LMFDB - Embedded newform 138.4.e.b.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,4,Mod(13,138)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.14226358079$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	138.25
Dual form			138.4.e.b.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68251 + 1.08128i) q^{2} +(0.426945 + 2.96946i) q^{3} +(1.66166 + 3.63853i) q^{4} +(16.0712 + 4.71893i) q^{5} +(-2.49249 + 5.45779i) q^{6} +(17.1563 - 19.7994i) q^{7} +(-1.13852 + 7.91857i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})$	\(q+(1.68251 + 1.08128i) q^{2} +(0.426945 + 2.96946i) q^{3} +(1.66166 + 3.63853i) q^{4} +(16.0712 + 4.71893i) q^{5} +(-2.49249 + 5.45779i) q^{6} +(17.1563 - 19.7994i) q^{7} +(-1.13852 + 7.91857i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(21.9374 + 25.3171i) q^{10} +(2.91288 - 1.87200i) q^{11} +(-10.0950 + 6.48769i) q^{12} +(-15.3367 - 17.6995i) q^{13} +(50.2742 - 14.7619i) q^{14} +(-7.15118 + 49.7376i) q^{15} +(-10.4778 + 12.0920i) q^{16} +(-29.3367 + 64.2383i) q^{17} +(-17.2709 - 5.07119i) q^{18} +(-2.36747 - 5.18404i) q^{19} +(9.53491 + 66.3167i) q^{20} +(66.1183 + 42.4917i) q^{21} +6.92510 q^{22} +(-80.0356 + 75.9032i) q^{23} -24.0000 q^{24} +(130.858 + 84.0975i) q^{25} +(-6.66595 - 46.3627i) q^{26} +(-11.2162 - 24.5601i) q^{27} +(100.548 + 29.5237i) q^{28} +(48.6772 - 106.588i) q^{29} +(-65.8122 + 75.9513i) q^{30} +(14.9079 - 103.687i) q^{31} +(-30.7038 + 9.01544i) q^{32} +(6.80247 + 7.85046i) q^{33} +(-118.819 + 76.3603i) q^{34} +(369.154 - 237.241i) q^{35} +(-23.5750 - 27.2070i) q^{36} +(-369.031 + 108.357i) q^{37} +(1.62212 - 11.2821i) q^{38} +(46.0100 - 53.0984i) q^{39} +(-55.6645 + 121.888i) q^{40} +(-324.440 - 95.2641i) q^{41} +(65.2991 + 142.985i) q^{42} +(-31.1314 - 216.524i) q^{43} +(11.6515 + 7.48799i) q^{44} -150.747 q^{45} +(-216.733 + 41.1667i) q^{46} +452.564 q^{47} +(-40.3802 - 25.9508i) q^{48} +(-48.8642 - 339.858i) q^{49} +(129.237 + 282.989i) q^{50} +(-203.279 - 59.6880i) q^{51} +(38.9156 - 85.2134i) q^{52} +(389.707 - 449.746i) q^{53} +(7.68500 - 53.4504i) q^{54} +(55.6473 - 16.3395i) q^{55} +(137.250 + 158.395i) q^{56} +(14.3830 - 9.24342i) q^{57} +(197.152 - 126.702i) q^{58} +(81.6101 + 94.1831i) q^{59} +(-192.854 + 56.6271i) q^{60} +(-83.4823 + 580.632i) q^{61} +(137.197 - 158.334i) q^{62} +(-97.9487 + 214.478i) q^{63} +(-61.4076 - 18.0309i) q^{64} +(-162.956 - 356.824i) q^{65} +(2.95663 + 20.5638i) q^{66} +(-587.346 - 377.464i) q^{67} -282.481 q^{68} +(-259.563 - 205.256i) q^{69} +877.627 q^{70} +(118.054 + 75.8687i) q^{71} +(-10.2467 - 71.2671i) q^{72} +(-265.030 - 580.336i) q^{73} +(-738.062 - 216.715i) q^{74} +(-193.855 + 424.484i) q^{75} +(14.9283 - 17.2282i) q^{76} +(12.9098 - 89.7898i) q^{77} +(134.826 - 39.5886i) q^{78} +(572.261 + 660.425i) q^{79} +(-225.452 + 144.889i) q^{80} +(68.1415 - 43.7919i) q^{81} +(-442.865 - 511.093i) q^{82} +(1026.52 - 301.412i) q^{83} +(-44.7410 + 311.180i) q^{84} +(-774.611 + 893.949i) q^{85} +(181.744 - 397.964i) q^{86} +(337.293 + 99.0380i) q^{87} +(11.5072 + 25.1972i) q^{88} +(-225.756 - 1570.17i) q^{89} +(-253.633 - 163.000i) q^{90} -613.558 q^{91} +(-409.168 - 165.086i) q^{92} +314.260 q^{93} +(761.441 + 489.349i) q^{94} +(-13.5850 - 94.4857i) q^{95} +(-39.8798 - 87.3247i) q^{96} +(-558.555 - 164.007i) q^{97} +(285.268 - 624.650i) q^{98} +(-20.4074 + 23.5514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 6 q^{5} + 18 q^{6} + 22 q^{7} - 24 q^{8} - 27 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 6 * q^5 + 18 * q^6 + 22 * q^7 - 24 * q^8 - 27 * q^9	\( 30 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 6 q^{5} + 18 q^{6} + 22 q^{7} - 24 q^{8} - 27 q^{9} - 56 q^{10} - 105 q^{11} + 36 q^{12} - 21 q^{13} - 114 q^{15} - 48 q^{16} + 41 q^{17} - 54 q^{18} - 149 q^{19} + 152 q^{20} - 33 q^{21} - 584 q^{22} + 472 q^{23} - 720 q^{24} + 281 q^{25} + 90 q^{26} + 81 q^{27} - 1505 q^{29} + 168 q^{30} - 991 q^{31} - 96 q^{32} + 315 q^{33} - 1392 q^{34} + 646 q^{35} - 108 q^{36} + 103 q^{37} - 606 q^{38} + 63 q^{39} + 40 q^{40} + 966 q^{41} - 132 q^{42} + 1532 q^{43} - 420 q^{44} - 54 q^{45} - 46 q^{46} + 1718 q^{47} + 144 q^{48} + 843 q^{49} + 122 q^{50} + 273 q^{51} - 40 q^{52} + 911 q^{53} + 162 q^{54} + 2112 q^{55} + 176 q^{56} - 972 q^{57} + 1060 q^{58} + 415 q^{59} + 72 q^{60} - 1424 q^{61} - 464 q^{62} + 198 q^{63} - 192 q^{64} + 5246 q^{65} + 300 q^{66} - 5 q^{67} - 144 q^{68} - 1449 q^{69} + 2744 q^{70} + 4415 q^{71} - 216 q^{72} + 2890 q^{73} + 206 q^{74} - 183 q^{75} - 464 q^{76} - 5116 q^{77} + 1050 q^{78} - 3436 q^{79} - 96 q^{80} - 243 q^{81} - 4668 q^{82} + 5757 q^{83} - 132 q^{84} + 568 q^{85} + 710 q^{86} - 138 q^{87} + 1624 q^{88} + 375 q^{89} - 108 q^{90} - 8002 q^{91} - 48 q^{92} - 690 q^{93} + 1082 q^{94} - 5577 q^{95} + 288 q^{96} + 3179 q^{97} - 4100 q^{98} - 945 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 6 * q^5 + 18 * q^6 + 22 * q^7 - 24 * q^8 - 27 * q^9 - 56 * q^10 - 105 * q^11 + 36 * q^12 - 21 * q^13 - 114 * q^15 - 48 * q^16 + 41 * q^17 - 54 * q^18 - 149 * q^19 + 152 * q^20 - 33 * q^21 - 584 * q^22 + 472 * q^23 - 720 * q^24 + 281 * q^25 + 90 * q^26 + 81 * q^27 - 1505 * q^29 + 168 * q^30 - 991 * q^31 - 96 * q^32 + 315 * q^33 - 1392 * q^34 + 646 * q^35 - 108 * q^36 + 103 * q^37 - 606 * q^38 + 63 * q^39 + 40 * q^40 + 966 * q^41 - 132 * q^42 + 1532 * q^43 - 420 * q^44 - 54 * q^45 - 46 * q^46 + 1718 * q^47 + 144 * q^48 + 843 * q^49 + 122 * q^50 + 273 * q^51 - 40 * q^52 + 911 * q^53 + 162 * q^54 + 2112 * q^55 + 176 * q^56 - 972 * q^57 + 1060 * q^58 + 415 * q^59 + 72 * q^60 - 1424 * q^61 - 464 * q^62 + 198 * q^63 - 192 * q^64 + 5246 * q^65 + 300 * q^66 - 5 * q^67 - 144 * q^68 - 1449 * q^69 + 2744 * q^70 + 4415 * q^71 - 216 * q^72 + 2890 * q^73 + 206 * q^74 - 183 * q^75 - 464 * q^76 - 5116 * q^77 + 1050 * q^78 - 3436 * q^79 - 96 * q^80 - 243 * q^81 - 4668 * q^82 + 5757 * q^83 - 132 * q^84 + 568 * q^85 + 710 * q^86 - 138 * q^87 + 1624 * q^88 + 375 * q^89 - 108 * q^90 - 8002 * q^91 - 48 * q^92 - 690 * q^93 + 1082 * q^94 - 5577 * q^95 + 288 * q^96 + 3179 * q^97 - 4100 * q^98 - 945 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	1.68251	+	1.08128i	0.594856	+	0.382291i
$2$	1.68251	+	1.08128i	0.594856	+	0.382291i
$3$	0.426945	+	2.96946i	0.0821655	+	0.571474i
$3$	0.426945	+	2.96946i	0.0821655	+	0.571474i
$4$	1.66166	+	3.63853i	0.207708	+	0.454816i
$5$	16.0712	+	4.71893i	1.43745	+	0.422074i	0.905371	−	0.424620i	$-0.139592\pi$
$5$	16.0712	+	4.71893i	1.43745	+	0.422074i	0.532080	+	0.846694i	$0.321411\pi$
$6$	−2.49249	+	5.45779i	−0.169592	+	0.371356i
$7$	17.1563	−	19.7994i	0.926351	−	1.06907i	−0.0710825	−	0.997470i	$-0.522645\pi$
$7$	17.1563	−	19.7994i	0.926351	−	1.06907i	0.997434	−	0.0715959i	$-0.0228092\pi$
$8$	−1.13852	+	7.91857i	−0.0503159	+	0.349955i
$9$	−8.63544	+	2.53559i	−0.319831	+	0.0939109i
$10$	21.9374	+	25.3171i	0.693722	+	0.800597i
$11$	2.91288	−	1.87200i	0.0798425	−	0.0513117i	−0.500110	−	0.865962i	$-0.666707\pi$
$11$	2.91288	−	1.87200i	0.0798425	−	0.0513117i	0.579953	+	0.814650i	$0.303071\pi$
$12$	−10.0950	+	6.48769i	−0.242849	+	0.156070i
$13$	−15.3367	−	17.6995i	−0.327202	−	0.377611i	0.568184	−	0.822901i	$-0.307646\pi$
$13$	−15.3367	−	17.6995i	−0.327202	−	0.377611i	−0.895386	+	0.445290i	$0.853101\pi$
$14$	50.2742	−	14.7619i	0.959740	−	0.281805i
$15$	−7.15118	+	49.7376i	−0.123095	+	0.856145i
$16$	−10.4778	+	12.0920i	−0.163715	+	0.188937i
$17$	−29.3367	+	64.2383i	−0.418540	+	0.916476i	0.576509	+	0.817091i	$0.304415\pi$
$17$	−29.3367	+	64.2383i	−0.418540	+	0.916476i	−0.995049	+	0.0993847i	$0.968313\pi$
$18$	−17.2709	−	5.07119i	−0.226155	−	0.0664050i
$19$	−2.36747	−	5.18404i	−0.0285861	−	0.0625948i	0.894800	−	0.446466i	$-0.147318\pi$
$19$	−2.36747	−	5.18404i	−0.0285861	−	0.0625948i	−0.923386	+	0.383872i	$0.874591\pi$
$20$	9.53491	+	66.3167i	0.106604	+	0.741444i
$21$	66.1183	+	42.4917i	0.687057	+	0.441545i
$22$	6.92510			0.0671108
$23$	−80.0356	+	75.9032i	−0.725590	+	0.688127i
$23$	−80.0356	+	75.9032i	−0.725590	+	0.688127i
$24$	−24.0000			−0.204124
$25$	130.858	+	84.0975i	1.04687	+	0.672780i
$26$	−6.66595	−	46.3627i	−0.0502808	−	0.349711i
$27$	−11.2162	−	24.5601i	−0.0799467	−	0.175059i
$28$	100.548	+	29.5237i	0.678639	+	0.199266i
$29$	48.6772	−	106.588i	0.311694	−	0.682515i	−0.687345	−	0.726331i	$-0.741224\pi$
$29$	48.6772	−	106.588i	0.311694	−	0.682515i	0.999040	+	0.0438154i	$0.0139514\pi$
$30$	−65.8122	+	75.9513i	−0.400520	+	0.462225i
$31$	14.9079	−	103.687i	0.0863724	−	0.600733i	−0.899961	−	0.435971i	$-0.856405\pi$
$31$	14.9079	−	103.687i	0.0863724	−	0.600733i	0.986333	−	0.164762i	$-0.0526857\pi$
$32$	−30.7038	+	9.01544i	−0.169616	+	0.0498038i
$33$	6.80247	+	7.85046i	0.0358836	+	0.0414118i
$34$	−118.819	+	76.3603i	−0.599332	+	0.385167i
$35$	369.154	−	237.241i	1.78281	−	1.14574i
$36$	−23.5750	−	27.2070i	−0.109143	−	0.125958i
$37$	−369.031	+	108.357i	−1.63969	+	0.481455i	−0.966210	−	0.257755i	$-0.917017\pi$
$37$	−369.031	+	108.357i	−1.63969	+	0.481455i	−0.673475	+	0.739210i	$0.735199\pi$
$38$	1.62212	−	11.2821i	0.00692480	−	0.0481631i
$39$	46.0100	−	53.0984i	0.188910	−	0.218014i
$40$	−55.6645	+	121.888i	−0.220033	+	0.481806i
$41$	−324.440	−	95.2641i	−1.23583	−	0.362872i	−0.402382	−	0.915472i	$-0.631818\pi$
$41$	−324.440	−	95.2641i	−1.23583	−	0.362872i	−0.833447	+	0.552600i	$0.813636\pi$
$42$	65.2991	+	142.985i	0.239902	+	0.525311i
$43$	−31.1314	−	216.524i	−0.110407	−	0.767896i	−0.967525	−	0.252776i	$-0.918656\pi$
$43$	−31.1314	−	216.524i	−0.110407	−	0.767896i	0.857118	−	0.515120i	$-0.172253\pi$
$44$	11.6515	+	7.48799i	0.0399212	+	0.0256558i
$45$	−150.747			−0.499379
$46$	−216.733	+	41.1667i	−0.694686	+	0.131950i
$47$	452.564			1.40454			0.702268	−	0.711913i	$-0.252171\pi$
$47$	452.564			1.40454			0.702268	+	0.711913i	$0.252171\pi$
$48$	−40.3802	−	25.9508i	−0.121424	−	0.0780348i
$49$	−48.8642	−	339.858i	−0.142461	−	0.990840i
$50$	129.237	+	282.989i	0.365537	+	0.800415i
$51$	−203.279	−	59.6880i	−0.558131	−	0.163882i
$52$	38.9156	−	85.2134i	0.103781	−	0.227249i
$53$	389.707	−	449.746i	1.01001	−	1.16561i	0.0238633	−	0.999715i	$-0.492403\pi$
$53$	389.707	−	449.746i	1.01001	−	1.16561i	0.986143	−	0.165895i	$-0.0530512\pi$
$54$	7.68500	−	53.4504i	0.0193666	−	0.134698i
$55$	55.6473	−	16.3395i	0.136427	−	0.0400586i
$56$	137.250	+	158.395i	0.327515	+	0.377972i
$57$	14.3830	−	9.24342i	0.0334225	−	0.0214793i
$58$	197.152	−	126.702i	0.446333	−	0.286841i
$59$	81.6101	+	94.1831i	0.180080	+	0.207824i	0.838612	−	0.544729i	$-0.183368\pi$
$59$	81.6101	+	94.1831i	0.180080	+	0.207824i	−0.658532	+	0.752553i	$0.728822\pi$
$60$	−192.854	+	56.6271i	−0.414956	+	0.121842i
$61$	−83.4823	+	580.632i	−0.175226	+	1.21873i	0.692401	+	0.721512i	$0.256553\pi$
$61$	−83.4823	+	580.632i	−0.175226	+	1.21873i	−0.867628	+	0.497214i	$0.834356\pi$
$62$	137.197	−	158.334i	0.281034	−	0.324330i
$63$	−97.9487	+	214.478i	−0.195879	+	0.428915i
$64$	−61.4076	−	18.0309i	−0.119937	−	0.0352166i
$65$	−162.956	−	356.824i	−0.310957	−	0.680901i
$66$	2.95663	+	20.5638i	0.00551419	+	0.0383520i
$67$	−587.346	−	377.464i	−1.07098	−	0.688278i	−0.118524	−	0.992951i	$-0.537816\pi$
$67$	−587.346	−	377.464i	−1.07098	−	0.688278i	−0.952457	+	0.304674i	$0.901453\pi$
$68$	−282.481			−0.503762
$69$	−259.563	−	205.256i	−0.452865	−	0.358116i
$70$	877.627			1.49852
$71$	118.054	+	75.8687i	0.197330	+	0.126816i	0.635575	−	0.772039i	$-0.280763\pi$
$71$	118.054	+	75.8687i	0.197330	+	0.126816i	−0.438245	+	0.898856i	$0.644400\pi$
$72$	−10.2467	−	71.2671i	−0.0167720	−	0.116652i
$73$	−265.030	−	580.336i	−0.424924	−	0.930454i	−0.994123	−	0.108254i	$-0.965474\pi$
$73$	−265.030	−	580.336i	−0.424924	−	0.930454i	0.569199	−	0.822200i	$-0.307253\pi$
$74$	−738.062	−	216.715i	−1.15943	−	0.340440i
$75$	−193.855	+	424.484i	−0.298460	+	0.653536i
$76$	14.9283	−	17.2282i	0.0225316	−	0.0260028i
$77$	12.9098	−	89.7898i	0.0191066	−	0.132890i
$78$	134.826	−	39.5886i	0.195719	−	0.0574683i
$79$	572.261	+	660.425i	0.814992	+	0.940551i	0.999103	−	0.0423541i	$-0.0134858\pi$
$79$	572.261	+	660.425i	0.814992	+	0.940551i	−0.184110	+	0.982906i	$0.558940\pi$
$80$	−225.452	+	144.889i	−0.315078	+	0.202488i
$81$	68.1415	−	43.7919i	0.0934726	−	0.0600712i
$82$	−442.865	−	511.093i	−0.596418	−	0.688303i
$83$	1026.52	−	301.412i	1.35753	−	0.398606i	0.479637	−	0.877467i	$-0.340768\pi$
$83$	1026.52	−	301.412i	1.35753	−	0.398606i	0.877891	+	0.478861i	$0.158950\pi$
$84$	−44.7410	+	311.180i	−0.0581147	+	0.404197i
$85$	−774.611	+	893.949i	−0.988452	+	1.14073i
$86$	181.744	−	397.964i	0.227883	−	0.498995i
$87$	337.293	+	99.0380i	0.415650	+	0.122046i
$88$	11.5072	+	25.1972i	0.0139394	+	0.0305230i
$89$	−225.756	−	1570.17i	−0.268878	−	1.87009i	−0.459156	−	0.888356i	$-0.651848\pi$
$89$	−225.756	−	1570.17i	−0.268878	−	1.87009i	0.190278	−	0.981730i	$-0.439061\pi$
$90$	−253.633	−	163.000i	−0.297058	−	0.190908i
$91$	−613.558			−0.706795
$92$	−409.168	−	165.086i	−0.463682	−	0.187081i
$93$	314.260			0.350400
$94$	761.441	+	489.349i	0.835497	+	0.536941i
$95$	−13.5850	−	94.4857i	−0.0146715	−	0.102042i
$96$	−39.8798	−	87.3247i	−0.0423981	−	0.0928389i
$97$	−558.555	−	164.007i	−0.584667	−	0.171674i	−0.0239953	−	0.999712i	$-0.507639\pi$
$97$	−558.555	−	164.007i	−0.584667	−	0.171674i	−0.560671	+	0.828038i	$0.689457\pi$
$98$	285.268	−	624.650i	0.294045	−	0.643869i
$99$	−20.4074	+	23.5514i	−0.0207174	+	0.0239091i
$100$	−88.5492	+	615.873i	−0.0885492	+	0.615873i
$101$	−194.953	+	57.2434i	−0.192065	+	0.0563953i	−0.376350	−	0.926477i	$-0.622821\pi$
$101$	−194.953	+	57.2434i	−0.192065	+	0.0563953i	0.184286	+	0.982873i	$0.441003\pi$
$102$	−277.478	−	320.227i	−0.269357	−	0.310855i
$103$	549.826	−	353.352i	0.525981	−	0.338027i	−0.250553	−	0.968103i	$-0.580612\pi$
$103$	549.826	−	353.352i	0.525981	−	0.338027i	0.776534	+	0.630076i	$0.216976\pi$
$104$	157.616	−	101.293i	0.148610	−	0.0955060i
$105$	862.085	+	994.900i	0.801247	+	0.924688i
$106$	1141.99	−	335.317i	1.04641	−	0.307254i
$107$	−164.001	+	1140.65i	−0.148174	+	1.03057i	0.771033	+	0.636796i	$0.219741\pi$
$107$	−164.001	+	1140.65i	−0.148174	+	1.03057i	−0.919206	+	0.393776i	$0.871169\pi$
$108$	70.7250	−	81.6210i	0.0630140	−	0.0727220i
$109$	−686.664	+	1503.59i	−0.603399	+	1.32126i	0.323599	+	0.946194i	$0.395107\pi$
$109$	−686.664	+	1503.59i	−0.603399	+	1.32126i	−0.926998	+	0.375066i	$0.877620\pi$
$110$	111.295	+	32.6791i	0.0964684	+	0.0283257i
$111$	−479.319	−	1049.56i	−0.409864	−	0.897478i
$112$	59.6546	+	414.907i	0.0503288	+	0.350045i
$113$	1697.88	+	1091.16i	1.41348	+	0.908387i	0.999998	−	0.00212551i	$-0.000676570\pi$
$113$	1697.88	+	1091.16i	1.41348	+	0.908387i	0.413481	+	0.910513i	$0.364313\pi$
$114$	34.1943			0.0280929
$115$	−1644.45	+	842.173i	−1.33344	+	0.682896i
$116$	468.709			0.375160
$117$	177.317	+	113.955i	0.140111	+	0.0900440i
$118$	35.4711	+	246.707i	0.0276727	+	0.192468i
$119$	768.572	+	1682.94i	0.592058	+	1.29643i
$120$	−385.709	−	113.254i	−0.293418	−	0.0861554i
$121$	−547.937	+	1199.81i	−0.411673	+	0.901438i
$122$	−768.286	+	886.650i	−0.570142	+	0.657979i
$123$	144.366	−	1004.09i	0.105829	−	0.736059i
$124$	402.040	−	118.050i	0.291163	−	0.0854932i
$125$	335.111	+	386.738i	0.239786	+	0.276727i
$126$	−396.710	+	254.950i	−0.280490	+	0.180260i
$127$	315.541	−	202.786i	0.220470	−	0.141688i	−0.425744	−	0.904844i	$-0.639988\pi$
$127$	315.541	−	202.786i	0.220470	−	0.141688i	0.646214	+	0.763156i	$0.276351\pi$
$128$	−83.8222	−	96.7359i	−0.0578821	−	0.0667995i
$129$	629.668	−	184.887i	0.429761	−	0.126189i
$130$	111.653	−	776.560i	0.0753275	−	0.523914i
$131$	−176.684	+	203.904i	−0.117839	+	0.135994i	−0.811604	−	0.584208i	$-0.801405\pi$
$131$	−176.684	+	203.904i	−0.117839	+	0.135994i	0.693765	+	0.720202i	$0.255951\pi$
$132$	−17.2607	+	37.7958i	−0.0113815	+	0.0249220i
$133$	−143.258	−	42.0643i	−0.0933987	−	0.0274243i
$134$	−580.068	−	1270.17i	−0.373957	−	0.818852i
$135$	−64.3606	−	447.638i	−0.0410317	−	0.285382i
$136$	−475.276	−	305.441i	−0.299666	−	0.192584i
$137$	−687.105			−0.428492			−0.214246	−	0.976780i	$-0.568729\pi$
$137$	−687.105			−0.428492			−0.214246	+	0.976780i	$0.568729\pi$
$138$	−214.776	−	626.006i	−0.132485	−	0.386153i
$139$	1387.12			0.846432			0.423216	−	0.906029i	$-0.360901\pi$
$139$	1387.12			0.846432			0.423216	+	0.906029i	$0.360901\pi$
$140$	1476.61	+	948.962i	0.891405	+	0.572871i
$141$	193.220	+	1343.87i	0.115404	+	0.802655i
$142$	116.591	+	255.299i	0.0689022	+	0.150875i
$143$	−77.8072	−	22.8463i	−0.0455005	−	0.0133601i
$144$	59.8198	−	130.987i	0.0346179	−	0.0758027i
$145$	1285.28	−	1483.30i	0.736117	−	0.849524i
$146$	181.591	−	1262.99i	0.102935	−	0.715931i
$147$	988.335	−	290.201i	0.554534	−	0.162826i
$148$	−1007.47	−	1162.68i	−0.559548	−	0.645753i
$149$	−2011.95	+	1293.00i	−1.10621	+	0.710919i	−0.960464	−	0.278403i	$-0.910195\pi$
$149$	−2011.95	+	1293.00i	−1.10621	+	0.710919i	−0.145747	+	0.989322i	$0.546559\pi$
$150$	−785.150	+	504.585i	−0.427381	+	0.274661i
$151$	356.532	+	411.460i	0.192147	+	0.221749i	0.843646	−	0.536900i	$-0.180405\pi$
$151$	356.532	+	411.460i	0.192147	+	0.221749i	−0.651499	+	0.758650i	$0.725859\pi$
$152$	43.7456	−	12.8449i	0.0233437	−	0.00685432i
$153$	90.4527	−	629.112i	0.0477952	−	0.332423i
$154$	118.809	−	137.113i	0.0621681	−	0.0717459i
$155$	728.879	−	1596.02i	0.377710	−	0.827069i
$156$	269.653	+	79.1772i	0.138394	+	0.0406362i
$157$	918.615	+	2011.49i	0.466965	+	1.02251i	0.985844	+	0.167663i	$0.0536220\pi$
$157$	918.615	+	2011.49i	0.466965	+	1.02251i	−0.518880	+	0.854847i	$0.673651\pi$
$158$	248.728	+	1729.94i	0.125239	+	0.871057i
$159$	1501.89	+	965.204i	0.749103	+	0.481419i
$160$	−535.990			−0.264836
$161$	129.725	+	2886.87i	0.0635017	+	1.41315i
$162$	162.000			0.0785674
$163$	−338.858	−	217.771i	−0.162831	−	0.104645i	0.456688	−	0.889627i	$-0.349036\pi$
$163$	−338.858	−	217.771i	−0.162831	−	0.104645i	−0.619518	+	0.784982i	$0.712672\pi$
$164$	−192.488	−	1338.78i	−0.0916509	−	0.637446i
$165$	72.2780	+	158.267i	0.0341020	+	0.0746730i
$166$	2053.03	+	602.825i	0.959917	+	0.281857i
$167$	−222.298	+	486.764i	−0.103006	+	0.225551i	−0.954117	−	0.299435i	$-0.903202\pi$
$167$	−222.298	+	486.764i	−0.103006	+	0.225551i	0.851111	+	0.524985i	$0.175929\pi$
$168$	−411.750	+	475.185i	−0.189091	+	0.218222i
$169$	234.608	−	1631.74i	0.106786	−	0.742711i
$170$	−2269.90	+	666.503i	−1.02408	+	0.300697i
$171$	33.5888	+	38.7635i	0.0150210	+	0.0173352i
$172$	736.097	−	473.061i	0.326319	−	0.209713i
$173$	−3297.21	+	2118.99i	−1.44903	+	0.931234i	−0.449754	+	0.893152i	$0.648489\pi$
$173$	−3297.21	+	2118.99i	−1.44903	+	0.931234i	−0.999275	+	0.0380822i	$0.987875\pi$
$174$	460.409	+	531.340i	0.200595	+	0.231499i
$175$	3910.12	−	1148.11i	1.68901	−	0.495939i
$176$	−7.88436	+	54.8369i	−0.00337674	+	0.0234857i
$177$	−244.830	+	282.549i	−0.103969	+	0.119987i
$178$	1317.96	−	2885.93i	0.554973	−	1.21522i
$179$	−1192.52	−	350.155i	−0.497949	−	0.146211i	0.0231076	−	0.999733i	$-0.492644\pi$
$179$	−1192.52	−	350.155i	−0.497949	−	0.146211i	−0.521057	+	0.853522i	$0.674462\pi$
$180$	−250.490	−	548.497i	−0.103725	−	0.227125i
$181$	−565.231	−	3931.27i	−0.232118	−	1.61441i	−0.688914	−	0.724843i	$-0.741912\pi$
$181$	−565.231	−	3931.27i	−0.232118	−	1.61441i	0.456797	−	0.889571i	$-0.348997\pi$
$182$	−1032.32	−	663.429i	−0.420442	−	0.270201i
$183$	−1759.81			−0.710868
$184$	−509.923	−	720.185i	−0.204305	−	0.288548i
$185$	−6442.10			−2.56018
$186$	528.744	+	339.803i	0.208438	+	0.133955i
$187$	34.7997	+	242.037i	0.0136086	+	0.0946497i
$188$	752.007	+	1646.67i	0.291733	+	0.638805i
$189$	−678.702	−	199.285i	−0.261208	−	0.0766976i
$190$	79.3088	−	173.662i	0.0302824	−	0.0663093i
$191$	2152.24	−	2483.82i	0.815345	−	0.940958i	−0.183772	−	0.982969i	$-0.558831\pi$
$191$	2152.24	−	2483.82i	0.815345	−	0.940958i	0.999117	+	0.0420106i	$0.0133763\pi$
$192$	27.3244	−	190.046i	0.0102707	−	0.0714342i
$193$	−988.723	+	290.315i	−0.368756	+	0.108276i	−0.460860	−	0.887473i	$-0.652459\pi$
$193$	−988.723	+	290.315i	−0.368756	+	0.108276i	0.0921041	+	0.995749i	$0.470641\pi$
$194$	−762.435	−	879.897i	−0.282163	−	0.325634i
$195$	990.003	−	636.236i	0.363567	−	0.233650i
$196$	1155.39	−	742.523i	0.421060	−	0.270599i
$197$	522.077	+	602.509i	0.188814	+	0.217903i	0.842262	−	0.539068i	$-0.181224\pi$
$197$	522.077	+	602.509i	0.188814	+	0.217903i	−0.653448	+	0.756972i	$0.726678\pi$
$198$	−59.8013	+	17.5592i	−0.0214641	+	0.00630243i
$199$	297.968	−	2072.41i	0.106143	−	0.738238i	−0.865350	−	0.501168i	$-0.832904\pi$
$199$	297.968	−	2072.41i	0.106143	−	0.738238i	0.971493	−	0.237070i	$-0.0761870\pi$
$200$	−814.917	+	940.464i	−0.288117	+	0.332504i
$201$	870.103	−	1905.26i	0.305335	−	0.668590i
$202$	−389.906	−	114.487i	−0.135810	−	0.0398775i
$203$	−1275.26	−	2792.44i	−0.440916	−	0.965471i
$204$	−120.604	−	838.816i	−0.0413918	−	0.287887i
$205$	−4764.59	−	3062.02i	−1.62329	−	1.04322i
$206$	1307.16			0.442108
$207$	498.683	−	858.395i	0.167444	−	0.288225i
$208$	374.716			0.124913
$209$	−16.6007	−	10.6686i	−0.00549422	−	0.00353092i
$210$	374.698	+	2606.08i	0.123127	+	0.856366i
$211$	−2186.29	−	4787.31i	−0.713320	−	1.56195i	−0.823035	−	0.567991i	$-0.807721\pi$
$211$	−2186.29	−	4787.31i	−0.713320	−	1.56195i	0.109715	−	0.993963i	$-0.465006\pi$
$212$	2283.97	+	670.635i	0.739924	+	0.217261i
$213$	−174.887	+	382.949i	−0.0562584	+	0.123189i
$214$	−1509.30	+	1741.83i	−0.482120	+	0.556396i
$215$	521.441	−	3626.70i	0.165404	−	1.15041i
$216$	207.250	−	60.8542i	0.0652852	−	0.0191695i
$217$	−1797.17	−	2074.05i	−0.562212	−	0.648828i
$218$	−2781.12	+	1787.32i	−0.864041	+	0.555286i
$219$	1610.13	−	1034.77i	0.496816	−	0.319284i
$220$	151.919	+	175.324i	0.0465562	+	0.0537287i
$221$	1586.91	−	465.959i	0.483019	−	0.141827i
$222$	328.415	−	2284.17i	0.0992872	−	0.690558i
$223$	−2989.08	+	3449.59i	−0.897596	+	1.03588i	0.101561	+	0.994829i	$0.467616\pi$
$223$	−2989.08	+	3449.59i	−0.897596	+	1.03588i	−0.999157	+	0.0410513i	$0.986929\pi$
$224$	−348.262	+	762.587i	−0.103880	+	0.227467i
$225$	−1343.26	−	394.415i	−0.398002	−	0.116864i
$226$	1676.84	+	3671.77i	0.493548	+	1.08072i
$227$	260.668	+	1812.99i	0.0762165	+	0.530098i	0.991783	+	0.127931i	$0.0408337\pi$
$227$	260.668	+	1812.99i	0.0762165	+	0.530098i	−0.915567	+	0.402167i	$0.868257\pi$
$228$	57.5322	+	36.9737i	0.0167112	+	0.0107397i
$229$	1440.98			0.415818			0.207909	−	0.978148i	$-0.433334\pi$
$229$	1440.98			0.415818			0.207909	+	0.978148i	$0.433334\pi$
$230$	−3677.42	−	361.151i	−1.05427	−	0.103537i
$231$	272.139			0.0775128
$232$	788.607	+	506.807i	0.223166	+	0.143420i
$233$	293.768	+	2043.20i	0.0825983	+	0.574484i	0.988526	+	0.151051i	$0.0482659\pi$
$233$	293.768	+	2043.20i	0.0825983	+	0.574484i	−0.905928	+	0.423433i	$0.860825\pi$
$234$	175.120	+	383.460i	0.0489230	+	0.107126i
$235$	7273.24	+	2135.61i	2.01895	+	0.592818i
$236$	−207.080	+	453.441i	−0.0571175	+	0.125070i
$237$	−1716.78	+	1981.27i	−0.470536	+	0.543028i
$238$	−526.602	+	3662.60i	−0.143422	+	0.997525i
$239$	3822.51	−	1122.39i	1.03455	−	0.303772i	0.279991	−	0.960003i	$-0.409669\pi$
$239$	3822.51	−	1122.39i	1.03455	−	0.303772i	0.754560	+	0.656231i	$0.227850\pi$
$240$	−526.498	−	607.611i	−0.141605	−	0.163421i
$241$	−4200.07	+	2699.22i	−1.12261	+	0.721461i	−0.964006	−	0.265881i	$-0.914337\pi$
$241$	−4200.07	+	2699.22i	−1.12261	+	0.721461i	−0.158609	+	0.987341i	$0.550701\pi$
$242$	−2219.24	+	1426.22i	−0.589498	+	0.378847i
$243$	159.131	+	183.647i	0.0420093	+	0.0484814i
$244$	−2251.37	+	661.061i	−0.590692	+	0.173443i
$245$	818.460	−	5692.51i	0.213426	−	1.48441i
$246$	1328.60	−	1533.28i	0.344342	−	0.397392i
$247$	−55.4456	+	121.409i	−0.0142831	+	0.0312756i
$248$	804.079	+	236.099i	0.205883	+	0.0604528i
$249$	1333.30	+	2919.52i	0.339335	+	0.743040i
$250$	145.653	+	1013.04i	0.0368476	+	0.256281i
$251$	2432.32	+	1563.16i	0.611661	+	0.393090i	0.809479	−	0.587148i	$-0.199749\pi$
$251$	2432.32	+	1563.16i	0.611661	+	0.393090i	−0.197819	+	0.980239i	$0.563386\pi$
$252$	−943.140			−0.235763
$253$	−91.0438	+	370.924i	−0.0226240	+	0.0921730i
$254$	750.169			0.185314
$255$	−2985.27	−	1918.51i	−0.733116	−	0.471145i
$256$	−36.4326	−	253.394i	−0.00889468	−	0.0618638i
$257$	2425.99	+	5312.18i	0.588830	+	1.28936i	0.936147	+	0.351609i	$0.114365\pi$
$257$	2425.99	+	5312.18i	0.588830	+	1.28936i	−0.347317	+	0.937748i	$0.612907\pi$
$258$	1259.34	+	369.774i	0.303887	+	0.0892292i
$259$	−4185.79	+	9165.60i	−1.00422	+	2.19893i
$260$	1027.54	−	1185.84i	0.245097	−	0.282857i
$261$	−150.085	+	1043.86i	−0.0355939	+	0.247561i
$262$	−517.749	+	152.025i	−0.122086	+	0.0358478i
$263$	−3874.42	−	4471.32i	−0.908392	−	1.04834i	−0.998625	−	0.0524194i	$-0.983307\pi$
$263$	−3874.42	−	4471.32i	−0.908392	−	1.04834i	0.0902333	−	0.995921i	$-0.471239\pi$
$264$	−69.9092	+	44.9279i	−0.0162978	+	0.0104739i
$265$	8385.37	−	5388.95i	1.94381	−	1.24921i
$266$	−195.549	−	225.676i	−0.0450747	−	0.0520190i
$267$	4566.18	−	1340.75i	1.04661	−	0.307313i
$268$	397.445	−	2764.29i	0.0905889	−	0.630060i
$269$	883.207	−	1019.27i	0.200186	−	0.231027i	−0.646776	−	0.762680i	$-0.723883\pi$
$269$	883.207	−	1019.27i	0.200186	−	0.231027i	0.846963	+	0.531653i	$0.178429\pi$
$270$	375.736	−	822.746i	0.0846909	−	0.185447i
$271$	6280.24	+	1844.04i	1.40774	+	0.413350i	0.895334	−	0.445394i	$-0.146937\pi$
$271$	6280.24	+	1844.04i	1.40774	+	0.413350i	0.512405	+	0.858744i	$0.328755\pi$
$272$	−469.387	−	1027.81i	−0.104635	−	0.229119i
$273$	−261.955	−	1821.94i	−0.0580742	−	0.403915i
$274$	−1156.06	−	742.954i	−0.254891	−	0.163808i
$275$	538.605			0.118106
$276$	315.526	−	1285.49i	0.0688132	−	0.280353i
$277$	−1090.55			−0.236551			−0.118276	−	0.992981i	$-0.537737\pi$
$277$	−1090.55			−0.236551			−0.118276	+	0.992981i	$0.537737\pi$
$278$	2333.84	+	1499.87i	0.503505	+	0.323583i
$279$	134.171	+	933.182i	0.0287908	+	0.200244i
$280$	1458.32	+	3193.27i	0.311254	+	0.681552i
$281$	6182.46	+	1815.33i	1.31251	+	0.385387i	0.861783	−	0.507276i	$-0.169348\pi$
$281$	6182.46	+	1815.33i	1.31251	+	0.385387i	0.450724	+	0.892663i	$0.351166\pi$
$282$	−1128.01	+	2470.00i	−0.238199	+	0.521582i
$283$	1633.40	−	1885.05i	0.343094	−	0.395952i	−0.557811	−	0.829968i	$-0.688358\pi$
$283$	1633.40	−	1885.05i	0.343094	−	0.395952i	0.900905	+	0.434016i	$0.142904\pi$
$284$	−79.8847	+	555.611i	−0.0166912	+	0.116090i
$285$	274.772	−	80.6803i	0.0571090	−	0.0167687i
$286$	−106.208	−	122.571i	−0.0219588	−	0.0253418i
$287$	−7452.35	+	4789.33i	−1.53275	+	0.985036i
$288$	242.281	−	155.705i	0.0495713	−	0.0318576i
$289$	−48.5944	−	56.0810i	−0.00989099	−	0.0114148i
$290$	3766.36	−	1105.90i	0.762649	−	0.223934i
$291$	248.540	−	1728.63i	0.0500675	−	0.348227i
$292$	1671.18	−	1928.64i	0.334926	−	0.386525i
$293$	1790.58	−	3920.83i	0.357021	−	0.781766i	−0.642855	−	0.765988i	$-0.722250\pi$
$293$	1790.58	−	3920.83i	0.357021	−	0.781766i	0.999876	−	0.0157783i	$-0.00502259\pi$
$294$	1976.67	+	580.402i	0.392115	+	0.115135i
$295$	867.129	+	1898.75i	0.171140	+	0.374743i
$296$	−437.886	−	3045.57i	−0.0859852	−	0.598040i
$297$	−78.6479	−	50.5439i	−0.0153657	−	0.00987493i
$298$	−4783.22			−0.929814
$299$	2570.93	+	252.484i	0.497259	+	0.0488346i
$300$	−1866.62			−0.359231
$301$	−4821.13	−	3098.35i	−0.923207	−	0.593309i
$302$	154.964	+	1077.80i	0.0295270	+	0.205365i
$303$	−253.216	−	554.466i	−0.0480095	−	0.105126i
$304$	87.4912	+	25.6897i	0.0165065	+	0.00484674i
$305$	−4081.62	+	8937.50i	−0.766272	+	1.67790i
$306$	832.435	−	960.681i	0.155513	−	0.179472i
$307$	−1413.09	+	9828.28i	−0.262702	+	1.82713i	0.249625	+	0.968342i	$0.419693\pi$
$307$	−1413.09	+	9828.28i	−0.262702	+	1.82713i	−0.512327	+	0.858790i	$0.671217\pi$
$308$	348.154	−	102.227i	0.0644089	−	0.0189122i
$309$	1284.01	+	1481.83i	0.236391	+	0.272810i
$310$	2952.10	−	1897.20i	0.540864	−	0.347592i
$311$	−4943.14	+	3176.76i	−0.901285	+	0.579221i	−0.907171	−	0.420762i	$-0.861763\pi$
$311$	−4943.14	+	3176.76i	−0.901285	+	0.579221i	0.00588618	+	0.999983i	$0.498126\pi$
$312$	368.080	+	424.787i	0.0667898	+	0.0770796i
$313$	−1831.46	+	537.766i	−0.330736	+	0.0971128i	−0.442885	−	0.896579i	$-0.646045\pi$
$313$	−1831.46	+	537.766i	−0.330736	+	0.0971128i	0.112149	+	0.993691i	$0.464227\pi$
$314$	−629.407	+	4377.62i	−0.113119	+	0.786763i
$315$	−2586.26	+	2984.70i	−0.462600	+	0.533869i
$316$	−1452.07	+	3179.59i	−0.258498	+	0.566031i
$317$	5077.95	+	1491.02i	0.899703	+	0.264177i	0.698701	−	0.715414i	$-0.253762\pi$
$317$	5077.95	+	1491.02i	0.899703	+	0.264177i	0.201002	+	0.979591i	$0.435580\pi$
$318$	1483.28	+	3247.93i	0.261566	+	0.572750i
$319$	−57.7418	−	401.603i	−0.0101345	−	0.0704873i
$320$	−901.806	−	579.556i	−0.157539	−	0.101244i
$321$	−3457.15			−0.601119
$322$	−2903.26	+	4997.45i	−0.502460	+	0.864898i
$323$	402.468			0.0693310
$324$	272.566	+	175.168i	0.0467363	+	0.0300356i
$325$	−518.450	−	3605.90i	−0.0884874	−	0.615443i
$326$	−334.659	−	732.801i	−0.0568560	−	0.124497i
$327$	−4758.01	−	1397.08i	−0.804644	−	0.236265i
$328$	1123.74	−	2460.64i	0.189171	−	0.414226i
$329$	7764.30	−	8960.48i	1.30109	−	1.50154i
$330$	−49.5227	+	344.438i	−0.00826101	+	0.0574566i
$331$	10466.5	−	3073.24i	1.73804	−	0.510335i	0.749593	−	0.661899i	$-0.230249\pi$
$331$	10466.5	−	3073.24i	1.73804	−	0.510335i	0.988447	+	0.151565i	$0.0484312\pi$
$332$	2802.42	+	3234.16i	0.463261	+	0.534632i
$333$	2912.00	−	1871.43i	0.479208	−	0.307968i
$334$	−900.347	+	578.618i	−0.147499	+	0.0947921i
$335$	−7658.12	−	8837.94i	−1.24898	−	1.44140i
$336$	−1206.58	+	354.284i	−0.195906	+	0.0575232i
$337$	492.145	−	3422.94i	0.0795515	−	0.553293i	−0.910600	−	0.413290i	$-0.864380\pi$
$337$	492.145	−	3422.94i	0.0795515	−	0.553293i	0.990151	−	0.140003i	$-0.0447112\pi$
$338$	2159.10	−	2491.73i	0.347454	−	0.400983i
$339$	−2515.26	+	5507.66i	−0.402980	+	0.882404i
$340$	−4539.80	−	1333.01i	−0.724133	−	0.212625i
$341$	−150.677	−	329.936i	−0.0239284	−	0.0523959i
$342$	14.5991	+	101.539i	0.00230827	+	0.0160544i
$343$	−7.78154	−	5.00089i	−0.00122497	−	0.000787239i
$344$	1750.00			0.274284
$345$	−3202.89	−	4523.57i	−0.499820	−	0.705916i
$346$	−7838.80			−1.21797
$347$	5084.48	+	3267.60i	0.786597	+	0.505515i	0.871217	−	0.490898i	$-0.163331\pi$
$347$	5084.48	+	3267.60i	0.786597	+	0.505515i	−0.0846200	+	0.996413i	$0.526968\pi$
$348$	200.113	+	1391.82i	0.0308252	+	0.214394i
$349$	4232.92	+	9268.80i	0.649235	+	1.42163i	0.892222	+	0.451597i	$0.149146\pi$
$349$	4232.92	+	9268.80i	0.649235	+	1.42163i	−0.242987	+	0.970030i	$0.578127\pi$
$350$	7820.24	+	2296.23i	1.19431	+	0.350682i
$351$	−262.681	+	575.190i	−0.0399455	+	0.0874683i
$352$	−72.5596	+	83.7383i	−0.0109871	+	0.0126797i
$353$	−855.175	+	5947.87i	−0.128941	+	0.896808i	0.817958	+	0.575278i	$0.195106\pi$
$353$	−855.175	+	5947.87i	−0.128941	+	0.896808i	−0.946899	+	0.321530i	$0.895803\pi$
$354$	−717.444	+	210.661i	−0.107717	+	0.0316285i
$355$	1539.25	+	1776.39i	0.230126	+	0.265580i
$356$	5337.98	−	3430.51i	0.794697	−	0.510721i
$357$	−4669.29	+	3000.77i	−0.692227	+	0.444867i
$358$	−1627.80	−	1878.59i	−0.240313	−	0.277336i
$359$	−11307.1	+	3320.07i	−1.66230	+	0.488097i	−0.971913	−	0.235340i	$-0.924380\pi$
$359$	−11307.1	+	3320.07i	−1.66230	+	0.488097i	−0.690391	+	0.723436i	$0.742561\pi$
$360$	171.628	−	1193.70i	0.0251267	−	0.174760i
$361$	4470.42	−	5159.14i	0.651760	−	0.752171i
$362$	3299.80	−	7225.56i	0.479099	−	1.04908i
$363$	−3796.74	−	1114.82i	−0.548974	−	0.161193i
$364$	−1019.53	−	2232.45i	−0.146807	−	0.321462i
$365$	−1520.79	−	10577.3i	−0.218088	−	1.51683i
$366$	−2960.89	−	1902.85i	−0.422864	−	0.271758i
$367$	−12231.4			−1.73972			−0.869858	−	0.493302i	$-0.835790\pi$
$367$	−12231.4			−1.73972			−0.869858	+	0.493302i	$0.835790\pi$
$368$	−79.2265	−	1763.09i	−0.0112227	−	0.249748i
$369$	3043.23			0.429334
$370$	−10838.9	−	6965.73i	−1.52294	−	0.978732i
$371$	−2218.77	−	15431.9i	−0.310493	−	2.15953i
$372$	522.193	+	1143.44i	0.0727807	+	0.159368i
$373$	4419.56	+	1297.70i	0.613502	+	0.180141i	0.573698	−	0.819067i	$-0.305508\pi$
$373$	4419.56	+	1297.70i	0.613502	+	0.180141i	0.0398043	+	0.999207i	$0.487327\pi$
$374$	−203.159	+	444.857i	−0.0280886	+	0.0615054i
$375$	−1005.33	+	1160.21i	−0.138440	+	0.159769i
$376$	−515.252	+	3583.66i	−0.0706705	+	0.491524i
$377$	−2633.10	+	773.148i	−0.359712	+	0.105621i
$378$	−926.438	−	1069.17i	−0.126060	−	0.145481i
$379$	−11237.1	+	7221.62i	−1.52298	+	0.978759i	−0.531706	+	0.846929i	$0.678449\pi$
$379$	−11237.1	+	7221.62i	−1.52298	+	0.978759i	−0.991272	+	0.131829i	$0.957915\pi$
$380$	321.215	−	206.432i	0.0433631	−	0.0278678i
$381$	736.884	+	850.410i	0.0990859	+	0.114351i
$382$	6306.88	−	1851.87i	0.844733	−	0.248036i
$383$	1624.15	−	11296.2i	0.216685	−	1.50707i	−0.533474	−	0.845816i	$-0.679114\pi$
$383$	1624.15	−	11296.2i	0.216685	−	1.50707i	0.750159	−	0.661258i	$-0.229977\pi$
$384$	251.467	−	290.208i	0.0334182	−	0.0385667i
$385$	631.188	−	1382.11i	0.0835540	−	0.182958i
$386$	−1977.45	−	580.631i	−0.260750	−	0.0765630i
$387$	817.849	+	1790.84i	0.107425	+	0.235229i
$388$	−331.386	−	2304.84i	−0.0433597	−	0.301574i
$389$	1903.59	+	1223.36i	0.248113	+	0.159452i	0.658786	−	0.752330i	$-0.271070\pi$
$389$	1903.59	+	1223.36i	0.248113	+	0.159452i	−0.410674	+	0.911782i	$0.634706\pi$
$390$	2353.64			0.305593
$391$	−2527.92	−	7368.10i	−0.326963	−	0.952995i
$392$	2746.82			0.353917
$393$	−680.920	−	437.600i	−0.0873991	−	0.0561680i
$394$	226.916	+	1578.24i	0.0290149	+	0.201803i
$395$	6080.42	+	13314.3i	0.774530	+	1.69598i
$396$	−119.603	−	35.1185i	−0.0151774	−	0.00445649i
$397$	−3671.42	+	8039.30i	−0.464140	+	1.01632i	0.522384	+	0.852710i	$0.325043\pi$
$397$	−3671.42	+	8039.30i	−0.464140	+	1.01632i	−0.986524	+	0.163615i	$0.947685\pi$
$398$	2742.19	−	3164.66i	0.345361	−	0.398568i
$399$	63.7453	−	443.358i	0.00799813	−	0.0556282i
$400$	−2388.01	+	701.183i	−0.298501	+	0.0876479i
$401$	5198.99	+	5999.96i	0.647445	+	0.747191i	0.980673	−	0.195655i	$-0.0626833\pi$
$401$	5198.99	+	5999.96i	0.647445	+	0.747191i	−0.333228	+	0.942846i	$0.608138\pi$
$402$	3524.08	−	2264.79i	0.437226	−	0.280988i
$403$	−2063.84	+	1326.35i	−0.255105	+	0.163946i
$404$	−532.227	−	614.223i	−0.0655428	−	0.0756404i
$405$	1301.77	−	382.233i	0.159717	−	0.0468971i
$406$	873.771	−	6077.21i	0.106809	−	0.742874i
$407$	−872.100	+	1006.46i	−0.106212	+	0.122576i
$408$	704.080	−	1541.72i	0.0854342	−	0.187075i
$409$	−4685.34	−	1375.74i	−0.566443	−	0.166323i	−0.0140421	−	0.999901i	$-0.504470\pi$
$409$	−4685.34	−	1375.74i	−0.566443	−	0.166323i	−0.552400	+	0.833579i	$0.686288\pi$
$410$	−4705.56	−	10303.7i	−0.566807	−	1.24113i
$411$	−293.356	−	2040.33i	−0.0352072	−	0.244872i
$412$	2199.31	+	1413.41i	0.262990	+	0.169014i
$413$	3264.89			0.388995
$414$	1767.20	−	905.040i	0.209791	−	0.107440i
$415$	17919.7			2.11962
$416$	630.462	+	405.173i	0.0743052	+	0.0477530i
$417$	592.224	+	4119.01i	0.0695475	+	0.483714i
$418$	−16.3950	−	35.9000i	−0.00191843	−	0.00420078i
$419$	10092.0	+	2963.28i	1.17667	+	0.345503i	0.810891	−	0.585197i	$-0.198983\pi$
$419$	10092.0	+	2963.28i	1.17667	+	0.345503i	0.365783	+	0.930700i	$0.380801\pi$
$420$	−2187.48	+	4789.91i	−0.254138	+	0.556485i
$421$	−3549.93	+	4096.83i	−0.410957	+	0.474269i	−0.923061	−	0.384654i	$-0.874321\pi$
$421$	−3549.93	+	4096.83i	−0.410957	+	0.474269i	0.512104	+	0.858923i	$0.328866\pi$
$422$	1497.98	−	10418.7i	0.172798	−	1.20183i
$423$	−3908.08	+	1147.52i	−0.449214	+	0.131901i
$424$	3117.66	+	3597.97i	0.357091	+	0.412105i
$425$	−9241.23	+	5938.98i	−1.05474	+	0.677842i
$426$	−708.324	+	455.212i	−0.0805596	+	0.0517725i
$427$	10063.9	+	11614.4i	1.14058	+	1.31630i
$428$	−4422.82	+	1298.66i	−0.499497	+	0.146666i
$429$	34.6218	−	240.800i	0.00389640	−	0.0271001i
$430$	4798.81	−	5538.12i	0.538184	−	0.621098i
$431$	1685.95	−	3691.71i	0.188420	−	0.412583i	−0.791721	−	0.610883i	$-0.790815\pi$
$431$	1685.95	−	3691.71i	0.188420	−	0.412583i	0.980141	+	0.198300i	$0.0635420\pi$
$432$	414.501	+	121.708i	0.0461636	+	0.0135549i
$433$	−2298.14	−	5032.21i	−0.255061	−	0.558505i	0.738176	−	0.674608i	$-0.235687\pi$
$433$	−2298.14	−	5032.21i	−0.255061	−	0.558505i	−0.993237	+	0.116102i	$0.962960\pi$
$434$	−781.126	−	5432.85i	−0.0863946	−	0.600888i
$435$	4953.34	+	3183.32i	0.545964	+	0.350870i
$436$	−6611.84			−0.726261
$437$	582.968	+	235.209i	0.0638149	+	0.0257473i
$438$	3827.94			0.417593
$439$	8296.01	+	5331.52i	0.901929	+	0.579635i	0.907362	−	0.420350i	$-0.138093\pi$
$439$	8296.01	+	5331.52i	0.901929	+	0.579635i	−0.00543241	+	0.999985i	$0.501729\pi$
$440$	66.0302	+	459.250i	0.00715424	+	0.0497589i
$441$	1283.71	+	2810.92i	0.138614	+	0.303523i
$442$	3173.82	+	931.918i	0.341546	+	0.100287i
$443$	1000.12	−	2189.95i	0.107262	−	0.234870i	−0.848389	−	0.529374i	$-0.822427\pi$
$443$	1000.12	−	2189.95i	0.107262	−	0.234870i	0.955650	+	0.294503i	$0.0951542\pi$
$444$	3022.40	−	3488.03i	0.323055	−	0.372826i
$445$	3781.34	−	26299.8i	0.402816	−	2.80164i
$446$	−8759.13	+	2571.91i	−0.929948	+	0.273057i
$447$	−4698.52	−	5422.38i	−0.497164	−	0.573758i
$448$	−1410.52	+	906.489i	−0.148752	+	0.0955973i
$449$	6605.18	−	4244.89i	0.694248	−	0.446166i	−0.145345	−	0.989381i	$-0.546429\pi$
$449$	6605.18	−	4244.89i	0.694248	−	0.446166i	0.839594	+	0.543215i	$0.182793\pi$
$450$	−1833.56	−	2116.04i	−0.192078	−	0.221669i
$451$	−1123.39	+	329.857i	−0.117291	+	0.0344398i
$452$	−1148.92	+	7990.92i	−0.119559	+	0.831551i
$453$	−1069.60	+	1234.38i	−0.110936	+	0.128027i
$454$	−1521.77	+	3332.22i	−0.157314	+	0.344469i
$455$	−9860.61	−	2895.34i	−1.01598	−	0.298320i
$456$	56.8193	+	124.417i	0.00583511	+	0.0127771i
$457$	−364.869	−	2537.72i	−0.0373476	−	0.259758i	0.962590	−	0.270963i	$-0.0873423\pi$
$457$	−364.869	−	2537.72i	−0.0373476	−	0.259758i	−0.999937	+	0.0112053i	$0.996433\pi$
$458$	2424.45	+	1558.10i	0.247352	+	0.158964i
$459$	1906.74			0.193898
$460$	−5796.79	−	4583.97i	−0.587558	−	0.464628i
$461$	4478.36			0.452447			0.226224	−	0.974075i	$-0.427362\pi$
$461$	4478.36			0.452447			0.226224	+	0.974075i	$0.427362\pi$
$462$	457.876	+	294.259i	0.0461089	+	0.0296324i
$463$	−1519.49	−	10568.3i	−0.152520	−	1.06080i	−0.911976	−	0.410243i	$-0.865444\pi$
$463$	−1519.49	−	10568.3i	−0.152520	−	1.06080i	0.759456	−	0.650559i	$-0.225465\pi$
$464$	778.836	+	1705.41i	0.0779236	+	0.170629i
$465$	5050.53	+	1482.97i	0.503683	+	0.147895i
$466$	−1715.01	+	3755.35i	−0.170486	+	0.373312i
$467$	−10338.5	+	11931.3i	−1.02443	+	1.18226i	−0.0413395	+	0.999145i	$0.513163\pi$
$467$	−10338.5	+	11931.3i	−1.02443	+	1.18226i	−0.983092	+	0.183112i	$0.941383\pi$
$468$	−119.987	+	834.529i	−0.0118513	+	0.0824276i
$469$	−17550.2	+	5153.21i	−1.72792	+	0.507363i
$470$	9928.07	+	11457.6i	0.974357	+	1.12447i
$471$	−5580.84	+	3586.59i	−0.545969	+	0.350873i
$472$	−838.710	+	539.006i	−0.0817898	+	0.0525631i
$473$	−496.014	−	572.430i	−0.0482172	−	0.0556456i
$474$	−5030.81	+	1477.18i	−0.487496	+	0.143142i
$475$	126.162	−	877.473i	0.0121867	−	0.0847605i
$476$	−4846.31	+	5592.94i	−0.466660	+	0.538555i
$477$	−2224.92	+	4871.89i	−0.213568	+	0.467649i
$478$	7645.02	+	2244.78i	0.731538	+	0.214799i
$479$	−1023.98	−	2242.21i	−0.0976764	−	0.213881i	0.854486	−	0.519475i	$-0.173872\pi$
$479$	−1023.98	−	2242.21i	−0.0976764	−	0.213881i	−0.952162	+	0.305593i	$0.901145\pi$
$480$	−228.838	−	1591.60i	−0.0217603	−	0.151347i
$481$	7577.57	+	4869.81i	0.718311	+	0.461631i
$482$	−9985.26			−0.943602
$483$	−8517.08	+	1617.75i	−0.802361	+	0.152402i
$484$	−5276.04			−0.495496
$485$	−8202.71	−	5271.56i	−0.767971	−	0.493545i
$486$	69.1650	+	481.053i	0.00645553	+	0.0448992i
$487$	−1793.21	−	3926.59i	−0.166855	−	0.365361i	0.807672	−	0.589632i	$-0.200727\pi$
$487$	−1793.21	−	3926.59i	−0.166855	−	0.365361i	−0.974527	+	0.224271i	$0.928000\pi$
$488$	−4502.73	−	1322.12i	−0.417682	−	0.122643i
$489$	501.989	−	1099.20i	0.0464227	−	0.101652i
$490$	7532.28	−	8692.71i	0.694436	−	0.801422i
$491$	−600.539	+	4176.84i	−0.0551974	+	0.383906i	0.943432	+	0.331566i	$0.107577\pi$
$491$	−600.539	+	4176.84i	−0.0551974	+	0.383906i	−0.998629	+	0.0523400i	$0.983332\pi$
$492$	3893.28	−	1143.17i	0.356753	−	0.104752i
$493$	5419.03	+	6253.89i	0.495052	+	0.571321i
$494$	−224.565	+	144.319i	−0.0204527	+	0.0131442i
$495$	−439.109	+	282.198i	−0.0398716	+	0.0256239i
$496$	1097.58	+	1266.67i	0.0993605	+	0.114668i
$497$	3527.52	−	1035.77i	0.318372	−	0.0934824i
$498$	−913.536	+	6353.78i	−0.0822018	+	0.571726i
$499$	10463.7	−	12075.8i	0.938716	−	1.08334i	−0.0576646	−	0.998336i	$-0.518365\pi$
$499$	10463.7	−	12075.8i	0.938716	−	1.08334i	0.996381	−	0.0850004i	$-0.0270891\pi$
$500$	−850.318	+	1861.94i	−0.0760547	+	0.166537i
$501$	−1540.34	−	452.284i	−0.137360	−	0.0403325i
$502$	2402.18	+	5260.05i	0.213575	+	0.467664i
$503$	853.022	+	5932.90i	0.0756151	+	0.525914i	0.992061	+	0.125756i	$0.0401357\pi$
$503$	853.022	+	5932.90i	0.0756151	+	0.525914i	−0.916446	+	0.400158i	$0.868955\pi$
$504$	−1586.84	−	1019.80i	−0.140245	−	0.0901300i
$505$	−3403.25			−0.299887
$506$	−554.255	+	525.638i	−0.0486949	+	0.0461807i
$507$	4945.55			0.433214
$508$	1262.16	+	811.144i	0.110235	+	0.0708439i
$509$	1550.40	+	10783.3i	0.135010	+	0.939018i	0.938888	+	0.344223i	$0.111858\pi$
$509$	1550.40	+	10783.3i	0.135010	+	0.939018i	−0.803877	+	0.594795i	$0.797233\pi$
$510$	−2948.28	−	6455.83i	−0.255984	−	0.560527i
$511$	−16037.2	−	4708.95i	−1.38835	−	0.407655i
$512$	212.692	−	465.732i	0.0183589	−	0.0402004i
$513$	−100.766	+	116.291i	−0.00867240	+	0.0100085i
$514$	−1662.22	+	11561.0i	−0.142640	+	0.992086i
$515$	10503.8	−	3084.20i	0.898744	−	0.263895i
$516$	1719.01	+	1983.84i	0.146657	+	0.169252i
$517$	1318.26	−	847.197i	0.112142	−	0.0720690i
$518$	−16953.2	+	10895.2i	−1.43799	+	0.924143i
$519$	−7699.98	−	8886.25i	−0.651236	−	0.751567i
$520$	3011.07	−	884.128i	0.253931	−	0.0745608i
$521$	2190.94	−	15238.4i	0.184236	−	1.28139i	−0.662373	−	0.749174i	$-0.730450\pi$
$521$	2190.94	−	15238.4i	0.184236	−	1.28139i	0.846609	−	0.532216i	$-0.178640\pi$
$522$	−1381.23	+	1594.02i	−0.115814	+	0.133656i
$523$	−332.355	+	727.756i	−0.0277875	+	0.0608462i	−0.923017	−	0.384760i	$-0.874284\pi$
$523$	−332.355	+	727.756i	−0.0277875	+	0.0608462i	0.895229	+	0.445606i	$0.147012\pi$
$524$	−1035.50	−	304.050i	−0.0863282	−	0.0253482i
$525$	5078.69	+	11120.8i	0.422194	+	0.924477i
$526$	−1683.98	−	11712.4i	−0.139592	−	0.970881i
$527$	6223.33	+	3999.49i	0.514407	+	0.330589i
$528$	−166.202			−0.0136989
$529$	644.399	−	12149.9i	0.0529628	−	0.998596i
$530$	19935.4			1.63385
$531$	−943.549	−	606.382i	−0.0771121	−	0.0495570i
$532$	−84.9937	−	591.144i	−0.00692659	−	0.0481755i
$533$	3289.70	+	7203.44i	0.267341	+	0.585396i
$534$	9132.35	+	2681.50i	0.740067	+	0.217303i
$535$	−8018.36	+	17557.8i	−0.647970	+	1.41886i
$536$	3657.68	−	4221.19i	0.294753	−	0.340164i
$537$	530.633	−	3690.64i	0.0426416	−	0.296579i
$538$	2588.12	−	759.942i	0.207401	−	0.0608986i
$539$	−778.549	−	898.494i	−0.0622161	−	0.0718012i
$540$	1521.80	−	978.000i	0.121274	−	0.0779378i
$541$	2626.60	−	1688.01i	0.208736	−	0.134146i	−0.432096	−	0.901828i	$-0.642226\pi$
$541$	2626.60	−	1688.01i	0.208736	−	0.134146i	0.640832	+	0.767681i	$0.278590\pi$
$542$	8572.62	+	9893.33i	0.679383	+	0.784049i
$543$	11432.4	−	3356.87i	0.903523	−	0.265298i
$544$	321.609	−	2236.84i	0.0253472	−	0.176294i
$545$	−18130.8	+	20924.1i	−1.42503	+	1.64457i
$546$	1529.29	−	3348.67i	0.119867	−	0.262473i
$547$	6233.27	+	1830.25i	0.487231	+	0.143064i	0.516116	−	0.856519i	$-0.327377\pi$
$547$	6233.27	+	1830.25i	0.487231	+	0.143064i	−0.0288849	+	0.999583i	$0.509196\pi$
$548$	−1141.74	−	2500.05i	−0.0890009	−	0.194885i
$549$	−751.341	−	5225.69i	−0.0584088	−	0.406242i
$550$	906.207	+	582.384i	0.0702560	+	0.0451508i
$551$	−667.800			−0.0516320
$552$	1920.85	−	1821.68i	0.148111	−	0.140463i
$553$	22893.9			1.76048
$554$	−1834.85	−	1179.19i	−0.140714	−	0.0904313i
$555$	−2750.42	−	19129.6i	−0.210358	−	1.46307i
$556$	2304.92	+	5047.08i	0.175810	+	0.384971i
$557$	16521.6	+	4851.17i	1.25681	+	0.369032i	0.841305	−	0.540561i	$-0.181788\pi$
$557$	16521.6	+	4851.17i	1.25681	+	0.369032i	0.415502	+	0.909592i	$0.363606\pi$
$558$	−783.289	+	1715.16i	−0.0594252	+	0.130123i
$559$	−3354.90	+	3871.76i	−0.253841	+	0.292948i
$560$	−999.195	+	6949.55i	−0.0753995	+	0.524415i
$561$	−703.863	+	206.673i	−0.0529717	+	0.0155539i
$562$	8439.14	+	9739.29i	0.633423	+	0.731009i
$563$	−10077.9	+	6476.64i	−0.754406	+	0.484828i	−0.860451	−	0.509534i	$-0.829818\pi$
$563$	−10077.9	+	6476.64i	−0.754406	+	0.484828i	0.106044	+	0.994361i	$0.466181\pi$
$564$	−4568.65	+	2936.09i	−0.341090	+	0.219205i
$565$	22137.8	+	25548.4i	1.64840	+	1.90235i
$566$	4786.48	−	1405.44i	0.355461	−	0.104373i
$567$	302.001	−	2100.47i	0.0223684	−	0.155575i
$568$	−735.178	+	848.441i	−0.0543088	+	0.0626757i
$569$	1627.39	−	3563.49i	0.119901	−	0.262547i	−0.840159	−	0.542340i	$-0.817539\pi$
$569$	1627.39	−	3563.49i	0.119901	−	0.262547i	0.960060	+	0.279793i	$0.0902658\pi$
$570$	549.544	+	161.361i	0.0403822	+	0.0118573i
$571$	−2146.58	−	4700.36i	−0.157324	−	0.344491i	0.814513	−	0.580145i	$-0.197004\pi$
$571$	−2146.58	−	4700.36i	−0.157324	−	0.344491i	−0.971837	+	0.235654i	$0.924277\pi$
$572$	−46.1624	−	321.067i	−0.00337438	−	0.0234693i
$573$	8294.51	+	5330.56i	0.604726	+	0.388634i
$574$	−17717.2			−1.28833
$575$	−16856.6	+	3201.77i	−1.22255	+	0.232214i
$576$	576.000			0.0416667
$577$	−2201.38	−	1414.74i	−0.158830	−	0.102074i	0.458812	−	0.888534i	$-0.348275\pi$
$577$	−2201.38	−	1414.74i	−0.158830	−	0.102074i	−0.617641	+	0.786460i	$0.711912\pi$
$578$	−21.1212	−	146.901i	−0.00151994	−	0.0105714i
$579$	−1284.21	−	2812.03i	−0.0921762	−	0.201838i
$580$	7532.72	+	2211.81i	0.539274	+	0.158345i
$581$	11643.4	−	25495.5i	0.831411	−	1.82054i
$582$	2287.31	−	2639.69i	0.162907	−	0.188005i
$583$	293.248	−	2039.59i	0.0208321	−	0.144890i
$584$	4897.17	−	1437.94i	0.346997	−	0.101888i
$585$	2311.96	+	2668.14i	0.163398	+	0.188571i
$586$	7252.20	−	4660.70i	0.511238	−	0.328553i
$587$	−12541.3	+	8059.81i	−0.881831	+	0.566719i	−0.901350	−	0.433091i	$-0.857423\pi$
$587$	−12541.3	+	8059.81i	−0.881831	+	0.566719i	0.0195188	+	0.999809i	$0.493787\pi$
$588$	2698.18	+	3113.87i	0.189237	+	0.218391i
$589$	−572.811	+	168.193i	−0.0400718	+	0.0117661i
$590$	−594.130	+	4132.27i	−0.0414575	+	0.288344i
$591$	−1566.23	+	1807.53i	−0.109012	+	0.125807i
$592$	2556.37	−	5597.67i	0.177476	−	0.388619i
$593$	−17460.7	−	5126.91i	−1.20915	−	0.355037i	−0.385803	−	0.922581i	$-0.626075\pi$
$593$	−17460.7	−	5126.91i	−1.20915	−	0.355037i	−0.823343	+	0.567544i	$0.807894\pi$
$594$	−77.6734	−	170.081i	−0.00536528	−	0.0117483i
$595$	4410.21	+	30673.7i	0.303867	+	2.11344i
$596$	−8047.81	−	5172.01i	−0.553106	−	0.355459i
$597$	6281.16			0.430605
$598$	4052.59	+	3204.70i	0.277129	+	0.219147i
$599$	22142.1			1.51036			0.755178	−	0.655520i	$-0.227551\pi$
$599$	22142.1			1.51036			0.755178	+	0.655520i	$0.227551\pi$
$600$	−3140.60	−	2018.34i	−0.213691	−	0.137331i
$601$	−3456.90	−	24043.3i	−0.234626	−	1.63186i	−0.677676	−	0.735361i	$-0.737013\pi$
$601$	−3456.90	−	24043.3i	−0.234626	−	1.63186i	0.443050	−	0.896497i	$-0.353897\pi$
$602$	−4761.40	−	10426.0i	−0.322359	−	0.705867i
$603$	6029.08	+	1770.30i	0.407170	+	0.119556i
$604$	−904.674	+	1980.96i	−0.0609448	+	0.133450i
$605$	−14467.8	+	16696.8i	−0.972233	+	1.12202i
$606$	173.496	−	1206.69i	0.0116300	−	0.0808886i
$607$	−16950.6	+	4977.14i	−1.13345	+	0.332811i	−0.794062	−	0.607836i	$-0.792038\pi$
$607$	−16950.6	+	4977.14i	−1.13345	+	0.332811i	−0.339387	+	0.940647i	$0.610219\pi$
$608$	119.427	+	137.826i	0.00796611	+	0.00919338i
$609$	7747.57	−	4979.06i	0.515513	−	0.331300i
$610$	−16531.3	+	10624.0i	−1.09727	+	0.705171i
$611$	−6940.82	−	8010.13i	−0.459567	−	0.530368i
$612$	2439.34	−	716.256i	0.161119	−	0.0473087i
$613$	476.742	−	3315.82i	0.0314118	−	0.218474i	−0.968069	−	0.250683i	$-0.919345\pi$
$613$	476.742	−	3315.82i	0.0314118	−	0.218474i	0.999481	+	0.0322085i	$0.0102541\pi$
$614$	−13004.7	+	15008.2i	−0.854766	+	0.986452i
$615$	7058.33	−	15455.6i	0.462796	−	1.01338i
$616$	696.309	+	204.455i	0.0455440	+	0.0133729i
$617$	9688.36	+	21214.6i	0.632154	+	1.38422i	0.906341	+	0.422547i	$0.138864\pi$
$617$	9688.36	+	21214.6i	0.632154	+	1.38422i	−0.274187	+	0.961676i	$0.588409\pi$
$618$	558.085	+	3881.56i	0.0363260	+	0.252653i
$619$	−2788.47	−	1792.04i	−0.181063	−	0.116362i	0.446970	−	0.894549i	$-0.352503\pi$
$619$	−2788.47	−	1792.04i	−0.181063	−	0.116362i	−0.628033	+	0.778187i	$0.716140\pi$
$620$	7018.33			0.454617
$621$	2761.88	+	1114.33i	0.178471	+	0.0720075i
$622$	−11751.8			−0.757565
$623$	−34961.5	−	22468.4i	−2.24832	−	1.44491i
$624$	159.983	+	1112.71i	0.0102635	+	0.0713844i
$625$	−4516.67	−	9890.12i	−0.289067	−	0.632968i
$626$	−3662.92	−	1075.53i	−0.233866	−	0.0686691i
$627$	24.5925	−	53.8500i	0.00156639	−	0.00342992i
$628$	−5792.42	+	6684.81i	−0.368062	+	0.424766i
$629$	3865.45	−	26884.8i	0.245033	−	1.70424i
$630$	−7578.69	+	2225.31i	−0.479274	+	0.140727i
$631$	−12701.6	−	14658.4i	−0.801333	−	0.924788i	0.197120	−	0.980379i	$-0.436841\pi$
$631$	−12701.6	−	14658.4i	−0.801333	−	0.924788i	−0.998454	+	0.0555916i	$0.982296\pi$
$632$	−5881.15	+	3779.58i	−0.370158	+	0.237886i
$633$	13282.3	−	8536.04i	0.834005	−	0.535983i
$634$	6931.47	+	7999.34i	0.434202	+	0.501095i
$635$	6028.05	−	1770.00i	0.376718	−	0.110614i
$636$	−1016.30	+	7068.50i	−0.0633629	+	0.440698i
$637$	−5265.89	+	6077.16i	−0.327539	+	0.378000i
$638$	337.095	−	738.135i	0.0209180	−	0.0458041i
$639$	−1211.82	−	355.822i	−0.0750217	−	0.0220283i
$640$	−890.632	−	1950.21i	−0.0550083	−	0.120451i
$641$	−1852.38	−	12883.6i	−0.114141	−	0.793869i	−0.963817	−	0.266564i	$-0.914112\pi$
$641$	−1852.38	−	12883.6i	−0.114141	−	0.793869i	0.849676	−	0.527305i	$-0.176797\pi$
$642$	−5816.68	−	3738.15i	−0.357580	−	0.229802i
$643$	2712.19			0.166343			0.0831713	−	0.996535i	$-0.473495\pi$
$643$	2712.19			0.166343			0.0831713	+	0.996535i	$0.473495\pi$
$644$	−10288.4	+	5269.01i	−0.629534	+	0.322404i
$645$	10992.0			0.671021
$646$	677.155	+	435.181i	0.0412420	+	0.0265046i
$647$	−2622.94	−	18242.9i	−0.159379	−	1.10851i	−0.899781	−	0.436341i	$-0.856274\pi$
$647$	−2622.94	−	18242.9i	−0.159379	−	1.10851i	0.740402	−	0.672164i	$-0.234635\pi$
$648$	269.189	+	589.442i	0.0163190	+	0.0357337i
$649$	414.031	+	121.571i	0.0250418	+	0.00735294i
$650$	3026.69	−	6627.54i	0.182641	−	0.399928i
$651$	5391.52	−	6222.15i	0.324593	−	0.374601i
$652$	229.298	−	1594.80i	0.0137730	−	0.0957935i
$653$	2717.62	−	797.964i	0.162861	−	0.0478204i	−0.199285	−	0.979941i	$-0.563862\pi$
$653$	2717.62	−	797.964i	0.162861	−	0.0478204i	0.362147	+	0.932121i	$0.382044\pi$
$654$	−6494.75	−	7495.34i	−0.388325	−	0.448151i
$655$	−3801.73	+	2443.22i	−0.226787	+	0.145747i
$656$	4551.34	−	2924.97i	0.270884	−	0.174087i
$657$	3760.15	+	4339.44i	0.223284	+	0.257683i
$658$	22752.3	−	6680.68i	1.34799	−	0.395805i
$659$	−1610.43	+	11200.8i	−0.0951948	+	0.662095i	0.885223	+	0.465167i	$0.154006\pi$
$659$	−1610.43	+	11200.8i	−0.0951948	+	0.662095i	−0.980418	+	0.196928i	$0.936904\pi$
$660$	−455.756	+	525.971i	−0.0268792	+	0.0310203i
$661$	10121.2	−	22162.3i	0.595564	−	1.30410i	−0.336457	−	0.941699i	$-0.609229\pi$
$661$	10121.2	−	22162.3i	0.595564	−	1.30410i	0.932021	−	0.362404i	$-0.118044\pi$
$662$	20933.0	+	6146.49i	1.22898	+	0.360861i
$663$	2061.17	+	4513.34i	0.120738	+	0.264379i
$664$	1218.05	+	8471.71i	0.0711889	+	0.495129i
$665$	−2103.83	−	1352.05i	−0.122681	−	0.0788423i
$666$	6922.99			0.402793
$667$	4194.48	+	12225.6i	0.243495	+	0.709712i
$668$	−2140.49			−0.123979
$669$	−11519.6	−	7403.19i	−0.665730	−	0.427839i
$670$	−3328.54	−	23150.5i	−0.191929	−	1.33490i
$671$	843.767	+	1847.59i	0.0485444	+	0.106297i
$672$	−2413.16	−	708.569i	−0.138527	−	0.0406751i
$673$	−6322.63	+	13844.6i	−0.362139	+	0.792974i	0.637605	+	0.770363i	$0.279925\pi$
$673$	−6322.63	+	13844.6i	−0.362139	+	0.792974i	−0.999744	+	0.0226105i	$0.992802\pi$
$674$	4529.20	−	5226.98i	0.258840	−	0.298718i
$675$	597.707	−	4157.14i	0.0340826	−	0.237050i
$676$	6326.96	−	1857.76i	0.359977	−	0.105699i
$677$	−2247.89	−	2594.20i	−0.127612	−	0.147272i	0.688348	−	0.725381i	$-0.258336\pi$
$677$	−2247.89	−	2594.20i	−0.127612	−	0.147272i	−0.815960	+	0.578109i	$0.803791\pi$
$678$	−10187.3	+	6546.96i	−0.577050	+	0.370848i
$679$	−12829.9	+	8245.31i	−0.725137	+	0.466017i
$680$	−6196.89	−	7151.59i	−0.349471	−	0.403310i
$681$	−5272.31	+	1548.09i	−0.296675	+	0.0871115i
$682$	103.239	−	718.043i	0.00579652	−	0.0403157i
$683$	4833.29	−	5577.91i	0.270777	−	0.312493i	−0.604033	−	0.796959i	$-0.706441\pi$
$683$	4833.29	−	5577.91i	0.270777	−	0.312493i	0.874810	+	0.484466i	$0.160986\pi$
$684$	−85.2290	+	186.625i	−0.00476435	+	0.0104325i
$685$	−11042.6	−	3242.40i	−0.615936	−	0.180855i
$686$	−7.68513	−	16.8281i	−0.000427725	−	0.000936588i
$687$	615.217	+	4278.93i	0.0341659	+	0.237629i
$688$	2944.39	+	1892.24i	0.163160	+	0.104856i
$689$	−13937.1			−0.770624
$690$	−497.631	−	11074.2i	−0.0274558	−	0.610995i
$691$	4550.81			0.250537			0.125269	−	0.992123i	$-0.460021\pi$
$691$	4550.81			0.250537			0.125269	+	0.992123i	$0.460021\pi$
$692$	−13188.8	−	8475.95i	−0.724515	−	0.465617i
$693$	116.188	+	808.108i	0.00636888	+	0.0442965i
$694$	5021.48	+	10995.5i	0.274658	+	0.601418i
$695$	22292.7	+	6545.72i	1.21670	+	0.357257i
$696$	−1168.25	+	2558.12i	−0.0636243	+	0.139318i
$697$	15637.6	−	18046.7i	0.849808	−	0.980731i
$698$	−2900.27	+	20171.8i	−0.157273	+	1.09386i
$699$	−5941.80	+	1744.67i	−0.321516	+	0.0944055i
$700$	10674.7	+	12319.3i	0.576381	+	0.665180i
$701$	−5666.51	+	3641.65i	−0.305309	+	0.196210i	−0.684320	−	0.729182i	$-0.739901\pi$
$701$	−5666.51	+	3641.65i	−0.305309	+	0.196210i	0.379011	+	0.925392i	$0.376264\pi$
$702$	−1063.90	+	683.730i	−0.0572001	+	0.0367603i
$703$	1435.40	+	1656.54i	0.0770087	+	0.0888728i
$704$	−212.627	+	62.4329i	−0.0113831	+	0.00334237i
$705$	−3236.36	+	22509.4i	−0.172891	+	1.20249i
$706$	−7870.16	+	9082.65i	−0.419543	+	0.484178i
$707$	−2211.28	+	4842.03i	−0.117629	+	0.257572i
$708$	−1434.89	−	421.321i	−0.0761672	−	0.0223647i
$709$	−12544.5	−	27468.5i	−0.664481	−	1.45501i	−0.878287	−	0.478134i	$-0.841313\pi$
$709$	−12544.5	−	27468.5i	−0.664481	−	1.45501i	0.213806	−	0.976876i	$-0.431414\pi$
$710$	669.022	+	4653.15i	0.0353633	+	0.245957i
$711$	−6616.29	−	4252.03i	−0.348988	−	0.224281i
$712$	12690.5			0.667974
$713$	6677.01	+	9430.21i	0.350710	+	0.495321i
$714$	−11100.8			−0.581844
$715$	−1142.65	−	734.334i	−0.0597658	−	0.0384091i
$716$	−707.511	−	4920.85i	−0.0369287	−	0.256845i
$717$	4964.90	+	10871.6i	0.258602	+	0.566259i
$718$	−22614.2	−	6640.14i	−1.17543	−	0.345136i
$719$	−5410.95	+	11848.3i	−0.280660	+	0.614559i	−0.996490	−	0.0837156i	$-0.973321\pi$
$719$	−5410.95	+	11848.3i	−0.280660	+	0.614559i	0.715830	+	0.698275i	$0.246049\pi$
$720$	1579.49	−	1822.83i	0.0817559	−	0.0943513i
$721$	2436.82	−	16948.4i	0.125869	−	0.875440i
$722$	13100.0	−	3846.51i	0.675251	−	0.198272i
$723$	−9808.43	−	11319.5i	−0.504536	−	0.582266i
$724$	13364.8	−	8589.04i	0.686049	−	0.440897i
$725$	15333.6	−	9854.32i	0.785485	−	0.504800i
$726$	−5182.61	−	5981.05i	−0.264938	−	0.305754i
$727$	−12176.2	+	3575.26i	−0.621171	+	0.182392i	−0.577150	−	0.816638i	$-0.695835\pi$
$727$	−12176.2	+	3575.26i	−0.621171	+	0.182392i	−0.0440211	+	0.999031i	$0.514017\pi$
$728$	698.548	−	4858.51i	0.0355630	−	0.247346i
$729$	−477.393	+	550.941i	−0.0242541	+	0.0279907i
$730$	8878.35	−	19440.9i	0.450140	−	0.985670i
$731$	14822.4	+	4352.25i	0.749968	+	0.220210i
$732$	−2924.20	−	6403.11i	−0.147653	−	0.323314i
$733$	−2195.81	−	15272.2i	−0.110647	−	0.769564i	−0.967293	−	0.253660i	$-0.918365\pi$
$733$	−2195.81	−	15272.2i	−0.110647	−	0.769564i	0.856647	−	0.515903i	$-0.172544\pi$
$734$	−20579.5	−	13225.6i	−1.03488	−	0.665078i
$735$	17253.2			0.865840
$736$	1773.09	−	3052.07i	0.0888004	−	0.152854i
$737$	−2417.48			−0.120826
$738$	5120.26	+	3290.59i	0.255392	+	0.164130i
$739$	−1053.29	−	7325.80i	−0.0524302	−	0.364660i	−0.999099	−	0.0424507i	$-0.986483\pi$
$739$	−1053.29	−	7325.80i	−0.0524302	−	0.364660i	0.946668	−	0.322210i	$-0.104426\pi$
$740$	−10704.6	−	23439.8i	−0.531768	−	1.16441i
$741$	−384.192	−	112.809i	−0.0190467	−	0.00559263i
$742$	12953.1	−	28363.4i	0.640869	−	1.40331i
$743$	−11882.8	+	13713.5i	−0.586726	+	0.677117i	−0.969037	−	0.246916i	$-0.920583\pi$
$743$	−11882.8	+	13713.5i	−0.586726	+	0.677117i	0.382311	+	0.924034i	$0.375128\pi$
$744$	−357.790	+	2488.49i	−0.0176307	+	0.122624i
$745$	−38436.1	+	11285.8i	−1.89019	+	0.555008i
$746$	6032.77	+	6962.18i	0.296079	+	0.341694i
$747$	−8100.16	+	5205.66i	−0.396746	+	0.254973i
$748$	−822.833	+	528.803i	−0.0402216	+	0.0258489i
$749$	19770.6	+	22816.5i	0.964488	+	1.11308i
$750$	−2946.00	+	865.023i	−0.143430	+	0.0421149i
$751$	5508.94	−	38315.5i	0.267675	−	1.86172i	−0.202679	−	0.979245i	$-0.564965\pi$
$751$	5508.94	−	38315.5i	0.267675	−	1.86172i	0.470354	−	0.882478i	$-0.344126\pi$
$752$	−4741.86	+	5472.40i	−0.229944	+	0.265369i
$753$	−3603.28	+	7890.08i	−0.174383	+	0.381846i
$754$	−5266.20	−	1546.30i	−0.254355	−	0.0746854i
$755$	3788.25	+	8295.10i	0.182607	+	0.399854i
$756$	−402.669	−	2800.62i	−0.0193716	−	0.134732i
$757$	−23726.0	−	15247.8i	−1.13915	−	0.732087i	−0.171700	−	0.985149i	$-0.554926\pi$
$757$	−23726.0	−	15247.8i	−1.13915	−	0.732087i	−0.967450	+	0.253062i	$0.918562\pi$
$758$	−26715.0			−1.28012
$759$	−1140.32	−	111.988i	−0.0545334	−	0.00535559i
$760$	763.658			0.0364484
$761$	−5699.27	−	3662.70i	−0.271483	−	0.174471i	0.397815	−	0.917466i	$-0.369769\pi$
$761$	−5699.27	−	3662.70i	−0.271483	−	0.174471i	−0.669298	+	0.742994i	$0.733405\pi$
$762$	320.280	+	2227.60i	0.0152264	+	0.105902i
$763$	17989.5	+	39391.4i	0.853555	+	1.86902i
$764$	12613.8	+	3703.73i	0.597316	+	0.175388i
$765$	4422.42	−	9683.74i	0.209010	−	0.457669i
$766$	14947.0	−	17249.8i	0.705037	−	0.813656i
$767$	415.363	−	2888.91i	0.0195539	−	0.136001i
$768$	736.891	−	216.371i	0.0346227	−	0.0101661i
$769$	12711.3	+	14669.6i	0.596075	+	0.687908i	0.970981	−	0.239155i	$-0.0768705\pi$
$769$	12711.3	+	14669.6i	0.596075	+	0.687908i	−0.374906	+	0.927063i	$0.622325\pi$
$770$	2556.43	−	1642.92i	0.119646	−	0.0768916i
$771$	−14738.6	+	9471.90i	−0.688452	+	0.442441i
$772$	−2699.24	−	3115.09i	−0.125839	−	0.145226i
$773$	−17936.5	+	5266.63i	−0.834581	+	0.245055i	−0.670984	−	0.741472i	$-0.734128\pi$
$773$	−17936.5	+	5266.63i	−0.834581	+	0.245055i	−0.163597	+	0.986527i	$0.552310\pi$
$774$	−560.365	+	3897.42i	−0.0260231	+	0.180995i
$775$	10670.6	−	12314.6i	0.494581	−	0.570777i
$776$	1934.62	−	4236.23i	0.0894960	−	0.195969i
$777$	−29004.0	−	8516.35i	−1.33914	−	0.393208i
$778$	1880.00	+	4116.63i	0.0866342	+	0.189702i
$779$	274.249	+	1907.44i	0.0126136	+	0.0877295i
$780$	3960.01	+	2544.95i	0.181784	+	0.116825i
$781$	485.903			0.0222625
$782$	3713.75	−	15130.3i	0.169825	−	0.691890i
$783$	−3163.79			−0.144399
$784$	4621.55	+	2970.09i	0.210530	+	0.135299i
$785$	5271.18	+	36661.9i	0.239664	+	1.66690i
$786$	−672.483	−	1472.53i	−0.0305174	−	0.0668238i
$787$	7253.21	+	2129.74i	0.328525	+	0.0964636i	0.441836	−	0.897096i	$-0.354327\pi$
$787$	7253.21	+	2129.74i	0.328525	+	0.0964636i	−0.113311	+	0.993560i	$0.536146\pi$
$788$	−1324.73	+	2900.75i	−0.0598878	+	0.131136i
$789$	11623.3	−	13414.0i	0.524460	−	0.605259i
$790$	−4166.12	+	28976.0i	−0.187625	+	1.30496i
$791$	50733.6	−	14896.7i	2.28050	−	0.669616i
$792$	−163.259	−	188.411i	−0.00732470	−	0.00845316i
$793$	11557.2	−	7427.37i	0.517539	−	0.332602i
$794$	−14869.9	+	9556.33i	−0.664628	+	0.427130i
$795$	19582.4	+	22599.3i	0.873605	+	1.00819i
$796$	8035.64	−	2359.48i	0.357809	−	0.105062i
$797$	−4.12538	+	28.6927i	−0.000183348	+	0.00127521i	−0.989913	−	0.141677i	$-0.954750\pi$
$797$	−4.12538	+	28.6927i	−0.000183348	+	0.00127521i	0.989730	+	0.142952i	$0.0456596\pi$
$798$	586.647	−	677.027i	0.0260239	−	0.0300332i
$799$	−13276.7	+	29071.9i	−0.587855	+	1.28722i
$800$	−4776.02	−	1402.37i	−0.211072	−	0.0619764i
$801$	5930.82	+	12986.7i	0.261617	+	0.572861i
$802$	2259.70	+	15716.5i	0.0994922	+	0.691983i
$803$	−1858.39	−	1194.31i	−0.0816702	−	0.0524862i
$804$	8378.15			0.367506
$805$	−11538.1	+	47007.6i	−0.505174	+	2.05814i
$806$	−4906.58			−0.214426
$807$	3403.78	+	2187.48i	0.148474	+	0.0954186i
$808$	−231.328	−	1608.92i	−0.0100719	−	0.0700516i
$809$	−974.606	−	2134.09i	−0.0423551	−	0.0927448i	0.887272	−	0.461247i	$-0.152598\pi$
$809$	−974.606	−	2134.09i	−0.0423551	−	0.0927448i	−0.929627	+	0.368502i	$0.879871\pi$
$810$	2603.53	+	764.466i	0.112937	+	0.0331612i
$811$	−12032.7	+	26348.0i	−0.520994	+	1.14082i	0.448068	+	0.894000i	$0.352112\pi$
$811$	−12032.7	+	26348.0i	−0.520994	+	1.14082i	−0.969062	+	0.246818i	$0.920615\pi$
$812$	8041.30	−	9280.16i	0.347530	−	0.401071i
$813$	−2794.51	+	19436.3i	−0.120551	+	0.838449i
$814$	−2555.58	+	750.386i	−0.110041	+	0.0323108i
$815$	−4418.20	−	5098.88i	−0.189893	−	0.219148i
$816$	2851.65	−	1832.65i	0.122338	−	0.0786219i
$817$	−1048.76	+	674.000i	−0.0449102	+	0.0288620i
$818$	−6395.55	−	7380.86i	−0.273368	−	0.315484i
$819$	5298.34	−	1555.73i	0.226055	−	0.0663758i
$820$	3224.10	−	22424.1i	0.137306	−	0.954981i
$821$	−2191.48	+	2529.11i	−0.0931587	+	0.107511i	−0.800415	−	0.599447i	$-0.795387\pi$
$821$	−2191.48	+	2529.11i	−0.0931587	+	0.107511i	0.707256	+	0.706958i	$0.249933\pi$
$822$	1712.60	−	3750.08i	0.0726690	−	0.159123i
$823$	25025.2	+	7348.07i	1.05993	+	0.311225i	0.764824	−	0.644239i	$-0.222826\pi$
$823$	25025.2	+	7348.07i	1.05993	+	0.311225i	0.295109	+	0.955464i	$0.404644\pi$
$824$	2172.06	+	4756.14i	0.0918291	+	0.201078i
$825$	229.954	+	1599.37i	0.00970423	+	0.0674944i
$826$	5493.20	+	3530.27i	0.231396	+	0.148709i
$827$	−1768.42			−0.0743578			−0.0371789	−	0.999309i	$-0.511837\pi$
$827$	−1768.42			−0.0743578			−0.0371789	+	0.999309i	$0.511837\pi$
$828$	3951.94	+	388.110i	0.165869	+	0.0162896i
$829$	−30759.7			−1.28870			−0.644349	−	0.764732i	$-0.722871\pi$
$829$	−30759.7			−1.28870			−0.644349	+	0.764732i	$0.722871\pi$
$830$	30150.0	+	19376.2i	1.26087	+	0.810312i
$831$	−465.603	−	3238.34i	−0.0194363	−	0.135183i
$832$	622.650	+	1363.41i	0.0259453	+	0.0568124i
$833$	23265.4	+	6831.35i	0.967707	+	0.284144i
$834$	−3457.38	+	7570.62i	−0.143548	+	0.314327i
$835$	−5869.60	+	6773.88i	−0.243264	+	0.280742i
$836$	11.2333	−	78.1296i	0.000464729	−	0.00323226i
$837$	−2713.77	+	796.834i	−0.112069	+	0.0329064i
$838$	13775.7	+	15898.0i	0.567869	+	0.655356i
$839$	30124.3	−	19359.7i	1.23958	−	0.796629i	0.254225	−	0.967145i	$-0.418180\pi$
$839$	30124.3	−	19359.7i	1.23958	−	0.796629i	0.985355	+	0.170516i	$0.0545434\pi$
$840$	−8859.68	+	5693.77i	−0.363914	+	0.233874i
$841$	6979.81	+	8055.13i	0.286187	+	0.330277i
$842$	−10402.6	+	3054.48i	−0.425769	+	0.125017i
$843$	−2751.00	+	19133.6i	−0.112396	+	0.781729i
$844$	13785.9	−	15909.8i	0.562240	−	0.648859i
$845$	11470.5	−	25116.8i	0.466978	−	1.02254i
$846$	−7816.17	−	2295.03i	−0.317642	−	0.0932682i
$847$	14355.0	+	31433.1i	0.582343	+	1.27515i
$848$	1355.06	+	9424.67i	0.0548739	+	0.381656i
$849$	6294.95	+	4045.52i	0.254467	+	0.163536i
$850$	−21970.1			−0.886553
$851$	21311.0	−	36683.1i	0.858438	−	1.47765i
$852$	−1683.97			−0.0677135
$853$	12441.3	+	7995.53i	0.499392	+	0.320940i	0.765973	−	0.642873i	$-0.222258\pi$
$853$	12441.3	+	7995.53i	0.499392	+	0.320940i	−0.266581	+	0.963813i	$0.585894\pi$
$854$	4374.20	+	30423.2i	0.175272	+	1.21904i
$855$	356.889	+	781.479i	0.0142753	+	0.0312585i
$856$	−8845.63	−	2597.31i	−0.353198	−	0.103708i
$857$	−11554.7	+	25301.3i	−0.460562	+	1.00849i	0.526798	+	0.849991i	$0.323393\pi$
$857$	−11554.7	+	25301.3i	−0.460562	+	1.00849i	−0.987359	+	0.158499i	$0.949335\pi$
$858$	318.624	−	367.712i	0.0126779	−	0.0146311i
$859$	3220.02	−	22395.7i	0.127899	−	0.889559i	−0.820311	−	0.571917i	$-0.806200\pi$
$859$	3220.02	−	22395.7i	0.127899	−	0.889559i	0.948211	−	0.317642i	$-0.102891\pi$
$860$	14062.3	−	4129.06i	0.557582	−	0.163721i
$861$	−17403.5	−	20084.7i	−0.688861	−	0.794988i
$862$	6828.39	−	4388.34i	0.269810	−	0.173396i
$863$	13172.8	−	8465.63i	0.519590	−	0.333921i	−0.254419	−	0.967094i	$-0.581884\pi$
$863$	13172.8	−	8465.63i	0.519590	−	0.333921i	0.774010	+	0.633173i	$0.218248\pi$
$864$	565.800	+	652.968i	0.0222788	+	0.0257111i
$865$	−62989.4	+	18495.4i	−2.47596	+	0.727007i
$866$	1574.61	−	10951.7i	0.0617869	−	0.429738i
$867$	145.783	−	168.243i	0.00571057	−	0.00659035i
$868$	4560.19	−	9985.43i	0.178321	−	0.390470i
$869$	2903.24	+	852.469i	0.113332	+	0.0332774i
$870$	4891.97	+	10711.9i	0.190636	+	0.417434i
$871$	2327.02	+	16184.7i	0.0905257	+	0.629620i
$872$	−11124.5	−	7149.26i	−0.432021	−	0.277643i
$873$	5239.22			0.203117
$874$	726.520	+	1026.09i	0.0281177	+	0.0397118i
$875$	13406.4			0.517966
$876$	6440.53	+	4139.08i	0.248408	+	0.159642i
$877$	1475.21	+	10260.3i	0.0568007	+	0.395057i	0.998312	+	0.0580764i	$0.0184967\pi$
$877$	1475.21	+	10260.3i	0.0568007	+	0.395057i	−0.941511	+	0.336981i	$0.890594\pi$
$878$	8193.22	+	17940.6i	0.314929	+	0.689599i
$879$	12407.3	+	3643.10i	0.476094	+	0.139794i
$880$	−385.483	+	844.089i	−0.0147666	+	0.0323344i
$881$	−30986.8	+	35760.7i	−1.18498	+	1.36755i	−0.270604	+	0.962691i	$0.587223\pi$
$881$	−30986.8	+	35760.7i	−1.18498	+	1.36755i	−0.914381	+	0.404854i	$0.867322\pi$
$882$	−879.556	+	6117.45i	−0.0335785	+	0.233543i
$883$	32325.6	−	9491.67i	1.23199	−	0.361744i	0.399988	−	0.916521i	$-0.369014\pi$
$883$	32325.6	−	9491.67i	1.23199	−	0.361744i	0.831999	+	0.554777i	$0.187196\pi$
$884$	4332.31	+	4999.75i	0.164832	+	0.190226i
$885$	−5268.05	+	3385.57i	−0.200094	+	0.128593i
$886$	4050.65	−	2603.20i	0.153594	−	0.0987089i
$887$	−2883.28	−	3327.48i	−0.109144	−	0.125959i	0.698549	−	0.715563i	$-0.253830\pi$
$887$	−2883.28	−	3327.48i	−0.109144	−	0.125959i	−0.807693	+	0.589603i	$0.799284\pi$
$888$	8856.75	−	2600.58i	0.334699	−	0.0982766i
$889$	1398.47	−	9726.57i	0.0527595	−	0.366950i
$890$	34799.7	−	40160.9i	1.31066	−	1.51258i
$891$	116.510	−	255.121i	0.00438073	−	0.00959247i
$892$	−17518.3	−	5143.82i	−0.657572	−	0.193081i
$893$	−1071.43	−	2346.11i	−0.0401502	−	0.0879166i
$894$	−2042.17	−	14203.6i	−0.0763987	−	0.531364i
$895$	−17512.8	−	11254.8i	−0.654066	−	0.420343i
$896$	−3353.39			−0.125032
$897$	347.899	+	7742.07i	0.0129499	+	0.288183i
$898$	15703.2			0.583543
$899$	−10326.1	−	6636.20i	−0.383088	−	0.246196i
$900$	−796.942	−	5542.86i	−0.0295164	−	0.205291i
$901$	17458.2	+	38228.2i	0.645525	+	1.41350i
$902$	−2246.78	−	659.714i	−0.0829374	−	0.0243526i
$903$	7142.09	−	15639.0i	0.263205	−	0.576338i
$904$	−10573.5	+	12202.5i	−0.389015	+	0.448947i
$905$	9467.44	−	65847.5i	0.347744	−	2.41861i
$906$	−3134.32	+	920.318i	−0.114935	+	0.0337478i
$907$	−19790.2	−	22839.1i	−0.724502	−	0.836119i	0.267339	−	0.963603i	$-0.413856\pi$
$907$	−19790.2	−	22839.1i	−0.724502	−	0.836119i	−0.991841	+	0.127483i	$0.959310\pi$
$908$	−6163.46	+	3961.02i	−0.225266	+	0.144770i
$909$	1538.36	−	988.643i	0.0561321	−	0.0360739i
$910$	−13459.9	−	15533.5i	−0.490319	−	0.565859i
$911$	−8888.08	+	2609.78i	−0.323244	+	0.0949130i	−0.439329	−	0.898326i	$-0.644784\pi$
$911$	−8888.08	+	2609.78i	−0.323244	+	0.0949130i	0.116085	+	0.993239i	$0.462966\pi$
$912$	−38.9309	+	270.770i	−0.00141352	+	0.00983125i
$913$	2425.88	−	2799.61i	0.0879353	−	0.101483i
$914$	2130.09	−	4664.26i	0.0770867	−	0.168796i
$915$	−28282.2	−	8304.41i	−1.02184	−	0.300039i
$916$	2394.41	+	5243.03i	0.0863686	+	0.189121i
$917$	1005.94	+	6996.46i	0.0362258	+	0.251956i
$918$	3208.11	+	2061.73i	0.115341	+	0.0741254i
$919$	9929.32			0.356407			0.178204	−	0.983994i	$-0.442971\pi$
$919$	9929.32			0.356407			0.178204	+	0.983994i	$0.442971\pi$
$920$	−4796.57	−	13980.5i	−0.171889	−	0.501005i
$921$	−29788.0			−1.06574
$922$	7534.88	+	4842.37i	0.269141	+	0.172966i
$923$	−467.720	−	3253.06i	−0.0166795	−	0.116009i
$924$	452.203	+	990.186i	0.0161000	+	0.0352540i
$925$	−57403.4	−	16855.1i	−2.04044	−	0.599128i
$926$	8870.76	−	19424.3i	0.314807	−	0.689331i
$927$	−3852.03	+	4445.49i	−0.136481	+	0.157507i
$928$	−533.634	+	3711.51i	−0.0188765	+	0.131289i
$929$	49144.8	−	14430.2i	1.73562	−	0.509623i	0.747624	−	0.664122i	$-0.231194\pi$
$929$	49144.8	−	14430.2i	1.73562	−	0.509623i	0.987993	+	0.154499i	$0.0493762\pi$
$930$	6894.04	+	7956.14i	0.243080	+	0.280529i
$931$	−1646.15	+	1057.92i	−0.0579490	+	0.0372416i
$932$	−6946.11	+	4464.00i	−0.244128	+	0.156892i
$933$	−11543.7	−	13322.2i	−0.405064	−	0.467469i
$934$	−30295.7	+	8895.62i	−1.06136	+	0.311642i
$935$	−582.883	+	4054.04i	−0.0203875	+	0.141798i
$936$	−1104.24	+	1274.36i	−0.0385611	+	0.0445019i
$937$	−5962.84	+	13056.8i	−0.207895	+	0.455226i	−0.984642	−	0.174587i	$-0.944141\pi$
$937$	−5962.84	+	13056.8i	−0.207895	+	0.455226i	0.776747	+	0.629813i	$0.216868\pi$
$938$	−35100.4	−	10306.4i	−1.22182	−	0.358760i
$939$	−2378.81	−	5208.86i	−0.0826725	−	0.181027i
$940$	4315.15	+	30012.5i	0.149728	+	1.04138i
$941$	16970.6	+	10906.3i	0.587912	+	0.377828i	0.800517	−	0.599310i	$-0.204558\pi$
$941$	16970.6	+	10906.3i	0.587912	+	0.377828i	−0.212605	+	0.977138i	$0.568195\pi$
$942$	−13267.9			−0.458909
$943$	33197.6	−	17001.5i	1.14641	−	0.587111i
$944$	−1993.95			−0.0687475
$945$	−9967.14	−	6405.50i	−0.343102	−	0.220498i
$946$	−215.588	−	1499.45i	−0.00740949	−	0.0515341i
$947$	8074.60	+	17680.9i	0.277074	+	0.606707i	0.996096	−	0.0882802i	$-0.0281371\pi$
$947$	8074.60	+	17680.9i	0.277074	+	0.606707i	−0.719022	+	0.694988i	$0.755410\pi$
$948$	−10061.6	−	2954.36i	−0.344712	−	0.101216i
$949$	−6206.94	+	13591.3i	−0.212314	+	0.464903i
$950$	1161.06	−	1339.94i	0.0396525	−	0.0457614i
$951$	−2259.53	+	15715.4i	−0.0770455	+	0.535863i
$952$	−14201.5	+	4169.94i	−0.483480	+	0.141963i
$953$	−11975.2	−	13820.1i	−0.407046	−	0.469756i	0.514801	−	0.857310i	$-0.327866\pi$
$953$	−11975.2	−	13820.1i	−0.407046	−	0.469756i	−0.921847	+	0.387553i	$0.873320\pi$
$954$	−9011.32	+	5791.23i	−0.305820	+	0.196539i
$955$	46310.1	−	29761.7i	1.56917	−	1.00845i
$956$	10435.6	+	12043.3i	0.353044	+	0.407435i
$957$	1167.89	−	342.924i	0.0394489	−	0.0115832i
$958$	701.602	−	4879.75i	0.0236615	−	0.164569i
$959$	−11788.2	+	13604.3i	−0.396934	+	0.458086i
$960$	1335.95	−	2925.32i	0.0449141	−	0.0983482i
$961$	18055.5	+	5301.58i	0.606073	+	0.177959i
$962$	7483.68	+	16387.0i	0.250815	+	0.549207i
$963$	−1476.01	−	10265.9i	−0.0493913	−	0.343524i
$964$	−16800.3	−	10796.9i	−0.561307	−	0.360730i
$965$	−17259.9			−0.575769
$966$	−16079.3	−	6487.49i	−0.535551	−	0.216078i
$967$	−32775.6			−1.08996			−0.544981	−	0.838449i	$-0.683463\pi$
$967$	−32775.6			−1.08996			−0.544981	+	0.838449i	$0.683463\pi$
$968$	−8876.98	−	5704.89i	−0.294749	−	0.189424i
$969$	171.832	+	1195.11i	0.00569662	+	0.0396209i
$970$	−8101.07	−	17738.9i	−0.268154	−	0.587176i
$971$	−53449.5	−	15694.2i	−1.76651	−	0.518693i	−0.773196	−	0.634168i	$-0.781343\pi$
$971$	−53449.5	−	15694.2i	−1.76651	−	0.518693i	−0.993310	+	0.115475i	$0.963161\pi$
$972$	−403.783	+	884.162i	−0.0133244	+	0.0291765i
$973$	23797.8	−	27464.1i	0.784093	−	0.904892i
$974$	1228.65	−	8545.48i	0.0404195	−	0.281124i
$975$	10486.2	−	3079.03i	0.344439	−	0.101136i
$976$	−6146.29	−	7093.20i	−0.201576	−	0.232631i
$977$	24141.2	−	15514.6i	0.790529	−	0.508042i	−0.0819838	−	0.996634i	$-0.526126\pi$
$977$	24141.2	−	15514.6i	0.790529	−	0.508042i	0.872513	+	0.488592i	$0.162489\pi$
$978$	2033.15	−	1306.62i	0.0664753	−	0.0427211i
$979$	−3596.95	−	4151.11i	−0.117425	−	0.135516i
$980$	22072.4	−	6481.03i	0.719465	−	0.211254i
$981$	2117.17	−	14725.2i	0.0689051	−	0.479246i
$982$	−5526.75	+	6378.21i	−0.179598	+	0.207268i
$983$	−16703.9	+	36576.5i	−0.541987	+	1.18678i	0.418438	+	0.908245i	$0.362578\pi$
$983$	−16703.9	+	36576.5i	−0.541987	+	1.18678i	−0.960425	+	0.278540i	$0.910150\pi$
$984$	7786.56	+	2286.34i	0.252263	+	0.0740710i
$985$	5547.20	+	12146.7i	0.179440	+	0.392919i
$986$	2355.33	+	16381.7i	0.0760742	+	0.529107i
$987$	29922.7	+	19230.2i	0.964997	+	0.620166i
$988$	−533.881			−0.0171913
$989$	18926.5	+	14966.6i	0.608520	+	0.481204i
$990$	−1043.94			−0.0335137
$991$	−4982.62	−	3202.13i	−0.159716	−	0.102643i	0.458342	−	0.888776i	$-0.348444\pi$
$991$	−4982.62	−	3202.13i	−0.159716	−	0.102643i	−0.618057	+	0.786133i	$0.712080\pi$
$992$	477.054	+	3317.98i	0.0152686	+	0.106196i
$993$	13594.5	+	29767.8i	0.434450	+	0.951312i
$994$	7055.04	+	2071.55i	0.225123	+	0.0661020i
$995$	14568.3	−	31900.0i	0.464165	−	1.01638i
$996$	−8407.26	+	9702.49i	−0.267464	+	0.308670i
$997$	−3440.57	+	23929.7i	−0.109292	+	0.760142i	0.859297	+	0.511476i	$0.170901\pi$
$997$	−3440.57	+	23929.7i	−0.109292	+	0.760142i	−0.968589	+	0.248666i	$0.920008\pi$
$998$	30662.5	−	9003.33i	0.972551	−	0.285567i
$999$	6800.39	+	7848.07i	0.215370	+	0.248551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.e.b.25.3	✓	30
23.12	even	11	inner	138.4.e.b.127.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.e.b.25.3	✓	30	1.1	even	1	trivial
138.4.e.b.127.3	yes	30	23.12	even	11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68251 + 1.08128i) q^{2} +(0.426945 + 2.96946i) q^{3} +(1.66166 + 3.63853i) q^{4} +(16.0712 + 4.71893i) q^{5} +(-2.49249 + 5.45779i) q^{6} +(17.1563 - 19.7994i) q^{7} +(-1.13852 + 7.91857i) q^{8} +(-8.63544 + 2.53559i) q^{9} +O(q^{10})\)	\(q+(1.68251 + 1.08128i) q^{2} +(0.426945 + 2.96946i) q^{3} +(1.66166 + 3.63853i) q^{4} +(16.0712 + 4.71893i) q^{5} +(-2.49249 + 5.45779i) q^{6} +(17.1563 - 19.7994i) q^{7} +(-1.13852 + 7.91857i) q^{8} +(-8.63544 + 2.53559i) q^{9} +(21.9374 + 25.3171i) q^{10} +(2.91288 - 1.87200i) q^{11} +(-10.0950 + 6.48769i) q^{12} +(-15.3367 - 17.6995i) q^{13} +(50.2742 - 14.7619i) q^{14} +(-7.15118 + 49.7376i) q^{15} +(-10.4778 + 12.0920i) q^{16} +(-29.3367 + 64.2383i) q^{17} +(-17.2709 - 5.07119i) q^{18} +(-2.36747 - 5.18404i) q^{19} +(9.53491 + 66.3167i) q^{20} +(66.1183 + 42.4917i) q^{21} +6.92510 q^{22} +(-80.0356 + 75.9032i) q^{23} -24.0000 q^{24} +(130.858 + 84.0975i) q^{25} +(-6.66595 - 46.3627i) q^{26} +(-11.2162 - 24.5601i) q^{27} +(100.548 + 29.5237i) q^{28} +(48.6772 - 106.588i) q^{29} +(-65.8122 + 75.9513i) q^{30} +(14.9079 - 103.687i) q^{31} +(-30.7038 + 9.01544i) q^{32} +(6.80247 + 7.85046i) q^{33} +(-118.819 + 76.3603i) q^{34} +(369.154 - 237.241i) q^{35} +(-23.5750 - 27.2070i) q^{36} +(-369.031 + 108.357i) q^{37} +(1.62212 - 11.2821i) q^{38} +(46.0100 - 53.0984i) q^{39} +(-55.6645 + 121.888i) q^{40} +(-324.440 - 95.2641i) q^{41} +(65.2991 + 142.985i) q^{42} +(-31.1314 - 216.524i) q^{43} +(11.6515 + 7.48799i) q^{44} -150.747 q^{45} +(-216.733 + 41.1667i) q^{46} +452.564 q^{47} +(-40.3802 - 25.9508i) q^{48} +(-48.8642 - 339.858i) q^{49} +(129.237 + 282.989i) q^{50} +(-203.279 - 59.6880i) q^{51} +(38.9156 - 85.2134i) q^{52} +(389.707 - 449.746i) q^{53} +(7.68500 - 53.4504i) q^{54} +(55.6473 - 16.3395i) q^{55} +(137.250 + 158.395i) q^{56} +(14.3830 - 9.24342i) q^{57} +(197.152 - 126.702i) q^{58} +(81.6101 + 94.1831i) q^{59} +(-192.854 + 56.6271i) q^{60} +(-83.4823 + 580.632i) q^{61} +(137.197 - 158.334i) q^{62} +(-97.9487 + 214.478i) q^{63} +(-61.4076 - 18.0309i) q^{64} +(-162.956 - 356.824i) q^{65} +(2.95663 + 20.5638i) q^{66} +(-587.346 - 377.464i) q^{67} -282.481 q^{68} +(-259.563 - 205.256i) q^{69} +877.627 q^{70} +(118.054 + 75.8687i) q^{71} +(-10.2467 - 71.2671i) q^{72} +(-265.030 - 580.336i) q^{73} +(-738.062 - 216.715i) q^{74} +(-193.855 + 424.484i) q^{75} +(14.9283 - 17.2282i) q^{76} +(12.9098 - 89.7898i) q^{77} +(134.826 - 39.5886i) q^{78} +(572.261 + 660.425i) q^{79} +(-225.452 + 144.889i) q^{80} +(68.1415 - 43.7919i) q^{81} +(-442.865 - 511.093i) q^{82} +(1026.52 - 301.412i) q^{83} +(-44.7410 + 311.180i) q^{84} +(-774.611 + 893.949i) q^{85} +(181.744 - 397.964i) q^{86} +(337.293 + 99.0380i) q^{87} +(11.5072 + 25.1972i) q^{88} +(-225.756 - 1570.17i) q^{89} +(-253.633 - 163.000i) q^{90} -613.558 q^{91} +(-409.168 - 165.086i) q^{92} +314.260 q^{93} +(761.441 + 489.349i) q^{94} +(-13.5850 - 94.4857i) q^{95} +(-39.8798 - 87.3247i) q^{96} +(-558.555 - 164.007i) q^{97} +(285.268 - 624.650i) q^{98} +(-20.4074 + 23.5514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 6 q^{5} + 18 q^{6} + 22 q^{7} - 24 q^{8} - 27 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 6 * q^5 + 18 * q^6 + 22 * q^7 - 24 * q^8 - 27 * q^9	\( 30 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 6 q^{5} + 18 q^{6} + 22 q^{7} - 24 q^{8} - 27 q^{9} - 56 q^{10} - 105 q^{11} + 36 q^{12} - 21 q^{13} - 114 q^{15} - 48 q^{16} + 41 q^{17} - 54 q^{18} - 149 q^{19} + 152 q^{20} - 33 q^{21} - 584 q^{22} + 472 q^{23} - 720 q^{24} + 281 q^{25} + 90 q^{26} + 81 q^{27} - 1505 q^{29} + 168 q^{30} - 991 q^{31} - 96 q^{32} + 315 q^{33} - 1392 q^{34} + 646 q^{35} - 108 q^{36} + 103 q^{37} - 606 q^{38} + 63 q^{39} + 40 q^{40} + 966 q^{41} - 132 q^{42} + 1532 q^{43} - 420 q^{44} - 54 q^{45} - 46 q^{46} + 1718 q^{47} + 144 q^{48} + 843 q^{49} + 122 q^{50} + 273 q^{51} - 40 q^{52} + 911 q^{53} + 162 q^{54} + 2112 q^{55} + 176 q^{56} - 972 q^{57} + 1060 q^{58} + 415 q^{59} + 72 q^{60} - 1424 q^{61} - 464 q^{62} + 198 q^{63} - 192 q^{64} + 5246 q^{65} + 300 q^{66} - 5 q^{67} - 144 q^{68} - 1449 q^{69} + 2744 q^{70} + 4415 q^{71} - 216 q^{72} + 2890 q^{73} + 206 q^{74} - 183 q^{75} - 464 q^{76} - 5116 q^{77} + 1050 q^{78} - 3436 q^{79} - 96 q^{80} - 243 q^{81} - 4668 q^{82} + 5757 q^{83} - 132 q^{84} + 568 q^{85} + 710 q^{86} - 138 q^{87} + 1624 q^{88} + 375 q^{89} - 108 q^{90} - 8002 q^{91} - 48 q^{92} - 690 q^{93} + 1082 q^{94} - 5577 q^{95} + 288 q^{96} + 3179 q^{97} - 4100 q^{98} - 945 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 + 9 * q^3 - 12 * q^4 - 6 * q^5 + 18 * q^6 + 22 * q^7 - 24 * q^8 - 27 * q^9 - 56 * q^10 - 105 * q^11 + 36 * q^12 - 21 * q^13 - 114 * q^15 - 48 * q^16 + 41 * q^17 - 54 * q^18 - 149 * q^19 + 152 * q^20 - 33 * q^21 - 584 * q^22 + 472 * q^23 - 720 * q^24 + 281 * q^25 + 90 * q^26 + 81 * q^27 - 1505 * q^29 + 168 * q^30 - 991 * q^31 - 96 * q^32 + 315 * q^33 - 1392 * q^34 + 646 * q^35 - 108 * q^36 + 103 * q^37 - 606 * q^38 + 63 * q^39 + 40 * q^40 + 966 * q^41 - 132 * q^42 + 1532 * q^43 - 420 * q^44 - 54 * q^45 - 46 * q^46 + 1718 * q^47 + 144 * q^48 + 843 * q^49 + 122 * q^50 + 273 * q^51 - 40 * q^52 + 911 * q^53 + 162 * q^54 + 2112 * q^55 + 176 * q^56 - 972 * q^57 + 1060 * q^58 + 415 * q^59 + 72 * q^60 - 1424 * q^61 - 464 * q^62 + 198 * q^63 - 192 * q^64 + 5246 * q^65 + 300 * q^66 - 5 * q^67 - 144 * q^68 - 1449 * q^69 + 2744 * q^70 + 4415 * q^71 - 216 * q^72 + 2890 * q^73 + 206 * q^74 - 183 * q^75 - 464 * q^76 - 5116 * q^77 + 1050 * q^78 - 3436 * q^79 - 96 * q^80 - 243 * q^81 - 4668 * q^82 + 5757 * q^83 - 132 * q^84 + 568 * q^85 + 710 * q^86 - 138 * q^87 + 1624 * q^88 + 375 * q^89 - 108 * q^90 - 8002 * q^91 - 48 * q^92 - 690 * q^93 + 1082 * q^94 - 5577 * q^95 + 288 * q^96 + 3179 * q^97 - 4100 * q^98 - 945 * q^99

Introduction

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