LMFDB - Embedded newform 207.4.m.a.4.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,4,Mod(4,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([22, 12]))

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

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

chi := DirichletCharacter("207.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	207.m (of order $33$, degree $20$, 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:	$12.2133953712$
Analytic rank:	$0$
Dimension:	$1400$
Relative dimension:	$70$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			4.19
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.69742 + 2.38370i) q^{2} +(3.62079 - 3.72691i) q^{3} +(-0.184220 - 0.532269i) q^{4} +(-15.8263 + 8.15904i) q^{5} +(2.73782 + 14.9570i) q^{6} +(16.2228 - 12.7578i) q^{7} +(-20.8807 - 6.13112i) q^{8} +(-0.779765 - 26.9887i) q^{9} +(7.41529 - 51.5745i) q^{10} +(56.8649 - 5.42994i) q^{11} +(-2.65074 - 1.24066i) q^{12} +(-60.9105 - 47.9006i) q^{13} +(2.87366 + 60.3256i) q^{14} +(-26.8958 + 88.5255i) q^{15} +(53.6000 - 42.1515i) q^{16} +(74.2870 + 85.7318i) q^{17} +(65.6565 + 43.9526i) q^{18} +(4.53566 - 5.23444i) q^{19} +(7.25834 + 6.92081i) q^{20} +(11.1923 - 106.654i) q^{21} +(-83.5804 + 144.765i) q^{22} +(102.651 - 40.3693i) q^{23} +(-98.4546 + 55.6210i) q^{24} +(111.396 - 156.433i) q^{25} +(217.571 - 63.8847i) q^{26} +(-103.408 - 94.8144i) q^{27} +(-9.77915 - 6.28468i) q^{28} +(-7.23513 + 20.9045i) q^{29} +(-165.364 - 214.377i) q^{30} +(131.852 - 125.721i) q^{31} +(1.21064 + 25.4145i) q^{32} +(185.659 - 231.591i) q^{33} +(-330.455 + 31.5546i) q^{34} +(-152.657 + 334.272i) q^{35} +(-14.2216 + 5.38691i) q^{36} +(309.042 - 198.609i) q^{37} +(4.77837 + 19.6967i) q^{38} +(-399.066 + 53.5704i) q^{39} +(380.488 - 73.3331i) q^{40} +(-39.4943 + 20.3607i) q^{41} +(235.233 + 207.717i) q^{42} +(263.902 + 251.630i) q^{43} +(-13.3658 - 29.2671i) q^{44} +(232.543 + 420.771i) q^{45} +(-78.0148 + 313.214i) q^{46} +(-71.2366 - 123.385i) q^{47} +(36.9793 - 352.384i) q^{48} +(19.5542 - 80.6034i) q^{49} +(183.804 + 531.067i) q^{50} +(588.493 + 33.5555i) q^{51} +(-14.2751 + 41.2451i) q^{52} +(-43.6213 - 303.393i) q^{53} +(401.536 - 85.5532i) q^{54} +(-855.659 + 549.899i) q^{55} +(-416.963 + 166.927i) q^{56} +(-3.08560 - 35.8568i) q^{57} +(-37.5490 - 52.7302i) q^{58} +(-86.7437 - 68.2160i) q^{59} +(52.0742 - 1.99239i) q^{60} +(-53.7861 - 221.709i) q^{61} +(75.8714 + 527.697i) q^{62} +(-356.966 - 427.886i) q^{63} +(396.277 + 254.672i) q^{64} +(1354.81 + 261.119i) q^{65} +(236.901 + 835.662i) q^{66} +(-258.935 - 24.7253i) q^{67} +(31.9472 - 55.3342i) q^{68} +(221.227 - 528.742i) q^{69} +(-537.679 - 931.287i) q^{70} +(-50.0821 - 109.664i) q^{71} +(-149.189 + 568.324i) q^{72} +(392.054 - 452.455i) q^{73} +(-51.1506 + 1073.78i) q^{74} +(-179.673 - 981.575i) q^{75} +(-3.62169 - 1.44991i) q^{76} +(853.236 - 813.559i) q^{77} +(549.687 - 1042.18i) q^{78} +(-42.7236 + 17.1040i) q^{79} +(-504.375 + 1104.43i) q^{80} +(-727.784 + 42.0897i) q^{81} +(18.5047 - 128.703i) q^{82} +(-389.922 - 201.019i) q^{83} +(-58.8307 + 13.6905i) q^{84} +(-1875.18 - 750.709i) q^{85} +(-1047.76 + 201.940i) q^{86} +(51.7125 + 102.656i) q^{87} +(-1220.67 - 235.265i) q^{88} +(-565.597 + 166.074i) q^{89} +(-1397.71 - 159.913i) q^{90} -1599.25 q^{91} +(-40.3978 - 47.2014i) q^{92} +(8.85850 - 946.611i) q^{93} +(415.032 + 39.6307i) q^{94} +(-29.0750 + 119.849i) q^{95} +(99.1013 + 87.5087i) q^{96} +(13.8833 - 291.446i) q^{97} +(158.942 + 183.429i) q^{98} +(-190.888 - 1530.48i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) $ 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.69742	+	2.38370i	−0.600129	+	0.842764i	−0.997181	−	0.0750325i	$-0.976094\pi$
$2$	−1.69742	+	2.38370i	−0.600129	+	0.842764i	0.397052	+	0.917796i	$0.370033\pi$
$3$	3.62079	−	3.72691i	0.696821	−	0.717245i
$3$	3.62079	−	3.72691i	0.696821	−	0.717245i
$4$	−0.184220	−	0.532269i	−0.0230275	−	0.0665337i
$5$	−15.8263	+	8.15904i	−1.41555	+	0.729767i	−0.984960	−	0.172781i	$-0.944725\pi$
$5$	−15.8263	+	8.15904i	−1.41555	+	0.729767i	−0.430590	+	0.902548i	$0.641694\pi$
$6$	2.73782	+	14.9570i	0.186285	+	1.01770i
$7$	16.2228	−	12.7578i	0.875951	−	0.688855i	−0.0753375	−	0.997158i	$-0.524003\pi$
$7$	16.2228	−	12.7578i	0.875951	−	0.688855i	0.951288	+	0.308303i	$0.0997610\pi$
$8$	−20.8807	−	6.13112i	−0.922804	−	0.270960i
$9$	−0.779765	−	26.9887i	−0.0288802	−	0.999583i
$10$	7.41529	−	51.5745i	0.234492	−	1.63093i
$11$	56.8649	−	5.42994i	1.55867	−	0.148835i	0.720196	−	0.693771i	$-0.244052\pi$
$11$	56.8649	−	5.42994i	1.55867	−	0.148835i	0.838478	+	0.544936i	$0.183446\pi$
$12$	−2.65074	−	1.24066i	−0.0637670	−	0.0298457i
$13$	−60.9105	−	47.9006i	−1.29950	−	1.02194i	−0.997645	−	0.0685881i	$-0.978151\pi$
$13$	−60.9105	−	47.9006i	−1.29950	−	1.02194i	−0.301858	−	0.953353i	$-0.597607\pi$
$14$	2.87366	+	60.3256i	0.0548585	+	1.15162i
$15$	−26.8958	+	88.5255i	−0.462964	+	1.52381i
$16$	53.6000	−	42.1515i	0.837499	−	0.658617i
$17$	74.2870	+	85.7318i	1.05984	+	1.22312i	0.973938	+	0.226815i	$0.0728312\pi$
$17$	74.2870	+	85.7318i	1.05984	+	1.22312i	0.0859003	+	0.996304i	$0.472623\pi$
$18$	65.6565	+	43.9526i	0.859744	+	0.575540i
$19$	4.53566	−	5.23444i	0.0547659	−	0.0632033i	−0.727706	−	0.685890i	$-0.759413\pi$
$19$	4.53566	−	5.23444i	0.0547659	−	0.0632033i	0.782472	+	0.622686i	$0.213959\pi$
$20$	7.25834	+	6.92081i	0.0811507	+	0.0773770i
$21$	11.1923	−	106.654i	0.116303	−	1.10828i
$22$	−83.5804	+	144.765i	−0.809973	+	1.40291i
$23$	102.651	−	40.3693i	0.930622	−	0.365981i
$23$	102.651	−	40.3693i	0.930622	−	0.365981i
$24$	−98.4546	+	55.6210i	−0.837374	+	0.473066i
$25$	111.396	−	156.433i	0.891166	−	1.25147i
$26$	217.571	−	63.8847i	1.64112	−	0.481878i
$27$	−103.408	−	94.8144i	−0.737070	−	0.675816i
$28$	−9.77915	−	6.28468i	−0.0660030	−	0.0424176i
$29$	−7.23513	+	20.9045i	−0.0463286	+	0.133858i	−0.965792	−	0.259318i	$-0.916502\pi$
$29$	−7.23513	+	20.9045i	−0.0463286	+	0.133858i	0.919463	+	0.393176i	$0.128624\pi$
$30$	−165.364	−	214.377i	−1.00638	−	1.30465i
$31$	131.852	−	125.721i	0.763915	−	0.728391i	−0.204192	−	0.978931i	$-0.565457\pi$
$31$	131.852	−	125.721i	0.763915	−	0.728391i	0.968106	+	0.250540i	$0.0806080\pi$
$32$	1.21064	+	25.4145i	0.00668792	+	0.140397i
$33$	185.659	−	231.591i	0.979365	−	1.22166i
$34$	−330.455	+	31.5546i	−1.66684	+	0.159164i
$35$	−152.657	+	334.272i	−0.737249	+	1.61435i
$36$	−14.2216	+	5.38691i	−0.0658409	+	0.0249394i
$37$	309.042	−	198.609i	1.37314	−	0.882462i	0.374147	−	0.927369i	$-0.377936\pi$
$37$	309.042	−	198.609i	1.37314	−	0.882462i	0.998991	+	0.0449071i	$0.0142992\pi$
$38$	4.77837	+	19.6967i	0.0203988	+	0.0840849i
$39$	−399.066	+	53.5704i	−1.63850	+	0.219952i
$40$	380.488	−	73.3331i	1.50401	−	0.289875i
$41$	−39.4943	+	20.3607i	−0.150439	+	0.0775565i	−0.531802	−	0.846869i	$-0.678485\pi$
$41$	−39.4943	+	20.3607i	−0.150439	+	0.0775565i	0.381363	+	0.924425i	$0.375455\pi$
$42$	235.233	+	207.717i	0.864221	+	0.763128i
$43$	263.902	+	251.630i	0.935923	+	0.892400i	0.994378	−	0.105890i	$-0.0337690\pi$
$43$	263.902	+	251.630i	0.935923	+	0.892400i	−0.0584553	+	0.998290i	$0.518618\pi$
$44$	−13.3658	−	29.2671i	−0.0457949	−	0.100277i
$45$	232.543	+	420.771i	0.770344	+	1.39388i
$46$	−78.0148	+	313.214i	−0.250058	+	1.00393i
$47$	−71.2366	−	123.385i	−0.221083	−	0.382928i	0.734054	−	0.679091i	$-0.237626\pi$
$47$	−71.2366	−	123.385i	−0.221083	−	0.382928i	−0.955137	+	0.296164i	$0.904293\pi$
$48$	36.9793	−	352.384i	0.111198	−	1.05963i
$49$	19.5542	−	80.6034i	0.0570092	−	0.234995i
$50$	183.804	+	531.067i	0.519876	+	1.50208i
$51$	588.493	+	33.5555i	1.61579	+	0.0921316i
$52$	−14.2751	+	41.2451i	−0.0380691	+	0.109993i
$53$	−43.6213	−	303.393i	−0.113054	−	0.786306i	−0.964920	−	0.262546i	$-0.915438\pi$
$53$	−43.6213	−	303.393i	−0.113054	−	0.786306i	0.851866	−	0.523760i	$-0.175471\pi$
$54$	401.536	−	85.5532i	1.01189	−	0.215598i
$55$	−855.659	+	549.899i	−2.09777	+	1.34815i
$56$	−416.963	+	166.927i	−0.994983	+	0.398331i
$57$	−3.08560	−	35.8568i	−0.00717014	−	0.0833220i
$58$	−37.5490	−	52.7302i	−0.0850073	−	0.119376i
$59$	−86.7437	−	68.2160i	−0.191408	−	0.150525i	0.517856	−	0.855468i	$-0.326730\pi$
$59$	−86.7437	−	68.2160i	−0.191408	−	0.150525i	−0.709264	+	0.704943i	$0.750973\pi$
$60$	52.0742	−	1.99239i	0.112046	−	0.00428695i
$61$	−53.7861	−	221.709i	−0.112895	−	0.465360i	−0.999993	−	0.00377838i	$-0.998797\pi$
$61$	−53.7861	−	221.709i	−0.112895	−	0.465360i	0.887098	−	0.461582i	$-0.152718\pi$
$62$	75.8714	+	527.697i	0.155414	+	1.08093i
$63$	−356.966	−	427.886i	−0.713866	−	0.855691i
$64$	396.277	+	254.672i	0.773978	+	0.497405i
$65$	1354.81	+	261.119i	2.58529	+	0.498274i
$66$	236.901	+	835.662i	0.441826	+	1.55853i
$67$	−258.935	−	24.7253i	−0.472149	−	0.0450848i	−0.143730	−	0.989617i	$-0.545910\pi$
$67$	−258.935	−	24.7253i	−0.472149	−	0.0450848i	−0.328419	+	0.944532i	$0.606516\pi$
$68$	31.9472	−	55.3342i	0.0569731	−	0.0986803i
$69$	221.227	−	528.742i	0.385979	−	0.922508i
$70$	−537.679	−	931.287i	−0.918070	−	1.59014i
$71$	−50.0821	−	109.664i	−0.0837134	−	0.183307i	0.863146	−	0.504954i	$-0.168491\pi$
$71$	−50.0821	−	109.664i	−0.0837134	−	0.183307i	−0.946859	+	0.321648i	$0.895763\pi$
$72$	−149.189	+	568.324i	−0.244196	+	0.930244i
$73$	392.054	−	452.455i	0.628582	−	0.725422i	−0.348731	−	0.937223i	$-0.613387\pi$
$73$	392.054	−	452.455i	0.628582	−	0.725422i	0.977313	+	0.211801i	$0.0679328\pi$
$74$	−51.1506	+	1073.78i	−0.0803533	+	1.68682i
$75$	−179.673	−	981.575i	−0.276625	−	1.51123i
$76$	−3.62169	−	1.44991i	−0.00546627	−	0.00218836i
$77$	853.236	−	813.559i	1.26280	−	1.20407i
$78$	549.687	−	1042.18i	0.797946	−	1.51287i
$79$	−42.7236	+	17.1040i	−0.0608454	+	0.0243588i	−0.401886	−	0.915690i	$-0.631645\pi$
$79$	−42.7236	+	17.1040i	−0.0608454	+	0.0243588i	0.341040	+	0.940049i	$0.389221\pi$
$80$	−504.375	+	1104.43i	−0.704886	+	1.54348i
$81$	−727.784	+	42.0897i	−0.998332	+	0.0577362i
$82$	18.5047	−	128.703i	0.0249208	−	0.173328i
$83$	−389.922	−	201.019i	−0.515657	−	0.265840i	0.180696	−	0.983539i	$-0.442165\pi$
$83$	−389.922	−	201.019i	−0.515657	−	0.265840i	−0.696353	+	0.717699i	$0.745195\pi$
$84$	−58.8307	+	13.6905i	−0.0764161	+	0.0177829i
$85$	−1875.18	−	750.709i	−2.39285	−	0.957951i
$86$	−1047.76	+	201.940i	−1.31376	+	0.253206i
$87$	51.7125	+	102.656i	0.0637260	+	0.126504i
$88$	−1220.67	−	235.265i	−1.47868	−	0.284992i
$89$	−565.597	+	166.074i	−0.673631	+	0.197796i	−0.600619	−	0.799535i	$-0.705079\pi$
$89$	−565.597	+	166.074i	−0.673631	+	0.197796i	−0.0730120	+	0.997331i	$0.523261\pi$
$90$	−1397.71	−	159.913i	−1.63702	−	0.187293i
$91$	−1599.25			−1.84227
$92$	−40.3978	−	47.2014i	−0.0457800	−	0.0534900i
$93$	8.85850	−	946.611i	0.00987724	−	1.05547i
$94$	415.032	+	39.6307i	0.455396	+	0.0434851i
$95$	−29.0750	+	119.849i	−0.0314003	+	0.129434i
$96$	99.1013	+	87.5087i	0.105359	+	0.0930346i
$97$	13.8833	−	291.446i	0.0145323	−	0.305071i	−0.979886	−	0.199559i	$-0.936049\pi$
$97$	13.8833	−	291.446i	0.0145323	−	0.305071i	0.994418	−	0.105512i	$-0.0336481\pi$
$98$	158.942	+	183.429i	0.163833	+	0.189073i
$99$	−190.888	−	1530.48i	−0.193788	−	1.55372i
$100$	−103.786	−	30.4743i	−0.103786	−	0.0304743i
$101$	−653.856	−	337.086i	−0.644169	−	0.332092i	0.104999	−	0.994472i	$-0.466516\pi$
$101$	−653.856	−	337.086i	−0.644169	−	0.332092i	−0.749168	+	0.662380i	$0.769546\pi$
$102$	−1078.91	+	1345.83i	−1.04733	+	1.30644i
$103$	−300.376	−	421.819i	−0.287348	−	0.403524i	0.645519	−	0.763744i	$-0.276641\pi$
$103$	−300.376	−	421.819i	−0.287348	−	0.403524i	−0.932867	+	0.360220i	$0.882702\pi$
$104$	978.169	+	1373.65i	0.922282	+	1.29516i
$105$	693.063	+	1779.27i	0.644153	+	1.65370i
$106$	797.240	+	411.006i	0.730517	+	0.376608i
$107$	−1746.70	−	512.878i	−1.57813	−	0.463381i	−0.628776	−	0.777586i	$-0.716444\pi$
$107$	−1746.70	−	512.878i	−1.57813	−	0.463381i	−0.949355	+	0.314205i	$0.898262\pi$
$108$	−31.4170	+	72.5077i	−0.0279916	+	0.0646023i
$109$	1238.69	+	1429.53i	1.08849	+	1.25618i	0.964552	+	0.263892i	$0.0850063\pi$
$109$	1238.69	+	1429.53i	1.08849	+	1.25618i	0.123936	+	0.992290i	$0.460448\pi$
$110$	141.623	−	2973.04i	0.122757	−	2.57699i
$111$	378.776	−	1870.89i	0.323890	−	1.59979i
$112$	331.784	−	1367.63i	0.279917	−	1.15383i
$113$	620.288	+	59.2303i	0.516388	+	0.0493090i	0.349997	−	0.936751i	$-0.386183\pi$
$113$	620.288	+	59.2303i	0.516388	+	0.0493090i	0.166391	+	0.986060i	$0.446789\pi$
$114$	90.7093	+	53.5090i	0.0745237	+	0.0439612i
$115$	−1295.22	+	1476.43i	−1.05026	+	1.19720i
$116$	12.4597			0.00997288
$117$	−1245.28	+	1681.25i	−0.983985	+	1.32848i
$118$	309.847	−	90.9792i	0.241726	−	0.0709773i
$119$	2298.89	+	443.075i	1.77092	+	0.341316i
$120$	1104.36	−	1683.57i	0.840117	−	1.28074i
$121$	1897.18	−	365.652i	1.42538	−	0.274720i
$122$	619.785	+	248.125i	0.459940	+	0.184132i
$123$	−67.1180	+	220.914i	−0.0492018	+	0.161944i
$124$	−91.2072	−	47.0206i	−0.0660536	−	0.0340530i
$125$	−169.887	+	1181.59i	−0.121561	+	0.845478i
$126$	1625.87	−	124.596i	1.14956	−	0.0880947i
$127$	−396.516	+	868.249i	−0.277048	+	0.606651i	−0.996093	−	0.0883132i	$-0.971852\pi$
$127$	−396.516	+	868.249i	−0.277048	+	0.606651i	0.719045	+	0.694964i	$0.244580\pi$
$128$	−1468.67	+	587.969i	−1.01417	+	0.406012i
$129$	1893.34	−	72.4404i	1.29224	−	0.0494420i
$130$	−2922.12	+	2786.23i	−1.97144	+	1.87976i
$131$	184.329	+	73.7940i	0.122938	+	0.0492169i	0.432316	−	0.901722i	$-0.357697\pi$
$131$	184.329	+	73.7940i	0.122938	+	0.0492169i	−0.309378	+	0.950939i	$0.600121\pi$
$132$	−157.471	−	56.1567i	−0.103834	−	0.0370289i
$133$	6.80156	−	142.782i	0.00443436	−	0.0930888i
$134$	498.461	−	575.254i	0.321346	−	0.370854i
$135$	2410.16	+	656.854i	1.53655	+	0.418763i
$136$	−1025.53	−	2245.60i	−0.646607	−	1.41587i
$137$	711.075	+	1231.62i	0.443440	+	0.768061i	0.997942	−	0.0641218i	$-0.0204246\pi$
$137$	711.075	+	1231.62i	0.443440	+	0.768061i	−0.554502	+	0.832182i	$0.687091\pi$
$138$	884.844	+	1424.83i	0.545819	+	0.878913i
$139$	228.242	−	395.327i	0.139275	−	0.241232i	−0.787947	−	0.615743i	$-0.788856\pi$
$139$	228.242	−	395.327i	0.139275	−	0.241232i	0.927222	+	0.374511i	$0.122189\pi$
$140$	206.045	+	19.6749i	0.124386	+	0.0118774i
$141$	−717.779	−	181.260i	−0.428709	−	0.108261i
$142$	346.417	+	66.7664i	0.204723	+	0.0394571i
$143$	−3723.77	−	2393.12i	−2.17760	−	1.39946i
$144$	−1179.41	−	1413.73i	−0.682529	−	0.818129i
$145$	−56.0554	−	389.874i	−0.0321045	−	0.223292i
$146$	413.033	+	1702.54i	0.234129	+	0.965093i
$147$	−229.600	−	364.725i	−0.128824	−	0.204639i
$148$	−162.645	−	127.906i	−0.0903334	−	0.0710390i
$149$	358.848	+	503.932i	0.197302	+	0.277072i	0.901360	−	0.433071i	$-0.142570\pi$
$149$	358.848	+	503.932i	0.197302	+	0.277072i	−0.704058	+	0.710142i	$0.748631\pi$
$150$	2644.76	+	1237.86i	1.43962	+	0.673806i
$151$	−582.499	+	233.197i	−0.313928	+	0.125678i	−0.523276	−	0.852164i	$-0.675290\pi$
$151$	−582.499	+	233.197i	−0.313928	+	0.125678i	0.209348	+	0.977841i	$0.432866\pi$
$152$	−126.801	+	81.4898i	−0.0676638	+	0.0434849i
$153$	2255.87	−	2071.76i	1.19200	−	1.09472i
$154$	490.975	+	3414.81i	0.256908	+	1.78684i
$155$	−1060.98	+	3065.49i	−0.549804	+	1.58855i
$156$	102.030	+	202.542i	0.0523649	+	0.103951i
$157$	−805.146	−	2326.32i	−0.409284	−	1.18255i	−0.941813	−	0.336138i	$-0.890879\pi$
$157$	−805.146	−	2326.32i	−0.409284	−	1.18255i	0.532528	−	0.846412i	$-0.321242\pi$
$158$	31.7494	−	130.873i	0.0159864	−	0.0658967i
$159$	−1288.66	−	935.948i	−0.642752	−	0.466827i
$160$	−226.518	−	392.341i	−0.111924	−	0.193858i
$161$	1150.28	−	1964.51i	0.563071	−	0.961646i
$162$	1135.03	−	1806.26i	0.550470	−	0.876007i
$163$	1076.02	+	2356.16i	0.517058	+	1.13220i	0.970541	+	0.240935i	$0.0774540\pi$
$163$	1076.02	+	2356.16i	0.517058	+	1.13220i	−0.453483	+	0.891265i	$0.649819\pi$
$164$	18.1131	+	17.2708i	0.00862434	+	0.00822329i
$165$	−1048.74	+	5180.04i	−0.494813	+	2.44403i
$166$	1141.03	−	588.242i	0.533501	−	0.275039i
$167$	2704.03	−	521.159i	1.25296	−	0.241488i	0.480750	−	0.876858i	$-0.340364\pi$
$167$	2704.03	−	521.159i	1.25296	−	0.241488i	0.772208	+	0.635370i	$0.219152\pi$
$168$	−887.614	+	2158.39i	−0.407624	+	0.991212i
$169$	897.666	+	3700.23i	0.408587	+	1.68422i
$170$	4972.43	−	3195.59i	2.24334	−	1.44171i
$171$	−144.808	−	118.330i	−0.0647585	−	0.0529178i
$172$	85.3188	−	186.822i	0.0378227	−	0.0828201i
$173$	−2154.09	+	205.691i	−0.946662	+	0.0903953i	−0.556954	−	0.830543i	$-0.688030\pi$
$173$	−2154.09	+	205.691i	−0.946662	+	0.0903953i	−0.389708	+	0.920939i	$0.627424\pi$
$174$	−332.478	−	50.9831i	−0.144857	−	0.0222127i
$175$	−188.588	−	3958.96i	−0.0814625	−	1.71011i
$176$	2819.08	−	2687.98i	1.20736	−	1.15122i
$177$	−568.316	+	76.2905i	−0.241340	+	0.0323974i
$178$	564.187	−	1630.11i	0.237571	−	0.686415i
$179$	−2246.71	−	1443.87i	−0.938139	−	0.602906i	−0.0202727	−	0.999794i	$-0.506453\pi$
$179$	−2246.71	−	1443.87i	−0.938139	−	0.602906i	−0.917867	+	0.396889i	$0.870090\pi$
$180$	181.124	−	201.290i	0.0750011	−	0.0833515i
$181$	−2569.17	+	754.376i	−1.05505	+	0.309792i	−0.762857	−	0.646567i	$-0.776204\pi$
$181$	−2569.17	+	754.376i	−1.05505	+	0.309792i	−0.292196	+	0.956358i	$0.594386\pi$
$182$	2714.60	−	3812.12i	1.10560	−	1.55260i
$183$	−1021.04	−	602.306i	−0.412445	−	0.243299i
$184$	−2390.94	+	213.569i	−0.957948	+	0.0855680i
$185$	−3270.54	+	5664.73i	−1.29975	+	2.25124i
$186$	2241.39	+	1627.91i	0.883586	+	0.641744i
$187$	4689.84	+	4471.75i	1.83398	+	1.74870i
$188$	−52.5510	+	60.6471i	−0.0203866	+	0.0235274i
$189$	−2887.19	−	218.902i	−1.11118	−	0.0842475i
$190$	−236.330	−	272.740i	−0.0902378	−	0.104140i
$191$	−1415.92	+	1113.49i	−0.536400	+	0.421830i	−0.849264	−	0.527968i	$-0.822954\pi$
$191$	−1415.92	+	1113.49i	−0.536400	+	0.421830i	0.312864	+	0.949798i	$0.398712\pi$
$192$	2383.97	−	554.777i	0.896086	−	0.208529i
$193$	92.4716	+	1941.22i	0.0344884	+	0.724000i	0.948207	+	0.317653i	$0.102895\pi$
$193$	92.4716	+	1941.22i	0.0344884	+	0.724000i	−0.913719	+	0.406347i	$0.866802\pi$
$194$	671.154	+	527.801i	0.248382	+	0.195329i
$195$	5878.66	−	4103.82i	2.15887	−	1.50708i
$196$	−46.5050	+	4.44069i	−0.0169479	+	0.00161833i
$197$	575.787	−	4004.69i	0.208239	−	1.44834i	−0.570660	−	0.821187i	$-0.693312\pi$
$197$	575.787	−	4004.69i	0.208239	−	1.44834i	0.778899	−	0.627149i	$-0.215778\pi$
$198$	3972.21	+	2142.85i	1.42572	+	0.769118i
$199$	1885.63	+	553.671i	0.671702	+	0.197230i	0.599761	−	0.800179i	$-0.295262\pi$
$199$	1885.63	+	553.671i	0.671702	+	0.197230i	0.0719413	+	0.997409i	$0.477081\pi$
$200$	−3285.13	+	2583.45i	−1.16147	+	0.913389i
$201$	−1029.70	+	875.505i	−0.361341	+	0.307231i
$202$	1913.38	−	986.416i	0.666460	−	0.343584i
$203$	149.321	+	431.435i	0.0516271	+	0.149167i
$204$	−90.5517	−	319.418i	−0.0310779	−	0.109626i
$205$	458.926	−	644.472i	0.156355	−	0.219570i
$206$	1515.35			0.512522
$207$	−1169.56	−	2738.95i	−0.392705	−	0.919664i
$208$	−5283.88			−1.76140
$209$	229.497	−	322.284i	0.0759553	−	0.106664i
$210$	−5417.65	−	1368.11i	−1.78025	−	0.449565i
$211$	187.766	+	542.513i	0.0612621	+	0.177005i	0.971478	−	0.237128i	$-0.0762060\pi$
$211$	187.766	+	542.513i	0.0612621	+	0.177005i	−0.910216	+	0.414133i	$0.864085\pi$
$212$	−153.451	+	79.1093i	−0.0497124	+	0.0256285i
$213$	−590.047	−	210.420i	−0.189809	−	0.0676891i
$214$	4187.44	−	3293.04i	1.33760	−	1.05190i
$215$	−6229.66	−	1829.19i	−1.97609	−	0.580232i
$216$	1577.91	+	2613.80i	0.497052	+	0.823362i
$217$	535.098	−	3721.69i	0.167396	−	1.16426i
$218$	−5510.14	+	526.155i	−1.71190	+	0.163466i
$219$	−266.714	−	3099.40i	−0.0822960	−	0.956337i
$220$	450.324	+	354.139i	0.138004	+	0.108527i
$221$	−418.260	−	8780.36i	−0.127309	−	2.67254i
$222$	3816.69	+	4078.58i	1.15387	+	1.23305i
$223$	2408.35	−	1893.94i	0.723205	−	0.568735i	−0.187265	−	0.982309i	$-0.559962\pi$
$223$	2408.35	−	1893.94i	0.723205	−	0.568735i	0.910470	+	0.413574i	$0.135720\pi$
$224$	343.873	+	396.851i	0.102571	+	0.118374i
$225$	−4308.80	−	2884.45i	−1.27668	−	0.854651i
$226$	−1194.08	+	1378.04i	−0.351455	+	0.405601i
$227$	3689.58	+	3518.00i	1.07879	+	1.02863i	0.999495	+	0.0317752i	$0.0101161\pi$
$227$	3689.58	+	3518.00i	1.07879	+	1.02863i	0.0792971	+	0.996851i	$0.474732\pi$
$228$	−18.5171	+	8.24792i	−0.00537860	+	0.00239575i
$229$	474.201	−	821.341i	0.136839	−	0.237012i	−0.789460	−	0.613803i	$-0.789639\pi$
$229$	474.201	−	821.341i	0.136839	−	0.237012i	0.926298	+	0.376791i	$0.122972\pi$
$230$	−1320.83	−	5593.55i	−0.378666	−	1.60360i
$231$	57.3247	−	6125.66i	0.0163277	−	1.74476i
$232$	279.243	−	392.141i	0.0790223	−	0.110971i
$233$	4744.44	−	1393.09i	1.33399	−	0.391693i	0.464465	−	0.885591i	$-0.346247\pi$
$233$	4744.44	−	1393.09i	1.33399	−	0.391693i	0.869520	+	0.493898i	$0.164428\pi$
$234$	−1893.82	−	5822.16i	−0.529073	−	1.62652i
$235$	2134.12	+	1371.52i	0.592403	+	0.380714i
$236$	−20.3293	+	58.7378i	−0.00560732	+	0.0162013i
$237$	−90.9483	+	221.157i	−0.0249271	+	0.0606148i
$238$	−4958.35	+	4727.78i	−1.35043	+	1.28763i
$239$	259.938	+	5456.76i	0.0703513	+	1.47686i	0.707827	+	0.706386i	$0.249676\pi$
$239$	259.938	+	5456.76i	0.0703513	+	1.47686i	−0.637476	+	0.770471i	$0.720021\pi$
$240$	2289.87	+	5878.66i	0.615877	+	1.58111i
$241$	1386.78	−	132.422i	0.370666	−	0.0353943i	0.0919390	−	0.995765i	$-0.470694\pi$
$241$	1386.78	−	132.422i	0.370666	−	0.0353943i	0.278727	+	0.960370i	$0.410087\pi$
$242$	−2348.72	+	5142.97i	−0.623889	+	1.36613i
$243$	−2478.29	+	2864.79i	−0.654248	+	0.756280i
$244$	−108.101	+	69.4720i	−0.0283624	+	0.0182274i
$245$	348.175	+	1435.20i	0.0907923	+	0.374251i
$246$	−412.664	−	534.973i	−0.106953	−	0.138653i
$247$	−527.002	+	101.571i	−0.135759	+	0.0261653i
$248$	−3523.97	+	1816.73i	−0.902308	+	0.465172i
$249$	−2161.01	+	725.360i	−0.549993	+	0.184610i
$250$	−2528.18	−	2410.62i	−0.639586	−	0.609844i
$251$	3092.66	+	6771.99i	0.777718	+	1.70296i	0.708873	+	0.705336i	$0.249204\pi$
$251$	3092.66	+	6771.99i	0.777718	+	1.70296i	0.0688448	+	0.997627i	$0.478069\pi$
$252$	−161.990	+	268.827i	−0.0404937	+	0.0672005i
$253$	5618.06	−	2852.98i	1.39606	−	0.708955i
$254$	−1396.59	−	2418.96i	−0.344998	−	0.597555i
$255$	−9587.46	+	4270.48i	−2.35447	+	1.04874i
$256$	202.979	−	836.691i	0.0495554	−	0.204270i
$257$	186.515	+	538.898i	0.0452703	+	0.130800i	0.965370	−	0.260884i	$-0.0840140\pi$
$257$	186.515	+	538.898i	0.0452703	+	0.130800i	−0.920100	+	0.391684i	$0.871893\pi$
$258$	−3041.12	+	4636.10i	−0.733843	+	1.11872i
$259$	2479.72	−	7164.68i	0.594913	−	1.71889i
$260$	−110.598	−	769.229i	−0.0263809	−	0.183483i
$261$	569.829	+	178.967i	0.135140	+	0.0424435i
$262$	−488.786	+	314.124i	−0.115257	+	0.0740711i
$263$	3639.54	−	1457.05i	0.853322	−	0.341619i	0.0965744	−	0.995326i	$-0.469211\pi$
$263$	3639.54	−	1457.05i	0.853322	−	0.341619i	0.756748	+	0.653707i	$0.226787\pi$
$264$	−5296.59	+	3697.48i	−1.23478	+	0.861986i
$265$	3165.76	+	4445.69i	0.733853	+	1.03055i
$266$	328.805	+	258.575i	0.0757906	+	0.0596024i
$267$	−1428.96	+	2709.25i	−0.327533	+	0.620987i
$268$	34.5406	+	142.378i	0.00787277	+	0.0324520i
$269$	394.517	+	2743.93i	0.0894206	+	0.621934i	0.984416	+	0.175858i	$0.0562699\pi$
$269$	394.517	+	2743.93i	0.0894206	+	0.621934i	−0.894995	+	0.446076i	$0.852821\pi$
$270$	−5656.81	+	4630.14i	−1.27505	+	1.04363i
$271$	5844.68	+	3756.15i	1.31011	+	0.841955i	0.994274	−	0.106859i	$-0.0340794\pi$
$271$	5844.68	+	3756.15i	1.31011	+	0.841955i	0.315834	+	0.948814i	$0.397716\pi$
$272$	7595.50	+	1463.91i	1.69318	+	0.326334i
$273$	−5790.54	+	5960.25i	−1.28373	+	1.32136i
$274$	−4142.80	−	395.589i	−0.913415	−	0.0872206i
$275$	5485.08	−	9500.44i	1.20277	−	2.08327i
$276$	−322.187	−	20.3472i	−0.0702659	−	0.00443754i
$277$	−1954.19	−	3384.76i	−0.423884	−	0.734189i	0.572431	−	0.819953i	$-0.306000\pi$
$277$	−1954.19	−	3384.76i	−0.423884	−	0.734189i	−0.996316	+	0.0857635i	$0.972667\pi$
$278$	554.916	+	1215.10i	0.119718	+	0.262146i
$279$	−3495.86	−	3460.49i	−0.750149	−	0.742560i
$280$	5237.03	−	6043.86i	1.11776	−	1.28996i
$281$	251.612	−	5281.98i	0.0534160	−	1.12134i	−0.799963	−	0.600049i	$-0.795148\pi$
$281$	251.612	−	5281.98i	0.0534160	−	1.12134i	0.853379	−	0.521291i	$-0.174549\pi$
$282$	1650.44	−	1403.29i	0.348519	−	0.296329i
$283$	−1543.27	−	617.833i	−0.324163	−	0.129775i	0.203873	−	0.978997i	$-0.434647\pi$
$283$	−1543.27	−	617.833i	−0.324163	−	0.129775i	−0.528036	+	0.849222i	$0.677071\pi$
$284$	−49.1449	+	46.8596i	−0.0102684	+	0.00979086i
$285$	341.391	+	542.306i	0.0709553	+	0.112714i
$286$	12025.3	−	4814.19i	2.48626	−	0.995347i
$287$	−380.952	+	834.169i	−0.0783516	+	0.171566i
$288$	684.962	−	52.4911i	0.140145	−	0.0107398i
$289$	−1132.19	+	7874.53i	−0.230447	+	1.60279i
$290$	1024.49	+	528.162i	0.207449	+	0.106947i
$291$	−1035.93	−	1107.01i	−0.208684	−	0.223003i
$292$	−313.052	−	125.327i	−0.0627397	−	0.0251172i
$293$	3627.39	−	699.122i	0.723257	−	0.139396i	0.185679	−	0.982610i	$-0.440552\pi$
$293$	3627.39	−	699.122i	0.723257	−	0.139396i	0.537578	+	0.843214i	$0.319339\pi$
$294$	1259.12	+	71.7943i	0.249774	+	0.0142419i
$295$	1929.41	+	371.864i	0.380796	+	0.0733923i
$296$	−7670.69	+	2252.32i	−1.50625	+	0.442275i
$297$	−6395.12	−	4830.11i	−1.24944	−	0.943675i
$298$	−1810.34			−0.351913
$299$	−8186.27	−	2458.15i	−1.58336	−	0.475447i
$300$	−489.362	+	276.460i	−0.0941779	+	0.0532048i
$301$	7491.48	+	715.349i	1.43456	+	0.136984i
$302$	432.875	−	1784.33i	0.0824806	−	0.339990i
$303$	−3623.77	+	1216.35i	−0.687062	+	0.230618i
$304$	22.4722	−	471.751i	0.00423971	−	0.0890025i
$305$	2660.17	+	3070.00i	0.499413	+	0.576353i
$306$	1109.30	+	8893.96i	0.207236	+	1.66155i
$307$	−1633.30	−	479.580i	−0.303640	−	0.0891567i	0.126364	−	0.991984i	$-0.459669\pi$
$307$	−1633.30	−	479.580i	−0.303640	−	0.0891567i	−0.430003	+	0.902827i	$0.641488\pi$
$308$	−590.215	−	304.277i	−0.109190	−	0.0562916i
$309$	−2659.68	−	407.842i	−0.489656	−	0.0750852i
$310$	−5506.27	−	7732.47i	−1.00882	−	1.41669i
$311$	950.408	+	1334.66i	0.173288	+	0.243350i	0.892082	−	0.451874i	$-0.149245\pi$
$311$	950.408	+	1334.66i	0.173288	+	0.243350i	−0.718793	+	0.695224i	$0.755305\pi$
$312$	8661.20	+	1328.13i	1.57162	+	0.240996i
$313$	−4098.49	−	2112.92i	−0.740128	−	0.381563i	0.0465581	−	0.998916i	$-0.485175\pi$
$313$	−4098.49	−	2112.92i	−0.740128	−	0.381563i	−0.786686	+	0.617353i	$0.788205\pi$
$314$	6911.91	+	2029.52i	1.24223	+	0.364753i
$315$	9140.61	+	3859.36i	1.63497	+	0.690318i
$316$	16.9745	+	19.5896i	0.00302180	+	0.00348734i
$317$	−326.795	+	6860.27i	−0.0579011	+	1.21549i	0.763754	+	0.645508i	$0.223354\pi$
$317$	−326.795	+	6860.27i	−0.0579011	+	1.21549i	−0.821655	+	0.569985i	$0.806949\pi$
$318$	4418.42	−	1483.08i	0.779159	−	0.261531i
$319$	−297.915	+	1228.02i	−0.0522885	+	0.215536i
$320$	−8349.48	−	797.279i	−1.45859	−	0.139279i
$321$	−8235.89	+	4652.78i	−1.43203	+	0.809013i
$322$	2730.29	+	6076.51i	0.472525	+	1.05165i
$323$	785.699			0.135348
$324$	156.476	+	379.623i	0.0268305	+	0.0650931i
$325$	−14278.4	+	4192.52i	−2.43700	+	0.715567i
$326$	−7442.83	−	1434.49i	−1.26448	−	0.243708i
$327$	9812.77	+	559.518i	1.65947	+	0.0946221i
$328$	949.502	−	183.002i	0.159840	−	0.0308066i
$329$	−2729.78	−	1092.84i	−0.457440	−	0.183131i
$330$	−10567.5	−	11292.6i	−1.76279	−	1.88375i
$331$	7543.04	+	3888.71i	1.25258	+	0.645748i	0.951440	−	0.307833i	$-0.0996037\pi$
$331$	7543.04	+	3888.71i	1.25258	+	0.645748i	0.301136	+	0.953581i	$0.402634\pi$
$332$	−35.1646	+	244.575i	−0.00581298	+	0.0404302i
$333$	−5601.18	−	8185.77i	−0.921751	−	1.34708i
$334$	−3347.59	+	7330.21i	−0.548420	+	1.20087i
$335$	4299.73	−	1721.35i	0.701252	−	0.280739i
$336$	−3895.73	−	6188.44i	−0.632528	−	1.00478i
$337$	−4434.10	+	4227.91i	−0.716738	+	0.683409i	−0.957908	−	0.287074i	$-0.907317\pi$
$337$	−4434.10	+	4227.91i	−0.716738	+	0.683409i	0.241170	+	0.970483i	$0.422469\pi$
$338$	−10343.9	−	4141.09i	−1.66460	−	0.666407i
$339$	2466.68	−	2097.30i	0.395197	−	0.336017i
$340$	−54.1332	+	1136.40i	−0.00863467	+	0.181264i
$341$	6815.10	−	7865.05i	1.08228	−	1.24902i
$342$	527.863	−	144.321i	0.0834607	−	0.0228186i
$343$	2229.61	+	4882.16i	0.350984	+	0.768548i
$344$	−3967.68	−	6872.22i	−0.621868	−	1.07711i
$345$	812.819	+	10173.0i	0.126843	+	1.58753i
$346$	3166.10	−	5483.84i	0.491938	−	0.852061i
$347$	−6127.90	−	585.143i	−0.948020	−	0.0905249i	−0.390422	−	0.920636i	$-0.627671\pi$
$347$	−6127.90	−	585.143i	−0.948020	−	0.0905249i	−0.557598	+	0.830111i	$0.688277\pi$
$348$	45.1140	−	46.4362i	0.00694932	−	0.00715300i
$349$	−6792.37	−	1309.12i	−1.04180	−	0.200790i	−0.360472	−	0.932770i	$-0.617384\pi$
$349$	−6792.37	−	1309.12i	−1.04180	−	0.200790i	−0.681326	+	0.731980i	$0.738596\pi$
$350$	9757.06	+	6270.48i	1.49010	+	0.957632i
$351$	1756.97	+	10728.5i	0.267180	+	1.63147i
$352$	206.842	+	1438.62i	0.0313203	+	0.217837i
$353$	−72.1752	−	297.510i	−0.0108824	−	0.0448580i	0.966111	−	0.258125i	$-0.0831047\pi$
$353$	−72.1752	−	297.510i	−0.0108824	−	0.0448580i	−0.976994	+	0.213267i	$0.931590\pi$
$354$	782.819	−	1484.19i	0.117532	−	0.222835i
$355$	1687.37	+	1326.96i	0.252272	+	0.198389i
$356$	192.591	+	270.456i	0.0286722	+	0.0402644i
$357$	9975.11	−	6963.49i	1.47882	−	1.03235i
$358$	7255.37	−	2904.61i	1.07111	−	0.428809i
$359$	−7068.94	+	4542.93i	−1.03923	+	0.667874i	−0.944797	−	0.327657i	$-0.893741\pi$
$359$	−7068.94	+	4542.93i	−1.03923	+	0.667874i	−0.0944353	+	0.995531i	$0.530105\pi$
$360$	−2275.86	−	10211.7i	−0.333190	−	1.49501i
$361$	969.310	+	6741.70i	0.141319	+	0.982899i
$362$	2562.76	−	7404.61i	0.372087	−	1.07508i
$363$	5506.55	−	8394.58i	0.796195	−	1.21378i
$364$	294.614	+	851.230i	0.0424229	+	0.122573i
$365$	−2513.18	+	10359.5i	−0.360400	+	1.48559i
$366$	3168.85	−	1411.48i	0.452564	−	0.201582i
$367$	−1770.34	−	3066.32i	−0.251801	−	0.436133i	0.712220	−	0.701956i	$-0.247690\pi$
$367$	−1770.34	−	3066.32i	−0.251801	−	0.436133i	−0.964022	+	0.265823i	$0.914356\pi$
$368$	3800.49	−	6490.70i	0.538354	−	0.919433i
$369$	580.307	+	1050.03i	0.0818688	+	0.148136i
$370$	−7951.52	−	17411.4i	−1.11724	−	2.44642i
$371$	−4578.28	−	4365.38i	−0.640680	−	0.610887i
$372$	−505.484	+	169.670i	−0.0704519	+	0.0236477i
$373$	1033.93	−	533.026i	0.143525	−	0.0739920i	−0.384968	−	0.922930i	$-0.625788\pi$
$373$	1033.93	−	533.026i	0.143525	−	0.0739920i	0.528493	+	0.848938i	$0.322757\pi$
$374$	−18619.9	+	3588.70i	−2.57437	+	0.496169i
$375$	3788.56	+	4911.45i	0.521708	+	0.676336i
$376$	730.977	+	3013.13i	0.100259	+	0.413272i
$377$	1442.04	−	926.740i	0.196999	−	0.126604i
$378$	5422.58	−	6510.62i	0.737850	−	0.885900i
$379$	2629.74	−	5758.34i	0.356414	−	0.780438i	−0.643474	−	0.765468i	$-0.722508\pi$
$379$	2629.74	−	5758.34i	0.356414	−	0.780438i	0.999888	−	0.0149698i	$-0.00476521\pi$
$380$	69.1479	−	6.60283i	0.00933477	−	0.000891363i
$381$	1800.19	+	4621.53i	0.242064	+	0.621438i
$382$	−250.812	−	5265.19i	−0.0335934	−	0.705211i
$383$	7946.18	−	7576.67i	1.06013	−	1.01083i	0.0602125	−	0.998186i	$-0.480822\pi$
$383$	7946.18	−	7576.67i	1.06013	−	1.01083i	0.999920	−	0.0126488i	$-0.00402633\pi$
$384$	−3126.45	+	7602.53i	−0.415485	+	1.01033i
$385$	−6865.73	+	19837.2i	−0.908858	+	2.62597i
$386$	−4784.24	−	3074.64i	−0.630858	−	0.405428i
$387$	6585.39	−	7318.59i	0.864998	−	0.961305i
$388$	−157.686	+	46.3007i	−0.0206321	+	0.00605814i
$389$	−4404.57	+	6185.35i	−0.574089	+	0.806195i	−0.994891	−	0.100958i	$-0.967809\pi$
$389$	−4404.57	+	6185.35i	−0.574089	+	0.806195i	0.420802	+	0.907153i	$0.361749\pi$
$390$	−196.323	+	20978.8i	−0.0254902	+	2.72386i
$391$	11086.6	+	5801.58i	1.43395	+	0.750380i
$392$	−902.493	+	1563.16i	−0.116283	+	0.201407i
$393$	942.439	−	419.784i	0.120966	−	0.0538812i
$394$	8568.60	+	8170.15i	1.09563	+	1.04469i
$395$	536.607	−	619.277i	0.0683534	−	0.0788841i
$396$	−779.460	+	383.549i	−0.0989125	+	0.0486718i
$397$	−7061.14	−	8148.99i	−0.892667	−	1.03019i	−0.999355	−	0.0358997i	$-0.988570\pi$
$397$	−7061.14	−	8148.99i	−0.892667	−	1.03019i	0.106689	−	0.994292i	$-0.465975\pi$
$398$	−4520.49	+	3554.95i	−0.569326	+	0.447723i
$399$	−507.511	−	542.334i	−0.0636775	−	0.0680468i
$400$	−623.092	−	13080.3i	−0.0778865	−	1.63504i
$401$	−2623.16	−	2062.88i	−0.326670	−	0.256896i	0.441332	−	0.897344i	$-0.354506\pi$
$401$	−2623.16	−	2062.88i	−0.326670	−	0.256896i	−0.768001	+	0.640448i	$0.778749\pi$
$402$	−339.101	−	3940.59i	−0.0420717	−	0.488903i
$403$	−14053.3	+	1341.93i	−1.73708	+	0.165871i
$404$	−58.9671	+	410.126i	−0.00726170	+	0.0505062i
$405$	11174.7	−	6604.14i	1.37105	−	0.810278i
$406$	−1281.87	−	376.391i	−0.156695	−	0.0460098i
$407$	16495.2	−	12971.9i	2.00893	−	1.57984i
$408$	−12082.4	−	4308.78i	−1.46610	−	0.522834i
$409$	−1899.68	+	979.353i	−0.229665	+	0.118401i	−0.569219	−	0.822186i	$-0.692754\pi$
$409$	−1899.68	+	979.353i	−0.229665	+	0.118401i	0.339554	+	0.940587i	$0.389724\pi$
$410$	757.233	+	2187.88i	0.0912124	+	0.263541i
$411$	7164.79	+	1809.32i	0.859886	+	0.217146i
$412$	−169.186	+	237.588i	−0.0202310	+	0.0284105i
$413$	−2277.51			−0.271354
$414$	8514.07	+	1861.29i	1.01073	+	0.220960i
$415$	7811.16			0.923940
$416$	1143.63	−	1606.00i	0.134786	−	0.189281i
$417$	−646.933	−	2282.04i	−0.0759723	−	0.267990i
$418$	378.673	+	1094.10i	0.0443098	+	0.128025i
$419$	−10223.6	+	5270.65i	−1.19202	+	0.614530i	−0.935952	−	0.352129i	$-0.885458\pi$
$419$	−10223.6	+	5270.65i	−1.19202	+	0.614530i	−0.256070	+	0.966658i	$0.582428\pi$
$420$	819.372	−	696.673i	0.0951935	−	0.0809385i
$421$	5647.95	−	4441.60i	0.653834	−	0.514181i	−0.235244	−	0.971936i	$-0.575589\pi$
$421$	5647.95	−	4441.60i	0.653834	−	0.514181i	0.889078	+	0.457755i	$0.151346\pi$
$422$	−1611.90	−	473.297i	−0.185939	−	0.0545966i
$423$	−3274.47	+	2018.80i	−0.376383	+	0.232050i
$424$	−949.295	+	6602.49i	−0.108731	+	0.756239i
$425$	21686.6	−	2070.82i	2.47518	−	0.236351i
$426$	1503.14	−	1049.32i	0.170956	−	0.119342i
$427$	−3701.08	−	2910.56i	−0.419456	−	0.329864i
$428$	48.7886	+	1024.20i	0.00551001	+	0.115669i
$429$	−22401.9	+	5213.17i	−2.52115	+	0.586700i
$430$	14934.6	−	11744.7i	1.67491	−	1.31716i
$431$	−7468.50	−	8619.11i	−0.834675	−	0.963267i	0.165060	−	0.986284i	$-0.447218\pi$
$431$	−7468.50	−	8619.11i	−0.834675	−	0.963267i	−0.999735	+	0.0230168i	$0.992673\pi$
$432$	−9539.24	−	723.248i	−1.06240	−	0.0805493i
$433$	−4104.84	+	4737.24i	−0.455580	+	0.525767i	−0.936344	−	0.351083i	$-0.885814\pi$
$433$	−4104.84	+	4737.24i	−0.455580	+	0.525767i	0.480765	+	0.876850i	$0.340359\pi$
$434$	7963.09	+	7592.79i	0.880739	+	0.839783i
$435$	−1655.99	−	1202.74i	−0.182526	−	0.132568i
$436$	532.701	−	922.666i	0.0585132	−	0.101348i
$437$	254.282	−	720.424i	0.0278352	−	0.0788617i
$438$	7840.74	+	4625.22i	0.855354	+	0.504570i
$439$	−6855.78	+	9627.60i	−0.745350	+	1.04670i	0.251536	+	0.967848i	$0.419064\pi$
$439$	−6855.78	+	9627.60i	−0.745350	+	1.04670i	−0.996886	+	0.0788500i	$0.974875\pi$
$440$	21238.2	−	6236.11i	2.30112	−	0.675670i
$441$	−2190.63	−	464.891i	−0.236544	−	0.0501987i
$442$	21639.7	+	13907.0i	2.32872	+	1.49658i
$443$	5123.94	−	14804.7i	0.549539	−	1.58779i	−0.237830	−	0.971307i	$-0.576436\pi$
$443$	5123.94	−	14804.7i	0.549539	−	1.58779i	0.787369	−	0.616482i	$-0.211443\pi$
$444$	−1065.60	+	143.045i	−0.113899	+	0.0152897i
$445$	7596.32	−	7243.08i	0.809214	−	0.771584i
$446$	426.607	+	8955.59i	0.0452925	+	0.950806i
$447$	3177.42	+	487.235i	0.336213	+	0.0515557i
$448$	9677.77	−	924.115i	1.02061	−	0.0974561i
$449$	−3433.52	+	7518.36i	−0.360886	+	0.790230i	0.638895	+	0.769294i	$0.279392\pi$
$449$	−3433.52	+	7518.36i	−0.360886	+	0.790230i	−0.999781	+	0.0209359i	$0.993335\pi$
$450$	14189.5	−	5374.75i	1.48644	−	0.563040i
$451$	−2135.28	+	1372.26i	−0.222941	+	0.143276i
$452$	−82.7431	−	341.072i	−0.00861042	−	0.0354926i
$453$	−1240.00	+	3015.28i	−0.128610	+	0.312738i
$454$	−14648.6	+	2823.29i	−1.51430	+	0.291858i
$455$	25310.2	−	13048.3i	2.60783	−	1.34443i
$456$	−155.413	+	767.633i	−0.0159603	+	0.0788326i
$457$	5889.44	+	5615.57i	0.602837	+	0.574804i	0.928801	−	0.370578i	$-0.120840\pi$
$457$	5889.44	+	5615.57i	0.602837	+	0.574804i	−0.325964	+	0.945382i	$0.605689\pi$
$458$	1152.91	+	2524.51i	0.117624	+	0.257561i
$459$	446.735	−	15908.8i	0.0454288	−	1.61778i
$460$	1024.47	+	417.418i	0.103839	+	0.0423091i
$461$	−2299.25	−	3982.43i	−0.232293	−	0.402343i	0.726190	−	0.687494i	$-0.241289\pi$
$461$	−2299.25	−	3982.43i	−0.232293	−	0.402343i	−0.958482	+	0.285152i	$0.907956\pi$
$462$	14504.4	+	10534.5i	1.46062	+	1.06084i
$463$	−1539.15	+	6344.47i	−0.154493	+	0.636831i	0.840920	+	0.541160i	$0.182015\pi$
$463$	−1539.15	+	6344.47i	−0.154493	+	0.636831i	−0.995413	+	0.0956705i	$0.969500\pi$
$464$	493.355	+	1425.45i	0.0493608	+	0.142619i
$465$	7583.24	+	15053.6i	0.756267	+	1.50128i
$466$	−4732.61	+	13674.0i	−0.470459	+	1.35930i
$467$	1319.02	+	9173.98i	0.130700	+	0.909039i	0.944644	+	0.328096i	$0.106407\pi$
$467$	1319.02	+	9173.98i	0.130700	+	0.909039i	−0.813944	+	0.580943i	$0.802684\pi$
$468$	1124.28	+	353.104i	0.111047	+	0.0348766i
$469$	−4516.11	+	2902.33i	−0.444636	+	0.285751i
$470$	−6891.78	+	2759.05i	−0.676370	+	0.270778i
$471$	−11585.2	−	5422.40i	−1.13338	−	0.530469i
$472$	1393.03	+	1956.23i	0.135846	+	0.190769i
$473$	16373.1	+	12875.9i	1.59162	+	1.25166i
$474$	−372.794	−	592.190i	−0.0361244	−	0.0573844i
$475$	−313.587	−	1292.62i	−0.0302913	−	0.124862i
$476$	−187.667	−	1305.25i	−0.0180708	−	0.125685i
$477$	−8154.17	+	1413.86i	−0.782713	+	0.135715i
$478$	−13448.5	−	8642.82i	−1.28686	−	0.827015i
$479$	−9240.03	−	1780.87i	−0.881394	−	0.169875i	−0.271577	−	0.962417i	$-0.587545\pi$
$479$	−9240.03	−	1780.87i	−0.881394	−	0.169875i	−0.609818	+	0.792542i	$0.708757\pi$
$480$	−2282.40	−	576.371i	−0.217035	−	0.0548075i
$481$	−28337.4	−	2705.89i	−2.68622	−	0.256503i
$482$	−2038.30	+	3530.45i	−0.192619	+	0.333625i
$483$	−3156.65	−	11400.1i	−0.297376	−	1.07395i
$484$	−544.125	−	942.452i	−0.0511011	−	0.0885097i
$485$	2158.20	+	4725.80i	0.202060	+	0.442449i
$486$	−2622.08	−	10770.2i	−0.244732	−	1.00524i
$487$	1104.38	−	1274.52i	0.102760	−	0.118592i	−0.702040	−	0.712138i	$-0.747727\pi$
$487$	1104.38	−	1274.52i	0.102760	−	0.118592i	0.804800	+	0.593546i	$0.202273\pi$
$488$	−236.236	+	4959.21i	−0.0219137	+	0.460026i
$489$	12677.2	+	4520.91i	1.17236	+	0.418084i
$490$	−4012.08	−	1606.19i	−0.369892	−	0.148083i
$491$	−1248.59	+	1190.52i	−0.114761	+	0.109425i	−0.745287	−	0.666743i	$-0.767688\pi$
$491$	−1248.59	+	1190.52i	−0.114761	+	0.109425i	0.630526	+	0.776168i	$0.282839\pi$
$492$	129.950	−	4.97198i	0.0119077	−	0.000455598i
$493$	−2329.66	+	932.656i	−0.212825	+	0.0852022i
$494$	652.430	−	1428.62i	0.0594215	−	0.130115i
$495$	15508.3	+	22664.4i	1.40817	+	2.05796i
$496$	1767.96	−	12296.4i	0.160047	−	1.11315i
$497$	−2211.55	−	1140.13i	−0.199601	−	0.102901i
$498$	1939.11	−	6382.43i	0.174485	−	0.574304i
$499$	−15106.2	−	6047.59i	−1.35520	−	0.542540i	−0.423542	−	0.905877i	$-0.639213\pi$
$499$	−15106.2	−	6047.59i	−1.35520	−	0.542540i	−0.931658	+	0.363337i	$0.881637\pi$
$500$	660.222	−	127.247i	0.0590520	−	0.0113813i
$501$	7848.40	−	11964.7i	0.699882	−	1.06695i
$502$	−21391.9	−	4122.95i	−1.90193	−	0.366566i
$503$	−14807.0	+	4347.73i	−1.31255	+	0.385399i	−0.861799	−	0.507250i	$-0.830662\pi$
$503$	−14807.0	+	4347.73i	−1.31255	+	0.385399i	−0.450751	+	0.892650i	$0.648844\pi$
$504$	4830.28	+	11123.1i	0.426900	+	0.983064i
$505$	13098.4			1.15420
$506$	−2735.57	+	18234.5i	−0.240338	+	1.60202i
$507$	17040.7	+	10052.2i	1.49271	+	0.880543i
$508$	535.188	+	51.1043i	0.0467424	+	0.00446336i
$509$	214.257	−	883.181i	0.0186577	−	0.0769083i	−0.961722	−	0.274028i	$-0.911644\pi$
$509$	214.257	−	883.181i	0.0186577	−	0.0769083i	0.980379	+	0.197120i	$0.0631589\pi$
$510$	6094.45	−	30102.4i	0.529151	−	2.61364i
$511$	587.914	−	12341.8i	0.0508959	−	1.06844i
$512$	−6638.02	−	7660.68i	−0.572972	−	0.661245i
$513$	−965.324	+	111.236i	−0.0830801	+	0.00957350i
$514$	−1601.16	−	470.144i	−0.137401	−	0.0403447i
$515$	8195.48	+	4225.06i	0.701235	+	0.361512i
$516$	−387.349	−	994.420i	−0.0330466	−	0.0848389i
$517$	−4720.83	−	6629.48i	−0.401590	−	0.563954i
$518$	12869.3	+	18072.4i	1.09159	+	1.53293i
$519$	−7032.92	+	8772.87i	−0.594819	+	0.741978i
$520$	−26688.5	−	13758.9i	−2.25070	−	1.16032i
$521$	−19290.0	−	5664.04i	−1.62209	−	0.476288i	−0.660510	−	0.750817i	$-0.729660\pi$
$521$	−19290.0	−	5664.04i	−1.62209	−	0.476288i	−0.961579	+	0.274529i	$0.911478\pi$
$522$	−1393.84	+	1054.52i	−0.116871	+	0.0884195i
$523$	6947.42	+	8017.75i	0.580860	+	0.670348i	0.967789	−	0.251761i	$-0.0810098\pi$
$523$	6947.42	+	8017.75i	0.580860	+	0.670348i	−0.386930	+	0.922109i	$0.626464\pi$
$524$	5.32125	−	111.707i	0.000443626	−	0.00931285i
$525$	−15437.5	−	13631.7i	−1.28333	−	1.13321i
$526$	−2704.67	+	11148.8i	−0.224200	+	0.924164i
$527$	20573.2	+	1964.50i	1.70054	+	0.162381i
$528$	189.400	−	20239.1i	0.0156109	−	1.66817i
$529$	8907.65	−	8287.93i	0.732115	−	0.681181i
$530$	−15970.8			−1.30892
$531$	−1773.42	+	2394.30i	−0.144934	+	0.195675i
$532$	−77.2517	+	22.6831i	−0.00629565	+	0.00184857i
$533$	3380.91	+	651.618i	0.274754	+	0.0529544i
$534$	−4032.48	−	8004.96i	−0.326784	−	0.648705i
$535$	31828.5	−	6134.44i	2.57208	−	0.495729i
$536$	5255.15	+	2103.85i	0.423485	+	0.169538i
$537$	−13516.0	+	3145.33i	−1.08615	+	0.252758i
$538$	−7210.35	−	3717.19i	−0.577807	−	0.297880i
$539$	674.274	−	4689.68i	0.0538832	−	0.374766i
$540$	−94.3778	−	1403.86i	−0.00752106	−	0.111875i
$541$	1473.60	−	3226.73i	0.117107	−	0.256429i	−0.841997	−	0.539482i	$-0.818620\pi$
$541$	1473.60	−	3226.73i	0.117107	−	0.256429i	0.959104	+	0.283053i	$0.0913473\pi$
$542$	−18874.4	+	7556.18i	−1.49580	+	0.598830i
$543$	−6490.92	+	12306.5i	−0.512987	+	0.972601i
$544$	−2088.90	+	1991.76i	−0.164634	+	0.156978i
$545$	−31267.5	−	12517.6i	−2.45753	−	0.983846i
$546$	−4378.45	−	23919.9i	−0.343187	−	1.87487i
$547$	−54.2708	+	1139.28i	−0.00424214	+	0.0890535i	−0.999995	−	0.00300788i	$-0.999043\pi$
$547$	−54.2708	+	1139.28i	−0.00424214	+	0.0890535i	0.995753	+	0.0920614i	$0.0293456\pi$
$548$	524.558	−	605.373i	0.0408906	−	0.0471902i
$549$	−5941.71	+	1624.50i	−0.461905	+	0.126288i
$550$	13335.7	+	29201.0i	1.03388	+	2.26388i
$551$	76.6074	+	132.688i	0.00592302	+	0.0102590i
$552$	−7861.14	+	9684.11i	−0.606145	+	0.746709i
$553$	−474.890	+	822.534i	−0.0365179	+	0.0632508i
$554$	11385.3	+	1087.17i	0.873134	+	0.0833742i
$555$	9270.05	+	32699.8i	0.708994	+	2.50095i
$556$	−252.467	−	48.6591i	−0.0192572	−	0.00371152i
$557$	14137.8	+	9085.80i	1.07547	+	0.691163i	0.953507	−	0.301372i	$-0.0974444\pi$
$557$	14137.8	+	9085.80i	1.07547	+	0.691163i	0.121964	+	0.992535i	$0.461081\pi$
$558$	14182.7	−	2459.15i	1.07599	−	0.186567i
$559$	−4021.19	−	27968.0i	−0.304254	−	2.11613i
$560$	5907.65	+	24351.7i	0.445792	+	1.83758i
$561$	33646.8	−	1287.35i	2.53221	−	0.0968840i
$562$	12163.5	+	9565.52i	0.912968	+	0.717966i
$563$	1977.14	+	2776.50i	0.148004	+	0.207843i	0.881922	−	0.471396i	$-0.156250\pi$
$563$	1977.14	+	2776.50i	0.148004	+	0.207843i	−0.733918	+	0.679239i	$0.762310\pi$
$564$	35.7503	+	415.443i	0.00266908	+	0.0310165i
$565$	−10300.1	+	4123.56i	−0.766957	+	0.307043i
$566$	4092.31	−	2629.97i	0.303909	−	0.195311i
$567$	−11269.7	+	9967.72i	−0.834718	+	0.738280i
$568$	373.382	+	2596.93i	0.0275823	+	0.191839i
$569$	4403.35	−	12722.7i	0.324426	−	0.937366i	−0.658374	−	0.752691i	$-0.728755\pi$
$569$	4403.35	−	12722.7i	0.324426	−	0.937366i	0.982800	−	0.184675i	$-0.0591233\pi$
$570$	−1872.18	−	106.751i	−0.137574	−	0.00784436i
$571$	7446.15	+	21514.3i	0.545730	+	1.57678i	0.793888	+	0.608064i	$0.208054\pi$
$571$	7446.15	+	21514.3i	0.545730	+	1.57678i	−0.248158	+	0.968720i	$0.579825\pi$
$572$	−587.791	+	2422.91i	−0.0429664	+	0.177110i
$573$	−976.862	+	9308.74i	−0.0712199	+	0.678671i
$574$	−1341.77	−	2324.01i	−0.0975686	−	0.168994i
$575$	5119.83	−	20555.1i	0.371325	−	1.49079i
$576$	6564.26	−	10893.6i	0.474845	−	0.788020i
$577$	2965.18	+	6492.84i	0.213938	+	0.468458i	0.985927	−	0.167177i	$-0.0534653\pi$
$577$	2965.18	+	6492.84i	0.213938	+	0.468458i	−0.771989	+	0.635636i	$0.780738\pi$
$578$	−16848.7	−	16065.2i	−1.21248	−	1.15610i
$579$	7569.57	+	6684.11i	0.543317	+	0.479762i
$580$	−197.191	+	101.659i	−0.0141171	+	0.00727788i
$581$	−8890.20	+	1713.45i	−0.634816	+	0.122351i
$582$	4397.18	−	590.275i	0.313177	−	0.0420407i
$583$	−4127.92	−	17015.5i	−0.293244	−	1.20877i
$584$	−10960.4	+	7043.83i	−0.776618	+	0.499102i
$585$	5990.83	−	36768.3i	0.423403	−	2.59860i
$586$	−4490.71	+	9833.29i	−0.316569	+	0.693190i
$587$	8308.01	−	793.319i	0.584171	−	0.0557815i	0.201213	−	0.979547i	$-0.435512\pi$
$587$	8308.01	−	793.319i	0.584171	−	0.0557815i	0.382958	+	0.923766i	$0.374906\pi$
$588$	−151.835	+	189.399i	−0.0106489	+	0.0132835i
$589$	−60.0402	−	1260.40i	−0.00420020	−	0.0881729i
$590$	−4161.44	+	3967.92i	−0.290379	+	0.276876i
$591$	−12840.3	−	16646.0i	−0.893706	−	1.15859i
$592$	8192.95	−	23672.0i	0.568798	−	1.64343i
$593$	11270.1	+	7242.83i	0.780448	+	0.501564i	0.869182	−	0.494492i	$-0.164646\pi$
$593$	11270.1	+	7242.83i	0.780448	+	0.501564i	−0.0887340	+	0.996055i	$0.528282\pi$
$594$	22368.7	−	7045.29i	1.54512	−	0.486653i
$595$	−39998.1	+	11744.5i	−2.75590	+	0.809207i
$596$	202.120	−	283.838i	0.0138912	−	0.0195075i
$597$	8890.95	−	5022.85i	0.609518	−	0.344341i
$598$	19755.0	−	15341.1i	1.35091	−	1.04907i
$599$	−9140.19	+	15831.3i	−0.623469	+	1.07988i	0.365365	+	0.930864i	$0.380944\pi$
$599$	−9140.19	+	15831.3i	−0.623469	+	1.07988i	−0.988835	+	0.149016i	$0.952389\pi$
$600$	−2266.45	+	21597.5i	−0.154213	+	1.46953i
$601$	−1943.31	−	1852.95i	−0.131896	−	0.125763i	0.621260	−	0.783604i	$-0.286621\pi$
$601$	−1943.31	−	1852.95i	−0.131896	−	0.125763i	−0.753156	+	0.657842i	$0.771470\pi$
$602$	−14421.4	+	16643.2i	−0.976364	+	1.12678i
$603$	−465.397	+	7007.62i	−0.0314302	+	0.473254i
$604$	231.432	+	267.087i	0.0155908	+	0.0179927i
$605$	−27042.1	+	21266.1i	−1.81722	+	1.42908i
$606$	3251.66	−	10702.6i	0.217970	−	0.717432i
$607$	−591.298	−	12412.9i	−0.0395388	−	0.830022i	−0.928341	−	0.371730i	$-0.878765\pi$
$607$	−591.298	−	12412.9i	−0.0395388	−	0.830022i	0.888802	−	0.458291i	$-0.151538\pi$
$608$	138.522	+	108.935i	0.00923981	+	0.00726626i
$609$	2148.58	+	1005.63i	0.142964	+	0.0669132i
$610$	−11833.4	+	1129.95i	−0.785442	+	0.0750006i
$611$	−1571.17	+	10927.7i	−0.104031	+	0.723550i
$612$	−1518.31	−	819.068i	−0.100285	−	0.0540994i
$613$	13732.2	+	4032.14i	0.904794	+	0.265671i	0.700848	−	0.713311i	$-0.252805\pi$
$613$	13732.2	+	4032.14i	0.904794	+	0.265671i	0.203946	+	0.978982i	$0.434623\pi$
$614$	3915.58	−	3079.24i	0.257361	−	0.202391i
$615$	−740.215	−	4043.88i	−0.0485339	−	0.265146i
$616$	−22804.2	+	11756.4i	−1.49157	+	0.768956i
$617$	−259.920	−	750.989i	−0.0169594	−	0.0490011i	0.936203	−	0.351459i	$-0.114314\pi$
$617$	−259.920	−	750.989i	−0.0169594	−	0.0490011i	−0.953163	+	0.302457i	$0.902193\pi$
$618$	5486.77	−	5647.58i	0.357136	−	0.367604i
$619$	−14527.2	+	20400.6i	−0.943292	+	1.32467i	0.00253478	+	0.999997i	$0.499193\pi$
$619$	−14527.2	+	20400.6i	−0.943292	+	1.32467i	−0.945827	+	0.324672i	$0.894746\pi$
$620$	1827.12			0.118353
$621$	−14442.6	−	5558.33i	−0.933270	−	0.359176i
$622$	−4794.67			−0.309082
$623$	−7056.85	+	9909.96i	−0.453815	+	0.637294i
$624$	−19131.8	+	19692.6i	−1.22738	+	1.26336i
$625$	899.415	+	2598.69i	0.0575625	+	0.166316i
$626$	11993.4	−	6183.03i	0.765740	−	0.394766i
$627$	−370.163	−	2022.24i	−0.0235771	−	0.128805i
$628$	−1089.90	+	857.109i	−0.0692546	+	0.0544624i
$629$	39984.9	+	11740.6i	2.53466	+	0.744243i
$630$	−24715.0	+	15237.5i	−1.56297	+	0.963611i
$631$	−1262.74	+	8782.52i	−0.0796652	+	0.554083i	0.910428	+	0.413668i	$0.135753\pi$
$631$	−1262.74	+	8782.52i	−0.0796652	+	0.554083i	−0.990093	+	0.140415i	$0.955156\pi$
$632$	996.965	−	95.1986i	0.0627486	−	0.00599177i
$633$	2701.76	+	1264.54i	0.169645	+	0.0794011i
$634$	−15798.1	−	12423.8i	−0.989626	−	0.778250i
$635$	−808.685	−	16976.4i	−0.0505381	−	1.06092i
$636$	−260.779	+	858.336i	−0.0162587	+	0.0535145i
$637$	−5052.00	+	3972.94i	−0.314235	+	0.247117i
$638$	−2421.54	−	2794.61i	−0.150266	−	0.173416i
$639$	−2920.65	+	1437.16i	−0.180813	+	0.0889724i
$640$	18446.5	−	21288.4i	1.13931	−	1.31484i
$641$	−2894.86	−	2760.24i	−0.178378	−	0.170083i	0.595630	−	0.803259i	$-0.296902\pi$
$641$	−2894.86	−	2760.24i	−0.178378	−	0.170083i	−0.774008	+	0.633176i	$0.781751\pi$
$642$	2888.96	−	27529.6i	0.177599	−	1.69238i
$643$	3729.75	−	6460.12i	0.228751	−	0.396209i	−0.728687	−	0.684847i	$-0.759869\pi$
$643$	3729.75	−	6460.12i	0.228751	−	0.396209i	0.957438	+	0.288638i	$0.0932024\pi$
$644$	−1257.55	−	250.354i	−0.0769479	−	0.0153189i
$645$	−29373.5	+	16594.3i	−1.79315	+	1.01302i
$646$	−1333.66	+	1872.87i	−0.0812264	+	0.114066i
$647$	−1334.91	+	391.964i	−0.0811137	+	0.0238171i	−0.322038	−	0.946727i	$-0.604368\pi$
$647$	−1334.91	+	391.964i	−0.0811137	+	0.0238171i	0.240924	+	0.970544i	$0.422550\pi$
$648$	15454.7	+	3583.27i	0.936909	+	0.217228i
$649$	−5303.08	−	3408.08i	−0.320746	−	0.206131i
$650$	14242.8	−	41151.9i	0.859460	−	2.48325i
$651$	−11932.9	−	15469.7i	−0.718416	−	0.931346i
$652$	1055.89	−	1006.78i	0.0634228	−	0.0604735i
$653$	−857.687	−	18005.1i	−0.0513995	−	1.07901i	−0.866337	−	0.499460i	$-0.833532\pi$
$653$	−857.687	−	18005.1i	−0.0513995	−	1.07901i	0.814938	−	0.579549i	$-0.196771\pi$
$654$	−17990.1	+	22440.9i	−1.07564	+	1.34176i
$655$	−3519.33	+	336.056i	−0.209942	+	0.0200470i
$656$	−1258.66	+	2756.08i	−0.0749122	+	0.164035i
$657$	−12516.9	−	10228.2i	−0.743273	−	0.607369i
$658$	7238.59	−	4651.96i	0.428860	−	0.275611i
$659$	−2652.75	−	10934.8i	−0.156808	−	0.646371i	−0.994902	−	0.100845i	$-0.967845\pi$
$659$	−2652.75	−	10934.8i	−0.156808	−	0.646371i	0.838094	−	0.545526i	$-0.183670\pi$
$660$	2950.37	−	396.057i	0.174005	−	0.0233583i
$661$	−20791.1	+	4007.16i	−1.22342	+	0.235795i	−0.759751	−	0.650214i	$-0.774679\pi$
$661$	−20791.1	+	4007.16i	−1.22342	+	0.235795i	−0.463668	+	0.886009i	$0.653467\pi$
$662$	−22073.2	+	11379.5i	−1.29592	+	0.668094i
$663$	−34238.1	−	30233.0i	−2.00558	−	1.77097i
$664$	6909.37	+	6588.07i	0.403819	+	0.385040i
$665$	1057.32	+	2315.22i	0.0616560	+	0.135008i
$666$	29020.0	+	543.193i	1.68844	+	0.0316040i
$667$	101.204	+	2437.96i	0.00587501	+	0.141526i
$668$	−775.533	−	1343.26i	−0.0449196	−	0.0778030i
$669$	1661.55	−	15833.3i	0.0960227	−	0.915022i
$670$	−3195.28	+	13171.1i	−0.184245	+	0.759470i
$671$	−4262.41	−	12315.4i	−0.245229	−	0.708541i
$672$	2724.12	+	155.328i	0.156377	+	0.00891652i
$673$	−7067.43	+	20420.0i	−0.404799	+	1.16959i	0.539923	+	0.841715i	$0.318453\pi$
$673$	−7067.43	+	20420.0i	−0.404799	+	1.16959i	−0.944721	+	0.327874i	$0.893668\pi$
$674$	−2551.50	−	17746.1i	−0.145816	−	1.01417i
$675$	−26351.4	+	5614.55i	−1.50261	+	0.320154i
$676$	1804.15	−	1159.46i	0.102649	−	0.0659682i
$677$	22979.8	−	9199.71i	1.30456	−	0.522265i	0.387811	−	0.921739i	$-0.373231\pi$
$677$	22979.8	−	9199.71i	1.30456	−	0.522265i	0.916745	+	0.399473i	$0.130807\pi$
$678$	812.328	+	9439.82i	0.0460137	+	0.534711i
$679$	−3492.98	−	4905.21i	−0.197420	−	0.277238i
$680$	34552.3	+	27172.3i	1.94856	+	1.53237i
$681$	26470.5	−	1012.78i	1.48950	−	0.0569894i
$682$	7179.78	+	29595.4i	0.403120	+	1.66168i
$683$	−2168.34	−	15081.2i	−0.121478	−	0.844897i	−0.955883	−	0.293746i	$-0.905098\pi$
$683$	−2168.34	−	15081.2i	−0.121478	−	0.844897i	0.834406	−	0.551151i	$-0.185811\pi$
$684$	−36.3071	+	98.8754i	−0.00202958	+	0.00552719i
$685$	−21302.5	−	13690.3i	−1.18822	−	0.763620i
$686$	−15422.2	−	2972.38i	−0.858340	−	0.165431i
$687$	−1344.08	−	4741.21i	−0.0746433	−	0.263302i
$688$	24751.7	+	2363.50i	1.37158	+	0.130970i
$689$	−11875.7	+	20569.3i	−0.656644	+	1.13734i
$690$	−25629.1	−	15330.4i	−1.41404	−	0.845825i
$691$	−17439.6	−	30206.2i	−0.960106	−	1.66295i	−0.722226	−	0.691657i	$-0.756881\pi$
$691$	−17439.6	−	30206.2i	−0.960106	−	1.66295i	−0.237880	−	0.971295i	$-0.576452\pi$
$692$	506.310	+	1108.66i	0.0278136	+	0.0609033i
$693$	−22622.2	−	22393.4i	−1.24004	−	1.22749i
$694$	11796.4	−	13613.8i	0.645225	−	0.744630i
$695$	−386.747	+	8118.81i	−0.0211081	+	0.443114i
$696$	−450.398	−	2460.57i	−0.0245292	−	0.134006i
$697$	−4679.48	−	1873.38i	−0.254301	−	0.101807i
$698$	14650.1	−	13968.8i	0.794432	−	0.757489i
$699$	11986.7	−	22726.2i	0.648609	−	1.22973i
$700$	−2072.49	+	829.699i	−0.111904	+	0.0447995i
$701$	−13649.8	+	29889.0i	−0.735445	+	1.61040i	0.0554592	+	0.998461i	$0.482338\pi$
$701$	−13649.8	+	29889.0i	−0.735445	+	1.61040i	−0.790904	+	0.611940i	$0.790390\pi$
$702$	−28555.8	−	14022.7i	−1.53528	−	0.753922i
$703$	362.103	−	2518.48i	0.0194267	−	0.135116i
$704$	23917.1	+	12330.1i	1.28041	+	0.660097i
$705$	12838.7	−	2987.71i	0.685864	−	0.159608i
$706$	831.686	+	332.957i	0.0443356	+	0.0177493i
$707$	−14907.9	+	2873.26i	−0.793024	+	0.152843i
$708$	145.302	+	288.443i	0.00771299	+	0.0153112i
$709$	34282.7	+	6607.45i	1.81596	+	0.349997i	0.980031	−	0.198845i	$-0.0637190\pi$
$709$	34282.7	+	6607.45i	1.81596	+	0.349997i	0.835926	+	0.548842i	$0.184931\pi$
$710$	−6027.26	+	1769.76i	−0.318590	+	0.0935466i
$711$	494.929	+	1139.72i	0.0261059	+	0.0601165i
$712$	12828.3			0.675224
$713$	8459.57	−	18228.2i	0.444338	−	0.957436i
$714$	−333.127	+	35597.6i	−0.0174607	+	1.86584i
$715$	78459.2	+	7491.94i	4.10378	+	0.391864i
$716$	−354.640	+	1461.84i	−0.0185105	+	0.0763013i
$717$	21278.1	+	18789.0i	1.10829	+	0.978646i
$718$	1170.01	−	24561.5i	0.0608137	−	1.27664i
$719$	2658.26	+	3067.80i	0.137881	+	0.159123i	0.820491	−	0.571660i	$-0.193700\pi$
$719$	2658.26	+	3067.80i	0.137881	+	0.159123i	−0.682609	+	0.730783i	$0.739155\pi$
$720$	30200.4	+	12751.3i	1.56320	+	0.660016i
$721$	−10254.4	−	3010.97i	−0.529673	−	0.155526i
$722$	−17715.5	−	9132.97i	−0.913161	−	0.470767i
$723$	4527.73	−	5647.89i	0.232902	−	0.290522i
$724$	874.823	+	1228.52i	0.0449068	+	0.0630628i
$725$	2464.21	+	3460.49i	0.126232	+	0.177268i
$726$	10663.2	+	27375.1i	0.545108	+	1.39943i
$727$	10730.4	+	5531.92i	0.547414	+	0.282211i	0.709666	−	0.704538i	$-0.248846\pi$
$727$	10730.4	+	5531.92i	0.547414	+	0.282211i	−0.162253	+	0.986749i	$0.551876\pi$
$728$	33393.3	+	9805.17i	1.70005	+	0.499181i
$729$	1703.45	+	19609.1i	0.0865442	+	0.996248i
$730$	−20427.9	−	23575.1i	−1.03571	−	1.19528i
$731$	−1968.20	+	41317.6i	−0.0995849	+	2.09054i
$732$	−132.493	+	654.425i	−0.00669001	+	0.0330440i
$733$	80.1641	−	330.441i	0.00403947	−	0.0166509i	−0.969756	−	0.244076i	$-0.921515\pi$
$733$	80.1641	−	330.441i	0.00403947	−	0.0166509i	0.973796	+	0.227425i	$0.0730306\pi$
$734$	10314.2	+	984.887i	0.518670	+	0.0495270i
$735$	6609.53	+	3898.93i	0.331696	+	0.195666i
$736$	1150.24	+	2559.97i	0.0576065	+	0.128209i
$737$	−14858.6			−0.742637
$738$	−3487.97	−	399.061i	−0.173975	−	0.0199047i
$739$	−4194.00	+	1231.47i	−0.208767	+	0.0612995i	−0.384444	−	0.923148i	$-0.625607\pi$
$739$	−4194.00	+	1231.47i	−0.208767	+	0.0612995i	0.175677	+	0.984448i	$0.443789\pi$
$740$	3617.66	+	697.247i	0.179713	+	0.0346369i
$741$	−1529.62	+	2331.86i	−0.0758325	+	0.115605i
$742$	18177.0	−	3503.33i	0.899325	−	0.173331i
$743$	28257.4	+	11312.6i	1.39524	+	0.558570i	0.942841	−	0.333244i	$-0.108143\pi$
$743$	28257.4	+	11312.6i	1.39524	+	0.558570i	0.452401	+	0.891815i	$0.350568\pi$
$744$	−5988.75	+	19711.5i	−0.295105	+	0.971318i
$745$	−9790.85	−	5047.53i	−0.481489	−	0.248225i
$746$	−484.437	+	3369.33i	−0.0237755	+	0.165362i
$747$	−5121.20	+	10680.3i	−0.250837	+	0.523120i
$748$	1516.21	−	3320.05i	0.0741153	−	0.162290i
$749$	−34879.6	+	13963.7i	−1.70157	+	0.681205i
$750$	−18138.2	+	693.980i	−0.883084	+	0.0337874i
$751$	18528.5	−	17666.9i	0.900285	−	0.858420i	−0.0902168	−	0.995922i	$-0.528756\pi$
$751$	18528.5	−	17666.9i	0.900285	−	0.858420i	0.990501	+	0.137503i	$0.0439075\pi$
$752$	−9019.15	−	3610.72i	−0.437360	−	0.175092i
$753$	36436.5	+	12993.9i	1.76337	+	0.628848i
$754$	−238.677	+	5010.44i	−0.0115280	+	0.242002i
$755$	7316.15	−	8443.29i	0.352665	−	0.406997i
$756$	415.365	+	1577.09i	0.0199824	+	0.0758707i
$757$	−15358.8	−	33631.1i	−0.737417	−	1.61472i	−0.787757	−	0.615986i	$-0.788758\pi$
$757$	−15358.8	−	33631.1i	−0.737417	−	1.61472i	0.0503401	−	0.998732i	$-0.483969\pi$
$758$	9262.34	+	16042.8i	0.443830	+	0.768736i
$759$	9708.99	−	31268.1i	0.464314	−	1.49534i
$760$	1341.91	−	2324.26i	0.0640476	−	0.110934i
$761$	26293.0	+	2510.68i	1.25246	+	0.119595i	0.700121	−	0.714025i	$-0.253130\pi$
$761$	26293.0	+	2510.68i	1.25246	+	0.119595i	0.552338	+	0.833620i	$0.313736\pi$
$762$	−14072.0	−	3553.58i	−0.668995	−	0.168941i
$763$	38332.7	+	7388.02i	1.81879	+	0.350543i
$764$	853.519	+	548.524i	0.0404179	+	0.0259750i
$765$	−18798.5	+	51194.1i	−0.888445	+	2.41951i
$766$	4572.45	+	31802.1i	0.215678	+	1.50007i
$767$	2016.02	+	8310.15i	0.0949078	+	0.391215i
$768$	−2383.33	−	3785.97i	−0.111980	−	0.177883i
$769$	−16382.0	−	12882.9i	−0.768203	−	0.604122i	0.155231	−	0.987878i	$-0.450388\pi$
$769$	−16382.0	−	12882.9i	−0.768203	−	0.604122i	−0.923434	+	0.383756i	$0.874630\pi$
$770$	−35631.9	−	50038.0i	−1.66764	−	2.34187i
$771$	2683.76	+	1256.11i	0.125361	+	0.0586742i
$772$	1016.22	−	406.831i	0.0473762	−	0.0189666i
$773$	−26378.1	+	16952.2i	−1.22736	+	0.788779i	−0.983479	−	0.181024i	$-0.942059\pi$
$773$	−26378.1	+	16952.2i	−1.22736	+	0.788779i	−0.243886	+	0.969804i	$0.578422\pi$
$774$	6267.10	+	28120.3i	0.291042	+	1.30590i
$775$	−4979.17	−	34630.9i	−0.230783	−	1.60513i
$776$	−2076.79	+	6000.48i	−0.0960725	+	0.277583i
$777$	−17723.6	−	35183.5i	−0.818315	−	1.62446i
$778$	−7267.58	−	20998.3i	−0.334904	−	0.967642i
$779$	−72.5561	+	299.080i	−0.00333709	+	0.0137557i
$780$	−3267.30	−	2373.03i	−0.149985	−	0.108933i
$781$	−3443.38	−	5964.11i	−0.157764	−	0.273256i
$782$	−32647.8	+	16579.4i	−1.49295	+	0.758154i
$783$	2730.22	−	1475.70i	0.124611	−	0.0673529i
$784$	−2349.45	−	5144.57i	−0.107027	−	0.234356i
$785$	31723.0	+	30247.8i	1.44235	+	1.37528i
$786$	−599.079	+	2959.04i	−0.0271863	+	0.134282i
$787$	9259.49	−	4773.60i	0.419397	−	0.216214i	−0.235593	−	0.971852i	$-0.575703\pi$
$787$	9259.49	−	4773.60i	0.419397	−	0.216214i	0.654990	+	0.755638i	$0.272673\pi$
$788$	−2237.64	+	431.270i	−0.101158	+	0.0194967i
$789$	7747.70	−	18839.9i	0.349589	−	0.850088i
$790$	565.320	+	2330.28i	0.0254597	+	0.104946i
$791$	10818.5	−	6952.62i	0.486297	−	0.312524i
$792$	−5397.66	+	33127.7i	−0.242168	+	1.48629i
$793$	−7343.86	+	16080.8i	−0.328863	+	0.720109i
$794$	31410.5	−	2999.34i	1.40392	−	0.134058i
$795$	28031.2	+	4298.39i	1.25052	+	0.191759i
$796$	−52.6691	−	1105.66i	−0.00234523	−	0.0492325i
$797$	−9763.30	+	9309.28i	−0.433919	+	0.413741i	−0.875301	−	0.483578i	$-0.839337\pi$
$797$	−9763.30	+	9309.28i	−0.433919	+	0.413741i	0.441382	+	0.897319i	$0.354488\pi$
$798$	2154.22	−	289.181i	0.0955621	−	0.0128282i
$799$	5286.09	−	15273.2i	0.234053	−	0.676253i
$800$	4110.54	+	2641.69i	0.181662	+	0.116747i
$801$	4923.17	+	15135.3i	0.217168	+	0.667638i
$802$	9369.89	−	2751.25i	0.412546	−	0.121135i
$803$	19837.3	−	27857.6i	0.871785	−	1.22425i
$804$	655.696	+	386.792i	0.0287620	+	0.0169665i
$805$	−2176.14	+	40476.1i	−0.0952781	+	1.77217i
$806$	20655.6	−	35776.6i	0.902684	−	1.56349i
$807$	11654.8	+	8464.85i	0.508389	+	0.369240i
$808$	11586.2	+	11047.5i	0.504458	+	0.481000i
$809$	29171.3	−	33665.5i	1.26775	−	1.46306i	0.444085	−	0.895985i	$-0.353529\pi$
$809$	29171.3	−	33665.5i	1.26775	−	1.46306i	0.823665	−	0.567076i	$-0.191926\pi$
$810$	−3225.98	+	37847.2i	−0.139937	+	1.64175i
$811$	11619.8	+	13410.0i	0.503117	+	0.580628i	0.949323	−	0.314302i	$-0.101771\pi$
$811$	11619.8	+	13410.0i	0.503117	+	0.580628i	−0.446206	+	0.894930i	$0.647225\pi$
$812$	202.132	−	158.958i	0.00873576	−	0.00686987i
$813$	35161.2	−	8182.40i	1.51680	−	0.352976i
$814$	2921.91	+	61338.3i	0.125814	+	2.64116i
$815$	−36253.5	−	28510.0i	−1.55816	−	1.22535i
$816$	32957.6	−	23007.3i	1.41391	−	0.987028i
$817$	2514.11	−	240.069i	0.107659	−	0.0102802i
$818$	890.079	−	6190.63i	0.0380451	−	0.264609i
$819$	1247.04	+	43161.7i	0.0532051	+	1.84150i
$820$	−427.576	−	125.548i	−0.0182093	−	0.00534673i
$821$	−510.220	+	401.242i	−0.0216892	+	0.0170565i	−0.628945	−	0.777450i	$-0.716513\pi$
$821$	−510.220	+	401.242i	−0.0216892	+	0.0170565i	0.607256	+	0.794507i	$0.292270\pi$
$822$	−16474.5	+	14007.5i	−0.699045	+	0.594365i
$823$	−13046.6	+	6726.00i	−0.552584	+	0.284877i	−0.711818	−	0.702364i	$-0.752128\pi$
$823$	−13046.6	+	6726.00i	−0.552584	+	0.284877i	0.159234	+	0.987241i	$0.449098\pi$
$824$	3685.82	+	10649.5i	0.155827	+	0.450234i
$825$	−15547.0	−	54841.5i	−0.656093	−	2.31435i
$826$	3865.90	−	5428.90i	0.162847	−	0.228687i
$827$	34640.4			1.45655			0.728275	−	0.685285i	$-0.240322\pi$
$827$	34640.4			1.45655			0.728275	+	0.685285i	$0.240322\pi$
$828$	−1242.40	+	1127.09i	−0.0521456	+	0.0473057i
$829$	−21346.4			−0.894322			−0.447161	−	0.894454i	$-0.647565\pi$
$829$	−21346.4			−0.894322			−0.447161	+	0.894454i	$0.647565\pi$
$830$	−13258.8	+	18619.4i	−0.554483	+	0.778663i
$831$	−19690.4	−	4972.40i	−0.821965	−	0.207570i
$832$	−11938.5	−	34494.1i	−0.497468	−	1.43734i
$833$	8362.89	−	4311.37i	0.347848	−	0.179328i
$834$	6537.80	+	2331.49i	0.271445	+	0.0968019i
$835$	−38542.7	+	30310.3i	−1.59739	+	1.25621i
$836$	−213.820	−	62.7832i	−0.00884583	−	0.00259737i
$837$	−25554.7	+	499.054i	−1.05532	+	0.0206091i
$838$	4790.19	−	33316.5i	0.197464	−	1.37339i
$839$	−2564.07	+	244.839i	−0.105509	+	0.0100748i	−0.147677	−	0.989036i	$-0.547180\pi$
$839$	−2564.07	+	244.839i	−0.105509	+	0.0100748i	0.0421682	+	0.999111i	$0.486573\pi$
$840$	−3562.74	−	41401.5i	−0.146341	−	1.70058i
$841$	18786.4	+	14773.8i	0.770282	+	0.605756i
$842$	1000.46	+	21002.3i	0.0409479	+	0.859603i
$843$	−18774.5	−	20062.7i	−0.767054	−	0.819686i
$844$	254.173	−	199.884i	0.0103661	−	0.00815199i
$845$	−44397.1	−	51237.0i	−1.80746	−	2.08592i
$846$	745.956	−	11232.1i	0.0303150	−	0.456462i
$847$	26112.8	−	30135.8i	1.05932	−	1.22252i
$848$	−15126.6	−	14423.1i	−0.612556	−	0.584071i
$849$	−7890.47	+	3514.60i	−0.318964	+	0.142074i
$850$	−31875.1	+	55209.2i	−1.28624	+	2.22784i
$851$	23705.9	−	32863.3i	0.954908	−	1.32378i
$852$	−3.30180	+	352.827i	−0.000132767	+	0.0141874i
$853$	−20846.4	+	29274.7i	−0.836774	+	1.17508i	0.145819	+	0.989311i	$0.453418\pi$
$853$	−20846.4	+	29274.7i	−0.836774	+	1.17508i	−0.982593	+	0.185773i	$0.940521\pi$
$854$	13220.2	−	3881.80i	0.529725	−	0.155541i
$855$	3257.23	+	691.243i	0.130287	+	0.0276491i
$856$	33327.8	+	21418.5i	1.33075	+	0.855220i
$857$	−3265.78	+	9435.85i	−0.130171	+	0.376105i	−0.991186	−	0.132474i	$-0.957708\pi$
$857$	−3265.78	+	9435.85i	−0.130171	+	0.376105i	0.861015	+	0.508579i	$0.169829\pi$
$858$	25598.9	−	62248.3i	1.01857	−	2.47683i
$859$	−30336.8	+	28926.1i	−1.20498	+	1.14895i	−0.220144	+	0.975467i	$0.570653\pi$
$859$	−30336.8	+	28926.1i	−1.20498	+	1.14895i	−0.984837	+	0.173480i	$0.944499\pi$
$860$	174.006	+	3652.83i	0.00689947	+	0.144838i
$861$	1729.53	+	4440.13i	0.0684578	+	0.175748i
$862$	33222.5	−	3172.37i	1.31272	−	0.125350i
$863$	−569.204	+	1246.38i	−0.0224518	+	0.0491627i	−0.920526	−	0.390682i	$-0.872239\pi$
$863$	−569.204	+	1246.38i	−0.0224518	+	0.0491627i	0.898074	+	0.439845i	$0.144966\pi$
$864$	2284.47	−	2742.85i	0.0899530	−	0.108002i
$865$	32413.1	−	20830.6i	1.27408	−	0.818801i
$866$	−4324.49	−	17825.8i	−0.169691	−	0.699474i
$867$	25248.3	+	32731.6i	0.989015	+	1.28215i
$868$	−2079.52	+	400.794i	−0.0813173	+	0.0156726i
$869$	−2336.60	+	1204.60i	−0.0912126	+	0.0470234i
$870$	5677.88	−	1905.83i	0.221262	−	0.0742684i
$871$	14587.5	+	13909.2i	0.567486	+	0.541097i
$872$	−17100.1	−	37444.0i	−0.664086	−	1.45415i
$873$	−7876.60	−	147.433i	−0.305364	−	0.00571576i
$874$	1285.65	+	1829.00i	0.0497571	+	0.0707857i
$875$	12318.4	+	21336.2i	0.475930	+	0.824336i
$876$	−1600.58	+	712.935i	−0.0617335	+	0.0274975i
$877$	5013.22	−	20664.8i	0.193027	−	0.795667i	−0.790135	−	0.612932i	$-0.789990\pi$
$877$	5013.22	−	20664.8i	0.193027	−	0.795667i	0.983162	−	0.182735i	$-0.0584950\pi$
$878$	−11312.1	−	32684.2i	−0.434812	−	1.25631i
$879$	10528.4	−	16050.3i	0.403999	−	0.615887i
$880$	−22684.3	+	65541.9i	−0.868962	+	2.51070i
$881$	−2974.16	−	20685.8i	−0.113737	−	0.791057i	−0.964229	−	0.265070i	$-0.914605\pi$
$881$	−2974.16	−	20685.8i	−0.113737	−	0.791057i	0.850492	−	0.525987i	$-0.176304\pi$
$882$	4826.58	−	4432.68i	0.184262	−	0.169225i
$883$	17203.1	−	11055.8i	0.655641	−	0.421355i	−0.170083	−	0.985430i	$-0.554403\pi$
$883$	17203.1	−	11055.8i	0.655641	−	0.421355i	0.825724	+	0.564075i	$0.190767\pi$
$884$	−4596.46	+	1840.15i	−0.174882	+	0.0700123i
$885$	8371.90	−	5844.31i	0.317987	−	0.221982i
$886$	26592.3	+	37343.7i	1.00834	+	1.41601i
$887$	−31788.8	−	24999.0i	−1.20334	−	0.946316i	−0.203873	−	0.978997i	$-0.565353\pi$
$887$	−31788.8	−	24999.0i	−1.20334	−	0.946316i	−0.999466	+	0.0326808i	$0.989596\pi$
$888$	−19379.8	+	36743.2i	−0.732367	+	1.38854i
$889$	4644.31	+	19144.1i	0.175214	+	0.722242i
$890$	4371.13	+	30401.9i	0.164630	+	1.14503i
$891$	−41156.8	+	6345.25i	−1.54748	+	0.238579i
$892$	−1451.75	−	932.986i	−0.0544936	−	0.0350209i
$893$	−968.958	−	186.751i	−0.0363101	−	0.00699820i
$894$	−6554.85	+	6746.97i	−0.245220	+	0.252408i
$895$	47337.8	+	4520.21i	1.76796	+	0.168820i
$896$	−16324.9	+	28275.5i	−0.608679	+	1.05426i
$897$	−38802.1	+	21609.1i	−1.44433	+	0.804354i
$898$	−12093.3	−	20946.3i	−0.449399	−	0.778382i
$899$	1674.17	+	3665.92i	0.0621097	+	0.136001i
$900$	−741.535	+	2824.82i	−0.0274643	+	0.104623i
$901$	22769.9	−	26277.9i	0.841926	−	0.971635i
$902$	353.419	−	7419.18i	0.0130461	−	0.273871i
$903$	29791.1	−	25330.0i	1.09788	−	0.933475i
$904$	−12588.9	−	5039.83i	−0.463164	−	0.185423i
$905$	34505.5	−	32900.9i	1.26741	−	1.20847i
$906$	−5082.71	−	8073.99i	−0.186382	−	0.296071i
$907$	−1835.35	+	734.761i	−0.0671903	+	0.0268990i	−0.405014	−	0.914310i	$-0.632733\pi$
$907$	−1835.35	+	734.761i	−0.0671903	+	0.0268990i	0.337824	+	0.941209i	$0.390309\pi$
$908$	1192.83	−	2611.94i	0.0435963	−	0.0954627i
$909$	−8587.68	+	17909.6i	−0.313350	+	0.653492i
$910$	−11858.9	+	82480.4i	−0.431998	+	3.00461i
$911$	−26992.6	−	13915.6i	−0.981672	−	0.506087i	−0.108815	−	0.994062i	$-0.534706\pi$
$911$	−26992.6	−	13915.6i	−0.981672	−	0.506087i	−0.872858	+	0.487975i	$0.837736\pi$
$912$	−1676.81	−	1791.86i	−0.0608822	−	0.0650597i
$913$	−23264.4	−	9313.67i	−0.843307	−	0.337609i
$914$	−23382.7	+	4506.64i	−0.846204	+	0.163092i
$915$	21073.5	+	1201.60i	0.761388	+	0.0434139i
$916$	−524.532	−	101.095i	−0.0189203	−	0.00364659i
$917$	3931.78	−	1154.47i	0.141591	−	0.0415748i
$918$	37163.5	+	28068.9i	1.33614	+	1.00916i
$919$	38977.4			1.39907			0.699536	−	0.714597i	$-0.253390\pi$
$919$	38977.4			1.39907			0.699536	+	0.714597i	$0.253390\pi$
$920$	36097.3	−	22887.8i	1.29358	−	0.820204i
$921$	−7701.19	+	4350.71i	−0.275530	+	0.155658i
$922$	13395.7	+	1279.13i	0.478486	+	0.0456898i
$923$	−2202.46	+	9078.68i	−0.0785428	+	0.323758i
$924$	−3271.06	+	1097.96i	−0.116461	+	0.0390911i
$925$	3356.83	−	70468.6i	0.119321	−	2.50486i
$926$	−12510.7	−	14438.1i	−0.443982	−	0.512382i
$927$	−11150.1	+	8435.68i	−0.395057	+	0.298882i
$928$	−540.039	−	158.570i	−0.0191031	−	0.00560916i
$929$	4137.19	+	2132.87i	0.146111	+	0.0753253i	0.529731	−	0.848165i	$-0.322293\pi$
$929$	4137.19	+	2132.87i	0.146111	+	0.0753253i	−0.383621	+	0.923491i	$0.625323\pi$
$930$	−48755.3	−	7476.27i	−1.71908	−	0.263609i
$931$	−333.222	−	467.945i	−0.0117303	−	0.0164729i
$932$	−1615.52	−	2268.68i	−0.0567792	−	0.0797352i
$933$	8415.40	+	1290.44i	0.295292	+	0.0452809i
$934$	−24106.9	−	12428.0i	−0.844542	−	0.435392i
$935$	−110708.	−	32506.9i	−3.87224	−	1.13699i
$936$	36310.2	−	27470.7i	1.26799	−	0.959302i
$937$	18101.5	+	20890.2i	0.631109	+	0.728339i	0.977777	−	0.209649i	$-0.0672322\pi$
$937$	18101.5	+	20890.2i	0.631109	+	0.728339i	−0.346667	+	0.937988i	$0.612687\pi$
$938$	747.478	−	15691.5i	0.0260192	−	0.546211i
$939$	−22714.4	+	7624.28i	−0.789411	+	0.264972i
$940$	336.868	−	1388.59i	0.0116887	−	0.0481816i
$941$	−12043.3	−	1150.00i	−0.417218	−	0.0398395i	−0.115663	−	0.993288i	$-0.536899\pi$
$941$	−12043.3	−	1150.00i	−0.417218	−	0.0398395i	−0.301554	+	0.953449i	$0.597505\pi$
$942$	32590.4	−	18411.6i	1.12723	−	0.636818i
$943$	−3232.20	+	3684.42i	−0.111617	+	0.127233i
$944$	−7524.86			−0.259442
$945$	47479.7	−	20092.3i	1.63441	−	0.691643i
$946$	−58484.4	+	17172.6i	−2.01003	+	0.590199i
$947$	−32761.6	−	6314.29i	−1.12419	−	0.216670i	−0.406920	−	0.913464i	$-0.633397\pi$
$947$	−32761.6	−	6314.29i	−1.12419	−	0.216670i	−0.717272	+	0.696793i	$0.754609\pi$
$948$	134.470	+	7.66738i	0.00460693	+	0.000262685i
$949$	−45553.1	+	8779.64i	−1.55818	+	0.300315i
$950$	3613.51	+	1446.63i	0.123408	+	0.0494052i
$951$	24384.4	+	26057.5i	0.831460	+	0.888511i
$952$	−45285.9	−	23346.5i	−1.54173	−	0.794815i
$953$	−1000.41	+	6958.03i	−0.0340048	+	0.236509i	−0.999735	−	0.0230412i	$-0.992665\pi$
$953$	−1000.41	+	6958.03i	−0.0340048	+	0.236509i	0.965730	+	0.259550i	$0.0835742\pi$
$954$	10470.9	−	21837.0i	0.355353	−	0.741088i
$955$	13323.8	−	29175.1i	0.451464	−	0.988569i
$956$	2856.58	−	1143.60i	0.0966406	−	0.0386891i
$957$	3498.04	+	5556.71i	0.118156	+	0.187694i
$958$	19929.3	−	19002.5i	0.672115	−	0.640860i
$959$	27248.4	+	10908.6i	0.917514	+	0.367317i
$960$	−33203.1	+	28231.0i	−1.11628	+	0.949117i
$961$	161.766	−	3395.89i	0.00543004	−	0.113991i
$962$	54550.5	−	62954.6i	1.82825	−	2.10992i
$963$	−12479.9	+	47541.2i	−0.417611	+	1.59086i
$964$	−325.958	−	713.747i	−0.0108904	−	0.0238467i
$965$	−17302.0	−	29967.9i	−0.577171	−	0.999690i
$966$	32532.4	+	11826.2i	1.08355	+	0.393895i
$967$	4113.14	−	7124.17i	0.136784	−	0.236916i	−0.789494	−	0.613759i	$-0.789657\pi$
$967$	4113.14	−	7124.17i	0.136784	−	0.236916i	0.926277	+	0.376842i	$0.122990\pi$
$968$	−41856.3	−	3996.79i	−1.38979	−	0.132708i
$969$	2844.85	−	2928.23i	0.0943135	−	0.0970777i
$970$	−14928.3	−	2877.19i	−0.494142	−	0.0952380i
$971$	−21839.7	−	14035.5i	−0.721802	−	0.463874i	0.127461	−	0.991844i	$-0.459317\pi$
$971$	−21839.7	−	14035.5i	−0.721802	−	0.463874i	−0.849263	+	0.527969i	$0.822954\pi$
$972$	1981.39	+	791.365i	0.0653838	+	0.0261142i
$973$	−1340.76	−	9325.19i	−0.0441755	−	0.307248i
$974$	1163.47	+	4795.91i	0.0382753	+	0.157773i
$975$	−36074.0	+	68394.7i	−1.18492	+	2.24655i
$976$	−12228.3	−	9616.44i	−0.401044	−	0.315384i
$977$	5747.99	+	8071.92i	0.188224	+	0.264323i	0.897895	−	0.440210i	$-0.145096\pi$
$977$	5747.99	+	8071.92i	0.188224	+	0.264323i	−0.709671	+	0.704533i	$0.751157\pi$
$978$	−32295.1	+	22544.8i	−1.05591	+	0.737120i
$979$	−31260.8	+	12515.0i	−1.02053	+	0.408559i
$980$	699.771	−	449.716i	0.0228096	−	0.0146588i
$981$	37615.2	−	34545.4i	1.22422	−	1.12431i
$982$	−718.470	−	4997.07i	−0.0233476	−	0.162386i
$983$	−8642.61	+	24971.2i	−0.280424	+	0.810231i	0.713549	+	0.700605i	$0.247086\pi$
$983$	−8642.61	+	24971.2i	−0.280424	+	0.810231i	−0.993973	+	0.109626i	$0.965035\pi$
$984$	2755.92	−	4201.32i	0.0892840	−	0.136111i
$985$	23561.8	+	68077.4i	0.762174	+	2.20216i
$986$	1731.25	−	7136.31i	0.0559171	−	0.230493i
$987$	−13956.9	+	6216.72i	−0.450104	+	0.200487i
$988$	151.148	+	261.796i	0.00486706	+	0.00842999i
$989$	37248.0	+	15176.7i	1.19759	+	0.487957i
$990$	−80349.1	−	1503.97i	−2.57946	−	0.0482820i
$991$	−3213.56	−	7036.71i	−0.103009	−	0.225558i	0.851109	−	0.524989i	$-0.175931\pi$
$991$	−3213.56	−	7036.71i	−0.103009	−	0.225558i	−0.954118	+	0.299431i	$0.903203\pi$
$992$	3354.76	+	3198.76i	0.107373	+	0.102380i
$993$	41804.6	−	14032.1i	1.33598	−	0.448433i
$994$	6471.66	−	3336.37i	0.206508	−	0.106462i
$995$	−34360.0	+	6622.35i	−1.09476	+	0.210998i
$996$	784.188	+	1016.61i	0.0249477	+	0.0323420i
$997$	3139.62	+	12941.7i	0.0997320	+	0.411101i	0.999691	−	0.0248746i	$-0.00791865\pi$
$997$	3139.62	+	12941.7i	0.0997320	+	0.411101i	−0.899959	+	0.435975i	$0.856403\pi$
$998$	40057.1	−	25743.2i	1.27053	−	0.816519i
$999$	−50788.4	−	8763.83i	−1.60848	−	0.277553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.19	✓	1400
9.7	even	3	inner	207.4.m.a.142.52	yes	1400
23.6	even	11	inner	207.4.m.a.121.52	yes	1400
207.52	even	33	inner	207.4.m.a.52.19	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.19	✓	1400	1.1	even	1	trivial
207.4.m.a.52.19	yes	1400	207.52	even	33	inner
207.4.m.a.121.52	yes	1400	23.6	even	11	inner
207.4.m.a.142.52	yes	1400	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	207.m (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69742 + 2.38370i) q^{2} +(3.62079 - 3.72691i) q^{3} +(-0.184220 - 0.532269i) q^{4} +(-15.8263 + 8.15904i) q^{5} +(2.73782 + 14.9570i) q^{6} +(16.2228 - 12.7578i) q^{7} +(-20.8807 - 6.13112i) q^{8} +(-0.779765 - 26.9887i) q^{9} +(7.41529 - 51.5745i) q^{10} +(56.8649 - 5.42994i) q^{11} +(-2.65074 - 1.24066i) q^{12} +(-60.9105 - 47.9006i) q^{13} +(2.87366 + 60.3256i) q^{14} +(-26.8958 + 88.5255i) q^{15} +(53.6000 - 42.1515i) q^{16} +(74.2870 + 85.7318i) q^{17} +(65.6565 + 43.9526i) q^{18} +(4.53566 - 5.23444i) q^{19} +(7.25834 + 6.92081i) q^{20} +(11.1923 - 106.654i) q^{21} +(-83.5804 + 144.765i) q^{22} +(102.651 - 40.3693i) q^{23} +(-98.4546 + 55.6210i) q^{24} +(111.396 - 156.433i) q^{25} +(217.571 - 63.8847i) q^{26} +(-103.408 - 94.8144i) q^{27} +(-9.77915 - 6.28468i) q^{28} +(-7.23513 + 20.9045i) q^{29} +(-165.364 - 214.377i) q^{30} +(131.852 - 125.721i) q^{31} +(1.21064 + 25.4145i) q^{32} +(185.659 - 231.591i) q^{33} +(-330.455 + 31.5546i) q^{34} +(-152.657 + 334.272i) q^{35} +(-14.2216 + 5.38691i) q^{36} +(309.042 - 198.609i) q^{37} +(4.77837 + 19.6967i) q^{38} +(-399.066 + 53.5704i) q^{39} +(380.488 - 73.3331i) q^{40} +(-39.4943 + 20.3607i) q^{41} +(235.233 + 207.717i) q^{42} +(263.902 + 251.630i) q^{43} +(-13.3658 - 29.2671i) q^{44} +(232.543 + 420.771i) q^{45} +(-78.0148 + 313.214i) q^{46} +(-71.2366 - 123.385i) q^{47} +(36.9793 - 352.384i) q^{48} +(19.5542 - 80.6034i) q^{49} +(183.804 + 531.067i) q^{50} +(588.493 + 33.5555i) q^{51} +(-14.2751 + 41.2451i) q^{52} +(-43.6213 - 303.393i) q^{53} +(401.536 - 85.5532i) q^{54} +(-855.659 + 549.899i) q^{55} +(-416.963 + 166.927i) q^{56} +(-3.08560 - 35.8568i) q^{57} +(-37.5490 - 52.7302i) q^{58} +(-86.7437 - 68.2160i) q^{59} +(52.0742 - 1.99239i) q^{60} +(-53.7861 - 221.709i) q^{61} +(75.8714 + 527.697i) q^{62} +(-356.966 - 427.886i) q^{63} +(396.277 + 254.672i) q^{64} +(1354.81 + 261.119i) q^{65} +(236.901 + 835.662i) q^{66} +(-258.935 - 24.7253i) q^{67} +(31.9472 - 55.3342i) q^{68} +(221.227 - 528.742i) q^{69} +(-537.679 - 931.287i) q^{70} +(-50.0821 - 109.664i) q^{71} +(-149.189 + 568.324i) q^{72} +(392.054 - 452.455i) q^{73} +(-51.1506 + 1073.78i) q^{74} +(-179.673 - 981.575i) q^{75} +(-3.62169 - 1.44991i) q^{76} +(853.236 - 813.559i) q^{77} +(549.687 - 1042.18i) q^{78} +(-42.7236 + 17.1040i) q^{79} +(-504.375 + 1104.43i) q^{80} +(-727.784 + 42.0897i) q^{81} +(18.5047 - 128.703i) q^{82} +(-389.922 - 201.019i) q^{83} +(-58.8307 + 13.6905i) q^{84} +(-1875.18 - 750.709i) q^{85} +(-1047.76 + 201.940i) q^{86} +(51.7125 + 102.656i) q^{87} +(-1220.67 - 235.265i) q^{88} +(-565.597 + 166.074i) q^{89} +(-1397.71 - 159.913i) q^{90} -1599.25 q^{91} +(-40.3978 - 47.2014i) q^{92} +(8.85850 - 946.611i) q^{93} +(415.032 + 39.6307i) q^{94} +(-29.0750 + 119.849i) q^{95} +(99.1013 + 87.5087i) q^{96} +(13.8833 - 291.446i) q^{97} +(158.942 + 183.429i) q^{98} +(-190.888 - 1530.48i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1400 q - 9 q^{2} - 14 q^{3} + 263 q^{4} + 19 q^{5} - 35 q^{6} - 9 q^{7} - 74 q^{8} - 78 q^{9} - 68 q^{10} + 79 q^{11} + 54 q^{12} - 9 q^{13} + 159 q^{14} - 868 q^{15} + 1031 q^{16} - 308 q^{17} - 87 q^{18}+ \cdots + 7484 q^{99}+O(q^{100}) \) 1400 * q - 9 * q^2 - 14 * q^3 + 263 * q^4 + 19 * q^5 - 35 * q^6 - 9 * q^7 - 74 * q^8 - 78 * q^9 - 68 * q^10 + 79 * q^11 + 54 * q^12 - 9 * q^13 + 159 * q^14 - 868 * q^15 + 1031 * q^16 - 308 * q^17 - 87 * q^18 - 36 * q^19 + 119 * q^20 - 660 * q^21 - 52 * q^22 - 116 * q^23 + 2420 * q^24 + 1397 * q^25 + 432 * q^26 + 274 * q^27 - 324 * q^28 - 45 * q^29 + 768 * q^30 - 45 * q^31 + 111 * q^32 - 1664 * q^33 + 403 * q^34 - 536 * q^35 - 121 * q^36 - 180 * q^37 - 117 * q^38 - 46 * q^39 - 473 * q^40 - 333 * q^41 - 332 * q^42 - 9 * q^43 - 1908 * q^44 + 1762 * q^45 + 484 * q^46 + 216 * q^47 + 1072 * q^48 + 4615 * q^49 - 105 * q^50 + 1298 * q^51 - 708 * q^52 - 1380 * q^53 + 4116 * q^54 - 1328 * q^55 - 3971 * q^56 + 2154 * q^57 - 338 * q^58 + 1917 * q^59 + 154 * q^60 + 27 * q^61 - 3854 * q^62 - 4850 * q^63 - 5854 * q^64 + 3363 * q^65 - 2017 * q^66 + 603 * q^67 - 18454 * q^68 - 4653 * q^69 + 542 * q^70 - 5296 * q^71 - 8044 * q^72 - 36 * q^73 + 3243 * q^74 + 5140 * q^75 - 1029 * q^76 - 1661 * q^77 + 14687 * q^78 - 9 * q^79 + 10312 * q^80 - 294 * q^81 - 770 * q^82 - 2735 * q^83 + 2298 * q^84 + 241 * q^85 + 10507 * q^86 - 10268 * q^87 + 2183 * q^88 - 2980 * q^89 + 33928 * q^90 - 1452 * q^91 - 1973 * q^92 - 11406 * q^93 + 2034 * q^94 - 3339 * q^95 - 4446 * q^96 - 5193 * q^97 + 14820 * q^98 + 7484 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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