LMFDB - Embedded newform 315.2.ce.a.107.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [315,2,Mod(53,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			107.16
Character	$\chi$	$=$	315.107
Dual form			315.2.ce.a.53.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.695956 + 2.59734i) q^{2} +(-4.52979 + 2.61528i) q^{4} +(-1.27254 - 1.83865i) q^{5} +(-1.50727 + 2.17442i) q^{7} +(-6.14253 - 6.14253i) q^{8} +(3.88997 - 4.58485i) q^{10} +(-3.60099 + 2.07903i) q^{11} +(-0.702126 + 0.702126i) q^{13} +(-6.69673 - 2.40161i) q^{14} +(6.44878 - 11.1696i) q^{16} +(-1.31583 - 0.352577i) q^{17} +(5.22461 + 3.01643i) q^{19} +(10.5729 + 5.00065i) q^{20} +(-7.90609 - 7.90609i) q^{22} +(-0.205581 + 0.0550852i) q^{23} +(-1.76127 + 4.67952i) q^{25} +(-2.31231 - 1.33501i) q^{26} +(1.14092 - 13.7916i) q^{28} +0.879133 q^{29} +(4.76368 + 8.25093i) q^{31} +(16.7177 + 4.47950i) q^{32} -3.66305i q^{34} +(5.91608 + 0.00430290i) q^{35} +(-3.13636 + 0.840384i) q^{37} +(-4.19861 + 15.6694i) q^{38} +(-3.47734 + 19.1106i) q^{40} +1.25212i q^{41} +(-4.28935 + 4.28935i) q^{43} +(10.8745 - 18.8352i) q^{44} +(-0.286150 - 0.495627i) q^{46} +(-0.0279906 - 0.104462i) q^{47} +(-2.45625 - 6.55491i) q^{49} +(-13.3801 - 1.31789i) q^{50} +(1.34423 - 5.01674i) q^{52} +(-1.29555 + 4.83507i) q^{53} +(8.40502 + 3.97530i) q^{55} +(22.6150 - 4.09799i) q^{56} +(0.611838 + 2.28341i) q^{58} +(0.113063 + 0.195831i) q^{59} +(5.96760 - 10.3362i) q^{61} +(-18.1152 + 18.1152i) q^{62} +20.7441i q^{64} +(2.18445 + 0.397480i) q^{65} +(0.825199 - 3.07969i) q^{67} +(6.88254 - 1.84417i) q^{68} +(4.10616 + 15.3691i) q^{70} -9.78757i q^{71} +(-6.60621 - 1.77013i) q^{73} +(-4.36553 - 7.56133i) q^{74} -31.5552 q^{76} +(0.906979 - 10.9637i) q^{77} +(1.88223 + 1.08671i) q^{79} +(-28.7434 + 2.35676i) q^{80} +(-3.25219 + 0.871421i) q^{82} +(-3.75964 - 3.75964i) q^{83} +(1.02619 + 2.86803i) q^{85} +(-14.1261 - 8.15572i) q^{86} +(34.8897 + 9.34867i) q^{88} +(-7.19793 + 12.4672i) q^{89} +(-0.468424 - 2.58502i) q^{91} +(0.787175 - 0.787175i) q^{92} +(0.251845 - 0.145403i) q^{94} +(-1.10238 - 13.4448i) q^{95} +(3.88891 + 3.88891i) q^{97} +(15.3159 - 10.9417i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.695956	+	2.59734i	0.492115	+	1.83660i	0.545621	+	0.838032i	$0.316294\pi$
$2$	0.695956	+	2.59734i	0.492115	+	1.83660i	−0.0535055	+	0.998568i	$0.517039\pi$
$3$		0			0
$3$		0			0
$4$	−4.52979	+	2.61528i	−2.26490	+	1.30764i
$5$	−1.27254	−	1.83865i	−0.569098	−	0.822270i
$5$	−1.27254	−	1.83865i	−0.569098	−	0.822270i
$6$		0			0
$7$	−1.50727	+	2.17442i	−0.569696	+	0.821855i
$7$	−1.50727	+	2.17442i	−0.569696	+	0.821855i
$8$	−6.14253	−	6.14253i	−2.17171	−	2.17171i
$9$		0			0
$10$	3.88997	−	4.58485i	1.23012	−	1.44986i
$11$	−3.60099	+	2.07903i	−1.08574	+	0.626852i	−0.932439	−	0.361328i	$-0.882323\pi$
$11$	−3.60099	+	2.07903i	−1.08574	+	0.626852i	−0.153300	+	0.988180i	$0.548990\pi$
$12$		0			0
$13$	−0.702126	+	0.702126i	−0.194735	+	0.194735i	−0.797738	−	0.603004i	$-0.793970\pi$
$13$	−0.702126	+	0.702126i	−0.194735	+	0.194735i	0.603004	+	0.797738i	$0.293970\pi$
$14$	−6.69673	−	2.40161i	−1.78978	−	0.641856i
$15$		0			0
$16$	6.44878	−	11.1696i	1.61220	−	2.79241i
$17$	−1.31583	−	0.352577i	−0.319137	−	0.0855124i	0.0956947	−	0.995411i	$-0.469493\pi$
$17$	−1.31583	−	0.352577i	−0.319137	−	0.0855124i	−0.414831	+	0.909898i	$0.636159\pi$
$18$		0			0
$19$	5.22461	+	3.01643i	1.19861	+	0.692016i	0.960245	−	0.279160i	$-0.0900559\pi$
$19$	5.22461	+	3.01643i	1.19861	+	0.692016i	0.238363	+	0.971176i	$0.423389\pi$
$20$	10.5729	+	5.00065i	2.36418	+	1.11818i
$21$		0			0
$22$	−7.90609	−	7.90609i	−1.68558	−	1.68558i
$23$	−0.205581	+	0.0550852i	−0.0428665	+	0.0114861i	−0.280189	−	0.959945i	$-0.590397\pi$
$23$	−0.205581	+	0.0550852i	−0.0428665	+	0.0114861i	0.237322	+	0.971431i	$0.423730\pi$
$24$		0			0
$25$	−1.76127	+	4.67952i	−0.352254	+	0.935904i
$26$	−2.31231	−	1.33501i	−0.453482	−	0.261818i
$27$		0			0
$28$	1.14092	−	13.7916i	0.215613	−	2.60637i
$29$	0.879133			0.163251			0.0816255	−	0.996663i	$-0.473989\pi$
$29$	0.879133			0.163251			0.0816255	+	0.996663i	$0.473989\pi$
$30$		0			0
$31$	4.76368	+	8.25093i	0.855582	+	1.48191i	0.876104	+	0.482122i	$0.160134\pi$
$31$	4.76368	+	8.25093i	0.855582	+	1.48191i	−0.0205224	+	0.999789i	$0.506533\pi$
$32$	16.7177	+	4.47950i	2.95530	+	0.791871i
$33$		0			0
$34$		−	3.66305i		−	0.628208i
$35$	5.91608	+	0.00430290i	1.00000	+	0.000727323i
$36$		0			0
$37$	−3.13636	+	0.840384i	−0.515614	+	0.138158i	−0.507237	−	0.861807i	$-0.669333\pi$
$37$	−3.13636	+	0.840384i	−0.515614	+	0.138158i	−0.00837687	+	0.999965i	$0.502666\pi$
$38$	−4.19861	+	15.6694i	−0.681104	+	2.54191i
$39$		0			0
$40$	−3.47734	+	19.1106i	−0.549815	+	3.02165i
$41$			1.25212i			0.195548i	0.995209	+	0.0977742i	$0.0311723\pi$
$41$			1.25212i			0.195548i	−0.995209	+	0.0977742i	$0.968828\pi$
$42$		0			0
$43$	−4.28935	+	4.28935i	−0.654120	+	0.654120i	−0.953982	−	0.299862i	$-0.903059\pi$
$43$	−4.28935	+	4.28935i	−0.654120	+	0.654120i	0.299862	+	0.953982i	$0.403059\pi$
$44$	10.8745	−	18.8352i	1.63939	−	2.83951i
$45$		0			0
$46$	−0.286150	−	0.495627i	−0.0421906	−	0.0730762i
$47$	−0.0279906	−	0.104462i	−0.00408285	−	0.0152374i	0.963854	−	0.266430i	$-0.0858440\pi$
$47$	−0.0279906	−	0.104462i	−0.00408285	−	0.0152374i	−0.967937	+	0.251192i	$0.919177\pi$
$48$		0			0
$49$	−2.45625	−	6.55491i	−0.350893	−	0.936416i
$50$	−13.3801	−	1.31789i	−1.89223	−	0.186377i
$51$		0			0
$52$	1.34423	−	5.01674i	0.186411	−	0.695697i
$53$	−1.29555	+	4.83507i	−0.177958	+	0.664148i	0.818071	+	0.575117i	$0.195044\pi$
$53$	−1.29555	+	4.83507i	−0.177958	+	0.664148i	−0.996029	+	0.0890305i	$0.971623\pi$
$54$		0			0
$55$	8.40502	+	3.97530i	1.13333	+	0.536030i
$56$	22.6150	−	4.09799i	3.02205	−	0.547618i
$57$		0			0
$58$	0.611838	+	2.28341i	0.0803383	+	0.299827i
$59$	0.113063	+	0.195831i	0.0147196	+	0.0254951i	0.873291	−	0.487198i	$-0.161981\pi$
$59$	0.113063	+	0.195831i	0.0147196	+	0.0254951i	−0.858572	+	0.512693i	$0.828648\pi$
$60$		0			0
$61$	5.96760	−	10.3362i	0.764073	−	1.32341i	−0.176662	−	0.984272i	$-0.556530\pi$
$61$	5.96760	−	10.3362i	0.764073	−	1.32341i	0.940735	−	0.339142i	$-0.110137\pi$
$62$	−18.1152	+	18.1152i	−2.30063	+	2.30063i
$63$		0			0
$64$			20.7441i			2.59301i
$65$	2.18445	+	0.397480i	0.270948	+	0.0493013i
$66$		0			0
$67$	0.825199	−	3.07969i	0.100814	−	0.376243i	−0.897023	−	0.441985i	$-0.854275\pi$
$67$	0.825199	−	3.07969i	0.100814	−	0.376243i	0.997837	+	0.0657413i	$0.0209412\pi$
$68$	6.88254	−	1.84417i	0.834630	−	0.223639i
$69$		0			0
$70$	4.10616	+	15.3691i	0.490779	+	1.83696i
$71$		−	9.78757i		−	1.16157i	−0.814057	−	0.580785i	$-0.802746\pi$
$71$		−	9.78757i		−	1.16157i	0.814057	−	0.580785i	$-0.197254\pi$
$72$		0			0
$73$	−6.60621	−	1.77013i	−0.773198	−	0.207178i	−0.149414	−	0.988775i	$-0.547739\pi$
$73$	−6.60621	−	1.77013i	−0.773198	−	0.207178i	−0.623784	+	0.781597i	$0.714406\pi$
$74$	−4.36553	−	7.56133i	−0.507483	−	0.878986i
$75$		0			0
$76$	−31.5552			−3.61963
$77$	0.906979	−	10.9637i	0.103360	−	1.24944i
$78$		0			0
$79$	1.88223	+	1.08671i	0.211767	+	0.122264i	0.602132	−	0.798396i	$-0.294318\pi$
$79$	1.88223	+	1.08671i	0.211767	+	0.122264i	−0.390365	+	0.920660i	$0.627651\pi$
$80$	−28.7434	+	2.35676i	−3.21361	+	0.263493i
$81$		0			0
$82$	−3.25219	+	0.871421i	−0.359144	+	0.0962324i
$83$	−3.75964	−	3.75964i	−0.412674	−	0.412674i	0.469995	−	0.882669i	$-0.344256\pi$
$83$	−3.75964	−	3.75964i	−0.412674	−	0.412674i	−0.882669	+	0.469995i	$0.844256\pi$
$84$		0			0
$85$	1.02619	+	2.86803i	0.111306	+	0.311081i
$86$	−14.1261	−	8.15572i	−1.52326	−	0.879454i
$87$		0			0
$88$	34.8897	+	9.34867i	3.71925	+	0.996571i
$89$	−7.19793	+	12.4672i	−0.762979	+	1.32152i	0.178330	+	0.983971i	$0.442931\pi$
$89$	−7.19793	+	12.4672i	−0.762979	+	1.32152i	−0.941309	+	0.337547i	$0.890403\pi$
$90$		0			0
$91$	−0.468424	−	2.58502i	−0.0491042	−	0.270984i
$92$	0.787175	−	0.787175i	0.0820686	−	0.0820686i
$93$		0			0
$94$	0.251845	−	0.145403i	0.0259758	−	0.0149971i
$95$	−1.10238	−	13.4448i	−0.113101	−	1.37940i
$96$		0			0
$97$	3.88891	+	3.88891i	0.394859	+	0.394859i	0.876415	−	0.481556i	$-0.159928\pi$
$97$	3.88891	+	3.88891i	0.394859	+	0.394859i	−0.481556	+	0.876415i	$0.659928\pi$
$98$	15.3159	−	10.9417i	1.54714	−	1.10527i
$99$		0			0
$100$	−4.26005	−	25.8035i	−0.426005	−	2.58035i
$101$	7.89380	−	4.55749i	0.785463	−	0.453487i	−0.0528999	−	0.998600i	$-0.516846\pi$
$101$	7.89380	−	4.55749i	0.785463	−	0.453487i	0.838363	+	0.545113i	$0.183513\pi$
$102$		0			0
$103$	2.32007	+	8.65861i	0.228603	+	0.853158i	0.980929	+	0.194367i	$0.0622652\pi$
$103$	2.32007	+	8.65861i	0.228603	+	0.853158i	−0.752326	+	0.658791i	$0.771068\pi$
$104$	8.62567			0.845816
$105$		0			0
$106$	−13.4600			−1.30735
$107$	3.50023	+	13.0630i	0.338380	+	1.26285i	0.900158	+	0.435564i	$0.143451\pi$
$107$	3.50023	+	13.0630i	0.338380	+	1.26285i	−0.561778	+	0.827288i	$0.689882\pi$
$108$		0			0
$109$	−3.19131	+	1.84250i	−0.305672	+	0.176480i	−0.644988	−	0.764192i	$-0.723138\pi$
$109$	−3.19131	+	1.84250i	−0.305672	+	0.176480i	0.339316	+	0.940672i	$0.389804\pi$
$110$	−4.47570	+	24.5974i	−0.426741	+	2.34527i
$111$		0			0
$112$	14.5674	+	30.8581i	1.37649	+	2.91581i
$113$	13.2212	+	13.2212i	1.24375	+	1.24375i	0.958434	+	0.285316i	$0.0920985\pi$
$113$	13.2212	+	13.2212i	1.24375	+	1.24375i	0.285316	+	0.958434i	$0.407901\pi$
$114$		0			0
$115$	0.362893	+	0.307893i	0.0338399	+	0.0287112i
$116$	−3.98229	+	2.29918i	−0.369746	+	0.213473i
$117$		0			0
$118$	−0.429954	+	0.429954i	−0.0395805	+	0.0395805i
$119$	2.74997	−	2.32975i	0.252090	−	0.213568i
$120$		0			0
$121$	3.14474	−	5.44685i	0.285886	−	0.495169i
$122$	30.9998	+	8.30638i	2.80659	+	0.752024i
$123$		0			0
$124$	−43.1569	−	24.9167i	−3.87561	−	2.23758i
$125$	10.8453	−	2.71653i	0.970033	−	0.242973i
$126$		0			0
$127$	−5.70267	−	5.70267i	−0.506030	−	0.506030i	0.407275	−	0.913305i	$-0.366479\pi$
$127$	−5.70267	−	5.70267i	−0.506030	−	0.506030i	−0.913305	+	0.407275i	$0.866479\pi$
$128$	−20.4440	+	5.47796i	−1.80701	+	0.484188i
$129$		0			0
$130$	0.487891	+	5.95040i	0.0427909	+	0.521885i
$131$	16.3919	+	9.46386i	1.43217	+	0.826862i	0.997286	−	0.0736266i	$-0.0234573\pi$
$131$	16.3919	+	9.46386i	1.43217	+	0.826862i	0.434880	+	0.900488i	$0.356791\pi$
$132$		0			0
$133$	−14.4339	+	6.81393i	−1.25158	+	0.590843i
$134$	8.57330			0.740621
$135$		0			0
$136$	5.91684	+	10.2483i	0.507365	+	0.878782i
$137$	−11.5217	−	3.08722i	−0.984361	−	0.263759i	−0.269481	−	0.963006i	$-0.586852\pi$
$137$	−11.5217	−	3.08722i	−0.984361	−	0.263759i	−0.714880	+	0.699247i	$0.753519\pi$
$138$		0			0
$139$		−	17.0047i		−	1.44232i	−0.692767	−	0.721161i	$-0.743609\pi$
$139$		−	17.0047i		−	1.44232i	0.692767	−	0.721161i	$-0.256391\pi$
$140$	−26.8098	+	15.4527i	−2.26585	+	1.30599i
$141$		0			0
$142$	25.4217	−	6.81172i	2.13334	−	0.571627i
$143$	1.06861	−	3.98809i	0.0893613	−	0.333501i
$144$		0			0
$145$	−1.11873	−	1.61642i	−0.0929058	−	0.134236i
$146$		−	18.3905i		−	1.52201i
$147$		0			0
$148$	12.0092	−	12.0092i	0.987150	−	0.987150i
$149$	−5.31610	+	9.20775i	−0.435512	+	0.754328i	−0.997337	−	0.0729275i	$-0.976766\pi$
$149$	−5.31610	+	9.20775i	−0.435512	+	0.754328i	0.561826	+	0.827256i	$0.310099\pi$
$150$		0			0
$151$	6.91806	+	11.9824i	0.562984	+	0.975116i	0.997234	+	0.0743241i	$0.0236799\pi$
$151$	6.91806	+	11.9824i	0.562984	+	0.975116i	−0.434251	+	0.900792i	$0.642987\pi$
$152$	−13.5638	−	50.6208i	−1.10017	−	4.10589i
$153$		0			0
$154$	29.1078	−	5.27455i	2.34558	−	0.425036i
$155$	9.10860	−	19.2584i	0.731620	−	1.54687i
$156$		0			0
$157$	5.26351	−	19.6437i	0.420074	−	1.56774i	−0.354376	−	0.935103i	$-0.615307\pi$
$157$	5.26351	−	19.6437i	0.420074	−	1.56774i	0.774450	−	0.632635i	$-0.218027\pi$
$158$	−1.51260	+	5.64509i	−0.120336	+	0.449100i
$159$		0			0
$160$	−13.0378	−	36.4384i	−1.03073	−	2.88071i
$161$	0.190088	−	0.530048i	0.0149810	−	0.0417737i
$162$		0			0
$163$	0.444770	+	1.65991i	0.0348371	+	0.130014i	0.981154	−	0.193225i	$-0.0618948\pi$
$163$	0.444770	+	1.65991i	0.0348371	+	0.130014i	−0.946317	+	0.323239i	$0.895228\pi$
$164$	−3.27464	−	5.67185i	−0.255707	−	0.442897i
$165$		0			0
$166$	7.14854	−	12.3816i	0.554834	−	0.961001i
$167$	−4.75534	+	4.75534i	−0.367980	+	0.367980i	−0.866740	−	0.498760i	$-0.833789\pi$
$167$	−4.75534	+	4.75534i	−0.367980	+	0.367980i	0.498760	+	0.866740i	$0.333789\pi$
$168$		0			0
$169$			12.0140i			0.924157i
$170$	−6.73507	+	4.66139i	−0.516556	+	0.357512i
$171$		0			0
$172$	8.21203	−	30.6477i	0.626161	−	2.33687i
$173$	−0.263351	+	0.0705647i	−0.0200222	+	0.00536494i	−0.268816	−	0.963191i	$-0.586632\pi$
$173$	−0.263351	+	0.0705647i	−0.0200222	+	0.00536494i	0.248794	+	0.968556i	$0.419966\pi$
$174$		0			0
$175$	−7.52055	−	10.8831i	−0.568500	−	0.822683i
$176$			53.6289i			4.04243i
$177$		0			0
$178$	−37.3910	−	10.0189i	−2.80257	−	0.750947i
$179$	−8.58944	−	14.8773i	−0.642005	−	1.11199i	−0.984985	−	0.172642i	$-0.944770\pi$
$179$	−8.58944	−	14.8773i	−0.642005	−	1.11199i	0.342980	−	0.939343i	$-0.388564\pi$
$180$		0			0
$181$	−4.07537			−0.302920			−0.151460	−	0.988463i	$-0.548397\pi$
$181$	−4.07537			−0.302920			−0.151460	+	0.988463i	$0.548397\pi$
$182$	6.38818	−	3.01572i	0.473523	−	0.223540i
$183$		0			0
$184$	1.60115	+	0.924424i	0.118038	+	0.0681494i
$185$	5.53632	+	4.69724i	0.407038	+	0.345348i
$186$		0			0
$187$	5.47132	−	1.46604i	0.400103	−	0.107207i
$188$	0.399990	+	0.399990i	0.0291723	+	0.0291723i
$189$		0			0
$190$	34.1535	−	12.2202i	2.47775	−	0.886548i
$191$	8.15870	+	4.71043i	0.590343	+	0.340834i	0.765233	−	0.643753i	$-0.222624\pi$
$191$	8.15870	+	4.71043i	0.590343	+	0.340834i	−0.174890	+	0.984588i	$0.555957\pi$
$192$		0			0
$193$	−11.2504	−	3.01454i	−0.809824	−	0.216992i	−0.169931	−	0.985456i	$-0.554355\pi$
$193$	−11.2504	−	3.01454i	−0.809824	−	0.216992i	−0.639893	+	0.768464i	$0.721021\pi$
$194$	−7.39433	+	12.8073i	−0.530882	+	0.919514i
$195$		0			0
$196$	28.2692	+	23.2686i	2.01923	+	1.66204i
$197$	8.07168	−	8.07168i	0.575083	−	0.575083i	−0.358461	−	0.933545i	$-0.616699\pi$
$197$	8.07168	−	8.07168i	0.575083	−	0.575083i	0.933545	+	0.358461i	$0.116699\pi$
$198$		0			0
$199$	16.4380	−	9.49049i	1.16526	−	0.672763i	0.212701	−	0.977117i	$-0.431774\pi$
$199$	16.4380	−	9.49049i	1.16526	−	0.672763i	0.952559	+	0.304354i	$0.0984407\pi$
$200$	39.5628	−	17.9254i	2.79751	−	1.26752i
$201$		0			0
$202$	17.3311	+	17.3311i	1.21941	+	1.21941i
$203$	−1.32509	+	1.91161i	−0.0930034	+	0.134169i
$204$		0			0
$205$	2.30221	−	1.59338i	0.160794	−	0.111286i
$206$	−20.8747	+	12.0520i	−1.45441	+	0.839704i
$207$		0			0
$208$	3.31463	+	12.3703i	0.229828	+	0.857729i
$209$	−25.0850			−1.73517
$210$		0			0
$211$	7.43148			0.511604			0.255802	−	0.966729i	$-0.417660\pi$
$211$	7.43148			0.511604			0.255802	+	0.966729i	$0.417660\pi$
$212$	−6.77645	−	25.2901i	−0.465409	−	1.73693i
$213$		0			0
$214$	−31.4932	+	18.1826i	−2.15283	+	1.24294i
$215$	13.3450	+	2.42824i	0.910122	+	0.165604i
$216$		0			0
$217$	−25.1212	−	2.07816i	−1.70534	−	0.141075i
$218$	−7.00663	−	7.00663i	−0.474549	−	0.474549i
$219$		0			0
$220$	−48.4695	+	3.97416i	−3.26781	+	0.267938i
$221$	1.17144	−	0.676328i	0.0787993	−	0.0454948i
$222$		0			0
$223$	−9.70762	+	9.70762i	−0.650071	+	0.650071i	−0.953010	−	0.302939i	$-0.902032\pi$
$223$	−9.70762	+	9.70762i	−0.650071	+	0.650071i	0.302939	+	0.953010i	$0.402032\pi$
$224$	−34.9385	+	29.5996i	−2.33443	+	1.97771i
$225$		0			0
$226$	−25.1387	+	43.5415i	−1.67220	+	2.89634i
$227$	−10.4034	−	2.78758i	−0.690498	−	0.185018i	−0.103527	−	0.994627i	$-0.533013\pi$
$227$	−10.4034	−	2.78758i	−0.690498	−	0.185018i	−0.586971	+	0.809608i	$0.699680\pi$
$228$		0			0
$229$	6.41630	+	3.70445i	0.424001	+	0.244797i	0.696788	−	0.717277i	$-0.254612\pi$
$229$	6.41630	+	3.70445i	0.424001	+	0.244797i	−0.272787	+	0.962075i	$0.587945\pi$
$230$	−0.547146	+	1.15684i	−0.0360778	+	0.0762796i
$231$		0			0
$232$	−5.40010	−	5.40010i	−0.354534	−	0.354534i
$233$	−21.5398	+	5.77156i	−1.41112	+	0.378107i	−0.882324	−	0.470643i	$-0.844022\pi$
$233$	−21.5398	+	5.77156i	−1.41112	+	0.378107i	−0.528793	+	0.848751i	$0.677355\pi$
$234$		0			0
$235$	−0.156451	+	0.184398i	−0.0102057	+	0.0120288i
$236$	−1.02431	−	0.591383i	−0.0666766	−	0.0384958i
$237$		0			0
$238$	7.96503	+	5.52122i	0.516296	+	0.357888i
$239$	11.9368			0.772124			0.386062	−	0.922473i	$-0.373835\pi$
$239$	11.9368			0.772124			0.386062	+	0.922473i	$0.373835\pi$
$240$		0			0
$241$	−7.36327	−	12.7536i	−0.474310	−	0.821529i	0.525257	−	0.850943i	$-0.323969\pi$
$241$	−7.36327	−	12.7536i	−0.474310	−	0.821529i	−0.999567	+	0.0294146i	$0.990636\pi$
$242$	16.3360	+	4.37721i	1.05012	+	0.281377i
$243$		0			0
$244$			62.4277i			3.99652i
$245$	−8.92651	+	12.8576i	−0.570294	+	0.821441i
$246$		0			0
$247$	−5.78625	+	1.55042i	−0.368170	+	0.0986510i
$248$	21.4206	−	79.9427i	1.36021	−	5.07636i
$249$		0			0
$250$	14.6036	+	26.2784i	0.923613	+	1.66199i
$251$			18.8368i			1.18897i	0.804108	+	0.594483i	$0.202643\pi$
$251$			18.8368i			1.18897i	−0.804108	+	0.594483i	$0.797357\pi$
$252$		0			0
$253$	0.625770	−	0.625770i	0.0393418	−	0.0393418i
$254$	10.8430	−	18.7806i	0.680350	−	1.17840i
$255$		0			0
$256$	−7.71224	−	13.3580i	−0.482015	−	0.834874i
$257$	3.87251	+	14.4524i	0.241561	+	0.901517i	0.975081	+	0.221849i	$0.0712093\pi$
$257$	3.87251	+	14.4524i	0.241561	+	0.901517i	−0.733520	+	0.679668i	$0.762124\pi$
$258$		0			0
$259$	2.90000	−	8.08646i	0.180197	−	0.502468i
$260$	−10.9346	+	3.91244i	−0.678137	+	0.242639i
$261$		0			0
$262$	−13.1729	+	49.1618i	−0.813823	+	3.03723i
$263$	−2.88720	+	10.7752i	−0.178032	+	0.664426i	0.817983	+	0.575243i	$0.195092\pi$
$263$	−2.88720	+	10.7752i	−0.178032	+	0.664426i	−0.996015	+	0.0891835i	$0.971574\pi$
$264$		0			0
$265$	10.5386	−	3.77076i	0.647384	−	0.231636i
$266$	−27.7435	−	32.7477i	−1.70106	−	2.00789i
$267$		0			0
$268$	4.31625	+	16.1085i	0.263657	+	0.983980i
$269$	−8.34045	−	14.4461i	−0.508526	−	0.880793i	−0.999951	−	0.00987349i	$-0.996857\pi$
$269$	−8.34045	−	14.4461i	−0.508526	−	0.880793i	0.491425	−	0.870920i	$-0.336476\pi$
$270$		0			0
$271$	5.86722	−	10.1623i	0.356408	−	0.617317i	−0.630950	−	0.775824i	$-0.717335\pi$
$271$	5.86722	−	10.1623i	0.356408	−	0.617317i	0.987358	+	0.158507i	$0.0506679\pi$
$272$	−12.4237	+	12.4237i	−0.753296	+	0.753296i
$273$		0			0
$274$		−	32.0743i		−	1.93768i
$275$	−3.38655	−	20.5126i	−0.204217	−	1.23696i
$276$		0			0
$277$	−3.17485	+	11.8487i	−0.190758	+	0.711919i	0.802566	+	0.596563i	$0.203468\pi$
$277$	−3.17485	+	11.8487i	−0.190758	+	0.711919i	−0.993324	+	0.115356i	$0.963199\pi$
$278$	44.1671	−	11.8345i	2.64897	−	0.709789i
$279$		0			0
$280$	−36.3133	−	36.3661i	−2.17013	−	2.17329i
$281$			20.0929i			1.19864i	0.800509	+	0.599320i	$0.204562\pi$
$281$			20.0929i			1.19864i	−0.800509	+	0.599320i	$0.795438\pi$
$282$		0			0
$283$	30.6875	+	8.22270i	1.82418	+	0.488789i	0.997290	−	0.0735682i	$-0.0234387\pi$
$283$	30.6875	+	8.22270i	1.82418	+	0.488789i	0.826895	+	0.562357i	$0.190105\pi$
$284$	25.5972	+	44.3356i	1.51891	+	2.63084i
$285$		0			0
$286$	11.1021			0.656484
$287$	−2.72264	−	1.88729i	−0.160713	−	0.111403i
$288$		0			0
$289$	−13.1153	−	7.57214i	−0.771490	−	0.445420i
$290$	3.41981	−	4.03069i	0.200818	−	0.236691i
$291$		0			0
$292$	34.5541	−	9.25875i	2.02213	−	0.541827i
$293$	−3.32527	−	3.32527i	−0.194265	−	0.194265i	0.603271	−	0.797536i	$-0.293864\pi$
$293$	−3.32527	−	3.32527i	−0.194265	−	0.194265i	−0.797536	+	0.603271i	$0.793864\pi$
$294$		0			0
$295$	0.216188	−	0.457088i	0.0125869	−	0.0266127i
$296$	24.4273	+	14.1031i	1.41981	+	0.819725i
$297$		0			0
$298$	−27.6155	−	7.39954i	−1.59972	−	0.428644i
$299$	0.105667	−	0.183020i	0.00611087	−	0.0105843i
$300$		0			0
$301$	−2.86164	−	15.7921i	−0.164942	−	0.910242i
$302$	−26.3078	+	26.3078i	−1.51385	+	1.51385i
$303$		0			0
$304$	67.3848	−	38.9046i	3.86478	−	2.23133i
$305$	−26.5987	+	2.18090i	−1.52304	+	0.124878i
$306$		0			0
$307$	−2.96830	−	2.96830i	−0.169410	−	0.169410i	0.617310	−	0.786720i	$-0.288222\pi$
$307$	−2.96830	−	2.96830i	−0.169410	−	0.169410i	−0.786720	+	0.617310i	$0.788222\pi$
$308$	24.5648	+	52.0355i	1.39971	+	2.96500i
$309$		0			0
$310$	56.3599	+	10.2552i	3.20103	+	0.582454i
$311$	8.09571	−	4.67406i	0.459065	−	0.265042i	−0.252586	−	0.967575i	$-0.581281\pi$
$311$	8.09571	−	4.67406i	0.459065	−	0.265042i	0.711651	+	0.702533i	$0.247948\pi$
$312$		0			0
$313$	5.38565	+	20.0995i	0.304415	+	1.13609i	0.933448	+	0.358714i	$0.116785\pi$
$313$	5.38565	+	20.0995i	0.304415	+	1.13609i	−0.629032	+	0.777379i	$0.716549\pi$
$314$	54.6846			3.08603
$315$		0			0
$316$	−11.3681			−0.639507
$317$	−3.73583	−	13.9423i	−0.209825	−	0.783078i	−0.987924	−	0.154937i	$-0.950483\pi$
$317$	−3.73583	−	13.9423i	−0.209825	−	0.783078i	0.778099	−	0.628141i	$-0.216184\pi$
$318$		0			0
$319$	−3.16575	+	1.82775i	−0.177248	+	0.102334i
$320$	38.1411	−	26.3977i	2.13215	−	1.47568i
$321$		0			0
$322$	1.50901	+	0.124833i	0.0840939	+	0.00695669i
$323$	−5.81120	−	5.81120i	−0.323344	−	0.323344i
$324$		0			0
$325$	−2.04898	−	4.52225i	−0.113657	−	0.250849i
$326$	−4.00180	+	2.31044i	−0.221639	+	0.127964i
$327$		0			0
$328$	7.69119	−	7.69119i	0.424675	−	0.424675i
$329$	0.269335	+	0.0965901i	0.0148489	+	0.00532518i
$330$		0			0
$331$	−5.77389	+	10.0007i	−0.317362	+	0.549687i	−0.979937	−	0.199309i	$-0.936130\pi$
$331$	−5.77389	+	10.0007i	−0.317362	+	0.549687i	0.662575	+	0.748996i	$0.269464\pi$
$332$	26.8629	+	7.19789i	1.47429	+	0.395036i
$333$		0			0
$334$	−15.6608	−	9.04175i	−0.856919	−	0.494743i
$335$	−6.71257	+	2.40178i	−0.366747	+	0.131223i
$336$		0			0
$337$	−20.7098	−	20.7098i	−1.12813	−	1.12813i	−0.990481	−	0.137653i	$-0.956044\pi$
$337$	−20.7098	−	20.7098i	−1.12813	−	1.12813i	−0.137653	−	0.990481i	$-0.543956\pi$
$338$	−31.2046	+	8.36124i	−1.69731	+	0.454792i
$339$		0			0
$340$	−12.1491	−	10.3078i	−0.658878	−	0.559019i
$341$	−34.3079	−	19.8077i	−1.85788	−	1.07265i
$342$		0			0
$343$	17.9554	+	4.53912i	0.969500	+	0.245089i
$344$	52.6950			2.84112
$345$		0			0
$346$	−0.366562	−	0.634904i	−0.0197065	−	0.0341326i
$347$	−20.5602	−	5.50909i	−1.10373	−	0.295743i	−0.339447	−	0.940625i	$-0.610240\pi$
$347$	−20.5602	−	5.50909i	−1.10373	−	0.295743i	−0.764282	+	0.644882i	$0.776907\pi$
$348$		0			0
$349$			6.84619i			0.366468i	0.983069	+	0.183234i	$0.0586566\pi$
$349$			6.84619i			0.366468i	−0.983069	+	0.183234i	$0.941343\pi$
$350$	23.0331	−	27.1076i	1.23117	−	1.44896i
$351$		0			0
$352$	−69.5133	+	18.6260i	−3.70507	+	0.992771i
$353$	−5.27279	+	19.6783i	−0.280642	+	1.04737i	0.671323	+	0.741165i	$0.265726\pi$
$353$	−5.27279	+	19.6783i	−0.280642	+	1.04737i	−0.951965	+	0.306206i	$0.900940\pi$
$354$		0			0
$355$	−17.9959	+	12.4551i	−0.955124	+	0.661048i
$356$		−	75.2983i		−	3.99080i
$357$		0			0
$358$	32.6637	−	32.6637i	1.72633	−	1.72633i
$359$	−7.96815	+	13.8012i	−0.420543	+	0.728402i	−0.995993	−	0.0894353i	$-0.971494\pi$
$359$	−7.96815	+	13.8012i	−0.420543	+	0.728402i	0.575450	+	0.817837i	$0.304827\pi$
$360$		0			0
$361$	8.69770	+	15.0649i	0.457774	+	0.792887i
$362$	−2.83628	−	10.5851i	−0.149072	−	0.556343i
$363$		0			0
$364$	8.88240	+	10.4845i	0.465564	+	0.549539i
$365$	5.15203	+	14.3991i	0.269670	+	0.753682i
$366$		0			0
$367$	−2.90688	+	10.8486i	−0.151738	+	0.566294i	0.847625	+	0.530596i	$0.178032\pi$
$367$	−2.90688	+	10.8486i	−0.151738	+	0.566294i	−0.999363	+	0.0356974i	$0.988635\pi$
$368$	−0.710465	+	2.65149i	−0.0370356	+	0.138219i
$369$		0			0
$370$	−8.34731	+	17.6488i	−0.433956	+	0.917518i
$371$	−8.56074	−	10.1049i	−0.444451	−	0.524618i
$372$		0			0
$373$	−7.97059	−	29.7467i	−0.412702	−	1.54022i	−0.789395	−	0.613885i	$-0.789606\pi$
$373$	−7.97059	−	29.7467i	−0.412702	−	1.54022i	0.376694	−	0.926338i	$-0.377061\pi$
$374$	7.61560	+	13.1906i	0.393793	+	0.682070i
$375$		0			0
$376$	−0.469731	+	0.813598i	−0.0242245	+	0.0419581i
$377$	−0.617263	+	0.617263i	−0.0317906	+	0.0317906i
$378$		0			0
$379$			5.79809i			0.297828i	0.988850	+	0.148914i	$0.0475777\pi$
$379$			5.79809i			0.297828i	−0.988850	+	0.148914i	$0.952422\pi$
$380$	40.1553	+	58.0190i	2.05992	+	2.97631i
$381$		0			0
$382$	−6.55650	+	24.4692i	−0.335460	+	1.25195i
$383$	9.09525	−	2.43707i	0.464746	−	0.124528i	−0.0188451	−	0.999822i	$-0.505999\pi$
$383$	9.09525	−	2.43707i	0.464746	−	0.124528i	0.483591	+	0.875294i	$0.339332\pi$
$384$		0			0
$385$	−21.3127	+	12.2842i	−1.08619	+	0.626062i
$386$		−	31.3192i		−	1.59411i
$387$		0			0
$388$	−27.7865	−	7.44538i	−1.41065	−	0.377982i
$389$	4.94348	+	8.56236i	0.250644	+	0.434129i	0.963703	−	0.266975i	$-0.0860242\pi$
$389$	4.94348	+	8.56236i	0.250644	+	0.434129i	−0.713059	+	0.701104i	$0.752691\pi$
$390$		0			0
$391$	0.289932			0.0146625
$392$	−25.1762	+	55.3513i	−1.27159	+	2.79566i
$393$		0			0
$394$	26.5825	+	15.3474i	1.33920	+	0.773190i
$395$	−0.397144	−	4.84364i	−0.0199825	−	0.243710i
$396$		0			0
$397$	20.9026	−	5.60083i	1.04907	−	0.281097i	0.307202	−	0.951644i	$-0.400607\pi$
$397$	20.9026	−	5.60083i	1.04907	−	0.281097i	0.741867	+	0.670547i	$0.233940\pi$
$398$	36.0902	+	36.0902i	1.80904	+	1.80904i
$399$		0			0
$400$	40.9104	+	49.8500i	2.04552	+	2.49250i
$401$	18.9003	+	10.9121i	0.943836	+	0.544924i	0.891161	−	0.453688i	$-0.149892\pi$
$401$	18.9003	+	10.9121i	0.943836	+	0.544924i	0.0526753	+	0.998612i	$0.483225\pi$
$402$		0			0
$403$	−9.13790	−	2.44849i	−0.455191	−	0.121968i
$404$	−23.8382	+	41.2890i	−1.18599	+	2.05420i
$405$		0			0
$406$	−5.88731	−	2.11133i	−0.292182	−	0.104784i
$407$	9.54680	−	9.54680i	0.473217	−	0.473217i
$408$		0			0
$409$	2.24712	−	1.29738i	0.111113	−	0.0641512i	−0.443414	−	0.896317i	$-0.646233\pi$
$409$	2.24712	−	1.29738i	0.111113	−	0.0641512i	0.554527	+	0.832166i	$0.312899\pi$
$410$	5.74079	+	4.87072i	0.283517	+	0.240548i
$411$		0			0
$412$	−33.1541	−	33.1541i	−1.63338	−	1.63338i
$413$	−0.596238	−	0.0493239i	−0.0293390	−	0.00242707i
$414$		0			0
$415$	−2.12836	+	11.6970i	−0.104477	+	0.574182i
$416$	−14.8831	+	8.59278i	−0.729705	+	0.421295i
$417$		0			0
$418$	−17.4581	−	65.1544i	−0.853902	−	3.18681i
$419$	−9.23892			−0.451351			−0.225675	−	0.974203i	$-0.572459\pi$
$419$	−9.23892			−0.451351			−0.225675	+	0.974203i	$0.572459\pi$
$420$		0			0
$421$	−4.60198			−0.224287			−0.112143	−	0.993692i	$-0.535772\pi$
$421$	−4.60198			−0.224287			−0.112143	+	0.993692i	$0.535772\pi$
$422$	5.17199	+	19.3021i	0.251768	+	0.939612i
$423$		0			0
$424$	37.6575	−	21.7416i	1.82881	−	1.05586i
$425$	3.96743	−	5.53649i	0.192449	−	0.268559i
$426$		0			0
$427$	13.4805	+	28.5556i	0.652365	+	1.38190i
$428$	−50.0188	−	50.0188i	−2.41775	−	2.41775i
$429$		0			0
$430$	2.98057	+	36.3515i	0.143736	+	1.75303i
$431$	−1.04639	+	0.604133i	−0.0504027	+	0.0291000i	−0.524990	−	0.851109i	$-0.675931\pi$
$431$	−1.04639	+	0.604133i	−0.0504027	+	0.0291000i	0.474587	+	0.880209i	$0.342597\pi$
$432$		0			0
$433$	21.2085	−	21.2085i	1.01922	−	1.01922i	0.0194062	−	0.999812i	$-0.493822\pi$
$433$	21.2085	−	21.2085i	1.01922	−	1.01922i	0.999812	−	0.0194062i	$-0.00617756\pi$
$434$	−12.0856	−	66.6947i	−0.580126	−	3.20145i
$435$		0			0
$436$	9.63732	−	16.6923i	0.461544	−	0.799417i
$437$	−1.24024	−	0.332321i	−0.0593287	−	0.0158971i
$438$		0			0
$439$	7.26004	+	4.19158i	0.346503	+	0.200053i	0.663144	−	0.748492i	$-0.269222\pi$
$439$	7.26004	+	4.19158i	0.346503	+	0.200053i	−0.316641	+	0.948545i	$0.602555\pi$
$440$	−27.2097	−	76.0465i	−1.29717	−	3.62538i
$441$		0			0
$442$	2.57193	+	2.57193i	0.122334	+	0.122334i
$443$	5.19257	−	1.39135i	0.246707	−	0.0661048i	−0.133347	−	0.991069i	$-0.542572\pi$
$443$	5.19257	−	1.39135i	0.246707	−	0.0661048i	0.380053	+	0.924965i	$0.375906\pi$
$444$		0			0
$445$	32.0824	−	2.63054i	1.52085	−	0.124699i
$446$	−31.9701	−	18.4580i	−1.51383	−	0.874010i
$447$		0			0
$448$	−45.1064	−	31.2670i	−2.13108	−	1.47723i
$449$	3.34892			0.158045			0.0790227	−	0.996873i	$-0.474820\pi$
$449$	3.34892			0.158045			0.0790227	+	0.996873i	$0.474820\pi$
$450$		0			0
$451$	−2.60320	−	4.50887i	−0.122580	−	0.212315i
$452$	−94.4666	−	25.3123i	−4.44334	−	1.19059i
$453$		0			0
$454$		−	28.9613i		−	1.35922i
$455$	−4.15686	+	4.15081i	−0.194876	+	0.194593i
$456$		0			0
$457$	−1.01059	+	0.270788i	−0.0472736	+	0.0126669i	−0.282378	−	0.959303i	$-0.591123\pi$
$457$	−1.01059	+	0.270788i	−0.0472736	+	0.0126669i	0.235105	+	0.971970i	$0.424457\pi$
$458$	−5.15628	+	19.2435i	−0.240937	+	0.899189i
$459$		0			0
$460$	−2.44905	−	0.445626i	−0.114188	−	0.0207774i
$461$			23.0551i			1.07378i	0.843651	+	0.536891i	$0.180401\pi$
$461$			23.0551i			1.07378i	−0.843651	+	0.536891i	$0.819599\pi$
$462$		0			0
$463$	−25.8069	+	25.8069i	−1.19935	+	1.19935i	−0.224987	+	0.974362i	$0.572234\pi$
$463$	−25.8069	+	25.8069i	−1.19935	+	1.19935i	−0.974362	+	0.224987i	$0.927766\pi$
$464$	5.66934	−	9.81958i	0.263192	−	0.455863i
$465$		0			0
$466$	−29.9815	−	51.9294i	−1.38886	−	2.40558i
$467$	6.24612	+	23.3108i	0.289036	+	1.07870i	0.945839	+	0.324635i	$0.105242\pi$
$467$	6.24612	+	23.3108i	0.289036	+	1.07870i	−0.656803	+	0.754062i	$0.728092\pi$
$468$		0			0
$469$	5.45274	+	6.43626i	0.251784	+	0.297199i
$470$	−0.587828	−	0.278024i	−0.0271145	−	0.0128243i
$471$		0			0
$472$	0.508405	−	1.89740i	0.0234013	−	0.0873347i
$473$	6.52821	−	24.3636i	0.300167	−	1.12024i
$474$		0			0
$475$	−23.3174	+	19.1359i	−1.06988	+	0.878016i
$476$	−6.36386	+	17.7452i	−0.291687	+	0.813351i
$477$		0			0
$478$	8.30746	+	31.0039i	0.379974	+	1.41808i
$479$	9.61925	+	16.6610i	0.439515	+	0.761262i	0.997652	−	0.0684867i	$-0.0218171\pi$
$479$	9.61925	+	16.6610i	0.439515	+	0.761262i	−0.558137	+	0.829749i	$0.688484\pi$
$480$		0			0
$481$	1.61206	−	2.79218i	0.0735038	−	0.127312i
$482$	28.0009	−	28.0009i	1.27540	−	1.27540i
$483$		0			0
$484$			32.8975i			1.49534i
$485$	2.20154	−	12.0991i	0.0999670	−	0.549394i
$486$		0			0
$487$	7.55036	−	28.1783i	0.342140	−	1.27688i	−0.553779	−	0.832664i	$-0.686815\pi$
$487$	7.55036	−	28.1783i	0.342140	−	1.27688i	0.895918	−	0.444219i	$-0.146519\pi$
$488$	−100.147	+	26.8342i	−4.53342	+	1.21473i
$489$		0			0
$490$	−39.6080	−	14.2369i	−1.78931	−	0.643158i
$491$			7.79240i			0.351666i	0.984420	+	0.175833i	$0.0562619\pi$
$491$			7.79240i			0.351666i	−0.984420	+	0.175833i	$0.943738\pi$
$492$		0			0
$493$	−1.15679	−	0.309962i	−0.0520993	−	0.0139600i
$494$	−8.05396	−	13.9499i	−0.362365	−	0.627634i
$495$		0			0
$496$	122.880			5.51746
$497$	21.2823	+	14.7525i	0.954643	+	0.661742i
$498$		0			0
$499$	−4.52229	−	2.61095i	−0.202446	−	0.116882i	0.395350	−	0.918530i	$-0.370623\pi$
$499$	−4.52229	−	2.61095i	−0.202446	−	0.116882i	−0.597796	+	0.801649i	$0.703957\pi$
$500$	−42.0225	+	40.6687i	−1.87930	+	1.81876i
$501$		0			0
$502$	−48.9256	+	13.1096i	−2.18366	+	0.585109i
$503$	−25.6241	−	25.6241i	−1.14252	−	1.14252i	−0.987987	−	0.154535i	$-0.950612\pi$
$503$	−25.6241	−	25.6241i	−1.14252	−	1.14252i	−0.154535	−	0.987987i	$-0.549388\pi$
$504$		0			0
$505$	−18.4248	−	8.71435i	−0.819894	−	0.387783i
$506$	2.06085	+	1.18983i	0.0916159	+	0.0528945i
$507$		0			0
$508$	40.7460	+	10.9178i	1.80781	+	0.484401i
$509$	17.7901	−	30.8133i	0.788532	−	1.36578i	−0.138335	−	0.990385i	$-0.544175\pi$
$509$	17.7901	−	30.8133i	0.788532	−	1.36578i	0.926866	−	0.375391i	$-0.122492\pi$
$510$		0			0
$511$	13.8064	−	11.6966i	0.610758	−	0.517429i
$512$	−0.604217	+	0.604217i	−0.0267029	+	0.0267029i
$513$		0			0
$514$	−34.8428	+	20.1165i	−1.53685	+	0.887300i
$515$	12.9678	−	15.2842i	0.571428	−	0.673504i
$516$		0			0
$517$	0.317975	+	0.317975i	0.0139845	+	0.0139845i
$518$	23.0216	+	1.90447i	1.01151	+	0.0836775i
$519$		0			0
$520$	−10.9765	−	15.8596i	−0.481353	−	0.695489i
$521$	20.0749	−	11.5902i	0.879495	−	0.507777i	0.00900344	−	0.999959i	$-0.497134\pi$
$521$	20.0749	−	11.5902i	0.879495	−	0.507777i	0.870492	+	0.492183i	$0.163801\pi$
$522$		0			0
$523$	0.305268	+	1.13928i	0.0133485	+	0.0498171i	0.972279	−	0.233824i	$-0.0751241\pi$
$523$	0.305268	+	1.13928i	0.0133485	+	0.0498171i	−0.958930	+	0.283642i	$0.908457\pi$
$524$	−99.0025			−4.32494
$525$		0			0
$526$	−29.9962			−1.30790
$527$	−3.35912	−	12.5364i	−0.146326	−	0.546095i
$528$		0			0
$529$	−19.8794	+	11.4774i	−0.864320	+	0.499015i
$530$	17.1284	+	24.7482i	0.744010	+	1.07499i
$531$		0			0
$532$	47.5623	−	68.6144i	2.06209	−	2.97481i
$533$	−0.879147	−	0.879147i	−0.0380801	−	0.0380801i
$534$		0			0
$535$	19.5642	−	23.0590i	0.845833	−	0.996926i
$536$	−23.9859	+	13.8483i	−1.03603	+	0.598153i
$537$		0			0
$538$	31.7169	−	31.7169i	1.36741	−	1.36741i
$539$	22.4728	+	18.4975i	0.967971	+	0.796745i
$540$		0			0
$541$	4.51761	−	7.82473i	0.194227	−	0.336411i	−0.752420	−	0.658684i	$-0.771113\pi$
$541$	4.51761	−	7.82473i	0.194227	−	0.336411i	0.946647	+	0.322273i	$0.104447\pi$
$542$	30.4784	+	8.16666i	1.30916	+	0.350788i
$543$		0			0
$544$	−20.4184	−	11.7886i	−0.875430	−	0.505430i
$545$	7.44880	+	3.52304i	0.319072	+	0.150911i
$546$		0			0
$547$	22.6405	+	22.6405i	0.968036	+	0.968036i	0.999505	−	0.0314683i	$-0.0100183\pi$
$547$	22.6405	+	22.6405i	0.968036	+	0.968036i	−0.0314683	+	0.999505i	$0.510018\pi$
$548$	60.2646	−	16.1479i	2.57438	−	0.689802i
$549$		0			0
$550$	50.9215	−	23.0719i	2.17130	−	0.983791i
$551$	4.59313	+	2.65184i	0.195674	+	0.112972i
$552$		0			0
$553$	−5.19999	+	2.45480i	−0.221126	+	0.104389i
$554$	−32.9847			−1.40139
$555$		0			0
$556$	44.4721	+	77.0279i	1.88604	+	3.26671i
$557$	29.0377	+	7.78063i	1.23037	+	0.329676i	0.814723	−	0.579851i	$-0.196889\pi$
$557$	29.0377	+	7.78063i	1.23037	+	0.329676i	0.415645	+	0.909527i	$0.363556\pi$
$558$		0			0
$559$		−	6.02334i		−	0.254760i
$560$	38.1996	−	66.0526i	1.61423	−	2.79123i
$561$		0			0
$562$	−52.1881	+	13.9838i	−2.20142	+	0.589870i
$563$	4.47706	−	16.7086i	0.188685	−	0.704184i	−0.805126	−	0.593104i	$-0.797902\pi$
$563$	4.47706	−	16.7086i	0.188685	−	0.704184i	0.993811	−	0.111080i	$-0.0354310\pi$
$564$		0			0
$565$	7.48465	−	41.1338i	0.314882	−	1.73051i
$566$			85.4287i			3.59084i
$567$		0			0
$568$	−60.1204	+	60.1204i	−2.52260	+	2.52260i
$569$	−7.00255	+	12.1288i	−0.293562	+	0.508465i	−0.974649	−	0.223738i	$-0.928174\pi$
$569$	−7.00255	+	12.1288i	−0.293562	+	0.508465i	0.681087	+	0.732202i	$0.261507\pi$
$570$		0			0
$571$	−2.55183	−	4.41990i	−0.106791	−	0.184967i	0.807678	−	0.589624i	$-0.200724\pi$
$571$	−2.55183	−	4.41990i	−0.106791	−	0.184967i	−0.914468	+	0.404657i	$0.867391\pi$
$572$	5.58940	+	20.8599i	0.233705	+	0.872197i
$573$		0			0
$574$	3.00710	−	8.38511i	0.125514	−	0.349988i
$575$	0.104311	−	1.05904i	0.00435008	−	0.0441650i
$576$		0			0
$577$	−3.25944	+	12.1644i	−0.135692	+	0.506411i	0.864302	+	0.502974i	$0.167761\pi$
$577$	−3.25944	+	12.1644i	−0.135692	+	0.506411i	−0.999994	+	0.00343709i	$0.998906\pi$
$578$	10.5398	−	39.3349i	0.438396	−	1.63612i
$579$		0			0
$580$	9.29501	+	4.39624i	0.385954	+	0.182544i
$581$	13.8419	−	2.50825i	0.574258	−	0.104060i
$582$		0			0
$583$	−5.38699	−	20.1045i	−0.223106	−	0.832644i
$584$	29.7058	+	51.4519i	1.22923	+	2.12910i
$585$		0			0
$586$	6.32263	−	10.9511i	0.261186	−	0.452387i
$587$	29.0630	−	29.0630i	1.19956	−	1.19956i	0.225260	−	0.974299i	$-0.427677\pi$
$587$	29.0630	−	29.0630i	1.19956	−	1.19956i	0.974299	−	0.225260i	$-0.0723232\pi$
$588$		0			0
$589$			57.4772i			2.36831i
$590$	1.33767	+	0.243401i	0.0550710	+	0.0100206i
$591$		0			0
$592$	−10.8389	+	40.4514i	−0.445477	+	1.66254i
$593$	−27.3282	+	7.32257i	−1.12224	+	0.300702i	−0.771788	−	0.635880i	$-0.780637\pi$
$593$	−27.3282	+	7.32257i	−1.12224	+	0.300702i	−0.350448	+	0.936582i	$0.613971\pi$
$594$		0			0
$595$	−7.78306	−	2.09153i	−0.319074	−	0.0857445i
$596$		−	55.6122i		−	2.27797i
$597$		0			0
$598$	0.548907	+	0.147079i	0.0224465	+	0.00601451i
$599$	13.6860	+	23.7049i	0.559195	+	0.968554i	0.997564	+	0.0697592i	$0.0222231\pi$
$599$	13.6860	+	23.7049i	0.559195	+	0.968554i	−0.438369	+	0.898795i	$0.644444\pi$
$600$		0			0
$601$	−39.4893			−1.61080			−0.805401	−	0.592731i	$-0.798050\pi$
$601$	−39.4893			−1.61080			−0.805401	+	0.592731i	$0.798050\pi$
$602$	39.0260	−	18.4233i	1.59058	−	0.750877i
$603$		0			0
$604$	−62.6747	−	36.1853i	−2.55020	−	1.47236i
$605$	−14.0167	+	1.14927i	−0.569859	+	0.0467245i
$606$		0			0
$607$	−3.88660	+	1.04141i	−0.157752	+	0.0422696i	−0.336831	−	0.941565i	$-0.609355\pi$
$607$	−3.88660	+	1.04141i	−0.157752	+	0.0422696i	0.179079	+	0.983835i	$0.442688\pi$
$608$	73.8314	+	73.8314i	2.99426	+	2.99426i
$609$		0			0
$610$	−24.1761	−	67.5681i	−0.978861	−	2.73575i
$611$	0.0929988	+	0.0536929i	0.00376233	+	0.00217218i
$612$		0			0
$613$	17.6850	+	4.73869i	0.714292	+	0.191394i	0.597623	−	0.801777i	$-0.296112\pi$
$613$	17.6850	+	4.73869i	0.714292	+	0.191394i	0.116668	+	0.993171i	$0.462779\pi$
$614$	5.64388	−	9.77549i	0.227769	−	0.394507i
$615$		0			0
$616$	−72.9163	+	61.7740i	−2.93788	+	2.48895i
$617$	21.3229	−	21.3229i	0.858426	−	0.858426i	−0.132727	−	0.991153i	$-0.542373\pi$
$617$	21.3229	−	21.3229i	0.858426	−	0.858426i	0.991153	+	0.132727i	$0.0423732\pi$
$618$		0			0
$619$	2.61954	−	1.51239i	0.105288	−	0.0607883i	−0.446431	−	0.894818i	$-0.647305\pi$
$619$	2.61954	−	1.51239i	0.105288	−	0.0607883i	0.551720	+	0.834030i	$0.313972\pi$
$620$	9.10598	+	111.058i	0.365705	+	4.46020i
$621$		0			0
$622$	17.7744	+	17.7744i	0.712688	+	0.712688i
$623$	−16.2597	−	34.4428i	−0.651431	−	1.37992i
$624$		0			0
$625$	−18.7958	−	16.4838i	−0.751834	−	0.659353i
$626$	−48.4572	+	27.9768i	−1.93674	+	1.11818i
$627$		0			0
$628$	27.5311	+	102.747i	1.09861	+	4.10007i
$629$	4.42323			0.176366
$630$		0			0
$631$	40.5296			1.61346			0.806730	−	0.590921i	$-0.201235\pi$
$631$	40.5296			1.61346			0.806730	+	0.590921i	$0.201235\pi$
$632$	−4.88653	−	18.2368i	−0.194376	−	0.725420i
$633$		0			0
$634$	33.6130	−	19.4065i	1.33494	−	0.770729i
$635$	−3.22833	+	17.7421i	−0.128112	+	0.704074i
$636$		0			0
$637$	6.32697	+	2.87778i	0.250684	+	0.114022i
$638$	−6.95051	−	6.95051i	−0.275173	−	0.275173i
$639$		0			0
$640$	36.0879	+	30.6185i	1.42650	+	1.21030i
$641$	37.2313	−	21.4955i	1.47055	−	0.849022i	0.471096	−	0.882082i	$-0.343859\pi$
$641$	37.2313	−	21.4955i	1.47055	−	0.849022i	0.999453	+	0.0330603i	$0.0105253\pi$
$642$		0			0
$643$	31.4639	−	31.4639i	1.24082	−	1.24082i	0.281152	−	0.959663i	$-0.409283\pi$
$643$	31.4639	−	31.4639i	1.24082	−	1.24082i	0.959663	−	0.281152i	$-0.0907166\pi$
$644$	0.525164	+	2.89814i	0.0206944	+	0.114203i
$645$		0			0
$646$	11.0493	−	19.1380i	0.434730	−	0.752975i
$647$	−16.5816	−	4.44301i	−0.651888	−	0.174673i	−0.0823057	−	0.996607i	$-0.526228\pi$
$647$	−16.5816	−	4.44301i	−0.651888	−	0.174673i	−0.569582	+	0.821934i	$0.692895\pi$
$648$		0			0
$649$	−0.814279	−	0.470124i	−0.0319632	−	0.0184540i
$650$	10.3198	−	8.46920i	0.404778	−	0.332189i
$651$		0			0
$652$	−6.35583	−	6.35583i	−0.248913	−	0.248913i
$653$	26.6769	−	7.14804i	1.04395	−	0.279724i	0.304198	−	0.952609i	$-0.401611\pi$
$653$	26.6769	−	7.14804i	1.04395	−	0.279724i	0.739748	+	0.672884i	$0.234945\pi$
$654$		0			0
$655$	−3.45864	−	42.1821i	−0.135140	−	1.64819i
$656$	13.9857	+	8.07466i	0.546051	+	0.315262i
$657$		0			0
$658$	−0.0634320	+	0.766779i	−0.00247284	+	0.0298922i
$659$	6.44855			0.251200			0.125600	−	0.992081i	$-0.459914\pi$
$659$	6.44855			0.251200			0.125600	+	0.992081i	$0.459914\pi$
$660$		0			0
$661$	3.39721	+	5.88414i	0.132136	+	0.228867i	0.924500	−	0.381182i	$-0.124483\pi$
$661$	3.39721	+	5.88414i	0.132136	+	0.228867i	−0.792364	+	0.610049i	$0.791150\pi$
$662$	−29.9936	−	8.03675i	−1.16573	−	0.312357i
$663$		0			0
$664$			46.1875i			1.79242i
$665$	30.8962	+	17.8679i	1.19810	+	0.692888i
$666$		0			0
$667$	−0.180733	+	0.0484272i	−0.00699800	+	0.00187511i
$668$	9.10418	−	33.9772i	0.352251	−	1.31462i
$669$		0			0
$670$	−10.9099	−	15.7633i	−0.421486	−	0.608990i
$671$			49.6273i			1.91584i
$672$		0			0
$673$	15.7865	−	15.7865i	0.608524	−	0.608524i	−0.334036	−	0.942560i	$-0.608411\pi$
$673$	15.7865	−	15.7865i	0.608524	−	0.608524i	0.942560	+	0.334036i	$0.108411\pi$
$674$	39.3773	−	68.2035i	1.51676	−	2.62710i
$675$		0			0
$676$	−31.4200	−	54.4211i	−1.20846	−	2.09312i
$677$	−4.56513	−	17.0373i	−0.175452	−	0.654797i	−0.996474	−	0.0839000i	$-0.973262\pi$
$677$	−4.56513	−	17.0373i	−0.175452	−	0.654797i	0.821022	−	0.570897i	$-0.193404\pi$
$678$		0			0
$679$	−14.3178	+	2.59449i	−0.549467	+	0.0995673i
$680$	11.3136	−	23.9204i	0.433855	−	0.917304i
$681$		0			0
$682$	27.5705	−	102.895i	1.05573	−	3.94004i
$683$	−6.77169	+	25.2723i	−0.259111	+	0.967017i	0.706645	+	0.707568i	$0.250208\pi$
$683$	−6.77169	+	25.2723i	−0.259111	+	0.967017i	−0.965757	+	0.259449i	$0.916459\pi$
$684$		0			0
$685$	8.98548	+	25.1129i	0.343318	+	0.959515i
$686$	0.706516	+	49.7954i	0.0269749	+	1.90120i
$687$		0			0
$688$	20.2493	+	75.5716i	0.771999	+	2.88114i
$689$	−2.48519	−	4.30447i	−0.0946781	−	0.163987i
$690$		0			0
$691$	−6.25564	+	10.8351i	−0.237976	+	0.412186i	−0.960133	−	0.279543i	$-0.909817\pi$
$691$	−6.25564	+	10.8351i	−0.237976	+	0.412186i	0.722158	+	0.691729i	$0.243151\pi$
$692$	1.00838	−	1.00838i	0.0383328	−	0.0383328i
$693$		0			0
$694$		−	57.2360i		−	2.17265i
$695$	−31.2658	+	21.6392i	−1.18598	+	0.820823i
$696$		0			0
$697$	0.441469	−	1.64758i	0.0167218	−	0.0624067i
$698$	−17.7819	+	4.76465i	−0.673055	+	0.180344i
$699$		0			0
$700$	62.5288	+	29.6297i	2.36336	+	1.11990i
$701$		−	15.0496i		−	0.568417i	−0.958763	−	0.284208i	$-0.908269\pi$
$701$		−	15.0496i		−	0.568417i	0.958763	−	0.284208i	$-0.0917307\pi$
$702$		0			0
$703$	−18.9212	−	5.06992i	−0.713627	−	0.191216i
$704$	−43.1275	−	74.6991i	−1.62543	−	2.81533i
$705$		0			0
$706$	−54.7810			−2.06171
$707$	−1.98821	+	24.0339i	−0.0747743	+	0.903887i
$708$		0			0
$709$	36.3774	+	21.0025i	1.36618	+	0.788766i	0.990438	−	0.137958i	$-0.0440539\pi$
$709$	36.3774	+	21.0025i	1.36618	+	0.788766i	0.375744	+	0.926724i	$0.377387\pi$
$710$	−44.8745	−	38.0734i	−1.68411	−	1.42887i
$711$		0			0
$712$	120.794	−	32.3665i	4.52693	−	1.21299i
$713$	−1.43382	−	1.43382i	−0.0536972	−	0.0536972i
$714$		0			0
$715$	−8.69255	+	3.11022i	−0.325083	+	0.116316i
$716$	77.8167	+	44.9275i	2.90815	+	1.67902i
$717$		0			0
$718$	−41.3921	−	11.0910i	−1.54474	−	0.413911i
$719$	20.7737	−	35.9811i	0.774729	−	1.34187i	−0.160217	−	0.987082i	$-0.551220\pi$
$719$	20.7737	−	35.9811i	0.774729	−	1.34187i	0.934947	−	0.354788i	$-0.115447\pi$
$720$		0			0
$721$	−22.3245	−	8.00608i	−0.831406	−	0.298162i
$722$	−33.0754	+	33.0754i	−1.23094	+	1.23094i
$723$		0			0
$724$	18.4606	−	10.6582i	0.686082	−	0.396110i
$725$	−1.54839	+	4.11392i	−0.0575058	+	0.152787i
$726$		0			0
$727$	5.40873	+	5.40873i	0.200599	+	0.200599i	0.800256	−	0.599658i	$-0.204697\pi$
$727$	5.40873	+	5.40873i	0.200599	+	0.200599i	−0.599658	+	0.800256i	$0.704697\pi$
$728$	−13.0012	+	18.7559i	−0.481858	+	0.695139i
$729$		0			0
$730$	−33.8138	+	23.4027i	−1.25150	+	0.866174i
$731$	7.15640	−	4.13175i	0.264689	−	0.152818i
$732$		0			0
$733$	9.15765	+	34.1768i	0.338246	+	1.26235i	0.900307	+	0.435255i	$0.143342\pi$
$733$	9.15765	+	34.1768i	0.338246	+	1.26235i	−0.562062	+	0.827095i	$0.689992\pi$
$734$	−30.2007			−1.11473
$735$		0			0
$736$	−3.68359			−0.135779
$737$	3.43123	+	12.8055i	0.126391	+	0.471698i
$738$		0			0
$739$	−17.4398	+	10.0689i	−0.641535	+	0.370390i	−0.785205	−	0.619235i	$-0.787443\pi$
$739$	−17.4398	+	10.0689i	−0.641535	+	0.370390i	0.143671	+	0.989626i	$0.454109\pi$
$740$	−37.3630	−	6.79851i	−1.37349	−	0.249918i
$741$		0			0
$742$	20.2879	−	29.2677i	0.744792	−	1.07445i
$743$	4.81639	+	4.81639i	0.176696	+	0.176696i	0.789914	−	0.613218i	$-0.210125\pi$
$743$	4.81639	+	4.81639i	0.176696	+	0.176696i	−0.613218	+	0.789914i	$0.710125\pi$
$744$		0			0
$745$	23.6948	−	1.94281i	0.868110	−	0.0711789i
$746$	71.7151	−	41.4047i	2.62568	−	1.51594i
$747$		0			0
$748$	−20.9498	+	20.9498i	−0.766002	+	0.766002i
$749$	−33.6804	−	12.0786i	−1.23066	−	0.441342i
$750$		0			0
$751$	1.34330	−	2.32666i	0.0490177	−	0.0849012i	−0.840476	−	0.541850i	$-0.817724\pi$
$751$	1.34330	−	2.32666i	0.0490177	−	0.0849012i	0.889493	+	0.456948i	$0.151058\pi$
$752$	−1.34731	−	0.361011i	−0.0491314	−	0.0131647i
$753$		0			0
$754$	−2.03283	−	1.17366i	−0.0740313	−	0.0427420i
$755$	13.2280	−	27.9680i	0.481415	−	1.01786i
$756$		0			0
$757$	26.4395	+	26.4395i	0.960959	+	0.960959i	0.999266	−	0.0383075i	$-0.0121966\pi$
$757$	26.4395	+	26.4395i	0.960959	+	0.960959i	−0.0383075	+	0.999266i	$0.512197\pi$
$758$	−15.0596	+	4.03521i	−0.546990	+	0.146566i
$759$		0			0
$760$	−75.8135	+	89.3563i	−2.75005	+	3.24129i
$761$	−22.8320	−	13.1820i	−0.827658	−	0.477849i	0.0253919	−	0.999678i	$-0.491917\pi$
$761$	−22.8320	−	13.1820i	−0.827658	−	0.477849i	−0.853050	+	0.521829i	$0.825250\pi$
$762$		0			0
$763$	0.803794	−	9.71643i	0.0290993	−	0.351758i
$764$	−49.2763			−1.78275
$765$		0			0
$766$	12.6598	+	21.9274i	0.457417	+	0.792270i
$767$	−0.216883	−	0.0581136i	−0.00783119	−	0.00209836i
$768$		0			0
$769$		−	3.56245i		−	0.128465i	−0.997935	−	0.0642326i	$-0.979540\pi$
$769$		−	3.56245i		−	0.128465i	0.997935	−	0.0642326i	$-0.0204600\pi$
$770$	−46.7390	−	46.8071i	−1.68436	−	1.68681i
$771$		0			0
$772$	58.8460	−	15.7677i	2.11791	−	0.567493i
$773$	0.795756	−	2.96980i	0.0286214	−	0.106816i	−0.950137	−	0.311831i	$-0.899058\pi$
$773$	0.795756	−	2.96980i	0.0286214	−	0.106816i	0.978759	+	0.205015i	$0.0657243\pi$
$774$		0			0
$775$	−47.0005	+	7.75960i	−1.68831	+	0.278733i
$776$		−	47.7755i		−	1.71504i
$777$		0			0
$778$	−18.7989	+	18.7989i	−0.673975	+	0.673975i
$779$	−3.77693	+	6.54184i	−0.135323	+	0.234386i
$780$		0			0
$781$	20.3487	+	35.2449i	0.728132	+	1.26116i
$782$	0.201780	+	0.753053i	0.00721563	+	0.0269291i
$783$		0			0
$784$	−89.0557	−	14.8358i	−3.18056	−	0.529851i
$785$	−42.8159	+	15.3197i	−1.52817	+	0.546783i
$786$		0			0
$787$	−10.9823	+	40.9866i	−0.391478	+	1.46101i	0.436220	+	0.899840i	$0.356317\pi$
$787$	−10.9823	+	40.9866i	−0.391478	+	1.46101i	−0.827698	+	0.561174i	$0.810350\pi$
$788$	−15.4533	+	57.6727i	−0.550503	+	2.05450i
$789$		0			0
$790$	12.3042	−	4.40248i	0.437764	−	0.156633i
$791$	−48.6766	+	8.82056i	−1.73074	+	0.313623i
$792$		0			0
$793$	3.06730	+	11.4473i	0.108923	+	0.406506i
$794$	29.0945	+	50.3932i	1.03253	+	1.78839i
$795$		0			0
$796$	−49.6405	+	85.9799i	−1.75946	+	3.04748i
$797$	37.3428	−	37.3428i	1.32275	−	1.32275i	0.411208	−	0.911542i	$-0.365107\pi$
$797$	37.3428	−	37.3428i	1.32275	−	1.32275i	0.911542	−	0.411208i	$-0.134893\pi$
$798$		0			0
$799$			0.147324i			0.00521195i
$800$	−50.4063	+	70.3413i	−1.78213	+	2.48694i
$801$		0			0
$802$	−15.1887	+	56.6849i	−0.536331	+	2.00161i
$803$	27.4690	−	7.36031i	0.969361	−	0.259740i
$804$		0			0
$805$	−1.21647	+	0.325004i	−0.0428749	+	0.0114549i
$806$		−	25.4383i		−	0.896027i
$807$		0			0
$808$	−76.4825	−	20.4934i	−2.69064	−	0.720956i
$809$	10.5010	+	18.1884i	0.369197	+	0.639468i	0.989440	−	0.144941i	$-0.0462993\pi$
$809$	10.5010	+	18.1884i	0.369197	+	0.639468i	−0.620243	+	0.784410i	$0.712966\pi$
$810$		0			0
$811$	−36.4188			−1.27884			−0.639419	−	0.768858i	$-0.720825\pi$
$811$	−36.4188			−1.27884			−0.639419	+	0.768858i	$0.720825\pi$
$812$	1.00302	−	12.1247i	0.0351990	−	0.425493i
$813$		0			0
$814$	31.4405	+	18.1522i	1.10199	+	0.636233i
$815$	2.48600	−	2.93008i	0.0870807	−	0.102636i
$816$		0			0
$817$	−35.3487	+	9.47166i	−1.23670	+	0.331371i
$818$	4.93364	+	4.93364i	0.172501	+	0.172501i
$819$		0			0
$820$	−6.26142	+	13.2386i	−0.218658	+	0.462311i
$821$	−21.3394	−	12.3203i	−0.744751	−	0.429982i	0.0790431	−	0.996871i	$-0.474814\pi$
$821$	−21.3394	−	12.3203i	−0.744751	−	0.429982i	−0.823794	+	0.566889i	$0.808147\pi$
$822$		0			0
$823$	−17.4572	−	4.67764i	−0.608519	−	0.163052i	−0.0586159	−	0.998281i	$-0.518669\pi$
$823$	−17.4572	−	4.67764i	−0.608519	−	0.163052i	−0.549903	+	0.835228i	$0.685335\pi$
$824$	38.9347	−	67.4368i	1.35635	−	2.34927i
$825$		0			0
$826$	−0.286844	−	1.58296i	−0.00998059	−	0.0550783i
$827$	−25.8068	+	25.8068i	−0.897391	+	0.897391i	−0.995205	−	0.0978136i	$-0.968815\pi$
$827$	−25.8068	+	25.8068i	−0.897391	+	0.897391i	0.0978136	+	0.995205i	$0.468815\pi$
$828$		0			0
$829$	−21.1695	+	12.2222i	−0.735248	+	0.424496i	−0.820339	−	0.571878i	$-0.806215\pi$
$829$	−21.1695	+	12.2222i	−0.735248	+	0.424496i	0.0850911	+	0.996373i	$0.472882\pi$
$830$	−31.8623	+	2.61249i	−1.10596	+	0.0906808i
$831$		0			0
$832$	−14.5650	−	14.5650i	−0.504949	−	0.504949i
$833$	0.920907	+	9.49119i	0.0319075	+	0.328850i
$834$		0			0
$835$	14.7948	+	2.69204i	0.511995	+	0.0931618i
$836$	113.630	−	65.6042i	3.92997	−	2.26897i
$837$		0			0
$838$	−6.42988	−	23.9966i	−0.222117	−	0.828950i
$839$	34.3012			1.18421			0.592105	−	0.805861i	$-0.298297\pi$
$839$	34.3012			1.18421			0.592105	+	0.805861i	$0.298297\pi$
$840$		0			0
$841$	−28.2271			−0.973349
$842$	−3.20278	−	11.9529i	−0.110375	−	0.411925i
$843$		0			0
$844$	−33.6631	+	19.4354i	−1.15873	+	0.668993i
$845$	22.0896	−	15.2884i	0.759906	−	0.525936i
$846$		0			0
$847$	7.10379	+	15.0479i	0.244089	+	0.517052i
$848$	45.6511	+	45.6511i	1.56767	+	1.56767i
$849$		0			0
$850$	17.1413	+	6.45163i	0.587943	+	0.221289i
$851$	0.598482	−	0.345534i	0.0205157	−	0.0118447i
$852$		0			0
$853$	38.7234	−	38.7234i	1.32586	−	1.32586i	0.416919	−	0.908944i	$-0.363110\pi$
$853$	38.7234	−	38.7234i	1.32586	−	1.32586i	0.908944	−	0.416919i	$-0.136890\pi$
$854$	−64.7869	+	54.8868i	−2.21696	+	1.87819i
$855$		0			0
$856$	58.7399	−	101.740i	2.00769	−	3.47742i
$857$	−36.7630	−	9.85063i	−1.25580	−	0.336491i	−0.431226	−	0.902244i	$-0.641919\pi$
$857$	−36.7630	−	9.85063i	−1.25580	−	0.336491i	−0.824575	+	0.565753i	$0.808586\pi$
$858$		0			0
$859$	21.3839	+	12.3460i	0.729608	+	0.421239i	0.818279	−	0.574822i	$-0.194929\pi$
$859$	21.3839	+	12.3460i	0.729608	+	0.421239i	−0.0886709	+	0.996061i	$0.528262\pi$
$860$	−66.8006	+	23.9015i	−2.27788	+	0.815033i
$861$		0			0
$862$	−2.29738	−	2.29738i	−0.0782491	−	0.0782491i
$863$	−14.5822	+	3.90728i	−0.496382	+	0.133005i	−0.498321	−	0.866993i	$-0.666050\pi$
$863$	−14.5822	+	3.90728i	−0.496382	+	0.133005i	0.00193811	+	0.999998i	$0.499383\pi$
$864$		0			0
$865$	0.464869	+	0.394414i	0.0158060	+	0.0134105i
$866$	69.8461	+	40.3257i	2.37347	+	1.37032i
$867$		0			0
$868$	119.229	−	56.2853i	4.04689	−	1.91045i
$869$	−9.03718			−0.306565
$870$		0			0
$871$	1.58293	+	2.74172i	0.0536357	+	0.0928997i
$872$	30.9204	+	8.28509i	1.04710	+	0.280569i
$873$		0			0
$874$		−	3.45261i		−	0.116786i
$875$	−10.4400	+	27.6768i	−0.352935	+	0.935648i
$876$		0			0
$877$	37.5967	−	10.0740i	1.26955	−	0.340175i	0.439692	−	0.898149i	$-0.355088\pi$
$877$	37.5967	−	10.0740i	1.26955	−	0.340175i	0.829859	+	0.557973i	$0.188421\pi$
$878$	−5.83432	+	21.7740i	−0.196899	+	0.734836i
$879$		0			0
$880$	98.6048	−	68.2450i	3.32397	−	2.30054i
$881$		−	40.0097i		−	1.34796i	−0.738750	−	0.673980i	$-0.764583\pi$
$881$		−	40.0097i		−	1.34796i	0.738750	−	0.673980i	$-0.235417\pi$
$882$		0			0
$883$	20.2833	−	20.2833i	0.682587	−	0.682587i	−0.277995	−	0.960582i	$-0.589670\pi$
$883$	20.2833	−	20.2833i	0.682587	−	0.682587i	0.960582	+	0.277995i	$0.0896700\pi$
$884$	−3.53757	+	6.12725i	−0.118981	+	0.206082i
$885$		0			0
$886$	7.22761	+	12.5186i	0.242816	+	0.420570i
$887$	−2.09272	−	7.81012i	−0.0702665	−	0.262238i	0.921852	−	0.387542i	$-0.126676\pi$
$887$	−2.09272	−	7.81012i	−0.0702665	−	0.262238i	−0.992118	+	0.125304i	$0.960009\pi$
$888$		0			0
$889$	20.9955	−	3.80454i	0.704167	−	0.127600i
$890$	29.1604	+	81.4984i	0.977458	+	2.73183i
$891$		0			0
$892$	18.5854	−	69.3616i	0.622285	−	2.32240i
$893$	0.168864	−	0.630208i	0.00565080	−	0.0210891i
$894$		0			0
$895$	−16.4238	+	34.7250i	−0.548988	+	1.16073i
$896$	18.9033	−	52.7108i	0.631516	−	1.76094i
$897$		0			0
$898$	2.33070	+	8.69830i	0.0777765	+	0.290266i
$899$	4.18791	+	7.25367i	0.139675	+	0.241923i
$900$		0			0
$901$	3.40946	−	5.90537i	0.113586	−	0.196736i
$902$	9.89938	−	9.89938i	0.329613	−	0.329613i
$903$		0			0
$904$		−	162.424i		−	5.40213i
$905$	5.18609	+	7.49319i	0.172391	+	0.249082i
$906$		0			0
$907$	3.38781	−	12.6435i	0.112491	−	0.419820i	−0.886596	−	0.462544i	$-0.846937\pi$
$907$	3.38781	−	12.6435i	0.112491	−	0.419820i	0.999087	+	0.0427234i	$0.0136034\pi$
$908$	54.4155	−	14.5806i	1.80584	−	0.483874i
$909$		0			0
$910$	−13.6741	−	7.90800i	−0.453291	−	0.262148i
$911$			18.3815i			0.609005i	0.952512	+	0.304502i	$0.0984901\pi$
$911$			18.3815i			0.609005i	−0.952512	+	0.304502i	$0.901510\pi$
$912$		0			0
$913$	21.3548	+	5.72201i	0.706742	+	0.189371i
$914$	−1.40666	−	2.43640i	−0.0465281	−	0.0805891i
$915$		0			0
$916$	−38.7527			−1.28042
$917$	−45.2855	+	21.3783i	−1.49546	+	0.705974i
$918$		0			0
$919$	−33.5697	−	19.3815i	−1.10736	−	0.639336i	−0.169218	−	0.985579i	$-0.554124\pi$
$919$	−33.5697	−	19.3815i	−1.10736	−	0.639336i	−0.938145	+	0.346242i	$0.887457\pi$
$920$	−0.337838	−	4.12032i	−0.0111382	−	0.135843i
$921$		0			0
$922$	−59.8820	+	16.0453i	−1.97211	+	0.528425i
$923$	6.87211	+	6.87211i	0.226198	+	0.226198i
$924$		0			0
$925$	1.59138	−	16.1568i	0.0523243	−	0.531232i
$926$	−84.9899	−	49.0689i	−2.79294	−	1.61251i
$927$		0			0
$928$	14.6971	+	3.93808i	0.482456	+	0.129274i
$929$	−4.37286	+	7.57402i	−0.143469	+	0.248496i	−0.928801	−	0.370580i	$-0.879159\pi$
$929$	−4.37286	+	7.57402i	−0.143469	+	0.248496i	0.785332	+	0.619075i	$0.212492\pi$
$930$		0			0
$931$	6.93949	−	41.6559i	0.227433	−	1.36522i
$932$	82.4764	−	82.4764i	2.70160	−	2.70160i
$933$		0			0
$934$	−56.1993	+	32.4467i	−1.83890	+	1.06169i
$935$	−9.65801	−	8.19425i	−0.315851	−	0.267981i
$936$		0			0
$937$	10.8936	+	10.8936i	0.355879	+	0.355879i	0.862291	−	0.506413i	$-0.169029\pi$
$937$	10.8936	+	10.8936i	0.355879	+	0.355879i	−0.506413	+	0.862291i	$0.669029\pi$
$938$	−12.9223	+	18.6420i	−0.421929	+	0.608683i
$939$		0			0
$940$	0.226438	−	1.24445i	0.00738558	−	0.0405894i
$941$	−47.6405	+	27.5052i	−1.55304	+	0.896646i	−0.555143	+	0.831755i	$0.687337\pi$
$941$	−47.6405	+	27.5052i	−1.55304	+	0.896646i	−0.997892	+	0.0648907i	$0.979330\pi$
$942$		0			0
$943$	−0.0689733	−	0.257412i	−0.00224608	−	0.00838249i
$944$	2.91648			0.0949234
$945$		0			0
$946$	67.8240			2.20515
$947$	−11.1538	−	41.6265i	−0.362449	−	1.35268i	−0.870846	−	0.491556i	$-0.836428\pi$
$947$	−11.1538	−	41.6265i	−0.362449	−	1.35268i	0.508396	−	0.861123i	$-0.330238\pi$
$948$		0			0
$949$	5.88125	−	3.39554i	0.190913	−	0.110224i
$950$	−65.9305	−	47.2456i	−2.13907	−	1.53285i
$951$		0			0
$952$	−31.2024	−	2.58123i	−1.01128	−	0.0836580i
$953$	15.9728	+	15.9728i	0.517408	+	0.517408i	0.916786	−	0.399378i	$-0.130774\pi$
$953$	15.9728	+	15.9728i	0.517408	+	0.517408i	−0.399378	+	0.916786i	$0.630774\pi$
$954$		0			0
$955$	−1.72146	−	20.9952i	−0.0557052	−	0.679389i
$956$	−54.0710	+	31.2179i	−1.74878	+	1.00966i
$957$		0			0
$958$	−36.5799	+	36.5799i	−1.18184	+	1.18184i
$959$	24.0792	−	20.3997i	0.777559	−	0.658740i
$960$		0			0
$961$	−29.8853	+	51.7628i	−0.964040	+	1.66977i
$962$	8.37417	+	2.24385i	0.269994	+	0.0723447i
$963$		0			0
$964$	66.7081	+	38.5140i	2.14852	+	1.24045i
$965$	8.77396	+	24.5217i	0.282444	+	0.789383i
$966$		0			0
$967$	16.1296	+	16.1296i	0.518694	+	0.518694i	0.917176	−	0.398482i	$-0.130463\pi$
$967$	16.1296	+	16.1296i	0.518694	+	0.518694i	−0.398482	+	0.917176i	$0.630463\pi$
$968$	−52.7742	+	14.1408i	−1.69623	+	0.454502i
$969$		0			0
$970$	32.9578	−	2.70231i	1.05821	−	0.0867660i
$971$	−38.0747	−	21.9824i	−1.22187	−	0.705449i	−0.256557	−	0.966529i	$-0.582588\pi$
$971$	−38.0747	−	21.9824i	−1.22187	−	0.705449i	−0.965317	+	0.261080i	$0.915921\pi$
$972$		0			0
$973$	36.9755	+	25.6308i	1.18538	+	0.821685i
$974$	78.4436			2.51349
$975$		0			0
$976$	−76.9676	−	133.312i	−2.46367	−	4.26720i
$977$	55.7479	+	14.9376i	1.78353	+	0.477896i	0.991220	−	0.132221i	$-0.0422108\pi$
$977$	55.7479	+	14.9376i	1.78353	+	0.477896i	0.792312	+	0.610117i	$0.208877\pi$
$978$		0			0
$979$		−	59.8589i		−	1.91310i
$980$	6.80909	−	81.5874i	0.217508	−	2.60622i
$981$		0			0
$982$	−20.2395	+	5.42317i	−0.645870	+	0.173060i
$983$	1.79419	−	6.69600i	0.0572257	−	0.213569i	−0.931392	−	0.364017i	$-0.881405\pi$
$983$	1.79419	−	6.69600i	0.0572257	−	0.213569i	0.988618	+	0.150448i	$0.0480716\pi$
$984$		0			0
$985$	−25.1125	−	4.56944i	−0.800152	−	0.145595i
$986$		−	3.22031i		−	0.102556i
$987$		0			0
$988$	22.1557	−	22.1557i	0.704868	−	0.704868i
$989$	0.645528	−	1.11809i	0.0205266	−	0.0355531i
$990$		0			0
$991$	−14.8019	−	25.6376i	−0.470197	−	0.814405i	0.529222	−	0.848483i	$-0.322484\pi$
$991$	−14.8019	−	25.6376i	−0.470197	−	0.814405i	−0.999419	+	0.0340783i	$0.989150\pi$
$992$	42.6778	+	159.276i	1.35502	+	5.05701i
$993$		0			0
$994$	−23.5059	+	65.5447i	−0.745561	+	2.07895i
$995$	−38.3678	−	18.1467i	−1.21634	−	0.575289i
$996$		0			0
$997$	4.53622	−	16.9294i	0.143663	−	0.536159i	−0.856148	−	0.516731i	$-0.827149\pi$
$997$	4.53622	−	16.9294i	0.143663	−	0.536159i	0.999811	−	0.0194282i	$-0.00618457\pi$
$998$	3.63421	−	13.5631i	0.115039	−	0.429331i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.107.16	yes	64
3.2	odd	2	inner	315.2.ce.a.107.1	yes	64
5.3	odd	4	inner	315.2.ce.a.233.16	yes	64
7.4	even	3	inner	315.2.ce.a.242.1	yes	64
15.8	even	4	inner	315.2.ce.a.233.1	yes	64
21.11	odd	6	inner	315.2.ce.a.242.16	yes	64
35.18	odd	12	inner	315.2.ce.a.53.1	✓	64
105.53	even	12	inner	315.2.ce.a.53.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.1	✓	64	35.18	odd	12	inner
315.2.ce.a.53.16	yes	64	105.53	even	12	inner
315.2.ce.a.107.1	yes	64	3.2	odd	2	inner
315.2.ce.a.107.16	yes	64	1.1	even	1	trivial
315.2.ce.a.233.1	yes	64	15.8	even	4	inner
315.2.ce.a.233.16	yes	64	5.3	odd	4	inner
315.2.ce.a.242.1	yes	64	7.4	even	3	inner
315.2.ce.a.242.16	yes	64	21.11	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.695956 + 2.59734i) q^{2} +(-4.52979 + 2.61528i) q^{4} +(-1.27254 - 1.83865i) q^{5} +(-1.50727 + 2.17442i) q^{7} +(-6.14253 - 6.14253i) q^{8} +(3.88997 - 4.58485i) q^{10} +(-3.60099 + 2.07903i) q^{11} +(-0.702126 + 0.702126i) q^{13} +(-6.69673 - 2.40161i) q^{14} +(6.44878 - 11.1696i) q^{16} +(-1.31583 - 0.352577i) q^{17} +(5.22461 + 3.01643i) q^{19} +(10.5729 + 5.00065i) q^{20} +(-7.90609 - 7.90609i) q^{22} +(-0.205581 + 0.0550852i) q^{23} +(-1.76127 + 4.67952i) q^{25} +(-2.31231 - 1.33501i) q^{26} +(1.14092 - 13.7916i) q^{28} +0.879133 q^{29} +(4.76368 + 8.25093i) q^{31} +(16.7177 + 4.47950i) q^{32} -3.66305i q^{34} +(5.91608 + 0.00430290i) q^{35} +(-3.13636 + 0.840384i) q^{37} +(-4.19861 + 15.6694i) q^{38} +(-3.47734 + 19.1106i) q^{40} +1.25212i q^{41} +(-4.28935 + 4.28935i) q^{43} +(10.8745 - 18.8352i) q^{44} +(-0.286150 - 0.495627i) q^{46} +(-0.0279906 - 0.104462i) q^{47} +(-2.45625 - 6.55491i) q^{49} +(-13.3801 - 1.31789i) q^{50} +(1.34423 - 5.01674i) q^{52} +(-1.29555 + 4.83507i) q^{53} +(8.40502 + 3.97530i) q^{55} +(22.6150 - 4.09799i) q^{56} +(0.611838 + 2.28341i) q^{58} +(0.113063 + 0.195831i) q^{59} +(5.96760 - 10.3362i) q^{61} +(-18.1152 + 18.1152i) q^{62} +20.7441i q^{64} +(2.18445 + 0.397480i) q^{65} +(0.825199 - 3.07969i) q^{67} +(6.88254 - 1.84417i) q^{68} +(4.10616 + 15.3691i) q^{70} -9.78757i q^{71} +(-6.60621 - 1.77013i) q^{73} +(-4.36553 - 7.56133i) q^{74} -31.5552 q^{76} +(0.906979 - 10.9637i) q^{77} +(1.88223 + 1.08671i) q^{79} +(-28.7434 + 2.35676i) q^{80} +(-3.25219 + 0.871421i) q^{82} +(-3.75964 - 3.75964i) q^{83} +(1.02619 + 2.86803i) q^{85} +(-14.1261 - 8.15572i) q^{86} +(34.8897 + 9.34867i) q^{88} +(-7.19793 + 12.4672i) q^{89} +(-0.468424 - 2.58502i) q^{91} +(0.787175 - 0.787175i) q^{92} +(0.251845 - 0.145403i) q^{94} +(-1.10238 - 13.4448i) q^{95} +(3.88891 + 3.88891i) q^{97} +(15.3159 - 10.9417i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73}+ \cdots + 208 q^{97}+O(q^{100}) \) 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

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