LMFDB - Embedded newform 207.4.m.a.4.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,4,Mod(4,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			4.16
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.16862 + 3.04540i) q^{2} +(3.13722 + 4.14221i) q^{3} +(-1.95501 - 5.64863i) q^{4} +(-16.6844 + 8.60138i) q^{5} +(-19.4181 + 0.571212i) q^{6} +(-19.7783 + 15.5539i) q^{7} +(-7.25554 - 2.13042i) q^{8} +(-7.31574 + 25.9900i) q^{9} +(9.98737 - 69.4637i) q^{10} +(8.43600 - 0.805540i) q^{11} +(17.2645 - 25.8190i) q^{12} +(48.3985 + 38.0610i) q^{13} +(-4.47603 - 93.9634i) q^{14} +(-87.9711 - 42.1256i) q^{15} +(59.8108 - 47.0357i) q^{16} +(72.3175 + 83.4588i) q^{17} +(-63.2849 - 78.6418i) q^{18} +(57.3795 - 66.2195i) q^{19} +(81.2041 + 77.4279i) q^{20} +(-126.476 - 33.1301i) q^{21} +(-15.8413 + 27.4379i) q^{22} +(-101.759 - 42.5694i) q^{23} +(-13.9376 - 36.7375i) q^{24} +(131.877 - 185.195i) q^{25} +(-220.869 + 64.8530i) q^{26} +(-130.607 + 51.2330i) q^{27} +(126.525 + 81.3125i) q^{28} +(-69.0040 + 199.374i) q^{29} +(319.065 - 176.553i) q^{30} +(-93.1315 + 88.8007i) q^{31} +(10.6573 + 223.724i) q^{32} +(29.8023 + 32.4165i) q^{33} +(-410.995 + 39.2452i) q^{34} +(196.204 - 429.627i) q^{35} +(161.110 - 9.48679i) q^{36} +(315.962 - 203.057i) q^{37} +(77.2305 + 318.348i) q^{38} +(-5.81992 + 319.882i) q^{39} +(139.378 - 26.8630i) q^{40} +(1.37017 - 0.706371i) q^{41} +(375.173 - 313.324i) q^{42} +(-35.0824 - 33.4510i) q^{43} +(-21.0427 - 46.0770i) q^{44} +(-101.492 - 496.552i) q^{45} +(350.317 - 217.579i) q^{46} +(-225.553 - 390.669i) q^{47} +(382.471 + 100.187i) q^{48} +(68.3949 - 281.928i) q^{49} +(278.002 + 803.235i) q^{50} +(-118.828 + 561.382i) q^{51} +(120.373 - 347.795i) q^{52} +(80.9085 + 562.731i) q^{53} +(127.212 - 508.855i) q^{54} +(-133.820 + 86.0012i) q^{55} +(176.639 - 70.7155i) q^{56} +(454.307 + 29.9328i) q^{57} +(-457.530 - 642.511i) q^{58} +(-362.926 - 285.408i) q^{59} +(-65.9676 + 579.272i) q^{60} +(41.1214 + 169.505i) q^{61} +(-68.4669 - 476.198i) q^{62} +(-259.552 - 627.827i) q^{63} +(-192.353 - 123.618i) q^{64} +(-1134.88 - 218.729i) q^{65} +(-163.351 + 20.4608i) q^{66} +(292.051 + 27.8875i) q^{67} +(330.046 - 571.657i) q^{68} +(-142.908 - 555.055i) q^{69} +(882.895 + 1529.22i) q^{70} +(-37.7703 - 82.7054i) q^{71} +(108.449 - 172.986i) q^{72} +(-522.876 + 603.431i) q^{73} +(-66.8133 + 1402.58i) q^{74} +(1180.84 - 34.7362i) q^{75} +(-486.226 - 194.656i) q^{76} +(-154.321 + 147.145i) q^{77} +(-961.549 - 711.428i) q^{78} +(-320.863 + 128.454i) q^{79} +(-593.332 + 1299.22i) q^{80} +(-621.960 - 380.272i) q^{81} +(-0.820193 + 5.70456i) q^{82} +(960.313 + 495.076i) q^{83} +(60.1224 + 779.187i) q^{84} +(-1924.43 - 770.426i) q^{85} +(177.952 - 34.2974i) q^{86} +(-1042.33 + 339.651i) q^{87} +(-62.9238 - 12.1276i) q^{88} +(814.628 - 239.196i) q^{89} +(1732.30 + 767.750i) q^{90} -1549.24 q^{91} +(-41.5193 + 658.021i) q^{92} +(-660.005 - 107.183i) q^{93} +(1678.88 + 160.314i) q^{94} +(-387.761 + 1598.37i) q^{95} +(-893.277 + 746.016i) q^{96} +(25.7115 - 539.750i) q^{97} +(710.261 + 819.684i) q^{98} +(-40.7796 + 225.145i) 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 $

$2$	−2.16862	+	3.04540i	−0.766723	+	1.07671i	0.227954	+	0.973672i	$0.426796\pi$
$2$	−2.16862	+	3.04540i	−0.766723	+	1.07671i	−0.994677	+	0.103040i	$0.967143\pi$
$3$	3.13722	+	4.14221i	0.603758	+	0.797168i
$3$	3.13722	+	4.14221i	0.603758	+	0.797168i
$4$	−1.95501	−	5.64863i	−0.244376	−	0.706078i
$5$	−16.6844	+	8.60138i	−1.49229	+	0.769331i	−0.995153	−	0.0983388i	$-0.968647\pi$
$5$	−16.6844	+	8.60138i	−1.49229	+	0.769331i	−0.497141	+	0.867670i	$0.665617\pi$
$6$	−19.4181	+	0.571212i	−1.32123	+	0.0388661i
$7$	−19.7783	+	15.5539i	−1.06793	+	0.839830i	−0.987608	−	0.156939i	$-0.949837\pi$
$7$	−19.7783	+	15.5539i	−1.06793	+	0.839830i	−0.0803219	+	0.996769i	$0.525595\pi$
$8$	−7.25554	−	2.13042i	−0.320652	−	0.0941520i
$9$	−7.31574	+	25.9900i	−0.270953	+	0.962592i
$10$	9.98737	−	69.4637i	0.315828	−	2.19663i
$11$	8.43600	−	0.805540i	0.231232	−	0.0220800i	0.0212031	−	0.999775i	$-0.493250\pi$
$11$	8.43600	−	0.805540i	0.231232	−	0.0220800i	0.210029	+	0.977695i	$0.432644\pi$
$12$	17.2645	−	25.8190i	0.415319	−	0.621109i
$13$	48.3985	+	38.0610i	1.03256	+	0.812018i	0.982412	−	0.186724i	$-0.0597869\pi$
$13$	48.3985	+	38.0610i	1.03256	+	0.812018i	0.0501523	+	0.998742i	$0.484029\pi$
$14$	−4.47603	−	93.9634i	−0.0854478	−	1.79377i
$15$	−87.9711	−	42.1256i	−1.51427	−	0.725119i
$16$	59.8108	−	47.0357i	0.934543	−	0.734933i
$17$	72.3175	+	83.4588i	1.03174	+	1.19069i	0.981403	+	0.191958i	$0.0614836\pi$
$17$	72.3175	+	83.4588i	1.03174	+	1.19069i	0.0503356	+	0.998732i	$0.483971\pi$
$18$	−63.2849	−	78.6418i	−0.828688	−	1.02978i
$19$	57.3795	−	66.2195i	0.692829	−	0.799568i	−0.294936	−	0.955517i	$-0.595298\pi$
$19$	57.3795	−	66.2195i	0.692829	−	0.799568i	0.987765	+	0.155949i	$0.0498437\pi$
$20$	81.2041	+	77.4279i	0.907889	+	0.865670i
$21$	−126.476	−	33.1301i	−1.31426	−	0.344266i
$22$	−15.8413	+	27.4379i	−0.153517	+	0.265899i
$23$	−101.759	−	42.5694i	−0.922529	−	0.385927i
$23$	−101.759	−	42.5694i	−0.922529	−	0.385927i
$24$	−13.9376	−	36.7375i	−0.118541	−	0.312459i
$25$	131.877	−	185.195i	1.05501	−	1.48156i
$26$	−220.869	+	64.8530i	−1.66600	+	0.489182i
$27$	−130.607	+	51.2330i	−0.930938	+	0.365177i
$28$	126.525	+	81.3125i	0.853962	+	0.548808i
$29$	−69.0040	+	199.374i	−0.441852	+	1.27665i	0.475901	+	0.879499i	$0.342122\pi$
$29$	−69.0040	+	199.374i	−0.441852	+	1.27665i	−0.917754	+	0.397150i	$0.869999\pi$
$30$	319.065	−	176.553i	1.94177	−	1.07447i
$31$	−93.1315	+	88.8007i	−0.539578	+	0.514487i	−0.910129	−	0.414326i	$-0.864017\pi$
$31$	−93.1315	+	88.8007i	−0.539578	+	0.514487i	0.370551	+	0.928812i	$0.379169\pi$
$32$	10.6573	+	223.724i	0.0588738	+	1.23591i
$33$	29.8023	+	32.4165i	0.157209	+	0.171000i
$34$	−410.995	+	39.2452i	−2.07309	+	0.197956i
$35$	196.204	−	429.627i	0.947559	−	2.07486i
$36$	161.110	−	9.48679i	0.745880	−	0.0439203i
$37$	315.962	−	203.057i	1.40389	−	0.902225i	0.403967	−	0.914773i	$-0.367631\pi$
$37$	315.962	−	203.057i	1.40389	−	0.902225i	0.999921	+	0.0125488i	$0.00399452\pi$
$38$	77.2305	+	318.348i	0.329696	+	1.35902i
$39$	−5.81992	+	319.882i	−0.0238957	+	1.31339i
$40$	139.378	−	26.8630i	0.550942	−	0.106185i
$41$	1.37017	−	0.706371i	0.00521913	−	0.00269065i	−0.455615	−	0.890177i	$-0.650581\pi$
$41$	1.37017	−	0.706371i	0.00521913	−	0.00269065i	0.460834	+	0.887486i	$0.347550\pi$
$42$	375.173	−	313.324i	1.37835	−	1.15112i
$43$	−35.0824	−	33.4510i	−0.124419	−	0.118633i	0.625316	−	0.780372i	$-0.284970\pi$
$43$	−35.0824	−	33.4510i	−0.124419	−	0.118633i	−0.749734	+	0.661739i	$0.769819\pi$
$44$	−21.0427	−	46.0770i	−0.0720977	−	0.157872i
$45$	−101.492	−	496.552i	−0.336210	−	1.64492i
$46$	350.317	−	217.579i	1.12286	−	0.697399i
$47$	−225.553	−	390.669i	−0.700006	−	1.21245i	−0.968464	−	0.249155i	$-0.919847\pi$
$47$	−225.553	−	390.669i	−0.700006	−	1.21245i	0.268458	−	0.963291i	$-0.413486\pi$
$48$	382.471	+	100.187i	1.15010	+	0.301266i
$49$	68.3949	−	281.928i	0.199402	−	0.821947i
$50$	278.002	+	803.235i	0.786310	+	2.27189i
$51$	−118.828	+	561.382i	−0.326260	+	1.54136i
$52$	120.373	−	347.795i	0.321014	−	0.927509i
$53$	80.9085	+	562.731i	0.209691	+	1.45843i	0.774165	+	0.632983i	$0.218170\pi$
$53$	80.9085	+	562.731i	0.209691	+	1.45843i	−0.564474	+	0.825451i	$0.690921\pi$
$54$	127.212	−	508.855i	0.320581	−	1.28234i
$55$	−133.820	+	86.0012i	−0.328079	+	0.210844i
$56$	176.639	−	70.7155i	0.421506	−	0.168746i
$57$	454.307	+	29.9328i	1.05569	+	0.0695562i
$58$	−457.530	−	642.511i	−1.03580	−	1.45458i
$59$	−362.926	−	285.408i	−0.800830	−	0.629779i	0.131530	−	0.991312i	$-0.458011\pi$
$59$	−362.926	−	285.408i	−0.800830	−	0.629779i	−0.932359	+	0.361533i	$0.882254\pi$
$60$	−65.9676	+	579.272i	−0.141940	+	1.24639i
$61$	41.1214	+	169.505i	0.0863125	+	0.355785i	0.998547	−	0.0538829i	$-0.0171598\pi$
$61$	41.1214	+	169.505i	0.0863125	+	0.355785i	−0.912235	+	0.409668i	$0.865645\pi$
$62$	−68.4669	−	476.198i	−0.140247	−	0.975439i
$63$	−259.552	−	627.827i	−0.519054	−	1.25554i
$64$	−192.353	−	123.618i	−0.375690	−	0.241441i
$65$	−1134.88	−	218.729i	−2.16560	−	0.417385i
$66$	−163.351	+	20.4608i	−0.304653	+	0.0381599i
$67$	292.051	+	27.8875i	0.532532	+	0.0508507i	0.357859	−	0.933776i	$-0.383507\pi$
$67$	292.051	+	27.8875i	0.532532	+	0.0508507i	0.174674	+	0.984626i	$0.444113\pi$
$68$	330.046	−	571.657i	0.588588	−	1.01946i
$69$	−142.908	−	555.055i	−0.249335	−	0.968417i
$70$	882.895	+	1529.22i	1.50752	+	2.61109i
$71$	−37.7703	−	82.7054i	−0.0631339	−	0.138244i	0.875435	−	0.483336i	$-0.160575\pi$
$71$	−37.7703	−	82.7054i	−0.0631339	−	0.138244i	−0.938569	+	0.345092i	$0.887848\pi$
$72$	108.449	−	172.986i	0.177512	−	0.283147i
$73$	−522.876	+	603.431i	−0.838328	+	0.967482i	−0.999812	−	0.0193931i	$-0.993827\pi$
$73$	−522.876	+	603.431i	−0.838328	+	0.967482i	0.161484	+	0.986875i	$0.448372\pi$
$74$	−66.8133	+	1402.58i	−0.104958	+	2.20334i
$75$	1180.84	−	34.7362i	1.81802	−	0.0534799i
$76$	−486.226	−	194.656i	−0.733868	−	0.293797i
$77$	−154.321	+	147.145i	−0.228396	+	0.217775i
$78$	−961.549	−	711.428i	−1.39582	−	1.03273i
$79$	−320.863	+	128.454i	−0.456962	+	0.182940i	−0.588712	−	0.808343i	$-0.700365\pi$
$79$	−320.863	+	128.454i	−0.456962	+	0.182940i	0.131750	+	0.991283i	$0.457940\pi$
$80$	−593.332	+	1299.22i	−0.829206	+	1.81571i
$81$	−621.960	−	380.272i	−0.853169	−	0.521635i
$82$	−0.820193	+	5.70456i	−0.00110457	+	0.00768249i
$83$	960.313	+	495.076i	1.26998	+	0.654719i	0.955624	−	0.294588i	$-0.0951823\pi$
$83$	960.313	+	495.076i	1.26998	+	0.654719i	0.314352	+	0.949306i	$0.398213\pi$
$84$	60.1224	+	779.187i	0.0780940	+	1.01210i
$85$	−1924.43	−	770.426i	−2.45569	−	0.983111i
$86$	177.952	−	34.2974i	0.223128	−	0.0430045i
$87$	−1042.33	+	339.651i	−1.28448	+	0.418556i
$88$	−62.9238	−	12.1276i	−0.0762239	−	0.0146910i
$89$	814.628	−	239.196i	0.970229	−	0.284885i	0.242044	−	0.970265i	$-0.422182\pi$
$89$	814.628	−	239.196i	0.970229	−	0.284885i	0.728185	+	0.685380i	$0.240364\pi$
$90$	1732.30	+	767.750i	2.02889	+	0.899199i
$91$	−1549.24			−1.78466
$92$	−41.5193	+	658.021i	−0.0470509	+	0.745689i
$93$	−660.005	−	107.183i	−0.735906	−	0.119509i
$94$	1678.88	+	160.314i	1.84217	+	0.175905i
$95$	−387.761	+	1598.37i	−0.418773	+	1.72621i
$96$	−893.277	+	746.016i	−0.949684	+	0.793124i
$97$	25.7115	−	539.750i	0.0269134	−	0.564982i	−0.944632	−	0.328131i	$-0.893581\pi$
$97$	25.7115	−	539.750i	0.0269134	−	0.564982i	0.971546	−	0.236852i	$-0.0761156\pi$
$98$	710.261	+	819.684i	0.732114	+	0.844904i
$99$	−40.7796	+	225.145i	−0.0413990	+	0.228565i
$100$	−1303.92	−	382.865i	−1.30392	−	0.382865i
$101$	−1046.54	−	539.528i	−1.03104	−	0.531536i	−0.142236	−	0.989833i	$-0.545429\pi$
$101$	−1046.54	−	539.528i	−1.03104	−	0.531536i	−0.888799	+	0.458297i	$0.848460\pi$
$102$	−1451.94	−	1579.30i	−1.40945	−	1.53308i
$103$	148.249	+	208.187i	0.141820	+	0.199158i	0.879376	−	0.476127i	$-0.157960\pi$
$103$	148.249	+	208.187i	0.141820	+	0.199158i	−0.737557	+	0.675285i	$0.764020\pi$
$104$	−270.071	−	379.262i	−0.254641	−	0.357594i
$105$	2395.14	−	535.116i	2.22611	−	0.497352i
$106$	−1889.20	−	973.950i	−1.73109	−	0.892438i
$107$	289.692	+	85.0613i	0.261735	+	0.0768522i	0.409967	−	0.912100i	$-0.365540\pi$
$107$	289.692	+	85.0613i	0.261735	+	0.0768522i	−0.148232	+	0.988953i	$0.547358\pi$
$108$	544.734	+	637.589i	0.485343	+	0.568075i
$109$	−355.829	−	410.648i	−0.312681	−	0.360853i	0.577556	−	0.816351i	$-0.304007\pi$
$109$	−355.829	−	410.648i	−0.312681	−	0.360853i	−0.890237	+	0.455498i	$0.849461\pi$
$110$	28.2977	−	594.041i	0.0245280	−	0.514905i
$111$	1832.34	+	671.748i	1.56683	+	0.574410i
$112$	−451.371	+	1860.58i	−0.380808	+	1.56971i
$113$	1200.56	+	114.639i	0.999460	+	0.0954369i	0.581941	−	0.813231i	$-0.302294\pi$
$113$	1200.56	+	114.639i	0.999460	+	0.0954369i	0.417519	+	0.908668i	$0.362900\pi$
$114$	−1076.38	+	1318.63i	−0.884314	+	1.08334i
$115$	2063.93	−	165.023i	1.67359	−	0.133813i
$116$	1261.09			1.00939
$117$	−1343.28	+	979.433i	−1.06142	+	0.773920i
$118$	1656.23	−	486.313i	1.29211	−	0.379396i
$119$	−2728.43	−	525.861i	−2.10180	−	0.405089i
$120$	548.532	+	493.059i	0.417283	+	0.375083i
$121$	−1236.43	+	238.302i	−0.928948	+	0.179040i
$122$	−605.387	−	242.360i	−0.449256	−	0.179855i
$123$	7.22445	+	3.45948i	0.00529599	+	0.00253602i
$124$	683.675	+	352.459i	0.495128	+	0.255256i
$125$	−273.421	+	1901.69i	−0.195644	+	1.36074i
$126$	2474.85	+	571.080i	1.74982	+	0.403776i
$127$	23.1695	−	50.7341i	0.0161887	−	0.0354482i	−0.901365	−	0.433060i	$-0.857434\pi$
$127$	23.1695	−	50.7341i	0.0161887	−	0.0354482i	0.917554	+	0.397612i	$0.130161\pi$
$128$	−869.863	+	348.240i	−0.600670	+	0.240472i
$129$	28.4998	−	250.261i	0.0194517	−	0.170808i
$130$	3127.23	−	2981.81i	2.10982	−	2.01171i
$131$	537.127	+	215.033i	0.358237	+	0.143416i	0.543797	−	0.839216i	$-0.316986\pi$
$131$	537.127	+	215.033i	0.358237	+	0.143416i	−0.185561	+	0.982633i	$0.559410\pi$
$132$	124.845	−	231.716i	0.0823209	−	0.152790i
$133$	−104.903	+	2202.18i	−0.0683928	+	1.43574i
$134$	−718.276	+	828.934i	−0.463056	+	0.534396i
$135$	1738.42	−	1978.19i	1.10829	−	1.26115i
$136$	−346.900	−	759.605i	−0.218724	−	0.478938i
$137$	−1212.74	−	2100.53i	−0.756288	−	1.30993i	−0.944731	−	0.327846i	$-0.893677\pi$
$137$	−1212.74	−	2100.53i	−0.756288	−	1.30993i	0.188443	−	0.982084i	$-0.439656\pi$
$138$	2000.28	+	768.491i	1.23388	+	0.474046i
$139$	583.269	−	1010.25i	0.355915	−	0.616463i	−0.631359	−	0.775491i	$-0.717502\pi$
$139$	583.269	−	1010.25i	0.355915	−	0.616463i	0.987274	+	0.159027i	$0.0508358\pi$
$140$	−2810.38	−	268.359i	−1.69658	−	0.162004i
$141$	910.624	−	2159.90i	0.543889	−	1.29005i
$142$	333.781	+	64.3309i	0.197255	+	0.0380178i
$143$	438.950	+	282.096i	0.256691	+	0.164965i
$144$	784.898	+	1898.58i	0.454223	+	1.09872i
$145$	−563.605	−	3919.96i	−0.322792	−	2.24507i
$146$	−703.769	−	2900.98i	−0.398934	−	1.64443i
$147$	1382.37	−	601.163i	0.775620	−	0.337300i
$148$	−1764.70	−	1387.78i	−0.980118	−	0.770773i
$149$	−200.557	−	281.643i	−0.110270	−	0.154853i	0.755753	−	0.654857i	$-0.227271\pi$
$149$	−200.557	−	281.643i	−0.110270	−	0.154853i	−0.866023	+	0.500004i	$0.833332\pi$
$150$	−2455.01	+	3671.47i	−1.33634	+	1.99849i
$151$	−1454.91	+	582.456i	−0.784096	+	0.313905i	−0.728944	−	0.684573i	$-0.759989\pi$
$151$	−1454.91	+	582.456i	−0.784096	+	0.313905i	−0.0551520	+	0.998478i	$0.517564\pi$
$152$	−557.394	+	358.215i	−0.297438	+	0.191152i
$153$	−2698.15	+	1268.97i	−1.42570	+	0.670523i
$154$	−113.451	−	789.070i	−0.0593646	−	0.412890i
$155$	790.030	−	2282.64i	0.409398	−	1.18288i
$156$	1818.27	−	592.499i	0.933195	−	0.304089i
$157$	467.266	+	1350.08i	0.237528	+	0.686291i	0.999262	+	0.0384022i	$0.0122268\pi$
$157$	467.266	+	1350.08i	0.237528	+	0.686291i	−0.761735	+	0.647889i	$0.775652\pi$
$158$	304.636	−	1255.73i	0.153389	−	0.632280i
$159$	−2077.12	+	2100.55i	−1.03601	+	1.04770i
$160$	−2102.15	−	3641.02i	−1.03868	−	1.79905i
$161$	2674.74	−	740.790i	1.30931	−	0.362624i
$162$	2506.88	−	1069.45i	1.21579	−	0.518667i
$163$	509.707	+	1116.10i	0.244928	+	0.536318i	0.991671	−	0.128794i	$-0.0411107\pi$
$163$	509.707	+	1116.10i	0.244928	+	0.536318i	−0.746743	+	0.665113i	$0.768383\pi$
$164$	−6.66872	−	6.35861i	−0.00317524	−	0.00302759i
$165$	−776.058	−	284.508i	−0.366158	−	0.134236i
$166$	−3590.26	+	1850.91i	−1.67866	+	0.865411i
$167$	1264.60	−	243.732i	0.585976	−	0.112938i	0.112358	−	0.993668i	$-0.464160\pi$
$167$	1264.60	−	243.732i	0.585976	−	0.112938i	0.473618	+	0.880730i	$0.342948\pi$
$168$	847.072	+	509.824i	0.389006	+	0.234130i
$169$	375.814	+	1549.13i	0.171058	+	0.705111i
$170$	6519.62	−	4189.90i	2.94136	−	1.89030i
$171$	1301.27	+	1975.74i	0.581933	+	0.883558i
$172$	−120.366	+	263.564i	−0.0533593	+	0.116841i
$173$	4314.92	−	412.025i	1.89628	−	0.181073i	0.919180	−	0.393838i	$-0.128853\pi$
$173$	4314.92	−	412.025i	1.89628	−	0.181073i	0.977103	+	0.212765i	$0.0682469\pi$
$174$	1226.04	−	3910.88i	0.534173	−	1.70393i
$175$	272.193	+	5714.04i	0.117577	+	2.46823i
$176$	466.675	−	444.973i	0.199869	−	0.190575i
$177$	43.6418	−	2398.70i	0.0185329	−	1.01863i
$178$	−1038.17	+	2999.60i	−0.437158	+	1.26309i
$179$	−135.311	−	86.9591i	−0.0565006	−	0.0363108i	0.512086	−	0.858934i	$-0.328873\pi$
$179$	−135.311	−	86.9591i	−0.0565006	−	0.0363108i	−0.568586	+	0.822624i	$0.692509\pi$
$180$	−2606.42	+	1544.05i	−1.07928	+	0.639371i
$181$	−76.8982	+	22.5793i	−0.0315790	+	0.00927243i	−0.297484	−	0.954727i	$-0.596147\pi$
$181$	−76.8982	+	22.5793i	−0.0315790	+	0.00927243i	0.265905	+	0.963999i	$0.414329\pi$
$182$	3359.71	−	4718.05i	1.36834	−	1.92157i
$183$	−573.117	+	702.107i	−0.231508	+	0.283613i
$184$	647.624	+	525.652i	0.259475	+	0.210607i
$185$	−3525.06	+	6105.58i	−1.40091	+	2.42644i
$186$	1757.71	−	1777.54i	0.692913	−	0.700729i
$187$	677.300	+	645.804i	0.264861	+	0.252545i
$188$	−1765.79	+	2037.83i	−0.685017	+	0.790552i
$189$	1786.32	−	3044.75i	0.687490	−	1.17181i
$190$	−4026.78	−	4647.15i	−1.53754	−	1.77442i
$191$	−2325.42	+	1828.73i	−0.880951	+	0.692788i	−0.952464	−	0.304652i	$-0.901460\pi$
$191$	−2325.42	+	1828.73i	−0.880951	+	0.692788i	0.0715127	+	0.997440i	$0.477217\pi$
$192$	−91.4030	−	1184.58i	−0.0343565	−	0.445260i
$193$	187.322	+	3932.37i	0.0698639	+	1.46662i	0.713158	+	0.701004i	$0.247264\pi$
$193$	187.322	+	3932.37i	0.0698639	+	1.46662i	−0.643294	+	0.765619i	$0.722433\pi$
$194$	1588.00	+	1248.81i	0.587688	+	0.462163i
$195$	−2654.33	−	5387.09i	−0.974772	−	1.97835i
$196$	−1726.22	+	164.834i	−0.629088	+	0.0600706i
$197$	329.745	−	2293.43i	0.119256	−	0.829442i	−0.839123	−	0.543942i	$-0.816931\pi$
$197$	329.745	−	2293.43i	0.119256	−	0.829442i	0.958379	−	0.285500i	$-0.0921598\pi$
$198$	−597.221	−	612.444i	−0.214357	−	0.219821i
$199$	−607.522	−	178.384i	−0.216412	−	0.0635444i	0.171729	−	0.985144i	$-0.445065\pi$
$199$	−607.522	−	178.384i	−0.216412	−	0.0635444i	−0.388141	+	0.921600i	$0.626883\pi$
$200$	−1351.38	+	1062.74i	−0.477785	+	0.375734i
$201$	800.711	+	1297.22i	0.280984	+	0.455219i
$202$	3912.63	−	2017.10i	1.36283	−	0.702587i
$203$	−1736.25	−	5016.57i	−0.600300	−	1.73445i
$204$	3403.35	−	426.292i	1.16805	−	0.146306i
$205$	−16.7846	+	23.5707i	−0.00571848	+	0.00803048i
$206$	−955.509			−0.323172
$207$	1850.82	−	2333.28i	0.621453	−	0.783451i
$208$	4684.98			1.56176
$209$	430.711	−	604.849i	0.142550	−	0.200183i
$210$	−3564.51	+	8454.62i	−1.17131	+	2.77821i
$211$	725.947	+	2097.49i	0.236854	+	0.684345i	0.999304	+	0.0372981i	$0.0118751\pi$
$211$	725.947	+	2097.49i	0.236854	+	0.684345i	−0.762450	+	0.647047i	$0.776004\pi$
$212$	3020.48	−	1557.17i	0.978525	−	0.504465i
$213$	224.089	−	415.917i	0.0720861	−	0.133794i
$214$	−887.278	+	697.764i	−0.283426	+	0.222888i
$215$	873.051	+	256.351i	0.276938	+	0.0813162i
$216$	1056.77	−	93.4752i	0.332890	−	0.0294453i
$217$	460.793	−	3204.89i	0.144151	−	1.00259i
$218$	2022.25	−	193.101i	0.628274	−	0.0599929i
$219$	−4139.91	−	272.766i	−1.27739	−	0.0841634i
$220$	747.409	+	587.769i	0.229047	+	0.180124i
$221$	323.532	+	6791.76i	0.0984755	+	2.06726i
$222$	−6019.40	+	4123.46i	−1.81980	+	1.24661i
$223$	−1654.11	+	1300.80i	−0.496714	+	0.390620i	−0.834850	−	0.550477i	$-0.814446\pi$
$223$	−1654.11	+	1300.80i	−0.496714	+	0.390620i	0.338136	+	0.941097i	$0.390204\pi$
$224$	−3690.56	−	4259.13i	−1.10083	−	1.27042i
$225$	3848.44	+	4782.32i	1.14028	+	1.41698i
$226$	−2952.68	+	3407.57i	−0.869067	+	1.00296i
$227$	−4074.71	−	3885.23i	−1.19140	−	1.13600i	−0.987601	−	0.156986i	$-0.949822\pi$
$227$	−4074.71	−	3885.23i	−1.19140	−	1.13600i	−0.203801	−	0.979012i	$-0.565329\pi$
$228$	−719.094	−	2624.73i	−0.208873	−	0.762398i
$229$	−821.395	+	1422.70i	−0.237027	+	0.410544i	−0.959860	−	0.280480i	$-0.909506\pi$
$229$	−821.395	+	1422.70i	−0.237027	+	0.410544i	0.722833	+	0.691023i	$0.242840\pi$
$230$	−3973.33	+	6643.38i	−1.13910	+	1.90457i
$231$	−1093.64	−	177.604i	−0.311499	−	0.0505866i
$232$	925.411	−	1299.56i	0.261880	−	0.367759i
$233$	−2786.56	+	818.209i	−0.783493	+	0.230054i	−0.648927	−	0.760850i	$-0.724782\pi$
$233$	−2786.56	+	818.209i	−0.783493	+	0.230054i	−0.134566	+	0.990905i	$0.542964\pi$
$234$	−69.7090	−	6214.84i	−0.0194744	−	1.73622i
$235$	7123.50	+	4578.00i	1.97739	+	1.27079i
$236$	−902.641	+	2608.01i	−0.248970	+	0.719352i
$237$	−1538.70	−	926.093i	−0.421728	−	0.253824i
$238$	7518.38	−	7168.76i	2.04766	−	1.95244i
$239$	57.8254	+	1213.91i	0.0156503	+	0.328540i	0.993092	+	0.117336i	$0.0374354\pi$
$239$	57.8254	+	1213.91i	0.0156503	+	0.328540i	−0.977442	+	0.211204i	$0.932262\pi$
$240$	−7243.03	+	1618.22i	−1.94806	+	0.435231i
$241$	3361.84	−	321.016i	0.898568	−	0.0858028i	0.364460	−	0.931219i	$-0.381254\pi$
$241$	3361.84	−	321.016i	0.898568	−	0.0858028i	0.534108	+	0.845416i	$0.320648\pi$
$242$	1955.62	−	4282.21i	0.519471	−	1.13748i
$243$	−376.058	−	3769.28i	−0.0992762	−	0.995060i
$244$	877.077	−	563.663i	0.230119	−	0.147889i
$245$	1283.84	+	5292.07i	0.334783	+	1.37999i
$246$	−26.2026	+	14.4991i	−0.00679113	+	0.00375783i
$247$	5297.47	−	1021.00i	1.36465	−	0.263016i
$248$	864.902	−	445.888i	0.221457	−	0.114169i
$249$	962.005	+	5530.98i	0.244838	+	1.40768i
$250$	−5198.45	−	4956.71i	−1.31511	−	1.25396i
$251$	−1983.41	−	4343.07i	−0.498772	−	1.09216i	−0.976866	−	0.213850i	$-0.931400\pi$
$251$	−1983.41	−	4343.07i	−0.498772	−	1.09216i	0.478094	−	0.878309i	$-0.341328\pi$
$252$	−3038.94	+	2693.52i	−0.759662	+	0.673316i
$253$	−892.729	−	277.145i	−0.221839	−	0.0688693i
$254$	104.260	+	180.583i	0.0257553	+	0.0446095i
$255$	−2846.09	−	10388.4i	−0.698939	−	2.55116i
$256$	1257.12	−	5181.93i	0.306914	−	1.26512i
$257$	−927.045	−	2678.52i	−0.225010	−	0.650123i	−0.999839	−	0.0179520i	$-0.994285\pi$
$257$	−927.045	−	2678.52i	−0.225010	−	0.650123i	0.774829	−	0.632171i	$-0.217836\pi$
$258$	700.341	+	629.515i	0.168997	+	0.151907i
$259$	−3090.90	+	8930.56i	−0.741540	+	2.14254i
$260$	983.172	+	6838.11i	0.234514	+	1.63108i
$261$	−4676.91	−	3251.98i	−1.10917	−	0.771236i
$262$	−1819.69	+	1169.44i	−0.429086	+	0.275757i
$263$	−2843.01	+	1138.17i	−0.666569	+	0.266854i	−0.680171	−	0.733054i	$-0.738094\pi$
$263$	−2843.01	+	1138.17i	−0.666569	+	0.266854i	0.0136020	+	0.999907i	$0.495670\pi$
$264$	−147.171	−	298.690i	−0.0343096	−	0.0696330i
$265$	−6190.17	−	8692.87i	−1.43494	−	2.01509i
$266$	−6479.04	−	5095.17i	−1.49344	−	1.17445i
$267$	3546.47	+	2623.95i	0.812885	+	0.601434i
$268$	−413.436	−	1704.21i	−0.0942336	−	0.388436i
$269$	724.891	+	5041.73i	0.164303	+	1.14275i	0.890407	+	0.455165i	$0.150420\pi$
$269$	724.891	+	5041.73i	0.164303	+	1.14275i	−0.726104	+	0.687585i	$0.758671\pi$
$270$	2254.41	+	9584.12i	0.508144	+	2.16026i
$271$	−2993.93	−	1924.08i	−0.671101	−	0.431290i	0.160221	−	0.987081i	$-0.448779\pi$
$271$	−2993.93	−	1924.08i	−0.671101	−	0.431290i	−0.831322	+	0.555791i	$0.812416\pi$
$272$	8250.91	+	1590.23i	1.83928	+	0.354492i
$273$	−4860.30	−	6417.27i	−1.07750	−	1.42268i
$274$	9026.93	+	861.967i	1.99028	+	0.190049i
$275$	963.330	−	1668.54i	0.211240	−	0.365879i
$276$	−2855.91	+	1892.37i	−0.622847	+	0.412708i
$277$	−855.109	−	1481.09i	−0.185482	−	0.321264i	0.758257	−	0.651956i	$-0.226051\pi$
$277$	−855.109	−	1481.09i	−0.185482	−	0.321264i	−0.943739	+	0.330692i	$0.892718\pi$
$278$	1811.73	+	3967.14i	0.390865	+	0.855875i
$279$	−1626.60	−	3070.13i	−0.349040	−	0.658796i
$280$	−2338.85	+	2699.18i	−0.499190	+	0.576096i
$281$	−48.8057	+	1024.56i	−0.0103612	+	0.217509i	0.987749	+	0.156053i	$0.0498772\pi$
$281$	−48.8057	+	1024.56i	−0.0103612	+	0.217509i	−0.998110	+	0.0614554i	$0.980426\pi$
$282$	4602.97	+	7457.22i	0.971995	+	1.57472i
$283$	4369.30	+	1749.20i	0.917766	+	0.367418i	0.781968	−	0.623318i	$-0.214216\pi$
$283$	4369.30	+	1749.20i	0.917766	+	0.367418i	0.135798	+	0.990737i	$0.456640\pi$
$284$	−393.331	+	375.040i	−0.0821827	+	0.0783611i
$285$	−7837.27	+	3408.25i	−1.62891	+	0.708377i
$286$	−1811.01	+	725.019i	−0.374431	+	0.149900i
$287$	−16.1129	+	35.2823i	−0.00331398	+	0.00725661i
$288$	−5892.55	−	1359.72i	−1.20563	−	0.278203i
$289$	−1036.36	+	7208.06i	−0.210943	+	1.46714i
$290$	13160.1	+	6784.49i	2.66478	+	1.37379i
$291$	2316.42	−	1586.81i	0.466635	−	0.319658i
$292$	4430.78	+	1773.82i	0.887986	+	0.355496i
$293$	880.206	−	169.646i	0.175502	−	0.0338253i	−0.100743	−	0.994912i	$-0.532122\pi$
$293$	880.206	−	169.646i	0.175502	−	0.0338253i	0.276245	+	0.961087i	$0.410910\pi$
$294$	−1167.06	+	5513.57i	−0.231511	+	1.09374i
$295$	8510.09	+	1640.19i	1.67958	+	0.323713i
$296$	−2725.07	+	800.153i	−0.535107	+	0.157121i
$297$	−1060.53	+	537.411i	−0.207199	+	0.104996i
$298$	1292.65			0.251279
$299$	−3304.74	−	5933.34i	−0.639191	−	1.14761i
$300$	−2504.77	−	6602.23i	−0.482043	−	1.27060i
$301$	1214.16	+	115.938i	0.232502	+	0.0222013i
$302$	1381.32	−	5693.90i	0.263200	−	1.08492i
$303$	−1048.38	−	6027.60i	−0.198772	−	1.14283i
$304$	317.232	−	6659.52i	0.0598504	−	1.25641i
$305$	−2144.06	−	2474.38i	−0.402520	−	0.464533i
$306$	1986.75	−	10968.9i	0.371159	−	2.04918i
$307$	1937.28	+	568.837i	0.360151	+	0.105750i	0.456802	−	0.889568i	$-0.348995\pi$
$307$	1937.28	+	568.837i	0.360151	+	0.105750i	−0.0966507	+	0.995318i	$0.530813\pi$
$308$	1132.86	+	584.032i	0.209581	+	0.108046i
$309$	−397.263	+	1267.21i	−0.0731376	+	0.233297i
$310$	5238.29	+	7356.14i	0.959725	+	1.34774i
$311$	2413.85	+	3389.78i	0.440118	+	0.618060i	0.973740	−	0.227664i	$-0.0731087\pi$
$311$	2413.85	+	3389.78i	0.440118	+	0.618060i	−0.533622	+	0.845723i	$0.679169\pi$
$312$	723.710	−	2308.52i	0.131321	−	0.418892i
$313$	3370.47	+	1737.60i	0.608659	+	0.313785i	0.734860	−	0.678219i	$-0.237248\pi$
$313$	3370.47	+	1737.60i	0.608659	+	0.313785i	−0.126201	+	0.992005i	$0.540278\pi$
$314$	−5124.84	−	1504.79i	−0.921056	−	0.270446i
$315$	9730.63	+	8242.39i	1.74050	+	1.47430i
$316$	1352.88	+	1561.31i	0.240840	+	0.277945i
$317$	−397.592	+	8346.48i	−0.0704448	+	1.47882i	0.636351	+	0.771400i	$0.280443\pi$
$317$	−397.592	+	8346.48i	−0.0704448	+	1.47882i	−0.706795	+	0.707418i	$0.749860\pi$
$318$	−1892.53	−	10880.9i	−0.333735	−	1.91878i
$319$	−421.514	+	1737.50i	−0.0739820	+	0.304958i
$320$	4272.58	+	407.982i	0.746388	+	0.0712715i
$321$	556.486	+	1466.82i	0.0967602	+	0.255047i
$322$	−3544.49	+	9752.14i	−0.613437	+	1.68778i
$323$	9676.14			1.66686
$324$	−932.078	+	4256.65i	−0.159821	+	0.729879i
$325$	13431.4	−	3943.80i	2.29242	−	0.673116i
$326$	−4504.34	−	868.140i	−0.765252	−	0.147490i
$327$	584.678	−	2762.21i	0.0988769	−	0.467127i
$328$	−11.4462	+	2.20607i	−0.00192686	+	0.000371371i
$329$	10537.5	+	4218.57i	1.76581	+	0.706922i
$330$	2549.42	−	1746.42i	0.425275	−	0.291325i
$331$	−4961.87	−	2558.02i	−0.823955	−	0.424778i	−0.00594516	−	0.999982i	$-0.501892\pi$
$331$	−4961.87	−	2558.02i	−0.823955	−	0.424778i	−0.818010	+	0.575204i	$0.804923\pi$
$332$	919.078	−	6392.33i	0.151931	−	1.05670i
$333$	2965.94	+	9697.37i	0.488086	+	1.59583i
$334$	−2000.18	+	4379.79i	−0.327680	+	0.717519i
$335$	−5112.55	+	2046.76i	−0.833816	+	0.333810i
$336$	−9122.94	+	3967.36i	−1.48124	+	0.644159i
$337$	5368.33	−	5118.69i	0.867750	−	0.827398i	−0.118450	−	0.992960i	$-0.537792\pi$
$337$	5368.33	−	5118.69i	0.867750	−	0.827398i	0.986199	+	0.165562i	$0.0529440\pi$
$338$	−5532.71	−	2214.96i	−0.890355	−	0.356444i
$339$	3291.55	+	5332.61i	0.527352	+	0.854358i
$340$	−589.569	+	12376.6i	−0.0940408	+	1.97416i
$341$	−714.125	+	824.144i	−0.113408	+	0.130880i
$342$	−8838.87	−	321.734i	−1.39752	−	0.0508695i
$343$	−552.880	−	1210.64i	−0.0870342	−	0.190578i
$344$	183.277	+	317.445i	0.0287256	+	0.0497543i
$345$	7158.57	+	8031.53i	1.11711	+	1.25334i
$346$	−8102.63	+	14034.2i	−1.25896	+	2.18058i
$347$	6373.99	+	608.642i	0.986091	+	0.0941603i	0.575624	−	0.817715i	$-0.304759\pi$
$347$	6373.99	+	608.642i	0.986091	+	0.0941603i	0.410468	+	0.911875i	$0.365365\pi$
$348$	3956.32	+	5223.71i	0.609428	+	0.804655i
$349$	−4486.93	−	864.784i	−0.688194	−	0.132639i	−0.166846	−	0.985983i	$-0.553358\pi$
$349$	−4486.93	−	864.784i	−0.688194	−	0.132639i	−0.521348	+	0.853344i	$0.674570\pi$
$350$	−17991.8	−	11562.6i	−2.74773	−	1.76586i
$351$	−8271.17	−	2491.44i	−1.25778	−	0.378869i
$352$	270.124	+	1878.75i	0.0409024	+	0.284482i
$353$	4.36807	+	18.0054i	0.000658609	+	0.00271482i	0.972140	−	0.234401i	$-0.0753130\pi$
$353$	4.36807	+	18.0054i	0.000658609	+	0.00271482i	−0.971481	+	0.237116i	$0.923798\pi$
$354$	7210.37	+	5334.78i	1.08256	+	0.800962i
$355$	1341.55	+	1055.01i	0.200570	+	0.157730i
$356$	−2943.74	−	4133.90i	−0.438252	−	0.615439i
$357$	−6381.44	−	12951.4i	−0.946055	−	1.92006i
$358$	558.263	−	223.495i	0.0824166	−	0.0329946i
$359$	8063.61	−	5182.17i	1.18546	−	0.761850i	0.209080	−	0.977899i	$-0.432953\pi$
$359$	8063.61	−	5182.17i	1.18546	−	0.761850i	0.976383	+	0.216048i	$0.0693168\pi$
$360$	−321.487	+	3818.97i	−0.0470663	+	0.559104i
$361$	−116.474	−	810.092i	−0.0169811	−	0.118106i
$362$	97.9998	−	283.152i	0.0142286	−	0.0411109i
$363$	−4866.05	−	4373.94i	−0.703585	−	0.632431i
$364$	3028.78	+	8751.07i	0.436129	+	1.26011i
$365$	3533.50	−	14565.3i	0.506718	−	2.08872i
$366$	−895.324	−	3267.98i	−0.127867	−	0.466721i
$367$	−751.401	−	1301.46i	−0.106874	−	0.185111i	0.807628	−	0.589692i	$-0.200751\pi$
$367$	−751.401	−	1301.46i	−0.106874	−	0.185111i	−0.914502	+	0.404581i	$0.867418\pi$
$368$	−8088.55	+	2240.19i	−1.14577	+	0.317331i
$369$	8.33479	+	40.7783i	0.00117586	+	0.00575294i
$370$	−10949.4	−	23975.9i	−1.53847	−	3.36878i
$371$	−10352.9	−	9871.44i	−1.44877	−	1.38140i
$372$	684.879	+	3937.66i	0.0954552	+	0.548813i
$373$	−10549.4	+	5438.60i	−1.46442	+	0.754960i	−0.991979	−	0.126403i	$-0.959657\pi$
$373$	−10549.4	+	5438.60i	−1.46442	+	0.754960i	−0.472439	+	0.881363i	$0.656626\pi$
$374$	−3435.54	+	662.145i	−0.474993	+	0.0915474i
$375$	−8734.96	+	4833.43i	−1.20286	+	0.665593i
$376$	804.219	+	3315.04i	0.110304	+	0.454681i
$377$	−10928.1	+	7023.05i	−1.49290	+	0.959431i
$378$	5398.62	+	12043.0i	0.734590	+	1.63868i
$379$	−2445.62	+	5355.17i	−0.331460	+	0.725796i	−0.999838	−	0.0180263i	$-0.994262\pi$
$379$	−2445.62	+	5355.17i	−0.331460	+	0.725796i	0.668378	+	0.743822i	$0.266989\pi$
$380$	9786.68	−	934.515i	1.32117	−	0.126157i
$381$	282.839	−	63.1911i	0.0380322	−	0.00849706i
$382$	−526.265	−	11047.7i	−0.0704871	−	1.47971i
$383$	5893.63	−	5619.56i	0.786293	−	0.749729i	−0.186237	−	0.982505i	$-0.559629\pi$
$383$	5893.63	−	5619.56i	0.786293	−	0.749729i	0.972530	+	0.232776i	$0.0747807\pi$
$384$	−4171.43	−	2510.64i	−0.554355	−	0.333648i
$385$	1309.10	−	3782.39i	0.173293	−	0.500697i
$386$	−12381.9	−	7957.35i	−1.63270	−	1.04927i
$387$	1126.04	−	667.072i	0.147907	−	0.0876206i
$388$	−3099.11	+	909.981i	−0.405499	+	0.119065i
$389$	−51.9936	+	73.0148i	−0.00677681	+	0.00951670i	−0.817950	−	0.575289i	$-0.804890\pi$
$389$	−51.9936	+	73.0148i	−0.00677681	+	0.00951670i	0.811174	+	0.584805i	$0.198829\pi$
$390$	22162.1	+	3599.06i	2.87749	+	0.467296i
$391$	−3806.15	−	11571.2i	−0.492289	−	1.49662i
$392$	−1096.87	+	1899.83i	−0.141327	+	0.244785i
$393$	794.372	+	2899.50i	0.101961	+	0.372163i
$394$	6269.32	+	5977.79i	0.801634	+	0.764357i
$395$	4248.51	−	4903.05i	0.541180	−	0.624555i
$396$	1351.48	−	209.811i	0.171501	−	0.0266248i
$397$	−1201.00	−	1386.03i	−0.151830	−	0.175221i	0.674739	−	0.738056i	$-0.264256\pi$
$397$	−1201.00	−	1386.03i	−0.151830	−	0.175221i	−0.826569	+	0.562835i	$0.809711\pi$
$398$	1860.74	−	1463.30i	0.234347	−	0.184293i
$399$	−9451.00	+	6474.20i	−1.18582	+	0.812319i
$400$	−823.127	−	17279.6i	−0.102891	−	2.15995i
$401$	1427.30	+	1122.44i	0.177746	+	0.139781i	0.703068	−	0.711122i	$-0.251813\pi$
$401$	1427.30	+	1122.44i	0.177746	+	0.139781i	−0.525322	+	0.850903i	$0.676055\pi$
$402$	−5687.00	−	374.699i	−0.705577	−	0.0464883i
$403$	−7887.28	+	753.144i	−0.974921	+	0.0930937i
$404$	−1001.60	+	6966.29i	−0.123345	+	0.857886i
$405$	13647.9	+	994.880i	1.67449	+	0.122064i
$406$	19042.7	+	5591.45i	2.32777	+	0.683495i
$407$	2501.89	−	1967.51i	0.304703	−	0.239621i
$408$	2058.14	−	3819.97i	0.249738	−	0.463522i
$409$	−4194.74	+	2162.54i	−0.507131	+	0.261444i	−0.692750	−	0.721178i	$-0.743601\pi$
$409$	−4194.74	+	2162.54i	−0.507131	+	0.261444i	0.185619	+	0.982622i	$0.440571\pi$
$410$	−35.3828	−	102.232i	−0.00426202	−	0.0123143i
$411$	4896.19	−	11613.2i	0.587619	−	1.39377i
$412$	886.142	−	1244.41i	0.105964	−	0.148805i
$413$	11617.3			1.38414
$414$	3092.06	+	10696.5i	0.367069	+	1.26982i
$415$	−20280.5			−2.39887
$416$	−7999.37	+	11233.5i	−0.942792	+	1.32397i
$417$	6014.51	−	753.358i	0.706312	−	0.0884703i
$418$	907.959	+	2623.38i	0.106243	+	0.306970i
$419$	−7202.02	+	3712.90i	−0.839717	+	0.432904i	−0.823740	−	0.566968i	$-0.808116\pi$
$419$	−7202.02	+	3712.90i	−0.839717	+	0.432904i	−0.0159776	+	0.999872i	$0.505086\pi$
$420$	−7705.19	−	12483.1i	−0.895178	−	1.45027i
$421$	1852.10	−	1456.51i	0.214408	−	0.168613i	−0.505179	−	0.863015i	$-0.668573\pi$
$421$	1852.10	−	1456.51i	0.214408	−	0.168613i	0.719587	+	0.694402i	$0.244331\pi$
$422$	−7961.99	−	2337.85i	−0.918444	−	0.269680i
$423$	11803.6	−	3004.09i	1.35676	−	0.345304i
$424$	611.817	−	4255.28i	0.0700766	−	0.487393i
$425$	24993.1	−	2386.56i	2.85258	−	0.272388i
$426$	780.670	+	1584.41i	0.0887878	+	0.180199i
$427$	−3449.77	−	2712.93i	−0.390974	−	0.307466i
$428$	−85.8713	−	1802.66i	−0.00969800	−	0.203586i
$429$	208.581	+	2703.22i	0.0234741	+	0.304225i
$430$	−2674.01	+	2102.86i	−0.299889	+	0.235835i
$431$	3780.54	+	4362.98i	0.422511	+	0.487604i	0.926600	−	0.376048i	$-0.122717\pi$
$431$	3780.54	+	4362.98i	0.422511	+	0.487604i	−0.504089	+	0.863652i	$0.668172\pi$
$432$	−5401.92	+	9207.47i	−0.601621	+	1.02545i
$433$	−8181.45	+	9441.89i	−0.908026	+	1.04792i	0.0906195	+	0.995886i	$0.471115\pi$
$433$	−8181.45	+	9441.89i	−0.908026	+	1.04792i	−0.998645	+	0.0520321i	$0.983430\pi$
$434$	8760.88	+	8353.48i	0.968976	+	0.923917i
$435$	14469.1	−	14632.3i	1.59481	−	1.61280i
$436$	−1623.95	+	2812.76i	−0.178379	+	0.308961i
$437$	−8657.79	+	4295.80i	−0.947730	+	0.470243i
$438$	9808.57	−	12016.2i	1.07003	−	1.31085i
$439$	5944.12	−	8347.36i	0.646236	−	0.907511i	−0.353373	−	0.935483i	$-0.614965\pi$
$439$	5944.12	−	8347.36i	0.646236	−	0.907511i	0.999609	+	0.0279711i	$0.00890465\pi$
$440$	1154.16	−	338.891i	0.125051	−	0.0367182i
$441$	6826.94	+	3840.10i	0.737171	+	0.414652i
$442$	−21385.3	−	13743.5i	−2.30134	−	1.47898i
$443$	730.619	−	2110.98i	0.0783583	−	0.226402i	−0.899017	−	0.437914i	$-0.855718\pi$
$443$	730.619	−	2110.98i	0.0783583	−	0.226402i	0.977375	+	0.211512i	$0.0678388\pi$
$444$	212.205	−	11663.5i	0.0226820	−	1.24668i
$445$	−11534.1	+	10997.8i	−1.22870	+	1.17156i
$446$	−374.340	−	7858.37i	−0.0397433	−	0.834316i
$447$	537.433	−	1714.32i	0.0568673	−	0.181398i
$448$	5727.17	−	546.878i	0.603980	−	0.0576731i
$449$	3175.43	−	6953.22i	0.333759	−	0.730830i	−0.666129	−	0.745837i	$-0.732050\pi$
$449$	3175.43	−	6953.22i	0.333759	−	0.730830i	0.999887	+	0.0150070i	$0.00477706\pi$
$450$	−22909.9	+	1349.02i	−2.39996	+	0.141319i
$451$	10.9897	−	7.06268i	0.00114742	−	0.000737402i
$452$	−1699.55	−	7005.62i	−0.176858	−	0.729020i
$453$	−6977.01	−	4199.23i	−0.723639	−	0.435534i
$454$	20668.6	−	3983.54i	2.13662	−	0.411799i
$455$	25848.1	−	13325.6i	2.66324	−	1.37300i
$456$	−3232.47	−	1185.04i	−0.331961	−	0.121699i
$457$	9273.59	+	8842.35i	0.949235	+	0.905094i	0.995588	−	0.0938314i	$-0.0299115\pi$
$457$	9273.59	+	8842.35i	0.949235	+	0.905094i	−0.0463532	+	0.998925i	$0.514760\pi$
$458$	−2551.39	−	5586.77i	−0.260303	−	0.569983i
$459$	−13721.0	−	7195.26i	−1.39530	−	0.731691i
$460$	−4967.17	−	11335.8i	−0.503468	−	1.14899i
$461$	1595.28	+	2763.11i	0.161171	+	0.279156i	0.935289	−	0.353885i	$-0.115140\pi$
$461$	1595.28	+	2763.11i	0.161171	+	0.279156i	−0.774118	+	0.633041i	$0.781806\pi$
$462$	2912.57	−	2945.42i	0.293301	−	0.296609i
$463$	−1860.95	+	7670.95i	−0.186794	+	0.769977i	0.798904	+	0.601458i	$0.205413\pi$
$463$	−1860.95	+	7670.95i	−0.186794	+	0.769977i	−0.985699	+	0.168518i	$0.946102\pi$
$464$	5250.51	+	15170.4i	0.525321	+	1.51782i
$465$	11933.7	−	3888.68i	1.19013	−	0.387813i
$466$	3551.22	−	10260.6i	0.353020	−	1.01998i
$467$	−170.759	−	1187.66i	−0.0169203	−	0.117683i	0.979611	−	0.200905i	$-0.0643882\pi$
$467$	−170.759	−	1187.66i	−0.0169203	−	0.117683i	−0.996531	+	0.0832214i	$0.973479\pi$
$468$	8158.57	+	5672.87i	0.805834	+	0.560318i
$469$	−6210.04	+	3990.95i	−0.611413	+	0.392931i
$470$	−29390.0	+	11766.0i	−2.88438	+	1.15473i
$471$	−4126.38	+	6170.99i	−0.403680	+	0.603703i
$472$	2025.18	+	2843.97i	0.197493	+	0.277340i
$473$	−322.901	−	253.932i	−0.0313890	−	0.0246846i
$474$	6157.19	−	2677.62i	0.596643	−	0.259467i
$475$	−4696.49	−	19359.2i	−0.453663	−	1.87002i
$476$	2363.70	+	16439.9i	0.227605	+	1.58303i
$477$	−15217.3	−	2013.98i	−1.46069	−	0.193320i
$478$	−3822.23	−	2456.40i	−0.365742	−	0.235048i
$479$	−2436.29	−	469.556i	−0.232394	−	0.0447903i	0.0717243	−	0.997424i	$-0.477150\pi$
$479$	−2436.29	−	469.556i	−0.232394	−	0.0447903i	−0.304119	+	0.952634i	$0.598362\pi$
$480$	8486.98	−	20130.2i	0.807033	−	1.91420i
$481$	23020.7	+	2198.21i	2.18223	+	0.208378i
$482$	−6312.92	+	10934.3i	−0.596568	+	1.03329i
$483$	11459.7	+	8755.30i	1.07958	+	0.824803i
$484$	3763.31	+	6518.25i	0.353429	+	0.612157i
$485$	4213.62	+	9226.53i	0.394496	+	0.863825i
$486$	12294.5	+	7028.89i	1.14751	+	0.656043i
$487$	2737.37	−	3159.09i	0.254706	−	0.293947i	−0.613968	−	0.789331i	$-0.710427\pi$
$487$	2737.37	−	3159.09i	0.254706	−	0.293947i	0.868674	+	0.495385i	$0.164973\pi$
$488$	62.7581	−	1317.45i	0.00582157	−	0.122210i
$489$	−3024.07	+	5612.77i	−0.279658	+	0.519055i
$490$	−18900.7	−	7566.68i	−1.74254	−	0.697608i
$491$	6539.13	−	6235.05i	0.601032	−	0.573083i	−0.327260	−	0.944934i	$-0.606125\pi$
$491$	6539.13	−	6235.05i	0.601032	−	0.573083i	0.928292	+	0.371851i	$0.121277\pi$
$492$	5.41746	−	47.5716i	0.000496418	−	0.00435913i
$493$	−21629.7	+	8659.23i	−1.97597	+	0.791059i
$494$	−8378.83	+	18347.1i	−0.763120	+	1.67100i
$495$	−1256.18	−	4107.16i	−0.114062	−	0.372935i
$496$	−1393.46	+	9691.75i	−0.126146	+	0.877363i
$497$	2033.42	+	1048.30i	0.183524	+	0.0946132i
$498$	−18930.3	−	9064.89i	−1.70338	−	0.815678i
$499$	−12299.6	−	4924.03i	−1.10342	−	0.441743i	−0.252798	−	0.967519i	$-0.581351\pi$
$499$	−12299.6	−	4924.03i	−1.10342	−	0.441743i	−0.850623	+	0.525776i	$0.823775\pi$
$500$	11276.5	−	2173.36i	1.00860	−	0.194391i
$501$	4976.93	+	4473.61i	0.443818	+	0.398934i
$502$	17527.6	+	3378.18i	1.55836	+	0.300349i
$503$	−3295.52	+	967.653i	−0.292127	+	0.0857763i	−0.424513	−	0.905422i	$-0.639555\pi$
$503$	−3295.52	+	967.653i	−0.292127	+	0.0857763i	0.132385	+	0.991198i	$0.457736\pi$
$504$	545.652	+	5108.17i	0.0482247	+	0.451461i
$505$	22101.5			1.94753
$506$	2780.01	−	2117.69i	0.244242	−	0.186053i
$507$	−5237.80	+	6416.65i	−0.458814	+	0.562078i
$508$	−331.875	−	31.6902i	−0.0289854	−	0.00276777i
$509$	1153.29	−	4753.91i	0.100429	−	0.413975i	−0.899298	−	0.437337i	$-0.855922\pi$
$509$	1153.29	−	4753.91i	0.100429	−	0.413975i	0.999727	+	0.0233615i	$0.00743687\pi$
$510$	37808.9	+	13861.0i	3.28276	+	1.20348i
$511$	955.937	−	20067.6i	0.0827557	−	1.73726i
$512$	8146.09	+	9401.09i	0.703144	+	0.811471i
$513$	−4101.54	+	11588.4i	−0.352997	+	0.997353i
$514$	10167.6	+	2985.47i	0.872515	+	0.256193i
$515$	−4264.14	−	2198.32i	−0.364855	−	0.188096i
$516$	−1469.35	+	328.278i	−0.125358	+	0.0280071i
$517$	−2217.47	−	3113.99i	−0.188634	−	0.264900i
$518$	−20494.1	−	28780.0i	−1.73834	−	2.44116i
$519$	15243.5	+	16580.7i	1.28924	+	1.40233i
$520$	7768.15	+	4004.76i	0.655107	+	0.337731i
$521$	10830.0	+	3179.98i	0.910694	+	0.267404i	0.703333	−	0.710860i	$-0.251694\pi$
$521$	10830.0	+	3179.98i	0.910694	+	0.267404i	0.207361	+	0.978264i	$0.433512\pi$
$522$	20046.0	−	7190.76i	1.68083	−	0.602933i
$523$	−6934.09	−	8002.36i	−0.579745	−	0.669061i	0.387805	−	0.921741i	$-0.373233\pi$
$523$	−6934.09	−	8002.36i	−0.579745	−	0.669061i	−0.967550	+	0.252680i	$0.918688\pi$
$524$	164.554	−	3454.42i	0.0137187	−	0.287991i
$525$	−22814.8	+	19053.7i	−1.89661	+	1.58394i
$526$	2699.23	−	11126.4i	0.223749	−	0.922306i
$527$	−14146.2	−	1350.80i	−1.16930	−	0.111654i
$528$	3307.23	+	537.084i	0.272592	+	0.0442682i
$529$	8542.70	+	8663.62i	0.702120	+	0.712059i
$530$	39897.4			3.26987
$531$	10072.8	−	7344.48i	0.823208	−	0.600232i
$532$	12644.4	−	3712.73i	1.03046	−	0.302570i
$533$	93.1994	+	17.9627i	0.00757395	+	0.00145976i
$534$	−15681.9	+	5110.07i	−1.27083	+	0.414109i
$535$	−5564.97	+	1072.56i	−0.449710	+	0.0866745i
$536$	−2059.57	−	824.528i	−0.165970	−	0.0664444i
$537$	−64.2974	−	833.295i	−0.00516693	−	0.0669634i
$538$	−16926.1	−	8726.01i	−1.35639	−	0.699266i
$539$	349.876	−	2433.44i	0.0279596	−	0.194463i
$540$	−14572.7	−	5952.30i	−1.16131	−	0.474345i
$541$	−2378.99	+	5209.26i	−0.189059	+	0.413981i	−0.980298	−	0.197527i	$-0.936709\pi$
$541$	−2378.99	+	5209.26i	−0.189059	+	0.413981i	0.791239	+	0.611507i	$0.209436\pi$
$542$	12352.3	−	4945.12i	0.978924	−	0.391902i
$543$	−334.775	−	247.692i	−0.0264577	−	0.0195755i
$544$	−17901.0	+	17068.6i	−1.41085	+	1.34524i
$545$	9468.91	+	3790.78i	0.744227	+	0.297943i
$546$	30083.3	−	884.944i	2.35796	−	0.0693628i
$547$	−901.931	+	18933.9i	−0.0705005	+	1.47999i	0.635678	+	0.771954i	$0.280721\pi$
$547$	−901.931	+	18933.9i	−0.0705005	+	1.47999i	−0.706179	+	0.708034i	$0.749582\pi$
$548$	−9494.19	+	10956.9i	−0.740094	+	0.854114i
$549$	−4706.27	−	171.308i	−0.365863	−	0.0133174i
$550$	2992.27	+	6552.15i	0.231983	+	0.507972i
$551$	9243.02	+	16009.4i	0.714639	+	1.23779i
$552$	−145.624	+	4331.68i	−0.0112285	+	0.334001i
$553$	4348.19	−	7531.28i	0.334365	−	0.579137i
$554$	6364.93	+	607.777i	0.488122	+	0.0466100i
$555$	−36349.5	+	4553.01i	−2.78009	+	0.348225i
$556$	−6846.83	−	1319.62i	−0.522249	−	0.100655i
$557$	2027.63	+	1303.08i	0.154243	+	0.0991261i	0.615486	−	0.788148i	$-0.288960\pi$
$557$	2027.63	+	1303.08i	0.154243	+	0.0991261i	−0.461243	+	0.887274i	$0.652596\pi$
$558$	12877.3	+	1704.28i	0.976950	+	0.129298i
$559$	−424.757	−	2954.25i	−0.0321383	−	0.223527i
$560$	−8472.70	−	34924.9i	−0.639351	−	2.63544i
$561$	−550.217	+	4831.54i	−0.0414085	+	0.363615i
$562$	−3014.35	−	2370.51i	−0.226250	−	0.177925i
$563$	2289.57	+	3215.24i	0.171392	+	0.240686i	0.891333	−	0.453349i	$-0.149771\pi$
$563$	2289.57	+	3215.24i	0.171392	+	0.240686i	−0.719941	+	0.694035i	$0.755831\pi$
$564$	−13980.8	−	921.148i	−1.04379	−	0.0687719i
$565$	−21016.6	+	8413.77i	−1.56491	+	0.626496i
$566$	−14802.4	+	9512.91i	−1.09928	+	0.706462i
$567$	18216.0	−	2152.73i	1.34921	−	0.159446i
$568$	97.8467	+	680.539i	0.00722809	+	0.0502725i
$569$	−6705.85	+	19375.3i	−0.494067	+	1.42751i	0.372304	+	0.928111i	$0.378568\pi$
$569$	−6705.85	+	19375.3i	−0.494067	+	1.42751i	−0.866371	+	0.499401i	$0.833553\pi$
$570$	6616.57	−	31258.8i	0.486206	−	2.29700i
$571$	−4909.38	−	14184.7i	−0.359809	−	1.03960i	−0.969103	−	0.246656i	$-0.920668\pi$
$571$	−4909.38	−	14184.7i	−0.359809	−	1.03960i	0.609294	−	0.792944i	$-0.291453\pi$
$572$	735.304	−	3030.96i	0.0537493	−	0.221558i
$573$	−14870.3	−	3895.25i	−1.08415	−	0.283990i
$574$	−72.5060	−	125.584i	−0.00527237	−	0.00913201i
$575$	−21303.3	+	13231.3i	−1.54506	+	0.959623i
$576$	4620.04	−	4094.91i	0.334204	−	0.296217i
$577$	−9901.96	−	21682.3i	−0.714426	−	1.56438i	−0.821554	−	0.570130i	$-0.806893\pi$
$577$	−9901.96	−	21682.3i	−0.714426	−	1.56438i	0.107128	−	0.994245i	$-0.465835\pi$
$578$	−19704.0	−	18787.7i	−1.41795	−	1.35202i
$579$	−15701.0	+	13112.6i	−1.12696	+	0.941178i
$580$	−21040.5	+	10847.1i	−1.50631	+	0.776557i
$581$	−26693.7	+	5144.80i	−1.90610	+	0.367370i
$582$	−190.956	+	10495.6i	−0.0136003	+	0.747520i
$583$	1135.85	+	4682.02i	0.0806894	+	0.332606i
$584$	5079.30	−	3264.27i	0.359902	−	0.231295i
$585$	13987.2	−	27895.3i	0.988549	−	1.97150i
$586$	−1392.19	+	3048.48i	−0.0981416	+	0.214900i
$587$	−18256.8	+	1743.31i	−1.28371	+	0.122580i	−0.714515	−	0.699621i	$-0.753352\pi$
$587$	−18256.8	+	1743.31i	−1.28371	+	0.122580i	−0.569198	+	0.822200i	$0.692746\pi$
$588$	−6098.30	−	6633.23i	−0.427703	−	0.465221i
$589$	536.497	+	11262.5i	0.0375314	+	0.787880i
$590$	−23450.2	+	22359.7i	−1.63632	+	1.56023i
$591$	10534.3	−	5829.11i	0.733206	−	0.405715i
$592$	9347.03	−	27006.5i	0.648920	−	1.87493i
$593$	−3662.60	−	2353.81i	−0.253634	−	0.163001i	0.407645	−	0.913140i	$-0.366350\pi$
$593$	−3662.60	−	2353.81i	−0.253634	−	0.163001i	−0.661280	+	0.750140i	$0.729986\pi$
$594$	663.257	−	4395.18i	0.0458144	−	0.303597i
$595$	50045.2	−	14694.6i	3.44815	−	1.01247i
$596$	−1198.81	+	1683.49i	−0.0823909	+	0.115702i
$597$	−1167.02	−	3076.11i	−0.0800051	−	0.210882i
$598$	25236.1	+	2802.90i	1.72572	+	0.191671i
$599$	−11849.1	+	20523.2i	−0.808246	+	1.39992i	0.105832	+	0.994384i	$0.466250\pi$
$599$	−11849.1	+	20523.2i	−0.808246	+	1.39992i	−0.914078	+	0.405539i	$0.867084\pi$
$600$	−8641.64	−	2263.66i	−0.587989	−	0.154022i
$601$	−4923.72	−	4694.75i	−0.334181	−	0.318641i	0.504346	−	0.863502i	$-0.331734\pi$
$601$	−4923.72	−	4694.75i	−0.334181	−	0.318641i	−0.838526	+	0.544861i	$0.816582\pi$
$602$	−2986.14	+	3446.18i	−0.202169	+	0.233316i
$603$	−2861.36	+	7386.38i	−0.193240	+	0.498834i
$604$	6134.43	+	7079.51i	0.413256	+	0.476922i
$605$	18579.3	−	14610.9i	1.24852	−	0.981849i
$606$	20630.0	+	9878.83i	1.38290	+	0.662211i
$607$	1413.20	+	29666.7i	0.0944974	+	1.98374i	0.165257	+	0.986251i	$0.447155\pi$
$607$	1413.20	+	29666.7i	0.0944974	+	1.98374i	−0.0707599	+	0.997493i	$0.522542\pi$
$608$	15426.4	+	12131.5i	1.02899	+	0.809203i
$609$	15332.7	−	22930.0i	1.02021	−	1.52573i
$610$	12185.1	−	1163.54i	0.808789	−	0.0772300i
$611$	3952.84	−	27492.6i	0.261726	−	1.82035i
$612$	12442.8	+	12760.0i	0.821849	+	0.842798i
$613$	−9759.23	−	2865.57i	−0.643021	−	0.188808i	−0.0560651	−	0.998427i	$-0.517855\pi$
$613$	−9759.23	−	2865.57i	−0.643021	−	0.188808i	−0.586955	+	0.809619i	$0.699674\pi$
$614$	−5933.56	+	4666.20i	−0.389998	+	0.306698i
$615$	−150.292	+	4.42105i	−0.00985422	+	0.000289876i
$616$	1433.16	−	738.845i	0.0937397	−	0.0483262i
$617$	646.929	+	1869.18i	0.0422113	+	0.121962i	0.964137	−	0.265405i	$-0.0855058\pi$
$617$	646.929	+	1869.18i	0.0422113	+	0.121962i	−0.921926	+	0.387367i	$0.873385\pi$
$618$	−2997.64	−	3957.92i	−0.195118	−	0.257623i
$619$	−17224.3	+	24188.1i	−1.11842	+	1.57060i	−0.342795	+	0.939410i	$0.611374\pi$
$619$	−17224.3	+	24188.1i	−1.11842	+	1.57060i	−0.775626	+	0.631192i	$0.782566\pi$
$620$	−14438.3			−0.935253
$621$	15471.4	+	346.456i	0.999749	+	0.0223877i
$622$	−15557.9			−1.00292
$623$	−12391.6	+	17401.5i	−0.796882	+	1.11906i
$624$	14697.8	+	19406.2i	0.942922	+	1.24498i
$625$	−2500.35	−	7224.29i	−0.160022	−	0.462354i
$626$	−12601.0	+	6496.24i	−0.804529	+	0.414764i
$627$	3856.64	−	113.449i	0.245645	−	0.00722601i
$628$	6712.56	−	5278.82i	0.426529	−	0.335426i
$629$	39796.5	+	11685.3i	2.52272	+	0.740736i
$630$	−46203.4	+	11759.1i	−2.92189	+	0.743639i
$631$	−2468.98	+	17172.2i	−0.155767	+	1.08338i	0.750560	+	0.660802i	$0.229784\pi$
$631$	−2468.98	+	17172.2i	−0.155767	+	1.08338i	−0.906327	+	0.422578i	$0.861125\pi$
$632$	2601.70	−	248.432i	0.163750	−	0.0156362i
$633$	−6410.76	+	9587.29i	−0.402536	+	0.601991i
$634$	−24556.2	−	19311.2i	−1.53825	−	1.20969i
$635$	49.8155	+	1045.76i	0.00311318	+	0.0653536i
$636$	15926.0	+	7626.28i	0.992935	+	0.475474i
$637$	14040.7	−	11041.7i	0.873331	−	0.686795i
$638$	−4377.29	−	5051.67i	−0.271628	−	0.313476i
$639$	2425.83	−	376.599i	0.150179	−	0.0233146i
$640$	11517.7	−	13292.2i	0.711373	−	0.820968i
$641$	17460.7	+	16648.7i	1.07590	+	1.02587i	0.999586	+	0.0287894i	$0.00916521\pi$
$641$	17460.7	+	16648.7i	1.07590	+	1.02587i	0.0763189	+	0.997083i	$0.475683\pi$
$642$	−5673.87	−	1486.25i	−0.348800	−	0.0913673i
$643$	1299.16	−	2250.21i	0.0796793	−	0.138009i	−0.823432	−	0.567415i	$-0.807944\pi$
$643$	1299.16	−	2250.21i	0.0796793	−	0.138009i	0.903112	+	0.429406i	$0.141277\pi$
$644$	−9413.58	−	13660.3i	−0.576005	−	0.835859i
$645$	1677.09	+	4420.59i	0.102381	+	0.269861i
$646$	−20983.9	+	29467.7i	−1.27802	+	1.79472i
$647$	−9527.86	+	2797.63i	−0.578947	+	0.169994i	−0.558079	−	0.829788i	$-0.688461\pi$
$647$	−9527.86	+	2797.63i	−0.578947	+	0.169994i	−0.0208683	+	0.999782i	$0.506643\pi$
$648$	3702.51	+	4084.11i	0.224458	+	0.247591i
$649$	−3291.55	−	2115.35i	−0.199083	−	0.127943i
$650$	−17117.1	+	49456.5i	−1.03290	+	2.98437i
$651$	14720.9	−	8145.72i	0.886264	−	0.490409i
$652$	5307.96	−	5061.13i	0.318828	−	0.304002i
$653$	−961.731	−	20189.2i	−0.0576347	−	1.20990i	−0.823658	−	0.567087i	$-0.808070\pi$
$653$	−961.731	−	20189.2i	−0.0576347	−	1.20990i	0.766023	−	0.642813i	$-0.222233\pi$
$654$	7144.09	+	7770.76i	0.427150	+	0.464619i
$655$	−10811.2	+	1032.34i	−0.644929	+	0.0615832i
$656$	48.7262	−	106.695i	0.00290006	−	0.00635024i
$657$	−11857.9	−	18004.1i	−0.704143	−	1.06911i
$658$	−35699.0	+	22942.4i	−2.11503	+	1.35925i
$659$	−1591.78	−	6561.39i	−0.0940922	−	0.387853i	0.905220	−	0.424944i	$-0.139706\pi$
$659$	−1591.78	−	6561.39i	−0.0940922	−	0.387853i	−0.999312	+	0.0370905i	$0.988191\pi$
$660$	−89.8758	+	4939.88i	−0.00530062	+	0.291340i
$661$	−11510.7	+	2218.50i	−0.677328	+	0.130544i	−0.516303	−	0.856406i	$-0.672692\pi$
$661$	−11510.7	+	2218.50i	−0.677328	+	0.130544i	−0.161025	+	0.986950i	$0.551480\pi$
$662$	18550.6	−	9563.51i	1.08911	−	0.561475i
$663$	−27117.9	+	22647.4i	−1.58849	+	1.32662i
$664$	−5912.87	−	5637.91i	−0.345578	−	0.329508i
$665$	−17191.6	−	37644.3i	−1.00250	−	2.19516i
$666$	−35964.4	−	11997.4i	−2.09248	−	0.698034i
$667$	15509.0	−	17350.6i	0.900316	−	1.00722i
$668$	−3849.07	−	6666.78i	−0.222941	−	0.386146i
$669$	−10577.5	−	2770.75i	−0.611285	−	0.160125i
$670$	4853.98	−	20008.4i	0.279889	−	1.15372i
$671$	483.444	+	1396.82i	0.0278139	+	0.0803630i
$672$	6064.11	−	28648.9i	0.348108	−	1.64457i
$673$	6635.56	−	19172.2i	0.380062	−	1.09812i	−0.579099	−	0.815257i	$-0.696595\pi$
$673$	6635.56	−	19172.2i	0.380062	−	1.09812i	0.959161	−	0.282861i	$-0.0912834\pi$
$674$	3946.60	+	27449.2i	0.225545	+	1.56870i
$675$	−7735.94	+	30944.2i	−0.441121	+	1.76451i
$676$	8015.73	−	5151.39i	0.456061	−	0.293093i
$677$	−10186.9	+	4078.22i	−0.578308	+	0.231520i	−0.642329	−	0.766429i	$-0.722032\pi$
$677$	−10186.9	+	4078.22i	−0.578308	+	0.231520i	0.0640209	+	0.997949i	$0.479608\pi$
$678$	−23378.0	−	1540.31i	−1.32423	−	0.0872494i
$679$	7886.66	+	11075.3i	0.445747	+	0.625964i
$680$	12321.4	+	9689.69i	0.694862	+	0.546445i
$681$	3310.17	−	29067.1i	0.186264	−	1.63561i
$682$	−961.184	−	3962.05i	−0.0539672	−	0.222456i
$683$	2084.49	+	14498.0i	0.116780	+	0.812225i	0.961063	+	0.276328i	$0.0891175\pi$
$683$	2084.49	+	14498.0i	0.116780	+	0.812225i	−0.844283	+	0.535897i	$0.819973\pi$
$684$	8616.21	−	11213.0i	0.481650	−	0.626811i
$685$	38301.3	+	24614.7i	2.13637	+	1.37296i
$686$	4885.87	+	941.674i	0.271929	+	0.0524100i
$687$	−8470.00	+	1060.92i	−0.470379	+	0.0589182i
$688$	−3671.69	−	350.604i	−0.203462	−	0.0194283i
$689$	−17502.3	+	30314.8i	−0.967755	+	1.67620i
$690$	−39983.4	+	4383.39i	−2.20601	+	0.241845i
$691$	−2714.64	−	4701.90i	−0.149450	−	0.258855i	0.781574	−	0.623812i	$-0.214417\pi$
$691$	−2714.64	−	4701.90i	−0.149450	−	0.258855i	−0.931024	+	0.364957i	$0.881084\pi$
$692$	−10763.1	−	23567.8i	−0.591258	−	1.29467i
$693$	−2695.32	−	5087.27i	−0.147744	−	0.278859i
$694$	−15676.3	+	18091.4i	−0.857442	+	0.989541i
$695$	−1041.91	+	21872.3i	−0.0568659	+	1.19376i
$696$	8286.25	−	243.752i	0.451278	−	0.0132750i
$697$	158.040	+	63.2697i	0.00858851	+	0.00343832i
$698$	12364.1	−	11789.1i	0.670467	−	0.639289i
$699$	−12131.2	−	8975.62i	−0.656432	−	0.485678i
$700$	31744.4	−	12708.5i	1.71403	−	0.686196i
$701$	−3269.23	+	7158.61i	−0.176144	+	0.385702i	−0.977026	−	0.213121i	$-0.931637\pi$
$701$	−3269.23	+	7158.61i	−0.176144	+	0.385702i	0.800882	+	0.598822i	$0.204364\pi$
$702$	25524.4	−	19786.0i	1.37230	−	1.06378i
$703$	4683.45	−	32574.1i	0.251266	−	1.74759i
$704$	−1722.27	−	887.893i	−0.0922025	−	0.0475337i
$705$	3384.97	+	43869.2i	0.180830	+	2.34356i
$706$	−64.3064	−	25.7444i	−0.00342805	−	0.00137238i
$707$	29090.6	−	5606.75i	1.54747	−	0.298251i
$708$	−13634.7	+	4442.97i	−0.723762	+	0.235843i
$709$	−5655.83	−	1090.07i	−0.299590	−	0.0577411i	0.0372414	−	0.999306i	$-0.488143\pi$
$709$	−5655.83	−	1090.07i	−0.299590	−	0.0577411i	−0.336831	+	0.941565i	$0.609355\pi$
$710$	−6122.25	+	1797.65i	−0.323611	+	0.0950208i
$711$	−991.175	−	9278.98i	−0.0522812	−	0.489436i
$712$	−6420.15			−0.337929
$713$	13257.1	−	5071.70i	0.696331	−	0.266391i
$714$	53281.2	+	8652.72i	2.79272	+	0.453529i
$715$	−9750.01	−	931.013i	−0.509972	−	0.0486964i
$716$	−226.665	+	934.327i	−0.0118308	+	0.0487674i
$717$	−4846.83	+	4047.81i	−0.252452	+	0.210834i
$718$	−1705.13	+	35795.1i	−0.0886279	+	1.86053i
$719$	−5900.68	−	6809.75i	−0.306062	−	0.353214i	0.581794	−	0.813336i	$-0.302351\pi$
$719$	−5900.68	−	6809.75i	−0.306062	−	0.353214i	−0.887856	+	0.460122i	$0.847806\pi$
$720$	−29425.9	−	24925.4i	−1.52311	−	1.29016i
$721$	−6170.24	−	1811.75i	−0.318712	−	0.0935824i
$722$	2719.64	+	1402.07i	0.140186	+	0.0722711i
$723$	11876.5	+	12918.3i	0.610916	+	0.664505i
$724$	277.879	+	390.226i	0.0142642	+	0.0200313i
$725$	27823.0	+	39072.0i	1.42527	+	2.00151i
$726$	23873.0	−	5333.64i	1.22040	−	0.272659i
$727$	−12227.1	−	6303.50i	−0.623765	−	0.321573i	0.117208	−	0.993107i	$-0.462605\pi$
$727$	−12227.1	−	6303.50i	−0.623765	−	0.321573i	−0.740974	+	0.671534i	$0.765636\pi$
$728$	11240.6	+	3300.53i	0.572257	+	0.168030i
$729$	14433.4	−	13382.8i	0.733291	−	0.679915i
$730$	36694.3	+	42347.5i	1.86044	+	2.14706i
$731$	254.710	−	5347.02i	0.0128875	−	0.270543i
$732$	5086.39	+	1864.70i	0.256828	+	0.0941548i
$733$	1935.81	−	7979.50i	0.0975452	−	0.402087i	−0.902016	−	0.431702i	$-0.857913\pi$
$733$	1935.81	−	7979.50i	0.0975452	−	0.402087i	0.999561	+	0.0296155i	$0.00942828\pi$
$734$	5592.98	+	534.065i	0.281255	+	0.0268566i
$735$	−17893.2	+	21920.3i	−0.897958	+	1.10006i
$736$	8439.32	−	23219.6i	0.422660	−	1.16289i
$737$	2486.20			0.124261
$738$	−142.261	−	63.0499i	−0.00709581	−	0.00314485i
$739$	−9683.26	+	2843.26i	−0.482009	+	0.141531i	−0.513705	−	0.857967i	$-0.671727\pi$
$739$	−9683.26	+	2843.26i	−0.482009	+	0.141531i	0.0316961	+	0.999498i	$0.489909\pi$
$740$	41379.7	+	7975.28i	2.05560	+	0.396185i
$741$	20848.5	+	18740.1i	1.03359	+	0.929061i
$742$	52513.9	−	10121.2i	2.59818	−	0.500758i
$743$	13970.5	+	5592.95i	0.689809	+	0.276158i	0.689966	−	0.723842i	$-0.257626\pi$
$743$	13970.5	+	5592.95i	0.689809	+	0.276158i	−0.000156466		1.00000i	$0.500050\pi$
$744$	4560.34	+	2183.75i	0.224718	+	0.107608i
$745$	5768.69	+	2973.96i	0.283689	+	0.146252i
$746$	6314.95	−	43921.5i	0.309929	−	2.15560i
$747$	−19892.4	+	21336.7i	−0.974332	+	1.04507i
$748$	2323.78	−	5088.36i	0.113591	−	0.248729i
$749$	−7052.67	+	2823.46i	−0.344057	+	0.137740i
$750$	4223.06	−	37083.3i	0.205606	−	1.80546i
$751$	23873.2	−	22763.1i	1.15998	−	1.10604i	0.167223	−	0.985919i	$-0.446520\pi$
$751$	23873.2	−	22763.1i	1.15998	−	1.10604i	0.992759	−	0.120122i	$-0.0383285\pi$
$752$	−31865.9	−	12757.2i	−1.54525	−	0.618626i
$753$	11767.5	−	21840.8i	0.569496	−	1.05700i
$754$	2310.85	−	48510.7i	0.111613	−	2.34304i
$755$	19264.2	−	22232.1i	0.928605	−	1.07167i
$756$	−20690.9	−	4137.75i	−0.995398	−	0.199059i
$757$	−3806.30	−	8334.64i	−0.182751	−	0.400169i	0.795978	−	0.605325i	$-0.206957\pi$
$757$	−3806.30	−	8334.64i	−0.182751	−	0.400169i	−0.978729	+	0.205157i	$0.934230\pi$
$758$	−11005.0	−	19061.2i	−0.527335	−	0.913371i
$759$	−1652.69	−	4567.33i	−0.0790368	−	0.218424i
$760$	6218.61	−	10771.0i	0.296806	−	0.514083i
$761$	−39307.0	−	3753.37i	−1.87238	−	0.178790i	−0.903875	−	0.427797i	$-0.859290\pi$
$761$	−39307.0	−	3753.37i	−1.87238	−	0.178790i	−0.968502	+	0.249007i	$0.919896\pi$
$762$	−420.928	+	998.395i	−0.0200113	+	0.0474646i
$763$	13424.9	+	2587.43i	0.636976	+	0.122767i
$764$	14876.0	+	9560.25i	0.704446	+	0.452720i
$765$	34102.0	−	44379.7i	1.61171	−	2.09745i
$766$	4332.78	+	30135.2i	0.204373	+	1.42145i
$767$	−6702.16	−	27626.7i	−0.315516	−	1.30058i
$768$	25408.5	−	11049.6i	1.19381	−	0.519163i
$769$	7191.04	+	5655.09i	0.337211	+	0.265186i	0.772377	−	0.635165i	$-0.219068\pi$
$769$	7191.04	+	5655.09i	0.337211	+	0.265186i	−0.435166	+	0.900350i	$0.643310\pi$
$770$	8679.95	+	12189.3i	0.406238	+	0.570482i
$771$	8186.64	−	12243.1i	0.382406	−	0.571887i
$772$	21846.3	−	8745.93i	1.01848	−	0.407737i
$773$	−32604.8	+	20953.9i	−1.51710	+	0.974978i	−0.524781	+	0.851238i	$0.675853\pi$
$773$	−32604.8	+	20953.9i	−1.51710	+	0.974978i	−0.992315	+	0.123740i	$0.960511\pi$
$774$	−410.460	+	4875.88i	−0.0190616	+	0.226434i
$775$	4163.57	+	28958.2i	0.192980	+	1.34221i
$776$	−1336.44	+	3861.40i	−0.0618241	+	0.178629i
$777$	−46689.0	+	15214.0i	−2.15567	+	0.702443i
$778$	−109.605	−	316.683i	−0.00505080	−	0.0145933i
$779$	31.8441	−	131.263i	0.00146461	−	0.00603721i
$780$	−25240.4	+	25525.1i	−1.15866	+	1.17173i
$781$	−385.253	−	667.278i	−0.0176510	−	0.0305724i
$782$	43492.9	+	13502.2i	1.98888	+	0.617441i
$783$	−1202.11	−	29574.9i	−0.0548660	−	1.34984i
$784$	−9169.92	−	20079.3i	−0.417726	−	0.914692i
$785$	−19408.5	−	18506.0i	−0.882446	−	0.841411i
$786$	−10552.8	−	3868.72i	−0.478889	−	0.175563i
$787$	−18693.2	+	9636.99i	−0.846682	+	0.436495i	−0.826255	−	0.563296i	$-0.809533\pi$
$787$	−18693.2	+	9636.99i	−0.846682	+	0.436495i	−0.0204274	+	0.999791i	$0.506503\pi$
$788$	−13599.4	+	2621.07i	−0.614795	+	0.118492i
$789$	−13633.7	−	8205.65i	−0.615174	−	0.370252i
$790$	5718.33	+	23571.3i	0.257530	+	1.06155i
$791$	−25528.1	+	16405.9i	−1.14750	+	0.737456i
$792$	775.530	−	1546.67i	0.0347945	−	0.0693920i
$793$	−4461.31	+	9768.92i	−0.199781	+	0.437458i
$794$	6825.53	−	651.760i	0.305075	−	0.0291311i
$795$	16587.8	−	52912.4i	0.740010	−	2.36051i
$796$	180.083	+	3780.41i	0.00801868	+	0.168333i
$797$	11007.6	−	10495.7i	0.489222	−	0.466472i	−0.404858	−	0.914380i	$-0.632679\pi$
$797$	11007.6	−	10495.7i	0.489222	−	0.466472i	0.894080	+	0.447908i	$0.147831\pi$
$798$	779.103	−	42822.2i	0.0345613	−	1.89961i
$799$	16293.4	−	47076.6i	0.721424	−	2.08442i
$800$	42838.0	+	27530.3i	1.89319	+	1.21668i
$801$	257.106	+	22922.1i	0.0113413	+	1.01113i
$802$	−6513.58	+	1912.56i	−0.286786	+	0.0842080i
$803$	−3924.89	+	5511.74i	−0.172486	+	0.242223i
$804$	5762.13	−	7059.00i	0.252755	−	0.309641i
$805$	−38254.5	+	35366.0i	−1.67490	+	1.54843i
$806$	14810.9	−	25653.2i	0.647260	−	1.12109i
$807$	−18609.7	+	18819.7i	−0.811765	+	0.820921i
$808$	6443.78	+	6144.13i	0.280559	+	0.267512i
$809$	947.359	−	1093.31i	0.0411711	−	0.0475139i	−0.734791	−	0.678294i	$-0.762720\pi$
$809$	947.359	−	1093.31i	0.0411711	−	0.0475139i	0.775962	+	0.630780i	$0.217265\pi$
$810$	−32626.8	+	39405.7i	−1.41530	+	1.70935i
$811$	−5657.24	−	6528.80i	−0.244948	−	0.282685i	0.619941	−	0.784648i	$-0.287157\pi$
$811$	−5657.24	−	6528.80i	−0.244948	−	0.282685i	−0.864889	+	0.501964i	$0.832611\pi$
$812$	−24942.3	+	19614.9i	−1.07796	+	0.847718i
$813$	−1422.66	−	18437.7i	−0.0613715	−	0.795375i
$814$	566.201	+	11886.0i	0.0243800	+	0.511800i
$815$	−18104.2	−	14237.3i	−0.778111	−	0.611914i
$816$	19297.8	+	39165.9i	0.827890	+	1.68024i
$817$	−4228.11	+	403.736i	−0.181056	+	0.0172888i
$818$	2511.00	−	17464.4i	0.107329	−	0.746489i
$819$	11333.8	−	40264.7i	0.483561	−	1.71790i
$820$	165.956	+	48.7291i	0.00706761	+	0.00207524i
$821$	32593.1	−	25631.5i	1.38551	−	1.08958i	0.400655	−	0.916229i	$-0.368783\pi$
$821$	32593.1	−	25631.5i	1.38551	−	1.08958i	0.984860	−	0.173352i	$-0.0554598\pi$
$822$	24749.0	+	40095.6i	1.05015	+	1.70133i
$823$	33754.4	−	17401.6i	1.42965	−	0.737037i	0.442493	−	0.896772i	$-0.354094\pi$
$823$	33754.4	−	17401.6i	1.42965	−	0.737037i	0.987160	+	0.159735i	$0.0510639\pi$
$824$	−632.103	−	1826.34i	−0.0267237	−	0.0772131i
$825$	9933.60	−	1244.25i	0.419204	−	0.0525082i
$826$	−25193.5	+	35379.3i	−1.06125	+	1.49032i
$827$	27598.9			1.16047			0.580235	−	0.814449i	$-0.302961\pi$
$827$	27598.9			1.16047			0.580235	+	0.814449i	$0.302961\pi$
$828$	−16798.2	−	5892.99i	−0.705046	−	0.247338i
$829$	30710.4			1.28663			0.643314	−	0.765602i	$-0.277559\pi$
$829$	30710.4			1.28663			0.643314	+	0.765602i	$0.277559\pi$
$830$	43980.8	−	61762.4i	1.83927	−	2.58290i
$831$	3452.33	−	8188.55i	0.144115	−	0.341826i
$832$	−4604.59	−	13304.1i	−0.191870	−	0.554371i
$833$	28475.5	−	14680.1i	1.18442	−	0.610608i
$834$	−10748.9	+	19950.3i	−0.446288	+	0.828326i
$835$	−19002.7	+	14943.9i	−0.787562	+	0.619346i
$836$	−4258.61	−	1250.44i	−0.176181	−	0.0517313i
$837$	7614.10	−	16369.4i	0.314435	−	0.675997i
$838$	4311.18	−	29984.9i	0.177717	−	1.23605i
$839$	17100.3	−	1632.88i	0.703655	−	0.0671909i	0.262906	−	0.964821i	$-0.415319\pi$
$839$	17100.3	−	1632.88i	0.703655	−	0.0671909i	0.440749	+	0.897630i	$0.354713\pi$
$840$	−18518.0	−	1220.10i	−0.760635	−	0.0501158i
$841$	−15817.4	−	12438.9i	−0.648546	−	0.510022i
$842$	419.148	+	8799.00i	0.0171553	+	0.360135i
$843$	−4397.04	+	3012.10i	−0.179647	+	0.123063i
$844$	10428.7	−	8201.21i	0.425320	−	0.334475i
$845$	−19594.9	−	22613.7i	−0.797732	−	0.920632i
$846$	−16448.8	+	42461.4i	−0.668466	+	1.72559i
$847$	20748.0	−	23944.5i	0.841688	−	0.971360i
$848$	31307.6	+	29851.8i	1.26782	+	1.20886i
$849$	6461.88	+	23586.2i	0.261214	+	0.953446i
$850$	−46932.6	+	81289.7i	−1.89385	+	3.28025i
$851$	−40795.9	+	7212.47i	−1.64332	+	0.290529i
$852$	−2787.46	−	452.675i	−0.112085	−	0.0182023i
$853$	5328.27	−	7482.51i	0.213876	−	0.300347i	−0.693675	−	0.720288i	$-0.744010\pi$
$853$	5328.27	−	7482.51i	0.213876	−	0.300347i	0.907552	+	0.419940i	$0.137949\pi$
$854$	15743.2	−	4622.62i	0.630821	−	0.185226i
$855$	−38704.9	−	21771.2i	−1.54816	−	0.870829i
$856$	−1920.66	−	1234.33i	−0.0766901	−	0.0492857i
$857$	−11130.4	+	32159.1i	−0.443648	+	1.28184i	0.472618	+	0.881267i	$0.343309\pi$
$857$	−11130.4	+	32159.1i	−0.443648	+	1.28184i	−0.916266	+	0.400570i	$0.868812\pi$
$858$	−8684.71	−	5227.04i	−0.345561	−	0.207981i
$859$	−14328.2	+	13662.0i	−0.569119	+	0.542654i	−0.919060	−	0.394118i	$-0.871050\pi$
$859$	−14328.2	+	13662.0i	−0.569119	+	0.542654i	0.349941	+	0.936772i	$0.386202\pi$
$860$	−258.792	−	5432.71i	−0.0102613	−	0.215411i
$861$	−196.696	+	43.9453i	−0.00778558	+	0.00173943i
$862$	−21485.6	+	2051.62i	−0.848957	+	0.0810656i
$863$	13403.5	−	29349.6i	0.528692	−	1.15767i	−0.437351	−	0.899291i	$-0.644083\pi$
$863$	13403.5	−	29349.6i	0.528692	−	1.15767i	0.966043	−	0.258382i	$-0.0831894\pi$
$864$	−12854.0	−	28673.9i	−0.506135	−	1.12906i
$865$	−68447.6	+	43988.6i	−2.69051	+	1.72908i
$866$	−11011.9	−	45391.7i	−0.432101	−	1.78114i
$867$	−33108.6	+	18320.4i	−1.29692	+	0.717641i
$868$	−19004.1	+	3662.73i	−0.743133	+	0.143227i
$869$	−2603.33	+	1342.11i	−0.101625	+	0.0523912i
$870$	13183.3	+	75796.2i	0.513741	+	2.95371i
$871$	13073.4	+	12465.5i	0.508583	+	0.484933i
$872$	1706.88	+	3737.54i	0.0662868	+	0.145148i
$873$	13840.0	+	4616.91i	0.536556	+	0.178991i
$874$	5693.01	−	35682.4i	0.220331	−	1.38098i
$875$	−24170.7	−	41864.9i	−0.933852	−	1.61748i
$876$	6552.80	+	23918.1i	0.252738	+	0.922507i
$877$	3155.10	−	13005.5i	0.121483	−	0.500758i	−0.878262	−	0.478179i	$-0.841297\pi$
$877$	3155.10	−	13005.5i	0.121483	−	0.500758i	0.999745	−	0.0225792i	$-0.00718780\pi$
$878$	12530.5	+	36204.5i	0.481644	+	1.39162i
$879$	3464.11	+	3113.78i	0.132925	+	0.119483i
$880$	−3958.78	+	11438.1i	−0.151648	+	0.438159i
$881$	−6767.36	−	47068.0i	−0.258795	−	1.79996i	−0.541447	−	0.840735i	$-0.682123\pi$
$881$	−6767.36	−	47068.0i	−0.258795	−	1.79996i	0.282652	−	0.959222i	$-0.408786\pi$
$882$	−26499.7	+	12463.1i	−1.01167	+	0.475798i
$883$	−11117.7	+	7144.89i	−0.423714	+	0.272304i	−0.735073	−	0.677988i	$-0.762852\pi$
$883$	−11117.7	+	7144.89i	−0.423714	+	0.272304i	0.311359	+	0.950292i	$0.399216\pi$
$884$	37731.6	−	15105.5i	1.43558	−	0.574719i
$885$	19904.0	+	40396.2i	0.756007	+	1.53435i
$886$	4844.36	+	6802.95i	0.183690	+	0.257957i
$887$	2206.90	+	1735.52i	0.0835404	+	0.0656969i	0.659056	−	0.752094i	$-0.270956\pi$
$887$	2206.90	+	1735.52i	0.0835404	+	0.0656969i	−0.575515	+	0.817791i	$0.695199\pi$
$888$	−11863.5	−	8777.55i	−0.448327	−	0.331706i
$889$	330.857	+	1363.81i	0.0124821	+	0.0514520i
$890$	−8479.47	−	58976.0i	−0.319362	−	2.22121i
$891$	−5553.18	−	2706.96i	−0.208797	−	0.101781i
$892$	10581.6	+	6800.35i	0.397194	+	0.255261i
$893$	−38812.0	−	7480.40i	−1.45442	−	0.280316i
$894$	4055.32	+	5354.42i	0.151712	+	0.200311i
$895$	3005.54	+	286.995i	0.112251	+	0.0107186i
$896$	11788.0	−	20417.3i	0.439518	−	0.761267i
$897$	14209.4	−	32303.1i	0.528917	−	1.20242i
$898$	14289.0	+	24749.3i	0.530993	+	0.919706i
$899$	−11278.1	−	24695.6i	−0.418405	−	0.916179i
$900$	19489.8	−	31087.9i	0.721844	−	1.15140i
$901$	−41113.7	+	47447.8i	−1.52020	+	1.75440i
$902$	−2.32389	+	48.7844i	−8.57838e−5	+	0.00180082i
$903$	3328.85	+	5393.04i	0.122677	+	0.198747i
$904$	−8466.46	−	3389.46i	−0.311494	−	0.124703i
$905$	1088.78	−	1038.15i	0.0399916	−	0.0381319i
$906$	27918.8	−	12141.3i	1.02377	−	0.445217i
$907$	35162.9	−	14077.1i	1.28728	−	0.515351i	0.375805	−	0.926699i	$-0.377366\pi$
$907$	35162.9	−	14077.1i	1.28728	−	0.515351i	0.911478	+	0.411348i	$0.134942\pi$
$908$	−13980.1	+	30612.2i	−0.510954	+	1.11883i
$909$	21678.6	−	23252.5i	0.791014	−	0.848445i
$910$	−15472.8	+	107616.i	−0.563647	+	3.92025i
$911$	−27366.4	−	14108.4i	−0.995269	−	0.513097i	−0.117958	−	0.993019i	$-0.537635\pi$
$911$	−27366.4	−	14108.4i	−0.995269	−	0.513097i	−0.877311	+	0.479922i	$0.840665\pi$
$912$	28580.3	−	19578.3i	1.03771	−	0.710859i
$913$	8500.01	+	3402.89i	0.308115	+	0.123351i
$914$	−47039.4	+	9066.10i	−1.70233	+	0.328096i
$915$	3523.00	−	16643.8i	0.127286	−	0.601341i
$916$	9642.12	+	1858.37i	0.347800	+	0.0670329i
$917$	−13968.1	+	4101.40i	−0.503017	+	0.147699i
$918$	51668.1	−	26182.2i	1.85763	−	0.941329i
$919$	37084.8			1.33114			0.665569	−	0.746336i	$-0.268189\pi$
$919$	37084.8			1.33114			0.665569	+	0.746336i	$0.268189\pi$
$920$	−15326.5	−	3199.71i	−0.549240	−	0.114664i
$921$	3721.43	+	9809.18i	0.133144	+	0.350948i
$922$	−11874.3	−	1133.86i	−0.424143	−	0.0405008i
$923$	1319.83	−	5440.40i	0.0470668	−	0.194012i
$924$	1134.86	+	6524.79i	0.0404049	+	0.232305i
$925$	4063.01	−	85293.1i	0.144423	−	3.03181i
$926$	−19325.4	−	22302.7i	−0.685823	−	0.791482i
$927$	−6495.33	+	2329.96i	−0.230135	+	0.0825521i
$928$	−45340.2	−	13313.1i	−1.60384	−	0.470930i
$929$	36169.6	+	18646.7i	1.27738	+	0.658535i	0.957366	−	0.288878i	$-0.0932822\pi$
$929$	36169.6	+	18646.7i	1.27738	+	0.658535i	0.320014	+	0.947413i	$0.396313\pi$
$930$	−14037.0	+	44775.9i	−0.494938	+	1.57877i
$931$	−14744.6	−	20706.0i	−0.519051	−	0.728905i
$932$	10069.5	+	14140.7i	0.353903	+	0.496988i
$933$	−6468.38	+	20633.1i	−0.226973	+	0.724006i
$934$	3987.20	+	2055.54i	0.139684	+	0.0720123i
$935$	−16855.1	−	4949.11i	−0.589541	−	0.173105i
$936$	11832.8	−	4244.57i	0.413213	−	0.148225i
$937$	2607.50	+	3009.21i	0.0909107	+	0.104916i	0.799382	−	0.600823i	$-0.205160\pi$
$937$	2607.50	+	3009.21i	0.0909107	+	0.104916i	−0.708471	+	0.705739i	$0.750615\pi$
$938$	1313.17	−	27566.9i	0.0457107	−	0.959586i
$939$	3376.41	+	19412.4i	0.117343	+	0.674654i
$940$	11932.9	−	49188.0i	0.414051	−	1.70674i
$941$	−34000.1	−	3246.61i	−1.17786	−	0.112472i	−0.512296	−	0.858809i	$-0.671205\pi$
$941$	−34000.1	−	3246.61i	−1.17786	−	0.112472i	−0.665568	+	0.746337i	$0.731811\pi$
$942$	−9844.59	−	25949.0i	−0.340503	−	0.897520i
$943$	−169.497	+	13.5522i	−0.00585320	+	0.000467997i
$944$	−35131.3			−1.21126
$945$	−3614.56	+	66164.4i	−0.124425	+	2.27760i
$946$	1473.57	−	432.680i	0.0506449	−	0.0148707i
$947$	−206.236	−	39.7487i	−0.00707683	−	0.00136395i	0.185712	−	0.982604i	$-0.440541\pi$
$947$	−206.236	−	39.7487i	−0.00707683	−	0.00136395i	−0.192788	+	0.981240i	$0.561753\pi$
$948$	−2222.98	+	10502.1i	−0.0761593	+	0.359801i
$949$	−48273.6	+	9303.98i	−1.65124	+	0.318251i
$950$	69141.4	+	27680.1i	2.36131	+	0.945326i
$951$	−35820.2	+	24537.8i	−1.22140	+	0.836691i
$952$	18675.9	+	9628.09i	0.635808	+	0.327782i
$953$	−5175.63	+	35997.3i	−0.175923	+	1.22357i	0.690153	+	0.723663i	$0.257543\pi$
$953$	−5175.63	+	35997.3i	−0.175923	+	1.22357i	−0.866077	+	0.499911i	$0.833366\pi$
$954$	39133.9	−	41975.1i	1.32810	−	1.42452i
$955$	23068.5	−	50513.1i	0.781655	−	1.71159i
$956$	6743.85	−	2699.83i	0.228150	−	0.0913376i
$957$	−8519.48	+	3704.93i	−0.287770	+	0.125145i
$958$	6713.37	−	6401.19i	0.226408	−	0.215880i
$959$	56657.4	+	22682.2i	1.90778	+	0.763760i
$960$	11714.1	+	18977.8i	0.393822	+	0.638028i
$961$	−629.601	+	13217.0i	−0.0211339	+	0.443656i
$962$	−56617.5	+	65340.1i	−1.89753	+	2.18986i
$963$	−4330.06	+	6906.82i	−0.144895	+	0.231121i
$964$	−8385.72	−	18362.2i	−0.280172	−	0.613491i
$965$	−36949.2	−	63997.8i	−1.23258	−	2.13488i
$966$	−51515.2	+	15912.6i	−1.71581	+	0.529999i
$967$	3734.16	−	6467.76i	0.124181	−	0.215087i	−0.797232	−	0.603673i	$-0.793703\pi$
$967$	3734.16	−	6467.76i	0.124181	−	0.215087i	0.921412	+	0.388586i	$0.127036\pi$
$968$	9478.64	+	905.101i	0.314726	+	0.0300527i
$969$	30356.1	+	40080.5i	1.00638	+	1.32876i
$970$	−37236.2	−	7176.69i	−1.23256	−	0.237556i
$971$	−1151.19	−	739.827i	−0.0380469	−	0.0244513i	0.521479	−	0.853264i	$-0.325380\pi$
$971$	−1151.19	−	739.827i	−0.0380469	−	0.0244513i	−0.559526	+	0.828813i	$0.689017\pi$
$972$	−20556.1	+	9493.19i	−0.678330	+	0.313266i
$973$	4177.22	+	29053.2i	0.137632	+	0.957248i
$974$	3684.38	+	15187.2i	0.121207	+	0.499621i
$975$	58473.1	+	43262.9i	1.92066	+	1.42105i
$976$	10432.3	+	8204.04i	0.342141	+	0.269062i
$977$	−27966.8	−	39273.9i	−0.915800	−	1.28606i	−0.957946	−	0.286950i	$-0.907359\pi$
$977$	−27966.8	−	39273.9i	−0.915800	−	1.28606i	0.0421453	−	0.999111i	$-0.486581\pi$
$978$	−10535.1	−	21381.4i	−0.344452	−	0.699083i
$979$	6679.52	−	2674.08i	0.218058	−	0.0872971i
$980$	27383.0	−	17598.0i	0.892570	−	0.573620i
$981$	13275.9	−	6243.79i	0.432076	−	0.203210i
$982$	4807.33	+	33435.7i	0.156220	+	1.08653i
$983$	−8060.54	+	23289.4i	−0.261538	+	0.755663i	0.735412	+	0.677620i	$0.236988\pi$
$983$	−8060.54	+	23289.4i	−0.261538	+	0.755663i	−0.996950	+	0.0780434i	$0.975133\pi$
$984$	−45.0471	−	40.4915i	−0.00145940	−	0.00131181i
$985$	14225.1	+	41100.7i	0.460151	+	1.32952i
$986$	20535.8	−	84649.7i	0.663279	−	2.73407i
$987$	15584.2	+	56883.0i	0.502583	+	1.83445i
$988$	−16123.9	−	27927.3i	−0.519199	−	0.899278i
$989$	2145.95	+	4897.36i	0.0689962	+	0.157459i
$990$	15232.1	+	5081.30i	0.488998	+	0.163126i
$991$	18091.1	+	39614.1i	0.579903	+	1.26981i	0.941354	+	0.337419i	$0.109554\pi$
$991$	18091.1	+	39614.1i	0.579903	+	1.26981i	−0.361452	+	0.932391i	$0.617719\pi$
$992$	−20859.4	−	19889.4i	−0.667627	−	0.636581i
$993$	−4970.61	−	28578.2i	−0.158850	−	0.913294i
$994$	−7602.22	+	3919.22i	−0.242583	+	0.125060i
$995$	11670.5	−	2249.30i	0.371838	−	0.0716658i
$996$	29361.7	−	16247.1i	0.934097	−	0.516877i
$997$	−3093.12	−	12750.0i	−0.0982550	−	0.405013i	0.901351	−	0.433090i	$-0.142577\pi$
$997$	−3093.12	−	12750.0i	−0.0982550	−	0.405013i	−0.999606	+	0.0280772i	$0.991062\pi$
$998$	41668.9	−	26779.0i	1.32165	−	0.849372i
$999$	−30863.7	+	42708.3i	−0.977461	+	1.35258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.16	✓	1400
9.7	even	3	inner	207.4.m.a.142.55	yes	1400
23.6	even	11	inner	207.4.m.a.121.55	yes	1400
207.52	even	33	inner	207.4.m.a.52.16	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.16	✓	1400	1.1	even	1	trivial
207.4.m.a.52.16	yes	1400	207.52	even	33	inner
207.4.m.a.121.55	yes	1400	23.6	even	11	inner
207.4.m.a.142.55	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+(-2.16862 + 3.04540i) q^{2} +(3.13722 + 4.14221i) q^{3} +(-1.95501 - 5.64863i) q^{4} +(-16.6844 + 8.60138i) q^{5} +(-19.4181 + 0.571212i) q^{6} +(-19.7783 + 15.5539i) q^{7} +(-7.25554 - 2.13042i) q^{8} +(-7.31574 + 25.9900i) q^{9} +(9.98737 - 69.4637i) q^{10} +(8.43600 - 0.805540i) q^{11} +(17.2645 - 25.8190i) q^{12} +(48.3985 + 38.0610i) q^{13} +(-4.47603 - 93.9634i) q^{14} +(-87.9711 - 42.1256i) q^{15} +(59.8108 - 47.0357i) q^{16} +(72.3175 + 83.4588i) q^{17} +(-63.2849 - 78.6418i) q^{18} +(57.3795 - 66.2195i) q^{19} +(81.2041 + 77.4279i) q^{20} +(-126.476 - 33.1301i) q^{21} +(-15.8413 + 27.4379i) q^{22} +(-101.759 - 42.5694i) q^{23} +(-13.9376 - 36.7375i) q^{24} +(131.877 - 185.195i) q^{25} +(-220.869 + 64.8530i) q^{26} +(-130.607 + 51.2330i) q^{27} +(126.525 + 81.3125i) q^{28} +(-69.0040 + 199.374i) q^{29} +(319.065 - 176.553i) q^{30} +(-93.1315 + 88.8007i) q^{31} +(10.6573 + 223.724i) q^{32} +(29.8023 + 32.4165i) q^{33} +(-410.995 + 39.2452i) q^{34} +(196.204 - 429.627i) q^{35} +(161.110 - 9.48679i) q^{36} +(315.962 - 203.057i) q^{37} +(77.2305 + 318.348i) q^{38} +(-5.81992 + 319.882i) q^{39} +(139.378 - 26.8630i) q^{40} +(1.37017 - 0.706371i) q^{41} +(375.173 - 313.324i) q^{42} +(-35.0824 - 33.4510i) q^{43} +(-21.0427 - 46.0770i) q^{44} +(-101.492 - 496.552i) q^{45} +(350.317 - 217.579i) q^{46} +(-225.553 - 390.669i) q^{47} +(382.471 + 100.187i) q^{48} +(68.3949 - 281.928i) q^{49} +(278.002 + 803.235i) q^{50} +(-118.828 + 561.382i) q^{51} +(120.373 - 347.795i) q^{52} +(80.9085 + 562.731i) q^{53} +(127.212 - 508.855i) q^{54} +(-133.820 + 86.0012i) q^{55} +(176.639 - 70.7155i) q^{56} +(454.307 + 29.9328i) q^{57} +(-457.530 - 642.511i) q^{58} +(-362.926 - 285.408i) q^{59} +(-65.9676 + 579.272i) q^{60} +(41.1214 + 169.505i) q^{61} +(-68.4669 - 476.198i) q^{62} +(-259.552 - 627.827i) q^{63} +(-192.353 - 123.618i) q^{64} +(-1134.88 - 218.729i) q^{65} +(-163.351 + 20.4608i) q^{66} +(292.051 + 27.8875i) q^{67} +(330.046 - 571.657i) q^{68} +(-142.908 - 555.055i) q^{69} +(882.895 + 1529.22i) q^{70} +(-37.7703 - 82.7054i) q^{71} +(108.449 - 172.986i) q^{72} +(-522.876 + 603.431i) q^{73} +(-66.8133 + 1402.58i) q^{74} +(1180.84 - 34.7362i) q^{75} +(-486.226 - 194.656i) q^{76} +(-154.321 + 147.145i) q^{77} +(-961.549 - 711.428i) q^{78} +(-320.863 + 128.454i) q^{79} +(-593.332 + 1299.22i) q^{80} +(-621.960 - 380.272i) q^{81} +(-0.820193 + 5.70456i) q^{82} +(960.313 + 495.076i) q^{83} +(60.1224 + 779.187i) q^{84} +(-1924.43 - 770.426i) q^{85} +(177.952 - 34.2974i) q^{86} +(-1042.33 + 339.651i) q^{87} +(-62.9238 - 12.1276i) q^{88} +(814.628 - 239.196i) q^{89} +(1732.30 + 767.750i) q^{90} -1549.24 q^{91} +(-41.5193 + 658.021i) q^{92} +(-660.005 - 107.183i) q^{93} +(1678.88 + 160.314i) q^{94} +(-387.761 + 1598.37i) q^{95} +(-893.277 + 746.016i) q^{96} +(25.7115 - 539.750i) q^{97} +(710.261 + 819.684i) q^{98} +(-40.7796 + 225.145i) 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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