LMFDB - Embedded newform 117.2.e.c.79.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(40,117)] 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("117.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.e (of order $3$, degree $2$, 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:	$0.934249703649$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.4
Root			$0.471837 + 1.66654i$ of defining polynomial
Character	$\chi$	$=$	117.79
Dual form			117.2.e.c.40.4

$q$-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} +(-1.67919 + 0.424649i) q^{3} +(0.876945 + 1.51891i) q^{4} +(0.663441 + 1.14911i) q^{5} +(-0.234075 + 0.826762i) q^{6} +(-1.56464 + 2.71004i) q^{7} +1.86228 q^{8} +(2.63935 - 1.42613i) q^{9} +0.658258 q^{10} +(1.70735 - 2.95722i) q^{11} +(-2.11756 - 2.17815i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.776210 + 1.34444i) q^{14} +(-1.60201 - 1.64785i) q^{15} +(-1.29196 + 2.23774i) q^{16} -0.912179 q^{17} +(0.0419726 - 1.48769i) q^{18} -1.03576 q^{19} +(-1.16360 + 2.01542i) q^{20} +(1.47651 - 5.21509i) q^{21} +(-0.847007 - 1.46706i) q^{22} +(-2.68611 - 4.65248i) q^{23} +(-3.12712 + 0.790817i) q^{24} +(1.61969 - 2.80539i) q^{25} +0.496094 q^{26} +(-3.82635 + 3.51554i) q^{27} -5.48843 q^{28} +(3.25212 - 5.63283i) q^{29} +(-1.10534 + 0.279529i) q^{30} +(-1.27269 - 2.20436i) q^{31} +(2.50321 + 4.33569i) q^{32} +(-1.61118 + 5.69075i) q^{33} +(-0.226263 + 0.391900i) q^{34} -4.15219 q^{35} +(4.48073 + 2.75830i) q^{36} +7.99800 q^{37} +(-0.256916 + 0.444991i) q^{38} +(-1.20735 - 1.24189i) q^{39} +(1.23551 + 2.13997i) q^{40} +(2.72681 + 4.72297i) q^{41} +(-1.87432 - 1.92794i) q^{42} +(-2.20468 + 3.81862i) q^{43} +5.98902 q^{44} +(3.38984 + 2.08675i) q^{45} -2.66513 q^{46} +(4.59865 - 7.96510i) q^{47} +(1.21919 - 4.30621i) q^{48} +(-1.39622 - 2.41832i) q^{49} +(-0.803520 - 1.39174i) q^{50} +(1.53172 - 0.387356i) q^{51} +(-0.876945 + 1.51891i) q^{52} -12.1878 q^{53} +(0.561267 + 2.51593i) q^{54} +4.53091 q^{55} +(-2.91381 + 5.04686i) q^{56} +(1.73923 - 0.439833i) q^{57} +(-1.61335 - 2.79441i) q^{58} +(3.54016 + 6.13174i) q^{59} +(1.09806 - 3.87839i) q^{60} +(7.18720 - 12.4486i) q^{61} -1.26274 q^{62} +(-0.264757 + 9.38413i) q^{63} -2.68417 q^{64} +(-0.663441 + 1.14911i) q^{65} +(2.04527 + 2.10379i) q^{66} +(4.67710 + 8.10098i) q^{67} +(-0.799931 - 1.38552i) q^{68} +(6.48616 + 6.67174i) q^{69} +(-1.02994 + 1.78391i) q^{70} -12.0670 q^{71} +(4.91521 - 2.65586i) q^{72} -5.22771 q^{73} +(1.98388 - 3.43618i) q^{74} +(-1.52846 + 5.39858i) q^{75} +(-0.908301 - 1.57322i) q^{76} +(5.34279 + 9.25399i) q^{77} +(-0.833035 + 0.210666i) q^{78} +(6.05439 - 10.4865i) q^{79} -3.42855 q^{80} +(4.93229 - 7.52811i) q^{81} +2.70551 q^{82} +(-5.50179 + 9.52938i) q^{83} +(9.21610 - 2.33066i) q^{84} +(-0.605177 - 1.04820i) q^{85} +(1.09373 + 1.89439i) q^{86} +(-3.06894 + 10.8396i) q^{87} +(3.17957 - 5.50718i) q^{88} -8.33216 q^{89} +(1.73737 - 0.938763i) q^{90} -3.12929 q^{91} +(4.71115 - 8.15994i) q^{92} +(3.07316 + 3.16108i) q^{93} +(-2.28136 - 3.95144i) q^{94} +(-0.687162 - 1.19020i) q^{95} +(-6.04452 - 6.21746i) q^{96} +(-7.01598 + 12.1520i) q^{97} -1.38531 q^{98} +(0.288905 - 10.2400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 6 q^{4} + 3 q^{5} - 7 q^{6} - 12 q^{8} - 2 q^{9} - 12 q^{10} + 7 q^{11} + 7 q^{12} + 6 q^{13} + 13 q^{14} - 12 q^{15} - 6 q^{16} - 28 q^{17} + 26 q^{18} - 6 q^{19} + 17 q^{20}+ \cdots - 11 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^3 - 6 * q^4 + 3 * q^5 - 7 * q^6 - 12 * q^8 - 2 * q^9 - 12 * q^10 + 7 * q^11 + 7 * q^12 + 6 * q^13 + 13 * q^14 - 12 * q^15 - 6 * q^16 - 28 * q^17 + 26 * q^18 - 6 * q^19 + 17 * q^20 - 18 * q^21 + 3 * q^22 + 17 * q^23 - 30 * q^24 - 3 * q^25 + 4 * q^26 + 13 * q^27 + 30 * q^28 + 14 * q^29 - 7 * q^30 - 6 * q^31 + 9 * q^32 + 19 * q^33 - 3 * q^34 - 26 * q^35 + 43 * q^36 - 18 * q^37 - 4 * q^38 - q^39 + 6 * q^40 - 4 * q^41 - 17 * q^42 + 3 * q^43 - 26 * q^44 + 18 * q^45 + 9 * q^47 - 3 * q^48 - 21 * q^50 - 4 * q^51 + 6 * q^52 - 56 * q^53 + 35 * q^54 + 30 * q^55 + 16 * q^56 - 30 * q^57 - 18 * q^58 + 17 * q^59 - 31 * q^60 + 6 * q^61 + 8 * q^62 - 60 * q^64 - 3 * q^65 - 19 * q^66 + 12 * q^67 + 22 * q^68 - 13 * q^69 - 9 * q^70 + 2 * q^71 - 18 * q^73 - 27 * q^74 + 18 * q^75 + 3 * q^76 + 15 * q^77 - 2 * q^78 + 6 * q^79 + 48 * q^80 - 2 * q^81 + 54 * q^82 + 28 * q^83 + 31 * q^84 - 27 * q^85 - 6 * q^86 + 23 * q^87 + 9 * q^88 + 18 * q^89 + 26 * q^90 + 44 * q^92 + 2 * q^93 + 24 * q^94 + 32 * q^95 - 57 * q^96 - 34 * q^98 - 11 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	$-0.777213\pi$
$2$	0.248047	−	0.429630i	0.175396	−	0.303794i	0.940298	+	0.340352i	$0.110546\pi$
$3$	−1.67919	+	0.424649i	−0.969480	+	0.245171i
$3$	−1.67919	+	0.424649i	−0.969480	+	0.245171i
$4$	0.876945	+	1.51891i	0.438473	+	0.759457i
$5$	0.663441	+	1.14911i	0.296700	+	0.513899i	0.975379	−	0.220536i	$-0.0707806\pi$
$5$	0.663441	+	1.14911i	0.296700	+	0.513899i	−0.678679	+	0.734435i	$0.737447\pi$
$6$	−0.234075	+	0.826762i	−0.0955609	+	0.337524i
$7$	−1.56464	+	2.71004i	−0.591380	+	1.02430i	0.402667	+	0.915346i	$0.368083\pi$
$7$	−1.56464	+	2.71004i	−0.591380	+	1.02430i	−0.994047	+	0.108953i	$0.965250\pi$
$8$	1.86228			0.658416
$9$	2.63935	−	1.42613i	0.879782	−	0.475377i
$10$	0.658258			0.208159
$11$	1.70735	−	2.95722i	0.514786	−	0.891635i	−0.485067	−	0.874477i	$-0.661205\pi$
$11$	1.70735	−	2.95722i	0.514786	−	0.891635i	0.999853	−	0.0171581i	$-0.00546187\pi$
$12$	−2.11756	−	2.17815i	−0.611288	−	0.628777i
$13$	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
$15$	−1.60201	−	1.64785i	−0.413638	−	0.425472i
$16$	−1.29196	+	2.23774i	−0.322989	+	0.559434i
$17$	−0.912179			−0.221236			−0.110618	−	0.993863i	$-0.535283\pi$
$17$	−0.912179			−0.221236			−0.110618	+	0.993863i	$0.535283\pi$
$18$	0.0419726	−	1.48769i	0.00989303	−	0.350652i
$19$	−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
$21$	1.47651	−	5.21509i	0.322202	−	1.13803i
$22$	−0.847007	−	1.46706i	−0.180582	−	0.312778i
$23$	−2.68611	−	4.65248i	−0.560093	−	0.970109i	−0.997488	−	0.0708399i	$-0.977432\pi$
$23$	−2.68611	−	4.65248i	−0.560093	−	0.970109i	0.437395	−	0.899270i	$-0.355901\pi$
$24$	−3.12712	+	0.790817i	−0.638321	+	0.161425i
$25$	1.61969	−	2.80539i	0.323938	−	0.561078i
$26$	0.496094			0.0972920
$27$	−3.82635	+	3.51554i	−0.736382	+	0.676566i
$28$	−5.48843			−1.03722
$29$	3.25212	−	5.63283i	0.603903	−	1.04599i	−0.388321	−	0.921524i	$-0.626945\pi$
$29$	3.25212	−	5.63283i	0.603903	−	1.04599i	0.992224	−	0.124466i	$-0.0397217\pi$
$30$	−1.10534	+	0.279529i	−0.201806	+	0.0510347i
$31$	−1.27269	−	2.20436i	−0.228581	−	0.395914i	0.728807	−	0.684720i	$-0.240075\pi$
$31$	−1.27269	−	2.20436i	−0.228581	−	0.395914i	−0.957388	+	0.288805i	$0.906742\pi$
$32$	2.50321	+	4.33569i	0.442510	+	0.766450i
$33$	−1.61118	+	5.69075i	−0.280471	+	0.990633i
$34$	−0.226263	+	0.391900i	−0.0388038	+	0.0672102i
$35$	−4.15219			−0.701849
$36$	4.48073	+	2.75830i	0.746789	+	0.459717i
$37$	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
$39$	−1.20735	−	1.24189i	−0.193331	−	0.198862i
$40$	1.23551	+	2.13997i	0.195352	+	0.338360i
$41$	2.72681	+	4.72297i	0.425856	+	0.737604i	0.996500	−	0.0835936i	$-0.0266398\pi$
$41$	2.72681	+	4.72297i	0.425856	+	0.737604i	−0.570644	+	0.821197i	$0.693306\pi$
$42$	−1.87432	−	1.92794i	−0.289213	−	0.297488i
$43$	−2.20468	+	3.81862i	−0.336211	+	0.582334i	−0.983717	−	0.179726i	$-0.942479\pi$
$43$	−2.20468	+	3.81862i	−0.336211	+	0.582334i	0.647506	+	0.762060i	$0.275812\pi$
$44$	5.98902			0.902878
$45$	3.38984	+	2.08675i	0.505327	+	0.311075i
$46$	−2.66513			−0.392952
$47$	4.59865	−	7.96510i	0.670782	−	1.16183i	−0.306901	−	0.951742i	$-0.599292\pi$
$47$	4.59865	−	7.96510i	0.670782	−	1.16183i	0.977683	−	0.210087i	$-0.0673747\pi$
$48$	1.21919	−	4.30621i	0.175974	−	0.621548i
$49$	−1.39622	−	2.41832i	−0.199460	−	0.345474i
$50$	−0.803520	−	1.39174i	−0.113635	−	0.196821i
$51$	1.53172	−	0.387356i	0.214484	−	0.0542407i
$52$	−0.876945	+	1.51891i	−0.121610	+	0.210635i
$53$	−12.1878			−1.67412			−0.837060	−	0.547111i	$-0.815728\pi$
$53$	−12.1878			−1.67412			−0.837060	+	0.547111i	$0.815728\pi$
$54$	0.561267	+	2.51593i	0.0763787	+	0.342375i
$55$	4.53091			0.610947
$56$	−2.91381	+	5.04686i	−0.389374	+	0.674415i
$57$	1.73923	−	0.439833i	0.230366	−	0.0582573i
$58$	−1.61335	−	2.79441i	−0.211844	−	0.366924i
$59$	3.54016	+	6.13174i	0.460890	+	0.798284i	0.999006	−	0.0445866i	$-0.0141971\pi$
$59$	3.54016	+	6.13174i	0.460890	+	0.798284i	−0.538116	+	0.842871i	$0.680864\pi$
$60$	1.09806	−	3.87839i	0.141759	−	0.500698i
$61$	7.18720	−	12.4486i	0.920226	−	1.59388i	0.121162	−	0.992633i	$-0.461338\pi$
$61$	7.18720	−	12.4486i	0.920226	−	1.59388i	0.799064	−	0.601246i	$-0.205329\pi$
$62$	−1.26274			−0.160369
$63$	−0.264757	+	9.38413i	−0.0333562	+	1.18229i
$64$	−2.68417			−0.335521
$65$	−0.663441	+	1.14911i	−0.0822897	+	0.142530i
$66$	2.04527	+	2.10379i	0.251755	+	0.258958i
$67$	4.67710	+	8.10098i	0.571399	+	0.989692i	0.996423	+	0.0845099i	$0.0269325\pi$
$67$	4.67710	+	8.10098i	0.571399	+	0.989692i	−0.425024	+	0.905182i	$0.639734\pi$
$68$	−0.799931	−	1.38552i	−0.0970059	−	0.168019i
$69$	6.48616	+	6.67174i	0.780842	+	0.803183i
$70$	−1.02994	+	1.78391i	−0.123101	+	0.213218i
$71$	−12.0670			−1.43209			−0.716045	−	0.698054i	$-0.754049\pi$
$71$	−12.0670			−1.43209			−0.716045	+	0.698054i	$0.754049\pi$
$72$	4.91521	−	2.65586i	0.579263	−	0.312996i
$73$	−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
$75$	−1.52846	+	5.39858i	−0.176492	+	0.623374i
$76$	−0.908301	−	1.57322i	−0.104189	−	0.180461i
$77$	5.34279	+	9.25399i	0.608868	+	1.05459i
$78$	−0.833035	+	0.210666i	−0.0943226	+	0.0238532i
$79$	6.05439	−	10.4865i	0.681172	−	1.17982i	−0.293451	−	0.955974i	$-0.594804\pi$
$79$	6.05439	−	10.4865i	0.681172	−	1.17982i	0.974623	−	0.223851i	$-0.0718629\pi$
$80$	−3.42855			−0.383323
$81$	4.93229	−	7.52811i	0.548033	−	0.836457i
$82$	2.70551			0.298773
$83$	−5.50179	+	9.52938i	−0.603900	+	1.04599i	0.388324	+	0.921523i	$0.373054\pi$
$83$	−5.50179	+	9.52938i	−0.603900	+	1.04599i	−0.992224	+	0.124463i	$0.960279\pi$
$84$	9.21610	−	2.33066i	1.00556	−	0.254296i
$85$	−0.605177	−	1.04820i	−0.0656407	−	0.113693i
$86$	1.09373	+	1.89439i	0.117940	+	0.204278i
$87$	−3.06894	+	10.8396i	−0.329024	+	1.16213i
$88$	3.17957	−	5.50718i	0.338943	−	0.587067i
$89$	−8.33216			−0.883207			−0.441604	−	0.897210i	$-0.645590\pi$
$89$	−8.33216			−0.883207			−0.441604	+	0.897210i	$0.645590\pi$
$90$	1.73737	−	0.938763i	0.183135	−	0.0989543i
$91$	−3.12929			−0.328038
$92$	4.71115	−	8.15994i	0.491171	−	0.850733i
$93$	3.07316	+	3.16108i	0.318672	+	0.327789i
$94$	−2.28136	−	3.95144i	−0.235305	−	0.407559i
$95$	−0.687162	−	1.19020i	−0.0705014	−	0.122112i
$96$	−6.04452	−	6.21746i	−0.616916	−	0.634567i
$97$	−7.01598	+	12.1520i	−0.712365	+	1.23385i	0.251602	+	0.967831i	$0.419043\pi$
$97$	−7.01598	+	12.1520i	−0.712365	+	1.23385i	−0.963967	+	0.266022i	$0.914291\pi$
$98$	−1.38531			−0.139937
$99$	0.288905	−	10.2400i	0.0290360	−	1.02916i
$100$	5.68153			0.568153
$101$	−5.91889	+	10.2518i	−0.588951	+	1.02009i	0.405419	+	0.914131i	$0.367126\pi$
$101$	−5.91889	+	10.2518i	−0.588951	+	1.02009i	−0.994370	+	0.105963i	$0.966208\pi$
$102$	0.213519	−	0.754156i	0.0211415	−	0.0746725i
$103$	−4.10294	−	7.10650i	−0.404275	−	0.700224i	0.589962	−	0.807431i	$-0.299143\pi$
$103$	−4.10294	−	7.10650i	−0.404275	−	0.700224i	−0.994237	+	0.107207i	$0.965809\pi$
$104$	0.931141	+	1.61278i	0.0913059	+	0.158146i
$105$	6.97231	−	1.76323i	0.680428	−	0.172073i
$106$	−3.02314	+	5.23624i	−0.293634	+	0.508588i
$107$	0.156610			0.0151401			0.00757005	−	0.999971i	$-0.497590\pi$
$107$	0.156610			0.0151401			0.00757005	+	0.999971i	$0.497590\pi$
$108$	−8.69531	−	2.72896i	−0.836706	−	0.262595i
$109$	−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
$111$	−13.4301	+	3.39634i	−1.27473	+	0.322367i
$112$	−4.04290	−	7.00252i	−0.382019	−	0.661676i
$113$	−8.53672	−	14.7860i	−0.803067	−	1.39095i	−0.917588	−	0.397532i	$-0.869867\pi$
$113$	−8.53672	−	14.7860i	−0.803067	−	1.39095i	0.114521	−	0.993421i	$-0.463467\pi$
$114$	0.242445	−	0.856324i	0.0227070	−	0.0802020i
$115$	3.56415	−	6.17329i	0.332359	−	0.575663i
$116$	11.4077			1.05918
$117$	2.55474	+	1.57267i	0.236186	+	0.145394i
$118$	3.51250			0.323352
$119$	1.42724	−	2.47204i	0.130834	−	0.226612i
$120$	−2.98340	−	3.06876i	−0.272346	−	0.280138i
$121$	−0.330096	−	0.571744i	−0.0300088	−	0.0519767i
$122$	−3.56552	−	6.17567i	−0.322807	−	0.559119i
$123$	−6.58443	−	6.77282i	−0.593698	−	0.610684i
$124$	2.23215	−	3.86620i	0.200453	−	0.347195i
$125$	10.9327			0.977849
$126$	3.96603	+	2.44145i	0.353322	+	0.217502i
$127$	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
$129$	2.08050	−	7.34840i	0.183178	−	0.646990i
$130$	0.329129	+	0.570068i	0.0288665	+	0.0499983i
$131$	−4.40550	−	7.63055i	−0.384910	−	0.666684i	0.606846	−	0.794819i	$-0.292434\pi$
$131$	−4.40550	−	7.63055i	−0.384910	−	0.666684i	−0.991757	+	0.128135i	$0.959101\pi$
$132$	−10.0567	+	2.54323i	−0.875322	+	0.221360i
$133$	1.62059	−	2.80694i	0.140523	−	0.243393i
$134$	4.64056			0.400884
$135$	−6.57831	−	2.06456i	−0.566171	−	0.177689i
$136$	−1.69874			−0.145665
$137$	5.09861	−	8.83104i	0.435603	−	0.754487i	−0.561741	−	0.827313i	$-0.689868\pi$
$137$	5.09861	−	8.83104i	0.435603	−	0.754487i	0.997345	+	0.0728259i	$0.0232018\pi$
$138$	4.47525	−	1.13174i	0.380959	−	0.0963405i
$139$	5.36283	+	9.28870i	0.454870	+	0.787857i	0.998681	−	0.0513505i	$-0.0163526\pi$
$139$	5.36283	+	9.28870i	0.454870	+	0.787857i	−0.543811	+	0.839208i	$0.683019\pi$
$140$	−3.64125	−	6.30682i	−0.307742	−	0.533024i
$141$	−4.33963	+	15.3277i	−0.365462	+	1.29083i
$142$	−2.99318	+	5.18434i	−0.251182	+	0.435061i
$143$	3.41470			0.285552
$144$	−0.218615	+	7.74866i	−0.0182179	+	0.645722i
$145$	8.63034			0.716711
$146$	−1.29672	+	2.24598i	−0.107317	+	0.185879i
$147$	3.37145	+	3.46791i	0.278072	+	0.286028i
$148$	7.01381	+	12.1483i	0.576531	+	0.998582i
$149$	7.56805	+	13.1083i	0.619999	+	1.07387i	0.989485	+	0.144634i	$0.0462004\pi$
$149$	7.56805	+	13.1083i	0.619999	+	1.07387i	−0.369486	+	0.929236i	$0.620466\pi$
$150$	1.94026	+	1.99577i	0.158422	+	0.162954i
$151$	−6.09490	+	10.5567i	−0.495996	+	0.859090i	−0.999989	−	0.00461712i	$-0.998530\pi$
$151$	−6.09490	+	10.5567i	−0.495996	+	0.859090i	0.503993	+	0.863708i	$0.331864\pi$
$152$	−1.92887			−0.156452
$153$	−2.40756	+	1.30089i	−0.194639	+	0.105171i
$154$	5.30105			0.427171
$155$	1.68870	−	2.92492i	0.135640	−	0.234935i
$156$	0.827551	−	2.92294i	0.0662571	−	0.234022i
$157$	1.92216	+	3.32928i	0.153405	+	0.265706i	0.932477	−	0.361229i	$-0.117643\pi$
$157$	1.92216	+	3.32928i	0.153405	+	0.265706i	−0.779072	+	0.626934i	$0.784309\pi$
$158$	−3.00355	−	5.20230i	−0.238949	−	0.413872i
$159$	20.4656	−	5.17553i	1.62303	−	0.410446i
$160$	−3.32147	+	5.75295i	−0.262585	+	0.454811i
$161$	16.8112			1.32491
$162$	−2.01086	−	3.98639i	−0.157988	−	0.313200i
$163$	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
$165$	−7.60824	+	1.92405i	−0.592301	+	0.149787i
$166$	2.72940	+	4.72747i	0.211843	+	0.366923i
$167$	−8.89187	−	15.4012i	−0.688074	−	1.19178i	−0.972460	−	0.233069i	$-0.925123\pi$
$167$	−8.89187	−	15.4012i	−0.688074	−	1.19178i	0.284386	−	0.958710i	$-0.408210\pi$
$168$	2.74968	−	9.71198i	0.212143	−	0.749295i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−0.600449			−0.0460524
$171$	−2.73372	+	1.47712i	−0.209052	+	0.112958i
$172$	−7.73354			−0.589677
$173$	−0.790406	+	1.36902i	−0.0600935	+	0.104085i	−0.894507	−	0.447054i	$-0.852473\pi$
$173$	−0.790406	+	1.36902i	−0.0600935	+	0.104085i	0.834414	+	0.551139i	$0.185807\pi$
$174$	3.89577	+	4.00723i	0.295338	+	0.303788i
$175$	5.06848	+	8.77887i	0.383141	+	0.663620i
$176$	4.41165	+	7.64120i	0.332541	+	0.575977i
$177$	−8.54843	−	8.79301i	−0.642540	−	0.660923i
$178$	−2.06677	+	3.57975i	−0.154911	+	0.268313i
$179$	15.2270			1.13812			0.569060	−	0.822296i	$-0.307307\pi$
$179$	15.2270			1.13812			0.569060	+	0.822296i	$0.307307\pi$
$180$	−0.196896	+	6.97884i	−0.0146757	+	0.520172i
$181$	−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
$183$	−6.78237	+	23.9556i	−0.501367	+	1.77085i
$184$	−5.00230	−	8.66423i	−0.368774	−	0.638736i
$185$	5.30620	+	9.19061i	0.390119	+	0.675707i
$186$	2.12038	−	0.536223i	0.155474	−	0.0393178i
$187$	−1.55741	+	2.69751i	−0.113889	+	0.197262i
$188$	16.1311			1.17648
$189$	−3.54039	−	15.8701i	−0.257525	−	1.15438i
$190$	−0.681794			−0.0494625
$191$	3.53659	−	6.12556i	0.255899	−	0.443230i	−0.709240	−	0.704967i	$-0.750962\pi$
$191$	3.53659	−	6.12556i	0.255899	−	0.443230i	0.965139	+	0.261737i	$0.0842952\pi$
$192$	4.50723	−	1.13983i	0.325281	−	0.0822602i
$193$	−4.00632	−	6.93914i	−0.288381	−	0.499490i	0.685043	−	0.728503i	$-0.259784\pi$
$193$	−4.00632	−	6.93914i	−0.288381	−	0.499490i	−0.973423	+	0.229013i	$0.926450\pi$
$194$	3.48059	+	6.02855i	0.249892	+	0.432825i
$195$	0.626072	−	2.21131i	0.0448339	−	0.158355i
$196$	2.44881	−	4.24147i	0.174915	−	0.302962i
$197$	10.2986			0.733748			0.366874	−	0.930271i	$-0.380428\pi$
$197$	10.2986			0.733748			0.366874	+	0.930271i	$0.380428\pi$
$198$	−4.32776	−	2.66413i	−0.307561	−	0.189332i
$199$	−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
$201$	−11.2938	−	11.6169i	−0.796604	−	0.819396i
$202$	2.93632	+	5.08586i	0.206599	+	0.357840i
$203$	10.1768	+	17.6267i	0.714271	+	1.23715i
$204$	1.93160	+	1.98686i	0.135239	+	0.139108i
$205$	−3.61815	+	6.26682i	−0.252703	+	0.437694i
$206$	−4.07089			−0.283632
$207$	−13.7246	−	8.44876i	−0.953928	−	0.587229i
$208$	−2.58391			−0.179162
$209$	−1.76840	+	3.06295i	−0.122323	+	0.211869i
$210$	0.971926	−	3.43288i	0.0670693	−	0.236891i
$211$	4.71574	+	8.16790i	0.324645	+	0.562302i	0.981440	−	0.191767i	$-0.0614218\pi$
$211$	4.71574	+	8.16790i	0.324645	+	0.562302i	−0.656795	+	0.754069i	$0.728089\pi$
$212$	−10.6880	−	18.5122i	−0.734056	−	1.27142i
$213$	20.2628	−	5.12424i	1.38838	−	0.351107i
$214$	0.0388468	−	0.0672846i	0.00265551	−	0.00459948i
$215$	−5.85070			−0.399014
$216$	−7.12575	+	6.54693i	−0.484846	+	0.445462i
$217$	7.96520			0.540713
$218$	−1.86721	+	3.23411i	−0.126464	+	0.219041i
$219$	8.77830	−	2.21994i	0.593183	−	0.150010i
$220$	3.97336	+	6.88206i	0.267884	+	0.463988i
$221$	−0.456090	−	0.789970i	−0.0306799	−	0.0531392i
$222$	−1.87214	+	6.61244i	−0.125649	+	0.443798i
$223$	9.31273	−	16.1301i	0.623626	−	1.08015i	−0.365178	−	0.930938i	$-0.618992\pi$
$223$	9.31273	−	16.1301i	0.623626	−	1.08015i	0.988805	−	0.149215i	$-0.0476746\pi$
$224$	−15.6666			−1.04677
$225$	0.274072	−	9.71429i	0.0182715	−	0.647619i
$226$	−8.47003			−0.563418
$227$	7.05046	−	12.2117i	0.467955	−	0.810522i	−0.531374	−	0.847137i	$-0.678324\pi$
$227$	7.05046	−	12.2117i	0.467955	−	0.810522i	0.999329	+	0.0366150i	$0.0116575\pi$
$228$	2.19328	+	2.25603i	0.145253	+	0.149409i
$229$	−1.02535	−	1.77595i	−0.0677569	−	0.117358i	0.830157	−	0.557530i	$-0.188251\pi$
$229$	−1.02535	−	1.77595i	−0.0677569	−	0.117358i	−0.897914	+	0.440172i	$0.854918\pi$
$230$	−1.76815	−	3.06253i	−0.116589	−	0.201937i
$231$	−12.9013	−	13.2704i	−0.848840	−	0.873126i
$232$	6.05636	−	10.4899i	0.397619	−	0.688697i
$233$	8.01472			0.525062			0.262531	−	0.964924i	$-0.415443\pi$
$233$	8.01472			0.525062			0.262531	+	0.964924i	$0.415443\pi$
$234$	1.30936	−	0.707496i	0.0855958	−	0.0462504i
$235$	12.2037			0.796084
$236$	−6.20905	+	10.7544i	−0.404175	+	0.700052i
$237$	−5.71337	+	20.1798i	−0.371123	+	1.31082i
$238$	−0.708043	−	1.22637i	−0.0458956	−	0.0794935i
$239$	1.74761	+	3.02695i	0.113043	+	0.195797i	0.916996	−	0.398897i	$-0.130607\pi$
$239$	1.74761	+	3.02695i	0.113043	+	0.195797i	−0.803953	+	0.594694i	$0.797273\pi$
$240$	5.75718	−	1.45593i	0.371624	−	0.0939799i
$241$	−3.56391	+	6.17288i	−0.229572	+	0.397630i	−0.957681	−	0.287831i	$-0.907066\pi$
$241$	−3.56391	+	6.17288i	−0.229572	+	0.397630i	0.728109	+	0.685461i	$0.240399\pi$
$242$	−0.327518			−0.0210536
$243$	−5.08544	+	14.7356i	−0.326231	+	0.945290i
$244$	25.2111			1.61398
$245$	1.85261	−	3.20882i	0.118359	−	0.205004i
$246$	−4.54305	+	1.14889i	−0.289654	+	0.0732506i
$247$	−0.517878	−	0.896990i	−0.0329518	−	0.0570741i
$248$	−2.37010	−	4.10513i	−0.150502	−	0.260676i
$249$	5.19190	−	18.3380i	0.329023	−	1.16212i
$250$	2.71182	−	4.69701i	0.171511	−	0.297065i
$251$	−10.8057			−0.682052			−0.341026	−	0.940054i	$-0.610774\pi$
$251$	−10.8057			−0.682052			−0.341026	+	0.940054i	$0.610774\pi$
$252$	−14.4859	+	7.82722i	−0.912523	+	0.493069i
$253$	−18.3445			−1.15331
$254$	0.118220	−	0.204763i	0.00741779	−	0.0128480i
$255$	1.46132	+	1.50313i	0.0915116	+	0.0941298i
$256$	0.129788	+	0.224800i	0.00811178	+	0.0140500i
$257$	−12.0213	−	20.8215i	−0.749870	−	1.29881i	−0.947885	−	0.318614i	$-0.896783\pi$
$257$	−12.0213	−	20.8215i	−0.749870	−	1.29881i	0.198015	−	0.980199i	$-0.436551\pi$
$258$	−2.64103	−	2.71659i	−0.164423	−	0.169128i
$259$	−12.5140	+	21.6749i	−0.777583	+	1.34681i
$260$	−2.32721			−0.144327
$261$	0.550298	−	19.5049i	0.0340626	−	1.20732i
$262$	−4.37108			−0.270047
$263$	0.587040	−	1.01678i	0.0361984	−	0.0626975i	−0.847359	−	0.531021i	$-0.821808\pi$
$263$	0.587040	−	1.01678i	0.0361984	−	0.0626975i	0.883557	+	0.468324i	$0.155142\pi$
$264$	−3.00048	+	10.5978i	−0.184667	+	0.652249i
$265$	−8.08587	−	14.0051i	−0.496711	−	0.860329i
$266$	−0.803964	−	1.39251i	−0.0492942	−	0.0853800i
$267$	13.9913	−	3.53825i	0.856252	−	0.216537i
$268$	−8.20313	+	14.2082i	−0.501086	+	0.867906i
$269$	−16.4749			−1.00449			−0.502247	−	0.864724i	$-0.667493\pi$
$269$	−16.4749			−1.00449			−0.502247	+	0.864724i	$0.667493\pi$
$270$	−2.51873	+	2.31413i	−0.153285	+	0.140834i
$271$	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
$273$	5.25466	−	1.32885i	0.318027	−	0.0804256i
$274$	−2.52939	−	4.38103i	−0.152806	−	0.264668i
$275$	−5.53077	−	9.57957i	−0.333518	−	0.577670i
$276$	−4.44579	+	15.7027i	−0.267605	+	0.945190i
$277$	8.42097	−	14.5856i	0.505967	−	0.876361i	−0.494009	−	0.869457i	$-0.664469\pi$
$277$	8.42097	−	14.5856i	0.505967	−	0.876361i	0.999976	−	0.00690414i	$-0.00219767\pi$
$278$	5.32094			0.319129
$279$	−6.50276	−	4.00304i	−0.389310	−	0.239656i
$280$	−7.73256			−0.462109
$281$	−10.8043	+	18.7136i	−0.644530	+	1.11636i	0.339879	+	0.940469i	$0.389614\pi$
$281$	−10.8043	+	18.7136i	−0.644530	+	1.11636i	−0.984410	+	0.175890i	$0.943720\pi$
$282$	5.50881	+	5.66642i	0.328045	+	0.337431i
$283$	−1.95826	−	3.39180i	−0.116406	−	0.201622i	0.801935	−	0.597412i	$-0.203804\pi$
$283$	−1.95826	−	3.39180i	−0.116406	−	0.201622i	−0.918341	+	0.395790i	$0.870471\pi$
$284$	−10.5821	−	18.3287i	−0.627932	−	1.08761i
$285$	1.65929	+	1.70677i	0.0982880	+	0.101100i
$286$	0.847007	−	1.46706i	0.0500845	−	0.0867490i
$287$	−17.0659			−1.00737
$288$	12.7901	+	7.87348i	0.753665	+	0.463949i
$289$	−16.1679			−0.951055
$290$	2.14073	−	3.70785i	0.125708	−	0.217733i
$291$	6.62080	−	23.3849i	0.388118	−	1.37085i
$292$	−4.58441	−	7.94044i	−0.268283	−	0.464679i
$293$	6.65319	+	11.5237i	0.388683	+	0.673219i	0.992273	−	0.124076i	$-0.0395966\pi$
$293$	6.65319	+	11.5237i	0.388683	+	0.673219i	−0.603589	+	0.797295i	$0.706263\pi$
$294$	2.32620	−	0.588271i	0.135666	−	0.0343086i
$295$	−4.69737	+	8.13609i	−0.273492	+	0.473701i
$296$	14.8945			0.865727
$297$	3.86330	+	17.3176i	0.224171	+	1.00487i
$298$	7.50893			0.434981
$299$	2.68611	−	4.65248i	0.155342	−	0.269060i
$300$	−9.54035	+	2.41266i	−0.550813	+	0.139295i
$301$	−6.89908	−	11.9496i	−0.397656	−	0.688761i
$302$	3.02364	+	5.23711i	0.173991	+	0.301362i
$303$	5.58550	−	19.7282i	0.320879	−	1.13335i
$304$	1.33815	−	2.31775i	0.0767483	−	0.132932i
$305$	19.0731			1.09212
$306$	−0.0382865	+	1.35704i	−0.00218869	+	0.0775768i
$307$	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
$309$	9.90737	+	10.1908i	0.563611	+	0.579736i
$310$	−0.837756	−	1.45104i	−0.0475813	−	0.0824133i
$311$	2.05648	+	3.56194i	0.116613	+	0.201979i	0.918423	−	0.395599i	$-0.129463\pi$
$311$	2.05648	+	3.56194i	0.116613	+	0.201979i	−0.801811	+	0.597578i	$0.796130\pi$
$312$	−2.24843	−	2.31276i	−0.127292	−	0.130934i
$313$	1.73971	−	3.01326i	0.0983340	−	0.170319i	−0.812661	−	0.582736i	$-0.801982\pi$
$313$	1.73971	−	3.01326i	0.0983340	−	0.170319i	0.910995	+	0.412417i	$0.135315\pi$
$314$	1.90715			0.107626
$315$	−10.9591	+	5.92158i	−0.617474	+	0.333643i
$316$	21.2375			1.19470
$317$	−12.5304	+	21.7033i	−0.703778	+	1.21898i	0.263353	+	0.964699i	$0.415172\pi$
$317$	−12.5304	+	21.7033i	−0.703778	+	1.21898i	−0.967131	+	0.254279i	$0.918162\pi$
$318$	2.85286	−	10.0764i	0.159980	−	0.565056i
$319$	−11.1050	−	19.2344i	−0.621761	−	1.07692i
$320$	−1.78079	−	3.08442i	−0.0995491	−	0.172424i
$321$	−0.262978	+	0.0665045i	−0.0146780	+	0.00371192i
$322$	4.16997	−	7.22261i	0.232384	−	0.402500i
$323$	0.944794			0.0525698
$324$	15.7599	+	0.889985i	0.875550	+	0.0494436i
$325$	3.23938			0.179689
$326$	1.30030	−	2.25219i	0.0720172	−	0.124738i
$327$	12.6404	−	3.19661i	0.699013	−	0.176773i
$328$	5.07809	+	8.79550i	0.280390	+	0.485650i
$329$	14.3905	+	24.9251i	0.793374	+	1.37416i
$330$	−1.06057	+	3.74598i	−0.0583827	+	0.206210i
$331$	−0.135093	+	0.233988i	−0.00742539	+	0.0128612i	−0.869714	−	0.493556i	$-0.835697\pi$
$331$	−0.135093	+	0.233988i	−0.00742539	+	0.0128612i	0.862289	+	0.506417i	$0.169030\pi$
$332$	−19.2991			−1.05917
$333$	21.1095	−	11.4062i	1.15679	−	0.625056i
$334$	−8.82241			−0.482741
$335$	−6.20596	+	10.7490i	−0.339068	+	0.587283i
$336$	9.76241	+	10.0417i	0.532583	+	0.547821i
$337$	12.3311	+	21.3581i	0.671718	+	1.16345i	0.977417	+	0.211321i	$0.0677765\pi$
$337$	12.3311	+	21.3581i	0.671718	+	1.16345i	−0.305699	+	0.952128i	$0.598890\pi$
$338$	0.248047	+	0.429630i	0.0134920	+	0.0233688i
$339$	20.6136	+	21.2034i	1.11958	+	1.15161i
$340$	1.06141	−	1.83842i	0.0575633	−	0.0997025i
$341$	−8.69169			−0.470681
$342$	−0.0434733	+	1.54088i	−0.00235077	+	0.0833214i
$343$	−13.1667			−0.710934
$344$	−4.10574	+	7.11135i	−0.221367	+	0.383418i
$345$	−3.36340	+	11.8796i	−0.181079	+	0.639578i
$346$	0.392116	+	0.679165i	0.0210803	+	0.0365121i
$347$	13.0725	+	22.6423i	0.701771	+	1.21550i	0.967844	+	0.251550i	$0.0809402\pi$
$347$	13.0725	+	22.6423i	0.701771	+	1.21550i	−0.266074	+	0.963953i	$0.585726\pi$
$348$	−19.1557	+	4.84428i	−1.02685	+	0.259680i
$349$	9.97134	−	17.2709i	0.533753	−	0.924488i	−0.465469	−	0.885064i	$-0.654114\pi$
$349$	9.97134	−	17.2709i	0.533753	−	0.924488i	0.999223	−	0.0394240i	$-0.0125523\pi$
$350$	5.02889			0.268805
$351$	−4.95772	−	1.55595i	−0.264624	−	0.0830503i
$352$	17.0955			0.911191
$353$	−8.57672	+	14.8553i	−0.456493	+	0.790669i	−0.998773	−	0.0495290i	$-0.984228\pi$
$353$	−8.57672	+	14.8553i	−0.456493	+	0.790669i	0.542280	+	0.840198i	$0.317561\pi$
$354$	−5.89816	+	1.49158i	−0.313483	+	0.0792767i
$355$	−8.00574	−	13.8663i	−0.424901	−	0.735949i
$356$	−7.30685	−	12.6558i	−0.387262	−	0.670758i
$357$	−1.34684	+	4.75710i	−0.0712826	+	0.251772i
$358$	3.77702	−	6.54198i	0.199621	−	0.345755i
$359$	3.15925			0.166739			0.0833694	−	0.996519i	$-0.473432\pi$
$359$	3.15925			0.166739			0.0833694	+	0.996519i	$0.473432\pi$
$360$	6.31283	+	3.88612i	0.332716	+	0.204817i
$361$	−17.9272			−0.943537
$362$	−5.69828	+	9.86972i	−0.299495	+	0.518741i
$363$	0.797084	+	0.819890i	0.0418361	+	0.0430331i
$364$	−2.74421	−	4.75312i	−0.143836	−	0.249131i
$365$	−3.46827	−	6.00723i	−0.181538	−	0.314433i
$366$	8.60968	+	8.85601i	0.450035	+	0.462911i
$367$	−2.01971	+	3.49824i	−0.105428	+	0.182607i	−0.913913	−	0.405910i	$-0.866955\pi$
$367$	−2.01971	+	3.49824i	−0.105428	+	0.182607i	0.808485	+	0.588517i	$0.200288\pi$
$368$	13.8814			0.723616
$369$	13.9326	+	8.57676i	0.725300	+	0.446488i
$370$	5.26475			0.273701
$371$	19.0695	−	33.0294i	0.990041	−	1.71480i
$372$	−2.10642	+	7.43996i	−0.109213	+	0.385744i
$373$	−5.92273	−	10.2585i	−0.306667	−	0.531164i	0.670964	−	0.741490i	$-0.265881\pi$
$373$	−5.92273	−	10.2585i	−0.306667	−	0.531164i	−0.977631	+	0.210327i	$0.932547\pi$
$374$	0.772622	+	1.33822i	0.0399513	+	0.0691977i
$375$	−18.3580	+	4.64256i	−0.948005	+	0.239741i
$376$	8.56399	−	14.8333i	0.441654	−	0.764967i
$377$	6.50423			0.334985
$378$	−7.69647	−	2.41548i	−0.395864	−	0.124239i
$379$	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
$381$	−0.800307	+	0.202389i	−0.0410010	+	0.0103687i
$382$	−1.75448	−	3.03885i	−0.0897672	−	0.155481i
$383$	−12.4042	−	21.4847i	−0.633826	−	1.09782i	−0.986763	−	0.162171i	$-0.948150\pi$
$383$	−12.4042	−	21.4847i	−0.633826	−	1.09782i	0.352937	−	0.935647i	$-0.385183\pi$
$384$	5.35274	−	18.9060i	0.273156	−	0.964795i
$385$	−7.08925	+	12.2789i	−0.361302	+	0.625793i
$386$	−3.97502			−0.202323
$387$	−0.373059	+	13.2228i	−0.0189636	+	0.672154i
$388$	−24.6105			−1.24941
$389$	−5.18742	+	8.98488i	−0.263013	+	0.455551i	−0.967041	−	0.254620i	$-0.918049\pi$
$389$	−5.18742	+	8.98488i	−0.263013	+	0.455551i	0.704028	+	0.710172i	$0.251383\pi$
$390$	−0.794749	−	0.817487i	−0.0402437	−	0.0413951i
$391$	2.45022	+	4.24390i	0.123913	+	0.214623i
$392$	−2.60015	−	4.50359i	−0.131327	−	0.227466i
$393$	10.6380	+	10.9423i	0.536615	+	0.551968i
$394$	2.55455	−	4.42461i	0.128696	−	0.222908i
$395$	16.0669			0.808415
$396$	15.8071	−	8.54113i	0.794336	−	0.429208i
$397$	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
$399$	−1.52931	+	5.40156i	−0.0765611	+	0.270416i
$400$	4.18515	+	7.24889i	0.209257	+	0.362444i
$401$	−11.1544	−	19.3199i	−0.557022	−	0.964790i	−0.997743	−	0.0671462i	$-0.978611\pi$
$401$	−11.1544	−	19.3199i	−0.557022	−	0.964790i	0.440721	−	0.897644i	$-0.354723\pi$
$402$	−7.79238	+	1.97061i	−0.388649	+	0.0982852i
$403$	1.27269	−	2.20436i	0.0633970	−	0.109807i
$404$	−20.7622			−1.03296
$405$	11.9229	+	0.673306i	0.592456	+	0.0334568i
$406$	10.0973			0.501120
$407$	13.6554	−	23.6518i	0.676873	−	1.17238i
$408$	2.85250	−	0.721367i	0.141220	−	0.0357130i
$409$	1.74980	+	3.03074i	0.0865220	+	0.149860i	0.906039	−	0.423195i	$-0.139091\pi$
$409$	1.74980	+	3.03074i	0.0865220	+	0.149860i	−0.819517	+	0.573055i	$0.805758\pi$
$410$	1.79494	+	3.10893i	0.0886459	+	0.153539i
$411$	−4.81142	+	16.9941i	−0.237330	+	0.838257i
$412$	7.19611	−	12.4640i	0.354527	−	0.614058i
$413$	−22.1564			−1.09024
$414$	−7.03419	+	3.80082i	−0.345712	+	0.186800i
$415$	−14.6004			−0.716708
$416$	−2.50321	+	4.33569i	−0.122730	+	0.212575i
$417$	−12.9496	−	13.3201i	−0.634147	−	0.652290i
$418$	0.877291	+	1.51951i	0.0429097	+	0.0743218i
$419$	10.6248	+	18.4026i	0.519054	+	0.899028i	0.999755	+	0.0221430i	$0.00704891\pi$
$419$	10.6248	+	18.4026i	0.519054	+	0.899028i	−0.480701	+	0.876885i	$0.659618\pi$
$420$	8.79253	+	9.04409i	0.429031	+	0.441306i
$421$	−1.11396	+	1.92943i	−0.0542911	+	0.0940349i	−0.891894	−	0.452245i	$-0.850623\pi$
$421$	−1.11396	+	1.92943i	−0.0542911	+	0.0940349i	0.837603	+	0.546280i	$0.183957\pi$
$422$	4.67890			0.227765
$423$	0.778148	−	27.5809i	0.0378348	−	1.34103i
$424$	−22.6971			−1.10227
$425$	−1.47745	+	2.55902i	−0.0716668	+	0.124131i
$426$	2.82459	−	9.97654i	0.136852	−	0.483365i
$427$	22.4908	+	38.9552i	1.08841	+	1.88517i
$428$	0.137339	+	0.237878i	0.00663852	+	0.0114983i
$429$	−5.73393	+	1.45005i	−0.276837	+	0.0700091i
$430$	−1.45125	+	2.51364i	−0.0699854	+	0.121218i
$431$	10.3044			0.496343			0.248172	−	0.968716i	$-0.420170\pi$
$431$	10.3044			0.496343			0.248172	+	0.968716i	$0.420170\pi$
$432$	−2.92337	−	13.1043i	−0.140651	−	0.630481i
$433$	−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
$435$	−14.4920	+	3.66487i	−0.694837	+	0.175717i
$436$	−6.60134	−	11.4339i	−0.316147	−	0.547583i
$437$	2.78215	+	4.81883i	0.133088	+	0.230516i
$438$	1.22368	−	4.32207i	0.0584696	−	0.206517i
$439$	−7.86943	+	13.6303i	−0.375587	+	0.650536i	−0.990415	−	0.138125i	$-0.955892\pi$
$439$	−7.86943	+	13.6303i	−0.375587	+	0.650536i	0.614827	+	0.788662i	$0.289226\pi$
$440$	8.43783			0.402258
$441$	−7.13394	−	4.39159i	−0.339711	−	0.209123i
$442$	−0.452527			−0.0215245
$443$	4.77962	−	8.27855i	0.227087	−	0.393326i	−0.729857	−	0.683600i	$-0.760413\pi$
$443$	4.77962	−	8.27855i	0.227087	−	0.393326i	0.956943	+	0.290275i	$0.0937466\pi$
$444$	−16.9363	−	17.4208i	−0.803759	−	0.826756i
$445$	−5.52790	−	9.57460i	−0.262047	−	0.453879i
$446$	−4.61999	−	8.00205i	−0.218763	−	0.378908i
$447$	−18.2746	−	18.7975i	−0.864359	−	0.889089i
$448$	4.19977	−	7.27421i	0.198420	−	0.343674i
$449$	−15.7163			−0.741696			−0.370848	−	0.928694i	$-0.620933\pi$
$449$	−15.7163			−0.741696			−0.370848	+	0.928694i	$0.620933\pi$
$450$	−4.10557	−	2.52735i	−0.193538	−	0.119140i
$451$	18.6225			0.876898
$452$	14.9725	−	25.9331i	0.704246	−	1.21979i
$453$	5.75160	−	20.3148i	0.270234	−	0.954475i
$454$	−3.49769	−	6.05817i	−0.164155	−	0.284324i
$455$	−2.07610	−	3.59590i	−0.0973289	−	0.168579i
$456$	3.23893	−	0.819093i	0.151677	−	0.0383575i
$457$	−16.4521	+	28.4958i	−0.769594	+	1.33298i	0.168189	+	0.985755i	$0.446208\pi$
$457$	−16.4521	+	28.4958i	−0.769594	+	1.33298i	−0.937783	+	0.347222i	$0.887125\pi$
$458$	−1.01734			−0.0475370
$459$	3.49032	−	3.20680i	0.162914	−	0.149681i
$460$	12.5023			0.582921
$461$	−6.38861	+	11.0654i	−0.297547	+	0.515367i	−0.975574	−	0.219670i	$-0.929502\pi$
$461$	−6.38861	+	11.0654i	−0.297547	+	0.515367i	0.678027	+	0.735037i	$0.262835\pi$
$462$	−8.90146	+	2.25109i	−0.414134	+	0.104730i
$463$	2.63733	+	4.56799i	0.122567	+	0.212293i	0.920779	−	0.390084i	$-0.127554\pi$
$463$	2.63733	+	4.56799i	0.122567	+	0.212293i	−0.798212	+	0.602376i	$0.794221\pi$
$464$	8.40319	+	14.5547i	0.390108	+	0.675687i
$465$	−1.59359	+	5.62860i	−0.0739008	+	0.261020i
$466$	1.98803	−	3.44336i	0.0920936	−	0.159511i
$467$	−18.5837			−0.859953			−0.429977	−	0.902840i	$-0.641478\pi$
$467$	−18.5837			−0.859953			−0.429977	+	0.902840i	$0.641478\pi$
$468$	−0.148390	+	5.25958i	−0.00685932	+	0.243124i
$469$	−29.2720			−1.35165
$470$	3.02710	−	5.24309i	0.139630	−	0.241846i
$471$	−4.64145	−	4.77424i	−0.213867	−	0.219986i
$472$	6.59278	+	11.4190i	0.303457	+	0.525603i
$473$	7.52833	+	13.0394i	0.346153	+	0.599554i
$474$	7.25267	+	7.46018i	0.333126	+	0.342657i
$475$	−1.67760	+	2.90570i	−0.0769738	+	0.133323i
$476$	5.00643			0.229469
$477$	−32.1678	+	17.3814i	−1.47286	+	0.795839i
$478$	1.73396			0.0793093
$479$	0.541178	−	0.937348i	0.0247271	−	0.0428285i	−0.853397	−	0.521261i	$-0.825462\pi$
$479$	0.541178	−	0.937348i	0.0247271	−	0.0428285i	0.878124	+	0.478433i	$0.158795\pi$
$480$	3.13438	−	11.0708i	0.143064	−	0.505308i
$481$	3.99900	+	6.92647i	0.182339	+	0.315820i
$482$	1.76804	+	3.06233i	0.0805318	+	0.139485i
$483$	−28.2292	+	7.13888i	−1.28447	+	0.324830i
$484$	0.578953	−	1.00278i	0.0263160	−	0.0455807i
$485$	−18.6188			−0.845434
$486$	5.06943	+	5.83998i	0.229954	+	0.264907i
$487$	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
$489$	−8.80259	+	2.22609i	−0.398067	+	0.100667i
$490$	−0.919071	−	1.59188i	−0.0415194	−	0.0719137i
$491$	8.40485	+	14.5576i	0.379306	+	0.656977i	0.990961	−	0.134147i	$-0.0428295\pi$
$491$	8.40485	+	14.5576i	0.379306	+	0.656977i	−0.611656	+	0.791124i	$0.709496\pi$
$492$	4.51314	−	15.9406i	0.203468	−	0.718656i
$493$	−2.96651	+	5.13815i	−0.133605	+	0.231411i
$494$	−0.513832			−0.0231184
$495$	11.9586	−	6.46167i	0.537500	−	0.290431i
$496$	6.57702			0.295317
$497$	18.8805	−	32.7021i	0.846908	−	1.46689i
$498$	−6.59070	−	6.77927i	−0.295336	−	0.303786i
$499$	10.4420	+	18.0861i	0.467449	+	0.809646i	0.999308	−	0.0371871i	$-0.0118397\pi$
$499$	10.4420	+	18.0861i	0.467449	+	0.809646i	−0.531859	+	0.846833i	$0.678506\pi$
$500$	9.58737	+	16.6058i	0.428760	+	0.742635i
$501$	21.4712	+	22.0855i	0.959264	+	0.986709i
$502$	−2.68033	+	4.64247i	−0.119629	+	0.207203i
$503$	2.96223			0.132079			0.0660397	−	0.997817i	$-0.478964\pi$
$503$	2.96223			0.132079			0.0660397	+	0.997817i	$0.478964\pi$
$504$	−0.493052	+	17.4759i	−0.0219623	+	0.778438i
$505$	−15.7073			−0.698967
$506$	−4.55031	+	7.88136i	−0.202286	+	0.350369i
$507$	0.471837	−	1.66654i	0.0209550	−	0.0740138i
$508$	0.417956	+	0.723920i	0.0185438	+	0.0321188i
$509$	−10.4883	−	18.1663i	−0.464885	−	0.805205i	0.534311	−	0.845288i	$-0.320571\pi$
$509$	−10.4883	−	18.1663i	−0.464885	−	0.805205i	−0.999196	+	0.0400828i	$0.987238\pi$
$510$	1.00827	−	0.254980i	0.0446468	−	0.0112907i
$511$	8.17950	−	14.1673i	0.361840	−	0.626725i
$512$	−22.5601			−0.997027
$513$	3.96316	−	3.64124i	0.174978	−	0.160765i
$514$	−11.9274			−0.526096
$515$	5.44411	−	9.42948i	0.239896	−	0.415513i
$516$	12.9861	−	3.28404i	0.571680	−	0.144572i
$517$	−15.7030	−	27.1984i	−0.690618	−	1.19619i
$518$	6.20813	+	10.7528i	0.272769	+	0.472450i
$519$	0.745886	−	2.63449i	0.0327408	−	0.115641i
$520$	−1.23551	+	2.13997i	−0.0541809	+	0.0938440i
$521$	34.1685			1.49695			0.748474	−	0.663164i	$-0.230787\pi$
$521$	34.1685			1.49695			0.748474	+	0.663164i	$0.230787\pi$
$522$	−8.24340	−	5.07456i	−0.360804	−	0.222108i
$523$	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
$525$	−12.2389	−	12.5890i	−0.534148	−	0.549431i
$526$	−0.291227	−	0.504420i	−0.0126981	−	0.0219937i
$527$	1.16092	+	2.01077i	0.0505704	+	0.0875905i
$528$	−10.6528	−	10.9576i	−0.463605	−	0.476869i
$529$	−2.93039	+	5.07558i	−0.127408	+	0.220678i
$530$	−8.02270			−0.348484
$531$	18.0884	+	11.1350i	0.784969	+	0.483220i
$532$	5.68467			0.246462
$533$	−2.72681	+	4.72297i	−0.118111	+	0.204574i
$534$	1.95035	−	6.88872i	0.0844001	−	0.298104i
$535$	0.103902	+	0.179963i	0.00449207	+	0.00778049i
$536$	8.71009	+	15.0863i	0.376218	+	0.651629i
$537$	−25.5690	+	6.46614i	−1.10338	+	0.279035i
$538$	−4.08656	+	7.07812i	−0.176184	+	0.305160i
$539$	−9.53533			−0.410716
$540$	−2.63293	−	11.8024i	−0.113303	−	0.507894i
$541$	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
$543$	38.5753	−	9.75530i	1.65543	−	0.418640i
$544$	−2.28338	−	3.95493i	−0.0978991	−	0.169566i
$545$	−4.99415	−	8.65013i	−0.213926	−	0.370531i
$546$	0.732489	−	2.58718i	0.0313476	−	0.110721i
$547$	10.8599	−	18.8099i	0.464335	−	0.804252i	−0.534836	−	0.844956i	$-0.679627\pi$
$547$	10.8599	−	18.8099i	0.464335	−	0.804252i	0.999171	+	0.0407040i	$0.0129601\pi$
$548$	17.8848			0.764001
$549$	1.21616	−	43.1060i	0.0519045	−	1.83972i
$550$	−5.48756			−0.233990
$551$	−3.36839	+	5.83423i	−0.143498	+	0.248547i
$552$	12.0791	+	12.4247i	0.514119	+	0.528829i
$553$	18.9459	+	32.8153i	0.805663	+	1.39545i
$554$	−4.17759	−	7.23580i	−0.177489	−	0.307420i
$555$	−12.8129	−	13.1795i	−0.543877	−	0.559438i
$556$	−9.40582	+	16.2914i	−0.398896	+	0.690908i
$557$	18.3186			0.776183			0.388091	−	0.921621i	$-0.373135\pi$
$557$	18.3186			0.776183			0.388091	+	0.921621i	$0.373135\pi$
$558$	−3.33282	+	1.80084i	−0.141089	+	0.0762356i
$559$	−4.40936			−0.186496
$560$	5.36446	−	9.29151i	0.226690	−	0.392638i
$561$	1.46969	−	5.19099i	0.0620503	−	0.219164i
$562$	5.35995	+	9.28370i	0.226096	+	0.391609i
$563$	22.4531	+	38.8899i	0.946286	+	1.63902i	0.753155	+	0.657843i	$0.228531\pi$
$563$	22.4531	+	38.8899i	0.946286	+	1.63902i	0.193131	+	0.981173i	$0.438136\pi$
$564$	−27.0871	+	6.85004i	−1.14057	+	0.288439i
$565$	11.3272	−	19.6193i	0.476540	−	0.825391i
$566$	−1.94296			−0.0816688
$567$	12.6842	+	25.1455i	0.532687	+	1.05601i
$568$	−22.4722			−0.942911
$569$	−17.1457	+	29.6973i	−0.718786	+	1.24497i	0.242695	+	0.970103i	$0.421969\pi$
$569$	−17.1457	+	29.6973i	−0.718786	+	1.24497i	−0.961481	+	0.274871i	$0.911365\pi$
$570$	1.14486	−	0.289523i	0.0479529	−	0.0121268i
$571$	−7.91642	−	13.7116i	−0.331292	−	0.573814i	0.651474	−	0.758671i	$-0.274151\pi$
$571$	−7.91642	−	13.7116i	−0.331292	−	0.573814i	−0.982765	+	0.184857i	$0.940818\pi$
$572$	2.99451	+	5.18664i	0.125207	+	0.216864i
$573$	−3.33739	+	11.7878i	−0.139422	+	0.492442i
$574$	−4.23315	+	7.33203i	−0.176688	+	0.306033i
$575$	−17.4027			−0.725743
$576$	−7.08445	+	3.82798i	−0.295186	+	0.159499i
$577$	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
$579$	9.67406	+	9.95085i	0.402040	+	0.413543i
$580$	7.56834	+	13.1088i	0.314258	+	0.544311i
$581$	−17.2167	−	29.8202i	−0.714268	−	1.23715i
$582$	−8.40458	−	8.64504i	−0.348381	−	0.358349i
$583$	−20.8088	+	36.0419i	−0.861813	+	1.49270i
$584$	−9.73547			−0.402856
$585$	−0.112262	+	3.97906i	−0.00464147	+	0.164514i
$586$	6.60121			0.272694
$587$	7.32790	−	12.6923i	0.302455	−	0.523867i	−0.674237	−	0.738515i	$-0.735527\pi$
$587$	7.32790	−	12.6923i	0.302455	−	0.523867i	0.976691	+	0.214648i	$0.0688605\pi$
$588$	−2.31088	+	8.16211i	−0.0952991	+	0.336600i
$589$	1.31819	+	2.28317i	0.0543151	+	0.0940765i
$590$	2.33034	+	4.03626i	0.0959385	+	0.166170i
$591$	−17.2934	+	4.37331i	−0.711354	+	0.179894i
$592$	−10.3331	+	17.8974i	−0.424687	+	0.735579i
$593$	20.3341			0.835021			0.417510	−	0.908672i	$-0.362903\pi$
$593$	20.3341			0.835021			0.417510	+	0.908672i	$0.362903\pi$
$594$	8.39845	+	2.63580i	0.344593	+	0.108148i
$595$	3.78754			0.155274
$596$	−13.2735	+	22.9904i	−0.543705	+	0.941725i
$597$	9.35215	−	2.36506i	0.382758	−	0.0967956i
$598$	−1.33256	−	2.30807i	−0.0544926	−	0.0943839i
$599$	22.9738	+	39.7918i	0.938684	+	1.62585i	0.767930	+	0.640534i	$0.221287\pi$
$599$	22.9738	+	39.7918i	0.938684	+	1.62585i	0.170754	+	0.985314i	$0.445380\pi$
$600$	−2.84643	+	10.0537i	−0.116205	+	0.410440i
$601$	−12.0518	+	20.8743i	−0.491602	+	0.851480i	−0.999953	−	0.00966978i	$-0.996922\pi$
$601$	−12.0518	+	20.8743i	−0.491602	+	0.851480i	0.508351	+	0.861150i	$0.330255\pi$
$602$	−6.84518			−0.278989
$603$	23.8976	+	14.7111i	0.973184	+	0.599083i
$604$	−21.3796			−0.869923
$605$	0.437999	−	0.758636i	0.0178072	−	0.0308429i
$606$	−7.09035	−	7.29321i	−0.288026	−	0.296266i
$607$	18.3605	+	31.8013i	0.745229	+	1.29077i	0.950088	+	0.311983i	$0.100993\pi$
$607$	18.3605	+	31.8013i	0.745229	+	1.29077i	−0.204859	+	0.978791i	$0.565674\pi$
$608$	−2.59272	−	4.49072i	−0.105149	−	0.182123i
$609$	−24.5739	−	25.2770i	−0.995786	−	1.02428i
$610$	4.73103	−	8.19438i	0.191554	−	0.331781i
$611$	9.19730			0.372083
$612$	−4.08723	−	2.51606i	−0.165217	−	0.101706i
$613$	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
$615$	3.41435	−	12.0596i	0.137680	−	0.486291i
$616$	9.94979	+	17.2335i	0.400888	+	0.694359i
$617$	−5.16646	−	8.94857i	−0.207994	−	0.360256i	0.743089	−	0.669193i	$-0.233360\pi$
$617$	−5.16646	−	8.94857i	−0.207994	−	0.360256i	−0.951082	+	0.308937i	$0.900027\pi$
$618$	6.83578	−	1.72870i	0.274976	−	0.0695385i
$619$	18.3253	−	31.7403i	0.736554	−	1.27575i	−0.217484	−	0.976064i	$-0.569785\pi$
$619$	18.3253	−	31.7403i	0.736554	−	1.27575i	0.954038	−	0.299685i	$-0.0968817\pi$
$620$	5.92360			0.237898
$621$	26.6340	+	8.35890i	1.06879	+	0.335431i
$622$	2.04042			0.0818133
$623$	13.0369	−	22.5805i	0.522311	−	0.904669i
$624$	4.33888	−	1.09726i	0.173694	−	0.0439255i
$625$	−0.845270	−	1.46405i	−0.0338108	−	0.0585620i
$626$	−0.863057	−	1.49486i	−0.0344947	−	0.0597466i
$627$	1.66879	−	5.89423i	0.0666451	−	0.235393i
$628$	−3.37126	+	5.83920i	−0.134528	+	0.233009i
$629$	−7.29561			−0.290895
$630$	−0.174278	+	6.17718i	−0.00694341	+	0.246105i
$631$	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
$633$	−11.3871	−	11.7129i	−0.452597	−	0.465546i
$634$	6.21626	+	10.7669i	0.246879	+	0.427607i
$635$	0.316198	+	0.547672i	0.0125480	+	0.0217337i
$636$	25.8084	+	26.5468i	1.02337	+	1.05265i
$637$	1.39622	−	2.41832i	0.0553201	−	0.0958173i
$638$	−11.0183			−0.436217
$639$	−31.8490	+	17.2091i	−1.25993	+	0.680783i
$640$	−15.0528			−0.595012
$641$	−3.31269	+	5.73775i	−0.130844	+	0.226628i	−0.924002	−	0.382388i	$-0.875102\pi$
$641$	−3.31269	+	5.73775i	−0.130844	+	0.226628i	0.793158	+	0.609015i	$0.208435\pi$
$642$	−0.0366587	+	0.129480i	−0.00144680	+	0.00511016i
$643$	−15.7291	−	27.2436i	−0.620294	−	1.07438i	−0.989431	−	0.145006i	$-0.953680\pi$
$643$	−15.7291	−	27.2436i	−0.620294	−	1.07438i	0.369137	−	0.929375i	$-0.379653\pi$
$644$	14.7425	+	25.5348i	0.580937	+	1.00621i
$645$	9.82443	−	2.48450i	0.386836	−	0.0978269i
$646$	0.234353	−	0.405912i	0.00922051	−	0.0159704i
$647$	20.2079			0.794456			0.397228	−	0.917720i	$-0.369972\pi$
$647$	20.2079			0.794456			0.397228	+	0.917720i	$0.369972\pi$
$648$	9.18532	−	14.0195i	0.360834	−	0.550737i
$649$	24.1772			0.949038
$650$	0.803520	−	1.39174i	0.0315166	−	0.0545884i
$651$	−13.3751	+	3.38242i	−0.524210	+	0.132567i
$652$	4.59710	+	7.96241i	0.180036	+	0.311832i
$653$	1.29686	+	2.24622i	0.0507500	+	0.0879015i	0.890284	−	0.455405i	$-0.150506\pi$
$653$	1.29686	+	2.24622i	0.0507500	+	0.0879015i	−0.839534	+	0.543306i	$0.817172\pi$
$654$	1.76204	−	6.22358i	0.0689012	−	0.243361i
$655$	5.84558	−	10.1248i	0.228406	−	0.395610i
$656$	−14.0917			−0.550187
$657$	−13.7977	+	7.45540i	−0.538301	+	0.290863i
$658$	14.2781			0.556617
$659$	7.95387	−	13.7765i	0.309839	−	0.536657i	−0.668488	−	0.743723i	$-0.733058\pi$
$659$	7.95387	−	13.7765i	0.309839	−	0.536657i	0.978327	+	0.207066i	$0.0663916\pi$
$660$	−9.59448	−	9.86898i	−0.373464	−	0.384150i
$661$	−18.5869	−	32.1934i	−0.722945	−	1.25218i	−0.959814	−	0.280636i	$-0.909455\pi$
$661$	−18.5869	−	32.1934i	−0.722945	−	1.25218i	0.236869	−	0.971542i	$-0.423879\pi$
$662$	0.0670189	+	0.116080i	0.00260476	+	0.00451158i
$663$	1.10132	+	1.13283i	0.0427718	+	0.0439955i
$664$	−10.2459	+	17.7464i	−0.397618	+	0.688694i
$665$	4.30066			0.166772
$666$	0.335697	−	11.8985i	0.0130080	−	0.461059i
$667$	−34.9422			−1.35297
$668$	15.5954	−	27.0120i	0.603403	−	1.04512i
$669$	−8.78818	+	31.0401i	−0.339771	+	1.20008i
$670$	3.07874	+	5.33253i	0.118942	+	0.206014i
$671$	−24.5421	−	42.5082i	−0.947439	−	1.64101i
$672$	26.3071	−	6.65279i	1.01482	−	0.256637i
$673$	20.1992	−	34.9860i	0.778621	−	1.34861i	−0.154116	−	0.988053i	$-0.549253\pi$
$673$	20.1992	−	34.9860i	0.778621	−	1.34861i	0.932737	−	0.360558i	$-0.117414\pi$
$674$	12.2348			0.471265
$675$	3.66495	+	16.4285i	0.141064	+	0.632333i
$676$	−1.75389			−0.0674573
$677$	0.401269	−	0.695018i	0.0154220	−	0.0267117i	−0.858211	−	0.513296i	$-0.828424\pi$
$677$	0.401269	−	0.695018i	0.0154220	−	0.0267117i	0.873633	+	0.486585i	$0.161757\pi$
$678$	14.2228	−	3.59679i	0.546222	−	0.138134i
$679$	−21.9550	−	38.0272i	−0.842556	−	1.45935i
$680$	−1.12701	−	1.95204i	−0.0432189	−	0.0748573i
$681$	−6.65333	+	23.4998i	−0.254956	+	0.900514i
$682$	−2.15595	+	3.73421i	−0.0825555	+	0.142990i
$683$	−50.3853			−1.92794			−0.963971	−	0.266008i	$-0.914295\pi$
$683$	−50.3853			−1.92794			−0.963971	+	0.266008i	$0.914295\pi$
$684$	−4.64094	−	2.85692i	−0.177451	−	0.109237i
$685$	13.5305			0.516974
$686$	−3.26596	+	5.65680i	−0.124695	+	0.215978i
$687$	2.47591	+	2.54675i	0.0944618	+	0.0971645i
$688$	−5.69671	−	9.86698i	−0.217185	−	0.376175i
$689$	−6.09389	−	10.5549i	−0.232159	−	0.402111i
$690$	4.26957	+	4.39172i	0.162540	+	0.167190i
$691$	8.72144	−	15.1060i	0.331779	−	0.574658i	−0.651082	−	0.759008i	$-0.725684\pi$
$691$	8.72144	−	15.1060i	0.331779	−	0.574658i	0.982861	+	0.184349i	$0.0590178\pi$
$692$	−2.77257			−0.105397
$693$	27.2989	+	16.8049i	1.03700	+	0.638367i
$694$	12.9704			0.492350
$695$	−7.11584	+	12.3250i	−0.269919	+	0.467514i
$696$	−5.71523	+	20.1864i	−0.216635	+	0.765162i
$697$	−2.48734	−	4.30819i	−0.0942146	−	0.163184i
$698$	−4.94672	−	8.56797i	−0.187236	−	0.324302i
$699$	−13.4582	+	3.40345i	−0.509037	+	0.128730i
$700$	−8.88956	+	15.3972i	−0.335994	+	0.581959i
$701$	−29.9544			−1.13136			−0.565680	−	0.824625i	$-0.691386\pi$
$701$	−29.9544			−1.13136			−0.565680	+	0.824625i	$0.691386\pi$
$702$	−1.89823	+	1.74404i	−0.0716441	+	0.0658245i
$703$	−8.28397			−0.312436
$704$	−4.58282	+	7.93768i	−0.172722	+	0.299163i
$705$	−20.4924	+	5.18231i	−0.771787	+	0.195177i
$706$	4.25486	+	7.36964i	0.160134	+	0.277360i
$707$	−18.5219	−	32.0809i	−0.696588	−	1.20652i
$708$	5.85932	−	20.6953i	0.220207	−	0.777778i
$709$	−1.71866	+	2.97681i	−0.0645458	+	0.111797i	−0.896492	−	0.443059i	$-0.853893\pi$
$709$	−1.71866	+	2.97681i	−0.0645458	+	0.111797i	0.831947	+	0.554856i	$0.187227\pi$
$710$	−7.94320			−0.298103
$711$	1.02448	−	36.3119i	0.0384209	−	1.36180i
$712$	−15.5168			−0.581518
$713$	−6.83715	+	11.8423i	−0.256053	+	0.443497i
$714$	1.70971	+	1.75863i	0.0639844	+	0.0658150i
$715$	2.26545	+	3.92388i	0.0847231	+	0.146745i
$716$	13.3533	+	23.1285i	0.499035	+	0.864354i
$717$	−4.21996	−	4.34069i	−0.157597	−	0.162106i
$718$	0.783643	−	1.35731i	0.0292453	−	0.0506543i
$719$	−34.0368			−1.26936			−0.634680	−	0.772775i	$-0.718868\pi$
$719$	−34.0368			−1.26936			−0.634680	+	0.772775i	$0.718868\pi$
$720$	−9.04913	+	4.88956i	−0.337241	+	0.182223i
$721$	25.6785			0.956319
$722$	−4.44679	+	7.70207i	−0.165492	+	0.286641i
$723$	3.36317	−	11.8788i	0.125078	−	0.441779i
$724$	−20.1457	−	34.8934i	−0.748710	−	1.29680i
$725$	−10.5349	−	18.2469i	−0.391255	−	0.677673i
$726$	0.549964	−	0.139080i	0.0204111	−	0.00516175i
$727$	18.5696	−	32.1635i	0.688708	−	1.19288i	−0.283548	−	0.958958i	$-0.591512\pi$
$727$	18.5696	−	32.1635i	0.688708	−	1.19288i	0.972256	−	0.233919i	$-0.0751551\pi$
$728$	−5.82762			−0.215986
$729$	2.28194	−	26.9034i	0.0845164	−	0.996422i
$730$	−3.44118			−0.127364
$731$	2.01106	−	3.48326i	0.0743819	−	0.128833i
$732$	−42.3342	+	10.7059i	−1.56472	+	0.395701i
$733$	−13.6999	−	23.7290i	−0.506018	−	0.876449i	−0.999976	−	0.00696311i	$-0.997784\pi$
$733$	−13.6999	−	23.7290i	−0.506018	−	0.876449i	0.493958	−	0.869486i	$-0.335550\pi$
$734$	1.00197	+	1.73546i	0.0369833	+	0.0640569i
$735$	−1.74826	+	6.17493i	−0.0644857	+	0.227766i
$736$	13.4478	−	23.2923i	0.495693	−	0.858566i
$737$	31.9418			1.17659
$738$	7.14076	−	3.85841i	0.262855	−	0.142030i
$739$	−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
$741$	1.25052	+	1.28630i	0.0459390	+	0.0472534i
$742$	−9.46028	−	16.3857i	−0.347298	−	0.601537i
$743$	8.88960	+	15.3972i	0.326128	+	0.564870i	0.981740	−	0.190228i	$-0.0609227\pi$
$743$	8.88960	+	15.3972i	0.326128	+	0.564870i	−0.655612	+	0.755098i	$0.727589\pi$
$744$	5.72309	+	5.88683i	0.209819	+	0.215822i
$745$	−10.0419	+	17.3931i	−0.367907	+	0.637234i
$746$	−5.87646			−0.215153
$747$	−0.930970	+	32.9976i	−0.0340624	+	1.20732i
$748$	−5.46306			−0.199749
$749$	−0.245040	+	0.424421i	−0.00895355	+	0.0155080i
$750$	−2.55907	+	9.03874i	−0.0934442	+	0.330048i
$751$	−13.9878	−	24.2276i	−0.510424	−	0.884079i	−0.999927	−	0.0120781i	$-0.996155\pi$
$751$	−13.9878	−	24.2276i	−0.510424	−	0.884079i	0.489504	−	0.872001i	$-0.337178\pi$
$752$	11.8825	+	20.5811i	0.433311	+	0.750516i
$753$	18.1449	−	4.58865i	0.661236	−	0.167220i
$754$	1.61335	−	2.79441i	0.0587549	−	0.101766i
$755$	−16.1744			−0.588648
$756$	21.0007	−	19.2948i	0.763786	−	0.701745i
$757$	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
$759$	30.8039	−	7.79000i	1.11811	−	0.282759i
$760$	−1.27969	−	2.21649i	−0.0464192	−	0.0804005i
$761$	−2.44851	−	4.24094i	−0.0887583	−	0.153734i	0.818228	−	0.574894i	$-0.194957\pi$
$761$	−2.44851	−	4.24094i	−0.0887583	−	0.153734i	−0.906987	+	0.421160i	$0.861623\pi$
$762$	−0.111561	+	0.394038i	−0.00404144	+	0.0142745i
$763$	11.7781	−	20.4003i	0.426396	−	0.738539i
$764$	12.4056			0.448819
$765$	−3.09214	−	1.90349i	−0.111797	−	0.0688209i
$766$	−12.3073			−0.444681
$767$	−3.54016	+	6.13174i	−0.127828	+	0.221404i
$768$	−0.313400	−	0.322367i	−0.0113089	−	0.0116324i
$769$	10.0123	+	17.3418i	0.361053	+	0.625362i	0.988134	−	0.153592i	$-0.0490840\pi$
$769$	10.0123	+	17.3418i	0.361053	+	0.625362i	−0.627081	+	0.778954i	$0.715751\pi$
$770$	3.51693	+	6.09151i	0.126742	+	0.219523i
$771$	29.0279	+	29.8584i	1.04542	+	1.07533i
$772$	7.02664	−	12.1705i	0.252894	−	0.438026i
$773$	−0.827218			−0.0297530			−0.0148765	−	0.999889i	$-0.504736\pi$
$773$	−0.827218			−0.0297530			−0.0148765	+	0.999889i	$0.504736\pi$
$774$	5.58838	+	3.44016i	0.200870	+	0.123654i
$775$	−8.24544			−0.296185
$776$	−13.0657	+	22.6305i	−0.469033	+	0.812388i
$777$	11.8091	−	41.7103i	0.423651	−	1.49635i
$778$	2.57345	+	4.45734i	0.0922626	+	0.159804i
$779$	−2.82430	−	4.89184i	−0.101191	−	0.175268i
$780$	3.90782	−	0.988246i	0.139922	−	0.0353849i
$781$	−20.6026	+	35.6848i	−0.737219	+	1.27690i
$782$	2.43107			0.0869350
$783$	7.35870	+	32.9861i	0.262979	+	1.17883i
$784$	7.21541			0.257693
$785$	−2.55048	+	4.41756i	−0.0910306	+	0.157670i
$786$	7.33987	−	1.85618i	0.261805	−	0.0662077i
$787$	2.10102	+	3.63908i	0.0748934	+	0.129719i	0.901040	−	0.433736i	$-0.142805\pi$
$787$	2.10102	+	3.63908i	0.0748934	+	0.129719i	−0.826147	+	0.563455i	$0.809472\pi$
$788$	9.03135	+	15.6428i	0.321728	+	0.557250i
$789$	−0.553974	+	1.95666i	−0.0197220	+	0.0696588i
$790$	3.98535	−	6.90283i	0.141792	−	0.245592i
$791$	53.4277			1.89967
$792$	0.538022	−	19.0698i	0.0191178	−	0.677617i
$793$	14.3744			0.510450
$794$	4.86002	−	8.41779i	0.172476	−	0.298736i
$795$	19.5250	+	20.0836i	0.692479	+	0.712292i
$796$	−4.88410	−	8.45951i	−0.173112	−	0.299840i
$797$	6.74376	+	11.6805i	0.238876	+	0.413746i	0.960392	−	0.278652i	$-0.0898876\pi$
$797$	6.74376	+	11.6805i	0.238876	+	0.413746i	−0.721516	+	0.692398i	$0.756554\pi$
$798$	1.94133	+	1.99688i	0.0687224	+	0.0706887i
$799$	−4.19479	+	7.26560i	−0.148401	+	0.257038i
$800$	16.2178			0.573384
$801$	−21.9915	+	11.8828i	−0.777030	+	0.419857i
$802$	−11.0672			−0.390797
$803$	−8.92553	+	15.4595i	−0.314975	+	0.545553i
$804$	7.74108	−	27.3418i	0.273007	−	0.964269i
$805$	11.1533	+	19.3180i	0.393101	+	0.680870i
$806$	−0.631372	−	1.09357i	−0.0222391	−	0.0385193i
$807$	27.6645	−	6.99607i	0.973837	−	0.246273i
$808$	−11.0226	+	19.0918i	−0.387775	+	0.671646i
$809$	3.02951			0.106512			0.0532559	−	0.998581i	$-0.483040\pi$
$809$	3.02951			0.106512			0.0532559	+	0.998581i	$0.483040\pi$
$810$	3.24672	−	4.95544i	0.114078	−	0.174116i
$811$	−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
$813$	−51.9697	+	13.1426i	−1.82266	+	0.460931i
$814$	−6.77436	−	11.7335i	−0.237441	−	0.411260i
$815$	3.47787	+	6.02385i	0.121825	+	0.211006i
$816$	−1.11212	+	3.92803i	−0.0389319	+	0.137509i
$817$	2.28351	−	3.95515i	0.0798899	−	0.138373i
$818$	1.73613			0.0607023
$819$	−8.25927	+	4.46278i	−0.288602	+	0.155942i
$820$	−12.6917			−0.443213
$821$	−11.9354	+	20.6727i	−0.416548	+	0.721483i	−0.995590	−	0.0938153i	$-0.970094\pi$
$821$	−11.9354	+	20.6727i	−0.416548	+	0.721483i	0.579041	+	0.815298i	$0.303427\pi$
$822$	6.10772	+	6.28247i	0.213031	+	0.219126i
$823$	9.40358	+	16.2875i	0.327788	+	0.567746i	0.982073	−	0.188503i	$-0.0603635\pi$
$823$	9.40358	+	16.2875i	0.327788	+	0.567746i	−0.654285	+	0.756248i	$0.727030\pi$
$824$	−7.64083	−	13.2343i	−0.266181	−	0.461039i
$825$	13.3552	+	13.7373i	0.464967	+	0.478270i
$826$	−5.49582	+	9.51903i	−0.191224	+	0.331209i
$827$	−53.8381			−1.87213			−0.936067	−	0.351822i	$-0.885562\pi$
$827$	−53.8381			−1.87213			−0.936067	+	0.351822i	$0.885562\pi$
$828$	0.797184	−	28.2556i	0.0277040	−	0.981951i
$829$	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
$831$	−7.94665	+	28.0678i	−0.275666	+	0.973663i
$832$	−1.34209	−	2.32456i	−0.0465284	−	0.0805896i
$833$	1.27360	+	2.20594i	0.0441276	+	0.0764313i
$834$	−8.93485	+	2.25953i	−0.309389	+	0.0782412i
$835$	11.7985	−	20.4355i	0.408303	−	0.707201i
$836$	−6.20315			−0.214541
$837$	12.6193	+	3.96047i	0.436185	+	0.136894i
$838$	10.5418			0.364159
$839$	−26.0416	+	45.1054i	−0.899056	+	1.55721i	−0.0703519	+	0.997522i	$0.522412\pi$
$839$	−26.0416	+	45.1054i	−0.899056	+	1.55721i	−0.828704	+	0.559688i	$0.810921\pi$
$840$	12.9844	−	3.28362i	0.448005	−	0.113296i
$841$	−6.65250	−	11.5225i	−0.229397	−	0.397327i
$842$	0.552629	+	0.957181i	0.0190448	+	0.0329866i
$843$	10.1957	−	36.0117i	0.351160	−	1.24031i
$844$	−8.27089	+	14.3256i	−0.284696	+	0.493108i
$845$	−1.32688			−0.0456461
$846$	−11.6566	−	7.17568i	−0.400761	−	0.246705i
$847$	2.06593			0.0709863
$848$	15.7461	−	27.2730i	0.540723	−	0.936560i
$849$	4.72861	+	4.86391i	0.162286	+	0.166929i
$850$	0.732954	+	1.26951i	0.0251401	+	0.0435440i
$851$	−21.4835	−	37.2105i	−0.736445	−	1.27556i
$852$	25.5526	+	26.2837i	0.875418	+	0.900465i
$853$	25.9591	−	44.9625i	0.888823	−	1.53949i	0.0475550	−	0.998869i	$-0.484857\pi$
$853$	25.9591	−	44.9625i	0.888823	−	1.53949i	0.841268	−	0.540618i	$-0.181810\pi$
$854$	22.3151			0.763607
$855$	−3.51104	−	2.16137i	−0.120075	−	0.0739171i
$856$	0.291653			0.00996849
$857$	14.4637	−	25.0518i	0.494069	−	0.855753i	−0.505908	−	0.862588i	$-0.668842\pi$
$857$	14.4637	−	25.0518i	0.494069	−	0.855753i	0.999977	+	0.00683492i	$0.00217564\pi$
$858$	−0.799298	+	2.82315i	−0.0272876	+	0.0963807i
$859$	3.13587	+	5.43148i	0.106994	+	0.185320i	0.914551	−	0.404470i	$-0.132544\pi$
$859$	3.13587	+	5.43148i	0.106994	+	0.185320i	−0.807557	+	0.589790i	$0.799211\pi$
$860$	−5.13075	−	8.88671i	−0.174957	−	0.303034i
$861$	28.6569	−	7.24703i	0.976624	−	0.246978i
$862$	2.55596	−	4.42706i	0.0870565	−	0.150786i
$863$	5.95115			0.202580			0.101290	−	0.994857i	$-0.467703\pi$
$863$	5.95115			0.202580			0.101290	+	0.994857i	$0.467703\pi$
$864$	−24.8205	−	7.78974i	−0.844410	−	0.265012i
$865$	−2.09755			−0.0713189
$866$	−2.49330	+	4.31853i	−0.0847259	+	0.146750i
$867$	27.1490	−	6.86570i	0.922028	−	0.233171i
$868$	6.98504	+	12.0985i	0.237088	+	0.410648i
$869$	−20.6739	−	35.8083i	−0.701316	−	1.21471i
$870$	−2.02015	+	7.13524i	−0.0684896	+	0.241907i
$871$	−4.67710	+	8.10098i	−0.158478	+	0.274491i
$872$	−14.0186			−0.474730
$873$	−1.18719	+	42.0791i	−0.0401803	+	1.42416i
$874$	2.76042			0.0933726
$875$	−17.1058	+	29.6280i	−0.578280	+	1.00161i
$876$	11.0700	+	11.3867i	0.374020	+	0.384722i
$877$	27.2757	+	47.2430i	0.921036	+	1.59528i	0.797815	+	0.602903i	$0.205989\pi$
$877$	27.2757	+	47.2430i	0.921036	+	1.59528i	0.123222	+	0.992379i	$0.460677\pi$
$878$	3.90398	+	6.76189i	0.131753	+	0.228203i
$879$	−16.0655	−	16.5251i	−0.541875	−	0.557379i
$880$	−5.85374	+	10.1390i	−0.197329	+	0.341785i
$881$	34.6855			1.16858			0.584292	−	0.811543i	$-0.301372\pi$
$881$	34.6855			1.16858			0.584292	+	0.811543i	$0.301372\pi$
$882$	−3.65631	+	1.97563i	−0.123114	+	0.0665231i
$883$	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
$885$	4.43279	−	15.6568i	0.149007	−	0.526296i
$886$	−2.37114	−	4.10694i	−0.0796600	−	0.137975i
$887$	−1.20709	−	2.09074i	−0.0405300	−	0.0702001i	0.845049	−	0.534689i	$-0.179571\pi$
$887$	−1.20709	−	2.09074i	−0.0405300	−	0.0702001i	−0.885579	+	0.464489i	$0.846238\pi$
$888$	−25.0107	+	6.32495i	−0.839305	+	0.212252i
$889$	−0.745715	+	1.29162i	−0.0250105	+	0.0433194i
$890$	−5.48471			−0.183848
$891$	−13.8411	−	27.4390i	−0.463695	−	0.919241i
$892$	32.6670			1.09377
$893$	−4.76308	+	8.24989i	−0.159390	+	0.276072i
$894$	−12.6089	+	3.18866i	−0.421705	+	0.106645i
$895$	10.1022	+	17.4976i	0.337680	+	0.584879i
$896$	−17.7500	−	30.7440i	−0.592987	−	1.02708i
$897$	−2.53481	+	8.95305i	−0.0846350	+	0.298934i
$898$	−3.89837	+	6.75218i	−0.130090	+	0.225323i
$899$	−16.5557			−0.552163
$900$	14.9955	−	8.10261i	0.499851	−	0.270087i
$901$	11.1174			0.370376
$902$	4.61925	−	8.00077i	0.153804	−	0.266397i
$903$	16.6592	+	17.1359i	0.554384	+	0.570246i
$904$	−15.8978	−	27.5358i	−0.528752	−	0.915826i
$905$	−15.2410	−	26.3981i	−0.506627	−	0.877503i
$906$	−7.30120	−	7.51010i	−0.242566	−	0.249506i
$907$	−23.2215	+	40.2207i	−0.771056	+	1.33551i	0.165929	+	0.986138i	$0.446938\pi$
$907$	−23.2215	+	40.2207i	−0.771056	+	1.33551i	−0.936985	+	0.349370i	$0.886396\pi$
$908$	24.7315			0.820742
$909$	−1.00155	+	35.4992i	−0.0332193	+	1.17743i
$910$	−2.05988			−0.0682843
$911$	−0.0724799	+	0.125539i	−0.00240137	+	0.00415929i	−0.867224	−	0.497919i	$-0.834098\pi$
$911$	−0.0724799	+	0.125539i	−0.00240137	+	0.00415929i	0.864822	+	0.502078i	$0.167431\pi$
$912$	−1.26278	+	4.46018i	−0.0418148	+	0.147691i
$913$	18.7870	+	32.5400i	0.621758	+	1.07692i
$914$	8.16176	+	14.1366i	0.269967	+	0.467597i
$915$	−32.0274	+	8.09939i	−1.05879	+	0.267757i
$916$	1.79835	−	3.11483i	0.0594191	−	0.102917i
$917$	27.5722			0.910513
$918$	−0.511976	−	2.29498i	−0.0168977	−	0.0757457i
$919$	−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
$921$	−4.20418	+	1.06319i	−0.138533	+	0.0350335i
$922$	3.16935	+	5.48947i	0.104377	+	0.180786i
$923$	−6.03350	−	10.4503i	−0.198595	−	0.343977i
$924$	8.84286	−	31.2333i	0.290909	−	1.02750i
$925$	12.9543	−	22.4375i	0.425935	−	0.737740i
$926$	2.61673			0.0859910
$927$	−20.9639	−	12.9052i	−0.688544	−	0.423861i
$928$	32.5630			1.06893
$929$	25.5801	−	44.3061i	0.839257	−	1.45364i	−0.0512606	−	0.998685i	$-0.516324\pi$
$929$	25.5801	−	44.3061i	0.839257	−	1.45364i	0.890517	−	0.454950i	$-0.150343\pi$
$930$	2.02293	+	2.08081i	0.0663345	+	0.0682324i
$931$	1.44614	+	2.50479i	0.0473953	+	0.0820910i
$932$	7.02847	+	12.1737i	0.230225	+	0.398762i
$933$	−4.96580	−	5.10788i	−0.162573	−	0.167224i
$934$	−4.60964	+	7.98413i	−0.150832	+	0.261249i
$935$	−4.13300			−0.135164
$936$	4.75765	+	2.92876i	0.155509	+	0.0957296i
$937$	−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
$939$	−1.64171	+	5.79859i	−0.0535753	+	0.189230i
$940$	10.7020	+	18.5364i	0.349061	+	0.604591i
$941$	8.43377	+	14.6077i	0.274933	+	0.476198i	0.970118	−	0.242633i	$-0.0780110\pi$
$941$	8.43377	+	14.6077i	0.274933	+	0.476198i	−0.695185	+	0.718831i	$0.744678\pi$
$942$	−3.20246	+	0.809868i	−0.104342	+	0.0263869i
$943$	14.6490	−	25.3728i	0.477038	−	0.826253i
$944$	−18.2949			−0.595450
$945$	15.8878	−	14.5972i	0.516829	−	0.474847i
$946$	7.46952			0.242855
$947$	−8.00694	+	13.8684i	−0.260191	+	0.450663i	−0.966292	−	0.257447i	$-0.917119\pi$
$947$	−8.00694	+	13.8684i	−0.260191	+	0.450663i	0.706102	+	0.708110i	$0.250452\pi$
$948$	−35.6617	+	9.01848i	−1.15824	+	0.292907i
$949$	−2.61385	−	4.52733i	−0.0848493	−	0.146963i
$950$	0.832250	+	1.44150i	0.0270017	+	0.0467684i
$951$	11.8246	−	41.7649i	0.383439	−	1.35432i
$952$	2.65791	−	4.60364i	0.0861435	−	0.149205i
$953$	35.3365			1.14466			0.572331	−	0.820023i	$-0.306039\pi$
$953$	35.3365			1.14466			0.572331	+	0.820023i	$0.306039\pi$
$954$	−0.511553	+	18.1316i	−0.0165621	+	0.587033i
$955$	9.38528			0.303701
$956$	−3.06512	+	5.30894i	−0.0991329	+	0.171703i
$957$	26.8153	+	27.5825i	0.866815	+	0.891616i
$958$	−0.268475	−	0.465013i	−0.00867404	−	0.0150239i
$959$	15.9550	+	27.6349i	0.515214	+	0.892376i
$960$	4.30007	+	4.42310i	0.138784	+	0.142755i
$961$	12.2605	−	21.2359i	0.395501	−	0.685028i
$962$	3.96776			0.127926
$963$	0.413349	−	0.223347i	0.0133200	−	0.00719727i
$964$	−12.5014			−0.402644
$965$	5.31591	−	9.20742i	0.171125	−	0.296397i
$966$	−3.93510	+	13.8989i	−0.126610	+	0.447189i
$967$	−26.6690	−	46.1920i	−0.857616	−	1.48543i	−0.874196	−	0.485572i	$-0.838611\pi$
$967$	−26.6690	−	46.1920i	−0.857616	−	1.48543i	0.0165803	−	0.999863i	$-0.494722\pi$
$968$	−0.614733	−	1.06475i	−0.0197583	−	0.0342223i
$969$	−1.58649	+	0.401206i	−0.0509653	+	0.0128886i
$970$	−4.61833	+	7.99917i	−0.148286	+	0.256838i
$971$	50.1657			1.60989			0.804946	−	0.593348i	$-0.202194\pi$
$971$	50.1657			1.60989			0.804946	+	0.593348i	$0.202194\pi$
$972$	−26.8418	+	5.19798i	−0.860951	+	0.166725i
$973$	−33.5637			−1.07600
$974$	4.32139	−	7.48487i	0.138466	−	0.239831i
$975$	−5.43954	+	1.37560i	−0.174205	+	0.0440545i
$976$	18.5711	+	32.1661i	0.594446	+	1.02961i
$977$	11.4716	+	19.8694i	0.367008	+	0.635677i	0.989096	−	0.147270i	$-0.0470488\pi$
$977$	11.4716	+	19.8694i	0.367008	+	0.635677i	−0.622088	+	0.782947i	$0.713715\pi$
$978$	−1.22706	+	4.33403i	−0.0392372	+	0.138587i
$979$	−14.2259	+	24.6400i	−0.454663	+	0.787499i
$980$	6.49857			0.207589
$981$	−19.8681	+	10.7354i	−0.634339	+	0.342756i
$982$	8.33919			0.266114
$983$	0.129157	−	0.223706i	0.00411946	−	0.00713511i	−0.863958	−	0.503563i	$-0.832022\pi$
$983$	0.129157	−	0.223706i	0.00411946	−	0.00713511i	0.868078	+	0.496428i	$0.165355\pi$
$984$	−12.2621	−	12.6129i	−0.390900	−	0.402084i
$985$	6.83254	+	11.8343i	0.217703	+	0.377072i
$986$	1.47167	+	2.54900i	0.0468675	+	0.0811768i
$987$	−34.7488	−	35.7430i	−1.10607	−	1.13771i
$988$	0.908301	−	1.57322i	0.0288969	−	0.0500509i
$989$	23.6881			0.753237
$990$	0.190174	−	6.74058i	0.00604412	−	0.214230i
$991$	−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
$993$	0.127484	−	0.450278i	0.00404558	−	0.0142891i
$994$	−9.36653	−	16.2233i	−0.297088	−	0.514572i
$995$	−3.69500	−	6.39993i	−0.117139	−	0.202891i
$996$	32.4068	−	8.19534i	1.02685	−	0.259679i
$997$	−20.8933	+	36.1882i	−0.661697	+	1.14609i	0.318473	+	0.947932i	$0.396830\pi$
$997$	−20.8933	+	36.1882i	−0.661697	+	1.14609i	−0.980170	+	0.198160i	$0.936503\pi$
$998$	10.3605			0.327954
$999$	−30.6032	+	28.1173i	−0.968241	+	0.889592i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.c.40.4	✓	12	9.4	even	3	inner
117.2.e.c.79.4	yes	12	1.1	even	1	trivial
351.2.e.c.118.3		12	9.5	odd	6
351.2.e.c.235.3		12	3.2	odd	2
1053.2.a.l.1.3		6	9.7	even	3
1053.2.a.m.1.4		6	9.2	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.248047 - 0.429630i) q^{2} +(-1.67919 + 0.424649i) q^{3} +(0.876945 + 1.51891i) q^{4} +(0.663441 + 1.14911i) q^{5} +(-0.234075 + 0.826762i) q^{6} +(-1.56464 + 2.71004i) q^{7} +1.86228 q^{8} +(2.63935 - 1.42613i) q^{9} +0.658258 q^{10} +(1.70735 - 2.95722i) q^{11} +(-2.11756 - 2.17815i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.776210 + 1.34444i) q^{14} +(-1.60201 - 1.64785i) q^{15} +(-1.29196 + 2.23774i) q^{16} -0.912179 q^{17} +(0.0419726 - 1.48769i) q^{18} -1.03576 q^{19} +(-1.16360 + 2.01542i) q^{20} +(1.47651 - 5.21509i) q^{21} +(-0.847007 - 1.46706i) q^{22} +(-2.68611 - 4.65248i) q^{23} +(-3.12712 + 0.790817i) q^{24} +(1.61969 - 2.80539i) q^{25} +0.496094 q^{26} +(-3.82635 + 3.51554i) q^{27} -5.48843 q^{28} +(3.25212 - 5.63283i) q^{29} +(-1.10534 + 0.279529i) q^{30} +(-1.27269 - 2.20436i) q^{31} +(2.50321 + 4.33569i) q^{32} +(-1.61118 + 5.69075i) q^{33} +(-0.226263 + 0.391900i) q^{34} -4.15219 q^{35} +(4.48073 + 2.75830i) q^{36} +7.99800 q^{37} +(-0.256916 + 0.444991i) q^{38} +(-1.20735 - 1.24189i) q^{39} +(1.23551 + 2.13997i) q^{40} +(2.72681 + 4.72297i) q^{41} +(-1.87432 - 1.92794i) q^{42} +(-2.20468 + 3.81862i) q^{43} +5.98902 q^{44} +(3.38984 + 2.08675i) q^{45} -2.66513 q^{46} +(4.59865 - 7.96510i) q^{47} +(1.21919 - 4.30621i) q^{48} +(-1.39622 - 2.41832i) q^{49} +(-0.803520 - 1.39174i) q^{50} +(1.53172 - 0.387356i) q^{51} +(-0.876945 + 1.51891i) q^{52} -12.1878 q^{53} +(0.561267 + 2.51593i) q^{54} +4.53091 q^{55} +(-2.91381 + 5.04686i) q^{56} +(1.73923 - 0.439833i) q^{57} +(-1.61335 - 2.79441i) q^{58} +(3.54016 + 6.13174i) q^{59} +(1.09806 - 3.87839i) q^{60} +(7.18720 - 12.4486i) q^{61} -1.26274 q^{62} +(-0.264757 + 9.38413i) q^{63} -2.68417 q^{64} +(-0.663441 + 1.14911i) q^{65} +(2.04527 + 2.10379i) q^{66} +(4.67710 + 8.10098i) q^{67} +(-0.799931 - 1.38552i) q^{68} +(6.48616 + 6.67174i) q^{69} +(-1.02994 + 1.78391i) q^{70} -12.0670 q^{71} +(4.91521 - 2.65586i) q^{72} -5.22771 q^{73} +(1.98388 - 3.43618i) q^{74} +(-1.52846 + 5.39858i) q^{75} +(-0.908301 - 1.57322i) q^{76} +(5.34279 + 9.25399i) q^{77} +(-0.833035 + 0.210666i) q^{78} +(6.05439 - 10.4865i) q^{79} -3.42855 q^{80} +(4.93229 - 7.52811i) q^{81} +2.70551 q^{82} +(-5.50179 + 9.52938i) q^{83} +(9.21610 - 2.33066i) q^{84} +(-0.605177 - 1.04820i) q^{85} +(1.09373 + 1.89439i) q^{86} +(-3.06894 + 10.8396i) q^{87} +(3.17957 - 5.50718i) q^{88} -8.33216 q^{89} +(1.73737 - 0.938763i) q^{90} -3.12929 q^{91} +(4.71115 - 8.15994i) q^{92} +(3.07316 + 3.16108i) q^{93} +(-2.28136 - 3.95144i) q^{94} +(-0.687162 - 1.19020i) q^{95} +(-6.04452 - 6.21746i) q^{96} +(-7.01598 + 12.1520i) q^{97} -1.38531 q^{98} +(0.288905 - 10.2400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 6 q^{4} + 3 q^{5} - 7 q^{6} - 12 q^{8} - 2 q^{9} - 12 q^{10} + 7 q^{11} + 7 q^{12} + 6 q^{13} + 13 q^{14} - 12 q^{15} - 6 q^{16} - 28 q^{17} + 26 q^{18} - 6 q^{19} + 17 q^{20}+ \cdots - 11 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 6 * q^4 + 3 * q^5 - 7 * q^6 - 12 * q^8 - 2 * q^9 - 12 * q^10 + 7 * q^11 + 7 * q^12 + 6 * q^13 + 13 * q^14 - 12 * q^15 - 6 * q^16 - 28 * q^17 + 26 * q^18 - 6 * q^19 + 17 * q^20 - 18 * q^21 + 3 * q^22 + 17 * q^23 - 30 * q^24 - 3 * q^25 + 4 * q^26 + 13 * q^27 + 30 * q^28 + 14 * q^29 - 7 * q^30 - 6 * q^31 + 9 * q^32 + 19 * q^33 - 3 * q^34 - 26 * q^35 + 43 * q^36 - 18 * q^37 - 4 * q^38 - q^39 + 6 * q^40 - 4 * q^41 - 17 * q^42 + 3 * q^43 - 26 * q^44 + 18 * q^45 + 9 * q^47 - 3 * q^48 - 21 * q^50 - 4 * q^51 + 6 * q^52 - 56 * q^53 + 35 * q^54 + 30 * q^55 + 16 * q^56 - 30 * q^57 - 18 * q^58 + 17 * q^59 - 31 * q^60 + 6 * q^61 + 8 * q^62 - 60 * q^64 - 3 * q^65 - 19 * q^66 + 12 * q^67 + 22 * q^68 - 13 * q^69 - 9 * q^70 + 2 * q^71 - 18 * q^73 - 27 * q^74 + 18 * q^75 + 3 * q^76 + 15 * q^77 - 2 * q^78 + 6 * q^79 + 48 * q^80 - 2 * q^81 + 54 * q^82 + 28 * q^83 + 31 * q^84 - 27 * q^85 - 6 * q^86 + 23 * q^87 + 9 * q^88 + 18 * q^89 + 26 * q^90 + 44 * q^92 + 2 * q^93 + 24 * q^94 + 32 * q^95 - 57 * q^96 - 34 * q^98 - 11 * q^99

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