LMFDB - Embedded newform 207.4.m.a.4.3

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			4.3
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.09157 + 4.34150i) q^{2} +(-4.81737 - 1.94756i) q^{3} +(-6.67428 - 19.2841i) q^{4} +(6.06640 - 3.12745i) q^{5} +(23.3485 - 14.8936i) q^{6} +(-10.1357 + 7.97080i) q^{7} +(63.4448 + 18.6291i) q^{8} +(19.4141 + 18.7642i) q^{9} +(-5.17688 + 36.0060i) q^{10} +(2.73664 - 0.261318i) q^{11} +(-5.40435 + 105.897i) q^{12} +(26.7276 + 21.0188i) q^{13} +(-3.27003 - 68.6464i) q^{14} +(-35.3150 + 3.25140i) q^{15} +(-148.698 + 116.937i) q^{16} +(-26.1804 - 30.2138i) q^{17} +(-141.485 + 26.2753i) q^{18} +(-8.51232 + 9.82374i) q^{19} +(-100.799 - 96.1114i) q^{20} +(64.3510 - 18.6584i) q^{21} +(-7.32600 + 12.6890i) q^{22} +(72.1943 - 83.3966i) q^{23} +(-269.356 - 213.305i) q^{24} +(-45.4868 + 63.8773i) q^{25} +(-173.883 + 51.0568i) q^{26} +(-56.9803 - 128.204i) q^{27} +(221.358 + 142.258i) q^{28} +(1.38007 - 3.98744i) q^{29} +(95.0626 - 163.372i) q^{30} +(-179.527 + 171.179i) q^{31} +(-22.8035 - 478.704i) q^{32} +(-13.6923 - 4.07090i) q^{33} +(212.112 - 20.2542i) q^{34} +(-36.5589 + 80.0529i) q^{35} +(232.275 - 499.619i) q^{36} +(338.967 - 217.841i) q^{37} +(-16.3333 - 67.3270i) q^{38} +(-87.8214 - 153.309i) q^{39} +(443.143 - 85.4088i) q^{40} +(-366.789 + 189.093i) q^{41} +(-117.940 + 337.063i) q^{42} +(-170.959 - 163.009i) q^{43} +(-23.3044 - 51.0295i) q^{44} +(176.457 + 53.1147i) q^{45} +(138.873 + 571.257i) q^{46} +(-85.9184 - 148.815i) q^{47} +(944.074 - 273.732i) q^{48} +(-41.6666 + 171.752i) q^{49} +(-136.698 - 394.962i) q^{50} +(67.2775 + 196.539i) q^{51} +(226.941 - 655.703i) q^{52} +(-25.7655 - 179.203i) q^{53} +(732.756 + 148.971i) q^{54} +(15.7843 - 10.1440i) q^{55} +(-791.546 + 316.887i) q^{56} +(60.1392 - 30.7463i) q^{57} +(13.0449 + 18.3190i) q^{58} +(-154.661 - 121.627i) q^{59} +(298.402 + 659.315i) q^{60} +(-67.5119 - 278.288i) q^{61} +(-188.152 - 1308.63i) q^{62} +(-346.340 - 35.4426i) q^{63} +(875.670 + 562.759i) q^{64} +(227.876 + 43.9194i) q^{65} +(60.0046 - 46.8598i) q^{66} +(-1057.58 - 100.987i) q^{67} +(-407.909 + 706.520i) q^{68} +(-510.206 + 261.149i) q^{69} +(-234.525 - 406.210i) q^{70} +(-312.431 - 684.129i) q^{71} +(882.161 + 1552.16i) q^{72} +(-529.976 + 611.625i) q^{73} +(-102.184 + 2145.10i) q^{74} +(343.531 - 219.132i) q^{75} +(246.255 + 98.5857i) q^{76} +(-25.6549 + 24.4619i) q^{77} +(937.096 + 92.6885i) q^{78} +(-959.966 + 384.313i) q^{79} +(-536.345 + 1174.43i) q^{80} +(24.8107 + 728.578i) q^{81} +(313.007 - 2177.01i) q^{82} +(-449.397 - 231.680i) q^{83} +(-789.307 - 1116.42i) q^{84} +(-253.313 - 101.411i) q^{85} +(1236.23 - 238.264i) q^{86} +(-14.4140 + 16.5212i) q^{87} +(178.494 + 34.4019i) q^{88} +(-32.8287 + 9.63938i) q^{89} +(-776.127 + 601.882i) q^{90} -438.440 q^{91} +(-2090.07 - 835.587i) q^{92} +(1198.23 - 474.992i) q^{93} +(911.702 + 87.0570i) q^{94} +(-20.9159 + 86.2166i) q^{95} +(-822.450 + 2350.50i) q^{96} +(-23.6792 + 497.087i) q^{97} +(-616.847 - 711.879i) q^{98} +(58.0327 + 46.2776i) 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 $

$2$	−3.09157	+	4.34150i	−1.09303	+	1.53495i	−0.273543	+	0.961860i	$0.588196\pi$
$2$	−3.09157	+	4.34150i	−1.09303	+	1.53495i	−0.819491	+	0.573092i	$0.805744\pi$
$3$	−4.81737	−	1.94756i	−0.927103	−	0.374807i
$3$	−4.81737	−	1.94756i	−0.927103	−	0.374807i
$4$	−6.67428	−	19.2841i	−0.834285	−	2.41051i
$5$	6.06640	−	3.12745i	0.542595	−	0.279727i	−0.165062	−	0.986283i	$-0.552782\pi$
$5$	6.06640	−	3.12745i	0.542595	−	0.279727i	0.707657	+	0.706556i	$0.249752\pi$
$6$	23.3485	−	14.8936i	1.58867	−	1.01338i
$7$	−10.1357	+	7.97080i	−0.547276	+	0.430383i	−0.853132	−	0.521695i	$-0.825300\pi$
$7$	−10.1357	+	7.97080i	−0.547276	+	0.430383i	0.305856	+	0.952078i	$0.401057\pi$
$8$	63.4448	+	18.6291i	2.80389	+	0.823296i
$9$	19.4141	+	18.7642i	0.719039	+	0.694970i
$10$	−5.17688	+	36.0060i	−0.163707	+	1.13861i
$11$	2.73664	−	0.261318i	0.0750117	−	0.00716275i	−0.0574827	−	0.998347i	$-0.518307\pi$
$11$	2.73664	−	0.261318i	0.0750117	−	0.00716275i	0.132494	+	0.991184i	$0.457701\pi$
$12$	−5.40435	+	105.897i	−0.130008	+	2.54749i
$13$	26.7276	+	21.0188i	0.570224	+	0.448429i	0.861175	−	0.508309i	$-0.169729\pi$
$13$	26.7276	+	21.0188i	0.570224	+	0.448429i	−0.290951	+	0.956738i	$0.593972\pi$
$14$	−3.27003	−	68.6464i	−0.0624252	−	1.31047i
$15$	−35.3150	+	3.25140i	−0.607886	+	0.0559673i
$16$	−148.698	+	116.937i	−2.32340	+	1.82714i
$17$	−26.1804	−	30.2138i	−0.373510	−	0.431054i	0.537610	−	0.843193i	$-0.319327\pi$
$17$	−26.1804	−	30.2138i	−0.373510	−	0.431054i	−0.911121	+	0.412139i	$0.864782\pi$
$18$	−141.485	+	26.2753i	−1.85268	+	0.344064i
$19$	−8.51232	+	9.82374i	−0.102782	+	0.118617i	−0.804810	−	0.593533i	$-0.797733\pi$
$19$	−8.51232	+	9.82374i	−0.102782	+	0.118617i	0.702028	+	0.712150i	$0.252278\pi$
$20$	−100.799	−	96.1114i	−1.12696	−	1.07456i
$21$	64.3510	−	18.6584i	0.668692	−	0.193886i
$22$	−7.32600	+	12.6890i	−0.0709959	+	0.122968i
$23$	72.1943	−	83.3966i	0.654502	−	0.756060i
$23$	72.1943	−	83.3966i	0.654502	−	0.756060i
$24$	−269.356	−	213.305i	−2.29092	−	1.81420i
$25$	−45.4868	+	63.8773i	−0.363895	+	0.511018i
$26$	−173.883	+	51.0568i	−1.31159	+	0.385118i
$27$	−56.9803	−	128.204i	−0.406143	−	0.913809i
$28$	221.358	+	142.258i	1.49403	+	0.960152i
$29$	1.38007	−	3.98744i	0.00883696	−	0.0255327i	−0.940496	−	0.339804i	$-0.889639\pi$
$29$	1.38007	−	3.98744i	0.00883696	−	0.0255327i	0.949333	+	0.314272i	$0.101760\pi$
$30$	95.0626	−	163.372i	0.578533	−	0.994249i
$31$	−179.527	+	171.179i	−1.04013	+	0.991762i	−0.999972	−	0.00743186i	$-0.997634\pi$
$31$	−179.527	+	171.179i	−1.04013	+	0.991762i	−0.0401572	+	0.999193i	$0.512786\pi$
$32$	−22.8035	−	478.704i	−0.125973	−	2.64449i
$33$	−13.6923	−	4.07090i	−0.0722282	−	0.0214743i
$34$	212.112	−	20.2542i	1.06991	−	0.102164i
$35$	−36.5589	+	80.0529i	−0.176560	+	0.386612i
$36$	232.275	−	499.619i	1.07535	−	2.31305i
$37$	338.967	−	217.841i	1.50610	−	0.967914i	0.512059	−	0.858951i	$-0.328883\pi$
$37$	338.967	−	217.841i	1.50610	−	0.967914i	0.994046	−	0.108964i	$-0.0347533\pi$
$38$	−16.3333	−	67.3270i	−0.0697268	−	0.287418i
$39$	−87.8214	−	153.309i	−0.360581	−	0.629464i
$40$	443.143	−	85.4088i	1.75168	−	0.337608i
$41$	−366.789	+	189.093i	−1.39714	+	0.720278i	−0.981894	−	0.189430i	$-0.939336\pi$
$41$	−366.789	+	189.093i	−1.39714	+	0.720278i	−0.415250	+	0.909708i	$0.636306\pi$
$42$	−117.940	+	337.063i	−0.433298	+	1.23833i
$43$	−170.959	−	163.009i	−0.606301	−	0.578107i	0.323473	−	0.946237i	$-0.395149\pi$
$43$	−170.959	−	163.009i	−0.606301	−	0.578107i	−0.929774	+	0.368131i	$0.879998\pi$
$44$	−23.3044	−	51.0295i	−0.0798470	−	0.174841i
$45$	176.457	+	53.1147i	0.584549	+	0.175953i
$46$	138.873	+	571.257i	0.445123	+	1.83103i
$47$	−85.9184	−	148.815i	−0.266649	−	0.461849i	0.701346	−	0.712821i	$-0.252583\pi$
$47$	−85.9184	−	148.815i	−0.266649	−	0.461849i	−0.967994	+	0.250973i	$0.919250\pi$
$48$	944.074	−	273.732i	2.83886	−	0.823122i
$49$	−41.6666	+	171.752i	−0.121477	+	0.500735i
$50$	−136.698	−	394.962i	−0.386639	−	1.11712i
$51$	67.2775	+	196.539i	0.184720	+	0.539626i
$52$	226.941	−	655.703i	0.605212	−	1.74865i
$53$	−25.7655	−	179.203i	−0.0667766	−	0.464441i	−0.995584	−	0.0938779i	$-0.970074\pi$
$53$	−25.7655	−	179.203i	−0.0667766	−	0.464441i	0.928807	−	0.370564i	$-0.120835\pi$
$54$	732.756	+	148.971i	1.84658	+	0.375415i
$55$	15.7843	−	10.1440i	0.0386974	−	0.0248693i
$56$	−791.546	+	316.887i	−1.88883	+	0.756175i
$57$	60.1392	−	30.7463i	0.139748	−	0.0714465i
$58$	13.0449	+	18.3190i	0.0295324	+	0.0414724i
$59$	−154.661	−	121.627i	−0.341273	−	0.268380i	0.432781	−	0.901499i	$-0.357532\pi$
$59$	−154.661	−	121.627i	−0.341273	−	0.268380i	−0.774055	+	0.633118i	$0.781775\pi$
$60$	298.402	+	659.315i	0.642060	+	1.41862i
$61$	−67.5119	−	278.288i	−0.141705	−	0.584117i	−0.997740	−	0.0671979i	$-0.978594\pi$
$61$	−67.5119	−	278.288i	−0.141705	−	0.584117i	0.856035	−	0.516919i	$-0.172921\pi$
$62$	−188.152	−	1308.63i	−0.385409	−	2.68058i
$63$	−346.340	−	35.4426i	−0.692616	−	0.0708785i
$64$	875.670	+	562.759i	1.71029	+	1.09914i
$65$	227.876	+	43.9194i	0.434839	+	0.0838083i
$66$	60.0046	−	46.8598i	0.111910	−	0.0873946i
$67$	−1057.58	−	100.987i	−1.92842	−	0.184142i	−0.940577	−	0.339579i	$-0.889715\pi$
$67$	−1057.58	−	100.987i	−1.92842	−	0.184142i	−0.987846	+	0.155437i	$0.950321\pi$
$68$	−407.909	+	706.520i	−0.727445	+	1.25997i
$69$	−510.206	+	261.149i	−0.890168	+	0.455633i
$70$	−234.525	−	406.210i	−0.400445	−	0.693591i
$71$	−312.431	−	684.129i	−0.522236	−	1.14354i	−0.968586	−	0.248679i	$-0.920004\pi$
$71$	−312.431	−	684.129i	−0.522236	−	1.14354i	0.446350	−	0.894858i	$-0.352724\pi$
$72$	882.161	+	1552.16i	1.44394	+	2.54060i
$73$	−529.976	+	611.625i	−0.849712	+	0.980620i	−0.999968	−	0.00802697i	$-0.997445\pi$
$73$	−529.976	+	611.625i	−0.849712	+	0.980620i	0.150256	+	0.988647i	$0.451990\pi$
$74$	−102.184	+	2145.10i	−0.160521	+	3.36976i
$75$	343.531	−	219.132i	0.528901	−	0.337376i
$76$	246.255	+	98.5857i	0.371676	+	0.148797i
$77$	−25.6549	+	24.4619i	−0.0379694	+	0.0362037i
$78$	937.096	+	92.6885i	1.36032	+	0.134550i
$79$	−959.966	+	384.313i	−1.36715	+	0.547323i	−0.935054	−	0.354505i	$-0.884649\pi$
$79$	−959.966	+	384.313i	−1.36715	+	0.547323i	−0.432094	+	0.901829i	$0.642225\pi$
$80$	−536.345	+	1174.43i	−0.749565	+	1.64132i
$81$	24.8107	+	728.578i	0.0340339	+	0.999421i
$82$	313.007	−	2177.01i	0.421534	−	2.93184i
$83$	−449.397	−	231.680i	−0.594310	−	0.306388i	0.134705	−	0.990886i	$-0.456991\pi$
$83$	−449.397	−	231.680i	−0.594310	−	0.306388i	−0.729015	+	0.684498i	$0.760022\pi$
$84$	−789.307	−	1116.42i	−1.02524	−	1.45013i
$85$	−253.313	−	101.411i	−0.323243	−	0.129407i
$86$	1236.23	−	238.264i	1.55007	−	0.298752i
$87$	−14.4140	+	16.5212i	−0.0177626	+	0.0203593i
$88$	178.494	+	34.4019i	0.216222	+	0.0416733i
$89$	−32.8287	+	9.63938i	−0.0390993	+	0.0114806i	−0.301224	−	0.953554i	$-0.597395\pi$
$89$	−32.8287	+	9.63938i	−0.0390993	+	0.0114806i	0.262124	+	0.965034i	$0.415577\pi$
$90$	−776.127	+	601.882i	−0.909011	+	0.704933i
$91$	−438.440			−0.505066
$92$	−2090.07	−	835.587i	−2.36853	−	0.946913i
$93$	1198.23	−	474.992i	1.33603	−	0.529617i
$94$	911.702	+	87.0570i	1.00037	+	0.0955239i
$95$	−20.9159	+	86.2166i	−0.0225887	+	0.0931119i
$96$	−822.450	+	2350.50i	−0.874385	+	2.49893i
$97$	−23.6792	+	497.087i	−0.0247861	+	0.520325i	0.951999	+	0.306102i	$0.0990250\pi$
$97$	−23.6792	+	497.087i	−0.0247861	+	0.520325i	−0.976785	+	0.214223i	$0.931278\pi$
$98$	−616.847	−	711.879i	−0.635826	−	0.733782i
$99$	58.0327	+	46.2776i	0.0589142	+	0.0469806i
$100$	1535.41	+	450.836i	1.53541	+	0.450836i
$101$	−524.675	−	270.489i	−0.516902	−	0.266482i	0.179976	−	0.983671i	$-0.442398\pi$
$101$	−524.675	−	270.489i	−0.516902	−	0.266482i	−0.696878	+	0.717189i	$0.745428\pi$
$102$	−1061.27	−	315.527i	−1.03021	−	0.306293i
$103$	712.013	+	999.882i	0.681133	+	0.956518i	0.999962	+	0.00870548i	$0.00277108\pi$
$103$	712.013	+	999.882i	0.681133	+	0.956518i	−0.318829	+	0.947812i	$0.603290\pi$
$104$	1304.17	+	1831.45i	1.22965	+	1.72681i
$105$	332.025	−	314.444i	0.308594	−	0.292253i
$106$	857.664	+	442.157i	0.785884	+	0.405151i
$107$	−74.0651	−	21.7475i	−0.0669172	−	0.0196487i	0.248103	−	0.968734i	$-0.420193\pi$
$107$	−74.0651	−	21.7475i	−0.0669172	−	0.0196487i	−0.315020	+	0.949085i	$0.602011\pi$
$108$	−2091.99	+	1954.48i	−1.86391	+	1.74139i
$109$	126.496	+	145.985i	0.111157	+	0.128282i	0.808601	−	0.588357i	$-0.200225\pi$
$109$	126.496	+	145.985i	0.111157	+	0.128282i	−0.697444	+	0.716639i	$0.745679\pi$
$110$	−4.75827	+	99.8883i	−0.00412439	+	0.0865816i
$111$	−2057.19	+	389.262i	−1.75909	+	0.332857i
$112$	575.072	−	2370.48i	0.485172	−	1.99990i
$113$	2306.17	+	220.213i	1.91988	+	0.183326i	0.985109	−	0.171929i	$-0.0549999\pi$
$113$	2306.17	+	220.213i	1.91988	+	0.183326i	0.934769	+	0.355255i	$0.115606\pi$
$114$	−52.4393	+	356.149i	−0.0430824	+	0.292600i
$115$	177.141	−	731.701i	0.143639	−	0.593317i
$116$	−86.1050			−0.0689194
$117$	124.490	+	909.583i	0.0983685	+	0.718726i
$118$	1006.19	−	295.443i	0.784974	−	0.230489i
$119$	506.184	+	97.5591i	0.389932	+	0.0751531i
$120$	−2301.12	−	451.600i	−1.75052	−	0.343544i
$121$	−1299.53	+	250.463i	−0.976353	+	0.188177i
$122$	1416.90	+	567.243i	1.05148	+	0.420949i
$123$	2135.23	−	196.588i	1.56526	−	0.144112i
$124$	4499.24	+	2319.52i	3.25841	+	1.67983i
$125$	−197.583	+	1374.22i	−0.141379	+	0.983310i
$126$	1224.61	−	1394.06i	0.865848	−	0.985659i
$127$	672.363	−	1472.27i	0.469784	−	1.02868i	−0.515363	−	0.856972i	$-0.672343\pi$
$127$	672.363	−	1472.27i	0.469784	−	1.02868i	0.985147	−	0.171711i	$-0.0549297\pi$
$128$	−1591.08	+	636.970i	−1.09869	+	0.439850i
$129$	506.102	+	1118.22i	0.345425	+	0.763210i
$130$	−895.169	+	853.542i	−0.603935	+	0.575851i
$131$	409.525	+	163.949i	0.273133	+	0.109346i	0.504185	−	0.863595i	$-0.331793\pi$
$131$	409.525	+	163.949i	0.273133	+	0.109346i	−0.231053	+	0.972941i	$0.574217\pi$
$132$	12.8830	+	291.214i	0.00849485	+	0.192022i
$133$	7.97522	−	167.420i	0.00519954	−	0.109152i
$134$	3708.02	−	4279.29i	2.39048	−	2.75876i
$135$	−746.616	−	599.534i	−0.475989	−	0.382220i
$136$	−1098.15	−	2404.62i	−0.692397	−	1.51614i
$137$	−1216.57	−	2107.16i	−0.758674	−	1.31406i	−0.943527	−	0.331295i	$-0.892514\pi$
$137$	−1216.57	−	2107.16i	−0.758674	−	1.31406i	0.184853	−	0.982766i	$-0.440819\pi$
$138$	443.556	−	3022.42i	0.273608	−	1.86439i
$139$	−1407.02	+	2437.04i	−0.858577	+	1.48710i	0.0147099	+	0.999892i	$0.495318\pi$
$139$	−1407.02	+	2437.04i	−0.858577	+	1.48710i	−0.873287	+	0.487207i	$0.838016\pi$
$140$	1787.75	+	170.710i	1.07923	+	0.103054i
$141$	124.075	+	884.227i	0.0741062	+	0.528123i
$142$	3936.05	+	758.611i	2.32610	+	0.448318i
$143$	78.6365	+	50.5366i	0.0459854	+	0.0295530i
$144$	−5081.06	−	519.968i	−2.94043	−	0.300907i
$145$	−4.09847	−	28.5055i	−0.00234731	−	0.0163259i
$146$	−1016.91	−	4191.77i	−0.576440	−	2.37612i
$147$	535.220	−	746.245i	0.300301	−	0.418702i
$148$	−6463.22	−	5082.73i	−3.58969	−	2.82296i
$149$	801.562	+	1125.64i	0.440715	+	0.618897i	0.973866	−	0.227123i	$-0.0729318\pi$
$149$	801.562	+	1125.64i	0.440715	+	0.618897i	−0.533152	+	0.846020i	$0.678992\pi$
$150$	−110.688	+	2168.90i	−0.0602508	+	1.18060i
$151$	−2056.15	+	823.159i	−1.10813	+	0.443628i	−0.852278	−	0.523089i	$-0.824780\pi$
$151$	−2056.15	+	823.159i	−1.10813	+	0.443628i	−0.255850	+	0.966717i	$0.582355\pi$
$152$	−723.069	+	464.688i	−0.385846	+	0.247968i
$153$	58.6696	−	1077.83i	0.0310010	−	0.569523i
$154$	−26.8874	−	187.006i	−0.0140692	−	0.0978531i
$155$	−553.731	+	1599.90i	−0.286947	+	0.829078i
$156$	−2370.28	+	2716.78i	−1.21650	+	1.39434i
$157$	−407.758	−	1178.14i	−0.207278	−	0.598890i	0.792664	−	0.609659i	$-0.208693\pi$
$157$	−407.758	−	1178.14i	−0.207278	−	0.598890i	−0.999942	+	0.0107685i	$0.996572\pi$
$158$	1299.31	−	5355.82i	0.654224	−	2.69675i
$159$	−224.886	+	913.465i	−0.112167	+	0.455613i
$160$	−1635.46	−	2832.69i	−0.808088	−	1.39965i
$161$	−67.0019	+	1420.73i	−0.0327981	+	0.695460i
$162$	−3239.82	−	2144.73i	−1.57126	−	1.04016i
$163$	34.6087	+	75.7824i	0.0166304	+	0.0364156i	0.917765	−	0.397124i	$-0.129992\pi$
$163$	34.6087	+	75.7824i	0.0166304	+	0.0364156i	−0.901135	+	0.433540i	$0.857264\pi$
$164$	6094.54	+	5811.13i	2.90185	+	2.76691i
$165$	−95.7948	+	18.1264i	−0.0451977	+	0.00855233i
$166$	2395.18	−	1234.80i	1.11989	−	0.577345i
$167$	877.302	−	169.086i	0.406513	−	0.0783490i	0.0181042	−	0.999836i	$-0.494237\pi$
$167$	877.302	−	169.086i	0.406513	−	0.0783490i	0.388409	+	0.921487i	$0.373025\pi$
$168$	4430.32	+	15.0182i	2.03456	+	0.00689692i
$169$	−245.388	−	1011.50i	−0.111692	−	0.460402i
$170$	1223.41	−	786.238i	0.551949	−	0.354716i
$171$	−349.593	+	30.9918i	−0.156339	+	0.0138597i
$172$	−2002.45	+	4384.74i	−0.887704	+	1.94380i
$173$	883.596	−	84.3732i	0.388315	−	0.0370796i	0.100927	−	0.994894i	$-0.467819\pi$
$173$	883.596	−	84.3732i	0.388315	−	0.0370796i	0.287388	+	0.957814i	$0.407213\pi$
$174$	−27.1648	−	113.655i	−0.0118354	−	0.0495182i
$175$	−48.1126	−	1010.01i	−0.0207827	−	0.436282i
$176$	−376.375	+	358.873i	−0.161195	+	0.153699i
$177$	508.183	+	887.131i	0.215805	+	0.376728i
$178$	59.6428	−	172.327i	0.0251147	−	0.0725642i
$179$	−3235.83	−	2079.54i	−1.35116	−	0.868336i	−0.353413	−	0.935467i	$-0.614979\pi$
$179$	−3235.83	−	2079.54i	−1.35116	−	0.868336i	−0.997744	+	0.0671310i	$0.978615\pi$
$180$	−153.460	−	3757.32i	−0.0635456	−	1.55586i
$181$	−1158.10	+	340.050i	−0.475586	+	0.139645i	−0.510737	−	0.859737i	$-0.670627\pi$
$181$	−1158.10	+	340.050i	−0.475586	+	0.139645i	0.0351501	+	0.999382i	$0.488809\pi$
$182$	1355.47	−	1903.49i	0.552054	−	0.775252i
$183$	−216.752	+	1472.10i	−0.0875560	+	0.594648i
$184$	6133.95	−	3946.16i	2.45761	−	1.58106i
$185$	1375.02	−	2381.61i	0.546453	−	0.946485i
$186$	−1642.23	+	6670.57i	−0.647387	+	2.62963i
$187$	−79.5418	−	75.8429i	−0.0311052	−	0.0296587i
$188$	−2296.31	+	2650.09i	−0.890830	+	1.02807i
$189$	1599.42	+	845.257i	0.615560	+	0.325309i
$190$	−309.646	−	357.351i	−0.118232	−	0.136447i
$191$	1058.40	−	832.332i	0.400957	−	0.315316i	−0.397237	−	0.917716i	$-0.630031\pi$
$191$	1058.40	−	832.332i	0.400957	−	0.315316i	0.798195	+	0.602400i	$0.205789\pi$
$192$	−3122.42	−	4416.44i	−1.17365	−	1.66005i
$193$	185.899	+	3902.51i	0.0693333	+	1.45549i	0.718864	+	0.695150i	$0.244662\pi$
$193$	185.899	+	3902.51i	0.0693333	+	1.45549i	−0.649531	+	0.760335i	$0.725035\pi$
$194$	−2084.90	−	1639.58i	−0.771582	−	0.606779i
$195$	−1012.23	−	655.377i	−0.371728	−	0.240680i
$196$	3590.18	−	342.820i	1.30837	−	0.124934i
$197$	−395.111	+	2748.06i	−0.142896	+	0.993864i	0.784592	+	0.620012i	$0.212872\pi$
$197$	−395.111	+	2748.06i	−0.142896	+	0.993864i	−0.927488	+	0.373852i	$0.878037\pi$
$198$	−380.326	+	108.879i	−0.136508	+	0.0390791i
$199$	−169.506	−	49.7713i	−0.0603816	−	0.0177296i	0.251402	−	0.967883i	$-0.419108\pi$
$199$	−169.506	−	49.7713i	−0.0603816	−	0.0177296i	−0.311784	+	0.950153i	$0.600926\pi$
$200$	−4075.88	+	3205.30i	−1.44104	+	1.13325i
$201$	4898.09	+	2546.19i	1.71883	+	0.893506i
$202$	2796.40	−	1441.64i	0.974028	−	0.502146i
$203$	17.7951	+	51.4157i	0.00615258	+	0.0177767i
$204$	3341.04	−	2609.14i	1.14666	−	0.895472i
$205$	−1633.71	+	2294.23i	−0.556602	+	0.781639i
$206$	−6542.22			−2.21271
$207$	2966.45	−	264.398i	0.996051	−	0.0887776i
$208$	−6432.22			−2.14420
$209$	−20.7281	+	29.1085i	−0.00686024	+	0.00963385i
$210$	338.678	+	2413.61i	0.111291	+	0.793119i
$211$	−622.318	−	1798.07i	−0.203043	−	0.586655i	0.796802	−	0.604241i	$-0.206523\pi$
$211$	−622.318	−	1798.07i	−0.203043	−	0.586655i	−0.999845	+	0.0175851i	$0.994402\pi$
$212$	−3283.79	+	1692.91i	−1.06383	+	0.548442i
$213$	172.716	+	3904.18i	0.0555602	+	1.25591i
$214$	323.394	−	254.320i	0.103303	−	0.0812380i
$215$	−1546.90	−	454.212i	−0.490688	−	0.144079i
$216$	−1226.78	−	9195.36i	−0.386444	−	2.89660i
$217$	455.201	−	3165.99i	0.142401	−	0.990421i
$218$	−1024.86	+	97.8626i	−0.318406	+	0.0304041i
$219$	3744.26	−	1914.26i	1.15531	−	0.590657i
$220$	−300.966	−	236.682i	−0.0922323	−	0.0725323i
$221$	−64.6811	−	1357.82i	−0.0196874	−	0.413290i
$222$	4669.95	−	10134.7i	1.41183	−	3.06395i
$223$	−1118.68	+	879.740i	−0.335930	+	0.264178i	−0.771847	−	0.635809i	$-0.780667\pi$
$223$	−1118.68	+	879.740i	−0.335930	+	0.264178i	0.435917	+	0.899987i	$0.356424\pi$
$224$	4046.78	+	4670.24i	1.20708	+	1.39305i
$225$	−2081.69	+	386.594i	−0.616797	+	0.114546i
$226$	−8085.74	+	9331.44i	−2.37989	+	2.74654i
$227$	−103.312	−	98.5082i	−0.0302074	−	0.0288027i	0.674825	−	0.737978i	$-0.264219\pi$
$227$	−103.312	−	98.5082i	−0.0302074	−	0.0288027i	−0.705032	+	0.709175i	$0.749068\pi$
$228$	−994.301	−	954.520i	−0.288812	−	0.277257i
$229$	3329.43	−	5766.74i	0.960763	−	1.66409i	0.240172	−	0.970730i	$-0.422796\pi$
$229$	3329.43	−	5766.74i	0.960763	−	1.66409i	0.720591	−	0.693360i	$-0.243870\pi$
$230$	2629.03	+	3031.16i	0.753711	+	0.868995i
$231$	171.230	−	67.8775i	0.0487710	−	0.0193334i
$232$	161.840	−	227.273i	0.0457989	−	0.0643155i
$233$	−3410.00	+	1001.27i	−0.958783	+	0.281524i	−0.723439	−	0.690388i	$-0.757440\pi$
$233$	−3410.00	+	1001.27i	−0.958783	+	0.281524i	−0.235344	+	0.971912i	$0.575622\pi$
$234$	−4333.82	−	2271.56i	−1.21073	−	0.634601i
$235$	−986.626	−	634.066i	−0.273874	−	0.176008i
$236$	−1313.21	+	3794.26i	−0.362214	+	1.04655i
$237$	5372.98	+	18.2138i	1.47263	+	0.00499203i
$238$	−1988.46	+	1895.99i	−0.541565	+	0.516381i
$239$	49.8419	+	1046.31i	0.0134896	+	0.283181i	0.995526	+	0.0944889i	$0.0301217\pi$
$239$	49.8419	+	1046.31i	0.0134896	+	0.283181i	−0.982036	+	0.188692i	$0.939575\pi$
$240$	4871.05	−	4613.11i	1.31010	−	1.24073i
$241$	5245.76	−	500.909i	1.40211	−	0.133886i	0.633571	−	0.773685i	$-0.281589\pi$
$241$	5245.76	−	500.909i	1.40211	−	0.133886i	0.768542	+	0.639799i	$0.220983\pi$
$242$	2930.19	−	6416.22i	0.778345	−	1.70434i
$243$	1299.42	−	3558.15i	0.343037	−	0.939322i
$244$	−4915.93	+	3159.28i	−1.28980	+	0.828901i
$245$	284.379	+	1172.23i	0.0741565	+	0.305677i
$246$	−5747.72	+	9877.86i	−1.48968	+	2.56012i
$247$	−433.997	+	83.6461i	−0.111800	+	0.0215477i
$248$	−14579.0	+	7515.97i	−3.73292	+	1.92446i
$249$	1713.70	+	1991.32i	0.436150	+	0.506805i
$250$	−5355.33	−	5106.29i	−1.35480	−	1.29180i
$251$	3020.58	+	6614.14i	0.759590	+	1.66327i	0.748324	+	0.663333i	$0.230859\pi$
$251$	3020.58	+	6614.14i	0.759590	+	1.66327i	0.0112655	+	0.999937i	$0.496414\pi$
$252$	1628.10	+	6915.41i	0.406986	+	1.72869i
$253$	175.777	−	247.092i	0.0436798	−	0.0614014i
$254$	4313.20	+	7470.68i	1.06549	+	1.84548i
$255$	1022.80	+	981.876i	0.251177	+	0.241127i
$256$	190.277	−	784.331i	0.0464543	−	0.191487i
$257$	−1280.70	−	3700.35i	−0.310849	−	0.898138i	−0.986907	−	0.161290i	$-0.948434\pi$
$257$	−1280.70	−	3700.35i	−0.310849	−	0.898138i	0.676058	−	0.736848i	$-0.263687\pi$
$258$	−6419.42	−	1259.83i	−1.54905	−	0.304005i
$259$	−1699.30	+	4909.81i	−0.407681	+	1.17792i
$260$	−673.961	−	4687.50i	−0.160759	−	1.11810i
$261$	101.614	−	51.5165i	0.0240986	−	0.0122176i
$262$	−1977.86	+	1271.09i	−0.466384	+	0.299727i
$263$	−2236.89	+	895.517i	−0.524459	+	0.209962i	−0.618757	−	0.785582i	$-0.712364\pi$
$263$	−2236.89	+	895.517i	−0.524459	+	0.209962i	0.0942980	+	0.995544i	$0.469939\pi$
$264$	−792.871	−	513.353i	−0.184840	−	0.119677i
$265$	−716.751	−	1006.54i	−0.166150	−	0.233325i
$266$	702.200	+	552.216i	0.161859	+	0.127288i
$267$	176.921	+	17.4993i	0.0405520	+	0.00401102i
$268$	5111.17	+	21068.5i	1.16498	+	4.80211i
$269$	−345.240	−	2401.20i	−0.0782515	−	0.544251i	−0.990805	−	0.135295i	$-0.956802\pi$
$269$	−345.240	−	2401.20i	−0.0782515	−	0.544251i	0.912554	−	0.408956i	$-0.134107\pi$
$270$	4911.09	−	1387.94i	1.10696	−	0.312841i
$271$	−1969.12	−	1265.48i	−0.441385	−	0.283661i	0.301013	−	0.953620i	$-0.402675\pi$
$271$	−1969.12	−	1265.48i	−0.441385	−	0.283661i	−0.742398	+	0.669959i	$0.766312\pi$
$272$	7426.08	+	1431.26i	1.65541	+	0.319055i
$273$	2112.13	+	853.886i	0.468248	+	0.189302i
$274$	12909.3	+	1232.69i	2.84628	+	0.271787i
$275$	−107.789	+	186.696i	−0.0236361	+	0.0409388i
$276$	8441.28	+	8095.86i	1.84096	+	1.76563i
$277$	−793.162	−	1373.80i	−0.172045	−	0.297991i	0.767090	−	0.641540i	$-0.221704\pi$
$277$	−793.162	−	1373.80i	−0.172045	−	0.297991i	−0.939135	+	0.343549i	$0.888371\pi$
$278$	−6230.48	−	13642.9i	−1.34417	−	2.94332i
$279$	−6697.38	−	45.4071i	−1.43714	−	0.00974356i
$280$	−3810.79	+	4397.88i	−0.813350	+	0.938656i
$281$	316.944	−	6653.46i	0.0672856	−	1.41250i	−0.672719	−	0.739898i	$-0.734874\pi$
$281$	316.944	−	6653.46i	0.0672856	−	1.41250i	0.740005	−	0.672602i	$-0.234823\pi$
$282$	−4222.46	−	2194.98i	−0.891644	−	0.463507i
$283$	−6723.26	−	2691.59i	−1.41221	−	0.565365i	−0.464811	−	0.885410i	$-0.653878\pi$
$283$	−6723.26	−	2691.59i	−1.41221	−	0.565365i	−0.947402	+	0.320045i	$0.896302\pi$
$284$	−11107.5	+	10591.0i	−2.32081	+	2.21289i
$285$	268.671	−	374.602i	0.0558411	−	0.0778579i
$286$	−462.515	+	185.163i	−0.0956261	+	0.0382829i
$287$	2210.44	−	4840.20i	0.454628	−	0.995497i
$288$	8539.78	−	9721.47i	1.74726	−	1.98904i
$289$	471.733	−	3280.98i	0.0960173	−	0.667815i
$290$	136.427	+	70.3331i	0.0276251	+	0.0142417i
$291$	1082.18	−	2348.53i	0.218001	−	0.473105i
$292$	15331.8	+	6137.94i	3.07270	+	1.23012i
$293$	9014.41	−	1737.38i	1.79736	−	0.346413i	0.822422	−	0.568878i	$-0.192622\pi$
$293$	9014.41	−	1737.38i	1.79736	−	0.346413i	0.974941	+	0.222465i	$0.0714102\pi$
$294$	1585.15	+	4630.73i	0.314449	+	0.918603i
$295$	−1318.62	−	254.142i	−0.260247	−	0.0501584i
$296$	25563.9	−	7506.23i	5.01983	−	1.47396i
$297$	−189.437	−	335.958i	−0.0370109	−	0.0656373i
$298$	−7365.03			−1.43169
$299$	3682.48	−	711.552i	0.712252	−	0.137626i
$300$	−6518.59	−	5162.13i	−1.25450	−	0.993453i
$301$	3032.09	+	289.530i	0.580621	+	0.0554426i
$302$	2782.99	−	11471.6i	0.530275	−	2.18582i
$303$	2000.76	+	2324.88i	0.379342	+	0.440795i
$304$	117.002	−	2456.17i	0.0220741	−	0.463392i
$305$	−1279.89	−	1477.07i	−0.240282	−	0.277300i
$306$	4498.00	+	3586.88i	0.840305	+	0.670093i
$307$	6867.10	+	2016.36i	1.27663	+	0.374853i	0.848660	−	0.528939i	$-0.177410\pi$
$307$	6867.10	+	2016.36i	1.27663	+	0.374853i	0.427972	+	0.903792i	$0.359228\pi$
$308$	642.952	+	331.465i	0.118947	+	0.0613213i
$309$	−1482.70	−	6203.49i	−0.272971	−	1.14208i
$310$	−5234.07	−	7350.22i	−0.958952	−	1.34666i
$311$	−880.098	−	1235.92i	−0.160469	−	0.225347i	0.726511	−	0.687154i	$-0.241140\pi$
$311$	−880.098	−	1235.92i	−0.160469	−	0.225347i	−0.886980	+	0.461808i	$0.847201\pi$
$312$	−2715.81	−	11362.7i	−0.492796	−	2.06181i
$313$	−3809.19	−	1963.77i	−0.687885	−	0.354630i	0.0785866	−	0.996907i	$-0.474959\pi$
$313$	−3809.19	−	1963.77i	−0.687885	−	0.354630i	−0.766472	+	0.642278i	$0.777990\pi$
$314$	6375.50	+	1872.02i	1.14583	+	0.336446i
$315$	−2211.89	+	868.153i	−0.395637	+	0.155285i
$316$	13818.2	+	15947.0i	2.45992	+	2.83890i
$317$	217.826	−	4572.74i	0.0385941	−	0.810190i	−0.893738	−	0.448588i	$-0.851927\pi$
$317$	217.826	−	4572.74i	0.0385941	−	0.810190i	0.932333	−	0.361602i	$-0.117770\pi$
$318$	−3270.56	−	3800.38i	−0.576742	−	0.670172i
$319$	2.73476	−	11.2728i	0.000479991	−	0.00197855i
$320$	7072.17	+	675.310i	1.23546	+	0.117972i
$321$	314.444	+	249.011i	0.0546747	+	0.0432974i
$322$	−5960.95	−	4683.17i	−1.03165	−	0.810505i
$323$	519.668			0.0895204
$324$	13884.3	−	5341.18i	2.38072	−	0.915841i
$325$	−2558.38	+	751.208i	−0.436657	+	0.128214i
$326$	−436.004	−	84.0329i	−0.0740737	−	0.0142765i
$327$	−325.066	−	949.620i	−0.0549731	−	0.160594i
$328$	−26793.5	+	5164.03i	−4.51044	+	0.869316i
$329$	2057.02	+	823.505i	0.344702	+	0.137998i
$330$	217.460	−	471.932i	0.0362752	−	0.0787242i
$331$	5669.94	+	2923.06i	0.941535	+	0.485395i	0.859444	−	0.511230i	$-0.170810\pi$
$331$	5669.94	+	2923.06i	0.941535	+	0.485395i	0.0820913	+	0.996625i	$0.473840\pi$
$332$	−1468.34	+	10212.5i	−0.242727	+	1.68821i
$333$	10668.3	+	2131.27i	1.75562	+	0.350729i
$334$	−1978.15	+	4331.55i	−0.324071	+	0.709616i
$335$	−6731.56	+	2694.91i	−1.09786	+	0.439518i
$336$	−7386.98	+	10299.5i	−1.19938	+	1.67227i
$337$	−8104.17	+	7727.31i	−1.30998	+	1.24906i	−0.361439	+	0.932396i	$0.617714\pi$
$337$	−8104.17	+	7727.31i	−1.30998	+	1.24906i	−0.948538	+	0.316664i	$0.897437\pi$
$338$	5150.08	+	2061.78i	0.828779	+	0.331793i
$339$	−10680.8	−	5552.24i	−1.71121	−	0.889547i
$340$	−264.939	+	5561.75i	−0.0422598	+	0.887142i
$341$	−446.569	+	515.369i	−0.0709182	+	0.0818439i
$342$	946.239	−	1613.57i	0.149610	−	0.255123i
$343$	−2783.97	−	6096.05i	−0.438252	−	0.959638i
$344$	−7809.73	−	13526.9i	−1.22405	−	2.12011i
$345$	−2278.38	+	3179.88i	−0.355548	+	0.496229i
$346$	−2365.39	+	4096.98i	−0.367527	+	0.636575i
$347$	−3915.25	−	373.861i	−0.605711	−	0.0578384i	−0.212306	−	0.977203i	$-0.568097\pi$
$347$	−3915.25	−	373.861i	−0.605711	−	0.0578384i	−0.393406	+	0.919365i	$0.628703\pi$
$348$	414.799	+	167.694i	0.0638954	+	0.0258315i
$349$	5441.56	+	1048.78i	0.834614	+	0.160859i	0.588617	−	0.808412i	$-0.299673\pi$
$349$	5441.56	+	1048.78i	0.834614	+	0.160859i	0.245997	+	0.969271i	$0.420885\pi$
$350$	4533.69	+	2913.62i	0.692388	+	0.444971i
$351$	1171.75	−	4624.24i	0.178186	−	0.703202i
$352$	−187.499	−	1304.08i	−0.0283912	−	0.197465i
$353$	1958.80	+	8074.30i	0.295345	+	1.21743i	0.905225	+	0.424933i	$0.139702\pi$
$353$	1958.80	+	8074.30i	0.295345	+	1.21743i	−0.609880	+	0.792494i	$0.708782\pi$
$354$	−5422.56	−	536.347i	−0.814141	−	0.0805269i
$355$	−4034.91	−	3173.09i	−0.603242	−	0.474394i
$356$	404.994	+	568.735i	0.0602940	+	0.0846711i
$357$	−2248.47	−	1455.80i	−0.333339	−	0.215824i
$358$	19032.1	−	7619.31i	2.80972	−	1.12484i
$359$	−3673.71	+	2360.95i	−0.540087	+	0.347093i	−0.782073	−	0.623187i	$-0.785837\pi$
$359$	−3673.71	+	2360.95i	−0.540087	+	0.347093i	0.241986	+	0.970280i	$0.422201\pi$
$360$	10205.8	+	6657.09i	1.49415	+	0.974609i
$361$	952.091	+	6621.94i	0.138809	+	0.965438i
$362$	2104.03	−	6079.19i	0.305484	−	0.882639i
$363$	6748.09	+	1324.33i	0.975710	+	0.191485i
$364$	2926.27	+	8454.90i	0.421369	+	1.21747i
$365$	−1302.22	+	5367.83i	−0.186744	+	0.769768i
$366$	−5721.01	−	5492.12i	−0.817055	−	0.784365i
$367$	1129.06	+	1955.60i	0.160590	+	0.278151i	0.935081	−	0.354435i	$-0.115327\pi$
$367$	1129.06	+	1955.60i	0.160590	+	0.278151i	−0.774490	+	0.632586i	$0.781994\pi$
$368$	−982.965	+	20843.1i	−0.139241	+	2.95250i
$369$	−10669.0	−	3211.44i	−1.50517	−	0.453065i
$370$	6088.79	+	13332.6i	0.855516	+	1.87332i
$371$	1689.54	+	1610.97i	0.236433	+	0.225438i
$372$	−17157.1	−	19936.5i	−2.39127	−	2.77865i
$373$	−3642.61	+	1877.90i	−0.505649	+	0.260680i	−0.692123	−	0.721780i	$-0.743324\pi$
$373$	−3642.61	+	1877.90i	−0.505649	+	0.260680i	0.186474	+	0.982460i	$0.440294\pi$
$374$	575.181	−	110.857i	0.0795238	−	0.0153269i
$375$	3628.20	−	6235.31i	0.499625	−	0.858640i
$376$	−2678.79	−	11042.1i	−0.367415	−	1.51450i
$377$	120.697	−	77.5674i	0.0164886	−	0.0105966i
$378$	−8614.41	+	4330.72i	−1.17216	+	0.589281i
$379$	4072.76	−	8918.10i	0.551988	−	1.20869i	−0.403859	−	0.914821i	$-0.632331\pi$
$379$	4072.76	−	8918.10i	0.551988	−	1.20869i	0.955847	−	0.293865i	$-0.0949415\pi$
$380$	1802.20	−	172.090i	0.243293	−	0.0232316i
$381$	−6106.35	+	5783.00i	−0.821096	+	0.777617i
$382$	341.465	+	7168.23i	0.0457353	+	0.960102i
$383$	−2458.21	+	2343.89i	−0.327959	+	0.312709i	−0.836112	−	0.548558i	$-0.815177\pi$
$383$	−2458.21	+	2343.89i	−0.327959	+	0.312709i	0.508153	+	0.861267i	$0.330328\pi$
$384$	8905.33	+	30.1880i	1.18346	+	0.00401178i
$385$	−79.1295	+	228.630i	−0.0104748	+	0.0302651i
$386$	−17517.5	−	11257.8i	−2.30988	−	1.48447i
$387$	−260.273	−	6372.56i	−0.0341872	−	0.837042i
$388$	9743.90	−	2861.07i	1.27493	−	0.374352i
$389$	−8058.17	+	11316.1i	−1.05030	+	1.47494i	−0.179207	+	0.983811i	$0.557353\pi$
$389$	−8058.17	+	11316.1i	−1.05030	+	1.47494i	−0.871090	+	0.491124i	$0.836586\pi$
$390$	5974.68	−	2368.43i	0.775743	−	0.307514i
$391$	−4409.80	+	2.09261i	−0.570366	+	0.000270659i
$392$	−5843.11	+	10120.6i	−0.752862	+	1.30399i
$393$	−1653.53	−	1587.38i	−0.212238	−	0.203747i
$394$	−10709.2	−	10211.2i	−1.36934	−	1.30567i
$395$	−4621.62	+	5333.64i	−0.588707	+	0.679404i
$396$	505.094	−	1427.98i	0.0640958	−	0.181208i
$397$	−4817.14	−	5559.27i	−0.608980	−	0.702801i	0.364595	−	0.931166i	$-0.381207\pi$
$397$	−4817.14	−	5559.27i	−0.608980	−	0.702801i	−0.973576	+	0.228365i	$0.926662\pi$
$398$	740.120	−	582.037i	0.0932132	−	0.0733037i
$399$	−364.480	+	790.993i	−0.0457314	+	0.0992461i
$400$	−705.845	−	14817.5i	−0.0882306	−	1.85219i
$401$	−3438.18	−	2703.82i	−0.428166	−	0.336714i	0.380708	−	0.924695i	$-0.375680\pi$
$401$	−3438.18	−	2703.82i	−0.428166	−	0.336714i	−0.808874	+	0.587982i	$0.799923\pi$
$402$	−26197.1	+	13393.3i	−3.25023	+	1.66169i
$403$	−8396.31	+	801.750i	−1.03784	+	0.0991018i
$404$	−1714.30	+	11923.2i	−0.211112	+	1.46832i
$405$	2429.10	+	4342.25i	0.298032	+	0.532761i
$406$	−278.236	−	81.6975i	−0.0340114	−	0.00998665i
$407$	870.706	−	684.731i	0.106043	−	0.0833928i
$408$	607.075	+	13722.7i	0.0736635	+	1.66513i
$409$	5635.73	−	2905.42i	0.681343	−	0.351256i	−0.0825618	−	0.996586i	$-0.526310\pi$
$409$	5635.73	−	2905.42i	0.681343	−	0.351256i	0.763904	+	0.645329i	$0.223280\pi$
$410$	−4909.66	−	14185.5i	−0.591392	−	1.70872i
$411$	1756.85	+	12520.3i	0.210849	+	1.50263i
$412$	14529.6	−	20404.0i	1.73744	−	2.43989i
$413$	2537.06			0.302277
$414$	−8023.10	+	13696.3i	−0.952449	+	1.62593i
$415$	−3450.79			−0.408175
$416$	9452.31	−	13273.9i	1.11403	−	1.56444i
$417$	11524.4	−	8999.84i	1.35336	−	1.05689i
$418$	−62.2922	−	179.982i	−0.00728903	−	0.0210603i
$419$	5234.17	−	2698.40i	0.610277	−	0.314619i	−0.125240	−	0.992127i	$-0.539970\pi$
$419$	5234.17	−	2698.40i	0.610277	−	0.314619i	0.735516	+	0.677507i	$0.236940\pi$
$420$	−8279.79	−	4304.12i	−0.961934	−	0.500046i
$421$	−9198.20	+	7233.54i	−1.06483	+	0.837390i	−0.987183	−	0.159591i	$-0.948982\pi$
$421$	−9198.20	+	7233.54i	−1.06483	+	0.837390i	−0.0776450	+	0.996981i	$0.524740\pi$
$422$	9730.26	+	2857.06i	1.12242	+	0.329573i
$423$	1124.37	−	4501.29i	0.129240	−	0.517400i
$424$	1703.70	−	11849.5i	0.195139	−	1.35722i
$425$	3120.84	−	298.004i	0.356195	−	0.0340125i
$426$	−17483.9	−	11320.2i	−1.98850	−	1.28748i
$427$	2902.46	+	2282.52i	0.328946	+	0.258686i
$428$	74.9515	+	1573.43i	0.00846476	+	0.177697i
$429$	−280.398	−	396.602i	−0.0315565	−	0.0446344i
$430$	6754.32	−	5311.66i	0.757494	−	0.595700i
$431$	−7851.32	−	9060.91i	−0.877459	−	1.01264i	−0.999797	−	0.0201535i	$-0.993584\pi$
$431$	−7851.32	−	9060.91i	−0.877459	−	1.01264i	0.122338	−	0.992489i	$-0.460961\pi$
$432$	23464.7	+	12400.5i	2.61330	+	1.38107i
$433$	4217.42	−	4867.16i	0.468074	−	0.540187i	−0.471801	−	0.881705i	$-0.656396\pi$
$433$	4217.42	−	4867.16i	0.468074	−	0.540187i	0.939875	+	0.341519i	$0.110941\pi$
$434$	12337.9	+	11764.1i	1.36460	+	1.30114i
$435$	−35.7722	+	145.303i	−0.00394286	+	0.0160156i
$436$	1970.90	−	3413.71i	0.216489	−	0.374970i
$437$	204.725	+	1419.12i	0.0224104	+	0.155344i
$438$	−3264.87	+	22173.8i	−0.356168	+	2.41896i
$439$	2871.37	−	4032.28i	0.312171	−	0.438383i	−0.628445	−	0.777854i	$-0.716308\pi$
$439$	2871.37	−	4032.28i	0.312171	−	0.438383i	0.940617	+	0.339470i	$0.110248\pi$
$440$	1190.40	−	349.534i	0.128978	−	0.0378714i
$441$	−4031.71	+	2552.56i	−0.435343	+	0.275625i
$442$	6094.96	+	3916.99i	0.655899	+	0.421521i
$443$	991.332	−	2864.27i	0.106320	−	0.307190i	−0.879275	−	0.476314i	$-0.841973\pi$
$443$	991.332	−	2864.27i	0.106320	−	0.307190i	0.985595	+	0.169124i	$0.0540937\pi$
$444$	21236.8	+	37072.9i	2.26994	+	3.96262i
$445$	−169.005	+	161.146i	−0.0180037	+	0.0171664i
$446$	−360.915	−	7576.53i	−0.0383179	−	0.804392i
$447$	−1669.18	−	6983.69i	−0.176621	−	0.738964i
$448$	−13361.2	+	1275.84i	−1.40905	+	0.134548i
$449$	−3280.17	+	7182.57i	−0.344768	+	0.754937i	−1.00000		0.000491176i	$-0.999844\pi$
$449$	−3280.17	+	7182.57i	−0.344768	+	0.754937i	0.655232	+	0.755428i	$0.272571\pi$
$450$	4757.28	−	10232.8i	0.498357	−	1.07196i
$451$	−954.358	+	613.329i	−0.0996430	+	0.0640366i
$452$	−11145.4	−	45942.1i	−1.15982	−	4.78083i
$453$	11508.4	+	39.0120i	1.19362	+	0.00404624i
$454$	747.071	−	143.986i	0.0772286	−	0.0148846i
$455$	−2659.75	+	1371.20i	−0.274046	+	0.141281i
$456$	4388.30	−	830.356i	0.450660	−	0.0852741i
$457$	−7628.61	−	7273.86i	−0.780856	−	0.744545i	0.190625	−	0.981663i	$-0.438949\pi$
$457$	−7628.61	−	7273.86i	−0.780856	−	0.744545i	−0.971481	+	0.237118i	$0.923797\pi$
$458$	14743.1	+	32283.0i	1.50415	+	3.29363i
$459$	−2381.76	+	5078.02i	−0.242203	+	0.516387i
$460$	−15292.5	+	1467.58i	−1.55003	+	0.148752i
$461$	9793.62	+	16963.0i	0.989445	+	1.71377i	0.620215	+	0.784432i	$0.287045\pi$
$461$	9793.62	+	16963.0i	0.989445	+	1.71377i	0.369230	+	0.929338i	$0.379621\pi$
$462$	−234.678	+	953.242i	−0.0236325	+	0.0959931i
$463$	3806.89	−	15692.2i	0.382119	−	1.57512i	−0.378299	−	0.925684i	$-0.623491\pi$
$463$	3806.89	−	15692.2i	0.382119	−	1.57512i	0.760418	−	0.649434i	$-0.224994\pi$
$464$	261.067	+	754.304i	0.0261201	+	0.0754692i
$465$	5783.42	−	6628.89i	0.576774	−	0.661091i
$466$	6195.25	−	17900.0i	0.615857	−	1.77940i
$467$	137.796	+	958.390i	0.0136540	+	0.0949658i	0.995509	−	0.0946681i	$-0.0301790\pi$
$467$	137.796	+	958.390i	0.0136540	+	0.0949658i	−0.981855	+	0.189634i	$0.939270\pi$
$468$	16709.6	−	8471.48i	1.65043	−	0.836740i
$469$	11524.3	−	7406.21i	1.13463	−	0.729183i
$470$	5803.02	−	2323.18i	0.569518	−	0.228001i
$471$	−330.173	+	6469.66i	−0.0323005	+	0.632922i
$472$	−7546.63	−	10597.8i	−0.735936	−	1.03348i
$473$	−510.450	−	401.422i	−0.0496205	−	0.0390220i
$474$	−16690.0	+	23270.5i	−1.61729	+	2.25496i
$475$	−240.316	−	990.594i	−0.0232135	−	0.0956875i
$476$	−1497.08	−	10412.4i	−0.144157	−	1.00263i
$477$	2862.38	−	3962.52i	0.274758	−	0.380359i
$478$	−4696.64	−	3018.35i	−0.449413	−	0.288820i
$479$	3749.09	+	722.579i	0.357621	+	0.0689258i	0.364897	−	0.931048i	$-0.381104\pi$
$479$	3749.09	+	722.579i	0.357621	+	0.0689258i	−0.00727643	+	0.999974i	$0.502316\pi$
$480$	2361.76	+	16831.3i	0.224582	+	1.60050i
$481$	13638.5	+	1302.32i	1.29286	+	0.123453i
$482$	−14042.9	+	24323.1i	−1.32705	+	2.29852i
$483$	3089.72	−	6713.68i	0.291071	−	0.632470i
$484$	13503.4	+	23388.5i	1.26816	+	2.19652i
$485$	1410.97	+	3089.59i	0.132100	+	0.289259i
$486$	11430.4	+	16641.7i	1.06686	+	1.55326i
$487$	−1823.80	+	2104.78i	−0.169701	+	0.195845i	−0.834229	−	0.551418i	$-0.814087\pi$
$487$	−1823.80	+	2104.78i	−0.169701	+	0.195845i	0.664528	+	0.747263i	$0.268632\pi$
$488$	900.966	−	18913.6i	0.0835754	−	1.75446i
$489$	−19.1321	−	432.474i	−0.00176930	−	0.0399942i
$490$	−5968.40	−	2389.39i	−0.550255	−	0.220289i
$491$	−3462.70	+	3301.68i	−0.318268	+	0.303468i	−0.832325	−	0.554288i	$-0.812990\pi$
$491$	−3462.70	+	3301.68i	−0.318268	+	0.303468i	0.514057	+	0.857756i	$0.328142\pi$
$492$	−18042.1	−	39863.8i	−1.65326	−	3.65285i
$493$	−156.606	+	62.6957i	−0.0143067	+	0.00572753i
$494$	978.583	−	2142.80i	0.0891265	−	0.195160i
$495$	496.781	+	99.2444i	0.0451083	+	0.00901152i
$496$	6678.11	−	46447.3i	0.604549	−	4.20473i
$497$	8619.76	+	4443.80i	0.777966	+	0.401069i
$498$	−13943.3	+	1283.74i	−1.25465	+	0.115514i
$499$	14462.6	+	5789.97i	1.29747	+	0.519428i	0.914594	−	0.404373i	$-0.132510\pi$
$499$	14462.6	+	5789.97i	1.29747	+	0.519428i	0.382874	+	0.923801i	$0.374934\pi$
$500$	27819.2	−	5361.72i	2.48823	−	0.479567i
$501$	−4555.59	−	894.045i	−0.406245	−	0.0797265i
$502$	−38053.6	−	7334.23i	−3.38330	−	0.652077i
$503$	8214.43	−	2411.97i	0.728158	−	0.213806i	0.103416	−	0.994638i	$-0.467023\pi$
$503$	8214.43	−	2411.97i	0.728158	−	0.213806i	0.624741	+	0.780832i	$0.285204\pi$
$504$	−21313.2	−	8700.65i	−1.88366	−	0.768964i
$505$	−4028.83			−0.355011
$506$	529.324	+	1527.04i	0.0465046	+	0.134160i
$507$	−787.836	+	5350.69i	−0.0690118	+	0.468703i
$508$	−32878.9	−	3139.55i	−2.87158	−	0.274203i
$509$	2405.94	−	9917.42i	0.209512	−	0.863619i	−0.765852	−	0.643017i	$-0.777683\pi$
$509$	2405.94	−	9917.42i	0.209512	−	0.863619i	0.975364	−	0.220602i	$-0.0708023\pi$
$510$	−7424.86	+	1404.94i	−0.644663	+	0.121984i
$511$	496.536	−	10423.6i	0.0429853	−	0.902372i
$512$	−6161.70	−	7110.98i	−0.531858	−	0.613797i
$513$	1744.48	+	531.553i	0.150137	+	0.0457478i
$514$	20024.5	+	5879.71i	1.71837	+	0.504558i
$515$	7446.44	+	3838.90i	0.637144	+	0.328471i
$516$	18186.0	−	17223.0i	1.55154	−	1.46938i
$517$	−274.016	−	384.801i	−0.0233099	−	0.0327341i
$518$	−16062.4	−	22556.5i	−1.36244	−	1.91328i
$519$	−4420.93	−	1314.40i	−0.373906	−	0.111167i
$520$	13639.3	+	7031.57i	1.15024	+	0.592990i
$521$	−16693.9	−	4901.77i	−1.40379	−	0.412189i	−0.509805	−	0.860290i	$-0.670282\pi$
$521$	−16693.9	−	4901.77i	−1.40379	−	0.412189i	−0.893983	+	0.448101i	$0.852100\pi$
$522$	−90.4867	+	600.423i	−0.00758716	+	0.0503444i
$523$	914.162	+	1055.00i	0.0764312	+	0.0882063i	0.792677	−	0.609642i	$-0.208687\pi$
$523$	914.162	+	1055.00i	0.0764312	+	0.0882063i	−0.716246	+	0.697848i	$0.754141\pi$
$524$	428.320	−	8991.55i	0.0357085	−	0.749614i
$525$	−1735.27	+	4959.28i	−0.144254	+	0.412268i
$526$	3027.62	−	12480.0i	0.250971	−	1.03452i
$527$	9872.05	+	942.666i	0.816002	+	0.0779187i
$528$	2512.06	−	995.810i	0.207052	−	0.0820778i
$529$	−1742.97	−	12041.5i	−0.143254	−	0.989686i
$530$	6585.76			0.539749
$531$	−720.369	−	5263.35i	−0.0588726	−	0.430151i
$532$	−3281.78	+	963.616i	−0.267449	+	0.0785302i
$533$	−13777.9	−	2655.48i	−1.11968	−	0.215800i
$534$	−622.937	+	714.003i	−0.0504815	+	0.0578613i
$535$	−517.323	+	99.7058i	−0.0418052	+	0.00805730i
$536$	−65216.8	−	26108.9i	−5.25548	−	2.10398i
$537$	11538.2	+	16319.9i	0.927203	+	1.31146i
$538$	11492.1	+	5924.60i	0.920931	+	0.474773i
$539$	−69.1448	+	480.912i	−0.00552556	+	0.0384311i
$540$	−6578.32	+	18399.3i	−0.524233	+	1.46626i
$541$	−2152.41	+	4713.12i	−0.171052	+	0.374553i	−0.975671	−	0.219239i	$-0.929642\pi$
$541$	−2152.41	+	4713.12i	−0.171052	+	0.374553i	0.804619	+	0.593792i	$0.202370\pi$
$542$	11581.7	−	4636.62i	0.917855	−	0.367454i
$543$	6241.28	+	617.327i	0.493257	+	0.0487882i
$544$	−13866.4	+	13221.6i	−1.09287	+	1.04205i
$545$	1223.94	+	489.990i	0.0961976	+	0.0385117i
$546$	−10236.9	+	6529.95i	−0.802381	+	0.511824i
$547$	−805.318	+	16905.7i	−0.0629486	+	1.32145i	0.717642	+	0.696412i	$0.245221\pi$
$547$	−805.318	+	16905.7i	−0.0629486	+	1.32145i	−0.780591	+	0.625042i	$0.785082\pi$
$548$	−32514.8	+	37524.1i	−2.53461	+	2.92509i
$549$	3911.17	−	6669.50i	0.304052	−	0.518483i
$550$	−477.303	−	1045.15i	−0.0370041	−	0.0810278i
$551$	27.4240	+	47.4998i	0.00212033	+	0.00367252i
$552$	−37234.9	+	7063.91i	−2.87105	+	0.544674i
$553$	6666.65	−	11547.0i	0.512649	−	0.887934i
$554$	8416.45	+	803.674i	0.645453	+	0.0616333i
$555$	−11262.3	+	8795.16i	−0.861368	+	0.672674i
$556$	56386.8	+	10867.7i	4.30096	+	0.828942i
$557$	6093.33	+	3915.94i	0.463523	+	0.297888i	0.751481	−	0.659755i	$-0.229340\pi$
$557$	6093.33	+	3915.94i	0.463523	+	0.297888i	−0.287958	+	0.957643i	$0.592976\pi$
$558$	20902.5	−	28936.3i	1.58580	−	2.19529i
$559$	−1143.06	−	7950.18i	−0.0864874	−	0.601533i
$560$	−3924.93	−	16178.8i	−0.296176	−	1.22086i
$561$	235.474	+	520.275i	0.0177214	+	0.0391551i
$562$	27906.2	+	21945.6i	2.09457	+	1.64719i
$563$	9749.96	+	13691.9i	0.729861	+	1.02495i	0.998101	+	0.0615947i	$0.0196186\pi$
$563$	9749.96	+	13691.9i	0.729861	+	1.02495i	−0.268240	+	0.963352i	$0.586442\pi$
$564$	16223.4	−	8294.25i	1.21122	−	0.619239i
$565$	14678.9	−	5876.53i	1.09300	−	0.437571i
$566$	32470.9	−	20867.8i	2.41140	−	1.54972i
$567$	−6058.82	−	7186.88i	−0.448759	−	0.532312i
$568$	−7077.44	−	49224.7i	−0.522822	−	3.63631i
$569$	−6810.07	+	19676.4i	−0.501745	+	1.44970i	0.355445	+	0.934697i	$0.384329\pi$
$569$	−6810.07	+	19676.4i	−0.501745	+	1.44970i	−0.857190	+	0.515000i	$0.827792\pi$
$570$	795.719	+	2324.54i	0.0584719	+	0.170815i
$571$	−554.769	−	1602.90i	−0.0406591	−	0.117477i	0.922844	−	0.385174i	$-0.125859\pi$
$571$	−554.769	−	1602.90i	−0.0406591	−	0.117477i	−0.963503	+	0.267697i	$0.913737\pi$
$572$	449.709	−	1853.73i	0.0328729	−	0.135504i
$573$	−6719.69	+	1948.36i	−0.489911	+	0.142049i
$574$	14180.0	+	24560.4i	1.03112	+	1.78595i
$575$	2043.26	+	8405.02i	0.148191	+	0.609589i
$576$	6440.59	+	27356.7i	0.465899	+	1.97893i
$577$	8484.61	+	18578.7i	0.612165	+	1.34045i	0.921083	+	0.389365i	$0.127306\pi$
$577$	8484.61	+	18578.7i	0.612165	+	1.34045i	−0.308919	+	0.951089i	$0.599967\pi$
$578$	12786.0	+	12191.4i	0.920114	+	0.877327i
$579$	6704.81	−	19161.9i	0.481248	−	1.37537i
$580$	−522.348	+	269.289i	−0.0373953	+	0.0192786i
$581$	6401.63	−	1233.81i	0.457116	−	0.0881019i
$582$	6850.54	+	11958.9i	0.487911	+	0.851741i
$583$	−117.340	−	483.681i	−0.00833570	−	0.0343602i
$584$	−45018.2	+	28931.4i	−3.18984	+	2.04999i
$585$	3599.88	+	5128.56i	0.254422	+	0.362461i
$586$	−20325.8	+	44507.3i	−1.43285	+	3.13751i
$587$	−23910.7	+	2283.20i	−1.68126	+	0.160541i	−0.891545	−	0.452931i	$-0.850378\pi$
$587$	−23910.7	+	2283.20i	−1.68126	+	0.160541i	−0.789716	+	0.613472i	$0.789772\pi$
$588$	−17962.9	−	5340.58i	−1.25982	−	0.374561i
$589$	−153.423	−	3220.75i	−0.0107329	−	0.225312i
$590$	5179.95	−	4939.07i	0.361449	−	0.344641i
$591$	7255.40	−	12468.9i	0.504987	−	0.867855i
$592$	−24929.9	+	72030.3i	−1.73077	+	5.00072i
$593$	12229.6	+	7859.47i	0.846895	+	0.544266i	0.890605	−	0.454778i	$-0.150281\pi$
$593$	12229.6	+	7859.47i	0.846895	+	0.544266i	−0.0437101	+	0.999044i	$0.513918\pi$
$594$	2044.22	+	216.199i	0.141204	+	0.0149339i
$595$	3375.83	−	991.233i	0.232597	−	0.0682968i
$596$	16357.0	−	22970.2i	1.12418	−	1.57868i
$597$	719.638	+	569.888i	0.0493347	+	0.0390686i
$598$	−8295.43	+	18187.3i	−0.567266	+	1.24370i
$599$	5494.34	−	9516.48i	0.374779	−	0.649137i	−0.615515	−	0.788125i	$-0.711052\pi$
$599$	5494.34	−	9516.48i	0.374779	−	0.649137i	0.990294	+	0.138989i	$0.0443852\pi$
$600$	25877.5	−	7503.13i	1.76074	−	0.510523i
$601$	−10585.0	−	10092.8i	−0.718421	−	0.685013i	0.239871	−	0.970805i	$-0.422895\pi$
$601$	−10585.0	−	10092.8i	−0.718421	−	0.685013i	−0.958292	+	0.285792i	$0.907743\pi$
$602$	−10630.9	+	12268.7i	−0.719741	+	0.830625i
$603$	−18637.0	−	21805.3i	−1.25864	−	1.47260i
$604$	29597.2	+	34157.0i	1.99386	+	2.30104i
$605$	−7100.14	+	5583.61i	−0.477127	+	0.375217i
$606$	−16278.9	+	1498.78i	−1.09123	+	0.100468i
$607$	180.190	+	3782.65i	0.0120489	+	0.252938i	0.996853	+	0.0792698i	$0.0252589\pi$
$607$	180.190	+	3782.65i	0.0120489	+	0.252938i	−0.984804	+	0.173668i	$0.944438\pi$
$608$	4896.77	+	3850.86i	0.326629	+	0.256864i
$609$	14.4092	−	282.345i	0.000958770	−	0.0187869i
$610$	10369.5	−	990.170i	0.688279	−	0.0657227i
$611$	831.523	−	5783.37i	0.0550570	−	0.382930i
$612$	−21176.4	+	6062.32i	−1.39870	+	0.400416i
$613$	22356.8	+	6564.54i	1.47305	+	0.432527i	0.917090	−	0.398681i	$-0.130532\pi$
$613$	22356.8	+	6564.54i	1.47305	+	0.432527i	0.555962	+	0.831208i	$0.312350\pi$
$614$	−29984.1	+	23579.8i	−1.97078	+	1.54984i
$615$	12338.3	−	7870.40i	0.808992	−	0.516041i
$616$	−2083.37	+	1074.05i	−0.136268	+	0.0702512i
$617$	2286.97	+	6607.77i	0.149222	+	0.431149i	0.994695	−	0.102870i	$-0.0328025\pi$
$617$	2286.97	+	6607.77i	0.149222	+	0.431149i	−0.845473	+	0.534018i	$0.820681\pi$
$618$	31516.3	+	12741.3i	2.05141	+	0.829340i
$619$	−12695.5	+	17828.3i	−0.824355	+	1.15764i	0.160971	+	0.986959i	$0.448537\pi$
$619$	−12695.5	+	17828.3i	−0.824355	+	1.15764i	−0.985326	+	0.170685i	$0.945402\pi$
$620$	34548.3			2.23790
$621$	−14805.4	−	4503.63i	−0.956717	−	0.291022i
$622$	8086.65			0.521294
$623$	255.908	−	359.373i	0.0164571	−	0.0231107i
$624$	30986.4	+	12527.1i	1.98790	+	0.803663i
$625$	−106.817	−	308.627i	−0.00683628	−	0.0197521i
$626$	20302.1	−	10466.5i	1.29622	−	0.668249i
$627$	156.545	−	99.8572i	0.00997098	−	0.00636030i
$628$	−19997.8	+	15726.5i	−1.27070	+	0.999290i
$629$	−15456.1	−	4538.32i	−0.979769	−	0.287686i
$630$	3069.11	−	12286.9i	0.194089	−	0.777016i
$631$	−1185.81	+	8247.50i	−0.0748121	+	0.520329i	0.917613	+	0.397476i	$0.130114\pi$
$631$	−1185.81	+	8247.50i	−0.0748121	+	0.520329i	−0.992425	+	0.122854i	$0.960795\pi$
$632$	−68064.2	+	6499.35i	−4.28394	+	0.409067i
$633$	−503.908	+	9873.97i	−0.0316407	+	0.619992i
$634$	19179.1	+	15082.6i	1.20142	+	0.944806i
$635$	−525.622	−	11034.2i	−0.0328483	−	0.689570i
$636$	19116.3	−	1760.01i	1.19184	−	0.109731i
$637$	−4723.68	+	3714.74i	−0.293813	+	0.231057i
$638$	40.4863	+	46.7237i	0.00251233	+	0.00289939i
$639$	6771.57	−	19144.2i	0.419216	−	1.18519i
$640$	−7660.01	+	8840.12i	−0.473107	+	0.545995i
$641$	2944.39	+	2807.47i	0.181430	+	0.172993i	0.775352	−	0.631530i	$-0.217573\pi$
$641$	2944.39	+	2807.47i	0.181430	+	0.172993i	−0.593922	+	0.804523i	$0.702421\pi$
$642$	−2053.21	+	595.324i	−0.126221	+	0.0365974i
$643$	1176.05	−	2036.99i	0.0721291	−	0.124931i	−0.827705	−	0.561163i	$-0.810354\pi$
$643$	1176.05	−	2036.99i	0.0721291	−	0.124931i	0.899834	+	0.436232i	$0.143687\pi$
$644$	27844.6	−	8190.27i	1.70378	−	0.501152i
$645$	6567.40	+	5200.79i	0.400917	+	0.317490i
$646$	−1606.59	+	2256.14i	−0.0978489	+	0.137410i
$647$	2104.43	−	617.916i	0.127873	−	0.0375468i	−0.217170	−	0.976134i	$-0.569683\pi$
$647$	2104.43	−	617.916i	0.127873	−	0.0375468i	0.345043	+	0.938587i	$0.387864\pi$
$648$	−11998.6	+	46686.7i	−0.727392	+	2.83029i
$649$	−455.035	−	292.433i	−0.0275218	−	0.0176872i
$650$	4648.03	−	13429.6i	0.280478	−	0.810389i
$651$	−8358.81	+	14365.2i	−0.503238	+	0.864849i
$652$	1230.41	−	1173.19i	0.0739055	−	0.0704687i
$653$	−254.718	−	5347.19i	−0.0152648	−	0.320447i	−0.993566	−	0.113258i	$-0.963871\pi$
$653$	−254.718	−	5347.19i	−0.0152648	−	0.320447i	0.978301	−	0.207189i	$-0.0664316\pi$
$654$	5127.74	+	1524.54i	0.306591	+	0.0911532i
$655$	2997.09	−	286.187i	0.178787	−	0.0170721i
$656$	32428.8	−	71009.1i	1.93008	−	4.22628i
$657$	−21765.6	+	1929.55i	−1.29248	+	0.114580i
$658$	−9934.65	+	6384.61i	−0.588591	+	0.378265i
$659$	2276.51	+	9383.92i	0.134568	+	0.554698i	0.998678	+	0.0513950i	$0.0163667\pi$
$659$	2276.51	+	9383.92i	0.134568	+	0.554698i	−0.864110	+	0.503303i	$0.832118\pi$
$660$	988.911	+	1726.33i	0.0583232	+	0.101814i
$661$	20011.3	−	3856.87i	1.17753	−	0.226951i	0.437310	−	0.899311i	$-0.355931\pi$
$661$	20011.3	−	3856.87i	1.17753	−	0.226951i	0.740225	+	0.672359i	$0.234719\pi$
$662$	−30219.5	+	15579.2i	−1.77419	+	0.914658i
$663$	−2332.84	+	6667.10i	−0.136652	+	0.390541i
$664$	−24195.9	−	23070.8i	−1.41413	−	1.34837i
$665$	−475.218	−	1040.58i	−0.0277115	−	0.0606797i
$666$	−42234.8	+	39727.6i	−2.45730	+	2.31143i
$667$	−232.906	−	402.963i	−0.0135205	−	0.0233925i
$668$	−9116.03	−	15789.4i	−0.528009	−	0.914538i
$669$	7102.44	−	2059.34i	0.410458	−	0.119011i
$670$	9111.12	−	37556.5i	0.525363	−	2.16558i
$671$	−257.478	−	743.932i	−0.0148134	−	0.0428006i
$672$	−10399.3	−	30379.6i	−0.596966	−	1.74392i
$673$	1422.43	−	4109.84i	0.0814720	−	0.235398i	−0.896907	−	0.442220i	$-0.854191\pi$
$673$	1422.43	−	4109.84i	0.0814720	−	0.235398i	0.978379	+	0.206822i	$0.0663122\pi$
$674$	−8493.52	−	59073.7i	−0.485398	−	3.37602i
$675$	10781.2	+	2191.84i	0.614767	+	0.124984i
$676$	−17868.1	+	11483.1i	−1.01662	+	0.653342i
$677$	3178.10	−	1272.32i	0.180420	−	0.0722291i	−0.279694	−	0.960089i	$-0.590233\pi$
$677$	3178.10	−	1272.32i	0.180420	−	0.0722291i	0.460114	+	0.887860i	$0.347809\pi$
$678$	57125.5	−	29205.5i	3.23583	−	1.65432i
$679$	−3722.18	−	5227.07i	−0.210374	−	0.295429i
$680$	−14182.2	−	11153.0i	−0.799797	−	0.628967i
$681$	305.844	+	675.757i	0.0172099	+	0.0380251i
$682$	−856.873	−	3532.08i	−0.0481105	−	0.198314i
$683$	−472.423	−	3285.78i	−0.0264667	−	0.184080i	0.972300	−	0.233738i	$-0.0750959\pi$
$683$	−472.423	−	3285.78i	−0.0264667	−	0.184080i	−0.998766	+	0.0496582i	$0.984187\pi$
$684$	2930.93	+	6534.73i	0.163841	+	0.365295i
$685$	−13970.2	−	8978.10i	−0.779232	−	0.500782i
$686$	35072.8	+	6759.74i	1.95202	+	0.376221i
$687$	−27270.1	+	21296.2i	−1.51444	+	1.18268i
$688$	44482.9	+	4247.61i	2.46497	+	0.235376i
$689$	3077.98	−	5331.22i	0.170191	−	0.294780i
$690$	−6761.67	−	19722.4i	−0.373061	−	1.08814i
$691$	1945.19	+	3369.17i	0.107089	+	0.185484i	0.914590	−	0.404383i	$-0.132514\pi$
$691$	1945.19	+	3369.17i	0.107089	+	0.185484i	−0.807501	+	0.589867i	$0.799180\pi$
$692$	−7524.43	−	16476.2i	−0.413347	−	0.905103i
$693$	−957.072	−	6.48879i	−0.0524620	−	0.000355684i
$694$	13727.4	−	15842.3i	0.750842	−	0.866518i
$695$	−913.867	+	19184.4i	−0.0498776	+	1.04706i
$696$	−1222.27	+	779.664i	−0.0665662	+	0.0424613i
$697$	15315.9	+	6131.57i	0.832326	+	0.333213i
$698$	−21376.2	+	20382.2i	−1.15917	+	1.10527i
$699$	18377.2	+	1817.70i	0.994408	+	0.0983572i
$700$	−19155.9	+	7668.88i	−1.03432	+	0.414080i
$701$	3474.30	−	7607.65i	0.187193	−	0.409896i	−0.792647	−	0.609681i	$-0.791297\pi$
$701$	3474.30	−	7607.65i	0.187193	−	0.409896i	0.979840	+	0.199786i	$0.0640246\pi$
$702$	16453.6	+	19383.3i	0.884618	+	1.04213i
$703$	−745.383	+	5184.26i	−0.0399896	+	0.278134i
$704$	2543.46	+	1311.24i	0.136165	+	0.0701979i
$705$	3518.06	+	4976.04i	0.187940	+	0.265828i
$706$	−41110.3	−	16458.1i	−2.19151	−	0.877349i
$707$	7473.96	−	1440.49i	0.397577	−	0.0766268i
$708$	13715.7	−	15720.8i	0.728063	−	0.834497i
$709$	−27005.4	−	5204.87i	−1.43048	−	0.275702i	−0.585574	−	0.810619i	$-0.699131\pi$
$709$	−27005.4	−	5204.87i	−1.43048	−	0.275702i	−0.844905	+	0.534917i	$0.820343\pi$
$710$	26250.2	−	7707.74i	1.38754	−	0.407417i
$711$	−25848.1	−	10551.9i	−1.36341	−	0.556580i
$712$	−2262.38			−0.119082
$713$	1314.89	+	27330.1i	0.0690646	+	1.43551i
$714$	13271.7	−	5261.05i	0.695630	−	0.275756i
$715$	635.091	+	60.6439i	0.0332183	+	0.00317196i
$716$	−18505.2	+	76279.4i	−0.965881	+	3.98142i
$717$	1797.64	−	5137.53i	0.0936320	−	0.267594i
$718$	1107.46	−	23248.5i	0.0575627	−	1.20839i
$719$	212.059	+	244.729i	0.0109993	+	0.0126938i	0.761223	−	0.648491i	$-0.224599\pi$
$719$	212.059	+	244.729i	0.0109993	+	0.0126938i	−0.750223	+	0.661185i	$0.770054\pi$
$720$	−32449.9	+	12736.4i	−1.67963	+	0.659247i
$721$	−15186.6	−	4459.19i	−0.784437	−	0.230331i
$722$	−31692.6	−	16338.7i	−1.63362	−	0.842192i
$723$	−26246.3	−	7803.35i	−1.35008	−	0.401396i
$724$	14287.1	+	20063.4i	0.733390	+	1.02990i
$725$	191.932	+	269.531i	0.00983197	+	0.0138071i
$726$	−26611.7	+	25202.6i	−1.36040	+	1.28837i
$727$	21410.8	+	11038.1i	1.09228	+	0.563107i	0.907661	−	0.419704i	$-0.137866\pi$
$727$	21410.8	+	11038.1i	1.09228	+	0.563107i	0.184614	+	0.982811i	$0.440896\pi$
$728$	−27816.7	−	8167.73i	−1.41615	−	0.415819i
$729$	−13189.5	+	14610.2i	−0.670096	+	0.742275i
$730$	−19278.5	−	22248.6i	−0.977439	−	1.12803i
$731$	−449.346	+	9432.94i	−0.0227355	+	0.477277i
$732$	29834.7	−	5645.34i	1.50645	−	0.285052i
$733$	−4703.16	+	19386.7i	−0.236992	+	0.976894i	0.721645	+	0.692263i	$0.243386\pi$
$733$	−4703.16	+	19386.7i	−0.236992	+	0.976894i	−0.958637	+	0.284631i	$0.908129\pi$
$734$	−11980.8	−	1144.03i	−0.602479	−	0.0575297i
$735$	913.019	−	6200.90i	0.0458194	−	0.311188i
$736$	−41568.5	−	32657.9i	−2.08184	−	1.63558i
$737$	−2920.62			−0.145973
$738$	46926.6	−	36391.3i	2.34064	−	1.81515i
$739$	−22576.1	+	6628.94i	−1.12378	+	0.329972i	−0.790261	−	0.612770i	$-0.790055\pi$
$739$	−22576.1	+	6628.94i	−1.12378	+	0.329972i	−0.333522	+	0.942742i	$0.608237\pi$
$740$	−55104.5	−	10620.5i	−2.73741	−	0.527592i
$741$	2253.63	+	442.280i	0.111726	+	0.0219265i
$742$	−12217.4	+	2354.70i	−0.604466	+	0.116501i
$743$	−15430.0	−	6177.24i	−0.761873	−	0.305008i	−0.0420037	−	0.999117i	$-0.513374\pi$
$743$	−15430.0	−	6177.24i	−0.761873	−	0.305008i	−0.719870	+	0.694109i	$0.755798\pi$
$744$	84870.0	−	7813.87i	4.18210	−	0.385041i
$745$	8382.96	+	4321.72i	0.412252	+	0.212531i
$746$	3108.49	−	21620.0i	0.152560	−	1.06108i
$747$	−4377.33	−	12930.4i	−0.214402	−	0.633333i
$748$	−931.676	+	2040.09i	−0.0455420	+	0.0997232i
$749$	924.046	−	369.932i	0.0450786	−	0.0180468i
$750$	15853.8	+	35028.7i	0.771864	+	1.70542i
$751$	7948.74	−	7579.11i	0.386223	−	0.368263i	−0.471948	−	0.881626i	$-0.656449\pi$
$751$	7948.74	−	7579.11i	0.386223	−	0.368263i	0.858171	+	0.513363i	$0.171601\pi$
$752$	30177.9	+	12081.4i	1.46340	+	0.585855i
$753$	−1669.82	−	37745.5i	−0.0808121	−	1.82672i
$754$	−36.3848	+	763.811i	−0.00175737	+	0.0368917i
$755$	−9899.06	+	11424.1i	−0.477170	+	0.550684i
$756$	5625.01	−	36484.9i	0.270608	−	1.75521i
$757$	−1613.92	−	3533.99i	−0.0774887	−	0.169677i	0.866923	−	0.498443i	$-0.166095\pi$
$757$	−1613.92	−	3533.99i	−0.0774887	−	0.169677i	−0.944411	+	0.328766i	$0.893367\pi$
$758$	26126.7	+	45252.8i	1.25193	+	2.16841i
$759$	−1328.01	+	847.998i	−0.0635094	+	0.0405539i
$760$	−2933.14	+	5080.35i	−0.139995	+	0.242478i
$761$	20077.0	+	1917.12i	0.956361	+	0.0913214i	0.561552	−	0.827442i	$-0.310205\pi$
$761$	20077.0	+	1917.12i	0.956361	+	0.0913214i	0.394809	+	0.918763i	$0.370811\pi$
$762$	−6228.70	−	44389.2i	−0.296118	−	2.11030i
$763$	−2445.74	−	471.378i	−0.116044	−	0.0223657i
$764$	−23114.8	−	14855.0i	−1.09459	−	0.703447i
$765$	−3014.93	−	6722.01i	−0.142490	−	0.317692i
$766$	−2576.31	−	17918.6i	−0.121522	−	0.845203i
$767$	−1577.27	−	6501.58i	−0.0742527	−	0.306074i
$768$	−2444.16	+	3407.84i	−0.114839	+	0.160117i
$769$	5958.62	+	4685.91i	0.279419	+	0.219738i	0.748026	−	0.663669i	$-0.231002\pi$
$769$	5958.62	+	4685.91i	0.279419	+	0.219738i	−0.468607	+	0.883407i	$0.655244\pi$
$770$	−747.962	−	1050.37i	−0.0350061	−	0.0491591i
$771$	−1037.02	+	20320.2i	−0.0484402	+	0.949175i
$772$	74015.5	−	29631.3i	3.45062	−	1.38142i
$773$	−20427.5	+	13128.0i	−0.950487	+	0.610841i	−0.921350	−	0.388735i	$-0.872912\pi$
$773$	−20427.5	+	13128.0i	−0.950487	+	0.610841i	−0.0291368	+	0.999575i	$0.509276\pi$
$774$	28471.1	+	18571.2i	1.32219	+	0.862440i
$775$	−2768.32	−	19254.1i	−0.128311	−	0.892422i
$776$	−10762.6	+	31096.5i	−0.497880	+	1.43853i
$777$	17748.3	−	20342.9i	0.819455	−	0.939249i
$778$	−24216.5	−	69969.1i	−1.11594	−	3.22431i
$779$	1264.63	−	5212.86i	0.0581643	−	0.239756i
$780$	−5882.46	+	23894.0i	−0.270033	+	1.09685i
$781$	−1033.79	−	1790.57i	−0.0473647	−	0.0820380i
$782$	13624.1	−	19151.6i	0.623014	−	0.875780i
$783$	−589.842	+	50.2756i	−0.0269211	+	0.00229464i
$784$	−13888.5	−	30411.5i	−0.632675	−	1.38537i
$785$	−6158.19	−	5871.82i	−0.279994	−	0.266974i
$786$	12003.6	−	2271.33i	0.544725	−	0.103073i
$787$	−1746.17	+	900.213i	−0.0790905	+	0.0407740i	−0.497318	−	0.867568i	$-0.665682\pi$
$787$	−1746.17	+	900.213i	−0.0790905	+	0.0407740i	0.418228	+	0.908342i	$0.362651\pi$
$788$	55630.9	−	10722.0i	2.51493	−	0.484714i
$789$	12520.0	+	42.4413i	0.564923	+	0.00191502i
$790$	−8867.93	−	36554.1i	−0.399375	−	1.64625i
$791$	−25129.9	+	16150.0i	−1.12960	+	0.725953i
$792$	2819.76	+	4017.17i	0.126510	+	0.180232i
$793$	4044.85	−	8856.99i	0.181131	−	0.396622i
$794$	39028.1	−	3726.73i	1.74440	−	0.166570i
$795$	1492.57	+	6244.77i	0.0665860	+	0.278590i
$796$	171.534	+	3600.94i	0.00763802	+	0.160342i
$797$	−26758.6	+	25514.3i	−1.18926	+	1.13395i	−0.201251	+	0.979540i	$0.564501\pi$
$797$	−26758.6	+	25514.3i	−1.18926	+	1.13395i	−0.988006	+	0.154415i	$0.950651\pi$
$798$	−2307.28	−	4027.80i	−0.102352	−	0.178675i
$799$	−2246.89	+	6491.95i	−0.0994858	+	0.287445i
$800$	31615.6	+	20318.1i	1.39722	+	0.897941i
$801$	−818.213	−	428.864i	−0.0360926	−	0.0189178i
$802$	22368.0	−	6567.84i	0.984840	−	0.289175i
$803$	−1290.53	+	1812.29i	−0.0567144	+	0.0796443i
$804$	16409.8	−	111449.i	0.719810	−	4.88869i
$805$	4036.79	+	8828.25i	0.176743	+	0.386528i
$806$	22477.0	−	38931.2i	0.982279	−	1.70136i
$807$	−3013.32	+	12239.8i	−0.131442	+	0.533906i
$808$	−28248.9	−	26935.3i	−1.22994	−	1.17275i
$809$	−8155.83	+	9412.33i	−0.354442	+	0.409048i	−0.904770	−	0.425901i	$-0.859957\pi$
$809$	−8155.83	+	9412.33i	−0.354442	+	0.409048i	0.550328	+	0.834949i	$0.314503\pi$
$810$	−26361.6	−	2878.43i	−1.14352	−	0.124861i
$811$	18196.5	+	20999.8i	0.787872	+	0.909253i	0.997651	−	0.0684960i	$-0.0218201\pi$
$811$	18196.5	+	20999.8i	0.787872	+	0.909253i	−0.209779	+	0.977749i	$0.567275\pi$
$812$	872.734	−	686.326i	0.0377179	−	0.0296617i
$813$	7021.38	+	9931.22i	0.302891	+	0.428417i
$814$	280.912	+	5897.06i	0.0120958	+	0.253921i
$815$	446.955	+	351.490i	0.0192100	+	0.0151069i
$816$	−32986.7	−	21357.6i	−1.41515	−	0.916257i
$817$	3056.61	−	291.871i	0.130890	−	0.0124985i
$818$	−4809.36	+	33449.8i	−0.205569	+	1.42976i
$819$	−8511.89	−	8226.97i	−0.363162	−	0.351005i
$820$	55145.9	+	16192.3i	2.34851	+	0.689585i
$821$	3897.64	−	3065.13i	0.165686	−	0.130297i	−0.531873	−	0.846824i	$-0.678512\pi$
$821$	3897.64	−	3065.13i	0.165686	−	0.130297i	0.697559	+	0.716527i	$0.254269\pi$
$822$	−59788.2	−	31079.9i	−2.53692	−	1.31878i
$823$	−341.772	+	176.195i	−0.0144756	+	0.00746268i	−0.465449	−	0.885075i	$-0.654107\pi$
$823$	−341.772	+	176.195i	−0.0144756	+	0.00746268i	0.450974	+	0.892537i	$0.351077\pi$
$824$	26546.6	+	76701.5i	1.12232	+	3.24274i
$825$	882.859	−	689.457i	0.0372572	−	0.0290955i
$826$	−7843.48	+	11014.6i	−0.330399	+	0.463981i
$827$	8726.96			0.366948			0.183474	−	0.983025i	$-0.441266\pi$
$827$	8726.96			0.366948			0.183474	+	0.983025i	$0.441266\pi$
$828$	−24897.6	−	55440.6i	−1.04499	−	2.32692i
$829$	−20695.3			−0.867040			−0.433520	−	0.901144i	$-0.642729\pi$
$829$	−20695.3			−0.867040			−0.433520	+	0.901144i	$0.642729\pi$
$830$	10668.4	−	14981.6i	0.446149	−	0.626529i
$831$	1145.41	+	8162.81i	0.0478143	+	0.340752i
$832$	11576.0	+	33446.8i	0.482364	+	1.39370i
$833$	6280.13	−	3237.63i	0.261217	−	0.134667i
$834$	3444.30	+	77856.8i	0.143005	+	3.23257i
$835$	4793.26	−	3769.46i	0.198656	−	0.156225i
$836$	699.675	+	205.443i	0.0289459	+	0.00849928i
$837$	32175.3	+	13262.3i	1.32872	+	0.547683i
$838$	−4466.68	+	31066.4i	−0.184127	+	1.28063i
$839$	37712.2	−	3601.08i	1.55181	−	0.148180i	0.716354	−	0.697737i	$-0.245810\pi$
$839$	37712.2	−	3601.08i	1.55181	−	0.148180i	0.835456	+	0.549557i	$0.185204\pi$
$840$	26923.1	−	13764.5i	1.10587	−	0.565381i
$841$	19157.1	+	15065.3i	0.785479	+	0.617708i
$842$	−2967.57	−	62296.9i	−0.121460	−	2.54976i
$843$	−14484.8	+	31434.9i	−0.591796	+	1.28431i
$844$	−30520.6	+	24001.7i	−1.24474	+	0.978876i
$845$	−4652.05	−	5368.75i	−0.189391	−	0.218569i
$846$	16066.3	+	18797.5i	0.652920	+	0.763913i
$847$	11175.2	−	12896.9i	0.453347	−	0.523190i
$848$	24786.7	+	23634.1i	1.00375	+	0.957074i
$849$	27146.4	+	26060.3i	1.09736	+	1.05346i
$850$	−8354.50	+	14470.4i	−0.337126	+	0.583919i
$851$	6304.30	−	43995.6i	0.253947	−	1.77221i
$852$	74135.7	−	29388.2i	2.98104	−	1.18172i
$853$	12321.8	−	17303.6i	0.494598	−	0.694565i	−0.489538	−	0.871982i	$-0.662835\pi$
$853$	12321.8	−	17303.6i	0.494598	−	0.694565i	0.984136	+	0.177417i	$0.0567740\pi$
$854$	−18882.7	+	5544.46i	−0.756619	+	0.222163i
$855$	−2023.85	+	1281.34i	−0.0809521	+	0.0512526i
$856$	−4293.91	−	2759.53i	−0.171452	−	0.110185i
$857$	7307.81	−	21114.5i	0.291284	−	0.841608i	−0.700497	−	0.713656i	$-0.747038\pi$
$857$	7307.81	−	21114.5i	0.291284	−	0.841608i	0.991780	−	0.127953i	$-0.0408406\pi$
$858$	2588.72	+	8.77544i	0.103004	+	0.000349171i
$859$	−32292.9	+	30791.3i	−1.28268	+	1.22303i	−0.321562	+	0.946889i	$0.604208\pi$
$859$	−32292.9	+	30791.3i	−1.28268	+	1.22303i	−0.961117	+	0.276143i	$0.910944\pi$
$860$	1565.42	+	32862.2i	0.0620701	+	1.30301i
$861$	−20075.1	+	19012.0i	−0.794607	+	0.752530i
$862$	63610.8	−	6074.10i	2.51345	−	0.240005i
$863$	15783.4	−	34560.9i	0.622566	−	1.36323i	−0.291072	−	0.956701i	$-0.594012\pi$
$863$	15783.4	−	34560.9i	0.622566	−	1.36323i	0.913638	−	0.406528i	$-0.133261\pi$
$864$	−60072.4	+	30200.2i	−2.36540	+	1.18916i
$865$	5096.38	−	3275.24i	0.200326	−	0.128742i
$866$	8092.34	+	33357.1i	0.317539	+	1.30891i
$867$	−8662.40	+	14886.9i	−0.339320	+	0.583145i
$868$	−64091.3	+	12352.6i	−2.50622	+	0.483035i
$869$	−2526.66	+	1302.58i	−0.0986317	+	0.0508482i
$870$	−520.242	−	604.520i	−0.0202734	−	0.0235577i
$871$	−26144.0	−	24928.3i	−1.01706	−	0.969763i
$872$	5305.98	+	11618.5i	0.206059	+	0.451205i
$873$	−9787.14	+	9206.15i	−0.379433	+	0.356908i
$874$	−6794.01	−	3498.48i	−0.262941	−	0.135398i
$875$	−8950.98	−	15503.6i	−0.345827	−	0.598989i
$876$	−61905.1	−	59428.3i	−2.38765	−	2.29212i
$877$	6115.93	−	25210.2i	0.235485	−	0.970682i	−0.724197	−	0.689593i	$-0.757789\pi$
$877$	6115.93	−	25210.2i	0.235485	−	0.970682i	0.959682	−	0.281089i	$-0.0906955\pi$
$878$	8629.10	+	24932.1i	0.331683	+	0.958336i
$879$	−46809.4	−	9186.44i	−1.79618	−	0.352504i
$880$	−1160.89	+	3354.16i	−0.0444698	+	0.128487i
$881$	−3615.49	−	25146.3i	−0.138262	−	0.961634i	−0.934326	−	0.356421i	$-0.883997\pi$
$881$	−3615.49	−	25146.3i	−0.138262	−	0.961634i	0.796064	−	0.605213i	$-0.206912\pi$
$882$	1382.34	−	25395.1i	0.0527729	−	0.969498i
$883$	5752.87	−	3697.14i	0.219252	−	0.140905i	−0.426405	−	0.904532i	$-0.640220\pi$
$883$	5752.87	−	3697.14i	0.219252	−	0.140905i	0.645657	+	0.763628i	$0.276584\pi$
$884$	−25752.7	+	10309.8i	−0.979814	+	0.392258i
$885$	5857.30	+	3792.38i	0.222476	+	0.144044i
$886$	9370.44	+	13158.9i	0.355312	+	0.498965i
$887$	14039.0	+	11040.4i	0.531436	+	0.417926i	0.847487	−	0.530816i	$-0.178115\pi$
$887$	14039.0	+	11040.4i	0.531436	+	0.417926i	−0.316051	+	0.948742i	$0.602357\pi$
$888$	−137769.	−	13626.8i	−5.20635	−	0.514962i
$889$	4920.30	+	20281.7i	0.185626	+	0.765161i
$890$	−177.125	−	1231.93i	−0.00667106	−	0.0463983i
$891$	258.288	+	1987.37i	0.00971154	+	0.0747245i
$892$	24431.4	+	15701.1i	0.917066	+	0.589362i
$893$	2193.28	+	422.721i	0.0821897	+	0.0158408i
$894$	35480.0	+	14343.8i	1.32733	+	0.536609i
$895$	−26133.5	−	2495.45i	−0.976029	−	0.0931995i
$896$	11049.5	−	19138.3i	0.411984	−	0.713577i
$897$	−19125.6	−	3744.03i	−0.711914	−	0.139364i
$898$	−21042.3	−	36446.3i	−0.781948	−	1.35437i
$899$	434.806	+	952.091i	0.0161308	+	0.0353215i
$900$	21348.9	+	37563.2i	0.790699	+	1.39123i
$901$	−4739.84	+	5470.07i	−0.175258	+	0.202258i
$902$	287.697	−	6039.49i	0.0106200	−	0.222941i
$903$	−14042.8	−	7299.95i	−0.517515	−	0.269022i
$904$	142212.	+	56933.2i	5.23220	+	2.09466i
$905$	−5962.03	+	5684.79i	−0.218989	+	0.208805i
$906$	−35748.3	+	49843.1i	−1.31088	+	1.82773i
$907$	−16196.7	+	6484.17i	−0.592946	+	0.237380i	−0.648674	−	0.761066i	$-0.724676\pi$
$907$	−16196.7	+	6484.17i	−0.592946	+	0.237380i	0.0557283	+	0.998446i	$0.482252\pi$
$908$	−1210.10	+	2649.76i	−0.0442276	+	0.0968450i
$909$	−5110.57	−	15096.4i	−0.186476	−	0.550842i
$910$	2269.75	−	15786.5i	0.0826830	−	0.575073i
$911$	−24451.7	−	12605.7i	−0.889266	−	0.458448i	−0.0478613	−	0.998854i	$-0.515241\pi$
$911$	−24451.7	−	12605.7i	−0.889266	−	0.458448i	−0.841405	+	0.540406i	$0.818271\pi$
$912$	−5347.18	+	11604.4i	−0.194148	+	0.421339i
$913$	−1290.38	−	516.591i	−0.0467748	−	0.0187258i
$914$	55163.8	−	10632.0i	1.99634	−	0.384763i
$915$	3289.01	+	9608.22i	0.118832	+	0.347145i
$916$	−133428.	−	25716.1i	−4.81286	−	0.927602i
$917$	−5457.63	+	1602.50i	−0.196539	+	0.0577092i
$918$	−14682.8	−	26039.4i	−0.527893	−	0.936198i
$919$	−23584.1			−0.846538			−0.423269	−	0.906004i	$-0.639118\pi$
$919$	−23584.1			−0.846538			−0.423269	+	0.906004i	$0.639118\pi$
$920$	24869.6	−	43122.6i	0.891224	−	1.54534i
$921$	−29154.3	−	23087.6i	−1.04307	−	0.826018i
$922$	−103923.	−	9923.41i	−3.71205	−	0.354458i
$923$	6029.05	−	24852.1i	0.215004	−	0.886258i
$924$	−2451.79	−	2848.97i	−0.0872922	−	0.101433i
$925$	−1503.45	+	31561.2i	−0.0534410	+	1.12187i
$926$	56358.5	+	65041.2i	2.00006	+	2.30819i
$927$	−4938.92	+	32772.1i	−0.174990	+	1.16114i
$928$	−1940.27	−	569.715i	−0.0686342	−	0.0201528i
$929$	−1245.87	−	642.291i	−0.0439997	−	0.0226834i	0.436086	−	0.899905i	$-0.356364\pi$
$929$	−1245.87	−	642.291i	−0.0439997	−	0.0226834i	−0.480086	+	0.877221i	$0.659395\pi$
$930$	10899.5	+	45602.4i	0.384309	+	1.60791i
$931$	−1332.57	−	1871.33i	−0.0469100	−	0.0658758i
$932$	42067.8	+	59075.9i	1.47852	+	2.07628i
$933$	1832.72	+	7667.94i	0.0643093	+	0.269064i
$934$	−4586.86	−	2364.69i	−0.160692	−	0.0828426i
$935$	−719.727	−	211.331i	−0.0251739	−	0.00739172i
$936$	−9046.43	+	60027.4i	−0.315910	+	2.09621i
$937$	7752.23	+	8946.55i	0.270282	+	0.311922i	0.874623	−	0.484804i	$-0.161109\pi$
$937$	7752.23	+	8946.55i	0.270282	+	0.311922i	−0.604341	+	0.796726i	$0.706563\pi$
$938$	−3474.06	+	72929.5i	−0.120930	+	2.53863i
$939$	14525.7	+	16878.8i	0.504823	+	0.586603i
$940$	−5642.36	+	23258.1i	−0.195780	+	0.807017i
$941$	−17132.0	−	1635.90i	−0.593503	−	0.0566727i	−0.206017	−	0.978548i	$-0.566050\pi$
$941$	−17132.0	−	1635.90i	−0.593503	−	0.0566727i	−0.387486	+	0.921876i	$0.626656\pi$
$942$	−27067.3	−	21434.8i	−0.936199	−	0.741385i
$943$	−10710.4	+	44240.4i	−0.369860	+	1.52775i
$944$	37220.4			1.28329
$945$	12346.2	+	125.561i	0.424998	+	0.00432221i
$946$	3320.86	−	975.093i	0.114134	−	0.0335127i
$947$	−14017.5	−	2701.65i	−0.481000	−	0.0927051i	−0.0570130	−	0.998373i	$-0.518158\pi$
$947$	−14017.5	−	2701.65i	−0.481000	−	0.0927051i	−0.423987	+	0.905668i	$0.639370\pi$
$948$	−35509.6	−	103735.i	−1.21656	−	3.55395i
$949$	−27020.6	+	5207.80i	−0.924264	+	0.178137i
$950$	5043.62	+	2019.16i	0.172249	+	0.0689581i
$951$	−9955.01	+	21604.3i	−0.339446	+	0.736664i
$952$	30297.3	+	15619.4i	1.03145	+	0.531750i
$953$	5554.14	−	38629.9i	0.188789	−	1.31306i	−0.646359	−	0.763033i	$-0.723709\pi$
$953$	5554.14	−	38629.9i	0.188789	−	1.31306i	0.835149	−	0.550025i	$-0.185382\pi$
$954$	8354.03	+	24677.4i	0.283513	+	0.837485i
$955$	3817.58	−	8359.34i	0.129355	−	0.283248i
$956$	19844.5	−	7944.52i	0.671355	−	0.268770i
$957$	−35.1288	+	48.9793i	−0.00118658	+	0.00165441i
$958$	−14727.6	+	14042.8i	−0.496690	+	0.473593i
$959$	29126.5	+	11660.5i	0.980754	+	0.392634i
$960$	−32754.0	−	17026.7i	−1.10118	−	0.572430i
$961$	1510.30	−	31705.2i	0.0506966	−	1.06425i
$962$	−47818.5	+	55185.5i	−1.60263	+	1.84953i
$963$	−1029.83	−	1811.98i	−0.0344609	−	0.0606336i
$964$	−44671.3	−	97816.4i	−1.49249	−	3.26811i
$965$	13332.6	+	23092.8i	0.444759	+	0.770345i
$966$	19595.4	+	34169.8i	0.652661	+	1.13809i
$967$	6951.72	−	12040.7i	0.231181	−	0.400418i	−0.726975	−	0.686664i	$-0.759074\pi$
$967$	6951.72	−	12040.7i	0.231181	−	0.400418i	0.958156	+	0.286247i	$0.0924076\pi$
$968$	−87114.0	−	8318.38i	−2.89251	−	0.276201i
$969$	−2503.43	−	1012.08i	−0.0829946	−	0.0335529i
$970$	−17775.5	−	3425.95i	−0.588390	−	0.113403i
$971$	6006.29	+	3860.01i	0.198508	+	0.127573i	0.636119	−	0.771591i	$-0.280539\pi$
$971$	6006.29	+	3860.01i	0.198508	+	0.127573i	−0.437611	+	0.899164i	$0.644175\pi$
$972$	−77288.3	−	1310.11i	−2.55043	−	0.0432323i
$973$	−5163.96	−	35916.2i	−0.170143	−	1.18337i
$974$	−3499.49	−	14425.1i	−0.115124	−	0.474548i
$975$	13787.7	+	1363.74i	0.452881	+	0.0447946i
$976$	42581.1	+	33486.1i	1.39650	+	1.09822i
$977$	−23115.7	−	32461.5i	−0.756947	−	1.06298i	−0.995766	−	0.0919194i	$-0.970700\pi$
$977$	−23115.7	−	32461.5i	−0.756947	−	1.06298i	0.238819	−	0.971064i	$-0.423240\pi$
$978$	1936.73	+	1253.96i	0.0633230	+	0.0409992i
$979$	−87.3215	+	34.9582i	−0.00285067	+	0.00114124i
$980$	20707.3	−	13307.8i	0.674970	−	0.433777i
$981$	−283.475	+	5207.75i	−0.00922596	+	0.169491i
$982$	−3629.06	−	25240.7i	−0.117931	−	0.820226i
$983$	17124.8	−	49478.8i	0.555641	−	1.60542i	−0.220860	−	0.975305i	$-0.570887\pi$
$983$	17124.8	−	49478.8i	0.555641	−	1.60542i	0.776502	−	0.630115i	$-0.216992\pi$
$984$	139131.	+	27304.9i	4.50747	+	0.884601i
$985$	6197.51	+	17906.5i	0.200476	+	0.579238i
$986$	211.966	−	873.734i	0.00684621	−	0.0282204i
$987$	−8305.58	−	7973.28i	−0.267852	−	0.257135i
$988$	4509.66	+	7810.96i	0.145214	+	0.251518i
$989$	−25936.6	+	2489.07i	−0.833909	+	0.0800280i
$990$	−1966.70	+	1849.95i	−0.0631372	+	0.0593892i
$991$	−2049.61	−	4488.01i	−0.0656992	−	0.143861i	0.873934	−	0.486045i	$-0.161561\pi$
$991$	−2049.61	−	4488.01i	−0.0656992	−	0.143861i	−0.939633	+	0.342184i	$0.888834\pi$
$992$	86037.8	+	82036.8i	2.75373	+	2.62568i
$993$	−21621.4	−	25124.0i	−0.690970	−	0.802906i
$994$	−45941.3	+	23684.4i	−1.46597	+	0.755758i
$995$	−1183.95	+	228.187i	−0.0377222	+	0.00727036i
$996$	26962.9	−	46337.7i	0.857785	−	1.47416i
$997$	5630.94	+	23211.0i	0.178870	+	0.737313i	0.988607	+	0.150520i	$0.0480947\pi$
$997$	5630.94	+	23211.0i	0.178870	+	0.737313i	−0.809737	+	0.586793i	$0.800390\pi$
$998$	−69849.3	+	44889.5i	−2.21547	+	1.42380i
$999$	−47242.5	−	31044.3i	−1.49618	−	0.983181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.3	✓	1400
9.7	even	3	inner	207.4.m.a.142.68	yes	1400
23.6	even	11	inner	207.4.m.a.121.68	yes	1400
207.52	even	33	inner	207.4.m.a.52.3	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.3	✓	1400	1.1	even	1	trivial
207.4.m.a.52.3	yes	1400	207.52	even	33	inner
207.4.m.a.121.68	yes	1400	23.6	even	11	inner
207.4.m.a.142.68	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+(-3.09157 + 4.34150i) q^{2} +(-4.81737 - 1.94756i) q^{3} +(-6.67428 - 19.2841i) q^{4} +(6.06640 - 3.12745i) q^{5} +(23.3485 - 14.8936i) q^{6} +(-10.1357 + 7.97080i) q^{7} +(63.4448 + 18.6291i) q^{8} +(19.4141 + 18.7642i) q^{9} +(-5.17688 + 36.0060i) q^{10} +(2.73664 - 0.261318i) q^{11} +(-5.40435 + 105.897i) q^{12} +(26.7276 + 21.0188i) q^{13} +(-3.27003 - 68.6464i) q^{14} +(-35.3150 + 3.25140i) q^{15} +(-148.698 + 116.937i) q^{16} +(-26.1804 - 30.2138i) q^{17} +(-141.485 + 26.2753i) q^{18} +(-8.51232 + 9.82374i) q^{19} +(-100.799 - 96.1114i) q^{20} +(64.3510 - 18.6584i) q^{21} +(-7.32600 + 12.6890i) q^{22} +(72.1943 - 83.3966i) q^{23} +(-269.356 - 213.305i) q^{24} +(-45.4868 + 63.8773i) q^{25} +(-173.883 + 51.0568i) q^{26} +(-56.9803 - 128.204i) q^{27} +(221.358 + 142.258i) q^{28} +(1.38007 - 3.98744i) q^{29} +(95.0626 - 163.372i) q^{30} +(-179.527 + 171.179i) q^{31} +(-22.8035 - 478.704i) q^{32} +(-13.6923 - 4.07090i) q^{33} +(212.112 - 20.2542i) q^{34} +(-36.5589 + 80.0529i) q^{35} +(232.275 - 499.619i) q^{36} +(338.967 - 217.841i) q^{37} +(-16.3333 - 67.3270i) q^{38} +(-87.8214 - 153.309i) q^{39} +(443.143 - 85.4088i) q^{40} +(-366.789 + 189.093i) q^{41} +(-117.940 + 337.063i) q^{42} +(-170.959 - 163.009i) q^{43} +(-23.3044 - 51.0295i) q^{44} +(176.457 + 53.1147i) q^{45} +(138.873 + 571.257i) q^{46} +(-85.9184 - 148.815i) q^{47} +(944.074 - 273.732i) q^{48} +(-41.6666 + 171.752i) q^{49} +(-136.698 - 394.962i) q^{50} +(67.2775 + 196.539i) q^{51} +(226.941 - 655.703i) q^{52} +(-25.7655 - 179.203i) q^{53} +(732.756 + 148.971i) q^{54} +(15.7843 - 10.1440i) q^{55} +(-791.546 + 316.887i) q^{56} +(60.1392 - 30.7463i) q^{57} +(13.0449 + 18.3190i) q^{58} +(-154.661 - 121.627i) q^{59} +(298.402 + 659.315i) q^{60} +(-67.5119 - 278.288i) q^{61} +(-188.152 - 1308.63i) q^{62} +(-346.340 - 35.4426i) q^{63} +(875.670 + 562.759i) q^{64} +(227.876 + 43.9194i) q^{65} +(60.0046 - 46.8598i) q^{66} +(-1057.58 - 100.987i) q^{67} +(-407.909 + 706.520i) q^{68} +(-510.206 + 261.149i) q^{69} +(-234.525 - 406.210i) q^{70} +(-312.431 - 684.129i) q^{71} +(882.161 + 1552.16i) q^{72} +(-529.976 + 611.625i) q^{73} +(-102.184 + 2145.10i) q^{74} +(343.531 - 219.132i) q^{75} +(246.255 + 98.5857i) q^{76} +(-25.6549 + 24.4619i) q^{77} +(937.096 + 92.6885i) q^{78} +(-959.966 + 384.313i) q^{79} +(-536.345 + 1174.43i) q^{80} +(24.8107 + 728.578i) q^{81} +(313.007 - 2177.01i) q^{82} +(-449.397 - 231.680i) q^{83} +(-789.307 - 1116.42i) q^{84} +(-253.313 - 101.411i) q^{85} +(1236.23 - 238.264i) q^{86} +(-14.4140 + 16.5212i) q^{87} +(178.494 + 34.4019i) q^{88} +(-32.8287 + 9.63938i) q^{89} +(-776.127 + 601.882i) q^{90} -438.440 q^{91} +(-2090.07 - 835.587i) q^{92} +(1198.23 - 474.992i) q^{93} +(911.702 + 87.0570i) q^{94} +(-20.9159 + 86.2166i) q^{95} +(-822.450 + 2350.50i) q^{96} +(-23.6792 + 497.087i) q^{97} +(-616.847 - 711.879i) q^{98} +(58.0327 + 46.2776i) 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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