LMFDB - Embedded newform 127.2.c.a.107.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [127,2,Mod(19,127)] 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("127.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(127, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	127.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.01410010567$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 12 x^{16} - 7 x^{15} + 92 x^{14} - 46 x^{13} + 388 x^{12} - 105 x^{11} + 1128 x^{10} + \cdots + 9 $ x^18 - x^17 + 12x^16 - 7x^15 + 92x^14 - 46x^13 + 388x^12 - 105x^11 + 1128x^10 - 250x^9 + 1865x^8 - 14x^7 + 1885x^6 - 360x^5 + 552x^4 - 129x^3 + 126x^2 - 27x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			107.1
Root			$1.23988 - 2.14754i$ of defining polynomial
Character	$\chi$	$=$	127.107
Dual form			127.2.c.a.19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.47976 q^{2} +(0.930662 + 1.61195i) q^{3} +4.14922 q^{4} +0.715813 q^{5} +(-2.30782 - 3.99726i) q^{6} +(0.241228 + 0.417820i) q^{7} -5.32956 q^{8} +(-0.232264 + 0.402292i) q^{9} -1.77505 q^{10} +(-0.520908 + 0.902239i) q^{11} +(3.86152 + 6.68836i) q^{12} +(2.53071 + 4.38331i) q^{13} +(-0.598189 - 1.03609i) q^{14} +(0.666180 + 1.15386i) q^{15} +4.91761 q^{16} +(-2.72880 + 4.72641i) q^{17} +(0.575959 - 0.997589i) q^{18} +6.02930 q^{19} +2.97007 q^{20} +(-0.449004 + 0.777698i) q^{21} +(1.29173 - 2.23734i) q^{22} +(-3.19458 - 5.53317i) q^{23} +(-4.96002 - 8.59101i) q^{24} -4.48761 q^{25} +(-6.27555 - 10.8696i) q^{26} +4.71934 q^{27} +(1.00091 + 1.73363i) q^{28} +(-1.80084 + 3.11915i) q^{29} +(-1.65197 - 2.86129i) q^{30} +(-3.70654 - 6.41992i) q^{31} -1.53537 q^{32} -1.93916 q^{33} +(6.76677 - 11.7204i) q^{34} +(0.172674 + 0.299081i) q^{35} +(-0.963713 + 1.66920i) q^{36} +(-0.299309 + 0.518418i) q^{37} -14.9512 q^{38} +(-4.71047 + 8.15877i) q^{39} -3.81497 q^{40} +(4.52412 - 7.83601i) q^{41} +(1.11342 - 1.92851i) q^{42} +(1.08385 - 1.87728i) q^{43} +(-2.16136 + 3.74359i) q^{44} +(-0.166257 + 0.287966i) q^{45} +(7.92180 + 13.7210i) q^{46} +10.1887 q^{47} +(4.57663 + 7.92695i) q^{48} +(3.38362 - 5.86060i) q^{49} +11.1282 q^{50} -10.1584 q^{51} +(10.5005 + 18.1873i) q^{52} +(-0.400099 + 0.692993i) q^{53} -11.7028 q^{54} +(-0.372873 + 0.645835i) q^{55} +(-1.28564 - 2.22680i) q^{56} +(5.61124 + 9.71896i) q^{57} +(4.46566 - 7.73474i) q^{58} +(2.68670 - 4.65351i) q^{59} +(2.76413 + 4.78761i) q^{60} -10.0527 q^{61} +(9.19134 + 15.9199i) q^{62} -0.224114 q^{63} -6.02786 q^{64} +(1.81151 + 3.13763i) q^{65} +4.80865 q^{66} +(-3.27584 - 5.67393i) q^{67} +(-11.3224 + 19.6109i) q^{68} +(5.94615 - 10.2990i) q^{69} +(-0.428192 - 0.741650i) q^{70} +(-1.04894 - 1.81682i) q^{71} +(1.23786 - 2.14404i) q^{72} -11.3725 q^{73} +(0.742215 - 1.28555i) q^{74} +(-4.17645 - 7.23382i) q^{75} +25.0169 q^{76} -0.502631 q^{77} +(11.6808 - 20.2318i) q^{78} +(-1.80468 - 3.12579i) q^{79} +3.52009 q^{80} +(5.08890 + 8.81423i) q^{81} +(-11.2188 + 19.4315i) q^{82} +(3.82785 - 6.63003i) q^{83} +(-1.86302 + 3.22684i) q^{84} +(-1.95331 + 3.38323i) q^{85} +(-2.68768 + 4.65521i) q^{86} -6.70390 q^{87} +(2.77621 - 4.80854i) q^{88} -0.516961 q^{89} +(0.412279 - 0.714088i) q^{90} +(-1.22096 + 2.11476i) q^{91} +(-13.2550 - 22.9584i) q^{92} +(6.89908 - 11.9495i) q^{93} -25.2657 q^{94} +4.31585 q^{95} +(-1.42891 - 2.47495i) q^{96} +(8.36629 + 14.4908i) q^{97} +(-8.39057 + 14.5329i) q^{98} +(-0.241976 - 0.419115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + 5 q^{7} - 6 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 8 q^{14} + 3 q^{15} - 6 q^{16} - 6 q^{17} + 16 q^{19} - 32 q^{20} + 3 q^{21} + 6 q^{22} + 13 q^{23} - 6 q^{24}+ \cdots + 17 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + 5 * q^7 - 6 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 8 * q^14 + 3 * q^15 - 6 * q^16 - 6 * q^17 + 16 * q^19 - 32 * q^20 + 3 * q^21 + 6 * q^22 + 13 * q^23 - 6 * q^24 + 6 * q^25 - 14 * q^26 + 10 * q^27 - 2 * q^28 - 5 * q^29 - 23 * q^30 - 11 * q^31 - 4 * q^32 - 16 * q^33 - 2 * q^34 - 16 * q^35 + 15 * q^36 - 4 * q^37 + 4 * q^38 - 7 * q^39 - 36 * q^40 - 11 * q^41 + 9 * q^43 - 15 * q^44 + 14 * q^45 + 15 * q^46 - 10 * q^47 + 20 * q^48 + 12 * q^49 + 32 * q^50 + 4 * q^51 + 26 * q^52 - 2 * q^53 + 2 * q^54 - q^55 + 12 * q^56 + 28 * q^57 + 10 * q^58 + 6 * q^60 + 28 * q^61 + 8 * q^62 - 12 * q^63 - 50 * q^64 + 15 * q^65 + 36 * q^66 - 12 * q^67 - 41 * q^68 + 33 * q^69 + 21 * q^70 - 4 * q^71 + 31 * q^72 + 52 * q^73 + 13 * q^74 - 11 * q^75 + 26 * q^76 - 40 * q^77 + q^78 - 35 * q^79 + 26 * q^80 + 27 * q^81 - 26 * q^82 + 13 * q^83 + 22 * q^84 + 15 * q^85 - 5 * q^86 - 64 * q^87 - q^88 + 8 * q^89 - 30 * q^90 - 16 * q^91 + 11 * q^92 - 6 * q^93 - 62 * q^94 - 38 * q^95 - 31 * q^96 + 28 * q^97 + 32 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/127\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.47976			−1.75346			−0.876729	−	0.480986i	$-0.840279\pi$
$2$	−2.47976			−1.75346			−0.876729	+	0.480986i	$0.840279\pi$
$3$	0.930662	+	1.61195i	0.537318	+	0.930662i	0.999047	+	0.0436411i	$0.0138958\pi$
$3$	0.930662	+	1.61195i	0.537318	+	0.930662i	−0.461729	+	0.887021i	$0.652771\pi$
$4$	4.14922			2.07461
$5$	0.715813			0.320121			0.160061	−	0.987107i	$-0.448831\pi$
$5$	0.715813			0.320121			0.160061	+	0.987107i	$0.448831\pi$
$6$	−2.30782	−	3.99726i	−0.942164	−	1.63188i
$7$	0.241228	+	0.417820i	0.0911757	+	0.157921i	0.908006	−	0.418957i	$-0.137604\pi$
$7$	0.241228	+	0.417820i	0.0911757	+	0.157921i	−0.816830	+	0.576878i	$0.804271\pi$
$8$	−5.32956			−1.88429
$9$	−0.232264	+	0.402292i	−0.0774212	+	0.134097i
$10$	−1.77505			−0.561319
$11$	−0.520908	+	0.902239i	−0.157060	+	0.272035i	−0.933807	−	0.357777i	$-0.883535\pi$
$11$	−0.520908	+	0.902239i	−0.157060	+	0.272035i	0.776747	+	0.629812i	$0.216868\pi$
$12$	3.86152	+	6.68836i	1.11473	+	1.93076i
$13$	2.53071	+	4.38331i	0.701892	+	1.21571i	0.967802	+	0.251714i	$0.0809944\pi$
$13$	2.53071	+	4.38331i	0.701892	+	1.21571i	−0.265910	+	0.963998i	$0.585672\pi$
$14$	−0.598189	−	1.03609i	−0.159873	−	0.276908i
$15$	0.666180	+	1.15386i	0.172007	+	0.297925i
$16$	4.91761			1.22940
$17$	−2.72880	+	4.72641i	−0.661830	+	1.14632i	0.318304	+	0.947989i	$0.396887\pi$
$17$	−2.72880	+	4.72641i	−0.661830	+	1.14632i	−0.980134	+	0.198335i	$0.936447\pi$
$18$	0.575959	−	0.997589i	0.135755	−	0.235134i
$19$	6.02930			1.38322			0.691608	−	0.722273i	$-0.256902\pi$
$19$	6.02930			1.38322			0.691608	+	0.722273i	$0.256902\pi$
$20$	2.97007			0.664127
$21$	−0.449004	+	0.777698i	−0.0979807	+	0.169708i
$22$	1.29173	−	2.23734i	0.275397	−	0.477002i
$23$	−3.19458	−	5.53317i	−0.666116	−	1.15375i	−0.978982	−	0.203949i	$-0.934622\pi$
$23$	−3.19458	−	5.53317i	−0.666116	−	1.15375i	0.312866	−	0.949797i	$-0.398711\pi$
$24$	−4.96002	−	8.59101i	−1.01246	−	1.75363i
$25$	−4.48761			−0.897522
$26$	−6.27555	−	10.8696i	−1.23074	−	2.13170i
$27$	4.71934			0.908237
$28$	1.00091	+	1.73363i	0.189154	+	0.327625i
$29$	−1.80084	+	3.11915i	−0.334408	+	0.579211i	−0.983371	−	0.181609i	$-0.941870\pi$
$29$	−1.80084	+	3.11915i	−0.334408	+	0.579211i	0.648963	+	0.760820i	$0.275203\pi$
$30$	−1.65197	−	2.86129i	−0.301607	−	0.522398i
$31$	−3.70654	−	6.41992i	−0.665715	−	1.15305i	−0.979091	−	0.203422i	$-0.934794\pi$
$31$	−3.70654	−	6.41992i	−0.665715	−	1.15305i	0.313377	−	0.949629i	$-0.398540\pi$
$32$	−1.53537			−0.271418
$33$	−1.93916			−0.337564
$34$	6.76677	−	11.7204i	1.16049	−	2.01003i
$35$	0.172674	+	0.299081i	0.0291873	+	0.0505539i
$36$	−0.963713	+	1.66920i	−0.160619	+	0.278200i
$37$	−0.299309	+	0.518418i	−0.0492061	+	0.0852274i	−0.889579	−	0.456781i	$-0.849002\pi$
$37$	−0.299309	+	0.518418i	−0.0492061	+	0.0852274i	0.840373	+	0.542008i	$0.182336\pi$
$38$	−14.9512			−2.42541
$39$	−4.71047	+	8.15877i	−0.754278	+	1.30645i
$40$	−3.81497			−0.603200
$41$	4.52412	−	7.83601i	0.706550	−	1.22378i	−0.259580	−	0.965722i	$-0.583584\pi$
$41$	4.52412	−	7.83601i	0.706550	−	1.22378i	0.966129	−	0.258058i	$-0.0830826\pi$
$42$	1.11342	−	1.92851i	0.171805	−	0.297575i
$43$	1.08385	−	1.87728i	0.165285	−	0.286282i	−0.771471	−	0.636264i	$-0.780479\pi$
$43$	1.08385	−	1.87728i	0.165285	−	0.286282i	0.936757	+	0.349982i	$0.113812\pi$
$44$	−2.16136	+	3.74359i	−0.325838	+	0.564368i
$45$	−0.166257	+	0.287966i	−0.0247842	+	0.0429275i
$46$	7.92180	+	13.7210i	1.16801	+	2.02304i
$47$	10.1887			1.48618			0.743091	−	0.669191i	$-0.233359\pi$
$47$	10.1887			1.48618			0.743091	+	0.669191i	$0.233359\pi$
$48$	4.57663	+	7.92695i	0.660580	+	1.14416i
$49$	3.38362	−	5.86060i	0.483374	−	0.837228i
$50$	11.1282			1.57377
$51$	−10.1584			−1.42245
$52$	10.5005	+	18.1873i	1.45615	+	2.52213i
$53$	−0.400099	+	0.692993i	−0.0549579	+	0.0951898i	−0.892195	−	0.451649i	$-0.850836\pi$
$53$	−0.400099	+	0.692993i	−0.0549579	+	0.0951898i	0.837238	+	0.546839i	$0.184169\pi$
$54$	−11.7028			−1.59255
$55$	−0.372873	+	0.645835i	−0.0502782	+	0.0870843i
$56$	−1.28564	−	2.22680i	−0.171801	−	0.297568i
$57$	5.61124	+	9.71896i	0.743227	+	1.28731i
$58$	4.46566	−	7.73474i	0.586369	−	1.01562i
$59$	2.68670	−	4.65351i	0.349779	−	0.605835i	−0.636431	−	0.771334i	$-0.719590\pi$
$59$	2.68670	−	4.65351i	0.349779	−	0.605835i	0.986210	+	0.165498i	$0.0529233\pi$
$60$	2.76413	+	4.78761i	0.356848	+	0.618078i
$61$	−10.0527			−1.28711			−0.643556	−	0.765399i	$-0.722542\pi$
$61$	−10.0527			−1.28711			−0.643556	+	0.765399i	$0.722542\pi$
$62$	9.19134	+	15.9199i	1.16730	+	2.02183i
$63$	−0.224114			−0.0282357
$64$	−6.02786			−0.753482
$65$	1.81151	+	3.13763i	0.224691	+	0.389176i
$66$	4.80865			0.591904
$67$	−3.27584	−	5.67393i	−0.400208	−	0.693181i	0.593543	−	0.804803i	$-0.297729\pi$
$67$	−3.27584	−	5.67393i	−0.400208	−	0.693181i	−0.993751	+	0.111622i	$0.964396\pi$
$68$	−11.3224	+	19.6109i	−1.37304	+	2.37818i
$69$	5.94615	−	10.2990i	0.715832	−	1.23986i
$70$	−0.428192	−	0.741650i	−0.0511787	−	0.0886441i
$71$	−1.04894	−	1.81682i	−0.124487	−	0.215617i	0.797046	−	0.603919i	$-0.206395\pi$
$71$	−1.04894	−	1.81682i	−0.124487	−	0.215617i	−0.921532	+	0.388302i	$0.873062\pi$
$72$	1.23786	−	2.14404i	0.145884	−	0.252678i
$73$	−11.3725			−1.33105			−0.665523	−	0.746378i	$-0.731791\pi$
$73$	−11.3725			−1.33105			−0.665523	+	0.746378i	$0.731791\pi$
$74$	0.742215	−	1.28555i	0.0862807	−	0.149443i
$75$	−4.17645	−	7.23382i	−0.482255	−	0.835290i
$76$	25.0169			2.86964
$77$	−0.502631			−0.0572802
$78$	11.6808	−	20.2318i	1.32259	−	2.29080i
$79$	−1.80468	−	3.12579i	−0.203042	−	0.351679i	0.746465	−	0.665424i	$-0.231749\pi$
$79$	−1.80468	−	3.12579i	−0.203042	−	0.351679i	−0.949507	+	0.313746i	$0.898416\pi$
$80$	3.52009			0.393558
$81$	5.08890	+	8.81423i	0.565433	+	0.979359i
$82$	−11.2188	+	19.4315i	−1.23890	+	2.14585i
$83$	3.82785	−	6.63003i	0.420161	−	0.727740i	−0.575794	−	0.817595i	$-0.695307\pi$
$83$	3.82785	−	6.63003i	0.420161	−	0.727740i	0.995955	+	0.0898548i	$0.0286403\pi$
$84$	−1.86302	+	3.22684i	−0.203272	+	0.352077i
$85$	−1.95331	+	3.38323i	−0.211866	+	0.366963i
$86$	−2.68768	+	4.65521i	−0.289820	+	0.501984i
$87$	−6.70390			−0.718733
$88$	2.77621	−	4.80854i	0.295945	−	0.512592i
$89$	−0.516961			−0.0547977			−0.0273989	−	0.999625i	$-0.508722\pi$
$89$	−0.516961			−0.0547977			−0.0273989	+	0.999625i	$0.508722\pi$
$90$	0.412279	−	0.714088i	0.0434580	−	0.0752714i
$91$	−1.22096	+	2.11476i	−0.127991	+	0.221687i
$92$	−13.2550	−	22.9584i	−1.38193	−	2.39358i
$93$	6.89908	−	11.9495i	0.715401	−	1.23911i
$94$	−25.2657			−2.60596
$95$	4.31585			0.442797
$96$	−1.42891	−	2.47495i	−0.145838	−	0.252598i
$97$	8.36629	+	14.4908i	0.849468	+	1.47132i	0.881684	+	0.471841i	$0.156410\pi$
$97$	8.36629	+	14.4908i	0.849468	+	1.47132i	−0.0322156	+	0.999481i	$0.510256\pi$
$98$	−8.39057	+	14.5329i	−0.847575	+	1.46804i
$99$	−0.241976	−	0.419115i	−0.0243195	−	0.0421226i
$100$	−18.6201			−1.86201
$101$	4.35664	+	7.54592i	0.433501	+	0.750847i	0.997172	−	0.0751531i	$-0.0239446\pi$
$101$	4.35664	+	7.54592i	0.433501	+	0.750847i	−0.563671	+	0.826000i	$0.690611\pi$
$102$	25.1903			2.49421
$103$	−3.39052	−	5.87256i	−0.334078	−	0.578641i	0.649229	−	0.760593i	$-0.275092\pi$
$103$	−3.39052	−	5.87256i	−0.334078	−	0.578641i	−0.983307	+	0.181952i	$0.941758\pi$
$104$	−13.4876	−	23.3611i	−1.32256	−	2.29075i
$105$	−0.321403	+	0.556686i	−0.0313657	+	0.0543270i
$106$	0.992152	−	1.71846i	0.0963663	−	0.166911i
$107$	−11.5284			−1.11450			−0.557248	−	0.830346i	$-0.688143\pi$
$107$	−11.5284			−1.11450			−0.557248	+	0.830346i	$0.688143\pi$
$108$	19.5816			1.88424
$109$	7.66816	−	13.2816i	0.734476	−	1.27215i	−0.220477	−	0.975392i	$-0.570761\pi$
$109$	7.66816	−	13.2816i	0.734476	−	1.27215i	0.954953	−	0.296758i	$-0.0959054\pi$
$110$	0.924636	−	1.60152i	0.0881606	−	0.152699i
$111$	−1.11422			−0.105757
$112$	1.18627	+	2.05467i	0.112092	+	0.194148i
$113$	−0.950103	−	1.64563i	−0.0893782	−	0.154808i	0.817870	−	0.575403i	$-0.195155\pi$
$113$	−0.950103	−	1.64563i	−0.0893782	−	0.154808i	−0.907248	+	0.420595i	$0.861821\pi$
$114$	−13.9145	−	24.1007i	−1.30322	−	2.25724i
$115$	−2.28672	−	3.96072i	−0.213238	−	0.369339i
$116$	−7.47209	+	12.9420i	−0.693766	+	1.20164i
$117$	−2.35116			−0.217365
$118$	−6.66239	+	11.5396i	−0.613323	+	1.06231i
$119$	−2.63305			−0.241372
$120$	−3.55045	−	6.14956i	−0.324110	−	0.561375i
$121$	4.95731	+	8.58631i	0.450664	+	0.780574i
$122$	24.9282			2.25689
$123$	16.8417			1.51857
$124$	−15.3793	−	26.6377i	−1.38110	−	2.39213i
$125$	−6.79136			−0.607437
$126$	0.555750			0.0495102
$127$	−10.8501	+	3.04542i	−0.962794	+	0.270237i
$127$	−10.8501	+	3.04542i	−0.962794	+	0.270237i
$128$	18.0184			1.59262
$129$	4.03478			0.355243
$130$	−4.49212	−	7.78059i	−0.393985	−	0.682403i
$131$	4.51877			0.394807			0.197403	−	0.980322i	$-0.436749\pi$
$131$	4.51877			0.394807			0.197403	+	0.980322i	$0.436749\pi$
$132$	−8.04600			−0.700314
$133$	1.45444	+	2.51916i	0.126116	+	0.218439i
$134$	8.12332	+	14.0700i	0.701748	+	1.21546i
$135$	3.37816			0.290746
$136$	14.5433	−	25.1897i	1.24708	−	2.16000i
$137$	3.37176			0.288069			0.144035	−	0.989573i	$-0.453992\pi$
$137$	3.37176			0.288069			0.144035	+	0.989573i	$0.453992\pi$
$138$	−14.7450	+	25.5391i	−1.25518	+	2.17404i
$139$	9.24640	+	16.0152i	0.784269	+	1.35839i	0.929435	+	0.368987i	$0.120295\pi$
$139$	9.24640	+	16.0152i	0.784269	+	1.35839i	−0.145166	+	0.989407i	$0.546372\pi$
$140$	0.716465	+	1.24095i	0.0605523	+	0.104880i
$141$	9.48228	+	16.4238i	0.798552	+	1.38313i
$142$	2.60113	+	4.50528i	0.218282	+	0.378075i
$143$	−5.27306			−0.440956
$144$	−1.14218	+	1.97832i	−0.0951817	+	0.164860i
$145$	−1.28907	+	2.23273i	−0.107051	+	0.185418i
$146$	28.2010			2.33393
$147$	12.5960			1.03890
$148$	−1.24190	+	2.15103i	−0.102083	+	0.176814i
$149$	−7.13696	+	12.3616i	−0.584682	+	1.01270i	0.410233	+	0.911981i	$0.365447\pi$
$149$	−7.13696	+	12.3616i	−0.584682	+	1.01270i	−0.994915	+	0.100719i	$0.967886\pi$
$150$	10.3566	+	17.9382i	0.845613	+	1.46465i
$151$	−8.54637	−	14.8028i	−0.695494	−	1.20463i	−0.970014	−	0.243050i	$-0.921852\pi$
$151$	−8.54637	−	14.8028i	−0.695494	−	1.20463i	0.274520	−	0.961581i	$-0.411481\pi$
$152$	−32.1335			−2.60637
$153$	−1.26760	−	2.19555i	−0.102479	−	0.177500i
$154$	1.24641			0.100438
$155$	−2.65319	−	4.59546i	−0.213109	−	0.369116i
$156$	−19.5448	+	33.8525i	−1.56483	+	2.71037i
$157$	−9.83030	−	17.0266i	−0.784544	−	1.35887i	−0.929271	−	0.369398i	$-0.879564\pi$
$157$	−9.83030	−	17.0266i	−0.784544	−	1.35887i	0.144728	−	0.989472i	$-0.453769\pi$
$158$	4.47517	+	7.75122i	0.356025	+	0.616654i
$159$	−1.48943			−0.118119
$160$	−1.09904			−0.0868866
$161$	1.54125	−	2.66952i	0.121467	−	0.210387i
$162$	−12.6193	−	21.8572i	−0.991463	−	1.71726i
$163$	−5.58096	+	9.66651i	−0.437135	+	0.757139i	−0.997467	−	0.0711283i	$-0.977340\pi$
$163$	−5.58096	+	9.66651i	−0.437135	+	0.757139i	0.560332	+	0.828268i	$0.310673\pi$
$164$	18.7716	−	32.5134i	1.46582	−	2.53887i
$165$	−1.38807			−0.108061
$166$	−9.49215	+	16.4409i	−0.736734	+	1.27606i
$167$	−17.9740			−1.39087			−0.695436	−	0.718588i	$-0.744789\pi$
$167$	−17.9740			−1.39087			−0.695436	+	0.718588i	$0.744789\pi$
$168$	2.39300	−	4.14479i	0.184624	−	0.319778i
$169$	−6.30896	+	10.9274i	−0.485304	+	0.840572i
$170$	4.84374	−	8.38961i	0.371498	−	0.643453i
$171$	−1.40039	+	2.42554i	−0.107090	+	0.185486i
$172$	4.49712	−	7.78925i	0.342903	−	0.593925i
$173$	−7.49195	−	12.9764i	−0.569602	−	0.986580i	−0.996605	−	0.0823297i	$-0.973764\pi$
$173$	−7.49195	−	12.9764i	−0.569602	−	0.986580i	0.427003	−	0.904250i	$-0.359569\pi$
$174$	16.6241			1.26027
$175$	−1.08254	−	1.87501i	−0.0818323	−	0.141738i
$176$	−2.56162	+	4.43686i	−0.193089	+	0.334441i
$177$	10.0017			0.751770
$178$	1.28194			0.0960855
$179$	4.92050	+	8.52255i	0.367775	+	0.637005i	0.989217	−	0.146455i	$-0.0467863\pi$
$179$	4.92050	+	8.52255i	0.367775	+	0.637005i	−0.621442	+	0.783460i	$0.713453\pi$
$180$	−0.689839	+	1.19484i	−0.0514175	+	0.0890578i
$181$	3.74745			0.278546			0.139273	−	0.990254i	$-0.455524\pi$
$181$	3.74745			0.278546			0.139273	+	0.990254i	$0.455524\pi$
$182$	3.02768	−	5.24410i	0.224427	−	0.388719i
$183$	−9.35563	−	16.2044i	−0.691588	−	1.19787i
$184$	17.0257	+	29.4894i	1.25515	+	2.17399i
$185$	−0.214249	+	0.371090i	−0.0157519	+	0.0272831i
$186$	−17.1081	+	29.6320i	−1.25442	+	2.17273i
$187$	−2.84291	−	4.92406i	−0.207894	−	0.360083i
$188$	42.2754			3.08325
$189$	1.13844	+	1.97183i	0.0828092	+	0.143430i
$190$	−10.7023			−0.776426
$191$	1.33315			0.0964635			0.0482317	−	0.998836i	$-0.484641\pi$
$191$	1.33315			0.0964635			0.0482317	+	0.998836i	$0.484641\pi$
$192$	−5.60990	−	9.71663i	−0.404860	−	0.701237i
$193$	13.9297			1.00268			0.501342	−	0.865249i	$-0.332840\pi$
$193$	13.9297			1.00268			0.501342	+	0.865249i	$0.332840\pi$
$194$	−20.7464	−	35.9338i	−1.48951	−	2.57990i
$195$	−3.37181	+	5.84015i	−0.241461	+	0.418222i
$196$	14.0394	−	24.3169i	1.00281	−	1.73692i
$197$	0.715839	+	1.23987i	0.0510014	+	0.0883370i	0.890399	−	0.455181i	$-0.150425\pi$
$197$	0.715839	+	1.23987i	0.0510014	+	0.0883370i	−0.839398	+	0.543518i	$0.817092\pi$
$198$	0.600043	+	1.03931i	0.0426432	+	0.0738602i
$199$	−5.32664	+	9.22601i	−0.377595	+	0.654014i	−0.990712	−	0.135978i	$-0.956582\pi$
$199$	−5.32664	+	9.22601i	−0.377595	+	0.654014i	0.613116	+	0.789993i	$0.289916\pi$
$200$	23.9170			1.69119
$201$	6.09741	−	10.5610i	0.430078	−	0.744917i
$202$	−10.8034	−	18.7121i	−0.760126	−	1.31658i
$203$	−1.73766			−0.121959
$204$	−42.1493			−2.95104
$205$	3.23843	−	5.60912i	0.226182	−	0.391758i
$206$	8.40770	+	14.5626i	0.585792	+	1.01462i
$207$	2.96794			0.206286
$208$	12.4450	+	21.5554i	0.862907	+	1.49460i
$209$	−3.14071	+	5.43987i	−0.217248	+	0.376284i
$210$	0.797003	−	1.38045i	0.0549985	−	0.0952601i
$211$	4.00956	−	6.94477i	0.276030	−	0.478098i	−0.694365	−	0.719623i	$-0.744314\pi$
$211$	4.00956	−	6.94477i	0.276030	−	0.478098i	0.970394	+	0.241526i	$0.0776478\pi$
$212$	−1.66010	+	2.87538i	−0.114016	+	0.197482i
$213$	1.95242	−	3.38169i	0.133778	−	0.231710i
$214$	28.5878			1.95422
$215$	0.775832	−	1.34378i	0.0529113	−	0.0916451i
$216$	−25.1520			−1.71138
$217$	1.78825	−	3.09733i	0.121394	−	0.210261i
$218$	−19.0152	+	32.9353i	−1.28787	+	2.23066i
$219$	−10.5839	−	18.3319i	−0.715195	−	1.23875i
$220$	−1.54713	+	2.67971i	−0.104308	+	0.180666i
$221$	−27.6231			−1.85813
$222$	2.76300			0.185441
$223$	−4.37048	−	7.56989i	−0.292669	−	0.506918i	0.681771	−	0.731566i	$-0.261210\pi$
$223$	−4.37048	−	7.56989i	−0.292669	−	0.506918i	−0.974440	+	0.224648i	$0.927877\pi$
$224$	−0.370375	−	0.641508i	−0.0247467	−	0.0428626i
$225$	1.04231	−	1.80533i	0.0694872	−	0.120355i
$226$	2.35603	+	4.08076i	0.156721	+	0.271448i
$227$	13.0104			0.863533			0.431767	−	0.901985i	$-0.357890\pi$
$227$	13.0104			0.863533			0.431767	+	0.901985i	$0.357890\pi$
$228$	23.2823	+	40.3261i	1.54191	+	2.67066i
$229$	0.789816			0.0521925			0.0260962	−	0.999659i	$-0.491692\pi$
$229$	0.789816			0.0521925			0.0260962	+	0.999659i	$0.491692\pi$
$230$	5.67053	+	9.82164i	0.373903	+	0.647620i
$231$	−0.467780	−	0.810218i	−0.0307777	−	0.0533085i
$232$	9.59769	−	16.6237i	0.630119	−	1.09140i
$233$	−5.41448	+	9.37815i	−0.354714	+	0.614383i	−0.987069	−	0.160296i	$-0.948755\pi$
$233$	−5.41448	+	9.37815i	−0.354714	+	0.614383i	0.632355	+	0.774679i	$0.282089\pi$
$234$	5.83033			0.381141
$235$	7.29324			0.475758
$236$	11.1477	−	19.3084i	0.725656	−	1.25687i
$237$	3.35909	−	5.81811i	0.218196	−	0.377927i
$238$	6.52935			0.423235
$239$	10.9620	+	18.9867i	0.709071	+	1.22815i	0.965202	+	0.261504i	$0.0842186\pi$
$239$	10.9620	+	18.9867i	0.709071	+	1.22815i	−0.256132	+	0.966642i	$0.582448\pi$
$240$	3.27601	+	5.67422i	0.211466	+	0.366269i
$241$	11.0967	+	19.2200i	0.714800	+	1.23807i	0.963036	+	0.269371i	$0.0868158\pi$
$241$	11.0967	+	19.2200i	0.714800	+	1.23807i	−0.248236	+	0.968700i	$0.579851\pi$
$242$	−12.2930	−	21.2920i	−0.790221	−	1.36870i
$243$	−2.39308	+	4.14494i	−0.153516	+	0.265898i
$244$	−41.7107			−2.67026
$245$	2.42204	−	4.19509i	0.154738	−	0.268015i
$246$	−41.7635			−2.66274
$247$	15.2584	+	26.4283i	0.970869	+	1.68159i
$248$	19.7542	+	34.2154i	1.25440	+	2.17268i
$249$	14.2497			0.903040
$250$	16.8410			1.06512
$251$	−2.71069	−	4.69505i	−0.171097	−	0.296349i	0.767706	−	0.640802i	$-0.221398\pi$
$251$	−2.71069	−	4.69505i	−0.171097	−	0.296349i	−0.938804	+	0.344452i	$0.888065\pi$
$252$	−0.929900			−0.0585782
$253$	6.65633			0.418480
$254$	26.9058	−	7.55192i	1.68822	−	0.473849i
$255$	−7.27148			−0.455358
$256$	−32.6256			−2.03910
$257$	8.62531	+	14.9395i	0.538032	+	0.931899i	0.999010	+	0.0444875i	$0.0141655\pi$
$257$	8.62531	+	14.9395i	0.538032	+	0.931899i	−0.460978	+	0.887412i	$0.652501\pi$
$258$	−10.0053			−0.622903
$259$	−0.288807			−0.0179456
$260$	7.51637	+	13.0187i	0.466146	+	0.807388i
$261$	−0.836539	−	1.44893i	−0.0517805	−	0.0896864i
$262$	−11.2055			−0.692276
$263$	13.1477	−	22.7726i	0.810725	−	1.40422i	−0.101633	−	0.994822i	$-0.532407\pi$
$263$	13.1477	−	22.7726i	0.810725	−	1.40422i	0.912357	−	0.409394i	$-0.134260\pi$
$264$	10.3349			0.636067
$265$	−0.286396	+	0.496053i	−0.0175932	+	0.0304723i
$266$	−3.60666	−	6.24692i	−0.221139	−	0.383023i
$267$	−0.481116	−	0.833317i	−0.0294438	−	0.0509982i
$268$	−13.5922	−	23.5424i	−0.830276	−	1.43808i
$269$	3.51249	+	6.08380i	0.214160	+	0.370936i	0.953012	−	0.302931i	$-0.0979653\pi$
$269$	3.51249	+	6.08380i	0.214160	+	0.370936i	−0.738852	+	0.673867i	$0.764632\pi$
$270$	−8.37704			−0.509811
$271$	5.31877	−	9.21238i	0.323092	−	0.559613i	−0.658032	−	0.752990i	$-0.728611\pi$
$271$	5.31877	−	9.21238i	0.323092	−	0.559613i	0.981124	+	0.193377i	$0.0619442\pi$
$272$	−13.4191	+	23.2426i	−0.813655	+	1.40929i
$273$	−4.54519			−0.275088
$274$	−8.36117			−0.505117
$275$	2.33763	−	4.04890i	0.140965	−	0.244158i
$276$	24.6719	−	42.7330i	1.48507	−	2.57222i
$277$	−1.38816	−	2.40436i	−0.0834062	−	0.144464i	0.821305	−	0.570490i	$-0.193247\pi$
$277$	−1.38816	−	2.40436i	−0.0834062	−	0.144464i	−0.904711	+	0.426026i	$0.859913\pi$
$278$	−22.9289	−	39.7140i	−1.37518	−	2.38189i
$279$	3.44358			0.206162
$280$	−0.920279	−	1.59397i	−0.0549972	−	0.0952580i
$281$	−23.1793			−1.38276			−0.691382	−	0.722490i	$-0.742998\pi$
$281$	−23.1793			−1.38276			−0.691382	+	0.722490i	$0.742998\pi$
$282$	−23.5138	−	40.7271i	−1.40023	−	2.42526i
$283$	−1.59964	+	2.77067i	−0.0950890	+	0.164699i	−0.909646	−	0.415385i	$-0.863647\pi$
$283$	−1.59964	+	2.77067i	−0.0950890	+	0.164699i	0.814557	+	0.580084i	$0.196980\pi$
$284$	−4.35229	−	7.53840i	−0.258261	−	0.447321i
$285$	4.01660	+	6.95696i	0.237923	+	0.412095i
$286$	13.0759			0.773197
$287$	4.36539			0.257681
$288$	0.356611	−	0.617668i	0.0210135	−	0.0363964i
$289$	−6.39266	−	11.0724i	−0.376039	−	0.651319i
$290$	3.19658	−	5.53663i	0.187709	−	0.325122i
$291$	−15.5724	+	26.9721i	−0.912869	+	1.58114i
$292$	−47.1869			−2.76140
$293$	14.4499	−	25.0279i	0.844172	−	1.46215i	−0.0421672	−	0.999111i	$-0.513426\pi$
$293$	14.4499	−	25.0279i	0.844172	−	1.46215i	0.886339	−	0.463037i	$-0.153240\pi$
$294$	−31.2351			−1.82167
$295$	1.92318	−	3.33104i	0.111972	−	0.193941i
$296$	1.59518	−	2.76294i	0.0927182	−	0.160593i
$297$	−2.45834	+	4.25797i	−0.142647	+	0.247073i
$298$	17.6980	−	30.6538i	1.02522	−	1.77572i
$299$	16.1691	−	28.0057i	0.935082	−	1.61961i
$300$	−17.3290	−	30.0147i	−1.00049	−	1.73290i
$301$	1.04582			0.0602800
$302$	21.1930	+	36.7073i	1.21952	+	2.11227i
$303$	−8.10911	+	14.0454i	−0.465856	+	0.806887i
$304$	29.6497			1.70053
$305$	−7.19583			−0.412032
$306$	3.14335	+	5.44444i	0.179693	+	0.311238i
$307$	−5.87033	+	10.1677i	−0.335038	+	0.580302i	−0.983492	−	0.180951i	$-0.942082\pi$
$307$	−5.87033	+	10.1677i	−0.335038	+	0.580302i	0.648454	+	0.761253i	$0.275416\pi$
$308$	−2.08553			−0.118834
$309$	6.31086	−	10.9307i	0.359013	−	0.621828i
$310$	6.57928	+	11.3957i	0.373678	+	0.647230i
$311$	6.94433	+	12.0279i	0.393777	+	0.682041i	0.992944	−	0.118582i	$-0.0378350\pi$
$311$	6.94433	+	12.0279i	0.393777	+	0.682041i	−0.599168	+	0.800624i	$0.704502\pi$
$312$	25.1047	−	43.4827i	1.42128	−	2.46172i
$313$	−16.2590	+	28.1615i	−0.919015	+	1.59178i	−0.118100	+	0.993002i	$0.537680\pi$
$313$	−16.2590	+	28.1615i	−0.919015	+	1.59178i	−0.800914	+	0.598779i	$0.795653\pi$
$314$	24.3768	+	42.2219i	1.37566	+	2.38272i
$315$	−0.160424			−0.00903886
$316$	−7.48800	−	12.9696i	−0.421233	−	0.729597i
$317$	−27.8671			−1.56517			−0.782587	−	0.622542i	$-0.786100\pi$
$317$	−27.8671			−1.56517			−0.782587	+	0.622542i	$0.786100\pi$
$318$	3.69343			0.207117
$319$	−1.87614	−	3.24958i	−0.105044	−	0.181941i
$320$	−4.31482			−0.241206
$321$	−10.7291	−	18.5833i	−0.598839	−	1.03722i
$322$	−3.82192	+	6.61977i	−0.212988	+	0.368905i
$323$	−16.4527	+	28.4970i	−0.915455	+	1.58561i
$324$	21.1150	+	36.5722i	1.17305	+	2.03179i
$325$	−11.3568	−	19.6706i	−0.629964	−	1.09113i
$326$	13.8395	−	23.9707i	0.766497	−	1.32761i
$327$	28.5458			1.57859
$328$	−24.1116	+	41.7625i	−1.33134	+	2.30595i
$329$	2.45781	+	4.25706i	0.135504	+	0.234699i
$330$	3.44210			0.189481
$331$	23.5958			1.29694			0.648472	−	0.761238i	$-0.275408\pi$
$331$	23.5958			1.29694			0.648472	+	0.761238i	$0.275408\pi$
$332$	15.8826	−	27.5095i	0.871671	−	1.50978i
$333$	−0.139037	−	0.240819i	−0.00761918	−	0.0131968i
$334$	44.5713			2.43883
$335$	−2.34489	−	4.06147i	−0.128115	−	0.221902i
$336$	−2.20803	+	3.82441i	−0.120458	+	0.208639i
$337$	5.44699	−	9.43447i	0.296717	−	0.513928i	−0.678666	−	0.734447i	$-0.737442\pi$
$337$	5.44699	−	9.43447i	0.296717	−	0.513928i	0.975383	+	0.220519i	$0.0707750\pi$
$338$	15.6447	−	27.0974i	0.850961	−	1.47391i
$339$	1.76845	−	3.06304i	0.0960490	−	0.166362i
$340$	−8.10471	+	14.0378i	−0.439540	+	0.761305i
$341$	7.72307			0.418228
$342$	3.47263	−	6.01477i	0.187778	−	0.325241i
$343$	6.64210			0.358639
$344$	−5.77643	+	10.0051i	−0.311444	+	0.539438i
$345$	4.25633	−	7.37218i	0.229153	−	0.396905i
$346$	18.5783	+	32.1785i	0.998773	+	1.72993i
$347$	−11.6693	+	20.2118i	−0.626441	+	1.08503i	0.361819	+	0.932248i	$0.382156\pi$
$347$	−11.6693	+	20.2118i	−0.626441	+	1.08503i	−0.988260	+	0.152780i	$0.951178\pi$
$348$	−27.8160			−1.49109
$349$	−11.0632			−0.592198			−0.296099	−	0.955157i	$-0.595686\pi$
$349$	−11.0632			−0.592198			−0.296099	+	0.955157i	$0.595686\pi$
$350$	2.68444	+	4.64959i	0.143489	+	0.248531i
$351$	11.9433	+	20.6863i	0.637484	+	1.10415i
$352$	0.799787	−	1.38527i	0.0426288	−	0.0738352i
$353$	−4.64909	−	8.05246i	−0.247446	−	0.428589i	0.715370	−	0.698745i	$-0.246258\pi$
$353$	−4.64909	−	8.05246i	−0.247446	−	0.428589i	−0.962817	+	0.270156i	$0.912925\pi$
$354$	−24.8017			−1.31820
$355$	−0.750846	−	1.30050i	−0.0398508	−	0.0690236i
$356$	−2.14499			−0.113684
$357$	−2.45048	−	4.24436i	−0.129693	−	0.224635i
$358$	−12.2017	−	21.1339i	−0.644878	−	1.11696i
$359$	−15.8051	+	27.3753i	−0.834163	+	1.44481i	0.0605470	+	0.998165i	$0.480716\pi$
$359$	−15.8051	+	27.3753i	−0.834163	+	1.44481i	−0.894710	+	0.446647i	$0.852618\pi$
$360$	0.886079	−	1.53473i	0.0467005	−	0.0808876i
$361$	17.3525			0.913288
$362$	−9.29278			−0.488418
$363$	−9.22716	+	15.9819i	−0.484300	+	0.838833i
$364$	−5.06602	+	8.77461i	−0.265532	+	0.459914i
$365$	−8.14055			−0.426096
$366$	23.1997	+	40.1831i	1.21267	+	2.10041i
$367$	5.92536	+	10.2630i	0.309301	+	0.535726i	0.978210	−	0.207619i	$-0.0665715\pi$
$367$	5.92536	+	10.2630i	0.309301	+	0.535726i	−0.668908	+	0.743345i	$0.733238\pi$
$368$	−15.7097	−	27.2100i	−0.818924	−	1.41842i
$369$	2.10158	+	3.64004i	0.109404	+	0.189493i
$370$	0.531287	−	0.920216i	0.0276203	−	0.0478398i
$371$	−0.386061			−0.0200433
$372$	28.6258	−	49.5813i	1.48418	−	2.57067i
$373$	−25.0064			−1.29478			−0.647390	−	0.762159i	$-0.724140\pi$
$373$	−25.0064			−1.29478			−0.647390	+	0.762159i	$0.724140\pi$
$374$	7.04973	+	12.2105i	0.364533	+	0.631389i
$375$	−6.32046	−	10.9474i	−0.326387	−	0.565319i
$376$	−54.3016			−2.80039
$377$	−18.2296			−0.938872
$378$	−2.82306	−	4.88968i	−0.145202	−	0.251498i
$379$	13.2820			0.682248			0.341124	−	0.940018i	$-0.389192\pi$
$379$	13.2820			0.682248			0.341124	+	0.940018i	$0.389192\pi$
$380$	17.9074			0.918632
$381$	−15.0069	−	14.6557i	−0.768826	−	0.750832i
$382$	−3.30590			−0.169145
$383$	−0.870286			−0.0444695			−0.0222348	−	0.999753i	$-0.507078\pi$
$383$	−0.870286			−0.0444695			−0.0222348	+	0.999753i	$0.507078\pi$
$384$	16.7690	+	29.0448i	0.855742	+	1.48219i
$385$	−0.359790			−0.0183366
$386$	−34.5424			−1.75816
$387$	0.503477	+	0.872047i	0.0255932	+	0.0443286i
$388$	34.7136	+	60.1257i	1.76232	+	3.05242i
$389$	12.0691			0.611926			0.305963	−	0.952043i	$-0.401022\pi$
$389$	12.0691			0.611926			0.305963	+	0.952043i	$0.401022\pi$
$390$	8.36130	−	14.4822i	0.423391	−	0.733334i
$391$	34.8694			1.76342
$392$	−18.0332	+	31.2344i	−0.910814	+	1.57758i
$393$	4.20545	+	7.28404i	0.212137	+	0.367431i
$394$	−1.77511	−	3.07458i	−0.0894287	−	0.154895i
$395$	−1.29181	−	2.23748i	−0.0649981	−	0.112580i
$396$	−1.00401	−	1.73900i	−0.0504535	−	0.0873881i
$397$	3.34691			0.167977			0.0839884	−	0.996467i	$-0.473234\pi$
$397$	3.34691			0.167977			0.0839884	+	0.996467i	$0.473234\pi$
$398$	13.2088	−	22.8783i	0.662097	−	1.14679i
$399$	−2.70718	+	4.68898i	−0.135529	+	0.234742i
$400$	−22.0683			−1.10342
$401$	−18.6964			−0.933656			−0.466828	−	0.884348i	$-0.654603\pi$
$401$	−18.6964			−0.933656			−0.466828	+	0.884348i	$0.654603\pi$
$402$	−15.1201	+	26.1888i	−0.754123	+	1.30618i
$403$	18.7603	−	32.4939i	0.934519	−	1.61863i
$404$	18.0767	+	31.3097i	0.899347	+	1.55772i
$405$	3.64270	+	6.30934i	0.181007	+	0.313514i
$406$	4.30897			0.213851
$407$	−0.311825	−	0.540096i	−0.0154566	−	0.0267716i
$408$	54.1396			2.68031
$409$	7.24790	+	12.5537i	0.358386	+	0.620742i	0.987691	−	0.156416i	$-0.0499940\pi$
$409$	7.24790	+	12.5537i	0.358386	+	0.620742i	−0.629306	+	0.777158i	$0.716661\pi$
$410$	−8.03053	+	13.9093i	−0.396600	+	0.686931i
$411$	3.13797	+	5.43512i	0.154785	+	0.268095i
$412$	−14.0680	−	24.3666i	−0.693083	−	1.20045i
$413$	2.59244			0.127566
$414$	−7.35978			−0.361713
$415$	2.74002	−	4.74586i	0.134502	−	0.232965i
$416$	−3.88557	−	6.73001i	−0.190506	−	0.329966i
$417$	−17.2105	+	29.8095i	−0.842804	+	1.45978i
$418$	7.78822	−	13.4896i	0.380934	−	0.659798i
$419$	29.3577			1.43422			0.717110	−	0.696960i	$-0.245465\pi$
$419$	29.3577			1.43422			0.717110	+	0.696960i	$0.245465\pi$
$420$	−1.33357	+	2.30982i	−0.0650717	+	0.112707i
$421$	26.0740			1.27077			0.635384	−	0.772196i	$-0.280842\pi$
$421$	26.0740			1.27077			0.635384	+	0.772196i	$0.280842\pi$
$422$	−9.94277	+	17.2214i	−0.484006	+	0.838324i
$423$	−2.36647	+	4.09885i	−0.115062	+	0.199293i
$424$	2.13236	−	3.69335i	0.103556	−	0.179365i
$425$	12.2458	−	21.2103i	0.594008	−	1.02885i
$426$	−4.84154	+	8.38579i	−0.234573	+	0.406293i
$427$	−2.42499	−	4.20020i	−0.117353	−	0.203262i
$428$	−47.8341			−2.31215
$429$	−4.90744	−	8.49994i	−0.236933	−	0.410381i
$430$	−1.92388	+	3.33226i	−0.0927777	+	0.160696i
$431$	9.62012			0.463385			0.231692	−	0.972789i	$-0.425574\pi$
$431$	9.62012			0.463385			0.231692	+	0.972789i	$0.425574\pi$
$432$	23.2078			1.11659
$433$	10.2357	+	17.7288i	0.491896	+	0.851990i	0.999956	−	0.00933207i	$-0.00297053\pi$
$433$	10.2357	+	17.7288i	0.491896	+	0.851990i	−0.508060	+	0.861322i	$0.669637\pi$
$434$	−4.43443	+	7.68065i	−0.212859	+	0.368683i
$435$	−4.79874			−0.230082
$436$	31.8169	−	55.1085i	1.52375	−	2.63922i
$437$	−19.2611	−	33.3612i	−0.921382	−	1.59588i
$438$	26.2456	+	45.4587i	1.25406	+	2.17210i
$439$	−12.5428	+	21.7247i	−0.598634	+	1.03686i	0.394389	+	0.918944i	$0.370956\pi$
$439$	−12.5428	+	21.7247i	−0.598634	+	1.03686i	−0.993023	+	0.117921i	$0.962377\pi$
$440$	1.98725	−	3.44202i	0.0947384	−	0.164092i
$441$	1.57178	+	2.72241i	0.0748468	+	0.129638i
$442$	68.4988			3.25816
$443$	−13.3771	−	23.1699i	−0.635568	−	1.10084i	−0.986395	−	0.164395i	$-0.947433\pi$
$443$	−13.3771	−	23.1699i	−0.635568	−	1.10084i	0.350827	−	0.936440i	$-0.385901\pi$
$444$	−4.62315			−0.219405
$445$	−0.370047			−0.0175419
$446$	10.8378	+	18.7715i	0.513183	+	0.888858i
$447$	−26.5684			−1.25664
$448$	−1.45409	−	2.51856i	−0.0686993	−	0.118991i
$449$	7.25394	−	12.5642i	0.342334	−	0.592941i	−0.642531	−	0.766259i	$-0.722116\pi$
$449$	7.25394	−	12.5642i	0.342334	−	0.592941i	0.984866	+	0.173319i	$0.0554491\pi$
$450$	−2.58468	+	4.47679i	−0.121843	+	0.211038i
$451$	4.71331	+	8.16369i	0.221941	+	0.384413i
$452$	−3.94219	−	6.82807i	−0.185425	−	0.321165i
$453$	15.9076	−	27.5527i	0.747403	−	1.29454i
$454$	−32.2628			−1.51417
$455$	−0.873977	+	1.51377i	−0.0409727	+	0.0709667i
$456$	−29.9055	−	51.7978i	−1.40045	−	2.42565i
$457$	11.0519			0.516984			0.258492	−	0.966013i	$-0.416774\pi$
$457$	11.0519			0.516984			0.258492	+	0.966013i	$0.416774\pi$
$458$	−1.95856			−0.0915173
$459$	−12.8781	+	22.3055i	−0.601099	+	1.04113i
$460$	−9.48812	−	16.4339i	−0.442386	−	0.766235i
$461$	−12.2842			−0.572132			−0.286066	−	0.958210i	$-0.592348\pi$
$461$	−12.2842			−0.572132			−0.286066	+	0.958210i	$0.592348\pi$
$462$	1.15998	+	2.00915i	0.0539673	+	0.0934741i
$463$	−3.18250	+	5.51225i	−0.147903	+	0.256176i	−0.930452	−	0.366413i	$-0.880586\pi$
$463$	−3.18250	+	5.51225i	−0.147903	+	0.256176i	0.782549	+	0.622589i	$0.213919\pi$
$464$	−8.85582	+	15.3387i	−0.411121	+	0.712083i
$465$	4.93845	−	8.55364i	0.229015	−	0.396666i
$466$	13.4266	−	23.2556i	0.621976	−	1.07729i
$467$	−8.71986	+	15.1032i	−0.403507	+	0.698894i	−0.994146	−	0.108041i	$-0.965542\pi$
$467$	−8.71986	+	15.1032i	−0.403507	+	0.698894i	0.590640	+	0.806936i	$0.298876\pi$
$468$	−9.75551			−0.450948
$469$	1.58045	−	2.73743i	0.0729786	−	0.126403i
$470$	−18.0855			−0.834222
$471$	18.2974	−	31.6920i	0.843099	−	1.46029i
$472$	−14.3190	+	24.8012i	−0.659084	+	1.14157i
$473$	1.12917	+	1.95578i	0.0519193	+	0.0899268i
$474$	−8.32974	+	14.4275i	−0.382598	+	0.662678i
$475$	−27.0572			−1.24147
$476$	−10.9251			−0.500752
$477$	−0.185857	−	0.321914i	−0.00850981	−	0.0147394i
$478$	−27.1831	−	47.0825i	−1.24332	−	2.15350i
$479$	−15.9384	+	27.6061i	−0.728244	+	1.26136i	0.229380	+	0.973337i	$0.426330\pi$
$479$	−15.9384	+	27.6061i	−0.728244	+	1.26136i	−0.957625	+	0.288019i	$0.907003\pi$
$480$	−1.02283	−	1.77160i	−0.0466857	−	0.0808620i
$481$	−3.02985			−0.138149
$482$	−27.5171	−	47.6611i	−1.25337	−	2.17090i
$483$	5.73752			0.261066
$484$	20.5690	+	35.6265i	0.934954	+	1.61939i
$485$	5.98870	+	10.3727i	0.271933	+	0.471002i
$486$	5.93428	−	10.2785i	0.269184	−	0.466241i
$487$	9.31639	−	16.1365i	0.422166	−	0.731213i	−0.573985	−	0.818866i	$-0.694603\pi$
$487$	9.31639	−	16.1365i	0.422166	−	0.731213i	0.996151	+	0.0876527i	$0.0279366\pi$
$488$	53.5763			2.42528
$489$	−20.7760			−0.939521
$490$	−6.00608	+	10.4028i	−0.271327	+	0.469952i
$491$	20.6220	−	35.7184i	0.930658	−	1.61195i	0.148458	−	0.988919i	$-0.452569\pi$
$491$	20.6220	−	35.7184i	0.930658	−	1.61195i	0.782199	−	0.623028i	$-0.214098\pi$
$492$	69.8801			3.15044
$493$	−9.82826	−	17.0230i	−0.442642	−	0.766679i
$494$	−37.8372	−	65.5360i	−1.70238	−	2.94860i
$495$	−0.173210	−	0.300008i	−0.00778519	−	0.0134843i
$496$	−18.2273	−	31.5706i	−0.818431	−	1.41756i
$497$	0.506069	−	0.876537i	0.0227003	−	0.0393181i
$498$	−35.3359			−1.58344
$499$	1.80796	−	3.13148i	0.0809355	−	0.140184i	−0.822716	−	0.568452i	$-0.807543\pi$
$499$	1.80796	−	3.13148i	0.0809355	−	0.140184i	0.903652	+	0.428267i	$0.140876\pi$
$500$	−28.1789			−1.26020
$501$	−16.7277	−	28.9733i	−0.747340	−	1.29443i
$502$	6.72187	+	11.6426i	0.300012	+	0.519636i
$503$	−16.0197			−0.714284			−0.357142	−	0.934050i	$-0.616249\pi$
$503$	−16.0197			−0.714284			−0.357142	+	0.934050i	$0.616249\pi$
$504$	1.19443			0.0532042
$505$	3.11854	+	5.40146i	0.138773	+	0.240362i
$506$	−16.5061			−0.733786
$507$	−23.4860			−1.04305
$508$	−45.0196	+	12.6361i	−1.99742	+	0.560637i
$509$	−16.1553			−0.716073			−0.358036	−	0.933708i	$-0.616554\pi$
$509$	−16.1553			−0.716073			−0.358036	+	0.933708i	$0.616554\pi$
$510$	18.0315			0.798450
$511$	−2.74336	−	4.75164i	−0.121359	−	0.210200i
$512$	44.8670			1.98286
$513$	28.4543			1.25629
$514$	−21.3887	−	37.0464i	−0.943417	−	1.63405i
$515$	−2.42698	−	4.20366i	−0.106946	−	0.185235i
$516$	16.7412			0.736991
$517$	−5.30740	+	9.19269i	−0.233419	+	0.404294i
$518$	0.716173			0.0314668
$519$	13.9449	−	24.1533i	0.612115	−	1.06021i
$520$	−9.65458	−	16.7222i	−0.423381	−	0.733318i
$521$	−15.4224	−	26.7125i	−0.675670	−	1.17029i	−0.976273	−	0.216545i	$-0.930521\pi$
$521$	−15.4224	−	26.7125i	−0.675670	−	1.17029i	0.300603	−	0.953749i	$-0.402812\pi$
$522$	2.07442	+	3.59300i	0.0907949	+	0.157261i
$523$	−7.79940	−	13.5090i	−0.341044	−	0.590705i	0.643583	−	0.765376i	$-0.277447\pi$
$523$	−7.79940	−	13.5090i	−0.341044	−	0.590705i	−0.984627	+	0.174671i	$0.944114\pi$
$524$	18.7494			0.819070
$525$	2.01496	−	3.49001i	0.0879399	−	0.152316i
$526$	−32.6033	+	56.4706i	−1.42157	+	2.46223i
$527$	40.4576			1.76236
$528$	−9.53601			−0.415002
$529$	−8.91067	+	15.4337i	−0.387420	+	0.671032i
$530$	0.710195	−	1.23009i	0.0308489	−	0.0534319i
$531$	1.24805	+	2.16168i	0.0541606	+	0.0938090i
$532$	6.03479	+	10.4526i	0.261641	+	0.453176i
$533$	45.7969			1.98369
$534$	1.19305	+	2.06643i	0.0516284	+	0.0894231i
$535$	−8.25221			−0.356774
$536$	17.4588	+	30.2396i	0.754106	+	1.30615i
$537$	−9.15864	+	15.8632i	−0.395224	+	0.684549i
$538$	−8.71013	−	15.0864i	−0.375520	−	0.650420i
$539$	3.52511	+	6.10567i	0.151837	+	0.262990i
$540$	14.0168			0.603185
$541$	−4.41492			−0.189812			−0.0949062	−	0.995486i	$-0.530255\pi$
$541$	−4.41492			−0.189812			−0.0949062	+	0.995486i	$0.530255\pi$
$542$	−13.1893	+	22.8445i	−0.566529	+	0.981256i
$543$	3.48761	+	6.04071i	0.149668	+	0.259232i
$544$	4.18971	−	7.25680i	0.179632	−	0.311133i
$545$	5.48897	−	9.50717i	0.235122	−	0.407242i
$546$	11.2710			0.482354
$547$	−1.49176	+	2.58380i	−0.0637828	+	0.110475i	−0.896153	−	0.443744i	$-0.853650\pi$
$547$	−1.49176	+	2.58380i	−0.0637828	+	0.110475i	0.832371	+	0.554219i	$0.186983\pi$
$548$	13.9902			0.597631
$549$	2.33487	−	4.04411i	0.0996497	−	0.172598i
$550$	−5.79678	+	10.0403i	−0.247175	+	0.428120i
$551$	−10.8578	+	18.8063i	−0.462558	+	0.801174i
$552$	−31.6904	+	54.8893i	−1.34883	+	2.33624i
$553$	0.870678	−	1.50806i	0.0370250	−	0.0641292i
$554$	3.44230	+	5.96223i	0.146249	+	0.253311i
$555$	−0.797574			−0.0338551
$556$	38.3654	+	66.4508i	1.62705	+	2.81814i
$557$	−10.0846	+	17.4671i	−0.427299	+	0.740103i	−0.996632	−	0.0820038i	$-0.973868\pi$
$557$	−10.0846	+	17.4671i	−0.427299	+	0.740103i	0.569333	+	0.822107i	$0.307201\pi$
$558$	−8.53926			−0.361496
$559$	10.9716			0.464049
$560$	0.849145	+	1.47076i	0.0358829	+	0.0621510i
$561$	5.29157	−	9.16526i	0.223410	−	0.386958i
$562$	57.4792			2.42462
$563$	7.68399	−	13.3091i	0.323842	−	0.560910i	−0.657436	−	0.753511i	$-0.728359\pi$
$563$	7.68399	−	13.3091i	0.323842	−	0.560910i	0.981277	+	0.192600i	$0.0616921\pi$
$564$	39.3441	+	68.1460i	1.65669	+	2.86946i
$565$	−0.680096	−	1.17796i	−0.0286119	−	0.0495572i
$566$	3.96674	−	6.87060i	0.166735	−	0.288793i
$567$	−2.45517	+	4.25248i	−0.103108	+	0.178588i
$568$	5.59040	+	9.68286i	0.234568	+	0.406284i
$569$	−19.2160			−0.805575			−0.402788	−	0.915293i	$-0.631959\pi$
$569$	−19.2160			−0.805575			−0.402788	+	0.915293i	$0.631959\pi$
$570$	−9.96022	−	17.2516i	−0.417188	−	0.722590i
$571$	−43.3111			−1.81251			−0.906256	−	0.422729i	$-0.861072\pi$
$571$	−43.3111			−1.81251			−0.906256	+	0.422729i	$0.861072\pi$
$572$	−21.8791			−0.914812
$573$	1.24071	+	2.14898i	0.0518316	+	0.0897749i
$574$	−10.8251			−0.451832
$575$	14.3360	+	24.8307i	0.597854	+	1.03551i
$576$	1.40005	−	2.42496i	0.0583355	−	0.101040i
$577$	16.1798	−	28.0243i	0.673576	−	1.16667i	−0.303307	−	0.952893i	$-0.598091\pi$
$577$	16.1798	−	28.0243i	0.673576	−	1.16667i	0.976883	−	0.213774i	$-0.0685758\pi$
$578$	15.8523	+	27.4570i	0.659368	+	1.14206i
$579$	12.9639	+	22.4541i	0.538760	+	0.933160i
$580$	−5.34862	+	9.26408i	−0.222089	+	0.384670i
$581$	3.69354			0.153234
$582$	38.6158	−	66.8845i	1.60068	−	2.77245i
$583$	−0.416830	−	0.721971i	−0.0172633	−	0.0299010i
$584$	60.6102			2.50807
$585$	−1.68299			−0.0695833
$586$	−35.8323	+	62.0634i	−1.48022	+	2.56381i
$587$	−3.73793	−	6.47429i	−0.154281	−	0.267223i	0.778516	−	0.627625i	$-0.215973\pi$
$587$	−3.73793	−	6.47429i	−0.154281	−	0.267223i	−0.932797	+	0.360402i	$0.882639\pi$
$588$	52.2637			2.15532
$589$	−22.3479	−	38.7076i	−0.920827	−	1.59492i
$590$	−4.76903	+	8.26020i	−0.196338	+	0.340067i
$591$	−1.33241	+	2.30780i	−0.0548079	+	0.0949301i
$592$	−1.47188	+	2.54938i	−0.0604940	+	0.104779i
$593$	−18.7610	+	32.4950i	−0.770421	+	1.33441i	0.166911	+	0.985972i	$0.446621\pi$
$593$	−18.7610	+	32.4950i	−0.770421	+	1.33441i	−0.937332	+	0.348436i	$0.886713\pi$
$594$	6.09610	−	10.5588i	0.250126	−	0.433231i
$595$	−1.88477			−0.0772682
$596$	−29.6128	+	51.2909i	−1.21299	+	2.10096i
$597$	−19.8292			−0.811555
$598$	−40.0955	+	69.4474i	−1.63963	+	2.83992i
$599$	14.4943	−	25.1048i	0.592220	−	1.02576i	−0.401712	−	0.915766i	$-0.631585\pi$
$599$	14.4943	−	25.1048i	0.592220	−	1.02576i	0.993933	−	0.109990i	$-0.0350818\pi$
$600$	22.2587	+	38.5531i	0.908706	+	1.57392i
$601$	10.5150	−	18.2125i	0.428915	−	0.742902i	−0.567862	−	0.823124i	$-0.692229\pi$
$601$	10.5150	−	18.2125i	0.428915	−	0.742902i	0.996777	+	0.0802212i	$0.0255627\pi$
$602$	−2.59338			−0.105698
$603$	3.04344			0.123938
$604$	−35.4608	−	61.4199i	−1.44288	−	2.49914i
$605$	3.54851	+	6.14619i	0.144267	+	0.249878i
$606$	20.1087	−	34.8292i	0.816859	−	1.41484i
$607$	−7.03063	−	12.1774i	−0.285364	−	0.494266i	0.687333	−	0.726342i	$-0.258781\pi$
$607$	−7.03063	−	12.1774i	−0.285364	−	0.494266i	−0.972697	+	0.232077i	$0.925448\pi$
$608$	−9.25721			−0.375429
$609$	−1.61717	−	2.80102i	−0.0655310	−	0.113503i
$610$	17.8439			0.722480
$611$	25.7847	+	44.6605i	1.04314	+	1.80677i
$612$	−5.25956	−	9.10982i	−0.212605	−	0.368243i
$613$	−10.1710	+	17.6166i	−0.410802	+	0.711529i	−0.994978	−	0.100098i	$-0.968084\pi$
$613$	−10.1710	+	17.6166i	−0.410802	+	0.711529i	0.584176	+	0.811627i	$0.301418\pi$
$614$	14.5570	−	25.2135i	0.587474	−	1.01754i
$615$	12.0555			0.486126
$616$	2.67881			0.107932
$617$	15.0707	−	26.1032i	0.606724	−	1.05088i	−0.385053	−	0.922894i	$-0.625817\pi$
$617$	15.0707	−	26.1032i	0.606724	−	1.05088i	0.991777	−	0.127982i	$-0.0408499\pi$
$618$	−15.6494	+	27.1056i	−0.629513	+	1.09035i
$619$	−37.9414			−1.52499			−0.762496	−	0.646993i	$-0.776026\pi$
$619$	−37.9414			−1.52499			−0.762496	+	0.646993i	$0.776026\pi$
$620$	−11.0087	−	19.0676i	−0.442119	−	0.765773i
$621$	−15.0763	−	26.1129i	−0.604991	−	1.04787i
$622$	−17.2203	−	29.8264i	−0.690470	−	1.19593i
$623$	−0.124706	−	0.215996i	−0.00499622	−	0.00865371i
$624$	−23.1642	+	40.1216i	−0.927311	+	1.60615i
$625$	17.5767			0.703069
$626$	40.3185	−	69.8338i	1.61145	−	2.79112i
$627$	−11.6918			−0.466924
$628$	−40.7881	−	70.6471i	−1.62762	−	2.81913i
$629$	−1.63351	−	2.82931i	−0.0651321	−	0.112812i
$630$	0.397813			0.0158493
$631$	−10.5943			−0.421753			−0.210876	−	0.977513i	$-0.567632\pi$
$631$	−10.5943			−0.421753			−0.210876	+	0.977513i	$0.567632\pi$
$632$	9.61814	+	16.6591i	0.382589	+	0.662663i
$633$	14.9262			0.593263
$634$	69.1038			2.74446
$635$	−7.76667	+	2.17995i	−0.308211	+	0.0865087i
$636$	−6.17997			−0.245052
$637$	34.2518			1.35711
$638$	4.65239	+	8.05818i	0.184190	+	0.319027i
$639$	0.974524			0.0385516
$640$	12.8978			0.509831
$641$	9.87475	+	17.1036i	0.390029	+	0.675550i	0.992453	−	0.122626i	$-0.0391316\pi$
$641$	9.87475	+	17.1036i	0.390029	+	0.675550i	−0.602424	+	0.798176i	$0.705798\pi$
$642$	26.6056	+	46.0822i	1.05004	+	1.81872i
$643$	−21.1476			−0.833978			−0.416989	−	0.908911i	$-0.636915\pi$
$643$	−21.1476			−0.833978			−0.416989	+	0.908911i	$0.636915\pi$
$644$	6.39497	−	11.0764i	0.251997	−	0.436472i
$645$	2.88815			0.113721
$646$	40.7989	−	70.6658i	1.60521	−	2.78031i
$647$	−14.9743	−	25.9362i	−0.588700	−	1.01966i	−0.994403	−	0.105654i	$-0.966306\pi$
$647$	−14.9743	−	25.9362i	−0.588700	−	1.01966i	0.405702	−	0.914005i	$-0.367027\pi$
$648$	−27.1216	−	46.9760i	−1.06544	−	1.84539i
$649$	2.79905	+	4.84810i	0.109872	+	0.190305i
$650$	28.1622	+	48.7784i	1.10461	+	1.91325i
$651$	6.65701			0.260909
$652$	−23.1567	+	40.1085i	−0.906885	+	1.57077i
$653$	−6.05762	+	10.4921i	−0.237053	+	0.410588i	−0.959867	−	0.280454i	$-0.909515\pi$
$653$	−6.05762	+	10.4921i	−0.237053	+	0.410588i	0.722814	+	0.691042i	$0.242848\pi$
$654$	−70.7869			−2.76799
$655$	3.23459			0.126386
$656$	22.2479	−	38.5344i	0.868633	−	1.50452i
$657$	2.64141	−	4.57505i	0.103051	−	0.178490i
$658$	−6.09480	−	10.5565i	−0.237600	−	0.411535i
$659$	7.45175	+	12.9068i	0.290279	+	0.502778i	0.973876	−	0.227082i	$-0.0729185\pi$
$659$	7.45175	+	12.9068i	0.290279	+	0.502778i	−0.683597	+	0.729860i	$0.739585\pi$
$660$	−5.75943			−0.224186
$661$	1.30071	+	2.25290i	0.0505918	+	0.0876275i	0.890212	−	0.455546i	$-0.150556\pi$
$661$	1.30071	+	2.25290i	0.0505918	+	0.0876275i	−0.839621	+	0.543173i	$0.817223\pi$
$662$	−58.5121			−2.27414
$663$	−25.7078	−	44.5272i	−0.998409	−	1.72929i
$664$	−20.4008	+	35.3351i	−0.791703	+	1.37127i
$665$	1.04111	+	1.80325i	0.0403724	+	0.0699270i
$666$	0.344779	+	0.597175i	0.0133599	+	0.0231400i
$667$	23.0117			0.891017
$668$	−74.5782			−2.88552
$669$	8.13488	−	14.0900i	0.314513	−	0.544752i
$670$	5.81478	+	10.0715i	0.224644	+	0.389096i
$671$	5.23651	−	9.06991i	0.202153	−	0.350140i
$672$	0.689388	−	1.19405i	0.0265937	−	0.0460616i
$673$	50.6581			1.95272			0.976362	−	0.216141i	$-0.0693471\pi$
$673$	50.6581			1.95272			0.976362	+	0.216141i	$0.0693471\pi$
$674$	−13.5073	+	23.3952i	−0.520280	+	0.901151i
$675$	−21.1785			−0.815163
$676$	−26.1773	+	45.3404i	−1.00682	+	1.74386i
$677$	−12.5258	+	21.6953i	−0.481405	+	0.833818i	−0.999772	−	0.0213403i	$-0.993207\pi$
$677$	−12.5258	+	21.6953i	−0.481405	+	0.833818i	0.518367	+	0.855158i	$0.326540\pi$
$678$	−4.38533	+	7.59562i	−0.168418	+	0.291708i
$679$	−4.03637	+	6.99120i	−0.154902	+	0.268298i
$680$	10.4103	−	18.0311i	0.399216	−	0.691463i
$681$	12.1083	+	20.9722i	0.463992	+	0.803657i
$682$	−19.1514			−0.733344
$683$	−16.1185	−	27.9181i	−0.616759	−	1.06826i	−0.990073	−	0.140552i	$-0.955112\pi$
$683$	−16.1185	−	27.9181i	−0.616759	−	1.06826i	0.373315	−	0.927705i	$-0.378221\pi$
$684$	−5.81052	+	10.0641i	−0.222171	+	0.384811i
$685$	2.41355			0.0922171
$686$	−16.4708			−0.628859
$687$	0.735052	+	1.27315i	0.0280440	+	0.0485736i
$688$	5.32993	−	9.23172i	0.203202	−	0.351956i
$689$	−4.05014			−0.154298
$690$	−10.5547	+	18.2813i	−0.401810	+	0.695955i
$691$	0.0634701	+	0.109933i	0.00241452	+	0.00418207i	0.867230	−	0.497908i	$-0.165898\pi$
$691$	0.0634701	+	0.109933i	0.00241452	+	0.00418207i	−0.864816	+	0.502090i	$0.832565\pi$
$692$	−31.0858	−	53.8421i	−1.18170	−	2.04677i
$693$	0.116743	−	0.202205i	0.00443470	−	0.00768112i
$694$	28.9371	−	50.1205i	1.09844	−	1.90255i
$695$	6.61869	+	11.4639i	0.251061	+	0.434851i
$696$	35.7288			1.35430
$697$	24.6908	+	42.7658i	0.935232	+	1.61987i
$698$	27.4340			1.03839
$699$	−20.1562			−0.762377
$700$	−4.49170	−	7.77985i	−0.169770	−	0.294051i
$701$	−12.4479			−0.470152			−0.235076	−	0.971977i	$-0.575534\pi$
$701$	−12.4479			−0.470152			−0.235076	+	0.971977i	$0.575534\pi$
$702$	−29.6164	−	51.2972i	−1.11780	−	1.93609i
$703$	−1.80462	+	3.12570i	−0.0680626	+	0.117888i
$704$	3.13996	−	5.43857i	0.118342	−	0.204974i
$705$	6.78754	+	11.7564i	0.255634	+	0.442770i
$706$	11.5286	+	19.9682i	0.433886	+	0.751513i
$707$	−2.10189	+	3.64058i	−0.0790496	+	0.136918i
$708$	41.4991			1.55963
$709$	−19.9948	+	34.6319i	−0.750919	+	1.30063i	0.196459	+	0.980512i	$0.437056\pi$
$709$	−19.9948	+	34.6319i	−0.750919	+	1.30063i	−0.947378	+	0.320117i	$0.896278\pi$
$710$	1.86192	+	3.22494i	0.0698767	+	0.121030i
$711$	1.67664			0.0628790
$712$	2.75518			0.103255
$713$	−23.6817	+	41.0179i	−0.886886	+	1.53613i
$714$	6.07661	+	10.5250i	0.227412	+	0.393888i
$715$	−3.77453			−0.141159
$716$	20.4162	+	35.3620i	0.762991	+	1.32154i
$717$	−20.4038	+	35.3404i	−0.761993	+	1.31981i
$718$	39.1930	−	67.8842i	1.46267	−	2.53342i
$719$	15.8752	−	27.4967i	0.592046	−	1.02545i	−0.401911	−	0.915679i	$-0.631654\pi$
$719$	15.8752	−	27.4967i	0.592046	−	1.02545i	0.993957	−	0.109774i	$-0.0350128\pi$
$720$	−0.817588	+	1.41610i	−0.0304697	+	0.0527751i
$721$	1.63578	−	2.83326i	0.0609197	−	0.105516i
$722$	−43.0300			−1.60141
$723$	−20.6545	+	35.7747i	−0.768150	+	1.33048i
$724$	15.5490			0.577874
$725$	8.08147	−	13.9975i	0.300138	−	0.519855i
$726$	22.8812	−	39.6313i	0.849200	−	1.47086i
$727$	19.8083	+	34.3089i	0.734648	+	1.27245i	0.954878	+	0.297000i	$0.0959860\pi$
$727$	19.8083	+	34.3089i	0.734648	+	1.27245i	−0.220230	+	0.975448i	$0.570681\pi$
$728$	6.50717	−	11.2707i	0.241172	−	0.417721i
$729$	21.6248			0.800918
$730$	20.1866			0.747141
$731$	5.91520	+	10.2454i	0.218782	+	0.378941i
$732$	−38.8186	−	67.2358i	−1.43478	−	2.48511i
$733$	12.7533	−	22.0894i	0.471054	−	0.815890i	−0.528398	−	0.848997i	$-0.677207\pi$
$733$	12.7533	−	22.0894i	0.471054	−	0.815890i	0.999452	+	0.0331072i	$0.0105403\pi$
$734$	−14.6935	−	25.4499i	−0.542347	−	0.939372i
$735$	9.01639			0.332575
$736$	4.90486	+	8.49547i	0.180796	+	0.313147i
$737$	6.82566			0.251426
$738$	−5.21142	−	9.02644i	−0.191835	−	0.332268i
$739$	9.39416	+	16.2712i	0.345570	+	0.598544i	0.985457	−	0.169924i	$-0.0543524\pi$
$739$	9.39416	+	16.2712i	0.345570	+	0.598544i	−0.639887	+	0.768469i	$0.721019\pi$
$740$	−0.888967	+	1.53974i	−0.0326791	+	0.0566018i
$741$	−28.4008	+	49.1917i	−1.04333	+	1.80710i
$742$	0.957340			0.0351451
$743$	−6.97471			−0.255877			−0.127939	−	0.991782i	$-0.540836\pi$
$743$	−6.97471			−0.255877			−0.127939	+	0.991782i	$0.540836\pi$
$744$	−36.7691	+	63.6859i	−1.34802	+	2.33484i
$745$	−5.10873	+	8.84858i	−0.187169	+	0.324187i
$746$	62.0098			2.27034
$747$	1.77814	+	3.07983i	0.0650587	+	0.112685i
$748$	−11.7958	−	20.4310i	−0.431299	−	0.747032i
$749$	−2.78099	−	4.81681i	−0.101615	−	0.176002i
$750$	15.6732	+	27.1468i	0.572306	+	0.991262i
$751$	−5.59543	+	9.69157i	−0.204180	+	0.353650i	−0.949871	−	0.312642i	$-0.898786\pi$
$751$	−5.59543	+	9.69157i	−0.204180	+	0.353650i	0.745691	+	0.666292i	$0.232119\pi$
$752$	50.1042			1.82711
$753$	5.04547	−	8.73902i	0.183867	−	0.318468i
$754$	45.2051			1.64627
$755$	−6.11761	−	10.5960i	−0.222642	−	0.385628i
$756$	4.72363	+	8.18157i	0.171797	+	0.297561i
$757$	44.6070			1.62127			0.810634	−	0.585553i	$-0.199122\pi$
$757$	44.6070			1.62127			0.810634	+	0.585553i	$0.199122\pi$
$758$	−32.9361			−1.19629
$759$	6.19479	+	10.7297i	0.224857	+	0.389463i
$760$	−23.0016			−0.834356
$761$	−36.4966			−1.32300			−0.661500	−	0.749945i	$-0.730080\pi$
$761$	−36.4966			−1.32300			−0.661500	+	0.749945i	$0.730080\pi$
$762$	37.2135	+	36.3426i	1.34810	+	1.31655i
$763$	7.39911			0.267866
$764$	5.53154			0.200124
$765$	−0.907365	−	1.57160i	−0.0328058	−	0.0568214i
$766$	2.15810			0.0779754
$767$	27.1971			0.982029
$768$	−30.3634	−	52.5910i	−1.09565	−	1.89772i
$769$	−14.6734	−	25.4150i	−0.529135	−	0.916488i	−0.999423	−	0.0339750i	$-0.989183\pi$
$769$	−14.6734	−	25.4150i	−0.529135	−	0.916488i	0.470288	−	0.882513i	$-0.344150\pi$
$770$	0.892194			0.0321524
$771$	−16.0545	+	27.8072i	−0.578189	+	1.00145i
$772$	57.7976			2.08018
$773$	7.06151	−	12.2309i	0.253985	−	0.439915i	−0.710634	−	0.703562i	$-0.751592\pi$
$773$	7.06151	−	12.2309i	0.253985	−	0.439915i	0.964619	+	0.263647i	$0.0849253\pi$
$774$	−1.24850	−	2.16247i	−0.0448765	−	0.0777284i
$775$	16.6335	+	28.8101i	0.597494	+	1.03489i
$776$	−44.5887	−	77.2298i	−1.60064	−	2.77239i
$777$	−0.268782	−	0.465544i	−0.00964249	−	0.0167013i
$778$	−29.9284			−1.07299
$779$	27.2773	−	47.2457i	0.977311	−	1.69275i
$780$	−13.9904	+	24.2321i	−0.500937	+	0.867648i
$781$	2.18561			0.0782073
$782$	−86.4679			−3.09209
$783$	−8.49877	+	14.7203i	−0.303721	+	0.526061i
$784$	16.6393	−	28.8201i	0.594261	−	1.02929i
$785$	−7.03666	−	12.1879i	−0.251149	−	0.435003i
$786$	−10.4285	−	18.0627i	−0.371972	−	0.644275i
$787$	0.194156			0.00692091			0.00346046	−	0.999994i	$-0.498899\pi$
$787$	0.194156			0.00692091			0.00346046	+	0.999994i	$0.498899\pi$
$788$	2.97017	+	5.14449i	0.105808	+	0.183265i
$789$	48.9444			1.74247
$790$	3.20338	+	5.54842i	0.113971	+	0.197404i
$791$	0.458384	−	0.793944i	0.0162982	−	0.0282294i
$792$	1.28963	+	2.23370i	0.0458249	+	0.0793710i
$793$	−25.4403	−	44.0640i	−0.903413	−	1.56476i
$794$	−8.29955			−0.294540
$795$	−1.06615			−0.0378126
$796$	−22.1014	+	38.2808i	−0.783364	+	1.35683i
$797$	13.6855	+	23.7040i	0.484766	+	0.839639i	0.999847	−	0.0175022i	$-0.00557141\pi$
$797$	13.6855	+	23.7040i	0.484766	+	0.839639i	−0.515081	+	0.857142i	$0.672238\pi$
$798$	6.71317	−	11.6275i	0.237644	−	0.411611i
$799$	−27.8030	+	48.1562i	−0.983600	+	1.70365i
$800$	6.89014			0.243603
$801$	0.120071	−	0.207969i	0.00424251	−	0.00734824i
$802$	46.3627			1.63713
$803$	5.92400	−	10.2607i	0.209054	−	0.362091i
$804$	25.2995	−	43.8200i	0.892245	−	1.54541i
$805$	1.10324	−	1.91087i	0.0388842	−	0.0673495i
$806$	−46.5212	+	80.5771i	−1.63864	+	2.83821i
$807$	−6.53787	+	11.3239i	−0.230144	+	0.398621i
$808$	−23.2190	−	40.2164i	−0.816840	−	1.41481i
$809$	−3.35744			−0.118041			−0.0590207	−	0.998257i	$-0.518798\pi$
$809$	−3.35744			−0.118041			−0.0590207	+	0.998257i	$0.518798\pi$
$810$	−9.03303	−	15.6457i	−0.317388	−	0.549733i
$811$	17.4343	−	30.1971i	0.612202	−	1.06036i	−0.378667	−	0.925533i	$-0.623617\pi$
$811$	17.4343	−	30.1971i	0.612202	−	1.06036i	0.990869	−	0.134831i	$-0.0430493\pi$
$812$	−7.20992			−0.253019
$813$	19.7999			0.694413
$814$	0.773251	+	1.33931i	0.0271024	+	0.0469428i
$815$	−3.99493	+	6.91941i	−0.139936	+	0.242377i
$816$	−49.9548			−1.74877
$817$	6.53484	−	11.3187i	0.228625	−	0.395991i
$818$	−17.9731	−	31.1303i	−0.628414	−	1.08844i
$819$	−0.567168	−	0.982363i	−0.0198184	−	0.0343265i
$820$	13.4370	−	23.2735i	0.469239	−	0.812746i
$821$	−1.42390	+	2.46626i	−0.0496943	+	0.0860731i	−0.889803	−	0.456346i	$-0.849158\pi$
$821$	−1.42390	+	2.46626i	−0.0496943	+	0.0860731i	0.840108	+	0.542419i	$0.182491\pi$
$822$	−7.78142	−	13.4778i	−0.271408	−	0.470093i
$823$	−17.2736			−0.602119			−0.301059	−	0.953605i	$-0.597340\pi$
$823$	−17.2736			−0.602119			−0.301059	+	0.953605i	$0.597340\pi$
$824$	18.0700	+	31.2982i	0.629499	+	1.09032i
$825$	8.70219			0.302971
$826$	−6.42863			−0.223681
$827$	14.1408	+	24.4925i	0.491723	+	0.851689i	0.999955	−	0.00953123i	$-0.00303393\pi$
$827$	14.1408	+	24.4925i	0.491723	+	0.851689i	−0.508232	+	0.861220i	$0.669701\pi$
$828$	12.3146			0.427963
$829$	5.71223	+	9.89387i	0.198394	+	0.343628i	0.948008	−	0.318247i	$-0.103094\pi$
$829$	5.71223	+	9.89387i	0.198394	+	0.343628i	−0.749614	+	0.661875i	$0.769761\pi$
$830$	−6.79461	+	11.7686i	−0.235844	+	0.408494i
$831$	2.58381	−	4.47529i	0.0896313	−	0.155246i
$832$	−15.2547	−	26.4220i	−0.528863	−	0.916018i
$833$	18.4664	+	31.9848i	0.639823	+	1.10821i
$834$	42.6781	−	73.9206i	1.47782	−	2.55966i
$835$	−12.8660			−0.445248
$836$	−13.0315	+	22.5713i	−0.450704	+	0.780643i
$837$	−17.4924	−	30.2978i	−0.604626	−	1.04724i
$838$	−72.8002			−2.51484
$839$	12.8448			0.443450			0.221725	−	0.975109i	$-0.428831\pi$
$839$	12.8448			0.443450			0.221725	+	0.975109i	$0.428831\pi$
$840$	1.71294	−	2.96690i	0.0591020	−	0.102368i
$841$	8.01395	+	13.8806i	0.276343	+	0.478640i
$842$	−64.6573			−2.22824
$843$	−21.5721	−	37.3640i	−0.742983	−	1.28689i
$844$	16.6366	−	28.8154i	0.572655	−	0.991867i
$845$	−4.51603	+	7.82200i	−0.155356	+	0.269085i
$846$	5.86830	−	10.1642i	0.201756	−	0.349452i
$847$	−2.39169	+	4.14252i	−0.0821793	+	0.142339i
$848$	−1.96753	+	3.40786i	−0.0675653	+	0.117027i
$849$	−5.95492			−0.204372
$850$	−30.3666	+	52.5965i	−1.04157	+	1.80405i
$851$	3.82466			0.131108
$852$	8.10103	−	14.0314i	0.277537	−	0.480708i
$853$	−24.3113	+	42.1085i	−0.832404	+	1.44177i	0.0637220	+	0.997968i	$0.479703\pi$
$853$	−24.3113	+	42.1085i	−0.832404	+	1.44177i	−0.896126	+	0.443799i	$0.853630\pi$
$854$	6.01339	+	10.4155i	0.205774	+	0.356411i
$855$	−1.00242	+	1.73623i	−0.0342819	+	0.0593780i
$856$	61.4415			2.10003
$857$	−36.6332			−1.25137			−0.625683	−	0.780078i	$-0.715180\pi$
$857$	−36.6332			−1.25137			−0.625683	+	0.780078i	$0.715180\pi$
$858$	12.1693	+	21.0778i	0.415453	+	0.719585i
$859$	4.15804	+	7.20193i	0.141870	+	0.245727i	0.928201	−	0.372079i	$-0.121355\pi$
$859$	4.15804	+	7.20193i	0.141870	+	0.245727i	−0.786331	+	0.617806i	$0.788022\pi$
$860$	3.21910	−	5.57565i	0.109770	−	0.190128i
$861$	4.06270	+	7.03681i	0.138456	+	0.239814i
$862$	−23.8556			−0.812526
$863$	−2.94345	−	5.09820i	−0.100196	−	0.173545i	0.811569	−	0.584256i	$-0.198614\pi$
$863$	−2.94345	−	5.09820i	−0.100196	−	0.173545i	−0.911765	+	0.410711i	$0.865280\pi$
$864$	−7.24593			−0.246511
$865$	−5.36283	−	9.28870i	−0.182342	−	0.315825i
$866$	−25.3821	−	43.9631i	−0.862519	−	1.49393i
$867$	11.8988	−	20.6094i	0.404105	−	0.699931i
$868$	7.41983	−	12.8515i	0.251845	−	0.436209i
$869$	3.76028			0.127559
$870$	11.8997			0.403439
$871$	16.5804	−	28.7181i	0.561806	−	0.973076i
$872$	−40.8679	+	70.7853i	−1.38396	+	2.39709i
$873$	−7.77274			−0.263067
$874$	47.7629	+	82.7278i	1.61560	+	2.79831i
$875$	−1.63827	−	2.83756i	−0.0553836	−	0.0959271i
$876$	−43.9150	−	76.0630i	−1.48375	−	2.56993i
$877$	18.9479	+	32.8187i	0.639825	+	1.10821i	0.985471	+	0.169844i	$0.0543265\pi$
$877$	18.9479	+	32.8187i	0.639825	+	1.10821i	−0.345646	+	0.938365i	$0.612340\pi$
$878$	31.1031	−	53.8722i	1.04968	−	1.81810i
$879$	53.7919			1.81435
$880$	−1.83364	+	3.17596i	−0.0618121	+	0.107062i
$881$	1.63106			0.0549517			0.0274758	−	0.999622i	$-0.491253\pi$
$881$	1.63106			0.0549517			0.0274758	+	0.999622i	$0.491253\pi$
$882$	−3.89765	−	6.75092i	−0.131241	−	0.227315i
$883$	−0.00895935	−	0.0155181i	−0.000301506	−	0.000522224i	0.865875	−	0.500261i	$-0.166763\pi$
$883$	−0.00895935	−	0.0155181i	−0.000301506	−	0.000522224i	−0.866176	+	0.499739i	$0.833429\pi$
$884$	−114.615			−3.85491
$885$	7.15932			0.240658
$886$	33.1722	+	57.4559i	1.11444	+	1.93027i
$887$	41.7725			1.40258			0.701291	−	0.712875i	$-0.252607\pi$
$887$	41.7725			1.40258			0.701291	+	0.712875i	$0.252607\pi$
$888$	5.93831			0.199277
$889$	−3.88980	−	3.79876i	−0.130460	−	0.127406i
$890$	0.917629			0.0307590
$891$	−10.6034			−0.355227
$892$	−18.1341	−	31.4092i	−0.607175	−	1.05166i
$893$	61.4310			2.05571
$894$	65.8833			2.20347
$895$	3.52216	+	6.10055i	0.117733	+	0.203919i
$896$	4.34655	+	7.52844i	0.145208	+	0.251508i
$897$	60.1918			2.00975
$898$	−17.9880	+	31.1562i	−0.600269	+	1.03970i
$899$	26.6996			0.890480
$900$	4.32477	−	7.49072i	0.144159	−	0.249691i
$901$	−2.18358	−	3.78207i	−0.0727456	−	0.125999i
$902$	−11.6879	−	20.2440i	−0.389164	−	0.674052i
$903$	0.973304	+	1.68581i	0.0323895	+	0.0561003i
$904$	5.06363	+	8.77047i	0.168414	+	0.291702i
$905$	2.68247			0.0891684
$906$	−39.4470	+	68.3242i	−1.31054	+	2.26992i
$907$	−14.5109	+	25.1336i	−0.481825	+	0.834546i	−0.999782	−	0.0208607i	$-0.993359\pi$
$907$	−14.5109	+	25.1336i	−0.481825	+	0.834546i	0.517957	+	0.855407i	$0.326693\pi$
$908$	53.9832			1.79150
$909$	−4.04755			−0.134249
$910$	2.16726	−	3.75380i	0.0718438	−	0.124437i
$911$	−10.6568	+	18.4582i	−0.353077	+	0.611547i	−0.986787	−	0.162023i	$-0.948198\pi$
$911$	−10.6568	+	18.4582i	−0.353077	+	0.611547i	0.633710	+	0.773571i	$0.281531\pi$
$912$	27.5939	+	47.7940i	0.913725	+	1.58262i
$913$	3.98791	+	6.90727i	0.131981	+	0.228597i
$914$	−27.4060			−0.906510
$915$	−6.69688	−	11.5993i	−0.221392	−	0.383462i
$916$	3.27712			0.108279
$917$	1.09005	+	1.88803i	0.0359968	+	0.0623483i
$918$	31.9347	−	55.3125i	1.05400	−	1.82558i
$919$	−28.3814	−	49.1581i	−0.936218	−	1.62158i	−0.772448	−	0.635078i	$-0.780968\pi$
$919$	−28.3814	−	49.1581i	−0.936218	−	1.62158i	−0.163770	−	0.986499i	$-0.552365\pi$
$920$	12.1872	+	21.1089i	0.401801	+	0.695940i
$921$	−21.8532			−0.720087
$922$	30.4619			1.00321
$923$	5.30913	−	9.19568i	0.174752	−	0.302680i
$924$	−1.94092	−	3.36178i	−0.0638517	−	0.110594i
$925$	1.34318	−	2.32646i	0.0441635	−	0.0764935i
$926$	7.89184	−	13.6691i	0.259342	−	0.449194i
$927$	3.14998			0.103459
$928$	2.76496	−	4.78905i	0.0907641	−	0.157208i
$929$	−37.2075			−1.22074			−0.610369	−	0.792117i	$-0.708979\pi$
$929$	−37.2075			−1.22074			−0.610369	+	0.792117i	$0.708979\pi$
$930$	−12.2462	+	21.2110i	−0.401568	+	0.695536i
$931$	20.4009	−	35.3353i	0.668611	−	1.15807i
$932$	−22.4659	+	38.9120i	−0.735894	+	1.27461i
$933$	−12.9256	+	22.3879i	−0.423167	+	0.732946i
$934$	21.6232	−	37.4524i	0.707532	−	1.22548i
$935$	−2.03499	−	3.52470i	−0.0665512	−	0.115270i
$936$	12.5307			0.409578
$937$	−10.9887	−	19.0330i	−0.358986	−	0.621782i	0.628806	−	0.777562i	$-0.283544\pi$
$937$	−10.9887	−	19.0330i	−0.358986	−	0.621782i	−0.987792	+	0.155781i	$0.950211\pi$
$938$	−3.91915	+	6.78817i	−0.127965	+	0.221641i
$939$	−60.5267			−1.97521
$940$	30.2613			0.987014
$941$	−19.9288	−	34.5178i	−0.649662	−	1.12525i	−0.983204	−	0.182512i	$-0.941577\pi$
$941$	−19.9288	−	34.5178i	−0.649662	−	1.12525i	0.333542	−	0.942735i	$-0.391756\pi$
$942$	−45.3732	+	78.5886i	−1.47834	+	2.56056i
$943$	−57.8107			−1.88258
$944$	13.2122	−	22.8841i	0.430019	−	0.744815i
$945$	0.814909	+	1.41146i	0.0265090	+	0.0459149i
$946$	−2.80007	−	4.84987i	−0.0910382	−	0.157683i
$947$	3.68775	−	6.38736i	0.119836	−	0.207561i	−0.799867	−	0.600178i	$-0.795097\pi$
$947$	3.68775	−	6.38736i	0.119836	−	0.207561i	0.919702	+	0.392616i	$0.128430\pi$
$948$	13.9376	−	24.1406i	0.452672	−	0.784051i
$949$	−28.7804	−	49.8490i	−0.934250	−	1.61817i
$950$	67.0953			2.17686
$951$	−25.9349	−	44.9205i	−0.840996	−	1.45665i
$952$	14.0330			0.454813
$953$	−25.3168			−0.820092			−0.410046	−	0.912065i	$-0.634487\pi$
$953$	−25.3168			−0.820092			−0.410046	+	0.912065i	$0.634487\pi$
$954$	0.460881	+	0.798270i	0.0149216	+	0.0258449i
$955$	0.954287			0.0308800
$956$	45.4836	+	78.7800i	1.47105	+	2.54793i
$957$	3.49211	−	6.04852i	0.112884	−	0.195521i
$958$	39.5235	−	68.4566i	1.27695	−	2.21173i
$959$	0.813365	+	1.40879i	0.0262649	+	0.0454922i
$960$	−4.01564	−	6.95529i	−0.129604	−	0.224481i
$961$	−11.9769	+	20.7446i	−0.386352	+	0.669181i
$962$	7.51331			0.242239
$963$	2.67764	−	4.63780i	0.0862856	−	0.149451i
$964$	46.0426	+	79.7482i	1.48293	+	2.56852i
$965$	9.97109			0.320981
$966$	−14.2277			−0.457768
$967$	16.4177	−	28.4363i	0.527958	−	0.914450i	−0.471511	−	0.881860i	$-0.656291\pi$
$967$	16.4177	−	28.4363i	0.527958	−	0.914450i	0.999469	−	0.0325895i	$-0.0103754\pi$
$968$	−26.4203	−	45.7613i	−0.849180	−	1.47082i
$969$	−61.2478			−1.96756
$970$	−14.8506	−	25.7219i	−0.476823	−	0.825881i
$971$	16.2185	−	28.0912i	0.520476	−	0.901490i	−0.479241	−	0.877683i	$-0.659088\pi$
$971$	16.2185	−	28.0912i	0.520476	−	0.901490i	0.999717	−	0.0238070i	$-0.00757872\pi$
$972$	−9.92944	+	17.1983i	−0.318487	+	0.551635i
$973$	−4.46099	+	7.72665i	−0.143013	+	0.247705i
$974$	−23.1024	+	40.0146i	−0.740250	+	1.28215i
$975$	21.1387	−	36.6134i	0.676982	−	1.17257i
$976$	−49.4350			−1.58238
$977$	2.70230	−	4.68052i	0.0864542	−	0.149743i	−0.819556	−	0.572999i	$-0.805780\pi$
$977$	2.70230	−	4.68052i	0.0864542	−	0.149743i	0.906010	+	0.423256i	$0.139113\pi$
$978$	51.5194			1.64741
$979$	0.269289	−	0.466422i	0.00860652	−	0.0149069i
$980$	10.0496	−	17.4064i	0.321022	−	0.556026i
$981$	3.56207	+	6.16968i	0.113728	+	0.196983i
$982$	−51.1377	+	88.5730i	−1.63187	+	2.82648i
$983$	−7.21576			−0.230147			−0.115074	−	0.993357i	$-0.536710\pi$
$983$	−7.21576			−0.230147			−0.115074	+	0.993357i	$0.536710\pi$
$984$	−89.7590			−2.86141
$985$	0.512407	+	0.887514i	0.0163266	+	0.0282786i
$986$	24.3717	+	42.2131i	0.776154	+	1.34434i
$987$	−4.57479	+	7.92377i	−0.145617	+	0.252216i
$988$	63.3105	+	109.657i	2.01418	+	3.48865i
$989$	−13.8497			−0.440396
$990$	0.429519	+	0.743948i	0.0136510	+	0.0236442i
$991$	−12.0502			−0.382787			−0.191394	−	0.981513i	$-0.561301\pi$
$991$	−12.0502			−0.382787			−0.191394	+	0.981513i	$0.561301\pi$
$992$	5.69091	+	9.85695i	0.180687	+	0.312959i
$993$	21.9597	+	38.0354i	0.696872	+	1.20702i
$994$	−1.25493	+	2.17360i	−0.0398040	+	0.0689426i
$995$	−3.81288	+	6.60410i	−0.120876	+	0.209364i
$996$	59.1253			1.87346
$997$	4.83338			0.153075			0.0765374	−	0.997067i	$-0.475614\pi$
$997$	4.83338			0.153075			0.0765374	+	0.997067i	$0.475614\pi$
$998$	−4.48332	+	7.76534i	−0.141917	+	0.245807i
$999$	−1.41254	+	2.44659i	−0.0446907	+	0.0774066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	127.2.c.a.107.1	yes	18
127.19	even	3	inner	127.2.c.a.19.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
127.2.c.a.19.1	✓	18	127.19	even	3	inner
127.2.c.a.107.1	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	127.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.47976 q^{2} +(0.930662 + 1.61195i) q^{3} +4.14922 q^{4} +0.715813 q^{5} +(-2.30782 - 3.99726i) q^{6} +(0.241228 + 0.417820i) q^{7} -5.32956 q^{8} +(-0.232264 + 0.402292i) q^{9} -1.77505 q^{10} +(-0.520908 + 0.902239i) q^{11} +(3.86152 + 6.68836i) q^{12} +(2.53071 + 4.38331i) q^{13} +(-0.598189 - 1.03609i) q^{14} +(0.666180 + 1.15386i) q^{15} +4.91761 q^{16} +(-2.72880 + 4.72641i) q^{17} +(0.575959 - 0.997589i) q^{18} +6.02930 q^{19} +2.97007 q^{20} +(-0.449004 + 0.777698i) q^{21} +(1.29173 - 2.23734i) q^{22} +(-3.19458 - 5.53317i) q^{23} +(-4.96002 - 8.59101i) q^{24} -4.48761 q^{25} +(-6.27555 - 10.8696i) q^{26} +4.71934 q^{27} +(1.00091 + 1.73363i) q^{28} +(-1.80084 + 3.11915i) q^{29} +(-1.65197 - 2.86129i) q^{30} +(-3.70654 - 6.41992i) q^{31} -1.53537 q^{32} -1.93916 q^{33} +(6.76677 - 11.7204i) q^{34} +(0.172674 + 0.299081i) q^{35} +(-0.963713 + 1.66920i) q^{36} +(-0.299309 + 0.518418i) q^{37} -14.9512 q^{38} +(-4.71047 + 8.15877i) q^{39} -3.81497 q^{40} +(4.52412 - 7.83601i) q^{41} +(1.11342 - 1.92851i) q^{42} +(1.08385 - 1.87728i) q^{43} +(-2.16136 + 3.74359i) q^{44} +(-0.166257 + 0.287966i) q^{45} +(7.92180 + 13.7210i) q^{46} +10.1887 q^{47} +(4.57663 + 7.92695i) q^{48} +(3.38362 - 5.86060i) q^{49} +11.1282 q^{50} -10.1584 q^{51} +(10.5005 + 18.1873i) q^{52} +(-0.400099 + 0.692993i) q^{53} -11.7028 q^{54} +(-0.372873 + 0.645835i) q^{55} +(-1.28564 - 2.22680i) q^{56} +(5.61124 + 9.71896i) q^{57} +(4.46566 - 7.73474i) q^{58} +(2.68670 - 4.65351i) q^{59} +(2.76413 + 4.78761i) q^{60} -10.0527 q^{61} +(9.19134 + 15.9199i) q^{62} -0.224114 q^{63} -6.02786 q^{64} +(1.81151 + 3.13763i) q^{65} +4.80865 q^{66} +(-3.27584 - 5.67393i) q^{67} +(-11.3224 + 19.6109i) q^{68} +(5.94615 - 10.2990i) q^{69} +(-0.428192 - 0.741650i) q^{70} +(-1.04894 - 1.81682i) q^{71} +(1.23786 - 2.14404i) q^{72} -11.3725 q^{73} +(0.742215 - 1.28555i) q^{74} +(-4.17645 - 7.23382i) q^{75} +25.0169 q^{76} -0.502631 q^{77} +(11.6808 - 20.2318i) q^{78} +(-1.80468 - 3.12579i) q^{79} +3.52009 q^{80} +(5.08890 + 8.81423i) q^{81} +(-11.2188 + 19.4315i) q^{82} +(3.82785 - 6.63003i) q^{83} +(-1.86302 + 3.22684i) q^{84} +(-1.95331 + 3.38323i) q^{85} +(-2.68768 + 4.65521i) q^{86} -6.70390 q^{87} +(2.77621 - 4.80854i) q^{88} -0.516961 q^{89} +(0.412279 - 0.714088i) q^{90} +(-1.22096 + 2.11476i) q^{91} +(-13.2550 - 22.9584i) q^{92} +(6.89908 - 11.9495i) q^{93} -25.2657 q^{94} +4.31585 q^{95} +(-1.42891 - 2.47495i) q^{96} +(8.36629 + 14.4908i) q^{97} +(-8.39057 + 14.5329i) q^{98} +(-0.241976 - 0.419115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + q^{3} + 10 q^{4} - 8 q^{5} + 5 q^{7} - 6 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 8 q^{14} + 3 q^{15} - 6 q^{16} - 6 q^{17} + 16 q^{19} - 32 q^{20} + 3 q^{21} + 6 q^{22} + 13 q^{23} - 6 q^{24}+ \cdots + 17 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 + q^3 + 10 * q^4 - 8 * q^5 + 5 * q^7 - 6 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 8 * q^14 + 3 * q^15 - 6 * q^16 - 6 * q^17 + 16 * q^19 - 32 * q^20 + 3 * q^21 + 6 * q^22 + 13 * q^23 - 6 * q^24 + 6 * q^25 - 14 * q^26 + 10 * q^27 - 2 * q^28 - 5 * q^29 - 23 * q^30 - 11 * q^31 - 4 * q^32 - 16 * q^33 - 2 * q^34 - 16 * q^35 + 15 * q^36 - 4 * q^37 + 4 * q^38 - 7 * q^39 - 36 * q^40 - 11 * q^41 + 9 * q^43 - 15 * q^44 + 14 * q^45 + 15 * q^46 - 10 * q^47 + 20 * q^48 + 12 * q^49 + 32 * q^50 + 4 * q^51 + 26 * q^52 - 2 * q^53 + 2 * q^54 - q^55 + 12 * q^56 + 28 * q^57 + 10 * q^58 + 6 * q^60 + 28 * q^61 + 8 * q^62 - 12 * q^63 - 50 * q^64 + 15 * q^65 + 36 * q^66 - 12 * q^67 - 41 * q^68 + 33 * q^69 + 21 * q^70 - 4 * q^71 + 31 * q^72 + 52 * q^73 + 13 * q^74 - 11 * q^75 + 26 * q^76 - 40 * q^77 + q^78 - 35 * q^79 + 26 * q^80 + 27 * q^81 - 26 * q^82 + 13 * q^83 + 22 * q^84 + 15 * q^85 - 5 * q^86 - 64 * q^87 - q^88 + 8 * q^89 - 30 * q^90 - 16 * q^91 + 11 * q^92 - 6 * q^93 - 62 * q^94 - 38 * q^95 - 31 * q^96 + 28 * q^97 + 32 * q^98 + 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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