LMFDB - Embedded newform 403.2.h.b.222.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			222.10
Character	$\chi$	$=$	403.222
Dual form			403.2.h.b.118.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.680422 q^{2} +(0.896149 - 1.55218i) q^{3} -1.53703 q^{4} +(-0.204382 - 0.354001i) q^{5} +(0.609760 - 1.05613i) q^{6} +(1.47430 - 2.55357i) q^{7} -2.40667 q^{8} +(-0.106167 - 0.183887i) q^{9} +O(q^{10})$	\(q+0.680422 q^{2} +(0.896149 - 1.55218i) q^{3} -1.53703 q^{4} +(-0.204382 - 0.354001i) q^{5} +(0.609760 - 1.05613i) q^{6} +(1.47430 - 2.55357i) q^{7} -2.40667 q^{8} +(-0.106167 - 0.183887i) q^{9} +(-0.139066 - 0.240870i) q^{10} +(-2.64506 - 4.58137i) q^{11} +(-1.37740 + 2.38574i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(1.00315 - 1.73750i) q^{14} -0.732628 q^{15} +1.43650 q^{16} +(-3.14250 + 5.44297i) q^{17} +(-0.0722385 - 0.125121i) q^{18} +(1.61734 - 2.80131i) q^{19} +(0.314141 + 0.544108i) q^{20} +(-2.64239 - 4.57676i) q^{21} +(-1.79975 - 3.11727i) q^{22} +1.03491 q^{23} +(-2.15674 + 3.73558i) q^{24} +(2.41646 - 4.18542i) q^{25} +(-0.340211 - 0.589263i) q^{26} +4.99633 q^{27} +(-2.26604 + 3.92490i) q^{28} -0.536694 q^{29} -0.498496 q^{30} +(4.66754 - 3.03546i) q^{31} +5.79077 q^{32} -9.48146 q^{33} +(-2.13823 + 3.70352i) q^{34} -1.20529 q^{35} +(0.163182 + 0.282639i) q^{36} +(-2.42298 + 4.19672i) q^{37} +(1.10047 - 1.90607i) q^{38} -1.79230 q^{39} +(0.491881 + 0.851963i) q^{40} +(-4.29037 - 7.43113i) q^{41} +(-1.79794 - 3.11413i) q^{42} +(-1.91684 + 3.32007i) q^{43} +(4.06552 + 7.04169i) q^{44} +(-0.0433974 + 0.0751665i) q^{45} +0.704175 q^{46} +5.01758 q^{47} +(1.28732 - 2.22970i) q^{48} +(-0.847142 - 1.46729i) q^{49} +(1.64421 - 2.84785i) q^{50} +(5.63230 + 9.75543i) q^{51} +(0.768513 + 1.33110i) q^{52} +(7.09395 + 12.2871i) q^{53} +3.39961 q^{54} +(-1.08121 + 1.87270i) q^{55} +(-3.54816 + 6.14560i) q^{56} +(-2.89875 - 5.02078i) q^{57} -0.365178 q^{58} +(-0.839102 + 1.45337i) q^{59} +1.12607 q^{60} +0.829504 q^{61} +(3.17590 - 2.06539i) q^{62} -0.626091 q^{63} +1.06716 q^{64} +(-0.204382 + 0.354001i) q^{65} -6.45139 q^{66} +(2.70677 + 4.68826i) q^{67} +(4.83011 - 8.36599i) q^{68} +(0.927433 - 1.60636i) q^{69} -0.820103 q^{70} +(3.75892 + 6.51064i) q^{71} +(0.255510 + 0.442555i) q^{72} +(6.20487 + 10.7471i) q^{73} +(-1.64865 + 2.85554i) q^{74} +(-4.33101 - 7.50153i) q^{75} +(-2.48589 + 4.30568i) q^{76} -15.5985 q^{77} -1.21952 q^{78} +(4.37564 - 7.57884i) q^{79} +(-0.293596 - 0.508522i) q^{80} +(4.79596 - 8.30684i) q^{81} +(-2.91926 - 5.05630i) q^{82} +(-5.05412 - 8.75399i) q^{83} +(4.06143 + 7.03460i) q^{84} +2.56909 q^{85} +(-1.30426 + 2.25905i) q^{86} +(-0.480958 + 0.833044i) q^{87} +(6.36578 + 11.0258i) q^{88} +17.4073 q^{89} +(-0.0295286 + 0.0511450i) q^{90} -2.94861 q^{91} -1.59068 q^{92} +(-0.528756 - 9.96508i) q^{93} +3.41407 q^{94} -1.32222 q^{95} +(5.18939 - 8.98829i) q^{96} +12.7634 q^{97} +(-0.576414 - 0.998378i) q^{98} +(-0.561637 + 0.972783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.680422			0.481131			0.240565	−	0.970633i	$-0.422667\pi$
$2$	0.680422			0.481131			0.240565	+	0.970633i	$0.422667\pi$
$3$	0.896149	−	1.55218i	0.517392	−	0.896149i	−0.482404	−	0.875949i	$-0.660236\pi$
$3$	0.896149	−	1.55218i	0.517392	−	0.896149i	0.999796	−	0.0202004i	$-0.00643043\pi$
$4$	−1.53703			−0.768513
$5$	−0.204382	−	0.354001i	−0.0914026	−	0.158314i	0.816699	−	0.577064i	$-0.195802\pi$
$5$	−0.204382	−	0.354001i	−0.0914026	−	0.158314i	−0.908102	+	0.418750i	$0.862468\pi$
$6$	0.609760	−	1.05613i	0.248933	−	0.431165i
$7$	1.47430	−	2.55357i	0.557234	−	0.965158i	−0.440492	−	0.897757i	$-0.645196\pi$
$7$	1.47430	−	2.55357i	0.557234	−	0.965158i	0.997726	−	0.0674015i	$-0.0214708\pi$
$8$	−2.40667			−0.850886
$9$	−0.106167	−	0.183887i	−0.0353891	−	0.0612957i
$10$	−0.139066	−	0.240870i	−0.0439766	−	0.0761697i
$11$	−2.64506	−	4.58137i	−0.797514	−	1.38134i	−0.921230	−	0.389018i	$-0.872814\pi$
$11$	−2.64506	−	4.58137i	−0.797514	−	1.38134i	0.123716	−	0.992318i	$-0.460519\pi$
$12$	−1.37740	+	2.38574i	−0.397623	+	0.688702i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	1.00315	−	1.73750i	0.268103	−	0.464367i
$15$	−0.732628			−0.189164
$16$	1.43650			0.359125
$17$	−3.14250	+	5.44297i	−0.762169	+	1.32011i	0.179562	+	0.983747i	$0.442532\pi$
$17$	−3.14250	+	5.44297i	−0.762169	+	1.32011i	−0.941731	+	0.336368i	$0.890801\pi$
$18$	−0.0722385	−	0.125121i	−0.0170268	−	0.0294913i
$19$	1.61734	−	2.80131i	0.371042	−	0.642664i	−0.618684	−	0.785640i	$-0.712334\pi$
$19$	1.61734	−	2.80131i	0.371042	−	0.642664i	0.989726	+	0.142976i	$0.0456671\pi$
$20$	0.314141	+	0.544108i	0.0702441	+	0.121666i
$21$	−2.64239	−	4.57676i	−0.576617	−	0.998730i
$22$	−1.79975	−	3.11727i	−0.383709	−	0.664603i
$23$	1.03491			0.215794			0.107897	−	0.994162i	$-0.465588\pi$
$23$	1.03491			0.215794			0.107897	+	0.994162i	$0.465588\pi$
$24$	−2.15674	+	3.73558i	−0.440242	+	0.762521i
$25$	2.41646	−	4.18542i	0.483291	−	0.837085i
$26$	−0.340211	−	0.589263i	−0.0667208	−	0.115564i
$27$	4.99633			0.961544
$28$	−2.26604	+	3.92490i	−0.428242	+	0.741737i
$29$	−0.536694			−0.0996616			−0.0498308	−	0.998758i	$-0.515868\pi$
$29$	−0.536694			−0.0996616			−0.0498308	+	0.998758i	$0.515868\pi$
$30$	−0.498496			−0.0910126
$31$	4.66754	−	3.03546i	0.838316	−	0.545185i
$31$	4.66754	−	3.03546i	0.838316	−	0.545185i
$32$	5.79077			1.02367
$33$	−9.48146			−1.65051
$34$	−2.13823	+	3.70352i	−0.366703	+	0.635148i
$35$	−1.20529			−0.203731
$36$	0.163182	+	0.282639i	0.0271970	+	0.0471065i
$37$	−2.42298	+	4.19672i	−0.398335	+	0.689936i	−0.993521	−	0.113652i	$-0.963745\pi$
$37$	−2.42298	+	4.19672i	−0.398335	+	0.689936i	0.595186	+	0.803588i	$0.297078\pi$
$38$	1.10047	−	1.90607i	0.178520	−	0.309206i
$39$	−1.79230			−0.286997
$40$	0.491881	+	0.851963i	0.0777732	+	0.134707i
$41$	−4.29037	−	7.43113i	−0.670043	−	1.16055i	−0.977892	−	0.209113i	$-0.932942\pi$
$41$	−4.29037	−	7.43113i	−0.670043	−	1.16055i	0.307849	−	0.951435i	$-0.400391\pi$
$42$	−1.79794	−	3.11413i	−0.277428	−	0.480520i
$43$	−1.91684	+	3.32007i	−0.292316	+	0.506306i	−0.974357	−	0.225008i	$-0.927759\pi$
$43$	−1.91684	+	3.32007i	−0.292316	+	0.506306i	0.682041	+	0.731314i	$0.261092\pi$
$44$	4.06552	+	7.04169i	0.612900	+	1.06157i
$45$	−0.0433974	+	0.0751665i	−0.00646931	+	0.0112052i
$46$	0.704175			0.103825
$47$	5.01758			0.731889			0.365944	−	0.930637i	$-0.380746\pi$
$47$	5.01758			0.731889			0.365944	+	0.930637i	$0.380746\pi$
$48$	1.28732	−	2.22970i	0.185809	−	0.321830i
$49$	−0.847142	−	1.46729i	−0.121020	−	0.209613i
$50$	1.64421	−	2.84785i	0.232526	−	0.402747i
$51$	5.63230	+	9.75543i	0.788680	+	1.36603i
$52$	0.768513	+	1.33110i	0.106574	+	0.184591i
$53$	7.09395	+	12.2871i	0.974429	+	1.68776i	0.681806	+	0.731533i	$0.261195\pi$
$53$	7.09395	+	12.2871i	0.974429	+	1.68776i	0.292623	+	0.956228i	$0.405472\pi$
$54$	3.39961			0.462629
$55$	−1.08121	+	1.87270i	−0.145790	+	0.252515i
$56$	−3.54816	+	6.14560i	−0.474143	+	0.821240i
$57$	−2.89875	−	5.02078i	−0.383949	−	0.665019i
$58$	−0.365178			−0.0479503
$59$	−0.839102	+	1.45337i	−0.109242	+	0.189212i	−0.915463	−	0.402401i	$-0.868176\pi$
$59$	−0.839102	+	1.45337i	−0.109242	+	0.189212i	0.806222	+	0.591614i	$0.201509\pi$
$60$	1.12607			0.145375
$61$	0.829504			0.106207			0.0531036	−	0.998589i	$-0.483089\pi$
$61$	0.829504			0.106207			0.0531036	+	0.998589i	$0.483089\pi$
$62$	3.17590	−	2.06539i	0.403340	−	0.262305i
$63$	−0.626091			−0.0788801
$64$	1.06716			0.133395
$65$	−0.204382	+	0.354001i	−0.0253505	+	0.0439084i
$66$	−6.45139			−0.794112
$67$	2.70677	+	4.68826i	0.330685	+	0.572763i	0.982646	−	0.185489i	$-0.0593870\pi$
$67$	2.70677	+	4.68826i	0.330685	+	0.572763i	−0.651962	+	0.758252i	$0.726054\pi$
$68$	4.83011	−	8.36599i	0.585737	−	1.01453i
$69$	0.927433	−	1.60636i	0.111650	−	0.193383i
$70$	−0.820103			−0.0980211
$71$	3.75892	+	6.51064i	0.446102	+	0.772671i	0.998128	−	0.0611556i	$-0.0194786\pi$
$71$	3.75892	+	6.51064i	0.446102	+	0.772671i	−0.552026	+	0.833827i	$0.686145\pi$
$72$	0.255510	+	0.442555i	0.0301121	+	0.0521557i
$73$	6.20487	+	10.7471i	0.726225	+	1.25786i	0.958468	+	0.285201i	$0.0920603\pi$
$73$	6.20487	+	10.7471i	0.726225	+	1.25786i	−0.232243	+	0.972658i	$0.574606\pi$
$74$	−1.64865	+	2.85554i	−0.191651	+	0.331950i
$75$	−4.33101	−	7.50153i	−0.500102	−	0.866202i
$76$	−2.48589	+	4.30568i	−0.285151	+	0.493896i
$77$	−15.5985			−1.77761
$78$	−1.21952			−0.138083
$79$	4.37564	−	7.57884i	0.492298	−	0.852686i	−0.507662	−	0.861556i	$-0.669490\pi$
$79$	4.37564	−	7.57884i	0.492298	−	0.852686i	0.999961	+	0.00887052i	$0.00282361\pi$
$80$	−0.293596	−	0.508522i	−0.0328250	−	0.0568545i
$81$	4.79596	−	8.30684i	0.532884	−	0.922983i
$82$	−2.91926	−	5.05630i	−0.322378	−	0.558375i
$83$	−5.05412	−	8.75399i	−0.554762	−	0.960875i	−0.997922	−	0.0644331i	$-0.979476\pi$
$83$	−5.05412	−	8.75399i	−0.554762	−	0.960875i	0.443160	−	0.896442i	$-0.353857\pi$
$84$	4.06143	+	7.03460i	0.443138	+	0.767537i
$85$	2.56909			0.278657
$86$	−1.30426	+	2.25905i	−0.140642	+	0.243599i
$87$	−0.480958	+	0.833044i	−0.0515641	+	0.0893117i
$88$	6.36578	+	11.0258i	0.678594	+	1.17536i
$89$	17.4073			1.84517			0.922583	−	0.385798i	$-0.126074\pi$
$89$	17.4073			1.84517			0.922583	+	0.385798i	$0.126074\pi$
$90$	−0.0295286	+	0.0511450i	−0.00311258	+	0.00539115i
$91$	−2.94861			−0.309098
$92$	−1.59068			−0.165840
$93$	−0.528756	−	9.96508i	−0.0548295	−	1.03333i
$94$	3.41407			0.352134
$95$	−1.32222			−0.135657
$96$	5.18939	−	8.98829i	0.529640	−	0.917364i
$97$	12.7634			1.29592			0.647962	−	0.761672i	$-0.275621\pi$
$97$	12.7634			1.29592			0.647962	+	0.761672i	$0.275621\pi$
$98$	−0.576414	−	0.998378i	−0.0582266	−	0.100851i
$99$	−0.561637	+	0.972783i	−0.0564466	+	0.0977684i
$100$	−3.71416	+	6.43311i	−0.371416	+	0.643311i
$101$	−14.2543			−1.41835			−0.709176	−	0.705031i	$-0.750933\pi$
$101$	−14.2543			−1.41835			−0.709176	+	0.705031i	$0.750933\pi$
$102$	3.83234	+	6.63781i	0.379458	+	0.657241i
$103$	−5.32940	−	9.23080i	−0.525122	−	0.909538i	−0.999572	−	0.0292552i	$-0.990686\pi$
$103$	−5.32940	−	9.23080i	−0.525122	−	0.909538i	0.474450	−	0.880282i	$-0.342647\pi$
$104$	1.20333	+	2.08424i	0.117997	+	0.204376i
$105$	−1.08012	+	1.87082i	−0.105409	+	0.182573i
$106$	4.82688	+	8.36040i	0.468828	+	0.812034i
$107$	4.16287	−	7.21031i	0.402440	−	0.697047i	−0.591580	−	0.806247i	$-0.701495\pi$
$107$	4.16287	−	7.21031i	0.402440	−	0.697047i	0.994020	+	0.109200i	$0.0348288\pi$
$108$	−7.67949			−0.738959
$109$	−8.84512			−0.847209			−0.423605	−	0.905847i	$-0.639235\pi$
$109$	−8.84512			−0.847209			−0.423605	+	0.905847i	$0.639235\pi$
$110$	−0.735676	+	1.27423i	−0.0701439	+	0.121493i
$111$	4.34270	+	7.52177i	0.412191	+	0.713935i
$112$	2.11784	−	3.66821i	0.200117	−	0.346613i
$113$	−3.58245	−	6.20498i	−0.337009	−	0.583716i	0.646860	−	0.762609i	$-0.276082\pi$
$113$	−3.58245	−	6.20498i	−0.337009	−	0.583716i	−0.983869	+	0.178893i	$0.942748\pi$
$114$	−1.97237	−	3.41625i	−0.184730	−	0.319961i
$115$	−0.211517	−	0.366358i	−0.0197241	−	0.0341631i
$116$	0.824913			0.0765912
$117$	−0.106167	+	0.183887i	−0.00981517	+	0.0170004i
$118$	−0.570944	+	0.988903i	−0.0525596	+	0.0910359i
$119$	9.26600	+	16.0492i	0.849413	+	1.47123i
$120$	1.76319			0.160957
$121$	−8.49264	+	14.7097i	−0.772058	+	1.33724i
$122$	0.564413			0.0510995
$123$	−15.3792			−1.38670
$124$	−7.17414	+	4.66559i	−0.644257	+	0.418982i
$125$	−4.01935			−0.359501
$126$	−0.426006			−0.0379516
$127$	5.33319	−	9.23736i	0.473245	−	0.819684i	−0.526286	−	0.850307i	$-0.676416\pi$
$127$	5.33319	−	9.23736i	0.473245	−	0.819684i	0.999531	+	0.0306238i	$0.00974938\pi$
$128$	−10.8554			−0.959492
$129$	3.43555	+	5.95055i	0.302484	+	0.523917i
$130$	−0.139066	+	0.240870i	−0.0121969	+	0.0211257i
$131$	−10.4218	+	18.0511i	−0.910555	+	1.57713i	−0.0972734	+	0.995258i	$0.531012\pi$
$131$	−10.4218	+	18.0511i	−0.910555	+	1.57713i	−0.813282	+	0.581870i	$0.802321\pi$
$132$	14.5733			1.26844
$133$	−4.76889	−	8.25996i	−0.413515	−	0.716229i
$134$	1.84175	+	3.19000i	0.159103	+	0.275574i
$135$	−1.02116	−	1.76870i	−0.0878876	−	0.152226i
$136$	7.56297	−	13.0994i	0.648519	−	1.12327i
$137$	5.41085	+	9.37187i	0.462280	+	0.800693i	0.999074	−	0.0430202i	$-0.0136980\pi$
$137$	5.41085	+	9.37187i	0.462280	+	0.800693i	−0.536794	+	0.843714i	$0.680365\pi$
$138$	0.631046	−	1.09300i	0.0537182	−	0.0930426i
$139$	0.890137			0.0755004			0.0377502	−	0.999287i	$-0.487981\pi$
$139$	0.890137			0.0755004			0.0377502	+	0.999287i	$0.487981\pi$
$140$	1.85256			0.156570
$141$	4.49650	−	7.78816i	0.378673	−	0.655882i
$142$	2.55765	+	4.42998i	0.214633	+	0.371756i
$143$	−2.64506	+	4.58137i	−0.221191	+	0.383114i
$144$	−0.152509	−	0.264154i	−0.0127091	−	0.0220128i
$145$	0.109691	+	0.189990i	0.00910932	+	0.0157778i
$146$	4.22193	+	7.31259i	0.349409	+	0.605195i
$147$	−3.03666			−0.250460
$148$	3.72418	−	6.45047i	0.306126	−	0.530225i
$149$	−2.08855	+	3.61748i	−0.171101	+	0.296355i	−0.938805	−	0.344449i	$-0.888066\pi$
$149$	−2.08855	+	3.61748i	−0.171101	+	0.296355i	0.767704	+	0.640804i	$0.221399\pi$
$150$	−2.94691	−	5.10420i	−0.240615	−	0.416757i
$151$	−11.9406			−0.971709			−0.485855	−	0.874040i	$-0.661492\pi$
$151$	−11.9406			−0.971709			−0.485855	+	0.874040i	$0.661492\pi$
$152$	−3.89239	+	6.74182i	−0.315715	+	0.546834i
$153$	1.33452			0.107890
$154$	−10.6135			−0.855263
$155$	−2.02852	−	1.03192i	−0.162935	−	0.0828857i
$156$	2.75481			0.220561
$157$	−4.11913			−0.328742			−0.164371	−	0.986399i	$-0.552559\pi$
$157$	−4.11913			−0.328742			−0.164371	+	0.986399i	$0.552559\pi$
$158$	2.97728	−	5.15680i	0.236860	−	0.410253i
$159$	25.4290			2.01665
$160$	−1.18353	−	2.04993i	−0.0935663	−	0.162062i
$161$	1.52577	−	2.64271i	0.120248	−	0.208275i
$162$	3.26328	−	5.65216i	0.256387	−	0.444075i
$163$	−21.5273			−1.68615			−0.843076	−	0.537794i	$-0.819258\pi$
$163$	−21.5273			−1.68615			−0.843076	+	0.537794i	$0.819258\pi$
$164$	6.59440	+	11.4218i	0.514937	+	0.891896i
$165$	1.93784	+	3.35644i	0.150861	+	0.261299i
$166$	−3.43893	−	5.95641i	−0.266913	−	0.462307i
$167$	−1.29365	+	2.24067i	−0.100106	+	0.173388i	−0.911728	−	0.410794i	$-0.865251\pi$
$167$	−1.29365	+	2.24067i	−0.100106	+	0.173388i	0.811622	+	0.584182i	$0.198585\pi$
$168$	6.35937	+	11.0147i	0.490636	+	0.849806i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	1.74806			0.134070
$171$	−0.686833			−0.0525234
$172$	2.94624	−	5.10303i	0.224648	−	0.389102i
$173$	−2.18057	−	3.77686i	−0.165786	−	0.287149i	0.771148	−	0.636656i	$-0.219683\pi$
$173$	−2.18057	−	3.77686i	−0.165786	−	0.287149i	−0.936934	+	0.349506i	$0.886349\pi$
$174$	−0.327254	+	0.566821i	−0.0248091	+	0.0429706i
$175$	−7.12518	−	12.3412i	−0.538613	−	0.932905i
$176$	−3.79963	−	6.58115i	−0.286408	−	0.496073i
$177$	1.50392	+	2.60487i	0.113042	+	0.195794i
$178$	11.8443			0.887766
$179$	−3.66673	+	6.35097i	−0.274064	+	0.474693i	−0.969899	−	0.243509i	$-0.921701\pi$
$179$	−3.66673	+	6.35097i	−0.274064	+	0.474693i	0.695834	+	0.718202i	$0.255035\pi$
$180$	0.0667030	−	0.115533i	0.00497175	−	0.00861132i
$181$	−7.88979	−	13.6655i	−0.586443	−	1.01575i	−0.994694	−	0.102879i	$-0.967194\pi$
$181$	−7.88979	−	13.6655i	−0.586443	−	1.01575i	0.408251	−	0.912870i	$-0.366139\pi$
$182$	−2.00630			−0.148717
$183$	0.743360	−	1.28754i	0.0549507	−	0.0951775i
$184$	−2.49068			−0.183616
$185$	1.98085			0.145635
$186$	−0.359777	−	6.78046i	−0.0263801	−	0.497167i
$187$	33.2484			2.43136
$188$	−7.71215			−0.562466
$189$	7.36611	−	12.7585i	0.535805	−	0.928042i
$190$	−0.899667			−0.0652687
$191$	−3.24740	−	5.62467i	−0.234974	−	0.406987i	0.724291	−	0.689494i	$-0.242167\pi$
$191$	−3.24740	−	5.62467i	−0.234974	−	0.406987i	−0.959265	+	0.282508i	$0.908834\pi$
$192$	0.956335	−	1.65642i	0.0690176	−	0.119542i
$193$	12.2799	−	21.2693i	0.883924	−	1.53100i	0.0369819	−	0.999316i	$-0.488226\pi$
$193$	12.2799	−	21.2693i	0.883924	−	1.53100i	0.846942	−	0.531685i	$-0.178441\pi$
$194$	8.68448			0.623509
$195$	0.366314	+	0.634475i	0.0262323	+	0.0454357i
$196$	1.30208	+	2.25527i	0.0930057	+	0.161091i
$197$	−7.18632	−	12.4471i	−0.512004	−	0.886818i	−0.999903	−	0.0139174i	$-0.995570\pi$
$197$	−7.18632	−	12.4471i	−0.512004	−	0.886818i	0.487899	−	0.872900i	$-0.337764\pi$
$198$	−0.382150	+	0.661903i	−0.0271582	+	0.0470394i
$199$	3.59714	+	6.23043i	0.254995	+	0.441664i	0.964894	−	0.262639i	$-0.0845930\pi$
$199$	3.59714	+	6.23043i	0.254995	+	0.441664i	−0.709899	+	0.704303i	$0.751260\pi$
$200$	−5.81561	+	10.0729i	−0.411226	+	0.712264i
$201$	9.70268			0.684374
$202$	−9.69892			−0.682413
$203$	−0.791250	+	1.37049i	−0.0555349	+	0.0961892i
$204$	−8.65700	−	14.9944i	−0.606111	−	1.04981i
$205$	−1.75375	+	3.03758i	−0.122487	+	0.212154i
$206$	−3.62624	−	6.28084i	−0.252652	−	0.437607i
$207$	−0.109873	−	0.190306i	−0.00763673	−	0.0132272i
$208$	−0.718251	−	1.24405i	−0.0498017	−	0.0862591i
$209$	−17.1118			−1.18365
$210$	−0.734935	+	1.27294i	−0.0507153	+	0.0878415i
$211$	−0.499763	+	0.865614i	−0.0344051	+	0.0595914i	−0.882715	−	0.469908i	$-0.844287\pi$
$211$	−0.499763	+	0.865614i	−0.0344051	+	0.0595914i	0.848310	+	0.529500i	$0.177620\pi$
$212$	−10.9036	−	18.8856i	−0.748862	−	1.29707i
$213$	13.4742			0.923238
$214$	2.83251	−	4.90605i	0.193626	−	0.335371i
$215$	1.56707			0.106874
$216$	−12.0245			−0.818165
$217$	−0.869885	−	16.3941i	−0.0590517	−	1.11290i
$218$	−6.01841			−0.407618
$219$	22.2420			1.50297
$220$	1.66184	−	2.87839i	0.112041	−	0.194061i
$221$	6.28500			0.422775
$222$	2.95487	+	5.11798i	0.198318	+	0.343496i
$223$	3.94546	−	6.83374i	0.264208	−	0.457621i	−0.703148	−	0.711043i	$-0.748223\pi$
$223$	3.94546	−	6.83374i	0.264208	−	0.457621i	0.967356	+	0.253423i	$0.0815563\pi$
$224$	8.53735	−	14.7871i	0.570426	−	0.988006i
$225$	−1.02619			−0.0684129
$226$	−2.43758	−	4.22201i	−0.162145	−	0.280844i
$227$	−2.16296	−	3.74636i	−0.143561	−	0.248655i	0.785274	−	0.619148i	$-0.212522\pi$
$227$	−2.16296	−	3.74636i	−0.143561	−	0.248655i	−0.928835	+	0.370493i	$0.879189\pi$
$228$	4.45545	+	7.71707i	0.295070	+	0.511076i
$229$	7.34153	−	12.7159i	0.485142	−	0.840290i	−0.514713	−	0.857363i	$-0.672101\pi$
$229$	7.34153	−	12.7159i	0.485142	−	0.840290i	0.999854	+	0.0170728i	$0.00543469\pi$
$230$	−0.143921	−	0.249278i	−0.00948986	−	0.0164369i
$231$	−13.9786	+	24.2116i	−0.919721	+	1.59300i
$232$	1.29165			0.0848007
$233$	−27.4006			−1.79507			−0.897537	−	0.440939i	$-0.854645\pi$
$233$	−27.4006			−1.79507			−0.897537	+	0.440939i	$0.854645\pi$
$234$	−0.0722385	+	0.125121i	−0.00472238	+	0.00817940i
$235$	−1.02550	−	1.77623i	−0.0668965	−	0.115868i
$236$	1.28972	−	2.23386i	0.0839538	−	0.145412i
$237$	−7.84246	−	13.5835i	−0.509422	−	0.882345i
$238$	6.30479	+	10.9202i	0.408679	+	0.707853i
$239$	5.29053	+	9.16346i	0.342216	+	0.592735i	0.984844	−	0.173443i	$-0.0554893\pi$
$239$	5.29053	+	9.16346i	0.342216	+	0.592735i	−0.642628	+	0.766178i	$0.722156\pi$
$240$	−1.05242			−0.0679335
$241$	−6.83191	+	11.8332i	−0.440082	+	0.762244i	−0.997695	−	0.0678567i	$-0.978384\pi$
$241$	−6.83191	+	11.8332i	−0.440082	+	0.762244i	0.557613	+	0.830101i	$0.311717\pi$
$242$	−5.77858	+	10.0088i	−0.371461	+	0.643390i
$243$	−1.10130	−	1.90750i	−0.0706482	−	0.122366i
$244$	−1.27497			−0.0816216
$245$	−0.346282	+	0.599777i	−0.0221231	+	0.0383184i
$246$	−10.4644			−0.667184
$247$	−3.23467			−0.205817
$248$	−11.2332	+	7.30536i	−0.713311	+	0.463891i
$249$	−18.1170			−1.14812
$250$	−2.73485			−0.172967
$251$	−10.2064	+	17.6780i	−0.644223	+	1.11583i	0.340257	+	0.940333i	$0.389486\pi$
$251$	−10.2064	+	17.6780i	−0.644223	+	1.11583i	−0.984480	+	0.175495i	$0.943847\pi$
$252$	0.962318			0.0606204
$253$	−2.73739	−	4.74130i	−0.172098	−	0.298083i
$254$	3.62882	−	6.28530i	0.227693	−	0.394375i
$255$	2.30229	−	3.98768i	0.144175	−	0.249718i
$256$	−9.52058			−0.595036
$257$	6.53703	+	11.3225i	0.407769	+	0.706277i	0.994639	−	0.103404i	$-0.0329735\pi$
$257$	6.53703	+	11.3225i	0.407769	+	0.706277i	−0.586870	+	0.809681i	$0.699640\pi$
$258$	2.33763	+	4.04889i	0.145534	+	0.252073i
$259$	7.14441	+	12.3745i	0.443932	+	0.768912i
$260$	0.314141	−	0.544108i	0.0194822	−	0.0337442i
$261$	0.0569793	+	0.0986911i	0.00352693	+	0.00610883i
$262$	−7.09121	+	12.2823i	−0.438096	+	0.758805i
$263$	10.8496			0.669012			0.334506	−	0.942394i	$-0.391431\pi$
$263$	10.8496			0.669012			0.334506	+	0.942394i	$0.391431\pi$
$264$	22.8187			1.40440
$265$	2.89976	−	5.02253i	0.178131	−	0.308531i
$266$	−3.24486	−	5.62026i	−0.198955	−	0.344600i
$267$	15.5995	−	27.0191i	0.954674	−	1.65354i
$268$	−4.16038	−	7.20598i	−0.254135	−	0.440176i
$269$	13.4683	+	23.3277i	0.821174	+	1.42232i	0.904809	+	0.425819i	$0.140014\pi$
$269$	13.4683	+	23.3277i	0.821174	+	1.42232i	−0.0836345	+	0.996496i	$0.526653\pi$
$270$	−0.694821	−	1.20346i	−0.0422854	−	0.0732405i
$271$	22.5954			1.37257			0.686285	−	0.727332i	$-0.259240\pi$
$271$	22.5954			1.37257			0.686285	+	0.727332i	$0.259240\pi$
$272$	−4.51421	+	7.81884i	−0.273714	+	0.474087i
$273$	−2.64239	+	4.57676i	−0.159925	+	0.276998i
$274$	3.68166	+	6.37683i	0.222417	+	0.385238i
$275$	−25.5666			−1.54173
$276$	−1.42549	+	2.46902i	−0.0858044	+	0.148618i
$277$	31.0264			1.86420			0.932098	−	0.362206i	$-0.117976\pi$
$277$	31.0264			1.86420			0.932098	+	0.362206i	$0.117976\pi$
$278$	0.605668			0.0363256
$279$	−1.05372	−	0.536034i	−0.0630847	−	0.0320915i
$280$	2.90073			0.173352
$281$	−3.38810			−0.202117			−0.101059	−	0.994880i	$-0.532223\pi$
$281$	−3.38810			−0.202117			−0.101059	+	0.994880i	$0.532223\pi$
$282$	3.05952	−	5.29924i	0.182191	−	0.315565i
$283$	26.5583			1.57872			0.789362	−	0.613928i	$-0.210411\pi$
$283$	26.5583			1.57872			0.789362	+	0.613928i	$0.210411\pi$
$284$	−5.77756	−	10.0070i	−0.342835	−	0.593808i
$285$	−1.18491	+	2.05232i	−0.0701878	+	0.121569i
$286$	−1.79975	+	3.11727i	−0.106422	+	0.184328i
$287$	−25.3012			−1.49348
$288$	−0.614790	−	1.06485i	−0.0362268	−	0.0627467i
$289$	−11.2506	−	19.4867i	−0.661802	−	1.14628i
$290$	0.0746360	+	0.129273i	0.00438278	+	0.00759119i
$291$	11.4379	−	19.8110i	0.670501	−	1.16134i
$292$	−9.53705	−	16.5186i	−0.558113	−	0.966681i
$293$	−1.34986	+	2.33803i	−0.0788597	+	0.136589i	−0.902758	−	0.430148i	$-0.858461\pi$
$293$	−1.34986	+	2.33803i	−0.0788597	+	0.136589i	0.823899	+	0.566737i	$0.191795\pi$
$294$	−2.06621			−0.120504
$295$	0.685991			0.0399399
$296$	5.83131	−	10.1001i	0.338938	−	0.587057i
$297$	−13.2156	−	22.8900i	−0.766845	−	1.32821i
$298$	−1.42110	+	2.46141i	−0.0823219	+	0.142586i
$299$	−0.517455	−	0.896258i	−0.0299252	−	0.0518319i
$300$	6.65688	+	11.5300i	0.384335	+	0.665688i
$301$	5.65201	+	9.78958i	0.325777	+	0.564262i
$302$	−8.12462			−0.467519
$303$	−12.7740	+	22.1251i	−0.733844	+	1.27106i
$304$	2.32331	−	4.02408i	0.133251	−	0.230797i
$305$	−0.169536	−	0.293645i	−0.00970760	−	0.0168141i
$306$	0.908039			0.0519091
$307$	−9.71769	+	16.8315i	−0.554618	+	0.960627i	0.443315	+	0.896366i	$0.353802\pi$
$307$	−9.71769	+	16.8315i	−0.554618	+	0.960627i	−0.997933	+	0.0642607i	$0.979531\pi$
$308$	23.9752			1.36612
$309$	−19.1038			−1.08678
$310$	−1.38025	−	0.702140i	−0.0783929	−	0.0398789i
$311$	3.42372			0.194141			0.0970705	−	0.995278i	$-0.469053\pi$
$311$	3.42372			0.194141			0.0970705	+	0.995278i	$0.469053\pi$
$312$	4.31347			0.244202
$313$	−11.6344	+	20.1514i	−0.657617	+	1.13903i	0.323614	+	0.946189i	$0.395102\pi$
$313$	−11.6344	+	20.1514i	−0.657617	+	1.13903i	−0.981231	+	0.192837i	$0.938231\pi$
$314$	−2.80274			−0.158168
$315$	0.127962	+	0.221637i	0.00720984	+	0.0124878i
$316$	−6.72548	+	11.6489i	−0.378338	+	0.655300i
$317$	0.550293	−	0.953136i	0.0309075	−	0.0535334i	−0.850158	−	0.526528i	$-0.823494\pi$
$317$	0.550293	−	0.953136i	0.0309075	−	0.0535334i	0.881065	+	0.472994i	$0.156827\pi$
$318$	17.3024			0.970271
$319$	1.41959	+	2.45879i	0.0794816	+	0.137666i
$320$	−0.218109	−	0.377775i	−0.0121927	−	0.0211183i
$321$	−7.46111	−	12.9230i	−0.416439	−	0.721293i
$322$	1.03817	−	1.79816i	0.0578548	−	0.100207i
$323$	10.1650	+	17.6062i	0.565594	+	0.979637i
$324$	−7.37151	+	12.7678i	−0.409529	+	0.709324i
$325$	−4.83291			−0.268082
$326$	−14.6477			−0.811260
$327$	−7.92655	+	13.7292i	−0.438339	+	0.759226i
$328$	10.3255	+	17.8843i	0.570130	+	0.987494i
$329$	7.39743	−	12.8127i	0.407834	−	0.706388i
$330$	1.31855	+	2.28380i	0.0725838	+	0.125719i
$331$	1.28540	+	2.22638i	0.0706521	+	0.122373i	0.899187	−	0.437564i	$-0.144159\pi$
$331$	1.28540	+	2.22638i	0.0706521	+	0.122373i	−0.828535	+	0.559937i	$0.810825\pi$
$332$	7.76831	+	13.4551i	0.426342	+	0.738445i
$333$	1.02896			0.0563868
$334$	−0.880227	+	1.52460i	−0.0481639	+	0.0834223i
$335$	1.10643	−	1.91640i	0.0604508	−	0.104704i
$336$	−3.79580	−	6.57452i	−0.207078	−	0.358669i
$337$	21.7924			1.18711			0.593553	−	0.804795i	$-0.297725\pi$
$337$	21.7924			1.18711			0.593553	+	0.804795i	$0.297725\pi$
$338$	−0.340211	+	0.589263i	−0.0185050	+	0.0320517i
$339$	−12.8416			−0.697462
$340$	−3.94876			−0.214151
$341$	−26.2525	−	13.3548i	−1.42165	−	0.723202i
$342$	−0.467336			−0.0252706
$343$	15.6445			0.844722
$344$	4.61321	−	7.99031i	0.248727	−	0.430809i
$345$	−0.758204			−0.0408203
$346$	−1.48371	−	2.56986i	−0.0797646	−	0.138156i
$347$	−17.8689	+	30.9498i	−0.959251	+	1.66147i	−0.234926	+	0.972013i	$0.575485\pi$
$347$	−17.8689	+	30.9498i	−0.959251	+	1.66147i	−0.724325	+	0.689459i	$0.757849\pi$
$348$	0.739245	−	1.28041i	0.0396277	−	0.0686372i
$349$	1.11201			0.0595244			0.0297622	−	0.999557i	$-0.490525\pi$
$349$	1.11201			0.0595244			0.0297622	+	0.999557i	$0.490525\pi$
$350$	−4.84813	−	8.39720i	−0.259143	−	0.448849i
$351$	−2.49816	−	4.32695i	−0.133342	−	0.230955i
$352$	−15.3169	−	26.5297i	−0.816394	−	1.41404i
$353$	−4.73709	+	8.20489i	−0.252130	+	0.436702i	−0.964112	−	0.265496i	$-0.914464\pi$
$353$	−4.73709	+	8.20489i	−0.252130	+	0.436702i	0.711982	+	0.702198i	$0.247798\pi$
$354$	1.02330	+	1.77241i	0.0543879	+	0.0942025i
$355$	1.53651	−	2.66132i	0.0815497	−	0.141248i
$356$	−26.7554			−1.41803
$357$	33.2149			1.75792
$358$	−2.49492	+	4.32134i	−0.131861	+	0.228390i
$359$	5.38733	+	9.33114i	0.284333	+	0.492479i	0.972447	−	0.233124i	$-0.0748947\pi$
$359$	5.38733	+	9.33114i	0.284333	+	0.492479i	−0.688114	+	0.725602i	$0.741561\pi$
$360$	0.104443	−	0.180901i	0.00550464	−	0.00953432i
$361$	4.26845	+	7.39317i	0.224655	+	0.389114i
$362$	−5.36838	−	9.29831i	−0.282156	−	0.488708i
$363$	15.2214	+	26.3642i	0.798914	+	1.38376i
$364$	4.53209			0.237546
$365$	2.53633	−	4.39305i	0.132758	−	0.229943i
$366$	0.505798	−	0.876068i	0.0264385	−	0.0457928i
$367$	2.84961	+	4.93567i	0.148748	+	0.257640i	0.930765	−	0.365618i	$-0.119142\pi$
$367$	2.84961	+	4.93567i	0.148748	+	0.257640i	−0.782017	+	0.623257i	$0.785809\pi$
$368$	1.48665			0.0774969
$369$	−0.910993	+	1.57789i	−0.0474244	+	0.0821415i
$370$	1.34782			0.0700697
$371$	41.8346			2.17194
$372$	0.812712	+	15.3166i	0.0421372	+	0.794128i
$373$	33.3823			1.72847			0.864234	−	0.503090i	$-0.167804\pi$
$373$	33.3823			1.72847			0.864234	+	0.503090i	$0.167804\pi$
$374$	22.6229			1.16980
$375$	−3.60193	+	6.23873i	−0.186003	+	0.322167i
$376$	−12.0756			−0.622754
$377$	0.268347	+	0.464791i	0.0138206	+	0.0239379i
$378$	5.01206	−	8.68114i	0.257793	−	0.446510i
$379$	−10.5145	+	18.2117i	−0.540096	+	0.935474i	0.458802	+	0.888539i	$0.348279\pi$
$379$	−10.5145	+	18.2117i	−0.540096	+	0.935474i	−0.998898	+	0.0469352i	$0.985055\pi$
$380$	2.03229			0.104254
$381$	−9.55868	−	16.5561i	−0.489706	−	0.848196i
$382$	−2.20960	−	3.82715i	−0.113053	−	0.195814i
$383$	−1.06401	−	1.84293i	−0.0543686	−	0.0941692i	0.837560	−	0.546345i	$-0.183981\pi$
$383$	−1.06401	−	1.84293i	−0.0543686	−	0.0941692i	−0.891929	+	0.452176i	$0.850648\pi$
$384$	−9.72807	+	16.8495i	−0.496434	+	0.859848i
$385$	3.18805	+	5.52186i	0.162478	+	0.281420i
$386$	8.35549	−	14.4721i	0.425283	−	0.736612i
$387$	0.814023			0.0413791
$388$	−19.6176			−0.995935
$389$	7.48510	−	12.9646i	0.379509	−	0.657330i	−0.611481	−	0.791259i	$-0.709426\pi$
$389$	7.48510	−	12.9646i	0.379509	−	0.657330i	0.990991	+	0.133929i	$0.0427595\pi$
$390$	0.249248	+	0.431710i	0.0126212	+	0.0218605i
$391$	−3.25220	+	5.63298i	−0.164471	+	0.284872i
$392$	2.03879	+	3.53129i	0.102974	+	0.178357i
$393$	18.6789	+	32.3529i	0.942228	+	1.63199i
$394$	−4.88973	−	8.46926i	−0.246341	−	0.426675i
$395$	−3.57722			−0.179989
$396$	0.863250	−	1.49519i	0.0433800	−	0.0751363i
$397$	16.7675	−	29.0422i	0.841538	−	1.45759i	−0.0470568	−	0.998892i	$-0.514984\pi$
$397$	16.7675	−	29.0422i	0.841538	−	1.45759i	0.888594	−	0.458694i	$-0.151682\pi$
$398$	2.44757	+	4.23932i	0.122686	+	0.212498i
$399$	−17.0945			−0.855798
$400$	3.47124	−	6.01237i	0.173562	−	0.300618i
$401$	2.73709			0.136684			0.0683418	−	0.997662i	$-0.478229\pi$
$401$	2.73709			0.136684			0.0683418	+	0.997662i	$0.478229\pi$
$402$	6.60192			0.329274
$403$	−4.96256	−	2.52448i	−0.247203	−	0.125753i
$404$	21.9092			1.09002
$405$	−3.92084			−0.194828
$406$	−0.538384	+	0.932508i	−0.0267195	+	0.0462796i
$407$	25.6356			1.27071
$408$	−13.5551	−	23.4781i	−0.671077	−	1.16234i
$409$	−16.8755	+	29.2292i	−0.834439	+	1.44529i	0.0600480	+	0.998195i	$0.480875\pi$
$409$	−16.8755	+	29.2292i	−0.834439	+	1.44529i	−0.894487	+	0.447095i	$0.852459\pi$
$410$	−1.19329	+	2.06684i	−0.0589324	+	0.102074i
$411$	19.3957			0.956721
$412$	8.19143	+	14.1880i	0.403563	+	0.698991i
$413$	2.47418	+	4.28541i	0.121747	+	0.210871i
$414$	−0.0747603	−	0.129489i	−0.00367427	−	0.00636402i
$415$	−2.06595	+	3.57832i	−0.101413	+	0.175653i
$416$	−2.89538	−	5.01495i	−0.141958	−	0.245878i
$417$	0.797695	−	1.38165i	0.0390633	−	0.0676596i
$418$	−11.6432			−0.569489
$419$	0.531174			0.0259495			0.0129748	−	0.999916i	$-0.495870\pi$
$419$	0.531174			0.0259495			0.0129748	+	0.999916i	$0.495870\pi$
$420$	1.66017	−	2.87549i	0.0810079	−	0.140310i
$421$	−10.8943	−	18.8694i	−0.530954	−	0.919639i	−0.999347	−	0.0361190i	$-0.988500\pi$
$421$	−10.8943	−	18.8694i	−0.530954	−	0.919639i	0.468394	−	0.883520i	$-0.344833\pi$
$422$	−0.340049	+	0.588983i	−0.0165533	+	0.0286712i
$423$	−0.532702	−	0.922667i	−0.0259009	−	0.0448616i
$424$	−17.0728	−	29.5710i	−0.829128	−	1.43609i
$425$	15.1874	+	26.3054i	0.736699	+	1.27600i
$426$	9.16815			0.444198
$427$	1.22294	−	2.11820i	0.0591823	−	0.102507i
$428$	−6.39845	+	11.0824i	−0.309281	+	0.535690i
$429$	4.74073	+	8.21119i	0.228885	+	0.396440i
$430$	1.06627			0.0514202
$431$	7.83106	−	13.5638i	0.377209	−	0.653345i	−0.613446	−	0.789737i	$-0.710217\pi$
$431$	7.83106	−	13.5638i	0.377209	−	0.653345i	0.990655	+	0.136392i	$0.0435505\pi$
$432$	7.17724			0.345315
$433$	−22.5130			−1.08190			−0.540952	−	0.841053i	$-0.681936\pi$
$433$	−22.5130			−1.08190			−0.540952	+	0.841053i	$0.681936\pi$
$434$	−0.591889	−	11.1549i	−0.0284116	−	0.535452i
$435$	0.393197			0.0188524
$436$	13.5952			0.651091
$437$	1.67380	−	2.89910i	0.0800685	−	0.138683i
$438$	15.1339			0.723126
$439$	−5.91881	−	10.2517i	−0.282489	−	0.489286i	0.689508	−	0.724278i	$-0.257827\pi$
$439$	−5.91881	−	10.2517i	−0.282489	−	0.489286i	−0.971997	+	0.234992i	$0.924493\pi$
$440$	2.60210	−	4.50698i	0.124050	−	0.214862i
$441$	−0.179877	+	0.311557i	−0.00856559	+	0.0148360i
$442$	4.27645			0.203410
$443$	−5.56160	−	9.63298i	−0.264240	−	0.457677i	0.703124	−	0.711067i	$-0.251788\pi$
$443$	−5.56160	−	9.63298i	−0.264240	−	0.457677i	−0.967364	+	0.253390i	$0.918454\pi$
$444$	−6.67484	−	11.5612i	−0.316774	−	0.548669i
$445$	−3.55774	−	6.16218i	−0.168653	−	0.292115i
$446$	2.68458	−	4.64982i	0.127118	−	0.220176i
$447$	3.74331	+	6.48360i	0.177052	+	0.306664i
$448$	1.57332	−	2.72507i	0.0743323	−	0.128747i
$449$	28.7985			1.35909			0.679543	−	0.733636i	$-0.262178\pi$
$449$	28.7985			1.35909			0.679543	+	0.733636i	$0.262178\pi$
$450$	−0.698245			−0.0329156
$451$	−22.6965	+	39.3115i	−1.06874	+	1.85111i
$452$	5.50632	+	9.53722i	0.258995	+	0.448593i
$453$	−10.7005	+	18.5339i	−0.502755	+	0.870797i
$454$	−1.47173	−	2.54911i	−0.0690716	−	0.119636i
$455$	0.602643	+	1.04381i	0.0282523	+	0.0489345i
$456$	6.97633	+	12.0834i	0.326697	+	0.565855i
$457$	9.67323			0.452495			0.226247	−	0.974070i	$-0.427354\pi$
$457$	9.67323			0.452495			0.226247	+	0.974070i	$0.427354\pi$
$458$	4.99533	−	8.65217i	0.233417	−	0.404289i
$459$	−15.7010	+	27.1949i	−0.732859	+	1.26935i
$460$	0.325107	+	0.563103i	0.0151582	+	0.0262548i
$461$	−30.3869			−1.41526			−0.707630	−	0.706583i	$-0.750236\pi$
$461$	−30.3869			−1.41526			−0.707630	+	0.706583i	$0.750236\pi$
$462$	−9.51131	+	16.4741i	−0.442506	+	0.766443i
$463$	−29.1462			−1.35454			−0.677269	−	0.735736i	$-0.736837\pi$
$463$	−29.1462			−1.35454			−0.677269	+	0.735736i	$0.736837\pi$
$464$	−0.770962			−0.0357910
$465$	−3.41958	+	2.22387i	−0.158579	+	0.103129i
$466$	−18.6440			−0.863665
$467$	−7.10315			−0.328695			−0.164347	−	0.986403i	$-0.552552\pi$
$467$	−7.10315			−0.328695			−0.164347	+	0.986403i	$0.552552\pi$
$468$	0.163182	−	0.282639i	0.00754308	−	0.0130650i
$469$	15.9624			0.737075
$470$	−0.697775	−	1.20858i	−0.0321860	−	0.0557477i
$471$	−3.69135	+	6.39361i	−0.170089	+	0.294602i
$472$	2.01944	−	3.49778i	0.0929524	−	0.160998i
$473$	20.2806			0.932504
$474$	−5.33618	−	9.24253i	−0.245099	−	0.424524i
$475$	−7.81644	−	13.5385i	−0.358643	−	0.621188i
$476$	−14.2421	−	24.6680i	−0.652785	−	1.13066i
$477$	1.50629	−	2.60897i	0.0689683	−	0.119457i
$478$	3.59979	+	6.23502i	0.164651	+	0.285183i
$479$	−5.31801	+	9.21106i	−0.242986	+	0.420864i	−0.961563	−	0.274583i	$-0.911460\pi$
$479$	−5.31801	+	9.21106i	−0.242986	+	0.420864i	0.718577	+	0.695447i	$0.244794\pi$
$480$	−4.24248			−0.193642
$481$	4.84595			0.220956
$482$	−4.64858	+	8.05158i	−0.211737	+	0.366739i
$483$	−2.73464	−	4.73653i	−0.124430	−	0.215520i
$484$	13.0534	−	22.6092i	0.593337	−	1.02769i
$485$	−2.60861	−	4.51824i	−0.118451	−	0.205163i
$486$	−0.749346	−	1.29791i	−0.0339910	−	0.0588742i
$487$	7.64778	+	13.2463i	0.346554	+	0.600249i	0.985635	−	0.168891i	$-0.0540185\pi$
$487$	7.64778	+	13.2463i	0.346554	+	0.600249i	−0.639081	+	0.769139i	$0.720685\pi$
$488$	−1.99634			−0.0903702
$489$	−19.2917	+	33.4142i	−0.872402	+	1.51104i
$490$	−0.235618	+	0.408102i	−0.0106441	+	0.0184362i
$491$	13.0040	+	22.5236i	0.586862	+	1.01647i	0.994641	+	0.103393i	$0.0329701\pi$
$491$	13.0040	+	22.5236i	0.586862	+	1.01647i	−0.407779	+	0.913081i	$0.633697\pi$
$492$	23.6383			1.06570
$493$	1.68656	−	2.92121i	0.0759589	−	0.131565i
$494$	−2.20094			−0.0990251
$495$	0.459154			0.0206375
$496$	6.70493	−	4.36045i	0.301060	−	0.195790i
$497$	22.1672			0.994333
$498$	−12.3272			−0.552395
$499$	0.700372	−	1.21308i	0.0313529	−	0.0543049i	−0.849923	−	0.526907i	$-0.823352\pi$
$499$	0.700372	−	1.21308i	0.0313529	−	0.0543049i	0.881276	+	0.472602i	$0.156685\pi$
$500$	6.17784			0.276281
$501$	2.31861	+	4.01594i	0.103588	+	0.179419i
$502$	−6.94467	+	12.0285i	−0.309956	+	0.536859i
$503$	8.00581	−	13.8665i	0.356961	−	0.618275i	−0.630490	−	0.776197i	$-0.717146\pi$
$503$	8.00581	−	13.8665i	0.356961	−	0.618275i	0.987452	+	0.157922i	$0.0504795\pi$
$504$	1.50679			0.0671180
$505$	2.91332	+	5.04602i	0.129641	+	0.224545i
$506$	−1.86258	−	3.22609i	−0.0828019	−	0.143417i
$507$	0.896149	+	1.55218i	0.0397994	+	0.0689346i
$508$	−8.19726	+	14.1981i	−0.363695	+	0.629938i
$509$	−2.70020	−	4.67688i	−0.119684	−	0.207299i	0.799958	−	0.600056i	$-0.204855\pi$
$509$	−2.70020	−	4.67688i	−0.119684	−	0.207299i	−0.919643	+	0.392756i	$0.871522\pi$
$510$	1.56653	−	2.71330i	0.0693669	−	0.120147i
$511$	36.5914			1.61871
$512$	15.2328			0.673202
$513$	8.08074	−	13.9963i	0.356774	−	0.617950i
$514$	4.44794	+	7.70406i	0.196190	+	0.339811i
$515$	−2.17847	+	3.77322i	−0.0959949	+	0.166268i
$516$	−5.28054	−	9.14616i	−0.232463	−	0.402637i
$517$	−13.2718	−	22.9874i	−0.583692	−	1.01098i
$518$	4.86121	+	8.41986i	0.213589	+	0.369948i
$519$	−7.81647			−0.343105
$520$	0.491881	−	0.851963i	0.0215704	−	0.0373610i
$521$	−3.54437	+	6.13903i	−0.155282	+	0.268956i	−0.933162	−	0.359457i	$-0.882962\pi$
$521$	−3.54437	+	6.13903i	−0.155282	+	0.268956i	0.777880	+	0.628413i	$0.216295\pi$
$522$	0.0387700	+	0.0671516i	0.00169692	+	0.00293914i
$523$	−15.0058			−0.656159			−0.328079	−	0.944650i	$-0.606401\pi$
$523$	−15.0058			−0.656159			−0.328079	+	0.944650i	$0.606401\pi$
$524$	16.0185	−	27.7449i	0.699774	−	1.21204i
$525$	−25.5409			−1.11470
$526$	7.38227			0.321882
$527$	1.85417	+	34.9443i	0.0807691	+	1.52220i
$528$	−13.6201			−0.592740
$529$	−21.9290			−0.953433
$530$	1.97306	−	3.41744i	0.0857042	−	0.148444i
$531$	0.356341			0.0154639
$532$	7.32991	+	12.6958i	0.317792	+	0.550432i
$533$	−4.29037	+	7.43113i	−0.185836	+	0.321878i
$534$	10.6142	−	18.3844i	0.459323	−	0.795571i
$535$	−3.40327			−0.147136
$536$	−6.51430	−	11.2831i	−0.281375	−	0.487356i
$537$	6.57188	+	11.3828i	0.283597	+	0.491205i
$538$	9.16409	+	15.8727i	0.395092	+	0.684320i
$539$	−4.48148	+	7.76214i	−0.193031	+	0.334339i
$540$	1.56955	+	2.71854i	0.0675428	+	0.116987i
$541$	−16.2396	+	28.1278i	−0.698194	+	1.20931i	0.270898	+	0.962608i	$0.412679\pi$
$541$	−16.2396	+	28.1278i	−0.698194	+	1.20931i	−0.969092	+	0.246699i	$0.920654\pi$
$542$	15.3744			0.660386
$543$	−28.2817			−1.21368
$544$	−18.1975	+	31.5190i	−0.780211	+	1.35137i
$545$	1.80779	+	3.13118i	0.0774371	+	0.134125i
$546$	−1.79794	+	3.11413i	−0.0769448	+	0.133272i
$547$	6.41812	+	11.1165i	0.274419	+	0.475308i	0.969988	−	0.243151i	$-0.0781812\pi$
$547$	6.41812	+	11.1165i	0.274419	+	0.475308i	−0.695569	+	0.718459i	$0.744848\pi$
$548$	−8.31662	−	14.4048i	−0.355269	−	0.615343i
$549$	−0.0880662	−	0.152535i	−0.00375857	−	0.00651004i
$550$	−17.3961			−0.741772
$551$	−0.868015	+	1.50345i	−0.0369787	+	0.0640489i
$552$	−2.23203	+	3.86598i	−0.0950013	+	0.164547i
$553$	−12.9021	−	22.3470i	−0.548651	−	0.950291i
$554$	21.1110			0.896922
$555$	1.77514	−	3.07464i	0.0753506	−	0.130511i
$556$	−1.36816			−0.0580230
$557$	−22.9685			−0.973206			−0.486603	−	0.873623i	$-0.661764\pi$
$557$	−22.9685			−0.973206			−0.486603	+	0.873623i	$0.661764\pi$
$558$	−0.716976	−	0.364729i	−0.0303520	−	0.0154402i
$559$	3.83368			0.162148
$560$	−1.73140			−0.0731648
$561$	29.7955	−	51.6073i	1.25797	−	2.17886i
$562$	−2.30534			−0.0972449
$563$	−14.3311	−	24.8222i	−0.603983	−	1.04613i	−0.992211	−	0.124566i	$-0.960246\pi$
$563$	−14.3311	−	24.8222i	−0.603983	−	1.04613i	0.388228	−	0.921563i	$-0.373087\pi$
$564$	−6.91123	+	11.9706i	−0.291015	+	0.504054i
$565$	−1.46438	+	2.53638i	−0.0616069	+	0.106706i
$566$	18.0708			0.759573
$567$	−14.1414	−	24.4936i	−0.593883	−	1.02864i
$568$	−9.04648	−	15.6690i	−0.379582	−	0.657455i
$569$	1.69071	+	2.92839i	0.0708781	+	0.122765i	0.899286	−	0.437360i	$-0.144087\pi$
$569$	1.69071	+	2.92839i	0.0708781	+	0.122765i	−0.828408	+	0.560125i	$0.810753\pi$
$570$	−0.806236	+	1.39644i	−0.0337695	+	0.0584905i
$571$	−2.92200	−	5.06105i	−0.122282	−	0.211798i	0.798385	−	0.602147i	$-0.205688\pi$
$571$	−2.92200	−	5.06105i	−0.122282	−	0.211798i	−0.920667	+	0.390349i	$0.872355\pi$
$572$	4.06552	−	7.04169i	0.169988	−	0.294428i
$573$	−11.6406			−0.486294
$574$	−17.2155			−0.718561
$575$	2.50081	−	4.33153i	0.104291	−	0.180637i
$576$	−0.113298	−	0.196237i	−0.00472073	−	0.00817654i
$577$	−13.9236	+	24.1163i	−0.579646	+	1.00398i	0.415874	+	0.909422i	$0.363476\pi$
$577$	−13.9236	+	24.1163i	−0.579646	+	1.00398i	−0.995520	+	0.0945536i	$0.969858\pi$
$578$	−7.65518	−	13.2592i	−0.318414	−	0.551508i
$579$	−22.0092	−	38.1210i	−0.914670	−	1.58426i
$580$	−0.168598	−	0.292020i	−0.00700063	−	0.0121255i
$581$	−29.8052			−1.23653
$582$	7.78259	−	13.4798i	0.322599	−	0.558758i
$583$	37.5278	−	65.0001i	1.55424	−	2.69203i
$584$	−14.9331	−	25.8648i	−0.617935	−	1.07029i
$585$	0.0867948			0.00358853
$586$	−0.918474	+	1.59084i	−0.0379418	+	0.0657172i
$587$	19.1762			0.791485			0.395742	−	0.918362i	$-0.370487\pi$
$587$	19.1762			0.791485			0.395742	+	0.918362i	$0.370487\pi$
$588$	4.66743			0.192482
$589$	−0.954279	−	17.9846i	−0.0393204	−	0.741042i
$590$	0.466763			0.0192163
$591$	−25.7601			−1.05963
$592$	−3.48061	+	6.02859i	−0.143052	+	0.247774i
$593$	17.9631			0.737655			0.368827	−	0.929498i	$-0.379759\pi$
$593$	17.9631			0.737655			0.368827	+	0.929498i	$0.379759\pi$
$594$	−8.99216	−	15.5749i	−0.368953	−	0.639045i
$595$	3.78762	−	6.56034i	0.155277	−	0.268948i
$596$	3.21016	−	5.56016i	0.131493	−	0.227753i
$597$	12.8943			0.527729
$598$	−0.352087	−	0.609833i	−0.0143979	−	0.0249379i
$599$	−17.9919	−	31.1629i	−0.735131	−	1.27328i	−0.954666	−	0.297679i	$-0.903787\pi$
$599$	−17.9919	−	31.1629i	−0.735131	−	1.27328i	0.219535	−	0.975605i	$-0.429546\pi$
$600$	10.4233	+	18.0537i	0.425530	+	0.737039i
$601$	−10.3208	+	17.8762i	−0.420995	+	0.729185i	−0.996037	−	0.0889391i	$-0.971652\pi$
$601$	−10.3208	+	17.8762i	−0.420995	+	0.729185i	0.575042	+	0.818124i	$0.304986\pi$
$602$	3.84575	+	6.66104i	0.156741	+	0.271484i
$603$	0.574741	−	0.995480i	0.0234053	−	0.0405391i
$604$	18.3530			0.746771
$605$	6.94299			0.282272
$606$	−8.69168	+	15.0544i	−0.353075	+	0.611544i
$607$	4.19470	+	7.26543i	0.170258	+	0.294895i	0.938510	−	0.345252i	$-0.112207\pi$
$607$	4.19470	+	7.26543i	0.170258	+	0.294895i	−0.768252	+	0.640147i	$0.778873\pi$
$608$	9.36562	−	16.2217i	0.379826	−	0.657878i
$609$	1.41816	+	2.45632i	0.0574666	+	0.0995351i
$610$	−0.115356	−	0.199802i	−0.00467063	−	0.00808977i
$611$	−2.50879	−	4.34535i	−0.101495	−	0.175794i
$612$	−2.05120			−0.0829147
$613$	19.7165	−	34.1501i	0.796344	−	1.37931i	−0.125639	−	0.992076i	$-0.540098\pi$
$613$	19.7165	−	34.1501i	0.796344	−	1.37931i	0.921982	−	0.387232i	$-0.126569\pi$
$614$	−6.61213	+	11.4525i	−0.266844	+	0.462187i
$615$	3.14324	+	5.44426i	0.126748	+	0.219534i
$616$	37.5403			1.51254
$617$	3.74354	−	6.48400i	0.150709	−	0.261036i	−0.780779	−	0.624807i	$-0.785178\pi$
$617$	3.74354	−	6.48400i	0.150709	−	0.261036i	0.931488	+	0.363771i	$0.118511\pi$
$618$	−12.9986			−0.522881
$619$	9.42029			0.378633			0.189317	−	0.981916i	$-0.439373\pi$
$619$	9.42029			0.378633			0.189317	+	0.981916i	$0.439373\pi$
$620$	3.11789	+	1.58609i	0.125217	+	0.0636987i
$621$	5.17075			0.207495
$622$	2.32957			0.0934073
$623$	25.6636	−	44.4506i	1.02819	−	1.78088i
$624$	−2.57464			−0.103068
$625$	−11.2608	−	19.5043i	−0.450432	−	0.780171i
$626$	−7.91632	+	13.7115i	−0.316400	+	0.548020i
$627$	−15.3347	+	26.5605i	−0.612409	+	1.06072i
$628$	6.33121			0.252643
$629$	−15.2284	−	26.3764i	−0.607197	−	1.05170i
$630$	0.0870681	+	0.150806i	0.00346888	+	0.00600827i
$631$	−18.7612	−	32.4954i	−0.746873	−	1.29362i	−0.949315	−	0.314327i	$-0.898221\pi$
$631$	−18.7612	−	32.4954i	−0.746873	−	1.29362i	0.202442	−	0.979294i	$-0.435112\pi$
$632$	−10.5307	+	18.2398i	−0.418890	+	0.725538i
$633$	0.895724	+	1.55144i	0.0356018	+	0.0616642i
$634$	0.374431	−	0.648534i	0.0148706	−	0.0257566i
$635$	−4.36004			−0.173023
$636$	−39.0850			−1.54982
$637$	−0.847142	+	1.46729i	−0.0335650	+	0.0581363i
$638$	0.965917	+	1.67302i	0.0382410	+	0.0662354i
$639$	0.798149	−	1.38243i	0.0315743	−	0.0546882i
$640$	2.21865	+	3.84282i	0.0877000	+	0.151901i
$641$	8.69151	+	15.0541i	0.343294	+	0.594603i	0.985042	−	0.172313i	$-0.0551240\pi$
$641$	8.69151	+	15.0541i	0.343294	+	0.594603i	−0.641748	+	0.766915i	$0.721791\pi$
$642$	−5.07670	−	8.79311i	−0.200362	−	0.347036i
$643$	38.2575			1.50873			0.754364	−	0.656456i	$-0.227945\pi$
$643$	38.2575			1.50873			0.754364	+	0.656456i	$0.227945\pi$
$644$	−2.34515	+	4.06192i	−0.0924118	+	0.160062i
$645$	1.40433	−	2.43238i	0.0552956	−	0.0957747i
$646$	6.91646	+	11.9797i	0.272125	+	0.471334i
$647$	2.68859			0.105699			0.0528496	−	0.998602i	$-0.483170\pi$
$647$	2.68859			0.105699			0.0528496	+	0.998602i	$0.483170\pi$
$648$	−11.5423	+	19.9918i	−0.453424	+	0.785353i
$649$	8.87789			0.348488
$650$	−3.28842			−0.128982
$651$	−26.2261	−	13.3413i	−1.02788	−	0.522888i
$652$	33.0881			1.29583
$653$	−5.73176			−0.224301			−0.112151	−	0.993691i	$-0.535774\pi$
$653$	−5.73176			−0.224301			−0.112151	+	0.993691i	$0.535774\pi$
$654$	−5.39340	+	9.34164i	−0.210899	+	0.365287i
$655$	8.52011			0.332908
$656$	−6.16312	−	10.6748i	−0.240629	−	0.416782i
$657$	1.31751	−	2.28199i	0.0514009	−	0.0890289i
$658$	5.03337	−	8.71806i	0.196221	−	0.339865i
$659$	4.96180			0.193284			0.0966422	−	0.995319i	$-0.469190\pi$
$659$	4.96180			0.193284			0.0966422	+	0.995319i	$0.469190\pi$
$660$	−2.97852	−	5.15894i	−0.115939	−	0.200811i
$661$	10.0969	+	17.4883i	0.392723	+	0.680216i	0.992808	−	0.119720i	$-0.0381997\pi$
$661$	10.0969	+	17.4883i	0.392723	+	0.680216i	−0.600085	+	0.799937i	$0.704866\pi$
$662$	0.874615	+	1.51488i	0.0339929	+	0.0588774i
$663$	5.63230	−	9.75543i	0.218741	−	0.378870i
$664$	12.1636	+	21.0680i	0.472039	+	0.817596i
$665$	−1.94935	+	3.37638i	−0.0755927	+	0.130930i
$666$	0.700129			0.0271294
$667$	−0.555430			−0.0215063
$668$	1.98837	−	3.44396i	0.0769324	−	0.133251i
$669$	−7.07144	−	12.2481i	−0.273398	−	0.473539i
$670$	0.752840	−	1.30396i	0.0290848	−	0.0503763i
$671$	−2.19409	−	3.80027i	−0.0847017	−	0.146708i
$672$	−15.3015	−	26.5029i	−0.590267	−	1.02237i
$673$	−23.6085	−	40.8910i	−0.910039	−	1.57623i	−0.814006	−	0.580856i	$-0.802718\pi$
$673$	−23.6085	−	40.8910i	−0.910039	−	1.57623i	−0.0960327	−	0.995378i	$-0.530615\pi$
$674$	14.8280			0.571153
$675$	12.0734	−	20.9118i	0.464706	−	0.804894i
$676$	0.768513	−	1.33110i	0.0295582	−	0.0511963i
$677$	7.75366	+	13.4297i	0.297997	+	0.516146i	0.975678	−	0.219210i	$-0.0703480\pi$
$677$	7.75366	+	13.4297i	0.297997	+	0.516146i	−0.677680	+	0.735357i	$0.737015\pi$
$678$	−8.73773			−0.335571
$679$	18.8171	−	32.5922i	0.722134	−	1.25077i
$680$	−6.18295			−0.237105
$681$	−7.75335			−0.297109
$682$	−17.8628	−	9.08689i	−0.684001	−	0.347955i
$683$	11.7610			0.450021			0.225011	−	0.974356i	$-0.427758\pi$
$683$	11.7610			0.450021			0.225011	+	0.974356i	$0.427758\pi$
$684$	1.05568			0.0403649
$685$	2.21177	−	3.83089i	0.0845072	−	0.146371i
$686$	10.6448			0.406422
$687$	−13.1582	−	22.7907i	−0.502017	−	0.869519i
$688$	−2.75355	+	4.76928i	−0.104978	+	0.181827i
$689$	7.09395	−	12.2871i	0.270258	−	0.468101i
$690$	−0.515898			−0.0196399
$691$	4.42430	+	7.66312i	0.168308	+	0.291519i	0.937825	−	0.347108i	$-0.112836\pi$
$691$	4.42430	+	7.66312i	0.168308	+	0.291519i	−0.769517	+	0.638627i	$0.779503\pi$
$692$	3.35159	+	5.80513i	0.127408	+	0.220678i
$693$	1.65605	+	2.86836i	0.0629080	+	0.108960i
$694$	−12.1584	+	21.0589i	−0.461525	+	0.799385i
$695$	−0.181928	−	0.315109i	−0.00690093	−	0.0119528i
$696$	1.15751	−	2.00486i	0.0438752	−	0.0759941i
$697$	53.9299			2.04274
$698$	0.756635			0.0286390
$699$	−24.5550	+	42.5306i	−0.928757	+	1.60865i
$700$	10.9516	+	18.9687i	0.413931	+	0.716950i
$701$	15.2515	−	26.4164i	0.576043	−	0.997735i	−0.419885	−	0.907577i	$-0.637930\pi$
$701$	15.2515	−	26.4164i	0.576043	−	0.997735i	0.995928	−	0.0901576i	$-0.0287371\pi$
$702$	−1.69981	−	2.94415i	−0.0641550	−	0.111120i
$703$	7.83754	+	13.5750i	0.295598	+	0.511991i
$704$	−2.82270	−	4.88906i	−0.106384	−	0.184263i
$705$	−3.67602			−0.138447
$706$	−3.22322	+	5.58278i	−0.121308	+	0.210111i
$707$	−21.0151	+	36.3993i	−0.790355	+	1.36893i
$708$	−2.31157	−	4.00375i	−0.0868740	−	0.150470i
$709$	−7.25645			−0.272522			−0.136261	−	0.990673i	$-0.543509\pi$
$709$	−7.25645			−0.272522			−0.136261	+	0.990673i	$0.543509\pi$
$710$	1.04548	−	1.81082i	0.0392361	−	0.0679589i
$711$	−1.85820			−0.0696879
$712$	−41.8935			−1.57003
$713$	4.83048	−	3.14143i	0.180903	−	0.117647i
$714$	22.6001			0.845789
$715$	2.16241			0.0808696
$716$	5.63586	−	9.76160i	0.210622	−	0.364808i
$717$	18.9644			0.708239
$718$	3.66566	+	6.34911i	0.136801	+	0.236947i
$719$	−0.680785	+	1.17915i	−0.0253890	+	0.0439750i	−0.878441	−	0.477851i	$-0.841416\pi$
$719$	−0.680785	+	1.17915i	−0.0253890	+	0.0439750i	0.853052	+	0.521826i	$0.174749\pi$
$720$	−0.0623405	+	0.107977i	−0.00232329	+	0.00402406i
$721$	−31.4286			−1.17046
$722$	2.90434	+	5.03047i	0.108089	+	0.187215i
$723$	12.2448	+	21.2086i	0.455390	+	0.788758i
$724$	12.1268	+	21.0042i	0.450689	+	0.780617i
$725$	−1.29690	+	2.24629i	−0.0481656	+	0.0834252i
$726$	10.3569	+	17.9387i	0.384382	+	0.665769i
$727$	−26.6852	+	46.2201i	−0.989698	+	1.71421i	−0.370860	+	0.928689i	$0.620937\pi$
$727$	−26.6852	+	46.2201i	−0.989698	+	1.71421i	−0.618838	+	0.785519i	$0.712396\pi$
$728$	7.09632			0.263007
$729$	24.8280			0.919557
$730$	1.72578	−	2.98913i	0.0638738	−	0.110633i
$731$	−12.0474	−	20.8666i	−0.445588	−	0.771781i
$732$	−1.14256	+	1.97898i	−0.0422304	+	0.0731451i
$733$	4.24541	+	7.35327i	0.156808	+	0.271599i	0.933716	−	0.358015i	$-0.116546\pi$
$733$	4.24541	+	7.35327i	0.156808	+	0.271599i	−0.776908	+	0.629614i	$0.783213\pi$
$734$	1.93894	+	3.35834i	0.0715674	+	0.123958i
$735$	0.620640	+	1.07498i	0.0228927	+	0.0396512i
$736$	5.99292			0.220902
$737$	14.3191	−	24.8014i	0.527451	−	0.913573i
$738$	−0.619859	+	1.07363i	−0.0228173	+	0.0395208i
$739$	−1.66531	−	2.88440i	−0.0612595	−	0.106105i	0.833769	−	0.552113i	$-0.186178\pi$
$739$	−1.66531	−	2.88440i	−0.0612595	−	0.106105i	−0.895029	+	0.446009i	$0.852845\pi$
$740$	−3.04463			−0.111923
$741$	−2.89875	+	5.02078i	−0.106488	+	0.184443i
$742$	28.4651			1.04499
$743$	−4.95373			−0.181735			−0.0908674	−	0.995863i	$-0.528964\pi$
$743$	−4.95373			−0.181735			−0.0908674	+	0.995863i	$0.528964\pi$
$744$	1.27254	+	23.9827i	0.0466536	+	0.879247i
$745$	1.70745			0.0625562
$746$	22.7140			0.831619
$747$	−1.07316	+	1.85877i	−0.0392650	+	0.0680090i
$748$	−51.1036			−1.86853
$749$	−12.2747	−	21.2604i	−0.448507	−	0.776837i
$750$	−2.45084	+	4.24497i	−0.0894918	+	0.155004i
$751$	−17.9872	+	31.1547i	−0.656362	+	1.13685i	0.325188	+	0.945649i	$0.394572\pi$
$751$	−17.9872	+	31.1547i	−0.656362	+	1.13685i	−0.981550	+	0.191203i	$0.938761\pi$
$752$	7.20776			0.262840
$753$	18.2929	+	31.6843i	0.666632	+	1.15464i
$754$	0.182589	+	0.316254i	0.00664951	+	0.0115173i
$755$	2.44044	+	4.22697i	0.0888167	+	0.153835i
$756$	−11.3219	+	19.6101i	−0.411773	+	0.713212i
$757$	−10.2957	−	17.8326i	−0.374203	−	0.648138i	0.616005	−	0.787743i	$-0.288750\pi$
$757$	−10.2957	−	17.8326i	−0.374203	−	0.648138i	−0.990207	+	0.139604i	$0.955417\pi$
$758$	−7.15433	+	12.3917i	−0.259857	+	0.450085i
$759$	−9.81245			−0.356169
$760$	3.18215			0.115429
$761$	1.56717	−	2.71441i	0.0568098	−	0.0983975i	−0.836222	−	0.548391i	$-0.815240\pi$
$761$	1.56717	−	2.71441i	0.0568098	−	0.0983975i	0.893032	+	0.449994i	$0.148574\pi$
$762$	−6.50393	−	11.2651i	−0.235613	−	0.408093i
$763$	−13.0404	+	22.5866i	−0.472094	+	0.817691i
$764$	4.99134	+	8.64526i	0.180580	+	0.312775i
$765$	−0.272753	−	0.472422i	−0.00986141	−	0.0170805i
$766$	−0.723979	−	1.25397i	−0.0261584	−	0.0453077i
$767$	1.67820			0.0605965
$768$	−8.53186	+	14.7776i	−0.307867	+	0.533241i
$769$	1.92429	−	3.33297i	0.0693917	−	0.120190i	−0.829242	−	0.558890i	$-0.811227\pi$
$769$	1.92429	−	3.33297i	0.0693917	−	0.120190i	0.898634	+	0.438700i	$0.144561\pi$
$770$	2.16922	+	3.75720i	0.0781732	+	0.135400i
$771$	23.4326			0.843906
$772$	−18.8745	+	32.6915i	−0.679307	+	1.17659i
$773$	−38.6195			−1.38905			−0.694523	−	0.719470i	$-0.744385\pi$
$773$	−38.6195			−1.38905			−0.694523	+	0.719470i	$0.744385\pi$
$774$	0.553879			0.0199088
$775$	−1.42578	−	26.8707i	−0.0512157	−	0.965224i
$776$	−30.7172			−1.10268
$777$	25.6098			0.918747
$778$	5.09302	−	8.82137i	0.182594	−	0.316262i
$779$	−27.7559			−0.994457
$780$	−0.563034	−	0.975204i	−0.0201599	−	0.0349179i
$781$	19.8851	−	34.4420i	0.711545	−	1.23243i
$782$	−2.21287	+	3.83281i	−0.0791321	+	0.137061i
$783$	−2.68150			−0.0958290
$784$	−1.21692	−	2.10777i	−0.0434615	−	0.0752774i
$785$	0.841877	+	1.45817i	0.0300479	+	0.0520444i
$786$	12.7096	+	22.0136i	0.453335	+	0.785199i
$787$	−23.5107	+	40.7217i	−0.838065	+	1.45157i	0.0534461	+	0.998571i	$0.482979\pi$
$787$	−23.5107	+	40.7217i	−0.838065	+	1.45157i	−0.891511	+	0.453000i	$0.850354\pi$
$788$	11.0456	+	19.1315i	0.393482	+	0.681531i
$789$	9.72282	−	16.8404i	0.346141	−	0.599535i
$790$	−2.43402			−0.0865984
$791$	−21.1265			−0.751171
$792$	1.35167	−	2.34117i	0.0480296	−	0.0831898i
$793$	−0.414752	−	0.718372i	−0.0147283	−	0.0255101i
$794$	11.4090	−	19.7609i	0.404890	−	0.701290i
$795$	−5.19723	−	9.00187i	−0.184327	−	0.319263i
$796$	−5.52890	−	9.57634i	−0.195967	−	0.339424i
$797$	17.5034	+	30.3167i	0.620001	+	1.07387i	0.989485	+	0.144636i	$0.0462010\pi$
$797$	17.5034	+	30.3167i	0.620001	+	1.07387i	−0.369484	+	0.929237i	$0.620466\pi$
$798$	−11.6315			−0.411751
$799$	−15.7677	+	27.3105i	−0.557823	+	0.966177i
$800$	13.9931	−	24.2368i	0.494732	−	0.856901i
$801$	−1.84808	−	3.20097i	−0.0652987	−	0.113101i
$802$	1.86237			0.0657627
$803$	32.8245	−	56.8536i	1.15835	−	2.00632i
$804$	−14.9133			−0.525951
$805$	−1.24736			−0.0439637
$806$	−3.37663	−	1.71771i	−0.118937	−	0.0605038i
$807$	48.2783			1.69948
$808$	34.3053			1.20686
$809$	−26.9563	+	46.6897i	−0.947734	+	1.64152i	−0.197551	+	0.980293i	$0.563299\pi$
$809$	−26.9563	+	46.6897i	−0.947734	+	1.64152i	−0.750183	+	0.661230i	$0.770035\pi$
$810$	−2.66782			−0.0937377
$811$	21.1572	+	36.6454i	0.742931	+	1.28679i	0.951155	+	0.308714i	$0.0998985\pi$
$811$	21.1572	+	36.6454i	0.742931	+	1.28679i	−0.208224	+	0.978081i	$0.566768\pi$
$812$	1.21617	−	2.10647i	0.0426793	−	0.0739227i
$813$	20.2488	−	35.0720i	0.710157	−	1.23003i
$814$	17.4430			0.611379
$815$	4.39981	+	7.62069i	0.154119	+	0.266941i
$816$	8.09081	+	14.0137i	0.283235	+	0.490578i
$817$	6.20036	+	10.7393i	0.216923	+	0.375722i
$818$	−11.4824	+	19.8882i	−0.401474	+	0.695374i
$819$	0.313046	+	0.542211i	0.0109387	+	0.0189464i
$820$	2.69556	−	4.66885i	0.0941330	−	0.163043i
$821$	29.8910			1.04320			0.521602	−	0.853189i	$-0.325335\pi$
$821$	29.8910			1.04320			0.521602	+	0.853189i	$0.325335\pi$
$822$	13.1973			0.460308
$823$	−10.0604	+	17.4251i	−0.350683	+	0.607401i	−0.986369	−	0.164547i	$-0.947384\pi$
$823$	−10.0604	+	17.4251i	−0.350683	+	0.607401i	0.635686	+	0.771947i	$0.280717\pi$
$824$	12.8261	+	22.2155i	0.446819	+	0.773913i
$825$	−22.9115	+	39.6839i	−0.797677	+	1.38162i
$826$	1.68349	+	2.91589i	0.0585760	+	0.101457i
$827$	−8.05125	−	13.9452i	−0.279970	−	0.484922i	0.691407	−	0.722465i	$-0.256991\pi$
$827$	−8.05125	−	13.9452i	−0.279970	−	0.484922i	−0.971377	+	0.237544i	$0.923658\pi$
$828$	0.168878	+	0.292506i	0.00586893	+	0.0101653i
$829$	−54.7301			−1.90086			−0.950428	−	0.310946i	$-0.899354\pi$
$829$	−54.7301			−1.90086			−0.950428	+	0.310946i	$0.899354\pi$
$830$	−1.40571	+	2.43477i	−0.0487931	+	0.0845121i
$831$	27.8043	−	48.1584i	0.964520	−	1.67060i
$832$	−0.533580	−	0.924188i	−0.0184986	−	0.0320405i
$833$	10.6486			0.368951
$834$	0.542769	−	0.940104i	0.0187946	−	0.0325531i
$835$	1.05760			0.0365996
$836$	26.3013			0.909648
$837$	23.3206	−	15.1662i	0.806077	−	0.524220i
$838$	0.361422			0.0124851
$839$	5.46607			0.188710			0.0943548	−	0.995539i	$-0.469921\pi$
$839$	5.46607			0.188710			0.0943548	+	0.995539i	$0.469921\pi$
$840$	2.59948	−	4.50244i	0.0896907	−	0.155349i
$841$	−28.7120			−0.990068
$842$	−7.41269	−	12.8392i	−0.255458	−	0.442467i
$843$	−3.03625	+	5.25893i	−0.104574	+	0.181127i
$844$	0.768148	−	1.33047i	0.0264408	−	0.0457967i
$845$	0.408765			0.0140619
$846$	−0.362462	−	0.627803i	−0.0124617	−	0.0215843i
$847$	25.0415	+	43.3731i	0.860435	+	1.49032i
$848$	10.1905	+	17.6504i	0.349942	+	0.606118i
$849$	23.8002	−	41.2231i	0.816820	−	1.41477i
$850$	10.3339	+	17.8988i	0.354449	+	0.613923i
$851$	−2.50756	+	4.34322i	−0.0859581	+	0.148884i
$852$	−20.7102			−0.709521
$853$	39.5220			1.35321			0.676603	−	0.736348i	$-0.263451\pi$
$853$	39.5220			1.35321			0.676603	+	0.736348i	$0.263451\pi$
$854$	0.832116	−	1.44127i	0.0284744	−	0.0493191i
$855$	0.140376	+	0.243139i	0.00480077	+	0.00831518i
$856$	−10.0187	+	17.3528i	−0.342431	+	0.593108i
$857$	2.68193	+	4.64524i	0.0916129	+	0.158678i	0.908190	−	0.418558i	$-0.137464\pi$
$857$	2.68193	+	4.64524i	0.0916129	+	0.158678i	−0.816577	+	0.577236i	$0.804131\pi$
$858$	3.22570	+	5.58707i	0.110123	+	0.190739i
$859$	0.669954	+	1.16039i	0.0228585	+	0.0395921i	0.877228	−	0.480073i	$-0.159390\pi$
$859$	0.669954	+	1.16039i	0.0228585	+	0.0395921i	−0.854370	+	0.519665i	$0.826057\pi$
$860$	−2.40863			−0.0821338
$861$	−22.6737	+	39.2719i	−0.772716	+	1.33838i
$862$	5.32842	−	9.22910i	0.181487	−	0.314344i
$863$	−4.09639	−	7.09516i	−0.139443	−	0.241522i	0.787843	−	0.615876i	$-0.211198\pi$
$863$	−4.09639	−	7.09516i	−0.139443	−	0.241522i	−0.927286	+	0.374354i	$0.877864\pi$
$864$	28.9326			0.984306
$865$	−0.891340	+	1.54385i	−0.0303065	+	0.0524923i
$866$	−15.3183			−0.520538
$867$	−40.3290			−1.36965
$868$	1.33704	+	25.1981i	0.0453820	+	0.855281i
$869$	−46.2953			−1.57046
$870$	0.267540			0.00907046
$871$	2.70677	−	4.68826i	0.0917154	−	0.158856i
$872$	21.2873			0.720879
$873$	−1.35505	−	2.34702i	−0.0458616	−	0.0794346i
$874$	1.13889	−	1.97261i	0.0385234	−	0.0667246i
$875$	−5.92574	+	10.2637i	−0.200326	+	0.346976i
$876$	−34.1865			−1.15505
$877$	4.21054	+	7.29287i	0.142180	+	0.246263i	0.928317	−	0.371789i	$-0.121256\pi$
$877$	4.21054	+	7.29287i	0.142180	+	0.246263i	−0.786137	+	0.618052i	$0.787922\pi$
$878$	−4.02728	−	6.97546i	−0.135914	−	0.235410i
$879$	2.41935	+	4.19044i	0.0816027	+	0.141340i
$880$	−1.55315	+	2.69014i	−0.0523568	+	0.0906846i
$881$	8.82678	+	15.2884i	0.297382	+	0.515081i	0.975536	−	0.219839i	$-0.0705532\pi$
$881$	8.82678	+	15.2884i	0.297382	+	0.515081i	−0.678154	+	0.734920i	$0.737220\pi$
$882$	−0.122393	+	0.211990i	−0.00412117	+	0.00713808i
$883$	14.3876			0.484180			0.242090	−	0.970254i	$-0.422167\pi$
$883$	14.3876			0.484180			0.242090	+	0.970254i	$0.422167\pi$
$884$	−9.66022			−0.324908
$885$	0.614750	−	1.06478i	0.0206646	−	0.0357921i
$886$	−3.78424	−	6.55449i	−0.127134	−	0.220202i
$887$	16.2678	−	28.1766i	0.546218	−	0.946078i	−0.452311	−	0.891860i	$-0.649400\pi$
$887$	16.2678	−	28.1766i	0.546218	−	0.946078i	0.998529	−	0.0542174i	$-0.0172664\pi$
$888$	−10.4514	−	18.1024i	−0.350727	−	0.607478i
$889$	−15.7255	−	27.2374i	−0.527416	−	0.913512i
$890$	−2.42076	−	4.19288i	−0.0811441	−	0.140546i
$891$	−50.7423			−1.69993
$892$	−6.06427	+	10.5036i	−0.203047	+	0.351688i
$893$	8.11511	−	14.0558i	0.271562	−	0.470359i
$894$	2.54703	+	4.41158i	0.0851854	+	0.147545i
$895$	2.99766			0.100201
$896$	−16.0042	+	27.7200i	−0.534662	+	0.926062i
$897$	−1.85487			−0.0619322
$898$	19.5951			0.653898
$899$	−2.50504	+	1.62911i	−0.0835479	+	0.0543340i
$900$	1.57729			0.0525762
$901$	−89.1710			−2.97072
$902$	−15.4432	+	26.7484i	−0.514203	+	0.890625i
$903$	20.2602			0.674217
$904$	8.62177	+	14.9333i	0.286756	+	0.496676i
$905$	−3.22507	+	5.58598i	−0.107205	+	0.185684i
$906$	−7.28087	+	12.6108i	−0.241891	+	0.418967i
$907$	34.9592			1.16080			0.580401	−	0.814331i	$-0.302896\pi$
$907$	34.9592			1.16080			0.580401	+	0.814331i	$0.302896\pi$
$908$	3.32453	+	5.75826i	0.110328	+	0.191094i
$909$	1.51334	+	2.62118i	0.0501942	+	0.0869389i
$910$	0.410052	+	0.710230i	0.0135931	+	0.0235439i
$911$	−6.02842	+	10.4415i	−0.199730	+	0.345943i	−0.948441	−	0.316954i	$-0.897340\pi$
$911$	−6.02842	+	10.4415i	−0.199730	+	0.345943i	0.748711	+	0.662897i	$0.230673\pi$
$912$	−4.16406	−	7.21236i	−0.137886	−	0.238825i
$913$	−26.7369	+	46.3096i	−0.884861	+	1.53262i
$914$	6.58188			0.217709
$915$	−0.607718			−0.0200905
$916$	−11.2841	+	19.5447i	−0.372838	+	0.645774i
$917$	30.7297	+	53.2255i	1.01479	+	1.75766i
$918$	−10.6833	+	18.5040i	−0.352601	+	0.610723i
$919$	−29.2474	−	50.6580i	−0.964784	−	1.67105i	−0.710195	−	0.704005i	$-0.751393\pi$
$919$	−29.2474	−	50.6580i	−0.964784	−	1.67105i	−0.254589	−	0.967049i	$-0.581940\pi$
$920$	0.509052	+	0.881704i	0.0167829	+	0.0290689i
$921$	17.4170	+	30.1671i	0.573910	+	0.994041i
$922$	−20.6759			−0.680925
$923$	3.75892	−	6.51064i	0.123726	−	0.214300i
$924$	21.4854	−	37.2138i	0.706818	−	1.22424i
$925$	11.7100	+	20.2824i	0.385023	+	0.666880i
$926$	−19.8317			−0.651710
$927$	−1.13162	+	1.96002i	−0.0371672	+	0.0643754i
$928$	−3.10787			−0.102021
$929$	29.0230			0.952215			0.476107	−	0.879387i	$-0.342047\pi$
$929$	29.0230			0.952215			0.476107	+	0.879387i	$0.342047\pi$
$930$	−2.32675	+	1.51317i	−0.0762973	+	0.0496187i
$931$	−5.48045			−0.179615
$932$	42.1155			1.37954
$933$	3.06816	−	5.31421i	0.100447	−	0.173979i
$934$	−4.83314			−0.158145
$935$	−6.79538	−	11.7699i	−0.222233	−	0.384918i
$936$	0.255510	−	0.442555i	0.00835159	−	0.0144654i
$937$	5.36280	−	9.28865i	0.175195	−	0.303447i	−0.765034	−	0.643990i	$-0.777278\pi$
$937$	5.36280	−	9.28865i	0.175195	−	0.303447i	0.940229	+	0.340543i	$0.110611\pi$
$938$	10.8612			0.354630
$939$	20.8524	+	36.1174i	0.680491	+	1.17865i
$940$	1.57623	+	2.73010i	0.0514108	+	0.0890462i
$941$	−26.7475	−	46.3281i	−0.871944	−	1.51025i	−0.859982	−	0.510324i	$-0.829526\pi$
$941$	−26.7475	−	46.3281i	−0.871944	−	1.51025i	−0.0119619	−	0.999928i	$-0.503808\pi$
$942$	−2.51168	+	4.35035i	−0.0818349	+	0.141742i
$943$	−4.44014	−	7.69055i	−0.144591	−	0.250439i
$944$	−1.20537	+	2.08777i	−0.0392315	+	0.0679510i
$945$	−6.02201			−0.195896
$946$	13.7994			0.448656
$947$	24.2324	−	41.9717i	0.787446	−	1.36390i	−0.140080	−	0.990140i	$-0.544736\pi$
$947$	24.2324	−	41.9717i	0.787446	−	1.36390i	0.927527	−	0.373757i	$-0.121931\pi$
$948$	12.0541	+	20.8782i	0.391498	+	0.678094i
$949$	6.20487	−	10.7471i	0.201419	−	0.348867i
$950$	−5.31848	−	9.21187i	−0.172554	−	0.298873i
$951$	−0.986290	−	1.70830i	−0.0319826	−	0.0553955i
$952$	−22.3002	−	38.6251i	−0.722754	−	1.25185i
$953$	−28.4984			−0.923154			−0.461577	−	0.887100i	$-0.652716\pi$
$953$	−28.4984			−0.923154			−0.461577	+	0.887100i	$0.652716\pi$
$954$	1.02491	−	1.77520i	0.0331828	−	0.0574743i
$955$	−1.32742	+	2.29916i	−0.0429544	+	0.0743992i
$956$	−8.13168	−	14.0845i	−0.262997	−	0.455525i
$957$	5.08864			0.164492
$958$	−3.61849	+	6.26741i	−0.116908	+	0.202491i
$959$	31.9090			1.03039
$960$	−0.781832			−0.0252335
$961$	12.5719	−	28.3363i	0.405546	−	0.914075i
$962$	3.29729			0.106309
$963$	−1.76784			−0.0569680
$964$	10.5008	−	18.1880i	0.338209	−	0.585795i
$965$	−10.0391			−0.323172
$966$	−1.86071	−	3.22284i	−0.0598672	−	0.103693i
$967$	9.32172	−	16.1457i	0.299766	−	0.519211i	−0.676316	−	0.736612i	$-0.736425\pi$
$967$	9.32172	−	16.1457i	0.299766	−	0.519211i	0.976082	+	0.217401i	$0.0697579\pi$
$968$	20.4390	−	35.4014i	0.656934	−	1.13784i
$969$	36.4373			1.17053
$970$	−1.77495	−	3.07431i	−0.0569904	−	0.0987102i
$971$	3.68434	+	6.38146i	0.118236	+	0.204791i	0.919069	−	0.394097i	$-0.128943\pi$
$971$	3.68434	+	6.38146i	0.118236	+	0.204791i	−0.800833	+	0.598888i	$0.795609\pi$
$972$	1.69272	+	2.93188i	0.0542941	+	0.0940401i
$973$	1.31233	−	2.27302i	0.0420714	−	0.0728698i
$974$	5.20371	+	9.01310i	0.166738	+	0.288798i
$975$	−4.33101	+	7.50153i	−0.138703	+	0.240241i
$976$	1.19158			0.0381417
$977$	−22.4574			−0.718477			−0.359238	−	0.933246i	$-0.616964\pi$
$977$	−22.4574			−0.718477			−0.359238	+	0.933246i	$0.616964\pi$
$978$	−13.1265	+	22.7358i	−0.419739	+	0.727010i
$979$	−46.0432	−	79.7491i	−1.47155	−	2.54879i
$980$	0.532244	−	0.921874i	0.0170019	−	0.0294482i
$981$	0.939062	+	1.62650i	0.0299820	+	0.0519303i
$982$	8.84819	+	15.3255i	0.282357	+	0.489057i
$983$	−2.84674	−	4.93069i	−0.0907968	−	0.157265i	0.817050	−	0.576567i	$-0.195608\pi$
$983$	−2.84674	−	4.93069i	−0.0907968	−	0.157265i	−0.907847	+	0.419302i	$0.862275\pi$
$984$	37.0127			1.17992
$985$	−2.93752	+	5.08793i	−0.0935970	+	0.162115i
$986$	1.14757	−	1.98766i	0.0365462	−	0.0632999i
$987$	−13.2584	−	22.9642i	−0.422020	−	0.730960i
$988$	4.97178			0.158173
$989$	−1.98376	+	3.43597i	−0.0630798	+	0.109257i
$990$	0.312419			0.00992932
$991$	7.72600			0.245424			0.122712	−	0.992442i	$-0.460841\pi$
$991$	7.72600			0.245424			0.122712	+	0.992442i	$0.460841\pi$
$992$	27.0287	−	17.5777i	0.858161	−	0.558091i
$993$	4.60765			0.146219
$994$	15.0830			0.478404
$995$	1.47038	−	2.54678i	0.0466143	−	0.0807384i
$996$	27.8463			0.882343
$997$	6.03306	+	10.4496i	0.191069	+	0.330941i	0.945605	−	0.325318i	$-0.105471\pi$
$997$	6.03306	+	10.4496i	0.191069	+	0.330941i	−0.754536	+	0.656259i	$0.772138\pi$
$998$	0.476548	−	0.825406i	0.0150849	−	0.0261278i
$999$	−12.1060	+	20.9682i	−0.383017	+	0.663404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.222.10	yes	34
31.25	even	3	inner	403.2.h.b.118.10	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.10	✓	34	31.25	even	3	inner
403.2.h.b.222.10	yes	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.680422 q^{2} +(0.896149 - 1.55218i) q^{3} -1.53703 q^{4} +(-0.204382 - 0.354001i) q^{5} +(0.609760 - 1.05613i) q^{6} +(1.47430 - 2.55357i) q^{7} -2.40667 q^{8} +(-0.106167 - 0.183887i) q^{9} +O(q^{10})\)	\(q+0.680422 q^{2} +(0.896149 - 1.55218i) q^{3} -1.53703 q^{4} +(-0.204382 - 0.354001i) q^{5} +(0.609760 - 1.05613i) q^{6} +(1.47430 - 2.55357i) q^{7} -2.40667 q^{8} +(-0.106167 - 0.183887i) q^{9} +(-0.139066 - 0.240870i) q^{10} +(-2.64506 - 4.58137i) q^{11} +(-1.37740 + 2.38574i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(1.00315 - 1.73750i) q^{14} -0.732628 q^{15} +1.43650 q^{16} +(-3.14250 + 5.44297i) q^{17} +(-0.0722385 - 0.125121i) q^{18} +(1.61734 - 2.80131i) q^{19} +(0.314141 + 0.544108i) q^{20} +(-2.64239 - 4.57676i) q^{21} +(-1.79975 - 3.11727i) q^{22} +1.03491 q^{23} +(-2.15674 + 3.73558i) q^{24} +(2.41646 - 4.18542i) q^{25} +(-0.340211 - 0.589263i) q^{26} +4.99633 q^{27} +(-2.26604 + 3.92490i) q^{28} -0.536694 q^{29} -0.498496 q^{30} +(4.66754 - 3.03546i) q^{31} +5.79077 q^{32} -9.48146 q^{33} +(-2.13823 + 3.70352i) q^{34} -1.20529 q^{35} +(0.163182 + 0.282639i) q^{36} +(-2.42298 + 4.19672i) q^{37} +(1.10047 - 1.90607i) q^{38} -1.79230 q^{39} +(0.491881 + 0.851963i) q^{40} +(-4.29037 - 7.43113i) q^{41} +(-1.79794 - 3.11413i) q^{42} +(-1.91684 + 3.32007i) q^{43} +(4.06552 + 7.04169i) q^{44} +(-0.0433974 + 0.0751665i) q^{45} +0.704175 q^{46} +5.01758 q^{47} +(1.28732 - 2.22970i) q^{48} +(-0.847142 - 1.46729i) q^{49} +(1.64421 - 2.84785i) q^{50} +(5.63230 + 9.75543i) q^{51} +(0.768513 + 1.33110i) q^{52} +(7.09395 + 12.2871i) q^{53} +3.39961 q^{54} +(-1.08121 + 1.87270i) q^{55} +(-3.54816 + 6.14560i) q^{56} +(-2.89875 - 5.02078i) q^{57} -0.365178 q^{58} +(-0.839102 + 1.45337i) q^{59} +1.12607 q^{60} +0.829504 q^{61} +(3.17590 - 2.06539i) q^{62} -0.626091 q^{63} +1.06716 q^{64} +(-0.204382 + 0.354001i) q^{65} -6.45139 q^{66} +(2.70677 + 4.68826i) q^{67} +(4.83011 - 8.36599i) q^{68} +(0.927433 - 1.60636i) q^{69} -0.820103 q^{70} +(3.75892 + 6.51064i) q^{71} +(0.255510 + 0.442555i) q^{72} +(6.20487 + 10.7471i) q^{73} +(-1.64865 + 2.85554i) q^{74} +(-4.33101 - 7.50153i) q^{75} +(-2.48589 + 4.30568i) q^{76} -15.5985 q^{77} -1.21952 q^{78} +(4.37564 - 7.57884i) q^{79} +(-0.293596 - 0.508522i) q^{80} +(4.79596 - 8.30684i) q^{81} +(-2.91926 - 5.05630i) q^{82} +(-5.05412 - 8.75399i) q^{83} +(4.06143 + 7.03460i) q^{84} +2.56909 q^{85} +(-1.30426 + 2.25905i) q^{86} +(-0.480958 + 0.833044i) q^{87} +(6.36578 + 11.0258i) q^{88} +17.4073 q^{89} +(-0.0295286 + 0.0511450i) q^{90} -2.94861 q^{91} -1.59068 q^{92} +(-0.528756 - 9.96508i) q^{93} +3.41407 q^{94} -1.32222 q^{95} +(5.18939 - 8.98829i) q^{96} +12.7634 q^{97} +(-0.576414 - 0.998378i) q^{98} +(-0.561637 + 0.972783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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