LMFDB - Embedded newform 351.2.bf.a.305.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(206,351)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("351.206"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bf (of order $12$, degree $4$, not 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.11
Character	$\chi$	$=$	351.305
Dual form			351.2.bf.a.206.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.477221 - 1.78101i) q^{2} +(-1.21221 - 0.699872i) q^{4} +(-0.672617 + 2.51024i) q^{5} +(1.99353 + 1.99353i) q^{7} +(0.782609 - 0.782609i) q^{8} +(4.14978 + 2.39588i) q^{10} +(6.08140 + 1.62951i) q^{11} +(-3.52535 + 0.756266i) q^{13} +(4.50185 - 2.59914i) q^{14} +(-2.42010 - 4.19174i) q^{16} +(-2.31896 - 4.01655i) q^{17} +(0.390218 + 0.104559i) q^{19} +(2.57220 - 2.57220i) q^{20} +(5.80434 - 10.0534i) q^{22} +4.26737 q^{23} +(-1.51877 - 0.876864i) q^{25} +(-0.335449 + 6.63959i) q^{26} +(-1.02137 - 3.81179i) q^{28} +(-5.22693 + 3.01777i) q^{29} +(-2.27098 - 0.608508i) q^{31} +(-6.48234 + 1.73694i) q^{32} +(-8.26018 + 2.21331i) q^{34} +(-6.34511 + 3.66335i) q^{35} +(1.60869 - 0.431046i) q^{37} +(0.372440 - 0.645085i) q^{38} +(1.43814 + 2.49093i) q^{40} +(1.18032 + 1.18032i) q^{41} -2.99100i q^{43} +(-6.23151 - 6.23151i) q^{44} +(2.03648 - 7.60024i) q^{46} +(-1.25642 - 4.68901i) q^{47} +0.948297i q^{49} +(-2.28650 + 2.28650i) q^{50} +(4.80276 + 1.55053i) q^{52} -0.186317i q^{53} +(-8.18091 + 14.1698i) q^{55} +3.12030 q^{56} +(2.88028 + 10.7494i) q^{58} +(-1.07545 - 4.01364i) q^{59} +0.0950990 q^{61} +(-2.16752 + 3.75426i) q^{62} +2.69361i q^{64} +(0.472797 - 9.35815i) q^{65} +(-2.70944 + 2.70944i) q^{67} +6.49189i q^{68} +(3.49646 + 13.0490i) q^{70} +(1.56243 - 5.83108i) q^{71} +(-1.49562 - 1.49562i) q^{73} -3.07079i q^{74} +(-0.399850 - 0.399850i) q^{76} +(8.87497 + 15.3719i) q^{77} +(-2.84121 + 4.92112i) q^{79} +(12.1501 - 3.25561i) q^{80} +(2.66543 - 1.53889i) q^{82} +(-15.0939 + 4.04440i) q^{83} +(11.6423 - 3.11954i) q^{85} +(-5.32701 - 1.42737i) q^{86} +(6.03462 - 3.48409i) q^{88} +(-0.0313812 - 0.117116i) q^{89} +(-8.53551 - 5.52023i) q^{91} +(-5.17297 - 2.98661i) q^{92} -8.95077 q^{94} +(-0.524935 + 0.909214i) q^{95} +(11.2137 - 11.2137i) q^{97} +(1.68893 + 0.452547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 2 q^{7} + 30 q^{8} - 12 q^{10} - 6 q^{11} - 2 q^{13} + 12 q^{14} + 14 q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 12 q^{23} - 48 q^{26} + 6 q^{29} + 6 q^{31} - 30 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) $ 48 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 + 2 * q^7 + 30 * q^8 - 12 * q^10 - 6 * q^11 - 2 * q^13 + 12 * q^14 + 14 * q^16 - 4 * q^19 + 6 * q^20 + 2 * q^22 + 12 * q^23 - 48 * q^26 + 6 * q^29 + 6 * q^31 - 30 * q^32 - 6 * q^34 + 6 * q^35 - 6 * q^37 + 36 * q^38 - 12 * q^40 - 18 * q^41 + 12 * q^44 - 12 * q^46 - 30 * q^47 + 12 * q^50 - 16 * q^52 - 4 * q^55 + 12 * q^56 - 28 * q^58 - 30 * q^59 - 4 * q^61 + 18 * q^62 - 30 * q^65 - 16 * q^67 - 46 * q^70 - 48 * q^71 - 22 * q^73 - 18 * q^76 + 72 * q^77 + 8 * q^79 - 54 * q^80 - 12 * q^82 - 72 * q^83 + 78 * q^85 - 102 * q^86 - 6 * q^88 - 16 * q^91 - 120 * q^92 - 52 * q^94 + 6 * q^95 + 48 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.477221	−	1.78101i	0.337446	−	1.25937i	−0.563747	−	0.825948i	$-0.690641\pi$
$2$	0.477221	−	1.78101i	0.337446	−	1.25937i	0.901193	−	0.433418i	$-0.142693\pi$
$3$		0			0
$3$		0			0
$4$	−1.21221	−	0.699872i	−0.606107	−	0.349936i
$5$	−0.672617	+	2.51024i	−0.300804	+	1.12261i	0.635694	+	0.771941i	$0.280714\pi$
$5$	−0.672617	+	2.51024i	−0.300804	+	1.12261i	−0.936498	+	0.350673i	$0.885953\pi$
$6$		0			0
$7$	1.99353	+	1.99353i	0.753482	+	0.753482i	0.975127	−	0.221645i	$-0.0711427\pi$
$7$	1.99353	+	1.99353i	0.753482	+	0.753482i	−0.221645	+	0.975127i	$0.571143\pi$
$8$	0.782609	−	0.782609i	0.276694	−	0.276694i
$9$		0			0
$10$	4.14978	+	2.39588i	1.31228	+	0.757644i
$11$	6.08140	+	1.62951i	1.83361	+	0.491315i	0.998290	−	0.0584482i	$-0.0186153\pi$
$11$	6.08140	+	1.62951i	1.83361	+	0.491315i	0.835321	+	0.549763i	$0.185282\pi$
$12$		0			0
$13$	−3.52535	+	0.756266i	−0.977755	+	0.209750i
$13$	−3.52535	+	0.756266i	−0.977755	+	0.209750i
$14$	4.50185	−	2.59914i	1.20317	−	0.694650i
$15$		0			0
$16$	−2.42010	−	4.19174i	−0.605026	−	1.04794i
$17$	−2.31896	−	4.01655i	−0.562430	−	0.974157i	−0.997284	−	0.0736558i	$-0.976533\pi$
$17$	−2.31896	−	4.01655i	−0.562430	−	0.974157i	0.434854	−	0.900501i	$-0.356800\pi$
$18$		0			0
$19$	0.390218	+	0.104559i	0.0895221	+	0.0239874i	0.303302	−	0.952894i	$-0.401911\pi$
$19$	0.390218	+	0.104559i	0.0895221	+	0.0239874i	−0.213780	+	0.976882i	$0.568578\pi$
$20$	2.57220	−	2.57220i	0.575162	−	0.575162i
$21$		0			0
$22$	5.80434	−	10.0534i	1.23749	−	2.14340i
$23$	4.26737			0.889808			0.444904	−	0.895578i	$-0.353238\pi$
$23$	4.26737			0.889808			0.444904	+	0.895578i	$0.353238\pi$
$24$		0			0
$25$	−1.51877	−	0.876864i	−0.303755	−	0.175373i
$26$	−0.335449	+	6.63959i	−0.0657869	+	1.30213i
$27$		0			0
$28$	−1.02137	−	3.81179i	−0.193020	−	0.720361i
$29$	−5.22693	+	3.01777i	−0.970617	+	0.560386i	−0.899424	−	0.437077i	$-0.856014\pi$
$29$	−5.22693	+	3.01777i	−0.970617	+	0.560386i	−0.0711925	+	0.997463i	$0.522680\pi$
$30$		0			0
$31$	−2.27098	−	0.608508i	−0.407881	−	0.109291i	0.0490441	−	0.998797i	$-0.484383\pi$
$31$	−2.27098	−	0.608508i	−0.407881	−	0.109291i	−0.456925	+	0.889505i	$0.651049\pi$
$32$	−6.48234	+	1.73694i	−1.14593	+	0.307050i
$33$		0			0
$34$	−8.26018	+	2.21331i	−1.41661	+	0.379579i
$35$	−6.34511	+	3.66335i	−1.07252	+	0.619220i
$36$		0			0
$37$	1.60869	−	0.431046i	0.264466	−	0.0708635i	−0.124149	−	0.992264i	$-0.539620\pi$
$37$	1.60869	−	0.431046i	0.264466	−	0.0708635i	0.388615	+	0.921400i	$0.372953\pi$
$38$	0.372440	−	0.645085i	0.0604178	−	0.104647i
$39$		0			0
$40$	1.43814	+	2.49093i	0.227390	+	0.393851i
$41$	1.18032	+	1.18032i	0.184335	+	0.184335i	0.793242	−	0.608907i	$-0.208392\pi$
$41$	1.18032	+	1.18032i	0.184335	+	0.184335i	−0.608907	+	0.793242i	$0.708392\pi$
$42$		0			0
$43$		−	2.99100i		−	0.456123i	−0.973647	−	0.228062i	$-0.926761\pi$
$43$		−	2.99100i		−	0.456123i	0.973647	−	0.228062i	$-0.0732388\pi$
$44$	−6.23151	−	6.23151i	−0.939436	−	0.939436i
$45$		0			0
$46$	2.03648	−	7.60024i	0.300262	−	1.12059i
$47$	−1.25642	−	4.68901i	−0.183267	−	0.683962i	−0.994995	−	0.0999262i	$-0.968139\pi$
$47$	−1.25642	−	4.68901i	−0.183267	−	0.683962i	0.811728	−	0.584036i	$-0.198527\pi$
$48$		0			0
$49$			0.948297i			0.135471i
$50$	−2.28650	+	2.28650i	−0.323359	+	0.323359i
$51$		0			0
$52$	4.80276	+	1.55053i	0.666023	+	0.215020i
$53$		−	0.186317i		−	0.0255926i	−0.999918	−	0.0127963i	$-0.995927\pi$
$53$		−	0.186317i		−	0.0255926i	0.999918	−	0.0127963i	$-0.00407330\pi$
$54$		0			0
$55$	−8.18091	+	14.1698i	−1.10311	+	1.91065i
$56$	3.12030			0.416968
$57$		0			0
$58$	2.88028	+	10.7494i	0.378200	+	1.41146i
$59$	−1.07545	−	4.01364i	−0.140012	−	0.522532i	−0.999927	−	0.0120945i	$-0.996150\pi$
$59$	−1.07545	−	4.01364i	−0.140012	−	0.522532i	0.859915	−	0.510438i	$-0.170517\pi$
$60$		0			0
$61$	0.0950990			0.0121762			0.00608809	−	0.999981i	$-0.498062\pi$
$61$	0.0950990			0.0121762			0.00608809	+	0.999981i	$0.498062\pi$
$62$	−2.16752	+	3.75426i	−0.275276	+	0.476791i
$63$		0			0
$64$			2.69361i			0.336702i
$65$	0.472797	−	9.35815i	0.0586433	−	1.16074i
$66$		0			0
$67$	−2.70944	+	2.70944i	−0.331010	+	0.331010i	−0.852970	−	0.521960i	$-0.825201\pi$
$67$	−2.70944	+	2.70944i	−0.331010	+	0.331010i	0.521960	+	0.852970i	$0.325201\pi$
$68$			6.49189i			0.787258i
$69$		0			0
$70$	3.49646	+	13.0490i	0.417907	+	1.55965i
$71$	1.56243	−	5.83108i	0.185427	−	0.692022i	−0.809112	−	0.587655i	$-0.800051\pi$
$71$	1.56243	−	5.83108i	0.185427	−	0.692022i	0.994539	−	0.104368i	$-0.0332819\pi$
$72$		0			0
$73$	−1.49562	−	1.49562i	−0.175049	−	0.175049i	0.614144	−	0.789194i	$-0.289501\pi$
$73$	−1.49562	−	1.49562i	−0.175049	−	0.175049i	−0.789194	+	0.614144i	$0.789501\pi$
$74$		−	3.07079i		−	0.356972i
$75$		0			0
$76$	−0.399850	−	0.399850i	−0.0458659	−	0.0458659i
$77$	8.87497	+	15.3719i	1.01140	+	1.75179i
$78$		0			0
$79$	−2.84121	+	4.92112i	−0.319661	+	0.553669i	−0.980417	−	0.196931i	$-0.936902\pi$
$79$	−2.84121	+	4.92112i	−0.319661	+	0.553669i	0.660756	+	0.750601i	$0.270236\pi$
$80$	12.1501	−	3.25561i	1.35842	−	0.363988i
$81$		0			0
$82$	2.66543	−	1.53889i	0.294348	−	0.169942i
$83$	−15.0939	+	4.04440i	−1.65677	+	0.443931i	−0.961498	−	0.274812i	$-0.911384\pi$
$83$	−15.0939	+	4.04440i	−1.65677	+	0.443931i	−0.695275	+	0.718743i	$0.744718\pi$
$84$		0			0
$85$	11.6423	−	3.11954i	1.26278	−	0.338362i
$86$	−5.32701	−	1.42737i	−0.574426	−	0.153917i
$87$		0			0
$88$	6.03462	−	3.48409i	0.643293	−	0.371405i
$89$	−0.0313812	−	0.117116i	−0.00332640	−	0.0124143i	0.964243	−	0.265021i	$-0.0853788\pi$
$89$	−0.0313812	−	0.117116i	−0.00332640	−	0.0124143i	−0.967569	+	0.252607i	$0.918712\pi$
$90$		0			0
$91$	−8.53551	−	5.52023i	−0.894764	−	0.578678i
$92$	−5.17297	−	2.98661i	−0.539319	−	0.311376i
$93$		0			0
$94$	−8.95077			−0.923201
$95$	−0.524935	+	0.909214i	−0.0538572	+	0.0932833i
$96$		0			0
$97$	11.2137	−	11.2137i	1.13858	−	1.13858i	0.149879	−	0.988704i	$-0.452112\pi$
$97$	11.2137	−	11.2137i	1.13858	−	1.13858i	0.988704	−	0.149879i	$-0.0478885\pi$
$98$	1.68893	+	0.452547i	0.170608	+	0.0457141i
$99$		0			0
$100$	1.22739	+	2.12589i	0.122739	+	0.212589i
$101$	1.75051	+	3.03197i	0.174182	+	0.301693i	0.939878	−	0.341510i	$-0.110938\pi$
$101$	1.75051	+	3.03197i	0.174182	+	0.301693i	−0.765696	+	0.643203i	$0.777605\pi$
$102$		0			0
$103$	−10.5831	+	6.11018i	−1.04279	+	0.602054i	−0.920622	−	0.390456i	$-0.872317\pi$
$103$	−10.5831	+	6.11018i	−1.04279	+	0.602054i	−0.122166	+	0.992510i	$0.538984\pi$
$104$	−2.16711	+	3.35083i	−0.212502	+	0.328576i
$105$		0			0
$106$	−0.331833	−	0.0889144i	−0.0322305	−	0.00863613i
$107$	−3.96991	−	2.29203i	−0.383786	−	0.221579i	0.295678	−	0.955288i	$-0.404454\pi$
$107$	−3.96991	−	2.29203i	−0.383786	−	0.221579i	−0.679464	+	0.733709i	$0.737788\pi$
$108$		0			0
$109$	−7.19868	+	7.19868i	−0.689508	+	0.689508i	−0.962123	−	0.272615i	$-0.912111\pi$
$109$	−7.19868	+	7.19868i	−0.689508	+	0.689508i	0.272615	+	0.962123i	$0.412111\pi$
$110$	21.3324	+	21.3324i	2.03396	+	2.03396i
$111$		0			0
$112$	3.53181	−	13.1809i	0.333724	−	1.24548i
$113$	−13.4282	−	7.75279i	−1.26322	−	0.729322i	−0.289525	−	0.957170i	$-0.593497\pi$
$113$	−13.4282	−	7.75279i	−1.26322	−	0.729322i	−0.973697	+	0.227849i	$0.926831\pi$
$114$		0			0
$115$	−2.87031	+	10.7121i	−0.267658	+	0.998912i
$116$	8.44821			0.784397
$117$		0			0
$118$	−7.66158			−0.705305
$119$	3.38420	−	12.6300i	0.310229	−	1.15779i
$120$		0			0
$121$	24.8019	+	14.3194i	2.25471	+	1.30176i
$122$	0.0453832	−	0.169372i	0.00410880	−	0.0153343i
$123$		0			0
$124$	2.32704	+	2.32704i	0.208974	+	0.208974i
$125$	−5.96543	+	5.96543i	−0.533564	+	0.533564i
$126$		0			0
$127$	2.41225	+	1.39271i	0.214052	+	0.123583i	0.603193	−	0.797595i	$-0.293895\pi$
$127$	2.41225	+	1.39271i	0.214052	+	0.123583i	−0.389141	+	0.921178i	$0.627228\pi$
$128$	−8.16731	−	2.18843i	−0.721895	−	0.193431i
$129$		0			0
$130$	−16.4413	−	5.30796i	−1.44200	−	0.465539i
$131$	11.1980	−	6.46515i	0.978370	−	0.564862i	0.0765926	−	0.997062i	$-0.475596\pi$
$131$	11.1980	−	6.46515i	0.978370	−	0.564862i	0.901778	+	0.432200i	$0.142263\pi$
$132$		0			0
$133$	0.569470	+	0.986350i	0.0493793	+	0.0855274i
$134$	3.53254	+	6.11854i	0.305165	+	0.528561i
$135$		0			0
$136$	−4.95822	−	1.32855i	−0.425164	−	0.113922i
$137$	0.300887	−	0.300887i	0.0257065	−	0.0257065i	−0.694137	−	0.719843i	$-0.744214\pi$
$137$	0.300887	−	0.300887i	0.0257065	−	0.0257065i	0.719843	+	0.694137i	$0.244214\pi$
$138$		0			0
$139$	−4.36753	+	7.56478i	−0.370449	+	0.641636i	−0.989635	−	0.143608i	$-0.954129\pi$
$139$	−4.36753	+	7.56478i	−0.370449	+	0.641636i	0.619186	+	0.785245i	$0.287463\pi$
$140$	10.2555			0.866749
$141$		0			0
$142$	−9.63961	−	5.56543i	−0.808938	−	0.467040i
$143$	−22.6714	−	1.14542i	−1.89588	−	0.0957845i
$144$		0			0
$145$	−4.05961	−	15.1507i	−0.337132	−	1.25819i
$146$	−3.37746	+	1.94998i	−0.279521	+	0.161381i
$147$		0			0
$148$	−2.25175	−	0.603354i	−0.185093	−	0.0495954i
$149$	−2.49557	+	0.668687i	−0.204445	+	0.0547810i	−0.359588	−	0.933111i	$-0.617083\pi$
$149$	−2.49557	+	0.668687i	−0.204445	+	0.0547810i	0.155143	+	0.987892i	$0.450416\pi$
$150$		0			0
$151$	1.31486	−	0.352316i	0.107002	−	0.0286711i	−0.204921	−	0.978779i	$-0.565694\pi$
$151$	1.31486	−	0.352316i	0.107002	−	0.0286711i	0.311923	+	0.950107i	$0.399027\pi$
$152$	0.387216	−	0.223559i	0.0314074	−	0.0181331i
$153$		0			0
$154$	31.6129	−	8.47064i	2.54744	−	0.682584i
$155$	3.05501	−	5.29143i	0.245384	−	0.425018i
$156$		0			0
$157$	−6.09285	−	10.5531i	−0.486263	−	0.842231i	0.513613	−	0.858022i	$-0.328307\pi$
$157$	−6.09285	−	10.5531i	−0.486263	−	0.842231i	−0.999875	+	0.0157906i	$0.994973\pi$
$158$	7.40869	+	7.40869i	0.589404	+	0.589404i
$159$		0			0
$160$		−	17.4405i		−	1.37879i
$161$	8.50712	+	8.50712i	0.670455	+	0.670455i
$162$		0			0
$163$	6.32949	−	23.6220i	0.495764	−	1.85022i	−0.0299426	−	0.999552i	$-0.509532\pi$
$163$	6.32949	−	23.6220i	0.495764	−	1.85022i	0.525707	−	0.850666i	$-0.323801\pi$
$164$	−0.604726	−	2.25687i	−0.0472212	−	0.176232i
$165$		0			0
$166$			28.8125i			2.23629i
$167$	5.44679	−	5.44679i	0.421485	−	0.421485i	−0.464230	−	0.885715i	$-0.653669\pi$
$167$	5.44679	−	5.44679i	0.421485	−	0.421485i	0.885715	+	0.464230i	$0.153669\pi$
$168$		0			0
$169$	11.8561	−	5.33220i	0.912009	−	0.410169i
$170$		−	22.2238i		−	1.70448i
$171$		0			0
$172$	−2.09332	+	3.62573i	−0.159614	+	0.276460i
$173$	11.6046			0.882279			0.441139	−	0.897439i	$-0.354574\pi$
$173$	11.6046			0.882279			0.441139	+	0.897439i	$0.354574\pi$
$174$		0			0
$175$	−1.27966	−	4.77577i	−0.0967334	−	0.361014i
$176$	−7.88714	−	29.4352i	−0.594516	−	2.21876i
$177$		0			0
$178$	−0.223561			−0.0167566
$179$	−2.75530	+	4.77232i	−0.205941	+	0.356700i	−0.950432	−	0.310932i	$-0.899359\pi$
$179$	−2.75530	+	4.77232i	−0.205941	+	0.356700i	0.744491	+	0.667632i	$0.232692\pi$
$180$		0			0
$181$			9.65258i			0.717471i	0.933439	+	0.358735i	$0.116792\pi$
$181$			9.65258i			0.717471i	−0.933439	+	0.358735i	$0.883208\pi$
$182$	−13.9049	+	12.5675i	−1.03070	+	0.931563i
$183$		0			0
$184$	3.33968	−	3.33968i	0.246205	−	0.246205i
$185$			4.32812i			0.318210i
$186$		0			0
$187$	−7.55751	−	28.2050i	−0.552660	−	2.06255i
$188$	−1.75866	+	6.56341i	−0.128264	+	0.478686i
$189$		0			0
$190$	1.36881	+	1.36881i	0.0993040	+	0.0993040i
$191$			7.27544i			0.526433i	0.964737	+	0.263216i	$0.0847833\pi$
$191$			7.27544i			0.526433i	−0.964737	+	0.263216i	$0.915217\pi$
$192$		0			0
$193$	−9.06750	−	9.06750i	−0.652693	−	0.652693i	0.300948	−	0.953641i	$-0.402697\pi$
$193$	−9.06750	−	9.06750i	−0.652693	−	0.652693i	−0.953641	+	0.300948i	$0.902697\pi$
$194$	−14.6204	−	25.3233i	−1.04968	−	1.81810i
$195$		0			0
$196$	0.663686	−	1.14954i	0.0474062	−	0.0821099i
$197$	15.2346	−	4.08211i	1.08542	−	0.290838i	0.328608	−	0.944467i	$-0.393421\pi$
$197$	15.2346	−	4.08211i	1.08542	−	0.290838i	0.756816	+	0.653628i	$0.226754\pi$
$198$		0			0
$199$	−21.4175	+	12.3654i	−1.51825	+	0.876560i	−0.518477	+	0.855091i	$0.673501\pi$
$199$	−21.4175	+	12.3654i	−1.51825	+	0.876560i	−0.999770	+	0.0214686i	$0.993166\pi$
$200$	−1.87485	+	0.502364i	−0.132572	+	0.0355225i
$201$		0			0
$202$	6.23536	−	1.67076i	0.438718	−	0.117554i
$203$	−16.4360	−	4.40402i	−1.15358	−	0.309102i
$204$		0			0
$205$	−3.75678	+	2.16898i	−0.262385	+	0.151488i
$206$	5.83181	+	21.7646i	0.406321	+	1.51641i
$207$		0			0
$208$	11.7018	+	12.9471i	0.811372	+	0.897719i
$209$	2.20269	+	1.27173i	0.152363	+	0.0879671i
$210$		0			0
$211$	14.4023			0.991498			0.495749	−	0.868466i	$-0.334894\pi$
$211$	14.4023			0.991498			0.495749	+	0.868466i	$0.334894\pi$
$212$	−0.130398	+	0.225856i	−0.00895578	+	0.0155119i
$213$		0			0
$214$	−5.97665	+	5.97665i	−0.408556	+	0.408556i
$215$	7.50814	+	2.01180i	0.512051	+	0.137204i
$216$		0			0
$217$	−3.31419	−	5.74035i	−0.224982	−	0.389680i
$218$	9.38557	+	16.2563i	0.635671	+	1.10101i
$219$		0			0
$220$	19.8340	−	11.4512i	1.33721	−	0.772038i
$221$	11.2127	+	12.4060i	0.754248	+	0.834517i
$222$		0			0
$223$	−0.984477	−	0.263790i	−0.0659254	−	0.0176647i	0.225706	−	0.974196i	$-0.427531\pi$
$223$	−0.984477	−	0.263790i	−0.0659254	−	0.0176647i	−0.291631	+	0.956531i	$0.594198\pi$
$224$	−16.3853	−	9.46008i	−1.09479	−	0.632078i
$225$		0			0
$226$	−20.2161	+	20.2161i	−1.34475	+	1.34475i
$227$	−5.49340	−	5.49340i	−0.364609	−	0.364609i	0.500897	−	0.865507i	$-0.333003\pi$
$227$	−5.49340	−	5.49340i	−0.364609	−	0.364609i	−0.865507	+	0.500897i	$0.833003\pi$
$228$		0			0
$229$	4.06263	−	15.1620i	0.268466	−	1.00193i	−0.691628	−	0.722254i	$-0.743106\pi$
$229$	4.06263	−	15.1620i	0.268466	−	1.00193i	0.960094	−	0.279676i	$-0.0902272\pi$
$230$	17.7087	+	10.2241i	1.16768	+	0.674158i
$231$		0			0
$232$	−1.72891	+	6.45237i	−0.113508	+	0.423619i
$233$	9.38345			0.614730			0.307365	−	0.951592i	$-0.400553\pi$
$233$	9.38345			0.614730			0.307365	+	0.951592i	$0.400553\pi$
$234$		0			0
$235$	12.6156			0.822953
$236$	−1.50536	+	5.61808i	−0.0979905	+	0.365706i
$237$		0			0
$238$	−20.8792	−	12.0546i	−1.35340	−	0.781384i
$239$	4.63155	−	17.2852i	0.299590	−	1.11809i	−0.637913	−	0.770108i	$-0.720202\pi$
$239$	4.63155	−	17.2852i	0.299590	−	1.11809i	0.937503	−	0.347977i	$-0.113131\pi$
$240$		0			0
$241$	−10.7084	−	10.7084i	−0.689788	−	0.689788i	0.272397	−	0.962185i	$-0.412184\pi$
$241$	−10.7084	−	10.7084i	−0.689788	−	0.689788i	−0.962185	+	0.272397i	$0.912184\pi$
$242$	37.3389	−	37.3389i	2.40024	−	2.40024i
$243$		0			0
$244$	−0.115280	−	0.0665571i	−0.00738006	−	0.00426088i
$245$	−2.38045	−	0.637841i	−0.152082	−	0.0407502i
$246$		0			0
$247$	−1.45473	−	0.0734965i	−0.0925621	−	0.00467647i
$248$	−2.25352	+	1.30107i	−0.143098	+	0.0826179i
$249$		0			0
$250$	7.77767	+	13.4713i	0.491903	+	0.852002i
$251$	8.02608	+	13.9016i	0.506602	+	0.877460i	0.999971	+	0.00763991i	$0.00243188\pi$
$251$	8.02608	+	13.9016i	0.506602	+	0.877460i	−0.493369	+	0.869820i	$0.664235\pi$
$252$		0			0
$253$	25.9516	+	6.95371i	1.63156	+	0.437176i
$254$	3.63161	−	3.63161i	0.227868	−	0.227868i
$255$		0			0
$256$	−10.4888	+	18.1672i	−0.655552	+	1.13545i
$257$	−14.3574			−0.895588			−0.447794	−	0.894137i	$-0.647790\pi$
$257$	−14.3574			−0.895588			−0.447794	+	0.894137i	$0.647790\pi$
$258$		0			0
$259$	4.06626	+	2.34766i	0.252665	+	0.145876i
$260$	−7.12264	+	11.0132i	−0.441727	+	0.683008i
$261$		0			0
$262$	−6.17060	−	23.0290i	−0.381221	−	1.42274i
$263$	15.6938	−	9.06082i	0.967721	−	0.558714i	0.0691806	−	0.997604i	$-0.477962\pi$
$263$	15.6938	−	9.06082i	0.967721	−	0.558714i	0.898541	+	0.438890i	$0.144628\pi$
$264$		0			0
$265$	0.467701	+	0.125320i	0.0287306	+	0.00769835i
$266$	2.02846	−	0.543525i	0.124373	−	0.0333257i
$267$		0			0
$268$	5.18067	−	1.38816i	0.316460	−	0.0847952i
$269$	2.52163	−	1.45587i	0.153747	−	0.0887657i	−0.421153	−	0.906990i	$-0.638374\pi$
$269$	2.52163	−	1.45587i	0.153747	−	0.0887657i	0.574900	+	0.818224i	$0.305041\pi$
$270$		0			0
$271$	13.0634	−	3.50032i	0.793544	−	0.212629i	0.160796	−	0.986988i	$-0.448594\pi$
$271$	13.0634	−	3.50032i	0.793544	−	0.212629i	0.632748	+	0.774358i	$0.281927\pi$
$272$	−11.2242	+	19.4409i	−0.680569	+	1.17878i
$273$		0			0
$274$	−0.392294	−	0.679474i	−0.0236994	−	0.0410485i
$275$	−7.80741	−	7.80741i	−0.470805	−	0.470805i
$276$		0			0
$277$			25.2517i			1.51723i	0.651540	+	0.758615i	$0.274123\pi$
$277$			25.2517i			1.51723i	−0.651540	+	0.758615i	$0.725877\pi$
$278$	11.3887	+	11.3887i	0.683048	+	0.683048i
$279$		0			0
$280$	−2.09877	+	7.83271i	−0.125425	+	0.468094i
$281$	5.40894	+	20.1864i	0.322670	+	1.20422i	0.916633	+	0.399729i	$0.130896\pi$
$281$	5.40894	+	20.1864i	0.322670	+	1.20422i	−0.593963	+	0.804492i	$0.702437\pi$
$282$		0			0
$283$		−	2.16398i		−	0.128635i	−0.997929	−	0.0643177i	$-0.979513\pi$
$283$		−	2.16398i		−	0.128635i	0.997929	−	0.0643177i	$-0.0204871\pi$
$284$	−5.97502	+	5.97502i	−0.354552	+	0.354552i
$285$		0			0
$286$	−12.8593	+	39.8314i	−0.760384	+	2.35528i
$287$			4.70599i			0.277786i
$288$		0			0
$289$	−2.25512	+	3.90599i	−0.132654	+	0.229764i
$290$	−28.9208			−1.69829
$291$		0			0
$292$	0.766270	+	2.85976i	0.0448425	+	0.167355i
$293$	8.29952	+	30.9742i	0.484863	+	1.80953i	0.580676	+	0.814135i	$0.302788\pi$
$293$	8.29952	+	30.9742i	0.484863	+	1.80953i	−0.0958129	+	0.995399i	$0.530545\pi$
$294$		0			0
$295$	10.7986			0.628718
$296$	0.921631	−	1.59631i	0.0535687	−	0.0927837i
$297$		0			0
$298$			4.76376i			0.275957i
$299$	−15.0440	+	3.22727i	−0.870015	+	0.186638i
$300$		0			0
$301$	5.96264	−	5.96264i	0.343681	−	0.343681i
$302$		−	2.50992i		−	0.144429i
$303$		0			0
$304$	−0.506085	−	1.88873i	−0.0290260	−	0.108326i
$305$	−0.0639652	+	0.238721i	−0.00366264	+	0.0136691i
$306$		0			0
$307$	18.5795	+	18.5795i	1.06039	+	1.06039i	0.998055	+	0.0623341i	$0.0198544\pi$
$307$	18.5795	+	18.5795i	1.06039	+	1.06039i	0.0623341	+	0.998055i	$0.480146\pi$
$308$		−	24.8454i		−	1.41570i
$309$		0			0
$310$	−7.96618	−	7.96618i	−0.452449	−	0.452449i
$311$	3.45338	+	5.98144i	0.195823	+	0.339176i	0.947170	−	0.320732i	$-0.103929\pi$
$311$	3.45338	+	5.98144i	0.195823	+	0.339176i	−0.751347	+	0.659908i	$0.770595\pi$
$312$		0			0
$313$	−14.0998	+	24.4216i	−0.796969	+	1.38039i	0.124613	+	0.992205i	$0.460231\pi$
$313$	−14.0998	+	24.4216i	−0.796969	+	1.38039i	−0.921582	+	0.388185i	$0.873102\pi$
$314$	−21.7029	+	5.81527i	−1.22476	+	0.328175i
$315$		0			0
$316$	6.88831	−	3.97697i	0.387498	−	0.223722i
$317$	0.698082	−	0.187051i	0.0392082	−	0.0105058i	−0.239162	−	0.970980i	$-0.576873\pi$
$317$	0.698082	−	0.187051i	0.0392082	−	0.0105058i	0.278370	+	0.960474i	$0.410206\pi$
$318$		0			0
$319$	−36.7045	+	9.83495i	−2.05506	+	0.550651i
$320$	−6.76162	−	1.81177i	−0.377986	−	0.101281i
$321$		0			0
$322$	19.2111	−	11.0915i	1.07059	−	0.618106i
$323$	−0.484934	−	1.80980i	−0.0269824	−	0.100700i
$324$		0			0
$325$	6.01734	+	1.94265i	0.333782	+	0.107759i
$326$	−39.0505	−	22.5458i	−2.16281	−	1.24870i
$327$		0			0
$328$	1.84745			0.102009
$329$	6.84296	−	11.8524i	0.377265	−	0.653442i
$330$		0			0
$331$	−3.42545	+	3.42545i	−0.188280	+	0.188280i	−0.794952	−	0.606672i	$-0.792504\pi$
$331$	−3.42545	+	3.42545i	−0.188280	+	0.188280i	0.606672	+	0.794952i	$0.292504\pi$
$332$	21.1276	+	5.66113i	1.15953	+	0.310695i
$333$		0			0
$334$	−7.10148	−	12.3001i	−0.388575	−	0.673032i
$335$	−4.97892	−	8.62375i	−0.272028	−	0.471166i
$336$		0			0
$337$	21.7282	−	12.5448i	1.18361	−	0.683359i	0.226765	−	0.973949i	$-0.427185\pi$
$337$	21.7282	−	12.5448i	1.18361	−	0.683359i	0.956848	+	0.290590i	$0.0938516\pi$
$338$	−3.83872	−	23.6605i	−0.208799	−	1.28696i
$339$		0			0
$340$	−16.2962	−	4.36656i	−0.883787	−	0.236810i
$341$	−12.8192	−	7.40117i	−0.694198	−	0.400796i
$342$		0			0
$343$	12.0642	−	12.0642i	0.651407	−	0.651407i
$344$	−2.34078	−	2.34078i	−0.126207	−	0.126207i
$345$		0			0
$346$	5.53794	−	20.6679i	0.297721	−	1.11111i
$347$	23.7482	+	13.7111i	1.27487	+	0.736048i	0.975901	−	0.218214i	$-0.0700230\pi$
$347$	23.7482	+	13.7111i	1.27487	+	0.736048i	0.298972	+	0.954262i	$0.403356\pi$
$348$		0			0
$349$	0.265695	−	0.991586i	0.0142223	−	0.0530784i	−0.958450	−	0.285261i	$-0.907920\pi$
$349$	0.265695	−	0.991586i	0.0142223	−	0.0530784i	0.972672	+	0.232182i	$0.0745865\pi$
$350$	−9.11638			−0.487291
$351$		0			0
$352$	−42.2520			−2.25204
$353$	4.96485	−	18.5291i	0.264252	−	0.986203i	−0.698454	−	0.715655i	$-0.746128\pi$
$353$	4.96485	−	18.5291i	0.264252	−	0.986203i	0.962706	−	0.270548i	$-0.0872049\pi$
$354$		0			0
$355$	13.5865	+	7.84418i	0.721097	+	0.416326i
$356$	−0.0439257	+	0.163933i	−0.00232806	+	0.00868842i
$357$		0			0
$358$	7.18467	+	7.18467i	0.379721	+	0.379721i
$359$	−18.1179	+	18.1179i	−0.956226	+	0.956226i	−0.999081	−	0.0428555i	$-0.986354\pi$
$359$	−18.1179	+	18.1179i	−0.956226	+	0.956226i	0.0428555	+	0.999081i	$0.486354\pi$
$360$		0			0
$361$	−16.3131	−	9.41840i	−0.858587	−	0.495705i
$362$	17.1914	+	4.60641i	0.903558	+	0.242108i
$363$		0			0
$364$	6.48340	+	12.6655i	0.339823	+	0.663851i
$365$	4.76035	−	2.74839i	0.249168	−	0.143857i
$366$		0			0
$367$	−11.6527	−	20.1831i	−0.608268	−	1.05355i	−0.991526	−	0.129910i	$-0.958531\pi$
$367$	−11.6527	−	20.1831i	−0.608268	−	1.05355i	0.383258	−	0.923641i	$-0.374802\pi$
$368$	−10.3275	−	17.8877i	−0.538357	−	0.932461i
$369$		0			0
$370$	7.70843	+	2.06547i	0.400742	+	0.107379i
$371$	0.371428	−	0.371428i	0.0192836	−	0.0192836i
$372$		0			0
$373$	−3.51100	+	6.08123i	−0.181793	+	0.314874i	−0.942491	−	0.334231i	$-0.891523\pi$
$373$	−3.51100	+	6.08123i	−0.181793	+	0.314874i	0.760698	+	0.649106i	$0.224857\pi$
$374$	−53.8401			−2.78400
$375$		0			0
$376$	−4.65294	−	2.68638i	−0.239957	−	0.138539i
$377$	16.1445	−	14.5916i	0.831484	−	0.751507i
$378$		0			0
$379$	2.49511	+	9.31188i	0.128165	+	0.478319i	0.999933	−	0.0116007i	$-0.00369271\pi$
$379$	2.49511	+	9.31188i	0.128165	+	0.478319i	−0.871767	+	0.489920i	$0.837026\pi$
$380$	1.27267	−	0.734774i	0.0652864	−	0.0376931i
$381$		0			0
$382$	12.9577	+	3.47199i	0.662971	+	0.177643i
$383$	−22.3537	+	5.98966i	−1.14222	+	0.306057i	−0.779844	−	0.625974i	$-0.784701\pi$
$383$	−22.3537	+	5.98966i	−1.14222	+	0.306057i	−0.362377	+	0.932032i	$0.618035\pi$
$384$		0			0
$385$	−44.5566	+	11.9389i	−2.27082	+	0.608463i
$386$	−20.4765	+	11.8221i	−1.04223	+	0.601731i
$387$		0			0
$388$	−21.4416	+	5.74527i	−1.08853	+	0.291672i
$389$	−2.26345	+	3.92041i	−0.114761	+	0.198772i	−0.917684	−	0.397310i	$-0.869944\pi$
$389$	−2.26345	+	3.92041i	−0.114761	+	0.198772i	0.802923	+	0.596083i	$0.203277\pi$
$390$		0			0
$391$	−9.89585	−	17.1401i	−0.500455	−	0.866813i
$392$	0.742145	+	0.742145i	0.0374840	+	0.0374840i
$393$		0			0
$394$		−	29.0812i		−	1.46509i
$395$	−10.4422	−	10.4422i	−0.525402	−	0.525402i
$396$		0			0
$397$	−2.03359	+	7.58947i	−0.102063	+	0.380905i	−0.997995	−	0.0632859i	$-0.979842\pi$
$397$	−2.03359	+	7.58947i	−0.102063	+	0.380905i	0.895932	+	0.444191i	$0.146509\pi$
$398$	11.8021	+	44.0459i	0.591583	+	2.20782i
$399$		0			0
$400$			8.48840i			0.424420i
$401$	0.183248	−	0.183248i	0.00915098	−	0.00915098i	−0.702516	−	0.711667i	$-0.747940\pi$
$401$	0.183248	−	0.183248i	0.00915098	−	0.00915098i	0.711667	+	0.702516i	$0.247940\pi$
$402$		0			0
$403$	8.46620	+	0.427734i	0.421731	+	0.0213069i
$404$		−	4.90053i		−	0.243811i
$405$		0			0
$406$	−15.6872	+	27.1711i	−0.778544	+	1.34848i
$407$	10.4855			0.519745
$408$		0			0
$409$	9.55921	+	35.6754i	0.472672	+	1.76404i	0.630108	+	0.776508i	$0.283011\pi$
$409$	9.55921	+	35.6754i	0.472672	+	1.76404i	−0.157435	+	0.987529i	$0.550323\pi$
$410$	2.07016	+	7.72596i	0.102238	+	0.381558i
$411$		0			0
$412$	17.1054			0.842721
$413$	5.85736	−	10.1453i	0.288222	−	0.499215i
$414$		0			0
$415$		−	40.6097i		−	1.99345i
$416$	21.5389	−	11.0257i	1.05603	−	0.540578i
$417$		0			0
$418$	3.31613	−	3.31613i	0.162197	−	0.162197i
$419$			29.1073i			1.42199i	0.703199	+	0.710993i	$0.251754\pi$
$419$			29.1073i			1.42199i	−0.703199	+	0.710993i	$0.748246\pi$
$420$		0			0
$421$	1.88779	+	7.04531i	0.0920051	+	0.343368i	0.996548	−	0.0830142i	$-0.0264547\pi$
$421$	1.88779	+	7.04531i	0.0920051	+	0.343368i	−0.904543	+	0.426382i	$0.859788\pi$
$422$	6.87309	−	25.6507i	0.334577	−	1.24866i
$423$		0			0
$424$	−0.145813	−	0.145813i	−0.00708132	−	0.00708132i
$425$			8.13364i			0.394540i
$426$		0			0
$427$	0.189582	+	0.189582i	0.00917453	+	0.00917453i
$428$	3.20825	+	5.55686i	0.155077	+	0.268601i
$429$		0			0
$430$	7.16608	−	12.4120i	0.345579	−	0.598560i
$431$	−14.6266	+	3.91918i	−0.704537	+	0.188780i	−0.593262	−	0.805009i	$-0.702160\pi$
$431$	−14.6266	+	3.91918i	−0.704537	+	0.188780i	−0.111275	+	0.993790i	$0.535494\pi$
$432$		0			0
$433$	26.0240	−	15.0250i	1.25063	−	0.722054i	0.279399	−	0.960175i	$-0.409865\pi$
$433$	26.0240	−	15.0250i	1.25063	−	0.722054i	0.971235	+	0.238121i	$0.0765316\pi$
$434$	−11.8052	+	3.16320i	−0.566669	+	0.151838i
$435$		0			0
$436$	13.7645	−	3.68818i	0.659199	−	0.176632i
$437$	1.66520	+	0.446190i	0.0796575	+	0.0213442i
$438$		0			0
$439$	13.5780	−	7.83924i	0.648041	−	0.374146i	−0.139664	−	0.990199i	$-0.544602\pi$
$439$	13.5780	−	7.83924i	0.648041	−	0.374146i	0.787705	+	0.616052i	$0.211269\pi$
$440$	4.68692	+	17.4918i	0.223440	+	0.833890i
$441$		0			0
$442$	27.4461	−	14.0496i	1.30548	−	0.668270i
$443$	−11.9145	−	6.87886i	−0.566076	−	0.326824i	0.189504	−	0.981880i	$-0.439312\pi$
$443$	−11.9145	−	6.87886i	−0.566076	−	0.326824i	−0.755581	+	0.655056i	$0.772645\pi$
$444$		0			0
$445$	0.315098			0.0149371
$446$	−0.939626	+	1.62748i	−0.0444926	+	0.0770634i
$447$		0			0
$448$	−5.36979	+	5.36979i	−0.253699	+	0.253699i
$449$	11.5500	+	3.09482i	0.545079	+	0.146054i	0.520843	−	0.853653i	$-0.325618\pi$
$449$	11.5500	+	3.09482i	0.545079	+	0.146054i	0.0242366	+	0.999706i	$0.492285\pi$
$450$		0			0
$451$	5.25465	+	9.10132i	0.247432	+	0.428564i
$452$	10.8519	+	18.7961i	0.510432	+	0.884094i
$453$		0			0
$454$	−12.4054	+	7.16224i	−0.582213	+	0.336141i
$455$	19.5983	−	17.7132i	0.918780	−	0.830407i
$456$		0			0
$457$	37.9781	+	10.1762i	1.77654	+	0.476023i	0.989946	−	0.141446i	$-0.0451750\pi$
$457$	37.9781	+	10.1762i	1.77654	+	0.476023i	0.786596	+	0.617468i	$0.211842\pi$
$458$	−25.0649	−	14.4712i	−1.17120	−	0.676195i
$459$		0			0
$460$	10.9765	−	10.9765i	0.511784	−	0.511784i
$461$	12.7210	+	12.7210i	0.592474	+	0.592474i	0.938299	−	0.345825i	$-0.112401\pi$
$461$	12.7210	+	12.7210i	0.592474	+	0.592474i	−0.345825	+	0.938299i	$0.612401\pi$
$462$		0			0
$463$	−8.75526	+	32.6751i	−0.406891	+	1.51854i	0.393649	+	0.919261i	$0.371213\pi$
$463$	−8.75526	+	32.6751i	−0.406891	+	1.51854i	−0.800540	+	0.599279i	$0.795454\pi$
$464$	25.2994	+	14.6066i	1.17450	+	0.678095i
$465$		0			0
$466$	4.47798	−	16.7120i	0.207438	−	0.774171i
$467$	−15.4828			−0.716459			−0.358229	−	0.933634i	$-0.616619\pi$
$467$	−15.4828			−0.716459			−0.358229	+	0.933634i	$0.616619\pi$
$468$		0			0
$469$	−10.8027			−0.498821
$470$	6.02044	−	22.4686i	0.277702	−	1.03640i
$471$		0			0
$472$	−3.98277	−	2.29945i	−0.183322	−	0.105841i
$473$	4.87385	−	18.1895i	0.224100	−	0.836353i
$474$		0			0
$475$	−0.500969	−	0.500969i	−0.0229860	−	0.0229860i
$476$	−12.9418	+	12.9418i	−0.593185	+	0.593185i
$477$		0			0
$478$	−28.5748	−	16.4977i	−1.30698	−	0.754587i
$479$	29.7901	+	7.98222i	1.36114	+	0.364717i	0.864236	−	0.503087i	$-0.167802\pi$
$479$	29.7901	+	7.98222i	1.36114	+	0.364717i	0.496907	+	0.867804i	$0.334469\pi$
$480$		0			0
$481$	−5.34519	+	2.73618i	−0.243720	+	0.124759i
$482$	−24.1820	+	13.9615i	−1.10146	+	0.635929i
$483$		0			0
$484$	−20.0434	−	34.7163i	−0.911065	−	1.57801i
$485$	20.6067	+	35.6918i	0.935700	+	1.62068i
$486$		0			0
$487$	−36.9964	−	9.91314i	−1.67647	−	0.449207i	−0.709623	−	0.704582i	$-0.751135\pi$
$487$	−36.9964	−	9.91314i	−1.67647	−	0.449207i	−0.966842	+	0.255374i	$0.917801\pi$
$488$	0.0744253	−	0.0744253i	0.00336907	−	0.00336907i
$489$		0			0
$490$	−2.27200	+	3.93523i	−0.102639	+	0.177775i
$491$	32.8792			1.48382			0.741909	−	0.670501i	$-0.233921\pi$
$491$	32.8792			1.48382			0.741909	+	0.670501i	$0.233921\pi$
$492$		0			0
$493$	24.2421	+	13.9962i	1.09181	+	0.630355i
$494$	−0.825124	+	2.55581i	−0.0371241	+	0.114991i
$495$		0			0
$496$	2.94531	+	10.9920i	0.132248	+	0.493557i
$497$	14.7392	−	8.50967i	0.661142	−	0.381711i
$498$		0			0
$499$	−18.6315	−	4.99230i	−0.834061	−	0.223486i	−0.183576	−	0.983005i	$-0.558767\pi$
$499$	−18.6315	−	4.99230i	−0.834061	−	0.223486i	−0.650485	+	0.759520i	$0.725434\pi$
$500$	11.4064	−	3.05634i	0.510110	−	0.136684i
$501$		0			0
$502$	28.5891	−	7.66043i	1.27599	−	0.341902i
$503$	14.1918	−	8.19366i	0.632783	−	0.365337i	−0.149046	−	0.988830i	$-0.547620\pi$
$503$	14.1918	−	8.19366i	0.632783	−	0.365337i	0.781829	+	0.623493i	$0.214287\pi$
$504$		0			0
$505$	−8.78841	+	2.35485i	−0.391079	+	0.104789i
$506$	24.7693	−	42.9016i	1.10113	−	1.90721i
$507$		0			0
$508$	−1.94944	−	3.37653i	−0.0864925	−	0.149809i
$509$	7.64282	+	7.64282i	0.338762	+	0.338762i	0.855901	−	0.517139i	$-0.173003\pi$
$509$	7.64282	+	7.64282i	0.338762	+	0.338762i	−0.517139	+	0.855901i	$0.673003\pi$
$510$		0			0
$511$		−	5.96312i		−	0.263793i
$512$	15.3927	+	15.3927i	0.680269	+	0.680269i
$513$		0			0
$514$	−6.85164	+	25.5707i	−0.302213	+	1.12787i
$515$	−8.21962	−	30.6761i	−0.362200	−	1.35175i
$516$		0			0
$517$		−	30.5631i		−	1.34416i
$518$	6.12171	−	6.12171i	0.268972	−	0.268972i
$519$		0			0
$520$	−6.95375	−	7.69378i	−0.304942	−	0.337395i
$521$		−	18.8001i		−	0.823648i	−0.911263	−	0.411824i	$-0.864892\pi$
$521$		−	18.8001i		−	0.823648i	0.911263	−	0.411824i	$-0.135108\pi$
$522$		0			0
$523$	−1.02893	+	1.78216i	−0.0449919	+	0.0779283i	−0.887644	−	0.460530i	$-0.847660\pi$
$523$	−1.02893	+	1.78216i	−0.0449919	+	0.0779283i	0.842652	+	0.538458i	$0.180993\pi$
$524$	−18.0991			−0.790663
$525$		0			0
$526$	−8.64803	−	32.2749i	−0.377072	−	1.40725i
$527$	2.82221	+	10.5326i	0.122937	+	0.458809i
$528$		0			0
$529$	−4.78954			−0.208241
$530$	0.446393	−	0.773176i	0.0193901	−	0.0335846i
$531$		0			0
$532$		−	1.59422i		−	0.0691183i
$533$	−5.05366	−	3.26839i	−0.218898	−	0.141570i
$534$		0			0
$535$	8.42378	−	8.42378i	0.364192	−	0.364192i
$536$			4.24085i			0.183177i
$537$		0			0
$538$	−1.38954	−	5.18583i	−0.0599073	−	0.223577i
$539$	−1.54526	+	5.76697i	−0.0665589	+	0.248401i
$540$		0			0
$541$	23.9398	+	23.9398i	1.02925	+	1.02925i	0.999559	+	0.0296937i	$0.00945319\pi$
$541$	23.9398	+	23.9398i	1.02925	+	1.02925i	0.0296937	+	0.999559i	$0.490547\pi$
$542$		−	24.9365i		−	1.07111i
$543$		0			0
$544$	22.0088	+	22.0088i	0.943618	+	0.943618i
$545$	−13.2285	−	22.9124i	−0.566645	−	0.981458i
$546$		0			0
$547$	−8.43825	+	14.6155i	−0.360793	+	0.624912i	−0.988092	−	0.153867i	$-0.950827\pi$
$547$	−8.43825	+	14.6155i	−0.360793	+	0.624912i	0.627298	+	0.778779i	$0.284161\pi$
$548$	−0.575322	+	0.154157i	−0.0245766	+	0.00658527i
$549$		0			0
$550$	−17.6310	+	10.1792i	−0.751787	+	0.434044i
$551$	−2.35518	+	0.631067i	−0.100334	+	0.0268844i
$552$		0			0
$553$	−15.4744	+	4.14636i	−0.658039	+	0.176321i
$554$	44.9736	+	12.0506i	1.91075	+	0.511983i
$555$		0			0
$556$	10.5888	−	6.11342i	0.449063	−	0.259267i
$557$	−6.49382	−	24.2353i	−0.275152	−	1.02688i	−0.955739	−	0.294215i	$-0.904942\pi$
$557$	−6.49382	−	24.2353i	−0.275152	−	1.02688i	0.680587	−	0.732667i	$-0.261725\pi$
$558$		0			0
$559$	2.26199	+	10.5443i	0.0956721	+	0.445977i
$560$	30.7117	+	17.7314i	1.29780	+	0.749288i
$561$		0			0
$562$	38.5335			1.62544
$563$	4.00167	−	6.93109i	0.168650	−	0.292111i	−0.769295	−	0.638893i	$-0.779393\pi$
$563$	4.00167	−	6.93109i	0.168650	−	0.292111i	0.937945	+	0.346783i	$0.112726\pi$
$564$		0			0
$565$	28.4935	−	28.4935i	1.19873	−	1.19873i
$566$	−3.85408	−	1.03270i	−0.161999	−	0.0434075i
$567$		0			0
$568$	−3.34068	−	5.78623i	−0.140172	−	0.242785i
$569$	−3.43410	−	5.94804i	−0.143965	−	0.249355i	0.785021	−	0.619469i	$-0.212652\pi$
$569$	−3.43410	−	5.94804i	−0.143965	−	0.249355i	−0.928986	+	0.370114i	$0.879319\pi$
$570$		0			0
$571$	−8.78114	+	5.06979i	−0.367479	+	0.212164i	−0.672357	−	0.740227i	$-0.734718\pi$
$571$	−8.78114	+	5.06979i	−0.367479	+	0.212164i	0.304877	+	0.952392i	$0.401384\pi$
$572$	26.6809	+	17.2556i	1.11559	+	0.721491i
$573$		0			0
$574$	8.38142	+	2.24579i	0.349834	+	0.0937377i
$575$	−6.48117	−	3.74191i	−0.270283	−	0.156048i
$576$		0			0
$577$	−6.26722	+	6.26722i	−0.260908	+	0.260908i	−0.825423	−	0.564515i	$-0.809063\pi$
$577$	−6.26722	+	6.26722i	−0.260908	+	0.260908i	0.564515	+	0.825423i	$0.309063\pi$
$578$	5.88042	+	5.88042i	0.244593	+	0.244593i
$579$		0			0
$580$	−5.68241	+	21.2071i	−0.235949	+	0.880575i
$581$	−38.1528	−	22.0275i	−1.58284	−	0.913855i
$582$		0			0
$583$	0.303605	−	1.13307i	0.0125740	−	0.0469269i
$584$	−2.34097			−0.0968701
$585$		0			0
$586$	59.1262			2.44248
$587$	2.97754	−	11.1123i	0.122896	−	0.458656i	−0.876860	−	0.480747i	$-0.840366\pi$
$587$	2.97754	−	11.1123i	0.122896	−	0.458656i	0.999756	+	0.0220910i	$0.00703235\pi$
$588$		0			0
$589$	−0.822554	−	0.474902i	−0.0338927	−	0.0195680i
$590$	5.15331	−	19.2324i	0.212158	−	0.791786i
$591$		0			0
$592$	−5.70002	−	5.70002i	−0.234269	−	0.234269i
$593$	12.5514	−	12.5514i	0.515426	−	0.515426i	−0.400758	−	0.916184i	$-0.631253\pi$
$593$	12.5514	−	12.5514i	0.515426	−	0.515426i	0.916184	+	0.400758i	$0.131253\pi$
$594$		0			0
$595$	29.4281	+	16.9903i	1.20643	+	0.696535i
$596$	3.49316	+	0.935990i	0.143086	+	0.0383397i
$597$		0			0
$598$	−1.43149	+	28.3336i	−0.0585378	+	1.15865i
$599$	−37.6976	+	21.7647i	−1.54028	+	0.889283i	−0.541462	+	0.840725i	$0.682129\pi$
$599$	−37.6976	+	21.7647i	−1.54028	+	0.889283i	−0.998820	+	0.0485576i	$0.984538\pi$
$600$		0			0
$601$	−14.2443	−	24.6718i	−0.581036	−	1.00638i	−0.995357	−	0.0962533i	$-0.969314\pi$
$601$	−14.2443	−	24.6718i	−0.581036	−	1.00638i	0.414321	−	0.910131i	$-0.364019\pi$
$602$	−7.77404	−	13.4650i	−0.316846	−	0.548794i
$603$		0			0
$604$	−1.84047	−	0.493152i	−0.0748876	−	0.0200661i
$605$	−52.6272	+	52.6272i	−2.13960	+	2.13960i
$606$		0			0
$607$	−14.8033	+	25.6401i	−0.600848	+	1.04070i	0.391845	+	0.920031i	$0.371837\pi$
$607$	−14.8033	+	25.6401i	−0.600848	+	1.04070i	−0.992693	+	0.120668i	$0.961496\pi$
$608$	−2.71114			−0.109951
$609$		0			0
$610$	0.394640	+	0.227846i	0.0159785	+	0.00922520i
$611$	7.97544	+	15.5802i	0.322652	+	0.630307i
$612$		0			0
$613$	−8.67578	−	32.3784i	−0.350411	−	1.30775i	−0.886161	−	0.463377i	$-0.846638\pi$
$613$	−8.67578	−	32.3784i	−0.350411	−	1.30775i	0.535750	−	0.844377i	$-0.320029\pi$
$614$	41.9569	−	24.2238i	1.69324	−	0.977594i
$615$		0			0
$616$	18.9758	+	5.08455i	0.764557	+	0.204862i
$617$	−32.7357	+	8.77151i	−1.31789	+	0.353128i	−0.848187	−	0.529697i	$-0.822306\pi$
$617$	−32.7357	+	8.77151i	−1.31789	+	0.353128i	−0.469703	+	0.882824i	$0.655639\pi$
$618$		0			0
$619$	−25.9724	+	6.95927i	−1.04392	+	0.279717i	−0.739736	−	0.672897i	$-0.765050\pi$
$619$	−25.9724	+	6.95927i	−1.04392	+	0.279717i	−0.304181	+	0.952614i	$0.598383\pi$
$620$	−7.40664	+	4.27623i	−0.297458	+	0.171737i
$621$		0			0
$622$	12.3010	−	3.29605i	0.493227	−	0.132160i
$623$	0.170915	−	0.296034i	0.00684757	−	0.0118603i
$624$		0			0
$625$	−15.3465	−	26.5810i	−0.613862	−	1.06324i
$626$	36.7664	+	36.7664i	1.46948	+	1.46948i
$627$		0			0
$628$			17.0569i			0.680643i
$629$	−5.46179	−	5.46179i	−0.217776	−	0.217776i
$630$		0			0
$631$	−0.0679900	+	0.253742i	−0.00270664	+	0.0101013i	−0.967266	−	0.253765i	$-0.918331\pi$
$631$	−0.0679900	+	0.253742i	−0.00270664	+	0.0101013i	0.964559	+	0.263866i	$0.0849977\pi$
$632$	1.62776	+	6.07486i	0.0647486	+	0.241645i
$633$		0			0
$634$		−	1.33256i		−	0.0529226i
$635$	−5.11857	+	5.11857i	−0.203124	+	0.203124i
$636$		0			0
$637$	−0.717165	−	3.34307i	−0.0284151	−	0.132457i
$638$			70.0647i			2.77389i
$639$		0			0
$640$	10.9870	−	19.0300i	0.434297	−	0.752225i
$641$	−31.2053			−1.23254			−0.616268	−	0.787537i	$-0.711356\pi$
$641$	−31.2053			−1.23254			−0.616268	+	0.787537i	$0.711356\pi$
$642$		0			0
$643$	−11.4741	−	42.8219i	−0.452494	−	1.68873i	−0.695352	−	0.718669i	$-0.744752\pi$
$643$	−11.4741	−	42.8219i	−0.452494	−	1.68873i	0.242858	−	0.970062i	$-0.421915\pi$
$644$	−4.35855	−	16.2663i	−0.171751	−	0.640984i
$645$		0			0
$646$	−3.45469			−0.135923
$647$	−5.33648	+	9.24306i	−0.209799	+	0.363382i	−0.951651	−	0.307181i	$-0.900614\pi$
$647$	−5.33648	+	9.24306i	−0.209799	+	0.363382i	0.741852	+	0.670563i	$0.233948\pi$
$648$		0			0
$649$		−	26.1610i		−	1.02691i
$650$	6.33149	−	9.78989i	0.248341	−	0.383991i
$651$		0			0
$652$	−24.2051	+	24.2051i	−0.947944	+	0.947944i
$653$		−	35.1382i		−	1.37506i	−0.726154	−	0.687532i	$-0.758694\pi$
$653$		−	35.1382i		−	1.37506i	0.726154	−	0.687532i	$-0.241306\pi$
$654$		0			0
$655$	8.69714	+	32.4582i	0.339825	+	1.26825i
$656$	2.09109	−	7.80407i	0.0816435	−	0.304698i
$657$		0			0
$658$	−17.8436	−	17.8436i	−0.695616	−	0.695616i
$659$			9.60362i			0.374104i	0.982350	+	0.187052i	$0.0598933\pi$
$659$			9.60362i			0.374104i	−0.982350	+	0.187052i	$0.940107\pi$
$660$		0			0
$661$	8.21987	+	8.21987i	0.319716	+	0.319716i	0.848658	−	0.528942i	$-0.177411\pi$
$661$	8.21987	+	8.21987i	0.319716	+	0.319716i	−0.528942	+	0.848658i	$0.677411\pi$
$662$	4.46607	+	7.73546i	0.173579	+	0.300647i
$663$		0			0
$664$	−8.64745	+	14.9778i	−0.335586	+	0.581252i
$665$	−2.85901	+	0.766070i	−0.110868	+	0.0297069i
$666$		0			0
$667$	−22.3053	+	12.8779i	−0.863663	+	0.498636i
$668$	−10.4147	+	2.79062i	−0.402958	+	0.107972i
$669$		0			0
$670$	−17.7351	+	4.75209i	−0.685165	+	0.183589i
$671$	0.578335	+	0.154964i	0.0223264	+	0.00598233i
$672$		0			0
$673$	−21.0558	+	12.1566i	−0.811640	+	0.468601i	−0.847525	−	0.530755i	$-0.821908\pi$
$673$	−21.0558	+	12.1566i	−0.811640	+	0.468601i	0.0358851	+	0.999356i	$0.488575\pi$
$674$	−11.9733	−	44.6849i	−0.461194	−	1.72120i
$675$		0			0
$676$	−18.1040	−	1.83400i	−0.696308	−	0.0705386i
$677$	36.2277	+	20.9161i	1.39234	+	0.803871i	0.993574	−	0.113180i	$-0.0361038\pi$
$677$	36.2277	+	20.9161i	1.39234	+	0.803871i	0.398770	+	0.917051i	$0.369437\pi$
$678$		0			0
$679$	44.7098			1.71580
$680$	6.66997	−	11.5527i	0.255782	−	0.443027i
$681$		0			0
$682$	−19.2992	+	19.2992i	−0.739003	+	0.739003i
$683$	−9.97708	−	2.67335i	−0.381763	−	0.102293i	0.0628338	−	0.998024i	$-0.479986\pi$
$683$	−9.97708	−	2.67335i	−0.381763	−	0.102293i	−0.444596	+	0.895731i	$0.646653\pi$
$684$		0			0
$685$	0.552918	+	0.957682i	0.0211259	+	0.0365911i
$686$	−15.7292	−	27.2438i	−0.600545	−	1.04017i
$687$		0			0
$688$	−12.5375	+	7.23853i	−0.477988	+	0.275966i
$689$	0.140905	+	0.656832i	0.00536806	+	0.0250233i
$690$		0			0
$691$	−0.659509	−	0.176715i	−0.0250889	−	0.00672256i	0.246253	−	0.969206i	$-0.420801\pi$
$691$	−0.659509	−	0.176715i	−0.0250889	−	0.00672256i	−0.271342	+	0.962483i	$0.587467\pi$
$692$	−14.0672	−	8.12171i	−0.534755	−	0.308741i
$693$		0			0
$694$	35.7527	−	35.7527i	1.35715	−	1.35715i
$695$	−16.0517	−	16.0517i	−0.608878	−	0.608878i
$696$		0			0
$697$	2.00370	−	7.47791i	0.0758955	−	0.283246i
$698$	−1.63923	−	0.946411i	−0.0620458	−	0.0358222i
$699$		0			0
$700$	−1.79120	+	6.68485i	−0.0677010	+	0.252664i
$701$	−48.1896			−1.82010			−0.910049	−	0.414502i	$-0.863956\pi$
$701$	−48.1896			−1.82010			−0.910049	+	0.414502i	$0.863956\pi$
$702$		0			0
$703$	0.672807			0.0253754
$704$	−4.38926	+	16.3809i	−0.165427	+	0.617380i
$705$		0			0
$706$	−30.6312	−	17.6849i	−1.15282	−	0.665581i
$707$	−2.55463	+	9.53401i	−0.0960767	+	0.358563i
$708$		0			0
$709$	13.1437	+	13.1437i	0.493620	+	0.493620i	0.909445	−	0.415824i	$-0.136507\pi$
$709$	13.1437	+	13.1437i	0.493620	+	0.493620i	−0.415824	+	0.909445i	$0.636507\pi$
$710$	20.4543	−	20.4543i	0.767638	−	0.767638i
$711$		0			0
$712$	−0.116215	−	0.0670970i	−0.00435536	−	0.00251457i
$713$	−9.69113	−	2.59673i	−0.362936	−	0.0972483i
$714$		0			0
$715$	18.1244	−	56.1402i	0.677815	−	2.09953i
$716$	6.68002	−	3.85671i	0.249644	−	0.144132i
$717$		0			0
$718$	23.6220	+	40.9144i	0.881563	+	1.52691i
$719$	17.7360	+	30.7196i	0.661439	+	1.14565i	0.980238	+	0.197824i	$0.0633875\pi$
$719$	17.7360	+	30.7196i	0.661439	+	1.14565i	−0.318798	+	0.947823i	$0.603279\pi$
$720$		0			0
$721$	−33.2786	−	8.91697i	−1.23936	−	0.332085i
$722$	−24.5593	+	24.5593i	−0.914001	+	0.914001i
$723$		0			0
$724$	6.75557	−	11.7010i	0.251069	−	0.434864i
$725$	10.5847			0.393106
$726$		0			0
$727$	−0.212677	−	0.122789i	−0.00788777	−	0.00455400i	0.496051	−	0.868293i	$-0.334783\pi$
$727$	−0.212677	−	0.122789i	−0.00788777	−	0.00455400i	−0.503939	+	0.863739i	$0.668116\pi$
$728$	−11.0001	+	2.35978i	−0.407692	+	0.0874592i
$729$		0			0
$730$	−2.62318	−	9.78984i	−0.0970882	−	0.362338i
$731$	−12.0135	+	6.93600i	−0.444336	+	0.256537i
$732$		0			0
$733$	0.851305	+	0.228106i	0.0314437	+	0.00842530i	0.274507	−	0.961585i	$-0.411485\pi$
$733$	0.851305	+	0.228106i	0.0314437	+	0.00842530i	−0.243063	+	0.970011i	$0.578152\pi$
$734$	−41.5073	+	11.1219i	−1.53206	+	0.410515i
$735$		0			0
$736$	−27.6625	+	7.41215i	−1.01965	+	0.273216i
$737$	−20.8922	+	12.0621i	−0.769574	+	0.444314i
$738$		0			0
$739$	−19.4340	+	5.20731i	−0.714890	+	0.191554i	−0.597890	−	0.801578i	$-0.703994\pi$
$739$	−19.4340	+	5.20731i	−0.714890	+	0.191554i	−0.116999	+	0.993132i	$0.537328\pi$
$740$	3.02913	−	5.24661i	0.111353	−	0.192869i
$741$		0			0
$742$	−0.484265	−	0.838771i	−0.0177779	−	0.0307923i
$743$	−21.9020	−	21.9020i	−0.803507	−	0.803507i	0.180135	−	0.983642i	$-0.442346\pi$
$743$	−21.9020	−	21.9020i	−0.803507	−	0.803507i	−0.983642	+	0.180135i	$0.942346\pi$
$744$		0			0
$745$		−	6.71426i		−	0.245992i
$746$	9.15522	+	9.15522i	0.335197	+	0.335197i
$747$		0			0
$748$	−10.5786	+	39.4798i	−0.386791	+	1.44352i
$749$	−3.34490	−	12.4833i	−0.122220	−	0.456131i
$750$		0			0
$751$		−	31.5860i		−	1.15259i	−0.817242	−	0.576295i	$-0.804498\pi$
$751$		−	31.5860i		−	1.15259i	0.817242	−	0.576295i	$-0.195502\pi$
$752$	−16.6144	+	16.6144i	−0.605867	+	0.605867i
$753$		0			0
$754$	−18.2834	−	35.7170i	−0.665842	−	1.30074i
$755$			3.53759i			0.128746i
$756$		0			0
$757$	6.66044	−	11.5362i	0.242078	−	0.419291i	−0.719228	−	0.694774i	$-0.755504\pi$
$757$	6.66044	−	11.5362i	0.242078	−	0.419291i	0.961306	+	0.275483i	$0.0888377\pi$
$758$	17.7753			0.645628
$759$		0			0
$760$	0.300740	+	1.12238i	0.0109090	+	0.0407129i
$761$	−1.86457	−	6.95866i	−0.0675905	−	0.252251i	0.923861	−	0.382729i	$-0.125016\pi$
$761$	−1.86457	−	6.95866i	−0.0675905	−	0.252251i	−0.991451	+	0.130478i	$0.958349\pi$
$762$		0			0
$763$	−28.7015			−1.03906
$764$	5.09188	−	8.81939i	0.184218	−	0.319074i
$765$		0			0
$766$			42.6706i			1.54175i
$767$	6.82673	+	13.3362i	0.246499	+	0.481541i
$768$		0			0
$769$	−27.9015	+	27.9015i	−1.00615	+	1.00615i	−0.00617137	+	0.999981i	$0.501964\pi$
$769$	−27.9015	+	27.9015i	−1.00615	+	1.00615i	−0.999981	+	0.00617137i	$0.998036\pi$
$770$			85.0534i			3.06511i
$771$		0			0
$772$	4.64566	+	17.3378i	0.167201	+	0.624003i
$773$	12.7625	−	47.6302i	0.459034	−	1.71314i	−0.216916	−	0.976190i	$-0.569600\pi$
$773$	12.7625	−	47.6302i	0.459034	−	1.71314i	0.675950	−	0.736947i	$-0.263733\pi$
$774$		0			0
$775$	2.91553	+	2.91553i	0.104729	+	0.104729i
$776$		−	17.5519i		−	0.630078i
$777$		0			0
$778$	5.90213	+	5.90213i	0.211601	+	0.211601i
$779$	0.337169	+	0.583993i	0.0120803	+	0.0209237i
$780$		0			0
$781$	19.0036	−	32.9152i	0.680001	−	1.17780i
$782$	−35.2493	+	9.44501i	−1.26051	+	0.337753i
$783$		0			0
$784$	3.97501	−	2.29498i	0.141965	−	0.0819634i
$785$	30.5891	−	8.19632i	1.09177	−	0.292539i
$786$		0			0
$787$	48.2254	−	12.9220i	1.71905	−	0.460618i	0.741436	−	0.671024i	$-0.234145\pi$
$787$	48.2254	−	12.9220i	1.71905	−	0.460618i	0.977614	+	0.210406i	$0.0674786\pi$
$788$	−21.3246	−	5.71391i	−0.759657	−	0.203550i
$789$		0			0
$790$	−23.5808	+	13.6144i	−0.838968	+	0.484378i
$791$	−11.3141	−	42.2249i	−0.402285	−	1.50135i
$792$		0			0
$793$	−0.335257	+	0.0719201i	−0.0119053	+	0.00255396i
$794$	12.5465	+	7.24371i	0.445257	+	0.257070i
$795$		0			0
$796$	34.6168			1.22696
$797$	−0.375653	+	0.650650i	−0.0133063	+	0.0230472i	−0.872602	−	0.488432i	$-0.837569\pi$
$797$	−0.375653	+	0.650650i	−0.0133063	+	0.0230472i	0.859296	+	0.511479i	$0.170902\pi$
$798$		0			0
$799$	−15.9201	+	15.9201i	−0.563212	+	0.563212i
$800$	11.3683	+	3.04612i	0.401929	+	0.107696i
$801$		0			0
$802$	−0.238917	−	0.413817i	−0.00843647	−	0.0146124i
$803$	−6.65835	−	11.5326i	−0.234968	−	0.406977i
$804$		0			0
$805$	−27.0770	+	15.6329i	−0.954337	+	0.550987i
$806$	4.80205	−	14.8743i	0.169145	−	0.523924i
$807$		0			0
$808$	3.74281	+	1.00288i	0.131672	+	0.0352813i
$809$	24.5450	+	14.1711i	0.862958	+	0.498229i	0.865002	−	0.501769i	$-0.167317\pi$
$809$	24.5450	+	14.1711i	0.862958	+	0.498229i	−0.00204394	+	0.999998i	$0.500651\pi$
$810$		0			0
$811$	−14.9696	+	14.9696i	−0.525652	+	0.525652i	−0.919273	−	0.393621i	$-0.871222\pi$
$811$	−14.9696	+	14.9696i	−0.525652	+	0.525652i	0.393621	+	0.919273i	$0.371222\pi$
$812$	16.8417	+	16.8417i	0.591029	+	0.591029i
$813$		0			0
$814$	5.00388	−	18.6747i	0.175386	−	0.654548i
$815$	55.0396	+	31.7771i	1.92795	+	1.11310i
$816$		0			0
$817$	0.312735	−	1.16714i	0.0109412	−	0.0408331i
$818$	68.1002			2.38107
$819$		0			0
$820$	6.07203			0.212045
$821$	−10.1140	+	37.7460i	−0.352981	+	1.31734i	0.530025	+	0.847982i	$0.322183\pi$
$821$	−10.1140	+	37.7460i	−0.352981	+	1.31734i	−0.883006	+	0.469362i	$0.844484\pi$
$822$		0			0
$823$	38.5876	+	22.2786i	1.34508	+	0.776582i	0.987548	−	0.157319i	$-0.0502851\pi$
$823$	38.5876	+	22.2786i	1.34508	+	0.776582i	0.357532	+	0.933901i	$0.383618\pi$
$824$	−3.50058	+	13.0643i	−0.121948	+	0.455118i
$825$		0			0
$826$	−15.2736	−	15.2736i	−0.531435	−	0.531435i
$827$	−6.18902	+	6.18902i	−0.215213	+	0.215213i	−0.806478	−	0.591265i	$-0.798629\pi$
$827$	−6.18902	+	6.18902i	−0.215213	+	0.215213i	0.591265	+	0.806478i	$0.298629\pi$
$828$		0			0
$829$	15.4468	+	8.91823i	0.536490	+	0.309743i	0.743655	−	0.668563i	$-0.233090\pi$
$829$	15.4468	+	8.91823i	0.536490	+	0.309743i	−0.207165	+	0.978306i	$0.566424\pi$
$830$	−72.3264	−	19.3798i	−2.51049	−	0.672683i
$831$		0			0
$832$	−2.03709	−	9.49592i	−0.0706234	−	0.329212i
$833$	3.80888	−	2.19906i	0.131970	−	0.0761929i
$834$		0			0
$835$	10.0092	+	17.3364i	0.346381	+	0.599949i
$836$	−1.78009	−	3.08321i	−0.0615657	−	0.106635i
$837$		0			0
$838$	51.8405	+	13.8906i	1.79080	+	0.479844i
$839$	23.4795	−	23.4795i	0.810604	−	0.810604i	−0.174121	−	0.984724i	$-0.555708\pi$
$839$	23.4795	−	23.4795i	0.810604	−	0.810604i	0.984724	+	0.174121i	$0.0557083\pi$
$840$		0			0
$841$	3.71387	−	6.43261i	0.128064	−	0.221814i
$842$	13.4487			0.463472
$843$		0			0
$844$	−17.4587	−	10.0798i	−0.600954	−	0.346961i
$845$	5.41048	+	33.3483i	0.186126	+	1.14722i
$846$		0			0
$847$	20.8971	+	77.9892i	0.718034	+	2.67974i
$848$	−0.780993	+	0.450906i	−0.0268194	+	0.0154842i
$849$		0			0
$850$	14.4861	+	3.88154i	0.496870	+	0.133136i
$851$	6.86486	−	1.83943i	0.235324	−	0.0630549i
$852$		0			0
$853$	18.1694	−	4.86849i	0.622110	−	0.166694i	0.0660230	−	0.997818i	$-0.478969\pi$
$853$	18.1694	−	4.86849i	0.622110	−	0.166694i	0.556087	+	0.831124i	$0.312302\pi$
$854$	0.428121	−	0.247176i	0.0146500	−	0.00845818i
$855$		0			0
$856$	−4.90065	+	1.31312i	−0.167501	+	0.0448817i
$857$	−16.1683	+	28.0043i	−0.552298	+	0.956607i	0.445811	+	0.895127i	$0.352915\pi$
$857$	−16.1683	+	28.0043i	−0.552298	+	0.956607i	−0.998108	+	0.0614802i	$0.980418\pi$
$858$		0			0
$859$	8.02856	+	13.9059i	0.273931	+	0.474462i	0.969865	−	0.243644i	$-0.0783427\pi$
$859$	8.02856	+	13.9059i	0.273931	+	0.474462i	−0.695934	+	0.718106i	$0.745009\pi$
$860$	−7.69346	−	7.69346i	−0.262345	−	0.262345i
$861$		0			0
$862$			27.9204i			0.950974i
$863$	−23.7439	−	23.7439i	−0.808250	−	0.808250i	0.176119	−	0.984369i	$-0.443646\pi$
$863$	−23.7439	−	23.7439i	−0.808250	−	0.808250i	−0.984369	+	0.176119i	$0.943646\pi$
$864$		0			0
$865$	−7.80543	+	29.1303i	−0.265393	+	0.990458i
$866$	−14.3405	−	53.5193i	−0.487308	−	1.81866i
$867$		0			0
$868$			9.27804i			0.314917i
$869$	−25.2975	+	25.2975i	−0.858160	+	0.858160i
$870$		0			0
$871$	7.50264	−	11.6007i	0.254217	−	0.393076i
$872$			11.2675i			0.381565i
$873$		0			0
$874$	1.58934	−	2.75282i	0.0537602	−	0.0931155i
$875$	−23.7845			−0.804062
$876$		0			0
$877$	8.33096	+	31.0916i	0.281317	+	1.04989i	0.951489	+	0.307683i	$0.0995535\pi$
$877$	8.33096	+	31.0916i	0.281317	+	1.04989i	−0.670172	+	0.742206i	$0.733780\pi$
$878$	−7.48210	−	27.9236i	−0.252508	−	0.942375i
$879$		0			0
$880$	79.1946			2.66965
$881$	21.3604	−	36.9973i	0.719650	−	1.24647i	−0.241489	−	0.970404i	$-0.577636\pi$
$881$	21.3604	−	36.9973i	0.719650	−	1.24647i	0.961139	−	0.276066i	$-0.0890309\pi$
$882$		0			0
$883$			30.7720i			1.03556i	0.855514	+	0.517780i	$0.173241\pi$
$883$			30.7720i			1.03556i	−0.855514	+	0.517780i	$0.826759\pi$
$884$	−4.90960	−	22.8862i	−0.165128	−	0.769745i
$885$		0			0
$886$	−17.9372	+	17.9372i	−0.602612	+	0.602612i
$887$		−	25.5690i		−	0.858525i	−0.903180	−	0.429262i	$-0.858774\pi$
$887$		−	25.5690i		−	0.858525i	0.903180	−	0.429262i	$-0.141226\pi$
$888$		0			0
$889$	2.03247	+	7.58529i	0.0681670	+	0.254403i
$890$	0.150371	−	0.561193i	0.00504045	−	0.0188112i
$891$		0			0
$892$	1.00878	+	1.00878i	0.0337764	+	0.0337764i
$893$		−	1.96110i		−	0.0656259i
$894$		0			0
$895$	−10.1264	−	10.1264i	−0.338488	−	0.338488i
$896$	−11.9191	−	20.6444i	−0.398188	−	0.689682i
$897$		0			0
$898$	11.0238	−	19.0938i	0.367870	−	0.637169i
$899$	13.7066	−	3.67268i	0.457141	−	0.122491i
$900$		0			0
$901$	−0.748352	+	0.432061i	−0.0249312	+	0.0143940i
$902$	18.7172	−	5.01525i	0.623214	−	0.166990i
$903$		0			0
$904$	−16.5765	+	4.44165i	−0.551325	+	0.147727i
$905$	−24.2303	−	6.49249i	−0.805443	−	0.215818i
$906$		0			0
$907$	−38.7229	+	22.3567i	−1.28577	+	0.742342i	−0.977898	−	0.209085i	$-0.932952\pi$
$907$	−38.7229	+	22.3567i	−1.28577	+	0.742342i	−0.307876	+	0.951426i	$0.599618\pi$
$908$	2.81450	+	10.5038i	0.0934023	+	0.348582i
$909$		0			0
$910$	−22.1947	−	43.3578i	−0.735747	−	1.43730i
$911$	−28.6386	−	16.5345i	−0.948840	−	0.547813i	−0.0561197	−	0.998424i	$-0.517873\pi$
$911$	−28.6386	−	16.5345i	−0.948840	−	0.547813i	−0.892720	+	0.450611i	$0.851206\pi$
$912$		0			0
$913$	−98.3826			−3.25599
$914$	36.2479	−	62.7832i	1.19897	−	2.07668i
$915$		0			0
$916$	−15.5362	+	15.5362i	−0.513331	+	0.513331i
$917$	35.2119	+	9.43499i	1.16280	+	0.311571i
$918$		0			0
$919$	−7.33901	−	12.7115i	−0.242092	−	0.419315i	0.719218	−	0.694784i	$-0.244500\pi$
$919$	−7.33901	−	12.7115i	−0.242092	−	0.419315i	−0.961310	+	0.275469i	$0.911167\pi$
$920$	6.13708	+	10.6297i	0.202334	+	0.350452i
$921$		0			0
$922$	28.7269	−	16.5855i	0.946069	−	0.546213i
$923$	−1.09827	+	21.7382i	−0.0361500	+	0.715522i
$924$		0			0
$925$	−2.82120	−	0.755938i	−0.0927604	−	0.0248551i
$926$	54.0165	+	31.1865i	1.77509	+	1.02485i
$927$		0			0
$928$	28.6411	−	28.6411i	0.940189	−	0.940189i
$929$	35.3524	+	35.3524i	1.15987	+	1.15987i	0.984502	+	0.175372i	$0.0561129\pi$
$929$	35.3524	+	35.3524i	1.15987	+	1.15987i	0.175372	+	0.984502i	$0.443887\pi$
$930$		0			0
$931$	−0.0991526	+	0.370042i	−0.00324959	+	0.0121277i
$932$	−11.3748	−	6.56722i	−0.372592	−	0.215116i
$933$		0			0
$934$	−7.38872	+	27.5751i	−0.241766	+	0.902284i
$935$	75.8847			2.48170
$936$		0			0
$937$	12.7044			0.415036			0.207518	−	0.978231i	$-0.433462\pi$
$937$	12.7044			0.415036			0.207518	+	0.978231i	$0.433462\pi$
$938$	−5.15526	+	19.2397i	−0.168325	+	0.628198i
$939$		0			0
$940$	−15.2928	−	8.82933i	−0.498798	−	0.287981i
$941$	−0.320048	+	1.19444i	−0.0104333	+	0.0389375i	−0.970946	−	0.239298i	$-0.923083\pi$
$941$	−0.320048	+	1.19444i	−0.0104333	+	0.0389375i	0.960513	+	0.278235i	$0.0897495\pi$
$942$		0			0
$943$	5.03685	+	5.03685i	0.164022	+	0.164022i
$944$	−14.2214	+	14.2214i	−0.462869	+	0.462869i
$945$		0			0
$946$	−30.0698	−	17.3608i	−0.977653	−	0.564448i
$947$	16.2266	+	4.34789i	0.527292	+	0.141287i	0.512638	−	0.858605i	$-0.328668\pi$
$947$	16.2266	+	4.34789i	0.527292	+	0.141287i	0.0146546	+	0.999893i	$0.495335\pi$
$948$		0			0
$949$	6.40367	+	4.14150i	0.207872	+	0.134439i
$950$	−1.13130	+	0.653159i	−0.0367044	+	0.0211913i
$951$		0			0
$952$	−7.23585	−	12.5329i	−0.234515	−	0.406192i
$953$	3.87222	+	6.70688i	0.125433	+	0.217257i	0.921902	−	0.387422i	$-0.126635\pi$
$953$	3.87222	+	6.70688i	0.125433	+	0.217257i	−0.796469	+	0.604680i	$0.793301\pi$
$954$		0			0
$955$	−18.2631	−	4.89359i	−0.590981	−	0.158353i
$956$	−17.7118	+	17.7118i	−0.572842	+	0.572842i
$957$		0			0
$958$	28.4329	−	49.2472i	0.918624	−	1.59110i
$959$	1.19965			0.0387388
$960$		0			0
$961$	−22.0597	−	12.7362i	−0.711603	−	0.410844i
$962$	2.32234	+	10.8256i	0.0748751	+	0.349031i
$963$		0			0
$964$	5.48636	+	20.4754i	0.176704	+	0.659467i
$965$	28.8606	−	16.6627i	0.929055	−	0.536390i
$966$		0			0
$967$	18.8877	+	5.06094i	0.607387	+	0.162749i	0.549387	−	0.835568i	$-0.314861\pi$
$967$	18.8877	+	5.06094i	0.607387	+	0.162749i	0.0579995	+	0.998317i	$0.481528\pi$
$968$	30.6166	−	8.20369i	0.984055	−	0.263677i
$969$		0			0
$970$	73.4014	−	19.6678i	2.35678	−	0.631497i
$971$	−46.5819	+	26.8941i	−1.49489	+	0.863073i	−0.999983	−	0.00587546i	$-0.998130\pi$
$971$	−46.5819	+	26.8941i	−1.49489	+	0.863073i	−0.494903	+	0.868948i	$0.664796\pi$
$972$		0			0
$973$	−23.7874	+	6.37381i	−0.762588	+	0.204335i
$974$	−35.3109	+	61.1602i	−1.13143	+	1.95970i
$975$		0			0
$976$	−0.230149	−	0.398630i	−0.00736690	−	0.0127598i
$977$	−31.2770	−	31.2770i	−1.00064	−	1.00064i	−1.00000		0.000639826i	$-0.999796\pi$
$977$	−31.2770	−	31.2770i	−1.00064	−	1.00064i	−0.000639826	−	1.00000i	$-0.500204\pi$
$978$		0			0
$979$		−	0.763367i		−	0.0243973i
$980$	2.43921	+	2.43921i	0.0779178	+	0.0779178i
$981$		0			0
$982$	15.6906	−	58.5583i	0.500708	−	1.86867i
$983$	12.5790	+	46.9456i	0.401209	+	1.49733i	0.810942	+	0.585127i	$0.198955\pi$
$983$	12.5790	+	46.9456i	0.401209	+	1.49733i	−0.409733	+	0.912206i	$0.634378\pi$
$984$		0			0
$985$			40.9883i			1.30600i
$986$	36.4961	−	36.4961i	1.16227	−	1.16227i
$987$		0			0
$988$	1.71200	+	1.10722i	0.0544661	+	0.0352252i
$989$		−	12.7637i		−	0.405862i
$990$		0			0
$991$	20.5994	−	35.6792i	0.654362	−	1.13339i	−0.327691	−	0.944785i	$-0.606271\pi$
$991$	20.5994	−	35.6792i	0.654362	−	1.13339i	0.982053	−	0.188604i	$-0.0603961\pi$
$992$	15.7782			0.500959
$993$		0			0
$994$	−8.12198	−	30.3116i	−0.257614	−	0.961427i
$995$	−16.6344	−	62.0803i	−0.527345	−	1.96808i
$996$		0			0
$997$	−30.0081			−0.950367			−0.475183	−	0.879887i	$-0.657618\pi$
$997$	−30.0081			−0.950367			−0.475183	+	0.879887i	$0.657618\pi$
$998$	−17.7827	+	30.8005i	−0.562901	+	0.974973i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bf.a.305.11		48
3.2	odd	2		117.2.bc.a.110.2	yes	48
9.4	even	3		117.2.x.a.32.11	yes	48
9.5	odd	6		351.2.ba.a.71.2		48
13.11	odd	12		351.2.ba.a.89.2		48
39.11	even	12		117.2.x.a.11.11	✓	48
117.50	even	12	inner	351.2.bf.a.206.11		48
117.76	odd	12		117.2.bc.a.50.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.11.11	✓	48	39.11	even	12
117.2.x.a.32.11	yes	48	9.4	even	3
117.2.bc.a.50.2	yes	48	117.76	odd	12
117.2.bc.a.110.2	yes	48	3.2	odd	2
351.2.ba.a.71.2		48	9.5	odd	6
351.2.ba.a.89.2		48	13.11	odd	12
351.2.bf.a.206.11		48	117.50	even	12	inner
351.2.bf.a.305.11		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.bf (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.477221 - 1.78101i) q^{2} +(-1.21221 - 0.699872i) q^{4} +(-0.672617 + 2.51024i) q^{5} +(1.99353 + 1.99353i) q^{7} +(0.782609 - 0.782609i) q^{8} +(4.14978 + 2.39588i) q^{10} +(6.08140 + 1.62951i) q^{11} +(-3.52535 + 0.756266i) q^{13} +(4.50185 - 2.59914i) q^{14} +(-2.42010 - 4.19174i) q^{16} +(-2.31896 - 4.01655i) q^{17} +(0.390218 + 0.104559i) q^{19} +(2.57220 - 2.57220i) q^{20} +(5.80434 - 10.0534i) q^{22} +4.26737 q^{23} +(-1.51877 - 0.876864i) q^{25} +(-0.335449 + 6.63959i) q^{26} +(-1.02137 - 3.81179i) q^{28} +(-5.22693 + 3.01777i) q^{29} +(-2.27098 - 0.608508i) q^{31} +(-6.48234 + 1.73694i) q^{32} +(-8.26018 + 2.21331i) q^{34} +(-6.34511 + 3.66335i) q^{35} +(1.60869 - 0.431046i) q^{37} +(0.372440 - 0.645085i) q^{38} +(1.43814 + 2.49093i) q^{40} +(1.18032 + 1.18032i) q^{41} -2.99100i q^{43} +(-6.23151 - 6.23151i) q^{44} +(2.03648 - 7.60024i) q^{46} +(-1.25642 - 4.68901i) q^{47} +0.948297i q^{49} +(-2.28650 + 2.28650i) q^{50} +(4.80276 + 1.55053i) q^{52} -0.186317i q^{53} +(-8.18091 + 14.1698i) q^{55} +3.12030 q^{56} +(2.88028 + 10.7494i) q^{58} +(-1.07545 - 4.01364i) q^{59} +0.0950990 q^{61} +(-2.16752 + 3.75426i) q^{62} +2.69361i q^{64} +(0.472797 - 9.35815i) q^{65} +(-2.70944 + 2.70944i) q^{67} +6.49189i q^{68} +(3.49646 + 13.0490i) q^{70} +(1.56243 - 5.83108i) q^{71} +(-1.49562 - 1.49562i) q^{73} -3.07079i q^{74} +(-0.399850 - 0.399850i) q^{76} +(8.87497 + 15.3719i) q^{77} +(-2.84121 + 4.92112i) q^{79} +(12.1501 - 3.25561i) q^{80} +(2.66543 - 1.53889i) q^{82} +(-15.0939 + 4.04440i) q^{83} +(11.6423 - 3.11954i) q^{85} +(-5.32701 - 1.42737i) q^{86} +(6.03462 - 3.48409i) q^{88} +(-0.0313812 - 0.117116i) q^{89} +(-8.53551 - 5.52023i) q^{91} +(-5.17297 - 2.98661i) q^{92} -8.95077 q^{94} +(-0.524935 + 0.909214i) q^{95} +(11.2137 - 11.2137i) q^{97} +(1.68893 + 0.452547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{2} - 6 q^{4} + 6 q^{5} + 2 q^{7} + 30 q^{8} - 12 q^{10} - 6 q^{11} - 2 q^{13} + 12 q^{14} + 14 q^{16} - 4 q^{19} + 6 q^{20} + 2 q^{22} + 12 q^{23} - 48 q^{26} + 6 q^{29} + 6 q^{31} - 30 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) \) 48 * q + 6 * q^2 - 6 * q^4 + 6 * q^5 + 2 * q^7 + 30 * q^8 - 12 * q^10 - 6 * q^11 - 2 * q^13 + 12 * q^14 + 14 * q^16 - 4 * q^19 + 6 * q^20 + 2 * q^22 + 12 * q^23 - 48 * q^26 + 6 * q^29 + 6 * q^31 - 30 * q^32 - 6 * q^34 + 6 * q^35 - 6 * q^37 + 36 * q^38 - 12 * q^40 - 18 * q^41 + 12 * q^44 - 12 * q^46 - 30 * q^47 + 12 * q^50 - 16 * q^52 - 4 * q^55 + 12 * q^56 - 28 * q^58 - 30 * q^59 - 4 * q^61 + 18 * q^62 - 30 * q^65 - 16 * q^67 - 46 * q^70 - 48 * q^71 - 22 * q^73 - 18 * q^76 + 72 * q^77 + 8 * q^79 - 54 * q^80 - 12 * q^82 - 72 * q^83 + 78 * q^85 - 102 * q^86 - 6 * q^88 - 16 * q^91 - 120 * q^92 - 52 * q^94 + 6 * q^95 + 48 * q^97 + 36 * q^98

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