LMFDB - Embedded newform 637.2.bl.b.53.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.27
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.04235 + 1.39245i) q^{2} +(2.02170 + 1.87586i) q^{3} +(1.50160 + 3.82602i) q^{4} +(-0.574996 + 0.177363i) q^{5} +(1.51697 + 6.64630i) q^{6} +(-0.954237 - 2.46768i) q^{7} +(-1.16067 + 5.08521i) q^{8} +(0.344217 + 4.59325i) q^{9} +O(q^{10})$	\(q+(2.04235 + 1.39245i) q^{2} +(2.02170 + 1.87586i) q^{3} +(1.50160 + 3.82602i) q^{4} +(-0.574996 + 0.177363i) q^{5} +(1.51697 + 6.64630i) q^{6} +(-0.954237 - 2.46768i) q^{7} +(-1.16067 + 5.08521i) q^{8} +(0.344217 + 4.59325i) q^{9} +(-1.42131 - 0.438418i) q^{10} +(0.197641 - 2.63733i) q^{11} +(-4.14130 + 10.5519i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(1.48724 - 6.36860i) q^{14} +(-1.49518 - 0.720040i) q^{15} +(-3.42552 + 3.17841i) q^{16} +(5.54927 - 0.836418i) q^{17} +(-5.69288 + 9.86036i) q^{18} +(-4.14229 - 7.17466i) q^{19} +(-1.54201 - 1.93362i) q^{20} +(2.69984 - 6.77892i) q^{21} +(4.07601 - 5.11116i) q^{22} +(-5.04591 - 0.760549i) q^{23} +(-11.8857 + 8.10351i) q^{24} +(-3.83203 + 2.61263i) q^{25} +(-2.44426 - 0.368413i) q^{26} +(-2.76181 + 3.46320i) q^{27} +(8.00850 - 7.35640i) q^{28} +(6.29803 + 7.89749i) q^{29} +(-2.05106 - 3.55254i) q^{30} +(-0.894638 + 1.54956i) q^{31} +(-1.10646 + 0.166773i) q^{32} +(5.34684 - 4.96114i) q^{33} +(12.4982 + 6.01884i) q^{34} +(0.986357 + 1.24966i) q^{35} +(-17.0570 + 8.21422i) q^{36} +(-0.315601 + 0.804139i) q^{37} +(1.53035 - 20.4212i) q^{38} +(-2.63540 - 0.812912i) q^{39} +(-0.234548 - 3.12983i) q^{40} +(-1.08013 + 4.73236i) q^{41} +(14.9534 - 10.0856i) q^{42} +(-1.53964 - 6.74561i) q^{43} +(10.3872 - 3.20404i) q^{44} +(-1.01260 - 2.58005i) q^{45} +(-9.24651 - 8.57951i) q^{46} +(-1.50564 - 1.02653i) q^{47} -12.8876 q^{48} +(-5.17886 + 4.70950i) q^{49} -11.4643 q^{50} +(12.7880 + 8.71868i) q^{51} +(-3.01294 - 2.79560i) q^{52} +(3.78968 + 9.65595i) q^{53} +(-10.4629 + 3.22738i) q^{54} +(0.354122 + 1.55151i) q^{55} +(13.6562 - 1.98835i) q^{56} +(5.08421 - 22.2754i) q^{57} +(1.86594 + 24.8992i) q^{58} +(-12.1884 - 3.75963i) q^{59} +(0.509724 - 6.80179i) q^{60} +(2.98424 - 7.60371i) q^{61} +(-3.98486 + 1.91901i) q^{62} +(11.0062 - 5.23247i) q^{63} +(5.92836 + 2.85495i) q^{64} +(0.441099 - 0.409280i) q^{65} +(17.8283 - 2.68718i) q^{66} +(-0.749615 + 1.29837i) q^{67} +(11.5329 + 19.9756i) q^{68} +(-8.77464 - 11.0030i) q^{69} +(0.274398 + 3.92570i) q^{70} +(0.383545 - 0.480950i) q^{71} +(-23.7572 - 3.58082i) q^{72} +(-6.42692 + 4.38180i) q^{73} +(-1.76430 + 1.20288i) q^{74} +(-12.6482 - 1.90640i) q^{75} +(21.2303 - 26.6220i) q^{76} +(-6.69667 + 2.02893i) q^{77} +(-4.25047 - 5.32992i) q^{78} +(2.12422 + 3.67926i) q^{79} +(1.40593 - 2.43513i) q^{80} +(1.58404 - 0.238755i) q^{81} +(-8.79560 + 8.16112i) q^{82} +(-1.44659 - 0.696640i) q^{83} +(29.9904 + 0.150414i) q^{84} +(-3.04246 + 1.46517i) q^{85} +(6.24846 - 15.9208i) q^{86} +(-2.08187 + 27.7806i) q^{87} +(13.1820 + 4.06610i) q^{88} +(-0.724459 - 9.66724i) q^{89} +(1.52452 - 6.67937i) q^{90} +(1.93042 + 1.80927i) q^{91} +(-4.66708 - 20.4478i) q^{92} +(-4.71545 + 1.45452i) q^{93} +(-1.64566 - 4.19306i) q^{94} +(3.65432 + 3.39071i) q^{95} +(-2.54978 - 1.73841i) q^{96} +12.2406 q^{97} +(-17.1348 + 2.40714i) q^{98} +12.1820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

Coefficient data

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

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

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

$2$	2.04235	+	1.39245i	1.44416	+	0.984613i	0.995876	+	0.0907233i	$0.0289179\pi$
$2$	2.04235	+	1.39245i	1.44416	+	0.984613i	0.448286	+	0.893890i	$0.352035\pi$
$3$	2.02170	+	1.87586i	1.16723	+	1.08303i	0.995192	+	0.0979397i	$0.0312252\pi$
$3$	2.02170	+	1.87586i	1.16723	+	1.08303i	0.172037	+	0.985091i	$0.444965\pi$
$4$	1.50160	+	3.82602i	0.750801	+	1.91301i
$5$	−0.574996	+	0.177363i	−0.257146	+	0.0793190i	−0.420648	−	0.907224i	$-0.638197\pi$
$5$	−0.574996	+	0.177363i	−0.257146	+	0.0793190i	0.163502	+	0.986543i	$0.447721\pi$
$6$	1.51697	+	6.64630i	0.619302	+	2.71334i
$7$	−0.954237	−	2.46768i	−0.360668	−	0.932694i
$7$	−0.954237	−	2.46768i	−0.360668	−	0.932694i
$8$	−1.16067	+	5.08521i	−0.410357	+	1.79789i
$9$	0.344217	+	4.59325i	0.114739	+	1.53108i
$10$	−1.42131	−	0.438418i	−0.449459	−	0.138640i
$11$	0.197641	−	2.63733i	0.0595909	−	0.795185i	−0.884718	−	0.466126i	$-0.845649\pi$
$11$	0.197641	−	2.63733i	0.0595909	−	0.795185i	0.944309	−	0.329059i	$-0.106732\pi$
$12$	−4.14130	+	10.5519i	−1.19549	+	3.04606i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	1.48724	−	6.36860i	0.397480	−	1.70208i
$15$	−1.49518	−	0.720040i	−0.386053	−	0.185913i
$16$	−3.42552	+	3.17841i	−0.856379	+	0.794604i
$17$	5.54927	−	0.836418i	1.34590	−	0.202861i	0.563744	−	0.825950i	$-0.309360\pi$
$17$	5.54927	−	0.836418i	1.34590	−	0.202861i	0.782151	+	0.623089i	$0.214122\pi$
$18$	−5.69288	+	9.86036i	−1.34182	+	2.32411i
$19$	−4.14229	−	7.17466i	−0.950308	−	1.64598i	−0.744758	−	0.667334i	$-0.767435\pi$
$19$	−4.14229	−	7.17466i	−0.950308	−	1.64598i	−0.205549	−	0.978647i	$-0.565898\pi$
$20$	−1.54201	−	1.93362i	−0.344803	−	0.432370i
$21$	2.69984	−	6.77892i	0.589154	−	1.47928i
$22$	4.07601	−	5.11116i	0.869008	−	1.08970i
$23$	−5.04591	−	0.760549i	−1.05215	−	0.158585i	−0.399874	−	0.916570i	$-0.630946\pi$
$23$	−5.04591	−	0.760549i	−1.05215	−	0.158585i	−0.652272	+	0.757985i	$0.726184\pi$
$24$	−11.8857	+	8.10351i	−2.42615	+	1.65412i
$25$	−3.83203	+	2.61263i	−0.766406	+	0.522527i
$26$	−2.44426	−	0.368413i	−0.479359	−	0.0722517i
$27$	−2.76181	+	3.46320i	−0.531510	+	0.666492i
$28$	8.00850	−	7.35640i	1.51346	−	1.39023i
$29$	6.29803	+	7.89749i	1.16952	+	1.46653i	0.856025	+	0.516935i	$0.172927\pi$
$29$	6.29803	+	7.89749i	1.16952	+	1.46653i	0.313491	+	0.949591i	$0.398501\pi$
$30$	−2.05106	−	3.55254i	−0.374471	−	0.648602i
$31$	−0.894638	+	1.54956i	−0.160682	+	0.278309i	−0.935113	−	0.354349i	$-0.884703\pi$
$31$	−0.894638	+	1.54956i	−0.160682	+	0.278309i	0.774432	+	0.632658i	$0.218036\pi$
$32$	−1.10646	+	0.166773i	−0.195597	+	0.0294815i
$33$	5.34684	−	4.96114i	0.930765	−	0.863624i
$34$	12.4982	+	6.01884i	2.14343	+	1.03222i
$35$	0.986357	+	1.24966i	0.166725	+	0.211231i
$36$	−17.0570	+	8.21422i	−2.84283	+	1.36904i
$37$	−0.315601	+	0.804139i	−0.0518845	+	0.132200i	−0.954466	−	0.298319i	$-0.903574\pi$
$37$	−0.315601	+	0.804139i	−0.0518845	+	0.132200i	0.902582	+	0.430519i	$0.141669\pi$
$38$	1.53035	−	20.4212i	0.248256	−	3.31275i
$39$	−2.63540	−	0.812912i	−0.422001	−	0.130170i
$40$	−0.234548	−	3.12983i	−0.0370854	−	0.494870i
$41$	−1.08013	+	4.73236i	−0.168688	+	0.739070i	0.817836	+	0.575452i	$0.195174\pi$
$41$	−1.08013	+	4.73236i	−0.168688	+	0.739070i	−0.986524	+	0.163618i	$0.947683\pi$
$42$	14.9534	−	10.0856i	2.30736	−	1.55623i
$43$	−1.53964	−	6.74561i	−0.234793	−	1.02870i	−0.945606	−	0.325315i	$-0.894530\pi$
$43$	−1.53964	−	6.74561i	−0.234793	−	1.02870i	0.710813	−	0.703381i	$-0.248327\pi$
$44$	10.3872	−	3.20404i	1.56594	−	0.483028i
$45$	−1.01260	−	2.58005i	−0.150949	−	0.384611i
$46$	−9.24651	−	8.57951i	−1.36332	−	1.26498i
$47$	−1.50564	−	1.02653i	−0.219620	−	0.149734i	0.448513	−	0.893776i	$-0.351954\pi$
$47$	−1.50564	−	1.02653i	−0.219620	−	0.149734i	−0.668133	+	0.744042i	$0.732906\pi$
$48$	−12.8876			−1.86017
$49$	−5.17886	+	4.70950i	−0.739838	+	0.672786i
$50$	−11.4643			−1.62130
$51$	12.7880	+	8.71868i	1.79067	+	1.22086i
$52$	−3.01294	−	2.79560i	−0.417820	−	0.387680i
$53$	3.78968	+	9.65595i	0.520553	+	1.32635i	0.913520	+	0.406794i	$0.133353\pi$
$53$	3.78968	+	9.65595i	0.520553	+	1.32635i	−0.392967	+	0.919553i	$0.628551\pi$
$54$	−10.4629	+	3.22738i	−1.42382	+	0.439191i
$55$	0.354122	+	1.55151i	0.0477497	+	0.209205i
$56$	13.6562	−	1.98835i	1.82489	−	0.265704i
$57$	5.08421	−	22.2754i	0.673421	−	2.95045i
$58$	1.86594	+	24.8992i	0.245009	+	3.26942i
$59$	−12.1884	−	3.75963i	−1.58680	−	0.489462i	−0.629120	−	0.777308i	$-0.716585\pi$
$59$	−12.1884	−	3.75963i	−1.58680	−	0.489462i	−0.957677	+	0.287846i	$0.907061\pi$
$60$	0.509724	−	6.80179i	0.0658050	−	0.878107i
$61$	2.98424	−	7.60371i	0.382092	−	0.973555i	−0.602411	−	0.798186i	$-0.705793\pi$
$61$	2.98424	−	7.60371i	0.382092	−	0.973555i	0.984503	−	0.175369i	$-0.0561117\pi$
$62$	−3.98486	+	1.91901i	−0.506077	+	0.243714i
$63$	11.0062	−	5.23247i	1.38665	−	0.659229i
$64$	5.92836	+	2.85495i	0.741044	+	0.356868i
$65$	0.441099	−	0.409280i	0.0547115	−	0.0507649i
$66$	17.8283	−	2.68718i	2.19451	−	0.330769i
$67$	−0.749615	+	1.29837i	−0.0915800	+	0.158621i	−0.908176	−	0.418588i	$-0.862525\pi$
$67$	−0.749615	+	1.29837i	−0.0915800	+	0.158621i	0.816596	+	0.577209i	$0.195858\pi$
$68$	11.5329	+	19.9756i	1.39857	+	2.42240i
$69$	−8.77464	−	11.0030i	−1.05634	−	1.32461i
$70$	0.274398	+	3.92570i	0.0327969	+	0.469211i
$71$	0.383545	−	0.480950i	0.0455184	−	0.0570783i	−0.758551	−	0.651613i	$-0.774092\pi$
$71$	0.383545	−	0.480950i	0.0455184	−	0.0570783i	0.804070	+	0.594535i	$0.202664\pi$
$72$	−23.7572	−	3.58082i	−2.79981	−	0.422003i
$73$	−6.42692	+	4.38180i	−0.752214	+	0.512850i	−0.877680	−	0.479247i	$-0.840910\pi$
$73$	−6.42692	+	4.38180i	−0.752214	+	0.512850i	0.125466	+	0.992098i	$0.459957\pi$
$74$	−1.76430	+	1.20288i	−0.205095	+	0.139832i
$75$	−12.6482	−	1.90640i	−1.46048	−	0.220133i
$76$	21.2303	−	26.6220i	2.43529	−	3.05375i
$77$	−6.69667	+	2.02893i	−0.763157	+	0.231217i
$78$	−4.25047	−	5.32992i	−0.481271	−	0.603495i
$79$	2.12422	+	3.67926i	0.238993	+	0.413949i	0.960426	−	0.278536i	$-0.0898492\pi$
$79$	2.12422	+	3.67926i	0.238993	+	0.413949i	−0.721432	+	0.692485i	$0.756516\pi$
$80$	1.40593	−	2.43513i	0.157187	−	0.272256i
$81$	1.58404	−	0.238755i	0.176004	−	0.0265284i
$82$	−8.79560	+	8.16112i	−0.971311	+	0.901245i
$83$	−1.44659	−	0.696640i	−0.158784	−	0.0764661i	0.352804	−	0.935697i	$-0.385228\pi$
$83$	−1.44659	−	0.696640i	−0.158784	−	0.0764661i	−0.511588	+	0.859231i	$0.670942\pi$
$84$	29.9904	+	0.150414i	3.27222	+	0.0164115i
$85$	−3.04246	+	1.46517i	−0.330001	+	0.158920i
$86$	6.24846	−	15.9208i	0.673788	−	1.71678i
$87$	−2.08187	+	27.7806i	−0.223200	+	2.97839i
$88$	13.1820	+	4.06610i	1.40520	+	0.433448i
$89$	−0.724459	−	9.66724i	−0.0767925	−	1.02473i	−0.893908	−	0.448251i	$-0.852047\pi$
$89$	−0.724459	−	9.66724i	−0.0767925	−	1.02473i	0.817115	−	0.576474i	$-0.195572\pi$
$90$	1.52452	−	6.67937i	0.160699	−	0.704068i
$91$	1.93042	+	1.80927i	0.202363	+	0.189663i
$92$	−4.66708	−	20.4478i	−0.486576	−	2.13183i
$93$	−4.71545	+	1.45452i	−0.488969	+	0.150827i
$94$	−1.64566	−	4.19306i	−0.169736	−	0.432481i
$95$	3.65432	+	3.39071i	0.374925	+	0.347880i
$96$	−2.54978	−	1.73841i	−0.260236	−	0.177426i
$97$	12.2406			1.24285			0.621423	−	0.783475i	$-0.286555\pi$
$97$	12.2406			1.24285			0.621423	+	0.783475i	$0.286555\pi$
$98$	−17.1348	+	2.40714i	−1.73088	+	0.243158i
$99$	12.1820			1.22433
$100$	−15.7502	−	10.7383i	−1.57502	−	1.07383i
$101$	−0.743015	−	0.689417i	−0.0739327	−	0.0685995i	0.642341	−	0.766419i	$-0.277963\pi$
$101$	−0.743015	−	0.689417i	−0.0739327	−	0.0685995i	−0.716274	+	0.697819i	$0.754154\pi$
$102$	13.9772	+	35.6133i	1.38395	+	3.52624i
$103$	1.10692	−	0.341440i	0.109068	−	0.0336431i	−0.239741	−	0.970837i	$-0.577062\pi$
$103$	1.10692	−	0.341440i	0.109068	−	0.0336431i	0.348809	+	0.937194i	$0.386586\pi$
$104$	−1.16067	−	5.08521i	−0.113813	−	0.498646i
$105$	−0.350071	+	4.37670i	−0.0341634	+	0.427123i
$106$	−5.70559	+	24.9978i	−0.554176	+	2.42800i
$107$	0.430429	+	5.74368i	0.0416112	+	0.555262i	0.978582	+	0.205856i	$0.0659977\pi$
$107$	0.430429	+	5.74368i	0.0416112	+	0.555262i	−0.936971	+	0.349407i	$0.886383\pi$
$108$	−17.3974	−	5.36638i	−1.67406	−	0.516380i
$109$	−1.16252	+	15.5128i	−0.111349	+	1.48585i	0.609514	+	0.792775i	$0.291365\pi$
$109$	−1.16252	+	15.5128i	−0.111349	+	1.48585i	−0.720863	+	0.693077i	$0.756254\pi$
$110$	−1.43716	+	3.66183i	−0.137028	+	0.349141i
$111$	−2.14651	+	1.03370i	−0.203737	+	0.0981148i
$112$	11.1121	+	5.42011i	1.04999	+	0.512152i
$113$	−15.0465	−	7.24601i	−1.41545	−	0.681647i	−0.439223	−	0.898378i	$-0.644746\pi$
$113$	−15.0465	−	7.24601i	−1.41545	−	0.681647i	−0.976231	+	0.216731i	$0.930461\pi$
$114$	41.4012	−	38.4147i	3.87758	−	3.59787i
$115$	3.03627	−	0.457644i	0.283134	−	0.0426756i
$116$	−20.7588	+	35.9553i	−1.92741	+	3.33836i
$117$	−2.30307	−	3.98903i	−0.212919	−	0.368786i
$118$	−19.6580	−	24.6503i	−1.80966	−	2.26924i
$119$	−7.35933	−	12.8957i	−0.674628	−	1.18214i
$120$	5.39695	−	6.76756i	0.492672	−	0.617791i
$121$	3.96069	+	0.596978i	0.360063	+	0.0542708i
$122$	16.6827	−	11.3741i	1.51038	−	1.02976i
$123$	−11.0610	+	7.54123i	−0.997333	+	0.679970i
$124$	−7.27203	−	1.09608i	−0.653048	−	0.0984311i
$125$	3.61588	−	4.53417i	0.323414	−	0.405548i
$126$	29.7645	+	4.63907i	2.65164	+	0.413281i
$127$	3.45296	+	4.32987i	0.306400	+	0.384214i	0.911063	−	0.412268i	$-0.135263\pi$
$127$	3.45296	+	4.32987i	0.306400	+	0.384214i	−0.604662	+	0.796482i	$0.706692\pi$
$128$	9.25138	+	16.0239i	0.817715	+	1.41632i
$129$	9.54115	−	16.5258i	0.840051	−	1.45501i
$130$	1.47078	−	0.221685i	0.128996	−	0.0194430i
$131$	1.54326	−	1.43194i	0.134835	−	0.125109i	−0.609872	−	0.792500i	$-0.708779\pi$
$131$	1.54326	−	1.43194i	0.134835	−	0.125109i	0.744708	+	0.667391i	$0.232589\pi$
$132$	27.0102	+	13.0074i	2.35094	+	1.13215i
$133$	−13.7520	+	17.0682i	−1.19245	+	1.48000i
$134$	−3.33890	+	1.60793i	−0.288437	+	0.138904i
$135$	0.973785	−	2.48116i	0.0838101	−	0.213545i
$136$	−2.18749	+	29.1900i	−0.187575	+	2.50302i
$137$	7.98078	+	2.46174i	0.681844	+	0.210321i	0.616280	−	0.787527i	$-0.288639\pi$
$137$	7.98078	+	2.46174i	0.681844	+	0.210321i	0.0655643	+	0.997848i	$0.479115\pi$
$138$	−2.59969	−	34.6904i	−0.221300	−	2.95304i
$139$	1.81222	−	7.93984i	0.153710	−	0.673448i	−0.838077	−	0.545551i	$-0.816320\pi$
$139$	1.81222	−	7.93984i	0.153710	−	0.673448i	0.991787	−	0.127897i	$-0.0408226\pi$
$140$	−3.30010	+	5.65031i	−0.278909	+	0.477538i
$141$	−1.11832	−	4.89970i	−0.0941799	−	0.412629i
$142$	1.45303	−	0.448202i	0.121936	−	0.0376123i
$143$	0.966226	+	2.46190i	0.0807999	+	0.205875i
$144$	−15.7784	−	14.6402i	−1.31487	−	1.22002i
$145$	−5.02206	−	3.42399i	−0.417060	−	0.284347i
$146$	−19.2275			−1.59128
$147$	−19.3045	−	0.193644i	−1.59221	−	0.0159715i
$148$	−3.55056			−0.291854
$149$	−15.2778	−	10.4162i	−1.25161	−	0.853332i	−0.257993	−	0.966147i	$-0.583061\pi$
$149$	−15.2778	−	10.4162i	−1.25161	−	0.853332i	−0.993616	+	0.112814i	$0.964013\pi$
$150$	−23.1774	−	21.5055i	−1.89243	−	1.75592i
$151$	3.20978	+	8.17839i	0.261208	+	0.665548i	0.999965	−	0.00842483i	$-0.00268174\pi$
$151$	3.20978	+	8.17839i	0.261208	+	0.665548i	−0.738756	+	0.673973i	$0.764587\pi$
$152$	41.2925	−	12.7370i	3.34926	−	1.03311i
$153$	5.75203	+	25.2013i	0.465024	+	2.03740i
$154$	−16.5022	−	5.18102i	−1.32978	−	0.417499i
$155$	0.239579	−	1.04967i	0.0192435	−	0.0843111i
$156$	−0.847098	−	11.3037i	−0.0678221	−	0.905024i
$157$	−8.98951	−	2.77290i	−0.717441	−	0.221301i	−0.0855228	−	0.996336i	$-0.527256\pi$
$157$	−8.98951	−	2.77290i	−0.717441	−	0.221301i	−0.631918	+	0.775035i	$0.717732\pi$
$158$	−0.784785	+	10.4722i	−0.0624341	+	0.833125i
$159$	−10.4516	+	26.6304i	−0.828870	+	2.11193i
$160$	0.606633	−	0.292139i	0.0479585	−	0.0230956i
$161$	2.93821	+	13.1774i	0.231563	+	1.03853i
$162$	3.56762	+	1.71808i	0.280299	+	0.134985i
$163$	4.38364	−	4.06743i	0.343353	−	0.318585i	−0.489580	−	0.871958i	$-0.662850\pi$
$163$	4.38364	−	4.06743i	0.343353	−	0.318585i	0.832934	+	0.553373i	$0.186660\pi$
$164$	−19.7280	+	2.97352i	−1.54050	+	0.232193i
$165$	−2.19449	+	3.80097i	−0.170841	+	0.295905i
$166$	−1.98441	−	3.43709i	−0.154020	−	0.266770i
$167$	2.93883	+	3.68518i	0.227413	+	0.285167i	0.882427	−	0.470450i	$-0.155908\pi$
$167$	2.93883	+	3.68518i	0.227413	+	0.285167i	−0.655013	+	0.755617i	$0.727337\pi$
$168$	31.3386	+	21.5973i	2.41783	+	1.66627i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	−8.25396	−	1.24408i	−0.633050	−	0.0954169i
$171$	31.5292	−	21.4963i	2.41110	−	1.64386i
$172$	23.4969	−	16.0199i	1.79162	−	1.22151i
$173$	8.50847	+	1.28245i	0.646887	+	0.0975026i	0.464287	−	0.885685i	$-0.346311\pi$
$173$	8.50847	+	1.28245i	0.646887	+	0.0975026i	0.182600	+	0.983187i	$0.441549\pi$
$174$	−42.9351	+	53.8389i	−3.25490	+	4.08152i
$175$	10.1038	+	6.96314i	0.763776	+	0.526364i
$176$	7.70551	+	9.66240i	0.580824	+	0.728331i
$177$	−17.5888	−	30.4646i	−1.32205	−	2.28986i
$178$	11.9816	−	20.7527i	0.898057	−	1.55548i
$179$	19.5112	−	2.94083i	1.45833	−	0.219808i	0.628495	−	0.777814i	$-0.283671\pi$
$179$	19.5112	−	2.94083i	1.45833	−	0.219808i	0.829837	+	0.558005i	$0.188433\pi$
$180$	8.35081	−	7.74842i	0.622433	−	0.577533i
$181$	−10.8220	−	5.21161i	−0.804395	−	0.387376i	−0.0139448	−	0.999903i	$-0.504439\pi$
$181$	−10.8220	−	5.21161i	−0.804395	−	0.387376i	−0.790450	+	0.612527i	$0.790153\pi$
$182$	1.42328	+	6.38320i	0.105501	+	0.473154i
$183$	20.2967	−	9.77440i	1.50038	−	0.722544i
$184$	9.72417	−	24.7768i	0.716875	−	1.82657i
$185$	0.0388452	−	0.518353i	0.00285595	−	0.0381100i
$186$	−11.6560	−	3.59539i	−0.854658	−	0.263627i
$187$	−1.10915	−	14.8006i	−0.0811090	−	1.08232i
$188$	1.66664	−	7.30203i	0.121552	−	0.532555i
$189$	11.1815	+	3.51054i	0.813332	+	0.255354i
$190$	2.74201	+	12.0135i	0.198926	+	0.871552i
$191$	−10.5628	+	3.25818i	−0.764295	+	0.235754i	−0.652306	−	0.757956i	$-0.726198\pi$
$191$	−10.5628	+	3.25818i	−0.764295	+	0.235754i	−0.111989	+	0.993709i	$0.535722\pi$
$192$	6.62987	+	16.8926i	0.478470	+	1.21912i
$193$	−8.01646	−	7.43819i	−0.577037	−	0.535412i	0.336756	−	0.941592i	$-0.390670\pi$
$193$	−8.01646	−	7.43819i	−0.577037	−	0.535412i	−0.913793	+	0.406180i	$0.866861\pi$
$194$	24.9997	+	17.0445i	1.79487	+	1.22372i
$195$	1.65952			0.118841
$196$	−25.7952	−	12.7426i	−1.84252	−	0.910188i
$197$	16.4996			1.17555			0.587773	−	0.809026i	$-0.300005\pi$
$197$	16.4996			1.17555			0.587773	+	0.809026i	$0.300005\pi$
$198$	24.8799	+	16.9628i	1.76814	+	1.20549i
$199$	−8.93883	−	8.29402i	−0.633657	−	0.587947i	0.296535	−	0.955022i	$-0.404169\pi$
$199$	−8.93883	−	8.29402i	−0.633657	−	0.587947i	−0.930191	+	0.367075i	$0.880359\pi$
$200$	−8.83808	−	22.5191i	−0.624947	−	1.59234i
$201$	−3.95106	+	1.21874i	−0.278686	+	0.0859634i
$202$	−0.557518	−	2.44265i	−0.0392268	−	0.171864i
$203$	13.4786	−	23.0776i	0.946014	−	1.61973i
$204$	−14.1554	+	62.0190i	−0.991078	+	4.34220i
$205$	−0.218274	−	2.91266i	−0.0152449	−	0.203429i
$206$	2.73617	+	0.843996i	0.190638	+	0.0588040i
$207$	1.75651	−	23.4390i	0.122086	−	1.62912i
$208$	1.70722	−	4.34993i	0.118374	−	0.301613i
$209$	−19.7406	+	9.50659i	−1.36549	+	0.657585i
$210$	−6.80933	+	8.45132i	−0.469888	+	0.583197i
$211$	5.11764	+	2.46453i	0.352313	+	0.169665i	0.601666	−	0.798748i	$-0.294504\pi$
$211$	5.11764	+	2.46453i	0.352313	+	0.169665i	−0.249353	+	0.968413i	$0.580218\pi$
$212$	−31.2533	+	28.9988i	−2.14648	+	1.99165i
$213$	1.67761	−	0.252859i	0.114948	−	0.0173256i
$214$	−7.11871	+	12.3300i	−0.486625	+	0.842860i
$215$	2.08171	+	3.60562i	0.141971	+	0.245901i
$216$	−14.4055	−	18.0640i	−0.980172	−	1.22910i
$217$	4.67751	+	0.729031i	0.317530	+	0.0494899i
$218$	−23.9751	+	30.0638i	−1.62380	+	2.03618i
$219$	−21.2129	−	3.19734i	−1.43344	−	0.216056i
$220$	−5.40435	+	3.68462i	−0.364361	+	0.248417i
$221$	−4.63681	+	3.16132i	−0.311906	+	0.212654i
$222$	−5.82331	−	0.877723i	−0.390835	−	0.0589089i
$223$	2.39147	−	2.99881i	0.160145	−	0.200815i	−0.695285	−	0.718734i	$-0.744722\pi$
$223$	2.39147	−	2.99881i	0.160145	−	0.200815i	0.855430	+	0.517919i	$0.173293\pi$
$224$	1.46737	+	2.57125i	0.0980428	+	0.171799i
$225$	−13.3195	−	16.7022i	−0.887970	−	1.11348i
$226$	−20.6405	−	35.7504i	−1.37299	−	2.37808i
$227$	10.8757	−	18.8373i	0.721846	−	1.25027i	−0.238414	−	0.971164i	$-0.576627\pi$
$227$	10.8757	−	18.8373i	0.721846	−	1.25027i	0.960259	−	0.279109i	$-0.0900392\pi$
$228$	92.8606	−	13.9965i	6.14984	−	0.926939i
$229$	−11.7583	+	10.9101i	−0.777008	+	0.720958i	−0.965297	−	0.261155i	$-0.915897\pi$
$229$	−11.7583	+	10.9101i	−0.777008	+	0.720958i	0.188288	+	0.982114i	$0.439706\pi$
$230$	6.83839	+	3.29320i	0.450910	+	0.217147i
$231$	−17.3447	−	8.46017i	−1.14119	−	0.556638i
$232$	−47.4703	+	22.8605i	−3.11658	+	1.50086i
$233$	−1.70513	+	4.34460i	−0.111707	+	0.284624i	−0.975784	−	0.218734i	$-0.929807\pi$
$233$	−1.70513	+	4.34460i	−0.111707	+	0.284624i	0.864078	+	0.503358i	$0.167902\pi$
$234$	0.850859	−	11.3539i	0.0556224	−	0.742229i
$235$	1.04780	+	0.323204i	0.0683511	+	0.0210835i
$236$	−3.91774	−	52.2786i	−0.255023	−	3.40305i
$237$	−2.60725	+	11.4231i	−0.169359	+	0.742010i
$238$	2.92626	−	36.5850i	0.189681	−	2.37146i
$239$	−0.216133	−	0.946942i	−0.0139805	−	0.0612526i	0.967456	−	0.253037i	$-0.0814296\pi$
$239$	−0.216133	−	0.946942i	−0.0139805	−	0.0612526i	−0.981437	+	0.191785i	$0.938572\pi$
$240$	7.41034	−	2.28579i	0.478335	−	0.147547i
$241$	7.21939	+	18.3947i	0.465042	+	1.18491i	0.950521	+	0.310659i	$0.100550\pi$
$241$	7.21939	+	18.3947i	0.465042	+	1.18491i	−0.485479	+	0.874248i	$0.661355\pi$
$242$	7.25787	+	6.73432i	0.466554	+	0.432899i
$243$	14.6300	+	9.97458i	0.938517	+	0.639870i
$244$	33.5731			2.14929
$245$	2.14254	−	3.62648i	0.136882	−	0.231687i
$246$	−33.0912			−2.10982
$247$	6.84505	+	4.66688i	0.435540	+	0.296946i
$248$	−6.84145	−	6.34794i	−0.434433	−	0.403094i
$249$	−1.61776	−	4.12200i	−0.102522	−	0.261221i
$250$	13.6985	−	4.22543i	0.866370	−	0.267240i
$251$	−3.65061	−	15.9944i	−0.230424	−	1.00956i	−0.949289	−	0.314405i	$-0.898195\pi$
$251$	−3.65061	−	15.9944i	−0.230424	−	1.00956i	0.718865	−	0.695150i	$-0.244662\pi$
$252$	36.5465	+	34.2529i	2.30221	+	2.15773i
$253$	−3.00310	+	13.1574i	−0.188803	+	0.827200i
$254$	1.02302	+	13.6512i	0.0641898	+	0.856553i
$255$	−8.89939	−	2.74510i	−0.557302	−	0.171905i
$256$	−2.43444	+	32.4854i	−0.152153	+	2.03034i
$257$	9.21184	−	23.4714i	0.574619	−	1.46411i	−0.287690	−	0.957724i	$-0.592887\pi$
$257$	9.21184	−	23.4714i	0.574619	−	1.46411i	0.862309	−	0.506382i	$-0.169017\pi$
$258$	42.4978	−	20.4658i	2.64579	−	1.27415i
$259$	2.28551	+	0.0114628i	0.142015	+	0.000712262i
$260$	2.22827	+	1.07308i	0.138191	+	0.0665494i
$261$	−34.1073	+	31.6469i	−2.11119	+	1.95890i
$262$	5.14579	−	0.775603i	0.317908	−	0.0479169i
$263$	−7.03361	+	12.1826i	−0.433711	+	0.751210i	−0.997189	−	0.0749212i	$-0.976129\pi$
$263$	−7.03361	+	12.1826i	−0.433711	+	0.751210i	0.563478	+	0.826131i	$0.309463\pi$
$264$	19.0225	+	32.9480i	1.17076	+	2.02781i
$265$	−3.89166	−	4.87998i	−0.239063	−	0.299775i
$266$	−51.8532	+	15.7102i	−3.17932	+	0.963255i
$267$	16.6698	−	20.9032i	1.02017	−	1.27926i
$268$	−6.09321	−	0.918404i	−0.372202	−	0.0561005i
$269$	22.7459	−	15.5079i	1.38684	−	0.945533i	0.387118	−	0.922030i	$-0.373471\pi$
$269$	22.7459	−	15.5079i	1.38684	−	0.945533i	0.999724	−	0.0235025i	$-0.00748176\pi$
$270$	5.44372	−	3.71147i	0.331294	−	0.225873i
$271$	6.33830	+	0.955346i	0.385025	+	0.0580331i	0.338703	−	0.940893i	$-0.390012\pi$
$271$	6.33830	+	0.955346i	0.385025	+	0.0580331i	0.0463219	+	0.998927i	$0.485250\pi$
$272$	−16.3506	+	20.5030i	−0.991402	+	1.24318i
$273$	0.508788	+	7.27902i	0.0307933	+	0.440546i
$274$	12.8717	+	16.1406i	0.777609	+	0.975090i
$275$	6.13301	+	10.6227i	0.369835	+	0.640572i
$276$	28.9218	−	50.0941i	1.74089	−	3.01531i
$277$	6.94518	−	1.04682i	0.417295	−	0.0628972i	0.0629611	−	0.998016i	$-0.479946\pi$
$277$	6.94518	−	1.04682i	0.417295	−	0.0628972i	0.354334	+	0.935119i	$0.384707\pi$
$278$	14.7570	−	13.6925i	0.885068	−	0.821223i
$279$	−7.42547	−	3.57592i	−0.444551	−	0.214084i
$280$	−7.49960	+	3.56539i	−0.448187	+	0.213073i
$281$	−13.5183	+	6.51007i	−0.806434	+	0.388358i	−0.791224	−	0.611526i	$-0.790556\pi$
$281$	−13.5183	+	6.51007i	−0.806434	+	0.388358i	−0.0152100	+	0.999884i	$0.504842\pi$
$282$	4.53859	−	11.5641i	0.270269	−	0.688634i
$283$	−2.19786	+	29.3284i	−0.130649	+	1.74339i	0.418988	+	0.907992i	$0.362385\pi$
$283$	−2.19786	+	29.3284i	−0.130649	+	1.74339i	−0.549638	+	0.835403i	$0.685234\pi$
$284$	2.41605	+	0.745254i	0.143366	+	0.0442227i
$285$	1.02742	+	13.7100i	0.0608593	+	0.812111i
$286$	−1.45471	+	6.37351i	−0.0860189	+	0.376873i
$287$	12.7086	−	1.85038i	0.750167	−	0.109225i
$288$	−1.14689	−	5.02486i	−0.0675813	−	0.296093i
$289$	13.8500	−	4.27217i	0.814708	−	0.251304i
$290$	−5.48909	−	13.9860i	−0.322331	−	0.821285i
$291$	24.7469	+	22.9617i	1.45069	+	1.34604i
$292$	−26.4155	−	18.0098i	−1.54585	−	1.05394i
$293$	−16.1346			−0.942593			−0.471296	−	0.881975i	$-0.656214\pi$
$293$	−16.1346			−0.942593			−0.471296	+	0.881975i	$0.656214\pi$
$294$	−39.1570	−	27.2761i	−2.28368	−	1.59077i
$295$	7.67511			0.446862
$296$	−3.72291	−	2.53823i	−0.216390	−	0.147532i
$297$	8.58774	+	7.96826i	0.498311	+	0.462365i
$298$	−16.6986	−	42.5473i	−0.967324	−	2.46470i
$299$	4.87620	−	1.50411i	0.281998	−	0.0869848i
$300$	−11.6986	−	51.2548i	−0.675417	−	2.95920i
$301$	−15.1768	+	10.2363i	−0.874777	+	0.590008i
$302$	−4.83252	+	21.1726i	−0.278080	+	1.21835i
$303$	−0.208901	−	2.78759i	−0.0120010	−	0.160143i
$304$	36.9936	+	11.4110i	2.12173	+	0.654466i
$305$	−0.367309	+	4.90139i	−0.0210320	+	0.280653i
$306$	−23.3439	+	59.4794i	−1.33448	+	3.40021i
$307$	−23.9773	+	11.5468i	−1.36846	+	0.659013i	−0.966505	−	0.256648i	$-0.917382\pi$
$307$	−23.9773	+	11.5468i	−1.36846	+	0.659013i	−0.401951	+	0.915661i	$0.631668\pi$
$308$	−17.8184	−	22.5750i	−1.01530	−	1.28633i
$309$	2.87836	+	1.38615i	0.163744	+	0.0788551i
$310$	1.95092	−	1.81019i	0.110805	−	0.102812i
$311$	5.88025	−	0.886305i	0.333438	−	0.0502577i	0.0198105	−	0.999804i	$-0.493694\pi$
$311$	5.88025	−	0.886305i	0.333438	−	0.0502577i	0.313628	+	0.949546i	$0.398456\pi$
$312$	7.19264	−	12.4580i	0.407203	−	0.705296i
$313$	−4.56714	−	7.91052i	−0.258150	−	0.447129i	0.707596	−	0.706617i	$-0.249780\pi$
$313$	−4.56714	−	7.91052i	−0.258150	−	0.447129i	−0.965746	+	0.259488i	$0.916446\pi$
$314$	−14.4986	−	18.1807i	−0.818205	−	1.02600i
$315$	−5.40048	+	4.96074i	−0.304282	+	0.279506i
$316$	−10.8872	+	13.6521i	−0.612451	+	0.767990i
$317$	−7.42655	−	1.11937i	−0.417117	−	0.0628702i	−0.0628688	−	0.998022i	$-0.520025\pi$
$317$	−7.42655	−	1.11937i	−0.417117	−	0.0628702i	−0.354248	+	0.935152i	$0.615263\pi$
$318$	−58.4275	+	39.8352i	−3.27645	+	2.23385i
$319$	22.0730	−	15.0491i	1.23585	−	0.842590i
$320$	−3.91514	−	0.590113i	−0.218863	−	0.0329883i
$321$	−9.90416	+	12.4194i	−0.552796	+	0.693184i
$322$	−12.3481	+	31.0043i	−0.688132	+	1.72780i
$323$	−28.9877	−	36.3495i	−1.61292	−	2.02254i
$324$	3.29208	+	5.70204i	0.182893	+	0.316780i
$325$	2.31896	−	4.01656i	0.128633	−	0.222799i
$326$	14.6167	−	2.20311i	0.809542	−	0.122019i
$327$	−31.4501	+	29.1814i	−1.73919	+	1.61374i
$328$	−22.8114	−	10.9854i	−1.25955	−	0.606565i
$329$	−1.09640	+	4.69498i	−0.0604465	+	0.258843i
$330$	−9.77459	+	4.70720i	−0.538074	+	0.259123i
$331$	−10.7161	+	27.3042i	−0.589010	+	1.50077i	0.256355	+	0.966583i	$0.417478\pi$
$331$	−10.7161	+	27.3042i	−0.589010	+	1.50077i	−0.845365	+	0.534190i	$0.820617\pi$
$332$	0.493159	−	6.58075i	0.0270656	−	0.361165i
$333$	−3.80225	−	1.17284i	−0.208362	−	0.0642712i
$334$	0.870695	+	11.6186i	0.0476423	+	0.635742i
$335$	0.200743	−	0.879512i	0.0109678	−	0.0480529i
$336$	12.2979	+	31.8025i	0.670904	+	1.73497i
$337$	−4.80563	−	21.0548i	−0.261779	−	1.14693i	−0.919320	−	0.393511i	$-0.871260\pi$
$337$	−4.80563	−	21.0548i	−0.261779	−	1.14693i	0.657540	−	0.753419i	$-0.271597\pi$
$338$	2.36205	−	0.728596i	0.128479	−	0.0396304i
$339$	−16.8270	−	42.8744i	−0.913915	−	2.32862i
$340$	−10.1743	−	9.44040i	−0.551780	−	0.511977i
$341$	3.90988	+	2.66571i	0.211732	+	0.144356i
$342$	94.3264			5.10059
$343$	16.5634	+	8.28578i	0.894339	+	0.447390i
$344$	36.0898			1.94583
$345$	6.99691	+	4.77041i	0.376701	+	0.256830i
$346$	15.5916	+	14.4669i	0.838208	+	0.777743i
$347$	−12.0122	−	30.6066i	−0.644849	−	1.64305i	−0.760174	−	0.649720i	$-0.774886\pi$
$347$	−12.0122	−	30.6066i	−0.644849	−	1.64305i	0.115325	−	0.993328i	$-0.463209\pi$
$348$	−109.415	+	33.7501i	−5.86527	+	1.80920i
$349$	5.66273	+	24.8100i	0.303119	+	1.32805i	0.865391	+	0.501098i	$0.167070\pi$
$349$	5.66273	+	24.8100i	0.303119	+	1.32805i	−0.562272	+	0.826953i	$0.690072\pi$
$350$	10.9397	+	28.2903i	0.584751	+	1.51218i
$351$	0.985677	−	4.31853i	0.0526116	−	0.230506i
$352$	0.221152	+	2.95107i	0.0117874	+	0.157293i
$353$	18.1121	+	5.58686i	0.964012	+	0.297358i	0.736516	−	0.676421i	$-0.236470\pi$
$353$	18.1121	+	5.58686i	0.964012	+	0.297358i	0.227496	+	0.973779i	$0.426946\pi$
$354$	6.49810	−	86.7111i	0.345370	−	4.60865i
$355$	−0.135234	+	0.344571i	−0.00717748	+	0.0182879i
$356$	35.8992	−	17.2881i	1.90265	−	0.916270i
$357$	9.31215	−	39.8763i	0.492851	−	2.11048i
$358$	43.9437	+	21.1622i	2.32250	+	1.11845i
$359$	12.4642	−	11.5651i	0.657835	−	0.610382i	−0.278942	−	0.960308i	$-0.589984\pi$
$359$	12.4642	−	11.5651i	0.657835	−	0.610382i	0.936777	+	0.349926i	$0.113793\pi$
$360$	14.2954	−	2.15468i	0.753433	−	0.113562i
$361$	−24.8172	+	42.9847i	−1.30617	+	2.26235i
$362$	−14.8455	−	25.7131i	−0.780261	−	1.35145i
$363$	6.88748	+	8.63663i	0.361499	+	0.453306i
$364$	−4.02358	+	10.1026i	−0.210893	+	0.529522i
$365$	2.91828	−	3.65941i	0.152750	−	0.191542i
$366$	55.0635	+	8.29949i	2.87822	+	0.433821i
$367$	−19.8666	+	13.5448i	−1.03703	+	0.707033i	−0.957097	−	0.289768i	$-0.906422\pi$
$367$	−19.8666	+	13.5448i	−1.03703	+	0.707033i	−0.0799297	+	0.996801i	$0.525470\pi$
$368$	19.7022	−	13.4327i	1.02705	−	0.700230i
$369$	−22.1087	−	3.33235i	−1.15093	−	0.173475i
$370$	0.801118	−	1.00457i	0.0416481	−	0.0522251i
$371$	20.2115	−	18.5658i	1.04933	−	0.963887i
$372$	−12.6458	−	15.8573i	−0.655652	−	0.822162i
$373$	0.468914	+	0.812183i	0.0242794	+	0.0420532i	0.877910	−	0.478826i	$-0.158938\pi$
$373$	0.468914	+	0.812183i	0.0242794	+	0.0420532i	−0.853630	+	0.520879i	$0.825604\pi$
$374$	18.3438	−	31.7724i	0.948536	−	1.64291i
$375$	15.8157	−	2.38383i	0.816719	−	0.123101i
$376$	6.96764	−	6.46503i	0.359329	−	0.333408i
$377$	−9.10092	−	4.38277i	−0.468721	−	0.225724i
$378$	17.9483	+	22.7394i	0.923159	+	1.16959i
$379$	−16.5967	+	7.99256i	−0.852517	+	0.410550i	−0.808511	−	0.588481i	$-0.799726\pi$
$379$	−16.5967	+	7.99256i	−0.852517	+	0.410550i	−0.0440056	+	0.999031i	$0.514012\pi$
$380$	−7.48560	+	19.0730i	−0.384003	+	0.978424i
$381$	−1.14140	+	15.2310i	−0.0584759	+	0.780307i
$382$	−26.1098	−	8.05380i	−1.33589	−	0.412068i
$383$	2.43436	+	32.4843i	0.124390	+	1.65987i	0.615027	+	0.788506i	$0.289145\pi$
$383$	2.43436	+	32.4843i	0.124390	+	1.65987i	−0.490637	+	0.871364i	$0.663236\pi$
$384$	−11.3551	+	49.7498i	−0.579461	+	2.53878i
$385$	3.49070	−	2.35436i	0.177903	−	0.119990i
$386$	−6.01512	−	26.3540i	−0.306161	−	1.34138i
$387$	30.4543	−	9.39392i	1.54808	−	0.477520i
$388$	18.3805	+	46.8328i	0.933130	+	2.37758i
$389$	1.55856	+	1.44613i	0.0790219	+	0.0733217i	0.718695	−	0.695325i	$-0.244740\pi$
$389$	1.55856	+	1.44613i	0.0790219	+	0.0733217i	−0.639673	+	0.768647i	$0.720930\pi$
$390$	3.38933	+	2.31081i	0.171625	+	0.117012i
$391$	−28.6373			−1.44825
$392$	−17.9379	−	31.8017i	−0.905998	−	1.60623i
$393$	5.80613			0.292881
$394$	33.6980	+	22.9749i	1.69768	+	1.15746i
$395$	−1.87398	−	1.73880i	−0.0942902	−	0.0874885i
$396$	18.2924	+	46.6084i	0.919230	+	2.34216i
$397$	4.55851	−	1.40611i	0.228785	−	0.0705709i	−0.178243	−	0.983987i	$-0.557041\pi$
$397$	4.55851	−	1.40611i	0.228785	−	0.0705709i	0.407028	+	0.913416i	$0.366565\pi$
$398$	−6.70721	−	29.3862i	−0.336202	−	1.47300i
$399$	−59.8200	+	8.70981i	−2.99475	+	0.436036i
$400$	4.82265	−	21.1294i	0.241132	−	1.05647i
$401$	−1.36624	−	18.2312i	−0.0682268	−	0.910424i	−0.921355	−	0.388722i	$-0.872917\pi$
$401$	−1.36624	−	18.2312i	−0.0682268	−	0.910424i	0.853128	−	0.521702i	$-0.174703\pi$
$402$	−9.76651	−	3.01257i	−0.487109	−	0.150253i
$403$	0.133713	−	1.78427i	0.00666071	−	0.0888810i
$404$	1.52201	−	3.87802i	0.0757228	−	0.192939i
$405$	−0.868469	+	0.418233i	−0.0431546	+	0.0207821i
$406$	59.6626	−	28.3643i	2.96101	−	1.40769i
$407$	2.05840	+	0.991275i	0.102031	+	0.0491357i
$408$	−59.1789	+	54.9100i	−2.92979	+	2.71845i
$409$	10.7503	−	1.62034i	0.531567	−	0.0801208i	0.122226	−	0.992502i	$-0.460997\pi$
$409$	10.7503	−	1.62034i	0.531567	−	0.0801208i	0.409341	+	0.912381i	$0.365759\pi$
$410$	3.60995	−	6.25262i	0.178283	−	0.308795i
$411$	11.5168	+	19.9478i	0.568084	+	0.983950i
$412$	2.96851	+	3.72240i	0.146248	+	0.183389i
$413$	2.35309	+	33.6647i	0.115788	+	1.65653i
$414$	36.2251	−	45.4248i	1.78036	−	2.23251i
$415$	0.955340	+	0.143994i	0.0468958	+	0.00706840i
$416$	0.924529	−	0.630333i	0.0453288	−	0.0309046i
$417$	18.5578	−	12.6525i	0.908780	−	0.619595i
$418$	−53.5549	−	8.07210i	−2.61945	−	0.394819i
$419$	−5.98691	+	7.50735i	−0.292480	+	0.366758i	−0.906261	−	0.422718i	$-0.861076\pi$
$419$	−5.98691	+	7.50735i	−0.292480	+	0.366758i	0.613782	+	0.789476i	$0.289648\pi$
$420$	−17.2710	+	5.23269i	−0.842739	+	0.255329i
$421$	11.6877	+	14.6559i	0.569622	+	0.714283i	0.980304	−	0.197496i	$-0.0632808\pi$
$421$	11.6877	+	14.6559i	0.569622	+	0.714283i	−0.410682	+	0.911779i	$0.634709\pi$
$422$	7.02030	+	12.1595i	0.341743	+	0.591916i
$423$	4.19683	−	7.26913i	0.204057	−	0.353437i
$424$	−53.5011	+	8.06399i	−2.59824	+	0.391622i
$425$	−19.0797	+	17.7034i	−0.925502	+	0.858740i
$426$	3.77837	+	1.81956i	0.183062	+	0.0881582i
$427$	−21.6112	−	0.108389i	−1.04584	−	0.00524529i
$428$	−21.3291	+	10.2715i	−1.03098	+	0.496494i
$429$	−2.66478	+	6.78974i	−0.128657	+	0.327812i
$430$	−0.769079	+	10.2626i	−0.0370883	+	0.494908i
$431$	−24.1059	−	7.43568i	−1.16114	−	0.358164i	−0.346454	−	0.938067i	$-0.612614\pi$
$431$	−24.1059	−	7.43568i	−1.16114	−	0.358164i	−0.814686	+	0.579903i	$0.803091\pi$
$432$	−1.54686	−	20.6414i	−0.0744233	−	0.993110i
$433$	4.69094	−	20.5523i	0.225432	−	0.987682i	−0.727882	−	0.685702i	$-0.759495\pi$
$433$	4.69094	−	20.5523i	0.225432	−	0.987682i	0.953314	−	0.301980i	$-0.0976476\pi$
$434$	8.53798	+	8.00215i	0.409836	+	0.384116i
$435$	−3.73018	−	16.3430i	−0.178848	−	0.783586i
$436$	−61.0977	+	18.8462i	−2.92605	+	0.902567i
$437$	15.4450	+	39.3532i	0.738833	+	1.88252i
$438$	−38.8722	−	36.0681i	−1.85739	−	1.72340i
$439$	2.59089	+	1.76644i	0.123657	+	0.0843076i	0.623569	−	0.781768i	$-0.285682\pi$
$439$	2.59089	+	1.76644i	0.123657	+	0.0843076i	−0.499912	+	0.866076i	$0.666634\pi$
$440$	−8.30076			−0.395723
$441$	−23.4146	−	22.1667i	−1.11498	−	1.05556i
$442$	−13.8720			−0.659824
$443$	7.42626	+	5.06314i	0.352832	+	0.240557i	0.726746	−	0.686907i	$-0.241032\pi$
$443$	7.42626	+	5.06314i	0.352832	+	0.240557i	−0.373913	+	0.927464i	$0.621984\pi$
$444$	−7.17816	−	6.66036i	−0.340661	−	0.316087i
$445$	2.13117	+	5.43013i	0.101027	+	0.257413i
$446$	9.05994	−	2.79462i	0.429001	−	0.132329i
$447$	−11.3477	−	49.7177i	−0.536729	−	2.35156i
$448$	1.38803	−	17.3536i	0.0655781	−	0.819879i
$449$	3.72297	−	16.3114i	0.175698	−	0.769782i	−0.807887	−	0.589337i	$-0.799389\pi$
$449$	3.72297	−	16.3114i	0.175698	−	0.769782i	0.983585	−	0.180445i	$-0.0577539\pi$
$450$	−3.94622	−	52.6586i	−0.186026	−	2.48235i
$451$	12.2673	+	3.78396i	0.577645	+	0.178180i
$452$	5.12953	−	68.4488i	0.241273	−	3.21956i
$453$	−8.85233	+	22.5554i	−0.415919	+	1.05974i
$454$	48.4420	−	23.3285i	2.27350	−	1.09486i
$455$	−1.43088	−	0.697939i	−0.0670808	−	0.0327199i
$456$	107.374	+	51.7086i	5.02825	+	2.42148i
$457$	26.8020	−	24.8686i	1.25374	−	1.16330i	0.274288	−	0.961648i	$-0.411558\pi$
$457$	26.8020	−	24.8686i	1.25374	−	1.16330i	0.979456	−	0.201657i	$-0.0646326\pi$
$458$	−39.2063	+	5.90940i	−1.83199	+	0.276128i
$459$	−12.4293	+	21.5282i	−0.580151	+	1.00485i
$460$	6.31023	+	10.9296i	0.294216	+	0.509597i
$461$	−3.73352	−	4.68169i	−0.173887	−	0.218048i	0.687249	−	0.726422i	$-0.258818\pi$
$461$	−3.73352	−	4.68169i	−0.173887	−	0.218048i	−0.861136	+	0.508374i	$0.830247\pi$
$462$	−23.6435	−	41.4303i	−1.10000	−	1.92751i
$463$	−5.54022	+	6.94721i	−0.257476	+	0.322864i	−0.893722	−	0.448622i	$-0.851915\pi$
$463$	−5.54022	+	6.94721i	−0.257476	+	0.322864i	0.636246	+	0.771486i	$0.280486\pi$
$464$	−46.6755	−	7.03520i	−2.16686	−	0.326601i
$465$	2.45339	−	1.67269i	0.113773	−	0.0775692i
$466$	−9.53212	+	6.49889i	−0.441567	+	0.301055i
$467$	2.67620	+	0.403373i	0.123840	+	0.0186659i	0.210670	−	0.977557i	$-0.432436\pi$
$467$	2.67620	+	0.403373i	0.123840	+	0.0186659i	−0.0868298	+	0.996223i	$0.527674\pi$
$468$	11.8038	−	14.8015i	0.545631	−	0.684200i
$469$	3.91927	+	0.610853i	0.180975	+	0.0282066i
$470$	1.68994	+	2.11912i	0.0779510	+	0.0977475i
$471$	−12.9725	−	22.4691i	−0.597742	−	1.03532i
$472$	33.2652	−	57.6170i	1.53115	−	2.65204i
$473$	−18.0947	+	2.72734i	−0.831995	+	0.125403i
$474$	−21.2311	+	19.6995i	−0.975175	+	0.904830i
$475$	34.6182	+	16.6712i	1.58839	+	0.764929i
$476$	38.2883	−	47.5211i	1.75494	−	2.17812i
$477$	−43.0478	+	20.7307i	−1.97102	+	0.949194i
$478$	0.877152	−	2.23495i	0.0401200	−	0.102224i
$479$	−1.37866	+	18.3970i	−0.0629926	+	0.840578i	0.872811	+	0.488058i	$0.162294\pi$
$479$	−1.37866	+	18.3970i	−0.0629926	+	0.840578i	−0.935804	+	0.352521i	$0.885325\pi$
$480$	1.77444	+	0.547343i	0.0809918	+	0.0249827i
$481$	−0.0645559	−	0.861439i	−0.00294350	−	0.0392782i
$482$	−10.8692	+	47.6212i	−0.495080	+	2.16909i
$483$	−18.7789	+	32.1525i	−0.854469	+	1.46299i
$484$	3.66333	+	16.0501i	0.166515	+	0.729551i
$485$	−7.03830	+	2.17103i	−0.319593	+	0.0985814i
$486$	15.9906	+	40.7433i	0.725346	+	1.84815i
$487$	14.8387	+	13.7683i	0.672406	+	0.623902i	0.940621	−	0.339457i	$-0.110243\pi$
$487$	14.8387	+	13.7683i	0.672406	+	0.623902i	−0.268215	+	0.963359i	$0.586434\pi$
$488$	35.2027	+	24.0008i	1.59355	+	1.08647i
$489$	16.4923			0.745810
$490$	9.42552	−	4.42318i	0.425802	−	0.199819i
$491$	10.0456			0.453351			0.226676	−	0.973970i	$-0.427214\pi$
$491$	10.0456			0.453351			0.226676	+	0.973970i	$0.427214\pi$
$492$	−45.4620	−	30.9955i	−2.04959	−	1.39738i
$493$	41.5551	+	38.5575i	1.87155	+	1.73654i
$494$	7.48161	+	19.0628i	0.336613	+	0.857677i
$495$	−7.00458	+	2.16063i	−0.314832	+	0.0971129i
$496$	−1.86054	−	8.15157i	−0.0835408	−	0.366016i
$497$	−1.55282	−	0.487524i	−0.0696536	−	0.0218685i
$498$	2.43564	−	10.6712i	0.109144	−	0.478190i
$499$	0.353972	+	4.72343i	0.0158460	+	0.211450i	0.999506	+	0.0314160i	$0.0100017\pi$
$499$	0.353972	+	4.72343i	0.0158460	+	0.211450i	−0.983660	+	0.180034i	$0.942379\pi$
$500$	22.7774	+	7.02590i	1.01864	+	0.314208i
$501$	−0.971455	+	12.9632i	−0.0434014	+	0.579151i
$502$	14.8156	−	37.7495i	0.661251	−	1.68484i
$503$	−28.0689	+	13.5173i	−1.25153	+	0.602705i	−0.937922	−	0.346847i	$-0.887252\pi$
$503$	−28.0689	+	13.5173i	−1.25153	+	0.602705i	−0.313609	+	0.949552i	$0.601538\pi$
$504$	13.8337	+	62.0420i	0.616201	+	2.76357i
$505$	0.549507	+	0.264629i	0.0244527	+	0.0117758i
$506$	−24.4545	+	22.6904i	−1.08713	+	1.00871i
$507$	2.72712	−	0.411047i	0.121116	−	0.0182552i
$508$	−11.3812	+	19.7128i	−0.504959	+	0.874615i
$509$	13.7496	+	23.8150i	0.609441	+	1.05558i	0.991333	+	0.131375i	$0.0419392\pi$
$509$	13.7496	+	23.8150i	0.609441	+	1.05558i	−0.381892	+	0.924207i	$0.624727\pi$
$510$	−14.3533	−	17.9985i	−0.635574	−	0.796985i
$511$	16.9457	+	11.6783i	0.749632	+	0.516617i
$512$	−27.1338	+	34.0247i	−1.19916	+	1.50369i
$513$	36.2875	+	5.46946i	1.60213	+	0.241482i
$514$	51.4967	−	35.1098i	2.27142	−	1.54863i
$515$	−0.575917	+	0.392654i	−0.0253779	+	0.0173024i
$516$	77.5549	+	11.6895i	3.41416	+	0.514602i
$517$	−3.00486	+	3.76798i	−0.132154	+	0.165716i
$518$	4.65187	+	3.20588i	0.204391	+	0.140858i
$519$	14.7959	+	18.5535i	0.649467	+	0.814406i
$520$	1.56930	+	2.71811i	0.0688185	+	0.119197i
$521$	−13.1753	+	22.8203i	−0.577220	+	0.999775i	0.418576	+	0.908182i	$0.362529\pi$
$521$	−13.1753	+	22.8203i	−0.577220	+	0.999775i	−0.995797	+	0.0915930i	$0.970804\pi$
$522$	−113.726	+	17.1414i	−4.97765	+	0.750260i
$523$	−16.9196	+	15.6991i	−0.739843	+	0.686474i	−0.957138	−	0.289632i	$-0.906467\pi$
$523$	−16.9196	+	15.6991i	−0.739843	+	0.686474i	0.217295	+	0.976106i	$0.430277\pi$
$524$	7.79598	+	3.75435i	0.340569	+	0.164009i
$525$	7.36496	+	33.0307i	0.321433	+	1.44158i
$526$	−31.3288	+	15.0871i	−1.36600	+	0.657831i
$527$	−3.66851	+	9.34721i	−0.159803	+	0.407171i
$528$	−2.54712	+	33.9890i	−0.110849	+	1.47918i
$529$	2.90463	+	0.895960i	0.126288	+	0.0389548i
$530$	−1.15299	−	15.3856i	−0.0500828	−	0.668308i
$531$	13.0735	−	57.2786i	0.567340	−	2.48568i
$532$	−85.9532	−	26.9859i	−3.72655	−	1.16999i
$533$	−1.08013	−	4.73236i	−0.0467856	−	0.204981i
$534$	63.1524	−	19.4799i	2.73287	−	0.842979i
$535$	−1.26621	−	3.22625i	−0.0547430	−	0.139483i
$536$	−5.73243	−	5.31892i	−0.247603	−	0.229742i
$537$	44.9623	+	30.6548i	1.94027	+	1.32285i
$538$	68.0492			2.93381
$539$	11.3969	+	14.5892i	0.490901	+	0.628399i
$540$	10.9552			0.471438
$541$	−5.11152	−	3.48497i	−0.219761	−	0.149831i	0.448436	−	0.893815i	$-0.351981\pi$
$541$	−5.11152	−	3.48497i	−0.219761	−	0.149831i	−0.668197	+	0.743984i	$0.732934\pi$
$542$	11.6148	+	10.7769i	0.498898	+	0.462910i
$543$	−12.1026	−	30.8370i	−0.519373	−	1.32334i
$544$	−6.00057	+	1.85093i	−0.257272	+	0.0793580i
$545$	−2.08294	−	9.12596i	−0.0892234	−	0.390913i
$546$	−9.09656	+	15.5748i	−0.389297	+	0.666540i
$547$	−1.13955	+	4.99268i	−0.0487235	+	0.213472i	−0.993429	−	0.114448i	$-0.963490\pi$
$547$	−1.13955	+	4.99268i	−0.0487235	+	0.213472i	0.944706	+	0.327919i	$0.106347\pi$
$548$	2.56527	+	34.2312i	0.109583	+	1.46228i
$549$	35.9530	+	11.0900i	1.53444	+	0.473311i
$550$	−2.26582	+	30.2352i	−0.0966148	+	1.28923i
$551$	30.5735	−	77.9000i	1.30247	−	3.31865i
$552$	66.1372	−	31.8500i	2.81499	−	1.35563i
$553$	7.05221	−	8.75277i	0.299890	−	0.372206i
$554$	15.6422	+	7.53287i	0.664572	+	0.320041i
$555$	1.05089	−	0.975085i	0.0446079	−	0.0413901i
$556$	33.0992	−	4.98890i	1.40372	−	0.211576i
$557$	−6.61547	+	11.4583i	−0.280306	+	0.485505i	−0.971460	−	0.237203i	$-0.923769\pi$
$557$	−6.61547	+	11.4583i	−0.280306	+	0.485505i	0.691154	+	0.722708i	$0.257103\pi$
$558$	−10.1861	−	17.6429i	−0.431213	−	0.746884i
$559$	4.31398	+	5.40956i	0.182462	+	0.228800i
$560$	−7.35071	−	1.14567i	−0.310624	−	0.0484136i
$561$	25.5215	−	32.0029i	1.07752	−	1.35116i
$562$	−36.6741	−	5.52774i	−1.54700	−	0.233173i
$563$	−17.6017	+	12.0006i	−0.741823	+	0.505766i	−0.874280	−	0.485423i	$-0.838666\pi$
$563$	−17.6017	+	12.0006i	−0.741823	+	0.505766i	0.132457	+	0.991189i	$0.457713\pi$
$564$	17.0671	−	11.6361i	0.718653	−	0.489969i
$565$	9.93684	+	1.49774i	0.418046	+	0.0630103i
$566$	−45.3273	+	56.8386i	−1.90525	+	2.38911i
$567$	−2.10072	−	3.68106i	−0.0882219	−	0.154590i
$568$	2.00056	+	2.50863i	0.0839417	+	0.105260i
$569$	−15.2340	−	26.3860i	−0.638642	−	1.10616i	−0.985731	−	0.168328i	$-0.946163\pi$
$569$	−15.2340	−	26.3860i	−0.638642	−	1.10616i	0.347089	−	0.937832i	$-0.387170\pi$
$570$	−16.9922	+	29.4313i	−0.711725	+	1.23274i
$571$	37.2444	−	5.61369i	1.55863	−	0.234925i	0.687575	−	0.726113i	$-0.258675\pi$
$571$	37.2444	−	5.61369i	1.55863	−	0.234925i	0.871054	+	0.491188i	$0.163437\pi$
$572$	−7.96841	+	7.39360i	−0.333176	+	0.309142i
$573$	−27.4667	−	13.2272i	−1.14744	−	0.552576i
$574$	28.5321	+	13.9170i	1.19091	+	0.580886i
$575$	21.3231	−	10.2687i	0.889236	−	0.428234i
$576$	−11.0729	+	28.2132i	−0.461369	+	1.17555i
$577$	0.665727	−	8.88351i	0.0277146	−	0.369825i	−0.966052	−	0.258347i	$-0.916822\pi$
$577$	0.665727	−	8.88351i	0.0277146	−	0.369825i	0.993767	−	0.111479i	$-0.0355587\pi$
$578$	34.2355	+	10.5603i	1.42401	+	0.439249i
$579$	−2.25385	−	30.0756i	−0.0936669	−	1.24990i
$580$	5.55909	−	24.3560i	0.230829	−	1.01133i
$581$	−0.338695	+	4.23447i	−0.0140514	+	0.175675i
$582$	18.5687	+	81.3548i	0.769698	+	3.37227i
$583$	26.2149	−	8.08623i	1.08571	−	0.334898i
$584$	−14.8228	−	37.7680i	−0.613374	−	1.56285i
$585$	2.03176	+	1.88520i	0.0840029	+	0.0779433i
$586$	−32.9525	−	22.4667i	−1.36126	−	0.928089i
$587$	30.4016			1.25481			0.627404	−	0.778694i	$-0.284117\pi$
$587$	30.4016			1.25481			0.627404	+	0.778694i	$0.284117\pi$
$588$	−28.2468	−	74.1501i	−1.16488	−	3.05790i
$589$	14.8234			0.610788
$590$	15.6753	+	10.6872i	0.645341	+	0.439986i
$591$	33.3572	+	30.9510i	1.37213	+	1.27315i
$592$	−1.47479	−	3.75770i	−0.0606135	−	0.154441i
$593$	29.9322	−	9.23285i	1.22917	−	0.379148i	0.388879	−	0.921289i	$-0.372862\pi$
$593$	29.9322	−	9.23285i	1.22917	−	0.379148i	0.840288	+	0.542141i	$0.182386\pi$
$594$	6.44378	+	28.2320i	0.264391	+	1.15837i
$595$	6.51879	+	6.10968i	0.267244	+	0.250473i
$596$	16.9115	−	74.0943i	0.692724	−	3.03502i
$597$	−2.51318	−	33.5360i	−0.102858	−	1.37254i
$598$	12.0533	+	3.71796i	0.492897	+	0.152039i
$599$	1.60597	−	21.4302i	0.0656181	−	0.875613i	−0.863149	−	0.504949i	$-0.831511\pi$
$599$	1.60597	−	21.4302i	0.0656181	−	0.875613i	0.928767	−	0.370664i	$-0.120870\pi$
$600$	24.3747	−	62.1058i	0.995095	−	2.53546i
$601$	−12.5854	+	6.06080i	−0.513368	+	0.247225i	−0.672587	−	0.740018i	$-0.734817\pi$
$601$	−12.5854	+	6.06080i	−0.513368	+	0.247225i	0.159219	+	0.987243i	$0.449103\pi$
$602$	−45.2499	−	0.226946i	−1.84425	−	0.00924965i
$603$	−6.22178	−	2.99625i	−0.253370	−	0.122017i
$604$	−26.4709	+	24.5614i	−1.07708	+	0.999388i
$605$	−2.38326	+	0.359219i	−0.0968935	+	0.0146043i
$606$	3.45494	−	5.98413i	0.140347	−	0.243088i
$607$	−23.6227	−	40.9158i	−0.958817	−	1.66072i	−0.725381	−	0.688347i	$-0.758336\pi$
$607$	−23.6227	−	40.9158i	−0.958817	−	1.66072i	−0.233436	−	0.972372i	$-0.574997\pi$
$608$	5.77984	+	7.24768i	0.234403	+	0.293932i
$609$	70.5402	−	21.3719i	2.85843	−	0.866033i
$610$	−7.57514	+	9.49892i	−0.306708	+	0.384600i
$611$	1.80193	+	0.271597i	0.0728981	+	0.0109876i
$612$	−87.7834	+	59.8497i	−3.54843	+	2.41928i
$613$	27.1089	−	18.4825i	1.09492	−	0.746502i	0.125543	−	0.992088i	$-0.459933\pi$
$613$	27.1089	−	18.4825i	1.09492	−	0.746502i	0.969375	+	0.245586i	$0.0789803\pi$
$614$	−65.0485	−	9.80449i	−2.62515	−	0.395677i
$615$	5.02247	−	6.29798i	0.202526	−	0.253959i
$616$	−2.54491	−	36.4089i	−0.102537	−	1.46696i
$617$	−18.6720	−	23.4140i	−0.751708	−	0.942612i	0.247950	−	0.968773i	$-0.420243\pi$
$617$	−18.6720	−	23.4140i	−0.751708	−	0.942612i	−0.999658	+	0.0261612i	$0.991672\pi$
$618$	3.94849	+	6.83898i	0.158832	+	0.275104i
$619$	−22.5916	+	39.1297i	−0.908031	+	1.57276i	−0.0912357	+	0.995829i	$0.529082\pi$
$619$	−22.5916	+	39.1297i	−0.908031	+	1.57276i	−0.816796	+	0.576927i	$0.804252\pi$
$620$	4.37579	−	0.659544i	0.175736	−	0.0264879i
$621$	16.5698	−	15.3745i	0.664922	−	0.616957i
$622$	13.2437	+	6.37782i	0.531023	+	0.255727i
$623$	−23.1643	+	11.0126i	−0.928059	+	0.441209i
$624$	11.6114	−	5.59174i	0.464826	−	0.223849i
$625$	7.19719	−	18.3382i	0.287888	−	0.733526i
$626$	1.68731	−	22.5156i	0.0674385	−	0.899904i
$627$	−57.7427	−	17.8113i	−2.30602	−	0.711314i
$628$	−2.88951	−	38.5578i	−0.115304	−	1.53862i
$629$	−1.07876	+	4.72636i	−0.0430130	+	0.188452i
$630$	−17.9373	+	2.61167i	−0.714639	+	0.104052i
$631$	−7.27177	−	31.8597i	−0.289485	−	1.26832i	−0.885234	−	0.465145i	$-0.846002\pi$
$631$	−7.27177	−	31.8597i	−0.289485	−	1.26832i	0.595750	−	0.803170i	$-0.296855\pi$
$632$	−21.1753	+	6.53171i	−0.842308	+	0.259818i
$633$	5.72322	+	14.5825i	0.227478	+	0.579604i
$634$	−13.6090	−	12.6273i	−0.540481	−	0.501493i
$635$	−2.75339	−	1.87723i	−0.109265	−	0.0744957i
$636$	−117.582			−4.66245
$637$	2.62262	−	6.49014i	0.103912	−	0.257149i
$638$	66.0361			2.61440
$639$	2.34115	+	1.59617i	0.0926144	+	0.0631434i
$640$	−8.16155	−	7.57281i	−0.322613	−	0.299341i
$641$	−3.59265	−	9.15393i	−0.141901	−	0.361558i	0.842200	−	0.539165i	$-0.181260\pi$
$641$	−3.59265	−	9.15393i	−0.141901	−	0.361558i	−0.984102	+	0.177606i	$0.943165\pi$
$642$	−37.5213	+	11.5738i	−1.48085	+	0.456780i
$643$	−2.71848	−	11.9104i	−0.107206	−	0.469701i	−0.999822	−	0.0188825i	$-0.993989\pi$
$643$	−2.71848	−	11.9104i	−0.107206	−	0.469701i	0.892615	−	0.450819i	$-0.148868\pi$
$644$	−46.0051	+	31.0289i	−1.81285	+	1.22271i
$645$	−2.55507	+	11.1945i	−0.100606	+	0.440783i
$646$	−8.58827	−	114.602i	−0.337901	−	4.50898i
$647$	6.33088	+	1.95282i	0.248893	+	0.0767732i	0.416691	−	0.909048i	$-0.363190\pi$
$647$	6.33088	+	1.95282i	0.248893	+	0.0767732i	−0.167799	+	0.985821i	$0.553666\pi$
$648$	−0.624418	+	8.33228i	−0.0245294	+	0.327323i
$649$	−12.3243	+	31.4018i	−0.483771	+	1.23263i
$650$	10.3290	−	4.97419i	0.405137	−	0.195104i
$651$	8.08895	+	10.2482i	0.317031	+	0.401660i
$652$	22.1445	+	10.6642i	0.867247	+	0.417644i
$653$	−24.2602	+	22.5102i	−0.949375	+	0.880891i	−0.992995	−	0.118157i	$-0.962301\pi$
$653$	−24.2602	+	22.5102i	−0.949375	+	0.880891i	0.0436202	+	0.999048i	$0.486111\pi$
$654$	−104.866	+	15.8060i	−4.10058	+	0.618063i
$655$	−0.633397	+	1.09708i	−0.0247489	+	0.0428663i
$656$	−11.3414	−	19.6439i	−0.442807	−	0.766964i
$657$	−22.3390	−	28.0122i	−0.871526	−	1.09286i
$658$	−8.77678	+	8.06212i	−0.342154	+	0.314294i
$659$	20.9431	−	26.2618i	0.815828	−	1.02302i	−0.183373	−	0.983043i	$-0.558702\pi$
$659$	20.9431	−	26.2618i	0.815828	−	1.02302i	0.999201	−	0.0399725i	$-0.0127270\pi$
$660$	−17.8378	−	2.68862i	−0.694336	−	0.104654i
$661$	35.5947	−	24.2680i	1.38447	−	0.943917i	0.384689	−	0.923046i	$-0.374309\pi$
$661$	35.5947	−	24.2680i	1.38447	−	0.943917i	0.999782	−	0.0208708i	$-0.00664385\pi$
$662$	−59.9058	+	40.8431i	−2.32831	+	1.58741i
$663$	−15.3044	−	2.30677i	−0.594376	−	0.0895877i
$664$	5.22156	−	6.54763i	0.202636	−	0.254097i
$665$	4.88010	−	12.2532i	0.189242	−	0.475160i
$666$	−6.13242	−	7.68981i	−0.237626	−	0.297974i
$667$	−25.7729	−	44.6400i	−0.997931	−	1.72847i
$668$	−9.68660	+	16.7777i	−0.374786	+	0.649148i
$669$	10.4602	−	1.57662i	0.404415	−	0.0609557i
$670$	1.63467	−	1.51675i	0.0631527	−	0.0585971i
$671$	−19.4637	−	9.37321i	−0.751387	−	0.361849i
$672$	−1.85674	+	7.95089i	−0.0716254	+	0.306712i
$673$	24.7315	−	11.9101i	0.953331	−	0.459100i	0.108478	−	0.994099i	$-0.465402\pi$
$673$	24.7315	−	11.9101i	0.953331	−	0.459100i	0.844853	+	0.534999i	$0.179688\pi$
$674$	19.5031	−	49.6931i	0.751231	−	1.91411i
$675$	1.53526	−	20.4867i	0.0590923	−	0.788532i
$676$	3.92754	+	1.21148i	0.151059	+	0.0465955i
$677$	0.748778	+	9.99175i	0.0287779	+	0.384014i	0.992933	+	0.118675i	$0.0378648\pi$
$677$	0.748778	+	9.99175i	0.0287779	+	0.384014i	−0.964155	+	0.265339i	$0.914516\pi$
$678$	25.3340	−	110.995i	0.972946	−	4.26276i
$679$	−11.6805	−	30.2059i	−0.448255	−	1.15920i
$680$	−3.91942	−	17.1721i	−0.150303	−	0.658520i
$681$	57.3235	−	17.6820i	2.19664	−	0.677575i
$682$	4.27348	+	10.8887i	0.163640	+	0.416948i
$683$	−6.13517	−	5.69260i	−0.234756	−	0.217821i	0.554019	−	0.832504i	$-0.313094\pi$
$683$	−6.13517	−	5.69260i	−0.234756	−	0.217821i	−0.788774	+	0.614683i	$0.789284\pi$
$684$	129.589	+	88.3526i	4.95497	+	3.37824i
$685$	−5.02554			−0.192016
$686$	22.2907	+	39.9862i	0.851064	+	1.52668i
$687$	−44.2375			−1.68777
$688$	26.7144	+	18.2136i	1.01848	+	0.694386i
$689$	−7.60395	−	7.05543i	−0.289687	−	0.268791i
$690$	7.64759	+	19.4857i	0.291139	+	0.741810i
$691$	11.5644	−	3.56715i	0.439932	−	0.135701i	−0.0668737	−	0.997761i	$-0.521302\pi$
$691$	11.5644	−	3.56715i	0.439932	−	0.135701i	0.506805	+	0.862060i	$0.330826\pi$
$692$	7.86968	+	34.4793i	0.299160	+	1.31071i
$693$	−11.6245	−	30.0611i	−0.441577	−	1.14193i
$694$	18.0851	−	79.2359i	0.686500	−	3.00775i
$695$	0.366215	+	4.88679i	0.0138913	+	0.185367i
$696$	−138.854	−	42.8307i	−5.26324	−	1.62349i
$697$	−2.03570	+	27.1646i	−0.0771077	+	1.02893i
$698$	−22.9815	+	58.5560i	−0.869863	+	2.21638i
$699$	−11.5971	+	5.58488i	−0.438644	+	0.211240i
$700$	−11.4692	+	49.1132i	−0.433496	+	1.85631i
$701$	26.0198	+	12.5305i	0.982756	+	0.473270i	0.855052	−	0.518542i	$-0.173525\pi$
$701$	26.0198	+	12.5305i	0.982756	+	0.473270i	0.127704	+	0.991812i	$0.459239\pi$
$702$	8.02646	−	7.44747i	0.302939	−	0.281086i
$703$	7.07674	−	1.06665i	0.266904	−	0.0402294i
$704$	8.70112	−	15.0708i	0.327936	−	0.568001i
$705$	1.51206	+	2.61896i	0.0569473	+	0.0986357i
$706$	29.2120	+	36.6306i	1.09941	+	1.37861i
$707$	−0.992246	+	2.49139i	−0.0373172	+	0.0936983i
$708$	90.1470	−	113.041i	3.38793	−	4.24833i
$709$	30.6025	+	4.61259i	1.14930	+	0.173229i	0.695942	−	0.718098i	$-0.254987\pi$
$709$	30.6025	+	4.61259i	1.14930	+	0.173229i	0.453360	+	0.891327i	$0.350225\pi$
$710$	−0.755995	+	0.515428i	−0.0283720	+	0.0193437i
$711$	−16.1686	+	11.0235i	−0.606369	+	0.413415i
$712$	50.0008	+	7.53640i	1.87386	+	0.282439i
$713$	5.69278	−	7.13852i	0.213196	−	0.267340i
$714$	74.5445	−	68.4747i	2.78976	−	2.56260i
$715$	−0.992226	−	1.24421i	−0.0371072	−	0.0465309i
$716$	40.5497	+	70.2341i	1.51541	+	2.62477i
$717$	1.33938	−	2.31987i	0.0500199	−	0.0866371i
$718$	41.5601	−	6.26418i	1.55101	−	0.233777i
$719$	0.469079	−	0.435241i	0.0174937	−	0.0162318i	−0.671377	−	0.741116i	$-0.734297\pi$
$719$	0.469079	−	0.435241i	0.0174937	−	0.0162318i	0.688871	+	0.724884i	$0.258107\pi$
$720$	11.6691	+	5.61956i	0.434883	+	0.209429i
$721$	−1.89883	−	2.40571i	−0.0707162	−	0.0895934i
$722$	−110.540	+	53.2331i	−4.11386	+	1.98113i
$723$	−19.9105	+	50.7312i	−0.740480	+	1.88671i
$724$	3.68936	−	49.2310i	0.137114	−	1.82966i
$725$	−44.7675	−	13.8089i	−1.66262	−	0.512851i
$726$	2.04057	+	27.2296i	0.0757328	+	1.01058i
$727$	8.78132	−	38.4735i	0.325681	−	1.42690i	−0.501593	−	0.865104i	$-0.667252\pi$
$727$	8.78132	−	38.4735i	0.325681	−	1.42690i	0.827274	−	0.561799i	$-0.189891\pi$
$728$	−11.4411	+	7.71664i	−0.424035	+	0.285998i
$729$	9.79718	+	42.9242i	0.362858	+	1.58979i
$730$	11.0557	−	3.41024i	0.409191	−	0.126219i
$731$	−14.1860	−	36.1454i	−0.524689	−	1.33689i
$732$	67.8746	+	62.9785i	2.50872	+	2.32775i
$733$	33.6603	+	22.9492i	1.24327	+	0.847648i	0.992719	−	0.120455i	$-0.0384355\pi$
$733$	33.6603	+	22.9492i	1.24327	+	0.847648i	0.250552	+	0.968103i	$0.419388\pi$
$734$	−59.4351			−2.19379
$735$	11.1343	−	3.31255i	0.410696	−	0.122185i
$736$	5.70996			0.210472
$737$	3.27608	+	2.23359i	0.120676	+	0.0822754i
$738$	−40.5137	−	37.5912i	−1.49133	−	1.38375i
$739$	14.0926	+	35.9072i	0.518403	+	1.32087i	0.915214	+	0.402969i	$0.132022\pi$
$739$	14.0926	+	35.9072i	0.518403	+	1.32087i	−0.396811	+	0.917900i	$0.629883\pi$
$740$	2.04156	−	0.629737i	0.0750491	−	0.0231496i
$741$	5.08421	+	22.2754i	0.186773	+	0.818307i
$742$	67.1311	−	9.77430i	2.46446	−	0.358826i
$743$	3.04671	−	13.3485i	0.111773	−	0.489710i	−0.887793	−	0.460244i	$-0.847762\pi$
$743$	3.04671	−	13.3485i	0.111773	−	0.489710i	0.999566	−	0.0294664i	$-0.00938080\pi$
$744$	−1.92349	−	25.6673i	−0.0705187	−	0.941007i
$745$	10.6321	+	3.27958i	0.389532	+	0.120155i
$746$	−0.173238	+	2.31171i	−0.00634271	+	0.0846376i
$747$	2.70190	−	6.88434i	0.0988575	−	0.251885i
$748$	54.9617	−	26.4682i	2.00960	−	0.967772i
$749$	13.7628	−	6.54299i	0.502882	−	0.239076i
$750$	35.6206	+	17.1540i	1.30068	+	0.626375i
$751$	−17.0021	+	15.7757i	−0.620417	+	0.575663i	−0.926478	−	0.376349i	$-0.877179\pi$
$751$	−17.0021	+	15.7757i	−0.620417	+	0.575663i	0.306061	+	0.952012i	$0.400989\pi$
$752$	8.42031	−	1.26916i	0.307057	−	0.0462814i
$753$	22.6228	−	39.1838i	0.824421	−	1.42794i
$754$	−12.4845	−	21.6238i	−0.454659	−	0.787492i
$755$	−3.29615	−	4.13325i	−0.119959	−	0.150424i
$756$	3.35873	+	48.0519i	0.122156	+	1.74763i
$757$	4.71232	−	5.90906i	0.171272	−	0.214769i	−0.688786	−	0.724965i	$-0.741856\pi$
$757$	4.71232	−	5.90906i	0.171272	−	0.214769i	0.860058	+	0.510196i	$0.170427\pi$
$758$	−45.0257	−	6.78653i	−1.63541	−	0.246498i
$759$	−30.7529	+	20.9670i	−1.11626	+	0.761052i
$760$	−21.4839	+	14.6475i	−0.779304	+	0.531320i
$761$	14.0136	+	2.11221i	0.507992	+	0.0765675i	0.398037	−	0.917369i	$-0.369691\pi$
$761$	14.0136	+	2.11221i	0.507992	+	0.0765675i	0.109954	+	0.993937i	$0.464929\pi$
$762$	−23.5396	+	29.5177i	−0.852749	+	1.06931i
$763$	39.3898	−	11.9341i	1.42601	−	0.432044i
$764$	−28.3269	−	35.5209i	−1.02483	−	1.28510i
$765$	−7.77716	−	13.4704i	−0.281184	−	0.487025i
$766$	−40.2610	+	69.7342i	−1.45469	+	2.51960i
$767$	12.6126	−	1.90105i	0.455416	−	0.0686428i
$768$	−65.8598	+	61.1090i	−2.37651	+	2.20508i
$769$	33.4830	+	16.1246i	1.20743	+	0.581467i	0.925784	−	0.378052i	$-0.123406\pi$
$769$	33.4830	+	16.1246i	1.20743	+	0.581467i	0.281644	+	0.959519i	$0.409120\pi$
$770$	10.4076	+	0.0521983i	0.375064	+	0.00188110i
$771$	62.6527	−	30.1720i	2.25638	−	1.08662i
$772$	16.4211	−	41.8403i	0.591009	−	1.50587i
$773$	−1.29017	+	17.2161i	−0.0464042	+	0.619221i	0.924720	+	0.380647i	$0.124299\pi$
$773$	−1.29017	+	17.2161i	−0.0464042	+	0.619221i	−0.971124	+	0.238573i	$0.923320\pi$
$774$	75.2791	+	23.2205i	2.70585	+	0.834645i
$775$	−0.620149	−	8.27532i	−0.0222764	−	0.297258i
$776$	−14.2073	+	62.2461i	−0.510011	+	2.23450i
$777$	4.59912	+	4.31049i	0.164993	+	0.154638i
$778$	1.16946	+	5.12372i	0.0419271	+	0.183694i
$779$	38.4273	−	11.8533i	1.37680	−	0.424687i
$780$	2.49194	+	6.34936i	0.0892258	+	0.227344i
$781$	−1.19262	−	1.10659i	−0.0426753	−	0.0395969i
$782$	−58.4874	−	39.8761i	−2.09151	−	1.42596i
$783$	−44.7445			−1.59904
$784$	2.77154	−	32.5930i	0.0989835	−	1.16404i
$785$	5.66074			0.202041
$786$	11.8582	+	8.08477i	0.422967	+	0.288374i
$787$	−31.2256	−	28.9732i	−1.11307	−	1.03278i	−0.999228	−	0.0392830i	$-0.987493\pi$
$787$	−31.2256	−	28.9732i	−1.11307	−	1.03278i	−0.113846	−	0.993498i	$-0.536317\pi$
$788$	24.7758	+	63.1277i	0.882601	+	2.24883i
$789$	−37.0727	+	11.4354i	−1.31982	+	0.407111i
$790$	−1.40613	−	6.16068i	−0.0500280	−	0.219187i
$791$	−3.52289	+	44.0443i	−0.125259	+	1.56603i
$792$	−14.1392	+	61.9478i	−0.502414	+	2.20122i
$793$	0.610422	+	8.14551i	0.0216767	+	0.289256i
$794$	11.2680	+	3.47573i	0.399888	+	0.123349i
$795$	1.28642	−	17.1661i	0.0456246	−	0.608818i
$796$	18.3105	−	46.6544i	0.648999	−	1.65362i
$797$	8.50397	−	4.09530i	0.301226	−	0.145063i	−0.277165	−	0.960822i	$-0.589395\pi$
$797$	8.50397	−	4.09530i	0.301226	−	0.145063i	0.578391	+	0.815759i	$0.303681\pi$
$798$	−134.302	−	65.5081i	−4.75423	−	2.31896i
$799$	−9.21379	−	4.43713i	−0.325961	−	0.156974i
$800$	3.80429	−	3.52986i	0.134502	−	0.124800i
$801$	44.1547	−	6.65525i	1.56013	−	0.235152i
$802$	22.5958	−	39.1370i	0.797885	−	1.38198i
$803$	10.2860	+	17.8159i	0.362986	+	0.628710i
$804$	−10.5958	−	13.2868i	−0.373687	−	0.468588i
$805$	−4.02664	−	7.05584i	−0.141921	−	0.248686i
$806$	2.75761	−	3.45793i	0.0971325	−	0.121800i
$807$	75.0761	+	11.3159i	2.64280	+	0.398338i
$808$	4.36822	−	2.97820i	0.153673	−	0.104773i
$809$	23.9578	−	16.3341i	0.842310	−	0.574277i	−0.0634900	−	0.997982i	$-0.520223\pi$
$809$	23.9578	−	16.3341i	0.842310	−	0.574277i	0.905800	+	0.423705i	$0.139271\pi$
$810$	−2.35609	−	0.355124i	−0.0827846	−	0.0124778i
$811$	9.95400	−	12.4819i	0.349532	−	0.438300i	−0.575723	−	0.817645i	$-0.695279\pi$
$811$	9.95400	−	12.4819i	0.349532	−	0.438300i	0.925255	+	0.379345i	$0.123851\pi$
$812$	108.535	+	16.9161i	3.80883	+	0.593640i
$813$	11.0221	+	13.8212i	0.386560	+	0.484731i
$814$	2.82369	+	4.89077i	0.0989701	+	0.171421i
$815$	−1.79917	+	3.11625i	−0.0630221	+	0.109157i
$816$	−71.5170	+	10.7794i	−2.50359	+	0.377356i
$817$	−42.0198	+	38.9887i	−1.47009	+	1.36404i
$818$	24.2121	+	11.6599i	0.846557	+	0.407680i
$819$	−7.64596	+	9.48971i	−0.267172	+	0.331597i
$820$	10.8161	−	5.20878i	0.377716	−	0.181898i
$821$	5.65655	−	14.4127i	0.197415	−	0.503005i	−0.797547	−	0.603257i	$-0.793869\pi$
$821$	5.65655	−	14.4127i	0.197415	−	0.503005i	0.994962	+	0.100251i	$0.0319647\pi$
$822$	−4.25485	+	56.7771i	−0.148405	+	1.98033i
$823$	47.5112	+	14.6553i	1.65614	+	0.510851i	0.975169	−	0.221462i	$-0.0710829\pi$
$823$	47.5112	+	14.6553i	1.65614	+	0.510851i	0.680968	+	0.732313i	$0.261559\pi$
$824$	0.451528	+	6.02523i	0.0157297	+	0.209899i
$825$	−7.52760	+	32.9806i	−0.262078	+	1.14824i
$826$	−42.0706	+	72.0317i	−1.46382	+	2.50630i
$827$	−4.31947	−	18.9248i	−0.150203	−	0.658081i	−0.992825	−	0.119576i	$-0.961846\pi$
$827$	−4.31947	−	18.9248i	−0.150203	−	0.658081i	0.842622	−	0.538505i	$-0.181011\pi$
$828$	92.3155	−	28.4755i	3.20818	−	0.989594i
$829$	0.980934	+	2.49938i	0.0340692	+	0.0868070i	0.946896	−	0.321540i	$-0.104201\pi$
$829$	0.980934	+	2.49938i	0.0340692	+	0.0868070i	−0.912827	+	0.408347i	$0.866105\pi$
$830$	1.75064	+	1.62435i	0.0607655	+	0.0563821i
$831$	16.0048	+	10.9119i	0.555199	+	0.378528i
$832$	−6.57998			−0.228120
$833$	−24.7998	+	30.4660i	−0.859262	+	1.05558i
$834$	55.5196			1.92249
$835$	−2.34343	−	1.59772i	−0.0810977	−	0.0552915i
$836$	−66.0150	−	61.2529i	−2.28318	−	2.11848i
$837$	−2.89561	−	7.37789i	−0.100087	−	0.255017i
$838$	−22.6810	+	6.99617i	−0.783503	+	0.241679i
$839$	0.568803	+	2.49209i	0.0196373	+	0.0860365i	0.983797	−	0.179286i	$-0.0573787\pi$
$839$	0.568803	+	2.49209i	0.0196373	+	0.0860365i	−0.964160	+	0.265322i	$0.914522\pi$
$840$	−21.8501	−	6.86007i	−0.753901	−	0.236695i
$841$	−16.2519	+	71.2044i	−0.560411	+	2.45532i
$842$	3.46274	+	46.2070i	0.119334	+	1.59240i
$843$	−39.5420	−	12.1971i	−1.36190	−	0.420090i
$844$	−1.74466	+	23.2809i	−0.0600538	+	0.801363i
$845$	−0.219836	+	0.560134i	−0.00756260	+	0.0192692i
$846$	18.6933	−	9.00224i	0.642690	−	0.309503i
$847$	−2.30629	−	10.3434i	−0.0792451	−	0.355402i
$848$	−43.6722	−	21.0314i	−1.49971	−	0.722223i
$849$	−59.4596	+	55.1704i	−2.04065	+	1.89344i
$850$	−63.6187	+	9.58897i	−2.18210	+	0.328899i
$851$	2.20408	−	3.81759i	0.0755550	−	0.130865i
$852$	3.48654	+	6.03887i	0.119447	+	0.206888i
$853$	9.88610	+	12.3968i	0.338494	+	0.424457i	0.921722	−	0.387850i	$-0.126782\pi$
$853$	9.88610	+	12.3968i	0.338494	+	0.424457i	−0.583229	+	0.812308i	$0.698211\pi$
$854$	−43.9867	−	30.3139i	−1.50519	−	1.03732i
$855$	−14.3165	+	17.9524i	−0.489615	+	0.613958i
$856$	−29.7074	−	4.47767i	−1.01538	−	0.153043i
$857$	−4.77076	+	3.25265i	−0.162966	+	0.111108i	−0.642057	−	0.766657i	$-0.721919\pi$
$857$	−4.77076	+	3.25265i	−0.162966	+	0.111108i	0.479091	+	0.877765i	$0.340966\pi$
$858$	−14.8968	+	10.1565i	−0.508569	+	0.346736i
$859$	17.5014	+	2.63791i	0.597139	+	0.0900042i	0.440655	−	0.897676i	$-0.354746\pi$
$859$	17.5014	+	2.63791i	0.597139	+	0.0900042i	0.156484	+	0.987681i	$0.449984\pi$
$860$	−10.6693	+	13.3789i	−0.363820	+	0.456215i
$861$	29.1641	+	20.0987i	0.993910	+	0.684963i
$862$	−38.8789	−	48.7526i	−1.32422	−	1.66052i
$863$	4.00319	+	6.93373i	0.136270	+	0.236027i	0.926082	−	0.377322i	$-0.123155\pi$
$863$	4.00319	+	6.93373i	0.136270	+	0.236027i	−0.789812	+	0.613349i	$0.789822\pi$
$864$	2.47827	−	4.29249i	0.0843125	−	0.146034i
$865$	−5.11980	+	0.771685i	−0.174078	+	0.0262381i
$866$	38.1987	−	35.4432i	1.29805	−	1.20441i
$867$	36.0146	+	17.3437i	1.22312	+	0.589024i
$868$	4.23446	+	18.9909i	0.143727	+	0.644595i
$869$	10.1232	−	4.87510i	0.343408	−	0.165376i
$870$	15.1385	−	38.5722i	0.513243	−	1.30772i
$871$	0.112038	−	1.49504i	0.00379625	−	0.0506574i
$872$	−77.5363	−	23.9168i	−2.62571	−	0.809924i
$873$	4.21343	+	56.2243i	0.142603	+	1.90290i
$874$	−23.2533	+	101.879i	−0.786556	+	3.44612i
$875$	−14.6393	−	4.59615i	−0.494898	−	0.155378i
$876$	−19.6203	−	85.9623i	−0.662909	−	2.90440i
$877$	−52.5107	+	16.1974i	−1.77316	+	0.546947i	−0.996547	−	0.0830307i	$-0.973540\pi$
$877$	−52.5107	+	16.1974i	−1.77316	+	0.546947i	−0.776613	+	0.629978i	$0.783064\pi$
$878$	2.83183	+	7.21539i	0.0955698	+	0.243508i
$879$	−32.6193	−	30.2663i	−1.10022	−	1.02086i
$880$	−6.14438	−	4.18917i	−0.207127	−	0.141217i
$881$	−49.2136			−1.65805			−0.829025	−	0.559212i	$-0.811104\pi$
$881$	−49.2136			−1.65805			−0.829025	+	0.559212i	$0.811104\pi$
$882$	−16.9547	−	77.8761i	−0.570895	−	2.62222i
$883$	−0.675936			−0.0227471			−0.0113735	−	0.999935i	$-0.503620\pi$
$883$	−0.675936			−0.0227471			−0.0113735	+	0.999935i	$0.503620\pi$
$884$	−19.0579	−	12.9935i	−0.640987	−	0.437018i
$885$	15.5168	+	14.3975i	0.521590	+	0.483965i
$886$	8.11687	+	20.6814i	0.272692	+	0.694807i
$887$	21.2069	−	6.54145i	0.712057	−	0.219640i	0.0824956	−	0.996591i	$-0.473711\pi$
$887$	21.2069	−	6.54145i	0.712057	−	0.219640i	0.629561	+	0.776951i	$0.283235\pi$
$888$	−2.76522	−	12.1152i	−0.0927947	−	0.406560i
$889$	7.38979	−	12.6525i	0.247845	−	0.424352i
$890$	−3.20860	+	14.0578i	−0.107553	+	0.471219i
$891$	−0.316606	−	4.22482i	−0.0106067	−	0.141537i
$892$	15.0646	+	4.64680i	0.504399	+	0.155586i
$893$	−1.12819	+	15.0546i	−0.0377534	+	0.503784i
$894$	46.0534	−	117.342i	1.54026	−	3.92451i
$895$	−10.6972	+	5.15152i	−0.357569	+	0.172196i
$896$	30.7137	−	38.1200i	1.02607	−	1.27350i
$897$	12.6797	+	6.10623i	0.423363	+	0.203881i
$898$	30.3165	−	28.1296i	1.01167	−	0.938696i
$899$	−17.8721	+	2.69378i	−0.596067	+	0.0898427i
$900$	43.9022	−	76.0409i	1.46341	−	2.53470i
$901$	29.1064	+	50.4137i	0.969674	+	1.67952i
$902$	19.7852	+	24.8099i	0.658775	+	0.826078i
$903$	−49.8848	−	7.77499i	−1.66006	−	0.258735i
$904$	54.3114	−	68.1043i	1.80637	−	2.26512i
$905$	7.14696	+	1.07723i	0.237573	+	0.0358084i
$906$	−49.4869	+	33.7396i	−1.64409	+	1.12092i
$907$	−5.74185	+	3.91473i	−0.190655	+	0.129986i	−0.654886	−	0.755728i	$-0.727283\pi$
$907$	−5.74185	+	3.91473i	−0.190655	+	0.129986i	0.464231	+	0.885714i	$0.346331\pi$
$908$	88.4027	+	13.3246i	2.93375	+	0.442191i
$909$	2.91091	−	3.65016i	0.0965487	−	0.121068i
$910$	−1.95052	−	3.41788i	−0.0646592	−	0.113302i
$911$	15.5826	+	19.5400i	0.516275	+	0.647388i	0.969813	−	0.243849i	$-0.0784100\pi$
$911$	15.5826	+	19.5400i	0.516275	+	0.647388i	−0.453539	+	0.891237i	$0.649839\pi$
$912$	53.3844	+	92.4645i	1.76773	+	3.06181i
$913$	−2.12317	+	3.67744i	−0.0702668	+	0.121706i
$914$	89.3675	−	13.4700i	2.95602	−	0.445548i
$915$	−9.93693	+	9.22012i	−0.328505	+	0.304808i
$916$	−59.3984	−	28.6048i	−1.96258	−	0.945128i
$917$	−5.00620	−	2.44186i	−0.165319	−	0.0806374i
$918$	−55.3621	+	26.6610i	−1.82722	+	0.879944i
$919$	−12.2122	+	31.1161i	−0.402843	+	1.02643i	0.575198	+	0.818014i	$0.304925\pi$
$919$	−12.2122	+	31.1161i	−0.402843	+	1.02643i	−0.978041	+	0.208413i	$0.933170\pi$
$920$	−1.19688	+	15.9712i	−0.0394599	+	0.526556i
$921$	−70.1352	−	21.6338i	−2.31103	−	0.712859i
$922$	−1.10614	−	14.7604i	−0.0364288	−	0.486108i
$923$	−0.136886	+	0.599735i	−0.00450564	+	0.0197405i
$924$	6.32400	−	79.0648i	0.208044	−	2.60104i
$925$	−0.891528	−	3.90604i	−0.0293132	−	0.128430i
$926$	−20.9888	+	6.47417i	−0.689733	+	0.212755i
$927$	1.94934	+	4.96685i	0.0640249	+	0.163133i
$928$	−8.28563	−	7.68794i	−0.271989	−	0.252369i
$929$	−24.7123	−	16.8485i	−0.810783	−	0.552783i	0.0854621	−	0.996341i	$-0.472763\pi$
$929$	−24.7123	−	16.8485i	−0.810783	−	0.552783i	−0.896245	+	0.443559i	$0.853716\pi$
$930$	7.33983			0.240682
$931$	55.2415	+	17.6485i	1.81047	+	0.578405i
$932$	−19.1829			−0.628358
$933$	13.5507	+	9.23870i	0.443629	+	0.302461i
$934$	4.90408	+	4.55032i	0.160466	+	0.148891i
$935$	3.26282	+	8.31354i	0.106706	+	0.271882i
$936$	22.9581	−	7.08165i	0.750410	−	0.231471i
$937$	5.25067	+	23.0047i	0.171532	+	0.751531i	0.985369	+	0.170437i	$0.0545180\pi$
$937$	5.25067	+	23.0047i	0.171532	+	0.751531i	−0.813836	+	0.581094i	$0.802625\pi$
$938$	7.15395	+	6.70498i	0.233585	+	0.218925i
$939$	5.60566	−	24.5600i	0.182934	−	0.801486i
$940$	0.336797	+	4.49424i	0.0109851	+	0.146586i
$941$	35.3039	+	10.8898i	1.15087	+	0.354998i	0.810755	−	0.585385i	$-0.199057\pi$
$941$	35.3039	+	10.8898i	1.15087	+	0.354998i	0.340118	+	0.940383i	$0.389533\pi$
$942$	4.79265	−	63.9534i	0.156153	−	2.08371i
$943$	9.04943	−	23.0576i	0.294690	−	0.750858i
$944$	53.7013	−	25.8612i	1.74783	−	0.841710i
$945$	−7.05194	−	0.0353683i	−0.229400	−	0.00115053i
$946$	−40.7535	−	19.6258i	−1.32501	−	0.638091i
$947$	7.61584	−	7.06647i	0.247482	−	0.229629i	−0.546671	−	0.837347i	$-0.684105\pi$
$947$	7.61584	−	7.06647i	0.247482	−	0.229629i	0.794153	+	0.607718i	$0.207915\pi$
$948$	−47.6200	+	7.17757i	−1.54663	+	0.233117i
$949$	3.88926	−	6.73640i	0.126251	−	0.218673i
$950$	47.4887	+	82.2528i	1.54074	+	2.66863i
$951$	−12.9145	−	16.1942i	−0.418780	−	0.525134i
$952$	74.1188	−	22.4562i	2.40221	−	0.727808i
$953$	−23.3291	+	29.2538i	−0.755704	+	0.947623i	−0.999755	−	0.0221394i	$-0.992952\pi$
$953$	−23.3291	+	29.2538i	−0.755704	+	0.947623i	0.244051	+	0.969762i	$0.421524\pi$
$954$	−116.785	−	17.6026i	−3.78107	−	0.569904i
$955$	5.49567	−	3.74688i	0.177836	−	0.121246i
$956$	3.29847	−	2.24886i	0.106680	−	0.0727333i
$957$	72.8551	+	10.9811i	2.35507	+	0.354970i
$958$	−28.4326	+	35.6534i	−0.918616	+	1.15191i
$959$	−1.54077	−	22.0431i	−0.0497539	−	0.711808i
$960$	−6.80827	−	8.53730i	−0.219736	−	0.275540i
$961$	13.8992	+	24.0742i	0.448363	+	0.776587i
$962$	1.06767	−	1.84925i	0.0344230	−	0.0596223i
$963$	−26.2340	+	3.95414i	−0.845379	+	0.127420i
$964$	−59.5378	+	55.2431i	−1.91758	+	1.77926i
$965$	5.92869	+	2.85511i	0.190851	+	0.0919091i
$966$	−83.1240	+	39.5180i	−2.67447	+	1.27147i
$967$	−44.7669	+	21.5586i	−1.43961	+	0.693277i	−0.980756	−	0.195237i	$-0.937452\pi$
$967$	−44.7669	+	21.5586i	−1.43961	+	0.693277i	−0.458849	+	0.888514i	$0.651738\pi$
$968$	−7.63280	+	19.4481i	−0.245327	+	0.625084i
$969$	9.58213	−	127.865i	0.307822	−	4.10761i
$970$	−17.3978	−	5.36650i	−0.558609	−	0.172308i
$971$	3.51628	+	46.9215i	0.112843	+	1.50578i	0.710309	+	0.703890i	$0.248555\pi$
$971$	3.51628	+	46.9215i	0.112843	+	1.50578i	−0.597466	+	0.801894i	$0.703826\pi$
$972$	−16.1945	+	70.9526i	−0.519438	+	2.27581i
$973$	−21.3222	+	3.10452i	−0.683560	+	0.0995265i
$974$	11.1342	+	48.7820i	0.356762	+	1.56308i
$975$	12.2228	−	3.77022i	0.391442	−	0.120744i
$976$	13.9452	+	35.5318i	0.446375	+	1.13734i
$977$	−14.1244	−	13.1055i	−0.451880	−	0.419283i	0.421119	−	0.907005i	$-0.361637\pi$
$977$	−14.1244	−	13.1055i	−0.451880	−	0.419283i	−0.872999	+	0.487722i	$0.837828\pi$
$978$	33.6832	+	22.9648i	1.07707	+	0.734334i
$979$	−25.6389			−0.819422
$980$	17.0922	+	2.75185i	0.545991	+	0.0879046i
$981$	−71.6542			−2.28774
$982$	20.5167	+	13.9880i	0.654713	+	0.446376i
$983$	−41.7764	−	38.7628i	−1.33246	−	1.23634i	−0.949954	−	0.312390i	$-0.898870\pi$
$983$	−41.7764	−	38.7628i	−1.33246	−	1.23634i	−0.382507	−	0.923953i	$-0.624939\pi$
$984$	−25.5107	−	65.0001i	−0.813250	−	2.07213i
$985$	−9.48719	+	2.92641i	−0.302287	+	0.0932432i
$986$	31.1807	+	136.612i	0.992996	+	4.35060i
$987$	−11.0237	+	7.43514i	−0.350889	+	0.236663i
$988$	−7.57702	+	33.1971i	−0.241057	+	1.05614i
$989$	2.63853	+	35.2087i	0.0839004	+	1.11957i
$990$	−17.3144	−	5.34078i	−0.550288	−	0.169741i
$991$	0.910053	−	12.1438i	0.0289088	−	0.385761i	−0.963918	−	0.266199i	$-0.914232\pi$
$991$	0.910053	−	12.1438i	0.0289088	−	0.385761i	0.992827	−	0.119562i	$-0.0381489\pi$
$992$	0.731461	−	1.86373i	0.0232239	−	0.0591735i
$993$	−72.8836	+	35.0989i	−2.31289	+	1.11383i
$994$	−2.49256	−	3.15793i	−0.0790591	−	0.100163i
$995$	6.61084	+	3.18361i	0.209578	+	0.100927i
$996$	13.3416	−	12.3792i	0.422745	−	0.392250i
$997$	−17.0856	+	2.57524i	−0.541106	+	0.0815587i	−0.413908	−	0.910319i	$-0.635837\pi$
$997$	−17.0856	+	2.57524i	−0.541106	+	0.0815587i	−0.127198	+	0.991877i	$0.540598\pi$
$998$	−5.85422	+	10.1398i	−0.185312	+	0.320970i
$999$	−1.91326	−	3.31387i	−0.0605329	−	0.104846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.27	✓	348
49.37	even	21	inner	637.2.bl.b.625.27	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.27	✓	348	1.1	even	1	trivial
637.2.bl.b.625.27	yes	348	49.37	even	21	inner

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04235 + 1.39245i) q^{2} +(2.02170 + 1.87586i) q^{3} +(1.50160 + 3.82602i) q^{4} +(-0.574996 + 0.177363i) q^{5} +(1.51697 + 6.64630i) q^{6} +(-0.954237 - 2.46768i) q^{7} +(-1.16067 + 5.08521i) q^{8} +(0.344217 + 4.59325i) q^{9} +O(q^{10})\)	\(q+(2.04235 + 1.39245i) q^{2} +(2.02170 + 1.87586i) q^{3} +(1.50160 + 3.82602i) q^{4} +(-0.574996 + 0.177363i) q^{5} +(1.51697 + 6.64630i) q^{6} +(-0.954237 - 2.46768i) q^{7} +(-1.16067 + 5.08521i) q^{8} +(0.344217 + 4.59325i) q^{9} +(-1.42131 - 0.438418i) q^{10} +(0.197641 - 2.63733i) q^{11} +(-4.14130 + 10.5519i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(1.48724 - 6.36860i) q^{14} +(-1.49518 - 0.720040i) q^{15} +(-3.42552 + 3.17841i) q^{16} +(5.54927 - 0.836418i) q^{17} +(-5.69288 + 9.86036i) q^{18} +(-4.14229 - 7.17466i) q^{19} +(-1.54201 - 1.93362i) q^{20} +(2.69984 - 6.77892i) q^{21} +(4.07601 - 5.11116i) q^{22} +(-5.04591 - 0.760549i) q^{23} +(-11.8857 + 8.10351i) q^{24} +(-3.83203 + 2.61263i) q^{25} +(-2.44426 - 0.368413i) q^{26} +(-2.76181 + 3.46320i) q^{27} +(8.00850 - 7.35640i) q^{28} +(6.29803 + 7.89749i) q^{29} +(-2.05106 - 3.55254i) q^{30} +(-0.894638 + 1.54956i) q^{31} +(-1.10646 + 0.166773i) q^{32} +(5.34684 - 4.96114i) q^{33} +(12.4982 + 6.01884i) q^{34} +(0.986357 + 1.24966i) q^{35} +(-17.0570 + 8.21422i) q^{36} +(-0.315601 + 0.804139i) q^{37} +(1.53035 - 20.4212i) q^{38} +(-2.63540 - 0.812912i) q^{39} +(-0.234548 - 3.12983i) q^{40} +(-1.08013 + 4.73236i) q^{41} +(14.9534 - 10.0856i) q^{42} +(-1.53964 - 6.74561i) q^{43} +(10.3872 - 3.20404i) q^{44} +(-1.01260 - 2.58005i) q^{45} +(-9.24651 - 8.57951i) q^{46} +(-1.50564 - 1.02653i) q^{47} -12.8876 q^{48} +(-5.17886 + 4.70950i) q^{49} -11.4643 q^{50} +(12.7880 + 8.71868i) q^{51} +(-3.01294 - 2.79560i) q^{52} +(3.78968 + 9.65595i) q^{53} +(-10.4629 + 3.22738i) q^{54} +(0.354122 + 1.55151i) q^{55} +(13.6562 - 1.98835i) q^{56} +(5.08421 - 22.2754i) q^{57} +(1.86594 + 24.8992i) q^{58} +(-12.1884 - 3.75963i) q^{59} +(0.509724 - 6.80179i) q^{60} +(2.98424 - 7.60371i) q^{61} +(-3.98486 + 1.91901i) q^{62} +(11.0062 - 5.23247i) q^{63} +(5.92836 + 2.85495i) q^{64} +(0.441099 - 0.409280i) q^{65} +(17.8283 - 2.68718i) q^{66} +(-0.749615 + 1.29837i) q^{67} +(11.5329 + 19.9756i) q^{68} +(-8.77464 - 11.0030i) q^{69} +(0.274398 + 3.92570i) q^{70} +(0.383545 - 0.480950i) q^{71} +(-23.7572 - 3.58082i) q^{72} +(-6.42692 + 4.38180i) q^{73} +(-1.76430 + 1.20288i) q^{74} +(-12.6482 - 1.90640i) q^{75} +(21.2303 - 26.6220i) q^{76} +(-6.69667 + 2.02893i) q^{77} +(-4.25047 - 5.32992i) q^{78} +(2.12422 + 3.67926i) q^{79} +(1.40593 - 2.43513i) q^{80} +(1.58404 - 0.238755i) q^{81} +(-8.79560 + 8.16112i) q^{82} +(-1.44659 - 0.696640i) q^{83} +(29.9904 + 0.150414i) q^{84} +(-3.04246 + 1.46517i) q^{85} +(6.24846 - 15.9208i) q^{86} +(-2.08187 + 27.7806i) q^{87} +(13.1820 + 4.06610i) q^{88} +(-0.724459 - 9.66724i) q^{89} +(1.52452 - 6.67937i) q^{90} +(1.93042 + 1.80927i) q^{91} +(-4.66708 - 20.4478i) q^{92} +(-4.71545 + 1.45452i) q^{93} +(-1.64566 - 4.19306i) q^{94} +(3.65432 + 3.39071i) q^{95} +(-2.54978 - 1.73841i) q^{96} +12.2406 q^{97} +(-17.1348 + 2.40714i) q^{98} +12.1820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

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