LMFDB - Embedded newform 725.2.p.b.274.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(149,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("725.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.p (of order $14$, degree $6$, not 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			274.6
Character	$\chi$	$=$	725.274
Dual form			725.2.p.b.299.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16693 + 0.561962i) q^{2} +(1.90343 - 2.38683i) q^{3} +(-0.201065 - 0.252127i) q^{4} +(3.56247 - 1.71559i) q^{6} +(2.58438 + 2.06098i) q^{7} +(-0.669356 - 2.93264i) q^{8} +(-1.40633 - 6.16153i) q^{9} +O(q^{10})$	\(q+(1.16693 + 0.561962i) q^{2} +(1.90343 - 2.38683i) q^{3} +(-0.201065 - 0.252127i) q^{4} +(3.56247 - 1.71559i) q^{6} +(2.58438 + 2.06098i) q^{7} +(-0.669356 - 2.93264i) q^{8} +(-1.40633 - 6.16153i) q^{9} +(-2.84528 - 0.649416i) q^{11} -0.984498 q^{12} +(-3.20613 - 0.731779i) q^{13} +(1.85759 + 3.85733i) q^{14} +(0.723424 - 3.16953i) q^{16} +2.25672 q^{17} +(1.82146 - 7.98036i) q^{18} +(3.50362 - 2.79405i) q^{19} +(9.83839 - 2.24555i) q^{21} +(-2.95528 - 2.35676i) q^{22} +(3.83109 + 7.95534i) q^{23} +(-8.27377 - 3.98444i) q^{24} +(-3.33009 - 2.65566i) q^{26} +(-9.13175 - 4.39762i) q^{27} -1.06598i q^{28} +(1.72439 + 5.10161i) q^{29} +(-2.38835 + 4.95945i) q^{31} +(-1.12565 + 1.41152i) q^{32} +(-6.96584 + 5.55507i) q^{33} +(2.63342 + 1.26819i) q^{34} +(-1.27073 + 1.59344i) q^{36} +(-0.970402 - 4.25161i) q^{37} +(5.65861 - 1.29154i) q^{38} +(-7.84928 + 6.25959i) q^{39} +1.22818i q^{41} +(12.7426 + 2.90841i) q^{42} +(-0.197744 + 0.0952283i) q^{43} +(0.408350 + 0.847948i) q^{44} +11.4362i q^{46} +(0.906190 - 3.97028i) q^{47} +(-6.18813 - 7.75967i) q^{48} +(0.873766 + 3.82822i) q^{49} +(4.29551 - 5.38640i) q^{51} +(0.460139 + 0.955489i) q^{52} +(5.59236 - 11.6127i) q^{53} +(-8.18478 - 10.2634i) q^{54} +(4.31423 - 8.95859i) q^{56} -13.6808i q^{57} +(-0.854673 + 6.92225i) q^{58} +5.20741 q^{59} +(10.0437 + 8.00960i) q^{61} +(-5.57405 + 4.44516i) q^{62} +(9.06429 - 18.8222i) q^{63} +(-7.96494 + 3.83571i) q^{64} +(-11.2504 + 2.56782i) q^{66} +(-3.77413 + 0.861420i) q^{67} +(-0.453747 - 0.568981i) q^{68} +(26.2802 + 5.99829i) q^{69} +(-1.67978 + 7.35960i) q^{71} +(-17.1282 + 8.24851i) q^{72} +(-5.36879 + 2.58547i) q^{73} +(1.25685 - 5.50664i) q^{74} +(-1.40891 - 0.321575i) q^{76} +(-6.01486 - 7.54240i) q^{77} +(-12.6772 + 2.89348i) q^{78} +(-5.30705 + 1.21130i) q^{79} +(-10.7957 + 5.19892i) q^{81} +(-0.690191 + 1.43320i) q^{82} +(-6.33189 + 5.04951i) q^{83} +(-2.54432 - 2.02903i) q^{84} -0.284267 q^{86} +(15.4589 + 5.59474i) q^{87} +8.77887i q^{88} +(-0.927897 + 1.92680i) q^{89} +(-6.77770 - 8.49897i) q^{91} +(1.23546 - 2.56546i) q^{92} +(7.29130 + 15.1405i) q^{93} +(3.28860 - 4.12378i) q^{94} +(1.22646 + 5.37346i) q^{96} +(4.29066 + 5.38032i) q^{97} +(-1.13169 + 4.95827i) q^{98} +18.4446i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{6} + 8 q^{9}+O(q^{10}) $ 48 * q + 8 * q^6 + 8 * q^9	$ 48 q + 8 q^{6} + 8 q^{9} - 28 q^{11} + 84 q^{14} - 20 q^{16} + 98 q^{21} - 76 q^{24} - 14 q^{29} + 14 q^{31} - 40 q^{34} - 56 q^{36} - 14 q^{39} + 42 q^{44} + 4 q^{49} + 12 q^{51} - 214 q^{54} - 84 q^{56} + 132 q^{59} + 112 q^{61} - 66 q^{64} - 140 q^{66} + 56 q^{69} + 106 q^{71} - 66 q^{74} - 84 q^{76} + 112 q^{79} - 58 q^{81} - 28 q^{84} + 60 q^{86} - 28 q^{89} - 62 q^{91} + 76 q^{94} - 2 q^{96}+O(q^{100}) $ 48 * q + 8 * q^6 + 8 * q^9 - 28 * q^11 + 84 * q^14 - 20 * q^16 + 98 * q^21 - 76 * q^24 - 14 * q^29 + 14 * q^31 - 40 * q^34 - 56 * q^36 - 14 * q^39 + 42 * q^44 + 4 * q^49 + 12 * q^51 - 214 * q^54 - 84 * q^56 + 132 * q^59 + 112 * q^61 - 66 * q^64 - 140 * q^66 + 56 * q^69 + 106 * q^71 - 66 * q^74 - 84 * q^76 + 112 * q^79 - 58 * q^81 - 28 * q^84 + 60 * q^86 - 28 * q^89 - 62 * q^91 + 76 * q^94 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.16693	+	0.561962i	0.825141	+	0.397367i	0.798291	−	0.602272i	$-0.205738\pi$
$2$	1.16693	+	0.561962i	0.825141	+	0.397367i	0.0268505	+	0.999639i	$0.491452\pi$
$3$	1.90343	−	2.38683i	1.09895	−	1.37803i	0.179993	−	0.983668i	$-0.442392\pi$
$3$	1.90343	−	2.38683i	1.09895	−	1.37803i	0.918953	−	0.394367i	$-0.129036\pi$
$4$	−0.201065	−	0.252127i	−0.100532	−	0.126064i
$5$		0			0
$5$		0			0
$6$	3.56247	−	1.71559i	1.45437	−	0.700388i
$7$	2.58438	+	2.06098i	0.976805	+	0.778976i	0.975269	−	0.221022i	$-0.0709394\pi$
$7$	2.58438	+	2.06098i	0.976805	+	0.778976i	0.00153671	+	0.999999i	$0.499511\pi$
$8$	−0.669356	−	2.93264i	−0.236653	−	1.03684i
$9$	−1.40633	−	6.16153i	−0.468777	−	2.05384i
$10$		0			0
$11$	−2.84528	−	0.649416i	−0.857884	−	0.195806i	−0.229116	−	0.973399i	$-0.573583\pi$
$11$	−2.84528	−	0.649416i	−0.857884	−	0.195806i	−0.628768	+	0.777593i	$0.716441\pi$
$12$	−0.984498			−0.284200
$13$	−3.20613	−	0.731779i	−0.889221	−	0.202959i	−0.246577	−	0.969123i	$-0.579306\pi$
$13$	−3.20613	−	0.731779i	−0.889221	−	0.202959i	−0.642645	+	0.766164i	$0.722163\pi$
$14$	1.85759	+	3.85733i	0.496463	+	1.03092i
$15$		0			0
$16$	0.723424	−	3.16953i	0.180856	−	0.792382i
$17$	2.25672			0.547335			0.273667	−	0.961824i	$-0.411763\pi$
$17$	2.25672			0.547335			0.273667	+	0.961824i	$0.411763\pi$
$18$	1.82146	−	7.98036i	0.429323	−	1.88099i
$19$	3.50362	−	2.79405i	0.803786	−	0.640998i	−0.132915	−	0.991127i	$-0.542434\pi$
$19$	3.50362	−	2.79405i	0.803786	−	0.640998i	0.936701	+	0.350129i	$0.113862\pi$
$20$		0			0
$21$	9.83839	−	2.24555i	2.14691	−	0.490019i
$22$	−2.95528	−	2.35676i	−0.630068	−	0.502463i
$23$	3.83109	+	7.95534i	0.798837	+	1.65880i	0.751325	+	0.659932i	$0.229415\pi$
$23$	3.83109	+	7.95534i	0.798837	+	1.65880i	0.0475120	+	0.998871i	$0.484871\pi$
$24$	−8.27377	−	3.98444i	−1.68888	−	0.813320i
$25$		0			0
$26$	−3.33009	−	2.65566i	−0.653084	−	0.520817i
$27$	−9.13175	−	4.39762i	−1.75741	−	0.846323i
$28$		−	1.06598i		−	0.201452i
$29$	1.72439	+	5.10161i	0.320212	+	0.947346i
$29$	1.72439	+	5.10161i	0.320212	+	0.947346i
$30$		0			0
$31$	−2.38835	+	4.95945i	−0.428960	+	0.890744i	0.568711	+	0.822537i	$0.307442\pi$
$31$	−2.38835	+	4.95945i	−0.428960	+	0.890744i	−0.997671	+	0.0682071i	$0.978272\pi$
$32$	−1.12565	+	1.41152i	−0.198989	+	0.249524i
$33$	−6.96584	+	5.55507i	−1.21260	+	0.967013i
$34$	2.63342	+	1.26819i	0.451629	+	0.217493i
$35$		0			0
$36$	−1.27073	+	1.59344i	−0.211788	+	0.265574i
$37$	−0.970402	−	4.25161i	−0.159533	−	0.698960i	−0.989903	−	0.141747i	$-0.954728\pi$
$37$	−0.970402	−	4.25161i	−0.159533	−	0.698960i	0.830370	−	0.557213i	$-0.188129\pi$
$38$	5.65861	−	1.29154i	0.917949	−	0.209516i
$39$	−7.84928	+	6.25959i	−1.25689	+	1.00234i
$40$		0			0
$41$			1.22818i			0.191810i	0.995391	+	0.0959049i	$0.0305745\pi$
$41$			1.22818i			0.191810i	−0.995391	+	0.0959049i	$0.969426\pi$
$42$	12.7426	+	2.90841i	1.96622	+	0.448778i
$43$	−0.197744	+	0.0952283i	−0.0301556	+	0.0145222i	−0.448901	−	0.893582i	$-0.648184\pi$
$43$	−0.197744	+	0.0952283i	−0.0301556	+	0.0145222i	0.418745	+	0.908104i	$0.362470\pi$
$44$	0.408350	+	0.847948i	0.0615611	+	0.127833i
$45$		0			0
$46$			11.4362i			1.68618i
$47$	0.906190	−	3.97028i	0.132181	−	0.579125i	−0.864843	−	0.502042i	$-0.832582\pi$
$47$	0.906190	−	3.97028i	0.132181	−	0.579125i	0.997025	−	0.0770828i	$-0.0245606\pi$
$48$	−6.18813	−	7.75967i	−0.893179	−	1.12001i
$49$	0.873766	+	3.82822i	0.124824	+	0.546889i
$50$		0			0
$51$	4.29551	−	5.38640i	0.601492	−	0.754247i
$52$	0.460139	+	0.955489i	0.0638098	+	0.132503i
$53$	5.59236	−	11.6127i	0.768170	−	1.59512i	−0.0350114	−	0.999387i	$-0.511147\pi$
$53$	5.59236	−	11.6127i	0.768170	−	1.59512i	0.803181	−	0.595735i	$-0.203139\pi$
$54$	−8.18478	−	10.2634i	−1.11381	−	1.39667i
$55$		0			0
$56$	4.31423	−	8.95859i	0.576513	−	1.19714i
$57$		−	13.6808i		−	1.81207i
$58$	−0.854673	+	6.92225i	−0.112224	+	0.908936i
$59$	5.20741			0.677947			0.338973	−	0.940796i	$-0.389920\pi$
$59$	5.20741			0.677947			0.338973	+	0.940796i	$0.389920\pi$
$60$		0			0
$61$	10.0437	+	8.00960i	1.28597	+	1.02552i	0.997687	+	0.0679786i	$0.0216550\pi$
$61$	10.0437	+	8.00960i	1.28597	+	1.02552i	0.288280	+	0.957546i	$0.406916\pi$
$62$	−5.57405	+	4.44516i	−0.707905	+	0.564535i
$63$	9.06429	−	18.8222i	1.14199	−	2.37137i
$64$	−7.96494	+	3.83571i	−0.995617	+	0.479464i
$65$		0			0
$66$	−11.2504	+	2.56782i	−1.38482	+	0.316077i
$67$	−3.77413	+	0.861420i	−0.461083	+	0.105239i	−0.446752	−	0.894658i	$-0.647419\pi$
$67$	−3.77413	+	0.861420i	−0.461083	+	0.105239i	−0.0143317	+	0.999897i	$0.504562\pi$
$68$	−0.453747	−	0.568981i	−0.0550249	−	0.0689991i
$69$	26.2802	+	5.99829i	3.16377	+	0.722109i
$70$		0			0
$71$	−1.67978	+	7.35960i	−0.199353	+	0.873424i	0.771969	+	0.635660i	$0.219272\pi$
$71$	−1.67978	+	7.35960i	−0.199353	+	0.873424i	−0.971323	+	0.237764i	$0.923585\pi$
$72$	−17.1282	+	8.24851i	−2.01858	+	0.972097i
$73$	−5.36879	+	2.58547i	−0.628369	+	0.302607i	−0.720832	−	0.693109i	$-0.756240\pi$
$73$	−5.36879	+	2.58547i	−0.628369	+	0.302607i	0.0924631	+	0.995716i	$0.470526\pi$
$74$	1.25685	−	5.50664i	0.146106	−	0.640134i
$75$		0			0
$76$	−1.40891	−	0.321575i	−0.161613	−	0.0368872i
$77$	−6.01486	−	7.54240i	−0.685457	−	0.859536i
$78$	−12.6772	+	2.89348i	−1.43541	+	0.327623i
$79$	−5.30705	+	1.21130i	−0.597089	+	0.136282i	−0.510376	−	0.859952i	$-0.670494\pi$
$79$	−5.30705	+	1.21130i	−0.597089	+	0.136282i	−0.0867136	+	0.996233i	$0.527637\pi$
$80$		0			0
$81$	−10.7957	+	5.19892i	−1.19952	+	0.577658i
$82$	−0.690191	+	1.43320i	−0.0762189	+	0.158270i
$83$	−6.33189	+	5.04951i	−0.695015	+	0.554256i	−0.906023	−	0.423228i	$-0.860897\pi$
$83$	−6.33189	+	5.04951i	−0.695015	+	0.554256i	0.211008	+	0.977484i	$0.432325\pi$
$84$	−2.54432	−	2.02903i	−0.277608	−	0.221385i
$85$		0			0
$86$	−0.284267			−0.0306533
$87$	15.4589	+	5.59474i	1.65737	+	0.599819i
$88$			8.77887i			0.935830i
$89$	−0.927897	+	1.92680i	−0.0983568	+	0.204240i	−0.944341	−	0.328968i	$-0.893299\pi$
$89$	−0.927897	+	1.92680i	−0.0983568	+	0.204240i	0.845984	+	0.533208i	$0.179014\pi$
$90$		0			0
$91$	−6.77770	−	8.49897i	−0.710496	−	0.890934i
$92$	1.23546	−	2.56546i	0.128806	−	0.267468i
$93$	7.29130	+	15.1405i	0.756073	+	1.57000i
$94$	3.28860	−	4.12378i	0.339193	−	0.425335i
$95$		0			0
$96$	1.22646	+	5.37346i	0.125175	+	0.548426i
$97$	4.29066	+	5.38032i	0.435651	+	0.546289i	0.950391	−	0.311057i	$-0.100683\pi$
$97$	4.29066	+	5.38032i	0.435651	+	0.546289i	−0.514740	+	0.857346i	$0.672112\pi$
$98$	−1.13169	+	4.95827i	−0.114318	+	0.500861i
$99$			18.4446i			1.85375i
$100$		0			0
$101$	3.88487	+	8.06703i	0.386559	+	0.802699i	0.999917	+	0.0128935i	$0.00410425\pi$
$101$	3.88487	+	8.06703i	0.386559	+	0.802699i	−0.613357	+	0.789805i	$0.710181\pi$
$102$	8.03949	−	3.87162i	0.796028	−	0.383347i
$103$	−13.8772	−	3.16739i	−1.36736	−	0.312092i	−0.525047	−	0.851073i	$-0.675952\pi$
$103$	−13.8772	−	3.16739i	−1.36736	−	0.312092i	−0.842318	+	0.538981i	$0.818809\pi$
$104$			9.89225i			0.970015i
$105$		0			0
$106$	13.0517	−	10.4084i	1.26770	−	1.01095i
$107$	11.3420	−	2.58874i	1.09648	−	0.250263i	0.364233	−	0.931308i	$-0.381331\pi$
$107$	11.3420	−	2.58874i	1.09648	−	0.250263i	0.732242	+	0.681044i	$0.238474\pi$
$108$	0.727314	+	3.18657i	0.0699859	+	0.306628i
$109$	4.05974	−	5.09075i	0.388852	−	0.487605i	−0.548420	−	0.836203i	$-0.684771\pi$
$109$	4.05974	−	5.09075i	0.388852	−	0.487605i	0.937273	+	0.348598i	$0.113342\pi$
$110$		0			0
$111$	−11.9949	−	5.77646i	−1.13851	−	0.548277i
$112$	8.40193	−	6.70032i	0.793908	−	0.633121i
$113$	−6.75963	+	8.47631i	−0.635893	+	0.797384i	−0.990483	−	0.137638i	$-0.956049\pi$
$113$	−6.75963	+	8.47631i	−0.635893	+	0.797384i	0.354590	+	0.935022i	$0.384620\pi$
$114$	7.68809	−	15.9645i	0.720056	−	1.49521i
$115$		0			0
$116$	0.939542	−	1.46052i	0.0872343	−	0.135606i
$117$			20.7838i			1.92147i
$118$	6.07666	+	2.92636i	0.559402	+	0.269394i
$119$	5.83223	+	4.65105i	0.534640	+	0.426361i
$120$		0			0
$121$	−2.23678	−	1.07718i	−0.203344	−	0.0979253i
$122$	7.21919	+	14.9908i	0.653595	+	1.35720i
$123$	2.93146	+	2.33776i	0.264320	+	0.210789i
$124$	1.73063	−	0.395004i	0.155415	−	0.0354724i
$125$		0			0
$126$	21.1547	−	16.8703i	1.88461	−	1.50293i
$127$	−2.20499	+	9.66067i	−0.195661	+	0.857246i	0.777822	+	0.628485i	$0.216325\pi$
$127$	−2.20499	+	9.66067i	−0.195661	+	0.857246i	−0.973483	+	0.228761i	$0.926532\pi$
$128$	−7.83921			−0.692895
$129$	−0.149098	+	0.653240i	−0.0131273	+	0.0575146i
$130$		0			0
$131$	−0.463506	−	0.962480i	−0.0404967	−	0.0840923i	0.879739	−	0.475457i	$-0.157717\pi$
$131$	−0.463506	−	0.962480i	−0.0404967	−	0.0840923i	−0.920236	+	0.391365i	$0.872003\pi$
$132$	2.80117	+	0.639349i	0.243811	+	0.0556482i
$133$	14.8132			1.28446
$134$	−4.88821	−	1.11570i	−0.422277	−	0.0963821i
$135$		0			0
$136$	−1.51055	−	6.61814i	−0.129528	−	0.567501i
$137$	−2.23008	−	9.77063i	−0.190529	−	0.834761i	−0.976331	−	0.216283i	$-0.930607\pi$
$137$	−2.23008	−	9.77063i	−0.190529	−	0.834761i	0.785802	−	0.618478i	$-0.212251\pi$
$138$	27.2963	+	21.7680i	2.32361	+	1.85302i
$139$	−5.66533	+	2.72828i	−0.480527	+	0.231409i	−0.658435	−	0.752638i	$-0.728781\pi$
$139$	−5.66533	+	2.72828i	−0.480527	+	0.231409i	0.177908	+	0.984047i	$0.443067\pi$
$140$		0			0
$141$	−7.75150	−	9.72007i	−0.652794	−	0.818578i
$142$	−6.09600	+	7.64414i	−0.511565	+	0.641482i
$143$	8.64712	+	4.16423i	0.723108	+	0.348231i
$144$	−20.5465			−1.71221
$145$		0			0
$146$	−7.71792			−0.638739
$147$	10.8005	+	5.20122i	0.890806	+	0.428990i
$148$	−0.876833	+	1.09951i	−0.0720752	+	0.0903795i
$149$	12.6383	+	15.8479i	1.03537	+	1.29831i	0.953411	+	0.301674i	$0.0975455\pi$
$149$	12.6383	+	15.8479i	1.03537	+	1.29831i	0.0819568	+	0.996636i	$0.473883\pi$
$150$		0			0
$151$	15.8338	−	7.62515i	1.28854	−	0.620526i	0.340966	−	0.940075i	$-0.389246\pi$
$151$	15.8338	−	7.62515i	1.28854	−	0.620526i	0.947570	+	0.319549i	$0.103531\pi$
$152$	−10.5391	−	8.40465i	−0.854834	−	0.681707i
$153$	−3.17369	−	13.9049i	−0.256578	−	1.12414i
$154$	−2.78036	−	12.1815i	−0.224048	−	0.981617i
$155$		0			0
$156$	3.15643	+	0.720435i	0.252717	+	0.0576809i
$157$	−15.8900			−1.26816			−0.634081	−	0.773267i	$-0.718621\pi$
$157$	−15.8900			−1.26816			−0.634081	+	0.773267i	$0.718621\pi$
$158$	−6.87363	−	1.56886i	−0.546837	−	0.124812i
$159$	−17.0727	−	35.4519i	−1.35396	−	2.81152i
$160$		0			0
$161$	−6.49477	+	28.4554i	−0.511859	+	2.24260i
$162$	−15.5194			−1.21932
$163$	−1.04194	+	4.56506i	−0.0816114	+	0.357563i	−0.999201	−	0.0399660i	$-0.987275\pi$
$163$	−1.04194	+	4.56506i	−0.0816114	+	0.357563i	0.917590	+	0.397529i	$0.130132\pi$
$164$	0.309658	−	0.246944i	0.0241802	−	0.0192831i
$165$		0			0
$166$	−10.2265	+	2.33413i	−0.793729	+	0.181163i
$167$	−7.87682	−	6.28156i	−0.609527	−	0.486081i	0.269406	−	0.963027i	$-0.413173\pi$
$167$	−7.87682	−	6.28156i	−0.609527	−	0.486081i	−0.878933	+	0.476945i	$0.841744\pi$
$168$	−13.1708	−	27.3494i	−1.01615	−	2.11005i
$169$	−1.96880	−	0.948126i	−0.151446	−	0.0729328i
$170$		0			0
$171$	−22.1429	−	17.6583i	−1.69331	−	1.35037i
$172$	0.0637690	+	0.0307095i	0.00486234	+	0.00234158i
$173$		−	1.83035i		−	0.139159i	−0.997576	−	0.0695796i	$-0.977834\pi$
$173$		−	1.83035i		−	0.139159i	0.997576	−	0.0695796i	$-0.0221658\pi$
$174$	14.8954	+	15.2160i	1.12922	+	1.15352i
$175$		0			0
$176$	−4.11669	+	8.54839i	−0.310307	+	0.644359i
$177$	9.91194	−	12.4292i	0.745027	−	0.934234i
$178$	−2.16557	+	1.72699i	−0.162317	+	0.129443i
$179$	−4.91340	−	2.36617i	−0.367245	−	0.176856i	0.241155	−	0.970487i	$-0.422474\pi$
$179$	−4.91340	−	2.36617i	−0.367245	−	0.176856i	−0.608400	+	0.793631i	$0.708188\pi$
$180$		0			0
$181$	6.36106	−	7.97652i	0.472814	−	0.592890i	−0.487044	−	0.873378i	$-0.661925\pi$
$181$	6.36106	−	7.97652i	0.472814	−	0.592890i	0.959858	+	0.280488i	$0.0904962\pi$
$182$	−3.13298	−	13.7265i	−0.232232	−	1.01747i
$183$	38.2351	−	8.72690i	2.82642	−	0.645111i
$184$	20.7658	−	16.5601i	1.53087	−	1.22083i
$185$		0			0
$186$			21.7653i			1.59591i
$187$	−6.42100	−	1.46555i	−0.469550	−	0.107172i
$188$	−1.18322	+	0.569808i	−0.0862951	+	0.0415575i
$189$	−14.5366	−	30.1855i	−1.05738	−	2.19567i
$190$		0			0
$191$			4.05183i			0.293180i	0.989197	+	0.146590i	$0.0468298\pi$
$191$			4.05183i			0.293180i	−0.989197	+	0.146590i	$0.953170\pi$
$192$	−6.00553	+	26.3119i	−0.433412	+	1.89890i
$193$	−14.6071	−	18.3168i	−1.05145	−	1.31847i	−0.946043	−	0.324041i	$-0.894958\pi$
$193$	−14.6071	−	18.3168i	−1.05145	−	1.31847i	−0.105402	−	0.994430i	$-0.533613\pi$
$194$	1.98335	+	8.68962i	0.142396	+	0.623879i
$195$		0			0
$196$	0.789516	−	0.990021i	0.0563940	−	0.0707158i
$197$	10.5479	+	21.9029i	0.751506	+	1.56052i	0.826243	+	0.563314i	$0.190474\pi$
$197$	10.5479	+	21.9029i	0.751506	+	1.56052i	−0.0747372	+	0.997203i	$0.523812\pi$
$198$	−10.3652	+	21.5235i	−0.736619	+	1.52961i
$199$	4.88750	+	6.12873i	0.346465	+	0.434454i	0.924281	−	0.381714i	$-0.124666\pi$
$199$	4.88750	+	6.12873i	0.346465	+	0.434454i	−0.577815	+	0.816168i	$0.696095\pi$
$200$		0			0
$201$	−5.12773	+	10.6478i	−0.361682	+	0.751041i
$202$			11.5968i			0.815946i
$203$	−6.05782	+	16.7385i	−0.425175	+	1.17481i
$204$	−2.22174			−0.155553
$205$		0			0
$206$	−14.4138	−	11.4946i	−1.00425	−	0.800866i
$207$	43.6293	−	34.7932i	3.03245	−	2.41830i
$208$	−4.63879	+	9.63254i	−0.321642	+	0.667897i
$209$	−11.7833	+	5.67453i	−0.815067	+	0.392515i
$210$		0			0
$211$	9.50058	−	2.16845i	0.654047	−	0.149282i	0.117395	−	0.993085i	$-0.462546\pi$
$211$	9.50058	−	2.16845i	0.654047	−	0.149282i	0.536653	+	0.843803i	$0.319689\pi$
$212$	−4.05230	+	0.924910i	−0.278313	+	0.0635231i
$213$	14.3687	+	18.0178i	0.984530	+	1.23456i
$214$	14.6901	+	3.35291i	1.00419	+	0.229201i
$215$		0			0
$216$	−6.78424	+	29.7237i	−0.461609	+	2.02244i
$217$	−16.3937	+	7.89481i	−1.11288	+	0.535934i
$218$	7.59822	−	3.65911i	0.514616	−	0.247826i
$219$	−4.04804	+	17.7356i	−0.273541	+	1.19846i
$220$		0			0
$221$	−7.23535	−	1.65142i	−0.486702	−	0.111087i
$222$	−10.7511	−	13.4814i	−0.721564	−	0.904812i
$223$	5.54244	−	1.26503i	0.371149	−	0.0847124i	−0.0328778	−	0.999459i	$-0.510467\pi$
$223$	5.54244	−	1.26503i	0.371149	−	0.0847124i	0.404027	+	0.914747i	$0.367610\pi$
$224$	−5.81822	+	1.32797i	−0.388746	+	0.0887288i
$225$		0			0
$226$	−12.6513	+	6.09257i	−0.841555	+	0.405272i
$227$	11.0814	−	23.0107i	0.735496	−	1.52727i	−0.110379	−	0.993890i	$-0.535206\pi$
$227$	11.0814	−	23.0107i	0.735496	−	1.52727i	0.845874	−	0.533383i	$-0.179079\pi$
$228$	−3.44931	+	2.75073i	−0.228436	+	0.182172i
$229$	−16.9638	−	13.5281i	−1.12100	−	0.893965i	−0.125819	−	0.992053i	$-0.540156\pi$
$229$	−16.9638	−	13.5281i	−1.12100	−	0.893965i	−0.995178	+	0.0980879i	$0.968727\pi$
$230$		0			0
$231$	−29.4513			−1.93775
$232$	13.8070	−	8.47182i	0.906471	−	0.556202i
$233$		−	12.5149i		−	0.819880i	−0.912112	−	0.409940i	$-0.865550\pi$
$233$		−	12.5149i		−	0.819880i	0.912112	−	0.409940i	$-0.134450\pi$
$234$	−11.6797	+	24.2532i	−0.763527	+	1.58548i
$235$		0			0
$236$	−1.04703	−	1.31293i	−0.0681556	−	0.0854645i
$237$	−7.21043	+	14.9726i	−0.468368	+	0.972576i
$238$	4.19207	+	8.70492i	0.271731	+	0.564256i
$239$	10.5358	−	13.2115i	0.681506	−	0.854581i	−0.313986	−	0.949427i	$-0.601665\pi$
$239$	10.5358	−	13.2115i	0.681506	−	0.854581i	0.995492	+	0.0948466i	$0.0302361\pi$
$240$		0			0
$241$	−4.62573	−	20.2666i	−0.297969	−	1.30549i	−0.873146	−	0.487459i	$-0.837924\pi$
$241$	−4.62573	−	20.2666i	−0.297969	−	1.30549i	0.575177	−	0.818029i	$-0.304933\pi$
$242$	−2.00483	−	2.51398i	−0.128875	−	0.161604i
$243$	−1.37382	+	6.01911i	−0.0881308	+	0.386126i
$244$		−	4.14275i		−	0.265212i
$245$		0			0
$246$	2.10706	+	4.37536i	0.134341	+	0.278963i
$247$	−13.2777	+	6.39421i	−0.844840	+	0.406854i
$248$	16.1429	+	3.68452i	1.02508	+	0.233967i
$249$			24.7245i			1.56685i
$250$		0			0
$251$	−4.85033	+	3.86801i	−0.306150	+	0.244146i	−0.764498	−	0.644627i	$-0.777013\pi$
$251$	−4.85033	+	3.86801i	−0.306150	+	0.244146i	0.458348	+	0.888773i	$0.348441\pi$
$252$	−6.56810	+	1.49913i	−0.413751	+	0.0944360i
$253$	−5.73419	−	25.1231i	−0.360506	−	1.57948i
$254$	−8.00199	+	10.0342i	−0.502089	+	0.629600i
$255$		0			0
$256$	6.78210	+	3.26609i	0.423881	+	0.204130i
$257$	−15.5566	+	12.4060i	−0.970393	+	0.773863i	−0.974097	−	0.226130i	$-0.927392\pi$
$257$	−15.5566	+	12.4060i	−0.970393	+	0.773863i	0.00370392	+	0.999993i	$0.498821\pi$
$258$	−0.541082	+	0.678496i	−0.0336863	+	0.0422413i
$259$	6.25458	−	12.9878i	0.388641	−	0.807020i
$260$		0			0
$261$	29.0087	−	17.7995i	1.79559	−	1.10176i
$262$		−	1.38362i		−	0.0854801i
$263$	−10.3840	−	5.00068i	−0.640306	−	0.308355i	0.0854137	−	0.996346i	$-0.472779\pi$
$263$	−10.3840	−	5.00068i	−0.640306	−	0.308355i	−0.725720	+	0.687990i	$0.758493\pi$
$264$	20.9536	+	16.7100i	1.28961	+	1.02843i
$265$		0			0
$266$	17.2859	+	8.32444i	1.05986	+	0.510404i
$267$	2.83274	+	5.88225i	0.173361	+	0.359988i
$268$	0.976033	+	0.778360i	0.0596207	+	0.0475459i
$269$	−2.90457	+	0.662949i	−0.177095	+	0.0404207i	−0.310149	−	0.950688i	$-0.600379\pi$
$269$	−2.90457	+	0.662949i	−0.177095	+	0.0404207i	0.133054	+	0.991109i	$0.457522\pi$
$270$		0			0
$271$	−12.3499	+	9.84868i	−0.750200	+	0.598265i	−0.922146	−	0.386842i	$-0.873566\pi$
$271$	−12.3499	+	9.84868i	−0.750200	+	0.598265i	0.171946	+	0.985106i	$0.444995\pi$
$272$	1.63257	−	7.15274i	0.0989888	−	0.433698i
$273$	−33.1864			−2.00854
$274$	2.88838	−	12.6548i	0.174493	−	0.764506i
$275$		0			0
$276$	−3.77170	−	7.83201i	−0.227030	−	0.471432i
$277$	−18.8229	−	4.29620i	−1.13096	−	0.258134i	−0.384213	−	0.923245i	$-0.625527\pi$
$277$	−18.8229	−	4.29620i	−1.13096	−	0.258134i	−0.746744	+	0.665111i	$0.768384\pi$
$278$	−8.14420			−0.488457
$279$	33.9167	+	7.74125i	2.03054	+	0.463457i
$280$		0			0
$281$	2.06142	+	9.03169i	0.122974	+	0.538785i	0.998457	+	0.0555355i	$0.0176866\pi$
$281$	2.06142	+	9.03169i	0.122974	+	0.538785i	−0.875482	+	0.483250i	$0.839456\pi$
$282$	−3.58311	−	15.6986i	−0.213371	−	0.934841i
$283$	−9.11363	−	7.26788i	−0.541749	−	0.432030i	0.313999	−	0.949423i	$-0.398331\pi$
$283$	−9.11363	−	7.26788i	−0.541749	−	0.432030i	−0.855748	+	0.517393i	$0.826903\pi$
$284$	2.19330	−	1.05624i	0.130149	−	0.0626762i
$285$		0			0
$286$	7.75040	+	9.71870i	0.458291	+	0.574679i
$287$	−2.53125	+	3.17409i	−0.149415	+	0.187361i
$288$	10.2802	+	4.95066i	0.605764	+	0.291721i
$289$	−11.9072			−0.700424
$290$		0			0
$291$	21.0089			1.23156
$292$	1.73134	+	0.833771i	0.101319	+	0.0487928i
$293$	−3.19463	+	4.00594i	−0.186632	+	0.234030i	−0.866341	−	0.499452i	$-0.833535\pi$
$293$	−3.19463	+	4.00594i	−0.186632	+	0.234030i	0.679709	+	0.733482i	$0.262106\pi$
$294$	9.68044	+	12.1389i	0.564575	+	0.707954i
$295$		0			0
$296$	−11.8189	+	5.69167i	−0.686959	+	0.330822i
$297$	23.1265	+	18.4428i	1.34194	+	1.07016i
$298$	5.84202	+	25.5955i	0.338419	+	1.48271i
$299$	−6.46143	−	28.3094i	−0.373674	−	1.63717i
$300$		0			0
$301$	−0.707309	−	0.161439i	−0.0407686	−	0.00930517i
$302$	22.7619			1.30980
$303$	26.6492	+	6.08250i	1.53096	+	0.349431i
$304$	−6.32120	−	13.1261i	−0.362546	−	0.752834i
$305$		0			0
$306$	4.11054	−	18.0094i	0.234984	−	1.02953i
$307$	−13.4126			−0.765498			−0.382749	−	0.923852i	$-0.625023\pi$
$307$	−13.4126			−0.765498			−0.382749	+	0.923852i	$0.625023\pi$
$308$	−0.692268	+	3.03302i	−0.0394456	+	0.172823i
$309$	−33.9744	+	27.0937i	−1.93273	+	1.54130i
$310$		0			0
$311$	8.43376	−	1.92495i	0.478235	−	0.109154i	0.0233933	−	0.999726i	$-0.492553\pi$
$311$	8.43376	−	1.92495i	0.478235	−	0.109154i	0.454842	+	0.890572i	$0.349696\pi$
$312$	23.6111	+	18.8292i	1.33671	+	1.06599i
$313$	−3.64566	−	7.57028i	−0.206065	−	0.427898i	0.772165	−	0.635422i	$-0.219174\pi$
$313$	−3.64566	−	7.57028i	−0.206065	−	0.427898i	−0.978230	+	0.207524i	$0.933459\pi$
$314$	−18.5425	−	8.92958i	−1.04641	−	0.503925i
$315$		0			0
$316$	1.37246	+	1.09450i	0.0772070	+	0.0615706i
$317$	−8.98359	−	4.32627i	−0.504569	−	0.242988i	0.164242	−	0.986420i	$-0.447482\pi$
$317$	−8.98359	−	4.32627i	−0.504569	−	0.242988i	−0.668811	+	0.743433i	$0.733196\pi$
$318$		−	50.9639i		−	2.85792i
$319$	−1.59331	−	15.6354i	−0.0892082	−	0.875412i
$320$		0			0
$321$	15.4099	−	31.9989i	0.860096	−	1.78601i
$322$	−23.5698	+	29.5556i	−1.31349	+	1.64707i
$323$	7.90669	−	6.30538i	0.439940	−	0.350841i
$324$	3.48142	+	1.67657i	0.193412	+	0.0931425i
$325$		0			0
$326$	−3.78126	+	4.74155i	−0.209425	+	0.262610i
$327$	−4.42331	−	19.3798i	−0.244609	−	1.07170i
$328$	3.60181	−	0.822090i	0.198877	−	0.0453923i
$329$	10.5246	−	8.39309i	0.580240	−	0.462726i
$330$		0			0
$331$			12.3448i			0.678531i	0.940691	+	0.339266i	$0.110179\pi$
$331$			12.3448i			0.678531i	−0.940691	+	0.339266i	$0.889821\pi$
$332$	2.54624	+	0.581163i	0.139743	+	0.0318955i
$333$	−24.8317	+	11.9583i	−1.36077	+	0.655312i
$334$	−5.66167	−	11.7566i	−0.309793	−	0.643292i
$335$		0			0
$336$		−	32.8075i		−	1.78980i
$337$	3.54168	−	15.5171i	0.192927	−	0.845270i	−0.782094	−	0.623160i	$-0.785849\pi$
$337$	3.54168	−	15.5171i	0.192927	−	0.845270i	0.975022	−	0.222110i	$-0.0712944\pi$
$338$	−1.76464	−	2.21278i	−0.0959836	−	0.120360i
$339$	7.36499	+	32.2681i	0.400011	+	1.75256i
$340$		0			0
$341$	10.0163	−	12.5600i	0.542411	−	0.680162i
$342$	−15.9158	−	33.0494i	−0.860626	−	1.78711i
$343$	4.40785	−	9.15299i	0.238001	−	0.494215i
$344$	0.411631	+	0.516169i	0.0221937	+	0.0278300i
$345$		0			0
$346$	1.02859	−	2.13589i	0.0552973	−	0.114826i
$347$		−	22.3607i		−	1.20038i	−0.799856	−	0.600192i	$-0.795091\pi$
$347$		−	22.3607i		−	1.20038i	0.799856	−	0.600192i	$-0.204909\pi$
$348$	−1.69766	−	5.02253i	−0.0910042	−	0.269236i
$349$	−8.24007			−0.441081			−0.220540	−	0.975378i	$-0.570782\pi$
$349$	−8.24007			−0.441081			−0.220540	+	0.975378i	$0.570782\pi$
$350$		0			0
$351$	26.0595	+	20.7818i	1.39096	+	1.10925i
$352$	4.11945	−	3.28515i	0.219567	−	0.175099i
$353$	−4.14838	+	8.61419i	−0.220796	+	0.458487i	−0.981714	−	0.190360i	$-0.939034\pi$
$353$	−4.14838	+	8.61419i	−0.220796	+	0.458487i	0.760919	+	0.648847i	$0.224749\pi$
$354$	18.5512	−	8.93380i	0.985986	−	0.474826i
$355$		0			0
$356$	0.672366	−	0.153463i	0.0356353	−	0.00813353i
$357$	22.2025	−	5.06757i	1.17508	−	0.268205i
$358$	−4.40388	−	5.52229i	−0.232752	−	0.291862i
$359$	12.3638	+	2.82196i	0.652538	+	0.148938i	0.535959	−	0.844244i	$-0.319950\pi$
$359$	12.3638	+	2.82196i	0.652538	+	0.148938i	0.116579	+	0.993181i	$0.462807\pi$
$360$		0			0
$361$	0.240782	−	1.05493i	0.0126727	−	0.0555228i
$362$	11.9054	−	5.73333i	0.625733	−	0.301337i
$363$	−6.82860	+	3.28848i	−0.358409	+	0.172601i
$364$	−0.780065	+	3.41769i	−0.0408865	+	0.179136i
$365$		0			0
$366$	49.5217	+	11.3030i	2.58854	+	0.590817i
$367$	11.9220	+	14.9498i	0.622326	+	0.780372i	0.988670	−	0.150108i	$-0.0479621\pi$
$367$	11.9220	+	14.9498i	0.622326	+	0.780372i	−0.366344	+	0.930479i	$0.619391\pi$
$368$	27.9862	−	6.38766i	1.45888	−	0.332980i
$369$	7.56748	−	1.72723i	0.393947	−	0.0899159i
$370$		0			0
$371$	38.3862	−	18.4858i	1.99291	−	0.959737i
$372$	2.35132	−	4.88257i	0.121910	−	0.253149i
$373$	−21.2829	+	16.9726i	−1.10199	+	0.878805i	−0.993334	−	0.115274i	$-0.963225\pi$
$373$	−21.2829	+	16.9726i	−1.10199	+	0.878805i	−0.108653	+	0.994080i	$0.534654\pi$
$374$	−6.66925	−	5.31855i	−0.344858	−	0.275015i
$375$		0			0
$376$	−12.2500			−0.631743
$377$	−1.79538	−	17.6183i	−0.0924668	−	0.907390i
$378$		−	43.3932i		−	2.23191i
$379$	−7.68735	+	15.9629i	−0.394873	+	0.819961i	0.604848	+	0.796341i	$0.293234\pi$
$379$	−7.68735	+	15.9629i	−0.394873	+	0.819961i	−0.999721	+	0.0236208i	$0.992481\pi$
$380$		0			0
$381$	18.8613	+	23.6513i	0.966295	+	1.21170i
$382$	−2.27697	+	4.72818i	−0.116500	+	0.241915i
$383$	−12.3108	−	25.5635i	−0.629050	−	1.30624i	−0.935155	−	0.354238i	$-0.884740\pi$
$383$	−12.3108	−	25.5635i	−0.629050	−	1.30624i	0.306105	−	0.951998i	$-0.400974\pi$
$384$	−14.9214	+	18.7108i	−0.761454	+	0.954834i
$385$		0			0
$386$	−6.75212	−	29.5830i	−0.343674	−	1.50573i
$387$	0.864846	+	1.08448i	0.0439626	+	0.0551273i
$388$	0.493825	−	2.16359i	0.0250701	−	0.109839i
$389$			15.0229i			0.761689i	0.924639	+	0.380845i	$0.124367\pi$
$389$			15.0229i			0.761689i	−0.924639	+	0.380845i	$0.875633\pi$
$390$		0			0
$391$	8.64570	+	17.9530i	0.437232	+	0.907921i
$392$	10.6419	−	5.12488i	0.537498	−	0.258846i
$393$	−3.17953	−	0.725706i	−0.160386	−	0.0366070i
$394$			31.4866i			1.58627i
$395$		0			0
$396$	4.65038	−	3.70856i	0.233691	−	0.186362i
$397$	14.0766	−	3.21289i	0.706483	−	0.161250i	0.145841	−	0.989308i	$-0.453411\pi$
$397$	14.0766	−	3.21289i	0.706483	−	0.161250i	0.560642	+	0.828058i	$0.310554\pi$
$398$	2.25924	+	9.89836i	0.113245	+	0.496160i
$399$	28.1958	−	35.3565i	1.41156	−	1.77004i
$400$		0			0
$401$	8.77169	+	4.22422i	0.438037	+	0.210948i	0.639887	−	0.768469i	$-0.278981\pi$
$401$	8.77169	+	4.22422i	0.438037	+	0.210948i	−0.201850	+	0.979416i	$0.564695\pi$
$402$	−11.9674	+	9.54366i	−0.596878	+	0.475994i
$403$	11.2866	−	14.1529i	0.562225	−	0.705008i
$404$	1.25281	−	2.60148i	0.0623294	−	0.129428i
$405$		0			0
$406$	−16.4754	+	16.1283i	−0.817661	+	0.800433i
$407$			12.7272i			0.630864i
$408$	−18.6716	−	8.99176i	−0.924381	−	0.445159i
$409$	5.71984	+	4.56142i	0.282828	+	0.225548i	0.754620	−	0.656162i	$-0.227821\pi$
$409$	5.71984	+	4.56142i	0.282828	+	0.225548i	−0.471792	+	0.881710i	$0.656393\pi$
$410$		0			0
$411$	−27.5656	−	13.2749i	−1.35971	−	0.654802i
$412$	1.99164	+	4.13568i	0.0981210	+	0.203750i
$413$	13.4579	+	10.7324i	0.662222	+	0.528104i
$414$	70.4646	−	16.0831i	3.46315	−	0.790441i
$415$		0			0
$416$	4.64190	−	3.70179i	0.227588	−	0.181495i
$417$	−4.27163	+	18.7152i	−0.209183	+	0.916489i
$418$	−16.9391			−0.828518
$419$	−6.39220	+	28.0061i	−0.312280	+	1.36819i	0.538483	+	0.842636i	$0.318998\pi$
$419$	−6.39220	+	28.0061i	−0.312280	+	1.36819i	−0.850763	+	0.525550i	$0.823860\pi$
$420$		0			0
$421$	−10.9771	−	22.7941i	−0.534989	−	1.11092i	−0.976868	−	0.213842i	$-0.931402\pi$
$421$	−10.9771	−	22.7941i	−0.534989	−	1.11092i	0.441879	−	0.897075i	$-0.354312\pi$
$422$	12.3051	+	2.80855i	0.599001	+	0.136718i
$423$	−25.7374			−1.25140
$424$	−37.7990	−	8.62738i	−1.83568	−	0.418982i
$425$		0			0
$426$	6.64192	+	29.1002i	0.321802	+	1.40991i
$427$	9.44923	+	41.3998i	0.457280	+	2.00348i
$428$	−2.93318	−	2.33913i	−0.141780	−	0.113066i
$429$	26.3985	−	12.7128i	1.27453	−	0.613782i
$430$		0			0
$431$	−5.26786	−	6.60569i	−0.253744	−	0.318185i	0.638602	−	0.769537i	$-0.279513\pi$
$431$	−5.26786	−	6.60569i	−0.253744	−	0.318185i	−0.892346	+	0.451353i	$0.850942\pi$
$432$	−20.5445	+	25.7620i	−0.988448	+	1.23948i
$433$	26.5580	+	12.7897i	1.27630	+	0.614632i	0.944436	−	0.328696i	$-0.106609\pi$
$433$	26.5580	+	12.7897i	1.27630	+	0.614632i	0.331861	+	0.943328i	$0.392324\pi$
$434$	−23.5668			−1.13124
$435$		0			0
$436$	−2.09979			−0.100562
$437$	35.6503	+	17.1683i	1.70538	+	0.821270i
$438$	−14.6905	+	18.4213i	−0.701940	+	0.880205i
$439$	−9.00472	−	11.2916i	−0.429772	−	0.538917i	0.519044	−	0.854748i	$-0.326288\pi$
$439$	−9.00472	−	11.2916i	−0.429772	−	0.538917i	−0.948815	+	0.315831i	$0.897717\pi$
$440$		0			0
$441$	22.3589	−	10.7675i	1.06471	−	0.512737i
$442$	−7.51508	−	5.99307i	−0.357456	−	0.285061i
$443$	2.52700	+	11.0715i	0.120061	+	0.526023i	0.998811	+	0.0487412i	$0.0155209\pi$
$443$	2.52700	+	11.0715i	0.120061	+	0.526023i	−0.878750	+	0.477282i	$0.841622\pi$
$444$	0.955358	+	4.18570i	0.0453393	+	0.198644i
$445$		0			0
$446$	7.17852	+	1.63845i	0.339913	+	0.0775828i
$447$	61.8823			2.92693
$448$	−28.4898	−	6.50261i	−1.34602	−	0.307219i
$449$	4.61925	+	9.59196i	0.217996	+	0.452673i	0.981074	−	0.193633i	$-0.0620272\pi$
$449$	4.61925	+	9.59196i	0.217996	+	0.452673i	−0.763078	+	0.646306i	$0.776313\pi$
$450$		0			0
$451$	0.797601	−	3.49452i	0.0375576	−	0.164550i
$452$	3.49623			0.164449
$453$	11.9386	−	52.3065i	0.560925	−	2.45757i
$454$	25.8622	−	20.6245i	1.21378	−	0.967953i
$455$		0			0
$456$	−40.1209	+	9.15733i	−1.87883	+	0.428831i
$457$	−26.4009	−	21.0540i	−1.23498	−	0.984866i	−0.999917	−	0.0128868i	$-0.995898\pi$
$457$	−26.4009	−	21.0540i	−1.23498	−	0.984866i	−0.235066	−	0.971979i	$-0.575531\pi$
$458$	−12.1931	−	25.3193i	−0.569748	−	1.18309i
$459$	−20.6078	−	9.92420i	−0.961890	−	0.463222i
$460$		0			0
$461$	−6.34335	−	5.05865i	−0.295439	−	0.235605i	0.464540	−	0.885552i	$-0.346220\pi$
$461$	−6.34335	−	5.05865i	−0.295439	−	0.235605i	−0.759979	+	0.649947i	$0.774791\pi$
$462$	−34.3674	−	16.5505i	−1.59892	−	0.769999i
$463$			10.7659i			0.500334i	0.968203	+	0.250167i	$0.0804855\pi$
$463$			10.7659i			0.500334i	−0.968203	+	0.250167i	$0.919515\pi$
$464$	17.4172	−	1.77488i	0.808572	−	0.0823969i
$465$		0			0
$466$	7.03291	−	14.6040i	0.325793	−	0.676517i
$467$	−11.1144	+	13.9370i	−0.514314	+	0.644930i	−0.969391	−	0.245523i	$-0.921040\pi$
$467$	−11.1144	+	13.9370i	−0.514314	+	0.644930i	0.455077	+	0.890452i	$0.349612\pi$
$468$	5.24017	−	4.17890i	0.242227	−	0.193170i
$469$	−11.5292	−	5.55215i	−0.532368	−	0.256375i
$470$		0			0
$471$	−30.2455	+	37.9267i	−1.39364	+	1.74757i
$472$	−3.48561	−	15.2714i	−0.160438	−	0.702925i
$473$	0.624479	−	0.142533i	0.0287136	−	0.00655368i
$474$	−16.8281	+	13.4199i	−0.772939	+	0.616399i
$475$		0			0
$476$		−	2.40563i		−	0.110262i
$477$	−79.4165	−	18.1263i	−3.63623	−	0.829946i
$478$	19.7189	−	9.49611i	0.901920	−	0.434342i
$479$	−1.34146	−	2.78556i	−0.0612927	−	0.127276i	0.868072	−	0.496438i	$-0.165359\pi$
$479$	−1.34146	−	2.78556i	−0.0612927	−	0.127276i	−0.929365	+	0.369162i	$0.879645\pi$
$480$		0			0
$481$			14.3413i			0.653909i
$482$	5.99119	−	26.2491i	0.272891	−	1.19562i
$483$	55.5559	+	69.6648i	2.52788	+	3.16986i
$484$	0.178153	+	0.780538i	0.00809785	+	0.0354790i
$485$		0			0
$486$	−4.98566	+	6.25182i	−0.226154	+	0.283588i
$487$	−18.9003	−	39.2469i	−0.856455	−	1.77845i	−0.573233	−	0.819392i	$-0.694311\pi$
$487$	−18.9003	−	39.2469i	−0.856455	−	1.77845i	−0.283222	−	0.959054i	$-0.591403\pi$
$488$	16.7664	−	34.8159i	0.758981	−	1.57604i
$489$	8.91273	+	11.1762i	0.403048	+	0.505406i
$490$		0			0
$491$	−7.86505	+	16.3319i	−0.354945	+	0.737050i	−0.999624	−	0.0274024i	$-0.991276\pi$
$491$	−7.86505	+	16.3319i	−0.354945	+	0.737050i	0.644680	+	0.764453i	$0.276991\pi$
$492$		−	1.20914i		−	0.0545123i
$493$	3.89147	+	11.5129i	0.175263	+	0.518516i
$494$	−19.0874			−0.858783
$495$		0			0
$496$	13.9913	+	11.1577i	0.628230	+	0.500997i
$497$	−19.5092	+	15.5580i	−0.875106	+	0.697874i
$498$	−13.8942	+	28.8517i	−0.622616	+	1.29287i
$499$	20.2290	−	9.74180i	0.905577	−	0.436103i	0.0776767	−	0.996979i	$-0.475250\pi$
$499$	20.2290	−	9.74180i	0.905577	−	0.436103i	0.827900	+	0.560876i	$0.189536\pi$
$500$		0			0
$501$	−29.9860	+	6.84410i	−1.33967	+	0.305772i
$502$	−7.83364	+	1.78798i	−0.349633	+	0.0798014i
$503$	6.87402	+	8.61975i	0.306497	+	0.384336i	0.911096	−	0.412195i	$-0.135238\pi$
$503$	6.87402	+	8.61975i	0.306497	+	0.384336i	−0.604598	+	0.796531i	$0.706666\pi$
$504$	−61.2659	−	13.9835i	−2.72900	−	0.622876i
$505$		0			0
$506$	7.42687	−	32.5392i	0.330164	−	1.44655i
$507$	−6.01049	+	2.89450i	−0.266935	+	0.128549i
$508$	2.87907	−	1.38649i	0.127738	−	0.0615153i
$509$	8.52190	−	37.3369i	0.377727	−	1.65493i	−0.326683	−	0.945134i	$-0.605931\pi$
$509$	8.52190	−	37.3369i	0.377727	−	1.65493i	0.704409	−	0.709794i	$-0.251212\pi$
$510$		0			0
$511$	−19.2036	−	4.38310i	−0.849518	−	0.193897i
$512$	15.8541	+	19.8804i	0.700660	+	0.878600i
$513$	−44.2814	+	10.1069i	−1.95507	+	0.446232i
$514$	−25.1251	+	5.73463i	−1.10822	+	0.252944i
$515$		0			0
$516$	0.194678	−	0.0937521i	0.00857023	−	0.00412720i
$517$	−5.15673	+	10.7081i	−0.226793	+	0.470940i
$518$	14.5973	−	11.6409i	0.641367	−	0.511473i
$519$	−4.36874	−	3.48395i	−0.191766	−	0.152929i
$520$		0			0
$521$	−8.30702			−0.363937			−0.181969	−	0.983304i	$-0.558247\pi$
$521$	−8.30702			−0.363937			−0.181969	+	0.983304i	$0.558247\pi$
$522$	43.8536	−	4.46887i	1.91942	−	0.195597i
$523$		−	17.4354i		−	0.762396i	−0.924493	−	0.381198i	$-0.875512\pi$
$523$		−	17.4354i		−	0.762396i	0.924493	−	0.381198i	$-0.124488\pi$
$524$	−0.149473	+	0.310384i	−0.00652975	+	0.0135592i
$525$		0			0
$526$	−9.30719	−	11.6708i	−0.405813	−	0.508873i
$527$	−5.38983	+	11.1921i	−0.234785	+	0.487536i
$528$	12.5677	+	26.0971i	0.546939	+	1.13573i
$529$	−34.2699	+	42.9731i	−1.49000	+	1.86840i
$530$		0			0
$531$	−7.32333	−	32.0856i	−0.317806	−	1.39240i
$532$	−2.97841	−	3.73481i	−0.129130	−	0.161924i
$533$	0.898757	−	3.93771i	0.0389295	−	0.170561i
$534$			8.45605i			0.365929i
$535$		0			0
$536$	5.05247	+	10.4916i	0.218233	+	0.453166i
$537$	−15.0000	+	7.22360i	−0.647296	+	0.311721i
$538$	−3.76197	−	0.858644i	−0.162190	−	0.0370188i
$539$		−	11.4598i		−	0.493608i
$540$		0			0
$541$	−12.6190	+	10.0633i	−0.542533	+	0.432656i	−0.856025	−	0.516935i	$-0.827073\pi$
$541$	−12.6190	+	10.0633i	−0.542533	+	0.432656i	0.313491	+	0.949591i	$0.398501\pi$
$542$	−19.9459	+	4.55253i	−0.856752	+	0.195548i
$543$	−6.93073	−	30.3655i	−0.297426	−	1.30311i
$544$	−2.54027	+	3.18540i	−0.108913	+	0.136573i
$545$		0			0
$546$	−38.7261	−	18.6495i	−1.65732	−	0.798126i
$547$	15.3494	−	12.2408i	0.656295	−	0.523378i	−0.237766	−	0.971322i	$-0.576415\pi$
$547$	15.3494	−	12.2408i	0.656295	−	0.523378i	0.894061	+	0.447945i	$0.147844\pi$
$548$	−2.01505	+	2.52680i	−0.0860788	+	0.107939i
$549$	35.2267	−	73.1489i	1.50344	−	3.12192i
$550$		0			0
$551$	20.2958	+	13.0561i	0.864629	+	0.556208i
$552$		−	81.0854i		−	3.45122i
$553$	−16.2119	−	7.80724i	−0.689400	−	0.331998i
$554$	−19.5506	−	15.5911i	−0.830625	−	0.662402i
$555$		0			0
$556$	1.82697	+	0.879823i	0.0774809	+	0.0373128i
$557$	−1.56803	−	3.25605i	−0.0664396	−	0.137963i	0.865104	−	0.501592i	$-0.167252\pi$
$557$	−1.56803	−	3.25605i	−0.0664396	−	0.137963i	−0.931544	+	0.363628i	$0.881538\pi$
$558$	35.2279	+	28.0933i	1.49132	+	1.18929i
$559$	0.703679	−	0.160610i	0.0297624	−	0.00679308i
$560$		0			0
$561$	−15.7199	+	12.5362i	−0.663696	+	0.529280i
$562$	−2.66994	+	11.6978i	−0.112624	+	0.493440i
$563$	39.1072			1.64817			0.824087	−	0.566464i	$-0.191689\pi$
$563$	39.1072			1.64817			0.824087	+	0.566464i	$0.191689\pi$
$564$	−0.892142	+	3.90873i	−0.0375660	+	0.164587i
$565$		0			0
$566$	−6.55066	−	13.6026i	−0.275345	−	0.571759i
$567$	−38.6151	−	8.81363i	−1.62168	−	0.370138i
$568$	22.7074			0.952782
$569$	12.9719	+	2.96075i	0.543811	+	0.124121i	0.485597	−	0.874183i	$-0.338602\pi$
$569$	12.9719	+	2.96075i	0.543811	+	0.124121i	0.0582140	+	0.998304i	$0.481459\pi$
$570$		0			0
$571$	0.390673	+	1.71165i	0.0163492	+	0.0716304i	0.982444	−	0.186556i	$-0.0597324\pi$
$571$	0.390673	+	1.71165i	0.0163492	+	0.0716304i	−0.966095	+	0.258186i	$0.916875\pi$
$572$	−0.688715	−	3.01746i	−0.0287966	−	0.126166i
$573$	9.67101	+	7.71237i	0.404012	+	0.322189i
$574$	−4.73751	+	2.28146i	−0.197740	+	0.0952264i
$575$		0			0
$576$	34.8352	+	43.6820i	1.45147	+	1.82008i
$577$	19.6694	−	24.6646i	0.818847	−	1.02680i	−0.180220	−	0.983626i	$-0.557681\pi$
$577$	19.6694	−	24.6646i	0.818847	−	1.02680i	0.999068	−	0.0431755i	$-0.0137475\pi$
$578$	−13.8948	−	6.69140i	−0.577949	−	0.278326i
$579$	−71.5227			−2.97238
$580$		0			0
$581$	−26.7710			−1.11065
$582$	24.5158	+	11.8062i	1.01621	+	0.489382i
$583$	−23.4533	+	29.4095i	−0.971336	+	1.21802i
$584$	11.1759	+	14.0141i	0.462461	+	0.579908i
$585$		0			0
$586$	−5.97908	+	2.87938i	−0.246994	+	0.118946i
$587$	24.6614	+	19.6668i	1.01788	+	0.811735i	0.982240	−	0.187629i	$-0.0600803\pi$
$587$	24.6614	+	19.6668i	1.01788	+	0.811735i	0.0356441	+	0.999365i	$0.488652\pi$
$588$	−0.860221	−	3.76887i	−0.0354749	−	0.155426i
$589$	5.48907	+	24.0492i	0.226173	+	0.990930i
$590$		0			0
$591$	72.3556	+	16.5147i	2.97631	+	0.679324i
$592$	−14.1776			−0.582696
$593$	−2.96467	−	0.676666i	−0.121744	−	0.0277873i	0.161215	−	0.986919i	$-0.448459\pi$
$593$	−2.96467	−	0.676666i	−0.121744	−	0.0277873i	−0.282959	+	0.959132i	$0.591316\pi$
$594$	16.6228	+	34.5176i	0.682041	+	1.41627i
$595$		0			0
$596$	1.45458	−	6.37291i	0.0595817	−	0.261045i
$597$	23.9312			0.979440
$598$	8.36878	−	36.6660i	0.342225	−	1.49939i
$599$	−4.43914	+	3.54009i	−0.181378	+	0.144644i	−0.709970	−	0.704232i	$-0.751292\pi$
$599$	−4.43914	+	3.54009i	−0.181378	+	0.144644i	0.528592	+	0.848876i	$0.322720\pi$
$600$		0			0
$601$	7.71975	−	1.76198i	0.314895	−	0.0718728i	−0.0621523	−	0.998067i	$-0.519796\pi$
$601$	7.71975	−	1.76198i	0.314895	−	0.0718728i	0.377048	+	0.926194i	$0.376939\pi$
$602$	−0.734655	−	0.585868i	−0.0299423	−	0.0238782i
$603$	10.6153	+	22.0430i	0.432290	+	0.897660i
$604$	−5.10613	−	2.45898i	−0.207766	−	0.100055i
$605$		0			0
$606$	27.6795	+	22.0737i	1.12440	+	0.896681i
$607$	−6.78995	−	3.26987i	−0.275596	−	0.132720i	0.290981	−	0.956729i	$-0.406018\pi$
$607$	−6.78995	−	3.26987i	−0.275596	−	0.132720i	−0.566577	+	0.824009i	$0.691733\pi$
$608$			8.09055i			0.328115i
$609$	28.4212	+	46.3195i	1.15168	+	1.87696i
$610$		0			0
$611$	−5.81073	+	12.0661i	−0.235077	+	0.488143i
$612$	−2.86768	+	3.59595i	−0.115919	+	0.145358i
$613$	22.4550	−	17.9073i	0.906951	−	0.723269i	−0.0544223	−	0.998518i	$-0.517332\pi$
$613$	22.4550	−	17.9073i	0.906951	−	0.723269i	0.961373	+	0.275249i	$0.0887603\pi$
$614$	−15.6515	−	7.53737i	−0.631644	−	0.304184i
$615$		0			0
$616$	−18.0930	+	22.6880i	−0.728990	+	0.914124i
$617$	2.29803	+	10.0683i	0.0925151	+	0.405335i	0.999888	−	0.0149923i	$-0.00477236\pi$
$617$	2.29803	+	10.0683i	0.0925151	+	0.405335i	−0.907373	+	0.420327i	$0.861915\pi$
$618$	−54.8712	+	12.5240i	−2.20724	+	0.503789i
$619$	6.88002	−	5.48663i	0.276531	−	0.220526i	−0.475397	−	0.879772i	$-0.657695\pi$
$619$	6.88002	−	5.48663i	0.276531	−	0.220526i	0.751928	+	0.659245i	$0.229124\pi$
$620$		0			0
$621$		−	89.4939i		−	3.59127i
$622$	10.9233	+	2.49318i	0.437986	+	0.0999673i
$623$	−6.36913	+	3.06721i	−0.255174	+	0.122885i
$624$	14.1616	+	29.4069i	0.566918	+	1.17722i
$625$		0			0
$626$		−	10.8827i		−	0.434959i
$627$	−8.88454	+	38.9257i	−0.354815	+	1.55454i
$628$	3.19492	+	4.00631i	0.127491	+	0.159869i
$629$	−2.18992	−	9.59469i	−0.0873180	−	0.382565i
$630$		0			0
$631$	−16.4385	+	20.6132i	−0.654406	+	0.820599i	−0.992721	−	0.120434i	$-0.961571\pi$
$631$	−16.4385	+	20.6132i	−0.654406	+	0.820599i	0.338316	+	0.941033i	$0.390143\pi$
$632$	7.10460	+	14.7529i	0.282606	+	0.586837i
$633$	12.9080	−	26.8037i	0.513047	−	1.06535i
$634$	−8.05199	−	10.0969i	−0.319785	−	0.400998i
$635$		0			0
$636$	−5.50567	+	11.4326i	−0.218314	+	0.453333i
$637$		−	12.9132i		−	0.511639i
$638$	6.92721	−	19.1407i	0.274251	−	0.757787i
$639$	47.7088			1.88733
$640$		0			0
$641$	−19.1175	−	15.2457i	−0.755095	−	0.602168i	0.168426	−	0.985714i	$-0.446131\pi$
$641$	−19.1175	−	15.2457i	−0.755095	−	0.602168i	−0.923522	+	0.383546i	$0.874703\pi$
$642$	35.9644	−	28.6806i	1.41940	−	1.13193i
$643$	−0.713633	+	1.48187i	−0.0281429	+	0.0584394i	−0.914566	−	0.404436i	$-0.867468\pi$
$643$	−0.713633	+	1.48187i	−0.0281429	+	0.0584394i	0.886423	+	0.462875i	$0.153182\pi$
$644$	8.48027	−	4.08388i	0.334169	−	0.160927i
$645$		0			0
$646$	12.7699	−	2.91465i	0.502425	−	0.114675i
$647$	17.9227	−	4.09073i	0.704613	−	0.160823i	0.144823	−	0.989458i	$-0.453739\pi$
$647$	17.9227	−	4.09073i	0.704613	−	0.160823i	0.559790	+	0.828634i	$0.310882\pi$
$648$	22.4727	+	28.1799i	0.882812	+	1.10701i
$649$	−14.8165	−	3.38178i	−0.581600	−	0.132746i
$650$		0			0
$651$	−12.3608	+	54.1562i	−0.484458	+	2.12255i
$652$	1.36047	−	0.655170i	0.0532803	−	0.0256584i
$653$	10.6609	−	5.13404i	0.417195	−	0.200911i	−0.213497	−	0.976944i	$-0.568485\pi$
$653$	10.6609	−	5.13404i	0.417195	−	0.200911i	0.630692	+	0.776033i	$0.282771\pi$
$654$	5.72902	−	25.1005i	0.224023	−	0.981507i
$655$		0			0
$656$	3.89276	+	0.888496i	0.151987	+	0.0346899i
$657$	23.4808	+	29.4440i	0.916072	+	1.14872i
$658$	16.9980	−	3.87969i	0.662652	−	0.151246i
$659$	9.65430	−	2.20353i	0.376078	−	0.0858374i	−0.0303036	−	0.999541i	$-0.509647\pi$
$659$	9.65430	−	2.20353i	0.376078	−	0.0858374i	0.406382	+	0.913703i	$0.366790\pi$
$660$		0			0
$661$	18.6871	−	8.99923i	0.726843	−	0.350029i	−0.0335984	−	0.999435i	$-0.510697\pi$
$661$	18.6871	−	8.99923i	0.726843	−	0.350029i	0.760442	+	0.649406i	$0.224982\pi$
$662$	−6.93730	+	14.4055i	−0.269626	+	0.559884i
$663$	−17.7136	+	14.1262i	−0.687940	+	0.548614i
$664$	19.0467	+	15.1892i	0.739155	+	0.589456i
$665$		0			0
$666$	−35.6969			−1.38323
$667$	−33.9788	+	33.2629i	−1.31566	+	1.28794i
$668$			3.24896i			0.125706i
$669$	7.53026	−	15.6367i	0.291137	−	0.604551i
$670$		0			0
$671$	−23.3756	−	29.3121i	−0.902406	−	1.13158i
$672$	−7.90494	+	16.4148i	−0.304940	+	0.633214i
$673$	11.8941	+	24.6983i	0.458483	+	0.952050i	0.994189	+	0.107646i	$0.0343313\pi$
$673$	11.8941	+	24.6983i	0.458483	+	0.952050i	−0.535706	+	0.844405i	$0.679954\pi$
$674$	12.8529	−	16.1170i	0.495075	−	0.620804i
$675$		0			0
$676$	0.156809	+	0.687024i	0.00603111	+	0.0264240i
$677$	12.1064	+	15.1810i	0.465288	+	0.583453i	0.958010	−	0.286734i	$-0.0925695\pi$
$677$	12.1064	+	15.1810i	0.465288	+	0.583453i	−0.492722	+	0.870187i	$0.663998\pi$
$678$	−9.53906	+	41.7934i	−0.366345	+	1.60506i
$679$			22.7478i			0.872979i
$680$		0			0
$681$	−33.8299	−	70.2485i	−1.29636	−	2.69193i
$682$	18.7465	−	9.02783i	0.717840	−	0.345693i
$683$	29.1518	+	6.65370i	1.11546	+	0.254597i	0.740243	−	0.672339i	$-0.234710\pi$
$683$	29.1518	+	6.65370i	1.11546	+	0.254597i	0.375219	+	0.926936i	$0.377568\pi$
$684$			9.13329i			0.349220i
$685$		0			0
$686$	10.2873	−	8.20381i	0.392769	−	0.313223i
$687$	−64.5787	+	14.7397i	−2.46383	+	0.562353i
$688$	0.158776	+	0.695645i	0.00605329	+	0.0265212i
$689$	−26.4278	+	33.1394i	−1.00682	+	1.26251i
$690$		0			0
$691$	32.4228	+	15.6140i	1.23342	+	0.593985i	0.933019	−	0.359827i	$-0.117164\pi$
$691$	32.4228	+	15.6140i	1.23342	+	0.593985i	0.300404	+	0.953812i	$0.402879\pi$
$692$	−0.461482	+	0.368020i	−0.0175429	+	0.0139900i
$693$	−38.0139	+	47.6679i	−1.44403	+	1.81075i
$694$	12.5659	−	26.0933i	0.476993	−	0.990487i
$695$		0			0
$696$	6.05983	−	49.0803i	0.229697	−	1.86039i
$697$			2.77166i			0.104984i
$698$	−9.61555	−	4.63060i	−0.363954	−	0.175271i
$699$	−29.8710	−	23.8213i	−1.12982	−	0.901005i
$700$		0			0
$701$	25.2036	+	12.1374i	0.951928	+	0.458424i	0.844362	−	0.535774i	$-0.179980\pi$
$701$	25.2036	+	12.1374i	0.951928	+	0.458424i	0.107566	+	0.994198i	$0.465694\pi$
$702$	18.7310	+	38.8953i	0.706955	+	1.46801i
$703$	−15.2791	−	12.1847i	−0.576262	−	0.459554i
$704$	25.1534	−	5.74111i	0.948006	−	0.216376i
$705$		0			0
$706$	−9.68169	+	7.72089i	−0.364375	+	0.290580i
$707$	−6.58595	+	28.8549i	−0.247690	+	1.08520i
$708$	−5.12668			−0.192672
$709$	8.49921	−	37.2375i	0.319194	−	1.39848i	−0.519775	−	0.854303i	$-0.673984\pi$
$709$	8.49921	−	37.2375i	0.319194	−	1.39848i	0.838969	−	0.544179i	$-0.183159\pi$
$710$		0			0
$711$	14.9269	+	30.9961i	0.559803	+	1.16244i
$712$	6.27169	+	1.43147i	0.235042	+	0.0536467i
$713$	−48.6041			−1.82024
$714$	28.7564	+	6.56347i	1.07618	+	0.245632i
$715$		0			0
$716$	0.391336	+	1.71456i	0.0146249	+	0.0640760i
$717$	−11.4794	−	50.2943i	−0.428704	−	1.87828i
$718$	12.8418	+	10.2410i	0.479253	+	0.382192i
$719$	24.7616	−	11.9246i	0.923452	−	0.444711i	0.0891496	−	0.996018i	$-0.471585\pi$
$719$	24.7616	−	11.9246i	0.923452	−	0.444711i	0.834302	+	0.551307i	$0.185871\pi$
$720$		0			0
$721$	−29.3362	−	36.7864i	−1.09254	−	1.37000i
$722$	0.873807	−	1.09572i	0.0325197	−	0.0407784i
$723$	−57.1777	−	27.5353i	−2.12646	−	1.02405i
$724$	−3.29009			−0.122275
$725$		0			0
$726$	−9.81648			−0.364324
$727$	−25.5217	−	12.2906i	−0.946549	−	0.455834i	−0.104074	−	0.994570i	$-0.533188\pi$
$727$	−25.5217	−	12.2906i	−0.946549	−	0.455834i	−0.842475	+	0.538736i	$0.818902\pi$
$728$	−20.3877	+	25.5654i	−0.755619	+	0.947516i
$729$	−10.6609	−	13.3684i	−0.394849	−	0.495125i
$730$		0			0
$731$	−0.446252	+	0.214904i	−0.0165052	+	0.00794850i
$732$	−9.88802	−	7.88543i	−0.365472	−	0.291454i
$733$	3.20181	+	14.0280i	0.118262	+	0.518138i	0.999007	+	0.0445482i	$0.0141848\pi$
$733$	3.20181	+	14.0280i	0.118262	+	0.518138i	−0.880746	+	0.473590i	$0.842958\pi$
$734$	5.51094	+	24.1450i	0.203412	+	0.891208i
$735$		0			0
$736$	−15.5416	−	3.54726i	−0.572870	−	0.130754i
$737$	11.2979			0.416162
$738$	9.80133	+	2.23709i	0.360792	+	0.0823484i
$739$	−2.90864	−	6.03986i	−0.106996	−	0.222180i	0.840596	−	0.541663i	$-0.182205\pi$
$739$	−2.90864	−	6.03986i	−0.106996	−	0.222180i	−0.947592	+	0.319483i	$0.896491\pi$
$740$		0			0
$741$	−10.0113	+	43.8625i	−0.367775	+	1.61133i
$742$	55.1822			2.02580
$743$	−9.58633	+	42.0005i	−0.351688	+	1.54085i	0.421593	+	0.906785i	$0.361471\pi$
$743$	−9.58633	+	42.0005i	−0.351688	+	1.54085i	−0.773282	+	0.634063i	$0.781386\pi$
$744$	39.5213	−	31.5172i	1.44892	−	1.15548i
$745$		0			0
$746$	−34.3735	+	7.84553i	−1.25850	+	0.287245i
$747$	40.0175	+	31.9129i	1.46416	+	1.16763i
$748$	0.921532	+	1.91358i	0.0336945	+	0.0699674i
$749$	34.6475	+	16.6854i	1.26599	+	0.609670i
$750$		0			0
$751$	36.4437	+	29.0629i	1.32985	+	1.06052i	0.992894	+	0.118998i	$0.0379683\pi$
$751$	36.4437	+	29.0629i	1.32985	+	1.06052i	0.336955	+	0.941521i	$0.390603\pi$
$752$	−11.9284	−	5.74439i	−0.434982	−	0.209476i
$753$			18.9394i			0.690189i
$754$	7.80575	−	21.5682i	0.284269	−	0.785468i
$755$		0			0
$756$	−4.68780	+	9.73431i	−0.170493	+	0.354033i
$757$	−26.3846	+	33.0852i	−0.958964	+	1.20250i	0.0202747	+	0.999794i	$0.493546\pi$
$757$	−26.3846	+	33.0852i	−0.958964	+	1.20250i	−0.979239	+	0.202709i	$0.935025\pi$
$758$	−17.9411	+	14.3076i	−0.651651	+	0.519675i
$759$	−70.8792	−	34.1336i	−2.57275	−	1.23897i
$760$		0			0
$761$	13.9561	−	17.5004i	0.505909	−	0.634390i	−0.461642	−	0.887066i	$-0.652739\pi$
$761$	13.9561	−	17.5004i	0.505909	−	0.634390i	0.967551	+	0.252677i	$0.0813109\pi$
$762$	8.71860	+	38.1987i	0.315842	+	1.38379i
$763$	20.9838	−	4.78943i	0.759666	−	0.173389i
$764$	1.02158	−	0.814680i	0.0369593	−	0.0294741i
$765$		0			0
$766$		−	36.7489i		−	1.32779i
$767$	−16.6956	−	3.81067i	−0.602845	−	0.137595i
$768$	20.7048	−	9.97092i	0.747121	−	0.359795i
$769$	2.77733	+	5.76719i	0.100153	+	0.207970i	0.945025	−	0.326999i	$-0.106037\pi$
$769$	2.77733	+	5.76719i	0.100153	+	0.207970i	−0.844871	+	0.534969i	$0.820323\pi$
$770$		0			0
$771$			60.7448i			2.18767i
$772$	−1.68118	+	7.36572i	−0.0605069	+	0.265098i
$773$	−19.6941	−	24.6956i	−0.708347	−	0.888239i	0.289269	−	0.957248i	$-0.406588\pi$
$773$	−19.6941	−	24.6956i	−0.708347	−	0.888239i	−0.997616	+	0.0690084i	$0.978016\pi$
$774$	0.399773	+	1.75152i	0.0143695	+	0.0629571i
$775$		0			0
$776$	12.9066	−	16.1843i	0.463318	−	0.580983i
$777$	−19.0944	−	39.6499i	−0.685007	−	1.42243i
$778$	−8.44227	+	17.5306i	−0.302670	+	0.628501i
$779$	3.43160	+	4.30308i	0.122950	+	0.154174i
$780$		0			0
$781$	9.55889	−	19.8492i	0.342044	−	0.710262i
$782$			25.8083i			0.922904i
$783$	6.68823	−	54.1699i	0.239018	−	1.93587i
$784$	12.7658			0.455920
$785$		0			0
$786$	−3.30245	−	2.63362i	−0.117795	−	0.0939380i
$787$	14.8017	−	11.8040i	0.527624	−	0.420766i	−0.323111	−	0.946361i	$-0.604729\pi$
$787$	14.8017	−	11.8040i	0.527624	−	0.420766i	0.850735	+	0.525595i	$0.176157\pi$
$788$	3.40151	−	7.06332i	0.121174	−	0.251620i
$789$	−31.7010	+	15.2664i	−1.12859	+	0.543498i
$790$		0			0
$791$	−34.9390	+	7.97459i	−1.24229	+	0.283544i
$792$	54.0913	−	12.3460i	1.92205	−	0.438695i
$793$	−26.3403	−	33.0296i	−0.935370	−	1.17292i
$794$	18.2318	+	4.16130i	0.647024	+	0.147679i
$795$		0			0
$796$	0.562516	−	2.46454i	0.0199379	−	0.0873534i
$797$	2.02763	−	0.976454i	0.0718222	−	0.0345878i	−0.397628	−	0.917547i	$-0.630166\pi$
$797$	2.02763	−	0.976454i	0.0718222	−	0.0345878i	0.469450	+	0.882959i	$0.344452\pi$
$798$	52.7715	−	25.4134i	1.86809	−	0.899624i
$799$	2.04502	−	8.95981i	0.0723475	−	0.316975i
$800$		0			0
$801$	13.1770	+	3.00755i	0.465585	+	0.106267i
$802$	7.86205	+	9.85870i	0.277619	+	0.348123i
$803$	16.9548	−	3.86981i	0.598320	−	0.136563i
$804$	3.71562	−	0.848066i	0.131040	−	0.0299090i
$805$		0			0
$806$	21.1240	−	10.1728i	0.744062	−	0.358321i
$807$	−3.94630	+	8.19458i	−0.138916	+	0.288463i
$808$	21.0573	−	16.7926i	0.740793	−	0.590763i
$809$	0.00308178	+	0.00245764i	0.000108350	+	8.64060e-5i	0.623544	−	0.781788i	$-0.285692\pi$
$809$	0.00308178	+	0.00245764i	0.000108350	+	8.64060e-5i	−0.623436	+	0.781875i	$0.714264\pi$
$810$		0			0
$811$	7.43379			0.261036			0.130518	−	0.991446i	$-0.458336\pi$
$811$	7.43379			0.261036			0.130518	+	0.991446i	$0.458336\pi$
$812$	5.43824	−	1.83818i	0.190845	−	0.0645073i
$813$			48.2232i			1.69126i
$814$	−7.15220	+	14.8517i	−0.250685	+	0.520552i
$815$		0			0
$816$	−13.9649	−	17.5114i	−0.488868	−	0.613021i
$817$	−0.426747	+	0.886149i	−0.0149300	+	0.0310024i
$818$	4.11129	+	8.53717i	0.143748	+	0.298495i
$819$	−42.8350	+	53.7134i	−1.49678	+	1.87690i
$820$		0			0
$821$	−3.67848	−	16.1165i	−0.128380	−	0.562469i	−0.997674	−	0.0681727i	$-0.978283\pi$
$821$	−3.67848	−	16.1165i	−0.128380	−	0.562469i	0.869294	−	0.494296i	$-0.164574\pi$
$822$	−24.7070	−	30.9816i	−0.861757	−	1.08061i
$823$	−10.3713	+	45.4395i	−0.361519	+	1.58392i	0.387821	+	0.921735i	$0.373228\pi$
$823$	−10.3713	+	45.4395i	−0.361519	+	1.58392i	−0.749340	+	0.662185i	$0.769629\pi$
$824$			42.8170i			1.49160i
$825$		0			0
$826$	9.67325	+	20.0867i	0.336575	+	0.698906i
$827$	−1.27250	+	0.612805i	−0.0442492	+	0.0213093i	−0.455878	−	0.890043i	$-0.650674\pi$
$827$	−1.27250	+	0.612805i	−0.0442492	+	0.0213093i	0.411628	+	0.911352i	$0.364960\pi$
$828$	−17.5446	−	4.00445i	−0.609719	−	0.139164i
$829$		−	50.9937i		−	1.77109i	−0.464558	−	0.885543i	$-0.653787\pi$
$829$		−	50.9937i		−	1.77109i	0.464558	−	0.885543i	$-0.346213\pi$
$830$		0			0
$831$	−46.0823	+	36.7494i	−1.59858	+	1.27482i
$832$	28.3435	−	6.46923i	0.982636	−	0.224280i
$833$	1.97185	+	8.63922i	0.0683204	+	0.299331i
$834$	−15.5019	+	19.4388i	−0.536788	+	0.673111i
$835$		0			0
$836$	3.79991	+	1.82994i	0.131423	+	0.0632898i
$837$	43.6196	−	34.7855i	1.50771	−	1.20236i
$838$	−23.1976	+	29.0888i	−0.801347	+	1.00486i
$839$	−21.4775	+	44.5985i	−0.741486	+	1.53971i	0.0973026	+	0.995255i	$0.468979\pi$
$839$	−21.4775	+	44.5985i	−0.741486	+	1.53971i	−0.838789	+	0.544457i	$0.816736\pi$
$840$		0			0
$841$	−23.0529	+	17.5944i	−0.794929	+	0.606703i
$842$		−	32.7677i		−	1.12925i
$843$	25.4809	+	12.2709i	0.877607	+	0.422633i
$844$	−2.45696	−	1.95936i	−0.0845720	−	0.0674439i
$845$		0			0
$846$	−30.0337	−	14.4634i	−1.03258	−	0.497263i
$847$	−3.56067	−	7.39381i	−0.122346	−	0.254054i
$848$	−32.7610	−	26.1260i	−1.12502	−	0.897171i
$849$	−34.6943	+	7.91875i	−1.19071	+	0.271771i
$850$		0			0
$851$	30.1053	−	24.0082i	1.03200	−	0.822989i
$852$	1.65374	−	7.24551i	0.0566562	−	0.248227i
$853$	−1.72427			−0.0590377			−0.0295189	−	0.999564i	$-0.509398\pi$
$853$	−1.72427			−0.0590377			−0.0295189	+	0.999564i	$0.509398\pi$
$854$	−12.2385	+	53.6206i	−0.418795	+	1.83486i
$855$		0			0
$856$	−15.1837	−	31.5293i	−0.518968	−	1.07765i
$857$	−33.6695	−	7.68485i	−1.15013	−	0.262509i	−0.395377	−	0.918519i	$-0.629386\pi$
$857$	−33.6695	−	7.68485i	−1.15013	−	0.262509i	−0.754752	+	0.656010i	$0.772243\pi$
$858$	37.9492			1.29556
$859$	15.5259	+	3.54368i	0.529736	+	0.120909i	0.479020	−	0.877804i	$-0.340992\pi$
$859$	15.5259	+	3.54368i	0.529736	+	0.120909i	0.0507167	+	0.998713i	$0.483849\pi$
$860$		0			0
$861$	2.75794	+	12.0833i	0.0939904	+	0.411799i
$862$	−2.43506	−	10.6687i	−0.0829384	−	0.363377i
$863$	29.2864	+	23.3551i	0.996920	+	0.795017i	0.978800	−	0.204819i	$-0.0656605\pi$
$863$	29.2864	+	23.3551i	0.996920	+	0.795017i	0.0181200	+	0.999836i	$0.494232\pi$
$864$	16.4865	−	7.93947i	0.560881	−	0.270106i
$865$		0			0
$866$	23.8039	+	29.8492i	0.808890	+	1.01432i
$867$	−22.6646	+	28.4205i	−0.769729	+	0.965209i
$868$	5.28670	+	2.54594i	0.179442	+	0.0864149i
$869$	15.8867			0.538918
$870$		0			0
$871$	12.7307			0.431364
$872$	−17.6467	−	8.49822i	−0.597594	−	0.287786i
$873$	27.1169	−	34.0036i	0.917769	−	1.15085i
$874$	31.9533	+	40.0682i	1.08084	+	1.35533i
$875$		0			0
$876$	5.28556	−	2.54539i	0.178583	−	0.0860008i
$877$	22.9707	+	18.3185i	0.775666	+	0.618573i	0.929203	−	0.369570i	$-0.120495\pi$
$877$	22.9707	+	18.3185i	0.775666	+	0.618573i	−0.153537	+	0.988143i	$0.549066\pi$
$878$	−4.16241	−	18.2367i	−0.140475	−	0.615459i
$879$	3.48073	+	15.2501i	0.117402	+	0.514372i
$880$		0			0
$881$	11.5912	+	2.64562i	0.390518	+	0.0891332i	0.413271	−	0.910608i	$-0.364386\pi$
$881$	11.5912	+	2.64562i	0.390518	+	0.0891332i	−0.0227533	+	0.999741i	$0.507243\pi$
$882$	32.1421			1.08228
$883$	−6.94857	−	1.58597i	−0.233838	−	0.0533720i	0.103996	−	0.994578i	$-0.466837\pi$
$883$	−6.94857	−	1.58597i	−0.233838	−	0.0533720i	−0.337834	+	0.941206i	$0.609694\pi$
$884$	1.03841	+	2.15627i	0.0349254	+	0.0725233i
$885$		0			0
$886$	−3.27295	+	14.3397i	−0.109957	+	0.481752i
$887$	19.7248			0.662296			0.331148	−	0.943579i	$-0.392564\pi$
$887$	19.7248			0.662296			0.331148	+	0.943579i	$0.392564\pi$
$888$	−8.91139	+	39.0433i	−0.299047	+	1.31021i
$889$	−25.6090	+	20.4225i	−0.858897	+	0.684948i
$890$		0			0
$891$	34.0930	−	7.78150i	1.14216	−	0.260690i
$892$	−1.43334	−	1.14305i	−0.0479917	−	0.0382721i
$893$	−7.91819	−	16.4423i	−0.264972	−	0.550220i
$894$	72.2120	+	34.7755i	2.41513	+	1.16307i
$895$		0			0
$896$	−20.2595	−	16.1564i	−0.676824	−	0.539749i
$897$	−79.8685	−	38.4626i	−2.66673	−	1.28423i
$898$			13.7889i			0.460143i
$899$	−29.4197	−	3.63238i	−0.981201	−	0.121147i
$900$		0			0
$901$	12.6204	−	26.2065i	0.420446	−	0.873066i
$902$	2.89453	−	3.62962i	0.0963772	−	0.120853i
$903$	−1.73164	+	1.38094i	−0.0576254	+	0.0459547i
$904$	29.3825	+	14.1499i	0.977249	+	0.470618i
$905$		0			0
$906$	43.3257	−	54.3287i	1.43940	−	1.80495i
$907$	−9.84131	−	43.1176i	−0.326775	−	1.43170i	−0.825238	−	0.564785i	$-0.808959\pi$
$907$	−9.84131	−	43.1176i	−0.326775	−	1.43170i	0.498463	−	0.866911i	$-0.333898\pi$
$908$	−8.02969	+	1.83273i	−0.266475	+	0.0608211i
$909$	44.2418	−	35.2817i	1.46741	−	1.17022i
$910$		0			0
$911$			27.1564i			0.899733i	0.893096	+	0.449866i	$0.148528\pi$
$911$			27.1564i			0.899733i	−0.893096	+	0.449866i	$0.851472\pi$
$912$	−43.3617	−	9.89703i	−1.43585	−	0.327723i
$913$	21.2952	−	10.2552i	0.704769	−	0.339399i
$914$	−18.9764	−	39.4048i	−0.627682	−	1.30340i
$915$		0			0
$916$			6.99707i			0.231190i
$917$	0.785773	−	3.44269i	0.0259485	−	0.113688i
$918$	−18.4708	−	23.1616i	−0.609626	−	0.764447i
$919$	−2.42668	−	10.6320i	−0.0800489	−	0.350717i	0.919003	−	0.394250i	$-0.128996\pi$
$919$	−2.42668	−	10.6320i	−0.0800489	−	0.350717i	−0.999052	+	0.0435332i	$0.986139\pi$
$920$		0			0
$921$	−25.5300	+	32.0136i	−0.841241	+	1.05488i
$922$	−4.55945	−	9.46779i	−0.150157	−	0.311805i
$923$	10.7712	−	22.3666i	0.354539	−	0.736207i
$924$	5.92162	+	7.42547i	0.194807	+	0.244280i
$925$		0			0
$926$	−6.05003	+	12.5630i	−0.198816	+	0.412846i
$927$			89.9595i			2.95466i
$928$	−9.14209	−	3.30861i	−0.300104	−	0.108611i
$929$	−8.35009			−0.273958			−0.136979	−	0.990574i	$-0.543739\pi$
$929$	−8.35009			−0.273958			−0.136979	+	0.990574i	$0.543739\pi$
$930$		0			0
$931$	13.7576	+	10.9713i	0.450886	+	0.359570i
$932$	−3.15536	+	2.51631i	−0.103357	+	0.0824246i
$933$	11.4586	−	23.7939i	0.375136	−	0.778979i
$934$	−20.8018	+	10.0176i	−0.680656	+	0.327786i
$935$		0			0
$936$	60.9514	−	13.9118i	1.99226	−	0.454720i
$937$	45.9699	−	10.4923i	1.50177	−	0.342769i	0.608960	−	0.793201i	$-0.291587\pi$
$937$	45.9699	−	10.4923i	1.50177	−	0.342769i	0.892811	+	0.450432i	$0.148730\pi$
$938$	−10.3336	−	12.9579i	−0.337403	−	0.423091i
$939$	−25.0082	−	5.70796i	−0.816112	−	0.186272i
$940$		0			0
$941$	−7.64160	+	33.4800i	−0.249109	+	1.09142i	0.683336	+	0.730104i	$0.260529\pi$
$941$	−7.64160	+	33.4800i	−0.249109	+	1.09142i	−0.932445	+	0.361313i	$0.882329\pi$
$942$	−56.6077	+	27.2608i	−1.84438	+	0.888205i
$943$	−9.77060	+	4.70527i	−0.318174	+	0.153225i
$944$	3.76716	−	16.5050i	0.122611	−	0.537193i
$945$		0			0
$946$	0.808819	+	0.184608i	0.0262970	+	0.00600211i
$947$	−8.57723	−	10.7555i	−0.278723	−	0.349507i	0.622690	−	0.782469i	$-0.286040\pi$
$947$	−8.57723	−	10.7555i	−0.278723	−	0.349507i	−0.901412	+	0.432962i	$0.857468\pi$
$948$	5.22477	−	1.19252i	0.169693	−	0.0387313i
$949$	19.1051	−	4.36060i	0.620176	−	0.141551i
$950$		0			0
$951$	−27.4257	+	13.2075i	−0.889339	+	0.428283i
$952$	9.73601	−	20.2170i	0.315546	−	0.655238i
$953$	−38.4724	+	30.6807i	−1.24624	+	0.993847i	−0.246550	+	0.969130i	$0.579297\pi$
$953$	−38.4724	+	30.6807i	−1.24624	+	0.993847i	−0.999694	+	0.0247169i	$0.992132\pi$
$954$	−82.4869	−	65.7811i	−2.67061	−	2.12974i
$955$		0			0
$956$	−5.44936			−0.176245
$957$	−40.3517	−	25.9579i	−1.30438	−	0.839099i
$958$		−	4.00439i		−	0.129376i
$959$	14.3737	−	29.8472i	0.464150	−	0.963817i
$960$		0			0
$961$	0.436200	+	0.546977i	0.0140710	+	0.0176444i
$962$	−8.05929	+	16.7353i	−0.259842	+	0.539567i
$963$	−31.9013	−	66.2437i	−1.02800	−	2.13467i
$964$	−4.17970	+	5.24118i	−0.134619	+	0.168807i
$965$		0			0
$966$	25.6806	+	112.514i	0.826259	+	3.62008i
$967$	−20.2151	−	25.3489i	−0.650072	−	0.815165i	0.342150	−	0.939645i	$-0.388845\pi$
$967$	−20.2151	−	25.3489i	−0.650072	−	0.815165i	−0.992222	+	0.124481i	$0.960274\pi$
$968$	−1.66177	+	7.28070i	−0.0534114	+	0.234010i
$969$		−	30.8738i		−	0.991808i
$970$		0			0
$971$	19.5883	+	40.6755i	0.628618	+	1.30534i	0.935411	+	0.353563i	$0.115030\pi$
$971$	19.5883	+	40.6755i	0.628618	+	1.30534i	−0.306792	+	0.951777i	$0.599256\pi$
$972$	1.79381	−	0.863854i	0.0575365	−	0.0277081i
$973$	−20.2643	−	4.62519i	−0.649644	−	0.148277i
$974$		−	56.4195i		−	1.80780i
$975$		0			0
$976$	32.6525	−	26.0395i	1.04518	−	0.833505i
$977$	28.8542	−	6.58578i	0.923127	−	0.210698i	0.265560	−	0.964094i	$-0.414443\pi$
$977$	28.8542	−	6.58578i	0.923127	−	0.210698i	0.657566	+	0.753397i	$0.271586\pi$
$978$	4.11989	+	18.0504i	0.131740	+	0.577189i
$979$	3.89142	−	4.87968i	0.124370	−	0.155955i
$980$		0			0
$981$	−37.0762	−	17.8549i	−1.18375	−	0.570064i
$982$	−18.3559	+	14.6383i	−0.585759	+	0.467127i
$983$	35.9942	−	45.1354i	1.14804	−	1.43959i	0.268810	−	0.963193i	$-0.413370\pi$
$983$	35.9942	−	45.1354i	1.14804	−	1.43959i	0.879228	−	0.476401i	$-0.158059\pi$
$984$	4.89361	−	10.1617i	0.156003	−	0.323943i
$985$		0			0
$986$	−1.92876	+	15.6216i	−0.0614242	+	0.497492i
$987$		−	41.0961i		−	1.30810i
$988$	4.28184	+	2.06202i	0.136223	+	0.0656017i
$989$	−1.51515	−	1.20829i	−0.0481789	−	0.0384214i
$990$		0			0
$991$	−20.7374	−	9.98659i	−0.658744	−	0.317234i	0.0744790	−	0.997223i	$-0.476271\pi$
$991$	−20.7374	−	9.98659i	−0.658744	−	0.317234i	−0.733223	+	0.679988i	$0.761985\pi$
$992$	−4.31192	−	8.95380i	−0.136904	−	0.284284i
$993$	29.4649	+	23.4975i	0.935040	+	0.745669i
$994$	−31.5088	+	7.19168i	−0.999398	+	0.228106i
$995$		0			0
$996$	6.23373	−	4.97123i	0.197523	−	0.157520i
$997$	−6.71662	+	29.4274i	−0.212717	+	0.931976i	0.749994	+	0.661445i	$0.230056\pi$
$997$	−6.71662	+	29.4274i	−0.212717	+	0.931976i	−0.962711	+	0.270531i	$0.912801\pi$
$998$	29.0803			0.920521
$999$	−9.83549	+	43.0921i	−0.311181	+	1.36337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.p.b.274.6		48
5.2	odd	4		145.2.m.a.71.1	✓	24
5.3	odd	4		725.2.q.b.651.4		24
5.4	even	2	inner	725.2.p.b.274.3		48
29.9	even	14	inner	725.2.p.b.299.3		48
145.9	even	14	inner	725.2.p.b.299.6		48
145.32	even	28		4205.2.a.y.1.7		24
145.38	odd	28		725.2.q.b.676.4		24
145.67	odd	28		145.2.m.a.96.1	yes	24
145.142	even	28		4205.2.a.y.1.18		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.m.a.71.1	✓	24	5.2	odd	4
145.2.m.a.96.1	yes	24	145.67	odd	28
725.2.p.b.274.3		48	5.4	even	2	inner
725.2.p.b.274.6		48	1.1	even	1	trivial
725.2.p.b.299.3		48	29.9	even	14	inner
725.2.p.b.299.6		48	145.9	even	14	inner
725.2.q.b.651.4		24	5.3	odd	4
725.2.q.b.676.4		24	145.38	odd	28
4205.2.a.y.1.7		24	145.32	even	28
4205.2.a.y.1.18		24	145.142	even	28

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.p (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.16693 + 0.561962i) q^{2} +(1.90343 - 2.38683i) q^{3} +(-0.201065 - 0.252127i) q^{4} +(3.56247 - 1.71559i) q^{6} +(2.58438 + 2.06098i) q^{7} +(-0.669356 - 2.93264i) q^{8} +(-1.40633 - 6.16153i) q^{9} +O(q^{10})\)	\(q+(1.16693 + 0.561962i) q^{2} +(1.90343 - 2.38683i) q^{3} +(-0.201065 - 0.252127i) q^{4} +(3.56247 - 1.71559i) q^{6} +(2.58438 + 2.06098i) q^{7} +(-0.669356 - 2.93264i) q^{8} +(-1.40633 - 6.16153i) q^{9} +(-2.84528 - 0.649416i) q^{11} -0.984498 q^{12} +(-3.20613 - 0.731779i) q^{13} +(1.85759 + 3.85733i) q^{14} +(0.723424 - 3.16953i) q^{16} +2.25672 q^{17} +(1.82146 - 7.98036i) q^{18} +(3.50362 - 2.79405i) q^{19} +(9.83839 - 2.24555i) q^{21} +(-2.95528 - 2.35676i) q^{22} +(3.83109 + 7.95534i) q^{23} +(-8.27377 - 3.98444i) q^{24} +(-3.33009 - 2.65566i) q^{26} +(-9.13175 - 4.39762i) q^{27} -1.06598i q^{28} +(1.72439 + 5.10161i) q^{29} +(-2.38835 + 4.95945i) q^{31} +(-1.12565 + 1.41152i) q^{32} +(-6.96584 + 5.55507i) q^{33} +(2.63342 + 1.26819i) q^{34} +(-1.27073 + 1.59344i) q^{36} +(-0.970402 - 4.25161i) q^{37} +(5.65861 - 1.29154i) q^{38} +(-7.84928 + 6.25959i) q^{39} +1.22818i q^{41} +(12.7426 + 2.90841i) q^{42} +(-0.197744 + 0.0952283i) q^{43} +(0.408350 + 0.847948i) q^{44} +11.4362i q^{46} +(0.906190 - 3.97028i) q^{47} +(-6.18813 - 7.75967i) q^{48} +(0.873766 + 3.82822i) q^{49} +(4.29551 - 5.38640i) q^{51} +(0.460139 + 0.955489i) q^{52} +(5.59236 - 11.6127i) q^{53} +(-8.18478 - 10.2634i) q^{54} +(4.31423 - 8.95859i) q^{56} -13.6808i q^{57} +(-0.854673 + 6.92225i) q^{58} +5.20741 q^{59} +(10.0437 + 8.00960i) q^{61} +(-5.57405 + 4.44516i) q^{62} +(9.06429 - 18.8222i) q^{63} +(-7.96494 + 3.83571i) q^{64} +(-11.2504 + 2.56782i) q^{66} +(-3.77413 + 0.861420i) q^{67} +(-0.453747 - 0.568981i) q^{68} +(26.2802 + 5.99829i) q^{69} +(-1.67978 + 7.35960i) q^{71} +(-17.1282 + 8.24851i) q^{72} +(-5.36879 + 2.58547i) q^{73} +(1.25685 - 5.50664i) q^{74} +(-1.40891 - 0.321575i) q^{76} +(-6.01486 - 7.54240i) q^{77} +(-12.6772 + 2.89348i) q^{78} +(-5.30705 + 1.21130i) q^{79} +(-10.7957 + 5.19892i) q^{81} +(-0.690191 + 1.43320i) q^{82} +(-6.33189 + 5.04951i) q^{83} +(-2.54432 - 2.02903i) q^{84} -0.284267 q^{86} +(15.4589 + 5.59474i) q^{87} +8.77887i q^{88} +(-0.927897 + 1.92680i) q^{89} +(-6.77770 - 8.49897i) q^{91} +(1.23546 - 2.56546i) q^{92} +(7.29130 + 15.1405i) q^{93} +(3.28860 - 4.12378i) q^{94} +(1.22646 + 5.37346i) q^{96} +(4.29066 + 5.38032i) q^{97} +(-1.13169 + 4.95827i) q^{98} +18.4446i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{6} + 8 q^{9}+O(q^{10}) \) 48 * q + 8 * q^6 + 8 * q^9	\( 48 q + 8 q^{6} + 8 q^{9} - 28 q^{11} + 84 q^{14} - 20 q^{16} + 98 q^{21} - 76 q^{24} - 14 q^{29} + 14 q^{31} - 40 q^{34} - 56 q^{36} - 14 q^{39} + 42 q^{44} + 4 q^{49} + 12 q^{51} - 214 q^{54} - 84 q^{56} + 132 q^{59} + 112 q^{61} - 66 q^{64} - 140 q^{66} + 56 q^{69} + 106 q^{71} - 66 q^{74} - 84 q^{76} + 112 q^{79} - 58 q^{81} - 28 q^{84} + 60 q^{86} - 28 q^{89} - 62 q^{91} + 76 q^{94} - 2 q^{96}+O(q^{100}) \) 48 * q + 8 * q^6 + 8 * q^9 - 28 * q^11 + 84 * q^14 - 20 * q^16 + 98 * q^21 - 76 * q^24 - 14 * q^29 + 14 * q^31 - 40 * q^34 - 56 * q^36 - 14 * q^39 + 42 * q^44 + 4 * q^49 + 12 * q^51 - 214 * q^54 - 84 * q^56 + 132 * q^59 + 112 * q^61 - 66 * q^64 - 140 * q^66 + 56 * q^69 + 106 * q^71 - 66 * q^74 - 84 * q^76 + 112 * q^79 - 58 * q^81 - 28 * q^84 + 60 * q^86 - 28 * q^89 - 62 * q^91 + 76 * q^94 - 2 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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