LMFDB - Embedded newform 207.4.m.a.4.12

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			4.12
Character	$\chi$	$=$	207.4
Dual form			207.4.m.a.52.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.33527 + 3.27943i) q^{2} +(-5.18945 - 0.263780i) q^{3} +(-2.68463 - 7.75672i) q^{4} +(-8.48781 + 4.37577i) q^{5} +(12.9838 - 16.4025i) q^{6} +(13.6708 - 10.7509i) q^{7} +(0.804118 + 0.236110i) q^{8} +(26.8608 + 2.73775i) q^{9} +(5.47131 - 38.0538i) q^{10} +(22.4044 - 2.13936i) q^{11} +(11.8857 + 40.9613i) q^{12} +(9.94578 + 7.82145i) q^{13} +(3.33159 + 69.9387i) q^{14} +(45.2013 - 20.4689i) q^{15} +(48.9643 - 38.5059i) q^{16} +(-7.97239 - 9.20063i) q^{17} +(-71.7057 + 81.6949i) q^{18} +(43.3151 - 49.9883i) q^{19} +(56.7283 + 54.0903i) q^{20} +(-73.7800 + 52.1850i) q^{21} +(-45.3045 + 78.4696i) q^{22} +(-31.6901 + 105.654i) q^{23} +(-4.11065 - 1.43739i) q^{24} +(-19.6115 + 27.5405i) q^{25} +(-48.8760 + 14.3513i) q^{26} +(-138.671 - 21.2928i) q^{27} +(-120.093 - 77.1788i) q^{28} +(8.00359 - 23.1249i) q^{29} +(-38.4310 + 196.035i) q^{30} +(63.9104 - 60.9385i) q^{31} +(12.2517 + 257.194i) q^{32} +(-116.831 + 5.19226i) q^{33} +(48.7905 - 4.65893i) q^{34} +(-68.9921 + 151.072i) q^{35} +(-50.8754 - 215.702i) q^{36} +(-17.4152 + 11.1921i) q^{37} +(62.7806 + 258.785i) q^{38} +(-49.5500 - 43.2125i) q^{39} +(-7.85837 + 1.51458i) q^{40} +(-151.557 + 78.1328i) q^{41} +(1.15933 - 363.823i) q^{42} +(24.3019 + 23.1719i) q^{43} +(-76.7419 - 168.041i) q^{44} +(-239.970 + 94.2994i) q^{45} +(-272.480 - 350.656i) q^{46} +(-74.6599 - 129.315i) q^{47} +(-264.255 + 186.909i) q^{48} +(-9.55467 + 39.3849i) q^{49} +(-44.5191 - 128.629i) q^{50} +(38.9454 + 49.8492i) q^{51} +(33.9681 - 98.1444i) q^{52} +(31.2655 + 217.457i) q^{53} +(393.663 - 405.037i) q^{54} +(-180.803 + 116.195i) q^{55} +(13.5314 - 5.41714i) q^{56} +(-237.968 + 247.986i) q^{57} +(57.1458 + 80.2501i) q^{58} +(421.987 + 331.854i) q^{59} +(-280.121 - 295.663i) q^{60} +(92.0080 + 379.262i) q^{61} +(50.5953 + 351.898i) q^{62} +(396.643 - 251.350i) q^{63} +(-452.838 - 291.021i) q^{64} +(-118.643 - 22.8665i) q^{65} +(255.804 - 395.264i) q^{66} +(333.361 + 31.8322i) q^{67} +(-49.9638 + 86.5399i) q^{68} +(192.324 - 539.926i) q^{69} +(-334.314 - 579.049i) q^{70} +(298.746 + 654.162i) q^{71} +(20.9529 + 8.54360i) q^{72} +(26.9422 - 31.0930i) q^{73} +(3.96562 - 83.2485i) q^{74} +(109.038 - 137.747i) q^{75} +(-504.030 - 201.783i) q^{76} +(283.287 - 270.113i) q^{77} +(257.425 - 61.5828i) q^{78} +(-476.817 + 190.889i) q^{79} +(-247.107 + 541.088i) q^{80} +(714.009 + 147.077i) q^{81} +(97.6946 - 679.481i) q^{82} +(882.537 + 454.979i) q^{83} +(602.856 + 432.194i) q^{84} +(107.928 + 43.2078i) q^{85} +(-132.742 + 25.5840i) q^{86} +(-47.6342 + 117.894i) q^{87} +(18.5209 + 3.56961i) q^{88} +(1214.64 - 356.650i) q^{89} +(251.146 - 1007.18i) q^{90} +220.054 q^{91} +(904.604 - 37.8301i) q^{92} +(-347.734 + 299.379i) q^{93} +(598.430 + 57.1432i) q^{94} +(-148.913 + 613.828i) q^{95} +(4.26334 - 1337.93i) q^{96} +(-14.4435 + 303.207i) q^{97} +(-106.847 - 123.308i) q^{98} +(607.658 + 3.87268i) 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 $

$2$	−2.33527	+	3.27943i	−0.825643	+	1.15945i	0.159411	+	0.987212i	$0.449040\pi$
$2$	−2.33527	+	3.27943i	−0.825643	+	1.15945i	−0.985055	+	0.172242i	$0.944899\pi$
$3$	−5.18945	−	0.263780i	−0.998711	−	0.0507646i
$3$	−5.18945	−	0.263780i	−0.998711	−	0.0507646i
$4$	−2.68463	−	7.75672i	−0.335579	−	0.969591i
$5$	−8.48781	+	4.37577i	−0.759173	+	0.391381i	−0.793925	−	0.608015i	$-0.791966\pi$
$5$	−8.48781	+	4.37577i	−0.759173	+	0.391381i	0.0347525	+	0.999396i	$0.488936\pi$
$6$	12.9838	−	16.4025i	0.883438	−	1.11605i
$7$	13.6708	−	10.7509i	0.738156	−	0.580492i	−0.176704	−	0.984264i	$-0.556544\pi$
$7$	13.6708	−	10.7509i	0.738156	−	0.580492i	0.914860	+	0.403772i	$0.132301\pi$
$8$	0.804118	+	0.236110i	0.0355373	+	0.0104347i
$9$	26.8608	+	2.73775i	0.994846	+	0.101398i
$10$	5.47131	−	38.0538i	0.173018	−	1.20337i
$11$	22.4044	−	2.13936i	0.614107	−	0.0586401i	0.216632	−	0.976253i	$-0.430493\pi$
$11$	22.4044	−	2.13936i	0.614107	−	0.0586401i	0.397475	+	0.917613i	$0.369887\pi$
$12$	11.8857	+	40.9613i	0.285925	+	0.985376i
$13$	9.94578	+	7.82145i	0.212190	+	0.166868i	0.718597	−	0.695426i	$-0.244785\pi$
$13$	9.94578	+	7.82145i	0.212190	+	0.166868i	−0.506408	+	0.862294i	$0.669027\pi$
$14$	3.33159	+	69.9387i	0.0636004	+	1.33514i
$15$	45.2013	−	20.4689i	0.778062	−	0.352337i
$16$	48.9643	−	38.5059i	0.765067	−	0.601655i
$17$	−7.97239	−	9.20063i	−0.113740	−	0.131264i	0.696024	−	0.718018i	$-0.254951\pi$
$17$	−7.97239	−	9.20063i	−0.113740	−	0.131264i	−0.809765	+	0.586755i	$0.800405\pi$
$18$	−71.7057	+	81.6949i	−0.938955	+	1.06976i
$19$	43.3151	−	49.9883i	0.523008	−	0.603584i	−0.431373	−	0.902174i	$-0.641971\pi$
$19$	43.3151	−	49.9883i	0.523008	−	0.603584i	0.954382	+	0.298590i	$0.0965162\pi$
$20$	56.7283	+	54.0903i	0.634241	+	0.604748i
$21$	−73.7800	+	52.1850i	−0.766672	+	0.542271i
$22$	−45.3045	+	78.4696i	−0.439043	+	0.760445i
$23$	−31.6901	+	105.654i	−0.287297	+	0.957841i
$23$	−31.6901	+	105.654i	−0.287297	+	0.957841i
$24$	−4.11065	−	1.43739i	−0.0349618	−	0.0122253i
$25$	−19.6115	+	27.5405i	−0.156892	+	0.220324i
$26$	−48.8760	+	14.3513i	−0.368668	+	0.108251i
$27$	−138.671	−	21.2928i	−0.988416	−	0.151770i
$28$	−120.093	−	77.1788i	−0.810549	−	0.520908i
$29$	8.00359	−	23.1249i	0.0512493	−	0.148075i	−0.916471	−	0.400100i	$-0.868975\pi$
$29$	8.00359	−	23.1249i	0.0512493	−	0.148075i	0.967721	+	0.252025i	$0.0810965\pi$
$30$	−38.4310	+	196.035i	−0.233883	+	1.19303i
$31$	63.9104	−	60.9385i	0.370279	−	0.353060i	−0.481978	−	0.876183i	$-0.660082\pi$
$31$	63.9104	−	60.9385i	0.370279	−	0.353060i	0.852257	+	0.523123i	$0.175233\pi$
$32$	12.2517	+	257.194i	0.0676815	+	1.42081i
$33$	−116.831	+	5.19226i	−0.616292	+	0.0273896i
$34$	48.7905	−	4.65893i	0.246103	−	0.0235000i
$35$	−68.9921	+	151.072i	−0.333194	+	0.729594i
$36$	−50.8754	−	215.702i	−0.235534	−	0.998620i
$37$	−17.4152	+	11.1921i	−0.0773795	+	0.0497288i	−0.578759	−	0.815499i	$-0.696463\pi$
$37$	−17.4152	+	11.1921i	−0.0773795	+	0.0497288i	0.501379	+	0.865228i	$0.332826\pi$
$38$	62.7806	+	258.785i	0.268009	+	1.10475i
$39$	−49.5500	−	43.2125i	−0.203445	−	0.177424i
$40$	−7.85837	+	1.51458i	−0.0310629	+	0.00598689i
$41$	−151.557	+	78.1328i	−0.577297	+	0.297617i	−0.722039	−	0.691852i	$-0.756795\pi$
$41$	−151.557	+	78.1328i	−0.577297	+	0.297617i	0.144742	+	0.989469i	$0.453765\pi$
$42$	1.15933	−	363.823i	0.00425926	−	1.33664i
$43$	24.3019	+	23.1719i	0.0861863	+	0.0821785i	0.731948	−	0.681361i	$-0.238611\pi$
$43$	24.3019	+	23.1719i	0.0861863	+	0.0821785i	−0.645761	+	0.763539i	$0.723460\pi$
$44$	−76.7419	−	168.041i	−0.262938	−	0.575754i
$45$	−239.970	+	94.2994i	−0.794945	+	0.312385i
$46$	−272.480	−	350.656i	−0.873368	−	1.12394i
$47$	−74.6599	−	129.315i	−0.231708	−	0.401330i	0.726603	−	0.687058i	$-0.241098\pi$
$47$	−74.6599	−	129.315i	−0.231708	−	0.401330i	−0.958311	+	0.285728i	$0.907765\pi$
$48$	−264.255	+	186.909i	−0.794623	+	0.562041i
$49$	−9.55467	+	39.3849i	−0.0278562	+	0.114825i
$50$	−44.5191	−	128.629i	−0.125919	−	0.363819i
$51$	38.9454	+	49.8492i	0.106930	+	0.136868i
$52$	33.9681	−	98.1444i	0.0905871	−	0.261734i
$53$	31.2655	+	217.457i	0.0810312	+	0.563584i	0.989378	+	0.145366i	$0.0464361\pi$
$53$	31.2655	+	217.457i	0.0810312	+	0.563584i	−0.908347	+	0.418218i	$0.862655\pi$
$54$	393.663	−	405.037i	0.992050	−	1.02071i
$55$	−180.803	+	116.195i	−0.443263	+	0.284868i
$56$	13.5314	−	5.41714i	0.0322893	−	0.0129267i
$57$	−237.968	+	247.986i	−0.552975	+	0.576255i
$58$	57.1458	+	80.2501i	0.129373	+	0.181678i
$59$	421.987	+	331.854i	0.931154	+	0.732267i	0.963640	−	0.267205i	$-0.0861001\pi$
$59$	421.987	+	331.854i	0.931154	+	0.732267i	−0.0324862	+	0.999472i	$0.510342\pi$
$60$	−280.121	−	295.663i	−0.602724	−	0.636165i
$61$	92.0080	+	379.262i	0.193122	+	0.796058i	0.983122	+	0.182952i	$0.0585651\pi$
$61$	92.0080	+	379.262i	0.193122	+	0.796058i	−0.790000	+	0.613106i	$0.789920\pi$
$62$	50.5953	+	351.898i	0.103639	+	0.720823i
$63$	396.643	−	251.350i	0.793212	−	0.502652i
$64$	−452.838	−	291.021i	−0.884449	−	0.568401i
$65$	−118.643	−	22.8665i	−0.226397	−	0.0436345i
$66$	255.804	−	395.264i	0.477080	−	0.737176i
$67$	333.361	+	31.8322i	0.607859	+	0.0580435i	0.394447	−	0.918919i	$-0.370936\pi$
$67$	333.361	+	31.8322i	0.607859	+	0.0580435i	0.213412	+	0.976962i	$0.431542\pi$
$68$	−49.9638	+	86.5399i	−0.0891030	+	0.154331i
$69$	192.324	−	539.926i	0.335551	−	0.942022i
$70$	−334.314	−	579.049i	−0.570831	−	0.988708i
$71$	298.746	+	654.162i	0.499361	+	1.09345i	0.976677	+	0.214716i	$0.0688825\pi$
$71$	298.746	+	654.162i	0.499361	+	1.09345i	−0.477316	+	0.878732i	$0.658390\pi$
$72$	20.9529	+	8.54360i	0.0342961	+	0.0139843i
$73$	26.9422	−	31.0930i	0.0431966	−	0.0498515i	−0.733740	−	0.679430i	$-0.762227\pi$
$73$	26.9422	−	31.0930i	0.0431966	−	0.0498515i	0.776937	+	0.629579i	$0.216772\pi$
$74$	3.96562	−	83.2485i	0.00622964	−	0.130776i
$75$	109.038	−	137.747i	0.167875	−	0.212076i
$76$	−504.030	−	201.783i	−0.760740	−	0.304554i
$77$	283.287	−	270.113i	0.419266	−	0.399770i
$78$	257.425	−	61.5828i	0.373688	−	0.0893959i
$79$	−476.817	+	190.889i	−0.679064	+	0.271856i	−0.685446	−	0.728123i	$-0.740393\pi$
$79$	−476.817	+	190.889i	−0.679064	+	0.271856i	0.00638191	+	0.999980i	$0.497969\pi$
$80$	−247.107	+	541.088i	−0.345342	+	0.756193i
$81$	714.009	+	147.077i	0.979437	+	0.201751i
$82$	97.6946	−	679.481i	0.131568	−	0.915074i
$83$	882.537	+	454.979i	1.16712	+	0.601693i	0.929195	−	0.369591i	$-0.120502\pi$
$83$	882.537	+	454.979i	1.16712	+	0.601693i	0.237926	+	0.971283i	$0.423532\pi$
$84$	602.856	+	432.194i	0.783060	+	0.561384i
$85$	107.928	+	43.2078i	0.137723	+	0.0551359i
$86$	−132.742	+	25.5840i	−0.166441	+	0.0320789i
$87$	−47.6342	+	117.894i	−0.0587002	+	0.145283i
$88$	18.5209	+	3.56961i	0.0224356	+	0.00432411i
$89$	1214.64	−	356.650i	1.44665	−	0.424774i	0.538215	−	0.842808i	$-0.319099\pi$
$89$	1214.64	−	356.650i	1.44665	−	0.424774i	0.908431	+	0.418034i	$0.137281\pi$
$90$	251.146	−	1007.18i	0.294146	−	1.17962i
$91$	220.054			0.253494
$92$	904.604	−	37.8301i	1.02512	−	0.0428702i
$93$	−347.734	+	299.379i	−0.387725	+	0.333808i
$94$	598.430	+	57.1432i	0.656631	+	0.0627007i
$95$	−148.913	+	613.828i	−0.160823	+	0.662920i
$96$	4.26334	−	1337.93i	0.00453256	−	1.42241i
$97$	−14.4435	+	303.207i	−0.0151188	+	0.317382i	0.978622	+	0.205668i	$0.0659368\pi$
$97$	−14.4435	+	303.207i	−0.0151188	+	0.317382i	−0.993740	+	0.111713i	$0.964366\pi$
$98$	−106.847	−	123.308i	−0.110135	−	0.127102i
$99$	607.658	+	3.87268i	0.616888	+	0.00393150i
$100$	266.274	+	78.1851i	0.266274	+	0.0781851i
$101$	1663.07	+	857.372i	1.63843	+	0.844670i	0.996993	+	0.0774957i	$0.0246924\pi$
$101$	1663.07	+	857.372i	1.63843	+	0.844670i	0.641439	+	0.767174i	$0.278338\pi$
$102$	−254.425	+	11.3073i	−0.246979	+	0.0109764i
$103$	650.313	+	913.237i	0.622110	+	0.873631i	0.998606	−	0.0527875i	$-0.0168106\pi$
$103$	650.313	+	913.237i	0.622110	+	0.873631i	−0.376496	+	0.926418i	$0.622871\pi$
$104$	6.15086	+	8.63767i	0.00579944	+	0.00814417i
$105$	397.881	−	765.781i	0.369802	−	0.711739i
$106$	−786.147	−	405.287i	−0.720353	−	0.371368i
$107$	138.839	+	40.7667i	0.125440	+	0.0368324i	0.343850	−	0.939025i	$-0.388269\pi$
$107$	138.839	+	40.7667i	0.125440	+	0.0368324i	−0.218410	+	0.975857i	$0.570087\pi$
$108$	207.117	+	1132.80i	0.184536	+	1.00929i
$109$	203.867	+	235.275i	0.179146	+	0.206745i	0.838219	−	0.545333i	$-0.183597\pi$
$109$	203.867	+	235.275i	0.179146	+	0.206745i	−0.659074	+	0.752079i	$0.729051\pi$
$110$	41.1706	−	864.277i	0.0356860	−	0.749142i
$111$	93.3277	−	53.4870i	0.0798042	−	0.0457365i
$112$	255.411	−	1052.82i	0.215482	−	0.888231i
$113$	−2344.59	−	223.881i	−1.95186	−	0.186380i	−0.957188	−	0.289468i	$-0.906522\pi$
$113$	−2344.59	−	223.881i	−1.95186	−	0.186380i	−0.994672	+	0.103088i	$0.967128\pi$
$114$	−257.534	−	1359.51i	−0.211582	−	1.11693i
$115$	−193.338	−	1035.44i	−0.156772	−	0.839610i
$116$	−200.860			−0.160770
$117$	245.739	+	237.320i	0.194176	+	0.187523i
$118$	−2073.75	+	608.908i	−1.61783	+	0.475038i
$119$	−207.904	−	40.0702i	−0.160156	−	0.0308675i
$120$	41.1802	−	5.78694i	0.0313268	−	0.00440227i
$121$	−809.567	+	156.031i	−0.608240	+	0.117229i
$122$	−1458.63	−	583.946i	−1.08244	−	0.433344i
$123$	807.106	−	365.489i	0.591661	−	0.267927i
$124$	−644.259	−	332.138i	−0.466582	−	0.240540i
$125$	215.825	−	1501.10i	0.154432	−	1.07410i
$126$	−101.986	+	1887.73i	−0.0721079	+	1.33470i
$127$	−632.884	+	1385.82i	−0.442200	+	0.968283i	0.548989	+	0.835829i	$0.315013\pi$
$127$	−632.884	+	1385.82i	−0.442200	+	0.968283i	−0.991189	+	0.132453i	$0.957714\pi$
$128$	99.5546	−	39.8556i	0.0687458	−	0.0275217i
$129$	−120.002	−	126.660i	−0.0819034	−	0.0864477i
$130$	352.052	−	335.681i	0.237516	−	0.226471i
$131$	−2186.67	−	875.412i	−1.45840	−	0.583855i	−0.499176	−	0.866501i	$-0.666364\pi$
$131$	−2186.67	−	875.412i	−1.45840	−	0.583855i	−0.959225	+	0.282645i	$0.908788\pi$
$132$	353.922	+	892.285i	0.233371	+	0.588360i
$133$	54.7363	−	1149.06i	0.0356860	−	0.749141i
$134$	−882.881	+	1018.90i	−0.569174	+	0.656862i
$135$	1270.18	−	426.063i	0.809779	−	0.271627i
$136$	−4.23838	−	9.28076i	−0.00267234	−	0.00585160i
$137$	−445.944	−	772.398i	−0.278099	−	0.481682i	0.692813	−	0.721117i	$-0.256371\pi$
$137$	−445.944	−	772.398i	−0.278099	−	0.481682i	−0.970912	+	0.239435i	$0.923038\pi$
$138$	1321.52	+	1891.59i	0.815185	+	1.16683i
$139$	−273.861	+	474.341i	−0.167112	+	0.289447i	−0.937403	−	0.348245i	$-0.886778\pi$
$139$	−273.861	+	474.341i	−0.167112	+	0.289447i	0.770291	+	0.637692i	$0.220111\pi$
$140$	1357.04	+	129.582i	0.819220	+	0.0782260i
$141$	353.333	+	690.767i	0.211036	+	0.412575i
$142$	−2842.93	−	547.931i	−1.68010	−	0.323812i
$143$	239.562	+	153.957i	0.140092	+	0.0900318i
$144$	1420.64	−	900.250i	0.822131	−	0.520978i
$145$	33.2561	+	231.301i	0.0190467	+	0.132473i
$146$	39.0499	+	160.966i	0.0221356	+	0.0912440i
$147$	59.9725	−	201.866i	0.0336493	−	0.113263i
$148$	133.567	+	105.038i	0.0741835	+	0.0583385i
$149$	−831.163	−	1167.21i	−0.456990	−	0.641753i	0.520219	−	0.854033i	$-0.325850\pi$
$149$	−831.163	−	1167.21i	−0.456990	−	0.641753i	−0.977209	+	0.212280i	$0.931911\pi$
$150$	197.100	+	679.259i	0.107287	+	0.369742i
$151$	2266.87	−	907.519i	1.22169	−	0.489092i	0.330970	−	0.943641i	$-0.392624\pi$
$151$	2266.87	−	907.519i	1.22169	−	0.489092i	0.890722	+	0.454549i	$0.150200\pi$
$152$	46.6332	−	29.9693i	0.0248846	−	0.0159923i
$153$	−188.956	−	268.963i	−0.0998444	−	0.142120i
$154$	224.266	+	1559.81i	0.117350	+	0.816187i
$155$	−275.807	+	796.892i	−0.142925	+	0.412954i
$156$	−202.164	+	500.355i	−0.103757	+	0.256798i
$157$	200.171	+	578.355i	0.101754	+	0.293999i	0.984375	−	0.176087i	$-0.0563441\pi$
$157$	200.171	+	578.355i	0.101754	+	0.293999i	−0.882621	+	0.470086i	$0.844223\pi$
$158$	487.491	−	2009.46i	0.245460	−	1.01180i
$159$	−104.890	−	1136.73i	−0.0523166	−	0.566971i
$160$	−1229.41	−	2129.40i	−0.607459	−	1.05215i
$161$	702.640	+	1785.07i	0.343949	+	0.873810i
$162$	−2149.73	+	1998.08i	−1.04259	+	0.969037i
$163$	1602.99	+	3510.07i	0.770284	+	1.68669i	0.726027	+	0.687666i	$0.241365\pi$
$163$	1602.99	+	3510.07i	0.770284	+	1.68669i	0.0442565	+	0.999020i	$0.485908\pi$
$164$	1012.93	+	965.825i	0.482295	+	0.459867i
$165$	968.918	−	555.296i	0.457152	−	0.261998i
$166$	−3553.04	+	1831.72i	−1.66126	+	0.856439i
$167$	−3719.16	+	716.809i	−1.72334	+	0.332146i	−0.952420	−	0.304790i	$-0.901414\pi$
$167$	−3719.16	+	716.809i	−1.72334	+	0.332146i	−0.770917	+	0.636936i	$0.780202\pi$
$168$	−71.6493	+	24.5427i	−0.0329039	+	0.0112709i
$169$	−480.219	−	1979.49i	−0.218579	−	0.900996i
$170$	−393.738	+	253.040i	−0.177637	+	0.114161i
$171$	1300.33	−	1224.14i	0.581515	−	0.547441i
$172$	114.496	−	250.711i	0.0507572	−	0.111143i
$173$	1203.86	−	114.954i	0.529061	−	0.0505192i	0.172892	−	0.984941i	$-0.444689\pi$
$173$	1203.86	−	114.954i	0.529061	−	0.0505192i	0.356169	+	0.934422i	$0.384083\pi$
$174$	−275.387	−	431.528i	−0.119983	−	0.188012i
$175$	27.9786	+	587.343i	0.0120856	+	0.253708i
$176$	1014.64	−	967.454i	0.434552	−	0.414344i
$177$	−2102.35	−	1833.45i	−0.892780	−	0.778593i
$178$	−1666.90	+	4816.20i	−0.701908	+	2.02803i
$179$	−1940.70	−	1247.21i	−0.810363	−	0.520789i	0.0686195	−	0.997643i	$-0.478141\pi$
$179$	−1940.70	−	1247.21i	−0.810363	−	0.520789i	−0.878982	+	0.476854i	$0.841777\pi$
$180$	1375.68	+	1608.22i	0.569652	+	0.665942i
$181$	3783.71	−	1111.00i	1.55382	−	0.456242i	0.611578	−	0.791184i	$-0.290535\pi$
$181$	3783.71	−	1111.00i	1.55382	−	0.456242i	0.942239	+	0.334943i	$0.108717\pi$
$182$	−513.887	+	721.653i	−0.209296	+	0.293915i
$183$	−377.429	−	1992.43i	−0.152461	−	0.804835i
$184$	−50.4286	+	77.4758i	−0.0202046	+	0.0310413i
$185$	98.8431	−	171.201i	0.0392815	−	0.0680376i
$186$	−169.738	−	1839.50i	−0.0669128	−	0.725155i
$187$	−198.300	−	189.079i	−0.0775461	−	0.0739401i
$188$	−802.625	+	926.279i	−0.311369	+	0.359339i
$189$	−2124.66	+	1199.74i	−0.817706	+	0.461737i
$190$	−1665.25	−	1921.81i	−0.635843	−	0.733802i
$191$	1675.98	−	1318.01i	0.634920	−	0.499306i	−0.248043	−	0.968749i	$-0.579788\pi$
$191$	1675.98	−	1318.01i	0.634920	−	0.499306i	0.882963	+	0.469443i	$0.155545\pi$
$192$	2273.22	+	1629.69i	0.854454	+	0.612567i
$193$	136.229	+	2859.79i	0.0508081	+	1.06659i	0.869993	+	0.493064i	$0.164123\pi$
$193$	136.229	+	2859.79i	0.0508081	+	1.06659i	−0.819185	+	0.573529i	$0.805574\pi$
$194$	−960.617	−	755.438i	−0.355507	−	0.279574i
$195$	609.659	+	149.960i	0.223890	+	0.0550712i
$196$	331.149	−	31.6209i	0.120681	−	0.0115236i
$197$	−259.709	+	1806.32i	−0.0939264	+	0.653272i	0.887411	+	0.460979i	$0.152502\pi$
$197$	−259.709	+	1806.32i	−0.0939264	+	0.653272i	−0.981337	+	0.192293i	$0.938407\pi$
$198$	−1431.75	+	1983.73i	−0.513888	+	0.712007i
$199$	−497.444	−	146.063i	−0.177201	−	0.0520308i	0.191929	−	0.981409i	$-0.438526\pi$
$199$	−497.444	−	146.063i	−0.177201	−	0.0520308i	−0.369129	+	0.929378i	$0.620344\pi$
$200$	−22.2726	+	17.5154i	−0.00787455	+	0.00619262i
$201$	−1721.57	−	253.126i	−0.604129	−	0.0888264i
$202$	−6695.41	+	3451.72i	−2.33212	+	1.20229i
$203$	−139.196	−	402.182i	−0.0481265	−	0.139052i
$204$	282.112	−	435.915i	0.0968227	−	0.149609i
$205$	944.492	−	1326.35i	0.321786	−	0.451886i
$206$	−4513.56			−1.52658
$207$	−1140.48	+	2751.19i	−0.382940	+	0.923773i
$208$	788.161			0.262736
$209$	863.505	−	1212.62i	0.285789	−	0.401334i
$210$	1582.16	+	3093.13i	0.519903	+	1.01641i
$211$	1312.32	+	3791.69i	0.428169	+	1.23711i	0.928517	+	0.371289i	$0.121084\pi$
$211$	1312.32	+	3791.69i	0.428169	+	1.23711i	−0.500348	+	0.865824i	$0.666795\pi$
$212$	1602.81	−	826.308i	0.519254	−	0.267694i
$213$	−1377.77	−	3473.55i	−0.443209	−	1.11739i
$214$	−457.918	+	360.110i	−0.146274	+	0.115031i
$215$	−307.665	−	90.3386i	−0.0975934	−	0.0286560i
$216$	−106.480	−	49.8636i	−0.0335420	−	0.0157073i
$217$	218.568	−	1520.17i	0.0683748	−	0.475557i
$218$	−1247.65	+	119.136i	−0.387622	+	0.0370134i
$219$	−148.017	+	154.249i	−0.0456716	+	0.0475944i
$220$	1386.68	+	1090.50i	0.424955	+	0.334188i
$221$	−7.32940	−	153.863i	−0.00223090	−	0.0468323i
$222$	−42.5387	+	430.968i	−0.0128604	+	0.130291i
$223$	−2253.85	+	1772.44i	−0.676810	+	0.532250i	−0.896346	−	0.443355i	$-0.853788\pi$
$223$	−2253.85	+	1772.44i	−0.676810	+	0.532250i	0.219536	+	0.975604i	$0.429546\pi$
$224$	2932.55	+	3384.34i	0.874727	+	1.00949i
$225$	−602.181	+	686.071i	−0.178424	+	0.203280i
$226$	6209.45	−	7166.09i	1.82764	−	2.10921i
$227$	2740.81	+	2613.36i	0.801384	+	0.764118i	0.975357	−	0.220632i	$-0.0708120\pi$
$227$	2740.81	+	2613.36i	0.801384	+	0.764118i	−0.173973	+	0.984750i	$0.555661\pi$
$228$	2562.41	+	1180.10i	0.744298	+	0.342780i
$229$	1534.77	−	2658.30i	0.442884	−	0.767097i	−0.555018	−	0.831838i	$-0.687289\pi$
$229$	1534.77	−	2658.30i	0.442884	−	0.767097i	0.997902	+	0.0647408i	$0.0206220\pi$
$230$	3847.15	+	1783.99i	1.10293	+	0.511448i
$231$	−1541.35	+	1327.01i	−0.439020	+	0.377970i
$232$	11.8959	−	16.7054i	0.00336638	−	0.00472743i
$233$	2990.17	−	877.994i	0.840742	−	0.246864i	0.167117	−	0.985937i	$-0.446554\pi$
$233$	2990.17	−	877.994i	0.840742	−	0.246864i	0.673625	+	0.739073i	$0.264736\pi$
$234$	−1352.14	+	251.677i	−0.377745	+	0.0703105i
$235$	1199.55	+	770.905i	0.332979	+	0.213993i
$236$	1441.22	−	4164.14i	0.397524	−	1.14857i
$237$	2524.77	−	864.833i	0.691989	−	0.237033i
$238$	616.920	−	588.232i	0.168021	−	0.160208i
$239$	70.3071	+	1475.93i	0.0190284	+	0.399455i	0.988210	+	0.153107i	$0.0489278\pi$
$239$	70.3071	+	1475.93i	0.0190284	+	0.399455i	−0.969181	+	0.246349i	$0.920769\pi$
$240$	1425.08	−	2742.77i	0.383284	−	0.737687i
$241$	4053.34	−	387.047i	1.08340	−	0.103452i	0.461948	−	0.886907i	$-0.347151\pi$
$241$	4053.34	−	387.047i	1.08340	−	0.103452i	0.621448	+	0.783455i	$0.286545\pi$
$242$	1378.87	−	3019.30i	0.366268	−	0.802015i
$243$	−3666.52	−	951.589i	−0.967932	−	0.251212i
$244$	2694.82	−	1731.86i	0.707043	−	0.454389i
$245$	−91.2411	−	376.101i	−0.0237926	−	0.0980743i
$246$	−686.215	+	3500.36i	−0.177852	+	0.907216i
$247$	821.783	−	158.386i	0.211696	−	0.0408010i
$248$	65.7797	−	33.9118i	0.0168428	−	0.00868307i
$249$	−4459.87	−	2593.89i	−1.13507	−	0.660165i
$250$	4418.73	+	4213.25i	1.11786	+	1.06588i
$251$	2566.74	+	5620.37i	0.645462	+	1.41336i	0.895470	+	0.445121i	$0.146839\pi$
$251$	2566.74	+	5620.37i	0.645462	+	1.41336i	−0.250008	+	0.968244i	$0.580433\pi$
$252$	−3014.49	−	2401.87i	−0.753552	−	0.600411i
$253$	−483.965	+	2434.91i	−0.120263	+	0.605064i
$254$	−3066.75	−	5311.78i	−0.757580	−	1.31217i
$255$	−548.690	−	252.694i	−0.134746	−	0.0620562i
$256$	913.470	−	3765.37i	0.223015	−	0.919280i
$257$	−654.837	−	1892.03i	−0.158940	−	0.459227i	0.837211	−	0.546880i	$-0.184185\pi$
$257$	−654.837	−	1892.03i	−0.158940	−	0.459227i	−0.996151	+	0.0876527i	$0.972063\pi$
$258$	695.608	−	97.7519i	0.167855	−	0.0235883i
$259$	−117.756	+	340.233i	−0.0282510	+	0.0816258i
$260$	141.142	+	981.668i	0.0336665	+	0.234156i
$261$	278.293	−	599.241i	0.0659997	−	0.142115i
$262$	7977.33	−	5126.72i	1.88107	−	1.20889i
$263$	−1875.74	+	750.932i	−0.439783	+	0.176063i	−0.580978	−	0.813919i	$-0.697330\pi$
$263$	−1875.74	+	750.932i	−0.439783	+	0.176063i	0.141195	+	0.989982i	$0.454906\pi$
$264$	−95.1717	−	23.4098i	−0.0221872	−	0.00545747i
$265$	−1216.92	−	1708.92i	−0.282093	−	0.396144i
$266$	3640.43	+	2862.86i	0.839131	+	0.659900i
$267$	−6397.39	+	1530.42i	−1.46634	+	0.350787i
$268$	−648.038	−	2671.25i	−0.147706	−	0.608853i
$269$	126.508	+	879.883i	0.0286741	+	0.199433i	0.999123	−	0.0418744i	$-0.0133329\pi$
$269$	126.508	+	879.883i	0.0286741	+	0.199433i	−0.970449	+	0.241307i	$0.922424\pi$
$270$	−1568.98	+	5160.46i	−0.353649	+	1.16317i
$271$	1884.79	+	1211.28i	0.422483	+	0.271513i	0.734560	−	0.678543i	$-0.237388\pi$
$271$	1884.79	+	1211.28i	0.422483	+	0.271513i	−0.312077	+	0.950057i	$0.601025\pi$
$272$	−744.641	−	143.518i	−0.165995	−	0.0319928i
$273$	−1141.96	−	58.0461i	−0.253167	−	0.0128685i
$274$	3574.43	+	341.316i	0.788098	+	0.0752543i
$275$	−380.465	+	658.985i	−0.0834288	+	0.144503i
$276$	−4704.38	−	42.2995i	−1.02598	−	0.00922512i
$277$	−813.909	−	1409.73i	−0.176545	−	0.305786i	0.764150	−	0.645039i	$-0.223159\pi$
$277$	−813.909	−	1409.73i	−0.176545	−	0.305786i	−0.940695	+	0.339254i	$0.889826\pi$
$278$	−916.030	−	2005.83i	−0.197625	−	0.432739i
$279$	1883.52	−	1461.89i	0.404170	−	0.313695i
$280$	−91.1474	+	105.190i	−0.0194539	+	0.0224510i
$281$	203.327	−	4268.35i	0.0431653	−	0.906152i	−0.868619	−	0.495481i	$-0.834992\pi$
$281$	203.327	−	4268.35i	0.0431653	−	0.906152i	0.911784	−	0.410670i	$-0.134705\pi$
$282$	−3090.45	−	454.396i	−0.652602	−	0.0959535i
$283$	6309.59	+	2525.98i	1.32532	+	0.530579i	0.922958	−	0.384900i	$-0.125764\pi$
$283$	6309.59	+	2525.98i	1.32532	+	0.530579i	0.402365	+	0.915479i	$0.368188\pi$
$284$	4272.14	−	4073.47i	0.892622	−	0.851113i
$285$	934.693	−	3146.15i	0.194268	−	0.653901i
$286$	−1064.33	+	426.095i	−0.220054	+	0.0880963i
$287$	−1231.91	+	2697.50i	−0.253370	+	0.554804i
$288$	−375.043	+	6941.98i	−0.0767349	+	1.42035i
$289$	678.100	−	4716.29i	0.138022	−	0.959961i
$290$	−836.199	−	431.091i	−0.169322	−	0.0872914i
$291$	154.934	−	1569.67i	0.0312110	−	0.316205i
$292$	−313.510	−	125.510i	−0.0628314	−	0.0251539i
$293$	5951.49	−	1147.06i	1.18666	−	0.228709i	0.442533	−	0.896752i	$-0.354080\pi$
$293$	5951.49	−	1147.06i	1.18666	−	0.228709i	0.744122	+	0.668043i	$0.232868\pi$
$294$	521.953	+	668.087i	0.103540	+	0.132529i
$295$	−5033.87	−	970.198i	−0.993502	−	0.191482i
$296$	−16.6465	+	4.88784i	−0.00326877	+	0.000959797i
$297$	−3152.39	−	180.385i	−0.615893	−	0.0352425i
$298$	5768.76			1.12139
$299$	−1141.55	+	802.948i	−0.220794	+	0.155303i
$300$	−1361.19	−	475.976i	−0.261962	−	0.0916016i
$301$	581.345	+	55.5117i	0.111323	+	0.0106300i
$302$	−2317.62	+	9553.36i	−0.441603	+	1.82031i
$303$	−8404.26	−	4887.98i	−1.59344	−	0.926755i
$304$	196.047	−	4115.53i	0.0369870	−	0.776453i
$305$	−2440.51	−	2816.50i	−0.458175	−	0.528762i
$306$	1323.31	+	8.43361i	0.247218	+	0.00157555i
$307$	−5346.25	−	1569.80i	−0.993897	−	0.291835i	−0.255948	−	0.966691i	$-0.582388\pi$
$307$	−5346.25	−	1569.80i	−0.993897	−	0.291835i	−0.737950	+	0.674856i	$0.764206\pi$
$308$	−2855.71	−	1472.22i	−0.528310	−	0.272363i
$309$	−3133.88	−	4910.74i	−0.576958	−	0.904085i
$310$	−1969.27	−	2765.45i	−0.360796	−	0.506667i
$311$	−3116.09	−	4375.93i	−0.568158	−	0.797866i	0.426123	−	0.904665i	$-0.359879\pi$
$311$	−3116.09	−	4375.93i	−0.568158	−	0.797866i	−0.994281	+	0.106799i	$0.965940\pi$
$312$	−29.6411	−	46.4473i	−0.00537852	−	0.00842807i
$313$	−1518.57	−	782.877i	−0.274232	−	0.141376i	0.315625	−	0.948884i	$-0.397786\pi$
$313$	−1518.57	−	782.877i	−0.274232	−	0.141376i	−0.589857	+	0.807507i	$0.700816\pi$
$314$	−2364.13	−	694.171i	−0.424890	−	0.124759i
$315$	−2266.78	+	3869.03i	−0.405457	+	0.692048i
$316$	2760.75	+	3186.07i	0.491469	+	0.567185i
$317$	173.275	−	3637.50i	0.0307007	−	0.644486i	−0.930110	−	0.367281i	$-0.880289\pi$
$317$	173.275	−	3637.50i	0.0307007	−	0.644486i	0.960811	−	0.277205i	$-0.0894082\pi$
$318$	3972.77	+	2310.59i	0.700572	+	0.407457i
$319$	129.843	−	535.221i	0.0227894	−	0.0939392i
$320$	5117.05	+	488.619i	0.893911	+	0.0853582i
$321$	−709.743	−	248.180i	−0.123408	−	0.0431528i
$322$	−7494.88	−	1864.37i	−1.29712	−	0.322662i
$323$	−805.248			−0.138716
$324$	−776.017	−	5933.22i	−0.133062	−	1.01736i
$325$	−410.459	+	120.522i	−0.0700559	+	0.0205703i
$326$	−15254.5	−	2940.06i	−2.59161	−	0.499493i
$327$	−995.896	−	1274.72i	−0.168420	−	0.215573i
$328$	−140.317	+	27.0440i	−0.0236211	+	0.00455260i
$329$	−2410.91	−	965.182i	−0.404005	−	0.161739i
$330$	−441.632	+	4474.27i	−0.0736699	+	0.746364i
$331$	5833.61	+	3007.44i	0.968714	+	0.499407i	0.868570	−	0.495566i	$-0.165039\pi$
$331$	5833.61	+	3007.44i	0.968714	+	0.499407i	0.100144	+	0.994973i	$0.468070\pi$
$332$	1159.87	−	8067.05i	0.191735	−	1.33354i
$333$	−498.428	+	252.950i	−0.0820231	+	0.0416264i
$334$	6334.52	−	13870.7i	1.03775	−	2.27236i
$335$	−2968.80	+	1188.53i	−0.484188	+	0.193839i
$336$	−1603.15	+	5396.17i	−0.260295	+	0.876147i
$337$	−6925.14	+	6603.11i	−1.11940	+	1.06734i	−0.122200	+	0.992506i	$0.538995\pi$
$337$	−6925.14	+	6603.11i	−1.11940	+	1.06734i	−0.997196	+	0.0748360i	$0.976157\pi$
$338$	7613.04	+	3047.80i	1.22513	+	0.490469i
$339$	12108.1	+	1780.28i	1.93988	+	0.285225i
$340$	45.4048	−	953.165i	0.00724242	−	0.152037i
$341$	1301.50	−	1502.02i	0.206687	−	0.238530i
$342$	977.849	+	7123.06i	0.154608	+	1.12623i
$343$	2770.90	+	6067.43i	0.436195	+	0.955133i
$344$	14.0705	+	24.3709i	0.00220532	+	0.00381973i
$345$	730.188	+	5424.36i	0.113948	+	0.846486i
$346$	−2434.35	+	4216.41i	−0.378241	+	0.655132i
$347$	1524.26	+	145.549i	0.235811	+	0.0225173i	0.212293	−	0.977206i	$-0.431907\pi$
$347$	1524.26	+	145.549i	0.235811	+	0.0225173i	0.0235188	+	0.999723i	$0.492513\pi$
$348$	1042.35	+	52.9829i	0.160563	+	0.00816144i
$349$	5710.28	+	1100.57i	0.875829	+	0.168802i	0.607303	−	0.794470i	$-0.292251\pi$
$349$	5710.28	+	1100.57i	0.875829	+	0.168802i	0.268526	+	0.963272i	$0.413463\pi$
$350$	−1991.49	−	1279.85i	−0.304142	−	0.195460i
$351$	−1212.65	−	1296.38i	−0.184406	−	0.197139i
$352$	824.721	+	5736.06i	0.124880	+	0.868560i
$353$	−146.274	−	602.951i	−0.0220549	−	0.0909117i	0.959720	−	0.280957i	$-0.0906517\pi$
$353$	−146.274	−	602.951i	−0.0220549	−	0.0909117i	−0.981775	+	0.190045i	$0.939137\pi$
$354$	10922.2	−	2612.88i	1.63986	−	0.392297i
$355$	−5398.16	−	4245.16i	−0.807056	−	0.634676i
$356$	−6027.29	−	8464.15i	−0.897320	−	1.26011i
$357$	1068.34	+	262.783i	0.158382	+	0.0389579i
$358$	8622.22	−	3451.82i	1.27290	−	0.509593i
$359$	2847.61	−	1830.05i	0.418639	−	0.269043i	−0.314318	−	0.949318i	$-0.601776\pi$
$359$	2847.61	−	1830.05i	0.418639	−	0.269043i	0.732957	+	0.680275i	$0.238140\pi$
$360$	−215.229	+	19.1685i	−0.0315099	+	0.00280631i
$361$	353.507	+	2458.69i	0.0515391	+	0.358462i
$362$	−5192.55	+	15002.9i	−0.753907	+	2.17827i
$363$	4242.37	−	596.169i	0.613407	−	0.0862005i
$364$	−590.764	−	1706.90i	−0.0850672	−	0.245786i
$365$	−92.6248	+	381.805i	−0.0132827	+	0.0547522i
$366$	7415.45	+	3415.12i	1.05905	+	0.487735i
$367$	808.794	+	1400.87i	0.115037	+	0.199251i	0.917795	−	0.397055i	$-0.129968\pi$
$367$	808.794	+	1400.87i	0.115037	+	0.199251i	−0.802757	+	0.596306i	$0.796635\pi$
$368$	2516.62	+	6393.52i	0.356489	+	0.905667i
$369$	−4284.85	+	1683.79i	−0.604499	+	0.237546i
$370$	330.617	+	723.950i	0.0464540	+	0.101720i
$371$	2765.27	+	2636.68i	0.386970	+	0.368975i
$372$	3255.74	+	1893.56i	0.453769	+	0.263915i
$373$	7422.01	−	3826.31i	1.03029	−	0.531150i	0.141725	−	0.989906i	$-0.454735\pi$
$373$	7422.01	−	3826.31i	1.03029	−	0.531150i	0.888562	+	0.458756i	$0.151705\pi$
$374$	1083.15	−	208.761i	0.149756	−	0.0288630i
$375$	−1515.97	+	7732.93i	−0.208759	+	1.06487i
$376$	−29.5028	−	121.612i	−0.00404652	−	0.0166800i
$377$	260.472	−	167.395i	0.0355835	−	0.0228681i
$378$	1027.20	−	9769.41i	0.139771	−	1.32932i
$379$	−4029.80	+	8824.04i	−0.546167	+	1.19594i	0.412383	+	0.911011i	$0.364697\pi$
$379$	−4029.80	+	8824.04i	−0.546167	+	1.19594i	−0.958549	+	0.284927i	$0.908031\pi$
$380$	5161.07	−	492.822i	0.696730	−	0.0665296i
$381$	3649.88	−	7024.72i	0.490784	−	0.944586i
$382$	408.438	+	8574.16i	0.0547055	+	1.14841i
$383$	−5440.39	+	5187.40i	−0.725825	+	0.692073i	−0.959962	−	0.280131i	$-0.909622\pi$
$383$	−5440.39	+	5187.40i	−0.725825	+	0.692073i	0.234137	+	0.972204i	$0.424774\pi$
$384$	−527.147	+	180.568i	−0.0700543	+	0.0239963i
$385$	−1222.53	+	3532.27i	−0.161833	+	0.467587i
$386$	−9696.63	−	6231.65i	−1.27862	−	0.821716i
$387$	589.332	+	688.948i	0.0774094	+	0.0904941i
$388$	2390.67	−	701.964i	0.312804	−	0.0918475i
$389$	−3183.56	+	4470.68i	−0.414943	+	0.582706i	−0.968160	−	0.250331i	$-0.919461\pi$
$389$	−3183.56	+	4470.68i	−0.414943	+	0.582706i	0.553217	+	0.833037i	$0.313400\pi$
$390$	−1915.51	+	1649.14i	−0.248706	+	0.214121i
$391$	1224.73	−	550.745i	0.158407	−	0.0712337i
$392$	−16.9823	+	29.4142i	−0.00218810	+	0.00378990i
$393$	11116.7	+	5119.71i	1.42688	+	0.657138i
$394$	−5317.20	−	5069.94i	−0.679889	−	0.648273i
$395$	3211.85	−	3706.67i	0.409128	−	0.472159i
$396$	−1601.30	−	4723.83i	−0.203202	−	0.599448i
$397$	−2318.91	−	2676.16i	−0.293155	−	0.338319i	0.589997	−	0.807405i	$-0.299129\pi$
$397$	−2318.91	−	2676.16i	−0.293155	−	0.338319i	−0.883152	+	0.469086i	$0.844583\pi$
$398$	1640.67	−	1290.24i	0.206632	−	0.162497i
$399$	−587.150	+	5948.53i	−0.0736698	+	0.746364i
$400$	100.210	+	2103.66i	0.0125262	+	0.262958i
$401$	622.641	+	489.650i	0.0775392	+	0.0609775i	0.656176	−	0.754608i	$-0.272173\pi$
$401$	622.641	+	489.650i	0.0775392	+	0.0609775i	−0.578637	+	0.815585i	$0.696415\pi$
$402$	4850.44	−	5054.64i	0.601785	−	0.627121i
$403$	1112.27	−	106.209i	0.137484	−	0.0131281i
$404$	2185.67	−	15201.7i	0.269162	−	1.87206i
$405$	−6703.95	+	1875.98i	−0.822524	+	0.230169i
$406$	1643.99	+	482.719i	0.200960	+	0.0590072i
$407$	−366.233	+	288.009i	−0.0446032	+	0.0350763i
$408$	19.5468	+	49.2800i	0.00237184	+	0.00597972i
$409$	556.755	−	287.027i	0.0673099	−	0.0347007i	−0.424243	−	0.905548i	$-0.639460\pi$
$409$	556.755	−	287.027i	0.0673099	−	0.0347007i	0.491553	+	0.870848i	$0.336429\pi$
$410$	2144.04	+	6194.79i	0.258260	+	0.746193i
$411$	2110.46	+	4125.95i	0.253288	+	0.495178i
$412$	5337.88	−	7496.01i	0.638297	−	0.896363i
$413$	9336.64			1.11241
$414$	−6359.02	−	10164.9i	−0.754901	−	1.20671i
$415$	−9481.70			−1.12154
$416$	−1889.78	+	2653.82i	−0.222726	+	0.312775i
$417$	1546.31	−	2389.33i	0.181590	−	0.280590i
$418$	1960.19	+	5663.61i	0.229369	+	0.662718i
$419$	12179.2	−	6278.82i	1.42003	−	0.732077i	0.434358	−	0.900740i	$-0.356975\pi$
$419$	12179.2	−	6278.82i	1.42003	−	0.732077i	0.985674	+	0.168663i	$0.0539449\pi$
$420$	−7008.11	−	1030.42i	−0.814193	−	0.119713i
$421$	−9084.20	+	7143.89i	−1.05163	+	0.827012i	−0.985308	−	0.170786i	$-0.945369\pi$
$421$	−9084.20	+	7143.89i	−1.05163	+	0.827012i	−0.0663231	+	0.997798i	$0.521127\pi$
$422$	−15499.2	−	4550.98i	−1.78789	−	0.524972i
$423$	−1651.40	−	3677.90i	−0.189819	−	0.422756i
$424$	−26.2026	+	182.243i	−0.00300120	+	0.0208738i
$425$	409.741	−	39.1255i	0.0467656	−	0.00446557i
$426$	14608.7	+	3593.37i	1.66149	+	0.408684i
$427$	5335.22	+	4195.66i	0.604659	+	0.475509i
$428$	−56.5141	−	1186.38i	−0.00638250	−	0.133985i
$429$	−1202.58	−	862.145i	−0.135341	−	0.0970274i
$430$	1014.74	−	798.001i	0.113803	−	0.0894954i
$431$	2952.67	+	3407.57i	0.329989	+	0.380828i	0.896363	−	0.443321i	$-0.146200\pi$
$431$	2952.67	+	3407.57i	0.329989	+	0.380828i	−0.566374	+	0.824148i	$0.691654\pi$
$432$	−7609.82	+	4297.07i	−0.847518	+	0.478571i
$433$	−7815.58	+	9019.65i	−0.867419	+	1.00106i	0.132532	+	0.991179i	$0.457689\pi$
$433$	−7815.58	+	9019.65i	−0.867419	+	1.00106i	−0.999951	+	0.00987655i	$0.996856\pi$
$434$	4474.88	+	4266.79i	0.494934	+	0.471918i
$435$	−111.568	−	1209.10i	−0.0122972	−	0.133269i
$436$	1277.66	−	2212.96i	0.140341	−	0.243077i
$437$	3908.79	+	6160.54i	0.427879	+	0.674367i
$438$	−160.188	−	845.625i	−0.0174751	−	0.0922501i
$439$	−7242.85	+	10171.2i	−0.787431	+	1.10579i	0.204482	+	0.978870i	$0.434449\pi$
$439$	−7242.85	+	10171.2i	−0.787431	+	1.10579i	−0.991913	+	0.126922i	$0.959490\pi$
$440$	−172.822	+	50.7450i	−0.0187249	+	0.00549812i
$441$	−364.473	+	1031.75i	−0.0393557	+	0.111408i
$442$	521.699	+	335.276i	0.0561419	+	0.0360802i
$443$	5469.31	−	15802.5i	0.586579	−	1.69481i	−0.124958	−	0.992162i	$-0.539880\pi$
$443$	5469.31	−	15802.5i	0.586579	−	1.69481i	0.711538	−	0.702648i	$-0.247999\pi$
$444$	−665.434	−	580.324i	−0.0711263	−	0.0620292i
$445$	−8749.01	+	8342.16i	−0.932006	+	0.888666i
$446$	−549.264	−	11530.5i	−0.0583148	−	1.22418i
$447$	4005.40	+	6276.40i	0.423823	+	0.664124i
$448$	−9319.40	+	889.895i	−0.982813	+	0.0938473i
$449$	5019.84	−	10991.9i	0.527619	−	1.15532i	−0.438855	−	0.898558i	$-0.644616\pi$
$449$	5019.84	−	10991.9i	0.527619	−	1.15532i	0.966474	−	0.256766i	$-0.0826568\pi$
$450$	−843.664	−	3576.97i	−0.0883793	−	0.374712i
$451$	−3228.38	+	2074.75i	−0.337070	+	0.216621i
$452$	4557.76	+	18787.3i	0.474290	+	1.95505i
$453$	−12003.2	+	4111.57i	−1.24495	+	0.426442i
$454$	−14970.9	+	2885.40i	−1.54762	+	0.298279i
$455$	−1867.78	+	962.908i	−0.192446	+	0.0992128i
$456$	−249.906	+	143.224i	−0.0256643	+	0.0147085i
$457$	−3750.91	−	3576.49i	−0.383939	−	0.366085i	0.473391	−	0.880852i	$-0.343030\pi$
$457$	−3750.91	−	3576.49i	−0.383939	−	0.366085i	−0.857330	+	0.514767i	$0.827878\pi$
$458$	5133.60	+	11241.0i	0.523750	+	1.14685i
$459$	909.631	+	1445.61i	0.0925010	+	0.147005i
$460$	−7512.57	+	4279.43i	−0.761469	+	0.433760i
$461$	−3490.53	−	6045.78i	−0.352647	−	0.610803i	0.634065	−	0.773280i	$-0.281385\pi$
$461$	−3490.53	−	6045.78i	−0.352647	−	0.610803i	−0.986712	+	0.162477i	$0.948052\pi$
$462$	−752.373	−	8153.70i	−0.0757653	−	0.821092i
$463$	2897.49	−	11943.6i	0.290837	−	1.19885i	−0.619505	−	0.784993i	$-0.712667\pi$
$463$	2897.49	−	11943.6i	0.290837	−	1.19885i	0.910343	−	0.413856i	$-0.135818\pi$
$464$	−498.554	−	1440.48i	−0.0498811	−	0.144122i
$465$	1641.49	−	4062.68i	0.163704	−	0.405166i
$466$	−4103.55	+	11856.4i	−0.407925	+	1.17862i
$467$	−2114.25	−	14704.9i	−0.209498	−	1.45709i	−0.774799	−	0.632208i	$-0.782149\pi$
$467$	−2114.25	−	14704.9i	−0.209498	−	1.45709i	0.565300	−	0.824885i	$-0.308760\pi$
$468$	1181.11	−	2543.24i	0.116660	−	0.251200i
$469$	4899.55	−	3148.75i	0.482389	−	0.310012i
$470$	−5329.41	+	2133.57i	−0.523037	+	0.209392i
$471$	−886.218	−	3054.15i	−0.0866980	−	0.298785i
$472$	260.973	+	366.486i	0.0254497	+	0.0357391i
$473$	594.043	+	467.161i	0.0577466	+	0.0454124i
$474$	−3059.87	+	10299.4i	−0.296507	+	0.998035i
$475$	527.229	+	2173.27i	0.0509283	+	0.209929i
$476$	247.331	+	1720.23i	0.0238160	+	0.165644i
$477$	244.476	+	5926.66i	0.0234671	+	0.568896i
$478$	−5004.39	−	3216.12i	−0.478861	−	0.307745i
$479$	−992.327	−	191.255i	−0.0946568	−	0.0182436i	0.141703	−	0.989909i	$-0.454742\pi$
$479$	−992.327	−	191.255i	−0.0946568	−	0.0182436i	−0.236360	+	0.971666i	$0.575954\pi$
$480$	5818.28	+	11374.7i	0.553264	+	1.08163i
$481$	−260.746	−	24.8982i	−0.0247173	−	0.00236021i
$482$	−8196.36	+	14196.5i	−0.774551	+	1.34156i
$483$	−3175.45	−	9448.89i	−0.299147	−	0.890144i
$484$	3383.68	+	5860.71i	0.317776	+	0.550404i
$485$	−1204.17	−	2636.77i	−0.112739	−	0.246865i
$486$	11683.0	−	9801.89i	1.09044	−	0.914861i
$487$	−209.884	+	242.219i	−0.0195293	+	0.0225380i	−0.765430	−	0.643519i	$-0.777474\pi$
$487$	−209.884	+	242.219i	−0.0195293	+	0.0225380i	0.745901	+	0.666057i	$0.232019\pi$
$488$	−15.5624	+	326.696i	−0.00144360	+	0.0303049i
$489$	−7392.78	−	18638.2i	−0.683667	−	1.72361i
$490$	1446.47	+	579.079i	0.133357	+	0.0533880i
$491$	−13164.8	+	12552.6i	−1.21002	+	1.15375i	−0.226292	+	0.974059i	$0.572660\pi$
$491$	−13164.8	+	12552.6i	−1.21002	+	1.15375i	−0.983724	+	0.179688i	$0.942491\pi$
$492$	−5001.78	−	5279.29i	−0.458328	−	0.483758i
$493$	−276.571	+	110.722i	−0.0252660	+	0.0101150i
$494$	−1399.67	+	3064.85i	−0.127478	+	0.279138i
$495$	−5174.63	+	2626.10i	−0.469863	+	0.238453i
$496$	782.835	−	5444.74i	0.0708676	−	0.492895i
$497$	11116.9	+	5731.17i	1.00334	+	0.517260i
$498$	18921.5	−	8568.40i	1.70260	−	0.771002i
$499$	1535.94	+	614.897i	0.137792	+	0.0551635i	0.439533	−	0.898226i	$-0.355144\pi$
$499$	1535.94	+	614.897i	0.137792	+	0.0551635i	−0.301742	+	0.953390i	$0.597568\pi$
$500$	−12223.0	+	2355.79i	−1.09326	+	0.210708i
$501$	19489.5	−	2738.81i	1.73798	−	0.244233i
$502$	−24425.6	−	4707.66i	−2.17165	−	0.418552i
$503$	14451.4	−	4243.32i	1.28103	−	0.376143i	0.430746	−	0.902473i	$-0.358250\pi$
$503$	14451.4	−	4243.32i	1.28103	−	0.376143i	0.850281	+	0.526330i	$0.176432\pi$
$504$	378.294	−	108.463i	0.0334337	−	0.00958600i
$505$	−17867.5			−1.57444
$506$	−6854.92	−	7273.30i	−0.602249	−	0.639007i
$507$	1969.92	+	10399.1i	0.172559	+	0.910931i
$508$	12448.5	+	1188.69i	1.08723	+	0.103818i
$509$	−1528.64	+	6301.12i	−0.133115	+	0.548708i	0.865723	+	0.500523i	$0.166859\pi$
$509$	−1528.64	+	6301.12i	−0.133115	+	0.548708i	−0.998838	+	0.0481850i	$0.984656\pi$
$510$	2110.03	−	1209.28i	0.183204	−	0.104996i
$511$	34.0463	−	714.720i	0.00294740	−	0.0618734i
$512$	10776.9	+	12437.2i	0.930225	+	1.07354i
$513$	−7070.93	+	6009.62i	−0.608556	+	0.517215i
$514$	7734.00	+	2270.91i	0.663681	+	0.194874i
$515$	−9515.86	−	4905.76i	−0.814211	−	0.419755i
$516$	−660.304	+	1270.85i	−0.0563339	+	0.108423i
$517$	−1949.36	−	2737.49i	−0.165827	−	0.232872i
$518$	−840.780	−	1180.71i	−0.0713161	−	0.100149i
$519$	−6277.68	+	278.996i	−0.530943	+	0.0235965i
$520$	−90.0038	−	46.4002i	−0.00759025	−	0.00391304i
$521$	−6654.98	−	1954.08i	−0.559616	−	0.164318i	−0.0103213	−	0.999947i	$-0.503285\pi$
$521$	−6654.98	−	1954.08i	−0.559616	−	0.164318i	−0.549295	+	0.835629i	$0.685104\pi$
$522$	1315.28	+	2312.04i	0.110284	+	0.193860i
$523$	1335.04	+	1540.71i	0.111620	+	0.128816i	0.808810	−	0.588070i	$-0.200112\pi$
$523$	1335.04	+	1540.71i	0.111620	+	0.128816i	−0.697190	+	0.716886i	$0.745567\pi$
$524$	−919.923	+	19311.6i	−0.0766928	+	1.60998i
$525$	9.73603	−	3055.37i	0.000809362	−	0.253995i
$526$	1917.73	−	7904.98i	0.158968	−	0.655273i
$527$	−1070.19	−	102.191i	−0.0884597	−	0.00844687i
$528$	−5520.61	+	4752.92i	−0.455026	+	0.391750i
$529$	−10158.5	−	6696.36i	−0.834920	−	0.550371i
$530$	8446.12			0.692219
$531$	10426.4	+	10069.2i	0.852104	+	0.822910i
$532$	−9059.85	+	2660.21i	−0.738336	+	0.216795i
$533$	−2118.46	−	408.300i	−0.172159	−	0.0331809i
$534$	9920.73	−	24553.7i	0.803955	−	1.98978i
$535$	−1356.82	+	261.506i	−0.109646	+	0.0211325i
$536$	260.546	+	104.307i	0.0209960	+	0.00840555i
$537$	9742.20	+	6984.28i	0.782880	+	0.561255i
$538$	−3180.95	−	1639.89i	−0.254908	−	0.131414i
$539$	−129.808	+	902.835i	−0.0103733	+	0.0721482i
$540$	−6714.83	−	8708.65i	−0.535111	−	0.694001i
$541$	5260.25	−	11518.3i	0.418033	−	0.915364i	−0.577086	−	0.816683i	$-0.695810\pi$
$541$	5260.25	−	11518.3i	0.418033	−	0.915364i	0.995119	−	0.0986811i	$-0.0314624\pi$
$542$	−8373.81	+	3352.37i	−0.663627	+	0.265676i
$543$	−19928.4	+	4767.40i	−1.57497	+	0.376775i
$544$	2268.67	−	2163.17i	0.178802	−	0.170488i
$545$	−2759.89	−	1104.89i	−0.216919	−	0.0868412i
$546$	2857.15	−	3609.43i	0.223946	−	0.282911i
$547$	701.282	−	14721.7i	0.0548165	−	1.15074i	−0.789100	−	0.614265i	$-0.789452\pi$
$547$	701.282	−	14721.7i	0.0548165	−	1.15074i	0.843916	−	0.536475i	$-0.180244\pi$
$548$	−4794.08	+	5532.67i	−0.373710	+	0.431284i
$549$	1433.09	+	10439.2i	0.111407	+	0.811537i
$550$	−1272.61	−	2786.62i	−0.0986620	−	0.216040i
$551$	−809.296	−	1401.74i	−0.0625720	−	0.108378i
$552$	282.133	−	388.755i	0.0217543	−	0.0299756i
$553$	−4466.26	+	7735.80i	−0.343445	+	0.594864i
$554$	6523.82	+	622.949i	0.500308	+	0.0477736i
$555$	−558.101	+	862.368i	−0.0426848	+	0.0659558i
$556$	4414.55	+	850.835i	0.336724	+	0.0648983i
$557$	7438.98	+	4780.74i	0.565888	+	0.363674i	0.792088	−	0.610407i	$-0.208994\pi$
$557$	7438.98	+	4780.74i	0.565888	+	0.363674i	−0.226200	+	0.974081i	$0.572630\pi$
$558$	395.622	+	9590.79i	0.0300144	+	0.727617i
$559$	60.4643	+	420.539i	0.00457490	+	0.0318191i
$560$	2439.01	+	10053.7i	0.184048	+	0.758656i
$561$	979.193	+	1033.52i	0.0736926	+	0.0777813i
$562$	13522.9	+	10634.6i	1.01500	+	0.798206i
$563$	−6739.14	−	9463.79i	−0.504477	−	0.708439i	0.481289	−	0.876562i	$-0.340169\pi$
$563$	−6739.14	−	9463.79i	−0.504477	−	0.708439i	−0.985766	+	0.168123i	$0.946229\pi$
$564$	4409.52	−	4595.16i	0.329210	−	0.343070i
$565$	20880.1	−	8359.12i	1.55474	−	0.622426i
$566$	−23018.4	+	14793.0i	−1.70943	+	1.09858i
$567$	11342.3	−	5665.56i	0.840092	−	0.419631i
$568$	85.7725	+	596.561i	0.00633615	+	0.0440689i
$569$	1435.89	−	4148.72i	0.105792	−	0.305665i	−0.879664	−	0.475595i	$-0.842233\pi$
$569$	1435.89	−	4148.72i	0.105792	−	0.305665i	0.985456	+	0.169930i	$0.0543540\pi$
$570$	8134.82	+	10412.4i	0.597772	+	0.765134i
$571$	−4612.74	−	13327.6i	−0.338069	−	0.976785i	−0.978046	−	0.208391i	$-0.933177\pi$
$571$	−4612.74	−	13327.6i	−0.338069	−	0.976785i	0.639977	−	0.768394i	$-0.278944\pi$
$572$	551.068	−	2271.53i	0.0402820	−	0.166045i
$573$	−9045.08	+	6397.64i	−0.659448	+	0.466431i
$574$	−5969.44	−	10339.4i	−0.434076	−	0.751841i
$575$	−2288.27	−	2944.80i	−0.165961	−	0.213577i
$576$	−11366.9	−	9056.84i	−0.822256	−	0.655153i
$577$	−5810.97	−	12724.2i	−0.419261	−	0.918054i	−0.994949	−	0.100384i	$-0.967993\pi$
$577$	−5810.97	−	12724.2i	−0.419261	−	0.918054i	0.575688	−	0.817670i	$-0.304734\pi$
$578$	13883.2	+	13237.6i	0.999075	+	0.952616i
$579$	47.4051	−	14876.7i	0.00340257	−	1.06780i
$580$	1704.86	−	878.917i	0.122053	−	0.0629225i
$581$	16956.4	−	3268.09i	1.21079	−	0.233362i
$582$	4785.81	+	4173.70i	0.340856	+	0.297260i
$583$	1165.70	+	4805.09i	0.0828104	+	0.341349i
$584$	29.0061	−	18.6411i	0.00205528	−	0.00132085i
$585$	−3124.24	−	939.029i	−0.220806	−	0.0663659i
$586$	−10136.7	+	22196.2i	−0.714576	+	1.56470i
$587$	5309.31	−	506.977i	0.373319	−	0.0356477i	0.0932897	−	0.995639i	$-0.470262\pi$
$587$	5309.31	−	506.977i	0.373319	−	0.0356477i	0.280030	+	0.959991i	$0.409656\pi$
$588$	−1726.82	+	76.7444i	−0.121110	+	0.00538246i
$589$	−277.923	−	5834.33i	−0.0194425	−	0.408148i
$590$	14937.2	−	14242.5i	1.04229	−	0.993824i
$591$	1824.22	−	9305.28i	0.126968	−	0.647662i
$592$	−421.762	+	1218.60i	−0.0292809	+	0.0846017i
$593$	−16583.6	−	10657.6i	−1.14841	−	0.738038i	−0.179087	−	0.983833i	$-0.557315\pi$
$593$	−16583.6	−	10657.6i	−1.14841	−	0.738038i	−0.969322	+	0.245795i	$0.920951\pi$
$594$	7953.25	−	9916.79i	0.549370	−	0.685002i
$595$	1939.99	−	569.632i	0.133667	−	0.0392481i
$596$	−6822.32	+	9580.61i	−0.468881	+	0.658452i
$597$	2542.94	+	889.203i	0.174331	+	0.0609592i
$598$	32.6158	−	5618.73i	0.00223037	−	0.384226i
$599$	−8958.15	+	15516.0i	−0.611052	+	1.05837i	0.380012	+	0.924982i	$0.375920\pi$
$599$	−8958.15	+	15516.0i	−0.611052	+	1.05837i	−0.991064	+	0.133391i	$0.957413\pi$
$600$	120.203	−	85.0201i	0.00817877	−	0.00578488i
$601$	145.412	+	138.650i	0.00986936	+	0.00941041i	0.694998	−	0.719012i	$-0.255405\pi$
$601$	145.412	+	138.650i	0.00986936	+	0.00941041i	−0.685128	+	0.728422i	$0.740254\pi$
$602$	−1539.65	+	1776.85i	−0.104238	+	0.120297i
$603$	8867.22	+	1767.70i	0.598841	+	0.119380i
$604$	−13125.1	−	15147.2i	−0.884192	−	1.02041i
$605$	6188.70	−	4866.85i	0.415878	−	0.327050i
$606$	35656.0	−	16146.4i	2.39014	−	1.08235i
$607$	−351.676	−	7382.59i	−0.0235158	−	0.493657i	−0.979648	−	0.200722i	$-0.935671\pi$
$607$	−351.676	−	7382.59i	−0.0235158	−	0.493657i	0.956132	−	0.292935i	$-0.0946319\pi$
$608$	13387.4	+	10527.9i	0.892975	+	0.702244i
$609$	616.266	+	2123.82i	0.0410055	+	0.141316i
$610$	14935.8	−	1426.19i	0.991364	−	0.0946637i
$611$	268.878	−	1870.09i	0.0178030	−	0.123823i
$612$	−1579.00	+	2187.75i	−0.104293	+	0.144501i
$613$	−7720.97	−	2267.08i	−0.508723	−	0.149374i	0.0172911	−	0.999850i	$-0.494496\pi$
$613$	−7720.97	−	2267.08i	−0.508723	−	0.149374i	−0.526014	+	0.850476i	$0.676314\pi$
$614$	17633.0	−	13866.7i	1.15897	−	0.911427i
$615$	−5251.26	+	6633.91i	−0.344311	+	0.434968i
$616$	291.573	−	150.316i	0.0190711	−	0.00983183i
$617$	542.550	+	1567.60i	0.0354007	+	0.102284i	0.961316	−	0.275447i	$-0.0888258\pi$
$617$	542.550	+	1567.60i	0.0354007	+	0.102284i	−0.925916	+	0.377731i	$0.876705\pi$
$618$	23422.9	+	1190.59i	1.52461	+	0.0774960i
$619$	17598.4	−	24713.5i	1.14271	−	1.60471i	0.430793	−	0.902451i	$-0.358234\pi$
$619$	17598.4	−	24713.5i	1.14271	−	1.60471i	0.711918	−	0.702263i	$-0.247827\pi$
$620$	6921.71			0.448359
$621$	6644.16	−	13976.3i	0.429341	−	0.903142i
$622$	21627.5			1.39418
$623$	12770.8	−	17934.1i	0.821272	−	1.15332i
$624$	−4090.12	−	207.901i	−0.262397	−	0.0133377i
$625$	3354.31	+	9691.64i	0.214676	+	0.620265i
$626$	6113.67	−	3151.81i	0.390337	−	0.201233i
$627$	−4800.98	+	6065.07i	−0.305794	+	0.386309i
$628$	3948.76	−	3105.34i	0.250912	−	0.197319i
$629$	241.815	+	71.0033i	0.0153288	+	0.00450093i
$630$	−7394.66	−	16469.0i	−0.467635	−	1.04149i
$631$	1437.58	−	9998.57i	0.0906958	−	0.630803i	−0.892878	−	0.450298i	$-0.851318\pi$
$631$	1437.58	−	9998.57i	0.0906958	−	0.630803i	0.983574	−	0.180505i	$-0.0577732\pi$
$632$	−428.488	+	40.9156i	−0.0269689	+	0.00257522i
$633$	−5810.04	−	20023.0i	−0.364816	−	1.25725i
$634$	11524.3	+	9062.79i	0.721905	+	0.567712i
$635$	−692.243	−	14532.0i	−0.0432611	−	0.908163i
$636$	−8535.69	+	3865.30i	−0.532173	+	0.240989i
$637$	−403.076	+	316.982i	−0.0250713	+	0.0197163i
$638$	1452.00	+	1675.70i	0.0901023	+	0.103984i
$639$	6233.63	+	18389.2i	0.385913	+	1.13845i
$640$	−670.601	+	773.915i	−0.0414185	+	0.0477995i
$641$	13573.1	+	12941.9i	0.836357	+	0.797465i	0.981403	−	0.191960i	$-0.0614843\pi$
$641$	13573.1	+	12941.9i	0.836357	+	0.797465i	−0.145045	+	0.989425i	$0.546333\pi$
$642$	2471.33	−	1747.99i	0.151925	−	0.107457i
$643$	−8920.80	+	15451.3i	−0.547126	+	0.947650i	0.451344	+	0.892350i	$0.350945\pi$
$643$	−8920.80	+	15451.3i	−0.547126	+	0.947650i	−0.998470	+	0.0552996i	$0.982389\pi$
$644$	11960.0	−	10242.4i	0.731816	−	0.626722i
$645$	1572.78	+	549.964i	0.0960129	+	0.0335734i
$646$	1880.47	−	2640.76i	0.114530	−	0.160835i
$647$	−5000.79	+	1468.36i	−0.303866	+	0.0892231i	−0.430111	−	0.902776i	$-0.641526\pi$
$647$	−5000.79	+	1468.36i	−0.303866	+	0.0892231i	0.126245	+	0.991999i	$0.459707\pi$
$648$	539.422	+	286.852i	0.0327014	+	0.0173898i
$649$	10164.3	+	6532.21i	0.614768	+	0.395087i
$650$	563.291	−	1627.52i	0.0339909	−	0.0982103i
$651$	−1535.24	+	7831.20i	−0.0924282	+	0.471473i
$652$	22923.2	−	21857.2i	1.37690	−	1.31288i
$653$	534.207	+	11214.4i	0.0320140	+	0.672056i	0.956656	+	0.291219i	$0.0940609\pi$
$653$	534.207	+	11214.4i	0.0320140	+	0.672056i	−0.924642	+	0.380837i	$0.875636\pi$
$654$	6506.06	−	289.146i	0.389002	−	0.0172882i
$655$	22390.7	−	2138.05i	1.33569	−	0.127543i
$656$	−4412.28	+	9661.55i	−0.262608	+	0.575031i
$657$	808.816	−	761.423i	0.0480288	−	0.0452145i
$658$	8795.38	−	5652.45i	0.521093	−	0.334886i
$659$	−1848.97	−	7621.57i	−0.109296	−	0.450522i	0.890696	−	0.454599i	$-0.150217\pi$
$659$	−1848.97	−	7621.57i	−0.109296	−	0.450522i	−0.999992	+	0.00407684i	$0.998702\pi$
$660$	−6908.46	−	6024.87i	−0.407442	−	0.355330i
$661$	−27749.6	+	5348.30i	−1.63288	+	0.314712i	−0.921584	−	0.388178i	$-0.873105\pi$
$661$	−27749.6	+	5348.30i	−1.63288	+	0.314712i	−0.711298	+	0.702890i	$0.751892\pi$
$662$	−23485.7	+	12107.7i	−1.37885	+	0.710847i
$663$	−2.55049	+	800.398i	−0.000149401	+	0.0468852i
$664$	602.239	+	574.233i	0.0351979	+	0.0335611i
$665$	4563.41	+	9992.48i	0.266108	+	0.582695i
$666$	334.434	−	2225.27i	0.0194580	−	0.129471i
$667$	2189.60	+	1578.44i	0.127109	+	0.0916303i
$668$	15544.7	+	26924.1i	0.900360	+	1.55947i
$669$	12163.8	−	8603.50i	0.702957	−	0.497205i
$670$	3035.26	−	12511.5i	0.175018	−	0.721436i
$671$	2872.76	+	8300.30i	0.165278	+	0.477540i
$672$	−14325.6	−	18336.4i	−0.822353	−	1.05259i
$673$	−45.7591	+	132.212i	−0.00262093	+	0.00757267i	−0.946304	−	0.323279i	$-0.895215\pi$
$673$	−45.7591	+	132.212i	−0.00262093	+	0.00757267i	0.943683	+	0.330852i	$0.107336\pi$
$674$	−5482.35	−	38130.6i	−0.313312	−	2.17913i
$675$	3305.96	−	3401.49i	0.188514	−	0.193960i
$676$	−14065.1	+	9039.12i	−0.800247	+	0.514288i
$677$	10680.6	−	4275.88i	0.606337	−	0.242741i	−0.0481181	−	0.998842i	$-0.515322\pi$
$677$	10680.6	−	4275.88i	0.606337	−	0.242741i	0.654455	+	0.756101i	$0.272898\pi$
$678$	−34113.9	+	35550.1i	−1.93236	+	2.01371i
$679$	3062.28	+	4300.38i	0.173078	+	0.243053i
$680$	76.5850	+	60.2271i	0.00431897	+	0.00339648i
$681$	−13534.0	−	14284.9i	−0.761561	−	0.803815i
$682$	1886.39	+	7775.81i	0.105914	+	0.436585i
$683$	2812.96	+	19564.6i	0.157591	+	1.09607i	0.903055	+	0.429526i	$0.141319\pi$
$683$	2812.96	+	19564.6i	0.157591	+	1.09607i	−0.745463	+	0.666547i	$0.767772\pi$
$684$	−12986.2	−	6799.98i	−0.725938	−	0.380122i
$685$	7164.92	+	4604.62i	0.399646	+	0.256837i
$686$	−26368.6	−	5082.12i	−1.46757	−	0.282852i
$687$	−8665.82	+	13390.3i	−0.481254	+	0.743626i
$688$	2082.18	+	198.824i	0.115381	+	0.0110176i
$689$	−1389.87	+	2407.32i	−0.0768500	+	0.133108i
$690$	−19494.0	−	10272.8i	−1.07554	−	0.566778i
$691$	9945.57	+	17226.2i	0.547536	+	0.948360i	0.998443	+	0.0557891i	$0.0177674\pi$
$691$	9945.57	+	17226.2i	0.547536	+	0.948360i	−0.450907	+	0.892571i	$0.648899\pi$
$692$	−4123.58	−	9029.37i	−0.226524	−	0.496019i
$693$	8348.82	−	6479.90i	0.457641	−	0.355196i
$694$	−4036.88	+	4658.81i	−0.220804	+	0.254821i
$695$	248.872	−	5224.48i	0.0135831	−	0.285145i
$696$	−66.1395	+	83.5539i	−0.00360203	+	0.00455044i
$697$	1927.14	+	771.510i	0.104728	+	0.0419269i
$698$	−16944.3	+	16156.4i	−0.918841	+	0.876113i
$699$	−15749.0	+	3767.56i	−0.852190	+	0.203866i
$700$	4480.75	−	1793.82i	0.241938	−	0.0968572i
$701$	−12058.9	+	26405.3i	−0.649727	+	1.42270i	0.242065	+	0.970260i	$0.422175\pi$
$701$	−12058.9	+	26405.3i	−0.649727	+	1.42270i	−0.891793	+	0.452445i	$0.850552\pi$
$702$	7083.26	−	949.399i	0.380827	−	0.0510438i
$703$	−194.869	+	1355.34i	−0.0104546	+	0.0727136i
$704$	−10768.2	−	5551.37i	−0.576478	−	0.297195i
$705$	−6021.66	−	4316.99i	−0.321687	−	0.230620i
$706$	2318.93	+	928.358i	0.123617	+	0.0494890i
$707$	31953.0	−	6158.44i	1.69974	−	0.327598i
$708$	−8577.59	+	21229.5i	−0.455318	+	1.12691i
$709$	−30622.5	−	5902.01i	−1.62208	−	0.312630i	−0.704354	−	0.709849i	$-0.748763\pi$
$709$	−30622.5	−	5902.01i	−1.62208	−	0.312630i	−0.917724	+	0.397219i	$0.869975\pi$
$710$	26527.9	−	7789.30i	1.40222	−	0.411728i
$711$	−13330.3	+	3822.02i	−0.703130	+	0.201599i
$712$	1060.92			0.0558423
$713$	4413.06	+	8683.53i	0.231796	+	0.456102i
$714$	−3356.64	+	2889.87i	−0.175937	+	0.151471i
$715$	−2707.04	−	258.491i	−0.141591	−	0.0135203i
$716$	−4464.23	+	18401.8i	−0.233011	+	0.960486i
$717$	24.4655	−	7677.80i	0.00127431	−	0.399906i
$718$	−648.430	+	13612.2i	−0.0337036	+	0.707526i
$719$	21374.6	+	24667.6i	1.10867	+	1.27948i	0.956694	+	0.291096i	$0.0940198\pi$
$719$	21374.6	+	24667.6i	1.10867	+	1.27948i	0.151981	+	0.988383i	$0.451435\pi$
$720$	−8118.85	+	13857.6i	−0.420239	+	0.717279i
$721$	18708.4	+	5493.29i	0.966349	+	0.283746i
$722$	−8888.65	−	4582.42i	−0.458174	−	0.236205i
$723$	−21136.7	+	939.370i	−1.08725	+	0.0483203i
$724$	−18775.5	−	26366.6i	−0.963795	−	1.35346i
$725$	479.909	+	673.937i	0.0245839	+	0.0345233i
$726$	−7951.99	+	15304.8i	−0.406510	+	0.782388i
$727$	17073.7	+	8802.09i	0.871014	+	0.449039i	0.834960	−	0.550311i	$-0.185491\pi$
$727$	17073.7	+	8802.09i	0.871014	+	0.449039i	0.0360544	+	0.999350i	$0.488521\pi$
$728$	176.950	+	51.9571i	0.00900851	+	0.00264514i
$729$	18776.2	+	5905.38i	0.953931	+	0.300025i
$730$	−1035.80	−	1195.37i	−0.0525159	−	0.0606066i
$731$	19.4511	−	408.328i	0.000984164	−	0.0206601i
$732$	−14441.5	+	8276.55i	−0.729198	+	0.417910i
$733$	123.150	−	507.630i	0.00620551	−	0.0255795i	−0.968625	−	0.248528i	$-0.920053\pi$
$733$	123.150	−	507.630i	0.00620551	−	0.0255795i	0.974830	+	0.222949i	$0.0715683\pi$
$734$	−6482.82	−	619.034i	−0.326002	−	0.0311294i
$735$	374.283	+	1975.82i	0.0187832	+	0.0991556i
$736$	−27561.8	−	6856.06i	−1.38035	−	0.343367i
$737$	7536.86			0.376694
$738$	4484.41	−	17984.0i	0.223677	−	0.897017i
$739$	−12880.9	+	3782.18i	−0.641181	+	0.188268i	−0.586131	−	0.810216i	$-0.699350\pi$
$739$	−12880.9	+	3782.18i	−0.641181	+	0.188268i	−0.0550493	+	0.998484i	$0.517532\pi$
$740$	−1593.32	−	307.087i	−0.0791507	−	0.0152550i
$741$	−4306.38	+	605.165i	−0.213494	+	0.0300017i
$742$	−15104.5	+	2911.15i	−0.747308	+	0.144032i
$743$	−29076.2	−	11640.4i	−1.43567	−	0.574756i	−0.482151	−	0.876088i	$-0.660144\pi$
$743$	−29076.2	−	11640.4i	−1.43567	−	0.574756i	−0.953519	+	0.301333i	$0.902569\pi$
$744$	−350.306	+	158.632i	−0.0172619	+	0.00781686i
$745$	12162.2	+	6270.04i	0.598104	+	0.308344i
$746$	−4784.29	+	33275.5i	−0.234806	+	1.63311i
$747$	22460.1	+	14637.3i	1.10009	+	0.716935i
$748$	−934.269	+	2045.76i	−0.0456688	+	0.100001i
$749$	2336.32	−	935.320i	0.113975	−	0.0456286i
$750$	−21819.4	−	23030.0i	−1.06231	−	1.12125i
$751$	−22212.6	+	21179.7i	−1.07929	+	1.02910i	−0.0798146	+	0.996810i	$0.525433\pi$
$751$	−22212.6	+	21179.7i	−1.07929	+	1.02910i	−0.999478	+	0.0322941i	$0.989719\pi$
$752$	−8635.06	−	3456.96i	−0.418734	−	0.167636i
$753$	−11837.4	−	29843.7i	−0.572881	−	1.44431i
$754$	−59.3120	+	1245.11i	−0.00286474	+	0.0601384i
$755$	−15269.7	+	17622.2i	−0.736054	+	0.849452i
$756$	15010.0	+	13259.6i	0.722101	+	0.637891i
$757$	−5627.60	−	12322.7i	−0.270196	−	0.591647i	0.725087	−	0.688657i	$-0.241799\pi$
$757$	−5627.60	−	12322.7i	−0.270196	−	0.591647i	−0.995283	+	0.0970098i	$0.969072\pi$
$758$	−19527.1	−	33822.0i	−0.935696	−	1.62067i
$759$	3153.80	−	12508.2i	0.150824	−	0.598179i
$760$	−264.675	+	458.430i	−0.0126326	+	0.0218803i
$761$	17698.1	+	1689.97i	0.843044	+	0.0805009i	0.507635	−	0.861572i	$-0.330520\pi$
$761$	17698.1	+	1689.97i	0.843044	+	0.0805009i	0.335408	+	0.942073i	$0.391126\pi$
$762$	14513.6	+	28374.2i	0.689992	+	1.34893i
$763$	5316.44	+	1024.66i	0.252252	+	0.0486175i
$764$	−14722.8	−	9461.76i	−0.697188	−	0.448056i
$765$	2780.74	+	1456.08i	0.131422	+	0.0688165i
$766$	−4306.94	−	29955.4i	−0.203154	−	1.41297i
$767$	1601.41	+	6601.10i	0.0753893	+	0.310759i
$768$	−5733.64	+	19299.3i	−0.269394	+	0.906774i
$769$	−30509.8	−	23993.2i	−1.43070	−	1.12512i	−0.971570	−	0.236752i	$-0.923917\pi$
$769$	−30509.8	−	23993.2i	−1.43070	−	1.12512i	−0.459134	−	0.888367i	$-0.651840\pi$
$770$	−8728.89	−	12258.0i	−0.408529	−	0.573699i
$771$	2899.17	+	9991.32i	0.135423	+	0.466704i
$772$	21816.9	−	8734.18i	1.01711	−	0.407189i
$773$	19561.4	−	12571.3i	0.910186	−	0.584941i	0.000391106	−	1.00000i	$-0.499876\pi$
$773$	19561.4	−	12571.3i	0.910186	−	0.584941i	0.909794	+	0.415059i	$0.136239\pi$
$774$	−3635.61	+	323.791i	−0.168836	+	0.0150367i
$775$	424.897	+	2955.22i	0.0196939	+	0.136974i
$776$	−83.2047	+	240.404i	−0.00384906	+	0.0111211i
$777$	700.836	−	1734.56i	0.0323582	−	0.0800864i
$778$	−7226.82	−	20880.5i	−0.333026	−	0.962215i
$779$	−2658.96	+	10960.4i	−0.122294	+	0.504103i
$780$	−473.508	−	5131.55i	−0.0217363	−	0.235563i
$781$	8092.71	+	14017.0i	0.370781	+	0.642211i
$782$	−1053.94	+	5302.55i	−0.0481955	+	0.242479i
$783$	−1602.26	+	3036.33i	−0.0731291	+	0.138582i
$784$	1048.72	+	2296.37i	0.0477731	+	0.104609i
$785$	−4229.76	−	4033.07i	−0.192314	−	0.183371i
$786$	−42750.3	+	24500.6i	−1.94002	+	1.11184i
$787$	−600.921	+	309.796i	−0.0272180	+	0.0140318i	−0.471782	−	0.881715i	$-0.656389\pi$
$787$	−600.921	+	309.796i	−0.0272180	+	0.0140318i	0.444564	+	0.895747i	$0.353359\pi$
$788$	14708.3	−	2834.79i	0.664926	−	0.128154i
$789$	9932.13	−	3402.14i	0.448154	−	0.153510i
$790$	4655.23	+	19189.1i	0.209653	+	0.864200i
$791$	−34459.4	+	22145.7i	−1.54897	+	0.995461i
$792$	487.714	+	146.588i	0.0218815	+	0.00657676i
$793$	−2051.29	+	4491.69i	−0.0918580	+	0.201141i
$794$	14191.6	−	1355.13i	0.634307	−	0.0605690i
$795$	5864.35	+	9189.36i	0.261619	+	0.409953i
$796$	202.484	+	4250.66i	0.00901615	+	0.189272i
$797$	9093.06	−	8670.21i	0.404131	−	0.385338i	−0.460571	−	0.887623i	$-0.652355\pi$
$797$	9093.06	−	8670.21i	0.404131	−	0.385338i	0.864702	+	0.502284i	$0.167507\pi$
$798$	−18136.6	−	15817.0i	−0.804549	−	0.701647i
$799$	−594.559	+	1717.87i	−0.0263254	+	0.0760622i
$800$	−7323.53	−	4706.55i	−0.323657	−	0.208002i
$801$	33602.6	−	6254.54i	1.48226	−	0.275897i
$802$	−3059.81	+	898.442i	−0.134720	+	0.0395575i
$803$	537.105	−	754.259i	0.0236040	−	0.0331472i
$804$	2658.34	+	14033.3i	0.116608	+	0.615566i
$805$	−13774.9	−	12076.8i	−0.603109	−	0.528758i
$806$	−2249.14	+	3895.63i	−0.0982911	+	0.170245i
$807$	−424.412	−	4599.48i	−0.0185130	−	0.200631i
$808$	1134.87	+	1082.10i	0.0494116	+	0.0471139i
$809$	16347.0	−	18865.5i	0.710422	−	0.819871i	−0.279699	−	0.960088i	$-0.590235\pi$
$809$	16347.0	−	18865.5i	0.710422	−	0.819871i	0.990121	+	0.140217i	$0.0447801\pi$
$810$	9503.40	−	26366.1i	0.412241	−	1.14372i
$811$	18030.4	+	20808.1i	0.780680	+	0.900953i	0.997158	−	0.0753344i	$-0.0240024\pi$
$811$	18030.4	+	20808.1i	0.780680	+	0.900953i	−0.216478	+	0.976287i	$0.569457\pi$
$812$	−2745.92	+	2159.42i	−0.118674	+	0.0933259i
$813$	−9461.52	−	6783.06i	−0.408155	−	0.292610i
$814$	−89.2513	−	1873.62i	−0.00384307	−	0.0806759i
$815$	−28965.2	−	22778.5i	−1.24492	−	0.979012i
$816$	3826.42	+	941.201i	0.164156	+	0.0403782i
$817$	2210.96	−	211.121i	0.0946778	−	0.00904063i
$818$	−358.889	+	2496.13i	−0.0153402	+	0.106693i
$819$	5910.85	+	602.455i	0.252188	+	0.0257039i
$820$	−12823.8	−	3765.40i	−0.546129	−	0.160358i
$821$	−12059.4	+	9483.58i	−0.512636	+	0.403142i	−0.840689	−	0.541518i	$-0.817850\pi$
$821$	−12059.4	+	9483.58i	−0.512636	+	0.403142i	0.328053	+	0.944659i	$0.393608\pi$
$822$	−18459.3	−	2714.11i	−0.783262	−	0.115165i
$823$	7839.43	−	4041.51i	0.332036	−	0.171176i	−0.284145	−	0.958781i	$-0.591710\pi$
$823$	7839.43	−	4041.51i	0.332036	−	0.171176i	0.616180	+	0.787605i	$0.288679\pi$
$824$	307.304	+	887.897i	0.0129920	+	0.0375380i
$825$	2148.23	−	3319.41i	0.0906568	−	0.140081i
$826$	−21803.6	+	30618.9i	−0.918455	+	1.28979i
$827$	39953.8			1.67996			0.839981	−	0.542615i	$-0.182566\pi$
$827$	39953.8			1.67996			0.839981	+	0.542615i	$0.182566\pi$
$828$	24402.0	+	1460.43i	1.02419	+	0.0612966i
$829$	20187.3			0.845760			0.422880	−	0.906186i	$-0.361019\pi$
$829$	20187.3			0.845760			0.422880	+	0.906186i	$0.361019\pi$
$830$	22142.3	−	31094.6i	0.925990	−	1.30037i
$831$	3851.88	+	7530.43i	0.160795	+	0.314353i
$832$	−2227.62	−	6436.28i	−0.0928231	−	0.268195i
$833$	438.539	−	226.083i	0.0182407	−	0.00940373i
$834$	4224.60	+	10650.8i	0.175403	+	0.442213i
$835$	28430.9	−	22358.3i	1.17832	−	0.926637i
$836$	−11724.2	−	3442.53i	−0.485035	−	0.142419i
$837$	−10160.1	+	7089.56i	−0.419574	+	0.292773i
$838$	−7850.82	+	54603.6i	−0.323630	+	2.25090i
$839$	10539.1	−	1006.36i	0.433669	−	0.0414104i	0.124061	−	0.992275i	$-0.460408\pi$
$839$	10539.1	−	1006.36i	0.433669	−	0.0414104i	0.309608	+	0.950864i	$0.399802\pi$
$840$	500.752	−	521.834i	0.0205686	−	0.0214345i
$841$	18700.3	+	14706.1i	0.766753	+	0.602981i
$842$	−2213.83	−	46473.9i	−0.0906099	−	1.90214i
$843$	−2181.06	+	22096.8i	−0.0891101	+	0.902792i
$844$	25888.0	−	20358.6i	1.05581	−	0.830298i
$845$	12737.8	+	14700.2i	0.518572	+	0.598464i
$846$	15917.9	+	3173.27i	0.646889	+	0.128959i
$847$	−9389.99	+	10836.6i	−0.380925	+	0.439611i
$848$	9904.27	+	9443.70i	0.401078	+	0.382427i
$849$	−32077.0	−	14772.8i	−1.29668	−	0.597175i
$850$	−828.547	+	1435.09i	−0.0334341	+	0.0579095i
$851$	−630.596	−	2194.66i	−0.0254014	−	0.0884043i
$852$	−23244.5	+	20012.2i	−0.934677	+	0.804702i
$853$	−11966.4	+	16804.4i	−0.480330	+	0.674529i	−0.981641	−	0.190738i	$-0.938912\pi$
$853$	−11966.4	+	16804.4i	−0.480330	+	0.674529i	0.501311	+	0.865267i	$0.332851\pi$
$854$	−26218.6	+	7698.47i	−1.05056	+	0.308473i
$855$	−5680.44	+	16080.2i	−0.227213	+	0.643196i
$856$	102.017	+	65.5625i	0.00407345	+	0.00261785i
$857$	−927.546	+	2679.97i	−0.0369713	+	0.106821i	−0.961976	−	0.273134i	$-0.911940\pi$
$857$	−927.546	+	2679.97i	−0.0369713	+	0.106821i	0.925005	+	0.379956i	$0.124061\pi$
$858$	5635.71	−	1930.45i	0.224242	−	0.0768118i
$859$	16478.4	−	15712.1i	0.654523	−	0.624087i	−0.288237	−	0.957559i	$-0.593069\pi$
$859$	16478.4	−	15712.1i	0.654523	−	0.624087i	0.942760	+	0.333473i	$0.108220\pi$
$860$	125.235	+	2629.00i	0.00496566	+	0.104242i
$861$	7104.48	−	13673.6i	0.281208	−	0.541226i
$862$	−18070.2	+	1725.49i	−0.714005	+	0.0681792i
$863$	5392.81	−	11808.6i	0.212716	−	0.465782i	−0.772956	−	0.634460i	$-0.781223\pi$
$863$	5392.81	−	11808.6i	0.212716	−	0.465782i	0.985671	+	0.168678i	$0.0539498\pi$
$864$	3777.43	−	35926.2i	0.148739	−	1.41462i
$865$	−9715.09	+	6243.51i	−0.381876	+	0.245417i
$866$	−11327.8	−	46694.0i	−0.444498	−	1.83225i
$867$	−4763.03	+	24296.1i	−0.186576	+	0.951717i
$868$	−12378.3	+	2385.73i	−0.484041	+	0.0932913i
$869$	−10274.4	+	5296.82i	−0.401076	+	0.206769i
$870$	4225.70	+	2457.70i	0.164672	+	0.0957744i
$871$	3066.57	+	2923.97i	0.119296	+	0.113748i
$872$	108.382	+	237.324i	0.00420904	+	0.00921651i
$873$	−1218.07	+	8104.86i	−0.0472228	+	0.314213i
$874$	−29331.2	−	1567.91i	−1.13517	−	0.0606812i
$875$	−13187.6	−	22841.5i	−0.509510	−	0.882496i
$876$	1593.84	+	734.028i	0.0614735	+	0.0283111i
$877$	11390.8	−	46953.4i	0.438585	−	1.80787i	−0.137522	−	0.990499i	$-0.543914\pi$
$877$	11390.8	−	46953.4i	0.438585	−	1.80787i	0.576107	−	0.817374i	$-0.304571\pi$
$878$	−16441.6	−	47504.8i	−0.631978	−	1.82598i
$879$	−31187.6	+	4382.71i	−1.19674	+	0.168174i
$880$	−4378.69	+	12651.4i	−0.167734	+	0.484634i
$881$	−4091.94	−	28460.1i	−0.156482	−	1.08836i	−0.905052	−	0.425302i	$-0.860168\pi$
$881$	−4091.94	−	28460.1i	−0.156482	−	1.08836i	0.748569	−	0.663056i	$-0.230741\pi$
$882$	−2532.42	−	3604.69i	−0.0966792	−	0.137615i
$883$	−24737.3	+	15897.7i	−0.942784	+	0.605890i	−0.919183	−	0.393831i	$-0.871149\pi$
$883$	−24737.3	+	15897.7i	−0.942784	+	0.605890i	−0.0236009	+	0.999721i	$0.507513\pi$
$884$	−1173.80	+	469.917i	−0.0446596	+	0.0178790i
$885$	25867.1	+	6362.63i	0.982501	+	0.241670i
$886$	39051.0	+	54839.4i	1.48075	+	2.07942i
$887$	−3340.16	−	2626.73i	−0.126439	−	0.0994330i	0.552937	−	0.833223i	$-0.313507\pi$
$887$	−3340.16	−	2626.73i	−0.126439	−	0.0994330i	−0.679376	+	0.733790i	$0.737750\pi$
$888$	87.6753	−	20.9742i	0.00331328	−	0.000792622i
$889$	6246.74	+	25749.4i	0.235668	+	0.971437i
$890$	−6926.23	−	48173.0i	−0.260863	−	1.81434i
$891$	16311.6	+	1767.64i	0.613310	+	0.0664626i
$892$	19799.1	+	12724.1i	0.743187	+	0.477617i
$893$	−9698.12	−	1869.16i	−0.363421	−	0.0700437i
$894$	−29936.7	−	1521.69i	−1.11995	−	0.0569271i
$895$	21929.8	+	2094.05i	0.819032	+	0.0782081i
$896$	932.511	−	1615.16i	0.0347690	−	0.0602217i
$897$	6135.82	−	3865.74i	0.228393	−	0.143894i
$898$	24324.5	+	42131.3i	0.903920	+	1.56563i
$899$	−897.681	−	1965.65i	−0.0333029	−	0.0729232i
$900$	6938.29	+	2829.11i	0.256974	+	0.104782i
$901$	1751.48	−	2021.31i	0.0647615	−	0.0747388i
$902$	735.134	−	15432.4i	0.0271367	−	0.569669i
$903$	−3002.22	−	441.423i	−0.110640	−	0.0162676i
$904$	−1832.46	−	733.608i	−0.0674191	−	0.0269905i
$905$	−27253.9	+	25986.6i	−1.00105	+	0.954500i
$906$	14547.2	−	48965.4i	0.533441	−	1.79555i
$907$	−25554.8	+	10230.6i	−0.935537	+	0.374532i	−0.788805	−	0.614644i	$-0.789300\pi$
$907$	−25554.8	+	10230.6i	−0.935537	+	0.374532i	−0.146732	+	0.989176i	$0.546875\pi$
$908$	12913.1	−	28275.6i	0.471955	−	1.03344i
$909$	42324.2	+	27582.8i	1.54434	+	1.00645i
$910$	1203.99	−	8373.91i	0.0438591	−	0.305047i
$911$	32844.9	+	16932.7i	1.19451	+	0.615814i	0.936616	−	0.350358i	$-0.113940\pi$
$911$	32844.9	+	16932.7i	1.19451	+	0.615814i	0.257897	+	0.966172i	$0.416970\pi$
$912$	−2102.97	+	21305.6i	−0.0763556	+	0.773574i
$913$	20746.1	+	8305.47i	0.752020	+	0.301064i
$914$	20488.2	−	3948.78i	0.741456	−	0.142904i
$915$	11922.0	+	15259.8i	0.430741	+	0.551339i
$916$	−24740.0	−	4768.24i	−0.892393	−	0.171995i
$917$	−39305.1	+	11541.0i	−1.41545	+	0.415614i
$918$	−6865.03	−	392.829i	−0.246819	−	0.0141234i
$919$	20902.2			0.750270			0.375135	−	0.926970i	$-0.377596\pi$
$919$	20902.2			0.750270			0.375135	+	0.926970i	$0.377596\pi$
$920$	89.0116	−	878.264i	0.00318981	−	0.0314734i
$921$	27330.0	+	9556.64i	0.977801	+	0.341913i
$922$	27978.1	+	2671.58i	0.999359	+	0.0954272i
$923$	−2145.24	+	8842.78i	−0.0765019	+	0.315345i
$924$	14431.2	+	8393.31i	0.513802	+	0.298831i
$925$	33.3031	−	699.118i	0.00118378	−	0.0248507i
$926$	32401.8	+	37393.7i	1.14988	+	1.32703i
$927$	14967.7	+	26310.7i	0.530319	+	0.932209i
$928$	6045.63	+	1775.16i	0.213855	+	0.0627935i
$929$	9905.12	+	5106.44i	0.349813	+	0.180341i	0.624173	−	0.781286i	$-0.285436\pi$
$929$	9905.12	+	5106.44i	0.349813	+	0.180341i	−0.274360	+	0.961627i	$0.588466\pi$
$930$	9489.95	+	14870.6i	0.334610	+	0.524330i
$931$	1554.92	+	2183.58i	0.0547374	+	0.0768679i
$932$	−14837.9	−	20836.9i	−0.521492	−	0.732333i
$933$	15016.5	+	23530.7i	0.526922	+	0.825680i
$934$	53161.1	+	27406.5i	1.86240	+	0.960136i
$935$	2510.50	+	737.148i	0.0878097	+	0.0257832i
$936$	141.569	+	248.855i	0.00494374	+	0.00869024i
$937$	16716.9	+	19292.3i	0.582836	+	0.672628i	0.968212	−	0.250131i	$-0.0804738\pi$
$937$	16716.9	+	19292.3i	0.582836	+	0.672628i	−0.385376	+	0.922760i	$0.625928\pi$
$938$	−1115.68	+	23420.9i	−0.0388360	+	0.815267i
$939$	7674.04	+	4463.27i	0.266702	+	0.155115i
$940$	2759.35	−	11374.2i	0.0957446	−	0.394665i
$941$	−21341.0	−	2037.82i	−0.739315	−	0.0705961i	−0.281398	−	0.959591i	$-0.590798\pi$
$941$	−21341.0	−	2037.82i	−0.739315	−	0.0705961i	−0.457917	+	0.888995i	$0.651404\pi$
$942$	12085.4	+	4225.98i	0.418009	+	0.146168i
$943$	−3452.20	−	18488.6i	−0.119214	−	0.638463i
$944$	33440.7			1.15297
$945$	12783.9	−	19480.2i	0.440065	−	0.670573i
$946$	−2919.27	+	857.176i	−0.100332	+	0.0294600i
$947$	−41889.0	−	8073.45i	−1.43739	−	0.277035i	−0.589743	−	0.807591i	$-0.700771\pi$
$947$	−41889.0	−	8073.45i	−1.43739	−	0.277035i	−0.847650	+	0.530556i	$0.821983\pi$
$948$	−13486.3	−	17262.2i	−0.462042	−	0.591403i
$949$	511.154	−	98.5169i	0.0174845	−	0.00336985i
$950$	−8358.31	−	3346.16i	−0.285452	−	0.114278i
$951$	−1858.71	+	18830.9i	−0.0633782	+	0.642097i
$952$	−157.718	−	81.3094i	−0.00536941	−	0.00276812i
$953$	−2039.29	+	14183.5i	−0.0693168	+	0.482109i	0.925362	+	0.379085i	$0.123761\pi$
$953$	−2039.29	+	14183.5i	−0.0693168	+	0.482109i	−0.994679	+	0.103024i	$0.967148\pi$
$954$	−20007.0	−	13038.6i	−0.678984	−	0.442496i
$955$	−8458.11	+	18520.7i	−0.286595	+	0.627555i
$956$	11259.6	−	4507.67i	0.380922	−	0.152498i
$957$	−814.996	+	2743.25i	−0.0275288	+	0.0926612i
$958$	2944.56	−	2807.64i	0.0993054	−	0.0946875i
$959$	−14400.4	−	5765.04i	−0.484893	−	0.194122i
$960$	−26425.8	−	3885.44i	−0.888426	−	0.130627i
$961$	−1046.47	+	21968.1i	−0.0351270	+	0.737406i
$962$	690.565	−	796.955i	0.0231442	−	0.0267098i
$963$	3617.71	+	1475.13i	0.121058	+	0.0493619i
$964$	−13883.9	−	30401.5i	−0.463870	−	1.01573i
$965$	−13670.1	−	23677.3i	−0.456016	−	0.789844i
$966$	38402.5	+	11652.1i	1.27907	+	0.388094i
$967$	22922.6	−	39703.1i	0.762296	−	1.32034i	−0.179368	−	0.983782i	$-0.557405\pi$
$967$	22922.6	−	39703.1i	0.762296	−	1.32034i	0.941664	−	0.336554i	$-0.109261\pi$
$968$	−687.829	−	65.6797i	−0.0228385	−	0.00218081i
$969$	4178.80	+	212.409i	0.138537	+	0.00704185i
$970$	11459.2	+	2208.57i	0.379311	+	0.0731062i
$971$	−29169.0	−	18745.8i	−0.964035	−	0.619548i	−0.0389233	−	0.999242i	$-0.512393\pi$
$971$	−29169.0	−	18745.8i	−0.964035	−	0.619548i	−0.925112	+	0.379694i	$0.876029\pi$
$972$	2462.03	+	30994.9i	0.0812446	+	1.02280i
$973$	1355.67	+	9428.89i	0.0446668	+	0.310664i
$974$	−304.205	−	1253.95i	−0.0100075	−	0.0412516i
$975$	2161.85	−	517.170i	0.0710098	−	0.0169874i
$976$	19109.0	+	15027.4i	0.626704	+	0.492845i
$977$	−16849.1	−	23661.3i	−0.551742	−	0.774813i	0.440684	−	0.897663i	$-0.354736\pi$
$977$	−16849.1	−	23661.3i	−0.551742	−	0.774813i	−0.992425	+	0.122850i	$0.960797\pi$
$978$	78386.8	+	19281.1i	2.56292	+	0.630411i
$979$	26450.2	−	10589.1i	0.863486	−	0.345688i
$980$	−2672.36	+	1717.42i	−0.0871076	+	0.0559807i
$981$	4831.91	+	6877.82i	0.157259	+	0.223845i
$982$	−10422.0	−	72486.7i	−0.338676	−	2.35554i
$983$	−3255.99	+	9407.58i	−0.105646	+	0.305244i	−0.985418	−	0.170152i	$-0.945574\pi$
$983$	−3255.99	+	9407.58i	−0.105646	+	0.305244i	0.879772	+	0.475396i	$0.157695\pi$
$984$	735.304	−	103.330i	0.0238218	−	0.00334761i
$985$	−5699.66	−	16468.1i	−0.184372	−	0.532708i
$986$	282.762	−	1165.56i	0.00913285	−	0.0376461i
$987$	12256.7	+	5644.72i	0.395274	+	0.182040i
$988$	−3434.74	−	5949.14i	−0.110601	−	0.191566i
$989$	−3218.33	+	1833.28i	−0.103475	+	0.0589432i
$990$	3472.06	−	23102.5i	0.111464	−	0.741662i
$991$	−12570.6	−	27525.8i	−0.402945	−	0.882327i	−0.996963	−	0.0778753i	$-0.975186\pi$
$991$	−12570.6	−	27525.8i	−0.402945	−	0.882327i	0.594018	−	0.804452i	$-0.297541\pi$
$992$	16456.0	+	15690.8i	0.526692	+	0.502200i
$993$	−29479.9	−	17145.7i	−0.942113	−	0.547939i
$994$	−44756.0	+	23073.3i	−1.42814	+	0.736259i
$995$	4861.35	−	936.949i	0.154890	−	0.0298525i
$996$	−8147.00	+	41557.6i	−0.259184	+	1.32209i
$997$	−14427.2	−	59469.6i	−0.458288	−	1.88909i	−0.457733	−	0.889090i	$-0.651338\pi$
$997$	−14427.2	−	59469.6i	−0.458288	−	1.88909i	−0.000555330	−	1.00000i	$-0.500177\pi$
$998$	−5603.35	+	3601.05i	−0.177726	+	0.114218i
$999$	2653.29	−	1181.20i	0.0840305	−	0.0374088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.4.m.a.4.12	✓	1400
9.7	even	3	inner	207.4.m.a.142.59	yes	1400
23.6	even	11	inner	207.4.m.a.121.59	yes	1400
207.52	even	33	inner	207.4.m.a.52.12	yes	1400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.4.m.a.4.12	✓	1400	1.1	even	1	trivial
207.4.m.a.52.12	yes	1400	207.52	even	33	inner
207.4.m.a.121.59	yes	1400	23.6	even	11	inner
207.4.m.a.142.59	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+(-2.33527 + 3.27943i) q^{2} +(-5.18945 - 0.263780i) q^{3} +(-2.68463 - 7.75672i) q^{4} +(-8.48781 + 4.37577i) q^{5} +(12.9838 - 16.4025i) q^{6} +(13.6708 - 10.7509i) q^{7} +(0.804118 + 0.236110i) q^{8} +(26.8608 + 2.73775i) q^{9} +(5.47131 - 38.0538i) q^{10} +(22.4044 - 2.13936i) q^{11} +(11.8857 + 40.9613i) q^{12} +(9.94578 + 7.82145i) q^{13} +(3.33159 + 69.9387i) q^{14} +(45.2013 - 20.4689i) q^{15} +(48.9643 - 38.5059i) q^{16} +(-7.97239 - 9.20063i) q^{17} +(-71.7057 + 81.6949i) q^{18} +(43.3151 - 49.9883i) q^{19} +(56.7283 + 54.0903i) q^{20} +(-73.7800 + 52.1850i) q^{21} +(-45.3045 + 78.4696i) q^{22} +(-31.6901 + 105.654i) q^{23} +(-4.11065 - 1.43739i) q^{24} +(-19.6115 + 27.5405i) q^{25} +(-48.8760 + 14.3513i) q^{26} +(-138.671 - 21.2928i) q^{27} +(-120.093 - 77.1788i) q^{28} +(8.00359 - 23.1249i) q^{29} +(-38.4310 + 196.035i) q^{30} +(63.9104 - 60.9385i) q^{31} +(12.2517 + 257.194i) q^{32} +(-116.831 + 5.19226i) q^{33} +(48.7905 - 4.65893i) q^{34} +(-68.9921 + 151.072i) q^{35} +(-50.8754 - 215.702i) q^{36} +(-17.4152 + 11.1921i) q^{37} +(62.7806 + 258.785i) q^{38} +(-49.5500 - 43.2125i) q^{39} +(-7.85837 + 1.51458i) q^{40} +(-151.557 + 78.1328i) q^{41} +(1.15933 - 363.823i) q^{42} +(24.3019 + 23.1719i) q^{43} +(-76.7419 - 168.041i) q^{44} +(-239.970 + 94.2994i) q^{45} +(-272.480 - 350.656i) q^{46} +(-74.6599 - 129.315i) q^{47} +(-264.255 + 186.909i) q^{48} +(-9.55467 + 39.3849i) q^{49} +(-44.5191 - 128.629i) q^{50} +(38.9454 + 49.8492i) q^{51} +(33.9681 - 98.1444i) q^{52} +(31.2655 + 217.457i) q^{53} +(393.663 - 405.037i) q^{54} +(-180.803 + 116.195i) q^{55} +(13.5314 - 5.41714i) q^{56} +(-237.968 + 247.986i) q^{57} +(57.1458 + 80.2501i) q^{58} +(421.987 + 331.854i) q^{59} +(-280.121 - 295.663i) q^{60} +(92.0080 + 379.262i) q^{61} +(50.5953 + 351.898i) q^{62} +(396.643 - 251.350i) q^{63} +(-452.838 - 291.021i) q^{64} +(-118.643 - 22.8665i) q^{65} +(255.804 - 395.264i) q^{66} +(333.361 + 31.8322i) q^{67} +(-49.9638 + 86.5399i) q^{68} +(192.324 - 539.926i) q^{69} +(-334.314 - 579.049i) q^{70} +(298.746 + 654.162i) q^{71} +(20.9529 + 8.54360i) q^{72} +(26.9422 - 31.0930i) q^{73} +(3.96562 - 83.2485i) q^{74} +(109.038 - 137.747i) q^{75} +(-504.030 - 201.783i) q^{76} +(283.287 - 270.113i) q^{77} +(257.425 - 61.5828i) q^{78} +(-476.817 + 190.889i) q^{79} +(-247.107 + 541.088i) q^{80} +(714.009 + 147.077i) q^{81} +(97.6946 - 679.481i) q^{82} +(882.537 + 454.979i) q^{83} +(602.856 + 432.194i) q^{84} +(107.928 + 43.2078i) q^{85} +(-132.742 + 25.5840i) q^{86} +(-47.6342 + 117.894i) q^{87} +(18.5209 + 3.56961i) q^{88} +(1214.64 - 356.650i) q^{89} +(251.146 - 1007.18i) q^{90} +220.054 q^{91} +(904.604 - 37.8301i) q^{92} +(-347.734 + 299.379i) q^{93} +(598.430 + 57.1432i) q^{94} +(-148.913 + 613.828i) q^{95} +(4.26334 - 1337.93i) q^{96} +(-14.4435 + 303.207i) q^{97} +(-106.847 - 123.308i) q^{98} +(607.658 + 3.87268i) 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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