LMFDB - Embedded newform 153.3.t.a.7.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(7,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([32, 33])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.t (of order $48$, degree $16$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			7.18
Character	$\chi$	$=$	153.7
Dual form			153.3.t.a.22.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0485999 - 0.0633367i) q^{2} +(-0.879538 + 2.86817i) q^{3} +(1.03363 - 3.85755i) q^{4} +(3.26851 - 2.86641i) q^{5} +(0.224406 - 0.0836860i) q^{6} +(-8.31214 - 7.28955i) q^{7} +(-0.589587 + 0.244215i) q^{8} +(-7.45283 - 5.04533i) q^{9} +(-0.340399 - 0.0677095i) q^{10} +(-0.315968 - 4.82074i) q^{11} +(10.1550 + 6.35748i) q^{12} +(12.6754 + 3.39635i) q^{13} +(-0.0577264 + 0.880735i) q^{14} +(5.34658 + 11.8958i) q^{15} +(-13.7902 - 7.96178i) q^{16} +(9.15087 - 14.3270i) q^{17} +(0.0426524 + 0.717240i) q^{18} +(-1.26468 + 3.05321i) q^{19} +(-7.67889 - 15.5712i) q^{20} +(28.2185 - 17.4292i) q^{21} +(-0.289974 + 0.254300i) q^{22} +(14.5130 - 29.4295i) q^{23} +(-0.181886 - 1.90583i) q^{24} +(-0.796275 + 6.04831i) q^{25} +(-0.400908 - 0.967877i) q^{26} +(21.0259 - 16.9384i) q^{27} +(-36.7114 + 24.5298i) q^{28} +(-5.23502 + 15.4219i) q^{29} +(0.493596 - 0.916769i) q^{30} +(-3.05911 + 46.6731i) q^{31} +(0.499119 + 3.79119i) q^{32} +(14.1046 + 3.33378i) q^{33} +(-1.35215 + 0.116703i) q^{34} -48.0632 q^{35} +(-27.1660 + 23.5346i) q^{36} +(10.9336 - 16.3633i) q^{37} +(0.254844 - 0.0682851i) q^{38} +(-20.8898 + 33.3679i) q^{39} +(-1.22705 + 2.48822i) q^{40} +(38.5388 - 13.0821i) q^{41} +(-2.47533 - 0.940209i) q^{42} +(-47.3643 - 6.23562i) q^{43} +(-18.9228 - 3.76399i) q^{44} +(-38.8217 + 4.87212i) q^{45} +(-2.56930 + 0.511065i) q^{46} +(8.09848 + 30.2239i) q^{47} +(34.9648 - 32.5500i) q^{48} +(9.55832 + 72.6027i) q^{49} +(0.421779 - 0.243514i) q^{50} +(33.0436 + 38.8474i) q^{51} +(26.2032 - 45.3852i) q^{52} +(-12.4306 + 30.0102i) q^{53} +(-2.09468 - 0.508506i) q^{54} +(-14.8510 - 14.8510i) q^{55} +(6.68094 + 2.26788i) q^{56} +(-7.64479 - 6.31273i) q^{57} +(1.23119 - 0.417933i) q^{58} +(-21.4012 - 16.4217i) q^{59} +(51.4149 - 8.32888i) q^{60} +(35.1729 - 40.1070i) q^{61} +(3.10479 - 2.07455i) q^{62} +(25.1707 + 96.2652i) q^{63} +(-44.8228 + 44.8228i) q^{64} +(51.1649 - 25.2317i) q^{65} +(-0.474334 - 1.05536i) q^{66} +(-41.8749 + 24.1765i) q^{67} +(-45.8083 - 50.1086i) q^{68} +(71.6441 + 67.5102i) q^{69} +(2.33587 + 3.04416i) q^{70} +(76.1317 - 113.939i) q^{71} +(5.62623 + 1.15457i) q^{72} +(-4.40542 - 22.1475i) q^{73} +(-1.56777 + 0.102757i) q^{74} +(-16.6472 - 7.60357i) q^{75} +(10.4707 + 8.03444i) q^{76} +(-32.5147 + 42.3740i) q^{77} +(3.12865 - 0.298588i) q^{78} +(8.34938 + 127.387i) q^{79} +(-67.8952 + 13.5052i) q^{80} +(30.0892 + 75.2040i) q^{81} +(-2.70156 - 1.80513i) q^{82} +(-4.10960 + 3.15341i) q^{83} +(-38.0666 - 126.870i) q^{84} +(-11.1572 - 73.0580i) q^{85} +(1.90696 + 3.30295i) q^{86} +(-39.6282 - 28.5791i) q^{87} +(1.36359 + 2.76508i) q^{88} +(79.3959 + 79.3959i) q^{89} +(2.19531 + 2.22205i) q^{90} +(-80.6014 - 120.629i) q^{91} +(-98.5246 - 86.4037i) q^{92} +(-131.176 - 49.8248i) q^{93} +(1.52070 - 1.98181i) q^{94} +(4.61812 + 13.6046i) q^{95} +(-11.3128 - 1.90293i) q^{96} +(42.4416 - 125.029i) q^{97} +(4.13388 - 4.13388i) q^{98} +(-21.9674 + 37.5223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) $ 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0485999	−	0.0633367i	−0.0243000	−	0.0316683i	0.781045	−	0.624474i	$-0.214687\pi$
$2$	−0.0485999	−	0.0633367i	−0.0243000	−	0.0316683i	−0.805345	+	0.592806i	$0.798020\pi$
$3$	−0.879538	+	2.86817i	−0.293179	+	0.956057i
$3$	−0.879538	+	2.86817i	−0.293179	+	0.956057i
$4$	1.03363	−	3.85755i	0.258407	−	0.964387i
$5$	3.26851	−	2.86641i	0.653703	−	0.573282i	−0.266928	−	0.963717i	$-0.586009\pi$
$5$	3.26851	−	2.86641i	0.653703	−	0.573282i	0.920631	+	0.390434i	$0.127675\pi$
$6$	0.224406	−	0.0836860i	0.0374010	−	0.0139477i
$7$	−8.31214	−	7.28955i	−1.18745	−	1.04136i	−0.998233	−	0.0594286i	$-0.981072\pi$
$7$	−8.31214	−	7.28955i	−1.18745	−	1.04136i	−0.189216	−	0.981936i	$-0.560595\pi$
$8$	−0.589587	+	0.244215i	−0.0736984	+	0.0305269i
$9$	−7.45283	−	5.04533i	−0.828092	−	0.560592i
$10$	−0.340399	−	0.0677095i	−0.0340399	−	0.00677095i
$11$	−0.315968	−	4.82074i	−0.0287244	−	0.438250i	−0.987865	−	0.155318i	$-0.950360\pi$
$11$	−0.315968	−	4.82074i	−0.0287244	−	0.438250i	0.959140	−	0.282931i	$-0.0913069\pi$
$12$	10.1550	+	6.35748i	0.846250	+	0.529790i
$13$	12.6754	+	3.39635i	0.975027	+	0.261258i	0.710949	−	0.703244i	$-0.248266\pi$
$13$	12.6754	+	3.39635i	0.975027	+	0.261258i	0.264078	+	0.964501i	$0.414932\pi$
$14$	−0.0577264	+	0.880735i	−0.00412332	+	0.0629096i
$15$	5.34658	+	11.8958i	0.356438	+	0.793052i
$16$	−13.7902	−	7.96178i	−0.861888	−	0.497611i
$17$	9.15087	−	14.3270i	0.538287	−	0.842762i
$17$	9.15087	−	14.3270i	0.538287	−	0.842762i
$18$	0.0426524	+	0.717240i	0.00236958	+	0.0398467i
$19$	−1.26468	+	3.05321i	−0.0665621	+	0.160695i	−0.953660	−	0.300886i	$-0.902718\pi$
$19$	−1.26468	+	3.05321i	−0.0665621	+	0.160695i	0.887098	+	0.461581i	$0.152718\pi$
$20$	−7.67889	−	15.5712i	−0.383944	−	0.778562i
$21$	28.2185	−	17.4292i	1.34374	−	0.829962i
$22$	−0.289974	+	0.254300i	−0.0131806	+	0.0115591i
$23$	14.5130	−	29.4295i	0.631001	−	1.27954i	−0.313048	−	0.949737i	$-0.601350\pi$
$23$	14.5130	−	29.4295i	0.631001	−	1.27954i	0.944049	−	0.329805i	$-0.106983\pi$
$24$	−0.181886	−	1.90583i	−0.00757860	−	0.0794097i
$25$	−0.796275	+	6.04831i	−0.0318510	+	0.241932i
$26$	−0.400908	−	0.967877i	−0.0154195	−	0.0372260i
$27$	21.0259	−	16.9384i	0.778738	−	0.627349i
$28$	−36.7114	+	24.5298i	−1.31112	+	0.876064i
$29$	−5.23502	+	15.4219i	−0.180518	+	0.531789i	−0.999092	−	0.0426129i	$-0.986432\pi$
$29$	−5.23502	+	15.4219i	−0.180518	+	0.531789i	0.818574	+	0.574401i	$0.194765\pi$
$30$	0.493596	−	0.916769i	0.0164532	−	0.0305590i
$31$	−3.05911	+	46.6731i	−0.0986811	+	1.50558i	0.605662	+	0.795722i	$0.292908\pi$
$31$	−3.05911	+	46.6731i	−0.0986811	+	1.50558i	−0.704343	+	0.709860i	$0.748758\pi$
$32$	0.499119	+	3.79119i	0.0155975	+	0.118475i
$33$	14.1046	+	3.33378i	0.427413	+	0.101024i
$34$	−1.35215	+	0.116703i	−0.0397692	+	0.00343245i
$35$	−48.0632			−1.37323
$36$	−27.1660	+	23.5346i	−0.754612	+	0.653740i
$37$	10.9336	−	16.3633i	0.295502	−	0.442250i	−0.653776	−	0.756688i	$-0.726816\pi$
$37$	10.9336	−	16.3633i	0.295502	−	0.442250i	0.949278	+	0.314438i	$0.101816\pi$
$38$	0.254844	−	0.0682851i	0.00670641	−	0.00179698i
$39$	−20.8898	+	33.3679i	−0.535635	+	0.855587i
$40$	−1.22705	+	2.48822i	−0.0306763	+	0.0622055i
$41$	38.5388	−	13.0821i	0.939970	−	0.319077i	0.190931	−	0.981603i	$-0.438849\pi$
$41$	38.5388	−	13.0821i	0.939970	−	0.319077i	0.749038	+	0.662527i	$0.230516\pi$
$42$	−2.47533	−	0.940209i	−0.0589364	−	0.0223859i
$43$	−47.3643	−	6.23562i	−1.10149	−	0.145014i	−0.442212	−	0.896910i	$-0.645806\pi$
$43$	−47.3643	−	6.23562i	−1.10149	−	0.145014i	−0.659282	+	0.751896i	$0.729140\pi$
$44$	−18.9228	−	3.76399i	−0.430065	−	0.0855452i
$45$	−38.8217	+	4.87212i	−0.862704	+	0.108269i
$46$	−2.56930	+	0.511065i	−0.0558543	+	0.0111101i
$47$	8.09848	+	30.2239i	0.172308	+	0.643062i	0.996995	+	0.0774722i	$0.0246849\pi$
$47$	8.09848	+	30.2239i	0.172308	+	0.643062i	−0.824686	+	0.565590i	$0.808648\pi$
$48$	34.9648	−	32.5500i	0.728433	−	0.678125i
$49$	9.55832	+	72.6027i	0.195068	+	1.48169i
$50$	0.421779	−	0.243514i	0.00843558	−	0.00487028i
$51$	33.0436	+	38.8474i	0.647914	+	0.761713i
$52$	26.2032	−	45.3852i	0.503907	−	0.872792i
$53$	−12.4306	+	30.0102i	−0.234540	+	0.566231i	−0.996701	−	0.0811569i	$-0.974139\pi$
$53$	−12.4306	+	30.0102i	−0.234540	+	0.566231i	0.762161	+	0.647388i	$0.224139\pi$
$54$	−2.09468	−	0.508506i	−0.0387904	−	0.00941677i
$55$	−14.8510	−	14.8510i	−0.270018	−	0.270018i
$56$	6.68094	+	2.26788i	0.119303	+	0.0404978i
$57$	−7.64479	−	6.31273i	−0.134119	−	0.110750i
$58$	1.23119	−	0.417933i	0.0212274	−	0.00720575i
$59$	−21.4012	−	16.4217i	−0.362732	−	0.278334i	0.411275	−	0.911511i	$-0.365084\pi$
$59$	−21.4012	−	16.4217i	−0.362732	−	0.278334i	−0.774007	+	0.633177i	$0.781750\pi$
$60$	51.4149	−	8.32888i	0.856915	−	0.138815i
$61$	35.1729	−	40.1070i	0.576604	−	0.657491i	−0.387856	−	0.921720i	$-0.626784\pi$
$61$	35.1729	−	40.1070i	0.576604	−	0.657491i	0.964460	+	0.264229i	$0.0851175\pi$
$62$	3.10479	−	2.07455i	0.0500772	−	0.0334605i
$63$	25.1707	+	96.2652i	0.399535	+	1.52802i
$64$	−44.8228	+	44.8228i	−0.700356	+	0.700356i
$65$	51.1649	−	25.2317i	0.787152	−	0.388181i
$66$	−0.474334	−	1.05536i	−0.00718688	−	0.0159903i
$67$	−41.8749	+	24.1765i	−0.624998	+	0.360843i	−0.778812	−	0.627257i	$-0.784178\pi$
$67$	−41.8749	+	24.1765i	−0.624998	+	0.360843i	0.153814	+	0.988100i	$0.450844\pi$
$68$	−45.8083	−	50.1086i	−0.673652	−	0.736892i
$69$	71.6441	+	67.5102i	1.03832	+	0.978408i
$70$	2.33587	+	3.04416i	0.0333695	+	0.0434880i
$71$	76.1317	−	113.939i	1.07228	−	1.60478i	0.318158	−	0.948038i	$-0.396936\pi$
$71$	76.1317	−	113.939i	1.07228	−	1.60478i	0.754119	−	0.656738i	$-0.228064\pi$
$72$	5.62623	+	1.15457i	0.0781421	+	0.0160357i
$73$	−4.40542	−	22.1475i	−0.0603482	−	0.303391i	0.938809	−	0.344438i	$-0.111931\pi$
$73$	−4.40542	−	22.1475i	−0.0603482	−	0.303391i	−0.999157	+	0.0410473i	$0.986931\pi$
$74$	−1.56777	+	0.102757i	−0.0211860	+	0.00138861i
$75$	−16.6472	−	7.60357i	−0.221963	−	0.101381i
$76$	10.4707	+	8.03444i	0.137772	+	0.105716i
$77$	−32.5147	+	42.3740i	−0.422269	+	0.550311i
$78$	3.12865	−	0.298588i	0.0401109	−	0.00382805i
$79$	8.34938	+	127.387i	0.105688	+	1.61249i	0.640798	+	0.767710i	$0.278604\pi$
$79$	8.34938	+	127.387i	0.105688	+	1.61249i	−0.535110	+	0.844783i	$0.679730\pi$
$80$	−67.8952	+	13.5052i	−0.848690	+	0.168815i
$81$	30.0892	+	75.2040i	0.371472	+	0.928444i
$82$	−2.70156	−	1.80513i	−0.0329459	−	0.0220137i
$83$	−4.10960	+	3.15341i	−0.0495132	+	0.0379928i	−0.633222	−	0.773971i	$-0.718268\pi$
$83$	−4.10960	+	3.15341i	−0.0495132	+	0.0379928i	0.583708	+	0.811963i	$0.301601\pi$
$84$	−38.0666	−	126.870i	−0.453174	−	1.51035i
$85$	−11.1572	−	73.0580i	−0.131261	−	0.859506i
$86$	1.90696	+	3.30295i	0.0221739	+	0.0384063i
$87$	−39.6282	−	28.5791i	−0.455496	−	0.328495i
$88$	1.36359	+	2.76508i	0.0154953	+	0.0314214i
$89$	79.3959	+	79.3959i	0.892088	+	0.892088i	0.994719	−	0.102631i	$-0.0327261\pi$
$89$	79.3959	+	79.3959i	0.892088	+	0.892088i	−0.102631	+	0.994719i	$0.532726\pi$
$90$	2.19531	+	2.22205i	0.0243924	+	0.0246895i
$91$	−80.6014	−	120.629i	−0.885730	−	1.32559i
$92$	−98.5246	−	86.4037i	−1.07092	−	0.939171i
$93$	−131.176	−	49.8248i	−1.41049	−	0.535750i
$94$	1.52070	−	1.98181i	0.0161776	−	0.0210831i
$95$	4.61812	+	13.6046i	0.0486118	+	0.143206i
$96$	−11.3128	−	1.90293i	−0.117841	−	0.0198222i
$97$	42.4416	−	125.029i	0.437542	−	1.28896i	−0.475004	−	0.879984i	$-0.657553\pi$
$97$	42.4416	−	125.029i	0.437542	−	1.28896i	0.912546	−	0.408974i	$-0.134113\pi$
$98$	4.13388	−	4.13388i	0.0421824	−	0.0421824i
$99$	−21.9674	+	37.5223i	−0.221893	+	0.379014i
$100$	22.5086	+	9.32337i	0.225086	+	0.0932337i
$101$	135.442	+	78.1974i	1.34101	+	0.774232i	0.986956	−	0.160993i	$-0.0514697\pi$
$101$	135.442	+	78.1974i	1.34101	+	0.774232i	0.354054	+	0.935225i	$0.384803\pi$
$102$	0.854545	−	3.98085i	0.00837789	−	0.0390280i
$103$	−21.2957	−	36.8853i	−0.206755	−	0.358109i	0.743936	−	0.668251i	$-0.232957\pi$
$103$	−21.2957	−	36.8853i	−0.206755	−	0.358109i	−0.950690	+	0.310142i	$0.899623\pi$
$104$	−8.30266	+	1.09307i	−0.0798333	+	0.0105103i
$105$	42.2734	−	137.854i	0.402604	−	1.31289i
$106$	2.50488	−	0.671180i	0.0236309	−	0.00633188i
$107$	−25.1350	−	126.362i	−0.234906	−	1.18095i	−0.900573	−	0.434705i	$-0.856853\pi$
$107$	−25.1350	−	126.362i	−0.234906	−	1.18095i	0.665666	−	0.746249i	$-0.268147\pi$
$108$	−43.6078	−	98.6165i	−0.403776	−	0.913116i
$109$	1.39726	−	7.02451i	0.0128189	−	0.0644451i	−0.973846	−	0.227208i	$-0.927040\pi$
$109$	1.39726	−	7.02451i	0.0128189	−	0.0644451i	0.986665	+	0.162762i	$0.0520404\pi$
$110$	−0.218855	+	1.66237i	−0.00198959	+	0.0151124i
$111$	37.3161	+	45.7515i	0.336181	+	0.412176i
$112$	56.5883	+	166.704i	0.505253	+	1.48843i
$113$	165.334	+	81.5339i	1.46314	+	0.721539i	0.987429	−	0.158064i	$-0.0505252\pi$
$113$	165.334	+	81.5339i	1.46314	+	0.721539i	0.475708	+	0.879603i	$0.342192\pi$
$114$	−0.0282910	+	0.790995i	−0.000248167	+	0.00693855i
$115$	−36.9210	−	137.791i	−0.321052	−	1.19818i
$116$	54.0795	+	36.1348i	0.466203	+	0.311507i
$117$	−77.3315	−	89.2638i	−0.660953	−	0.762938i
$118$			2.15357i			0.0182506i
$119$	−180.500	+	52.3819i	−1.51681	+	0.440184i
$120$	−6.05740	−	5.70788i	−0.0504783	−	0.0475657i
$121$	96.8251	−	12.7473i	0.800207	−	0.105349i
$122$	−4.24964	−	0.278536i	−0.0348331	−	0.00228308i
$123$	3.62556	+	122.042i	0.0294761	+	0.992212i
$124$	176.882	+	60.0432i	1.42646	+	0.484219i
$125$	75.1158	+	112.419i	0.600927	+	0.899350i
$126$	4.87383	−	6.27272i	0.0386812	−	0.0497835i
$127$	11.0182	−	4.56390i	0.0867578	−	0.0359363i	−0.338882	−	0.940829i	$-0.610049\pi$
$127$	11.0182	−	4.56390i	0.0867578	−	0.0359363i	0.425640	+	0.904892i	$0.360049\pi$
$128$	20.1821	+	2.65702i	0.157672	+	0.0207580i
$129$	59.5435	−	130.364i	0.461577	−	1.01058i
$130$	−4.08471	−	2.01435i	−0.0314208	−	0.0154950i
$131$	−17.3508	−	19.7848i	−0.132449	−	0.151029i	0.681813	−	0.731526i	$-0.261192\pi$
$131$	−17.3508	−	19.7848i	−0.132449	−	0.151029i	−0.814262	+	0.580497i	$0.802858\pi$
$132$	27.4391	−	50.9634i	0.207872	−	0.386086i
$133$	32.7687	−	16.1597i	0.246381	−	0.121502i
$134$	3.56637	+	1.47724i	0.0266147	+	0.0110242i
$135$	20.1711	−	115.632i	0.149415	−	0.856537i
$136$	−1.89638	+	10.6818i	−0.0139440	+	0.0785424i
$137$	14.7864	−	25.6109i	0.107930	−	0.186941i	−0.807001	−	0.590550i	$-0.798911\pi$
$137$	14.7864	−	25.6109i	0.107930	−	0.186941i	0.914932	+	0.403609i	$0.132244\pi$
$138$	0.793972	−	7.81869i	0.00575342	−	0.0566572i
$139$	152.671	+	10.0066i	1.09835	+	0.0719897i	0.603783	−	0.797149i	$-0.293659\pi$
$139$	152.671	+	10.0066i	1.09835	+	0.0719897i	0.494568	+	0.869139i	$0.335326\pi$
$140$	−49.6794	+	185.406i	−0.354853	+	1.32433i
$141$	−93.8104	−	3.35526i	−0.665322	−	0.0237962i
$142$	−10.9165	+	0.715506i	−0.0768769	+	0.00503878i
$143$	12.3679	−	62.1778i	0.0864890	−	0.434810i
$144$	62.6062	+	128.914i	0.434765	+	0.895236i
$145$	27.0947	+	65.4123i	0.186860	+	0.451119i
$146$	−1.18865	+	1.35539i	−0.00814142	+	0.00928351i
$147$	−216.644	−	36.4419i	−1.47377	−	0.247904i
$148$	−51.8208	−	59.0903i	−0.350140	−	0.399259i
$149$	−262.204	−	70.2573i	−1.75976	−	0.471526i	−0.773093	−	0.634292i	$-0.781292\pi$
$149$	−262.204	−	70.2573i	−1.75976	−	0.471526i	−0.986665	+	0.162766i	$0.947958\pi$
$150$	0.327470	+	1.42391i	0.00218313	+	0.00949277i
$151$	56.4674	−	43.3290i	0.373956	−	0.286947i	−0.404635	−	0.914478i	$-0.632601\pi$
$151$	56.4674	−	43.3290i	0.373956	−	0.286947i	0.778591	+	0.627532i	$0.215935\pi$
$152$		−	2.10899i		−	0.0138749i
$153$	−140.484	+	60.6071i	−0.918197	+	0.396125i
$154$	4.26404			0.0276886
$155$	123.785	+	161.320i	0.798615	+	1.04078i
$156$	107.126	+	115.073i	0.686705	+	0.737649i
$157$	38.1210	−	142.270i	0.242809	−	0.906176i	−0.731663	−	0.681667i	$-0.761256\pi$
$157$	38.1210	−	142.270i	0.242809	−	0.906176i	0.974472	−	0.224509i	$-0.0720778\pi$
$158$	7.66248	−	6.71982i	0.0484967	−	0.0425305i
$159$	−75.1413	−	62.0484i	−0.472587	−	0.390241i
$160$	12.4985	+	10.9609i	0.0781155	+	0.0685054i
$161$	−335.162	+	138.829i	−2.08175	+	0.862289i
$162$	3.30083	−	5.56066i	0.0203755	−	0.0343251i
$163$	97.6358	+	19.4210i	0.598993	+	0.119147i	0.485268	−	0.874365i	$-0.338722\pi$
$163$	97.6358	+	19.4210i	0.598993	+	0.119147i	0.113724	+	0.993512i	$0.463722\pi$
$164$	−10.6303	−	162.187i	−0.0648189	−	0.988946i
$165$	55.6572	−	29.5332i	0.337316	−	0.178989i
$166$	0.399453	+	0.107033i	0.00240634	+	0.000644777i
$167$	−7.73019	+	117.940i	−0.0462886	+	0.706227i	0.910147	+	0.414285i	$0.135968\pi$
$167$	−7.73019	+	117.940i	−0.0462886	+	0.706227i	−0.956436	+	0.291942i	$0.905698\pi$
$168$	−12.3808	+	17.1674i	−0.0736952	+	0.102187i
$169$	2.77105	+	1.59986i	0.0163967	+	0.00946666i
$170$	−4.08501	+	4.25727i	−0.0240295	+	0.0250428i
$171$	24.8299	−	16.3743i	0.145204	−	0.0957561i
$172$	−73.0112	+	176.265i	−0.424484	+	1.02479i
$173$	−63.8610	−	129.497i	−0.369139	−	0.748539i	0.630479	−	0.776207i	$-0.282859\pi$
$173$	−63.8610	−	129.497i	−0.369139	−	0.748539i	−0.999617	+	0.0276677i	$0.991192\pi$
$174$	0.115825	+	3.89886i	0.000665661	+	0.0224072i
$175$	50.7082	−	44.4699i	0.289761	−	0.254114i
$176$	−34.0244	+	68.9947i	−0.193321	+	0.392016i
$177$	65.9234	−	46.9388i	0.372449	−	0.265191i
$178$	1.17004	−	8.88731i	0.00657324	−	0.0499287i
$179$	117.173	+	282.880i	0.654597	+	1.58034i	0.806033	+	0.591870i	$0.201610\pi$
$179$	117.173	+	282.880i	0.654597	+	1.58034i	−0.151436	+	0.988467i	$0.548390\pi$
$180$	−21.3327	+	154.792i	−0.118515	+	0.859957i
$181$	−276.587	+	184.809i	−1.52810	+	1.02105i	−0.544905	+	0.838498i	$0.683434\pi$
$181$	−276.587	+	184.809i	−1.52810	+	1.02105i	−0.983197	+	0.182548i	$0.941566\pi$
$182$	−3.72299	+	10.9676i	−0.0204560	+	0.0602614i
$183$	84.0978	+	136.157i	0.459551	+	0.744029i
$184$	−1.36957	+	20.8955i	−0.00744329	+	0.113563i
$185$	−11.1672	−	84.8236i	−0.0603635	−	0.458506i
$186$	3.21940	+	10.7297i	0.0173086	+	0.0576867i
$187$	−71.9580	−	39.5872i	−0.384802	−	0.211696i
$188$	124.961			0.664686
$189$	−298.244	−	12.4749i	−1.57801	−	0.0660050i
$190$	0.637227	−	0.953677i	0.00335382	−	0.00501935i
$191$	−35.9148	+	9.62335i	−0.188036	+	0.0503840i	−0.351608	−	0.936147i	$-0.614365\pi$
$191$	−35.9148	+	9.62335i	−0.188036	+	0.0503840i	0.163572	+	0.986531i	$0.447698\pi$
$192$	−89.1361	−	167.983i	−0.464251	−	0.874910i
$193$	−50.9867	+	103.391i	−0.264180	+	0.535704i	−0.988032	−	0.154252i	$-0.950703\pi$
$193$	−50.9867	+	103.391i	−0.264180	+	0.535704i	0.723852	+	0.689956i	$0.242370\pi$
$194$	−9.98157	+	3.38829i	−0.0514514	+	0.0174654i
$195$	27.3675	+	168.942i	0.140346	+	0.866369i
$196$	289.948	+	38.1724i	1.47933	+	0.194757i
$197$	156.433	+	31.1164i	0.794075	+	0.157951i	0.575428	−	0.817853i	$-0.304836\pi$
$197$	156.433	+	31.1164i	0.794075	+	0.157951i	0.218647	+	0.975804i	$0.429836\pi$
$198$	3.44416	−	0.432241i	0.0173947	−	0.00218304i
$199$	−260.367	+	51.7902i	−1.30838	+	0.260252i	−0.799541	−	0.600611i	$-0.794924\pi$
$199$	−260.367	+	51.7902i	−1.30838	+	0.260252i	−0.508836	+	0.860863i	$0.669924\pi$
$200$	−1.00761	−	3.76047i	−0.00503807	−	0.0188023i
$201$	−32.5117	−	141.368i	−0.161750	−	0.703325i
$202$	−1.62970	−	12.3788i	−0.00806784	−	0.0612814i
$203$	155.933	−	90.0278i	0.768141	−	0.443487i
$204$	184.010	−	87.3137i	0.902011	−	0.428008i
$205$	88.4657	−	153.227i	0.431540	−	0.747449i
$206$	−1.30122	+	3.14142i	−0.00631660	+	0.0152496i
$207$	−256.644	+	146.110i	−1.23983	+	0.705845i
$208$	−147.755	−	147.755i	−0.710359	−	0.710359i
$209$	15.1183	+	5.13198i	0.0723365	+	0.0245549i
$210$	−10.7857	+	4.02222i	−0.0513603	+	0.0191534i
$211$	−3.69910	+	1.25568i	−0.0175313	+	0.00595107i	−0.330191	−	0.943914i	$-0.607113\pi$
$211$	−3.69910	+	1.25568i	−0.0175313	+	0.00595107i	0.312660	+	0.949865i	$0.398780\pi$
$212$	102.917	+	78.9712i	0.485459	+	0.372505i
$213$	259.836	+	318.572i	1.21989	+	1.49565i
$214$	−6.78180	+	7.73316i	−0.0316906	+	0.0361363i
$215$	−172.685	+	115.384i	−0.803184	+	0.536671i
$216$	−8.25999	+	15.1215i	−0.0382407	+	0.0700071i
$217$	365.653	−	365.653i	1.68504	−	1.68504i
$218$	−0.512816	+	0.252893i	−0.00235237	+	0.00116006i
$219$	67.3977	+	6.84409i	0.307752	+	0.0312516i
$220$	−72.6387	+	41.9380i	−0.330176	+	0.190627i
$221$	164.650	−	150.520i	0.745022	−	0.681084i
$222$	1.08418	−	4.58700i	0.00488372	−	0.0206622i
$223$	12.0120	+	15.6544i	0.0538655	+	0.0701989i	0.819509	−	0.573066i	$-0.194246\pi$
$223$	12.0120	+	15.6544i	0.0538655	+	0.0701989i	−0.765644	+	0.643265i	$0.777579\pi$
$224$	23.4873	−	35.1512i	0.104854	−	0.156925i
$225$	36.4502	−	41.0595i	0.162001	−	0.182487i
$226$	−2.87116	−	14.4343i	−0.0127042	−	0.0638685i
$227$	−64.2051	+	4.20823i	−0.282842	+	0.0185384i	−0.206164	−	0.978517i	$-0.566098\pi$
$227$	−64.2051	+	4.20823i	−0.282842	+	0.0185384i	−0.0766780	+	0.997056i	$0.524431\pi$
$228$	−32.2535	+	22.9651i	−0.141463	+	0.100724i
$229$	42.1985	+	32.3800i	0.184273	+	0.141397i	0.696779	−	0.717286i	$-0.254616\pi$
$229$	42.1985	+	32.3800i	0.184273	+	0.141397i	−0.512506	+	0.858684i	$0.671283\pi$
$230$	−6.93286	+	9.03508i	−0.0301429	+	0.0392830i
$231$	−92.9379	−	130.527i	−0.402329	−	0.565053i
$232$	−0.679751	−	10.3710i	−0.00292996	−	0.0447026i
$233$	304.861	−	60.6406i	1.30842	−	0.260260i	0.508858	−	0.860850i	$-0.330068\pi$
$233$	304.861	−	60.6406i	1.30842	−	0.260260i	0.799557	+	0.600590i	$0.205068\pi$
$234$	−1.89537	+	9.23613i	−0.00809985	+	0.0394707i
$235$	113.104	+	75.5738i	0.481294	+	0.321591i
$236$	−85.4683	+	65.5822i	−0.362154	+	0.277890i
$237$	−372.711	−	88.0941i	−1.57262	−	0.371705i
$238$	12.0900	+	8.88654i	0.0507983	+	0.0373384i
$239$	89.1299	+	154.377i	0.372928	+	0.645931i	0.990015	−	0.140965i	$-0.0450204\pi$
$239$	89.1299	+	154.377i	0.372928	+	0.645931i	−0.617086	+	0.786896i	$0.711687\pi$
$240$	20.9812	−	206.614i	0.0874216	−	0.860890i
$241$	−49.0844	−	99.5333i	−0.203670	−	0.413001i	0.770941	−	0.636906i	$-0.219786\pi$
$241$	−49.0844	−	99.5333i	−0.203670	−	0.413001i	−0.974611	+	0.223905i	$0.928119\pi$
$242$	−5.51306	−	5.51306i	−0.0227813	−	0.0227813i
$243$	−242.163	+	20.1564i	−0.996554	+	0.0829482i
$244$	−118.359	−	177.137i	−0.485077	−	0.725969i
$245$	239.351	+	209.905i	0.976941	+	0.856754i
$246$	7.55354	−	6.16087i	0.0307054	−	0.0250442i
$247$	−26.4000	+	34.4052i	−0.106883	+	0.139292i
$248$	−9.59464	−	28.2649i	−0.0386881	−	0.113971i
$249$	−5.42996	−	14.5606i	−0.0218071	−	0.0584762i
$250$	3.46961	−	10.2211i	0.0138784	−	0.0408845i
$251$	130.833	−	130.833i	0.521248	−	0.521248i	−0.396700	−	0.917948i	$-0.629845\pi$
$251$	130.833	−	130.833i	0.521248	−	0.521248i	0.917948	+	0.396700i	$0.129845\pi$
$252$	397.365	+	2.40507i	1.57684	+	0.00954392i
$253$	−146.458	−	60.6648i	−0.578884	−	0.239782i
$254$	−0.824548	−	0.476053i	−0.00324625	−	0.00187423i
$255$	219.356	+	32.2566i	0.860220	+	0.126496i
$256$	125.965	+	218.178i	0.492052	+	0.852259i
$257$	−55.2024	+	7.26753i	−0.214795	+	0.0282783i	−0.237156	−	0.971472i	$-0.576215\pi$
$257$	−55.2024	+	7.26753i	−0.214795	+	0.0282783i	0.0223605	+	0.999750i	$0.492882\pi$
$258$	−11.1507	+	2.56441i	−0.0432196	+	0.00993959i
$259$	−210.162	+	56.3128i	−0.811437	+	0.217424i
$260$	−44.4472	−	223.451i	−0.170951	−	0.859428i
$261$	116.824	−	88.5241i	0.447602	−	0.339173i
$262$	−0.409856	+	2.06049i	−0.00156434	+	0.00786445i
$263$	50.0343	−	380.048i	0.190245	−	1.44505i	−0.583789	−	0.811906i	$-0.698430\pi$
$263$	50.0343	−	380.048i	0.190245	−	1.44505i	0.774033	−	0.633145i	$-0.218236\pi$
$264$	−9.13007	+	1.47901i	−0.0345836	+	0.00560231i
$265$	45.3919	+	133.720i	0.171290	+	0.504605i
$266$	−2.61606	−	1.29010i	−0.00983482	−	0.00485000i
$267$	−297.553	+	157.889i	−1.11443	+	0.591346i
$268$	49.9789	+	186.524i	0.186488	+	0.695984i
$269$	−421.449	−	281.604i	−1.56673	−	1.04685i	−0.969597	−	0.244709i	$-0.921308\pi$
$269$	−421.449	−	281.604i	−1.56673	−	1.04685i	−0.597130	−	0.802145i	$-0.703692\pi$
$270$	−8.30409	+	4.34216i	−0.0307559	+	0.0160821i
$271$			427.149i			1.57620i	0.615549	+	0.788099i	$0.288934\pi$
$271$			427.149i			1.57620i	−0.615549	+	0.788099i	$0.711066\pi$
$272$	−240.260	+	124.714i	−0.883310	+	0.458509i
$273$	416.875	−	125.081i	1.52702	−	0.458174i
$274$	−2.34073	+	0.308163i	−0.00854280	+	0.00112468i
$275$	29.4090	+	1.92757i	0.106942	+	0.00700933i
$276$	334.477	−	206.590i	1.21187	−	0.748515i
$277$	−424.173	−	143.987i	−1.53131	−	0.519810i	−0.576520	−	0.817083i	$-0.695590\pi$
$277$	−424.173	−	143.987i	−1.53131	−	0.519810i	−0.954793	+	0.297273i	$0.903923\pi$
$278$	−6.78601	−	10.1560i	−0.0244101	−	0.0365323i
$279$	258.280	−	332.412i	0.925735	−	1.19144i
$280$	28.3374	−	11.7377i	0.101205	−	0.0419205i
$281$	−152.305	−	20.0513i	−0.542011	−	0.0713571i	−0.145450	−	0.989366i	$-0.546463\pi$
$281$	−152.305	−	20.0513i	−0.542011	−	0.0713571i	−0.396561	+	0.918009i	$0.629796\pi$
$282$	4.34667	+	6.10470i	0.0154137	+	0.0216479i
$283$	−360.468	−	177.763i	−1.27374	−	0.628139i	−0.325454	−	0.945558i	$-0.605517\pi$
$283$	−360.468	−	177.763i	−1.27374	−	0.628139i	−0.948285	+	0.317419i	$0.897184\pi$
$284$	−360.834	−	411.452i	−1.27054	−	1.44877i
$285$	−43.0820	+	1.27986i	−0.151165	+	0.00449072i
$286$	−4.53921	+	2.23849i	−0.0158714	+	0.00782690i
$287$	−415.702	−	172.190i	−1.44844	−	0.599964i
$288$	15.4079	−	30.7733i	0.0534998	−	0.106852i
$289$	−121.523	−	262.208i	−0.420495	−	0.907295i
$290$	2.82620	−	4.89512i	0.00974552	−	0.0168797i
$291$	321.275	+	231.697i	1.10404	+	0.796211i
$292$	−89.9887	−	5.89817i	−0.308180	−	0.0201992i
$293$	49.0532	−	183.069i	0.167417	−	0.624809i	−0.830303	−	0.557313i	$-0.811832\pi$
$293$	49.0532	−	183.069i	0.167417	−	0.624809i	0.997720	−	0.0674957i	$-0.0215009\pi$
$294$	8.22077	+	15.4926i	0.0279618	+	0.0526958i
$295$	−117.021	+	7.66999i	−0.396683	+	0.0260000i
$296$	−2.45014	+	12.3177i	−0.00827751	+	0.0416139i
$297$	−88.2994	−	96.0086i	−0.297304	−	0.323261i
$298$	8.29323	+	20.0216i	0.0278296	+	0.0671867i
$299$	283.910	−	323.738i	0.949533	−	1.08273i
$300$	−46.5382	+	56.3583i	−0.155127	+	0.187861i
$301$	348.243	+	397.095i	1.15695	+	1.31925i
$302$	−5.48863	−	1.47067i	−0.0181743	−	0.00486978i
$303$	−343.410	+	319.693i	−1.13337	+	1.05509i
$304$	41.7492	−	32.0353i	0.137333	−	0.105379i
$305$		−	231.910i		−	0.760361i
$306$	10.6662	+	5.95229i	0.0348568	+	0.0194519i
$307$	210.995			0.687280			0.343640	−	0.939101i	$-0.388340\pi$
$307$	210.995			0.687280			0.343640	+	0.939101i	$0.388340\pi$
$308$	129.852	+	169.226i	0.421596	+	0.549434i
$309$	124.524	−	28.6378i	0.402989	−	0.0926790i
$310$	4.20153	−	15.6803i	0.0135533	−	0.0505816i
$311$	−79.8538	+	70.0299i	−0.256765	+	0.225177i	−0.778044	−	0.628209i	$-0.783788\pi$
$311$	−79.8538	+	70.0299i	−0.256765	+	0.225177i	0.521280	+	0.853386i	$0.325455\pi$
$312$	4.16740	−	24.7749i	0.0133571	−	0.0794066i
$313$	−133.588	−	117.153i	−0.426798	−	0.374292i	0.418830	−	0.908065i	$-0.362440\pi$
$313$	−133.588	−	117.153i	−0.426798	−	0.374292i	−0.845628	+	0.533773i	$0.820774\pi$
$314$	−10.8636	+	4.49983i	−0.0345973	+	0.0143307i
$315$	358.207	+	242.495i	1.13716	+	0.769825i
$316$	500.031	+	99.4624i	1.58238	+	0.314754i
$317$	19.2392	+	293.534i	0.0606916	+	0.925975i	0.914294	+	0.405050i	$0.132746\pi$
$317$	19.2392	+	293.534i	0.0606916	+	0.925975i	−0.853603	+	0.520924i	$0.825587\pi$
$318$	−0.278075	+	7.77475i	−0.000874449	+	0.0244489i
$319$	75.9990	+	20.3639i	0.238241	+	0.0638366i
$320$	−18.0234	+	274.984i	−0.0563232	+	0.859326i
$321$	384.536	+	39.0488i	1.19793	+	0.121647i
$322$	25.0818	+	14.4810i	0.0778938	+	0.0449720i
$323$	32.1702	+	46.0585i	0.0995983	+	0.142596i
$324$	321.204	−	38.3379i	0.991370	−	0.118327i
$325$	−30.6353	+	73.9601i	−0.0942623	+	0.227569i
$326$	−3.51504	−	7.12779i	−0.0107823	−	0.0218644i
$327$	18.9186	+	10.1859i	0.0578549	+	0.0311496i
$328$	−19.5271	+	17.1248i	−0.0595338	+	0.0522098i
$329$	153.003	−	310.260i	0.465055	−	0.943039i
$330$	−4.57547	−	2.08983i	−0.0138651	−	0.00633282i
$331$	−33.4308	+	253.932i	−0.101000	+	0.767167i	0.863736	+	0.503945i	$0.168119\pi$
$331$	−33.4308	+	253.932i	−0.101000	+	0.767167i	−0.964735	+	0.263222i	$0.915215\pi$
$332$	7.91662	+	19.1124i	0.0238452	+	0.0575675i
$333$	−164.044	+	66.7890i	−0.492625	+	0.200567i
$334$	7.84561	−	5.24227i	0.0234898	−	0.0156954i
$335$	−67.5689	+	199.052i	−0.201698	+	0.594184i
$336$	−527.907	+	15.6827i	−1.57115	+	0.0466749i
$337$	10.6510	−	162.503i	0.0316054	−	0.482206i	−0.952491	−	0.304568i	$-0.901488\pi$
$337$	10.6510	−	162.503i	0.0316054	−	0.482206i	0.984096	−	0.177638i	$-0.0568455\pi$
$338$	−0.0333426	−	0.253262i	−9.86468e−5	−	0.000749297i
$339$	−379.271	+	402.496i	−1.11879	+	1.18730i
$340$	−293.357	−	32.4754i	−0.862815	−	0.0955159i
$341$	225.965			0.662655
$342$	−2.24383	−	0.776853i	−0.00656089	−	0.00227150i
$343$	148.821	−	222.727i	0.433881	−	0.649349i
$344$	29.4482	−	7.89062i	0.0856052	−	0.0229378i
$345$	427.682	+	15.2966i	1.23966	+	0.0443381i
$346$	−5.09829	+	10.3383i	−0.0147349	+	0.0298795i
$347$	191.279	−	64.9305i	0.551237	−	0.187120i	−0.0319037	−	0.999491i	$-0.510157\pi$
$347$	191.279	−	64.9305i	0.551237	−	0.187120i	0.583141	+	0.812371i	$0.301824\pi$
$348$	−151.206	+	123.328i	−0.434499	+	0.354389i
$349$	−187.467	−	24.6805i	−0.537156	−	0.0707179i	−0.142932	−	0.989732i	$-0.545653\pi$
$349$	−187.467	−	24.6805i	−0.537156	−	0.0707179i	−0.394224	+	0.919015i	$0.628986\pi$
$350$	−5.28099	−	1.05046i	−0.0150886	−	0.00300130i
$351$	324.040	−	143.289i	0.923190	−	0.408231i
$352$	18.1186	−	3.60402i	0.0514734	−	0.0102387i
$353$	−18.3559	−	68.5053i	−0.0519999	−	0.194066i	0.935040	−	0.354543i	$-0.115363\pi$
$353$	−18.3559	−	68.5053i	−0.0519999	−	0.194066i	−0.987040	+	0.160477i	$0.948697\pi$
$354$	−6.17682	−	1.89415i	−0.0174486	−	0.00535070i
$355$	−77.7587	−	590.636i	−0.219039	−	1.66376i
$356$	388.339	−	224.208i	1.09084	−	0.629797i
$357$	8.51662	−	563.778i	0.0238561	−	1.57921i
$358$	12.2221	−	21.1693i	0.0341400	−	0.0591322i
$359$	106.758	−	257.736i	0.297375	−	0.717928i	−0.702604	−	0.711581i	$-0.747980\pi$
$359$	106.758	−	257.736i	0.297375	−	0.717928i	0.999980	−	0.00634722i	$-0.00202040\pi$
$360$	21.6989	−	12.3534i	0.0602747	−	0.0343149i
$361$	247.543	+	247.543i	0.685714	+	0.685714i
$362$	25.1473	+	8.53636i	0.0694677	+	0.0235811i
$363$	−48.6000	+	288.923i	−0.133884	+	0.795930i
$364$	−548.642	+	186.239i	−1.50726	+	0.511645i
$365$	−77.8831	−	59.7618i	−0.213378	−	0.163731i
$366$	4.53661	−	11.9437i	0.0123951	−	0.0326331i
$367$	−262.285	+	299.079i	−0.714673	+	0.814928i	−0.989188	−	0.146654i	$-0.953149\pi$
$367$	−262.285	+	299.079i	−0.714673	+	0.814928i	0.274515	+	0.961583i	$0.411483\pi$
$368$	−434.448	+	290.289i	−1.18057	+	0.788829i
$369$	−353.227	−	96.9419i	−0.957253	−	0.262715i
$370$	−4.82972	+	4.82972i	−0.0130533	+	0.0130533i
$371$	322.086	−	158.835i	0.868157	−	0.428128i
$372$	−327.788	+	454.516i	−0.881151	+	1.22182i
$373$	7.70549	−	4.44877i	0.0206582	−	0.0119270i	−0.489635	−	0.871927i	$-0.662870\pi$
$373$	7.70549	−	4.44877i	0.0206582	−	0.0119270i	0.510294	+	0.860000i	$0.329537\pi$
$374$	0.989834	+	6.48151i	0.00264662	+	0.0173302i
$375$	−388.504	+	116.569i	−1.03601	+	0.310850i
$376$	−12.1559	−	15.8419i	−0.0323295	−	0.0421326i
$377$	−118.734	+	177.698i	−0.314944	+	0.471347i
$378$	13.7045	+	19.4961i	0.0362553	+	0.0515769i
$379$	19.4627	+	97.8454i	0.0513527	+	0.258167i	0.997930	−	0.0643096i	$-0.0204845\pi$
$379$	19.4627	+	97.8454i	0.0513527	+	0.258167i	−0.946577	+	0.322477i	$0.895485\pi$
$380$	57.2536	−	3.75260i	0.150667	−	0.00987526i
$381$	3.39911	+	35.6163i	0.00892154	+	0.0934812i
$382$	2.35497	+	1.80703i	0.00616484	+	0.00473045i
$383$	−362.160	+	471.976i	−0.945588	+	1.23231i	0.0269664	+	0.999636i	$0.491415\pi$
$383$	−362.160	+	471.976i	−0.945588	+	1.23231i	−0.972554	+	0.232677i	$0.925251\pi$
$384$	−25.3717	+	55.5487i	−0.0660721	+	0.144658i
$385$	15.1864	+	231.700i	0.0394453	+	0.601819i
$386$	9.02639	−	1.79546i	0.0233844	−	0.00465145i
$387$	321.537	+	285.441i	0.830844	+	0.737575i
$388$	−438.436	−	292.954i	−1.12999	−	0.755035i
$389$	−268.891	+	206.328i	−0.691238	+	0.530405i	−0.893577	−	0.448910i	$-0.851812\pi$
$389$	−268.891	+	206.328i	−0.691238	+	0.530405i	0.202339	+	0.979315i	$0.435146\pi$
$390$	9.37017	−	9.94394i	0.0240261	−	0.0254973i
$391$	−288.828	−	477.233i	−0.738691	−	1.22054i
$392$	−23.3661	−	40.4713i	−0.0596074	−	0.103243i
$393$	72.0071	−	32.3637i	0.183224	−	0.0823503i
$394$	−5.63182	−	11.4202i	−0.0142939	−	0.0289853i
$395$	392.433	+	392.433i	0.993502	+	0.993502i
$396$	122.038	+	123.524i	0.308177	+	0.311930i
$397$	324.384	+	485.475i	0.817089	+	1.22286i	0.972011	+	0.234933i	$0.0754872\pi$
$397$	324.384	+	485.475i	0.817089	+	1.22286i	−0.154923	+	0.987927i	$0.549513\pi$
$398$	15.9341	+	13.9738i	0.0400353	+	0.0351100i
$399$	17.5276	+	108.199i	0.0439288	+	0.271176i
$400$	59.1361	−	77.0677i	0.147840	−	0.192669i
$401$	−103.002	−	303.434i	−0.256863	−	0.756693i	−0.996493	−	0.0836795i	$-0.973333\pi$
$401$	−103.002	−	303.434i	−0.256863	−	0.756693i	0.739630	−	0.673014i	$-0.235001\pi$
$402$	−7.37374	+	8.92968i	−0.0183426	+	0.0222131i
$403$	−197.293	+	581.208i	−0.489562	+	1.44220i
$404$	441.647	−	441.647i	1.09318	−	1.09318i
$405$	313.913	+	159.557i	0.775093	+	0.393968i
$406$	−13.2804	−	5.50091i	−0.0327103	−	0.0135490i
$407$	−82.3377	−	47.5377i	−0.202304	−	0.116800i
$408$	−28.9692	−	14.8342i	−0.0710029	−	0.0363582i
$409$	−154.823	−	268.162i	−0.378541	−	0.655652i	0.612309	−	0.790618i	$-0.290241\pi$
$409$	−154.823	−	268.162i	−0.378541	−	0.655652i	−0.990850	+	0.134966i	$0.956907\pi$
$410$	−14.0043	+	1.84370i	−0.0341569	+	0.00449684i
$411$	60.4511	+	64.9358i	0.147083	+	0.157995i
$412$	−164.298	+	44.0236i	−0.398783	+	0.106854i
$413$	58.1827	+	292.504i	0.140878	+	0.708243i
$414$	21.7270	+	9.15408i	0.0524807	+	0.0221113i
$415$	−4.39333	+	22.0867i	−0.0105863	+	0.0532211i
$416$	−6.54969	+	49.7498i	−0.0157444	+	0.119591i
$417$	−162.980	+	429.085i	−0.390840	+	1.02898i
$418$	−0.409708	−	1.20696i	−0.000980162	−	0.00288746i
$419$	638.513	+	314.880i	1.52390	+	0.751503i	0.995251	−	0.0973390i	$-0.0310331\pi$
$419$	638.513	+	314.880i	1.52390	+	0.751503i	0.528646	+	0.848842i	$0.322700\pi$
$420$	−488.081	−	305.561i	−1.16210	−	0.727525i
$421$	185.835	+	693.546i	0.441413	+	1.64738i	0.725236	+	0.688500i	$0.241731\pi$
$421$	185.835	+	693.546i	0.441413	+	1.64738i	−0.283822	+	0.958877i	$0.591603\pi$
$422$	0.259307	+	0.173263i	0.000614471	+	0.000410576i
$423$	92.1332	−	266.113i	0.217809	−	0.629109i
$424$		−	20.7294i		−	0.0488901i
$425$	79.3673	+	66.7555i	0.186747	+	0.157072i
$426$	7.54929	−	31.9398i	0.0177213	−	0.0749760i
$427$	−584.723	+	76.9803i	−1.36938	+	0.180282i
$428$	−513.428	−	33.6519i	−1.19960	−	0.0786258i
$429$	167.459	+	90.1611i	0.390346	+	0.210166i
$430$	15.7005	+	5.32961i	0.0365128	+	0.0123944i
$431$	−319.095	−	477.560i	−0.740360	−	1.10803i	−0.990189	−	0.139737i	$-0.955374\pi$
$431$	−319.095	−	477.560i	−0.740360	−	1.10803i	0.249828	−	0.968290i	$-0.419626\pi$
$432$	−424.812	+	66.1807i	−0.983361	+	0.153196i
$433$	72.8127	−	30.1600i	0.168159	−	0.0696536i	−0.297016	−	0.954872i	$-0.595991\pi$
$433$	72.8127	−	30.1600i	0.168159	−	0.0696536i	0.465175	+	0.885219i	$0.345991\pi$
$434$	−40.9300	−	5.38854i	−0.0943087	−	0.0124160i
$435$	−211.445	+	20.1796i	−0.486080	+	0.0463898i
$436$	−25.6531	−	12.6507i	−0.0588375	−	0.0290154i
$437$	71.5000	+	81.5301i	0.163616	+	0.186568i
$438$	−2.84204	−	4.60137i	−0.00648868	−	0.0105054i
$439$	460.161	−	226.926i	1.04820	−	0.516917i	0.165189	−	0.986262i	$-0.447177\pi$
$439$	460.161	−	226.926i	1.04820	−	0.516917i	0.883015	+	0.469345i	$0.155510\pi$
$440$	12.3828	+	5.12911i	0.0281427	+	0.0116571i
$441$	295.068	−	589.320i	0.669089	−	1.33633i
$442$	−17.5354	−	3.11313i	−0.0396728	−	0.00704329i
$443$	−34.6008	+	59.9304i	−0.0781057	+	0.135283i	−0.902433	−	0.430831i	$-0.858221\pi$
$443$	−34.6008	+	59.9304i	−0.0781057	+	0.135283i	0.824327	+	0.566114i	$0.191554\pi$
$444$	215.059	−	96.6588i	0.484368	−	0.217700i
$445$	487.088	+	31.9254i	1.09458	+	0.0717425i
$446$	0.407712	−	1.52160i	0.000914152	−	0.00341166i
$447$	432.128	−	690.252i	0.966730	−	1.54419i
$448$	699.311	−	45.8352i	1.56096	−	0.102311i
$449$	−89.8732	+	451.823i	−0.200163	+	1.00629i	0.741813	+	0.670607i	$0.233966\pi$
$449$	−89.8732	+	451.823i	−0.200163	+	1.00629i	−0.941976	+	0.335680i	$0.891034\pi$
$450$	−4.37206	−	0.313146i	−0.00971568	−	0.000695880i
$451$	−75.2427	−	181.652i	−0.166835	−	0.402776i
$452$	485.415	−	553.510i	1.07393	−	1.22458i
$453$	74.6097	+	200.068i	0.164701	+	0.441651i
$454$	3.38690	+	3.86202i	0.00746014	+	0.00850665i
$455$	−609.218	−	163.239i	−1.33894	−	0.358768i
$456$	6.04894	+	1.85493i	0.0132652	+	0.00406784i
$457$	−25.2826	+	19.4000i	−0.0553229	+	0.0424508i	−0.636053	−	0.771646i	$-0.719434\pi$
$457$	−25.2826	+	19.4000i	−0.0553229	+	0.0424508i	0.580730	+	0.814096i	$0.302767\pi$
$458$		−	4.24638i		−	0.00927157i
$459$	−50.2705	−	456.239i	−0.109522	−	0.993984i
$460$	−569.698			−1.23847
$461$	109.280	+	142.416i	0.237050	+	0.308929i	0.896696	−	0.442647i	$-0.145961\pi$
$461$	109.280	+	142.416i	0.237050	+	0.308929i	−0.659646	+	0.751576i	$0.729294\pi$
$462$	−3.75038	+	12.2300i	−0.00811771	+	0.0264719i
$463$	52.1613	−	194.669i	0.112659	−	0.420451i	−0.886442	−	0.462840i	$-0.846830\pi$
$463$	52.1613	−	194.669i	0.112659	−	0.420451i	0.999101	+	0.0423896i	$0.0134971\pi$
$464$	194.978	−	170.991i	0.420210	−	0.368514i
$465$	−571.568	+	213.151i	−1.22918	+	0.458388i
$466$	−18.6570	−	16.3617i	−0.0400365	−	0.0351110i
$467$	8.26510	−	3.42352i	0.0176983	−	0.00733087i	−0.373817	−	0.927503i	$-0.621951\pi$
$467$	8.26510	−	3.42352i	0.0176983	−	0.00733087i	0.391515	+	0.920172i	$0.371951\pi$
$468$	−424.271	+	206.044i	−0.906562	+	0.440266i
$469$	524.305	+	104.291i	1.11792	+	0.222368i
$470$	−0.710264	−	10.8365i	−0.00151120	−	0.0230564i
$471$	374.525	+	234.469i	0.795169	+	0.497811i
$472$	16.6283	+	4.45553i	0.0352294	+	0.00943969i
$473$	−15.0947	+	230.301i	−0.0319128	+	0.486895i
$474$	12.5342	+	27.8877i	0.0264434	+	0.0588347i
$475$	−17.4597	−	10.0804i	−0.0367573	−	0.0212218i
$476$	15.4956	+	750.432i	0.0325538	+	1.57654i
$477$	244.055	−	160.944i	0.511646	−	0.337409i
$478$	5.44605	−	13.1479i	0.0113934	−	0.0275061i
$479$	−292.491	−	593.113i	−0.610628	−	1.23823i	−0.954218	−	0.299111i	$-0.903310\pi$
$479$	−292.491	−	593.113i	−0.610628	−	1.23823i	0.343590	−	0.939120i	$-0.388357\pi$
$480$	−42.4305	+	26.2073i	−0.0883970	+	0.0545985i
$481$	194.162	−	170.276i	0.403664	−	0.354004i
$482$	−3.91861	+	7.94616i	−0.00812990	+	0.0164858i
$483$	−103.397	−	1083.41i	−0.214072	−	2.24308i
$484$	50.9078	−	386.683i	0.105181	−	0.798932i
$485$	−219.663	−	530.314i	−0.452914	−	1.09343i
$486$	13.0457	+	14.3582i	0.0268431	+	0.0295436i
$487$	550.105	−	367.569i	1.12958	−	0.754761i	0.157061	−	0.987589i	$-0.449798\pi$
$487$	550.105	−	367.569i	1.12958	−	0.754761i	0.972518	+	0.232828i	$0.0747979\pi$
$488$	−10.9427	+	32.2363i	−0.0224236	+	0.0660579i
$489$	−141.577	+	262.955i	−0.289524	+	0.537740i
$490$	1.66225	−	25.3610i	0.00339235	−	0.0517572i
$491$	62.8678	+	477.528i	0.128040	+	0.972562i	0.928019	+	0.372534i	$0.121511\pi$
$491$	62.8678	+	477.528i	0.128040	+	0.972562i	−0.799978	+	0.600029i	$0.795156\pi$
$492$	474.530	+	112.160i	0.964493	+	0.227968i
$493$	173.043	+	216.125i	0.351001	+	0.438388i
$494$	3.46215			0.00700840
$495$	35.7536	+	185.610i	0.0722296	+	0.374970i
$496$	413.786	−	619.275i	0.834247	−	1.24854i
$497$	−1463.38	+	392.112i	−2.94443	+	0.788957i
$498$	−0.658323	+	1.05156i	−0.00132193	+	0.00211156i
$499$	−336.636	+	682.630i	−0.674621	+	1.36800i	0.242799	+	0.970077i	$0.421935\pi$
$499$	−336.636	+	682.630i	−0.674621	+	1.36800i	−0.917420	+	0.397920i	$0.869732\pi$
$500$	511.303	−	173.564i	1.02261	−	0.347128i
$501$	−331.473	−	125.904i	−0.661623	−	0.251306i
$502$	−14.6450	−	1.92806i	−0.0291734	−	0.00384075i
$503$	467.775	+	93.0462i	0.929970	+	0.184982i	0.636757	−	0.771065i	$-0.280276\pi$
$503$	467.775	+	93.0462i	0.929970	+	0.184982i	0.293213	+	0.956047i	$0.405276\pi$
$504$	−38.3497	−	50.6097i	−0.0760907	−	0.100416i
$505$	666.840	−	132.643i	1.32048	−	0.262659i
$506$	3.27553	+	12.2244i	0.00647338	+	0.0241590i
$507$	−7.02593	+	6.54070i	−0.0138578	+	0.0129008i
$508$	−6.21673	−	47.2207i	−0.0122377	−	0.0929542i
$509$	−206.118	+	119.002i	−0.404946	+	0.233796i	−0.688616	−	0.725126i	$-0.741781\pi$
$509$	−206.118	+	119.002i	−0.404946	+	0.233796i	0.283670	+	0.958922i	$0.408448\pi$
$510$	−8.61767	−	15.4610i	−0.0168974	−	0.0303156i
$511$	−124.827	+	216.207i	−0.244280	+	0.423105i
$512$	38.8567	−	93.8084i	0.0758920	−	0.183220i
$513$	25.1255	+	85.6182i	0.0489776	+	0.166897i
$514$	3.14314	+	3.14314i	0.00611505	+	0.00611505i
$515$	−175.334	−	59.5178i	−0.340454	−	0.115568i
$516$	−441.341	−	364.440i	−0.855312	−	0.706279i
$517$	143.143	−	48.5905i	0.276872	−	0.0939855i
$518$	13.7805	+	10.5742i	0.0266033	+	0.0204135i
$519$	427.589	−	69.2666i	0.823870	−	0.133462i
$520$	−24.0042	+	27.3715i	−0.0461619	+	0.0526376i
$521$	−540.926	+	361.435i	−1.03824	+	0.693733i	−0.953106	−	0.302636i	$-0.902133\pi$
$521$	−540.926	+	361.435i	−1.03824	+	0.693733i	−0.0851386	+	0.996369i	$0.527133\pi$
$522$	−11.2845	−	3.09699i	−0.0216178	−	0.00593293i
$523$	322.408	−	322.408i	0.616458	−	0.616458i	−0.328163	−	0.944621i	$-0.606430\pi$
$523$	322.408	−	322.408i	0.616458	−	0.616458i	0.944621	+	0.328163i	$0.106430\pi$
$524$	−94.2552	+	46.4815i	−0.179876	+	0.0887052i
$525$	82.9476	+	184.553i	0.157995	+	0.351529i
$526$	−26.5027	+	15.3013i	−0.0503853	+	0.0290900i
$527$	640.689	+	470.927i	1.21573	+	0.893599i
$528$	−167.963	−	158.271i	−0.318112	−	0.299757i
$529$	−333.432	−	434.537i	−0.630306	−	0.821431i
$530$	6.26335	−	9.37377i	0.0118176	−	0.0176864i
$531$	76.6463	+	230.364i	0.144343	+	0.433831i
$532$	−28.4663	−	143.110i	−0.0535082	−	0.269004i
$533$	532.924	−	34.9297i	0.999857	−	0.0655341i
$534$	24.4612	+	11.1726i	0.0458076	+	0.0209224i
$535$	−444.360	−	340.969i	−0.830579	−	0.637326i
$536$	18.7846	−	24.4806i	0.0350459	−	0.0456727i
$537$	−914.408	+	87.2681i	−1.70281	+	0.162510i
$538$	2.64659	+	40.3791i	0.00491931	+	0.0750541i
$539$	346.979	−	69.0184i	0.643746	−	0.128049i
$540$	−425.208	−	197.332i	−0.787423	−	0.365429i
$541$	360.699	+	241.012i	0.666727	+	0.445493i	0.842326	−	0.538969i	$-0.181186\pi$
$541$	360.699	+	241.012i	0.666727	+	0.445493i	−0.175599	+	0.984462i	$0.556186\pi$
$542$	27.0542	−	20.7594i	0.0499156	−	0.0383016i
$543$	−286.796	−	955.845i	−0.528170	−	1.76030i
$544$	58.8835	+	27.5418i	0.108242	+	0.0506283i
$545$	−15.5682	−	26.9648i	−0.0285654	−	0.0494768i
$546$	−28.1824	−	20.3246i	−0.0516160	−	0.0372245i
$547$	157.057	+	318.479i	0.287124	+	0.582229i	0.991874	−	0.127226i	$-0.0406075\pi$
$547$	157.057	+	318.479i	0.287124	+	0.582229i	−0.704750	+	0.709456i	$0.748941\pi$
$548$	−83.5114	−	83.5114i	−0.152393	−	0.152393i
$549$	−464.490	+	121.451i	−0.846066	+	0.221223i
$550$	−1.30719	−	1.95635i	−0.00237671	−	0.00355699i
$551$	−40.4656	−	35.4873i	−0.0734402	−	0.0644053i
$552$	−58.7274	−	22.3066i	−0.106390	−	0.0404104i
$553$	859.192	−	1119.72i	1.55369	−	2.02481i
$554$	11.4951	+	33.8635i	0.0207493	+	0.0611255i
$555$	253.111	+	42.5760i	0.456056	+	0.0767136i
$556$	196.405	−	578.592i	0.353247	−	1.04063i
$557$	−211.668	+	211.668i	−0.380014	+	0.380014i	−0.871107	−	0.491093i	$-0.836597\pi$
$557$	−211.668	+	211.668i	−0.380014	+	0.380014i	0.491093	+	0.871107i	$0.336597\pi$
$558$	−33.6063	−	0.203403i	−0.0602263	−	0.000364522i
$559$	−579.180	−	239.904i	−1.03610	−	0.429167i
$560$	662.801	+	382.668i	1.18357	+	0.683337i
$561$	176.833	−	171.569i	0.315209	−	0.305828i
$562$	6.13203	+	10.6210i	0.0109111	+	0.0188986i
$563$	−696.148	+	91.6496i	−1.23650	+	0.162788i	−0.720288	−	0.693675i	$-0.755991\pi$
$563$	−696.148	+	91.6496i	−1.23650	+	0.162788i	−0.516209	+	0.856463i	$0.672657\pi$
$564$	−109.908	+	358.410i	−0.194872	+	0.635478i
$565$	774.108	−	207.422i	1.37010	−	0.367118i
$566$	6.25980	+	31.4701i	0.0110597	+	0.0556010i
$567$	298.097	−	844.443i	0.525744	−	1.48932i
$568$	−17.0606	+	85.7695i	−0.0300363	+	0.151003i
$569$	5.12388	−	38.9197i	0.00900506	−	0.0684002i	−0.986352	−	0.164649i	$-0.947351\pi$
$569$	5.12388	−	38.9197i	0.00900506	−	0.0684002i	0.995357	+	0.0962484i	$0.0306843\pi$
$570$	2.17485	+	2.66647i	0.00381552	+	0.00467802i
$571$	−69.8682	−	205.825i	−0.122361	−	0.360464i	0.868439	−	0.495796i	$-0.165123\pi$
$571$	−69.8682	−	205.825i	−0.122361	−	0.360464i	−0.990800	+	0.135331i	$0.956790\pi$
$572$	−227.070	−	111.978i	−0.396975	−	0.195767i
$573$	3.98702	−	111.474i	0.00695816	−	0.194545i
$574$	9.29720	+	34.6976i	0.0161972	+	0.0604488i
$575$	166.442	+	111.213i	0.289465	+	0.193414i
$576$	560.202	−	107.911i	0.972573	−	0.187345i
$577$			715.808i			1.24057i	0.784377	+	0.620284i	$0.212983\pi$
$577$			715.808i			1.24057i	−0.784377	+	0.620284i	$0.787017\pi$
$578$	−10.7014	+	20.4402i	−0.0185145	+	0.0353636i
$579$	−251.698	−	237.175i	−0.434712	−	0.409629i
$580$	280.337	−	36.9070i	0.483339	−	0.0636328i
$581$	57.1465	+	3.74558i	0.0983588	+	0.00644678i
$582$	−0.939022	−	31.6090i	−0.00161344	−	0.0543110i
$583$	148.599	+	50.4427i	0.254887	+	0.0865226i
$584$	8.00613	+	11.9820i	0.0137091	+	0.0205172i
$585$	−508.626	−	70.0962i	−0.869446	−	0.119823i
$586$	−13.9790	+	5.79027i	−0.0238549	+	0.00988101i
$587$	4.28867	+	0.564614i	0.00730608	+	0.000961864i	0.134178	−	0.990957i	$-0.457160\pi$
$587$	4.28867	+	0.564614i	0.00730608	+	0.000961864i	−0.126872	+	0.991919i	$0.540494\pi$
$588$	−364.505	+	798.047i	−0.619907	+	1.35722i
$589$	−138.634	−	68.3666i	−0.235371	−	0.116072i
$590$	6.17303	+	7.03899i	0.0104628	+	0.0119305i
$591$	−226.836	+	421.308i	−0.383817	+	0.712873i
$592$	−281.057	+	138.602i	−0.474758	+	0.234125i
$593$	874.918	+	362.403i	1.47541	+	0.611134i	0.968085	−	0.250621i	$-0.0806348\pi$
$593$	874.918	+	362.403i	1.47541	+	0.611134i	0.507324	+	0.861755i	$0.330635\pi$
$594$	−1.78952	+	10.2586i	−0.00301266	+	0.0172704i
$595$	−439.820	+	688.599i	−0.739193	+	1.15731i
$596$	−542.042	+	938.844i	−0.909466	+	1.57524i
$597$	80.4594	−	792.329i	0.134773	−	1.32718i
$598$	−34.3025	−	2.24830i	−0.0573620	−	0.00375971i
$599$	207.569	−	774.658i	0.346526	−	1.29325i	−0.544294	−	0.838894i	$-0.683202\pi$
$599$	207.569	−	774.658i	0.346526	−	1.29325i	0.890820	−	0.454357i	$-0.150131\pi$
$600$	11.6719	+	0.417462i	0.0194532	+	0.000695770i
$601$	−413.507	+	27.1027i	−0.688032	+	0.0450960i	−0.405409	−	0.914135i	$-0.632871\pi$
$601$	−413.507	+	27.1027i	−0.688032	+	0.0450960i	−0.282623	+	0.959231i	$0.591204\pi$
$602$	8.22610	−	41.3554i	0.0136646	−	0.0686967i
$603$	434.064	+	31.0896i	0.719841	+	0.0515582i
$604$	−108.777	−	262.612i	−0.180095	−	0.434788i
$605$	279.935	−	319.205i	0.462703	−	0.527612i
$606$	36.9380	+	6.21338i	0.0609538	+	0.0102531i
$607$	−2.14110	−	2.44145i	−0.00352734	−	0.00402216i	0.750073	−	0.661355i	$-0.230018\pi$
$607$	−2.14110	−	2.44145i	−0.00352734	−	0.00402216i	−0.753601	+	0.657332i	$0.771685\pi$
$608$	−12.2065	−	3.27072i	−0.0200765	−	0.00537948i
$609$	121.066	+	526.425i	0.198796	+	0.864408i
$610$	−14.6884	+	11.2708i	−0.0240794	+	0.0184767i
$611$			410.604i			0.672020i
$612$	88.5866	+	604.569i	0.144749	+	0.987858i
$613$	−802.629			−1.30935			−0.654673	−	0.755912i	$-0.727194\pi$
$613$	−802.629			−1.30935			−0.654673	+	0.755912i	$0.727194\pi$
$614$	−10.2543	−	13.3637i	−0.0167009	−	0.0217650i
$615$	361.673	+	388.504i	0.588086	+	0.631714i
$616$	8.82188	−	32.9237i	0.0143212	−	0.0534476i
$617$	−857.096	+	751.653i	−1.38913	+	1.21824i	−0.442157	+	0.896937i	$0.645787\pi$
$617$	−857.096	+	751.653i	−1.38913	+	1.21824i	−0.946977	+	0.321301i	$0.895880\pi$
$618$	−7.86567	−	6.49512i	−0.0127276	−	0.0105099i
$619$	382.928	+	335.819i	0.618624	+	0.542519i	0.910274	−	0.414007i	$-0.135871\pi$
$619$	382.928	+	335.819i	0.618624	+	0.542519i	−0.291650	+	0.956525i	$0.594204\pi$
$620$	750.248	−	310.763i	1.21008	−	0.501231i
$621$	−193.340	−	864.610i	−0.311336	−	1.39229i
$622$	8.31636	+	1.65423i	0.0133703	+	0.00265953i
$623$	−81.1893	−	1238.71i	−0.130320	−	1.98830i
$624$	553.742	−	293.830i	0.887407	−	0.470882i
$625$	420.440	+	112.656i	0.672704	+	0.180250i
$626$	−0.927745	+	14.1547i	−0.00148202	+	0.0226113i
$627$	−28.0166	+	38.8482i	−0.0446835	+	0.0619589i
$628$	−509.409	−	294.107i	−0.811160	−	0.468324i
$629$	−134.384	−	306.383i	−0.213647	−	0.487095i
$630$	−2.05001	−	34.4728i	−0.00325398	−	0.0547188i
$631$	−451.308	+	1089.55i	−0.715226	+	1.72671i	−0.0287165	+	0.999588i	$0.509142\pi$
$631$	−451.308	+	1089.55i	−0.715226	+	1.72671i	−0.686510	+	0.727121i	$0.740858\pi$
$632$	−36.0325	−	73.0666i	−0.0570134	−	0.115612i
$633$	−0.347995	−	11.7141i	−0.000549755	−	0.0185057i
$634$	17.6564	−	15.4843i	0.0278493	−	0.0244232i
$635$	22.9313	−	46.5000i	0.0361122	−	0.0732283i
$636$	−317.023	+	225.726i	−0.498463	+	0.354915i
$637$	−125.429	+	952.728i	−0.196906	+	1.49565i
$638$	−2.40377	−	5.80321i	−0.00376766	−	0.00909594i
$639$	−1142.26	+	465.059i	−1.78757	+	0.727791i
$640$	73.5815	−	49.1656i	0.114971	−	0.0768212i
$641$	124.601	−	367.063i	0.194386	−	0.572641i	−0.805413	−	0.592714i	$-0.798056\pi$
$641$	124.601	−	367.063i	0.194386	−	0.572641i	0.999799	+	0.0200727i	$0.00638978\pi$
$642$	−16.2152	−	26.2530i	−0.0252573	−	0.0408925i
$643$	47.1283	−	719.040i	0.0732945	−	1.11826i	−0.789850	−	0.613300i	$-0.789842\pi$
$643$	47.1283	−	719.040i	0.0732945	−	1.11826i	0.863144	−	0.504957i	$-0.168492\pi$
$644$	189.106	+	1436.40i	0.293642	+	2.23043i
$645$	−179.059	−	596.774i	−0.277611	−	0.925231i
$646$	1.35372	−	4.27600i	0.00209555	−	0.00661919i
$647$	277.082			0.428256			0.214128	−	0.976806i	$-0.431309\pi$
$647$	277.082			0.428256			0.214128	+	0.976806i	$0.431309\pi$
$648$	−36.1062	−	36.9910i	−0.0557194	−	0.0570849i
$649$	−72.4027	+	108.358i	−0.111560	+	0.166962i
$650$	6.17326	−	1.65412i	0.00949732	−	0.00254480i
$651$	727.151	+	1370.36i	1.11698	+	2.10501i
$652$	175.836	−	356.561i	0.269688	−	0.546872i
$653$	175.387	−	59.5360i	0.268587	−	0.0911730i	−0.183897	−	0.982946i	$-0.558871\pi$
$653$	175.387	−	59.5360i	0.268587	−	0.0911730i	0.452484	+	0.891773i	$0.350538\pi$
$654$	−0.274299	−	1.69327i	−0.000419418	−	0.00258910i
$655$	−113.423	−	14.9324i	−0.173165	−	0.0227976i
$656$	−635.615	−	126.432i	−0.968925	−	0.192731i
$657$	−78.9088	+	187.288i	−0.120105	+	0.285066i
$658$	−27.0868	+	5.38789i	−0.0411653	+	0.00818829i
$659$	100.668	+	375.698i	0.152759	+	0.570103i	0.999287	+	0.0377593i	$0.0120220\pi$
$659$	100.668	+	375.698i	0.152759	+	0.570103i	−0.846528	+	0.532344i	$0.821311\pi$
$660$	−56.3969	−	245.226i	−0.0854498	−	0.371555i
$661$	62.0852	+	471.584i	0.0939262	+	0.713440i	0.972011	+	0.234935i	$0.0754878\pi$
$661$	62.0852	+	471.584i	0.0939262	+	0.713440i	−0.878085	+	0.478505i	$0.841179\pi$
$662$	17.7080	−	10.2237i	0.0267492	−	0.0154437i
$663$	286.900	+	604.632i	0.432731	+	0.911964i
$664$	1.65286	−	2.86283i	0.00248924	−	0.00431149i
$665$	60.7846	−	146.747i	0.0914054	−	0.220672i
$666$	12.2027	+	7.14407i	0.0183224	+	0.0107268i
$667$	377.882	+	377.882i	0.566539	+	0.566539i
$668$	446.968	+	151.725i	0.669115	+	0.227134i
$669$	−55.4644	+	20.6839i	−0.0829064	+	0.0309177i
$670$	15.8911	−	5.39431i	0.0237181	−	0.00805120i
$671$	−204.459	−	156.887i	−0.304708	−	0.233810i
$672$	80.1618	+	98.2824i	0.119288	+	0.146254i
$673$	289.962	−	330.639i	0.430851	−	0.491291i	−0.495153	−	0.868806i	$-0.664888\pi$
$673$	289.962	−	330.639i	0.430851	−	0.491291i	0.926004	+	0.377515i	$0.123221\pi$
$674$	−10.8101	+	7.22305i	−0.0160387	+	0.0107167i
$675$	85.7065	+	140.659i	0.126973	+	0.208384i
$676$	9.03578	−	9.03578i	0.0133665	−	0.0133665i
$677$	−264.961	+	130.664i	−0.391375	+	0.193005i	−0.627320	−	0.778762i	$-0.715848\pi$
$677$	−264.961	+	130.664i	−0.391375	+	0.193005i	0.235945	+	0.971766i	$0.424182\pi$
$678$	43.9253	+	4.46052i	0.0647866	+	0.00657894i
$679$	−1264.18	+	729.877i	−1.86183	+	1.07493i
$680$	24.4200	+	40.3493i	0.0359117	+	0.0593372i
$681$	44.4009	−	187.853i	0.0651996	−	0.275848i
$682$	−10.9819	−	14.3119i	−0.0161025	−	0.0209852i
$683$	−196.038	+	293.392i	−0.287025	+	0.429563i	−0.946762	−	0.321933i	$-0.895667\pi$
$683$	−196.038	+	293.392i	−0.287025	+	0.429563i	0.659738	+	0.751496i	$0.270667\pi$
$684$	−37.4998	−	112.707i	−0.0548243	−	0.164777i
$685$	−25.0815	−	126.093i	−0.0366154	−	0.184078i
$686$	−21.3395	+	1.39866i	−0.0311071	+	0.00203887i
$687$	−129.987	+	92.5530i	−0.189209	+	0.134721i
$688$	603.516	+	463.094i	0.877204	+	0.673102i
$689$	−259.488	+	338.171i	−0.376615	+	0.490815i
$690$	−19.8165	−	27.8313i	−0.0287195	−	0.0403353i
$691$	−53.7239	−	819.669i	−0.0777481	−	1.18621i	−0.841340	−	0.540507i	$-0.818233\pi$
$691$	−53.7239	−	819.669i	−0.0777481	−	1.18621i	0.763592	−	0.645700i	$-0.223434\pi$
$692$	−565.550	+	112.495i	−0.817269	+	0.162565i
$693$	456.117	−	151.758i	0.658177	−	0.218988i
$694$	−13.4086	−	8.95937i	−0.0193208	−	0.0129098i
$695$	527.690	−	404.911i	0.759266	−	0.582605i
$696$	30.3437	+	7.17204i	0.0435973	+	0.0103047i
$697$	165.236	−	671.856i	0.237067	−	0.963925i
$698$	7.54772	+	13.0730i	0.0108134	+	0.0187293i
$699$	−94.2089	+	927.729i	−0.134777	+	1.32722i
$700$	−119.131	−	241.575i	−0.170188	−	0.345107i
$701$	−515.665	−	515.665i	−0.735614	−	0.735614i	0.236112	−	0.971726i	$-0.424127\pi$
$701$	−515.665	−	515.665i	−0.735614	−	0.735614i	−0.971726	+	0.236112i	$0.924127\pi$
$702$	−24.8238	−	13.5598i	−0.0353615	−	0.0193159i
$703$	36.1329	+	54.0768i	0.0513982	+	0.0769229i
$704$	230.242	+	201.917i	0.327048	+	0.286813i
$705$	−316.238	+	257.932i	−0.448565	+	0.365861i
$706$	−3.44680	+	4.49196i	−0.00488216	+	0.00636255i
$707$	−555.788	−	1637.30i	−0.786122	−	2.31584i
$708$	−112.928	−	302.820i	−0.159503	−	0.427712i
$709$	61.3883	−	180.844i	0.0865844	−	0.255069i	−0.895010	−	0.446045i	$-0.852832\pi$
$709$	61.3883	−	180.844i	0.0865844	−	0.255069i	0.981595	+	0.190976i	$0.0611653\pi$
$710$	−33.6299	+	33.6299i	−0.0473660	+	0.0473660i
$711$	580.483	−	991.518i	0.816431	−	1.39454i
$712$	−66.2004	−	27.4211i	−0.0929781	−	0.0385128i
$713$	1329.17	+	767.395i	1.86419	+	1.07629i
$714$	−36.1217	+	26.8602i	−0.0505907	+	0.0376193i
$715$	−137.802	−	238.681i	−0.192730	−	0.333819i
$716$	1212.34	−	159.607i	1.69321	−	0.222915i
$717$	−521.174	+	119.859i	−0.726882	+	0.167167i
$718$	−21.5126	+	5.76428i	−0.0299618	+	0.00802824i
$719$	42.8362	+	215.352i	0.0595775	+	0.299516i	0.999073	−	0.0430446i	$-0.0137058\pi$
$719$	42.8362	+	215.352i	0.0595775	+	0.299516i	−0.939496	+	0.342561i	$0.888706\pi$
$720$	574.150	+	241.902i	0.797430	+	0.335975i
$721$	−91.8640	+	461.832i	−0.127412	+	0.640543i
$722$	3.64797	−	27.7091i	0.00505260	−	0.0383783i
$723$	328.650	−	53.2392i	0.454565	−	0.0736365i
$724$	427.023	+	1257.97i	0.589811	+	1.73753i
$725$	−89.1078	−	43.9431i	−0.122907	−	0.0606112i
$726$	20.6614	−	10.9635i	0.0284592	−	0.0151012i
$727$	−254.147	−	948.488i	−0.349583	−	1.30466i	−0.887166	−	0.461450i	$-0.847329\pi$
$727$	−254.147	−	948.488i	−0.349583	−	1.30466i	0.537584	−	0.843210i	$-0.319337\pi$
$728$	76.9808	+	51.4369i	0.105743	+	0.0706551i
$729$	155.179	−	712.292i	0.212866	−	0.977081i
$730$			7.83727i			0.0107360i
$731$	−522.762	+	621.524i	−0.715132	+	0.850238i
$732$	612.159	−	183.675i	0.836283	−	0.250923i
$733$	−322.641	+	42.4765i	−0.440165	+	0.0579488i	−0.347352	−	0.937735i	$-0.612919\pi$
$733$	−322.641	+	42.4765i	−0.440165	+	0.0579488i	−0.0928128	+	0.995684i	$0.529586\pi$
$734$	31.6897	+	2.07705i	0.0431740	+	0.00282977i
$735$	−812.561	+	501.880i	−1.10553	+	0.682829i
$736$	118.816	+	40.3327i	0.161435	+	0.0547999i
$737$	129.780	+	194.229i	0.176092	+	0.263540i
$738$	11.0268	+	27.0836i	0.0149415	+	0.0366986i
$739$	583.125	−	241.538i	0.789073	−	0.326845i	0.0485022	−	0.998823i	$-0.484555\pi$
$739$	583.125	−	241.538i	0.789073	−	0.326845i	0.740571	+	0.671978i	$0.234555\pi$
$740$	−338.754	−	44.5978i	−0.457776	−	0.0602673i
$741$	−75.4602	−	105.981i	−0.101836	−	0.143024i
$742$	−25.7135	−	12.6805i	−0.0346543	−	0.0170896i
$743$	76.8443	+	87.6242i	0.103424	+	0.117933i	0.801236	−	0.598348i	$-0.204176\pi$
$743$	76.8443	+	87.6242i	0.103424	+	0.117933i	−0.697812	+	0.716281i	$0.745843\pi$
$744$	89.5075	−	2.65904i	0.120306	−	0.00357397i
$745$	−1058.40	+	521.947i	−1.42068	+	0.700600i
$746$	−0.656257	−	0.271831i	−0.000879701	−	0.000364384i
$747$	46.5381	−	2.76750i	0.0623000	−	0.00370481i
$748$	−227.087	+	236.663i	−0.303592	+	0.316394i
$749$	−712.197	+	1233.56i	−0.950864	+	1.64695i
$750$	26.2643	+	18.9413i	0.0350191	+	0.0252551i
$751$	1353.17	+	88.6915i	1.80182	+	0.118098i	0.929033	−	0.369996i	$-0.120641\pi$
$751$	1353.17	+	88.6915i	1.80182	+	0.118098i	0.872791	+	0.488094i	$0.162308\pi$
$752$	128.957	−	481.273i	0.171485	−	0.639990i
$753$	260.180	+	490.325i	0.345524	+	0.651163i
$754$	17.0252	−	1.11589i	0.0225799	−	0.00147996i
$755$	60.3660	−	303.480i	0.0799549	−	0.401961i
$756$	−356.396	+	1137.60i	−0.471423	+	1.50476i
$757$	−223.039	−	538.465i	−0.294636	−	0.711314i	−0.999997	−	0.00246584i	$-0.999215\pi$
$757$	−223.039	−	538.465i	−0.294636	−	0.711314i	0.705361	−	0.708848i	$-0.250785\pi$
$758$	5.25132	−	5.98798i	0.00692786	−	0.00789971i
$759$	302.812	−	366.709i	0.398962	−	0.483147i
$760$	−6.04522	−	6.89325i	−0.00795424	−	0.00907007i
$761$	−1075.50	−	288.178i	−1.41327	−	0.378684i	−0.530177	−	0.847887i	$-0.677875\pi$
$761$	−1075.50	−	288.178i	−1.41327	−	0.378684i	−0.883090	+	0.469203i	$0.844541\pi$
$762$	2.09062	−	1.94624i	0.00274360	−	0.00255412i
$763$	−62.8198	+	48.2033i	−0.0823326	+	0.0631760i
$764$			148.490i			0.194359i
$765$	−285.449	+	600.780i	−0.373137	+	0.785334i
$766$	47.4944			0.0620031
$767$	−215.494	−	280.837i	−0.280956	−	0.366150i
$768$	−736.565	+	169.394i	−0.959068	+	0.220565i
$769$	104.470	−	389.889i	0.135852	−	0.507007i	−0.864141	−	0.503250i	$-0.832137\pi$
$769$	104.470	−	389.889i	0.135852	−	0.507007i	0.999993	−	0.00375701i	$-0.00119590\pi$
$770$	13.9371	−	12.2225i	0.0181001	−	0.0158734i
$771$	27.7081	−	164.722i	0.0359378	−	0.213647i
$772$	346.134	+	303.551i	0.448360	+	0.393201i
$773$	−109.626	+	45.4087i	−0.141819	+	0.0587435i	−0.452464	−	0.891783i	$-0.649455\pi$
$773$	−109.626	+	45.4087i	−0.141819	+	0.0587435i	0.310645	+	0.950526i	$0.399455\pi$
$774$	2.45224	−	34.2375i	0.00316827	−	0.0442345i
$775$	−279.857	−	55.6671i	−0.361106	−	0.0718285i
$776$	5.51091	+	84.0803i	0.00710169	+	0.108351i
$777$	23.3308	−	652.310i	0.0300268	−	0.839524i
$778$	26.1362	+	7.00318i	0.0335941	+	0.00900152i
$779$	−8.79669	+	134.212i	−0.0112923	+	0.172287i
$780$	679.990	+	69.0515i	0.871782	+	0.0885276i
$781$	−573.326	−	331.010i	−0.734093	−	0.423829i
$782$	−16.1893	+	41.4869i	−0.0207024	+	0.0530523i
$783$	151.151	+	412.932i	0.193041	+	0.527372i
$784$	446.235	−	1077.31i	0.569178	−	1.37412i
$785$	−283.204	−	574.281i	−0.360769	−	0.731568i
$786$	−5.54935	−	2.98781i	−0.00706024	−	0.00380129i
$787$	−482.779	+	423.386i	−0.613443	+	0.537975i	−0.908704	−	0.417442i	$-0.862927\pi$
$787$	−482.779	+	423.386i	−0.613443	+	0.537975i	0.295261	+	0.955417i	$0.404593\pi$
$788$	281.726	−	571.284i	0.357520	−	0.724980i
$789$	1046.04	+	477.774i	1.32578	+	0.605544i
$790$	5.78318	−	43.9276i	0.00732049	−	0.0556046i
$791$	−779.937	−	1882.94i	−0.986014	−	2.38045i
$792$	3.78818	−	27.4874i	0.00478305	−	0.0347064i
$793$	582.046	−	388.910i	0.733979	−	0.490429i
$794$	14.9833	−	44.1395i	0.0188707	−	0.0555913i
$795$	−423.456	+	12.5798i	−0.532650	+	0.0158236i
$796$	−69.3391	+	1057.91i	−0.0871094	+	1.32903i
$797$	−65.8532	−	500.205i	−0.0826264	−	0.627610i	−0.981786	−	0.189989i	$-0.939155\pi$
$797$	−65.8532	−	500.205i	−0.0826264	−	0.627610i	0.899160	−	0.437620i	$-0.144179\pi$
$798$	6.00115	−	6.36863i	0.00752024	−	0.00798073i
$799$	507.125	+	160.549i	0.634700	+	0.200937i
$800$	−23.3277			−0.0291596
$801$	−191.145	−	992.302i	−0.238633	−	1.23883i
$802$	−14.2126	+	21.2707i	−0.0177215	+	0.0265220i
$803$	−105.376	+	28.2353i	−0.131227	+	0.0351623i
$804$	−578.940	−	20.7066i	−0.720075	−	0.0257545i
$805$	−697.542	+	1414.47i	−0.866511	+	1.75711i
$806$	46.4002	−	15.7507i	0.0575685	−	0.0195419i
$807$	1178.37	−	961.109i	1.46018	−	1.19096i
$808$	−98.9518	−	13.0272i	−0.122465	−	0.0161228i
$809$	−1289.52	−	256.502i	−1.59397	−	0.317060i	−0.683281	−	0.730155i	$-0.739448\pi$
$809$	−1289.52	−	256.502i	−1.59397	−	0.317060i	−0.910688	+	0.413095i	$0.864448\pi$
$810$	−5.15031	−	27.6367i	−0.00635841	−	0.0341193i
$811$	−26.3660	+	5.24451i	−0.0325104	+	0.00646673i	−0.211319	−	0.977417i	$-0.567776\pi$
$811$	−26.3660	+	5.24451i	−0.0325104	+	0.00646673i	0.178808	+	0.983884i	$0.442776\pi$
$812$	−186.110	−	694.573i	−0.229200	−	0.855385i
$813$	−1225.14	−	375.694i	−1.50694	−	0.462108i
$814$	0.990728	+	7.52533i	0.00121711	+	0.00924488i
$815$	374.793	−	216.387i	0.459868	−	0.265505i
$816$	−146.384	−	798.799i	−0.179393	−	0.978921i
$817$	78.9393	−	136.727i	0.0966209	−	0.167352i
$818$	−9.46008	+	22.8386i	−0.0115649	+	0.0279201i
$819$	−7.90271	+	1305.68i	−0.00964922	+	1.59424i
$820$	−499.640	−	499.640i	−0.609317	−	0.609317i
$821$	−1358.14	−	461.025i	−1.65425	−	0.561541i	−0.670626	−	0.741796i	$-0.733974\pi$
$821$	−1358.14	−	461.025i	−1.65425	−	0.561541i	−0.983620	+	0.180255i	$0.942308\pi$
$822$	1.17489	−	6.98465i	0.00142931	−	0.00849714i
$823$	−1114.33	+	378.263i	−1.35398	+	0.459615i	−0.901739	−	0.432280i	$-0.857709\pi$
$823$	−1114.33	+	378.263i	−1.35398	+	0.459615i	−0.452242	+	0.891895i	$0.649376\pi$
$824$	21.5636	+	16.5463i	0.0261694	+	0.0200805i
$825$	−31.3949	+	82.6546i	−0.0380544	+	0.100187i
$826$	15.6986	−	17.9008i	0.0190055	−	0.0216717i
$827$	975.913	−	652.084i	1.18006	−	0.788493i	0.198589	−	0.980083i	$-0.436364\pi$
$827$	975.913	−	652.084i	1.18006	−	0.788493i	0.981475	+	0.191589i	$0.0613642\pi$
$828$	298.351	+	1141.04i	0.360327	+	1.37807i
$829$	62.8242	−	62.8242i	0.0757831	−	0.0757831i	−0.668199	−	0.743982i	$-0.732935\pi$
$829$	62.8242	−	62.8242i	0.0757831	−	0.0757831i	0.743982	+	0.668199i	$0.232935\pi$
$830$	1.61242	−	0.795156i	0.00194267	−	0.000958019i
$831$	786.058	−	1089.96i	0.945918	−	1.31162i
$832$	−720.378	+	415.910i	−0.865839	+	0.499892i
$833$	1127.64	+	527.436i	1.35371	+	0.633177i
$834$	35.0977	−	10.5309i	0.0420835	−	0.0126269i
$835$	312.798	+	407.646i	0.374608	+	0.488199i
$836$	35.4236	−	53.0151i	0.0423727	−	0.0634152i
$837$	726.248	+	1033.16i	0.867679	+	1.23436i
$838$	−11.0883	−	55.7444i	−0.0132318	−	0.0665208i
$839$	805.316	−	52.7832i	0.959852	−	0.0629120i	0.422584	−	0.906324i	$-0.361123\pi$
$839$	805.316	−	52.7832i	0.959852	−	0.0629120i	0.537268	+	0.843412i	$0.319456\pi$
$840$	8.74204	+	91.6004i	0.0104072	+	0.109048i
$841$	456.782	+	350.501i	0.543141	+	0.416767i
$842$	34.8953	−	45.4765i	0.0414434	−	0.0540101i
$843$	191.469	−	419.201i	0.227128	−	0.497273i
$844$	1.02034	+	15.5674i	0.00120893	+	0.0184447i
$845$	13.6431	−	2.71378i	0.0161457	−	0.00321157i
$846$	−21.3324	+	7.09768i	−0.0252156	+	0.00838969i
$847$	−897.745	−	599.854i	−1.05991	−	0.708210i
$848$	410.356	−	314.877i	0.483910	−	0.371317i
$849$	826.901	−	877.535i	0.973970	−	1.03361i
$850$	0.370829	−	8.27117i	0.000436269	−	0.00973079i
$851$	−322.883	−	559.250i	−0.379416	−	0.657168i
$852$	1497.48	−	673.046i	1.75761	−	0.789960i
$853$	183.974	+	373.062i	0.215678	+	0.437353i	0.977645	−	0.210264i	$-0.0674324\pi$
$853$	183.974	+	373.062i	0.215678	+	0.437353i	−0.761966	+	0.647617i	$0.775766\pi$
$854$	33.2932	+	33.2932i	0.0389850	+	0.0389850i
$855$	34.2214	−	124.692i	0.0400250	−	0.145839i
$856$	45.6788	+	68.3631i	0.0533631	+	0.0798635i
$857$	1039.82	+	911.895i	1.21332	+	1.06406i	0.996127	+	0.0879271i	$0.0280242\pi$
$857$	1039.82	+	911.895i	1.21332	+	1.06406i	0.217196	+	0.976128i	$0.430309\pi$
$858$	−2.42797	−	14.9881i	−0.00282981	−	0.0174686i
$859$	75.5698	−	98.4845i	0.0879742	−	0.114650i	−0.747292	−	0.664495i	$-0.768647\pi$
$859$	75.5698	−	98.4845i	0.0879742	−	0.114650i	0.835267	+	0.549845i	$0.185313\pi$
$860$	266.608	+	785.403i	0.310010	+	0.913260i
$861$	859.496	−	1040.86i	0.998253	−	1.20890i
$862$	−14.7390	+	43.4198i	−0.0170987	+	0.0503710i
$863$	732.987	−	732.987i	0.849347	−	0.849347i	−0.140704	−	0.990052i	$-0.544937\pi$
$863$	732.987	−	732.987i	0.849347	−	0.849347i	0.990052	+	0.140704i	$0.0449367\pi$
$864$	74.7112	+	71.2589i	0.0864713	+	0.0824756i
$865$	−579.923	−	240.212i	−0.670431	−	0.277702i
$866$	−5.44893	−	3.14594i	−0.00629207	−	0.00363273i
$867$	858.942	−	117.927i	0.990706	−	0.136018i
$868$	−1032.58	−	1788.47i	−1.18960	−	2.06045i
$869$	611.462	−	80.5004i	0.703638	−	0.0926357i
$870$	11.5543	+	12.4115i	0.0132808	+	0.0142661i
$871$	−612.890	+	164.223i	−0.703663	+	0.188546i
$872$	0.891683	+	4.48279i	0.00102257	+	0.00514082i
$873$	−947.122	+	717.687i	−1.08490	+	0.822092i
$874$	1.68895	−	8.49094i	0.00193244	−	0.00971503i
$875$	195.109	−	1482.00i	0.222982	−	1.69372i
$876$	96.0654	−	252.915i	0.109664	−	0.288716i
$877$	383.320	+	1129.22i	0.437081	+	1.28760i	0.912946	+	0.408080i	$0.133802\pi$
$877$	383.320	+	1129.22i	0.437081	+	1.28760i	−0.475866	+	0.879518i	$0.657865\pi$
$878$	−36.7366	−	18.1165i	−0.0418412	−	0.0206338i
$879$	481.929	+	301.709i	0.548270	+	0.343241i
$880$	86.5579	+	323.038i	0.0983612	+	0.367089i
$881$	925.283	+	618.254i	1.05026	+	0.701764i	0.955876	−	0.293771i	$-0.0949104\pi$
$881$	925.283	+	618.254i	1.05026	+	0.701764i	0.0943885	+	0.995535i	$0.469910\pi$
$882$	−51.6659	+	9.95229i	−0.0585781	+	0.0112838i
$883$		−	3.78609i		−	0.00428776i	−0.999998	−	0.00214388i	$-0.999318\pi$
$883$		−	3.78609i		−	0.00428776i	0.999998	−	0.00214388i	$-0.000682418\pi$
$884$	−410.450	−	790.726i	−0.464310	−	0.894486i
$885$	80.9259	−	342.384i	0.0914417	−	0.386874i
$886$	5.47739	−	0.721112i	0.00618216	−	0.000813897i
$887$	−145.336	−	9.52583i	−0.163851	−	0.0107394i	−0.0167433	−	0.999860i	$-0.505330\pi$
$887$	−145.336	−	9.52583i	−0.163851	−	0.0107394i	−0.147108	+	0.989120i	$0.546996\pi$
$888$	−33.1743	−	17.8613i	−0.0373584	−	0.0201141i
$889$	−124.854	−	42.3822i	−0.140443	−	0.0476740i
$890$	−21.6504	−	32.4021i	−0.0243263	−	0.0364069i
$891$	353.032	−	168.815i	0.396220	−	0.189466i
$892$	72.8033	−	30.1561i	0.0816181	−	0.0338073i
$893$	−102.522	−	13.4973i	−0.114806	−	0.0151145i
$894$	−64.7197	+	6.17664i	−0.0723934	+	0.00690899i
$895$	1193.83	+	588.733i	1.33389	+	0.657802i
$896$	−148.388	−	169.204i	−0.165611	−	0.188843i
$897$	678.826	+	1099.04i	0.756773	+	1.22524i
$898$	32.9848	−	16.2663i	0.0367314	−	0.0181139i
$899$	−703.771	−	291.512i	−0.782838	−	0.324262i
$900$	−120.713	−	183.049i	−0.134126	−	0.203388i
$901$	316.204	+	452.713i	0.350948	+	0.502456i
$902$	−7.84844	+	13.5939i	−0.00870116	+	0.0150708i
$903$	−1445.23	+	649.562i	−1.60048	+	0.719337i
$904$	−117.391	−	7.69420i	−0.129857	−	0.00851129i
$905$	−374.288	+	1396.86i	−0.413578	+	1.54349i
$906$	9.04560	−	14.4488i	0.00998411	−	0.0159479i
$907$	548.003	−	35.9180i	0.604193	−	0.0396009i	0.239763	−	0.970832i	$-0.422930\pi$
$907$	548.003	−	35.9180i	0.604193	−	0.0396009i	0.364431	+	0.931231i	$0.381264\pi$
$908$	−50.1307	+	252.024i	−0.0552100	+	0.277560i
$909$	−614.893	−	1266.14i	−0.676450	−	1.39289i
$910$	19.2689	+	46.5193i	0.0211746	+	0.0511201i
$911$	237.727	−	271.076i	0.260952	−	0.297558i	−0.606496	−	0.795086i	$-0.707426\pi$
$911$	237.727	−	271.076i	0.260952	−	0.297558i	0.867448	+	0.497528i	$0.165759\pi$
$912$	55.1627	+	147.920i	0.0604854	+	0.162193i
$913$	16.5003	+	18.8149i	0.0180726	+	0.0206078i
$914$	2.45746	+	0.658475i	0.00268869	+	0.000720433i
$915$	665.158	+	203.974i	0.726948	+	0.222922i
$916$	168.525	−	129.314i	0.183979	−	0.141172i
$917$			290.934i			0.317267i
$918$	−26.4535	+	25.3572i	−0.0288165	+	0.0276222i
$919$	−1042.38			−1.13425			−0.567125	−	0.823632i	$-0.691944\pi$
$919$	−1042.38			−1.13425			−0.567125	+	0.823632i	$0.691944\pi$
$920$	55.4187	+	72.2231i	0.0602377	+	0.0785034i
$921$	−185.578	+	605.170i	−0.201496	+	0.657079i
$922$	3.70918	−	13.8429i	0.00402297	−	0.0150139i
$923$	1351.97	−	1185.65i	1.46476	−	1.28456i
$924$	−599.578	+	223.596i	−0.648894	+	0.241987i
$925$	90.2639	+	79.1593i	0.0975826	+	0.0855777i
$926$	−14.8647	+	6.15716i	−0.0160526	+	0.00664920i
$927$	−27.3851	+	382.343i	−0.0295417	+	0.412453i
$928$	−61.0801	−	12.1496i	−0.0658191	−	0.0130922i
$929$	46.5939	+	710.886i	0.0501549	+	0.765216i	0.946670	+	0.322204i	$0.104424\pi$
$929$	46.5939	+	710.886i	0.0501549	+	0.765216i	−0.896515	+	0.443012i	$0.853910\pi$
$930$	41.2784	+	25.8421i	0.0443854	+	0.0277872i
$931$	−233.759	−	62.6356i	−0.251084	−	0.0672778i
$932$	81.1883	−	1238.69i	0.0871119	−	1.32907i
$933$	−130.623	−	290.629i	−0.140004	−	0.311499i
$934$	−0.618518	−	0.357101i	−0.000662224	−	0.000382335i
$935$	−348.669	+	76.8699i	−0.372908	+	0.0822138i
$936$	67.3932	+	33.7433i	0.0720013	+	0.0360505i
$937$	170.452	−	411.507i	0.181912	−	0.439175i	−0.806448	−	0.591304i	$-0.798613\pi$
$937$	170.452	−	411.507i	0.181912	−	0.439175i	0.988361	+	0.152130i	$0.0486132\pi$
$938$	−18.8758	−	38.2763i	−0.0201234	−	0.0408063i
$939$	453.512	−	280.112i	0.482973	−	0.298309i
$940$	408.437	−	358.190i	0.434507	−	0.381053i
$941$	−123.179	+	249.782i	−0.130902	+	0.265443i	−0.952449	−	0.304698i	$-0.901445\pi$
$941$	−123.179	+	249.782i	−0.130902	+	0.265443i	0.821547	+	0.570141i	$0.193111\pi$
$942$	−3.35139	−	35.1163i	−0.00355774	−	0.0372785i
$943$	174.313	−	1324.04i	0.184849	−	1.40407i
$944$	164.381	+	396.850i	0.174132	+	0.420392i
$945$	−1010.57	+	814.115i	−1.06939	+	0.861497i
$946$	15.3201	−	10.2366i	0.0161946	−	0.0108209i
$947$	−78.0523	+	229.935i	−0.0824206	+	0.242803i	−0.980326	−	0.197385i	$-0.936755\pi$
$947$	−78.0523	+	229.935i	−0.0824206	+	0.242803i	0.897905	+	0.440188i	$0.145088\pi$
$948$	−725.071	+	1346.69i	−0.764843	+	1.42056i
$949$	19.3805	−	295.690i	0.0204221	−	0.311581i
$950$	0.210084	+	1.59575i	0.000221141	+	0.00167973i
$951$	−858.828	−	202.993i	−0.903079	−	0.213452i
$952$	93.6282	−	74.9645i	0.0983490	−	0.0787443i
$953$	−399.254			−0.418944			−0.209472	−	0.977815i	$-0.567175\pi$
$953$	−399.254			−0.418944			−0.209472	+	0.977815i	$0.567175\pi$
$954$	−22.0547	−	7.63575i	−0.0231182	−	0.00800393i
$955$	−89.8037	+	134.401i	−0.0940353	+	0.140734i
$956$	687.645	−	184.254i	0.719294	−	0.192734i
$957$	−125.251	+	200.067i	−0.130879	+	0.209057i
$958$	−23.3508	+	47.3506i	−0.0243745	+	0.0494266i
$959$	−309.598	+	105.095i	−0.322835	+	0.109588i
$960$	−772.850	−	293.553i	−0.805052	−	0.305785i
$961$	−1216.24	−	160.121i	−1.26560	−	0.166619i
$962$	−20.2210	−	4.02220i	−0.0210197	−	0.00418108i
$963$	−450.212	+	1068.57i	−0.467510	+	1.10963i
$964$	−434.689	+	86.4651i	−0.450923	+	0.0896941i
$965$	129.710	+	484.084i	0.134414	+	0.501641i
$966$	−63.5943	+	59.2023i	−0.0658326	+	0.0612861i
$967$	−57.5311	−	436.992i	−0.0594945	−	0.451905i	−0.995101	−	0.0988614i	$-0.968480\pi$
$967$	−57.5311	−	436.992i	−0.0594945	−	0.451905i	0.935607	−	0.353044i	$-0.114853\pi$
$968$	−53.9737	+	31.1618i	−0.0557580	+	0.0321919i
$969$	−160.399	+	51.7596i	−0.165530	+	0.0534155i
$970$	−22.9127	+	39.6860i	−0.0236213	+	0.0409134i
$971$	−216.042	+	521.572i	−0.222495	+	0.537149i	−0.995227	−	0.0975819i	$-0.968889\pi$
$971$	−216.042	+	521.572i	−0.222495	+	0.537149i	0.772733	+	0.634731i	$0.218889\pi$
$972$	−172.551	+	954.988i	−0.177522	+	0.982498i
$973$	−1196.08	−	1196.08i	−1.22927	−	1.22927i
$974$	−50.0157	−	16.9780i	−0.0513508	−	0.0174312i
$975$	−185.185	−	152.918i	−0.189934	−	0.156839i
$976$	−804.364	+	273.045i	−0.824143	+	0.279759i
$977$	503.015	+	385.977i	0.514856	+	0.395063i	0.833251	−	0.552895i	$-0.186477\pi$
$977$	503.015	+	385.977i	0.514856	+	0.395063i	−0.318395	+	0.947958i	$0.603144\pi$
$978$	23.5353	−	3.81257i	0.0240648	−	0.00389833i
$979$	357.661	−	407.834i	0.365333	−	0.416582i
$980$	1057.12	−	706.343i	1.07869	−	0.720758i
$981$	−45.8545	+	45.3028i	−0.0467427	+	0.0461802i
$982$	27.1897	−	27.1897i	0.0276881	−	0.0276881i
$983$	−1582.22	+	780.264i	−1.60958	+	0.793758i	−0.609583	+	0.792722i	$0.708663\pi$
$983$	−1582.22	+	780.264i	−1.60958	+	0.793758i	−0.999999	+	0.00103575i	$0.999670\pi$
$984$	−31.9421	−	71.0690i	−0.0324615	−	0.0722246i
$985$	600.495	−	346.696i	0.609640	−	0.351976i
$986$	5.27877	−	21.4637i	0.00535372	−	0.0217684i
$987$	755.306	+	711.725i	0.765255	+	0.721099i
$988$	105.432	+	137.402i	0.106712	+	0.139070i
$989$	−870.909	+	1303.41i	−0.880596	+	1.31790i
$990$	10.0183	−	11.2851i	0.0101195	−	0.0113991i
$991$	46.3798	+	233.167i	0.0468010	+	0.235284i	0.997105	−	0.0760397i	$-0.0242276\pi$
$991$	46.3798	+	233.167i	0.0468010	+	0.235284i	−0.950304	+	0.311324i	$0.899228\pi$
$992$	−178.473	+	11.6977i	−0.179912	+	0.0117921i
$993$	−698.918	−	319.229i	−0.703845	−	0.321479i
$994$	95.9553	+	73.6291i	0.0965345	+	0.0740735i
$995$	−702.562	+	915.596i	−0.706092	+	0.920197i
$996$	−61.7807	+	5.89614i	−0.0620288	+	0.00591982i
$997$	−33.1821	−	506.261i	−0.0332819	−	0.507784i	−0.981660	−	0.190641i	$-0.938943\pi$
$997$	−33.1821	−	506.261i	−0.0332819	−	0.507784i	0.948378	−	0.317143i	$-0.102723\pi$
$998$	59.5960	−	11.8544i	0.0597155	−	0.0118781i
$999$	−47.2793	−	529.250i	−0.0473266	−	0.529780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.7.18	✓	544
9.4	even	3	inner	153.3.t.a.58.17	yes	544
17.5	odd	16	inner	153.3.t.a.124.17	yes	544
153.22	odd	48	inner	153.3.t.a.22.18	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.18	✓	544	1.1	even	1	trivial
153.3.t.a.22.18	yes	544	153.22	odd	48	inner
153.3.t.a.58.17	yes	544	9.4	even	3	inner
153.3.t.a.124.17	yes	544	17.5	odd	16	inner

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.t (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0485999 - 0.0633367i) q^{2} +(-0.879538 + 2.86817i) q^{3} +(1.03363 - 3.85755i) q^{4} +(3.26851 - 2.86641i) q^{5} +(0.224406 - 0.0836860i) q^{6} +(-8.31214 - 7.28955i) q^{7} +(-0.589587 + 0.244215i) q^{8} +(-7.45283 - 5.04533i) q^{9} +(-0.340399 - 0.0677095i) q^{10} +(-0.315968 - 4.82074i) q^{11} +(10.1550 + 6.35748i) q^{12} +(12.6754 + 3.39635i) q^{13} +(-0.0577264 + 0.880735i) q^{14} +(5.34658 + 11.8958i) q^{15} +(-13.7902 - 7.96178i) q^{16} +(9.15087 - 14.3270i) q^{17} +(0.0426524 + 0.717240i) q^{18} +(-1.26468 + 3.05321i) q^{19} +(-7.67889 - 15.5712i) q^{20} +(28.2185 - 17.4292i) q^{21} +(-0.289974 + 0.254300i) q^{22} +(14.5130 - 29.4295i) q^{23} +(-0.181886 - 1.90583i) q^{24} +(-0.796275 + 6.04831i) q^{25} +(-0.400908 - 0.967877i) q^{26} +(21.0259 - 16.9384i) q^{27} +(-36.7114 + 24.5298i) q^{28} +(-5.23502 + 15.4219i) q^{29} +(0.493596 - 0.916769i) q^{30} +(-3.05911 + 46.6731i) q^{31} +(0.499119 + 3.79119i) q^{32} +(14.1046 + 3.33378i) q^{33} +(-1.35215 + 0.116703i) q^{34} -48.0632 q^{35} +(-27.1660 + 23.5346i) q^{36} +(10.9336 - 16.3633i) q^{37} +(0.254844 - 0.0682851i) q^{38} +(-20.8898 + 33.3679i) q^{39} +(-1.22705 + 2.48822i) q^{40} +(38.5388 - 13.0821i) q^{41} +(-2.47533 - 0.940209i) q^{42} +(-47.3643 - 6.23562i) q^{43} +(-18.9228 - 3.76399i) q^{44} +(-38.8217 + 4.87212i) q^{45} +(-2.56930 + 0.511065i) q^{46} +(8.09848 + 30.2239i) q^{47} +(34.9648 - 32.5500i) q^{48} +(9.55832 + 72.6027i) q^{49} +(0.421779 - 0.243514i) q^{50} +(33.0436 + 38.8474i) q^{51} +(26.2032 - 45.3852i) q^{52} +(-12.4306 + 30.0102i) q^{53} +(-2.09468 - 0.508506i) q^{54} +(-14.8510 - 14.8510i) q^{55} +(6.68094 + 2.26788i) q^{56} +(-7.64479 - 6.31273i) q^{57} +(1.23119 - 0.417933i) q^{58} +(-21.4012 - 16.4217i) q^{59} +(51.4149 - 8.32888i) q^{60} +(35.1729 - 40.1070i) q^{61} +(3.10479 - 2.07455i) q^{62} +(25.1707 + 96.2652i) q^{63} +(-44.8228 + 44.8228i) q^{64} +(51.1649 - 25.2317i) q^{65} +(-0.474334 - 1.05536i) q^{66} +(-41.8749 + 24.1765i) q^{67} +(-45.8083 - 50.1086i) q^{68} +(71.6441 + 67.5102i) q^{69} +(2.33587 + 3.04416i) q^{70} +(76.1317 - 113.939i) q^{71} +(5.62623 + 1.15457i) q^{72} +(-4.40542 - 22.1475i) q^{73} +(-1.56777 + 0.102757i) q^{74} +(-16.6472 - 7.60357i) q^{75} +(10.4707 + 8.03444i) q^{76} +(-32.5147 + 42.3740i) q^{77} +(3.12865 - 0.298588i) q^{78} +(8.34938 + 127.387i) q^{79} +(-67.8952 + 13.5052i) q^{80} +(30.0892 + 75.2040i) q^{81} +(-2.70156 - 1.80513i) q^{82} +(-4.10960 + 3.15341i) q^{83} +(-38.0666 - 126.870i) q^{84} +(-11.1572 - 73.0580i) q^{85} +(1.90696 + 3.30295i) q^{86} +(-39.6282 - 28.5791i) q^{87} +(1.36359 + 2.76508i) q^{88} +(79.3959 + 79.3959i) q^{89} +(2.19531 + 2.22205i) q^{90} +(-80.6014 - 120.629i) q^{91} +(-98.5246 - 86.4037i) q^{92} +(-131.176 - 49.8248i) q^{93} +(1.52070 - 1.98181i) q^{94} +(4.61812 + 13.6046i) q^{95} +(-11.3128 - 1.90293i) q^{96} +(42.4416 - 125.029i) q^{97} +(4.13388 - 4.13388i) q^{98} +(-21.9674 + 37.5223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) \) 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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