LMFDB - Embedded newform 197.4.g.a.37.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(16,197)]

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([2]))

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

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

chi := DirichletCharacter("197.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.g (of order $49$, 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:	$2058$
Relative dimension:	$49$ over $\Q(\zeta_{49})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{49}]$

Embedding invariants

Embedding label			37.13
Character	$\chi$	$=$	197.37
Dual form			197.4.g.a.16.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.99065 + 0.192006i) q^{2} +(-1.86534 - 2.67411i) q^{3} +(0.972802 - 0.125429i) q^{4} +(10.2745 + 6.68798i) q^{5} +(6.09203 + 7.63916i) q^{6} +(-26.7473 - 1.71723i) q^{7} +(20.6471 - 4.02103i) q^{8} +(5.65350 - 15.3624i) q^{9} +(-32.0116 - 18.0286i) q^{10} +(5.46837 + 18.4248i) q^{11} +(-2.15002 - 2.36741i) q^{12} +(1.98068 + 61.7650i) q^{13} +80.3215 q^{14} +(-1.28114 - 39.9505i) q^{15} +(-68.5665 + 17.9802i) q^{16} +(89.0575 - 86.2474i) q^{17} +(-13.9580 + 47.0291i) q^{18} +(10.6340 - 5.12106i) q^{19} +(10.8339 + 5.21735i) q^{20} +(45.3008 + 74.7284i) q^{21} +(-19.8917 - 54.0521i) q^{22} +(-3.56179 + 22.0309i) q^{23} +(-49.2666 - 47.7120i) q^{24} +(10.2389 + 23.1300i) q^{25} +(-17.7828 - 184.337i) q^{26} +(-136.779 + 35.8676i) q^{27} +(-26.2352 + 1.68436i) q^{28} +(-83.5450 - 91.9923i) q^{29} +(11.5022 + 119.232i) q^{30} +(-236.991 - 95.9469i) q^{31} +(41.8987 - 13.9113i) q^{32} +(39.0694 - 48.9915i) q^{33} +(-249.780 + 275.035i) q^{34} +(-263.331 - 196.529i) q^{35} +(3.57285 - 15.6537i) q^{36} +(-356.028 - 93.3617i) q^{37} +(-30.8193 + 17.3571i) q^{38} +(161.472 - 120.509i) q^{39} +(239.032 + 96.7733i) q^{40} +(12.1535 - 11.7700i) q^{41} +(-149.827 - 214.788i) q^{42} +(-105.520 - 355.530i) q^{43} +(7.63064 + 17.2378i) q^{44} +(160.830 - 120.031i) q^{45} +(6.42200 - 66.5707i) q^{46} +(142.710 - 273.548i) q^{47} +(175.981 + 149.815i) q^{48} +(372.285 + 48.0009i) q^{49} +(-35.0622 - 67.2077i) q^{50} +(-396.757 - 77.2685i) q^{51} +(9.67394 + 59.8367i) q^{52} +(27.5130 - 285.201i) q^{53} +(402.171 - 133.530i) q^{54} +(-67.0394 + 225.878i) q^{55} +(-559.160 + 72.0957i) q^{56} +(-33.5303 - 18.8839i) q^{57} +(267.517 + 259.076i) q^{58} +(-325.453 + 183.291i) q^{59} +(-6.25725 - 38.7033i) q^{60} +(46.4269 - 66.5564i) q^{61} +(727.179 + 241.440i) q^{62} +(-177.597 + 401.194i) q^{63} +(403.001 - 163.157i) q^{64} +(-392.732 + 647.853i) q^{65} +(-107.436 + 154.018i) q^{66} +(179.655 - 344.365i) q^{67} +(75.8174 - 95.0720i) q^{68} +(65.5571 - 31.5706i) q^{69} +(825.266 + 537.189i) q^{70} +(-226.871 + 616.482i) q^{71} +(54.9560 - 339.922i) q^{72} +(433.349 + 113.637i) q^{73} +(1082.68 + 210.852i) q^{74} +(42.7529 - 70.5253i) q^{75} +(9.70244 - 6.31559i) q^{76} +(-114.625 - 502.203i) q^{77} +(-459.767 + 391.405i) q^{78} +(-359.315 + 233.888i) q^{79} +(-824.739 - 273.832i) q^{80} +(14.5087 + 12.3514i) q^{81} +(-34.0870 + 37.5336i) q^{82} +(-904.472 - 435.571i) q^{83} +(53.4418 + 67.0139i) q^{84} +(1491.84 - 290.537i) q^{85} +(383.836 + 1043.01i) q^{86} +(-90.1574 + 395.006i) q^{87} +(186.993 + 358.430i) q^{88} +(-229.136 + 92.7670i) q^{89} +(-457.941 + 389.851i) q^{90} +(53.0870 - 1655.45i) q^{91} +(-0.701601 + 21.8785i) q^{92} +(185.496 + 812.713i) q^{93} +(-374.272 + 845.487i) q^{94} +(143.509 + 18.5034i) q^{95} +(-115.356 - 86.0923i) q^{96} +(-583.126 - 961.928i) q^{97} +(-1122.59 - 72.0728i) q^{98} +(313.964 + 20.1572i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2058 q - 42 q^{2} - 42 q^{3} - 84 q^{4} - 42 q^{5} - 119 q^{6} - 84 q^{7} - 98 q^{8} - 42 q^{9} + 168 q^{10} - 140 q^{11} + 14 q^{12} - 42 q^{13} - 812 q^{14} + 1638 q^{15} + 672 q^{16} - 42 q^{17} + 147 q^{18}+ \cdots + 6237 q^{99}+O(q^{100}) $ 2058 * q - 42 * q^2 - 42 * q^3 - 84 * q^4 - 42 * q^5 - 119 * q^6 - 84 * q^7 - 98 * q^8 - 42 * q^9 + 168 * q^10 - 140 * q^11 + 14 * q^12 - 42 * q^13 - 812 * q^14 + 1638 * q^15 + 672 * q^16 - 42 * q^17 + 147 * q^18 - 567 * q^19 - 35 * q^20 - 42 * q^21 + 1302 * q^22 - 42 * q^23 - 434 * q^24 - 42 * q^25 + 364 * q^26 - 1596 * q^27 - 147 * q^28 + 4676 * q^29 - 847 * q^30 + 882 * q^31 + 910 * q^32 - 287 * q^33 - 882 * q^34 - 42 * q^35 - 17787 * q^36 - 1400 * q^37 + 14 * q^38 + 168 * q^39 + 3962 * q^40 - 392 * q^41 + 1764 * q^42 + 294 * q^43 - 12978 * q^44 + 2814 * q^45 + 840 * q^46 + 28 * q^47 + 3654 * q^48 + 1554 * q^49 - 4998 * q^50 - 98 * q^51 - 3703 * q^52 - 42 * q^53 - 1365 * q^54 + 4046 * q^55 - 3073 * q^56 + 14567 * q^57 - 10402 * q^58 + 4004 * q^59 - 4536 * q^60 - 1050 * q^61 + 210 * q^62 + 2254 * q^63 + 3822 * q^64 - 1106 * q^65 - 875 * q^66 - 3612 * q^67 + 819 * q^68 + 4333 * q^69 - 5292 * q^70 + 11424 * q^71 - 1876 * q^72 - 714 * q^73 + 1288 * q^74 - 1316 * q^75 + 8715 * q^76 + 6629 * q^77 + 13986 * q^78 - 1512 * q^79 + 406 * q^80 + 1078 * q^81 - 42 * q^82 - 5999 * q^83 - 7595 * q^84 + 30492 * q^85 + 7749 * q^86 - 35 * q^87 + 8897 * q^88 - 196 * q^89 - 14910 * q^90 - 8232 * q^91 - 7938 * q^92 - 2639 * q^93 - 11116 * q^94 + 3703 * q^95 + 14497 * q^96 - 2674 * q^97 - 10024 * q^98 + 6237 * q^99

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{48}{49}\right)$

Coefficient data

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

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

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

$2$	−2.99065	+	0.192006i	−1.05735	+	0.0678844i	−0.583018	−	0.812459i	$-0.698128\pi$
$2$	−2.99065	+	0.192006i	−1.05735	+	0.0678844i	−0.474336	+	0.880344i	$0.657312\pi$
$3$	−1.86534	−	2.67411i	−0.358985	−	0.514632i	0.599270	−	0.800547i	$-0.295458\pi$
$3$	−1.86534	−	2.67411i	−0.358985	−	0.514632i	−0.958255	+	0.285915i	$0.907703\pi$
$4$	0.972802	−	0.125429i	0.121600	−	0.0156786i
$5$	10.2745	+	6.68798i	0.918982	+	0.598191i	0.915726	−	0.401804i	$-0.131617\pi$
$5$	10.2745	+	6.68798i	0.918982	+	0.598191i	0.00325583	+	0.999995i	$0.498964\pi$
$6$	6.09203	+	7.63916i	0.414510	+	0.519779i
$7$	−26.7473	−	1.71723i	−1.44422	−	0.0927219i	−0.677887	−	0.735167i	$-0.737104\pi$
$7$	−26.7473	−	1.71723i	−1.44422	−	0.0927219i	−0.766332	+	0.642445i	$0.777920\pi$
$8$	20.6471	−	4.02103i	0.912483	−	0.177706i
$9$	5.65350	−	15.3624i	0.209389	−	0.568978i
$10$	−32.0116	−	18.0286i	−1.01230	−	0.570115i
$11$	5.46837	+	18.4248i	0.149889	+	0.505025i	0.999759	−	0.0219675i	$-0.00699304\pi$
$11$	5.46837	+	18.4248i	0.149889	+	0.505025i	−0.849870	+	0.526993i	$0.823320\pi$
$12$	−2.15002	−	2.36741i	−0.0517214	−	0.0569510i
$13$	1.98068	+	61.7650i	0.0422572	+	1.31773i	0.772705	+	0.634765i	$0.218903\pi$
$13$	1.98068	+	61.7650i	0.0422572	+	1.31773i	−0.730448	+	0.682968i	$0.760689\pi$
$14$	80.3215			1.53335
$15$	−1.28114	−	39.9505i	−0.0220525	−	0.687679i
$16$	−68.5665	+	17.9802i	−1.07135	+	0.280941i
$17$	89.0575	−	86.2474i	1.27057	−	1.23047i	0.310541	−	0.950560i	$-0.399490\pi$
$17$	89.0575	−	86.2474i	1.27057	−	1.23047i	0.960025	−	0.279914i	$-0.0903061\pi$
$18$	−13.9580	+	47.0291i	−0.182774	+	0.615825i
$19$	10.6340	−	5.12106i	0.128400	−	0.0618343i	−0.368581	−	0.929596i	$-0.620156\pi$
$19$	10.6340	−	5.12106i	0.128400	−	0.0618343i	0.496981	+	0.867761i	$0.334442\pi$
$20$	10.8339	+	5.21735i	0.121127	+	0.0583318i
$21$	45.3008	+	74.7284i	0.470735	+	0.776527i
$22$	−19.8917	−	54.0521i	−0.192769	−	0.523815i
$23$	−3.56179	+	22.0309i	−0.0322907	+	0.199729i	−0.998263	−	0.0589166i	$-0.981235\pi$
$23$	−3.56179	+	22.0309i	−0.0322907	+	0.199729i	0.965972	+	0.258646i	$0.0832762\pi$
$24$	−49.2666	−	47.7120i	−0.419021	−	0.405799i
$25$	10.2389	+	23.1300i	0.0819116	+	0.185040i
$26$	−17.7828	−	184.337i	−0.134134	−	1.39044i
$27$	−136.779	+	35.8676i	−0.974929	+	0.255656i
$28$	−26.2352	+	1.68436i	−0.177071	+	0.0113683i
$29$	−83.5450	−	91.9923i	−0.534963	−	0.589053i	0.411684	−	0.911327i	$-0.364941\pi$
$29$	−83.5450	−	91.9923i	−0.534963	−	0.589053i	−0.946647	+	0.322273i	$0.895553\pi$
$30$	11.5022	+	119.232i	0.0700000	+	0.725624i
$31$	−236.991	−	95.9469i	−1.37306	−	0.555890i	−0.434394	−	0.900723i	$-0.643038\pi$
$31$	−236.991	−	95.9469i	−1.37306	−	0.555890i	−0.938664	+	0.344833i	$0.887935\pi$
$32$	41.8987	−	13.9113i	0.231460	−	0.0768499i
$33$	39.0694	−	48.9915i	0.206094	−	0.258434i
$34$	−249.780	+	275.035i	−1.25991	+	1.38730i
$35$	−263.331	−	196.529i	−1.27174	−	0.949128i
$36$	3.57285	−	15.6537i	0.0165410	−	0.0724708i
$37$	−356.028	−	93.3617i	−1.58191	−	0.414826i	−0.644940	−	0.764233i	$-0.723118\pi$
$37$	−356.028	−	93.3617i	−1.58191	−	0.414826i	−0.936971	+	0.349407i	$0.886383\pi$
$38$	−30.8193	+	17.3571i	−0.131567	+	0.0740972i
$39$	161.472	−	120.509i	0.662979	−	0.494794i
$40$	239.032	+	96.7733i	0.944857	+	0.382530i
$41$	12.1535	−	11.7700i	0.0462942	−	0.0448334i	−0.672174	−	0.740393i	$-0.734639\pi$
$41$	12.1535	−	11.7700i	0.0462942	−	0.0448334i	0.718468	+	0.695560i	$0.244843\pi$
$42$	−149.827	−	214.788i	−0.550448	−	0.789109i
$43$	−105.520	−	355.530i	−0.374223	−	1.26088i	−0.909323	−	0.416092i	$-0.863400\pi$
$43$	−105.520	−	355.530i	−0.374223	−	1.26088i	0.535100	−	0.844789i	$-0.320274\pi$
$44$	7.63064	+	17.2378i	0.0261446	+	0.0590611i
$45$	160.830	−	120.031i	0.532782	−	0.397625i
$46$	6.42200	−	66.5707i	0.0205842	−	0.213376i
$47$	142.710	−	273.548i	0.442901	−	0.848959i	−0.556929	−	0.830560i	$-0.688021\pi$
$47$	142.710	−	273.548i	0.442901	−	0.848959i	0.999831	−	0.0183990i	$-0.00585691\pi$
$48$	175.981	+	149.815i	0.529181	+	0.450498i
$49$	372.285	+	48.0009i	1.08538	+	0.139944i
$50$	−35.0622	−	67.2077i	−0.0991709	−	0.190092i
$51$	−396.757	−	77.2685i	−1.08936	−	0.212152i
$52$	9.67394	+	59.8367i	0.0257987	+	0.159574i
$53$	27.5130	−	285.201i	0.0713058	−	0.739159i	−0.888571	−	0.458738i	$-0.848302\pi$
$53$	27.5130	−	285.201i	0.0713058	−	0.739159i	0.959877	−	0.280421i	$-0.0904740\pi$
$54$	402.171	−	133.530i	1.01349	−	0.336502i
$55$	−67.0394	+	225.878i	−0.164356	+	0.553771i
$56$	−559.160	+	72.0957i	−1.33430	+	0.172039i
$57$	−33.5303	−	18.8839i	−0.0779157	−	0.0438813i
$58$	267.517	+	259.076i	0.605633	+	0.586523i
$59$	−325.453	+	183.291i	−0.718141	+	0.404449i	−0.806182	−	0.591667i	$-0.798470\pi$
$59$	−325.453	+	183.291i	−0.718141	+	0.404449i	0.0880413	+	0.996117i	$0.471939\pi$
$60$	−6.25725	−	38.7033i	−0.0134635	−	0.0832762i
$61$	46.4269	−	66.5564i	0.0974484	−	0.139700i	−0.768468	−	0.639888i	$-0.778981\pi$
$61$	46.4269	−	66.5564i	0.0974484	−	0.139700i	0.865917	+	0.500188i	$0.166736\pi$
$62$	727.179	+	241.440i	1.48955	+	0.494563i
$63$	−177.597	+	401.194i	−0.355160	+	0.802313i
$64$	403.001	−	163.157i	0.787111	−	0.318666i
$65$	−392.732	+	647.853i	−0.749422	+	1.23625i
$66$	−107.436	+	154.018i	−0.200371	+	0.287247i
$67$	179.655	−	344.365i	0.327587	−	0.627923i	−0.665355	−	0.746527i	$-0.731720\pi$
$67$	179.655	−	344.365i	0.327587	−	0.627923i	0.992942	+	0.118605i	$0.0378421\pi$
$68$	75.8174	−	95.0720i	0.135209	−	0.169547i
$69$	65.5571	−	31.5706i	0.114379	−	0.0550820i
$70$	825.266	+	537.189i	1.40912	+	0.917233i
$71$	−226.871	+	616.482i	−0.379220	+	1.03046i	0.594774	+	0.803893i	$0.297241\pi$
$71$	−226.871	+	616.482i	−0.379220	+	1.03046i	−0.973995	+	0.226571i	$0.927248\pi$
$72$	54.9560	−	339.922i	0.0899531	−	0.556392i
$73$	433.349	+	113.637i	0.694790	+	0.182195i	0.584127	−	0.811663i	$-0.301437\pi$
$73$	433.349	+	113.637i	0.694790	+	0.182195i	0.110663	+	0.993858i	$0.464702\pi$
$74$	1082.68	+	210.852i	1.70080	+	0.331231i
$75$	42.7529	−	70.5253i	0.0658224	−	0.108581i
$76$	9.70244	−	6.31559i	0.0146440	−	0.00953221i
$77$	−114.625	−	502.203i	−0.169645	−	0.743265i
$78$	−459.767	+	391.405i	−0.667415	+	0.568178i
$79$	−359.315	+	233.888i	−0.511722	+	0.333094i	−0.775352	−	0.631530i	$-0.782427\pi$
$79$	−359.315	+	233.888i	−0.511722	+	0.333094i	0.263629	+	0.964624i	$0.415080\pi$
$80$	−824.739	−	273.832i	−1.15261	−	0.382692i
$81$	14.5087	+	12.3514i	0.0199022	+	0.0169430i
$82$	−34.0870	+	37.5336i	−0.0459059	+	0.0505475i
$83$	−904.472	−	435.571i	−1.19613	−	0.576025i	−0.273559	−	0.961855i	$-0.588201\pi$
$83$	−904.472	−	435.571i	−1.19613	−	0.576025i	−0.922570	+	0.385830i	$0.873915\pi$
$84$	53.4418	+	67.0139i	0.0694164	+	0.0870454i
$85$	1491.84	−	290.537i	1.90368	−	0.370743i
$86$	383.836	+	1043.01i	0.481280	+	1.30779i
$87$	−90.1574	+	395.006i	−0.111102	+	0.486771i
$88$	186.993	+	358.430i	0.226517	+	0.434190i
$89$	−229.136	+	92.7670i	−0.272903	+	0.110486i	−0.507630	−	0.861575i	$-0.669478\pi$
$89$	−229.136	+	92.7670i	−0.272903	+	0.110486i	0.234727	+	0.972061i	$0.424580\pi$
$90$	−457.941	+	389.851i	−0.536347	+	0.456599i
$91$	53.0870	−	1655.45i	0.0611542	−	1.90701i
$92$	−0.701601	+	21.8785i	−0.000795075	+	0.0247934i
$93$	185.496	+	812.713i	0.206829	+	0.906176i
$94$	−374.272	+	845.487i	−0.410673	+	0.927716i
$95$	143.509	+	18.5034i	0.154986	+	0.0199833i
$96$	−115.356	−	86.0923i	−0.122640	−	0.0915287i
$97$	−583.126	−	961.928i	−0.610387	−	1.00690i	−0.996431	−	0.0844163i	$-0.973097\pi$
$97$	−583.126	−	961.928i	−0.610387	−	1.00690i	0.386044	−	0.922480i	$-0.373841\pi$
$98$	−1122.59	−	72.0728i	−1.15713	−	0.0742903i
$99$	313.964	+	20.1572i	0.318733	+	0.0204633i
$100$	12.8616	+	21.2166i	0.0128616	+	0.0212166i
$101$	1059.61	+	790.804i	1.04391	+	0.779089i	0.975817	−	0.218590i	$-0.0701458\pi$
$101$	1059.61	+	790.804i	1.04391	+	0.779089i	0.0680912	+	0.997679i	$0.478309\pi$
$102$	1201.40	+	154.903i	1.16624	+	0.150370i
$103$	145.232	−	328.081i	0.138933	−	0.313853i	−0.831380	−	0.555704i	$-0.812449\pi$
$103$	145.232	−	328.081i	0.138933	−	0.313853i	0.970313	+	0.241852i	$0.0777548\pi$
$104$	289.254	+	1267.31i	0.272728	+	1.19490i
$105$	−34.3375	+	1070.77i	−0.0319142	+	0.995204i
$106$	−27.5215	+	858.220i	−0.0252181	+	0.786394i
$107$	1160.97	−	988.349i	1.04893	−	0.892966i	0.0545139	−	0.998513i	$-0.482639\pi$
$107$	1160.97	−	988.349i	1.04893	−	0.892966i	0.994414	+	0.105547i	$0.0336595\pi$
$108$	−128.560	+	52.0481i	−0.114543	+	0.0463734i
$109$	307.506	+	589.430i	0.270217	+	0.517956i	0.983041	−	0.183388i	$-0.0587063\pi$
$109$	307.506	+	589.430i	0.270217	+	0.517956i	−0.712823	+	0.701344i	$0.752584\pi$
$110$	157.121	−	688.394i	0.136190	−	0.596689i
$111$	414.456	+	1126.21i	0.354400	+	0.963019i
$112$	1864.84	−	363.178i	1.57331	−	0.306403i
$113$	−217.528	−	272.771i	−0.181091	−	0.227081i	0.682998	−	0.730421i	$-0.260676\pi$
$113$	−217.528	−	272.771i	−0.181091	−	0.227081i	−0.864089	+	0.503339i	$0.832105\pi$
$114$	103.903	+	50.0371i	0.0853634	+	0.0411088i
$115$	−183.938	+	202.536i	−0.149151	+	0.164231i
$116$	−92.8113	−	79.0114i	−0.0742872	−	0.0632416i
$117$	960.057	+	318.761i	0.758609	+	0.251876i
$118$	938.122	−	610.650i	0.731874	−	0.476397i
$119$	−2530.16	+	2153.95i	−1.94907	+	1.65926i
$120$	−187.094	−	819.712i	−0.142327	−	0.623576i
$121$	805.926	−	524.600i	0.605504	−	0.394140i
$122$	−126.067	+	207.961i	−0.0935541	+	0.154327i
$123$	−54.1448	−	10.5447i	−0.0396917	−	0.00772995i
$124$	−242.580	−	63.6119i	−0.175680	−	0.0460687i
$125$	195.084	−	1206.66i	0.139591	−	0.863419i
$126$	454.098	−	1233.93i	0.321066	−	0.872439i
$127$	−2145.48	−	1396.55i	−1.49906	−	0.975779i	−0.993603	−	0.112927i	$-0.963977\pi$
$127$	−2145.48	−	1396.55i	−1.49906	−	0.975779i	−0.505456	−	0.862853i	$-0.668676\pi$
$128$	−1492.11	+	718.564i	−1.03036	+	0.496193i
$129$	−753.896	+	945.356i	−0.514549	+	0.645224i
$130$	1050.13	−	2012.91i	0.708483	−	1.35803i
$131$	259.467	−	371.966i	0.173052	−	0.248083i	−0.724212	−	0.689577i	$-0.757796\pi$
$131$	259.467	−	371.966i	0.173052	−	0.248083i	0.897264	+	0.441494i	$0.145552\pi$
$132$	31.8619	−	52.5595i	0.0210092	−	0.0346569i
$133$	−293.225	+	118.713i	−0.191171	+	0.0773967i
$134$	−471.165	+	1064.37i	−0.303749	+	0.686175i
$135$	−1645.22	−	546.250i	−1.04887	−	0.348250i
$136$	1491.98	−	2138.86i	0.940706	−	1.34857i
$137$	126.334	+	781.422i	0.0787845	+	0.487310i	0.996032	+	0.0889927i	$0.0283648\pi$
$137$	126.334	+	781.422i	0.0787845	+	0.487310i	−0.917248	+	0.398317i	$0.869594\pi$
$138$	−189.997	+	107.004i	−0.117200	+	0.0660057i
$139$	247.618	+	239.805i	0.151098	+	0.146331i	0.767374	−	0.641200i	$-0.221563\pi$
$139$	247.618	+	239.805i	0.151098	+	0.146331i	−0.616275	+	0.787531i	$0.711359\pi$
$140$	−280.819	−	158.155i	−0.169526	−	0.0954750i
$141$	−997.699	+	128.639i	−0.595897	+	0.0768324i
$142$	560.124	−	1887.24i	0.331018	−	1.11531i
$143$	−1127.18	+	374.248i	−0.659155	+	0.218854i
$144$	−111.421	+	1155.00i	−0.0644798	+	0.668401i
$145$	−243.143	−	1503.92i	−0.139255	−	0.861339i
$146$	−1317.81	−	256.644i	−0.747007	−	0.145480i
$147$	−566.080	−	1085.07i	−0.317616	−	0.608810i
$148$	−358.055	−	46.1661i	−0.198865	−	0.0256408i
$149$	−2418.44	−	2058.85i	−1.32971	−	1.13200i	−0.980838	−	0.194827i	$-0.937585\pi$
$149$	−2418.44	−	2058.85i	−1.32971	−	1.13200i	−0.348871	−	0.937171i	$-0.613435\pi$
$150$	−114.318	+	219.125i	−0.0622266	+	0.119277i
$151$	−53.5691	+	555.299i	−0.0288701	+	0.299269i	0.969633	+	0.244566i	$0.0786456\pi$
$151$	−53.5691	+	555.299i	−0.0288701	+	0.299269i	−0.998503	+	0.0547027i	$0.982579\pi$
$152$	198.969	−	148.495i	0.106175	−	0.0792402i
$153$	−821.480	−	1855.74i	−0.434070	−	0.980571i
$154$	439.228	+	1479.91i	0.229831	+	0.774378i
$155$	−1793.28	−	2570.80i	−0.929287	−	1.33220i
$156$	141.965	−	137.485i	0.0728607	−	0.0705616i
$157$	3100.42	+	1255.22i	1.57605	+	0.638073i	0.985614	−	0.169011i	$-0.0540572\pi$
$157$	3100.42	+	1255.22i	1.57605	+	0.638073i	0.590438	+	0.807083i	$0.298955\pi$
$158$	1029.68	−	768.468i	0.518460	−	0.386937i
$159$	−813.981	+	458.425i	−0.405993	+	0.228651i
$160$	523.528	+	137.285i	0.258678	+	0.0678334i
$161$	133.101	−	583.152i	0.0651540	−	0.285458i
$162$	−45.7619	−	34.1530i	−0.0221938	−	0.0165637i
$163$	−551.101	+	606.823i	−0.264819	+	0.291595i	−0.858188	−	0.513335i	$-0.828410\pi$
$163$	−551.101	+	606.823i	−0.264819	+	0.291595i	0.593369	+	0.804931i	$0.297798\pi$
$164$	10.3467	−	12.9743i	0.00492646	−	0.00617759i
$165$	729.074	−	242.069i	0.343990	−	0.114212i
$166$	2788.59	+	1128.98i	1.30383	+	0.527864i
$167$	53.3907	+	553.450i	0.0247395	+	0.256451i	0.999455	+	0.0330024i	$0.0105069\pi$
$167$	53.3907	+	553.450i	0.0247395	+	0.256451i	−0.974716	+	0.223448i	$0.928269\pi$
$168$	1235.82	+	1360.77i	0.567531	+	0.624915i
$169$	−1618.51	+	103.912i	−0.736691	+	0.0472971i
$170$	−4405.80	+	1155.34i	−1.98770	+	0.521237i
$171$	−18.5524	−	192.316i	−0.00829673	−	0.0860043i
$172$	−147.243	−	332.625i	−0.0652744	−	0.147456i
$173$	−1267.02	−	1227.04i	−0.556818	−	0.539248i	0.362900	−	0.931828i	$-0.381787\pi$
$173$	−1267.02	−	1227.04i	−0.556818	−	0.539248i	−0.919718	+	0.392580i	$0.871583\pi$
$174$	193.786	−	1198.63i	0.0844303	−	0.522231i
$175$	−234.145	−	636.247i	−0.101141	−	0.274833i
$176$	−706.229	−	1165.00i	−0.302466	−	0.498949i
$177$	1097.22	+	528.394i	0.465945	+	0.224387i
$178$	667.455	−	321.429i	0.281055	−	0.135349i
$179$	−223.814	+	754.103i	−0.0934560	+	0.314884i	−0.992379	−	0.123222i	$-0.960677\pi$
$179$	−223.814	+	754.103i	−0.0934560	+	0.314884i	0.898923	+	0.438106i	$0.144351\pi$
$180$	141.401	−	136.939i	0.0585522	−	0.0567046i
$181$	1233.74	−	323.524i	0.506647	−	0.132858i	0.00852190	−	0.999964i	$-0.497287\pi$
$181$	1233.74	−	323.524i	0.506647	−	0.132858i	0.498125	+	0.867105i	$0.334022\pi$
$182$	159.092	+	4961.06i	0.0647948	+	2.02054i
$183$	−264.581			−0.106876
$184$	15.0463	+	469.198i	0.00602839	+	0.187988i
$185$	−3033.62	−	3340.36i	−1.20560	−	1.32750i
$186$	−710.801	−	2394.92i	−0.280207	−	0.944109i
$187$	2076.09	+	1169.23i	0.811864	+	0.457233i
$188$	104.518	−	284.008i	0.0405464	−	0.110178i
$189$	3720.06	−	724.481i	1.43172	−	0.278827i
$190$	−432.737	−	27.7826i	−0.165232	−	0.0106082i
$191$	2432.67	+	3050.48i	0.921582	+	1.15563i	0.987471	+	0.157800i	$0.0504401\pi$
$191$	2432.67	+	3050.48i	0.921582	+	1.15563i	−0.0658895	+	0.997827i	$0.520988\pi$
$192$	−1188.03	−	773.324i	−0.446557	−	0.290676i
$193$	−1769.64	+	228.170i	−0.660008	+	0.0850987i	−0.450595	−	0.892728i	$-0.648788\pi$
$193$	−1769.64	+	228.170i	−0.660008	+	0.0850987i	−0.209414	+	0.977827i	$0.567155\pi$
$194$	1928.62	+	2764.83i	0.713748	+	1.02321i
$195$	2465.01	−	158.259i	0.905246	−	0.0581187i
$196$	368.181			0.134177
$197$	−2681.76	−	673.457i	−0.969885	−	0.243563i
$197$	−2681.76	−	673.457i	−0.969885	−	0.243563i
$198$	−942.827			−0.338403
$199$	−407.777	+	26.1802i	−0.145259	+	0.00932595i	−0.136530	−	0.990636i	$-0.543595\pi$
$199$	−407.777	+	26.1802i	−0.145259	+	0.00932595i	−0.00872926	+	0.999962i	$0.502779\pi$
$200$	304.411	+	436.396i	0.107626	+	0.154289i
$201$	−1255.99	+	161.941i	−0.440748	+	0.0568282i
$202$	−3320.75	−	2161.57i	−1.15667	−	0.752908i
$203$	2076.63	+	2604.01i	0.717985	+	0.900325i
$204$	−395.658	−	25.4021i	−0.135792	−	0.00871815i
$205$	203.589	−	39.6490i	0.0693624	−	0.0135083i
$206$	−371.344	+	1009.06i	−0.125596	+	0.341285i
$207$	318.311	+	179.270i	0.106880	+	0.0601937i
$208$	−1246.36	−	4199.40i	−0.415478	−	1.39988i
$209$	152.505	+	167.925i	0.0504736	+	0.0555771i
$210$	−102.903	−	3208.89i	−0.0338141	−	1.05445i
$211$	−5645.95			−1.84210			−0.921051	−	0.389443i	$-0.872668\pi$
$211$	−5645.95			−1.84210			−0.921051	+	0.389443i	$0.872668\pi$
$212$	−9.00777	−	280.895i	−0.00291819	−	0.0909999i
$213$	2071.73	−	543.272i	0.666445	−	0.174762i
$214$	−3282.29	+	3178.72i	−1.04847	+	1.01539i
$215$	1293.61	−	4358.62i	0.410343	−	1.38258i
$216$	−2679.86	+	1290.55i	−0.844174	+	0.406533i
$217$	6174.10	+	2973.29i	1.93145	+	0.930139i
$218$	−1032.82	−	1703.74i	−0.320877	−	0.529320i
$219$	−504.465	−	1370.79i	−0.155656	−	0.422967i
$220$	−36.8844	+	228.143i	−0.0113034	+	0.0699155i
$221$	5503.47	+	5329.81i	1.67513	+	1.62227i
$222$	−1455.73	−	3288.52i	−0.440100	−	0.994194i
$223$	278.351	+	2885.40i	0.0835864	+	0.866460i	0.937947	+	0.346779i	$0.112725\pi$
$223$	278.351	+	2885.40i	0.0835864	+	0.866460i	−0.854360	+	0.519681i	$0.826051\pi$
$224$	−1144.57	+	300.141i	−0.341404	+	0.0895267i
$225$	413.218	−	26.5295i	0.122435	−	0.00786058i
$226$	702.924	+	773.997i	0.206893	+	0.227812i
$227$	−333.478	−	3456.85i	−0.0975054	−	1.01075i	−0.906294	−	0.422647i	$-0.861101\pi$
$227$	−333.478	−	3456.85i	−0.0975054	−	1.01075i	0.808789	−	0.588099i	$-0.200123\pi$
$228$	−34.9869	−	14.1646i	−0.0101626	−	0.00411437i
$229$	−2877.92	+	955.537i	−0.830474	+	0.275736i	−0.698584	−	0.715528i	$-0.746186\pi$
$229$	−2877.92	+	955.537i	−0.830474	+	0.275736i	−0.131890	+	0.991264i	$0.542105\pi$
$230$	511.206	−	641.032i	0.146556	−	0.183776i
$231$	−1129.13	+	1243.30i	−0.321608	+	0.354126i
$232$	−2094.87	−	1563.44i	−0.592822	−	0.442435i
$233$	−128.403	+	562.571i	−0.0361028	+	0.158177i	−0.989766	−	0.142699i	$-0.954422\pi$
$233$	−128.403	+	562.571i	−0.0361028	+	0.158177i	0.953663	+	0.300876i	$0.0972790\pi$
$234$	−2932.40	−	768.965i	−0.819217	−	0.214824i
$235$	3295.76	−	1856.14i	0.914857	−	0.515238i
$236$	−293.611	+	219.127i	−0.0809849	+	0.0604406i
$237$	1295.69	+	524.565i	0.355122	+	0.143773i
$238$	7153.24	−	6927.52i	1.94822	−	1.88674i
$239$	3637.61	+	5214.79i	0.984508	+	1.41137i	0.910218	+	0.414130i	$0.135914\pi$
$239$	3637.61	+	5214.79i	0.984508	+	1.41137i	0.0742902	+	0.997237i	$0.476331\pi$
$240$	806.164	+	2716.23i	0.216823	+	0.730550i
$241$	2280.80	+	5152.36i	0.609622	+	1.37715i	0.906489	+	0.422229i	$0.138752\pi$
$241$	2280.80	+	5152.36i	0.609622	+	1.37715i	−0.296867	+	0.954919i	$0.595942\pi$
$242$	−2309.52	+	1723.64i	−0.613477	+	0.457850i
$243$	−360.640	+	3738.41i	−0.0952060	+	0.986910i
$244$	36.8161	−	70.5695i	0.00965946	−	0.0185154i
$245$	3504.03	+	2983.02i	0.913731	+	0.777871i
$246$	163.953	+	21.1394i	0.0424929	+	0.00547885i
$247$	337.365	+	646.666i	0.0869070	+	0.166584i
$248$	−5278.98	−	1028.08i	−1.35168	−	0.263239i
$249$	522.386	+	3231.14i	0.132951	+	0.822351i
$250$	−351.742	+	3646.17i	−0.0889844	+	0.922416i
$251$	3544.26	−	1176.78i	0.891282	−	0.295926i	0.167432	−	0.985884i	$-0.446452\pi$
$251$	3544.26	−	1176.78i	0.891282	−	0.295926i	0.723850	+	0.689958i	$0.242371\pi$
$252$	−122.445	+	412.558i	−0.0306084	+	0.103130i
$253$	−425.392	+	54.8482i	−0.105708	+	0.0136296i
$254$	6684.52	+	3764.65i	1.65128	+	0.929982i
$255$	−3559.73	−	3447.40i	−0.874191	−	0.846606i
$256$	1293.80	−	728.652i	0.315868	−	0.177894i
$257$	−419.675	−	2595.84i	−0.101862	−	0.630054i	−0.986498	−	0.163772i	$-0.947634\pi$
$257$	−419.675	−	2595.84i	−0.101862	−	0.630054i	0.884636	−	0.466282i	$-0.154407\pi$
$258$	2073.13	−	2971.98i	0.500260	−	0.717161i
$259$	9362.48	+	3108.56i	2.24616	+	0.745777i
$260$	−300.791	+	679.493i	−0.0717473	+	0.162078i
$261$	−1885.55	+	763.373i	−0.447174	+	0.181041i
$262$	−704.557	+	1162.24i	−0.166136	+	0.274059i
$263$	1930.98	−	2768.21i	0.452736	−	0.649031i	−0.526873	−	0.849944i	$-0.676636\pi$
$263$	1930.98	−	2768.21i	0.452736	−	0.649031i	0.979609	+	0.200913i	$0.0643908\pi$
$264$	609.675	−	1168.63i	0.142132	−	0.272441i
$265$	2190.10	−	2746.30i	0.507687	−	0.636619i
$266$	854.139	−	411.331i	0.196882	−	0.0948133i
$267$	675.486	+	439.693i	0.154828	+	0.100782i
$268$	131.575	−	357.533i	0.0299897	−	0.0814917i
$269$	1305.26	−	8073.47i	0.295847	−	1.82992i	−0.222720	−	0.974882i	$-0.571494\pi$
$269$	1305.26	−	8073.47i	0.295847	−	1.82992i	0.518567	−	0.855037i	$-0.326466\pi$
$270$	5025.16	+	1317.75i	1.13267	+	0.297021i
$271$	−2493.52	−	485.613i	−0.558932	−	0.108852i	−0.0962192	−	0.995360i	$-0.530675\pi$
$271$	−2493.52	−	485.613i	−0.558932	−	0.108852i	−0.462713	+	0.886508i	$0.653124\pi$
$272$	−4555.61	+	7514.95i	−1.01553	+	1.67522i
$273$	−4525.88	+	2946.02i	−1.00336	+	0.653118i
$274$	−527.860	−	2312.70i	−0.116384	−	0.509911i
$275$	−370.174	+	315.134i	−0.0811721	+	0.0691028i
$276$	59.8142	−	38.9347i	0.0130449	−	0.00849129i
$277$	−7057.09	−	2343.11i	−1.53076	−	0.508246i	−0.579059	−	0.815286i	$-0.696580\pi$
$277$	−7057.09	−	2343.11i	−1.53076	−	0.508246i	−0.951697	+	0.307040i	$0.900662\pi$
$278$	−786.583	−	669.628i	−0.169698	−	0.144466i
$279$	−2813.80	+	3098.31i	−0.603792	+	0.664842i
$280$	−6227.28	−	2998.90i	−1.32911	−	0.640066i
$281$	−2491.51	−	3124.25i	−0.528936	−	0.663264i	0.443544	−	0.896253i	$-0.353721\pi$
$281$	−2491.51	−	3124.25i	−0.528936	−	0.663264i	−0.972480	+	0.232988i	$0.925150\pi$
$282$	2959.07	−	576.279i	0.624858	−	0.121691i
$283$	−2091.85	−	5684.24i	−0.439391	−	1.19397i	−0.943804	−	0.330505i	$-0.892781\pi$
$283$	−2091.85	−	5684.24i	−0.439391	−	1.19397i	0.504413	−	0.863463i	$-0.331709\pi$
$284$	−143.376	+	628.171i	−0.0299570	+	0.131250i
$285$	−218.213	−	418.273i	−0.0453537	−	0.0869346i
$286$	3299.13	−	1335.67i	0.682103	−	0.276153i
$287$	−345.286	+	293.946i	−0.0710160	+	0.0604568i
$288$	23.1631	−	722.312i	0.00473924	−	0.147787i
$289$	335.159	−	10451.5i	0.0682187	−	2.12731i
$290$	1015.92	+	4451.03i	0.205713	+	0.901287i
$291$	−1484.57	+	3353.67i	−0.299062	+	0.675586i
$292$	435.816	+	56.1923i	0.0873432	+	0.0112617i
$293$	−1464.48	−	1092.97i	−0.291999	−	0.217925i	0.442102	−	0.896965i	$-0.354233\pi$
$293$	−1464.48	−	1092.97i	−0.291999	−	0.217925i	−0.734101	+	0.679040i	$0.762396\pi$
$294$	1901.29	+	3136.37i	0.377161	+	0.622166i
$295$	−4569.72	−	293.386i	−0.901896	−	0.0579037i
$296$	−7726.37	−	496.050i	−1.51718	−	0.0974064i
$297$	−1408.81	−	2323.98i	−0.275244	−	0.454043i
$298$	7628.03	+	5692.95i	1.48282	+	1.10666i
$299$	−1367.80	−	176.358i	−0.264554	−	0.0341105i
$300$	32.7442	−	73.9696i	0.00630162	−	0.0142355i
$301$	2211.83	+	9690.68i	0.423548	+	1.85569i
$302$	53.5855	−	1670.99i	0.0102103	−	0.318393i
$303$	138.169	−	4308.62i	0.0261967	−	0.816910i
$304$	−637.057	+	542.335i	−0.120190	+	0.102319i
$305$	922.142	−	373.334i	0.173120	−	0.0700887i
$306$	2813.07	+	5392.13i	0.525531	+	1.00735i
$307$	852.005	−	3732.88i	0.158392	−	0.693963i	−0.831896	−	0.554932i	$-0.812744\pi$
$307$	852.005	−	3732.88i	0.158392	−	0.693963i	0.990288	−	0.139030i	$-0.0443986\pi$
$308$	−174.498	−	474.167i	−0.0322823	−	0.0877214i
$309$	−1148.23	+	223.618i	−0.211394	+	0.0411689i
$310$	5856.67	+	7344.04i	1.07302	+	1.34553i
$311$	5460.33	+	2629.55i	0.995584	+	0.479448i	0.859438	−	0.511241i	$-0.170814\pi$
$311$	5460.33	+	2629.55i	0.995584	+	0.479448i	0.136146	+	0.990689i	$0.456528\pi$
$312$	2849.35	−	3137.46i	0.517029	−	0.569306i
$313$	7410.80	+	6308.91i	1.33828	+	1.13930i	0.978496	+	0.206264i	$0.0661307\pi$
$313$	7410.80	+	6308.91i	1.33828	+	1.13930i	0.359788	+	0.933034i	$0.382849\pi$
$314$	−9513.27	−	3158.62i	−1.70976	−	0.567680i
$315$	−4507.90	+	2934.32i	−0.806322	+	0.524857i
$316$	−320.206	+	272.595i	−0.0570031	+	0.0485274i
$317$	642.849	+	2816.51i	0.113899	+	0.499025i	0.999408	+	0.0344023i	$0.0109528\pi$
$317$	642.849	+	2816.51i	0.113899	+	0.499025i	−0.885509	+	0.464622i	$0.846190\pi$
$318$	2346.31	−	1527.28i	0.413757	−	0.269326i
$319$	1238.08	−	2042.35i	0.217302	−	0.358462i
$320$	5231.83	+	1018.90i	0.913964	+	0.177994i
$321$	−4808.56	−	1260.95i	−0.836099	−	0.219251i
$322$	−286.089	+	1769.56i	−0.0495127	+	0.306254i
$323$	505.359	−	1373.22i	0.0870554	−	0.236558i
$324$	15.6633	+	10.1957i	0.00268575	+	0.00174823i
$325$	−1408.34	+	678.222i	−0.240372	+	0.115757i
$326$	1531.64	−	1920.61i	0.260213	−	0.326297i
$327$	1002.60	−	1921.79i	0.169553	−	0.325001i
$328$	203.608	−	291.887i	0.0342755	−	0.0491365i
$329$	−4286.85	+	7071.60i	−0.718363	+	1.18502i
$330$	−2133.93	+	863.931i	−0.355966	+	0.144115i
$331$	3076.97	−	6950.94i	0.510954	−	1.15425i	−0.453800	−	0.891103i	$-0.649932\pi$
$331$	3076.97	−	6950.94i	0.510954	−	1.15425i	0.964755	−	0.263151i	$-0.0847618\pi$
$332$	−934.505	−	310.277i	−0.154481	−	0.0512912i
$333$	−3447.07	+	4941.63i	−0.567262	+	0.813212i
$334$	−265.939	−	1644.92i	−0.0435674	−	0.269480i
$335$	4148.97	−	2336.66i	0.676664	−	0.381090i
$336$	−4449.75	−	4309.34i	−0.722482	−	0.699684i
$337$	5109.55	+	2877.65i	0.825920	+	0.465150i	0.845063	−	0.534667i	$-0.179563\pi$
$337$	5109.55	+	2877.65i	0.825920	+	0.465150i	−0.0191425	+	0.999817i	$0.506094\pi$
$338$	4820.45	−	621.528i	0.775733	−	0.100020i
$339$	−323.656	+	1090.51i	−0.0518543	+	0.174714i
$340$	1414.83	−	469.755i	0.225676	−	0.0749295i
$341$	471.846	−	4891.17i	0.0749322	−	0.776750i
$342$	92.4096	+	571.586i	0.0146109	+	0.0903738i
$343$	−851.519	−	165.833i	−0.134046	−	0.0261054i
$344$	−3608.27	−	6916.38i	−0.565538	−	1.08403i
$345$	884.711	+	114.071i	0.138062	+	0.0178011i
$346$	4024.81	+	3426.37i	0.625361	+	0.532377i
$347$	−1378.12	+	2641.60i	−0.213203	+	0.408671i	−0.969333	−	0.245751i	$-0.920965\pi$
$347$	−1378.12	+	2641.60i	−0.213203	+	0.408671i	0.756130	+	0.654422i	$0.227088\pi$
$348$	−38.1602	+	395.571i	−0.00587817	+	0.0609334i
$349$	−6872.06	+	5128.76i	−1.05402	+	0.786636i	−0.977607	−	0.210440i	$-0.932510\pi$
$349$	−6872.06	+	5128.76i	−1.05402	+	0.786636i	−0.0764139	+	0.997076i	$0.524347\pi$
$350$	822.408	+	1857.83i	0.125599	+	0.283730i
$351$	−2486.28	−	8377.10i	−0.378085	−	1.27389i
$352$	485.431	+	695.901i	0.0735044	+	0.105374i
$353$	295.458	−	286.135i	0.0445485	−	0.0431429i	−0.673074	−	0.739575i	$-0.735026\pi$
$353$	295.458	−	286.135i	0.0445485	−	0.0431429i	0.717622	+	0.696433i	$0.245230\pi$
$354$	−3382.86	−	1369.57i	−0.507901	−	0.205626i
$355$	−6454.01	+	4816.75i	−0.964910	+	0.720131i
$356$	−211.269	+	118.984i	−0.0314528	+	0.0177139i
$357$	10479.5	+	2748.05i	1.55360	+	0.407401i
$358$	524.556	−	2298.23i	0.0774404	−	0.339289i
$359$	−7538.67	−	5626.26i	−1.10829	−	0.827138i	−0.122061	−	0.992523i	$-0.538950\pi$
$359$	−7538.67	−	5626.26i	−1.10829	−	0.827138i	−0.986229	+	0.165385i	$0.947113\pi$
$360$	2838.04	−	3125.00i	0.415494	−	0.457505i
$361$	−4189.66	+	5253.67i	−0.610827	+	0.765952i
$362$	−3627.56	+	1204.43i	−0.526686	+	0.174872i
$363$	−2906.16	−	1176.58i	−0.420204	−	0.170122i
$364$	−155.998	−	1617.08i	−0.0224630	−	0.232852i
$365$	3692.45	+	4065.80i	0.529511	+	0.583051i
$366$	791.270	−	50.8012i	0.113006	−	0.00725525i
$367$	4688.14	−	1229.38i	0.666809	−	0.174858i	0.0952936	−	0.995449i	$-0.469621\pi$
$367$	4688.14	−	1229.38i	0.666809	−	0.174858i	0.571516	+	0.820591i	$0.306356\pi$
$368$	−151.902	−	1574.63i	−0.0215175	−	0.223052i
$369$	−112.106	−	253.249i	−0.0158157	−	0.0357280i
$370$	9713.87	+	9407.36i	1.36487	+	1.32180i
$371$	−1225.66	+	7581.12i	−0.171517	+	1.06090i
$372$	282.389	+	767.342i	0.0393580	+	0.106948i
$373$	3869.73	+	6383.52i	0.537177	+	0.886129i	1.00000		0.000321544i	$-0.000102351\pi$
$373$	3869.73	+	6383.52i	0.537177	+	0.886129i	−0.462823	+	0.886451i	$0.653164\pi$
$374$	−6433.35	−	3098.14i	−0.889467	−	0.428345i
$375$	−3590.65	+	1729.17i	−0.494454	+	0.238117i
$376$	1846.60	−	6221.82i	0.253275	−	0.853366i
$377$	5516.43	−	5342.37i	0.753610	−	0.729830i
$378$	−10986.3	+	2880.94i	−1.49490	+	0.392010i
$379$	12.4500	+	388.236i	0.00168737	+	0.0526183i	0.999984	−	0.00573132i	$-0.00182435\pi$
$379$	12.4500	+	388.236i	0.00168737	+	0.0526183i	−0.998296	+	0.0583496i	$0.981416\pi$
$380$	141.926			0.0191597
$381$	267.521	+	8342.29i	0.0359725	+	1.12175i
$382$	−7860.99	−	8655.82i	−1.05289	−	1.15935i
$383$	−782.857	−	2637.70i	−0.104444	−	0.351907i	0.890160	−	0.455648i	$-0.150592\pi$
$383$	−782.857	−	2637.70i	−0.104444	−	0.351907i	−0.994604	+	0.103741i	$0.966919\pi$
$384$	4704.82	+	2649.71i	0.625239	+	0.352128i
$385$	2181.01	−	5926.51i	0.288713	−	0.784527i
$386$	5248.57	−	1022.16i	0.692086	−	0.134784i
$387$	−6058.35	−	388.959i	−0.795771	−	0.0510902i
$388$	−687.920	−	862.625i	−0.0900099	−	0.112869i
$389$	8697.71	+	5661.58i	1.13365	+	0.737927i	0.968666	−	0.248369i	$-0.0798945\pi$
$389$	8697.71	+	5661.58i	1.13365	+	0.737927i	0.164988	+	0.986296i	$0.447241\pi$
$390$	−7341.59	+	946.594i	−0.953221	+	0.122904i
$391$	1582.91	+	2269.22i	0.204734	+	0.293502i
$392$	7879.64	−	505.889i	1.01526	−	0.0651818i
$393$	−1478.67			−0.189794
$394$	8149.51	+	1499.16i	1.04205	+	0.191692i
$395$	−5256.02			−0.669517
$396$	307.953	−	19.7712i	0.0390789	−	0.00250895i
$397$	−2380.70	−	3412.91i	−0.300967	−	0.431459i	0.640809	−	0.767701i	$-0.278599\pi$
$397$	−2380.70	−	3412.91i	−0.300967	−	0.431459i	−0.941776	+	0.336242i	$0.890844\pi$
$398$	1214.49	−	156.591i	0.152957	−	0.0197217i
$399$	864.417	+	562.673i	0.108459	+	0.0705987i
$400$	−1117.93	−	1401.84i	−0.139741	−	0.175230i
$401$	−8193.29	−	526.027i	−1.02033	−	0.0655075i	−0.455101	−	0.890440i	$-0.650397\pi$
$401$	−8193.29	−	526.027i	−1.02033	−	0.0655075i	−0.565232	+	0.824932i	$0.691213\pi$
$402$	3725.12	−	725.467i	0.462169	−	0.0900075i
$403$	5456.76	−	14827.8i	0.674493	−	1.83282i
$404$	1129.98	+	636.391i	0.139155	+	0.0783704i
$405$	66.4638	+	223.939i	0.00815460	+	0.0274756i
$406$	−6710.46	−	7388.97i	−0.820283	−	0.903222i
$407$	−226.730	−	7070.28i	−0.0276132	−	0.861083i
$408$	−8502.60			−1.03172
$409$	345.172	+	10763.7i	0.0417302	+	1.30130i	0.779565	+	0.626321i	$0.215440\pi$
$409$	345.172	+	10763.7i	0.0417302	+	1.30130i	−0.737835	+	0.674981i	$0.764152\pi$
$410$	−601.252	+	157.667i	−0.0724237	+	0.0189917i
$411$	1853.95	−	1795.45i	0.222503	−	0.215482i
$412$	100.131	−	337.375i	0.0119735	−	0.0403428i
$413$	9019.73	−	4343.67i	1.07465	−	0.517526i
$414$	−986.379	−	475.015i	−0.117096	−	0.0563906i
$415$	−6379.93	−	10524.4i	−0.754647	−	1.24487i
$416$	942.222	+	2560.32i	0.111049	+	0.301755i
$417$	179.371	−	1109.47i	0.0210644	−	0.130291i
$418$	−488.332	−	472.923i	−0.0571413	−	0.0553383i
$419$	2439.11	+	5510.00i	0.284388	+	0.642437i	0.998330	−	0.0577675i	$-0.0183982\pi$
$419$	2439.11	+	5510.00i	0.284388	+	0.642437i	−0.713942	+	0.700205i	$0.753092\pi$
$420$	100.902	+	1045.95i	0.0117226	+	0.121517i
$421$	11774.7	−	3087.69i	1.36310	−	0.357446i	0.501551	−	0.865128i	$-0.332763\pi$
$421$	11774.7	−	3087.69i	1.36310	−	0.357446i	0.861544	+	0.507682i	$0.169498\pi$
$422$	16885.1	−	1084.06i	1.94775	−	0.125050i
$423$	−3395.54	−	3738.87i	−0.390300	−	0.429764i
$424$	−578.738	−	5999.22i	−0.0662877	−	0.687141i
$425$	2906.75	+	1176.81i	0.331761	+	0.134315i
$426$	−6091.51	+	2022.52i	−0.692805	+	0.230027i
$427$	−1356.09	+	1700.48i	−0.153690	+	0.192721i
$428$	1005.43	−	1107.09i	0.113549	−	0.125031i
$429$	3103.35	+	2316.09i	0.349256	+	0.260657i
$430$	−3031.87	+	13283.5i	−0.340022	+	1.48974i
$431$	−6742.23	−	1768.02i	−0.753508	−	0.197593i	−0.143131	−	0.989704i	$-0.545717\pi$
$431$	−6742.23	−	1768.02i	−0.753508	−	0.197593i	−0.610377	+	0.792111i	$0.708982\pi$
$432$	8733.53	−	4918.63i	0.972667	−	0.547796i
$433$	6670.23	−	4978.12i	0.740302	−	0.552502i	−0.160341	−	0.987062i	$-0.551259\pi$
$433$	6670.23	−	4978.12i	0.740302	−	0.552502i	0.900643	+	0.434560i	$0.143096\pi$
$434$	−19035.5	−	7706.61i	−2.10537	−	0.852371i
$435$	−3568.11	+	3455.52i	−0.393282	+	0.380873i
$436$	373.074	+	534.829i	0.0409793	+	0.0587469i
$437$	74.9457	+	252.517i	0.00820398	+	0.0276419i
$438$	1771.88	+	4002.71i	0.193296	+	0.436659i
$439$	−9992.82	+	7457.83i	−1.08640	+	0.810804i	−0.982958	−	0.183831i	$-0.941150\pi$
$439$	−9992.82	+	7457.83i	−1.08640	+	0.810804i	−0.103446	+	0.994635i	$0.532987\pi$
$440$	−475.909	+	4933.30i	−0.0515638	+	0.534513i
$441$	2842.13	−	5447.82i	0.306892	−	0.588254i
$442$	−17482.3	−	14882.9i	−1.88133	−	1.60160i
$443$	5759.43	+	742.597i	0.617695	+	0.0796430i	0.430366	−	0.902654i	$-0.358384\pi$
$443$	5759.43	+	742.597i	0.617695	+	0.0796430i	0.187329	+	0.982297i	$0.440017\pi$
$444$	544.443	+	1043.59i	0.0581939	+	0.111547i
$445$	−2974.69	−	579.321i	−0.316885	−	0.0617134i
$446$	−1386.46	−	8575.78i	−0.147200	−	0.910482i
$447$	−994.366	+	10307.6i	−0.105217	+	1.09068i
$448$	−11059.4	+	3671.96i	−1.16631	+	0.387241i
$449$	−4340.48	+	14624.5i	−0.456214	+	1.53714i	0.344909	+	0.938636i	$0.387910\pi$
$449$	−4340.48	+	14624.5i	−0.456214	+	1.53714i	−0.801123	+	0.598500i	$0.795764\pi$
$450$	−1230.70	+	158.681i	−0.128923	+	0.0166228i
$451$	283.320	+	159.563i	0.0295810	+	0.0166597i
$452$	−245.825	−	238.068i	−0.0255811	−	0.0247739i
$453$	1584.86	−	892.574i	0.164377	−	0.0925757i
$454$	1661.05	+	10274.2i	0.171712	+	1.06210i
$455$	11617.0	−	16653.9i	1.19696	−	1.71593i
$456$	−768.237	−	255.072i	−0.0788947	−	0.0261948i
$457$	5142.50	−	11617.0i	0.526381	−	1.18910i	−0.431546	−	0.902091i	$-0.642032\pi$
$457$	5142.50	−	11617.0i	0.526381	−	1.18910i	0.957927	−	0.287013i	$-0.0926622\pi$
$458$	8423.40	−	3410.25i	0.859387	−	0.347927i
$459$	−9087.69	+	14991.1i	−0.924133	+	1.52445i
$460$	−153.531	+	220.099i	−0.0155618	+	0.0223091i
$461$	−3517.21	+	6741.84i	−0.355343	+	0.681125i	−0.996253	−	0.0864908i	$-0.972435\pi$
$461$	−3517.21	+	6741.84i	−0.355343	+	0.681125i	0.640910	+	0.767616i	$0.278557\pi$
$462$	3138.12	−	3935.07i	0.316014	−	0.396269i
$463$	−3827.68	+	1843.31i	−0.384206	+	0.185024i	−0.616009	−	0.787739i	$-0.711252\pi$
$463$	−3827.68	+	1843.31i	−0.384206	+	0.185024i	0.231804	+	0.972763i	$0.425537\pi$
$464$	7382.43	+	4805.43i	0.738622	+	0.480790i
$465$	−3529.52	+	9590.83i	−0.351994	+	0.956482i
$466$	275.992	−	1707.11i	0.0274358	−	0.169700i
$467$	12613.4	+	3307.61i	1.24984	+	0.327748i	0.818535	−	0.574457i	$-0.194787\pi$
$467$	12613.4	+	3307.61i	1.24984	+	0.327748i	0.431309	+	0.902204i	$0.358052\pi$
$468$	973.927	+	189.672i	0.0961961	+	0.0187342i
$469$	−5396.64	+	8902.32i	−0.531329	+	0.876484i
$470$	−9500.07	+	6183.86i	−0.932352	+	0.606894i
$471$	−2426.74	−	10632.3i	−0.237406	−	1.04015i
$472$	−5982.64	+	5093.09i	−0.583418	+	0.496671i
$473$	5973.54	−	3888.34i	0.580684	−	0.377984i
$474$	−3975.66	−	1320.01i	−0.385250	−	0.127912i
$475$	227.331	+	193.530i	0.0219593	+	0.0186942i
$476$	−2191.17	+	2412.72i	−0.210992	+	0.232326i
$477$	−4225.83	−	2035.05i	−0.405634	−	0.195343i
$478$	−11880.1	−	14897.2i	−1.13678	−	1.42548i
$479$	−10211.7	+	1988.73i	−0.974083	+	0.189703i	−0.653008	−	0.757351i	$-0.726493\pi$
$479$	−10211.7	+	1988.73i	−0.974083	+	0.189703i	−0.321075	+	0.947054i	$0.604044\pi$
$480$	−609.443	−	1656.05i	−0.0579524	−	0.157475i
$481$	5061.31	−	22175.0i	0.479783	−	2.10207i
$482$	−7810.35	−	14971.0i	−0.738074	−	1.41475i
$483$	−1807.69	+	731.852i	−0.170295	+	0.0689450i
$484$	718.207	−	611.418i	0.0674499	−	0.0574210i
$485$	442.003	−	13783.3i	0.0413821	−	1.29045i
$486$	360.750	−	11249.5i	0.0336707	−	1.04998i
$487$	1788.00	+	7833.73i	0.166369	+	0.728912i	0.987428	+	0.158068i	$0.0505266\pi$
$487$	1788.00	+	7833.73i	0.166369	+	0.728912i	−0.821059	+	0.570844i	$0.806616\pi$
$488$	690.957	−	1560.88i	0.0640945	−	0.144791i
$489$	2650.70	+	341.770i	0.245131	+	0.0316061i
$490$	−11052.1	−	8248.38i	−1.01894	−	0.760457i
$491$	−9125.58	−	15053.6i	−0.838761	−	1.38362i	−0.922039	−	0.387097i	$-0.873478\pi$
$491$	−9125.58	−	15053.6i	−0.838761	−	1.38362i	0.0832782	−	0.996526i	$-0.473461\pi$
$492$	−53.9948	−	3.46658i	−0.00494771	−	0.000317654i
$493$	−15374.4	−	987.070i	−1.40452	−	0.0901732i
$494$	−1133.10	−	1869.17i	−0.103200	−	0.170239i
$495$	3091.02	+	2306.89i	0.280669	+	0.209469i
$496$	17974.8	+	2317.59i	1.62720	+	0.209804i
$497$	7126.83	−	16099.6i	0.643224	−	1.45305i
$498$	−2182.67	−	9562.91i	−0.196401	−	0.860491i
$499$	448.838	−	13996.4i	0.0402660	−	1.25564i	−0.757565	−	0.652760i	$-0.773611\pi$
$499$	448.838	−	13996.4i	0.0402660	−	1.25564i	0.797831	−	0.602882i	$-0.205981\pi$
$500$	38.4276	−	1198.32i	0.00343707	−	0.107181i
$501$	1380.39	−	1175.15i	0.123097	−	0.104794i
$502$	−10373.7	+	4199.84i	−0.922312	+	0.373403i
$503$	9850.36	+	18881.3i	0.873173	+	1.67371i	0.729389	+	0.684099i	$0.239804\pi$
$503$	9850.36	+	18881.3i	0.873173	+	1.67371i	0.143783	+	0.989609i	$0.454073\pi$
$504$	−2053.65	+	8997.63i	−0.181502	+	0.795211i
$505$	5598.07	+	15211.8i	0.493288	+	1.34042i
$506$	1261.67	−	245.710i	0.110846	−	0.0215872i
$507$	3296.95	+	4134.24i	0.288802	+	0.362146i
$508$	−2262.29	−	1089.46i	−0.197585	−	0.0951518i
$509$	−11646.2	+	12823.8i	−1.01416	+	1.11671i	−0.0210226	+	0.999779i	$0.506692\pi$
$509$	−11646.2	+	12823.8i	−1.01416	+	1.11671i	−0.993140	+	0.116927i	$0.962696\pi$
$510$	11307.8	+	9626.48i	0.981801	+	0.835819i
$511$	−11395.8	−	3783.66i	−0.986535	−	0.327552i
$512$	7374.42	−	4800.22i	0.636536	−	0.414339i
$513$	−1270.82	+	1081.87i	−0.109373	+	0.0931104i
$514$	1753.52	+	7682.66i	0.150475	+	0.659275i
$515$	3686.39	−	2399.57i	0.315421	−	0.205316i
$516$	−614.817	+	1014.20i	−0.0524531	+	0.0865269i
$517$	5820.45	+	1133.53i	0.495131	+	0.0964268i
$518$	−28596.8	−	7498.95i	−2.42562	−	0.636072i
$519$	−917.811	+	5676.99i	−0.0776251	+	0.480139i
$520$	−5503.76	+	14955.5i	−0.464146	+	1.26123i
$521$	16686.9	+	10862.0i	1.40320	+	0.913381i	0.999999	−	0.00173080i	$-0.000550930\pi$
$521$	16686.9	+	10862.0i	1.40320	+	0.913381i	0.403200	+	0.915112i	$0.367898\pi$
$522$	5492.43	−	2645.02i	0.460531	−	0.221780i
$523$	14463.0	−	18136.0i	1.20922	−	1.51632i	0.413675	−	0.910425i	$-0.364245\pi$
$523$	14463.0	−	18136.0i	1.20922	−	1.51632i	0.795547	−	0.605892i	$-0.207183\pi$
$524$	205.755	−	394.394i	0.0171535	−	0.0328801i
$525$	−1264.63	+	1812.95i	−0.105130	+	0.150711i
$526$	−5243.39	+	8649.51i	−0.434644	+	0.716990i
$527$	−29381.0	+	11895.0i	−2.42857	+	0.983218i
$528$	−1797.97	+	4061.65i	−0.148195	+	0.334774i
$529$	11074.5	+	3676.98i	0.910207	+	0.302209i
$530$	−6022.53	+	8633.75i	−0.493588	+	0.707596i
$531$	975.849	+	6035.97i	0.0797519	+	0.493293i
$532$	−270.359	+	152.264i	−0.0220330	+	0.0124088i
$533$	751.049	+	727.350i	0.0610348	+	0.0591089i
$534$	−2104.57	−	1185.27i	−0.170550	−	0.0960518i
$535$	18538.5	−	2390.27i	1.49811	−	0.193160i
$536$	2324.66	−	7832.54i	0.187332	−	0.631183i
$537$	2434.04	−	808.158i	0.195599	−	0.0649433i
$538$	−2353.41	+	24395.5i	−0.188592	+	1.95496i
$539$	1151.39	+	7121.76i	0.0920110	+	0.569120i
$540$	−1668.99	−	325.035i	−0.133003	−	0.0259024i
$541$	−5199.23	−	9965.96i	−0.413184	−	0.791996i	0.586657	−	0.809836i	$-0.300444\pi$
$541$	−5199.23	−	9965.96i	−0.413184	−	0.791996i	−0.999841	+	0.0178393i	$0.994321\pi$
$542$	7550.49	+	973.528i	0.598379	+	0.0771524i
$543$	−3166.48	−	2695.67i	−0.250252	−	0.213043i
$544$	2531.58	−	4852.56i	0.199523	−	0.382448i
$545$	−782.623	+	8112.71i	−0.0615117	+	0.637633i
$546$	12969.7	−	9679.51i	1.01658	−	0.758690i
$547$	4010.13	+	9058.96i	0.313457	+	0.708105i	0.999816	−	0.0191578i	$-0.00609849\pi$
$547$	4010.13	+	9058.96i	0.313457	+	0.708105i	−0.686360	+	0.727262i	$0.740792\pi$
$548$	220.911	+	744.323i	0.0172206	+	0.0580218i
$549$	−759.992	−	1089.51i	−0.0590814	−	0.0846976i
$550$	1046.55	−	1013.53i	0.0811366	−	0.0785765i
$551$	−1359.52	−	550.407i	−0.105113	−	0.0425556i
$552$	1226.62	−	915.449i	0.0945804	−	0.0705872i
$553$	10012.3	−	5638.84i	0.769924	−	0.433613i
$554$	21555.2	+	5652.43i	1.65305	+	0.433482i
$555$	−3273.73	+	14343.1i	−0.250382	+	1.09700i
$556$	270.962	+	202.224i	0.0206679	+	0.0154248i
$557$	14647.8	−	16128.9i	1.11427	−	1.22693i	0.142803	−	0.989751i	$-0.454389\pi$
$557$	14647.8	−	16128.9i	1.11427	−	1.22693i	0.971465	−	0.237182i	$-0.0762237\pi$
$558$	7820.21	−	9806.23i	0.593290	−	0.743962i
$559$	21750.3	−	7221.61i	1.64569	−	0.546407i
$560$	21589.3	+	8740.55i	1.62913	+	0.659563i
$561$	−745.964	−	7732.70i	−0.0561401	−	0.581951i
$562$	8051.10	+	8865.16i	0.604298	+	0.665399i
$563$	3813.52	−	244.836i	0.285472	−	0.0183279i	0.0793246	−	0.996849i	$-0.474724\pi$
$563$	3813.52	−	244.836i	0.285472	−	0.0183279i	0.206148	+	0.978521i	$0.433907\pi$
$564$	−954.429	+	250.281i	−0.0712566	+	0.0186857i
$565$	−410.708	−	4257.42i	−0.0305816	−	0.317011i
$566$	7347.41	+	16597.9i	0.545644	+	1.23262i
$567$	−366.858	−	355.282i	−0.0271721	−	0.0263147i
$568$	−2205.34	+	13640.8i	−0.162912	+	1.00767i
$569$	764.916	+	2078.52i	0.0563567	+	0.153139i	0.963518	−	0.267644i	$-0.0862451\pi$
$569$	764.916	+	2078.52i	0.0563567	+	0.153139i	−0.907161	+	0.420783i	$0.861755\pi$
$570$	732.909	+	1209.01i	0.0538565	+	0.0888418i
$571$	−4134.81	−	1991.22i	−0.303041	−	0.145937i	0.276183	−	0.961105i	$-0.410930\pi$
$571$	−4134.81	−	1991.22i	−0.303041	−	0.145937i	−0.579224	+	0.815168i	$0.696645\pi$
$572$	−1049.58	+	505.450i	−0.0767220	+	0.0369474i
$573$	3619.53	−	12195.4i	0.263889	−	0.889129i
$574$	976.190	−	945.387i	0.0709850	−	0.0687451i
$575$	−546.044	+	143.190i	−0.0396028	+	0.0103851i
$576$	−228.115	−	7113.47i	−0.0165014	−	0.514574i
$577$	−18506.5			−1.33524			−0.667622	−	0.744501i	$-0.732688\pi$
$577$	−18506.5			−1.33524			−0.667622	+	0.744501i	$0.732688\pi$
$578$	1004.41	+	31321.1i	0.0722799	+	2.25395i
$579$	3911.14	+	4306.60i	0.280728	+	0.309113i
$580$	−425.166	−	1432.52i	−0.0304380	−	0.102556i
$581$	23444.2	+	13203.5i	1.67406	+	0.942813i
$582$	3795.90	−	10314.7i	0.270353	−	0.734635i
$583$	5405.22	−	1052.67i	0.383982	−	0.0747804i
$584$	9404.35	+	603.779i	0.666361	+	0.0427818i
$585$	7732.26	+	9695.95i	0.546478	+	0.685262i
$586$	4589.60	+	2987.50i	0.323540	+	0.210602i
$587$	−15423.7	+	1988.67i	−1.08451	+	0.139832i	−0.649325	−	0.760511i	$-0.724948\pi$
$587$	−15423.7	+	1988.67i	−1.08451	+	0.139832i	−0.435181	+	0.900343i	$0.643316\pi$
$588$	−686.783	−	984.555i	−0.0481674	−	0.0690516i
$589$	−3011.51	+	193.345i	−0.210674	+	0.0135257i
$590$	13722.8			0.957555
$591$	3201.50	+	8427.54i	0.222829	+	0.586570i
$592$	26090.3			1.81132
$593$	−10644.2	+	683.380i	−0.737107	+	0.0473238i	−0.428094	−	0.903734i	$-0.640815\pi$
$593$	−10644.2	+	683.380i	−0.737107	+	0.0473238i	−0.309013	+	0.951058i	$0.599999\pi$
$594$	4659.47	+	6679.71i	0.321853	+	0.461400i
$595$	−40401.7	+	5209.23i	−2.78371	+	0.358920i
$596$	−2610.91	−	1699.51i	−0.179441	−	0.116803i
$597$	830.653	+	1041.61i	0.0569453	+	0.0714072i
$598$	4124.46	+	264.799i	0.282043	+	0.0181078i
$599$	−14383.7	+	2801.23i	−0.981139	+	0.191077i	−0.656141	−	0.754638i	$-0.727812\pi$
$599$	−14383.7	+	2801.23i	−0.981139	+	0.191077i	−0.324997	+	0.945715i	$0.605363\pi$
$600$	599.140	−	1628.06i	0.0407663	−	0.110775i
$601$	7176.75	+	4041.87i	0.487098	+	0.274328i	0.714707	−	0.699424i	$-0.246560\pi$
$601$	7176.75	+	4041.87i	0.487098	+	0.274328i	−0.227609	+	0.973753i	$0.573091\pi$
$602$	−8475.49	−	28556.7i	−0.573813	−	1.93337i
$603$	−4274.59	−	4706.80i	−0.288681	−	0.317870i
$604$	17.5385	+	546.916i	0.00118151	+	0.0368438i
$605$	11789.0			0.792218
$606$	414.066	+	12912.1i	0.0277562	+	0.865542i
$607$	−2019.82	+	529.658i	−0.135061	+	0.0354171i	−0.320566	−	0.947226i	$-0.603873\pi$
$607$	−2019.82	+	529.658i	−0.135061	+	0.0354171i	0.185505	+	0.982643i	$0.440608\pi$
$608$	374.310	−	362.499i	0.0249675	−	0.0241797i
$609$	3089.79	−	10410.5i	0.205590	−	0.692702i
$610$	−2686.12	+	1293.57i	−0.178292	+	0.0858607i
$611$	17178.4	+	8272.66i	1.13742	+	0.547751i
$612$	−1031.90	−	1702.23i	−0.0681570	−	0.112432i
$613$	7193.50	+	19547.1i	0.473968	+	1.28793i	0.919652	+	0.392735i	$0.128471\pi$
$613$	7193.50	+	19547.1i	0.473968	+	1.28793i	−0.445684	+	0.895191i	$0.647039\pi$
$614$	−1831.31	+	11327.3i	−0.120368	+	0.744517i
$615$	−485.790	−	470.461i	−0.0318519	−	0.0308469i
$616$	−4386.04	−	9908.14i	−0.286881	−	0.648069i
$617$	−859.107	−	8905.54i	−0.0560556	−	0.581075i	−0.980061	−	0.198696i	$-0.936329\pi$
$617$	−859.107	−	8905.54i	−0.0560556	−	0.581075i	0.924006	−	0.382379i	$-0.124895\pi$
$618$	3391.02	−	889.231i	0.220723	−	0.0578805i
$619$	8912.25	−	572.185i	0.578697	−	0.0371536i	0.228031	−	0.973654i	$-0.426771\pi$
$619$	8912.25	−	572.185i	0.578697	−	0.0371536i	0.350667	+	0.936500i	$0.385955\pi$
$620$	−2066.96	−	2275.95i	−0.133889	−	0.147426i
$621$	−303.020	−	3141.12i	−0.0195809	−	0.202977i
$622$	−16834.8	−	6815.66i	−1.08523	−	0.439362i
$623$	6288.08	−	2087.79i	0.404377	−	0.134262i
$624$	−8904.75	+	11166.2i	−0.571275	+	0.716356i
$625$	12200.3	−	13433.8i	0.780817	−	0.859766i
$626$	−23374.5	−	17444.8i	−1.49238	−	1.11379i
$627$	164.575	−	721.052i	0.0104825	−	0.0459267i
$628$	3173.53	+	832.198i	0.201652	+	0.0528795i
$629$	−39759.2	+	22392.0i	−2.52035	+	1.41944i
$630$	12918.1	−	9641.06i	0.816939	−	0.609697i
$631$	−15644.8	−	6333.88i	−0.987020	−	0.399600i	−0.175854	−	0.984416i	$-0.556269\pi$
$631$	−15644.8	−	6333.88i	−0.987020	−	0.399600i	−0.811166	+	0.584816i	$0.801167\pi$
$632$	−6478.34	+	6273.93i	−0.407745	+	0.394879i
$633$	10531.6	+	15097.9i	0.661287	+	0.948005i
$634$	−2463.32	−	8299.76i	−0.154308	−	0.519914i
$635$	−12703.7	−	28697.8i	−0.793905	−	1.79345i
$636$	−734.342	+	548.054i	−0.0457839	+	0.0341694i
$637$	−2227.40	+	23089.3i	−0.138544	+	1.43616i
$638$	−3310.53	+	6345.66i	−0.205431	+	0.393773i
$639$	8188.02	+	6970.57i	0.506907	+	0.431536i
$640$	−20136.5	−	2596.31i	−1.24370	−	0.160357i
$641$	9887.88	+	18953.2i	0.609279	+	1.16787i	0.971780	+	0.235890i	$0.0758006\pi$
$641$	9887.88	+	18953.2i	0.609279	+	1.16787i	−0.362501	+	0.931983i	$0.618077\pi$
$642$	14622.8	+	2847.80i	0.898936	+	0.175068i
$643$	2989.61	+	18491.8i	0.183358	+	1.13413i	0.899741	+	0.436424i	$0.143755\pi$
$643$	2989.61	+	18491.8i	0.183358	+	1.13413i	−0.716383	+	0.697707i	$0.754204\pi$
$644$	56.3364	−	583.986i	0.00344715	−	0.0357333i
$645$	−14068.4	+	4671.04i	−0.858828	+	0.285151i
$646$	−1247.68	+	4203.86i	−0.0759899	+	0.256035i
$647$	6469.38	−	834.134i	0.393103	−	0.0506850i	0.0712105	−	0.997461i	$-0.477314\pi$
$647$	6469.38	−	834.134i	0.393103	−	0.0506850i	0.321892	+	0.946776i	$0.395681\pi$
$648$	349.228	+	196.681i	0.0211712	+	0.0119234i
$649$	−5156.80	−	4994.08i	−0.311898	−	0.302057i
$650$	4081.64	−	2298.74i	0.246300	−	0.138714i
$651$	−3565.91	−	22056.4i	−0.214684	−	1.32789i
$652$	−459.999	+	659.443i	−0.0276303	+	0.0396101i
$653$	−23779.3	−	7895.27i	−1.42505	−	0.473148i	−0.504375	−	0.863485i	$-0.668277\pi$
$653$	−23779.3	−	7895.27i	−1.42505	−	0.473148i	−0.920672	+	0.390336i	$0.872359\pi$
$654$	−2629.42	+	5939.91i	−0.157215	+	0.355151i
$655$	5153.60	−	2086.46i	0.307432	−	0.124465i
$656$	−621.696	+	1025.55i	−0.0370018	+	0.0610383i
$657$	4195.68	−	6014.83i	0.249146	−	0.357170i
$658$	11462.7	−	21971.8i	0.679121	−	1.30175i
$659$	18534.0	−	23240.9i	1.09557	−	1.37380i	0.174389	−	0.984677i	$-0.444205\pi$
$659$	18534.0	−	23240.9i	1.09557	−	1.37380i	0.921184	−	0.389128i	$-0.127223\pi$
$660$	678.882	−	326.932i	0.0400386	−	0.0192815i
$661$	−8751.85	−	5696.82i	−0.514989	−	0.335220i	0.261654	−	0.965162i	$-0.415732\pi$
$661$	−8751.85	−	5696.82i	−0.514989	−	0.335220i	−0.776643	+	0.629941i	$0.783079\pi$
$662$	−7867.53	+	21378.6i	−0.461904	+	1.25514i
$663$	3986.64	−	24658.8i	0.233527	−	1.44445i
$664$	−20426.2	−	5356.37i	−1.19381	−	0.313054i
$665$	−3806.70	−	741.354i	−0.221981	−	0.0432308i
$666$	9360.15	−	15440.5i	0.544592	−	0.898362i
$667$	2324.25	−	1512.92i	0.134925	−	0.0878267i
$668$	121.357	+	531.701i	0.00702912	+	0.0307966i
$669$	7196.65	−	6126.60i	0.415902	−	0.354063i
$670$	−11959.5	+	7784.75i	−0.689604	+	0.448882i
$671$	1480.17	+	491.449i	0.0851583	+	0.0282745i
$672$	2937.62	+	2500.83i	0.168632	+	0.143559i
$673$	−14131.8	+	15560.7i	−0.809422	+	0.891263i	−0.995832	−	0.0912087i	$-0.970927\pi$
$673$	−14131.8	+	15560.7i	−0.809422	+	0.891263i	0.186410	+	0.982472i	$0.440315\pi$
$674$	−15833.4	−	7624.97i	−0.904867	−	0.435761i
$675$	−2230.09	−	2796.44i	−0.127165	−	0.159459i
$676$	−1561.46	+	304.094i	−0.0888403	+	0.0173016i
$677$	−1246.60	−	3387.40i	−0.0707689	−	0.192302i	0.898145	−	0.439699i	$-0.144915\pi$
$677$	−1246.60	−	3387.40i	−0.0707689	−	0.192302i	−0.968914	+	0.247397i	$0.920425\pi$
$678$	758.559	−	3323.46i	0.0429680	−	0.188255i
$679$	13945.2	+	26730.3i	0.788171	+	1.51078i
$680$	29634.0	−	11997.5i	1.67120	−	0.676592i
$681$	−8621.94	+	7339.97i	−0.485159	+	0.413022i
$682$	−471.990	+	14718.4i	−0.0265006	+	0.826387i
$683$	65.9196	−	2055.62i	0.00369304	−	0.115162i	−0.995980	−	0.0895796i	$-0.971448\pi$
$683$	65.9196	−	2055.62i	0.00369304	−	0.115162i	0.999673	−	0.0255829i	$-0.00814418\pi$
$684$	−42.1698	−	184.758i	−0.00235731	−	0.0103281i
$685$	−3928.11	+	8873.67i	−0.219103	+	0.494957i
$686$	2578.44	+	332.453i	0.143506	+	0.0185031i
$687$	7923.52	+	5913.48i	0.440031	+	0.328403i
$688$	13627.6	+	22480.2i	0.755157	+	1.24571i
$689$	17670.0	+	1134.45i	0.977028	+	0.0627273i
$690$	−2667.76	−	171.276i	−0.147188	−	0.00944981i
$691$	1558.25	+	2570.49i	0.0857864	+	0.141514i	0.895104	−	0.445858i	$-0.147101\pi$
$691$	1558.25	+	2570.49i	0.0857864	+	0.141514i	−0.809317	+	0.587372i	$0.800163\pi$
$692$	−1386.46	−	1034.74i	−0.0761639	−	0.0568426i
$693$	−8363.08	−	1078.30i	−0.458423	−	0.0591071i
$694$	3614.28	−	8164.72i	0.197689	−	0.446583i
$695$	940.350	+	4119.94i	0.0513230	+	0.224861i
$696$	−273.164	+	8518.25i	−0.0148768	+	0.463913i
$697$	67.2281	−	2096.42i	0.00365344	−	0.113928i
$698$	19567.2	−	16657.8i	1.06107	−	0.903305i
$699$	1743.89	−	706.023i	0.0943633	−	0.0382035i
$700$	−307.580	−	589.574i	−0.0166078	−	0.0318340i
$701$	−685.895	+	3005.10i	−0.0369557	+	0.161913i	−0.990039	−	0.140796i	$-0.955034\pi$
$701$	−685.895	+	3005.10i	−0.0369557	+	0.161913i	0.953083	+	0.302709i	$0.0978911\pi$
$702$	9044.05	+	24575.6i	0.486247	+	1.32129i
$703$	−4264.11	+	830.436i	−0.228768	+	0.0445526i
$704$	5209.89	+	6532.99i	0.278913	+	0.349746i
$705$	−11111.2	−	5350.88i	−0.593578	−	0.285852i
$706$	−828.671	+	912.459i	−0.0441749	+	0.0486414i
$707$	−26983.6	−	22971.5i	−1.43539	−	1.22197i
$708$	1133.66	+	376.399i	0.0601771	+	0.0199802i
$709$	−15662.2	+	10195.0i	−0.829630	+	0.540029i	−0.888841	−	0.458216i	$-0.848488\pi$
$709$	−15662.2	+	10195.0i	−0.829630	+	0.540029i	0.0592110	+	0.998245i	$0.481142\pi$
$710$	18376.8	−	15644.4i	0.971367	−	0.826937i
$711$	1561.69	+	6842.22i	0.0823742	+	0.360905i
$712$	−4357.99	+	2836.73i	−0.229385	+	0.149313i
$713$	2957.91	−	4879.39i	0.155364	−	0.256290i
$714$	−31868.2	−	6206.33i	−1.67036	−	0.325302i
$715$	−14084.2	−	3693.30i	−0.736668	−	0.193177i
$716$	−123.140	+	761.666i	−0.00642733	+	0.0397553i
$717$	7159.52	−	19454.7i	0.372911	−	1.01332i
$718$	23625.8	+	15378.7i	1.22800	+	0.799343i
$719$	−18514.2	+	8915.95i	−0.960308	+	0.462460i	−0.847289	−	0.531133i	$-0.821766\pi$
$719$	−18514.2	+	8915.95i	−0.960308	+	0.462460i	−0.113019	+	0.993593i	$0.536052\pi$
$720$	−8869.39	+	11121.9i	−0.459087	+	0.575677i
$721$	−4447.95	+	8525.89i	−0.229751	+	0.440390i
$722$	11521.1	−	16516.3i	0.593864	−	0.851349i
$723$	9523.50	−	15710.0i	0.489879	−	0.808107i
$724$	1159.60	−	469.472i	0.0595254	−	0.0240991i
$725$	1272.37	−	2874.30i	0.0651786	−	0.147240i
$726$	8917.23	+	2960.73i	0.455853	+	0.151354i
$727$	11530.1	−	16529.2i	0.588208	−	0.843240i	−0.409401	−	0.912355i	$-0.634262\pi$
$727$	11530.1	−	16529.2i	0.588208	−	0.843240i	0.997609	+	0.0691146i	$0.0220174\pi$
$728$	−5560.51	−	34393.7i	−0.283086	−	1.75098i
$729$	11117.9	−	6261.48i	0.564847	−	0.318116i
$730$	−11823.5	−	11450.4i	−0.599461	−	0.580546i
$731$	−40060.9	−	22561.9i	−2.02696	−	1.14156i
$732$	−257.385	+	33.1861i	−0.0129962	+	0.00167568i
$733$	2145.07	−	7227.44i	0.108090	−	0.364190i	−0.887170	−	0.461443i	$-0.847332\pi$
$733$	2145.07	−	7227.44i	0.108090	−	0.364190i	0.995260	+	0.0972524i	$0.0310054\pi$
$734$	−13784.5	+	4576.78i	−0.693184	+	0.230153i
$735$	1440.71	−	14934.5i	0.0723014	−	0.749479i
$736$	157.245	+	972.617i	0.00787518	+	0.0487108i
$737$	7327.26	+	1426.98i	0.366218	+	0.0713210i
$738$	383.895	+	735.855i	0.0191482	+	0.0367035i
$739$	24319.9	+	3135.71i	1.21059	+	0.156088i	0.706593	−	0.707620i	$-0.250231\pi$
$739$	24319.9	+	3135.71i	1.21059	+	0.156088i	0.503993	+	0.863708i	$0.331864\pi$
$740$	−3370.09	−	2869.00i	−0.167415	−	0.142522i
$741$	1099.95	−	2108.40i	0.0545314	−	0.104526i
$742$	2209.89	−	22907.8i	0.109336	−	1.13339i
$743$	2771.67	−	2068.55i	0.136854	−	0.102137i	−0.527499	−	0.849556i	$-0.676870\pi$
$743$	2771.67	−	2068.55i	0.136854	−	0.102137i	0.664354	+	0.747418i	$0.268707\pi$
$744$	7097.91	+	16034.3i	0.349761	+	0.790115i
$745$	−11078.8	−	37328.2i	−0.544827	−	1.83570i
$746$	−12798.7	−	18347.9i	−0.628140	−	0.900487i
$747$	−11804.8	+	11432.4i	−0.578202	+	0.559957i
$748$	2166.28	+	877.029i	0.105892	+	0.0428708i
$749$	−32750.1	+	24442.0i	−1.59768	+	1.19238i
$750$	10406.4	−	5860.76i	0.506649	−	0.285339i
$751$	−3207.79	−	841.181i	−0.155864	−	0.0408724i	0.174898	−	0.984587i	$-0.444040\pi$
$751$	−3207.79	−	841.181i	−0.155864	−	0.0408724i	−0.330762	+	0.943714i	$0.607306\pi$
$752$	−4866.65	+	21322.2i	−0.235995	+	1.03396i
$753$	−9758.08	−	7282.65i	−0.472250	−	0.352449i
$754$	−15472.0	+	17036.3i	−0.747288	+	0.822848i
$755$	−4264.23	+	5347.17i	−0.205551	+	0.257753i
$756$	3528.01	−	1171.38i	0.169725	−	0.0563527i
$757$	−6466.51	−	2618.00i	−0.310475	−	0.125697i	0.214729	−	0.976674i	$-0.431113\pi$
$757$	−6466.51	−	2618.00i	−0.310475	−	0.125697i	−0.525204	+	0.850976i	$0.676011\pi$
$758$	−111.777	−	1158.69i	−0.00535611	−	0.0555217i
$759$	940.172	+	1035.23i	0.0449619	+	0.0495080i
$760$	3037.45	−	195.010i	0.144973	−	0.00930759i
$761$	−9041.77	+	2371.03i	−0.430701	+	0.112943i	−0.462639	−	0.886547i	$-0.653097\pi$
$761$	−9041.77	+	2371.03i	−0.430701	+	0.112943i	0.0319378	+	0.999490i	$0.489832\pi$
$762$	−2401.83	−	24897.5i	−0.114185	−	1.18365i
$763$	−7212.75	−	16293.7i	−0.342227	−	0.773097i
$764$	2749.13	+	2662.38i	0.130183	+	0.126075i
$765$	3970.81	−	24560.9i	0.187666	−	1.16078i
$766$	2847.71	+	7738.14i	0.134323	+	0.365000i
$767$	−11965.6	−	19738.5i	−0.563303	−	0.929228i
$768$	−4361.87	−	2100.56i	−0.204942	−	0.0986948i
$769$	−21762.4	+	10480.2i	−1.02051	+	0.491451i	−0.867849	−	0.496827i	$-0.834498\pi$
$769$	−21762.4	+	10480.2i	−1.02051	+	0.491451i	−0.152660	+	0.988279i	$0.548784\pi$
$770$	−5384.71	+	18142.9i	−0.252015	+	0.849122i
$771$	−6158.71	+	5964.38i	−0.287679	+	0.278601i
$772$	−1692.89	+	443.929i	−0.0789230	+	0.0206960i
$773$	83.6765	+	2609.34i	0.00389345	+	0.121412i	0.999588	+	0.0287136i	$0.00914108\pi$
$773$	83.6765	+	2609.34i	0.00389345	+	0.121412i	−0.995694	+	0.0926984i	$0.970451\pi$
$774$	18193.1			0.844880
$775$	−207.287	−	6463.98i	−0.00960772	−	0.299604i
$776$	−15907.8	−	17516.3i	−0.735899	−	0.810306i
$777$	−9151.60	−	30834.8i	−0.422538	−	1.42367i
$778$	−27098.9	−	15261.8i	−1.24877	−	0.703293i
$779$	68.9654	−	187.401i	0.00317194	−	0.00861919i
$780$	2378.12	−	463.138i	0.109167	−	0.0212603i
$781$	−12599.2	−	808.892i	−0.577251	−	0.0370607i
$782$	−5169.62	−	6482.50i	−0.236401	−	0.296437i
$783$	14726.7	+	9586.04i	0.672146	+	0.437519i
$784$	−26389.4	+	3402.53i	−1.20214	+	0.154999i
$785$	23460.4	+	33632.3i	1.06667	+	1.52916i
$786$	4422.19	−	283.914i	0.200680	−	0.0128841i
$787$	−4229.94			−0.191589			−0.0957947	−	0.995401i	$-0.530539\pi$
$787$	−4229.94			−0.191589			−0.0957947	+	0.995401i	$0.530539\pi$
$788$	−2693.29	−	318.770i	−0.121757	−	0.0144108i
$789$	−11004.4			−0.496538
$790$	15718.9	−	1009.19i	0.707917	−	0.0454498i
$791$	5349.87	+	7669.45i	0.240480	+	0.344746i
$792$	6563.51	−	846.270i	0.294475	−	0.0379683i
$793$	4202.82	+	2735.73i	0.188205	+	0.122508i
$794$	7775.15	+	9749.72i	0.347518	+	0.435774i
$795$	−11429.2	−	733.779i	−0.509877	−	0.0327352i
$796$	−393.403	+	76.6152i	−0.0175173	+	0.00341150i
$797$	7695.61	−	20911.5i	0.342023	−	0.929388i	−0.644330	−	0.764747i	$-0.722864\pi$
$797$	7695.61	−	20911.5i	0.342023	−	0.929388i	0.986354	−	0.164641i	$-0.0526465\pi$
$798$	−2693.21	−	1516.78i	−0.119472	−	0.0672852i
$799$	−10883.4	−	36669.8i	−0.481887	−	1.62364i
$800$	750.767	+	826.678i	0.0331795	+	0.0365344i
$801$	129.701	+	4044.54i	0.00572128	+	0.178411i
$802$	24604.3			1.08330
$803$	275.970	+	8605.76i	0.0121280	+	0.378195i
$804$	−1201.51	+	315.074i	−0.0527041	+	0.0138206i
$805$	5267.65	−	5101.44i	0.230634	−	0.223356i
$806$	−13472.2	+	45392.4i	−0.588759	+	1.98372i
$807$	−24024.1	+	11569.4i	−1.04794	+	0.504661i
$808$	25057.7	+	12067.1i	1.09100	+	0.525396i
$809$	18639.0	+	30746.9i	0.810026	+	1.33622i	0.938770	+	0.344545i	$0.111967\pi$
$809$	18639.0	+	30746.9i	0.810026	+	1.33622i	−0.128743	+	0.991678i	$0.541094\pi$
$810$	−241.768	−	656.961i	−0.0104875	−	0.0284978i
$811$	6844.65	−	42336.6i	0.296360	−	1.83309i	−0.218522	−	0.975832i	$-0.570124\pi$
$811$	6844.65	−	42336.6i	0.296360	−	1.83309i	0.514883	−	0.857261i	$-0.327836\pi$
$812$	2346.77	+	2272.72i	0.101423	+	0.0982227i
$813$	3352.69	+	7573.78i	0.144630	+	0.326721i
$814$	2035.61	+	21101.2i	0.0876511	+	0.908595i
$815$	−9720.71	+	2549.07i	−0.417794	+	0.109558i
$816$	28593.6	−	1835.77i	1.22669	−	0.0787558i
$817$	−2942.79	−	3240.33i	−0.126016	−	0.138758i
$818$	−3098.99	−	32124.3i	−0.132462	−	1.37311i
$819$	−25131.5	−	10174.6i	−1.07224	−	0.434103i
$820$	193.079	−	64.1067i	0.00822270	−	0.00273012i
$821$	22197.8	−	27835.1i	0.943614	−	1.18325i	−0.0393072	−	0.999227i	$-0.512515\pi$
$821$	22197.8	−	27835.1i	0.943614	−	1.18325i	0.982921	−	0.184027i	$-0.0589135\pi$
$822$	−5199.78	+	5725.54i	−0.220637	+	0.242945i
$823$	18650.4	+	13919.1i	0.789928	+	0.589539i	0.915394	−	0.402559i	$-0.131879\pi$
$823$	18650.4	+	13919.1i	0.789928	+	0.589539i	−0.125466	+	0.992098i	$0.540043\pi$
$824$	1679.40	−	7357.92i	0.0710007	−	0.311074i
$825$	1533.20	+	402.053i	0.0647021	+	0.0169669i
$826$	−26140.9	+	14722.3i	−1.10116	+	0.620161i
$827$	27017.5	−	20163.7i	1.13602	−	0.847835i	0.146075	−	0.989274i	$-0.453336\pi$
$827$	27017.5	−	20163.7i	1.13602	−	0.847835i	0.989947	+	0.141439i	$0.0451728\pi$
$828$	332.140	+	134.468i	0.0139404	+	0.00564384i
$829$	21266.7	−	20595.7i	0.890981	−	0.862867i	−0.100256	−	0.994962i	$-0.531966\pi$
$829$	21266.7	−	20595.7i	0.890981	−	0.862867i	0.991237	+	0.132095i	$0.0421703\pi$
$830$	21100.9	+	30249.7i	0.882437	+	1.26504i
$831$	6898.14	+	23242.1i	0.287959	+	0.970229i
$832$	10875.6	+	24568.2i	0.453178	+	1.02374i
$833$	37294.8	−	27833.8i	1.55124	−	1.15772i
$834$	−323.411	+	3352.49i	−0.0134278	+	0.139193i
$835$	−3152.90	+	6043.51i	−0.130671	+	0.250472i
$836$	169.420	+	144.229i	0.00700898	+	0.00596683i
$837$	35856.7	+	4623.21i	1.48075	+	0.190922i
$838$	−8352.49	−	16010.2i	−0.344310	−	0.659978i
$839$	33822.3	+	6586.90i	1.39175	+	0.271043i	0.830691	−	0.556734i	$-0.187946\pi$
$839$	33822.3	+	6586.90i	1.39175	+	0.271043i	0.561057	+	0.827777i	$0.310395\pi$
$840$	3596.62	+	22246.4i	0.147732	+	0.913777i
$841$	859.083	−	8905.30i	0.0352242	−	0.365136i
$842$	−34621.1	+	11495.0i	−1.41701	+	0.470480i
$843$	−3707.07	+	12490.4i	−0.151457	+	0.510309i
$844$	−5492.39	+	708.166i	−0.224000	+	0.0288816i
$845$	−17324.4	−	9756.91i	−0.705298	−	0.397217i
$846$	10872.8	+	10529.7i	0.441860	+	0.427917i
$847$	−22457.2	+	12647.7i	−0.911026	+	0.513080i
$848$	3241.52	+	20049.9i	0.131267	+	0.811932i
$849$	−11298.2	+	16196.9i	−0.456719	+	0.654742i
$850$	−8919.04	−	2961.33i	−0.359907	−	0.119497i
$851$	3324.94	−	7511.11i	0.133934	−	0.302559i
$852$	1947.24	−	788.351i	0.0782998	−	0.0317001i
$853$	−21843.9	+	36033.7i	−0.876811	+	1.44639i	0.0179470	+	0.999839i	$0.494287\pi$
$853$	−21843.9	+	36033.7i	−0.876811	+	1.44639i	−0.894758	+	0.446552i	$0.852652\pi$
$854$	3729.08	−	5345.92i	0.149422	−	0.214208i
$855$	1095.58	−	2100.03i	0.0438224	−	0.0839994i
$856$	19996.5	−	25074.9i	0.798443	−	1.00122i
$857$	−4272.54	+	2057.55i	−0.170300	+	0.0820122i	−0.517092	−	0.855930i	$-0.672985\pi$
$857$	−4272.54	+	2057.55i	−0.170300	+	0.0820122i	0.346792	+	0.937942i	$0.387271\pi$
$858$	−9725.73	−	6330.75i	−0.386982	−	0.251898i
$859$	−8007.43	+	21758.8i	−0.318056	+	0.864260i	0.674031	+	0.738703i	$0.264562\pi$
$859$	−8007.43	+	21758.8i	−0.318056	+	0.864260i	−0.992086	+	0.125557i	$0.959928\pi$
$860$	711.734	−	4402.33i	0.0282209	−	0.174556i
$861$	1430.12	+	375.022i	0.0566067	+	0.0148440i
$862$	20503.1	+	3992.99i	0.810139	+	0.157775i
$863$	−14768.7	+	24362.5i	−0.582540	+	0.960960i	0.416126	+	0.909307i	$0.363388\pi$
$863$	−14768.7	+	24362.5i	−0.582540	+	0.960960i	−0.998665	+	0.0516528i	$0.983551\pi$
$864$	−5231.89	+	3405.58i	−0.206010	+	0.134097i
$865$	−4811.60	−	21081.0i	−0.189132	−	0.828643i
$866$	−18992.5	+	16168.5i	−0.745255	+	0.634445i
$867$	−28573.6	+	18599.3i	−1.11927	+	0.728566i
$868$	6379.12	+	2118.01i	0.249448	+	0.0828226i
$869$	−6274.20	−	5341.30i	−0.244922	−	0.208505i
$870$	10007.5	−	11019.4i	0.389984	−	0.429415i
$871$	21625.5	+	10414.3i	0.841278	+	0.405138i
$872$	8719.22	+	10933.6i	0.338612	+	0.424607i
$873$	−18074.2	+	3519.96i	−0.700710	+	0.136463i
$874$	−272.621	−	740.800i	−0.0105510	−	0.0286704i
$875$	−7290.10	+	31940.0i	−0.281658	+	1.23402i
$876$	−662.682	−	1270.24i	−0.0255593	−	0.0489924i
$877$	−1170.22	+	473.770i	−0.0450576	+	0.0182418i	−0.397685	−	0.917522i	$-0.630186\pi$
$877$	−1170.22	+	473.770i	−0.0450576	+	0.0182418i	0.352627	+	0.935764i	$0.385288\pi$
$878$	28453.1	−	24222.4i	1.09367	−	0.931057i
$879$	−190.963	+	5954.94i	−0.00732768	+	0.228504i
$880$	535.313	−	16693.0i	0.0205062	−	0.639457i
$881$	−3428.86	−	15022.8i	−0.131125	−	0.574496i	−0.997213	−	0.0746048i	$-0.976230\pi$
$881$	−3428.86	−	15022.8i	−0.131125	−	0.574496i	0.866088	−	0.499891i	$-0.166627\pi$
$882$	−7453.79	+	16838.2i	−0.284560	+	0.642827i
$883$	22906.1	+	2953.41i	0.872991	+	0.112560i	0.551322	−	0.834293i	$-0.314124\pi$
$883$	22906.1	+	2953.41i	0.872991	+	0.112560i	0.321669	+	0.946852i	$0.395756\pi$
$884$	6022.30	+	4494.56i	0.229131	+	0.171005i
$885$	7739.54	+	12767.2i	0.293968	+	0.484931i
$886$	−17367.0	−	1115.00i	−0.658529	−	0.0422790i
$887$	−2001.81	−	128.520i	−0.0757769	−	0.00486504i	0.0261356	−	0.999658i	$-0.491680\pi$
$887$	−2001.81	−	128.520i	−0.0757769	−	0.00486504i	−0.101912	+	0.994793i	$0.532496\pi$
$888$	13085.8	+	21586.5i	0.494518	+	0.815759i
$889$	54987.6	+	41038.3i	2.07449	+	1.54823i
$890$	9007.49	+	1161.39i	0.339249	+	0.0437413i
$891$	−148.233	+	334.861i	−0.00557351	+	0.0125907i
$892$	632.693	+	2772.01i	0.0237490	+	0.104051i
$893$	116.719	−	3639.73i	0.00437386	−	0.136393i
$894$	994.670	−	31017.5i	0.0372111	−	1.16038i
$895$	−7343.00	+	6251.19i	−0.274245	+	0.233468i
$896$	41144.0	−	16657.3i	1.53407	−	0.621075i
$897$	2079.81	+	3986.60i	0.0774167	+	0.148393i
$898$	10172.9	−	44570.2i	0.378032	−	1.65627i
$899$	10973.0	+	29817.2i	0.407086	+	1.10618i
$900$	398.651	−	77.6374i	0.0147649	−	0.00287546i
$901$	−22147.6	−	27772.3i	−0.818918	−	1.02689i
$902$	−877.949	−	422.798i	−0.0324085	−	0.0156071i
$903$	21788.1	−	23991.1i	0.802948	−	0.884135i
$904$	−5588.15	−	4757.26i	−0.205596	−	0.175027i
$905$	14839.8	+	4927.16i	0.545074	+	0.180977i
$906$	−4568.37	+	2973.68i	−0.167521	+	0.109044i
$907$	−29003.4	+	24690.9i	−1.06179	+	0.903913i	−0.995582	−	0.0938928i	$-0.970069\pi$
$907$	−29003.4	+	24690.9i	−1.06179	+	0.903913i	−0.0662056	+	0.997806i	$0.521089\pi$
$908$	−757.998	−	3321.01i	−0.0277038	−	0.121378i
$909$	18139.1	−	11807.3i	0.661867	−	0.430828i
$910$	−31544.9	+	52036.6i	−1.14912	+	1.89560i
$911$	−17570.2	−	3421.79i	−0.638996	−	0.124444i	−0.138749	−	0.990328i	$-0.544308\pi$
$911$	−17570.2	−	3421.79i	−0.638996	−	0.124444i	−0.500246	+	0.865883i	$0.666757\pi$
$912$	2638.59	+	691.920i	0.0958032	+	0.0251225i
$913$	3079.30	−	19046.5i	0.111621	−	0.690414i
$914$	−13148.9	+	35729.8i	−0.475850	+	1.29304i
$915$	−2718.45	−	1769.51i	−0.0982175	−	0.0639325i
$916$	−2679.80	+	1290.52i	−0.0966627	+	0.0465503i
$917$	−7578.81	+	9503.52i	−0.272927	+	0.342240i
$918$	24299.7	−	46578.0i	0.873649	−	1.67462i
$919$	16010.5	−	22952.3i	0.574688	−	0.823858i	−0.421879	−	0.906652i	$-0.638629\pi$
$919$	16010.5	−	22952.3i	0.574688	−	0.823858i	0.996567	+	0.0827939i	$0.0263843\pi$
$920$	−2983.39	+	4921.41i	−0.106912	+	0.176363i
$921$	−11571.4	+	4684.74i	−0.413996	+	0.167608i
$922$	9224.28	−	20837.8i	0.329485	−	0.744313i
$923$	−38526.4	−	12791.6i	−1.37390	−	0.456167i
$924$	−942.476	+	1351.11i	−0.0335554	+	0.0481042i
$925$	−1485.91	−	9190.85i	−0.0528176	−	0.326695i
$926$	11093.3	−	6247.64i	0.393681	−	0.221717i
$927$	−4219.05	−	4085.92i	−0.149484	−	0.144767i
$928$	−4780.16	−	2692.14i	−0.169091	−	0.0952303i
$929$	−1282.25	+	165.327i	−0.0452843	+	0.00583877i	−0.150486	−	0.988612i	$-0.548084\pi$
$929$	−1282.25	+	165.327i	−0.0452843	+	0.00583877i	0.105202	+	0.994451i	$0.466451\pi$
$930$	8714.05	−	29360.5i	0.307253	−	1.03524i
$931$	4204.69	−	1396.05i	0.148016	−	0.0491448i
$932$	−54.3481	+	563.375i	−0.00191012	+	0.0198004i
$933$	−3153.66	−	19506.5i	−0.110661	−	0.684474i
$934$	−38357.2	−	7470.07i	−1.34378	−	0.261700i
$935$	13511.0	+	25898.1i	0.472575	+	0.905838i
$936$	21104.2	+	2721.08i	0.736978	+	0.0950227i
$937$	−2462.47	−	2096.34i	−0.0858544	−	0.0730889i	0.604270	−	0.796779i	$-0.293465\pi$
$937$	−2462.47	−	2096.34i	−0.0858544	−	0.0730889i	−0.690125	+	0.723691i	$0.742444\pi$
$938$	14430.2	−	27659.9i	0.502304	−	0.962823i
$939$	3047.02	−	31585.5i	0.105895	−	1.09772i
$940$	2973.31	−	2219.04i	0.103169	−	0.0769968i
$941$	−1240.36	−	2802.00i	−0.0429699	−	0.0970697i	0.891639	−	0.452748i	$-0.149556\pi$
$941$	−1240.36	−	2802.00i	−0.0429699	−	0.0970697i	−0.934609	+	0.355678i	$0.884250\pi$
$942$	9299.00	+	31331.4i	0.321633	+	1.08369i
$943$	216.017	+	309.676i	0.00745967	+	0.0106940i
$944$	19019.5	−	18419.4i	0.655754	−	0.635063i
$945$	43067.1	+	17435.9i	1.48251	+	0.600202i
$946$	−17118.2	+	12775.6i	−0.588330	+	0.439082i
$947$	−17971.6	+	10121.4i	−0.616681	+	0.347308i	−0.767305	−	0.641283i	$-0.778403\pi$
$947$	−17971.6	+	10121.4i	−0.616681	+	0.347308i	0.150623	+	0.988591i	$0.451872\pi$
$948$	1326.24	+	347.782i	0.0454371	+	0.0119150i
$949$	−6160.50	+	26990.9i	−0.210725	+	0.923247i
$950$	−717.026	−	535.130i	−0.0244878	−	0.0182757i
$951$	6332.51	−	6972.80i	0.215926	−	0.237759i
$952$	−43579.3	+	54646.7i	−1.48363	+	1.86041i
$953$	−30806.4	+	10228.4i	−1.04713	+	0.347672i	−0.786387	−	0.617735i	$-0.788051\pi$
$953$	−30806.4	+	10228.4i	−1.04713	+	0.347672i	−0.260747	+	0.965407i	$0.583969\pi$
$954$	13028.7	+	5274.75i	0.442160	+	0.179011i
$955$	4593.06	+	47611.9i	0.155631	+	1.61328i
$956$	4192.76	+	4616.69i	0.141845	+	0.156187i
$957$	−7770.90	+	498.908i	−0.262484	+	0.0168521i
$958$	30157.8	−	7908.32i	1.01707	−	0.266708i
$959$	−2037.22	−	21117.9i	−0.0685977	−	0.711087i
$960$	−7034.51	−	15891.1i	−0.236498	−	0.534253i
$961$	25558.5	+	24752.0i	0.857926	+	0.830855i
$962$	−10878.9	+	67289.6i	−0.364603	+	2.25520i
$963$	−8619.86	−	23422.9i	−0.288443	−	0.783794i
$964$	2865.02	+	4726.15i	0.0957220	+	0.157903i
$965$	−19708.2	−	9490.98i	−0.657441	−	0.316607i
$966$	5265.65	−	2535.80i	0.175382	−	0.0844597i
$967$	−8968.50	+	30217.9i	−0.298250	+	1.00490i	0.667323	+	0.744769i	$0.267440\pi$
$967$	−8968.50	+	30217.9i	−0.298250	+	1.00490i	−0.965573	+	0.260134i	$0.916233\pi$
$968$	14530.6	−	14072.1i	0.482471	−	0.467247i
$969$	−4614.81	+	1210.15i	−0.152992	+	0.0401192i
$970$	1324.60	+	41305.9i	0.0438457	+	1.36727i
$971$	−24667.0			−0.815245			−0.407622	−	0.913151i	$-0.633642\pi$
$971$	−24667.0			−0.815245			−0.407622	+	0.913151i	$0.633642\pi$
$972$	118.074	+	3681.97i	0.00389631	+	0.121501i
$973$	−6211.31	−	6839.35i	−0.204651	−	0.225344i
$974$	−6851.40	−	23084.6i	−0.225393	−	0.759425i
$975$	4440.68	+	2500.94i	0.145862	+	0.0821480i
$976$	−1986.63	+	5398.31i	−0.0651541	+	0.177045i
$977$	−10773.4	+	2098.12i	−0.352785	+	0.0687049i	−0.364439	−	0.931227i	$-0.618739\pi$
$977$	−10773.4	+	2098.12i	−0.352785	+	0.0687049i	0.0116541	+	0.999932i	$0.496290\pi$
$978$	−7992.94	−	513.164i	−0.261335	−	0.0167783i
$979$	−2962.21	−	3714.50i	−0.0967035	−	0.121262i
$980$	3782.88	+	2462.38i	0.123306	+	0.0802632i
$981$	10793.5	−	1391.67i	0.351286	−	0.0452933i
$982$	30181.8	+	43267.9i	0.980794	+	1.40604i
$983$	29634.2	−	1902.58i	0.961531	−	0.0617323i	0.424620	−	0.905372i	$-0.360408\pi$
$983$	29634.2	−	1902.58i	0.961531	−	0.0617323i	0.536910	+	0.843639i	$0.319591\pi$
$984$	−1160.34			−0.0375916
$985$	−23049.7	−	24855.0i	−0.745610	−	0.804006i
$986$	46169.0			1.49120
$987$	26906.7	−	1727.47i	0.867729	−	0.0557100i
$988$	409.300	+	586.762i	0.0131797	+	0.0188941i
$989$	8208.50	−	1058.37i	0.263918	−	0.0340285i
$990$	−9687.10	−	6305.60i	−0.310986	−	0.202430i
$991$	1192.69	+	1495.59i	0.0382312	+	0.0479405i	0.800580	−	0.599226i	$-0.204525\pi$
$991$	1192.69	+	1495.59i	0.0382312	+	0.0479405i	−0.762348	+	0.647167i	$0.775954\pi$
$992$	−11264.4	−	723.196i	−0.360528	−	0.0231467i
$993$	−24327.2	+	4737.72i	−0.777442	+	0.151407i
$994$	−18222.6	+	49516.8i	−0.581476	+	1.58006i
$995$	−4364.81	−	2458.22i	−0.139069	−	0.0783223i
$996$	913.457	+	3077.74i	0.0290602	+	0.0979136i
$997$	−4759.04	−	5240.23i	−0.151174	−	0.166459i	0.659997	−	0.751268i	$-0.270557\pi$
$997$	−4759.04	−	5240.23i	−0.151174	−	0.166459i	−0.811171	+	0.584809i	$0.801170\pi$
$998$	1345.08	+	41944.5i	0.0426631	+	1.33039i
$999$	52045.8			1.64830

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.g.a.37.13	yes	2058
197.16	even	49	inner	197.4.g.a.16.13	✓	2058

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.g.a.16.13	✓	2058	197.16	even	49	inner
197.4.g.a.37.13	yes	2058	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.g (of order \(49\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.99065 + 0.192006i) q^{2} +(-1.86534 - 2.67411i) q^{3} +(0.972802 - 0.125429i) q^{4} +(10.2745 + 6.68798i) q^{5} +(6.09203 + 7.63916i) q^{6} +(-26.7473 - 1.71723i) q^{7} +(20.6471 - 4.02103i) q^{8} +(5.65350 - 15.3624i) q^{9} +(-32.0116 - 18.0286i) q^{10} +(5.46837 + 18.4248i) q^{11} +(-2.15002 - 2.36741i) q^{12} +(1.98068 + 61.7650i) q^{13} +80.3215 q^{14} +(-1.28114 - 39.9505i) q^{15} +(-68.5665 + 17.9802i) q^{16} +(89.0575 - 86.2474i) q^{17} +(-13.9580 + 47.0291i) q^{18} +(10.6340 - 5.12106i) q^{19} +(10.8339 + 5.21735i) q^{20} +(45.3008 + 74.7284i) q^{21} +(-19.8917 - 54.0521i) q^{22} +(-3.56179 + 22.0309i) q^{23} +(-49.2666 - 47.7120i) q^{24} +(10.2389 + 23.1300i) q^{25} +(-17.7828 - 184.337i) q^{26} +(-136.779 + 35.8676i) q^{27} +(-26.2352 + 1.68436i) q^{28} +(-83.5450 - 91.9923i) q^{29} +(11.5022 + 119.232i) q^{30} +(-236.991 - 95.9469i) q^{31} +(41.8987 - 13.9113i) q^{32} +(39.0694 - 48.9915i) q^{33} +(-249.780 + 275.035i) q^{34} +(-263.331 - 196.529i) q^{35} +(3.57285 - 15.6537i) q^{36} +(-356.028 - 93.3617i) q^{37} +(-30.8193 + 17.3571i) q^{38} +(161.472 - 120.509i) q^{39} +(239.032 + 96.7733i) q^{40} +(12.1535 - 11.7700i) q^{41} +(-149.827 - 214.788i) q^{42} +(-105.520 - 355.530i) q^{43} +(7.63064 + 17.2378i) q^{44} +(160.830 - 120.031i) q^{45} +(6.42200 - 66.5707i) q^{46} +(142.710 - 273.548i) q^{47} +(175.981 + 149.815i) q^{48} +(372.285 + 48.0009i) q^{49} +(-35.0622 - 67.2077i) q^{50} +(-396.757 - 77.2685i) q^{51} +(9.67394 + 59.8367i) q^{52} +(27.5130 - 285.201i) q^{53} +(402.171 - 133.530i) q^{54} +(-67.0394 + 225.878i) q^{55} +(-559.160 + 72.0957i) q^{56} +(-33.5303 - 18.8839i) q^{57} +(267.517 + 259.076i) q^{58} +(-325.453 + 183.291i) q^{59} +(-6.25725 - 38.7033i) q^{60} +(46.4269 - 66.5564i) q^{61} +(727.179 + 241.440i) q^{62} +(-177.597 + 401.194i) q^{63} +(403.001 - 163.157i) q^{64} +(-392.732 + 647.853i) q^{65} +(-107.436 + 154.018i) q^{66} +(179.655 - 344.365i) q^{67} +(75.8174 - 95.0720i) q^{68} +(65.5571 - 31.5706i) q^{69} +(825.266 + 537.189i) q^{70} +(-226.871 + 616.482i) q^{71} +(54.9560 - 339.922i) q^{72} +(433.349 + 113.637i) q^{73} +(1082.68 + 210.852i) q^{74} +(42.7529 - 70.5253i) q^{75} +(9.70244 - 6.31559i) q^{76} +(-114.625 - 502.203i) q^{77} +(-459.767 + 391.405i) q^{78} +(-359.315 + 233.888i) q^{79} +(-824.739 - 273.832i) q^{80} +(14.5087 + 12.3514i) q^{81} +(-34.0870 + 37.5336i) q^{82} +(-904.472 - 435.571i) q^{83} +(53.4418 + 67.0139i) q^{84} +(1491.84 - 290.537i) q^{85} +(383.836 + 1043.01i) q^{86} +(-90.1574 + 395.006i) q^{87} +(186.993 + 358.430i) q^{88} +(-229.136 + 92.7670i) q^{89} +(-457.941 + 389.851i) q^{90} +(53.0870 - 1655.45i) q^{91} +(-0.701601 + 21.8785i) q^{92} +(185.496 + 812.713i) q^{93} +(-374.272 + 845.487i) q^{94} +(143.509 + 18.5034i) q^{95} +(-115.356 - 86.0923i) q^{96} +(-583.126 - 961.928i) q^{97} +(-1122.59 - 72.0728i) q^{98} +(313.964 + 20.1572i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2058 q - 42 q^{2} - 42 q^{3} - 84 q^{4} - 42 q^{5} - 119 q^{6} - 84 q^{7} - 98 q^{8} - 42 q^{9} + 168 q^{10} - 140 q^{11} + 14 q^{12} - 42 q^{13} - 812 q^{14} + 1638 q^{15} + 672 q^{16} - 42 q^{17} + 147 q^{18}+ \cdots + 6237 q^{99}+O(q^{100}) \) 2058 * q - 42 * q^2 - 42 * q^3 - 84 * q^4 - 42 * q^5 - 119 * q^6 - 84 * q^7 - 98 * q^8 - 42 * q^9 + 168 * q^10 - 140 * q^11 + 14 * q^12 - 42 * q^13 - 812 * q^14 + 1638 * q^15 + 672 * q^16 - 42 * q^17 + 147 * q^18 - 567 * q^19 - 35 * q^20 - 42 * q^21 + 1302 * q^22 - 42 * q^23 - 434 * q^24 - 42 * q^25 + 364 * q^26 - 1596 * q^27 - 147 * q^28 + 4676 * q^29 - 847 * q^30 + 882 * q^31 + 910 * q^32 - 287 * q^33 - 882 * q^34 - 42 * q^35 - 17787 * q^36 - 1400 * q^37 + 14 * q^38 + 168 * q^39 + 3962 * q^40 - 392 * q^41 + 1764 * q^42 + 294 * q^43 - 12978 * q^44 + 2814 * q^45 + 840 * q^46 + 28 * q^47 + 3654 * q^48 + 1554 * q^49 - 4998 * q^50 - 98 * q^51 - 3703 * q^52 - 42 * q^53 - 1365 * q^54 + 4046 * q^55 - 3073 * q^56 + 14567 * q^57 - 10402 * q^58 + 4004 * q^59 - 4536 * q^60 - 1050 * q^61 + 210 * q^62 + 2254 * q^63 + 3822 * q^64 - 1106 * q^65 - 875 * q^66 - 3612 * q^67 + 819 * q^68 + 4333 * q^69 - 5292 * q^70 + 11424 * q^71 - 1876 * q^72 - 714 * q^73 + 1288 * q^74 - 1316 * q^75 + 8715 * q^76 + 6629 * q^77 + 13986 * q^78 - 1512 * q^79 + 406 * q^80 + 1078 * q^81 - 42 * q^82 - 5999 * q^83 - 7595 * q^84 + 30492 * q^85 + 7749 * q^86 - 35 * q^87 + 8897 * q^88 - 196 * q^89 - 14910 * q^90 - 8232 * q^91 - 7938 * q^92 - 2639 * q^93 - 11116 * q^94 + 3703 * q^95 + 14497 * q^96 - 2674 * q^97 - 10024 * q^98 + 6237 * q^99

Introduction

L-functions

Modular forms

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