LMFDB - Embedded newform 197.4.h.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(4,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(98))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("197.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.h (of order $98$, degree $42$, 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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$2016$
Relative dimension:	$48$ over $\Q(\zeta_{98})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{98}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	197.4
Dual form			197.4.h.a.148.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.65231 - 0.149190i) q^{2} +(0.203946 - 0.106399i) q^{3} +(13.6382 + 0.875598i) q^{4} +(-0.723623 + 0.214768i) q^{5} +(-0.964694 + 0.464572i) q^{6} +(-0.222342 - 6.93345i) q^{7} +(-26.2527 - 2.53257i) q^{8} +(-15.4169 + 22.1013i) q^{9} +(3.39856 - 0.891207i) q^{10} +(-10.9231 - 14.6360i) q^{11} +(2.87461 - 1.27250i) q^{12} +(34.1828 + 35.2966i) q^{13} +32.2897i q^{14} +(-0.124729 + 0.120793i) q^{15} +(13.3257 + 1.71816i) q^{16} +(43.8584 - 108.331i) q^{17} +(75.0214 - 100.522i) q^{18} +(4.40062 - 19.2804i) q^{19} +(-10.0569 + 2.29543i) q^{20} +(-0.783055 - 1.39039i) q^{21} +(48.6342 + 69.7207i) q^{22} +(2.09296 + 1.78176i) q^{23} +(-5.62360 + 2.27674i) q^{24} +(-104.284 + 67.8810i) q^{25} +(-153.763 - 169.310i) q^{26} +(-1.58690 + 12.3077i) q^{27} +(3.03858 - 94.7541i) q^{28} +(-0.223311 - 0.504464i) q^{29} +(0.598300 - 0.543360i) q^{30} +(49.7989 + 255.707i) q^{31} +(146.553 + 23.6936i) q^{32} +(-3.78497 - 1.82275i) q^{33} +(-220.205 + 497.446i) q^{34} +(1.64997 + 4.96945i) q^{35} +(-229.610 + 287.921i) q^{36} +(-159.502 + 20.5655i) q^{37} +(-23.3495 + 89.0417i) q^{38} +(10.7270 + 3.56160i) q^{39} +(19.5410 - 3.80561i) q^{40} +(-431.046 - 174.511i) q^{41} +(3.43558 + 6.58536i) q^{42} +(-382.124 + 285.187i) q^{43} +(-136.156 - 209.172i) q^{44} +(6.40938 - 19.3040i) q^{45} +(-9.47127 - 8.60156i) q^{46} +(-313.132 + 516.544i) q^{47} +(2.90053 - 1.06742i) q^{48} +(294.272 - 18.8929i) q^{49} +(495.286 - 300.245i) q^{50} +(-2.58152 - 26.7601i) q^{51} +(435.285 + 511.311i) q^{52} +(-363.642 + 400.410i) q^{53} +(9.21892 - 57.0223i) q^{54} +(11.0476 + 8.24501i) q^{55} +(-11.7223 + 182.585i) q^{56} +(-1.15391 - 4.40038i) q^{57} +(0.963652 + 2.38024i) q^{58} +(2.00254 + 0.525127i) q^{59} +(-1.80684 + 1.53819i) q^{60} +(16.9342 - 32.4598i) q^{61} +(-193.531 - 1197.06i) q^{62} +(156.666 + 101.978i) q^{63} +(-783.782 - 152.642i) q^{64} +(-32.3161 - 18.2001i) q^{65} +(17.3369 + 9.04466i) q^{66} +(345.982 + 209.736i) q^{67} +(693.001 - 1439.03i) q^{68} +(0.616428 + 0.140696i) q^{69} +(-6.93479 - 23.3656i) q^{70} +(-178.711 - 124.661i) q^{71} +(460.708 - 541.174i) q^{72} +(39.4844 + 306.233i) q^{73} +(745.121 - 71.8809i) q^{74} +(-14.0458 + 24.9397i) q^{75} +(76.8982 - 259.096i) q^{76} +(-99.0492 + 78.9891i) q^{77} +(-49.3738 - 18.1700i) q^{78} +(272.938 + 81.0065i) q^{79} +(-10.0118 + 1.61863i) q^{80} +(-250.292 - 680.124i) q^{81} +(1979.32 + 876.188i) q^{82} +(-133.553 - 585.134i) q^{83} +(-9.46199 - 19.6480i) q^{84} +(-8.47094 + 87.8102i) q^{85} +(1820.31 - 1269.77i) q^{86} +(-0.0992177 - 0.0791235i) q^{87} +(249.695 + 411.898i) q^{88} +(26.1044 - 134.041i) q^{89} +(-32.6984 + 88.8521i) q^{90} +(237.127 - 244.853i) q^{91} +(26.9840 + 26.1325i) q^{92} +(37.3631 + 46.8519i) q^{93} +(1533.85 - 2356.41i) q^{94} +(0.956409 + 14.8968i) q^{95} +(32.4099 - 10.7608i) q^{96} +(-1438.55 + 810.177i) q^{97} +(-1371.86 + 43.9930i) q^{98} +(491.874 - 15.7734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2016 q - 42 q^{2} - 42 q^{3} - 42 q^{5} - 119 q^{6} - 98 q^{8} - 42 q^{9} - 252 q^{10} - 140 q^{11} + 14 q^{12} - 42 q^{13} - 1722 q^{15} + 168 q^{16} - 42 q^{17} + 147 q^{18} - 567 q^{19} - 49 q^{20} - 42 q^{21}+ \cdots - 14763 q^{99}+O(q^{100}) $ 2016 * q - 42 * q^2 - 42 * q^3 - 42 * q^5 - 119 * q^6 - 98 * q^8 - 42 * q^9 - 252 * q^10 - 140 * q^11 + 14 * q^12 - 42 * q^13 - 1722 * q^15 + 168 * q^16 - 42 * q^17 + 147 * q^18 - 567 * q^19 - 49 * q^20 - 42 * q^21 - 1386 * q^22 - 42 * q^23 + 1246 * q^24 - 42 * q^25 + 1134 * q^26 - 504 * q^27 + 525 * q^28 - 3269 * q^29 - 847 * q^30 - 966 * q^31 - 994 * q^32 - 1631 * q^33 + 798 * q^34 - 42 * q^35 - 4207 * q^36 - 2149 * q^37 + 14 * q^38 - 252 * q^39 - 686 * q^40 - 392 * q^41 + 1176 * q^42 - 378 * q^43 + 12894 * q^44 + 3759 * q^45 + 2520 * q^46 + 28 * q^47 + 3654 * q^48 + 2646 * q^49 + 4914 * q^50 + 14 * q^51 - 3703 * q^52 - 42 * q^53 + 4305 * q^54 - 4130 * q^55 + 2989 * q^56 - 11585 * q^57 + 13286 * q^58 - 3136 * q^59 - 4914 * q^60 - 1050 * q^61 + 3836 * q^62 - 2198 * q^63 - 2562 * q^64 + 2359 * q^65 - 4683 * q^66 + 3528 * q^67 - 49 * q^68 - 49 * q^69 + 5208 * q^70 - 8792 * q^71 + 4928 * q^72 + 630 * q^73 + 266 * q^74 + 1232 * q^75 - 7903 * q^76 - 49 * q^77 - 4788 * q^78 - 1512 * q^79 - 490 * q^80 + 1078 * q^81 - 42 * q^82 - 5607 * q^83 + 10535 * q^84 - 19824 * q^85 - 7833 * q^86 - 49 * q^87 - 2373 * q^88 - 196 * q^89 - 8484 * q^90 + 14084 * q^91 - 1554 * q^92 - 2639 * q^93 + 7784 * q^94 + 7651 * q^95 + 15211 * q^96 - 1442 * q^97 + 18788 * q^98 - 14763 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{98}\right)$

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 $

$2$	−4.65231	−	0.149190i	−1.64484	−	0.0527468i	−0.804206	−	0.594351i	$-0.797409\pi$
$2$	−4.65231	−	0.149190i	−1.64484	−	0.0527468i	−0.840634	+	0.541604i	$0.817817\pi$
$3$	0.203946	−	0.106399i	0.0392494	−	0.0204764i	−0.442800	−	0.896620i	$-0.646015\pi$
$3$	0.203946	−	0.106399i	0.0392494	−	0.0204764i	0.482050	+	0.876144i	$0.339892\pi$
$4$	13.6382	+	0.875598i	1.70477	+	0.109450i
$5$	−0.723623	+	0.214768i	−0.0647228	+	0.0192094i	−0.316727	−	0.948517i	$-0.602584\pi$
$5$	−0.723623	+	0.214768i	−0.0647228	+	0.0192094i	0.252004	+	0.967726i	$0.418910\pi$
$6$	−0.964694	+	0.464572i	−0.0656391	+	0.0316101i
$7$	−0.222342	−	6.93345i	−0.0120054	−	0.374371i	−0.987804	−	0.155701i	$-0.950236\pi$
$7$	−0.222342	−	6.93345i	−0.0120054	−	0.374371i	0.975799	−	0.218670i	$-0.0701718\pi$
$8$	−26.2527	−	2.53257i	−1.16022	−	0.111925i
$9$	−15.4169	+	22.1013i	−0.570995	+	0.818565i
$10$	3.39856	−	0.891207i	0.107472	−	0.0281825i
$11$	−10.9231	−	14.6360i	−0.299404	−	0.401174i	0.626203	−	0.779660i	$-0.284608\pi$
$11$	−10.9231	−	14.6360i	−0.299404	−	0.401174i	−0.925607	+	0.378486i	$0.876445\pi$
$12$	2.87461	−	1.27250i	0.0691524	−	0.0306117i
$13$	34.1828	+	35.2966i	0.729278	+	0.753039i	0.976406	−	0.215944i	$-0.0692827\pi$
$13$	34.1828	+	35.2966i	0.729278	+	0.753039i	−0.247128	+	0.968983i	$0.579487\pi$
$14$			32.2897i			0.616414i
$15$	−0.124729	+	0.120793i	−0.00214700	+	0.00207925i
$16$	13.3257	+	1.71816i	0.208214	+	0.0268462i
$17$	43.8584	−	108.331i	0.625718	−	1.54554i	−0.199004	−	0.979999i	$-0.563771\pi$
$17$	43.8584	−	108.331i	0.625718	−	1.54554i	0.824722	−	0.565538i	$-0.191331\pi$
$18$	75.0214	−	100.522i	0.982372	−	1.31629i
$19$	4.40062	−	19.2804i	0.0531354	−	0.232801i	−0.941387	−	0.337330i	$-0.890476\pi$
$19$	4.40062	−	19.2804i	0.0531354	−	0.232801i	0.994522	+	0.104529i	$0.0333334\pi$
$20$	−10.0569	+	2.29543i	−0.112440	+	0.0256637i
$21$	−0.783055	−	1.39039i	−0.00813698	−	0.0144480i
$22$	48.6342	+	69.7207i	0.471311	+	0.675660i
$23$	2.09296	+	1.78176i	0.0189744	+	0.0161532i	0.657665	−	0.753310i	$-0.271544\pi$
$23$	2.09296	+	1.78176i	0.0189744	+	0.0161532i	−0.638691	+	0.769463i	$0.720524\pi$
$24$	−5.62360	+	2.27674i	−0.0478297	+	0.0193641i
$25$	−104.284	+	67.8810i	−0.834268	+	0.543048i
$26$	−153.763	−	169.310i	−1.15982	−	1.27710i
$27$	−1.58690	+	12.3077i	−0.0113111	+	0.0877263i
$28$	3.03858	−	94.7541i	0.0205085	−	0.639530i
$29$	−0.223311	−	0.504464i	−0.00142993	−	0.00323023i	0.913696	−	0.406398i	$-0.133215\pi$
$29$	−0.223311	−	0.504464i	−0.00142993	−	0.00323023i	−0.915126	+	0.403168i	$0.867909\pi$
$30$	0.598300	−	0.543360i	0.00364114	−	0.00330678i
$31$	49.7989	+	255.707i	0.288521	+	1.48149i	0.788274	+	0.615325i	$0.210975\pi$
$31$	49.7989	+	255.707i	0.288521	+	1.48149i	−0.499753	+	0.866168i	$0.666576\pi$
$32$	146.553	+	23.6936i	0.809600	+	0.130890i
$33$	−3.78497	−	1.82275i	−0.0199660	−	0.00961514i
$34$	−220.205	+	497.446i	−1.11073	+	2.50915i
$35$	1.64997	+	4.96945i	0.00796846	+	0.0239997i
$36$	−229.610	+	287.921i	−1.06301	+	1.33297i
$37$	−159.502	+	20.5655i	−0.708702	+	0.0913770i	−0.473788	−	0.880639i	$-0.657114\pi$
$37$	−159.502	+	20.5655i	−0.708702	+	0.0913770i	−0.234914	+	0.972016i	$0.575481\pi$
$38$	−23.3495	+	89.0417i	−0.0996786	+	0.380118i
$39$	10.7270	+	3.56160i	0.0440433	+	0.0146234i
$40$	19.5410	−	3.80561i	0.0772426	−	0.0150430i
$41$	−431.046	−	174.511i	−1.64191	−	0.664734i	−0.646719	−	0.762729i	$-0.723859\pi$
$41$	−431.046	−	174.511i	−1.64191	−	0.664734i	−0.995187	+	0.0979948i	$0.968757\pi$
$42$	3.43558	+	6.58536i	0.0126219	+	0.0241939i
$43$	−382.124	+	285.187i	−1.35520	+	1.01141i	−0.358224	+	0.933636i	$0.616618\pi$
$43$	−382.124	+	285.187i	−1.35520	+	1.01141i	−0.996971	+	0.0777727i	$0.975219\pi$
$44$	−136.156	−	209.172i	−0.466506	−	0.716679i
$45$	6.40938	−	19.3040i	0.0212323	−	0.0639483i
$46$	−9.47127	−	8.60156i	−0.0303579	−	0.0275702i
$47$	−313.132	+	516.544i	−0.971809	+	1.60310i	−0.187934	+	0.982182i	$0.560179\pi$
$47$	−313.132	+	516.544i	−0.971809	+	1.60310i	−0.783875	+	0.620919i	$0.786760\pi$
$48$	2.90053	−	1.06742i	0.00872199	−	0.00320977i
$49$	294.272	−	18.8929i	0.857936	−	0.0550813i
$50$	495.286	−	300.245i	1.40088	−	0.849222i
$51$	−2.58152	−	26.7601i	−0.00708794	−	0.0734739i
$52$	435.285	+	511.311i	1.16083	+	1.36358i
$53$	−363.642	+	400.410i	−0.942454	+	1.03775i	0.0567716	+	0.998387i	$0.481919\pi$
$53$	−363.642	+	400.410i	−0.942454	+	1.03775i	−0.999225	+	0.0393589i	$0.987468\pi$
$54$	9.21892	−	57.0223i	0.0232322	−	0.143699i
$55$	11.0476	+	8.24501i	0.0270846	+	0.0202138i
$56$	−11.7223	+	182.585i	−0.0279726	+	0.435696i
$57$	−1.15391	−	4.40038i	−0.00268140	−	0.0102253i
$58$	0.963652	+	2.38024i	0.00218162	+	0.00538863i
$59$	2.00254	+	0.525127i	0.00441878	+	0.00115874i	0.255863	−	0.966713i	$-0.417640\pi$
$59$	2.00254	+	0.525127i	0.00441878	+	0.00115874i	−0.251445	+	0.967872i	$0.580906\pi$
$60$	−1.80684	+	1.53819i	−0.00388770	+	0.00330965i
$61$	16.9342	−	32.4598i	0.0355444	−	0.0681319i	−0.868172	−	0.496263i	$-0.834705\pi$
$61$	16.9342	−	32.4598i	0.0355444	−	0.0681319i	0.903717	+	0.428131i	$0.140828\pi$
$62$	−193.531	−	1197.06i	−0.396426	−	2.45204i
$63$	156.666	+	101.978i	0.313302	+	0.203937i
$64$	−783.782	−	152.642i	−1.53082	−	0.298128i
$65$	−32.3161	−	18.2001i	−0.0616664	−	0.0347298i
$66$	17.3369	+	9.04466i	0.0323338	+	0.0168685i
$67$	345.982	+	209.736i	0.630872	+	0.382438i	0.797272	−	0.603620i	$-0.206276\pi$
$67$	345.982	+	209.736i	0.630872	+	0.382438i	−0.166400	+	0.986058i	$0.553214\pi$
$68$	693.001	−	1439.03i	1.23586	−	2.56630i
$69$	0.616428	+	0.140696i	0.00107550	+	0.000245475i
$70$	−6.93479	−	23.3656i	−0.0118409	−	0.0398960i
$71$	−178.711	−	124.661i	−0.298720	−	0.208374i	0.413190	−	0.910645i	$-0.364415\pi$
$71$	−178.711	−	124.661i	−0.298720	−	0.208374i	−0.711910	+	0.702271i	$0.752170\pi$
$72$	460.708	−	541.174i	0.754097	−	0.885805i
$73$	39.4844	+	306.233i	0.0633055	+	0.490985i	0.992580	+	0.121595i	$0.0388008\pi$
$73$	39.4844	+	306.233i	0.0633055	+	0.490985i	−0.929274	+	0.369390i	$0.879567\pi$
$74$	745.121	−	71.8809i	1.17052	−	0.112919i
$75$	−14.0458	+	24.9397i	−0.0216249	+	0.0383972i
$76$	76.8982	−	259.096i	0.116064	−	0.391057i
$77$	−99.0492	+	78.9891i	−0.146594	+	0.116904i
$78$	−49.3738	−	18.1700i	−0.0716728	−	0.0263762i
$79$	272.938	+	81.0065i	0.388707	+	0.115366i	0.472973	−	0.881077i	$-0.343181\pi$
$79$	272.938	+	81.0065i	0.388707	+	0.115366i	−0.0842654	+	0.996443i	$0.526854\pi$
$80$	−10.0118	+	1.61863i	−0.0139919	+	0.00226210i
$81$	−250.292	−	680.124i	−0.343336	−	0.932954i
$82$	1979.32	+	876.188i	2.66561	+	1.17999i
$83$	−133.553	−	585.134i	−0.176619	−	0.773816i	−0.983176	−	0.182661i	$-0.941529\pi$
$83$	−133.553	−	585.134i	−0.176619	−	0.773816i	0.806557	−	0.591156i	$-0.201328\pi$
$84$	−9.46199	−	19.6480i	−0.0122903	−	0.0255211i
$85$	−8.47094	+	87.8102i	−0.0108094	+	0.112051i
$86$	1820.31	−	1269.77i	2.28243	−	1.59212i
$87$	−0.0992177	−	0.0791235i	−0.000122267	−	9.75049e-5i
$88$	249.695	+	411.898i	0.302472	+	0.498960i
$89$	26.1044	−	134.041i	0.0310906	−	0.159644i	−0.962763	−	0.270347i	$-0.912861\pi$
$89$	26.1044	−	134.041i	0.0310906	−	0.159644i	0.993853	+	0.110704i	$0.0353104\pi$
$90$	−32.6984	+	88.8521i	−0.0382968	+	0.104065i
$91$	237.127	−	244.853i	0.273161	−	0.282061i
$92$	26.9840	+	26.1325i	0.0305791	+	0.0296142i
$93$	37.3631	+	46.8519i	0.0416599	+	0.0522399i
$94$	1533.85	−	2356.41i	1.68303	−	2.58558i
$95$	0.956409	+	14.8968i	0.00103290	+	0.0160883i
$96$	32.4099	−	10.7608i	0.0344565	−	0.0114403i
$97$	−1438.55	+	810.177i	−1.50580	+	0.848052i	−0.999894	−	0.0145360i	$-0.995373\pi$
$97$	−1438.55	+	810.177i	−1.50580	+	0.848052i	−0.505907	+	0.862588i	$0.668842\pi$
$98$	−1371.86	+	43.9930i	−1.41407	+	0.0453465i
$99$	491.874	−	15.7734i	0.499345	−	0.0160130i
$100$	−1481.67	+	834.461i	−1.48167	+	0.834461i
$101$	−215.294	+	71.4826i	−0.212105	+	0.0704237i	−0.419187	−	0.907900i	$-0.637685\pi$
$101$	−215.294	+	71.4826i	−0.212105	+	0.0704237i	0.207082	+	0.978324i	$0.433603\pi$
$102$	8.01766	+	124.882i	0.00778301	+	0.121227i
$103$	−630.615	+	968.795i	−0.603266	+	0.926778i	0.396695	+	0.917950i	$0.370157\pi$
$103$	−630.615	+	968.795i	−0.603266	+	0.926778i	−0.999961	+	0.00882790i	$0.997190\pi$
$104$	−808.001	−	1013.20i	−0.761837	−	0.955314i
$105$	0.865248	+	0.837946i	0.000804186	+	0.000778811i
$106$	1751.51	−	1808.58i	1.60492	−	1.65721i
$107$	−43.1501	+	117.253i	−0.0389858	+	0.105937i	−0.956465	−	0.291846i	$-0.905731\pi$
$107$	−43.1501	+	117.253i	−0.0389858	+	0.105937i	0.917480	+	0.397783i	$0.130220\pi$
$108$	−32.4189	+	166.464i	−0.0288844	+	0.148315i
$109$	404.515	+	667.290i	0.355464	+	0.586375i	0.981044	−	0.193785i	$-0.0620765\pi$
$109$	404.515	+	667.290i	0.355464	+	0.586375i	−0.625580	+	0.780160i	$0.715138\pi$
$110$	−50.1666	−	40.0065i	−0.0434836	−	0.0346770i
$111$	−30.3417	+	21.1650i	−0.0259451	+	0.0180982i
$112$	8.94990	−	92.7750i	0.00755077	−	0.0782716i
$113$	313.769	+	651.547i	0.261211	+	0.542411i	0.989787	−	0.142555i	$-0.0455316\pi$
$113$	313.769	+	651.547i	0.261211	+	0.542411i	−0.728576	+	0.684965i	$0.759817\pi$
$114$	4.71187	+	20.6441i	0.00387112	+	0.0169605i
$115$	−1.89718	−	0.839825i	−0.00153837	−	0.000680992i
$116$	−2.60385	−	7.07549i	−0.00208415	−	0.00566330i
$117$	−1307.09	+	211.320i	−1.03283	+	0.166979i
$118$	−9.23807	−	2.74181i	−0.00720706	−	0.00213902i
$119$	−760.859	−	280.003i	−0.586116	−	0.215696i
$120$	3.58040	−	2.85527i	0.00272370	−	0.00217208i
$121$	283.809	−	956.246i	0.213230	−	0.718442i
$122$	−83.6260	+	148.486i	−0.0620586	+	0.110191i
$123$	−106.478	+	10.2718i	−0.0780552	+	0.00752989i
$124$	455.268	+	3530.97i	0.329712	+	2.55718i
$125$	122.045	−	143.362i	0.0873286	−	0.102581i
$126$	−713.643	−	497.807i	−0.504575	−	0.351969i
$127$	534.692	+	1801.55i	0.373592	+	1.25876i	0.909933	+	0.414755i	$0.136133\pi$
$127$	534.692	+	1801.55i	0.373592	+	1.25876i	−0.536341	+	0.844001i	$0.680194\pi$
$128$	2465.75	+	562.791i	1.70268	+	0.388627i
$129$	−47.5893	+	98.8201i	−0.0324806	+	0.0674467i
$130$	147.629	+	89.4935i	0.0995994	+	0.0603777i
$131$	−2110.45	−	1101.02i	−1.40756	−	0.734324i	−0.422474	−	0.906375i	$-0.638838\pi$
$131$	−2110.45	−	1101.02i	−1.40756	−	0.734324i	−0.985088	+	0.172051i	$0.944961\pi$
$132$	−50.0241	−	28.1730i	−0.0329851	−	0.0185769i
$133$	−134.658	−	26.2246i	−0.0877920	−	0.0170975i
$134$	−1578.32	−	1027.37i	−1.01751	−	0.662326i
$135$	−1.49497	−	9.24693i	−0.000953086	−	0.00589518i
$136$	−1425.76	+	2732.91i	−0.898953	+	1.72313i
$137$	782.387	−	666.056i	0.487911	−	0.415365i	−0.370103	−	0.928991i	$-0.620678\pi$
$137$	782.387	−	666.056i	0.487911	−	0.415365i	0.858014	+	0.513626i	$0.171698\pi$
$138$	−2.84682	−	0.746524i	−0.00175607	−	0.000460495i
$139$	366.779	+	905.951i	0.223811	+	0.552819i	0.996650	−	0.0817840i	$-0.0260618\pi$
$139$	366.779	+	905.951i	0.223811	+	0.552819i	−0.772839	+	0.634603i	$0.781164\pi$
$140$	18.1513	+	69.2189i	0.0109576	+	0.0417862i
$141$	−8.90252	+	138.664i	−0.00531722	+	0.0828199i
$142$	812.822	+	606.625i	0.480356	+	0.358499i
$143$	143.217	−	885.848i	0.0837511	−	0.518030i
$144$	−243.414	+	268.026i	−0.140865	+	0.155108i
$145$	0.269936	+	0.317082i	0.000154600	+	0.000181602i
$146$	−138.007	−	1430.58i	−0.0782295	−	0.810930i
$147$	58.0054	−	35.1632i	0.0325456	−	0.0197294i
$148$	−2193.32	+	140.816i	−1.21817	+	0.0782094i
$149$	1212.46	−	446.196i	0.666635	−	0.245328i	0.0104698	−	0.999945i	$-0.496667\pi$
$149$	1212.46	−	446.196i	0.666635	−	0.245328i	0.656165	+	0.754617i	$0.272178\pi$
$150$	69.0660	−	113.932i	0.0375948	−	0.0620165i
$151$	−2378.26	−	2159.88i	−1.28172	−	1.16403i	−0.977386	−	0.211464i	$-0.932177\pi$
$151$	−2378.26	−	2159.88i	−1.28172	−	1.16403i	−0.304338	−	0.952564i	$-0.598435\pi$
$152$	−164.357	+	495.018i	−0.0877048	+	0.264153i
$153$	1718.09	+	2639.45i	0.907840	+	1.39469i
$154$	472.592	−	352.704i	0.247289	−	0.184557i
$155$	−90.9531	−	174.340i	−0.0471325	−	0.0903441i
$156$	143.177	+	57.9661i	0.0734831	+	0.0297500i
$157$	2131.82	−	415.171i	1.08368	−	0.211046i	0.382445	−	0.923978i	$-0.375082\pi$
$157$	2131.82	−	415.171i	1.08368	−	0.211046i	0.701233	+	0.712932i	$0.252633\pi$
$158$	−1257.70	−	417.587i	−0.633276	−	0.210262i
$159$	−31.5603	+	120.353i	−0.0157415	+	0.0600290i
$160$	−111.138	+	14.3297i	−0.0549139	+	0.00708037i
$161$	11.8884	−	14.9076i	0.00581949	−	0.00729741i
$162$	1062.97	+	3201.49i	0.515522	+	1.55267i
$163$	849.417	−	1918.85i	0.408168	−	0.922059i	−0.585601	−	0.810600i	$-0.699141\pi$
$163$	849.417	−	1918.85i	0.408168	−	0.922059i	0.993769	−	0.111460i	$-0.0355526\pi$
$164$	−5725.87	−	2757.44i	−2.72631	−	1.31292i
$165$	3.13036	+	0.506093i	0.00147696	+	0.000238783i
$166$	534.033	+	2742.15i	0.249693	+	1.28212i
$167$	−1949.53	+	1770.51i	−0.903348	+	0.820397i	−0.984333	−	0.176319i	$-0.943581\pi$
$167$	−1949.53	+	1770.51i	−0.903348	+	0.820397i	0.0809853	+	0.996715i	$0.474193\pi$
$168$	17.0361	+	38.4847i	0.00782357	+	0.0176736i
$169$	−6.96527	+	217.203i	−0.00317035	+	0.0988633i
$170$	52.5099	−	407.256i	0.0236901	−	0.183736i
$171$	358.277	+	394.502i	0.160223	+	0.176423i
$172$	−5461.18	+	3554.83i	−2.42099	+	1.57589i
$173$	2974.05	−	1204.06i	1.30701	−	0.529149i	0.387374	−	0.921923i	$-0.373382\pi$
$173$	2974.05	−	1204.06i	1.30701	−	0.529149i	0.919635	+	0.392773i	$0.128484\pi$
$174$	0.449787	+	0.382909i	0.000195967	+	0.000166829i
$175$	493.836	+	707.952i	0.213317	+	0.305806i
$176$	−120.411	−	213.802i	−0.0515701	−	0.0915679i
$177$	0.464282	−	0.105969i	0.000197161	−	4.50008e-5i
$178$	−141.444	+	619.705i	−0.0595598	+	0.260948i
$179$	−960.405	+	1286.86i	−0.401028	+	0.537341i	−0.955550	−	0.294828i	$-0.904738\pi$
$179$	−960.405	+	1286.86i	−0.401028	+	0.537341i	0.554522	+	0.832169i	$0.312901\pi$
$180$	104.315	−	257.659i	0.0431953	−	0.106693i
$181$	−1948.18	−	251.190i	−0.800039	−	0.103154i	−0.283005	−	0.959118i	$-0.591331\pi$
$181$	−1948.18	−	251.190i	−0.800039	−	0.103154i	−0.517034	+	0.855965i	$0.672964\pi$
$182$	−1139.72	+	1103.75i	−0.464184	+	0.449537i
$183$		−	8.42182i		−	0.00340196i
$184$	−50.4334	−	52.0767i	−0.0202065	−	0.0208649i
$185$	111.003	−	49.1376i	0.0441139	−	0.0195279i
$186$	−166.835	−	223.543i	−0.0657684	−	0.0881237i
$187$	−2064.60	+	541.402i	−0.807372	+	0.211718i
$188$	−4722.83	+	6770.53i	−1.83217	+	2.62655i
$189$	85.6874	+	8.26616i	0.0329780	+	0.00318135i
$190$	−2.22704	−	69.4474i	−0.000850351	−	0.0265171i
$191$	3215.74	−	1548.62i	1.21823	−	0.586671i	0.289415	−	0.957204i	$-0.406539\pi$
$191$	3215.74	−	1548.62i	1.21823	−	0.586671i	0.928819	+	0.370533i	$0.120825\pi$
$192$	−176.090	+	52.2626i	−0.0661886	+	0.0196444i
$193$	2038.75	+	130.892i	0.760377	+	0.0488178i	0.439427	−	0.898278i	$-0.355182\pi$
$193$	2038.75	+	130.892i	0.760377	+	0.0488178i	0.320950	+	0.947096i	$0.395998\pi$
$194$	6813.46	−	3554.58i	2.52153	−	1.31548i
$195$	−8.52719	−	0.273450i	−0.00313151	−	0.000100422i
$196$	4029.87			1.46861
$197$	−2755.61	−	227.982i	−0.996595	−	0.0824519i
$197$	−2755.61	−	227.982i	−0.996595	−	0.0824519i
$198$	−2290.70			−0.822188
$199$	90.6390	+	2.90662i	0.0322876	+	0.00103540i	0.0481912	−	0.998838i	$-0.484654\pi$
$199$	90.6390	+	2.90662i	0.0322876	+	0.00103540i	−0.0159036	+	0.999874i	$0.505062\pi$
$200$	2909.64	−	1517.96i	1.02871	−	0.536679i
$201$	92.8773	+	5.96292i	0.0325923	+	0.00209250i
$202$	1012.28	−	300.439i	0.352593	−	0.104648i
$203$	−3.44803	+	1.66048i	−0.00119214	+	0.000574103i
$204$	−11.7760	−	367.219i	−0.00404159	−	0.126032i
$205$	349.395	+	33.7057i	0.119038	+	0.0114834i
$206$	3078.35	−	4413.05i	1.04116	−	1.49258i
$207$	−71.6461	+	18.7878i	−0.0240567	+	0.00630842i
$208$	394.865	+	529.083i	0.131630	+	0.176372i
$209$	−330.256	+	146.194i	−0.109303	+	0.0483851i
$210$	−3.90039	−	4.02747i	−0.00128168	−	0.00132344i
$211$		−	2395.72i		−	0.781651i	−0.920465	−	0.390825i	$-0.872190\pi$
$211$		−	2395.72i		−	0.781651i	0.920465	−	0.390825i	$-0.127810\pi$
$212$	−5310.00	+	5142.45i	−1.72025	+	1.66597i
$213$	−49.7113	−	6.40956i	−0.0159914	−	0.00206186i
$214$	218.241	−	539.059i	0.0697132	−	0.172193i
$215$	215.265	−	288.436i	0.0682835	−	0.0914937i
$216$	72.8304	−	319.091i	0.0229420	−	0.100516i
$217$	1761.86	−	402.132i	0.551164	−	0.125800i
$218$	−1782.38	−	3164.79i	−0.553751	−	0.983241i
$219$	40.6355	+	58.2540i	0.0125383	+	0.0179746i
$220$	143.449	+	122.120i	0.0439606	+	0.0374242i
$221$	5322.92	−	2155.01i	1.62017	−	0.655935i
$222$	144.316	−	93.9396i	0.0436301	−	0.0284001i
$223$	−362.666	−	399.335i	−0.108905	−	0.119917i	0.683393	−	0.730051i	$-0.260503\pi$
$223$	−362.666	−	399.335i	−0.108905	−	0.119917i	−0.792299	+	0.610134i	$0.791116\pi$
$224$	131.693	−	1021.39i	0.0392819	−	0.304662i
$225$	107.470	−	3351.31i	0.0318430	−	0.992981i
$226$	−1362.54	−	3078.01i	−0.401040	−	0.905957i
$227$	−1192.49	+	1082.99i	−0.348671	+	0.316653i	−0.827727	−	0.561130i	$-0.810367\pi$
$227$	−1192.49	+	1082.99i	−0.348671	+	0.316653i	0.479057	+	0.877784i	$0.340979\pi$
$228$	−11.8843	−	61.0234i	−0.00345200	−	0.0177253i
$229$	−3305.01	−	534.328i	−0.953716	−	0.154189i	−0.337114	−	0.941464i	$-0.609451\pi$
$229$	−3305.01	−	534.328i	−0.953716	−	0.154189i	−0.616603	+	0.787275i	$0.711491\pi$
$230$	8.70097	+	4.19016i	0.00249446	+	0.00120127i
$231$	−11.7964	+	26.6482i	−0.00335993	+	0.00759014i
$232$	4.58494	+	13.8091i	0.00129748	+	0.00390781i
$233$	3698.83	−	4638.19i	1.03999	−	1.30411i	0.0886214	−	0.996065i	$-0.471754\pi$
$233$	3698.83	−	4638.19i	1.03999	−	1.30411i	0.951372	−	0.308045i	$-0.0996747\pi$
$234$	6112.52	−	788.122i	1.70764	−	0.220176i
$235$	115.653	−	441.034i	0.0321036	−	0.122425i
$236$	26.8511	+	8.91518i	0.00740618	+	0.00245902i
$237$	64.2835	−	12.5192i	0.0176188	−	0.00343127i
$238$	3497.98	+	1416.17i	0.952690	+	0.385701i
$239$	2185.04	+	4188.31i	0.591373	+	1.13355i	0.977466	+	0.211092i	$0.0677020\pi$
$239$	2185.04	+	4188.31i	0.591373	+	1.13355i	−0.386093	+	0.922460i	$0.626176\pi$
$240$	−1.86964	+	1.39535i	−0.000502854	+	0.000375290i
$241$	−758.364	−	1165.05i	−0.202699	−	0.311400i	0.722149	−	0.691738i	$-0.243155\pi$
$241$	−758.364	−	1165.05i	−0.202699	−	0.311400i	−0.924848	+	0.380338i	$0.875808\pi$
$242$	−1463.03	+	4406.41i	−0.388624	+	1.17047i
$243$	−371.446	−	337.338i	−0.0980588	−	0.0890544i
$244$	259.374	−	427.864i	0.0680520	−	0.112259i
$245$	−208.884	+	76.8714i	−0.0544700	+	0.0200454i
$246$	496.901	−	31.9021i	0.128785	−	0.00826830i
$247$	830.957	−	503.731i	0.214059	−	0.129764i
$248$	−659.761	−	6839.12i	−0.168931	−	1.75115i
$249$	−89.4950	−	105.126i	−0.0227772	−	0.0267553i
$250$	−589.181	+	648.754i	−0.149052	+	0.164123i
$251$	−1010.91	+	6252.81i	−0.254214	+	1.57241i	0.469896	+	0.882722i	$0.344292\pi$
$251$	−1010.91	+	6252.81i	−0.254214	+	1.57241i	−0.724110	+	0.689684i	$0.757749\pi$
$252$	2047.34	+	1527.97i	0.511787	+	0.381956i
$253$	3.21620	−	50.0949i	0.000799212	−	0.0124484i
$254$	−2218.78	−	8461.15i	−0.548104	−	2.09016i
$255$	7.61526	+	18.8098i	0.00187014	+	0.00461928i
$256$	−5208.33	−	1365.79i	−1.27157	−	0.333444i
$257$	−3291.74	+	2802.30i	−0.798961	+	0.680166i	−0.951335	−	0.308157i	$-0.900288\pi$
$257$	−3291.74	+	2802.30i	−0.798961	+	0.680166i	0.152374	+	0.988323i	$0.451308\pi$
$258$	236.143	−	452.642i	0.0569830	−	0.109226i
$259$	178.054	+	1101.33i	0.0427171	+	0.264221i
$260$	−424.795	−	276.511i	−0.101326	−	0.0659557i
$261$	14.5921	+	2.84180i	0.00346063	+	0.000673958i
$262$	9654.19	+	5437.14i	2.27648	+	1.28209i
$263$	−539.867	−	281.648i	−0.126577	−	0.0660349i	0.398070	−	0.917355i	$-0.369680\pi$
$263$	−539.867	−	281.648i	−0.126577	−	0.0660349i	−0.524647	+	0.851320i	$0.675803\pi$
$264$	94.7496	+	57.4378i	0.0220888	+	0.0133903i
$265$	177.145	−	367.844i	0.0410638	−	0.0852698i
$266$	622.558	+	142.095i	0.143502	+	0.0327534i
$267$	−8.93785	−	30.1146i	−0.00204864	−	0.00690255i
$268$	4534.91	+	3163.36i	1.03363	+	0.721018i
$269$	3567.96	−	4191.13i	0.808708	−	0.949954i	−0.190790	−	0.981631i	$-0.561105\pi$
$269$	3567.96	−	4191.13i	0.808708	−	0.949954i	0.999498	+	0.0316765i	$0.0100846\pi$
$270$	5.57551	+	43.2426i	0.00125672	+	0.00974689i
$271$	−4667.10	+	450.230i	−1.04615	+	0.100921i	−0.604770	−	0.796400i	$-0.706735\pi$
$271$	−4667.10	+	450.230i	−1.04615	+	0.100921i	−0.441379	+	0.897321i	$0.645511\pi$
$272$	770.573	−	1368.23i	0.171775	−	0.305004i
$273$	22.3091	−	75.1667i	0.00494581	−	0.0166641i
$274$	−3739.27	+	2981.97i	−0.824444	+	0.657472i
$275$	2132.61	+	784.819i	0.467640	+	0.172096i
$276$	8.28374	+	2.45857i	0.00180660	+	0.000536190i
$277$	−3098.11	+	500.879i	−0.672013	+	0.108646i	−0.486077	−	0.873916i	$-0.661573\pi$
$277$	−3098.11	+	500.879i	−0.672013	+	0.108646i	−0.185936	+	0.982562i	$0.559532\pi$
$278$	−1571.21	−	4269.48i	−0.338974	−	0.921103i
$279$	−6419.18	−	2841.58i	−1.37744	−	0.609753i
$280$	−30.7308	−	134.640i	−0.00655899	−	0.0287368i
$281$	2867.66	+	5954.75i	0.608790	+	1.26417i	0.946436	+	0.322893i	$0.104655\pi$
$281$	2867.66	+	5954.75i	0.608790	+	1.26417i	−0.337645	+	0.941273i	$0.609630\pi$
$282$	62.1046	−	643.779i	0.0131145	−	0.135945i
$283$	5042.95	−	3517.75i	1.05927	−	0.738899i	0.0927986	−	0.995685i	$-0.470419\pi$
$283$	5042.95	−	3517.75i	1.05927	−	0.738899i	0.966468	+	0.256786i	$0.0826636\pi$
$284$	−2328.14	−	1856.63i	−0.486443	−	0.387925i
$285$	1.78006	+	2.93639i	0.000369970	+	0.000610305i
$286$	−798.450	+	4099.87i	−0.165082	+	0.847659i
$287$	−1114.13	+	3027.44i	−0.229146	+	0.622662i
$288$	−2783.05	+	2873.73i	−0.569420	+	0.587973i
$289$	−6282.80	−	6084.55i	−1.27881	−	1.23846i
$290$	−1.20852	−	1.51543i	−0.000244713	−	0.000306860i
$291$	−207.185	+	318.292i	−0.0417368	+	0.0641190i
$292$	270.357	+	4211.03i	0.0541830	+	0.843944i
$293$	−626.404	+	207.981i	−0.124897	+	0.0414688i	−0.376874	−	0.926265i	$-0.623001\pi$
$293$	−626.404	+	207.981i	−0.124897	+	0.0414688i	0.251977	+	0.967733i	$0.418919\pi$
$294$	−275.105	+	154.936i	−0.0545730	+	0.0307349i
$295$	−1.56186	+	0.0500859i	−0.000308255	+	9.88513e-6i
$296$	4239.45	−	135.951i	0.832476	−	0.0266959i
$297$	197.469	−	111.212i	0.0385801	−	0.0217279i
$298$	−5707.31	+	1894.96i	−1.10945	+	0.368362i
$299$	8.65316	+	134.780i	0.00167366	+	0.0260687i
$300$	−213.395	+	327.833i	−0.0410680	+	0.0630914i
$301$	2062.29	+	2586.03i	0.394912	+	0.495204i
$302$	10742.2	+	10403.2i	2.04683	+	1.98225i
$303$	−36.3028	+	37.4856i	−0.00688297	+	0.00710723i
$304$	91.7681	−	249.363i	0.0173134	−	0.0470460i
$305$	−5.28271	+	27.1256i	−0.000991760	+	0.00509248i
$306$	−7599.31	−	12535.9i	−1.41969	−	2.34192i
$307$	5556.27	+	4430.98i	1.03294	+	0.823744i	0.984553	−	0.175085i	$-0.0560199\pi$
$307$	5556.27	+	4430.98i	1.03294	+	0.823744i	0.0483888	+	0.998829i	$0.484591\pi$
$308$	−1420.01	+	990.538i	−0.262703	+	0.183250i
$309$	−25.5332	+	264.678i	−0.00470075	+	0.0487282i
$310$	397.132	+	824.653i	0.0727600	+	0.151088i
$311$	277.924	+	1217.66i	0.0506740	+	0.222017i	0.993924	−	0.110065i	$-0.0351059\pi$
$311$	277.924	+	1217.66i	0.0506740	+	0.222017i	−0.943250	+	0.332082i	$0.892249\pi$
$312$	−272.592	−	120.668i	−0.0494631	−	0.0218958i
$313$	−989.371	−	2688.44i	−0.178666	−	0.485494i	0.817197	−	0.576359i	$-0.195527\pi$
$313$	−989.371	−	2688.44i	−0.178666	−	0.485494i	−0.995863	+	0.0908644i	$0.971037\pi$
$314$	−9979.81	+	1613.46i	−1.79361	+	0.289977i
$315$	−135.269	−	40.1470i	−0.0241953	−	0.00718104i
$316$	3651.44	+	1343.76i	0.650029	+	0.239217i
$317$	−4255.96	+	3394.02i	−0.754065	+	0.601347i	−0.923233	−	0.384240i	$-0.874463\pi$
$317$	−4255.96	+	3394.02i	−0.754065	+	0.601347i	0.169168	+	0.985587i	$0.445892\pi$
$318$	164.784	−	555.211i	0.0290585	−	0.0979078i
$319$	−4.94407	+	8.77870i	−0.000867758	+	0.00154079i
$320$	599.945	−	57.8760i	0.104806	−	0.0101105i
$321$	3.67523	+	28.5044i	0.000639039	+	0.00495626i
$322$	−57.5326	+	67.5811i	−0.00995704	+	0.0116961i
$323$	−1895.66	−	1322.33i	−0.326555	−	0.227791i
$324$	−2818.00	−	9494.79i	−0.483197	−	1.62805i
$325$	−5960.67	−	1360.48i	−1.01735	−	0.232203i
$326$	−4238.02	+	8800.34i	−0.720007	+	1.49511i
$327$	153.498	+	93.0514i	0.0259586	+	0.0157363i
$328$	10874.2	+	5673.05i	1.83057	+	0.955006i
$329$	3651.06	+	2056.24i	0.611821	+	0.344571i
$330$	−14.4879	−	2.82152i	−0.00241677	−	0.000470665i
$331$	4689.34	+	3052.42i	0.778698	+	0.506876i	0.872441	−	0.488720i	$-0.162536\pi$
$331$	4689.34	+	3052.42i	0.778698	+	0.506876i	−0.0937423	+	0.995596i	$0.529883\pi$
$332$	−1309.07	−	8097.08i	−0.216400	−	1.33851i
$333$	2004.50	−	3842.25i	0.329868	−	0.632295i
$334$	9333.95	−	7946.11i	1.52914	−	1.30177i
$335$	−295.405	−	77.4643i	−0.0481782	−	0.0126338i
$336$	−8.04583	−	19.8734i	−0.00130636	−	0.00322673i
$337$	700.563	+	2671.55i	0.113241	+	0.431836i	0.999509	−	0.0313367i	$-0.00997641\pi$
$337$	700.563	+	2671.55i	0.113241	+	0.431836i	−0.886268	+	0.463172i	$0.846711\pi$
$338$	64.8092	−	1009.45i	0.0104294	−	0.162447i
$339$	133.316	+	99.4960i	0.0213590	+	0.0159406i
$340$	−192.414	+	1190.15i	−0.0306916	+	0.189838i
$341$	3198.56	−	3521.97i	0.507952	−	0.559312i
$342$	−1607.96	−	1888.80i	−0.254235	−	0.298639i
$343$	−424.899	−	4404.52i	−0.0668874	−	0.693358i
$344$	10754.1	−	6519.17i	1.68552	−	1.02177i
$345$	−0.476278	+	0.0305781i	−7.43245e−5	+	4.77179e-6i
$346$	−14015.8	+	5157.95i	−2.17773	+	0.801425i
$347$	−3962.66	+	6536.83i	−0.613046	+	1.01128i	0.383112	+	0.923702i	$0.374852\pi$
$347$	−3962.66	+	6536.83i	−0.613046	+	1.01128i	−0.996157	+	0.0875811i	$0.972086\pi$
$348$	−1.28387	−	1.16597i	−0.000197766	−	0.000179605i
$349$	607.617	−	1830.04i	0.0931948	−	0.280688i	−0.892024	−	0.451988i	$-0.850715\pi$
$349$	607.617	−	1830.04i	0.0931948	−	0.280688i	0.985219	+	0.171300i	$0.0547967\pi$
$350$	−2191.86	−	3367.29i	−0.334742	−	0.514254i
$351$	−488.663	+	364.699i	−0.0743103	+	0.0554592i
$352$	−1254.04	−	2403.76i	−0.189888	−	0.363980i
$353$	−2884.13	−	1167.65i	−0.434863	−	0.176057i	0.147365	−	0.989082i	$-0.452921\pi$
$353$	−2884.13	−	1167.65i	−0.434863	−	0.176057i	−0.582228	+	0.813026i	$0.697819\pi$
$354$	−2.17579	+	0.423736i	−0.000326673	+	6.36195e-5i
$355$	156.093	+	51.8264i	0.0233368	+	0.00774834i
$356$	473.382	−	1805.21i	0.0704753	−	0.268753i
$357$	−184.966	+	23.8487i	−0.0274214	+	0.00353560i
$358$	4660.09	−	5843.57i	0.687970	−	0.862687i
$359$	318.558	+	959.447i	0.0468325	+	0.141052i	0.969848	−	0.243711i	$-0.0783648\pi$
$359$	318.558	+	959.447i	0.0468325	+	0.141052i	−0.923015	+	0.384763i	$0.874283\pi$
$360$	−217.152	+	490.551i	−0.0317915	+	0.0718175i
$361$	5827.38	+	2806.32i	0.849596	+	0.409144i
$362$	9026.06	+	1459.26i	1.31050	+	0.211871i
$363$	−43.8615	−	225.219i	−0.00634196	−	0.0325646i
$364$	3448.36	−	3131.71i	0.496548	−	0.450952i
$365$	−94.3408	−	213.118i	−0.0135288	−	0.0305619i
$366$	−1.25646	+	39.1809i	−0.000179443	+	0.00559568i
$367$	470.800	−	3651.43i	0.0669633	−	0.519354i	−0.923710	−	0.383093i	$-0.874859\pi$
$367$	470.800	−	3651.43i	0.0669633	−	0.519354i	0.990673	−	0.136261i	$-0.0435086\pi$
$368$	24.8288	+	27.3392i	0.00351709	+	0.00387271i
$369$	10502.3	−	6836.24i	1.48165	−	0.964446i
$370$	−523.749	+	212.043i	−0.0735903	+	0.0297934i
$371$	2857.08	+	2432.26i	0.399817	+	0.340369i
$372$	468.540	+	671.688i	0.0653029	+	0.0936166i
$373$	4956.83	+	8801.36i	0.688083	+	1.22176i	0.965348	+	0.260968i	$0.0840416\pi$
$373$	4956.83	+	8801.36i	0.688083	+	1.22176i	−0.277264	+	0.960794i	$0.589428\pi$
$374$	9685.93	−	2210.75i	1.33916	−	0.305656i
$375$	9.63723	−	42.2235i	0.00132711	−	0.00581443i
$376$	9528.76	−	12767.7i	1.30694	−	1.75118i
$377$	10.1724	−	25.1261i	0.00138968	−	0.00343253i
$378$	−397.411	−	51.2405i	−0.0540757	−	0.00697229i
$379$	−3180.00	+	3079.66i	−0.430991	+	0.417392i	−0.879137	−	0.476569i	$-0.841880\pi$
$379$	−3180.00	+	3079.66i	−0.430991	+	0.417392i	0.448146	+	0.893960i	$0.352084\pi$
$380$			204.003i			0.0275398i
$381$	300.731	+	310.529i	0.0404381	+	0.0417556i
$382$	−15191.7	+	6724.90i	−2.03475	+	0.900722i
$383$	−3747.05	−	5020.70i	−0.499909	−	0.669832i	0.478122	−	0.878294i	$-0.341318\pi$
$383$	−3747.05	−	5020.70i	−0.499909	−	0.669832i	−0.978031	+	0.208461i	$0.933154\pi$
$384$	562.760	−	147.573i	0.0747871	−	0.0196115i
$385$	54.7100	−	78.4309i	0.00724229	−	0.0103824i
$386$	−9465.38	−	913.114i	−1.24812	−	0.120405i
$387$	−411.821	−	12842.1i	−0.0540932	−	1.68682i
$388$	−20328.6	+	9789.72i	−2.65986	+	1.28092i
$389$	5694.51	−	1690.10i	0.742218	−	0.220286i	0.108765	−	0.994067i	$-0.465310\pi$
$389$	5694.51	−	1690.10i	0.742218	−	0.220286i	0.633453	+	0.773781i	$0.281637\pi$
$390$	39.6303	+	2.54435i	0.00514554	+	0.000330354i
$391$	284.814	−	148.587i	0.0368380	−	0.0192184i
$392$	−7773.29	−	249.274i	−1.00156	−	0.0321180i
$393$	−547.564			−0.0702823
$394$	12785.9	+	1471.75i	1.63489	+	0.188187i
$395$	−214.902			−0.0273744
$396$	6722.06	+	215.563i	0.853021	+	0.0273547i
$397$	2402.90	−	1253.59i	0.303774	−	0.158479i	−0.303813	−	0.952732i	$-0.598260\pi$
$397$	2402.90	−	1253.59i	0.303774	−	0.158479i	0.607587	+	0.794253i	$0.292137\pi$
$398$	−421.247	−	27.0449i	−0.0530533	−	0.00340613i
$399$	−30.2532	+	8.97900i	−0.00379588	+	0.00112660i
$400$	−1506.28	+	725.386i	−0.188285	+	0.0906733i
$401$	−144.833	−	4516.44i	−0.0180365	−	0.562444i	−0.968126	−	0.250465i	$-0.919416\pi$
$401$	−144.833	−	4516.44i	−0.0180365	−	0.562444i	0.950089	−	0.311979i	$-0.100992\pi$
$402$	−431.204	−	41.5977i	−0.0534988	−	0.00516096i
$403$	−7323.31	+	10498.5i	−0.905211	+	1.29769i
$404$	−2998.81	+	786.380i	−0.369298	+	0.0968412i
$405$	327.186	+	438.399i	0.0401432	+	0.0537882i
$406$	16.2890	−	7.21066i	0.00199116	−	0.000881426i
$407$	2043.26	+	2109.83i	0.248846	+	0.256954i
$408$			709.064i			0.0860390i
$409$	4500.00	−	4358.01i	0.544036	−	0.526870i	−0.371858	−	0.928290i	$-0.621279\pi$
$409$	4500.00	−	4358.01i	0.544036	−	0.526870i	0.915894	+	0.401420i	$0.131483\pi$
$410$	−1620.46	−	208.936i	−0.195193	−	0.0251673i
$411$	88.6974	−	219.084i	0.0106451	−	0.0262935i
$412$	−9448.70	+	12660.4i	−1.12986	+	1.51392i
$413$	3.19569	−	14.0012i	0.000380750	−	0.00166817i
$414$	336.123	−	76.7178i	0.0399022	−	0.00910742i
$415$	222.310	+	394.733i	0.0262958	+	0.0466909i
$416$	4173.30	+	5982.74i	0.491858	+	0.705116i
$417$	171.195	+	145.740i	0.0201042	+	0.0171150i
$418$	1558.26	−	630.871i	0.182338	−	0.0738203i
$419$	−13651.0	+	8885.81i	−1.59163	+	1.03604i	−0.624749	+	0.780826i	$0.714799\pi$
$419$	−13651.0	+	8885.81i	−1.59163	+	1.03604i	−0.966885	+	0.255213i	$0.917854\pi$
$420$	11.0667	+	12.1856i	0.00128571	+	0.00141571i
$421$	1291.28	−	10014.9i	0.149485	−	1.15937i	−0.730000	−	0.683447i	$-0.760480\pi$
$421$	1291.28	−	10014.9i	0.149485	−	1.15937i	0.879485	−	0.475927i	$-0.157887\pi$
$422$	−357.419	+	11145.6i	−0.0412296	+	1.28569i
$423$	−6588.75	−	14884.1i	−0.757343	−	1.71085i
$424$	10560.7	−	9590.91i	1.20960	−	1.09853i
$425$	2779.92	+	14274.3i	0.317284	+	1.62919i
$426$	230.316	+	37.2357i	0.0261945	+	0.00423492i
$427$	−228.823	−	110.196i	−0.0259334	−	0.0124888i
$428$	−691.155	+	1561.33i	−0.0780566	+	0.176331i
$429$	−65.0444	−	195.903i	−0.00732021	−	0.0220473i
$430$	−1044.51	+	1309.78i	−0.117141	+	0.146891i
$431$	−13967.1	+	1800.85i	−1.56095	+	0.201262i	−0.859379	−	0.511338i	$-0.829150\pi$
$431$	−13967.1	+	1800.85i	−1.56095	+	0.201262i	−0.701570	+	0.712601i	$0.747517\pi$
$432$	−42.2930	+	161.282i	−0.00471024	+	0.0179622i
$433$	8395.82	+	2787.60i	0.931819	+	0.309385i	0.740433	−	0.672130i	$-0.234620\pi$
$433$	8395.82	+	2787.60i	0.931819	+	0.309385i	0.191385	+	0.981515i	$0.438702\pi$
$434$	−8256.70	+	1607.99i	−0.913212	+	0.177848i
$435$	0.0887894	+	0.0359468i	9.78650e−6	+	3.96211e-6i
$436$	4932.56	+	9454.80i	0.541805	+	1.03854i
$437$	43.5634	−	32.5122i	0.00476869	−	0.00355897i
$438$	−180.358	−	277.078i	−0.0196754	−	0.0302267i
$439$	−26.4456	+	79.6498i	−0.00287512	+	0.00865940i	−0.950483	−	0.310775i	$-0.899411\pi$
$439$	−26.4456	+	79.6498i	−0.00287512	+	0.00865940i	0.947608	+	0.319435i	$0.103493\pi$
$440$	−269.147	−	244.433i	−0.0291616	−	0.0264838i
$441$	−4119.20	+	6795.05i	−0.444790	+	0.733727i
$442$	−25085.4	+	9231.64i	−2.69952	+	0.993449i
$443$	−3898.51	+	250.292i	−0.418112	+	0.0268437i	−0.271705	−	0.962381i	$-0.587587\pi$
$443$	−3898.51	+	250.292i	−0.418112	+	0.0268437i	−0.146407	+	0.989224i	$0.546771\pi$
$444$	−432.336	+	262.085i	−0.0462112	+	0.0280135i
$445$	9.89784	+	102.601i	0.00105439	+	0.0109298i
$446$	1627.66	+	1911.94i	0.172807	+	0.202988i
$447$	199.802	−	220.004i	0.0211416	−	0.0232793i
$448$	−884.065	+	5468.25i	−0.0932324	+	0.576676i
$449$	−12706.0	−	9482.73i	−1.33549	−	0.996698i	−0.998475	−	0.0551972i	$-0.982421\pi$
$449$	−12706.0	−	9482.73i	−1.33549	−	0.996698i	−0.337010	−	0.941501i	$-0.609415\pi$
$450$	−999.967	+	15575.3i	−0.104753	+	1.63161i
$451$	2154.23	+	8214.99i	0.224919	+	0.857714i
$452$	3708.73	+	9160.64i	0.385938	+	0.953275i
$453$	−714.845	−	187.454i	−0.0741421	−	0.0194423i
$454$	5709.40	−	4860.48i	0.590210	−	0.502453i
$455$	−119.004	+	228.108i	−0.0122615	+	0.0235030i
$456$	19.1492	+	118.444i	0.00196654	+	0.0121637i
$457$	−4295.37	−	2795.98i	−0.439670	−	0.286193i	0.306598	−	0.951839i	$-0.400809\pi$
$457$	−4295.37	−	2795.98i	−0.439670	−	0.286193i	−0.746268	+	0.665646i	$0.768156\pi$
$458$	15296.2	+	2978.93i	1.56058	+	0.303922i
$459$	1263.70	+	711.704i	0.128507	+	0.0723736i
$460$	−25.1387	−	13.1148i	−0.00254803	−	0.00132931i
$461$	11127.8	+	6745.76i	1.12424	+	0.681521i	0.952777	−	0.303670i	$-0.0982119\pi$
$461$	11127.8	+	6745.76i	1.12424	+	0.681521i	0.171463	+	0.985191i	$0.445151\pi$
$462$	58.8560	−	122.216i	0.00592690	−	0.0123073i
$463$	−3616.36	−	825.411i	−0.362995	−	0.0828512i	0.0371336	−	0.999310i	$-0.488177\pi$
$463$	−3616.36	−	825.411i	−0.362995	−	0.0828512i	−0.400128	+	0.916459i	$0.631034\pi$
$464$	−2.10903	−	7.10602i	−0.000211011	−	0.000710967i
$465$	−37.0991	−	25.8787i	−0.00369985	−	0.00258085i
$466$	−17900.1	+	21026.4i	−1.77941	+	2.09020i
$467$	−761.123	−	5903.12i	−0.0754188	−	0.584934i	−0.985396	−	0.170276i	$-0.945534\pi$
$467$	−761.123	−	5903.12i	−0.0754188	−	0.584934i	0.909978	−	0.414657i	$-0.136099\pi$
$468$	−18011.3	+	1737.53i	−1.77901	+	0.171618i
$469$	1377.27	−	2445.48i	0.135600	−	0.240771i
$470$	−603.850	+	2034.57i	−0.0592628	+	0.199676i
$471$	390.602	−	311.495i	0.0382123	−	0.0304733i
$472$	−51.2421	−	18.8576i	−0.00499705	−	0.00183896i
$473$	8347.97	+	2477.64i	0.811502	+	0.240849i
$474$	−300.935	+	48.6528i	−0.0291611	+	0.00471455i
$475$	849.860	+	2309.34i	0.0820932	+	0.223074i
$476$	−10131.5	−	4484.93i	−0.975585	−	0.431862i
$477$	−3243.34	−	14210.0i	−0.311326	−	1.36401i
$478$	−9540.61	−	19811.3i	−0.912923	−	1.89570i
$479$	1247.60	−	12932.7i	0.119007	−	1.23363i	−0.721726	−	0.692178i	$-0.756651\pi$
$479$	1247.60	−	12932.7i	0.119007	−	1.23363i	0.840733	−	0.541450i	$-0.182124\pi$
$480$	−21.1415	+	14.7474i	−0.00201036	+	0.00140234i
$481$	−6178.12	−	4926.89i	−0.585651	−	0.467041i
$482$	3354.33	+	5533.31i	0.316982	+	0.522895i
$483$	0.838448	−	4.30525i	7.89870e−5	−	0.000405581i
$484$	4707.91	−	12792.9i	0.442141	−	1.20144i
$485$	866.970	−	895.217i	0.0811692	−	0.0838139i
$486$	1677.75	+	1624.81i	0.156594	+	0.151652i
$487$	8603.65	+	10788.6i	0.800552	+	1.00386i	0.999715	+	0.0238936i	$0.00760630\pi$
$487$	8603.65	+	10788.6i	0.800552	+	1.00386i	−0.199163	+	0.979966i	$0.563822\pi$
$488$	−526.777	+	809.270i	−0.0488649	+	0.0750696i
$489$	−30.9273	−	481.718i	−0.00286009	−	0.0445481i
$490$	983.263	−	326.466i	0.0906517	−	0.0300984i
$491$	826.204	−	465.309i	0.0759390	−	0.0427681i	−0.452282	−	0.891875i	$-0.649390\pi$
$491$	826.204	−	465.309i	0.0759390	−	0.0427681i	0.528221	+	0.849107i	$0.322859\pi$
$492$	−1461.16	+	46.8564i	−0.133890	+	0.00429360i
$493$	−64.4432	+	2.06657i	−0.00588717	+	0.000188790i
$494$	−3941.02	+	2219.54i	−0.358937	+	0.202150i
$495$	−352.544	+	117.053i	−0.0320114	+	0.0106285i
$496$	224.260	+	3493.03i	0.0203016	+	0.316213i
$497$	−824.598	+	1266.80i	−0.0744231	+	0.114334i
$498$	400.674	+	502.430i	0.0360535	+	0.0452097i
$499$	4572.75	+	4428.46i	0.410230	+	0.397285i	0.871835	−	0.489800i	$-0.162930\pi$
$499$	4572.75	+	4428.46i	0.410230	+	0.397285i	−0.461605	+	0.887086i	$0.652726\pi$
$500$	1790.00	−	1848.32i	0.160103	−	0.165319i
$501$	−209.219	+	568.516i	−0.0186571	+	0.0506974i
$502$	5635.91	−	28939.2i	0.501081	−	2.57295i
$503$	10936.0	+	18040.1i	0.969407	+	1.59914i	0.787950	+	0.615739i	$0.211142\pi$
$503$	10936.0	+	18040.1i	0.969407	+	1.59914i	0.181456	+	0.983399i	$0.441919\pi$
$504$	−3854.64	−	3073.97i	−0.340673	−	0.271678i
$505$	140.440	−	97.9647i	0.0123752	−	0.00863242i
$506$	−22.4364	+	232.577i	−0.00197119	+	0.0204334i
$507$	21.6895	+	45.0387i	0.00189993	+	0.00394525i
$508$	5714.77	+	25038.0i	0.499118	+	2.18678i
$509$	6709.98	+	2970.31i	0.584312	+	0.258657i	0.675723	−	0.737156i	$-0.263832\pi$
$509$	6709.98	+	2970.31i	0.584312	+	0.258657i	−0.0914111	+	0.995813i	$0.529138\pi$
$510$	−32.6223	−	88.6453i	−0.00283243	−	0.00769662i
$511$	2114.47	−	341.852i	0.183051	−	0.0295942i
$512$	4629.99	+	1374.16i	0.399646	+	0.118613i
$513$	230.313	+	84.7574i	0.0198218	+	0.00729460i
$514$	15732.3	−	12546.1i	1.35004	−	1.07662i
$515$	248.262	−	836.478i	0.0212422	−	0.0715721i
$516$	−735.556	+	1306.06i	−0.0627540	+	0.111426i
$517$	10980.5	−	1059.28i	0.934086	−	0.0901101i
$518$	−664.055	−	5150.28i	−0.0563260	−	0.436854i
$519$	478.435	−	561.997i	0.0404643	−	0.0475317i
$520$	802.292	+	559.644i	0.0676593	+	0.0471962i
$521$	−463.571	−	1561.92i	−0.0389816	−	0.131342i	0.936925	−	0.349530i	$-0.113659\pi$
$521$	−463.571	−	1561.92i	−0.0389816	−	0.131342i	−0.975907	+	0.218188i	$0.929985\pi$
$522$	−67.4628	−	15.3979i	−0.00565664	−	0.00129109i
$523$	−3712.29	+	7708.65i	−0.310377	+	0.644504i	−0.996555	−	0.0829290i	$-0.973573\pi$
$523$	−3712.29	+	7708.65i	−0.310377	+	0.644504i	0.686179	+	0.727433i	$0.259287\pi$
$524$	−27818.5	−	16863.8i	−2.31920	−	1.40591i
$525$	176.041	+	91.8405i	0.0146344	+	0.00763476i
$526$	2469.61	+	1390.86i	0.204715	+	0.115293i
$527$	29885.1	+	5820.11i	2.47023	+	0.481078i
$528$	−47.3056	−	30.7926i	−0.00389908	−	0.00253802i
$529$	−1940.65	−	12003.6i	−0.159501	−	0.986569i
$530$	−879.010	+	1684.90i	−0.0720410	+	0.138089i
$531$	−42.4788	+	36.1627i	−0.00347161	+	0.00295542i
$532$	−1813.52	−	475.562i	−0.147794	−	0.0387561i
$533$	−8574.73	−	21179.8i	−0.696835	−	1.72119i
$534$	37.0888	+	141.436i	0.00300560	+	0.0114617i
$535$	6.04233	−	94.1142i	0.000488285	−	0.00760544i
$536$	−8551.79	−	6382.37i	−0.689144	−	0.514322i
$537$	−58.9513	+	364.635i	−0.00473731	+	0.0293020i
$538$	−17224.5	+	18966.1i	−1.38030	+	1.51987i
$539$	−3490.88	−	4100.59i	−0.278967	−	0.327690i
$540$	−12.2921	−	127.420i	−0.000979566	−	0.0101542i
$541$	3303.99	−	2002.90i	0.262569	−	0.159171i	−0.380963	−	0.924590i	$-0.624407\pi$
$541$	3303.99	−	2002.90i	0.262569	−	0.159171i	0.643532	+	0.765420i	$0.277469\pi$
$542$	21780.0	−	1398.32i	1.72607	−	0.110817i
$543$	−424.050	+	156.054i	−0.0335133	+	0.0123332i
$544$	8994.34	−	14837.1i	0.708877	−	1.16937i
$545$	−436.029	−	395.990i	−0.0342705	−	0.0311236i
$546$	−115.003	+	346.370i	−0.00901405	+	0.0271489i
$547$	3615.33	+	5554.12i	0.282597	+	0.434144i	0.950787	−	0.309846i	$-0.100278\pi$
$547$	3615.33	+	5554.12i	0.282597	+	0.434144i	−0.668190	+	0.743991i	$0.732931\pi$
$548$	11253.5	−	8398.71i	0.877237	−	0.654699i
$549$	456.329	+	874.696i	0.0354747	+	0.0679984i
$550$	−9804.46	−	3969.38i	−0.760115	−	0.307737i
$551$	−10.7090	+	2.08557i	−0.000827981	+	0.000161249i
$552$	−15.8266	−	5.25479i	−0.00122033	−	0.000405179i
$553$	500.969	−	1910.41i	0.0385232	−	0.146906i
$554$	14488.1	−	1868.03i	1.11108	−	0.143258i
$555$	17.4104	−	21.8319i	0.00133158	−	0.00166975i
$556$	4208.94	+	12676.7i	0.321041	+	0.966924i
$557$	367.325	−	829.794i	0.0279427	−	0.0631229i	−0.899896	−	0.436104i	$-0.856358\pi$
$557$	367.325	−	829.794i	0.0279427	−	0.0631229i	0.927839	+	0.372981i	$0.121664\pi$
$558$	29440.1	+	14177.6i	2.23351	+	1.07560i
$559$	−23128.2	−	3739.19i	−1.74994	−	0.282917i
$560$	13.4487	+	69.0563i	0.00101484	+	0.00521100i
$561$	−363.463	+	330.087i	−0.0273537	+	0.0248419i
$562$	−12452.8	−	28131.2i	−0.934681	−	2.11146i
$563$	165.586	−	5163.57i	0.0123954	−	0.386534i	−0.974425	−	0.224714i	$-0.927855\pi$
$563$	165.586	−	5163.57i	0.0123954	−	0.386534i	0.986820	−	0.161820i	$-0.0517365\pi$
$564$	−242.828	+	1883.32i	−0.0181293	+	0.140607i
$565$	−366.982	−	404.087i	−0.0273257	−	0.0300887i
$566$	−23986.2	+	15613.3i	−1.78130	+	1.15950i
$567$	−4659.95	+	1886.61i	−0.345149	+	0.139735i
$568$	4375.95	+	3725.30i	0.323258	+	0.275194i
$569$	8908.42	+	12770.9i	0.656345	+	0.940920i	0.999998	+	0.00182357i	$0.000580461\pi$
$569$	8908.42	+	12770.9i	0.656345	+	0.940920i	−0.343653	+	0.939097i	$0.611664\pi$
$570$	−7.84330	−	13.9266i	−0.000576350	−	0.00102337i
$571$	−17747.1	+	4050.66i	−1.30069	+	0.296874i	−0.816122	−	0.577880i	$-0.803880\pi$
$571$	−17747.1	+	4050.66i	−1.30069	+	0.296874i	−0.484568	+	0.874754i	$0.661023\pi$
$572$	2728.86	−	11955.9i	0.199475	−	0.873955i
$573$	491.067	−	657.985i	0.0358021	−	0.0479716i
$574$	5634.92	−	13918.4i	0.409751	−	1.01209i
$575$	−339.209	−	43.7362i	−0.0246017	−	0.00317204i
$576$	15457.0	−	14969.3i	1.11813	−	1.08285i
$577$		−	18600.7i		−	1.34204i	−0.741440	−	0.671019i	$-0.765857\pi$
$577$		−	18600.7i		−	1.34204i	0.741440	−	0.671019i	$-0.234143\pi$
$578$	28321.7	+	29244.5i	2.03811	+	2.10452i
$579$	429.722	−	190.225i	0.0308440	−	0.0136537i
$580$	3.40379	+	4.56077i	0.000243680	+	0.000326510i
$581$	−4027.30	+	1056.08i	−0.287574	+	0.0754108i
$582$	1011.38	−	1449.88i	0.0720324	−	0.103264i
$583$	9832.50	+	948.529i	0.698491	+	0.0673826i
$584$	−261.016	−	8139.45i	−0.0184948	−	0.576735i
$585$	900.457	−	433.637i	0.0636398	−	0.0306473i
$586$	2945.25	−	874.136i	0.207623	−	0.0616215i
$587$	−19169.0	−	1230.69i	−1.34785	−	0.0865351i	−0.626673	−	0.779282i	$-0.715584\pi$
$587$	−19169.0	−	1230.69i	−1.34785	−	0.0865351i	−0.721181	+	0.692747i	$0.756400\pi$
$588$	821.876	−	428.772i	0.0576422	−	0.0300719i
$589$	5149.27	+	165.127i	0.360224	+	0.0115517i
$590$	7.27374			0.000507551
$591$	−586.253	+	246.697i	−0.0408041	+	0.0171705i
$592$	−2160.81			−0.150015
$593$	14959.1	+	479.708i	1.03591	+	0.0332197i	0.545368	−	0.838197i	$-0.316390\pi$
$593$	14959.1	+	479.708i	1.03591	+	0.0332197i	0.490544	+	0.871417i	$0.336798\pi$
$594$	−935.277	+	487.933i	−0.0646042	+	0.0337039i
$595$	610.711	+	39.2089i	0.0420785	+	0.00270153i
$596$	16926.4	−	5023.67i	1.16331	−	0.345264i
$597$	18.7947	−	9.05106i	0.00128847	−	0.000620495i
$598$	−20.1493	−	628.329i	−0.00137787	−	0.0429670i
$599$	11985.8	+	1156.26i	0.817576	+	0.0788706i	0.496340	−	0.868128i	$-0.334677\pi$
$599$	11985.8	+	1156.26i	0.817576	+	0.0788706i	0.321237	+	0.946999i	$0.395902\pi$
$600$	431.901	−	619.163i	0.0293872	−	0.0421287i
$601$	24300.2	−	6372.25i	1.64929	−	0.432495i	0.692065	−	0.721835i	$-0.256701\pi$
$601$	24300.2	−	6372.25i	1.64929	−	0.432495i	0.957226	+	0.289340i	$0.0934358\pi$
$602$	−9208.60	−	12338.7i	−0.623446	−	0.835361i
$603$	−9969.39	+	4413.15i	−0.673275	+	0.298039i
$604$	−30543.9	−	31539.1i	−2.05764	−	2.12468i
$605$			752.915i			0.0505956i
$606$	174.484	−	168.979i	0.0116963	−	0.0113272i
$607$	2142.74	+	276.276i	0.143281	+	0.0184740i	0.199183	−	0.979962i	$-0.436171\pi$
$607$	2142.74	+	276.276i	0.143281	+	0.0184740i	−0.0559028	+	0.998436i	$0.517804\pi$
$608$	1101.75	−	2721.34i	0.0734897	−	0.181521i
$609$	−0.526538	+	0.705514i	−3.50352e−5	+	4.69439e-5i
$610$	28.6237	−	125.408i	0.00189990	−	0.00832400i
$611$	−28936.0	+	6604.45i	−1.91592	+	0.437295i
$612$	21120.5	+	37501.6i	1.39501	+	2.47698i
$613$	−6054.68	−	8679.84i	−0.398933	−	0.571901i	0.569243	−	0.822169i	$-0.307236\pi$
$613$	−6054.68	−	8679.84i	−0.398933	−	0.571901i	−0.968177	+	0.250268i	$0.919481\pi$
$614$	−25188.4	−	21443.2i	−1.65557	−	1.40941i
$615$	74.8439	−	30.3009i	0.00490731	−	0.00198675i
$616$	2800.36	−	1822.83i	0.183165	−	0.119227i
$617$	12298.7	+	13542.2i	0.802473	+	0.883612i	0.995222	−	0.0976363i	$-0.0311282\pi$
$617$	12298.7	+	13542.2i	0.802473	+	0.883612i	−0.192749	+	0.981248i	$0.561740\pi$
$618$	158.276	−	1227.56i	0.0103022	−	0.0799022i
$619$	569.870	−	17770.7i	0.0370033	−	1.15390i	−0.797649	−	0.603121i	$-0.793923\pi$
$619$	569.870	−	17770.7i	0.0370033	−	1.15390i	0.834653	−	0.550777i	$-0.185668\pi$
$620$	−1087.78	−	2457.32i	−0.0704618	−	0.159174i
$621$	−25.2506	+	22.9320i	−0.00163168	+	0.00148185i
$622$	−1111.32	−	5706.41i	−0.0716399	−	0.367856i
$623$	−935.170	−	151.191i	−0.0601393	−	0.00972285i
$624$	136.825	+	65.8913i	0.00877784	+	0.00422719i
$625$	6238.39	−	14092.6i	0.399257	−	0.901928i
$626$	4201.77	+	12655.1i	0.268269	+	0.807984i
$627$	−51.7995	+	64.9545i	−0.00329932	+	0.00413721i
$628$	29437.6	−	3795.55i	1.87052	−	0.241177i
$629$	−4767.62	+	18181.0i	−0.302221	+	1.15250i
$630$	623.322	+	206.957i	0.0394186	+	0.0130879i
$631$	10583.4	−	2061.12i	0.667700	−	0.130035i	0.154088	−	0.988057i	$-0.450756\pi$
$631$	10583.4	−	2061.12i	0.667700	−	0.130035i	0.513612	+	0.858022i	$0.328307\pi$
$632$	−6960.20	−	2817.87i	−0.438073	−	0.177356i
$633$	−254.901	−	488.598i	−0.0160054	−	0.0306793i
$634$	20306.4	−	15155.1i	1.27204	−	0.949344i
$635$	−773.831	−	1188.81i	−0.0483599	−	0.0742938i
$636$	−535.805	+	1613.76i	−0.0334057	+	0.100613i
$637$	10725.9	+	9740.98i	0.667152	+	0.605890i
$638$	24.3111	−	40.1036i	0.00150860	−	0.00248859i
$639$	5510.34	−	2027.86i	0.341136	−	0.125541i
$640$	−1905.14	+	122.314i	−0.117668	+	0.00755453i
$641$	−4391.05	+	2661.88i	−0.270571	+	0.164022i	−0.647150	−	0.762363i	$-0.724039\pi$
$641$	−4391.05	+	2661.88i	−0.270571	+	0.164022i	0.376579	+	0.926385i	$0.377100\pi$
$642$	−12.8457	−	133.159i	−0.000789689	−	0.00818596i
$643$	−10848.1	−	12742.8i	−0.665329	−	0.781533i	0.320866	−	0.947125i	$-0.396026\pi$
$643$	−10848.1	−	12742.8i	−0.665329	−	0.781533i	−0.986194	+	0.165592i	$0.947047\pi$
$644$	175.189	−	192.902i	0.0107196	−	0.0118035i
$645$	13.2133	−	81.7292i	0.000806628	−	0.00498928i
$646$	8621.91	+	6434.70i	0.525115	+	0.391904i
$647$	−871.072	+	13567.7i	−0.0529295	+	0.824419i	0.882369	+	0.470559i	$0.155948\pi$
$647$	−871.072	+	13567.7i	−0.0529295	+	0.824419i	−0.935298	+	0.353861i	$0.884869\pi$
$648$	4848.38	+	18489.0i	0.293924	+	1.12086i
$649$	−14.1882	−	35.0451i	−0.000858144	−	0.00211963i
$650$	27527.9	+	7218.67i	1.66113	+	0.435599i
$651$	316.538	−	269.472i	0.0190570	−	0.0162234i
$652$	13264.6	−	25425.8i	0.796752	−	1.52722i
$653$	3498.25	+	21637.9i	0.209643	+	1.29672i	0.849240	+	0.528007i	$0.177061\pi$
$653$	3498.25	+	21637.9i	0.209643	+	1.29672i	−0.639596	+	0.768711i	$0.720898\pi$
$654$	−700.238	−	455.804i	−0.0418677	−	0.0272528i
$655$	1763.63	+	343.467i	0.105207	+	0.0204891i
$656$	−5444.15	−	3066.09i	−0.324022	−	0.182486i
$657$	−7376.86	−	3848.51i	−0.438050	−	0.228530i
$658$	−16679.1	−	10110.9i	−0.988173	−	0.599036i
$659$	8597.77	−	17853.4i	0.508227	−	1.05534i	−0.476166	−	0.879356i	$-0.657974\pi$
$659$	8597.77	−	17853.4i	0.508227	−	1.05534i	0.984392	−	0.175988i	$-0.0563120\pi$
$660$	42.2492	+	9.64311i	0.00249174	+	0.000568724i
$661$	−4264.46	−	14368.4i	−0.250935	−	0.845484i	−0.985894	−	0.167372i	$-0.946472\pi$
$661$	−4264.46	−	14368.4i	−0.250935	−	0.845484i	0.734959	−	0.678112i	$-0.237202\pi$
$662$	−21360.8	−	14900.4i	−1.25410	−	0.874804i
$663$	856.298	−	1005.86i	0.0501597	−	0.0589204i
$664$	2024.24	+	15699.6i	0.118307	+	0.917563i
$665$	103.074	−	9.94341i	0.00601058	−	0.000579833i
$666$	−9898.78	+	17576.3i	−0.575931	+	1.02262i
$667$	0.431454	−	1.45371i	2.50464e−5	−	8.43896e-5i
$668$	−28138.2	+	22439.5i	−1.62979	+	1.29972i
$669$	−116.453	−	42.8558i	−0.00672994	−	0.00247668i
$670$	1362.76	+	404.460i	0.0785790	+	0.0233218i
$671$	−660.056	+	106.713i	−0.0379749	+	0.00613949i
$672$	−81.8158	−	222.320i	−0.00469660	−	0.0127622i
$673$	−6500.00	−	2877.36i	−0.372298	−	0.164805i	0.210158	−	0.977667i	$-0.432602\pi$
$673$	−6500.00	−	2877.36i	−0.372298	−	0.164805i	−0.582456	+	0.812862i	$0.697908\pi$
$674$	−2860.66	−	12533.4i	−0.163485	−	0.716273i
$675$	−669.970	−	1391.21i	−0.0382032	−	0.0793297i
$676$	−285.176	+	2956.14i	−0.0162253	+	0.168192i
$677$	26294.2	−	18341.7i	1.49271	−	1.04125i	0.509154	−	0.860675i	$-0.329958\pi$
$677$	26294.2	−	18341.7i	1.49271	−	1.04125i	0.983561	−	0.180578i	$-0.0577967\pi$
$678$	−605.381	−	482.775i	−0.0342913	−	0.0273464i
$679$	5937.17	+	9793.99i	0.335564	+	0.553548i
$680$	444.771	−	2283.80i	0.0250826	−	0.128794i
$681$	−127.975	+	347.750i	−0.00720120	+	0.0195680i
$682$	−15406.1	+	15908.1i	−0.865002	+	0.893186i
$683$	−10907.6	−	10563.4i	−0.611080	−	0.591798i	0.324077	−	0.946031i	$-0.394946\pi$
$683$	−10907.6	−	10563.4i	−0.611080	−	0.591798i	−0.935157	+	0.354232i	$0.884742\pi$
$684$	4540.81	+	5693.99i	0.253833	+	0.318297i
$685$	−423.106	+	650.005i	−0.0236001	+	0.0362561i
$686$	1319.65	+	20554.6i	0.0734466	+	1.14399i
$687$	−730.895	+	242.674i	−0.0405901	+	0.0134768i
$688$	−5582.06	+	3143.76i	−0.309323	+	0.174207i
$689$	−26563.4	+	851.837i	−1.46877	+	0.0471007i
$690$	2.22036	−	0.0712025i	0.000122504	−	3.92845e-6i
$691$	−6092.02	+	3430.96i	−0.335386	+	0.188886i	−0.649236	−	0.760587i	$-0.724911\pi$
$691$	−6092.02	+	3430.96i	−0.335386	+	0.188886i	0.313851	+	0.949472i	$0.398381\pi$
$692$	41614.8	−	13817.1i	2.28606	−	0.759025i
$693$	−218.729	−	3406.88i	−0.0119896	−	0.186748i
$694$	19410.8	−	29820.1i	1.06170	−	1.63106i
$695$	−459.979	−	576.795i	−0.0251050	−	0.0314807i
$696$	2.40435	+	2.32848i	0.000130943	+	0.000126812i
$697$	−37810.0	+	39041.9i	−2.05474	+	2.12169i
$698$	−3099.85	+	8423.28i	−0.168096	+	0.456771i
$699$	260.866	−	1339.49i	0.0141157	−	0.0724809i
$700$	6115.13	+	10087.6i	0.330186	+	0.544677i
$701$	−7562.49	−	6030.89i	−0.407463	−	0.324941i	0.398218	−	0.917291i	$-0.369629\pi$
$701$	−7562.49	−	6030.89i	−0.407463	−	0.324941i	−0.805681	+	0.592350i	$0.798200\pi$
$702$	2327.82	−	1623.79i	0.125154	−	0.0873018i
$703$	−305.397	+	3165.76i	−0.0163845	+	0.169842i
$704$	6327.29	+	13138.7i	0.338734	+	0.703388i
$705$	−23.3385	−	102.252i	−0.00124678	−	0.00546248i
$706$	13243.7	+	5862.57i	0.705994	+	0.312522i
$707$	543.490	+	1476.84i	0.0289110	+	0.0785605i
$708$	6.42474	−	1.03870i	0.000341040	−	5.51367e-5i
$709$	−28000.2	−	8310.32i	−1.48317	−	0.440198i	−0.561275	−	0.827629i	$-0.689689\pi$
$709$	−28000.2	−	8310.32i	−1.48317	−	0.440198i	−0.921899	+	0.387431i	$0.873363\pi$
$710$	−718.460	−	264.400i	−0.0379765	−	0.0139757i
$711$	−5998.19	+	4783.40i	−0.316385	+	0.252309i
$712$	−1024.78	+	3452.83i	−0.0539400	+	0.181742i
$713$	−351.382	+	623.913i	−0.0184563	+	0.0327710i
$714$	864.077	−	83.3565i	0.0452903	−	0.00436910i
$715$	86.6163	+	671.779i	0.00453044	+	0.0351372i
$716$	−14224.9	+	16709.4i	−0.742472	+	0.872150i
$717$	891.259	+	621.704i	0.0464221	+	0.0323821i
$718$	−1338.89	−	4511.17i	−0.0695919	−	0.234478i
$719$	2622.37	+	598.539i	0.136019	+	0.0310456i	0.289989	−	0.957030i	$-0.406348\pi$
$719$	2622.37	+	598.539i	0.136019	+	0.0310456i	−0.153969	+	0.988076i	$0.549206\pi$
$720$	118.577	−	246.227i	0.00613763	−	0.0127449i
$721$	6857.30	+	4156.94i	0.354201	+	0.214719i
$722$	−26692.1	−	13925.2i	−1.37587	−	0.717789i
$723$	−278.625	−	156.919i	−0.0143322	−	0.00807174i
$724$	−26349.6	−	5131.59i	−1.35259	−	0.263417i
$725$	57.5312	+	37.4487i	0.00294711	+	0.00191836i
$726$	170.457	+	1054.33i	0.00871382	+	0.0538981i
$727$	−5422.69	+	10394.3i	−0.276639	+	0.530265i	−0.984347	−	0.176239i	$-0.943607\pi$
$727$	−5422.69	+	10394.3i	−0.276639	+	0.530265i	0.707708	+	0.706505i	$0.249729\pi$
$728$	−6845.33	+	5827.52i	−0.348496	+	0.296679i
$729$	18815.8	+	4934.07i	0.955939	+	0.250677i
$730$	407.107	+	1005.56i	0.0206407	+	0.0509830i
$731$	14135.2	+	53903.7i	0.715198	+	2.72736i
$732$	7.37413	−	114.858i	0.000372344	−	0.00579956i
$733$	−103.040	−	76.9004i	−0.00519216	−	0.00387501i	0.595511	−	0.803347i	$-0.296949\pi$
$733$	−103.040	−	76.9004i	−0.00519216	−	0.00387501i	−0.600703	+	0.799472i	$0.705113\pi$
$734$	−2735.06	+	16917.3i	−0.137538	+	0.850722i
$735$	−34.4222	+	37.9026i	−0.00172746	+	0.00190212i
$736$	264.514	+	310.713i	0.0132474	+	0.0155612i
$737$	−709.505	−	7354.76i	−0.0354612	−	0.367593i
$738$	−49879.9	+	30237.5i	−2.48794	+	1.50821i
$739$	−28588.3	+	1835.43i	−1.42305	+	0.0913630i	−0.756451	−	0.654051i	$-0.773068\pi$
$739$	−28588.3	+	1835.43i	−1.42305	+	0.0913630i	−0.666602	+	0.745414i	$0.732252\pi$
$740$	1556.90	−	572.952i	0.0773414	−	0.0284623i
$741$	115.874	−	191.147i	0.00574459	−	0.00947631i
$742$	−12929.1	−	11741.9i	−0.639681	−	0.580941i
$743$	3775.06	−	11369.9i	0.186398	−	0.561401i	−0.813396	−	0.581711i	$-0.802384\pi$
$743$	3775.06	−	11369.9i	0.186398	−	0.561401i	0.999794	+	0.0203098i	$0.00646524\pi$
$744$	−862.228	−	1324.61i	−0.0424876	−	0.0652724i
$745$	−781.536	+	583.275i	−0.0384339	+	0.0286840i
$746$	−21747.6	−	41686.1i	−1.06734	−	2.04590i
$747$	14991.2	+	6069.25i	0.734267	+	0.297272i
$748$	−28631.4	+	5575.96i	−1.39955	+	0.272563i
$749$	822.561	+	273.109i	0.0401278	+	0.0133233i
$750$	−51.1347	+	194.999i	−0.00248957	+	0.00949380i
$751$	−7065.46	+	910.991i	−0.343305	+	0.0442643i	−0.297600	−	0.954691i	$-0.596186\pi$
$751$	−7065.46	+	910.991i	−0.343305	+	0.0442643i	−0.0457054	+	0.998955i	$0.514554\pi$
$752$	−5060.21	+	6345.30i	−0.245381	+	0.307698i
$753$	459.120	+	1382.80i	0.0222195	+	0.0669215i
$754$	−51.0739	+	115.377i	−0.00246685	+	0.00557265i
$755$	2184.84	+	1052.16i	0.105317	+	0.0507180i
$756$	1161.38	+	187.763i	0.0558717	+	0.00903290i
$757$	3631.51	+	18647.1i	0.174359	+	0.895296i	0.960718	+	0.277526i	$0.0895145\pi$
$757$	3631.51	+	18647.1i	0.174359	+	0.895296i	−0.786359	+	0.617769i	$0.788036\pi$
$758$	15253.8	−	13853.1i	0.730928	−	0.663809i
$759$	−4.67409	−	10.5589i	−0.000223529	−	0.000504957i
$760$	12.6189	−	393.505i	0.000602285	−	0.0187815i
$761$	−409.276	+	3174.27i	−0.0194957	+	0.151205i	−0.998652	−	0.0519025i	$-0.983471\pi$
$761$	−409.276	+	3174.27i	−0.0194957	+	0.151205i	0.979156	+	0.203108i	$0.0651041\pi$
$762$	−1352.77	−	1489.54i	−0.0643117	−	0.0708143i
$763$	4536.68	−	2953.05i	0.215254	−	0.140115i
$764$	45212.7	−	18304.6i	2.14102	−	0.866803i
$765$	−1810.12	−	1540.98i	−0.0855490	−	0.0728289i
$766$	16683.4	+	23916.9i	0.786938	+	1.12814i
$767$	49.9172	+	88.6330i	0.00234994	+	0.00417256i
$768$	−1207.54	+	275.612i	−0.0567359	+	0.0129496i
$769$	−8610.85	+	37726.6i	−0.403791	+	1.76912i	0.208026	+	0.978123i	$0.433296\pi$
$769$	−8610.85	+	37726.6i	−0.403791	+	1.76912i	−0.611817	+	0.790999i	$0.709561\pi$
$770$	−266.229	+	356.723i	−0.0124600	+	0.0166953i
$771$	−373.177	+	921.754i	−0.0174314	+	0.0430560i
$772$	27690.2	+	3570.26i	1.29092	+	0.166446i
$773$	−25907.7	+	25090.2i	−1.20548	+	1.16744i	−0.224265	+	0.974528i	$0.571998\pi$
$773$	−25907.7	+	25090.2i	−1.20548	+	1.16744i	−0.981216	+	0.192915i	$0.938206\pi$
$774$			59806.9i			2.77741i
$775$	−22550.8	−	23285.6i	−1.04523	−	1.07928i
$776$	39817.7	−	17626.1i	1.84198	−	0.815388i
$777$	153.493	+	205.667i	0.00708691	+	0.00949582i
$778$	−26744.7	+	7013.30i	−1.23245	+	0.323186i
$779$	−5261.52	+	7542.78i	−0.241994	+	0.346917i
$780$	−116.056	−	11.1958i	−0.00532751	−	0.000513939i
$781$	127.545	+	3977.31i	0.00584366	+	0.182227i
$782$	−1347.21	+	648.782i	−0.0616063	+	0.0296680i
$783$	6.56315	−	1.94791i	0.000299550	−	8.89049e-5i
$784$	3953.84	+	253.845i	0.180113	+	0.0115636i
$785$	−1453.47	+	758.273i	−0.0660847	+	0.0344763i
$786$	2547.44	+	81.6913i	0.115603	+	0.00370717i
$787$	−24861.8			−1.12609			−0.563043	−	0.826428i	$-0.690369\pi$
$787$	−24861.8			−1.12609			−0.563043	+	0.826428i	$0.690369\pi$
$788$	−37381.8	−	5522.06i	−1.68994	−	0.249639i
$789$	−140.071			−0.00632022
$790$	999.788	+	32.0613i	0.0450264	+	0.00144391i
$791$	4447.71	−	2320.37i	0.199927	−	0.104302i
$792$	−12953.0	−	831.609i	−0.581141	−	0.0373105i
$793$	1724.58	−	511.846i	0.0772278	−	0.0229208i
$794$	−11366.1	+	5473.61i	−0.508018	+	0.244649i
$795$	−3.01018	−	93.8683i	−0.000134289	−	0.00418763i
$796$	1233.60	+	119.004i	0.0549295	+	0.00529899i
$797$	−7689.08	+	11022.9i	−0.341733	+	0.489900i	−0.953607	−	0.301056i	$-0.902661\pi$
$797$	−7689.08	+	11022.9i	−0.341733	+	0.489900i	0.611874	+	0.790955i	$0.290416\pi$
$798$	142.087	−	37.2596i	0.00630304	−	0.00165285i
$799$	42224.3	+	56576.7i	1.86957	+	2.50506i
$800$	−16891.4	+	7477.34i	−0.746503	+	0.330455i
$801$	2560.02	+	2643.43i	0.112926	+	0.116606i
$802$			21033.5i			0.926081i
$803$	4050.73	−	3922.91i	0.178016	−	0.172399i
$804$	1261.45	+	162.646i	0.0553334	+	0.00713445i
$805$	−5.40106	+	13.3407i	−0.000236475	+	0.000584098i
$806$	35636.6	−	47749.7i	1.55737	−	2.08674i
$807$	281.742	−	1234.39i	0.0122897	−	0.0538446i
$808$	5833.10	−	1331.37i	0.253970	−	0.0579670i
$809$	−13632.8	−	24206.3i	−0.592462	−	1.05198i	−0.990877	−	0.134771i	$-0.956970\pi$
$809$	−13632.8	−	24206.3i	−0.592462	−	1.05198i	0.398414	−	0.917206i	$-0.369561\pi$
$810$	−1456.76	−	2088.38i	−0.0631919	−	0.0905903i
$811$	−31570.2	−	26876.1i	−1.36693	−	1.16368i	−0.969227	−	0.246170i	$-0.920828\pi$
$811$	−31570.2	−	26876.1i	−1.36693	−	1.16368i	−0.397703	−	0.917514i	$-0.630193\pi$
$812$	−48.4786	+	19.6268i	−0.00209515	+	0.000848234i
$813$	−903.934	+	588.396i	−0.0389943	+	0.0253825i
$814$	−9191.09	−	10120.4i	−0.395759	−	0.435774i
$815$	−202.552	+	1570.95i	−0.00870561	+	0.0675190i
$816$	11.5776	−	361.033i	0.000496688	−	0.0154886i
$817$	3816.92	+	8622.50i	0.163448	+	0.369233i
$818$	−21585.6	+	19603.4i	−0.922643	+	0.837920i
$819$	1755.80	+	9015.67i	0.0749116	+	0.384655i
$820$	4735.58	+	765.612i	0.201675	+	0.0326053i
$821$	−19944.0	−	9604.52i	−0.847807	−	0.408282i	−0.0410441	−	0.999157i	$-0.513068\pi$
$821$	−19944.0	−	9604.52i	−0.847807	−	0.408282i	−0.806763	+	0.590875i	$0.798783\pi$
$822$	−445.333	+	1006.01i	−0.0188963	+	0.0426871i
$823$	8689.51	+	26171.4i	0.368041	+	1.10848i	0.954426	+	0.298448i	$0.0964688\pi$
$823$	8689.51	+	26171.4i	0.368041	+	1.10848i	−0.586385	+	0.810032i	$0.699450\pi$
$824$	19008.9	−	23836.4i	0.803649	−	1.00774i
$825$	518.440	−	66.8455i	0.0218785	−	0.00282092i
$826$	−16.9562	+	64.6613i	−0.000714264	+	0.00272380i
$827$	−1805.27	−	599.392i	−0.0759076	−	0.0252030i	0.276902	−	0.960898i	$-0.410692\pi$
$827$	−1805.27	−	599.392i	−0.0759076	−	0.0252030i	−0.352810	+	0.935695i	$0.614774\pi$
$828$	−993.570	+	193.498i	−0.0417016	+	0.00812139i
$829$	21477.7	+	8695.34i	0.899819	+	0.364296i	0.778006	−	0.628257i	$-0.216231\pi$
$829$	21477.7	+	8695.34i	0.899819	+	0.364296i	0.121813	+	0.992553i	$0.461129\pi$
$830$	−975.363	−	1869.59i	−0.0407896	−	0.0781860i
$831$	−578.555	+	431.787i	−0.0241515	+	0.0180247i
$832$	−21404.2	−	32882.5i	−0.891894	−	1.37019i
$833$	10859.6	−	32707.4i	0.451696	−	1.36044i
$834$	−774.709	−	703.570i	−0.0321654	−	0.0292118i
$835$	1030.48	−	1699.88i	0.0427079	−	0.0704512i
$836$	−4632.09	+	1704.65i	−0.191632	+	0.0705222i
$837$	−3226.18	+	207.128i	−0.133229	+	0.00855361i
$838$	64834.3	−	39302.9i	2.67263	−	1.62016i
$839$	−2140.87	−	22192.3i	−0.0880940	−	0.913187i	−0.928525	−	0.371269i	$-0.878923\pi$
$839$	−2140.87	−	22192.3i	−0.0880940	−	0.913187i	0.840431	−	0.541918i	$-0.182302\pi$
$840$	−20.5930	−	24.1897i	−0.000845863	−	0.000993598i
$841$	16396.5	−	18054.4i	0.672293	−	0.740269i
$842$	−7501.55	+	46399.8i	−0.307032	+	1.89910i
$843$	1218.42	+	909.333i	0.0497803	+	0.0371520i
$844$	2097.69	−	32673.2i	0.0855515	−	1.33253i
$845$	−41.6079	−	158.669i	−0.00169391	−	0.00645962i
$846$	28432.3	+	70228.4i	1.15547	+	2.85402i
$847$	−6693.19	−	1755.16i	−0.271524	−	0.0712019i
$848$	−5533.75	+	4710.95i	−0.224091	+	0.190772i
$849$	654.208	−	1253.99i	0.0264456	−	0.0506913i
$850$	−10803.4	−	66823.1i	−0.435947	−	2.69649i
$851$	−370.474	−	241.152i	−0.0149233	−	0.00971396i
$852$	−672.358	−	130.942i	−0.0270359	−	0.00526524i
$853$	24631.3	+	13872.1i	0.988700	+	0.556825i	0.898442	−	0.439093i	$-0.144700\pi$
$853$	24631.3	+	13872.1i	0.988700	+	0.556825i	0.0902581	+	0.995918i	$0.471231\pi$
$854$	1048.12	+	546.802i	0.0419975	+	0.0219100i
$855$	−343.984	−	208.525i	−0.0137591	−	0.00834082i
$856$	1429.76	−	2968.93i	0.0570890	−	0.118547i
$857$	−24971.8	−	5699.65i	−0.995357	−	0.227184i	−0.306335	−	0.951924i	$-0.599103\pi$
$857$	−24971.8	−	5699.65i	−0.995357	−	0.227184i	−0.689022	+	0.724740i	$0.741960\pi$
$858$	273.380	+	921.107i	0.0108777	+	0.0366504i
$859$	−34121.5	−	23801.7i	−1.35531	−	0.945404i	−0.999943	−	0.0106762i	$-0.996602\pi$
$859$	−34121.5	−	23801.7i	−1.35531	−	0.945404i	−0.355365	−	0.934728i	$-0.615643\pi$
$860$	3188.37	−	3745.24i	0.126422	−	0.148502i
$861$	94.8936	+	735.976i	0.00375606	+	0.0291312i
$862$	65247.7	−	6294.37i	2.57813	−	0.248709i
$863$	18076.3	−	32096.2i	0.713005	−	1.26601i	−0.242246	−	0.970215i	$-0.577884\pi$
$863$	18076.3	−	32096.2i	0.713005	−	1.26601i	0.955251	−	0.295797i	$-0.0955854\pi$
$864$	−524.178	+	1766.13i	−0.0206399	+	0.0695428i
$865$	−1893.50	+	1510.01i	−0.0744287	+	0.0593549i
$866$	−38644.1	−	14221.4i	−1.51637	−	0.558039i
$867$	−1928.74	−	572.439i	−0.0755518	−	0.0224234i
$868$	24380.6	−	3941.66i	0.953377	−	0.154135i
$869$	−1795.72	−	4879.55i	−0.0700986	−	0.190480i
$870$	−0.407713	−	0.180482i	−1.58882e−5	−	7.03325e-6i
$871$	4423.67	+	19381.4i	0.172090	+	0.753975i
$872$	−8929.67	−	18542.7i	−0.346785	−	0.720107i
$873$	4272.04	−	44284.2i	0.165621	−	1.71683i
$874$	−207.521	+	144.757i	−0.00803146	+	0.00560240i
$875$	−1021.13	−	814.321i	−0.0394518	−	0.0314618i
$876$	503.185	+	830.057i	0.0194076	+	0.0320149i
$877$	4413.82	−	22664.0i	0.169948	−	0.872646i	−0.794276	−	0.607557i	$-0.792150\pi$
$877$	4413.82	−	22664.0i	0.169948	−	0.872646i	0.964224	−	0.265089i	$-0.0854013\pi$
$878$	134.916	−	366.610i	0.00518587	−	0.0140917i
$879$	−105.624	+	109.065i	−0.00405302	+	0.00418507i
$880$	133.050	+	128.852i	0.00509673	+	0.00493590i
$881$	−8844.24	−	11090.3i	−0.338218	−	0.424112i	0.583415	−	0.812174i	$-0.301716\pi$
$881$	−8844.24	−	11090.3i	−0.338218	−	0.424112i	−0.921633	+	0.388062i	$0.873145\pi$
$882$	20177.5	−	30998.1i	0.770310	−	1.18340i
$883$	1510.15	+	23521.9i	0.0575546	+	0.896459i	0.920397	+	0.390986i	$0.127866\pi$
$883$	1510.15	+	23521.9i	0.0575546	+	0.896459i	−0.862842	+	0.505473i	$0.831318\pi$
$884$	74481.7	−	24729.6i	2.83381	−	0.940890i
$885$	−0.313207	+	0.176395i	−1.18964e−5	+	6.69993e-6i
$886$	18174.4	−	582.817i	0.689143	−	0.0220995i
$887$	625.084	−	20.0452i	0.0236621	−	0.000758796i	−0.0202183	−	0.999796i	$-0.506436\pi$
$887$	625.084	−	20.0452i	0.0236621	−	0.000758796i	0.0438804	+	0.999037i	$0.486028\pi$
$888$	850.154	−	478.798i	0.0321276	−	0.0180939i
$889$	12372.1	−	4107.82i	0.466757	−	0.154974i
$890$	−30.7406	−	478.810i	−0.00115778	−	0.0180334i
$891$	−7220.31	+	11092.3i	−0.271481	+	0.417068i
$892$	−4596.43	−	5763.74i	−0.172534	−	0.216350i
$893$	8581.19	+	8310.42i	0.321566	+	0.311420i
$894$	−962.362	+	993.718i	−0.0360025	+	0.0371755i
$895$	418.597	−	1137.46i	0.0156337	−	0.0424818i
$896$	3353.85	−	17221.3i	0.125049	−	0.642101i
$897$	16.1052	+	26.5672i	0.000599483	+	0.000988909i
$898$	57697.5	+	46012.2i	2.14409	+	1.70985i
$899$	117.874	−	82.2240i	0.00437300	−	0.00305041i
$900$	4400.09	−	45611.6i	0.162966	−	1.68932i
$901$	27428.1	+	56955.0i	1.01416	+	2.10593i
$902$	−8796.52	−	38540.1i	−0.324714	−	1.42267i
$903$	695.746	+	307.986i	0.0256401	+	0.0113501i
$904$	−6587.19	−	17899.5i	−0.242353	−	0.658550i
$905$	1463.70	−	236.639i	0.0537623	−	0.00869188i
$906$	3297.71	+	978.744i	0.120926	+	0.0358903i
$907$	45996.9	+	16927.3i	1.68391	+	0.619693i	0.994505	−	0.104687i	$-0.0333840\pi$
$907$	45996.9	+	16927.3i	1.68391	+	0.619693i	0.689401	+	0.724380i	$0.257874\pi$
$908$	−17211.6	+	13725.8i	−0.629061	+	0.501659i
$909$	1739.31	−	5860.31i	0.0634646	−	0.213833i
$910$	587.675	−	1043.48i	0.0214079	−	0.0380120i
$911$	25349.7	−	2445.46i	0.921925	−	0.0889370i	0.375857	−	0.926678i	$-0.377349\pi$
$911$	25349.7	−	2445.46i	0.921925	−	0.0889370i	0.546068	+	0.837741i	$0.316124\pi$
$912$	−7.81617	−	60.6207i	−0.000283793	−	0.00220104i
$913$	−7105.19	+	8346.16i	−0.257555	+	0.302539i
$914$	19566.3	+	13648.6i	0.708091	+	0.493933i
$915$	1.80873	+	6.09423i	6.53496e−5	+	0.000220185i
$916$	−44606.3	−	10181.1i	−1.60899	−	0.367241i
$917$	−7164.62	+	14877.5i	−0.258011	+	0.535766i
$918$	−5772.95	−	3499.60i	−0.207555	−	0.125821i
$919$	−8506.64	−	4437.91i	−0.305341	−	0.159296i	0.302959	−	0.953004i	$-0.402026\pi$
$919$	−8506.64	−	4437.91i	−0.305341	−	0.159296i	−0.608299	+	0.793708i	$0.708148\pi$
$920$	47.6792	+	26.8524i	0.00170863	+	0.000962281i
$921$	1604.63	+	312.502i	0.0574097	+	0.0111805i
$922$	−50763.7	−	33043.5i	−1.81325	−	1.18029i
$923$	−1708.74	−	10569.2i	−0.0609360	−	0.376911i
$924$	−184.214	+	353.103i	−0.00655865	+	0.0125717i
$925$	15237.4	−	12971.8i	0.541625	−	0.461092i
$926$	16701.3	+	4379.59i	0.592698	+	0.155424i
$927$	−11689.5	−	28873.2i	−0.414166	−	1.02300i
$928$	−20.7744	−	79.2219i	−0.000734865	−	0.00280236i
$929$	−29.6602	+	461.982i	−0.00104749	+	0.0163155i	−0.998436	−	0.0559103i	$-0.982194\pi$
$929$	−29.6602	+	461.982i	−0.00104749	+	0.0163155i	0.997388	+	0.0722258i	$0.0230102\pi$
$930$	168.735	+	125.931i	0.00594952	+	0.00444024i
$931$	930.717	−	5756.82i	0.0327637	−	0.202655i
$932$	54506.4	−	60017.6i	1.91568	−	2.10938i
$933$	186.239	+	218.767i	0.00653505	+	0.00767644i
$934$	2660.29	+	27576.7i	0.0931985	+	0.966100i
$935$	1377.72	−	835.180i	0.0481884	−	0.0292121i
$936$	34849.9	−	2237.44i	1.21699	−	0.0781335i
$937$	−45137.8	+	16611.1i	−1.57373	+	0.579148i	−0.975079	−	0.221860i	$-0.928787\pi$
$937$	−45137.8	+	16611.1i	−1.57373	+	0.579148i	−0.598654	+	0.801008i	$0.704297\pi$
$938$	−6772.32	+	11171.7i	−0.235740	+	0.388878i
$939$	−487.824	−	443.029i	−0.0169537	−	0.0153969i
$940$	1963.46	−	5913.62i	0.0681287	−	0.205193i
$941$	−14685.8	−	22561.3i	−0.508759	−	0.781590i	0.487018	−	0.873392i	$-0.338084\pi$
$941$	−14685.8	−	22561.3i	−0.508759	−	0.781590i	−0.995777	+	0.0918013i	$0.970738\pi$
$942$	−1863.67	+	1390.90i	−0.0644605	+	0.0481081i
$943$	−591.225	−	1133.27i	−0.0204167	−	0.0391349i
$944$	25.7829	+	10.4384i	0.000888944	+	0.000359893i
$945$	−63.7807	+	12.4213i	−0.00219554	+	0.000427582i
$946$	−38467.7	−	12772.2i	−1.32209	−	0.438963i
$947$	−1262.08	+	4812.86i	−0.0433074	+	0.165150i	−0.985418	−	0.170154i	$-0.945574\pi$
$947$	−1262.08	+	4812.86i	−0.0433074	+	0.165150i	0.942110	+	0.335304i	$0.108839\pi$
$948$	887.670	−	114.452i	0.0304116	−	0.00392114i
$949$	−9459.30	+	11861.6i	−0.323563	+	0.405736i
$950$	−3609.28	−	10870.6i	−0.123264	−	0.371251i
$951$	−506.868	+	1145.02i	−0.0172832	+	0.0390431i
$952$	19265.5	+	9277.77i	0.655881	+	0.315855i
$953$	−30475.4	−	4927.02i	−1.03588	−	0.167473i	−0.382071	−	0.924133i	$-0.624789\pi$
$953$	−30475.4	−	4927.02i	−1.03588	−	0.167473i	−0.653809	+	0.756660i	$0.726830\pi$
$954$	12969.0	+	66593.2i	0.440134	+	2.25999i
$955$	−1994.39	+	1811.25i	−0.0675780	+	0.0613726i
$956$	26132.6	+	59034.0i	0.884088	+	1.99717i
$957$	−0.0742832	+	2.31642i	−2.50913e−6	+	7.82438e-5i
$958$	−7733.64	+	59980.6i	−0.260817	+	2.02284i
$959$	−4792.02	−	5276.55i	−0.161358	−	0.177673i
$960$	116.199	−	75.6369i	0.00390656	−	0.00254289i
$961$	−35292.2	+	14288.2i	−1.18466	+	0.479616i
$962$	28007.5	+	23843.1i	0.938667	+	0.799099i
$963$	−1926.19	−	2761.34i	−0.0644556	−	0.0924020i
$964$	−9322.56	−	16553.2i	−0.311473	−	0.553051i
$965$	−1503.40	+	343.141i	−0.0501515	+	0.0114468i
$966$	−4.54302	+	19.9043i	−0.000151314	+	0.000662950i
$967$	−6914.38	+	9264.64i	−0.229939	+	0.308098i	−0.901438	−	0.432908i	$-0.857488\pi$
$967$	−6914.38	+	9264.64i	−0.229939	+	0.308098i	0.671499	+	0.741006i	$0.265651\pi$
$968$	−9872.51	+	24385.3i	−0.327804	+	0.809683i
$969$	−527.306	−	67.9886i	−0.0174814	−	0.00225398i
$970$	−4166.97	+	4035.48i	−0.137931	+	0.133579i
$971$			36769.1i			1.21522i	0.794237	+	0.607608i	$0.207871\pi$
$971$			36769.1i			1.21522i	−0.794237	+	0.607608i	$0.792129\pi$
$972$	−4770.47	−	4925.90i	−0.157421	−	0.162550i
$973$	6199.82	−	2744.48i	0.204272	−	0.0904253i
$974$	−38417.3	−	51475.6i	−1.26383	−	1.69341i
$975$	−1360.41	+	356.741i	−0.0446851	+	0.0117178i
$976$	281.432	−	403.453i	0.00922992	−	0.0132318i
$977$	2881.73	+	277.997i	0.0943651	+	0.00910329i	0.143098	−	0.989709i	$-0.454294\pi$
$977$	2881.73	+	277.997i	0.0943651	+	0.00910329i	−0.0487325	+	0.998812i	$0.515518\pi$
$978$	72.0157	+	2245.71i	0.00235461	+	0.0734254i
$979$	−2246.96	+	1082.08i	−0.0733536	+	0.0353252i
$980$	−2916.11	+	865.485i	−0.0950527	+	0.0282111i
$981$	−20984.3	−	1347.24i	−0.682954	−	0.0438471i
$982$	−3913.18	+	2041.50i	−0.127163	+	0.0663411i
$983$	1963.99	+	62.9814i	0.0637250	+	0.00204354i	0.0638978	−	0.997956i	$-0.479647\pi$
$983$	1963.99	+	62.9814i	0.0637250	+	0.00204354i	−0.000172811		1.00000i	$0.500055\pi$
$984$	2821.35			0.0914038
$985$	2042.99	−	426.843i	0.0660863	−	0.0138075i
$986$	300.118			0.00969340
$987$	963.399	+	30.8943i	0.0310692	+	0.000996330i
$988$	11773.8	−	6142.38i	0.379124	−	0.197788i
$989$	−1307.91	−	83.9703i	−0.0420515	−	0.00269980i
$990$	1657.61	−	491.969i	0.0532143	−	0.0157937i
$991$	27657.7	−	13319.3i	0.886556	−	0.426943i	0.0655415	−	0.997850i	$-0.479123\pi$
$991$	27657.7	−	13319.3i	0.886556	−	0.426943i	0.821015	+	0.570907i	$0.193408\pi$
$992$	1239.58	+	38654.6i	0.0396740	+	1.23718i
$993$	1281.14	+	123.590i	0.0409425	+	0.00394967i
$994$	4025.28	−	5770.54i	0.128445	−	0.184135i
$995$	−66.2127	+	17.3630i	−0.00210963	+	0.000553211i
$996$	−1128.50	−	1512.08i	−0.0359014	−	0.0481046i
$997$	−26423.5	+	11696.9i	−0.839359	+	0.371559i	−0.779312	−	0.626636i	$-0.784431\pi$
$997$	−26423.5	+	11696.9i	−0.839359	+	0.371559i	−0.0600470	+	0.998196i	$0.519125\pi$
$998$	−20613.2	−	21284.8i	−0.653806	−	0.675109i
$999$		−	1995.73i		−	0.0632054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.h.a.4.6	✓	2016
197.148	even	98	inner	197.4.h.a.148.6	yes	2016

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.h.a.4.6	✓	2016	1.1	even	1	trivial
197.4.h.a.148.6	yes	2016	197.148	even	98	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.h (of order \(98\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.65231 - 0.149190i) q^{2} +(0.203946 - 0.106399i) q^{3} +(13.6382 + 0.875598i) q^{4} +(-0.723623 + 0.214768i) q^{5} +(-0.964694 + 0.464572i) q^{6} +(-0.222342 - 6.93345i) q^{7} +(-26.2527 - 2.53257i) q^{8} +(-15.4169 + 22.1013i) q^{9} +(3.39856 - 0.891207i) q^{10} +(-10.9231 - 14.6360i) q^{11} +(2.87461 - 1.27250i) q^{12} +(34.1828 + 35.2966i) q^{13} +32.2897i q^{14} +(-0.124729 + 0.120793i) q^{15} +(13.3257 + 1.71816i) q^{16} +(43.8584 - 108.331i) q^{17} +(75.0214 - 100.522i) q^{18} +(4.40062 - 19.2804i) q^{19} +(-10.0569 + 2.29543i) q^{20} +(-0.783055 - 1.39039i) q^{21} +(48.6342 + 69.7207i) q^{22} +(2.09296 + 1.78176i) q^{23} +(-5.62360 + 2.27674i) q^{24} +(-104.284 + 67.8810i) q^{25} +(-153.763 - 169.310i) q^{26} +(-1.58690 + 12.3077i) q^{27} +(3.03858 - 94.7541i) q^{28} +(-0.223311 - 0.504464i) q^{29} +(0.598300 - 0.543360i) q^{30} +(49.7989 + 255.707i) q^{31} +(146.553 + 23.6936i) q^{32} +(-3.78497 - 1.82275i) q^{33} +(-220.205 + 497.446i) q^{34} +(1.64997 + 4.96945i) q^{35} +(-229.610 + 287.921i) q^{36} +(-159.502 + 20.5655i) q^{37} +(-23.3495 + 89.0417i) q^{38} +(10.7270 + 3.56160i) q^{39} +(19.5410 - 3.80561i) q^{40} +(-431.046 - 174.511i) q^{41} +(3.43558 + 6.58536i) q^{42} +(-382.124 + 285.187i) q^{43} +(-136.156 - 209.172i) q^{44} +(6.40938 - 19.3040i) q^{45} +(-9.47127 - 8.60156i) q^{46} +(-313.132 + 516.544i) q^{47} +(2.90053 - 1.06742i) q^{48} +(294.272 - 18.8929i) q^{49} +(495.286 - 300.245i) q^{50} +(-2.58152 - 26.7601i) q^{51} +(435.285 + 511.311i) q^{52} +(-363.642 + 400.410i) q^{53} +(9.21892 - 57.0223i) q^{54} +(11.0476 + 8.24501i) q^{55} +(-11.7223 + 182.585i) q^{56} +(-1.15391 - 4.40038i) q^{57} +(0.963652 + 2.38024i) q^{58} +(2.00254 + 0.525127i) q^{59} +(-1.80684 + 1.53819i) q^{60} +(16.9342 - 32.4598i) q^{61} +(-193.531 - 1197.06i) q^{62} +(156.666 + 101.978i) q^{63} +(-783.782 - 152.642i) q^{64} +(-32.3161 - 18.2001i) q^{65} +(17.3369 + 9.04466i) q^{66} +(345.982 + 209.736i) q^{67} +(693.001 - 1439.03i) q^{68} +(0.616428 + 0.140696i) q^{69} +(-6.93479 - 23.3656i) q^{70} +(-178.711 - 124.661i) q^{71} +(460.708 - 541.174i) q^{72} +(39.4844 + 306.233i) q^{73} +(745.121 - 71.8809i) q^{74} +(-14.0458 + 24.9397i) q^{75} +(76.8982 - 259.096i) q^{76} +(-99.0492 + 78.9891i) q^{77} +(-49.3738 - 18.1700i) q^{78} +(272.938 + 81.0065i) q^{79} +(-10.0118 + 1.61863i) q^{80} +(-250.292 - 680.124i) q^{81} +(1979.32 + 876.188i) q^{82} +(-133.553 - 585.134i) q^{83} +(-9.46199 - 19.6480i) q^{84} +(-8.47094 + 87.8102i) q^{85} +(1820.31 - 1269.77i) q^{86} +(-0.0992177 - 0.0791235i) q^{87} +(249.695 + 411.898i) q^{88} +(26.1044 - 134.041i) q^{89} +(-32.6984 + 88.8521i) q^{90} +(237.127 - 244.853i) q^{91} +(26.9840 + 26.1325i) q^{92} +(37.3631 + 46.8519i) q^{93} +(1533.85 - 2356.41i) q^{94} +(0.956409 + 14.8968i) q^{95} +(32.4099 - 10.7608i) q^{96} +(-1438.55 + 810.177i) q^{97} +(-1371.86 + 43.9930i) q^{98} +(491.874 - 15.7734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2016 q - 42 q^{2} - 42 q^{3} - 42 q^{5} - 119 q^{6} - 98 q^{8} - 42 q^{9} - 252 q^{10} - 140 q^{11} + 14 q^{12} - 42 q^{13} - 1722 q^{15} + 168 q^{16} - 42 q^{17} + 147 q^{18} - 567 q^{19} - 49 q^{20} - 42 q^{21}+ \cdots - 14763 q^{99}+O(q^{100}) \) 2016 * q - 42 * q^2 - 42 * q^3 - 42 * q^5 - 119 * q^6 - 98 * q^8 - 42 * q^9 - 252 * q^10 - 140 * q^11 + 14 * q^12 - 42 * q^13 - 1722 * q^15 + 168 * q^16 - 42 * q^17 + 147 * q^18 - 567 * q^19 - 49 * q^20 - 42 * q^21 - 1386 * q^22 - 42 * q^23 + 1246 * q^24 - 42 * q^25 + 1134 * q^26 - 504 * q^27 + 525 * q^28 - 3269 * q^29 - 847 * q^30 - 966 * q^31 - 994 * q^32 - 1631 * q^33 + 798 * q^34 - 42 * q^35 - 4207 * q^36 - 2149 * q^37 + 14 * q^38 - 252 * q^39 - 686 * q^40 - 392 * q^41 + 1176 * q^42 - 378 * q^43 + 12894 * q^44 + 3759 * q^45 + 2520 * q^46 + 28 * q^47 + 3654 * q^48 + 2646 * q^49 + 4914 * q^50 + 14 * q^51 - 3703 * q^52 - 42 * q^53 + 4305 * q^54 - 4130 * q^55 + 2989 * q^56 - 11585 * q^57 + 13286 * q^58 - 3136 * q^59 - 4914 * q^60 - 1050 * q^61 + 3836 * q^62 - 2198 * q^63 - 2562 * q^64 + 2359 * q^65 - 4683 * q^66 + 3528 * q^67 - 49 * q^68 - 49 * q^69 + 5208 * q^70 - 8792 * q^71 + 4928 * q^72 + 630 * q^73 + 266 * q^74 + 1232 * q^75 - 7903 * q^76 - 49 * q^77 - 4788 * q^78 - 1512 * q^79 - 490 * q^80 + 1078 * q^81 - 42 * q^82 - 5607 * q^83 + 10535 * q^84 - 19824 * q^85 - 7833 * q^86 - 49 * q^87 - 2373 * q^88 - 196 * q^89 - 8484 * q^90 + 14084 * q^91 - 1554 * q^92 - 2639 * q^93 + 7784 * q^94 + 7651 * q^95 + 15211 * q^96 - 1442 * q^97 + 18788 * q^98 - 14763 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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