LMFDB - Embedded newform 144.3.v.a.43.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(43,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("144.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.v (of order $12$, degree $4$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.19
Character	$\chi$	$=$	144.43
Dual form			144.3.v.a.67.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.661532 - 1.88743i) q^{2} +(2.43372 + 1.75414i) q^{3} +(-3.12475 + 2.49718i) q^{4} +(1.97813 - 7.38249i) q^{5} +(1.70082 - 5.75389i) q^{6} +(0.0635994 - 0.110157i) q^{7} +(6.78037 + 4.24577i) q^{8} +(2.84600 + 8.53817i) q^{9} +O(q^{10})$	\(q+(-0.661532 - 1.88743i) q^{2} +(2.43372 + 1.75414i) q^{3} +(-3.12475 + 2.49718i) q^{4} +(1.97813 - 7.38249i) q^{5} +(1.70082 - 5.75389i) q^{6} +(0.0635994 - 0.110157i) q^{7} +(6.78037 + 4.24577i) q^{8} +(2.84600 + 8.53817i) q^{9} +(-15.2425 + 1.15017i) q^{10} +(-5.19143 - 19.3747i) q^{11} +(-11.9852 + 0.596210i) q^{12} +(17.4564 + 4.67742i) q^{13} +(-0.249987 - 0.0471665i) q^{14} +(17.7641 - 14.4970i) q^{15} +(3.52814 - 15.6062i) q^{16} +11.3896 q^{17} +(14.2324 - 11.0199i) q^{18} +(-22.0659 - 22.0659i) q^{19} +(12.2543 + 28.0082i) q^{20} +(0.348014 - 0.156530i) q^{21} +(-33.1340 + 22.6154i) q^{22} +(10.9224 + 18.9182i) q^{23} +(9.05388 + 22.2267i) q^{24} +(-28.9375 - 16.7071i) q^{25} +(-2.71966 - 36.0419i) q^{26} +(-8.05073 + 25.7718i) q^{27} +(0.0763511 + 0.503034i) q^{28} +(2.73750 + 10.2165i) q^{29} +(-39.1135 - 23.9382i) q^{30} +(-17.9433 + 10.3595i) q^{31} +(-31.7894 + 3.66488i) q^{32} +(21.3513 - 56.2590i) q^{33} +(-7.53459 - 21.4970i) q^{34} +(-0.687428 - 0.687428i) q^{35} +(-30.2144 - 19.5726i) q^{36} +(10.1299 + 10.1299i) q^{37} +(-27.0504 + 56.2449i) q^{38} +(34.2791 + 42.0044i) q^{39} +(44.7568 - 41.6573i) q^{40} +(-20.7267 + 11.9665i) q^{41} +(-0.525662 - 0.553302i) q^{42} +(14.3992 + 53.7384i) q^{43} +(64.6041 + 47.5771i) q^{44} +(68.6627 - 4.12097i) q^{45} +(28.4811 - 33.1302i) q^{46} +(40.5547 + 23.4142i) q^{47} +(35.9619 - 31.7922i) q^{48} +(24.4919 + 42.4212i) q^{49} +(-12.3903 + 65.6696i) q^{50} +(27.7191 + 19.9789i) q^{51} +(-66.2272 + 28.9760i) q^{52} +(-1.03374 - 1.03374i) q^{53} +(53.9682 - 1.85371i) q^{54} -153.303 q^{55} +(0.898930 - 0.476880i) q^{56} +(-14.9956 - 92.4087i) q^{57} +(17.4719 - 11.9253i) q^{58} +(-11.6087 - 3.11053i) q^{59} +(-19.3067 + 89.6598i) q^{60} +(5.43623 + 20.2883i) q^{61} +(31.4229 + 27.0134i) q^{62} +(1.12155 + 0.229514i) q^{63} +(27.9469 + 57.5758i) q^{64} +(69.0620 - 119.619i) q^{65} +(-120.309 - 3.08193i) q^{66} +(7.34023 - 27.3941i) q^{67} +(-35.5897 + 28.4419i) q^{68} +(-6.60296 + 65.2010i) q^{69} +(-0.842713 + 1.75222i) q^{70} -50.8622 q^{71} +(-16.9541 + 69.9754i) q^{72} +58.3319i q^{73} +(12.4182 - 25.8208i) q^{74} +(-41.1193 - 91.4206i) q^{75} +(124.053 + 13.8478i) q^{76} +(-2.46444 - 0.660344i) q^{77} +(56.6035 - 92.4865i) q^{78} +(-41.2927 - 23.8404i) q^{79} +(-108.233 - 56.9175i) q^{80} +(-64.8005 + 48.5993i) q^{81} +(36.2973 + 31.2038i) q^{82} +(-48.8308 + 13.0842i) q^{83} +(-0.696573 + 1.35817i) q^{84} +(22.5301 - 84.0836i) q^{85} +(91.9017 - 62.7270i) q^{86} +(-11.2588 + 29.6660i) q^{87} +(47.0606 - 153.409i) q^{88} -53.6042i q^{89} +(-53.2006 - 126.870i) q^{90} +(1.62547 - 1.62547i) q^{91} +(-81.3720 - 31.8393i) q^{92} +(-61.8409 - 6.26269i) q^{93} +(17.3644 - 92.0332i) q^{94} +(-206.550 + 119.252i) q^{95} +(-83.7954 - 46.8438i) q^{96} +(-17.1573 + 29.7172i) q^{97} +(63.8647 - 74.2897i) q^{98} +(150.649 - 99.4657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) $ 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 56 q^{12} - 2 q^{13} + 14 q^{14} - 2 q^{16} - 16 q^{17} + 38 q^{18} - 8 q^{19} - 44 q^{20} + 14 q^{21} - 2 q^{22} - 4 q^{23} + 120 q^{24} - 104 q^{26} - 52 q^{27} + 56 q^{28} - 2 q^{29} - 130 q^{30} - 182 q^{32} - 8 q^{33} - 10 q^{34} + 92 q^{35} - 2 q^{36} - 8 q^{37} - 254 q^{38} + 184 q^{39} - 2 q^{40} - 252 q^{42} - 2 q^{43} - 140 q^{44} - 54 q^{45} + 176 q^{46} + 162 q^{48} - 480 q^{49} - 96 q^{50} - 120 q^{51} - 2 q^{52} - 8 q^{53} + 94 q^{54} - 16 q^{55} + 260 q^{56} + 88 q^{58} + 142 q^{59} - 434 q^{60} - 2 q^{61} - 636 q^{62} + 244 q^{64} - 4 q^{65} - 100 q^{66} - 2 q^{67} - 112 q^{68} + 14 q^{69} - 100 q^{70} - 16 q^{71} + 98 q^{72} + 82 q^{74} - 296 q^{75} + 154 q^{76} + 194 q^{77} + 228 q^{78} + 592 q^{80} - 8 q^{81} - 420 q^{82} + 238 q^{83} - 22 q^{84} - 52 q^{85} - 170 q^{86} - 456 q^{87} - 26 q^{88} + 808 q^{90} + 188 q^{91} + 176 q^{92} + 26 q^{93} - 18 q^{94} - 202 q^{96} - 4 q^{97} + 408 q^{98} - 38 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 56 * q^12 - 2 * q^13 + 14 * q^14 - 2 * q^16 - 16 * q^17 + 38 * q^18 - 8 * q^19 - 44 * q^20 + 14 * q^21 - 2 * q^22 - 4 * q^23 + 120 * q^24 - 104 * q^26 - 52 * q^27 + 56 * q^28 - 2 * q^29 - 130 * q^30 - 182 * q^32 - 8 * q^33 - 10 * q^34 + 92 * q^35 - 2 * q^36 - 8 * q^37 - 254 * q^38 + 184 * q^39 - 2 * q^40 - 252 * q^42 - 2 * q^43 - 140 * q^44 - 54 * q^45 + 176 * q^46 + 162 * q^48 - 480 * q^49 - 96 * q^50 - 120 * q^51 - 2 * q^52 - 8 * q^53 + 94 * q^54 - 16 * q^55 + 260 * q^56 + 88 * q^58 + 142 * q^59 - 434 * q^60 - 2 * q^61 - 636 * q^62 + 244 * q^64 - 4 * q^65 - 100 * q^66 - 2 * q^67 - 112 * q^68 + 14 * q^69 - 100 * q^70 - 16 * q^71 + 98 * q^72 + 82 * q^74 - 296 * q^75 + 154 * q^76 + 194 * q^77 + 228 * q^78 + 592 * q^80 - 8 * q^81 - 420 * q^82 + 238 * q^83 - 22 * q^84 - 52 * q^85 - 170 * q^86 - 456 * q^87 - 26 * q^88 + 808 * q^90 + 188 * q^91 + 176 * q^92 + 26 * q^93 - 18 * q^94 - 202 * q^96 - 4 * q^97 + 408 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.661532	−	1.88743i	−0.330766	−	0.943713i
$2$	−0.661532	−	1.88743i	−0.330766	−	0.943713i
$3$	2.43372	+	1.75414i	0.811241	+	0.584712i
$3$	2.43372	+	1.75414i	0.811241	+	0.584712i
$4$	−3.12475	+	2.49718i	−0.781188	+	0.624296i
$5$	1.97813	−	7.38249i	0.395626	−	1.47650i	−0.425085	−	0.905154i	$-0.639756\pi$
$5$	1.97813	−	7.38249i	0.395626	−	1.47650i	0.820711	−	0.571344i	$-0.193578\pi$
$6$	1.70082	−	5.75389i	0.283470	−	0.958981i
$7$	0.0635994	−	0.110157i	0.00908563	−	0.0157368i	−0.861447	−	0.507848i	$-0.830441\pi$
$7$	0.0635994	−	0.110157i	0.00908563	−	0.0157368i	0.870532	+	0.492111i	$0.163775\pi$
$8$	6.78037	+	4.24577i	0.847547	+	0.530721i
$9$	2.84600	+	8.53817i	0.316223	+	0.948685i
$10$	−15.2425	+	1.15017i	−1.52425	+	0.115017i
$11$	−5.19143	−	19.3747i	−0.471948	−	1.76133i	−0.632759	−	0.774349i	$-0.718078\pi$
$11$	−5.19143	−	19.3747i	−0.471948	−	1.76133i	0.160811	−	0.986985i	$-0.448589\pi$
$12$	−11.9852	+	0.596210i	−0.998765	+	0.0496842i
$13$	17.4564	+	4.67742i	1.34280	+	0.359801i	0.857471	−	0.514532i	$-0.172034\pi$
$13$	17.4564	+	4.67742i	1.34280	+	0.359801i	0.485326	+	0.874333i	$0.338701\pi$
$14$	−0.249987	−	0.0471665i	−0.0178562	−	0.00336904i
$15$	17.7641	−	14.4970i	1.18427	−	0.966467i
$16$	3.52814	−	15.6062i	0.220509	−	0.975385i
$17$	11.3896			0.669977			0.334988	−	0.942222i	$-0.391268\pi$
$17$	11.3896			0.669977			0.334988	+	0.942222i	$0.391268\pi$
$18$	14.2324	−	11.0199i	0.790691	−	0.612216i
$19$	−22.0659	−	22.0659i	−1.16136	−	1.16136i	−0.984178	−	0.177183i	$-0.943302\pi$
$19$	−22.0659	−	22.0659i	−1.16136	−	1.16136i	−0.177183	−	0.984178i	$-0.556698\pi$
$20$	12.2543	+	28.0082i	0.612713	+	1.40041i
$21$	0.348014	−	0.156530i	0.0165721	−	0.00745383i
$22$	−33.1340	+	22.6154i	−1.50609	+	1.02797i
$23$	10.9224	+	18.9182i	0.474887	+	0.822529i	0.999586	−	0.0287588i	$-0.00915549\pi$
$23$	10.9224	+	18.9182i	0.474887	+	0.822529i	−0.524699	+	0.851288i	$0.675822\pi$
$24$	9.05388	+	22.2267i	0.377245	+	0.926113i
$25$	−28.9375	−	16.7071i	−1.15750	−	0.668282i
$26$	−2.71966	−	36.0419i	−0.104602	−	1.38623i
$27$	−8.05073	+	25.7718i	−0.298175	+	0.954511i
$28$	0.0763511	+	0.503034i	0.00272682	+	0.0179655i
$29$	2.73750	+	10.2165i	0.0943964	+	0.352292i	0.996927	−	0.0783330i	$-0.0249597\pi$
$29$	2.73750	+	10.2165i	0.0943964	+	0.352292i	−0.902531	+	0.430625i	$0.858293\pi$
$30$	−39.1135	−	23.9382i	−1.30378	−	0.797941i
$31$	−17.9433	+	10.3595i	−0.578815	+	0.334179i	−0.760662	−	0.649148i	$-0.775126\pi$
$31$	−17.9433	+	10.3595i	−0.578815	+	0.334179i	0.181848	+	0.983327i	$0.441792\pi$
$32$	−31.7894	+	3.66488i	−0.993420	+	0.114527i
$33$	21.3513	−	56.2590i	0.647011	−	1.70482i
$34$	−7.53459	−	21.4970i	−0.221605	−	0.632266i
$35$	−0.687428	−	0.687428i	−0.0196408	−	0.0196408i
$36$	−30.2144	−	19.5726i	−0.839290	−	0.543685i
$37$	10.1299	+	10.1299i	0.273782	+	0.273782i	0.830621	−	0.556839i	$-0.187986\pi$
$37$	10.1299	+	10.1299i	0.273782	+	0.273782i	−0.556839	+	0.830621i	$0.687986\pi$
$38$	−27.0504	+	56.2449i	−0.711853	+	1.48013i
$39$	34.2791	+	42.0044i	0.878951	+	1.07704i
$40$	44.7568	−	41.6573i	1.11892	−	1.04143i
$41$	−20.7267	+	11.9665i	−0.505528	+	0.291867i	−0.730994	−	0.682384i	$-0.760943\pi$
$41$	−20.7267	+	11.9665i	−0.505528	+	0.291867i	0.225465	+	0.974251i	$0.427610\pi$
$42$	−0.525662	−	0.553302i	−0.0125158	−	0.0131738i
$43$	14.3992	+	53.7384i	0.334864	+	1.24973i	0.904017	+	0.427497i	$0.140605\pi$
$43$	14.3992	+	53.7384i	0.334864	+	1.24973i	−0.569153	+	0.822232i	$0.692729\pi$
$44$	64.6041	+	47.5771i	1.46827	+	1.08130i
$45$	68.6627	−	4.12097i	1.52584	−	0.0915772i
$46$	28.4811	−	33.1302i	0.619155	−	0.720222i
$47$	40.5547	+	23.4142i	0.862865	+	0.498176i	0.864971	−	0.501822i	$-0.167337\pi$
$47$	40.5547	+	23.4142i	0.862865	+	0.498176i	−0.00210545	+	0.999998i	$0.500670\pi$
$48$	35.9619	−	31.7922i	0.749205	−	0.662338i
$49$	24.4919	+	42.4212i	0.499835	+	0.865739i
$50$	−12.3903	+	65.6696i	−0.247805	+	1.31339i
$51$	27.7191	+	19.9789i	0.543512	+	0.391744i
$52$	−66.2272	+	28.9760i	−1.27360	+	0.557231i
$53$	−1.03374	−	1.03374i	−0.0195045	−	0.0195045i	0.697287	−	0.716792i	$-0.254390\pi$
$53$	−1.03374	−	1.03374i	−0.0195045	−	0.0195045i	−0.716792	+	0.697287i	$0.754390\pi$
$54$	53.9682	−	1.85371i	0.999411	−	0.0343280i
$55$	−153.303			−2.78732
$56$	0.898930	−	0.476880i	0.0160523	−	0.00851571i
$57$	−14.9956	−	92.4087i	−0.263081	−	1.62121i
$58$	17.4719	−	11.9253i	0.301240	−	0.205609i
$59$	−11.6087	−	3.11053i	−0.196757	−	0.0527209i	0.159095	−	0.987263i	$-0.449143\pi$
$59$	−11.6087	−	3.11053i	−0.196757	−	0.0527209i	−0.355852	+	0.934542i	$0.615809\pi$
$60$	−19.3067	+	89.6598i	−0.321779	+	1.49433i
$61$	5.43623	+	20.2883i	0.0891185	+	0.332595i	0.996062	−	0.0886572i	$-0.0282576\pi$
$61$	5.43623	+	20.2883i	0.0891185	+	0.332595i	−0.906944	+	0.421252i	$0.861591\pi$
$62$	31.4229	+	27.0134i	0.506821	+	0.435700i
$63$	1.12155	+	0.229514i	0.0178023	+	0.00364308i
$64$	27.9469	+	57.5758i	0.436671	+	0.899622i
$65$	69.0620	−	119.619i	1.06249	−	1.84029i
$66$	−120.309	−	3.08193i	−1.82287	−	0.0466959i
$67$	7.34023	−	27.3941i	0.109556	−	0.408867i	−0.889266	−	0.457390i	$-0.848784\pi$
$67$	7.34023	−	27.3941i	0.109556	−	0.408867i	0.998822	+	0.0485222i	$0.0154512\pi$
$68$	−35.5897	+	28.4419i	−0.523378	+	0.418264i
$69$	−6.60296	+	65.2010i	−0.0956951	+	0.944941i
$70$	−0.842713	+	1.75222i	−0.0120388	+	0.0250318i
$71$	−50.8622			−0.716369			−0.358184	−	0.933651i	$-0.616604\pi$
$71$	−50.8622			−0.716369			−0.358184	+	0.933651i	$0.616604\pi$
$72$	−16.9541	+	69.9754i	−0.235474	+	0.971881i
$73$			58.3319i			0.799067i	0.916719	+	0.399533i	$0.130828\pi$
$73$			58.3319i			0.799067i	−0.916719	+	0.399533i	$0.869172\pi$
$74$	12.4182	−	25.8208i	0.167814	−	0.348929i
$75$	−41.1193	−	91.4206i	−0.548257	−	1.21894i
$76$	124.053	+	13.8478i	1.63227	+	0.182208i
$77$	−2.46444	−	0.660344i	−0.0320057	−	0.00857589i
$78$	56.6035	−	92.4865i	0.725685	−	1.18572i
$79$	−41.2927	−	23.8404i	−0.522693	−	0.301777i	0.215343	−	0.976539i	$-0.430913\pi$
$79$	−41.2927	−	23.8404i	−0.522693	−	0.301777i	−0.738036	+	0.674762i	$0.764246\pi$
$80$	−108.233	−	56.9175i	−1.35291	−	0.711468i
$81$	−64.8005	+	48.5993i	−0.800006	+	0.599991i
$82$	36.2973	+	31.2038i	0.442650	+	0.380534i
$83$	−48.8308	+	13.0842i	−0.588323	+	0.157641i	−0.540687	−	0.841224i	$-0.681836\pi$
$83$	−48.8308	+	13.0842i	−0.588323	+	0.157641i	−0.0476365	+	0.998865i	$0.515169\pi$
$84$	−0.696573	+	1.35817i	−0.00829254	+	0.0161687i
$85$	22.5301	−	84.0836i	0.265060	−	0.989219i
$86$	91.9017	−	62.7270i	1.06862	−	0.729383i
$87$	−11.2588	+	29.6660i	−0.129411	+	0.340988i
$88$	47.0606	−	153.409i	0.534779	−	1.74329i
$89$		−	53.6042i		−	0.602295i	−0.953578	−	0.301147i	$-0.902630\pi$
$89$		−	53.6042i		−	0.602295i	0.953578	−	0.301147i	$-0.0973696\pi$
$90$	−53.2006	−	126.870i	−0.591117	−	1.40966i
$91$	1.62547	−	1.62547i	0.0178623	−	0.0178623i
$92$	−81.3720	−	31.8393i	−0.884478	−	0.346079i
$93$	−61.8409	−	6.26269i	−0.664956	−	0.0673407i
$94$	17.3644	−	92.0332i	0.184728	−	0.979077i
$95$	−206.550	+	119.252i	−2.17421	+	1.25528i
$96$	−83.7954	−	46.8438i	−0.872868	−	0.487956i
$97$	−17.1573	+	29.7172i	−0.176879	+	0.306363i	−0.940810	−	0.338935i	$-0.889933\pi$
$97$	−17.1573	+	29.7172i	−0.176879	+	0.306363i	0.763931	+	0.645298i	$0.223267\pi$
$98$	63.8647	−	74.2897i	0.651681	−	0.758058i
$99$	150.649	−	99.4657i	1.52171	−	1.00470i
$100$	132.143	−	20.0568i	1.32143	−	0.200568i
$101$	143.393	−	38.4220i	1.41973	−	0.380416i	0.534342	−	0.845268i	$-0.320559\pi$
$101$	143.393	−	38.4220i	1.41973	−	0.380416i	0.885388	+	0.464853i	$0.153893\pi$
$102$	19.3717	−	65.5345i	0.189918	−	0.642495i
$103$	31.6543	+	54.8269i	0.307324	+	0.532300i	0.977776	−	0.209652i	$-0.0672332\pi$
$103$	31.6543	+	54.8269i	0.307324	+	0.532300i	−0.670452	+	0.741953i	$0.733900\pi$
$104$	98.5014	+	105.830i	0.947129	+	1.01760i
$105$	−0.467165	−	2.87885i	−0.00444919	−	0.0274176i
$106$	−1.26725	+	2.63496i	−0.0119552	+	0.0248581i
$107$	−32.4055	+	32.4055i	−0.302856	+	0.302856i	−0.842130	−	0.539275i	$-0.818699\pi$
$107$	−32.4055	+	32.4055i	−0.302856	+	0.302856i	0.539275	+	0.842130i	$0.318699\pi$
$108$	−39.2004	−	100.635i	−0.362967	−	0.931802i
$109$	−14.3542	+	14.3542i	−0.131690	+	0.131690i	−0.769879	−	0.638189i	$-0.779684\pi$
$109$	−14.3542	+	14.3542i	−0.131690	+	0.131690i	0.638189	+	0.769879i	$0.279684\pi$
$110$	101.415	+	289.347i	0.921951	+	2.63043i
$111$	6.88414	+	42.4227i	0.0620193	+	0.382187i
$112$	−1.49475	−	1.38119i	−0.0133460	−	0.0123321i
$113$	−85.9347	−	148.843i	−0.760484	−	1.31720i	−0.942601	−	0.333921i	$-0.891628\pi$
$113$	−85.9347	−	148.843i	−0.760484	−	1.31720i	0.182117	−	0.983277i	$-0.441705\pi$
$114$	−164.494	+	89.4344i	−1.44293	+	0.784512i
$115$	161.269	−	43.2119i	1.40234	−	0.375756i
$116$	−34.0664	−	25.0879i	−0.293676	−	0.216275i
$117$	9.74431	+	162.357i	0.0832847	+	1.38767i
$118$	1.80860	+	23.9682i	0.0153272	+	0.203120i
$119$	0.724372	−	1.25465i	0.00608716	−	0.0105433i
$120$	181.998	−	22.8728i	1.51665	−	0.190607i
$121$	−243.638	+	140.664i	−2.01354	+	1.16252i
$122$	34.6964	−	23.6818i	0.284396	−	0.194113i
$123$	−71.4339	−	7.23417i	−0.580763	−	0.0588144i
$124$	30.1985	−	77.1786i	0.243536	−	0.622408i
$125$	−45.4729	+	45.4729i	−0.363783	+	0.363783i
$126$	−0.308748	−	2.26867i	−0.00245038	−	0.0180053i
$127$		−	52.4869i		−	0.413283i	−0.978417	−	0.206642i	$-0.933747\pi$
$127$		−	52.4869i		−	0.413283i	0.978417	−	0.206642i	$-0.0662534\pi$
$128$	90.1822	−	90.8359i	0.704549	−	0.709656i
$129$	−59.2209	+	156.042i	−0.459077	+	1.20963i
$130$	−271.458	−	51.2176i	−2.08814	−	0.393982i
$131$	27.3331	−	102.009i	0.208650	−	0.778691i	−0.779656	−	0.626208i	$-0.784606\pi$
$131$	27.3331	−	102.009i	0.208650	−	0.778691i	0.988306	−	0.152484i	$-0.0487271\pi$
$132$	73.7716	+	229.114i	0.558876	+	1.73571i
$133$	−3.83409	+	1.02734i	−0.0288278	+	0.00772438i
$134$	−56.5602	+	4.26794i	−0.422091	+	0.0318503i
$135$	174.335	+	110.414i	1.29137	+	0.817885i
$136$	77.2258	+	48.3576i	0.567836	+	0.355571i
$137$	−99.5439	−	57.4717i	−0.726598	−	0.419502i	0.0905783	−	0.995889i	$-0.471128\pi$
$137$	−99.5439	−	57.4717i	−0.726598	−	0.419502i	−0.817176	+	0.576388i	$0.804462\pi$
$138$	127.430	−	30.6699i	0.923406	−	0.222246i
$139$	68.9203	+	18.4671i	0.495829	+	0.132857i	0.498064	−	0.867140i	$-0.334045\pi$
$139$	68.9203	+	18.4671i	0.495829	+	0.132857i	−0.00223442	+	0.999998i	$0.500711\pi$
$140$	3.86467	+	0.431406i	0.0276048	+	0.00308147i
$141$	57.6270	+	128.122i	0.408702	+	0.908668i
$142$	33.6470	+	95.9986i	0.236950	+	0.676047i
$143$		−	362.494i		−	2.53492i
$144$	143.289	−	14.2914i	0.995063	−	0.0992456i
$145$	80.8381			0.557504
$146$	110.097	−	38.5884i	0.754090	−	0.264304i
$147$	−14.8062	+	146.204i	−0.100722	+	0.994583i
$148$	−56.9498	−	6.35720i	−0.384796	−	0.0429541i
$149$	51.9800	−	193.992i	0.348859	−	1.30196i	−0.539179	−	0.842191i	$-0.681265\pi$
$149$	51.9800	−	193.992i	0.348859	−	1.30196i	0.888038	−	0.459769i	$-0.152068\pi$
$150$	−145.348	+	138.087i	−0.968986	+	0.920582i
$151$	37.7658	−	65.4123i	0.250105	−	0.433194i	−0.713450	−	0.700706i	$-0.752868\pi$
$151$	37.7658	−	65.4123i	0.250105	−	0.433194i	0.963554	+	0.267512i	$0.0862016\pi$
$152$	−55.9282	−	243.301i	−0.367949	−	1.60067i
$153$	32.4149	+	97.2463i	0.211862	+	0.635597i
$154$	0.383954	+	5.08828i	0.00249320	+	0.0330408i
$155$	40.9851	+	152.958i	0.264420	+	0.986828i
$156$	−212.006	−	45.6520i	−1.35902	−	0.292641i
$157$	114.681	+	30.7286i	0.730451	+	0.195724i	0.604830	−	0.796355i	$-0.293241\pi$
$157$	114.681	+	30.7286i	0.730451	+	0.195724i	0.125621	+	0.992078i	$0.459908\pi$
$158$	−17.6805	+	93.7082i	−0.111902	+	0.593090i
$159$	−0.702513	−	4.32915i	−0.00441832	−	0.0272274i
$160$	−35.8278	+	241.935i	−0.223924	+	1.51209i
$161$	2.77863			0.0172586
$162$	134.595	+	90.1562i	0.830834	+	0.556520i
$163$	−106.075	−	106.075i	−0.650765	−	0.650765i	0.302412	−	0.953177i	$-0.402208\pi$
$163$	−106.075	−	106.075i	−0.650765	−	0.650765i	−0.953177	+	0.302412i	$0.902208\pi$
$164$	34.8830	−	89.1507i	0.212701	−	0.543602i
$165$	−373.096	−	268.914i	−2.26119	−	1.62978i
$166$	56.9986	+	83.5090i	0.343365	+	0.503066i
$167$	110.487	+	191.369i	0.661600	+	1.14592i	0.980195	+	0.198034i	$0.0634556\pi$
$167$	110.487	+	191.369i	0.661600	+	1.14592i	−0.318595	+	0.947891i	$0.603211\pi$
$168$	3.02426	+	0.416254i	0.0180015	+	0.00247770i
$169$	136.488	+	78.8015i	0.807622	+	0.466281i
$170$	−173.606	+	13.1000i	−1.02121	+	0.0770590i
$171$	125.602	−	251.201i	0.734517	−	1.46901i
$172$	−179.188	−	131.962i	−1.04179	−	0.767219i
$173$	2.43826	+	9.09971i	0.0140940	+	0.0525995i	0.972615	−	0.232423i	$-0.0746655\pi$
$173$	2.43826	+	9.09971i	0.0140940	+	0.0525995i	−0.958521	+	0.285023i	$0.907999\pi$
$174$	63.4404	+	1.62513i	0.364600	+	0.00933985i
$175$	−3.68081	+	2.12512i	−0.0210332	+	0.0121435i
$176$	−320.680	+	12.6617i	−1.82205	+	0.0719417i
$177$	−22.7960	−	27.9334i	−0.128791	−	0.157816i
$178$	−101.174	+	35.4609i	−0.568393	+	0.199219i
$179$	25.0125	+	25.0125i	0.139735	+	0.139735i	0.773514	−	0.633779i	$-0.218497\pi$
$179$	25.0125	+	25.0125i	0.139735	+	0.139735i	−0.633779	+	0.773514i	$0.718497\pi$
$180$	−204.263	+	184.340i	−1.13479	+	1.02411i
$181$	8.07943	+	8.07943i	0.0446377	+	0.0446377i	0.729073	−	0.684436i	$-0.239951\pi$
$181$	8.07943	+	8.07943i	0.0446377	+	0.0446377i	−0.684436	+	0.729073i	$0.739951\pi$
$182$	−4.14325	−	1.99265i	−0.0227651	−	0.0109486i
$183$	−22.3582	+	58.9119i	−0.122176	+	0.321923i
$184$	−6.26414	+	174.646i	−0.0340442	+	0.949164i
$185$	94.8224	−	54.7457i	0.512554	−	0.295923i
$186$	29.0894	+	120.863i	0.156395	+	0.649802i
$187$	−59.1283	−	220.670i	−0.316194	−	1.18005i
$188$	−185.193	+	28.1088i	−0.985069	+	0.149515i
$189$	2.32693	+	2.52592i	0.0123118	+	0.0133646i
$190$	361.718	+	310.959i	1.90378	+	1.63663i
$191$	68.7827	+	39.7117i	0.360119	+	0.207915i	0.669133	−	0.743143i	$-0.266666\pi$
$191$	68.7827	+	39.7117i	0.360119	+	0.207915i	−0.309014	+	0.951057i	$0.599999\pi$
$192$	−32.9808	+	189.146i	−0.171775	+	0.985136i
$193$	63.0589	+	109.221i	0.326730	+	0.565913i	0.981861	−	0.189602i	$-0.0607198\pi$
$193$	63.0589	+	109.221i	0.326730	+	0.565913i	−0.655131	+	0.755516i	$0.727386\pi$
$194$	67.4391	+	12.7241i	0.347624	+	0.0655883i
$195$	377.905	−	169.975i	1.93798	−	0.871666i
$196$	−182.465	−	71.3950i	−0.930943	−	0.364260i
$197$	135.334	+	135.334i	0.686977	+	0.686977i	0.961563	−	0.274586i	$-0.0885407\pi$
$197$	135.334	+	135.334i	0.686977	+	0.686977i	−0.274586	+	0.961563i	$0.588541\pi$
$198$	−287.393	−	218.540i	−1.45148	−	1.10374i
$199$	−190.840			−0.958995			−0.479498	−	0.877543i	$-0.659181\pi$
$199$	−190.840			−0.958995			−0.479498	+	0.877543i	$0.659181\pi$
$200$	−125.273	−	236.142i	−0.626363	−	1.18071i
$201$	65.9171	−	53.7939i	0.327946	−	0.267631i
$202$	−167.377	−	245.226i	−0.828601	−	1.21399i
$203$	1.29952	+	0.348206i	0.00640159	+	0.00171530i
$204$	−136.506	+	6.79060i	−0.669149	+	0.0332872i
$205$	47.3428	+	176.686i	0.230940	+	0.861881i
$206$	82.5414	−	96.0150i	0.400686	−	0.466092i
$207$	−130.441	+	147.098i	−0.630151	+	0.710621i
$208$	134.585	−	255.924i	0.647043	−	1.23041i
$209$	−312.966	+	542.072i	−1.49744	+	2.59365i
$210$	−5.12457	+	2.78619i	−0.0244027	+	0.0132676i
$211$	−41.1780	+	153.678i	−0.195156	+	0.728333i	0.797070	+	0.603887i	$0.206382\pi$
$211$	−41.1780	+	153.678i	−0.195156	+	0.728333i	−0.992226	+	0.124446i	$0.960285\pi$
$212$	5.81161	+	0.648740i	0.0274133	+	0.00306009i
$213$	−123.784	−	89.2193i	−0.581148	−	0.418870i
$214$	82.6004	+	39.7257i	0.385983	+	0.185634i
$215$	425.206			1.97770
$216$	−164.008	+	140.561i	−0.759297	+	0.650745i
$217$			2.63544i			0.0121449i
$218$	36.5883	+	17.5967i	0.167836	+	0.0807190i
$219$	−102.322	+	141.964i	−0.467224	+	0.648236i
$220$	479.032	−	382.825i	2.17742	−	1.74011i
$221$	198.821	+	53.2739i	0.899643	+	0.241059i
$222$	75.5157	−	41.0573i	0.340161	−	0.184943i
$223$	226.931	+	131.019i	1.01763	+	0.587529i	0.913416	−	0.407026i	$-0.133434\pi$
$223$	226.931	+	131.019i	1.01763	+	0.587529i	0.104213	+	0.994555i	$0.466768\pi$
$224$	−1.61808	+	3.73493i	−0.00722356	+	0.0166738i
$225$	60.2915	−	294.621i	0.267962	−	1.30943i
$226$	−224.082	+	260.660i	−0.991514	+	1.15336i
$227$	−185.730	+	49.7663i	−0.818195	+	0.219235i	−0.643557	−	0.765398i	$-0.722542\pi$
$227$	−185.730	+	49.7663i	−0.818195	+	0.219235i	−0.174638	+	0.984633i	$0.555876\pi$
$228$	277.619	+	251.307i	1.21763	+	1.10223i
$229$	−80.9030	+	301.934i	−0.353288	+	1.31849i	0.529337	+	0.848412i	$0.322441\pi$
$229$	−80.9030	+	301.934i	−0.353288	+	1.31849i	−0.882625	+	0.470078i	$0.844226\pi$
$230$	−188.244	−	275.797i	−0.818452	−	1.19912i
$231$	−4.83942	−	5.93005i	−0.0209499	−	0.0256712i
$232$	−24.8155	+	80.8943i	−0.106963	+	0.348682i
$233$		−	227.184i		−	0.975037i	−0.873113	−	0.487519i	$-0.837902\pi$
$233$		−	227.184i		−	0.975037i	0.873113	−	0.487519i	$-0.162098\pi$
$234$	299.991	−	125.796i	1.28201	−	0.537591i
$235$	253.078	−	253.078i	1.07693	−	1.07693i
$236$	44.0418	−	19.2693i	0.186618	−	0.0816498i
$237$	−58.6758	−	130.454i	−0.247577	−	0.550439i
$238$	−2.84725	−	0.537208i	−0.0119632	−	0.00225718i
$239$	−79.1629	+	45.7047i	−0.331226	+	0.191233i	−0.656385	−	0.754426i	$-0.727915\pi$
$239$	−79.1629	+	45.7047i	−0.331226	+	0.191233i	0.325159	+	0.945659i	$0.394582\pi$
$240$	−163.568	−	328.377i	−0.681535	−	1.36824i
$241$	238.034	−	412.286i	0.987691	−	1.71073i	0.358386	−	0.933573i	$-0.383327\pi$
$241$	238.034	−	412.286i	0.987691	−	1.71073i	0.629305	−	0.777158i	$-0.283340\pi$
$242$	426.668	+	366.795i	1.76309	+	1.51568i
$243$	−242.956	+	4.60816i	−0.999820	+	0.0189636i
$244$	−67.6504	−	49.8205i	−0.277256	−	0.204183i
$245$	361.622	−	96.8964i	1.47601	−	0.395496i
$246$	33.6018	+	139.612i	0.136593	+	0.567527i
$247$	−281.978	−	488.401i	−1.14161	−	1.97733i
$248$	−165.646	−	5.94133i	−0.667928	−	0.0239570i
$249$	−141.792	−	53.8127i	−0.569446	−	0.216115i
$250$	115.908	+	55.7449i	0.463634	+	0.222980i
$251$	−145.998	+	145.998i	−0.581666	+	0.581666i	−0.935361	−	0.353695i	$-0.884925\pi$
$251$	−145.998	+	145.998i	−0.581666	+	0.581666i	0.353695	+	0.935361i	$0.384925\pi$
$252$	−4.07769	+	2.08353i	−0.0161813	+	0.00826799i
$253$	309.830	−	309.830i	1.22463	−	1.22463i
$254$	−99.0652	+	34.7218i	−0.390021	+	0.136700i
$255$	202.326	−	165.115i	0.793436	−	0.647510i
$256$	−231.104	−	110.121i	−0.902752	−	0.430162i
$257$	−114.285	−	197.947i	−0.444688	−	0.770223i	0.553342	−	0.832954i	$-0.313352\pi$
$257$	−114.285	−	197.947i	−0.444688	−	0.770223i	−0.998030	+	0.0627311i	$0.980019\pi$
$258$	333.695	+	8.54815i	1.29339	+	0.0331324i
$259$	1.76014	−	0.471629i	0.00679592	−	0.00182096i
$260$	82.9089	+	546.240i	0.318880	+	2.10092i
$261$	−79.4390	+	52.4493i	−0.304364	+	0.200955i
$262$	−210.615	+	15.8927i	−0.803875	+	0.0606592i
$263$	155.868	−	269.971i	0.592653	−	1.02651i	−0.401220	−	0.915982i	$-0.631414\pi$
$263$	155.868	−	269.971i	0.592653	−	1.02651i	0.993873	−	0.110524i	$-0.0352529\pi$
$264$	383.633	−	290.804i	1.45316	−	1.10153i
$265$	−9.67643	+	5.58669i	−0.0365148	+	0.0210819i
$266$	4.47541	+	6.55695i	0.0168248	+	0.0246502i
$267$	94.0292	−	130.458i	0.352169	−	0.488606i
$268$	45.4718	+	103.930i	0.169671	+	0.387797i
$269$	−349.579	+	349.579i	−1.29955	+	1.29955i	−0.370863	+	0.928688i	$0.620938\pi$
$269$	−349.579	+	349.579i	−1.29955	+	1.29955i	−0.928688	+	0.370863i	$0.879062\pi$
$270$	93.0712	−	402.086i	0.344708	−	1.48921i
$271$			68.3144i			0.252083i	0.992025	+	0.126041i	$0.0402272\pi$
$271$			68.3144i			0.252083i	−0.992025	+	0.126041i	$0.959773\pi$
$272$	40.1841	−	177.748i	0.147736	−	0.653485i
$273$	6.80723	−	1.10464i	0.0249349	−	0.00404631i
$274$	−42.6221	+	225.901i	−0.155555	+	0.824457i
$275$	−173.467	+	647.388i	−0.630789	+	2.35414i
$276$	−142.186	−	220.226i	−0.515167	−	0.797919i
$277$	−47.5880	+	12.7512i	−0.171798	+	0.0460331i	−0.343692	−	0.939082i	$-0.611678\pi$
$277$	−47.5880	+	12.7512i	−0.171798	+	0.0460331i	0.171895	+	0.985115i	$0.445011\pi$
$278$	−10.7376	−	142.298i	−0.0386245	−	0.511865i
$279$	−139.518	−	123.719i	−0.500065	−	0.443438i
$280$	−1.74236	−	7.57967i	−0.00622270	−	0.0270703i
$281$	−168.955	−	97.5462i	−0.601263	−	0.347139i	0.168275	−	0.985740i	$-0.446180\pi$
$281$	−168.955	−	97.5462i	−0.601263	−	0.347139i	−0.769538	+	0.638601i	$0.779514\pi$
$282$	203.699	−	193.524i	0.722337	−	0.686254i
$283$	−7.64261	−	2.04783i	−0.0270057	−	0.00723615i	0.245291	−	0.969450i	$-0.421117\pi$
$283$	−7.64261	−	2.04783i	−0.0270057	−	0.00723615i	−0.272297	+	0.962213i	$0.587783\pi$
$284$	158.932	−	127.012i	0.559619	−	0.447226i
$285$	−711.869	−	72.0916i	−2.49779	−	0.252953i
$286$	−684.180	+	239.801i	−2.39224	+	0.838466i
$287$			3.04426i			0.0106072i
$288$	−121.764	−	260.993i	−0.422792	−	0.906227i
$289$	−159.277			−0.551131
$290$	−53.4770	−	152.576i	−0.184403	−	0.526124i
$291$	−93.8841	+	42.2273i	−0.322626	+	0.145111i
$292$	−145.665	−	182.273i	−0.498854	−	0.624221i
$293$	−101.174	+	377.586i	−0.345304	+	1.28869i	0.546954	+	0.837163i	$0.315787\pi$
$293$	−101.174	+	377.586i	−0.345304	+	1.28869i	−0.892257	+	0.451528i	$0.850879\pi$
$294$	285.743	−	68.7728i	0.971916	−	0.233921i
$295$	−45.9269	+	79.5478i	−0.155685	+	0.269654i
$296$	25.6754	+	111.694i	0.0867411	+	0.377345i
$297$	541.115	+	22.1879i	1.82194	+	0.0747066i
$298$	−400.532	+	30.2235i	−1.34407	+	0.101421i
$299$	102.177	+	381.331i	0.341730	+	1.27535i
$300$	356.782	+	182.984i	1.18927	+	0.609948i
$301$	6.83546	+	1.83155i	0.0227092	+	0.00608490i
$302$	−148.444	−	28.0078i	−0.491537	−	0.0927412i
$303$	416.375	+	158.022i	1.37418	+	0.521525i
$304$	−422.215	+	266.512i	−1.38886	+	0.876684i
$305$	160.531			0.526333
$306$	162.102	−	125.512i	0.529744	−	0.410170i
$307$	49.9701	+	49.9701i	0.162769	+	0.162769i	0.783792	−	0.621023i	$-0.213283\pi$
$307$	49.9701	+	49.9701i	0.162769	+	0.162769i	−0.621023	+	0.783792i	$0.713283\pi$
$308$	9.34975	−	4.09074i	0.0303563	−	0.0132816i
$309$	−19.1361	+	188.960i	−0.0619291	+	0.611520i
$310$	261.585	−	178.543i	0.843821	−	0.575945i
$311$	−71.6417	−	124.087i	−0.230359	−	0.398994i	0.727555	−	0.686050i	$-0.240657\pi$
$311$	−71.6417	−	124.087i	−0.230359	−	0.398994i	−0.957914	+	0.287056i	$0.907323\pi$
$312$	54.0842	+	430.347i	0.173347	+	1.37932i
$313$	−7.63331	−	4.40709i	−0.0243876	−	0.0140802i	0.487757	−	0.872980i	$-0.337815\pi$
$313$	−7.63331	−	4.40709i	−0.0243876	−	0.0140802i	−0.512144	+	0.858899i	$0.671149\pi$
$314$	−17.8670	−	236.779i	−0.0569013	−	0.754075i
$315$	3.91295	−	7.82579i	0.0124221	−	0.0248438i
$316$	188.563	−	28.6204i	0.596719	−	0.0905708i
$317$	−63.1151	−	235.549i	−0.199101	−	0.743056i	−0.991167	−	0.132620i	$-0.957661\pi$
$317$	−63.1151	−	235.549i	−0.199101	−	0.743056i	0.792066	−	0.610436i	$-0.209006\pi$
$318$	−7.70622	+	4.18981i	−0.0242334	+	0.0131755i
$319$	183.729	−	106.076i	0.575954	−	0.332527i
$320$	480.335	−	92.4253i	1.50105	−	0.288829i
$321$	−135.710	+	22.0223i	−0.422772	+	0.0686053i
$322$	−1.83816	−	5.24447i	−0.00570856	−	0.0162872i
$323$	−251.321	−	251.321i	−0.778085	−	0.778085i
$324$	81.1241	−	313.680i	0.250383	−	0.968147i
$325$	−426.997	−	426.997i	−1.31384	−	1.31384i
$326$	−130.036	+	270.380i	−0.398884	+	0.829386i
$327$	−60.1134	+	9.75490i	−0.183833	+	0.0298315i
$328$	−191.342	−	6.86296i	−0.583359	−	0.0209237i
$329$	5.15851	−	2.97826i	0.0156793	−	0.00905248i
$330$	−260.740	+	882.086i	−0.790121	+	2.67299i
$331$	66.7251	+	249.021i	0.201586	+	0.752330i	0.990463	+	0.137779i	$0.0439963\pi$
$331$	66.7251	+	249.021i	0.201586	+	0.752330i	−0.788877	+	0.614551i	$0.789337\pi$
$332$	119.911	−	162.824i	0.361176	−	0.490435i
$333$	−57.6612	+	115.321i	−0.173157	+	0.346309i
$334$	288.105	−	335.133i	0.862589	−	1.00339i
$335$	−187.717	−	108.378i	−0.560349	−	0.323517i
$336$	−1.21500	−	5.98343i	−0.00361606	−	0.0178078i
$337$	258.037	+	446.934i	0.765689	+	1.32621i	0.939881	+	0.341501i	$0.110935\pi$
$337$	258.037	+	446.934i	0.765689	+	1.32621i	−0.174192	+	0.984712i	$0.555731\pi$
$338$	58.4406	−	309.741i	0.172901	−	0.916393i
$339$	51.9504	−	512.985i	0.153246	−	1.51323i
$340$	139.571	+	319.002i	0.410504	+	0.938242i
$341$	293.864	+	293.864i	0.861771	+	0.861771i
$342$	−557.214	−	70.8874i	−1.62928	−	0.207273i
$343$	12.4634			0.0363365
$344$	−130.529	+	425.502i	−0.379445	+	1.23692i
$345$	468.284	+	177.722i	1.35734	+	0.515137i
$346$	15.5620	−	10.6218i	0.0449770	−	0.0306988i
$347$	287.812	+	77.1189i	0.829428	+	0.222245i	0.648464	−	0.761245i	$-0.275412\pi$
$347$	287.812	+	77.1189i	0.829428	+	0.222245i	0.180964	+	0.983490i	$0.442078\pi$
$348$	−38.9005	−	120.814i	−0.111783	−	0.347167i
$349$	−163.593	−	610.537i	−0.468747	−	1.74939i	−0.644157	−	0.764894i	$-0.722792\pi$
$349$	−163.593	−	610.537i	−0.468747	−	1.74939i	0.175409	−	0.984496i	$-0.443875\pi$
$350$	6.44598	+	5.54143i	0.0184171	+	0.0158326i
$351$	−261.082	+	412.225i	−0.743823	+	1.17443i
$352$	236.038	+	596.884i	0.670564	+	1.69569i
$353$	98.0473	−	169.823i	0.277754	−	0.481085i	−0.693072	−	0.720868i	$-0.743743\pi$
$353$	98.0473	−	169.823i	0.277754	−	0.481085i	0.970826	+	0.239784i	$0.0770766\pi$
$354$	−37.6419	+	61.5045i	−0.106333	+	0.173742i
$355$	−100.612	+	375.489i	−0.283414	+	1.05772i
$356$	133.860	+	167.500i	0.376010	+	0.470505i
$357$	3.96375	−	1.78282i	0.0111029	−	0.00499389i
$358$	30.6627	−	63.7558i	0.0856499	−	0.178089i
$359$	−234.925			−0.654388			−0.327194	−	0.944957i	$-0.606103\pi$
$359$	−234.925			−0.654388			−0.327194	+	0.944957i	$0.606103\pi$
$360$	483.055	+	263.584i	1.34182	+	0.732178i
$361$			612.804i			1.69752i
$362$	9.90452	−	20.5941i	0.0273606	−	0.0568898i
$363$	−839.692	−	85.0364i	−2.31320	−	0.234260i
$364$	−1.02009	+	9.13827i	−0.00280244	+	0.0251051i
$365$	430.634	+	115.388i	1.17982	+	0.316132i
$366$	125.982	+	3.22725i	0.344214	+	0.00881763i
$367$	−488.198	−	281.861i	−1.33024	−	0.768014i	−0.344904	−	0.938638i	$-0.612088\pi$
$367$	−488.198	−	281.861i	−1.33024	−	0.768014i	−0.985336	+	0.170624i	$0.945422\pi$
$368$	333.776	−	103.711i	0.906999	−	0.281823i
$369$	−161.160	−	142.911i	−0.436749	−	0.387292i
$370$	−166.057	−	142.754i	−0.448802	−	0.385822i
$371$	−0.179619	+	0.0481288i	−0.000484149	+	0.000129727i
$372$	208.877	−	134.859i	0.561496	−	0.362524i
$373$	146.529	−	546.853i	0.392838	−	1.46609i	−0.432593	−	0.901589i	$-0.642401\pi$
$373$	146.529	−	546.853i	0.392838	−	1.46609i	0.825431	−	0.564503i	$-0.190932\pi$
$374$	−377.383	+	257.580i	−1.00904	+	0.688718i
$375$	−190.434	+	30.9026i	−0.507824	+	0.0824071i
$376$	175.564	+	330.943i	0.466926	+	0.880168i
$377$			191.147i			0.507021i
$378$	3.22814	−	6.06289i	0.00854006	−	0.0160394i
$379$	194.843	−	194.843i	0.514098	−	0.514098i	−0.401682	−	0.915779i	$-0.631574\pi$
$379$	194.843	−	194.843i	0.514098	−	0.514098i	0.915779	+	0.401682i	$0.131574\pi$
$380$	347.624	−	888.426i	0.914800	−	2.33796i
$381$	92.0693	−	127.739i	0.241652	−	0.335272i
$382$	29.4510	−	156.093i	0.0770967	−	0.408620i
$383$	255.158	−	147.315i	0.666208	−	0.384635i	−0.128430	−	0.991719i	$-0.540994\pi$
$383$	255.158	−	147.315i	0.666208	−	0.384635i	0.794638	+	0.607083i	$0.207661\pi$
$384$	378.817	−	62.8774i	0.986503	−	0.163743i
$385$	−9.74995	+	16.8874i	−0.0253246	+	0.0438634i
$386$	164.432	−	191.272i	0.425989	−	0.495524i
$387$	−417.847	+	275.882i	−1.07971	+	0.712873i
$388$	−20.5973	−	135.704i	−0.0530858	−	0.349752i
$389$	−617.288	+	165.402i	−1.58686	+	0.425198i	−0.941041	−	0.338293i	$-0.890150\pi$
$389$	−617.288	+	165.402i	−1.58686	+	0.425198i	−0.645819	+	0.763491i	$0.723484\pi$
$390$	−570.811	−	600.825i	−1.46362	−	1.54058i
$391$	124.402	+	215.470i	0.318163	+	0.551075i
$392$	−14.0464	+	391.619i	−0.0358327	+	0.999027i
$393$	245.458	−	200.314i	0.624576	−	0.509706i
$394$	165.906	−	344.962i	0.421080	−	0.875538i
$395$	−257.684	+	257.684i	−0.652364	+	0.652364i
$396$	−222.358	+	687.005i	−0.561509	+	1.73486i
$397$	−248.977	+	248.977i	−0.627145	+	0.627145i	−0.947349	−	0.320203i	$-0.896249\pi$
$397$	−248.977	+	248.977i	−0.627145	+	0.627145i	0.320203	+	0.947349i	$0.396249\pi$
$398$	126.247	+	360.196i	0.317203	+	0.905016i
$399$	−11.1332	−	4.22526i	−0.0279028	−	0.0105896i
$400$	−362.828	+	392.658i	−0.907071	+	0.981645i
$401$	256.606	+	444.454i	0.639915	+	1.10836i	0.985451	+	0.169959i	$0.0543636\pi$
$401$	256.606	+	444.454i	0.639915	+	1.10836i	−0.345537	+	0.938405i	$0.612303\pi$
$402$	−145.138	−	88.8273i	−0.361040	−	0.220963i
$403$	−361.680	+	96.9118i	−0.897469	+	0.240476i
$404$	−352.120	+	478.137i	−0.871584	+	1.18351i
$405$	230.600	+	574.525i	0.569382	+	1.41858i
$406$	−0.202463	−	2.68310i	−0.000498677	−	0.00660863i
$407$	143.675	−	248.853i	0.353011	−	0.611432i
$408$	103.120	+	253.154i	0.252745	+	0.620474i
$409$	−318.798	+	184.058i	−0.779458	+	0.450020i	−0.836238	−	0.548366i	$-0.815250\pi$
$409$	−318.798	+	184.058i	−0.779458	+	0.450020i	0.0567800	+	0.998387i	$0.481917\pi$
$410$	302.162	−	206.239i	0.736981	−	0.503022i
$411$	−141.449	−	314.484i	−0.344158	−	0.765168i
$412$	−235.825	−	92.2738i	−0.572391	−	0.223965i
$413$	−1.08095	+	1.08095i	−0.00261732	+	0.00261732i
$414$	363.928	+	148.888i	0.879054	+	0.359632i
$415$			386.375i			0.931025i
$416$	−572.070	−	84.7171i	−1.37517	−	0.203647i
$417$	135.339	+	165.839i	0.324554	+	0.397697i
$418$	1230.16	+	232.101i	2.94296	+	0.555266i
$419$	87.8999	−	328.047i	0.209785	−	0.782928i	−0.778153	−	0.628075i	$-0.783843\pi$
$419$	87.8999	−	328.047i	0.209785	−	0.782928i	0.987938	−	0.154853i	$-0.0494904\pi$
$420$	8.64879	+	7.82909i	0.0205924	+	0.0186407i
$421$	558.068	−	149.534i	1.32558	−	0.355187i	0.474512	−	0.880249i	$-0.342625\pi$
$421$	558.068	−	149.534i	1.32558	−	0.355187i	0.851064	+	0.525062i	$0.175958\pi$
$422$	317.297	−	23.9427i	0.751889	−	0.0567364i
$423$	−84.4960	+	412.900i	−0.199754	+	0.976122i
$424$	−2.62012	−	11.3981i	−0.00617953	−	0.0268824i
$425$	−329.586	−	190.287i	−0.775497	−	0.447734i
$426$	−86.5074	+	292.655i	−0.203069	+	0.686984i
$427$	2.58064	+	0.691481i	0.00604366	+	0.00161939i
$428$	20.3366	−	182.182i	0.0475155	−	0.425659i
$429$	635.864	−	882.209i	1.48220	−	2.05643i
$430$	−281.287	−	802.545i	−0.654157	−	1.86638i
$431$			309.517i			0.718137i	0.933311	+	0.359069i	$0.116906\pi$
$431$			309.517i			0.718137i	−0.933311	+	0.359069i	$0.883094\pi$
$432$	373.795	+	216.567i	0.865266	+	0.501314i
$433$	−206.506			−0.476920			−0.238460	−	0.971152i	$-0.576643\pi$
$433$	−206.506			−0.476920			−0.238460	+	0.971152i	$0.576643\pi$
$434$	4.97420	−	1.74343i	0.0114613	−	0.00401712i
$435$	196.737	+	141.801i	0.452270	+	0.325980i
$436$	9.00822	−	80.6985i	0.0206611	−	0.185088i
$437$	176.433	−	658.458i	0.403737	−	1.50677i
$438$	335.635	+	99.2120i	0.766290	+	0.226511i
$439$	390.298	−	676.015i	0.889061	−	1.53990i	0.0480730	−	0.998844i	$-0.484692\pi$
$439$	390.298	−	676.015i	0.889061	−	1.53990i	0.840988	−	0.541054i	$-0.181975\pi$
$440$	−1039.45	−	650.887i	−2.36238	−	1.47929i
$441$	−292.495	+	329.847i	−0.663255	+	0.747952i
$442$	−30.9759	−	410.502i	−0.0700812	−	0.928738i
$443$	116.703	+	435.541i	0.263437	+	0.983162i	0.963200	+	0.268786i	$0.0866225\pi$
$443$	116.703	+	435.541i	0.263437	+	0.983162i	−0.699762	+	0.714376i	$0.746711\pi$
$444$	−127.449	−	115.369i	−0.287046	−	0.259841i
$445$	−395.733	−	106.036i	−0.889287	−	0.238284i
$446$	97.1661	−	514.989i	0.217861	−	1.15468i
$447$	466.794	−	380.943i	1.04428	−	0.852221i
$448$	8.11980	+	0.583226i	0.0181246	+	0.00130184i
$449$	129.052			0.287421			0.143711	−	0.989620i	$-0.454097\pi$
$449$	129.052			0.287421			0.143711	+	0.989620i	$0.454097\pi$
$450$	−595.960	+	81.1057i	−1.32436	+	0.180235i
$451$	339.449	+	339.449i	0.752658	+	0.752658i
$452$	640.214	+	250.503i	1.41640	+	0.554211i
$453$	206.654	−	92.9489i	0.456189	−	0.205185i
$454$	216.797	+	317.630i	0.477526	+	0.699626i
$455$	−8.78460	−	15.2154i	−0.0193068	−	0.0334404i
$456$	290.670	−	690.233i	0.637434	−	1.51367i
$457$	202.429	+	116.872i	0.442952	+	0.255738i	0.704849	−	0.709357i	$-0.251015\pi$
$457$	202.429	+	116.872i	0.442952	+	0.255738i	−0.261897	+	0.965096i	$0.584348\pi$
$458$	623.398	−	47.0407i	1.36113	−	0.102709i
$459$	−91.6947	+	293.531i	−0.199770	+	0.639500i
$460$	−396.018	+	537.745i	−0.860908	+	1.16901i
$461$	−203.655	−	760.052i	−0.441769	−	1.64870i	−0.724329	−	0.689454i	$-0.757850\pi$
$461$	−203.655	−	760.052i	−0.441769	−	1.64870i	0.282561	−	0.959249i	$-0.408816\pi$
$462$	−7.99110	+	13.0570i	−0.0172968	+	0.0282618i
$463$	−143.716	+	82.9742i	−0.310401	+	0.179210i	−0.647106	−	0.762400i	$-0.724021\pi$
$463$	−143.716	+	82.9742i	−0.310401	+	0.179210i	0.336705	+	0.941610i	$0.390687\pi$
$464$	169.098	−	6.67667i	0.364436	−	0.0143894i
$465$	−168.564	+	444.151i	−0.362503	+	0.955164i
$466$	−428.792	+	150.289i	−0.920155	+	0.322509i
$467$	−541.992	−	541.992i	−1.16058	−	1.16058i	−0.984348	−	0.176234i	$-0.943608\pi$
$467$	−541.992	−	541.992i	−1.16058	−	1.16058i	−0.176234	−	0.984348i	$-0.556392\pi$
$468$	−435.885	−	482.993i	−0.931377	−	1.03204i
$469$	−2.55083	−	2.55083i	−0.00543887	−	0.00543887i
$470$	−645.085	−	310.247i	−1.37252	−	0.660099i
$471$	225.199	+	275.951i	0.478129	+	0.585883i
$472$	−65.5045	−	70.3783i	−0.138781	−	0.149107i
$473$	966.411	−	557.958i	2.04315	−	1.17961i
$474$	−207.406	+	197.046i	−0.437566	+	0.415708i
$475$	269.875	+	1007.19i	0.568157	+	2.12039i
$476$	0.869608	+	5.72936i	0.00182691	+	0.0120365i
$477$	5.88421	−	11.7683i	0.0123359	−	0.0246714i
$478$	138.633	+	119.179i	0.290027	+	0.249328i
$479$	630.680	+	364.123i	1.31666	+	0.760174i	0.983190	−	0.182587i	$-0.0584470\pi$
$479$	630.680	+	364.123i	1.31666	+	0.760174i	0.333470	+	0.942761i	$0.391780\pi$
$480$	−511.582	+	525.955i	−1.06580	+	1.09574i
$481$	129.450	+	224.214i	0.269126	+	0.466141i
$482$	−935.627	−	176.530i	−1.94113	−	0.366245i
$483$	6.76242	+	4.87411i	0.0140009	+	0.0100913i
$484$	410.043	−	1047.95i	0.847196	−	2.16519i
$485$	185.448	+	185.448i	0.382367	+	0.382367i
$486$	169.421	+	455.514i	0.348603	+	0.937271i
$487$	−721.954			−1.48245			−0.741226	−	0.671255i	$-0.765755\pi$
$487$	−721.954			−1.48245			−0.741226	+	0.671255i	$0.765755\pi$
$488$	−49.2796	+	160.643i	−0.100983	+	0.329186i
$489$	−72.0867	−	444.226i	−0.147417	−	0.908438i
$490$	−422.110	−	618.435i	−0.861448	−	1.26211i
$491$	−759.444	−	203.492i	−1.54673	−	0.414445i	−0.618296	−	0.785945i	$-0.712177\pi$
$491$	−759.444	−	203.492i	−1.54673	−	0.414445i	−0.928433	+	0.371501i	$0.878843\pi$
$492$	241.278	−	155.779i	0.490403	−	0.316623i
$493$	31.1790	+	116.362i	0.0632434	+	0.236028i
$494$	−735.283	+	855.306i	−1.48843	+	1.73139i
$495$	−436.300	−	1308.92i	−0.881414	−	2.64429i
$496$	98.3664	+	316.575i	0.198319	+	0.638256i
$497$	−3.23481	+	5.60285i	−0.00650866	+	0.0112733i
$498$	−7.76751	+	303.221i	−0.0155974	+	0.608877i
$499$	−7.16071	+	26.7241i	−0.0143501	+	0.0535554i	−0.972730	−	0.231942i	$-0.925492\pi$
$499$	−7.16071	+	26.7241i	−0.0143501	+	0.0535554i	0.958380	+	0.285497i	$0.0921587\pi$
$500$	28.5372	−	255.645i	0.0570745	−	0.511291i
$501$	−66.7932	+	659.550i	−0.133320	+	1.31647i
$502$	372.143	+	178.978i	0.741321	+	0.356530i
$503$	6.95957			0.0138361			0.00691806	−	0.999976i	$-0.497798\pi$
$503$	6.95957			0.0138361			0.00691806	+	0.999976i	$0.497798\pi$
$504$	6.63004	+	6.31801i	0.0131548	+	0.0125357i
$505$		−	1134.60i		−	2.24673i
$506$	−789.745	−	379.819i	−1.56076	−	0.750631i
$507$	193.946	+	431.200i	0.382536	+	0.850493i
$508$	131.070	+	164.009i	0.258011	+	0.322852i
$509$	−689.437	−	184.734i	−1.35449	−	0.362936i	−0.492702	−	0.870198i	$-0.663991\pi$
$509$	−689.437	−	184.734i	−1.35449	−	0.362936i	−0.861792	+	0.507262i	$0.830658\pi$
$510$	−445.488	−	272.647i	−0.873506	−	0.534602i
$511$	6.42569	+	3.70987i	0.0125747	+	0.00726003i
$512$	−54.9629	+	509.041i	−0.107349	+	0.994221i
$513$	746.323	−	391.031i	1.45482	−	0.762243i
$514$	−298.008	+	346.653i	−0.579782	+	0.674422i
$515$	467.376	−	125.233i	0.907525	−	0.243171i
$516$	−204.616	−	635.479i	−0.396542	−	1.23155i
$517$	243.107	−	907.287i	0.470226	−	1.75491i
$518$	−2.05456	−	3.01014i	−0.00396633	−	0.00581109i
$519$	−10.0281	+	26.4232i	−0.0193220	+	0.0509118i
$520$	976.140	−	517.839i	1.87719	−	0.995845i
$521$			466.290i			0.894990i	0.894287	+	0.447495i	$0.147684\pi$
$521$			466.290i			0.894990i	−0.894287	+	0.447495i	$0.852316\pi$
$522$	151.546	+	115.238i	0.290317	+	0.220763i
$523$	368.440	−	368.440i	0.704475	−	0.704475i	−0.260893	−	0.965368i	$-0.584017\pi$
$523$	368.440	−	368.440i	0.704475	−	0.704475i	0.965368	+	0.260893i	$0.0840170\pi$
$524$	169.325	+	387.007i	0.323139	+	0.738563i
$525$	−12.6858	−	1.28470i	−0.0241635	−	0.00244706i
$526$	−612.662	−	115.595i	−1.16476	−	0.219761i
$527$	−204.367	+	117.991i	−0.387792	+	0.223892i
$528$	−802.657	−	531.702i	−1.52018	−	1.00701i
$529$	25.9020	−	44.8636i	0.0489641	−	0.0848083i
$530$	16.9457	+	14.5678i	0.0319731	+	0.0274864i
$531$	−6.48007	−	107.969i	−0.0122035	−	0.203332i
$532$	9.41512	−	12.7846i	0.0176976	−	0.0240313i
$533$	−417.785	+	111.945i	−0.783836	+	0.210028i
$534$	−308.433	−	91.1711i	−0.577589	−	0.170732i
$535$	175.131	+	303.336i	0.327348	+	0.566983i
$536$	166.079	−	154.577i	0.309848	−	0.288391i
$537$	16.9981	+	104.749i	0.0316538	+	0.195063i
$538$	891.062	+	428.547i	1.65625	+	0.796555i
$539$	694.750	−	694.750i	1.28896	−	1.28896i
$540$	−820.477	+	90.3280i	−1.51940	+	0.167274i
$541$	383.939	−	383.939i	0.709683	−	0.709683i	−0.256785	−	0.966468i	$-0.582663\pi$
$541$	383.939	−	383.939i	0.709683	−	0.709683i	0.966468	+	0.256785i	$0.0826633\pi$
$542$	128.938	−	45.1921i	0.237894	−	0.0833803i
$543$	5.49066	+	33.8355i	0.0101117	+	0.0623122i
$544$	−362.069	+	41.7415i	−0.665568	+	0.0767307i
$545$	77.5753	+	134.364i	0.142340	+	0.246540i
$546$	−6.58813	−	12.1174i	−0.0120662	−	0.0221930i
$547$	571.312	−	153.083i	1.04445	−	0.279859i	0.304491	−	0.952515i	$-0.401514\pi$
$547$	571.312	−	153.083i	1.04445	−	0.279859i	0.739955	+	0.672657i	$0.234847\pi$
$548$	454.568	−	68.9948i	0.829503	−	0.125903i
$549$	−157.753	+	104.156i	−0.287346	+	0.189719i
$550$	1336.65	−	100.862i	2.43027	−	0.183385i
$551$	165.030	−	285.840i	0.299510	−	0.518767i
$552$	−321.599	+	414.052i	−0.582606	+	0.750095i
$553$	−5.25239	+	3.03247i	−0.00949799	+	0.00548367i
$554$	55.5478	+	81.3834i	0.100267	+	0.146902i
$555$	326.803	+	33.0956i	0.588834	+	0.0596318i
$556$	−261.475	+	114.401i	−0.470278	+	0.205758i
$557$	156.162	−	156.162i	0.280362	−	0.280362i	−0.552891	−	0.833253i	$-0.686476\pi$
$557$	156.162	−	156.162i	0.280362	−	0.280362i	0.833253	+	0.552891i	$0.186476\pi$
$558$	−141.215	+	345.174i	−0.253074	+	0.618592i
$559$			1005.43i			1.79862i
$560$	−13.1534	+	8.30277i	−0.0234883	+	0.0148264i
$561$	243.183	−	640.768i	0.433482	−	1.14219i
$562$	−72.3421	+	383.420i	−0.128723	+	0.682241i
$563$	49.9967	−	186.590i	0.0888041	−	0.331421i	−0.907203	−	0.420693i	$-0.861787\pi$
$563$	49.9967	−	186.590i	0.0888041	−	0.331421i	0.996007	+	0.0892711i	$0.0284538\pi$
$564$	−500.015	−	256.445i	−0.886551	−	0.454690i
$565$	−1268.82	+	339.980i	−2.24571	+	0.601735i
$566$	1.19070	+	15.7796i	0.00210371	+	0.0278791i
$567$	1.23230	+	10.2291i	0.00217336	+	0.0180408i
$568$	−344.865	−	215.949i	−0.607156	−	0.380192i
$569$	−660.098	−	381.108i	−1.16010	−	0.669785i	−0.208774	−	0.977964i	$-0.566947\pi$
$569$	−660.098	−	381.108i	−1.16010	−	0.669785i	−0.951328	+	0.308179i	$0.900281\pi$
$570$	334.857	+	1391.29i	0.587468	+	2.44086i
$571$	1013.81	+	271.650i	1.77550	+	0.475744i	0.989751	−	0.142803i	$-0.0456117\pi$
$571$	1013.81	+	271.650i	1.77550	+	0.475744i	0.785748	+	0.618547i	$0.212278\pi$
$572$	905.214	+	1132.70i	1.58254	+	1.98025i
$573$	97.7382	+	217.302i	0.170573	+	0.379235i
$574$	5.74581	−	2.01387i	0.0100101	−	0.00350849i
$575$		−	729.925i		−	1.26944i
$576$	−412.054	+	402.476i	−0.715372	+	0.698743i
$577$	−870.365			−1.50843			−0.754216	−	0.656627i	$-0.771983\pi$
$577$	−870.365			−1.50843			−0.754216	+	0.656627i	$0.771983\pi$
$578$	105.367	+	300.623i	0.182295	+	0.520110i
$579$	−38.1212	+	376.428i	−0.0658398	+	0.650135i
$580$	−252.599	+	201.868i	−0.435515	+	0.348048i
$581$	−1.66429	+	6.21122i	−0.00286453	+	0.0106906i
$582$	141.808	+	149.265i	0.243657	+	0.256468i
$583$	−14.6618	+	25.3949i	−0.0251488	+	0.0435591i
$584$	−247.664	+	395.512i	−0.424082	+	0.677247i
$585$	1217.88	+	249.227i	2.08184	+	0.426029i
$586$	779.596	−	58.8271i	1.33037	−	0.100388i
$587$	−299.012	−	1115.93i	−0.509391	−	1.90107i	−0.426433	−	0.904519i	$-0.640230\pi$
$587$	−299.012	−	1115.93i	−0.509391	−	1.90107i	−0.0829574	−	0.996553i	$-0.526437\pi$
$588$	−318.832	−	493.824i	−0.542231	−	0.839836i
$589$	624.525	+	167.341i	1.06031	+	0.284110i
$590$	180.523	+	34.0603i	0.305971	+	0.0577293i
$591$	91.9712	+	566.762i	0.155620	+	0.958988i
$592$	193.829	−	122.350i	0.327414	−	0.206672i
$593$	−706.677			−1.19170			−0.595849	−	0.803096i	$-0.703184\pi$
$593$	−706.677			−1.19170			−0.595849	+	0.803096i	$0.703184\pi$
$594$	−316.087	−	1035.99i	−0.532133	−	1.74410i
$595$	−7.82953	−	7.82953i	−0.0131589	−	0.0131589i
$596$	322.010	+	735.981i	0.540284	+	1.23487i
$597$	−464.452	−	334.760i	−0.777976	−	0.560737i
$598$	652.140	−	445.115i	1.09054	−	0.744339i
$599$	−560.848	−	971.417i	−0.936307	−	1.62173i	−0.772287	−	0.635274i	$-0.780887\pi$
$599$	−560.848	−	971.417i	−0.936307	−	1.62173i	−0.164020	−	0.986457i	$-0.552446\pi$
$600$	109.347	−	794.449i	0.182244	−	1.32408i
$601$	715.847	+	413.294i	1.19109	+	0.687678i	0.958554	−	0.284910i	$-0.0919636\pi$
$601$	715.847	+	413.294i	1.19109	+	0.687678i	0.232538	+	0.972587i	$0.425297\pi$
$602$	−1.06495	−	14.1130i	−0.00176902	−	0.0234436i
$603$	254.786	−	15.2917i	0.422530	−	0.0253593i
$604$	45.3378	+	298.705i	0.0750627	+	0.494545i
$605$	556.506	+	2076.91i	0.919844	+	3.43290i
$606$	22.8095	−	890.414i	0.0376394	−	1.46933i
$607$	−12.4843	+	7.20784i	−0.0205673	+	0.0118745i	−0.510248	−	0.860027i	$-0.670447\pi$
$607$	−12.4843	+	7.20784i	−0.0205673	+	0.0118745i	0.489681	+	0.871902i	$0.337113\pi$
$608$	782.330	+	620.593i	1.28673	+	1.02071i
$609$	2.55188	+	3.12698i	0.00419027	+	0.00513461i
$610$	−106.197	−	302.991i	−0.174093	−	0.496707i
$611$	598.419	+	598.419i	0.979409	+	0.979409i
$612$	−344.130	−	222.925i	−0.562305	−	0.364256i
$613$	846.490	+	846.490i	1.38090	+	1.38090i	0.843029	+	0.537868i	$0.180770\pi$
$613$	846.490	+	846.490i	1.38090	+	1.38090i	0.537868	+	0.843029i	$0.319230\pi$
$614$	61.2580	−	127.372i	0.0997687	−	0.207446i
$615$	−194.712	+	513.049i	−0.316604	+	0.834227i
$616$	−13.9061	−	14.9408i	−0.0225749	−	0.0242545i
$617$	−816.298	+	471.290i	−1.32301	+	0.763841i	−0.984208	−	0.177016i	$-0.943356\pi$
$617$	−816.298	+	471.290i	−1.32301	+	0.763841i	−0.338804	+	0.940857i	$0.610022\pi$
$618$	369.306	−	88.8848i	0.597583	−	0.143827i
$619$	−147.899	−	551.967i	−0.238932	−	0.891707i	−0.976337	−	0.216256i	$-0.930616\pi$
$619$	−147.899	−	551.967i	−0.238932	−	0.891707i	0.737405	−	0.675451i	$-0.236051\pi$
$620$	−510.033	−	375.609i	−0.822634	−	0.605822i
$621$	−575.489	+	129.185i	−0.926713	+	0.208027i
$622$	−186.812	+	217.306i	−0.300341	+	0.349366i
$623$	−5.90490	−	3.40920i	−0.00947818	−	0.00547223i
$624$	776.469	−	386.768i	1.24434	−	0.619820i
$625$	−171.925	−	297.783i	−0.275080	−	0.476452i
$626$	−3.26838	+	17.3227i	−0.00522106	+	0.0276721i
$627$	−1712.54	+	770.268i	−2.73132	+	1.22850i
$628$	−435.084	+	190.360i	−0.692809	+	0.303121i
$629$	115.376	+	115.376i	0.183428	+	0.183428i
$630$	−17.3591	−	2.20839i	−0.0275542	−	0.00350538i
$631$	296.277			0.469536			0.234768	−	0.972051i	$-0.424567\pi$
$631$	296.277			0.469536			0.234768	+	0.972051i	$0.424567\pi$
$632$	−178.759	−	336.966i	−0.282847	−	0.533174i
$633$	−369.789	+	301.778i	−0.584184	+	0.476743i
$634$	−402.828	+	274.948i	−0.635376	+	0.433672i
$635$	−387.484	−	103.826i	−0.610211	−	0.163506i
$636$	13.0059	+	11.7732i	0.0204495	+	0.0185114i
$637$	229.118	+	855.079i	0.359683	+	1.34235i
$638$	−321.754	−	276.603i	−0.504316	−	0.433547i
$639$	−144.754	−	434.270i	−0.226532	−	0.679608i
$640$	−492.203	−	845.454i	−0.769067	−	1.32102i
$641$	4.62426	−	8.00946i	0.00721414	−	0.0124953i	−0.862396	−	0.506235i	$-0.831037\pi$
$641$	4.62426	−	8.00946i	0.00721414	−	0.0124953i	0.869610	+	0.493739i	$0.164370\pi$
$642$	131.342	+	241.574i	0.204582	+	0.376283i
$643$	−25.9755	+	96.9419i	−0.0403974	+	0.150765i	−0.983179	−	0.182647i	$-0.941533\pi$
$643$	−25.9755	+	96.9419i	−0.0403974	+	0.150765i	0.942781	+	0.333412i	$0.108200\pi$
$644$	−8.68254	+	6.93876i	−0.0134822	+	0.0107745i
$645$	1034.83	+	745.870i	1.60439	+	1.15639i
$646$	−308.093	+	640.608i	−0.476925	+	0.991653i
$647$	570.038			0.881048			0.440524	−	0.897741i	$-0.354793\pi$
$647$	570.038			0.881048			0.440524	+	0.897741i	$0.354793\pi$
$648$	−645.713	+	54.3934i	−0.996471	+	0.0839405i
$649$			241.062i			0.371437i
$650$	−523.453	+	1088.40i	−0.805312	+	1.67446i
$651$	−4.62293	+	6.41393i	−0.00710127	+	0.00985243i
$652$	596.345	+	66.5689i	0.914640	+	0.102100i
$653$	−555.297	−	148.791i	−0.850378	−	0.227858i	−0.192794	−	0.981239i	$-0.561755\pi$
$653$	−555.297	−	148.791i	−0.850378	−	0.227858i	−0.657584	+	0.753381i	$0.728422\pi$
$654$	58.1786	+	107.006i	0.0889581	+	0.163618i
$655$	−699.008	−	403.573i	−1.06719	−	0.616141i
$656$	113.625	+	365.683i	0.173209	+	0.557444i
$657$	−498.047	+	166.013i	−0.758063	+	0.252683i
$658$	−9.03377	−	7.76608i	−0.0137291	−	0.0118026i
$659$	587.306	−	157.368i	0.891208	−	0.238798i	0.215971	−	0.976400i	$-0.430708\pi$
$659$	587.306	−	157.368i	0.891208	−	0.238798i	0.675236	+	0.737601i	$0.264042\pi$
$660$	1837.36	−	91.4006i	2.78388	−	0.138486i
$661$	256.334	−	956.653i	0.387798	−	1.44728i	−0.445911	−	0.895077i	$-0.647120\pi$
$661$	256.334	−	956.653i	0.387798	−	1.44728i	0.833709	−	0.552204i	$-0.186213\pi$
$662$	425.868	−	290.674i	0.643306	−	0.439085i
$663$	390.425	+	478.413i	0.588877	+	0.721589i
$664$	−386.644	−	118.609i	−0.582295	−	0.178628i
$665$			30.3374i			0.0456201i
$666$	255.804	+	32.5428i	0.384090	+	0.0488631i
$667$	−163.377	+	163.377i	−0.244943	+	0.244943i
$668$	−823.130	−	322.075i	−1.23223	−	0.482148i
$669$	322.463	+	716.933i	0.482007	+	1.07165i
$670$	−80.3754	+	425.997i	−0.119963	+	0.635817i
$671$	364.857	−	210.650i	0.543751	−	0.313935i
$672$	−10.4895	+	6.25144i	−0.0156094	+	0.00930274i
$673$	−363.782	+	630.088i	−0.540537	+	0.936238i	0.458336	+	0.888779i	$0.348446\pi$
$673$	−363.782	+	630.088i	−0.540537	+	0.936238i	−0.998873	+	0.0474591i	$0.984888\pi$
$674$	672.854	−	782.687i	0.998300	−	1.16126i
$675$	663.539	−	611.267i	0.983020	−	0.905580i
$676$	−623.273	+	94.6011i	−0.922002	+	0.139942i
$677$	−532.142	+	142.587i	−0.786030	+	0.210616i	−0.629442	−	0.777048i	$-0.716716\pi$
$677$	−532.142	+	142.587i	−0.786030	+	0.210616i	−0.156588	+	0.987664i	$0.550050\pi$
$678$	−1002.59	+	241.303i	−1.47874	+	0.355904i
$679$	2.18238	+	3.78000i	0.00321411	+	0.00556700i
$680$	509.762	−	474.460i	0.749650	−	0.697736i
$681$	−539.313	−	204.679i	−0.791943	−	0.300557i
$682$	360.246	−	749.046i	0.528220	−	1.09831i
$683$	63.9582	−	63.9582i	0.0936431	−	0.0936431i	−0.658733	−	0.752376i	$-0.728907\pi$
$683$	63.9582	−	63.9582i	0.0936431	−	0.0936431i	0.752376	+	0.658733i	$0.228907\pi$
$684$	234.820	+	1098.59i	0.343304	+	1.60613i
$685$	−621.195	+	621.195i	−0.906854	+	0.906854i
$686$	−8.24495	−	23.5238i	−0.0120189	−	0.0342912i
$687$	−726.529	+	592.909i	−1.05754	+	0.863040i
$688$	889.452	−	35.1191i	1.29281	−	0.0510452i
$689$	−13.2101	−	22.8805i	−0.0191728	−	0.0332083i
$690$	25.6530	−	1001.42i	0.0371783	−	1.45133i
$691$	−613.121	+	164.285i	−0.887295	+	0.237750i	−0.673552	−	0.739140i	$-0.735232\pi$
$691$	−613.121	+	164.285i	−0.887295	+	0.237750i	−0.213743	+	0.976890i	$0.568566\pi$
$692$	−30.3426	−	22.3455i	−0.0438477	−	0.0322912i
$693$	−1.37567	−	22.9211i	−0.00198510	−	0.0330752i
$694$	−44.8404	−	594.240i	−0.0646115	−	0.856253i
$695$	272.667	−	472.273i	0.392326	−	0.679529i
$696$	−202.294	+	153.344i	−0.290652	+	0.220322i
$697$	−236.068	+	136.294i	−0.338692	+	0.195544i
$698$	−1044.12	+	712.659i	−1.49588	+	1.02100i
$699$	398.511	−	552.902i	0.570117	−	0.790990i
$700$	6.19481	−	15.8321i	0.00884973	−	0.0226173i
$701$	122.440	−	122.440i	0.174665	−	0.174665i	−0.614360	−	0.789026i	$-0.710586\pi$
$701$	122.440	−	122.440i	0.174665	−	0.174665i	0.789026	+	0.614360i	$0.210586\pi$
$702$	950.759	+	220.073i	1.35436	+	0.313494i
$703$		−	447.051i		−	0.635919i
$704$	970.428	−	840.363i	1.37845	−	1.19370i
$705$	1059.85	−	171.988i	1.50334	−	0.243954i
$706$	−385.389	−	72.7137i	−0.545877	−	0.102994i
$707$	4.88723	−	18.2394i	0.00691263	−	0.0257983i
$708$	140.987	+	30.3591i	0.199134	+	0.0428801i
$709$	−1287.77	+	345.056i	−1.81632	+	0.486680i	−0.996322	−	0.0856928i	$-0.972690\pi$
$709$	−1287.77	+	345.056i	−1.81632	+	0.486680i	−0.819993	+	0.572373i	$0.806023\pi$
$710$	775.267	−	58.5004i	1.09192	−	0.0823950i
$711$	86.0338	−	420.414i	0.121004	−	0.591300i
$712$	227.591	−	363.457i	0.319651	−	0.510473i
$713$	−391.967	−	226.302i	−0.549743	−	0.317394i
$714$	−5.98708	−	6.30189i	−0.00838527	−	0.00882617i
$715$	−2676.11	−	717.061i	−3.74281	−	1.00288i
$716$	−140.619	−	15.6970i	−0.196395	−	0.0219232i
$717$	−272.833	−	27.6300i	−0.380520	−	0.0385356i
$718$	155.410	+	443.404i	0.216449	+	0.617554i
$719$			413.989i			0.575784i	0.957663	+	0.287892i	$0.0929545\pi$
$719$			413.989i			0.575784i	−0.957663	+	0.287892i	$0.907046\pi$
$720$	177.939	−	1086.10i	0.247137	−	1.50847i
$721$	8.05279			0.0111689
$722$	1156.62	−	405.390i	1.60197	−	0.561481i
$723$	1302.51	−	585.847i	1.80154	−	0.810300i
$724$	−45.4220	−	5.07038i	−0.0627376	−	0.00700329i
$725$	91.4710	−	341.374i	0.126167	−	0.470861i
$726$	394.983	+	1641.11i	0.544054	+	2.26048i
$727$	−642.004	+	1111.98i	−0.883087	+	1.52955i	−0.0351966	+	0.999380i	$0.511206\pi$
$727$	−642.004	+	1111.98i	−0.883087	+	1.52955i	−0.847891	+	0.530171i	$0.822128\pi$
$728$	17.9226	−	4.11992i	0.0246190	−	0.00565923i
$729$	−599.371	−	414.964i	−0.822183	−	0.569223i
$730$	−67.0919	−	889.123i	−0.0919067	−	1.21798i
$731$	164.001	+	612.059i	0.224351	+	0.837290i
$732$	−77.2502	−	239.917i	−0.105533	−	0.327756i
$733$	−986.400	−	264.305i	−1.34570	−	0.360580i	−0.487156	−	0.873315i	$-0.661966\pi$
$733$	−986.400	−	264.305i	−1.34570	−	0.360580i	−0.858547	+	0.512735i	$0.828632\pi$
$734$	−209.034	+	1107.90i	−0.284787	+	1.50940i
$735$	1050.06	+	398.516i	1.42865	+	0.542199i
$736$	−416.550	−	561.369i	−0.565965	−	0.762729i
$737$	−568.858			−0.771857
$738$	−163.121	+	398.718i	−0.221031	+	0.540269i
$739$	−299.587	−	299.587i	−0.405395	−	0.405395i	0.474734	−	0.880129i	$-0.342544\pi$
$739$	−299.587	−	299.587i	−0.405395	−	0.405395i	−0.880129	+	0.474734i	$0.842544\pi$
$740$	−159.586	+	407.856i	−0.215657	+	0.551157i
$741$	170.465	−	1683.26i	0.230048	−	2.27161i
$742$	0.209663	+	0.307179i	0.000282565	+	0.000413988i
$743$	355.542	+	615.817i	0.478523	+	0.828825i	0.999697	−	0.0246249i	$-0.00783914\pi$
$743$	355.542	+	615.817i	0.478523	+	0.828825i	−0.521174	+	0.853450i	$0.674506\pi$
$744$	−392.715	−	305.026i	−0.527842	−	0.409981i
$745$	−1329.32	−	767.484i	−1.78432	−	1.03018i
$746$	−1129.08	+	85.1984i	−1.51351	+	0.114207i
$747$	−250.688	−	379.688i	−0.335593	−	0.508284i
$748$	735.815	+	541.884i	0.983709	+	0.724444i
$749$	1.50874	+	5.63068i	0.00201434	+	0.00751760i
$750$	184.305	+	338.987i	0.245739	+	0.451982i
$751$	869.284	−	501.881i	1.15750	−	0.668284i	0.206798	−	0.978384i	$-0.433696\pi$
$751$	869.284	−	501.881i	1.15750	−	0.668284i	0.950704	+	0.310100i	$0.100362\pi$
$752$	508.489	−	550.294i	0.676182	−	0.731774i
$753$	−611.420	+	99.2181i	−0.811978	+	0.131764i
$754$	360.776	−	126.450i	0.478482	−	0.167705i
$755$	−408.200	−	408.200i	−0.540662	−	0.540662i
$756$	−13.5788	−	2.08209i	−0.0179613	−	0.00275408i
$757$	−1.93857	−	1.93857i	−0.00256085	−	0.00256085i	0.705825	−	0.708386i	$-0.250576\pi$
$757$	−1.93857	−	1.93857i	−0.00256085	−	0.00256085i	−0.708386	+	0.705825i	$0.750576\pi$
$758$	−496.647	−	238.857i	−0.655207	−	0.315115i
$759$	1297.53	−	210.556i	1.70952	−	0.277412i
$760$	−1906.80	−	68.3924i	−2.50895	−	0.0899900i
$761$	−88.6701	+	51.1937i	−0.116518	+	0.0672716i	−0.557126	−	0.830428i	$-0.688096\pi$
$761$	−88.6701	+	51.1937i	−0.116518	+	0.0672716i	0.440608	+	0.897699i	$0.354763\pi$
$762$	−302.004	−	89.2708i	−0.396331	−	0.117153i
$763$	0.668303	+	2.49414i	0.000875889	+	0.00326886i
$764$	−314.096	+	47.6739i	−0.411121	+	0.0624004i
$765$	782.040	−	46.9363i	1.02228	−	0.0613546i
$766$	−446.842	−	384.137i	−0.583344	−	0.501485i
$767$	−188.096	−	108.597i	−0.245236	−	0.141587i
$768$	−369.276	−	673.394i	−0.480828	−	0.876815i
$769$	−642.532	−	1112.90i	−0.835542	−	1.44720i	−0.893589	−	0.448887i	$-0.851821\pi$
$769$	−642.532	−	1112.90i	−0.835542	−	1.44720i	0.0580467	−	0.998314i	$-0.481513\pi$
$770$	38.3236	+	7.23075i	0.0497710	+	0.00939058i
$771$	69.0890	−	682.220i	0.0896097	−	0.884851i
$772$	−469.789	−	183.820i	−0.608535	−	0.238108i
$773$	130.960	+	130.960i	0.169418	+	0.169418i	0.786724	−	0.617305i	$-0.211776\pi$
$773$	130.960	+	130.960i	0.169418	+	0.169418i	−0.617305	+	0.786724i	$0.711776\pi$
$774$	797.126	+	606.150i	1.02988	+	0.783140i
$775$	692.310			0.893303
$776$	−242.505	+	128.648i	−0.312506	+	0.165784i
$777$	5.11100	+	1.93972i	0.00657787	+	0.00249642i
$778$	720.540	+	1055.67i	0.926144	+	1.35690i
$779$	721.403	+	193.299i	0.926063	+	0.248138i
$780$	−756.402	+	1474.83i	−0.969746	+	1.89081i
$781$	264.047	+	985.438i	0.338089	+	1.26177i
$782$	324.389	−	377.340i	0.414819	−	0.482532i
$783$	−285.336	−	11.6999i	−0.364414	−	0.0149424i
$784$	748.443	−	232.557i	0.954647	−	0.296628i
$785$	453.707	−	785.844i	0.577971	−	1.00108i
$786$	−540.457	−	330.770i	−0.687604	−	0.420827i
$787$	−210.002	+	783.736i	−0.266838	+	0.995853i	0.694278	+	0.719707i	$0.255724\pi$
$787$	−210.002	+	783.736i	−0.266838	+	0.995853i	−0.961116	+	0.276146i	$0.910943\pi$
$788$	−760.842	−	84.9314i	−0.965535	−	0.107781i
$789$	852.905	−	383.621i	1.08100	−	0.486211i
$790$	656.825	+	315.893i	0.831424	+	0.399864i
$791$	−21.8616			−0.0276379
$792$	1443.77	−	34.7922i	1.82294	−	0.0439296i
$793$			379.587i			0.478672i
$794$	634.631	+	305.219i	0.799284	+	0.384407i
$795$	−33.3496	−	3.37734i	−0.0419491	−	0.00424823i
$796$	596.328	−	476.563i	0.749155	−	0.598697i
$797$	928.208	+	248.713i	1.16463	+	0.312061i	0.788812	−	0.614634i	$-0.210696\pi$
$797$	928.208	+	248.713i	1.16463	+	0.312061i	0.375815	+	0.926695i	$0.377363\pi$
$798$	−0.609889	+	23.8083i	−0.000764271	+	0.0298349i
$799$	461.902	+	266.679i	0.578100	+	0.333766i
$800$	981.135	+	425.056i	1.22642	+	0.531320i
$801$	457.682	−	152.558i	0.571388	−	0.190459i
$802$	669.121	−	778.345i	0.834316	−	0.970505i
$803$	1130.16	−	302.826i	1.40742	−	0.377118i
$804$	−71.6413	+	332.700i	−0.0891062	+	0.413806i
$805$	5.49650	−	20.5132i	0.00682796	−	0.0254823i
$806$	422.177	+	618.534i	0.523792	+	0.767411i
$807$	−1463.99	+	237.569i	−1.81411	+	0.294385i
$808$	1135.39	+	348.297i	1.40518	+	0.431061i
$809$			652.810i			0.806935i	0.914994	+	0.403467i	$0.132195\pi$
$809$			652.810i			0.806935i	−0.914994	+	0.403467i	$0.867805\pi$
$810$	931.824	−	815.306i	1.15040	−	1.00655i
$811$	250.396	−	250.396i	0.308749	−	0.308749i	−0.535675	−	0.844424i	$-0.679943\pi$
$811$	250.396	−	250.396i	0.308749	−	0.308749i	0.844424	+	0.535675i	$0.179943\pi$
$812$	−4.93022	+	2.15709i	−0.00607170	+	0.00265652i
$813$	−119.833	+	166.258i	−0.147396	+	0.204500i
$814$	−564.737	−	106.552i	−0.693780	−	0.130900i
$815$	−992.925	+	573.266i	−1.21831	+	0.703393i
$816$	409.591	−	362.101i	0.501950	−	0.443751i
$817$	868.054	−	1503.51i	1.06249	−	1.84028i
$818$	558.292	+	479.948i	0.682508	+	0.586733i
$819$	18.5046	+	9.25242i	0.0225941	+	0.0112972i
$820$	−589.151	−	433.875i	−0.718477	−	0.529116i
$821$	166.460	−	44.6030i	0.202753	−	0.0543276i	−0.156013	−	0.987755i	$-0.549864\pi$
$821$	166.460	−	44.6030i	0.202753	−	0.0543276i	0.358766	+	0.933427i	$0.383197\pi$
$822$	−499.992	+	475.016i	−0.608263	+	0.577878i
$823$	637.405	+	1104.02i	0.774490	+	1.34146i	0.935081	+	0.354435i	$0.115327\pi$
$823$	637.405	+	1104.02i	0.774490	+	1.34146i	−0.160591	+	0.987021i	$0.551340\pi$
$824$	−18.1542	+	506.144i	−0.0220318	+	0.614252i
$825$	−1557.78	+	1271.28i	−1.88821	+	1.54094i
$826$	2.75530	+	1.32513i	0.00333572	+	0.00160428i
$827$	−782.646	+	782.646i	−0.946367	+	0.946367i	−0.998633	−	0.0522660i	$-0.983356\pi$
$827$	−782.646	+	782.646i	−0.946367	+	0.946367i	0.0522660	+	0.998633i	$0.483356\pi$
$828$	40.2642	−	785.382i	0.0486282	−	0.948529i
$829$	449.400	−	449.400i	0.542099	−	0.542099i	−0.382045	−	0.924144i	$-0.624780\pi$
$829$	449.400	−	449.400i	0.542099	−	0.542099i	0.924144	+	0.382045i	$0.124780\pi$
$830$	729.254	−	255.600i	0.878620	−	0.307951i
$831$	−138.183	−	52.4431i	−0.166285	−	0.0631084i
$832$	218.545	+	1135.78i	0.262675	+	1.36512i
$833$	278.953	+	483.161i	0.334878	+	0.580025i
$834$	223.479	−	365.150i	0.267960	−	0.437830i
$835$	1631.34	−	437.116i	1.95370	−	0.523493i
$836$	−375.715	−	2475.37i	−0.449420	−	2.96097i
$837$	−122.528	−	545.832i	−0.146389	−	0.652129i
$838$	−677.313	+	51.1090i	−0.808249	+	0.0609892i
$839$	−688.965	+	1193.32i	−0.821174	+	1.42232i	0.0836338	+	0.996497i	$0.473347\pi$
$839$	−688.965	+	1193.32i	−0.821174	+	1.42232i	−0.904808	+	0.425819i	$0.859986\pi$
$840$	9.05537	−	21.5031i	0.0107802	−	0.0255990i
$841$	631.445	−	364.565i	0.750826	−	0.433490i
$842$	−651.413	−	954.390i	−0.773650	−	1.13348i
$843$	−240.080	−	533.770i	−0.284792	−	0.633180i
$844$	−255.092	−	583.036i	−0.302242	−	0.690800i
$845$	851.742	−	851.742i	1.00798	−	1.00798i
$846$	835.214	−	113.666i	0.987250	−	0.134357i
$847$			35.7847i			0.0422488i
$848$	−19.7799	+	12.4855i	−0.0233253	+	0.0147235i
$849$	−15.0078	−	18.3900i	−0.0176770	−	0.0216608i
$850$	−141.120	+	747.950i	−0.166024	+	0.879942i
$851$	−80.9965	+	302.283i	−0.0951780	+	0.355209i
$852$	609.593	−	30.3246i	0.715484	−	0.0355922i
$853$	−391.748	+	104.968i	−0.459259	+	0.123058i	−0.481028	−	0.876705i	$-0.659737\pi$
$853$	−391.748	+	104.968i	−0.459259	+	0.123058i	0.0217697	+	0.999763i	$0.493070\pi$
$854$	−0.402058	−	5.32821i	−0.000470794	−	0.00623912i
$855$	−1606.03	−	1424.17i	−1.87840	−	1.66569i
$856$	−357.308	+	82.1353i	−0.417416	+	0.0959524i
$857$	980.321	+	565.989i	1.14390	+	0.660430i	0.947393	−	0.320072i	$-0.103707\pi$
$857$	980.321	+	565.989i	1.14390	+	0.660430i	0.196506	+	0.980503i	$0.437041\pi$
$858$	−2085.75	−	616.537i	−2.43094	−	0.718574i
$859$	−448.978	−	120.303i	−0.522675	−	0.140050i	−0.0121716	−	0.999926i	$-0.503874\pi$
$859$	−448.978	−	120.303i	−0.522675	−	0.140050i	−0.510504	+	0.859875i	$0.670541\pi$
$860$	−1328.66	+	1061.82i	−1.54496	+	1.23467i
$861$	−5.34005	+	7.40888i	−0.00620215	+	0.00860497i
$862$	584.191	−	204.756i	0.677715	−	0.237535i
$863$		−	483.935i		−	0.560759i	−0.959889	−	0.280380i	$-0.909540\pi$
$863$		−	483.935i		−	0.560759i	0.959889	−	0.280380i	$-0.0904603\pi$
$864$	161.478	−	848.776i	0.186896	−	0.982380i
$865$	72.0017			0.0832389
$866$	136.610	+	389.765i	0.157749	+	0.450075i
$867$	−387.636	−	279.394i	−0.447100	−	0.322253i
$868$	−6.58119	−	8.23510i	−0.00758201	−	0.00948744i
$869$	−247.531	+	923.799i	−0.284846	+	1.06306i
$870$	137.491	−	465.133i	0.158036	−	0.534636i
$871$	256.268	−	443.868i	0.294222	−	0.509608i
$872$	−158.272	+	36.3823i	−0.181504	+	0.0417228i
$873$	−302.560	−	61.9161i	−0.346575	−	0.0709234i
$874$	−1359.51	+	102.586i	−1.55550	+	0.117376i
$875$	2.11713	+	7.90122i	0.00241957	+	0.00902996i
$876$	−34.7781	−	699.118i	−0.0397010	−	0.798080i
$877$	117.383	+	31.4528i	0.133846	+	0.0358640i	0.325120	−	0.945673i	$-0.394595\pi$
$877$	117.383	+	31.4528i	0.133846	+	0.0358640i	−0.191274	+	0.981537i	$0.561262\pi$
$878$	−1534.12	−	289.452i	−1.74729	−	0.329672i
$879$	−908.568	+	741.467i	−1.03364	+	0.843535i
$880$	−540.873	+	2392.47i	−0.614628	+	2.71871i
$881$	338.986			0.384774			0.192387	−	0.981319i	$-0.438377\pi$
$881$	338.986			0.384774			0.192387	+	0.981319i	$0.438377\pi$
$882$	816.057	+	333.859i	0.925234	+	0.378525i
$883$	0.181357	+	0.181357i	0.000205387	+	0.000205387i	0.707209	−	0.707004i	$-0.249954\pi$
$883$	0.181357	+	0.181357i	0.000205387	+	0.000205387i	−0.707004	+	0.707209i	$0.749954\pi$
$884$	−754.301	+	330.025i	−0.853282	+	0.373332i
$885$	−251.311	+	113.035i	−0.283967	+	0.127723i
$886$	744.848	−	508.392i	0.840686	−	0.573806i
$887$	483.461	+	837.378i	0.545051	+	0.944057i	0.998604	+	0.0528271i	$0.0168232\pi$
$887$	483.461	+	837.378i	0.545051	+	0.944057i	−0.453552	+	0.891230i	$0.649843\pi$
$888$	−133.440	+	316.870i	−0.150270	+	0.356836i
$889$	−5.78183	−	3.33814i	−0.00650374	−	0.00375494i
$890$	61.6543	+	817.062i	0.0692744	+	0.918048i
$891$	1278.00	+	1003.19i	1.43435	+	1.12591i
$892$	−1036.28	+	157.288i	−1.16175	+	0.176332i
$893$	−378.218	−	1411.53i	−0.423536	−	1.58066i
$894$	−1027.80	−	629.033i	−1.14966	−	0.703616i
$895$	234.133	−	135.176i	0.261601	−	0.151035i
$896$	−4.27071	−	15.7113i	−0.00476642	−	0.0175350i
$897$	−420.236	+	1107.29i	−0.468490	+	1.23443i
$898$	−85.3721	−	243.576i	−0.0950692	−	0.271243i
$899$	−154.958	−	154.958i	−0.172367	−	0.172367i
$900$	547.328	+	1071.18i	0.608142	+	1.19020i
$901$	−11.7739	−	11.7739i	−0.0130676	−	0.0130676i
$902$	416.128	−	865.241i	0.461339	−	0.959247i
$903$	13.4228	+	16.4478i	0.0148647	+	0.0182146i
$904$	49.2847	−	1374.07i	0.0545184	−	1.51999i
$905$	75.6285	−	43.6641i	0.0835674	−	0.0482476i
$906$	−312.142	−	328.555i	−0.344528	−	0.362643i
$907$	296.354	+	1106.01i	0.326741	+	1.21941i	0.912550	+	0.408964i	$0.134110\pi$
$907$	296.354	+	1106.01i	0.326741	+	1.21941i	−0.585810	+	0.810449i	$0.699223\pi$
$908$	456.085	−	619.310i	0.502297	−	0.682060i
$909$	736.149	+	1114.96i	0.809845	+	1.22658i
$910$	−22.9066	+	26.6457i	−0.0251721	+	0.0292810i
$911$	−914.422	−	527.942i	−1.00376	−	0.579519i	−0.0943985	−	0.995534i	$-0.530093\pi$
$911$	−914.422	−	527.942i	−1.00376	−	0.579519i	−0.909357	+	0.416016i	$0.863426\pi$
$912$	−1495.05	−	92.0067i	−1.63931	−	0.100885i
$913$	507.004	+	878.156i	0.555316	+	0.961836i
$914$	86.6748	−	459.384i	0.0948302	−	0.502609i
$915$	390.689	+	281.594i	0.426982	+	0.307753i
$916$	−501.184	−	1145.50i	−0.547144	−	1.25054i
$917$	−9.49863	−	9.49863i	−0.0103584	−	0.0103584i
$918$	614.676	−	21.1130i	0.669582	−	0.0229989i
$919$	642.206			0.698810			0.349405	−	0.936972i	$-0.386384\pi$
$919$	642.206			0.698810			0.349405	+	0.936972i	$0.386384\pi$
$920$	1276.93	+	391.718i	1.38797	+	0.425781i
$921$	33.9589	+	209.268i	0.0368717	+	0.227218i
$922$	−1299.82	+	887.183i	−1.40978	+	0.962238i
$923$	−887.869	−	237.904i	−0.961938	−	0.257751i
$924$	29.9304	+	6.44501i	0.0323922	+	0.00697512i
$925$	−123.893	−	462.376i	−0.133939	−	0.499866i
$926$	251.680	+	216.362i	0.271793	+	0.233653i
$927$	−378.033	+	426.308i	−0.407803	+	0.459879i
$928$	−124.466	−	314.743i	−0.134122	−	0.339163i
$929$	−155.772	+	269.806i	−0.167677	+	0.290426i	−0.937603	−	0.347708i	$-0.886960\pi$
$929$	−155.772	+	269.806i	−0.167677	+	0.290426i	0.769925	+	0.638134i	$0.220293\pi$
$930$	949.813	+	24.3311i	1.02130	+	0.0261624i
$931$	395.626	−	1476.50i	0.424947	−	1.58592i
$932$	567.320	+	709.893i	0.608712	+	0.761687i
$933$	43.3098	−	427.663i	0.0464199	−	0.458374i
$934$	−664.425	+	1381.51i	−0.711375	+	1.47914i
$935$	−1746.06			−1.86744
$936$	−623.261	+	1142.21i	−0.665877	+	1.22032i
$937$		−	1531.27i		−	1.63422i	−0.576479	−	0.817112i	$-0.695574\pi$
$937$		−	1531.27i		−	1.63422i	0.576479	−	0.817112i	$-0.304426\pi$
$938$	−3.12705	+	6.50196i	−0.00333374	+	0.00693173i
$939$	−10.8467	−	24.1155i	−0.0115513	−	0.0256821i
$940$	−158.823	+	1422.79i	−0.168961	+	1.51360i
$941$	−35.3950	−	9.48407i	−0.0376143	−	0.0100787i	0.239963	−	0.970782i	$-0.422865\pi$
$941$	−35.3950	−	9.48407i	−0.0376143	−	0.0100787i	−0.277577	+	0.960703i	$0.589531\pi$
$942$	371.860	−	607.596i	0.394756	−	0.645007i
$943$	−452.770	−	261.407i	−0.480138	−	0.277208i
$944$	−89.5005	+	170.192i	−0.0948098	+	0.180289i
$945$	23.2505	−	12.1819i	0.0246037	−	0.0128910i
$946$	−1692.42	−	1454.92i	−1.78902	−	1.53797i
$947$	414.035	−	110.940i	0.437207	−	0.117149i	−0.0335005	−	0.999439i	$-0.510666\pi$
$947$	414.035	−	110.940i	0.437207	−	0.117149i	0.470707	+	0.882290i	$0.343999\pi$
$948$	509.115	+	261.112i	0.537041	+	0.275435i
$949$	−272.843	+	1018.26i	−0.287505	+	1.07298i
$950$	1722.46	−	1175.65i	1.81311	−	1.23753i
$951$	259.580	−	683.973i	0.272955	−	0.719214i
$952$	10.2385	−	5.43147i	0.0107547	−	0.00570533i
$953$		−	932.178i		−	0.978151i	−0.872241	−	0.489076i	$-0.837334\pi$
$953$		−	932.178i		−	0.978151i	0.872241	−	0.489076i	$-0.162666\pi$
$954$	−26.1043	−	3.32093i	−0.0273630	−	0.00348106i
$955$	429.233	−	429.233i	0.449458	−	0.449458i
$956$	133.231	−	340.500i	0.139363	−	0.356172i
$957$	633.218	+	64.1266i	0.661670	+	0.0670079i
$958$	270.041	−	1431.24i	0.281880	−	1.49399i
$959$	−12.6619	+	7.31033i	−0.0132032	+	0.00762287i
$960$	1331.13	+	617.636i	1.38659	+	0.643371i
$961$	−265.860	+	460.483i	−0.276649	+	0.479170i
$962$	337.551	−	392.651i	0.350885	−	0.408162i
$963$	−368.910	−	184.458i	−0.383084	−	0.191545i
$964$	285.759	+	1882.71i	0.296431	+	1.95301i
$965$	931.064	−	249.478i	0.964833	−	0.258526i
$966$	4.72595	−	15.9879i	0.00489229	−	0.0165507i
$967$	548.468	+	949.974i	0.567185	+	0.982393i	0.996843	+	0.0794012i	$0.0253008\pi$
$967$	548.468	+	949.974i	0.567185	+	0.982393i	−0.429658	+	0.902992i	$0.641366\pi$
$968$	−2249.19	−	80.6729i	−2.32354	−	0.0833397i
$969$	−170.794	−	1052.50i	−0.176258	−	1.08617i
$970$	227.339	−	472.698i	0.234370	−	0.487318i
$971$	1068.71	−	1068.71i	1.10063	−	1.10063i	0.106297	−	0.994334i	$-0.466101\pi$
$971$	1068.71	−	1068.71i	1.10063	−	1.10063i	0.994334	−	0.106297i	$-0.0338994\pi$
$972$	747.671	−	621.106i	0.769208	−	0.638998i
$973$	6.41758	−	6.41758i	0.00659566	−	0.00659566i
$974$	477.596	+	1362.63i	0.490345	+	1.39901i
$975$	−290.181	−	1788.20i	−0.297621	−	1.83406i
$976$	335.802	−	13.2588i	0.344059	−	0.0135848i
$977$	−98.9088	−	171.315i	−0.101237	−	0.175348i	0.810957	−	0.585105i	$-0.198947\pi$
$977$	−98.9088	−	171.315i	−0.101237	−	0.175348i	−0.912195	+	0.409757i	$0.865613\pi$
$978$	−790.756	+	429.928i	−0.808544	+	0.439599i
$979$	−1038.56	+	278.283i	−1.06084	+	0.284252i
$980$	−888.012	+	1205.82i	−0.906134	+	1.23042i
$981$	−163.411	−	81.7065i	−0.166576	−	0.0832890i
$982$	118.320	+	1568.01i	0.120488	+	1.59675i
$983$	−845.462	+	1464.38i	−0.860083	+	1.48971i	0.0117650	+	0.999931i	$0.496255\pi$
$983$	−845.462	+	1464.38i	−0.860083	+	1.48971i	−0.871848	+	0.489777i	$0.837078\pi$
$984$	−453.634	−	352.342i	−0.461010	−	0.358071i
$985$	1266.81	−	731.396i	1.28611	−	0.742534i
$986$	198.998	−	135.825i	0.201823	−	0.137753i
$987$	17.7787	+	1.80046i	0.0180128	+	0.00182417i
$988$	2100.74	+	821.979i	2.12625	+	0.831963i
$989$	−859.358	+	859.358i	−0.868916	+	0.868916i
$990$	−2181.87	+	1689.38i	−2.20391	+	1.70644i
$991$			31.0089i			0.0312905i	0.999878	+	0.0156452i	$0.00498024\pi$
$991$			31.0089i			0.0312905i	−0.999878	+	0.0156452i	$0.995020\pi$
$992$	532.440	−	395.084i	0.536733	−	0.398270i
$993$	−274.427	+	723.093i	−0.276362	+	0.728191i
$994$	12.7149	+	2.39899i	0.0127916	+	0.00241347i
$995$	−377.507	+	1408.87i	−0.379404	+	1.41595i
$996$	577.445	−	185.930i	0.579764	−	0.186676i
$997$	1378.53	−	369.376i	1.38268	−	0.370488i	0.510586	−	0.859827i	$-0.329429\pi$
$997$	1378.53	−	369.376i	1.38268	−	0.370488i	0.872094	+	0.489339i	$0.162762\pi$
$998$	55.1768	−	4.16356i	0.0552874	−	0.00417190i
$999$	−342.620	+	179.513i	−0.342963	+	0.179693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.v.a.43.19	✓	184
3.2	odd	2		432.3.w.a.235.28		184
9.4	even	3	inner	144.3.v.a.139.44	yes	184
9.5	odd	6		432.3.w.a.91.3		184
16.3	odd	4	inner	144.3.v.a.115.44	yes	184
48.35	even	4		432.3.w.a.19.3		184
144.67	odd	12	inner	144.3.v.a.67.19	yes	184
144.131	even	12		432.3.w.a.307.28		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.v.a.43.19	✓	184	1.1	even	1	trivial
144.3.v.a.67.19	yes	184	144.67	odd	12	inner
144.3.v.a.115.44	yes	184	16.3	odd	4	inner
144.3.v.a.139.44	yes	184	9.4	even	3	inner
432.3.w.a.19.3		184	48.35	even	4
432.3.w.a.91.3		184	9.5	odd	6
432.3.w.a.235.28		184	3.2	odd	2
432.3.w.a.307.28		184	144.131	even	12

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.661532 - 1.88743i) q^{2} +(2.43372 + 1.75414i) q^{3} +(-3.12475 + 2.49718i) q^{4} +(1.97813 - 7.38249i) q^{5} +(1.70082 - 5.75389i) q^{6} +(0.0635994 - 0.110157i) q^{7} +(6.78037 + 4.24577i) q^{8} +(2.84600 + 8.53817i) q^{9} +O(q^{10})\)	\(q+(-0.661532 - 1.88743i) q^{2} +(2.43372 + 1.75414i) q^{3} +(-3.12475 + 2.49718i) q^{4} +(1.97813 - 7.38249i) q^{5} +(1.70082 - 5.75389i) q^{6} +(0.0635994 - 0.110157i) q^{7} +(6.78037 + 4.24577i) q^{8} +(2.84600 + 8.53817i) q^{9} +(-15.2425 + 1.15017i) q^{10} +(-5.19143 - 19.3747i) q^{11} +(-11.9852 + 0.596210i) q^{12} +(17.4564 + 4.67742i) q^{13} +(-0.249987 - 0.0471665i) q^{14} +(17.7641 - 14.4970i) q^{15} +(3.52814 - 15.6062i) q^{16} +11.3896 q^{17} +(14.2324 - 11.0199i) q^{18} +(-22.0659 - 22.0659i) q^{19} +(12.2543 + 28.0082i) q^{20} +(0.348014 - 0.156530i) q^{21} +(-33.1340 + 22.6154i) q^{22} +(10.9224 + 18.9182i) q^{23} +(9.05388 + 22.2267i) q^{24} +(-28.9375 - 16.7071i) q^{25} +(-2.71966 - 36.0419i) q^{26} +(-8.05073 + 25.7718i) q^{27} +(0.0763511 + 0.503034i) q^{28} +(2.73750 + 10.2165i) q^{29} +(-39.1135 - 23.9382i) q^{30} +(-17.9433 + 10.3595i) q^{31} +(-31.7894 + 3.66488i) q^{32} +(21.3513 - 56.2590i) q^{33} +(-7.53459 - 21.4970i) q^{34} +(-0.687428 - 0.687428i) q^{35} +(-30.2144 - 19.5726i) q^{36} +(10.1299 + 10.1299i) q^{37} +(-27.0504 + 56.2449i) q^{38} +(34.2791 + 42.0044i) q^{39} +(44.7568 - 41.6573i) q^{40} +(-20.7267 + 11.9665i) q^{41} +(-0.525662 - 0.553302i) q^{42} +(14.3992 + 53.7384i) q^{43} +(64.6041 + 47.5771i) q^{44} +(68.6627 - 4.12097i) q^{45} +(28.4811 - 33.1302i) q^{46} +(40.5547 + 23.4142i) q^{47} +(35.9619 - 31.7922i) q^{48} +(24.4919 + 42.4212i) q^{49} +(-12.3903 + 65.6696i) q^{50} +(27.7191 + 19.9789i) q^{51} +(-66.2272 + 28.9760i) q^{52} +(-1.03374 - 1.03374i) q^{53} +(53.9682 - 1.85371i) q^{54} -153.303 q^{55} +(0.898930 - 0.476880i) q^{56} +(-14.9956 - 92.4087i) q^{57} +(17.4719 - 11.9253i) q^{58} +(-11.6087 - 3.11053i) q^{59} +(-19.3067 + 89.6598i) q^{60} +(5.43623 + 20.2883i) q^{61} +(31.4229 + 27.0134i) q^{62} +(1.12155 + 0.229514i) q^{63} +(27.9469 + 57.5758i) q^{64} +(69.0620 - 119.619i) q^{65} +(-120.309 - 3.08193i) q^{66} +(7.34023 - 27.3941i) q^{67} +(-35.5897 + 28.4419i) q^{68} +(-6.60296 + 65.2010i) q^{69} +(-0.842713 + 1.75222i) q^{70} -50.8622 q^{71} +(-16.9541 + 69.9754i) q^{72} +58.3319i q^{73} +(12.4182 - 25.8208i) q^{74} +(-41.1193 - 91.4206i) q^{75} +(124.053 + 13.8478i) q^{76} +(-2.46444 - 0.660344i) q^{77} +(56.6035 - 92.4865i) q^{78} +(-41.2927 - 23.8404i) q^{79} +(-108.233 - 56.9175i) q^{80} +(-64.8005 + 48.5993i) q^{81} +(36.2973 + 31.2038i) q^{82} +(-48.8308 + 13.0842i) q^{83} +(-0.696573 + 1.35817i) q^{84} +(22.5301 - 84.0836i) q^{85} +(91.9017 - 62.7270i) q^{86} +(-11.2588 + 29.6660i) q^{87} +(47.0606 - 153.409i) q^{88} -53.6042i q^{89} +(-53.2006 - 126.870i) q^{90} +(1.62547 - 1.62547i) q^{91} +(-81.3720 - 31.8393i) q^{92} +(-61.8409 - 6.26269i) q^{93} +(17.3644 - 92.0332i) q^{94} +(-206.550 + 119.252i) q^{95} +(-83.7954 - 46.8438i) q^{96} +(-17.1573 + 29.7172i) q^{97} +(63.8647 - 74.2897i) q^{98} +(150.649 - 99.4657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 56 q^{12} - 2 q^{13} + 14 q^{14} - 2 q^{16} - 16 q^{17} + 38 q^{18} - 8 q^{19} - 44 q^{20} + 14 q^{21} - 2 q^{22} - 4 q^{23} + 120 q^{24} - 104 q^{26} - 52 q^{27} + 56 q^{28} - 2 q^{29} - 130 q^{30} - 182 q^{32} - 8 q^{33} - 10 q^{34} + 92 q^{35} - 2 q^{36} - 8 q^{37} - 254 q^{38} + 184 q^{39} - 2 q^{40} - 252 q^{42} - 2 q^{43} - 140 q^{44} - 54 q^{45} + 176 q^{46} + 162 q^{48} - 480 q^{49} - 96 q^{50} - 120 q^{51} - 2 q^{52} - 8 q^{53} + 94 q^{54} - 16 q^{55} + 260 q^{56} + 88 q^{58} + 142 q^{59} - 434 q^{60} - 2 q^{61} - 636 q^{62} + 244 q^{64} - 4 q^{65} - 100 q^{66} - 2 q^{67} - 112 q^{68} + 14 q^{69} - 100 q^{70} - 16 q^{71} + 98 q^{72} + 82 q^{74} - 296 q^{75} + 154 q^{76} + 194 q^{77} + 228 q^{78} + 592 q^{80} - 8 q^{81} - 420 q^{82} + 238 q^{83} - 22 q^{84} - 52 q^{85} - 170 q^{86} - 456 q^{87} - 26 q^{88} + 808 q^{90} + 188 q^{91} + 176 q^{92} + 26 q^{93} - 18 q^{94} - 202 q^{96} - 4 q^{97} + 408 q^{98} - 38 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 56 * q^12 - 2 * q^13 + 14 * q^14 - 2 * q^16 - 16 * q^17 + 38 * q^18 - 8 * q^19 - 44 * q^20 + 14 * q^21 - 2 * q^22 - 4 * q^23 + 120 * q^24 - 104 * q^26 - 52 * q^27 + 56 * q^28 - 2 * q^29 - 130 * q^30 - 182 * q^32 - 8 * q^33 - 10 * q^34 + 92 * q^35 - 2 * q^36 - 8 * q^37 - 254 * q^38 + 184 * q^39 - 2 * q^40 - 252 * q^42 - 2 * q^43 - 140 * q^44 - 54 * q^45 + 176 * q^46 + 162 * q^48 - 480 * q^49 - 96 * q^50 - 120 * q^51 - 2 * q^52 - 8 * q^53 + 94 * q^54 - 16 * q^55 + 260 * q^56 + 88 * q^58 + 142 * q^59 - 434 * q^60 - 2 * q^61 - 636 * q^62 + 244 * q^64 - 4 * q^65 - 100 * q^66 - 2 * q^67 - 112 * q^68 + 14 * q^69 - 100 * q^70 - 16 * q^71 + 98 * q^72 + 82 * q^74 - 296 * q^75 + 154 * q^76 + 194 * q^77 + 228 * q^78 + 592 * q^80 - 8 * q^81 - 420 * q^82 + 238 * q^83 - 22 * q^84 - 52 * q^85 - 170 * q^86 - 456 * q^87 - 26 * q^88 + 808 * q^90 + 188 * q^91 + 176 * q^92 + 26 * q^93 - 18 * q^94 - 202 * q^96 - 4 * q^97 + 408 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

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