.968968	−	0.769550i
$216$		0			0
$217$	−0.985072	+	13.9485i	−0.0668711	+	0.946888i
$218$	−27.3804	−	27.3804i	−1.85444	−	1.85444i
$219$		0			0
$220$	21.4075	+	9.28890i	1.44329	+	0.626257i
$221$	8.41432	−	4.85801i	0.566009	−	0.326785i
$222$		0			0
$223$	−1.84347	+	1.84347i	−0.123448	+	0.123448i	−0.766132	−	0.642684i	$-0.777821\pi$
$223$	−1.84347	+	1.84347i	−0.123448	+	0.123448i	0.642684	+	0.766132i	$0.277821\pi$
$224$	−7.63024	−	8.78986i	−0.509817	−	0.587297i
$225$		0			0
$226$	22.7590	−	39.4198i	1.51391	−	2.62216i
$227$	−6.53177	−	1.75018i	−0.433529	−	0.116164i	0.0354533	−	0.999371i	$-0.488712\pi$
$227$	−6.53177	−	1.75018i	−0.433529	−	0.116164i	−0.468982	+	0.883208i	$0.655379\pi$
$228$		0			0
$229$	22.0329	+	12.7207i	1.45597	+	0.840606i	0.998810	−	0.0487763i	$-0.0155321\pi$
$229$	22.0329	+	12.7207i	1.45597	+	0.840606i	0.457163	+	0.889383i	$0.348865\pi$
$230$	31.4076	−	23.2774i	2.07096	−	1.53487i
$231$		0			0
$232$	3.02475	+	3.02475i	0.198585	+	0.198585i
$233$	10.2722	−	2.75243i	0.672954	−	0.180317i	0.0938688	−	0.995585i	$-0.470077\pi$
$233$	10.2722	−	2.75243i	0.672954	−	0.180317i	0.579085	+	0.815267i	$0.303410\pi$
$234$		0			0
$235$	−16.7996	+	6.63232i	−1.09589	+	0.432645i
$236$	17.7723	+	10.2608i	1.15688	+	0.667923i
$237$		0			0
$238$	13.3914	−	19.8240i	0.868037	−	1.28500i
$239$	−15.7861			−1.02112			−0.510558	−	0.859843i	$-0.670561\pi$
$239$	−15.7861			−1.02112			−0.510558	+	0.859843i	$0.670561\pi$
$240$		0			0
$241$	1.41218	+	2.44597i	0.0909664	+	0.157559i	0.907918	−	0.419148i	$-0.137671\pi$
$241$	1.41218	+	2.44597i	0.0909664	+	0.157559i	−0.816952	+	0.576706i	$0.804338\pi$
$242$	4.22940	+	1.13326i	0.271876	+	0.0728490i
$243$		0			0
$244$		−	25.6461i		−	1.64182i
$245$	13.7603	−	7.46015i	0.879114	−	0.476611i
$246$		0			0
$247$	−10.6317	+	2.84876i	−0.676479	+	0.181262i
$248$	4.64768	−	17.3454i	0.295128	−	1.10143i
$249$		0			0
$250$	21.4859	−	14.8392i	1.35889	−	0.938511i
$251$		−	22.0003i		−	1.38865i	−0.719663	−	0.694324i	$-0.755704\pi$
$251$		−	22.0003i		−	1.38865i	0.719663	−	0.694324i	$-0.244296\pi$
$252$		0			0
$253$	−15.9895	+	15.9895i	−1.00525	+	1.00525i
$254$	21.7744	−	37.7143i	1.36625	−	2.36641i
$255$		0			0
$256$	11.0179	+	19.0836i	0.688619	+	1.19272i
$257$	−2.56986	−	9.59086i	−0.160304	−	0.598261i	−0.998593	−	0.0530353i	$-0.983110\pi$
$257$	−2.56986	−	9.59086i	−0.160304	−	0.598261i	0.838289	−	0.545226i	$-0.183556\pi$
$258$		0			0
$259$	−19.0675	−	6.58022i	−1.18480	−	0.408875i
$260$	−19.1761	−	2.85098i	−1.18925	−	0.176810i
$261$		0			0
$262$	6.32969	−	23.6227i	0.391049	−	1.45942i
$263$	−2.27029	+	8.47285i	−0.139992	+	0.522458i	0.859935	+	0.510404i	$0.170504\pi$
$263$	−2.27029	+	8.47285i	−0.139992	+	0.522458i	−0.999927	+	0.0120549i	$0.996163\pi$
$264$		0			0
$265$	4.03516	+	0.599922i	0.247878	+	0.0368529i
$266$	−20.4659	+	17.7659i	−1.25485	+	1.08930i
$267$		0			0
$268$	8.66803	+	32.3495i	0.529484	+	1.97606i
$269$	10.3843	+	17.9862i	0.633143	+	1.09664i	0.986905	+	0.161300i	$0.0515687\pi$
$269$	10.3843	+	17.9862i	0.633143	+	1.09664i	−0.353763	+	0.935335i	$0.615098\pi$
$270$		0			0
$271$	−11.8493	+	20.5237i	−0.719796	+	1.24672i	0.241284	+	0.970455i	$0.422432\pi$
$271$	−11.8493	+	20.5237i	−0.719796	+	1.24672i	−0.961080	+	0.276269i	$0.910902\pi$
$272$	−2.80837	+	2.80837i	−0.170283	+	0.170283i
$273$		0			0
$274$		−	38.7176i		−	2.33901i
$275$	−11.0307	+	10.3177i	−0.665175	+	0.622180i
$276$		0			0
$277$	−1.55791	+	5.81419i	−0.0936056	+	0.349341i	−0.996804	−	0.0798818i	$-0.974546\pi$
$277$	−1.55791	+	5.81419i	−0.0936056	+	0.349341i	0.903199	+	0.429223i	$0.141212\pi$
$278$	−17.1025	+	4.58260i	−1.02574	+	0.274846i
$279$		0			0
$280$	−19.1701	+	6.04576i	−1.14563	+	0.361303i
$281$		−	1.10459i		−	0.0658940i	−0.999457	−	0.0329470i	$-0.989511\pi$
$281$		−	1.10459i		−	0.0658940i	0.999457	−	0.0329470i	$-0.0104893\pi$
$282$		0			0
$283$	13.4052	+	3.59192i	0.796858	+	0.213517i	0.634204	−	0.773166i	$-0.281328\pi$
$283$	13.4052	+	3.59192i	0.796858	+	0.213517i	0.162654	+	0.986683i	$0.447995\pi$
$284$	−1.85344	−	3.21026i	−0.109982	−	0.190494i
$285$		0			0
$286$	17.7058			1.04697
$287$	−15.9498	+	23.6113i	−0.941485	+	1.39373i
$288$		0			0
$289$	−1.74177	−	1.00561i	−0.102457	−	0.0591534i
$290$	−6.11569	+	2.41441i	−0.359126	+	0.141779i
$291$		0			0
$292$	7.16520	−	1.91991i	0.419311	−	0.112354i
$293$	2.68196	+	2.68196i	0.156682	+	0.156682i	0.781095	−	0.624413i	$-0.214662\pi$
$293$	2.68196	+	2.68196i	0.156682	+	0.156682i	−0.624413	+	0.781095i	$0.714662\pi$
$294$		0			0
$295$	−10.6712	+	7.90884i	−0.621302	+	0.460471i
$296$	22.4331	+	12.9517i	1.30390	+	0.752804i
$297$		0			0
$298$	−7.67691	−	2.05702i	−0.444712	−	0.119160i
$299$	9.39299	−	16.2691i	0.543211	−	0.940868i
$300$		0			0
$301$	−21.0761	+	4.08166i	−1.21481	+	0.235263i
$302$	−26.0262	+	26.0262i	−1.49764	+	1.49764i
$303$		0			0
$304$	3.89646	−	2.24962i	0.223477	−	0.129025i
$305$	15.2275	+	6.60735i	0.871925	+	0.378336i
$306$		0			0
$307$	−15.8583	−	15.8583i	−0.905081	−	0.905081i	0.0907893	−	0.995870i	$-0.471061\pi$
$307$	−15.8583	−	15.8583i	−0.905081	−	0.905081i	−0.995870	+	0.0907893i	$0.971061\pi$
$308$	24.8254	−	12.0869i	1.41456	−	0.688715i
$309$		0			0
$310$	21.6142	+	17.1659i	1.22761	+	0.974958i
$311$	22.0623	−	12.7377i	1.25104	−	0.722288i	0.279723	−	0.960081i	$-0.409757\pi$
$311$	22.0623	−	12.7377i	1.25104	−	0.722288i	0.971316	+	0.237793i	$0.0764241\pi$
$312$		0			0
$313$	1.63905	+	6.11703i	0.0926448	+	0.345755i	0.996652	−	0.0817624i	$-0.0260549\pi$
$313$	1.63905	+	6.11703i	0.0926448	+	0.345755i	−0.904007	+	0.427518i	$0.859388\pi$
$314$	−14.5120			−0.818959
$315$		0			0
$316$	22.9380			1.29036
$317$	−0.647369	−	2.41602i	−0.0363599	−	0.135697i	0.945360	−	0.326028i	$-0.105710\pi$
$317$	−0.647369	−	2.41602i	−0.0363599	−	0.135697i	−0.981720	+	0.190331i	$0.939044\pi$
$318$		0			0
$319$	3.29365	−	1.90159i	0.184409	−	0.106469i
$320$	−27.3837	+	3.14108i	−1.53080	+	0.175592i
$321$		0			0
$322$	3.25855	−	46.1408i	0.181592	−	2.57133i
$323$	−12.0066	−	12.0066i	−0.668068	−	0.668068i
$324$		0			0
$325$	6.63324	−	10.6514i	0.367946	−	0.590835i
$326$	−7.35362	+	4.24561i	−0.407279	+	0.235143i
$327$		0			0
$328$	25.8740	−	25.8740i	1.42865	−	1.42865i
$329$	−6.97155	+	20.2015i	−0.384354	+	1.11374i
$330$		0			0
$331$	−0.708836	+	1.22774i	−0.0389611	+	0.0674827i	−0.884848	−	0.465879i	$-0.845738\pi$
$331$	−0.708836	+	1.22774i	−0.0389611	+	0.0674827i	0.845887	+	0.533362i	$0.179072\pi$
$332$	5.90256	+	1.58159i	0.323945	+	0.0868008i
$333$		0			0
$334$	17.5007	+	10.1040i	0.957593	+	0.552867i
$335$	−21.4409	−	3.18770i	−1.17144	−	0.174162i
$336$		0			0
$337$	7.38849	+	7.38849i	0.402477	+	0.402477i	0.879105	−	0.476628i	$-0.158141\pi$
$337$	7.38849	+	7.38849i	0.402477	+	0.402477i	−0.476628	+	0.879105i	$0.658141\pi$
$338$	15.1192	−	4.05117i	0.822375	−	0.220355i
$339$		0			0
$340$	−10.9825	−	27.8185i	−0.595607	−	1.50867i
$341$	−13.8265	−	7.98274i	−0.748748	−	0.432290i
$342$		0			0
$343$	3.88816	−	18.1075i	0.209941	−	0.977714i
$344$	27.5687			1.48641
$345$		0			0
$346$	27.5134	+	47.6546i	1.47913	+	2.56193i
$347$	10.1880	+	2.72987i	0.546922	+	0.146547i	0.521691	−	0.853134i	$-0.325301\pi$
$347$	10.1880	+	2.72987i	0.546922	+	0.146547i	0.0252308	+	0.999682i	$0.491968\pi$
$348$		0			0
$349$			8.10936i			0.434084i	0.976162	+	0.217042i	$0.0696409\pi$
$349$			8.10936i			0.434084i	−0.976162	+	0.217042i	$0.930359\pi$
$350$	3.20406	−	30.7297i	0.171264	−	1.64257i
$351$		0			0
$352$	12.8368	−	3.43962i	0.684206	−	0.183332i
$353$	2.68249	−	10.0112i	0.142774	−	0.532841i	−0.857070	−	0.515200i	$-0.827718\pi$
$353$	2.68249	−	10.0112i	0.142774	−	0.532841i	0.999844	−	0.0176413i	$-0.00561568\pi$
$354$		0			0
$355$	2.38362	−	0.273416i	0.126510	−	0.0145114i
$356$			16.8730i			0.894269i
$357$		0			0
$358$	−0.756221	+	0.756221i	−0.0399675	+	0.0399675i
$359$	−1.45427	+	2.51888i	−0.0767537	+	0.132941i	−0.901848	−	0.432054i	$-0.857789\pi$
$359$	−1.45427	+	2.51888i	−0.0767537	+	0.132941i	0.825094	+	0.564996i	$0.191122\pi$
$360$		0			0
$361$	0.117833	+	0.204093i	0.00620174	+	0.0107417i
$362$	7.84028	+	29.2603i	0.412076	+	1.53789i
$363$		0			0
$364$	−17.3226	+	15.0373i	−0.907952	+	0.788168i
$365$	−0.706053	+	4.74902i	−0.0369565	+	0.248575i
$366$		0			0
$367$	2.80371	−	10.4636i	0.146352	−	0.546194i	−0.853339	−	0.521356i	$-0.825426\pi$
$367$	2.80371	−	10.4636i	0.146352	−	0.546194i	0.999691	−	0.0248380i	$-0.00790698\pi$
$368$	−1.98752	+	7.41752i	−0.103607	+	0.386665i
$369$		0			0
$370$	−31.9879	+	23.7074i	−1.66297	+	1.23249i
$371$	3.64513	−	3.16424i	0.189246	−	0.164279i
$372$		0			0
$373$	4.65126	+	17.3587i	0.240833	+	0.898801i	0.975432	+	0.220300i	$0.0707036\pi$
$373$	4.65126	+	17.3587i	0.240833	+	0.898801i	−0.734599	+	0.678501i	$0.762630\pi$
$374$	13.6572	+	23.6550i	0.706199	+	1.22317i
$375$		0			0
$376$	13.7220	−	23.7672i	0.707658	−	1.22570i
$377$	−2.23416	+	2.23416i	−0.115065	+	0.115065i
$378$		0			0
$379$		−	7.37508i		−	0.378832i	−0.981897	−	0.189416i	$-0.939340\pi$
$379$		−	7.37508i		−	0.378832i	0.981897	−	0.189416i	$-0.0606595\pi$
$380$	3.86105	+	33.6603i	0.198068	+	1.72674i
$381$		0			0
$382$	4.08024	−	15.2277i	0.208763	−	0.779114i
$383$	8.84543	−	2.37013i	0.451981	−	0.121108i	−0.0256454	−	0.999671i	$-0.508164\pi$
$383$	8.84543	−	2.37013i	0.451981	−	0.121108i	0.477626	+	0.878563i	$0.341497\pi$
$384$		0			0
$385$	0.780766	+	17.8542i	0.0397915	+	0.909936i
$386$		−	11.9230i		−	0.606867i
$387$		0			0
$388$	−12.6990	−	3.40269i	−0.644695	−	0.172746i
$389$	−4.50787	−	7.80786i	−0.228558	−	0.395874i	0.728823	−	0.684702i	$-0.240068\pi$
$389$	−4.50787	−	7.80786i	−0.228558	−	0.395874i	−0.957381	+	0.288828i	$0.906734\pi$
$390$		0			0
$391$	28.9809			1.46563
$392$	−9.32328	+	21.8801i	−0.470897	+	1.10511i
$393$		0			0
$394$	−15.2969	−	8.83167i	−0.770647	−	0.444933i
$395$	−5.90965	+	13.6196i	−0.297347	+	0.685276i
$396$		0			0
$397$	14.8688	−	3.98408i	0.746244	−	0.199955i	0.134393	−	0.990928i	$-0.457092\pi$
$397$	14.8688	−	3.98408i	0.746244	−	0.199955i	0.611851	+	0.790973i	$0.290425\pi$
$398$	−28.5274	−	28.5274i	−1.42995	−	1.42995i
$399$		0			0
$400$	−1.49219	+	4.90743i	−0.0746096	+	0.245371i
$401$	−16.5088	−	9.53134i	−0.824408	−	0.475972i	0.0275261	−	0.999621i	$-0.491237\pi$
$401$	−16.5088	−	9.53134i	−0.824408	−	0.475972i	−0.851934	+	0.523649i	$0.824570\pi$
$402$		0			0
$403$	12.8118	+	3.43290i	0.638200	+	0.171005i
$404$	21.7340	−	37.6445i	1.08131	−	1.87288i
$405$		0			0
$406$	−2.53790	+	7.35408i	−0.125954	+	0.364977i
$407$	16.2849	−	16.2849i	0.807213	−	0.807213i
$408$		0			0
$409$	−14.2422	+	8.22271i	−0.704229	+	0.406587i	−0.808921	−	0.587918i	$-0.799948\pi$
$409$	−14.2422	+	8.22271i	−0.704229	+	0.406587i	0.104691	+	0.994505i	$0.466615\pi$
$410$	20.6531	+	52.3141i	1.01998	+	2.58361i
$411$		0			0
$412$	33.5570	+	33.5570i	1.65323	+	1.65323i
$413$	−1.10714	+	15.6770i	−0.0544788	+	0.771415i
$414$		0			0
$415$	−2.45979	+	3.09721i	−0.120746	+	0.152036i
$416$	−9.56155	+	5.52036i	−0.468794	+	0.270658i
$417$		0			0
$418$	−8.00866	−	29.8887i	−0.391716	−	1.46190i
$419$	0.432905			0.0211488			0.0105744	−	0.999944i	$-0.496634\pi$
$419$	0.432905			0.0211488			0.0105744	+	0.999944i	$0.496634\pi$
$420$		0			0
$421$	2.44053			0.118944			0.0594721	−	0.998230i	$-0.481058\pi$
$421$	2.44053			0.118944			0.0594721	+	0.998230i	$0.481058\pi$
$422$	−6.71614	−	25.0650i	−0.326937	−	1.22014i
$423$		0			0
$424$	−5.36826	+	3.09937i	−0.260706	+	0.150519i
$425$	19.3469	+	0.646142i	0.938462	+	0.0313425i
$426$		0			0
$427$	17.6587	−	8.59761i	0.854564	−	0.416067i
$428$	7.42739	+	7.42739i	0.359016	+	0.359016i
$429$		0			0
$430$	−16.8674	+	38.8733i	−0.813420	+	1.87464i
$431$	−1.41023	+	0.814199i	−0.0679286	+	0.0392186i	−0.533580	−	0.845750i	$-0.679154\pi$
$431$	−1.41023	+	0.814199i	−0.0679286	+	0.0392186i	0.465651	+	0.884968i	$0.345820\pi$
$432$		0			0
$433$	12.1563	−	12.1563i	0.584193	−	0.584193i	−0.351860	−	0.936053i	$-0.614451\pi$
$433$	12.1563	−	12.1563i	0.584193	−	0.584193i	0.936053	+	0.351860i	$0.114451\pi$
$434$	32.0628	−	6.20937i	1.53906	−	0.298059i
$435$		0			0
$436$	−28.6388	+	49.6039i	−1.37155	+	2.37560i
$437$	−31.7122	−	8.49725i	−1.51700	−	0.406478i
$438$		0			0
$439$	−32.5150	−	18.7725i	−1.55185	−	0.895964i	−0.997991	−	0.0633566i	$-0.979819\pi$
$439$	−32.5150	−	18.7725i	−1.55185	−	0.895964i	−0.553864	−	0.832607i	$-0.686847\pi$
$440$	3.37499	−	22.7007i	0.160896	−	1.08221i
$441$		0			0
$442$	−16.0458	−	16.0458i	−0.763221	−	0.763221i
$443$	−12.1431	+	3.25374i	−0.576937	+	0.154590i	−0.535476	−	0.844550i	$-0.679868\pi$
$443$	−12.1431	+	3.25374i	−0.576937	+	0.154590i	−0.0414608	+	0.999140i	$0.513201\pi$
$444$		0			0
$445$	−10.0185	−	4.34710i	−0.474921	−	0.206072i
$446$	5.27315	+	3.04446i	0.249691	+	0.144159i
$447$		0			0
$448$	−18.2558	+	27.0250i	−0.862507	+	1.27681i
$449$	24.2617			1.14498			0.572491	−	0.819911i	$-0.305977\pi$
$449$	24.2617			1.14498			0.572491	+	0.819911i	$0.305977\pi$
$450$		0			0
$451$	−16.2664	−	28.1742i	−0.765953	−	1.32667i
$452$	−65.0365	−	17.4265i	−3.05906	−	0.819673i
$453$		0			0
$454$			15.7934i			0.741220i
$455$	−4.46556	−	14.1596i	−0.209349	−	0.663810i
$456$		0			0
$457$	−31.6281	+	8.47473i	−1.47950	+	0.396431i	−0.906177	−	0.422898i	$-0.861013\pi$
$457$	−31.6281	+	8.47473i	−1.47950	+	0.396431i	−0.573323	+	0.819329i	$0.694346\pi$
$458$	15.3789	−	57.3947i	0.718608	−	2.68188i
$459$		0			0
$460$	−45.2833	−	35.9638i	−2.11135	−	1.67682i
$461$			11.3402i			0.528165i	0.964500	+	0.264083i	$0.0850691\pi$
$461$			11.3402i			0.528165i	−0.964500	+	0.264083i	$0.914931\pi$
$462$		0			0
$463$	10.8990	−	10.8990i	0.506520	−	0.506520i	−0.406937	−	0.913456i	$-0.633403\pi$
$463$	10.8990	−	10.8990i	0.506520	−	0.506520i	0.913456	+	0.406937i	$0.133403\pi$
$464$	0.645775	−	1.11851i	0.0299793	−	0.0519257i
$465$		0			0
$466$	−12.4187	−	21.5099i	−0.575287	−	0.996426i
$467$	5.98056	+	22.3197i	0.276747	+	1.03283i	0.954661	+	0.297694i	$0.0962174\pi$
$467$	5.98056	+	22.3197i	0.276747	+	1.03283i	−0.677914	+	0.735141i	$0.737116\pi$
$468$		0			0
$469$	−19.3685	+	16.8133i	−0.894354	+	0.776365i
$470$	25.1173	+	33.8902i	1.15858	+	1.56324i
$471$		0			0
$472$	5.22361	−	19.4948i	0.240436	−	0.897319i
$473$	6.34388	−	23.6757i	0.291692	−	1.08861i
$474$		0			0
$475$	−20.9808	−	6.37958i	−0.962664	−	0.292715i
$476$	−33.4516	−	11.5442i	−1.53325	−	0.529127i
$477$		0			0
$478$	9.54242	+	35.6128i	0.436460	+	1.62889i
$479$	−4.96946	−	8.60736i	−0.227061	−	0.393280i	0.729875	−	0.683581i	$-0.239578\pi$
$479$	−4.96946	−	8.60736i	−0.227061	−	0.393280i	−0.956936	+	0.290300i	$0.906245\pi$
$480$		0			0
$481$	−9.56651	+	16.5697i	−0.436195	+	0.755512i
$482$	4.66437	−	4.66437i	0.212456	−	0.212456i
$483$		0			0
$484$		−	6.47687i		−	0.294403i
$485$	5.29209	−	6.66347i	0.240301	−	0.302572i
$486$		0			0
$487$	−1.20024	+	4.47934i	−0.0543879	+	0.202978i	−0.987773	−	0.155897i	$-0.950173\pi$
$487$	−1.20024	+	4.47934i	−0.0543879	+	0.202978i	0.933385	+	0.358876i	$0.116840\pi$
$488$	−24.3628	+	6.52798i	−1.10285	+	0.295508i
$489$		0			0
$490$	−25.1477	−	26.5332i	−1.13606	−	1.19865i
$491$		−	1.99747i		−	0.0901445i	−0.998984	−	0.0450722i	$-0.985648\pi$
$491$		−	1.99747i		−	0.0901445i	0.998984	−	0.0450722i	$-0.0143518\pi$
$492$		0			0
$493$	−4.70817	−	1.26155i	−0.212045	−	0.0568173i
$494$	12.8534	+	22.2627i	0.578300	+	1.00165i
$495$		0			0
$496$	−5.42183			−0.243448
$497$	1.58908	−	2.35240i	0.0712801	−	0.105520i
$498$		0			0
$499$	0.178762	+	0.103208i	0.00800250	+	0.00462025i	0.503996	−	0.863706i	$-0.331863\pi$
$499$	0.178762	+	0.103208i	0.00800250	+	0.00462025i	−0.495993	+	0.868326i	$0.665196\pi$
$500$	−29.4282	−	25.0181i	−1.31607	−	1.11884i
$501$		0			0
$502$	−49.6319	+	13.2988i	−2.21518	+	0.593555i
$503$	20.3423	+	20.3423i	0.907017	+	0.907017i	0.996030	−	0.0890134i	$-0.0283714\pi$
$503$	20.3423	+	20.3423i	0.907017	+	0.907017i	−0.0890134	+	0.996030i	$0.528371\pi$
$504$		0			0
$505$	16.7522	+	22.6033i	0.745462	+	1.00583i
$506$	45.7371	+	26.4063i	2.03326	+	1.17391i
$507$		0			0
$508$	−62.2228	−	16.6726i	−2.76069	−	0.739725i
$509$	−2.36278	+	4.09245i	−0.104728	+	0.181395i	−0.913627	−	0.406553i	$-0.866731\pi$
$509$	−2.36278	+	4.09245i	−0.104728	+	0.181395i	0.808899	+	0.587948i	$0.200064\pi$
$510$		0			0
$511$	3.72402	+	4.28999i	0.164741	+	0.189778i
$512$	8.12052	−	8.12052i	0.358880	−	0.358880i
$513$		0			0
$514$	−20.0832	+	11.5950i	−0.885831	+	0.511435i
$515$	−28.5701	+	11.2792i	−1.25895	+	0.497020i
$516$		0			0
$517$	−17.2534	−	17.2534i	−0.758803	−	0.758803i
$518$	−3.31875	+	46.9932i	−0.145817	+	2.06476i
$519$		0			0
$520$	2.17279	+	18.9423i	0.0952833	+	0.830673i
$521$	10.9951	−	6.34804i	0.481705	−	0.278113i	−0.239422	−	0.970916i	$-0.576958\pi$
$521$	10.9951	−	6.34804i	0.481705	−	0.278113i	0.721127	+	0.692803i	$0.243625\pi$
$522$		0			0
$523$	8.48338	+	31.6604i	0.370952	+	1.38441i	0.859170	+	0.511691i	$0.170981\pi$
$523$	8.48338	+	31.6604i	0.370952	+	1.38441i	−0.488217	+	0.872722i	$0.662353\pi$
$524$	−36.1756			−1.58034
$525$		0			0
$526$	20.4868			0.893266
$527$	5.29590	+	19.7645i	0.230693	+	0.860957i
$528$		0			0
$529$	28.6089	−	16.5173i	1.24386	−	0.718145i
$530$	−1.08579	−	9.46581i	−0.0471636	−	0.411169i
$531$		0			0
$532$	33.2194	+	22.4402i	1.44025	+	0.972908i
$533$	19.1112	+	19.1112i	0.827800	+	0.827800i
$534$		0			0
$535$	−6.32362	+	2.49650i	−0.273394	+	0.107933i
$536$	28.5244	−	16.4686i	1.23207	−	0.711334i
$537$		0			0
$538$	34.2989	−	34.2989i	1.47873	−	1.47873i
$539$	16.6449	+	13.0416i	0.716948	+	0.561740i
$540$		0			0
$541$	21.0600	−	36.4771i	0.905442	−	1.56827i	0.0851189	−	0.996371i	$-0.472873\pi$
$541$	21.0600	−	36.4771i	0.905442	−	1.56827i	0.820323	−	0.571901i	$-0.193794\pi$
$542$	53.4633	+	14.3255i	2.29645	+	0.615331i
$543$		0			0
$544$	−14.7505	−	8.51619i	−0.632421	−	0.365129i
$545$	−22.0742	−	29.7842i	−0.945556	−	1.27582i
$546$		0			0
$547$	19.7948	+	19.7948i	0.846364	+	0.846364i	0.989677	−	0.143313i	$-0.0457757\pi$
$547$	19.7948	+	19.7948i	0.846364	+	0.846364i	−0.143313	+	0.989677i	$0.545776\pi$
$548$	−55.3200	+	14.8229i	−2.36315	+	0.633205i
$549$		0			0
$550$	29.9442	+	18.6479i	1.27682	+	0.795150i
$551$	4.78199	+	2.76089i	0.203720	+	0.117618i
$552$		0			0
$553$	7.68975	+	15.7940i	0.327002	+	0.671631i
$554$	14.0583			0.597280
$555$		0			0
$556$	13.0953	+	22.6818i	0.555365	+	0.961921i
$557$	−39.6153	−	10.6149i	−1.67855	−	0.449767i	−0.711157	−	0.703033i	$-0.751829\pi$
$557$	−39.6153	−	10.6149i	−1.67855	−	0.449767i	−0.967397	+	0.253266i	$0.918495\pi$
$558$		0			0
$559$			20.3630i			0.861264i
$560$	3.26125	+	5.11836i	0.137813	+	0.216290i
$561$		0			0
$562$	−2.49190	+	0.667703i	−0.105115	+	0.0281654i
$563$	1.85140	−	6.90950i	0.0780270	−	0.291201i	−0.915876	−	0.401462i	$-0.868502\pi$
$563$	1.85140	−	6.90950i	0.0780270	−	0.291201i	0.993903	+	0.110261i	$0.0351688\pi$
$564$		0			0
$565$	27.1028	−	34.1262i	1.14022	−	1.43570i
$566$		−	32.4129i		−	1.36242i
$567$		0			0
$568$	−2.57784	+	2.57784i	−0.108164	+	0.108164i
$569$	−19.8667	+	34.4101i	−0.832855	+	1.44255i	0.0629097	+	0.998019i	$0.479962\pi$
$569$	−19.8667	+	34.4101i	−0.832855	+	1.44255i	−0.895765	+	0.444528i	$0.853371\pi$
$570$		0			0
$571$	−13.4380	−	23.2753i	−0.562362	−	0.974040i	−0.997290	−	0.0735743i	$-0.976559\pi$
$571$	−13.4380	−	23.2753i	−0.562362	−	0.974040i	0.434928	−	0.900465i	$-0.356774\pi$
$572$	−6.77863	−	25.2982i	−0.283429	−	1.05777i
$573$		0			0
$574$	62.9074	+	21.7095i	2.62571	+	0.906135i
$575$	33.0203	−	17.6217i	1.37704	−	0.734876i
$576$		0			0
$577$	−4.11210	+	15.3466i	−0.171189	+	0.638886i	0.825980	+	0.563699i	$0.190622\pi$
$577$	−4.11210	+	15.3466i	−0.171189	+	0.638886i	−0.997169	+	0.0751873i	$0.976045\pi$
$578$	−1.21575	+	4.53723i	−0.0505684	+	0.188724i
$579$		0			0
$580$	5.79111	+	7.81379i	0.240463	+	0.324450i
$581$	0.889770	+	4.59443i	0.0369139	+	0.190609i
$582$		0			0
$583$	1.42640	+	5.32340i	0.0590755	+	0.220473i
$584$	−3.64767	−	6.31796i	−0.150942	−	0.261439i
$585$		0			0
$586$	4.42920	−	7.67160i	0.182969	−	0.316911i
$587$	4.67480	−	4.67480i	0.192950	−	0.192950i	−0.604020	−	0.796969i	$-0.706435\pi$
$587$	4.67480	−	4.67480i	0.192950	−	0.192950i	0.796969	+	0.604020i	$0.206435\pi$
$588$		0			0
$589$		−	23.1800i		−	0.955116i
$590$	24.2926	+	19.2931i	1.00011	+	0.794283i
$591$		0			0
$592$	2.02423	−	7.55454i	0.0831955	−	0.310490i
$593$	−9.58856	+	2.56925i	−0.393755	+	0.105506i	−0.450263	−	0.892896i	$-0.648670\pi$
$593$	−9.58856	+	2.56925i	−0.393755	+	0.105506i	0.0565085	+	0.998402i	$0.482003\pi$
$594$		0			0
$595$	15.4728	−	16.8879i	0.634321	−	0.692336i
$596$			11.7564i			0.481559i
$597$		0			0
$598$	−42.3804	−	11.3558i	−1.73307	−	0.464373i
$599$	−8.98437	−	15.5614i	−0.367092	−	0.635821i	0.622018	−	0.783003i	$-0.286313\pi$
$599$	−8.98437	−	15.5614i	−0.367092	−	0.635821i	−0.989109	+	0.147182i	$0.952980\pi$
$600$		0			0
$601$	39.8874			1.62704			0.813520	−	0.581538i	$-0.197549\pi$
$601$	39.8874			1.62704			0.813520	+	0.581538i	$0.197549\pi$
$602$	21.9482	+	45.0796i	0.894543	+	1.83731i
$603$		0			0
$604$	47.1506	+	27.2224i	1.91853	+	1.10766i
$605$	3.84568	+	1.66867i	0.156349	+	0.0678412i
$606$		0			0
$607$	30.9589	−	8.29542i	1.25658	−	0.336701i	0.431708	−	0.902014i	$-0.357911\pi$
$607$	30.9589	−	8.29542i	1.25658	−	0.336701i	0.824877	+	0.565313i	$0.191245\pi$
$608$	13.6437	+	13.6437i	0.553323	+	0.553323i
$609$		0			0
$610$	5.70114	−	38.3467i	0.230833	−	1.55261i
$611$	17.5551	+	10.1354i	0.710203	+	0.410036i
$612$		0			0
$613$	16.2623	+	4.35747i	0.656828	+	0.175996i	0.571814	−	0.820383i	$-0.306240\pi$
$613$	16.2623	+	4.35747i	0.656828	+	0.175996i	0.0850137	+	0.996380i	$0.472907\pi$
$614$	−26.1896	+	45.3618i	−1.05693	+	1.83065i
$615$		0			0
$616$	−17.8011	−	20.5065i	−0.717229	−	0.826231i
$617$	10.1234	−	10.1234i	0.407552	−	0.407552i	−0.473332	−	0.880884i	$-0.656949\pi$
$617$	10.1234	−	10.1234i	0.407552	−	0.407552i	0.880884	+	0.473332i	$0.156949\pi$
$618$		0			0
$619$	28.0328	−	16.1847i	1.12673	−	0.650520i	0.183622	−	0.982997i	$-0.441218\pi$
$619$	28.0328	−	16.1847i	1.12673	−	0.650520i	0.943111	+	0.332477i	$0.107885\pi$
$620$	16.2518	−	37.4545i	0.652689	−	1.50421i
$621$		0			0
$622$	−42.0720	−	42.0720i	−1.68693	−	1.68693i
$623$	−11.6180	+	5.65653i	−0.465465	+	0.226624i
$624$		0			0
$625$	22.4364	−	11.0276i	0.897456	−	0.441104i
$626$	12.8090	−	7.39529i	0.511951	−	0.295575i
$627$		0			0
$628$	5.55589	+	20.7349i	0.221704	+	0.827411i
$629$	−29.5163			−1.17689
$630$		0			0
$631$	−8.76242			−0.348827			−0.174413	−	0.984673i	$-0.555803\pi$
$631$	−8.76242			−0.348827			−0.174413	+	0.984673i	$0.555803\pi$
$632$	−5.83867	−	21.7902i	−0.232250	−	0.866768i
$633$		0			0
$634$	−5.05911	+	2.92088i	−0.200923	+	0.116003i
$635$	25.9303	−	32.6497i	1.02901	−	1.29567i
$636$		0			0
$637$	−16.1612	−	6.88643i	−0.640331	−	0.272850i
$638$	−6.28087	−	6.28087i	−0.248662	−	0.248662i
$639$		0			0
$640$	16.4144	+	41.5777i	0.648838	+	1.64350i
$641$	−3.35536	+	1.93722i	−0.132529	+	0.0765156i	−0.564799	−	0.825229i	$-0.691046\pi$
$641$	−3.35536	+	1.93722i	−0.132529	+	0.0765156i	0.432270	+	0.901744i	$0.357713\pi$
$642$		0			0
$643$	−22.2135	+	22.2135i	−0.876016	+	0.876016i	−0.993120	−	0.117103i	$-0.962639\pi$
$643$	−22.2135	+	22.2135i	−0.876016	+	0.876016i	0.117103	+	0.993120i	$0.462639\pi$
$644$	−67.1739	+	13.0091i	−2.64702	+	0.512629i
$645$		0			0
$646$	−19.8287	+	34.3444i	−0.780151	+	1.35126i
$647$	−3.37217	−	0.903571i	−0.132574	−	0.0355231i	0.191922	−	0.981410i	$-0.438528\pi$
$647$	−3.37217	−	0.903571i	−0.132574	−	0.0355231i	−0.324496	+	0.945887i	$0.605195\pi$
$648$		0			0
$649$	−15.5399	−	8.97194i	−0.609993	−	0.352179i
$650$	−28.0389	−	8.52573i	−1.09978	−	0.334407i
$651$		0			0
$652$	8.88149	+	8.88149i	0.347826	+	0.347826i
$653$	20.0441	−	5.37079i	0.784385	−	0.210175i	0.155668	−	0.987809i	$-0.450247\pi$
$653$	20.0441	−	5.37079i	0.784385	−	0.210175i	0.628717	+	0.777634i	$0.283580\pi$
$654$		0			0
$655$	9.32014	−	21.4795i	0.364168	−	0.839274i
$656$	−9.56788	−	5.52402i	−0.373563	−	0.215677i
$657$		0			0
$658$	49.7879	+	3.51612i	1.94093	+	0.137073i
$659$	8.70064			0.338929			0.169464	−	0.985536i	$-0.445796\pi$
$659$	8.70064			0.338929			0.169464	+	0.985536i	$0.445796\pi$
$660$		0			0
$661$	−21.7101	−	37.6029i	−0.844424	−	1.46258i	−0.886121	−	0.463455i	$-0.846610\pi$
$661$	−21.7101	−	37.6029i	−0.844424	−	1.46258i	0.0416969	−	0.999130i	$-0.486724\pi$
$662$	3.19821	+	0.856958i	0.124302	+	0.0333066i
$663$		0			0
$664$		−	6.00977i		−	0.233224i
$665$	−21.8825	+	13.9428i	−0.848569	+	0.540680i
$666$		0			0
$667$	−9.10326	+	2.43921i	−0.352480	+	0.0944466i
$668$	7.73660	−	28.8734i	0.299338	−	1.11714i
$669$		0			0
$670$	5.76935	+	50.2968i	0.222890	+	1.94314i
$671$			22.4246i			0.865693i
$672$		0			0
$673$	12.2145	−	12.2145i	0.470833	−	0.470833i	−0.431351	−	0.902184i	$-0.641963\pi$
$673$	12.2145	−	12.2145i	0.470833	−	0.470833i	0.902184	+	0.431351i	$0.141963\pi$
$674$	12.2019	−	21.1344i	0.470001	−	0.814065i
$675$		0			0
$676$	−11.5767	−	20.0514i	−0.445258	−	0.771209i
$677$	5.44169	+	20.3087i	0.209141	+	0.780526i	0.988147	+	0.153509i	$0.0490575\pi$
$677$	5.44169	+	20.3087i	0.209141	+	0.780526i	−0.779006	+	0.627017i	$0.784276\pi$
$678$		0			0
$679$	−1.91429	−	9.88467i	−0.0734637	−	0.379339i
$680$	−23.6310	+	17.5139i	−0.906207	+	0.671626i
$681$		0			0
$682$	−9.65086	+	36.0175i	−0.369551	+	1.37918i
$683$	−4.56461	+	17.0354i	−0.174660	+	0.651840i	0.821949	+	0.569561i	$0.192887\pi$
$683$	−4.56461	+	17.0354i	−0.174660	+	0.651840i	−0.996609	+	0.0822793i	$0.973780\pi$
$684$		0			0
$685$	5.45119	−	36.6655i	0.208279	−	1.40092i
$686$	−43.2002	+	2.17415i	−1.64939	+	0.0830093i
$687$		0			0
$688$	−2.15437	−	8.04020i	−0.0821344	−	0.306530i
$689$	−2.28928	−	3.96515i	−0.0872146	−	0.151060i
$690$		0			0
$691$	15.0811	−	26.1213i	0.573714	−	0.993701i	−0.422467	−	0.906378i	$-0.638836\pi$
$691$	15.0811	−	26.1213i	0.573714	−	0.993701i	0.996180	−	0.0873225i	$-0.0278310\pi$
$692$	57.5559	−	57.5559i	2.18795	−	2.18795i
$693$		0			0
$694$		−	24.6340i		−	0.935093i
$695$	−16.8413	+	1.93180i	−0.638825	+	0.0732772i
$696$		0			0
$697$	−10.7914	+	40.2741i	−0.408754	+	1.52549i
$698$	18.2944	−	4.90197i	0.692454	−	0.185542i
$699$		0			0
$700$	−45.1336	+	7.18684i	−1.70589	+	0.271637i
$701$			25.9117i			0.978670i	0.872096	+	0.489335i	$0.162760\pi$
$701$			25.9117i			0.978670i	−0.872096	+	0.489335i	$0.837240\pi$
$702$		0			0
$703$	32.2980	+	8.65422i	1.21814	+	0.326400i
$704$	−18.6182	−	32.2477i	−0.701700	−	1.21538i
$705$		0			0
$706$	−24.2063			−0.911018
$707$	33.2064	+	2.34510i	1.24885	+	0.0881964i
$708$		0			0
$709$	12.4525	+	7.18943i	0.467662	+	0.270005i	0.715260	−	0.698858i	$-0.246308\pi$
$709$	12.4525	+	7.18943i	0.467662	+	0.270005i	−0.247599	+	0.968863i	$0.579641\pi$
$710$	−2.05768	−	5.21209i	−0.0772232	−	0.195606i
$711$		0			0
$712$	16.0287	−	4.29488i	0.600702	−	0.160958i
$713$	27.9752	+	27.9752i	1.04768	+	1.04768i
$714$		0			0
$715$	16.7674	+	2.49286i	0.627064	+	0.0932278i
$716$	1.37001	+	0.790977i	0.0511998	+	0.0295602i
$717$		0			0
$718$	6.56158	+	1.75817i	0.244876	+	0.0656143i
$719$	3.38386	−	5.86102i	0.126197	−	0.218579i	−0.796003	−	0.605292i	$-0.793056\pi$
$719$	3.38386	−	5.86102i	0.126197	−	0.218579i	0.922200	+	0.386713i	$0.126390\pi$
$720$		0			0
$721$	−11.8561	+	34.3554i	−0.441544	+	1.27946i
$722$	0.389198	−	0.389198i	0.0144844	−	0.0144844i
$723$		0			0
$724$	38.8058	−	22.4045i	1.44221	−	0.832658i
$725$	−6.13148	+	1.42539i	−0.227718	+	0.0529378i
$726$		0			0
$727$	16.4806	+	16.4806i	0.611233	+	0.611233i	0.943267	−	0.332034i	$-0.107735\pi$
$727$	16.4806	+	16.4806i	0.611233	+	0.611233i	−0.332034	+	0.943267i	$0.607735\pi$
$728$	18.6941	+	12.6282i	0.692851	+	0.468032i
$729$		0			0
$730$	11.1404	−	1.27787i	0.412325	−	0.0472962i
$731$	−27.2051	+	15.7069i	−1.00622	+	0.580940i
$732$		0			0
$733$	−13.5666	−	50.6311i	−0.501093	−	1.87010i	−0.492810	−	0.870137i	$-0.664030\pi$
$733$	−13.5666	−	50.6311i	−0.501093	−	1.87010i	−0.00828279	−	0.999966i	$-0.502637\pi$
$734$	−25.3002			−0.933848
$735$		0			0
$736$	−32.9322			−1.21390
$737$	−7.57921	−	28.2860i	−0.279184	−	1.04193i
$738$		0			0
$739$	−37.8928	+	21.8774i	−1.39391	+	0.804773i	−0.993745	−	0.111671i	$-0.964380\pi$
$739$	−37.8928	+	21.8774i	−1.39391	+	0.804773i	−0.400163	+	0.916444i	$0.631046\pi$
$740$	46.1199	+	36.6282i	1.69540	+	1.34648i
$741$		0			0
$742$	−9.34183	−	6.31055i	−0.342949	−	0.231668i
$743$	−16.4879	−	16.4879i	−0.604881	−	0.604881i	0.336723	−	0.941604i	$-0.390681\pi$
$743$	−16.4879	−	16.4879i	−0.604881	−	0.604881i	−0.941604	+	0.336723i	$0.890681\pi$
$744$		0			0
$745$	−6.98041	−	3.02886i	−0.255743	−	0.110969i
$746$	36.3490	−	20.9861i	1.33083	−	0.768356i
$747$		0			0
$748$	28.5699	−	28.5699i	1.04462	−	1.04462i
$749$	−2.62419	+	7.60411i	−0.0958859	+	0.277848i
$750$		0			0
$751$	−1.48307	+	2.56876i	−0.0541181	+	0.0937353i	−0.891815	−	0.452400i	$-0.850568\pi$
$751$	−1.48307	+	2.56876i	−0.0541181	+	0.0937353i	0.837697	+	0.546135i	$0.183901\pi$
$752$	−8.00382	−	2.14462i	−0.291869	−	0.0782061i
$753$		0			0
$754$	6.39070	+	3.68967i	0.232736	+	0.134370i
$755$	−28.3111	+	20.9825i	−1.03035	+	0.763631i
$756$		0			0
$757$	−31.2106	−	31.2106i	−1.13437	−	1.13437i	−0.989443	−	0.144925i	$-0.953706\pi$
$757$	−31.2106	−	31.2106i	−1.13437	−	1.13437i	−0.144925	−	0.989443i	$-0.546294\pi$
$758$	−16.6379	+	4.45811i	−0.604316	+	0.161926i
$759$		0			0
$760$	30.9932	−	12.2358i	1.12424	−	0.443838i
$761$	−34.8304	−	20.1094i	−1.26260	−	0.728963i	−0.289025	−	0.957322i	$-0.593331\pi$
$761$	−34.8304	−	20.1094i	−1.26260	−	0.728963i	−0.973577	+	0.228358i	$0.926664\pi$
$762$		0			0
$763$	−43.7558	−	3.09012i	−1.58407	−	0.111870i
$764$	−23.3195			−0.843670
$765$		0			0
$766$	−10.6938	−	18.5223i	−0.386384	−	0.669236i
$767$	14.3994	+	3.85830i	0.519931	+	0.139315i
$768$		0			0
$769$			24.6136i			0.887589i	0.896129	+	0.443794i	$0.146368\pi$
$769$			24.6136i			0.887589i	−0.896129	+	0.443794i	$0.853632\pi$
$770$	39.8065	−	12.5540i	1.43453	−	0.452413i
$771$		0			0
$772$	−17.0357	+	4.56471i	−0.613130	+	0.164288i
$773$	13.3233	−	49.7233i	0.479206	−	1.78842i	−0.125637	−	0.992076i	$-0.540097\pi$
$773$	13.3233	−	49.7233i	0.479206	−	1.78842i	0.604843	−	0.796345i	$-0.293236\pi$
$774$		0			0
$775$	18.0518	+	19.2992i	0.648440	+	0.693249i
$776$			12.9297i			0.464149i
$777$		0			0
$778$	−14.8893	+	14.8893i	−0.533807	+	0.533807i
$779$	23.6169	−	40.9056i	0.846162	−	1.46560i
$780$		0			0
$781$	1.62063	+	2.80701i	0.0579906	+	0.100443i
$782$	−17.5185	−	65.3798i	−0.626459	−	2.33798i
$783$		0			0
$784$	7.10972	+	1.00924i	0.253918	+	0.0360442i
$785$	−13.7429	−	2.04320i	−0.490503	−	0.0729248i
$786$		0			0
$787$	−6.64831	+	24.8118i	−0.236987	+	0.884446i	0.740257	+	0.672324i	$0.234704\pi$
$787$	−6.64831	+	24.8118i	−0.236987	+	0.884446i	−0.977243	+	0.212121i	$0.931963\pi$
$788$	−6.76238	+	25.2375i	−0.240900	+	0.899050i
$789$		0			0
$790$	34.2976	+	5.09914i	1.22025	+	0.181419i
$791$	−9.80382	−	50.6232i	−0.348584	−	1.79995i
$792$		0			0
$793$	−4.82175	−	17.9950i	−0.171225	−	0.639022i
$794$	−17.9759	−	31.1351i	−0.637940	−	1.10494i
$795$		0			0
$796$	−29.8386	+	51.6819i	−1.05760	+	1.83182i
$797$	1.12818	−	1.12818i	0.0399621	−	0.0399621i	−0.686843	−	0.726805i	$-0.741004\pi$
$797$	1.12818	−	1.12818i	0.0399621	−	0.0399621i	0.726805	+	0.686843i	$0.241004\pi$
$798$		0			0
$799$			31.2716i			1.10631i
$800$	−21.9847	−	0.734239i	−0.777276	−	0.0259593i
$801$		0			0
$802$	−11.5231	+	43.0047i	−0.406893	+	1.51855i
$803$	−6.26516	+	1.67874i	−0.221093	+	0.0592416i
$804$		0			0
$805$	9.58218	−	43.2365i	0.337727	−	1.52389i
$806$		−	30.9780i		−	1.09115i
$807$		0			0
$808$	−41.2930	−	11.0644i	−1.45268	−	0.389245i
$809$	18.4134	+	31.8929i	0.647381	+	1.12130i	0.983746	+	0.179565i	$0.0574689\pi$
$809$	18.4134	+	31.8929i	0.647381	+	1.12130i	−0.336366	+	0.941731i	$0.609198\pi$
$810$		0			0
$811$	9.33779			0.327894			0.163947	−	0.986469i	$-0.447577\pi$
$811$	9.33779			0.327894			0.163947	+	0.986469i	$0.447577\pi$
$812$	11.4792	+	0.810683i	0.402841	+	0.0284494i
$813$		0			0
$814$	−46.5821	−	26.8942i	−1.63270	−	0.942640i
$815$	−7.56163	+	2.98525i	−0.264872	+	0.104569i
$816$		0			0
$817$	34.3743	−	9.21057i	1.20261	−	0.322237i
$818$	27.1593	+	27.1593i	0.949602	+	0.949602i
$819$		0			0
$820$	66.8399	−	49.5376i	2.33415	−	1.72993i
$821$	−13.7473	−	7.93699i	−0.479783	−	0.277003i	0.240543	−	0.970639i	$-0.422675\pi$
$821$	−13.7473	−	7.93699i	−0.479783	−	0.277003i	−0.720326	+	0.693636i	$0.756008\pi$
$822$		0			0
$823$	−13.2164	−	3.54133i	−0.460696	−	0.123443i	0.0210040	−	0.999779i	$-0.493314\pi$
$823$	−13.2164	−	3.54133i	−0.460696	−	0.123443i	−0.481700	+	0.876336i	$0.659980\pi$
$824$	23.3362	−	40.4194i	0.812954	−	1.40808i
$825$		0			0
$826$	36.0360	−	6.97882i	1.25385	−	0.242824i
$827$	−1.84947	+	1.84947i	−0.0643124	+	0.0643124i	−0.738531	−	0.674219i	$-0.764480\pi$
$827$	−1.84947	+	1.84947i	−0.0643124	+	0.0643124i	0.674219	+	0.738531i	$0.264480\pi$
$828$		0			0
$829$	28.8636	−	16.6644i	1.00247	−	0.578778i	0.0934940	−	0.995620i	$-0.470196\pi$
$829$	28.8636	−	16.6644i	1.00247	−	0.578778i	0.908979	+	0.416842i	$0.136863\pi$
$830$	8.47408	+	3.67697i	0.294139	+	0.127630i
$831$		0			0
$832$	21.8744	+	21.8744i	0.758359	+	0.758359i
$833$	−3.26554	−	26.9033i	−0.113144	−	0.932144i
$834$		0			0
$835$	15.1505	+	12.0325i	0.524306	+	0.416401i
$836$	−39.6392	+	22.8857i	−1.37095	+	0.791518i
$837$		0			0
$838$	−0.261684	−	0.976617i	−0.00903971	−	0.0337367i
$839$	26.2661			0.906808			0.453404	−	0.891305i	$-0.350210\pi$
$839$	26.2661			0.906808			0.453404	+	0.891305i	$0.350210\pi$
$840$		0			0
$841$	−27.4149			−0.945342
$842$	−1.47526	−	5.50574i	−0.0508408	−	0.189740i
$843$		0			0
$844$	−33.2418	+	19.1922i	−1.14423	+	0.660621i
$845$	14.8882	−	1.70777i	0.512171	−	0.0587492i
$846$		0			0
$847$	4.45967	−	2.17131i	0.153236	−	0.0746071i
$848$	1.32341	+	1.32341i	0.0454461	+	0.0454461i
$849$		0			0
$850$	−10.2372	−	44.0364i	−0.351133	−	1.51044i
$851$	−49.4239	+	28.5349i	−1.69423	+	0.978164i
$852$		0			0
$853$	−19.2905	+	19.2905i	−0.660495	+	0.660495i	−0.955497	−	0.295002i	$-0.904680\pi$
$853$	−19.2905	+	19.2905i	−0.660495	+	0.660495i	0.295002	+	0.955497i	$0.404680\pi$
$854$	−30.0702	−	34.6402i	−1.02898	−	1.18536i
$855$		0			0
$856$	5.16515	−	8.94630i	0.176541	−	0.305778i
$857$	32.5286	+	8.71601i	1.11116	+	0.297733i	0.767299	−	0.641289i	$-0.221600\pi$
$857$	32.5286	+	8.71601i	1.11116	+	0.297733i	0.343856	+	0.939022i	$0.388267\pi$
$858$		0			0
$859$	−3.29570	−	1.90278i	−0.112448	−	0.0649219i	0.442721	−	0.896659i	$-0.354013\pi$
$859$	−3.29570	−	1.90278i	−0.112448	−	0.0649219i	−0.555169	+	0.831737i	$0.687346\pi$
$860$	62.0001	+	9.21777i	2.11419	+	0.314323i
$861$		0			0
$862$	2.68926	+	2.68926i	0.0915967	+	0.0915967i
$863$	26.6306	−	7.13565i	0.906517	−	0.242901i	0.224704	−	0.974427i	$-0.427858\pi$
$863$	26.6306	−	7.13565i	0.906517	−	0.242901i	0.681813	+	0.731527i	$0.261192\pi$
$864$		0			0
$865$	19.3457	+	49.0026i	0.657774	+	1.66614i
$866$	−34.7723	−	20.0758i	−1.18161	−	0.682204i
$867$		0			0
$868$	−21.1472	−	43.4344i	−0.717782	−	1.47426i
$869$	−20.0567			−0.680378
$870$		0			0
$871$	12.1641	+	21.0689i	0.412166	+	0.713893i
$872$	54.4115	+	14.5795i	1.84261	+	0.493725i
$873$		0			0
$874$			76.6778i			2.59367i
$875$	7.36079	−	28.6499i	0.248840	−	0.968545i
$876$		0			0
$877$	−16.6920	+	4.47261i	−0.563649	+	0.151029i	−0.529382	−	0.848384i	$-0.677576\pi$
$877$	−16.6920	+	4.47261i	−0.563649	+	0.151029i	−0.0342666	+	0.999413i	$0.510910\pi$
$878$	−22.6953	+	84.7002i	−0.765931	+	2.85849i
$879$		0			0
$880$	−6.88422	+	0.789663i	−0.232067	+	0.0266195i
$881$		−	55.6733i		−	1.87568i	−0.347064	−	0.937841i	$-0.612822\pi$
$881$		−	55.6733i		−	1.87568i	0.347064	−	0.937841i	$-0.387178\pi$
$882$		0			0
$883$	−13.5326	+	13.5326i	−0.455408	+	0.455408i	−0.897145	−	0.441737i	$-0.854362\pi$
$883$	−13.5326	+	13.5326i	−0.455408	+	0.455408i	0.441737	+	0.897145i	$0.354362\pi$
$884$	−16.7833	+	29.0695i	−0.564483	+	0.977713i
$885$		0			0
$886$	14.6806	+	25.4276i	0.493205	+	0.854256i
$887$	12.1926	+	45.5036i	0.409389	+	1.52786i	0.795815	+	0.605540i	$0.207043\pi$
$887$	12.1926	+	45.5036i	0.409389	+	1.52786i	−0.386426	+	0.922321i	$0.626290\pi$
$888$		0			0
$889$	−9.37967	−	48.4330i	−0.314584	−	1.62439i
$890$	−3.75089	+	25.2290i	−0.125730	+	0.845679i
$891$		0			0
$892$	2.33113	−	8.69989i	0.0780519	−	0.291294i
$893$	9.16890	−	34.2188i	0.306825	−	1.14509i
$894$		0			0
$895$	−0.822612	+	0.609670i	−0.0274969	+	0.0203790i
$896$	49.9969	+	17.2540i	1.67028	+	0.576416i
$897$		0			0
$898$	−14.6658	−	54.7335i	−0.489404	−	1.82648i
$899$	−3.32701	−	5.76256i	−0.110962	−	0.192192i
$900$		0			0
$901$	3.53164	−	6.11698i	0.117656	−	0.203786i
$902$	−53.7271	+	53.7271i	−1.78892	+	1.78892i
$903$		0			0
$904$			66.2179i			2.20237i
$905$	3.30507	+	28.8134i	0.109864	+	0.957789i
$906$		0			0
$907$	0.109787	−	0.409732i	0.00364543	−	0.0136049i	−0.964079	−	0.265615i	$-0.914425\pi$
$907$	0.109787	−	0.409732i	0.00364543	−	0.0136049i	0.967725	+	0.252010i	$0.0810916\pi$
$908$	22.5657	−	6.04646i	0.748870	−	0.200659i
$909$		0			0
$910$	−29.2440	+	18.6333i	−0.969431	+	0.617689i
$911$			0.818653i			0.0271232i	0.999908	+	0.0135616i	$0.00431692\pi$
$911$			0.818653i			0.0271232i	−0.999908	+	0.0135616i	$0.995683\pi$
$912$		0			0
$913$	−5.16112	−	1.38292i	−0.170808	−	0.0457679i
$914$	38.2373	+	66.2290i	1.26478	+	2.19066i
$915$		0			0
$916$	−87.8939			−2.90410
$917$	−12.1275	−	24.9088i	−0.400487	−	0.822563i
$918$		0			0
$919$	−15.9425	−	9.20443i	−0.525896	−	0.303626i	0.213448	−	0.976954i	$-0.431531\pi$
$919$	−15.9425	−	9.20443i	−0.525896	−	0.303626i	−0.739343	+	0.673328i	$0.764864\pi$
$920$	−22.6377	+	52.1716i	−0.746343	+	1.72005i
$921$		0			0
$922$	25.5830	−	6.85495i	0.842532	−	0.225756i
$923$	−1.90406	−	1.90406i	−0.0626730	−	0.0626730i
$924$		0			0
$925$	−33.6303	+	17.9472i	−1.10576	+	0.590102i
$926$	−31.1760	−	17.9995i	−1.02451	−	0.591499i
$927$		0			0
$928$	5.35009	+	1.43355i	0.175625	+	0.0470586i
$929$	−18.2734	+	31.6505i	−0.599532	+	1.03842i	0.393358	+	0.919386i	$0.371313\pi$
$929$	−18.2734	+	31.6505i	−0.599532	+	1.03842i	−0.992890	+	0.119035i	$0.962020\pi$
$930$		0			0
$931$	−4.31480	+	30.3962i	−0.141412	+	0.996196i
$932$	−25.9790	+	25.9790i	−0.850971	+	0.850971i
$933$		0			0
$934$	46.7373	−	26.9838i	1.52929	−	0.882938i
$935$	9.60292	+	24.3242i	0.314049	+	0.795485i
$936$		0			0
$937$	−9.73540	−	9.73540i	−0.318042	−	0.318042i	0.529973	−	0.848015i	$-0.322202\pi$
$937$	−9.73540	−	9.73540i	−0.318042	−	0.318042i	−0.848015	+	0.529973i	$0.822202\pi$
$938$	49.6380	+	33.5312i	1.62074	+	1.09483i
$939$		0			0
$940$	38.8065	−	48.8627i	1.26573	−	1.59372i
$941$	−26.9972	+	15.5869i	−0.880084	+	0.508117i	−0.870686	−	0.491839i	$-0.836325\pi$
$941$	−26.9972	+	15.5869i	−0.880084	+	0.508117i	−0.00939807	+	0.999956i	$0.502992\pi$
$942$		0			0
$943$	20.8652	+	77.8701i	0.679465	+	2.53580i
$944$	−6.09369			−0.198333
$945$		0			0
$946$	−57.2462			−1.86123
$947$	2.02380	+	7.55291i	0.0657645	+	0.245437i	0.990981	−	0.134003i	$-0.0427833\pi$
$947$	2.02380	+	7.55291i	0.0657645	+	0.245437i	−0.925216	+	0.379440i	$0.876117\pi$
$948$		0			0
$949$	4.66662	−	2.69427i	0.151485	−	0.0874598i
$950$	−1.70957	+	51.1882i	−0.0554657	+	1.66076i
$951$		0			0
$952$	−2.45172	+	34.7162i	−0.0794608	+	1.12516i
$953$	−14.8359	−	14.8359i	−0.480583	−	0.480583i	0.424735	−	0.905318i	$-0.360367\pi$
$953$	−14.8359	−	14.8359i	−0.480583	−	0.480583i	−0.905318	+	0.424735i	$0.860367\pi$
$954$		0			0
$955$	6.00794	−	13.8461i	0.194412	−	0.448049i
$956$	47.2305	−	27.2686i	1.52754	−	0.881928i
$957$		0			0
$958$	−16.4139	+	16.4139i	−0.530310	+	0.530310i
$959$	−28.7519	−	33.1215i	−0.928447	−	1.06955i
$960$		0			0
$961$	1.53342	−	2.65597i	0.0494653	−	0.0856764i
$962$	43.1634	+	11.5656i	1.39164	+	0.372889i
$963$		0			0
$964$	−8.45023	−	4.87874i	−0.272164	−	0.157134i
$965$	1.67869	−	11.2911i	0.0540389	−	0.363474i
$966$		0			0
$967$	−38.1841	−	38.1841i	−1.22792	−	1.22792i	−0.964750	−	0.263167i	$-0.915233\pi$
$967$	−38.1841	−	38.1841i	−1.22792	−	1.22792i	−0.263167	−	0.964750i	$-0.584767\pi$
$968$	−6.15277	+	1.64863i	−0.197758	+	0.0529890i
$969$		0			0
$970$	−18.2315	−	7.91080i	−0.585378	−	0.254000i
$971$	34.5090	+	19.9238i	1.10745	+	0.639384i	0.938167	−	0.346184i	$-0.112523\pi$
$971$	34.5090	+	19.9238i	1.10745	+	0.639384i	0.169279	+	0.985568i	$0.445856\pi$
$972$		0			0
$973$	−11.2275	+	16.6207i	−0.359938	+	0.532834i
$974$	10.8308			0.347040
$975$		0			0
$976$	3.80767	+	6.59508i	0.121881	+	0.211103i
$977$	15.9726	+	4.27984i	0.511008	+	0.136924i	0.505104	−	0.863058i	$-0.331454\pi$
$977$	15.9726	+	4.27984i	0.511008	+	0.136924i	0.00590397	+	0.999983i	$0.498121\pi$
$978$		0			0
$979$		−	14.7536i		−	0.471526i
$980$	−28.2831	+	46.0894i	−0.903471	+	1.47227i
$981$		0			0
$982$	−4.50621	+	1.20744i	−0.143799	+	0.0385308i
$983$	0.230258	−	0.859334i	0.00734408	−	0.0274085i	−0.962157	−	0.272497i	$-0.912150\pi$
$983$	0.230258	−	0.859334i	0.00734408	−	0.0274085i	0.969501	+	0.245089i	$0.0788171\pi$
$984$		0			0
$985$	−13.2427	−	10.5173i	−0.421948	−	0.335109i
$986$			11.3840i			0.362541i
$987$		0			0
$988$	26.8882	−	26.8882i	0.855428	−	0.855428i
$989$	−30.3693	+	52.6012i	−0.965689	+	1.67262i
$990$		0			0
$991$	−25.8144	−	44.7119i	−0.820021	−	1.42032i	−0.905665	−	0.423993i	$-0.860628\pi$
$991$	−25.8144	−	44.7119i	−0.820021	−	1.42032i	0.0856440	−	0.996326i	$-0.472705\pi$
$992$	−6.01795	−	22.4593i	−0.191070	−	0.713083i
$993$		0			0
$994$	−6.26750	−	2.16292i	−0.198793	−	0.0686038i
$995$	−22.9990	−	31.0319i	−0.729116	−	0.983778i
$996$		0			0
$997$	6.08631	−	22.7144i	0.192755	−	0.719373i	−0.800081	−	0.599892i	$-0.795210\pi$
$997$	6.08631	−	22.7144i	0.192755	−	0.719373i	0.992836	−	0.119481i	$-0.0381230\pi$
$998$	0.124776	−	0.465669i	0.00394970	−	0.0147405i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.107.2	yes	64
3.2	odd	2	inner	315.2.ce.a.107.15	yes	64
5.3	odd	4	inner	315.2.ce.a.233.2	yes	64
7.4	even	3	inner	315.2.ce.a.242.15	yes	64
15.8	even	4	inner	315.2.ce.a.233.15	yes	64
21.11	odd	6	inner	315.2.ce.a.242.2	yes	64
35.18	odd	12	inner	315.2.ce.a.53.15	yes	64
105.53	even	12	inner	315.2.ce.a.53.2	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.2	✓	64	105.53	even	12	inner
315.2.ce.a.53.15	yes	64	35.18	odd	12	inner
315.2.ce.a.107.2	yes	64	1.1	even	1	trivial
315.2.ce.a.107.15	yes	64	3.2	odd	2	inner
315.2.ce.a.233.2	yes	64	5.3	odd	4	inner
315.2.ce.a.233.15	yes	64	15.8	even	4	inner
315.2.ce.a.242.2	yes	64	21.11	odd	6	inner
315.2.ce.a.242.15	yes	64	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	315.2.ce.a.107.2

Level	$315$
Weight	$2$
Character	315.107
Analytic conductor	$2.515$
Analytic rank	$0$
Dimension	$64$
Inner twists	$8$