LMFDB - Embedded newform 425.2.r.a.69.11

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			69.11
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46986 + 0.477587i) q^{2} +(-1.10052 - 1.51474i) q^{3} +(0.314369 - 0.228403i) q^{4} +(-2.19230 + 0.440256i) q^{5} +(2.34104 + 1.70086i) q^{6} -4.04029i q^{7} +(1.46385 - 2.01482i) q^{8} +(-0.156235 + 0.480841i) q^{9} +(3.01211 - 1.69413i) q^{10} +(0.248930 + 0.766128i) q^{11} +(-0.691941 - 0.224825i) q^{12} +(-0.183422 - 0.0595974i) q^{13} +(1.92959 + 5.93867i) q^{14} +(3.07955 + 2.83625i) q^{15} +(-1.42956 + 4.39975i) q^{16} +(-0.587785 + 0.809017i) q^{17} -0.781385i q^{18} +(-4.15318 - 3.01746i) q^{19} +(-0.588636 + 0.639130i) q^{20} +(-6.11999 + 4.44643i) q^{21} +(-0.731785 - 1.00722i) q^{22} +(0.742309 - 0.241191i) q^{23} -4.66293 q^{24} +(4.61235 - 1.93035i) q^{25} +0.298068 q^{26} +(-4.44176 + 1.44322i) q^{27} +(-0.922813 - 1.27014i) q^{28} +(-5.56276 + 4.04158i) q^{29} +(-5.88107 - 2.69814i) q^{30} +(4.10415 + 2.98184i) q^{31} -2.16885i q^{32} +(0.886531 - 1.22021i) q^{33} +(0.477587 - 1.46986i) q^{34} +(1.77876 + 8.85753i) q^{35} +(0.0607100 + 0.186846i) q^{36} +(-6.94342 - 2.25605i) q^{37} +(7.54571 + 2.45175i) q^{38} +(0.111585 + 0.343425i) q^{39} +(-2.32216 + 5.06155i) q^{40} +(-3.27121 + 10.0678i) q^{41} +(6.87198 - 9.45847i) q^{42} +0.147653i q^{43} +(0.253242 + 0.183991i) q^{44} +(0.130820 - 1.12293i) q^{45} +(-0.975901 + 0.709034i) q^{46} +(7.76309 + 10.6850i) q^{47} +(8.23774 - 2.67660i) q^{48} -9.32395 q^{49} +(-5.85760 + 5.04014i) q^{50} +1.87232 q^{51} +(-0.0712744 + 0.0231585i) q^{52} +(-1.46489 - 2.01625i) q^{53} +(5.83951 - 4.24265i) q^{54} +(-0.883022 - 1.56999i) q^{55} +(-8.14045 - 5.91439i) q^{56} +9.61178i q^{57} +(6.24627 - 8.59726i) q^{58} +(3.04084 - 9.35875i) q^{59} +(1.61592 + 0.188253i) q^{60} +(0.115763 + 0.356282i) q^{61} +(-7.45661 - 2.42280i) q^{62} +(1.94274 + 0.631234i) q^{63} +(-1.82331 - 5.61158i) q^{64} +(0.428354 + 0.0499026i) q^{65} +(-0.720324 + 2.21693i) q^{66} +(5.40626 - 7.44108i) q^{67} +0.388582i q^{68} +(-1.18227 - 0.858969i) q^{69} +(-6.84478 - 12.1698i) q^{70} +(0.509940 - 0.370493i) q^{71} +(0.740103 + 1.01866i) q^{72} +(-3.33920 + 1.08497i) q^{73} +11.2833 q^{74} +(-7.99997 - 4.86212i) q^{75} -1.99483 q^{76} +(3.09538 - 1.00575i) q^{77} +(-0.328030 - 0.451495i) q^{78} +(-7.86290 + 5.71273i) q^{79} +(1.19702 - 10.2749i) q^{80} +(8.30144 + 6.03135i) q^{81} -16.3605i q^{82} +(-4.90590 + 6.75239i) q^{83} +(-0.908360 + 2.79564i) q^{84} +(0.932426 - 2.03238i) q^{85} +(-0.0705170 - 0.217029i) q^{86} +(12.2439 + 3.97828i) q^{87} +(1.90801 + 0.619949i) q^{88} +(4.42157 + 13.6082i) q^{89} +(0.344010 + 1.71303i) q^{90} +(-0.240791 + 0.741078i) q^{91} +(0.178271 - 0.245368i) q^{92} -9.49829i q^{93} +(-16.5137 - 11.9979i) q^{94} +(10.4335 + 4.78672i) q^{95} +(-3.28525 + 2.38687i) q^{96} +(-2.18751 - 3.01084i) q^{97} +(13.7049 - 4.45300i) q^{98} -0.407277 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 $

$2$	−1.46986	+	0.477587i	−1.03935	+	0.337705i	−0.778480	−	0.627669i	$-0.784009\pi$
$2$	−1.46986	+	0.477587i	−1.03935	+	0.337705i	−0.260869	+	0.965374i	$0.584009\pi$
$3$	−1.10052	−	1.51474i	−0.635387	−	0.874535i	0.362972	−	0.931800i	$-0.381762\pi$
$3$	−1.10052	−	1.51474i	−0.635387	−	0.874535i	−0.998359	+	0.0572648i	$0.981762\pi$
$4$	0.314369	−	0.228403i	0.157185	−	0.114201i
$5$	−2.19230	+	0.440256i	−0.980426	+	0.196889i
$5$	−2.19230	+	0.440256i	−0.980426	+	0.196889i
$6$	2.34104	+	1.70086i	0.955724	+	0.694374i
$7$		−	4.04029i		−	1.52709i	−0.645757	−	0.763543i	$-0.723458\pi$
$7$		−	4.04029i		−	1.52709i	0.645757	−	0.763543i	$-0.276542\pi$
$8$	1.46385	−	2.01482i	0.517550	−	0.712346i
$9$	−0.156235	+	0.480841i	−0.0520782	+	0.160280i
$10$	3.01211	−	1.69413i	0.952514	−	0.535731i
$11$	0.248930	+	0.766128i	0.0750552	+	0.230996i	0.981545	−	0.191232i	$-0.0612482\pi$
$11$	0.248930	+	0.766128i	0.0750552	+	0.230996i	−0.906490	+	0.422228i	$0.861248\pi$
$12$	−0.691941	−	0.224825i	−0.199746	−	0.0649015i
$13$	−0.183422	−	0.0595974i	−0.0508721	−	0.0165293i	0.283470	−	0.958981i	$-0.408514\pi$
$13$	−0.183422	−	0.0595974i	−0.0508721	−	0.0165293i	−0.334342	+	0.942452i	$0.608514\pi$
$14$	1.92959	+	5.93867i	0.515705	+	1.58718i
$15$	3.07955	+	2.83625i	0.795136	+	0.732316i
$16$	−1.42956	+	4.39975i	−0.357391	+	1.09994i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$		−	0.781385i		−	0.184174i
$19$	−4.15318	−	3.01746i	−0.952806	−	0.692254i	−0.00133692	−	0.999999i	$-0.500426\pi$
$19$	−4.15318	−	3.01746i	−0.952806	−	0.692254i	−0.951469	+	0.307745i	$0.900426\pi$
$20$	−0.588636	+	0.639130i	−0.131623	+	0.142914i
$21$	−6.11999	+	4.44643i	−1.33549	+	0.970291i
$22$	−0.731785	−	1.00722i	−0.156017	−	0.214739i
$23$	0.742309	−	0.241191i	0.154782	−	0.0502917i	−0.230601	−	0.973048i	$-0.574069\pi$
$23$	0.742309	−	0.241191i	0.154782	−	0.0502917i	0.385383	+	0.922757i	$0.374069\pi$
$24$	−4.66293			−0.951816
$25$	4.61235	−	1.93035i	0.922470	−	0.386069i
$26$	0.298068			0.0584559
$27$	−4.44176	+	1.44322i	−0.854817	+	0.277747i
$28$	−0.922813	−	1.27014i	−0.174395	−	0.240035i
$29$	−5.56276	+	4.04158i	−1.03298	+	0.750502i	−0.968902	−	0.247443i	$-0.920410\pi$
$29$	−5.56276	+	4.04158i	−1.03298	+	0.750502i	−0.0640752	+	0.997945i	$0.520410\pi$
$30$	−5.88107	−	2.69814i	−1.07373	−	0.492611i
$31$	4.10415	+	2.98184i	0.737127	+	0.535554i	0.891810	−	0.452410i	$-0.149436\pi$
$31$	4.10415	+	2.98184i	0.737127	+	0.535554i	−0.154683	+	0.987964i	$0.549436\pi$
$32$		−	2.16885i		−	0.383403i
$33$	0.886531	−	1.22021i	0.154325	−	0.212410i
$34$	0.477587	−	1.46986i	0.0819055	−	0.252079i
$35$	1.77876	+	8.85753i	0.300666	+	1.49720i
$36$	0.0607100	+	0.186846i	0.0101183	+	0.0311410i
$37$	−6.94342	−	2.25605i	−1.14149	−	0.370893i	−0.323559	−	0.946208i	$-0.604879\pi$
$37$	−6.94342	−	2.25605i	−1.14149	−	0.370893i	−0.817932	+	0.575315i	$0.804879\pi$
$38$	7.54571	+	2.45175i	1.22408	+	0.397726i
$39$	0.111585	+	0.343425i	0.0178680	+	0.0549920i
$40$	−2.32216	+	5.06155i	−0.367166	+	0.800302i
$41$	−3.27121	+	10.0678i	−0.510878	+	1.57232i	0.279781	+	0.960064i	$0.409738\pi$
$41$	−3.27121	+	10.0678i	−0.510878	+	1.57232i	−0.790659	+	0.612256i	$0.790262\pi$
$42$	6.87198	−	9.45847i	1.06037	−	1.45947i
$43$			0.147653i			0.0225168i	0.999937	+	0.0112584i	$0.00358374\pi$
$43$			0.147653i			0.0225168i	−0.999937	+	0.0112584i	$0.996416\pi$
$44$	0.253242	+	0.183991i	0.0381776	+	0.0277377i
$45$	0.130820	−	1.12293i	0.0195015	−	0.167397i
$46$	−0.975901	+	0.709034i	−0.143889	+	0.104541i
$47$	7.76309	+	10.6850i	1.13236	+	1.55856i	0.783503	+	0.621388i	$0.213431\pi$
$47$	7.76309	+	10.6850i	1.13236	+	1.55856i	0.348860	+	0.937175i	$0.386569\pi$
$48$	8.23774	−	2.67660i	1.18902	−	0.386334i
$49$	−9.32395			−1.33199
$50$	−5.85760	+	5.04014i	−0.828390	+	0.712784i
$51$	1.87232			0.262177
$52$	−0.0712744	+	0.0231585i	−0.00988399	+	0.00321150i
$53$	−1.46489	−	2.01625i	−0.201218	−	0.276953i	0.696469	−	0.717587i	$-0.254754\pi$
$53$	−1.46489	−	2.01625i	−0.201218	−	0.276953i	−0.897687	+	0.440634i	$0.854754\pi$
$54$	5.83951	−	4.24265i	0.794657	−	0.577352i
$55$	−0.883022	−	1.56999i	−0.119067	−	0.211697i
$56$	−8.14045	−	5.91439i	−1.08781	−	0.790343i
$57$			9.61178i			1.27311i
$58$	6.24627	−	8.59726i	0.820176	−	1.12888i
$59$	3.04084	−	9.35875i	0.395884	−	1.21840i	−0.532387	−	0.846501i	$-0.678705\pi$
$59$	3.04084	−	9.35875i	0.395884	−	1.21840i	0.928271	−	0.371904i	$-0.121295\pi$
$60$	1.61592	+	0.188253i	0.208615	+	0.0243033i
$61$	0.115763	+	0.356282i	0.0148219	+	0.0456172i	0.958194	−	0.286120i	$-0.0923654\pi$
$61$	0.115763	+	0.356282i	0.0148219	+	0.0456172i	−0.943372	+	0.331737i	$0.892365\pi$
$62$	−7.45661	−	2.42280i	−0.946991	−	0.307696i
$63$	1.94274	+	0.631234i	0.244762	+	0.0795280i
$64$	−1.82331	−	5.61158i	−0.227914	−	0.701447i
$65$	0.428354	+	0.0499026i	0.0531307	+	0.00618966i
$66$	−0.720324	+	2.21693i	−0.0886657	+	0.272885i
$67$	5.40626	−	7.44108i	0.660480	−	0.909072i	−0.339017	−	0.940780i	$-0.610095\pi$
$67$	5.40626	−	7.44108i	0.660480	−	0.909072i	0.999497	+	0.0317077i	$0.0100946\pi$
$68$			0.388582i			0.0471225i
$69$	−1.18227	−	0.858969i	−0.142328	−	0.103408i
$70$	−6.84478	−	12.1698i	−0.818107	−	1.45457i
$71$	0.509940	−	0.370493i	0.0605188	−	0.0439695i	−0.557115	−	0.830436i	$-0.688092\pi$
$71$	0.509940	−	0.370493i	0.0605188	−	0.0439695i	0.617633	+	0.786466i	$0.288092\pi$
$72$	0.740103	+	1.01866i	0.0872220	+	0.120051i
$73$	−3.33920	+	1.08497i	−0.390824	+	0.126986i	−0.497836	−	0.867271i	$-0.665872\pi$
$73$	−3.33920	+	1.08497i	−0.390824	+	0.126986i	0.107012	+	0.994258i	$0.465872\pi$
$74$	11.2833			1.31166
$75$	−7.99997	−	4.86212i	−0.923757	−	0.561429i
$76$	−1.99483			−0.228823
$77$	3.09538	−	1.00575i	0.352751	−	0.114616i
$78$	−0.328030	−	0.451495i	−0.0371421	−	0.0511217i
$79$	−7.86290	+	5.71273i	−0.884646	+	0.642733i	−0.934476	−	0.356025i	$-0.884132\pi$
$79$	−7.86290	+	5.71273i	−0.884646	+	0.642733i	0.0498306	+	0.998758i	$0.484132\pi$
$80$	1.19702	−	10.2749i	0.133830	−	1.14877i
$81$	8.30144	+	6.03135i	0.922382	+	0.670150i
$82$		−	16.3605i		−	1.80672i
$83$	−4.90590	+	6.75239i	−0.538492	+	0.741171i	−0.988395	−	0.151907i	$-0.951459\pi$
$83$	−4.90590	+	6.75239i	−0.538492	+	0.741171i	0.449903	+	0.893078i	$0.351459\pi$
$84$	−0.908360	+	2.79564i	−0.0991102	+	0.305030i
$85$	0.932426	−	2.03238i	0.101136	−	0.220443i
$86$	−0.0705170	−	0.217029i	−0.00760404	−	0.0234028i
$87$	12.2439	+	3.97828i	1.31268	+	0.426516i
$88$	1.90801	+	0.619949i	0.203394	+	0.0660867i
$89$	4.42157	+	13.6082i	0.468685	+	1.44246i	0.854288	+	0.519800i	$0.173993\pi$
$89$	4.42157	+	13.6082i	0.468685	+	1.44246i	−0.385603	+	0.922665i	$0.626007\pi$
$90$	0.344010	+	1.71303i	0.0362618	+	0.180569i
$91$	−0.240791	+	0.741078i	−0.0252417	+	0.0776861i
$92$	0.178271	−	0.245368i	0.0185860	−	0.0255814i
$93$		−	9.49829i		−	0.984927i
$94$	−16.5137	−	11.9979i	−1.70325	−	1.23749i
$95$	10.4335	+	4.78672i	1.07045	+	0.491107i
$96$	−3.28525	+	2.38687i	−0.335299	+	0.243609i
$97$	−2.18751	−	3.01084i	−0.222108	−	0.305705i	0.683392	−	0.730051i	$-0.260504\pi$
$97$	−2.18751	−	3.01084i	−0.222108	−	0.305705i	−0.905500	+	0.424346i	$0.860504\pi$
$98$	13.7049	−	4.45300i	1.38441	−	0.449821i
$99$	−0.407277			−0.0409329
$100$	1.00908	−	1.66031i	0.100908	−	0.166031i
$101$	4.56840			0.454573			0.227286	−	0.973828i	$-0.427015\pi$
$101$	4.56840			0.454573			0.227286	+	0.973828i	$0.427015\pi$
$102$	−2.75205	+	0.894196i	−0.272494	+	0.0885386i
$103$	3.38668	+	4.66137i	0.333700	+	0.459299i	0.942588	−	0.333957i	$-0.108384\pi$
$103$	3.38668	+	4.66137i	0.333700	+	0.459299i	−0.608888	+	0.793256i	$0.708384\pi$
$104$	−0.388580	+	0.282320i	−0.0381034	+	0.0276838i
$105$	11.4593	−	12.4423i	1.11831	−	1.21424i
$106$	3.11612	+	2.26399i	0.302664	+	0.219898i
$107$		−	18.3893i		−	1.77777i	−0.458135	−	0.888883i	$-0.651482\pi$
$107$		−	18.3893i		−	1.77777i	0.458135	−	0.888883i	$-0.348518\pi$
$108$	−1.06672	+	1.46821i	−0.102645	+	0.141279i
$109$	3.71848	−	11.4443i	0.356165	−	1.09616i	−0.599165	−	0.800625i	$-0.704501\pi$
$109$	3.71848	−	11.4443i	0.356165	−	1.09616i	0.955331	−	0.295539i	$-0.0954992\pi$
$110$	2.04773	+	1.88595i	0.195243	+	0.179818i
$111$	4.22406	+	13.0003i	0.400930	+	1.23393i
$112$	17.7763	+	5.77586i	1.67970	+	0.545767i
$113$	−8.31035	−	2.70020i	−0.781772	−	0.254013i	−0.109175	−	0.994023i	$-0.534821\pi$
$113$	−8.31035	−	2.70020i	−0.781772	−	0.254013i	−0.672596	+	0.740009i	$0.734821\pi$
$114$	−4.59046	−	14.1280i	−0.429936	−	1.32321i
$115$	−1.52118	+	0.855568i	−0.141850	+	0.0797822i
$116$	−0.825652	+	2.54110i	−0.0766599	+	0.235935i
$117$	0.0573137	−	0.0788856i	0.00529866	−	0.00729297i
$118$			15.2083i			1.40004i
$119$	3.26866	+	2.37482i	0.299638	+	0.217700i
$120$	10.2225	−	2.05288i	0.933185	−	0.187402i
$121$	8.37420	−	6.08421i	0.761291	−	0.553110i
$122$	−0.340311	−	0.468398i	−0.0308103	−	0.0424068i
$123$	18.8501	−	6.12476i	1.69965	−	0.552251i
$124$	1.97128			0.177026
$125$	−9.26180	+	6.26251i	−0.828400	+	0.560136i
$126$	−3.15702			−0.281250
$127$	−14.4286	+	4.68815i	−1.28033	+	0.416006i	−0.868698	−	0.495342i	$-0.835043\pi$
$127$	−14.4286	+	4.68815i	−1.28033	+	0.416006i	−0.411636	+	0.911348i	$0.635043\pi$
$128$	7.90967	+	10.8867i	0.699123	+	0.962260i
$129$	0.223655	−	0.162495i	0.0196918	−	0.0143069i
$130$	−0.653454	+	0.131226i	−0.0573117	+	0.0115093i
$131$	2.79358	+	2.02966i	0.244077	+	0.177332i	0.703098	−	0.711093i	$-0.251800\pi$
$131$	2.79358	+	2.02966i	0.244077	+	0.177332i	−0.459021	+	0.888425i	$0.651800\pi$
$132$		−	0.586081i		−	0.0510118i
$133$	−12.1914	+	16.7801i	−1.05713	+	1.45502i
$134$	−4.39269	+	13.5193i	−0.379471	+	1.16789i
$135$	9.10228	−	5.11947i	0.783400	−	0.440614i
$136$	0.769592	+	2.36856i	0.0659920	+	0.203102i
$137$	−16.1214	−	5.23815i	−1.37734	−	0.447525i	−0.475547	−	0.879690i	$-0.657750\pi$
$137$	−16.1214	−	5.23815i	−1.37734	−	0.447525i	−0.901795	+	0.432165i	$0.857750\pi$
$138$	2.14800	+	0.697929i	0.182850	+	0.0594116i
$139$	5.57059	+	17.1445i	0.472491	+	1.45418i	0.849311	+	0.527892i	$0.177017\pi$
$139$	5.57059	+	17.1445i	0.472491	+	1.45418i	−0.376820	+	0.926286i	$0.622983\pi$
$140$	2.58227	+	2.37826i	0.218242	+	0.201000i
$141$	7.64150	−	23.5181i	0.643530	−	1.98058i
$142$	−0.572599	+	0.788115i	−0.0480514	+	0.0661371i
$143$		−	0.155360i		−	0.0129919i
$144$	−1.89223	−	1.37479i	−0.157686	−	0.114566i
$145$	10.4159	−	11.3094i	0.864993	−	0.939193i
$146$	4.38999	−	3.18951i	0.363318	−	0.263966i
$147$	10.2612	+	14.1234i	0.846331	+	1.16488i
$148$	−2.69809	+	0.876661i	−0.221781	+	0.0720611i
$149$	−6.96110			−0.570275			−0.285138	−	0.958487i	$-0.592039\pi$
$149$	−6.96110			−0.570275			−0.285138	+	0.958487i	$0.592039\pi$
$150$	14.0809	+	3.32596i	1.14970	+	0.271563i
$151$	14.8532			1.20874			0.604370	−	0.796704i	$-0.293425\pi$
$151$	14.8532			1.20874			0.604370	+	0.796704i	$0.293425\pi$
$152$	−12.1593	+	3.95079i	−0.986248	+	0.320452i
$153$	−0.297176	−	0.409028i	−0.0240253	−	0.0330679i
$154$	−4.06945	+	2.95663i	−0.327925	+	0.238252i
$155$	−10.3103	−	4.73020i	−0.828142	−	0.379939i
$156$	0.113518	+	0.0824758i	0.00908873	+	0.00660335i
$157$			4.78609i			0.381971i	0.981593	+	0.190986i	$0.0611684\pi$
$157$			4.78609i			0.381971i	−0.981593	+	0.190986i	$0.938832\pi$
$158$	8.82905	−	12.1521i	0.702402	−	0.966773i
$159$	−1.44195	+	4.43785i	−0.114354	+	0.351945i
$160$	0.954852	+	4.75478i	0.0754877	+	0.375898i
$161$	−0.974481	−	2.99914i	−0.0767998	−	0.236366i
$162$	−15.0825	−	4.90059i	−1.18499	−	0.385026i
$163$	−21.0881	−	6.85193i	−1.65175	−	0.536685i	−0.672628	−	0.739981i	$-0.734835\pi$
$163$	−21.0881	−	6.85193i	−1.65175	−	0.536685i	−0.979117	+	0.203296i	$0.934835\pi$
$164$	1.27113	+	3.91215i	0.0992589	+	0.305488i
$165$	−1.40634	+	3.06536i	−0.109483	+	0.238638i
$166$	3.98614	−	12.2681i	0.309384	−	0.952187i
$167$	5.86556	−	8.07325i	0.453891	−	0.624727i	−0.519337	−	0.854570i	$-0.673821\pi$
$167$	5.86556	−	8.07325i	0.453891	−	0.624727i	0.973228	+	0.229842i	$0.0738211\pi$
$168$			18.8396i			1.45351i
$169$	−10.4871	−	7.61935i	−0.806702	−	0.586103i
$170$	−0.399897	+	3.43264i	−0.0306707	+	0.263271i
$171$	2.09979	−	1.52559i	0.160575	−	0.116665i
$172$	0.0337243	+	0.0464175i	0.00257145	+	0.00353930i
$173$	−9.89434	+	3.21487i	−0.752253	+	0.244422i	−0.659950	−	0.751309i	$-0.729423\pi$
$173$	−9.89434	+	3.21487i	−0.752253	+	0.244422i	−0.0923024	+	0.995731i	$0.529423\pi$
$174$	−19.8968			−1.50837
$175$	−7.79917	−	18.6352i	−0.589561	−	1.40869i
$176$	−3.72663			−0.280905
$177$	−17.5226	+	5.69343i	−1.31708	+	0.427944i
$178$	−12.9982	−	17.8905i	−0.974255	−	1.34095i
$179$	−12.2846	+	8.92526i	−0.918192	+	0.667105i	−0.943073	−	0.332585i	$-0.892079\pi$
$179$	−12.2846	+	8.92526i	−0.918192	+	0.667105i	0.0248815	+	0.999690i	$0.492079\pi$
$180$	−0.215355	−	0.382895i	−0.0160516	−	0.0285393i
$181$	−14.0943	−	10.2401i	−1.04762	−	0.761139i	−0.0758597	−	0.997119i	$-0.524170\pi$
$181$	−14.0943	−	10.2401i	−1.04762	−	0.761139i	−0.971758	+	0.235980i	$0.924170\pi$
$182$		−	1.20428i		−	0.0892672i
$183$	0.412274	−	0.567447i	0.0304762	−	0.0419469i
$184$	0.600674	−	1.84868i	0.0442823	−	0.136287i
$185$	16.2153	+	1.88906i	1.19217	+	0.138886i
$186$	4.53626	+	13.9612i	0.332615	+	1.02368i
$187$	−0.766128	−	0.248930i	−0.0560248	−	0.0182036i
$188$	4.88095	+	1.58592i	0.355980	+	0.115665i
$189$	5.83101	+	17.9460i	0.424144	+	1.30538i
$190$	−17.6218	−	2.05292i	−1.27842	−	0.148934i
$191$	−2.83596	+	8.72819i	−0.205203	+	0.631550i	0.794502	+	0.607261i	$0.207732\pi$
$191$	−2.83596	+	8.72819i	−0.205203	+	0.631550i	−0.999705	+	0.0242882i	$0.992268\pi$
$192$	−6.49348	+	8.93751i	−0.468627	+	0.645009i
$193$			9.47890i			0.682306i	0.940008	+	0.341153i	$0.110817\pi$
$193$			9.47890i			0.682306i	−0.940008	+	0.341153i	$0.889183\pi$
$194$	4.65327	+	3.38080i	0.334085	+	0.242727i
$195$	−0.395824	−	0.703763i	−0.0283455	−	0.0503975i
$196$	−2.93116	+	2.12962i	−0.209369	+	0.152115i
$197$	−3.16518	−	4.35649i	−0.225510	−	0.310387i	0.681237	−	0.732063i	$-0.261442\pi$
$197$	−3.16518	−	4.35649i	−0.225510	−	0.310387i	−0.906747	+	0.421675i	$0.861442\pi$
$198$	0.598641	−	0.194510i	0.0425436	−	0.0138232i
$199$	−0.499551			−0.0354122			−0.0177061	−	0.999843i	$-0.505636\pi$
$199$	−0.499551			−0.0354122			−0.0177061	+	0.999843i	$0.505636\pi$
$200$	2.86249	−	12.1188i	0.202409	−	0.856928i
$201$	−17.2210			−1.21468
$202$	−6.71491	+	2.18181i	−0.472460	+	0.153511i
$203$	16.3292	+	22.4751i	1.14608	+	1.57745i
$204$	0.588600	−	0.427643i	0.0412103	−	0.0299410i
$205$	2.73908	−	23.5117i	0.191306	−	1.64213i
$206$	−7.20417	−	5.23413i	−0.501938	−	0.364679i
$207$			0.394615i			0.0274276i
$208$	0.524427	−	0.721812i	0.0363625	−	0.0500486i
$209$	1.27791	−	3.93301i	0.0883950	−	0.272052i
$210$	−10.9013	+	23.7612i	−0.752260	+	1.63968i
$211$	6.29922	+	19.3870i	0.433657	+	1.33466i	0.894457	+	0.447154i	$0.147562\pi$
$211$	6.29922	+	19.3870i	0.433657	+	1.33466i	−0.460801	+	0.887504i	$0.652438\pi$
$212$	−0.921033	−	0.299262i	−0.0632568	−	0.0205534i
$213$	−1.12240	−	0.364690i	−0.0769057	−	0.0249882i
$214$	8.78251	+	27.0298i	0.600360	+	1.84772i
$215$	−0.0650050	−	0.323699i	−0.00443331	−	0.0220761i
$216$	−3.59426	+	11.0620i	−0.244558	+	0.752673i
$217$	12.0475	−	16.5819i	0.817837	−	1.12566i
$218$			18.5974i			1.25958i
$219$	5.31831	+	3.86398i	0.359378	+	0.261104i
$220$	−0.636185	−	0.291872i	−0.0428916	−	0.0196780i
$221$	0.156028	−	0.113361i	0.0104956	−	0.00762548i
$222$	−12.4176	−	17.0913i	−0.833412	−	1.14709i
$223$	−6.89999	+	2.24194i	−0.462057	+	0.150131i	−0.530790	−	0.847504i	$-0.678105\pi$
$223$	−6.89999	+	2.24194i	−0.462057	+	0.150131i	0.0687324	+	0.997635i	$0.478105\pi$
$224$	−8.76280			−0.585489
$225$	0.207581	+	2.51939i	0.0138387	+	0.167960i
$226$	13.5046			0.898315
$227$	−8.18540	+	2.65960i	−0.543284	+	0.176524i	−0.567786	−	0.823176i	$-0.692200\pi$
$227$	−8.18540	+	2.65960i	−0.543284	+	0.176524i	0.0245022	+	0.999700i	$0.492200\pi$
$228$	2.19536	+	3.02165i	0.145391	+	0.200114i
$229$	11.2825	−	8.19719i	0.745566	−	0.541685i	−0.148883	−	0.988855i	$-0.547568\pi$
$229$	11.2825	−	8.19719i	0.745566	−	0.541685i	0.894449	+	0.447169i	$0.147568\pi$
$230$	1.82731	−	1.98406i	0.120489	−	0.130825i
$231$	−4.92998	−	3.58184i	−0.324369	−	0.235668i
$232$			17.1242i			1.12426i
$233$	−7.71644	+	10.6208i	−0.505521	+	0.695790i	−0.983156	−	0.182768i	$-0.941494\pi$
$233$	−7.71644	+	10.6208i	−0.505521	+	0.695790i	0.477635	+	0.878558i	$0.341494\pi$
$234$	−0.0465685	+	0.143323i	−0.00304428	+	0.00936933i
$235$	−21.7231	−	20.0069i	−1.41706	−	1.30511i
$236$	−1.18162	−	3.63664i	−0.0769166	−	0.236725i
$237$	17.3066	+	5.62326i	1.12419	+	0.365270i
$238$	−5.93867	−	1.92959i	−0.384947	−	0.125077i
$239$	−2.16364	−	6.65901i	−0.139954	−	0.430736i	0.856373	−	0.516357i	$-0.172712\pi$
$239$	−2.16364	−	6.65901i	−0.139954	−	0.430736i	−0.996328	+	0.0856218i	$0.972712\pi$
$240$	−16.8812	+	9.49463i	−1.08968	+	0.612876i
$241$	5.35790	−	16.4899i	0.345133	−	1.06221i	−0.616380	−	0.787449i	$-0.711402\pi$
$241$	5.35790	−	16.4899i	0.345133	−	1.06221i	0.961513	−	0.274760i	$-0.0885985\pi$
$242$	−9.40317	+	12.9424i	−0.604459	+	0.831966i
$243$		−	5.20112i		−	0.333652i
$244$	0.117768	+	0.0855635i	0.00753933	+	0.00547764i
$245$	20.4409	−	4.10493i	1.30592	−	0.262254i
$246$	−24.7819	+	18.0051i	−1.58004	+	1.14796i
$247$	0.581952	+	0.800988i	0.0370287	+	0.0509656i
$248$	12.0157	−	3.90414i	0.762999	−	0.247913i
$249$	15.6272			0.990331
$250$	10.6227	−	13.6283i	0.671836	−	0.861932i
$251$	2.98335			0.188307			0.0941536	−	0.995558i	$-0.469986\pi$
$251$	2.98335			0.188307			0.0941536	+	0.995558i	$0.469986\pi$
$252$	0.754913	−	0.245286i	0.0475550	−	0.0154516i
$253$	0.369566	+	0.508664i	0.0232344	+	0.0319794i
$254$	18.9691	−	13.7819i	1.19023	−	0.864750i
$255$	−4.10469	+	0.824301i	−0.257045	+	0.0516198i
$256$	−7.27850	−	5.28814i	−0.454906	−	0.330509i
$257$		−	11.1966i		−	0.698424i	−0.937044	−	0.349212i	$-0.886449\pi$
$257$		−	11.1966i		−	0.698424i	0.937044	−	0.349212i	$-0.113551\pi$
$258$	−0.251137	+	0.345660i	−0.0156351	+	0.0215199i
$259$	−9.11511	+	28.0534i	−0.566385	+	1.74316i
$260$	0.146059	−	0.0821493i	0.00905821	−	0.00509468i
$261$	−1.07426	−	3.30624i	−0.0664951	−	0.204651i
$262$	−5.07552	−	1.64914i	−0.313567	−	0.101884i
$263$	1.91892	+	0.623495i	0.118326	+	0.0384464i	0.367581	−	0.929991i	$-0.380186\pi$
$263$	1.91892	+	0.623495i	0.118326	+	0.0384464i	−0.249256	+	0.968438i	$0.580186\pi$
$264$	−1.16074	−	3.57240i	−0.0714388	−	0.219866i
$265$	4.09914	+	3.77529i	0.251808	+	0.231914i
$266$	9.90578	−	30.4869i	0.607362	−	1.86927i
$267$	15.7468	−	21.6736i	0.963689	−	1.32640i
$268$		−	3.57405i		−	0.218320i
$269$	−5.30521	−	3.85446i	−0.323464	−	0.235010i	0.414188	−	0.910191i	$-0.364066\pi$
$269$	−5.30521	−	3.85446i	−0.323464	−	0.235010i	−0.737652	+	0.675181i	$0.764066\pi$
$270$	−10.9341	+	11.8720i	−0.665428	+	0.722510i
$271$	4.95397	−	3.59927i	0.300933	−	0.218640i	−0.427063	−	0.904222i	$-0.640452\pi$
$271$	4.95397	−	3.59927i	0.300933	−	0.218640i	0.727996	+	0.685581i	$0.240452\pi$
$272$	−2.71919	−	3.74265i	−0.164875	−	0.226931i
$273$	1.38754	−	0.450838i	0.0839775	−	0.0272859i
$274$	26.1979			1.58267
$275$	2.62705	+	3.05313i	0.158417	+	0.184111i
$276$	−0.567860			−0.0341811
$277$	11.4225	−	3.71138i	0.686309	−	0.222995i	0.0549536	−	0.998489i	$-0.482499\pi$
$277$	11.4225	−	3.71138i	0.686309	−	0.222995i	0.631355	+	0.775494i	$0.282499\pi$
$278$	−16.3760	−	22.5396i	−0.982167	−	1.35184i
$279$	−2.07500	+	1.50758i	−0.124227	+	0.0902562i
$280$	20.4502	+	9.38221i	1.22213	+	0.560695i
$281$	−15.5721	−	11.3138i	−0.928957	−	0.674926i	0.0167806	−	0.999859i	$-0.494658\pi$
$281$	−15.5721	−	11.3138i	−0.928957	−	0.674926i	−0.945737	+	0.324933i	$0.894658\pi$
$282$			38.2178i			2.27584i
$283$	−3.48529	+	4.79709i	−0.207179	+	0.285157i	−0.899944	−	0.436007i	$-0.856392\pi$
$283$	−3.48529	+	4.79709i	−0.207179	+	0.285157i	0.692765	+	0.721164i	$0.256392\pi$
$284$	0.0756879	−	0.232943i	0.00449125	−	0.0138227i
$285$	−4.23165	−	21.0719i	−0.250661	−	1.24819i
$286$	0.0741980	+	0.228358i	0.00438742	+	0.0135031i
$287$	40.6767	+	13.2167i	2.40107	+	0.780155i
$288$	1.04287	+	0.338850i	0.0614519	+	0.0199669i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−9.90870	+	21.5977i	−0.581859	+	1.26826i
$291$	−2.15324	+	6.62701i	−0.126225	+	0.388482i
$292$	−0.801931	+	1.10376i	−0.0469295	+	0.0645929i
$293$			9.03672i			0.527931i	0.964532	+	0.263965i	$0.0850305\pi$
$293$			9.03672i			0.527931i	−0.964532	+	0.263965i	$0.914970\pi$
$294$	−21.8277	−	15.8588i	−1.27302	−	0.924901i
$295$	−2.54618	+	21.8559i	−0.148245	+	1.27250i
$296$	−14.7097	+	10.6872i	−0.854982	+	0.621181i
$297$	−2.21138	−	3.04370i	−0.128317	−	0.176613i
$298$	10.2318	−	3.32453i	0.592715	−	0.192585i
$299$	−0.150530			−0.00870538
$300$	−3.62547	+	0.298714i	−0.209316	+	0.0172463i
$301$	0.596560			0.0343851
$302$	−21.8322	+	7.09371i	−1.25630	+	0.408197i
$303$	−5.02763	−	6.91993i	−0.288830	−	0.397540i
$304$	19.2133	−	13.9593i	1.10196	−	0.800621i
$305$	−0.410643	−	0.730111i	−0.0235133	−	0.0418060i
$306$	0.632154	+	0.459287i	0.0361378	+	0.0262557i
$307$			10.9385i			0.624292i	0.950034	+	0.312146i	$0.101048\pi$
$307$			10.9385i			0.624292i	−0.950034	+	0.312146i	$0.898952\pi$
$308$	0.743377	−	1.02317i	0.0423578	−	0.0583005i
$309$	3.33364	−	10.2599i	0.189644	−	0.583665i
$310$	17.4138	+	2.02868i	0.989036	+	0.115221i
$311$	−8.82131	−	27.1492i	−0.500211	−	1.53949i	−0.808676	−	0.588255i	$-0.799815\pi$
$311$	−8.82131	−	27.1492i	−0.500211	−	1.53949i	0.308465	−	0.951236i	$-0.400185\pi$
$312$	0.855283	+	0.277898i	0.0484209	+	0.0157329i
$313$	−11.7381	−	3.81395i	−0.663479	−	0.215577i	−0.0421308	−	0.999112i	$-0.513415\pi$
$313$	−11.7381	−	3.81395i	−0.663479	−	0.215577i	−0.621348	+	0.783535i	$0.713415\pi$
$314$	−2.28577	−	7.03489i	−0.128994	−	0.397002i
$315$	−4.53697	−	0.528550i	−0.255629	−	0.0297804i
$316$	−1.16705	+	3.59182i	−0.0656518	+	0.202056i
$317$	−5.86986	+	8.07917i	−0.329684	+	0.453771i	−0.941393	−	0.337312i	$-0.890482\pi$
$317$	−5.86986	+	8.07917i	−0.329684	+	0.453771i	0.611709	+	0.791083i	$0.290482\pi$
$318$		−	7.21169i		−	0.404411i
$319$	−4.48110	−	3.25571i	−0.250894	−	0.182285i
$320$	6.46778	+	11.4995i	0.361560	+	0.642843i
$321$	−27.8551	+	20.2379i	−1.55472	+	1.12957i
$322$	2.86470	+	3.94293i	0.159644	+	0.219731i
$323$	4.88236	−	1.58638i	0.271662	−	0.0882683i
$324$	3.98729			0.221516
$325$	−0.961049	+	0.0791841i	−0.0533094	+	0.00439234i
$326$	34.2689			1.89798
$327$	−21.4274	+	6.96218i	−1.18494	+	0.385009i
$328$	15.4961	+	21.3286i	0.855631	+	1.17768i
$329$	43.1704	−	31.3651i	2.38006	−	1.72922i
$330$	0.603148	−	5.17730i	0.0332022	−	0.285001i
$331$	−16.1138	−	11.7074i	−0.885694	−	0.643494i	0.0490577	−	0.998796i	$-0.484378\pi$
$331$	−16.1138	−	11.7074i	−0.885694	−	0.643494i	−0.934752	+	0.355302i	$0.884378\pi$
$332$			3.24326i			0.177997i
$333$	2.16961	−	2.98621i	0.118894	−	0.163643i
$334$	−4.76588	+	14.6679i	−0.260778	+	0.802591i
$335$	−8.57615	+	18.6932i	−0.468565	+	1.02132i
$336$	−10.8143	−	33.2829i	−0.589966	−	1.81573i
$337$	−0.541058	−	0.175800i	−0.0294733	−	0.00957646i	0.294243	−	0.955731i	$-0.404932\pi$
$337$	−0.541058	−	0.175800i	−0.0294733	−	0.00957646i	−0.323717	+	0.946154i	$0.604932\pi$
$338$	19.0535	+	6.19087i	1.03638	+	0.336739i
$339$	5.05563	+	15.5596i	0.274584	+	0.845084i
$340$	−0.171076	−	0.851888i	−0.00927788	−	0.0462001i
$341$	−1.26282	+	3.88657i	−0.0683857	+	0.210470i
$342$	−2.35780	+	3.24524i	−0.127495	+	0.175482i
$343$			9.38944i			0.506982i
$344$	0.297493	+	0.216142i	0.0160398	+	0.0116536i
$345$	2.97005	+	1.36261i	0.159902	+	0.0733607i
$346$	13.0079	−	9.45081i	0.699311	−	0.508079i
$347$	−8.97386	−	12.3515i	−0.481742	−	0.663061i	0.497097	−	0.867695i	$-0.334399\pi$
$347$	−8.97386	−	12.3515i	−0.481742	−	0.663061i	−0.978838	+	0.204634i	$0.934399\pi$
$348$	4.75775	−	1.54589i	0.255042	−	0.0828682i
$349$	13.2971			0.711776			0.355888	−	0.934529i	$-0.384178\pi$
$349$	13.2971			0.711776			0.355888	+	0.934529i	$0.384178\pi$
$350$	20.3636	+	23.6664i	1.08848	+	1.26502i
$351$	0.900728			0.0480773
$352$	1.66162	−	0.539893i	0.0885646	−	0.0287764i
$353$	−6.57748	−	9.05312i	−0.350084	−	0.481849i	0.597269	−	0.802041i	$-0.296253\pi$
$353$	−6.57748	−	9.05312i	−0.350084	−	0.481849i	−0.947353	+	0.320192i	$0.896253\pi$
$354$	23.0367	−	16.7371i	1.22438	−	0.889567i
$355$	−0.954829	+	1.03674i	−0.0506771	+	0.0550243i
$356$	4.49815	+	3.26810i	0.238401	+	0.173209i
$357$		−	7.56472i		−	0.400368i
$358$	13.7940	−	18.9858i	0.729037	−	1.00343i
$359$	−9.63448	+	29.6519i	−0.508488	+	1.56497i	0.286338	+	0.958129i	$0.407562\pi$
$359$	−9.63448	+	29.6519i	−0.508488	+	1.56497i	−0.794826	+	0.606837i	$0.792438\pi$
$360$	−2.07100	−	1.90738i	−0.109151	−	0.100528i
$361$	2.27252	+	6.99410i	0.119606	+	0.368110i
$362$	25.6071	+	8.32026i	1.34588	+	0.437303i
$363$	−18.4320	−	5.98892i	−0.967429	−	0.314337i
$364$	0.0935669	+	0.287969i	0.00490424	+	0.0150937i
$365$	6.84286	−	3.84868i	0.358171	−	0.201449i
$366$	−0.334981	+	1.03097i	−0.0175097	+	0.0538894i
$367$	0.556855	−	0.766445i	0.0290676	−	0.0400081i	−0.794236	−	0.607610i	$-0.792129\pi$
$367$	0.556855	−	0.766445i	0.0290676	−	0.0400081i	0.823303	+	0.567601i	$0.192129\pi$
$368$			3.61077i			0.188224i
$369$	−4.32991	−	3.14587i	−0.225406	−	0.163767i
$370$	−24.7364	+	4.96756i	−1.28598	+	0.258251i
$371$	−8.14623	+	5.91858i	−0.422931	+	0.307278i
$372$	−2.16944	−	2.98597i	−0.112480	−	0.154815i
$373$	−33.7687	+	10.9721i	−1.74848	+	0.568115i	−0.995906	−	0.0903934i	$-0.971188\pi$
$373$	−33.7687	+	10.9721i	−1.74848	+	0.568115i	−0.752573	+	0.658509i	$0.771188\pi$
$374$	1.24499			0.0643768
$375$	19.6789	+	7.13717i	1.01621	+	0.368562i
$376$	32.8923			1.69629
$377$	1.26120	−	0.409788i	0.0649550	−	0.0211052i
$378$	−17.1416	−	23.5933i	−0.881667	−	1.21351i
$379$	7.30169	−	5.30498i	0.375062	−	0.272499i	−0.384245	−	0.923231i	$-0.625538\pi$
$379$	7.30169	−	5.30498i	0.375062	−	0.272499i	0.759307	+	0.650733i	$0.225538\pi$
$380$	4.37327	−	0.878237i	0.224344	−	0.0450526i
$381$	22.9804	+	16.6962i	1.17732	+	0.855373i
$382$		−	14.1836i		−	0.725699i
$383$	22.8721	−	31.4807i	1.16871	−	1.60859i	0.497069	−	0.867711i	$-0.334410\pi$
$383$	22.8721	−	31.4807i	1.16871	−	1.60859i	0.671640	−	0.740878i	$-0.265590\pi$
$384$	7.78579	−	23.9622i	0.397317	−	1.22282i
$385$	−6.34321	+	3.56767i	−0.323280	+	0.181825i
$386$	−4.52700	−	13.9327i	−0.230418	−	0.709154i
$387$	−0.0709975	−	0.0230685i	−0.00360900	−	0.00117264i
$388$	−1.37537	−	0.446885i	−0.0698238	−	0.0226871i
$389$	−9.13243	−	28.1067i	−0.463032	−	1.42507i	−0.861440	−	0.507859i	$-0.830437\pi$
$389$	−9.13243	−	28.1067i	−0.463032	−	1.42507i	0.398408	−	0.917208i	$-0.369563\pi$
$390$	0.917914	+	0.845394i	0.0464804	+	0.0428082i
$391$	−0.241191	+	0.742309i	−0.0121975	+	0.0375402i
$392$	−13.6489	+	18.7861i	−0.689373	+	0.948840i
$393$		−	6.46524i		−	0.326128i
$394$	6.73298	+	4.89180i	0.339203	+	0.246445i
$395$	14.7228	−	15.9857i	0.740783	−	0.804329i
$396$	−0.128035	+	0.0930232i	−0.00643402	+	0.00467459i
$397$	16.8726	+	23.2231i	0.846811	+	1.16554i	0.984556	+	0.175068i	$0.0560144\pi$
$397$	16.8726	+	23.2231i	0.846811	+	1.16554i	−0.137745	+	0.990468i	$0.543986\pi$
$398$	0.734271	−	0.238579i	0.0368057	−	0.0119589i
$399$	38.8344			1.94415
$400$	1.89939	+	23.0527i	0.0949695	+	1.15264i
$401$	−32.6286			−1.62939			−0.814697	−	0.579887i	$-0.803097\pi$
$401$	−32.6286			−1.62939			−0.814697	+	0.579887i	$0.803097\pi$
$402$	25.3125	−	8.22453i	1.26247	−	0.410202i
$403$	−0.575081	−	0.791531i	−0.0286468	−	0.0394290i
$404$	1.43616	−	1.04343i	0.0714519	−	0.0519128i
$405$	−20.8546	−	9.56775i	−1.03627	−	0.475426i
$406$	−34.7354	−	25.2368i	−1.72389	−	1.25248i
$407$		−	5.88115i		−	0.291518i
$408$	2.74080	−	3.77239i	0.135690	−	0.186761i
$409$	1.59808	−	4.91839i	0.0790200	−	0.243199i	−0.903741	−	0.428080i	$-0.859190\pi$
$409$	1.59808	−	4.91839i	0.0790200	−	0.243199i	0.982761	+	0.184881i	$0.0591901\pi$
$410$	7.20282	+	35.8671i	0.355722	+	1.77135i
$411$	9.80750	+	30.1844i	0.483768	+	1.48889i
$412$	2.12934	+	0.691864i	0.104905	+	0.0340857i
$413$	−37.8121	−	12.2859i	−1.86061	−	0.604549i
$414$	−0.188463	−	0.580029i	−0.00926244	−	0.0285069i
$415$	7.78241	−	16.9631i	0.382023	−	0.832686i
$416$	−0.129258	+	0.397815i	−0.00633740	+	0.0195045i
$417$	19.8389	−	27.3059i	0.971516	−	1.33718i
$418$			6.39129i			0.312608i
$419$	−19.4290	−	14.1160i	−0.949167	−	0.689610i	0.00144284	−	0.999999i	$-0.499541\pi$
$419$	−19.4290	−	14.1160i	−0.949167	−	0.689610i	−0.950610	+	0.310389i	$0.899541\pi$
$420$	0.760596	−	6.52880i	0.0371133	−	0.318573i
$421$	27.2557	−	19.8024i	1.32836	−	0.965110i	0.328573	−	0.944478i	$-0.393432\pi$
$421$	27.2557	−	19.8024i	1.32836	−	0.965110i	0.999787	−	0.0206319i	$-0.00656780\pi$
$422$	−18.5180	−	25.4878i	−0.901441	−	1.24073i
$423$	−6.35064	+	2.06345i	−0.308778	+	0.100328i
$424$	−6.20676			−0.301427
$425$	−1.14939	+	4.86610i	−0.0557534	+	0.236040i
$426$	1.82395			0.0883705
$427$	1.43948	−	0.467716i	0.0696614	−	0.0226344i
$428$	−4.20018	−	5.78105i	−0.203023	−	0.279437i
$429$	−0.235330	+	0.170977i	−0.0113619	+	0.00825487i
$430$	0.250143	+	0.444747i	0.0120630	+	0.0214476i
$431$	0.791092	+	0.574762i	0.0381055	+	0.0276853i	0.606675	−	0.794950i	$-0.292503\pi$
$431$	0.791092	+	0.574762i	0.0381055	+	0.0276853i	−0.568569	+	0.822635i	$0.692503\pi$
$432$		−	21.6058i		−	1.03951i
$433$	−2.74612	+	3.77971i	−0.131970	+	0.181641i	−0.869888	−	0.493249i	$-0.835809\pi$
$433$	−2.74612	+	3.77971i	−0.131970	+	0.181641i	0.737918	+	0.674890i	$0.235809\pi$
$434$	−9.78882	+	30.1269i	−0.469878	+	1.44614i
$435$	−28.5937	−	3.33113i	−1.37096	−	0.159715i
$436$	−1.44493	−	4.44704i	−0.0691997	−	0.212975i
$437$	−3.81073	−	1.23818i	−0.182292	−	0.0592302i
$438$	−9.66257	−	3.13956i	−0.461695	−	0.150014i
$439$	3.95697	+	12.1783i	0.188856	+	0.581238i	0.999993	−	0.00361713i	$-0.00115137\pi$
$439$	3.95697	+	12.1783i	0.188856	+	0.581238i	−0.811138	+	0.584855i	$0.801151\pi$
$440$	−4.45585	−	0.519101i	−0.212425	−	0.0247472i
$441$	1.45672	−	4.48334i	0.0693679	−	0.213492i
$442$	−0.175200	+	0.241142i	−0.00833340	+	0.0114699i
$443$		−	34.4806i		−	1.63822i	−0.573634	−	0.819112i	$-0.694467\pi$
$443$		−	34.4806i		−	1.63822i	0.573634	−	0.819112i	$-0.305533\pi$
$444$	4.29722	+	3.12211i	0.203937	+	0.148169i
$445$	−15.6845	−	27.8866i	−0.743516	−	1.32195i
$446$	9.07130	−	6.59069i	0.429539	−	0.312078i
$447$	7.66085	+	10.5442i	0.362346	+	0.498726i
$448$	−22.6724	+	7.36671i	−1.07117	+	0.348044i
$449$	30.1349			1.42215			0.711077	−	0.703114i	$-0.248208\pi$
$449$	30.1349			1.42215			0.711077	+	0.703114i	$0.248208\pi$
$450$	−1.50834	−	3.60402i	−0.0711041	−	0.169895i
$451$	−8.52750			−0.401544
$452$	−3.22925	+	1.04925i	−0.151891	+	0.0493524i
$453$	−16.3463	−	22.4988i	−0.768017	−	1.05709i
$454$	10.7612	−	7.81848i	0.505049	−	0.366939i
$455$	0.201621	−	1.73067i	0.00945214	−	0.0811352i
$456$	19.3660	+	14.0702i	0.906896	+	0.658898i
$457$		−	13.0571i		−	0.610788i	−0.952226	−	0.305394i	$-0.901212\pi$
$457$		−	13.0571i		−	0.610788i	0.952226	−	0.305394i	$-0.0987881\pi$
$458$	−12.6688	+	17.4371i	−0.591973	+	0.814781i
$459$	1.44322	−	4.44176i	0.0673635	−	0.207324i
$460$	−0.282797	+	0.616405i	−0.0131855	+	0.0287400i
$461$	9.39291	+	28.9084i	0.437471	+	1.34640i	0.890533	+	0.454919i	$0.150332\pi$
$461$	9.39291	+	28.9084i	0.437471	+	1.34640i	−0.453061	+	0.891479i	$0.649668\pi$
$462$	8.95704	+	2.91032i	0.416719	+	0.135400i
$463$	28.5551	+	9.27813i	1.32707	+	0.431191i	0.884917	−	0.465749i	$-0.154215\pi$
$463$	28.5551	+	9.27813i	1.32707	+	0.431191i	0.442153	+	0.896940i	$0.354215\pi$
$464$	−9.82960	−	30.2524i	−0.456328	−	1.40443i
$465$	4.18168	+	20.8231i	0.193921	+	0.965648i
$466$	6.26976	−	19.2963i	0.290441	−	0.893885i
$467$	−1.06874	+	1.47099i	−0.0494553	+	0.0680694i	−0.833028	−	0.553230i	$-0.813395\pi$
$467$	−1.06874	+	1.47099i	−0.0494553	+	0.0680694i	0.783573	+	0.621300i	$0.213395\pi$
$468$		−	0.0378898i		−	0.00175146i
$469$	−30.0641	−	21.8429i	−1.38823	−	1.00861i
$470$	41.4850	+	19.0327i	1.91356	+	0.877913i
$471$	7.24968	−	5.26720i	0.334047	−	0.242700i
$472$	−14.4048	−	19.8266i	−0.663036	−	0.912591i
$473$	−0.113121	+	0.0367552i	−0.00520130	+	0.00169001i
$474$	−28.1239			−1.29177
$475$	−24.9807	−	5.90051i	−1.14619	−	0.270734i
$476$	1.56998			0.0719601
$477$	1.19836	−	0.389371i	0.0548692	−	0.0178281i
$478$	6.36051	+	8.75449i	0.290923	+	0.400421i
$479$	−14.3891	+	10.4543i	−0.657455	+	0.477669i	−0.865802	−	0.500386i	$-0.833191\pi$
$479$	−14.3891	+	10.4543i	−0.657455	+	0.477669i	0.208348	+	0.978055i	$0.433191\pi$
$480$	6.15141	−	6.67909i	0.280772	−	0.304857i
$481$	1.13912	+	0.827619i	0.0519394	+	0.0377362i
$482$			26.7968i			1.22056i
$483$	−3.47048	+	4.77671i	−0.157912	+	0.217348i
$484$	1.24294	−	3.82538i	0.0564973	−	0.173881i
$485$	6.12121	+	5.63761i	0.277950	+	0.255991i
$486$	2.48399	+	7.64492i	0.112676	+	0.346781i
$487$	17.2658	+	5.61000i	0.782389	+	0.254214i	0.672860	−	0.739770i	$-0.265066\pi$
$487$	17.2658	+	5.61000i	0.782389	+	0.254214i	0.109529	+	0.993984i	$0.465066\pi$
$488$	0.887303	+	0.288302i	0.0401663	+	0.0130508i
$489$	12.8290	+	39.4836i	0.580148	+	1.78551i
$490$	−28.0848	+	15.7960i	−1.26874	+	0.713590i
$491$	9.87732	−	30.3993i	0.445757	−	1.37190i	−0.435894	−	0.899998i	$-0.643568\pi$
$491$	9.87732	−	30.3993i	0.445757	−	1.37190i	0.881651	−	0.471902i	$-0.156432\pi$
$492$	4.52698	−	6.23085i	0.204092	−	0.280908i
$493$		−	6.87594i		−	0.309677i
$494$	−1.23793	−	0.899409i	−0.0556971	−	0.0404663i
$495$	0.892873	−	0.179306i	0.0401317	−	0.00805922i
$496$	−18.9865	+	13.7945i	−0.852518	+	0.619390i
$497$	−1.49690	−	2.06031i	−0.0671452	−	0.0924174i
$498$	−22.9698	+	7.46333i	−1.02930	+	0.334440i
$499$	31.3302			1.40253			0.701267	−	0.712899i	$-0.252618\pi$
$499$	31.3302			1.40253			0.701267	+	0.712899i	$0.252618\pi$
$500$	−1.48125	+	4.08416i	−0.0662435	+	0.182649i
$501$	−18.6841			−0.834742
$502$	−4.38510	+	1.42481i	−0.195717	+	0.0635922i
$503$	−11.3818	−	15.6657i	−0.507490	−	0.698500i	0.476003	−	0.879443i	$-0.342085\pi$
$503$	−11.3818	−	15.6657i	−0.507490	−	0.698500i	−0.983494	+	0.180943i	$0.942085\pi$
$504$	4.11570	−	2.99023i	0.183328	−	0.133195i
$505$	−10.0153	+	2.01127i	−0.445675	+	0.0895002i
$506$	−0.786142	−	0.571166i	−0.0349483	−	0.0253914i
$507$			24.2705i			1.07789i
$508$	−3.46513	+	4.76935i	−0.153740	+	0.211606i
$509$	−0.475320	+	1.46288i	−0.0210682	+	0.0648412i	−0.961038	−	0.276417i	$-0.910853\pi$
$509$	−0.475320	+	1.46288i	−0.0210682	+	0.0648412i	0.939970	+	0.341258i	$0.110853\pi$
$510$	5.63965	−	3.17195i	0.249728	−	0.140456i
$511$	4.38360	+	13.4913i	0.193919	+	0.596821i
$512$	−12.3723	−	4.02001i	−0.546784	−	0.177661i
$513$	22.8023	+	7.40892i	1.00675	+	0.327112i
$514$	5.34735	+	16.4574i	0.235861	+	0.725907i
$515$	−9.47682	−	8.72811i	−0.417599	−	0.384607i
$516$	0.0331961	−	0.102167i	0.00146138	−	0.00449765i
$517$	−6.25359	+	8.60733i	−0.275033	+	0.378550i
$518$		−	45.5879i		−	2.00302i
$519$	15.7586	+	11.4493i	0.691727	+	0.502569i
$520$	0.727591	−	0.790005i	0.0319070	−	0.0346440i
$521$	−5.14851	+	3.74061i	−0.225560	+	0.163879i	−0.694826	−	0.719178i	$-0.744519\pi$
$521$	−5.14851	+	3.74061i	−0.225560	+	0.163879i	0.469266	+	0.883057i	$0.344519\pi$
$522$	3.15803	+	4.34665i	0.138223	+	0.190248i
$523$	−12.1562	+	3.94979i	−0.531554	+	0.172712i	−0.562482	−	0.826809i	$-0.690154\pi$
$523$	−12.1562	+	3.94979i	−0.531554	+	0.172712i	0.0309285	+	0.999522i	$0.490154\pi$
$524$	1.34180			0.0586167
$525$	−19.6444	+	32.3222i	−0.857350	+	1.41066i
$526$	−3.11832			−0.135965
$527$	−4.82471	+	1.56764i	−0.210168	+	0.0682877i
$528$	4.10124	+	5.64487i	0.178484	+	0.245662i
$529$	−18.1145	+	13.1610i	−0.787589	+	0.572217i
$530$	−7.82820	−	3.59146i	−0.340035	−	0.156003i
$531$	4.02498	+	2.92432i	0.174669	+	0.126905i
$532$			8.05970i			0.349432i
$533$	1.20002	−	1.65169i	0.0519788	−	0.0715427i
$534$	−12.7946	+	39.3777i	−0.553676	+	1.70404i
$535$	8.09603	+	40.3149i	0.350022	+	1.74297i
$536$	−7.07846	−	21.7853i	−0.305743	−	0.940980i
$537$	27.0389	+	8.78547i	1.16681	+	0.379121i
$538$	9.63876	+	3.13182i	0.415556	+	0.135022i
$539$	−2.32101	−	7.14334i	−0.0999731	−	0.307685i
$540$	1.69218	−	3.68839i	0.0728197	−	0.158723i
$541$	−9.39158	+	28.9043i	−0.403776	+	1.24269i	0.518138	+	0.855297i	$0.326625\pi$
$541$	−9.39158	+	28.9043i	−0.403776	+	1.24269i	−0.921913	+	0.387396i	$0.873375\pi$
$542$	−5.56269	+	7.65639i	−0.238938	+	0.328870i
$543$			32.6186i			1.39980i
$544$	1.75464	+	1.27482i	0.0752296	+	0.0546575i
$545$	−3.11359	+	26.7264i	−0.133371	+	1.14483i
$546$	−1.82417	+	1.32534i	−0.0780673	+	0.0567192i
$547$	−1.10161	−	1.51624i	−0.0471014	−	0.0648296i	0.784817	−	0.619728i	$-0.212757\pi$
$547$	−1.10161	−	1.51624i	−0.0471014	−	0.0648296i	−0.831918	+	0.554898i	$0.812757\pi$
$548$	−6.26447	+	2.03545i	−0.267605	+	0.0869501i
$549$	−0.189401			−0.00808344
$550$	−5.31953	−	3.23303i	−0.226825	−	0.137857i
$551$	35.2985			1.50377
$552$	−3.46133	+	1.12465i	−0.147324	+	0.0478685i
$553$	23.0811	+	31.7684i	0.981509	+	1.35093i
$554$	−15.0169	+	10.9104i	−0.638008	+	0.463540i
$555$	−14.9839	−	26.6409i	−0.636029	−	1.13084i
$556$	5.66708	+	4.11737i	0.240338	+	0.174615i
$557$			35.9262i			1.52224i	0.648611	+	0.761120i	$0.275350\pi$
$557$			35.9262i			1.52224i	−0.648611	+	0.761120i	$0.724650\pi$
$558$	2.32996	−	3.20692i	0.0986352	−	0.135760i
$559$	0.00879971	−	0.0270827i	0.000372188	−	0.00114548i
$560$	−41.5137	−	4.83629i	−1.75428	−	0.204371i
$561$	0.466077	+	1.43444i	0.0196778	+	0.0605620i
$562$	28.2922	+	9.19271i	1.19344	+	0.387771i
$563$	1.30658	+	0.424533i	0.0550658	+	0.0178919i	0.336420	−	0.941712i	$-0.390784\pi$
$563$	1.30658	+	0.424533i	0.0550658	+	0.0178919i	−0.281355	+	0.959604i	$0.590784\pi$
$564$	−2.96935	−	9.13871i	−0.125032	−	0.384809i
$565$	19.4075	+	2.26095i	0.816482	+	0.0951190i
$566$	2.83186	−	8.71558i	0.119032	−	0.366343i
$567$	24.3684	−	33.5402i	1.02338	−	1.40856i
$568$		−	1.56978i		−	0.0658667i
$569$	−11.2077	−	8.14285i	−0.469850	−	0.341366i	0.327533	−	0.944840i	$-0.393783\pi$
$569$	−11.2077	−	8.14285i	−0.469850	−	0.341366i	−0.797383	+	0.603474i	$0.793783\pi$
$570$	16.2836	+	28.9518i	0.682045	+	1.21266i
$571$	22.3204	−	16.2167i	0.934078	−	0.678647i	−0.0129101	−	0.999917i	$-0.504110\pi$
$571$	22.3204	−	16.2167i	0.934078	−	0.678647i	0.946988	+	0.321270i	$0.104110\pi$
$572$	−0.0354847	−	0.0488405i	−0.00148369	−	0.00204212i
$573$	16.3420	−	5.30983i	0.682696	−	0.221821i
$574$	−66.1012			−2.75901
$575$	2.95820	−	2.54537i	0.123366	−	0.106149i
$576$	2.98314			0.124298
$577$	−10.1223	+	3.28894i	−0.421398	+	0.136921i	−0.512037	−	0.858963i	$-0.671109\pi$
$577$	−10.1223	+	3.28894i	−0.421398	+	0.136921i	0.0906391	+	0.995884i	$0.471109\pi$
$578$	0.908424	+	1.25034i	0.0377855	+	0.0520072i
$579$	14.3581	−	10.4317i	0.596701	−	0.433528i
$580$	0.691343	−	5.93434i	0.0287064	−	0.246410i
$581$	27.2816	+	19.8212i	1.13183	+	0.822324i
$582$		−	10.7691i		−	0.446395i
$583$	1.18005	−	1.62420i	0.0488726	−	0.0672674i
$584$	−2.70207	+	8.31612i	−0.111812	+	0.344123i
$585$	−0.0909189	+	0.198174i	−0.00375904	+	0.00819347i
$586$	−4.31582	−	13.2827i	−0.178285	−	0.548704i
$587$	−12.7494	−	4.14253i	−0.526224	−	0.170981i	0.0338441	−	0.999427i	$-0.489225\pi$
$587$	−12.7494	−	4.14253i	−0.526224	−	0.170981i	−0.560068	+	0.828447i	$0.689225\pi$
$588$	6.45163	+	2.09626i	0.266061	+	0.0864483i
$589$	−8.04769	−	24.7682i	−0.331599	−	1.02056i
$590$	−6.69556	−	33.3412i	−0.275652	−	1.37264i
$591$	−3.11560	+	9.58884i	−0.128159	+	0.394432i
$592$	19.8521	−	27.3241i	0.815917	−	1.12301i
$593$		−	36.9595i		−	1.51774i	−0.651240	−	0.758872i	$-0.725751\pi$
$593$		−	36.9595i		−	1.51774i	0.651240	−	0.758872i	$-0.274249\pi$
$594$	4.70405	+	3.41769i	0.193009	+	0.140229i
$595$	−8.21142	−	3.76727i	−0.336635	−	0.154443i
$596$	−2.18836	+	1.58993i	−0.0896385	+	0.0651262i
$597$	0.549767	+	0.756690i	0.0225005	+	0.0309692i
$598$	0.221258	−	0.0718912i	0.00904792	−	0.00293985i
$599$	−42.9288			−1.75402			−0.877012	−	0.480469i	$-0.840466\pi$
$599$	−42.9288			−1.75402			−0.877012	+	0.480469i	$0.840466\pi$
$600$	−21.5070	+	9.00107i	−0.878021	+	0.367467i
$601$	−27.9496			−1.14009			−0.570043	−	0.821615i	$-0.693074\pi$
$601$	−27.9496			−1.14009			−0.570043	+	0.821615i	$0.693074\pi$
$602$	−0.876860	+	0.284909i	−0.0357382	+	0.0116120i
$603$	2.73333	+	3.76211i	0.111310	+	0.153205i
$604$	4.66940	−	3.39252i	0.189995	−	0.138040i
$605$	−15.6801	+	17.0252i	−0.637488	+	0.692173i
$606$	10.6948	+	7.77022i	0.434446	+	0.315643i
$607$			29.5119i			1.19785i	0.800805	+	0.598925i	$0.204405\pi$
$607$			29.5119i			1.19785i	−0.800805	+	0.598925i	$0.795595\pi$
$608$	−6.54444	+	9.00765i	−0.265412	+	0.365308i
$609$	16.0734	−	49.4688i	0.651327	−	2.00458i
$610$	0.952279	+	0.877044i	0.0385567	+	0.0355105i
$611$	−0.787124	−	2.42252i	−0.0318436	−	0.0980046i
$612$	−0.186846	−	0.0607100i	−0.00755281	−	0.00245406i
$613$	3.66489	+	1.19079i	0.148023	+	0.0480957i	0.382092	−	0.924124i	$-0.375204\pi$
$613$	3.66489	+	1.19079i	0.148023	+	0.0480957i	−0.234068	+	0.972220i	$0.575204\pi$
$614$	−5.22407	−	16.0780i	−0.210826	−	0.648857i
$615$	−38.6285	+	21.7262i	−1.55765	+	0.876084i
$616$	2.50477	−	7.70890i	0.100920	−	0.310600i
$617$	−11.7364	+	16.1537i	−0.472488	+	0.650324i	−0.977040	−	0.213058i	$-0.931658\pi$
$617$	−11.7364	+	16.1537i	−0.472488	+	0.650324i	0.504552	+	0.863382i	$0.331658\pi$
$618$			16.6727i			0.670675i
$619$	−28.4449	−	20.6664i	−1.14330	−	0.830653i	−0.155721	−	0.987801i	$-0.549770\pi$
$619$	−28.4449	−	20.6664i	−1.14330	−	0.830653i	−0.987575	+	0.157148i	$0.949770\pi$
$620$	−4.32163	+	0.867868i	−0.173561	+	0.0348544i
$621$	−2.94907	+	2.14262i	−0.118342	+	0.0859805i
$622$	25.9322	+	35.6926i	1.03979	+	1.43114i
$623$	54.9810	−	17.8644i	2.20277	−	0.715723i
$624$	−1.67050			−0.0668735
$625$	17.5475	−	17.8069i	0.701901	−	0.712275i
$626$	19.0749			0.762387
$627$	−7.36385	+	2.39266i	−0.294084	+	0.0955537i
$628$	1.09316	+	1.50460i	0.0436217	+	0.0600401i
$629$	5.90642	−	4.29127i	0.235505	−	0.171104i
$630$	6.92114	−	1.38990i	0.275745	−	0.0553749i
$631$	−6.90178	−	5.01443i	−0.274755	−	0.199621i	0.441871	−	0.897078i	$-0.354315\pi$
$631$	−6.90178	−	5.01443i	−0.274755	−	0.199621i	−0.716627	+	0.697457i	$0.754315\pi$
$632$			24.2049i			0.962820i
$633$	22.4338	−	30.8775i	0.891665	−	1.22727i
$634$	4.76938	−	14.6786i	0.189416	−	0.582963i
$635$	29.5679	−	16.6301i	1.17337	−	0.659946i
$636$	0.560314	+	1.72447i	0.0222179	+	0.0683797i
$637$	1.71022	+	0.555683i	0.0677613	+	0.0220170i
$638$	8.14149	+	2.64533i	0.322324	+	0.104730i
$639$	0.0984780	+	0.303084i	0.00389573	+	0.0119898i
$640$	−22.1333	−	20.3847i	−0.874896	−	0.805776i
$641$	5.93277	−	18.2592i	0.234330	−	0.721194i	−0.762879	−	0.646541i	$-0.776215\pi$
$641$	5.93277	−	18.2592i	0.234330	−	0.721194i	0.997210	−	0.0746533i	$-0.0237850\pi$
$642$	31.2777	−	43.0501i	1.23443	−	1.69905i
$643$		−	32.8364i		−	1.29494i	−0.762091	−	0.647470i	$-0.775827\pi$
$643$		−	32.8364i		−	1.29494i	0.762091	−	0.647470i	$-0.224173\pi$
$644$	−0.991359	−	0.720265i	−0.0390650	−	0.0283824i
$645$	−0.418780	+	0.454704i	−0.0164894	+	0.0179039i
$646$	−6.41876	+	4.66350i	−0.252543	+	0.183483i
$647$	23.1982	+	31.9295i	0.912013	+	1.25528i	0.966474	+	0.256763i	$0.0826560\pi$
$647$	23.1982	+	31.9295i	0.912013	+	1.25528i	−0.0544610	+	0.998516i	$0.517344\pi$
$648$	24.3041	−	7.89689i	0.954757	−	0.310219i
$649$	7.92695			0.311160
$650$	1.37479	−	0.575374i	0.0539238	−	0.0225680i
$651$	−38.3759			−1.50407
$652$	−8.19444	+	2.66254i	−0.320919	+	0.104273i
$653$	−2.01971	−	2.77989i	−0.0790374	−	0.108786i	0.767668	−	0.640848i	$-0.221417\pi$
$653$	−2.01971	−	2.77989i	−0.0790374	−	0.108786i	−0.846705	+	0.532062i	$0.821417\pi$
$654$	28.1702	−	20.4669i	1.10154	−	0.800318i
$655$	−7.01794	−	3.21972i	−0.274214	−	0.125805i
$656$	−39.6192	−	28.7850i	−1.54687	−	1.12387i
$657$		−	1.77513i		−	0.0692546i
$658$	−48.4749	+	66.7200i	−1.88975	+	2.60102i
$659$	−3.91811	+	12.0587i	−0.152628	+	0.469741i	−0.997913	−	0.0645753i	$-0.979431\pi$
$659$	−3.91811	+	12.0587i	−0.152628	+	0.469741i	0.845285	+	0.534316i	$0.179431\pi$
$660$	0.258026	+	1.28487i	0.0100437	+	0.0500133i
$661$	12.2355	+	37.6569i	0.475905	+	1.46468i	0.844734	+	0.535187i	$0.179759\pi$
$661$	12.2355	+	37.6569i	0.475905	+	1.46468i	−0.368829	+	0.929497i	$0.620241\pi$
$662$	29.2763	+	9.51245i	1.13786	+	0.369712i
$663$	−0.343425	−	0.111585i	−0.0133375	−	0.00433362i
$664$	6.42333	+	19.7690i	0.249274	+	0.767185i
$665$	19.3397	−	42.1543i	0.749963	−	1.63467i
$666$	−1.76285	+	5.42548i	−0.0683089	+	0.210233i
$667$	−3.15449	+	4.34178i	−0.122142	+	0.168115i
$668$		−	3.87769i		−	0.150032i
$669$	10.9895	+	7.98437i	0.424880	+	0.308694i
$670$	3.67813	−	31.5723i	0.142098	−	1.21974i
$671$	−0.244141	+	0.177379i	−0.00942494	+	0.00684762i
$672$	9.64366	+	13.2734i	0.372012	+	0.512031i
$673$	−25.8056	+	8.38476i	−0.994734	+	0.323209i	−0.760759	−	0.649034i	$-0.775173\pi$
$673$	−25.8056	+	8.38476i	−0.994734	+	0.323209i	−0.233975	+	0.972243i	$0.575173\pi$
$674$	0.879240			0.0338671
$675$	−17.7010	+	15.2308i	−0.681313	+	0.586232i
$676$	−5.03711			−0.193735
$677$	28.2521	−	9.17968i	1.08582	−	0.352804i	0.289189	−	0.957272i	$-0.406614\pi$
$677$	28.2521	−	9.17968i	1.08582	−	0.352804i	0.796629	+	0.604468i	$0.206614\pi$
$678$	−14.8622	−	20.4560i	−0.570778	−	0.785608i
$679$	−12.1647	+	8.83816i	−0.466838	+	0.339178i
$680$	−2.72995	−	4.85378i	−0.104689	−	0.186134i
$681$	13.0368	+	9.47180i	0.499572	+	0.362960i
$682$		−	6.31583i		−	0.241846i
$683$	−8.33150	+	11.4673i	−0.318796	+	0.438785i	−0.938099	−	0.346367i	$-0.887415\pi$
$683$	−8.33150	+	11.4673i	−0.318796	+	0.438785i	0.619303	+	0.785152i	$0.287415\pi$
$684$	0.311662	−	0.959196i	0.0119167	−	0.0366758i
$685$	37.6490	+	4.38606i	1.43849	+	0.167583i
$686$	−4.48428	−	13.8012i	−0.171210	−	0.526932i
$687$	−24.8332	−	8.06880i	−0.947446	−	0.307844i
$688$	−0.649634	−	0.211079i	−0.0247671	−	0.00804731i
$689$	0.148530	+	0.457128i	0.00565854	+	0.0174152i
$690$	−5.01633	−	0.584396i	−0.190969	−	0.0222476i
$691$	−0.0313524	+	0.0964927i	−0.00119270	+	0.00367075i	−0.951651	−	0.307181i	$-0.900614\pi$
$691$	−0.0313524	+	0.0964927i	−0.00119270	+	0.00367075i	0.950458	+	0.310852i	$0.100614\pi$
$692$	−2.37619	+	3.27055i	−0.0903293	+	0.124328i
$693$			1.64552i			0.0625081i
$694$	19.0892	+	13.8691i	0.724617	+	0.526465i
$695$	−19.7604	−	35.1334i	−0.749554	−	1.33269i
$696$	25.9387	−	18.8456i	0.983205	−	0.714340i
$697$	−6.22222	−	8.56415i	−0.235683	−	0.324390i
$698$	−19.5449	+	6.35051i	−0.739784	+	0.240370i
$699$	24.5798			0.929694
$700$	−6.70816	−	4.07700i	−0.253544	−	0.154096i
$701$	−23.3937			−0.883568			−0.441784	−	0.897121i	$-0.645654\pi$
$701$	−23.3937			−0.883568			−0.441784	+	0.897121i	$0.645654\pi$
$702$	−1.32395	+	0.430176i	−0.0499691	+	0.0162359i
$703$	22.0297	+	30.3213i	0.830867	+	1.14359i
$704$	3.84531	−	2.79378i	0.144926	−	0.105295i
$705$	−6.39845	+	54.9229i	−0.240979	+	2.06852i
$706$	13.9916	+	10.1655i	0.526582	+	0.382584i
$707$		−	18.4577i		−	0.694172i
$708$	−4.20817	+	5.79204i	−0.158153	+	0.217678i
$709$	−5.72379	+	17.6160i	−0.214962	+	0.661584i	0.784195	+	0.620515i	$0.213076\pi$
$709$	−5.72379	+	17.6160i	−0.214962	+	0.661584i	−0.999156	+	0.0410690i	$0.986924\pi$
$710$	0.908335	−	1.97987i	0.0340892	−	0.0743033i
$711$	−1.51846	−	4.67333i	−0.0569466	−	0.175264i
$712$	33.8905	+	11.0117i	1.27010	+	0.412681i
$713$	3.76574	+	1.22356i	0.141028	+	0.0458227i
$714$	3.61281	+	11.1191i	0.135206	+	0.416122i
$715$	0.0683983	+	0.340596i	0.00255795	+	0.0127376i
$716$	−1.82334	+	5.61166i	−0.0681413	+	0.209717i
$717$	−7.70553	+	10.6057i	−0.287768	+	0.396079i
$718$		−	48.1854i		−	1.79826i
$719$	16.6367	+	12.0873i	0.620445	+	0.450780i	0.853077	−	0.521785i	$-0.174734\pi$
$719$	16.6367	+	12.0873i	0.620445	+	0.450780i	−0.232632	+	0.972565i	$0.574734\pi$
$720$	4.75359	+	2.18088i	0.177156	+	0.0812764i
$721$	18.8333	−	13.6832i	0.701389	−	0.509589i
$722$	−6.68058	−	9.19503i	−0.248625	−	0.342203i
$723$	−30.8744	+	10.0317i	−1.14823	+	0.373083i
$724$	−6.76966			−0.251593
$725$	−17.8557	+	29.3792i	−0.663145	+	1.09112i
$726$	29.9527			1.11165
$727$	−35.4108	+	11.5057i	−1.31331	+	0.426722i	−0.880194	−	0.474614i	$-0.842588\pi$
$727$	−35.4108	+	11.5057i	−1.31331	+	0.426722i	−0.433121	+	0.901336i	$0.642588\pi$
$728$	1.14066	+	1.56998i	0.0422755	+	0.0581872i
$729$	17.0260	−	12.3701i	0.630592	−	0.458152i
$730$	−8.21997	+	8.92509i	−0.304235	+	0.330332i
$731$	−0.119454	−	0.0867881i	−0.00441815	−	0.00320997i
$732$		−	0.272553i		−	0.0100738i
$733$	−18.3553	+	25.2640i	−0.677970	+	0.933146i	−0.999907	−	0.0136154i	$-0.995666\pi$
$733$	−18.3553	+	25.2640i	−0.677970	+	0.933146i	0.321937	+	0.946761i	$0.395666\pi$
$734$	−0.452455	+	1.39251i	−0.0167004	+	0.0513986i
$735$	−28.7136	−	26.4451i	−1.05912	−	0.975441i
$736$	−0.523108	−	1.60996i	−0.0192820	−	0.0593439i
$737$	7.04660	+	2.28958i	0.259565	+	0.0843377i
$738$	7.86680	+	2.55608i	0.289581	+	0.0940905i
$739$	9.23759	+	28.4304i	0.339810	+	1.04583i	0.964304	+	0.264798i	$0.0853053\pi$
$739$	9.23759	+	28.4304i	0.339810	+	1.04583i	−0.624494	+	0.781030i	$0.714695\pi$
$740$	5.52906	−	3.10975i	0.203252	−	0.114317i
$741$	0.572837	−	1.76301i	0.0210437	−	0.0647658i
$742$	9.14719	−	12.5900i	0.335804	−	0.462195i
$743$			2.70349i			0.0991814i	0.998770	+	0.0495907i	$0.0157917\pi$
$743$			2.70349i			0.0991814i	−0.998770	+	0.0495907i	$0.984208\pi$
$744$	−19.1373	−	13.9041i	−0.701609	−	0.509749i
$745$	15.2608	−	3.06467i	0.559113	−	0.112281i
$746$	44.3952	−	32.2550i	1.62542	−	1.18094i
$747$	−2.48035	−	3.41391i	−0.0907514	−	0.124909i
$748$	−0.297703	+	0.0967297i	−0.0108851	+	0.00353679i
$749$	−74.2983			−2.71480
$750$	−32.3339	−	1.09227i	−1.18067	−	0.0398841i
$751$	−51.4248			−1.87652			−0.938259	−	0.345934i	$-0.887562\pi$
$751$	−51.4248			−1.87652			−0.938259	+	0.345934i	$0.887562\pi$
$752$	−58.1090	+	18.8808i	−2.11902	+	0.688511i
$753$	−3.28324	−	4.51899i	−0.119648	−	0.164681i
$754$	−1.65808	+	1.20466i	−0.0603836	+	0.0438713i
$755$	−32.5627	+	6.53923i	−1.18508	+	0.237987i
$756$	5.93201	+	4.30986i	0.215745	+	0.156748i
$757$			18.8169i			0.683913i	0.939716	+	0.341956i	$0.111090\pi$
$757$			18.8169i			0.683913i	−0.939716	+	0.341956i	$0.888910\pi$
$758$	−8.19887	+	11.2848i	−0.297797	+	0.409882i
$759$	0.363778	−	1.11959i	0.0132043	−	0.0406386i
$760$	24.9174	−	14.0145i	0.903850	−	0.508360i
$761$	−0.844230	−	2.59827i	−0.0306033	−	0.0941873i	0.934588	−	0.355732i	$-0.115768\pi$
$761$	−0.844230	−	2.59827i	−0.0306033	−	0.0941873i	−0.965191	+	0.261544i	$0.915768\pi$
$762$	−41.7518	−	13.5660i	−1.51251	−	0.491444i
$763$	−46.2383	−	15.0237i	−1.67394	−	0.543895i
$764$	1.10200	+	3.39162i	0.0398691	+	0.122704i
$765$	0.831576	+	0.765877i	0.0300657	+	0.0276904i
$766$	−18.5840	+	57.1957i	−0.671467	+	2.06656i
$767$	−1.11551	+	1.53537i	−0.0402789	+	0.0554391i
$768$			16.8447i			0.607832i
$769$	4.13363	+	3.00326i	0.149062	+	0.108300i	0.659817	−	0.751426i	$-0.270634\pi$
$769$	4.13363	+	3.00326i	0.149062	+	0.108300i	−0.510754	+	0.859727i	$0.670634\pi$
$770$	7.61977	−	8.27341i	0.274597	−	0.298153i
$771$	−16.9599	+	12.3221i	−0.610797

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+(-1.46986 + 0.477587i) q^{2} +(-1.10052 - 1.51474i) q^{3} +(0.314369 - 0.228403i) q^{4} +(-2.19230 + 0.440256i) q^{5} +(2.34104 + 1.70086i) q^{6} -4.04029i q^{7} +(1.46385 - 2.01482i) q^{8} +(-0.156235 + 0.480841i) q^{9} +(3.01211 - 1.69413i) q^{10} +(0.248930 + 0.766128i) q^{11} +(-0.691941 - 0.224825i) q^{12} +(-0.183422 - 0.0595974i) q^{13} +(1.92959 + 5.93867i) q^{14} +(3.07955 + 2.83625i) q^{15} +(-1.42956 + 4.39975i) q^{16} +(-0.587785 + 0.809017i) q^{17} -0.781385i q^{18} +(-4.15318 - 3.01746i) q^{19} +(-0.588636 + 0.639130i) q^{20} +(-6.11999 + 4.44643i) q^{21} +(-0.731785 - 1.00722i) q^{22} +(0.742309 - 0.241191i) q^{23} -4.66293 q^{24} +(4.61235 - 1.93035i) q^{25} +0.298068 q^{26} +(-4.44176 + 1.44322i) q^{27} +(-0.922813 - 1.27014i) q^{28} +(-5.56276 + 4.04158i) q^{29} +(-5.88107 - 2.69814i) q^{30} +(4.10415 + 2.98184i) q^{31} -2.16885i q^{32} +(0.886531 - 1.22021i) q^{33} +(0.477587 - 1.46986i) q^{34} +(1.77876 + 8.85753i) q^{35} +(0.0607100 + 0.186846i) q^{36} +(-6.94342 - 2.25605i) q^{37} +(7.54571 + 2.45175i) q^{38} +(0.111585 + 0.343425i) q^{39} +(-2.32216 + 5.06155i) q^{40} +(-3.27121 + 10.0678i) q^{41} +(6.87198 - 9.45847i) q^{42} +0.147653i q^{43} +(0.253242 + 0.183991i) q^{44} +(0.130820 - 1.12293i) q^{45} +(-0.975901 + 0.709034i) q^{46} +(7.76309 + 10.6850i) q^{47} +(8.23774 - 2.67660i) q^{48} -9.32395 q^{49} +(-5.85760 + 5.04014i) q^{50} +1.87232 q^{51} +(-0.0712744 + 0.0231585i) q^{52} +(-1.46489 - 2.01625i) q^{53} +(5.83951 - 4.24265i) q^{54} +(-0.883022 - 1.56999i) q^{55} +(-8.14045 - 5.91439i) q^{56} +9.61178i q^{57} +(6.24627 - 8.59726i) q^{58} +(3.04084 - 9.35875i) q^{59} +(1.61592 + 0.188253i) q^{60} +(0.115763 + 0.356282i) q^{61} +(-7.45661 - 2.42280i) q^{62} +(1.94274 + 0.631234i) q^{63} +(-1.82331 - 5.61158i) q^{64} +(0.428354 + 0.0499026i) q^{65} +(-0.720324 + 2.21693i) q^{66} +(5.40626 - 7.44108i) q^{67} +0.388582i q^{68} +(-1.18227 - 0.858969i) q^{69} +(-6.84478 - 12.1698i) q^{70} +(0.509940 - 0.370493i) q^{71} +(0.740103 + 1.01866i) q^{72} +(-3.33920 + 1.08497i) q^{73} +11.2833 q^{74} +(-7.99997 - 4.86212i) q^{75} -1.99483 q^{76} +(3.09538 - 1.00575i) q^{77} +(-0.328030 - 0.451495i) q^{78} +(-7.86290 + 5.71273i) q^{79} +(1.19702 - 10.2749i) q^{80} +(8.30144 + 6.03135i) q^{81} -16.3605i q^{82} +(-4.90590 + 6.75239i) q^{83} +(-0.908360 + 2.79564i) q^{84} +(0.932426 - 2.03238i) q^{85} +(-0.0705170 - 0.217029i) q^{86} +(12.2439 + 3.97828i) q^{87} +(1.90801 + 0.619949i) q^{88} +(4.42157 + 13.6082i) q^{89} +(0.344010 + 1.71303i) q^{90} +(-0.240791 + 0.741078i) q^{91} +(0.178271 - 0.245368i) q^{92} -9.49829i q^{93} +(-16.5137 - 11.9979i) q^{94} +(10.4335 + 4.78672i) q^{95} +(-3.28525 + 2.38687i) q^{96} +(-2.18751 - 3.01084i) q^{97} +(13.7049 - 4.45300i) q^{98} -0.407277 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

Modular forms

Varieties

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