LMFDB - Embedded newform 351.2.e.c.118.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [351,2,Mod(118,351)] 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("351.118"); 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, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 3 x^{10} - x^{9} - 2 x^{8} + 9 x^{7} + 24 x^{6} + 27 x^{5} - 18 x^{4} - 27 x^{3} + \cdots + 729 $ x^12 - x^11 - 3x^10 - x^9 - 2x^8 + 9x^7 + 24x^6 + 27x^5 - 18x^4 - 27x^3 - 243x^2 - 243*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 117)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.3
Root			$0.471837 - 1.66654i$ of defining polynomial
Character	$\chi$	$=$	351.118
Dual form			351.2.e.c.235.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.248047 - 0.429630i) q^{2} +(0.876945 - 1.51891i) q^{4} +(-0.663441 + 1.14911i) q^{5} +(-1.56464 - 2.71004i) q^{7} -1.86228 q^{8} +0.658258 q^{10} +(-1.70735 - 2.95722i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.776210 + 1.34444i) q^{14} +(-1.29196 - 2.23774i) q^{16} +0.912179 q^{17} -1.03576 q^{19} +(1.16360 + 2.01542i) q^{20} +(-0.847007 + 1.46706i) q^{22} +(2.68611 - 4.65248i) q^{23} +(1.61969 + 2.80539i) q^{25} -0.496094 q^{26} -5.48843 q^{28} +(-3.25212 - 5.63283i) q^{29} +(-1.27269 + 2.20436i) q^{31} +(-2.50321 + 4.33569i) q^{32} +(-0.226263 - 0.391900i) q^{34} +4.15219 q^{35} +7.99800 q^{37} +(0.256916 + 0.444991i) q^{38} +(1.23551 - 2.13997i) q^{40} +(-2.72681 + 4.72297i) q^{41} +(-2.20468 - 3.81862i) q^{43} -5.98902 q^{44} -2.66513 q^{46} +(-4.59865 - 7.96510i) q^{47} +(-1.39622 + 2.41832i) q^{49} +(0.803520 - 1.39174i) q^{50} +(-0.876945 - 1.51891i) q^{52} +12.1878 q^{53} +4.53091 q^{55} +(2.91381 + 5.04686i) q^{56} +(-1.61335 + 2.79441i) q^{58} +(-3.54016 + 6.13174i) q^{59} +(7.18720 + 12.4486i) q^{61} +1.26274 q^{62} -2.68417 q^{64} +(0.663441 + 1.14911i) q^{65} +(4.67710 - 8.10098i) q^{67} +(0.799931 - 1.38552i) q^{68} +(-1.02994 - 1.78391i) q^{70} +12.0670 q^{71} -5.22771 q^{73} +(-1.98388 - 3.43618i) q^{74} +(-0.908301 + 1.57322i) q^{76} +(-5.34279 + 9.25399i) q^{77} +(6.05439 + 10.4865i) q^{79} +3.42855 q^{80} +2.70551 q^{82} +(5.50179 + 9.52938i) q^{83} +(-0.605177 + 1.04820i) q^{85} +(-1.09373 + 1.89439i) q^{86} +(3.17957 + 5.50718i) q^{88} +8.33216 q^{89} -3.12929 q^{91} +(-4.71115 - 8.15994i) q^{92} +(-2.28136 + 3.95144i) q^{94} +(0.687162 - 1.19020i) q^{95} +(-7.01598 - 12.1520i) q^{97} +1.38531 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + 12 q^{8} - 12 q^{10} - 7 q^{11} + 6 q^{13} - 13 q^{14} - 6 q^{16} + 28 q^{17} - 6 q^{19} - 17 q^{20} + 3 q^{22} - 17 q^{23} - 3 q^{25} - 4 q^{26} + 30 q^{28} - 14 q^{29}+ \cdots + 34 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + 12 * q^8 - 12 * q^10 - 7 * q^11 + 6 * q^13 - 13 * q^14 - 6 * q^16 + 28 * q^17 - 6 * q^19 - 17 * q^20 + 3 * q^22 - 17 * q^23 - 3 * q^25 - 4 * q^26 + 30 * q^28 - 14 * q^29 - 6 * q^31 - 9 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 + 4 * q^38 + 6 * q^40 + 4 * q^41 + 3 * q^43 + 26 * q^44 - 9 * q^47 + 21 * q^50 + 6 * q^52 + 56 * q^53 + 30 * q^55 - 16 * q^56 - 18 * q^58 - 17 * q^59 + 6 * q^61 - 8 * q^62 - 60 * q^64 + 3 * q^65 + 12 * q^67 - 22 * q^68 - 9 * q^70 - 2 * q^71 - 18 * q^73 + 27 * q^74 + 3 * q^76 - 15 * q^77 + 6 * q^79 - 48 * q^80 + 54 * q^82 - 28 * q^83 - 27 * q^85 + 6 * q^86 + 9 * q^88 - 18 * q^89 - 44 * q^92 + 24 * q^94 - 32 * q^95 + 34 * q^98

Character values

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

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

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 $

$2$	−0.248047	−	0.429630i	−0.175396	−	0.303794i	0.764902	−	0.644146i	$-0.222787\pi$
$2$	−0.248047	−	0.429630i	−0.175396	−	0.303794i	−0.940298	+	0.340352i	$0.889454\pi$
$3$		0			0
$3$		0			0
$4$	0.876945	−	1.51891i	0.438473	−	0.759457i
$5$	−0.663441	+	1.14911i	−0.296700	+	0.513899i	−0.975379	−	0.220536i	$-0.929219\pi$
$5$	−0.663441	+	1.14911i	−0.296700	+	0.513899i	0.678679	+	0.734435i	$0.262553\pi$
$6$		0			0
$7$	−1.56464	−	2.71004i	−0.591380	−	1.02430i	−0.994047	−	0.108953i	$-0.965250\pi$
$7$	−1.56464	−	2.71004i	−0.591380	−	1.02430i	0.402667	−	0.915346i	$-0.368083\pi$
$8$	−1.86228			−0.658416
$9$		0			0
$10$	0.658258			0.208159
$11$	−1.70735	−	2.95722i	−0.514786	−	0.891635i	−0.999853	−	0.0171581i	$-0.994538\pi$
$11$	−1.70735	−	2.95722i	−0.514786	−	0.891635i	0.485067	−	0.874477i	$-0.338795\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−0.776210	+	1.34444i	−0.207451	+	0.359315i
$15$		0			0
$16$	−1.29196	−	2.23774i	−0.322989	−	0.559434i
$17$	0.912179			0.221236			0.110618	−	0.993863i	$-0.464717\pi$
$17$	0.912179			0.221236			0.110618	+	0.993863i	$0.464717\pi$
$18$		0			0
$19$	−1.03576			−0.237619			−0.118809	−	0.992917i	$-0.537908\pi$
$19$	−1.03576			−0.237619			−0.118809	+	0.992917i	$0.537908\pi$
$20$	1.16360	+	2.01542i	0.260190	+	0.450661i
$21$		0			0
$22$	−0.847007	+	1.46706i	−0.180582	+	0.312778i
$23$	2.68611	−	4.65248i	0.560093	−	0.970109i	−0.437395	−	0.899270i	$-0.644099\pi$
$23$	2.68611	−	4.65248i	0.560093	−	0.970109i	0.997488	−	0.0708399i	$-0.0225679\pi$
$24$		0			0
$25$	1.61969	+	2.80539i	0.323938	+	0.561078i
$26$	−0.496094			−0.0972920
$27$		0			0
$28$	−5.48843			−1.03722
$29$	−3.25212	−	5.63283i	−0.603903	−	1.04599i	−0.992224	−	0.124466i	$-0.960278\pi$
$29$	−3.25212	−	5.63283i	−0.603903	−	1.04599i	0.388321	−	0.921524i	$-0.373055\pi$
$30$		0			0
$31$	−1.27269	+	2.20436i	−0.228581	+	0.395914i	−0.957388	−	0.288805i	$-0.906742\pi$
$31$	−1.27269	+	2.20436i	−0.228581	+	0.395914i	0.728807	+	0.684720i	$0.240075\pi$
$32$	−2.50321	+	4.33569i	−0.442510	+	0.766450i
$33$		0			0
$34$	−0.226263	−	0.391900i	−0.0388038	−	0.0672102i
$35$	4.15219			0.701849
$36$		0			0
$37$	7.99800			1.31486			0.657431	−	0.753514i	$-0.271643\pi$
$37$	7.99800			1.31486			0.657431	+	0.753514i	$0.271643\pi$
$38$	0.256916	+	0.444991i	0.0416773	+	0.0721871i
$39$		0			0
$40$	1.23551	−	2.13997i	0.195352	−	0.338360i
$41$	−2.72681	+	4.72297i	−0.425856	+	0.737604i	−0.996500	−	0.0835936i	$-0.973360\pi$
$41$	−2.72681	+	4.72297i	−0.425856	+	0.737604i	0.570644	+	0.821197i	$0.306694\pi$
$42$		0			0
$43$	−2.20468	−	3.81862i	−0.336211	−	0.582334i	0.647506	−	0.762060i	$-0.275812\pi$
$43$	−2.20468	−	3.81862i	−0.336211	−	0.582334i	−0.983717	+	0.179726i	$0.942479\pi$
$44$	−5.98902			−0.902878
$45$		0			0
$46$	−2.66513			−0.392952
$47$	−4.59865	−	7.96510i	−0.670782	−	1.16183i	−0.977683	−	0.210087i	$-0.932625\pi$
$47$	−4.59865	−	7.96510i	−0.670782	−	1.16183i	0.306901	−	0.951742i	$-0.400708\pi$
$48$		0			0
$49$	−1.39622	+	2.41832i	−0.199460	+	0.345474i
$50$	0.803520	−	1.39174i	0.113635	−	0.196821i
$51$		0			0
$52$	−0.876945	−	1.51891i	−0.121610	−	0.210635i
$53$	12.1878			1.67412			0.837060	−	0.547111i	$-0.184272\pi$
$53$	12.1878			1.67412			0.837060	+	0.547111i	$0.184272\pi$
$54$		0			0
$55$	4.53091			0.610947
$56$	2.91381	+	5.04686i	0.389374	+	0.674415i
$57$		0			0
$58$	−1.61335	+	2.79441i	−0.211844	+	0.366924i
$59$	−3.54016	+	6.13174i	−0.460890	+	0.798284i	−0.999006	−	0.0445866i	$-0.985803\pi$
$59$	−3.54016	+	6.13174i	−0.460890	+	0.798284i	0.538116	+	0.842871i	$0.319136\pi$
$60$		0			0
$61$	7.18720	+	12.4486i	0.920226	+	1.59388i	0.799064	+	0.601246i	$0.205329\pi$
$61$	7.18720	+	12.4486i	0.920226	+	1.59388i	0.121162	+	0.992633i	$0.461338\pi$
$62$	1.26274			0.160369
$63$		0			0
$64$	−2.68417			−0.335521
$65$	0.663441	+	1.14911i	0.0822897	+	0.142530i
$66$		0			0
$67$	4.67710	−	8.10098i	0.571399	−	0.989692i	−0.425024	−	0.905182i	$-0.639734\pi$
$67$	4.67710	−	8.10098i	0.571399	−	0.989692i	0.996423	−	0.0845099i	$-0.0269325\pi$
$68$	0.799931	−	1.38552i	0.0970059	−	0.168019i
$69$		0			0
$70$	−1.02994	−	1.78391i	−0.123101	−	0.213218i
$71$	12.0670			1.43209			0.716045	−	0.698054i	$-0.245951\pi$
$71$	12.0670			1.43209			0.716045	+	0.698054i	$0.245951\pi$
$72$		0			0
$73$	−5.22771			−0.611857			−0.305928	−	0.952055i	$-0.598967\pi$
$73$	−5.22771			−0.611857			−0.305928	+	0.952055i	$0.598967\pi$
$74$	−1.98388	−	3.43618i	−0.230621	−	0.399448i
$75$		0			0
$76$	−0.908301	+	1.57322i	−0.104189	+	0.180461i
$77$	−5.34279	+	9.25399i	−0.608868	+	1.05459i
$78$		0			0
$79$	6.05439	+	10.4865i	0.681172	+	1.17982i	0.974623	+	0.223851i	$0.0718629\pi$
$79$	6.05439	+	10.4865i	0.681172	+	1.17982i	−0.293451	+	0.955974i	$0.594804\pi$
$80$	3.42855			0.383323
$81$		0			0
$82$	2.70551			0.298773
$83$	5.50179	+	9.52938i	0.603900	+	1.04599i	0.992224	+	0.124463i	$0.0397207\pi$
$83$	5.50179	+	9.52938i	0.603900	+	1.04599i	−0.388324	+	0.921523i	$0.626946\pi$
$84$		0			0
$85$	−0.605177	+	1.04820i	−0.0656407	+	0.113693i
$86$	−1.09373	+	1.89439i	−0.117940	+	0.204278i
$87$		0			0
$88$	3.17957	+	5.50718i	0.338943	+	0.587067i
$89$	8.33216			0.883207			0.441604	−	0.897210i	$-0.354410\pi$
$89$	8.33216			0.883207			0.441604	+	0.897210i	$0.354410\pi$
$90$		0			0
$91$	−3.12929			−0.328038
$92$	−4.71115	−	8.15994i	−0.491171	−	0.850733i
$93$		0			0
$94$	−2.28136	+	3.95144i	−0.235305	+	0.407559i
$95$	0.687162	−	1.19020i	0.0705014	−	0.122112i
$96$		0			0
$97$	−7.01598	−	12.1520i	−0.712365	−	1.23385i	−0.963967	−	0.266022i	$-0.914291\pi$
$97$	−7.01598	−	12.1520i	−0.712365	−	1.23385i	0.251602	−	0.967831i	$-0.419043\pi$
$98$	1.38531			0.139937
$99$		0			0
$100$	5.68153			0.568153
$101$	5.91889	+	10.2518i	0.588951	+	1.02009i	0.994370	+	0.105963i	$0.0337924\pi$
$101$	5.91889	+	10.2518i	0.588951	+	1.02009i	−0.405419	+	0.914131i	$0.632874\pi$
$102$		0			0
$103$	−4.10294	+	7.10650i	−0.404275	+	0.700224i	−0.994237	−	0.107207i	$-0.965809\pi$
$103$	−4.10294	+	7.10650i	−0.404275	+	0.700224i	0.589962	+	0.807431i	$0.299143\pi$
$104$	−0.931141	+	1.61278i	−0.0913059	+	0.158146i
$105$		0			0
$106$	−3.02314	−	5.23624i	−0.293634	−	0.508588i
$107$	−0.156610			−0.0151401			−0.00757005	−	0.999971i	$-0.502410\pi$
$107$	−0.156610			−0.0151401			−0.00757005	+	0.999971i	$0.502410\pi$
$108$		0			0
$109$	−7.52766			−0.721019			−0.360509	−	0.932756i	$-0.617397\pi$
$109$	−7.52766			−0.721019			−0.360509	+	0.932756i	$0.617397\pi$
$110$	−1.12388	−	1.94661i	−0.107158	−	0.185602i
$111$		0			0
$112$	−4.04290	+	7.00252i	−0.382019	+	0.661676i
$113$	8.53672	−	14.7860i	0.803067	−	1.39095i	−0.114521	−	0.993421i	$-0.536533\pi$
$113$	8.53672	−	14.7860i	0.803067	−	1.39095i	0.917588	−	0.397532i	$-0.130133\pi$
$114$		0			0
$115$	3.56415	+	6.17329i	0.332359	+	0.575663i
$116$	−11.4077			−1.05918
$117$		0			0
$118$	3.51250			0.323352
$119$	−1.42724	−	2.47204i	−0.130834	−	0.226612i
$120$		0			0
$121$	−0.330096	+	0.571744i	−0.0300088	+	0.0519767i
$122$	3.56552	−	6.17567i	0.322807	−	0.559119i
$123$		0			0
$124$	2.23215	+	3.86620i	0.200453	+	0.347195i
$125$	−10.9327			−0.977849
$126$		0			0
$127$	0.476604			0.0422917			0.0211459	−	0.999776i	$-0.493269\pi$
$127$	0.476604			0.0422917			0.0211459	+	0.999776i	$0.493269\pi$
$128$	5.67223	+	9.82459i	0.501359	+	0.868379i
$129$		0			0
$130$	0.329129	−	0.570068i	0.0288665	−	0.0499983i
$131$	4.40550	−	7.63055i	0.384910	−	0.666684i	−0.606846	−	0.794819i	$-0.707566\pi$
$131$	4.40550	−	7.63055i	0.384910	−	0.666684i	0.991757	+	0.128135i	$0.0408990\pi$
$132$		0			0
$133$	1.62059	+	2.80694i	0.140523	+	0.243393i
$134$	−4.64056			−0.400884
$135$		0			0
$136$	−1.69874			−0.145665
$137$	−5.09861	−	8.83104i	−0.435603	−	0.754487i	0.561741	−	0.827313i	$-0.310132\pi$
$137$	−5.09861	−	8.83104i	−0.435603	−	0.754487i	−0.997345	+	0.0728259i	$0.976798\pi$
$138$		0			0
$139$	5.36283	−	9.28870i	0.454870	−	0.787857i	−0.543811	−	0.839208i	$-0.683019\pi$
$139$	5.36283	−	9.28870i	0.454870	−	0.787857i	0.998681	+	0.0513505i	$0.0163526\pi$
$140$	3.64125	−	6.30682i	0.307742	−	0.533024i
$141$		0			0
$142$	−2.99318	−	5.18434i	−0.251182	−	0.435061i
$143$	−3.41470			−0.285552
$144$		0			0
$145$	8.63034			0.716711
$146$	1.29672	+	2.24598i	0.107317	+	0.185879i
$147$		0			0
$148$	7.01381	−	12.1483i	0.576531	−	0.998582i
$149$	−7.56805	+	13.1083i	−0.619999	+	1.07387i	0.369486	+	0.929236i	$0.379534\pi$
$149$	−7.56805	+	13.1083i	−0.619999	+	1.07387i	−0.989485	+	0.144634i	$0.953800\pi$
$150$		0			0
$151$	−6.09490	−	10.5567i	−0.495996	−	0.859090i	0.503993	−	0.863708i	$-0.331864\pi$
$151$	−6.09490	−	10.5567i	−0.495996	−	0.859090i	−0.999989	+	0.00461712i	$0.998530\pi$
$152$	1.92887			0.156452
$153$		0			0
$154$	5.30105			0.427171
$155$	−1.68870	−	2.92492i	−0.135640	−	0.234935i
$156$		0			0
$157$	1.92216	−	3.32928i	0.153405	−	0.265706i	−0.779072	−	0.626934i	$-0.784309\pi$
$157$	1.92216	−	3.32928i	0.153405	−	0.265706i	0.932477	+	0.361229i	$0.117643\pi$
$158$	3.00355	−	5.20230i	0.238949	−	0.413872i
$159$		0			0
$160$	−3.32147	−	5.75295i	−0.262585	−	0.454811i
$161$	−16.8112			−1.32491
$162$		0			0
$163$	5.24217			0.410599			0.205299	−	0.978699i	$-0.434183\pi$
$163$	5.24217			0.410599			0.205299	+	0.978699i	$0.434183\pi$
$164$	4.78252	+	8.28357i	0.373452	+	0.646838i
$165$		0			0
$166$	2.72940	−	4.72747i	0.211843	−	0.366923i
$167$	8.89187	−	15.4012i	0.688074	−	1.19178i	−0.284386	−	0.958710i	$-0.591790\pi$
$167$	8.89187	−	15.4012i	0.688074	−	1.19178i	0.972460	−	0.233069i	$-0.0748768\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.600449			0.0460524
$171$		0			0
$172$	−7.73354			−0.589677
$173$	0.790406	+	1.36902i	0.0600935	+	0.104085i	0.894507	−	0.447054i	$-0.147527\pi$
$173$	0.790406	+	1.36902i	0.0600935	+	0.104085i	−0.834414	+	0.551139i	$0.814193\pi$
$174$		0			0
$175$	5.06848	−	8.77887i	0.383141	−	0.663620i
$176$	−4.41165	+	7.64120i	−0.332541	+	0.575977i
$177$		0			0
$178$	−2.06677	−	3.57975i	−0.154911	−	0.268313i
$179$	−15.2270			−1.13812			−0.569060	−	0.822296i	$-0.692693\pi$
$179$	−15.2270			−1.13812			−0.569060	+	0.822296i	$0.692693\pi$
$180$		0			0
$181$	−22.9726			−1.70754			−0.853770	−	0.520650i	$-0.825690\pi$
$181$	−22.9726			−1.70754			−0.853770	+	0.520650i	$0.825690\pi$
$182$	0.776210	+	1.34444i	0.0575365	+	0.0996562i
$183$		0			0
$184$	−5.00230	+	8.66423i	−0.368774	+	0.638736i
$185$	−5.30620	+	9.19061i	−0.390119	+	0.675707i
$186$		0			0
$187$	−1.55741	−	2.69751i	−0.113889	−	0.197262i
$188$	−16.1311			−1.17648
$189$		0			0
$190$	−0.681794			−0.0494625
$191$	−3.53659	−	6.12556i	−0.255899	−	0.443230i	0.709240	−	0.704967i	$-0.249038\pi$
$191$	−3.53659	−	6.12556i	−0.255899	−	0.443230i	−0.965139	+	0.261737i	$0.915705\pi$
$192$		0			0
$193$	−4.00632	+	6.93914i	−0.288381	+	0.499490i	−0.973423	−	0.229013i	$-0.926450\pi$
$193$	−4.00632	+	6.93914i	−0.288381	+	0.499490i	0.685043	+	0.728503i	$0.259784\pi$
$194$	−3.48059	+	6.02855i	−0.249892	+	0.432825i
$195$		0			0
$196$	2.44881	+	4.24147i	0.174915	+	0.302962i
$197$	−10.2986			−0.733748			−0.366874	−	0.930271i	$-0.619572\pi$
$197$	−10.2986			−0.733748			−0.366874	+	0.930271i	$0.619572\pi$
$198$		0			0
$199$	−5.56945			−0.394808			−0.197404	−	0.980322i	$-0.563251\pi$
$199$	−5.56945			−0.394808			−0.197404	+	0.980322i	$0.563251\pi$
$200$	−3.01632	−	5.22443i	−0.213286	−	0.369423i
$201$		0			0
$202$	2.93632	−	5.08586i	0.206599	−	0.357840i
$203$	−10.1768	+	17.6267i	−0.714271	+	1.23715i
$204$		0			0
$205$	−3.61815	−	6.26682i	−0.252703	−	0.437694i
$206$	4.07089			0.283632
$207$		0			0
$208$	−2.58391			−0.179162
$209$	1.76840	+	3.06295i	0.122323	+	0.211869i
$210$		0			0
$211$	4.71574	−	8.16790i	0.324645	−	0.562302i	−0.656795	−	0.754069i	$-0.728089\pi$
$211$	4.71574	−	8.16790i	0.324645	−	0.562302i	0.981440	+	0.191767i	$0.0614218\pi$
$212$	10.6880	−	18.5122i	0.734056	−	1.27142i
$213$		0			0
$214$	0.0388468	+	0.0672846i	0.00265551	+	0.00459948i
$215$	5.85070			0.399014
$216$		0			0
$217$	7.96520			0.540713
$218$	1.86721	+	3.23411i	0.126464	+	0.219041i
$219$		0			0
$220$	3.97336	−	6.88206i	0.267884	−	0.463988i
$221$	0.456090	−	0.789970i	0.0306799	−	0.0531392i
$222$		0			0
$223$	9.31273	+	16.1301i	0.623626	+	1.08015i	0.988805	+	0.149215i	$0.0476746\pi$
$223$	9.31273	+	16.1301i	0.623626	+	1.08015i	−0.365178	+	0.930938i	$0.618992\pi$
$224$	15.6666			1.04677
$225$		0			0
$226$	−8.47003			−0.563418
$227$	−7.05046	−	12.2117i	−0.467955	−	0.810522i	0.531374	−	0.847137i	$-0.321676\pi$
$227$	−7.05046	−	12.2117i	−0.467955	−	0.810522i	−0.999329	+	0.0366150i	$0.988342\pi$
$228$		0			0
$229$	−1.02535	+	1.77595i	−0.0677569	+	0.117358i	−0.897914	−	0.440172i	$-0.854918\pi$
$229$	−1.02535	+	1.77595i	−0.0677569	+	0.117358i	0.830157	+	0.557530i	$0.188251\pi$
$230$	1.76815	−	3.06253i	0.116589	−	0.201937i
$231$		0			0
$232$	6.05636	+	10.4899i	0.397619	+	0.688697i
$233$	−8.01472			−0.525062			−0.262531	−	0.964924i	$-0.584557\pi$
$233$	−8.01472			−0.525062			−0.262531	+	0.964924i	$0.584557\pi$
$234$		0			0
$235$	12.2037			0.796084
$236$	6.20905	+	10.7544i	0.404175	+	0.700052i
$237$		0			0
$238$	−0.708043	+	1.22637i	−0.0458956	+	0.0794935i
$239$	−1.74761	+	3.02695i	−0.113043	+	0.195797i	−0.916996	−	0.398897i	$-0.869393\pi$
$239$	−1.74761	+	3.02695i	−0.113043	+	0.195797i	0.803953	+	0.594694i	$0.202727\pi$
$240$		0			0
$241$	−3.56391	−	6.17288i	−0.229572	−	0.397630i	0.728109	−	0.685461i	$-0.240399\pi$
$241$	−3.56391	−	6.17288i	−0.229572	−	0.397630i	−0.957681	+	0.287831i	$0.907066\pi$
$242$	0.327518			0.0210536
$243$		0			0
$244$	25.2111			1.61398
$245$	−1.85261	−	3.20882i	−0.118359	−	0.205004i
$246$		0			0
$247$	−0.517878	+	0.896990i	−0.0329518	+	0.0570741i
$248$	2.37010	−	4.10513i	0.150502	−	0.260676i
$249$		0			0
$250$	2.71182	+	4.69701i	0.171511	+	0.297065i
$251$	10.8057			0.682052			0.341026	−	0.940054i	$-0.389226\pi$
$251$	10.8057			0.682052			0.341026	+	0.940054i	$0.389226\pi$
$252$		0			0
$253$	−18.3445			−1.15331
$254$	−0.118220	−	0.204763i	−0.00741779	−	0.0128480i
$255$		0			0
$256$	0.129788	−	0.224800i	0.00811178	−	0.0140500i
$257$	12.0213	−	20.8215i	0.749870	−	1.29881i	−0.198015	−	0.980199i	$-0.563449\pi$
$257$	12.0213	−	20.8215i	0.749870	−	1.29881i	0.947885	−	0.318614i	$-0.103217\pi$
$258$		0			0
$259$	−12.5140	−	21.6749i	−0.777583	−	1.34681i
$260$	2.32721			0.144327
$261$		0			0
$262$	−4.37108			−0.270047
$263$	−0.587040	−	1.01678i	−0.0361984	−	0.0626975i	0.847359	−	0.531021i	$-0.178192\pi$
$263$	−0.587040	−	1.01678i	−0.0361984	−	0.0626975i	−0.883557	+	0.468324i	$0.844858\pi$
$264$		0			0
$265$	−8.08587	+	14.0051i	−0.496711	+	0.860329i
$266$	0.803964	−	1.39251i	0.0492942	−	0.0853800i
$267$		0			0
$268$	−8.20313	−	14.2082i	−0.501086	−	0.867906i
$269$	16.4749			1.00449			0.502247	−	0.864724i	$-0.332507\pi$
$269$	16.4749			1.00449			0.502247	+	0.864724i	$0.332507\pi$
$270$		0			0
$271$	30.9493			1.88004			0.940018	−	0.341124i	$-0.110807\pi$
$271$	30.9493			1.88004			0.940018	+	0.341124i	$0.110807\pi$
$272$	−1.17850	−	2.04122i	−0.0714569	−	0.123767i
$273$		0			0
$274$	−2.52939	+	4.38103i	−0.152806	+	0.264668i
$275$	5.53077	−	9.57957i	0.333518	−	0.577670i
$276$		0			0
$277$	8.42097	+	14.5856i	0.505967	+	0.876361i	0.999976	+	0.00690414i	$0.00219767\pi$
$277$	8.42097	+	14.5856i	0.505967	+	0.876361i	−0.494009	+	0.869457i	$0.664469\pi$
$278$	−5.32094			−0.319129
$279$		0			0
$280$	−7.73256			−0.462109
$281$	10.8043	+	18.7136i	0.644530	+	1.11636i	0.984410	+	0.175890i	$0.0562804\pi$
$281$	10.8043	+	18.7136i	0.644530	+	1.11636i	−0.339879	+	0.940469i	$0.610386\pi$
$282$		0			0
$283$	−1.95826	+	3.39180i	−0.116406	+	0.201622i	−0.918341	−	0.395790i	$-0.870471\pi$
$283$	−1.95826	+	3.39180i	−0.116406	+	0.201622i	0.801935	+	0.597412i	$0.203804\pi$
$284$	10.5821	−	18.3287i	0.627932	−	1.08761i
$285$		0			0
$286$	0.847007	+	1.46706i	0.0500845	+	0.0867490i
$287$	17.0659			1.00737
$288$		0			0
$289$	−16.1679			−0.951055
$290$	−2.14073	−	3.70785i	−0.125708	−	0.217733i
$291$		0			0
$292$	−4.58441	+	7.94044i	−0.268283	+	0.464679i
$293$	−6.65319	+	11.5237i	−0.388683	+	0.673219i	−0.992273	−	0.124076i	$-0.960403\pi$
$293$	−6.65319	+	11.5237i	−0.388683	+	0.673219i	0.603589	+	0.797295i	$0.293737\pi$
$294$		0			0
$295$	−4.69737	−	8.13609i	−0.273492	−	0.473701i
$296$	−14.8945			−0.865727
$297$		0			0
$298$	7.50893			0.434981
$299$	−2.68611	−	4.65248i	−0.155342	−	0.269060i
$300$		0			0
$301$	−6.89908	+	11.9496i	−0.397656	+	0.688761i
$302$	−3.02364	+	5.23711i	−0.173991	+	0.301362i
$303$		0			0
$304$	1.33815	+	2.31775i	0.0767483	+	0.132932i
$305$	−19.0731			−1.09212
$306$		0			0
$307$	2.50370			0.142894			0.0714469	−	0.997444i	$-0.477238\pi$
$307$	2.50370			0.142894			0.0714469	+	0.997444i	$0.477238\pi$
$308$	9.37067	+	16.2305i	0.533944	+	0.924817i
$309$		0			0
$310$	−0.837756	+	1.45104i	−0.0475813	+	0.0824133i
$311$	−2.05648	+	3.56194i	−0.116613	+	0.201979i	−0.918423	−	0.395599i	$-0.870537\pi$
$311$	−2.05648	+	3.56194i	−0.116613	+	0.201979i	0.801811	+	0.597578i	$0.203870\pi$
$312$		0			0
$313$	1.73971	+	3.01326i	0.0983340	+	0.170319i	0.910995	−	0.412417i	$-0.135315\pi$
$313$	1.73971	+	3.01326i	0.0983340	+	0.170319i	−0.812661	+	0.582736i	$0.801982\pi$
$314$	−1.90715			−0.107626
$315$		0			0
$316$	21.2375			1.19470
$317$	12.5304	+	21.7033i	0.703778	+	1.21898i	0.967131	+	0.254279i	$0.0818382\pi$
$317$	12.5304	+	21.7033i	0.703778	+	1.21898i	−0.263353	+	0.964699i	$0.584828\pi$
$318$		0			0
$319$	−11.1050	+	19.2344i	−0.621761	+	1.07692i
$320$	1.78079	−	3.08442i	0.0995491	−	0.172424i
$321$		0			0
$322$	4.16997	+	7.22261i	0.232384	+	0.402500i
$323$	−0.944794			−0.0525698
$324$		0			0
$325$	3.23938			0.179689
$326$	−1.30030	−	2.25219i	−0.0720172	−	0.124738i
$327$		0			0
$328$	5.07809	−	8.79550i	0.280390	−	0.485650i
$329$	−14.3905	+	24.9251i	−0.793374	+	1.37416i
$330$		0			0
$331$	−0.135093	−	0.233988i	−0.00742539	−	0.0128612i	0.862289	−	0.506417i	$-0.169030\pi$
$331$	−0.135093	−	0.233988i	−0.00742539	−	0.0128612i	−0.869714	+	0.493556i	$0.835697\pi$
$332$	19.2991			1.05917
$333$		0			0
$334$	−8.82241			−0.482741
$335$	6.20596	+	10.7490i	0.339068	+	0.587283i
$336$		0			0
$337$	12.3311	−	21.3581i	0.671718	−	1.16345i	−0.305699	−	0.952128i	$-0.598890\pi$
$337$	12.3311	−	21.3581i	0.671718	−	1.16345i	0.977417	−	0.211321i	$-0.0677765\pi$
$338$	−0.248047	+	0.429630i	−0.0134920	+	0.0233688i
$339$		0			0
$340$	1.06141	+	1.83842i	0.0575633	+	0.0997025i
$341$	8.69169			0.470681
$342$		0			0
$343$	−13.1667			−0.710934
$344$	4.10574	+	7.11135i	0.221367	+	0.383418i
$345$		0			0
$346$	0.392116	−	0.679165i	0.0210803	−	0.0365121i
$347$	−13.0725	+	22.6423i	−0.701771	+	1.21550i	0.266074	+	0.963953i	$0.414274\pi$
$347$	−13.0725	+	22.6423i	−0.701771	+	1.21550i	−0.967844	+	0.251550i	$0.919060\pi$
$348$		0			0
$349$	9.97134	+	17.2709i	0.533753	+	0.924488i	0.999223	+	0.0394240i	$0.0125523\pi$
$349$	9.97134	+	17.2709i	0.533753	+	0.924488i	−0.465469	+	0.885064i	$0.654114\pi$
$350$	−5.02889			−0.268805
$351$		0			0
$352$	17.0955			0.911191
$353$	8.57672	+	14.8553i	0.456493	+	0.790669i	0.998773	−	0.0495290i	$-0.0157720\pi$
$353$	8.57672	+	14.8553i	0.456493	+	0.790669i	−0.542280	+	0.840198i	$0.682439\pi$
$354$		0			0
$355$	−8.00574	+	13.8663i	−0.424901	+	0.735949i
$356$	7.30685	−	12.6558i	0.387262	−	0.670758i
$357$		0			0
$358$	3.77702	+	6.54198i	0.199621	+	0.345755i
$359$	−3.15925			−0.166739			−0.0833694	−	0.996519i	$-0.526568\pi$
$359$	−3.15925			−0.166739			−0.0833694	+	0.996519i	$0.526568\pi$
$360$		0			0
$361$	−17.9272			−0.943537
$362$	5.69828	+	9.86972i	0.299495	+	0.518741i
$363$		0			0
$364$	−2.74421	+	4.75312i	−0.143836	+	0.249131i
$365$	3.46827	−	6.00723i	0.181538	−	0.314433i
$366$		0			0
$367$	−2.01971	−	3.49824i	−0.105428	−	0.182607i	0.808485	−	0.588517i	$-0.200288\pi$
$367$	−2.01971	−	3.49824i	−0.105428	−	0.182607i	−0.913913	+	0.405910i	$0.866955\pi$
$368$	−13.8814			−0.723616
$369$		0			0
$370$	5.26475			0.273701
$371$	−19.0695	−	33.0294i	−0.990041	−	1.71480i
$372$		0			0
$373$	−5.92273	+	10.2585i	−0.306667	+	0.531164i	−0.977631	−	0.210327i	$-0.932547\pi$
$373$	−5.92273	+	10.2585i	−0.306667	+	0.531164i	0.670964	+	0.741490i	$0.265881\pi$
$374$	−0.772622	+	1.33822i	−0.0399513	+	0.0691977i
$375$		0			0
$376$	8.56399	+	14.8333i	0.441654	+	0.764967i
$377$	−6.50423			−0.334985
$378$		0			0
$379$	0.705984			0.0362640			0.0181320	−	0.999836i	$-0.494228\pi$
$379$	0.705984			0.0362640			0.0181320	+	0.999836i	$0.494228\pi$
$380$	−1.20521	−	2.08748i	−0.0618258	−	0.107086i
$381$		0			0
$382$	−1.75448	+	3.03885i	−0.0897672	+	0.155481i
$383$	12.4042	−	21.4847i	0.633826	−	1.09782i	−0.352937	−	0.935647i	$-0.614817\pi$
$383$	12.4042	−	21.4847i	0.633826	−	1.09782i	0.986763	−	0.162171i	$-0.0518497\pi$
$384$		0			0
$385$	−7.08925	−	12.2789i	−0.361302	−	0.625793i
$386$	3.97502			0.202323
$387$		0			0
$388$	−24.6105			−1.24941
$389$	5.18742	+	8.98488i	0.263013	+	0.455551i	0.967041	−	0.254620i	$-0.0819505\pi$
$389$	5.18742	+	8.98488i	0.263013	+	0.455551i	−0.704028	+	0.710172i	$0.748617\pi$
$390$		0			0
$391$	2.45022	−	4.24390i	0.123913	−	0.214623i
$392$	2.60015	−	4.50359i	0.131327	−	0.227466i
$393$		0			0
$394$	2.55455	+	4.42461i	0.128696	+	0.222908i
$395$	−16.0669			−0.808415
$396$		0			0
$397$	19.5931			0.983351			0.491675	−	0.870779i	$-0.336385\pi$
$397$	19.5931			0.983351			0.491675	+	0.870779i	$0.336385\pi$
$398$	1.38148	+	2.39280i	0.0692476	+	0.119940i
$399$		0			0
$400$	4.18515	−	7.24889i	0.209257	−	0.362444i
$401$	11.1544	−	19.3199i	0.557022	−	0.964790i	−0.440721	−	0.897644i	$-0.645277\pi$
$401$	11.1544	−	19.3199i	0.557022	−	0.964790i	0.997743	−	0.0671462i	$-0.0213894\pi$
$402$		0			0
$403$	1.27269	+	2.20436i	0.0633970	+	0.109807i
$404$	20.7622			1.03296
$405$		0			0
$406$	10.0973			0.501120
$407$	−13.6554	−	23.6518i	−0.676873	−	1.17238i
$408$		0			0
$409$	1.74980	−	3.03074i	0.0865220	−	0.149860i	−0.819517	−	0.573055i	$-0.805758\pi$
$409$	1.74980	−	3.03074i	0.0865220	−	0.149860i	0.906039	+	0.423195i	$0.139091\pi$
$410$	−1.79494	+	3.10893i	−0.0886459	+	0.153539i
$411$		0			0
$412$	7.19611	+	12.4640i	0.354527	+	0.614058i
$413$	22.1564			1.09024
$414$		0			0
$415$	−14.6004			−0.716708
$416$	2.50321	+	4.33569i	0.122730	+	0.212575i
$417$		0			0
$418$	0.877291	−	1.51951i	0.0429097	−	0.0743218i
$419$	−10.6248	+	18.4026i	−0.519054	+	0.899028i	0.480701	+	0.876885i	$0.340382\pi$
$419$	−10.6248	+	18.4026i	−0.519054	+	0.899028i	−0.999755	+	0.0221430i	$0.992951\pi$
$420$		0			0
$421$	−1.11396	−	1.92943i	−0.0542911	−	0.0940349i	0.837603	−	0.546280i	$-0.183957\pi$
$421$	−1.11396	−	1.92943i	−0.0542911	−	0.0940349i	−0.891894	+	0.452245i	$0.850623\pi$
$422$	−4.67890			−0.227765
$423$		0			0
$424$	−22.6971			−1.10227
$425$	1.47745	+	2.55902i	0.0716668	+	0.124131i
$426$		0			0
$427$	22.4908	−	38.9552i	1.08841	−	1.88517i
$428$	−0.137339	+	0.237878i	−0.00663852	+	0.0114983i
$429$		0			0
$430$	−1.45125	−	2.51364i	−0.0699854	−	0.121218i
$431$	−10.3044			−0.496343			−0.248172	−	0.968716i	$-0.579830\pi$
$431$	−10.3044			−0.496343			−0.248172	+	0.968716i	$0.579830\pi$
$432$		0			0
$433$	−10.0517			−0.483056			−0.241528	−	0.970394i	$-0.577649\pi$
$433$	−10.0517			−0.483056			−0.241528	+	0.970394i	$0.577649\pi$
$434$	−1.97574	−	3.42209i	−0.0948387	−	0.164265i
$435$		0			0
$436$	−6.60134	+	11.4339i	−0.316147	+	0.547583i
$437$	−2.78215	+	4.81883i	−0.133088	+	0.230516i
$438$		0			0
$439$	−7.86943	−	13.6303i	−0.375587	−	0.650536i	0.614827	−	0.788662i	$-0.289226\pi$
$439$	−7.86943	−	13.6303i	−0.375587	−	0.650536i	−0.990415	+	0.138125i	$0.955892\pi$
$440$	−8.43783			−0.402258
$441$		0			0
$442$	−0.452527			−0.0215245
$443$	−4.77962	−	8.27855i	−0.227087	−	0.393326i	0.729857	−	0.683600i	$-0.239587\pi$
$443$	−4.77962	−	8.27855i	−0.227087	−	0.393326i	−0.956943	+	0.290275i	$0.906253\pi$
$444$		0			0
$445$	−5.52790	+	9.57460i	−0.262047	+	0.453879i
$446$	4.61999	−	8.00205i	0.218763	−	0.378908i
$447$		0			0
$448$	4.19977	+	7.27421i	0.198420	+	0.343674i
$449$	15.7163			0.741696			0.370848	−	0.928694i	$-0.379067\pi$
$449$	15.7163			0.741696			0.370848	+	0.928694i	$0.379067\pi$
$450$		0			0
$451$	18.6225			0.876898
$452$	−14.9725	−	25.9331i	−0.704246	−	1.21979i
$453$		0			0
$454$	−3.49769	+	6.05817i	−0.164155	+	0.284324i
$455$	2.07610	−	3.59590i	0.0973289	−	0.168579i
$456$		0			0
$457$	−16.4521	−	28.4958i	−0.769594	−	1.33298i	−0.937783	−	0.347222i	$-0.887125\pi$
$457$	−16.4521	−	28.4958i	−0.769594	−	1.33298i	0.168189	−	0.985755i	$-0.446208\pi$
$458$	1.01734			0.0475370
$459$		0			0
$460$	12.5023			0.582921
$461$	6.38861	+	11.0654i	0.297547	+	0.515367i	0.975574	−	0.219670i	$-0.0704982\pi$
$461$	6.38861	+	11.0654i	0.297547	+	0.515367i	−0.678027	+	0.735037i	$0.737165\pi$
$462$		0			0
$463$	2.63733	−	4.56799i	0.122567	−	0.212293i	−0.798212	−	0.602376i	$-0.794221\pi$
$463$	2.63733	−	4.56799i	0.122567	−	0.212293i	0.920779	+	0.390084i	$0.127554\pi$
$464$	−8.40319	+	14.5547i	−0.390108	+	0.675687i
$465$		0			0
$466$	1.98803	+	3.44336i	0.0920936	+	0.159511i
$467$	18.5837			0.859953			0.429977	−	0.902840i	$-0.358522\pi$
$467$	18.5837			0.859953			0.429977	+	0.902840i	$0.358522\pi$
$468$		0			0
$469$	−29.2720			−1.35165
$470$	−3.02710	−	5.24309i	−0.139630	−	0.241846i
$471$		0			0
$472$	6.59278	−	11.4190i	0.303457	−	0.525603i
$473$	−7.52833	+	13.0394i	−0.346153	+	0.599554i
$474$		0			0
$475$	−1.67760	−	2.90570i	−0.0769738	−	0.133323i
$476$	−5.00643			−0.229469
$477$		0			0
$478$	1.73396			0.0793093
$479$	−0.541178	−	0.937348i	−0.0247271	−	0.0428285i	0.853397	−	0.521261i	$-0.174538\pi$
$479$	−0.541178	−	0.937348i	−0.0247271	−	0.0428285i	−0.878124	+	0.478433i	$0.841205\pi$
$480$		0			0
$481$	3.99900	−	6.92647i	0.182339	−	0.315820i
$482$	−1.76804	+	3.06233i	−0.0805318	+	0.139485i
$483$		0			0
$484$	0.578953	+	1.00278i	0.0263160	+	0.0455807i
$485$	18.6188			0.845434
$486$		0			0
$487$	17.4217			0.789451			0.394726	−	0.918799i	$-0.370840\pi$
$487$	17.4217			0.789451			0.394726	+	0.918799i	$0.370840\pi$
$488$	−13.3846	−	23.1828i	−0.605892	−	1.04944i
$489$		0			0
$490$	−0.919071	+	1.59188i	−0.0415194	+	0.0719137i
$491$	−8.40485	+	14.5576i	−0.379306	+	0.656977i	−0.990961	−	0.134147i	$-0.957170\pi$
$491$	−8.40485	+	14.5576i	−0.379306	+	0.656977i	0.611656	+	0.791124i	$0.290504\pi$
$492$		0			0
$493$	−2.96651	−	5.13815i	−0.133605	−	0.231411i
$494$	0.513832			0.0231184
$495$		0			0
$496$	6.57702			0.295317
$497$	−18.8805	−	32.7021i	−0.846908	−	1.46689i
$498$		0			0
$499$	10.4420	−	18.0861i	0.467449	−	0.809646i	−0.531859	−	0.846833i	$-0.678506\pi$
$499$	10.4420	−	18.0861i	0.467449	−	0.809646i	0.999308	+	0.0371871i	$0.0118397\pi$
$500$	−9.58737	+	16.6058i	−0.428760	+	0.742635i
$501$		0			0
$502$	−2.68033	−	4.64247i	−0.119629	−	0.207203i
$503$	−2.96223			−0.132079			−0.0660397	−	0.997817i	$-0.521036\pi$
$503$	−2.96223			−0.132079			−0.0660397	+	0.997817i	$0.521036\pi$
$504$		0			0
$505$	−15.7073			−0.698967
$506$	4.55031	+	7.88136i	0.202286	+	0.350369i
$507$		0			0
$508$	0.417956	−	0.723920i	0.0185438	−	0.0321188i
$509$	10.4883	−	18.1663i	0.464885	−	0.805205i	−0.534311	−	0.845288i	$-0.679429\pi$
$509$	10.4883	−	18.1663i	0.464885	−	0.805205i	0.999196	+	0.0400828i	$0.0127622\pi$
$510$		0			0
$511$	8.17950	+	14.1673i	0.361840	+	0.626725i
$512$	22.5601			0.997027
$513$		0			0
$514$	−11.9274			−0.526096
$515$	−5.44411	−	9.42948i	−0.239896	−	0.415513i
$516$		0			0
$517$	−15.7030	+	27.1984i	−0.690618	+	1.19619i
$518$	−6.20813	+	10.7528i	−0.272769	+	0.472450i
$519$		0			0
$520$	−1.23551	−	2.13997i	−0.0541809	−	0.0938440i
$521$	−34.1685			−1.49695			−0.748474	−	0.663164i	$-0.769213\pi$
$521$	−34.1685			−1.49695			−0.748474	+	0.663164i	$0.769213\pi$
$522$		0			0
$523$	19.3302			0.845250			0.422625	−	0.906305i	$-0.361109\pi$
$523$	19.3302			0.845250			0.422625	+	0.906305i	$0.361109\pi$
$524$	−7.72677	−	13.3832i	−0.337545	−	0.584646i
$525$		0			0
$526$	−0.291227	+	0.504420i	−0.0126981	+	0.0219937i
$527$	−1.16092	+	2.01077i	−0.0505704	+	0.0875905i
$528$		0			0
$529$	−2.93039	−	5.07558i	−0.127408	−	0.220678i
$530$	8.02270			0.348484
$531$		0			0
$532$	5.68467			0.246462
$533$	2.72681	+	4.72297i	0.118111	+	0.204574i
$534$		0			0
$535$	0.103902	−	0.179963i	0.00449207	−	0.00778049i
$536$	−8.71009	+	15.0863i	−0.376218	+	0.651629i
$537$		0			0
$538$	−4.08656	−	7.07812i	−0.176184	−	0.305160i
$539$	9.53533			0.410716
$540$		0			0
$541$	8.72119			0.374953			0.187477	−	0.982269i	$-0.439969\pi$
$541$	8.72119			0.374953			0.187477	+	0.982269i	$0.439969\pi$
$542$	−7.67688	−	13.2968i	−0.329750	−	0.571144i
$543$		0			0
$544$	−2.28338	+	3.95493i	−0.0978991	+	0.169566i
$545$	4.99415	−	8.65013i	0.213926	−	0.370531i
$546$		0			0
$547$	10.8599	+	18.8099i	0.464335	+	0.804252i	0.999171	−	0.0407040i	$-0.0129601\pi$
$547$	10.8599	+	18.8099i	0.464335	+	0.804252i	−0.534836	+	0.844956i	$0.679627\pi$
$548$	−17.8848			−0.764001
$549$		0			0
$550$	−5.48756			−0.233990
$551$	3.36839	+	5.83423i	0.143498	+	0.248547i
$552$		0			0
$553$	18.9459	−	32.8153i	0.805663	−	1.39545i
$554$	4.17759	−	7.23580i	0.177489	−	0.307420i
$555$		0			0
$556$	−9.40582	−	16.2914i	−0.398896	−	0.690908i
$557$	−18.3186			−0.776183			−0.388091	−	0.921621i	$-0.626865\pi$
$557$	−18.3186			−0.776183			−0.388091	+	0.921621i	$0.626865\pi$
$558$		0			0
$559$	−4.40936			−0.186496
$560$	−5.36446	−	9.29151i	−0.226690	−	0.392638i
$561$		0			0
$562$	5.35995	−	9.28370i	0.226096	−	0.391609i
$563$	−22.4531	+	38.8899i	−0.946286	+	1.63902i	−0.193131	+	0.981173i	$0.561864\pi$
$563$	−22.4531	+	38.8899i	−0.946286	+	1.63902i	−0.753155	+	0.657843i	$0.771469\pi$
$564$		0			0
$565$	11.3272	+	19.6193i	0.476540	+	0.825391i
$566$	1.94296			0.0816688
$567$		0			0
$568$	−22.4722			−0.942911
$569$	17.1457	+	29.6973i	0.718786	+	1.24497i	0.961481	+	0.274871i	$0.0886352\pi$
$569$	17.1457	+	29.6973i	0.718786	+	1.24497i	−0.242695	+	0.970103i	$0.578031\pi$
$570$		0			0
$571$	−7.91642	+	13.7116i	−0.331292	+	0.573814i	−0.982765	−	0.184857i	$-0.940818\pi$
$571$	−7.91642	+	13.7116i	−0.331292	+	0.573814i	0.651474	+	0.758671i	$0.274151\pi$
$572$	−2.99451	+	5.18664i	−0.125207	+	0.216864i
$573$		0			0
$574$	−4.23315	−	7.33203i	−0.176688	−	0.306033i
$575$	17.4027			0.725743
$576$		0			0
$577$	17.1698			0.714789			0.357395	−	0.933953i	$-0.383665\pi$
$577$	17.1698			0.714789			0.357395	+	0.933953i	$0.383665\pi$
$578$	4.01041	+	6.94623i	0.166811	+	0.288925i
$579$		0			0
$580$	7.56834	−	13.1088i	0.314258	−	0.544311i
$581$	17.2167	−	29.8202i	0.714268	−	1.23715i
$582$		0			0
$583$	−20.8088	−	36.0419i	−0.861813	−	1.49270i
$584$	9.73547			0.402856
$585$		0			0
$586$	6.60121			0.272694
$587$	−7.32790	−	12.6923i	−0.302455	−	0.523867i	0.674237	−	0.738515i	$-0.264473\pi$
$587$	−7.32790	−	12.6923i	−0.302455	−	0.523867i	−0.976691	+	0.214648i	$0.931139\pi$
$588$		0			0
$589$	1.31819	−	2.28317i	0.0543151	−	0.0940765i
$590$	−2.33034	+	4.03626i	−0.0959385	+	0.166170i
$591$		0			0
$592$	−10.3331	−	17.8974i	−0.424687	−	0.735579i
$593$	−20.3341			−0.835021			−0.417510	−	0.908672i	$-0.637097\pi$
$593$	−20.3341			−0.835021			−0.417510	+	0.908672i	$0.637097\pi$
$594$		0			0
$595$	3.78754			0.155274
$596$	13.2735	+	22.9904i	0.543705	+	0.941725i
$597$		0			0
$598$	−1.33256	+	2.30807i	−0.0544926	+	0.0943839i
$599$	−22.9738	+	39.7918i	−0.938684	+	1.62585i	−0.170754	+	0.985314i	$0.554620\pi$
$599$	−22.9738	+	39.7918i	−0.938684	+	1.62585i	−0.767930	+	0.640534i	$0.778713\pi$
$600$		0			0
$601$	−12.0518	−	20.8743i	−0.491602	−	0.851480i	0.508351	−	0.861150i	$-0.330255\pi$
$601$	−12.0518	−	20.8743i	−0.491602	−	0.851480i	−0.999953	+	0.00966978i	$0.996922\pi$
$602$	6.84518			0.278989
$603$		0			0
$604$	−21.3796			−0.869923
$605$	−0.437999	−	0.758636i	−0.0178072	−	0.0308429i
$606$		0			0
$607$	18.3605	−	31.8013i	0.745229	−	1.29077i	−0.204859	−	0.978791i	$-0.565674\pi$
$607$	18.3605	−	31.8013i	0.745229	−	1.29077i	0.950088	−	0.311983i	$-0.100993\pi$
$608$	2.59272	−	4.49072i	0.105149	−	0.182123i
$609$		0			0
$610$	4.73103	+	8.19438i	0.191554	+	0.331781i
$611$	−9.19730			−0.372083
$612$		0			0
$613$	12.6282			0.510047			0.255024	−	0.966935i	$-0.417917\pi$
$613$	12.6282			0.510047			0.255024	+	0.966935i	$0.417917\pi$
$614$	−0.621035	−	1.07566i	−0.0250629	−	0.0434103i
$615$		0			0
$616$	9.94979	−	17.2335i	0.400888	−	0.694359i
$617$	5.16646	−	8.94857i	0.207994	−	0.360256i	−0.743089	−	0.669193i	$-0.766640\pi$
$617$	5.16646	−	8.94857i	0.207994	−	0.360256i	0.951082	+	0.308937i	$0.0999733\pi$
$618$		0			0
$619$	18.3253	+	31.7403i	0.736554	+	1.27575i	0.954038	+	0.299685i	$0.0968817\pi$
$619$	18.3253	+	31.7403i	0.736554	+	1.27575i	−0.217484	+	0.976064i	$0.569785\pi$
$620$	−5.92360			−0.237898
$621$		0			0
$622$	2.04042			0.0818133
$623$	−13.0369	−	22.5805i	−0.522311	−	0.904669i
$624$		0			0
$625$	−0.845270	+	1.46405i	−0.0338108	+	0.0585620i
$626$	0.863057	−	1.49486i	0.0344947	−	0.0597466i
$627$		0			0
$628$	−3.37126	−	5.83920i	−0.134528	−	0.233009i
$629$	7.29561			0.290895
$630$		0			0
$631$	5.45904			0.217321			0.108660	−	0.994079i	$-0.465344\pi$
$631$	5.45904			0.217321			0.108660	+	0.994079i	$0.465344\pi$
$632$	−11.2750	−	19.5288i	−0.448495	−	0.776816i
$633$		0			0
$634$	6.21626	−	10.7669i	0.246879	−	0.427607i
$635$	−0.316198	+	0.547672i	−0.0125480	+	0.0217337i
$636$		0			0
$637$	1.39622	+	2.41832i	0.0553201	+	0.0958173i
$638$	11.0183			0.436217
$639$		0			0
$640$	−15.0528			−0.595012
$641$	3.31269	+	5.73775i	0.130844	+	0.226628i	0.924002	−	0.382388i	$-0.124898\pi$
$641$	3.31269	+	5.73775i	0.130844	+	0.226628i	−0.793158	+	0.609015i	$0.791565\pi$
$642$		0			0
$643$	−15.7291	+	27.2436i	−0.620294	+	1.07438i	0.369137	+	0.929375i	$0.379653\pi$
$643$	−15.7291	+	27.2436i	−0.620294	+	1.07438i	−0.989431	+	0.145006i	$0.953680\pi$
$644$	−14.7425	+	25.5348i	−0.580937	+	1.00621i
$645$		0			0
$646$	0.234353	+	0.405912i	0.00922051	+	0.0159704i
$647$	−20.2079			−0.794456			−0.397228	−	0.917720i	$-0.630028\pi$
$647$	−20.2079			−0.794456			−0.397228	+	0.917720i	$0.630028\pi$
$648$		0			0
$649$	24.1772			0.949038
$650$	−0.803520	−	1.39174i	−0.0315166	−	0.0545884i
$651$		0			0
$652$	4.59710	−	7.96241i	0.180036	−	0.311832i
$653$	−1.29686	+	2.24622i	−0.0507500	+	0.0879015i	−0.890284	−	0.455405i	$-0.849494\pi$
$653$	−1.29686	+	2.24622i	−0.0507500	+	0.0879015i	0.839534	+	0.543306i	$0.182828\pi$
$654$		0			0
$655$	5.84558	+	10.1248i	0.228406	+	0.395610i
$656$	14.0917			0.550187
$657$		0			0
$658$	14.2781			0.556617
$659$	−7.95387	−	13.7765i	−0.309839	−	0.536657i	0.668488	−	0.743723i	$-0.266942\pi$
$659$	−7.95387	−	13.7765i	−0.309839	−	0.536657i	−0.978327	+	0.207066i	$0.933608\pi$
$660$		0			0
$661$	−18.5869	+	32.1934i	−0.722945	+	1.25218i	0.236869	+	0.971542i	$0.423879\pi$
$661$	−18.5869	+	32.1934i	−0.722945	+	1.25218i	−0.959814	+	0.280636i	$0.909455\pi$
$662$	−0.0670189	+	0.116080i	−0.00260476	+	0.00451158i
$663$		0			0
$664$	−10.2459	−	17.7464i	−0.397618	−	0.688694i
$665$	−4.30066			−0.166772
$666$		0			0
$667$	−34.9422			−1.35297
$668$	−15.5954	−	27.0120i	−0.603403	−	1.04512i
$669$		0			0
$670$	3.07874	−	5.33253i	0.118942	−	0.206014i
$671$	24.5421	−	42.5082i	0.947439	−	1.64101i
$672$		0			0
$673$	20.1992	+	34.9860i	0.778621	+	1.34861i	0.932737	+	0.360558i	$0.117414\pi$
$673$	20.1992	+	34.9860i	0.778621	+	1.34861i	−0.154116	+	0.988053i	$0.549253\pi$
$674$	−12.2348			−0.471265
$675$		0			0
$676$	−1.75389			−0.0674573
$677$	−0.401269	−	0.695018i	−0.0154220	−	0.0267117i	0.858211	−	0.513296i	$-0.171576\pi$
$677$	−0.401269	−	0.695018i	−0.0154220	−	0.0267117i	−0.873633	+	0.486585i	$0.838243\pi$
$678$		0			0
$679$	−21.9550	+	38.0272i	−0.842556	+	1.45935i
$680$	1.12701	−	1.95204i	0.0432189	−	0.0748573i
$681$		0			0
$682$	−2.15595	−	3.73421i	−0.0825555	−	0.142990i
$683$	50.3853			1.92794			0.963971	−	0.266008i	$-0.0857049\pi$
$683$	50.3853			1.92794			0.963971	+	0.266008i	$0.0857049\pi$
$684$		0			0
$685$	13.5305			0.516974
$686$	3.26596	+	5.65680i	0.124695	+	0.215978i
$687$		0			0
$688$	−5.69671	+	9.86698i	−0.217185	+	0.376175i
$689$	6.09389	−	10.5549i	0.232159	−	0.402111i
$690$		0			0
$691$	8.72144	+	15.1060i	0.331779	+	0.574658i	0.982861	−	0.184349i	$-0.0590178\pi$
$691$	8.72144	+	15.1060i	0.331779	+	0.574658i	−0.651082	+	0.759008i	$0.725684\pi$
$692$	2.77257			0.105397
$693$		0			0
$694$	12.9704			0.492350
$695$	7.11584	+	12.3250i	0.269919	+	0.467514i
$696$		0			0
$697$	−2.48734	+	4.30819i	−0.0942146	+	0.163184i
$698$	4.94672	−	8.56797i	0.187236	−	0.324302i
$699$		0			0
$700$	−8.88956	−	15.3972i	−0.335994	−	0.581959i
$701$	29.9544			1.13136			0.565680	−	0.824625i	$-0.308614\pi$
$701$	29.9544			1.13136			0.565680	+	0.824625i	$0.308614\pi$
$702$		0			0
$703$	−8.28397			−0.312436
$704$	4.58282	+	7.93768i	0.172722	+	0.299163i
$705$		0			0
$706$	4.25486	−	7.36964i	0.160134	−	0.277360i
$707$	18.5219	−	32.0809i	0.696588	−	1.20652i
$708$		0			0
$709$	−1.71866	−	2.97681i	−0.0645458	−	0.111797i	0.831947	−	0.554856i	$-0.187227\pi$
$709$	−1.71866	−	2.97681i	−0.0645458	−	0.111797i	−0.896492	+	0.443059i	$0.853893\pi$
$710$	7.94320			0.298103
$711$		0			0
$712$	−15.5168			−0.581518
$713$	6.83715	+	11.8423i	0.256053	+	0.443497i
$714$		0			0
$715$	2.26545	−	3.92388i	0.0847231	−	0.146745i
$716$	−13.3533	+	23.1285i	−0.499035	+	0.864354i
$717$		0			0
$718$	0.783643	+	1.35731i	0.0292453	+	0.0506543i
$719$	34.0368			1.26936			0.634680	−	0.772775i	$-0.281132\pi$
$719$	34.0368			1.26936			0.634680	+	0.772775i	$0.281132\pi$
$720$		0			0
$721$	25.6785			0.956319
$722$	4.44679	+	7.70207i	0.165492	+	0.286641i
$723$		0			0
$724$	−20.1457	+	34.8934i	−0.748710	+	1.29680i
$725$	10.5349	−	18.2469i	0.391255	−	0.677673i
$726$		0			0
$727$	18.5696	+	32.1635i	0.688708	+	1.19288i	0.972256	+	0.233919i	$0.0751551\pi$
$727$	18.5696	+	32.1635i	0.688708	+	1.19288i	−0.283548	+	0.958958i	$0.591512\pi$
$728$	5.82762			0.215986
$729$		0			0
$730$	−3.44118			−0.127364
$731$	−2.01106	−	3.48326i	−0.0743819	−	0.128833i
$732$		0			0
$733$	−13.6999	+	23.7290i	−0.506018	+	0.876449i	0.493958	+	0.869486i	$0.335550\pi$
$733$	−13.6999	+	23.7290i	−0.506018	+	0.876449i	−0.999976	+	0.00696311i	$0.997784\pi$
$734$	−1.00197	+	1.73546i	−0.0369833	+	0.0640569i
$735$		0			0
$736$	13.4478	+	23.2923i	0.495693	+	0.858566i
$737$	−31.9418			−1.17659
$738$		0			0
$739$	−22.9544			−0.844390			−0.422195	−	0.906505i	$-0.638740\pi$
$739$	−22.9544			−0.844390			−0.422195	+	0.906505i	$0.638740\pi$
$740$	9.30649	+	16.1193i	0.342113	+	0.592558i
$741$		0			0
$742$	−9.46028	+	16.3857i	−0.347298	+	0.601537i
$743$	−8.88960	+	15.3972i	−0.326128	+	0.564870i	−0.981740	−	0.190228i	$-0.939077\pi$
$743$	−8.88960	+	15.3972i	−0.326128	+	0.564870i	0.655612	+	0.755098i	$0.272411\pi$
$744$		0			0
$745$	−10.0419	−	17.3931i	−0.367907	−	0.637234i
$746$	5.87646			0.215153
$747$		0			0
$748$	−5.46306			−0.199749
$749$	0.245040	+	0.424421i	0.00895355	+	0.0155080i
$750$		0			0
$751$	−13.9878	+	24.2276i	−0.510424	+	0.884079i	0.489504	+	0.872001i	$0.337178\pi$
$751$	−13.9878	+	24.2276i	−0.510424	+	0.884079i	−0.999927	+	0.0120781i	$0.996155\pi$
$752$	−11.8825	+	20.5811i	−0.433311	+	0.750516i
$753$		0			0
$754$	1.61335	+	2.79441i	0.0587549	+	0.101766i
$755$	16.1744			0.588648
$756$		0			0
$757$	25.6113			0.930860			0.465430	−	0.885085i	$-0.345900\pi$
$757$	25.6113			0.930860			0.465430	+	0.885085i	$0.345900\pi$
$758$	−0.175117	−	0.303312i	−0.00636054	−	0.0110168i
$759$		0			0
$760$	−1.27969	+	2.21649i	−0.0464192	+	0.0804005i
$761$	2.44851	−	4.24094i	0.0887583	−	0.153734i	−0.818228	−	0.574894i	$-0.805043\pi$
$761$	2.44851	−	4.24094i	0.0887583	−	0.153734i	0.906987	+	0.421160i	$0.138377\pi$
$762$		0			0
$763$	11.7781	+	20.4003i	0.426396	+	0.738539i
$764$	−12.4056			−0.448819
$765$		0			0
$766$	−12.3073			−0.444681
$767$	3.54016	+	6.13174i	0.127828	+	0.221404i
$768$		0			0
$769$	10.0123	−	17.3418i	0.361053	−	0.625362i	−0.627081	−	0.778954i	$-0.715751\pi$
$769$	10.0123	−	17.3418i	0.361053	−	0.625362i	0.988134	+	0.153592i	$0.0490840\pi$
$770$	−3.51693	+	6.09151i	−0.126742	+	0.219523i
$771$		0			0
$772$	7.02664	+	12.1705i	0.252894	+	0.438026i
$773$	0.827218			0.0297530			0.0148765	−	0.999889i	$-0.495264\pi$
$773$	0.827218			0.0297530			0.0148765	+	0.999889i	$0.495264\pi$
$774$		0			0
$775$	−8.24544			−0.296185
$776$	13.0657	+	22.6305i	0.469033	+	0.812388i
$777$		0			0
$778$	2.57345	−	4.45734i	0.0922626	−	0.159804i
$779$	2.82430	−	4.89184i	0.101191	−	0.175268i
$780$		0			0
$781$	−20.6026	−	35.6848i	−0.737219	−	1.27690i
$782$	−2.43107			−0.0869350
$783$		0			0
$784$	7.21541			0.257693
$785$	2.55048	+	4.41756i	0.0910306	+	0.157670i
$786$		0			0
$787$	2.10102	−	3.63908i	0.0748934	−	0.129719i	−0.826147	−	0.563455i	$-0.809472\pi$
$787$	2.10102	−	3.63908i	0.0748934	−	0.129719i	0.901040	+	0.433736i	$0.142805\pi$
$788$	−9.03135	+	15.6428i	−0.321728	+	0.557250i
$789$		0			0
$790$	3.98535	+	6.90283i	0.141792	+	0.245592i
$791$	−53.4277			−1.89967
$792$		0			0
$793$	14.3744			0.510450
$794$	−4.86002	−	8.41779i	−0.172476	−	0.298736i
$795$		0			0
$796$	−4.88410	+	8.45951i	−0.173112	+	0.299840i
$797$	−6.74376	+	11.6805i	−0.238876	+	0.413746i	−0.960392	−	0.278652i	$-0.910112\pi$
$797$	−6.74376	+	11.6805i	−0.238876	+	0.413746i	0.721516	+	0.692398i	$0.243446\pi$
$798$		0			0
$799$	−4.19479	−	7.26560i	−0.148401	−	0.257038i
$800$	−16.2178			−0.573384
$801$		0			0
$802$	−11.0672			−0.390797
$803$	8.92553	+	15.4595i	0.314975	+	0.545553i
$804$		0			0
$805$	11.1533	−	19.3180i	0.393101	−	0.680870i
$806$	0.631372	−	1.09357i	0.0222391	−	0.0385193i
$807$		0			0
$808$	−11.0226	−	19.0918i	−0.387775	−	0.671646i
$809$	−3.02951			−0.106512			−0.0532559	−	0.998581i	$-0.516960\pi$
$809$	−3.02951			−0.106512			−0.0532559	+	0.998581i	$0.516960\pi$
$810$		0			0
$811$	−31.9363			−1.12143			−0.560717	−	0.828008i	$-0.689474\pi$
$811$	−31.9363			−1.12143			−0.560717	+	0.828008i	$0.689474\pi$
$812$	17.8490	+	30.9154i	0.626377	+	1.08492i
$813$		0			0
$814$	−6.77436	+	11.7335i	−0.237441	+	0.411260i
$815$	−3.47787	+	6.02385i	−0.121825	+	0.211006i
$816$		0			0
$817$	2.28351	+	3.95515i	0.0798899	+	0.138373i
$818$	−1.73613			−0.0607023
$819$		0			0
$820$	−12.6917			−0.443213
$821$	11.9354	+	20.6727i	0.416548	+	0.721483i	0.995590	−	0.0938153i	$-0.0299063\pi$
$821$	11.9354	+	20.6727i	0.416548	+	0.721483i	−0.579041	+	0.815298i	$0.696573\pi$
$822$		0			0
$823$	9.40358	−	16.2875i	0.327788	−	0.567746i	−0.654285	−	0.756248i	$-0.727030\pi$
$823$	9.40358	−	16.2875i	0.327788	−	0.567746i	0.982073	+	0.188503i	$0.0603635\pi$
$824$	7.64083	−	13.2343i	0.266181	−	0.461039i
$825$		0			0
$826$	−5.49582	−	9.51903i	−0.191224	−	0.331209i
$827$	53.8381			1.87213			0.936067	−	0.351822i	$-0.114438\pi$
$827$	53.8381			1.87213			0.936067	+	0.351822i	$0.114438\pi$
$828$		0			0
$829$	31.1172			1.08074			0.540372	−	0.841426i	$-0.318283\pi$
$829$	31.1172			1.08074			0.540372	+	0.841426i	$0.318283\pi$
$830$	3.62160	+	6.27279i	0.125707	+	0.217732i
$831$		0			0
$832$	−1.34209	+	2.32456i	−0.0465284	+	0.0805896i
$833$	−1.27360	+	2.20594i	−0.0441276	+	0.0764313i
$834$		0			0
$835$	11.7985	+	20.4355i	0.408303	+	0.707201i
$836$	6.20315			0.214541
$837$		0			0
$838$	10.5418			0.364159
$839$	26.0416	+	45.1054i	0.899056	+	1.55721i	0.828704	+	0.559688i	$0.189079\pi$
$839$	26.0416	+	45.1054i	0.899056	+	1.55721i	0.0703519	+	0.997522i	$0.477588\pi$
$840$		0			0
$841$	−6.65250	+	11.5225i	−0.229397	+	0.397327i
$842$	−0.552629	+	0.957181i	−0.0190448	+	0.0329866i
$843$		0			0
$844$	−8.27089	−	14.3256i	−0.284696	−	0.493108i
$845$	1.32688			0.0456461
$846$		0			0
$847$	2.06593			0.0709863
$848$	−15.7461	−	27.2730i	−0.540723	−	0.936560i
$849$		0			0
$850$	0.732954	−	1.26951i	0.0251401	−	0.0435440i
$851$	21.4835	−	37.2105i	0.736445	−	1.27556i
$852$		0			0
$853$	25.9591	+	44.9625i	0.888823	+	1.53949i	0.841268	+	0.540618i	$0.181810\pi$
$853$	25.9591	+	44.9625i	0.888823	+	1.53949i	0.0475550	+	0.998869i	$0.484857\pi$
$854$	−22.3151			−0.763607
$855$		0			0
$856$	0.291653			0.00996849
$857$	−14.4637	−	25.0518i	−0.494069	−	0.855753i	0.505908	−	0.862588i	$-0.331158\pi$
$857$	−14.4637	−	25.0518i	−0.494069	−	0.855753i	−0.999977	+	0.00683492i	$0.997824\pi$
$858$		0			0
$859$	3.13587	−	5.43148i	0.106994	−	0.185320i	−0.807557	−	0.589790i	$-0.799211\pi$
$859$	3.13587	−	5.43148i	0.106994	−	0.185320i	0.914551	+	0.404470i	$0.132544\pi$
$860$	5.13075	−	8.88671i	0.174957	−	0.303034i
$861$		0			0
$862$	2.55596	+	4.42706i	0.0870565	+	0.150786i
$863$	−5.95115			−0.202580			−0.101290	−	0.994857i	$-0.532297\pi$
$863$	−5.95115			−0.202580			−0.101290	+	0.994857i	$0.532297\pi$
$864$		0			0
$865$	−2.09755			−0.0713189
$866$	2.49330	+	4.31853i	0.0847259	+	0.146750i
$867$		0			0
$868$	6.98504	−	12.0985i	0.237088	−	0.410648i
$869$	20.6739	−	35.8083i	0.701316	−	1.21471i
$870$		0			0
$871$	−4.67710	−	8.10098i	−0.158478	−	0.274491i
$872$	14.0186			0.474730
$873$		0			0
$874$	2.76042			0.0933726
$875$	17.1058	+	29.6280i	0.578280	+	1.00161i
$876$		0			0
$877$	27.2757	−	47.2430i	0.921036	−	1.59528i	0.123222	−	0.992379i	$-0.460677\pi$
$877$	27.2757	−	47.2430i	0.921036	−	1.59528i	0.797815	−	0.602903i	$-0.205989\pi$
$878$	−3.90398	+	6.76189i	−0.131753	+	0.228203i
$879$		0			0
$880$	−5.85374	−	10.1390i	−0.197329	−	0.341785i
$881$	−34.6855			−1.16858			−0.584292	−	0.811543i	$-0.698628\pi$
$881$	−34.6855			−1.16858			−0.584292	+	0.811543i	$0.698628\pi$
$882$		0			0
$883$	29.1891			0.982290			0.491145	−	0.871078i	$-0.336578\pi$
$883$	29.1891			0.982290			0.491145	+	0.871078i	$0.336578\pi$
$884$	−0.799931	−	1.38552i	−0.0269046	−	0.0466001i
$885$		0			0
$886$	−2.37114	+	4.10694i	−0.0796600	+	0.137975i
$887$	1.20709	−	2.09074i	0.0405300	−	0.0702001i	−0.845049	−	0.534689i	$-0.820429\pi$
$887$	1.20709	−	2.09074i	0.0405300	−	0.0702001i	0.885579	+	0.464489i	$0.153762\pi$
$888$		0			0
$889$	−0.745715	−	1.29162i	−0.0250105	−	0.0433194i
$890$	5.48471			0.183848
$891$		0			0
$892$	32.6670			1.09377
$893$	4.76308	+	8.24989i	0.159390	+	0.276072i
$894$		0			0
$895$	10.1022	−	17.4976i	0.337680	−	0.584879i
$896$	17.7500	−	30.7440i	0.592987	−	1.02708i
$897$		0			0
$898$	−3.89837	−	6.75218i	−0.130090	−	0.225323i
$899$	16.5557			0.552163
$900$		0			0
$901$	11.1174			0.370376
$902$	−4.61925	−	8.00077i	−0.153804	−	0.266397i
$903$		0			0
$904$	−15.8978	+	27.5358i	−0.528752	+	0.915826i
$905$	15.2410	−	26.3981i	0.506627	−	0.877503i
$906$		0			0
$907$	−23.2215	−	40.2207i	−0.771056	−	1.33551i	−0.936985	−	0.349370i	$-0.886396\pi$
$907$	−23.2215	−	40.2207i	−0.771056	−	1.33551i	0.165929	−	0.986138i	$-0.446938\pi$
$908$	−24.7315			−0.820742
$909$		0			0
$910$	−2.05988			−0.0682843
$911$	0.0724799	+	0.125539i	0.00240137	+	0.00415929i	0.867224	−	0.497919i	$-0.165902\pi$
$911$	0.0724799	+	0.125539i	0.00240137	+	0.00415929i	−0.864822	+	0.502078i	$0.832569\pi$
$912$		0			0
$913$	18.7870	−	32.5400i	0.621758	−	1.07692i
$914$	−8.16176	+	14.1366i	−0.269967	+	0.467597i
$915$		0			0
$916$	1.79835	+	3.11483i	0.0594191	+	0.102917i
$917$	−27.5722			−0.910513
$918$		0			0
$919$	−37.8928			−1.24997			−0.624983	−	0.780638i	$-0.714894\pi$
$919$	−37.8928			−1.24997			−0.624983	+	0.780638i	$0.714894\pi$
$920$	−6.63746	−	11.4964i	−0.218831	−	0.379026i
$921$		0			0
$922$	3.16935	−	5.48947i	0.104377	−	0.180786i
$923$	6.03350	−	10.4503i	0.198595	−	0.343977i
$924$		0			0
$925$	12.9543	+	22.4375i	0.425935	+	0.737740i
$926$	−2.61673			−0.0859910
$927$		0			0
$928$	32.5630			1.06893
$929$	−25.5801	−	44.3061i	−0.839257	−	1.45364i	−0.890517	−	0.454950i	$-0.849657\pi$
$929$	−25.5801	−	44.3061i	−0.839257	−	1.45364i	0.0512606	−	0.998685i	$-0.483676\pi$
$930$		0			0
$931$	1.44614	−	2.50479i	0.0473953	−	0.0820910i
$932$	−7.02847	+	12.1737i	−0.230225	+	0.398762i
$933$		0			0
$934$	−4.60964	−	7.98413i	−0.150832	−	0.261249i
$935$	4.13300			0.135164
$936$		0			0
$937$	−33.4925			−1.09415			−0.547076	−	0.837083i	$-0.684259\pi$
$937$	−33.4925			−1.09415			−0.547076	+	0.837083i	$0.684259\pi$
$938$	7.26083	+	12.5761i	0.237074	+	0.410625i
$939$		0			0
$940$	10.7020	−	18.5364i	0.349061	−	0.604591i
$941$	−8.43377	+	14.6077i	−0.274933	+	0.476198i	−0.970118	−	0.242633i	$-0.921989\pi$
$941$	−8.43377	+	14.6077i	−0.274933	+	0.476198i	0.695185	+	0.718831i	$0.255322\pi$
$942$		0			0
$943$	14.6490	+	25.3728i	0.477038	+	0.826253i
$944$	18.2949			0.595450
$945$		0			0
$946$	7.46952			0.242855
$947$	8.00694	+	13.8684i	0.260191	+	0.450663i	0.966292	−	0.257447i	$-0.0828812\pi$
$947$	8.00694	+	13.8684i	0.260191	+	0.450663i	−0.706102	+	0.708110i	$0.749548\pi$
$948$		0			0
$949$	−2.61385	+	4.52733i	−0.0848493	+	0.146963i
$950$	−0.832250	+	1.44150i	−0.0270017	+	0.0467684i
$951$		0			0
$952$	2.65791	+	4.60364i	0.0861435	+	0.149205i
$953$	−35.3365			−1.14466			−0.572331	−	0.820023i	$-0.693961\pi$
$953$	−35.3365			−1.14466			−0.572331	+	0.820023i	$0.693961\pi$
$954$		0			0
$955$	9.38528			0.303701
$956$	3.06512	+	5.30894i	0.0991329	+	0.171703i
$957$		0			0
$958$	−0.268475	+	0.465013i	−0.00867404	+	0.0150239i
$959$	−15.9550	+	27.6349i	−0.515214	+	0.892376i
$960$		0			0
$961$	12.2605	+	21.2359i	0.395501	+	0.685028i
$962$	−3.96776			−0.127926
$963$		0			0
$964$	−12.5014			−0.402644
$965$	−5.31591	−	9.20742i	−0.171125	−	0.296397i
$966$		0			0
$967$	−26.6690	+	46.1920i	−0.857616	+	1.48543i	0.0165803	+	0.999863i	$0.494722\pi$
$967$	−26.6690	+	46.1920i	−0.857616	+	1.48543i	−0.874196	+	0.485572i	$0.838611\pi$
$968$	0.614733	−	1.06475i	0.0197583	−	0.0342223i
$969$		0			0
$970$	−4.61833	−	7.99917i	−0.148286	−	0.256838i
$971$	−50.1657			−1.60989			−0.804946	−	0.593348i	$-0.797806\pi$
$971$	−50.1657			−1.60989			−0.804946	+	0.593348i	$0.797806\pi$
$972$		0			0
$973$	−33.5637			−1.07600
$974$	−4.32139	−	7.48487i	−0.138466	−	0.239831i
$975$		0			0
$976$	18.5711	−	32.1661i	0.594446	−	1.02961i
$977$	−11.4716	+	19.8694i	−0.367008	+	0.635677i	−0.989096	−	0.147270i	$-0.952951\pi$
$977$	−11.4716	+	19.8694i	−0.367008	+	0.635677i	0.622088	+	0.782947i	$0.286285\pi$
$978$		0			0
$979$	−14.2259	−	24.6400i	−0.454663	−	0.787499i
$980$	−6.49857			−0.207589
$981$		0			0
$982$	8.33919			0.266114
$983$	−0.129157	−	0.223706i	−0.00411946	−	0.00713511i	0.863958	−	0.503563i	$-0.167978\pi$
$983$	−0.129157	−	0.223706i	−0.00411946	−	0.00713511i	−0.868078	+	0.496428i	$0.834645\pi$
$984$		0			0
$985$	6.83254	−	11.8343i	0.217703	−	0.377072i
$986$	−1.47167	+	2.54900i	−0.0468675	+	0.0811768i
$987$		0			0
$988$	0.908301	+	1.57322i	0.0288969	+	0.0500509i
$989$	−23.6881			−0.753237
$990$		0			0
$991$	−23.1558			−0.735568			−0.367784	−	0.929911i	$-0.619883\pi$
$991$	−23.1558			−0.735568			−0.367784	+	0.929911i	$0.619883\pi$
$992$	−6.37161	−	11.0360i	−0.202299	−	0.350392i
$993$		0			0
$994$	−9.36653	+	16.2233i	−0.297088	+	0.514572i
$995$	3.69500	−	6.39993i	0.117139	−	0.202891i
$996$		0			0
$997$	−20.8933	−	36.1882i	−0.661697	−	1.14609i	−0.980170	−	0.198160i	$-0.936503\pi$
$997$	−20.8933	−	36.1882i	−0.661697	−	1.14609i	0.318473	−	0.947932i	$-0.396830\pi$
$998$	−10.3605			−0.327954
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.e.c.118.3		12
3.2	odd	2		117.2.e.c.40.4	✓	12
9.2	odd	6		117.2.e.c.79.4	yes	12
9.4	even	3		1053.2.a.m.1.4		6
9.5	odd	6		1053.2.a.l.1.3		6
9.7	even	3	inner	351.2.e.c.235.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.c.40.4	✓	12	3.2	odd	2
117.2.e.c.79.4	yes	12	9.2	odd	6
351.2.e.c.118.3		12	1.1	even	1	trivial
351.2.e.c.235.3		12	9.7	even	3	inner
1053.2.a.l.1.3		6	9.5	odd	6
1053.2.a.m.1.4		6	9.4	even	3

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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.248047 - 0.429630i) q^{2} +(0.876945 - 1.51891i) q^{4} +(-0.663441 + 1.14911i) q^{5} +(-1.56464 - 2.71004i) q^{7} -1.86228 q^{8} +0.658258 q^{10} +(-1.70735 - 2.95722i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.776210 + 1.34444i) q^{14} +(-1.29196 - 2.23774i) q^{16} +0.912179 q^{17} -1.03576 q^{19} +(1.16360 + 2.01542i) q^{20} +(-0.847007 + 1.46706i) q^{22} +(2.68611 - 4.65248i) q^{23} +(1.61969 + 2.80539i) q^{25} -0.496094 q^{26} -5.48843 q^{28} +(-3.25212 - 5.63283i) q^{29} +(-1.27269 + 2.20436i) q^{31} +(-2.50321 + 4.33569i) q^{32} +(-0.226263 - 0.391900i) q^{34} +4.15219 q^{35} +7.99800 q^{37} +(0.256916 + 0.444991i) q^{38} +(1.23551 - 2.13997i) q^{40} +(-2.72681 + 4.72297i) q^{41} +(-2.20468 - 3.81862i) q^{43} -5.98902 q^{44} -2.66513 q^{46} +(-4.59865 - 7.96510i) q^{47} +(-1.39622 + 2.41832i) q^{49} +(0.803520 - 1.39174i) q^{50} +(-0.876945 - 1.51891i) q^{52} +12.1878 q^{53} +4.53091 q^{55} +(2.91381 + 5.04686i) q^{56} +(-1.61335 + 2.79441i) q^{58} +(-3.54016 + 6.13174i) q^{59} +(7.18720 + 12.4486i) q^{61} +1.26274 q^{62} -2.68417 q^{64} +(0.663441 + 1.14911i) q^{65} +(4.67710 - 8.10098i) q^{67} +(0.799931 - 1.38552i) q^{68} +(-1.02994 - 1.78391i) q^{70} +12.0670 q^{71} -5.22771 q^{73} +(-1.98388 - 3.43618i) q^{74} +(-0.908301 + 1.57322i) q^{76} +(-5.34279 + 9.25399i) q^{77} +(6.05439 + 10.4865i) q^{79} +3.42855 q^{80} +2.70551 q^{82} +(5.50179 + 9.52938i) q^{83} +(-0.605177 + 1.04820i) q^{85} +(-1.09373 + 1.89439i) q^{86} +(3.17957 + 5.50718i) q^{88} +8.33216 q^{89} -3.12929 q^{91} +(-4.71115 - 8.15994i) q^{92} +(-2.28136 + 3.95144i) q^{94} +(0.687162 - 1.19020i) q^{95} +(-7.01598 - 12.1520i) q^{97} +1.38531 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} - 3 q^{5} + 12 q^{8} - 12 q^{10} - 7 q^{11} + 6 q^{13} - 13 q^{14} - 6 q^{16} + 28 q^{17} - 6 q^{19} - 17 q^{20} + 3 q^{22} - 17 q^{23} - 3 q^{25} - 4 q^{26} + 30 q^{28} - 14 q^{29}+ \cdots + 34 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 - 3 * q^5 + 12 * q^8 - 12 * q^10 - 7 * q^11 + 6 * q^13 - 13 * q^14 - 6 * q^16 + 28 * q^17 - 6 * q^19 - 17 * q^20 + 3 * q^22 - 17 * q^23 - 3 * q^25 - 4 * q^26 + 30 * q^28 - 14 * q^29 - 6 * q^31 - 9 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 + 4 * q^38 + 6 * q^40 + 4 * q^41 + 3 * q^43 + 26 * q^44 - 9 * q^47 + 21 * q^50 + 6 * q^52 + 56 * q^53 + 30 * q^55 - 16 * q^56 - 18 * q^58 - 17 * q^59 + 6 * q^61 - 8 * q^62 - 60 * q^64 + 3 * q^65 + 12 * q^67 - 22 * q^68 - 9 * q^70 - 2 * q^71 - 18 * q^73 + 27 * q^74 + 3 * q^76 - 15 * q^77 + 6 * q^79 - 48 * q^80 + 54 * q^82 - 28 * q^83 - 27 * q^85 + 6 * q^86 + 9 * q^88 - 18 * q^89 - 44 * q^92 + 24 * q^94 - 32 * q^95 + 34 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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