LMFDB - Embedded newform 385.2.i.c.331.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, 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("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 17 x^{14} - 28 x^{13} + 127 x^{12} - 178 x^{11} + 612 x^{10} - 527 x^{9} + 1556 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 17x^14 - 28x^13 + 127x^12 - 178x^11 + 612x^10 - 527x^9 + 1556x^8 - 1065x^7 + 2812x^6 - 1224x^5 + 2359x^4 - 1154x^3 + 1351x^2 - 333*x + 81
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			331.2
Root			$1.25936 - 2.18128i$ of defining polynomial
Character	$\chi$	$=$	385.331
Dual form			385.2.i.c.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25936 + 2.18128i) q^{2} +(1.64549 + 2.85007i) q^{3} +(-2.17198 - 3.76198i) q^{4} +(-0.500000 + 0.866025i) q^{5} -8.28906 q^{6} +(-0.160806 + 2.64086i) q^{7} +5.90377 q^{8} +(-3.91527 + 6.78146i) q^{9} +O(q^{10})$	\(q+(-1.25936 + 2.18128i) q^{2} +(1.64549 + 2.85007i) q^{3} +(-2.17198 - 3.76198i) q^{4} +(-0.500000 + 0.866025i) q^{5} -8.28906 q^{6} +(-0.160806 + 2.64086i) q^{7} +5.90377 q^{8} +(-3.91527 + 6.78146i) q^{9} +(-1.25936 - 2.18128i) q^{10} +(0.500000 + 0.866025i) q^{11} +(7.14794 - 12.3806i) q^{12} +5.30061 q^{13} +(-5.55793 - 3.67656i) q^{14} -3.29098 q^{15} +(-3.09102 + 5.35380i) q^{16} +(-0.896554 - 1.55288i) q^{17} +(-9.86149 - 17.0806i) q^{18} +(2.74517 - 4.75477i) q^{19} +4.34396 q^{20} +(-7.79125 + 3.88720i) q^{21} -2.51872 q^{22} +(0.254764 - 0.441264i) q^{23} +(9.71460 + 16.8262i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-6.67538 + 11.5621i) q^{26} -15.8972 q^{27} +(10.2841 - 5.13094i) q^{28} +4.77451 q^{29} +(4.14453 - 7.17854i) q^{30} +(-2.80992 - 4.86692i) q^{31} +(-1.88165 - 3.25911i) q^{32} +(-1.64549 + 2.85007i) q^{33} +4.51634 q^{34} +(-2.20665 - 1.45969i) q^{35} +34.0156 q^{36} +(3.09749 - 5.36501i) q^{37} +(6.91432 + 11.9759i) q^{38} +(8.72211 + 15.1071i) q^{39} +(-2.95189 + 5.11282i) q^{40} +1.28221 q^{41} +(1.33293 - 21.8902i) q^{42} +6.22470 q^{43} +(2.17198 - 3.76198i) q^{44} +(-3.91527 - 6.78146i) q^{45} +(0.641679 + 1.11142i) q^{46} +(-5.58621 + 9.67560i) q^{47} -20.3450 q^{48} +(-6.94828 - 0.849331i) q^{49} +2.51872 q^{50} +(2.95054 - 5.11049i) q^{51} +(-11.5128 - 19.9408i) q^{52} +(-0.942640 - 1.63270i) q^{53} +(20.0204 - 34.6763i) q^{54} -1.00000 q^{55} +(-0.949360 + 15.5910i) q^{56} +18.0686 q^{57} +(-6.01283 + 10.4145i) q^{58} +(2.90126 + 5.02513i) q^{59} +(7.14794 + 12.3806i) q^{60} +(-0.971912 + 1.68340i) q^{61} +14.1548 q^{62} +(-17.2793 - 11.4302i) q^{63} -2.88540 q^{64} +(-2.65031 + 4.59047i) q^{65} +(-4.14453 - 7.17854i) q^{66} +(-0.889722 - 1.54104i) q^{67} +(-3.89459 + 6.74563i) q^{68} +1.67685 q^{69} +(5.96296 - 2.97503i) q^{70} -3.97341 q^{71} +(-23.1149 + 40.0362i) q^{72} +(-1.49881 - 2.59601i) q^{73} +(7.80171 + 13.5130i) q^{74} +(1.64549 - 2.85007i) q^{75} -23.8498 q^{76} +(-2.36745 + 1.18117i) q^{77} -43.9371 q^{78} +(-2.31838 + 4.01556i) q^{79} +(-3.09102 - 5.35380i) q^{80} +(-14.4129 - 24.9639i) q^{81} +(-1.61477 + 2.79686i) q^{82} +4.07571 q^{83} +(31.5460 + 20.8676i) q^{84} +1.79311 q^{85} +(-7.83915 + 13.5778i) q^{86} +(7.85640 + 13.6077i) q^{87} +(2.95189 + 5.11282i) q^{88} +(-1.55858 + 2.69955i) q^{89} +19.7230 q^{90} +(-0.852369 + 13.9982i) q^{91} -2.21337 q^{92} +(9.24739 - 16.0169i) q^{93} +(-14.0701 - 24.3701i) q^{94} +(2.74517 + 4.75477i) q^{95} +(6.19246 - 10.7257i) q^{96} +12.0725 q^{97} +(10.6030 - 14.0865i) q^{98} -7.83055 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.25936	+	2.18128i	−0.890502	+	1.54240i	−0.0512281	+	0.998687i	$0.516314\pi$
$2$	−1.25936	+	2.18128i	−0.890502	+	1.54240i	−0.839274	+	0.543708i	$0.817020\pi$
$3$	1.64549	+	2.85007i	0.950024	+	1.64549i	0.745365	+	0.666657i	$0.232275\pi$
$3$	1.64549	+	2.85007i	0.950024	+	1.64549i	0.204659	+	0.978833i	$0.434391\pi$
$4$	−2.17198	−	3.76198i	−1.08599	−	1.88099i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−8.28906			−3.38399
$7$	−0.160806	+	2.64086i	−0.0607788	+	0.998151i
$7$	−0.160806	+	2.64086i	−0.0607788	+	0.998151i
$8$	5.90377			2.08730
$9$	−3.91527	+	6.78146i	−1.30509	+	2.26049i
$10$	−1.25936	−	2.18128i	−0.398245	−	0.689780i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	7.14794	−	12.3806i	2.06343	−	3.57397i
$13$	5.30061			1.47013			0.735063	−	0.677999i	$-0.237153\pi$
$13$	5.30061			1.47013			0.735063	+	0.677999i	$0.237153\pi$
$14$	−5.55793	−	3.67656i	−1.48542	−	0.982601i
$15$	−3.29098			−0.849727
$16$	−3.09102	+	5.35380i	−0.772755	+	1.33845i
$17$	−0.896554	−	1.55288i	−0.217446	−	0.376628i	0.736580	−	0.676350i	$-0.236439\pi$
$17$	−0.896554	−	1.55288i	−0.217446	−	0.376628i	−0.954027	+	0.299722i	$0.903106\pi$
$18$	−9.86149	−	17.0806i	−2.32437	−	4.02593i
$19$	2.74517	−	4.75477i	0.629785	−	1.09082i	−0.357810	−	0.933795i	$-0.616476\pi$
$19$	2.74517	−	4.75477i	0.629785	−	1.09082i	0.987595	−	0.157025i	$-0.0501903\pi$
$20$	4.34396			0.971338
$21$	−7.79125	+	3.88720i	−1.70019	+	0.848257i
$22$	−2.51872			−0.536993
$23$	0.254764	−	0.441264i	0.0531219	−	0.0920099i	−0.838242	−	0.545299i	$-0.816416\pi$
$23$	0.254764	−	0.441264i	0.0531219	−	0.0920099i	0.891364	+	0.453289i	$0.149749\pi$
$24$	9.71460	+	16.8262i	1.98298	+	3.43463i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−6.67538	+	11.5621i	−1.30915	+	2.26751i
$27$	−15.8972			−3.05943
$28$	10.2841	−	5.13094i	1.94352	−	0.969657i
$29$	4.77451			0.886604			0.443302	−	0.896372i	$-0.353807\pi$
$29$	4.77451			0.886604			0.443302	+	0.896372i	$0.353807\pi$
$30$	4.14453	−	7.17854i	0.756684	−	1.31062i
$31$	−2.80992	−	4.86692i	−0.504676	−	0.874125i	−0.999985	−	0.00540823i	$-0.998278\pi$
$31$	−2.80992	−	4.86692i	−0.504676	−	0.874125i	0.495309	−	0.868717i	$-0.335055\pi$
$32$	−1.88165	−	3.25911i	−0.332631	−	0.576134i
$33$	−1.64549	+	2.85007i	−0.286443	+	0.496134i
$34$	4.51634			0.774546
$35$	−2.20665	−	1.45969i	−0.372992	−	0.246733i
$36$	34.0156			5.66926
$37$	3.09749	−	5.36501i	0.509224	−	0.882002i	−0.490719	−	0.871318i	$-0.663266\pi$
$37$	3.09749	−	5.36501i	0.509224	−	0.882002i	0.999943	−	0.0106838i	$-0.00340083\pi$
$38$	6.91432	+	11.9759i	1.12165	+	1.94275i
$39$	8.72211	+	15.1071i	1.39665	+	2.41908i
$40$	−2.95189	+	5.11282i	−0.466734	+	0.808407i
$41$	1.28221			0.200248			0.100124	−	0.994975i	$-0.468076\pi$
$41$	1.28221			0.200248			0.100124	+	0.994975i	$0.468076\pi$
$42$	1.33293	−	21.8902i	0.205675	−	3.37774i
$43$	6.22470			0.949259			0.474629	−	0.880186i	$-0.342582\pi$
$43$	6.22470			0.949259			0.474629	+	0.880186i	$0.342582\pi$
$44$	2.17198	−	3.76198i	0.327438	−	0.567139i
$45$	−3.91527	−	6.78146i	−0.583655	−	1.01092i
$46$	0.641679	+	1.11142i	0.0946104	+	0.163870i
$47$	−5.58621	+	9.67560i	−0.814833	+	1.41133i	0.0946154	+	0.995514i	$0.469838\pi$
$47$	−5.58621	+	9.67560i	−0.814833	+	1.41133i	−0.909448	+	0.415818i	$0.863495\pi$
$48$	−20.3450			−2.93654
$49$	−6.94828	−	0.849331i	−0.992612	−	0.121333i
$50$	2.51872			0.356201
$51$	2.95054	−	5.11049i	0.413158	−	0.715611i
$52$	−11.5128	−	19.9408i	−1.59654	−	2.76529i
$53$	−0.942640	−	1.63270i	−0.129482	−	0.224269i	0.793994	−	0.607925i	$-0.207998\pi$
$53$	−0.942640	−	1.63270i	−0.129482	−	0.224269i	−0.923476	+	0.383657i	$0.874665\pi$
$54$	20.0204	−	34.6763i	2.72443	−	4.71884i
$55$	−1.00000			−0.134840
$56$	−0.949360	+	15.5910i	−0.126864	+	2.08344i
$57$	18.0686			2.39324
$58$	−6.01283	+	10.4145i	−0.789523	+	1.36749i
$59$	2.90126	+	5.02513i	0.377712	+	0.654216i	0.990729	−	0.135854i	$-0.0433778\pi$
$59$	2.90126	+	5.02513i	0.377712	+	0.654216i	−0.613017	+	0.790069i	$0.710044\pi$
$60$	7.14794	+	12.3806i	0.922795	+	1.59833i
$61$	−0.971912	+	1.68340i	−0.124441	+	0.215537i	−0.921514	−	0.388345i	$-0.873047\pi$
$61$	−0.971912	+	1.68340i	−0.124441	+	0.215537i	0.797074	+	0.603882i	$0.206380\pi$
$62$	14.1548			1.79766
$63$	−17.2793	−	11.4302i	−2.17698	−	1.44007i
$64$	−2.88540			−0.360675
$65$	−2.65031	+	4.59047i	−0.328730	+	0.569377i
$66$	−4.14453	−	7.17854i	−0.510156	−	0.883617i
$67$	−0.889722	−	1.54104i	−0.108697	−	0.188269i	0.806546	−	0.591172i	$-0.201334\pi$
$67$	−0.889722	−	1.54104i	−0.108697	−	0.188269i	−0.915243	+	0.402903i	$0.868001\pi$
$68$	−3.89459	+	6.74563i	−0.472288	+	0.818028i
$69$	1.67685			0.201868
$70$	5.96296	−	2.97503i	0.712710	−	0.355584i
$71$	−3.97341			−0.471557			−0.235779	−	0.971807i	$-0.575764\pi$
$71$	−3.97341			−0.471557			−0.235779	+	0.971807i	$0.575764\pi$
$72$	−23.1149	+	40.0362i	−2.72412	+	4.71831i
$73$	−1.49881	−	2.59601i	−0.175422	−	0.303840i	0.764885	−	0.644167i	$-0.222796\pi$
$73$	−1.49881	−	2.59601i	−0.175422	−	0.303840i	−0.940307	+	0.340327i	$0.889462\pi$
$74$	7.80171	+	13.5130i	0.906930	+	1.57085i
$75$	1.64549	−	2.85007i	0.190005	−	0.329098i
$76$	−23.8498			−2.73576
$77$	−2.36745	+	1.18117i	−0.269797	+	0.134607i
$78$	−43.9371			−4.97490
$79$	−2.31838	+	4.01556i	−0.260839	+	0.451786i	−0.966465	−	0.256798i	$-0.917332\pi$
$79$	−2.31838	+	4.01556i	−0.260839	+	0.451786i	0.705626	+	0.708584i	$0.250666\pi$
$80$	−3.09102	−	5.35380i	−0.345587	−	0.598573i
$81$	−14.4129	−	24.9639i	−1.60144	−	2.77377i
$82$	−1.61477	+	2.79686i	−0.178321	+	0.308861i
$83$	4.07571			0.447367			0.223684	−	0.974662i	$-0.428192\pi$
$83$	4.07571			0.447367			0.223684	+	0.974662i	$0.428192\pi$
$84$	31.5460	+	20.8676i	3.44195	+	2.27684i
$85$	1.79311			0.194490
$86$	−7.83915	+	13.5778i	−0.845317	+	1.46413i
$87$	7.85640	+	13.6077i	0.842295	+	1.45890i
$88$	2.95189	+	5.11282i	0.314672	+	0.545028i
$89$	−1.55858	+	2.69955i	−0.165210	+	0.286151i	−0.936730	−	0.350054i	$-0.886163\pi$
$89$	−1.55858	+	2.69955i	−0.165210	+	0.286151i	0.771520	+	0.636205i	$0.219497\pi$
$90$	19.7230			2.07898
$91$	−0.852369	+	13.9982i	−0.0893525	+	1.46741i
$92$	−2.21337			−0.230759
$93$	9.24739	−	16.0169i	0.958909	−	1.66088i
$94$	−14.0701	−	24.3701i	−1.45122	−	2.51359i
$95$	2.74517	+	4.75477i	0.281648	+	0.487829i
$96$	6.19246	−	10.7257i	0.632015	−	1.09468i
$97$	12.0725			1.22578			0.612891	−	0.790168i	$-0.290007\pi$
$97$	12.0725			1.22578			0.612891	+	0.790168i	$0.290007\pi$
$98$	10.6030	−	14.0865i	1.07107	−	1.42295i
$99$	−7.83055			−0.787000
$100$	−2.17198	+	3.76198i	−0.217198	+	0.376198i
$101$	−3.90210	−	6.75864i	−0.388274	−	0.672510i	0.603944	−	0.797027i	$-0.293595\pi$
$101$	−3.90210	−	6.75864i	−0.388274	−	0.672510i	−0.992217	+	0.124517i	$0.960262\pi$
$102$	7.43159	+	12.8719i	0.735837	+	1.27451i
$103$	−4.80085	+	8.31531i	−0.473041	+	0.819332i	−0.999524	−	0.0308542i	$-0.990177\pi$
$103$	−4.80085	+	8.31531i	−0.473041	+	0.819332i	0.526482	+	0.850186i	$0.323511\pi$
$104$	31.2936			3.06859
$105$	0.529208	−	8.69102i	0.0516454	−	0.848156i
$106$	4.74850			0.461215
$107$	−5.72515	+	9.91625i	−0.553471	+	0.958640i	0.444550	+	0.895754i	$0.353364\pi$
$107$	−5.72515	+	9.91625i	−0.553471	+	0.958640i	−0.998021	+	0.0628859i	$0.979970\pi$
$108$	34.5285	+	59.8050i	3.32250	+	5.75474i
$109$	−3.82026	−	6.61688i	−0.365914	−	0.633782i	0.623008	−	0.782215i	$-0.285910\pi$
$109$	−3.82026	−	6.61688i	−0.365914	−	0.633782i	−0.988922	+	0.148433i	$0.952577\pi$
$110$	1.25936	−	2.18128i	0.120075	−	0.207977i
$111$	20.3875			1.93510
$112$	−13.6416	−	9.02387i	−1.28901	−	0.852676i
$113$	−2.21984			−0.208825			−0.104413	−	0.994534i	$-0.533296\pi$
$113$	−2.21984			−0.208825			−0.104413	+	0.994534i	$0.533296\pi$
$114$	−22.7549	+	39.4126i	−2.13119	+	3.69133i
$115$	0.254764	+	0.441264i	0.0237568	+	0.0411481i
$116$	−10.3701	−	17.9616i	−0.962842	−	1.66769i
$117$	−20.7534	+	35.9459i	−1.91865	+	3.32320i
$118$	−14.6149			−1.34541
$119$	4.24510	−	2.11796i	0.389148	−	0.194153i
$120$	−19.4292			−1.77363
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−2.44797	−	4.24002i	−0.221629	−	0.383873i
$123$	2.10987	+	3.65440i	0.190240	+	0.329506i
$124$	−12.2062	+	21.1417i	−1.09615	+	1.89858i
$125$	1.00000			0.0894427
$126$	46.6932	−	23.2961i	4.15976	−	2.07539i
$127$	−2.58387			−0.229281			−0.114641	−	0.993407i	$-0.536572\pi$
$127$	−2.58387			−0.229281			−0.114641	+	0.993407i	$0.536572\pi$
$128$	7.39705	−	12.8121i	0.653813	−	1.13244i
$129$	10.2427	+	17.7409i	0.901818	+	1.56200i
$130$	−6.67538	−	11.5621i	−0.585470	−	1.01406i
$131$	7.99801	−	13.8530i	0.698790	−	1.21034i	−0.270097	−	0.962833i	$-0.587056\pi$
$131$	7.99801	−	13.8530i	0.698790	−	1.21034i	0.968886	−	0.247506i	$-0.0796110\pi$
$132$	14.2959			1.24430
$133$	12.1152	+	8.01420i	1.05053	+	0.694919i
$134$	4.48193			0.387179
$135$	7.94862	−	13.7674i	0.684108	−	1.18491i
$136$	−5.29305	−	9.16783i	−0.453875	−	0.786135i
$137$	−2.54234	−	4.40346i	−0.217207	−	0.376213i	0.736746	−	0.676169i	$-0.236361\pi$
$137$	−2.54234	−	4.40346i	−0.217207	−	0.376213i	−0.953953	+	0.299956i	$0.903028\pi$
$138$	−2.11175	+	3.65766i	−0.179764	+	0.311361i
$139$	−5.27535			−0.447450			−0.223725	−	0.974652i	$-0.571822\pi$
$139$	−5.27535			−0.447450			−0.223725	+	0.974652i	$0.571822\pi$
$140$	−0.698533	+	11.4718i	−0.0590368	+	0.969542i
$141$	−36.7682			−3.09644
$142$	5.00396	−	8.66711i	0.419923	−	0.727328i
$143$	2.65031	+	4.59047i	0.221630	+	0.383874i
$144$	−24.2044	−	41.9232i	−2.01703	−	3.49360i
$145$	−2.38725	+	4.13484i	−0.198251	+	0.343380i
$146$	7.55015			0.624855
$147$	−9.01268	−	21.2007i	−0.743353	−	1.74860i
$148$	−26.9107			−2.21205
$149$	6.39221	−	11.0716i	0.523670	−	0.907024i	−0.475950	−	0.879472i	$-0.657896\pi$
$149$	6.39221	−	11.0716i	0.523670	−	0.907024i	0.999620	−	0.0275514i	$-0.00877101\pi$
$150$	4.14453	+	7.17854i	0.338399	+	0.586125i
$151$	2.92268	+	5.06223i	0.237844	+	0.411958i	0.960095	−	0.279673i	$-0.0902259\pi$
$151$	2.92268	+	5.06223i	0.237844	+	0.411958i	−0.722251	+	0.691631i	$0.756893\pi$
$152$	16.2068	−	28.0711i	1.31455	−	2.27687i
$153$	14.0410			1.13515
$154$	0.405025	−	6.65159i	0.0326378	−	0.536000i
$155$	5.61984			0.451396
$156$	37.8884	−	65.6247i	3.03350	−	5.25418i
$157$	−4.88908	−	8.46814i	−0.390191	−	0.675831i	0.602283	−	0.798282i	$-0.294258\pi$
$157$	−4.88908	−	8.46814i	−0.390191	−	0.675831i	−0.992475	+	0.122451i	$0.960924\pi$
$158$	−5.83936	−	10.1141i	−0.464555	−	0.804633i
$159$	3.10221	−	5.37319i	0.246021	−	0.426121i
$160$	3.76329			0.297514
$161$	1.12435	+	0.743753i	0.0886111	+	0.0586160i
$162$	72.6043			5.70433
$163$	8.62783	−	14.9438i	0.675784	−	1.17049i	−0.300455	−	0.953796i	$-0.597138\pi$
$163$	8.62783	−	14.9438i	0.675784	−	1.17049i	0.976239	−	0.216696i	$-0.0695282\pi$
$164$	−2.78494	−	4.82365i	−0.217467	−	0.376664i
$165$	−1.64549	−	2.85007i	−0.128101	−	0.221878i
$166$	−5.13279	+	8.89025i	−0.398382	+	0.690017i
$167$	−9.48832			−0.734228			−0.367114	−	0.930176i	$-0.619654\pi$
$167$	−9.48832			−0.734228			−0.367114	+	0.930176i	$0.619654\pi$
$168$	−45.9977	+	22.9491i	−3.54880	+	1.77056i
$169$	15.0965			1.16127
$170$	−2.25817	+	3.91126i	−0.173194	+	0.299980i
$171$	21.4962	+	37.2325i	1.64385	+	2.84724i
$172$	−13.5199	−	23.4172i	−1.03088	−	1.78554i
$173$	0.347422	−	0.601752i	0.0264140	−	0.0457504i	−0.852516	−	0.522701i	$-0.824925\pi$
$173$	0.347422	−	0.601752i	0.0264140	−	0.0457504i	0.878930	+	0.476950i	$0.158258\pi$
$174$	−39.5762			−3.00026
$175$	2.36745	−	1.18117i	0.178963	−	0.0892879i
$176$	−6.18204			−0.465989
$177$	−9.54798	+	16.5376i	−0.717670	+	1.24304i
$178$	−3.92564	−	6.79940i	−0.294239	−	0.509637i
$179$	−1.50595	−	2.60838i	−0.112560	−	0.194959i	0.804242	−	0.594302i	$-0.202572\pi$
$179$	−1.50595	−	2.60838i	−0.112560	−	0.194959i	−0.916802	+	0.399343i	$0.869238\pi$
$180$	−17.0078	+	29.4583i	−1.26769	+	2.19570i
$181$	−22.1739			−1.64817			−0.824085	−	0.566466i	$-0.808310\pi$
$181$	−22.1739			−1.64817			−0.824085	+	0.566466i	$0.808310\pi$
$182$	−29.4605	−	19.4880i	−2.18375	−	1.44455i
$183$	−6.39708			−0.472886
$184$	1.50407	−	2.60512i	0.110881	−	0.192052i
$185$	3.09749	+	5.36501i	0.227732	+	0.394443i
$186$	23.2916	+	40.3422i	1.70782	+	2.95803i
$187$	0.896554	−	1.55288i	0.0655625	−	0.113558i
$188$	48.5325			3.53960
$189$	2.55637	−	41.9824i	0.185948	−	3.05377i
$190$	−13.8286			−1.00323
$191$	−10.3182	+	17.8716i	−0.746595	+	1.29314i	0.202850	+	0.979210i	$0.434979\pi$
$191$	−10.3182	+	17.8716i	−0.746595	+	1.29314i	−0.949446	+	0.313931i	$0.898354\pi$
$192$	−4.74789	−	8.22359i	−0.342649	−	0.593486i
$193$	2.26204	+	3.91796i	0.162825	+	0.282021i	0.935881	−	0.352317i	$-0.114606\pi$
$193$	2.26204	+	3.91796i	0.162825	+	0.282021i	−0.773056	+	0.634338i	$0.781273\pi$
$194$	−15.2037	+	26.3336i	−1.09156	+	1.89064i
$195$	−17.4442			−1.24921
$196$	11.8964	+	27.9840i	0.849740	+	1.99886i
$197$	10.9741			0.781871			0.390935	−	0.920418i	$-0.372152\pi$
$197$	10.9741			0.781871			0.390935	+	0.920418i	$0.372152\pi$
$198$	9.86149	−	17.0806i	0.700825	−	1.21386i
$199$	5.71858	+	9.90487i	0.405379	+	0.702138i	0.994366	−	0.106005i	$-0.0338061\pi$
$199$	5.71858	+	9.90487i	0.405379	+	0.702138i	−0.588986	+	0.808143i	$0.700473\pi$
$200$	−2.95189	−	5.11282i	−0.208730	−	0.361531i
$201$	2.92806	−	5.07155i	0.206529	−	0.357719i
$202$	19.6566			1.38303
$203$	−0.767768	+	12.6088i	−0.0538867	+	0.884965i
$204$	−25.6340			−1.79474
$205$	−0.641106	+	1.11043i	−0.0447768	+	0.0775557i
$206$	−12.0920	−	20.9439i	−0.842489	−	1.45923i
$207$	1.99494	+	3.45534i	0.138658	+	0.240163i
$208$	−16.3843	+	28.3784i	−1.13605	+	1.96769i
$209$	5.49034			0.379775
$210$	18.2910	+	12.0995i	1.26220	+	0.834943i
$211$	20.3863			1.40345			0.701724	−	0.712449i	$-0.252414\pi$
$211$	20.3863			1.40345			0.701724	+	0.712449i	$0.252414\pi$
$212$	−4.09479	+	7.09238i	−0.281231	+	0.487107i
$213$	−6.53821	−	11.3245i	−0.447991	−	0.775943i
$214$	−14.4201	−	24.9763i	−0.985735	−	1.70734i
$215$	−3.11235	+	5.39075i	−0.212261	+	0.367646i
$216$	−93.8537			−6.38593
$217$	13.3047	−	6.63797i	0.903183	−	0.450615i
$218$	19.2443			1.30339
$219$	4.93254	−	8.54341i	0.333310	−	0.577310i
$220$	2.17198	+	3.76198i	0.146435	+	0.253632i
$221$	−4.75229	−	8.23120i	−0.319673	−	0.553690i
$222$	−25.6753	+	44.4709i	−1.72321	+	2.98469i
$223$	15.0377			1.00700			0.503501	−	0.863995i	$-0.332045\pi$
$223$	15.0377			1.00700			0.503501	+	0.863995i	$0.332045\pi$
$224$	8.90942	−	4.44508i	0.595286	−	0.296999i
$225$	7.83055			0.522037
$226$	2.79558	−	4.84209i	0.185959	−	0.322091i
$227$	10.3170	+	17.8695i	0.684763	+	1.18604i	0.973511	+	0.228639i	$0.0734274\pi$
$227$	10.3170	+	17.8695i	0.684763	+	1.18604i	−0.288749	+	0.957405i	$0.593239\pi$
$228$	−39.2446	−	67.9736i	−2.59904	−	4.50166i
$229$	11.0890	−	19.2067i	0.732781	−	1.26921i	−0.222909	−	0.974839i	$-0.571555\pi$
$229$	11.0890	−	19.2067i	0.732781	−	1.26921i	0.955690	−	0.294374i	$-0.0951113\pi$
$230$	−1.28336			−0.0846221
$231$	−7.26204	−	4.80382i	−0.477807	−	0.316068i
$232$	28.1876			1.85061
$233$	12.8249	−	22.2135i	0.840190	−	1.45525i	−0.0495433	−	0.998772i	$-0.515777\pi$
$233$	12.8249	−	22.2135i	0.840190	−	1.45525i	0.889734	−	0.456480i	$-0.150890\pi$
$234$	−52.2719	−	90.5376i	−3.41712	−	5.91863i
$235$	−5.58621	−	9.67560i	−0.364404	−	0.631167i
$236$	12.6029	−	21.8289i	0.820381	−	1.42094i
$237$	−15.2595			−0.991212
$238$	−0.726253	+	11.9270i	−0.0470760	+	0.773114i
$239$	−27.3883			−1.77160			−0.885799	−	0.464068i	$-0.846389\pi$
$239$	−27.3883			−1.77160			−0.885799	+	0.464068i	$0.846389\pi$
$240$	10.1725	−	17.6193i	0.656631	−	1.13732i
$241$	11.8476	+	20.5206i	0.763169	+	1.32185i	0.941209	+	0.337824i	$0.109691\pi$
$241$	11.8476	+	20.5206i	0.763169	+	1.32185i	−0.178041	+	0.984023i	$0.556976\pi$
$242$	−1.25936	−	2.18128i	−0.0809548	−	0.140218i
$243$	23.5868	−	40.8535i	1.51309	−	2.62076i
$244$	8.44388			0.540564
$245$	4.20968	−	5.59272i	0.268947	−	0.357306i
$246$	−10.6283			−0.677638
$247$	14.5511	−	25.2032i	0.925863	−	1.60364i
$248$	−16.5891	−	28.7332i	−1.05341	−	1.82456i
$249$	6.70654	+	11.6161i	0.425010	+	0.736138i
$250$	−1.25936	+	2.18128i	−0.0796490	+	0.137956i
$251$	21.5663			1.36125			0.680626	−	0.732631i	$-0.261708\pi$
$251$	21.5663			1.36125			0.680626	+	0.732631i	$0.261708\pi$
$252$	−5.46990	+	89.8303i	−0.344571	+	5.65878i
$253$	0.509528			0.0320337
$254$	3.25402	−	5.63613i	0.204175	−	0.353642i
$255$	2.95054	+	5.11049i	0.184770	+	0.320031i
$256$	15.7457	+	27.2724i	0.984106	+	1.70452i
$257$	−2.16024	+	3.74165i	−0.134752	+	0.233398i	−0.925503	−	0.378741i	$-0.876357\pi$
$257$	−2.16024	+	3.74165i	−0.134752	+	0.233398i	0.790751	+	0.612138i	$0.209690\pi$
$258$	−51.5970			−3.21229
$259$	13.6701	+	9.04276i	0.849421	+	0.561890i
$260$	23.0256			1.42799
$261$	−18.6935	+	32.3781i	−1.15710	+	2.00415i
$262$	20.1448	+	34.8918i	1.24455	+	2.15562i
$263$	−7.35395	−	12.7374i	−0.453464	−	0.785422i	0.545135	−	0.838349i	$-0.316479\pi$
$263$	−7.35395	−	12.7374i	−0.453464	−	0.785422i	−0.998598	+	0.0529261i	$0.983145\pi$
$264$	−9.71460	+	16.8262i	−0.597892	+	1.03558i
$265$	1.88528			0.115812
$266$	−32.7387	+	16.3339i	−2.00734	+	1.00150i
$267$	−10.2585			−0.627812
$268$	−3.86491	+	6.69423i	−0.236087	+	0.408915i
$269$	8.42786	+	14.5975i	0.513855	+	0.890024i	0.999871	+	0.0160735i	$0.00511658\pi$
$269$	8.42786	+	14.5975i	0.513855	+	0.890024i	−0.486015	+	0.873950i	$0.661550\pi$
$270$	20.0204	+	34.6763i	1.21840	+	2.11033i
$271$	10.2708	−	17.7896i	0.623907	−	1.08064i	−0.364844	−	0.931069i	$-0.618878\pi$
$271$	10.2708	−	17.7896i	0.623907	−	1.08064i	0.988751	−	0.149571i	$-0.0477891\pi$
$272$	11.0851			0.672131
$273$	−41.2984	+	20.6045i	−2.49949	+	1.24704i
$274$	12.8069			0.773692
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−3.64207	−	6.30825i	−0.219227	−	0.379712i
$277$	−5.56694	−	9.64222i	−0.334485	−	0.579345i	0.648901	−	0.760873i	$-0.275229\pi$
$277$	−5.56694	−	9.64222i	−0.334485	−	0.579345i	−0.983386	+	0.181528i	$0.941896\pi$
$278$	6.64357	−	11.5070i	0.398455	−	0.690144i
$279$	44.0064			2.63460
$280$	−13.0275	−	8.61769i	−0.778545	−	0.515005i
$281$	10.6506			0.635364			0.317682	−	0.948197i	$-0.397096\pi$
$281$	10.6506			0.635364			0.317682	+	0.948197i	$0.397096\pi$
$282$	46.3044	−	80.2016i	2.75739	−	4.77594i
$283$	12.7198	+	22.0313i	0.756113	+	1.30963i	0.944819	+	0.327593i	$0.106237\pi$
$283$	12.7198	+	22.0313i	0.756113	+	1.30963i	−0.188706	+	0.982034i	$0.560429\pi$
$284$	8.63016	+	14.9479i	0.512106	+	0.886993i
$285$	−9.03430	+	15.6479i	−0.535146	+	0.926899i
$286$	−13.3508			−0.789447
$287$	−0.206187	+	3.38614i	−0.0121708	+	0.199878i
$288$	29.4686			1.73646
$289$	6.89238	−	11.9380i	0.405434	−	0.702233i
$290$	−6.01283	−	10.4145i	−0.353085	−	0.611562i
$291$	19.8653	+	34.4076i	1.16452	+	2.01701i
$292$	−6.51075	+	11.2769i	−0.381013	+	0.659934i
$293$	−4.15823			−0.242926			−0.121463	−	0.992596i	$-0.538759\pi$
$293$	−4.15823			−0.242926			−0.121463	+	0.992596i	$0.538759\pi$
$294$	57.5947	+	7.04015i	3.35899	+	0.410590i
$295$	−5.80252			−0.337836
$296$	18.2869	−	31.6738i	1.06290	−	1.84100i
$297$	−7.94862	−	13.7674i	−0.461226	−	0.798867i
$298$	16.1002	+	27.8864i	0.932660	+	1.61541i
$299$	1.35040	−	2.33897i	0.0780959	−	0.135266i
$300$	−14.2959			−0.825373
$301$	−1.00097	+	16.4386i	−0.0576948	+	0.947504i
$302$	−14.7228			−0.847203
$303$	12.8417	−	22.2425i	0.737739	−	1.27780i
$304$	16.9707	+	29.3942i	0.973339	+	1.68587i
$305$	−0.971912	−	1.68340i	−0.0556515	−	0.0963912i
$306$	−17.6827	+	30.6273i	−1.01085	+	1.75085i
$307$	16.8008			0.958872			0.479436	−	0.877577i	$-0.340841\pi$
$307$	16.8008			0.958872			0.479436	+	0.877577i	$0.340841\pi$
$308$	9.58559	+	6.34084i	0.546189	+	0.361303i
$309$	−31.5990			−1.79760
$310$	−7.07740	+	12.2584i	−0.401969	+	0.696231i
$311$	−2.41248	−	4.17854i	−0.136799	−	0.236943i	0.789484	−	0.613771i	$-0.210348\pi$
$311$	−2.41248	−	4.17854i	−0.136799	−	0.236943i	−0.926283	+	0.376828i	$0.877015\pi$
$312$	51.4933	+	89.1890i	2.91523	+	5.04933i
$313$	−12.9322	+	22.3993i	−0.730973	+	1.26608i	0.225494	+	0.974244i	$0.427600\pi$
$313$	−12.9322	+	22.3993i	−0.730973	+	1.26608i	−0.956468	+	0.291839i	$0.905733\pi$
$314$	24.6285			1.38986
$315$	18.5385	−	9.24920i	1.04452	−	0.521133i
$316$	20.1419			1.13307
$317$	4.49988	−	7.79402i	0.252738	−	0.437756i	−0.711540	−	0.702645i	$-0.752002\pi$
$317$	4.49988	−	7.79402i	0.252738	−	0.437756i	0.964279	+	0.264890i	$0.0853355\pi$
$318$	7.81360	+	13.5336i	0.438165	+	0.758924i
$319$	2.38725	+	4.13484i	0.133661	+	0.231507i
$320$	1.44270	−	2.49883i	0.0806493	−	0.139689i
$321$	−37.6827			−2.10324
$322$	−3.03829	+	1.51586i	−0.169317	+	0.0844757i
$323$	−9.84477			−0.547778
$324$	−62.6091	+	108.442i	−3.47829	+	6.02457i
$325$	−2.65031	−	4.59047i	−0.147013	−	0.254633i
$326$	21.7311	+	37.6394i	1.20357	+	2.08465i
$327$	12.5724	−	21.7760i	0.695254	−	1.20422i
$328$	7.56989			0.417977
$329$	−24.6536	−	16.3083i	−1.35920	−	0.899105i
$330$	8.28906			0.456298
$331$	12.5469	−	21.7318i	0.689639	−	1.19449i	−0.282316	−	0.959321i	$-0.591103\pi$
$331$	12.5469	−	21.7318i	0.689639	−	1.19449i	0.971955	−	0.235168i	$-0.0755640\pi$
$332$	−8.85235	−	15.3327i	−0.485836	−	0.841492i
$333$	24.2550	+	42.0110i	1.32917	+	2.30219i
$334$	11.9492	−	20.6966i	0.653832	−	1.13247i
$335$	1.77944			0.0972215
$336$	3.27159	−	53.7282i	0.178480	−	2.93111i
$337$	−23.0416			−1.25516			−0.627578	−	0.778554i	$-0.715954\pi$
$337$	−23.0416			−1.25516			−0.627578	+	0.778554i	$0.715954\pi$
$338$	−19.0119	+	32.9296i	−1.03411	+	1.79114i
$339$	−3.65273	−	6.32671i	−0.198389	−	0.343620i
$340$	−3.89459	−	6.74563i	−0.211214	−	0.365833i
$341$	2.80992	−	4.86692i	0.152166	−	0.263559i
$342$	−108.286			−5.85542
$343$	3.36029	−	18.2129i	0.181438	−	0.983402i
$344$	36.7492			1.98139
$345$	−0.838423	+	1.45219i	−0.0451392	+	0.0781833i
$346$	0.875059	+	1.51565i	0.0470435	+	0.0814816i
$347$	−5.50593	−	9.53654i	−0.295574	−	0.511948i	0.679545	−	0.733634i	$-0.262177\pi$
$347$	−5.50593	−	9.53654i	−0.295574	−	0.511948i	−0.975118	+	0.221686i	$0.928844\pi$
$348$	34.1279	−	59.1112i	1.82945	−	3.16869i
$349$	−34.2561			−1.83369			−0.916844	−	0.399245i	$-0.869272\pi$
$349$	−34.2561			−1.83369			−0.916844	+	0.399245i	$0.869272\pi$
$350$	−0.405025	+	6.65159i	−0.0216495	+	0.355542i
$351$	−84.2651			−4.49774
$352$	1.88165	−	3.25911i	0.100292	−	0.173711i
$353$	0.747336	+	1.29442i	0.0397767	+	0.0688952i	0.885228	−	0.465157i	$-0.154002\pi$
$353$	0.747336	+	1.29442i	0.0397767	+	0.0688952i	−0.845452	+	0.534052i	$0.820669\pi$
$354$	−24.0487	−	41.6536i	−1.27817	−	2.21386i
$355$	1.98671	−	3.44107i	0.105443	−	0.182633i
$356$	13.5408			0.717663
$357$	13.0216	+	8.61376i	0.689177	+	0.455889i
$358$	7.58612			0.400939
$359$	−9.49155	+	16.4398i	−0.500945	+	0.867662i	0.499055	+	0.866571i	$0.333681\pi$
$359$	−9.49155	+	16.4398i	−0.500945	+	0.867662i	−0.999999	+	0.00109139i	$0.999653\pi$
$360$	−23.1149	−	40.0362i	−1.21826	−	2.11009i
$361$	−5.57191	−	9.65083i	−0.293258	−	0.507938i
$362$	27.9249	−	48.3673i	1.46770	−	2.54213i
$363$	−3.29098			−0.172732
$364$	54.5121	−	27.1971i	2.85721	−	1.42552i
$365$	2.99761			0.156902
$366$	8.05624	−	13.9538i	0.421106	−	0.729377i
$367$	7.32783	+	12.6922i	0.382509	+	0.662526i	0.991420	−	0.130713i	$-0.0417266\pi$
$367$	7.32783	+	12.6922i	0.382509	+	0.662526i	−0.608911	+	0.793239i	$0.708393\pi$
$368$	1.57496	+	2.72791i	0.0821005	+	0.142202i
$369$	−5.02021	+	8.69526i	−0.261342	+	0.452657i
$370$	−15.6034			−0.811183
$371$	4.46332	−	2.22683i	0.231724	−	0.115611i
$372$	−80.3405			−4.16546
$373$	−12.7808	+	22.1370i	−0.661765	+	1.14621i	0.318386	+	0.947961i	$0.396859\pi$
$373$	−12.7808	+	22.1370i	−0.661765	+	1.14621i	−0.980151	+	0.198250i	$0.936474\pi$
$374$	2.25817	+	3.91126i	0.116767	+	0.202247i
$375$	1.64549	+	2.85007i	0.0849727	+	0.147177i
$376$	−32.9797	+	57.1225i	−1.70080	+	2.94587i
$377$	25.3078			1.30342
$378$	88.3558	+	58.4471i	4.54453	+	3.00620i
$379$	−30.9775			−1.59121			−0.795604	−	0.605817i	$-0.792846\pi$
$379$	−30.9775			−1.59121			−0.795604	+	0.605817i	$0.792846\pi$
$380$	11.9249	−	20.6545i	0.611734	−	1.05955i
$381$	−4.25173	−	7.36421i	−0.217823	−	0.377280i
$382$	−25.9885	−	45.0135i	−1.32969	−	2.30309i
$383$	17.2216	−	29.8286i	0.879980	−	1.52417i	0.0286190	−	0.999590i	$-0.490889\pi$
$383$	17.2216	−	29.8286i	0.879980	−	1.52417i	0.851361	−	0.524580i	$-0.175778\pi$
$384$	48.6871			2.48455
$385$	0.160806	−	2.64086i	0.00819542	−	0.134591i
$386$	−11.3949			−0.579984
$387$	−24.3714	+	42.2126i	−1.23887	+	2.14578i
$388$	−26.2213	−	45.4166i	−1.33119	−	2.30568i
$389$	2.71565	+	4.70364i	0.137689	+	0.238484i	0.926621	−	0.375996i	$-0.122699\pi$
$389$	2.71565	+	4.70364i	0.137689	+	0.238484i	−0.788933	+	0.614480i	$0.789366\pi$
$390$	21.9686	−	38.0507i	1.11242	−	1.92677i
$391$	−0.913638			−0.0462047
$392$	−41.0211	−	5.01425i	−2.07188	−	0.253258i
$393$	52.6426			2.65547
$394$	−13.8203	+	23.9375i	−0.696258	+	1.20595i
$395$	−2.31838	−	4.01556i	−0.116651	−	0.202045i
$396$	17.0078	+	29.4583i	0.854673	+	1.48034i
$397$	−15.1045	+	26.1617i	−0.758072	+	1.31302i	0.185760	+	0.982595i	$0.440525\pi$
$397$	−15.1045	+	26.1617i	−0.758072	+	1.31302i	−0.943832	+	0.330424i	$0.892808\pi$
$398$	−28.8070			−1.44397
$399$	−2.90553	+	47.7166i	−0.145459	+	2.38882i
$400$	6.18204			0.309102
$401$	3.24446	−	5.61958i	0.162021	−	0.280628i	−0.773572	−	0.633708i	$-0.781532\pi$
$401$	3.24446	−	5.61958i	0.162021	−	0.280628i	0.935593	+	0.353080i	$0.114865\pi$
$402$	7.37496	+	12.7738i	0.367830	+	0.637100i
$403$	−14.8943	−	25.7977i	−0.741938	−	1.28507i
$404$	−16.9506	+	29.3592i	−0.843322	+	1.46068i
$405$	28.8259			1.43237
$406$	−26.5364	−	17.5537i	−1.31698	−	0.871178i
$407$	6.19498			0.307074
$408$	17.4193	−	30.1711i	0.862385	−	1.49369i
$409$	−1.86660	−	3.23305i	−0.0922974	−	0.159864i	0.816180	−	0.577798i	$-0.196088\pi$
$409$	−1.86660	−	3.23305i	−0.0922974	−	0.159864i	−0.908477	+	0.417934i	$0.862754\pi$
$410$	−1.61477	−	2.79686i	−0.0797477	−	0.138127i
$411$	8.36679	−	14.4917i	0.412703	−	0.714823i
$412$	41.7093			2.05487
$413$	−13.7372	+	6.85375i	−0.675963	+	0.337251i
$414$	−10.0494			−0.493901
$415$	−2.03785	+	3.52967i	−0.100034	+	0.173265i
$416$	−9.97388	−	17.2753i	−0.489010	−	0.846989i
$417$	−8.68054	−	15.0351i	−0.425088	−	0.736274i
$418$	−6.91432	+	11.9759i	−0.338190	+	0.585763i
$419$	−24.0207			−1.17349			−0.586744	−	0.809773i	$-0.699590\pi$
$419$	−24.0207			−1.17349			−0.586744	+	0.809773i	$0.699590\pi$
$420$	−33.8448	+	16.8858i	−1.65146	+	0.823944i
$421$	32.8926			1.60309			0.801544	−	0.597935i	$-0.204012\pi$
$421$	32.8926			1.60309			0.801544	+	0.597935i	$0.204012\pi$
$422$	−25.6736	+	44.4680i	−1.24977	+	2.16467i
$423$	−43.7431	−	75.7653i	−2.12686	−	3.68383i
$424$	−5.56513	−	9.63909i	−0.270267	−	0.468116i
$425$	−0.896554	+	1.55288i	−0.0434893	+	0.0753256i
$426$	32.9358			1.59575
$427$	−4.28934	−	2.83738i	−0.207576	−	0.137311i
$428$	49.7396			2.40425
$429$	−8.72211	+	15.1071i	−0.421107	+	0.729379i
$430$	−7.83915	−	13.5778i	−0.378037	−	0.654780i
$431$	−10.4365	−	18.0766i	−0.502711	−	0.870721i	−0.999995	−	0.00313303i	$-0.999003\pi$
$431$	−10.4365	−	18.0766i	−0.502711	−	0.870721i	0.497284	−	0.867588i	$-0.334331\pi$
$432$	49.1387	−	85.1107i	2.36419	−	4.09489i
$433$	−26.2218			−1.26014			−0.630069	−	0.776539i	$-0.716973\pi$
$433$	−26.2218			−1.26014			−0.630069	+	0.776539i	$0.716973\pi$
$434$	−2.27617	+	37.3809i	−0.109260	+	1.79434i
$435$	−15.7128			−0.753372
$436$	−16.5950	+	28.7434i	−0.794757	+	1.37656i
$437$	−1.39874	−	2.42269i	−0.0669108	−	0.115893i
$438$	12.4237	+	21.5185i	0.593627	+	1.02819i
$439$	−12.9144	+	22.3684i	−0.616371	+	1.06759i	0.373772	+	0.927521i	$0.378064\pi$
$439$	−12.9144	+	22.3684i	−0.616371	+	1.06759i	−0.990142	+	0.140065i	$0.955269\pi$
$440$	−5.90377			−0.281451
$441$	32.9641	−	43.7941i	1.56972	−	2.08543i
$442$	23.9394			1.13868
$443$	−8.29263	+	14.3632i	−0.393995	+	0.682419i	−0.992972	−	0.118347i	$-0.962240\pi$
$443$	−8.29263	+	14.3632i	−0.393995	+	0.682419i	0.598978	+	0.800766i	$0.295574\pi$
$444$	−44.2813	−	76.6975i	−2.10150	−	3.63990i
$445$	−1.55858	−	2.69955i	−0.0738839	−	0.127971i
$446$	−18.9379	+	32.8015i	−0.896737	+	1.55319i
$447$	42.0733			1.99000
$448$	0.463988	−	7.61993i	0.0219214	−	0.360008i
$449$	−36.6076			−1.72762			−0.863810	−	0.503818i	$-0.831928\pi$
$449$	−36.6076			−1.72762			−0.863810	+	0.503818i	$0.831928\pi$
$450$	−9.86149	+	17.0806i	−0.464875	+	0.805187i
$451$	0.641106	+	1.11043i	0.0301885	+	0.0522880i
$452$	4.82145	+	8.35099i	0.226782	+	0.392798i
$453$	−9.61848	+	16.6597i	−0.451915	+	0.782741i
$454$	−51.9712			−2.43913
$455$	−11.6966	−	7.73726i	−0.548345	−	0.362728i
$456$	106.673			4.99541
$457$	11.7200	−	20.2997i	0.548240	−	0.949579i	−0.450156	−	0.892950i	$-0.648632\pi$
$457$	11.7200	−	20.2997i	0.548240	−	0.949579i	0.998395	−	0.0566288i	$-0.0180351\pi$
$458$	27.9301	+	48.3763i	1.30509	+	2.26048i
$459$	14.2527	+	24.6865i	0.665261	+	1.15227i
$460$	1.10668	−	1.91683i	0.0515993	−	0.0893727i
$461$	−24.2805			−1.13086			−0.565428	−	0.824798i	$-0.691289\pi$
$461$	−24.2805			−1.13086			−0.565428	+	0.824798i	$0.691289\pi$
$462$	19.6240	−	9.79078i	0.912990	−	0.455508i
$463$	31.0998			1.44533			0.722665	−	0.691198i	$-0.242917\pi$
$463$	31.0998			1.44533			0.722665	+	0.691198i	$0.242917\pi$
$464$	−14.7581	+	25.5618i	−0.685127	+	1.18668i
$465$	9.24739	+	16.0169i	0.428837	+	0.742768i
$466$	32.3025	+	55.9495i	1.49638	+	2.59181i
$467$	3.81976	−	6.61602i	0.176757	−	0.306153i	−0.764011	−	0.645204i	$-0.776773\pi$
$467$	3.81976	−	6.61602i	0.176757	−	0.306153i	0.940768	+	0.339051i	$0.110106\pi$
$468$	180.303			8.33452
$469$	4.21276	−	2.10182i	0.194527	−	0.0970532i
$470$	28.1402			1.29801
$471$	16.0899	−	27.8685i	0.741382	−	1.28411i
$472$	17.1284	+	29.6672i	0.788397	+	1.36554i
$473$	3.11235	+	5.39075i	0.143106	+	0.247867i
$474$	19.2172	−	33.2852i	0.882677	−	1.52884i
$475$	−5.49034			−0.251914
$476$	−17.1880	−	11.3698i	−0.787810	−	0.521134i
$477$	14.7628			0.675942
$478$	34.4917	−	59.7414i	1.57761	−	2.73251i
$479$	−16.9556	−	29.3680i	−0.774723	−	1.34186i	−0.934950	−	0.354779i	$-0.884556\pi$
$479$	−16.9556	−	29.3680i	−0.774723	−	1.34186i	0.160228	−	0.987080i	$-0.448777\pi$
$480$	6.19246	+	10.7257i	0.282646	+	0.489557i
$481$	16.4186	−	28.4378i	0.748623	−	1.29665i
$482$	−59.6814			−2.71841
$483$	−0.269646	+	4.42831i	−0.0122693	+	0.201495i
$484$	4.34396			0.197453
$485$	−6.03627	+	10.4551i	−0.274093	+	0.474743i
$486$	59.4086	+	102.899i	2.69483	+	4.66758i
$487$	−11.3372	−	19.6367i	−0.513739	−	0.889822i	−0.999873	−	0.0159378i	$-0.994927\pi$
$487$	−11.3372	−	19.6367i	−0.513739	−	0.889822i	0.486134	−	0.873884i	$-0.338407\pi$
$488$	−5.73794	+	9.93841i	−0.259745	+	0.449891i
$489$	56.7881			2.56804
$490$	6.89777	+	16.2257i	0.311609	+	0.733004i
$491$	18.6463			0.841498			0.420749	−	0.907177i	$-0.361767\pi$
$491$	18.6463			0.841498			0.420749	+	0.907177i	$0.361767\pi$
$492$	9.16517	−	15.8745i	0.413198	−	0.715680i
$493$	−4.28060	−	7.41422i	−0.192789	−	0.333920i
$494$	36.6501	+	63.4799i	1.64897	+	2.85609i
$495$	3.91527	−	6.78146i	0.175979	−	0.304804i
$496$	34.7421			1.55996
$497$	0.638947	−	10.4932i	0.0286607	−	0.470685i
$498$	−33.7838			−1.51389
$499$	16.6753	−	28.8825i	0.746489	−	1.29296i	−0.203006	−	0.979177i	$-0.565071\pi$
$499$	16.6753	−	28.8825i	0.746489	−	1.29296i	0.949496	−	0.313780i	$-0.101595\pi$
$500$	−2.17198	−	3.76198i	−0.0971338	−	0.168241i
$501$	−15.6129	−	27.0424i	−0.697535	−	1.20817i
$502$	−27.1597	+	47.0420i	−1.21220	+	2.09959i
$503$	21.1300			0.942142			0.471071	−	0.882095i	$-0.343868\pi$
$503$	21.1300			0.942142			0.471071	+	0.882095i	$0.343868\pi$
$504$	−102.013	−	67.4812i	−4.54401	−	3.00585i
$505$	7.80420			0.347282
$506$	−0.641679	+	1.11142i	−0.0285261	+	0.0494087i
$507$	24.8411	+	43.0261i	1.10323	+	1.91086i
$508$	5.61211	+	9.72045i	0.248997	+	0.431275i
$509$	−2.84160	+	4.92180i	−0.125952	+	0.218155i	−0.922105	−	0.386941i	$-0.873532\pi$
$509$	−2.84160	+	4.92180i	−0.125952	+	0.218155i	0.796153	+	0.605096i	$0.206865\pi$
$510$	−14.8632			−0.658153
$511$	7.09671	−	3.54069i	0.313940	−	0.156631i
$512$	−49.7299			−2.19777
$513$	−43.6406	+	75.5878i	−1.92678	+	3.33728i
$514$	−5.44104	−	9.42417i	−0.239994	−	0.415682i
$515$	−4.80085	−	8.31531i	−0.211551	−	0.366416i
$516$	44.4938	−	77.0655i	1.95873	−	3.39262i
$517$	−11.1724			−0.491363
$518$	−36.9404	+	18.4303i	−1.62307	+	0.809779i
$519$	2.28672			0.100376
$520$	−15.6468	+	27.1011i	−0.686158	+	1.18846i
$521$	−1.41053	−	2.44311i	−0.0617964	−	0.107034i	0.833472	−	0.552562i	$-0.186350\pi$
$521$	−1.41053	−	2.44311i	−0.0617964	−	0.107034i	−0.895268	+	0.445527i	$0.853016\pi$
$522$	−47.0837	−	81.5514i	−2.06080	−	3.56941i
$523$	−12.6788	+	21.9602i	−0.554403	+	0.960254i	0.443547	+	0.896251i	$0.353720\pi$
$523$	−12.6788	+	21.9602i	−0.554403	+	0.960254i	−0.997950	+	0.0640030i	$0.979613\pi$
$524$	−69.4860			−3.03551
$525$	7.26204	+	4.80382i	0.316941	+	0.209656i
$526$	37.0451			1.61524
$527$	−5.03849	+	8.72692i	−0.219480	+	0.380150i
$528$	−10.1725	−	17.6193i	−0.442701	−	0.766780i
$529$	11.3702	+	19.6937i	0.494356	+	0.856250i
$530$	−2.37425	+	4.11232i	−0.103131	+	0.178628i
$531$	−45.4369			−1.97179
$532$	3.83518	−	62.9839i	0.166276	−	2.73070i
$533$	6.79651			0.294390
$534$	12.9192	−	22.3767i	0.559068	−	0.968335i
$535$	−5.72515	−	9.91625i	−0.247520	−	0.428717i
$536$	−5.25272	−	9.09797i	−0.226883	−	0.392973i
$537$	4.95604	−	8.58411i	0.213869	−	0.370432i
$538$	−42.4548			−1.83036
$539$	−2.73860	−	6.44205i	−0.117960	−	0.277479i
$540$	−69.0569			−2.97174
$541$	15.5040	−	26.8537i	0.666568	−	1.15453i	−0.312289	−	0.949987i	$-0.601096\pi$
$541$	15.5040	−	26.8537i	0.666568	−	1.15453i	0.978858	−	0.204543i	$-0.0655708\pi$
$542$	25.8693	+	44.8070i	1.11118	+	1.92462i
$543$	−36.4869	−	63.1971i	−1.56580	−	2.71205i
$544$	−3.37399	+	5.84393i	−0.144659	+	0.250556i
$545$	7.64051			0.327284
$546$	7.06534	−	116.032i	0.302368	−	4.96570i
$547$	20.2066			0.863971			0.431986	−	0.901880i	$-0.357813\pi$
$547$	20.2066			0.863971			0.431986	+	0.901880i	$0.357813\pi$
$548$	−11.0438	+	19.1284i	−0.471768	+	0.817126i
$549$	−7.61060	−	13.1820i	−0.324813	−	0.562592i
$550$	1.25936	+	2.18128i	0.0536993	+	0.0930099i
$551$	13.1068	−	22.7017i	0.558370	−	0.967125i
$552$	9.89971			0.421360
$553$	−10.2317	−	6.76825i	−0.435097	−	0.287815i
$554$	28.0431			1.19144
$555$	−10.1938	+	17.6561i	−0.432702	+	0.749461i
$556$	11.4579	+	19.8457i	0.485925	+	0.841647i
$557$	−2.43273	−	4.21361i	−0.103078	−	0.178537i	0.809873	−	0.586605i	$-0.199536\pi$
$557$	−2.43273	−	4.21361i	−0.103078	−	0.178537i	−0.912951	+	0.408068i	$0.866203\pi$
$558$	−55.4200	+	95.9902i	−2.34611	+	4.06359i
$559$	32.9948			1.39553
$560$	14.6357	−	7.30203i	0.618471	−	0.308567i
$561$	5.90108			0.249144
$562$	−13.4130	+	23.2320i	−0.565793	+	0.979982i
$563$	16.5816	+	28.7202i	0.698831	+	1.21041i	0.968872	+	0.247562i	$0.0796294\pi$
$563$	16.5816	+	28.7202i	0.698831	+	1.21041i	−0.270041	+	0.962849i	$0.587037\pi$
$564$	79.8598	+	138.321i	3.36270	+	5.82437i
$565$	1.10992	−	1.92244i	0.0466947	−	0.0808776i
$566$	−64.0752			−2.69328
$567$	68.2439	−	34.0482i	2.86598	−	1.42989i
$568$	−23.4581			−0.984280
$569$	18.2546	−	31.6179i	0.765273	−	1.32549i	−0.174829	−	0.984599i	$-0.555937\pi$
$569$	18.2546	−	31.6179i	0.765273	−	1.32549i	0.940102	−	0.340893i	$-0.110729\pi$
$570$	−22.7549	−	39.4126i	−0.953097	−	1.65081i
$571$	−0.885873	−	1.53438i	−0.0370727	−	0.0642117i	0.846894	−	0.531762i	$-0.178470\pi$
$571$	−0.885873	−	1.53438i	−0.0370727	−	0.0642117i	−0.883966	+	0.467550i	$0.845137\pi$
$572$	11.5128	−	19.9408i	0.481375	−	0.833766i
$573$	−67.9137			−2.83713
$574$	−7.12645	−	4.71413i	−0.297452	−	0.196764i
$575$	−0.509528			−0.0212488
$576$	11.2971	−	19.5672i	0.470713	−	0.815299i
$577$	3.79548	+	6.57396i	0.158008	+	0.273677i	0.934150	−	0.356880i	$-0.116160\pi$
$577$	3.79548	+	6.57396i	0.158008	+	0.273677i	−0.776142	+	0.630558i	$0.782826\pi$
$578$	17.3600	+	30.0684i	0.722080	+	1.25068i
$579$	−7.44432	+	12.8939i	−0.309375	+	0.535854i
$580$	20.7402			0.861192
$581$	−0.655397	+	10.7634i	−0.0271905	+	0.446540i
$582$	−100.070			−4.14804
$583$	0.942640	−	1.63270i	0.0390402	−	0.0676196i
$584$	−8.84861	−	15.3262i	−0.366158	−	0.634204i
$585$	−20.7534	−	35.9459i	−0.858046	−	1.48618i
$586$	5.23670	−	9.07024i	0.216326	−	0.374688i
$587$	−18.3651			−0.758009			−0.379004	−	0.925395i	$-0.623733\pi$
$587$	−18.3651			−0.758009			−0.379004	+	0.925395i	$0.623733\pi$
$588$	−60.1811	+	79.9529i	−2.48183	+	3.29720i
$589$	−30.8548			−1.27135
$590$	7.30746	−	12.6569i	0.300843	−	0.521076i
$591$	18.0577	+	31.2769i	0.742796	+	1.28656i
$592$	19.1488	+	33.1667i	0.787011	+	1.36314i
$593$	16.0687	−	27.8318i	0.659863	−	1.14292i	−0.320787	−	0.947151i	$-0.603948\pi$
$593$	16.0687	−	27.8318i	0.659863	−	1.14292i	0.980651	−	0.195766i	$-0.0627192\pi$
$594$	40.0407			1.64289
$595$	−0.288342	+	4.73535i	−0.0118209	+	0.194130i
$596$	−55.5350			−2.27480
$597$	−18.8197	+	32.5967i	−0.770240	+	1.33410i
$598$	3.40129	+	5.89121i	0.139089	+	0.240909i
$599$	−20.1171	−	34.8438i	−0.821961	−	1.42368i	−0.904220	−	0.427067i	$-0.859547\pi$
$599$	−20.1171	−	34.8438i	−0.821961	−	1.42368i	0.0822591	−	0.996611i	$-0.473786\pi$
$600$	9.71460	−	16.8262i	0.396597	−	0.686926i
$601$	12.5052			0.510099			0.255049	−	0.966928i	$-0.417908\pi$
$601$	12.5052			0.510099			0.255049	+	0.966928i	$0.417908\pi$
$602$	−34.5965	−	22.8855i	−1.41005	−	0.932742i
$603$	13.9340			0.567438
$604$	12.6960	−	21.9901i	0.516592	−	0.894764i
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	32.3448	+	56.0228i	1.31392	+	2.27577i
$607$	−1.30522	+	2.26071i	−0.0529773	+	0.0917594i	−0.891298	−	0.453418i	$-0.850204\pi$
$607$	−1.30522	+	2.26071i	−0.0529773	+	0.0917594i	0.838321	+	0.545178i	$0.183538\pi$
$608$	−20.6617			−0.837944
$609$	−37.1994	+	18.5595i	−1.50739	+	0.752068i
$610$	4.89595			0.198231
$611$	−29.6103	+	51.2866i	−1.19791	+	2.07483i
$612$	−30.4968	−	52.8220i	−1.23276	−	2.13520i
$613$	7.05232	+	12.2150i	0.284840	+	0.493358i	0.972570	−	0.232608i	$-0.0747261\pi$
$613$	7.05232	+	12.2150i	0.284840	+	0.493358i	−0.687730	+	0.725967i	$0.741393\pi$
$614$	−21.1582	+	36.6472i	−0.853877	+	1.47896i
$615$	−4.21973			−0.170156
$616$	−13.9769	+	6.97335i	−0.563146	+	0.280964i
$617$	14.3444			0.577483			0.288742	−	0.957407i	$-0.406763\pi$
$617$	14.3444			0.577483			0.288742	+	0.957407i	$0.406763\pi$
$618$	39.7945	−	68.9261i	1.60077	−	2.77261i
$619$	21.3583	+	36.9936i	0.858461	+	1.48690i	0.873396	+	0.487010i	$0.161912\pi$
$619$	21.3583	+	36.9936i	0.858461	+	1.48690i	−0.0149351	+	0.999888i	$0.504754\pi$
$620$	−12.2062	−	21.1417i	−0.490211	−	0.849071i
$621$	−4.05004	+	7.01488i	−0.162523	+	0.281497i
$622$	12.1527			0.487280
$623$	−6.87849	−	4.55010i	−0.275581	−	0.182296i
$624$	−107.841			−4.31709
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−32.5727	−	56.4176i	−1.30187	−	2.25490i
$627$	9.03430	+	15.6479i	0.360795	+	0.624915i
$628$	−21.2380	+	36.7852i	−0.847487	+	1.46789i
$629$	−11.1083			−0.442915
$630$	−3.17157	+	52.0856i	−0.126358	+	2.07514i
$631$	−24.9795			−0.994417			−0.497209	−	0.867631i	$-0.665642\pi$
$631$	−24.9795			−0.994417			−0.497209	+	0.867631i	$0.665642\pi$
$632$	−13.6872	+	23.7069i	−0.544448	+	0.943011i
$633$	33.5454	+	58.1023i	1.33331	+	2.30936i
$634$	11.3339	+	19.6310i	0.450128	+	0.779645i
$635$	1.29193	−	2.23770i	0.0512688	−	0.0888002i
$636$	−26.9517			−1.06871
$637$	−36.8302	−	4.50197i	−1.45926	−	0.178375i
$638$	−12.0257			−0.476100
$639$	15.5570	−	26.9455i	0.615425	−	1.06595i
$640$	7.39705	+	12.8121i	0.292394	+	0.506441i
$641$	−21.2883	−	36.8724i	−0.840836	−	1.45637i	−0.889189	−	0.457540i	$-0.848731\pi$
$641$	−21.2883	−	36.8724i	−0.840836	−	1.45637i	0.0483531	−	0.998830i	$-0.484603\pi$
$642$	47.4561	−	82.1964i	1.87294	−	3.24403i
$643$	24.9393			0.983508			0.491754	−	0.870734i	$-0.336356\pi$
$643$	24.9393			0.983508			0.491754	+	0.870734i	$0.336356\pi$
$644$	0.355922	−	5.84519i	0.0140253	−	0.230333i
$645$	−20.4854			−0.806611
$646$	12.3981	−	21.4742i	0.487797	−	0.844890i
$647$	10.0701	+	17.4419i	0.395895	+	0.685711i	0.993215	−	0.116292i	$-0.0371009\pi$
$647$	10.0701	+	17.4419i	0.395895	+	0.685711i	−0.597320	+	0.802003i	$0.703768\pi$
$648$	−85.0906	−	147.381i	−3.34268	−	5.78968i
$649$	−2.90126	+	5.02513i	−0.113884	+	0.197253i
$650$	13.3508			0.523660
$651$	40.8115	+	26.9967i	1.59953	+	1.05808i
$652$	−74.9579			−2.93558
$653$	−2.23790	+	3.87616i	−0.0875759	+	0.151686i	−0.906486	−	0.422236i	$-0.861245\pi$
$653$	−2.23790	+	3.87616i	−0.0875759	+	0.151686i	0.818910	+	0.573922i	$0.194579\pi$
$654$	31.6663	+	54.8477i	1.23825	+	2.14471i
$655$	7.99801	+	13.8530i	0.312508	+	0.541280i
$656$	−3.96334	+	6.86471i	−0.154743	+	0.268022i
$657$	23.4730			0.915767
$658$	66.6207	−	33.2383i	2.59714	−	1.29576i
$659$	9.01118			0.351026			0.175513	−	0.984477i	$-0.443842\pi$
$659$	9.01118			0.351026			0.175513	+	0.984477i	$0.443842\pi$
$660$	−7.14794	+	12.3806i	−0.278233	+	0.481914i
$661$	−16.9754	−	29.4022i	−0.660266	−	1.14361i	−0.980546	−	0.196292i	$-0.937110\pi$
$661$	−16.9754	−	29.4022i	−0.660266	−	1.14361i	0.320279	−	0.947323i	$-0.396223\pi$
$662$	31.6021	+	54.7364i	1.22825	+	2.12739i
$663$	15.6397	−	27.0887i	0.607395	−	1.05204i
$664$	24.0621			0.933789
$665$	−12.9981	+	6.48501i	−0.504046	+	0.251478i
$666$	−122.183			−4.73451
$667$	1.21637	−	2.10682i	0.0470981	−	0.0815763i
$668$	20.6084	+	35.6948i	0.797364	+	1.38107i
$669$	24.7444	+	42.8586i	0.956675	+	1.65701i
$670$	−2.24096	+	3.88146i	−0.0865759	+	0.149954i
$671$	−1.94382			−0.0750405
$672$	27.3292	+	18.0782i	1.05425	+	0.697380i
$673$	−7.57324			−0.291927			−0.145963	−	0.989290i	$-0.546628\pi$
$673$	−7.57324			−0.291927			−0.145963	+	0.989290i	$0.546628\pi$
$674$	29.0177	−	50.2601i	1.11772	−	1.93595i
$675$	7.94862	+	13.7674i	0.305943	+	0.529908i
$676$	−32.7893	−	56.7927i	−1.26113	−	2.18433i
$677$	−19.5149	+	33.8008i	−0.750019	+	1.29907i	0.197794	+	0.980244i	$0.436622\pi$
$677$	−19.5149	+	33.8008i	−0.750019	+	1.29907i	−0.947813	+	0.318827i	$0.896711\pi$
$678$	18.4004			0.706663
$679$	−1.94133	+	31.8819i	−0.0745016	+	1.22352i
$680$	10.5861			0.405958
$681$	−33.9530	+	58.8083i	−1.30108	+	2.25354i
$682$	7.07740	+	12.2584i	0.271008	+	0.469399i
$683$	15.4266	+	26.7196i	0.590281	+	1.02240i	0.994194	+	0.107600i	$0.0343165\pi$
$683$	15.4266	+	26.7196i	0.590281	+	1.02240i	−0.403913	+	0.914797i	$0.632350\pi$
$684$	93.3785	−	161.736i	3.57042	−	6.18414i
$685$	5.08468			0.194276
$686$	35.4955	+	30.2663i	1.35522	+	1.15557i
$687$	72.9873			2.78464
$688$	−19.2407	+	33.3258i	−0.733544	+	1.27054i
$689$	−4.99657	−	8.65432i	−0.190354	−	0.329703i
$690$	−2.11175	−	3.65766i	−0.0803930	−	0.139245i
$691$	−4.68338	+	8.11186i	−0.178164	+	0.308590i	−0.941252	−	0.337706i	$-0.890349\pi$
$691$	−4.68338	+	8.11186i	−0.178164	+	0.308590i	0.763087	+	0.646295i	$0.223683\pi$
$692$	−3.01837			−0.114741
$693$	1.25920	−	20.6794i	0.0478329	−	0.785545i
$694$	27.7358			1.05284
$695$	2.63768	−	4.56859i	0.100053	−	0.173296i
$696$	46.3824	+	80.3367i	1.75812	+	3.04515i
$697$	−1.14957	−	1.99112i	−0.0435432	−	0.0754190i
$698$	43.1408	−	74.7221i	1.63290	−	2.82827i
$699$	84.4133			3.19280
$700$	−9.58559	−	6.34084i	−0.362301	−	0.239661i
$701$	−23.8625			−0.901276			−0.450638	−	0.892707i	$-0.648803\pi$
$701$	−23.8625			−0.901276			−0.450638	+	0.892707i	$0.648803\pi$
$702$	106.120	−	183.806i	4.00525	−	6.93729i
$703$	−17.0063	−	29.4557i	−0.641403	−	1.11094i
$704$	−1.44270	−	2.49883i	−0.0543737	−	0.0941781i
$705$	18.3841	−	31.8422i	0.692386	−	1.19925i
$706$	−3.76466			−0.141685
$707$	18.4761	−	9.21808i	0.694865	−	0.346681i
$708$	82.9520			3.11753
$709$	8.83962	−	15.3107i	0.331979	−	0.575004i	−0.650921	−	0.759146i	$-0.725617\pi$
$709$	8.83962	−	15.3107i	0.331979	−	0.575004i	0.982900	+	0.184141i	$0.0589504\pi$
$710$	5.00396	+	8.66711i	0.187795	+	0.325271i
$711$	−18.1542	−	31.4440i	−0.680837	−	1.17924i
$712$	−9.20152	+	15.9375i	−0.344842	+	0.597283i
$713$	−2.86346			−0.107238
$714$	−35.1879	+	17.5559i	−1.31687	+	0.657014i
$715$	−5.30061			−0.198232
$716$	−6.54177	+	11.3307i	−0.244477	+	0.423447i
$717$	−45.0671	−	78.0585i	−1.68306	−	2.91515i
$718$	−23.9066	−	41.4074i	−0.892185	−	1.54531i
$719$	−12.5563	+	21.7482i	−0.468273	+	0.811072i	−0.999343	−	0.0362559i	$-0.988457\pi$
$719$	−12.5563	+	21.7482i	−0.468273	+	0.811072i	0.531070	+	0.847328i	$0.321790\pi$
$720$	48.4088			1.80409
$721$	−21.1876	−	14.0155i	−0.789066	−	0.521965i
$722$	28.0682			1.04459
$723$	−38.9901	+	67.5328i	−1.45006	+	2.51157i
$724$	48.1611	+	83.4175i	1.78989	+	3.10019i
$725$	−2.38725	−	4.13484i	−0.0886604	−	0.153564i
$726$	4.14453	−	7.17854i	0.153818	−	0.266421i
$727$	−34.6511			−1.28514			−0.642570	−	0.766227i	$-0.722132\pi$
$727$	−34.6511			−1.28514			−0.642570	+	0.766227i	$0.722132\pi$
$728$	−5.03219	+	82.6420i	−0.186505	+	3.06292i
$729$	68.7698			2.54703
$730$	−3.77508	+	6.53862i	−0.139722	+	0.242005i
$731$	−5.58078	−	9.66620i	−0.206413	−	0.357517i
$732$	13.8943	+	24.0657i	0.513549	+	0.889493i
$733$	0.212651	−	0.368322i	0.00785444	−	0.0136043i	−0.862071	−	0.506787i	$-0.830833\pi$
$733$	0.212651	−	0.368322i	0.00785444	−	0.0136043i	0.869926	+	0.493182i	$0.164166\pi$
$734$	−36.9135			−1.36250
$735$	22.8667	+	2.79513i	0.843450	+	0.103100i
$736$	−1.91750			−0.0706800
$737$	0.889722	−	1.54104i	0.0327733	−	0.0567651i
$738$	−12.6445	−	21.9009i	−0.465451	−	0.806185i
$739$	8.75016	+	15.1557i	0.321880	+	0.557513i	0.980876	−	0.194634i	$-0.0623519\pi$
$739$	8.75016	+	15.1557i	0.321880	+	0.557513i	−0.658996	+	0.752146i	$0.729019\pi$
$740$	13.4554	−	23.3054i	0.494629	−	0.856722i
$741$	95.7746			3.51837
$742$	−0.763585	+	12.5401i	−0.0280321	+	0.460362i
$743$	−15.1702			−0.556540			−0.278270	−	0.960503i	$-0.589761\pi$
$743$	−15.1702			−0.556540			−0.278270	+	0.960503i	$0.589761\pi$
$744$	54.5945	−	94.5604i	2.00153	−	3.46675i
$745$	6.39221	+	11.0716i	0.234193	+	0.405633i
$746$	−32.1913	−	55.7570i	−1.17861	−	2.04141i
$747$	−15.9575	+	27.6392i	−0.583855	+	1.01127i
$748$	−7.78918			−0.284801
$749$	−25.2668	−	16.7139i	−0.923228	−	0.610713i
$750$	−8.28906			−0.302674
$751$	4.01273	−	6.95025i	0.146427	−	0.253618i	−0.783478	−	0.621420i	$-0.786556\pi$
$751$	4.01273	−	6.95025i	0.146427	−	0.253618i	0.929904	+	0.367802i	$0.119889\pi$
$752$	−34.5342	−	59.8150i	−1.25933	−	2.18123i
$753$	35.4871	+	61.4655i	1.29322	+	2.23993i
$754$	−31.8717	+	55.2033i	−1.16070	+	2.01039i
$755$	−5.84536			−0.212734
$756$	−163.489	+	81.5678i	−5.94604	+	2.96659i
$757$	4.81301			0.174932			0.0874658	−	0.996168i	$-0.472123\pi$
$757$	4.81301			0.174932			0.0874658	+	0.996168i	$0.472123\pi$
$758$	39.0118	−	67.5705i	1.41697	−	2.45427i
$759$	0.838423	+	1.45219i	0.0304328	+	0.0527112i
$760$	16.2068	+	28.0711i	0.587884	+	1.01825i
$761$	−2.21721	+	3.84032i	−0.0803737	+	0.139211i	−0.903411	−	0.428777i	$-0.858945\pi$
$761$	−2.21721	+	3.84032i	−0.0803737	+	0.139211i	0.823037	+	0.567988i	$0.192278\pi$
$762$	21.4178			0.775887
$763$	18.0886	−	9.02473i	0.654850	−	0.326717i
$764$	89.6432			3.24318
$765$	−7.02051	+	12.1599i	−0.253827	+	0.439641i
$766$	43.3763	+	75.1299i	1.56725	+	2.71455i
$767$	15.3784	+	26.6362i	0.555283	+	0.961779i
$768$	−51.8188	+	89.7528i	−1.86985	+	3.23867i
$769$	−3.82639			−0.137983			−0.0689915	−	0.997617i	$-0.521978\pi$
$769$	−3.82639			−0.137983			−0.0689915	+	0.997617i	$0.521978\pi$
$770$	5.55793	+	3.67656i	0.200294	+	0.132494i
$771$	−14.2186			−0.512071
$772$	9.82619	−	17.0195i	0.353652	−	0.612544i
$773$	−1.09937	−	1.90417i	−0.0395417	−	0.0684883i	0.845577	−	0.533853i	$-0.179256\pi$
$773$	−1.09937	−	1.90417i	−0.0395417	−	0.0684883i	−0.885119	+	0.465365i	$0.845923\pi$
$774$	−61.3848	−	106.322i	−2.20643	−	3.82165i
$775$	−2.80992	+	4.86692i	−0.100935	+	0.174825i
$776$	71.2736			2.55857
$777$	−3.27843	+	53.8406i	−0.117613	+	1.93152i
$778$	−13.6799			−0.490449
$779$	3.51989	−	6.09663i	0.126113	−	0.218434i
$780$	37.8884	+	65.6247i	1.35662	+	2.34974i
$781$	−1.98671	−	3.44107i	−0.0710899	−	0.123131i
$782$	1.15060	−	1.99290i	0.0411454	−	0.0712658i
$783$	−75.9015			−2.71250
$784$	26.0244	−	34.5744i	0.929444	−	1.23480i
$785$	9.77817			0.348998
$786$	−66.2960	+	114.828i	−2.36470	+	4.09578i
$787$	7.69997	+	13.3367i	0.274474	+	0.475403i	0.970002	−	0.243096i	$-0.0781628\pi$
$787$	7.69997	+	13.3367i	0.274474	+	0.475403i	−0.695528	+	0.718499i	$0.744830\pi$
$788$	−23.8355	−	41.2842i	−0.849103	−	1.47069i
$789$	24.2017	−	41.9186i	0.861603	−	1.49234i
$790$	11.6787			0.415510
$791$	0.356963	−	5.86229i	0.0126921	−	0.208439i
$792$	−46.2298			−1.64270
$793$	−5.15173	+	8.92306i	−0.182943	+	0.316867i
$794$	−38.0440	−	65.8941i	−1.35013	−	2.33849i
$795$	3.10221	+	5.37319i	0.110024	+	0.190567i
$796$	24.8413	−	43.0263i	0.880475	−	1.52503i
$797$	19.3677			0.686039			0.343019	−	0.939328i	$-0.388550\pi$
$797$	19.3677			0.686039			0.343019	+	0.939328i	$0.388550\pi$
$798$	−100.424	−	66.4302i	−3.55497	−	2.35160i
$799$	20.0334			0.708729
$800$	−1.88165	+	3.25911i	−0.0665262	+	0.115227i
$801$	−12.2046	−	21.1389i	−0.431227	−	0.746907i
$802$	8.17190	+	14.1541i	0.288560	+	0.499800i
$803$	1.49881	−	2.59601i	0.0528917	−	0.0916112i
$804$	−25.4387			−0.897154
$805$	−1.20628	+	0.601838i	−0.0425159	+	0.0212120i
$806$	75.0291			2.64279
$807$	−27.7359	+	48.0400i	−0.976350	+	1.69109i
$808$	−23.0371	−	39.9014i	−0.810443	−	1.40373i
$809$	−3.66189	−	6.34258i	−0.128745	−	0.222993i	0.794445	−	0.607335i	$-0.207762\pi$
$809$	−3.66189	−	6.34258i	−0.128745	−	0.222993i	−0.923191	+	0.384342i	$0.874428\pi$
$810$	−36.3022	+	62.8772i	−1.27553	+	2.20928i
$811$	−31.3236			−1.09992			−0.549960	−	0.835191i	$-0.685357\pi$
$811$	−31.3236			−1.09992			−0.549960	+	0.835191i	$0.685357\pi$
$812$	49.1016	−	24.4977i	1.72313	−	0.859702i
$813$	67.6021			2.37091
$814$	−7.80171	+	13.5130i	−0.273450	+	0.473629i
$815$	8.62783	+	14.9438i	0.302220	+	0.523460i
$816$	18.2404	+	31.5932i	0.638540	+	1.10598i
$817$	17.0879	−	29.5971i	0.597829	−	1.03547i
$818$	9.40289			0.328764
$819$	−91.5908	−	60.5870i	−3.20044	−	2.11708i
$820$	5.56987			0.194508
$821$	23.5909	−	40.8606i	0.823328	−	1.42605i	−0.0798622	−	0.996806i	$-0.525448\pi$
$821$	23.5909	−	40.8606i	0.823328	−	1.42605i	0.903190	−	0.429240i	$-0.141219\pi$
$822$	21.0736	+	36.5005i	0.735026	+	1.27310i
$823$	25.1075	+	43.4875i	0.875193	+	1.51588i	0.856557	+	0.516052i	$0.172599\pi$
$823$	25.1075	+	43.4875i	0.875193	+	1.51588i	0.0186353	+	0.999826i	$0.494068\pi$
$824$	−28.3431	+	49.0917i	−0.987378	+	1.71019i
$825$	3.29098			0.114577
$826$	2.35016	−	38.5960i	0.0817726	−	1.34292i
$827$	0.0456538			0.00158754			0.000793769	−	1.00000i	$-0.499747\pi$
$827$	0.0456538			0.00158754			0.000793769		1.00000i	$0.499747\pi$
$828$	8.66593	−	15.0098i	0.301162	−	0.521628i
$829$	−12.1812	−	21.0985i	−0.423071	−	0.732780i	0.573167	−	0.819438i	$-0.305715\pi$
$829$	−12.1812	−	21.0985i	−0.423071	−	0.732780i	−0.996238	+	0.0866581i	$0.972381\pi$
$830$	−5.13279	−	8.89025i	−0.178162	−	0.308585i
$831$	18.3207	−	31.7323i	0.635537	−	1.10078i
$832$	−15.2944			−0.530237
$833$	4.91060	+	11.5513i	0.170142	+	0.400229i
$834$	43.7277			1.51417
$835$	4.74416	−	8.21713i	0.164178	−	0.284365i
$836$	−11.9249	−	20.6545i	−0.412431	−	0.714352i
$837$	44.6700	+	77.3707i	1.54402	+	2.67432i
$838$	30.2507	−	52.3958i	1.04499	−	1.80998i
$839$	−13.2346			−0.456908			−0.228454	−	0.973555i	$-0.573367\pi$
$839$	−13.2346			−0.456908			−0.228454	+	0.973555i	$0.573367\pi$
$840$	3.12432	−	51.3098i	0.107799	−	1.77036i
$841$	−6.20408			−0.213934
$842$	−41.4237	+	71.7479i	−1.42755	+	2.47260i
$843$	17.5255	+	30.3551i	0.603611	+	1.04548i
$844$	−44.2785	−	76.6926i	−1.52413	−	2.63987i
$845$	−7.54825	+	13.0740i	−0.259668	+	0.449758i
$846$	220.353			7.57590
$847$	−2.20665	−	1.45969i	−0.0758214	−	0.0501556i
$848$	11.6549			0.400230
$849$	−41.8606	+	72.5046i	−1.43665	+	2.48835i
$850$	−2.25817	−	3.91126i	−0.0774546	−	0.134155i
$851$	−1.57826	−	2.73362i	−0.0541019	−	0.0937072i
$852$	−28.4017	+	49.1932i	−0.973026	+	1.68533i
$853$	−17.6903			−0.605704			−0.302852	−	0.953038i	$-0.597939\pi$
$853$	−17.6903			−0.605704			−0.302852	+	0.953038i	$0.597939\pi$
$854$	11.5909	−	5.78294i	0.396634	−	0.197888i
$855$	−42.9924			−1.47031
$856$	−33.8000	+	58.5433i	−1.15526	+	2.00097i
$857$	−20.3525	−	35.2515i	−0.695227	−	1.20417i	−0.970104	−	0.242690i	$-0.921970\pi$
$857$	−20.3525	−	35.2515i	−0.695227	−	1.20417i	0.274876	−	0.961480i	$-0.411363\pi$
$858$	−21.9686	−	38.0507i	−0.749994	−	1.29903i
$859$	−13.2219	+	22.9009i	−0.451124	+	0.781370i	−0.998456	−	0.0555457i	$-0.982310\pi$
$859$	−13.2219	+	22.9009i	−0.451124	+	0.781370i	0.547332	+	0.836916i	$0.315643\pi$
$860$	27.0398			0.922051
$861$	−9.99003	+	4.98422i	−0.340459	+	0.169862i
$862$	52.5735			1.79066
$863$	−11.4105	+	19.7636i	−0.388419	+	0.672762i	−0.992237	−	0.124361i	$-0.960312\pi$
$863$	−11.4105	+	19.7636i	−0.388419	+	0.672762i	0.603818	+	0.797122i	$0.293645\pi$
$864$	29.9130	+	51.8108i	1.01766	+	1.76264i
$865$	0.347422	+	0.601752i	0.0118127	+	0.0204602i
$866$	33.0227	−	57.1969i	1.12216	−	1.94363i
$867$	45.3654			1.54069
$868$	−53.8694	−	35.6345i	−1.82845	−	1.20951i
$869$	−4.63677			−0.157292
$870$	19.7881	−	34.2740i	0.670879	−	1.16200i
$871$	−4.71607	−	8.16848i	−0.159798	−	0.276778i
$872$	−22.5539	−	39.0645i	−0.763772	−	1.32289i
$873$	−47.2673	+	81.8694i	−1.59976	+	2.77086i
$874$	7.04607			0.238337
$875$	−0.160806	+	2.64086i	−0.00543622	+	0.0892774i
$876$	−42.8535			−1.44789
$877$	9.11423	−	15.7863i	0.307766	−	0.533066i	−0.670108	−	0.742264i	$-0.733752\pi$
$877$	9.11423	−	15.7863i	0.307766	−	0.533066i	0.977873	+	0.209198i	$0.0670854\pi$
$878$	−32.5278	−	56.3398i	−1.09776	−	1.90137i
$879$	−6.84232	−	11.8512i	−0.230786	−	0.399733i
$880$	3.09102	−	5.35380i	0.104198	−	0.180477i
$881$	49.1054			1.65440			0.827201	−	0.561906i	$-0.189932\pi$
$881$	49.1054			1.65440			0.827201	+	0.561906i	$0.189932\pi$
$882$	54.0133	+	127.056i	1.81872	+	4.27821i
$883$	−14.4898			−0.487619			−0.243810	−	0.969823i	$-0.578397\pi$
$883$	−14.4898			−0.487619			−0.243810	+	0.969823i	$0.578397\pi$
$884$	−20.6437	+	35.7560i	−0.694323	+	1.20260i
$885$	−9.54798	−	16.5376i	−0.320952	−	0.555905i
$886$	−20.8868	−	36.1770i	−0.701706	−	1.21539i
$887$	−5.95626	+	10.3165i	−0.199992	+	0.346396i	−0.948525	−	0.316701i	$-0.897425\pi$
$887$	−5.95626	+	10.3165i	−0.199992	+	0.346396i	0.748534	+	0.663097i	$0.230758\pi$
$888$	120.363			4.03913
$889$	0.415501	−	6.82364i	0.0139354	−	0.228857i
$890$	7.85127			0.263175
$891$	14.4129	−	24.9639i	0.482851	−	0.836323i
$892$	−32.6616	−	56.5716i	−1.09359	−	1.89416i
$893$	30.6702	+	53.1223i	1.02634	+	1.77767i
$894$	−52.9854	+	91.7735i	−1.77210	+	3.06936i
$895$	3.01189			0.100676
$896$	32.6454	+	21.5948i	1.09061	+	0.721432i
$897$	8.88831			0.296772
$898$	46.1022	−	79.8513i	1.53845	−	2.66467i
$899$	−13.4160	−	23.2372i	−0.447448	−	0.775003i
$900$	−17.0078	−	29.4583i	−0.566926	−	0.981945i
$901$	−1.69026	+	2.92761i	−0.0563106	+	0.0975328i
$902$	−3.22953			−0.107532
$903$	−48.4982	+	24.1967i	−1.61392	+	0.805215i
$904$	−13.1054			−0.435880
$905$	11.0869	−	19.2031i	0.368542	−	0.638334i
$906$	−24.2263	−	41.9611i	−0.804864	−	1.39406i
$907$	8.88064	+	15.3817i	0.294877	+	0.510741i	0.974956	−	0.222397i	$-0.0713881\pi$
$907$	8.88064	+	15.3817i	0.294877	+	0.510741i	−0.680079	+	0.733138i	$0.738055\pi$
$908$	44.8165	−	77.6245i	1.48729	−	2.57606i
$909$	61.1112			2.02693
$910$	31.6073	−	15.7695i	1.04777	−	0.522754i
$911$	5.00677			0.165882			0.0829408	−	0.996554i	$-0.473569\pi$
$911$	5.00677			0.165882			0.0829408	+	0.996554i	$0.473569\pi$
$912$	−55.8504	+	96.7357i	−1.84939	+	3.20324i
$913$	2.03785	+	3.52967i	0.0674432	+	0.116815i
$914$	29.5195	+	51.1292i	0.976417	+	1.69120i
$915$	3.19854	−	5.54004i	0.105741	−	0.183148i
$916$	−96.3401			−3.18317
$917$	35.2976	+	23.3493i	1.16563	+	0.771061i
$918$	−71.7973			−2.36967
$919$	−5.48413	+	9.49879i	−0.180905	+	0.313336i	−0.942189	−	0.335082i	$-0.891236\pi$
$919$	−5.48413	+	9.49879i	−0.180905	+	0.313336i	0.761284	+	0.648418i	$0.224569\pi$
$920$	1.50407	+	2.60512i	0.0495876	+	0.0858883i
$921$	27.6455	+	47.8835i	0.910951	+	1.57781i
$922$	30.5779	−	52.9625i	1.00703	−	1.74423i
$923$	−21.0615			−0.693248
$924$	−2.29886	+	37.7534i	−0.0756268	+	1.24200i
$925$	−6.19498			−0.203690
$926$	−39.1659	+	67.8373i	−1.28707	+	2.22927i
$927$	−37.5933	−	65.1134i	−1.23472	−	2.13861i
$928$	−8.98393	−	15.5606i	−0.294912	−	0.510803i
$929$	9.23973	−	16.0037i	0.303146	−	0.525064i	−0.673701	−	0.739004i	$-0.735296\pi$
$929$	9.23973	−	16.0037i	0.303146	−	0.525064i	0.976847	+	0.213940i	$0.0686298\pi$
$930$	−46.5832			−1.52752
$931$	−23.1126	+	30.7059i	−0.757484	+	1.00635i
$932$	−111.422			−3.64975
$933$	7.93943	−	13.7515i	0.259925	−	0.450204i
$934$	9.62091	+	16.6639i	0.314806	+	0.545259i
$935$	0.896554	+	1.55288i	0.0293204	+	0.0507845i
$936$	−122.523	+	212.216i	−4.00479	+	6.93650i
$937$	42.7809			1.39759			0.698795	−	0.715322i	$-0.253720\pi$
$937$	42.7809			1.39759			0.698795	+	0.715322i	$0.253720\pi$
$938$	−0.720719	+	11.8361i	−0.0235323	+	0.386464i
$939$	−85.1195			−2.77777
$940$	−24.2663	+	42.0304i	−0.791478	+	1.37088i
$941$	15.5124	+	26.8683i	0.505691	+	0.875882i	0.999978	+	0.00658343i	$0.00209558\pi$
$941$	15.5124	+	26.8683i	0.505691	+	0.875882i	−0.494288	+	0.869298i	$0.664571\pi$
$942$	40.5259	+	70.1929i	1.32041	+	2.28701i
$943$	0.326661	−	0.565794i	0.0106376	−	0.0184248i
$944$	−35.8714			−1.16751
$945$	35.0796	+	23.2051i	1.14114	+	0.754861i
$946$	−15.6783			−0.509745
$947$	−3.09896	+	5.36755i	−0.100703	+	0.174422i	−0.911974	−	0.410247i	$-0.865442\pi$
$947$	−3.09896	+	5.36755i	−0.100703	+	0.174422i	0.811272	+	0.584669i	$0.198776\pi$
$948$	33.1433	+	57.4059i	1.07645	+	1.86446i
$949$	−7.94459	−	13.7604i	−0.257892	−	0.446683i
$950$	6.91432	−	11.9759i	0.224330	−	0.388551i
$951$	29.6180			0.960430
$952$	25.0621	−	12.5040i	0.812267	−	0.405256i
$953$	−2.74266			−0.0888435			−0.0444217	−	0.999013i	$-0.514145\pi$
$953$	−2.74266			−0.0888435			−0.0444217	+	0.999013i	$0.514145\pi$
$954$	−18.5917	+	32.2017i	−0.601928	+	1.04257i
$955$	−10.3182	−	17.8716i	−0.333888	−	0.578310i
$956$	59.4867	+	103.034i	1.92394	+	3.33236i
$957$	−7.85640	+	13.6077i	−0.253961	+	0.439874i
$958$	85.4130			2.75957
$959$	12.0377	−	6.00586i	0.388719	−	0.193939i
$960$	9.49578			0.306475
$961$	−0.291290	+	0.504528i	−0.00939644	+	0.0162751i
$962$	41.3538	+	71.6270i	1.33330	+	2.30935i
$963$	−44.8311	−	77.6497i	−1.44466	−	2.50223i
$964$	51.4653	−	89.1405i	1.65759	−	2.87102i
$965$	−4.52408			−0.145635
$966$	−9.31979	−	6.16502i	−0.299859	−	0.198356i
$967$	16.4386			0.528629			0.264315	−	0.964437i	$-0.414854\pi$
$967$	16.4386			0.528629			0.264315	+	0.964437i	$0.414854\pi$
$968$	−2.95189	+	5.11282i	−0.0948772	+	0.164332i
$969$	−16.1995	−	28.0583i	−0.520402	−	0.901363i
$970$	−15.2037	−	26.3336i	−0.488161	−	0.845520i
$971$	−5.02029	+	8.69540i	−0.161109	+	0.279049i	−0.935267	−	0.353944i	$-0.884840\pi$
$971$	−5.02029	+	8.69540i	−0.161109	+	0.279049i	0.774158	+	0.632993i	$0.218174\pi$
$972$	−204.920			−6.57281
$973$	0.848306	−	13.9315i	0.0271955	−	0.446622i
$974$	57.1106			1.82994
$975$	8.72211	−	15.1071i	0.279331	−	0.483815i
$976$	−6.00840	−	10.4068i	−0.192324	−	0.333115i
$977$	−26.8421	−	46.4919i	−0.858756	−	1.48741i	−0.873116	−	0.487512i	$-0.837904\pi$
$977$	−26.8421	−	46.4919i	−0.858756	−	1.48741i	0.0143600	−	0.999897i	$-0.495429\pi$
$978$	−71.5166	+	123.870i	−2.28685	+	3.96094i
$979$	−3.11717			−0.0996251
$980$	−30.1830	−	3.68945i	−0.964162	−	0.117855i
$981$	59.8294			1.91021
$982$	−23.4825	+	40.6728i	−0.749356	+	1.29792i
$983$	−5.90418	−	10.2263i	−0.188314	−	0.326169i	0.756374	−	0.654139i	$-0.226969\pi$
$983$	−5.90418	−	10.2263i	−0.188314	−	0.326169i	−0.944688	+	0.327970i	$0.893636\pi$
$984$	12.4562	+	21.5747i	0.397088	+	0.687777i
$985$	−5.48704	+	9.50383i	−0.174832	+	0.302817i
$986$	21.5633			0.686715
$987$	5.91254	−	97.0997i	0.188198	−	3.09072i
$988$	−126.418			−4.02191
$989$	1.58583	−	2.74674i	0.0504264	−	0.0873411i
$990$	9.86149	+	17.0806i	0.313419	+	0.542857i
$991$	−1.39027	−	2.40801i	−0.0441633	−	0.0764931i	0.843099	−	0.537759i	$-0.180729\pi$
$991$	−1.39027	−	2.40801i	−0.0441633	−	0.0764931i	−0.887262	+	0.461266i	$0.847396\pi$
$992$	−10.5745	+	18.3157i	−0.335742	+	0.581522i
$993$	82.5830			2.62069
$994$	22.0840	+	14.6085i	0.700460	+	0.463353i
$995$	−11.4372			−0.362582
$996$	29.1329	−	50.4597i	0.923112	−	1.59888i
$997$	−2.53263	−	4.38665i	−0.0802093	−	0.138927i	0.823130	−	0.567852i	$-0.192226\pi$
$997$	−2.53263	−	4.38665i	−0.0802093	−	0.138927i	−0.903340	+	0.428926i	$0.858892\pi$
$998$	42.0005	+	72.7469i	1.32950	+	2.30276i
$999$	−49.2415	+	85.2888i	−1.55793	+	2.69842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.c.331.2	yes	16
7.2	even	3		2695.2.a.t.1.7		8
7.4	even	3	inner	385.2.i.c.221.2	✓	16
7.5	odd	6		2695.2.a.s.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.2	✓	16	7.4	even	3	inner
385.2.i.c.331.2	yes	16	1.1	even	1	trivial
2695.2.a.s.1.7		8	7.5	odd	6
2695.2.a.t.1.7		8	7.2	even	3

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25936 + 2.18128i) q^{2} +(1.64549 + 2.85007i) q^{3} +(-2.17198 - 3.76198i) q^{4} +(-0.500000 + 0.866025i) q^{5} -8.28906 q^{6} +(-0.160806 + 2.64086i) q^{7} +5.90377 q^{8} +(-3.91527 + 6.78146i) q^{9} +O(q^{10})\)	\(q+(-1.25936 + 2.18128i) q^{2} +(1.64549 + 2.85007i) q^{3} +(-2.17198 - 3.76198i) q^{4} +(-0.500000 + 0.866025i) q^{5} -8.28906 q^{6} +(-0.160806 + 2.64086i) q^{7} +5.90377 q^{8} +(-3.91527 + 6.78146i) q^{9} +(-1.25936 - 2.18128i) q^{10} +(0.500000 + 0.866025i) q^{11} +(7.14794 - 12.3806i) q^{12} +5.30061 q^{13} +(-5.55793 - 3.67656i) q^{14} -3.29098 q^{15} +(-3.09102 + 5.35380i) q^{16} +(-0.896554 - 1.55288i) q^{17} +(-9.86149 - 17.0806i) q^{18} +(2.74517 - 4.75477i) q^{19} +4.34396 q^{20} +(-7.79125 + 3.88720i) q^{21} -2.51872 q^{22} +(0.254764 - 0.441264i) q^{23} +(9.71460 + 16.8262i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-6.67538 + 11.5621i) q^{26} -15.8972 q^{27} +(10.2841 - 5.13094i) q^{28} +4.77451 q^{29} +(4.14453 - 7.17854i) q^{30} +(-2.80992 - 4.86692i) q^{31} +(-1.88165 - 3.25911i) q^{32} +(-1.64549 + 2.85007i) q^{33} +4.51634 q^{34} +(-2.20665 - 1.45969i) q^{35} +34.0156 q^{36} +(3.09749 - 5.36501i) q^{37} +(6.91432 + 11.9759i) q^{38} +(8.72211 + 15.1071i) q^{39} +(-2.95189 + 5.11282i) q^{40} +1.28221 q^{41} +(1.33293 - 21.8902i) q^{42} +6.22470 q^{43} +(2.17198 - 3.76198i) q^{44} +(-3.91527 - 6.78146i) q^{45} +(0.641679 + 1.11142i) q^{46} +(-5.58621 + 9.67560i) q^{47} -20.3450 q^{48} +(-6.94828 - 0.849331i) q^{49} +2.51872 q^{50} +(2.95054 - 5.11049i) q^{51} +(-11.5128 - 19.9408i) q^{52} +(-0.942640 - 1.63270i) q^{53} +(20.0204 - 34.6763i) q^{54} -1.00000 q^{55} +(-0.949360 + 15.5910i) q^{56} +18.0686 q^{57} +(-6.01283 + 10.4145i) q^{58} +(2.90126 + 5.02513i) q^{59} +(7.14794 + 12.3806i) q^{60} +(-0.971912 + 1.68340i) q^{61} +14.1548 q^{62} +(-17.2793 - 11.4302i) q^{63} -2.88540 q^{64} +(-2.65031 + 4.59047i) q^{65} +(-4.14453 - 7.17854i) q^{66} +(-0.889722 - 1.54104i) q^{67} +(-3.89459 + 6.74563i) q^{68} +1.67685 q^{69} +(5.96296 - 2.97503i) q^{70} -3.97341 q^{71} +(-23.1149 + 40.0362i) q^{72} +(-1.49881 - 2.59601i) q^{73} +(7.80171 + 13.5130i) q^{74} +(1.64549 - 2.85007i) q^{75} -23.8498 q^{76} +(-2.36745 + 1.18117i) q^{77} -43.9371 q^{78} +(-2.31838 + 4.01556i) q^{79} +(-3.09102 - 5.35380i) q^{80} +(-14.4129 - 24.9639i) q^{81} +(-1.61477 + 2.79686i) q^{82} +4.07571 q^{83} +(31.5460 + 20.8676i) q^{84} +1.79311 q^{85} +(-7.83915 + 13.5778i) q^{86} +(7.85640 + 13.6077i) q^{87} +(2.95189 + 5.11282i) q^{88} +(-1.55858 + 2.69955i) q^{89} +19.7230 q^{90} +(-0.852369 + 13.9982i) q^{91} -2.21337 q^{92} +(9.24739 - 16.0169i) q^{93} +(-14.0701 - 24.3701i) q^{94} +(2.74517 + 4.75477i) q^{95} +(6.19246 - 10.7257i) q^{96} +12.0725 q^{97} +(10.6030 - 14.0865i) q^{98} -7.83055 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more