LMFDB - Embedded newform 207.4.m.a.4.11

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			4.11
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.41610 + 3.39293i) q^{2} +(4.94150 - 1.60674i) q^{3} +(-3.05792 - 8.83529i) q^{4} +(19.5280 - 10.0674i) q^{5} +(-6.48755 + 20.6482i) q^{6} +(-0.748547 + 0.588664i) q^{7} +(5.39337 + 1.58363i) q^{8} +(21.8367 - 15.8794i) q^{9} +(-13.0236 + 90.5811i) q^{10} +(-0.805518 + 0.0769176i) q^{11} +(-29.3068 - 38.7462i) q^{12} +(-14.8688 - 11.6930i) q^{13} +(-0.188735 - 3.96204i) q^{14} +(80.3220 - 81.1246i) q^{15} +(40.3896 - 31.7627i) q^{16} +(-21.8127 - 25.1732i) q^{17} +(1.11817 + 112.457i) q^{18} +(17.6392 - 20.3567i) q^{19} +(-148.664 - 141.751i) q^{20} +(-2.75311 + 4.11160i) q^{21} +(1.68523 - 2.91891i) q^{22} +(-5.38270 - 110.173i) q^{23} +(29.1958 - 0.840233i) q^{24} +(207.485 - 291.371i) q^{25} +(75.5979 - 22.1976i) q^{26} +(82.3920 - 113.554i) q^{27} +(7.49002 + 4.81354i) q^{28} +(-61.1578 + 176.704i) q^{29} +(81.1846 + 468.532i) q^{30} +(-35.0330 + 33.4039i) q^{31} +(12.3233 + 258.699i) q^{32} +(-3.85688 + 1.67435i) q^{33} +(138.113 - 13.1882i) q^{34} +(-8.69134 + 19.0314i) q^{35} +(-207.075 - 144.376i) q^{36} +(191.287 - 122.932i) q^{37} +(26.4510 + 109.032i) q^{38} +(-92.2618 - 33.8904i) q^{39} +(121.265 - 23.3719i) q^{40} +(-340.032 + 175.299i) q^{41} +(-7.29861 - 19.2751i) q^{42} +(214.386 + 204.416i) q^{43} +(3.14280 + 6.88178i) q^{44} +(266.564 - 529.934i) q^{45} +(386.814 + 247.925i) q^{46} +(-6.02669 - 10.4385i) q^{47} +(148.550 - 221.851i) q^{48} +(-80.6515 + 332.450i) q^{49} +(487.301 + 1407.96i) q^{50} +(-148.235 - 89.3460i) q^{51} +(-57.8430 + 167.127i) q^{52} +(75.5486 + 525.452i) q^{53} +(186.215 + 553.908i) q^{54} +(-14.9558 + 9.61153i) q^{55} +(-4.96942 + 1.98945i) q^{56} +(54.4560 - 128.934i) q^{57} +(-451.781 - 634.438i) q^{58} +(506.768 + 398.526i) q^{59} +(-962.378 - 461.595i) q^{60} +(-142.144 - 585.925i) q^{61} +(-28.6941 - 199.572i) q^{62} +(-6.99818 + 24.7410i) q^{63} +(-561.713 - 360.991i) q^{64} +(-408.077 - 78.6503i) q^{65} +(3.63763 - 17.1315i) q^{66} +(668.490 + 63.8330i) q^{67} +(-155.711 + 269.700i) q^{68} +(-203.618 - 535.769i) q^{69} +(-43.5731 - 75.4708i) q^{70} +(-26.7193 - 58.5071i) q^{71} +(142.921 - 51.0622i) q^{72} +(-129.968 + 149.991i) q^{73} +(-45.0654 + 946.039i) q^{74} +(557.125 - 1773.19i) q^{75} +(-233.797 - 93.5982i) q^{76} +(0.557689 - 0.531756i) q^{77} +(337.901 - 231.156i) q^{78} +(264.634 - 105.944i) q^{79} +(468.962 - 1026.88i) q^{80} +(224.687 - 693.510i) q^{81} +(226.773 - 1577.24i) q^{82} +(-373.649 - 192.629i) q^{83} +(44.7460 + 11.7516i) q^{84} +(-679.390 - 271.987i) q^{85} +(-1211.55 + 233.506i) q^{86} +(-18.2931 + 971.446i) q^{87} +(-4.46626 - 0.860801i) q^{88} +(-447.432 + 131.378i) q^{89} +(1153.98 + 2184.80i) q^{90} +18.0132 q^{91} +(-956.948 + 384.457i) q^{92} +(-119.444 + 221.354i) q^{93} +(49.9783 + 4.77235i) q^{94} +(139.520 - 575.108i) q^{95} +(476.558 + 1258.56i) q^{96} +(-19.2330 + 403.751i) q^{97} +(-933.119 - 1076.88i) q^{98} +(-16.3685 + 14.4708i) 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 $

$2$	−2.41610	+	3.39293i	−0.854219	+	1.19958i	0.124057	+	0.992275i	$0.460409\pi$
$2$	−2.41610	+	3.39293i	−0.854219	+	1.19958i	−0.978276	+	0.207307i	$0.933530\pi$
$3$	4.94150	−	1.60674i	0.950991	−	0.309218i
$3$	4.94150	−	1.60674i	0.950991	−	0.309218i
$4$	−3.05792	−	8.83529i	−0.382240	−	1.10441i
$5$	19.5280	−	10.0674i	1.74664	−	0.900456i	0.788078	−	0.615575i	$-0.211076\pi$
$5$	19.5280	−	10.0674i	1.74664	−	0.900456i	0.958563	−	0.284881i	$-0.0919541\pi$
$6$	−6.48755	+	20.6482i	−0.441422	+	1.40493i
$7$	−0.748547	+	0.588664i	−0.0404177	+	0.0317849i	−0.638164	−	0.769901i	$-0.720306\pi$
$7$	−0.748547	+	0.588664i	−0.0404177	+	0.0317849i	0.597746	+	0.801686i	$0.296063\pi$
$8$	5.39337	+	1.58363i	0.238355	+	0.0699874i
$9$	21.8367	−	15.8794i	0.808768	−	0.588127i
$10$	−13.0236	+	90.5811i	−0.411842	+	2.86443i
$11$	−0.805518	+	0.0769176i	−0.0220793	+	0.00210832i	−0.106090	−	0.994357i	$-0.533833\pi$
$11$	−0.805518	+	0.0769176i	−0.0220793	+	0.00210832i	0.0840105	+	0.996465i	$0.473227\pi$
$12$	−29.3068	−	38.7462i	−0.705011	−	0.932090i
$13$	−14.8688	−	11.6930i	−0.317221	−	0.249465i	0.446834	−	0.894617i	$-0.352552\pi$
$13$	−14.8688	−	11.6930i	−0.317221	−	0.249465i	−0.764054	+	0.645152i	$0.776794\pi$
$14$	−0.188735	−	3.96204i	−0.00360297	−	0.0756357i
$15$	80.3220	−	81.1246i	1.38260	−	1.39642i
$16$	40.3896	−	31.7627i	0.631088	−	0.496293i
$17$	−21.8127	−	25.1732i	−0.311198	−	0.359142i	0.578507	−	0.815677i	$-0.303636\pi$
$17$	−21.8127	−	25.1732i	−0.311198	−	0.359142i	−0.889705	+	0.456536i	$0.849090\pi$
$18$	1.11817	+	112.457i	0.0146419	+	1.47257i
$19$	17.6392	−	20.3567i	0.212985	−	0.245798i	−0.639197	−	0.769043i	$-0.720733\pi$
$19$	17.6392	−	20.3567i	0.212985	−	0.245798i	0.852182	+	0.523245i	$0.175279\pi$
$20$	−148.664	−	141.751i	−1.66211	−	1.58482i
$21$	−2.75311	+	4.11160i	−0.0286085	+	0.0427250i
$22$	1.68523	−	2.91891i	0.0163315	−	0.0282870i
$23$	−5.38270	−	110.173i	−0.0487987	−	0.998809i
$23$	−5.38270	−	110.173i	−0.0487987	−	0.998809i
$24$	29.1958	−	0.840233i	0.248315	−	0.00714633i
$25$	207.485	−	291.371i	1.65988	−	2.33097i
$26$	75.5979	−	22.1976i	0.570230	−	0.167435i
$27$	82.3920	−	113.554i	0.587272	−	0.809390i
$28$	7.49002	+	4.81354i	0.0505529	+	0.0324884i
$29$	−61.1578	+	176.704i	−0.391611	+	1.13149i	0.561137	+	0.827723i	$0.310364\pi$
$29$	−61.1578	+	176.704i	−0.391611	+	1.13149i	−0.952748	+	0.303762i	$0.901757\pi$
$30$	81.1846	+	468.532i	0.494074	+	2.85139i
$31$	−35.0330	+	33.4039i	−0.202971	+	0.193533i	−0.784747	−	0.619817i	$-0.787207\pi$
$31$	−35.0330	+	33.4039i	−0.202971	+	0.193533i	0.581775	+	0.813350i	$0.302358\pi$
$32$	12.3233	+	258.699i	0.0680774	+	1.42912i
$33$	−3.85688	+	1.67435i	−0.0203453	+	0.00883233i
$34$	138.113	−	13.1882i	0.696651	−	0.0665221i
$35$	−8.69134	+	19.0314i	−0.0419744	+	0.0919112i
$36$	−207.075	−	144.376i	−0.958678	−	0.668407i
$37$	191.287	−	122.932i	0.849928	−	0.546215i	−0.0416246	−	0.999133i	$-0.513253\pi$
$37$	191.287	−	122.932i	0.849928	−	0.546215i	0.891552	+	0.452918i	$0.149617\pi$
$38$	26.4510	+	109.032i	0.112919	+	0.465458i
$39$	−92.2618	−	33.8904i	−0.378813	−	0.139149i
$40$	121.265	−	23.3719i	0.479342	−	0.0923856i
$41$	−340.032	+	175.299i	−1.29522	+	0.667732i	−0.961465	−	0.274927i	$-0.911346\pi$
$41$	−340.032	+	175.299i	−1.29522	+	0.667732i	−0.333755	+	0.942660i	$0.608316\pi$
$42$	−7.29861	−	19.2751i	−0.0268143	−	0.0708147i
$43$	214.386	+	204.416i	0.760314	+	0.724958i	0.967369	−	0.253371i	$-0.0815395\pi$
$43$	214.386	+	204.416i	0.760314	+	0.724958i	−0.207055	+	0.978329i	$0.566388\pi$
$44$	3.14280	+	6.88178i	0.0107681	+	0.0235788i
$45$	266.564	−	529.934i	0.883045	−	1.75551i
$46$	386.814	+	247.925i	1.23984	+	0.794663i
$47$	−6.02669	−	10.4385i	−0.0187039	−	0.0323961i	0.856522	−	0.516111i	$-0.172621\pi$
$47$	−6.02669	−	10.4385i	−0.0187039	−	0.0323961i	−0.875226	+	0.483714i	$0.839287\pi$
$48$	148.550	−	221.851i	0.446696	−	0.667114i
$49$	−80.6515	+	332.450i	−0.235136	+	0.969242i
$50$	487.301	+	1407.96i	1.37829	+	3.98232i
$51$	−148.235	−	89.3460i	−0.407000	−	0.245313i
$52$	−57.8430	+	167.127i	−0.154257	+	0.445698i
$53$	75.5486	+	525.452i	0.195800	+	1.36182i	0.816307	+	0.577618i	$0.196018\pi$
$53$	75.5486	+	525.452i	0.195800	+	1.36182i	−0.620507	+	0.784201i	$0.713073\pi$
$54$	186.215	+	553.908i	0.469271	+	1.39588i
$55$	−14.9558	+	9.61153i	−0.0366662	+	0.0235640i
$56$	−4.96942	+	1.98945i	−0.0118583	+	0.00474736i
$57$	54.4560	−	128.934i	0.126542	−	0.299610i
$58$	−451.781	−	634.438i	−1.02279	−	1.43631i
$59$	506.768	+	398.526i	1.11823	+	0.879385i	0.993615	−	0.112820i	$-0.0359884\pi$
$59$	506.768	+	398.526i	1.11823	+	0.879385i	0.124614	+	0.992205i	$0.460231\pi$
$60$	−962.378	−	461.595i	−2.07071	−	0.993195i
$61$	−142.144	−	585.925i	−0.298355	−	1.22984i	−0.901702	−	0.432357i	$-0.857682\pi$
$61$	−142.144	−	585.925i	−0.298355	−	1.22984i	0.603347	−	0.797478i	$-0.293833\pi$
$62$	−28.6941	−	199.572i	−0.0587766	−	0.408800i
$63$	−6.99818	+	24.7410i	−0.0139951	+	0.0494774i
$64$	−561.713	−	360.991i	−1.09710	−	0.705061i
$65$	−408.077	−	78.6503i	−0.778703	−	0.150083i
$66$	3.63763	−	17.1315i	0.00678426	−	0.0319506i
$67$	668.490	+	63.8330i	1.21894	+	0.116395i	0.684628	−	0.728892i	$-0.259965\pi$
$67$	668.490	+	63.8330i	1.21894	+	0.116395i	0.534312	+	0.845287i	$0.320571\pi$
$68$	−155.711	+	269.700i	−0.277688	+	0.480969i
$69$	−203.618	−	535.769i	−0.355257	−	0.934769i
$70$	−43.5731	−	75.4708i	−0.0743997	−	0.128864i
$71$	−26.7193	−	58.5071i	−0.0446619	−	0.0977959i	0.885986	−	0.463712i	$-0.153483\pi$
$71$	−26.7193	−	58.5071i	−0.0446619	−	0.0977959i	−0.930648	+	0.365916i	$0.880756\pi$
$72$	142.921	−	51.0622i	0.233936	−	0.0835796i
$73$	−129.968	+	149.991i	−0.208377	+	0.240480i	−0.850312	−	0.526279i	$-0.823587\pi$
$73$	−129.968	+	149.991i	−0.208377	+	0.240480i	0.641934	+	0.766760i	$0.278132\pi$
$74$	−45.0654	+	946.039i	−0.0707938	+	1.48615i
$75$	557.125	−	1773.19i	0.857750	−	2.73000i
$76$	−233.797	−	93.5982i	−0.352873	−	0.141269i
$77$	0.557689	−	0.531756i	0.000825385	−	0.000787003i
$78$	337.901	−	231.156i	0.490510	−	0.335554i
$79$	264.634	−	105.944i	0.376882	−	0.150881i	−0.175484	−	0.984482i	$-0.556149\pi$
$79$	264.634	−	105.944i	0.376882	−	0.150881i	0.552366	+	0.833601i	$0.313725\pi$
$80$	468.962	−	1026.88i	0.655394	−	1.43511i
$81$	224.687	−	693.510i	0.308213	−	0.951317i
$82$	226.773	−	1577.24i	0.305401	−	2.12411i
$83$	−373.649	−	192.629i	−0.494136	−	0.254745i	0.193100	−	0.981179i	$-0.438146\pi$
$83$	−373.649	−	192.629i	−0.494136	−	0.254745i	−0.687236	+	0.726434i	$0.741176\pi$
$84$	44.7460	+	11.7516i	0.0581213	+	0.0152643i
$85$	−679.390	−	271.987i	−0.866943	−	0.347072i
$86$	−1211.55	+	233.506i	−1.51912	+	0.292787i
$87$	−18.2931	+	971.446i	−0.0225428	+	1.19713i
$88$	−4.46626	−	0.860801i	−0.00541029	−	0.00104275i
$89$	−447.432	+	131.378i	−0.532895	+	0.156472i	−0.537099	−	0.843519i	$-0.680480\pi$
$89$	−447.432	+	131.378i	−0.532895	+	0.156472i	0.00420419	+	0.999991i	$0.498662\pi$
$90$	1153.98	+	2184.80i	1.35156	+	2.55887i
$91$	18.0132			0.0207506
$92$	−956.948	+	384.457i	−1.08444	+	0.435679i
$93$	−119.444	+	221.354i	−0.133180	+	0.246810i
$94$	49.9783	+	4.77235i	0.0548390	+	0.00523649i
$95$	139.520	−	575.108i	0.150678	−	0.621104i
$96$	476.558	+	1258.56i	0.506651	+	1.33803i
$97$	−19.2330	+	403.751i	−0.0201322	+	0.422626i	0.966193	+	0.257818i	$0.0830035\pi$
$97$	−19.2330	+	403.751i	−0.0201322	+	0.422626i	−0.986326	+	0.164808i	$0.947300\pi$
$98$	−933.119	−	1076.88i	−0.961829	−	1.11001i
$99$	−16.3685	+	14.4708i	−0.0166171	+	0.0146906i
$100$	−3208.82	−	942.196i	−3.20882	−	0.942196i
$101$	−931.546	−	480.245i	−0.917746	−	0.473131i	−0.0664338	−	0.997791i	$-0.521162\pi$
$101$	−931.546	−	480.245i	−0.917746	−	0.473131i	−0.851312	+	0.524660i	$0.824192\pi$
$102$	661.294	−	287.081i	0.641940	−	0.278679i
$103$	995.652	+	1398.20i	0.952471	+	1.33756i	0.941282	+	0.337621i	$0.109622\pi$
$103$	995.652	+	1398.20i	0.952471	+	1.33756i	0.0111888	+	0.999937i	$0.496438\pi$
$104$	−61.6756	−	86.6112i	−0.0581518	−	0.0816628i
$105$	−12.3697	+	108.008i	−0.0114967	+	0.100386i
$106$	−1965.36	−	1013.21i	−1.80087	−	0.928413i
$107$	628.889	+	184.659i	0.568197	+	0.166838i	0.553198	−	0.833050i	$-0.313407\pi$
$107$	628.889	+	184.659i	0.568197	+	0.166838i	0.0149988	+	0.999888i	$0.495226\pi$
$108$	−1255.23	−	380.717i	−1.11838	−	0.339208i
$109$	1010.94	+	1166.68i	0.888351	+	1.02521i	0.999507	+	0.0314090i	$0.00999944\pi$
$109$	1010.94	+	1166.68i	0.888351	+	1.02521i	−0.111155	+	0.993803i	$0.535455\pi$
$110$	3.52346	−	73.9665i	0.00305408	−	0.0641130i
$111$	747.721	−	914.819i	0.639374	−	0.782259i
$112$	−11.5359	+	47.5518i	−0.00973254	+	0.0401181i
$113$	−2258.17	−	215.629i	−1.87992	−	0.179511i	−0.908662	−	0.417533i	$-0.862895\pi$
$113$	−2258.17	−	215.629i	−1.87992	−	0.179511i	−0.971260	+	0.238022i	$0.923501\pi$
$114$	305.895	+	496.283i	0.251313	+	0.407730i
$115$	−1214.27	−	2097.27i	−0.984617	−	1.70062i
$116$	1748.25			1.39931
$117$	−510.364	−	19.2279i	−0.403275	−	0.0151934i
$118$	−2576.57	+	756.550i	−2.01011	+	0.590221i
$119$	31.1465	+	6.00299i	0.0239932	+	0.00462431i
$120$	561.678	−	310.334i	0.427283	−	0.236079i
$121$	−1306.30	+	251.769i	−0.981446	+	0.189158i
$122$	2331.44	+	933.366i	1.73015	+	0.692647i
$123$	−1398.61	+	1412.58i	−1.02527	+	1.03551i
$124$	402.262	+	207.380i	0.291324	+	0.150188i
$125$	727.576	−	5060.40i	0.520611	−	3.62093i
$126$	−67.0363	−	83.5210i	−0.0473974	−	0.0590527i
$127$	−706.083	+	1546.11i	−0.493344	+	1.08027i	0.485231	+	0.874386i	$0.338735\pi$
$127$	−706.083	+	1546.11i	−0.493344	+	1.08027i	−0.978576	+	0.205888i	$0.933992\pi$
$128$	658.453	−	263.605i	0.454684	−	0.182028i
$129$	1387.83	+	665.659i	0.947222	+	0.454326i
$130$	1252.81	−	1194.55i	0.845219	−	0.805915i
$131$	524.139	+	209.834i	0.349575	+	0.139949i	0.539803	−	0.841791i	$-0.318499\pi$
$131$	524.139	+	209.834i	0.349575	+	0.139949i	−0.190229	+	0.981740i	$0.560923\pi$
$132$	26.5874	+	28.9566i	0.0175313	+	0.0190935i
$133$	−1.22050	+	25.6215i	−0.000795723	+	0.0167043i
$134$	−1831.72	+	2113.91i	−1.18087	+	1.36279i
$135$	465.758	−	3046.97i	0.296934	−	1.94253i
$136$	−77.7789	−	170.312i	−0.0490403	−	0.107383i
$137$	819.411	+	1419.26i	0.511000	+	0.885078i	0.999919	+	0.0127489i	$0.00405822\pi$
$137$	819.411	+	1419.26i	0.511000	+	0.885078i	−0.488918	+	0.872329i	$0.662608\pi$
$138$	2309.79	+	603.608i	1.42480	+	0.372337i
$139$	1200.23	−	2078.86i	0.732389	−	1.26853i	−0.223471	−	0.974711i	$-0.571739\pi$
$139$	1200.23	−	2078.86i	0.732389	−	1.26853i	0.955860	−	0.293824i	$-0.0949280\pi$
$140$	194.725	+	18.5940i	0.117552	+	0.0112249i
$141$	−46.5529	−	41.8986i	−0.0278047	−	0.0250248i
$142$	263.067	+	50.7020i	0.155465	+	0.0299635i
$143$	12.8765	+	8.27522i	0.00752998	+	0.00483922i
$144$	377.603	−	1334.96i	0.218520	−	0.772546i
$145$	584.657	+	4066.38i	0.334849	+	2.32893i
$146$	−194.894	−	803.363i	−0.110476	−	0.455389i
$147$	135.623	+	1772.39i	0.0760953	+	0.994449i
$148$	−1671.08	−	1314.15i	−0.928123	−	0.729884i
$149$	−165.105	−	231.858i	−0.0907782	−	0.127480i	0.766689	−	0.642018i	$-0.221903\pi$
$149$	−165.105	−	231.858i	−0.0907782	−	0.127480i	−0.857467	+	0.514538i	$0.827963\pi$
$150$	4670.23	+	6174.47i	2.54215	+	3.36096i
$151$	1167.60	−	467.436i	0.629258	−	0.251917i	−0.0350388	−	0.999386i	$-0.511155\pi$
$151$	1167.60	−	467.436i	0.629258	−	0.251917i	0.664297	+	0.747469i	$0.268731\pi$
$152$	127.372	−	81.8572i	0.0679688	−	0.0436809i
$153$	−876.056	−	203.328i	−0.462908	−	0.107438i
$154$	0.456780	+	3.17698i	0.000239016	+	0.00166239i
$155$	−347.835	+	1005.00i	−0.180250	+	0.520799i
$156$	−17.3016	+	918.794i	−0.00887973	+	0.471554i
$157$	365.747	+	1056.76i	0.185922	+	0.537188i	0.998988	−	0.0449850i	$-0.0143240\pi$
$157$	365.747	+	1056.76i	0.185922	+	0.537188i	−0.813065	+	0.582173i	$0.802203\pi$
$158$	−279.922	+	1153.86i	−0.140946	+	0.580986i
$159$	1217.59	+	2475.13i	0.607303	+	1.23453i
$160$	2845.07	+	4927.81i	1.40577	+	2.43486i
$161$	68.8839	+	79.3009i	0.0337193	+	0.0388185i
$162$	1810.17	+	2437.94i	0.877903	+	1.18236i
$163$	−177.982	−	389.725i	−0.0855251	−	0.187274i	0.862037	−	0.506845i	$-0.169188\pi$
$163$	−177.982	−	389.725i	−0.0855251	−	0.187274i	−0.947562	+	0.319571i	$0.896461\pi$
$164$	2588.60	+	2468.23i	1.23254	+	1.17522i
$165$	−58.4609	+	71.5255i	−0.0275829	+	0.0337470i
$166$	1556.35	−	802.354i	0.727688	−	0.375149i
$167$	−2519.37	+	485.569i	−1.16739	+	0.224997i	−0.735882	−	0.677110i	$-0.763232\pi$
$167$	−2519.37	+	485.569i	−1.16739	+	0.224997i	−0.431513	+	0.902107i	$0.642020\pi$
$168$	−21.3598	+	17.8155i	−0.00980919	+	0.00818150i
$169$	−433.606	−	1787.35i	−0.197363	−	0.813541i
$170$	2564.30	−	1647.98i	1.15690	−	0.743494i
$171$	61.9295	−	724.625i	0.0276951	−	0.324055i
$172$	1150.50	−	2519.25i	0.510029	−	1.11681i
$173$	1462.88	−	139.688i	0.642896	−	0.0613891i	0.231484	−	0.972839i	$-0.425642\pi$
$173$	1462.88	−	139.688i	0.642896	−	0.0613891i	0.411412	+	0.911450i	$0.365036\pi$
$174$	−3251.85	−	2409.17i	−1.41679	−	1.04965i
$175$	16.2078	+	340.244i	0.00700112	+	0.146972i
$176$	−30.0914	+	28.6921i	−0.0128877	+	0.0122884i
$177$	3144.52	+	1155.07i	1.33535	+	0.490511i
$178$	635.282	−	1835.53i	0.267508	−	0.772913i
$179$	−179.158	−	115.138i	−0.0748095	−	0.0480771i	0.502701	−	0.864460i	$-0.332340\pi$
$179$	−179.158	−	115.138i	−0.0748095	−	0.0480771i	−0.577511	+	0.816383i	$0.695976\pi$
$180$	−5497.25	−	734.675i	−2.27634	−	0.304219i
$181$	1077.49	−	316.381i	0.442483	−	0.129925i	−0.0528991	−	0.998600i	$-0.516846\pi$
$181$	1077.49	−	316.381i	0.442483	−	0.129925i	0.495382	+	0.868675i	$0.335028\pi$
$182$	−43.5217	+	61.1177i	−0.0177255	+	0.0248920i
$183$	−1643.83	−	2666.96i	−0.664020	−	1.07731i
$184$	145.442	−	602.726i	0.0582726	−	0.241487i
$185$	2497.84	−	4326.39i	0.992676	−	1.71936i
$186$	−462.452	−	940.078i	−0.182305	−	0.370591i
$187$	19.5068	+	18.5997i	0.00762824	+	0.00727351i
$188$	−73.7984	+	85.1678i	−0.0286292	+	0.0330399i
$189$	5.17099	+	133.502i	0.00199013	+	0.0513801i
$190$	1614.21	+	1862.90i	0.616353	+	0.711309i
$191$	−2901.04	+	2281.40i	−1.09901	+	0.864275i	−0.991523	−	0.129931i	$-0.958524\pi$
$191$	−2901.04	+	2281.40i	−1.09901	+	0.864275i	−0.107491	+	0.994206i	$0.534282\pi$
$192$	−3355.72	−	881.307i	−1.26135	−	0.331265i
$193$	−145.415	−	3052.64i	−0.0542343	−	1.13852i	−0.847897	−	0.530161i	$-0.822132\pi$
$193$	−145.415	−	3052.64i	−0.0542343	−	1.13852i	0.793663	−	0.608358i	$-0.208171\pi$
$194$	−1323.43	−	1040.76i	−0.489778	−	0.385165i
$195$	−2142.88	+	267.025i	−0.786948	+	0.0980617i
$196$	3183.92	−	304.027i	1.16032	−	0.110797i
$197$	−432.490	+	3008.03i	−0.156414	+	1.08789i	0.748759	+	0.662842i	$0.230650\pi$
$197$	−432.490	+	3008.03i	−0.156414	+	1.08789i	−0.905173	+	0.425043i	$0.860259\pi$
$198$	−9.55062	−	90.5000i	−0.00342794	−	0.0324826i
$199$	−5174.95	−	1519.50i	−1.84343	−	0.541279i	−0.999992	−	0.00405050i	$-0.998711\pi$
$199$	−5174.95	−	1519.50i	−1.84343	−	0.541279i	−0.843436	−	0.537229i	$-0.819471\pi$
$200$	1580.47	−	1242.89i	0.558779	−	0.439429i
$201$	3405.90	−	758.661i	1.19519	−	0.266228i
$202$	3880.14	−	2000.35i	1.35151	−	0.696754i
$203$	−58.2397	−	168.273i	−0.0201361	−	0.0581794i
$204$	−336.108	+	1582.91i	−0.115354	+	0.543263i
$205$	−4875.35	+	6846.47i	−1.66102	+	2.33258i
$206$	−7149.58			−2.41813
$207$	−1867.02	−	2320.34i	−0.626893	−	0.779105i
$208$	−971.946			−0.324002
$209$	−12.6429	+	17.7545i	−0.00418434	+	0.00587609i
$210$	−336.578	−	302.928i	−0.110601	−	0.0995428i
$211$	−754.638	−	2180.38i	−0.246215	−	0.711393i	−0.998611	−	0.0526816i	$-0.983223\pi$
$211$	−754.638	−	2180.38i	−0.246215	−	0.711393i	0.752396	−	0.658711i	$-0.228898\pi$
$212$	4411.50	−	2274.29i	1.42916	−	0.736786i
$213$	−226.039	−	246.181i	−0.0727133	−	0.0791928i
$214$	−2145.99	+	1687.63i	−0.685500	+	0.539083i
$215$	6244.47	+	1833.54i	1.98079	+	0.581612i
$216$	624.198	−	481.961i	0.196627	−	0.151821i
$217$	6.56018	−	45.6271i	0.00205223	−	0.0142736i
$218$	−6401.00	+	611.222i	−1.98867	+	0.189895i
$219$	−401.238	+	950.002i	−0.123804	+	0.293129i
$220$	130.654	+	102.748i	0.0400396	+	0.0314875i
$221$	29.9797	+	629.352i	0.00912514	+	0.191560i
$222$	1297.35	+	4747.25i	0.392219	+	1.43520i
$223$	−2926.52	+	2301.44i	−0.878808	+	0.691103i	−0.951961	−	0.306218i	$-0.900936\pi$
$223$	−2926.52	+	2301.44i	−0.878808	+	0.691103i	0.0731529	+	0.997321i	$0.476694\pi$
$224$	−161.511	−	186.394i	−0.0481760	−	0.0555980i
$225$	−96.0239	−	9657.34i	−0.0284515	−	2.86144i
$226$	6187.58	−	7140.85i	1.82120	−	2.10178i
$227$	−1578.05	−	1504.67i	−0.461406	−	0.439949i	0.423377	−	0.905954i	$-0.360845\pi$
$227$	−1578.05	−	1504.67i	−0.461406	−	0.439949i	−0.884782	+	0.466004i	$0.845693\pi$
$228$	−1305.69	−	86.8631i	−0.379262	−	0.0252309i
$229$	−605.347	+	1048.49i	−0.174683	+	0.302560i	−0.940052	−	0.341032i	$-0.889223\pi$
$229$	−605.347	+	1048.49i	−0.174683	+	0.302560i	0.765368	+	0.643592i	$0.222557\pi$
$230$	10049.7	+	947.274i	2.88111	+	0.271571i
$231$	1.90142	−	3.52373i	0.000541578	−	0.00100366i
$232$	−609.681	+	856.177i	−0.172532	+	0.242288i
$233$	−2960.75	+	869.355i	−0.832469	+	0.244435i	−0.670077	−	0.742291i	$-0.733739\pi$
$233$	−2960.75	+	869.355i	−0.832469	+	0.244435i	−0.162392	+	0.986726i	$0.551921\pi$
$234$	1298.33	−	1685.17i	0.362711	−	0.470783i
$235$	−222.779	−	143.171i	−0.0618403	−	0.0397423i
$236$	1971.44	−	5696.10i	0.543770	−	1.57112i
$237$	1137.46	−	948.719i	0.311756	−	0.260025i
$238$	−95.6205	+	91.1740i	−0.0260427	+	0.0248316i
$239$	105.409	+	2212.81i	0.0285287	+	0.598890i	0.967191	+	0.254052i	$0.0817633\pi$
$239$	105.409	+	2212.81i	0.0285287	+	0.598890i	−0.938662	+	0.344839i	$0.887934\pi$
$240$	667.434	−	5827.84i	0.179511	−	1.56744i
$241$	−4658.89	+	444.870i	−1.24525	+	0.118907i	−0.696794	−	0.717272i	$-0.745391\pi$
$241$	−4658.89	+	444.870i	−1.24525	+	0.118907i	−0.548457	+	0.836179i	$0.684785\pi$
$242$	2301.92	−	5040.50i	0.611459	−	1.33891i
$243$	−4.00383	−	3787.99i	−0.00105698	−	0.999999i
$244$	−4742.15	+	3047.59i	−1.24420	+	0.799599i
$245$	1771.94	+	7304.05i	0.462063	+	1.90465i
$246$	−1413.63	−	8158.30i	−0.366380	−	2.11445i
$247$	−500.305	+	96.4258i	−0.128881	+	0.0248398i
$248$	−241.845	+	124.680i	−0.0619242	+	0.0319241i
$249$	−2155.89	−	351.519i	−0.548691	−	0.0894643i
$250$	15411.7	+	14695.0i	3.89889	+	3.71758i
$251$	492.020	+	1077.37i	0.123729	+	0.270929i	0.961353	−	0.275318i	$-0.0887832\pi$
$251$	492.020	+	1077.37i	0.123729	+	0.270929i	−0.837624	+	0.546247i	$0.816056\pi$
$252$	239.994	−	13.8252i	0.0599928	−	0.00345596i
$253$	12.8101	+	88.3321i	0.00318325	+	0.0219502i
$254$	−3539.87	−	6131.23i	−0.874453	−	1.51460i
$255$	−3794.21	−	252.415i	−0.931776	−	0.0619876i
$256$	562.856	−	2320.12i	0.137416	−	0.566436i
$257$	25.5696	+	73.8785i	0.00620618	+	0.0179316i	0.948061	−	0.318087i	$-0.103041\pi$
$257$	25.5696	+	73.8785i	0.00620618	+	0.0179316i	−0.941855	+	0.336019i	$0.890919\pi$
$258$	−5611.67	+	3100.52i	−1.35414	+	0.748177i
$259$	−70.8211	+	204.624i	−0.0169908	+	0.0490916i
$260$	552.969	+	3845.98i	0.131899	+	0.917376i
$261$	1470.47	+	4829.79i	0.348735	+	1.14543i
$262$	−1978.32	+	1271.39i	−0.466493	+	0.299797i
$263$	6946.16	−	2780.82i	1.62859	−	0.651988i	0.635798	−	0.771855i	$-0.280671\pi$
$263$	6946.16	−	2780.82i	1.62859	−	0.651988i	0.992790	+	0.119867i	$0.0382467\pi$
$264$	−23.4531	+	2.92249i	−0.00546757	+	0.000681315i
$265$	6765.25	+	9500.47i	1.56825	+	2.20230i
$266$	−83.9833	−	66.0452i	−0.0193584	−	0.0152236i
$267$	−1999.89	+	1368.11i	−0.458394	+	0.313584i
$268$	−1480.21	−	6101.50i	−0.337381	−	1.39070i
$269$	50.0267	+	347.943i	0.0113390	+	0.0788643i	0.994705	−	0.102770i	$-0.0327705\pi$
$269$	50.0267	+	347.943i	0.0113390	+	0.0788643i	−0.983366	+	0.181634i	$0.941861\pi$
$270$	9212.83	+	8942.04i	2.07657	+	2.01554i
$271$	−6367.56	−	4092.18i	−1.42731	−	0.917279i	−0.999913	−	0.0132165i	$-0.995793\pi$
$271$	−6367.56	−	4092.18i	−1.42731	−	0.917279i	−0.427401	−	0.904062i	$-0.640571\pi$
$272$	−1680.58	−	323.905i	−0.374633	−	0.0722045i
$273$	89.0123	−	28.9427i	0.0197336	−	0.00641645i
$274$	−6795.24	−	648.866i	−1.49823	−	0.143064i
$275$	−144.721	+	250.664i	−0.0317346	+	0.0549659i
$276$	−4111.03	+	3437.37i	−0.896576	+	0.749656i
$277$	1316.91	+	2280.95i	0.285651	+	0.494761i	0.972767	−	0.231786i	$-0.0744570\pi$
$277$	1316.91	+	2280.95i	0.285651	+	0.494761i	−0.687116	+	0.726548i	$0.741124\pi$
$278$	4153.55	+	9095.01i	0.896092	+	1.96217i
$279$	−234.572	+	1285.74i	−0.0503349	+	0.275896i
$280$	−77.0143	+	88.8793i	−0.0164375	+	0.0189698i
$281$	234.532	−	4923.44i	0.0497901	−	1.04522i	−0.826347	−	0.563161i	$-0.809585\pi$
$281$	234.532	−	4923.44i	0.0497901	−	1.04522i	0.876137	−	0.482062i	$-0.160112\pi$
$282$	254.636	−	56.7198i	0.0537707	−	0.0119774i
$283$	6134.00	+	2455.68i	1.28844	+	0.515814i	0.911834	−	0.410560i	$-0.134667\pi$
$283$	6134.00	+	2455.68i	1.28844	+	0.515814i	0.376607	+	0.926373i	$0.377091\pi$
$284$	−435.221	+	414.983i	−0.0909353	+	0.0867067i
$285$	−234.616	−	3066.07i	−0.0487629	−	0.637256i
$286$	−59.1881	+	23.6953i	−0.0122373	+	0.00489907i
$287$	151.338	−	331.384i	0.0311261	−	0.0681566i
$288$	4377.09	+	5453.45i	0.895564	+	1.11579i
$289$	541.296	−	3764.80i	0.110176	−	0.766293i
$290$	−15209.5	−	7841.06i	−3.07978	−	1.58773i
$291$	553.685	+	2026.04i	0.111538	+	0.408139i
$292$	1722.64	+	689.641i	0.345239	+	0.138213i
$293$	−3508.62	+	676.232i	−0.699577	+	0.134832i	−0.526625	−	0.850098i	$-0.676543\pi$
$293$	−3508.62	+	676.232i	−0.699577	+	0.134832i	−0.172952	+	0.984930i	$0.555331\pi$
$294$	−6341.27	−	3822.10i	−1.25793	−	0.758194i
$295$	13908.3	+	2680.61i	2.74499	+	0.529054i
$296$	1226.36	−	360.091i	0.240813	−	0.0707091i
$297$	−57.6339	+	97.8074i	−0.0112601	+	0.0191089i
$298$	1185.59			0.230467
$299$	−1208.21	+	1701.08i	−0.233688	+	0.329016i
$300$	−17370.3	+	499.903i	−3.34291	+	0.0962064i
$301$	−280.810	−	26.8141i	−0.0537729	−	0.00513469i
$302$	−1235.05	+	5090.96i	−0.235329	+	0.970039i
$303$	−5374.86	−	876.374i	−1.01907	−	0.166160i
$304$	65.8551	−	1382.47i	0.0124245	−	0.260823i
$305$	−8674.53	−	10010.9i	−1.62853	−	1.87943i
$306$	2806.51	−	2481.14i	0.524306	−	0.463521i
$307$	6947.83	+	2040.07i	1.29164	+	0.379260i	0.854180	−	0.519978i	$-0.174060\pi$
$307$	6947.83	+	2040.07i	1.29164	+	0.379260i	0.437461	+	0.899238i	$0.355878\pi$
$308$	−6.40359	−	3.30128i	−0.00118467	−	0.000610740i
$309$	7166.56	+	5309.43i	1.31939	+	0.977485i
$310$	−2569.51	−	3608.37i	−0.470769	−	0.661102i
$311$	−2216.39	−	3112.48i	−0.404116	−	0.567501i	0.561499	−	0.827477i	$-0.310225\pi$
$311$	−2216.39	−	3112.48i	−0.404116	−	0.567501i	−0.965615	+	0.259976i	$0.916285\pi$
$312$	−443.932	−	328.892i	−0.0805534	−	0.0596790i
$313$	−896.479	−	462.167i	−0.161891	−	0.0834608i	0.375377	−	0.926872i	$-0.377513\pi$
$313$	−896.479	−	462.167i	−0.161891	−	0.0834608i	−0.537268	+	0.843412i	$0.680544\pi$
$314$	−4469.19	−	1312.27i	−0.803219	−	0.235846i
$315$	112.417	+	553.597i	0.0201079	+	0.0990211i
$316$	−1745.27	−	2014.15i	−0.310694	−	0.358560i
$317$	0.612919	−	12.8668i	0.000108596	−	0.00227971i	−0.998812	−	0.0487217i	$-0.984485\pi$
$317$	0.612919	−	12.8668i	0.000108596	−	0.00227971i	0.998921	+	0.0464420i	$0.0147883\pi$
$318$	−11339.8	−	1848.95i	−1.99969	−	0.326051i
$319$	35.6721	−	147.042i	0.00626098	−	0.0258081i
$320$	−14603.4	−	1394.46i	−2.55111	−	0.243601i
$321$	3404.35	−	97.9748i	0.591939	−	0.0170356i
$322$	−435.493	+	42.1199i	−0.0753697	+	0.00728960i
$323$	−897.204			−0.154557
$324$	−6814.44	+	135.527i	−1.16846	+	0.0232385i
$325$	−6492.05	+	1906.24i	−1.10804	+	0.325351i
$326$	1752.33	+	337.734i	0.297708	+	0.0573785i
$327$	6870.11	+	4140.85i	1.16183	+	0.700273i
$328$	−2111.52	+	406.963i	−0.355455	+	0.0685084i
$329$	10.6561	+	4.26604i	0.00178568	+	0.000714877i
$330$	−101.434	−	371.166i	−0.0169205	−	0.0619152i
$331$	8654.26	+	4461.58i	1.43710	+	0.740878i	0.988267	−	0.152736i	$-0.0488083\pi$
$331$	8654.26	+	4461.58i	1.43710	+	0.740878i	0.448836	+	0.893614i	$0.351839\pi$
$332$	−559.347	+	3890.34i	−0.0924643	+	0.643103i
$333$	2224.98	−	5721.97i	0.366150	−	0.941627i
$334$	4439.54	−	9721.24i	0.727308	−	1.59258i
$335$	13696.9	−	5483.42i	2.23386	−	0.894303i
$336$	19.3988	+	253.512i	0.00314967	+	0.0411614i
$337$	7307.88	−	6968.05i	1.18126	−	1.12633i	0.191817	−	0.981431i	$-0.438562\pi$
$337$	7307.88	−	6968.05i	1.18126	−	1.12633i	0.989446	−	0.144901i	$-0.0462863\pi$
$338$	7111.99	+	2847.21i	1.14450	+	0.458189i
$339$	−11505.2	+	2562.78i	−1.84330	+	0.410592i
$340$	−325.559	+	6834.32i	−0.0519291	+	1.09013i
$341$	25.6504	−	29.6021i	0.00407345	−	0.00470101i
$342$	2308.98	+	1960.89i	0.365074	+	0.310037i
$343$	−271.019	−	593.448i	−0.0426636	−	0.0934203i
$344$	832.539	+	1442.00i	0.130487	+	0.226010i
$345$	−9370.07	−	8412.62i	−1.46222	−	1.31281i
$346$	−3060.51	+	5300.97i	−0.475533	+	0.823647i
$347$	7205.56	+	688.048i	1.11474	+	0.106445i	0.636129	−	0.771582i	$-0.280534\pi$
$347$	7205.56	+	688.048i	1.11474	+	0.106445i	0.478611	+	0.878027i	$0.341140\pi$
$348$	8638.95	−	2808.98i	1.33074	−	0.432693i
$349$	−5041.56	−	971.682i	−0.773263	−	0.149034i	−0.212668	−	0.977125i	$-0.568215\pi$
$349$	−5041.56	−	971.682i	−0.773263	−	0.149034i	−0.560595	+	0.828090i	$0.689427\pi$
$350$	−1193.58	−	767.070i	−0.182285	−	0.117147i
$351$	−2552.86	+	725.010i	−0.388209	+	0.110251i
$352$	−29.8251	−	207.438i	−0.00451615	−	0.0314105i
$353$	2833.22	+	11678.7i	0.427188	+	1.76089i	0.624973	+	0.780647i	$0.285110\pi$
$353$	2833.22	+	11678.7i	0.427188	+	1.76089i	−0.197785	+	0.980245i	$0.563375\pi$
$354$	−11516.5	+	7878.38i	−1.72909	+	1.18286i
$355$	−1110.79	−	873.535i	−0.166069	−	0.130598i
$356$	2528.97	+	3551.45i	0.376504	+	0.528725i
$357$	163.555	−	20.3806i	0.0242472	−	0.00302145i
$358$	823.518	−	329.687i	0.121576	−	0.0486717i
$359$	2050.35	−	1317.68i	0.301430	−	0.193717i	−0.381179	−	0.924501i	$-0.624482\pi$
$359$	2050.35	−	1317.68i	0.301430	−	0.193717i	0.682609	+	0.730784i	$0.260845\pi$
$360$	2276.90	−	2435.99i	0.333342	−	0.356633i
$361$	872.883	+	6071.03i	0.127261	+	0.885119i
$362$	−1529.87	+	4420.27i	−0.222122	+	0.641779i
$363$	−6050.57	+	3343.01i	−0.874855	+	0.483368i
$364$	−55.0831	−	159.152i	−0.00793170	−	0.0229171i
$365$	−1028.00	+	4237.46i	−0.147419	+	0.607668i
$366$	13020.5	+	866.203i	1.85954	+	0.123708i
$367$	−3276.38	−	5674.85i	−0.466009	−	0.807152i	0.533237	−	0.845966i	$-0.320975\pi$
$367$	−3276.38	−	5674.85i	−0.466009	−	0.807152i	−0.999246	+	0.0388139i	$0.987642\pi$
$368$	−3716.79	−	4278.86i	−0.526498	−	0.606117i
$369$	−4641.54	+	9227.46i	−0.654822	+	1.30180i
$370$	8644.12	+	18928.0i	1.21456	+	2.65951i
$371$	−365.866	−	348.853i	−0.0511990	−	0.0488182i
$372$	2320.98	+	378.437i	0.323487	+	0.0527448i
$373$	−1527.16	+	787.304i	−0.211993	+	0.109290i	−0.560953	−	0.827848i	$-0.689565\pi$
$373$	−1527.16	+	787.304i	−0.211993	+	0.109290i	0.348960	+	0.937138i	$0.386535\pi$
$374$	−110.238	+	21.2466i	−0.0152414	+	0.00293753i
$375$	−4535.46	−	26175.0i	−0.624560	−	3.60445i
$376$	−15.9733	−	65.8429i	−0.00219085	−	0.00903082i
$377$	2975.54	−	1912.26i	0.406493	−	0.261237i
$378$	−465.456	−	305.009i	−0.0633346	−	0.0415025i
$379$	639.928	−	1401.25i	0.0867306	−	0.189914i	−0.861297	−	0.508102i	$-0.830347\pi$
$379$	639.928	−	1401.25i	0.0867306	−	0.189914i	0.948027	+	0.318189i	$0.103075\pi$
$380$	−5507.89	+	525.939i	−0.743549	+	0.0710003i
$381$	−1004.91	+	8774.57i	−0.135126	+	1.17988i
$382$	−731.454	−	15355.1i	−0.0979698	−	2.05664i
$383$	4352.58	−	4150.18i	0.580696	−	0.553693i	−0.341764	−	0.939786i	$-0.611024\pi$
$383$	4352.58	−	4150.18i	0.580696	−	0.553693i	0.922460	+	0.386093i	$0.126176\pi$
$384$	2830.20	−	2360.57i	0.376114	−	0.313704i
$385$	5.53718	−	15.9986i	0.000732989	−	0.00211783i
$386$	10708.7	+	6882.10i	1.41208	+	0.907486i
$387$	7927.50	+	1059.46i	1.04129	+	0.139162i
$388$	3626.07	−	1064.71i	0.474448	−	0.139311i
$389$	1083.51	−	1521.57i	0.141224	−	0.198321i	−0.737906	−	0.674903i	$-0.764185\pi$
$389$	1083.51	−	1521.57i	0.141224	−	0.198321i	0.879130	+	0.476583i	$0.158125\pi$
$390$	4271.41	−	7915.80i	0.554593	−	1.02778i
$391$	−2655.99	+	2538.67i	−0.343528	+	0.328353i
$392$	−961.463	+	1665.30i	−0.123881	+	0.214567i
$393$	2927.18	+	194.735i	0.375717	+	0.0249951i
$394$	−9161.11	−	8735.10i	−1.17140	−	1.11692i
$395$	4101.21	−	4733.05i	0.522416	−	0.602900i
$396$	177.907	+	100.370i	0.0225762	+	0.0127368i
$397$	6282.68	+	7250.60i	0.794253	+	0.916617i	0.998051	−	0.0623956i	$-0.0198741\pi$
$397$	6282.68	+	7250.60i	0.794253	+	0.916617i	−0.203798	+	0.979013i	$0.565329\pi$
$398$	17658.7	−	13887.0i	2.22400	−	1.74897i
$399$	35.1361	+	128.570i	0.00440854	+	0.0161317i
$400$	−874.531	−	18358.7i	−0.109316	−	2.29483i
$401$	5673.06	+	4461.35i	0.706482	+	0.555584i	0.905466	−	0.424419i	$-0.139522\pi$
$401$	5673.06	+	4461.35i	0.706482	+	0.555584i	−0.198984	+	0.980003i	$0.563764\pi$
$402$	−5654.90	+	13389.0i	−0.701594	+	1.66115i
$403$	911.490	−	87.0368i	0.112666	−	0.0107583i
$404$	−1394.51	+	9699.03i	−0.171731	+	1.19442i
$405$	−2594.15	−	15804.9i	−0.318283	−	1.93914i
$406$	711.650	+	208.959i	0.0869916	+	0.0255430i
$407$	−144.629	+	113.738i	−0.0176142	+	0.0138520i
$408$	−657.992	−	716.625i	−0.0798418	−	0.0869564i
$409$	−11104.8	+	5724.93i	−1.34254	+	0.692126i	−0.971621	−	0.236541i	$-0.923986\pi$
$409$	−11104.8	+	5724.93i	−1.34254	+	0.692126i	−0.370915	+	0.928667i	$0.620956\pi$
$410$	−11450.3	−	33083.5i	−1.37924	−	3.98506i
$411$	6329.51	+	5696.69i	0.759639	+	0.683691i
$412$	9308.85	−	13072.5i	1.11314	−	1.56319i
$413$	−613.938			−0.0731474
$414$	12383.7	−	728.513i	1.47010	−	0.0864842i
$415$	−9235.91			−1.09247
$416$	2841.72	−	3990.64i	0.334920	−	0.470330i
$417$	2590.73	−	12201.1i	0.304242	−	1.43283i
$418$	−29.6933	−	85.7930i	−0.00347451	−	0.0100389i
$419$	−6497.02	+	3349.44i	−0.757518	+	0.390528i	−0.793299	−	0.608832i	$-0.791638\pi$
$419$	−6497.02	+	3349.44i	−0.757518	+	0.390528i	0.0357813	+	0.999360i	$0.488608\pi$
$420$	992.110	−	220.991i	0.115262	−	0.0256745i
$421$	−100.986	+	79.4163i	−0.0116906	+	0.00919362i	−0.623987	−	0.781435i	$-0.714488\pi$
$421$	−100.986	+	79.4163i	−0.0116906	+	0.00919362i	0.612297	+	0.790628i	$0.290246\pi$
$422$	9221.18	+	2707.58i	1.06370	+	0.312329i
$423$	−297.361	−	132.243i	−0.0341802	−	0.0152007i
$424$	−424.663	+	2953.60i	−0.0486402	+	0.338300i
$425$	−11860.6	+	1132.55i	−1.35370	+	0.129263i
$426$	1381.41	−	172.137i	0.157111	−	0.0195777i
$427$	451.314	+	354.917i	0.0511490	+	0.0402240i
$428$	−291.584	−	6121.09i	−0.0329304	−	0.691295i
$429$	76.9253	+	20.2027i	0.00865731	+	0.00227365i
$430$	−21308.3	+	16757.1i	−2.38972	+	1.87930i
$431$	−37.6788	−	43.4837i	−0.00421096	−	0.00485971i	0.753640	−	0.657287i	$-0.228296\pi$
$431$	−37.6788	−	43.4837i	−0.00421096	−	0.00485971i	−0.757851	+	0.652427i	$0.773751\pi$
$432$	−279.013	−	7203.41i	−0.0310741	−	0.802255i
$433$	−8173.39	+	9432.60i	−0.907132	+	1.04689i	0.0915620	+	0.995799i	$0.470814\pi$
$433$	−8173.39	+	9432.60i	−0.907132	+	1.04689i	−0.998694	+	0.0510870i	$0.983731\pi$
$434$	138.960	+	132.498i	0.0153693	+	0.0146546i
$435$	9422.71	+	19154.6i	1.03858	+	2.11125i
$436$	7216.63	−	12499.6i	0.792692	−	1.37298i
$437$	−2337.70	−	1833.78i	−0.255898	−	0.200736i
$438$	−2253.86	−	3656.67i	−0.245876	−	0.398909i
$439$	2713.89	−	3811.12i	0.295050	−	0.414339i	−0.640266	−	0.768153i	$-0.721176\pi$
$439$	2713.89	−	3811.12i	0.295050	−	0.414339i	0.935316	+	0.353814i	$0.115115\pi$
$440$	−95.8834	+	28.1539i	−0.0103888	+	0.00305042i
$441$	3517.95	+	8540.33i	0.379867	+	0.922182i
$442$	−2207.78	−	1418.86i	−0.237587	−	0.152688i
$443$	−1213.09	+	3504.99i	−0.130103	+	0.375908i	−0.991172	−	0.132580i	$-0.957674\pi$
$443$	−1213.09	+	3504.99i	−0.130103	+	0.375908i	0.861069	+	0.508487i	$0.169795\pi$
$444$	−10369.2	−	3808.88i	−1.10833	−	0.407121i
$445$	−7414.83	+	7070.03i	−0.789880	+	0.753149i
$446$	−737.879	−	15490.0i	−0.0783399	−	1.64456i
$447$	−1188.40	−	880.443i	−0.125748	−	0.0931623i
$448$	632.971	−	60.4414i	0.0667524	−	0.00637408i
$449$	−1037.09	+	2270.92i	−0.109005	+	0.238689i	−0.956272	−	0.292480i	$-0.905520\pi$
$449$	−1037.09	+	2270.92i	−0.109005	+	0.238689i	0.847266	+	0.531168i	$0.178247\pi$
$450$	32998.7	+	23007.3i	3.45683	+	2.41016i
$451$	260.418	−	167.361i	0.0271898	−	0.0174738i
$452$	5000.17	+	20611.0i	0.520328	+	2.14482i
$453$	5018.64	−	4185.87i	0.520521	−	0.434148i
$454$	8917.97	−	1718.80i	0.921897	−	0.177681i
$455$	351.763	−	181.347i	0.0362438	−	0.0186850i
$456$	497.886	−	609.152i	0.0511308	−	0.0625573i
$457$	2769.38	+	2640.60i	0.283471	+	0.270289i	0.818452	−	0.574575i	$-0.194833\pi$
$457$	2769.38	+	2640.60i	0.283471	+	0.270289i	−0.534981	+	0.844864i	$0.679681\pi$
$458$	−2094.88	−	4587.16i	−0.213728	−	0.467999i
$459$	−4655.72	+	402.855i	−0.473444	+	0.0409666i
$460$	−14816.8	+	17141.7i	−1.50182	+	1.73747i
$461$	−1601.13	−	2773.24i	−0.161761	−	0.280179i	0.773739	−	0.633504i	$-0.218384\pi$
$461$	−1601.13	−	2773.24i	−0.161761	−	0.280179i	−0.935500	+	0.353325i	$0.885051\pi$
$462$	7.36176	+	14.9651i	0.000741342	+	0.00150701i
$463$	−4192.06	+	17279.9i	−0.420781	+	1.73448i	0.228143	+	0.973628i	$0.426735\pi$
$463$	−4192.06	+	17279.9i	−0.420781	+	1.73448i	−0.648924	+	0.760854i	$0.724781\pi$
$464$	3142.46	+	9079.54i	0.314407	+	0.908420i
$465$	−104.042	+	5525.11i	−0.0103760	+	0.551012i
$466$	4203.80	−	12146.1i	0.417891	−	1.20742i
$467$	2069.98	+	14397.0i	0.205112	+	1.42658i	0.788822	+	0.614622i	$0.210691\pi$
$467$	2069.98	+	14397.0i	0.205112	+	1.42658i	−0.583710	+	0.811962i	$0.698399\pi$
$468$	1390.77	+	4568.01i	0.137368	+	0.451189i
$469$	−537.972	+	345.734i	−0.0529664	+	0.0340395i
$470$	1024.02	−	409.957i	0.100499	−	0.0402339i
$471$	3505.28	+	4634.30i	0.342919	+	0.453370i
$472$	2102.06	+	2951.93i	0.204990	+	0.287868i
$473$	−188.415	−	148.171i	−0.0183157	−	0.0144036i
$474$	470.716	+	6151.54i	0.0456133	+	0.596096i
$475$	−2271.50	−	9363.27i	−0.219418	−	0.904455i
$476$	−42.2053	−	293.545i	−0.00406403	−	0.0282660i
$477$	9993.62	+	10274.5i	0.959279	+	0.986240i
$478$	−7762.59	−	4988.71i	−0.742788	−	0.477361i
$479$	−1625.26	−	313.244i	−0.155032	−	0.0298799i	0.111145	−	0.993804i	$-0.464548\pi$
$479$	−1625.26	−	313.244i	−0.155032	−	0.0298799i	−0.266176	+	0.963924i	$0.585760\pi$
$480$	21976.6	+	19779.5i	2.08978	+	1.88084i
$481$	−4281.65	−	408.848i	−0.405876	−	0.0387565i
$482$	9746.91	−	16882.1i	0.921078	−	1.59535i
$483$	467.806	+	281.186i	0.0440702	+	0.0264895i
$484$	6219.03	+	10771.7i	0.584057	+	1.01162i
$485$	3689.14	+	8078.10i	0.345393	+	0.756304i
$486$	12862.1	+	9138.57i	1.20048	+	0.852950i
$487$	9120.01	−	10525.1i	0.848598	−	0.979334i	−0.151360	−	0.988479i	$-0.548365\pi$
$487$	9120.01	−	10525.1i	0.848598	−	0.979334i	0.999958	+	0.00914446i	$0.00291081\pi$
$488$	161.257	−	3385.21i	0.0149586	−	0.314019i
$489$	−1505.68	−	1639.86i	−0.139242	−	0.151650i
$490$	−29063.3	−	11635.2i	−2.67948	−	1.07270i
$491$	−2737.64	+	2610.34i	−0.251625	+	0.239924i	−0.805385	−	0.592753i	$-0.798041\pi$
$491$	−2737.64	+	2610.34i	−0.251625	+	0.239924i	0.553759	+	0.832677i	$0.313193\pi$
$492$	16757.4	+	8037.52i	1.53553	+	0.736503i
$493$	5782.23	−	2314.86i	0.528232	−	0.211472i
$494$	881.618	−	1930.47i	0.0802953	−	0.175822i
$495$	−173.961	+	447.375i	−0.0157959	+	0.0406222i
$496$	−353.970	+	2461.92i	−0.0320438	+	0.222869i
$497$	54.4416	+	28.0666i	0.00491356	+	0.00253312i
$498$	6401.52	−	6465.49i	0.576022	−	0.581778i
$499$	5825.63	+	2332.23i	0.522627	+	0.209228i	0.617949	−	0.786218i	$-0.287964\pi$
$499$	5825.63	+	2332.23i	0.522627	+	0.209228i	−0.0953220	+	0.995446i	$0.530388\pi$
$500$	−46935.0	+	9045.98i	−4.19799	+	0.809097i
$501$	−11669.3	+	6447.42i	−1.04061	+	0.574949i
$502$	−4844.22	−	933.647i	−0.430693	−	0.0830093i
$503$	13265.0	−	3894.97i	1.17586	−	0.345264i	0.365285	−	0.930896i	$-0.380972\pi$
$503$	13265.0	−	3894.97i	1.17586	−	0.345264i	0.810577	+	0.585632i	$0.199153\pi$
$504$	−76.9245	+	122.355i	−0.00679859	+	0.0108137i
$505$	−23026.1			−2.02901
$506$	−330.655	−	169.955i	−0.0290502	−	0.0149317i
$507$	−5014.47	−	8135.48i	−0.439252	−	0.712642i
$508$	15819.4	+	1510.57i	1.38164	+	0.131931i
$509$	2814.16	−	11600.1i	0.245060	−	1.01015i	−0.707721	−	0.706492i	$-0.750277\pi$
$509$	2814.16	−	11600.1i	0.245060	−	1.01015i	0.952781	−	0.303658i	$-0.0982080\pi$
$510$	10023.6	−	12263.6i	0.870300	−	1.06479i
$511$	8.99281	−	188.782i	0.000778509	−	0.0163429i
$512$	10227.8	+	11803.5i	0.882833	+	1.01884i
$513$	−858.263	−	3680.24i	−0.0738660	−	0.316738i
$514$	−312.444	−	91.7417i	−0.0268119	−	0.00787267i
$515$	33519.4	+	17280.4i	2.86804	+	1.47858i
$516$	1637.41	−	14297.4i	0.139696	−	1.21978i
$517$	5.65752	+	7.94487i	0.000481271	+	0.000675851i
$518$	−523.165	−	734.683i	−0.0443756	−	0.0623168i
$519$	7004.39	−	3040.75i	0.592406	−	0.257176i
$520$	−2076.35	−	1070.43i	−0.175104	−	0.0902724i
$521$	−17629.2	−	5176.41i	−1.48244	−	0.435284i	−0.562320	−	0.826920i	$-0.690091\pi$
$521$	−17629.2	−	5176.41i	−1.48244	−	0.435284i	−0.920120	+	0.391636i	$0.871909\pi$
$522$	−19939.9	−	6680.03i	−1.67193	−	0.560109i
$523$	−2798.44	−	3229.58i	−0.233972	−	0.270018i	0.626607	−	0.779336i	$-0.284443\pi$
$523$	−2798.44	−	3229.58i	−0.233972	−	0.270018i	−0.860579	+	0.509318i	$0.829898\pi$
$524$	251.164	−	5272.58i	0.0209392	−	0.439568i
$525$	626.776	+	1655.27i	0.0521043	+	0.137604i
$526$	−7347.45	+	30286.6i	−0.609057	+	2.51057i
$527$	1605.05	+	153.264i	0.132670	+	0.0126685i
$528$	−102.596	+	190.131i	−0.00845627	+	0.0156712i
$529$	−12109.1	+	1186.05i	−0.995237	+	0.0974812i
$530$	−48579.9			−3.98147
$531$	17394.5	+	655.338i	1.42158	+	0.0535579i
$532$	230.106	−	67.5652i	0.0187525	−	0.00550624i
$533$	7105.63	+	1369.50i	0.577446	+	0.111294i
$534$	190.021	−	10091.0i	0.0153989	−	0.817752i
$535$	14140.0	−	2725.26i	1.14267	−	0.220231i
$536$	3504.32	+	1402.92i	0.282395	+	0.113054i
$537$	−1070.31	−	281.092i	−0.0860095	−	0.0225885i
$538$	−1301.42	−	670.928i	−0.104290	−	0.0537653i
$539$	39.3950	−	273.998i	0.00314817	−	0.0218960i
$540$	−28345.1	+	5202.28i	−2.25885	+	0.414575i
$541$	10443.6	−	22868.3i	0.829955	−	1.81735i	0.373233	−	0.927738i	$-0.378249\pi$
$541$	10443.6	−	22868.3i	0.829955	−	1.81735i	0.456722	−	0.889610i	$-0.349024\pi$
$542$	29269.1	−	11717.6i	2.31959	−	0.928624i
$543$	4816.09	−	3294.65i	0.380623	−	0.260381i
$544$	6243.48	−	5953.14i	0.492071	−	0.469189i
$545$	31487.1	+	12605.5i	2.47479	+	0.990756i
$546$	−116.862	+	371.941i	−0.00915975	+	0.0291531i
$547$	934.990	−	19627.9i	0.0730846	−	1.53424i	−0.603197	−	0.797592i	$-0.706107\pi$
$547$	934.990	−	19627.9i	0.0730846	−	1.53424i	0.676282	−	0.736643i	$-0.263590\pi$
$548$	10033.9	−	11579.7i	0.782166	−	0.902667i
$549$	−12408.1	−	10537.5i	−0.964600	−	0.819182i
$550$	−500.826	−	1096.66i	−0.0388278	−	0.0850211i
$551$	2518.34	+	4361.89i	0.194709	+	0.337246i
$552$	−249.723	−	3212.06i	−0.0192553	−	0.247671i
$553$	−135.726	+	235.084i	−0.0104370	+	0.0180774i
$554$	−10920.9	−	1042.82i	−0.837515	−	0.0799730i
$555$	5391.67	−	25392.2i	0.412367	−	1.94205i
$556$	−22037.5	−	4247.38i	−1.68093	−	0.323973i
$557$	8484.55	+	5452.69i	0.645426	+	0.414790i	0.821992	−	0.569499i	$-0.192863\pi$
$557$	8484.55	+	5452.69i	0.645426	+	0.414790i	−0.176566	+	0.984289i	$0.556499\pi$
$558$	−3795.67	−	3902.35i	−0.287963	−	0.296057i
$559$	−797.428	−	5546.23i	−0.0603356	−	0.419643i
$560$	253.449	+	1044.73i	0.0191253	+	0.0788356i
$561$	126.278	+	60.5679i	0.00950349	+	0.00455825i
$562$	16138.2	+	12691.2i	1.21130	+	0.952576i
$563$	126.326	+	177.400i	0.00945651	+	0.0132798i	0.819277	−	0.573398i	$-0.194375\pi$
$563$	126.326	+	177.400i	0.00945651	+	0.0132798i	−0.809821	+	0.586678i	$0.800436\pi$
$564$	−227.831	+	539.432i	−0.0170096	+	0.0402733i
$565$	−46268.5	+	18523.1i	−3.44519	+	1.37925i
$566$	−23152.3	+	14879.1i	−1.71937	+	1.10497i
$567$	240.056	+	651.390i	0.0177802	+	0.0482466i
$568$	−51.4530	−	357.864i	−0.00380092	−	0.0264359i
$569$	−3569.70	+	10314.0i	−0.263004	+	0.759901i	0.733751	+	0.679418i	$0.237768\pi$
$569$	−3569.70	+	10314.0i	−0.263004	+	0.759901i	−0.996756	+	0.0804835i	$0.974354\pi$
$570$	10969.8	+	6611.87i	0.806096	+	0.485861i
$571$	6381.08	+	18436.9i	0.467670	+	1.35124i	0.894563	+	0.446942i	$0.147487\pi$
$571$	6381.08	+	18436.9i	0.467670	+	1.35124i	−0.426892	+	0.904302i	$0.640392\pi$
$572$	33.7386	−	139.073i	0.00246623	−	0.0101659i
$573$	−10669.8	+	15934.8i	−0.777904	+	1.16175i
$574$	758.715	+	1314.13i	0.0551710	+	0.0955590i
$575$	−33218.0	−	21290.8i	−2.40919	−	1.54415i
$576$	−17998.3	+	1036.82i	−1.30196	+	0.0750011i
$577$	−1496.26	−	3276.34i	−0.107955	−	0.236388i	0.847943	−	0.530087i	$-0.177841\pi$
$577$	−1496.26	−	3276.34i	−0.107955	−	0.236388i	−0.955898	+	0.293699i	$0.905114\pi$
$578$	11465.9	+	10932.7i	0.825117	+	0.786747i
$579$	−5623.39	−	14851.0i	−0.403627	−	1.06595i
$580$	34139.8	−	17600.3i	2.44410	−	1.26002i
$581$	393.088	−	75.7615i	0.0280689	−	0.00540984i
$582$	−8211.96	−	3016.49i	−0.584874	−	0.214841i
$583$	−101.272	−	417.450i	−0.00719429	−	0.0296552i
$584$	−938.493	+	603.133i	−0.0664985	+	0.0427360i
$585$	−10160.0	+	4762.56i	−0.718058	+	0.336594i
$586$	6182.76	−	13538.4i	0.435849	−	0.954377i
$587$	−6614.62	+	631.620i	−0.465102	+	0.0444118i	−0.324977	−	0.945722i	$-0.605356\pi$
$587$	−6614.62	+	631.620i	−0.465102	+	0.0444118i	−0.140125	+	0.990134i	$0.544750\pi$
$588$	15244.8	−	6618.09i	1.06919	−	0.464159i
$589$	62.0398	+	1302.38i	0.00434008	+	0.0911094i
$590$	−42698.9	+	40713.3i	−2.97947	+	2.84092i
$591$	2695.99	+	15559.1i	0.187645	+	1.08294i
$592$	3821.32	−	11041.0i	0.265296	−	0.766523i
$593$	1451.17	+	932.610i	0.100493	+	0.0645830i	0.589922	−	0.807460i	$-0.299158\pi$
$593$	1451.17	+	932.610i	0.100493	+	0.0645830i	−0.489429	+	0.872043i	$0.662795\pi$
$594$	−192.605	−	431.860i	−0.0133041	−	0.0298307i
$595$	668.664	−	196.337i	0.0460715	−	0.0135278i
$596$	−1543.65	+	2167.76i	−0.106091	+	0.148985i
$597$	−28013.4	+	806.206i	−1.92046	+	0.0552694i
$598$	−2852.49	−	8209.35i	−0.195062	−	0.561380i
$599$	10294.7	−	17831.0i	0.702223	−	1.21629i	−0.265461	−	0.964121i	$-0.585524\pi$
$599$	10294.7	−	17831.0i	0.702223	−	1.21629i	0.967684	−	0.252164i	$-0.0811424\pi$
$600$	5812.86	−	8681.15i	0.395515	−	0.590678i
$601$	12852.5	+	12254.9i	0.872323	+	0.831759i	0.986846	−	0.161662i	$-0.0516854\pi$
$601$	12852.5	+	12254.9i	0.872323	+	0.831759i	−0.114523	+	0.993421i	$0.536534\pi$
$602$	769.443	−	887.984i	0.0520933	−	0.0601188i
$603$	15611.3	−	9221.34i	1.05430	−	0.622756i
$604$	−7700.37	−	8886.70i	−0.518747	−	0.598667i
$605$	−22974.9	+	18067.7i	−1.54390	+	1.21414i
$606$	15959.7	−	16119.1i	1.06983	−	1.08052i
$607$	−350.803	−	7364.26i	−0.0234574	−	0.492432i	−0.979775	−	0.200102i	$-0.935873\pi$
$607$	−350.803	−	7364.26i	−0.0234574	−	0.492432i	0.956318	−	0.292330i	$-0.0944304\pi$
$608$	5483.63	+	4312.37i	0.365774	+	0.287648i
$609$	−558.162	−	737.942i	−0.0371394	−	0.0491016i
$610$	54924.9	−	5244.70i	3.64565	−	0.348117i
$611$	−32.4477	+	225.679i	−0.00214843	+	0.0149427i
$612$	882.453	+	8361.97i	0.0582861	+	0.552308i
$613$	−8356.64	−	2453.73i	−0.550606	−	0.161672i	−0.00541644	−	0.999985i	$-0.501724\pi$
$613$	−8356.64	−	2453.73i	−0.550606	−	0.161672i	−0.545189	+	0.838313i	$0.683542\pi$
$614$	−23708.4	+	18644.5i	−1.55830	+	1.22546i
$615$	−13091.0	+	41665.3i	−0.858341	+	2.73188i
$616$	3.84993	−	1.98478i	0.000251815	−	0.000129820i
$617$	−6831.12	−	19737.2i	−0.445722	−	1.28783i	−0.914526	−	0.404527i	$-0.867436\pi$
$617$	−6831.12	−	19737.2i	−0.445722	−	1.28783i	0.468804	−	0.883302i	$-0.344685\pi$
$618$	−35329.6	+	11487.5i	−2.29962	+	0.747730i
$619$	3377.01	−	4742.34i	0.219278	−	0.307933i	−0.690253	−	0.723568i	$-0.742501\pi$
$619$	3377.01	−	4742.34i	0.219278	−	0.307933i	0.909532	+	0.415634i	$0.136440\pi$
$620$	9943.16			0.644076
$621$	−12954.1	−	8466.12i	−0.837083	−	0.547075i
$622$	15915.5			1.02597
$623$	257.586	−	361.729i	0.0165650	−	0.0232622i
$624$	−4802.87	+	1561.67i	−0.308123	+	0.100187i
$625$	−22113.1	−	63891.6i	−1.41524	−	4.08906i
$626$	3734.08	−	1925.05i	0.238409	−	0.122908i
$627$	−33.9480	+	108.048i	−0.00216228	+	0.00688198i
$628$	8218.33	−	6462.97i	0.522209	−	0.410670i
$629$	−7267.09	−	2133.81i	−0.460665	−	0.135263i
$630$	−2149.93	−	956.120i	−0.135961	−	0.0604647i
$631$	2407.18	−	16742.3i	0.151867	−	1.05626i	−0.761219	−	0.648495i	$-0.775399\pi$
$631$	2407.18	−	16742.3i	0.151867	−	1.05626i	0.913086	−	0.407766i	$-0.133692\pi$
$632$	1595.05	−	152.308i	0.100392	−	0.00958624i
$633$	−7232.36	−	9561.85i	−0.454124	−	0.600394i
$634$	42.1751	+	33.1669i	0.00264194	+	0.00207764i
$635$	1776.86	+	37300.9i	0.111043	+	2.33109i
$636$	18145.2	−	18326.5i	1.13130	−	1.14260i
$637$	5086.52	−	4000.08i	0.316382	−	0.248805i
$638$	412.717	+	476.301i	0.0256107	+	0.0295563i
$639$	−1512.52	−	853.317i	−0.0936376	−	0.0528274i
$640$	10204.5	−	11776.6i	0.630262	−	0.727361i
$641$	−22796.1	−	21736.1i	−1.40467	−	1.33935i	−0.868901	−	0.494986i	$-0.835173\pi$
$641$	−22796.1	−	21736.1i	−1.40467	−	1.33935i	−0.535769	−	0.844364i	$-0.679978\pi$
$642$	−7892.82	+	11787.5i	−0.485210	+	0.724632i
$643$	−6177.53	+	10699.8i	−0.378877	+	0.656235i	−0.990899	−	0.134606i	$-0.957023\pi$
$643$	−6177.53	+	10699.8i	−0.378877	+	0.656235i	0.612022	+	0.790841i	$0.290356\pi$
$644$	490.004	−	851.105i	0.0299827	−	0.0520780i
$645$	33803.1	−	972.827i	2.06356	−	0.0593877i
$646$	2167.73	−	3044.15i	0.132025	−	0.185403i
$647$	16508.5	−	4847.33i	1.00312	−	0.294541i	0.261382	−	0.965236i	$-0.415822\pi$
$647$	16508.5	−	4847.33i	1.00312	−	0.294541i	0.741734	+	0.670694i	$0.234004\pi$
$648$	2310.09	−	3384.53i	0.140044	−	0.205181i
$649$	−438.864	−	282.041i	−0.0265438	−	0.0170587i
$650$	9217.68	−	26632.7i	0.556226	−	1.60711i
$651$	−40.8939	−	236.006i	−0.00246200	−	0.0142086i
$652$	−2899.08	+	2764.27i	−0.174136	+	0.166039i
$653$	485.789	+	10198.0i	0.0291124	+	0.611145i	0.965535	+	0.260272i	$0.0838121\pi$
$653$	485.789	+	10198.0i	0.0291124	+	0.611145i	−0.936423	+	0.350873i	$0.885885\pi$
$654$	−30648.5	+	13305.1i	−1.83249	+	0.795522i
$655$	12347.9	−	1179.08i	0.736599	−	0.0703367i
$656$	−8165.78	+	17880.6i	−0.486007	+	1.06421i
$657$	−456.303	+	5339.12i	−0.0270960	+	0.317045i
$658$	−40.2204	+	25.8481i	−0.00238291	+	0.00153140i
$659$	2794.30	+	11518.3i	0.165175	+	0.680861i	0.992821	+	0.119610i	$0.0381645\pi$
$659$	2794.30	+	11518.3i	0.165175	+	0.680861i	−0.827646	+	0.561251i	$0.810320\pi$
$660$	810.717	+	297.799i	0.0478138	+	0.0175634i
$661$	−142.885	+	27.5389i	−0.00840785	+	0.00162048i	−0.193453	−	0.981109i	$-0.561969\pi$
$661$	−142.885	+	27.5389i	−0.00840785	+	0.00162048i	0.185046	+	0.982730i	$0.440757\pi$
$662$	−36047.4	+	18583.7i	−2.11635	+	1.09105i
$663$	1159.35	+	3061.77i	0.0679118	+	0.179350i
$664$	−1710.17	−	1630.64i	−0.0999510	−	0.0953031i
$665$	234.108	+	512.626i	0.0136516	+	0.0298929i
$666$	14038.5	+	21374.0i	0.816787	+	1.24358i
$667$	19797.1	+	5786.78i	1.14925	+	0.335929i
$668$	11994.2	+	20774.5i	0.694714	+	1.20328i
$669$	−10763.6	+	16074.7i	−0.622038	+	0.928976i
$670$	−14488.2	+	59721.2i	−0.835416	+	3.44363i
$671$	159.567	+	461.039i	0.00918037	+	0.0265249i
$672$	−1097.59	−	661.557i	−0.0630068	−	0.0379763i
$673$	7011.17	−	20257.5i	0.401576	−	1.16028i	−0.545178	−	0.838321i	$-0.683538\pi$
$673$	7011.17	−	20257.5i	0.401576	−	1.16028i	0.946754	−	0.321958i	$-0.104341\pi$
$674$	5985.58	+	41630.6i	0.342071	+	2.37916i
$675$	−15991.4	−	47567.4i	−0.911865	−	2.71240i
$676$	−14465.8	+	9296.61i	−0.823043	+	0.528938i
$677$	−16422.2	+	6574.47i	−0.932286	+	0.373231i	−0.787558	−	0.616241i	$-0.788655\pi$
$677$	−16422.2	+	6574.47i	−0.932286	+	0.373231i	−0.144728	+	0.989471i	$0.546231\pi$
$678$	19102.4	−	45228.3i	1.08204	−	2.56192i
$679$	−223.277	−	313.549i	−0.0126194	−	0.0177215i
$680$	−3233.47	−	2542.83i	−0.182350	−	0.143401i
$681$	−10215.6	−	4899.80i	−0.574833	−	0.275713i
$682$	38.4642	+	158.551i	0.00215963	+	0.00890213i
$683$	−4039.31	−	28094.0i	−0.226296	−	1.57392i	−0.713514	−	0.700641i	$-0.752897\pi$
$683$	−4039.31	−	28094.0i	−0.226296	−	1.57392i	0.487218	−	0.873280i	$-0.338012\pi$
$684$	−6591.65	+	1668.68i	−0.368477	+	0.0932803i
$685$	30289.8	+	19466.1i	1.68951	+	1.08578i
$686$	2668.34	+	514.279i	0.148509	+	0.0286229i
$687$	−1306.66	+	6153.75i	−0.0725651	+	0.341747i
$688$	15151.8	+	1446.82i	0.839616	+	0.0801736i
$689$	5020.77	−	8696.24i	0.277614	−	0.480842i
$690$	51182.4	−	11466.3i	2.82389	−	0.632630i
$691$	9162.67	+	15870.2i	0.504435	+	0.873707i	0.999987	+	0.00512861i	$0.00163250\pi$
$691$	9162.67	+	15870.2i	0.504435	+	0.873707i	−0.495552	+	0.868578i	$0.665034\pi$
$692$	−5707.58	−	12497.8i	−0.313540	−	0.686556i
$693$	3.73414	−	20.4676i	0.000204687	−	0.00112193i
$694$	−19743.8	+	22785.6i	−1.07992	+	1.24630i
$695$	2509.42	−	52679.2i	0.136961	−	2.87516i
$696$	−1637.08	+	5210.39i	−0.0891570	+	0.283764i
$697$	11829.9	+	4735.96i	0.642881	+	0.257371i
$698$	15477.7	−	14758.0i	0.839314	−	0.800285i
$699$	−13233.7	+	9053.08i	−0.716087	+	0.489870i
$700$	2956.59	−	1183.64i	0.159641	−	0.0639106i
$701$	9211.95	−	20171.4i	0.496335	−	1.08682i	−0.481309	−	0.876551i	$-0.659838\pi$
$701$	9211.95	−	20171.4i	0.496335	−	1.08682i	0.977643	−	0.210270i	$-0.0674344\pi$
$702$	3708.04	−	10413.4i	0.199360	−	0.559868i
$703$	871.641	−	6062.40i	0.0467633	−	0.325246i
$704$	480.237	+	247.579i	0.0257097	+	0.0132542i
$705$	−1330.90	−	349.531i	−0.0710986	−	0.0186725i
$706$	−46470.4	−	18603.9i	−2.47725	−	0.991740i
$707$	980.009	−	188.881i	0.0521316	−	0.0100475i
$708$	589.683	−	31314.9i	0.0313018	−	1.66227i
$709$	−26137.0	−	5037.50i	−1.38448	−	0.266837i	−0.558019	−	0.829828i	$-0.688438\pi$
$709$	−26137.0	−	5037.50i	−1.38448	−	0.266837i	−0.826463	+	0.562992i	$0.809650\pi$
$710$	5647.62	−	1658.29i	0.298523	−	0.0876542i
$711$	4096.43	−	6515.71i	0.216073	−	0.343682i
$712$	−2621.22			−0.137969
$713$	3868.77	+	3679.88i	0.203207	+	0.193285i
$714$	−326.015	+	604.174i	−0.0170880	+	0.0316675i
$715$	334.763	+	31.9660i	0.0175097	+	0.00167197i
$716$	−469.425	+	1935.00i	−0.0245017	+	0.100997i
$717$	4076.30	+	10765.2i	0.212318	+	0.560718i
$718$	−483.044	+	10140.3i	−0.0251073	+	0.527067i
$719$	5143.19	+	5935.55i	0.266771	+	0.307870i	0.873292	−	0.487197i	$-0.161981\pi$
$719$	5143.19	+	5935.55i	0.266771	+	0.307870i	−0.606521	+	0.795068i	$0.707435\pi$
$720$	−6065.72	−	29870.6i	−0.313967	−	1.54613i
$721$	−1568.36	−	460.512i	−0.0810108	−	0.0237869i
$722$	−22707.6	−	11706.6i	−1.17048	−	0.603425i
$723$	−22307.1	+	9683.96i	−1.14745	+	0.498133i
$724$	−6090.21	−	8552.50i	−0.312625	−	0.439021i
$725$	38797.1	+	54483.0i	1.98743	+	2.79096i
$726$	3276.13	−	28606.2i	0.167477	−	1.46236i
$727$	−23253.9	−	11988.2i	−1.18630	−	0.611578i	−0.251879	−	0.967759i	$-0.581049\pi$
$727$	−23253.9	−	11988.2i	−1.18630	−	0.611578i	−0.934417	+	0.356180i	$0.884079\pi$
$728$	97.1520	+	28.5264i	0.00494601	+	0.00145228i
$729$	−6106.12	−	18711.9i	−0.310223	−	0.950664i
$730$	−11893.7	−	13726.0i	−0.603020	−	0.695922i
$731$	469.483	−	9855.66i	0.0237544	−	0.498666i
$732$	−18536.6	+	22679.1i	−0.935974	+	1.14514i
$733$	−6580.88	+	27126.8i	−0.331611	+	1.36692i	0.525065	+	0.851062i	$0.324041\pi$
$733$	−6580.88	+	27126.8i	−0.331611	+	1.36692i	−0.856676	+	0.515855i	$0.827474\pi$
$734$	27170.4	+	2594.46i	1.36632	+	0.130468i
$735$	20491.8	+	33245.9i	1.02837	+	1.66843i
$736$	28435.2	−	2750.19i	1.42410	−	0.137736i
$737$	−543.390			−0.0271588
$738$	−20093.7	−	38042.9i	−1.00225	−	1.89753i
$739$	20139.0	−	5913.35i	1.00247	−	0.294352i	0.261002	−	0.965338i	$-0.415947\pi$
$739$	20139.0	−	5913.35i	1.00247	−	0.294352i	0.741470	+	0.670986i	$0.234129\pi$
$740$	−45863.1	−	8839.39i	−2.27833	−	0.439111i
$741$	−2317.32	+	1280.35i	−0.114884	+	0.0634748i
$742$	2067.60	−	398.498i	0.102297	−	0.0197160i
$743$	7961.60	+	3187.34i	0.393113	+	0.157379i	0.559793	−	0.828632i	$-0.310881\pi$
$743$	7961.60	+	3187.34i	0.393113	+	0.157379i	−0.166680	+	0.986011i	$0.553305\pi$
$744$	−994.749	+	1004.69i	−0.0490178	+	0.0495077i
$745$	−5558.39	−	2865.55i	−0.273347	−	0.140920i
$746$	1018.49	−	7083.74i	0.0499859	−	0.347660i
$747$	−11218.1	+	1726.93i	−0.549464	+	0.0845853i
$748$	104.684	−	229.225i	0.00511712	−	0.0112049i
$749$	−579.455	+	231.979i	−0.0282681	+	0.0113169i
$750$	99768.0	+	47852.8i	4.85735	+	2.32978i
$751$	−19757.0	+	18838.3i	−0.959979	+	0.915338i	−0.996466	−	0.0839961i	$-0.973232\pi$
$751$	−19757.0	+	18838.3i	−0.959979	+	0.915338i	0.0364872	+	0.999334i	$0.488383\pi$
$752$	−574.972	−	230.184i	−0.0278818	−	0.0111622i
$753$	4162.37	+	4533.28i	0.201441	+	0.219392i
$754$	−701.009	+	14716.0i	−0.0338584	+	0.710776i
$755$	18095.1	−	20882.8i	0.872247	−	1.00663i
$756$	1163.72	−	453.926i	0.0559840	−	0.0218375i
$757$	−12591.4	−	27571.4i	−0.604548	−	1.32378i	−0.926241	−	0.376931i	$-0.876979\pi$
$757$	−12591.4	−	27571.4i	−0.604548	−	1.32378i	0.321693	−	0.946844i	$-0.395748\pi$
$758$	3208.21	+	5556.78i	0.153730	+	0.266268i
$759$	205.228	+	415.910i	0.00981463	+	0.0198901i
$760$	1663.24	−	2880.82i	0.0793844	−	0.137498i
$761$	33192.9	+	3169.54i	1.58113	+	0.150980i	0.848333	−	0.529463i	$-0.177606\pi$
$761$	33192.9	+	3169.54i	1.58113	+	0.150980i	0.732801	+	0.680443i	$0.238213\pi$
$762$	−27343.6	−	24609.8i	−1.29994	−	1.16997i
$763$	−1443.52	−	278.216i	−0.0684914	−	0.0132006i
$764$	29028.0	+	18655.2i	1.37460	+	0.883403i
$765$	−19154.6	+	4849.02i	−0.905278	+	0.229172i
$766$	3565.02	+	24795.2i	0.168158	+	1.16957i
$767$	−2875.08	−	11851.2i	−0.135349	−	0.557918i
$768$	−946.495	−	12369.2i	−0.0444710	−	0.581168i
$769$	518.764	+	407.960i	0.0243265	+	0.0191306i	0.630248	−	0.776394i	$-0.282953\pi$
$769$	518.764	+	407.960i	0.0243265	+	0.0191306i	−0.605922	+	0.795524i	$0.707196\pi$
$770$	40.9039	+	57.4415i	0.00191438	+	0.00268837i
$771$	245.056	+	323.987i	0.0114468	+	0.0151337i
$772$	−26526.3	+	10619.5i	−1.23666	+	0.495085i
$773$	−10977.7	+	7054.93i	−0.510789	+	0.328264i	−0.770519	−	0.637417i	$-0.780003\pi$
$773$	−10977.7	+	7054.93i	−0.510789	+	0.328264i	0.259730	+	0.965681i	$0.416367\pi$
$774$	−22748.3	+	24337.7i	−1.05642	+	1.13023i
$775$	2464.13	+	17138.4i	0.114212	+	0.794361i
$776$	−743.126	+	2147.12i	−0.0343771	+	0.0993262i
$777$	−21.1835	+	1124.94i	−0.000978063	+	0.0519396i
$778$	2544.74	+	7352.54i	0.117266	+	0.338819i
$779$	−2429.38	+	10014.1i	−0.111735	+	0.460579i
$780$	8912.00	+	18116.4i	0.409104	+	0.831631i
$781$	26.0231	+	45.0733i	0.00119229	+	0.00206511i
$782$	−2196.40	−	15145.3i	−0.100439	−	0.692575i
$783$	15026.6	+	21503.7i	0.685830	+	0.981456i
$784$	7302.04	+	15989.2i	0.332637	+	0.728373i
$785$	17781.1	+	16954.3i	0.808454	+	0.770859i
$786$	−7733.07	+	9461.23i	−0.350928	+	0.429352i
$787$	24665.4	−	12715.9i	1.11719	−	0.575949i	0.202163	−	0.979352i	$-0.435203\pi$
$787$	24665.4	−	12715.9i	1.11719	−	0.575949i	0.915023	+	0.403402i	$0.132172\pi$
$788$	27899.4	−	5377.16i	1.26126	−	0.243088i
$789$	29856.4	−	24902.1i	1.34717	−	1.12362i
$790$	6150.00	+	25350.6i	0.276971	+	1.14169i
$791$	1817.28	−	1167.90i	0.0816879	−	0.0524976i
$792$	−111.198	+	52.1246i	−0.00498894	+	0.00233860i
$793$	−4737.69	+	10374.1i	−0.212157	+	0.464558i
$794$	−39780.3	+	3798.56i	−1.77802	+	0.169781i
$795$	48695.3	+	36076.5i	2.17238	+	1.60944i
$796$	2399.36	+	50368.7i	0.106838	+	2.24280i
$797$	11132.1	−	10614.5i	0.494756	−	0.471749i	−0.401137	−	0.916018i	$-0.631385\pi$
$797$	11132.1	−	10614.5i	0.494756	−	0.471749i	0.895894	+	0.444269i	$0.146536\pi$
$798$	−521.121	−	191.422i	−0.0231171	−	0.00849157i
$799$	−131.313	+	379.405i	−0.00581418	+	0.0167990i
$800$	77934.3	+	50085.3i	3.44424	+	2.21348i
$801$	−7684.25	+	9973.83i	−0.338963	+	0.439960i
$802$	−28843.7	+	8469.28i	−1.26996	+	0.372894i
$803$	93.1543	−	130.817i	0.00409383	−	0.00574898i
$804$	−17118.0	−	27772.2i	−0.750877	−	1.21822i
$805$	2143.52	+	855.108i	0.0938500	+	0.0374393i
$806$	−1906.94	+	3302.91i	−0.0833363	+	0.144343i
$807$	806.263	+	1638.98i	0.0351695	+	0.0714930i
$808$	−4263.63	−	4065.37i	−0.185636	−	0.177004i
$809$	−1464.40	+	1690.01i	−0.0636411	+	0.0734457i	−0.786677	−	0.617364i	$-0.788200\pi$
$809$	−1464.40	+	1690.01i	−0.0636411	+	0.0734457i	0.723036	+	0.690810i	$0.242746\pi$
$810$	59892.7	+	29384.4i	2.59804	+	1.27465i
$811$	12290.5	+	14184.0i	0.532154	+	0.614138i	0.956632	−	0.291300i	$-0.0940878\pi$
$811$	12290.5	+	14184.0i	0.532154	+	0.614138i	−0.424478	+	0.905438i	$0.639542\pi$
$812$	−1308.64	+	1029.13i	−0.0565571	+	0.0444770i
$813$	−38040.4	−	9990.47i	−1.64100	−	0.430973i
$814$	−36.4661	−	765.518i	−0.00157019	−	0.0329624i
$815$	−7399.16	−	5818.76i	−0.318014	−	0.250089i
$816$	−8825.01	+	1099.69i	−0.378599	+	0.0471773i
$817$	7942.84	−	758.449i	0.340128	−	0.0324783i
$818$	7405.99	−	51509.8i	0.316558	−	2.20171i
$819$	393.351	−	286.040i	0.0167824	−	0.0122040i
$820$	75399.0	+	22139.2i	3.21103	+	0.942845i
$821$	−26493.7	+	20834.9i	−1.12623	+	0.885678i	−0.994409	−	0.105596i	$-0.966325\pi$
$821$	−26493.7	+	20834.9i	−1.12623	+	0.885678i	−0.131822	+	0.991273i	$0.542083\pi$
$822$	−34621.2	+	7711.83i	−1.46904	+	0.327228i
$823$	−20422.4	+	10528.5i	−0.864983	+	0.445930i	−0.832814	−	0.553553i	$-0.813272\pi$
$823$	−20422.4	+	10528.5i	−0.864983	+	0.445930i	−0.0321690	+	0.999482i	$0.510241\pi$
$824$	3155.68	+	9117.74i	0.133414	+	0.385475i
$825$	−312.385	+	1471.19i	−0.0131828	+	0.0620850i
$826$	1483.33	−	2083.05i	0.0624839	−	0.0877464i
$827$	15677.3			0.659195			0.329597	−	0.944122i	$-0.393087\pi$
$827$	15677.3			0.659195			0.329597	+	0.944122i	$0.393087\pi$
$828$	−14791.7	+	23591.1i	−0.620828	+	0.990154i
$829$	2941.59			0.123239			0.0616197	−	0.998100i	$-0.480373\pi$
$829$	2941.59			0.123239			0.0616197	+	0.998100i	$0.480373\pi$
$830$	22314.8	−	31336.8i	0.933204	−	1.31050i
$831$	10172.4	+	9155.36i	0.424640	+	0.382185i
$832$	4130.95	+	11935.6i	0.172133	+	0.497347i
$833$	10128.1	−	5221.39i	0.421269	−	0.217179i
$834$	35138.1	+	38269.3i	1.45891	+	1.58892i
$835$	−44310.0	+	34845.8i	−1.83642	+	1.44418i
$836$	195.527	+	57.4119i	0.00808904	+	0.00237516i
$837$	906.715	+	6730.36i	0.0374440	+	0.277939i
$838$	4332.98	−	30136.5i	0.178616	−	1.24230i
$839$	−29915.3	+	2856.56i	−1.23098	+	0.117544i	−0.690198	−	0.723621i	$-0.742477\pi$
$839$	−29915.3	+	2856.56i	−1.23098	+	0.117544i	−0.540779	+	0.841165i	$0.681870\pi$
$840$	−237.760	+	562.939i	−0.00976606	+	0.0231229i
$841$	−8312.92	−	6537.35i	−0.340847	−	0.268045i
$842$	−25.4622	−	534.516i	−0.00104214	−	0.0218773i
$843$	−6751.76	−	24706.0i	−0.275852	−	1.00939i
$844$	−16956.7	+	13334.9i	−0.691557	+	0.543846i
$845$	−26461.4	−	30538.1i	−1.07728	−	1.24325i
$846$	1167.15	−	689.415i	0.0474318	−	0.0280172i
$847$	829.623	−	957.436i	0.0336555	−	0.0388405i
$848$	19741.2	+	18823.2i	0.799428	+	0.762253i
$849$	34256.8	+	2278.98i	1.38479	+	0.0921253i
$850$	24813.6	−	42978.5i	1.00129	−	1.73429i
$851$	−14573.4	−	20412.9i	−0.587040	−	0.822260i
$852$	−1483.87	+	2749.92i	−0.0596674	+	0.110576i
$853$	25515.1	−	35830.9i	1.02417	−	1.43825i	0.129473	−	0.991583i	$-0.458672\pi$
$853$	25515.1	−	35830.9i	1.02417	−	1.43825i	0.894700	−	0.446667i	$-0.147389\pi$
$854$	−2294.63	+	673.764i	−0.0919445	+	0.0269973i
$855$	−6085.73	−	14774.0i	−0.243424	−	0.590947i
$856$	3099.40	+	1991.86i	0.123756	+	0.0795332i
$857$	−11910.4	+	34412.8i	−0.474738	+	1.37167i	0.412754	+	0.910843i	$0.364567\pi$
$857$	−11910.4	+	34412.8i	−0.474738	+	1.37167i	−0.887492	+	0.460823i	$0.847554\pi$
$858$	−254.405	+	212.191i	−0.0101227	+	0.00844297i
$859$	4343.02	−	4141.06i	0.172505	−	0.164483i	−0.598908	−	0.800818i	$-0.704399\pi$
$859$	4343.02	−	4141.06i	0.172505	−	0.164483i	0.771413	+	0.636334i	$0.219550\pi$
$860$	−2895.24	−	60778.6i	−0.114799	−	2.40992i
$861$	215.386	−	1880.69i	0.00852538	−	0.0744411i
$862$	238.573	−	22.7809i	0.00942670	−	0.000900141i
$863$	17173.7	−	37605.1i	0.677403	−	1.48330i	−0.187969	−	0.982175i	$-0.560191\pi$
$863$	17173.7	−	37605.1i	0.677403	−	1.48330i	0.865372	−	0.501130i	$-0.167082\pi$
$864$	30391.7	+	19915.3i	1.19670	+	0.784182i
$865$	27161.0	−	17455.3i	1.06763	−	0.686124i
$866$	−12256.5	−	50521.8i	−0.480937	−	1.98245i
$867$	−3374.25	−	19473.5i	−0.132175	−	0.762806i
$868$	−423.189	+	81.5630i	−0.0165484	+	0.00318943i
$869$	−205.019	+	105.694i	−0.00800320	+	0.00412594i
$870$	−87756.4	−	14308.7i	−3.41980	−	0.557599i
$871$	−9193.26	−	8765.75i	−0.357637	−	0.341006i
$872$	3604.75	+	7893.31i	0.139991	+	0.306538i
$873$	5991.36	+	9122.03i	0.232276	+	0.353647i
$874$	11870.0	−	3501.06i	0.459393	−	0.135498i
$875$	2434.25	+	4216.25i	0.0940488	+	0.162897i
$876$	9620.50	+	640.016i	0.371058	+	0.0246851i
$877$	172.749	−	712.079i	0.00665143	−	0.0274176i	−0.968389	−	0.249444i	$-0.919752\pi$
$877$	172.749	−	712.079i	0.00665143	−	0.0274176i	0.975041	+	0.222027i	$0.0712672\pi$
$878$	6373.86	+	18416.1i	0.244997	+	0.707873i
$879$	−16251.3	+	8979.06i	−0.623599	+	0.344546i
$880$	−298.772	+	863.244i	−0.0114450	+	0.0330681i
$881$	3035.34	+	21111.3i	0.116076	+	0.807329i	0.961809	+	0.273722i	$0.0882548\pi$
$881$	3035.34	+	21111.3i	0.116076	+	0.807329i	−0.845732	+	0.533607i	$0.820836\pi$
$882$	−37476.5	−	8698.08i	−1.43072	−	0.332063i
$883$	26646.8	−	17124.9i	1.01556	−	0.652659i	0.0767312	−	0.997052i	$-0.475552\pi$
$883$	26646.8	−	17124.9i	1.01556	−	0.652659i	0.938826	+	0.344393i	$0.111915\pi$
$884$	5468.83	−	2189.39i	0.208073	−	0.0833000i
$885$	73034.9	−	9100.89i	2.77406	−	0.345676i
$886$	−8961.25	−	12584.3i	−0.339796	−	0.477176i
$887$	−36469.7	−	28680.1i	−1.38053	−	1.08566i	−0.985993	−	0.166786i	$-0.946661\pi$
$887$	−36469.7	−	28680.1i	−1.38053	−	1.08566i	−0.394542	−	0.918878i	$-0.629097\pi$
$888$	5481.47	−	3749.83i	0.207146	−	0.141707i
$889$	−381.601	−	1572.98i	−0.0143965	−	0.0593431i
$890$	−6073.18	−	42239.9i	−0.228734	−	1.59088i
$891$	−127.646	+	575.917i	−0.00479945	+	0.0216543i
$892$	29283.0	+	18819.0i	1.09918	+	0.706399i
$893$	−318.801	−	61.4438i	−0.0119465	−	0.00230251i
$894$	5858.58	−	1904.94i	0.219173	−	0.0712647i
$895$	−4657.74	−	444.761i	−0.173957	−	0.0166108i
$896$	−337.708	+	584.928i	−0.0125916	+	0.0218092i
$897$	−3237.17	+	10347.2i	−0.120497	+	0.385152i
$898$	−5199.35	−	9005.54i	−0.193212	−	0.334654i
$899$	−3760.06	−	8233.38i	−0.139494	−	0.305449i
$900$	−85031.8	+	30379.8i	−3.14933	+	1.12518i
$901$	11579.4	−	13363.4i	0.428153	−	0.494115i
$902$	−61.3521	+	1287.94i	−0.00226475	+	0.0475429i
$903$	−1430.71	+	318.688i	−0.0527253	+	0.0117445i
$904$	−11837.7	−	4739.09i	−0.435526	−	0.174358i
$905$	17856.2	−	17025.9i	0.655868	−	0.625369i
$906$	2076.86	+	27141.4i	0.0761578	+	0.995266i
$907$	−15597.1	+	6244.12i	−0.570994	+	0.228592i	−0.639149	−	0.769083i	$-0.720713\pi$
$907$	−15597.1	+	6244.12i	−0.570994	+	0.228592i	0.0681543	+	0.997675i	$0.478289\pi$
$908$	−8468.64	+	18543.7i	−0.309517	+	0.677748i
$909$	−27968.0	+	4305.43i	−1.02050	+	0.157098i
$910$	−234.597	+	1631.66i	−0.00854596	+	0.0594384i
$911$	−24451.5	−	12605.6i	−0.889258	−	0.458444i	−0.0478562	−	0.998854i	$-0.515239\pi$
$911$	−24451.5	−	12605.6i	−0.889258	−	0.458444i	−0.841402	+	0.540410i	$0.818269\pi$
$912$	−1895.85	−	6937.28i	−0.0688355	−	0.251882i
$913$	315.798	+	126.426i	0.0114473	+	0.00458280i
$914$	−15650.5	+	3016.38i	−0.566380	+	0.109161i
$915$	−58950.2	−	35531.3i	−2.12987	−	1.28375i
$916$	11114.8	+	2142.21i	0.400922	+	0.0772713i
$917$	−515.865	+	151.472i	−0.0185773	+	0.00545478i
$918$	9881.82	−	16769.9i	0.355282	−	0.602929i
$919$	2086.73			0.0749020			0.0374510	−	0.999298i	$-0.488076\pi$
$919$	2086.73			0.0749020			0.0374510	+	0.999298i	$0.488076\pi$
$920$	−3227.68	−	13234.3i	−0.115667	−	0.474262i
$921$	37610.5	−	1082.40i	1.34561	−	0.0387257i
$922$	13277.9	+	1267.88i	0.474277	+	0.0452880i
$923$	−286.837	+	1182.36i	−0.0102290	+	0.0421645i
$924$	−36.9476	−	6.02433i	−0.00131546	−	0.000214487i
$925$	3870.04	−	81242.0i	0.137563	−	2.88781i
$926$	−48501.1	−	55973.2i	−1.72121	−	1.98639i
$927$	43944.4	+	14721.7i	1.55698	+	0.521601i
$928$	−46466.7	−	13643.8i	−1.64369	−	0.482631i
$929$	34407.7	+	17738.4i	1.21516	+	0.626457i	0.942032	−	0.335522i	$-0.108913\pi$
$929$	34407.7	+	17738.4i	1.21516	+	0.626457i	0.273124	+	0.961979i	$0.411943\pi$
$930$	−18494.9	−	13702.2i	−0.652121	−	0.483132i
$931$	5344.97	+	7505.96i	0.188157	+	0.264230i
$932$	16734.8	+	23500.7i	0.588160	+	0.825955i
$933$	−15953.2	−	11819.2i	−0.559792	−	0.414729i
$934$	−53849.4	−	27761.3i	−1.88652	−	0.972567i
$935$	568.181	+	166.833i	0.0198733	+	0.00583532i
$936$	−2722.13	−	911.934i	−0.0950594	−	0.0318456i
$937$	−15924.0	−	18377.3i	−0.555193	−	0.640727i	0.406892	−	0.913476i	$-0.366612\pi$
$937$	−15924.0	−	18377.3i	−0.555193	−	0.640727i	−0.962085	+	0.272749i	$0.912067\pi$
$938$	126.741	−	2660.63i	0.00441178	−	0.0926148i
$939$	−5172.53	−	843.384i	−0.179765	−	0.0293107i
$940$	−583.718	+	2406.12i	−0.0202540	+	0.0834882i
$941$	15738.6	+	1502.86i	0.545233	+	0.0520634i	0.364039	−	0.931384i	$-0.381398\pi$
$941$	15738.6	+	1502.86i	0.545233	+	0.0520634i	0.181194	+	0.983447i	$0.442004\pi$
$942$	−24193.0	+	696.256i	−0.836782	+	0.0240820i
$943$	21143.4	+	36518.6i	0.730142	+	1.26109i
$944$	33126.4			1.14213
$945$	1445.00	+	2554.97i	0.0497415	+	0.0879505i
$946$	957.962	−	281.283i	0.0329239	−	0.00966733i
$947$	8206.75	+	1581.72i	0.281609	+	0.0542756i	0.328100	−	0.944643i	$-0.393592\pi$
$947$	8206.75	+	1581.72i	0.281609	+	0.0542756i	−0.0464911	+	0.998919i	$0.514804\pi$
$948$	−11860.5	−	7148.72i	−0.406340	−	0.244915i
$949$	3686.30	−	710.476i	0.126093	−	0.0243024i
$950$	37257.1	+	14915.5i	1.27240	+	0.509392i
$951$	−17.6448	−	64.5658i	−0.000601654	−	0.00220157i
$952$	158.478	+	81.7009i	0.00539526	+	0.00278145i
$953$	−832.648	+	5791.19i	−0.0283023	+	0.196847i	−0.999067	−	0.0431861i	$-0.986249\pi$
$953$	−832.648	+	5791.19i	−0.0283023	+	0.196847i	0.970765	+	0.240033i	$0.0771583\pi$
$954$	−59006.2	+	9083.50i	−2.00251	+	0.308270i
$955$	−33683.8	+	73757.2i	−1.14134	+	2.49919i
$956$	19228.5	−	7697.92i	0.650516	−	0.260427i
$957$	−59.9859	−	783.924i	−0.00202620	−	0.0264793i
$958$	4989.60	−	4757.58i	0.168274	−	0.160449i
$959$	−1448.84	−	580.027i	−0.0487856	−	0.0195308i
$960$	−74403.2	+	16573.2i	−2.50141	+	0.557186i
$961$	−1306.02	+	27416.8i	−0.0438395	+	0.920304i
$962$	11732.1	−	13539.5i	0.393199	−	0.453775i
$963$	16665.2	−	5954.07i	0.557661	−	0.199239i
$964$	18177.1	+	39802.2i	0.607307	+	1.32982i
$965$	−33571.9	−	58148.2i	−1.11991	−	1.93975i
$966$	−2084.31	+	907.860i	−0.0694219	+	0.0302380i
$967$	−768.675	+	1331.38i	−0.0255625	+	0.0442755i	−0.878524	−	0.477699i	$-0.841471\pi$
$967$	−768.675	+	1331.38i	−0.0255625	+	0.0442755i	0.852961	+	0.521974i	$0.174804\pi$
$968$	−7444.09	−	710.824i	−0.247171	−	0.0236020i
$969$	−4433.53	+	1441.58i	−0.146982	+	0.0477917i
$970$	−36321.8	−	7000.45i	−1.20229	−	0.231722i
$971$	−40281.2	−	25887.2i	−1.33129	−	0.855571i	−0.335053	−	0.942199i	$-0.608754\pi$
$971$	−40281.2	−	25887.2i	−1.33129	−	0.855571i	−0.996241	+	0.0866286i	$0.972391\pi$
$972$	−33455.8	+	11618.8i	−1.10401	+	0.383408i
$973$	325.320	+	2262.65i	0.0107187	+	0.0745502i
$974$	13676.0	+	56373.1i	0.449904	+	1.85453i
$975$	−29017.6	+	19850.7i	−0.953135	+	0.652033i
$976$	−24351.7	−	19150.4i	−0.798647	−	0.628063i
$977$	14621.6	+	20533.2i	0.478799	+	0.672379i	0.981363	−	0.192161i	$-0.0615495\pi$
$977$	14621.6	+	20533.2i	0.478799	+	0.672379i	−0.502565	+	0.864540i	$0.667610\pi$
$978$	9201.80	−	1146.64i	0.300860	−	0.0374902i
$979$	350.309	−	140.243i	0.0114361	−	0.00457832i
$980$	59114.9	−	37990.9i	1.92690	−	1.23834i
$981$	40601.9	+	9423.47i	1.32143	+	0.306696i
$982$	−2242.29	−	15595.4i	−0.0728658	−	0.506793i
$983$	7919.04	−	22880.5i	0.256946	−	0.742397i	−0.740571	−	0.671978i	$-0.765445\pi$
$983$	7919.04	−	22880.5i	0.256946	−	0.742397i	0.997517	−	0.0704193i	$-0.0224337\pi$
$984$	−9780.20	+	5403.68i	−0.316851	+	0.175064i
$985$	21837.4	+	63095.0i	0.706393	+	2.04099i
$986$	−6116.27	+	25211.6i	−0.197547	+	0.814302i
$987$	59.5113	+	3.95907i	0.00191921	+	0.000127678i
$988$	2381.84	+	4125.47i	0.0766969	+	0.132843i
$989$	21367.1	−	24719.8i	0.686992	−	0.794785i
$990$	−1097.60	−	1671.14i	−0.0352365	−	0.0536487i
$991$	−12895.3	−	28236.7i	−0.413353	−	0.905116i	−0.995740	−	0.0922045i	$-0.970609\pi$
$991$	−12895.3	−	28236.7i	−0.413353	−	0.905116i	0.582388	−	0.812911i	$-0.302119\pi$
$992$	−9073.27	−	8651.34i	−0.290400	−	0.276896i
$993$	49933.6	+	8141.70i	1.59577	+	0.260190i
$994$	−226.764	+	116.905i	−0.00723594	+	0.00373039i
$995$	−116354.	+	22425.4i	−3.70721	+	0.714505i
$996$	3486.78	+	20122.8i	0.110926	+	0.640177i
$997$	5522.96	+	22765.9i	0.175440	+	0.723174i	0.989758	+	0.142755i	$0.0455961\pi$
$997$	5522.96	+	22765.9i	0.175440	+	0.723174i	−0.814318	+	0.580419i	$0.802889\pi$
$998$	−21988.4	+	14131.1i	−0.697424	+	0.448207i
$999$	1800.99	−	31850.0i	0.0570378	−	1.00870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.11	✓	1400
9.7	even	3	inner	207.4.m.a.142.60	yes	1400
23.6	even	11	inner	207.4.m.a.121.60	yes	1400
207.52	even	33	inner	207.4.m.a.52.11	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.11	✓	1400	1.1	even	1	trivial
207.4.m.a.52.11	yes	1400	207.52	even	33	inner
207.4.m.a.121.60	yes	1400	23.6	even	11	inner
207.4.m.a.142.60	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+(-2.41610 + 3.39293i) q^{2} +(4.94150 - 1.60674i) q^{3} +(-3.05792 - 8.83529i) q^{4} +(19.5280 - 10.0674i) q^{5} +(-6.48755 + 20.6482i) q^{6} +(-0.748547 + 0.588664i) q^{7} +(5.39337 + 1.58363i) q^{8} +(21.8367 - 15.8794i) q^{9} +(-13.0236 + 90.5811i) q^{10} +(-0.805518 + 0.0769176i) q^{11} +(-29.3068 - 38.7462i) q^{12} +(-14.8688 - 11.6930i) q^{13} +(-0.188735 - 3.96204i) q^{14} +(80.3220 - 81.1246i) q^{15} +(40.3896 - 31.7627i) q^{16} +(-21.8127 - 25.1732i) q^{17} +(1.11817 + 112.457i) q^{18} +(17.6392 - 20.3567i) q^{19} +(-148.664 - 141.751i) q^{20} +(-2.75311 + 4.11160i) q^{21} +(1.68523 - 2.91891i) q^{22} +(-5.38270 - 110.173i) q^{23} +(29.1958 - 0.840233i) q^{24} +(207.485 - 291.371i) q^{25} +(75.5979 - 22.1976i) q^{26} +(82.3920 - 113.554i) q^{27} +(7.49002 + 4.81354i) q^{28} +(-61.1578 + 176.704i) q^{29} +(81.1846 + 468.532i) q^{30} +(-35.0330 + 33.4039i) q^{31} +(12.3233 + 258.699i) q^{32} +(-3.85688 + 1.67435i) q^{33} +(138.113 - 13.1882i) q^{34} +(-8.69134 + 19.0314i) q^{35} +(-207.075 - 144.376i) q^{36} +(191.287 - 122.932i) q^{37} +(26.4510 + 109.032i) q^{38} +(-92.2618 - 33.8904i) q^{39} +(121.265 - 23.3719i) q^{40} +(-340.032 + 175.299i) q^{41} +(-7.29861 - 19.2751i) q^{42} +(214.386 + 204.416i) q^{43} +(3.14280 + 6.88178i) q^{44} +(266.564 - 529.934i) q^{45} +(386.814 + 247.925i) q^{46} +(-6.02669 - 10.4385i) q^{47} +(148.550 - 221.851i) q^{48} +(-80.6515 + 332.450i) q^{49} +(487.301 + 1407.96i) q^{50} +(-148.235 - 89.3460i) q^{51} +(-57.8430 + 167.127i) q^{52} +(75.5486 + 525.452i) q^{53} +(186.215 + 553.908i) q^{54} +(-14.9558 + 9.61153i) q^{55} +(-4.96942 + 1.98945i) q^{56} +(54.4560 - 128.934i) q^{57} +(-451.781 - 634.438i) q^{58} +(506.768 + 398.526i) q^{59} +(-962.378 - 461.595i) q^{60} +(-142.144 - 585.925i) q^{61} +(-28.6941 - 199.572i) q^{62} +(-6.99818 + 24.7410i) q^{63} +(-561.713 - 360.991i) q^{64} +(-408.077 - 78.6503i) q^{65} +(3.63763 - 17.1315i) q^{66} +(668.490 + 63.8330i) q^{67} +(-155.711 + 269.700i) q^{68} +(-203.618 - 535.769i) q^{69} +(-43.5731 - 75.4708i) q^{70} +(-26.7193 - 58.5071i) q^{71} +(142.921 - 51.0622i) q^{72} +(-129.968 + 149.991i) q^{73} +(-45.0654 + 946.039i) q^{74} +(557.125 - 1773.19i) q^{75} +(-233.797 - 93.5982i) q^{76} +(0.557689 - 0.531756i) q^{77} +(337.901 - 231.156i) q^{78} +(264.634 - 105.944i) q^{79} +(468.962 - 1026.88i) q^{80} +(224.687 - 693.510i) q^{81} +(226.773 - 1577.24i) q^{82} +(-373.649 - 192.629i) q^{83} +(44.7460 + 11.7516i) q^{84} +(-679.390 - 271.987i) q^{85} +(-1211.55 + 233.506i) q^{86} +(-18.2931 + 971.446i) q^{87} +(-4.46626 - 0.860801i) q^{88} +(-447.432 + 131.378i) q^{89} +(1153.98 + 2184.80i) q^{90} +18.0132 q^{91} +(-956.948 + 384.457i) q^{92} +(-119.444 + 221.354i) q^{93} +(49.9783 + 4.77235i) q^{94} +(139.520 - 575.108i) q^{95} +(476.558 + 1258.56i) q^{96} +(-19.2330 + 403.751i) q^{97} +(-933.119 - 1076.88i) q^{98} +(-16.3685 + 14.4708i) 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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