LMFDB - Embedded newform 425.2.r.a.69.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(69,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([9, 0]))

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

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

chi := DirichletCharacter("425.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.13
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17389 + 0.381421i) q^{2} +(-1.02469 - 1.41037i) q^{3} +(-0.385489 + 0.280074i) q^{4} +(0.897862 + 2.04789i) q^{5} +(1.74082 + 1.26478i) q^{6} +2.70715i q^{7} +(1.79671 - 2.47296i) q^{8} +(-0.0120917 + 0.0372143i) q^{9} +(-1.83510 - 2.06154i) q^{10} +(0.0960804 + 0.295705i) q^{11} +(0.790016 + 0.256692i) q^{12} +(-4.63378 - 1.50561i) q^{13} +(-1.03256 - 3.17791i) q^{14} +(1.96824 - 3.36477i) q^{15} +(-0.871420 + 2.68195i) q^{16} +(0.587785 - 0.809017i) q^{17} -0.0482977i q^{18} +(1.98990 + 1.44575i) q^{19} +(-0.919677 - 0.537971i) q^{20} +(3.81808 - 2.77399i) q^{21} +(-0.225576 - 0.310479i) q^{22} +(-4.14812 + 1.34781i) q^{23} -5.32885 q^{24} +(-3.38769 + 3.67744i) q^{25} +6.01384 q^{26} +(-4.90908 + 1.59506i) q^{27} +(-0.758204 - 1.04358i) q^{28} +(-5.88501 + 4.27571i) q^{29} +(-1.02711 + 4.70061i) q^{30} +(2.74830 + 1.99676i) q^{31} +2.63278i q^{32} +(0.318600 - 0.438515i) q^{33} +(-0.381421 + 1.17389i) q^{34} +(-5.54394 + 2.43065i) q^{35} +(-0.00576157 - 0.0177323i) q^{36} +(-9.64260 - 3.13307i) q^{37} +(-2.88737 - 0.938162i) q^{38} +(2.62474 + 8.07812i) q^{39} +(6.67754 + 1.45908i) q^{40} +(-2.17215 + 6.68518i) q^{41} +(-3.42396 + 4.71267i) q^{42} -2.68539i q^{43} +(-0.119857 - 0.0870815i) q^{44} +(-0.0870674 + 0.00865097i) q^{45} +(4.35537 - 3.16436i) q^{46} +(-2.74728 - 3.78131i) q^{47} +(4.67548 - 1.51915i) q^{48} -0.328661 q^{49} +(2.57413 - 5.60906i) q^{50} -1.74331 q^{51} +(2.20796 - 0.717409i) q^{52} +(1.19539 + 1.64531i) q^{53} +(5.15435 - 3.74486i) q^{54} +(-0.519304 + 0.462264i) q^{55} +(6.69467 + 4.86396i) q^{56} -4.28793i q^{57} +(5.27753 - 7.26389i) q^{58} +(-4.07893 + 12.5537i) q^{59} +(0.183650 + 1.84834i) q^{60} +(-4.51850 - 13.9065i) q^{61} +(-3.98782 - 1.29572i) q^{62} +(-0.100745 - 0.0327340i) q^{63} +(-2.74704 - 8.45452i) q^{64} +(-1.07719 - 10.8413i) q^{65} +(-0.206744 + 0.636291i) q^{66} +(1.24381 - 1.71196i) q^{67} +0.476491i q^{68} +(6.15145 + 4.46929i) q^{69} +(5.58089 - 4.96790i) q^{70} +(-4.92386 + 3.57740i) q^{71} +(0.0703043 + 0.0967656i) q^{72} +(-8.18801 + 2.66045i) q^{73} +12.5144 q^{74} +(8.65788 + 1.00964i) q^{75} -1.17200 q^{76} +(-0.800518 + 0.260104i) q^{77} +(-6.16233 - 8.48172i) q^{78} +(6.02713 - 4.37897i) q^{79} +(-6.27476 + 0.623457i) q^{80} +(7.37488 + 5.35817i) q^{81} -8.67619i q^{82} +(3.54246 - 4.87577i) q^{83} +(-0.694903 + 2.13869i) q^{84} +(2.18453 + 0.477332i) q^{85} +(1.02426 + 3.15236i) q^{86} +(12.0606 + 3.91874i) q^{87} +(0.903895 + 0.293693i) q^{88} +(-2.85571 - 8.78896i) q^{89} +(0.0989082 - 0.0433647i) q^{90} +(4.07591 - 12.5443i) q^{91} +(1.22157 - 1.68135i) q^{92} -5.92218i q^{93} +(4.66728 + 3.39098i) q^{94} +(-1.17407 + 5.37317i) q^{95} +(3.71319 - 2.69779i) q^{96} +(-5.70529 - 7.85266i) q^{97} +(0.385813 - 0.125358i) q^{98} -0.0121662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.17389	+	0.381421i	−0.830068	+	0.269706i	−0.693074	−	0.720866i	$-0.743744\pi$
$2$	−1.17389	+	0.381421i	−0.830068	+	0.269706i	−0.136994	+	0.990572i	$0.543744\pi$
$3$	−1.02469	−	1.41037i	−0.591606	−	0.814276i	0.403301	−	0.915067i	$-0.367863\pi$
$3$	−1.02469	−	1.41037i	−0.591606	−	0.814276i	−0.994908	+	0.100791i	$0.967863\pi$
$4$	−0.385489	+	0.280074i	−0.192745	+	0.140037i
$5$	0.897862	+	2.04789i	0.401536	+	0.915843i
$5$	0.897862	+	2.04789i	0.401536	+	0.915843i
$6$	1.74082	+	1.26478i	0.710688	+	0.516345i
$7$			2.70715i			1.02321i	0.859222	+	0.511603i	$0.170948\pi$
$7$			2.70715i			1.02321i	−0.859222	+	0.511603i	$0.829052\pi$
$8$	1.79671	−	2.47296i	0.635233	−	0.874323i
$9$	−0.0120917	+	0.0372143i	−0.00403056	+	0.0124048i
$10$	−1.83510	−	2.06154i	−0.580311	−	0.651916i
$11$	0.0960804	+	0.295705i	0.0289693	+	0.0891584i	0.964496	−	0.264098i	$-0.0850743\pi$
$11$	0.0960804	+	0.295705i	0.0289693	+	0.0891584i	−0.935526	+	0.353257i	$0.885074\pi$
$12$	0.790016	+	0.256692i	0.228058	+	0.0741005i
$13$	−4.63378	−	1.50561i	−1.28518	−	0.417580i	−0.414778	−	0.909922i	$-0.636141\pi$
$13$	−4.63378	−	1.50561i	−1.28518	−	0.417580i	−0.870402	+	0.492342i	$0.836141\pi$
$14$	−1.03256	−	3.17791i	−0.275964	−	0.849331i
$15$	1.96824	−	3.36477i	0.508198	−	0.868780i
$16$	−0.871420	+	2.68195i	−0.217855	+	0.670489i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$17$	0.587785	−	0.809017i	0.142559	−	0.196215i
$18$		−	0.0482977i		−	0.0113839i
$19$	1.98990	+	1.44575i	0.456514	+	0.331677i	0.792162	−	0.610311i	$-0.208955\pi$
$19$	1.98990	+	1.44575i	0.456514	+	0.331677i	−0.335648	+	0.941987i	$0.608955\pi$
$20$	−0.919677	−	0.537971i	−0.205646	−	0.120294i
$21$	3.81808	−	2.77399i	0.833172	−	0.605335i
$22$	−0.225576	−	0.310479i	−0.0480930	−	0.0661944i
$23$	−4.14812	+	1.34781i	−0.864943	+	0.281037i	−0.707691	−	0.706522i	$-0.750263\pi$
$23$	−4.14812	+	1.34781i	−0.864943	+	0.281037i	−0.157251	+	0.987559i	$0.550263\pi$
$24$	−5.32885			−1.08775
$25$	−3.38769	+	3.67744i	−0.677537	+	0.735489i
$26$	6.01384			1.17941
$27$	−4.90908	+	1.59506i	−0.944753	+	0.306969i
$28$	−0.758204	−	1.04358i	−0.143287	−	0.197218i
$29$	−5.88501	+	4.27571i	−1.09282	+	0.793979i	−0.979873	−	0.199622i	$-0.936029\pi$
$29$	−5.88501	+	4.27571i	−1.09282	+	0.793979i	−0.112945	+	0.993601i	$0.536029\pi$
$30$	−1.02711	+	4.70061i	−0.187524	+	0.858210i
$31$	2.74830	+	1.99676i	0.493610	+	0.358629i	0.806571	−	0.591137i	$-0.201321\pi$
$31$	2.74830	+	1.99676i	0.493610	+	0.358629i	−0.312961	+	0.949766i	$0.601321\pi$
$32$			2.63278i			0.465415i
$33$	0.318600	−	0.438515i	0.0554611	−	0.0763357i
$34$	−0.381421	+	1.17389i	−0.0654132	+	0.201321i
$35$	−5.54394	+	2.43065i	−0.937097	+	0.410855i
$36$	−0.00576157	−	0.0177323i	−0.000960262	−	0.00295538i
$37$	−9.64260	−	3.13307i	−1.58523	−	0.515074i	−0.621836	−	0.783148i	$-0.713613\pi$
$37$	−9.64260	−	3.13307i	−1.58523	−	0.515074i	−0.963398	+	0.268074i	$0.913613\pi$
$38$	−2.88737	−	0.938162i	−0.468393	−	0.152190i
$39$	2.62474	+	8.07812i	0.420295	+	1.29353i
$40$	6.67754	+	1.45908i	1.05581	+	0.230701i
$41$	−2.17215	+	6.68518i	−0.339232	+	1.04405i	0.625368	+	0.780330i	$0.284949\pi$
$41$	−2.17215	+	6.68518i	−0.339232	+	1.04405i	−0.964600	+	0.263719i	$0.915051\pi$
$42$	−3.42396	+	4.71267i	−0.528328	+	0.727181i
$43$		−	2.68539i		−	0.409518i	−0.978812	−	0.204759i	$-0.934359\pi$
$43$		−	2.68539i		−	0.409518i	0.978812	−	0.204759i	$-0.0656410\pi$
$44$	−0.119857	−	0.0870815i	−0.0180692	−	0.0131280i
$45$	−0.0870674	+	0.00865097i	−0.0129792	+	0.00128961i
$46$	4.35537	−	3.16436i	0.642164	−	0.466560i
$47$	−2.74728	−	3.78131i	−0.400732	−	0.551560i	0.560196	−	0.828360i	$-0.310726\pi$
$47$	−2.74728	−	3.78131i	−0.400732	−	0.551560i	−0.960927	+	0.276800i	$0.910726\pi$
$48$	4.67548	−	1.51915i	0.674847	−	0.219271i
$49$	−0.328661			−0.0469516
$50$	2.57413	−	5.60906i	0.364037	−	0.793241i
$51$	−1.74331			−0.244112
$52$	2.20796	−	0.717409i	0.306188	−	0.0994867i
$53$	1.19539	+	1.64531i	0.164200	+	0.226001i	0.883186	−	0.469023i	$-0.155394\pi$
$53$	1.19539	+	1.64531i	0.164200	+	0.226001i	−0.718987	+	0.695024i	$0.755394\pi$
$54$	5.15435	−	3.74486i	0.701419	−	0.509610i
$55$	−0.519304	+	0.462264i	−0.0700229	+	0.0623317i
$56$	6.69467	+	4.86396i	0.894613	+	0.649974i
$57$		−	4.28793i		−	0.567950i
$58$	5.27753	−	7.26389i	0.692973	−	0.953796i
$59$	−4.07893	+	12.5537i	−0.531032	+	1.63435i	0.221038	+	0.975265i	$0.429055\pi$
$59$	−4.07893	+	12.5537i	−0.531032	+	1.63435i	−0.752070	+	0.659083i	$0.770945\pi$
$60$	0.183650	+	1.84834i	0.0237091	+	0.238619i
$61$	−4.51850	−	13.9065i	−0.578535	−	1.78055i	−0.623813	−	0.781573i	$-0.714418\pi$
$61$	−4.51850	−	13.9065i	−0.578535	−	1.78055i	0.0452784	−	0.998974i	$-0.485582\pi$
$62$	−3.98782	−	1.29572i	−0.506454	−	0.164557i
$63$	−0.100745	−	0.0327340i	−0.0126926	−	0.00412409i
$64$	−2.74704	−	8.45452i	−0.343380	−	1.05681i
$65$	−1.07719	−	10.8413i	−0.133608	−	1.34470i
$66$	−0.206744	+	0.636291i	−0.0254484	+	0.0783220i
$67$	1.24381	−	1.71196i	0.151956	−	0.209149i	−0.726252	−	0.687429i	$-0.758739\pi$
$67$	1.24381	−	1.71196i	0.151956	−	0.209149i	0.878208	+	0.478279i	$0.158739\pi$
$68$			0.476491i			0.0577830i
$69$	6.15145	+	4.46929i	0.740547	+	0.538039i
$70$	5.58089	−	4.96790i	0.667044	−	0.593778i
$71$	−4.92386	+	3.57740i	−0.584355	+	0.424559i	−0.840292	−	0.542135i	$-0.817616\pi$
$71$	−4.92386	+	3.57740i	−0.584355	+	0.424559i	0.255936	+	0.966694i	$0.417616\pi$
$72$	0.0703043	+	0.0967656i	0.00828544	+	0.0114039i
$73$	−8.18801	+	2.66045i	−0.958334	+	0.311382i	−0.746098	−	0.665837i	$-0.768075\pi$
$73$	−8.18801	+	2.66045i	−0.958334	+	0.311382i	−0.212237	+	0.977218i	$0.568075\pi$
$74$	12.5144			1.45477
$75$	8.65788	+	1.00964i	0.999726	+	0.116583i
$76$	−1.17200			−0.134438
$77$	−0.800518	+	0.260104i	−0.0912275	+	0.0296416i
$78$	−6.16233	−	8.48172i	−0.697747	−	0.960366i
$79$	6.02713	−	4.37897i	0.678105	−	0.492672i	−0.194623	−	0.980878i	$-0.562348\pi$
$79$	6.02713	−	4.37897i	0.678105	−	0.492672i	0.872729	+	0.488206i	$0.162348\pi$
$80$	−6.27476	+	0.623457i	−0.701539	+	0.0697046i
$81$	7.37488	+	5.35817i	0.819431	+	0.595352i
$82$		−	8.67619i		−	0.958125i
$83$	3.54246	−	4.87577i	0.388835	−	0.535186i	−0.569063	−	0.822294i	$-0.692694\pi$
$83$	3.54246	−	4.87577i	0.388835	−	0.535186i	0.957898	+	0.287108i	$0.0926939\pi$
$84$	−0.694903	+	2.13869i	−0.0758201	+	0.233350i
$85$	2.18453	+	0.477332i	0.236945	+	0.0517739i
$86$	1.02426	+	3.15236i	0.110449	+	0.339928i
$87$	12.0606	+	3.91874i	1.29304	+	0.420133i
$88$	0.903895	+	0.293693i	0.0963555	+	0.0313078i
$89$	−2.85571	−	8.78896i	−0.302704	−	0.931628i	−0.980524	−	0.196400i	$-0.937075\pi$
$89$	−2.85571	−	8.78896i	−0.302704	−	0.931628i	0.677820	−	0.735228i	$-0.262925\pi$
$90$	0.0989082	−	0.0433647i	0.0104258	−	0.00457104i
$91$	4.07591	−	12.5443i	0.427271	−	1.31500i
$92$	1.22157	−	1.68135i	0.127358	−	0.175293i
$93$		−	5.92218i		−	0.614102i
$94$	4.66728	+	3.39098i	0.481394	+	0.349753i
$95$	−1.17407	+	5.37317i	−0.120457	+	0.551275i
$96$	3.71319	−	2.69779i	0.378976	−	0.275342i
$97$	−5.70529	−	7.85266i	−0.579285	−	0.797317i	0.414332	−	0.910126i	$-0.364015\pi$
$97$	−5.70529	−	7.85266i	−0.579285	−	0.797317i	−0.993617	+	0.112809i	$0.964015\pi$
$98$	0.385813	−	0.125358i	0.0389730	−	0.0126631i
$99$	−0.0121662			−0.00122275
$100$	0.275959	−	2.36642i	0.0275959	−	0.236642i
$101$	2.17224			0.216146			0.108073	−	0.994143i	$-0.465532\pi$
$101$	2.17224			0.216146			0.108073	+	0.994143i	$0.465532\pi$
$102$	2.04646	−	0.664935i	0.202630	−	0.0658384i
$103$	11.3764	+	15.6582i	1.12095	+	1.54285i	0.804216	+	0.594337i	$0.202585\pi$
$103$	11.3764	+	15.6582i	1.12095	+	1.54285i	0.316732	+	0.948515i	$0.397415\pi$
$104$	−12.0489	+	8.75402i	−1.18149	+	0.858402i
$105$	9.10894	+	5.32832i	0.888941	+	0.519991i
$106$	−2.03082	−	1.47548i	−0.197251	−	0.143311i
$107$			19.1209i			1.84848i	0.381809	+	0.924241i	$0.375301\pi$
$107$			19.1209i			1.84848i	−0.381809	+	0.924241i	$0.624699\pi$
$108$	1.44566	−	1.98979i	0.139109	−	0.191467i
$109$	−2.93784	+	9.04174i	−0.281394	+	0.866042i	0.706062	+	0.708150i	$0.250470\pi$
$109$	−2.93784	+	9.04174i	−0.281394	+	0.866042i	−0.987456	+	0.157892i	$0.949530\pi$
$110$	0.433290	−	0.740723i	0.0413126	−	0.0706251i
$111$	5.46191	+	16.8100i	0.518422	+	1.59554i
$112$	−7.26045	−	2.35906i	−0.686048	−	0.222911i
$113$	12.3629	+	4.01696i	1.16301	+	0.377884i	0.826029	−	0.563628i	$-0.190595\pi$
$113$	12.3629	+	4.01696i	1.16301	+	0.377884i	0.336979	+	0.941512i	$0.390595\pi$
$114$	1.63551	+	5.03358i	0.153179	+	0.471438i
$115$	−6.48460	−	7.28474i	−0.604692	−	0.679305i
$116$	1.07109	−	3.29648i	0.0994483	−	0.306071i
$117$	0.112060	−	0.154238i	0.0103600	−	0.0142593i
$118$		−	16.2925i		−	1.49984i
$119$	2.19013	+	1.59122i	0.200769	+	0.145867i
$120$	−4.78458	−	10.9129i	−0.436770	−	0.996206i
$121$	8.82098	−	6.40881i	0.801907	−	0.582620i
$122$	10.6085	+	14.6013i	0.960447	+	1.32194i
$123$	11.6543	−	3.78672i	1.05084	−	0.341437i
$124$	−1.61868			−0.145362
$125$	−10.5727	−	3.63576i	−0.945648	−	0.325192i
$126$	0.130749			0.0116481
$127$	−2.18189	+	0.708938i	−0.193611	+	0.0629081i	−0.404218	−	0.914663i	$-0.632456\pi$
$127$	−2.18189	+	0.708938i	−0.193611	+	0.0629081i	0.210606	+	0.977571i	$0.432456\pi$
$128$	3.35444	+	4.61699i	0.296494	+	0.408088i
$129$	−3.78738	+	2.75169i	−0.333460	+	0.242273i
$130$	5.39960	+	12.3157i	0.473576	+	1.08016i
$131$	7.13168	+	5.18147i	0.623098	+	0.452707i	0.854002	−	0.520269i	$-0.174168\pi$
$131$	7.13168	+	5.18147i	0.623098	+	0.452707i	−0.230904	+	0.972976i	$0.574168\pi$
$132$			0.258275i			0.0224799i
$133$	−3.91385	+	5.38695i	−0.339374	+	0.467108i
$134$	−0.807125	+	2.48408i	−0.0697250	+	0.214591i
$135$	−7.67418	−	8.62111i	−0.660488	−	0.741987i
$136$	−0.944586	−	2.90714i	−0.0809976	−	0.249285i
$137$	−1.57440	−	0.511555i	−0.134510	−	0.0437051i	0.240988	−	0.970528i	$-0.422528\pi$
$137$	−1.57440	−	0.511555i	−0.134510	−	0.0437051i	−0.375499	+	0.926823i	$0.622528\pi$
$138$	−8.92583	−	2.90018i	−0.759817	−	0.246879i
$139$	2.35186	+	7.23829i	0.199483	+	0.613944i	0.999895	+	0.0144944i	$0.00461387\pi$
$139$	2.35186	+	7.23829i	0.199483	+	0.613944i	−0.800412	+	0.599450i	$0.795386\pi$
$140$	1.45637	−	2.48970i	0.123085	−	0.210418i
$141$	−2.51792	+	7.74935i	−0.212047	+	0.652613i
$142$	4.41560	−	6.07755i	0.370549	−	0.510017i
$143$		−	1.51489i		−	0.126682i
$144$	−0.0892702	−	0.0648586i	−0.00743919	−	0.00540488i
$145$	−14.0401	−	8.21283i	−1.16597	−	0.682039i
$146$	8.59710	−	6.24616i	0.711501	−	0.516936i
$147$	0.336777	+	0.463533i	0.0277769	+	0.0382316i
$148$	4.59461	−	1.49288i	0.377675	−	0.122714i
$149$	−1.72497			−0.141315			−0.0706576	−	0.997501i	$-0.522510\pi$
$149$	−1.72497			−0.141315			−0.0706576	+	0.997501i	$0.522510\pi$
$150$	−10.5485	+	2.11709i	−0.861284	+	0.172860i
$151$	0.794765			0.0646771			0.0323385	−	0.999477i	$-0.489705\pi$
$151$	0.794765			0.0646771			0.0323385	+	0.999477i	$0.489705\pi$
$152$	7.15054	−	2.32335i	0.579985	−	0.188449i
$153$	0.0229997	+	0.0316564i	0.00185942	+	0.00255927i
$154$	0.840514	−	0.610669i	0.0677305	−	0.0492091i
$155$	−1.62154	+	7.42104i	−0.130245	+	0.596072i
$156$	−3.27428	−	2.37891i	−0.262153	−	0.190465i
$157$		−	20.8413i		−	1.66331i	−0.555290	−	0.831657i	$-0.687393\pi$
$157$		−	20.8413i		−	1.66331i	0.555290	−	0.831657i	$-0.312607\pi$
$158$	−5.40498	+	7.43932i	−0.429997	+	0.591840i
$159$	1.09559	−	3.37188i	0.0868860	−	0.267407i
$160$	−5.39164	+	2.36388i	−0.426247	+	0.186881i
$161$	−3.64871	−	11.2296i	−0.287559	−	0.885015i
$162$	−10.7010	−	3.47698i	−0.840754	−	0.273177i
$163$	17.6170	+	5.72411i	1.37987	+	0.448347i	0.902626	−	0.430425i	$-0.141636\pi$
$163$	17.6170	+	5.72411i	1.37987	+	0.448347i	0.477243	+	0.878772i	$0.341636\pi$
$164$	−1.03501	−	3.18543i	−0.0808205	−	0.248740i
$165$	1.18409	+	0.258730i	0.0921812	+	0.0201421i
$166$	−2.29874	+	7.07481i	−0.178417	+	0.549112i
$167$	−12.3156	+	16.9510i	−0.953010	+	1.31171i	−0.00283333	+	0.999996i	$0.500902\pi$
$167$	−12.3156	+	16.9510i	−0.953010	+	1.31171i	−0.950177	+	0.311710i	$0.899098\pi$
$168$		−	14.4260i		−	1.11299i
$169$	8.68787	+	6.31211i	0.668298	+	0.485547i
$170$	−2.74647	+	0.272887i	−0.210644	+	0.0209295i
$171$	−0.0778636	+	0.0565712i	−0.00595438	+	0.00432611i
$172$	0.752108	+	1.03519i	0.0573477	+	0.0789324i
$173$	−4.54162	+	1.47566i	−0.345293	+	0.112192i	−0.476529	−	0.879159i	$-0.658105\pi$
$173$	−4.54162	+	1.47566i	−0.345293	+	0.112192i	0.131236	+	0.991351i	$0.458105\pi$
$174$	−15.6526			−1.18662
$175$	−9.95539	−	9.17097i	−0.752557	−	0.693260i
$176$	−0.876794			−0.0660908
$177$	21.8849	−	7.11085i	1.64497	−	0.534484i
$178$	6.70459	+	9.22808i	0.502530	+	0.691674i
$179$	−0.459604	+	0.333922i	−0.0343524	+	0.0249585i	−0.604829	−	0.796355i	$-0.706759\pi$
$179$	−0.459604	+	0.333922i	−0.0343524	+	0.0249585i	0.570477	+	0.821314i	$0.306759\pi$
$180$	0.0311406	−	0.0277202i	0.00232109	−	0.00206614i
$181$	−0.694976	−	0.504930i	−0.0516572	−	0.0375311i	0.561657	−	0.827370i	$-0.310164\pi$
$181$	−0.694976	−	0.504930i	−0.0516572	−	0.0375311i	−0.613314	+	0.789839i	$0.710164\pi$
$182$			16.2804i			1.20678i
$183$	−14.9832	+	20.6226i	−1.10759	+	1.52447i
$184$	−4.11990	+	12.6797i	−0.303723	+	0.934763i
$185$	−2.24155	−	22.5600i	−0.164802	−	1.65865i
$186$	2.25885	+	6.95201i	0.165627	+	0.509746i
$187$	0.295705	+	0.0960804i	0.0216241	+	0.00702609i
$188$	2.11809	+	0.688211i	0.154478	+	0.0501929i
$189$	−4.31806	−	13.2896i	−0.314093	−	0.966678i
$190$	−0.671208	−	6.75534i	−0.0486945	−	0.490084i
$191$	0.998462	−	3.07295i	0.0722462	−	0.222351i	−0.908413	−	0.418074i	$-0.862705\pi$
$191$	0.998462	−	3.07295i	0.0722462	−	0.222351i	0.980659	+	0.195723i	$0.0627053\pi$
$192$	−9.10911	+	12.5376i	−0.657393	+	0.904824i
$193$		−	4.57315i		−	0.329182i	−0.986362	−	0.164591i	$-0.947370\pi$
$193$		−	4.57315i		−	0.329182i	0.986362	−	0.164591i	$-0.0526305\pi$
$194$	9.69258	+	7.04207i	0.695887	+	0.505591i
$195$	−14.1864	+	12.6282i	−1.01591	+	0.904325i
$196$	0.126695	−	0.0920496i	0.00904967	−	0.00657497i
$197$	2.68644	+	3.69757i	0.191401	+	0.263441i	0.893922	−	0.448222i	$-0.147943\pi$
$197$	2.68644	+	3.69757i	0.191401	+	0.263441i	−0.702522	+	0.711662i	$0.747943\pi$
$198$	0.0142819	−	0.00464046i	0.00101497	−	0.000329783i
$199$	17.5439			1.24366			0.621828	−	0.783154i	$-0.286390\pi$
$199$	17.5439			1.24366			0.621828	+	0.783154i	$0.286390\pi$
$200$	3.00748	+	14.9849i	0.212661	+	1.05959i
$201$	−3.68902			−0.260203
$202$	−2.54998	+	0.828540i	−0.179416	+	0.0582959i
$203$	−11.5750	−	15.9316i	−0.812405	−	1.11818i
$204$	0.672028	−	0.488257i	0.0470513	−	0.0341848i
$205$	−15.6408	+	1.55406i	−1.09240	+	0.108540i
$206$	−19.3270	−	14.0419i	−1.34658	−	0.978347i
$207$		−	0.170667i		−	0.0118622i
$208$	8.07594	−	11.1156i	0.559966	−	0.770727i
$209$	−0.236324	+	0.727331i	−0.0163469	+	0.0503105i
$210$	−12.7253	−	2.78055i	−0.878126	−	0.191876i
$211$	−6.20296	−	19.0908i	−0.427030	−	1.31426i	−0.901037	−	0.433741i	$-0.857193\pi$
$211$	−6.20296	−	19.0908i	−0.427030	−	1.31426i	0.474008	−	0.880521i	$-0.342807\pi$
$212$	−0.921621	−	0.299453i	−0.0632972	−	0.0205665i
$213$	10.0909	+	3.27873i	0.691416	+	0.224655i
$214$	−7.29310	−	22.4459i	−0.498546	−	1.53437i
$215$	5.49937	−	2.41111i	0.375054	−	0.164436i
$216$	−4.87569	+	15.0058i	−0.331748	+	1.02102i
$217$	−5.40553	+	7.44007i	−0.366951	+	0.505065i
$218$		−	11.7346i		−	0.794767i
$219$	12.1424	+	8.82197i	0.820507	+	0.596133i
$220$	0.0707176	−	0.323642i	0.00476778	−	0.0218199i
$221$	−3.94173	+	2.86384i	−0.265150	+	0.192642i
$222$	−12.8234	−	17.6499i	−0.860651	−	1.18458i
$223$	−12.0383	+	3.91148i	−0.806144	+	0.261932i	−0.682964	−	0.730452i	$-0.739309\pi$
$223$	−12.0383	+	3.91148i	−0.806144	+	0.261932i	−0.123180	+	0.992384i	$0.539309\pi$
$224$	−7.12734			−0.476215
$225$	−0.0958908	−	0.170537i	−0.00639272	−	0.0113691i
$226$	−16.0449			−1.06729
$227$	14.7399	−	4.78930i	0.978324	−	0.317877i	0.224153	−	0.974554i	$-0.428039\pi$
$227$	14.7399	−	4.78930i	0.978324	−	0.317877i	0.754172	+	0.656677i	$0.228039\pi$
$228$	1.20094	+	1.65295i	0.0795342	+	0.109469i
$229$	−11.3805	+	8.26840i	−0.752043	+	0.546391i	−0.896459	−	0.443126i	$-0.853870\pi$
$229$	−11.3805	+	8.26840i	−0.752043	+	0.546391i	0.144416	+	0.989517i	$0.453870\pi$
$230$	10.3908	+	6.07815i	0.685148	+	0.400781i
$231$	1.18713	+	0.862498i	0.0781072	+	0.0567482i
$232$			22.2356i			1.45984i
$233$	1.78494	−	2.45676i	0.116935	−	0.160948i	−0.746537	−	0.665344i	$-0.768285\pi$
$233$	1.78494	−	2.45676i	0.116935	−	0.160948i	0.863472	+	0.504396i	$0.168285\pi$
$234$	−0.0727174	+	0.223801i	−0.00475368	+	0.0146303i
$235$	5.27701	−	9.02121i	0.344234	−	0.588479i
$236$	−1.94358	−	5.98171i	−0.126516	−	0.389376i
$237$	−12.3519	−	4.01338i	−0.802342	−	0.260697i
$238$	−3.17791	−	1.03256i	−0.205993	−	0.0669312i
$239$	−1.16487	−	3.58511i	−0.0753493	−	0.231901i	0.906287	−	0.422663i	$-0.138904\pi$
$239$	−1.16487	−	3.58511i	−0.0753493	−	0.231901i	−0.981636	+	0.190761i	$0.938904\pi$
$240$	7.30899	+	8.21086i	0.471794	+	0.530009i
$241$	−1.66068	+	5.11105i	−0.106974	+	0.329231i	−0.990189	−	0.139737i	$-0.955374\pi$
$241$	−1.66068	+	5.11105i	−0.106974	+	0.329231i	0.883215	+	0.468969i	$0.155374\pi$
$242$	−7.91043	+	10.8878i	−0.508502	+	0.699893i
$243$		−	0.406619i		−	0.0260847i
$244$	5.63670	+	4.09530i	0.360853	+	0.262175i
$245$	−0.295093	−	0.673061i	−0.0188528	−	0.0430003i
$246$	−12.2366	+	8.89042i	−0.780178	+	0.566832i
$247$	−7.04403	−	9.69528i	−0.448201	−	0.616896i
$248$	9.87581	−	3.20885i	0.627115	−	0.203762i
$249$	−10.5066			−0.665826
$250$	13.7979	+	0.235360i	0.872659	+	0.0148854i
$251$	−6.32674			−0.399340			−0.199670	−	0.979863i	$-0.563987\pi$
$251$	−6.32674			−0.399340			−0.199670	+	0.979863i	$0.563987\pi$
$252$	0.0480040	−	0.0155974i	0.00302397	−	0.000982546i
$253$	−0.797106	−	1.09712i	−0.0501136	−	0.0689755i
$254$	2.29090	−	1.66444i	0.143744	−	0.104436i
$255$	−1.56525	−	3.57010i	−0.0980199	−	0.223568i
$256$	8.68490	+	6.30995i	0.542807	+	0.394372i
$257$			9.85114i			0.614497i	0.951629	+	0.307249i	$0.0994083\pi$
$257$			9.85114i			0.614497i	−0.951629	+	0.307249i	$0.900592\pi$
$258$	3.39643	−	4.67478i	0.211452	−	0.291039i
$259$	8.48169	−	26.1040i	0.527027	−	1.62202i
$260$	3.45161	+	3.87751i	0.214060	+	0.240473i
$261$	−0.0879581	−	0.270707i	−0.00544447	−	0.0167563i
$262$	−10.3482	−	3.36232i	−0.639311	−	0.207725i
$263$	24.1994	+	7.86287i	1.49220	+	0.484845i	0.937732	−	0.347360i	$-0.112922\pi$
$263$	24.1994	+	7.86287i	1.49220	+	0.484845i	0.554468	+	0.832205i	$0.312922\pi$
$264$	−0.511998	−	1.57577i	−0.0315113	−	0.0969819i
$265$	−2.29612	+	3.92529i	−0.141050	+	0.241129i
$266$	2.53975	−	7.81654i	0.155722	−	0.479263i
$267$	−9.46944	+	13.0336i	−0.579520	+	0.797641i
$268$			1.00830i			0.0615919i
$269$	12.9038	+	9.37519i	0.786761	+	0.571615i	0.907000	−	0.421130i	$-0.138366\pi$
$269$	12.9038	+	9.37519i	0.786761	+	0.571615i	−0.120239	+	0.992745i	$0.538366\pi$
$270$	12.2969	+	7.19317i	0.748368	+	0.437762i
$271$	0.891542	−	0.647743i	0.0541573	−	0.0393476i	−0.560377	−	0.828237i	$-0.689344\pi$
$271$	0.891542	−	0.647743i	0.0541573	−	0.0393476i	0.614535	+	0.788890i	$0.289344\pi$
$272$	1.65754	+	2.28141i	0.100503	+	0.138331i
$273$	−21.8687	+	7.10557i	−1.32355	+	0.430048i
$274$	2.04330			0.123440
$275$	−1.41293	−	0.648426i	−0.0852028	−	0.0391015i
$276$	−3.62305			−0.218082
$277$	2.74300	−	0.891256i	0.164811	−	0.0535504i	−0.225449	−	0.974255i	$-0.572385\pi$
$277$	2.74300	−	0.891256i	0.164811	−	0.0535504i	0.390260	+	0.920705i	$0.372385\pi$
$278$	−5.52168	−	7.59994i	−0.331168	−	0.455814i
$279$	−0.107540	+	0.0781322i	−0.00643823	+	0.00467765i
$280$	−3.94996	+	18.0771i	−0.236055	+	1.08031i
$281$	−6.11951	−	4.44609i	−0.365060	−	0.265231i	0.390100	−	0.920773i	$-0.372441\pi$
$281$	−6.11951	−	4.44609i	−0.365060	−	0.265231i	−0.755159	+	0.655541i	$0.772441\pi$
$282$		−	10.0573i		−	0.598903i
$283$	−9.58958	+	13.1989i	−0.570041	+	0.784594i	−0.992560	−	0.121760i	$-0.961146\pi$
$283$	−9.58958	+	13.1989i	−0.570041	+	0.784594i	0.422518	+	0.906354i	$0.361146\pi$
$284$	0.896160	−	2.75810i	0.0531773	−	0.163663i
$285$	8.78120	−	3.84997i	0.520153	−	0.228053i
$286$	0.577812	+	1.77832i	0.0341667	+	0.105154i
$287$	−18.0978	−	5.88032i	−1.06828	−	0.347104i
$288$	−0.0979772	−	0.0318347i	−0.00577336	−	0.00187588i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	19.6141	+	4.28581i	1.15178	+	0.251671i
$291$	−5.22897	+	16.0931i	−0.306528	+	0.943396i
$292$	2.41127	−	3.31883i	0.141109	−	0.194220i
$293$			31.4868i			1.83948i	0.392528	+	0.919740i	$0.371601\pi$
$293$			31.4868i			1.83948i	−0.392528	+	0.919740i	$0.628399\pi$
$294$	−0.572141	−	0.415685i	−0.0333680	−	0.0242432i
$295$	−29.3708	+	2.91827i	−1.71004	+	0.169908i
$296$	−25.0729	+	18.2165i	−1.45733	+	1.05881i
$297$	−0.943333	−	1.29839i	−0.0547377	−	0.0753400i
$298$	2.02493	−	0.657941i	0.117301	−	0.0381135i
$299$	21.2508			1.22896
$300$	−3.62029	+	2.03565i	−0.209018	+	0.117528i
$301$	7.26974			0.419021
$302$	−0.932970	+	0.303140i	−0.0536864	+	0.0174438i
$303$	−2.22588	−	3.06366i	−0.127873	−	0.176003i
$304$	−5.61146	+	4.07697i	−0.321839	+	0.233830i
$305$	24.4220	−	21.7395i	1.39840	−	1.24480i
$306$	−0.0390737	−	0.0283887i	−0.00223369	−	0.00162287i
$307$		−	27.5113i		−	1.57015i	−0.619400	−	0.785076i	$-0.712624\pi$
$307$		−	27.5113i		−	1.57015i	0.619400	−	0.785076i	$-0.287376\pi$
$308$	0.235743	−	0.324472i	0.0134327	−	0.0184885i
$309$	10.4266	−	32.0897i	0.593148	−	1.82552i
$310$	−0.927024	−	9.33000i	−0.0526514	−	0.529908i
$311$	2.14648	+	6.60618i	0.121716	+	0.374602i	0.993288	−	0.115664i	$-0.0368996\pi$
$311$	2.14648	+	6.60618i	0.121716	+	0.374602i	−0.871573	+	0.490266i	$0.836900\pi$
$312$	24.6928	+	8.02316i	1.39795	+	0.454222i
$313$	27.4778	+	8.92807i	1.55314	+	0.504644i	0.954963	−	0.296724i	$-0.0958940\pi$
$313$	27.4778	+	8.92807i	1.55314	+	0.504644i	0.598172	+	0.801368i	$0.295894\pi$
$314$	7.94930	+	24.4654i	0.448605	+	1.38066i
$315$	−0.0234195	−	0.235705i	−0.00131954	−	0.0132804i
$316$	−1.09696	+	3.37609i	−0.0617087	+	0.189920i
$317$	−3.02948	+	4.16972i	−0.170153	+	0.234195i	−0.885574	−	0.464498i	$-0.846235\pi$
$317$	−3.02948	+	4.16972i	−0.170153	+	0.234195i	0.715421	+	0.698693i	$0.246235\pi$
$318$			4.37611i			0.245400i
$319$	−1.82978	−	1.32941i	−0.102448	−	0.0744329i
$320$	14.8474	−	13.2166i	0.829997	−	0.738832i
$321$	26.9674	−	19.5930i	1.50517	−	1.09357i
$322$	8.56640	+	11.7906i	0.477387	+	0.657067i
$323$	2.33927	−	0.760073i	0.130160	−	0.0422916i
$324$	−4.34363			−0.241313
$325$	21.2346	−	11.9399i	1.17788	−	0.662309i
$326$	−22.8638			−1.26631
$327$	15.7626	−	5.12156i	0.871671	−	0.283223i
$328$	12.6295	+	17.3829i	0.697345	+	0.959813i
$329$	10.2366	−	7.43730i	0.564360	−	0.410031i
$330$	−1.48868	+	0.147914i	−0.0819491	+	0.00814242i
$331$	−4.49159	−	3.26333i	−0.246880	−	0.179369i	0.457463	−	0.889229i	$-0.348758\pi$
$331$	−4.49159	−	3.26333i	−0.246880	−	0.179369i	−0.704343	+	0.709860i	$0.748758\pi$
$332$			2.87171i			0.157606i
$333$	0.233190	−	0.320959i	0.0127787	−	0.0175884i
$334$	7.99175	−	24.5961i	0.437289	−	1.34584i
$335$	4.62267	+	1.01008i	0.252564	+	0.0551867i
$336$	4.11258	+	12.6572i	0.224360	+	0.690508i
$337$	30.5702	+	9.93285i	1.66526	+	0.541077i	0.981965	−	0.189063i	$-0.0605451\pi$
$337$	30.5702	+	9.93285i	1.66526	+	0.541077i	0.683298	+	0.730140i	$0.260545\pi$
$338$	−12.6062	−	4.09601i	−0.685688	−	0.222793i
$339$	−7.00281	−	21.5524i	−0.380341	−	1.17057i
$340$	−0.975800	+	0.427824i	−0.0529202	+	0.0232020i
$341$	−0.326394	+	1.00454i	−0.0176752	+	0.0543987i
$342$	0.0698262	−	0.0961075i	0.00377577	−	0.00519690i
$343$			18.0603i			0.975165i
$344$	−6.64085	−	4.82486i	−0.358051	−	0.260139i
$345$	−3.62945	+	16.6103i	−0.195403	+	0.894267i
$346$	4.76853	−	3.46454i	0.256358	−	0.186255i
$347$	−9.14206	−	12.5830i	−0.490771	−	0.675489i	0.489759	−	0.871858i	$-0.337085\pi$
$347$	−9.14206	−	12.5830i	−0.490771	−	0.675489i	−0.980530	+	0.196369i	$0.937085\pi$
$348$	−5.74679	+	1.86724i	−0.308060	+	0.100095i
$349$	−29.1685			−1.56135			−0.780676	−	0.624936i	$-0.785125\pi$
$349$	−29.1685			−1.56135			−0.780676	+	0.624936i	$0.785125\pi$
$350$	15.1846	+	6.96855i	0.811650	+	0.372485i
$351$	25.1492			1.34236
$352$	−0.778527	+	0.252959i	−0.0414956	+	0.0134828i
$353$	9.17133	+	12.6232i	0.488141	+	0.671868i	0.980044	−	0.198782i	$-0.0636986\pi$
$353$	9.17133	+	12.6232i	0.488141	+	0.671868i	−0.491903	+	0.870650i	$0.663699\pi$
$354$	−22.9784	+	16.6948i	−1.22129	+	0.887316i
$355$	−11.7471	−	6.87151i	−0.623469	−	0.364702i
$356$	3.56241	+	2.58824i	0.188807	+	0.137176i
$357$		−	4.71940i		−	0.249777i
$358$	0.412161	−	0.567291i	0.0217834	−	0.0299823i
$359$	7.68786	−	23.6608i	0.405750	−	1.24877i	−0.514518	−	0.857480i	$-0.672029\pi$
$359$	7.68786	−	23.6608i	0.405750	−	1.24877i	0.920267	−	0.391290i	$-0.127971\pi$
$360$	−0.135041	+	0.230857i	−0.00711731	+	0.0121673i
$361$	−4.00181	−	12.3163i	−0.210622	−	0.648226i
$362$	1.00842	+	0.327655i	0.0530014	+	0.0172212i
$363$	−18.0776	−	5.87376i	−0.948826	−	0.308292i
$364$	1.94213	+	5.97727i	0.101795	+	0.313294i
$365$	−12.8000	−	14.3794i	−0.669983	−	0.752653i
$366$	9.72281	−	29.9237i	0.508219	−	1.56414i
$367$	−11.3166	+	15.5759i	−0.590720	+	0.813056i	−0.994819	−	0.101659i	$-0.967585\pi$
$367$	−11.3166	+	15.5759i	−0.590720	+	0.813056i	0.404100	+	0.914715i	$0.367585\pi$
$368$		−	12.2996i		−	0.641160i
$369$	−0.222519	−	0.161670i	−0.0115839	−	0.00841620i
$370$	11.2362	+	25.6281i	0.584143	+	1.33234i
$371$	−4.45411	+	3.23610i	−0.231246	+	0.168010i
$372$	1.65865	+	2.28294i	0.0859971	+	0.118365i
$373$	−23.4416	+	7.61664i	−1.21376	+	0.394375i	−0.844806	−	0.535073i	$-0.820284\pi$
$373$	−23.4416	+	7.61664i	−1.21376	+	0.394375i	−0.368955	+	0.929447i	$0.620284\pi$
$374$	−0.383773			−0.0198445
$375$	5.70596	+	18.6369i	0.294655	+	0.962404i
$376$	−14.2871			−0.736800
$377$	33.7074	−	10.9522i	1.73602	−	0.564067i
$378$	10.1379	+	13.9536i	0.521437	+	0.717696i
$379$	−0.691636	+	0.502503i	−0.0355270	+	0.0258118i	−0.605407	−	0.795916i	$-0.706990\pi$
$379$	−0.691636	+	0.502503i	−0.0355270	+	0.0258118i	0.569880	+	0.821728i	$0.306990\pi$
$380$	−1.05230	−	2.40013i	−0.0539816	−	0.123124i
$381$	3.23563	+	2.35082i	0.165766	+	0.120436i
$382$			3.98815i			0.204052i
$383$	−8.77206	+	12.0737i	−0.448231	+	0.616938i	−0.972016	−	0.234913i	$-0.924520\pi$
$383$	−8.77206	+	12.0737i	−0.448231	+	0.616938i	0.523785	+	0.851850i	$0.324520\pi$
$384$	3.07439	−	9.46199i	0.156889	−	0.482855i
$385$	−1.25142	−	1.40583i	−0.0637782	−	0.0716479i
$386$	1.74430	+	5.36839i	0.0887823	+	0.273244i
$387$	0.0999349	+	0.0324708i	0.00507997	+	0.00165058i
$388$	4.39866	+	1.42921i	0.223308	+	0.0725572i
$389$	−9.27582	−	28.5480i	−0.470303	−	1.44744i	−0.852189	−	0.523233i	$-0.824726\pi$
$389$	−9.27582	−	28.5480i	−0.470303	−	1.44744i	0.381887	−	0.924209i	$-0.375274\pi$
$390$	11.8367	−	20.2352i	0.599374	−	1.02465i
$391$	−1.34781	+	4.14812i	−0.0681615	+	0.209779i
$392$	−0.590509	+	0.812766i	−0.0298252	+	0.0410509i
$393$		−	15.3677i		−	0.775198i
$394$	−4.56392	−	3.31588i	−0.229927	−	0.167052i
$395$	14.3792	+	8.41117i	0.723494	+	0.423212i
$396$	0.00468996	−	0.00340745i	0.000235679	−	0.000171231i
$397$	−6.30516	−	8.67831i	−0.316447	−	0.435552i	0.620931	−	0.783865i	$-0.286755\pi$
$397$	−6.30516	−	8.67831i	−0.316447	−	0.435552i	−0.937378	+	0.348313i	$0.886755\pi$
$398$	−20.5947	+	6.69163i	−1.03232	+	0.335421i
$399$	11.6081			0.581131
$400$	−6.91064	−	12.2902i	−0.345532	−	0.614511i
$401$	24.4193			1.21944			0.609721	−	0.792616i	$-0.291282\pi$
$401$	24.4193			1.21944			0.609721	+	0.792616i	$0.291282\pi$
$402$	4.33051	−	1.40707i	0.215986	−	0.0701782i
$403$	−9.72871	−	13.3904i	−0.484622	−	0.667024i
$404$	−0.837377	+	0.608390i	−0.0416611	+	0.0302685i
$405$	−4.35129	+	19.9138i	−0.216217	+	0.989526i
$406$	19.6645	+	14.2871i	0.975930	+	0.709055i
$407$		−	3.15239i		−	0.156258i
$408$	−3.13222	+	4.31113i	−0.155068	+	0.213433i
$409$	6.26658	−	19.2866i	0.309862	−	0.953659i	−0.667955	−	0.744201i	$-0.732830\pi$
$409$	6.26658	−	19.2866i	0.309862	−	0.953659i	0.977818	−	0.209457i	$-0.0671697\pi$
$410$	17.7679	−	7.79002i	0.877492	−	0.384722i
$411$	0.891798	+	2.74467i	0.0439892	+	0.135385i
$412$	−8.77095	−	2.84985i	−0.432113	−	0.140402i
$413$	−33.9847	−	11.0423i	−1.67228	−	0.543355i
$414$	0.0650959	+	0.200345i	0.00319929	+	0.00984640i
$415$	13.1657	+	2.87678i	0.646278	+	0.141216i
$416$	3.96394	−	12.1997i	0.194348	−	0.598142i
$417$	7.79872	−	10.7340i	0.381905	−	0.525647i
$418$		−	0.943948i		−	0.0461700i
$419$	−1.89280	−	1.37520i	−0.0924693	−	0.0671829i	0.540590	−	0.841286i	$-0.318201\pi$
$419$	−1.89280	−	1.37520i	−0.0924693	−	0.0671829i	−0.633059	+	0.774103i	$0.718201\pi$
$420$	−5.00373	+	0.497168i	−0.244157	+	0.0242593i
$421$	−14.3141	+	10.3998i	−0.697627	+	0.506856i	−0.879158	−	0.476530i	$-0.841895\pi$
$421$	−14.3141	+	10.3998i	−0.697627	+	0.506856i	0.181532	+	0.983385i	$0.441895\pi$
$422$	14.5632	+	20.0446i	0.708928	+	0.975755i
$423$	0.173938	−	0.0565159i	0.00845715	−	0.00274790i
$424$	6.21657			0.301903
$425$	0.983882	+	4.90224i	0.0477253	+	0.237794i
$426$	−13.0962			−0.634513
$427$	37.6470	−	12.2323i	1.82187	−	0.591961i
$428$	−5.35526	−	7.37089i	−0.258856	−	0.356285i
$429$	−2.13655	+	1.55230i	−0.103154	+	0.0749457i
$430$	−5.53603	+	4.92796i	−0.266971	+	0.237647i
$431$	−31.2012	−	22.6690i	−1.50291	−	1.09193i	−0.969204	−	0.246260i	$-0.920798\pi$
$431$	−31.2012	−	22.6690i	−1.50291	−	1.09193i	−0.533707	−	0.845669i	$-0.679202\pi$
$432$		−	14.5559i		−	0.700321i
$433$	9.32722	−	12.8378i	0.448237	−	0.616946i	−0.523780	−	0.851853i	$-0.675479\pi$
$433$	9.32722	−	12.8378i	0.448237	−	0.616946i	0.972018	+	0.234908i	$0.0754787\pi$
$434$	3.50772	−	10.7956i	0.168376	−	0.518207i
$435$	2.80366	+	28.2173i	0.134425	+	1.35292i
$436$	−1.39985	−	4.30831i	−0.0670409	−	0.206331i
$437$	−10.2029	−	3.31513i	−0.488072	−	0.158584i
$438$	−17.6188	−	5.72468i	−0.841857	−	0.273536i
$439$	7.73662	+	23.8109i	0.369249	+	1.13643i	0.947278	+	0.320414i	$0.103822\pi$
$439$	7.73662	+	23.8109i	0.369249	+	1.13643i	−0.578029	+	0.816016i	$0.696178\pi$
$440$	0.210123	+	2.11477i	0.0100172	+	0.100818i
$441$	0.00397406	−	0.0122309i	0.000189241	−	0.000582424i
$442$	3.53485	−	4.86530i	0.168136	−	0.231419i
$443$		−	10.0237i		−	0.476242i	−0.971235	−	0.238121i	$-0.923468\pi$
$443$		−	10.0237i		−	0.476242i	0.971235	−	0.238121i	$-0.0765316\pi$
$444$	−6.81357	−	4.95035i	−0.323358	−	0.234933i
$445$	15.4348	−	13.7394i	0.731678	−	0.651312i
$446$	12.6398	−	9.18332i	0.598510	−	0.434843i
$447$	1.76756	+	2.43284i	0.0836029	+	0.115070i
$448$	22.8876	−	7.43665i	1.08134	−	0.351349i
$449$	−13.2950			−0.627432			−0.313716	−	0.949517i	$-0.601574\pi$
$449$	−13.2950			−0.627432			−0.313716	+	0.949517i	$0.601574\pi$
$450$	0.177612	+	0.163617i	0.00837271	+	0.00771300i
$451$	−2.18554			−0.102913
$452$	−5.89083	+	1.91405i	−0.277082	+	0.0900292i
$453$	−0.814389	−	1.12091i	−0.0382633	−	0.0526650i
$454$	−15.4764	+	11.2443i	−0.726343	+	0.527719i
$455$	29.3490	−	2.91610i	1.37590	−	0.136709i
$456$	−10.6039	−	7.70417i	−0.496572	−	0.360781i
$457$			8.51249i			0.398197i	0.979979	+	0.199099i	$0.0638014\pi$
$457$			8.51249i			0.398197i	−0.979979	+	0.199099i	$0.936199\pi$
$458$	10.2057	−	14.0470i	0.476882	−	0.656372i
$459$	−1.59506	+	4.90908i	−0.0744509	+	0.229136i
$460$	4.54001	+	0.992020i	0.211679	+	0.0462532i
$461$	4.44873	+	13.6918i	0.207198	+	0.637690i	0.999616	+	0.0277115i	$0.00882197\pi$
$461$	4.44873	+	13.6918i	0.207198	+	0.637690i	−0.792418	+	0.609979i	$0.791178\pi$
$462$	−1.72254	−	0.559686i	−0.0801396	−	0.0260389i
$463$	33.0017	+	10.7229i	1.53372	+	0.498336i	0.949635	−	0.313357i	$-0.101454\pi$
$463$	33.0017	+	10.7229i	1.53372	+	0.498336i	0.584084	+	0.811693i	$0.301454\pi$
$464$	−6.33894	−	19.5093i	−0.294278	−	0.905695i
$465$	12.1280	−	5.31731i	0.562421	−	0.246584i
$466$	−1.15827	+	3.56479i	−0.0536559	+	0.165136i
$467$	6.53419	−	8.99354i	0.302366	−	0.416171i	−0.630615	−	0.776096i	$-0.717197\pi$
$467$	6.53419	−	8.99354i	0.302366	−	0.416171i	0.932982	+	0.359924i	$0.117197\pi$
$468$			0.0908423i			0.00419919i
$469$	4.63453	+	3.36719i	0.214003	+	0.155482i
$470$	−2.75377	+	12.6027i	−0.127022	+	0.581320i
$471$	−29.3938	+	21.3559i	−1.35440	+	0.984027i
$472$	23.7160	+	32.6423i	1.09162	+	1.50249i
$473$	0.794082	−	0.258013i	0.0365119	−	0.0118635i
$474$	16.0306			0.736310
$475$	−12.0578	+	2.42000i	−0.553250	+	0.111037i
$476$	−1.28993			−0.0591240
$477$	−0.0756835	+	0.0245911i	−0.00346531	+	0.00112595i
$478$	2.73487	+	3.76423i	0.125090	+	0.172172i
$479$	−32.2651	+	23.4420i	−1.47423	+	1.07109i	−0.494870	+	0.868967i	$0.664784\pi$
$479$	−32.2651	+	23.4420i	−1.47423	+	1.07109i	−0.979360	+	0.202123i	$0.935216\pi$
$480$	8.85871	+	5.18195i	0.404343	+	0.236523i
$481$	39.9645	+	29.0359i	1.82223	+	1.32392i
$482$		−	6.63325i		−	0.302136i
$483$	−12.0990	+	16.6529i	−0.550525	+	0.757733i
$484$	−1.60545	+	4.94106i	−0.0729749	+	0.224594i
$485$	10.9588	−	18.7344i	0.497614	−	0.850686i
$486$	0.155093	+	0.477328i	0.00703517	+	0.0216520i
$487$	−15.8228	−	5.14116i	−0.717002	−	0.232968i	−0.0722789	−	0.997384i	$-0.523027\pi$
$487$	−15.8228	−	5.14116i	−0.717002	−	0.232968i	−0.644723	+	0.764416i	$0.723027\pi$
$488$	−42.5087	−	13.8119i	−1.92428	−	0.625236i
$489$	−9.97889	−	30.7119i	−0.451261	−	1.38884i
$490$	0.603127	+	0.677548i	0.0272465	+	0.0306085i
$491$	−6.20620	+	19.1007i	−0.280082	+	0.862003i	0.707748	+	0.706465i	$0.249711\pi$
$491$	−6.20620	+	19.1007i	−0.280082	+	0.862003i	−0.987830	+	0.155538i	$0.950289\pi$
$492$	−3.43206	+	4.72382i	−0.154729	+	0.212966i
$493$			7.27427i			0.327617i
$494$	11.9669	+	8.69448i	0.538418	+	0.391183i
$495$	−0.0109236	−	0.0249151i	−0.000490980	−	0.00111985i
$496$	−7.75015	+	5.63081i	−0.347992	+	0.252831i
$497$	−9.68455	−	13.3296i	−0.434411	−	0.597916i
$498$	12.3336	−	4.00742i	0.552681	−	0.179577i
$499$	7.60821			0.340590			0.170295	−	0.985393i	$-0.445528\pi$
$499$	7.60821			0.340590			0.170295	+	0.985393i	$0.445528\pi$
$500$	5.09393	−	1.55959i	0.227808	−	0.0697468i
$501$	36.5268			1.63190
$502$	7.42692	−	2.41315i	0.331480	−	0.107704i
$503$	−21.2860	−	29.2977i	−0.949097	−	1.30632i	−0.951927	−	0.306324i	$-0.900901\pi$
$503$	−21.2860	−	29.2977i	−0.949097	−	1.30632i	0.00283060	−	0.999996i	$-0.499099\pi$
$504$	−0.261959	+	0.190324i	−0.0116686	+	0.00847772i
$505$	1.95038	+	4.44851i	0.0867906	+	0.197956i
$506$	1.35418	+	0.983872i	0.0602008	+	0.0437384i
$507$		−	18.7211i		−	0.831431i
$508$	0.642539	−	0.884379i	0.0285081	−	0.0392380i
$509$	−2.35794	+	7.25699i	−0.104514	+	0.321660i	−0.989616	−	0.143736i	$-0.954088\pi$
$509$	−2.35794	+	7.25699i	−0.104514	+	0.321660i	0.885102	+	0.465397i	$0.154088\pi$
$510$	3.19915	+	3.59390i	0.141661	+	0.159141i
$511$	−7.20223	−	22.1662i	−0.318608	−	0.980574i
$512$	−23.4571	−	7.62168i	−1.03667	−	0.336834i
$513$	−12.0746	−	3.92328i	−0.533108	−	0.173217i
$514$	−3.75743	−	11.5642i	−0.165733	−	0.510075i
$515$	−21.8519	+	37.3565i	−0.962909	+	1.64612i
$516$	0.689316	−	2.12150i	0.0303455	−	0.0933937i
$517$	0.854191	−	1.17569i	0.0375673	−	0.0517070i
$518$			33.8784i			1.48853i
$519$	6.73498	+	4.89325i	0.295633	+	0.214790i
$520$	−28.7455	−	16.8148i	−1.26057	−	0.737379i
$521$	−18.0567	+	13.1190i	−0.791080	+	0.574753i	−0.908284	−	0.418355i	$-0.862607\pi$
$521$	−18.0567	+	13.1190i	−0.791080	+	0.574753i	0.117204	+	0.993108i	$0.462607\pi$
$522$	0.206507	+	0.284232i	0.00903856	+	0.0124405i
$523$	−8.39118	+	2.72646i	−0.366921	+	0.119220i	−0.486673	−	0.873584i	$-0.661790\pi$
$523$	−8.39118	+	2.72646i	−0.366921	+	0.119220i	0.119753	+	0.992804i	$0.461790\pi$
$524$	−4.20038			−0.183495
$525$	−2.73324	+	23.4382i	−0.119288	+	1.02293i
$526$	−31.4066			−1.36939
$527$	3.23083	−	1.04976i	0.140737	−	0.0457282i
$528$	0.898444	+	1.23660i	0.0390997	+	0.0538162i
$529$	−3.21707	+	2.33734i	−0.139873	+	0.101623i
$530$	1.19821	−	5.48367i	0.0520471	−	0.238195i
$531$	−0.417855	−	0.303590i	−0.0181334	−	0.0131747i
$532$		−	3.17278i		−	0.137558i
$533$	20.1305	−	27.7073i	0.871949	−	1.20013i
$534$	6.14484	−	18.9119i	0.265913	−	0.818397i
$535$	−39.1574	+	17.1679i	−1.69292	+	0.742233i
$536$	−1.99884	−	6.15179i	−0.0863367	−	0.265717i
$537$	0.941904	+	0.306043i	0.0406462	+	0.0132067i
$538$	−18.7236	−	6.08368i	−0.807233	−	0.262286i
$539$	−0.0315779	−	0.0971868i	−0.00136016	−	0.00418613i
$540$	5.37287	+	1.17400i	0.231211	+	0.0505211i
$541$	−6.50662	+	20.0253i	−0.279742	+	0.860956i	0.708184	+	0.706028i	$0.249515\pi$
$541$	−6.50662	+	20.0253i	−0.279742	+	0.860956i	−0.987926	+	0.154928i	$0.950485\pi$
$542$	−0.799512	+	1.10043i	−0.0343420	+	0.0472677i
$543$			1.49757i			0.0642669i
$544$	2.12997	+	1.54751i	0.0913215	+	0.0663490i
$545$	−21.1542	+	2.10187i	−0.906148	+	0.0900344i
$546$	22.9613	−	16.6824i	0.982653	−	0.713939i
$547$	−1.18186	−	1.62669i	−0.0505327	−	0.0695523i	0.783003	−	0.622018i	$-0.213687\pi$
$547$	−1.18186	−	1.62669i	−0.0505327	−	0.0695523i	−0.833536	+	0.552466i	$0.813687\pi$
$548$	0.750189	−	0.243751i	0.0320465	−	0.0104125i
$549$	0.572158			0.0244191
$550$	1.90595	+	0.222262i	0.0812700	+	0.00947728i
$551$	−17.8922			−0.762231
$552$	22.1047	−	7.18226i	0.940840	−	0.305697i
$553$	11.8545	+	16.3163i	0.504105	+	0.693842i
$554$	−2.88005	+	2.09248i	−0.122362	+	0.0889009i
$555$	−29.5210	+	26.2785i	−1.25310	+	1.11546i
$556$	−2.93388	−	2.13159i	−0.124424	−	0.0903995i
$557$		−	17.0724i		−	0.723381i	−0.932298	−	0.361691i	$-0.882200\pi$
$557$		−	17.0724i		−	0.723381i	0.932298	−	0.361691i	$-0.117800\pi$
$558$	0.0964389	−	0.132737i	0.00408258	−	0.00561920i
$559$	−4.04314	+	12.4435i	−0.171007	+	0.526304i
$560$	−1.68779	−	16.9867i	−0.0713222	−	0.717819i
$561$	−0.167498	−	0.515506i	−0.00707177	−	0.0217647i
$562$	8.87949	+	2.88512i	0.374559	+	0.121702i
$563$	−8.75831	−	2.84575i	−0.369119	−	0.119934i	0.118583	−	0.992944i	$-0.462165\pi$
$563$	−8.75831	−	2.84575i	−0.369119	−	0.119934i	−0.487702	+	0.873010i	$0.662165\pi$
$564$	−1.19976	−	3.69249i	−0.0505192	−	0.155482i
$565$	2.87393	+	28.9246i	0.120907	+	1.21687i
$566$	6.22280	−	19.1518i	0.261564	−	0.805010i
$567$	−14.5054	+	19.9649i	−0.609168	+	0.838448i
$568$			18.6041i			0.780609i
$569$	3.54787	+	2.57768i	0.148734	+	0.108062i	0.659664	−	0.751561i	$-0.270699\pi$
$569$	3.54787	+	2.57768i	0.148734	+	0.108062i	−0.510929	+	0.859623i	$0.670699\pi$
$570$	−8.83974	+	7.86880i	−0.370256	+	0.329588i
$571$	22.9341	−	16.6626i	0.959761	−	0.697307i	0.00666545	−	0.999978i	$-0.497878\pi$
$571$	22.9341	−	16.6626i	0.959761	−	0.697307i	0.953095	+	0.302671i	$0.0978783\pi$
$572$	0.424283	+	0.583975i	0.0177401	+	0.0244172i
$573$	−5.35711	+	1.74063i	−0.223796	+	0.0727158i
$574$	23.4877			0.980360
$575$	9.09605	−	19.8204i	0.379332	−	0.826569i
$576$	0.347845			0.0144936
$577$	15.5281	−	5.04538i	0.646442	−	0.210042i	0.0325976	−	0.999469i	$-0.489622\pi$
$577$	15.5281	−	5.04538i	0.646442	−	0.210042i	0.613845	+	0.789427i	$0.289622\pi$
$578$	0.725506	+	0.998574i	0.0301771	+	0.0415352i
$579$	−6.44982	+	4.68607i	−0.268045	+	0.194746i
$580$	7.71251	−	0.766311i	0.320245	−	0.0318194i
$581$	13.1995	+	9.58996i	0.547606	+	0.397859i
$582$		−	20.8861i		−	0.865755i
$583$	−0.371674	+	0.511566i	−0.0153932	+	0.0211869i
$584$	−8.13231	+	25.0287i	−0.336517	+	1.03569i
$585$	0.416476	+	0.0910026i	0.0172192	+	0.00376249i
$586$	−12.0097	−	36.9622i	−0.496118	−	1.52689i
$587$	1.16852	+	0.379676i	0.0482300	+	0.0156709i	0.333033	−	0.942915i	$-0.391928\pi$
$587$	1.16852	+	0.379676i	0.0482300	+	0.0156709i	−0.284803	+	0.958586i	$0.591928\pi$
$588$	−0.259648	−	0.0843646i	−0.0107077	−	0.00347914i
$589$	2.58204	+	7.94670i	0.106391	+	0.327438i
$590$	33.3651	−	14.6284i	1.37362	−	0.602241i
$591$	2.46215	−	7.57773i	0.101279	−	0.311706i
$592$	16.8055	−	23.1308i	0.690702	−	0.950670i
$593$			13.5555i			0.556657i	0.960486	+	0.278329i	$0.0897805\pi$
$593$			13.5555i			0.556657i	−0.960486	+	0.278329i	$0.910220\pi$
$594$	1.60261	+	1.16436i	0.0657557	+	0.0477743i
$595$	−1.29221	+	5.91384i	−0.0529754	+	0.242444i
$596$	0.664958	−	0.483120i	0.0272377	−	0.0197894i
$597$	−17.9771	−	24.7434i	−0.735755	−	1.01268i
$598$	−24.9461	+	8.10549i	−1.02012	+	0.331458i
$599$	28.7909			1.17637			0.588183	−	0.808728i	$-0.299844\pi$
$599$	28.7909			1.17637			0.588183	+	0.808728i	$0.299844\pi$
$600$	18.0525	−	19.5966i	0.736990	−	0.800026i
$601$	−2.55531			−0.104233			−0.0521166	−	0.998641i	$-0.516597\pi$
$601$	−2.55531			−0.104233			−0.0521166	+	0.998641i	$0.516597\pi$
$602$	−8.53391	+	2.77283i	−0.347816	+	0.113012i
$603$	0.0486697	+	0.0669881i	0.00198198	+	0.00272797i
$604$	−0.306374	+	0.222593i	−0.0124662	+	0.00905720i
$605$	21.0446	+	12.3101i	0.855583	+	0.500478i
$606$	3.78149	+	2.74742i	0.153613	+	0.111606i
$607$		−	6.96166i		−	0.282565i	−0.989969	−	0.141282i	$-0.954877\pi$
$607$		−	6.96166i		−	0.282565i	0.989969	−	0.141282i	$-0.0451226\pi$
$608$	−3.80633	+	5.23897i	−0.154367	+	0.212468i
$609$	−10.6086	+	32.6500i	−0.429883	+	1.32304i
$610$	−20.3769	+	34.8350i	−0.825037	+	1.41043i
$611$	7.03714	+	21.6581i	0.284692	+	0.876192i
$612$	−0.0177323	−	0.00576157i	−0.000716786	−	0.000232898i
$613$	18.6779	+	6.06881i	0.754393	+	0.245117i	0.660870	−	0.750500i	$-0.270187\pi$
$613$	18.6779	+	6.06881i	0.754393	+	0.245117i	0.0935225	+	0.995617i	$0.470187\pi$
$614$	10.4934	+	32.2953i	0.423479	+	1.30333i
$615$	18.2188	+	20.4668i	0.734652	+	0.825301i
$616$	−0.795072	+	2.44698i	−0.0320344	+	0.0985916i
$617$	−3.94807	+	5.43406i	−0.158943	+	0.218767i	−0.881060	−	0.473005i	$-0.843169\pi$
$617$	−3.94807	+	5.43406i	−0.158943	+	0.218767i	0.722117	+	0.691771i	$0.243169\pi$
$618$			41.6469i			1.67528i
$619$	−6.91132	−	5.02137i	−0.277789	−	0.201826i	0.440163	−	0.897918i	$-0.354921\pi$
$619$	−6.91132	−	5.02137i	−0.277789	−	0.201826i	−0.717953	+	0.696092i	$0.754921\pi$
$620$	−1.45336	−	3.31488i	−0.0583682	−	0.133129i
$621$	18.2136	−	13.2330i	0.730888	−	0.531021i
$622$	−5.03947	−	6.93624i	−0.202065	−	0.278118i
$623$	23.7930	−	7.73082i	0.953248	−	0.309729i
$624$	−23.9524			−0.958863
$625$	−2.04717	−	24.9160i	−0.0818867	−	0.996642i
$626$	−35.6613			−1.42531
$627$	1.26796	−	0.411986i	0.0506376	−	0.0164531i
$628$	5.83710	+	8.03409i	0.232926	+	0.320595i
$629$	−8.20249	+	5.95945i	−0.327055	+	0.237619i
$630$	0.117395	+	0.267759i	0.00467712	+	0.0106678i
$631$	−30.0428	−	21.8274i	−1.19599	−	0.868935i	−0.202102	−	0.979364i	$-0.564777\pi$
$631$	−30.0428	−	21.8274i	−1.19599	−	0.868935i	−0.993884	+	0.110430i	$0.964777\pi$
$632$		−	22.7726i		−	0.905845i
$633$	−20.5689	+	28.3106i	−0.817539	+	1.12525i
$634$	1.96587	−	6.05032i	0.0780746	−	0.240289i
$635$	−3.41086	−	3.83173i	−0.135356	−	0.152058i
$636$	0.522039	+	1.60667i	0.0207002	+	0.0637086i
$637$	1.52295	+	0.494835i	0.0603413	+	0.0196061i
$638$	2.65504	+	0.862674i	0.105114	+	0.0341536i
$639$	−0.0735927	−	0.226495i	−0.00291128	−	0.00896000i
$640$	−6.44326	+	11.0149i	−0.254692	+	0.435404i
$641$	2.98461	−	9.18570i	0.117885	−	0.362813i	−0.874653	−	0.484750i	$-0.838911\pi$
$641$	2.98461	−	9.18570i	0.117885	−	0.362813i	0.992538	+	0.121937i	$0.0389106\pi$
$642$	−24.1837	+	33.2860i	−0.954455	+	1.31369i
$643$		−	3.72549i		−	0.146919i	−0.997298	−	0.0734595i	$-0.976596\pi$
$643$		−	3.72549i		−	0.146919i	0.997298	−	0.0734595i	$-0.0234040\pi$
$644$	4.55166	+	3.30697i	0.179361	+	0.130313i
$645$	−9.03571	−	5.28549i	−0.355781	−	0.208116i
$646$	−2.45614	+	1.78449i	−0.0966356	+	0.0702099i
$647$	19.1221	+	26.3193i	0.751766	+	1.03472i	0.997855	+	0.0654695i	$0.0208545\pi$
$647$	19.1221	+	26.3193i	0.751766	+	1.03472i	−0.246089	+	0.969247i	$0.579145\pi$
$648$	26.5011	−	8.61071i	1.04106	−	0.338261i
$649$	−4.10409			−0.161100
$650$	−20.3730	+	22.1156i	−0.799095	+	0.867443i
$651$	16.0322			0.628353
$652$	−8.39434	+	2.72749i	−0.328748	+	0.106817i
$653$	−17.6170	−	24.2477i	−0.689406	−	0.948885i	0.310593	−	0.950543i	$-0.399472\pi$
$653$	−17.6170	−	24.2477i	−0.689406	−	0.948885i	−0.999999	+	0.00165762i	$0.999472\pi$
$654$	−16.5501	+	12.0243i	−0.647160	+	0.470189i
$655$	−4.20780	+	19.2571i	−0.164412	+	0.752438i
$656$	−16.0365	−	11.6512i	−0.626120	−	0.454903i
$657$		−	0.336881i		−	0.0131430i
$658$	−9.17989	+	12.6350i	−0.357870	+	0.492565i
$659$	−0.941458	+	2.89751i	−0.0366740	+	0.112871i	−0.967718	−	0.252037i	$-0.918900\pi$
$659$	−0.941458	+	2.89751i	−0.0366740	+	0.112871i	0.931044	+	0.364908i	$0.118900\pi$
$660$	−0.528917	+	0.231895i	−0.0205881	+	0.00902651i
$661$	6.36053	+	19.5757i	0.247396	+	0.761406i	0.995233	+	0.0975240i	$0.0310923\pi$
$661$	6.36053	+	19.5757i	0.247396	+	0.761406i	−0.747837	+	0.663882i	$0.768908\pi$
$662$	6.51736	+	2.11762i	0.253304	+	0.0823035i
$663$	8.07812	+	2.62474i	0.313728	+	0.101936i
$664$	−5.69282	−	17.5207i	−0.220924	−	0.679935i
$665$	−14.5460	−	3.17838i	−0.564069	−	0.123252i
$666$	−0.151320	+	0.465715i	−0.00586353	+	0.0180461i
$667$	18.6489	−	25.6680i	0.722088	−	0.993869i
$668$		−	9.98371i		−	0.386281i
$669$	17.8522	+	12.9704i	0.690204	+	0.501463i
$670$	−5.81179	+	0.577457i	−0.224529	+	0.0223091i
$671$	3.67809	−	2.67229i	0.141991	−	0.103163i
$672$	7.30333	+	10.0522i	0.281732	+	0.387771i
$673$	−11.0653	+	3.59533i	−0.426536	+	0.138590i	−0.514415	−	0.857541i	$-0.671991\pi$
$673$	−11.0653	+	3.59533i	−0.426536	+	0.138590i	0.0878794	+	0.996131i	$0.471991\pi$
$674$	−39.6747			−1.52821
$675$	10.7647	−	23.4564i	0.414333	−	0.902838i
$676$	−5.11694			−0.196806
$677$	38.4375	−	12.4891i	1.47727	−	0.479995i	0.543976	−	0.839101i	$-0.316918\pi$
$677$	38.4375	−	12.4891i	1.47727	−	0.479995i	0.933297	+	0.359106i	$0.116918\pi$
$678$	16.4411	+	22.6293i	0.631417	+	0.869072i
$679$	21.2583	−	15.4451i	0.815820	−	0.592728i
$680$	5.10538	−	4.54462i	0.195782	−	0.174278i
$681$	−21.8586	−	15.8812i	−0.837622	−	0.608568i
$682$		−	1.30371i		−	0.0499218i
$683$	17.3088	−	23.8236i	0.662304	−	0.911584i	−0.337251	−	0.941415i	$-0.609497\pi$
$683$	17.3088	−	23.8236i	0.662304	−	0.911584i	0.999555	+	0.0298313i	$0.00949699\pi$
$684$	0.0141714	−	0.0436152i	0.000541859	−	0.00166767i
$685$	−0.365991	−	3.68351i	−0.0139838	−	0.140740i
$686$	−6.88859	−	21.2009i	−0.263007	−	0.809454i
$687$	23.3230	+	7.57809i	0.889826	+	0.289122i
$688$	7.20208	+	2.34010i	0.274577	+	0.0892154i
$689$	−3.06198	−	9.42382i	−0.116652	−	0.359019i
$690$	−2.07493	−	20.8830i	−0.0789912	−	0.795004i
$691$	6.22003	−	19.1433i	0.236621	−	0.728245i	−0.760281	−	0.649594i	$-0.774939\pi$
$691$	6.22003	−	19.1433i	0.236621	−	0.728245i	0.996902	−	0.0786507i	$-0.0250612\pi$
$692$	1.33745	−	1.84084i	0.0508422	−	0.0699783i
$693$		−	0.0329358i		−	0.00125113i
$694$	15.5312	+	11.2841i	0.589557	+	0.428338i
$695$	−12.7116	+	11.3153i	−0.482177	+	0.429216i
$696$	31.3603	−	22.7846i	1.18871	−	0.863649i
$697$	4.13167	+	5.68675i	0.156498	+	0.215401i
$698$	34.2407	−	11.1255i	1.29603	−	0.421105i
$699$	−5.29395			−0.200236
$700$	6.40625	+	0.747063i	0.242134	+	0.0282363i
$701$	−44.6351			−1.68584			−0.842921	−	0.538037i	$-0.819166\pi$
$701$	−44.6351			−1.68584			−0.842921	+	0.538037i	$0.819166\pi$
$702$	−29.5224	+	9.59242i	−1.11425	+	0.362043i
$703$	−14.6582	−	20.1752i	−0.552843	−	0.760924i
$704$	2.23611	−	1.62463i	0.0842764	−	0.0612304i
$705$	−18.1305	+	1.80144i	−0.682835	+	0.0678462i
$706$	−15.5809	−	11.3202i	−0.586396	−	0.426042i
$707$			5.88059i			0.221162i
$708$	−6.44484	+	8.87057i	−0.242212	+	0.333376i
$709$	4.56771	−	14.0580i	0.171544	−	0.527958i	−0.827915	−	0.560854i	$-0.810473\pi$
$709$	4.56771	−	14.0580i	0.171544	−	0.527958i	0.999459	+	0.0328956i	$0.0104729\pi$
$710$	16.4107	+	3.58585i	0.615884	+	0.134574i
$711$	0.0900822	+	0.277245i	0.00337835	+	0.0103975i
$712$	−26.8656	−	8.72916i	−1.00683	−	0.327139i
$713$	−14.0915	−	4.57862i	−0.527733	−	0.171471i
$714$	1.80008	+	5.54008i	0.0673663	+	0.207332i
$715$	3.10233	−	1.36017i	0.116021	−	0.0508673i
$716$	0.0836494	−	0.257446i	0.00312613	−	0.00962122i
$717$	−3.86269	+	5.31653i	−0.144255	+	0.198549i
$718$			30.7076i			1.14600i
$719$	28.0820	+	20.4028i	1.04728	+	0.760896i	0.971694	−	0.236243i	$-0.0759163\pi$
$719$	28.0820	+	20.4028i	1.04728	+	0.760896i	0.0755890	+	0.997139i	$0.475916\pi$
$720$	0.0526708	−	0.241049i	0.00196292	−	0.00898338i
$721$	−42.3892	+	30.7976i	−1.57866	+	1.14696i
$722$	9.39540	+	12.9317i	0.349660	+	0.481266i
$723$	8.91014	−	2.89508i	0.331372	−	0.107669i
$724$	0.409324			0.0152124
$725$	4.21289	−	36.1265i	0.156463	−	1.34171i
$726$	23.4615			0.870739
$727$	−15.2595	+	4.95812i	−0.565945	+	0.183887i	−0.577994	−	0.816041i	$-0.696164\pi$
$727$	−15.2595	+	4.95812i	−0.565945	+	0.183887i	0.0120495	+	0.999927i	$0.496164\pi$
$728$	−23.6984	−	32.6181i	−0.878322	−	1.20891i
$729$	21.5512	−	15.6578i	0.798191	−	0.579920i
$730$	20.5105	+	11.9977i	0.759126	+	0.444055i
$731$	−2.17252	−	1.57843i	−0.0803537	−	0.0583804i
$732$		−	12.1462i		−	0.448938i
$733$	−31.1272	+	42.8430i	−1.14971	+	1.58244i	−0.406099	+	0.913829i	$0.633111\pi$
$733$	−31.1272	+	42.8430i	−1.14971	+	1.58244i	−0.743611	+	0.668612i	$0.766889\pi$
$734$	7.34346	−	22.6008i	0.271052	−	0.834212i
$735$	−0.646885	+	1.10587i	−0.0238607	+	0.0407906i
$736$	−3.54848	−	10.9211i	−0.130799	−	0.402557i
$737$	0.625741	+	0.203316i	0.0230495	+	0.00748923i
$738$	0.322879	+	0.104910i	0.0118853	+	0.00386178i
$739$	3.15502	+	9.71015i	0.116059	+	0.357194i	0.992166	−	0.124923i	$-0.0398683\pi$
$739$	3.15502	+	9.71015i	0.116059	+	0.357194i	−0.876107	+	0.482116i	$0.839868\pi$
$740$	7.18258	+	8.06885i	0.264037	+	0.296617i
$741$	−6.45594	+	19.8693i	−0.237165	+	0.729919i
$742$	3.99434	−	5.49773i	0.146637	−	0.201828i
$743$		−	35.1178i		−	1.28835i	−0.764880	−	0.644173i	$-0.777202\pi$
$743$		−	35.1178i		−	1.28835i	0.764880	−	0.644173i	$-0.222798\pi$
$744$	−14.6453	−	10.6404i	−0.536923	−	0.390098i
$745$	−1.54879	−	3.53255i	−0.0567432	−	0.129423i
$746$	24.6128	−	17.8823i	0.901139	−	0.654716i
$747$	0.138614	+	0.190786i	0.00507164	+	0.00698051i
$748$	−0.140901	+	0.0457815i	−0.00515184	+	0.00167394i
$749$	−51.7630			−1.89138
$750$	−13.8067	−	19.7013i	−0.504149	−	0.719391i
$751$	12.5728			0.458788			0.229394	−	0.973334i	$-0.426326\pi$
$751$	12.5728			0.458788			0.229394	+	0.973334i	$0.426326\pi$
$752$	12.5353	−	4.07297i	0.457116	−	0.148526i
$753$	6.48296	+	8.92303i	0.236252	+	0.325173i
$754$	−35.3915	+	25.7134i	−1.28888	+	0.936428i
$755$	0.713590	+	1.62759i	0.0259702	+	0.0592340i
$756$	5.38665	+	3.91363i	0.195911	+	0.142337i
$757$		−	17.4575i		−	0.634502i	−0.948342	−	0.317251i	$-0.897240\pi$
$757$		−	17.4575i		−	0.634502i	0.948342	−	0.317251i	$-0.102760\pi$
$758$	0.620242	−	0.853690i	0.0225282	−	0.0310074i
$759$	−0.730558	+	2.24842i	−0.0265176	+	0.0816127i
$760$	11.1782	+	12.5575i	0.405475	+	0.455507i
$761$	8.88365	+	27.3411i	0.322032	+	0.991113i	0.972763	+	0.231804i	$0.0744628\pi$
$761$	8.88365	+	27.3411i	0.322032	+	0.991113i	−0.650730	+	0.759309i	$0.725537\pi$
$762$	−4.69493	−	1.52548i	−0.170079	−	0.0552622i
$763$	−24.4773	−	7.95317i	−0.886139	−	0.287924i
$764$	0.475758	+	1.46423i	0.0172123	+	0.0529741i
$765$	−0.0441782	+	0.0755239i	−0.00159726	+	0.00273057i
$766$	5.69230	−	17.5191i	0.205671	−	0.632991i
$767$	37.8018	−	52.0297i	1.36494	−	1.87868i
$768$		−	18.7147i		−	0.675307i
$769$	−39.2929	−	28.5480i	−1.41694	−	1.02947i	−0.992267	−	0.124119i	$-0.960389\pi$
$769$	−39.2929	−	28.5480i	−1.41694	−	1.02947i	−0.424672	−	0.905347i	$-0.639611\pi$
$770$	2.00525	+	1.17298i	0.0722641	+	0.0422713i
$771$	13.8937	−

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17389 + 0.381421i) q^{2} +(-1.02469 - 1.41037i) q^{3} +(-0.385489 + 0.280074i) q^{4} +(0.897862 + 2.04789i) q^{5} +(1.74082 + 1.26478i) q^{6} +2.70715i q^{7} +(1.79671 - 2.47296i) q^{8} +(-0.0120917 + 0.0372143i) q^{9} +(-1.83510 - 2.06154i) q^{10} +(0.0960804 + 0.295705i) q^{11} +(0.790016 + 0.256692i) q^{12} +(-4.63378 - 1.50561i) q^{13} +(-1.03256 - 3.17791i) q^{14} +(1.96824 - 3.36477i) q^{15} +(-0.871420 + 2.68195i) q^{16} +(0.587785 - 0.809017i) q^{17} -0.0482977i q^{18} +(1.98990 + 1.44575i) q^{19} +(-0.919677 - 0.537971i) q^{20} +(3.81808 - 2.77399i) q^{21} +(-0.225576 - 0.310479i) q^{22} +(-4.14812 + 1.34781i) q^{23} -5.32885 q^{24} +(-3.38769 + 3.67744i) q^{25} +6.01384 q^{26} +(-4.90908 + 1.59506i) q^{27} +(-0.758204 - 1.04358i) q^{28} +(-5.88501 + 4.27571i) q^{29} +(-1.02711 + 4.70061i) q^{30} +(2.74830 + 1.99676i) q^{31} +2.63278i q^{32} +(0.318600 - 0.438515i) q^{33} +(-0.381421 + 1.17389i) q^{34} +(-5.54394 + 2.43065i) q^{35} +(-0.00576157 - 0.0177323i) q^{36} +(-9.64260 - 3.13307i) q^{37} +(-2.88737 - 0.938162i) q^{38} +(2.62474 + 8.07812i) q^{39} +(6.67754 + 1.45908i) q^{40} +(-2.17215 + 6.68518i) q^{41} +(-3.42396 + 4.71267i) q^{42} -2.68539i q^{43} +(-0.119857 - 0.0870815i) q^{44} +(-0.0870674 + 0.00865097i) q^{45} +(4.35537 - 3.16436i) q^{46} +(-2.74728 - 3.78131i) q^{47} +(4.67548 - 1.51915i) q^{48} -0.328661 q^{49} +(2.57413 - 5.60906i) q^{50} -1.74331 q^{51} +(2.20796 - 0.717409i) q^{52} +(1.19539 + 1.64531i) q^{53} +(5.15435 - 3.74486i) q^{54} +(-0.519304 + 0.462264i) q^{55} +(6.69467 + 4.86396i) q^{56} -4.28793i q^{57} +(5.27753 - 7.26389i) q^{58} +(-4.07893 + 12.5537i) q^{59} +(0.183650 + 1.84834i) q^{60} +(-4.51850 - 13.9065i) q^{61} +(-3.98782 - 1.29572i) q^{62} +(-0.100745 - 0.0327340i) q^{63} +(-2.74704 - 8.45452i) q^{64} +(-1.07719 - 10.8413i) q^{65} +(-0.206744 + 0.636291i) q^{66} +(1.24381 - 1.71196i) q^{67} +0.476491i q^{68} +(6.15145 + 4.46929i) q^{69} +(5.58089 - 4.96790i) q^{70} +(-4.92386 + 3.57740i) q^{71} +(0.0703043 + 0.0967656i) q^{72} +(-8.18801 + 2.66045i) q^{73} +12.5144 q^{74} +(8.65788 + 1.00964i) q^{75} -1.17200 q^{76} +(-0.800518 + 0.260104i) q^{77} +(-6.16233 - 8.48172i) q^{78} +(6.02713 - 4.37897i) q^{79} +(-6.27476 + 0.623457i) q^{80} +(7.37488 + 5.35817i) q^{81} -8.67619i q^{82} +(3.54246 - 4.87577i) q^{83} +(-0.694903 + 2.13869i) q^{84} +(2.18453 + 0.477332i) q^{85} +(1.02426 + 3.15236i) q^{86} +(12.0606 + 3.91874i) q^{87} +(0.903895 + 0.293693i) q^{88} +(-2.85571 - 8.78896i) q^{89} +(0.0989082 - 0.0433647i) q^{90} +(4.07591 - 12.5443i) q^{91} +(1.22157 - 1.68135i) q^{92} -5.92218i q^{93} +(4.66728 + 3.39098i) q^{94} +(-1.17407 + 5.37317i) q^{95} +(3.71319 - 2.69779i) q^{96} +(-5.70529 - 7.85266i) q^{97} +(0.385813 - 0.125358i) q^{98} -0.0121662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

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