LMFDB - Embedded newform 483.2.i.h.415.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, degree $2$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 245x^16 - 416x^15 + 1707x^14 - 2021x^13 + 7135x^12 - 6640x^11 + 20315x^10 - 10565x^9 + 29358x^8 - 9009x^7 + 30661x^6 - 4026x^5 + 15786x^4 - 84x^3 + 5800x^2 + 152*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.7
Root			$-0.384545 - 0.666052i$ of defining polynomial
Character	$\chi$	$=$	483.415
Dual form			483.2.i.h.277.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.384545 - 0.666052i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.704250 + 1.21980i) q^{4} +(2.01355 - 3.48756i) q^{5} +0.769091 q^{6} +(2.63574 + 0.229917i) q^{7} +2.62145 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.54860 - 2.68225i) q^{10} +(-2.73557 - 4.73814i) q^{11} +(-0.704250 + 1.21980i) q^{12} -4.39956 q^{13} +(1.16670 - 1.66713i) q^{14} +4.02709 q^{15} +(-0.400435 + 0.693574i) q^{16} +(1.12483 + 1.94826i) q^{17} +(0.384545 + 0.666052i) q^{18} +(-1.78076 + 3.08437i) q^{19} +5.67216 q^{20} +(1.11876 + 2.39758i) q^{21} -4.20780 q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.31072 + 2.27024i) q^{24} +(-5.60873 - 9.71461i) q^{25} +(-1.69183 + 2.93033i) q^{26} -1.00000 q^{27} +(1.57577 + 3.37699i) q^{28} -4.70941 q^{29} +(1.54860 - 2.68225i) q^{30} +(5.27462 + 9.13592i) q^{31} +(2.92942 + 5.07390i) q^{32} +(2.73557 - 4.73814i) q^{33} +1.73019 q^{34} +(6.10904 - 8.72937i) q^{35} -1.40850 q^{36} +(1.96275 - 3.39958i) q^{37} +(1.36957 + 2.37216i) q^{38} +(-2.19978 - 3.81013i) q^{39} +(5.27840 - 9.14246i) q^{40} -3.97807 q^{41} +(2.02712 + 0.176827i) q^{42} +2.61087 q^{43} +(3.85304 - 6.67367i) q^{44} +(2.01355 + 3.48756i) q^{45} +(0.384545 + 0.666052i) q^{46} +(0.259175 - 0.448904i) q^{47} -0.800870 q^{48} +(6.89428 + 1.21200i) q^{49} -8.62724 q^{50} +(-1.12483 + 1.94826i) q^{51} +(-3.09839 - 5.36656i) q^{52} +(6.31816 + 10.9434i) q^{53} +(-0.384545 + 0.666052i) q^{54} -22.0328 q^{55} +(6.90945 + 0.602714i) q^{56} -3.56152 q^{57} +(-1.81098 + 3.13671i) q^{58} +(-0.421445 - 0.729964i) q^{59} +(2.83608 + 4.91223i) q^{60} +(-4.50466 + 7.80230i) q^{61} +8.11333 q^{62} +(-1.51698 + 2.16766i) q^{63} +2.90423 q^{64} +(-8.85871 + 15.3437i) q^{65} +(-2.10390 - 3.64406i) q^{66} +(0.699842 + 1.21216i) q^{67} +(-1.58432 + 2.74412i) q^{68} -1.00000 q^{69} +(-3.46501 - 7.42577i) q^{70} -7.10801 q^{71} +(-1.31072 + 2.27024i) q^{72} +(-2.66304 - 4.61252i) q^{73} +(-1.50953 - 2.61458i) q^{74} +(5.60873 - 9.71461i) q^{75} -5.01640 q^{76} +(-6.12087 - 13.1175i) q^{77} -3.38366 q^{78} +(6.72171 - 11.6423i) q^{79} +(1.61259 + 2.79309i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.52975 + 2.64960i) q^{82} +3.39713 q^{83} +(-2.13667 + 3.05315i) q^{84} +9.05955 q^{85} +(1.00400 - 1.73898i) q^{86} +(-2.35471 - 4.07847i) q^{87} +(-7.17114 - 12.4208i) q^{88} +(-6.50780 + 11.2718i) q^{89} +3.09720 q^{90} +(-11.5961 - 1.01153i) q^{91} -1.40850 q^{92} +(-5.27462 + 9.13592i) q^{93} +(-0.199329 - 0.345248i) q^{94} +(7.17128 + 12.4210i) q^{95} +(-2.92942 + 5.07390i) q^{96} -6.35615 q^{97} +(3.45842 - 4.12588i) q^{98} +5.47113 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) $ 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.384545	−	0.666052i	0.271915	−	0.470970i	−0.697437	−	0.716646i	$-0.745677\pi$
$2$	0.384545	−	0.666052i	0.271915	−	0.470970i	0.969352	+	0.245676i	$0.0790098\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.704250	+	1.21980i	0.352125	+	0.609898i
$5$	2.01355	−	3.48756i	0.900485	−	1.55969i	0.0736191	−	0.997286i	$-0.476545\pi$
$5$	2.01355	−	3.48756i	0.900485	−	1.55969i	0.826866	−	0.562399i	$-0.190122\pi$
$6$	0.769091			0.313980
$7$	2.63574	+	0.229917i	0.996217	+	0.0869003i
$7$	2.63574	+	0.229917i	0.996217	+	0.0869003i
$8$	2.62145			0.926821
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.54860	−	2.68225i	−0.489710	−	0.848203i
$11$	−2.73557	−	4.73814i	−0.824804	−	1.42860i	−0.902069	−	0.431592i	$-0.857952\pi$
$11$	−2.73557	−	4.73814i	−0.824804	−	1.42860i	0.0772644	−	0.997011i	$-0.475381\pi$
$12$	−0.704250	+	1.21980i	−0.203299	+	0.352125i
$13$	−4.39956			−1.22022			−0.610109	−	0.792318i	$-0.708874\pi$
$13$	−4.39956			−1.22022			−0.610109	+	0.792318i	$0.708874\pi$
$14$	1.16670	−	1.66713i	0.311813	−	0.445559i
$15$	4.02709			1.03979
$16$	−0.400435	+	0.693574i	−0.100109	+	0.173394i
$17$	1.12483	+	1.94826i	0.272810	+	0.472521i	0.969580	−	0.244773i	$-0.0787135\pi$
$17$	1.12483	+	1.94826i	0.272810	+	0.472521i	−0.696770	+	0.717295i	$0.745380\pi$
$18$	0.384545	+	0.666052i	0.0906382	+	0.156990i
$19$	−1.78076	+	3.08437i	−0.408534	+	0.707602i	−0.994726	−	0.102570i	$-0.967293\pi$
$19$	−1.78076	+	3.08437i	−0.408534	+	0.707602i	0.586191	+	0.810173i	$0.300627\pi$
$20$	5.67216			1.26833
$21$	1.11876	+	2.39758i	0.244133	+	0.523194i
$22$	−4.20780			−0.897105
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	1.31072	+	2.27024i	0.267550	+	0.463410i
$25$	−5.60873	−	9.71461i	−1.12175	−	1.94292i
$26$	−1.69183	+	2.93033i	−0.331795	+	0.574686i
$27$	−1.00000			−0.192450
$28$	1.57577	+	3.37699i	0.297792	+	0.638191i
$29$	−4.70941			−0.874516			−0.437258	−	0.899336i	$-0.644050\pi$
$29$	−4.70941			−0.874516			−0.437258	+	0.899336i	$0.644050\pi$
$30$	1.54860	−	2.68225i	0.282734	−	0.489710i
$31$	5.27462	+	9.13592i	0.947350	+	1.64086i	0.750975	+	0.660330i	$0.229584\pi$
$31$	5.27462	+	9.13592i	0.947350	+	1.64086i	0.196375	+	0.980529i	$0.437083\pi$
$32$	2.92942	+	5.07390i	0.517852	+	0.896947i
$33$	2.73557	−	4.73814i	0.476201	−	0.824804i
$34$	1.73019			0.296724
$35$	6.10904	−	8.72937i	1.03262	−	1.47553i
$36$	−1.40850			−0.234750
$37$	1.96275	−	3.39958i	0.322673	−	0.558887i	−0.658365	−	0.752699i	$-0.728752\pi$
$37$	1.96275	−	3.39958i	0.322673	−	0.558887i	0.981039	+	0.193812i	$0.0620851\pi$
$38$	1.36957	+	2.37216i	0.222173	+	0.384815i
$39$	−2.19978	−	3.81013i	−0.352246	−	0.610109i
$40$	5.27840	−	9.14246i	0.834588	−	1.44555i
$41$	−3.97807			−0.621270			−0.310635	−	0.950529i	$-0.600542\pi$
$41$	−3.97807			−0.621270			−0.310635	+	0.950529i	$0.600542\pi$
$42$	2.02712	+	0.176827i	0.312792	+	0.0272849i
$43$	2.61087			0.398155			0.199077	−	0.979984i	$-0.436206\pi$
$43$	2.61087			0.398155			0.199077	+	0.979984i	$0.436206\pi$
$44$	3.85304	−	6.67367i	0.580868	−	1.00609i
$45$	2.01355	+	3.48756i	0.300162	+	0.519895i
$46$	0.384545	+	0.666052i	0.0566981	+	0.0982040i
$47$	0.259175	−	0.448904i	0.0378046	−	0.0654794i	−0.846504	−	0.532382i	$-0.821297\pi$
$47$	0.259175	−	0.448904i	0.0378046	−	0.0654794i	0.884309	+	0.466903i	$0.154630\pi$
$48$	−0.800870			−0.115596
$49$	6.89428	+	1.21200i	0.984897	+	0.173143i
$50$	−8.62724			−1.22008
$51$	−1.12483	+	1.94826i	−0.157507	+	0.272810i
$52$	−3.09839	−	5.36656i	−0.429669	−	0.744208i
$53$	6.31816	+	10.9434i	0.867865	+	1.50319i	0.864174	+	0.503194i	$0.167842\pi$
$53$	6.31816	+	10.9434i	0.867865	+	1.50319i	0.00369181	+	0.999993i	$0.498825\pi$
$54$	−0.384545	+	0.666052i	−0.0523300	+	0.0906382i
$55$	−22.0328			−2.97090
$56$	6.90945	+	0.602714i	0.923315	+	0.0805410i
$57$	−3.56152			−0.471735
$58$	−1.81098	+	3.13671i	−0.237794	+	0.411871i
$59$	−0.421445	−	0.729964i	−0.0548675	−	0.0950332i	0.837287	−	0.546763i	$-0.184140\pi$
$59$	−0.421445	−	0.729964i	−0.0548675	−	0.0950332i	−0.892155	+	0.451730i	$0.850807\pi$
$60$	2.83608	+	4.91223i	0.366136	+	0.634166i
$61$	−4.50466	+	7.80230i	−0.576762	+	0.998982i	0.419085	+	0.907947i	$0.362351\pi$
$61$	−4.50466	+	7.80230i	−0.576762	+	0.998982i	−0.995848	+	0.0910347i	$0.970983\pi$
$62$	8.11333			1.03039
$63$	−1.51698	+	2.16766i	−0.191122	+	0.273100i
$64$	2.90423			0.363029
$65$	−8.85871	+	15.3437i	−1.09879	+	1.90316i
$66$	−2.10390	−	3.64406i	−0.258972	−	0.448553i
$67$	0.699842	+	1.21216i	0.0854993	+	0.148089i	0.905604	−	0.424125i	$-0.139418\pi$
$67$	0.699842	+	1.21216i	0.0854993	+	0.148089i	−0.820105	+	0.572214i	$0.806085\pi$
$68$	−1.58432	+	2.74412i	−0.192127	+	0.332773i
$69$	−1.00000			−0.120386
$70$	−3.46501	−	7.42577i	−0.414148	−	0.887550i
$71$	−7.10801			−0.843565			−0.421783	−	0.906697i	$-0.638596\pi$
$71$	−7.10801			−0.843565			−0.421783	+	0.906697i	$0.638596\pi$
$72$	−1.31072	+	2.27024i	−0.154470	+	0.267550i
$73$	−2.66304	−	4.61252i	−0.311685	−	0.539854i	0.667042	−	0.745020i	$-0.267560\pi$
$73$	−2.66304	−	4.61252i	−0.311685	−	0.539854i	−0.978727	+	0.205166i	$0.934227\pi$
$74$	−1.50953	−	2.61458i	−0.175479	−	0.303939i
$75$	5.60873	−	9.71461i	0.647640	−	1.12175i
$76$	−5.01640			−0.575420
$77$	−6.12087	−	13.1175i	−0.697538	−	1.49487i
$78$	−3.38366			−0.383124
$79$	6.72171	−	11.6423i	0.756251	−	1.30987i	−0.188498	−	0.982073i	$-0.560362\pi$
$79$	6.72171	−	11.6423i	0.756251	−	1.30987i	0.944750	−	0.327792i	$-0.106305\pi$
$80$	1.61259	+	2.79309i	0.180293	+	0.312277i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.52975	+	2.64960i	−0.168932	+	0.292600i
$83$	3.39713			0.372883			0.186442	−	0.982466i	$-0.440304\pi$
$83$	3.39713			0.372883			0.186442	+	0.982466i	$0.440304\pi$
$84$	−2.13667	+	3.05315i	−0.233130	+	0.333126i
$85$	9.05955			0.982646
$86$	1.00400	−	1.73898i	0.108264	−	0.187519i
$87$	−2.35471	−	4.07847i	−0.252451	−	0.437258i
$88$	−7.17114	−	12.4208i	−0.764446	−	1.32406i
$89$	−6.50780	+	11.2718i	−0.689826	+	1.19481i	0.282068	+	0.959394i	$0.408980\pi$
$89$	−6.50780	+	11.2718i	−0.689826	+	1.19481i	−0.971894	+	0.235419i	$0.924354\pi$
$90$	3.09720			0.326473
$91$	−11.5961	−	1.01153i	−1.21560	−	0.106037i
$92$	−1.40850			−0.146846
$93$	−5.27462	+	9.13592i	−0.546953	+	0.947350i
$94$	−0.199329	−	0.345248i	−0.0205592	−	0.0356096i
$95$	7.17128	+	12.4210i	0.735758	+	1.27437i
$96$	−2.92942	+	5.07390i	−0.298982	+	0.517852i
$97$	−6.35615			−0.645369			−0.322684	−	0.946507i	$-0.604585\pi$
$97$	−6.35615			−0.645369			−0.322684	+	0.946507i	$0.604585\pi$
$98$	3.45842	−	4.12588i	0.349353	−	0.416777i
$99$	5.47113			0.549870
$100$	7.89990	−	13.6830i	0.789990	−	1.36830i
$101$	−1.41794	−	2.45594i	−0.141090	−	0.244375i	0.786817	−	0.617186i	$-0.211727\pi$
$101$	−1.41794	−	2.45594i	−0.141090	−	0.244375i	−0.927907	+	0.372811i	$0.878394\pi$
$102$	0.865093	+	1.49838i	0.0856570	+	0.148362i
$103$	−5.29469	+	9.17067i	−0.521701	+	0.903613i	0.477980	+	0.878371i	$0.341369\pi$
$103$	−5.29469	+	9.17067i	−0.521701	+	0.903613i	−0.999681	+	0.0252423i	$0.991964\pi$
$104$	−11.5332			−1.13092
$105$	10.6144	+	0.925895i	1.03586	+	0.0903581i
$106$	9.71847			0.943941
$107$	9.42702	−	16.3281i	0.911344	−	1.57849i	0.0991766	−	0.995070i	$-0.468379\pi$
$107$	9.42702	−	16.3281i	0.911344	−	1.57849i	0.812167	−	0.583424i	$-0.198288\pi$
$108$	−0.704250	−	1.21980i	−0.0677665	−	0.117375i
$109$	−5.56722	−	9.64271i	−0.533243	−	0.923604i	−0.999246	−	0.0388209i	$-0.987640\pi$
$109$	−5.56722	−	9.64271i	−0.533243	−	0.923604i	0.466003	−	0.884783i	$-0.345694\pi$
$110$	−8.47259	+	14.6750i	−0.807830	+	1.39920i
$111$	3.92549			0.372591
$112$	−1.21491	+	1.73602i	−0.114798	+	0.164038i
$113$	−1.29979			−0.122274			−0.0611370	−	0.998129i	$-0.519473\pi$
$113$	−1.29979			−0.122274			−0.0611370	+	0.998129i	$0.519473\pi$
$114$	−1.36957	+	2.37216i	−0.128272	+	0.222173i
$115$	2.01355	+	3.48756i	0.187764	+	0.325217i
$116$	−3.31660	−	5.74453i	−0.307939	−	0.533366i
$117$	2.19978	−	3.81013i	0.203370	−	0.352246i
$118$	−0.648259			−0.0596771
$119$	2.51681	+	5.39371i	0.230716	+	0.494441i
$120$	10.5568			0.963699
$121$	−9.46665	+	16.3967i	−0.860604	+	1.49061i
$122$	3.46449	+	6.00067i	0.313660	+	0.543275i
$123$	−1.98904	−	3.44511i	−0.179345	−	0.310635i
$124$	−7.42931	+	12.8679i	−0.667171	+	1.15557i
$125$	−25.0383			−2.23949
$126$	0.860426	+	1.84395i	0.0766528	+	0.164273i
$127$	−0.0947076			−0.00840394			−0.00420197	−	0.999991i	$-0.501338\pi$
$127$	−0.0947076			−0.00840394			−0.00420197	+	0.999991i	$0.501338\pi$
$128$	−4.74202	+	8.21343i	−0.419140	+	0.725971i
$129$	1.30544	+	2.26108i	0.114937	+	0.199077i
$130$	6.81315	+	11.8007i	0.597553	+	1.03499i
$131$	6.86302	−	11.8871i	0.599625	−	1.03858i	−0.393251	−	0.919431i	$-0.628650\pi$
$131$	6.86302	−	11.8871i	0.599625	−	1.03858i	0.992876	−	0.119150i	$-0.0380169\pi$
$132$	7.70609			0.670729
$133$	−5.40277	+	7.72017i	−0.468480	+	0.669424i
$134$	1.07648			0.0929941
$135$	−2.01355	+	3.48756i	−0.173298	+	0.300162i
$136$	2.94867	+	5.10724i	0.252846	+	0.437943i
$137$	0.515909	+	0.893580i	0.0440771	+	0.0763437i	0.887222	−	0.461342i	$-0.152632\pi$
$137$	0.515909	+	0.893580i	0.0440771	+	0.0763437i	−0.843145	+	0.537686i	$0.819299\pi$
$138$	−0.384545	+	0.666052i	−0.0327347	+	0.0566981i
$139$	0.281873			0.0239081			0.0119541	−	0.999929i	$-0.496195\pi$
$139$	0.281873			0.0239081			0.0119541	+	0.999929i	$0.496195\pi$
$140$	14.9503	+	1.30412i	1.26353	+	0.110218i
$141$	0.518350			0.0436530
$142$	−2.73335	+	4.73430i	−0.229378	+	0.397294i
$143$	12.0353	+	20.8457i	1.00644	+	1.74321i
$144$	−0.400435	−	0.693574i	−0.0333696	−	0.0577978i
$145$	−9.48262	+	16.4244i	−0.787489	+	1.36397i
$146$	−4.09623			−0.339007
$147$	2.39751	+	6.57662i	0.197744	+	0.542430i
$148$	5.52905			0.454485
$149$	2.85125	−	4.93851i	0.233584	−	0.404579i	−0.725277	−	0.688458i	$-0.758288\pi$
$149$	2.85125	−	4.93851i	0.233584	−	0.404579i	0.958860	+	0.283879i	$0.0916214\pi$
$150$	−4.31362	−	7.47141i	−0.352206	−	0.610038i
$151$	−1.43814	−	2.49093i	−0.117034	−	0.202709i	0.801557	−	0.597919i	$-0.204005\pi$
$151$	−1.43814	−	2.49093i	−0.117034	−	0.202709i	−0.918591	+	0.395209i	$0.870672\pi$
$152$	−4.66816	+	8.08550i	−0.378638	+	0.655821i
$153$	−2.24965			−0.181874
$154$	−11.0907	−	0.967442i	−0.893712	−	0.0779587i
$155$	42.4828			3.41230
$156$	3.09839	−	5.36656i	0.248069	−	0.429669i
$157$	−8.37042	−	14.4980i	−0.668032	−	1.15707i	−0.978454	−	0.206466i	$-0.933804\pi$
$157$	−8.37042	−	14.4980i	−0.668032	−	1.15707i	0.310422	−	0.950599i	$-0.399530\pi$
$158$	−5.16960	−	8.95402i	−0.411272	−	0.712343i
$159$	−6.31816	+	10.9434i	−0.501062	+	0.867865i
$160$	23.5940			1.86527
$161$	−1.51698	+	2.16766i	−0.119555	+	0.170836i
$162$	−0.769091			−0.0604255
$163$	0.343687	−	0.595284i	0.0269197	−	0.0466262i	−0.852252	−	0.523132i	$-0.824764\pi$
$163$	0.343687	−	0.595284i	0.0269197	−	0.0466262i	0.879171	+	0.476506i	$0.158097\pi$
$164$	−2.80156	−	4.85244i	−0.218765	−	0.378912i
$165$	−11.0164	−	19.0809i	−0.857624	−	1.48545i
$166$	1.30635	−	2.26267i	0.101392	−	0.175617i
$167$	−12.4022			−0.959714			−0.479857	−	0.877347i	$-0.659312\pi$
$167$	−12.4022			−0.959714			−0.479857	+	0.877347i	$0.659312\pi$
$168$	2.93276	+	6.28512i	0.226267	+	0.484908i
$169$	6.35609			0.488930
$170$	3.48381	−	6.03413i	0.267196	−	0.462797i
$171$	−1.78076	−	3.08437i	−0.136178	−	0.235867i
$172$	1.83871	+	3.18473i	0.140200	+	0.242834i
$173$	1.60350	−	2.77735i	0.121912	−	0.211158i	−0.798610	−	0.601850i	$-0.794431\pi$
$173$	1.60350	−	2.77735i	0.121912	−	0.211158i	0.920522	+	0.390691i	$0.127764\pi$
$174$	−3.62197			−0.274581
$175$	−12.5496	−	26.8947i	−0.948662	−	2.03305i
$176$	4.38167			0.330281
$177$	0.421445	−	0.729964i	0.0316777	−	0.0548675i
$178$	5.00509	+	8.66907i	0.375147	+	0.649774i
$179$	−5.57358	−	9.65373i	−0.416589	−	0.721553i	0.579005	−	0.815324i	$-0.303441\pi$
$179$	−5.57358	−	9.65373i	−0.416589	−	0.721553i	−0.995594	+	0.0937708i	$0.970108\pi$
$180$	−2.83608	+	4.91223i	−0.211389	+	0.366136i
$181$	18.5663			1.38002			0.690011	−	0.723799i	$-0.257606\pi$
$181$	18.5663			1.38002			0.690011	+	0.723799i	$0.257606\pi$
$182$	−5.13296	+	7.33462i	−0.380480	+	0.543678i
$183$	−9.00931			−0.665988
$184$	−1.31072	+	2.27024i	−0.0966277	+	0.167364i
$185$	−7.90416	−	13.6904i	−0.581125	−	1.00654i
$186$	4.05666	+	7.02635i	0.297449	+	0.515197i
$187$	6.15407	−	10.6592i	0.450030	−	0.779475i
$188$	0.730096			0.0532477
$189$	−2.63574	−	0.229917i	−0.191722	−	0.0167240i
$190$	11.0307			0.800253
$191$	11.4693	−	19.8655i	0.829892	−	1.43742i	−0.0682304	−	0.997670i	$-0.521735\pi$
$191$	11.4693	−	19.8655i	0.829892	−	1.43742i	0.898122	−	0.439746i	$-0.144931\pi$
$192$	1.45212	+	2.51514i	0.104797	+	0.181514i
$193$	5.06476	+	8.77242i	0.364569	+	0.631453i	0.988707	−	0.149862i	$-0.0478829\pi$
$193$	5.06476	+	8.77242i	0.364569	+	0.631453i	−0.624138	+	0.781314i	$0.714550\pi$
$194$	−2.44423	+	4.23352i	−0.175485	+	0.303949i
$195$	−17.7174			−1.26877
$196$	3.37690	+	9.26317i	0.241207	+	0.661655i
$197$	−4.51568			−0.321729			−0.160864	−	0.986977i	$-0.551428\pi$
$197$	−4.51568			−0.321729			−0.160864	+	0.986977i	$0.551428\pi$
$198$	2.10390	−	3.64406i	0.149518	−	0.258972i
$199$	−10.4038	−	18.0199i	−0.737506	−	1.27740i	−0.953615	−	0.301029i	$-0.902670\pi$
$199$	−10.4038	−	18.0199i	−0.737506	−	1.27740i	0.216109	−	0.976369i	$-0.430663\pi$
$200$	−14.7030	−	25.4663i	−1.03966	−	1.80074i
$201$	−0.699842	+	1.21216i	−0.0493631	+	0.0854993i
$202$	−2.18104			−0.153458
$203$	−12.4128	−	1.08277i	−0.871208	−	0.0759957i
$204$	−3.16863			−0.221849
$205$	−8.01003	+	13.8738i	−0.559445	+	0.968986i
$206$	4.07209	+	7.05308i	0.283716	+	0.491411i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	1.76174	−	3.05142i	0.122154	−	0.211578i
$209$	19.4856			1.34784
$210$	4.69840	−	6.71368i	0.324221	−	0.463288i
$211$	26.2315			1.80585			0.902925	−	0.429799i	$-0.141416\pi$
$211$	26.2315			1.80585			0.902925	+	0.429799i	$0.141416\pi$
$212$	−8.89912	+	15.4137i	−0.611194	+	1.05862i
$213$	−3.55400	−	6.15572i	−0.243516	−	0.421783i
$214$	−7.25023	−	12.5578i	−0.495615	−	0.858431i
$215$	5.25711	−	9.10559i	0.358532	−	0.620996i
$216$	−2.62145			−0.178367
$217$	11.8021	+	25.2926i	0.801176	+	1.71698i
$218$	−8.56339			−0.579986
$219$	2.66304	−	4.61252i	0.179951	−	0.311685i
$220$	−15.5166	−	26.8755i	−1.04613	−	1.81194i
$221$	−4.94873	−	8.57146i	−0.332888	−	0.576579i
$222$	1.50953	−	2.61458i	0.101313	−	0.175479i
$223$	−1.20377			−0.0806102			−0.0403051	−	0.999187i	$-0.512833\pi$
$223$	−1.20377			−0.0806102			−0.0403051	+	0.999187i	$0.512833\pi$
$224$	6.55461	+	14.0470i	0.437949	+	0.938555i
$225$	11.2175			0.747831
$226$	−0.499829	+	0.865729i	−0.0332481	+	0.0575874i
$227$	−7.12657	−	12.3436i	−0.473007	−	0.819273i	0.526515	−	0.850166i	$-0.323498\pi$
$227$	−7.12657	−	12.3436i	−0.473007	−	0.819273i	−0.999523	+	0.0308929i	$0.990165\pi$
$228$	−2.50820	−	4.34433i	−0.166110	−	0.287710i
$229$	−6.17854	+	10.7015i	−0.408289	+	0.707178i	−0.994698	−	0.102837i	$-0.967208\pi$
$229$	−6.17854	+	10.7015i	−0.408289	+	0.707178i	0.586409	+	0.810015i	$0.300541\pi$
$230$	3.09720			0.204223
$231$	8.29963	−	11.8596i	0.546075	−	0.780302i
$232$	−12.3455			−0.810520
$233$	−5.99138	+	10.3774i	−0.392508	+	0.679844i	−0.992780	−	0.119952i	$-0.961726\pi$
$233$	−5.99138	+	10.3774i	−0.392508	+	0.679844i	0.600271	+	0.799796i	$0.295059\pi$
$234$	−1.69183	−	2.93033i	−0.110598	−	0.191562i
$235$	−1.04372	−	1.80778i	−0.0680849	−	0.117926i
$236$	0.593605	−	1.02815i	0.0386404	−	0.0669271i
$237$	13.4434			0.873244
$238$	4.56032	+	0.397798i	0.295602	+	0.0257854i
$239$	6.53934			0.422995			0.211497	−	0.977379i	$-0.432166\pi$
$239$	6.53934			0.422995			0.211497	+	0.977379i	$0.432166\pi$
$240$	−1.61259	+	2.79309i	−0.104092	+	0.180293i
$241$	−0.250032	−	0.433069i	−0.0161060	−	0.0278964i	0.857860	−	0.513883i	$-0.171794\pi$
$241$	−0.250032	−	0.433069i	−0.0161060	−	0.0278964i	−0.873966	+	0.485987i	$0.838460\pi$
$242$	7.28071	+	12.6106i	0.468022	+	0.810638i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−12.6896			−0.812369
$245$	18.1089	−	21.6038i	1.15693	−	1.38022i
$246$	−3.05950			−0.195066
$247$	7.83455	−	13.5698i	0.498501	−	0.863428i
$248$	13.8271	+	23.9493i	0.878024	+	1.52078i
$249$	1.69857	+	2.94200i	0.107642	+	0.186442i
$250$	−9.62835	+	16.6768i	−0.608951	+	1.05473i
$251$	5.10076			0.321957			0.160978	−	0.986958i	$-0.448535\pi$
$251$	5.10076			0.321957			0.160978	+	0.986958i	$0.448535\pi$
$252$	−3.71244	−	0.323837i	−0.233862	−	0.0203998i
$253$	5.47113			0.343967
$254$	−0.0364194	+	0.0630802i	−0.00228515	+	0.00395800i
$255$	4.52978	+	7.84580i	0.283666	+	0.491323i
$256$	6.55128	+	11.3471i	0.409455	+	0.709197i
$257$	4.42971	−	7.67248i	0.276318	−	0.478596i	−0.694149	−	0.719831i	$-0.744219\pi$
$257$	4.42971	−	7.67248i	0.276318	−	0.478596i	0.970467	+	0.241235i	$0.0775525\pi$
$258$	2.00800			0.125013
$259$	5.95491	−	8.50914i	0.370020	−	0.528732i
$260$	−24.9550			−1.54764
$261$	2.35471	−	4.07847i	0.145753	−	0.252451i
$262$	−5.27829	−	9.14226i	−0.326094	−	0.564811i
$263$	−13.0804	−	22.6559i	−0.806573	−	1.39703i	−0.915224	−	0.402945i	$-0.867987\pi$
$263$	−13.0804	−	22.6559i	−0.806573	−	1.39703i	0.108651	−	0.994080i	$-0.465347\pi$
$264$	7.17114	−	12.4208i	0.441353	−	0.764446i
$265$	50.8876			3.12600
$266$	3.06442	+	6.56728i	0.187892	+	0.402666i
$267$	−13.0156			−0.796542
$268$	−0.985728	+	1.70733i	−0.0602129	+	0.104292i
$269$	7.87844	+	13.6459i	0.480357	+	0.832002i	0.999746	−	0.0225354i	$-0.00717385\pi$
$269$	7.87844	+	13.6459i	0.480357	+	0.832002i	−0.519389	+	0.854538i	$0.673841\pi$
$270$	1.54860	+	2.68225i	0.0942447	+	0.163237i
$271$	2.97558	−	5.15386i	0.180754	−	0.313075i	−0.761384	−	0.648302i	$-0.775480\pi$
$271$	2.97558	−	5.15386i	0.180754	−	0.313075i	0.942137	+	0.335227i	$0.108813\pi$
$272$	−1.80168			−0.109243
$273$	−4.92204	−	10.5483i	−0.297895	−	0.638411i
$274$	0.793561			0.0479408
$275$	−30.6861	+	53.1499i	−1.85044	+	3.20506i
$276$	−0.704250	−	1.21980i	−0.0423909	−	0.0734231i
$277$	−7.61827	−	13.1952i	−0.457738	−	0.792825i	0.541103	−	0.840956i	$-0.318007\pi$
$277$	−7.61827	−	13.1952i	−0.457738	−	0.792825i	−0.998841	+	0.0481311i	$0.984673\pi$
$278$	0.108393	−	0.187742i	0.00650097	−	0.0112600i
$279$	−10.5492			−0.631567
$280$	16.0145	−	22.8836i	0.957050	−	1.36755i
$281$	1.78254			0.106338			0.0531688	−	0.998586i	$-0.483068\pi$
$281$	1.78254			0.106338			0.0531688	+	0.998586i	$0.483068\pi$
$282$	0.199329	−	0.345248i	0.0118699	−	0.0205592i
$283$	9.99956	+	17.3197i	0.594412	+	1.02955i	0.993630	+	0.112696i	$0.0359485\pi$
$283$	9.99956	+	17.3197i	0.594412	+	1.02955i	−0.399218	+	0.916856i	$0.630718\pi$
$284$	−5.00581	−	8.67032i	−0.297040	−	0.514489i
$285$	−7.17128	+	12.4210i	−0.424790	+	0.735758i
$286$	18.5124			1.09466
$287$	−10.4852	−	0.914624i	−0.618920	−	0.0539886i
$288$	−5.85883			−0.345235
$289$	5.96953	−	10.3395i	0.351149	−	0.608208i
$290$	7.29299	+	12.6318i	0.428259	+	0.741767i
$291$	−3.17807	−	5.50458i	−0.186302	−	0.322684i
$292$	3.75089	−	6.49673i	0.219504	−	0.380192i
$293$	−17.4319			−1.01838			−0.509191	−	0.860653i	$-0.670055\pi$
$293$	−17.4319			−1.01838			−0.509191	+	0.860653i	$0.670055\pi$
$294$	5.30232	+	0.932139i	0.309238	+	0.0543635i
$295$	−3.39439			−0.197629
$296$	5.14523	−	8.91180i	0.299060	−	0.517988i
$297$	2.73557	+	4.73814i	0.158734	+	0.274935i
$298$	−2.19287	−	3.79816i	−0.127030	−	0.220022i
$299$	2.19978	−	3.81013i	0.127216	−	0.220345i
$300$	15.7998			0.912201
$301$	6.88159	+	0.600283i	0.396648	+	0.0345997i
$302$	−2.21212			−0.127293
$303$	1.41794	−	2.45594i	0.0814582	−	0.141090i
$304$	−1.42616	−	2.47018i	−0.0817958	−	0.141674i
$305$	18.1407	+	31.4206i	1.03873	+	1.79914i
$306$	−0.865093	+	1.49838i	−0.0494541	+	0.0856570i
$307$	−22.1407			−1.26363			−0.631817	−	0.775117i	$-0.717691\pi$
$307$	−22.1407			−1.26363			−0.631817	+	0.775117i	$0.717691\pi$
$308$	11.6900	−	16.7042i	0.666101	−	0.951810i
$309$	−10.5894			−0.602409
$310$	16.3366	−	28.2957i	0.927854	−	1.60709i
$311$	3.44517	+	5.96722i	0.195358	+	0.338370i	0.947018	−	0.321181i	$-0.104080\pi$
$311$	3.44517	+	5.96722i	0.195358	+	0.338370i	−0.751660	+	0.659551i	$0.770746\pi$
$312$	−5.76660	−	9.98804i	−0.326469	−	0.565461i
$313$	−6.78694	+	11.7553i	−0.383620	+	0.664450i	−0.991577	−	0.129520i	$-0.958656\pi$
$313$	−6.78694	+	11.7553i	−0.383620	+	0.664450i	0.607956	+	0.793970i	$0.291990\pi$
$314$	−12.8752			−0.726591
$315$	4.50534	+	9.65527i	0.253847	+	0.544013i
$316$	18.9350			1.06518
$317$	12.3294	−	21.3551i	0.692486	−	1.19942i	−0.278534	−	0.960426i	$-0.589849\pi$
$317$	12.3294	−	21.3551i	0.692486	−	1.19942i	0.971021	−	0.238995i	$-0.0768181\pi$
$318$	4.85923	+	8.41644i	0.272492	+	0.471971i
$319$	12.8829	+	22.3139i	0.721305	+	1.24934i
$320$	5.84780	−	10.1287i	0.326902	−	0.566211i
$321$	18.8540			1.05233
$322$	0.860426	+	1.84395i	0.0479497	+	0.102760i
$323$	−8.01218			−0.445810
$324$	0.704250	−	1.21980i	0.0391250	−	0.0677665i
$325$	24.6759	+	42.7400i	1.36877	+	2.37079i
$326$	−0.264327	−	0.457827i	−0.0146397	−	0.0253567i
$327$	5.56722	−	9.64271i	0.307868	−	0.533243i
$328$	−10.4283			−0.575806
$329$	0.786329	−	1.12361i	0.0433517	−	0.0619465i
$330$	−16.9452			−0.932802
$331$	−11.4838	+	19.8905i	−0.631207	+	1.09328i	0.356099	+	0.934448i	$0.384107\pi$
$331$	−11.4838	+	19.8905i	−0.631207	+	1.09328i	−0.987305	+	0.158834i	$0.949227\pi$
$332$	2.39243	+	4.14381i	0.131302	+	0.227421i
$333$	1.96275	+	3.39958i	0.107558	+	0.186296i
$334$	−4.76922	+	8.26054i	−0.260960	+	0.451997i
$335$	5.63666			0.307963
$336$	−2.11089	−	0.184133i	−0.115158	−	0.0100453i
$337$	−19.9238			−1.08532			−0.542659	−	0.839953i	$-0.682582\pi$
$337$	−19.9238			−1.08532			−0.542659	+	0.839953i	$0.682582\pi$
$338$	2.44420	−	4.23349i	0.132947	−	0.230271i
$339$	−0.649896	−	1.12565i	−0.0352975	−	0.0611370i
$340$	6.38019	+	11.0508i	0.346014	+	0.599314i
$341$	28.8582	−	49.9838i	1.56276	−	2.70678i
$342$	−2.73913			−0.148115
$343$	17.8929	+	4.77963i	0.966125	+	0.258076i
$344$	6.84426			0.369018
$345$	−2.01355	+	3.48756i	−0.108406	+	0.187764i
$346$	−1.23324	−	2.13603i	−0.0662994	−	0.114834i
$347$	−6.31573	−	10.9392i	−0.339046	−	0.587246i	0.645207	−	0.764008i	$-0.276771\pi$
$347$	−6.31573	−	10.9392i	−0.339046	−	0.587246i	−0.984254	+	0.176762i	$0.943438\pi$
$348$	3.31660	−	5.74453i	0.177789	−	0.307939i
$349$	14.9697			0.801308			0.400654	−	0.916229i	$-0.368783\pi$
$349$	14.9697			0.801308			0.400654	+	0.916229i	$0.368783\pi$
$350$	−22.7392	−	1.98355i	−1.21546	−	0.106025i
$351$	4.39956			0.234831
$352$	16.0272	−	27.7600i	0.854254	−	1.47961i
$353$	−1.36603	−	2.36603i	−0.0727064	−	0.125931i	0.827380	−	0.561642i	$-0.189830\pi$
$353$	−1.36603	−	2.36603i	−0.0727064	−	0.125931i	−0.900087	+	0.435711i	$0.856497\pi$
$354$	−0.324129	−	0.561409i	−0.0172273	−	0.0298385i
$355$	−14.3123	+	24.7896i	−0.759618	+	1.31570i
$356$	−18.3325			−0.971619
$357$	−3.41269	+	4.87648i	−0.180619	+	0.258091i
$358$	−8.57318			−0.453107
$359$	−8.33886	+	14.4433i	−0.440108	+	0.762290i	−0.997697	−	0.0678274i	$-0.978393\pi$
$359$	−8.33886	+	14.4433i	−0.440108	+	0.762290i	0.557589	+	0.830117i	$0.311727\pi$
$360$	5.27840	+	9.14246i	0.278196	+	0.481850i
$361$	3.15779	+	5.46945i	0.166199	+	0.287866i
$362$	7.13959	−	12.3661i	0.375248	−	0.649949i
$363$	−18.9333			−0.993740
$364$	−6.93269	−	14.8572i	−0.363372	−	0.778731i
$365$	−21.4486			−1.12267
$366$	−3.46449	+	6.00067i	−0.181092	+	0.313660i
$367$	14.0388	+	24.3158i	0.732817	+	1.26928i	0.955674	+	0.294425i	$0.0951283\pi$
$367$	14.0388	+	24.3158i	0.732817	+	1.26928i	−0.222857	+	0.974851i	$0.571538\pi$
$368$	−0.400435	−	0.693574i	−0.0208741	−	0.0361551i
$369$	1.98904	−	3.44511i	0.103545	−	0.179345i
$370$	−12.1580			−0.632066
$371$	14.1370	+	30.2965i	0.733955	+	1.57292i
$372$	−14.8586			−0.770383
$373$	−11.1699	+	19.3468i	−0.578356	+	1.00174i	0.417312	+	0.908763i	$0.362972\pi$
$373$	−11.1699	+	19.3468i	−0.578356	+	1.00174i	−0.995668	+	0.0929784i	$0.970361\pi$
$374$	−4.73304	−	8.19786i	−0.244740	−	0.423901i
$375$	−12.5191	−	21.6838i	−0.646486	−	1.11975i
$376$	0.679413	−	1.17678i	0.0350381	−	0.0606877i
$377$	20.7193			1.06710
$378$	−1.16670	+	1.66713i	−0.0600085	+	0.0857478i
$379$	27.7949			1.42773			0.713864	−	0.700284i	$-0.246943\pi$
$379$	27.7949			1.42773			0.713864	+	0.700284i	$0.246943\pi$
$380$	−10.1007	+	17.4950i	−0.518157	+	0.897475i
$381$	−0.0473538	−	0.0820192i	−0.00242601	−	0.00420197i
$382$	−8.82096	−	15.2783i	−0.451319	−	0.781708i
$383$	−3.29578	+	5.70845i	−0.168406	+	0.291688i	−0.937860	−	0.347015i	$-0.887195\pi$
$383$	−3.29578	+	5.70845i	−0.168406	+	0.291688i	0.769453	+	0.638703i	$0.220529\pi$
$384$	−9.48405			−0.483981
$385$	−58.0727	−	5.06569i	−2.95966	−	0.258172i
$386$	7.79052			0.396527
$387$	−1.30544	+	2.26108i	−0.0663591	+	0.114937i
$388$	−4.47632	−	7.75321i	−0.227250	−	0.393609i
$389$	−4.49456	−	7.78481i	−0.227883	−	0.394706i	0.729297	−	0.684197i	$-0.239847\pi$
$389$	−4.49456	−	7.78481i	−0.227883	−	0.394706i	−0.957181	+	0.289491i	$0.906514\pi$
$390$	−6.81315	+	11.8007i	−0.344997	+	0.597553i
$391$	−2.24965			−0.113770
$392$	18.0730	+	3.17720i	0.912823	+	0.160473i
$393$	13.7260			0.692387
$394$	−1.73648	+	3.00767i	−0.0874827	+	0.151524i
$395$	−27.0689	−	46.8848i	−1.36199	−	2.35903i
$396$	3.85304	+	6.67367i	0.193623	+	0.335364i
$397$	1.27586	−	2.20985i	0.0640334	−	0.110909i	−0.832231	−	0.554428i	$-0.812937\pi$
$397$	1.27586	−	2.20985i	0.0640334	−	0.110909i	0.896265	+	0.443519i	$0.146270\pi$
$398$	−16.0029			−0.802155
$399$	−9.38725	−	0.818852i	−0.469950	−	0.0409939i
$400$	8.98373			0.449187
$401$	−18.6811	+	32.3567i	−0.932892	+	1.61582i	−0.154540	+	0.987986i	$0.549390\pi$
$401$	−18.6811	+	32.3567i	−0.932892	+	1.61582i	−0.778351	+	0.627829i	$0.783944\pi$
$402$	0.538242	+	0.932263i	0.0268451	+	0.0464970i
$403$	−23.2060	−	40.1940i	−1.15597	−	2.00220i
$404$	1.99716	−	3.45918i	0.0993625	−	0.172101i
$405$	−4.02709			−0.200108
$406$	−5.49447	+	7.85120i	−0.272686	+	0.389648i
$407$	−21.4769			−1.06457
$408$	−2.94867	+	5.10724i	−0.145981	+	0.252846i
$409$	5.38652	+	9.32973i	0.266346	+	0.461326i	0.967916	−	0.251276i	$-0.0808501\pi$
$409$	5.38652	+	9.32973i	0.266346	+	0.461326i	−0.701569	+	0.712601i	$0.747517\pi$
$410$	6.16044	+	10.6702i	0.304242	+	0.526963i
$411$	−0.515909	+	0.893580i	−0.0254479	+	0.0440771i
$412$	−14.9151			−0.734816
$413$	−0.942990	−	2.02089i	−0.0464015	−	0.0994417i
$414$	−0.769091			−0.0377987
$415$	6.84028	−	11.8477i	0.335776	−	0.581581i
$416$	−12.8881	−	22.3229i	−0.631893	−	1.09447i
$417$	0.140936	+	0.244109i	0.00690168	+	0.0119541i
$418$	7.49308	−	12.9784i	0.366498	−	0.634794i
$419$	19.8186			0.968200			0.484100	−	0.875013i	$-0.339147\pi$
$419$	19.8186			0.968200			0.484100	+	0.875013i	$0.339147\pi$
$420$	6.34577	+	13.5994i	0.309642	+	0.663585i
$421$	3.68979			0.179830			0.0899148	−	0.995949i	$-0.471341\pi$
$421$	3.68979			0.179830			0.0899148	+	0.995949i	$0.471341\pi$
$422$	10.0872	−	17.4715i	0.491037	−	0.850501i
$423$	0.259175	+	0.448904i	0.0126015	+	0.0218265i
$424$	16.5627	+	28.6874i	0.804356	+	1.39318i
$425$	12.6177	−	21.8545i	0.612048	−	1.06010i
$426$	−5.46670			−0.264863
$427$	−13.6670	+	19.5291i	−0.661392	+	0.945082i
$428$	26.5559			1.28363
$429$	−12.0353	+	20.8457i	−0.581069	+	1.00644i
$430$	−4.04320	−	7.00302i	−0.194980	−	0.337716i
$431$	−4.59503	−	7.95882i	−0.221335	−	0.383363i	0.733879	−	0.679280i	$-0.237708\pi$
$431$	−4.59503	−	7.95882i	−0.221335	−	0.383363i	−0.955213	+	0.295918i	$0.904375\pi$
$432$	0.400435	−	0.693574i	0.0192659	−	0.0333696i
$433$	33.6161			1.61549			0.807743	−	0.589535i	$-0.200689\pi$
$433$	33.6161			1.61549			0.807743	+	0.589535i	$0.200689\pi$
$434$	21.3846	+	1.86539i	1.02650	+	0.0895415i
$435$	−18.9652			−0.909313
$436$	7.84143	−	13.5818i	0.375536	−	0.650448i
$437$	−1.78076	−	3.08437i	−0.0851853	−	0.147545i
$438$	−2.04812	−	3.54744i	−0.0978628	−	0.169503i
$439$	1.15356	−	1.99803i	0.0550565	−	0.0953606i	−0.837184	−	0.546922i	$-0.815799\pi$
$439$	1.15356	−	1.99803i	0.0550565	−	0.0953606i	0.892240	+	0.451561i	$0.149133\pi$
$440$	−57.7576			−2.75349
$441$	−4.49676	+	5.36462i	−0.214132	+	0.255458i
$442$	−7.61205			−0.362068
$443$	5.69780	−	9.86889i	0.270711	−	0.468885i	−0.698333	−	0.715773i	$-0.746075\pi$
$443$	5.69780	−	9.86889i	0.270711	−	0.468885i	0.969044	+	0.246888i	$0.0794079\pi$
$444$	2.76453	+	4.78830i	0.131199	+	0.227243i
$445$	26.2075	+	45.3928i	1.24236	+	2.15182i
$446$	−0.462903	+	0.801771i	−0.0219191	+	0.0379650i
$447$	5.70250			0.269719
$448$	7.65481	+	0.667731i	0.361656	+	0.0315473i
$449$	3.16307			0.149275			0.0746373	−	0.997211i	$-0.476220\pi$
$449$	3.16307			0.149275			0.0746373	+	0.997211i	$0.476220\pi$
$450$	4.31362	−	7.47141i	0.203346	−	0.352206i
$451$	10.8823	+	18.8487i	0.512426	+	0.887549i
$452$	−0.915378	−	1.58548i	−0.0430557	−	0.0745747i
$453$	1.43814	−	2.49093i	0.0675698	−	0.117034i
$454$	−10.9620			−0.514470
$455$	−26.8770	+	38.4054i	−1.26002	+	1.80047i
$456$	−9.33633			−0.437214
$457$	−5.45681	+	9.45147i	−0.255259	+	0.442121i	−0.964966	−	0.262376i	$-0.915494\pi$
$457$	−5.45681	+	9.45147i	−0.255259	+	0.442121i	0.709707	+	0.704497i	$0.248827\pi$
$458$	4.75185	+	8.23045i	0.222040	+	0.384584i
$459$	−1.12483	−	1.94826i	−0.0525024	−	0.0909368i
$460$	−2.83608	+	4.91223i	−0.132233	+	0.229034i
$461$	34.5807			1.61058			0.805291	−	0.592880i	$-0.202009\pi$
$461$	34.5807			1.61058			0.805291	+	0.592880i	$0.202009\pi$
$462$	−4.70751	−	10.0885i	−0.219013	−	0.469361i
$463$	−1.07364			−0.0498961			−0.0249480	−	0.999689i	$-0.507942\pi$
$463$	−1.07364			−0.0498961			−0.0249480	+	0.999689i	$0.507942\pi$
$464$	1.88581	−	3.26633i	0.0875468	−	0.151635i
$465$	21.2414	+	36.7912i	0.985046	+	1.70615i
$466$	4.60791	+	7.98114i	0.213457	+	0.369719i
$467$	6.74418	−	11.6813i	0.312083	−	0.540544i	−0.666730	−	0.745299i	$-0.732307\pi$
$467$	6.74418	−	11.6813i	0.312083	−	0.540544i	0.978813	+	0.204755i	$0.0656399\pi$
$468$	6.19677			0.286446
$469$	1.56591	+	3.35585i	0.0723069	+	0.154959i
$470$	−1.60543			−0.0740531
$471$	8.37042	−	14.4980i	0.385688	−	0.668032i
$472$	−1.10479	−	1.91356i	−0.0508523	−	0.0880788i
$473$	−7.14222	−	12.3707i	−0.328400	−	0.568805i
$474$	5.16960	−	8.95402i	0.237448	−	0.411272i
$475$	39.9512			1.83309
$476$	−4.80677	+	6.86852i	−0.220318	+	0.314818i
$477$	−12.6363			−0.578577
$478$	2.51467	−	4.35554i	0.115018	−	0.199218i
$479$	3.15470	+	5.46409i	0.144142	+	0.249661i	0.929052	−	0.369948i	$-0.120625\pi$
$479$	3.15470	+	5.46409i	0.144142	+	0.249661i	−0.784911	+	0.619609i	$0.787291\pi$
$480$	11.7970	+	20.4330i	0.538458	+	0.932637i
$481$	−8.63521	+	14.9566i	−0.393732	+	0.681963i
$482$	−0.384595			−0.0175178
$483$	−2.63574	−	0.229917i	−0.119930	−	0.0104616i
$484$	−26.6675			−1.21216
$485$	−12.7984	+	22.1675i	−0.581145	+	1.00657i
$486$	−0.384545	−	0.666052i	−0.0174433	−	0.0302127i
$487$	9.29842	+	16.1053i	0.421352	+	0.729803i	0.996072	−	0.0885474i	$-0.0282225\pi$
$487$	9.29842	+	16.1053i	0.421352	+	0.729803i	−0.574720	+	0.818350i	$0.694889\pi$
$488$	−11.8087	+	20.4533i	−0.534555	+	0.925877i
$489$	0.687374			0.0310841
$490$	−7.42558	−	20.3691i	−0.335453	−	0.920182i
$491$	−27.5620			−1.24386			−0.621928	−	0.783074i	$-0.713651\pi$
$491$	−27.5620			−1.24386			−0.621928	+	0.783074i	$0.713651\pi$
$492$	2.80156	−	4.85244i	0.126304	−	0.218765i
$493$	−5.29727	−	9.17514i	−0.238577	−	0.413227i
$494$	−6.02548	−	10.4364i	−0.271099	−	0.469558i
$495$	11.0164	−	19.0809i	0.495149	−	0.857624i
$496$	−8.44858			−0.379352
$497$	−18.7349	−	1.63425i	−0.840374	−	0.0733061i
$498$	2.61270			0.117078
$499$	4.66878	−	8.08657i	0.209004	−	0.362005i	−0.742397	−	0.669960i	$-0.766311\pi$
$499$	4.66878	−	8.08657i	0.209004	−	0.362005i	0.951401	+	0.307955i	$0.0996447\pi$
$500$	−17.6332	−	30.5416i	−0.788581	−	1.36586i
$501$	−6.20112	−	10.7407i	−0.277046	−	0.479857i
$502$	1.96147	−	3.39737i	0.0875448	−	0.151632i
$503$	32.9700			1.47006			0.735029	−	0.678035i	$-0.237168\pi$
$503$	32.9700			1.47006			0.735029	+	0.678035i	$0.237168\pi$
$504$	−3.97669	+	5.68241i	−0.177136	+	0.253114i
$505$	−11.4203			−0.508197
$506$	2.10390	−	3.64406i	0.0935297	−	0.161998i
$507$	3.17805	+	5.50454i	0.141142	+	0.244465i
$508$	−0.0666978	−	0.115524i	−0.00295924	−	0.00512555i
$509$	−11.0073	+	19.0653i	−0.487892	+	0.845053i	−0.999903	−	0.0139256i	$-0.995567\pi$
$509$	−11.0073	+	19.0653i	−0.487892	+	0.845053i	0.512011	+	0.858979i	$0.328901\pi$
$510$	6.96762			0.308531
$511$	−5.95859	−	12.7697i	−0.263592	−	0.564897i
$512$	−8.89104			−0.392932
$513$	1.78076	−	3.08437i	0.0786225	−	0.136178i
$514$	−3.40685	−	5.90083i	−0.150270	−	0.260275i
$515$	21.3222	+	36.9311i	0.939568	+	1.62738i
$516$	−1.83871	+	3.18473i	−0.0809446	+	0.140200i
$517$	−2.83596			−0.124725
$518$	−3.37760	−	7.23843i	−0.148403	−	0.318038i
$519$	3.20701			0.140772
$520$	−23.2226	+	40.2227i	−1.01838	+	1.76388i
$521$	9.09504	+	15.7531i	0.398461	+	0.690155i	0.993536	−	0.113515i	$-0.0362110\pi$
$521$	9.09504	+	15.7531i	0.398461	+	0.690155i	−0.595075	+	0.803670i	$0.702878\pi$
$522$	−1.81098	−	3.13671i	−0.0792646	−	0.137290i
$523$	−19.5821	+	33.9172i	−0.856265	+	1.48309i	0.0192022	+	0.999816i	$0.493887\pi$
$523$	−19.5821	+	33.9172i	−0.856265	+	1.48309i	−0.875467	+	0.483278i	$0.839446\pi$
$524$	19.3331			0.844572
$525$	17.0167	−	24.3157i	0.742671	−	1.06122i
$526$	−20.1200			−0.877276
$527$	−11.8661	+	20.5526i	−0.516894	+	0.895287i
$528$	2.19083	+	3.79464i	0.0953438	+	0.165140i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	19.5686	−	33.8938i	0.850005	−	1.47225i
$531$	0.842890			0.0365783
$532$	−13.2219	−	1.15335i	−0.573244	−	0.0500042i
$533$	17.5017			0.758085
$534$	−5.00509	+	8.66907i	−0.216591	+	0.375147i
$535$	−37.9635	−	65.7546i	−1.64130	−	2.84282i
$536$	1.83460	+	3.17762i	0.0792426	+	0.137252i
$537$	5.57358	−	9.65373i	0.240518	−	0.416589i
$538$	12.1185			0.522464
$539$	−13.1171	−	35.9816i	−0.564994	−	1.54984i
$540$	−5.67216			−0.244091
$541$	−6.20655	+	10.7501i	−0.266841	+	0.462182i	−0.968044	−	0.250780i	$-0.919313\pi$
$541$	−6.20655	+	10.7501i	−0.266841	+	0.462182i	0.701204	+	0.712961i	$0.252646\pi$
$542$	−2.28849	−	3.96378i	−0.0982991	−	0.170259i
$543$	9.28315	+	16.0789i	0.398378	+	0.690011i
$544$	−6.59016	+	11.4145i	−0.282551	+	0.489393i
$545$	−44.8394			−1.92071
$546$	−8.91845	−	0.777959i	−0.381674	−	0.0332936i
$547$	25.5889			1.09410			0.547052	−	0.837099i	$-0.315750\pi$
$547$	25.5889			1.09410			0.547052	+	0.837099i	$0.315750\pi$
$548$	−0.726657	+	1.25861i	−0.0310413	+	0.0537651i
$549$	−4.50466	−	7.80230i	−0.192254	−	0.332994i
$550$	23.6004	+	40.8771i	1.00632	+	1.74301i
$551$	8.38634	−	14.5256i	0.357270	−	0.618810i
$552$	−2.62145			−0.111576
$553$	20.3935	−	29.1408i	0.867218	−	1.23919i
$554$	−11.7183			−0.497862
$555$	7.90416	−	13.6904i	0.335513	−	0.581125i
$556$	0.198509	+	0.343827i	0.00841865	+	0.0145815i
$557$	−13.7923	−	23.8889i	−0.584398	−	1.01221i	−0.994950	−	0.100369i	$-0.967998\pi$
$557$	−13.7923	−	23.8889i	−0.584398	−	1.01221i	0.410553	−	0.911837i	$-0.365336\pi$
$558$	−4.05666	+	7.02635i	−0.171732	+	0.297449i
$559$	−11.4867			−0.485835
$560$	3.60819	+	7.73262i	0.152474	+	0.326763i
$561$	12.3081			0.519650
$562$	0.685469	−	1.18727i	0.0289148	−	0.0500818i
$563$	−12.6669	−	21.9397i	−0.533845	−	0.924647i	−0.999218	−	0.0395326i	$-0.987413\pi$
$563$	−12.6669	−	21.9397i	−0.533845	−	0.924647i	0.465373	−	0.885115i	$-0.345920\pi$
$564$	0.365048	+	0.632282i	0.0153713	+	0.0266239i
$565$	−2.61719	+	4.53310i	−0.110106	+	0.190709i
$566$	15.3811			0.646517
$567$	−1.11876	−	2.39758i	−0.0469834	−	0.100689i
$568$	−18.6333			−0.781834
$569$	11.1027	−	19.2305i	0.465450	−	0.806183i	−0.533772	−	0.845629i	$-0.679226\pi$
$569$	11.1027	−	19.2305i	0.465450	−	0.806183i	0.999222	+	0.0394454i	$0.0125591\pi$
$570$	5.51537	+	9.55289i	0.231013	+	0.400127i
$571$	−4.33227	−	7.50371i	−0.181300	−	0.314020i	0.761024	−	0.648724i	$-0.224697\pi$
$571$	−4.33227	−	7.50371i	−0.181300	−	0.314020i	−0.942323	+	0.334704i	$0.891364\pi$
$572$	−16.9517	+	29.3612i	−0.708786	+	1.22765i
$573$	22.9387			0.958277
$574$	−4.64121	+	6.63195i	−0.193720	+	0.276812i
$575$	11.2175			0.467800
$576$	−1.45212	+	2.51514i	−0.0605048	+	0.104797i
$577$	−20.2143	−	35.0122i	−0.841532	−	1.45758i	−0.888599	−	0.458684i	$-0.848321\pi$
$577$	−20.2143	−	35.0122i	−0.841532	−	1.45758i	0.0470678	−	0.998892i	$-0.485012\pi$
$578$	−4.59111	−	7.95204i	−0.190965	−	0.330761i
$579$	−5.06476	+	8.77242i	−0.210484	+	0.364569i
$580$	−26.7125			−1.10918
$581$	8.95396	+	0.781056i	0.371473	+	0.0324037i
$582$	−4.88845			−0.202633
$583$	34.5675	−	59.8726i	1.43164	−	2.47967i
$584$	−6.98101	−	12.0915i	−0.288876	−	0.500348i
$585$	−8.85871	−	15.3437i	−0.366262	−	0.634385i
$586$	−6.70335	+	11.6105i	−0.276913	+	0.479627i
$587$	−46.9106			−1.93621			−0.968104	−	0.250547i	$-0.919389\pi$
$587$	−46.9106			−1.93621			−0.968104	+	0.250547i	$0.919389\pi$
$588$	−6.33369	+	7.55606i	−0.261197	+	0.311607i
$589$	−37.5714			−1.54810
$590$	−1.30530	+	2.26084i	−0.0537383	+	0.0930774i
$591$	−2.25784	−	3.91069i	−0.0928750	−	0.160864i
$592$	1.57191	+	2.72262i	0.0646049	+	0.111899i
$593$	−2.84222	+	4.92286i	−0.116716	+	0.202158i	−0.918464	−	0.395504i	$-0.870570\pi$
$593$	−2.84222	+	4.92286i	−0.116716	+	0.202158i	0.801749	+	0.597662i	$0.203903\pi$
$594$	4.20780			0.172648
$595$	23.8786	+	2.08294i	0.978929	+	0.0853922i
$596$	8.03197			0.329002
$597$	10.4038	−	18.0199i	0.425799	−	0.737506i
$598$	−1.69183	−	2.93033i	−0.0691840	−	0.119830i
$599$	−2.40028	−	4.15741i	−0.0980730	−	0.169867i	0.812814	−	0.582523i	$-0.197935\pi$
$599$	−2.40028	−	4.15741i	−0.0980730	−	0.169867i	−0.910887	+	0.412656i	$0.864601\pi$
$600$	14.7030	−	25.4663i	0.600247	−	1.03966i
$601$	8.92677			0.364131			0.182065	−	0.983286i	$-0.441722\pi$
$601$	8.92677			0.364131			0.182065	+	0.983286i	$0.441722\pi$
$602$	3.04610	−	4.35266i	0.124150	−	0.177401i
$603$	−1.39968			−0.0569996
$604$	2.02562	−	3.50848i	0.0824214	−	0.142758i
$605$	38.1231	+	66.0311i	1.54992	+	2.68454i
$606$	−1.09052	−	1.88884i	−0.0442994	−	0.0767288i
$607$	−1.66241	+	2.87939i	−0.0674753	+	0.116871i	−0.897789	−	0.440425i	$-0.854828\pi$
$607$	−1.66241	+	2.87939i	−0.0674753	+	0.116871i	0.830314	+	0.557296i	$0.188161\pi$
$608$	−20.8663			−0.846242
$609$	−5.26869	−	11.2912i	−0.213498	−	0.457542i
$610$	27.9036			1.12978
$611$	−1.14026	+	1.97498i	−0.0461298	+	0.0798991i
$612$	−1.58432	−	2.74412i	−0.0640422	−	0.110924i
$613$	−12.8126	−	22.1921i	−0.517497	−	0.896330i	−0.999793	−	0.0203225i	$-0.993531\pi$
$613$	−12.8126	−	22.1921i	−0.517497	−	0.896330i	0.482297	−	0.876008i	$-0.339803\pi$
$614$	−8.51409	+	14.7468i	−0.343601	+	0.595134i
$615$	−16.0201			−0.645991
$616$	−16.0455	−	34.3867i	−0.646493	−	1.38548i
$617$	29.3425			1.18128			0.590642	−	0.806934i	$-0.298875\pi$
$617$	29.3425			1.18128			0.590642	+	0.806934i	$0.298875\pi$
$618$	−4.07209	+	7.05308i	−0.163804	+	0.283716i
$619$	−2.99870	−	5.19390i	−0.120528	−	0.208760i	0.799448	−	0.600735i	$-0.205125\pi$
$619$	−2.99870	−	5.19390i	−0.120528	−	0.208760i	−0.919976	+	0.391975i	$0.871792\pi$
$620$	29.9185	+	51.8203i	1.20156	+	2.08116i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	5.29930			0.212483
$623$	−19.7445	+	28.2134i	−0.791046	+	1.13035i
$624$	3.52347			0.141052
$625$	−22.3721	+	38.7496i	−0.894883	+	1.54998i
$626$	5.21977	+	9.04091i	0.208624	+	0.361347i
$627$	9.74278	+	16.8750i	0.389089	+	0.673922i
$628$	11.7897	−	20.4204i	0.470461	−	0.814863i
$629$	8.83099			0.352115
$630$	8.16342	+	0.712097i	0.325238	+	0.0283706i
$631$	16.3993			0.652846			0.326423	−	0.945224i	$-0.394157\pi$
$631$	16.3993			0.652846			0.326423	+	0.945224i	$0.394157\pi$
$632$	17.6206	−	30.5198i	0.700909	−	1.21401i
$633$	13.1157	+	22.7171i	0.521304	+	0.902925i
$634$	−9.48240	−	16.4240i	−0.376594	−	0.652280i
$635$	−0.190698	+	0.330299i	−0.00756762	+	0.0131075i
$636$	−17.7982			−0.705746
$637$	−30.3318	−	5.33227i	−1.20179	−	0.211272i
$638$	19.8163			0.784533
$639$	3.55400	−	6.15572i	0.140594	−	0.243516i
$640$	19.0966	+	33.0762i	0.754858	+	1.30745i
$641$	24.2326	+	41.9721i	0.957130	+	1.65780i	0.729416	+	0.684070i	$0.239792\pi$
$641$	24.2326	+	41.9721i	0.957130	+	1.65780i	0.227714	+	0.973728i	$0.426875\pi$
$642$	7.25023	−	12.5578i	0.286144	−	0.495615i
$643$	−19.8571			−0.783088			−0.391544	−	0.920159i	$-0.628059\pi$
$643$	−19.8571			−0.783088			−0.391544	+	0.920159i	$0.628059\pi$
$644$	−3.71244	−	0.323837i	−0.146291	−	0.0127610i
$645$	10.5142			0.413997
$646$	−3.08105	+	5.33653i	−0.121222	+	0.209963i
$647$	14.7065	+	25.4724i	0.578172	+	1.00142i	0.995689	+	0.0927538i	$0.0295670\pi$
$647$	14.7065	+	25.4724i	0.578172	+	1.00142i	−0.417517	+	0.908669i	$0.637100\pi$
$648$	−1.31072	−	2.27024i	−0.0514900	−	0.0891834i
$649$	−2.30578	+	3.99373i	−0.0905098	+	0.156768i
$650$	37.9560			1.48876
$651$	−16.0031	+	22.8672i	−0.627209	+	0.896236i
$652$	0.968166			0.0379163
$653$	−11.5894	+	20.0734i	−0.453528	+	0.785534i	−0.998602	−	0.0528537i	$-0.983168\pi$
$653$	−11.5894	+	20.0734i	−0.453528	+	0.785534i	0.545074	+	0.838388i	$0.316502\pi$
$654$	−4.28170	−	7.41612i	−0.167428	−	0.289993i
$655$	−27.6380	−	47.8704i	−1.07991	−	1.87045i
$656$	1.59296	−	2.75909i	0.0621946	−	0.107724i
$657$	5.32607			0.207790
$658$	−0.446002	−	0.955814i	−0.0173870	−	0.0372615i
$659$	33.1492			1.29131			0.645654	−	0.763630i	$-0.276585\pi$
$659$	33.1492			1.29131			0.645654	+	0.763630i	$0.276585\pi$
$660$	15.5166	−	26.8755i	0.603981	−	1.04613i
$661$	−7.52823	−	13.0393i	−0.292814	−	0.507169i	0.681660	−	0.731669i	$-0.261258\pi$
$661$	−7.52823	−	13.0393i	−0.292814	−	0.507169i	−0.974474	+	0.224500i	$0.927925\pi$
$662$	8.83208	+	15.2976i	0.343269	+	0.594559i
$663$	4.94873	−	8.57146i	0.192193	−	0.332888i
$664$	8.90539			0.345596
$665$	16.0459	+	34.3874i	0.622232	+	1.33349i
$666$	3.01906			0.116986
$667$	2.35471	−	4.07847i	0.0911746	−	0.157919i
$668$	−8.73428	−	15.1282i	−0.337939	−	0.585328i
$669$	−0.601883	−	1.04249i	−0.0232701	−	0.0403051i
$670$	2.16755	−	3.75431i	0.0837398	−	0.145042i
$671$	49.2912			1.90286
$672$	−8.88776	+	12.7000i	−0.342853	+	0.489912i
$673$	−23.8903			−0.920904			−0.460452	−	0.887684i	$-0.652313\pi$
$673$	−23.8903			−0.920904			−0.460452	+	0.887684i	$0.652313\pi$
$674$	−7.66160	+	13.2703i	−0.295114	+	0.511152i
$675$	5.60873	+	9.71461i	0.215880	+	0.373915i
$676$	4.47628	+	7.75314i	0.172164	+	0.298198i
$677$	4.29280	−	7.43534i	0.164986	−	0.285763i	−0.771665	−	0.636030i	$-0.780576\pi$
$677$	4.29280	−	7.43534i	0.164986	−	0.285763i	0.936650	+	0.350266i	$0.113909\pi$
$678$	−0.999657			−0.0383916
$679$	−16.7532	−	1.46138i	−0.642927	−	0.0560827i
$680$	23.7491			0.910737
$681$	7.12657	−	12.3436i	0.273091	−	0.473007i
$682$	−22.1945	−	38.4421i	−0.849873	−	1.47202i
$683$	4.69158	+	8.12606i	0.179518	+	0.310935i	0.941716	−	0.336410i	$-0.109213\pi$
$683$	4.69158	+	8.12606i	0.179518	+	0.310935i	−0.762197	+	0.647345i	$0.775879\pi$
$684$	2.50820	−	4.34433i	0.0959034	−	0.166110i
$685$	4.15522			0.158763
$686$	10.0641	−	10.0796i	0.384249	−	0.384841i
$687$	−12.3571			−0.471452
$688$	−1.04549	+	1.81083i	−0.0398588	+	0.0690374i
$689$	−27.7971	−	48.1460i	−1.05898	−	1.83421i
$690$	1.54860	+	2.68225i	0.0589542	+	0.102112i
$691$	10.6397	−	18.4284i	0.404751	−	0.701050i	−0.589541	−	0.807738i	$-0.700691\pi$
$691$	10.6397	−	18.4284i	0.404751	−	0.701050i	0.994293	+	0.106688i	$0.0340247\pi$
$692$	4.51707			0.171713
$693$	14.4205	+	1.25790i	0.547789	+	0.0477838i
$694$	−9.71474			−0.368767
$695$	0.567564	−	0.983049i	0.0215289	−	0.0372892i
$696$	−6.17273	−	10.6915i	−0.233977	−	0.405260i
$697$	−4.47464	−	7.75030i	−0.169489	−	0.293563i
$698$	5.75651	−	9.97058i	0.217887	−	0.377392i
$699$	−11.9828			−0.453230
$700$	23.9680	−	34.2486i	0.905907	−	1.29448i
$701$	−4.27651			−0.161521			−0.0807607	−	0.996734i	$-0.525735\pi$
$701$	−4.27651			−0.161521			−0.0807607	+	0.996734i	$0.525735\pi$
$702$	1.69183	−	2.93033i	0.0638540	−	0.110598i
$703$	6.99036	+	12.1077i	0.263646	+	0.456649i
$704$	−7.94472	−	13.7607i	−0.299428	−	0.518624i
$705$	1.04372	−	1.80778i	0.0393088	−	0.0680849i
$706$	−2.10120			−0.0790797
$707$	−3.17265	−	6.79922i	−0.119320	−	0.255711i
$708$	1.18721			0.0446181
$709$	6.86581	−	11.8919i	0.257851	−	0.446611i	−0.707815	−	0.706398i	$-0.750319\pi$
$709$	6.86581	−	11.8919i	0.257851	−	0.446611i	0.965666	+	0.259787i	$0.0836523\pi$
$710$	11.0075	+	19.0655i	0.413102	+	0.715514i
$711$	6.72171	+	11.6423i	0.252084	+	0.436622i
$712$	−17.0599	+	29.5485i	−0.639345	+	1.10738i
$713$	−10.5492			−0.395072
$714$	1.93566	+	4.14826i	0.0724402	+	0.155245i
$715$	96.9343			3.62514
$716$	7.85039	−	13.5973i	0.293383	−	0.508154i
$717$	3.26967	+	5.66324i	0.122108	+	0.211497i
$718$	6.41334	+	11.1082i	0.239344	+	0.414556i
$719$	−8.84409	+	15.3184i	−0.329829	+	0.571280i	−0.982478	−	0.186380i	$-0.940324\pi$
$719$	−8.84409	+	15.3184i	−0.329829	+	0.571280i	0.652649	+	0.757660i	$0.273658\pi$
$720$	−3.22518			−0.120195
$721$	−16.0639	+	22.9542i	−0.598252	+	0.854859i
$722$	4.85725			0.180768
$723$	0.250032	−	0.433069i	0.00929880	−	0.0161060i
$724$	13.0753	+	22.6471i	0.485940	+	0.841673i
$725$	26.4138	+	45.7501i	0.980985	+	1.69912i
$726$	−7.28071	+	12.6106i	−0.270213	+	0.468022i
$727$	25.0455			0.928885			0.464442	−	0.885603i	$-0.346255\pi$
$727$	25.0455			0.928885			0.464442	+	0.885603i	$0.346255\pi$
$728$	−30.3985	−	2.65167i	−1.12664	−	0.0982775i
$729$	1.00000			0.0370370
$730$	−8.24795	+	14.2859i	−0.305270	+	0.528744i
$731$	2.93678	+	5.08665i	0.108621	+	0.188137i
$732$	−6.34481	−	10.9895i	−0.234511	−	0.406185i
$733$	−7.89251	+	13.6702i	−0.291517	+	0.504922i	−0.974169	−	0.225822i	$-0.927493\pi$
$733$	−7.89251	+	13.6702i	−0.291517	+	0.504922i	0.682652	+	0.730744i	$0.260827\pi$
$734$	21.5942			0.797055
$735$	27.7639	+	4.88084i	1.02409	+	0.180033i
$736$	−5.85883			−0.215959
$737$	3.82893	−	6.63190i	0.141040	−	0.244289i
$738$	−1.52975	−	2.64960i	−0.0563108	−	0.0975332i
$739$	4.99929	+	8.65903i	0.183902	+	0.318528i	0.943206	−	0.332209i	$-0.107794\pi$
$739$	4.99929	+	8.65903i	0.183902	+	0.318528i	−0.759304	+	0.650736i	$0.774460\pi$
$740$	11.1330	−	19.2829i	0.409257	−	0.708854i
$741$	15.6691			0.575619
$742$	25.6154	+	2.23444i	0.940370	+	0.0820288i
$743$	−7.14322			−0.262059			−0.131030	−	0.991378i	$-0.541828\pi$
$743$	−7.14322			−0.262059			−0.131030	+	0.991378i	$0.541828\pi$
$744$	−13.8271	+	23.9493i	−0.506927	+	0.878024i
$745$	−11.4822	−	19.8878i	−0.420677	−	0.728634i
$746$	8.59067	+	14.8795i	0.314527	+	0.544776i
$747$	−1.69857	+	2.94200i	−0.0621472	+	0.107642i
$748$	17.3360			0.633867
$749$	28.6013	−	40.8692i	1.04507	−	1.49333i
$750$	−19.2567			−0.703156
$751$	10.6810	−	18.5000i	0.389754	−	0.675073i	−0.602663	−	0.797996i	$-0.705893\pi$
$751$	10.6810	−	18.5000i	0.389754	−	0.675073i	0.992416	+	0.122923i	$0.0392268\pi$
$752$	0.207566	+	0.359514i	0.00756914	+	0.0131101i
$753$	2.55038	+	4.41738i	0.0929409	+	0.160978i
$754$	7.96752	−	13.8001i	0.290160	−	0.502572i
$755$	−11.5831			−0.421550
$756$	−1.57577	−	3.37699i	−0.0573102	−	0.122820i
$757$	−6.60015			−0.239887			−0.119943	−	0.992781i	$-0.538271\pi$
$757$	−6.60015			−0.239887			−0.119943	+	0.992781i	$0.538271\pi$
$758$	10.6884	−	18.5129i	0.388220	−	0.672417i
$759$	2.73557	+	4.73814i	0.0992948	+	0.171984i
$760$	18.7991	+	32.5610i	0.681916	+	1.18111i
$761$	−6.57699	+	11.3917i	−0.238416	+	0.412948i	−0.960260	−	0.279108i	$-0.909961\pi$
$761$	−6.57699	+	11.3917i	−0.238416	+	0.412948i	0.721844	+	0.692056i	$0.243295\pi$
$762$	−0.0728387			−0.00263867
$763$	−12.4567	−	26.6957i	−0.450964	−	0.966449i
$764$	32.3091			1.16890
$765$	−4.52978	+	7.84580i	−0.163774	+	0.283666i
$766$	2.53475	+	4.39032i	0.0915843	+	0.158629i
$767$	1.85417	+	3.21152i	0.0669502	+	0.115961i
$768$	−6.55128	+	11.3471i	−0.236399	+	0.409455i
$769$	−23.8184			−0.858915			−0.429457	−	0.903087i	$-0.641295\pi$
$769$	−23.8184			−0.858915			−0.429457	+	0.903087i	$0.641295\pi$
$770$	−25.7056	+	36.7314i	−0.926365	+	1.32371i
$771$	8.85942			0.319064
$772$	−7.13371	+	12.3560i	−0.256748	+	0.444700i
$773$	0.897935	+	1.55527i	0.0322965	+	0.0559391i	0.881722	−	0.471770i	$-0.156385\pi$
$773$	0.897935	+	1.55527i	0.0322965	+	0.0559391i	−0.849425	+	0.527709i	$0.823051\pi$
$774$	1.00400	+	1.73898i	0.0360880	+	0.0625063i
$775$	59.1679	−	102.482i	2.12537	−	3.68126i
$776$	−16.6623			−0.598141
$777$	10.3466	+	0.902536i	0.371182	+	0.0323783i
$778$	−6.91345			−0.247859
$779$	7.08399	−	12.2698i	0.253810	−	0.439612i
$780$	−12.4775	−	21.6116i	−0.446766	−	0.773821i
$781$	19.4444	+	33.6787i	0.695776	+	1.20512i
$782$	−0.865093	+	1.49838i	−0.0309357	+	0.0535821i
$783$	4.70941			0.168301
$784$	−3.60132	+	4.29636i	−0.128619	+	0.153442i
$785$	−67.4169			−2.40621
$786$	5.27829	−	9.14226i	0.188270	−	0.326094i
$787$	7.53744	+	13.0552i	0.268681	+	0.465369i	0.968521	−	0.248930i	$-0.0800790\pi$
$787$	7.53744	+	13.0552i	0.268681	+	0.465369i	−0.699841	+	0.714299i	$0.746746\pi$
$788$	−3.18016	−	5.50820i	−0.113289	−	0.196222i
$789$	13.0804	−	22.6559i	0.465675	−	0.806573i
$790$	−41.6369			−1.48138
$791$	−3.42591	−	0.298844i	−0.121812	−	0.0106257i
$792$	14.3423			0.509631
$793$	19.8185	−	34.3266i	0.703775	−	1.21897i
$794$	−0.981249	−	1.69957i	−0.0348232	−	0.0603156i
$795$	25.4438	+	44.0699i	0.902398	+	1.56300i
$796$	14.6538	−	25.3811i	0.519389	−	0.899608i
$797$	20.9322			0.741456			0.370728	−	0.928742i	$-0.379108\pi$
$797$	20.9322			0.741456			0.370728	+	0.928742i	$0.379108\pi$
$798$	−4.15522	+	5.93751i	−0.147093	+	0.210186i
$799$	1.16611			0.0412539
$800$	32.8606	−	56.9163i	1.16180	−	2.01229i
$801$	−6.50780	−	11.2718i	−0.229942	−	0.398271i
$802$	14.3675	+	24.8852i	0.507334	+	0.878728i
$803$	−14.5698	+	25.2357i	−0.514158	+	0.890548i
$804$	−1.97146			−0.0695279
$805$	4.50534	+	9.65527i	0.158792	+	0.340303i
$806$	−35.6950			−1.25730
$807$	−7.87844	+	13.6459i	−0.277334	+	0.480357i
$808$	−3.71704	−	6.43810i	−0.130765	−	0.226492i
$809$	−12.4493	−	21.5628i	−0.437694	−	0.758108i	0.559817	−	0.828616i	$-0.310871\pi$
$809$	−12.4493	−	21.5628i	−0.437694	−	0.758108i	−0.997511	+	0.0705081i	$0.977538\pi$
$810$	−1.54860	+	2.68225i	−0.0544122	+	0.0942447i
$811$	33.0135			1.15926			0.579630	−	0.814880i	$-0.303197\pi$
$811$	33.0135			1.15926			0.579630	+	0.814880i	$0.303197\pi$
$812$	−7.42095	−	15.9036i	−0.260424	−	0.558108i
$813$	5.95116			0.208716
$814$	−8.25884	+	14.3047i	−0.289472	+	0.501380i
$815$	−1.38406	−	2.39726i	−0.0484815	−	0.0839724i
$816$	−0.900840	−	1.56030i	−0.0315357	−	0.0546214i
$817$	−4.64934	+	8.05289i	−0.162660	+	0.281735i
$818$	8.28545			0.289694
$819$	6.67406	−	9.53675i	0.233211	−	0.333241i
$820$	−22.5642			−0.787977
$821$	−3.53329	+	6.11983i	−0.123312	+	0.213584i	−0.921072	−	0.389392i	$-0.872685\pi$
$821$	−3.53329	+	6.11983i	−0.123312	+	0.213584i	0.797760	+	0.602976i	$0.206018\pi$
$822$	0.396781	+	0.687244i	0.0138393	+	0.0239704i
$823$	−19.1629	−	33.1911i	−0.667975	−	1.15697i	−0.978469	−	0.206392i	$-0.933828\pi$
$823$	−19.1629	−	33.1911i	−0.667975	−	1.15697i	0.310494	−	0.950575i	$-0.399506\pi$
$824$	−13.8797	+	24.0404i	−0.483523	+	0.837487i
$825$	−61.3722			−2.13671
$826$	−1.70864	−	0.149045i	−0.0594513	−	0.00518595i
$827$	−18.8543			−0.655629			−0.327815	−	0.944742i	$-0.606312\pi$
$827$	−18.8543			−0.655629			−0.327815	+	0.944742i	$0.606312\pi$
$828$	0.704250	−	1.21980i	0.0244744	−	0.0423909i
$829$	−24.5960	−	42.6016i	−0.854255	−	1.47961i	−0.877334	−	0.479879i	$-0.840680\pi$
$829$	−24.5960	−	42.6016i	−0.854255	−	1.47961i	0.0230794	−	0.999734i	$-0.492653\pi$
$830$	−5.26079	−	9.11196i	−0.182605	−	0.316281i
$831$	7.61827	−	13.1952i	0.264275	−	0.457738i
$832$	−12.7773			−0.442974
$833$	5.39357	+	14.7951i	0.186876	+	0.512620i
$834$	0.216786			0.00750668
$835$	−24.9725	+	43.2536i	−0.864208	+	1.49685i
$836$	13.7227	+	23.7684i	0.474609	+	0.822047i
$837$	−5.27462	−	9.13592i	−0.182318	−	0.315783i
$838$	7.62113	−	13.2002i	0.263268	−	0.455993i
$839$	3.42024			0.118080			0.0590399	−	0.998256i	$-0.481196\pi$
$839$	3.42024			0.118080			0.0590399	+	0.998256i	$0.481196\pi$
$840$	27.8250	+	2.42718i	0.960054	+	0.0837458i
$841$	−6.82142			−0.235222
$842$	1.41889	−	2.45759i	0.0488983	−	0.0846943i
$843$	0.891272	+	1.54373i	0.0306970	+	0.0531688i
$844$	18.4735	+	31.9971i	0.635884	+	1.10138i
$845$	12.7983	−	22.1673i	0.440274	−	0.762577i
$846$	0.398658			0.0137062
$847$	−28.7215	+	41.0410i	−0.986883	+	1.41018i
$848$	−10.1200			−0.347524
$849$	−9.99956	+	17.3197i	−0.343184	+	0.594412i
$850$	−9.70415	−	16.8081i	−0.332849	−	0.576512i
$851$	1.96275	+	3.39958i	0.0672821	+	0.116536i
$852$	5.00581	−	8.67032i	0.171496	−	0.297040i
$853$	26.9555			0.922939			0.461469	−	0.887156i	$-0.347322\pi$
$853$	26.9555			0.922939			0.461469	+	0.887156i	$0.347322\pi$
$854$	7.75185	+	16.6128i	0.265263	+	0.568477i
$855$	−14.3426			−0.490505
$856$	24.7124	−	42.8031i	0.844653	−	1.46298i
$857$	−10.5721	−	18.3114i	−0.361137	−	0.625507i	0.627012	−	0.779010i	$-0.284278\pi$
$857$	−10.5721	−	18.3114i	−0.361137	−	0.625507i	−0.988148	+	0.153503i	$0.950945\pi$
$858$	9.25622	+	16.0322i	0.316002	+	0.547332i
$859$	−20.6665	+	35.7955i	−0.705133	+	1.22133i	0.261511	+	0.965201i	$0.415779\pi$
$859$	−20.6665	+	35.7955i	−0.705133	+	1.22133i	−0.966644	+	0.256125i	$0.917554\pi$
$860$	14.8093			0.504992
$861$	−4.45050	−	9.53774i	−0.151673	−	0.325045i
$862$	−7.06798			−0.240736
$863$	0.688390	−	1.19233i	0.0234331	−	0.0405873i	−0.854071	−	0.520156i	$-0.825874\pi$
$863$	0.688390	−	1.19233i	0.0234331	−	0.0405873i	0.877504	+	0.479569i	$0.159207\pi$
$864$	−2.92942	−	5.07390i	−0.0996608	−	0.172617i
$865$	−6.45746	−	11.1846i	−0.219560	−	0.380289i
$866$	12.9269	−	22.3901i	0.439274	−	0.760845i
$867$	11.9391			0.405472
$868$	−22.5403	+	32.2084i	−0.765067	+	1.09323i
$869$	−73.5507			−2.49504
$870$	−7.29299	+	12.6318i	−0.247256	+	0.428259i
$871$	−3.07900	−	5.33298i	−0.104328	−	0.180701i
$872$	−14.5942	−	25.2778i	−0.494221	−	0.856015i
$873$	3.17807	−	5.50458i	0.107561	−	0.186302i
$874$	−2.73913			−0.0926525
$875$	−65.9945	−	5.75672i	−2.23102	−	0.194613i
$876$	7.50177			0.253461
$877$	11.2162	−	19.4271i	0.378745	−	0.656006i	−0.612135	−	0.790753i	$-0.709689\pi$
$877$	11.2162	−	19.4271i	0.378745	−	0.656006i	0.990880	+	0.134748i	$0.0430224\pi$
$878$	−0.887193	−	1.53666i	−0.0299413	−	0.0518599i
$879$	−8.71595	−	15.0965i	−0.293982	−	0.509191i
$880$	8.82269	−	15.2813i	0.297413	−	0.515134i
$881$	−51.4107			−1.73207			−0.866036	−	0.499982i	$-0.833340\pi$
$881$	−51.4107			−1.73207			−0.866036	+	0.499982i	$0.833340\pi$
$882$	1.84391	+	5.05802i	0.0620875	+	0.170312i
$883$	47.4947			1.59833			0.799163	−	0.601115i	$-0.205277\pi$
$883$	47.4947			1.59833			0.799163	+	0.601115i	$0.205277\pi$
$884$	6.97029	−	12.0729i	0.234436	−	0.406055i
$885$	−1.69720	−	2.93963i	−0.0570507	−	0.0988146i
$886$	−4.38213	−	7.59007i	−0.147220	−	0.254993i
$887$	8.01467	−	13.8818i	0.269106	−	0.466106i	−0.699525	−	0.714608i	$-0.746605\pi$
$887$	8.01467	−	13.8818i	0.269106	−	0.466106i	0.968631	+	0.248502i	$0.0799384\pi$
$888$	10.2905			0.345325
$889$	−0.249625	−	0.0217748i	−0.00837215	−	0.000730305i
$890$	40.3119			1.35126
$891$	−2.73557	+	4.73814i	−0.0916449	+	0.158734i
$892$	−0.847752	−	1.46835i	−0.0283848	−	0.0491640i
$893$	0.923057	+	1.59878i	0.0308889	+	0.0535012i
$894$	2.19287	−	3.79816i	0.0733405	−	0.127030i
$895$	−44.8906			−1.50053
$896$	−14.3872	+	20.5582i	−0.480641	+	0.686801i
$897$	4.39956			0.146897
$898$	1.21634	−	2.10677i	0.0405899	−	0.0703038i
$899$	−24.8404	−	43.0248i	−0.828473	−	1.43496i
$900$	7.89990	+	13.6830i	0.263330	+	0.456101i
$901$	−14.2136	+	24.6188i	−0.473525	+	0.820170i
$902$	16.7389			0.557345
$903$	2.92094	+	6.25977i	0.0972026	+	0.208312i
$904$	−3.40733			−0.113326
$905$	37.3841	−	64.7512i	1.24269	−	2.15240i
$906$	−1.10606	−	1.91575i	−0.0367464	−	0.0636467i
$907$	14.4438	+	25.0173i	0.479597	+	0.830686i	0.999726	−	0.0234013i	$-0.00744954\pi$
$907$	14.4438	+	25.0173i	0.479597	+	0.830686i	−0.520129	+	0.854088i	$0.674116\pi$
$908$	10.0378	−	17.3859i	0.333115	−	0.576973i
$909$	2.83587			0.0940599
$910$	15.2445	+	32.6701i	0.505351	+	1.08300i
$911$	41.9126			1.38863			0.694314	−	0.719672i	$-0.255708\pi$
$911$	41.9126			1.38863			0.694314	+	0.719672i	$0.255708\pi$
$912$	1.42616	−	2.47018i	0.0472248	−	0.0817958i
$913$	−9.29308	−	16.0961i	−0.307556	−	0.532702i
$914$	4.19678	+	7.26904i	0.138817	+	0.240438i
$915$	−18.1407	+	31.4206i	−0.599712	+	1.03873i
$916$	−17.4049			−0.575075
$917$	20.8222	−	29.7534i	0.687610	−	0.982544i
$918$	−1.73019			−0.0571046
$919$	−2.49499	+	4.32146i	−0.0823023	+	0.142552i	−0.904238	−	0.427028i	$-0.859561\pi$
$919$	−2.49499	+	4.32146i	−0.0823023	+	0.142552i	0.821936	+	0.569580i	$0.192894\pi$
$920$	5.27840	+	9.14246i	0.174024	+	0.301418i
$921$	−11.0703	−	19.1744i	−0.364780	−	0.631817i
$922$	13.2978	−	23.0325i	0.437941	−	0.758536i
$923$	31.2721			1.02933
$924$	20.3113	+	1.77176i	0.668192	+	0.0582865i
$925$	−44.0341			−1.44783
$926$	−0.412862	+	0.715097i	−0.0135675	+	0.0234996i
$927$	−5.29469	−	9.17067i	−0.173900	−	0.301204i
$928$	−13.7958	−	23.8951i	−0.452870	−	0.784394i
$929$	18.4714	−	31.9935i	0.606028	−	1.04967i	−0.385860	−	0.922557i	$-0.626095\pi$
$929$	18.4714	−	31.9935i	0.606028	−	1.04967i	0.991888	−	0.127114i	$-0.0405715\pi$
$930$	32.6731			1.07139
$931$	−16.0153	+	19.1062i	−0.524881	+	0.626180i
$932$	−16.8777			−0.552848
$933$	−3.44517	+	5.96722i	−0.112790	+	0.195358i
$934$	−5.18688	−	8.98395i	−0.169720	−	0.293964i
$935$	−24.7830	−	42.9254i	−0.810491	−	1.40381i
$936$	5.76660	−	9.98804i	0.188487	−	0.326469i
$937$	−7.79921			−0.254789			−0.127395	−	0.991852i	$-0.540661\pi$
$937$	−7.79921			−0.254789			−0.127395	+	0.991852i	$0.540661\pi$
$938$	2.83734	+	0.247502i	0.0926423	+	0.00808121i
$939$	−13.5739			−0.442967
$940$	1.47008	−	2.54626i	0.0479488	−	0.0830497i
$941$	11.6540	+	20.1854i	0.379910	+	0.658024i	0.991049	−	0.133500i	$-0.0426216\pi$
$941$	11.6540	+	20.1854i	0.379910	+	0.658024i	−0.611139	+	0.791524i	$0.709288\pi$
$942$	−6.43761	−	11.1503i	−0.209749	−	0.363295i
$943$	1.98904	−	3.44511i	0.0647719	−	0.112188i
$944$	0.675046			0.0219709
$945$	−6.10904	+	8.72937i	−0.198727	+	0.283966i
$946$	−10.9860			−0.357187
$947$	−18.7793	+	32.5267i	−0.610244	+	1.05697i	0.380954	+	0.924594i	$0.375595\pi$
$947$	−18.7793	+	32.5267i	−0.610244	+	1.05697i	−0.991199	+	0.132381i	$0.957738\pi$
$948$	9.46752	+	16.3982i	0.307491	+	0.532590i
$949$	11.7162	+	20.2930i	0.380323	+	0.658739i
$950$	15.3631	−	26.6096i	0.498443	−	0.863329i
$951$	24.6587			0.799614
$952$	6.59769	+	14.1393i	0.213832	+	0.458258i
$953$	−16.0283			−0.519209			−0.259604	−	0.965715i	$-0.583592\pi$
$953$	−16.0283			−0.519209			−0.259604	+	0.965715i	$0.583592\pi$
$954$	−4.85923	+	8.41644i	−0.157324	+	0.272492i
$955$	−46.1881	−	80.0001i	−1.49461	−	2.58874i
$956$	4.60533	+	7.97667i	0.148947	+	0.257984i
$957$	−12.8829	+	22.3139i	−0.416445	+	0.721305i
$958$	4.85249			0.156777
$959$	1.15435	+	2.47386i	0.0372760	+	0.0798852i
$960$	11.6956			0.377474
$961$	−40.1433	+	69.5303i	−1.29495	+	2.24291i
$962$	6.64126	+	11.5030i	0.214123	+	0.370872i
$963$	9.42702	+	16.3281i	0.303781	+	0.526165i
$964$	0.352170	−	0.609977i	0.0113426	−	0.0196460i
$965$	40.7925			1.31316
$966$	−1.16670	+	1.66713i	−0.0375379	+	0.0536390i
$967$	−49.3526			−1.58707			−0.793536	−	0.608523i	$-0.791762\pi$
$967$	−49.3526			−1.58707			−0.793536	+	0.608523i	$0.791762\pi$
$968$	−24.8163	+	42.9831i	−0.797626	+	1.38153i
$969$	−4.00609	−	6.93875i	−0.128694	−	0.222905i
$970$	9.84312	+	17.0488i	0.316044	+	0.547404i
$971$	7.59831	−	13.1607i	0.243841	−	0.422346i	−0.717964	−	0.696080i	$-0.754926\pi$
$971$	7.59831	−	13.1607i	0.243841	−	0.422346i	0.961805	+	0.273735i	$0.0882590\pi$
$972$	1.40850			0.0451776
$973$	0.742944	+	0.0648072i	0.0238177	+	0.00207762i
$974$	14.3027			0.458287
$975$	−24.6759	+	42.7400i	−0.790262	+	1.36877i
$976$	−3.60765	−	6.24863i	−0.115478	−	0.200014i
$977$	24.1383	+	41.8088i	0.772253	+	1.33758i	0.936326	+	0.351133i	$0.114203\pi$
$977$	24.1383	+	41.8088i	0.772253	+	1.33758i	−0.164073	+	0.986448i	$0.552463\pi$
$978$	0.264327	−	0.457827i	0.00845223	−	0.0146397i
$979$	71.2101			2.27589
$980$	39.1054	+	6.87466i	1.24918	+	0.219603i
$981$	11.1344			0.355495
$982$	−10.5988	+	18.3577i	−0.338223	+	0.585819i
$983$	6.63330	+	11.4892i	0.211570	+	0.366449i	0.952206	−	0.305457i	$-0.0988092\pi$
$983$	6.63330	+	11.4892i	0.211570	+	0.366449i	−0.740636	+	0.671906i	$0.765476\pi$
$984$	−5.21415	−	9.03117i	−0.166221	−	0.287903i
$985$	−9.09252	+	15.7487i	−0.289712	+	0.501795i
$986$	−8.14816			−0.259490
$987$	1.36624	+	0.119177i	0.0434878	+	0.00379345i
$988$	22.0699			0.702138
$989$	−1.30544	+	2.26108i	−0.0415105	+	0.0718983i
$990$	−8.47259	−	14.6750i	−0.269277	−	0.466401i
$991$	−0.702165	−	1.21618i	−0.0223050	−	0.0386334i	0.854657	−	0.519192i	$-0.173767\pi$
$991$	−0.702165	−	1.21618i	−0.0223050	−	0.0386334i	−0.876962	+	0.480559i	$0.840434\pi$
$992$	−30.9031	+	53.5258i	−0.981176	+	1.69945i
$993$	−22.9676			−0.728855
$994$	−8.29291	+	11.8500i	−0.263035	+	0.375858i
$995$	−83.7942			−2.65645
$996$	−2.39243	+	4.14381i	−0.0758070	+	0.131302i
$997$	−5.03552	−	8.72178i	−0.159477	−	0.276221i	0.775204	−	0.631712i	$-0.217647\pi$
$997$	−5.03552	−	8.72178i	−0.159477	−	0.276221i	−0.934680	+	0.355490i	$0.884314\pi$
$998$	−3.59072	−	6.21931i	−0.113662	−	0.196869i
$999$	−1.96275	+	3.39958i	−0.0620985	+	0.107558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.415.7	yes	20
7.2	even	3		3381.2.a.bi.1.4		10
7.4	even	3	inner	483.2.i.h.277.7	✓	20
7.5	odd	6		3381.2.a.bj.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.7	✓	20	7.4	even	3	inner
483.2.i.h.415.7	yes	20	1.1	even	1	trivial
3381.2.a.bi.1.4		10	7.2	even	3
3381.2.a.bj.1.4		10	7.5	odd	6

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.384545 - 0.666052i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.704250 + 1.21980i) q^{4} +(2.01355 - 3.48756i) q^{5} +0.769091 q^{6} +(2.63574 + 0.229917i) q^{7} +2.62145 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.54860 - 2.68225i) q^{10} +(-2.73557 - 4.73814i) q^{11} +(-0.704250 + 1.21980i) q^{12} -4.39956 q^{13} +(1.16670 - 1.66713i) q^{14} +4.02709 q^{15} +(-0.400435 + 0.693574i) q^{16} +(1.12483 + 1.94826i) q^{17} +(0.384545 + 0.666052i) q^{18} +(-1.78076 + 3.08437i) q^{19} +5.67216 q^{20} +(1.11876 + 2.39758i) q^{21} -4.20780 q^{22} +(-0.500000 + 0.866025i) q^{23} +(1.31072 + 2.27024i) q^{24} +(-5.60873 - 9.71461i) q^{25} +(-1.69183 + 2.93033i) q^{26} -1.00000 q^{27} +(1.57577 + 3.37699i) q^{28} -4.70941 q^{29} +(1.54860 - 2.68225i) q^{30} +(5.27462 + 9.13592i) q^{31} +(2.92942 + 5.07390i) q^{32} +(2.73557 - 4.73814i) q^{33} +1.73019 q^{34} +(6.10904 - 8.72937i) q^{35} -1.40850 q^{36} +(1.96275 - 3.39958i) q^{37} +(1.36957 + 2.37216i) q^{38} +(-2.19978 - 3.81013i) q^{39} +(5.27840 - 9.14246i) q^{40} -3.97807 q^{41} +(2.02712 + 0.176827i) q^{42} +2.61087 q^{43} +(3.85304 - 6.67367i) q^{44} +(2.01355 + 3.48756i) q^{45} +(0.384545 + 0.666052i) q^{46} +(0.259175 - 0.448904i) q^{47} -0.800870 q^{48} +(6.89428 + 1.21200i) q^{49} -8.62724 q^{50} +(-1.12483 + 1.94826i) q^{51} +(-3.09839 - 5.36656i) q^{52} +(6.31816 + 10.9434i) q^{53} +(-0.384545 + 0.666052i) q^{54} -22.0328 q^{55} +(6.90945 + 0.602714i) q^{56} -3.56152 q^{57} +(-1.81098 + 3.13671i) q^{58} +(-0.421445 - 0.729964i) q^{59} +(2.83608 + 4.91223i) q^{60} +(-4.50466 + 7.80230i) q^{61} +8.11333 q^{62} +(-1.51698 + 2.16766i) q^{63} +2.90423 q^{64} +(-8.85871 + 15.3437i) q^{65} +(-2.10390 - 3.64406i) q^{66} +(0.699842 + 1.21216i) q^{67} +(-1.58432 + 2.74412i) q^{68} -1.00000 q^{69} +(-3.46501 - 7.42577i) q^{70} -7.10801 q^{71} +(-1.31072 + 2.27024i) q^{72} +(-2.66304 - 4.61252i) q^{73} +(-1.50953 - 2.61458i) q^{74} +(5.60873 - 9.71461i) q^{75} -5.01640 q^{76} +(-6.12087 - 13.1175i) q^{77} -3.38366 q^{78} +(6.72171 - 11.6423i) q^{79} +(1.61259 + 2.79309i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.52975 + 2.64960i) q^{82} +3.39713 q^{83} +(-2.13667 + 3.05315i) q^{84} +9.05955 q^{85} +(1.00400 - 1.73898i) q^{86} +(-2.35471 - 4.07847i) q^{87} +(-7.17114 - 12.4208i) q^{88} +(-6.50780 + 11.2718i) q^{89} +3.09720 q^{90} +(-11.5961 - 1.01153i) q^{91} -1.40850 q^{92} +(-5.27462 + 9.13592i) q^{93} +(-0.199329 - 0.345248i) q^{94} +(7.17128 + 12.4210i) q^{95} +(-2.92942 + 5.07390i) q^{96} -6.35615 q^{97} +(3.45842 - 4.12588i) q^{98} +5.47113 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22}+ \cdots + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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