LMFDB - Embedded newform 925.2.y.b.393.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(193,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.193"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [68] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			393.13
Character	$\chi$	$=$	925.393
Dual form			925.2.y.b.732.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14153 + 0.659061i) q^{2} +(1.18821 + 0.318379i) q^{3} +(-0.131277 - 0.227378i) q^{4} +(1.14654 + 1.14654i) q^{6} +(-4.13076 - 1.10683i) q^{7} -2.98232i q^{8} +(-1.28760 - 0.743399i) q^{9} -4.89589i q^{11} +(-0.0835914 - 0.311968i) q^{12} +(-2.57679 + 1.48771i) q^{13} +(-3.98591 - 3.98591i) q^{14} +(1.70298 - 2.94965i) q^{16} +(-2.10881 + 3.65256i) q^{17} +(-0.979891 - 1.69722i) q^{18} +(4.90693 + 1.31481i) q^{19} +(-4.55581 - 2.63030i) q^{21} +(3.22669 - 5.58880i) q^{22} -6.57051i q^{23} +(0.949509 - 3.54362i) q^{24} -3.92197 q^{26} +(-3.90274 - 3.90274i) q^{27} +(0.290603 + 1.08454i) q^{28} +(-0.417950 - 0.417950i) q^{29} +(3.03803 - 3.03803i) q^{31} +(-1.27754 + 0.737586i) q^{32} +(1.55875 - 5.81734i) q^{33} +(-4.81453 + 2.77967i) q^{34} +0.390363i q^{36} +(-0.219784 + 6.07879i) q^{37} +(4.73486 + 4.73486i) q^{38} +(-3.53541 + 0.947311i) q^{39} +(-0.897477 + 0.518158i) q^{41} +(-3.46706 - 6.00512i) q^{42} +3.17618i q^{43} +(-1.11322 + 0.642716i) q^{44} +(4.33037 - 7.50041i) q^{46} +(4.44958 - 4.44958i) q^{47} +(2.96260 - 2.96260i) q^{48} +(9.77595 + 5.64415i) q^{49} +(-3.66860 + 3.66860i) q^{51} +(0.676543 + 0.390602i) q^{52} +(6.40827 - 1.71709i) q^{53} +(-1.88294 - 7.02724i) q^{54} +(-3.30094 + 12.3193i) q^{56} +(5.41184 + 3.12453i) q^{57} +(-0.201647 - 0.752555i) q^{58} +(1.57132 + 5.86425i) q^{59} +(1.68182 + 0.450642i) q^{61} +(5.47024 - 1.46575i) q^{62} +(4.49597 + 4.49597i) q^{63} -8.75638 q^{64} +(5.61334 - 5.61334i) q^{66} +(3.09017 - 11.5327i) q^{67} +1.10735 q^{68} +(2.09191 - 7.80712i) q^{69} +(-1.78413 - 3.09021i) q^{71} +(-2.21705 + 3.84005i) q^{72} +(-2.50291 + 2.50291i) q^{73} +(-4.25718 + 6.79426i) q^{74} +(-0.345207 - 1.28833i) q^{76} +(-5.41895 + 20.2238i) q^{77} +(-4.66011 - 1.24867i) q^{78} +(-3.97409 - 1.06485i) q^{79} +(-1.16452 - 2.01701i) q^{81} -1.36599 q^{82} +(-2.57020 + 0.688684i) q^{83} +1.38119i q^{84} +(-2.09329 + 3.62569i) q^{86} +(-0.363544 - 0.629677i) q^{87} -14.6011 q^{88} +(-11.4703 + 3.07346i) q^{89} +(12.2907 - 3.29330i) q^{91} +(-1.49399 + 0.862553i) q^{92} +(4.57706 - 2.64257i) q^{93} +(8.01187 - 2.14677i) q^{94} +(-1.75281 + 0.469664i) q^{96} +10.2570 q^{97} +(7.43968 + 12.8859i) q^{98} +(-3.63960 + 6.30397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.14153	+	0.659061i	0.807182	+	0.466027i	0.845976	−	0.533221i	$-0.179018\pi$
$2$	1.14153	+	0.659061i	0.807182	+	0.466027i	−0.0387944	+	0.999247i	$0.512352\pi$
$3$	1.18821	+	0.318379i	0.686012	+	0.183816i	0.584957	−	0.811064i	$-0.301111\pi$
$3$	1.18821	+	0.318379i	0.686012	+	0.183816i	0.101055	+	0.994881i	$0.467778\pi$
$4$	−0.131277	−	0.227378i	−0.0656383	−	0.113689i
$5$		0			0
$5$		0			0
$6$	1.14654	+	1.14654i	0.468073	+	0.468073i
$7$	−4.13076	−	1.10683i	−1.56128	−	0.418344i	−0.628213	−	0.778041i	$-0.716213\pi$
$7$	−4.13076	−	1.10683i	−1.56128	−	0.418344i	−0.933069	+	0.359697i	$0.882880\pi$
$8$		−	2.98232i		−	1.05441i
$9$	−1.28760	−	0.743399i	−0.429201	−	0.247800i
$10$		0			0
$11$		−	4.89589i		−	1.47617i	−0.674709	−	0.738084i	$-0.735731\pi$
$11$		−	4.89589i		−	1.47617i	0.674709	−	0.738084i	$-0.264269\pi$
$12$	−0.0835914	−	0.311968i	−0.0241308	−	0.0900573i
$13$	−2.57679	+	1.48771i	−0.714672	+	0.412616i	−0.812789	−	0.582559i	$-0.802052\pi$
$13$	−2.57679	+	1.48771i	−0.714672	+	0.412616i	0.0981164	+	0.995175i	$0.468718\pi$
$14$	−3.98591	−	3.98591i	−1.06528	−	1.06528i
$15$		0			0
$16$	1.70298	−	2.94965i	0.425745	−	0.737412i
$17$	−2.10881	+	3.65256i	−0.511461	+	0.885877i	0.488450	+	0.872592i	$0.337562\pi$
$17$	−2.10881	+	3.65256i	−0.511461	+	0.885877i	−0.999912	+	0.0132853i	$0.995771\pi$
$18$	−0.979891	−	1.69722i	−0.230962	−	0.400039i
$19$	4.90693	+	1.31481i	1.12573	+	0.301638i	0.773199	−	0.634164i	$-0.218655\pi$
$19$	4.90693	+	1.31481i	1.12573	+	0.301638i	0.352528	+	0.935801i	$0.385322\pi$
$20$		0			0
$21$	−4.55581	−	2.63030i	−0.994160	−	0.573978i
$22$	3.22669	−	5.58880i	0.687933	−	1.19154i
$23$		−	6.57051i		−	1.37005i	−0.728522	−	0.685023i	$-0.759792\pi$
$23$		−	6.57051i		−	1.37005i	0.728522	−	0.685023i	$-0.240208\pi$
$24$	0.949509	−	3.54362i	0.193818	−	0.723338i
$25$		0			0
$26$	−3.92197			−0.769161
$27$	−3.90274	−	3.90274i	−0.751083	−	0.751083i
$28$	0.290603	+	1.08454i	0.0549188	+	0.204960i
$29$	−0.417950	−	0.417950i	−0.0776113	−	0.0776113i	0.667236	−	0.744847i	$-0.267477\pi$
$29$	−0.417950	−	0.417950i	−0.0776113	−	0.0776113i	−0.744847	+	0.667236i	$0.767477\pi$
$30$		0			0
$31$	3.03803	−	3.03803i	0.545646	−	0.545646i	−0.379532	−	0.925179i	$-0.623915\pi$
$31$	3.03803	−	3.03803i	0.545646	−	0.545646i	0.925179	+	0.379532i	$0.123915\pi$
$32$	−1.27754	+	0.737586i	−0.225839	+	0.130388i
$33$	1.55875	−	5.81734i	0.271344	−	1.01267i
$34$	−4.81453	+	2.77967i	−0.825685	+	0.476709i
$35$		0			0
$36$			0.390363i			0.0650605i
$37$	−0.219784	+	6.07879i	−0.0361323	+	0.999347i
$37$	−0.219784	+	6.07879i	−0.0361323	+	0.999347i
$38$	4.73486	+	4.73486i	0.768095	+	0.768095i
$39$	−3.53541	+	0.947311i	−0.566119	+	0.151691i
$40$		0			0
$41$	−0.897477	+	0.518158i	−0.140162	+	0.0809228i	−0.568441	−	0.822724i	$-0.692453\pi$
$41$	−0.897477	+	0.518158i	−0.140162	+	0.0809228i	0.428279	+	0.903647i	$0.359120\pi$
$42$	−3.46706	−	6.00512i	−0.534978	−	0.926610i
$43$			3.17618i			0.484362i	0.970231	+	0.242181i	$0.0778628\pi$
$43$			3.17618i			0.484362i	−0.970231	+	0.242181i	$0.922137\pi$
$44$	−1.11322	+	0.642716i	−0.167824	+	0.0968931i
$45$		0			0
$46$	4.33037	−	7.50041i	0.638478	−	1.10588i
$47$	4.44958	−	4.44958i	0.649038	−	0.649038i	−0.303722	−	0.952761i	$-0.598230\pi$
$47$	4.44958	−	4.44958i	0.649038	−	0.649038i	0.952761	+	0.303722i	$0.0982295\pi$
$48$	2.96260	−	2.96260i	0.427615	−	0.427615i
$49$	9.77595	+	5.64415i	1.39656	+	0.806307i
$50$		0			0
$51$	−3.66860	+	3.66860i	−0.513707	+	0.513707i
$52$	0.676543	+	0.390602i	0.0938197	+	0.0541668i
$53$	6.40827	−	1.71709i	0.880243	−	0.235861i	0.209731	−	0.977759i	$-0.432741\pi$
$53$	6.40827	−	1.71709i	0.880243	−	0.235861i	0.670512	+	0.741899i	$0.266074\pi$
$54$	−1.88294	−	7.02724i	−0.256236	−	0.956286i
$55$		0			0
$56$	−3.30094	+	12.3193i	−0.441106	+	1.64623i
$57$	5.41184	+	3.12453i	0.716816	+	0.413854i
$58$	−0.201647	−	0.752555i	−0.0264775	−	0.0988154i
$59$	1.57132	+	5.86425i	0.204568	+	0.763460i	0.989581	+	0.143979i	$0.0459899\pi$
$59$	1.57132	+	5.86425i	0.204568	+	0.763460i	−0.785012	+	0.619480i	$0.787343\pi$
$60$		0			0
$61$	1.68182	+	0.450642i	0.215335	+	0.0576988i	0.364874	−	0.931057i	$-0.381112\pi$
$61$	1.68182	+	0.450642i	0.215335	+	0.0576988i	−0.149539	+	0.988756i	$0.547779\pi$
$62$	5.47024	−	1.46575i	0.694722	−	0.186150i
$63$	4.49597	+	4.49597i	0.566439	+	0.566439i
$64$	−8.75638			−1.09455
$65$		0			0
$66$	5.61334	−	5.61334i	0.690954	−	0.690954i
$67$	3.09017	−	11.5327i	0.377524	−	1.40894i	−0.472097	−	0.881547i	$-0.656503\pi$
$67$	3.09017	−	11.5327i	0.377524	−	1.40894i	0.849621	−	0.527394i	$-0.176831\pi$
$68$	1.10735			0.134286
$69$	2.09191	−	7.80712i	0.251837	−	0.939867i
$70$		0			0
$71$	−1.78413	−	3.09021i	−0.211738	−	0.366741i	0.740521	−	0.672034i	$-0.234579\pi$
$71$	−1.78413	−	3.09021i	−0.211738	−	0.366741i	−0.952258	+	0.305293i	$0.901246\pi$
$72$	−2.21705	+	3.84005i	−0.261282	+	0.452554i
$73$	−2.50291	+	2.50291i	−0.292943	+	0.292943i	−0.838242	−	0.545298i	$-0.816416\pi$
$73$	−2.50291	+	2.50291i	−0.292943	+	0.292943i	0.545298	+	0.838242i	$0.316416\pi$
$74$	−4.25718	+	6.79426i	−0.494888	+	0.789816i
$75$		0			0
$76$	−0.345207	−	1.28833i	−0.0395979	−	0.147781i
$77$	−5.41895	+	20.2238i	−0.617546	+	2.30471i
$78$	−4.66011	−	1.24867i	−0.527653	−	0.141384i
$79$	−3.97409	−	1.06485i	−0.447120	−	0.119805i	0.0282316	−	0.999601i	$-0.491012\pi$
$79$	−3.97409	−	1.06485i	−0.447120	−	0.119805i	−0.475351	+	0.879796i	$0.657679\pi$
$80$		0			0
$81$	−1.16452	−	2.01701i	−0.129391	−	0.224112i
$82$	−1.36599			−0.150849
$83$	−2.57020	+	0.688684i	−0.282117	+	0.0755929i	−0.397103	−	0.917774i	$-0.629984\pi$
$83$	−2.57020	+	0.688684i	−0.282117	+	0.0755929i	0.114986	+	0.993367i	$0.463318\pi$
$84$			1.38119i			0.150700i
$85$		0			0
$86$	−2.09329	+	3.62569i	−0.225726	+	0.390968i
$87$	−0.363544	−	0.629677i	−0.0389760	−	0.0675085i
$88$	−14.6011			−1.55649
$89$	−11.4703	+	3.07346i	−1.21585	+	0.325786i	−0.809055	−	0.587734i	$-0.800020\pi$
$89$	−11.4703	+	3.07346i	−1.21585	+	0.325786i	−0.406795	+	0.913519i	$0.633354\pi$
$90$		0			0
$91$	12.2907	−	3.29330i	1.28842	−	0.345231i
$92$	−1.49399	+	0.862553i	−0.155759	+	0.0899274i
$93$	4.57706	−	2.64257i	0.474619	−	0.274021i
$94$	8.01187	−	2.14677i	0.826361	−	0.221423i
$95$		0			0
$96$	−1.75281	+	0.469664i	−0.178895	+	0.0479349i
$97$	10.2570			1.04144			0.520719	−	0.853728i	$-0.325664\pi$
$97$	10.2570			1.04144			0.520719	+	0.853728i	$0.325664\pi$
$98$	7.43968	+	12.8859i	0.751521	+	1.30167i
$99$	−3.63960	+	6.30397i	−0.365794	+	0.633573i
$100$		0			0
$101$		−	19.0134i		−	1.89190i	−0.324311	−	0.945951i	$-0.605132\pi$
$101$		−	19.0134i		−	1.89190i	0.324311	−	0.945951i	$-0.394868\pi$
$102$	−6.60565	+	1.76998i	−0.654056	+	0.175254i
$103$	18.1801			1.79133			0.895667	−	0.444724i	$-0.146698\pi$
$103$	18.1801			1.79133			0.895667	+	0.444724i	$0.146698\pi$
$104$	4.43683	+	7.68481i	0.435067	+	0.753558i
$105$		0			0
$106$	8.44688	+	2.26334i	0.820434	+	0.219835i
$107$	−6.32701	−	1.69532i	−0.611656	−	0.163893i	−0.0603240	−	0.998179i	$-0.519213\pi$
$107$	−6.32701	−	1.69532i	−0.611656	−	0.163893i	−0.551332	+	0.834286i	$0.685880\pi$
$108$	−0.375058	+	1.39974i	−0.0360900	+	0.134690i
$109$	−1.79221	−	6.68861i	−0.171662	−	0.640652i	−0.997096	−	0.0761534i	$-0.975736\pi$
$109$	−1.79221	−	6.68861i	−0.171662	−	0.640652i	0.825434	−	0.564499i	$-0.190931\pi$
$110$		0			0
$111$	−2.19651	+	7.15289i	−0.208483	+	0.678922i
$112$	−10.2994	+	10.2994i	−0.973200	+	0.973200i
$113$	−0.777094	+	1.34597i	−0.0731029	+	0.126618i	−0.900260	−	0.435353i	$-0.856623\pi$
$113$	−0.777094	+	1.34597i	−0.0731029	+	0.126618i	0.827157	+	0.561971i	$0.189957\pi$
$114$	4.11851	+	7.13347i	0.385734	+	0.668111i
$115$		0			0
$116$	−0.0401654	+	0.149899i	−0.00372926	+	0.0139178i
$117$	4.42384			0.408984
$118$	−2.07119	+	7.72979i	−0.190669	+	0.711585i
$119$	12.7538	−	12.7538i	1.16914	−	1.16914i
$120$		0			0
$121$	−12.9698			−1.17907
$122$	1.62284	+	1.62284i	0.146925	+	0.146925i
$123$	−1.23136	+	0.329942i	−0.111028	+	0.0297498i
$124$	−1.08960	−	0.291958i	−0.0978492	−	0.0262186i
$125$		0			0
$126$	2.16915	+	8.09539i	0.193244	+	0.721195i
$127$	−4.21459	−	15.7291i	−0.373984	−	1.39573i	−0.854823	−	0.518920i	$-0.826334\pi$
$127$	−4.21459	−	15.7291i	−0.373984	−	1.39573i	0.480839	−	0.876809i	$-0.340332\pi$
$128$	−7.44057	−	4.29582i	−0.657660	−	0.379700i
$129$	−1.01123	+	3.77396i	−0.0890337	+	0.332278i
$130$		0			0
$131$	3.68624	+	13.7572i	0.322068	+	1.20197i	0.917227	+	0.398366i	$0.130423\pi$
$131$	3.68624	+	13.7572i	0.322068	+	1.20197i	−0.595158	+	0.803608i	$0.702911\pi$
$132$	−1.52736	+	0.409255i	−0.132940	+	0.0356211i
$133$	−18.8141	−	10.8623i	−1.63139	−	0.941883i
$134$	11.1283	−	11.1283i	0.961335	−	0.961335i
$135$		0			0
$136$	10.8931	+	6.28915i	0.934078	+	0.539290i
$137$	7.34260	−	7.34260i	0.627321	−	0.627321i	−0.320072	−	0.947393i	$-0.603707\pi$
$137$	7.34260	−	7.34260i	0.627321	−	0.627321i	0.947393	+	0.320072i	$0.103707\pi$
$138$	7.53335	−	7.53335i	0.641281	−	0.641281i
$139$	4.37561	−	7.57878i	0.371135	−	0.642824i	−0.618606	−	0.785702i	$-0.712302\pi$
$139$	4.37561	−	7.57878i	0.371135	−	0.642824i	0.989740	+	0.142877i	$0.0456355\pi$
$140$		0			0
$141$	6.70368	−	3.87037i	0.564552	−	0.325944i
$142$		−	4.70341i		−	0.394702i
$143$	7.28366	+	12.6157i	0.609091	+	1.05498i
$144$	−4.38553	+	2.53199i	−0.365461	+	0.210999i
$145$		0			0
$146$	−4.50671	+	1.20757i	−0.372978	+	0.0999392i
$147$	9.81888	+	9.81888i	0.809848	+	0.809848i
$148$	1.41103	−	0.748029i	0.115986	−	0.0614876i
$149$		−	16.7086i		−	1.36883i	−0.729095	−	0.684413i	$-0.760059\pi$
$149$		−	16.7086i		−	1.36883i	0.729095	−	0.684413i	$-0.239941\pi$
$150$		0			0
$151$	−3.85044	+	2.22305i	−0.313344	+	0.180909i	−0.648422	−	0.761281i	$-0.724571\pi$
$151$	−3.85044	+	2.22305i	−0.313344	+	0.180909i	0.335078	+	0.942190i	$0.391237\pi$
$152$	3.92118	−	14.6340i	0.318050	−	1.18698i
$153$	5.43062	−	3.13537i	0.439040	−	0.253480i
$154$	−19.5146	+	19.5146i	−1.57253	+	1.57253i
$155$		0			0
$156$	0.679514	+	0.679514i	0.0544047	+	0.0544047i
$157$	−2.50499	−	9.34877i	−0.199920	−	0.746113i	−0.990938	−	0.134320i	$-0.957115\pi$
$157$	−2.50499	−	9.34877i	−0.199920	−	0.746113i	0.791018	−	0.611793i	$-0.209552\pi$
$158$	−3.83473	−	3.83473i	−0.305075	−	0.305075i
$159$	8.16104			0.647213
$160$		0			0
$161$	−7.27247	+	27.1412i	−0.573151	+	2.13903i
$162$		−	3.06996i		−	0.241199i
$163$	−8.18322	+	14.1737i	−0.640959	+	1.11017i	0.344260	+	0.938874i	$0.388130\pi$
$163$	−8.18322	+	14.1737i	−0.640959	+	1.11017i	−0.985219	+	0.171299i	$0.945203\pi$
$164$	0.235635	+	0.136044i	0.0184000	+	0.0106233i
$165$		0			0
$166$	−3.38784	−	0.907770i	−0.262948	−	0.0704566i
$167$	4.92891	+	8.53712i	0.381411	+	0.660623i	0.991264	−	0.131892i	$-0.0421051\pi$
$167$	4.92891	+	8.53712i	0.381411	+	0.660623i	−0.609854	+	0.792514i	$0.708772\pi$
$168$	−7.84440	+	13.5869i	−0.605209	+	1.04825i
$169$	−2.07344	+	3.59131i	−0.159496	+	0.276255i
$170$		0			0
$171$	−5.34076	−	5.34076i	−0.408418	−	0.408418i
$172$	0.722191	−	0.416957i	0.0550666	−	0.0317927i
$173$	−1.95280	−	7.28794i	−0.148468	−	0.554092i	−0.999576	−	0.0291012i	$-0.990735\pi$
$173$	−1.95280	−	7.28794i	−0.148468	−	0.554092i	0.851108	−	0.524991i	$-0.175931\pi$
$174$		−	0.958392i		−	0.0726555i
$175$		0			0
$176$	−14.4412	−	8.33761i	−1.08854	−	0.628471i
$177$			7.46822i			0.561346i
$178$	−15.1193	−	4.05119i	−1.13324	−	0.303650i
$179$	15.1099	+	15.1099i	1.12937	+	1.12937i	0.990280	+	0.139089i	$0.0444174\pi$
$179$	15.1099	+	15.1099i	1.12937	+	1.12937i	0.139089	+	0.990280i	$0.455583\pi$
$180$		0			0
$181$	−0.167025	−	0.289295i	−0.0124148	−	0.0215032i	0.859751	−	0.510713i	$-0.170619\pi$
$181$	−0.167025	−	0.289295i	−0.0124148	−	0.0215032i	−0.872166	+	0.489210i	$0.837285\pi$
$182$	16.2007	+	4.34097i	1.20088	+	0.321774i
$183$	1.85487	+	1.07091i	0.137116	+	0.0791641i
$184$	−19.5954			−1.44459
$185$		0			0
$186$	6.96645			0.510805
$187$	17.8826	+	10.3245i	1.30770	+	0.755003i
$188$	−1.59586	−	0.427610i	−0.116390	−	0.0311866i
$189$	11.8016	+	20.4410i	0.858442	+	1.48686i
$190$		0			0
$191$	−2.98486	−	2.98486i	−0.215977	−	0.215977i	0.590824	−	0.806801i	$-0.298803\pi$
$191$	−2.98486	−	2.98486i	−0.215977	−	0.215977i	−0.806801	+	0.590824i	$0.798803\pi$
$192$	−10.4044	−	2.78785i	−0.750872	−	0.201196i
$193$		−	7.99715i		−	0.575648i	−0.957683	−	0.287824i	$-0.907068\pi$
$193$		−	7.99715i		−	0.575648i	0.957683	−	0.287824i	$-0.0929318\pi$
$194$	11.7086	+	6.75997i	0.840629	+	0.485338i
$195$		0			0
$196$		−	2.96378i		−	0.211698i
$197$	1.27223	+	4.74803i	0.0906426	+	0.338283i	0.996323	−	0.0856786i	$-0.0273058\pi$
$197$	1.27223	+	4.74803i	0.0906426	+	0.338283i	−0.905680	+	0.423962i	$0.860639\pi$
$198$	−8.30941	+	4.79744i	−0.590524	+	0.340939i
$199$	7.98996	+	7.98996i	0.566393	+	0.566393i	0.931116	−	0.364723i	$-0.118836\pi$
$199$	7.98996	+	7.98996i	0.566393	+	0.566393i	−0.364723	+	0.931116i	$0.618836\pi$
$200$		0			0
$201$	7.34353	−	12.7194i	0.517973	−	0.897155i
$202$	12.5310	−	21.7043i	0.881676	−	1.52711i
$203$	1.26385	+	2.18905i	0.0887049	+	0.153641i
$204$	1.31576	+	0.352557i	0.0921216	+	0.0246839i
$205$		0			0
$206$	20.7530	+	11.9818i	1.44593	+	0.834810i
$207$	−4.88451	+	8.46021i	−0.339497	+	0.588025i
$208$			10.1342i			0.702677i
$209$	6.43716	−	24.0238i	0.445268	−	1.66176i
$210$		0			0
$211$	−16.1514			−1.11191			−0.555955	−	0.831213i	$-0.687647\pi$
$211$	−16.1514			−1.11191			−0.555955	+	0.831213i	$0.687647\pi$
$212$	−1.23168	−	1.23168i	−0.0845923	−	0.0845923i
$213$	−1.13606	−	4.23984i	−0.0778417	−	0.290509i
$214$	−6.10514	−	6.10514i	−0.417339	−	0.417339i
$215$		0			0
$216$	−11.6392	+	11.6392i	−0.791950	+	0.791950i
$217$	−15.9120	+	9.18679i	−1.08018	+	0.623640i
$218$	2.36235	−	8.81640i	0.159998	−	0.597122i
$219$	−3.77085	+	2.17710i	−0.254811	+	0.147115i
$220$		0			0
$221$		−	12.5492i		−	0.844149i
$222$	−7.22157	+	6.71759i	−0.484680	+	0.450855i
$223$	2.37166	+	2.37166i	0.158818	+	0.158818i	0.782043	−	0.623225i	$-0.214178\pi$
$223$	2.37166	+	2.37166i	0.158818	+	0.158818i	−0.623225	+	0.782043i	$0.714178\pi$
$224$	6.09359	−	1.63277i	0.407145	−	0.109094i
$225$		0			0
$226$	−1.77415	+	1.02431i	−0.118015	+	0.0681358i
$227$	2.15053	+	3.72482i	0.142735	+	0.247225i	0.928526	−	0.371268i	$-0.121077\pi$
$227$	2.15053	+	3.72482i	0.142735	+	0.247225i	−0.785790	+	0.618493i	$0.787744\pi$
$228$		−	1.64071i		−	0.108659i
$229$	−6.37880	+	3.68280i	−0.421523	+	0.243366i	−0.695729	−	0.718305i	$-0.744918\pi$
$229$	−6.37880	+	3.68280i	−0.421523	+	0.243366i	0.274206	+	0.961671i	$0.411585\pi$
$230$		0			0
$231$	−12.8777	+	22.3048i	−0.847288	+	1.46755i
$232$	−1.24646	+	1.24646i	−0.0818341	+	0.0818341i
$233$	−2.31125	+	2.31125i	−0.151415	+	0.151415i	−0.778750	−	0.627335i	$-0.784146\pi$
$233$	−2.31125	+	2.31125i	−0.151415	+	0.151415i	0.627335	+	0.778750i	$0.284146\pi$
$234$	5.04994	+	2.91558i	0.330125	+	0.190598i
$235$		0			0
$236$	1.12712	−	1.12712i	0.0733693	−	0.0733693i
$237$	−4.38301	−	2.53053i	−0.284707	−	0.164376i
$238$	22.9643	−	6.15327i	1.48856	−	0.398857i
$239$	−4.53201	−	16.9137i	−0.293151	−	1.09406i	−0.942675	−	0.333713i	$-0.891698\pi$
$239$	−4.53201	−	16.9137i	−0.293151	−	1.09406i	0.649523	−	0.760342i	$-0.274968\pi$
$240$		0			0
$241$	−5.49887	+	20.5221i	−0.354213	+	1.32194i	0.527258	+	0.849705i	$0.323220\pi$
$241$	−5.49887	+	20.5221i	−0.354213	+	1.32194i	−0.881472	+	0.472237i	$0.843447\pi$
$242$	−14.8054	−	8.54788i	−0.951724	−	0.549478i
$243$	3.54399	+	13.2264i	0.227347	+	0.848471i
$244$	−0.118317	−	0.441567i	−0.00757450	−	0.0282684i
$245$		0			0
$246$	−1.62308	−	0.434904i	−0.103484	−	0.0277284i
$247$	−14.6002	+	3.91210i	−0.928986	+	0.248921i
$248$	−9.06039	−	9.06039i	−0.575335	−	0.575335i
$249$	−3.27320			−0.207431
$250$		0			0
$251$	17.7562	−	17.7562i	1.12076	−	1.12076i	0.129136	−	0.991627i	$-0.458780\pi$
$251$	17.7562	−	17.7562i	1.12076	−	1.12076i	0.991627	−	0.129136i	$-0.0412203\pi$
$252$	0.432068	−	1.61250i	0.0272177	−	0.101578i
$253$	−32.1685			−2.02242
$254$	5.55535	−	20.7328i	0.348573	−	1.30089i
$255$		0			0
$256$	3.09396	+	5.35890i	0.193373	+	0.334931i
$257$	2.64029	−	4.57311i	0.164696	−	0.285263i	−0.771851	−	0.635803i	$-0.780669\pi$
$257$	2.64029	−	4.57311i	0.164696	−	0.285263i	0.936547	+	0.350541i	$0.114002\pi$
$258$	−3.64161	+	3.64161i	−0.226717	+	0.226717i
$259$	7.63609	−	24.8668i	0.474484	−	1.54515i
$260$		0			0
$261$	0.227451	+	0.848857i	0.0140788	+	0.0525429i
$262$	−4.85891	+	18.1337i	−0.300185	+	1.12030i
$263$	−16.7100	−	4.47743i	−1.03038	−	0.276090i	−0.296261	−	0.955107i	$-0.595740\pi$
$263$	−16.7100	−	4.47743i	−1.03038	−	0.276090i	−0.734123	+	0.679017i	$0.762406\pi$
$264$	−17.3492	−	4.64870i	−1.06777	−	0.286108i
$265$		0			0
$266$	−14.3179	−	24.7993i	−0.877885	−	1.52054i
$267$	−14.6076			−0.893972
$268$	−3.02794	+	0.811334i	−0.184961	+	0.0495601i
$269$		−	0.173030i		−	0.0105498i	−0.999986	−	0.00527492i	$-0.998321\pi$
$269$		−	0.173030i		−	0.0105498i	0.999986	−	0.00527492i	$-0.00167907\pi$
$270$		0			0
$271$	−9.17400	+	15.8898i	−0.557281	+	0.965239i	0.440441	+	0.897781i	$0.354822\pi$
$271$	−9.17400	+	15.8898i	−0.557281	+	0.965239i	−0.997722	+	0.0674574i	$0.978511\pi$
$272$	7.18252	+	12.4405i	0.435504	+	0.754315i
$273$	15.6525			0.947331
$274$	13.2210	−	3.54256i	0.798710	−	0.214014i
$275$		0			0
$276$	−2.04978	+	0.549238i	−0.123383	+	0.0330602i
$277$	1.59242	−	0.919384i	0.0956793	−	0.0552405i	−0.451397	−	0.892323i	$-0.649074\pi$
$277$	1.59242	−	0.919384i	0.0956793	−	0.0552405i	0.547076	+	0.837083i	$0.315741\pi$
$278$	9.98977	−	5.76759i	0.599146	−	0.345917i
$279$	−6.17025	+	1.65331i	−0.369403	+	0.0989813i
$280$		0			0
$281$	3.28246	−	0.879533i	0.195815	−	0.0524686i	−0.159578	−	0.987185i	$-0.551013\pi$
$281$	3.28246	−	0.879533i	0.195815	−	0.0524686i	0.355394	+	0.934717i	$0.384347\pi$
$282$	10.2032			0.607595
$283$	−6.28759	−	10.8904i	−0.373758	−	0.647369i	0.616382	−	0.787447i	$-0.288598\pi$
$283$	−6.28759	−	10.8904i	−0.373758	−	0.647369i	−0.990140	+	0.140079i	$0.955264\pi$
$284$	−0.468430	+	0.811344i	−0.0277962	+	0.0481444i
$285$		0			0
$286$			19.2015i			1.13541i
$287$	4.28078	−	1.14703i	0.252686	−	0.0677071i
$288$	2.19328			0.129240
$289$	−0.394151	−	0.682690i	−0.0231854	−	0.0401582i
$290$		0			0
$291$	12.1874	+	3.26561i	0.714438	+	0.191433i
$292$	0.897679	+	0.240532i	0.0525327	+	0.0140761i
$293$	2.72847	−	10.1828i	0.159399	−	0.594885i	−0.839290	−	0.543685i	$-0.817029\pi$
$293$	2.72847	−	10.1828i	0.159399	−	0.594885i	0.998688	−	0.0512000i	$-0.0163046\pi$
$294$	4.73728	+	17.6798i	0.276284	+	1.03110i
$295$		0			0
$296$	18.1289	+	0.655467i	1.05372	+	0.0380982i
$297$	−19.1074	+	19.1074i	−1.10872	+	1.10872i
$298$	11.0120	−	19.0734i	0.637909	−	1.10489i
$299$	9.77500	+	16.9308i	0.565303	+	0.979133i
$300$		0			0
$301$	3.51550	−	13.1200i	0.202630	−	0.756226i
$302$	−5.86051			−0.337234
$303$	6.05346	−	22.5918i	0.347762	−	1.29787i
$304$	12.2346	−	12.2346i	0.701704	−	0.701704i
$305$		0			0
$306$	8.26561			0.472513
$307$	−7.96428	−	7.96428i	−0.454546	−	0.454546i	0.442314	−	0.896860i	$-0.354158\pi$
$307$	−7.96428	−	7.96428i	−0.454546	−	0.454546i	−0.896860	+	0.442314i	$0.854158\pi$
$308$	5.30982	−	1.42276i	0.302555	−	0.0810693i
$309$	21.6017	+	5.78816i	1.22888	+	0.329277i
$310$		0			0
$311$	0.179038	+	0.668180i	0.0101523	+	0.0378890i	0.970816	−	0.239825i	$-0.0770900\pi$
$311$	0.179038	+	0.668180i	0.0101523	+	0.0378890i	−0.960664	+	0.277714i	$0.910423\pi$
$312$	2.82519	+	10.5437i	0.159945	+	0.596922i
$313$	20.1350	+	11.6249i	1.13810	+	0.657081i	0.945959	−	0.324287i	$-0.105124\pi$
$313$	20.1350	+	11.6249i	1.13810	+	0.657081i	0.192139	+	0.981368i	$0.438458\pi$
$314$	3.30189	−	12.3228i	0.186336	−	0.695417i
$315$		0			0
$316$	0.279581	+	1.04341i	0.0157276	+	0.0586963i
$317$	31.3969	−	8.41276i	1.76342	−	0.472508i	0.776017	−	0.630713i	$-0.217237\pi$
$317$	31.3969	−	8.41276i	1.76342	−	0.472508i	0.987406	+	0.158205i	$0.0505706\pi$
$318$	9.31605	+	5.37862i	0.522418	+	0.301618i
$319$	−2.04624	+	2.04624i	−0.114567	+	0.114567i
$320$		0			0
$321$	−6.97805	−	4.02878i	−0.389477	−	0.224865i
$322$	−26.1894	+	26.1894i	−1.45948	+	1.45948i
$323$	−15.1502	+	15.1502i	−0.842979	+	0.842979i
$324$	−0.305748	+	0.529572i	−0.0169860	+	0.0294207i
$325$		0			0
$326$	−18.6827	+	10.7865i	−1.03474	+	0.597408i
$327$		−	8.51805i		−	0.471049i
$328$	1.54532	+	2.67656i	0.0853258	+	0.147789i
$329$	−23.3051	+	13.4552i	−1.28485	+	0.741810i
$330$		0			0
$331$	20.5568	−	5.50817i	1.12990	−	0.302757i	0.355018	−	0.934859i	$-0.384475\pi$
$331$	20.5568	−	5.50817i	1.12990	−	0.302757i	0.774885	+	0.632103i	$0.217808\pi$
$332$	0.493999	+	0.493999i	0.0271117	+	0.0271117i
$333$	4.80196	−	7.66369i	0.263146	−	0.419968i
$334$			12.9938i			0.710990i
$335$		0			0
$336$	−15.5169	+	8.95869i	−0.846517	+	0.488737i
$337$	0.488128	−	1.82172i	0.0265900	−	0.0992352i	−0.951356	−	0.308095i	$-0.900309\pi$
$337$	0.488128	−	1.82172i	0.0265900	−	0.0992352i	0.977946	+	0.208860i	$0.0669752\pi$
$338$	−4.73379	+	2.73305i	−0.257484	+	0.148659i
$339$	−1.35188	+	1.35188i	−0.0734239	+	0.0734239i
$340$		0			0
$341$	−14.8739	−	14.8739i	−0.805466	−	0.805466i
$342$	−2.57674	−	9.61651i	−0.139334	−	0.520001i
$343$	−12.9675	−	12.9675i	−0.700179	−	0.700179i
$344$	9.47238			0.510716
$345$		0			0
$346$	2.57403	−	9.60640i	0.138381	−	0.516443i
$347$			6.76364i			0.363091i	0.983383	+	0.181546i	$0.0581100\pi$
$347$			6.76364i			0.363091i	−0.983383	+	0.181546i	$0.941890\pi$
$348$	−0.0954497	+	0.165324i	−0.00511664	+	0.00886228i
$349$	−12.1596	−	7.02035i	−0.650888	−	0.375790i	0.137908	−	0.990445i	$-0.455962\pi$
$349$	−12.1596	−	7.02035i	−0.650888	−	0.375790i	−0.788796	+	0.614655i	$0.789295\pi$
$350$		0			0
$351$	15.8627	+	4.25039i	0.846688	+	0.226869i
$352$	3.61114	+	6.25468i	0.192475	+	0.333376i
$353$	−7.21056	+	12.4891i	−0.383779	+	0.664725i	−0.991599	−	0.129350i	$-0.958711\pi$
$353$	−7.21056	+	12.4891i	−0.383779	+	0.664725i	0.607820	+	0.794075i	$0.292044\pi$
$354$	−4.92201	+	8.52517i	−0.261602	+	0.453108i
$355$		0			0
$356$	2.20462	+	2.20462i	0.116844	+	0.116844i
$357$	19.2147	−	11.0936i	1.01695	−	0.587135i
$358$	7.29003	+	27.2068i	0.385290	+	1.43792i
$359$			2.87625i			0.151803i	0.997115	+	0.0759013i	$0.0241834\pi$
$359$			2.87625i			0.151803i	−0.997115	+	0.0759013i	$0.975817\pi$
$360$		0			0
$361$	5.89475	+	3.40334i	0.310250	+	0.179123i
$362$		−	0.440318i		−	0.0231426i
$363$	−15.4108	−	4.12931i	−0.808856	−	0.216732i
$364$	−2.36231	−	2.36231i	−0.123819	−	0.123819i
$365$		0			0
$366$	1.41159	+	2.44495i	0.0737852	+	0.127800i
$367$	25.2940	+	6.77750i	1.32033	+	0.353783i	0.849103	−	0.528227i	$-0.177143\pi$
$367$	25.2940	+	6.77750i	1.32033	+	0.353783i	0.471231	+	0.882010i	$0.343810\pi$
$368$	−19.3807	−	11.1894i	−1.01029	−	0.583290i
$369$	1.54079			0.0802105
$370$		0			0
$371$	−28.3716			−1.47298
$372$	−1.20172	−	0.693814i	−0.0623063	−	0.0359726i
$373$	33.2235	+	8.90222i	1.72025	+	0.460939i	0.977900	−	0.209074i	$-0.0670448\pi$
$373$	33.2235	+	8.90222i	1.72025	+	0.460939i	0.742349	+	0.670013i	$0.233712\pi$
$374$	13.6090	+	23.5714i	0.703703	+	1.21885i
$375$		0			0
$376$	−13.2701	−	13.2701i	−0.684352	−	0.684352i
$377$	1.69875	+	0.455180i	0.0874903	+	0.0234430i
$378$			31.1120i			1.60023i
$379$	1.99724	+	1.15311i	0.102591	+	0.0592312i	0.550418	−	0.834889i	$-0.314468\pi$
$379$	1.99724	+	1.15311i	0.102591	+	0.0592312i	−0.447826	+	0.894121i	$0.647802\pi$
$380$		0			0
$381$		−	20.0312i		−	1.02623i
$382$	−1.44009	−	5.37450i	−0.0736816	−	0.274983i
$383$	−0.121710	+	0.0702694i	−0.00621910	+	0.00359060i	−0.503106	−	0.864225i	$-0.667810\pi$
$383$	−0.121710	+	0.0702694i	−0.00621910	+	0.00359060i	0.496887	+	0.867815i	$0.334476\pi$
$384$	−7.47325	−	7.47325i	−0.381367	−	0.381367i
$385$		0			0
$386$	5.27061	−	9.12897i	0.268267	−	0.464652i
$387$	2.36116	−	4.08966i	0.120025	−	0.207889i
$388$	−1.34650	−	2.33220i	−0.0683581	−	0.118400i
$389$	−5.08702	−	1.36306i	−0.257922	−	0.0691101i	0.127541	−	0.991833i	$-0.459292\pi$
$389$	−5.08702	−	1.36306i	−0.257922	−	0.0691101i	−0.385463	+	0.922723i	$0.625958\pi$
$390$		0			0
$391$	23.9992	+	13.8559i	1.21369	+	0.700725i
$392$	16.8327	−	29.1550i	0.850178	−	1.47255i
$393$			17.5201i			0.883770i
$394$	−1.67696	+	6.25848i	−0.0844838	+	0.315298i
$395$		0			0
$396$	1.91118			0.0960402
$397$	−3.01599	−	3.01599i	−0.151368	−	0.151368i	0.627361	−	0.778729i	$-0.284135\pi$
$397$	−3.01599	−	3.01599i	−0.151368	−	0.151368i	−0.778729	+	0.627361i	$0.784135\pi$
$398$	3.85489	+	14.3866i	0.193228	+	0.721137i
$399$	−18.8967	−	18.8967i	−0.946019	−	0.946019i
$400$		0			0
$401$	−6.97260	+	6.97260i	−0.348195	+	0.348195i	−0.859437	−	0.511242i	$-0.829186\pi$
$401$	−6.97260	+	6.97260i	−0.348195	+	0.348195i	0.511242	+	0.859437i	$0.329186\pi$
$402$	16.7657	−	9.67967i	0.836196	−	0.482778i
$403$	−3.30865	+	12.3481i	−0.164816	+	0.615101i
$404$	−4.32321	+	2.49601i	−0.215088	+	0.124181i
$405$		0			0
$406$			3.33182i			0.165355i
$407$	29.7611	+	1.07604i	1.47520	+	0.0533373i
$408$	10.9410	+	10.9410i	0.541658	+	0.541658i
$409$	−8.95729	+	2.40010i	−0.442910	+	0.118677i	−0.473380	−	0.880858i	$-0.656966\pi$
$409$	−8.95729	+	2.40010i	−0.442910	+	0.118677i	0.0304703	+	0.999536i	$0.490300\pi$
$410$		0			0
$411$	11.0623	−	6.38680i	0.545661	−	0.315038i
$412$	−2.38662	−	4.13374i	−0.117580	−	0.203655i
$413$		−	25.9630i		−	1.27756i
$414$	−11.1516	+	6.43838i	−0.548071	+	0.316429i
$415$		0			0
$416$	2.19463	−	3.80120i	0.107600	−	0.186369i
$417$	7.61206	−	7.61206i	0.372764	−	0.372764i
$418$	23.1814	−	23.1814i	1.13384	−	1.13384i
$419$	−29.2106	−	16.8648i	−1.42703	−	0.823898i	−0.430147	−	0.902759i	$-0.641538\pi$
$419$	−29.2106	−	16.8648i	−1.42703	−	0.823898i	−0.996886	+	0.0788607i	$0.974872\pi$
$420$		0			0
$421$	6.17988	−	6.17988i	0.301189	−	0.301189i	−0.540290	−	0.841479i	$-0.681685\pi$
$421$	6.17988	−	6.17988i	0.301189	−	0.301189i	0.841479	+	0.540290i	$0.181685\pi$
$422$	−18.4373	−	10.6448i	−0.897513	−	0.518179i
$423$	−9.03711	+	2.42149i	−0.439400	+	0.117737i
$424$	−5.12092	−	19.1115i	−0.248694	−	0.928138i
$425$		0			0
$426$	1.49747	−	5.58863i	0.0725526	−	0.270770i
$427$	−6.44841	−	3.72299i	−0.312060	−	0.180168i
$428$	0.445111	+	1.66118i	0.0215153	+	0.0802960i
$429$	4.63794	+	17.3090i	0.223922	+	0.835687i
$430$		0			0
$431$	3.98861	+	1.06874i	0.192124	+	0.0514796i	0.353598	−	0.935397i	$-0.384958\pi$
$431$	3.98861	+	1.06874i	0.192124	+	0.0514796i	−0.161474	+	0.986877i	$0.551625\pi$
$432$	−18.1580	+	4.86542i	−0.873628	+	0.234088i
$433$	2.42155	+	2.42155i	0.116372	+	0.116372i	0.762895	−	0.646523i	$-0.223777\pi$
$433$	2.42155	+	2.42155i	0.116372	+	0.116372i	−0.646523	+	0.762895i	$0.723777\pi$
$434$	−24.2186			−1.16253
$435$		0			0
$436$	−1.28556	+	1.28556i	−0.0615674	+	0.0615674i
$437$	8.63895	−	32.2410i	0.413257	−	1.54230i
$438$	−5.73937			−0.274238
$439$	−2.19354	+	8.18640i	−0.104692	+	0.390716i	−0.998310	−	0.0581125i	$-0.981492\pi$
$439$	−2.19354	+	8.18640i	−0.104692	+	0.390716i	0.893618	+	0.448828i	$0.148158\pi$
$440$		0			0
$441$	−8.39170	−	14.5349i	−0.399605	−	0.692136i
$442$	8.27068	−	14.3252i	0.393396	−	0.681382i
$443$	21.9112	−	21.9112i	1.04103	−	1.04103i	0.0419105	−	0.999121i	$-0.486656\pi$
$443$	21.9112	−	21.9112i	1.04103	−	1.04103i	0.999121	−	0.0419105i	$-0.0133444\pi$
$444$	1.91476	−	0.439569i	0.0908704	−	0.0208610i
$445$		0			0
$446$	1.14425	+	4.27038i	0.0541816	+	0.202209i
$447$	5.31969	−	19.8533i	0.251613	−	0.939031i
$448$	36.1705	+	9.69186i	1.70890	+	0.457898i
$449$	24.7248	+	6.62498i	1.16683	+	0.312652i	0.789692	−	0.613503i	$-0.210240\pi$
$449$	24.7248	+	6.62498i	1.16683	+	0.312652i	0.377142	+	0.926155i	$0.376907\pi$
$450$		0			0
$451$	2.53685	+	4.39395i	0.119456	+	0.206903i
$452$	0.408057			0.0191934
$453$	−5.28289	+	1.41555i	−0.248212	+	0.0665082i
$454$			5.66931i			0.266074i
$455$		0			0
$456$	9.31835	−	16.1399i	0.436372	−	0.755818i
$457$	−13.3314	−	23.0907i	−0.623617	−	1.08014i	−0.988807	−	0.149203i	$-0.952329\pi$
$457$	−13.3314	−	23.0907i	−0.623617	−	1.08014i	0.365190	−	0.930933i	$-0.381004\pi$
$458$	−9.70877			−0.453661
$459$	22.4852	−	6.02488i	1.04952	−	0.281217i
$460$		0			0
$461$	28.6141	−	7.66712i	1.33269	−	0.357094i	0.478973	−	0.877829i	$-0.341009\pi$
$461$	28.6141	−	7.66712i	1.33269	−	0.357094i	0.853718	+	0.520736i	$0.174342\pi$
$462$	−29.4004	+	16.9743i	−1.36783	+	0.789718i
$463$	−16.3053	+	9.41385i	−0.757770	+	0.437499i	−0.828495	−	0.559997i	$-0.810802\pi$
$463$	−16.3053	+	9.41385i	−0.757770	+	0.437499i	0.0707245	+	0.997496i	$0.477469\pi$
$464$	−1.94456	+	0.521044i	−0.0902741	+	0.0241889i
$465$		0			0
$466$	−4.16161	+	1.11510i	−0.192783	+	0.0516560i
$467$	−22.1604			−1.02546			−0.512731	−	0.858549i	$-0.671366\pi$
$467$	−22.1604			−1.02546			−0.512731	+	0.858549i	$0.671366\pi$
$468$	−0.580747	−	1.00588i	−0.0268450	−	0.0464970i
$469$	−25.5295	+	44.2185i	−1.17884	+	2.04182i
$470$		0			0
$471$		−	11.9058i		−	0.548591i
$472$	17.4891	−	4.68618i	0.805000	−	0.215699i
$473$	15.5502			0.715000
$474$	−3.33555	−	5.77735i	−0.153207	−	0.265362i
$475$		0			0
$476$	−4.57420	−	1.22565i	−0.209658	−	0.0561777i
$477$	−9.52780	−	2.55297i	−0.436248	−	0.116892i
$478$	5.97374	−	22.2943i	0.273233	−	1.01972i
$479$	1.61172	+	6.01501i	0.0736412	+	0.274833i	0.992922	−	0.118770i	$-0.0378952\pi$
$479$	1.61172	+	6.01501i	0.0736412	+	0.274833i	−0.919281	+	0.393603i	$0.871228\pi$
$480$		0			0
$481$	−8.47713	−	15.9907i	−0.386524	−	0.729114i
$482$	−19.8024	+	19.8024i	−0.901975	+	0.901975i
$483$	−17.2824	+	29.9340i	−0.786376	+	1.36204i
$484$	1.70263	+	2.94904i	0.0773921	+	0.134047i
$485$		0			0
$486$	−4.67141	+	17.4340i	−0.211900	+	0.790820i
$487$	−13.1383			−0.595352			−0.297676	−	0.954667i	$-0.596212\pi$
$487$	−13.1383			−0.595352			−0.297676	+	0.954667i	$0.596212\pi$
$488$	1.34396	−	5.01572i	0.0608382	−	0.227051i
$489$	−14.2360	+	14.2360i	−0.643774	+	0.643774i
$490$		0			0
$491$	−1.90585			−0.0860099			−0.0430050	−	0.999075i	$-0.513693\pi$
$491$	−1.90585			−0.0860099			−0.0430050	+	0.999075i	$0.513693\pi$
$492$	0.236670	+	0.236670i	0.0106699	+	0.0106699i
$493$	2.40796	−	0.645212i	0.108449	−	0.0290589i
$494$	−19.2448	−	5.15663i	−0.865865	−	0.232008i
$495$		0			0
$496$	−3.78742	−	14.1348i	−0.170060	−	0.634672i
$497$	3.94948	+	14.7397i	0.177159	+	0.661165i
$498$	−3.73645	−	2.15724i	−0.167434	−	0.0966682i
$499$	−5.11290	+	19.0816i	−0.228885	+	0.854210i	0.751926	+	0.659248i	$0.229125\pi$
$499$	−5.11290	+	19.0816i	−0.228885	+	0.854210i	−0.980811	+	0.194962i	$0.937542\pi$
$500$		0			0
$501$	3.13853	+	11.7131i	0.140219	+	0.523304i
$502$	31.9717	−	8.56678i	1.42696	−	0.382354i
$503$	−11.0969	−	6.40682i	−0.494788	−	0.285666i	0.231770	−	0.972770i	$-0.425548\pi$
$503$	−11.0969	−	6.40682i	−0.494788	−	0.285666i	−0.726559	+	0.687104i	$0.758882\pi$
$504$	13.4084	−	13.4084i	0.597259	−	0.597259i
$505$		0			0
$506$	−36.7212	−	21.2010i	−1.63246	−	0.942500i
$507$	−3.60708	+	3.60708i	−0.160196	+	0.160196i
$508$	−3.02316	+	3.02316i	−0.134131	+	0.134131i
$509$	16.2560	−	28.1562i	0.720534	−	1.24800i	−0.240252	−	0.970711i	$-0.577230\pi$
$509$	16.2560	−	28.1562i	0.720534	−	1.24800i	0.960786	−	0.277291i	$-0.0894366\pi$
$510$		0			0
$511$	13.1092	−	7.56862i	0.579919	−	0.334816i
$512$			25.3397i			1.11987i
$513$	−14.0191	−	24.2818i	−0.618960	−	1.07207i
$514$	6.02792	−	3.48022i	0.265880	−	0.153506i
$515$		0			0
$516$	0.990864	−	0.265501i	0.0436203	−	0.0116880i
$517$	−21.7847	−	21.7847i	−0.958089	−	0.958089i
$518$	25.1055	−	23.3535i	1.10307	−	1.02609i
$519$		−	9.28132i		−	0.407405i
$520$		0			0
$521$	24.6860	−	14.2524i	1.08151	−	0.624411i	0.150208	−	0.988654i	$-0.452006\pi$
$521$	24.6860	−	14.2524i	1.08151	−	0.624411i	0.931304	+	0.364244i	$0.118672\pi$
$522$	−0.299808	+	1.11890i	−0.0131222	+	0.0489728i
$523$	23.1609	−	13.3720i	1.01276	−	0.584716i	0.100760	−	0.994911i	$-0.467873\pi$
$523$	23.1609	−	13.3720i	1.01276	−	0.584716i	0.911998	+	0.410195i	$0.134539\pi$
$524$	2.64417	−	2.64417i	0.115511	−	0.115511i
$525$		0			0
$526$	−16.1240	−	16.1240i	−0.703041	−	0.703041i
$527$	4.68998	+	17.5032i	0.204299	+	0.762453i
$528$	−14.5046	−	14.5046i	−0.631231	−	0.631231i
$529$	−20.1715			−0.877024
$530$		0			0
$531$	2.33623	−	8.71894i	0.101384	−	0.378370i
$532$			5.70387i			0.247294i
$533$	1.54174	−	2.67037i	0.0667801	−	0.115666i
$534$	−16.6750	−	9.62732i	−0.721598	−	0.416615i
$535$		0			0
$536$	−34.3942	−	9.21589i	−1.48560	−	0.398066i
$537$	13.1430	+	22.7644i	0.567164	+	0.982357i
$538$	0.114037	−	0.197519i	0.00491650	−	0.00851563i
$539$	27.6331	−	47.8620i	1.19024	−	2.06156i
$540$		0			0
$541$	17.2856	+	17.2856i	0.743165	+	0.743165i	0.973186	−	0.230021i	$-0.0738794\pi$
$541$	17.2856	+	17.2856i	0.743165	+	0.743165i	−0.230021	+	0.973186i	$0.573879\pi$
$542$	−20.9448	+	12.0925i	−0.899654	+	0.519416i
$543$	−0.106354	−	0.396920i	−0.00456410	−	0.0170335i
$544$		−	6.22171i		−	0.266754i
$545$		0			0
$546$	17.8677	+	10.3159i	0.764669	+	0.441482i
$547$			13.5842i			0.580818i	0.956903	+	0.290409i	$0.0937913\pi$
$547$			13.5842i			0.580818i	−0.956903	+	0.290409i	$0.906209\pi$
$548$	−2.63345	−	0.705632i	−0.112496	−	0.0301431i
$549$	−1.83051	−	1.83051i	−0.0781243	−	0.0781243i
$550$		0			0
$551$	−1.50133	−	2.60037i	−0.0639586	−	0.110780i
$552$	−23.2834	−	6.23876i	−0.991006	−	0.265539i
$553$	15.2374	+	8.79732i	0.647960	+	0.374100i
$554$	2.42372			0.102974
$555$		0			0
$556$	−2.29766			−0.0974425
$557$	−35.3898	−	20.4323i	−1.49951	−	0.865744i	−0.499513	−	0.866307i	$-0.666488\pi$
$557$	−35.3898	−	20.4323i	−1.49951	−	0.865744i	−1.00000		0.000562636i	$0.999821\pi$
$558$	−8.13315	−	2.17927i	−0.344303	−	0.0922558i
$559$	−4.72522	−	8.18433i	−0.199856	−	0.346160i
$560$		0			0
$561$	17.9611	+	17.9611i	0.758318	+	0.758318i
$562$	4.32669	+	1.15933i	0.182510	+	0.0489035i
$563$			27.8829i			1.17512i	0.809180	+	0.587561i	$0.199912\pi$
$563$			27.8829i			1.17512i	−0.809180	+	0.587561i	$0.800088\pi$
$564$	−1.76007	−	1.01618i	−0.0741124	−	0.0427888i
$565$		0			0
$566$		−	16.5756i		−	0.696726i
$567$	2.57786	+	9.62072i	0.108260	+	0.404032i
$568$	−9.21600	+	5.32086i	−0.386695	+	0.223258i
$569$	10.7860	+	10.7860i	0.452173	+	0.452173i	0.896075	−	0.443902i	$-0.146406\pi$
$569$	10.7860	+	10.7860i	0.452173	+	0.452173i	−0.443902	+	0.896075i	$0.646406\pi$
$570$		0			0
$571$	16.7650	−	29.0378i	0.701594	−	1.21520i	−0.266313	−	0.963887i	$-0.585805\pi$
$571$	16.7650	−	29.0378i	0.701594	−	1.21520i	0.967907	−	0.251310i	$-0.0808612\pi$
$572$	1.91235	−	3.31228i	0.0799593	−	0.138494i
$573$	−2.59631	−	4.49695i	−0.108463	−	0.187863i
$574$	5.64259	+	1.51193i	0.235517	+	0.0631067i
$575$		0			0
$576$	11.2747	+	6.50948i	0.469781	+	0.271228i
$577$	−8.95508	+	15.5106i	−0.372805	+	0.645717i	−0.989996	−	0.141097i	$-0.954937\pi$
$577$	−8.95508	+	15.5106i	−0.372805	+	0.645717i	0.617191	+	0.786813i	$0.288271\pi$
$578$		−	1.03908i		−	0.0432200i
$579$	2.54613	−	9.50228i	0.105813	−	0.394901i
$580$		0			0
$581$	11.3792			0.472087
$582$	11.7600	+	11.7600i	0.487469	+	0.487469i
$583$	−8.40669	−	31.3742i	−0.348170	−	1.29939i
$584$	7.46448	+	7.46448i	0.308883	+	0.308883i
$585$		0			0
$586$	9.82570	−	9.82570i	0.405896	−	0.405896i
$587$	32.4251	−	18.7207i	1.33833	−	0.772684i	0.351769	−	0.936087i	$-0.385580\pi$
$587$	32.4251	−	18.7207i	1.33833	−	0.772684i	0.986560	+	0.163402i	$0.0522469\pi$
$588$	0.943605	−	3.52158i	0.0389136	−	0.145228i
$589$	18.9018	−	10.9130i	0.778836	−	0.449661i
$590$		0			0
$591$			6.04669i			0.248728i
$592$	17.5560	+	11.0003i	0.721547	+	0.452111i
$593$	−8.22207	−	8.22207i	−0.337640	−	0.337640i	0.517839	−	0.855478i	$-0.326737\pi$
$593$	−8.22207	−	8.22207i	−0.337640	−	0.337640i	−0.855478	+	0.517839i	$0.826737\pi$
$594$	−34.4046	+	9.21869i	−1.41164	+	0.378247i
$595$		0			0
$596$	−3.79917	+	2.19345i	−0.155620	+	0.0898473i
$597$	6.94990	+	12.0376i	0.284440	+	0.492665i
$598$			25.7693i			1.05378i
$599$	15.7152	−	9.07320i	0.642107	−	0.370721i	−0.143318	−	0.989677i	$-0.545777\pi$
$599$	15.7152	−	9.07320i	0.642107	−	0.370721i	0.785426	+	0.618956i	$0.212444\pi$
$600$		0			0
$601$	−21.7617	+	37.6924i	−0.887679	+	1.53751i	−0.0450671	+	0.998984i	$0.514350\pi$
$601$	−21.7617	+	37.6924i	−0.887679	+	1.53751i	−0.842612	+	0.538521i	$0.818983\pi$
$602$	12.6599	−	12.6599i	0.515981	−	0.515981i
$603$	−12.5523	+	12.5523i	−0.511169	+	0.511169i
$604$	1.01094	+	0.583669i	0.0411347	+	0.0237492i
$605$		0			0
$606$	21.7996	−	21.7996i	0.885548	−	0.885548i
$607$	−12.4039	−	7.16138i	−0.503458	−	0.290671i	0.226683	−	0.973969i	$-0.427212\pi$
$607$	−12.4039	−	7.16138i	−0.503458	−	0.290671i	−0.730140	+	0.683297i	$0.760545\pi$
$608$	−7.23856	+	1.93957i	−0.293563	+	0.0786598i
$609$	0.804767	+	3.00343i	0.0326108	+	0.121705i
$610$		0			0
$611$	−4.84594	+	18.0853i	−0.196046	+	0.731653i
$612$	−1.42583	−	0.823201i	−0.0576356	−	0.0332759i
$613$	−0.0869843	−	0.324630i	−0.00351326	−	0.0131117i	0.964147	−	0.265369i	$-0.0854938\pi$
$613$	−0.0869843	−	0.324630i	−0.00351326	−	0.0131117i	−0.967660	+	0.252257i	$0.918827\pi$
$614$	−3.84250	−	14.3404i	−0.155071	−	0.578731i
$615$		0			0
$616$	60.3138	+	16.1610i	2.43011	+	0.651147i
$617$	25.9211	−	6.94555i	1.04355	−	0.279617i	0.303964	−	0.952684i	$-0.401690\pi$
$617$	25.9211	−	6.94555i	1.04355	−	0.279617i	0.739582	+	0.673066i	$0.235023\pi$
$618$	20.8442	+	20.8442i	0.838476	+	0.838476i
$619$	−45.2493			−1.81872			−0.909361	−	0.416008i	$-0.863429\pi$
$619$	−45.2493			−1.81872			−0.909361	+	0.416008i	$0.863429\pi$
$620$		0			0
$621$	−25.6430	+	25.6430i	−1.02902	+	1.02902i
$622$	−0.235995	+	0.880744i	−0.00946252	+	0.0353146i
$623$	50.7829			2.03457
$624$	−3.22650	+	12.0415i	−0.129164	+	0.482045i
$625$		0			0
$626$	15.3231	+	26.5404i	0.612434	+	1.06077i
$627$	15.2974	−	26.4958i	0.610918	−	1.05814i
$628$	−1.79685	+	1.79685i	−0.0717023	+	0.0717023i
$629$	−21.7397	−	13.6218i	−0.866818	−	0.543136i
$630$		0			0
$631$	−8.96677	−	33.4644i	−0.356961	−	1.33220i	−0.877998	−	0.478664i	$-0.841121\pi$
$631$	−8.96677	−	33.4644i	−0.356961	−	1.33220i	0.521037	−	0.853534i	$-0.325545\pi$
$632$	−3.17574	+	11.8520i	−0.126324	+	0.471448i
$633$	−19.1912	−	5.14227i	−0.762783	−	0.204387i
$634$	41.3849	+	11.0890i	1.64360	+	0.440402i
$635$		0			0
$636$	−1.07135	−	1.85564i	−0.0424819	−	0.0735808i
$637$	−33.5874			−1.33078
$638$	−3.68443	+	0.987240i	−0.145868	+	0.0390852i
$639$			5.30529i			0.209874i
$640$		0			0
$641$	−5.16086	+	8.93888i	−0.203842	+	0.353065i	−0.949763	−	0.312970i	$-0.898676\pi$
$641$	−5.16086	+	8.93888i	−0.203842	+	0.353065i	0.745921	+	0.666034i	$0.232010\pi$
$642$	−5.31043	−	9.19793i	−0.209586	−	0.363013i
$643$	9.55874			0.376960			0.188480	−	0.982077i	$-0.439644\pi$
$643$	9.55874			0.376960			0.188480	+	0.982077i	$0.439644\pi$
$644$	7.12601	−	1.90941i	0.280804	−	0.0752412i
$645$		0			0
$646$	−27.2793	+	7.30946i	−1.07329	+	0.287587i
$647$	−1.47670	+	0.852572i	−0.0580550	+	0.0335181i	−0.528747	−	0.848780i	$-0.677338\pi$
$647$	−1.47670	+	0.852572i	−0.0580550	+	0.0335181i	0.470692	+	0.882298i	$0.344004\pi$
$648$	−6.01537	+	3.47298i	−0.236306	+	0.136431i
$649$	28.7107	−	7.69301i	1.12699	−	0.301977i
$650$		0			0
$651$	−21.8316	+	5.84977i	−0.855649	+	0.229270i
$652$	4.29706			0.168286
$653$	14.4314	+	24.9960i	0.564746	+	0.978168i	0.997073	+	0.0764516i	$0.0243591\pi$
$653$	14.4314	+	24.9960i	0.564746	+	0.978168i	−0.432328	+	0.901717i	$0.642308\pi$
$654$	5.61392	−	9.72359i	0.219522	−	0.380223i
$655$		0			0
$656$			3.52965i			0.137810i
$657$	5.08342	−	1.36210i	0.198323	−	0.0531405i
$658$	−35.4713			−1.38281
$659$	11.5673	+	20.0352i	0.450598	+	0.780459i	0.998423	−	0.0561341i	$-0.0178774\pi$
$659$	11.5673	+	20.0352i	0.450598	+	0.780459i	−0.547825	+	0.836593i	$0.684544\pi$
$660$		0			0
$661$	−32.1200	−	8.60652i	−1.24932	−	0.334755i	−0.427247	−	0.904135i	$-0.640517\pi$
$661$	−32.1200	−	8.60652i	−1.24932	−	0.334755i	−0.822074	+	0.569380i	$0.807183\pi$
$662$	27.0964	+	7.26045i	1.05313	+	0.282185i
$663$	3.99540	−	14.9110i	0.155168	−	0.579096i
$664$	2.05388	+	7.66518i	0.0797059	+	0.297466i
$665$		0			0
$666$	10.5324	−	5.58353i	0.408123	−	0.216357i
$667$	−2.74614	+	2.74614i	−0.106331	+	0.106331i
$668$	1.29410	−	2.24145i	0.0500703	−	0.0867242i
$669$	2.06294	+	3.57311i	0.0797577	+	0.138144i
$670$		0			0
$671$	2.20629	−	8.23400i	0.0851731	−	0.317870i
$672$	7.76029			0.299360
$673$	9.06446	−	33.8290i	0.349409	−	1.30401i	−0.537966	−	0.842966i	$-0.680807\pi$
$673$	9.06446	−	33.8290i	0.349409	−	1.30401i	0.887376	−	0.461047i	$-0.152526\pi$
$674$	1.75783	−	1.75783i	0.0677092	−	0.0677092i
$675$		0			0
$676$	1.08878			0.0418761
$677$	−9.71006	−	9.71006i	−0.373188	−	0.373188i	0.495449	−	0.868637i	$-0.335004\pi$
$677$	−9.71006	−	9.71006i	−0.373188	−	0.373188i	−0.868637	+	0.495449i	$0.835004\pi$
$678$	−2.43418	+	0.652235i	−0.0934839	+	0.0250489i
$679$	−42.3691	−	11.3528i	−1.62598	−	0.435679i
$680$		0			0
$681$	1.36937	+	5.11054i	0.0524742	+	0.195836i
$682$	−7.17614	−	26.7817i	−0.274789	−	1.02553i
$683$	4.90289	+	2.83069i	0.187604	+	0.108313i	0.590860	−	0.806774i	$-0.298788\pi$
$683$	4.90289	+	2.83069i	0.187604	+	0.108313i	−0.403256	+	0.915087i	$0.632122\pi$
$684$	−0.513253	+	1.91548i	−0.0196247	+	0.0732404i
$685$		0			0
$686$	−6.25638	−	23.3491i	−0.238870	−	0.891474i
$687$	−8.75186	+	2.34506i	−0.333904	+	0.0894694i
$688$	9.36860	+	5.40896i	0.357174	+	0.206215i
$689$	−13.9582	+	13.9582i	−0.531766	+	0.531766i
$690$		0			0
$691$	27.9652	+	16.1457i	1.06385	+	0.614212i	0.926494	−	0.376310i	$-0.122807\pi$
$691$	27.9652	+	16.1457i	1.06385	+	0.614212i	0.137353	+	0.990522i	$0.456141\pi$
$692$	−1.40076	+	1.40076i	−0.0532488	+	0.0532488i
$693$	22.0118	−	22.0118i	0.836159	−	0.836159i
$694$	−4.45765	+	7.72088i	−0.169210	+	0.293081i
$695$		0			0
$696$	−1.87790	+	1.08421i	−0.0711816	+	0.0410967i
$697$		−	4.37079i		−	0.165555i
$698$	−9.25368	−	16.0278i	−0.350257	−	0.606663i
$699$	−3.48210	+	2.01039i	−0.131705	+	0.0760399i
$700$		0			0
$701$	−45.2722	+	12.1306i	−1.70991	+	0.458168i	−0.975402	−	0.220435i	$-0.929252\pi$
$701$	−45.2722	+	12.1306i	−1.70991	+	0.458168i	−0.734505	+	0.678603i	$0.762586\pi$
$702$	15.3064	+	15.3064i	0.577704	+	0.577704i
$703$	−9.07091	+	29.5392i	−0.342116	+	1.11409i
$704$			42.8703i			1.61573i
$705$		0			0
$706$	−16.4621	+	9.50440i	−0.619559	+	0.357703i
$707$	−21.0447	+	78.5397i	−0.791466	+	2.95379i
$708$	1.69811	−	0.980401i	0.0638187	−	0.0368457i
$709$	21.6799	−	21.6799i	0.814204	−	0.814204i	−0.171057	−	0.985261i	$-0.554718\pi$
$709$	21.6799	−	21.6799i	0.814204	−	0.814204i	0.985261	+	0.171057i	$0.0547181\pi$
$710$		0			0
$711$	4.32544	+	4.32544i	0.162217	+	0.162217i
$712$	9.16604	+	34.2081i	0.343512	+	1.28200i
$713$	−19.9614	−	19.9614i	−0.747560	−	0.747560i
$714$	29.2454			1.09448
$715$		0			0
$716$	1.45208	−	5.41924i	0.0542668	−	0.202526i
$717$		−	21.5399i		−	0.804421i
$718$	−1.89562	+	3.28332i	−0.0707440	+	0.122532i
$719$	4.69821	+	2.71251i	0.175214	+	0.101160i	0.585042	−	0.811003i	$-0.301078\pi$
$719$	4.69821	+	2.71251i	0.175214	+	0.101160i	−0.409828	+	0.912163i	$0.634411\pi$
$720$		0			0
$721$	−75.0976	−	20.1223i	−2.79678	−	0.749395i
$722$	4.48602	+	7.77001i	0.166952	+	0.289170i
$723$	−13.0676	+	22.6337i	−0.485989	+	0.841758i
$724$	−0.0438528	+	0.0759554i	−0.00162978	+	0.00282286i
$725$		0			0
$726$	−14.8704	−	14.8704i	−0.551891	−	0.551891i
$727$	22.1381	−	12.7814i	0.821057	−	0.474037i	−0.0297241	−	0.999558i	$-0.509463\pi$
$727$	22.1381	−	12.7814i	0.821057	−	0.474037i	0.850781	+	0.525521i	$0.176130\pi$
$728$	−9.82167	−	36.6550i	−0.364015	−	1.35852i
$729$			23.8311i			0.882634i
$730$		0			0
$731$	−11.6012	−	6.69795i	−0.429085	−	0.247733i
$732$		−	0.562343i		−	0.0207848i
$733$	−20.1942	−	5.41101i	−0.745889	−	0.199860i	−0.134195	−	0.990955i	$-0.542845\pi$
$733$	−20.1942	−	5.41101i	−0.745889	−	0.199860i	−0.611694	+	0.791095i	$0.709511\pi$
$734$	24.4070	+	24.4070i	0.900878	+	0.900878i
$735$		0			0
$736$	4.84631	+	8.39406i	0.178637	+	0.309409i
$737$	−56.4628	−	15.1291i	−2.07983	−	0.557289i
$738$	1.75886	+	1.01548i	0.0647445	+	0.0373802i
$739$	23.1549			0.851767			0.425884	−	0.904778i	$-0.359963\pi$
$739$	23.1549			0.851767			0.425884	+	0.904778i	$0.359963\pi$
$740$		0			0
$741$	−18.5936			−0.683051
$742$	−32.3869	−	18.6986i	−1.18896	−	0.686448i
$743$	24.2877	+	6.50787i	0.891029	+	0.238750i	0.675159	−	0.737672i	$-0.264075\pi$
$743$	24.2877	+	6.50787i	0.891029	+	0.238750i	0.215869	+	0.976422i	$0.430741\pi$
$744$	−7.88098	−	13.6503i	−0.288931	−	0.500443i
$745$		0			0
$746$	32.0585	+	32.0585i	1.17374	+	1.17374i
$747$	3.82137	+	1.02393i	0.139817	+	0.0374638i
$748$		−	5.42146i		−	0.198228i
$749$	24.2590	+	14.0059i	0.886403	+	0.511765i
$750$		0			0
$751$			49.5019i			1.80635i	0.429272	+	0.903175i	$0.358770\pi$
$751$			49.5019i			1.80635i	−0.429272	+	0.903175i	$0.641230\pi$
$752$	−5.54715	−	20.7022i	−0.202284	−	0.754933i
$753$	26.7513	−	15.4449i	0.974871	−	0.562842i
$754$	1.63918	+	1.63918i	0.0596955	+	0.0596955i
$755$		0			0
$756$	3.09855	−	5.36685i	0.112693	−	0.195190i
$757$	−17.8035	+	30.8365i	−0.647078	+	1.12077i	0.336740	+	0.941598i	$0.390676\pi$
$757$	−17.8035	+	30.8365i	−0.647078	+	1.12077i	−0.983817	+	0.179174i	$0.942658\pi$
$758$	1.51994	+	2.63261i	0.0552067	+	0.0956207i
$759$	−38.2229	−	10.2418i	−1.38740	−	0.371753i
$760$		0			0
$761$	9.14549	+	5.28015i	0.331524	+	0.191405i	0.656517	−	0.754311i	$-0.272029\pi$
$761$	9.14549	+	5.28015i	0.331524	+	0.191405i	−0.324994	+	0.945716i	$0.605362\pi$
$762$	13.2018	−	22.8662i	0.478251	−	0.828355i
$763$			29.6127i			1.07205i
$764$	−0.286848	+	1.07053i	−0.0103778	+	0.0387305i
$765$		0			0
$766$	−0.185247			−0.00669326
$767$	−12.7732	−	12.7732i	−0.461215	−	0.461215i
$768$	1.97011	+	7.35254i	0.0710901	+	0.265312i
$769$	−10.0805	−	10.0805i	−0.363511	−	0.363511i	0.501593	−	0.865104i	$-0.332748\pi$
$769$	−10.0805	−	10.0805i	−0.363511	−	0.363511i	−0.865104	+	0.501593i	$0.832748\pi$
$770$		0			0
$771$	4.59319	−	4.59319i	0.165420	−	0.165420i
$772$	−1.81837	+	1.04984i	−0.0654447	+	0.0377845i
$773$	0.806988	−	3.01172i	0.0290253	−	0.108324i	−0.949893	−	0.312574i	$-0.898809\pi$
$773$	0.806988	−	3.01172i	0.0290253	−	0.108324i	0.978919	+	0.204250i	$0.0654755\pi$
$774$	5.39067	−	3.11230i	0.193764	−	0.111869i
$775$		0			0
$776$		−	30.5896i		−	1.09810i
$777$	16.9903	−	27.1157i	0.609525	−	0.972771i
$778$	−4.90864	−	4.90864i	−0.175983	−	0.175983i
$779$	−5.08513	+	1.36256i	−0.182194	+	0.0488187i
$780$		0			0
$781$	−15.1293	+	8.73493i	−0.541370	+	0.312560i
$782$	18.2638	+	31.6339i	0.653113	+	1.13123i
$783$			3.26230i			0.116585i
$784$	33.2965	−	19.2237i	1.18916	−	0.686562i
$785$		0			0
$786$	−11.5468	+	19.9996i	−0.411861	+	0.713363i
$787$	−14.6240	+	14.6240i	−0.521288	+	0.521288i	−0.917960	−	0.396673i	$-0.870165\pi$
$787$	−14.6240	+	14.6240i	−0.521288	+	0.521288i	0.396673	+	0.917960i	$0.370165\pi$
$788$	0.912581	−	0.912581i	0.0325094	−	0.0325094i
$789$	−18.4294	−	10.6402i	−0.656105	−	0.378803i
$790$		0			0
$791$	4.69976	−	4.69976i	0.167104	−	0.167104i
$792$	18.8005	+	10.8545i	0.668046	+	0.385697i
$793$	−5.00411	+	1.34085i	−0.177701	+	0.0476149i
$794$	−1.45512	−	5.43057i	−0.0516401	−	0.192724i
$795$		0			0
$796$	0.767844	−	2.86563i	0.0272155	−	0.101570i
$797$	8.17798	+	4.72156i	0.289679	+	0.167246i	0.637797	−	0.770204i	$-0.279846\pi$
$797$	8.17798	+	4.72156i	0.289679	+	0.167246i	−0.348118	+	0.937451i	$0.613179\pi$
$798$	−9.11703	−	34.0252i	−0.322739	−	1.20448i
$799$	6.86907	+	25.6357i	0.243010	+	0.906926i
$800$		0			0
$801$	17.0540	+	4.56961i	0.602574	+	0.161459i
$802$	−12.5548	+	3.36405i	−0.443325	+	0.118789i
$803$	12.2540	+	12.2540i	0.432434	+	0.432434i
$804$	−3.85613			−0.135995
$805$		0			0
$806$	−11.9151	+	11.9151i	−0.419690	+	0.419690i
$807$	0.0550892	−	0.205596i	0.00193923	−	0.00723731i
$808$	−56.7040			−1.99484
$809$	0.700060	−	2.61266i	0.0246128	−	0.0918562i	−0.952527	−	0.304454i	$-0.901526\pi$
$809$	0.700060	−	2.61266i	0.0246128	−	0.0918562i	0.977140	+	0.212598i	$0.0681925\pi$
$810$		0			0
$811$	−6.24691	−	10.8200i	−0.219359	−	0.379940i	0.735253	−	0.677792i	$-0.237063\pi$
$811$	−6.24691	−	10.8200i	−0.219359	−	0.379940i	−0.954612	+	0.297852i	$0.903730\pi$
$812$	0.331828	−	0.574742i	0.0116449	−	0.0201695i
$813$	−15.9596	+	15.9596i	−0.559728	+	0.559728i
$814$	33.2640	+	20.8427i	1.16590	+	0.730537i
$815$		0			0
$816$	4.57353	+	17.0686i	0.160106	+	0.597522i
$817$	−4.17606	+	15.5853i	−0.146102	+	0.545260i
$818$	−11.8068	−	3.16362i	−0.412815	−	0.110614i
$819$	−18.2739	−	4.89646i	−0.638540	−	0.171096i
$820$		0			0
$821$	−12.5053	−	21.6598i	−0.436438	−	0.755932i	0.560974	−	0.827833i	$-0.310427\pi$
$821$	−12.5053	−	21.6598i	−0.436438	−	0.755932i	−0.997412	+	0.0719010i	$0.977093\pi$
$822$	16.8372			0.587264
$823$	−1.31661	+	0.352784i	−0.0458940	+	0.0122973i	−0.281693	−	0.959505i	$-0.590896\pi$
$823$	−1.31661	+	0.352784i	−0.0458940	+	0.0122973i	0.235799	+	0.971802i	$0.424229\pi$
$824$		−	54.2188i		−	1.88880i
$825$		0			0
$826$	17.1112	−	29.6375i	0.595375	−	1.03122i
$827$	−16.4986	−	28.5764i	−0.573712	−	0.993698i	−0.996180	−	0.0873203i	$-0.972170\pi$
$827$	−16.4986	−	28.5764i	−0.573712	−	0.993698i	0.422469	−	0.906378i	$-0.361164\pi$
$828$	2.56488			0.0891359
$829$	−37.2077	+	9.96978i	−1.29228	+	0.346265i	−0.838525	−	0.544863i	$-0.816582\pi$
$829$	−37.2077	+	9.96978i	−1.29228	+	0.346265i	−0.453752	+	0.891128i	$0.649915\pi$
$830$		0			0
$831$	2.18484	−	0.585426i	0.0757912	−	0.0203082i
$832$	22.5633	−	13.0269i	0.782242	−	0.451628i
$833$	−41.2312	+	23.8049i	−1.42858	+	0.824790i
$834$	13.7062	−	3.67256i	0.474607	−	0.127171i
$835$		0			0
$836$	−6.30752	+	1.69010i	−0.218150	+	0.0584532i
$837$	−23.7133			−0.819652
$838$	−22.2298	−	38.5032i	−0.767917	−	1.33007i
$839$	21.2111	−	36.7387i	0.732288	−	1.26836i	−0.223614	−	0.974678i	$-0.571786\pi$
$839$	21.2111	−	36.7387i	0.732288	−	1.26836i	0.955903	−	0.293683i	$-0.0948810\pi$
$840$		0			0
$841$		−	28.6506i		−	0.987953i
$842$	11.1274	−	2.98158i	0.383476	−	0.102752i
$843$	4.18027			0.143976
$844$	2.12030	+	3.67247i	0.0729838	+	0.126412i
$845$		0			0
$846$	−11.9120	−	3.19182i	−0.409544	−	0.109737i
$847$	53.5751	+	14.3554i	1.84086	+	0.493257i
$848$	5.84834	−	21.8263i	0.200833	−	0.749518i
$849$	−4.00368	−	14.9419i	−0.137406	−	0.512806i
$850$		0			0
$851$	39.9407	+	1.44409i	1.36915	+	0.0495028i
$852$	−0.814907	+	0.814907i	−0.0279183	+	0.0279183i
$853$	−20.9962	+	36.3664i	−0.718895	+	1.24516i	0.242543	+	0.970141i	$0.422019\pi$
$853$	−20.9962	+	36.3664i	−0.718895	+	1.24516i	−0.961438	+	0.275022i	$0.911315\pi$
$854$	−4.90736	−	8.49979i	−0.167926	−	0.290857i
$855$		0			0
$856$	−5.05599	+	18.8692i	−0.172810	+	0.644936i
$857$	26.5861			0.908164			0.454082	−	0.890960i	$-0.349967\pi$
$857$	26.5861			0.908164			0.454082	+	0.890960i	$0.349967\pi$
$858$	−6.11337	+	22.8154i	−0.208707	+	0.778905i
$859$	8.37407	−	8.37407i	0.285720	−	0.285720i	−0.549665	−	0.835385i	$-0.685245\pi$
$859$	8.37407	−	8.37407i	0.285720	−	0.285720i	0.835385	+	0.549665i	$0.185245\pi$
$860$		0			0
$861$	5.45165			0.185792
$862$	3.84874	+	3.84874i	0.131089	+	0.131089i
$863$	29.3868	−	7.87417i	1.00034	−	0.268040i	0.278751	−	0.960363i	$-0.410080\pi$
$863$	29.3868	−	7.87417i	1.00034	−	0.268040i	0.721587	+	0.692324i	$0.243413\pi$
$864$	7.86451	+	2.10729i	0.267556	+	0.0716914i
$865$		0			0
$866$	1.16831	+	4.36021i	0.0397009	+	0.148166i
$867$	−0.250979	−	0.936666i	−0.00852369	−	0.0318109i
$868$	4.17774	+	2.41202i	0.141802	+	0.0818693i
$869$	−5.21341	+	19.4567i	−0.176853	+	0.660024i
$870$		0			0
$871$	9.19455	+	34.3145i	0.311545	+	1.16270i
$872$	−19.9476	+	5.34494i	−0.675510	+	0.181002i
$873$	−13.2069	−	7.62502i	−0.446986	−	0.258068i
$874$	31.1104	−	31.1104i	1.05233	−	1.05233i
$875$		0			0
$876$	0.990049	+	0.571605i	0.0334506	+	0.0193127i
$877$	−29.7086	+	29.7086i	−1.00319	+	1.00319i	−0.00319179	+	0.999995i	$0.501016\pi$
$877$	−29.7086	+	29.7086i	−1.00319	+	1.00319i	−0.999995	+	0.00319179i	$0.998984\pi$
$878$	−7.89932	+	7.89932i	−0.266589	+	0.266589i
$879$	6.48398	−	11.2306i	0.218699	−	0.378798i
$880$		0			0
$881$	32.3408	−	18.6720i	1.08959	−	0.629074i	0.156122	−	0.987738i	$-0.450101\pi$
$881$	32.3408	−	18.6720i	1.08959	−	0.629074i	0.933467	+	0.358664i	$0.116767\pi$
$882$		−	22.1226i		−	0.744906i
$883$	−22.4292	−	38.8484i	−0.754801	−	1.30735i	−0.945473	−	0.325700i	$-0.894400\pi$
$883$	−22.4292	−	38.8484i	−0.754801	−	1.30735i	0.190672	−	0.981654i	$-0.438933\pi$
$884$	−2.85340	+	1.64741i	−0.0959703	+	0.0554085i
$885$		0			0
$886$	39.4530	−	10.5714i	1.32545	−	0.355153i
$887$	24.0980	+	24.0980i	0.809132	+	0.809132i	0.984503	−	0.175370i	$-0.0561122\pi$
$887$	24.0980	+	24.0980i	0.809132	+	0.809132i	−0.175370	+	0.984503i	$0.556112\pi$
$888$	21.3322	+	6.55070i	0.715863	+	0.219827i
$889$			69.6379i			2.33558i
$890$		0			0
$891$	−9.87506	+	5.70137i	−0.330827	+	0.191003i
$892$	0.227919	−	0.850605i	0.00763129	−	0.0284804i
$893$	27.6841	−	15.9834i	0.926414	−	0.534865i
$894$	19.1571	−	19.1571i	0.640710	−	0.640710i
$895$		0			0
$896$	25.9805	+	25.9805i	0.867947	+	0.867947i
$897$	6.22431	+	23.2295i	0.207824	+	0.775609i
$898$	23.8577	+	23.8577i	0.796143	+	0.796143i
$899$	−2.53949			−0.0846966
$900$		0			0
$901$	−7.24203	+	27.0276i	−0.241267	+	0.900421i
$902$			6.68775i			0.222678i
$903$	8.35429	−	14.4701i	0.278013	−	0.481533i
$904$	4.01411	+	2.31755i	0.133507	+	0.0770804i
$905$		0			0
$906$	−6.96350	−	1.86586i	−0.231347	−	0.0619892i
$907$	−3.65102	−	6.32376i	−0.121230	−	0.209977i	0.799023	−	0.601301i	$-0.205351\pi$
$907$	−3.65102	−	6.32376i	−0.121230	−	0.209977i	−0.920253	+	0.391324i	$0.872017\pi$
$908$	0.564627	−	0.977963i	0.0187378	−	0.0324548i
$909$	−14.1345	+	24.4817i	−0.468812	+	0.812007i
$910$		0			0
$911$	38.5071	+	38.5071i	1.27580	+	1.27580i	0.942998	+	0.332797i	$0.107992\pi$
$911$	38.5071	+	38.5071i	1.27580	+	1.27580i	0.332797	+	0.942998i	$0.392008\pi$
$912$	18.4325	−	10.6420i	0.610362	−	0.352392i
$913$	3.37172	+	12.5834i	0.111588	+	0.416451i
$914$		−	35.1449i		−	1.16249i
$915$		0			0
$916$	1.67477	+	0.966931i	0.0553361	+	0.0319483i
$917$		−	60.9079i		−	2.01136i
$918$	29.6382	+	7.94153i	0.978206	+	0.262110i
$919$	−9.38503	−	9.38503i	−0.309583	−	0.309583i	0.535164	−	0.844748i	$-0.320250\pi$
$919$	−9.38503	−	9.38503i	−0.309583	−	0.309583i	−0.844748	+	0.535164i	$0.820250\pi$
$920$		0			0
$921$	−6.92756	−	11.9989i	−0.228271	−	0.395377i
$922$	37.7169	+	10.1062i	1.24214	+	0.332830i
$923$	9.19467	+	5.30854i	0.302646	+	0.174733i
$924$	6.76214			0.222458
$925$		0			0
$926$	−24.8172			−0.815544
$927$	−23.4087	−	13.5150i	−0.768844	−	0.443892i
$928$	0.842219	+	0.225672i	0.0276472	+	0.00740805i
$929$	3.03772	+	5.26148i	0.0996643	+	0.172624i	0.911546	−	0.411199i	$-0.134890\pi$
$929$	3.03772	+	5.26148i	0.0996643	+	0.172624i	−0.811881	+	0.583822i	$0.801556\pi$
$930$		0			0
$931$	40.5489	+	40.5489i	1.32894	+	1.32894i
$932$	0.828939	+	0.222113i	0.0271528	+	0.00727557i
$933$			0.850939i			0.0278585i
$934$	−25.2967	−	14.6051i	−0.827734	−	0.477892i
$935$		0			0
$936$		−	13.1933i		−	0.431237i
$937$	8.90460	+	33.2324i	0.290901	+	1.08566i	0.944419	+	0.328745i	$0.106626\pi$
$937$	8.90460	+	33.2324i	0.290901	+	1.08566i	−0.653518	+	0.756911i	$0.726708\pi$
$938$	−58.2853	+	33.6511i	−1.90308	+	1.09875i
$939$	20.2234	+	20.2234i	0.659966	+	0.659966i
$940$		0			0
$941$	−27.4941	+	47.6211i	−0.896281	+	1.55240i	−0.0640700	+	0.997945i	$0.520408\pi$
$941$	−27.4941	+	47.6211i	−0.896281	+	1.55240i	−0.832211	+	0.554459i	$0.812925\pi$
$942$	7.84666	−	13.5908i	0.255658	−	0.442813i
$943$	3.40456	+	5.89688i	0.110868	+	0.192029i
$944$	19.9734	+	5.35185i	0.650078	+	0.174188i
$945$		0			0
$946$	17.7510	+	10.2485i	0.577135	+	0.333209i
$947$	−19.3878	+	33.5806i	−0.630018	+	1.09122i	0.357530	+	0.933902i	$0.383619\pi$
$947$	−19.3878	+	33.5806i	−0.630018	+	1.09122i	−0.987548	+	0.157321i	$0.949714\pi$
$948$			1.32880i			0.0431574i
$949$	2.72587	−	10.1731i	0.0884853	−	0.330232i
$950$		0			0
$951$	39.9844			1.29658
$952$	−38.0359	−	38.0359i	−1.23275	−	1.23275i
$953$	10.5419	+	39.3428i	0.341485	+	1.27444i	0.896666	+	0.442708i	$0.145982\pi$
$953$	10.5419	+	39.3428i	0.341485	+	1.27444i	−0.555181	+	0.831729i	$0.687351\pi$
$954$	−9.19368	−	9.19368i	−0.297656	−	0.297656i
$955$		0			0
$956$	−3.25085	+	3.25085i	−0.105140	+	0.105140i
$957$	−3.08283	+	1.77987i	−0.0996538	+	0.0575352i
$958$	−2.12444	+	7.92852i	−0.0686375	+	0.256159i
$959$	−38.4576	+	22.2035i	−1.24186	+	0.716988i
$960$		0			0
$961$			12.5407i			0.404540i
$962$	0.861985	−	23.8408i	0.0277915	−	0.768658i
$963$	6.88639	+	6.88639i	0.221911	+	0.221911i
$964$	5.38813	−	1.44374i	0.173540	−	0.0464999i
$965$		0			0
$966$	−39.4567	+	22.7803i	−1.26950	+	0.732945i
$967$	23.0800	+	39.9757i	0.742202	+	1.28553i	0.951491	+	0.307678i	$0.0995519\pi$
$967$	23.0800	+	39.9757i	0.742202	+	1.28553i	−0.209288	+	0.977854i	$0.567115\pi$
$968$			38.6800i			1.24322i
$969$	−22.8251	+	13.1781i	−0.733247	+	0.423341i
$970$		0			0
$971$	−2.87600	+	4.98139i	−0.0922954	+	0.159860i	−0.908477	−	0.417936i	$-0.862754\pi$
$971$	−2.87600	+	4.98139i	−0.0922954	+	0.159860i	0.816181	+	0.577796i	$0.196087\pi$
$972$	2.54213	−	2.54213i	0.0815390	−	0.0815390i
$973$	−26.4631	+	26.4631i	−0.848368	+	0.848368i
$974$	−14.9977	−	8.65893i	−0.480557	−	0.277450i
$975$		0			0
$976$	4.19334	−	4.19334i	0.134225	−	0.134225i
$977$	−41.8050	−	24.1361i	−1.33746	−	0.772184i	−0.351031	−	0.936364i	$-0.614169\pi$
$977$	−41.8050	−	24.1361i	−1.33746	−	0.772184i	−0.986430	+	0.164180i	$0.947502\pi$
$978$	−25.6332	+	6.86838i	−0.819658	+	0.219627i
$979$	15.0473	+	56.1574i	0.480915	+	1.79480i
$980$		0			0
$981$	−2.66465	+	9.94460i	−0.0850757	+	0.317507i
$982$	−2.17558	−	1.25607i	−0.0694257	−	0.0400829i
$983$	7.98131	+	29.7867i	0.254564	+	0.950047i	0.968332	+	0.249665i	$0.0803204\pi$
$983$	7.98131	+	29.7867i	0.254564	+	0.950047i	−0.713768	+	0.700382i	$0.753013\pi$
$984$	0.983993	+	3.67231i	0.0313685	+	0.117069i
$985$		0			0
$986$	3.17399	+	0.850468i	0.101080	+	0.0270844i
$987$	−31.9752	+	8.56773i	−1.01778	+	0.272714i
$988$	2.80618	+	2.80618i	0.0892766	+	0.0892766i
$989$	20.8691			0.663598
$990$		0			0
$991$	−18.7066	+	18.7066i	−0.594235	+	0.594235i	−0.938773	−	0.344537i	$-0.888036\pi$
$991$	−18.7066	+	18.7066i	−0.594235	+	0.594235i	0.344537	+	0.938773i	$0.388036\pi$
$992$	−1.64039	+	6.12200i	−0.0520823	+	0.194374i
$993$	26.1794			0.830778
$994$	−5.20590	+	19.4287i	−0.165121	+	0.616241i
$995$		0			0
$996$	0.429694	+	0.744252i	0.0136154	+	0.0235825i
$997$	−16.0200	+	27.7475i	−0.507359	+	0.878771i	0.492605	+	0.870253i	$0.336045\pi$
$997$	−16.0200	+	27.7475i	−0.507359	+	0.878771i	−0.999964	+	0.00851805i	$0.997289\pi$
$998$	−18.4125	+	18.4125i	−0.582836	+	0.582836i
$999$	24.5817	−	22.8662i	0.777731	−	0.723455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.y.b.393.13		68
5.2	odd	4		925.2.t.b.282.5		68
5.3	odd	4		185.2.p.a.97.13	✓	68
5.4	even	2		185.2.u.a.23.5	yes	68
37.29	odd	12		925.2.t.b.843.5		68
185.29	odd	12		185.2.p.a.103.13	yes	68
185.103	even	12		185.2.u.a.177.5	yes	68
185.177	even	12	inner	925.2.y.b.732.13		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.13	✓	68	5.3	odd	4
185.2.p.a.103.13	yes	68	185.29	odd	12
185.2.u.a.23.5	yes	68	5.4	even	2
185.2.u.a.177.5	yes	68	185.103	even	12
925.2.t.b.282.5		68	5.2	odd	4
925.2.t.b.843.5		68	37.29	odd	12
925.2.y.b.393.13		68	1.1	even	1	trivial
925.2.y.b.732.13		68	185.177	even	12	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14153 + 0.659061i) q^{2} +(1.18821 + 0.318379i) q^{3} +(-0.131277 - 0.227378i) q^{4} +(1.14654 + 1.14654i) q^{6} +(-4.13076 - 1.10683i) q^{7} -2.98232i q^{8} +(-1.28760 - 0.743399i) q^{9} -4.89589i q^{11} +(-0.0835914 - 0.311968i) q^{12} +(-2.57679 + 1.48771i) q^{13} +(-3.98591 - 3.98591i) q^{14} +(1.70298 - 2.94965i) q^{16} +(-2.10881 + 3.65256i) q^{17} +(-0.979891 - 1.69722i) q^{18} +(4.90693 + 1.31481i) q^{19} +(-4.55581 - 2.63030i) q^{21} +(3.22669 - 5.58880i) q^{22} -6.57051i q^{23} +(0.949509 - 3.54362i) q^{24} -3.92197 q^{26} +(-3.90274 - 3.90274i) q^{27} +(0.290603 + 1.08454i) q^{28} +(-0.417950 - 0.417950i) q^{29} +(3.03803 - 3.03803i) q^{31} +(-1.27754 + 0.737586i) q^{32} +(1.55875 - 5.81734i) q^{33} +(-4.81453 + 2.77967i) q^{34} +0.390363i q^{36} +(-0.219784 + 6.07879i) q^{37} +(4.73486 + 4.73486i) q^{38} +(-3.53541 + 0.947311i) q^{39} +(-0.897477 + 0.518158i) q^{41} +(-3.46706 - 6.00512i) q^{42} +3.17618i q^{43} +(-1.11322 + 0.642716i) q^{44} +(4.33037 - 7.50041i) q^{46} +(4.44958 - 4.44958i) q^{47} +(2.96260 - 2.96260i) q^{48} +(9.77595 + 5.64415i) q^{49} +(-3.66860 + 3.66860i) q^{51} +(0.676543 + 0.390602i) q^{52} +(6.40827 - 1.71709i) q^{53} +(-1.88294 - 7.02724i) q^{54} +(-3.30094 + 12.3193i) q^{56} +(5.41184 + 3.12453i) q^{57} +(-0.201647 - 0.752555i) q^{58} +(1.57132 + 5.86425i) q^{59} +(1.68182 + 0.450642i) q^{61} +(5.47024 - 1.46575i) q^{62} +(4.49597 + 4.49597i) q^{63} -8.75638 q^{64} +(5.61334 - 5.61334i) q^{66} +(3.09017 - 11.5327i) q^{67} +1.10735 q^{68} +(2.09191 - 7.80712i) q^{69} +(-1.78413 - 3.09021i) q^{71} +(-2.21705 + 3.84005i) q^{72} +(-2.50291 + 2.50291i) q^{73} +(-4.25718 + 6.79426i) q^{74} +(-0.345207 - 1.28833i) q^{76} +(-5.41895 + 20.2238i) q^{77} +(-4.66011 - 1.24867i) q^{78} +(-3.97409 - 1.06485i) q^{79} +(-1.16452 - 2.01701i) q^{81} -1.36599 q^{82} +(-2.57020 + 0.688684i) q^{83} +1.38119i q^{84} +(-2.09329 + 3.62569i) q^{86} +(-0.363544 - 0.629677i) q^{87} -14.6011 q^{88} +(-11.4703 + 3.07346i) q^{89} +(12.2907 - 3.29330i) q^{91} +(-1.49399 + 0.862553i) q^{92} +(4.57706 - 2.64257i) q^{93} +(8.01187 - 2.14677i) q^{94} +(-1.75281 + 0.469664i) q^{96} +10.2570 q^{97} +(7.43968 + 12.8859i) q^{98} +(-3.63960 + 6.30397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 4 q^{3} + 30 q^{4} - 8 q^{6} + 2 q^{7} + 10 q^{12} + 6 q^{13} - 26 q^{16} + 10 q^{17} + 8 q^{18} - 4 q^{19} - 12 q^{21} + 14 q^{22} - 24 q^{26} - 68 q^{27} - 14 q^{28} - 14 q^{29} - 24 q^{31}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q + 6 * q^2 + 4 * q^3 + 30 * q^4 - 8 * q^6 + 2 * q^7 + 10 * q^12 + 6 * q^13 - 26 * q^16 + 10 * q^17 + 8 * q^18 - 4 * q^19 - 12 * q^21 + 14 * q^22 - 24 * q^26 - 68 * q^27 - 14 * q^28 - 14 * q^29 - 24 * q^31 - 18 * q^32 - 10 * q^33 + 18 * q^37 + 36 * q^38 - 52 * q^39 - 18 * q^41 + 40 * q^42 + 36 * q^44 - 52 * q^46 + 24 * q^47 - 60 * q^48 + 36 * q^49 - 8 * q^51 + 78 * q^52 + 38 * q^53 - 40 * q^54 + 16 * q^56 - 90 * q^57 - 16 * q^58 + 8 * q^59 + 4 * q^61 + 22 * q^62 + 48 * q^63 + 20 * q^64 + 80 * q^66 + 56 * q^67 + 20 * q^68 - 8 * q^69 + 4 * q^71 - 32 * q^72 - 60 * q^73 + 44 * q^74 + 72 * q^76 - 6 * q^77 + 24 * q^78 - 56 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^83 - 4 * q^86 + 32 * q^87 + 36 * q^88 + 22 * q^89 + 44 * q^91 - 156 * q^92 + 30 * q^93 + 20 * q^94 - 8 * q^96 - 16 * q^97 - 48 * q^98 - 32 * q^99

Introduction

L-functions

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Database

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