LMFDB - Embedded newform 144.3.v.a.43.12

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			43.12
Character	$\chi$	$=$	144.43
Dual form			144.3.v.a.67.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35588 + 1.47023i) q^{2} +(-2.99965 + 0.0461027i) q^{3} +(-0.323163 - 3.98692i) q^{4} +(0.803565 - 2.99895i) q^{5} +(3.99939 - 4.47268i) q^{6} +(-0.723340 + 1.25286i) q^{7} +(6.29987 + 4.93068i) q^{8} +(8.99575 - 0.276584i) q^{9} +O(q^{10})$	\(q+(-1.35588 + 1.47023i) q^{2} +(-2.99965 + 0.0461027i) q^{3} +(-0.323163 - 3.98692i) q^{4} +(0.803565 - 2.99895i) q^{5} +(3.99939 - 4.47268i) q^{6} +(-0.723340 + 1.25286i) q^{7} +(6.29987 + 4.93068i) q^{8} +(8.99575 - 0.276584i) q^{9} +(3.31960 + 5.24765i) q^{10} +(4.92392 + 18.3763i) q^{11} +(1.15318 + 11.9445i) q^{12} +(-12.8872 - 3.45311i) q^{13} +(-0.861232 - 2.76221i) q^{14} +(-2.27215 + 9.03282i) q^{15} +(-15.7911 + 2.57685i) q^{16} +2.84649 q^{17} +(-11.7905 + 13.6009i) q^{18} +(4.69705 + 4.69705i) q^{19} +(-12.2162 - 2.23461i) q^{20} +(2.11200 - 3.79149i) q^{21} +(-33.6937 - 17.6768i) q^{22} +(19.5797 + 33.9130i) q^{23} +(-19.1247 - 14.4998i) q^{24} +(13.3027 + 7.68031i) q^{25} +(22.5504 - 14.2651i) q^{26} +(-26.9713 + 1.24438i) q^{27} +(5.22882 + 2.47902i) q^{28} +(12.2769 + 45.8179i) q^{29} +(-10.1996 - 15.5880i) q^{30} +(8.24185 - 4.75843i) q^{31} +(17.6224 - 26.7105i) q^{32} +(-15.6172 - 54.8954i) q^{33} +(-3.85951 + 4.18501i) q^{34} +(3.17601 + 3.17601i) q^{35} +(-4.00981 - 35.7760i) q^{36} +(-14.6089 - 14.6089i) q^{37} +(-13.2744 + 0.537102i) q^{38} +(38.8162 + 9.76397i) q^{39} +(19.8492 - 14.9309i) q^{40} +(45.1434 - 26.0636i) q^{41} +(2.71074 + 8.24595i) q^{42} +(9.64369 + 35.9907i) q^{43} +(71.6737 - 25.5698i) q^{44} +(6.39921 - 27.2000i) q^{45} +(-76.4076 - 17.1954i) q^{46} +(-37.1642 - 21.4567i) q^{47} +(47.2490 - 8.45765i) q^{48} +(23.4536 + 40.6228i) q^{49} +(-29.3287 + 9.14443i) q^{50} +(-8.53848 + 0.131231i) q^{51} +(-9.60263 + 52.4961i) q^{52} +(-22.5827 - 22.5827i) q^{53} +(34.7404 - 41.3413i) q^{54} +59.0662 q^{55} +(-10.7344 + 4.32631i) q^{56} +(-14.3060 - 13.8729i) q^{57} +(-84.0089 - 44.0738i) q^{58} +(-31.8699 - 8.53952i) q^{59} +(36.7474 + 6.13982i) q^{60} +(-12.6438 - 47.1874i) q^{61} +(-4.17898 + 18.5693i) q^{62} +(-6.16046 + 11.4705i) q^{63} +(15.3768 + 62.1253i) q^{64} +(-20.7114 + 35.8732i) q^{65} +(101.884 + 51.4708i) q^{66} +(8.40472 - 31.3668i) q^{67} +(-0.919881 - 11.3488i) q^{68} +(-60.2955 - 100.824i) q^{69} +(-8.97577 + 0.363173i) q^{70} +26.3288 q^{71} +(58.0358 + 42.6127i) q^{72} +17.2047i q^{73} +(41.2865 - 1.67051i) q^{74} +(-40.2574 - 22.4249i) q^{75} +(17.2089 - 20.2447i) q^{76} +(-26.5846 - 7.12333i) q^{77} +(-66.9855 + 43.8300i) q^{78} +(-49.7868 - 28.7444i) q^{79} +(-4.96136 + 49.4274i) q^{80} +(80.8470 - 4.97615i) q^{81} +(-22.8897 + 101.710i) q^{82} +(-131.432 + 35.2171i) q^{83} +(-15.7989 - 7.19513i) q^{84} +(2.28734 - 8.53648i) q^{85} +(-65.9904 - 34.6208i) q^{86} +(-38.9386 - 136.871i) q^{87} +(-59.5876 + 140.047i) q^{88} +147.204i q^{89} +(31.3137 + 46.2884i) q^{90} +(13.6481 - 13.6481i) q^{91} +(128.881 - 89.0220i) q^{92} +(-24.5032 + 14.6536i) q^{93} +(81.9367 - 25.5471i) q^{94} +(17.8606 - 10.3118i) q^{95} +(-51.6294 + 80.9346i) q^{96} +(20.4564 - 35.4315i) q^{97} +(-91.5251 - 20.5975i) q^{98} +(49.3769 + 163.947i) 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 $

$2$	−1.35588	+	1.47023i	−0.677941	+	0.735116i
$2$	−1.35588	+	1.47023i	−0.677941	+	0.735116i
$3$	−2.99965	+	0.0461027i	−0.999882	+	0.0153676i
$3$	−2.99965	+	0.0461027i	−0.999882	+	0.0153676i
$4$	−0.323163	−	3.98692i	−0.0807907	−	0.996731i
$5$	0.803565	−	2.99895i	0.160713	−	0.599789i	−0.837835	−	0.545923i	$-0.816179\pi$
$5$	0.803565	−	2.99895i	0.160713	−	0.599789i	0.998548	−	0.0538658i	$-0.0171543\pi$
$6$	3.99939	−	4.47268i	0.666564	−	0.745447i
$7$	−0.723340	+	1.25286i	−0.103334	+	0.178980i	−0.913056	−	0.407833i	$-0.866284\pi$
$7$	−0.723340	+	1.25286i	−0.103334	+	0.178980i	0.809722	+	0.586813i	$0.199618\pi$
$8$	6.29987	+	4.93068i	0.787484	+	0.616335i
$9$	8.99575	−	0.276584i	0.999528	−	0.0307315i
$10$	3.31960	+	5.24765i	0.331960	+	0.524765i
$11$	4.92392	+	18.3763i	0.447629	+	1.67057i	0.708901	+	0.705308i	$0.249191\pi$
$11$	4.92392	+	18.3763i	0.447629	+	1.67057i	−0.261272	+	0.965265i	$0.584142\pi$
$12$	1.15318	+	11.9445i	0.0960985	+	0.995372i
$13$	−12.8872	−	3.45311i	−0.991322	−	0.265624i	−0.273516	−	0.961867i	$-0.588187\pi$
$13$	−12.8872	−	3.45311i	−0.991322	−	0.265624i	−0.717806	+	0.696244i	$0.754853\pi$
$14$	−0.861232	−	2.76221i	−0.0615166	−	0.197301i
$15$	−2.27215	+	9.03282i	−0.151477	+	0.602188i
$16$	−15.7911	+	2.57685i	−0.986946	+	0.161053i
$17$	2.84649			0.167441			0.0837204	−	0.996489i	$-0.473320\pi$
$17$	2.84649			0.167441			0.0837204	+	0.996489i	$0.473320\pi$
$18$	−11.7905	+	13.6009i	−0.655030	+	0.755603i
$19$	4.69705	+	4.69705i	0.247213	+	0.247213i	0.819826	−	0.572613i	$-0.194070\pi$
$19$	4.69705	+	4.69705i	0.247213	+	0.247213i	−0.572613	+	0.819826i	$0.694070\pi$
$20$	−12.2162	−	2.23461i	−0.610812	−	0.111730i
$21$	2.11200	−	3.79149i	0.100572	−	0.180547i
$22$	−33.6937	−	17.6768i	−1.53153	−	0.803492i
$23$	19.5797	+	33.9130i	0.851289	+	1.47448i	0.880045	+	0.474890i	$0.157512\pi$
$23$	19.5797	+	33.9130i	0.851289	+	1.47448i	−0.0287557	+	0.999586i	$0.509154\pi$
$24$	−19.1247	−	14.4998i	−0.796863	−	0.604160i
$25$	13.3027	+	7.68031i	0.532107	+	0.307212i
$26$	22.5504	−	14.2651i	0.867322	−	0.548659i
$27$	−26.9713	+	1.24438i	−0.998937	+	0.0460882i
$28$	5.22882	+	2.47902i	0.186744	+	0.0885366i
$29$	12.2769	+	45.8179i	0.423340	+	1.57993i	0.767521	+	0.641023i	$0.221490\pi$
$29$	12.2769	+	45.8179i	0.423340	+	1.57993i	−0.344181	+	0.938903i	$0.611844\pi$
$30$	−10.1996	−	15.5880i	−0.339986	−	0.519601i
$31$	8.24185	−	4.75843i	0.265866	−	0.153498i	−0.361141	−	0.932511i	$-0.617613\pi$
$31$	8.24185	−	4.75843i	0.265866	−	0.153498i	0.627008	+	0.779013i	$0.284280\pi$
$32$	17.6224	−	26.7105i	0.550699	−	0.834704i
$33$	−15.6172	−	54.8954i	−0.473249	−	1.66350i
$34$	−3.85951	+	4.18501i	−0.113515	+	0.123088i
$35$	3.17601	+	3.17601i	0.0907432	+	0.0907432i
$36$	−4.00981	−	35.7760i	−0.111384	−	0.993777i
$37$	−14.6089	−	14.6089i	−0.394836	−	0.394836i	0.481571	−	0.876407i	$-0.340066\pi$
$37$	−14.6089	−	14.6089i	−0.394836	−	0.394836i	−0.876407	+	0.481571i	$0.840066\pi$
$38$	−13.2744	+	0.537102i	−0.349327	+	0.0141343i
$39$	38.8162	+	9.76397i	0.995287	+	0.250358i
$40$	19.8492	−	14.9309i	0.496230	−	0.373271i
$41$	45.1434	−	26.0636i	1.10106	−	0.635697i	0.164560	−	0.986367i	$-0.447380\pi$
$41$	45.1434	−	26.0636i	1.10106	−	0.635697i	0.936499	+	0.350670i	$0.114046\pi$
$42$	2.71074	+	8.24595i	0.0645414	+	0.196332i
$43$	9.64369	+	35.9907i	0.224272	+	0.836994i	0.982695	+	0.185231i	$0.0593034\pi$
$43$	9.64369	+	35.9907i	0.224272	+	0.836994i	−0.758423	+	0.651763i	$0.774030\pi$
$44$	71.6737	−	25.5698i	1.62895	−	0.581132i
$45$	6.39921	−	27.2000i	0.142205	−	0.604445i
$46$	−76.4076	−	17.1954i	−1.66104	−	0.373812i
$47$	−37.1642	−	21.4567i	−0.790727	−	0.456527i	0.0494913	−	0.998775i	$-0.484240\pi$
$47$	−37.1642	−	21.4567i	−0.790727	−	0.456527i	−0.840218	+	0.542248i	$0.817573\pi$
$48$	47.2490	−	8.45765i	0.984354	−	0.176201i
$49$	23.4536	+	40.6228i	0.478644	+	0.829036i
$50$	−29.3287	+	9.14443i	−0.586574	+	0.182889i
$51$	−8.53848	+	0.131231i	−0.167421	+	0.00257316i
$52$	−9.60263	+	52.4961i	−0.184666	+	1.00954i
$53$	−22.5827	−	22.5827i	−0.426089	−	0.426089i	0.461205	−	0.887294i	$-0.347417\pi$
$53$	−22.5827	−	22.5827i	−0.426089	−	0.426089i	−0.887294	+	0.461205i	$0.847417\pi$
$54$	34.7404	−	41.3413i	0.643341	−	0.765580i
$55$	59.0662			1.07393
$56$	−10.7344	+	4.32631i	−0.191686	+	0.0772556i
$57$	−14.3060	−	13.8729i	−0.250983	−	0.243385i
$58$	−84.0089	−	44.0738i	−1.44843	−	0.759894i
$59$	−31.8699	−	8.53952i	−0.540168	−	0.144738i	−0.0215886	−	0.999767i	$-0.506872\pi$
$59$	−31.8699	−	8.53952i	−0.540168	−	0.144738i	−0.518580	+	0.855029i	$0.673539\pi$
$60$	36.7474	+	6.13982i	0.612457	+	0.102330i
$61$	−12.6438	−	47.1874i	−0.207276	−	0.773564i	−0.988744	−	0.149619i	$-0.952195\pi$
$61$	−12.6438	−	47.1874i	−0.207276	−	0.773564i	0.781468	−	0.623946i	$-0.214471\pi$
$62$	−4.17898	+	18.5693i	−0.0674029	+	0.299505i
$63$	−6.16046	+	11.4705i	−0.0977851	+	0.182071i
$64$	15.3768	+	62.1253i	0.240263	+	0.970708i
$65$	−20.7114	+	35.8732i	−0.318637	+	0.551895i
$66$	101.884	+	51.4708i	1.54370	+	0.779861i
$67$	8.40472	−	31.3668i	0.125444	−	0.468162i	−0.874411	−	0.485185i	$-0.838752\pi$
$67$	8.40472	−	31.3668i	0.125444	−	0.468162i	0.999855	+	0.0170232i	$0.00541890\pi$
$68$	−0.919881	−	11.3488i	−0.0135277	−	0.166894i
$69$	−60.2955	−	100.824i	−0.873848	−	1.46122i
$70$	−8.97577	+	0.363173i	−0.128225	+	0.00518819i
$71$	26.3288			0.370829			0.185414	−	0.982660i	$-0.440637\pi$
$71$	26.3288			0.370829			0.185414	+	0.982660i	$0.440637\pi$
$72$	58.0358	+	42.6127i	0.806053	+	0.591843i
$73$			17.2047i			0.235681i	0.993033	+	0.117840i	$0.0375971\pi$
$73$			17.2047i			0.235681i	−0.993033	+	0.117840i	$0.962403\pi$
$74$	41.2865	−	1.67051i	0.557926	−	0.0225745i
$75$	−40.2574	−	22.4249i	−0.536765	−	0.298999i
$76$	17.2089	−	20.2447i	0.226433	−	0.266378i
$77$	−26.5846	−	7.12333i	−0.345255	−	0.0925108i
$78$	−66.9855	+	43.8300i	−0.858788	+	0.561923i
$79$	−49.7868	−	28.7444i	−0.630213	−	0.363854i	0.150621	−	0.988592i	$-0.451873\pi$
$79$	−49.7868	−	28.7444i	−0.630213	−	0.363854i	−0.780835	+	0.624738i	$0.785206\pi$
$80$	−4.96136	+	49.4274i	−0.0620171	+	0.617843i
$81$	80.8470	−	4.97615i	0.998111	−	0.0614340i
$82$	−22.8897	+	101.710i	−0.279143	+	1.24037i
$83$	−131.432	+	35.2171i	−1.58352	+	0.424302i	−0.940012	−	0.341141i	$-0.889187\pi$
$83$	−131.432	+	35.2171i	−1.58352	+	0.424302i	−0.643504	+	0.765443i	$0.722520\pi$
$84$	−15.7989	−	7.19513i	−0.188082	−	0.0856563i
$85$	2.28734	−	8.53648i	0.0269099	−	0.100429i
$86$	−65.9904	−	34.6208i	−0.767331	−	0.402567i
$87$	−38.9386	−	136.871i	−0.447570	−	1.57323i
$88$	−59.5876	+	140.047i	−0.677132	+	1.59144i
$89$			147.204i			1.65398i	0.562217	+	0.826990i	$0.309948\pi$
$89$			147.204i			1.65398i	−0.562217	+	0.826990i	$0.690052\pi$
$90$	31.3137	+	46.2884i	0.347930	+	0.514315i
$91$	13.6481	−	13.6481i	0.149979	−	0.149979i
$92$	128.881	−	89.0220i	1.40088	−	0.967631i
$93$	−24.5032	+	14.6536i	−0.263476	+	0.157565i
$94$	81.9367	−	25.5471i	0.871667	−	0.271778i
$95$	17.8606	−	10.3118i	0.188006	−	0.108545i
$96$	−51.6294	+	80.9346i	−0.537806	+	0.843068i
$97$	20.4564	−	35.4315i	0.210891	−	0.365273i	−0.741103	−	0.671391i	$-0.765697\pi$
$97$	20.4564	−	35.4315i	0.210891	−	0.365273i	0.951993	+	0.306118i	$0.0990303\pi$
$98$	−91.5251	−	20.5975i	−0.933930	−	0.210179i
$99$	49.3769	+	163.947i	0.498757	+	1.65603i
$100$	26.3219	−	55.5188i	0.263219	−	0.555188i
$101$	39.1674	−	10.4949i	0.387796	−	0.103910i	−0.0596526	−	0.998219i	$-0.518999\pi$
$101$	39.1674	−	10.4949i	0.387796	−	0.103910i	0.447449	+	0.894309i	$0.352333\pi$
$102$	11.3842	−	12.7315i	0.111610	−	0.124818i
$103$	43.7297	+	75.7421i	0.424560	+	0.735360i	0.996379	−	0.0850197i	$-0.0270953\pi$
$103$	43.7297	+	75.7421i	0.424560	+	0.735360i	−0.571819	+	0.820380i	$0.693762\pi$
$104$	−64.1614	−	85.2967i	−0.616937	−	0.820161i
$105$	−9.67333	−	9.38049i	−0.0921270	−	0.0893380i
$106$	63.8214	−	2.58231i	0.602089	−	0.0243614i
$107$	−89.5196	+	89.5196i	−0.836632	+	0.836632i	−0.988414	−	0.151782i	$-0.951499\pi$
$107$	−89.5196	+	89.5196i	−0.836632	+	0.836632i	0.151782	+	0.988414i	$0.451499\pi$
$108$	13.6774	+	107.130i	0.126642	+	0.991948i
$109$	42.4414	−	42.4414i	0.389370	−	0.389370i	−0.485093	−	0.874463i	$-0.661214\pi$
$109$	42.4414	−	42.4414i	0.389370	−	0.389370i	0.874463	+	0.485093i	$0.161214\pi$
$110$	−80.0869	+	86.8410i	−0.728063	+	0.789464i
$111$	44.4951	+	43.1481i	0.400857	+	0.388722i
$112$	8.19392	−	21.6480i	0.0731600	−	0.193286i
$113$	−28.9994	−	50.2284i	−0.256632	−	0.444499i	0.708706	−	0.705504i	$-0.249279\pi$
$113$	−28.9994	−	50.2284i	−0.256632	−	0.444499i	−0.965337	+	0.261005i	$0.915946\pi$
$114$	39.7938	−	2.22310i	0.349068	−	0.0195009i
$115$	117.437	−	31.4670i	1.02119	−	0.273627i
$116$	178.705	−	63.7535i	1.54056	−	0.549600i
$117$	−116.885	−	27.4989i	−0.999016	−	0.235034i
$118$	55.7670	−	35.2776i	0.472602	−	0.298963i
$119$	−2.05898	+	3.56626i	−0.0173024	+	0.0299686i
$120$	−58.8522	+	45.7024i	−0.490435	+	0.380853i
$121$	−208.655	+	120.467i	−1.72442	+	0.995594i
$122$	86.5200	+	45.3913i	0.709180	+	0.372060i
$123$	−134.213	+	80.2627i	−1.09116	+	0.652542i
$124$	−21.6350	−	31.3219i	−0.174476	−	0.252596i
$125$	88.6069	−	88.6069i	0.708855	−	0.708855i
$126$	−8.51141	−	24.6100i	−0.0675509	−	0.195317i
$127$		−	93.0923i		−	0.733011i	−0.930416	−	0.366505i	$-0.880554\pi$
$127$		−	93.0923i		−	0.733011i	0.930416	−	0.366505i	$-0.119446\pi$
$128$	−112.188	−	61.6272i	−0.876467	−	0.481462i
$129$	−30.5869	−	107.515i	−0.237108	−	0.833449i
$130$	−24.6596	−	79.0903i	−0.189690	−	0.608387i
$131$	−1.63648	+	6.10744i	−0.0124922	+	0.0466217i	−0.971891	−	0.235433i	$-0.924349\pi$
$131$	−1.63648	+	6.10744i	−0.0124922	+	0.0466217i	0.959398	+	0.282055i	$0.0910159\pi$
$132$	−213.817	+	80.0048i	−1.61983	+	0.606097i
$133$	−9.28232	+	2.48719i	−0.0697919	+	0.0187007i
$134$	34.7207	+	54.8867i	0.259110	+	0.409602i
$135$	−17.9414	+	81.8854i	−0.132899	+	0.606559i
$136$	17.9326	+	14.0352i	0.131857	+	0.103200i
$137$	108.154	+	62.4427i	0.789445	+	0.455786i	0.839767	−	0.542947i	$-0.182692\pi$
$137$	108.154	+	62.4427i	0.789445	+	0.455786i	−0.0503222	+	0.998733i	$0.516025\pi$
$138$	229.989	+	48.0574i	1.66658	+	0.348242i
$139$	257.017	+	68.8674i	1.84904	+	0.495449i	0.999486	−	0.0320537i	$-0.0102048\pi$
$139$	257.017	+	68.8674i	1.84904	+	0.495449i	0.849554	+	0.527502i	$0.176871\pi$
$140$	11.6362	−	13.6889i	0.0831154	−	0.0977778i
$141$	112.469	+	62.6493i	0.797650	+	0.444321i
$142$	−35.6988	+	38.7095i	−0.251400	+	0.272602i
$143$		−	253.822i		−	1.77498i
$144$	−141.340	+	27.5483i	−0.981530	+	0.191307i
$145$	147.271			1.01566
$146$	−25.2949	−	23.3275i	−0.173253	−	0.159778i
$147$	−72.2252	−	120.773i	−0.491328	−	0.821582i
$148$	−53.5236	+	62.9658i	−0.361646	+	0.425444i
$149$	−2.21004	+	8.24800i	−0.0148325	+	0.0553557i	−0.972945	−	0.231035i	$-0.925789\pi$
$149$	−2.21004	+	8.24800i	−0.0148325	+	0.0553557i	0.958113	+	0.286391i	$0.0924555\pi$
$150$	87.5541	−	28.7822i	0.583694	−	0.191881i
$151$	112.403	−	194.688i	0.744393	−	1.28933i	−0.206085	−	0.978534i	$-0.566072\pi$
$151$	112.403	−	194.688i	0.744393	−	1.28933i	0.950478	−	0.310793i	$-0.100594\pi$
$152$	6.43118	+	52.7505i	0.0423104	+	0.347043i
$153$	25.6064	−	0.787294i	0.167362	−	0.00514571i
$154$	46.5186	−	29.4272i	0.302069	−	0.191086i
$155$	−7.64742	−	28.5406i	−0.0493382	−	0.184133i
$156$	26.3843	−	157.913i	0.169130	−	1.01226i
$157$	−92.7362	−	24.8486i	−0.590677	−	0.158271i	−0.0489141	−	0.998803i	$-0.515576\pi$
$157$	−92.7362	−	24.8486i	−0.590677	−	0.158271i	−0.541762	+	0.840532i	$0.682243\pi$
$158$	109.766	−	34.2241i	0.694722	−	0.216608i
$159$	68.7813	+	66.6991i	0.432587	+	0.419491i
$160$	−65.9427	−	74.3121i	−0.412142	−	0.464451i
$161$	−56.6510			−0.351870
$162$	−102.303	+	125.611i	−0.631500	+	0.775376i
$163$	−108.362	−	108.362i	−0.664799	−	0.664799i	0.291708	−	0.956507i	$-0.405776\pi$
$163$	−108.362	−	108.362i	−0.664799	−	0.664799i	−0.956507	+	0.291708i	$0.905776\pi$
$164$	−118.502	−	171.561i	−0.722574	−	1.04610i
$165$	−177.178	+	2.72311i	−1.07380	+	0.0165037i
$166$	126.429	−	240.985i	0.761620	−	1.45172i
$167$	−78.3148	−	135.645i	−0.468951	−	0.812247i	0.530419	−	0.847736i	$-0.322035\pi$
$167$	−78.3148	−	135.645i	−0.468951	−	0.812247i	−0.999370	+	0.0354887i	$0.988701\pi$
$168$	32.0000	−	13.4723i	0.190476	−	0.0801922i
$169$	7.79718	+	4.50171i	0.0461372	+	0.0266373i
$170$	9.44924	+	14.9374i	0.0555837	+	0.0878670i
$171$	43.5526	+	40.9544i	0.254694	+	0.239499i
$172$	140.376	−	50.0795i	0.816139	−	0.291160i
$173$	56.4535	+	210.687i	0.326321	+	1.21785i	0.912977	+	0.408011i	$0.133777\pi$
$173$	56.4535	+	210.687i	0.326321	+	1.21785i	−0.586656	+	0.809836i	$0.699556\pi$
$174$	254.029	+	128.333i	1.45994	+	0.737545i
$175$	−19.2447	+	11.1109i	−0.109970	+	0.0634911i
$176$	−125.107	−	277.495i	−0.710837	−	1.57667i
$177$	95.9922	+	24.1463i	0.542329	+	0.136420i
$178$	−216.424	−	199.592i	−1.21587	−	1.12130i
$179$	40.8955	+	40.8955i	0.228467	+	0.228467i	0.812052	−	0.583585i	$-0.198351\pi$
$179$	40.8955	+	40.8955i	0.228467	+	0.228467i	−0.583585	+	0.812052i	$0.698351\pi$
$180$	−110.512	−	16.7231i	−0.613958	−	0.0929063i
$181$	−102.039	−	102.039i	−0.563751	−	0.563751i	0.366620	−	0.930371i	$-0.380515\pi$
$181$	−102.039	−	102.039i	−0.563751	−	0.563751i	−0.930371	+	0.366620i	$0.880515\pi$
$182$	1.56064	+	38.5710i	0.00857495	+	0.211929i
$183$	40.1025	+	140.963i	0.219139	+	0.770288i
$184$	−43.8645	+	310.188i	−0.238394	+	1.68581i
$185$	−55.5506	+	32.0722i	−0.300274	+	0.173363i
$186$	11.6794	−	55.8940i	0.0627923	−	0.300505i
$187$	14.0159	+	52.3081i	0.0749514	+	0.279722i
$188$	−73.5364	+	155.105i	−0.391151	+	0.825025i
$189$	17.9504	−	34.6914i	0.0949756	−	0.183553i
$190$	−9.05611	+	40.2408i	−0.0476637	+	0.211794i
$191$	−319.944	−	184.720i	−1.67510	−	0.967118i	−0.964713	−	0.263305i	$-0.915187\pi$
$191$	−319.944	−	184.720i	−1.67510	−	0.967118i	−0.710385	−	0.703813i	$-0.751479\pi$
$192$	−48.9891	−	185.645i	−0.255152	−	0.966901i
$193$	172.896	+	299.465i	0.895836	+	1.55163i	0.832766	+	0.553625i	$0.186756\pi$
$193$	172.896	+	299.465i	0.895836	+	1.55163i	0.0630702	+	0.998009i	$0.479911\pi$
$194$	24.3560	+	78.1166i	0.125547	+	0.402663i
$195$	60.4729	−	108.562i	0.310118	−	0.556726i
$196$	154.381	−	106.635i	0.787656	−	0.544058i
$197$	249.540	+	249.540i	1.26670	+	1.26670i	0.947783	+	0.318915i	$0.103318\pi$
$197$	249.540	+	249.540i	1.26670	+	1.26670i	0.318915	+	0.947783i	$0.396682\pi$
$198$	−307.989	−	149.697i	−1.55550	−	0.756046i
$199$	−302.176			−1.51847			−0.759236	−	0.650816i	$-0.774427\pi$
$199$	−302.176			−1.51847			−0.759236	+	0.650816i	$0.774427\pi$
$200$	45.9361	+	113.976i	0.229680	+	0.569881i
$201$	−23.7651	+	94.4769i	−0.118234	+	0.470034i
$202$	−37.6765	+	71.8150i	−0.186518	+	0.355520i
$203$	−66.2838	−	17.7607i	−0.326521	−	0.0874911i
$204$	3.28253	+	33.9998i	0.0160908	+	0.166666i
$205$	−41.8875	−	156.326i	−0.204329	−	0.762568i
$206$	−170.651	−	38.4046i	−0.828402	−	0.186430i
$207$	185.513	+	299.657i	0.896200	+	1.44762i
$208$	212.401	+	21.3202i	1.02116	+	0.102501i
$209$	−63.1866	+	109.442i	−0.302328	+	0.523648i
$210$	26.9074	−	1.50320i	0.128130	−	0.00715809i
$211$	67.4797	−	251.838i	0.319809	−	1.19354i	−0.599619	−	0.800285i	$-0.704681\pi$
$211$	67.4797	−	251.838i	0.319809	−	1.19354i	0.919428	−	0.393258i	$-0.128652\pi$
$212$	−82.7378	+	97.3335i	−0.390272	+	0.459121i
$213$	−78.9772	+	1.21383i	−0.370785	+	0.00569874i
$214$	−10.2365	−	252.993i	−0.0478339	−	1.18221i
$215$	115.684			0.538063
$216$	−176.051	−	125.147i	−0.815053	−	0.579386i
$217$			13.7679i			0.0634464i
$218$	4.85312	+	119.944i	0.0222620	+	0.550202i
$219$	−0.793182	−	51.6079i	−0.00362184	−	0.235653i
$220$	−19.0880	−	235.493i	−0.0867637	−	1.07042i
$221$	−36.6833	−	9.82926i	−0.165988	−	0.0444763i
$222$	−123.768	+	6.91437i	−0.557513	+	0.0311458i
$223$	312.971	+	180.694i	1.40346	+	0.810288i	0.994746	−	0.102375i	$-0.0326442\pi$
$223$	312.971	+	180.694i	1.40346	+	0.810288i	0.408714	+	0.912663i	$0.365977\pi$
$224$	20.7176	+	41.3992i	0.0924895	+	0.184818i
$225$	121.792	+	65.4108i	0.541297	+	0.290715i
$226$	113.167	+	25.4680i	0.500740	+	0.112690i
$227$	299.748	−	80.3174i	1.32048	−	0.353821i	0.471321	−	0.881962i	$-0.343777\pi$
$227$	299.748	−	80.3174i	1.32048	−	0.353821i	0.849157	+	0.528141i	$0.177111\pi$
$228$	−50.6872	+	61.5203i	−0.222312	+	0.269826i
$229$	−44.1284	+	164.690i	−0.192701	+	0.719169i	0.800149	+	0.599801i	$0.204753\pi$
$229$	−44.1284	+	164.690i	−0.192701	+	0.719169i	−0.992850	+	0.119368i	$0.961913\pi$
$230$	−112.966	+	215.325i	−0.491159	+	0.936194i
$231$	80.0729	+	20.1418i	0.346636	+	0.0871942i
$232$	−148.571	+	349.180i	−0.640390	+	1.50509i
$233$		−	166.801i		−	0.715886i	−0.933743	−	0.357943i	$-0.883478\pi$
$233$		−	166.801i		−	0.715886i	0.933743	−	0.357943i	$-0.116522\pi$
$234$	198.912	−	134.563i	0.850052	−	0.575054i
$235$	−94.2114	+	94.2114i	−0.400900	+	0.400900i
$236$	−23.7473	+	129.823i	−0.100624	+	0.550096i
$237$	150.668	+	83.9279i	0.635730	+	0.354126i
$238$	−2.45149	−	7.86262i	−0.0103004	−	0.0330362i
$239$	301.402	−	174.014i	1.26110	−	0.728094i	0.287809	−	0.957688i	$-0.407073\pi$
$239$	301.402	−	174.014i	1.26110	−	0.728094i	0.973287	+	0.229594i	$0.0737397\pi$
$240$	12.6036	−	148.493i	0.0525150	−	0.618723i
$241$	−137.804	+	238.683i	−0.571800	+	0.990387i	0.424581	+	0.905390i	$0.360421\pi$
$241$	−137.804	+	238.683i	−0.571800	+	0.990387i	−0.996381	+	0.0849968i	$0.972912\pi$
$242$	105.797	−	470.110i	0.437178	−	1.94260i
$243$	−242.283	+	18.6540i	−0.997049	+	0.0767653i
$244$	−184.047	+	65.6592i	−0.754290	+	0.269095i
$245$	140.672	−	37.6929i	0.574171	−	0.153849i
$246$	63.9719	−	306.151i	0.260048	−	1.24451i
$247$	−44.3123	−	76.7512i	−0.179402	−	0.310734i
$248$	75.3849	+	10.6604i	0.303971	+	0.0429854i
$249$	392.625	−	111.698i	1.57681	−	0.448587i
$250$	10.1321	+	250.413i	0.0405284	+	1.00165i
$251$	−189.053	+	189.053i	−0.753201	+	0.753201i	−0.975075	−	0.221875i	$-0.928782\pi$
$251$	−189.053	+	189.053i	−0.753201	+	0.753201i	0.221875	+	0.975075i	$0.428782\pi$
$252$	47.7228	+	20.8545i	0.189376	+	0.0827558i
$253$	−526.786	+	526.786i	−2.08216	+	2.08216i
$254$	136.867	+	126.222i	0.538848	+	0.496938i
$255$	−6.46766	+	25.7119i	−0.0253634	+	0.100831i
$256$	242.720	−	81.3828i	0.948124	−	0.317902i
$257$	−182.188	−	315.558i	−0.708902	−	1.22785i	−0.965265	−	0.261273i	$-0.915858\pi$
$257$	−182.188	−	315.558i	−0.708902	−	1.22785i	0.256363	−	0.966581i	$-0.417476\pi$
$258$	199.544	+	100.808i	0.773427	+	0.390728i
$259$	28.8702	−	7.73574i	0.111468	−	0.0298677i
$260$	149.717	+	70.9818i	0.575833	+	0.273007i
$261$	123.112	+	408.770i	0.471694	+	1.56617i
$262$	−6.76048	−	10.6870i	−0.0258033	−	0.0407900i
$263$	8.27352	−	14.3302i	0.0314583	−	0.0544873i	−0.849868	−	0.526996i	$-0.823318\pi$
$263$	8.27352	−	14.3302i	0.0314583	−	0.0544873i	0.881326	+	0.472509i	$0.156652\pi$
$264$	172.285	−	422.838i	0.652596	−	1.60166i
$265$	−85.8711	+	49.5777i	−0.324042	+	0.187086i
$266$	8.92900	−	17.0195i	0.0335677	−	0.0639831i
$267$	−6.78651	−	441.560i	−0.0254176	−	1.65378i
$268$	−127.773	−	23.3724i	−0.476766	−	0.0872104i
$269$	255.676	−	255.676i	0.950469	−	0.950469i	−0.0483612	−	0.998830i	$-0.515400\pi$
$269$	255.676	−	255.676i	0.950469	−	0.950469i	0.998830	+	0.0483612i	$0.0153998\pi$
$270$	−96.0641	−	137.405i	−0.355793	−	0.508907i
$271$		−	69.5228i		−	0.256542i	−0.991739	−	0.128271i	$-0.959057\pi$
$271$		−	69.5228i		−	0.256542i	0.991739	−	0.128271i	$-0.0409427\pi$
$272$	−44.9494	+	7.33499i	−0.165255	+	0.0269669i
$273$	−40.3102	+	41.5686i	−0.147656	+	0.152266i
$274$	−238.449	+	74.3464i	−0.870253	+	0.271337i
$275$	−75.6344	+	282.271i	−0.275034	+	1.02644i
$276$	−382.493	+	272.976i	−1.38584	+	0.989044i
$277$	394.147	−	105.611i	1.42291	−	0.381269i	0.536397	−	0.843966i	$-0.319785\pi$
$277$	394.147	−	105.611i	1.42291	−	0.381269i	0.886516	+	0.462697i	$0.153118\pi$
$278$	−449.735	+	284.498i	−1.61775	+	1.02337i
$279$	72.8255	−	45.0852i	0.261023	−	0.161596i
$280$	4.34858	+	35.6684i	0.0155306	+	0.127387i
$281$	56.1393	+	32.4120i	0.199784	+	0.115345i	0.596555	−	0.802572i	$-0.296536\pi$
$281$	56.1393	+	32.4120i	0.199784	+	0.115345i	−0.396771	+	0.917918i	$0.629869\pi$
$282$	−244.603	+	80.4098i	−0.867387	+	0.285141i
$283$	135.000	+	36.1732i	0.477032	+	0.127820i	0.489320	−	0.872104i	$-0.337245\pi$
$283$	135.000	+	36.1732i	0.477032	+	0.127820i	−0.0122881	+	0.999924i	$0.503912\pi$
$284$	−8.50850	−	104.971i	−0.0299595	−	0.369617i
$285$	−53.1000	+	31.7552i	−0.186316	+	0.111422i
$286$	373.177	+	344.152i	1.30481	+	1.20333i
$287$			75.4113i			0.262757i
$288$	151.139	−	245.155i	0.524787	−	0.851234i
$289$	−280.897			−0.971964
$290$	−199.682	+	216.522i	−0.688557	+	0.746627i
$291$	−59.7284	+	107.225i	−0.205252	+	0.368471i
$292$	68.5938	−	5.55991i	0.234910	−	0.0190408i
$293$	−56.6251	+	211.328i	−0.193260	+	0.721256i	0.799451	+	0.600732i	$0.205124\pi$
$293$	−56.6251	+	211.328i	−0.193260	+	0.721256i	−0.992710	+	0.120524i	$0.961543\pi$
$294$	275.493	+	57.5658i	0.937050	+	0.195802i
$295$	−51.2191	+	88.7141i	−0.173624	+	0.300726i
$296$	−20.0025	−	164.066i	−0.0675759	−	0.554278i
$297$	−155.672	−	489.506i	−0.524147	−	1.64817i
$298$	−9.12990	−	14.4326i	−0.0306373	−	0.0484315i
$299$	−135.221	−	504.653i	−0.452246	−	1.68780i
$300$	−76.3967	+	167.750i	−0.254656	+	0.559167i
$301$	−52.0671	−	13.9513i	−0.172980	−	0.0463499i
$302$	133.831	+	429.234i	0.443150	+	1.42130i
$303$	−117.005	+	33.2866i	−0.386154	+	0.109857i
$304$	−86.2754	−	62.0682i	−0.283801	−	0.204172i
$305$	−151.673			−0.497287
$306$	−33.5617	+	38.7148i	−0.109679	+	0.126519i
$307$	−156.734	−	156.734i	−0.510536	−	0.510536i	0.404155	−	0.914691i	$-0.367566\pi$
$307$	−156.734	−	156.734i	−0.510536	−	0.510536i	−0.914691	+	0.404155i	$0.867566\pi$
$308$	−19.8090	+	108.293i	−0.0643150	+	0.351600i
$309$	−134.666	−	225.183i	−0.435811	−	0.728749i
$310$	52.3302	+	27.4542i	0.168807	+	0.0885619i
$311$	171.086	+	296.329i	0.550115	+	0.952827i	0.998266	+	0.0588691i	$0.0187495\pi$
$311$	171.086	+	296.329i	0.550115	+	0.952827i	−0.448151	+	0.893958i	$0.647917\pi$
$312$	196.394	+	252.902i	0.629468	+	0.810583i
$313$	−121.870	−	70.3617i	−0.389361	−	0.224798i	0.292522	−	0.956259i	$-0.405506\pi$
$313$	−121.870	−	70.3617i	−0.389361	−	0.224798i	−0.681883	+	0.731461i	$0.738839\pi$
$314$	162.273	−	102.652i	0.516792	−	0.326917i
$315$	29.4490	+	27.6922i	0.0934890	+	0.0879117i
$316$	−98.5127	+	207.786i	−0.311749	+	0.657549i
$317$	−84.0328	−	313.615i	−0.265088	−	0.989320i	−0.962197	−	0.272355i	$-0.912197\pi$
$317$	−84.0328	−	313.615i	−0.265088	−	0.989320i	0.697109	−	0.716965i	$-0.254469\pi$
$318$	−191.323	+	10.6883i	−0.601643	+	0.0336112i
$319$	−781.513	+	451.207i	−2.44988	+	1.41444i
$320$	198.667	+	3.80749i	0.620833	+	0.0118984i
$321$	264.400	−	272.654i	0.823676	−	0.849390i
$322$	76.8121	−	83.2901i	0.238547	−	0.258665i
$323$	13.3701	+	13.3701i	0.0413936	+	0.0413936i
$324$	−45.9663	−	320.723i	−0.141871	−	0.989885i
$325$	−144.913	−	144.913i	−0.445886	−	0.445886i
$326$	306.244	−	12.3911i	0.939399	−	0.0380095i
$327$	−125.352	+	129.266i	−0.383341	+	0.395308i
$328$	412.909	+	58.3905i	1.25887	+	0.178020i
$329$	53.7647	−	31.0410i	0.163418	−	0.0943497i
$330$	236.229	−	264.185i	0.715845	−	0.800559i
$331$	16.0812	+	60.0158i	0.0485836	+	0.181317i	0.985954	−	0.167018i	$-0.0534139\pi$
$331$	16.0812	+	60.0158i	0.0485836	+	0.181317i	−0.937370	+	0.348335i	$0.886747\pi$
$332$	182.882	+	512.628i	0.550848	+	1.54406i
$333$	−135.459	−	127.378i	−0.406783	−	0.382516i
$334$	305.616	+	68.7781i	0.915017	+	0.205923i
$335$	−87.3137	−	50.4106i	−0.260638	−	0.150479i
$336$	−23.5808	+	65.3142i	−0.0701810	+	0.194388i
$337$	−155.973	−	270.153i	−0.462827	−	0.801640i	0.536273	−	0.844044i	$-0.319832\pi$
$337$	−155.973	−	270.153i	−0.462827	−	0.801640i	−0.999101	+	0.0424043i	$0.986498\pi$
$338$	−17.1906	+	5.35988i	−0.0508598	+	0.0158576i
$339$	89.3035	+	149.330i	0.263432	+	0.440503i
$340$	−34.7735	−	6.36079i	−0.102275	−	0.0187082i
$341$	128.025	+	128.025i	0.375439	+	0.375439i
$342$	−119.265	+	8.50312i	−0.348727	+	0.0248629i
$343$	−138.747			−0.404510
$344$	−116.705	+	274.287i	−0.339258	+	0.797346i
$345$	−350.818	+	99.8041i	−1.01686	+	0.289287i
$346$	−386.304	−	202.668i	−1.11648	−	0.585745i
$347$	353.625	+	94.7534i	1.01909	+	0.273065i	0.729423	−	0.684063i	$-0.239789\pi$
$347$	353.625	+	94.7534i	1.01909	+	0.273065i	0.289668	+	0.957127i	$0.406455\pi$
$348$	−533.112	+	199.477i	−1.53193	+	0.573209i
$349$	−92.1429	−	343.882i	−0.264020	−	0.985335i	−0.962848	−	0.270045i	$-0.912961\pi$
$349$	−92.1429	−	343.882i	−0.264020	−	0.985335i	0.698828	−	0.715290i	$-0.253705\pi$
$350$	9.75792	−	43.3593i	0.0278798	−	0.123884i
$351$	351.881	+	77.0983i	1.00251	+	0.219653i
$352$	577.612	+	192.313i	1.64094	+	0.546345i
$353$	−86.9363	+	150.578i	−0.246278	+	0.426567i	−0.962490	−	0.271316i	$-0.912541\pi$
$353$	−86.9363	+	150.578i	−0.246278	+	0.426567i	0.716212	+	0.697883i	$0.245874\pi$
$354$	−165.655	+	108.391i	−0.467951	+	0.306190i
$355$	21.1569	−	78.9588i	0.0595970	−	0.222419i
$356$	586.892	−	47.5709i	1.64857	−	0.133626i
$357$	6.01181	−	10.7925i	0.0168398	−	0.0302310i
$358$	−115.575	+	4.67635i	−0.322836	+	0.0130624i
$359$	−266.450			−0.742202			−0.371101	−	0.928593i	$-0.621020\pi$
$359$	−266.450			−0.742202			−0.371101	+	0.928593i	$0.621020\pi$
$360$	174.429	−	139.804i	0.484524	−	0.388345i
$361$		−	316.875i		−	0.877771i
$362$	288.374	−	11.6680i	0.796612	−	0.0322321i
$363$	620.336	−	370.977i	1.70892	−	1.02198i
$364$	−58.8244	−	50.0033i	−0.161606	−	0.137372i
$365$	51.5959	+	13.8251i	0.141359	+	0.0378769i
$366$	−261.622	−	132.169i	−0.714814	−	0.361117i
$367$	−317.602	−	183.368i	−0.865401	−	0.499640i	0.000415917	−	1.00000i	$-0.499868\pi$
$367$	−317.602	−	183.368i	−0.865401	−	0.499640i	−0.865817	+	0.500360i	$0.833201\pi$
$368$	−396.574	−	485.070i	−1.07765	−	1.31813i
$369$	398.890	−	246.947i	1.08100	−	0.669234i
$370$	28.1666	−	125.158i	0.0761260	−	0.338266i
$371$	44.6280	−	11.9580i	0.120291	−	0.0322319i
$372$	66.3413	+	92.9571i	0.178337	+	0.249885i
$373$	100.152	−	373.772i	0.268503	−	1.00207i	−0.691568	−	0.722312i	$-0.743080\pi$
$373$	100.152	−	373.772i	0.268503	−	1.00207i	0.960071	−	0.279757i	$-0.0902538\pi$
$374$	−95.9089	−	50.3170i	−0.256441	−	0.134537i
$375$	−261.704	+	269.874i	−0.697878	+	0.719665i
$376$	−128.333	−	318.419i	−0.341312	−	0.846860i
$377$		−	632.857i		−	1.67866i
$378$	26.6658	+	73.4287i	0.0705445	+	0.194256i
$379$	243.272	−	243.272i	0.641880	−	0.641880i	−0.309137	−	0.951017i	$-0.600040\pi$
$379$	243.272	−	243.272i	0.641880	−	0.641880i	0.951017	+	0.309137i	$0.100040\pi$
$380$	−46.8843	−	67.8764i	−0.123380	−	0.178622i
$381$	4.29181	+	279.244i	0.0112646	+	0.732924i
$382$	705.387	−	219.933i	1.84656	−	0.575741i
$383$	56.1042	−	32.3918i	0.146486	−	0.0845739i	−0.424965	−	0.905210i	$-0.639714\pi$
$383$	56.1042	−	32.3918i	0.146486	−	0.0845739i	0.571452	+	0.820636i	$0.306380\pi$
$384$	339.365	+	179.687i	0.883762	+	0.467936i
$385$	−42.7250	+	74.0018i	−0.110974	+	0.192212i
$386$	−674.711	−	151.842i	−1.74796	−	0.393374i
$387$	96.7067	+	321.096i	0.249888	+	0.829706i
$388$	−147.873	−	70.1079i	−0.381117	−	0.180691i
$389$	508.627	−	136.286i	1.30753	−	0.350350i	0.463235	−	0.886236i	$-0.346689\pi$
$389$	508.627	−	136.286i	1.30753	−	0.350350i	0.844291	+	0.535885i	$0.180022\pi$
$390$	77.6165	+	236.106i	0.199017	+	0.605400i
$391$	55.7334	+	96.5331i	0.142541	+	0.246888i
$392$	−52.5433	+	371.560i	−0.134039	+	0.947858i
$393$	4.62730	−	18.3956i	0.0117743	−	0.0468082i
$394$	−705.227	+	28.5345i	−1.78992	+	0.0724227i
$395$	−126.210	+	126.210i	−0.319519	+	0.319519i
$396$	637.687	−	249.844i	1.61032	−	0.630918i
$397$	233.601	−	233.601i	0.588416	−	0.588416i	−0.348786	−	0.937202i	$-0.613406\pi$
$397$	233.601	−	233.601i	0.588416	−	0.588416i	0.937202	+	0.348786i	$0.113406\pi$
$398$	409.715	−	444.269i	1.02943	−	1.11625i
$399$	27.7290	−	7.88863i	0.0694963	−	0.0197710i
$400$	−229.855	−	87.0017i	−0.574638	−	0.217504i
$401$	−46.0102	−	79.6920i	−0.114739	−	0.198733i	0.802937	−	0.596064i	$-0.203270\pi$
$401$	−46.0102	−	79.6920i	−0.114739	−	0.198733i	−0.917675	+	0.397331i	$0.869936\pi$
$402$	−106.680	−	163.040i	−0.265374	−	0.405572i
$403$	−122.646	+	32.8628i	−0.304331	+	0.0815454i
$404$	−54.4997	−	152.766i	−0.134900	−	0.378134i
$405$	50.0426	−	246.454i	0.123562	−	0.608529i
$406$	115.985	−	73.3711i	0.285678	−	0.180717i
$407$	196.525	−	340.391i	0.482863	−	0.836342i
$408$	−54.4384	−	41.2737i	−0.133427	−	0.101161i
$409$	216.521	−	125.008i	0.529391	−	0.305644i	−0.211378	−	0.977404i	$-0.567795\pi$
$409$	216.521	−	125.008i	0.529391	−	0.305644i	0.740768	+	0.671761i	$0.234462\pi$
$410$	286.631	+	150.376i	0.699099	+	0.366771i
$411$	−327.302	−	182.320i	−0.796356	−	0.443601i
$412$	287.846	−	198.824i	0.698656	−	0.482583i
$413$	33.7516	−	33.7516i	0.0817231	−	0.0817231i
$414$	−692.100	−	133.552i	−1.67174	−	0.322590i
$415$			422.456i			1.01797i
$416$	−319.337	+	283.372i	−0.767637	+	0.681182i
$417$	−774.133	−	194.729i	−1.85644	−	0.466975i
$418$	−75.2321	−	241.290i	−0.179981	−	0.577249i
$419$	−84.9463	+	317.024i	−0.202736	+	0.756620i	0.787392	+	0.616453i	$0.211431\pi$
$419$	−84.9463	+	317.024i	−0.202736	+	0.756620i	−0.990128	+	0.140168i	$0.955236\pi$
$420$	−34.2732	+	41.5983i	−0.0816029	+	0.0990435i
$421$	303.306	−	81.2707i	0.720442	−	0.193042i	0.120073	−	0.992765i	$-0.461687\pi$
$421$	303.306	−	81.2707i	0.720442	−	0.193042i	0.600369	+	0.799723i	$0.295020\pi$
$422$	278.765	+	440.673i	0.660581	+	1.04425i
$423$	−340.254	−	182.741i	−0.804383	−	0.432011i
$424$	−30.9202	−	253.617i	−0.0729249	−	0.598152i
$425$	37.8660	+	21.8620i	0.0890965	+	0.0514399i
$426$	105.299	−	117.761i	0.247181	−	0.276433i
$427$	68.2651	+	18.2916i	0.159871	+	0.0428374i
$428$	385.837	+	327.979i	0.901489	+	0.766305i
$429$	11.7019	+	761.375i	0.0272771	+	1.77477i
$430$	−156.853	+	170.082i	−0.364775	+	0.395539i
$431$		−	44.8510i		−	0.104063i	−0.998645	−	0.0520313i	$-0.983430\pi$
$431$		−	44.8510i		−	0.104063i	0.998645	−	0.0520313i	$-0.0165696\pi$
$432$	422.701	−	89.1512i	0.978474	−	0.206369i
$433$	320.449			0.740068			0.370034	−	0.929018i	$-0.379346\pi$
$433$	320.449			0.740068			0.370034	+	0.929018i	$0.379346\pi$
$434$	−20.2419	−	18.6676i	−0.0466404	−	0.0430129i
$435$	−441.759	+	6.78957i	−1.01554	+	0.0156082i
$436$	−182.926	−	155.495i	−0.419555	−	0.356640i
$437$	−67.3243	+	251.258i	−0.154060	+	0.574960i
$438$	76.9511	+	68.8082i	0.175687	+	0.157096i
$439$	−6.58046	+	11.3977i	−0.0149897	+	0.0259628i	−0.873423	−	0.486962i	$-0.838105\pi$
$439$	−6.58046	+	11.3977i	−0.0149897	+	0.0259628i	0.858433	+	0.512925i	$0.171438\pi$
$440$	372.110	+	291.237i	0.845704	+	0.661901i
$441$	222.218	+	358.945i	0.503895	+	0.813935i
$442$	64.1895	−	40.6056i	0.145225	−	0.0918679i
$443$	27.8651	+	103.994i	0.0629009	+	0.234750i	0.990218	−	0.139526i	$-0.0445580\pi$
$443$	27.8651	+	103.994i	0.0629009	+	0.234750i	−0.927317	+	0.374276i	$0.877891\pi$
$444$	157.649	−	191.343i	0.355065	−	0.430952i
$445$	441.457	+	118.288i	0.992039	+	0.265816i
$446$	−690.015	+	215.140i	−1.54712	+	0.482378i
$447$	6.24909	−	24.8430i	0.0139801	−	0.0555771i
$448$	−88.9571	−	25.6727i	−0.198565	−	0.0573051i
$449$	−598.999			−1.33407			−0.667037	−	0.745025i	$-0.732438\pi$
$449$	−598.999			−1.33407			−0.667037	+	0.745025i	$0.732438\pi$
$450$	−261.304	+	90.3728i	−0.580677	+	0.200828i
$451$	701.235	+	701.235i	1.55484	+	1.55484i
$452$	−190.885	+	131.850i	−0.422313	+	0.291704i
$453$	−328.195	+	589.178i	−0.724491	+	1.30061i
$454$	−288.339	+	549.601i	−0.635107	+	1.21057i
$455$	−29.9627	−	51.8970i	−0.0658521	−	0.114059i
$456$	−21.7232	−	157.936i	−0.0476386	−	0.346352i
$457$	368.786	+	212.919i	0.806971	+	0.465905i	0.845903	−	0.533337i	$-0.179062\pi$
$457$	368.786	+	212.919i	0.806971	+	0.465905i	−0.0389319	+	0.999242i	$0.512396\pi$
$458$	−182.299	−	288.179i	−0.398032	−	0.629211i
$459$	−76.7737	+	3.54212i	−0.167263	+	0.00771705i
$460$	−163.408	−	458.042i	−0.355235	−	0.995743i
$461$	5.83135	+	21.7629i	0.0126494	+	0.0472080i	0.971962	−	0.235138i	$-0.0755541\pi$
$461$	5.83135	+	21.7629i	0.0126494	+	0.0472080i	−0.959313	+	0.282346i	$0.908887\pi$
$462$	−138.183	+	90.4157i	−0.299097	+	0.195705i
$463$	−336.245	+	194.131i	−0.726232	+	0.419290i	−0.817042	−	0.576578i	$-0.804388\pi$
$463$	−336.245	+	194.131i	−0.726232	+	0.419290i	0.0908100	+	0.995868i	$0.471054\pi$
$464$	−311.931	−	691.880i	−0.672266	−	1.49112i
$465$	24.2553	+	85.2590i	0.0521620	+	0.183353i
$466$	245.237	+	226.163i	0.526259	+	0.485329i
$467$	154.492	+	154.492i	0.330818	+	0.330818i	0.852897	−	0.522079i	$-0.174843\pi$
$467$	154.492	+	154.492i	0.330818	+	0.330818i	−0.522079	+	0.852897i	$0.674843\pi$
$468$	−71.8633	+	474.898i	−0.153554	+	1.01474i
$469$	33.2188	+	33.2188i	0.0708291	+	0.0708291i
$470$	−10.7730	−	266.252i	−0.0229212	−	0.566494i
$471$	279.321	+	70.2616i	0.593039	+	0.149175i
$472$	−158.671	−	210.938i	−0.336167	−	0.446903i
$473$	−613.892	+	354.431i	−1.29787	+	0.749325i
$474$	−327.682	+	107.721i	−0.691312	+	0.227259i
$475$	26.4086	+	98.5582i	0.0555970	+	0.207491i
$476$	14.8838	+	7.05653i	0.0312685	+	0.0148246i
$477$	−209.395	−	196.903i	−0.438982	−	0.412794i
$478$	−152.824	+	679.074i	−0.319716	+	1.42066i
$479$	415.748	+	240.032i	0.867949	+	0.501111i	0.866666	−	0.498889i	$-0.166258\pi$
$479$	415.748	+	240.032i	0.867949	+	0.501111i	0.00128289	+	0.999999i	$0.499592\pi$
$480$	201.231	+	219.870i	0.419231	+	0.458062i
$481$	137.822	+	238.714i	0.286532	+	0.496287i
$482$	−164.074	−	526.230i	−0.340402	−	1.09176i
$483$	169.933	−	2.61176i	0.351828	−	0.00540738i
$484$	547.722	+	792.960i	1.13166	+	1.63835i
$485$	−89.8191	−	89.8191i	−0.185194	−	0.185194i
$486$	301.082	−	381.505i	0.619510	−	0.784989i
$487$	−378.056			−0.776295			−0.388148	−	0.921597i	$-0.626885\pi$
$487$	−378.056			−0.776295			−0.388148	+	0.921597i	$0.626885\pi$
$488$	153.012	−	359.618i	0.313548	−	0.736921i
$489$	330.044	+	320.052i	0.674937	+	0.654504i
$490$	−135.317	+	257.927i	−0.276158	+	0.526382i
$491$	220.859	+	59.1789i	0.449814	+	0.120527i	0.476612	−	0.879114i	$-0.341865\pi$
$491$	220.859	+	59.1789i	0.449814	+	0.120527i	−0.0267984	+	0.999641i	$0.508531\pi$
$492$	363.374	+	509.158i	0.738565	+	1.03487i
$493$	34.9460	+	130.420i	0.0708844	+	0.264544i
$494$	172.924	+	38.9163i	0.350049	+	0.0787779i
$495$	531.345	−	16.3367i	1.07342	−	0.0330035i
$496$	−117.886	+	96.3791i	−0.237674	+	0.194313i
$497$	−19.0447	+	32.9864i	−0.0383193	+	0.0663710i
$498$	−368.132	+	728.700i	−0.739221	+	1.46325i
$499$	−13.7167	+	51.1915i	−0.0274884	+	0.102588i	−0.978307	−	0.207160i	$-0.933578\pi$
$499$	−13.7167	+	51.1915i	−0.0274884	+	0.102588i	0.950819	+	0.309748i	$0.100245\pi$
$500$	−381.903	−	324.635i	−0.763807	−	0.649269i
$501$	241.170	+	403.277i	0.481378	+	0.804944i
$502$	−21.6180	−	534.287i	−0.0430638	−	1.06432i
$503$	−374.165			−0.743867			−0.371934	−	0.928259i	$-0.621305\pi$
$503$	−374.165			−0.743867			−0.371934	+	0.928259i	$0.621305\pi$
$504$	−95.3675	+	41.8874i	−0.189221	+	0.0831099i
$505$		−	125.894i		−	0.249296i
$506$	−60.2374	−	1488.76i	−0.119046	−	2.94221i
$507$	−23.5963	−	13.1440i	−0.0465411	−	0.0259251i
$508$	−371.152	+	30.0840i	−0.730614	+	0.0592204i
$509$	−104.080	−	27.8883i	−0.204480	−	0.0547903i	0.155125	−	0.987895i	$-0.450422\pi$
$509$	−104.080	−	27.8883i	−0.204480	−	0.0547903i	−0.359605	+	0.933105i	$0.617089\pi$
$510$	−29.0330	−	44.3713i	−0.0569275	−	0.0870025i
$511$	−21.5551	−	12.4448i	−0.0421822	−	0.0243539i
$512$	−209.448	+	467.200i	−0.409078	+	0.912499i
$513$	−132.531	−	120.841i	−0.258344	−	0.235557i
$514$	710.969	+	160.002i	1.38321	+	0.311288i
$515$	262.286	−	70.2793i	0.509293	−	0.136465i
$516$	−418.769	+	156.693i	−0.811568	+	0.303668i
$517$	211.303	−	788.592i	0.408709	−	1.52532i
$518$	−27.7713	+	52.9346i	−0.0536125	+	0.102190i
$519$	−179.054	−	629.385i	−0.344998	−	1.21269i
$520$	−307.358	+	123.875i	−0.591073	+	0.238222i
$521$		−	312.931i		−	0.600636i	−0.953839	−	0.300318i	$-0.902907\pi$
$521$		−	312.931i		−	0.600636i	0.953839	−	0.300318i	$-0.0970927\pi$
$522$	−767.913	−	373.242i	−1.47110	−	0.715022i
$523$	568.260	−	568.260i	1.08654	−	1.08654i	0.0906572	−	0.995882i	$-0.471103\pi$
$523$	568.260	−	568.260i	1.08654	−	1.08654i	0.995882	−	0.0906572i	$-0.0288967\pi$
$524$	24.8788	+	4.55084i	0.0474786	+	0.00868481i
$525$	57.2151	−	34.2161i	0.108981	−	0.0651736i
$526$	9.85073	+	31.5940i	0.0187276	+	0.0600647i
$527$	23.4604	−	13.5449i	0.0445168	−	0.0257018i
$528$	388.071	+	826.617i	0.734982	+	1.56556i
$529$	−502.226	+	869.881i	−0.949387	+	1.64439i
$530$	43.5404	−	193.472i	0.0821518	−	0.365041i
$531$	−289.056	−	68.0047i	−0.544361	−	0.128069i
$532$	12.9159	+	36.2042i	0.0242781	+	0.0680529i
$533$	−671.772	+	180.001i	−1.26036	+	0.337712i
$534$	658.398	+	588.726i	1.23295	+	1.10248i
$535$	196.530	+	340.399i	0.367345	+	0.636260i
$536$	207.609	−	156.166i	0.387329	−	0.291355i
$537$	−124.557	−	120.787i	−0.231951	−	0.224929i
$538$	29.2362	+	722.570i	0.0543425	+	1.34307i
$539$	−631.013	+	631.013i	−1.17071	+	1.17071i
$540$	332.269	+	45.0686i	0.615313	+	0.0834603i
$541$	−68.7920	+	68.7920i	−0.127157	+	0.127157i	−0.767821	−	0.640664i	$-0.778659\pi$
$541$	−68.7920	+	68.7920i	−0.127157	+	0.127157i	0.640664	+	0.767821i	$0.278659\pi$
$542$	102.215	+	94.2648i	0.188588	+	0.173920i
$543$	310.785	+	301.376i	0.572348	+	0.555021i
$544$	50.1620	−	76.0314i	0.0922095	−	0.139764i
$545$	−93.1749	−	161.384i	−0.170963	−	0.296117i
$546$	−6.45960	−	115.628i	−0.0118308	−	0.211772i
$547$	−206.625	+	55.3650i	−0.377742	+	0.101216i	−0.442694	−	0.896673i	$-0.645977\pi$
$547$	−206.625	+	55.3650i	−0.377742	+	0.101216i	0.0649518	+	0.997888i	$0.479311\pi$
$548$	214.003	−	451.381i	0.390516	−	0.823687i
$549$	−126.792	−	420.989i	−0.230951	−	0.766829i
$550$	−312.453	−	493.927i	−0.568096	−	0.898049i
$551$	−157.544	+	272.874i	−0.285924	+	0.495234i
$552$	117.278	−	932.477i	0.212459	−	1.68927i
$553$	72.0256	−	41.5840i	0.130245	−	0.0751971i
$554$	−379.144	+	722.684i	−0.684376	+	1.30448i
$555$	165.154	−	98.7661i	0.297574	−	0.177957i
$556$	191.511	−	1046.96i	0.344444	−	1.88302i
$557$	−32.8619	+	32.8619i	−0.0589981	+	0.0589981i	−0.735990	−	0.676992i	$-0.763283\pi$
$557$	−32.8619	+	32.8619i	−0.0589981	+	0.0589981i	0.676992	+	0.735990i	$0.263283\pi$
$558$	−32.4571	+	168.201i	−0.0581669	+	0.301435i
$559$		−	497.120i		−	0.889302i
$560$	−58.3369	−	41.9687i	−0.104173	−	0.0749441i
$561$	−44.4543	−	156.260i	−0.0792412	−	0.278537i
$562$	−123.771	+	38.5908i	−0.220234	+	0.0686669i
$563$	247.190	−	922.527i	0.439059	−	1.63859i	−0.292102	−	0.956387i	$-0.594355\pi$
$563$	247.190	−	922.527i	0.439059	−	1.63859i	0.731161	−	0.682205i	$-0.238979\pi$
$564$	213.432	−	468.650i	0.378426	−	0.830939i
$565$	−173.935	+	46.6058i	−0.307850	+	0.0824881i
$566$	−236.227	+	149.435i	−0.417363	+	0.264019i
$567$	−52.2454	+	104.890i	−0.0921436	+	0.184990i
$568$	165.868	+	129.819i	0.292022	+	0.228555i
$569$	−410.015	−	236.722i	−0.720589	−	0.416033i	0.0943801	−	0.995536i	$-0.469913\pi$
$569$	−410.015	−	236.722i	−0.720589	−	0.416033i	−0.814970	+	0.579504i	$0.803246\pi$
$570$	25.3099	−	121.126i	0.0444034	−	0.212501i
$571$	132.148	+	35.4089i	0.231432	+	0.0620121i	0.372671	−	0.927963i	$-0.378442\pi$
$571$	132.148	+	35.4089i	0.231432	+	0.0620121i	−0.141239	+	0.989976i	$0.545109\pi$
$572$	−1011.97	+	82.0257i	−1.76917	+	0.143402i
$573$	968.234	+	539.343i	1.68976	+	0.941262i
$574$	−110.872	−	102.249i	−0.193157	−	0.178134i
$575$			601.511i			1.04611i
$576$	155.509	+	554.611i	0.269981	+	0.962866i
$577$	1044.11			1.80955			0.904776	−	0.425888i	$-0.140038\pi$
$577$	1044.11			1.80955			0.904776	+	0.425888i	$0.140038\pi$
$578$	380.864	−	412.984i	0.658934	−	0.714506i
$579$	−532.434	−	890.319i	−0.919575	−	1.53768i
$580$	−47.5923	−	587.156i	−0.0820558	−	1.01234i
$581$	50.9478	−	190.140i	0.0876899	−	0.327263i
$582$	−76.6609	−	233.199i	−0.131720	−	0.400686i
$583$	303.792	−	526.183i	0.521084	−	0.902543i
$584$	−84.8307	+	108.387i	−0.145258	+	0.185595i
$585$	−176.392	+	328.434i	−0.301525	+	0.561426i
$586$	−233.924	−	369.788i	−0.399188	−	0.631038i
$587$	171.686	+	640.740i	0.292480	+	1.09155i	0.943198	+	0.332230i	$0.107801\pi$
$587$	171.686	+	640.740i	0.292480	+	1.09155i	−0.650718	+	0.759319i	$0.725532\pi$
$588$	−458.171	+	326.986i	−0.779202	+	0.556098i
$589$	61.0630	+	16.3618i	0.103672	+	0.0277789i
$590$	−60.9832	−	195.590i	−0.103361	−	0.331508i
$591$	−760.035	−	737.026i	−1.28601	−	1.24708i
$592$	268.337	+	193.046i	0.453271	+	0.326092i
$593$	481.014			0.811153			0.405577	−	0.914061i	$-0.367071\pi$
$593$	481.014			0.811153			0.405577	+	0.914061i	$0.367071\pi$
$594$	930.760	+	434.839i	1.56694	+	0.732053i
$595$	9.04050	+	9.04050i	0.0151941	+	0.0151941i
$596$	33.5983	+	6.14583i	0.0563731	+	0.0103118i
$597$	906.420	−	13.9311i	1.51829	−	0.0233352i
$598$	925.302	+	485.444i	1.54733	+	0.811779i
$599$	237.845	+	411.960i	0.397070	+	0.687746i	0.993363	−	0.115021i	$-0.0366936\pi$
$599$	237.845	+	411.960i	0.397070	+	0.687746i	−0.596293	+	0.802767i	$0.703360\pi$
$600$	−143.047	−	339.770i	−0.238411	−	0.566284i
$601$	327.303	+	188.968i	0.544597	+	0.314423i	0.746940	−	0.664892i	$-0.231522\pi$
$601$	327.303	+	188.968i	0.544597	+	0.314423i	−0.202343	+	0.979315i	$0.564856\pi$
$602$	91.1085	−	57.6343i	0.151343	−	0.0957380i
$603$	66.9312	−	284.493i	0.110997	−	0.471796i
$604$	−812.532	−	385.228i	−1.34525	−	0.637794i
$605$	193.606	+	722.547i	0.320010	+	1.19429i
$606$	109.705	−	217.157i	0.181032	−	0.358344i
$607$	153.390	−	88.5597i	0.252702	−	0.145897i	−0.368299	−	0.929707i	$-0.620060\pi$
$607$	153.390	−	88.5597i	0.252702	−	0.145897i	0.621001	+	0.783810i	$0.286726\pi$
$608$	208.234	−	42.6876i	0.342490	−	0.0702099i
$609$	199.647	+	50.2199i	0.327827	+	0.0824629i
$610$	205.650	−	222.994i	0.337132	−	0.365564i
$611$	404.849	+	404.849i	0.662601	+	0.662601i
$612$	−11.4139	−	101.836i	−0.0186502	−	0.166399i
$613$	542.679	+	542.679i	0.885283	+	0.885283i	0.994066	−	0.108782i	$-0.0346952\pi$
$613$	542.679	+	542.679i	0.885283	+	0.885283i	−0.108782	+	0.994066i	$0.534695\pi$
$614$	442.950	−	17.9224i	0.721416	−	0.0291896i
$615$	132.855	+	466.993i	0.216024	+	0.759338i
$616$	−132.357	−	175.956i	−0.214865	−	0.285643i
$617$	272.476	−	157.314i	0.441615	−	0.254967i	−0.262667	−	0.964886i	$-0.584602\pi$
$617$	272.476	−	157.314i	0.441615	−	0.254967i	0.704282	+	0.709920i	$0.251269\pi$
$618$	513.663	+	107.333i	0.831169	+	0.173678i
$619$	−155.199	−	579.212i	−0.250726	−	0.935723i	−0.970418	−	0.241429i	$-0.922384\pi$
$619$	−155.199	−	579.212i	−0.250726	−	0.935723i	0.719692	−	0.694293i	$-0.244283\pi$
$620$	−111.318	+	39.7129i	−0.179545	+	0.0640531i
$621$	−570.290	−	890.312i	−0.918341	−	1.43368i
$622$	−667.645	−	150.252i	−1.07338	−	0.241563i
$623$	−184.426	−	106.479i	−0.296030	−	0.170913i
$624$	−638.112	−	54.1607i	−1.02261	−	0.0867959i
$625$	−2.51815	−	4.36156i	−0.00402904	−	0.00697850i
$626$	268.690	−	83.7750i	0.429217	−	0.133826i
$627$	184.492	−	331.202i	0.294245	−	0.528232i
$628$	−69.1006	+	377.762i	−0.110033	+	0.601533i
$629$	−41.5842	−	41.5842i	−0.0661117	−	0.0661117i
$630$	−80.6434	+	5.74957i	−0.128005	+	0.00912630i
$631$	588.990			0.933423			0.466711	−	0.884410i	$-0.345439\pi$
$631$	588.990			0.933423			0.466711	+	0.884410i	$0.345439\pi$
$632$	−171.921	−	426.569i	−0.272027	−	0.674951i
$633$	−190.805	+	758.535i	−0.301429	+	1.19832i
$634$	575.025	+	301.677i	0.906979	+	0.475831i
$635$	−279.179	−	74.8057i	−0.439652	−	0.117804i
$636$	243.697	−	295.781i	0.383171	−	0.465064i
$637$	−161.975	−	604.501i	−0.254279	−	0.948980i
$638$	396.262	−	1760.79i	0.621100	−	2.75986i
$639$	236.848	−	7.28212i	0.370654	−	0.0113961i
$640$	−274.967	+	286.923i	−0.429635	+	0.448318i
$641$	−223.902	+	387.809i	−0.349300	+	0.605006i	−0.986125	−	0.166002i	$-0.946914\pi$
$641$	−223.902	+	387.809i	−0.349300	+	0.605006i	0.636825	+	0.771008i	$0.280247\pi$
$642$	42.3694	+	758.417i	0.0659959	+	1.18133i
$643$	61.3454	−	228.944i	0.0954050	−	0.356056i	−0.901676	−	0.432413i	$-0.857662\pi$
$643$	61.3454	−	228.944i	0.0954050	−	0.356056i	0.997081	+	0.0763569i	$0.0243288\pi$
$644$	18.3075	+	225.863i	0.0284278	+	0.350719i
$645$	−347.010	+	5.33333i	−0.538000	+	0.00826872i
$646$	−37.7855	+	1.52886i	−0.0584916	+	0.00236665i
$647$	−367.597			−0.568156			−0.284078	−	0.958801i	$-0.591688\pi$
$647$	−367.597			−0.568156			−0.284078	+	0.958801i	$0.591688\pi$
$648$	533.862	+	367.281i	0.823861	+	0.566792i
$649$		−	627.700i		−	0.967180i
$650$	409.541	−	16.5706i	0.630063	−	0.0254933i
$651$	−0.634736	−	41.2987i	−0.000975016	−	0.0634389i
$652$	−397.013	+	467.051i	−0.608916	+	0.716335i
$653$	−948.905	−	254.258i	−1.45315	−	0.389369i	−0.556029	−	0.831163i	$-0.687676\pi$
$653$	−948.905	−	254.258i	−1.45315	−	0.389369i	−0.897117	+	0.441793i	$0.854342\pi$
$654$	−20.0874	−	359.566i	−0.0307146	−	0.549795i
$655$	17.0009	+	9.81545i	0.0259555	+	0.0149854i
$656$	−645.704	+	527.901i	−0.984304	+	0.804727i
$657$	4.75853	+	154.769i	0.00724282	+	0.235569i
$658$	−27.2611	+	121.135i	−0.0414302	+	0.184095i
$659$	−369.076	+	98.8935i	−0.560054	+	0.150066i	−0.527731	−	0.849411i	$-0.676957\pi$
$659$	−369.076	+	98.8935i	−0.560054	+	0.150066i	−0.0323228	+	0.999477i	$0.510290\pi$
$660$	68.1141	+	705.514i	0.103203	+	1.06896i
$661$	−224.889	+	839.298i	−0.340226	+	1.26974i	0.557866	+	0.829931i	$0.311620\pi$
$661$	−224.889	+	839.298i	−0.340226	+	1.26974i	−0.898091	+	0.439809i	$0.855046\pi$
$662$	−110.041	−	57.7313i	−0.166226	−	0.0872074i
$663$	110.490	+	27.7931i	0.166652	+	0.0419202i
$664$	−1001.65	−	426.185i	−1.50851	−	0.641845i
$665$			29.8358i			0.0448659i
$666$	370.941	−	26.4467i	0.556969	−	0.0397097i
$667$	−1313.44	+	1313.44i	−1.96918	+	1.96918i
$668$	−515.499	+	356.071i	−0.771705	+	0.533040i
$669$	−947.134	−	527.590i	−1.41575	−	0.788624i
$670$	192.502	−	60.0205i	0.287317	−	0.0895829i
$671$	804.874	−	464.694i	1.19951	−	0.692540i
$672$	−64.0542	−	123.228i	−0.0953187	−	0.183375i
$673$	419.388	−	726.402i	0.623163	−	1.07935i	−0.365731	−	0.930721i	$-0.619181\pi$
$673$	419.388	−	726.402i	0.623163	−	1.07935i	0.988893	−	0.148628i	$-0.0474858\pi$
$674$	608.668	+	136.979i	0.903068	+	0.203233i
$675$	−368.348	−	190.594i	−0.545701	−	0.282362i
$676$	15.4282	−	32.5416i	0.0228228	−	0.0481384i
$677$	−754.235	+	202.097i	−1.11408	+	0.298518i	−0.768487	−	0.639865i	$-0.778990\pi$
$677$	−754.235	+	202.097i	−1.11408	+	0.298518i	−0.345597	+	0.938383i	$0.612324\pi$
$678$	−340.635	−	71.1777i	−0.502412	−	0.104982i
$679$	29.5938	+	51.2580i	0.0435844	+	0.0754905i
$680$	56.5006	−	42.5006i	0.0830891	−	0.0625009i
$681$	−895.436	+	254.743i	−1.31488	+	0.374072i
$682$	−361.812	+	14.6395i	−0.530517	+	0.0214655i
$683$	447.481	−	447.481i	0.655170	−	0.655170i	−0.299064	−	0.954233i	$-0.596674\pi$
$683$	447.481	−	447.481i	0.655170	−	0.655170i	0.954233	+	0.299064i	$0.0966742\pi$
$684$	149.207	−	186.876i	0.218140	−	0.273211i
$685$	274.171	−	274.171i	0.400250	−	0.400250i
$686$	188.125	−	203.990i	0.274234	−	0.297362i
$687$	124.777	−	496.045i	0.181626	−	0.722045i
$688$	−245.028	−	543.484i	−0.356145	−	0.789948i
$689$	213.047	+	369.008i	0.309212	+	0.535571i
$690$	328.932	−	651.106i	0.476714	−	0.943632i
$691$	−880.365	+	235.893i	−1.27405	+	0.341379i	−0.831579	−	0.555406i	$-0.812563\pi$
$691$	−880.365	+	235.893i	−1.27405	+	0.341379i	−0.442466	+	0.896785i	$0.645896\pi$
$692$	821.751	−	293.162i	1.18750	−	0.423645i
$693$	−241.119	−	56.7268i	−0.347935	−	0.0818569i
$694$	−618.783	+	391.436i	−0.891618	+	0.564028i
$695$	413.059	−	715.439i	0.594329	−	1.02941i
$696$	429.561	−	1054.27i	0.617185	−	1.51475i
$697$	128.501	−	74.1898i	0.184362	−	0.106442i
$698$	630.521	+	330.792i	0.903325	+	0.473914i
$699$	7.68999	+	500.345i	0.0110014	+	0.715801i
$700$	50.5177	+	73.1366i	0.0721681	+	0.104481i
$701$	716.091	−	716.091i	1.02153	−	1.02153i	0.0217641	−	0.999763i	$-0.493072\pi$
$701$	716.091	−	716.091i	1.02153	−	1.02153i	0.999763	−	0.0217641i	$-0.00692827\pi$
$702$	−590.462	+	412.811i	−0.841114	+	0.588049i
$703$		−	137.238i		−	0.195217i
$704$	−1065.92	+	588.469i	−1.51409	+	0.835893i
$705$	278.258	−	286.944i	0.394692	−	0.407013i
$706$	−103.509	−	331.983i	−0.146614	−	0.470231i
$707$	−15.1827	+	56.6627i	−0.0214749	+	0.0801453i
$708$	65.2482	−	390.517i	0.0921585	−	0.551577i
$709$	−181.423	+	48.6121i	−0.255886	+	0.0685644i	−0.384481	−	0.923133i	$-0.625620\pi$
$709$	−181.423	+	48.6121i	−0.255886	+	0.0685644i	0.128596	+	0.991697i	$0.458953\pi$
$710$	87.4013	+	138.164i	0.123100	+	0.194598i
$711$	−455.820	−	244.808i	−0.641097	−	0.344315i
$712$	−725.816	+	927.368i	−1.01940	+	1.30248i
$713$	322.745	+	186.337i	0.452658	+	0.261342i
$714$	7.71610	+	23.4721i	0.0108069	+	0.0328740i
$715$	−761.197	−	203.962i	−1.06461	−	0.285262i
$716$	149.831	−	176.263i	0.209262	−	0.246178i
$717$	−896.076	+	535.877i	−1.24976	+	0.747388i
$718$	361.276	−	391.744i	0.503169	−	0.545604i
$719$		−	334.014i		−	0.464553i	−0.972650	−	0.232277i	$-0.925383\pi$
$719$		−	334.014i		−	0.464553i	0.972650	−	0.232277i	$-0.0746174\pi$
$720$	−30.9604	+	446.009i	−0.0430005	+	0.619457i
$721$	−126.526			−0.175487
$722$	465.880	+	429.646i	0.645263	+	0.595077i
$723$	402.359	−	722.318i	0.556513	−	0.999057i
$724$	−373.846	+	439.796i	−0.516362	+	0.607454i
$725$	−188.580	+	703.791i	−0.260110	+	0.970746i
$726$	−295.681	+	1415.04i	−0.407274	+	1.94909i
$727$	91.4920	−	158.469i	0.125849	−	0.217976i	−0.796216	−	0.605013i	$-0.793168\pi$
$727$	91.4920	−	158.469i	0.125849	−	0.217976i	0.922064	+	0.387037i	$0.126501\pi$
$728$	153.275	−	18.6869i	0.210543	−	0.0256688i
$729$	725.903	−	67.1252i	0.995752	−	0.0920784i
$730$	−90.2841	+	57.1127i	−0.123677	+	0.0782366i
$731$	27.4507	+	102.447i	0.0375523	+	0.140147i
$732$	549.048	−	205.439i	0.750065	−	0.280655i
$733$	633.868	+	169.844i	0.864759	+	0.231711i	0.663820	−	0.747892i	$-0.268934\pi$
$733$	633.868	+	169.844i	0.864759	+	0.231711i	0.200939	+	0.979604i	$0.435601\pi$
$734$	700.225	−	218.324i	0.953985	−	0.297444i
$735$	−420.228	+	119.551i	−0.571739	+	0.162654i
$736$	1250.87	+	74.6433i	1.69956	+	0.101418i
$737$	617.791			0.838251
$738$	−177.779	+	921.292i	−0.240893	+	1.24836i
$739$	180.573	+	180.573i	0.244348	+	0.244348i	0.818646	−	0.574298i	$-0.194725\pi$
$739$	180.573	+	180.573i	0.244348	+	0.244348i	−0.574298	+	0.818646i	$0.694725\pi$
$740$	145.821	+	211.112i	0.197056	+	0.285286i
$741$	136.460	+	228.184i	0.184156	+	0.307940i
$742$	−42.9293	+	81.8273i	−0.0578562	+	0.110279i
$743$	504.966	+	874.627i	0.679631	+	1.17716i	0.975092	+	0.221801i	$0.0711935\pi$
$743$	504.966	+	874.627i	0.679631	+	1.17716i	−0.295461	+	0.955355i	$0.595473\pi$
$744$	−226.619	−	28.5019i	−0.304596	−	0.0383090i
$745$	22.9594	+	13.2556i	0.0308179	+	0.0177928i
$746$	413.737	+	654.037i	0.554607	+	0.876725i
$747$	−1172.59	+	353.156i	−1.56973	+	0.472765i
$748$	204.019	−	72.7844i	0.272753	−	0.0973053i
$749$	−47.4026	−	176.909i	−0.0632878	−	0.236193i
$750$	−41.9374	−	750.684i	−0.0559165	−	1.00091i
$751$	−230.020	+	132.802i	−0.306286	+	0.176834i	−0.645263	−	0.763960i	$-0.723252\pi$
$751$	−230.020	+	132.802i	−0.306286	+	0.176834i	0.338978	+	0.940794i	$0.389919\pi$
$752$	642.155	+	243.060i	0.853930	+	0.323218i
$753$	558.377	−	575.809i	0.741537	−	0.764687i
$754$	930.446	+	858.079i	1.23401	+	1.13804i
$755$	−493.536	−	493.536i	−0.653690	−	0.653690i
$756$	−144.113	−	60.3559i	−0.190626	−	0.0798358i
$757$	−917.824	−	917.824i	−1.21245	−	1.21245i	−0.970219	−	0.242230i	$-0.922121\pi$
$757$	−917.824	−	917.824i	−1.21245	−	1.21245i	−0.242230	−	0.970219i	$-0.577879\pi$
$758$	27.8179	+	687.516i	0.0366991	+	0.907013i
$759$	1555.89	−	1604.46i	2.04992	−	2.11391i
$760$	163.364	+	23.1017i	0.214952	+	0.0303970i
$761$	−288.702	+	166.682i	−0.379372	+	0.219030i	−0.677545	−	0.735481i	$-0.736956\pi$
$761$	−288.702	+	166.682i	−0.379372	+	0.219030i	0.298173	+	0.954512i	$0.403623\pi$
$762$	−416.373	−	372.312i	−0.546421	−	0.488599i
$763$	22.4736	+	83.8727i	0.0294543	+	0.109925i
$764$	−633.069	+	1335.29i	−0.828624	+	1.74776i
$765$	18.2153	−	77.4247i	0.0238109	−	0.101209i
$766$	−28.4473	+	126.406i	−0.0371375	+	0.165021i
$767$	381.226	+	220.101i	0.497035	+	0.286963i
$768$	−724.321	+	255.310i	−0.943126	+	0.332434i
$769$	−397.311	−	688.164i	−0.516660	−	0.894881i	−0.999813	−	0.0193453i	$-0.993842\pi$
$769$	−397.311	−	688.164i	−0.516660	−	0.894881i	0.483153	−	0.875536i	$-0.339492\pi$
$770$	−50.8698	−	163.153i	−0.0660646	−	0.211888i
$771$	561.047	+	938.164i	0.727687	+	1.21681i
$772$	1138.07	−	786.101i	1.47419	−	1.01827i
$773$	−641.509	−	641.509i	−0.829895	−	0.829895i	0.157607	−	0.987502i	$-0.449622\pi$
$773$	−641.509	−	641.509i	−0.829895	−	0.829895i	−0.987502	+	0.157607i	$0.949622\pi$
$774$	−603.209	−	293.188i	−0.779340	−	0.378796i
$775$	146.185			0.188626
$776$	303.574	−	122.350i	0.391204	−	0.157668i
$777$	−86.2437	+	24.5355i	−0.110996	+	0.0315772i
$778$	−489.267	+	932.589i	−0.628878	+	1.19870i
$779$	334.463	+	89.6191i	0.429349	+	0.115044i
$780$	−452.369	−	206.018i	−0.579961	−	0.264126i
$781$	129.641	+	483.827i	0.165994	+	0.619497i
$782$	−217.494	−	48.9465i	−0.278125	−	0.0625915i
$783$	−388.138	−	1220.49i	−0.495706	−	1.55874i
$784$	−475.037	−	581.043i	−0.605915	−	0.741126i
$785$	−149.039	+	258.143i	−0.189859	+	0.328845i
$786$	20.7717	+	31.7455i	0.0264271	+	0.0403887i
$787$	380.559	−	1420.27i	0.483556	−	1.80466i	−0.102918	−	0.994690i	$-0.532818\pi$
$787$	380.559	−	1420.27i	0.483556	−	1.80466i	0.586475	−	0.809968i	$-0.300515\pi$
$788$	914.253	−	1075.54i	1.16022	−	1.36489i
$789$	−24.1570	+	43.3668i	−0.0306172	+	0.0549643i
$790$	−14.4320	−	356.684i	−0.0182683	−	0.451499i
$791$	83.9056			0.106075
$792$	−497.301	+	1276.31i	−0.627905	+	1.61150i
$793$			651.774i			0.821909i
$794$	26.7120	+	660.184i	0.0336423	+	0.831466i
$795$	255.297	−	152.674i	0.321128	−	0.192043i
$796$	97.6520	+	1204.75i	0.122678	+	1.51351i
$797$	399.181	+	106.960i	0.500854	+	0.134203i	0.500396	−	0.865796i	$-0.333188\pi$
$797$	399.181	+	106.960i	0.500854	+	0.134203i	0.000457774		1.00000i	$0.499854\pi$
$798$	−25.9992	+	51.4641i	−0.0325804	+	0.0644914i
$799$	−105.788	−	61.0765i	−0.132400	−	0.0764412i
$800$	439.570	−	219.977i	0.549462	−	0.274971i
$801$	40.7142	+	1324.21i	0.0508293	+	1.65320i
$802$	179.550	+	40.4074i	0.223878	+	0.0503832i
$803$	−316.159	+	84.7144i	−0.393722	+	0.105497i
$804$	384.352	+	64.2182i	0.478050	+	0.0798734i
$805$	−45.5227	+	169.893i	−0.0565500	+	0.211047i
$806$	117.977	−	224.876i	0.146374	−	0.279002i
$807$	−755.150	+	778.725i	−0.935750	+	0.964963i
$808$	298.497	+	127.006i	0.369427	+	0.157185i
$809$			1085.23i			1.34145i	0.741707	+	0.670724i	$0.234017\pi$
$809$			1085.23i			1.34145i	−0.741707	+	0.670724i	$0.765983\pi$
$810$	294.493	+	407.738i	0.363572	+	0.503380i
$811$	393.094	−	393.094i	0.484703	−	0.484703i	−0.421927	−	0.906630i	$-0.638646\pi$
$811$	393.094	−	393.094i	0.484703	−	0.484703i	0.906630	+	0.421927i	$0.138646\pi$
$812$	−49.3901	+	270.008i	−0.0608252	+	0.332522i
$813$	3.20519	+	208.544i	0.00394242	+	0.256511i
$814$	233.989	+	750.468i	0.287456	+	0.921951i
$815$	−412.048	+	237.896i	−0.505581	+	0.291897i
$816$	134.494	−	24.0747i	0.164821	−	0.0295033i
$817$	−123.753	+	214.347i	−0.151473	+	0.262359i
$818$	−109.786	+	487.832i	−0.134212	+	0.596372i
$819$	119.000	−	126.550i	0.145299	−	0.154517i
$820$	−609.725	+	217.521i	−0.743567	+	0.265270i
$821$	−0.201220	+	0.0539169i	−0.000245092	+	6.56722e-5i	−0.258942	−	0.965893i	$-0.583374\pi$
$821$	−0.201220	+	0.0539169i	−0.000245092	+	6.56722e-5i	0.258696	+	0.965959i	$0.416707\pi$
$822$	711.836	−	234.006i	0.865980	−	0.284679i
$823$	49.9481	+	86.5127i	0.0606903	+	0.105119i	0.894774	−	0.446519i	$-0.147336\pi$
$823$	49.9481	+	86.5127i	0.0606903	+	0.105119i	−0.834084	+	0.551638i	$0.814003\pi$
$824$	−97.9682	+	692.783i	−0.118893	+	0.840756i
$825$	213.863	−	850.201i	0.259228	−	1.03055i
$826$	3.85946	+	95.3860i	0.00467247	+	0.115479i
$827$	−338.637	+	338.637i	−0.409477	+	0.409477i	−0.881556	−	0.472079i	$-0.843504\pi$
$827$	−338.637	+	338.637i	−0.409477	+	0.409477i	0.472079	+	0.881556i	$0.343504\pi$
$828$	1134.76	−	836.466i	1.37048	−	1.01022i
$829$	−1083.03	+	1083.03i	−1.30643	+	1.30643i	−0.382450	+	0.923976i	$0.624920\pi$
$829$	−1083.03	+	1083.03i	−1.30643	+	1.30643i	−0.923976	+	0.382450i	$0.875080\pi$
$830$	−621.108	−	572.801i	−0.748323	−	0.690122i
$831$	−1177.43	+	334.968i	−1.41689	+	0.403090i
$832$	16.3617	−	853.718i	0.0196655	−	1.02610i
$833$	66.7604	+	115.632i	0.0801446	+	0.138814i
$834$	1335.93	−	874.126i	1.60184	−	1.04811i
$835$	−469.724	+	125.862i	−0.562543	+	0.150733i
$836$	456.758	+	216.553i	0.546361	+	0.259034i
$837$	−216.372	+	138.597i	−0.258509	+	0.165588i
$838$	−350.921	−	554.738i	−0.418761	−	0.661979i
$839$	326.394	−	565.331i	0.389027	−	0.673815i	−0.603292	−	0.797521i	$-0.706145\pi$
$839$	326.394	−	565.331i	0.389027	−	0.673815i	0.992319	+	0.123706i	$0.0394779\pi$
$840$	−14.6886	−	106.792i	−0.0174864	−	0.127133i
$841$	−1220.23	+	704.499i	−1.45093	+	0.837692i
$842$	−291.761	+	556.124i	−0.346510	+	0.660480i
$843$	−169.892	−	94.6364i	−0.201533	−	0.112261i
$844$	−1025.86	−	187.652i	−1.21548	−	0.222336i
$845$	19.7659	−	19.7659i	0.0233916	−	0.0233916i
$846$	730.016	−	252.478i	0.862903	−	0.298437i
$847$		−	348.554i		−	0.411516i
$848$	414.799	+	298.415i	0.489150	+	0.351904i
$849$	−406.620	−	102.283i	−0.478940	−	0.120474i
$850$	−83.4840	+	26.0296i	−0.0982165	+	0.0306230i
$851$	209.394	−	781.470i	0.246057	−	0.918296i
$852$	30.3619	+	314.484i	0.0356361	+	0.369113i
$853$	−243.964	+	65.3700i	−0.286007	+	0.0766354i	−0.398970	−	0.916964i	$-0.630632\pi$
$853$	−243.964	+	65.3700i	−0.286007	+	0.0766354i	0.112963	+	0.993599i	$0.463966\pi$
$854$	−119.452	+	75.5643i	−0.139874	+	0.0884828i
$855$	157.817	−	97.7025i	0.184582	−	0.114272i
$856$	−1005.35	+	122.570i	−1.17448	+	0.143189i
$857$	282.113	+	162.878i	0.329187	+	0.190056i	0.655480	−	0.755213i	$-0.272466\pi$
$857$	282.113	+	162.878i	0.329187	+	0.190056i	−0.326293	+	0.945269i	$0.605800\pi$
$858$	−1135.26	−	1015.13i	−1.32315	−	1.18314i
$859$	−121.770	−	32.6282i	−0.141758	−	0.0379840i	0.187242	−	0.982314i	$-0.440045\pi$
$859$	−121.770	−	32.6282i	−0.141758	−	0.0379840i	−0.329000	+	0.944330i	$0.606712\pi$
$860$	−37.3846	−	461.222i	−0.0434705	−	0.536304i
$861$	−3.47666	−	226.207i	−0.00403794	−	0.262726i
$862$	65.9413	+	60.8127i	0.0764981	+	0.0705484i
$863$			625.046i			0.724271i	0.932125	+	0.362136i	$0.117952\pi$
$863$			625.046i			0.724271i	−0.932125	+	0.362136i	$0.882048\pi$
$864$	−442.060	+	742.347i	−0.511644	+	0.859198i
$865$	677.204			0.782895
$866$	−434.492	+	471.135i	−0.501723	+	0.544036i
$867$	842.593	−	12.9501i	0.971849	−	0.0149367i
$868$	54.8914	−	4.44926i	0.0632390	−	0.00512588i
$869$	283.071	−	1056.43i	0.325743	−	1.21569i
$870$	588.992	−	658.695i	0.677002	−	0.757120i
$871$	−216.626	+	375.208i	−0.248710	+	0.430778i
$872$	476.640	−	58.1105i	0.546605	−	0.0666405i
$873$	174.221	−	324.391i	0.199566	−	0.371582i
$874$	−278.123	−	439.658i	−0.318219	−	0.503042i
$875$	46.9193	+	175.105i	0.0536220	+	0.200120i
$876$	−205.501	+	19.8401i	−0.234590	+	0.0226485i
$877$	1352.27	+	362.339i	1.54193	+	0.413158i	0.926887	−	0.375340i	$-0.122474\pi$
$877$	1352.27	+	362.339i	1.54193	+	0.413158i	0.615038	+	0.788497i	$0.289141\pi$
$878$	−7.83491	−	25.1287i	−0.00892359	−	0.0286204i
$879$	160.113	−	636.519i	0.182153	−	0.724140i
$880$	−932.723	+	152.205i	−1.05991	+	0.172960i
$881$	919.435			1.04363			0.521813	−	0.853060i	$-0.325256\pi$
$881$	919.435			1.04363			0.521813	+	0.853060i	$0.325256\pi$
$882$	−829.034	−	159.976i	−0.939948	−	0.181379i
$883$	900.546	+	900.546i	1.01987	+	1.01987i	0.999799	+	0.0200729i	$0.00638984\pi$
$883$	900.546	+	900.546i	1.01987	+	1.01987i	0.0200729	+	0.999799i	$0.493610\pi$
$884$	−27.3338	+	149.430i	−0.0309206	+	0.169038i
$885$	149.549	−	268.472i	0.168982	−	0.303359i
$886$	−190.677	−	100.036i	−0.215211	−	0.112907i
$887$	−409.791	−	709.779i	−0.461996	−	0.800201i	0.537064	−	0.843542i	$-0.319533\pi$
$887$	−409.791	−	709.779i	−0.461996	−	0.800201i	−0.999060	+	0.0433403i	$0.986200\pi$
$888$	67.5642	+	491.219i	0.0760858	+	0.553174i
$889$	116.632	+	67.3374i	0.131194	+	0.0757451i
$890$	−772.475	+	488.660i	−0.867950	+	0.549056i
$891$	489.527	+	1461.17i	0.549413	+	1.63992i
$892$	619.273	−	1306.19i	0.694252	−	1.46434i
$893$	−73.7786	−	275.346i	−0.0826189	−	0.308338i
$894$	28.0519	+	42.8718i	0.0313779	+	0.0479550i
$895$	155.506	−	89.7812i	0.173749	−	0.100314i
$896$	158.360	−	95.9783i	0.176741	−	0.107119i
$897$	428.882	+	1507.55i	0.478130	+	1.68065i
$898$	812.173	−	880.667i	0.904424	−	0.980699i
$899$	319.205	+	319.205i	0.355067	+	0.355067i
$900$	221.429	−	506.713i	0.246033	−	0.563015i
$901$	−64.2816	−	64.2816i	−0.0713448	−	0.0713448i
$902$	−1981.77	+	80.1853i	−2.19708	+	0.0888972i
$903$	156.826	+	39.4486i	0.173672	+	0.0436862i
$904$	64.9677	−	459.419i	0.0718669	−	0.508207i
$905$	−388.004	+	224.014i	−0.428733	+	0.247529i
$906$	−421.235	−	1281.38i	−0.464939	−	1.41433i
$907$	62.0778	+	231.678i	0.0684430	+	0.255433i	0.991667	−	0.128830i	$-0.0411222\pi$
$907$	62.0778	+	231.678i	0.0684430	+	0.255433i	−0.923224	+	0.384263i	$0.874456\pi$
$908$	−417.087	−	1169.12i	−0.459347	−	1.28758i
$909$	349.438	−	105.242i	0.384420	−	0.115778i
$910$	116.927	+	26.3141i	0.128491	+	0.0289165i
$911$	−574.180	−	331.503i	−0.630275	−	0.363889i	0.150584	−	0.988597i	$-0.451885\pi$
$911$	−574.180	−	331.503i	−0.630275	−	0.363889i	−0.780859	+	0.624708i	$0.785218\pi$
$912$	261.657	+	182.205i	0.286905	+	0.199786i
$913$	−1294.32	−	2241.83i	−1.41766	−	2.45545i
$914$	−813.070	+	253.508i	−0.889573	+	0.277361i
$915$	454.964	−	6.99252i	0.497229	−	0.00764210i
$916$	670.866	+	122.715i	0.732386	+	0.133969i
$917$	−6.46805	−	6.46805i	−0.00705349	−	0.00705349i
$918$	98.8884	−	117.678i	0.107722	−	0.128189i
$919$	180.060			0.195930			0.0979652	−	0.995190i	$-0.468767\pi$
$919$	180.060			0.195930			0.0979652	+	0.995190i	$0.468767\pi$
$920$	894.990	+	380.804i	0.972815	+	0.413917i
$921$	477.374	+	462.922i	0.518321	+	0.502630i
$922$	−39.9031	−	20.9345i	−0.0432789	−	0.0227055i
$923$	−339.305	−	90.9164i	−0.367611	−	0.0985010i
$924$	54.4274	−	325.754i	0.0589042	−	0.352547i
$925$	−82.1369	−	306.539i	−0.0887966	−	0.331393i
$926$	170.491	−	757.578i	0.184116	−	0.818119i
$927$	414.331	+	669.262i	0.446959	+	0.721966i
$928$	1440.17	+	479.497i	1.55190	+	0.516700i
$929$	349.631	−	605.578i	0.376352	−	0.651860i	−0.614177	−	0.789169i	$-0.710512\pi$
$929$	349.631	−	605.578i	0.376352	−	0.651860i	0.990528	+	0.137308i	$0.0438451\pi$
$930$	−158.238	−	79.9402i	−0.170148	−	0.0859573i
$931$	−80.6446	+	300.970i	−0.0866215	+	0.323276i
$932$	−665.025	+	53.9040i	−0.713546	+	0.0578369i
$933$	−526.858	−	880.995i	−0.564693	−	0.944261i
$934$	−436.612	+	17.6660i	−0.467465	+	0.0189143i
$935$	168.132			0.179820
$936$	−600.772	−	749.562i	−0.641850	−	0.800814i
$937$			700.846i			0.747968i	0.927435	+	0.373984i	$0.122009\pi$
$937$			700.846i			0.747968i	−0.927435	+	0.373984i	$0.877991\pi$
$938$	−93.8803	+	3.79853i	−0.100086	+	0.00404961i
$939$	368.811	+	205.442i	0.392770	+	0.218788i
$940$	406.060	+	345.168i	0.431978	+	0.367200i
$941$	411.062	+	110.144i	0.436835	+	0.117050i	0.470533	−	0.882382i	$-0.344062\pi$
$941$	411.062	+	110.144i	0.436835	+	0.117050i	−0.0336977	+	0.999432i	$0.510728\pi$
$942$	−482.028	+	315.401i	−0.511707	+	0.334820i
$943$	1767.79	+	1020.63i	1.87464	+	1.08232i
$944$	525.267	+	52.7247i	0.556427	+	0.0558524i
$945$	−89.6134	−	81.7090i	−0.0948290	−	0.0864646i
$946$	311.271	−	1383.13i	0.329039	−	1.46208i
$947$	−639.153	+	171.260i	−0.674924	+	0.180845i	−0.579972	−	0.814637i	$-0.696936\pi$
$947$	−639.153	+	171.260i	−0.674924	+	0.180845i	−0.0949519	+	0.995482i	$0.530270\pi$
$948$	285.924	−	627.825i	0.301607	−	0.662262i
$949$	59.4097	−	221.720i	0.0626024	−	0.233635i
$950$	−180.710	−	94.8066i	−0.190221	−	0.0997965i
$951$	266.527	+	936.858i	0.280260	+	0.985130i
$952$	−30.5554	+	12.3148i	−0.0320960	+	0.0129357i
$953$		−	57.2479i		−	0.0600713i	−0.999549	−	0.0300356i	$-0.990438\pi$
$953$		−	57.2479i		−	0.0600713i	0.999549	−	0.0300356i	$-0.00956208\pi$
$954$	573.407	−	40.8817i	0.601056	−	0.0428530i
$955$	−811.059	+	811.059i	−0.849277	+	0.849277i
$956$	−791.184	−	1145.43i	−0.827599	−	1.19815i
$957$	2323.46	−	1389.49i	2.42786	−	1.45192i
$958$	−916.608	+	285.790i	−0.956793	+	0.298319i
$959$	−156.464	+	90.3346i	−0.163153	+	0.0941967i
$960$	−596.105	−	2.26205i	−0.620943	−	0.00235630i
$961$	−435.215	+	753.814i	−0.452877	+	0.784406i
$962$	−537.835	−	121.039i	−0.559080	−	0.125820i
$963$	−780.536	+	830.056i	−0.810526	+	0.861948i
$964$	996.145	+	472.280i	1.03335	+	0.489917i
$965$	1037.01	−	277.867i	1.07463	−	0.287945i
$966$	−226.569	+	253.382i	−0.234544	+	0.262300i
$967$	−335.018	−	580.269i	−0.346451	−	0.600071i	0.639165	−	0.769070i	$-0.279280\pi$
$967$	−335.018	−	580.269i	−0.346451	−	0.600071i	−0.985616	+	0.168998i	$0.945947\pi$
$968$	−1908.48	−	269.883i	−1.97157	−	0.278805i
$969$	−40.7221	−	39.4893i	−0.0420248	−	0.0407526i
$970$	253.839	−	10.2707i	0.261690	−	0.0105884i
$971$	781.797	−	781.797i	0.805146	−	0.805146i	−0.178749	−	0.983895i	$-0.557205\pi$
$971$	781.797	−	781.797i	0.805146	−	0.805146i	0.983895	+	0.178749i	$0.0572050\pi$
$972$	152.669	+	959.936i	0.157067	+	0.987588i
$973$	−272.192	+	272.192i	−0.279745	+	0.279745i
$974$	512.599	−	555.830i	0.526283	−	0.570667i
$975$	441.369	+	428.007i	0.452686	+	0.438982i
$976$	321.255	+	712.562i	0.329155	+	0.730084i
$977$	−338.739	−	586.714i	−0.346714	−	0.600526i	0.638950	−	0.769248i	$-0.279369\pi$
$977$	−338.739	−	586.714i	−0.346714	−	0.600526i	−0.985664	+	0.168723i	$0.946036\pi$
$978$	−918.052	+	51.2876i	−0.938704	+	0.0524413i
$979$	−2705.07	+	724.821i	−2.76309	+	0.740369i
$980$	−195.739	−	548.667i	−0.199733	−	0.559864i
$981$	370.053	−	393.530i	0.377220	−	0.401152i
$982$	−386.465	+	244.474i	−0.393549	+	0.248955i
$983$	−434.498	+	752.573i	−0.442012	+	0.765588i	−0.997839	−	0.0657106i	$-0.979069\pi$
$983$	−434.498	+	752.573i	−0.442012	+	0.765588i	0.555826	+	0.831298i	$0.312402\pi$
$984$	−1241.27	−	156.115i	−1.26146	−	0.158653i
$985$	948.876	−	547.834i	0.963326	−	0.556177i
$986$	−239.131	−	125.456i	−0.242526	−	0.127237i
$987$	−159.844	+	95.5908i	−0.161949	+	0.0968499i
$988$	−291.681	+	201.473i	−0.295224	+	0.203920i
$989$	−1031.73	+	1031.73i	−1.04321	+	1.04321i
$990$	−696.423	+	803.351i	−0.703457	+	0.811466i
$991$		−	954.956i		−	0.963629i	−0.876273	−	0.481815i	$-0.839978\pi$
$991$		−	954.956i		−	0.963629i	0.876273	−	0.481815i	$-0.160022\pi$
$992$	18.1405	−	303.999i	0.0182868	−	0.306451i
$993$	−51.0047	−	179.285i	−0.0513643	−	0.180549i
$994$	−22.6753	−	72.7258i	−0.0228121	−	0.0731648i
$995$	−242.818	+	906.209i	−0.244038	+	0.910763i
$996$	−572.214	−	1529.27i	−0.574512	−	1.53541i
$997$	−1180.62	+	316.347i	−1.18418	+	0.317299i	−0.796581	−	0.604531i	$-0.793360\pi$
$997$	−1180.62	+	316.347i	−1.18418	+	0.317299i	−0.387594	+	0.921830i	$0.626694\pi$
$998$	−56.6651	−	89.5764i	−0.0567787	−	0.0897559i
$999$	412.201	+	375.843i	0.412614	+	0.376219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.v.a.43.12	✓	184
3.2	odd	2		432.3.w.a.235.35		184
9.4	even	3	inner	144.3.v.a.139.20	yes	184
9.5	odd	6		432.3.w.a.91.27		184
16.3	odd	4	inner	144.3.v.a.115.20	yes	184
48.35	even	4		432.3.w.a.19.27		184
144.67	odd	12	inner	144.3.v.a.67.12	yes	184
144.131	even	12		432.3.w.a.307.35		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.v.a.43.12	✓	184	1.1	even	1	trivial
144.3.v.a.67.12	yes	184	144.67	odd	12	inner
144.3.v.a.115.20	yes	184	16.3	odd	4	inner
144.3.v.a.139.20	yes	184	9.4	even	3	inner
432.3.w.a.19.27		184	48.35	even	4
432.3.w.a.91.27		184	9.5	odd	6
432.3.w.a.235.35		184	3.2	odd	2
432.3.w.a.307.35		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)

\(f(q)\)	\(=\)	\(q+(-1.35588 + 1.47023i) q^{2} +(-2.99965 + 0.0461027i) q^{3} +(-0.323163 - 3.98692i) q^{4} +(0.803565 - 2.99895i) q^{5} +(3.99939 - 4.47268i) q^{6} +(-0.723340 + 1.25286i) q^{7} +(6.29987 + 4.93068i) q^{8} +(8.99575 - 0.276584i) q^{9} +O(q^{10})\)	\(q+(-1.35588 + 1.47023i) q^{2} +(-2.99965 + 0.0461027i) q^{3} +(-0.323163 - 3.98692i) q^{4} +(0.803565 - 2.99895i) q^{5} +(3.99939 - 4.47268i) q^{6} +(-0.723340 + 1.25286i) q^{7} +(6.29987 + 4.93068i) q^{8} +(8.99575 - 0.276584i) q^{9} +(3.31960 + 5.24765i) q^{10} +(4.92392 + 18.3763i) q^{11} +(1.15318 + 11.9445i) q^{12} +(-12.8872 - 3.45311i) q^{13} +(-0.861232 - 2.76221i) q^{14} +(-2.27215 + 9.03282i) q^{15} +(-15.7911 + 2.57685i) q^{16} +2.84649 q^{17} +(-11.7905 + 13.6009i) q^{18} +(4.69705 + 4.69705i) q^{19} +(-12.2162 - 2.23461i) q^{20} +(2.11200 - 3.79149i) q^{21} +(-33.6937 - 17.6768i) q^{22} +(19.5797 + 33.9130i) q^{23} +(-19.1247 - 14.4998i) q^{24} +(13.3027 + 7.68031i) q^{25} +(22.5504 - 14.2651i) q^{26} +(-26.9713 + 1.24438i) q^{27} +(5.22882 + 2.47902i) q^{28} +(12.2769 + 45.8179i) q^{29} +(-10.1996 - 15.5880i) q^{30} +(8.24185 - 4.75843i) q^{31} +(17.6224 - 26.7105i) q^{32} +(-15.6172 - 54.8954i) q^{33} +(-3.85951 + 4.18501i) q^{34} +(3.17601 + 3.17601i) q^{35} +(-4.00981 - 35.7760i) q^{36} +(-14.6089 - 14.6089i) q^{37} +(-13.2744 + 0.537102i) q^{38} +(38.8162 + 9.76397i) q^{39} +(19.8492 - 14.9309i) q^{40} +(45.1434 - 26.0636i) q^{41} +(2.71074 + 8.24595i) q^{42} +(9.64369 + 35.9907i) q^{43} +(71.6737 - 25.5698i) q^{44} +(6.39921 - 27.2000i) q^{45} +(-76.4076 - 17.1954i) q^{46} +(-37.1642 - 21.4567i) q^{47} +(47.2490 - 8.45765i) q^{48} +(23.4536 + 40.6228i) q^{49} +(-29.3287 + 9.14443i) q^{50} +(-8.53848 + 0.131231i) q^{51} +(-9.60263 + 52.4961i) q^{52} +(-22.5827 - 22.5827i) q^{53} +(34.7404 - 41.3413i) q^{54} +59.0662 q^{55} +(-10.7344 + 4.32631i) q^{56} +(-14.3060 - 13.8729i) q^{57} +(-84.0089 - 44.0738i) q^{58} +(-31.8699 - 8.53952i) q^{59} +(36.7474 + 6.13982i) q^{60} +(-12.6438 - 47.1874i) q^{61} +(-4.17898 + 18.5693i) q^{62} +(-6.16046 + 11.4705i) q^{63} +(15.3768 + 62.1253i) q^{64} +(-20.7114 + 35.8732i) q^{65} +(101.884 + 51.4708i) q^{66} +(8.40472 - 31.3668i) q^{67} +(-0.919881 - 11.3488i) q^{68} +(-60.2955 - 100.824i) q^{69} +(-8.97577 + 0.363173i) q^{70} +26.3288 q^{71} +(58.0358 + 42.6127i) q^{72} +17.2047i q^{73} +(41.2865 - 1.67051i) q^{74} +(-40.2574 - 22.4249i) q^{75} +(17.2089 - 20.2447i) q^{76} +(-26.5846 - 7.12333i) q^{77} +(-66.9855 + 43.8300i) q^{78} +(-49.7868 - 28.7444i) q^{79} +(-4.96136 + 49.4274i) q^{80} +(80.8470 - 4.97615i) q^{81} +(-22.8897 + 101.710i) q^{82} +(-131.432 + 35.2171i) q^{83} +(-15.7989 - 7.19513i) q^{84} +(2.28734 - 8.53648i) q^{85} +(-65.9904 - 34.6208i) q^{86} +(-38.9386 - 136.871i) q^{87} +(-59.5876 + 140.047i) q^{88} +147.204i q^{89} +(31.3137 + 46.2884i) q^{90} +(13.6481 - 13.6481i) q^{91} +(128.881 - 89.0220i) q^{92} +(-24.5032 + 14.6536i) q^{93} +(81.9367 - 25.5471i) q^{94} +(17.8606 - 10.3118i) q^{95} +(-51.6294 + 80.9346i) q^{96} +(20.4564 - 35.4315i) q^{97} +(-91.5251 - 20.5975i) q^{98} +(49.3769 + 163.947i) 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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