LMFDB - Embedded newform 151.2.k.a.99.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [151,2,Mod(5,151)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(151, base_ring=CyclotomicField(150))

chi = DirichletCharacter(H, H._module([112]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("151.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	151.k (of order $75$, degree $40$, 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:	$1.20574107052$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$12$ over $\Q(\zeta_{75})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{75}]$

Embedding invariants

Embedding label			99.11
Character	$\chi$	$=$	151.99
Dual form			151.2.k.a.90.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.209259 + 1.99097i) q^{2} +(0.655371 + 0.615435i) q^{3} +(-1.96386 + 0.417431i) q^{4} +(2.90813 + 1.44361i) q^{5} +(-1.08817 + 1.43361i) q^{6} +(-1.33686 - 2.55717i) q^{7} +(-0.00478326 - 0.0147213i) q^{8} +(-0.137620 - 2.18740i) q^{9} +O(q^{10})$	\(q+(0.209259 + 1.99097i) q^{2} +(0.655371 + 0.615435i) q^{3} +(-1.96386 + 0.417431i) q^{4} +(2.90813 + 1.44361i) q^{5} +(-1.08817 + 1.43361i) q^{6} +(-1.33686 - 2.55717i) q^{7} +(-0.00478326 - 0.0147213i) q^{8} +(-0.137620 - 2.18740i) q^{9} +(-2.26562 + 6.09206i) q^{10} +(-0.564053 - 2.40485i) q^{11} +(-1.54396 - 0.935054i) q^{12} +(-4.62849 + 0.388665i) q^{13} +(4.81149 - 3.19675i) q^{14} +(1.01746 + 2.73586i) q^{15} +(-3.64000 + 1.62063i) q^{16} +(-0.461160 + 0.0193283i) q^{17} +(4.32625 - 0.731730i) q^{18} +(0.488653 - 1.50392i) q^{19} +(-6.31375 - 1.62110i) q^{20} +(0.697635 - 2.49865i) q^{21} +(4.66995 - 1.62625i) q^{22} +(-1.41355 - 1.56990i) q^{23} +(0.00592522 - 0.0125917i) q^{24} +(3.35020 + 4.41373i) q^{25} +(-1.74237 - 9.13382i) q^{26} +(2.97522 - 3.59642i) q^{27} +(3.69284 + 4.46388i) q^{28} +(-1.43582 + 7.52686i) q^{29} +(-5.23409 + 2.59822i) q^{30} +(3.48813 - 2.76466i) q^{31} +(-4.00380 - 6.93479i) q^{32} +(1.11037 - 1.92321i) q^{33} +(-0.134984 - 0.914110i) q^{34} +(-0.196200 - 9.36648i) q^{35} +(1.18336 + 4.23830i) q^{36} +(5.11442 + 7.35868i) q^{37} +(3.09651 + 0.658183i) q^{38} +(-3.27257 - 2.59381i) q^{39} +(0.00734152 - 0.0497167i) q^{40} +(9.60349 + 1.21320i) q^{41} +(5.12071 + 0.866103i) q^{42} +(-3.42817 + 6.55748i) q^{43} +(2.11158 + 4.48734i) q^{44} +(2.75753 - 6.55991i) q^{45} +(2.82982 - 3.14284i) q^{46} +(2.81890 + 6.70589i) q^{47} +(-3.38295 - 1.17807i) q^{48} +(-0.756953 + 1.08911i) q^{49} +(-8.08652 + 7.59374i) q^{50} +(-0.314127 - 0.271147i) q^{51} +(8.92745 - 2.69536i) q^{52} +(-9.03434 - 4.96667i) q^{53} +(7.78294 + 5.17098i) q^{54} +(1.83132 - 7.80789i) q^{55} +(-0.0312505 + 0.0319120i) q^{56} +(1.24581 - 0.684892i) q^{57} +(-15.2862 - 1.28362i) q^{58} +(-7.68794 - 5.58561i) q^{59} +(-3.14017 - 4.94812i) q^{60} +(-9.97213 - 3.01076i) q^{61} +(6.23426 + 6.36622i) q^{62} +(-5.40959 + 3.27617i) q^{63} +(6.52208 - 4.73857i) q^{64} +(-14.0213 - 5.55142i) q^{65} +(4.06140 + 1.80825i) q^{66} +(0.175822 - 2.79461i) q^{67} +(0.897585 - 0.230461i) q^{68} +(0.0397745 - 1.89881i) q^{69} +(18.6073 - 2.35065i) q^{70} +(6.52637 + 0.273536i) q^{71} +(-0.0315433 + 0.0124889i) q^{72} +(-7.69742 + 12.1292i) q^{73} +(-13.5806 + 11.7225i) q^{74} +(-0.520735 + 4.95446i) q^{75} +(-0.331863 + 3.15746i) q^{76} +(-5.39557 + 4.65733i) q^{77} +(4.47937 - 7.05836i) q^{78} +(13.7644 - 5.44970i) q^{79} +(-12.9251 - 0.541724i) q^{80} +(-2.36010 + 0.298150i) q^{81} +(-0.405829 + 19.3741i) q^{82} +(-2.98033 + 0.765220i) q^{83} +(-0.327043 + 5.19820i) q^{84} +(-1.36901 - 0.609525i) q^{85} +(-13.7731 - 5.45315i) q^{86} +(-5.57329 + 4.04923i) q^{87} +(-0.0327047 + 0.0198067i) q^{88} +(-0.00333036 - 0.00340085i) q^{89} +(13.6376 + 4.11743i) q^{90} +(7.18151 + 11.3163i) q^{91} +(3.43133 + 2.49301i) q^{92} +(3.98749 + 0.334839i) q^{93} +(-12.7613 + 7.01559i) q^{94} +(3.59213 - 3.66816i) q^{95} +(1.64393 - 7.00894i) q^{96} +(3.92895 + 2.61039i) q^{97} +(-2.32679 - 1.27916i) q^{98} +(-5.18276 + 1.56477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9}+O(q^{10}) $ 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9} - 10 q^{10} - 50 q^{11} - 65 q^{12} - 40 q^{13} - 65 q^{14} + 25 q^{16} - 20 q^{17} - 15 q^{18} - 30 q^{19} + 70 q^{20} - 40 q^{21} - 65 q^{23} + 80 q^{24} + 20 q^{25} - 65 q^{26} + 5 q^{27} - 110 q^{28} - 75 q^{29} - 135 q^{30} - 45 q^{31} + 10 q^{32} + 40 q^{33} + 20 q^{34} - 10 q^{36} - 60 q^{37} - 70 q^{38} + 25 q^{39} - 50 q^{41} + 50 q^{42} - 50 q^{43} - 30 q^{44} + 10 q^{45} - 85 q^{46} + 30 q^{47} + 175 q^{48} - 50 q^{49} + 10 q^{50} + 80 q^{51} - 145 q^{52} + 95 q^{53} + 10 q^{54} + 70 q^{55} + 140 q^{56} - 70 q^{57} + 240 q^{58} - 30 q^{59} - 60 q^{60} - 60 q^{61} + 10 q^{62} + 90 q^{63} - 160 q^{64} + 45 q^{65} - 55 q^{66} - 10 q^{67} + 10 q^{68} - 105 q^{69} + 75 q^{70} - 25 q^{71} + 310 q^{72} + 40 q^{73} + 170 q^{74} - 80 q^{75} - 15 q^{76} + 45 q^{77} - 80 q^{78} + 160 q^{79} - 85 q^{80} + 160 q^{81} - 50 q^{82} - 5 q^{83} + 70 q^{84} - 85 q^{85} + 150 q^{86} + 10 q^{87} + 95 q^{88} - 50 q^{89} - 90 q^{90} + 270 q^{91} + 90 q^{92} + 100 q^{93} - 35 q^{94} + 60 q^{95} + 255 q^{96} + 210 q^{97} - 30 q^{98}+O(q^{100}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9 - 10 * q^10 - 50 * q^11 - 65 * q^12 - 40 * q^13 - 65 * q^14 + 25 * q^16 - 20 * q^17 - 15 * q^18 - 30 * q^19 + 70 * q^20 - 40 * q^21 - 65 * q^23 + 80 * q^24 + 20 * q^25 - 65 * q^26 + 5 * q^27 - 110 * q^28 - 75 * q^29 - 135 * q^30 - 45 * q^31 + 10 * q^32 + 40 * q^33 + 20 * q^34 - 10 * q^36 - 60 * q^37 - 70 * q^38 + 25 * q^39 - 50 * q^41 + 50 * q^42 - 50 * q^43 - 30 * q^44 + 10 * q^45 - 85 * q^46 + 30 * q^47 + 175 * q^48 - 50 * q^49 + 10 * q^50 + 80 * q^51 - 145 * q^52 + 95 * q^53 + 10 * q^54 + 70 * q^55 + 140 * q^56 - 70 * q^57 + 240 * q^58 - 30 * q^59 - 60 * q^60 - 60 * q^61 + 10 * q^62 + 90 * q^63 - 160 * q^64 + 45 * q^65 - 55 * q^66 - 10 * q^67 + 10 * q^68 - 105 * q^69 + 75 * q^70 - 25 * q^71 + 310 * q^72 + 40 * q^73 + 170 * q^74 - 80 * q^75 - 15 * q^76 + 45 * q^77 - 80 * q^78 + 160 * q^79 - 85 * q^80 + 160 * q^81 - 50 * q^82 - 5 * q^83 + 70 * q^84 - 85 * q^85 + 150 * q^86 + 10 * q^87 + 95 * q^88 - 50 * q^89 - 90 * q^90 + 270 * q^91 + 90 * q^92 + 100 * q^93 - 35 * q^94 + 60 * q^95 + 255 * q^96 + 210 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/151\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{53}{75}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.209259	+	1.99097i	0.147968	+	1.40783i	0.776537	+	0.630071i	$0.216974\pi$
$2$	0.209259	+	1.99097i	0.147968	+	1.40783i	−0.628569	+	0.777754i	$0.716359\pi$
$3$	0.655371	+	0.615435i	0.378379	+	0.355321i	0.850280	−	0.526330i	$-0.176432\pi$
$3$	0.655371	+	0.615435i	0.378379	+	0.355321i	−0.471902	+	0.881651i	$0.656432\pi$
$4$	−1.96386	+	0.417431i	−0.981929	+	0.208715i
$5$	2.90813	+	1.44361i	1.30055	+	0.645600i	0.956055	−	0.293187i	$-0.0947158\pi$
$5$	2.90813	+	1.44361i	1.30055	+	0.645600i	0.344498	+	0.938787i	$0.388049\pi$
$6$	−1.08817	+	1.43361i	−0.444242	+	0.585268i
$7$	−1.33686	−	2.55717i	−0.505285	−	0.966521i	−0.995486	−	0.0949114i	$-0.969743\pi$
$7$	−1.33686	−	2.55717i	−0.505285	−	0.966521i	0.490201	−	0.871610i	$-0.336923\pi$
$8$	−0.00478326	−	0.0147213i	−0.00169114	−	0.00520478i
$9$	−0.137620	−	2.18740i	−0.0458733	−	0.729135i
$10$	−2.26562	+	6.09206i	−0.716451	+	1.92648i
$11$	−0.564053	−	2.40485i	−0.170069	−	0.725091i	−0.988592	−	0.150618i	$-0.951874\pi$
$11$	−0.564053	−	2.40485i	−0.170069	−	0.725091i	0.818524	−	0.574473i	$-0.194793\pi$
$12$	−1.54396	−	0.935054i	−0.445702	−	0.269927i
$13$	−4.62849	+	0.388665i	−1.28371	+	0.107796i	−0.705863	−	0.708348i	$-0.749441\pi$
$13$	−4.62849	+	0.388665i	−1.28371	+	0.107796i	−0.577848	+	0.816145i	$0.696107\pi$
$14$	4.81149	−	3.19675i	1.28593	−	0.854367i
$15$	1.01746	+	2.73586i	0.262706	+	0.706396i
$16$	−3.64000	+	1.62063i	−0.910000	+	0.405158i
$17$	−0.461160	+	0.0193283i	−0.111848	+	0.00468781i	−0.0977339	−	0.995213i	$-0.531159\pi$
$17$	−0.461160	+	0.0193283i	−0.111848	+	0.00468781i	−0.0141139	+	0.999900i	$0.504493\pi$
$18$	4.32625	−	0.731730i	1.01971	−	0.172470i
$19$	0.488653	−	1.50392i	0.112105	−	0.345023i	−0.879227	−	0.476402i	$-0.841941\pi$
$19$	0.488653	−	1.50392i	0.112105	−	0.345023i	0.991332	+	0.131379i	$0.0419406\pi$
$20$	−6.31375	−	1.62110i	−1.41180	−	0.362488i
$21$	0.697635	−	2.49865i	0.152236	−	0.545250i
$22$	4.66995	−	1.62625i	0.995636	−	0.346717i
$23$	−1.41355	−	1.56990i	−0.294745	−	0.327347i	0.577524	−	0.816373i	$-0.304019\pi$
$23$	−1.41355	−	1.56990i	−0.294745	−	0.327347i	−0.872269	+	0.489026i	$0.837352\pi$
$24$	0.00592522	−	0.0125917i	0.00120948	−	0.00257028i
$25$	3.35020	+	4.41373i	0.670040	+	0.882745i
$26$	−1.74237	−	9.13382i	−0.341707	−	1.79129i
$27$	2.97522	−	3.59642i	0.572581	−	0.692132i
$28$	3.69284	+	4.46388i	0.697882	+	0.843594i
$29$	−1.43582	+	7.52686i	−0.266626	+	1.39770i	0.556973	+	0.830530i	$0.311963\pi$
$29$	−1.43582	+	7.52686i	−0.266626	+	1.39770i	−0.823599	+	0.567172i	$0.808037\pi$
$30$	−5.23409	+	2.59822i	−0.955610	+	0.474369i
$31$	3.48813	−	2.76466i	0.626487	−	0.496547i	−0.256129	−	0.966643i	$-0.582447\pi$
$31$	3.48813	−	2.76466i	0.626487	−	0.496547i	0.882616	+	0.470095i	$0.155780\pi$
$32$	−4.00380	−	6.93479i	−0.707779	−	1.22591i
$33$	1.11037	−	1.92321i	0.193290	−	0.334788i
$34$	−0.134984	−	0.914110i	−0.0231496	−	0.156768i
$35$	−0.196200	−	9.36648i	−0.0331638	−	1.58322i
$36$	1.18336	+	4.23830i	0.197226	+	0.706384i
$37$	5.11442	+	7.35868i	0.840805	+	1.20976i	0.975746	+	0.218907i	$0.0702490\pi$
$37$	5.11442	+	7.35868i	0.840805	+	1.20976i	−0.134940	+	0.990854i	$0.543084\pi$
$38$	3.09651	+	0.658183i	0.502320	+	0.106771i
$39$	−3.27257	−	2.59381i	−0.524031	−	0.415342i
$40$	0.00734152	−	0.0497167i	0.00116080	−	0.00786090i
$41$	9.60349	+	1.21320i	1.49981	+	0.189470i	0.831965	−	0.554828i	$-0.187216\pi$
$41$	9.60349	+	1.21320i	1.49981	+	0.189470i	0.667848	+	0.744298i	$0.267216\pi$
$42$	5.12071	+	0.866103i	0.790142	+	0.133643i
$43$	−3.42817	+	6.55748i	−0.522791	+	1.00001i	0.470283	+	0.882515i	$0.344152\pi$
$43$	−3.42817	+	6.55748i	−0.522791	+	1.00001i	−0.993074	+	0.117491i	$0.962515\pi$
$44$	2.11158	+	4.48734i	0.318333	+	0.676492i
$45$	2.75753	−	6.55991i	0.411069	−	0.977894i
$46$	2.82982	−	3.14284i	0.417234	−	0.463386i
$47$	2.81890	+	6.70589i	0.411178	+	0.978154i	0.987021	+	0.160593i	$0.0513408\pi$
$47$	2.81890	+	6.70589i	0.411178	+	0.978154i	−0.575843	+	0.817561i	$0.695326\pi$
$48$	−3.38295	−	1.17807i	−0.488286	−	0.170039i
$49$	−0.756953	+	1.08911i	−0.108136	+	0.155588i
$50$	−8.08652	+	7.59374i	−1.14361	+	1.07392i
$51$	−0.314127	−	0.271147i	−0.0439865	−	0.0379681i
$52$	8.92745	−	2.69536i	1.23801	−	0.373779i
$53$	−9.03434	−	4.96667i	−1.24096	−	0.682224i	−0.280291	−	0.959915i	$-0.590431\pi$
$53$	−9.03434	−	4.96667i	−1.24096	−	0.682224i	−0.960671	+	0.277691i	$0.910431\pi$
$54$	7.78294	+	5.17098i	1.05912	+	0.703681i
$55$	1.83132	−	7.80789i	0.246936	−	1.05282i
$56$	−0.0312505	+	0.0319120i	−0.00417603	+	0.00426442i
$57$	1.24581	−	0.684892i	0.165012	−	0.0907161i
$58$	−15.2862	−	1.28362i	−2.00717	−	0.168547i
$59$	−7.68794	−	5.58561i	−1.00088	−	0.727185i	−0.0386066	−	0.999254i	$-0.512292\pi$
$59$	−7.68794	−	5.58561i	−1.00088	−	0.727185i	−0.962278	+	0.272070i	$0.912292\pi$
$60$	−3.14017	−	4.94812i	−0.405395	−	0.638800i
$61$	−9.97213	−	3.01076i	−1.27680	−	0.385489i	−0.423019	−	0.906121i	$-0.639030\pi$
$61$	−9.97213	−	3.01076i	−1.27680	−	0.385489i	−0.853781	+	0.520632i	$0.825696\pi$
$62$	6.23426	+	6.36622i	0.791752	+	0.808510i
$63$	−5.40959	+	3.27617i	−0.681545	+	0.412758i
$64$	6.52208	−	4.73857i	0.815260	−	0.592321i
$65$	−14.0213	−	5.55142i	−1.73913	−	0.688569i
$66$	4.06140	+	1.80825i	0.499924	+	0.222580i
$67$	0.175822	−	2.79461i	0.0214800	−	0.341416i	−0.972579	−	0.232573i	$-0.925286\pi$
$67$	0.175822	−	2.79461i	0.0214800	−	0.341416i	0.994059	−	0.108843i	$-0.0347144\pi$
$68$	0.897585	−	0.230461i	0.108848	−	0.0279475i
$69$	0.0397745	−	1.89881i	0.00478828	−	0.228590i
$70$	18.6073	−	2.35065i	2.22400	−	0.280956i
$71$	6.52637	+	0.273536i	0.774538	+	0.0324628i	0.425871	−	0.904784i	$-0.359968\pi$
$71$	6.52637	+	0.273536i	0.774538	+	0.0324628i	0.348667	+	0.937247i	$0.386634\pi$
$72$	−0.0315433	+	0.0124889i	−0.00371741	+	0.00147183i
$73$	−7.69742	+	12.1292i	−0.900915	+	1.41961i	0.00677731	+	0.999977i	$0.497843\pi$
$73$	−7.69742	+	12.1292i	−0.900915	+	1.41961i	−0.907692	+	0.419637i	$0.862157\pi$
$74$	−13.5806	+	11.7225i	−1.57872	+	1.36271i
$75$	−0.520735	+	4.95446i	−0.0601293	+	0.572092i
$76$	−0.331863	+	3.15746i	−0.0380673	+	0.362186i
$77$	−5.39557	+	4.65733i	−0.614882	+	0.530752i
$78$	4.47937	−	7.05836i	0.507189	−	0.799202i
$79$	13.7644	−	5.44970i	1.54861	−	0.613139i	0.570516	−	0.821287i	$-0.306743\pi$
$79$	13.7644	−	5.44970i	1.54861	−	0.613139i	0.978097	+	0.208148i	$0.0667434\pi$
$80$	−12.9251	−	0.541724i	−1.44507	−	0.0605665i
$81$	−2.36010	+	0.298150i	−0.262234	+	0.0331278i
$82$	−0.405829	+	19.3741i	−0.0448163	+	2.13951i
$83$	−2.98033	+	0.765220i	−0.327134	+	0.0839938i	−0.408685	−	0.912675i	$-0.634013\pi$
$83$	−2.98033	+	0.765220i	−0.327134	+	0.0839938i	0.0815511	+	0.996669i	$0.474013\pi$
$84$	−0.327043	+	5.19820i	−0.0356833	+	0.567170i
$85$	−1.36901	−	0.609525i	−0.148490	−	0.0661122i
$86$	−13.7731	−	5.45315i	−1.48519	−	0.588028i
$87$	−5.57329	+	4.04923i	−0.597519	+	0.434123i
$88$	−0.0327047	+	0.0198067i	−0.00348633	+	0.00211140i
$89$	−0.00333036	−	0.00340085i	−0.000353018	−	0.000360490i	0.714296	−	0.699844i	$-0.246747\pi$
$89$	−0.00333036	−	0.00340085i	−0.000353018	−	0.000360490i	−0.714649	+	0.699483i	$0.753414\pi$
$90$	13.6376	+	4.11743i	1.43753	+	0.434016i
$91$	7.18151	+	11.3163i	0.752827	+	1.18627i
$92$	3.43133	+	2.49301i	0.357741	+	0.259914i
$93$	3.98749	+	0.334839i	0.413483	+	0.0347212i
$94$	−12.7613	+	7.01559i	−1.31623	+	0.723603i
$95$	3.59213	−	3.66816i	0.368545	−	0.376346i
$96$	1.64393	−	7.00894i	0.167783	−	0.715347i
$97$	3.92895	+	2.61039i	0.398925	+	0.265045i	0.736752	−	0.676163i	$-0.236359\pi$
$97$	3.92895	+	2.61039i	0.398925	+	0.265045i	−0.337827	+	0.941208i	$0.609692\pi$
$98$	−2.32679	−	1.27916i	−0.235041	−	0.129215i
$99$	−5.18276	+	1.56477i	−0.520887	+	0.157265i
$100$	−8.42174	−	7.26946i	−0.842174	−	0.726946i
$101$	1.84870	−	1.73604i	0.183952	−	0.172743i	−0.587100	−	0.809514i	$-0.699731\pi$
$101$	1.84870	−	1.73604i	0.183952	−	0.172743i	0.771052	+	0.636772i	$0.219731\pi$
$102$	0.474110	−	0.682155i	0.0469439	−	0.0675434i
$103$	0.625188	+	0.217713i	0.0616016	+	0.0214519i	0.359492	−	0.933148i	$-0.382950\pi$
$103$	0.625188	+	0.217713i	0.0616016	+	0.0214519i	−0.297891	+	0.954600i	$0.596283\pi$
$104$	0.0278609	+	0.0662785i	0.00273199	+	0.00649914i
$105$	5.63587	−	6.25927i	0.550005	−	0.610842i
$106$	7.99795	−	19.0264i	0.776829	−	1.84800i
$107$	−2.68483	−	5.70556i	−0.259553	−	0.551577i	0.731997	−	0.681308i	$-0.238589\pi$
$107$	−2.68483	−	5.70556i	−0.259553	−	0.551577i	−0.991549	+	0.129731i	$0.958589\pi$
$108$	−4.34165	+	8.30481i	−0.417776	+	0.799131i
$109$	−3.33438	−	0.563968i	−0.319375	−	0.0540183i	0.00487932	−	0.999988i	$-0.498447\pi$
$109$	−3.33438	−	0.563968i	−0.319375	−	0.0540183i	−0.324255	+	0.945970i	$0.605114\pi$
$110$	15.9285	+	2.01223i	1.51872	+	0.191859i
$111$	−1.17695	+	7.97026i	−0.111711	+	0.756504i
$112$	9.01040	+	7.14156i	0.851403	+	0.674814i
$113$	14.1242	+	3.00220i	1.32870	+	0.282423i	0.816948	−	0.576712i	$-0.195664\pi$
$113$	14.1242	+	3.00220i	1.32870	+	0.282423i	0.511749	+	0.859135i	$0.328998\pi$
$114$	1.62429	+	2.33705i	0.152129	+	0.218885i
$115$	−1.84445	−	6.60607i	−0.171996	−	0.616019i
$116$	−0.322187	−	15.3810i	−0.0299143	−	1.42809i
$117$	1.48714	+	10.0709i	0.137486	+	0.931053i
$118$	9.51199	−	16.4753i	0.875650	−	1.51667i
$119$	0.665932	+	1.15343i	0.0610459	+	0.105735i
$120$	0.0354088	−	0.0280647i	0.00323236	−	0.00256194i
$121$	4.38766	−	2.17805i	0.398878	−	0.198005i
$122$	3.90757	−	20.4842i	0.353775	−	1.85455i
$123$	5.54720	+	6.70542i	0.500175	+	0.604607i
$124$	−5.69614	+	6.88545i	−0.511529	+	0.618332i
$125$	0.329248	+	1.72598i	0.0294489	+	0.154376i
$126$	−7.65474	−	10.0847i	−0.681938	−	0.898421i
$127$	−6.63946	+	14.1096i	−0.589157	+	1.25202i	0.358737	+	0.933439i	$0.383207\pi$
$127$	−6.63946	+	14.1096i	−0.589157	+	1.25202i	−0.947895	+	0.318584i	$0.896793\pi$
$128$	0.0828589	+	0.0920241i	0.00732376	+	0.00813386i
$129$	−6.28242	+	2.18777i	−0.553136	+	0.192622i
$130$	8.11861	−	29.0776i	0.712049	−	2.55027i
$131$	−11.1072	−	2.85185i	−0.970444	−	0.249168i	−0.269988	−	0.962864i	$-0.587020\pi$
$131$	−11.1072	−	2.85185i	−0.970444	−	0.249168i	−0.700456	+	0.713696i	$0.747020\pi$
$132$	−1.37779	+	4.24041i	−0.119922	+	0.369081i
$133$	−4.49904	+	0.760956i	−0.390117	+	0.0659833i
$134$	5.60076	−	0.234741i	0.483832	−	0.0202786i
$135$	13.8441	−	6.16380i	1.19151	−	0.530496i
$136$	0.00249039	+	0.00669645i	0.000213549	+	0.000574216i
$137$	17.7128	−	11.7684i	1.51331	−	1.00544i	0.525319	−	0.850906i	$-0.323946\pi$
$137$	17.7128	−	11.7684i	1.51331	−	1.00544i	0.987988	−	0.154533i	$-0.0493872\pi$
$138$	3.78879	−	0.318154i	0.322524	−	0.0270831i
$139$	−2.70317	−	1.63710i	−0.229280	−	0.138857i	0.398714	−	0.917076i	$-0.369457\pi$
$139$	−2.70317	−	1.63710i	−0.229280	−	0.138857i	−0.627993	+	0.778219i	$0.716123\pi$
$140$	4.29517	+	18.3125i	0.363008	+	1.54769i
$141$	−2.27961	+	6.12969i	−0.191978	+	0.516213i
$142$	0.821101	+	13.0510i	0.0689053	+	1.09522i
$143$	3.54540	+	10.9116i	0.296481	+	0.912474i
$144$	4.04591	+	7.73912i	0.337159	+	0.644927i
$145$	−15.0414	+	19.8163i	−1.24912	+	1.64565i
$146$	−25.7595	−	12.7872i	−2.13188	−	1.05827i
$147$	−1.16636	+	0.247918i	−0.0962000	+	0.0204480i
$148$	−13.1157	−	12.3165i	−1.07811	−	1.01241i
$149$	1.80930	+	17.2143i	0.148223	+	1.41025i	0.775448	+	0.631412i	$0.217524\pi$
$149$	1.80930	+	17.2143i	0.148223	+	1.41025i	−0.627224	+	0.778839i	$0.715809\pi$
$150$	−9.97312			−0.814302
$151$	−9.57701	−	7.69941i	−0.779366	−	0.626569i
$151$	−9.57701	−	7.69941i	−0.779366	−	0.626569i
$152$	−0.0244771			−0.00198535
$153$	0.105744	+	1.00608i	0.00854887	+	0.0813371i
$154$	−10.4017	−	9.76781i	−0.838189	−	0.787112i
$155$	14.1350	−	3.00449i	1.13535	−	0.241326i
$156$	7.50961	+	3.72780i	0.601250	+	0.298463i
$157$	3.65361	−	4.81345i	0.291590	−	0.384155i	−0.627229	−	0.778835i	$-0.715811\pi$
$157$	3.65361	−	4.81345i	0.291590	−	0.384155i	0.918819	+	0.394680i	$0.129144\pi$
$158$	13.7305	+	26.2640i	1.09234	+	2.08945i
$159$	−2.86419	−	8.81506i	−0.227145	−	0.699079i
$160$	−1.63246	−	25.9472i	−0.129057	−	2.05130i
$161$	−2.12480	+	5.71342i	−0.167458	+	0.450280i
$162$	−1.08748	−	4.63649i	−0.0854404	−	0.364277i
$163$	−8.65477	−	5.24152i	−0.677894	−	0.410547i	0.136673	−	0.990616i	$-0.456359\pi$
$163$	−8.65477	−	5.24152i	−0.677894	−	0.410547i	−0.814567	+	0.580069i	$0.803026\pi$
$164$	−19.3663	+	1.62624i	−1.51226	+	0.126988i
$165$	6.00544	−	3.99001i	0.467523	−	0.310622i
$166$	−2.14719	−	5.77361i	−0.166654	−	0.448119i
$167$	21.0740	−	9.38276i	1.63076	−	0.726060i	0.631955	−	0.775005i	$-0.282253\pi$
$167$	21.0740	−	9.38276i	1.63076	−	0.726060i	0.998801	+	0.0489454i	$0.0155860\pi$
$168$	−0.0401204	+	0.00168154i	−0.00309536	+	0.000129734i
$169$	8.45387	−	1.42987i	0.650298	−	0.109990i
$170$	0.927064	−	2.85321i	0.0711025	−	0.218831i
$171$	−3.35693	−	0.861913i	−0.256711	−	0.0659121i
$172$	3.99514	−	14.3090i	0.304627	−	1.09105i
$173$	5.06289	−	1.76308i	0.384924	−	0.134045i	−0.129503	−	0.991579i	$-0.541338\pi$
$173$	5.06289	−	1.76308i	0.384924	−	0.134045i	0.514427	+	0.857534i	$0.328005\pi$
$174$	−9.22814	−	10.2489i	−0.699583	−	0.776966i
$175$	6.80792	−	14.4676i	0.514631	−	1.09365i
$176$	5.95054	+	7.83955i	0.448539	+	0.590928i
$177$	−1.60087	−	8.39207i	−0.120329	−	0.630787i
$178$	0.00607407	−	0.00734229i	0.000455271	−	0.000550328i
$179$	−14.6389	−	17.6954i	−1.09416	−	1.32262i	−0.942508	−	0.334184i	$-0.891539\pi$
$179$	−14.6389	−	17.6954i	−1.09416	−	1.32262i	−0.151656	−	0.988433i	$-0.548461\pi$
$180$	−2.67709	+	14.0338i	−0.199539	+	1.04602i
$181$	−5.91877	+	2.93810i	−0.439939	+	0.218387i	−0.650988	−	0.759088i	$-0.725645\pi$
$181$	−5.91877	+	2.93810i	−0.439939	+	0.218387i	0.211049	+	0.977475i	$0.432312\pi$
$182$	−21.0275	+	16.6662i	−1.55866	+	1.23538i
$183$	−4.68252	−	8.11036i	−0.346142	−	0.599535i
$184$	−0.0163497	+	0.0283185i	−0.00120532	+	0.00208767i
$185$	4.25033	+	28.7832i	0.312491	+	2.11618i
$186$	0.167765	+	8.00902i	0.0123011	+	0.587250i
$187$	0.306601	+	1.09812i	0.0224209	+	0.0803026i
$188$	−8.33515	−	11.9927i	−0.607904	−	0.874659i
$189$	−13.1741	−	2.80025i	−0.958276	−	0.203688i
$190$	8.05487	+	6.38422i	0.584362	+	0.463160i
$191$	0.163484	−	1.10711i	0.0118293	−	0.0801080i	−0.982546	−	0.186017i	$-0.940442\pi$
$191$	0.163484	−	1.10711i	0.0118293	−	0.0801080i	0.994376	+	0.105909i	$0.0337753\pi$
$192$	7.19067	+	0.908392i	0.518942	+	0.0655576i
$193$	4.35374	+	0.736380i	0.313389	+	0.0530058i	0.321344	−	0.946963i	$-0.395865\pi$
$193$	4.35374	+	0.736380i	0.313389	+	0.0530058i	−0.00795481	+	0.999968i	$0.502532\pi$
$194$	−4.37503	+	8.36866i	−0.314109	+	0.600835i
$195$	−5.77262	−	12.2674i	−0.413386	−	0.878489i
$196$	1.03192	−	2.45484i	0.0737085	−	0.175346i
$197$	0.280400	−	0.311416i	0.0199777	−	0.0221874i	−0.733073	−	0.680150i	$-0.761915\pi$
$197$	0.280400	−	0.311416i	0.0199777	−	0.0221874i	0.753051	+	0.657962i	$0.228581\pi$
$198$	−4.19994	−	9.99126i	−0.298477	−	0.710048i
$199$	9.56830	+	3.33203i	0.678279	+	0.236202i	0.646068	−	0.763279i	$-0.276412\pi$
$199$	9.56830	+	3.33203i	0.678279	+	0.236202i	0.0322103	+	0.999481i	$0.489745\pi$
$200$	0.0489511	−	0.0704315i	0.00346137	−	0.00498026i
$201$	1.83513	−	1.72330i	0.129440	−	0.121552i
$202$	3.84325	+	3.31741i	0.270410	+	0.233412i
$203$	21.1670	−	6.39069i	1.48563	−	0.448538i
$204$	0.730085	+	0.401368i	0.0511162	+	0.0281014i
$205$	26.1768	+	17.3918i	1.82826	+	1.21470i
$206$	−0.302634	+	1.29029i	−0.0210855	+	0.0898984i
$207$	−3.23948	+	3.30804i	−0.225159	+	0.229925i
$208$	16.2178	−	8.91581i	1.12450	−	0.618200i
$209$	−3.89233	−	0.326848i	−0.269238	−	0.0226086i
$210$	13.6413	+	9.91102i	0.941342	+	0.683925i
$211$	2.85095	+	4.49238i	0.196268	+	0.309269i	0.928181	−	0.372130i	$-0.121372\pi$
$211$	2.85095	+	4.49238i	0.196268	+	0.309269i	−0.731913	+	0.681398i	$0.761372\pi$
$212$	19.8154	+	5.98262i	1.36093	+	0.410888i
$213$	4.10886	+	4.19582i	0.281534	+	0.287493i
$214$	10.7977	−	6.53935i	0.738119	−	0.447021i
$215$	−19.4360	+	14.1210i	−1.32552	+	0.963048i
$216$	−0.0671754	−	0.0265966i	−0.00457071	−	0.00180967i
$217$	−11.7328	−	5.22380i	−0.796478	−	0.354615i
$218$	0.425092	−	6.75665i	0.0287909	−	0.457618i
$219$	−12.5094	+	3.21187i	−0.845306	+	0.217038i
$220$	−0.337206	+	16.0980i	−0.0227344	+	1.08533i
$221$	2.12696	−	0.268698i	0.143075	−	0.0180746i
$222$	−16.1148	−	0.675410i	−1.08155	−	0.0453306i
$223$	−27.3687	+	10.8360i	−1.83274	+	0.725635i	−0.854089	+	0.520127i	$0.825885\pi$
$223$	−27.3687	+	10.8360i	−1.83274	+	0.725635i	−0.978655	+	0.205508i	$0.934115\pi$
$224$	−12.3810	+	19.5093i	−0.827237	+	1.30352i
$225$	9.19355	−	7.93566i	0.612903	−	0.529044i
$226$	−3.02165	+	28.7491i	−0.200997	+	1.91236i
$227$	−1.06402	+	10.1235i	−0.0706216	+	0.671920i	0.900747	+	0.434344i	$0.143020\pi$
$227$	−1.06402	+	10.1235i	−0.0706216	+	0.671920i	−0.971369	+	0.237576i	$0.923647\pi$
$228$	−2.16071	+	1.86507i	−0.143096	+	0.123517i
$229$	−1.88068	+	2.96347i	−0.124279	+	0.195832i	−0.900770	−	0.434296i	$-0.856997\pi$
$229$	−1.88068	+	2.96347i	−0.124279	+	0.195832i	0.776492	+	0.630127i	$0.216997\pi$
$230$	12.7665	−	5.05461i	0.841798	−	0.333291i
$231$	−6.40239	−	0.268339i	−0.421246	−	0.0176554i
$232$	0.117673	−	0.0148656i	0.00772564	−	0.000975975i
$233$	−0.220937	+	10.5474i	−0.0144740	+	0.690984i	0.930951	+	0.365144i	$0.118980\pi$
$233$	−0.220937	+	10.5474i	−0.0144740	+	0.690984i	−0.945425	+	0.325840i	$0.894353\pi$
$234$	−19.7396	+	5.06826i	−1.29042	+	0.331323i
$235$	−1.48296	+	23.5709i	−0.0967375	+	1.53760i
$236$	17.4296	+	7.76017i	1.13457	+	0.505144i
$237$	12.3747	+	4.89949i	0.803824	+	0.318256i
$238$	−2.15708	+	1.56721i	−0.139823	+	0.101587i
$239$	11.9640	−	7.24564i	0.773885	−	0.468681i	−0.0750494	−	0.997180i	$-0.523911\pi$
$239$	11.9640	−	7.24564i	0.773885	−	0.468681i	0.848934	+	0.528498i	$0.177245\pi$
$240$	−8.13737	−	8.30960i	−0.525265	−	0.536383i
$241$	−25.3382	−	7.65007i	−1.63218	−	0.492784i	−0.664993	−	0.746850i	$-0.731565\pi$
$241$	−25.3382	−	7.65007i	−1.63218	−	0.492784i	−0.967187	+	0.254066i	$0.918232\pi$
$242$	5.25459	+	8.27991i	0.337778	+	0.532252i
$243$	−13.0587	−	9.48767i	−0.837713	−	0.608634i
$244$	20.8406	+	1.75004i	1.33419	+	0.112035i
$245$	−3.77357	+	2.07454i	−0.241084	+	0.132537i
$246$	−12.1895	+	12.4475i	−0.777171	+	0.793621i
$247$	−1.67720	+	7.15079i	−0.106718	+	0.454994i
$248$	−0.0573841	−	0.0381259i	−0.00364390	−	0.00242100i
$249$	−2.42417	−	1.33270i	−0.153625	−	0.0844563i
$250$	−3.36747	+	1.01670i	−0.212977	+	0.0643017i
$251$	15.0813	+	13.0179i	0.951926	+	0.821680i	0.984066	−	0.177803i	$-0.0568991\pi$
$251$	15.0813	+	13.0179i	0.951926	+	0.821680i	−0.0321405	+	0.999483i	$0.510232\pi$
$252$	9.25610	−	8.69206i	0.583080	−	0.547548i
$253$	−2.97807	+	4.28488i	−0.187230	+	0.269388i
$254$	−29.4811	−	10.2664i	−1.84981	−	0.644171i
$255$	−0.522090	−	1.24200i	−0.0326946	−	0.0777773i
$256$	10.6228	−	11.7978i	0.663927	−	0.737366i
$257$	5.64565	−	13.4305i	0.352166	−	0.837770i	−0.645116	−	0.764085i	$-0.723191\pi$
$257$	5.64565	−	13.4305i	0.352166	−	0.837770i	0.997282	−	0.0736849i	$-0.0234759\pi$
$258$	−5.67043	−	12.0503i	−0.353025	−	0.750217i
$259$	11.9802	−	22.9160i	0.744412	−	1.42393i
$260$	29.8532	+	5.04929i	1.85142	+	0.313143i
$261$	16.6619	+	2.10488i	1.03134	+	0.130289i
$262$	3.35365	−	22.7109i	0.207189	−	1.40308i
$263$	13.2565	+	10.5070i	0.817433	+	0.647890i	0.938702	−	0.344730i	$-0.112030\pi$
$263$	13.2565	+	10.5070i	0.817433	+	0.647890i	−0.121269	+	0.992620i	$0.538696\pi$
$264$	−0.0336234	−	0.00714688i	−0.00206938	−	0.000439860i
$265$	−19.1031	−	27.4857i	−1.17349	−	1.68843i
$266$	−2.45650	−	8.79820i	−0.150618	−	0.539453i
$267$	−8.96206e−5	−	0.00427844i	−5.48469e−6	−	0.000261836i
$268$	0.821266	+	5.56160i	0.0501668	+	0.339729i
$269$	0.0279579	−	0.0484245i	0.00170462	−	0.00295250i	−0.865172	−	0.501476i	$-0.832791\pi$
$269$	0.0279579	−	0.0484245i	0.00170462	−	0.00295250i	0.866876	+	0.498523i	$0.166124\pi$
$270$	15.1689	+	26.2733i	0.923151	+	1.59895i
$271$	−1.30225	+	1.03215i	−0.0791062	+	0.0626988i	−0.659909	−	0.751345i	$-0.729405\pi$
$271$	−1.30225	+	1.03215i	−0.0791062	+	0.0626988i	0.580803	+	0.814044i	$0.302739\pi$
$272$	1.64730	−	0.817727i	0.0998822	−	0.0495820i
$273$	−2.25786	+	11.8361i	−0.136652	+	0.716353i
$274$	27.1369	+	32.8029i	1.63940	+	1.98170i
$275$	8.72468	−	10.5463i	0.526118	−	0.635967i
$276$	0.714512	+	3.74560i	0.0430086	+	0.225459i
$277$	7.05883	+	9.29966i	0.424124	+	0.558762i	0.957988	−	0.286808i	$-0.0925941\pi$
$277$	7.05883	+	9.29966i	0.424124	+	0.558762i	−0.533864	+	0.845570i	$0.679261\pi$
$278$	2.69374	−	5.72449i	0.161560	−	0.343332i
$279$	−6.52746	−	7.24948i	−0.390789	−	0.434015i
$280$	−0.136949	+	0.0476906i	−0.00818425	+	0.00285006i
$281$	7.46258	−	26.7280i	0.445180	−	1.59446i	−0.317881	−	0.948131i	$-0.602971\pi$
$281$	7.46258	−	26.7280i	0.445180	−	1.59446i	0.763061	−	0.646326i	$-0.223695\pi$
$282$	−12.6810	−	3.25594i	−0.755144	−	0.193888i
$283$	2.75889	−	8.49098i	0.163999	−	0.504737i	−0.834962	−	0.550307i	$-0.814511\pi$
$283$	2.75889	−	8.49098i	0.163999	−	0.504737i	0.998961	+	0.0455707i	$0.0145106\pi$
$284$	−12.9311	+	2.18712i	−0.767317	+	0.129782i
$285$	4.61170	−	0.193287i	0.273173	−	0.0114494i
$286$	−20.9827	+	9.34211i	−1.24073	+	0.552411i
$287$	−9.73613	−	26.1797i	−0.574706	−	1.54534i
$288$	−14.6182	+	9.71230i	−0.861385	+	0.572303i
$289$	−16.7281	+	1.40470i	−0.984005	+	0.0826292i
$290$	−42.6011	−	25.8001i	−2.50162	−	1.51504i
$291$	0.968399	+	4.12879i	0.0567685	+	0.242034i
$292$	10.0535	−	27.0331i	0.588339	−	1.58200i
$293$	0.300385	+	4.77448i	0.0175487	+	0.278928i	0.997009	+	0.0772896i	$0.0246266\pi$
$293$	0.300385	+	4.77448i	0.0175487	+	0.278928i	−0.979460	+	0.201638i	$0.935373\pi$
$294$	−0.737668	−	2.27031i	−0.0430217	−	0.132407i
$295$	−14.2941	−	27.3420i	−0.832232	−	1.59191i
$296$	0.0838662	−	0.110490i	0.00487462	−	0.00642208i
$297$	−10.3271	−	5.12639i	−0.599236	−	0.297464i
$298$	−33.8945	+	7.20449i	−1.96345	+	0.417345i
$299$	7.15274	+	6.71687i	0.413654	+	0.388447i
$300$	−1.04550	−	9.94723i	−0.0603617	−	0.574303i
$301$	21.3516			1.23069
$302$	13.3252	−	20.6787i	0.766779	−	1.18992i
$303$	2.28000			0.130983
$304$	0.658604	+	6.26620i	0.0377735	+	0.359391i
$305$	−24.6539	−	23.1515i	−1.41168	−	1.32565i
$306$	−1.98095	+	0.421064i	−0.113243	+	0.0240706i
$307$	−30.3532	−	15.0675i	−1.73235	−	0.859945i	−0.979418	−	0.201845i	$-0.935306\pi$
$307$	−30.3532	−	15.0675i	−1.73235	−	0.859945i	−0.752930	−	0.658100i	$-0.771360\pi$
$308$	8.65202	−	11.3986i	0.492995	−	0.649497i
$309$	0.275742	+	0.527445i	0.0156864	+	0.0300053i
$310$	8.93970	+	27.5136i	0.507741	+	1.56267i
$311$	0.883490	+	14.0427i	0.0500981	+	0.796287i	0.940221	+	0.340566i	$0.110619\pi$
$311$	0.883490	+	14.0427i	0.0500981	+	0.796287i	−0.890123	+	0.455721i	$0.849381\pi$
$312$	−0.0225308	+	0.0605836i	−0.00127556	+	0.00342987i
$313$	5.42113	+	23.1131i	0.306420	+	1.30643i	0.875129	+	0.483890i	$0.160776\pi$
$313$	5.42113	+	23.1131i	0.306420	+	1.30643i	−0.568709	+	0.822539i	$0.692557\pi$
$314$	10.3480	+	6.26695i	0.583969	+	0.353664i
$315$	−20.4613	+	1.71818i	−1.15286	+	0.0968085i
$316$	−24.7564	+	16.4481i	−1.39266	+	0.925279i
$317$	7.06591	+	18.9997i	0.396861	+	1.06713i	0.969019	+	0.246984i	$0.0794396\pi$
$317$	7.06591	+	18.9997i	0.396861	+	1.06713i	−0.572158	+	0.820143i	$0.693894\pi$
$318$	16.9511	−	7.54712i	0.950571	−	0.423222i
$319$	18.9109	−	0.792601i	1.05881	−	0.0443771i
$320$	25.8077	−	4.36504i	1.44269	−	0.244013i
$321$	1.75184	−	5.39160i	0.0977780	−	0.300930i
$322$	−11.8198	−	3.03482i	−0.658694	−	0.169124i
$323$	−0.196279	+	0.702993i	−0.0109213	+	0.0391156i
$324$	4.51045	−	1.57070i	0.250580	−	0.0872614i
$325$	−17.2218	−	19.1268i	−0.955294	−	1.06096i
$326$	8.62459	−	18.3282i	0.477672	−	1.01510i
$327$	−1.83817	−	2.42170i	−0.101651	−	0.133920i
$328$	−0.0280760	−	0.147179i	−0.00155024	−	0.00812662i
$329$	13.3797	−	16.1732i	0.737644	−	0.891659i
$330$	9.20066	+	11.1217i	0.506479	+	0.612229i
$331$	−2.14574	+	11.2484i	−0.117941	+	0.618267i	0.873406	+	0.486994i	$0.161906\pi$
$331$	−2.14574	+	11.2484i	−0.117941	+	0.618267i	−0.991346	+	0.131273i	$0.958094\pi$
$332$	5.53353	−	2.74687i	0.303692	−	0.150754i
$333$	15.3926	−	12.2000i	0.843508	−	0.668556i
$334$	23.0907	+	39.9942i	1.26347	+	2.18839i
$335$	4.54562	−	7.87325i	0.248354	−	0.430162i
$336$	1.51000	+	10.2257i	0.0823771	+	0.557857i
$337$	−0.156501	−	7.47128i	−0.00852516	−	0.406987i	−0.983115	−	0.182989i	$-0.941423\pi$
$337$	−0.156501	−	7.47128i	−0.00852516	−	0.406987i	0.974590	−	0.223997i	$-0.0719107\pi$
$338$	4.61586	+	16.5321i	0.251070	+	0.899230i
$339$	7.40896	+	10.6601i	0.402400	+	0.578977i
$340$	2.94299	+	0.625551i	0.159606	+	0.0339253i
$341$	−8.61609	−	6.82903i	−0.466588	−	0.369813i
$342$	1.01357	−	6.86389i	0.0548076	−	0.371157i
$343$	−16.2425	−	2.05190i	−0.877013	−	0.110792i
$344$	0.112933	+	0.0191011i	0.00608893	+	0.00102986i
$345$	2.85681	−	5.46457i	0.153805	−	0.294202i
$346$	4.56969	+	9.71109i	0.245668	+	0.522072i
$347$	9.89045	−	23.5284i	0.530947	−	1.26307i	−0.406087	−	0.913835i	$-0.633107\pi$
$347$	9.89045	−	23.5284i	0.530947	−	1.26307i	0.937034	−	0.349239i	$-0.113560\pi$
$348$	9.25487	−	10.2786i	0.496113	−	0.550990i
$349$	0.150537	+	0.358114i	0.00805808	+	0.0191694i	0.925842	−	0.377910i	$-0.123357\pi$
$349$	0.150537	+	0.358114i	0.00805808	+	0.0191694i	−0.917784	+	0.397079i	$0.870024\pi$
$350$	30.2290	+	10.5269i	1.61581	+	0.562685i
$351$	−12.3730	+	17.8024i	−0.660420	+	0.950219i
$352$	−14.4188	+	13.5402i	−0.768525	+	0.721693i
$353$	−17.7758	−	15.3437i	−0.946113	−	0.816663i	0.0370653	−	0.999313i	$-0.488199\pi$
$353$	−17.7758	−	15.3437i	−0.946113	−	0.816663i	−0.983178	+	0.182650i	$0.941532\pi$
$354$	16.3733	−	4.94340i	0.870233	−	0.262739i
$355$	18.5846	+	10.2170i	0.986370	+	0.542262i
$356$	0.00795998	+	0.00528860i	0.000421878	+	0.000280295i
$357$	−0.273427	+	1.16576i	−0.0144713	+	0.0616986i
$358$	32.1676	−	32.8485i	1.70011	−	1.73610i
$359$	−16.4089	+	9.02086i	−0.866028	+	0.476103i	−0.851843	−	0.523796i	$-0.824515\pi$
$359$	−16.4089	+	9.02086i	−0.866028	+	0.476103i	−0.0141846	+	0.999899i	$0.504515\pi$
$360$	−0.109761	−	0.00921687i	−0.00578490	−	0.000485772i
$361$	13.3483	+	9.69813i	0.702544	+	0.510428i
$362$	−7.08821	−	11.1692i	−0.372548	−	0.587042i
$363$	4.21600	+	1.27288i	0.221283	+	0.0668091i
$364$	−18.8272	−	19.2257i	−0.986815	−	1.00770i
$365$	−39.8948	+	24.1612i	−2.08819	+	1.26465i
$366$	15.1676	−	11.0199i	0.792823	−	0.576020i
$367$	25.3906	+	10.0529i	1.32538	+	0.524756i	0.920903	−	0.389792i	$-0.127453\pi$
$367$	25.3906	+	10.0529i	1.32538	+	0.524756i	0.404478	+	0.914548i	$0.367453\pi$
$368$	7.68954	+	3.42360i	0.400845	+	0.178468i
$369$	1.33213	−	21.1737i	0.0693481	−	1.10226i
$370$	−56.4169	+	14.4854i	−2.93298	+	0.753060i
$371$	−0.623008	+	29.7421i	−0.0323450	+	1.54413i
$372$	−7.97063	+	1.00693i	−0.413258	+	0.0522066i
$373$	25.7446	+	1.07902i	1.33301	+	0.0558695i	0.697699	−	0.716391i	$-0.254207\pi$
$373$	25.7446	+	1.07902i	1.33301	+	0.0558695i	0.635306	+	0.772260i	$0.280874\pi$
$374$	−2.12216	+	0.840223i	−0.109734	+	0.0434469i
$375$	−0.846448	+	1.33379i	−0.0437104	+	0.0688765i
$376$	0.0852362	−	0.0735739i	0.00439572	−	0.00379428i
$377$	3.72027	−	35.3960i	0.191604	−	1.82299i
$378$	2.81839	−	26.8152i	0.144962	−	1.37923i
$379$	19.1405	−	16.5216i	0.983180	−	0.848658i	−0.00530372	−	0.999986i	$-0.501688\pi$
$379$	19.1405	−	16.5216i	0.983180	−	0.848658i	0.988484	+	0.151328i	$0.0483549\pi$
$380$	−5.52323	+	8.70322i	−0.283336	+	0.446466i
$381$	−13.0348	+	5.16086i	−0.667795	+	0.264399i
$382$	2.23844	+	0.0938183i	0.114528	+	0.00480016i
$383$	−1.41876	+	0.179231i	−0.0724953	+	0.00915829i	−0.161497	−	0.986873i	$-0.551632\pi$
$383$	−1.41876	+	0.179231i	−0.0724953	+	0.00915829i	0.0890019	+	0.996031i	$0.471632\pi$
$384$	−0.00233149	+	0.111304i	−0.000118978	+	0.00567997i
$385$	−22.4143	+	5.75503i	−1.14234	+	0.293303i
$386$	−0.555048	+	8.82224i	−0.0282512	+	0.449040i
$387$	14.8156	+	6.59635i	0.753121	+	0.335311i
$388$	−8.80557	−	3.48637i	−0.447035	−	0.176994i
$389$	4.11511	−	2.98981i	0.208645	−	0.151589i	−0.478556	−	0.878057i	$-0.658840\pi$
$389$	4.11511	−	2.98981i	0.208645	−	0.151589i	0.687200	+	0.726468i	$0.258840\pi$
$390$	23.2161	−	14.0602i	1.17559	−	0.711963i
$391$	0.682215	+	0.696655i	0.0345011	+	0.0352313i
$392$	0.0196539	+	0.00593387i	0.000992673	+	0.000299706i
$393$	−5.52424	−	8.70480i	−0.278661	−	0.439099i
$394$	0.678694	+	0.493100i	0.0341921	+	0.0248420i
$395$	47.8957	+	4.02192i	2.40990	+	0.202365i
$396$	9.52503	−	5.23643i	0.478651	−	0.263140i
$397$	5.72974	−	5.85102i	0.287568	−	0.293654i	−0.555439	−	0.831557i	$-0.687450\pi$
$397$	5.72974	−	5.85102i	0.287568	−	0.293654i	0.843007	+	0.537903i	$0.180783\pi$
$398$	−4.63171	+	19.7474i	−0.232167	+	0.989848i
$399$	−3.41686	−	2.27016i	−0.171057	−	0.113650i
$400$	−19.3478	−	10.6365i	−0.967388	−	0.531826i
$401$	10.7186	−	3.23615i	0.535263	−	0.161605i	−0.00987577	−	0.999951i	$-0.503144\pi$
$401$	10.7186	−	3.23615i	0.535263	−	0.161605i	0.545139	+	0.838346i	$0.316477\pi$
$402$	3.81504	+	3.29306i	0.190277	+	0.164243i
$403$	−15.0702	+	14.1519i	−0.750702	+	0.704956i
$404$	−2.90590	+	4.18104i	−0.144574	+	0.208015i
$405$	−7.29388	−	2.54000i	−0.362436	−	0.126214i
$406$	17.1530	+	40.8054i	0.851290	+	2.02514i
$407$	14.8118	−	16.4501i	0.734192	−	0.815402i
$408$	−0.00248910	+	0.00592133i	−0.000123229	+	0.000293150i
$409$	−12.5798	−	26.7335i	−0.622033	−	1.32189i	−0.928969	−	0.370157i	$-0.879304\pi$
$409$	−12.5798	−	26.7335i	−0.622033	−	1.32189i	0.306936	−	0.951730i	$-0.400696\pi$
$410$	−29.1487	+	55.7564i	−1.43955	+	2.75361i
$411$	18.8511	+	3.18843i	0.929857	+	0.157274i
$412$	−1.31866	−	0.166586i	−0.0649657	−	0.00820708i
$413$	−4.00570	+	27.1266i	−0.197108	+	1.33481i
$414$	−7.26409	−	5.75745i	−0.357010	−	0.282963i
$415$	−9.77186	−	2.07707i	−0.479682	−	0.101960i
$416$	21.2269	+	30.5414i	1.04073	+	1.49742i
$417$	−0.764052	−	2.73653i	−0.0374158	−	0.134008i
$418$	−0.163762	−	7.81790i	−0.00800984	−	0.382386i
$419$	2.43104	+	16.4630i	0.118764	+	0.804268i	0.963234	+	0.268665i	$0.0865824\pi$
$419$	2.43104	+	16.4630i	0.118764	+	0.804268i	−0.844470	+	0.535603i	$0.820084\pi$
$420$	−8.45524	+	14.6449i	−0.412574	+	0.714598i
$421$	1.84821	+	3.20120i	0.0900764	+	0.156017i	0.907543	−	0.419959i	$-0.137956\pi$
$421$	1.84821	+	3.20120i	0.0900764	+	0.156017i	−0.817467	+	0.575976i	$0.804622\pi$
$422$	−8.34759	+	6.61622i	−0.406355	+	0.322073i
$423$	14.2805	−	7.08892i	0.694344	−	0.344675i
$424$	−0.0299025	+	0.156754i	−0.00145219	+	0.00761267i
$425$	−1.63029	−	1.97068i	−0.0790807	−	0.0955921i
$426$	−7.49393	+	9.05860i	−0.363082	+	0.438891i
$427$	5.63228	+	29.5254i	0.272565	+	1.42884i
$428$	7.65431	+	10.0842i	0.369985	+	0.487437i
$429$	−4.39183	+	9.33311i	−0.212040	+	0.450607i
$430$	−32.1817	−	35.7414i	−1.55194	−	1.72360i
$431$	4.35050	−	1.51500i	0.209556	−	0.0729752i	−0.222058	−	0.975033i	$-0.571277\pi$
$431$	4.35050	−	1.51500i	0.209556	−	0.0729752i	0.431614	+	0.902058i	$0.357944\pi$
$432$	−5.00132	+	17.9127i	−0.240626	+	0.861826i
$433$	20.0316	+	5.14325i	0.962659	+	0.247169i	0.697139	−	0.716936i	$-0.254456\pi$
$433$	20.0316	+	5.14325i	0.962659	+	0.247169i	0.265521	+	0.964105i	$0.414456\pi$
$434$	7.94520	−	24.4528i	0.381382	−	1.17377i
$435$	−22.0533	+	3.73004i	−1.05738	+	0.178842i
$436$	6.78366	−	0.284320i	0.324879	−	0.0136164i
$437$	−3.05174	+	1.35872i	−0.145984	+	0.0649965i
$438$	−9.01241	−	24.2337i	−0.430630	−	1.15793i
$439$	−20.2754	+	13.4709i	−0.967692	+	0.642933i	−0.934292	−	0.356509i	$-0.883967\pi$
$439$	−20.2754	+	13.4709i	−0.967692	+	0.642933i	−0.0333999	+	0.999442i	$0.510633\pi$
$440$	−0.123702	+	0.0103876i	−0.00589728	+	0.000495208i
$441$	2.48650	+	1.50588i	0.118405	+	0.0717085i
$442$	0.980053	+	4.17848i	0.0466164	+	0.198750i
$443$	1.31299	−	3.53052i	0.0623820	−	0.167740i	−0.902331	−	0.431044i	$-0.858145\pi$
$443$	1.31299	−	3.53052i	0.0623820	−	0.167740i	0.964713	+	0.263304i	$0.0848121\pi$
$444$	−1.01568	−	16.1438i	−0.0482020	−	0.766149i
$445$	−0.00477562	−	0.0146978i	−0.000226386	−	0.000696745i
$446$	−27.3013	−	52.2226i	−1.29276	−	2.47281i
$447$	−9.40852	+	12.3953i	−0.445008	+	0.586276i
$448$	−20.8364	−	10.3433i	−0.984429	−	0.488675i
$449$	18.6220	−	3.95824i	0.878828	−	0.186801i	0.253663	−	0.967293i	$-0.418365\pi$
$449$	18.6220	−	3.95824i	0.878828	−	0.186801i	0.625166	+	0.780492i	$0.285031\pi$
$450$	17.7234	+	16.6434i	0.835491	+	0.784579i
$451$	−2.49930	−	23.7793i	−0.117688	−	1.11972i
$452$	−28.9912			−1.36363
$453$	−1.53801	−	10.9400i	−0.0722620	−	0.514006i
$454$	−20.3782			−0.956395
$455$	4.54853	+	43.2764i	0.213238	+	2.02883i
$456$	−0.0160416	−	0.0150640i	−0.000751216	−	0.000705438i
$457$	4.65157	−	0.988722i	0.217591	−	0.0462505i	−0.0978260	−	0.995204i	$-0.531189\pi$
$457$	4.65157	−	0.988722i	0.217591	−	0.0462505i	0.315417	+	0.948953i	$0.397856\pi$
$458$	−6.29372	−	3.12423i	−0.294086	−	0.145986i
$459$	−1.30254	+	1.71603i	−0.0607974	+	0.0800976i
$460$	6.37981	+	12.2035i	0.297460	+	0.568989i
$461$	2.54333	+	7.82756i	0.118455	+	0.364566i	0.992652	−	0.121005i	$-0.0386117\pi$
$461$	2.54333	+	7.82756i	0.118455	+	0.364566i	−0.874197	+	0.485571i	$0.838612\pi$
$462$	−0.805502	−	12.8031i	−0.0374753	−	0.595653i
$463$	−9.98535	+	26.8498i	−0.464059	+	1.24782i	0.467425	+	0.884033i	$0.345182\pi$
$463$	−9.98535	+	26.8498i	−0.464059	+	1.24782i	−0.931484	+	0.363783i	$0.881485\pi$
$464$	−6.97187	−	29.7247i	−0.323661	−	1.37993i
$465$	11.1127	+	6.73011i	0.515341	+	0.312102i
$466$	−21.0458	+	1.76726i	−0.974926	+	0.0818668i
$467$	−13.1924	+	8.76502i	−0.610472	+	0.405597i	−0.820129	−	0.572178i	$-0.806099\pi$
$467$	−13.1924	+	8.76502i	−0.610472	+	0.405597i	0.209657	+	0.977775i	$0.432765\pi$
$468$	−7.12442	−	19.1570i	−0.329327	−	0.885533i
$469$	−7.38134	+	3.28639i	−0.340839	+	0.151751i
$470$	−47.2392	+	1.97991i	−2.17898	+	0.0913265i
$471$	5.35683	−	0.906041i	0.246830	−	0.0417482i
$472$	−0.0454544	+	0.139894i	−0.00209221	+	0.00643915i
$473$	17.7035	+	4.54547i	0.814006	+	0.209001i
$474$	−7.16521	+	25.6629i	−0.329109	+	1.17874i
$475$	8.27498	−	2.88165i	0.379682	−	0.132219i
$476$	−1.78927	−	1.98719i	−0.0820112	−	0.0910826i
$477$	−9.62081	+	20.4453i	−0.440506	+	0.936124i
$478$	16.9294	+	22.3036i	0.774332	+	1.02014i
$479$	−2.03288	−	10.6567i	−0.0928847	−	0.486919i	−0.998081	−	0.0619247i	$-0.980276\pi$
$479$	−2.03288	−	10.6567i	−0.0928847	−	0.486919i	0.905196	−	0.424994i	$-0.139724\pi$
$480$	14.8989	−	18.0097i	0.680039	−	0.822026i
$481$	−26.5321	−	32.0718i	−1.20976	−	1.46235i
$482$	9.92876	−	52.0484i	0.452243	−	2.37074i
$483$	−4.90877	+	2.43673i	−0.223357	+	0.110875i
$484$	−7.70756	+	6.10894i	−0.350344	+	0.277679i
$485$	7.65752	+	13.2632i	0.347710	+	0.602251i
$486$	16.1570	−	27.9847i	0.732896	−	1.26941i
$487$	2.50594	+	16.9702i	0.113555	+	0.768993i	0.968272	+	0.249899i	$0.0803973\pi$
$487$	2.50594	+	16.9702i	0.113555	+	0.768993i	−0.854717	+	0.519094i	$0.826269\pi$
$488$	0.00337675	+	0.161204i	0.000152858	+	0.00729738i
$489$	−2.44628	−	8.76159i	−0.110625	−	0.396213i
$490$	−4.91998	−	7.07892i	−0.222262	−	0.319793i
$491$	40.7498	+	8.66163i	1.83901	+	0.390894i	0.990412	−	0.138144i	$-0.0441135\pi$
$491$	40.7498	+	8.66163i	1.83901	+	0.390894i	0.848599	+	0.529037i	$0.177447\pi$
$492$	−13.6930	−	10.8529i	−0.617327	−	0.489287i
$493$	0.516664	−	3.49884i	0.0232694	−	0.157580i
$494$	−14.5880	−	1.84289i	−0.656343	−	0.0829154i
$495$	−17.3310	−	2.93132i	−0.778972	−	0.131753i
$496$	−8.21630	+	15.7163i	−0.368923	+	0.705684i
$497$	−8.02536	−	17.0548i	−0.359986	−	0.765010i
$498$	2.14608	−	5.10531i	0.0961680	−	0.228775i
$499$	1.38999	−	1.54374i	0.0622246	−	0.0691074i	−0.711229	−	0.702961i	$-0.751861\pi$
$499$	1.38999	−	1.54374i	0.0622246	−	0.0691074i	0.773453	+	0.633853i	$0.218528\pi$
$500$	−1.36707	−	3.25214i	−0.0611374	−	0.145440i
$501$	19.5858	+	6.82049i	0.875028	+	0.304717i
$502$	−22.7622	+	32.7505i	−1.01593	+	1.46173i
$503$	−15.7086	+	14.7514i	−0.700414	+	0.657732i	−0.950583	−	0.310470i	$-0.899514\pi$
$503$	−15.7086	+	14.7514i	−0.700414	+	0.657732i	0.250169	+	0.968202i	$0.419514\pi$
$504$	0.0741051	+	0.0639658i	0.00330090	+	0.00284926i
$505$	7.88240	−	2.37984i	0.350762	−	0.105901i
$506$	−9.15423	−	5.03258i	−0.406955	−	0.223726i
$507$	6.42041	+	4.26571i	0.285141	+	0.189447i
$508$	7.14919	−	30.4807i	0.317194	−	1.35236i
$509$	−21.9242	+	22.3882i	−0.971772	+	0.992341i	−0.999974	−	0.00726131i	$-0.997689\pi$
$509$	−21.9242	+	22.3882i	−0.971772	+	0.992341i	0.0282016	+	0.999602i	$0.491022\pi$
$510$	2.36353	−	1.29936i	0.104659	−	0.0575368i
$511$	41.3068	+	3.46863i	1.82731	+	0.153443i
$512$	25.9124	+	18.8265i	1.14518	+	0.832020i
$513$	−3.95488	−	6.23189i	−0.174612	−	0.275145i
$514$	27.9210	+	8.42985i	1.23154	+	0.371825i
$515$	1.50383	+	1.53566i	0.0662667	+	0.0676694i
$516$	11.4245	−	6.91895i	0.502937	−	0.304590i
$517$	14.5367	−	10.5615i	0.639322	−	0.464495i
$518$	48.1319	+	19.0568i	2.11479	+	0.837306i
$519$	4.40313	+	1.96040i	0.193276	+	0.0860521i
$520$	−0.0146570	+	0.232966i	−0.000642752	+	0.0102162i
$521$	−1.81952	+	0.467172i	−0.0797144	+	0.0204672i	−0.288336	−	0.957529i	$-0.593102\pi$
$521$	−1.81952	+	0.467172i	−0.0797144	+	0.0204672i	0.208622	+	0.977996i	$0.433102\pi$
$522$	−0.704106	+	33.6137i	−0.0308179	+	1.47123i
$523$	−25.6278	+	3.23754i	−1.12063	+	0.141568i	−0.663744	−	0.747960i	$-0.731034\pi$
$523$	−25.6278	+	3.23754i	−1.12063	+	0.141568i	−0.456881	+	0.889528i	$0.651034\pi$
$524$	23.0035	+	0.964132i	1.00491	+	0.0421183i
$525$	13.3656	−	5.29180i	0.583321	−	0.230953i
$526$	−18.1450	+	28.5920i	−0.791161	+	1.24667i
$527$	−1.55515	+	1.34237i	−0.0677435	+	0.0584746i
$528$	−0.924915	+	8.79998i	−0.0402518	+	0.382970i
$529$	1.93768	−	18.4358i	0.0842468	−	0.801554i
$530$	50.7256	−	43.7852i	2.20338	−	1.90191i
$531$	−11.1600	+	17.5853i	−0.484302	+	0.763138i
$532$	8.51784	−	3.37245i	0.369295	−	0.146214i
$533$	−44.9211	−	1.88275i	−1.94575	−	0.0815511i
$534$	0.00849948	−	0.00107373i	0.000367808	−	4.64650e-5i
$535$	0.428750	−	20.4683i	0.0185365	−	0.884923i
$536$	−0.0419814	+	0.0107790i	−0.00181332	+	0.000465581i
$537$	1.29644	−	20.6064i	0.0559456	−	0.889230i
$538$	0.102262	+	0.0455300i	0.00440883	+	0.00196294i
$539$	3.04612	+	1.20604i	0.131206	+	0.0519480i
$540$	−24.6149	+	17.8838i	−1.05926	+	0.769596i
$541$	36.6357	−	22.1874i	1.57509	−	0.953910i	0.585393	−	0.810750i	$-0.300940\pi$
$541$	36.6357	−	22.1874i	1.57509	−	0.953910i	0.989700	−	0.143160i	$-0.0457264\pi$
$542$	−2.32749	−	2.37675i	−0.0999742	−	0.102090i
$543$	−5.68720	−	1.71707i	−0.244061	−	0.0736864i
$544$	1.98043	+	3.12066i	0.0849104	+	0.133797i
$545$	−8.88264	−	6.45362i	−0.380491	−	0.276443i
$546$	−24.0377	−	2.01851i	−1.02872	−	0.0863841i
$547$	13.1954	−	7.25422i	0.564194	−	0.310168i	−0.174012	−	0.984743i	$-0.555673\pi$
$547$	13.1954	−	7.25422i	0.564194	−	0.310168i	0.738206	+	0.674575i	$0.235673\pi$
$548$	−29.8729	+	30.5052i	−1.27611	+	1.30312i
$549$	−5.21339	+	22.2274i	−0.222502	+	0.948643i
$550$	22.8231	+	15.1636i	0.973179	+	0.646579i
$551$	10.6182	+	5.83739i	0.452349	+	0.248681i
$552$	−0.0281433	+	0.00849697i	−0.00119786	+	0.000361655i
$553$	−32.3368	−	27.9124i	−1.37510	−	1.18696i
$554$	−17.0382	+	15.9999i	−0.723883	+	0.679771i
$555$	−14.9286	+	21.4795i	−0.633685	+	0.911753i
$556$	5.99201	+	2.08664i	0.254118	+	0.0884932i
$557$	−9.69687	−	23.0679i	−0.410870	−	0.977420i	−0.987096	−	0.160130i	$-0.948809\pi$
$557$	−9.69687	−	23.0679i	−0.410870	−	0.977420i	0.576226	−	0.817290i	$-0.304525\pi$
$558$	13.0675	−	14.5130i	0.553193	−	0.614383i
$559$	13.3186	−	31.6836i	0.563315	−	1.34007i
$560$	15.8938	+	33.7760i	0.671635	+	1.42730i
$561$	−0.474884	+	0.908370i	−0.0200496	+	0.0383514i
$562$	54.7761	+	9.26468i	2.31059	+	0.390807i
$563$	7.46864	+	0.943508i	0.314766	+	0.0397641i	0.281129	−	0.959670i	$-0.409291\pi$
$563$	7.46864	+	0.943508i	0.314766	+	0.0397641i	0.0336365	+	0.999434i	$0.489291\pi$
$564$	1.91811	−	12.9894i	0.0807671	−	0.546953i
$565$	36.7411	+	29.1206i	1.54571	+	1.22511i
$566$	17.4826	+	3.71604i	0.734847	+	0.156197i
$567$	3.91754	+	5.63661i	0.164521	+	0.236715i
$568$	−0.0271905	−	0.0973854i	−0.00114089	−	0.00408620i
$569$	0.380055	+	18.1436i	0.0159327	+	0.760621i	0.932588	+	0.360943i	$0.117545\pi$
$569$	0.380055	+	18.1436i	0.0159327	+	0.760621i	−0.916655	+	0.399679i	$0.869122\pi$
$570$	1.34987	+	9.14128i	0.0565397	+	0.382886i
$571$	−12.2119	+	21.1516i	−0.511050	+	0.885165i	0.488868	+	0.872358i	$0.337410\pi$
$571$	−12.2119	+	21.1516i	−0.511050	+	0.885165i	−0.999918	+	0.0128072i	$0.995923\pi$
$572$	−11.5175	−	19.9489i	−0.481571	−	0.834105i
$573$	0.788500	−	0.624957i	0.0329400	−	0.0261080i
$574$	50.0854	−	24.8626i	2.09053	−	1.03775i
$575$	2.19345	−	11.4985i	0.0914733	−	0.479520i
$576$	−11.2627	−	13.6143i	−0.469281	−	0.567263i
$577$	9.32805	−	11.2757i	0.388332	−	0.469413i	−0.539730	−	0.841838i	$-0.681474\pi$
$577$	9.32805	−	11.2757i	0.388332	−	0.469413i	0.928062	+	0.372425i	$0.121474\pi$
$578$	−6.29720	−	33.0111i	−0.261929	−	1.37308i
$579$	2.40012	+	3.16205i	0.0997457	+	0.131410i
$580$	21.2672	−	45.1951i	0.883072	−	1.87662i
$581$	5.94108	+	6.59824i	0.246478	+	0.273741i
$582$	−8.01763	+	2.79203i	−0.332341	+	0.115734i
$583$	−6.84826	+	24.5277i	−0.283626	+	1.01583i
$584$	0.215377	+	0.0552994i	0.00891235	+	0.00228830i
$585$	−10.2136	+	31.4342i	−0.422280	+	1.29965i
$586$	−9.44296	+	1.59716i	−0.390085	+	0.0659780i
$587$	−33.2171	+	1.39221i	−1.37102	+	0.0574626i	−0.715973	−	0.698128i	$-0.754017\pi$
$587$	−33.2171	+	1.39221i	−1.37102	+	0.0574626i	−0.655044	+	0.755591i	$0.727350\pi$
$588$	2.18708	−	0.973752i	0.0901938	−	0.0401569i
$589$	−2.45334	−	6.59683i	−0.101088	−	0.271818i
$590$	51.4459	−	34.1805i	2.11799	−	1.40719i
$591$	0.375422	−	0.0315251i	0.0154428	−	0.00129677i
$592$	−30.5422	−	18.4970i	−1.25528	−	0.760223i
$593$	−4.43187	−	18.8954i	−0.181995	−	0.775940i	−0.983934	−	0.178534i	$-0.942865\pi$
$593$	−4.43187	−	18.8954i	−0.181995	−	0.775940i	0.801939	−	0.597406i	$-0.203802\pi$
$594$	8.04545	−	21.6335i	0.330109	−	0.887635i
$595$	0.271518	+	4.31566i	0.0111312	+	0.176925i
$596$	−10.7390	−	33.0512i	−0.439886	−	1.35383i
$597$	4.22014	+	8.07238i	0.172719	+	0.330381i
$598$	−11.8763	+	15.6464i	−0.485657	+	0.639830i
$599$	−9.05063	−	4.49277i	−0.369799	−	0.183570i	0.250159	−	0.968205i	$-0.419517\pi$
$599$	−9.05063	−	4.49277i	−0.369799	−	0.183570i	−0.619958	+	0.784635i	$0.712850\pi$
$600$	0.0754271	−	0.0160325i	0.00307930	−	0.000654525i
$601$	−0.00369467	−	0.00346952i	−0.000150709	−	0.000141525i	0.684472	−	0.729039i	$-0.260033\pi$
$601$	−0.00369467	−	0.00346952i	−0.000150709	−	0.000141525i	−0.684622	+	0.728898i	$0.740033\pi$
$602$	4.46801	+	42.5103i	0.182102	+	1.73259i
$603$	−6.13713			−0.249923
$604$	22.0219	+	11.1228i	0.896057	+	0.452581i
$605$	15.9041			0.646595
$606$	0.477111	+	4.53941i	0.0193813	+	0.184401i
$607$	−3.00888	−	2.82553i	−0.122127	−	0.114685i	0.621078	−	0.783749i	$-0.286695\pi$
$607$	−3.00888	−	2.82553i	−0.122127	−	0.114685i	−0.743205	+	0.669064i	$0.766695\pi$
$608$	−12.3858	+	2.63269i	−0.502312	+	0.106770i
$609$	17.8053	+	8.83862i	0.721506	+	0.358159i
$610$	40.9348	−	53.9296i	1.65740	−	2.18355i
$611$	−15.6536	−	29.9425i	−0.633275	−	1.21134i
$612$	−0.627636	−	1.93167i	−0.0253707	−	0.0780829i
$613$	−0.168920	−	2.68491i	−0.00682263	−	0.108443i	0.993141	−	0.116919i	$-0.0373018\pi$
$613$	−0.168920	−	2.68491i	−0.00682263	−	0.108443i	−0.999964	+	0.00847649i	$0.997302\pi$
$614$	23.6471	−	63.5851i	0.954319	−	2.56609i
$615$	6.45198	+	27.5082i	0.260169	+	1.10924i
$616$	0.0943706	+	0.0571529i	0.00380230	+	0.00230275i
$617$	−32.0127	+	2.68818i	−1.28878	+	0.108222i	−0.708219	−	0.705993i	$-0.750501\pi$
$617$	−32.0127	+	2.68818i	−1.28878	+	0.108222i	−0.580563	+	0.814215i	$0.697168\pi$
$618$	−0.992424	+	0.659365i	−0.0399211	+	0.0265235i
$619$	−5.74549	−	15.4492i	−0.230931	−	0.620954i	0.768900	−	0.639369i	$-0.220805\pi$
$619$	−5.74549	−	15.4492i	−0.230931	−	0.620954i	−0.999830	+	0.0184154i	$0.994138\pi$
$620$	−26.5050	+	11.8008i	−1.06447	+	0.473930i
$621$	−9.85163	+	0.412906i	−0.395332	+	0.0165693i
$622$	−27.7736	+	4.69755i	−1.11362	+	0.188355i
$623$	−0.00424435	+	0.0130628i	−0.000170046	+	0.000523349i
$624$	16.1158	+	4.13783i	0.645148	+	0.165646i
$625$	5.91654	−	21.1907i	0.236662	−	0.847627i
$626$	−44.8829	+	15.6299i	−1.79388	+	0.624696i
$627$	−2.34977	−	2.60968i	−0.0938408	−	0.104221i
$628$	−5.16588	+	10.9781i	−0.206141	+	0.438072i
$629$	−2.50080	−	3.29468i	−0.0997134	−	0.131368i
$630$	−7.70254	−	40.3781i	−0.306877	−	1.60870i
$631$	5.35497	−	6.47305i	0.213178	−	0.257688i	−0.653075	−	0.757293i	$-0.726521\pi$
$631$	5.35497	−	6.47305i	0.213178	−	0.257688i	0.866253	+	0.499605i	$0.166521\pi$
$632$	−0.146065	−	0.176563i	−0.00581017	−	0.00702329i
$633$	−0.896336	+	4.69876i	−0.0356261	+	0.186759i
$634$	−36.3491	+	18.0438i	−1.44361	+	0.716612i
$635$	−39.6771	+	31.4477i	−1.57454	+	1.24796i
$636$	9.30453	+	16.1159i	0.368949	+	0.639038i
$637$	3.08025	−	5.33515i	0.122044	−	0.211386i
$638$	5.53531	+	37.4850i	0.219145	+	1.48405i
$639$	−0.299824	−	14.3135i	−0.0118609	−	0.566232i
$640$	0.108117	+	0.387233i	0.00427372	+	0.0153067i
$641$	0.730897	+	1.05162i	0.0288687	+	0.0415366i	0.835321	−	0.549763i	$-0.185282\pi$
$641$	0.730897	+	1.05162i	0.0288687	+	0.0415366i	−0.806452	+	0.591299i	$0.798615\pi$
$642$	11.1011	+	2.35961i	0.438124	+	0.0931262i
$643$	−27.0472	−	21.4374i	−1.06664	−	0.845408i	−0.0781867	−	0.996939i	$-0.524913\pi$
$643$	−27.0472	−	21.4374i	−1.06664	−	0.845408i	−0.988453	+	0.151531i	$0.951580\pi$
$644$	1.78785	−	12.1073i	0.0704512	−	0.477094i
$645$	−21.4284	−	2.70703i	−0.843741	−	0.106589i
$646$	−1.44071	−	0.243677i	−0.0566839	−	0.00958736i
$647$	−15.9437	+	30.4975i	−0.626812	+	1.19898i	0.339256	+	0.940694i	$0.389825\pi$
$647$	−15.9437	+	30.4975i	−0.626812	+	1.19898i	−0.966068	+	0.258287i	$0.916842\pi$
$648$	0.0156781	+	0.0333178i	0.000615896	+	0.00130885i
$649$	−9.09618	+	21.6390i	−0.357056	+	0.849403i
$650$	34.4769	−	38.2905i	1.35230	−	1.50188i
$651$	−4.47446	−	10.6443i	−0.175368	−	0.417184i
$652$	19.1847	+	6.68082i	0.751331	+	0.261641i
$653$	13.0038	−	18.7100i	0.508877	−	0.732178i	−0.480588	−	0.876946i	$-0.659577\pi$
$653$	13.0038	−	18.7100i	0.508877	−	0.732178i	0.989466	+	0.144768i	$0.0462436\pi$
$654$	4.43687	−	4.16650i	0.173495	−	0.162923i
$655$	−28.1843	−	24.3280i	−1.10125	−	0.950575i
$656$	−36.9229	+	11.1477i	−1.44160	+	0.435243i
$657$	27.5908	+	15.1681i	1.07642	+	0.591766i
$658$	35.0001	+	23.2540i	1.36445	+	0.906537i
$659$	4.72053	−	20.1261i	0.183886	−	0.784002i	−0.799231	−	0.601024i	$-0.794760\pi$
$659$	4.72053	−	20.1261i	0.183886	−	0.784002i	0.983117	−	0.182978i	$-0.0585736\pi$
$660$	−10.1283	+	10.3427i	−0.394243	+	0.402588i
$661$	37.6307	−	20.6876i	1.46366	−	0.804656i	0.466844	−	0.884340i	$-0.345391\pi$
$661$	37.6307	−	20.6876i	1.46366	−	0.804656i	0.996820	+	0.0796836i	$0.0253910\pi$
$662$	−22.8441	−	1.91828i	−0.887863	−	0.0745559i
$663$	1.55932	+	1.13291i	0.0605588	+	0.0439985i
$664$	0.0255208	+	0.0402143i	0.000990398	+	0.00156062i
$665$	−14.1823	−	4.28189i	−0.549966	−	0.166045i
$666$	27.5108	+	28.0931i	1.06602	+	1.08859i
$667$	13.8460	−	8.38545i	0.536120	−	0.324686i
$668$	−37.4697	+	27.2234i	−1.44975	+	1.05330i
$669$	−24.6055	−	9.74202i	−0.951305	−	0.376648i
$670$	16.6266	+	7.40263i	0.642341	+	0.285989i
$671$	−1.61563	+	25.6798i	−0.0623708	+	0.991356i
$672$	−20.1208	+	5.16614i	−0.776176	+	0.199288i
$673$	0.0992985	−	4.74046i	0.00382767	−	0.182731i	−0.993683	−	0.112220i	$-0.964204\pi$
$673$	0.0992985	−	4.74046i	0.00382767	−	0.182731i	0.997511	−	0.0705108i	$-0.0224629\pi$
$674$	14.8423	−	1.87502i	0.571705	−	0.0722231i
$675$	25.8412	+	1.08307i	0.994628	+	0.0416873i
$676$	−16.0053	+	6.33696i	−0.615590	+	0.243729i
$677$	−10.3194	+	16.2608i	−0.396607	+	0.624952i	−0.982681	−	0.185305i	$-0.940673\pi$
$677$	−10.3194	+	16.2608i	−0.396607	+	0.624952i	0.586074	+	0.810257i	$0.300673\pi$
$678$	−19.6735	+	16.9817i	−0.755556	+	0.652179i
$679$	1.42277	−	13.5367i	0.0546009	−	0.519492i
$680$	−0.00242468	+	0.0230693i	−9.29821e−5	+	0.000884666i
$681$	−6.92768	+	5.97981i	−0.265469	+	0.229147i
$682$	11.7934	−	18.5834i	0.451591	−	0.711594i
$683$	9.26917	−	3.66992i	0.354675	−	0.140426i	−0.184029	−	0.982921i	$-0.558914\pi$
$683$	9.26917	−	3.66992i	0.354675	−	0.140426i	0.538704	+	0.842495i	$0.318914\pi$
$684$	6.95232	+	0.291389i	0.265829	+	0.0111415i
$685$	68.4999	−	8.65355i	2.61725	−	0.330635i
$686$	0.686384	−	32.7676i	0.0262063	−	1.25107i
$687$	−3.05637	+	0.784742i	−0.116608	+	0.0299398i
$688$	1.85127	−	29.4250i	0.0705788	−	1.12182i
$689$	43.7457	+	19.4768i	1.66658	+	0.742008i
$690$	11.4776	+	4.54429i	0.436944	+	0.172998i
$691$	−17.3714	+	12.6211i	−0.660841	+	0.480129i	−0.866947	−	0.498401i	$-0.833921\pi$
$691$	−17.3714	+	12.6211i	−0.660841	+	0.480129i	0.206106	+	0.978530i	$0.433921\pi$
$692$	−9.20683	+	5.57585i	−0.349991	+	0.211962i
$693$	10.9300	+	11.1614i	0.415196	+	0.423985i
$694$	48.9140	+	14.7680i	1.85675	+	0.560586i
$695$	−5.49783	−	8.66319i	−0.208544	−	0.328613i
$696$	0.0862686	+	0.0626778i	0.00327000	+	0.00237580i
$697$	−4.45220	−	0.373861i	−0.168639	−	0.0141610i
$698$	−0.681491	+	0.374653i	−0.0257948	+	0.0141808i
$699$	−6.63604	+	6.77650i	−0.250998	+	0.256311i
$700$	−7.33058	+	31.2541i	−0.277070	+	1.18129i
$701$	−22.0175	−	14.6284i	−0.831590	−	0.552507i	0.0637112	−	0.997968i	$-0.479706\pi$
$701$	−22.0175	−	14.6284i	−0.831590	−	0.552507i	−0.895301	+	0.445461i	$0.853040\pi$
$702$	−38.0330	−	20.9088i	−1.43546	−	0.789153i
$703$	13.5660	−	4.09583i	0.511653	−	0.154477i
$704$	−15.0744	−	13.0118i	−0.568137	−	0.490402i
$705$	−15.4783	+	14.5351i	−0.582945	+	0.547422i
$706$	26.8290	−	38.6019i	1.00972	−	1.45280i
$707$	−6.91080	−	2.40660i	−0.259907	−	0.0905094i
$708$	6.64700	+	15.8126i	0.249810	+	0.594274i
$709$	−3.82714	+	4.25047i	−0.143731	+	0.159630i	−0.810712	−	0.585445i	$-0.800920\pi$
$709$	−3.82714	+	4.25047i	−0.143731	+	0.159630i	0.666981	+	0.745075i	$0.267586\pi$
$710$	−16.4527	+	39.1394i	−0.617458	+	1.46887i
$711$	−13.8149	−	29.3583i	−0.518101	−	1.10102i
$712$	−3.41352e−5	0	6.52946e-5i	−1.27927e−6	0	2.44702e-6i
$713$	−9.27087	−	1.56805i	−0.347197	−	0.0587239i
$714$	−2.37821	−	0.300437i	−0.0890022	−	0.0112436i
$715$	−5.44160	+	36.8505i	−0.203504	+	1.37813i
$716$	36.1354	+	28.6405i	1.35044	+	1.07035i
$717$	12.3001	+	2.61446i	0.459354	+	0.0976387i
$718$	−21.3939	−	30.7818i	−0.798414	−	1.14877i
$719$	−4.67614	−	16.7481i	−0.174391	−	0.624597i	−0.998322	−	0.0579074i	$-0.981557\pi$
$719$	−4.67614	−	16.7481i	−0.174391	−	0.624597i	0.823931	−	0.566690i	$-0.191776\pi$
$720$	0.593786	+	28.3470i	0.0221291	+	1.05643i
$721$	−0.279056	−	1.88977i	−0.0103926	−	0.0703785i
$722$	−16.5154	+	28.6055i	−0.614639	+	1.06459i
$723$	−11.8978	−	20.6077i	−0.442485	−	0.766407i
$724$	10.3972	−	8.24069i	0.386408	−	0.306263i
$725$	−38.0318	+	18.8791i	−1.41247	+	0.701154i
$726$	−1.65203	+	8.66027i	−0.0613128	+	0.321413i
$727$	−3.56948	−	4.31475i	−0.132385	−	0.160025i	0.700155	−	0.713991i	$-0.253114\pi$
$727$	−3.56948	−	4.31475i	−0.132385	−	0.160025i	−0.832540	+	0.553965i	$0.813114\pi$
$728$	0.132239	−	0.159850i	0.00490112	−	0.00592444i
$729$	−1.38197	−	7.24453i	−0.0511840	−	0.268316i
$730$	−56.4524	−	74.3733i	−2.08940	−	2.75268i
$731$	1.45419	−	3.09031i	0.0537851	−	0.114299i
$732$	12.5813	+	13.9730i	0.465019	+	0.516456i
$733$	−25.0574	+	8.72590i	−0.925515	+	0.322299i	−0.749436	−	0.662077i	$-0.769675\pi$
$733$	−25.0574	+	8.72590i	−0.925515	+	0.322299i	−0.176080	+	0.984376i	$0.556342\pi$
$734$	−14.7017	+	52.6556i	−0.542649	+	1.94355i
$735$	−3.74983	−	0.962792i	−0.138314	−	0.0355131i
$736$	−5.22738	+	16.0882i	−0.192684	+	0.593020i
$737$	−6.81979	+	1.15348i	−0.251210	+	0.0424890i
$738$	42.4348	−	1.77854i	1.56205	−	0.0654691i
$739$	−7.41357	+	3.30073i	−0.272713	+	0.121419i	−0.538537	−	0.842602i	$-0.681023\pi$
$739$	−7.41357	+	3.30073i	−0.272713	+	0.121419i	0.265824	+	0.964022i	$0.414356\pi$
$740$	−20.3620	−	54.7519i	−0.748524	−	2.01272i
$741$	−5.50004	+	3.65422i	−0.202049	+	0.134241i
$742$	−59.3459	+	4.98341i	−2.17865	+	0.182947i
$743$	40.1065	+	24.2893i	1.47136	+	0.891090i	0.999958	+	0.00917360i	$0.00292009\pi$
$743$	40.1065	+	24.2893i	1.47136	+	0.891090i	0.471406	+	0.881916i	$0.343747\pi$
$744$	−0.0141439	−	0.0603028i	−0.000518540	−	0.00221081i
$745$	−19.5890	+	52.6733i	−0.717686	+	1.92980i
$746$	3.23900	+	51.4824i	0.118588	+	1.88491i
$747$	2.08400	+	6.41388i	0.0762495	+	0.234672i
$748$	−1.06051	−	2.02857i	−0.0387761	−	0.0741718i
$749$	−11.0009	+	14.4931i	−0.401963	+	0.529567i
$750$	−2.83265	−	1.40614i	−0.103434	−	0.0513450i
$751$	4.29764	−	0.913492i	0.156823	−	0.0333338i	−0.128831	−	0.991667i	$-0.541122\pi$
$751$	4.29764	−	0.913492i	0.156823	−	0.0333338i	0.285654	+	0.958333i	$0.407789\pi$
$752$	−21.1286	−	19.8410i	−0.770479	−	0.723528i
$753$	1.87223	+	17.8131i	0.0682280	+	0.649146i
$754$	71.2507			2.59480
$755$	−16.7362	−	36.2163i	−0.609093	−	1.31805i
$756$	27.0410			0.983472
$757$	−1.77395	−	16.8780i	−0.0644754	−	0.613442i	−0.978280	−	0.207288i	$-0.933536\pi$
$757$	−1.77395	−	16.8780i	−0.0644754	−	0.613442i	0.913805	−	0.406154i	$-0.133130\pi$
$758$	36.8993	+	34.6507i	1.34024	+	1.25857i
$759$	−4.58880	+	0.975380i	−0.166563	+	0.0354041i
$760$	−0.0711824	−	0.0353353i	−0.00258206	−	0.00128174i
$761$	−3.09434	+	4.07664i	−0.112170	+	0.147778i	−0.849180	−	0.528103i	$-0.822903\pi$
$761$	−3.09434	+	4.07664i	−0.112170	+	0.147778i	0.737011	+	0.675881i	$0.236237\pi$
$762$	−13.0027	−	24.8720i	−0.471040	−	0.901016i
$763$	3.01543	+	9.28053i	0.109166	+	0.335978i
$764$	0.141084	+	2.24246i	0.00510422	+	0.0811293i
$765$	−1.14487	+	3.07847i	−0.0413930	+	0.111302i
$766$	−0.653731	−	2.78720i	−0.0236203	−	0.100706i
$767$	37.7544	+	22.8649i	1.36323	+	0.825604i
$768$	14.2227	−	1.19431i	0.513218	−	0.0430961i
$769$	−22.9641	+	15.2573i	−0.828107	+	0.550193i	−0.894225	−	0.447619i	$-0.852272\pi$
$769$	−22.9641	+	15.2573i	−0.828107	+	0.550193i	0.0661172	+	0.997812i	$0.478939\pi$
$770$	−16.1485	−	43.4219i	−0.581950	−	1.56482i
$771$	11.9656	−	5.32742i	0.430930	−	0.191862i
$772$	−8.85752	+	0.371240i	−0.318789	+	0.0133612i
$773$	−5.37381	+	0.908912i	−0.193283	+	0.0326913i	−0.262607	−	0.964903i	$-0.584582\pi$
$773$	−5.37381	+	0.908912i	−0.193283	+	0.0326913i	0.0693245	+	0.997594i	$0.477916\pi$
$774$	−10.0328	+	30.8778i	−0.360621	+	1.10988i
$775$	23.8884	+	6.13349i	0.858096	+	0.220322i
$776$	0.0196353	−	0.0703257i	0.000704865	−	0.00252454i
$777$	21.9548	−	7.64545i	0.787622	−	0.274279i
$778$	6.81372	+	7.56741i	0.244284	+	0.271305i
$779$	6.51733	−	13.8500i	0.233508	−	0.496229i
$780$	16.4574	+	21.6818i	0.589270	+	0.776334i
$781$	−3.02341	−	15.8493i	−0.108186	−	0.567131i
$782$	−1.24426	+	1.50405i	−0.0444945	+	0.0537846i
$783$	22.7979	+	27.5579i	0.814729	+	0.984838i
$784$	0.990258	−	5.19112i	0.0353664	−	0.185397i
$785$	17.5739	−	8.72375i	0.627239	−	0.311364i
$786$	16.1750	−	12.8201i	0.576942	−	0.457278i
$787$	9.69563	+	16.7933i	0.345612	+	0.598617i	0.985465	−	0.169880i	$-0.0543381\pi$
$787$	9.69563	+	16.7933i	0.345612	+	0.598617i	−0.639853	+	0.768497i	$0.721005\pi$
$788$	−0.420671	+	0.728624i	−0.0149858	+	0.0259561i
$789$	2.22158	+	15.0445i	0.0790904	+	0.535599i
$790$	2.01511	+	96.2004i	0.0716944	+	3.42266i
$791$	−11.2050	−	40.1317i	−0.398402	−	1.42692i
$792$	0.0478260	+	0.0688126i	0.00169942	+	0.00244515i
$793$	47.3260	+	10.0595i	1.68060	+	0.357222i
$794$	12.8482	+	10.1833i	0.455965	+	0.361393i
$795$	4.39606	−	29.7700i	0.155912	−	1.05583i
$796$	−20.1817	−	2.54954i	−0.715321	−	0.0903660i
$797$	−7.17641	−	1.21380i	−0.254202	−	0.0429950i	0.0382766	−	0.999267i	$-0.487813\pi$
$797$	−7.17641	−	1.21380i	−0.254202	−	0.0429950i	−0.292478	+	0.956272i	$0.594480\pi$
$798$	3.80480	−	7.27791i	0.134688	−	0.257635i
$799$	−1.42958	−	3.03800i	−0.0505748	−	0.107477i
$800$	17.1947	−	40.9046i	0.607925	−	1.44620i
$801$	−0.00698072	+	0.00775287i	−0.000246652	+	0.000273934i
$802$	8.68602	+	20.6632i	0.306714	+	0.729644i
$803$	33.5107	+	11.6697i	1.18257	+	0.411813i
$804$	−2.88457	+	4.15035i	−0.101731	+	0.146372i
$805$	−14.4271	+	13.5480i	−0.508489	+	0.477503i
$806$	−31.3295	−	27.0429i	−1.10354	−	0.952546i
$807$	0.0481249	−	0.0145298i	0.00169408	−	0.000511472i
$808$	−0.0343997	−	0.0189114i	−0.00121018	−	0.000665300i
$809$	1.63254	+	1.08465i	0.0573969	+	0.0381344i	0.581761	−	0.813359i	$-0.302364\pi$
$809$	1.63254	+	1.08465i	0.0573969	+	0.0381344i	−0.524365	+	0.851494i	$0.675697\pi$
$810$	3.53074	−	15.0534i	0.124058	−	0.528922i
$811$	−16.9020	+	17.2597i	−0.593509	+	0.606071i	−0.943779	−	0.330577i	$-0.892756\pi$
$811$	−16.9020	+	17.2597i	−0.593509	+	0.606071i	0.350270	+	0.936649i	$0.386090\pi$
$812$	−38.9013	+	21.3862i	−1.36517	+	0.750507i
$813$	−1.48868	−	0.125008i	−0.0522103	−	0.00438422i
$814$	35.8511	+	26.0474i	1.25658	+	0.912960i
$815$	−17.6025	−	27.7371i	−0.616588	−	0.971587i
$816$	1.58285	+	0.477891i	0.0554108	+	0.0167295i
$817$	8.18674	+	8.36002i	0.286418	+	0.292480i
$818$	50.5931	−	30.6402i	1.76894	−	1.07131i
$819$	23.7649	−	17.2662i	0.830413	−	0.603330i
$820$	−58.6673	−	23.2280i	−2.04875	−	0.811158i
$821$	−18.8398	−	8.38804i	−0.657515	−	0.292745i	0.0507288	−	0.998712i	$-0.483846\pi$
$821$	−18.8398	−	8.38804i	−0.657515	−	0.292745i	−0.708244	+	0.705968i	$0.750512\pi$
$822$	−2.40328	+	38.1991i	−0.0838242	+	1.33235i
$823$	27.2317	−	6.99192i	0.949239	−	0.243723i	0.257833	−	0.966190i	$-0.416992\pi$
$823$	27.2317	−	6.99192i	0.949239	−	0.243723i	0.691406	+	0.722466i	$0.256992\pi$
$824$	0.000214602	−	0.0102450i	7.47601e−6	−	0.000356901i
$825$	12.2085	−	1.54229i	0.425044	−	0.0536956i
$826$	−54.8463	−	2.29874i	−1.90835	−	0.0799834i
$827$	−41.0487	+	16.2523i	−1.42740	+	0.565148i	−0.949641	−	0.313341i	$-0.898552\pi$
$827$	−41.0487	+	16.2523i	−1.42740	+	0.565148i	−0.477761	+	0.878490i	$0.658552\pi$
$828$	4.98099	−	7.84879i	0.173101	−	0.272764i
$829$	2.41942	−	2.08839i	0.0840301	−	0.0725328i	−0.610398	−	0.792095i	$-0.708991\pi$
$829$	2.41942	−	2.08839i	0.0840301	−	0.0725328i	0.694428	+	0.719562i	$0.255657\pi$
$830$	2.09053	−	19.8901i	0.0725634	−	0.690395i
$831$	−1.09718	+	10.4390i	−0.0380608	+	0.362124i
$832$	−28.3456	+	24.4673i	−0.982708	+	0.848251i
$833$	0.328026	−	0.516886i	0.0113654	−	0.0179091i
$834$	5.28845	−	2.09384i	0.183124	−	0.0725039i
$835$	74.8309	+	3.13634i	2.58963	+	0.108538i
$836$	7.78043	−	0.982897i	0.269092	−	0.0339942i
$837$	0.435075	−	20.7703i	0.0150384	−	0.717925i
$838$	−32.2685	+	8.28513i	−1.11470	+	0.286205i
$839$	−2.67471	+	42.5132i	−0.0923411	+	1.46772i	0.630222	+	0.776415i	$0.282964\pi$
$839$	−2.67471	+	42.5132i	−0.0923411	+	1.46772i	−0.722563	+	0.691305i	$0.757036\pi$
$840$	−0.119103	−	0.0530279i	−0.00410943	−	0.00182964i
$841$	−27.6285	−	10.9389i	−0.952706	−	0.377203i
$842$	−5.98672	+	4.34961i	−0.206316	+	0.149897i
$843$	21.3401	−	12.9240i	0.734991	−	0.445127i
$844$	−7.47413	−	7.63233i	−0.257270	−	0.262716i
$845$	26.6491	+	8.04583i	0.916756	+	0.276785i
$846$	17.1021	+	26.9486i	0.587983	+	0.926514i
$847$	−11.4353	−	8.30827i	−0.392923	−	0.285475i
$848$	40.9341	+	3.43733i	1.40568	+	0.118039i
$849$	7.03374	−	3.86683i	0.241397	−	0.132709i
$850$	3.58241	−	3.65823i	0.122876	−	0.125476i
$851$	4.32294	−	18.4310i	0.148189	−	0.631805i
$852$	−9.82068	−	6.52484i	−0.336451	−	0.223537i
$853$	−34.6627	−	19.0560i	−1.18683	−	0.652465i	−0.238931	−	0.971037i	$-0.576797\pi$
$853$	−34.6627	−	19.0560i	−1.18683	−	0.652465i	−0.947899	+	0.318572i	$0.896797\pi$
$854$	−57.6055	+	17.3921i	−1.97122	+	0.595147i
$855$	−8.51811	−	7.35263i	−0.291313	−	0.251455i
$856$	−0.0711513	+	0.0668155i	−0.00243190	+	0.00228371i
$857$	19.4419	−	27.9733i	0.664124	−	0.955549i	−0.335783	−	0.941939i	$-0.609001\pi$
$857$	19.4419	−	27.9733i	0.664124	−	0.955549i	0.999907	−	0.0136099i	$-0.00433231\pi$
$858$	−19.5009	−	6.79094i	−0.665751	−	0.231839i
$859$	3.00384	+	7.14585i	0.102490	+	0.243813i	0.965012	−	0.262206i	$-0.0844499\pi$
$859$	3.00384	+	7.14585i	0.102490	+	0.243813i	−0.862522	+	0.506019i	$0.831117\pi$
$860$	32.2749	−	35.8449i	1.10057	−	1.22230i
$861$	9.73109	−	23.1494i	0.331635	−	0.788928i
$862$	3.92670	+	8.34467i	0.133744	+	0.284220i
$863$	−0.918025	+	1.75602i	−0.0312499	+	0.0597756i	−0.901324	−	0.433145i	$-0.857404\pi$
$863$	−0.918025	+	1.75602i	−0.0312499	+	0.0597756i	0.870074	+	0.492920i	$0.164071\pi$
$864$	−36.8526	−	6.23316i	−1.25375	−	0.212056i
$865$	17.2687	+	2.18155i	0.587154	+	0.0741748i
$866$	−6.04824	+	40.9586i	−0.205527	+	1.39183i
$867$	−11.8276	−	9.37444i	−0.401687	−	0.318373i
$868$	25.2222	+	5.36115i	0.856098	+	0.181969i
$869$	−20.8696	−	30.0274i	−0.707952	−	1.01861i
$870$	−12.0412	−	43.1268i	−0.408236	−	1.46214i
$871$	0.272377	+	13.0031i	0.00922913	+	0.440594i
$872$	0.00764682	+	0.0517841i	0.000258954	+	0.00175363i
$873$	5.16928	−	8.95345i	0.174954	−	0.303028i
$874$	−3.34377	−	5.79158i	−0.113105	−	0.195903i
$875$	3.97347	−	3.14934i	0.134328	−	0.106467i
$876$	23.2259	−	11.5295i	0.784732	−	0.389544i
$877$	−2.57715	+	13.5099i	−0.0870242	+	0.456197i	0.911925	+	0.410358i	$0.134596\pi$
$877$	−2.57715	+	13.5099i	−0.0870242	+	0.456197i	−0.998949	+	0.0458390i	$0.985404\pi$
$878$	−31.0630	−	37.5487i	−1.04832	−	1.26721i
$879$	−2.74152	+	3.31392i	−0.0924691	+	0.111776i
$880$	5.98770	+	31.3886i	0.201845	+	1.05811i
$881$	−12.0135	−	15.8272i	−0.404745	−	0.533232i	0.548211	−	0.836340i	$-0.315309\pi$
$881$	−12.0135	−	15.8272i	−0.404745	−	0.533232i	−0.952956	+	0.303108i	$0.901976\pi$
$882$	−2.47783	+	5.26566i	−0.0834329	+	0.177304i
$883$	−7.27864	−	8.08375i	−0.244946	−	0.272040i	0.608118	−	0.793847i	$-0.291925\pi$
$883$	−7.27864	−	8.08375i	−0.244946	−	0.272040i	−0.853064	+	0.521807i	$0.825258\pi$
$884$	−4.06489	+	1.41554i	−0.136717	+	0.0476099i
$885$	7.45931	−	26.7162i	0.250742	−	0.898056i
$886$	7.30390	+	1.87532i	0.245379	+	0.0630027i
$887$	7.85247	−	24.1674i	0.263660	−	0.811462i	−0.728339	−	0.685217i	$-0.759707\pi$
$887$	7.85247	−	24.1674i	0.263660	−	0.811462i	0.991999	−	0.126245i	$-0.0402926\pi$
$888$	0.122963	−	0.0207976i	0.00412636	−	0.000697921i
$889$	44.9567	−	1.88424i	1.50780	−	0.0631955i
$890$	0.0282636	−	0.0125837i	0.000947396	−	0.000421808i
$891$	2.04823	+	5.50753i	0.0686183	+	0.184509i
$892$	49.2250	−	32.7050i	1.64817	−	1.09504i
$893$	11.4626	−	0.962540i	0.383581	−	0.0322102i
$894$	−26.6474	−	16.1382i	−0.891221	−	0.539743i
$895$	−17.0266	−	72.5933i	−0.569137	−	2.42653i
$896$	0.124551	−	0.334908i	0.00416096	−	0.0111885i
$897$	0.553906	+	8.80409i	0.0184944	+	0.293960i
$898$	11.7775	+	36.2475i	0.393022	+	1.20960i
$899$	15.8008	+	30.2242i	0.526988	+	1.00803i
$900$	−14.7422	+	19.4222i	−0.491408	+	0.647406i
$901$	4.26227	+	2.11581i	0.141997	+	0.0704879i
$902$	46.8208	−	9.95206i	1.55896	−	0.331367i
$903$	13.9932	+	13.1405i	0.465665	+	0.437289i
$904$	−0.0233634	−	0.222288i	−0.000777056	−	0.00739319i
$905$	−21.4540			−0.713155
$906$	21.4593	−	5.35141i	0.712938	−	0.177789i
$907$	−54.1829			−1.79911			−0.899557	−	0.436804i	$-0.856110\pi$
$907$	−54.1829			−1.79911			−0.899557	+	0.436804i	$0.856110\pi$
$908$	−2.13627	−	20.3253i	−0.0708946	−	0.674518i
$909$	−4.05184	−	3.80493i	−0.134391	−	0.126202i
$910$	−85.2099	+	18.1119i	−2.82468	+	0.600404i
$911$	39.5014	+	19.6087i	1.30874	+	0.649664i	0.957989	−	0.286805i	$-0.0925932\pi$
$911$	39.5014	+	19.6087i	1.30874	+	0.649664i	0.350751	+	0.936469i	$0.385926\pi$
$912$	−3.42480	+	4.51201i	−0.113407	+	0.149408i
$913$	3.52131	+	6.73564i	0.116538	+	0.222917i
$914$	2.94189	+	9.05422i	0.0973092	+	0.299487i
$915$	−1.90919	−	30.3457i	−0.0631158	−	1.00320i
$916$	2.45634	−	6.60490i	0.0811597	−	0.218232i
$917$	7.55612	+	32.2157i	0.249525	+	1.06385i
$918$	−3.68913	−	2.23422i	−0.121759	−	0.0737402i
$919$	−20.2924	+	1.70400i	−0.669384	+	0.0562098i	−0.413509	−	0.910500i	$-0.635697\pi$
$919$	−20.2924	+	1.70400i	−0.669384	+	0.0562098i	−0.255875	+	0.966710i	$0.582364\pi$
$920$	−0.0884278	+	0.0587513i	−0.00291538	+	0.00193697i
$921$	−10.6196	−	28.5552i	−0.349927	−	0.940925i
$922$	−15.0522	+	6.70167i	−0.495717	+	0.220708i
$923$	−30.3135	+	1.27051i	−0.997782	+	0.0418195i
$924$	12.6854	−	2.14557i	0.417319	−	0.0705842i
$925$	−15.3449	+	47.2267i	−0.504537	+	1.55280i
$926$	−55.5465	−	14.2619i	−1.82537	−	0.468676i
$927$	0.390189	−	1.39750i	0.0128155	−	0.0458999i
$928$	57.9460	−	20.1789i	1.90217	−	0.662405i
$929$	15.9853	+	17.7535i	0.524462	+	0.582474i	0.945931	−	0.324369i	$-0.105152\pi$
$929$	15.9853	+	17.7535i	0.524462	+	0.582474i	−0.421469	+	0.906843i	$0.638485\pi$
$930$	−11.0740	+	23.5334i	−0.363130	+	0.771691i
$931$	1.26805	+	1.67060i	0.0415587	+	0.0547516i
$932$	−3.96893	−	20.8058i	−0.130007	−	0.681518i
$933$	−8.06333	+	9.74689i	−0.263982	+	0.319099i
$934$	−20.2115	−	24.4315i	−0.661340	−	0.799422i
$935$	−0.693620	+	3.63608i	−0.0226838	+	0.118913i
$936$	0.141144	−	0.0700643i	0.00461342	−	0.00229012i
$937$	4.52646	−	3.58763i	0.147873	−	0.117203i	−0.544441	−	0.838799i	$-0.683258\pi$
$937$	4.52646	−	3.58763i	0.147873	−	0.117203i	0.692314	+	0.721597i	$0.256591\pi$
$938$	−8.08769	−	14.0083i	−0.264072	−	0.457387i
$939$	−10.6717	+	18.4840i	−0.348259	+	0.603203i
$940$	−6.92692	−	46.9090i	−0.225931	−	1.53000i
$941$	−0.367467	−	17.5427i	−0.0119791	−	0.571876i	−0.964009	−	0.265870i	$-0.914341\pi$
$941$	−0.367467	−	17.5427i	−0.0119791	−	0.571876i	0.952030	−	0.306005i	$-0.0989926\pi$
$942$	2.92486	+	10.4757i	0.0952971	+	0.341316i
$943$	−11.6704	−	16.7914i	−0.380039	−	0.546805i
$944$	37.0363	+	7.87231i	1.20543	+	0.256222i
$945$	−34.2696	−	27.1617i	−1.11479	−	0.883571i
$946$	−5.34528	+	36.1981i	−0.173790	+	1.17690i
$947$	5.93207	+	0.749395i	0.192767	+	0.0243521i	0.221124	−	0.975246i	$-0.429028\pi$
$947$	5.93207	+	0.749395i	0.192767	+	0.0243521i	−0.0283571	+	0.999598i	$0.509028\pi$
$948$	−26.3474	−	4.45633i	−0.855723	−	0.144735i
$949$	30.9132	−	59.1315i	1.00348	−	1.91949i
$950$	7.46888	+	15.8722i	0.242322	+	0.514961i
$951$	−7.06226	+	16.8004i	−0.229009	+	0.544792i
$952$	0.0137947	−	0.0153206i	0.000447089	−	0.000496542i
$953$	4.76728	+	11.3409i	0.154427	+	0.367368i	0.980592	−	0.196061i	$-0.0628151\pi$
$953$	4.76728	+	11.3409i	0.154427	+	0.367368i	−0.826164	+	0.563429i	$0.809482\pi$
$954$	−42.7190	−	14.8763i	−1.38308	−	0.481639i
$955$	2.07367	−	2.98362i	0.0671024	−	0.0965477i
$956$	−20.4710	+	19.2235i	−0.662079	+	0.621734i
$957$	12.8814	+	11.1190i	0.416398	+	0.359425i
$958$	20.7918	−	6.27741i	0.671753	−	0.202814i
$959$	−53.7732	−	29.5621i	−1.73643	−	0.954609i
$960$	19.6000	+	13.0222i	0.632587	+	0.420290i
$961$	−2.55516	+	10.8940i	−0.0824244	+	0.351418i
$962$	58.3017	−	59.5357i	1.87972	−	1.91951i
$963$	−12.1109	+	6.65801i	−0.390267	+	0.214551i
$964$	52.9541	+	4.44668i	1.70554	+	0.143218i
$965$	11.5982	+	8.42657i	0.373359	+	0.271261i
$966$	−5.87865	−	9.26328i	−0.189143	−	0.298041i
$967$	−39.2131	−	11.8391i	−1.26101	−	0.380721i	−0.413014	−	0.910725i	$-0.635524\pi$
$967$	−39.2131	−	11.8391i	−1.26101	−	0.380721i	−0.847995	+	0.530004i	$0.822191\pi$
$968$	−0.0530512	−	0.0541741i	−0.00170513	−	0.00174122i
$969$	−0.561282	+	0.339924i	−0.0180310	+	0.0109199i
$970$	−24.8042	+	18.0213i	−0.796414	+	0.578629i
$971$	41.9126	+	16.5944i	1.34504	+	0.532539i	0.926717	−	0.375760i	$-0.122618\pi$
$971$	41.9126	+	16.5944i	1.34504	+	0.532539i	0.418322	+	0.908299i	$0.362618\pi$
$972$	29.6058	+	13.1814i	0.949607	+	0.422792i
$973$	−0.572588	+	9.10103i	−0.0183563	+	0.291766i
$974$	−33.2627	+	8.54040i	−1.06580	+	0.273652i
$975$	0.484589	−	23.1340i	0.0155193	−	0.740882i
$976$	41.1779	−	5.20198i	1.31807	−	0.166511i
$977$	−11.7991	−	0.494529i	−0.377487	−	0.0158214i	−0.147622	−	0.989044i	$-0.547162\pi$
$977$	−11.7991	−	0.494529i	−0.377487	−	0.0158214i	−0.229865	+	0.973222i	$0.573829\pi$
$978$	16.9321	−	6.70390i	0.541429	−	0.214367i
$979$	−0.00630006	+	0.00992730i	−0.000201351	+	0.000317278i
$980$	6.54477	−	5.64930i	0.209065	−	0.180460i
$981$	−0.774749	+	7.37124i	−0.0247358	+	0.235346i
$982$	−8.71775	+	82.9439i	−0.278195	+	2.64685i
$983$	0.138848	−	0.119851i	0.00442857	−	0.00382264i	−0.651204	−	0.758903i	$-0.725736\pi$
$983$	0.138848	−	0.119851i	0.00442857	−	0.00382264i	0.655632	+	0.755080i	$0.272402\pi$
$984$	0.0721791	−	0.113736i	0.00230099	−	0.00362577i
$985$	1.26500	−	0.500849i	0.0403062	−	0.0159584i
$986$	7.07419	+	0.296496i	0.225288	+	0.00944236i
$987$	18.7222	−	2.36516i	0.595934	−	0.0752840i
$988$	0.308827	−	14.7433i	0.00982511	−	0.469046i
$989$	15.1405	−	3.88741i	0.481439	−	0.123612i
$990$	2.20949	−	35.1189i	0.0702223	−	1.11615i
$991$	−55.0020	−	24.4885i	−1.74720	−	0.777902i	−0.992560	−	0.121759i	$-0.961146\pi$
$991$	−55.0020	−	24.4885i	−1.74720	−	0.777902i	−0.754637	−	0.656143i	$-0.772187\pi$
$992$	−33.1381	−	13.1203i	−1.05214	−	0.416570i
$993$	−8.32890	+	6.05130i	−0.264310	+	0.192032i
$994$	32.2760	−	19.5471i	1.02373	−	0.619995i
$995$	23.0157	+	23.5028i	0.729646	+	0.745090i
$996$	5.31703	+	1.60531i	0.168477	+	0.0508661i
$997$	−1.74897	−	2.75594i	−0.0553906	−	0.0872816i	0.815504	−	0.578751i	$-0.196460\pi$
$997$	−1.74897	−	2.75594i	−0.0553906	−	0.0872816i	−0.870895	+	0.491470i	$0.836460\pi$
$998$	3.36441	+	2.44438i	0.106498	+	0.0773756i
$999$	41.6815	+	3.50009i	1.31874	+	0.110738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	151.2.k.a.99.11	yes	480
151.90	even	75	inner	151.2.k.a.90.11	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
151.2.k.a.90.11	✓	480	151.90	even	75	inner
151.2.k.a.99.11	yes	480	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	151.k (of order \(75\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(0.209259 + 1.99097i) q^{2} +(0.655371 + 0.615435i) q^{3} +(-1.96386 + 0.417431i) q^{4} +(2.90813 + 1.44361i) q^{5} +(-1.08817 + 1.43361i) q^{6} +(-1.33686 - 2.55717i) q^{7} +(-0.00478326 - 0.0147213i) q^{8} +(-0.137620 - 2.18740i) q^{9} +O(q^{10})\)	\(q+(0.209259 + 1.99097i) q^{2} +(0.655371 + 0.615435i) q^{3} +(-1.96386 + 0.417431i) q^{4} +(2.90813 + 1.44361i) q^{5} +(-1.08817 + 1.43361i) q^{6} +(-1.33686 - 2.55717i) q^{7} +(-0.00478326 - 0.0147213i) q^{8} +(-0.137620 - 2.18740i) q^{9} +(-2.26562 + 6.09206i) q^{10} +(-0.564053 - 2.40485i) q^{11} +(-1.54396 - 0.935054i) q^{12} +(-4.62849 + 0.388665i) q^{13} +(4.81149 - 3.19675i) q^{14} +(1.01746 + 2.73586i) q^{15} +(-3.64000 + 1.62063i) q^{16} +(-0.461160 + 0.0193283i) q^{17} +(4.32625 - 0.731730i) q^{18} +(0.488653 - 1.50392i) q^{19} +(-6.31375 - 1.62110i) q^{20} +(0.697635 - 2.49865i) q^{21} +(4.66995 - 1.62625i) q^{22} +(-1.41355 - 1.56990i) q^{23} +(0.00592522 - 0.0125917i) q^{24} +(3.35020 + 4.41373i) q^{25} +(-1.74237 - 9.13382i) q^{26} +(2.97522 - 3.59642i) q^{27} +(3.69284 + 4.46388i) q^{28} +(-1.43582 + 7.52686i) q^{29} +(-5.23409 + 2.59822i) q^{30} +(3.48813 - 2.76466i) q^{31} +(-4.00380 - 6.93479i) q^{32} +(1.11037 - 1.92321i) q^{33} +(-0.134984 - 0.914110i) q^{34} +(-0.196200 - 9.36648i) q^{35} +(1.18336 + 4.23830i) q^{36} +(5.11442 + 7.35868i) q^{37} +(3.09651 + 0.658183i) q^{38} +(-3.27257 - 2.59381i) q^{39} +(0.00734152 - 0.0497167i) q^{40} +(9.60349 + 1.21320i) q^{41} +(5.12071 + 0.866103i) q^{42} +(-3.42817 + 6.55748i) q^{43} +(2.11158 + 4.48734i) q^{44} +(2.75753 - 6.55991i) q^{45} +(2.82982 - 3.14284i) q^{46} +(2.81890 + 6.70589i) q^{47} +(-3.38295 - 1.17807i) q^{48} +(-0.756953 + 1.08911i) q^{49} +(-8.08652 + 7.59374i) q^{50} +(-0.314127 - 0.271147i) q^{51} +(8.92745 - 2.69536i) q^{52} +(-9.03434 - 4.96667i) q^{53} +(7.78294 + 5.17098i) q^{54} +(1.83132 - 7.80789i) q^{55} +(-0.0312505 + 0.0319120i) q^{56} +(1.24581 - 0.684892i) q^{57} +(-15.2862 - 1.28362i) q^{58} +(-7.68794 - 5.58561i) q^{59} +(-3.14017 - 4.94812i) q^{60} +(-9.97213 - 3.01076i) q^{61} +(6.23426 + 6.36622i) q^{62} +(-5.40959 + 3.27617i) q^{63} +(6.52208 - 4.73857i) q^{64} +(-14.0213 - 5.55142i) q^{65} +(4.06140 + 1.80825i) q^{66} +(0.175822 - 2.79461i) q^{67} +(0.897585 - 0.230461i) q^{68} +(0.0397745 - 1.89881i) q^{69} +(18.6073 - 2.35065i) q^{70} +(6.52637 + 0.273536i) q^{71} +(-0.0315433 + 0.0124889i) q^{72} +(-7.69742 + 12.1292i) q^{73} +(-13.5806 + 11.7225i) q^{74} +(-0.520735 + 4.95446i) q^{75} +(-0.331863 + 3.15746i) q^{76} +(-5.39557 + 4.65733i) q^{77} +(4.47937 - 7.05836i) q^{78} +(13.7644 - 5.44970i) q^{79} +(-12.9251 - 0.541724i) q^{80} +(-2.36010 + 0.298150i) q^{81} +(-0.405829 + 19.3741i) q^{82} +(-2.98033 + 0.765220i) q^{83} +(-0.327043 + 5.19820i) q^{84} +(-1.36901 - 0.609525i) q^{85} +(-13.7731 - 5.45315i) q^{86} +(-5.57329 + 4.04923i) q^{87} +(-0.0327047 + 0.0198067i) q^{88} +(-0.00333036 - 0.00340085i) q^{89} +(13.6376 + 4.11743i) q^{90} +(7.18151 + 11.3163i) q^{91} +(3.43133 + 2.49301i) q^{92} +(3.98749 + 0.334839i) q^{93} +(-12.7613 + 7.01559i) q^{94} +(3.59213 - 3.66816i) q^{95} +(1.64393 - 7.00894i) q^{96} +(3.92895 + 2.61039i) q^{97} +(-2.32679 - 1.27916i) q^{98} +(-5.18276 + 1.56477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9}+O(q^{10}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9	\( 480 q - 45 q^{2} - 40 q^{3} + 15 q^{4} - 40 q^{5} - 60 q^{6} - 40 q^{7} - 50 q^{8} - 40 q^{9} - 10 q^{10} - 50 q^{11} - 65 q^{12} - 40 q^{13} - 65 q^{14} + 25 q^{16} - 20 q^{17} - 15 q^{18} - 30 q^{19} + 70 q^{20} - 40 q^{21} - 65 q^{23} + 80 q^{24} + 20 q^{25} - 65 q^{26} + 5 q^{27} - 110 q^{28} - 75 q^{29} - 135 q^{30} - 45 q^{31} + 10 q^{32} + 40 q^{33} + 20 q^{34} - 10 q^{36} - 60 q^{37} - 70 q^{38} + 25 q^{39} - 50 q^{41} + 50 q^{42} - 50 q^{43} - 30 q^{44} + 10 q^{45} - 85 q^{46} + 30 q^{47} + 175 q^{48} - 50 q^{49} + 10 q^{50} + 80 q^{51} - 145 q^{52} + 95 q^{53} + 10 q^{54} + 70 q^{55} + 140 q^{56} - 70 q^{57} + 240 q^{58} - 30 q^{59} - 60 q^{60} - 60 q^{61} + 10 q^{62} + 90 q^{63} - 160 q^{64} + 45 q^{65} - 55 q^{66} - 10 q^{67} + 10 q^{68} - 105 q^{69} + 75 q^{70} - 25 q^{71} + 310 q^{72} + 40 q^{73} + 170 q^{74} - 80 q^{75} - 15 q^{76} + 45 q^{77} - 80 q^{78} + 160 q^{79} - 85 q^{80} + 160 q^{81} - 50 q^{82} - 5 q^{83} + 70 q^{84} - 85 q^{85} + 150 q^{86} + 10 q^{87} + 95 q^{88} - 50 q^{89} - 90 q^{90} + 270 q^{91} + 90 q^{92} + 100 q^{93} - 35 q^{94} + 60 q^{95} + 255 q^{96} + 210 q^{97} - 30 q^{98}+O(q^{100}) \) 480 * q - 45 * q^2 - 40 * q^3 + 15 * q^4 - 40 * q^5 - 60 * q^6 - 40 * q^7 - 50 * q^8 - 40 * q^9 - 10 * q^10 - 50 * q^11 - 65 * q^12 - 40 * q^13 - 65 * q^14 + 25 * q^16 - 20 * q^17 - 15 * q^18 - 30 * q^19 + 70 * q^20 - 40 * q^21 - 65 * q^23 + 80 * q^24 + 20 * q^25 - 65 * q^26 + 5 * q^27 - 110 * q^28 - 75 * q^29 - 135 * q^30 - 45 * q^31 + 10 * q^32 + 40 * q^33 + 20 * q^34 - 10 * q^36 - 60 * q^37 - 70 * q^38 + 25 * q^39 - 50 * q^41 + 50 * q^42 - 50 * q^43 - 30 * q^44 + 10 * q^45 - 85 * q^46 + 30 * q^47 + 175 * q^48 - 50 * q^49 + 10 * q^50 + 80 * q^51 - 145 * q^52 + 95 * q^53 + 10 * q^54 + 70 * q^55 + 140 * q^56 - 70 * q^57 + 240 * q^58 - 30 * q^59 - 60 * q^60 - 60 * q^61 + 10 * q^62 + 90 * q^63 - 160 * q^64 + 45 * q^65 - 55 * q^66 - 10 * q^67 + 10 * q^68 - 105 * q^69 + 75 * q^70 - 25 * q^71 + 310 * q^72 + 40 * q^73 + 170 * q^74 - 80 * q^75 - 15 * q^76 + 45 * q^77 - 80 * q^78 + 160 * q^79 - 85 * q^80 + 160 * q^81 - 50 * q^82 - 5 * q^83 + 70 * q^84 - 85 * q^85 + 150 * q^86 + 10 * q^87 + 95 * q^88 - 50 * q^89 - 90 * q^90 + 270 * q^91 + 90 * q^92 + 100 * q^93 - 35 * q^94 + 60 * q^95 + 255 * q^96 + 210 * q^97 - 30 * q^98

Introduction

L-functions

Modular forms

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Database

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