LMFDB - Embedded newform 507.2.t.b.127.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			127.12
Character	$\chi$	$=$	507.127
Dual form			507.2.t.b.4.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.81864 - 0.0732885i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(1.30855 - 0.105637i) q^{4} +(-3.76569 + 1.42814i) q^{5} +(-0.576371 - 1.72644i) q^{6} +(-1.29170 + 3.03172i) q^{7} +(-1.24165 + 0.150763i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})$	\(q+(1.81864 - 0.0732885i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(1.30855 - 0.105637i) q^{4} +(-3.76569 + 1.42814i) q^{5} +(-0.576371 - 1.72644i) q^{6} +(-1.29170 + 3.03172i) q^{7} +(-1.24165 + 0.150763i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(-6.74376 + 2.87325i) q^{10} +(-0.0893553 + 0.141304i) q^{11} +(-0.465528 - 1.22750i) q^{12} +(-2.65571 - 2.43868i) q^{13} +(-2.12694 + 5.60827i) q^{14} +(2.41944 + 3.21968i) q^{15} +(-4.83867 + 0.786360i) q^{16} +(-1.24661 - 0.531132i) q^{17} +(-1.49792 + 1.03394i) q^{18} +(5.53158 + 3.19366i) q^{19} +(-4.77674 + 2.26659i) q^{20} +(3.27140 + 0.397220i) q^{21} +(-0.152149 + 0.263530i) q^{22} +(-1.39113 - 2.40951i) q^{23} +(0.490258 + 1.15068i) q^{24} +(8.39832 - 7.44026i) q^{25} +(-5.00851 - 4.24045i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-1.36999 + 4.10362i) q^{28} +(-0.0325697 - 0.808209i) q^{29} +(4.63604 + 5.67812i) q^{30} +(-4.06789 + 4.59170i) q^{31} +(-6.29117 + 1.28435i) q^{32} +(0.160585 + 0.0465141i) q^{33} +(-2.30606 - 0.874573i) q^{34} +(0.534411 - 13.2613i) q^{35} +(-1.04952 + 0.788660i) q^{36} +(4.10676 + 0.838401i) q^{37} +(10.2940 + 5.40270i) q^{38} +(-1.60353 + 3.22935i) q^{39} +(4.46035 - 2.34097i) q^{40} +(-4.95862 + 1.43628i) q^{41} +(5.97859 + 0.482642i) q^{42} +(1.64561 + 8.06074i) q^{43} +(-0.101999 + 0.194343i) q^{44} +(2.41944 - 3.21968i) q^{45} +(-2.70656 - 4.28008i) q^{46} +(-0.289367 - 0.199736i) q^{47} +(2.10152 + 4.42885i) q^{48} +(-2.67380 - 2.78372i) q^{49} +(14.7282 - 14.1466i) q^{50} +(-0.163332 + 1.34516i) q^{51} +(-3.73276 - 2.91060i) q^{52} +(1.02150 + 8.41284i) q^{53} +(1.40987 + 1.15112i) q^{54} +(0.134683 - 0.659720i) q^{55} +(1.14676 - 3.95907i) q^{56} +(1.52859 - 6.20171i) q^{57} +(-0.118465 - 1.46745i) q^{58} +(0.463934 - 2.85470i) q^{59} +(3.50608 + 3.95754i) q^{60} +(-11.7410 - 8.82282i) q^{61} +(-7.06150 + 8.64877i) q^{62} +(-0.528623 - 3.25275i) q^{63} +(-1.82782 + 0.450517i) q^{64} +(13.4834 + 5.39061i) q^{65} +(0.295455 + 0.0728232i) q^{66} +(-0.455998 + 5.64855i) q^{67} +(-1.68736 - 0.563325i) q^{68} +(-1.92734 + 2.00658i) q^{69} -24.1566i q^{70} +(-10.7562 - 10.3315i) q^{71} +(0.968849 - 0.791041i) q^{72} +(1.49389 + 2.84636i) q^{73} +(7.53015 + 1.22377i) q^{74} +(-9.48307 - 5.99673i) q^{75} +(7.57573 + 3.59473i) q^{76} +(-0.312975 - 0.453423i) q^{77} +(-2.67957 + 5.99053i) q^{78} +(2.80535 - 4.06424i) q^{79} +(17.0979 - 9.87149i) q^{80} +(0.428693 - 0.903450i) q^{81} +(-8.91267 + 2.97549i) q^{82} +(3.96026 + 16.0674i) q^{83} +(4.32275 + 0.174201i) q^{84} +(5.45289 + 0.219744i) q^{85} +(3.58353 + 14.5390i) q^{86} +(-0.767238 + 0.256142i) q^{87} +(0.0896442 - 0.188921i) q^{88} +(-1.00113 + 0.578001i) q^{89} +(4.16411 - 6.03275i) q^{90} +(10.8238 - 4.90135i) q^{91} +(-2.07490 - 3.00602i) q^{92} +(5.54217 + 2.62979i) q^{93} +(-0.540891 - 0.342039i) q^{94} +(-25.3912 - 4.12648i) q^{95} +(2.98396 + 5.68546i) q^{96} +(-4.48931 + 3.66541i) q^{97} +(-5.06668 - 4.86661i) q^{98} -0.167186i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	$ 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) $ 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{77}{78}\right)$

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 $

$2$	1.81864	−	0.0732885i	1.28597	−	0.0518228i	0.612164	−	0.790731i	$-0.290299\pi$
$2$	1.81864	−	0.0732885i	1.28597	−	0.0518228i	0.673806	+	0.738908i	$0.264658\pi$
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$3$	−0.278217	−	0.960518i	−0.160629	−	0.554555i
$4$	1.30855	−	0.105637i	0.654276	−	0.0528186i
$5$	−3.76569	+	1.42814i	−1.68407	+	0.638683i	−0.996196	−	0.0871464i	$-0.972225\pi$
$5$	−3.76569	+	1.42814i	−1.68407	+	0.638683i	−0.687874	+	0.725830i	$0.741456\pi$
$6$	−0.576371	−	1.72644i	−0.235303	−	0.704817i
$7$	−1.29170	+	3.03172i	−0.488215	+	1.14588i	0.475684	+	0.879616i	$0.342201\pi$
$7$	−1.29170	+	3.03172i	−0.488215	+	1.14588i	−0.963899	+	0.266267i	$0.914210\pi$
$8$	−1.24165	+	0.150763i	−0.438988	+	0.0533028i
$9$	−0.845190	+	0.534466i	−0.281730	+	0.178155i
$10$	−6.74376	+	2.87325i	−2.13256	+	0.908601i
$11$	−0.0893553	+	0.141304i	−0.0269417	+	0.0426048i	−0.858392	−	0.512994i	$-0.828536\pi$
$11$	−0.0893553	+	0.141304i	−0.0269417	+	0.0426048i	0.831451	+	0.555598i	$0.187511\pi$
$12$	−0.465528	−	1.22750i	−0.134386	−	0.354348i
$13$	−2.65571	−	2.43868i	−0.736563	−	0.676369i
$13$	−2.65571	−	2.43868i	−0.736563	−	0.676369i
$14$	−2.12694	+	5.60827i	−0.568447	+	1.49887i
$15$	2.41944	+	3.21968i	0.624696	+	0.831319i
$16$	−4.83867	+	0.786360i	−1.20967	+	0.196590i
$17$	−1.24661	−	0.531132i	−0.302348	−	0.128818i	0.235465	−	0.971883i	$-0.424339\pi$
$17$	−1.24661	−	0.531132i	−0.302348	−	0.128818i	−0.537812	+	0.843065i	$0.680749\pi$
$18$	−1.49792	+	1.03394i	−0.353064	+	0.243702i
$19$	5.53158	+	3.19366i	1.26903	+	0.732676i	0.974805	−	0.223060i	$-0.0716046\pi$
$19$	5.53158	+	3.19366i	1.26903	+	0.732676i	0.294227	+	0.955736i	$0.404938\pi$
$20$	−4.77674	+	2.26659i	−1.06811	+	0.506825i
$21$	3.27140	+	0.397220i	0.713878	+	0.0866804i
$22$	−0.152149	+	0.263530i	−0.0324383	+	0.0561847i
$23$	−1.39113	−	2.40951i	−0.290071	−	0.502418i	0.683755	−	0.729712i	$-0.260346\pi$
$23$	−1.39113	−	2.40951i	−0.290071	−	0.502418i	−0.973826	+	0.227293i	$0.927012\pi$
$24$	0.490258	+	1.15068i	0.100074	+	0.234881i
$25$	8.39832	−	7.44026i	1.67966	−	1.48805i
$26$	−5.00851	−	4.24045i	−0.982249	−	0.831620i
$27$	0.748511	+	0.663123i	0.144051	+	0.127618i
$28$	−1.36999	+	4.10362i	−0.258904	+	0.775511i
$29$	−0.0325697	−	0.808209i	−0.00604805	−	0.150081i	−0.999391	−	0.0348881i	$-0.988893\pi$
$29$	−0.0325697	−	0.808209i	−0.00604805	−	0.150081i	0.993343	−	0.115193i	$-0.0367485\pi$
$30$	4.63604	+	5.67812i	0.846421	+	1.03668i
$31$	−4.06789	+	4.59170i	−0.730615	+	0.824694i	−0.989998	−	0.141080i	$-0.954942\pi$
$31$	−4.06789	+	4.59170i	−0.730615	+	0.824694i	0.259383	+	0.965775i	$0.416481\pi$
$32$	−6.29117	+	1.28435i	−1.11213	+	0.227043i
$33$	0.160585	+	0.0465141i	0.0279543	+	0.00809707i
$34$	−2.30606	−	0.874573i	−0.395486	−	0.149988i
$35$	0.534411	−	13.2613i	0.0903319	−	2.24156i
$36$	−1.04952	+	0.788660i	−0.174919	+	0.131443i
$37$	4.10676	+	0.838401i	0.675147	+	0.137832i	0.525352	−	0.850885i	$-0.323934\pi$
$37$	4.10676	+	0.838401i	0.675147	+	0.137832i	0.149795	+	0.988717i	$0.452139\pi$
$38$	10.2940	+	5.40270i	1.66991	+	0.876434i
$39$	−1.60353	+	3.22935i	−0.256771	+	0.517109i
$40$	4.46035	−	2.34097i	0.705243	−	0.370140i
$41$	−4.95862	+	1.43628i	−0.774407	+	0.224310i	−0.641813	−	0.766861i	$-0.721818\pi$
$41$	−4.95862	+	1.43628i	−0.774407	+	0.224310i	−0.132593	+	0.991171i	$0.542330\pi$
$42$	5.97859	+	0.482642i	0.922517	+	0.0744733i
$43$	1.64561	+	8.06074i	0.250954	+	1.22925i	0.888513	+	0.458851i	$0.151739\pi$
$43$	1.64561	+	8.06074i	0.250954	+	1.22925i	−0.637560	+	0.770401i	$0.720056\pi$
$44$	−0.101999	+	0.194343i	−0.0153769	+	0.0292983i
$45$	2.41944	−	3.21968i	0.360668	−	0.479962i
$46$	−2.70656	−	4.28008i	−0.399060	−	0.631063i
$47$	−0.289367	−	0.199736i	−0.0422085	−	0.0291344i	0.546774	−	0.837280i	$-0.315856\pi$
$47$	−0.289367	−	0.199736i	−0.0422085	−	0.0291344i	−0.588982	+	0.808146i	$0.700471\pi$
$48$	2.10152	+	4.42885i	0.303328	+	0.639249i
$49$	−2.67380	−	2.78372i	−0.381971	−	0.397674i
$50$	14.7282	−	14.1466i	2.08288	−	2.00064i
$51$	−0.163332	+	1.34516i	−0.0228711	+	0.188361i
$52$	−3.73276	−	2.91060i	−0.517640	−	0.403628i
$53$	1.02150	+	8.41284i	0.140314	+	1.15559i	0.877388	+	0.479781i	$0.159284\pi$
$53$	1.02150	+	8.41284i	0.140314	+	1.15559i	−0.737074	+	0.675812i	$0.763793\pi$
$54$	1.40987	+	1.15112i	0.191859	+	0.156648i
$55$	0.134683	−	0.659720i	0.0181606	−	0.0889567i
$56$	1.14676	−	3.95907i	0.153242	−	0.529053i
$57$	1.52859	−	6.20171i	0.202466	−	0.821437i
$58$	−0.118465	−	1.46745i	−0.0155552	−	0.192686i
$59$	0.463934	−	2.85470i	0.0603991	−	0.371650i	−0.939201	−	0.343368i	$-0.888432\pi$
$59$	0.463934	−	2.85470i	0.0603991	−	0.371650i	0.999600	−	0.0282823i	$-0.00900373\pi$
$60$	3.50608	+	3.95754i	0.452632	+	0.510916i
$61$	−11.7410	−	8.82282i	−1.50329	−	1.12965i	−0.956255	−	0.292533i	$-0.905502\pi$
$61$	−11.7410	−	8.82282i	−1.50329	−	1.12965i	−0.547030	−	0.837113i	$-0.684242\pi$
$62$	−7.06150	+	8.64877i	−0.896811	+	1.09839i
$63$	−0.528623	−	3.25275i	−0.0666003	−	0.409808i
$64$	−1.82782	+	0.450517i	−0.228477	+	0.0563146i
$65$	13.4834	+	5.39061i	1.67241	+	0.668623i
$66$	0.295455	+	0.0728232i	0.0363681	+	0.00896392i
$67$	−0.455998	+	5.64855i	−0.0557091	+	0.690081i	0.907278	+	0.420532i	$0.138157\pi$
$67$	−0.455998	+	5.64855i	−0.0557091	+	0.690081i	−0.962987	+	0.269549i	$0.913125\pi$
$68$	−1.68736	−	0.563325i	−0.204623	−	0.0683132i
$69$	−1.92734	+	2.00658i	−0.232025	+	0.241564i
$70$		−	24.1566i		−	2.88726i
$71$	−10.7562	−	10.3315i	−1.27653	−	1.22612i	−0.960791	−	0.277272i	$-0.910570\pi$
$71$	−10.7562	−	10.3315i	−1.27653	−	1.22612i	−0.315734	−	0.948848i	$-0.602251\pi$
$72$	0.968849	−	0.791041i	0.114180	−	0.0932250i
$73$	1.49389	+	2.84636i	0.174846	+	0.333141i	0.957070	−	0.289856i	$-0.0936073\pi$
$73$	1.49389	+	2.84636i	0.174846	+	0.333141i	−0.782224	+	0.622997i	$0.785915\pi$
$74$	7.53015	+	1.22377i	0.875362	+	0.142260i
$75$	−9.48307	−	5.99673i	−1.09501	−	0.692442i
$76$	7.57573	+	3.59473i	0.868996	+	0.412343i
$77$	−0.312975	−	0.453423i	−0.0356668	−	0.0516723i
$78$	−2.67957	+	5.99053i	−0.303402	+	0.678294i
$79$	2.80535	−	4.06424i	0.315626	−	0.457263i	−0.632775	−	0.774335i	$-0.718084\pi$
$79$	2.80535	−	4.06424i	0.315626	−	0.457263i	0.948401	+	0.317072i	$0.102700\pi$
$80$	17.0979	−	9.87149i	1.91161	−	1.10367i
$81$	0.428693	−	0.903450i	0.0476325	−	0.100383i
$82$	−8.91267	+	2.97549i	−0.984240	+	0.328588i
$83$	3.96026	+	16.0674i	0.434695	+	1.76363i	0.623714	+	0.781653i	$0.285623\pi$
$83$	3.96026	+	16.0674i	0.434695	+	1.76363i	−0.189019	+	0.981973i	$0.560531\pi$
$84$	4.32275	+	0.174201i	0.471651	+	0.0190069i
$85$	5.45289	+	0.219744i	0.591449	+	0.0238346i
$86$	3.58353	+	14.5390i	0.386422	+	1.56778i
$87$	−0.767238	+	0.256142i	−0.0822566	+	0.0274613i
$88$	0.0896442	−	0.188921i	0.00955611	−	0.0201391i
$89$	−1.00113	+	0.578001i	−0.106119	+	0.0612680i	−0.552120	−	0.833764i	$-0.686181\pi$
$89$	−1.00113	+	0.578001i	−0.106119	+	0.0612680i	0.446001	+	0.895032i	$0.352848\pi$
$90$	4.16411	−	6.03275i	0.438936	−	0.635908i
$91$	10.8238	−	4.90135i	1.13464	−	0.513801i
$92$	−2.07490	−	3.00602i	−0.216324	−	0.313399i
$93$	5.54217	+	2.62979i	0.574697	+	0.272697i
$94$	−0.540891	−	0.342039i	−0.0557887	−	0.0352786i
$95$	−25.3912	−	4.12648i	−2.60509	−	0.423368i
$96$	2.98396	+	5.68546i	0.304549	+	0.580269i
$97$	−4.48931	+	3.66541i	−0.455821	+	0.372166i	−0.832361	−	0.554234i	$-0.813011\pi$
$97$	−4.48931	+	3.66541i	−0.455821	+	0.372166i	0.376540	+	0.926400i	$0.377114\pi$
$98$	−5.06668	−	4.86661i	−0.511812	−	0.491602i
$99$		−	0.167186i		−	0.0168029i
$100$	10.2037	−	10.6231i	1.02037	−	1.06231i
$101$	−15.8491	−	5.29122i	−1.57705	−	0.526496i	−0.612515	−	0.790459i	$-0.709842\pi$
$101$	−15.8491	−	5.29122i	−1.57705	−	0.526496i	−0.964533	+	0.263963i	$0.914970\pi$
$102$	−0.198457	+	2.45833i	−0.0196502	+	0.243411i
$103$	−14.3227	−	3.53022i	−1.41125	−	0.347843i	−0.541239	−	0.840869i	$-0.682045\pi$
$103$	−14.3227	−	3.53022i	−1.41125	−	0.347843i	−0.870015	+	0.493026i	$0.835891\pi$
$104$	3.66512	+	2.62760i	0.359395	+	0.257657i
$105$	−12.8864	+	3.17621i	−1.25758	+	0.309966i
$106$	2.47431	+	15.2250i	0.240326	+	1.47879i
$107$	−1.49352	+	1.82923i	−0.144384	+	0.176838i	−0.841734	−	0.539892i	$-0.818465\pi$
$107$	−1.49352	+	1.82923i	−0.144384	+	0.176838i	0.697350	+	0.716731i	$0.254362\pi$
$108$	1.04952	+	0.788660i	0.100990	+	0.0758888i
$109$	8.89357	+	10.0388i	0.851850	+	0.961540i	0.999622	−	0.0274816i	$-0.00874875\pi$
$109$	8.89357	+	10.0388i	0.851850	+	0.961540i	−0.147772	+	0.989021i	$0.547210\pi$
$110$	0.196589	−	1.20966i	0.0187440	−	0.115337i
$111$	−0.337273	−	4.17788i	−0.0320125	−	0.396546i
$112$	3.86607	−	15.6852i	0.365309	−	1.48212i
$113$	1.79790	−	6.20709i	0.169133	−	0.583913i	−0.830505	−	0.557011i	$-0.811948\pi$
$113$	1.79790	−	6.20709i	0.169133	−	0.583913i	0.999638	−	0.0269030i	$-0.00856452\pi$
$114$	2.32543	−	11.3907i	0.217796	−	1.06684i
$115$	8.67971	+	7.08676i	0.809387	+	0.660844i
$116$	−0.127996	−	1.05414i	−0.0118841	−	0.0978748i
$117$	3.54798	+	0.641763i	0.328011	+	0.0593310i
$118$	0.634510	−	5.22566i	0.0584114	−	0.481061i
$119$	3.22049	−	3.09332i	0.295222	−	0.283564i
$120$	−3.48949	−	3.63295i	−0.318546	−	0.331641i
$121$	4.70364	+	9.91270i	0.427603	+	0.901155i
$122$	−21.9993	−	15.1850i	−1.99172	−	1.37479i
$123$	2.75915	+	4.36325i	0.248784	+	0.393421i
$124$	−4.83800	+	6.43820i	−0.434465	+	0.578168i
$125$	−11.6416	+	22.1812i	−1.04126	+	1.98395i
$126$	−1.19976	−	5.87683i	−0.106883	−	0.523549i
$127$	15.3019	+	1.23530i	1.35783	+	0.109615i	0.737828	−	0.674989i	$-0.235852\pi$
$127$	15.3019	+	1.23530i	1.35783	+	0.109615i	0.619997	+	0.784604i	$0.287134\pi$
$128$	9.04373	−	2.61955i	0.799360	−	0.231538i
$129$	7.28465	−	3.82328i	0.641378	−	0.336621i
$130$	24.9165	+	8.81538i	2.18532	+	0.773160i
$131$	−3.95776	−	2.07719i	−0.345791	−	0.181485i	0.282882	−	0.959155i	$-0.408709\pi$
$131$	−3.95776	−	2.07719i	−0.345791	−	0.181485i	−0.628673	+	0.777669i	$0.716402\pi$
$132$	0.215048	+	0.0439024i	0.0187175	+	0.00382121i
$133$	−16.8274	+	12.6450i	−1.45912	+	1.09646i
$134$	−0.415321	+	10.3061i	−0.0358783	+	0.890310i
$135$	−3.76569	−	1.42814i	−0.324099	−	0.122915i
$136$	1.62793	+	0.471534i	0.139593	+	0.0404337i
$137$	18.3496	−	3.74609i	1.56771	−	0.320050i	0.663846	−	0.747869i	$-0.268923\pi$
$137$	18.3496	−	3.74609i	1.56771	−	0.320050i	0.903864	+	0.427819i	$0.140718\pi$
$138$	−3.35808	+	3.79049i	−0.285859	+	0.322668i
$139$	−2.99240	−	3.66502i	−0.253812	−	0.310863i	0.631944	−	0.775014i	$-0.282257\pi$
$139$	−2.99240	−	3.66502i	−0.253812	−	0.310863i	−0.885756	+	0.464151i	$0.846360\pi$
$140$	−0.701579	−	17.4095i	−0.0592943	−	1.47137i
$141$	−0.111343	+	0.333512i	−0.00937675	+	0.0280868i
$142$	−20.3188	−	18.0009i	−1.70511	−	1.51060i
$143$	0.581899	−	0.157354i	0.0486608	−	0.0131586i
$144$	3.66931	−	3.25073i	0.305776	−	0.270894i
$145$	1.27688	+	2.99696i	0.106039	+	0.248884i
$146$	2.92544	+	5.06701i	0.242111	+	0.419349i
$147$	−1.92991	+	3.34271i	−0.159177	+	0.275702i
$148$	5.46248	+	0.663265i	0.449013	+	0.0545200i
$149$	−14.9887	+	7.11222i	−1.22792	+	0.582656i	−0.928453	−	0.371451i	$-0.878860\pi$
$149$	−14.9887	+	7.11222i	−1.22792	+	0.582656i	−0.299468	+	0.954106i	$0.596809\pi$
$150$	−17.6857	−	10.2109i	−1.44403	−	0.833714i
$151$	13.2191	−	9.12452i	1.07576	−	0.742543i	0.107931	−	0.994158i	$-0.465577\pi$
$151$	13.2191	−	9.12452i	1.07576	−	0.742543i	0.967827	+	0.251616i	$0.0809619\pi$
$152$	−7.34975	−	3.13143i	−0.596143	−	0.253993i
$153$	1.33750	−	0.217364i	0.108130	−	0.0175729i
$154$	−0.602419	−	0.801674i	−0.0485443	−	0.0646007i
$155$	8.76085	−	23.1005i	0.703689	−	1.85547i
$156$	−1.75717	+	4.39516i	−0.140686	+	0.351894i
$157$	7.50573	+	19.7910i	0.599022	+	1.57949i	0.800068	+	0.599910i	$0.204797\pi$
$157$	7.50573	+	19.7910i	0.599022	+	1.57949i	−0.201046	+	0.979582i	$0.564434\pi$
$158$	4.80404	−	7.59698i	0.382189	−	0.604383i
$159$	7.79649	−	3.32177i	0.618302	−	0.263434i
$160$	21.8564	−	13.8211i	1.72790	−	1.09266i
$161$	9.10190	−	1.10517i	0.717331	−	0.0870997i
$162$	0.713423	−	1.67447i	0.0560518	−	0.131558i
$163$	−3.10676	−	9.30589i	−0.243340	−	0.728894i	−0.997398	−	0.0720858i	$-0.977034\pi$
$163$	−3.10676	−	9.30589i	−0.243340	−	0.728894i	0.754058	−	0.656808i	$-0.228094\pi$
$164$	−6.33689	+	2.40327i	−0.494828	+	0.187664i
$165$	−0.671144	+	0.0541804i	−0.0522485	+	0.00421794i
$166$	8.37982	+	28.9305i	0.650400	+	2.24544i
$167$	−5.51497	+	0.222246i	−0.426761	+	0.0171979i	−0.252718	−	0.967540i	$-0.581324\pi$
$167$	−5.51497	+	0.222246i	−0.426761	+	0.0171979i	−0.174043	+	0.984738i	$0.555683\pi$
$168$	−4.12180			−0.318004
$169$	1.10564	+	12.9529i	0.0850493	+	0.996377i
$170$	9.93293			0.761821
$171$	−6.38214	+	0.257191i	−0.488054	+	0.0196679i
$172$	3.00488	+	10.3741i	0.229120	+	0.791015i
$173$	−1.89584	+	0.153048i	−0.144138	+	0.0116360i	−0.152325	−	0.988330i	$-0.548676\pi$
$173$	−1.89584	+	0.153048i	−0.144138	+	0.0116360i	0.00818687	+	0.999966i	$0.497394\pi$
$174$	−1.37656	+	0.522059i	−0.104356	+	0.0395772i
$175$	11.7087	+	35.0719i	0.885097	+	2.65119i
$176$	0.321245	−	0.753990i	0.0242148	−	0.0568341i
$177$	−2.87107	+	0.348611i	−0.215803	+	0.0262032i
$178$	−1.77832	+	1.12454i	−0.133291	+	0.0842882i
$179$	0.0238416	−	0.0101580i	0.00178200	−	0.000759241i	−0.391075	−	0.920359i	$-0.627897\pi$
$179$	0.0238416	−	0.0101580i	0.00178200	−	0.000759241i	0.392857	+	0.919599i	$0.371487\pi$
$180$	2.82584	−	4.46871i	0.210626	−	0.333078i
$181$	6.75541	+	17.8126i	0.502126	+	1.32400i	0.911376	+	0.411575i	$0.135021\pi$
$181$	6.75541	+	17.8126i	0.502126	+	1.32400i	−0.409250	+	0.912422i	$0.634210\pi$
$182$	19.3253	−	9.70704i	1.43249	−	0.719533i
$183$	−5.20791	+	13.7321i	−0.384980	+	1.01511i
$184$	2.09056	+	2.78203i	0.154118	+	0.205094i
$185$	−16.6622	+	2.70787i	−1.22503	+	0.199086i
$186$	10.2719	+	4.37646i	0.753175	+	0.320898i
$187$	0.186443	−	0.128692i	0.0136340	−	0.00941089i
$188$	−0.399751	−	0.230796i	−0.0291548	−	0.0168326i
$189$	−2.97725	+	1.41272i	−0.216563	+	0.102761i
$190$	−46.4798	−	5.64367i	−3.37200	−	0.409435i
$191$	4.18713	−	7.25233i	0.302970	−	0.524760i	−0.673837	−	0.738880i	$-0.735355\pi$
$191$	4.18713	−	7.25233i	0.302970	−	0.524760i	0.976807	+	0.214120i	$0.0686883\pi$
$192$	0.941260	+	1.63031i	0.0679296	+	0.117658i
$193$	−1.93115	−	4.53258i	−0.139007	−	0.326262i	0.835897	−	0.548886i	$-0.184948\pi$
$193$	−1.93115	−	4.53258i	−0.139007	−	0.326262i	−0.974904	+	0.222624i	$0.928538\pi$
$194$	−7.89579	+	6.99506i	−0.566885	+	0.502216i
$195$	1.42646	−	14.4508i	0.102151	−	1.03484i
$196$	−3.79287	−	3.36019i	−0.270919	−	0.240013i
$197$	2.51298	−	7.52731i	0.179043	−	0.536298i	−0.820323	−	0.571900i	$-0.806207\pi$
$197$	2.51298	−	7.52731i	0.179043	−	0.536298i	0.999366	+	0.0356016i	$0.0113347\pi$
$198$	−0.0122528	−	0.304051i	−0.000870771	−	0.0216080i
$199$	−2.22422	−	2.72417i	−0.157671	−	0.193111i	0.689728	−	0.724068i	$-0.257730\pi$
$199$	−2.22422	−	2.72417i	−0.157671	−	0.193111i	−0.847399	+	0.530957i	$0.821833\pi$
$200$	−9.30602	+	10.5043i	−0.658035	+	0.742768i
$201$	5.55241	−	1.13353i	0.391636	−	0.0799532i
$202$	−29.2116	−	8.46124i	−2.05532	−	0.595331i
$203$	2.49234	+	0.945219i	0.174928	+	0.0663414i
$204$	−0.0716296	+	1.77747i	−0.00501507	+	0.124448i
$205$	16.6215	−	12.4902i	1.16089	−	0.872354i
$206$	−26.3064	−	5.37050i	−1.83286	−	0.374180i
$207$	2.46358	+	1.29298i	0.171230	+	0.0898686i
$208$	14.7678	+	9.71164i	1.02396	+	0.673381i
$209$	−0.945553	+	0.496265i	−0.0654053	+	0.0343274i
$210$	−23.2028	+	6.72078i	−1.60115	+	0.463778i
$211$	9.61061	+	0.775848i	0.661621	+	0.0534116i	0.406716	−	0.913555i	$-0.366674\pi$
$211$	9.61061	+	0.775848i	0.661621	+	0.0534116i	0.254905	+	0.966966i	$0.417956\pi$
$212$	2.22540	+	10.9007i	0.152841	+	0.748665i
$213$	−6.93100	+	13.2059i	−0.474904	+	0.904855i
$214$	−2.58211	+	3.43616i	−0.176509	+	0.234891i
$215$	−17.7087	−	28.0041i	−1.20773	−	1.90987i
$216$	−1.02936	−	0.710516i	−0.0700390	−	0.0483445i
$217$	−8.66629	−	18.2638i	−0.588306	−	1.23983i
$218$	16.9099	+	17.6051i	1.14528	+	1.19237i
$219$	2.31836	−	2.22681i	0.156660	−	0.150474i
$220$	0.106548	−	0.877506i	0.00718350	−	0.0591614i
$221$	2.01538	+	4.45063i	0.135569	+	0.299382i
$222$	−0.919567	−	7.57332i	−0.0617173	−	0.508288i
$223$	15.4323	+	12.6001i	1.03342	+	0.843763i	0.987883	−	0.155200i	$-0.0496022\pi$
$223$	15.4323	+	12.6001i	1.03342	+	0.843763i	0.0455384	+	0.998963i	$0.485500\pi$
$224$	4.23249	−	20.7321i	0.282795	−	1.38522i
$225$	−3.12161	+	10.7771i	−0.208107	+	0.718470i
$226$	2.81483	−	11.4202i	0.187239	−	0.759660i
$227$	1.33010	+	16.4762i	0.0882817	+	1.09357i	0.877540	+	0.479504i	$0.159183\pi$
$227$	1.33010	+	16.4762i	0.0882817	+	1.09357i	−0.789258	+	0.614062i	$0.789535\pi$
$228$	1.34510	−	8.27674i	0.0890815	−	0.548140i
$229$	−14.6938	−	16.5859i	−0.970995	−	1.09603i	−0.995350	−	0.0963230i	$-0.969292\pi$
$229$	−14.6938	−	16.5859i	−0.970995	−	1.09603i	0.0243555	−	0.999703i	$-0.492247\pi$
$230$	16.3046	+	12.2521i	1.07509	+	0.807881i
$231$	−0.348446	+	0.426768i	−0.0229260	+	0.0280793i
$232$	0.162288	+	0.998599i	0.0106547	+	0.0655613i
$233$	−21.6210	+	5.32909i	−1.41644	+	0.349120i	−0.871927	−	0.489635i	$-0.837130\pi$
$233$	−21.6210	+	5.32909i	−1.41644	+	0.349120i	−0.544508	+	0.838755i	$0.683284\pi$
$234$	6.49951	+	0.907107i	0.424886	+	0.0592994i
$235$	1.37492	+	0.338887i	0.0896897	+	0.0221065i
$236$	0.305519	−	3.78453i	0.0198876	−	0.246352i
$237$	−4.68428	−	1.56384i	−0.304276	−	0.101582i
$238$	5.63019	−	5.86165i	0.364951	−	0.379954i
$239$			18.9252i			1.22417i	0.790792	+	0.612085i	$0.209669\pi$
$239$			18.9252i			1.22417i	−0.790792	+	0.612085i	$0.790331\pi$
$240$	−14.2387	−	13.6764i	−0.919103	−	0.882810i
$241$	10.2920	−	8.40316i	0.662966	−	0.541295i	−0.240126	−	0.970742i	$-0.577189\pi$
$241$	10.2920	−	8.40316i	0.662966	−	0.541295i	0.903092	+	0.429447i	$0.141291\pi$
$242$	9.28069	+	17.6829i	0.596585	+	1.13670i
$243$	−0.987050	−	0.160411i	−0.0633193	−	0.0102904i
$244$	−16.2958	−	10.3048i	−1.04323	−	0.659699i
$245$	14.0442	+	6.66407i	0.897254	+	0.425752i
$246$	5.33767	+	7.73295i	0.340317	+	0.493035i
$247$	−6.90197	−	21.9712i	−0.439162	−	1.39800i
$248$	4.35862	−	6.31456i	0.276773	−	0.400975i
$249$	14.3312	−	8.27413i	0.908204	−	0.524352i
$250$	−19.5462	+	41.1928i	−1.23621	+	2.60526i
$251$	0.481538	−	0.160761i	0.0303944	−	0.0101471i	−0.301430	−	0.953488i	$-0.597464\pi$
$251$	0.481538	−	0.160761i	0.0303944	−	0.0101471i	0.331825	+	0.943341i	$0.392336\pi$
$252$	−1.03534	−	4.20055i	−0.0652205	−	0.264610i
$253$	0.464780	+	0.0187300i	0.0292204	+	0.00117754i
$254$	27.9191	+	1.12510i	1.75180	+	0.0705953i
$255$	−1.30602	−	5.29874i	−0.0817862	−	0.331820i
$256$	19.8265	−	6.61907i	1.23916	−	0.413692i
$257$	−0.706617	+	1.48916i	−0.0440776	+	0.0928915i	−0.924295	−	0.381680i	$-0.875346\pi$
$257$	−0.706617	+	1.48916i	−0.0440776	+	0.0928915i	0.880217	+	0.474571i	$0.157397\pi$
$258$	12.9679	−	7.48704i	0.807348	−	0.466123i
$259$	−7.84649	+	11.3676i	−0.487557	+	0.706349i
$260$	18.2132	+	5.62954i	1.12953	+	0.349129i
$261$	0.459488	+	0.665683i	0.0284416	+	0.0412048i
$262$	−7.34996	−	3.48760i	−0.454082	−	0.215465i
$263$	1.16714	+	0.738055i	0.0719689	+	0.0455104i	0.569966	−	0.821669i	$-0.306956\pi$
$263$	1.16714	+	0.738055i	0.0719689	+	0.0455104i	−0.497997	+	0.867179i	$0.665931\pi$
$264$	−0.206403	−	0.0335437i	−0.0127032	−	0.00206447i
$265$	−15.8614	−	30.2213i	−0.974357	−	1.85648i
$266$	−29.6762	+	24.2299i	−1.81957	+	1.48563i
$267$	0.833711	+	0.800791i	0.0510223	+	0.0490076i
$268$			7.43960i			0.454446i
$269$	3.06430	−	3.19027i	0.186833	−	0.194514i	−0.621198	−	0.783654i	$-0.713354\pi$
$269$	3.06430	−	3.19027i	0.186833	−	0.194514i	0.808031	+	0.589140i	$0.200533\pi$
$270$	−6.95309	−	2.32128i	−0.423152	−	0.141269i
$271$	2.44107	−	30.2380i	0.148284	−	1.83683i	−0.313208	−	0.949684i	$-0.601404\pi$
$271$	2.44107	−	30.2380i	0.148284	−	1.83683i	0.461492	−	0.887144i	$-0.347314\pi$
$272$	6.44960	+	1.58968i	0.391065	+	0.0963888i
$273$	−7.71921	−	9.03281i	−0.467188	−	0.546690i
$274$	33.0967	−	8.15759i	1.99944	−	0.492818i
$275$	0.300905	+	1.85154i	0.0181453	+	0.111652i
$276$	−2.31006	+	2.82931i	−0.139049	+	0.170304i
$277$	0.872739	+	0.655821i	0.0524378	+	0.0394044i	0.626638	−	0.779310i	$-0.284430\pi$
$277$	0.872739	+	0.655821i	0.0524378	+	0.0394044i	−0.574200	+	0.818715i	$0.694687\pi$
$278$	−5.71069	−	6.44603i	−0.342504	−	0.386607i
$279$	0.984035	−	6.05501i	0.0589127	−	0.362504i
$280$	1.33576	+	16.5464i	0.0798270	+	0.988834i
$281$	4.99875	−	20.2807i	0.298201	−	1.20985i	−0.610370	−	0.792116i	$-0.708979\pi$
$281$	4.99875	−	20.2807i	0.298201	−	1.20985i	0.908571	−	0.417731i	$-0.137175\pi$
$282$	−0.178049	+	0.614697i	−0.0106027	+	0.0366047i
$283$	2.14795	−	10.5214i	0.127683	−	0.625431i	−0.864705	−	0.502280i	$-0.832495\pi$
$283$	2.14795	−	10.5214i	0.127683	−	0.625431i	0.992388	−	0.123151i	$-0.0393001\pi$
$284$	−15.1664	−	12.3830i	−0.899962	−	0.734796i
$285$	3.10073	+	25.5368i	0.183671	+	1.51267i
$286$	1.04673	−	0.328816i	0.0618944	−	0.0194433i
$287$	2.05063	−	16.8884i	0.121045	−	0.996892i
$288$	4.63079	−	4.44794i	0.272872	−	0.262097i
$289$	−10.5044	−	10.9362i	−0.617904	−	0.643307i
$290$	2.54183	+	5.35679i	0.149261	+	0.314562i
$291$	4.76970	+	3.29228i	0.279605	+	0.192997i
$292$	2.25551	+	3.56680i	0.131994	+	0.208731i
$293$	−15.7122	+	20.9091i	−0.917914	+	1.22152i	0.0568728	+	0.998381i	$0.481887\pi$
$293$	−15.7122	+	20.9091i	−0.917914	+	1.22152i	−0.974786	+	0.223140i	$0.928369\pi$
$294$	−3.26483	+	6.22061i	−0.190409	+	0.362793i
$295$	2.32988	+	11.4125i	0.135651	+	0.664461i
$296$	−5.22554	−	0.421849i	−0.303728	−	0.0245195i
$297$	−0.160585	+	0.0465141i	−0.00931811	+	0.00269902i
$298$	−26.7377	+	14.0330i	−1.54887	+	0.812912i
$299$	−2.18159	+	9.79152i	−0.126165	+	0.566258i
$300$	−13.0426	−	6.84526i	−0.753013	−	0.395211i
$301$	−26.5636	−	5.42299i	−1.53110	−	0.312576i
$302$	23.3721	−	17.5630i	1.34491	−	1.01064i
$303$	−0.672805	+	16.6955i	−0.0386517	+	0.959131i
$304$	−29.2768	−	11.1032i	−1.67914	−	0.636815i
$305$	56.8134	+	16.4562i	3.25312	+	0.942279i
$306$	2.41649	−	0.493330i	0.138141	−	0.0282018i
$307$	−12.2316	+	13.8067i	−0.698097	+	0.787989i	−0.985474	−	0.169829i	$-0.945678\pi$
$307$	−12.2316	+	13.8067i	−0.698097	+	0.787989i	0.287377	+	0.957818i	$0.407217\pi$
$308$	−0.457443	−	0.560265i	−0.0260652	−	0.0319241i
$309$	0.593975	+	14.7393i	0.0337901	+	0.838492i
$310$	14.2398	−	42.6534i	0.808767	−	2.42255i
$311$	−12.4918	−	11.0668i	−0.708346	−	0.627540i	0.230019	−	0.973186i	$-0.426121\pi$
$311$	−12.4918	−	11.0668i	−0.708346	−	0.627540i	−0.938365	+	0.345646i	$0.887660\pi$
$312$	1.50415	−	4.25146i	0.0851560	−	0.240691i
$313$	−2.31012	+	2.04658i	−0.130575	+	0.115680i	−0.725883	−	0.687818i	$-0.758569\pi$
$313$	−2.31012	+	2.04658i	−0.130575	+	0.115680i	0.595308	+	0.803498i	$0.297030\pi$
$314$	15.1006	+	35.4425i	0.852178	+	2.00014i
$315$	6.63602	+	11.4939i	0.373897	+	0.647609i
$316$	3.24160	−	5.61462i	0.182354	−	0.315847i
$317$	−5.09965	−	0.619210i	−0.286425	−	0.0347783i	−0.0239367	−	0.999713i	$-0.507620\pi$
$317$	−5.09965	−	0.619210i	−0.286425	−	0.0347783i	−0.262488	+	0.964935i	$0.584543\pi$
$318$	13.9355	−	6.61249i	0.781466	−	0.370810i
$319$	0.117114	+	0.0676156i	0.00655711	+	0.00378575i
$320$	6.23960	−	4.30689i	0.348804	−	0.240762i
$321$	2.17253	+	0.925629i	0.121259	+	0.0516636i
$322$	16.4721	−	2.67697i	0.917952	−	0.149182i
$323$	−5.19948	−	6.91925i	−0.289307	−	0.384997i
$324$	0.465528	−	1.22750i	0.0258627	−	0.0681943i
$325$	−40.4480	−	0.721635i	−2.24365	−	0.0400291i
$326$	−6.33209	−	16.6963i	−0.350702	−	0.924725i
$327$	7.16807	−	11.3354i	0.396395	−	0.626849i
$328$	5.94032	−	2.53093i	0.327999	−	0.139747i
$329$	0.979317	−	0.619283i	0.0539915	−	0.0341422i
$330$	−1.21660	+	0.147722i	−0.0669714	+	0.00813181i
$331$	−5.54755	+	13.0206i	−0.304921	+	0.715675i	−0.999995	−	0.00326288i	$-0.998961\pi$
$331$	−5.54755	+	13.0206i	−0.304921	+	0.715675i	0.695074	+	0.718938i	$0.255372\pi$
$332$	6.87952	+	20.6067i	0.377563	+	1.13094i
$333$	−3.91909	+	1.48632i	−0.214765	+	0.0814496i
$334$	−10.0134	+	0.808368i	−0.547911	+	0.0442319i
$335$	−6.34977	−	21.9220i	−0.346925	−	1.19772i
$336$	−16.1416	+	0.650483i	−0.880595	+	0.0354868i
$337$	−21.8026			−1.18767			−0.593833	−	0.804589i	$-0.702386\pi$
$337$	−21.8026			−1.18767			−0.593833	+	0.804589i	$0.702386\pi$
$338$	2.96006	+	23.4756i	0.161006	+	1.27690i
$339$	−6.46223			−0.350980
$340$	7.15860	−	0.288482i	0.388230	−	0.0156451i
$341$	−0.285339	−	0.985104i	−0.0154520	−	0.0533464i
$342$	−11.5879	+	0.935475i	−0.626604	+	0.0505847i
$343$	−9.67574	+	3.66952i	−0.522441	+	0.198136i
$344$	−3.25853	−	9.76049i	−0.175688	−	0.526250i
$345$	4.39212	−	10.3087i	0.236464	−	0.555001i
$346$	−3.43663	+	0.417282i	−0.184754	+	0.0224332i
$347$	14.3088	−	9.04835i	0.768138	−	0.485741i	−0.0920275	−	0.995756i	$-0.529335\pi$
$347$	14.3088	−	9.04835i	0.768138	−	0.485741i	0.860165	+	0.510016i	$0.170360\pi$
$348$	−0.976913	+	0.416224i	−0.0523680	+	0.0223119i
$349$	−9.53336	+	15.0758i	−0.510309	+	0.806989i	−0.997811	−	0.0661331i	$-0.978934\pi$
$349$	−9.53336	+	15.0758i	−0.510309	+	0.806989i	0.487502	+	0.873122i	$0.337908\pi$
$350$	23.8643	+	62.9250i	1.27560	+	3.36348i
$351$	−0.370684	−	3.58645i	−0.0197857	−	0.191430i
$352$	0.380666	−	1.00373i	0.0202895	−	0.0534991i
$353$	22.0449	+	29.3365i	1.17333	+	1.56142i	0.758707	+	0.651433i	$0.225832\pi$
$353$	22.0449	+	29.3365i	1.17333	+	1.56142i	0.414627	+	0.909991i	$0.363912\pi$
$354$	−5.19588	+	0.844412i	−0.276158	+	0.0448800i
$355$	55.2593	+	23.5438i	2.93286	+	1.24958i
$356$	−1.24897	+	0.862100i	−0.0661952	+	0.0456912i
$357$	−3.86719	−	2.23272i	−0.204673	−	0.118168i
$358$	0.0426147	−	0.0202209i	0.00225226	−	0.00106871i
$359$	−11.3825	−	1.38208i	−0.600745	−	0.0729436i	−0.185486	−	0.982647i	$-0.559386\pi$
$359$	−11.3825	−	1.38208i	−0.600745	−	0.0729436i	−0.415259	+	0.909703i	$0.636309\pi$
$360$	−2.51867	+	4.36247i	−0.132746	+	0.229922i
$361$	10.8989	+	18.8775i	0.573627	+	0.993551i
$362$	13.5911	+	31.8995i	0.714332	+	1.67660i
$363$	8.21270	−	7.27581i	0.431055	−	0.381881i
$364$	13.6457	−	7.55707i	0.715231	−	0.396098i
$365$	−9.69051	−	8.58505i	−0.507225	−	0.449362i
$366$	−8.46489	+	25.3554i	−0.442467	+	1.32535i
$367$	−0.627741	−	15.5772i	−0.0327678	−	0.813124i	−0.929119	−	0.369780i	$-0.879433\pi$
$367$	−0.627741	−	15.5772i	−0.0327678	−	0.813124i	0.896351	−	0.443344i	$-0.146208\pi$
$368$	8.62598	+	10.5649i	0.449660	+	0.550734i
$369$	3.42334	−	3.86415i	0.178212	−	0.201159i
$370$	−30.1040	+	6.14577i	−1.56503	+	0.319503i
$371$	−26.8249	−	7.76992i	−1.39268	−	0.403394i
$372$	7.53003	+	2.85576i	0.390414	+	0.148064i
$373$	−1.38901	+	34.4678i	−0.0719200	+	1.78468i	0.413607	+	0.910456i	$0.364269\pi$
$373$	−1.38901	+	34.4678i	−0.0719200	+	1.78468i	−0.485527	+	0.874222i	$0.661372\pi$
$374$	0.329640	−	0.247708i	0.0170453	−	0.0128087i
$375$	24.5444	+	5.01077i	1.26747	+	0.258755i
$376$	0.389404	+	0.204375i	0.0200820	+	0.0105398i
$377$	−1.88447	+	2.22580i	−0.0970552	+	0.114635i
$378$	−5.31100	+	2.78743i	−0.273169	+	0.143370i
$379$	−30.6484	+	8.87741i	−1.57430	+	0.456002i	−0.946589	−	0.322444i	$-0.895496\pi$
$379$	−30.6484	+	8.87741i	−1.57430	+	0.456002i	−0.627712	+	0.778445i	$0.716009\pi$
$380$	−33.6616	−	2.71745i	−1.72681	−	0.139402i
$381$	−3.07073	−	15.0414i	−0.157318	−	0.770597i
$382$	7.08336	−	13.4962i	0.362416	−	0.690527i
$383$	8.34721	−	11.1081i	0.426523	−	0.567599i	−0.534112	−	0.845414i	$-0.679354\pi$
$383$	8.34721	−	11.1081i	0.426523	−	0.567599i	0.960635	+	0.277815i	$0.0896103\pi$
$384$	−5.03225	−	7.95786i	−0.256801	−	0.406098i
$385$	1.82612	+	1.26048i	0.0930677	+	0.0642400i
$386$	−3.84425	−	8.10158i	−0.195667	−	0.412360i
$387$	−5.69905	−	5.93334i	−0.289699	−	0.301608i
$388$	−5.48729	+	5.27062i	−0.278575	+	0.267575i
$389$	−1.09255	+	8.99792i	−0.0553943	+	0.456213i	0.938449	+	0.345418i	$0.112263\pi$
$389$	−1.09255	+	8.99792i	−0.0553943	+	0.456213i	−0.993843	+	0.110795i	$0.964660\pi$
$390$	1.53514	−	26.3853i	0.0777347	−	1.33607i
$391$	0.454434	+	3.74260i	0.0229817	+	0.189272i
$392$	3.73959	+	3.05328i	0.188878	+	0.154214i
$393$	−0.894064	+	4.37941i	−0.0450996	+	0.220912i
$394$	4.01854	−	13.8736i	0.202451	−	0.698942i
$395$	−4.75977	+	19.3111i	−0.239490	+	0.971648i
$396$	−0.0176611	−	0.218772i	−0.000887503	−	0.0109937i
$397$	1.58195	−	9.73411i	0.0793956	−	0.488541i	−0.916650	−	0.399692i	$-0.869117\pi$
$397$	1.58195	−	9.73411i	0.0793956	−	0.488541i	0.996045	−	0.0888488i	$-0.0283188\pi$
$398$	−4.24469	−	4.79127i	−0.212767	−	0.240164i
$399$	16.8274	+	12.6450i	0.842424	+	0.633041i
$400$	−34.7860	+	42.6051i	−1.73930	+	2.13025i
$401$	2.11827	+	13.0342i	0.105781	+	0.650898i	0.984744	+	0.174008i	$0.0556719\pi$
$401$	2.11827	+	13.0342i	0.105781	+	0.650898i	−0.878963	+	0.476890i	$0.841764\pi$
$402$	10.0147	−	2.46841i	0.499489	−	0.123113i
$403$	22.0009	−	2.27395i	1.09594	−	0.113273i
$404$	−21.2984	−	5.24957i	−1.05963	−	0.261176i
$405$	−0.324072	+	4.01435i	−0.0161033	+	0.199475i
$406$	4.60193	+	1.53635i	0.228390	+	0.0762478i
$407$	−0.485431	+	0.505387i	−0.0240619	+	0.0250511i
$408$		−	1.69484i		−	0.0839071i
$409$	−20.2717	−	19.4713i	−1.00237	−	0.962793i	−0.00306574	−	0.999995i	$-0.500976\pi$
$409$	−20.2717	−	19.4713i	−1.00237	−	0.962793i	−0.999308	+	0.0372025i	$0.988155\pi$
$410$	29.3130	−	23.9333i	1.44767	−	1.18198i
$411$	−8.70336	−	16.5829i	−0.429305	−	0.817973i
$412$	−19.1149	−	3.10647i	−0.941722	−	0.153045i
$413$	8.05540	+	5.09393i	0.396380	+	0.250656i
$414$	4.57511	+	2.17092i	0.224854	+	0.106695i
$415$	−37.8596	−	54.8491i	−1.85846	−	2.69244i
$416$	19.8397	+	11.9313i	0.972721	+	0.584980i
$417$	−2.68778	+	3.89393i	−0.131621	+	0.190686i
$418$	−1.68325	+	0.971823i	−0.0823303	+	0.0475334i
$419$	14.0047	−	29.5143i	0.684175	−	1.44187i	−0.202410	−	0.979301i	$-0.564877\pi$
$419$	14.0047	−	29.5143i	0.684175	−	1.44187i	0.886584	−	0.462567i	$-0.153071\pi$
$420$	−16.5270	+	5.51751i	−0.806433	+	0.269227i
$421$	−2.63785	−	10.7022i	−0.128561	−	0.521593i	−0.999542	−	0.0302755i	$-0.990362\pi$
$421$	−2.63785	−	10.7022i	−0.128561	−	0.521593i	0.870980	−	0.491318i	$-0.163485\pi$
$422$	17.5351	+	0.706639i	0.853593	+	0.0343986i
$423$	0.351322	+	0.0141578i	0.0170819	+	0.000688375i
$424$	−2.53669	−	10.2918i	−0.123193	−	0.499812i
$425$	−14.4212	+	4.81451i	−0.699531	+	0.233538i
$426$	−11.6371	+	24.5247i	−0.563821	+	1.18823i
$427$	41.9142	−	24.1992i	2.02837	−	1.17108i
$428$	−1.76111	+	2.55141i	−0.0851266	+	0.123327i
$429$	−0.313036	−	0.515145i	−0.0151135	−	0.0248715i
$430$	−34.2581	−	49.6315i	−1.65207	−	2.39344i
$431$	8.44018	+	4.00492i	0.406549	+	0.192910i	0.620975	−	0.783830i	$-0.286737\pi$
$431$	8.44018	+	4.00492i	0.406549	+	0.192910i	−0.214426	+	0.976740i	$0.568788\pi$
$432$	−4.14325	−	2.62003i	−0.199342	−	0.126056i
$433$	−28.3964	−	4.61486i	−1.36464	−	0.221776i	−0.566410	−	0.824124i	$-0.691668\pi$
$433$	−28.3964	−	4.61486i	−1.36464	−	0.221776i	−0.798234	+	0.602348i	$0.794232\pi$
$434$	−17.0994	−	32.5801i	−0.820795	−	1.56390i
$435$	2.52338	−	2.06028i	0.120987	−	0.0987826i
$436$	12.6982	+	12.1968i	0.608132	+	0.584119i
$437$		−	17.7712i		−	0.850113i
$438$	4.05305	−	4.21967i	0.193662	−	0.201624i
$439$	29.3909	+	9.81213i	1.40275	+	0.468307i	0.914567	−	0.404433i	$-0.132531\pi$
$439$	29.3909	+	9.81213i	1.40275	+	0.468307i	0.488184	+	0.872741i	$0.337659\pi$
$440$	−0.0677669	+	0.839444i	−0.00323066	+	0.0400189i
$441$	3.74767	+	0.923717i	0.178460	+	0.0439865i
$442$	3.99143	+	7.94637i	0.189853	+	0.377970i
$443$	−33.9087	+	8.35775i	−1.61105	+	0.397089i	−0.939138	−	0.343540i	$-0.888374\pi$
$443$	−33.9087	+	8.35775i	−1.61105	+	0.397089i	−0.671914	+	0.740629i	$0.734528\pi$
$444$	−0.882679	−	5.43134i	−0.0418901	−	0.257760i
$445$	2.94447	−	3.60632i	0.139581	−	0.170956i
$446$	28.9891	+	21.7839i	1.37268	+	1.03150i
$447$	11.0015	+	12.4182i	0.520354	+	0.587359i
$448$	0.995145	−	6.12337i	0.0470162	−	0.289302i
$449$	0.298206	+	3.69395i	0.0140732	+	0.174328i	0.999975	+	0.00700574i	$0.00223001\pi$
$449$	0.298206	+	3.69395i	0.0140732	+	0.174328i	−0.985902	+	0.167322i	$0.946488\pi$
$450$	−4.88724	+	19.8283i	−0.230387	+	0.934716i
$451$	0.240127	−	0.829014i	0.0113071	−	0.0390367i
$452$	1.69695	−	8.31222i	0.0798179	−	0.390974i
$453$	−12.4421	−	10.1586i	−0.584579	−	0.477294i
$454$	3.62648	+	29.8668i	0.170199	+	1.40172i
$455$	−33.7593	+	33.9149i	−1.58266	+	1.58995i
$456$	−0.962972	+	7.93078i	−0.0450953	+	0.371393i
$457$	6.52403	−	6.26641i	0.305181	−	0.293131i	−0.524451	−	0.851440i	$-0.675729\pi$
$457$	6.52403	−	6.26641i	0.305181	−	0.293131i	0.829632	+	0.558310i	$0.188550\pi$
$458$	−27.9383	−	29.0868i	−1.30547	−	1.35914i
$459$	−0.580897	−	1.22421i	−0.0271139	−	0.0571414i
$460$	12.1065	+	8.35649i	0.564467	+	0.389624i
$461$	9.92152	+	15.6896i	0.462091	+	0.730739i	0.993182	−	0.116576i	$-0.0371919\pi$
$461$	9.92152	+	15.6896i	0.462091	+	0.730739i	−0.531090	+	0.847315i	$0.678218\pi$
$462$	−0.602419	+	0.801674i	−0.0280271	+	0.0372972i
$463$	11.0049	−	20.9681i	0.511442	−	0.974472i	−0.483625	−	0.875275i	$-0.660680\pi$
$463$	11.0049	−	20.9681i	0.511442	−	0.974472i	0.995068	−	0.0991970i	$-0.0316274\pi$
$464$	0.793138	+	3.88505i	0.0368205	+	0.180359i
$465$	−24.6258	−	1.98800i	−1.14200	−	0.0921915i
$466$	−38.9301	+	11.2762i	−1.80340	+	0.522362i
$467$	36.2734	−	19.0378i	1.67853	−	0.880962i	0.691131	−	0.722729i	$-0.257113\pi$
$467$	36.2734	−	19.0378i	1.67853	−	0.880962i	0.987402	−	0.158233i	$-0.0505797\pi$
$468$	4.71051	+	0.464981i	0.217743	+	0.0214938i
$469$	−16.5358	−	8.67868i	−0.763554	−	0.400744i
$470$	2.52531	+	0.515546i	0.116484	+	0.0237804i
$471$	16.9214	−	12.7156i	0.779695	−	0.585903i
$472$	−0.145658	+	3.61447i	−0.00670446	+	0.166369i
$473$	−1.28606	−	0.487739i	−0.0591332	−	0.0224262i
$474$	−8.63361	−	2.50075i	−0.396555	−	0.114863i
$475$	70.2176	−	14.3350i	3.22181	−	0.657736i
$476$	3.88741	−	4.38797i	0.178179	−	0.201123i
$477$	−5.35974	−	6.56449i	−0.245406	−	0.300567i
$478$	1.38700	+	34.4181i	0.0634400	+	1.57425i
$479$	1.39909	−	4.19080i	0.0639262	−	0.191482i	−0.911729	−	0.410792i	$-0.865252\pi$
$479$	1.39909	−	4.19080i	0.0639262	−	0.191482i	0.975655	+	0.219310i	$0.0703805\pi$
$480$	−19.3563	−	17.1482i	−0.883490	−	0.782704i
$481$	−8.86179	−	12.2416i	−0.404063	−	0.558171i
$482$	18.1015	−	16.0366i	0.824503	−	0.730446i
$483$	−3.59385	−	8.43507i	−0.163526	−	0.383809i
$484$	7.20210	+	12.4744i	0.327368	+	0.567018i
$485$	11.6707	−	20.2142i	0.529937	−	0.917879i
$486$	−1.80684	−	0.219390i	−0.0819600	−	0.00995175i
$487$	−22.1804	+	10.5247i	−1.00509	+	0.476922i	−0.858795	−	0.512319i	$-0.828787\pi$
$487$	−22.1804	+	10.5247i	−1.00509	+	0.476922i	−0.146296	+	0.989241i	$0.546735\pi$
$488$	15.9084	+	9.18470i	0.720138	+	0.415772i
$489$	−8.07412	+	5.57316i	−0.365124	+	0.252027i
$490$	26.0298	+	11.0902i	1.17590	+	0.501006i
$491$	17.7351	−	2.88224i	0.800375	−	0.130074i	0.253552	−	0.967322i	$-0.418401\pi$
$491$	17.7351	−	2.88224i	0.800375	−	0.130074i	0.546823	+	0.837248i	$0.315837\pi$
$492$	4.07141	+	5.41807i	0.183554	+	0.244265i
$493$	−0.388664	+	1.02482i	−0.0175045	+	0.0461557i
$494$	−14.1624	−	39.4518i	−0.637197	−	1.77502i
$495$	0.238765	+	0.629572i	0.0107317	+	0.0282972i
$496$	16.0725	−	25.4166i	0.721675	−	1.14124i
$497$	45.2159	−	19.2647i	2.02821	−	0.864140i
$498$	25.4569	−	16.0979i	1.14075	−	0.721366i
$499$	20.6688	−	2.50964i	0.925261	−	0.112347i	0.355983	−	0.934492i	$-0.384146\pi$
$499$	20.6688	−	2.50964i	0.925261	−	0.112347i	0.569278	+	0.822145i	$0.307223\pi$
$500$	−12.8905	+	30.2551i	−0.576480	+	1.35305i
$501$	1.74783	+	5.23539i	0.0780874	+	0.233900i
$502$	0.863960	−	0.327657i	0.0385604	−	0.0146240i
$503$	36.3690	−	2.93601i	1.62161	−	0.130910i	0.764004	−	0.645212i	$-0.223231\pi$
$503$	36.3690	−	2.93601i	1.62161	−	0.130910i	0.857609	+	0.514302i	$0.171949\pi$
$504$	1.14676	+	3.95907i	0.0510806	+	0.176351i
$505$	67.2396	−	2.70966i	2.99212	−	0.120578i
$506$	0.846638			0.0376376
$507$	12.1339	−	4.66571i	0.538885	−	0.207211i
$508$	20.1538			0.894182
$509$	0.0473149	−	0.00190672i	0.00209719	−	8.45141e-5i	−0.0392173	−	0.999231i	$-0.512486\pi$
$509$	0.0473149	−	0.00190672i	0.00209719	−	8.45141e-5i	0.0413145	+	0.999146i	$0.486845\pi$
$510$	−2.76351	−	9.54076i	−0.122370	−	0.422472i
$511$	−10.5590	+	0.852412i	−0.467104	+	0.0377085i
$512$	17.9649	−	6.81320i	0.793946	−	0.301104i
$513$	2.02266	+	6.05860i	0.0893026	+	0.267494i
$514$	−1.17594	+	2.76003i	−0.0518685	+	0.121740i
$515$	58.9764	−	7.16103i	2.59881	−	0.315553i
$516$	9.12846	−	5.77249i	0.401858	−	0.254120i
$517$	0.0540799	−	0.0230413i	0.00237843	−	0.00101336i
$518$	−13.4368	+	21.2486i	−0.590379	+	0.933610i
$519$	0.674462	+	1.77841i	0.0296056	+	0.0780635i
$520$	−17.5543	−	4.66043i	−0.769807	−	0.204373i
$521$	−11.3833	+	30.0152i	−0.498710	+	1.31499i	0.415443	+	0.909619i	$0.363627\pi$
$521$	−11.3833	+	30.0152i	−0.498710	+	1.31499i	−0.914153	+	0.405370i	$0.867143\pi$
$522$	0.884428	+	1.17696i	0.0387104	+	0.0515142i
$523$	−3.01497	+	0.489980i	−0.131835	+	0.0214253i	−0.225971	−	0.974134i	$-0.572555\pi$
$523$	−3.01497	+	0.489980i	−0.131835	+	0.0214253i	0.0941355	+	0.995559i	$0.469991\pi$
$524$	−5.39837	−	2.30003i	−0.235829	−	0.100477i
$525$	30.4297	−	21.0041i	1.32806	−	0.916693i
$526$	2.17669	+	1.25671i	0.0949084	+	0.0547954i
$527$	7.50988	−	3.56348i	0.327136	−	0.155228i
$528$	−0.813597	−	0.0987885i	−0.0354072	−	0.00429922i
$529$	7.62949	−	13.2147i	0.331717	−	0.574551i
$530$	−31.0610	−	53.7992i	−1.34920	−	2.33689i
$531$	1.13363	+	2.66072i	0.0491952	+	0.115465i
$532$	−20.6838	+	18.3242i	−0.896755	+	0.794455i
$533$	16.6713	+	8.27816i	0.722115	+	0.358567i
$534$	1.57491	+	1.39525i	0.0681529	+	0.0603782i
$535$	3.01174	−	9.02128i	0.130209	−	0.390024i
$536$	−0.285405	−	7.08225i	−0.0123276	−	0.305907i
$537$	−0.0163901	−	0.0200742i	−0.000707283	−	0.000866264i
$538$	5.33903	−	6.02652i	0.230182	−	0.259822i
$539$	0.632269	−	0.129079i	0.0272338	−	0.00555981i
$540$	−5.07847	−	1.47100i	−0.218543	−	0.0633016i
$541$	26.0458	+	9.87786i	1.11980	+	0.424683i	0.843898	−	0.536504i	$-0.180255\pi$
$541$	26.0458	+	9.87786i	1.11980	+	0.424683i	0.275898	+	0.961187i	$0.411025\pi$
$542$	2.22331	−	55.1709i	0.0954993	−	2.36979i
$543$	15.2298	−	11.4445i	0.653574	−	0.491129i
$544$	8.52481	+	1.74035i	0.365498	+	0.0746170i
$545$	−47.8273	−	25.1017i	−2.04869	−	1.07524i
$546$	−14.7004	−	15.8617i	−0.629120	−	0.678816i
$547$	−26.1274	+	13.7127i	−1.11713	+	0.586314i	−0.919156	−	0.393894i	$-0.871128\pi$
$547$	−26.1274	+	13.7127i	−1.11713	+	0.586314i	−0.197972	+	0.980208i	$0.563435\pi$
$548$	23.6156	−	6.84036i	1.00881	−	0.292206i
$549$	14.6389	+	1.18177i	0.624773	+	0.0504369i
$550$	0.682934	+	3.34523i	0.0291204	+	0.142641i
$551$	2.40098	−	4.57469i	0.102285	−	0.194888i
$552$	2.09056	−	2.78203i	0.0889802	−	0.118411i
$553$	8.69801	+	13.7548i	0.369877	+	0.584914i
$554$	1.63526	+	1.12874i	0.0694755	+	0.0479555i
$555$	7.23666	+	15.2509i	0.307179	+	0.647366i
$556$	−4.30287	−	4.47976i	−0.182482	−	0.189984i
$557$	2.95238	−	2.83580i	0.125096	−	0.120157i	−0.627566	−	0.778563i	$-0.715949\pi$
$557$	2.95238	−	2.83580i	0.125096	−	0.120157i	0.752662	+	0.658407i	$0.228769\pi$
$558$	1.34584	−	11.0840i	0.0569739	−	0.469222i
$559$	15.2873	−	25.4202i	0.646585	−	1.07516i
$560$	7.84230	+	64.5871i	0.331398	+	2.72930i
$561$	−0.175483	−	0.143277i	−0.00740888	−	0.00604916i
$562$	7.60457	−	37.2496i	0.320779	−	1.57128i
$563$	12.7177	−	43.9067i	0.535988	−	1.85045i	0.0100051	−	0.999950i	$-0.496815\pi$
$563$	12.7177	−	43.9067i	0.535988	−	1.85045i	0.525983	−	0.850495i	$-0.323698\pi$
$564$	−0.110466	+	0.448180i	−0.00465147	+	0.0188718i
$565$	2.09423	+	25.9416i	0.0881048	+	1.09137i
$566$	3.13525	−	19.2920i	0.131784	−	0.810902i
$567$	2.18527	+	2.46666i	0.0917728	+	0.103590i
$568$	14.9130	+	11.2064i	0.625735	+	0.470209i
$569$	2.13481	−	2.61467i	0.0894959	−	0.109613i	−0.727916	−	0.685667i	$-0.759511\pi$
$569$	2.13481	−	2.61467i	0.0894959	−	0.109613i	0.817412	+	0.576054i	$0.195408\pi$
$570$	7.51065	+	46.2149i	0.314587	+	1.93573i
$571$	16.3328	−	4.02567i	0.683506	−	0.168469i	0.117752	−	0.993043i	$-0.462431\pi$
$571$	16.3328	−	4.02567i	0.683506	−	0.168469i	0.565754	+	0.824574i	$0.308585\pi$
$572$	0.744822	−	0.267376i	0.0311426	−	0.0111796i
$573$	−8.13093	−	2.00409i	−0.339674	−	0.0837222i
$574$	2.49161	−	30.8642i	0.103998	−	1.28825i
$575$	−29.6106	−	9.88547i	−1.23485	−	0.412253i
$576$	1.30407	−	1.35768i	0.0543362	−	0.0565699i
$577$		−	11.8200i		−	0.492072i	−0.969261	−	0.246036i	$-0.920872\pi$
$577$		−	11.8200i		−	0.492072i	0.969261	−	0.246036i	$-0.0791282\pi$
$578$	−19.9051	−	19.1191i	−0.827944	−	0.795251i
$579$	−3.81635	+	3.11595i	−0.158602	+	0.129494i
$580$	1.98746	+	3.78679i	0.0825247	+	0.157238i
$581$	−53.8274	−	8.74780i	−2.23314	−	0.362920i
$582$	8.91563	+	5.63790i	0.369565	+	0.233699i
$583$	−1.28005	−	0.607390i	−0.0530141	−	0.0251555i
$584$	−2.28400	−	3.30895i	−0.0945127	−	0.136925i
$585$	−14.2771	+	2.65032i	−0.590286	+	0.109577i
$586$	−27.0423	+	39.1775i	−1.11711	+	1.61841i
$587$	3.53034	−	2.03824i	0.145713	−	0.0841273i	−0.425371	−	0.905019i	$-0.639856\pi$
$587$	3.53034	−	2.03824i	0.145713	−	0.0841273i	0.571084	+	0.820892i	$0.306523\pi$
$588$	−2.17228	+	4.57798i	−0.0895832	+	0.188793i
$589$	−37.1662	+	12.4079i	−1.53141	+	0.511259i
$590$	5.07360	+	20.5844i	0.208877	+	0.847447i
$591$	−7.92927	−	0.319539i	−0.326167	−	0.0131441i
$592$	−20.5305	−	0.827353i	−0.843800	−	0.0340040i
$593$	10.1738	+	41.2768i	0.417788	+	1.69503i	0.682648	+	0.730747i	$0.260828\pi$
$593$	10.1738	+	41.2768i	0.417788	+	1.69503i	−0.264860	+	0.964287i	$0.585326\pi$
$594$	−0.288638	+	0.0963614i	−0.0118429	+	0.00395375i
$595$	−7.70968	+	16.2478i	−0.316066	+	0.666095i
$596$	−18.8621	+	10.8901i	−0.772624	+	0.446075i
$597$	−1.99780	+	2.89431i	−0.0817645	+	0.118456i
$598$	−3.24991	+	17.9671i	−0.132899	+	0.734729i
$599$	4.11798	+	5.96593i	0.168256	+	0.243761i	0.898037	−	0.439920i	$-0.144993\pi$
$599$	4.11798	+	5.96593i	0.168256	+	0.243761i	−0.729781	+	0.683681i	$0.760378\pi$
$600$	12.6787	+	6.01611i	0.517605	+	0.245607i
$601$	18.5774	+	11.7476i	0.757787	+	0.479195i	0.856645	−	0.515906i	$-0.172545\pi$
$601$	18.5774	+	11.7476i	0.757787	+	0.479195i	−0.0988583	+	0.995102i	$0.531519\pi$
$602$	−48.7069	−	7.91565i	−1.98515	−	0.322618i
$603$	−2.63355	−	5.01782i	−0.107247	−	0.204341i
$604$	16.3340	−	13.3363i	0.664623	−	0.542648i
$605$	−31.8692	−	30.6108i	−1.29567	−	1.24450i
$606$			30.4123i			1.23542i
$607$	−20.9658	+	21.8277i	−0.850974	+	0.885957i	−0.994611	−	0.103673i	$-0.966940\pi$
$607$	−20.9658	+	21.8277i	−0.850974	+	0.885957i	0.143638	+	0.989630i	$0.454120\pi$
$608$	−38.9019	−	12.9874i	−1.57768	−	0.526707i
$609$	0.214488	−	2.65691i	0.00869150	−	0.107664i
$610$	104.529	+	25.7641i	4.23225	+	1.04316i
$611$	0.281384	+	1.23612i	0.0113836	+	0.0500079i
$612$	1.72722	−	0.425722i	0.0698188	−	0.0172088i
$613$	−1.86468	−	11.4738i	−0.0753138	−	0.463424i	−0.997124	−	0.0757835i	$-0.975854\pi$
$613$	−1.86468	−	11.4738i	−0.0753138	−	0.463424i	0.921811	−	0.387641i	$-0.126710\pi$
$614$	−21.2330	+	26.0058i	−0.856896	+	1.04951i
$615$	−16.6215	−	12.4902i	−0.670242	−	0.503654i
$616$	0.456964	+	0.515805i	0.0184116	+	0.0207824i
$617$	−0.766957	+	4.71928i	−0.0308765	+	0.189991i	−0.997907	−	0.0646712i	$-0.979400\pi$
$617$	−0.766957	+	4.71928i	−0.0308765	+	0.189991i	0.967030	+	0.254662i	$0.0819643\pi$
$618$	2.16045	+	26.7620i	0.0869060	+	1.07652i
$619$	−4.98635	+	20.2304i	−0.200418	+	0.813130i	0.781512	+	0.623890i	$0.214449\pi$
$619$	−4.98635	+	20.2304i	−0.200418	+	0.813130i	−0.981931	+	0.189240i	$0.939398\pi$
$620$	9.02376	−	31.1536i	0.362403	−	1.25116i
$621$	0.556525	−	2.72604i	0.0223326	−	0.109392i
$622$	−23.5292	−	19.2110i	−0.943433	−	0.770289i
$623$	−0.459187	−	3.78174i	−0.0183969	−	0.151512i
$624$	5.21954	−	16.8867i	0.208949	−	0.676009i
$625$	5.39873	−	44.4625i	0.215949	−	1.77850i
$626$	−4.05127	+	3.89130i	−0.161921	+	0.155528i
$627$	0.739741	+	0.770152i	0.0295424	+	0.0307569i
$628$	11.9123	+	25.1046i	0.475352	+	1.00178i
$629$	−4.67424	−	3.22639i	−0.186374	−	0.128645i
$630$	12.9109	+	20.4169i	0.514381	+	0.813429i
$631$	5.97850	−	7.95594i	0.238000	−	0.316721i	−0.664601	−	0.747199i	$-0.731398\pi$
$631$	5.97850	−	7.95594i	0.238000	−	0.316721i	0.902601	+	0.430477i	$0.141655\pi$
$632$	−2.87051	+	5.46929i	−0.114183	+	0.217557i
$633$	−1.92862	−	9.44701i	−0.0766558	−	0.375485i
$634$	−9.31979	−	0.752371i	−0.370136	−	0.0298805i
$635$	−59.3865	+	17.2015i	−2.35668	+	0.682621i
$636$	9.85121	−	5.17031i	0.390626	−	0.205016i
$637$	0.312234	+	13.9133i	0.0123712	+	0.551265i
$638$	0.217943	+	0.114385i	0.00862843	+	0.00452855i
$639$	14.6128	+	2.98323i	0.578075	+	0.118015i
$640$	−30.3148	+	22.7801i	−1.19830	+	0.900464i
$641$	−1.08696	+	26.9727i	−0.0429324	+	1.06536i	0.823893	+	0.566745i	$0.191797\pi$
$641$	−1.08696	+	26.9727i	−0.0429324	+	1.06536i	−0.866826	+	0.498611i	$0.833844\pi$
$642$	4.01888	+	1.52416i	0.158613	+	0.0601538i
$643$	−23.2743	−	6.74149i	−0.917850	−	0.265858i	−0.214518	−	0.976720i	$-0.568818\pi$
$643$	−23.2743	−	6.74149i	−0.917850	−	0.265858i	−0.703332	+	0.710862i	$0.748305\pi$
$644$	11.7936	−	2.40767i	0.464732	−	0.0948756i
$645$	−21.9716	+	24.8008i	−0.865131	+	0.976531i
$646$	−9.96306	−	12.2025i	−0.391991	−	0.480102i
$647$	1.52636	+	37.8762i	0.0600074	+	1.48907i	0.696373	+	0.717680i	$0.254796\pi$
$647$	1.52636	+	37.8762i	0.0600074	+	1.48907i	−0.636365	+	0.771388i	$0.719563\pi$
$648$	−0.396077	+	1.18640i	−0.0155594	+	0.0466060i
$649$	0.361926	+	0.320639i	0.0142068	+	0.0125862i
$650$	−73.6131	+	1.65198i	−2.88734	+	0.0647961i
$651$	−15.1316	+	13.4054i	−0.593055	+	0.525401i
$652$	−5.04841	−	11.8491i	−0.197711	−	0.464045i
$653$	15.7966	+	27.3605i	0.618168	+	1.07070i	0.989820	+	0.142326i	$0.0454582\pi$
$653$	15.7966	+	27.3605i	0.618168	+	1.07070i	−0.371652	+	0.928372i	$0.621209\pi$
$654$	12.2054	−	21.1403i	0.477267	−	0.826651i
$655$	17.8702	+	2.16984i	0.698248	+	0.0847827i
$656$	22.8637	−	10.8490i	0.892678	−	0.423581i
$657$	−2.78390	−	1.60728i	−0.108610	−	0.0627062i
$658$	1.73564	−	1.19802i	0.0676621	−	0.0467038i
$659$	−9.23467	−	3.93452i	−0.359732	−	0.153267i	0.204536	−	0.978859i	$-0.434431\pi$
$659$	−9.23467	−	3.93452i	−0.359732	−	0.153267i	−0.564268	+	0.825592i	$0.690842\pi$
$660$	−0.872504	+	0.141796i	−0.0339622	+	0.00551939i
$661$	6.97482	+	9.28180i	0.271289	+	0.361020i	0.914442	−	0.404718i	$-0.132630\pi$
$661$	6.97482	+	9.28180i	0.271289	+	0.361020i	−0.643152	+	0.765738i	$0.722374\pi$
$662$	−9.13471	+	24.0863i	−0.355031	+	0.936139i
$663$	3.71419	−	3.17405i	0.144247	−	0.123270i
$664$	−7.33961	−	19.3530i	−0.284832	−	0.751040i
$665$	45.3081	−	71.6490i	1.75697	−	2.77843i
$666$	−7.01847	+	2.99029i	−0.271960	+	0.115871i
$667$	−1.90208	+	1.20280i	−0.0736490	+	0.0465728i
$668$	−7.19314	+	0.873406i	−0.278311	+	0.0337931i
$669$	7.80906	−	18.3285i	0.301916	−	0.708622i
$670$	−13.1546	−	39.4027i	−0.508205	−	1.52226i
$671$	2.29582	−	0.870692i	0.0886293	−	0.0336127i
$672$	−21.0911	+	1.70265i	−0.813607	+	0.0656811i
$673$	−2.23108	−	7.70257i	−0.0860017	−	0.296912i	0.905975	−	0.423330i	$-0.139139\pi$
$673$	−2.23108	−	7.70257i	−0.0860017	−	0.296912i	−0.991977	+	0.126418i	$0.959652\pi$
$674$	−39.6511	+	1.59788i	−1.52730	+	0.0615482i
$675$	11.2200			0.431859
$676$	2.81510	+	16.8327i	0.108273	+	0.647413i
$677$	35.0813			1.34828			0.674141	−	0.738603i	$-0.264514\pi$
$677$	35.0813			1.34828			0.674141	+	0.738603i	$0.264514\pi$
$678$	−11.7524	+	0.473607i	−0.451350	+	0.0181888i
$679$	−5.31368	−	18.3450i	−0.203920	−	0.704015i
$680$	−6.80369	+	0.549250i	−0.260909	+	0.0210628i
$681$	15.4557	−	5.86156i	0.592262	−	0.224615i
$682$	−0.591124	−	1.77063i	−0.0226353	−	0.0678011i
$683$	−16.9282	+	39.7320i	−0.647740	+	1.52030i	0.194332	+	0.980936i	$0.437746\pi$
$683$	−16.9282	+	39.7320i	−0.647740	+	1.52030i	−0.842072	+	0.539366i	$0.818664\pi$
$684$	−8.32419	+	1.01074i	−0.318283	+	0.0386466i
$685$	−63.7490	+	40.3124i	−2.43572	+	1.54026i
$686$	−17.3277	+	7.38265i	−0.661575	+	0.281871i
$687$	−11.8430	+	18.7282i	−0.451838	+	0.714524i
$688$	−14.3012	−	37.7092i	−0.545229	−	1.43765i
$689$	17.8034	−	24.8332i	0.678257	−	0.946071i
$690$	7.23216	−	19.0696i	0.275323	−	0.725968i
$691$	−15.9401	−	21.2124i	−0.606390	−	0.806959i	0.386959	−	0.922097i	$-0.373525\pi$
$691$	−15.9401	−	21.2124i	−0.606390	−	0.806959i	−0.993349	+	0.115138i	$0.963269\pi$
$692$	−2.46464	+	0.400543i	−0.0936915	+	0.0152264i
$693$	0.506863	+	0.215954i	0.0192541	+	0.00820341i
$694$	25.3594	−	17.5043i	0.962629	−	0.664455i
$695$	16.5026	+	9.52779i	0.625980	+	0.361410i
$696$	0.914021	−	0.433709i	0.0346459	−	0.0164397i
$697$	6.94433	+	0.843195i	0.263035	+	0.0319383i
$698$	−16.2328	+	28.1161i	−0.614421	+	1.06421i
$699$	11.1340	+	19.2847i	0.421127	+	0.729413i
$700$	19.0264	+	44.6566i	0.719130	+	1.68786i
$701$	−19.7138	+	17.4649i	−0.744580	+	0.659640i	−0.947573	−	0.319540i	$-0.896472\pi$
$701$	−19.7138	+	17.4649i	−0.744580	+	0.659640i	0.202993	+	0.979180i	$0.434933\pi$
$702$	−0.936985	−	6.49527i	−0.0353642	−	0.245148i
$703$	20.0393	+	17.7533i	0.755797	+	0.669578i
$704$	0.0996654	−	0.298534i	0.00375628	−	0.0112514i
$705$	−0.0570192	−	1.41492i	−0.00214747	−	0.0532889i
$706$	42.2418	+	51.7368i	1.58979	+	1.94714i
$707$	36.5138	−	41.2155i	1.37324	−	1.55007i
$708$	−3.72011	+	0.759466i	−0.139810	+	0.0285425i
$709$	13.0847	+	3.79003i	0.491406	+	0.142338i	0.514664	−	0.857392i	$-0.327917\pi$
$709$	13.0847	+	3.79003i	0.491406	+	0.142338i	−0.0232578	+	0.999730i	$0.507404\pi$
$710$	102.222	+	38.7677i	3.83633	+	1.45493i
$711$	−0.198850	+	4.93442i	−0.00745747	+	0.185055i
$712$	1.15590	−	0.868605i	0.0433193	−	0.0325524i
$713$	16.7228	+	3.41398i	0.626272	+	0.127854i
$714$	−7.19664	−	3.77709i	−0.269327	−	0.141354i
$715$	−1.96653	+	1.42358i	−0.0735440	+	0.0532389i
$716$	0.0301249	−	0.0158108i	0.00112582	−	0.000590876i
$717$	18.1780	−	5.26533i	0.678871	−	0.196637i
$718$	−20.8019	−	1.67930i	−0.776320	−	0.0626710i
$719$	3.33111	+	16.3169i	0.124230	+	0.608517i	0.993467	+	0.114122i	$0.0364053\pi$
$719$	3.33111	+	16.3169i	0.124230	+	0.608517i	−0.869237	+	0.494395i	$0.835390\pi$
$720$	−9.17502	+	17.4815i	−0.341933	+	0.651498i
$721$	29.2032	−	38.8624i	1.08758	−	1.44731i
$722$	21.2047	+	33.5325i	0.789156	+	1.24795i
$723$	−10.9348	−	7.54775i	−0.406670	−	0.280704i
$724$	10.7215	+	22.5950i	0.398460	+	0.839738i
$725$	−6.28682	−	6.54527i	−0.233487	−	0.243085i
$726$	14.4027	−	13.8340i	0.534533	−	0.513426i
$727$	1.87645	−	15.4540i	0.0695937	−	0.573156i	−0.915647	−	0.401983i	$-0.868321\pi$
$727$	1.87645	−	15.4540i	0.0695937	−	0.573156i	0.985241	−	0.171173i	$-0.0547557\pi$
$728$	−12.7004	+	7.71757i	−0.470707	+	0.286032i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−18.2527	−	14.9029i	−0.675563	−	0.551580i
$731$	2.22988	−	10.9227i	0.0824750	−	0.403989i
$732$	−5.36420	+	18.5194i	−0.198267	+	0.684495i
$733$	−5.83757	+	23.6839i	−0.215615	+	0.874786i	0.759034	+	0.651050i	$0.225671\pi$
$733$	−5.83757	+	23.6839i	−0.215615	+	0.874786i	−0.974650	+	0.223736i	$0.928175\pi$
$734$	−2.28326	−	28.2833i	−0.0842768	−	1.04396i
$735$	2.49361	−	15.3438i	0.0919782	−	0.565965i
$736$	11.8465	+	13.3720i	0.436669	+	0.492897i
$737$	−0.757418	−	0.569163i	−0.0278999	−	0.0209654i
$738$	5.94260	−	7.27837i	0.218750	−	0.267920i
$739$	−5.36998	−	33.0428i	−0.197538	−	1.21550i	−0.876527	−	0.481352i	$-0.840146\pi$
$739$	−5.36998	−	33.0428i	−0.197538	−	1.21550i	0.678989	−	0.734148i	$-0.262418\pi$
$740$	−21.5173	+	5.30353i	−0.790990	+	0.194962i
$741$	−19.1835	+	12.7422i	−0.704724	+	0.468098i
$742$	−49.3542	−	12.1647i	−1.81185	−	0.446580i
$743$	−1.47992	+	18.3320i	−0.0542928	+	0.672538i	0.911176	+	0.412018i	$0.135176\pi$
$743$	−1.47992	+	18.3320i	−0.0542928	+	0.672538i	−0.965469	+	0.260520i	$0.916106\pi$
$744$	−7.27789	−	2.42972i	−0.266820	−	0.0890778i
$745$	46.2856	−	48.1884i	1.69577	−	1.76549i
$746$			62.7863i			2.29877i
$747$	−11.9346	−	11.4634i	−0.436666	−	0.419423i
$748$	0.230375	−	0.188095i	0.00842335	−	0.00687745i
$749$	−3.61654	−	6.89075i	−0.132146	−	0.251783i
$750$	45.0046	+	7.31395i	1.64333	+	0.267068i
$751$	−21.3259	−	13.4857i	−0.778195	−	0.492101i	0.0853632	−	0.996350i	$-0.472795\pi$
$751$	−21.3259	−	13.4857i	−0.778195	−	0.492101i	−0.863558	+	0.504249i	$0.831769\pi$
$752$	1.55721	+	0.738908i	0.0567858	+	0.0269452i
$753$	−0.288386	−	0.417799i	−0.0105094	−	0.0152255i
$754$	−3.26404	+	4.18603i	−0.118869	+	0.152446i
$755$	−36.7482	+	53.2389i	−1.33740	+	1.93756i
$756$	−3.74665	+	2.16313i	−0.136264	+	0.0786723i
$757$	−16.1277	+	33.9885i	−0.586172	+	1.23533i	0.366241	+	0.930520i	$0.380645\pi$
$757$	−16.1277	+	33.9885i	−0.586172	+	1.23533i	−0.952413	+	0.304811i	$0.901407\pi$
$758$	−55.0876	+	18.3910i	−2.00087	+	0.667989i
$759$	−0.111319	−	0.451640i	−0.00404064	−	0.0163935i
$760$	32.1490	+	1.29556i	1.16617	+	0.0469950i
$761$	9.22727	+	0.371846i	0.334488	+	0.0134794i	0.206942	−	0.978353i	$-0.433649\pi$
$761$	9.22727	+	0.371846i	0.334488	+	0.0134794i	0.127546	+	0.991833i	$0.459290\pi$
$762$	−6.68691	−	27.1299i	−0.242241	−	0.982812i
$763$	−41.9226	+	13.9958i	−1.51770	+	0.506682i
$764$	4.71297	−	9.93237i	0.170509	−	0.359340i
$765$	−4.72617	+	2.72866i	−0.170875	+	0.0986548i
$766$	14.3664	−	20.8134i	0.519081	−	0.752018i
$767$	−8.19379	+	6.44988i	−0.295861	+	0.232892i
$768$	−11.8738	−	17.2022i	−0.428460	−	0.620732i
$769$	−15.4850	−	7.34772i	−0.558403	−	0.264966i	0.128506	−	0.991709i	$-0.458982\pi$
$769$	−15.4850	−	7.34772i	−0.558403	−	0.264966i	−0.686909	+	0.726743i	$0.741033\pi$
$770$	3.41343	+	2.15852i	0.123011	+	0.0777877i
$771$	1.62696	+	0.264407i	0.0585936	+	0.00952239i
$772$	−3.00582	−	5.72712i	−0.108182	−	0.206123i
$773$	14.2849	−	11.6632i	0.513790	−	0.419497i	−0.339756	−	0.940514i	$-0.610345\pi$
$773$	14.2849	−	11.6632i	0.513790	−	0.419497i	0.853547	+	0.521017i	$0.174447\pi$
$774$	−10.7993	−	10.3729i	−0.388174	−	0.372846i
$775$			68.8288i			2.47240i
$776$	5.02153	−	5.22796i	0.180262	−	0.187673i
$777$	13.1018	+	4.37403i	0.470025	+	0.156917i
$778$	−1.32750	+	16.4440i	−0.0475931	+	0.589547i
$779$	−32.0160	−	7.89124i	−1.14709	−	0.282733i
$780$	0.340056	−	19.0603i	0.0121760	−	0.682469i
$781$	2.42100	−	0.596724i	0.0866303	−	0.0213525i
$782$	1.10074	+	6.77313i	0.0393624	+	0.242207i
$783$	0.511563	−	0.626551i	0.0182818	−	0.0223911i
$784$	15.1266	+	11.3669i	0.540237	+	0.405961i
$785$	−56.5285	−	63.8075i	−2.01759	−	2.27739i
$786$	−1.30502	+	8.03009i	−0.0465484	+	0.286424i
$787$	2.70513	+	33.5091i	0.0964275	+	1.19447i	0.846234	+	0.532812i	$0.178865\pi$
$787$	2.70513	+	33.5091i	0.0964275	+	1.19447i	−0.749806	+	0.661658i	$0.769853\pi$
$788$	2.49321	−	10.1153i	0.0888168	−	0.360344i
$789$	0.384196	−	1.32640i	0.0136777	−	0.0472210i
$790$	−7.24100	+	35.4688i	−0.257623	+	1.26192i
$791$	16.4958	+	13.4684i	0.586524	+	0.478882i
$792$	0.0252055	+	0.207586i	0.000895639	+	0.00737625i
$793$	9.66478	+	52.0636i	0.343206	+	1.84883i
$794$	2.16359	−	17.8187i	0.0767828	−	0.632363i
$795$	−24.6152	+	23.6433i	−0.873013	+	0.838540i
$796$	−3.19828	−	3.32976i	−0.113360	−	0.118020i
$797$	−12.3638	−	26.0562i	−0.437948	−	0.922957i	−0.995673	−	0.0929304i	$-0.970377\pi$
$797$	−12.3638	−	26.0562i	−0.437948	−	0.922957i	0.557724	−	0.830026i	$-0.311675\pi$
$798$	31.5297	+	21.7634i	1.11614	+	0.770415i
$799$	0.254642	+	0.402685i	0.00900860	+	0.0142460i
$800$	−43.2794	+	57.5944i	−1.53016	+	2.03627i
$801$	0.537221	−	1.02359i	0.0189818	−	0.0361667i
$802$	4.80762	+	23.5493i	0.169763	+	0.831554i
$803$	−0.535689	−	0.0432453i	−0.0189041	−	0.00152609i
$804$	7.14587	−	2.06983i	0.252015	−	0.0729971i
$805$	−32.6967	+	17.1605i	−1.15241	+	0.604829i
$806$	39.8449	−	5.74789i	1.40348	−	0.202461i
$807$	−3.91685	−	2.05572i	−0.137880	−	0.0723649i
$808$	20.4767	+	4.18035i	0.720369	+	0.147064i
$809$	0.410075	−	0.308151i	0.0144175	−	0.0108340i	−0.593509	−	0.804827i	$-0.702258\pi$
$809$	0.410075	−	0.308151i	0.0144175	−	0.0108340i	0.607927	+	0.793993i	$0.292001\pi$
$810$	−0.295163	+	7.32440i	−0.0103710	+	0.257353i
$811$	26.6025	+	10.0890i	0.934141	+	0.354273i	0.774263	−	0.632864i	$-0.218121\pi$
$811$	26.6025	+	10.0890i	0.934141	+	0.354273i	0.159878	+	0.987137i	$0.448890\pi$
$812$	3.36120	+	0.973584i	0.117955	+	0.0341661i
$813$	−29.7233	+	6.06806i	−1.04244	+	0.212816i
$814$	−0.845783	+	0.954691i	−0.0296447	+	0.0334619i
$815$	24.9892	+	30.6063i	0.875335	+	1.07209i
$816$	−0.267472	−	6.63724i	−0.00936338	−	0.232350i
$817$	−16.6404	+	49.8442i	−0.582175	+	1.74383i
$818$	−38.2940	−	33.9255i	−1.33892	−	1.18618i
$819$	−6.52856	+	9.92752i	−0.228126	+	0.346896i
$820$	20.4306	−	18.0999i	0.713467	−	0.632077i
$821$	4.43905	+	10.4188i	0.154924	+	0.363620i	0.979298	−	0.202426i	$-0.0648826\pi$
$821$	4.43905	+	10.4188i	0.154924	+	0.363620i	−0.824374	+	0.566046i	$0.808472\pi$
$822$	−17.0436	−	29.5204i	−0.594463	−	1.02964i
$823$	2.88563	−	4.99806i	0.100587	−	0.174222i	−0.811340	−	0.584575i	$-0.801261\pi$
$823$	2.88563	−	4.99806i	0.100587	−	0.174222i	0.911927	+	0.410353i	$0.134595\pi$
$824$	18.3159	+	2.22395i	0.638065	+	0.0774751i
$825$	1.69473	−	0.804157i	0.0590028	−	0.0279972i
$826$	15.0232	+	8.67363i	0.522723	+	0.301794i
$827$	8.37084	−	5.77797i	0.291083	−	0.200920i	−0.413570	−	0.910472i	$-0.635718\pi$
$827$	8.37084	−	5.77797i	0.291083	−	0.200920i	0.704653	+	0.709553i	$0.251103\pi$
$828$	3.36030	+	1.43169i	0.116779	+	0.0497547i
$829$	28.7208	−	4.66759i	0.997516	−	0.162112i	0.360332	−	0.932824i	$-0.382663\pi$
$829$	28.7208	−	4.66759i	0.997516	−	0.162112i	0.637184	+	0.770712i	$0.280099\pi$
$830$	−72.8727	−	96.9759i	−2.52945	−	3.36608i
$831$	0.387116	−	1.02074i	0.0134289	−	0.0354092i
$832$	5.95283	+	3.26103i	0.206377	+	0.113056i
$833$	1.85467	+	4.89035i	0.0642604	+	0.169441i
$834$	−4.60272	+	7.27862i	−0.159379	+	0.252038i
$835$	20.4503	−	8.71305i	0.707711	−	0.301528i
$836$	−1.18488	+	0.749274i	−0.0409800	+	0.0259142i
$837$	−6.08973	+	0.739427i	−0.210492	+	0.0255583i
$838$	23.3064	−	54.7021i	0.805106	−	1.88965i
$839$	−2.58859	−	7.75378i	−0.0893681	−	0.267690i	0.894362	−	0.447345i	$-0.147630\pi$
$839$	−2.58859	−	7.75378i	−0.0893681	−	0.267690i	−0.983730	+	0.179655i	$0.942502\pi$
$840$	15.5215	−	5.88651i	0.535541	−	0.203104i
$841$	28.2538	−	2.28088i	0.974270	−	0.0786512i
$842$	−5.58165	−	19.2701i	−0.192356	−	0.664091i
$843$	−20.8708	+	0.841063i	−0.718827	+	0.0289677i
$844$	12.6579			0.435704
$845$	−22.6621	−	47.1976i	−0.779598	−	1.62365i
$846$	0.639964			0.0220024
$847$	−36.1282	+	1.45592i	−1.24138	+	0.0500259i
$848$	−11.5582	−	39.9037i	−0.396912	−	1.37030i
$849$	−10.7036	+	0.864082i	−0.367346	+	0.0296552i
$850$	−25.8741	+	9.81274i	−0.887473	+	0.336574i
$851$	−3.69291	−	11.0616i	−0.126591	−	0.379188i
$852$	−7.67454	+	18.0128i	−0.262925	+	0.617108i
$853$	−19.9925	+	2.42753i	−0.684531	+	0.0831171i	−0.455411	−	0.890281i	$-0.650508\pi$
$853$	−19.9925	+	2.42753i	−0.684531	+	0.0831171i	−0.229120	+	0.973398i	$0.573585\pi$
$854$	74.4531	−	47.0813i	2.54773	−	1.61109i
$855$	23.6659	−	10.0831i	0.809356	−	0.344834i
$856$	1.57864	−	2.49642i	0.0539569	−	0.0853260i
$857$	15.6814	+	41.3486i	0.535668	+	1.41244i	0.880621	+	0.473821i	$0.157126\pi$
$857$	15.6814	+	41.3486i	0.535668	+	1.41244i	−0.344953	+	0.938620i	$0.612105\pi$
$858$	−0.607053	−	0.913920i	−0.0207244	−	0.0312007i
$859$	−13.5626	+	35.7617i	−0.462750	+	1.22017i	0.477180	+	0.878806i	$0.341659\pi$
$859$	−13.5626	+	35.7617i	−0.462750	+	1.22017i	−0.939930	+	0.341367i	$0.889110\pi$
$860$	−26.1311	−	34.7742i	−0.891063	−	1.18579i
$861$	−16.7922	+	2.72899i	−0.572275	+	0.0930037i
$862$	15.6431	+	6.66492i	0.532807	+	0.227008i
$863$	−0.501640	+	0.346257i	−0.0170760	+	0.0117867i	−0.576572	−	0.817046i	$-0.695610\pi$
$863$	−0.501640	+	0.346257i	−0.0170760	+	0.0117867i	0.559496	+	0.828833i	$0.310995\pi$
$864$	−5.56069	−	3.21047i	−0.189179	−	0.109222i
$865$	6.92059	−	3.28386i	0.235307	−	0.111655i
$866$	−51.9809	−	6.31163i	−1.76638	−	0.214478i
$867$	−7.58193	+	13.1323i	−0.257496	+	0.445996i
$868$	−13.2696	−	22.9837i	−0.450401	−	0.780117i
$869$	0.323622	+	0.759569i	0.0109781	+	0.0257666i
$870$	4.43811	−	3.93183i	0.150466	−	0.133301i
$871$	14.9860	−	13.8889i	0.507783	−	0.470608i
$872$	−12.5561	−	11.1238i	−0.425205	−	0.376698i
$873$	1.83529	−	5.49735i	0.0621150	−	0.186057i
$874$	−1.30243	−	32.3194i	−0.0440553	−	1.09322i
$875$	−52.2100	−	63.9456i	−1.76502	−	2.16176i
$876$	2.79845	−	3.15880i	0.0945510	−	0.106726i
$877$	−3.56714	+	0.728238i	−0.120454	+	0.0245908i	−0.259874	−	0.965642i	$-0.583681\pi$
$877$	−3.56714	+	0.728238i	−0.120454	+	0.0245908i	0.139420	+	0.990233i	$0.455476\pi$
$878$	54.1705	+	15.6907i	1.82817	+	0.529535i
$879$	24.4549	+	9.27454i	0.824845	+	0.312822i
$880$	−0.132908	+	3.29808i	−0.00448033	+	0.111178i
$881$	−27.0604	+	20.3346i	−0.911688	+	0.685089i	−0.949356	−	0.314202i	$-0.898263\pi$
$881$	−27.0604	+	20.3346i	−0.911688	+	0.685089i	0.0376687	+	0.999290i	$0.488007\pi$
$882$	6.88334	+	1.40524i	0.231774	+	0.0473170i
$883$	4.39123	+	2.30469i	0.147777	+	0.0775591i	0.536991	−	0.843588i	$-0.319561\pi$
$883$	4.39123	+	2.30469i	0.147777	+	0.0775591i	−0.389214	+	0.921147i	$0.627253\pi$
$884$	3.10739	+	5.61098i	0.104513	+	0.188718i
$885$	10.3137	−	5.41304i	0.346691	−	0.181957i
$886$	−61.0551	+	17.6848i	−2.05119	+	0.594133i
$887$	−42.7501	−	3.45114i	−1.43541	−	0.115878i	−0.661865	−	0.749623i	$-0.730235\pi$
$887$	−42.7501	−	3.45114i	−1.43541	−	0.115878i	−0.773542	+	0.633745i	$0.781517\pi$
$888$	1.04864	+	5.13659i	0.0351902	+	0.172373i
$889$	−23.5105	+	44.7955i	−0.788517	+	1.50239i
$890$	5.09062	−	6.77439i	0.170638	−	0.227078i
$891$	0.0893553	+	0.141304i	0.00299352	+	0.00473387i
$892$	21.5250	+	14.8576i	0.720709	+	0.497470i
$893$	−0.962769	−	2.02899i	−0.0322178	−	0.0678976i
$894$	20.9179	+	21.7778i	0.699599	+	0.728359i
$895$	−0.0752732	+	0.0723009i	−0.00251611	+	0.00241675i
$896$	−3.74001	+	30.8017i	−0.124945	+	1.02901i
$897$	10.0119	−	0.628715i	0.334287	−	0.0209922i
$898$	0.813052	+	6.69609i	0.0271319	+	0.223451i
$899$	3.84355	+	3.13816i	0.128190	+	0.104663i
$900$	−2.94633	+	14.4321i	−0.0982111	+	0.481070i
$901$	3.19491	−	11.0301i	0.106438	−	0.367466i
$902$	0.375946	−	1.52527i	0.0125176	−	0.0507860i
$903$	2.18157	+	27.0236i	0.0725980	+	0.899288i
$904$	−1.29656	+	7.97806i	−0.0431230	+	0.265346i
$905$	−50.8776	−	57.4290i	−1.69123	−	1.90900i
$906$	−23.3721	−	17.5630i	−0.776486	−	0.583491i
$907$	6.61189	−	8.09810i	0.219544	−	0.268893i	−0.653076	−	0.757293i	$-0.726522\pi$
$907$	6.61189	−	8.09810i	0.219544	−	0.268893i	0.872620	+	0.488400i	$0.162419\pi$
$908$	3.48100	+	21.4195i	0.115521	+	0.710831i
$909$	16.2235	−	3.99874i	0.538100	−	0.132630i
$910$	−58.9103	+	64.1530i	−1.95286	+	2.12665i
$911$	10.7378	+	2.64663i	0.355759	+	0.0876866i	0.413145	−	0.910665i	$-0.364430\pi$
$911$	10.7378	+	2.64663i	0.355759	+	0.0876866i	−0.0573860	+	0.998352i	$0.518277\pi$
$912$	−2.51954	+	31.2101i	−0.0834302	+	1.03347i
$913$	−2.62426	−	0.876107i	−0.0868503	−	0.0289949i
$914$	11.4056	−	11.8745i	0.377263	−	0.392772i
$915$		−	59.1487i		−	1.95539i
$916$	−20.9797	−	20.1513i	−0.693189	−	0.665817i
$917$	11.4097	−	9.31574i	0.376782	−	0.307633i
$918$	−1.14616	−	2.18383i	−0.0378290	−	0.0720770i
$919$	−21.1929	−	3.44418i	−0.699089	−	0.113613i	−0.199528	−	0.979892i	$-0.563941\pi$
$919$	−21.1929	−	3.44418i	−0.699089	−	0.113613i	−0.499560	+	0.866279i	$0.666505\pi$
$920$	−11.8455	−	7.49067i	−0.390536	−	0.246960i
$921$	16.6646	+	7.90746i	0.549118	+	0.260560i
$922$	19.1935	+	27.8066i	0.632104	+	0.915761i
$923$	3.37021	+	53.6684i	0.110932	+	1.76652i
$924$	−0.410877	+	0.595258i	−0.0135168	+	0.0195825i
$925$	40.7278	−	23.5142i	1.33912	−	0.773143i
$926$	18.4772	−	38.9400i	0.607200	−	1.27965i
$927$	13.9922	−	4.67127i	0.459563	−	0.153425i
$928$	1.24293	+	5.04275i	0.0408011	+	0.165536i
$929$	20.6041	+	0.830318i	0.675999	+	0.0272418i	0.375892	−	0.926664i	$-0.377336\pi$
$929$	20.6041	+	0.830318i	0.675999	+	0.0272418i	0.300108	+	0.953905i	$0.402977\pi$
$930$	−44.9312	−	1.81066i	−1.47335	−	0.0593740i
$931$	−5.90008	−	23.9375i	−0.193367	−	0.784521i
$932$	−27.7292	+	9.25736i	−0.908300	+	0.303235i
$933$	−7.15441	+	15.0776i	−0.234225	+	0.493618i
$934$	64.5729	−	37.2812i	2.11289	−	1.21988i
$935$	−0.518296	+	0.750881i	−0.0169501	+	0.0245564i
$936$	−4.50208	−	0.261938i	−0.147155	−	0.00856171i
$937$	−16.6990	−	24.1927i	−0.545533	−	0.790341i	0.449136	−	0.893464i	$-0.351732\pi$
$937$	−16.6990	−	24.1927i	−0.545533	−	0.790341i	−0.994669	+	0.103122i	$0.967117\pi$
$938$	−30.7087	−	14.5715i	−1.00268	−	0.475775i
$939$	2.60850	+	1.64951i	0.0851251	+	0.0538298i
$940$	1.83495	+	0.298208i	0.0598495	+	0.00972649i
$941$	10.0070	+	19.0667i	0.326219	+	0.621558i	0.992235	−	0.124379i	$-0.0396940\pi$
$941$	10.0070	+	19.0667i	0.326219	+	0.621558i	−0.666016	+	0.745938i	$0.732002\pi$
$942$	29.8419	−	24.3652i	0.972302	−	0.793860i
$943$	10.3589	+	9.94981i	0.337331	+	0.324011i
$944$			14.1778i			0.461447i
$945$	9.19386	−	9.57182i	0.299076	−	0.311371i
$946$	−2.37462	−	0.792766i	−0.0772056	−	0.0257750i
$947$	−0.832986	+	10.3184i	−0.0270684	+	0.335302i	0.969023	+	0.246971i	$0.0794353\pi$
$947$	−0.832986	+	10.3184i	−0.0270684	+	0.335302i	−0.996091	+	0.0883309i	$0.971847\pi$
$948$	−6.29482	−	1.55153i	−0.204446	−	0.0503915i
$949$	2.97404	−	11.2022i	0.0965414	−	0.363640i
$950$	126.650	−	31.2164i	4.10906	−	1.01279i
$951$	0.824050	+	5.07058i	0.0267216	+	0.164425i
$952$	−3.53235	+	4.32634i	−0.114484	+	0.140217i
$953$	−13.7404	−	10.3252i	−0.445095	−	0.334467i	0.354448	−	0.935076i	$-0.384669\pi$
$953$	−13.7404	−	10.3252i	−0.445095	−	0.334467i	−0.799543	+	0.600609i	$0.794925\pi$
$954$	−10.2285	−	11.5456i	−0.331161	−	0.373803i
$955$	−5.41013	+	33.2899i	−0.175068	+	1.07724i
$956$	1.99921	+	24.7646i	0.0646590	+	0.800946i
$957$	0.0323629	−	0.131302i	0.00104615	−	0.00424438i
$958$	2.23731	−	7.72407i	0.0722840	−	0.249553i
$959$	−12.3450	+	60.4697i	−0.398640	+	1.95267i
$960$	−5.87281	−	4.79500i	−0.189544	−	0.154758i
$961$	−0.799340	−	6.58315i	−0.0257852	−	0.212360i
$962$	−17.0135	−	21.6136i	−0.548539	−	0.696852i
$963$	0.284647	−	2.34428i	0.00917264	−	0.0755434i
$964$	12.5799	−	12.0832i	0.405172	−	0.389173i
$965$	13.7453	+	14.3104i	0.442476	+	0.460667i
$966$	−7.15409	−	15.0769i	−0.230179	−	0.485092i
$967$	−34.7863	−	24.0112i	−1.11865	−	0.772149i	−0.142619	−	0.989778i	$-0.545552\pi$
$967$	−34.7863	−	24.0112i	−1.11865	−	0.772149i	−0.976032	+	0.217629i	$0.930168\pi$
$968$	−7.33472	−	11.5989i	−0.235747	−	0.372804i
$969$	−5.19948	+	6.91925i	−0.167031	+	0.222278i
$970$	19.7432	−	37.6176i	0.633917	−	1.20783i
$971$	7.15240	+	35.0348i	0.229531	+	1.12432i	0.917241	+	0.398333i	$0.130411\pi$
$971$	7.15240	+	35.0348i	0.229531	+	1.12432i	−0.687710	+	0.725986i	$0.741384\pi$
$972$	−1.30855	−	0.105637i	−0.0419718	−	0.00338832i
$973$	14.9766	−	4.33803i	0.480128	−	0.139071i
$974$	−39.5668	+	20.7663i	−1.26780	+	0.665394i
$975$	10.5602	+	39.0518i	0.338197	+	1.25066i
$976$	63.7489	+	33.4580i	2.04055	+	1.07096i
$977$	−0.731675	−	0.149373i	−0.0234084	−	0.00477885i	0.188307	−	0.982110i	$-0.439700\pi$
$977$	−0.731675	−	0.149373i	−0.0234084	−	0.00477885i	−0.211716	+	0.977331i	$0.567905\pi$
$978$	−14.2754	+	10.7273i	−0.456478	+	0.343021i
$979$	0.00778210	−	0.193111i	0.000248717	−	0.00617185i
$980$	19.0816	+	7.23669i	0.609539	+	0.231168i
$981$	−12.8821	−	3.73136i	−0.411295	−	0.119133i
$982$	32.0425	−	6.54152i	1.02252	−	0.208748i
$983$	5.79314	−	6.53910i	0.184772	−	0.208565i	−0.648825	−	0.760938i	$-0.724739\pi$
$983$	5.79314	−	6.53910i	0.184772	−	0.208565i	0.833597	+	0.552373i	$0.186278\pi$
$984$	−4.08371	−	5.00163i	−0.130184	−	0.159446i
$985$	1.28691	+	31.9344i	0.0410045	+	1.01752i
$986$	−0.631730	+	1.89226i	−0.0201184	+	0.0602619i
$987$	−0.867295	−	0.768357i	−0.0276063	−	0.0244571i
$988$	−11.3526	−	28.0214i	−0.361173	−	0.891479i
$989$	17.1332	−	15.1787i	0.544804	−	0.482655i
$990$	0.480368	+	1.12746i	0.0152671	+	0.0358332i
$991$	−0.0944192	−	0.163539i	−0.00299933	−	0.00519498i	0.864522	−	0.502595i	$-0.167621\pi$
$991$	−0.0944192	−	0.163539i	−0.00299933	−	0.00519498i	−0.867521	+	0.497400i	$0.834288\pi$
$992$	19.6945	−	34.1118i	0.625300	−	1.08305i
$993$	14.0499	+	1.70597i	0.445861	+	0.0541373i
$994$	80.8194	−	38.3493i	2.56344	−	1.21637i
$995$	12.2662	+	7.08190i	0.388865	+	0.224511i
$996$	17.8791	−	12.3410i	0.566520	−	0.391041i
$997$	−37.5443	−	15.9961i	−1.18904	−	0.506602i	−0.295394	−	0.955376i	$-0.595451\pi$
$997$	−37.5443	−	15.9961i	−1.18904	−	0.506602i	−0.893646	+	0.448773i	$0.851861\pi$
$998$	37.4050	−	6.07891i	1.18404	−	0.192425i
$999$	2.51799	+	3.35084i	0.0796657	+	0.106016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.b.127.12	yes	360
169.4	even	78	inner	507.2.t.b.4.12	✓	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.b.4.12	✓	360	169.4	even	78	inner
507.2.t.b.127.12	yes	360	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.81864 - 0.0732885i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(1.30855 - 0.105637i) q^{4} +(-3.76569 + 1.42814i) q^{5} +(-0.576371 - 1.72644i) q^{6} +(-1.29170 + 3.03172i) q^{7} +(-1.24165 + 0.150763i) q^{8} +(-0.845190 + 0.534466i) q^{9} +O(q^{10})\)	\(q+(1.81864 - 0.0732885i) q^{2} +(-0.278217 - 0.960518i) q^{3} +(1.30855 - 0.105637i) q^{4} +(-3.76569 + 1.42814i) q^{5} +(-0.576371 - 1.72644i) q^{6} +(-1.29170 + 3.03172i) q^{7} +(-1.24165 + 0.150763i) q^{8} +(-0.845190 + 0.534466i) q^{9} +(-6.74376 + 2.87325i) q^{10} +(-0.0893553 + 0.141304i) q^{11} +(-0.465528 - 1.22750i) q^{12} +(-2.65571 - 2.43868i) q^{13} +(-2.12694 + 5.60827i) q^{14} +(2.41944 + 3.21968i) q^{15} +(-4.83867 + 0.786360i) q^{16} +(-1.24661 - 0.531132i) q^{17} +(-1.49792 + 1.03394i) q^{18} +(5.53158 + 3.19366i) q^{19} +(-4.77674 + 2.26659i) q^{20} +(3.27140 + 0.397220i) q^{21} +(-0.152149 + 0.263530i) q^{22} +(-1.39113 - 2.40951i) q^{23} +(0.490258 + 1.15068i) q^{24} +(8.39832 - 7.44026i) q^{25} +(-5.00851 - 4.24045i) q^{26} +(0.748511 + 0.663123i) q^{27} +(-1.36999 + 4.10362i) q^{28} +(-0.0325697 - 0.808209i) q^{29} +(4.63604 + 5.67812i) q^{30} +(-4.06789 + 4.59170i) q^{31} +(-6.29117 + 1.28435i) q^{32} +(0.160585 + 0.0465141i) q^{33} +(-2.30606 - 0.874573i) q^{34} +(0.534411 - 13.2613i) q^{35} +(-1.04952 + 0.788660i) q^{36} +(4.10676 + 0.838401i) q^{37} +(10.2940 + 5.40270i) q^{38} +(-1.60353 + 3.22935i) q^{39} +(4.46035 - 2.34097i) q^{40} +(-4.95862 + 1.43628i) q^{41} +(5.97859 + 0.482642i) q^{42} +(1.64561 + 8.06074i) q^{43} +(-0.101999 + 0.194343i) q^{44} +(2.41944 - 3.21968i) q^{45} +(-2.70656 - 4.28008i) q^{46} +(-0.289367 - 0.199736i) q^{47} +(2.10152 + 4.42885i) q^{48} +(-2.67380 - 2.78372i) q^{49} +(14.7282 - 14.1466i) q^{50} +(-0.163332 + 1.34516i) q^{51} +(-3.73276 - 2.91060i) q^{52} +(1.02150 + 8.41284i) q^{53} +(1.40987 + 1.15112i) q^{54} +(0.134683 - 0.659720i) q^{55} +(1.14676 - 3.95907i) q^{56} +(1.52859 - 6.20171i) q^{57} +(-0.118465 - 1.46745i) q^{58} +(0.463934 - 2.85470i) q^{59} +(3.50608 + 3.95754i) q^{60} +(-11.7410 - 8.82282i) q^{61} +(-7.06150 + 8.64877i) q^{62} +(-0.528623 - 3.25275i) q^{63} +(-1.82782 + 0.450517i) q^{64} +(13.4834 + 5.39061i) q^{65} +(0.295455 + 0.0728232i) q^{66} +(-0.455998 + 5.64855i) q^{67} +(-1.68736 - 0.563325i) q^{68} +(-1.92734 + 2.00658i) q^{69} -24.1566i q^{70} +(-10.7562 - 10.3315i) q^{71} +(0.968849 - 0.791041i) q^{72} +(1.49389 + 2.84636i) q^{73} +(7.53015 + 1.22377i) q^{74} +(-9.48307 - 5.99673i) q^{75} +(7.57573 + 3.59473i) q^{76} +(-0.312975 - 0.453423i) q^{77} +(-2.67957 + 5.99053i) q^{78} +(2.80535 - 4.06424i) q^{79} +(17.0979 - 9.87149i) q^{80} +(0.428693 - 0.903450i) q^{81} +(-8.91267 + 2.97549i) q^{82} +(3.96026 + 16.0674i) q^{83} +(4.32275 + 0.174201i) q^{84} +(5.45289 + 0.219744i) q^{85} +(3.58353 + 14.5390i) q^{86} +(-0.767238 + 0.256142i) q^{87} +(0.0896442 - 0.188921i) q^{88} +(-1.00113 + 0.578001i) q^{89} +(4.16411 - 6.03275i) q^{90} +(10.8238 - 4.90135i) q^{91} +(-2.07490 - 3.00602i) q^{92} +(5.54217 + 2.62979i) q^{93} +(-0.540891 - 0.342039i) q^{94} +(-25.3912 - 4.12648i) q^{95} +(2.98396 + 5.68546i) q^{96} +(-4.48931 + 3.66541i) q^{97} +(-5.06668 - 4.86661i) q^{98} -0.167186i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9}+O(q^{10}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9	\( 360 q - 15 q^{3} - 14 q^{4} + 3 q^{7} + 15 q^{9} + 6 q^{11} - 28 q^{12} + 6 q^{13} + 4 q^{14} - 6 q^{15} + 20 q^{16} - 6 q^{19} - 12 q^{20} - 28 q^{22} + 46 q^{23} - 6 q^{25} - 39 q^{26} + 30 q^{27} - 6 q^{28} + 43 q^{29} + 26 q^{31} - 195 q^{32} + 19 q^{33} + 65 q^{34} + 84 q^{35} - 14 q^{36} - 65 q^{38} - 2 q^{39} + 12 q^{41} - 128 q^{42} + 83 q^{43} - 39 q^{44} - 6 q^{45} - 20 q^{48} + 72 q^{49} - 52 q^{50} - 55 q^{52} + 49 q^{53} - 49 q^{55} - 2 q^{56} + 26 q^{57} + 26 q^{58} - 202 q^{59} - 182 q^{60} - 3 q^{61} - 65 q^{62} - 3 q^{63} - 14 q^{64} - 58 q^{65} + 48 q^{66} - 41 q^{67} + 139 q^{68} + 6 q^{69} - 60 q^{71} - 52 q^{73} - 269 q^{74} + 23 q^{75} - 14 q^{76} + 70 q^{77} - 65 q^{78} + 18 q^{79} + 492 q^{80} + 15 q^{81} - 65 q^{82} + 78 q^{83} - 6 q^{84} - 91 q^{85} - 169 q^{86} + 48 q^{87} - 522 q^{88} - 12 q^{89} + 373 q^{91} + 72 q^{92} - 3 q^{93} - 13 q^{94} - 110 q^{95} + 65 q^{96} - 121 q^{97} - 104 q^{98}+O(q^{100}) \) 360 * q - 15 * q^3 - 14 * q^4 + 3 * q^7 + 15 * q^9 + 6 * q^11 - 28 * q^12 + 6 * q^13 + 4 * q^14 - 6 * q^15 + 20 * q^16 - 6 * q^19 - 12 * q^20 - 28 * q^22 + 46 * q^23 - 6 * q^25 - 39 * q^26 + 30 * q^27 - 6 * q^28 + 43 * q^29 + 26 * q^31 - 195 * q^32 + 19 * q^33 + 65 * q^34 + 84 * q^35 - 14 * q^36 - 65 * q^38 - 2 * q^39 + 12 * q^41 - 128 * q^42 + 83 * q^43 - 39 * q^44 - 6 * q^45 - 20 * q^48 + 72 * q^49 - 52 * q^50 - 55 * q^52 + 49 * q^53 - 49 * q^55 - 2 * q^56 + 26 * q^57 + 26 * q^58 - 202 * q^59 - 182 * q^60 - 3 * q^61 - 65 * q^62 - 3 * q^63 - 14 * q^64 - 58 * q^65 + 48 * q^66 - 41 * q^67 + 139 * q^68 + 6 * q^69 - 60 * q^71 - 52 * q^73 - 269 * q^74 + 23 * q^75 - 14 * q^76 + 70 * q^77 - 65 * q^78 + 18 * q^79 + 492 * q^80 + 15 * q^81 - 65 * q^82 + 78 * q^83 - 6 * q^84 - 91 * q^85 - 169 * q^86 + 48 * q^87 - 522 * q^88 - 12 * q^89 + 373 * q^91 + 72 * q^92 - 3 * q^93 - 13 * q^94 - 110 * q^95 + 65 * q^96 - 121 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

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