LMFDB - Embedded newform 197.3.i.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,3,Mod(2,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(196))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("197.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	197.i (of order $196$, degree $84$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.36786120790$
Analytic rank:	$0$
Dimension:	$2688$
Relative dimension:	$32$ over $\Q(\zeta_{196})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{196}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	197.2
Dual form			197.3.i.a.99.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.90099 - 0.0465026i) q^{2} +(-0.438834 + 0.107589i) q^{3} +(4.41565 + 0.141601i) q^{4} +(-1.33348 - 9.17958i) q^{5} +(1.27806 - 0.291708i) q^{6} +(6.15258 - 6.35304i) q^{7} +(-1.21114 - 0.0582831i) q^{8} +(-7.79839 + 4.06842i) q^{9} +O(q^{10})$	\(q+(-2.90099 - 0.0465026i) q^{2} +(-0.438834 + 0.107589i) q^{3} +(4.41565 + 0.141601i) q^{4} +(-1.33348 - 9.17958i) q^{5} +(1.27806 - 0.291708i) q^{6} +(6.15258 - 6.35304i) q^{7} +(-1.21114 - 0.0582831i) q^{8} +(-7.79839 + 4.06842i) q^{9} +(3.44154 + 26.6919i) q^{10} +(15.1946 + 7.61973i) q^{11} +(-1.95297 + 0.412936i) q^{12} +(-17.2282 - 7.29847i) q^{13} +(-18.1440 + 18.1440i) q^{14} +(1.57280 + 3.88484i) q^{15} +(-14.1246 - 0.906828i) q^{16} +(12.9627 - 8.73674i) q^{17} +(22.8123 - 11.4398i) q^{18} +(4.74138 - 3.78112i) q^{19} +(-4.58834 - 40.7226i) q^{20} +(-2.01644 + 3.44988i) q^{21} +(-43.7251 - 22.8114i) q^{22} +(6.08495 - 16.5348i) q^{23} +(0.537758 - 0.104728i) q^{24} +(-58.5198 + 17.3684i) q^{25} +(49.6396 + 21.9740i) q^{26} +(6.03823 - 5.30967i) q^{27} +(28.0672 - 27.1816i) q^{28} +(-33.2570 - 21.6479i) q^{29} +(-4.38202 - 11.3430i) q^{30} +(-19.0625 + 23.1330i) q^{31} +(45.7677 + 3.67582i) q^{32} +(-7.48771 - 1.70902i) q^{33} +(-38.0110 + 24.7424i) q^{34} +(-66.5226 - 48.0064i) q^{35} +(-35.0111 + 16.8604i) q^{36} +(-50.1136 + 3.21740i) q^{37} +(-13.9305 + 10.7485i) q^{38} +(8.34557 + 1.34925i) q^{39} +(1.08001 + 11.1954i) q^{40} +(8.45826 - 43.4314i) q^{41} +(6.01011 - 9.91430i) q^{42} +(12.7732 + 38.4710i) q^{43} +(66.0151 + 35.7976i) q^{44} +(47.7453 + 66.1608i) q^{45} +(-18.4213 + 47.6843i) q^{46} +(12.8822 + 22.8736i) q^{47} +(6.29591 - 1.12170i) q^{48} +(-0.936398 - 29.2003i) q^{49} +(170.573 - 47.6642i) q^{50} +(-4.74850 + 5.22862i) q^{51} +(-75.0404 - 34.6670i) q^{52} +(9.32717 + 21.0702i) q^{53} +(-17.7638 + 15.1225i) q^{54} +(49.6842 - 149.641i) q^{55} +(-7.82188 + 7.33581i) q^{56} +(-1.67387 + 2.16940i) q^{57} +(95.4717 + 64.3470i) q^{58} +(-60.4494 - 7.79409i) q^{59} +(6.39483 + 17.3768i) q^{60} +(-4.06681 - 6.70863i) q^{61} +(56.3758 - 66.2222i) q^{62} +(-22.1334 + 74.5748i) q^{63} +(-76.2478 - 7.35554i) q^{64} +(-44.0234 + 167.880i) q^{65} +(21.6423 + 5.30605i) q^{66} +(38.0471 + 10.6317i) q^{67} +(58.4759 - 36.7428i) q^{68} +(-0.891322 + 7.91070i) q^{69} +(190.749 + 142.360i) q^{70} +(-34.9925 - 10.9988i) q^{71} +(9.68204 - 4.47289i) q^{72} +(-33.6462 - 29.5865i) q^{73} +(145.529 - 7.00324i) q^{74} +(23.8118 - 13.9179i) q^{75} +(21.4717 - 16.0247i) q^{76} +(141.894 - 49.6510i) q^{77} +(-24.1477 - 4.30225i) q^{78} +(9.25861 - 63.7356i) q^{79} +(10.5105 + 130.867i) q^{80} +(43.2118 - 61.9473i) q^{81} +(-26.5570 + 125.601i) q^{82} +(24.6037 + 19.6208i) q^{83} +(-9.39241 + 14.9479i) q^{84} +(-97.4851 - 107.342i) q^{85} +(-35.2661 - 112.198i) q^{86} +(16.9234 + 5.92175i) q^{87} +(-17.9586 - 10.1141i) q^{88} +(55.7211 + 67.6197i) q^{89} +(-135.432 - 194.152i) q^{90} +(-152.366 + 64.5473i) q^{91} +(29.2104 - 72.1502i) q^{92} +(5.87639 - 12.2025i) q^{93} +(-36.3075 - 66.9553i) q^{94} +(-41.0316 - 38.4818i) q^{95} +(-20.4799 + 3.31103i) q^{96} +(9.92086 + 37.8325i) q^{97} +(1.35859 + 84.7535i) q^{98} +(-149.494 + 2.39637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9}+O(q^{10}) $ 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 140 * q^8 - 84 * q^9	\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9} - 84 q^{10} - 140 q^{11} - 140 q^{12} - 84 q^{13} - 28 q^{14} - 84 q^{15} + 112 q^{16} - 84 q^{17} - 210 q^{18} - 98 q^{19} - 84 q^{20} - 84 q^{21} - 84 q^{22} - 84 q^{23} - 308 q^{24} - 84 q^{25} + 70 q^{26} - 126 q^{27} - 910 q^{28} - 294 q^{29} + 70 q^{30} - 84 q^{31} - 84 q^{32} - 98 q^{33} - 84 q^{34} - 84 q^{35} + 2198 q^{36} + 126 q^{37} - 140 q^{38} - 84 q^{39} + 476 q^{40} + 28 q^{41} - 588 q^{42} - 84 q^{43} - 84 q^{44} - 966 q^{45} - 448 q^{46} + 266 q^{47} - 1428 q^{48} + 756 q^{49} - 84 q^{50} - 84 q^{51} + 126 q^{52} - 84 q^{53} - 588 q^{54} - 84 q^{55} - 84 q^{56} - 672 q^{57} + 532 q^{58} + 616 q^{59} - 378 q^{60} - 364 q^{61} - 854 q^{62} + 1036 q^{63} - 1428 q^{64} + 28 q^{65} + 406 q^{66} - 84 q^{67} - 966 q^{68} - 504 q^{69} - 84 q^{70} + 434 q^{71} - 532 q^{72} - 84 q^{73} + 546 q^{74} - 84 q^{75} - 308 q^{76} + 700 q^{77} + 2310 q^{78} - 1400 q^{79} - 84 q^{80} - 700 q^{81} - 84 q^{82} - 98 q^{83} - 588 q^{84} + 1666 q^{85} - 84 q^{86} - 84 q^{87} + 420 q^{88} + 868 q^{89} - 1890 q^{90} + 1260 q^{91} + 924 q^{92} - 98 q^{93} - 420 q^{94} - 1834 q^{95} + 364 q^{96} + 504 q^{97} - 980 q^{98} + 630 q^{99}+O(q^{100}) \) 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 140 * q^8 - 84 * q^9 - 84 * q^10 - 140 * q^11 - 140 * q^12 - 84 * q^13 - 28 * q^14 - 84 * q^15 + 112 * q^16 - 84 * q^17 - 210 * q^18 - 98 * q^19 - 84 * q^20 - 84 * q^21 - 84 * q^22 - 84 * q^23 - 308 * q^24 - 84 * q^25 + 70 * q^26 - 126 * q^27 - 910 * q^28 - 294 * q^29 + 70 * q^30 - 84 * q^31 - 84 * q^32 - 98 * q^33 - 84 * q^34 - 84 * q^35 + 2198 * q^36 + 126 * q^37 - 140 * q^38 - 84 * q^39 + 476 * q^40 + 28 * q^41 - 588 * q^42 - 84 * q^43 - 84 * q^44 - 966 * q^45 - 448 * q^46 + 266 * q^47 - 1428 * q^48 + 756 * q^49 - 84 * q^50 - 84 * q^51 + 126 * q^52 - 84 * q^53 - 588 * q^54 - 84 * q^55 - 84 * q^56 - 672 * q^57 + 532 * q^58 + 616 * q^59 - 378 * q^60 - 364 * q^61 - 854 * q^62 + 1036 * q^63 - 1428 * q^64 + 28 * q^65 + 406 * q^66 - 84 * q^67 - 966 * q^68 - 504 * q^69 - 84 * q^70 + 434 * q^71 - 532 * q^72 - 84 * q^73 + 546 * q^74 - 84 * q^75 - 308 * q^76 + 700 * q^77 + 2310 * q^78 - 1400 * q^79 - 84 * q^80 - 700 * q^81 - 84 * q^82 - 98 * q^83 - 588 * q^84 + 1666 * q^85 - 84 * q^86 - 84 * q^87 + 420 * q^88 + 868 * q^89 - 1890 * q^90 + 1260 * q^91 + 924 * q^92 - 98 * q^93 - 420 * q^94 - 1834 * q^95 + 364 * q^96 + 504 * q^97 - 980 * q^98 + 630 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{196}\right)$

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 $

$2$	−2.90099	−	0.0465026i	−1.45050	−	0.0232513i	−0.714215	−	0.699927i	$-0.753216\pi$
$2$	−2.90099	−	0.0465026i	−1.45050	−	0.0232513i	−0.736282	+	0.676675i	$0.763420\pi$
$3$	−0.438834	+	0.107589i	−0.146278	+	0.0358630i	−0.310581	−	0.950547i	$-0.600524\pi$
$3$	−0.438834	+	0.107589i	−0.146278	+	0.0358630i	0.164303	+	0.986410i	$0.447462\pi$
$4$	4.41565	+	0.141601i	1.10391	+	0.0354003i
$5$	−1.33348	−	9.17958i	−0.266696	−	1.83592i	−0.503061	−	0.864251i	$-0.667793\pi$
$5$	−1.33348	−	9.17958i	−0.266696	−	1.83592i	0.236365	−	0.971664i	$-0.424044\pi$
$6$	1.27806	−	0.291708i	0.213009	−	0.0486180i
$7$	6.15258	−	6.35304i	0.878940	−	0.907577i	−0.117398	−	0.993085i	$-0.537455\pi$
$7$	6.15258	−	6.35304i	0.878940	−	0.907577i	0.996338	+	0.0855076i	$0.0272512\pi$
$8$	−1.21114	−	0.0582831i	−0.151392	−	0.00728539i
$9$	−7.79839	+	4.06842i	−0.866488	+	0.452046i
$10$	3.44154	+	26.6919i	0.344154	+	2.66919i
$11$	15.1946	+	7.61973i	1.38133	+	0.692703i	0.975244	−	0.221133i	$-0.0709755\pi$
$11$	15.1946	+	7.61973i	1.38133	+	0.692703i	0.406085	+	0.913836i	$0.366894\pi$
$12$	−1.95297	+	0.412936i	−0.162748	+	0.0344113i
$13$	−17.2282	−	7.29847i	−1.32525	−	0.561421i	−0.391773	−	0.920062i	$-0.628138\pi$
$13$	−17.2282	−	7.29847i	−1.32525	−	0.561421i	−0.933476	+	0.358641i	$0.883240\pi$
$14$	−18.1440	+	18.1440i	−1.29600	+	1.29600i
$15$	1.57280	+	3.88484i	0.104853	+	0.258989i
$16$	−14.1246	−	0.906828i	−0.882787	−	0.0566768i
$17$	12.9627	−	8.73674i	0.762512	−	0.513926i	−0.115067	−	0.993358i	$-0.536708\pi$
$17$	12.9627	−	8.73674i	0.762512	−	0.513926i	0.877579	+	0.479432i	$0.159157\pi$
$18$	22.8123	−	11.4398i	1.26735	−	0.635545i
$19$	4.74138	−	3.78112i	0.249546	−	0.199006i	−0.490726	−	0.871314i	$-0.663268\pi$
$19$	4.74138	−	3.78112i	0.249546	−	0.199006i	0.740272	+	0.672308i	$0.234697\pi$
$20$	−4.58834	−	40.7226i	−0.229417	−	2.03613i
$21$	−2.01644	+	3.44988i	−0.0960210	+	0.164280i
$22$	−43.7251	−	22.8114i	−1.98751	−	1.03688i
$23$	6.08495	−	16.5348i	0.264563	−	0.718904i	−0.734619	−	0.678479i	$-0.762639\pi$
$23$	6.08495	−	16.5348i	0.264563	−	0.718904i	0.999183	−	0.0404243i	$-0.0128710\pi$
$24$	0.537758	−	0.104728i	0.0224066	−	0.00436368i
$25$	−58.5198	+	17.3684i	−2.34079	+	0.694735i
$26$	49.6396	+	21.9740i	1.90921	+	0.845153i
$27$	6.03823	−	5.30967i	0.223638	−	0.196655i
$28$	28.0672	−	27.1816i	1.00240	−	0.970771i
$29$	−33.2570	−	21.6479i	−1.14679	−	0.746480i	−0.175528	−	0.984474i	$-0.556163\pi$
$29$	−33.2570	−	21.6479i	−1.14679	−	0.746480i	−0.971267	+	0.237994i	$0.923510\pi$
$30$	−4.38202	−	11.3430i	−0.146067	−	0.378101i
$31$	−19.0625	+	23.1330i	−0.614918	+	0.746226i	−0.983008	−	0.183564i	$-0.941236\pi$
$31$	−19.0625	+	23.1330i	−0.614918	+	0.746226i	0.368090	+	0.929790i	$0.380012\pi$
$32$	45.7677	+	3.67582i	1.43024	+	0.114869i
$33$	−7.48771	−	1.70902i	−0.226900	−	0.0517885i
$34$	−38.0110	+	24.7424i	−1.11797	+	0.727718i
$35$	−66.5226	−	48.0064i	−1.90064	−	1.37161i
$36$	−35.0111	+	16.8604i	−0.972530	+	0.468346i
$37$	−50.1136	+	3.21740i	−1.35442	+	0.0869568i	−0.724271	−	0.689515i	$-0.757824\pi$
$37$	−50.1136	+	3.21740i	−1.35442	+	0.0869568i	−0.630151	+	0.776472i	$0.717007\pi$
$38$	−13.9305	+	10.7485i	−0.366593	+	0.282856i
$39$	8.34557	+	1.34925i	0.213989	+	0.0345961i
$40$	1.08001	+	11.1954i	0.0270003	+	0.279886i
$41$	8.45826	−	43.4314i	0.206299	−	1.05930i	−0.723245	−	0.690591i	$-0.757350\pi$
$41$	8.45826	−	43.4314i	0.206299	−	1.05930i	0.929544	−	0.368711i	$-0.120201\pi$
$42$	6.01011	−	9.91430i	0.143098	−	0.236055i
$43$	12.7732	+	38.4710i	0.297052	+	0.894674i	0.985542	+	0.169428i	$0.0541922\pi$
$43$	12.7732	+	38.4710i	0.297052	+	0.894674i	−0.688490	+	0.725246i	$0.741726\pi$
$44$	66.0151	+	35.7976i	1.50034	+	0.813582i
$45$	47.7453	+	66.1608i	1.06101	+	1.47024i
$46$	−18.4213	+	47.6843i	−0.400463	+	1.03662i
$47$	12.8822	+	22.8736i	0.274089	+	0.486673i	0.973695	−	0.227856i	$-0.0731716\pi$
$47$	12.8822	+	22.8736i	0.274089	+	0.486673i	−0.699606	+	0.714529i	$0.746641\pi$
$48$	6.29591	−	1.12170i	0.131165	−	0.0233688i
$49$	−0.936398	−	29.2003i	−0.0191102	−	0.595925i
$50$	170.573	−	47.6642i	3.41146	−	0.953283i
$51$	−4.74850	+	5.22862i	−0.0931078	+	0.102522i
$52$	−75.0404	−	34.6670i	−1.44308	−	0.666674i
$53$	9.32717	+	21.0702i	0.175984	+	0.397551i	0.980538	−	0.196328i	$-0.0629017\pi$
$53$	9.32717	+	21.0702i	0.175984	+	0.397551i	−0.804554	+	0.593879i	$0.797596\pi$
$54$	−17.7638	+	15.1225i	−0.328959	+	0.280047i
$55$	49.6842	−	149.641i	0.903349	−	2.72074i
$56$	−7.82188	+	7.33581i	−0.139676	+	0.130997i
$57$	−1.67387	+	2.16940i	−0.0293661	+	0.0380597i
$58$	95.4717	+	64.3470i	1.64606	+	1.10943i
$59$	−60.4494	−	7.79409i	−1.02457	−	0.132103i	−0.402785	−	0.915295i	$-0.631958\pi$
$59$	−60.4494	−	7.79409i	−1.02457	−	0.132103i	−0.621781	+	0.783191i	$0.713591\pi$
$60$	6.39483	+	17.3768i	0.106580	+	0.289613i
$61$	−4.06681	−	6.70863i	−0.0666691	−	0.109978i	0.820038	−	0.572308i	$-0.193952\pi$
$61$	−4.06681	−	6.70863i	−0.0666691	−	0.109978i	−0.886707	+	0.462331i	$0.847013\pi$
$62$	56.3758	−	66.2222i	0.909287	−	1.06810i
$63$	−22.1334	+	74.5748i	−0.351324	+	1.18373i
$64$	−76.2478	−	7.35554i	−1.19137	−	0.114930i
$65$	−44.0234	+	167.880i	−0.677283	+	2.58277i
$66$	21.6423	+	5.30605i	0.327914	+	0.0803948i
$67$	38.0471	+	10.6317i	0.567867	+	0.158682i	0.541098	−	0.840960i	$-0.318009\pi$
$67$	38.0471	+	10.6317i	0.567867	+	0.158682i	0.0267688	+	0.999642i	$0.491478\pi$
$68$	58.4759	−	36.7428i	0.859940	−	0.540336i
$69$	−0.891322	+	7.91070i	−0.0129177	+	0.114648i
$70$	190.749	+	142.360i	2.72499	+	2.03371i
$71$	−34.9925	−	10.9988i	−0.492852	−	0.154913i	0.0432539	−	0.999064i	$-0.486228\pi$
$71$	−34.9925	−	10.9988i	−0.492852	−	0.154913i	−0.536106	+	0.844151i	$0.680105\pi$
$72$	9.68204	−	4.47289i	0.134473	−	0.0621235i
$73$	−33.6462	−	29.5865i	−0.460907	−	0.405295i	0.398033	−	0.917371i	$-0.369693\pi$
$73$	−33.6462	−	29.5865i	−0.460907	−	0.405295i	−0.858940	+	0.512076i	$0.828877\pi$
$74$	145.529	−	7.00324i	1.96661	−	0.0946384i
$75$	23.8118	−	13.9179i	0.317491	−	0.185572i
$76$	21.4717	−	16.0247i	0.282522	−	0.210852i
$77$	141.894	−	49.6510i	1.84279	−	0.644818i
$78$	−24.1477	−	4.30225i	−0.309586	−	0.0551570i
$79$	9.25861	−	63.7356i	0.117198	−	0.806780i	−0.845066	−	0.534662i	$-0.820439\pi$
$79$	9.25861	−	63.7356i	0.117198	−	0.806780i	0.962264	−	0.272118i	$-0.0877242\pi$
$80$	10.5105	+	130.867i	0.131382	+	1.63584i
$81$	43.2118	−	61.9473i	0.533478	−	0.764781i
$82$	−26.5570	+	125.601i	−0.323866	+	1.53172i
$83$	24.6037	+	19.6208i	0.296430	+	0.236395i	0.760399	−	0.649457i	$-0.225004\pi$
$83$	24.6037	+	19.6208i	0.296430	+	0.236395i	−0.463969	+	0.885852i	$0.653575\pi$
$84$	−9.39241	+	14.9479i	−0.111814	+	0.177952i
$85$	−97.4851	−	107.342i	−1.14688	−	1.26285i
$86$	−35.2661	−	112.198i	−0.410071	−	1.30463i
$87$	16.9234	+	5.92175i	0.194522	+	0.0680661i
$88$	−17.9586	−	10.1141i	−0.204075	−	0.114933i
$89$	55.7211	+	67.6197i	0.626080	+	0.759771i	0.984803	−	0.173672i	$-0.0555634\pi$
$89$	55.7211	+	67.6197i	0.626080	+	0.759771i	−0.358723	+	0.933444i	$0.616788\pi$
$90$	−135.432	−	194.152i	−1.50480	−	2.15725i
$91$	−152.366	+	64.5473i	−1.67435	+	0.709311i
$92$	29.2104	−	72.1502i	0.317504	−	0.784241i
$93$	5.87639	−	12.2025i	0.0631870	−	0.131209i
$94$	−36.3075	−	66.9553i	−0.386249	−	0.712290i
$95$	−41.0316	−	38.4818i	−0.431912	−	0.405071i
$96$	−20.4799	+	3.31103i	−0.213332	+	0.0344899i
$97$	9.92086	+	37.8325i	0.102277	+	0.390026i	0.998571	−	0.0534331i	$-0.0170164\pi$
$97$	9.92086	+	37.8325i	0.102277	+	0.390026i	−0.896295	+	0.443459i	$0.853751\pi$
$98$	1.35859	+	84.7535i	0.0138632	+	0.864832i
$99$	−149.494	+	2.39637i	−1.51004	+	0.0242058i
$100$	−260.862	+	68.4061i	−2.60862	+	0.684061i
$101$	8.97185	+	55.4940i	0.0888301	+	0.549446i	0.992600	+	0.121428i	$0.0387473\pi$
$101$	8.97185	+	55.4940i	0.0888301	+	0.549446i	−0.903770	+	0.428018i	$0.859212\pi$
$102$	14.0185	−	14.9474i	0.137436	−	0.146543i
$103$	114.885	−	62.2979i	1.11539	−	0.604834i	0.189215	−	0.981936i	$-0.439406\pi$
$103$	114.885	−	62.2979i	1.11539	−	0.604834i	0.926172	+	0.377102i	$0.123079\pi$
$104$	20.4404	+	9.84356i	0.196542	+	0.0946496i
$105$	34.3573	+	13.9097i	0.327213	+	0.132474i
$106$	−26.0782	−	61.5583i	−0.246021	−	0.580739i
$107$	−15.2314	+	10.6248i	−0.142349	+	0.0992968i	−0.641133	−	0.767430i	$-0.721535\pi$
$107$	−15.2314	+	10.6248i	−0.142349	+	0.0992968i	0.498784	+	0.866727i	$0.333780\pi$
$108$	27.4146	−	22.5906i	0.253839	−	0.209173i
$109$	34.1773	−	60.6853i	0.313554	−	0.556746i	−0.668877	−	0.743373i	$-0.733225\pi$
$109$	34.1773	−	60.6853i	0.313554	−	0.556746i	0.982431	+	0.186627i	$0.0597555\pi$
$110$	−151.092	+	431.797i	−1.37356	+	3.92542i
$111$	21.6454	−	6.80358i	0.195004	−	0.0612935i
$112$	−92.6637	+	84.1547i	−0.827355	+	0.751382i
$113$	−186.040	−	116.897i	−1.64637	−	1.03448i	−0.947763	−	0.318977i	$-0.896661\pi$
$113$	−186.040	−	116.897i	−1.64637	−	1.03448i	−0.698607	−	0.715506i	$-0.746196\pi$
$114$	4.95676	−	6.21558i	0.0434804	−	0.0545227i
$115$	−159.897	−	33.8085i	−1.39040	−	0.293987i
$116$	−143.786	−	100.299i	−1.23954	−	0.864646i
$117$	164.046	−	13.1753i	1.40210	−	0.112609i
$118$	175.001	+	25.4216i	1.48306	+	0.215438i
$119$	24.2492	−	136.106i	0.203775	−	1.14375i
$120$	−1.67845	−	4.79674i	−0.0139871	−	0.0399728i
$121$	100.445	+	134.587i	0.830120	+	1.11229i
$122$	11.4858	+	19.6508i	0.0941461	+	0.161072i
$123$	0.960971	+	19.9692i	0.00781277	+	0.162351i
$124$	−87.4488	+	99.4480i	−0.705232	+	0.802000i
$125$	140.214	+	303.508i	1.12171	+	2.42806i
$126$	67.6768	−	215.312i	0.537117	−	1.70882i
$127$	77.4290	−	103.748i	0.609677	−	0.816912i	−0.384674	−	0.923052i	$-0.625686\pi$
$127$	77.4290	−	103.748i	0.609677	−	0.816912i	0.994351	+	0.106141i	$0.0338494\pi$
$128$	38.3468	+	4.32064i	0.299584	+	0.0337550i
$129$	−9.74439	−	15.5081i	−0.0755379	−	0.120218i
$130$	135.518	−	484.972i	1.04245	−	3.73056i
$131$	28.6126	−	116.705i	0.218416	−	0.890876i	−0.753859	−	0.657037i	$-0.771810\pi$
$131$	28.6126	−	116.705i	0.218416	−	0.890876i	0.972275	−	0.233840i	$-0.0751291\pi$
$132$	−32.8211	−	8.60671i	−0.248645	−	0.0652023i
$133$	5.15006	−	53.3858i	0.0387223	−	0.401397i
$134$	−109.880	−	32.6118i	−0.819999	−	0.243371i
$135$	−56.7924	−	48.3481i	−0.420685	−	0.358134i
$136$	−16.2088	+	9.82587i	−0.119182	+	0.0722490i
$137$	203.166	−	74.7670i	1.48296	−	0.545745i	0.529781	−	0.848135i	$-0.322274\pi$
$137$	203.166	−	74.7670i	1.48296	−	0.545745i	0.953184	+	0.302390i	$0.0977845\pi$
$138$	2.95359	−	22.9074i	0.0214028	−	0.165996i
$139$	−120.884	+	179.355i	−0.869668	+	1.29033i	0.0861245	+	0.996284i	$0.472552\pi$
$139$	−120.884	+	179.355i	−0.869668	+	1.29033i	−0.955792	+	0.294042i	$0.904999\pi$
$140$	−286.943	−	221.399i	−2.04959	−	1.58142i
$141$	−8.11409	−	8.65174i	−0.0575468	−	0.0613599i
$142$	101.001	+	33.5348i	0.711278	+	0.236160i
$143$	−206.164	−	242.172i	−1.44171	−	1.69351i
$144$	113.838	−	50.3929i	0.790545	−	0.349951i
$145$	−154.371	+	334.153i	−1.06463	+	2.30450i
$146$	96.2315	+	87.3949i	0.659120	+	0.598595i
$147$	3.55256	+	12.7134i	0.0241671	+	0.0864854i
$148$	−221.740	+	7.11076i	−1.49824	+	0.0480457i
$149$	−13.1914	−	74.0406i	−0.0885326	−	0.496917i	−0.996896	−	0.0787343i	$-0.974912\pi$
$149$	−13.1914	−	74.0406i	−0.0885326	−	0.496917i	0.908363	−	0.418183i	$-0.137333\pi$
$150$	−69.7251	+	39.2684i	−0.464834	+	0.261790i
$151$	41.6942	+	16.1072i	0.276121	+	0.106670i	0.494454	−	0.869204i	$-0.335368\pi$
$151$	41.6942	+	16.1072i	0.276121	+	0.106670i	−0.218333	+	0.975874i	$0.570062\pi$
$152$	−5.96283	+	4.30311i	−0.0392291	+	0.0283099i
$153$	−65.5436	+	120.870i	−0.428389	+	0.790001i
$154$	−413.944	+	137.439i	−2.68795	+	0.892460i
$155$	237.771	+	144.138i	1.53400	+	0.929922i
$156$	36.6601	+	7.13954i	0.235000	+	0.0457663i
$157$	258.650	−	24.9516i	1.64745	−	0.158928i	0.769819	−	0.638262i	$-0.220347\pi$
$157$	258.650	−	24.9516i	1.64745	−	0.158928i	0.877632	+	0.479335i	$0.159122\pi$
$158$	−29.8230	+	184.466i	−0.188753	+	1.16751i
$159$	−6.36000	−	8.24283i	−0.0400000	−	0.0518417i
$160$	−27.2878	−	425.030i	−0.170549	−	2.65644i
$161$	−67.6080	−	140.390i	−0.419926	−	0.871985i
$162$	−128.238	+	177.699i	−0.791591	+	1.09691i
$163$	−40.5463	−	62.2900i	−0.248750	−	0.382147i	0.691641	−	0.722241i	$-0.256888\pi$
$163$	−40.5463	−	62.2900i	−0.248750	−	0.382147i	−0.940391	+	0.340094i	$0.889541\pi$
$164$	43.4987	−	190.580i	0.265236	−	1.16207i
$165$	−5.70338	+	71.0129i	−0.0345660	+	0.430381i
$166$	−70.4627	−	58.0639i	−0.424474	−	0.349782i
$167$	207.189	−	80.0410i	1.24066	−	0.479288i	0.351196	−	0.936302i	$-0.385775\pi$
$167$	207.189	−	80.0410i	1.24066	−	0.479288i	0.889459	+	0.457015i	$0.151081\pi$
$168$	2.64325	−	4.06075i	0.0157337	−	0.0241711i
$169$	125.974	+	130.079i	0.745409	+	0.769696i
$170$	277.812	+	315.931i	1.63419	+	1.85842i
$171$	−21.5919	+	48.7766i	−0.126269	+	0.285243i
$172$	50.9546	+	171.683i	0.296248	+	0.998158i
$173$	−0.839333	−	4.30980i	−0.00485164	−	0.0249121i	0.979054	−	0.203599i	$-0.0652640\pi$
$173$	−0.839333	−	4.30980i	−0.00485164	−	0.0249121i	−0.983906	+	0.178687i	$0.942815\pi$
$174$	−48.8193	−	17.9659i	−0.280570	−	0.103253i
$175$	−249.706	+	478.639i	−1.42689	+	2.73508i
$176$	−207.708	−	121.404i	−1.18016	−	0.689798i
$177$	27.3658	−	3.08338i	0.154609	−	0.0174203i
$178$	−158.502	−	198.755i	−0.890461	−	1.11660i
$179$	−127.054	−	253.360i	−0.709798	−	1.41542i	−0.900979	−	0.433863i	$-0.857150\pi$
$179$	−127.054	−	253.360i	−0.709798	−	1.41542i	0.191181	−	0.981555i	$-0.438768\pi$
$180$	201.458	+	298.904i	1.11921	+	1.66058i
$181$	14.9242	−	232.457i	0.0824543	−	1.28429i	−0.722673	−	0.691190i	$-0.757087\pi$
$181$	14.9242	−	232.457i	0.0824543	−	1.28429i	0.805127	−	0.593102i	$-0.202097\pi$
$182$	445.013	−	180.166i	2.44513	−	0.989922i
$183$	2.50643	+	2.50643i	0.0136963	+	0.0136963i
$184$	−8.33341	+	19.6712i	−0.0452902	+	0.106909i
$185$	96.3599	+	455.732i	0.520864	+	2.46341i
$186$	−17.6148	+	35.1260i	−0.0947033	+	0.188849i
$187$	263.535	−	33.9791i	1.40928	−	0.181706i
$188$	53.6443	+	102.826i	0.285342	+	0.546947i
$189$	3.41812	−	71.0293i	0.0180853	−	0.375817i
$190$	117.243	+	113.543i	0.617068	+	0.597597i
$191$	50.2370	+	220.103i	0.263021	+	1.15237i	0.917955	+	0.396684i	$0.129839\pi$
$191$	50.2370	+	220.103i	0.263021	+	1.15237i	−0.654934	+	0.755686i	$0.727304\pi$
$192$	34.2515	−	4.97557i	0.178393	−	0.0259145i
$193$	7.86891	−	245.382i	0.0407715	−	1.27141i	−0.750882	−	0.660436i	$-0.770371\pi$
$193$	7.86891	−	245.382i	0.0407715	−	1.27141i	0.791653	−	0.610970i	$-0.209221\pi$
$194$	−27.0210	−	110.213i	−0.139284	−	0.568110i
$195$	1.25687	−	78.4080i	0.00644550	−	0.402092i
$196$		−	129.071i		−	0.658526i
$197$	77.8456	−	180.967i	0.395155	−	0.918614i
$197$	77.8456	−	180.967i	0.395155	−	0.918614i
$198$	433.792			2.19087
$199$	36.8008	+	0.589913i	0.184929	+	0.00296439i	0.108423	−	0.994105i	$-0.465420\pi$
$199$	36.8008	+	0.589913i	0.184929	+	0.00296439i	0.0765051	+	0.997069i	$0.475624\pi$
$200$	71.8877	−	17.6247i	0.359438	−	0.0881237i
$201$	−17.8402	−	0.572100i	−0.0887572	−	0.00284627i
$202$	−23.4466	−	161.405i	−0.116072	−	0.799035i
$203$	−342.147	+	78.0928i	−1.68545	+	0.384693i
$204$	−21.7081	+	22.4154i	−0.106412	+	0.109879i
$205$	−409.961	−	19.7284i	−1.99981	−	0.0962362i
$206$	−336.177	+	175.383i	−1.63193	+	0.851375i
$207$	19.8175	+	153.701i	0.0957369	+	0.742516i
$208$	236.723	+	118.711i	1.13809	+	0.570726i
$209$	100.854	−	21.3247i	0.482557	−	0.102032i
$210$	−99.0235	−	41.9497i	−0.471540	−	0.199761i
$211$	−145.026	+	145.026i	−0.687327	+	0.687327i	−0.961640	−	0.274314i	$-0.911549\pi$
$211$	−145.026	+	145.026i	−0.687327	+	0.687327i	0.274314	+	0.961640i	$0.411549\pi$
$212$	38.2019	+	94.3595i	0.180198	+	0.445092i
$213$	16.5392	+	1.06185i	0.0776490	+	0.00498523i
$214$	44.6802	−	30.1140i	0.208786	−	0.140720i
$215$	336.115	−	168.553i	1.56332	−	0.783969i
$216$	−7.62259	+	6.07881i	−0.0352897	+	0.0281426i
$217$	29.6817	+	263.432i	0.136782	+	1.21397i
$218$	−101.970	+	174.458i	−0.467753	+	0.800268i
$219$	17.9483	+	9.36360i	0.0819556	+	0.0427562i
$220$	240.577	−	653.726i	1.09353	−	2.97148i
$221$	−287.089	+	55.9107i	−1.29905	+	0.252989i
$222$	−63.1095	+	18.7306i	−0.284277	+	0.0843720i
$223$	−48.5475	−	21.4905i	−0.217702	−	0.0963701i	0.293054	−	0.956096i	$-0.405328\pi$
$223$	−48.5475	−	21.4905i	−0.217702	−	0.0963701i	−0.510756	+	0.859726i	$0.670634\pi$
$224$	304.942	−	268.148i	1.36135	−	1.19709i
$225$	385.699	−	373.528i	1.71422	−	1.66013i
$226$	534.264	+	347.767i	2.36400	+	1.53879i
$227$	152.059	+	393.612i	0.669865	+	1.73397i	0.679132	+	0.734016i	$0.262356\pi$
$227$	152.059	+	393.612i	0.669865	+	1.73397i	−0.00926681	+	0.999957i	$0.502950\pi$
$228$	−7.69841	+	9.34231i	−0.0337649	+	0.0409750i
$229$	−121.691	−	9.77355i	−0.531400	−	0.0426793i	−0.188540	−	0.982066i	$-0.560375\pi$
$229$	−121.691	−	9.77355i	−0.531400	−	0.0426793i	−0.342861	+	0.939386i	$0.611396\pi$
$230$	462.286	+	105.514i	2.00994	+	0.458756i
$231$	−56.9262	+	37.0548i	−0.246434	+	0.160411i
$232$	39.0171	+	28.1569i	0.168177	+	0.121366i
$233$	230.442	−	110.975i	0.989022	−	0.476288i	0.131823	−	0.991273i	$-0.457917\pi$
$233$	230.442	−	110.975i	0.989022	−	0.476288i	0.857199	+	0.514985i	$0.172203\pi$
$234$	−476.508	+	30.5929i	−2.03636	+	0.130739i
$235$	192.792	−	148.755i	0.820392	−	0.632998i
$236$	−265.820	−	42.9757i	−1.12635	−	0.182100i
$237$	2.79426	+	28.9655i	0.0117901	+	0.122217i
$238$	−76.6760	+	393.715i	−0.322168	+	1.65426i
$239$	104.017	−	171.586i	0.435216	−	0.717934i	−0.558544	−	0.829475i	$-0.688640\pi$
$239$	104.017	−	171.586i	0.435216	−	0.717934i	0.993760	+	0.111541i	$0.0355786\pi$
$240$	−18.6922	−	56.2980i	−0.0778843	−	0.234575i
$241$	−165.304	−	89.6387i	−0.685911	−	0.371945i	0.0959603	−	0.995385i	$-0.469408\pi$
$241$	−165.304	−	89.6387i	−0.685911	−	0.371945i	−0.781871	+	0.623440i	$0.785734\pi$
$242$	−285.130	−	395.106i	−1.17822	−	1.63267i
$243$	−38.3760	+	99.3379i	−0.157926	+	0.408798i
$244$	−17.0077	−	30.1988i	−0.0697036	−	0.123766i
$245$	−266.798	+	47.5338i	−1.08897	+	0.194015i
$246$	−1.85915	−	57.9751i	−0.00755752	−	0.235671i
$247$	−109.282	+	30.5372i	−0.442437	+	0.123633i
$248$	24.4355	−	26.9062i	0.0985302	−	0.108493i
$249$	−12.9079	−	5.96317i	−0.0518390	−	0.0239485i
$250$	−392.646	−	886.994i	−1.57058	−	3.54797i
$251$	62.3496	−	53.0790i	0.248405	−	0.211470i	−0.515344	−	0.856983i	$-0.672336\pi$
$251$	62.3496	−	53.0790i	0.248405	−	0.211470i	0.763749	+	0.645513i	$0.223356\pi$
$252$	−108.293	+	326.162i	−0.429735	+	1.29429i
$253$	218.449	−	204.874i	0.863435	−	0.809778i
$254$	−229.445	+	297.371i	−0.903328	+	1.17075i
$255$	54.3286	+	36.6169i	0.213053	+	0.143596i
$256$	192.849	+	24.8651i	0.753316	+	0.0971293i
$257$	−68.5363	−	186.235i	−0.266678	−	0.724650i	−0.999043	−	0.0437381i	$-0.986073\pi$
$257$	−68.5363	−	186.235i	−0.266678	−	0.724650i	0.732365	−	0.680912i	$-0.238417\pi$
$258$	27.5472	+	45.4420i	0.106772	+	0.176132i
$259$	−287.888	+	338.169i	−1.11154	+	1.30567i
$260$	−218.164	+	735.067i	−0.839092	+	2.82718i
$261$	347.424	+	33.5156i	1.33113	+	0.128412i
$262$	−88.4319	+	337.229i	−0.337526	+	1.28713i
$263$	−250.220	−	61.3465i	−0.951407	−	0.233257i	−0.268102	−	0.963390i	$-0.586397\pi$
$263$	−250.220	−	61.3465i	−0.951407	−	0.233257i	−0.683304	+	0.730134i	$0.739458\pi$
$264$	8.96903	+	2.50626i	0.0339736	+	0.00949342i
$265$	180.978	−	113.716i	0.682937	−	0.429118i
$266$	−17.4229	+	154.632i	−0.0654995	+	0.581324i
$267$	−31.7274	−	23.6788i	−0.118829	−	0.0886847i
$268$	166.497	+	52.3334i	0.621258	+	0.195274i
$269$	47.1284	−	21.7723i	0.175199	−	0.0809380i	−0.329831	−	0.944040i	$-0.606992\pi$
$269$	47.1284	−	21.7723i	0.175199	−	0.0809380i	0.505030	+	0.863102i	$0.331482\pi$
$270$	162.506	+	142.898i	0.601874	+	0.529253i
$271$	199.217	−	9.58687i	0.735119	−	0.0353759i	0.322865	−	0.946445i	$-0.395354\pi$
$271$	199.217	−	9.58687i	0.735119	−	0.0353759i	0.412254	+	0.911069i	$0.364742\pi$
$272$	−191.016	+	111.648i	−0.702263	+	0.410470i
$273$	59.9186	−	44.7184i	0.219482	−	0.163804i
$274$	−592.860	+	207.451i	−2.16372	+	0.757120i
$275$	−1021.53	−	181.999i	−3.71465	−	0.661816i
$276$	−5.05593	+	34.8047i	−0.0183186	+	0.126104i
$277$	−13.1132	−	163.273i	−0.0473401	−	0.589432i	−0.975896	−	0.218238i	$-0.929969\pi$
$277$	−13.1132	−	163.273i	−0.0473401	−	0.589432i	0.928555	−	0.371194i	$-0.121051\pi$
$278$	359.024	−	514.687i	1.29145	−	1.85139i
$279$	54.5418	−	257.954i	0.195490	−	0.924567i
$280$	77.7699	+	62.0194i	0.277750	+	0.221498i
$281$	33.4940	−	53.3054i	0.119196	−	0.189699i	−0.781797	−	0.623533i	$-0.785697\pi$
$281$	33.4940	−	53.3054i	0.119196	−	0.189699i	0.900993	+	0.433834i	$0.142840\pi$
$282$	23.1366	+	25.4760i	0.0820447	+	0.0903403i
$283$	69.1301	+	219.935i	0.244276	+	0.777156i	0.993397	+	0.114724i	$0.0365983\pi$
$283$	69.1301	+	219.935i	0.244276	+	0.777156i	−0.749122	+	0.662433i	$0.769524\pi$
$284$	−152.957	−	53.5220i	−0.538581	−	0.188458i
$285$	22.1463	+	12.4726i	0.0777062	+	0.0437633i
$286$	586.818	+	712.126i	2.05181	+	2.48995i
$287$	−223.881	−	320.951i	−0.780074	−	1.11829i
$288$	−371.870	+	157.537i	−1.29121	+	0.547002i
$289$	−16.7511	+	41.3754i	−0.0579621	+	0.143168i
$290$	463.369	−	962.196i	1.59782	−	3.31792i
$291$	−8.42398	−	15.5348i	−0.0289484	−	0.0533843i
$292$	−144.380	−	135.408i	−0.494453	−	0.463726i
$293$	−83.2864	+	13.4651i	−0.284254	+	0.0459560i	−0.300064	−	0.953919i	$-0.597008\pi$
$293$	−83.2864	+	13.4651i	−0.284254	+	0.0459560i	0.0158102	+	0.999875i	$0.494967\pi$
$294$	−9.71475	−	37.0465i	−0.0330434	−	0.126009i
$295$	9.06160	+	565.293i	0.0307173	+	1.91625i
$296$	60.8819	−	0.975932i	0.205682	−	0.00329707i
$297$	132.207	−	34.6687i	0.445141	−	0.116730i
$298$	34.8250	+	215.405i	0.116862	+	0.722835i
$299$	−225.512	+	240.454i	−0.754220	+	0.804195i
$300$	107.115	−	58.0848i	0.357051	−	0.193616i
$301$	322.996	+	155.547i	1.07308	+	0.516767i
$302$	−120.206	−	48.6658i	−0.398032	−	0.161145i
$303$	−9.90770	−	23.3874i	−0.0326987	−	0.0771861i
$304$	−70.3988	+	49.1071i	−0.231575	+	0.161537i
$305$	−56.1594	+	46.2774i	−0.184129	+	0.151729i
$306$	195.762	−	347.596i	0.639746	−	1.13593i
$307$	−21.9304	+	62.6736i	−0.0714346	+	0.204148i	−0.974065	−	0.226268i	$-0.927348\pi$
$307$	−21.9304	+	62.6736i	−0.0714346	+	0.204148i	0.902630	+	0.430416i	$0.141633\pi$
$308$	633.587	−	199.149i	2.05710	−	0.646588i
$309$	−43.7128	+	39.6988i	−0.141465	+	0.128475i
$310$	−683.068	−	429.200i	−2.20344	−	1.38452i
$311$	281.109	−	352.500i	0.903888	−	1.13344i	−0.0866550	−	0.996238i	$-0.527618\pi$
$311$	281.109	−	352.500i	0.903888	−	1.13344i	0.990543	−	0.137202i	$-0.0438108\pi$
$312$	−10.0290	−	2.12053i	−0.0321442	−	0.00679656i
$313$	54.7905	+	38.2195i	0.175049	+	0.122107i	0.656374	−	0.754435i	$-0.272089\pi$
$313$	54.7905	+	38.2195i	0.175049	+	0.122107i	−0.481325	+	0.876542i	$0.659844\pi$
$314$	−751.501	+	60.3566i	−2.39332	+	0.192219i
$315$	714.079	+	103.731i	2.26692	+	0.329306i
$316$	49.9078	−	280.123i	0.157936	−	0.886466i
$317$	6.85023	+	19.5768i	0.0216096	+	0.0617566i	0.954183	−	0.299224i	$-0.0967278\pi$
$317$	6.85023	+	19.5768i	0.0216096	+	0.0617566i	−0.932573	+	0.360981i	$0.882442\pi$
$318$	18.0670	+	24.2081i	0.0568145	+	0.0761262i
$319$	−340.376	−	582.342i	−1.06701	−	1.82552i
$320$	34.1542	+	709.731i	0.106732	+	2.21791i
$321$	5.54094	−	6.30123i	0.0172615	−	0.0196300i
$322$	189.602	+	410.413i	0.588826	+	1.27457i
$323$	28.4264	−	90.4377i	0.0880074	−	0.279993i
$324$	199.580	−	267.419i	0.615987	−	0.825366i
$325$	1134.96	+	127.879i	3.49217	+	0.393473i
$326$	114.728	+	182.588i	0.351926	+	0.560087i
$327$	−8.46909	+	30.3079i	−0.0258994	+	0.0926846i
$328$	−12.7754	+	52.1083i	−0.0389495	+	0.158867i
$329$	224.576	+	58.8907i	0.682601	+	0.178999i
$330$	19.8478	−	205.743i	0.0601447	−	0.623463i
$331$	−448.298	−	133.052i	−1.35437	−	0.401971i	−0.475790	−	0.879559i	$-0.657838\pi$
$331$	−448.298	−	133.052i	−1.35437	−	0.401971i	−0.878584	+	0.477587i	$0.841511\pi$
$332$	105.863	+	90.1224i	0.318864	+	0.271453i
$333$	377.716	−	228.974i	1.13428	−	0.687609i
$334$	−604.777	+	222.564i	−1.81071	+	0.666358i
$335$	46.8595	−	363.433i	0.139879	−	1.08488i
$336$	31.6098	−	46.8995i	0.0940769	−	0.139582i
$337$	190.362	+	146.880i	0.564873	+	0.435845i	0.853123	−	0.521710i	$-0.174706\pi$
$337$	190.362	+	146.880i	0.564873	+	0.435845i	−0.288249	+	0.957555i	$0.593073\pi$
$338$	−359.401	−	383.215i	−1.06332	−	1.13377i
$339$	94.2173	+	31.2823i	0.277927	+	0.0922782i
$340$	−415.260	−	487.788i	−1.22135	−	1.43467i
$341$	−465.914	+	206.246i	−1.36632	+	0.604828i
$342$	64.9063	−	140.496i	0.189784	−	0.410808i
$343$	129.530	+	117.635i	0.377637	+	0.342960i
$344$	−13.2279	−	47.3381i	−0.0384533	−	0.137611i
$345$	73.8054	−	2.36680i	0.213929	−	0.00686028i
$346$	2.23448	+	12.5417i	0.00645804	+	0.0362478i
$347$	−148.060	+	83.3857i	−0.426685	+	0.240305i	−0.689123	−	0.724644i	$-0.742004\pi$
$347$	−148.060	+	83.3857i	−0.426685	+	0.240305i	0.262438	+	0.964949i	$0.415474\pi$
$348$	73.8893	+	28.5448i	0.212325	+	0.0820252i
$349$	−517.773	+	373.654i	−1.48359	+	1.07064i	−0.505410	+	0.862879i	$0.668659\pi$
$349$	−517.773	+	373.654i	−1.48359	+	1.07064i	−0.978179	+	0.207762i	$0.933382\pi$
$350$	746.652	−	1376.92i	2.13329	−	3.93404i
$351$	−142.781	+	47.4064i	−0.406782	+	0.135061i
$352$	667.414	+	404.590i	1.89606	+	1.14940i
$353$	234.587	+	45.6857i	0.664551	+	0.129421i	0.512148	−	0.858897i	$-0.328850\pi$
$353$	234.587	+	45.6857i	0.664551	+	0.129421i	0.152403	+	0.988318i	$0.451299\pi$
$354$	−79.5314	+	7.67229i	−0.224665	+	0.0216731i
$355$	−54.3029	+	335.883i	−0.152966	+	0.946149i
$356$	236.470	+	306.475i	0.664241	+	0.860885i
$357$	4.00216	+	62.3369i	0.0112105	+	0.174613i
$358$	356.800	+	740.903i	0.996649	+	2.06956i
$359$	−33.7330	+	46.7439i	−0.0939639	+	0.130206i	−0.855261	−	0.518197i	$-0.826603\pi$
$359$	−33.7330	+	46.7439i	−0.0939639	+	0.130206i	0.761298	+	0.648403i	$0.224563\pi$
$360$	−53.9700	−	82.9125i	−0.149917	−	0.230312i
$361$	−72.1463	+	316.094i	−0.199851	+	0.875605i
$362$	−54.1049	+	673.661i	−0.149461	+	1.86094i
$363$	−58.5585	−	48.2544i	−0.161318	−	0.132932i
$364$	−681.933	+	263.443i	−1.87344	+	0.723745i
$365$	−226.725	+	348.311i	−0.621165	+	0.954276i
$366$	−7.15458	−	7.38769i	−0.0195480	−	0.0201850i
$367$	48.5825	+	55.2487i	0.132377	+	0.150541i	0.813365	−	0.581753i	$-0.197633\pi$
$367$	48.5825	+	55.2487i	0.132377	+	0.150541i	−0.680988	+	0.732295i	$0.738449\pi$
$368$	−100.942	+	228.029i	−0.274298	+	0.619644i
$369$	110.736	+	373.107i	0.300098	+	1.01113i
$370$	−258.347	−	1326.55i	−0.698234	−	3.58528i
$371$	191.246	+	70.3804i	0.515488	+	0.189704i
$372$	27.6760	−	53.0497i	0.0743978	−	0.142607i
$373$	−66.0000	−	38.5768i	−0.176944	−	0.103423i	0.413491	−	0.910508i	$-0.364309\pi$
$373$	−66.0000	−	38.5768i	−0.176944	−	0.103423i	−0.590435	+	0.807085i	$0.701044\pi$
$374$	−766.093	+	86.3179i	−2.04838	+	0.230797i
$375$	−94.1847	−	118.104i	−0.251159	−	0.314944i
$376$	−14.2689	−	28.4539i	−0.0379493	−	0.0756752i
$377$	414.963	+	615.681i	1.10070	+	1.63311i
$378$	−13.2190	+	205.897i	−0.0349709	+	0.544700i
$379$	173.054	−	70.0620i	0.456608	−	0.184860i	−0.135402	−	0.990791i	$-0.543233\pi$
$379$	173.054	−	70.0620i	0.456608	−	0.184860i	0.592010	+	0.805931i	$0.298335\pi$
$380$	−175.732	−	175.732i	−0.462453	−	0.462453i
$381$	−22.8163	+	53.8585i	−0.0598854	+	0.141361i
$382$	−135.502	−	640.852i	−0.354717	−	1.67762i
$383$	21.9978	−	43.8661i	0.0574355	−	0.114533i	−0.863345	−	0.504614i	$-0.831635\pi$
$383$	21.9978	−	43.8661i	0.0574355	−	0.114533i	0.920780	+	0.390081i	$0.127553\pi$
$384$	−17.2927	+	2.22965i	−0.0450331	+	0.00580638i
$385$	−644.989	−	1236.32i	−1.67530	−	3.21123i
$386$	−34.2385	+	711.484i	−0.0887009	+	1.84322i
$387$	−256.127	−	248.045i	−0.661826	−	0.640943i
$388$	38.4499	+	168.460i	0.0990977	+	0.434175i
$389$	−663.179	+	96.3373i	−1.70483	+	0.247654i	−0.925442	−	0.378888i	$-0.876306\pi$
$389$	−663.179	+	96.3373i	−1.70483	+	0.247654i	−0.779388	+	0.626542i	$0.784470\pi$
$390$	−7.29236	+	227.403i	−0.0186983	+	0.583083i
$391$	−65.5826	−	267.498i	−0.167731	−	0.684139i
$392$	−0.567782	+	35.4202i	−0.00144842	+	0.0903575i
$393$			54.2924i			0.138149i
$394$	−234.245	+	521.364i	−0.594530	+	1.32326i
$395$	−597.412			−1.51244
$396$	−660.452	−	10.5870i	−1.66781	−	0.0267348i
$397$	−237.047	+	58.1168i	−0.597095	+	0.146390i	−0.525137	−	0.851018i	$-0.675986\pi$
$397$	−237.047	+	58.1168i	−0.597095	+	0.146390i	−0.0719579	+	0.997408i	$0.522925\pi$
$398$	−106.731	−	3.42267i	−0.268169	−	0.00859966i
$399$	3.48371	+	23.9816i	0.00873109	+	0.0601042i
$400$	842.318	−	192.254i	2.10579	−	0.480634i
$401$	−143.844	+	148.531i	−0.358713	+	0.370400i	−0.873422	−	0.486965i	$-0.838104\pi$
$401$	−143.844	+	148.531i	−0.358713	+	0.370400i	0.514709	+	0.857365i	$0.327900\pi$
$402$	51.7277	+	2.48927i	0.128676	+	0.00619223i
$403$	497.248	−	259.414i	1.23387	−	0.643707i
$404$	31.7585	+	246.313i	0.0786101	+	0.609685i
$405$	−626.272	−	314.060i	−1.54635	−	0.775457i
$406$	996.197	−	210.636i	2.45369	−	0.518807i
$407$	−785.973	−	332.965i	−1.93114	−	0.818096i
$408$	6.05581	−	6.05581i	0.0148427	−	0.0148427i
$409$	−10.3283	−	25.5110i	−0.0252525	−	0.0623741i	0.913766	−	0.406242i	$-0.133161\pi$
$409$	−10.3283	−	25.5110i	−0.0252525	−	0.0623741i	−0.939018	+	0.343867i	$0.888263\pi$
$410$	1188.38	+	76.2962i	2.89848	+	0.186088i
$411$	−81.1121	+	54.6688i	−0.197353	+	0.133014i
$412$	516.113	−	258.818i	1.25270	−	0.628199i
$413$	−421.436	+	336.084i	−1.02043	+	0.813762i
$414$	−50.3430	−	446.807i	−0.121602	−	1.07924i
$415$	147.302	−	252.015i	0.354944	−	0.607266i
$416$	−761.669	−	397.362i	−1.83094	−	0.955198i
$417$	33.7512	−	91.7130i	0.0809382	−	0.219935i
$418$	−293.570	+	57.1727i	−0.702320	+	0.136777i
$419$	602.873	−	178.930i	1.43884	−	0.427040i	0.531362	−	0.847145i	$-0.321680\pi$
$419$	602.873	−	178.930i	1.43884	−	0.427040i	0.907475	+	0.420105i	$0.138007\pi$
$420$	149.740	+	66.2856i	0.356524	+	0.157823i
$421$	358.417	−	315.171i	0.851346	−	0.748625i	−0.118341	−	0.992973i	$-0.537758\pi$
$421$	358.417	−	315.171i	0.851346	−	0.748625i	0.969688	+	0.244348i	$0.0785740\pi$
$422$	427.463	−	413.975i	1.01295	−	0.980984i
$423$	−193.520	−	125.967i	−0.457494	−	0.297795i
$424$	−10.0684	−	26.0625i	−0.0237463	−	0.0614682i
$425$	−606.832	+	736.413i	−1.42784	+	1.73274i
$426$	−47.9308	−	3.84955i	−0.112514	−	0.00903650i
$427$	−67.6416	−	15.4388i	−0.158411	−	0.0361563i
$428$	−68.7609	+	44.7584i	−0.160656	+	0.104576i
$429$	116.527	+	84.0922i	0.271624	+	0.196019i
$430$	−982.904	+	473.342i	−2.28582	+	1.10079i
$431$	821.195	−	52.7225i	1.90532	−	0.122326i	0.933581	−	0.358366i	$-0.116666\pi$
$431$	821.195	−	52.7225i	1.90532	−	0.122326i	0.971743	+	0.236040i	$0.0758495\pi$
$432$	−90.1025	+	69.5213i	−0.208571	+	0.160929i
$433$	−362.578	−	58.6187i	−0.837362	−	0.135378i	−0.274146	−	0.961688i	$-0.588395\pi$
$433$	−362.578	−	58.6187i	−0.837362	−	0.135378i	−0.563216	+	0.826310i	$0.690436\pi$
$434$	−73.8560	−	765.595i	−0.170175	−	1.76404i
$435$	31.7922	−	163.246i	0.0730855	−	0.375278i
$436$	159.508	−	263.126i	0.365845	−	0.603499i
$437$	−33.6690	−	101.406i	−0.0770457	−	0.232049i
$438$	−51.6324	−	27.9984i	−0.117882	−	0.0639232i
$439$	128.450	+	177.994i	0.292598	+	0.405453i	0.931446	−	0.363879i	$-0.118548\pi$
$439$	128.450	+	177.994i	0.292598	+	0.405453i	−0.638848	+	0.769333i	$0.720589\pi$
$440$	−68.8958	+	178.340i	−0.156581	+	0.405317i
$441$	126.102	+	223.906i	0.285945	+	0.507724i
$442$	835.444	−	148.846i	1.89015	−	0.336756i
$443$	−10.2233	−	318.800i	−0.0230774	−	0.719638i	−0.944010	−	0.329916i	$-0.892979\pi$
$443$	−10.2233	−	318.800i	−0.0230774	−	0.719638i	0.920933	−	0.389722i	$-0.127429\pi$
$444$	96.5419	−	26.9772i	0.217437	−	0.0607595i
$445$	546.417	−	601.666i	1.22790	−	1.35206i
$446$	139.837	+	64.6015i	0.313535	+	0.144846i
$447$	13.7548	+	31.0723i	0.0307713	+	0.0695129i
$448$	−515.851	+	439.150i	−1.15145	+	0.980246i
$449$	9.22619	−	27.7878i	0.0205483	−	0.0618882i	−0.938277	−	0.345885i	$-0.887579\pi$
$449$	9.22619	−	27.7878i	0.0205483	−	0.0618882i	0.958825	+	0.283997i	$0.0916604\pi$
$450$	−1136.28	+	1065.67i	−2.52506	+	2.36815i
$451$	459.455	−	595.473i	1.01875	−	1.32034i
$452$	−804.934	−	542.518i	−1.78083	−	1.20026i
$453$	−20.0298	−	2.58255i	−0.0442159	−	0.00570100i
$454$	−422.819	−	1148.94i	−0.931320	−	2.53070i
$455$	795.693	+	1312.58i	1.74878	+	2.88479i
$456$	2.15372	−	2.52988i	0.00472307	−	0.00554799i
$457$	70.0115	−	235.892i	0.153198	−	0.516175i	−0.846675	−	0.532110i	$-0.821399\pi$
$457$	70.0115	−	235.892i	0.153198	−	0.516175i	0.999873	+	0.0159353i	$0.00507258\pi$
$458$	352.569	+	34.0119i	0.769802	+	0.0742619i
$459$	31.8826	−	121.582i	0.0694610	−	0.264885i
$460$	−701.260	−	171.928i	−1.52448	−	0.373757i
$461$	767.347	+	214.424i	1.66453	+	0.465128i	0.967699	−	0.252109i	$-0.0811243\pi$
$461$	767.347	+	214.424i	1.66453	+	0.465128i	0.696829	+	0.717237i	$0.254594\pi$
$462$	166.866	−	104.849i	0.361181	−	0.226945i
$463$	−18.6088	+	165.157i	−0.0401917	+	0.356711i	0.957479	+	0.288502i	$0.0931572\pi$
$463$	−18.6088	+	165.157i	−0.0401917	+	0.356711i	−0.997671	+	0.0682094i	$0.978271\pi$
$464$	450.111	+	335.926i	0.970067	+	0.723980i
$465$	−119.849	−	37.6711i	−0.257741	−	0.0810131i
$466$	−673.671	+	311.222i	−1.44565	+	0.667858i
$467$	−222.350	−	195.522i	−0.476124	−	0.418676i	0.388228	−	0.921564i	$-0.373087\pi$
$467$	−222.350	−	195.522i	−0.476124	−	0.418676i	−0.864352	+	0.502887i	$0.832271\pi$
$468$	726.234	−	34.9484i	1.55178	−	0.0746760i
$469$	301.631	−	176.302i	0.643137	−	0.375911i
$470$	−566.206	+	422.571i	−1.20469	+	0.899086i
$471$	−110.820	+	38.7775i	−0.235286	+	0.0823302i
$472$	72.7582	+	12.9629i	0.154149	+	0.0274637i
$473$	−99.0539	+	681.880i	−0.209416	+	1.44161i
$474$	−6.75917	−	84.1586i	−0.0142598	−	0.177550i
$475$	−211.792	+	303.620i	−0.445879	+	0.639201i
$476$	126.349	−	597.563i	0.265438	−	1.25538i
$477$	−158.459	−	126.367i	−0.332200	−	0.264921i
$478$	−309.731	+	492.933i	−0.647972	+	1.03124i
$479$	575.329	+	633.501i	1.20110	+	1.32255i	0.933309	+	0.359074i	$0.116907\pi$
$479$	575.329	+	633.501i	1.20110	+	1.32255i	0.267796	+	0.963476i	$0.413705\pi$
$480$	57.7034	+	183.582i	0.120215	+	0.382462i
$481$	886.852	+	310.323i	1.84377	+	0.645162i
$482$	475.379	+	267.728i	0.986262	+	0.555453i
$483$	44.7731	+	54.3338i	0.0926979	+	0.112492i
$484$	424.470	+	608.510i	0.877005	+	1.25725i
$485$	334.057	−	141.518i	0.688778	−	0.291790i
$486$	115.948	−	286.394i	0.238576	−	0.589288i
$487$	98.8714	−	205.308i	0.203021	−	0.421578i	−0.774453	−	0.632631i	$-0.781975\pi$
$487$	98.8714	−	205.308i	0.203021	−	0.421578i	0.977475	+	0.211053i	$0.0676893\pi$
$488$	4.53446	+	8.36209i	0.00929193	+	0.0171354i
$489$	24.4948	+	22.9726i	0.0500916	+	0.0469787i
$490$	776.190	−	125.488i	1.58406	−	0.256099i
$491$	18.0436	+	68.8080i	0.0367486	+	0.140138i	0.983128	−	0.182919i	$-0.0585546\pi$
$491$	18.0436	+	68.8080i	0.0367486	+	0.140138i	−0.946379	+	0.323057i	$0.895289\pi$
$492$	1.41565	+	88.3130i	0.00287733	+	0.179498i
$493$	−620.233	+	9.94228i	−1.25808	+	0.0201669i
$494$	318.446	−	83.5064i	0.644628	−	0.169041i
$495$	221.345	+	1369.09i	0.447161	+	2.76585i
$496$	290.227	−	309.458i	0.585135	−	0.623907i
$497$	−285.170	+	154.637i	−0.573783	+	0.311142i
$498$	37.1684	+	17.8994i	0.0746354	+	0.0359425i
$499$	−400.062	−	161.967i	−0.801727	−	0.324583i	−0.0625048	−	0.998045i	$-0.519909\pi$
$499$	−400.062	−	161.967i	−0.801727	−	0.324583i	−0.739223	+	0.673461i	$0.764807\pi$
$500$	576.159	+	1360.04i	1.15232	+	2.72008i
$501$	−82.3102	+	57.4160i	−0.164292	+	0.114603i
$502$	−183.344	+	151.082i	−0.365227	+	0.300961i
$503$	467.495	−	830.084i	0.929413	−	1.65027i	0.184793	−	0.982777i	$-0.440839\pi$
$503$	467.495	−	830.084i	0.929413	−	1.65027i	0.744620	−	0.667489i	$-0.232631\pi$
$504$	31.1530	−	89.0302i	0.0618115	−	0.176647i
$505$	497.448	−	156.358i	0.985046	−	0.309620i
$506$	−643.246	+	584.179i	−1.27124	+	1.15450i
$507$	−69.2767	−	43.5294i	−0.136640	−	0.0858569i
$508$	356.590	−	447.150i	0.701949	−	0.880216i
$509$	409.610	+	86.6079i	0.804734	+	0.170153i	0.590929	−	0.806723i	$-0.298761\pi$
$509$	409.610	+	86.6079i	0.804734	+	0.170153i	0.213805	+	0.976876i	$0.431414\pi$
$510$	−155.904	−	108.752i	−0.305694	−	0.213239i
$511$	−394.975	+	31.7223i	−0.772946	+	0.0620789i
$512$	−711.051	−	103.291i	−1.38877	−	0.201741i
$513$	8.55301	−	48.0064i	0.0166725	−	0.0935798i
$514$	190.163	+	543.454i	0.369966	+	1.05730i
$515$	−725.065	−	971.521i	−1.40789	−	1.88645i
$516$	−40.8318	−	69.8582i	−0.0791315	−	0.135384i
$517$	21.4490	+	445.715i	0.0414874	+	0.862117i
$518$	850.886	−	967.639i	1.64264	−	1.86803i
$519$	0.832015	+	1.80098i	0.00160311	+	0.00347010i
$520$	63.1029	−	200.760i	0.121352	−	0.386077i
$521$	154.748	−	207.348i	0.297021	−	0.397982i	−0.627805	−	0.778370i	$-0.716047\pi$
$521$	154.748	−	207.348i	0.297021	−	0.397982i	0.924827	+	0.380389i	$0.124210\pi$
$522$	−1006.32	−	113.385i	−1.92781	−	0.217212i
$523$	−193.767	−	308.378i	−0.370490	−	0.589632i	0.608496	−	0.793557i	$-0.291773\pi$
$523$	−193.767	−	308.378i	−0.370490	−	0.589632i	−0.978987	+	0.203925i	$0.934630\pi$
$524$	142.869	−	511.276i	0.272650	−	0.975717i
$525$	58.0829	−	236.908i	0.110634	−	0.451254i
$526$	723.033	+	189.602i	1.37459	+	0.360460i
$527$	−44.9940	+	466.410i	−0.0853776	+	0.885028i
$528$	104.211	+	30.9293i	0.197369	+	0.0585782i
$529$	166.432	+	141.686i	0.314617	+	0.267837i
$530$	−530.305	+	321.474i	−1.00057	+	0.606554i
$531$	503.118	−	185.152i	0.947491	−	0.348685i
$532$	30.3004	−	235.004i	0.0569556	−	0.441736i
$533$	−462.704	+	686.514i	−0.868112	+	1.28802i
$534$	90.9400	+	70.1675i	0.170300	+	0.131400i
$535$	117.842	+	125.650i	0.220264	+	0.234859i
$536$	−45.4605	−	15.0939i	−0.0848144	−	0.0281603i
$537$	83.0143	+	97.5133i	0.154589	+	0.181589i
$538$	−137.732	+	60.9697i	−0.256007	+	0.113327i
$539$	208.270	−	450.823i	0.386402	−	0.836406i
$540$	−243.929	−	221.530i	−0.451721	−	0.410241i
$541$	31.6079	+	113.113i	0.0584249	+	0.209082i	0.986627	−	0.162995i	$-0.0521153\pi$
$541$	31.6079	+	113.113i	0.0584249	+	0.209082i	−0.928202	+	0.372076i	$0.878646\pi$
$542$	−578.373	+	18.5473i	−1.06711	+	0.0342201i
$543$	18.4606	+	103.616i	0.0339973	+	0.190821i
$544$	625.388	−	352.212i	1.14961	−	0.647449i
$545$	−602.640	−	232.811i	−1.10576	−	0.427176i
$546$	−175.903	+	126.941i	−0.322166	+	0.232493i
$547$	174.783	−	322.322i	0.319531	−	0.589253i	−0.668463	−	0.743745i	$-0.733048\pi$
$547$	174.783	−	322.322i	0.319531	−	0.589253i	0.987994	+	0.154492i	$0.0493741\pi$
$548$	907.698	−	301.376i	1.65638	−	0.549957i
$549$	59.0081	+	35.7711i	0.107483	+	0.0651568i
$550$	2954.98	+	575.482i	5.37269	+	1.04633i
$551$	−239.538	+	23.1079i	−0.434732	+	0.0419381i
$552$	1.54057	−	9.52898i	0.00279089	−	0.0172626i
$553$	−347.951	−	450.959i	−0.629206	−	0.815477i
$554$	30.4487	+	474.263i	0.0549615	+	0.856070i
$555$	−91.3177	−	189.623i	−0.164536	−	0.341663i
$556$	−559.178	+	774.853i	−1.00572	+	1.39362i
$557$	260.279	+	399.858i	0.467287	+	0.717879i	0.990977	−	0.134030i	$-0.0427920\pi$
$557$	260.279	+	399.858i	0.467287	+	0.717879i	−0.523690	+	0.851909i	$0.675445\pi$
$558$	−170.221	+	745.787i	−0.305056	+	1.33654i
$559$	60.7189	−	756.012i	0.108621	−	1.35244i
$560$	896.070	+	738.395i	1.60013	+	1.31856i
$561$	−111.992	+	43.2646i	−0.199630	+	0.0771205i
$562$	−99.6448	+	153.081i	−0.177304	+	0.272386i
$563$	−420.934	−	434.649i	−0.747663	−	0.772024i	0.231991	−	0.972718i	$-0.425476\pi$
$563$	−420.934	−	434.649i	−0.747663	−	0.772024i	−0.979654	+	0.200694i	$0.935680\pi$
$564$	−34.6039	−	39.3520i	−0.0613544	−	0.0697731i
$565$	−824.980	+	1863.65i	−1.46014	+	3.29849i
$566$	−190.318	−	641.245i	−0.336251	−	1.13294i
$567$	−127.690	−	655.662i	−0.225203	−	1.15637i
$568$	41.7396	+	15.3606i	0.0734852	+	0.0270432i
$569$	−52.3875	+	100.417i	−0.0920694	+	0.176480i	−0.928232	−	0.372002i	$-0.878671\pi$
$569$	−52.3875	+	100.417i	−0.0920694	+	0.176480i	0.836163	+	0.548482i	$0.184794\pi$
$570$	−63.6662	−	37.2126i	−0.111695	−	0.0652853i
$571$	540.494	−	60.8991i	0.946575	−	0.106653i	0.374838	−	0.927090i	$-0.377698\pi$
$571$	540.494	−	60.8991i	0.946575	−	0.106653i	0.571737	+	0.820437i	$0.306270\pi$
$572$	−876.056	−	1098.54i	−1.53157	−	1.92052i
$573$	−45.7263	−	91.1835i	−0.0798016	−	0.159134i
$574$	634.553	+	941.486i	1.10549	+	1.64022i
$575$	−68.9080	+	1073.30i	−0.119840	+	1.86660i
$576$	624.536	−	252.847i	1.08426	−	0.438970i
$577$	−171.407	−	171.407i	−0.297066	−	0.297066i	0.542798	−	0.839863i	$-0.317365\pi$
$577$	−171.407	−	171.407i	−0.297066	−	0.297066i	−0.839863	+	0.542798i	$0.817365\pi$
$578$	50.5188	−	119.251i	0.0874027	−	0.206316i
$579$	22.9472	+	108.528i	0.0396325	+	0.187441i
$580$	−728.966	+	1453.64i	−1.25684	+	2.50628i
$581$	276.028	−	35.5898i	0.475091	−	0.0612561i
$582$	23.7155	+	45.4581i	0.0407483	+	0.0781068i
$583$	−18.8268	+	391.224i	−0.0322929	+	0.671054i
$584$	39.0257	+	37.7943i	0.0668249	+	0.0647163i
$585$	−339.695	−	1488.30i	−0.580676	−	2.54411i
$586$	242.239	−	35.1891i	0.413378	−	0.0600497i
$587$	16.2161	−	505.678i	0.0276254	−	0.861461i	−0.888099	−	0.459653i	$-0.847974\pi$
$587$	16.2161	−	505.678i	0.0276254	−	0.861461i	0.915724	−	0.401808i	$-0.131618\pi$
$588$	13.8866	+	56.6408i	0.0236167	+	0.0963278i
$589$	−2.91359	+	181.760i	−0.00494667	+	0.308590i
$590$		−	1640.33i		−	2.78022i
$591$	−14.6912	+	87.7898i	−0.0248582	+	0.148544i
$592$	710.752			1.20059
$593$	49.0775	+	0.786707i	0.0827613	+	0.00132666i	0.0573948	−	0.998352i	$-0.481721\pi$
$593$	49.0775	+	0.786707i	0.0827613	+	0.00132666i	0.0253665	+	0.999678i	$0.491925\pi$
$594$	−385.143	+	94.4257i	−0.648389	+	0.158966i
$595$	−1281.73	−	41.1026i	−2.15417	−	0.0690801i
$596$	−47.7642	−	328.805i	−0.0801413	−	0.551687i
$597$	−16.2129	+	3.70049i	−0.0271573	+	0.00619847i
$598$	665.390	−	687.069i	1.11269	−	1.14895i
$599$	−345.676	−	16.6348i	−0.577088	−	0.0277710i	−0.242526	−	0.970145i	$-0.577976\pi$
$599$	−345.676	−	16.6348i	−0.577088	−	0.0277710i	−0.334562	+	0.942374i	$0.608588\pi$
$600$	−29.6505	+	15.4687i	−0.0494175	+	0.0257811i
$601$	16.0753	+	124.677i	0.0267476	+	0.207449i	0.999725	−	0.0234513i	$-0.00746547\pi$
$601$	16.0753	+	124.677i	0.0267476	+	0.207449i	−0.972977	+	0.230900i	$0.925833\pi$
$602$	−929.776	−	466.260i	−1.54448	−	0.774518i
$603$	−339.960	+	71.8812i	−0.563781	+	0.119206i
$604$	181.826	+	77.0278i	0.301037	+	0.127529i
$605$	1101.51	−	1101.51i	1.82067	−	1.82067i
$606$	27.6546	+	68.3074i	0.0456346	+	0.112718i
$607$	−498.628	−	32.0130i	−0.821464	−	0.0527397i	−0.352340	−	0.935872i	$-0.614614\pi$
$607$	−498.628	−	32.0130i	−0.821464	−	0.0527397i	−0.469124	+	0.883132i	$0.655430\pi$
$608$	230.901	−	155.625i	0.379771	−	0.255962i
$609$	141.744	−	71.0810i	0.232748	−	0.116718i
$610$	165.070	−	131.639i	0.270607	−	0.215802i
$611$	−54.9948	−	488.093i	−0.0900079	−	0.798842i
$612$	−306.533	+	524.439i	−0.500871	+	0.856927i
$613$	−147.779	−	77.0960i	−0.241074	−	0.125768i	0.337706	−	0.941251i	$-0.390349\pi$
$613$	−147.779	−	77.0960i	−0.241074	−	0.125768i	−0.578781	+	0.815483i	$0.696471\pi$
$614$	66.5345	−	180.796i	0.108362	−	0.294456i
$615$	182.027	−	35.4498i	0.295979	−	0.0576419i
$616$	−174.747	+	51.8641i	−0.283681	+	0.0841949i
$617$	−230.715	−	102.131i	−0.373931	−	0.165528i	0.209266	−	0.977859i	$-0.432892\pi$
$617$	−230.715	−	102.131i	−0.373931	−	0.165528i	−0.583197	+	0.812330i	$0.698199\pi$
$618$	128.656	−	113.133i	0.208182	−	0.183063i
$619$	514.951	−	498.702i	0.831907	−	0.805657i	−0.151235	−	0.988498i	$-0.548325\pi$
$619$	514.951	−	498.702i	0.831907	−	0.805657i	0.983143	+	0.182841i	$0.0585292\pi$
$620$	1029.50	+	670.131i	1.66049	+	1.08086i
$621$	−51.0519	−	132.150i	−0.0822092	−	0.212802i
$622$	−831.888	+	1009.53i	−1.33744	+	1.62303i
$623$	772.419	+	62.0366i	1.23984	+	0.0995772i
$624$	−116.654	−	26.6255i	−0.186946	−	0.0426691i
$625$	1320.12	−	859.302i	2.11219	−	1.37488i
$626$	−157.169	−	113.422i	−0.251069	−	0.181186i
$627$	−41.9641	+	20.2088i	−0.0669283	+	0.0322310i
$628$	1145.64	−	73.5525i	1.82427	−	0.117122i
$629$	−621.499	+	479.536i	−0.988074	+	0.762378i
$630$	−2066.72	−	334.130i	−3.28050	−	0.530366i
$631$	78.2215	+	810.848i	0.123964	+	1.28502i	0.822219	+	0.569171i	$0.192736\pi$
$631$	78.2215	+	810.848i	0.123964	+	1.28502i	−0.698255	+	0.715849i	$0.746040\pi$
$632$	−14.9281	+	76.6529i	−0.0236205	+	0.121286i
$633$	48.0391	−	79.2455i	0.0758911	−	0.125190i
$634$	−18.9621	−	57.1108i	−0.0299087	−	0.0900801i
$635$	−1055.61	−	572.420i	−1.66238	−	0.901448i
$636$	−26.9163	−	37.2980i	−0.0423213	−	0.0586447i
$637$	−196.985	+	509.905i	−0.309239	+	0.800478i
$638$	960.349	+	1705.20i	1.50525	+	2.67272i
$639$	317.633	−	56.5907i	0.497078	−	0.0885614i
$640$	−11.4729	−	357.769i	−0.0179265	−	0.559014i
$641$	−182.018	+	50.8622i	−0.283959	+	0.0793482i	−0.408165	−	0.912908i	$-0.633831\pi$
$641$	−182.018	+	50.8622i	−0.283959	+	0.0793482i	0.124206	+	0.992256i	$0.460362\pi$
$642$	−16.3672	+	18.0222i	−0.0254942	+	0.0280719i
$643$	−6.62564	−	3.06090i	−0.0103043	−	0.00476035i	0.414229	−	0.910173i	$-0.364051\pi$
$643$	−6.62564	−	3.06090i	−0.0103043	−	0.00476035i	−0.424533	+	0.905413i	$0.639562\pi$
$644$	−278.654	−	629.484i	−0.432693	−	0.977460i
$645$	−129.364	+	110.129i	−0.200564	+	0.170743i
$646$	−86.6703	+	261.037i	−0.134165	+	0.404082i
$647$	293.601	−	275.355i	0.453788	−	0.425588i	−0.423247	−	0.906014i	$-0.639110\pi$
$647$	293.601	−	275.355i	0.453788	−	0.425588i	0.877035	+	0.480426i	$0.159518\pi$
$648$	−55.9458	+	72.5081i	−0.0863361	+	0.111895i
$649$	−859.116	−	579.036i	−1.32375	−	0.892197i
$650$	−3286.55	−	423.754i	−5.05623	−	0.651929i
$651$	−41.3677	−	112.410i	−0.0635449	−	0.172672i
$652$	−170.218	−	280.792i	−0.261070	−	0.430663i
$653$	11.7039	−	13.7481i	0.0179233	−	0.0210537i	−0.752412	−	0.658693i	$-0.771109\pi$
$653$	11.7039	−	13.7481i	0.0179233	−	0.0210537i	0.770335	+	0.637640i	$0.220089\pi$
$654$	25.9782	−	87.5291i	0.0397220	−	0.133837i
$655$	−1109.45	−	107.028i	−1.69382	−	0.163401i
$656$	−158.854	+	605.780i	−0.242156	+	0.923445i
$657$	382.757	+	93.8406i	0.582582	+	0.142832i
$658$	−648.754	−	181.285i	−0.985949	−	0.275509i
$659$	−264.783	+	166.374i	−0.401795	+	0.252465i	−0.717738	−	0.696314i	$-0.754822\pi$
$659$	−264.783	+	166.374i	−0.401795	+	0.252465i	0.315942	+	0.948778i	$0.397679\pi$
$660$	−35.2397	+	312.761i	−0.0533934	+	0.473880i
$661$	−278.156	−	207.593i	−0.420810	−	0.314059i	0.366724	−	0.930330i	$-0.380479\pi$
$661$	−278.156	−	207.593i	−0.420810	−	0.314059i	−0.787534	+	0.616271i	$0.788643\pi$
$662$	1294.32	+	406.831i	1.95517	+	0.614549i
$663$	119.969	−	55.4232i	0.180949	−	0.0835945i
$664$	−28.6548	−	25.1974i	−0.0431549	−	0.0379479i
$665$	−496.927	+	23.9134i	−0.747258	+	0.0359601i
$666$	−1106.40	+	646.686i	−1.66126	+	0.971000i
$667$	−560.311	+	418.171i	−0.840047	+	0.626944i
$668$	926.210	−	324.095i	1.38654	−	0.485172i
$669$	23.6164	+	4.20759i	0.0353011	+	0.00628938i
$670$	−152.840	+	1052.14i	−0.228119	+	1.57035i
$671$	−10.6757	−	132.923i	−0.0159101	−	0.198097i
$672$	−104.969	+	150.481i	−0.156204	+	0.223930i
$673$	−12.9397	+	61.1981i	−0.0192269	+	0.0909333i	−0.986926	−	0.161176i	$-0.948471\pi$
$673$	−12.9397	+	61.1981i	−0.0192269	+	0.0909333i	0.967699	+	0.252109i	$0.0811243\pi$
$674$	−545.409	−	434.949i	−0.809212	−	0.645325i
$675$	−261.136	+	415.595i	−0.386868	+	0.615696i
$676$	537.838	+	592.220i	0.795619	+	0.876064i
$677$	−186.980	−	594.870i	−0.276189	−	0.878686i	−0.984891	−	0.173178i	$-0.944596\pi$
$677$	−186.980	−	594.870i	−0.276189	−	0.878686i	0.708702	−	0.705508i	$-0.249281\pi$
$678$	−271.869	−	95.1311i	−0.400987	−	0.140311i
$679$	301.391	+	169.740i	0.443874	+	0.249985i
$680$	111.811	+	135.687i	0.164429	+	0.199540i
$681$	−109.077	−	156.370i	−0.160172	−	0.229619i
$682$	1361.20	−	576.652i	1.99590	−	0.845531i
$683$	−93.5910	+	231.171i	−0.137029	+	0.338465i	−0.979852	−	0.199727i	$-0.935994\pi$
$683$	−93.5910	+	231.171i	−0.137029	+	0.338465i	0.842822	+	0.538192i	$0.180892\pi$
$684$	−102.249	+	212.323i	−0.149487	+	0.310413i
$685$	−957.248	−	1765.28i	−1.39744	−	2.57705i
$686$	−370.294	−	347.283i	−0.539787	−	0.506243i
$687$	54.4535	−	8.80362i	0.0792628	−	0.0128146i
$688$	−145.530	−	554.970i	−0.211526	−	0.806642i
$689$	−6.91012	−	431.077i	−0.0100292	−	0.625656i
$690$	−214.219	+	3.43391i	−0.310462	+	0.00497668i
$691$	−290.388	+	76.1486i	−0.420243	+	0.110201i	−0.457719	−	0.889097i	$-0.651333\pi$
$691$	−290.388	+	76.1486i	−0.420243	+	0.110201i	0.0374763	+	0.999298i	$0.488068\pi$
$692$	−3.09593	−	19.1494i	−0.00447389	−	0.0276726i
$693$	−904.548	+	964.484i	−1.30526	+	1.39175i
$694$	433.398	−	235.016i	0.624493	−	0.338640i
$695$	1807.60	+	870.496i	2.60087	+	1.25251i
$696$	−20.1514	−	8.15839i	−0.0289532	−	0.0117218i
$697$	−269.807	−	636.886i	−0.387097	−	0.913753i
$698$	1519.43	−	1059.89i	2.17684	−	1.51847i
$699$	−89.1861	+	73.4927i	−0.127591	+	0.105140i
$700$	−1170.39	+	2078.14i	−1.67198	+	2.96878i
$701$	382.283	−	1092.50i	0.545339	−	1.55849i	−0.259958	−	0.965620i	$-0.583709\pi$
$701$	382.283	−	1092.50i	0.545339	−	1.55849i	0.805298	−	0.592871i	$-0.202005\pi$
$702$	416.410	−	130.886i	0.593177	−	0.186447i
$703$	−225.442	+	204.741i	−0.320686	+	0.291238i
$704$	−1102.51	−	692.752i	−1.56606	−	0.984023i
$705$	−68.5994	+	86.0209i	−0.0973040	+	0.122015i
$706$	−678.409	−	143.443i	−0.960920	−	0.203177i
$707$	407.756	+	284.433i	0.576741	+	0.402310i
$708$	121.274	−	9.74011i	0.171292	−	0.0137572i
$709$	−1146.93	−	166.610i	−1.61768	−	0.234993i	−0.726009	−	0.687685i	$-0.758627\pi$
$709$	−1146.93	−	166.610i	−1.61768	−	0.234993i	−0.891667	+	0.452691i	$0.850464\pi$
$710$	173.152	−	971.868i	0.243876	−	1.36883i
$711$	187.101	+	534.703i	0.263152	+	0.752044i
$712$	−63.5448	−	85.1442i	−0.0892483	−	0.119585i
$713$	266.505	+	455.957i	0.373780	+	0.639491i
$714$	−8.71141	−	181.025i	−0.0122009	−	0.253536i
$715$	−1948.12	+	2215.43i	−2.72464	+	3.09850i
$716$	−525.149	−	1136.74i	−0.733448	−	1.58762i
$717$	−27.1852	+	86.4889i	−0.0379152	+	0.120626i
$718$	100.033	−	134.035i	0.139322	−	0.186678i
$719$	−77.2640	−	8.70556i	−0.107460	−	0.0121079i	0.0580705	−	0.998312i	$-0.481505\pi$
$719$	−77.2640	−	8.70556i	−0.107460	−	0.0121079i	−0.165531	+	0.986205i	$0.552934\pi$
$720$	−614.387	−	977.791i	−0.853315	−	1.35804i
$721$	311.057	−	1113.16i	0.431424	−	1.54391i
$722$	223.995	−	913.630i	0.310242	−	1.26542i
$723$	82.1853	+	21.5515i	0.113673	+	0.0298085i
$724$	98.8163	−	1024.33i	0.136487	−	1.41483i
$725$	2322.18	+	689.212i	3.20301	+	0.950637i
$726$	167.634	+	142.709i	0.230901	+	0.196569i
$727$	147.809	−	89.6028i	0.203314	−	0.123250i	−0.413060	−	0.910704i	$-0.635540\pi$
$727$	147.809	−	89.6028i	0.203314	−	0.123250i	0.616374	+	0.787454i	$0.288601\pi$
$728$	188.297	−	69.2952i	0.258650	−	0.0951857i
$729$	−80.7736	+	626.464i	−0.110801	+	0.859347i
$730$	673.925	−	999.904i	0.923186	−	1.36973i
$731$	501.687	+	387.091i	0.686302	+	0.529537i
$732$	10.7126	+	11.4224i	0.0146347	+	0.0156044i
$733$	−14.6421	−	4.86150i	−0.0199755	−	0.00663234i	0.305103	−	0.952319i	$-0.401309\pi$
$733$	−14.6421	−	4.86150i	−0.0199755	−	0.00663234i	−0.325079	+	0.945687i	$0.605391\pi$
$734$	−138.368	−	162.535i	−0.188513	−	0.221438i
$735$	111.966	−	49.5640i	0.152335	−	0.0674340i
$736$	339.273	−	734.392i	0.460969	−	0.997816i
$737$	497.100	+	451.453i	0.674491	+	0.612555i
$738$	−303.894	−	1087.53i	−0.411781	−	1.47362i
$739$	−996.557	+	31.9577i	−1.34852	+	0.0432445i	−0.697921	−	0.716175i	$-0.745891\pi$
$739$	−996.557	+	31.9577i	−1.34852	+	0.0432445i	−0.650601	+	0.759420i	$0.725483\pi$
$740$	360.959	+	2026.00i	0.487783	+	2.73783i
$741$	44.6711	−	25.1583i	0.0602849	−	0.0339518i
$742$	−551.531	−	213.066i	−0.743303	−	0.287151i
$743$	−749.439	+	540.837i	−1.00867	+	0.727910i	−0.962572	−	0.271027i	$-0.912637\pi$
$743$	−749.439	+	540.837i	−1.00867	+	0.727910i	−0.0460944	+	0.998937i	$0.514677\pi$
$744$	−7.82831	+	14.4363i	−0.0105219	+	0.0194037i
$745$	−662.071	+	219.823i	−0.888686	+	0.295064i
$746$	189.672	+	114.980i	0.254252	+	0.154129i
$747$	−271.695	−	52.9125i	−0.363714	−	0.0708334i
$748$	1168.49	−	112.723i	1.56215	−	0.150699i
$749$	−26.2128	+	162.135i	−0.0349970	+	0.216469i
$750$	267.737	+	346.998i	0.356983	+	0.462665i
$751$	66.0703	+	1029.10i	0.0879765	+	1.37030i	0.769565	+	0.638569i	$0.220473\pi$
$751$	66.0703	+	1029.10i	0.0879765	+	1.37030i	−0.681588	+	0.731736i	$0.738710\pi$
$752$	−161.213	−	334.763i	−0.214379	−	0.445163i
$753$	−21.6504	+	30.0010i	−0.0287522	+	0.0398419i
$754$	−1175.17	−	1805.38i	−1.55859	−	2.39441i
$755$	92.2592	−	404.214i	0.122198	−	0.535382i
$756$	25.1511	−	313.157i	0.0332686	−	0.414228i
$757$	550.623	+	453.733i	0.727375	+	0.599384i	0.924584	−	0.380978i	$-0.124412\pi$
$757$	550.623	+	453.733i	0.727375	+	0.599384i	−0.197210	+	0.980361i	$0.563188\pi$
$758$	−505.288	+	195.202i	−0.666607	+	0.257522i
$759$	−73.8206	+	113.408i	−0.0972604	+	0.149418i
$760$	47.4520	+	48.9981i	0.0624369	+	0.0644712i
$761$	−309.286	−	351.724i	−0.406420	−	0.462186i	0.511307	−	0.859398i	$-0.329162\pi$
$761$	−309.286	−	351.724i	−0.406420	−	0.462186i	−0.917727	+	0.397212i	$0.869978\pi$
$762$	68.6946	−	155.182i	0.0901503	−	0.203651i
$763$	−175.258	−	590.501i	−0.229695	−	0.773920i
$764$	190.662	+	979.010i	0.249558	+	1.28143i
$765$	1196.94	+	440.484i	1.56463	+	0.575797i
$766$	−65.8554	+	126.232i	−0.0859731

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	197.i (of order \(196\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.90099 - 0.0465026i) q^{2} +(-0.438834 + 0.107589i) q^{3} +(4.41565 + 0.141601i) q^{4} +(-1.33348 - 9.17958i) q^{5} +(1.27806 - 0.291708i) q^{6} +(6.15258 - 6.35304i) q^{7} +(-1.21114 - 0.0582831i) q^{8} +(-7.79839 + 4.06842i) q^{9} +O(q^{10})\)	\(q+(-2.90099 - 0.0465026i) q^{2} +(-0.438834 + 0.107589i) q^{3} +(4.41565 + 0.141601i) q^{4} +(-1.33348 - 9.17958i) q^{5} +(1.27806 - 0.291708i) q^{6} +(6.15258 - 6.35304i) q^{7} +(-1.21114 - 0.0582831i) q^{8} +(-7.79839 + 4.06842i) q^{9} +(3.44154 + 26.6919i) q^{10} +(15.1946 + 7.61973i) q^{11} +(-1.95297 + 0.412936i) q^{12} +(-17.2282 - 7.29847i) q^{13} +(-18.1440 + 18.1440i) q^{14} +(1.57280 + 3.88484i) q^{15} +(-14.1246 - 0.906828i) q^{16} +(12.9627 - 8.73674i) q^{17} +(22.8123 - 11.4398i) q^{18} +(4.74138 - 3.78112i) q^{19} +(-4.58834 - 40.7226i) q^{20} +(-2.01644 + 3.44988i) q^{21} +(-43.7251 - 22.8114i) q^{22} +(6.08495 - 16.5348i) q^{23} +(0.537758 - 0.104728i) q^{24} +(-58.5198 + 17.3684i) q^{25} +(49.6396 + 21.9740i) q^{26} +(6.03823 - 5.30967i) q^{27} +(28.0672 - 27.1816i) q^{28} +(-33.2570 - 21.6479i) q^{29} +(-4.38202 - 11.3430i) q^{30} +(-19.0625 + 23.1330i) q^{31} +(45.7677 + 3.67582i) q^{32} +(-7.48771 - 1.70902i) q^{33} +(-38.0110 + 24.7424i) q^{34} +(-66.5226 - 48.0064i) q^{35} +(-35.0111 + 16.8604i) q^{36} +(-50.1136 + 3.21740i) q^{37} +(-13.9305 + 10.7485i) q^{38} +(8.34557 + 1.34925i) q^{39} +(1.08001 + 11.1954i) q^{40} +(8.45826 - 43.4314i) q^{41} +(6.01011 - 9.91430i) q^{42} +(12.7732 + 38.4710i) q^{43} +(66.0151 + 35.7976i) q^{44} +(47.7453 + 66.1608i) q^{45} +(-18.4213 + 47.6843i) q^{46} +(12.8822 + 22.8736i) q^{47} +(6.29591 - 1.12170i) q^{48} +(-0.936398 - 29.2003i) q^{49} +(170.573 - 47.6642i) q^{50} +(-4.74850 + 5.22862i) q^{51} +(-75.0404 - 34.6670i) q^{52} +(9.32717 + 21.0702i) q^{53} +(-17.7638 + 15.1225i) q^{54} +(49.6842 - 149.641i) q^{55} +(-7.82188 + 7.33581i) q^{56} +(-1.67387 + 2.16940i) q^{57} +(95.4717 + 64.3470i) q^{58} +(-60.4494 - 7.79409i) q^{59} +(6.39483 + 17.3768i) q^{60} +(-4.06681 - 6.70863i) q^{61} +(56.3758 - 66.2222i) q^{62} +(-22.1334 + 74.5748i) q^{63} +(-76.2478 - 7.35554i) q^{64} +(-44.0234 + 167.880i) q^{65} +(21.6423 + 5.30605i) q^{66} +(38.0471 + 10.6317i) q^{67} +(58.4759 - 36.7428i) q^{68} +(-0.891322 + 7.91070i) q^{69} +(190.749 + 142.360i) q^{70} +(-34.9925 - 10.9988i) q^{71} +(9.68204 - 4.47289i) q^{72} +(-33.6462 - 29.5865i) q^{73} +(145.529 - 7.00324i) q^{74} +(23.8118 - 13.9179i) q^{75} +(21.4717 - 16.0247i) q^{76} +(141.894 - 49.6510i) q^{77} +(-24.1477 - 4.30225i) q^{78} +(9.25861 - 63.7356i) q^{79} +(10.5105 + 130.867i) q^{80} +(43.2118 - 61.9473i) q^{81} +(-26.5570 + 125.601i) q^{82} +(24.6037 + 19.6208i) q^{83} +(-9.39241 + 14.9479i) q^{84} +(-97.4851 - 107.342i) q^{85} +(-35.2661 - 112.198i) q^{86} +(16.9234 + 5.92175i) q^{87} +(-17.9586 - 10.1141i) q^{88} +(55.7211 + 67.6197i) q^{89} +(-135.432 - 194.152i) q^{90} +(-152.366 + 64.5473i) q^{91} +(29.2104 - 72.1502i) q^{92} +(5.87639 - 12.2025i) q^{93} +(-36.3075 - 66.9553i) q^{94} +(-41.0316 - 38.4818i) q^{95} +(-20.4799 + 3.31103i) q^{96} +(9.92086 + 37.8325i) q^{97} +(1.35859 + 84.7535i) q^{98} +(-149.494 + 2.39637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9}+O(q^{10}) \) 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 140 * q^8 - 84 * q^9	\( 2688 q - 84 q^{2} - 84 q^{3} - 84 q^{4} - 84 q^{5} - 98 q^{6} - 84 q^{7} - 140 q^{8} - 84 q^{9} - 84 q^{10} - 140 q^{11} - 140 q^{12} - 84 q^{13} - 28 q^{14} - 84 q^{15} + 112 q^{16} - 84 q^{17} - 210 q^{18} - 98 q^{19} - 84 q^{20} - 84 q^{21} - 84 q^{22} - 84 q^{23} - 308 q^{24} - 84 q^{25} + 70 q^{26} - 126 q^{27} - 910 q^{28} - 294 q^{29} + 70 q^{30} - 84 q^{31} - 84 q^{32} - 98 q^{33} - 84 q^{34} - 84 q^{35} + 2198 q^{36} + 126 q^{37} - 140 q^{38} - 84 q^{39} + 476 q^{40} + 28 q^{41} - 588 q^{42} - 84 q^{43} - 84 q^{44} - 966 q^{45} - 448 q^{46} + 266 q^{47} - 1428 q^{48} + 756 q^{49} - 84 q^{50} - 84 q^{51} + 126 q^{52} - 84 q^{53} - 588 q^{54} - 84 q^{55} - 84 q^{56} - 672 q^{57} + 532 q^{58} + 616 q^{59} - 378 q^{60} - 364 q^{61} - 854 q^{62} + 1036 q^{63} - 1428 q^{64} + 28 q^{65} + 406 q^{66} - 84 q^{67} - 966 q^{68} - 504 q^{69} - 84 q^{70} + 434 q^{71} - 532 q^{72} - 84 q^{73} + 546 q^{74} - 84 q^{75} - 308 q^{76} + 700 q^{77} + 2310 q^{78} - 1400 q^{79} - 84 q^{80} - 700 q^{81} - 84 q^{82} - 98 q^{83} - 588 q^{84} + 1666 q^{85} - 84 q^{86} - 84 q^{87} + 420 q^{88} + 868 q^{89} - 1890 q^{90} + 1260 q^{91} + 924 q^{92} - 98 q^{93} - 420 q^{94} - 1834 q^{95} + 364 q^{96} + 504 q^{97} - 980 q^{98} + 630 q^{99}+O(q^{100}) \) 2688 * q - 84 * q^2 - 84 * q^3 - 84 * q^4 - 84 * q^5 - 98 * q^6 - 84 * q^7 - 140 * q^8 - 84 * q^9 - 84 * q^10 - 140 * q^11 - 140 * q^12 - 84 * q^13 - 28 * q^14 - 84 * q^15 + 112 * q^16 - 84 * q^17 - 210 * q^18 - 98 * q^19 - 84 * q^20 - 84 * q^21 - 84 * q^22 - 84 * q^23 - 308 * q^24 - 84 * q^25 + 70 * q^26 - 126 * q^27 - 910 * q^28 - 294 * q^29 + 70 * q^30 - 84 * q^31 - 84 * q^32 - 98 * q^33 - 84 * q^34 - 84 * q^35 + 2198 * q^36 + 126 * q^37 - 140 * q^38 - 84 * q^39 + 476 * q^40 + 28 * q^41 - 588 * q^42 - 84 * q^43 - 84 * q^44 - 966 * q^45 - 448 * q^46 + 266 * q^47 - 1428 * q^48 + 756 * q^49 - 84 * q^50 - 84 * q^51 + 126 * q^52 - 84 * q^53 - 588 * q^54 - 84 * q^55 - 84 * q^56 - 672 * q^57 + 532 * q^58 + 616 * q^59 - 378 * q^60 - 364 * q^61 - 854 * q^62 + 1036 * q^63 - 1428 * q^64 + 28 * q^65 + 406 * q^66 - 84 * q^67 - 966 * q^68 - 504 * q^69 - 84 * q^70 + 434 * q^71 - 532 * q^72 - 84 * q^73 + 546 * q^74 - 84 * q^75 - 308 * q^76 + 700 * q^77 + 2310 * q^78 - 1400 * q^79 - 84 * q^80 - 700 * q^81 - 84 * q^82 - 98 * q^83 - 588 * q^84 + 1666 * q^85 - 84 * q^86 - 84 * q^87 + 420 * q^88 + 868 * q^89 - 1890 * q^90 + 1260 * q^91 + 924 * q^92 - 98 * q^93 - 420 * q^94 - 1834 * q^95 + 364 * q^96 + 504 * q^97 - 980 * q^98 + 630 * q^99

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