LMFDB - Embedded newform 315.2.ce.a.53.16

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			53.16
Character	$\chi$	$=$	315.53
Dual form			315.2.ce.a.107.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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	−0.0535055	−	0.998568i	$-0.517039\pi$
$2$	0.695956	−	2.59734i	0.492115	−	1.83660i	0.545621	−	0.838032i	$-0.316294\pi$
$3$		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	−0.153300	−	0.988180i	$-0.548990\pi$
$11$	−3.60099	−	2.07903i	−1.08574	−	0.626852i	−0.932439	+	0.361328i	$0.882323\pi$
$12$		0			0
$13$	−0.702126	−	0.702126i	−0.194735	−	0.194735i	0.603004	−	0.797738i	$-0.293970\pi$
$13$	−0.702126	−	0.702126i	−0.194735	−	0.194735i	−0.797738	+	0.603004i	$0.793970\pi$
$14$	−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	−0.414831	−	0.909898i	$-0.636159\pi$
$17$	−1.31583	+	0.352577i	−0.319137	+	0.0855124i	0.0956947	+	0.995411i	$0.469493\pi$
$18$		0			0
$19$	5.22461	−	3.01643i	1.19861	−	0.692016i	0.238363	−	0.971176i	$-0.423389\pi$
$19$	5.22461	−	3.01643i	1.19861	−	0.692016i	0.960245	+	0.279160i	$0.0900559\pi$
$20$	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	0.237322	−	0.971431i	$-0.423730\pi$
$23$	−0.205581	−	0.0550852i	−0.0428665	−	0.0114861i	−0.280189	+	0.959945i	$0.590397\pi$
$24$		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	−0.0205224	−	0.999789i	$-0.506533\pi$
$31$	4.76368	−	8.25093i	0.855582	−	1.48191i	0.876104	−	0.482122i	$-0.160134\pi$
$32$	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	−0.00837687	−	0.999965i	$-0.502666\pi$
$37$	−3.13636	−	0.840384i	−0.515614	−	0.138158i	−0.507237	+	0.861807i	$0.669333\pi$
$38$	−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	$-0.968828\pi$
$41$		−	1.25212i		−	0.195548i	0.995209	−	0.0977742i	$-0.0311723\pi$
$42$		0			0
$43$	−4.28935	−	4.28935i	−0.654120	−	0.654120i	0.299862	−	0.953982i	$-0.403059\pi$
$43$	−4.28935	−	4.28935i	−0.654120	−	0.654120i	−0.953982	+	0.299862i	$0.903059\pi$
$44$	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	−0.967937	−	0.251192i	$-0.919177\pi$
$47$	−0.0279906	+	0.104462i	−0.00408285	+	0.0152374i	0.963854	+	0.266430i	$0.0858440\pi$
$48$		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	−0.996029	−	0.0890305i	$-0.971623\pi$
$53$	−1.29555	−	4.83507i	−0.177958	−	0.664148i	0.818071	−	0.575117i	$-0.195044\pi$
$54$		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	−0.858572	−	0.512693i	$-0.828648\pi$
$59$	0.113063	−	0.195831i	0.0147196	−	0.0254951i	0.873291	+	0.487198i	$0.161981\pi$
$60$		0			0
$61$	5.96760	+	10.3362i	0.764073	+	1.32341i	0.940735	+	0.339142i	$0.110137\pi$
$61$	5.96760	+	10.3362i	0.764073	+	1.32341i	−0.176662	+	0.984272i	$0.556530\pi$
$62$	−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	0.997837	−	0.0657413i	$-0.0209412\pi$
$67$	0.825199	+	3.07969i	0.100814	+	0.376243i	−0.897023	+	0.441985i	$0.854275\pi$
$68$	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	$0.197254\pi$
$71$			9.78757i			1.16157i	−0.814057	+	0.580785i	$0.802746\pi$
$72$		0			0
$73$	−6.60621	+	1.77013i	−0.773198	+	0.207178i	−0.623784	−	0.781597i	$-0.714406\pi$
$73$	−6.60621	+	1.77013i	−0.773198	+	0.207178i	−0.149414	+	0.988775i	$0.547739\pi$
$74$	−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	−0.390365	−	0.920660i	$-0.627651\pi$
$79$	1.88223	−	1.08671i	0.211767	−	0.122264i	0.602132	+	0.798396i	$0.294318\pi$
$80$	−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	−0.882669	−	0.469995i	$-0.844256\pi$
$83$	−3.75964	+	3.75964i	−0.412674	+	0.412674i	0.469995	+	0.882669i	$0.344256\pi$
$84$		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	−0.941309	−	0.337547i	$-0.890403\pi$
$89$	−7.19793	−	12.4672i	−0.762979	−	1.32152i	0.178330	−	0.983971i	$-0.442931\pi$
$90$		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	−0.481556	−	0.876415i	$-0.659928\pi$
$97$	3.88891	−	3.88891i	0.394859	−	0.394859i	0.876415	+	0.481556i	$0.159928\pi$
$98$	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	0.838363	−	0.545113i	$-0.183513\pi$
$101$	7.89380	+	4.55749i	0.785463	+	0.453487i	−0.0528999	+	0.998600i	$0.516846\pi$
$102$		0			0
$103$	2.32007	−	8.65861i	0.228603	−	0.853158i	−0.752326	−	0.658791i	$-0.771068\pi$
$103$	2.32007	−	8.65861i	0.228603	−	0.853158i	0.980929	−	0.194367i	$-0.0622652\pi$
$104$	8.62567			0.845816
$105$		0			0
$106$	−13.4600			−1.30735
$107$	3.50023	−	13.0630i	0.338380	−	1.26285i	−0.561778	−	0.827288i	$-0.689882\pi$
$107$	3.50023	−	13.0630i	0.338380	−	1.26285i	0.900158	−	0.435564i	$-0.143451\pi$
$108$		0			0
$109$	−3.19131	−	1.84250i	−0.305672	−	0.176480i	0.339316	−	0.940672i	$-0.389804\pi$
$109$	−3.19131	−	1.84250i	−0.305672	−	0.176480i	−0.644988	+	0.764192i	$0.723138\pi$
$110$	−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	0.285316	−	0.958434i	$-0.407901\pi$
$113$	13.2212	−	13.2212i	1.24375	−	1.24375i	0.958434	−	0.285316i	$-0.0920985\pi$
$114$		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	−0.913305	−	0.407275i	$-0.866479\pi$
$127$	−5.70267	+	5.70267i	−0.506030	+	0.506030i	0.407275	+	0.913305i	$0.366479\pi$
$128$	−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	0.434880	−	0.900488i	$-0.356791\pi$
$131$	16.3919	−	9.46386i	1.43217	−	0.826862i	0.997286	+	0.0736266i	$0.0234573\pi$
$132$		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	−0.714880	−	0.699247i	$-0.753519\pi$
$137$	−11.5217	+	3.08722i	−0.984361	+	0.263759i	−0.269481	+	0.963006i	$0.586852\pi$
$138$		0			0
$139$			17.0047i			1.44232i	0.692767	+	0.721161i	$0.256391\pi$
$139$			17.0047i			1.44232i	−0.692767	+	0.721161i	$0.743609\pi$
$140$	−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	0.561826	−	0.827256i	$-0.310099\pi$
$149$	−5.31610	−	9.20775i	−0.435512	−	0.754328i	−0.997337	+	0.0729275i	$0.976766\pi$
$150$		0			0
$151$	6.91806	−	11.9824i	0.562984	−	0.975116i	−0.434251	−	0.900792i	$-0.642987\pi$
$151$	6.91806	−	11.9824i	0.562984	−	0.975116i	0.997234	−	0.0743241i	$-0.0236799\pi$
$152$	−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	0.774450	+	0.632635i	$0.218027\pi$
$157$	5.26351	+	19.6437i	0.420074	+	1.56774i	−0.354376	+	0.935103i	$0.615307\pi$
$158$	−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	−0.946317	−	0.323239i	$-0.895228\pi$
$163$	0.444770	−	1.65991i	0.0348371	−	0.130014i	0.981154	+	0.193225i	$0.0618948\pi$
$164$	−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	0.498760	−	0.866740i	$-0.333789\pi$
$167$	−4.75534	−	4.75534i	−0.367980	−	0.367980i	−0.866740	+	0.498760i	$0.833789\pi$
$168$		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	0.248794	−	0.968556i	$-0.419966\pi$
$173$	−0.263351	−	0.0705647i	−0.0200222	−	0.00536494i	−0.268816	+	0.963191i	$0.586632\pi$
$174$		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	0.342980	+	0.939343i	$0.388564\pi$
$179$	−8.58944	+	14.8773i	−0.642005	+	1.11199i	−0.984985	+	0.172642i	$0.944770\pi$
$180$		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	−0.174890	−	0.984588i	$-0.555957\pi$
$191$	8.15870	−	4.71043i	0.590343	−	0.340834i	0.765233	+	0.643753i	$0.222624\pi$
$192$		0			0
$193$	−11.2504	+	3.01454i	−0.809824	+	0.216992i	−0.639893	−	0.768464i	$-0.721021\pi$
$193$	−11.2504	+	3.01454i	−0.809824	+	0.216992i	−0.169931	+	0.985456i	$0.554355\pi$
$194$	−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	0.933545	−	0.358461i	$-0.116699\pi$
$197$	8.07168	+	8.07168i	0.575083	+	0.575083i	−0.358461	+	0.933545i	$0.616699\pi$
$198$		0			0
$199$	16.4380	+	9.49049i	1.16526	+	0.672763i	0.952559	−	0.304354i	$-0.0984407\pi$
$199$	16.4380	+	9.49049i	1.16526	+	0.672763i	0.212701	+	0.977117i	$0.431774\pi$
$200$	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	0.302939	−	0.953010i	$-0.402032\pi$
$223$	−9.70762	−	9.70762i	−0.650071	−	0.650071i	−0.953010	+	0.302939i	$0.902032\pi$
$224$	−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	−0.586971	−	0.809608i	$-0.699680\pi$
$227$	−10.4034	+	2.78758i	−0.690498	+	0.185018i	−0.103527	+	0.994627i	$0.533013\pi$
$228$		0			0
$229$	6.41630	−	3.70445i	0.424001	−	0.244797i	−0.272787	−	0.962075i	$-0.587945\pi$
$229$	6.41630	−	3.70445i	0.424001	−	0.244797i	0.696788	+	0.717277i	$0.254612\pi$
$230$	−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	−0.528793	−	0.848751i	$-0.677355\pi$
$233$	−21.5398	−	5.77156i	−1.41112	−	0.378107i	−0.882324	+	0.470643i	$0.844022\pi$
$234$		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	−0.999567	−	0.0294146i	$-0.990636\pi$
$241$	−7.36327	+	12.7536i	−0.474310	+	0.821529i	0.525257	+	0.850943i	$0.323969\pi$
$242$	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	$-0.797357\pi$
$251$		−	18.8368i		−	1.18897i	0.804108	−	0.594483i	$-0.202643\pi$
$252$		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	−0.733520	−	0.679668i	$-0.762124\pi$
$257$	3.87251	−	14.4524i	0.241561	−	0.901517i	0.975081	−	0.221849i	$-0.0712093\pi$
$258$		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	−0.996015	−	0.0891835i	$-0.971574\pi$
$263$	−2.88720	−	10.7752i	−0.178032	−	0.664426i	0.817983	−	0.575243i	$-0.195092\pi$
$264$		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	0.491425	+	0.870920i	$0.336476\pi$
$269$	−8.34045	+	14.4461i	−0.508526	+	0.880793i	−0.999951	+	0.00987349i	$0.996857\pi$
$270$		0			0
$271$	5.86722	+	10.1623i	0.356408	+	0.617317i	0.987358	−	0.158507i	$-0.0506679\pi$
$271$	5.86722	+	10.1623i	0.356408	+	0.617317i	−0.630950	+	0.775824i	$0.717335\pi$
$272$	−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	−0.993324	−	0.115356i	$-0.963199\pi$
$277$	−3.17485	−	11.8487i	−0.190758	−	0.711919i	0.802566	−	0.596563i	$-0.203468\pi$
$278$	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	$-0.795438\pi$
$281$		−	20.0929i		−	1.19864i	0.800509	−	0.599320i	$-0.204562\pi$
$282$		0			0
$283$	30.6875	−	8.22270i	1.82418	−	0.488789i	0.826895	−	0.562357i	$-0.190105\pi$
$283$	30.6875	−	8.22270i	1.82418	−	0.488789i	0.997290	+	0.0735682i	$0.0234387\pi$
$284$	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	−0.797536	−	0.603271i	$-0.793864\pi$
$293$	−3.32527	+	3.32527i	−0.194265	+	0.194265i	0.603271	+	0.797536i	$0.293864\pi$
$294$		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	−0.786720	−	0.617310i	$-0.788222\pi$
$307$	−2.96830	+	2.96830i	−0.169410	+	0.169410i	0.617310	+	0.786720i	$0.288222\pi$
$308$	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	0.711651	−	0.702533i	$-0.247948\pi$
$311$	8.09571	+	4.67406i	0.459065	+	0.265042i	−0.252586	+	0.967575i	$0.581281\pi$
$312$		0			0
$313$	5.38565	−	20.0995i	0.304415	−	1.13609i	−0.629032	−	0.777379i	$-0.716549\pi$
$313$	5.38565	−	20.0995i	0.304415	−	1.13609i	0.933448	−	0.358714i	$-0.116785\pi$
$314$	54.6846			3.08603
$315$		0			0
$316$	−11.3681			−0.639507
$317$	−3.73583	+	13.9423i	−0.209825	+	0.783078i	0.778099	+	0.628141i	$0.216184\pi$
$317$	−3.73583	+	13.9423i	−0.209825	+	0.783078i	−0.987924	+	0.154937i	$0.950483\pi$
$318$		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	0.662575	−	0.748996i	$-0.269464\pi$
$331$	−5.77389	−	10.0007i	−0.317362	−	0.549687i	−0.979937	+	0.199309i	$0.936130\pi$
$332$	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	−0.137653	+	0.990481i	$0.543956\pi$
$337$	−20.7098	+	20.7098i	−1.12813	+	1.12813i	−0.990481	+	0.137653i	$0.956044\pi$
$338$	−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	−0.764282	−	0.644882i	$-0.776907\pi$
$347$	−20.5602	+	5.50909i	−1.10373	+	0.295743i	−0.339447	+	0.940625i	$0.610240\pi$
$348$		0			0
$349$		−	6.84619i		−	0.366468i	−0.983069	−	0.183234i	$-0.941343\pi$
$349$		−	6.84619i		−	0.366468i	0.983069	−	0.183234i	$-0.0586566\pi$
$350$	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	−0.951965	−	0.306206i	$-0.900940\pi$
$353$	−5.27279	−	19.6783i	−0.280642	−	1.04737i	0.671323	−	0.741165i	$-0.265726\pi$
$354$		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	0.575450	−	0.817837i	$-0.304827\pi$
$359$	−7.96815	−	13.8012i	−0.420543	−	0.728402i	−0.995993	+	0.0894353i	$0.971494\pi$
$360$		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	−0.999363	−	0.0356974i	$-0.988635\pi$
$367$	−2.90688	−	10.8486i	−0.151738	−	0.566294i	0.847625	−	0.530596i	$-0.178032\pi$
$368$	−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	0.376694	+	0.926338i	$0.377061\pi$
$373$	−7.97059	+	29.7467i	−0.412702	+	1.54022i	−0.789395	+	0.613885i	$0.789606\pi$
$374$	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	$-0.952422\pi$
$379$		−	5.79809i		−	0.297828i	0.988850	−	0.148914i	$-0.0475777\pi$
$380$	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	0.483591	−	0.875294i	$-0.339332\pi$
$383$	9.09525	+	2.43707i	0.464746	+	0.124528i	−0.0188451	+	0.999822i	$0.505999\pi$
$384$		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	−0.713059	−	0.701104i	$-0.752691\pi$
$389$	4.94348	−	8.56236i	0.250644	−	0.434129i	0.963703	+	0.266975i	$0.0860242\pi$
$390$		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	0.741867	−	0.670547i	$-0.233940\pi$
$397$	20.9026	+	5.60083i	1.04907	+	0.281097i	0.307202	+	0.951644i	$0.400607\pi$
$398$	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	0.0526753	−	0.998612i	$-0.483225\pi$
$401$	18.9003	−	10.9121i	0.943836	−	0.544924i	0.891161	+	0.453688i	$0.149892\pi$
$402$		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	0.554527	−	0.832166i	$-0.312899\pi$
$409$	2.24712	+	1.29738i	0.111113	+	0.0641512i	−0.443414	+	0.896317i	$0.646233\pi$
$410$	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	0.474587	−	0.880209i	$-0.342597\pi$
$431$	−1.04639	−	0.604133i	−0.0504027	−	0.0291000i	−0.524990	+	0.851109i	$0.675931\pi$
$432$		0			0
$433$	21.2085	+	21.2085i	1.01922	+	1.01922i	0.999812	+	0.0194062i	$0.00617756\pi$
$433$	21.2085	+	21.2085i	1.01922	+	1.01922i	0.0194062	+	0.999812i	$0.493822\pi$
$434$	−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	−0.316641	−	0.948545i	$-0.602555\pi$
$439$	7.26004	−	4.19158i	0.346503	−	0.200053i	0.663144	+	0.748492i	$0.269222\pi$
$440$	−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	0.380053	−	0.924965i	$-0.375906\pi$
$443$	5.19257	+	1.39135i	0.246707	+	0.0661048i	−0.133347	+	0.991069i	$0.542572\pi$
$444$		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	0.235105	−	0.971970i	$-0.424457\pi$
$457$	−1.01059	−	0.270788i	−0.0472736	−	0.0126669i	−0.282378	+	0.959303i	$0.591123\pi$
$458$	−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	$-0.819599\pi$
$461$		−	23.0551i		−	1.07378i	0.843651	−	0.536891i	$-0.180401\pi$
$462$		0			0
$463$	−25.8069	−	25.8069i	−1.19935	−	1.19935i	−0.974362	−	0.224987i	$-0.927766\pi$
$463$	−25.8069	−	25.8069i	−1.19935	−	1.19935i	−0.224987	−	0.974362i	$-0.572234\pi$
$464$	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	−0.656803	−	0.754062i	$-0.728092\pi$
$467$	6.24612	−	23.3108i	0.289036	−	1.07870i	0.945839	−	0.324635i	$-0.105242\pi$
$468$		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	−0.558137	−	0.829749i	$-0.688484\pi$
$479$	9.61925	−	16.6610i	0.439515	−	0.761262i	0.997652	+	0.0684867i	$0.0218171\pi$
$480$		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	0.895918	+	0.444219i	$0.146519\pi$
$487$	7.55036	+	28.1783i	0.342140	+	1.27688i	−0.553779	+	0.832664i	$0.686815\pi$
$488$	−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	$-0.943738\pi$
$491$		−	7.79240i		−	0.351666i	0.984420	−	0.175833i	$-0.0562619\pi$
$492$		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	−0.597796	−	0.801649i	$-0.703957\pi$
$499$	−4.52229	+	2.61095i	−0.202446	+	0.116882i	0.395350	+	0.918530i	$0.370623\pi$
$500$	−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	−0.154535	+	0.987987i	$0.549388\pi$
$503$	−25.6241	+	25.6241i	−1.14252	+	1.14252i	−0.987987	+	0.154535i	$0.950612\pi$
$504$		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	0.926866	+	0.375391i	$0.122492\pi$
$509$	17.7901	+	30.8133i	0.788532	+	1.36578i	−0.138335	+	0.990385i	$0.544175\pi$
$510$		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	0.870492	−	0.492183i	$-0.163801\pi$
$521$	20.0749	+	11.5902i	0.879495	+	0.507777i	0.00900344	+	0.999959i	$0.497134\pi$
$522$		0			0
$523$	0.305268	−	1.13928i	0.0133485	−	0.0498171i	−0.958930	−	0.283642i	$-0.908457\pi$
$523$	0.305268	−	1.13928i	0.0133485	−	0.0498171i	0.972279	+	0.233824i	$0.0751241\pi$
$524$	−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	0.946647	−	0.322273i	$-0.104447\pi$
$541$	4.51761	+	7.82473i	0.194227	+	0.336411i	−0.752420	+	0.658684i	$0.771113\pi$
$542$	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	−0.0314683	−	0.999505i	$-0.510018\pi$
$547$	22.6405	−	22.6405i	0.968036	−	0.968036i	0.999505	+	0.0314683i	$0.0100183\pi$
$548$	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	0.415645	−	0.909527i	$-0.363556\pi$
$557$	29.0377	−	7.78063i	1.23037	−	0.329676i	0.814723	+	0.579851i	$0.196889\pi$
$558$		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	0.993811	+	0.111080i	$0.0354310\pi$
$563$	4.47706	+	16.7086i	0.188685	+	0.704184i	−0.805126	+	0.593104i	$0.797902\pi$
$564$		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	0.681087	−	0.732202i	$-0.261507\pi$
$569$	−7.00255	−	12.1288i	−0.293562	−	0.508465i	−0.974649	+	0.223738i	$0.928174\pi$
$570$		0			0
$571$	−2.55183	+	4.41990i	−0.106791	+	0.184967i	−0.914468	−	0.404657i	$-0.867391\pi$
$571$	−2.55183	+	4.41990i	−0.106791	+	0.184967i	0.807678	+	0.589624i	$0.200724\pi$
$572$	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	−0.999994	−	0.00343709i	$-0.998906\pi$
$577$	−3.25944	−	12.1644i	−0.135692	−	0.506411i	0.864302	−	0.502974i	$-0.167761\pi$
$578$	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	0.974299	+	0.225260i	$0.0723232\pi$
$587$	29.0630	+	29.0630i	1.19956	+	1.19956i	0.225260	+	0.974299i	$0.427677\pi$
$588$		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	−0.350448	−	0.936582i	$-0.613971\pi$
$593$	−27.3282	−	7.32257i	−1.12224	−	0.300702i	−0.771788	+	0.635880i	$0.780637\pi$
$594$		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	−0.438369	−	0.898795i	$-0.644444\pi$
$599$	13.6860	−	23.7049i	0.559195	−	0.968554i	0.997564	−	0.0697592i	$-0.0222231\pi$
$600$		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	0.179079	−	0.983835i	$-0.442688\pi$
$607$	−3.88660	−	1.04141i	−0.157752	−	0.0422696i	−0.336831	+	0.941565i	$0.609355\pi$
$608$	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	0.116668	−	0.993171i	$-0.462779\pi$
$613$	17.6850	−	4.73869i	0.714292	−	0.191394i	0.597623	+	0.801777i	$0.296112\pi$
$614$	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	0.991153	−	0.132727i	$-0.0423732\pi$
$617$	21.3229	+	21.3229i	0.858426	+	0.858426i	−0.132727	+	0.991153i	$0.542373\pi$
$618$		0			0
$619$	2.61954	+	1.51239i	0.105288	+	0.0607883i	0.551720	−	0.834030i	$-0.313972\pi$
$619$	2.61954	+	1.51239i	0.105288	+	0.0607883i	−0.446431	+	0.894818i	$0.647305\pi$
$620$	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	0.999453	−	0.0330603i	$-0.0105253\pi$
$641$	37.2313	+	21.4955i	1.47055	+	0.849022i	0.471096	+	0.882082i	$0.343859\pi$
$642$		0			0
$643$	31.4639	+	31.4639i	1.24082	+	1.24082i	0.959663	+	0.281152i	$0.0907166\pi$
$643$	31.4639	+	31.4639i	1.24082	+	1.24082i	0.281152	+	0.959663i	$0.409283\pi$
$644$	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	−0.569582	−	0.821934i	$-0.692895\pi$
$647$	−16.5816	+	4.44301i	−0.651888	+	0.174673i	−0.0823057	+	0.996607i	$0.526228\pi$
$648$		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	0.739748	−	0.672884i	$-0.234945\pi$
$653$	26.6769	+	7.14804i	1.04395	+	0.279724i	0.304198	+	0.952609i	$0.401611\pi$
$654$		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	−0.792364	−	0.610049i	$-0.791150\pi$
$661$	3.39721	−	5.88414i	0.132136	−	0.228867i	0.924500	+	0.381182i	$0.124483\pi$
$662$	−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	0.942560	−	0.334036i	$-0.108411\pi$
$673$	15.7865	+	15.7865i	0.608524	+	0.608524i	−0.334036	+	0.942560i	$0.608411\pi$
$674$	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	0.821022	+	0.570897i	$0.193404\pi$
$677$	−4.56513	+	17.0373i	−0.175452	+	0.654797i	−0.996474	+	0.0839000i	$0.973262\pi$
$678$		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	−0.965757	−	0.259449i	$-0.916459\pi$
$683$	−6.77169	−	25.2723i	−0.259111	−	0.967017i	0.706645	−	0.707568i	$-0.250208\pi$
$684$		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	0.722158	−	0.691729i	$-0.243151\pi$
$691$	−6.25564	−	10.8351i	−0.237976	−	0.412186i	−0.960133	+	0.279543i	$0.909817\pi$
$692$	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	$0.0917307\pi$
$701$			15.0496i			0.568417i	−0.958763	+	0.284208i	$0.908269\pi$
$702$		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	0.375744	−	0.926724i	$-0.377387\pi$
$709$	36.3774	−	21.0025i	1.36618	−	0.788766i	0.990438	+	0.137958i	$0.0440539\pi$
$710$	−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	0.934947	+	0.354788i	$0.115447\pi$
$719$	20.7737	+	35.9811i	0.774729	+	1.34187i	−0.160217	+	0.987082i	$0.551220\pi$
$720$		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	−0.599658	−	0.800256i	$-0.704697\pi$
$727$	5.40873	−	5.40873i	0.200599	−	0.200599i	0.800256	+	0.599658i	$0.204697\pi$
$728$	−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	−0.562062	−	0.827095i	$-0.689992\pi$
$733$	9.15765	−	34.1768i	0.338246	−	1.26235i	0.900307	−	0.435255i	$-0.143342\pi$
$734$	−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	0.143671	−	0.989626i	$-0.454109\pi$
$739$	−17.4398	−	10.0689i	−0.641535	−	0.370390i	−0.785205	+	0.619235i	$0.787443\pi$
$740$	−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	−0.613218	−	0.789914i	$-0.710125\pi$
$743$	4.81639	−	4.81639i	0.176696	−	0.176696i	0.789914	+	0.613218i	$0.210125\pi$
$744$		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	0.889493	−	0.456948i	$-0.151058\pi$
$751$	1.34330	+	2.32666i	0.0490177	+	0.0849012i	−0.840476	+	0.541850i	$0.817724\pi$
$752$	−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	−0.0383075	−	0.999266i	$-0.512197\pi$
$757$	26.4395	−	26.4395i	0.960959	−	0.960959i	0.999266	+	0.0383075i	$0.0121966\pi$
$758$	−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	−0.853050	−	0.521829i	$-0.825250\pi$
$761$	−22.8320	+	13.1820i	−0.827658	+	0.477849i	0.0253919	+	0.999678i	$0.491917\pi$
$762$		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	$0.0204600\pi$
$769$			3.56245i			0.128465i	−0.997935	+	0.0642326i	$0.979540\pi$
$770$	−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	0.978759	−	0.205015i	$-0.0657243\pi$
$773$	0.795756	+	2.96980i	0.0286214	+	0.106816i	−0.950137	+	0.311831i	$0.899058\pi$
$774$		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	−0.827698	−	0.561174i	$-0.810350\pi$
$787$	−10.9823	−	40.9866i	−0.391478	−	1.46101i	0.436220	−	0.899840i	$-0.356317\pi$
$788$	−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	0.911542	+	0.411208i	$0.134893\pi$
$797$	37.3428	+	37.3428i	1.32275	+	1.32275i	0.411208	+	0.911542i	$0.365107\pi$
$798$		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	−0.620243	−	0.784410i	$-0.712966\pi$
$809$	10.5010	−	18.1884i	0.369197	−	0.639468i	0.989440	+	0.144941i	$0.0462993\pi$
$810$		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	−0.823794	−	0.566889i	$-0.808147\pi$
$821$	−21.3394	+	12.3203i	−0.744751	+	0.429982i	0.0790431	+	0.996871i	$0.474814\pi$
$822$		0			0
$823$	−17.4572	+	4.67764i	−0.608519	+	0.163052i	−0.549903	−	0.835228i	$-0.685335\pi$
$823$	−17.4572	+	4.67764i	−0.608519	+	0.163052i	−0.0586159	+	0.998281i	$0.518669\pi$
$824$	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	0.0978136	−	0.995205i	$-0.468815\pi$
$827$	−25.8068	−	25.8068i	−0.897391	−	0.897391i	−0.995205	+	0.0978136i	$0.968815\pi$
$828$		0			0
$829$	−21.1695	−	12.2222i	−0.735248	−	0.424496i	0.0850911	−	0.996373i	$-0.472882\pi$
$829$	−21.1695	−	12.2222i	−0.735248	−	0.424496i	−0.820339	+	0.571878i	$0.806215\pi$
$830$	−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	0.908944	+	0.416919i	$0.136890\pi$
$853$	38.7234	+	38.7234i	1.32586	+	1.32586i	0.416919	+	0.908944i	$0.363110\pi$
$854$	−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	−0.824575	−	0.565753i	$-0.808586\pi$
$857$	−36.7630	+	9.85063i	−1.25580	+	0.336491i	−0.431226	+	0.902244i	$0.641919\pi$
$858$		0			0
$859$	21.3839	−	12.3460i	0.729608	−	0.421239i	−0.0886709	−	0.996061i	$-0.528262\pi$
$859$	21.3839	−	12.3460i	0.729608	−	0.421239i	0.818279	+	0.574822i	$0.194929\pi$
$860$	−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	0.00193811	−	0.999998i	$-0.499383\pi$
$863$	−14.5822	−	3.90728i	−0.496382	−	0.133005i	−0.498321	+	0.866993i	$0.666050\pi$
$864$		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	0.829859	−	0.557973i	$-0.188421\pi$
$877$	37.5967	+	10.0740i	1.26955	+	0.340175i	0.439692	+	0.898149i	$0.355088\pi$
$878$	−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	$0.235417\pi$
$881$			40.0097i			1.34796i	−0.738750	+	0.673980i	$0.764583\pi$
$882$		0			0
$883$	20.2833	+	20.2833i	0.682587	+	0.682587i	0.960582	−	0.277995i	$-0.0896700\pi$
$883$	20.2833	+	20.2833i	0.682587	+	0.682587i	−0.277995	+	0.960582i	$0.589670\pi$
$884$	−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	−0.992118	−	0.125304i	$-0.960009\pi$
$887$	−2.09272	+	7.81012i	−0.0702665	+	0.262238i	0.921852	+	0.387542i	$0.126676\pi$
$888$		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	0.999087	−	0.0427234i	$-0.0136034\pi$
$907$	3.38781	+	12.6435i	0.112491	+	0.419820i	−0.886596	+	0.462544i	$0.846937\pi$
$908$	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	$-0.901510\pi$
$911$		−	18.3815i		−	0.609005i	0.952512	−	0.304502i	$-0.0984901\pi$
$912$		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	−0.938145	−	0.346242i	$-0.887457\pi$
$919$	−33.5697	+	19.3815i	−1.10736	+	0.639336i	−0.169218	+	0.985579i	$0.554124\pi$
$920$	−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	0.785332	−	0.619075i	$-0.212492\pi$
$929$	−4.37286	−	7.57402i	−0.143469	−	0.248496i	−0.928801	+	0.370580i	$0.879159\pi$
$930$		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	−0.506413	−	0.862291i	$-0.669029\pi$
$937$	10.8936	−	10.8936i	0.355879	−	0.355879i	0.862291	+	0.506413i	$0.169029\pi$
$938$	−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	−0.997892	−	0.0648907i	$-0.979330\pi$
$941$	−47.6405	−	27.5052i	−1.55304	−	0.896646i	−0.555143	−	0.831755i	$-0.687337\pi$
$942$		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	0.508396	+	0.861123i	$0.330238\pi$
$947$	−11.1538	+	41.6265i	−0.362449	+	1.35268i	−0.870846	+	0.491556i	$0.836428\pi$
$948$		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	−0.399378	−	0.916786i	$-0.630774\pi$
$953$	15.9728	−	15.9728i	0.517408	−	0.517408i	0.916786	+	0.399378i	$0.130774\pi$
$954$		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	−0.398482	−	0.917176i	$-0.630463\pi$
$967$	16.1296	−	16.1296i	0.518694	−	0.518694i	0.917176	+	0.398482i	$0.130463\pi$
$968$	−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	−0.965317	−	0.261080i	$-0.915921\pi$
$971$	−38.0747	+	21.9824i	−1.22187	+	0.705449i	−0.256557	+	0.966529i	$0.582588\pi$
$972$		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	0.792312	−	0.610117i	$-0.208877\pi$
$977$	55.7479	−	14.9376i	1.78353	−	0.477896i	0.991220	+	0.132221i	$0.0422108\pi$
$978$		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	0.988618	−	0.150448i	$-0.0480716\pi$
$983$	1.79419	+	6.69600i	0.0572257	+	0.213569i	−0.931392	+	0.364017i	$0.881405\pi$
$984$		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	−0.999419	−	0.0340783i	$-0.989150\pi$
$991$	−14.8019	+	25.6376i	−0.470197	+	0.814405i	0.529222	+	0.848483i	$0.322484\pi$
$992$	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	0.999811	+	0.0194282i	$0.00618457\pi$
$997$	4.53622	+	16.9294i	0.143663	+	0.536159i	−0.856148	+	0.516731i	$0.827149\pi$
$998$	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.53.16	yes	64
3.2	odd	2	inner	315.2.ce.a.53.1	✓	64
5.2	odd	4	inner	315.2.ce.a.242.16	yes	64
7.2	even	3	inner	315.2.ce.a.233.1	yes	64
15.2	even	4	inner	315.2.ce.a.242.1	yes	64
21.2	odd	6	inner	315.2.ce.a.233.16	yes	64
35.2	odd	12	inner	315.2.ce.a.107.1	yes	64
105.2	even	12	inner	315.2.ce.a.107.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.1	✓	64	3.2	odd	2	inner
315.2.ce.a.53.16	yes	64	1.1	even	1	trivial
315.2.ce.a.107.1	yes	64	35.2	odd	12	inner
315.2.ce.a.107.16	yes	64	105.2	even	12	inner
315.2.ce.a.233.1	yes	64	7.2	even	3	inner
315.2.ce.a.233.16	yes	64	21.2	odd	6	inner
315.2.ce.a.242.1	yes	64	15.2	even	4	inner
315.2.ce.a.242.16	yes	64	5.2	odd	4	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.695956 - 2.59734i) q^{2} +(-4.52979 - 2.61528i) q^{4} +(-1.27254 + 1.83865i) q^{5} +(-1.50727 - 2.17442i) q^{7} +(-6.14253 + 6.14253i) q^{8} +O(q^{10})\)	\(q+(0.695956 - 2.59734i) q^{2} +(-4.52979 - 2.61528i) q^{4} +(-1.27254 + 1.83865i) q^{5} +(-1.50727 - 2.17442i) q^{7} +(-6.14253 + 6.14253i) q^{8} +(3.88997 + 4.58485i) q^{10} +(-3.60099 - 2.07903i) q^{11} +(-0.702126 - 0.702126i) q^{13} +(-6.69673 + 2.40161i) q^{14} +(6.44878 + 11.1696i) q^{16} +(-1.31583 + 0.352577i) q^{17} +(5.22461 - 3.01643i) q^{19} +(10.5729 - 5.00065i) q^{20} +(-7.90609 + 7.90609i) q^{22} +(-0.205581 - 0.0550852i) q^{23} +(-1.76127 - 4.67952i) q^{25} +(-2.31231 + 1.33501i) q^{26} +(1.14092 + 13.7916i) q^{28} +0.879133 q^{29} +(4.76368 - 8.25093i) q^{31} +(16.7177 - 4.47950i) q^{32} +3.66305i q^{34} +(5.91608 - 0.00430290i) q^{35} +(-3.13636 - 0.840384i) q^{37} +(-4.19861 - 15.6694i) q^{38} +(-3.47734 - 19.1106i) q^{40} -1.25212i q^{41} +(-4.28935 - 4.28935i) q^{43} +(10.8745 + 18.8352i) q^{44} +(-0.286150 + 0.495627i) q^{46} +(-0.0279906 + 0.104462i) q^{47} +(-2.45625 + 6.55491i) q^{49} +(-13.3801 + 1.31789i) q^{50} +(1.34423 + 5.01674i) q^{52} +(-1.29555 - 4.83507i) q^{53} +(8.40502 - 3.97530i) q^{55} +(22.6150 + 4.09799i) q^{56} +(0.611838 - 2.28341i) q^{58} +(0.113063 - 0.195831i) q^{59} +(5.96760 + 10.3362i) q^{61} +(-18.1152 - 18.1152i) q^{62} -20.7441i q^{64} +(2.18445 - 0.397480i) q^{65} +(0.825199 + 3.07969i) q^{67} +(6.88254 + 1.84417i) q^{68} +(4.10616 - 15.3691i) q^{70} +9.78757i q^{71} +(-6.60621 + 1.77013i) q^{73} +(-4.36553 + 7.56133i) q^{74} -31.5552 q^{76} +(0.906979 + 10.9637i) q^{77} +(1.88223 - 1.08671i) q^{79} +(-28.7434 - 2.35676i) q^{80} +(-3.25219 - 0.871421i) q^{82} +(-3.75964 + 3.75964i) q^{83} +(1.02619 - 2.86803i) q^{85} +(-14.1261 + 8.15572i) q^{86} +(34.8897 - 9.34867i) q^{88} +(-7.19793 - 12.4672i) q^{89} +(-0.468424 + 2.58502i) q^{91} +(0.787175 + 0.787175i) q^{92} +(0.251845 + 0.145403i) q^{94} +(-1.10238 + 13.4448i) q^{95} +(3.88891 - 3.88891i) q^{97} +(15.3159 + 10.9417i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7}+O(q^{10}) \) 64 * q + 8 * q^7	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73} - 320 q^{76} - 56 q^{82} + 16 q^{85} + 120 q^{88} - 128 q^{91} + 208 q^{97}+O(q^{100}) \) 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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