LMFDB - Embedded newform 351.2.t.c.64.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(64,351)] 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("351.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(351, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,12,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			64.10
Root			$-1.66095 + 0.491165i$ of defining polynomial
Character	$\chi$	$=$	351.64
Dual form			351.2.t.c.181.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.14539 - 1.23864i) q^{2} +(2.06847 - 3.58269i) q^{4} +(0.771397 + 0.445366i) q^{5} +(0.850723 - 0.491165i) q^{7} -5.29379i q^{8} +2.20660 q^{10} +(-2.49915 + 1.44288i) q^{11} +(0.714352 + 3.53408i) q^{13} +(1.21676 - 2.10748i) q^{14} +(-2.42018 - 4.19187i) q^{16} -5.34353 q^{17} -7.19723i q^{19} +(3.19122 - 1.84245i) q^{20} +(-3.57443 + 6.19110i) q^{22} +(-2.31688 + 4.01296i) q^{23} +(-2.10330 - 3.64302i) q^{25} +(5.91002 + 6.69715i) q^{26} -4.06384i q^{28} +(0.971133 + 1.68205i) q^{29} +(8.73604 + 5.04375i) q^{31} +(-1.21534 - 0.701678i) q^{32} +(-11.4640 + 6.61872i) q^{34} +0.874993 q^{35} +4.82809i q^{37} +(-8.91479 - 15.4409i) q^{38} +(2.35768 - 4.08361i) q^{40} +(-2.39352 - 1.38190i) q^{41} +(-2.45501 - 4.25220i) q^{43} +11.9382i q^{44} +11.4791i q^{46} +(3.82403 - 2.20780i) q^{47} +(-3.01751 + 5.22649i) q^{49} +(-9.02479 - 5.21047i) q^{50} +(14.1391 + 4.75082i) q^{52} -6.30850 q^{53} -2.57044 q^{55} +(-2.60013 - 4.50355i) q^{56} +(4.16692 + 2.40577i) q^{58} +(2.74727 + 1.58614i) q^{59} +(2.76034 + 4.78105i) q^{61} +24.9896 q^{62} +6.20421 q^{64} +(-1.02291 + 3.04432i) q^{65} +(-3.15059 - 1.81899i) q^{67} +(-11.0529 + 19.1442i) q^{68} +(1.87720 - 1.08380i) q^{70} +6.69715i q^{71} -9.33980i q^{73} +(5.98027 + 10.3581i) q^{74} +(-25.7854 - 14.8872i) q^{76} +(-1.41739 + 2.45499i) q^{77} +(-2.37380 - 4.11154i) q^{79} -4.31146i q^{80} -6.84670 q^{82} +(4.78313 - 2.76154i) q^{83} +(-4.12198 - 2.37983i) q^{85} +(-10.5339 - 6.08176i) q^{86} +(7.63833 + 13.2300i) q^{88} -17.5838i q^{89} +(2.34353 + 2.65566i) q^{91} +(9.58479 + 16.6013i) q^{92} +(5.46935 - 9.47320i) q^{94} +(3.20540 - 5.55192i) q^{95} +(0.213335 - 0.123169i) q^{97} +14.9505i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) $ 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Character values

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

$n$	$28$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.14539	−	1.23864i	1.51702	−	0.875852i	0.517220	−	0.855852i	$-0.326967\pi$
$2$	2.14539	−	1.23864i	1.51702	−	0.875852i	0.999800	−	0.0199997i	$-0.00636654\pi$
$3$		0			0
$3$		0			0
$4$	2.06847	−	3.58269i	1.03423	−	1.79135i
$5$	0.771397	+	0.445366i	0.344979	+	0.199174i	0.662472	−	0.749087i	$-0.269508\pi$
$5$	0.771397	+	0.445366i	0.344979	+	0.199174i	−0.317493	+	0.948261i	$0.602841\pi$
$6$		0			0
$7$	0.850723	−	0.491165i	0.321543	−	0.185643i	−0.330537	−	0.943793i	$-0.607230\pi$
$7$	0.850723	−	0.491165i	0.321543	−	0.185643i	0.652080	+	0.758150i	$0.273897\pi$
$8$		−	5.29379i		−	1.87164i
$9$		0			0
$10$	2.20660			0.697787
$11$	−2.49915	+	1.44288i	−0.753521	+	0.435046i	−0.826965	−	0.562254i	$-0.809934\pi$
$11$	−2.49915	+	1.44288i	−0.753521	+	0.435046i	0.0734436	+	0.997299i	$0.476601\pi$
$12$		0			0
$13$	0.714352	+	3.53408i	0.198126	+	0.980177i
$13$	0.714352	+	3.53408i	0.198126	+	0.980177i
$14$	1.21676	−	2.10748i	0.325191	−	0.563248i
$15$		0			0
$16$	−2.42018	−	4.19187i	−0.605045	−	1.04797i
$17$	−5.34353			−1.29600			−0.647998	−	0.761642i	$-0.724394\pi$
$17$	−5.34353			−1.29600			−0.647998	+	0.761642i	$0.724394\pi$
$18$		0			0
$19$		−	7.19723i		−	1.65116i	−0.564287	−	0.825579i	$-0.690849\pi$
$19$		−	7.19723i		−	1.65116i	0.564287	−	0.825579i	$-0.309151\pi$
$20$	3.19122	−	1.84245i	0.713578	−	0.411984i
$21$		0			0
$22$	−3.57443	+	6.19110i	−0.762071	+	1.31995i
$23$	−2.31688	+	4.01296i	−0.483103	+	0.836759i	−0.999812	−	0.0194021i	$-0.993824\pi$
$23$	−2.31688	+	4.01296i	−0.483103	+	0.836759i	0.516709	+	0.856161i	$0.327157\pi$
$24$		0			0
$25$	−2.10330	−	3.64302i	−0.420660	−	0.728604i
$26$	5.91002	+	6.69715i	1.15905	+	1.31342i
$27$		0			0
$28$		−	4.06384i		−	0.767993i
$29$	0.971133	+	1.68205i	0.180335	+	0.312349i	0.941995	−	0.335628i	$-0.108949\pi$
$29$	0.971133	+	1.68205i	0.180335	+	0.312349i	−0.761660	+	0.647977i	$0.775615\pi$
$30$		0			0
$31$	8.73604	+	5.04375i	1.56904	+	0.905885i	0.996281	+	0.0861597i	$0.0274595\pi$
$31$	8.73604	+	5.04375i	1.56904	+	0.905885i	0.572757	+	0.819725i	$0.305874\pi$
$32$	−1.21534	−	0.701678i	−0.214844	−	0.124040i
$33$		0			0
$34$	−11.4640	+	6.61872i	−1.96605	+	1.13510i
$35$	0.874993			0.147901
$36$		0			0
$37$			4.82809i			0.793732i	0.917876	+	0.396866i	$0.129902\pi$
$37$			4.82809i			0.793732i	−0.917876	+	0.396866i	$0.870098\pi$
$38$	−8.91479	−	15.4409i	−1.44617	−	2.50484i
$39$		0			0
$40$	2.35768	−	4.08361i	0.372781	−	0.645676i
$41$	−2.39352	−	1.38190i	−0.373804	−	0.215816i	0.301315	−	0.953525i	$-0.402574\pi$
$41$	−2.39352	−	1.38190i	−0.373804	−	0.215816i	−0.675119	+	0.737709i	$0.735908\pi$
$42$		0			0
$43$	−2.45501	−	4.25220i	−0.374386	−	0.648455i	0.615849	−	0.787864i	$-0.288813\pi$
$43$	−2.45501	−	4.25220i	−0.374386	−	0.648455i	−0.990235	+	0.139409i	$0.955480\pi$
$44$			11.9382i			1.79976i
$45$		0			0
$46$			11.4791i			1.69251i
$47$	3.82403	−	2.20780i	0.557791	−	0.322041i	−0.194467	−	0.980909i	$-0.562298\pi$
$47$	3.82403	−	2.20780i	0.557791	−	0.322041i	0.752259	+	0.658868i	$0.228964\pi$
$48$		0			0
$49$	−3.01751	+	5.22649i	−0.431073	+	0.746641i
$50$	−9.02479	−	5.21047i	−1.27630	−	0.736871i
$51$		0			0
$52$	14.1391	+	4.75082i	1.96074	+	0.658820i
$53$	−6.30850			−0.866540			−0.433270	−	0.901264i	$-0.642640\pi$
$53$	−6.30850			−0.866540			−0.433270	+	0.901264i	$0.642640\pi$
$54$		0			0
$55$	−2.57044			−0.346599
$56$	−2.60013	−	4.50355i	−0.347456	−	0.601812i
$57$		0			0
$58$	4.16692	+	2.40577i	0.547143	+	0.315893i
$59$	2.74727	+	1.58614i	0.357664	+	0.206498i	0.668056	−	0.744111i	$-0.267127\pi$
$59$	2.74727	+	1.58614i	0.357664	+	0.206498i	−0.310391	+	0.950609i	$0.600460\pi$
$60$		0			0
$61$	2.76034	+	4.78105i	0.353426	+	0.612151i	0.986847	−	0.161656i	$-0.0516834\pi$
$61$	2.76034	+	4.78105i	0.353426	+	0.612151i	−0.633422	+	0.773807i	$0.718350\pi$
$62$	24.9896			3.17368
$63$		0			0
$64$	6.20421			0.775526
$65$	−1.02291	+	3.04432i	−0.126876	+	0.377602i
$66$		0			0
$67$	−3.15059	−	1.81899i	−0.384906	−	0.222225i	0.295045	−	0.955483i	$-0.404665\pi$
$67$	−3.15059	−	1.81899i	−0.384906	−	0.222225i	−0.679950	+	0.733258i	$0.737999\pi$
$68$	−11.0529	+	19.1442i	−1.34036	+	2.32158i
$69$		0			0
$70$	1.87720	−	1.08380i	0.224369	−	0.129539i
$71$			6.69715i			0.794805i	0.917644	+	0.397403i	$0.130088\pi$
$71$			6.69715i			0.794805i	−0.917644	+	0.397403i	$0.869912\pi$
$72$		0			0
$73$		−	9.33980i		−	1.09314i	−0.837413	−	0.546570i	$-0.815933\pi$
$73$		−	9.33980i		−	1.09314i	0.837413	−	0.546570i	$-0.184067\pi$
$74$	5.98027	+	10.3581i	0.695192	+	1.20411i
$75$		0			0
$76$	−25.7854	−	14.8872i	−2.95779	−	1.70768i
$77$	−1.41739	+	2.45499i	−0.161526	+	0.279772i
$78$		0			0
$79$	−2.37380	−	4.11154i	−0.267073	−	0.462584i	0.701031	−	0.713130i	$-0.252723\pi$
$79$	−2.37380	−	4.11154i	−0.267073	−	0.462584i	−0.968105	+	0.250546i	$0.919390\pi$
$80$		−	4.31146i		−	0.482036i
$81$		0			0
$82$	−6.84670			−0.756092
$83$	4.78313	−	2.76154i	0.525016	−	0.303118i	−0.213968	−	0.976841i	$-0.568639\pi$
$83$	4.78313	−	2.76154i	0.525016	−	0.303118i	0.738985	+	0.673722i	$0.235306\pi$
$84$		0			0
$85$	−4.12198	−	2.37983i	−0.447092	−	0.258129i
$86$	−10.5339	−	6.08176i	−1.13590	−	0.655813i
$87$		0			0
$88$	7.63833	+	13.2300i	0.814248	+	1.41032i
$89$		−	17.5838i		−	1.86388i	−0.362615	−	0.931939i	$-0.618116\pi$
$89$		−	17.5838i		−	1.86388i	0.362615	−	0.931939i	$-0.381884\pi$
$90$		0			0
$91$	2.34353	+	2.65566i	0.245669	+	0.278388i
$92$	9.58479	+	16.6013i	0.999283	+	1.73081i
$93$		0			0
$94$	5.46935	−	9.47320i	0.564121	−	0.977086i
$95$	3.20540	−	5.55192i	0.328867	−	0.569615i
$96$		0			0
$97$	0.213335	−	0.123169i	0.0216609	−	0.0125059i	−0.489130	−	0.872211i	$-0.662686\pi$
$97$	0.213335	−	0.123169i	0.0216609	−	0.0125059i	0.510791	+	0.859705i	$0.329352\pi$
$98$			14.9505i			1.51023i
$99$		0			0
$100$	−17.4024			−1.74024
$101$	−2.38713	−	4.13463i	−0.237528	−	0.411411i	0.722476	−	0.691396i	$-0.243004\pi$
$101$	−2.38713	−	4.13463i	−0.237528	−	0.411411i	−0.960004	+	0.279985i	$0.909671\pi$
$102$		0			0
$103$	1.71676	−	2.97351i	0.169157	−	0.292988i	−0.768967	−	0.639289i	$-0.779229\pi$
$103$	1.71676	−	2.97351i	0.169157	−	0.292988i	0.938124	+	0.346300i	$0.112562\pi$
$104$	18.7087	−	3.78163i	1.83454	−	0.370820i
$105$		0			0
$106$	−13.5342	+	7.81398i	−1.31456	+	0.758960i
$107$	2.34075			0.226289			0.113144	−	0.993579i	$-0.463908\pi$
$107$	2.34075			0.226289			0.113144	+	0.993579i	$0.463908\pi$
$108$		0			0
$109$		−	10.2127i		−	0.978195i	−0.872229	−	0.489097i	$-0.837326\pi$
$109$		−	10.2127i		−	0.978195i	0.872229	−	0.489097i	$-0.162674\pi$
$110$	−5.51461	+	3.18386i	−0.525797	+	0.303569i
$111$		0			0
$112$	−4.11780	−	2.37742i	−0.389096	−	0.224645i
$113$	−0.605276	+	1.04837i	−0.0569396	+	0.0986222i	−0.893090	−	0.449878i	$-0.851468\pi$
$113$	−0.605276	+	1.04837i	−0.0569396	+	0.0986222i	0.836151	+	0.548500i	$0.184801\pi$
$114$		0			0
$115$	−3.57447	+	2.06372i	−0.333321	+	0.192443i
$116$	8.03503			0.746034
$117$		0			0
$118$	7.85863			0.723446
$119$	−4.54586	+	2.62456i	−0.416719	+	0.240593i
$120$		0			0
$121$	−1.33618	+	2.31432i	−0.121471	+	0.210393i
$122$	11.8440	+	6.83815i	1.07231	+	0.619097i
$123$		0			0
$124$	36.1404	−	20.8657i	3.24550	−	1.87379i
$125$		−	8.20061i		−	0.733485i
$126$		0			0
$127$	7.58237			0.672827			0.336413	−	0.941714i	$-0.390786\pi$
$127$	7.58237			0.672827			0.336413	+	0.941714i	$0.390786\pi$
$128$	15.7411	−	9.08815i	1.39133	−	0.803286i
$129$		0			0
$130$	1.57629	+	7.79828i	0.138250	+	0.683955i
$131$	9.40603	−	16.2917i	0.821809	−	1.42342i	−0.0825247	−	0.996589i	$-0.526298\pi$
$131$	9.40603	−	16.2917i	0.821809	−	1.42342i	0.904334	−	0.426826i	$-0.140368\pi$
$132$		0			0
$133$	−3.53503	−	6.12285i	−0.306526	−	0.530918i
$134$	−9.01232			−0.778546
$135$		0			0
$136$			28.2875i			2.42564i
$137$	−15.6417	+	9.03076i	−1.33636	+	0.771550i	−0.986266	−	0.165163i	$-0.947185\pi$
$137$	−15.6417	+	9.03076i	−1.33636	+	0.771550i	−0.350098	+	0.936713i	$0.613852\pi$
$138$		0			0
$139$	2.42577	−	4.20155i	0.205751	−	0.356371i	−0.744621	−	0.667488i	$-0.767370\pi$
$139$	2.42577	−	4.20155i	0.205751	−	0.356371i	0.950372	+	0.311117i	$0.100703\pi$
$140$	1.80989	−	3.13483i	0.152964	−	0.264941i
$141$		0			0
$142$	8.29537	+	14.3680i	0.696132	+	1.20574i
$143$	−6.88453	−	7.80145i	−0.575713	−	0.652390i
$144$		0			0
$145$			1.73004i			0.143672i
$146$	−11.5687	−	20.0375i	−0.957429	−	1.65832i
$147$		0			0
$148$	17.2975	+	9.98674i	1.42185	+	0.820905i
$149$	10.6241	+	6.13383i	0.870360	+	0.502503i	0.867468	−	0.497493i	$-0.165746\pi$
$149$	10.6241	+	6.13383i	0.870360	+	0.502503i	0.00289232	+	0.999996i	$0.499079\pi$
$150$		0			0
$151$	−4.82142	+	2.78365i	−0.392362	+	0.226530i	−0.683183	−	0.730247i	$-0.739405\pi$
$151$	−4.82142	+	2.78365i	−0.392362	+	0.226530i	0.290821	+	0.956777i	$0.406072\pi$
$152$	−38.1006			−3.09037
$153$		0			0
$154$			7.02254i			0.565893i
$155$	4.49263	+	7.78147i	0.360857	+	0.625023i
$156$		0			0
$157$	2.02526	−	3.50785i	0.161633	−	0.279957i	−0.773821	−	0.633404i	$-0.781657\pi$
$157$	2.02526	−	3.50785i	0.161633	−	0.279957i	0.935455	+	0.353447i	$0.114991\pi$
$158$	−10.1855	−	5.88057i	−0.810311	−	0.467833i
$159$		0			0
$160$	−0.625007	−	1.08254i	−0.0494111	−	0.0855826i
$161$			4.55188i			0.358739i
$162$		0			0
$163$			10.3387i			0.809787i	0.914364	+	0.404894i	$0.132691\pi$
$163$			10.3387i			0.809787i	−0.914364	+	0.404894i	$0.867309\pi$
$164$	−9.90182	+	5.71682i	−0.773202	+	0.446409i
$165$		0			0
$166$	6.84112	−	11.8492i	0.530974	−	0.919673i
$167$	−11.4388	−	6.60418i	−0.885159	−	0.511047i	−0.0128030	−	0.999918i	$-0.504075\pi$
$167$	−11.4388	−	6.60418i	−0.885159	−	0.511047i	−0.872356	+	0.488871i	$0.837409\pi$
$168$		0			0
$169$	−11.9794	+	5.04915i	−0.921492	+	0.388396i
$170$	−11.7910			−0.904330
$171$		0			0
$172$	−20.3124			−1.54881
$173$	5.71416	+	9.89721i	0.434439	+	0.752471i	0.997250	−	0.0741150i	$-0.0236132\pi$
$173$	5.71416	+	9.89721i	0.434439	+	0.752471i	−0.562810	+	0.826586i	$0.690280\pi$
$174$		0			0
$175$	−3.57865	−	2.06613i	−0.270520	−	0.156185i
$176$	12.0968	+	6.98407i	0.911828	+	0.526444i
$177$		0			0
$178$	−21.7800	−	37.7241i	−1.63248	−	2.82754i
$179$	−0.150491			−0.0112482			−0.00562411	−	0.999984i	$-0.501790\pi$
$179$	−0.150491			−0.0112482			−0.00562411	+	0.999984i	$0.501790\pi$
$180$		0			0
$181$	−22.0219			−1.63687			−0.818436	−	0.574598i	$-0.805159\pi$
$181$	−22.0219			−1.63687			−0.818436	+	0.574598i	$0.805159\pi$
$182$	8.31719	+	2.79462i	0.616511	+	0.207151i
$183$		0			0
$184$	21.2438	+	12.2651i	1.56611	+	0.904195i
$185$	−2.15027	+	3.72437i	−0.158091	+	0.273821i
$186$		0			0
$187$	13.3543	−	7.71009i	0.976561	−	0.563818i
$188$		−	18.2671i		−	1.33226i
$189$		0			0
$190$		−	15.8814i		−	1.15216i
$191$	−9.97868	−	17.2836i	−0.722032	−	1.25060i	−0.960184	−	0.279369i	$-0.909875\pi$
$191$	−9.97868	−	17.2836i	−0.722032	−	1.25060i	0.238152	−	0.971228i	$-0.423458\pi$
$192$		0			0
$193$	−8.70542	−	5.02608i	−0.626630	−	0.361785i	0.152816	−	0.988255i	$-0.451166\pi$
$193$	−8.70542	−	5.02608i	−0.626630	−	0.361785i	−0.779446	+	0.626470i	$0.784499\pi$
$194$	0.305125	−	0.528492i	0.0219067	−	0.0379435i
$195$		0			0
$196$	12.4833	+	21.6216i	0.891661	+	1.54440i
$197$			3.94715i			0.281223i	0.990065	+	0.140611i	$0.0449068\pi$
$197$			3.94715i			0.281223i	−0.990065	+	0.140611i	$0.955093\pi$
$198$		0			0
$199$	11.4749			0.813433			0.406716	−	0.913554i	$-0.366674\pi$
$199$	11.4749			0.813433			0.406716	+	0.913554i	$0.366674\pi$
$200$	−19.2854	+	11.1344i	−1.36368	+	0.787323i
$201$		0			0
$202$	−10.2427	−	5.91360i	−0.720670	−	0.416079i
$203$	1.65233	+	0.953973i	0.115971	+	0.0669558i
$204$		0			0
$205$	−1.23090	−	2.13198i	−0.0859698	−	0.148904i
$206$		−	8.50578i		−	0.592626i
$207$		0			0
$208$	13.0855	−	11.5476i	0.907319	−	0.800680i
$209$	10.3848	+	17.9869i	0.718329	+	1.24418i
$210$		0			0
$211$	−5.48306	+	9.49694i	−0.377469	+	0.653796i	−0.990693	−	0.136113i	$-0.956539\pi$
$211$	−5.48306	+	9.49694i	−0.377469	+	0.653796i	0.613224	+	0.789909i	$0.289872\pi$
$212$	−13.0489	+	22.6014i	−0.896204	+	1.55227i
$213$		0			0
$214$	5.02182	−	2.89935i	0.343285	−	0.198195i
$215$		−	4.37351i		−	0.298271i
$216$		0			0
$217$	9.90926			0.672684
$218$	−12.6498	−	21.9101i	−0.856754	−	1.48394i
$219$		0			0
$220$	−5.31688	+	9.20911i	−0.358464	+	0.620878i
$221$	−3.81716	−	18.8845i	−0.256770	−	1.27031i
$222$		0			0
$223$	−11.1218	+	6.42116i	−0.744770	+	0.429993i	−0.823801	−	0.566879i	$-0.808151\pi$
$223$	−11.1218	+	6.42116i	−0.744770	+	0.429993i	0.0790313	+	0.996872i	$0.474817\pi$
$224$	−1.37856			−0.0921088
$225$		0			0
$226$			2.99888i			0.199482i
$227$	20.4534	−	11.8088i	1.35754	−	0.783777i	0.368249	−	0.929727i	$-0.379957\pi$
$227$	20.4534	−	11.8088i	1.35754	−	0.783777i	0.989292	+	0.145950i	$0.0466240\pi$
$228$		0			0
$229$	10.7715	+	6.21892i	0.711800	+	0.410958i	0.811727	−	0.584037i	$-0.198528\pi$
$229$	10.7715	+	6.21892i	0.711800	+	0.410958i	−0.0999271	+	0.994995i	$0.531861\pi$
$230$	−5.11242	+	8.85497i	−0.337103	+	0.583880i
$231$		0			0
$232$	8.90443	−	5.14098i	0.584605	−	0.337522i
$233$	18.7821			1.23046			0.615230	−	0.788348i	$-0.289063\pi$
$233$	18.7821			1.23046			0.615230	+	0.788348i	$0.289063\pi$
$234$		0			0
$235$	3.93312			0.256568
$236$	11.3653	−	6.56175i	0.739817	−	0.427134i
$237$		0			0
$238$	−6.50177	+	11.2614i	−0.421447	+	0.729968i
$239$	17.1326	+	9.89154i	1.10822	+	0.639830i	0.938367	−	0.345639i	$-0.112338\pi$
$239$	17.1326	+	9.89154i	1.10822	+	0.639830i	0.169851	+	0.985470i	$0.445671\pi$
$240$		0			0
$241$	−9.86550	+	5.69585i	−0.635493	+	0.366902i	−0.782876	−	0.622178i	$-0.786248\pi$
$241$	−9.86550	+	5.69585i	−0.635493	+	0.366902i	0.147384	+	0.989079i	$0.452915\pi$
$242$			6.62017i			0.425561i
$243$		0			0
$244$	22.8387			1.46210
$245$	−4.65540	+	2.68780i	−0.297423	+	0.171717i
$246$		0			0
$247$	25.4356	−	5.14136i	1.61843	−	0.327137i
$248$	26.7006	−	46.2468i	1.69549	−	2.93667i
$249$		0			0
$250$	−10.1576	−	17.5935i	−0.642424	−	1.11271i
$251$	18.6950			1.18002			0.590010	−	0.807396i	$-0.299124\pi$
$251$	18.6950			1.18002			0.590010	+	0.807396i	$0.299124\pi$
$252$		0			0
$253$		−	13.3720i		−	0.840688i
$254$	16.2672	−	9.39184i	1.02069	−	0.589297i
$255$		0			0
$256$	16.3097	−	28.2492i	1.01936	−	1.76558i
$257$	−4.37976	+	7.58598i	−0.273202	+	0.473200i	−0.969680	−	0.244378i	$-0.921416\pi$
$257$	−4.37976	+	7.58598i	−0.273202	+	0.473200i	0.696478	+	0.717578i	$0.254749\pi$
$258$		0			0
$259$	2.37139	+	4.10736i	0.147351	+	0.255219i
$260$	8.79102	+	9.96185i	0.545196	+	0.617808i
$261$		0			0
$262$		−	46.6028i		−	2.87913i
$263$	3.86402	+	6.69268i	0.238266	+	0.412688i	0.960217	−	0.279256i	$-0.0900878\pi$
$263$	3.86402	+	6.69268i	0.238266	+	0.412688i	−0.721951	+	0.691944i	$0.756754\pi$
$264$		0			0
$265$	−4.86636	−	2.80959i	−0.298938	−	0.172592i
$266$	−15.1680	−	8.75727i	−0.930012	−	0.536942i
$267$		0			0
$268$	−13.0338	+	7.52505i	−0.796165	+	0.459666i
$269$	−14.8448			−0.905102			−0.452551	−	0.891739i	$-0.649486\pi$
$269$	−14.8448			−0.905102			−0.452551	+	0.891739i	$0.649486\pi$
$270$		0			0
$271$			19.3486i			1.17534i	0.809100	+	0.587671i	$0.199955\pi$
$271$			19.3486i			1.17534i	−0.809100	+	0.587671i	$0.800045\pi$
$272$	12.9323	+	22.3994i	0.784136	+	1.35816i
$273$		0			0
$274$	−22.3718	+	38.7490i	−1.35153	+	2.34091i
$275$	10.5129	+	6.06963i	0.633952	+	0.366012i
$276$		0			0
$277$	−0.587762	−	1.01803i	−0.0353152	−	0.0611677i	0.847828	−	0.530272i	$-0.177910\pi$
$277$	−0.587762	−	1.01803i	−0.0353152	−	0.0611677i	−0.883143	+	0.469104i	$0.844577\pi$
$278$		−	12.0186i		−	0.720829i
$279$		0			0
$280$		−	4.63203i		−	0.276817i
$281$	−3.96724	+	2.29048i	−0.236665	+	0.136639i	−0.613643	−	0.789583i	$-0.710297\pi$
$281$	−3.96724	+	2.29048i	−0.236665	+	0.136639i	0.376978	+	0.926222i	$0.376963\pi$
$282$		0			0
$283$	−0.0159162	+	0.0275676i	−0.000946118	+	0.00163872i	−0.866498	−	0.499180i	$-0.833634\pi$
$283$	−0.0159162	+	0.0275676i	−0.000946118	+	0.00163872i	0.865552	+	0.500819i	$0.166968\pi$
$284$	23.9938	+	13.8528i	1.42377	+	0.822014i
$285$		0			0
$286$	−24.4332	−	8.20969i	−1.44477	−	0.485449i
$287$	−2.71496			−0.160259
$288$		0			0
$289$	11.5533			0.679607
$290$	2.14290	+	3.71161i	0.125835	+	0.217953i
$291$		0			0
$292$	−33.4616	−	19.3191i	−1.95819	−	1.13056i
$293$	−9.44674	−	5.45408i	−0.551884	−	0.318631i	0.197997	−	0.980203i	$-0.436556\pi$
$293$	−9.44674	−	5.45408i	−0.551884	−	0.318631i	−0.749882	+	0.661572i	$0.769890\pi$
$294$		0			0
$295$	1.41282	+	2.44708i	0.0822578	+	0.142475i
$296$	25.5589			1.48558
$297$		0			0
$298$	30.3905			1.76047
$299$	−15.8372	−	5.32137i	−0.915887	−	0.307743i
$300$		0			0
$301$	−4.17707	−	2.41163i	−0.240762	−	0.139004i
$302$	−6.89589	+	11.9440i	−0.396814	+	0.687302i
$303$		0			0
$304$	−30.1699	+	17.4186i	−1.73036	+	0.999025i
$305$			4.91745i			0.281572i
$306$		0			0
$307$		−	6.90363i		−	0.394011i	−0.980402	−	0.197005i	$-0.936878\pi$
$307$		−	6.90363i		−	0.394011i	0.980402	−	0.197005i	$-0.0631217\pi$
$308$	5.86364	+	10.1561i	0.334112	+	0.578699i
$309$		0			0
$310$	19.2769	+	11.1295i	1.09485	+	0.632115i
$311$	−7.69804	+	13.3334i	−0.436516	+	0.756067i	−0.997418	−	0.0718148i	$-0.977121\pi$
$311$	−7.69804	+	13.3334i	−0.436516	+	0.756067i	0.560902	+	0.827882i	$0.310454\pi$
$312$		0			0
$313$	8.67077	+	15.0182i	0.490101	+	0.848879i	0.999935	−	0.0113932i	$-0.00362663\pi$
$313$	8.67077	+	15.0182i	0.490101	+	0.848879i	−0.509834	+	0.860273i	$0.670293\pi$
$314$		−	10.0343i		−	0.566267i
$315$		0			0
$316$	−19.6405			−1.10486
$317$	9.21059	−	5.31774i	0.517318	−	0.298674i	−0.218518	−	0.975833i	$-0.570122\pi$
$317$	9.21059	−	5.31774i	0.517318	−	0.298674i	0.735837	+	0.677159i	$0.236789\pi$
$318$		0			0
$319$	−4.85401	−	2.80246i	−0.271772	−	0.156908i
$320$	4.78591	+	2.76314i	0.267540	+	0.154464i
$321$		0			0
$322$	5.63815	+	9.76557i	0.314202	+	0.544214i
$323$			38.4586i			2.13989i
$324$		0			0
$325$	11.3722	−	10.0356i	0.630817	−	0.556676i
$326$	12.8059	+	22.1805i	0.709254	+	1.22846i
$327$		0			0
$328$	−7.31548	+	12.6708i	−0.403930	+	0.699627i
$329$	2.16879	−	3.75646i	0.119569	−	0.207100i
$330$		0			0
$331$	27.4350	−	15.8396i	1.50796	−	0.870623i	0.508006	−	0.861353i	$-0.330383\pi$
$331$	27.4350	−	15.8396i	1.50796	−	0.870623i	0.999957	−	0.00926968i	$-0.00295067\pi$
$332$		−	22.8486i		−	1.25398i
$333$		0			0
$334$	−32.7208			−1.79041
$335$	−1.62024	−	2.80633i	−0.0885229	−	0.153326i
$336$		0			0
$337$	−12.1482	+	21.0414i	−0.661757	+	1.14620i	0.318397	+	0.947958i	$0.396856\pi$
$337$	−12.1482	+	21.0414i	−0.661757	+	1.14620i	−0.980154	+	0.198239i	$0.936478\pi$
$338$	−19.4464	+	25.6706i	−1.05774	+	1.39630i
$339$		0			0
$340$	−17.0524	+	9.84519i	−0.924795	+	0.533930i
$341$	−29.1102			−1.57641
$342$		0			0
$343$			12.8047i			0.691389i
$344$	−22.5103	+	12.9963i	−1.21367	+	0.700714i
$345$		0			0
$346$	24.5182	+	14.1556i	1.31811	+	0.761009i
$347$	1.91224	−	3.31209i	0.102654	−	0.177802i	−0.810123	−	0.586260i	$-0.800600\pi$
$347$	1.91224	−	3.31209i	0.102654	−	0.177802i	0.912777	+	0.408457i	$0.133933\pi$
$348$		0			0
$349$	20.3799	−	11.7664i	1.09091	−	0.629839i	0.157093	−	0.987584i	$-0.449788\pi$
$349$	20.3799	−	11.7664i	1.09091	−	0.629839i	0.933819	+	0.357745i	$0.116454\pi$
$350$	−10.2368			−0.547180
$351$		0			0
$352$	4.04976			0.215853
$353$	−20.4327	+	11.7968i	−1.08752	+	0.627881i	−0.932916	−	0.360095i	$-0.882744\pi$
$353$	−20.4327	+	11.7968i	−1.08752	+	0.627881i	−0.154606	+	0.987976i	$0.549411\pi$
$354$		0			0
$355$	−2.98268	+	5.16616i	−0.158304	+	0.274191i
$356$	−62.9973	−	36.3715i	−3.33885	−	1.92769i
$357$		0			0
$358$	−0.322862	+	0.186404i	−0.0170638	+	0.00985177i
$359$			0.220474i			0.0116362i	0.999983	+	0.00581809i	$0.00185196\pi$
$359$			0.220474i			0.0116362i	−0.999983	+	0.00581809i	$0.998148\pi$
$360$		0			0
$361$	−32.8001			−1.72632
$362$	−47.2455	+	27.2772i	−2.48317	+	1.43366i
$363$		0			0
$364$	14.3619	−	2.90301i	0.752768	−	0.152159i
$365$	4.15963	−	7.20469i	0.217725	−	0.377111i
$366$		0			0
$367$	10.2569	+	17.7655i	0.535407	+	0.927353i	0.999144	+	0.0413794i	$0.0131752\pi$
$367$	10.2569	+	17.7655i	0.535407	+	0.927353i	−0.463736	+	0.885973i	$0.653491\pi$
$368$	22.4291			1.16920
$369$		0			0
$370$			10.6536i			0.553856i
$371$	−5.36679	+	3.09852i	−0.278630	+	0.160867i
$372$		0			0
$373$	−5.42755	+	9.40079i	−0.281028	+	0.486754i	−0.971638	−	0.236473i	$-0.924009\pi$
$373$	−5.42755	+	9.40079i	−0.281028	+	0.486754i	0.690610	+	0.723227i	$0.257342\pi$
$374$	19.1001	−	33.0823i	0.987642	−	1.71065i
$375$		0			0
$376$	−11.6876	−	20.2436i	−0.602744	−	1.04398i
$377$	−5.25077	+	4.63364i	−0.270428	+	0.238644i
$378$		0			0
$379$			19.6987i			1.01185i	0.862577	+	0.505927i	$0.168849\pi$
$379$			19.6987i			1.01185i	−0.862577	+	0.505927i	$0.831151\pi$
$380$	−13.2605	−	22.9679i	−0.680251	−	1.17823i
$381$		0			0
$382$	−42.8164	−	24.7200i	−2.19068	−	1.26479i
$383$	17.6164	+	10.1708i	0.900156	+	0.519705i	0.877251	−	0.480032i	$-0.159375\pi$
$383$	17.6164	+	10.1708i	0.900156	+	0.519705i	0.0229052	+	0.999738i	$0.492708\pi$
$384$		0			0
$385$	−2.18674	+	1.26251i	−0.111446	+	0.0643436i
$386$	−24.9020			−1.26748
$387$		0			0
$388$		−	1.01909i		−	0.0517362i
$389$	10.6980	+	18.5295i	0.542412	+	0.939485i	0.998765	+	0.0496861i	$0.0158221\pi$
$389$	10.6980	+	18.5295i	0.542412	+	0.939485i	−0.456353	+	0.889799i	$0.650845\pi$
$390$		0			0
$391$	12.3803	−	21.4434i	0.626100	−	1.08444i
$392$	27.6679	+	15.9741i	1.39744	+	0.806814i
$393$		0			0
$394$	4.88911	+	8.46818i	0.246310	+	0.426621i
$395$		−	4.22884i		−	0.212776i
$396$		0			0
$397$			27.7995i			1.39522i	0.716479	+	0.697608i	$0.245752\pi$
$397$			27.7995i			1.39522i	−0.716479	+	0.697608i	$0.754248\pi$
$398$	24.6181	−	14.2133i	1.23399	−	0.712447i
$399$		0			0
$400$	−10.1807	+	17.6335i	−0.509036	+	0.881676i
$401$	13.1515	+	7.59301i	0.656754	+	0.379177i	0.791039	−	0.611766i	$-0.209541\pi$
$401$	13.1515	+	7.59301i	0.656754	+	0.379177i	−0.134285	+	0.990943i	$0.542874\pi$
$402$		0			0
$403$	−11.5844	+	34.4768i	−0.577060	+	1.71741i
$404$	−19.7508			−0.982639
$405$		0			0
$406$	4.72652			0.234573
$407$	−6.96636	−	12.0661i	−0.345310	−	0.598094i
$408$		0			0
$409$	−2.06606	−	1.19284i	−0.102160	−	0.0589823i	0.448049	−	0.894009i	$-0.352119\pi$
$409$	−2.06606	−	1.19284i	−0.102160	−	0.0589823i	−0.550210	+	0.835027i	$0.685452\pi$
$410$	−5.28152	−	3.04929i	−0.260836	−	0.150594i
$411$		0			0
$412$	−7.10210	−	12.3012i	−0.349896	−	0.606037i
$413$	3.11622			0.153339
$414$		0			0
$415$	4.91958			0.241493
$416$	1.61160	−	4.79636i	0.0790153	−	0.235161i
$417$		0			0
$418$	44.5587	+	25.7260i	2.17944	+	1.25830i
$419$	16.6455	−	28.8308i	0.813183	−	1.40848i	−0.0974415	−	0.995241i	$-0.531066\pi$
$419$	16.6455	−	28.8308i	0.813183	−	1.40848i	0.910625	−	0.413234i	$-0.135601\pi$
$420$		0			0
$421$	21.0487	−	12.1525i	1.02585	−	0.592275i	0.110057	−	0.993925i	$-0.464897\pi$
$421$	21.0487	−	12.1525i	1.02585	−	0.592275i	0.915793	+	0.401650i	$0.131563\pi$
$422$			27.1662i			1.32243i
$423$		0			0
$424$			33.3959i			1.62185i
$425$	11.2390	+	19.4666i	0.545173	+	0.944268i
$426$		0			0
$427$	4.69657	+	2.71157i	0.227283	+	0.131222i
$428$	4.84176	−	8.38618i	0.234035	−	0.405361i
$429$		0			0
$430$	−5.41722	−	9.38289i	−0.261241	−	0.452483i
$431$		−	12.1410i		−	0.584812i	−0.956294	−	0.292406i	$-0.905544\pi$
$431$		−	12.1410i		−	0.584812i	0.956294	−	0.292406i	$-0.0944559\pi$
$432$		0			0
$433$	−13.2730			−0.637859			−0.318930	−	0.947778i	$-0.603323\pi$
$433$	−13.2730			−0.637859			−0.318930	+	0.947778i	$0.603323\pi$
$434$	21.2592	−	12.2740i	1.02048	−	0.589172i
$435$		0			0
$436$	−36.5888	−	21.1245i	−1.75228	−	1.01168i
$437$	28.8822	+	16.6751i	1.38162	+	0.797680i
$438$		0			0
$439$	6.55074	+	11.3462i	0.312650	+	0.541526i	0.978935	−	0.204171i	$-0.0654500\pi$
$439$	6.55074	+	11.3462i	0.312650	+	0.541526i	−0.666285	+	0.745697i	$0.732117\pi$
$440$			13.6074i			0.648708i
$441$		0			0
$442$	−31.5804	−	35.7864i	−1.50213	−	1.70219i
$443$	−17.2195	−	29.8250i	−0.818123	−	1.41703i	−0.907064	−	0.420993i	$-0.861682\pi$
$443$	−17.2195	−	29.8250i	−0.818123	−	1.41703i	0.0889410	−	0.996037i	$-0.471652\pi$
$444$		0			0
$445$	7.83122	−	13.5641i	0.371236	−	0.642999i
$446$	−15.9070	+	27.5518i	−0.753220	+	1.30462i
$447$		0			0
$448$	5.27806	−	3.04729i	0.249365	−	0.143971i
$449$		−	5.32385i		−	0.251248i	−0.992078	−	0.125624i	$-0.959907\pi$
$449$		−	5.32385i		−	0.251248i	0.992078	−	0.125624i	$-0.0400933\pi$
$450$		0			0
$451$	7.97567			0.375559
$452$	2.50399	+	4.33703i	0.117778	+	0.203997i
$453$		0			0
$454$	29.2537	−	50.6689i	1.37294	−	2.37801i
$455$	0.625053	+	3.09229i	0.0293029	+	0.144969i
$456$		0			0
$457$	10.7297	−	6.19481i	0.501916	−	0.289781i	−0.227589	−	0.973757i	$-0.573084\pi$
$457$	10.7297	−	6.19481i	0.501916	−	0.289781i	0.729504	+	0.683976i	$0.239751\pi$
$458$	30.8121			1.43975
$459$		0			0
$460$			17.0750i			0.796124i
$461$	−11.2633	+	6.50288i	−0.524585	+	0.302869i	−0.738809	−	0.673915i	$-0.764611\pi$
$461$	−11.2633	+	6.50288i	−0.524585	+	0.302869i	0.214223	+	0.976785i	$0.431278\pi$
$462$		0			0
$463$	5.56377	+	3.21224i	0.258570	+	0.149286i	0.623682	−	0.781678i	$-0.285636\pi$
$463$	5.56377	+	3.21224i	0.258570	+	0.149286i	−0.365112	+	0.930964i	$0.618969\pi$
$464$	4.70063	−	8.14173i	0.218221	−	0.377971i
$465$		0			0
$466$	40.2950	−	23.2644i	1.86663	−	1.07770i
$467$	−13.9598			−0.645982			−0.322991	−	0.946402i	$-0.604688\pi$
$467$	−13.9598			−0.645982			−0.322991	+	0.946402i	$0.604688\pi$
$468$		0			0
$469$	−3.57370			−0.165018
$470$	8.43808	−	4.87173i	0.389220	−	0.224716i
$471$		0			0
$472$	8.39669	−	14.5435i	0.386489	−	0.669419i
$473$	12.2709	+	7.08459i	0.564215	+	0.325750i
$474$		0			0
$475$	−26.2196	+	15.1379i	−1.20304	+	0.694575i
$476$			21.7152i			0.995316i
$477$		0			0
$478$	49.0083			2.24159
$479$	29.9863	−	17.3126i	1.37011	−	0.791033i	0.379168	−	0.925328i	$-0.376210\pi$
$479$	29.9863	−	17.3126i	1.37011	−	0.791033i	0.990941	+	0.134295i	$0.0428769\pi$
$480$		0			0
$481$	−17.0628	+	3.44895i	−0.777998	+	0.157259i
$482$	−14.1102	+	24.4396i	−0.642703	+	1.11319i
$483$		0			0
$484$	5.52767	+	9.57421i	0.251258	+	0.435191i
$485$	0.219421			0.00996341
$486$		0			0
$487$			5.78811i			0.262284i	0.991364	+	0.131142i	$0.0418644\pi$
$487$			5.78811i			0.262284i	−0.991364	+	0.131142i	$0.958136\pi$
$488$	25.3099	−	14.6127i	1.14573	−	0.661485i
$489$		0			0
$490$	−6.65843	+	11.5327i	−0.300797	+	0.520996i
$491$	−12.4622	+	21.5851i	−0.562410	+	0.974123i	0.434875	+	0.900491i	$0.356793\pi$
$491$	−12.4622	+	21.5851i	−0.562410	+	0.974123i	−0.997285	+	0.0736326i	$0.976541\pi$
$492$		0			0
$493$	−5.18928	−	8.98810i	−0.233713	−	0.404803i
$494$	48.2009	−	42.5358i	2.16866	−	1.91378i
$495$		0			0
$496$		−	48.8272i		−	2.19240i
$497$	3.28941	+	5.69742i	0.147550	+	0.255564i
$498$		0			0
$499$	−34.4839	−	19.9093i	−1.54371	−	0.891262i	−0.998600	−	0.0528989i	$-0.983154\pi$
$499$	−34.4839	−	19.9093i	−1.54371	−	0.891262i	−0.545112	−	0.838363i	$-0.683513\pi$
$500$	−29.3803	−	16.9627i	−1.31392	−	0.758595i
$501$		0			0
$502$	40.1082	−	23.1565i	1.79011	−	1.03352i
$503$	12.9120			0.575720			0.287860	−	0.957673i	$-0.407056\pi$
$503$	12.9120			0.575720			0.287860	+	0.957673i	$0.407056\pi$
$504$		0			0
$505$		−	4.25259i		−	0.189238i
$506$	−16.5631	−	28.6881i	−0.736318	−	1.27534i
$507$		0			0
$508$	15.6839	−	27.1653i	0.695860	−	1.20527i
$509$	−32.1750	−	18.5763i	−1.42613	−	0.823378i	−0.429319	−	0.903153i	$-0.641247\pi$
$509$	−32.1750	−	18.5763i	−1.42613	−	0.823378i	−0.996813	+	0.0797749i	$0.974580\pi$
$510$		0			0
$511$	−4.58738	−	7.94558i	−0.202934	−	0.351492i
$512$		−	44.4550i		−	1.96465i
$513$		0			0
$514$			21.6998i			0.957139i
$515$	2.64860	−	1.52917i	0.116711	−	0.0673832i
$516$		0			0
$517$	−6.37120	+	11.0352i	−0.280205	+	0.485329i
$518$	10.1751	+	5.87460i	0.447068	+	0.258115i
$519$		0			0
$520$	16.1160	+	5.41507i	0.706734	+	0.237466i
$521$	24.6907			1.08172			0.540859	−	0.841114i	$-0.318099\pi$
$521$	24.6907			1.08172			0.540859	+	0.841114i	$0.318099\pi$
$522$		0			0
$523$	−33.4434			−1.46238			−0.731189	−	0.682175i	$-0.761034\pi$
$523$	−33.4434			−1.46238			−0.731189	+	0.682175i	$0.761034\pi$
$524$	−38.9121	−	67.3978i	−1.69989	−	2.94429i
$525$		0			0
$526$	16.5797	+	9.57227i	0.722908	+	0.417371i
$527$	−46.6813	−	26.9515i	−2.03347	−	1.17402i
$528$		0			0
$529$	0.764121	+	1.32350i	0.0332227	+	0.0575433i
$530$	−13.9203			−0.604660
$531$		0			0
$532$	−29.2484			−1.26808
$533$	3.17392	−	9.44603i	0.137478	−	0.409153i
$534$		0			0
$535$	1.80565	+	1.04249i	0.0780649	+	0.0450708i
$536$	−9.62937	+	16.6786i	−0.415925	+	0.720404i
$537$		0			0
$538$	−31.8478	+	18.3874i	−1.37306	+	0.792735i
$539$		−	17.4157i		−	0.750146i
$540$		0			0
$541$		−	10.9418i		−	0.470423i	−0.971944	−	0.235211i	$-0.924422\pi$
$541$		−	10.9418i		−	0.470423i	0.971944	−	0.235211i	$-0.0755782\pi$
$542$	23.9659	+	41.5102i	1.02943	+	1.78302i
$543$		0			0
$544$	6.49422	+	3.74944i	0.278437	+	0.160756i
$545$	4.54837	−	7.87800i	0.194831	−	0.337457i
$546$		0			0
$547$	−5.47407	−	9.48136i	−0.234054	−	0.405394i	0.724943	−	0.688809i	$-0.241866\pi$
$547$	−5.47407	−	9.48136i	−0.234054	−	0.405394i	−0.958997	+	0.283415i	$0.908533\pi$
$548$			74.7194i			3.19185i
$549$		0			0
$550$	30.0724			1.28229
$551$	12.1061	−	6.98947i	0.515738	−	0.297761i
$552$		0			0
$553$	−4.03889	−	2.33185i	−0.171751	−	0.0991605i
$554$	−2.52196	−	1.45605i	−0.107148	−	0.0618618i
$555$		0			0
$556$	−10.0352	−	17.3815i	−0.425589	−	0.737141i
$557$		−	12.5825i		−	0.533136i	−0.963816	−	0.266568i	$-0.914110\pi$
$557$		−	12.5825i		−	0.533136i	0.963816	−	0.266568i	$-0.0858898\pi$
$558$		0			0
$559$	13.2739	−	11.7138i	0.561425	−	0.495440i
$560$	−2.11764	−	3.66786i	−0.0894866	−	0.154995i
$561$		0			0
$562$	−5.67418	+	9.82797i	−0.239351	+	0.414568i
$563$	−6.07784	+	10.5271i	−0.256151	+	0.443666i	−0.965207	−	0.261486i	$-0.915788\pi$
$563$	−6.07784	+	10.5271i	−0.256151	+	0.443666i	0.709057	+	0.705151i	$0.249121\pi$
$564$		0			0
$565$	−0.933815	+	0.539139i	−0.0392859	+	0.0226817i
$566$			0.0788577i			0.00331464i
$567$		0			0
$568$	35.4533			1.48759
$569$	17.6882	+	30.6369i	0.741529	+	1.28437i	0.951799	+	0.306722i	$0.0992323\pi$
$569$	17.6882	+	30.6369i	0.741529	+	1.28437i	−0.210270	+	0.977643i	$0.567434\pi$
$570$		0			0
$571$	6.24561	−	10.8177i	0.261371	−	0.452707i	−0.705236	−	0.708973i	$-0.749159\pi$
$571$	6.24561	−	10.8177i	0.261371	−	0.452707i	0.966606	+	0.256266i	$0.0824922\pi$
$572$	−42.1906	+	8.52810i	−1.76408	+	0.356578i
$573$		0			0
$574$	−5.82465	+	3.36286i	−0.243116	+	0.140363i
$575$	19.4924			0.812888
$576$		0			0
$577$		−	25.1610i		−	1.04747i	−0.851882	−	0.523734i	$-0.824539\pi$
$577$		−	25.1610i		−	1.04747i	0.851882	−	0.523734i	$-0.175461\pi$
$578$	24.7864	−	14.3104i	1.03098	−	0.595235i
$579$		0			0
$580$	6.19819	+	3.57853i	0.257366	+	0.148590i
$581$	2.71274	−	4.69861i	0.112544	−	0.194931i
$582$		0			0
$583$	15.7659	−	9.10243i	0.652956	−	0.376984i
$584$	−49.4430			−2.04596
$585$		0			0
$586$	−27.0226			−1.11629
$587$	3.21529	−	1.85635i	0.132709	−	0.0766197i	−0.432176	−	0.901789i	$-0.642254\pi$
$587$	3.21529	−	1.85635i	0.132709	−	0.0766197i	0.564885	+	0.825170i	$0.308921\pi$
$588$		0			0
$589$	36.3011	−	62.8753i	1.49576	−	2.59073i
$590$	6.06212	+	3.49997i	0.249574	+	0.144091i
$591$		0			0
$592$	20.2387	−	11.6848i	0.831806	−	0.480244i
$593$			31.6710i			1.30057i	0.759689	+	0.650287i	$0.225351\pi$
$593$			31.6710i			1.30057i	−0.759689	+	0.650287i	$0.774649\pi$
$594$		0			0
$595$	−4.67555			−0.191679
$596$	43.9512	−	25.3752i	1.80031	−	1.03941i
$597$		0			0
$598$	−40.5682	+	8.20015i	−1.65896	+	0.335329i
$599$	−14.2298	+	24.6468i	−0.581415	+	1.00704i	0.413897	+	0.910324i	$0.364167\pi$
$599$	−14.2298	+	24.6468i	−0.581415	+	1.00704i	−0.995312	+	0.0967168i	$0.969166\pi$
$600$		0			0
$601$	−0.635544	−	1.10079i	−0.0259244	−	0.0449023i	0.852772	−	0.522283i	$-0.174920\pi$
$601$	−0.635544	−	1.10079i	−0.0259244	−	0.0449023i	−0.878697	+	0.477381i	$0.841586\pi$
$602$	−11.9486			−0.486988
$603$		0			0
$604$			23.0315i			0.937140i
$605$	−2.06144	+	1.19017i	−0.0838096	+	0.0483875i
$606$		0			0
$607$	0.373604	−	0.647101i	0.0151641	−	0.0262650i	−0.858344	−	0.513075i	$-0.828506\pi$
$607$	0.373604	−	0.647101i	0.0151641	−	0.0262650i	0.873508	+	0.486810i	$0.161840\pi$
$608$	−5.05014	+	8.74709i	−0.204810	+	0.354741i
$609$		0			0
$610$	6.09096	+	10.5499i	0.246616	+	0.427151i
$611$	10.5342	+	11.9373i	0.426170	+	0.482930i
$612$		0			0
$613$			41.1308i			1.66126i	0.556826	+	0.830629i	$0.312019\pi$
$613$			41.1308i			1.66126i	−0.556826	+	0.830629i	$0.687981\pi$
$614$	−8.55112	−	14.8110i	−0.345095	−	0.597723i
$615$		0			0
$616$	12.9962	+	7.50336i	0.523632	+	0.302319i
$617$	−10.9623	−	6.32908i	−0.441325	−	0.254799i	0.262835	−	0.964841i	$-0.415343\pi$
$617$	−10.9623	−	6.32908i	−0.441325	−	0.254799i	−0.704159	+	0.710042i	$0.748676\pi$
$618$		0			0
$619$	7.38692	−	4.26484i	0.296905	−	0.171418i	−0.344147	−	0.938916i	$-0.611832\pi$
$619$	7.38692	−	4.26484i	0.296905	−	0.171418i	0.641052	+	0.767498i	$0.278498\pi$
$620$	37.1715			1.49284
$621$		0			0
$622$			38.1404i			1.52929i
$623$	−8.63654	−	14.9589i	−0.346016	−	0.599317i
$624$		0			0
$625$	−6.86422	+	11.8892i	−0.274569	+	0.475567i
$626$	37.2044	+	21.4800i	1.48699	+	0.858512i
$627$		0			0
$628$	−8.37836	−	14.5117i	−0.334333	−	0.579082i
$629$		−	25.7990i		−	1.02867i
$630$		0			0
$631$		−	2.50848i		−	0.0998612i	−0.998753	−	0.0499306i	$-0.984100\pi$
$631$		−	2.50848i		−	0.0998612i	0.998753	−	0.0499306i	$-0.0159000\pi$
$632$	−21.7656	+	12.5664i	−0.865791	+	0.499865i
$633$		0			0
$634$	13.1735	−	22.8173i	0.523188	−	0.906189i
$635$	5.84902	+	3.37693i	0.232111	+	0.134009i
$636$		0			0
$637$	−20.6264	−	6.93057i	−0.817247	−	0.274599i
$638$	−13.8850			−0.549712
$639$		0			0
$640$	16.1902			0.639974
$641$	−20.6692	−	35.8000i	−0.816383	−	1.41402i	−0.908331	−	0.418253i	$-0.862643\pi$
$641$	−20.6692	−	35.8000i	−0.816383	−	1.41402i	0.0919475	−	0.995764i	$-0.470691\pi$
$642$		0			0
$643$	17.6848	+	10.2103i	0.697419	+	0.402655i	0.806385	−	0.591390i	$-0.201421\pi$
$643$	17.6848	+	10.2103i	0.697419	+	0.402655i	−0.108966	+	0.994045i	$0.534754\pi$
$644$	16.3080	+	9.41542i	0.642625	+	0.371020i
$645$		0			0
$646$	47.6365	+	82.5088i	1.87423	+	3.24626i
$647$	−15.7134			−0.617756			−0.308878	−	0.951102i	$-0.599953\pi$
$647$	−15.7134			−0.617756			−0.308878	+	0.951102i	$0.599953\pi$
$648$		0			0
$649$	−9.15445			−0.359344
$650$	11.9673	−	35.6164i	0.469396	−	1.39699i
$651$		0			0
$652$	37.0403	+	21.3852i	1.45061	+	0.837509i
$653$	−16.1168	+	27.9151i	−0.630700	+	1.09240i	0.356709	+	0.934215i	$0.383899\pi$
$653$	−16.1168	+	27.9151i	−0.630700	+	1.09240i	−0.987409	+	0.158188i	$0.949435\pi$
$654$		0			0
$655$	14.5116	−	8.37826i	0.567014	−	0.327366i
$656$			13.3778i			0.522314i
$657$		0			0
$658$		−	10.7454i		−	0.418900i
$659$	−2.33379	−	4.04224i	−0.0909115	−	0.157463i	0.816983	−	0.576661i	$-0.195645\pi$
$659$	−2.33379	−	4.04224i	−0.0909115	−	0.157463i	−0.907895	+	0.419198i	$0.862311\pi$
$660$		0			0
$661$	−19.5539	−	11.2894i	−0.760557	−	0.439108i	0.0689389	−	0.997621i	$-0.478039\pi$
$661$	−19.5539	−	11.2894i	−0.760557	−	0.439108i	−0.829496	+	0.558513i	$0.811372\pi$
$662$	39.2392	−	67.9642i	1.52507	−	2.64151i
$663$		0			0
$664$	−14.6190	−	25.3209i	−0.567328	−	0.982641i
$665$		−	6.29753i		−	0.244208i
$666$		0			0
$667$	−9.00000			−0.348481
$668$	−47.3215	+	27.3211i	−1.83092	+	1.05708i
$669$		0			0
$670$	−6.95207	−	4.01378i	−0.268582	−	0.155066i
$671$	−13.7970	−	7.96570i	−0.532627	−	0.307512i
$672$		0			0
$673$	1.89964	+	3.29028i	0.0732259	+	0.126831i	0.900313	−	0.435242i	$-0.143337\pi$
$673$	1.89964	+	3.29028i	0.0732259	+	0.126831i	−0.827088	+	0.562073i	$0.810004\pi$
$674$			60.1893i			2.31841i
$675$		0			0
$676$	−6.68945	+	53.3625i	−0.257287	+	2.05240i
$677$	−14.9160	−	25.8352i	−0.573267	−	0.992927i	−0.996228	−	0.0867791i	$-0.972343\pi$
$677$	−14.9160	−	25.8352i	−0.573267	−	0.992927i	0.422961	−	0.906148i	$-0.360991\pi$
$678$		0			0
$679$	0.120993	−	0.209566i	0.00464327	−	0.00804239i
$680$	−12.5983	+	21.8209i	−0.483123	+	0.836794i
$681$		0			0
$682$	−62.4527	+	36.0571i	−2.39144	+	1.38070i
$683$			0.0316640i			0.00121159i	1.00000		0.000605795i	$0.000192831\pi$
$683$			0.0316640i			0.00121159i	−1.00000		0.000605795i	$0.999807\pi$
$684$		0			0
$685$	−16.0880			−0.614690
$686$	15.8604	+	27.4711i	0.605554	+	1.04885i
$687$		0			0
$688$	−11.8831	+	20.5822i	−0.453040	+	0.784689i
$689$	−4.50649	−	22.2947i	−0.171684	−	0.849362i
$690$		0			0
$691$	6.85148	−	3.95570i	0.260642	−	0.150482i	−0.363985	−	0.931405i	$-0.618584\pi$
$691$	6.85148	−	3.95570i	0.260642	−	0.150482i	0.624628	+	0.780923i	$0.285251\pi$
$692$	47.2782			1.79725
$693$		0			0
$694$		−	9.47431i		−	0.359640i
$695$	3.74246	−	2.16071i	0.141959	−	0.0819603i
$696$		0			0
$697$	12.7898	+	7.38421i	0.484449	+	0.279697i
$698$	29.1486	−	50.4869i	1.10329	−	1.91096i
$699$		0			0
$700$	−14.8046	+	8.54746i	−0.559562	+	0.323064i
$701$	−35.2396			−1.33098			−0.665491	−	0.746406i	$-0.731778\pi$
$701$	−35.2396			−1.33098			−0.665491	+	0.746406i	$0.731778\pi$
$702$		0			0
$703$	34.7488			1.31058
$704$	−15.5052	+	8.95195i	−0.584375	+	0.337389i
$705$		0			0
$706$	−29.2241	+	50.6175i	−1.09986	+	1.90502i
$707$	−4.06157	−	2.34495i	−0.152751	−	0.0881909i
$708$		0			0
$709$	19.4230	−	11.2139i	0.729447	−	0.421147i	−0.0887726	−	0.996052i	$-0.528294\pi$
$709$	19.4230	−	11.2139i	0.729447	−	0.421147i	0.818220	+	0.574905i	$0.194961\pi$
$710$			14.7779i			0.554605i
$711$		0			0
$712$	−93.0849			−3.48851
$713$	−40.4807	+	23.3716i	−1.51601	+	0.875272i
$714$		0			0
$715$	−1.83620	−	9.08415i	−0.0686701	−	0.339728i
$716$	−0.311285	+	0.539162i	−0.0116333	+	0.0201494i
$717$		0			0
$718$	0.273088	+	0.473003i	0.0101916	+	0.0176523i
$719$	37.6708			1.40488			0.702442	−	0.711741i	$-0.252093\pi$
$719$	37.6708			1.40488			0.702442	+	0.711741i	$0.252093\pi$
$720$		0			0
$721$		−	3.37284i		−	0.125611i
$722$	−70.3691	+	40.6276i	−2.61887	+	1.51200i
$723$		0			0
$724$	−45.5515	+	78.8975i	−1.69291	+	2.93220i
$725$	4.08516	−	7.07571i	0.151719	−	0.262785i
$726$		0			0
$727$	−22.0067	−	38.1168i	−0.816185	−	1.41367i	−0.908474	−	0.417941i	$-0.862752\pi$
$727$	−22.0067	−	38.1168i	−0.816185	−	1.41367i	0.0922894	−	0.995732i	$-0.470582\pi$
$728$	14.0585	−	12.4062i	0.521042	−	0.459803i
$729$		0			0
$730$		−	20.6092i		−	0.762779i
$731$	13.1184	+	22.7218i	0.485202	+	0.840395i
$732$		0			0
$733$	15.2722	+	8.81743i	0.564093	+	0.325679i	0.754787	−	0.655970i	$-0.227740\pi$
$733$	15.2722	+	8.81743i	0.564093	+	0.325679i	−0.190694	+	0.981650i	$0.561074\pi$
$734$	44.0102	+	25.4093i	1.62445	+	0.937875i
$735$		0			0
$736$	5.63161	−	3.25141i	0.207584	−	0.119849i
$737$	10.4984			0.386713
$738$		0			0
$739$		−	13.4319i		−	0.494100i	−0.969003	−	0.247050i	$-0.920539\pi$
$739$		−	13.4319i		−	0.494100i	0.969003	−	0.247050i	$-0.0794612\pi$
$740$	8.89551	+	15.4075i	0.327005	+	0.566390i
$741$		0			0
$742$	−7.67590	+	13.2951i	−0.281791	+	0.488077i
$743$	−28.3946	−	16.3936i	−1.04170	−	0.601423i	−0.121383	−	0.992606i	$-0.538733\pi$
$743$	−28.3946	−	16.3936i	−1.04170	−	0.601423i	−0.920313	+	0.391182i	$0.872066\pi$
$744$		0			0
$745$	5.46360	+	9.46323i	0.200171	+	0.346706i
$746$			26.8911i			0.984555i
$747$		0			0
$748$		−	63.7923i		−	2.33248i
$749$	1.99133	−	1.14969i	0.0727616	−	0.0420089i
$750$		0			0
$751$	−12.4916	+	21.6360i	−0.455824	+	0.789511i	−0.998735	−	0.0502796i	$-0.983989\pi$
$751$	−12.4916	+	21.6360i	−0.455824	+	0.789511i	0.542911	+	0.839790i	$0.317322\pi$
$752$	−18.5097	−	10.6866i	−0.674978	−	0.389699i
$753$		0			0
$754$	−5.52554	+	16.4448i	−0.201228	+	0.598884i
$755$	−4.95897			−0.180475
$756$		0			0
$757$	21.6436			0.786652			0.393326	−	0.919399i	$-0.371324\pi$
$757$	21.6436			0.786652			0.393326	+	0.919399i	$0.371324\pi$
$758$	24.3996	+	42.2614i	0.886234	+	1.53500i
$759$		0			0
$760$	−29.3907	−	16.9687i	−1.06611	−	0.615521i
$761$	17.2650	+	9.96794i	0.625855	+	0.361338i	0.779145	−	0.626844i	$-0.215654\pi$
$761$	17.2650	+	9.96794i	0.625855	+	0.361338i	−0.153290	+	0.988181i	$0.548987\pi$
$762$		0			0
$763$	−5.01610	−	8.68813i	−0.181595	−	0.314532i
$764$	−82.5623			−2.98700
$765$		0			0
$766$	50.3921			1.82074
$767$	−3.64302	+	10.8421i	−0.131542	+	0.391487i
$768$		0			0
$769$	−32.9151	−	19.0035i	−1.18695	−	0.685285i	−0.229337	−	0.973347i	$-0.573656\pi$
$769$	−32.9151	−	19.0035i	−1.18695	−	0.685285i	−0.957612	+	0.288062i	$0.906989\pi$
$770$	−3.12760	+	5.41717i	−0.112711	+	0.195221i
$771$		0			0
$772$	−36.0138	+	20.7926i	−1.29616	+	0.748341i
$773$		−	36.5619i		−	1.31504i	−0.753437	−	0.657520i	$-0.771605\pi$
$773$		−	36.5619i		−	1.31504i	0.753437	−	0.657520i	$-0.228395\pi$
$774$		0			0
$775$		−	42.4341i		−	1.52428i
$776$	−0.652032	−	1.12935i	−0.0234066	−	0.0405414i
$777$		0			0
$778$	45.9029	+	26.5021i	1.64570	+	0.950145i
$779$	−9.94583	+	17.2267i	−0.356346	+	0.617210i
$780$		0			0
$781$	−9.66320	−	16.7372i	−0.345777	−	0.598903i
$782$		−	61.3392i		−	2.19348i
$783$		0			0
$784$	29.2117			1.04328
$785$	3.12456	−	1.80396i	0.111520	−	0.0643862i
$786$		0			0
$787$	−1.39487	−	0.805329i	−0.0497218	−	0.0287069i	0.474933	−	0.880022i	$-0.342472\pi$
$787$	−1.39487	−	0.805329i	−0.0497218	−	0.0287069i	−0.524655	+	0.851315i	$0.675806\pi$
$788$	14.1414	+	8.16455i	0.503767	+	0.290850i
$789$		0			0
$790$	−5.23802	−	9.07251i	−0.186360	−	0.322785i
$791$			1.18916i			0.0422817i
$792$		0			0
$793$	−14.9247	+	13.1706i	−0.529993	+	0.467702i
$794$	34.4336	+	59.6408i	1.22200	+	2.11657i
$795$		0			0
$796$	23.7354	−	41.1109i	0.841280	−	1.45714i
$797$	0.0491630	−	0.0851528i	0.00174144	−	0.00301627i	−0.865153	−	0.501507i	$-0.832779\pi$
$797$	0.0491630	−	0.0851528i	0.00174144	−	0.00301627i	0.866895	+	0.498491i	$0.166112\pi$
$798$		0			0
$799$	−20.4338	+	11.7975i	−0.722896	+	0.417364i
$800$			5.90335i			0.208715i
$801$		0			0
$802$	37.6201			1.32841
$803$	13.4762	+	23.3415i	0.475566	+	0.823705i
$804$		0			0
$805$	−2.02725	+	3.51131i	−0.0714513	+	0.123757i
$806$	17.8514	+	88.3152i	0.628788	+	3.11077i
$807$		0			0
$808$	−21.8879	+	12.6370i	−0.770013	+	0.444567i
$809$	−33.5971			−1.18121			−0.590605	−	0.806961i	$-0.701111\pi$
$809$	−33.5971			−1.18121			−0.590605	+	0.806961i	$0.701111\pi$
$810$		0			0
$811$		−	13.9011i		−	0.488134i	−0.969758	−	0.244067i	$-0.921518\pi$
$811$		−	13.9011i		−	0.488134i	0.969758	−	0.244067i	$-0.0784817\pi$
$812$	6.83558	−	3.94652i	0.239882	−	0.138496i
$813$		0			0
$814$	−29.8911	−	17.2577i	−1.04768	−	0.604881i
$815$	−4.60449	+	7.97521i	−0.161288	+	0.279360i
$816$		0			0
$817$	−30.6041	+	17.6693i	−1.07070	+	0.618170i
$818$	−5.91002			−0.206639
$819$		0			0
$820$	−10.1843			−0.355651
$821$	36.3185	−	20.9685i	1.26753	−	0.731806i	0.293007	−	0.956110i	$-0.405344\pi$
$821$	36.3185	−	20.9685i	1.26753	−	0.731806i	0.974519	+	0.224304i	$0.0720109\pi$
$822$		0			0
$823$	−22.4560	+	38.8949i	−0.782766	+	1.35579i	0.147558	+	0.989053i	$0.452859\pi$
$823$	−22.4560	+	38.8949i	−0.782766	+	1.35579i	−0.930324	+	0.366737i	$0.880475\pi$
$824$	−15.7411	−	9.08815i	−0.548368	−	0.316601i
$825$		0			0
$826$	6.68552	−	3.85988i	0.232619	−	0.134303i
$827$		−	17.5703i		−	0.610980i	−0.952195	−	0.305490i	$-0.901180\pi$
$827$		−	17.5703i		−	0.610980i	0.952195	−	0.305490i	$-0.0988202\pi$
$828$		0			0
$829$	0.797445			0.0276964			0.0138482	−	0.999904i	$-0.495592\pi$
$829$	0.797445			0.0276964			0.0138482	+	0.999904i	$0.495592\pi$
$830$	10.5544	−	6.09360i	0.366350	−	0.211512i
$831$		0			0
$832$	4.43199	+	21.9261i	0.153652	+	0.760152i
$833$	16.1242	−	27.9279i	0.558670	−	0.967644i
$834$		0			0
$835$	−5.88255	−	10.1889i	−0.203574	−	0.352601i
$836$	85.9222			2.97168
$837$		0			0
$838$		−	82.4710i		−	2.84891i
$839$	14.4922	−	8.36709i	0.500327	−	0.288864i	−0.228522	−	0.973539i	$-0.573389\pi$
$839$	14.4922	−	8.36709i	0.500327	−	0.288864i	0.728849	+	0.684675i	$0.240056\pi$
$840$		0			0
$841$	12.6138	−	21.8477i	0.434959	−	0.753371i
$842$	30.1051	−	52.1436i	1.03749	−	1.79699i
$843$		0			0
$844$	22.6831	+	39.2882i	0.780783	+	1.35236i
$845$	−11.4896	−	1.44032i	−0.395254	−	0.0495485i
$846$		0			0
$847$			2.62513i			0.0902006i
$848$	15.2677	+	26.4444i	0.524295	+	0.908106i
$849$		0			0
$850$	48.2243	+	27.8423i	1.65408	+	0.954983i
$851$	−19.3749	−	11.1861i	−0.664163	−	0.383455i
$852$		0			0
$853$	−19.7398	+	11.3968i	−0.675876	+	0.390217i	−0.798300	−	0.602261i	$-0.794267\pi$
$853$	−19.7398	+	11.3968i	−0.675876	+	0.390217i	0.122423	+	0.992478i	$0.460933\pi$
$854$	13.4346			0.459724
$855$		0			0
$856$		−	12.3914i		−	0.423531i
$857$	21.7623	+	37.6934i	0.743386	+	1.28758i	0.950945	+	0.309360i	$0.100115\pi$
$857$	21.7623	+	37.6934i	0.743386	+	1.28758i	−0.207559	+	0.978223i	$0.566552\pi$
$858$		0			0
$859$	8.51911	−	14.7555i	0.290668	−	0.503452i	−0.683300	−	0.730138i	$-0.739456\pi$
$859$	8.51911	−	14.7555i	0.290668	−	0.503452i	0.973968	+	0.226686i	$0.0727890\pi$
$860$	−15.6689	−	9.04647i	−0.534307	−	0.308482i
$861$		0			0
$862$	−15.0384	−	26.0472i	−0.512209	−	0.887172i
$863$			47.3664i			1.61237i	0.591663	+	0.806186i	$0.298472\pi$
$863$			47.3664i			1.61237i	−0.591663	+	0.806186i	$0.701528\pi$
$864$		0			0
$865$			10.1796i			0.346116i
$866$	−28.4758	+	16.4405i	−0.967646	+	0.558671i
$867$		0			0
$868$	20.4970	−	35.5018i	0.695713	−	1.20501i
$869$	11.8649	+	6.85023i	0.402491	+	0.232378i
$870$		0			0
$871$	4.17783	−	12.4338i	0.141560	−	0.421304i
$872$	−54.0637			−1.83083
$873$		0			0
$874$	82.6180			2.79460
$875$	−4.02785	−	6.97645i	−0.136166	−	0.235847i
$876$		0			0
$877$	40.4664	+	23.3633i	1.36645	+	0.788922i	0.990473	−	0.137706i	$-0.0439728\pi$
$877$	40.4664	+	23.3633i	1.36645	+	0.788922i	0.375980	+	0.926628i	$0.377306\pi$
$878$	28.1078	+	16.2281i	0.948593	+	0.547670i
$879$		0			0
$880$	6.22094	+	10.7750i	0.209708	+	0.363225i
$881$	15.7253			0.529797			0.264899	−	0.964276i	$-0.414662\pi$
$881$	15.7253			0.529797			0.264899	+	0.964276i	$0.414662\pi$
$882$		0			0
$883$	−24.3745			−0.820269			−0.410134	−	0.912025i	$-0.634518\pi$
$883$	−24.3745			−0.820269			−0.410134	+	0.912025i	$0.634518\pi$
$884$	−75.5528	−	25.3862i	−2.54112	−	0.853829i
$885$		0			0
$886$	−73.8851	−	42.6576i	−2.48222	−	1.43311i
$887$	−1.96001	+	3.39484i	−0.0658107	+	0.113987i	−0.897053	−	0.441922i	$-0.854297\pi$
$887$	−1.96001	+	3.39484i	−0.0658107	+	0.113987i	0.831243	+	0.555910i	$0.187630\pi$
$888$		0			0
$889$	6.45050	−	3.72420i	0.216343	−	0.124906i
$890$		−	38.8003i		−	1.30059i
$891$		0			0
$892$			53.1279i			1.77885i
$893$	−15.8901	−	27.5224i	−0.531741	−	0.921002i
$894$		0			0
$895$	−0.116088	−	0.0670235i	−0.00388040	−	0.00224035i
$896$	8.92756	−	15.4630i	0.298249	−	0.516582i
$897$		0			0
$898$	−6.59435	−	11.4217i	−0.220056	−	0.381149i
$899$			19.5926i			0.653450i
$900$		0			0
$901$	33.7097			1.12303
$902$	17.1109	−	9.87899i	0.569731	−	0.328934i
$903$		0			0
$904$	5.54985	+	3.20420i	0.184585	+	0.106570i
$905$	−16.9876	−	9.80779i	−0.564687	−	0.326022i
$906$		0			0
$907$	−21.7796	−	37.7234i	−0.723181	−	1.25259i	−0.959718	−	0.280964i	$-0.909346\pi$
$907$	−21.7796	−	37.7234i	−0.723181	−	1.25259i	0.236537	−	0.971622i	$-0.423987\pi$
$908$		−	97.7044i		−	3.24243i
$909$		0			0
$910$	5.17123	+	5.85996i	0.171424	+	0.194256i
$911$	−14.0645	−	24.3604i	−0.465976	−	0.807095i	0.533269	−	0.845946i	$-0.320963\pi$
$911$	−14.0645	−	24.3604i	−0.465976	−	0.807095i	−0.999245	+	0.0388513i	$0.987630\pi$
$912$		0			0
$913$	−7.96916	+	13.8030i	−0.263741	+	0.456812i
$914$	15.3463	−	26.5806i	0.507611	−	0.879208i
$915$		0			0
$916$	44.5609	−	25.7273i	1.47234	−	0.850053i
$917$		−	18.4797i		−	0.610252i
$918$		0			0
$919$	−17.9402			−0.591793			−0.295897	−	0.955220i	$-0.595618\pi$
$919$	−17.9402			−0.591793			−0.295897	+	0.955220i	$0.595618\pi$
$920$	10.9249	+	18.9225i	0.360184	+	0.623856i
$921$		0			0
$922$	−16.1095	+	27.9024i	−0.530538	+	0.918918i
$923$	−23.6682	+	4.78412i	−0.779050	+	0.157471i
$924$		0			0
$925$	17.5888	−	10.1549i	0.578316	−	0.333891i
$926$	15.9153			0.523008
$927$		0			0
$928$		−	2.72569i		−	0.0894752i
$929$	37.2632	−	21.5139i	1.22257	−	0.705849i	0.257101	−	0.966384i	$-0.417233\pi$
$929$	37.2632	−	21.5139i	1.22257	−	0.705849i	0.965464	+	0.260536i	$0.0838992\pi$
$930$		0			0
$931$	37.6162	+	21.7177i	1.23282	+	0.711770i
$932$	38.8503	−	67.2906i	1.27258	−	2.20418i
$933$		0			0
$934$	−29.9492	+	17.2912i	−0.979967	+	0.565784i
$935$	13.7353			0.449191
$936$		0			0
$937$	20.5616			0.671719			0.335860	−	0.941912i	$-0.390973\pi$
$937$	20.5616			0.671719			0.335860	+	0.941912i	$0.390973\pi$
$938$	−7.66699	+	4.42654i	−0.250336	+	0.144532i
$939$		0			0
$940$	8.13553	−	14.0912i	0.265352	−	0.459603i
$941$	31.2579	+	18.0468i	1.01898	+	0.588308i	0.913808	−	0.406147i	$-0.133128\pi$
$941$	31.2579	+	18.0468i	1.01898	+	0.588308i	0.105171	+	0.994454i	$0.466461\pi$
$942$		0			0
$943$	11.0910	−	6.40338i	0.361172	−	0.208523i
$944$		−	15.3550i		−	0.499761i
$945$		0			0
$946$	35.1011			1.14123
$947$	−5.32031	+	3.07168i	−0.172887	+	0.0998163i	−0.583946	−	0.811792i	$-0.698492\pi$
$947$	−5.32031	+	3.07168i	−0.172887	+	0.0998163i	0.411059	+	0.911609i	$0.365159\pi$
$948$		0			0
$949$	33.0076	−	6.67191i	1.07147	−	0.216579i
$950$	−37.5009	+	64.9535i	−1.21669	+	2.10737i
$951$		0			0
$952$	13.8939	+	24.0649i	0.450302	+	0.779947i
$953$	−19.7667			−0.640305			−0.320152	−	0.947366i	$-0.603734\pi$
$953$	−19.7667			−0.640305			−0.320152	+	0.947366i	$0.603734\pi$
$954$		0			0
$955$		−	17.7767i		−	0.575240i
$956$	70.8766	−	40.9206i	2.29231	−	1.32347i
$957$		0			0
$958$	42.8882	−	74.2846i	1.38566	−	2.40003i
$959$	−8.87119	+	15.3654i	−0.286466	+	0.496173i
$960$		0			0
$961$	35.3789	+	61.2780i	1.14125	+	1.97671i
$962$	−32.3344	+	28.5341i	−1.04250	+	0.919976i
$963$		0			0
$964$			47.1267i			1.51785i
$965$	−4.47689	−	7.75420i	−0.144116	−	0.249617i
$966$		0			0
$967$	−26.4324	−	15.2608i	−0.850009	−	0.490753i	0.0106449	−	0.999943i	$-0.496612\pi$
$967$	−26.4324	−	15.2608i	−0.850009	−	0.490753i	−0.860654	+	0.509190i	$0.829945\pi$
$968$	12.2516	+	7.07344i	0.393780	+	0.227349i
$969$		0			0
$970$	0.470745	−	0.271784i	0.0151147	−	0.00872647i
$971$	4.05102			0.130004			0.0650018	−	0.997885i	$-0.479295\pi$
$971$	4.05102			0.130004			0.0650018	+	0.997885i	$0.479295\pi$
$972$		0			0
$973$		−	4.76581i		−	0.152785i
$974$	7.16940	+	12.4178i	0.229722	+	0.397891i
$975$		0			0
$976$	13.3610	−	23.1420i	0.427677	−	0.740758i
$977$	25.1440	+	14.5169i	0.804426	+	0.464436i	0.845017	−	0.534740i	$-0.179590\pi$
$977$	25.1440	+	14.5169i	0.804426	+	0.464436i	−0.0405902	+	0.999176i	$0.512924\pi$
$978$		0			0
$979$	25.3714	+	43.9445i	0.810872	+	1.40447i
$980$			22.2385i			0.710382i
$981$		0			0
$982$			61.7447i			1.97035i
$983$	5.23002	−	3.01955i	0.166812	−	0.0963088i	−0.414270	−	0.910154i	$-0.635963\pi$
$983$	5.23002	−	3.01955i	0.166812	−	0.0963088i	0.581082	+	0.813845i	$0.302630\pi$
$984$		0			0
$985$	−1.75793	+	3.04482i	−0.0560122	+	0.0970160i
$986$	−22.2661	−	12.8553i	−0.709096	−	0.409397i
$987$		0			0
$988$	34.1927	−	101.762i	1.08782	−	3.23750i
$989$	22.7519			0.723467
$990$		0			0
$991$	−49.4199			−1.56987			−0.784937	−	0.619575i	$-0.787305\pi$
$991$	−49.4199			−1.56987			−0.784937	+	0.619575i	$0.787305\pi$
$992$	−7.07818	−	12.2598i	−0.224732	−	0.389248i
$993$		0			0
$994$	14.1141	+	8.14879i	0.447673	+	0.258464i
$995$	8.85169	+	5.11052i	0.280617	+	0.162014i
$996$		0			0
$997$	10.6174	+	18.3899i	0.336257	+	0.582414i	0.983725	−	0.179678i	$-0.0575056\pi$
$997$	10.6174	+	18.3899i	0.336257	+	0.582414i	−0.647469	+	0.762092i	$0.724172\pi$
$998$	−98.6419			−3.12246
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.t.c.64.10		20
3.2	odd	2		117.2.t.c.103.1	yes	20
9.2	odd	6		117.2.t.c.25.10	yes	20
9.4	even	3		1053.2.b.i.649.10		10
9.5	odd	6		1053.2.b.j.649.1		10
9.7	even	3	inner	351.2.t.c.181.1		20
13.12	even	2	inner	351.2.t.c.64.1		20
39.38	odd	2		117.2.t.c.103.10	yes	20
117.25	even	6	inner	351.2.t.c.181.10		20
117.38	odd	6		117.2.t.c.25.1	✓	20
117.77	odd	6		1053.2.b.j.649.10		10
117.103	even	6		1053.2.b.i.649.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.1	✓	20	117.38	odd	6
117.2.t.c.25.10	yes	20	9.2	odd	6
117.2.t.c.103.1	yes	20	3.2	odd	2
117.2.t.c.103.10	yes	20	39.38	odd	2
351.2.t.c.64.1		20	13.12	even	2	inner
351.2.t.c.64.10		20	1.1	even	1	trivial
351.2.t.c.181.1		20	9.7	even	3	inner
351.2.t.c.181.10		20	117.25	even	6	inner
1053.2.b.i.649.1		10	117.103	even	6
1053.2.b.i.649.10		10	9.4	even	3
1053.2.b.j.649.1		10	9.5	odd	6
1053.2.b.j.649.10		10	117.77	odd	6

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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.14539 - 1.23864i) q^{2} +(2.06847 - 3.58269i) q^{4} +(0.771397 + 0.445366i) q^{5} +(0.850723 - 0.491165i) q^{7} -5.29379i q^{8} +2.20660 q^{10} +(-2.49915 + 1.44288i) q^{11} +(0.714352 + 3.53408i) q^{13} +(1.21676 - 2.10748i) q^{14} +(-2.42018 - 4.19187i) q^{16} -5.34353 q^{17} -7.19723i q^{19} +(3.19122 - 1.84245i) q^{20} +(-3.57443 + 6.19110i) q^{22} +(-2.31688 + 4.01296i) q^{23} +(-2.10330 - 3.64302i) q^{25} +(5.91002 + 6.69715i) q^{26} -4.06384i q^{28} +(0.971133 + 1.68205i) q^{29} +(8.73604 + 5.04375i) q^{31} +(-1.21534 - 0.701678i) q^{32} +(-11.4640 + 6.61872i) q^{34} +0.874993 q^{35} +4.82809i q^{37} +(-8.91479 - 15.4409i) q^{38} +(2.35768 - 4.08361i) q^{40} +(-2.39352 - 1.38190i) q^{41} +(-2.45501 - 4.25220i) q^{43} +11.9382i q^{44} +11.4791i q^{46} +(3.82403 - 2.20780i) q^{47} +(-3.01751 + 5.22649i) q^{49} +(-9.02479 - 5.21047i) q^{50} +(14.1391 + 4.75082i) q^{52} -6.30850 q^{53} -2.57044 q^{55} +(-2.60013 - 4.50355i) q^{56} +(4.16692 + 2.40577i) q^{58} +(2.74727 + 1.58614i) q^{59} +(2.76034 + 4.78105i) q^{61} +24.9896 q^{62} +6.20421 q^{64} +(-1.02291 + 3.04432i) q^{65} +(-3.15059 - 1.81899i) q^{67} +(-11.0529 + 19.1442i) q^{68} +(1.87720 - 1.08380i) q^{70} +6.69715i q^{71} -9.33980i q^{73} +(5.98027 + 10.3581i) q^{74} +(-25.7854 - 14.8872i) q^{76} +(-1.41739 + 2.45499i) q^{77} +(-2.37380 - 4.11154i) q^{79} -4.31146i q^{80} -6.84670 q^{82} +(4.78313 - 2.76154i) q^{83} +(-4.12198 - 2.37983i) q^{85} +(-10.5339 - 6.08176i) q^{86} +(7.63833 + 13.2300i) q^{88} -17.5838i q^{89} +(2.34353 + 2.65566i) q^{91} +(9.58479 + 16.6013i) q^{92} +(5.46935 - 9.47320i) q^{94} +(3.20540 - 5.55192i) q^{95} +(0.213335 - 0.123169i) q^{97} +14.9505i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 12 q^{4} - 16 q^{10} - 4 q^{13} + 18 q^{14} + 4 q^{16} + 12 q^{17} - 10 q^{22} - 24 q^{23} - 12 q^{25} + 12 q^{26} - 12 q^{29} + 12 q^{35} - 12 q^{38} - 8 q^{40} + 4 q^{43} - 10 q^{49} - 108 q^{53}+ \cdots - 24 q^{95}+O(q^{100}) \) 20 * q + 12 * q^4 - 16 * q^10 - 4 * q^13 + 18 * q^14 + 4 * q^16 + 12 * q^17 - 10 * q^22 - 24 * q^23 - 12 * q^25 + 12 * q^26 - 12 * q^29 + 12 * q^35 - 12 * q^38 - 8 * q^40 + 4 * q^43 - 10 * q^49 - 108 * q^53 + 20 * q^55 - 36 * q^56 - 2 * q^61 + 72 * q^62 + 8 * q^64 + 24 * q^65 - 24 * q^68 + 42 * q^74 + 6 * q^77 - 14 * q^79 - 4 * q^82 + 22 * q^88 - 72 * q^91 + 84 * q^92 + 20 * q^94 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more