LMFDB - Embedded newform 475.2.u.c.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.1
Character	$\chi$	$=$	475.149
Dual form			475.2.u.c.424.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16796 + 1.39192i) q^{2} +(0.0605732 + 0.166424i) q^{3} +(-0.226016 - 1.28180i) q^{4} +(-0.302396 - 0.110063i) q^{6} +(0.929646 - 0.536732i) q^{7} +(-1.09903 - 0.634528i) q^{8} +(2.27411 - 1.90820i) q^{9} +O(q^{10})$	\(q+(-1.16796 + 1.39192i) q^{2} +(0.0605732 + 0.166424i) q^{3} +(-0.226016 - 1.28180i) q^{4} +(-0.302396 - 0.110063i) q^{6} +(0.929646 - 0.536732i) q^{7} +(-1.09903 - 0.634528i) q^{8} +(2.27411 - 1.90820i) q^{9} +(1.65508 - 2.86668i) q^{11} +(0.199631 - 0.115257i) q^{12} +(-0.908963 + 2.49736i) q^{13} +(-0.338702 + 1.92087i) q^{14} +(4.61300 - 1.67899i) q^{16} +(2.57109 - 3.06411i) q^{17} +5.39408i q^{18} +(-0.281925 - 4.34977i) q^{19} +(0.145636 + 0.122203i) q^{21} +(2.05712 + 5.65190i) q^{22} +(1.72714 - 0.304541i) q^{23} +(0.0390283 - 0.221341i) q^{24} +(-2.41449 - 4.18202i) q^{26} +(0.915450 + 0.528535i) q^{27} +(-0.898098 - 1.07031i) q^{28} +(-1.72552 + 1.44789i) q^{29} +(4.02636 + 6.97386i) q^{31} +(-2.18269 + 5.99689i) q^{32} +(0.577336 + 0.101800i) q^{33} +(1.26206 + 7.15751i) q^{34} +(-2.95992 - 2.48367i) q^{36} -5.64805i q^{37} +(6.38382 + 4.68794i) q^{38} -0.470678 q^{39} +(0.842126 - 0.306509i) q^{41} +(-0.340195 + 0.0599856i) q^{42} +(8.38279 + 1.47811i) q^{43} +(-4.04858 - 1.47356i) q^{44} +(-1.59333 + 2.75973i) q^{46} +(-4.04709 - 4.82313i) q^{47} +(0.558849 + 0.666010i) q^{48} +(-2.92384 + 5.06424i) q^{49} +(0.665679 + 0.242287i) q^{51} +(3.40655 + 0.600667i) q^{52} +(-3.34778 + 0.590304i) q^{53} +(-1.80489 + 0.656926i) q^{54} -1.36228 q^{56} +(0.706828 - 0.310399i) q^{57} -4.09287i q^{58} +(1.13893 + 0.955673i) q^{59} +(2.38416 + 13.5212i) q^{61} +(-14.4097 - 2.54082i) q^{62} +(1.08992 - 2.99454i) q^{63} +(-0.888845 - 1.53952i) q^{64} +(-0.816002 + 0.684707i) q^{66} +(8.26605 + 9.85110i) q^{67} +(-4.50868 - 2.60309i) q^{68} +(0.155301 + 0.268989i) q^{69} +(1.91469 - 10.8587i) q^{71} +(-3.71013 + 0.654195i) q^{72} +(-0.892893 - 2.45320i) q^{73} +(7.86164 + 6.59670i) q^{74} +(-5.51182 + 1.34449i) q^{76} -3.55333i q^{77} +(0.549733 - 0.655146i) q^{78} +(-6.17425 + 2.24724i) q^{79} +(1.51398 - 8.58623i) q^{81} +(-0.556934 + 1.53016i) q^{82} +(-2.33730 + 1.34944i) q^{83} +(0.123724 - 0.214297i) q^{84} +(-11.8482 + 9.94180i) q^{86} +(-0.345483 - 0.199465i) q^{87} +(-3.63797 + 2.10038i) q^{88} +(0.742205 + 0.270140i) q^{89} +(0.495396 + 2.80953i) q^{91} +(-0.780722 - 2.14502i) q^{92} +(-0.916725 + 1.09251i) q^{93} +11.4403 q^{94} -1.13024 q^{96} +(12.0317 - 14.3388i) q^{97} +(-3.63409 - 9.98458i) q^{98} +(-1.70638 - 9.67734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) $ 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9	$ 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9 - 48 * q^14 + 42 * q^16 + 24 * q^19 + 6 * q^21 - 42 * q^24 - 42 * q^26 + 18 * q^29 + 60 * q^31 - 48 * q^34 - 42 * q^36 - 24 * q^39 - 12 * q^41 + 60 * q^44 + 42 * q^46 + 6 * q^49 + 54 * q^51 - 60 * q^54 - 144 * q^56 - 36 * q^59 + 12 * q^61 + 48 * q^64 - 66 * q^66 - 54 * q^69 + 48 * q^71 + 78 * q^74 + 54 * q^76 - 18 * q^79 + 30 * q^81 + 24 * q^84 - 66 * q^86 + 12 * q^89 - 12 * q^91 + 132 * q^94 - 36 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−1.16796	+	1.39192i	−0.825873	+	0.984237i	−1.00000		0.000486534i	$-0.999845\pi$
$2$	−1.16796	+	1.39192i	−0.825873	+	0.984237i	0.174127	+	0.984723i	$0.444290\pi$
$3$	0.0605732	+	0.166424i	0.0349720	+	0.0960847i	0.955950	−	0.293531i	$-0.0948302\pi$
$3$	0.0605732	+	0.166424i	0.0349720	+	0.0960847i	−0.920978	+	0.389615i	$0.872608\pi$
$4$	−0.226016	−	1.28180i	−0.113008	−	0.640900i
$5$		0			0
$5$		0			0
$6$	−0.302396	−	0.110063i	−0.123452	−	0.0449330i
$7$	0.929646	−	0.536732i	0.351373	−	0.202865i	−0.313917	−	0.949451i	$-0.601641\pi$
$7$	0.929646	−	0.536732i	0.351373	−	0.202865i	0.665290	+	0.746585i	$0.268308\pi$
$8$	−1.09903	−	0.634528i	−0.388567	−	0.224339i
$9$	2.27411	−	1.90820i	0.758035	−	0.636067i
$10$		0			0
$11$	1.65508	−	2.86668i	0.499024	−	0.864335i	−0.500975	−	0.865462i	$-0.667025\pi$
$11$	1.65508	−	2.86668i	0.499024	−	0.864335i	0.999999	+	0.00112649i	$0.000358574\pi$
$12$	0.199631	−	0.115257i	0.0576286	−	0.0332719i
$13$	−0.908963	+	2.49736i	−0.252101	+	0.692642i	0.747496	+	0.664266i	$0.231256\pi$
$13$	−0.908963	+	2.49736i	−0.252101	+	0.692642i	−0.999597	+	0.0283760i	$0.990966\pi$
$14$	−0.338702	+	1.92087i	−0.0905219	+	0.513375i
$15$		0			0
$16$	4.61300	−	1.67899i	1.15325	−	0.419749i
$17$	2.57109	−	3.06411i	0.623581	−	0.743155i	−0.358101	−	0.933683i	$-0.616576\pi$
$17$	2.57109	−	3.06411i	0.623581	−	0.743155i	0.981682	+	0.190528i	$0.0610200\pi$
$18$			5.39408i			1.27140i
$19$	−0.281925	−	4.34977i	−0.0646780	−	0.997906i
$19$	−0.281925	−	4.34977i	−0.0646780	−	0.997906i
$20$		0			0
$21$	0.145636	+	0.122203i	0.0317805	+	0.0266670i
$22$	2.05712	+	5.65190i	0.438580	+	1.20499i
$23$	1.72714	−	0.304541i	0.360133	−	0.0635012i	0.00934578	−	0.999956i	$-0.497025\pi$
$23$	1.72714	−	0.304541i	0.360133	−	0.0635012i	0.350787	+	0.936455i	$0.385914\pi$
$24$	0.0390283	−	0.221341i	0.00796662	−	0.0451810i
$25$		0			0
$26$	−2.41449	−	4.18202i	−0.473520	−	0.820161i
$27$	0.915450	+	0.528535i	0.176178	+	0.101717i
$28$	−0.898098	−	1.07031i	−0.169725	−	0.202270i
$29$	−1.72552	+	1.44789i	−0.320422	+	0.268866i	−0.788784	−	0.614671i	$-0.789289\pi$
$29$	−1.72552	+	1.44789i	−0.320422	+	0.268866i	0.468362	+	0.883537i	$0.344844\pi$
$30$		0			0
$31$	4.02636	+	6.97386i	0.723156	+	1.25254i	0.959729	+	0.280929i	$0.0906425\pi$
$31$	4.02636	+	6.97386i	0.723156	+	1.25254i	−0.236573	+	0.971614i	$0.576024\pi$
$32$	−2.18269	+	5.99689i	−0.385848	+	1.06011i
$33$	0.577336	+	0.101800i	0.100501	+	0.0177211i
$34$	1.26206	+	7.15751i	0.216442	+	1.22750i
$35$		0			0
$36$	−2.95992	−	2.48367i	−0.493320	−	0.413944i
$37$		−	5.64805i		−	0.928534i	−0.885695	−	0.464267i	$-0.846318\pi$
$37$		−	5.64805i		−	0.928534i	0.885695	−	0.464267i	$-0.153682\pi$
$38$	6.38382	+	4.68794i	1.03559	+	0.760485i
$39$	−0.470678			−0.0753688
$40$		0			0
$41$	0.842126	−	0.306509i	0.131518	−	0.0478686i	−0.275423	−	0.961323i	$-0.588818\pi$
$41$	0.842126	−	0.306509i	0.131518	−	0.0478686i	0.406941	+	0.913455i	$0.366596\pi$
$42$	−0.340195	+	0.0599856i	−0.0524933	+	0.00925598i
$43$	8.38279	+	1.47811i	1.27836	+	0.225410i	0.771285	−	0.636490i	$-0.219614\pi$
$43$	8.38279	+	1.47811i	1.27836	+	0.225410i	0.507079	+	0.861900i	$0.330725\pi$
$44$	−4.04858	−	1.47356i	−0.610346	−	0.222148i
$45$		0			0
$46$	−1.59333	+	2.75973i	−0.234924	+	0.406900i
$47$	−4.04709	−	4.82313i	−0.590329	−	0.703527i	0.385340	−	0.922775i	$-0.374084\pi$
$47$	−4.04709	−	4.82313i	−0.590329	−	0.703527i	−0.975669	+	0.219248i	$0.929640\pi$
$48$	0.558849	+	0.666010i	0.0806629	+	0.0961303i
$49$	−2.92384	+	5.06424i	−0.417691	+	0.723462i
$50$		0			0
$51$	0.665679	+	0.242287i	0.0932137	+	0.0339270i
$52$	3.40655	+	0.600667i	0.472404	+	0.0832976i
$53$	−3.34778	+	0.590304i	−0.459853	+	0.0810846i	−0.398776	−	0.917048i	$-0.630565\pi$
$53$	−3.34778	+	0.590304i	−0.459853	+	0.0810846i	−0.0610776	+	0.998133i	$0.519454\pi$
$54$	−1.80489	+	0.656926i	−0.245614	+	0.0893963i
$55$		0			0
$56$	−1.36228			−0.182043
$57$	0.706828	−	0.310399i	0.0936216	−	0.0411133i
$58$		−	4.09287i		−	0.537420i
$59$	1.13893	+	0.955673i	0.148276	+	0.124418i	0.713908	−	0.700239i	$-0.246923\pi$
$59$	1.13893	+	0.955673i	0.148276	+	0.124418i	−0.565632	+	0.824657i	$0.691368\pi$
$60$		0			0
$61$	2.38416	+	13.5212i	0.305260	+	1.73122i	0.622277	+	0.782797i	$0.286208\pi$
$61$	2.38416	+	13.5212i	0.305260	+	1.73122i	−0.317016	+	0.948420i	$0.602681\pi$
$62$	−14.4097	−	2.54082i	−1.83003	−	0.322684i
$63$	1.08992	−	2.99454i	0.137317	−	0.377276i
$64$	−0.888845	−	1.53952i	−0.111106	−	0.192441i
$65$		0			0
$66$	−0.816002	+	0.684707i	−0.100443	+	0.0842816i
$67$	8.26605	+	9.85110i	1.00986	+	1.20350i	0.978975	+	0.203980i	$0.0653878\pi$
$67$	8.26605	+	9.85110i	1.00986	+	1.20350i	0.0308840	+	0.999523i	$0.490168\pi$
$68$	−4.50868	−	2.60309i	−0.546758	−	0.315671i
$69$	0.155301	+	0.268989i	0.0186961	+	0.0323825i
$70$		0			0
$71$	1.91469	−	10.8587i	0.227231	−	1.28869i	−0.631141	−	0.775668i	$-0.717413\pi$
$71$	1.91469	−	10.8587i	0.227231	−	1.28869i	0.858373	−	0.513026i	$-0.171476\pi$
$72$	−3.71013	+	0.654195i	−0.437243	+	0.0770977i
$73$	−0.892893	−	2.45320i	−0.104505	−	0.287126i	0.876409	−	0.481568i	$-0.159933\pi$
$73$	−0.892893	−	2.45320i	−0.104505	−	0.287126i	−0.980914	+	0.194442i	$0.937710\pi$
$74$	7.86164	+	6.59670i	0.913897	+	0.766851i
$75$		0			0
$76$	−5.51182	+	1.34449i	−0.632249	+	0.154224i
$77$		−	3.55333i		−	0.404939i
$78$	0.549733	−	0.655146i	0.0622450	−	0.0741807i
$79$	−6.17425	+	2.24724i	−0.694657	+	0.252835i	−0.665128	−	0.746729i	$-0.731623\pi$
$79$	−6.17425	+	2.24724i	−0.694657	+	0.252835i	−0.0295293	+	0.999564i	$0.509401\pi$
$80$		0			0
$81$	1.51398	−	8.58623i	0.168221	−	0.954026i
$82$	−0.556934	+	1.53016i	−0.0615030	+	0.168978i
$83$	−2.33730	+	1.34944i	−0.256552	+	0.148120i	−0.622761	−	0.782412i	$-0.713989\pi$
$83$	−2.33730	+	1.34944i	−0.256552	+	0.148120i	0.366209	+	0.930533i	$0.380656\pi$
$84$	0.123724	−	0.214297i	0.0134994	−	0.0233817i
$85$		0			0
$86$	−11.8482	+	9.94180i	−1.27762	+	1.07205i
$87$	−0.345483	−	0.199465i	−0.0370397	−	0.0213849i
$88$	−3.63797	+	2.10038i	−0.387809	+	0.223902i
$89$	0.742205	+	0.270140i	0.0786736	+	0.0286348i	0.381057	−	0.924551i	$-0.375560\pi$
$89$	0.742205	+	0.270140i	0.0786736	+	0.0286348i	−0.302384	+	0.953186i	$0.597782\pi$
$90$		0			0
$91$	0.495396	+	2.80953i	0.0519316	+	0.294519i
$92$	−0.780722	−	2.14502i	−0.0813959	−	0.223633i
$93$	−0.916725	+	1.09251i	−0.0950600	+	0.113288i
$94$	11.4403			1.17997
$95$		0			0
$96$	−1.13024			−0.115354
$97$	12.0317	−	14.3388i	1.22163	−	1.45588i	0.372222	−	0.928144i	$-0.378596\pi$
$97$	12.0317	−	14.3388i	1.22163	−	1.45588i	0.849408	−	0.527737i	$-0.176959\pi$
$98$	−3.63409	−	9.98458i	−0.367098	−	1.00859i
$99$	−1.70638	−	9.67734i	−0.171497	−	0.972609i
$100$		0			0
$101$	−17.7763	−	6.47005i	−1.76881	−	0.643794i	−0.999991	−	0.00432656i	$-0.998623\pi$
$101$	−17.7763	−	6.47005i	−1.76881	−	0.643794i	−0.768818	−	0.639467i	$-0.779155\pi$
$102$	−1.11473	+	0.643590i	−0.110375	+	0.0637249i
$103$	−10.0838	−	5.82191i	−0.993591	−	0.573650i	−0.0872452	−	0.996187i	$-0.527806\pi$
$103$	−10.0838	−	5.82191i	−0.993591	−	0.573650i	−0.906346	+	0.422537i	$0.861140\pi$
$104$	2.58362	−	2.16792i	0.253345	−	0.212582i
$105$		0			0
$106$	3.08842	−	5.34930i	0.299974	−	0.519570i
$107$	9.86907	−	5.69791i	0.954079	−	0.550838i	0.0597335	−	0.998214i	$-0.480975\pi$
$107$	9.86907	−	5.69791i	0.954079	−	0.550838i	0.894346	+	0.447376i	$0.147642\pi$
$108$	0.470571	−	1.29288i	0.0452807	−	0.124408i
$109$	2.21184	−	12.5440i	0.211856	−	1.20149i	−0.674424	−	0.738344i	$-0.735608\pi$
$109$	2.21184	−	12.5440i	0.211856	−	1.20149i	0.886280	−	0.463150i	$-0.153281\pi$
$110$		0			0
$111$	0.939969	−	0.342121i	0.0892179	−	0.0324727i
$112$	3.38729	−	4.03681i	0.320069	−	0.381443i
$113$		−	16.5894i		−	1.56060i	−0.625406	−	0.780300i	$-0.715067\pi$
$113$		−	16.5894i		−	1.56060i	0.625406	−	0.780300i	$-0.284933\pi$
$114$	−0.393496	+	1.34638i	−0.0368543	+	0.126100i
$115$		0			0
$116$	2.24590	+	1.88453i	0.208526	+	0.174974i
$117$	2.69838	+	7.41374i	0.249465	+	0.685400i
$118$	−2.66044	+	0.469108i	−0.244914	+	0.0431849i
$119$	0.745602	−	4.22852i	0.0683492	−	0.387628i
$120$		0			0
$121$	0.0214486	+	0.0371501i	0.00194987	+	0.00337728i
$122$	−21.6051	−	12.4737i	−1.95603	−	1.12932i
$123$	0.102021	+	0.121583i	0.00919889	+	0.0109628i
$124$	8.02908	−	6.73720i	0.721033	−	0.605018i
$125$		0			0
$126$	2.89517	+	5.01458i	0.257922	+	0.446735i
$127$	−3.32559	+	9.13699i	−0.295099	+	0.810777i	0.700202	+	0.713945i	$0.253093\pi$
$127$	−3.32559	+	9.13699i	−0.295099	+	0.810777i	−0.995301	+	0.0968322i	$0.969129\pi$
$128$	−9.38857	−	1.65546i	−0.829840	−	0.146323i
$129$	0.261780	+	1.48463i	0.0230484	+	0.130714i
$130$		0			0
$131$	11.3300	+	9.50703i	0.989910	+	0.830633i	0.985555	−	0.169358i	$-0.0541693\pi$
$131$	11.3300	+	9.50703i	0.989910	+	0.830633i	0.00435510	+	0.999991i	$0.498614\pi$
$132$		−	0.763038i		−	0.0664139i
$133$	−2.59675	−	3.89243i	−0.225167	−	0.337517i
$134$	−23.3664			−2.01855
$135$		0			0
$136$	−4.76998	+	1.73613i	−0.409022	+	0.148872i
$137$	−3.54166	+	0.624490i	−0.302584	+	0.0533538i	−0.322879	−	0.946440i	$-0.604651\pi$
$137$	−3.54166	+	0.624490i	−0.302584	+	0.0533538i	0.0202946	+	0.999794i	$0.493540\pi$
$138$	−0.555798	−	0.0980021i	−0.0473126	−	0.00834249i
$139$	−5.50159	−	2.00242i	−0.466639	−	0.169843i	0.0979902	−	0.995187i	$-0.468759\pi$
$139$	−5.50159	−	2.00242i	−0.466639	−	0.169843i	−0.564629	+	0.825345i	$0.690981\pi$
$140$		0			0
$141$	0.557538	−	0.965684i	0.0469532	−	0.0813253i
$142$	12.8782	+	15.3477i	1.08072	+	1.28795i
$143$	5.65471	+	6.73902i	0.472870	+	0.563545i
$144$	7.28659	−	12.6207i	0.607216	−	1.05173i
$145$		0			0
$146$	4.45753	+	1.62241i	0.368908	+	0.134271i
$147$	−1.01991	−	0.179838i	−0.0841212	−	0.0148328i
$148$	−7.23968	+	1.27655i	−0.595098	+	0.104932i
$149$	9.45957	−	3.44300i	0.774958	−	0.282062i	0.0758895	−	0.997116i	$-0.475820\pi$
$149$	9.45957	−	3.44300i	0.774958	−	0.282062i	0.699069	+	0.715054i	$0.253598\pi$
$150$		0			0
$151$	−2.12653			−0.173054			−0.0865272	−	0.996249i	$-0.527577\pi$
$151$	−2.12653			−0.173054			−0.0865272	+	0.996249i	$0.527577\pi$
$152$	−2.45021	+	4.95944i	−0.198738	+	0.402264i
$153$		−	11.8743i		−	0.959977i
$154$	4.94595	+	4.15014i	0.398556	+	0.334428i
$155$		0			0
$156$	0.106381	+	0.603315i	0.00851728	+	0.0483039i
$157$	−11.3744	−	2.00562i	−0.907779	−	0.160066i	−0.299784	−	0.954007i	$-0.596915\pi$
$157$	−11.3744	−	2.00562i	−0.907779	−	0.160066i	−0.607995	+	0.793941i	$0.708026\pi$
$158$	4.08329	−	11.2188i	0.324849	−	0.892516i
$159$	−0.301027	−	0.521393i	−0.0238730	−	0.0413492i
$160$		0			0
$161$	1.44217	−	1.21012i	0.113659	−	0.0953712i
$162$	10.1831	+	12.1357i	0.800059	+	0.953473i
$163$	15.9620	+	9.21567i	1.25024	+	0.721827i	0.971157	−	0.238439i	$-0.0766358\pi$
$163$	15.9620	+	9.21567i	1.25024	+	0.721827i	0.279084	+	0.960267i	$0.409969\pi$
$164$	−0.583217	−	1.01016i	−0.0455416	−	0.0788804i
$165$		0			0
$166$	0.851559	−	4.82943i	0.0660938	−	0.374836i
$167$	−1.91311	+	0.337332i	−0.148041	+	0.0261035i	−0.247177	−	0.968970i	$-0.579503\pi$
$167$	−1.91311	+	0.337332i	−0.148041	+	0.0261035i	0.0991367	+	0.995074i	$0.468392\pi$
$168$	−0.0825180	−	0.226716i	−0.00636640	−	0.0174915i
$169$	4.54800	+	3.81623i	0.349846	+	0.293556i
$170$		0			0
$171$	−8.94137	−	9.35387i	−0.683763	−	0.715309i
$172$		−	11.0791i		−	0.844777i
$173$	−7.74653	+	9.23195i	−0.588958	+	0.701892i	−0.975405	−	0.220419i	$-0.929258\pi$
$173$	−7.74653	+	9.23195i	−0.588958	+	0.701892i	0.386448	+	0.922311i	$0.373702\pi$
$174$	0.681149	−	0.247918i	0.0516378	−	0.0187946i
$175$		0			0
$176$	2.82173	−	16.0028i	0.212696	−	1.20626i
$177$	−0.0900581	+	0.247432i	−0.00676918	+	0.0185982i
$178$	−1.24288	+	0.717577i	−0.0931578	+	0.0537847i
$179$	−9.15519	+	15.8573i	−0.684291	+	1.18523i	0.289368	+	0.957218i	$0.406555\pi$
$179$	−9.15519	+	15.8573i	−0.684291	+	1.18523i	−0.973659	+	0.228009i	$0.926778\pi$
$180$		0			0
$181$	−19.6501	+	16.4884i	−1.46058	+	1.22557i	−0.536206	+	0.844087i	$0.680143\pi$
$181$	−19.6501	+	16.4884i	−1.46058	+	1.22557i	−0.924375	+	0.381486i	$0.875412\pi$
$182$	−4.48924	−	2.59187i	−0.332765	−	0.192122i
$183$	−2.10584	+	1.21581i	−0.155668	+	0.0898749i
$184$	−2.09142	−	0.761216i	−0.154182	−	0.0561176i
$185$		0			0
$186$	−0.449990	−	2.55202i	−0.0329948	−	0.187123i
$187$	−4.52845	−	12.4418i	−0.331153	−	0.909835i
$188$	−5.26759	+	6.27767i	−0.384178	+	0.457846i
$189$	1.13473			0.0825392
$190$		0			0
$191$	9.22171			0.667259			0.333630	−	0.942704i	$-0.391726\pi$
$191$	9.22171			0.667259			0.333630	+	0.942704i	$0.391726\pi$
$192$	0.202373	−	0.241179i	0.0146050	−	0.0174056i
$193$	4.10492	+	11.2782i	0.295479	+	0.811821i	0.995241	+	0.0974450i	$0.0310670\pi$
$193$	4.10492	+	11.2782i	0.295479	+	0.811821i	−0.699762	+	0.714376i	$0.746711\pi$
$194$	5.90593	+	33.4942i	0.424021	+	2.40474i
$195$		0			0
$196$	7.15218	+	2.60318i	0.510870	+	0.185941i
$197$	−23.2937	+	13.4486i	−1.65961	+	0.958174i	−0.686710	+	0.726931i	$0.740946\pi$
$197$	−23.2937	+	13.4486i	−1.65961	+	0.958174i	−0.972896	+	0.231243i	$0.925721\pi$
$198$	15.4631	+	8.92761i	1.09891	+	0.634457i
$199$	3.50384	−	2.94007i	0.248381	−	0.208416i	−0.510094	−	0.860119i	$-0.670389\pi$
$199$	3.50384	−	2.94007i	0.248381	−	0.208416i	0.758475	+	0.651702i	$0.225945\pi$
$200$		0			0
$201$	−1.13875	+	1.97238i	−0.0803215	+	0.139121i
$202$	29.7678	−	17.1865i	2.09446	−	1.20923i
$203$	−0.827000	+	2.27217i	−0.0580441	+	0.159475i
$204$	0.160110	−	0.908028i	0.0112099	−	0.0635747i
$205$		0			0
$206$	19.8812	−	7.23615i	1.38519	−	0.504167i
$207$	3.34657	−	3.98829i	0.232603	−	0.277205i
$208$			13.0465i			0.904609i
$209$	−12.9360	−	6.39102i	−0.894801	−	0.442076i
$210$		0			0
$211$	−11.9217	−	10.0035i	−0.820721	−	0.688667i	0.132419	−	0.991194i	$-0.457725\pi$
$211$	−11.9217	−	10.0035i	−0.820721	−	0.688667i	−0.953141	+	0.302527i	$0.902170\pi$
$212$	1.51331	+	4.15777i	0.103934	+	0.285557i
$213$	1.92313	−	0.339099i	0.131770	−	0.0232347i
$214$	−3.59564	+	20.3919i	−0.245793	+	1.39396i
$215$		0			0
$216$	−0.670741	−	1.16176i	−0.0456381	−	0.0790475i
$217$	7.48618	+	4.32215i	0.508195	+	0.293407i
$218$	14.8769	+	17.7296i	1.00759	+	1.20080i
$219$	0.354186	−	0.297197i	0.0239336	−	0.0200827i
$220$		0			0
$221$	5.31514	+	9.20609i	0.357535	+	0.619269i
$222$	−0.621642	+	1.70795i	−0.0417219	+	0.114630i
$223$	19.8226	+	3.49526i	1.32742	+	0.234060i	0.791998	−	0.610524i	$-0.209041\pi$
$223$	19.8226	+	3.49526i	1.32742	+	0.234060i	0.535423	+	0.844584i	$0.320152\pi$
$224$	1.18959	+	6.74650i	0.0794828	+	0.450770i
$225$		0			0
$226$	23.0911	+	19.3758i	1.53600	+	1.28886i
$227$			13.8680i			0.920453i	0.887802	+	0.460226i	$0.152232\pi$
$227$			13.8680i			0.920453i	−0.887802	+	0.460226i	$0.847768\pi$
$228$	−0.557624	−	0.835857i	−0.0369295	−	0.0553560i
$229$	−8.70352			−0.575145			−0.287572	−	0.957759i	$-0.592848\pi$
$229$	−8.70352			−0.575145			−0.287572	+	0.957759i	$0.592848\pi$
$230$		0			0
$231$	0.591357	−	0.215236i	0.0389084	−	0.0141615i
$232$	2.81513	−	0.496384i	0.184823	−	0.0325892i
$233$	−15.4818	−	2.72986i	−1.01425	−	0.178839i	−0.358268	−	0.933619i	$-0.616633\pi$
$233$	−15.4818	−	2.72986i	−1.01425	−	0.178839i	−0.655978	+	0.754780i	$0.727744\pi$
$234$	−13.4709	−	4.90302i	−0.880623	−	0.320520i
$235$		0			0
$236$	0.967567	−	1.67587i	0.0629832	−	0.109090i
$237$	−0.747988	−	0.891418i	−0.0485871	−	0.0579038i
$238$	5.01493	+	5.97656i	0.325070	+	0.387403i
$239$	−6.91731	+	11.9811i	−0.447443	+	0.774995i	−0.998219	−	0.0596587i	$-0.980999\pi$
$239$	−6.91731	+	11.9811i	−0.447443	+	0.774995i	0.550775	+	0.834653i	$0.314332\pi$
$240$		0			0
$241$	−11.4424	−	4.16469i	−0.737070	−	0.268271i	−0.0539155	−	0.998546i	$-0.517170\pi$
$241$	−11.4424	−	4.16469i	−0.737070	−	0.268271i	−0.683154	+	0.730274i	$0.739392\pi$
$242$	−0.0767611	−	0.0135351i	−0.00493439	−	0.000870066i
$243$	4.64369	−	0.818808i	0.297893	−	0.0525266i
$244$	16.7927	−	6.11203i	1.07504	−	0.391283i
$245$		0			0
$246$	−0.288390			−0.0183871
$247$	11.1192	+	3.24972i	0.707497	+	0.206775i
$248$		−	10.2194i		−	0.648929i
$249$	−0.366156	−	0.307242i	−0.0232042	−	0.0194707i
$250$		0			0
$251$	0.761116	+	4.31650i	0.0480412	+	0.272455i	0.999361	−	0.0357511i	$-0.0113824\pi$
$251$	0.761116	+	4.31650i	0.0480412	+	0.272455i	−0.951320	+	0.308206i	$0.900271\pi$
$252$	−4.08474	−	0.720250i	−0.257314	−	0.0453715i
$253$	1.98552	−	5.45518i	0.124829	−	0.342964i
$254$	−8.83381	−	15.3006i	−0.554282	−	0.960045i
$255$		0			0
$256$	15.9933	−	13.4200i	0.999582	−	0.838749i
$257$	14.8859	+	17.7403i	0.928558	+	1.10661i	0.994068	+	0.108761i	$0.0346882\pi$
$257$	14.8859	+	17.7403i	0.928558	+	1.10661i	−0.0655097	+	0.997852i	$0.520867\pi$
$258$	−2.37223	−	1.36961i	−0.147689	−	0.0852682i
$259$	−3.03149	−	5.25069i	−0.188368	−	0.326262i
$260$		0			0
$261$	−1.16116	+	6.58529i	−0.0718743	+	0.407619i
$262$	−26.4661	+	4.66668i	−1.63508	+	0.288308i
$263$	10.9475	+	30.0779i	0.675050	+	1.85468i	0.489375	+	0.872074i	$0.337225\pi$
$263$	10.9475	+	30.0779i	0.675050	+	1.85468i	0.185675	+	0.982611i	$0.440553\pi$
$264$	−0.569917	−	0.478217i	−0.0350760	−	0.0294322i
$265$		0			0
$266$	8.45086	+	0.931735i	0.518155	+	0.0571283i
$267$			0.139884i			0.00856074i
$268$	10.7589	−	12.8219i	0.657203	−	0.783224i
$269$	3.55876	−	1.29528i	0.216981	−	0.0789748i	−0.231242	−	0.972896i	$-0.574279\pi$
$269$	3.55876	−	1.29528i	0.216981	−	0.0789748i	0.448224	+	0.893921i	$0.352057\pi$
$270$		0			0
$271$	2.90657	−	16.4840i	0.176562	−	1.00133i	−0.759764	−	0.650199i	$-0.774686\pi$
$271$	2.90657	−	16.4840i	0.176562	−	1.00133i	0.936326	−	0.351132i	$-0.114203\pi$
$272$	6.71582	−	18.4516i	0.407207	−	1.11879i
$273$	−0.437564	+	0.252628i	−0.0264826	+	0.0152897i
$274$	3.26728	−	5.65909i	0.197383	−	0.341878i
$275$		0			0
$276$	0.309690	−	0.259861i	0.0186412	−	0.0156418i
$277$	−10.0366	−	5.79462i	−0.603040	−	0.348165i	0.167197	−	0.985924i	$-0.446528\pi$
$277$	−10.0366	−	5.79462i	−0.603040	−	0.348165i	−0.770236	+	0.637758i	$0.779862\pi$
$278$	9.21285	−	5.31904i	0.552550	−	0.319015i
$279$	22.4639	+	8.17619i	1.34488	+	0.489496i
$280$		0			0
$281$	−0.442986	−	2.51230i	−0.0264263	−	0.149871i	0.968739	−	0.248080i	$-0.0797997\pi$
$281$	−0.442986	−	2.51230i	−0.0264263	−	0.149871i	−0.995166	+	0.0982092i	$0.968689\pi$
$282$	0.692974	+	1.90393i	0.0412660	+	0.113377i
$283$	−0.333538	+	0.397495i	−0.0198268	+	0.0236286i	−0.775867	−	0.630897i	$-0.782687\pi$
$283$	−0.333538	+	0.397495i	−0.0198268	+	0.0236286i	0.756040	+	0.654525i	$0.227132\pi$
$284$	−14.3515			−0.851603
$285$		0			0
$286$	−15.9847			−0.945192
$287$	0.618366	−	0.736940i	0.0365010	−	0.0435002i
$288$	6.47960	+	17.8026i	0.381814	+	1.04903i
$289$	0.173778	+	0.985542i	0.0102222	+	0.0579731i
$290$		0			0
$291$	3.11510	+	1.13381i	0.182611	+	0.0664649i
$292$	−2.94271	+	1.69897i	−0.172209	+	0.0994250i
$293$	1.00495	+	0.580211i	0.0587100	+	0.0338963i	0.529068	−	0.848580i	$-0.322542\pi$
$293$	1.00495	+	0.580211i	0.0587100	+	0.0338963i	−0.470358	+	0.882476i	$0.655875\pi$
$294$	1.44154	−	1.20960i	0.0840724	−	0.0705451i
$295$		0			0
$296$	−3.58385	+	6.20741i	−0.208307	+	0.360798i
$297$	3.03028	−	1.74953i	0.175835	−	0.101518i
$298$	−6.25602	+	17.1883i	−0.362401	+	0.995689i
$299$	−0.809358	+	4.59010i	−0.0468064	+	0.265452i
$300$		0			0
$301$	8.58638	−	3.12519i	0.494911	−	0.180133i
$302$	2.48370	−	2.95996i	0.142921	−	0.170327i
$303$		−	3.35031i		−	0.192470i
$304$	−8.60376	−	19.5922i	−0.493460	−	1.12369i
$305$		0			0
$306$	16.5280	+	13.8687i	0.944844	+	0.792819i
$307$	5.12048	+	14.0684i	0.292241	+	0.802926i	0.995738	+	0.0922276i	$0.0293987\pi$
$307$	5.12048	+	14.0684i	0.292241	+	0.802926i	−0.703497	+	0.710698i	$0.748379\pi$
$308$	−4.55465	+	0.803108i	−0.259526	+	0.0457614i
$309$	0.358092	−	2.03084i	0.0203712	−	0.115531i
$310$		0			0
$311$	−5.60315	−	9.70495i	−0.317726	−	0.550317i	0.662287	−	0.749250i	$-0.269586\pi$
$311$	−5.60315	−	9.70495i	−0.317726	−	0.550317i	−0.980013	+	0.198933i	$0.936252\pi$
$312$	0.517291	+	0.298658i	0.0292858	+	0.0169082i
$313$	−8.75749	−	10.4368i	−0.495003	−	0.589921i	0.459480	−	0.888188i	$-0.348036\pi$
$313$	−8.75749	−	10.4368i	−0.495003	−	0.589921i	−0.954482	+	0.298267i	$0.903591\pi$
$314$	16.0765	−	13.4898i	0.907252	−	0.761275i
$315$		0			0
$316$	4.27600	+	7.40624i	0.240544	+	0.416634i
$317$	−2.97044	+	8.16123i	−0.166837	+	0.458380i	−0.994733	−	0.102501i	$-0.967315\pi$
$317$	−2.97044	+	8.16123i	−0.166837	+	0.458380i	0.827896	+	0.560881i	$0.189538\pi$
$318$	1.07733	+	0.189962i	0.0604134	+	0.0106525i
$319$	1.29475	+	7.34288i	0.0724919	+	0.411122i
$320$		0			0
$321$	1.54607	+	1.29731i	0.0862931	+	0.0724085i
$322$			3.42076i			0.190632i
$323$	−14.0530	−	10.3198i	−0.781931	−	0.574210i
$324$	−11.3480			−0.630446
$325$		0			0
$326$	−31.4705	+	11.4543i	−1.74299	+	0.634396i
$327$	2.22159	−	0.391726i	0.122854	−	0.0216625i
$328$	−1.12001	−	0.197489i	−0.0618424	−	0.0109045i
$329$	−6.35109	−	2.31161i	−0.350147	−	0.127443i
$330$		0			0
$331$	11.6700	−	20.2130i	0.641439	−	1.11101i	−0.343672	−	0.939090i	$-0.611671\pi$
$331$	11.6700	−	20.2130i	0.641439	−	1.11101i	0.985112	−	0.171916i	$-0.0549957\pi$
$332$	2.25798	+	2.69096i	0.123923	+	0.147685i
$333$	−10.7776	−	12.8443i	−0.590610	−	0.703862i
$334$	1.76489	−	3.05688i	0.0965706	−	0.167265i
$335$		0			0
$336$	0.877000	+	0.319202i	0.0478443	+	0.0174139i
$337$	−12.6588	−	2.23209i	−0.689568	−	0.121589i	−0.182126	−	0.983275i	$-0.558298\pi$
$337$	−12.6588	−	2.23209i	−0.689568	−	0.121589i	−0.507442	+	0.861686i	$0.669409\pi$
$338$	−10.6238	+	1.87326i	−0.577857	+	0.101892i
$339$	2.76087	−	1.00487i	0.149950	−	0.0545772i
$340$		0			0
$341$	26.6557			1.44349
$342$	23.4630	−	1.52072i	1.26873	−	0.0822313i
$343$			13.7915i			0.744671i
$344$	−8.27507	−	6.94361i	−0.446162	−	0.374374i
$345$		0			0
$346$	−3.80251	−	21.5651i	−0.204424	−	1.15935i
$347$	−31.9415	−	5.63215i	−1.71471	−	0.302350i	−0.771916	−	0.635725i	$-0.780701\pi$
$347$	−31.9415	−	5.63215i	−1.71471	−	0.302350i	−0.942794	+	0.333376i	$0.891812\pi$
$348$	−0.177589	+	0.487923i	−0.00951978	+	0.0261554i
$349$	6.05424	+	10.4863i	0.324076	+	0.561316i	0.981325	−	0.192357i	$-0.0616133\pi$
$349$	6.05424	+	10.4863i	0.324076	+	0.561316i	−0.657249	+	0.753674i	$0.728280\pi$
$350$		0			0
$351$	−2.15205	+	1.80579i	−0.114868	+	0.0963857i
$352$	13.5786	+	16.1824i	0.723742	+	0.862523i
$353$	−20.0019	−	11.5481i	−1.06459	−	0.614643i	−0.137894	−	0.990447i	$-0.544033\pi$
$353$	−20.0019	−	11.5481i	−1.06459	−	0.614643i	−0.926699	+	0.375804i	$0.877367\pi$
$354$	−0.239222	−	0.414345i	−0.0127145	−	0.0220222i
$355$		0			0
$356$	0.178516	−	1.01241i	0.00946133	−	0.0536579i
$357$	0.748889	−	0.132049i	0.0396354	−	0.00698879i
$358$	−11.3791	−	31.2639i	−0.601406	−	1.65235i
$359$	4.93802	+	4.14349i	0.260619	+	0.218685i	0.763729	−	0.645537i	$-0.223366\pi$
$359$	4.93802	+	4.14349i	0.260619	+	0.218685i	−0.503110	+	0.864222i	$0.667811\pi$
$360$		0			0
$361$	−18.8410	+	2.45262i	−0.991634	+	0.129085i
$362$		−	46.6092i		−	2.44972i
$363$	−0.00488344	+	0.00581986i	−0.000256314	+	0.000305463i
$364$	3.48929	−	1.27000i	0.182888	−	0.0665659i
$365$		0			0
$366$	0.767229	−	4.35117i	0.0401037	−	0.227439i
$367$	−2.94780	+	8.09901i	−0.153874	+	0.422765i	−0.992546	−	0.121872i	$-0.961110\pi$
$367$	−2.94780	+	8.09901i	−0.153874	+	0.422765i	0.838672	+	0.544637i	$0.183333\pi$
$368$	7.45597	−	4.30470i	0.388669	−	0.224398i
$369$	1.33020	−	2.30398i	0.0692476	−	0.119940i
$370$		0			0
$371$	−2.79542	+	2.34563i	−0.145131	+	0.121779i
$372$	1.60758	+	0.928134i	0.0833489	+	0.0481215i
$373$	8.23228	−	4.75291i	0.426251	−	0.246096i	−0.271497	−	0.962439i	$-0.587519\pi$
$373$	8.23228	−	4.75291i	0.426251	−	0.246096i	0.697748	+	0.716343i	$0.254185\pi$
$374$	22.6071	+	8.22830i	1.16898	+	0.425475i
$375$		0			0
$376$	1.38748	+	7.86878i	0.0715538	+	0.405801i
$377$	−2.04745	−	5.62532i	−0.105449	−	0.289719i
$378$	−1.32532	+	1.57945i	−0.0681669	+	0.0812381i
$379$	11.3635			0.583706			0.291853	−	0.956463i	$-0.405728\pi$
$379$	11.3635			0.583706			0.291853	+	0.956463i	$0.405728\pi$
$380$		0			0
$381$	−1.72205			−0.0882234
$382$	−10.7706	+	12.8359i	−0.551071	+	0.656741i
$383$	−0.934706	−	2.56808i	−0.0477612	−	0.131223i	0.913519	−	0.406797i	$-0.133354\pi$
$383$	−0.934706	−	2.56808i	−0.0477612	−	0.131223i	−0.961280	+	0.275574i	$0.911132\pi$
$384$	−0.293189	−	1.66276i	−0.0149617	−	0.0848521i
$385$		0			0
$386$	−20.4927	−	7.45874i	−1.04305	−	0.379640i
$387$	21.8839	−	12.6347i	1.11242	−	0.642256i
$388$	−21.0988	−	12.1814i	−1.07113	−	0.618416i
$389$	16.9706	−	14.2400i	0.860445	−	0.721999i	−0.101619	−	0.994823i	$-0.532402\pi$
$389$	16.9706	−	14.2400i	0.860445	−	0.721999i	0.962064	+	0.272824i	$0.0879578\pi$
$390$		0			0
$391$	3.50748	−	6.07514i	0.177381	−	0.307233i
$392$	6.42680	−	3.71051i	0.324602	−	0.187409i
$393$	−0.895897	+	2.46146i	−0.0451920	+	0.124164i
$394$	8.48669	−	48.1304i	0.427553	−	2.42478i
$395$		0			0
$396$	−12.0188	+	4.37447i	−0.603965	+	0.219825i
$397$	−10.9022	+	12.9927i	−0.547165	+	0.652086i	−0.966778	−	0.255617i	$-0.917721\pi$
$397$	−10.9022	+	12.9927i	−0.547165	+	0.652086i	0.419613	+	0.907703i	$0.362166\pi$
$398$			8.31096i			0.416591i
$399$	0.490499	−	0.667938i	0.0245557	−	0.0334387i
$400$		0			0
$401$	5.07050	+	4.25465i	0.253208	+	0.212467i	0.760552	−	0.649276i	$-0.224928\pi$
$401$	5.07050	+	4.25465i	0.253208	+	0.212467i	−0.507344	+	0.861744i	$0.669373\pi$
$402$	−1.41538	−	3.88871i	−0.0705926	−	0.193951i
$403$	−21.0760	+	3.71627i	−1.04987	+	0.185121i
$404$	−4.27558	+	24.2480i	−0.212718	+	1.20638i
$405$		0			0
$406$	−2.19677	−	3.80492i	−0.109024	−	0.188835i
$407$	−16.1911	−	9.34796i	−0.802565	−	0.463361i
$408$	−0.577866	−	0.688674i	−0.0286086	−	0.0340944i
$409$	−27.3969	+	22.9888i	−1.35469	+	1.13672i	−0.377109	+	0.926169i	$0.623082\pi$
$409$	−27.3969	+	22.9888i	−1.35469	+	1.13672i	−0.977583	+	0.210552i	$0.932474\pi$
$410$		0			0
$411$	−0.318460	−	0.551588i	−0.0157085	−	0.0272078i
$412$	−5.18342	+	14.2413i	−0.255369	+	0.701620i
$413$	1.57174	+	0.277140i	0.0773402	+	0.0136372i
$414$	1.64272	+	9.31632i	0.0807352	+	0.457872i
$415$		0			0
$416$	−12.9924	−	10.9019i	−0.637004	−	0.534510i
$417$		−	1.03689i		−	0.0507766i
$418$	24.0045	−	10.5414i	1.17410	−	0.515598i
$419$	29.6681			1.44938			0.724691	−	0.689074i	$-0.241982\pi$
$419$	29.6681			1.44938			0.724691	+	0.689074i	$0.241982\pi$
$420$		0			0
$421$	−11.6019	+	4.22276i	−0.565444	+	0.205805i	−0.608895	−	0.793251i	$-0.708387\pi$
$421$	−11.6019	+	4.22276i	−0.565444	+	0.205805i	0.0434509	+	0.999056i	$0.486165\pi$
$422$	27.8481	−	4.91037i	1.35562	−	0.239033i
$423$	−18.4070	−	3.24565i	−0.894980	−	0.157809i
$424$	4.05389	+	1.47550i	0.196874	+	0.0716564i
$425$		0			0
$426$	−1.77414	+	3.07289i	−0.0859572	+	0.148882i
$427$	9.47370	+	11.2903i	0.458465	+	0.546377i
$428$	−9.53416	−	11.3624i	−0.460851	−	0.549221i
$429$	−0.779008	+	1.34928i	−0.0376108	+	0.0651439i
$430$		0			0
$431$	16.0374	+	5.83712i	0.772492	+	0.281164i	0.698038	−	0.716060i	$-0.254056\pi$
$431$	16.0374	+	5.83712i	0.772492	+	0.281164i	0.0744539	+	0.997224i	$0.476279\pi$
$432$	5.11038	+	0.901098i	0.245873	+	0.0433541i
$433$	−2.75763	+	0.486245i	−0.132523	+	0.0233674i	−0.239516	−	0.970892i	$-0.576989\pi$
$433$	−2.75763	+	0.486245i	−0.132523	+	0.0233674i	0.106993	+	0.994260i	$0.465878\pi$
$434$	−14.7597	+	5.37207i	−0.708486	+	0.257868i
$435$		0			0
$436$	−16.5788			−0.793979
$437$	−1.81161	−	7.42680i	−0.0866609	−	0.355272i
$438$			0.840113i			0.0401421i
$439$	−16.2517	−	13.6368i	−0.775651	−	0.650848i	0.166498	−	0.986042i	$-0.446754\pi$
$439$	−16.2517	−	13.6368i	−0.775651	−	0.650848i	−0.942149	+	0.335193i	$0.891198\pi$
$440$		0			0
$441$	3.01447	+	17.0959i	0.143546	+	0.814090i
$442$	−19.0220	−	3.35410i	−0.904785	−	0.159538i
$443$	−7.79086	+	21.4052i	−0.370155	+	1.01699i	0.605146	+	0.796114i	$0.293115\pi$
$443$	−7.79086	+	21.4052i	−0.370155	+	1.01699i	−0.975301	+	0.220878i	$0.929108\pi$
$444$	−0.650979	−	1.12753i	−0.0308941	−	0.0535101i
$445$		0			0
$446$	−28.0172	+	23.5092i	−1.32665	+	1.11319i
$447$	1.14599	+	1.36574i	0.0542036	+	0.0645974i
$448$	−1.65262	−	0.954142i	−0.0780791	−	0.0450790i
$449$	−14.8849	−	25.7814i	−0.702461	−	1.21670i	−0.967600	−	0.252488i	$-0.918751\pi$
$449$	−14.8849	−	25.7814i	−0.702461	−	1.21670i	0.265139	−	0.964210i	$-0.414582\pi$
$450$		0			0
$451$	0.515121	−	2.92140i	0.0242561	−	0.137563i
$452$	−21.2643	+	3.74947i	−1.00019	+	0.176360i
$453$	−0.128811	−	0.353904i	−0.00605205	−	0.0166279i
$454$	−19.3032	−	16.1973i	−0.905943	−	0.760177i
$455$		0			0
$456$	−0.973784	−	0.107363i	−0.0456016	−	0.00502773i
$457$		−	36.7666i		−	1.71987i	−0.510406	−	0.859934i	$-0.670505\pi$
$457$		−	36.7666i		−	1.71987i	0.510406	−	0.859934i	$-0.329495\pi$
$458$	10.1654	−	12.1146i	0.474996	−	0.566078i
$459$	3.97319	−	1.44612i	0.185453	−	0.0674993i
$460$		0			0
$461$	−4.46796	+	25.3390i	−0.208093	+	1.18016i	0.684404	+	0.729103i	$0.260063\pi$
$461$	−4.46796	+	25.3390i	−0.208093	+	1.18016i	−0.892497	+	0.451053i	$0.851048\pi$
$462$	−0.391090	+	1.07451i	−0.0181951	+	0.0499907i
$463$	30.8035	−	17.7844i	1.43156	−	0.826511i	0.434320	−	0.900759i	$-0.356989\pi$
$463$	30.8035	−	17.7844i	1.43156	−	0.826511i	0.997240	+	0.0742472i	$0.0236554\pi$
$464$	−5.52885	+	9.57625i	−0.256670	+	0.444566i
$465$		0			0
$466$	21.8819	−	18.3611i	1.01366	−	0.850560i
$467$	6.16238	+	3.55785i	0.285161	+	0.164638i	0.635758	−	0.771889i	$-0.280688\pi$
$467$	6.16238	+	3.55785i	0.285161	+	0.164638i	−0.350596	+	0.936527i	$0.614021\pi$
$468$	8.89306	−	5.13441i	0.411082	−	0.237338i
$469$	12.9719	+	4.72139i	0.598987	+	0.218013i
$470$		0			0
$471$	−0.355204	−	2.01446i	−0.0163669	−	0.0928215i
$472$	−0.645319	−	1.77300i	−0.0297032	−	0.0816089i
$473$	18.1114	−	21.5844i	0.832764	−	0.992449i
$474$	2.11440			0.0971178
$475$		0			0
$476$	−5.58864			−0.256155
$477$	−6.48679	+	7.73066i	−0.297010	+	0.353963i
$478$	−8.59764	−	23.6218i	−0.393247	−	1.08044i
$479$	1.53032	+	8.67887i	0.0699220	+	0.396547i	0.999603	+	0.0281814i	$0.00897159\pi$
$479$	1.53032	+	8.67887i	0.0699220	+	0.396547i	−0.929681	+	0.368366i	$0.879917\pi$
$480$		0			0
$481$	14.1052	+	5.13387i	0.643142	+	0.234085i
$482$	19.1612	−	11.0627i	0.872768	−	0.503893i
$483$	0.288750	+	0.166710i	0.0131386	+	0.00758557i
$484$	0.0427713	−	0.0358894i	0.00194415	−	0.00163133i
$485$		0			0
$486$	−4.28393	+	7.41999i	−0.194323	+	0.336577i
$487$	−4.14225	+	2.39153i	−0.187703	+	0.108370i	−0.590907	−	0.806740i	$-0.701230\pi$
$487$	−4.14225	+	2.39153i	−0.187703	+	0.108370i	0.403204	+	0.915110i	$0.367897\pi$
$488$	5.95933	−	16.3731i	0.269766	−	0.741177i
$489$	−0.566835	+	3.21468i	−0.0256331	+	0.145373i
$490$		0			0
$491$	−9.46362	+	3.44448i	−0.427087	+	0.155447i	−0.546615	−	0.837384i	$-0.684084\pi$
$491$	−9.46362	+	3.44448i	−0.427087	+	0.155447i	0.119528	+	0.992831i	$0.461862\pi$
$492$	0.132787	−	0.158250i	0.00598652	−	0.00713445i
$493$			9.00984i			0.405783i
$494$	−17.5101	+	11.6815i	−0.787818	+	0.525575i
$495$		0			0
$496$	30.2827	+	25.4102i	1.35973	+	1.14095i
$497$	−4.04824	−	11.1224i	−0.181588	−	0.498910i
$498$	0.855312	−	0.150815i	0.0383275	−	0.00675817i
$499$	0.333774	−	1.89292i	0.0149418	−	0.0847390i	−0.976425	−	0.215857i	$-0.930746\pi$
$499$	0.333774	−	1.89292i	0.0149418	−	0.0847390i	0.991367	+	0.131118i	$0.0418567\pi$
$500$		0			0
$501$	−0.172023	−	0.297953i	−0.00768542	−	0.0133115i
$502$	−6.89718	−	3.98209i	−0.307836	−	0.177729i
$503$	10.4320	+	12.4324i	0.465140	+	0.554332i	0.946715	−	0.322073i	$-0.104380\pi$
$503$	10.4320	+	12.4324i	0.465140	+	0.554332i	−0.481575	+	0.876405i	$0.659935\pi$
$504$	−3.09798	+	2.59951i	−0.137995	+	0.115791i
$505$		0			0
$506$	5.27417	+	9.13513i	0.234465	+	0.406106i
$507$	−0.359623	+	0.988056i	−0.0159714	+	0.0438811i
$508$	12.4634	+	2.19764i	0.552976	+	0.0975045i
$509$	5.87363	+	33.3110i	0.260344	+	1.47649i	0.781973	+	0.623313i	$0.214214\pi$
$509$	5.87363	+	33.3110i	0.260344	+	1.47649i	−0.521629	+	0.853173i	$0.674675\pi$
$510$		0			0
$511$	−2.14679	−	1.80137i	−0.0949683	−	0.0796878i
$512$			18.8686i			0.833884i
$513$	2.04092	−	4.13101i	0.0901088	−	0.182388i
$514$	−42.0793			−1.85604
$515$		0			0
$516$	1.84383	−	0.671099i	0.0811701	−	0.0295435i
$517$	−20.5246	+	3.61904i	−0.902671	+	0.159165i
$518$	10.8492	+	1.91301i	0.476687	+	0.0840527i
$519$	−2.00565	−	0.729996i	−0.0880381	−	0.0320433i
$520$		0			0
$521$	−3.44419	+	5.96551i	−0.150893	+	0.261354i	−0.931556	−	0.363598i	$-0.881548\pi$
$521$	−3.44419	+	5.96551i	−0.150893	+	0.261354i	0.780663	+	0.624952i	$0.214881\pi$
$522$	−7.81001	−	9.30761i	−0.341835	−	0.407383i
$523$	12.9773	+	15.4658i	0.567459	+	0.676271i	0.971107	−	0.238643i	$-0.0767026\pi$
$523$	12.9773	+	15.4658i	0.567459	+	0.676271i	−0.403648	+	0.914914i	$0.632258\pi$
$524$	9.62535	−	16.6716i	0.420485	−	0.728302i
$525$		0			0
$526$	−54.6523	−	19.8918i	−2.38295	−	0.867324i
$527$	31.7208	+	5.59323i	1.38178	+	0.243645i
$528$	2.83417	−	0.499741i	0.123341	−	0.0217484i
$529$	−18.7227	+	6.81449i	−0.814029	+	0.296282i
$530$		0			0
$531$	4.41366			0.191536
$532$	−4.40241	+	4.20827i	−0.190869	+	0.182452i
$533$			2.38169i			0.103163i
$534$	−0.194707	−	0.163379i	−0.00842580	−	0.00707008i
$535$		0			0
$536$	−2.83388	−	16.0717i	−0.122405	−	0.694193i
$537$	−3.19358	−	0.563114i	−0.137813	−	0.0243002i
$538$	−2.35356	+	6.46635i	−0.101469	+	0.278784i
$539$	9.67835	+	16.7634i	0.416876	+	0.722050i
$540$		0			0
$541$	2.00813	−	1.68502i	0.0863363	−	0.0724447i	−0.598598	−	0.801050i	$-0.704275\pi$
$541$	2.00813	−	1.68502i	0.0863363	−	0.0724447i	0.684934	+	0.728605i	$0.259831\pi$
$542$	19.5496	+	23.2983i	0.839729	+	1.00075i
$543$	−3.93433	−	2.27149i	−0.168838	−	0.0974788i
$544$	12.7632	+	22.1065i	0.547218	+	0.947810i
$545$		0			0
$546$	0.159420	−	0.904113i	0.00682253	−	0.0386925i
$547$	−26.1665	+	4.61386i	−1.11880	+	0.197274i	−0.702313	−	0.711868i	$-0.747849\pi$
$547$	−26.1665	+	4.61386i	−1.11880	+	0.197274i	−0.416485	+	0.909143i	$0.636738\pi$
$548$	1.60094	+	4.39856i	0.0683889	+	0.187897i
$549$	31.2231	+	26.1993i	1.33257	+	1.11816i
$550$		0			0
$551$	6.78444	+	7.09744i	0.289027	+	0.302361i
$552$		−	0.394172i		−	0.0167771i
$553$	−4.53370	+	5.40306i	−0.192793	+	0.229761i
$554$	19.7880	−	7.20224i	0.840711	−	0.305994i
$555$		0			0
$556$	−1.32325	+	7.50453i	−0.0561183	+	0.318263i
$557$	5.96029	−	16.3758i	0.252546	−	0.693864i	−0.747032	−	0.664789i	$-0.768522\pi$
$557$	5.96029	−	16.3758i	0.252546	−	0.693864i	0.999577	−	0.0290750i	$-0.00925616\pi$
$558$	−37.6176	+	21.7185i	−1.59248	+	0.919418i
$559$	−11.3110	+	19.5913i	−0.478405	+	0.828622i
$560$		0			0
$561$	1.79631	−	1.50728i	0.0758402	−	0.0636375i
$562$	4.01431	+	2.31766i	0.169333	+	0.0977647i
$563$	1.95146	−	1.12668i	0.0822443	−	0.0474838i	−0.458314	−	0.888790i	$-0.651546\pi$
$563$	1.95146	−	1.12668i	0.0822443	−	0.0474838i	0.540558	+	0.841307i	$0.318213\pi$
$564$	−1.36383	−	0.496392i	−0.0574275	−	0.0209019i
$565$		0			0
$566$	−0.163723	−	0.928516i	−0.00688177	−	0.0390285i
$567$	−3.20103	−	8.79476i	−0.134431	−	0.369345i
$568$	−8.99447	+	10.7192i	−0.377400	+	0.449767i
$569$	8.49148			0.355982			0.177991	−	0.984032i	$-0.443040\pi$
$569$	8.49148			0.355982			0.177991	+	0.984032i	$0.443040\pi$
$570$		0			0
$571$	−2.29006			−0.0958359			−0.0479179	−	0.998851i	$-0.515259\pi$
$571$	−2.29006			−0.0958359			−0.0479179	+	0.998851i	$0.515259\pi$
$572$	7.36002	−	8.77133i	0.307738	−	0.366748i
$573$	0.558589	+	1.53471i	0.0233354	+	0.0641134i
$574$	0.303535	+	1.72143i	0.0126693	+	0.0718513i
$575$		0			0
$576$	−4.95905	−	1.80495i	−0.206627	−	0.0752061i
$577$	−1.73999	+	1.00458i	−0.0724366	+	0.0418213i	−0.535781	−	0.844357i	$-0.679983\pi$
$577$	−1.73999	+	1.00458i	−0.0724366	+	0.0418213i	0.463344	+	0.886178i	$0.346649\pi$
$578$	−1.57476	−	0.909189i	−0.0655015	−	0.0378173i
$579$	−1.62831	+	1.36631i	−0.0676701	+	0.0567819i
$580$		0			0
$581$	−1.44857	+	2.50900i	−0.0600970	+	0.104091i
$582$	−5.21649	+	3.01174i	−0.216230	+	0.124841i
$583$	−3.84862	+	10.5740i	−0.159394	+	0.437931i
$584$	−0.575306	+	3.26272i	−0.0238063	+	0.135012i
$585$		0			0
$586$	−1.98135	+	0.721154i	−0.0818490	+	0.0297906i
$587$	4.74974	−	5.66052i	0.196043	−	0.233635i	−0.659064	−	0.752087i	$-0.729047\pi$
$587$	4.74974	−	5.66052i	0.196043	−	0.233635i	0.855106	+	0.518452i	$0.173492\pi$
$588$			1.34797i			0.0555895i
$589$	29.1996	−	19.4799i	1.20315	−	0.802654i
$590$		0			0
$591$	−3.64914	−	3.06199i	−0.150106	−	0.125954i
$592$	−9.48305	−	26.0545i	−0.389751	−	1.07083i
$593$	−23.1188	+	4.07647i	−0.949377	+	0.167401i	−0.626833	−	0.779154i	$-0.715649\pi$
$593$	−23.1188	+	4.07647i	−0.949377	+	0.167401i	−0.322544	+	0.946555i	$0.604538\pi$
$594$	−1.10403	+	6.26129i	−0.0452991	+	0.256904i
$595$		0			0
$596$	−6.55126	−	11.3471i	−0.268350	−	0.464796i
$597$	0.701537	+	0.405033i	0.0287120	+	0.0165769i
$598$	−5.44375	−	6.48761i	−0.222612	−	0.265298i
$599$	24.7199	−	20.7425i	1.01003	−	0.847514i	0.0216857	−	0.999765i	$-0.493097\pi$
$599$	24.7199	−	20.7425i	1.01003	−	0.847514i	0.988342	+	0.152251i	$0.0486522\pi$
$600$		0			0
$601$	−14.9179	−	25.8385i	−0.608513	−	1.05397i	−0.991486	−	0.130215i	$-0.958433\pi$
$601$	−14.9179	−	25.8385i	−0.608513	−	1.05397i	0.382973	−	0.923759i	$-0.374900\pi$
$602$	−5.67854	+	15.6017i	−0.231440	+	0.635876i
$603$	37.5958	+	6.62915i	1.53102	+	0.269960i
$604$	0.480630	+	2.72579i	0.0195565	+	0.110911i
$605$		0			0
$606$	4.66336	+	3.91303i	0.189436	+	0.158956i
$607$		−	9.11607i		−	0.370010i	−0.982738	−	0.185005i	$-0.940770\pi$
$607$		−	9.11607i		−	0.370010i	0.982738	−	0.185005i	$-0.0592301\pi$
$608$	26.7004	+	7.80353i	1.08285	+	0.316475i
$609$	−0.428236			−0.0173530
$610$		0			0
$611$	15.7237	−	5.72298i	0.636115	−	0.231527i
$612$	−15.2204	+	2.68377i	−0.615250	+	0.108485i
$613$	−41.4127	−	7.30218i	−1.67264	−	0.294932i	−0.744631	−	0.667477i	$-0.767374\pi$
$613$	−41.4127	−	7.30218i	−1.67264	−	0.294932i	−0.928014	+	0.372544i	$0.878485\pi$
$614$	−25.5626	−	9.30403i	−1.03162	−	0.375480i
$615$		0			0
$616$	−2.25468	+	3.90523i	−0.0908438	+	0.157346i
$617$	21.6512	+	25.8029i	0.871643	+	1.03878i	0.998899	+	0.0469138i	$0.0149386\pi$
$617$	21.6512	+	25.8029i	0.871643	+	1.03878i	−0.127256	+	0.991870i	$0.540617\pi$
$618$	2.40853	+	2.87038i	0.0968854	+	0.115464i
$619$	−20.8458	+	36.1060i	−0.837865	+	1.45122i	0.0538116	+	0.998551i	$0.482863\pi$
$619$	−20.8458	+	36.1060i	−0.837865	+	1.45122i	−0.891676	+	0.452673i	$0.850470\pi$
$620$		0			0
$621$	1.74207	+	0.634061i	0.0699068	+	0.0254440i
$622$	20.0528	+	3.53585i	0.804043	+	0.141775i
$623$	0.834981	−	0.147230i	0.0334528	−	0.00589863i
$624$	−2.17124	+	0.790266i	−0.0869191	+	0.0316360i
$625$		0			0
$626$	24.7556			0.989431
$627$	0.280041	−	2.53998i	0.0111838	−	0.101437i
$628$			15.0331i			0.599884i
$629$	−17.3062	−	14.5217i	−0.690045	−	0.579016i
$630$		0			0
$631$	−1.44547	−	8.19764i	−0.0575431	−	0.326343i	0.942424	−	0.334420i	$-0.108540\pi$
$631$	−1.44547	−	8.19764i	−0.0575431	−	0.326343i	−0.999967	+	0.00807654i	$0.997429\pi$
$632$	8.21165	+	1.44794i	0.326642	+	0.0575958i
$633$	0.942679	−	2.58999i	0.0374681	−	0.102943i
$634$	−7.89042	−	13.6666i	−0.313369	−	0.542770i
$635$		0			0
$636$	−0.600286	+	0.503699i	−0.0238029	+	0.0199730i
$637$	−9.98954	−	11.9051i	−0.395800	−	0.471696i
$638$	−11.7329	−	6.77400i	−0.464511	−	0.268185i
$639$	−16.3664	−	28.3475i	−0.647446	−	1.12141i
$640$		0			0
$641$	−1.26074	+	7.15002i	−0.0497963	+	0.282409i	−0.999530	−	0.0306495i	$-0.990242\pi$
$641$	−1.26074	+	7.15002i	−0.0497963	+	0.282409i	0.949734	+	0.313058i	$0.101354\pi$
$642$	−3.61149	+	0.636804i	−0.142534	+	0.0251326i
$643$	1.22168	+	3.35653i	0.0481783	+	0.132369i	0.961448	−	0.274986i	$-0.0886733\pi$
$643$	1.22168	+	3.35653i	0.0481783	+	0.132369i	−0.913270	+	0.407355i	$0.866451\pi$
$644$	−1.87709	−	1.57507i	−0.0739678	−	0.0620664i
$645$		0			0
$646$	30.7777	−	7.50756i	1.21093	−	0.295381i
$647$			21.0229i			0.826494i	0.910619	+	0.413247i	$0.135605\pi$
$647$			21.0229i			0.826494i	−0.910619	+	0.413247i	$0.864395\pi$
$648$	−7.11213	+	8.47590i	−0.279391	+	0.332965i
$649$	4.62461	−	1.68322i	0.181532	−	0.0660722i
$650$		0			0
$651$	−0.265845	+	1.50768i	−0.0104193	+	0.0590908i
$652$	8.20498	−	22.5430i	0.321332	−	0.882852i
$653$	20.1477	−	11.6323i	0.788441	−	0.455207i	−0.0509725	−	0.998700i	$-0.516232\pi$
$653$	20.1477	−	11.6323i	0.788441	−	0.455207i	0.839413	+	0.543494i	$0.182899\pi$
$654$	−2.04948	+	3.54980i	−0.0801409	+	0.138808i
$655$		0			0
$656$	3.37010	−	2.82785i	0.131580	−	0.110409i
$657$	−6.71174	−	3.87503i	−0.261850	−	0.151179i
$658$	10.6354	−	6.14035i	0.414611	−	0.239376i
$659$	−22.1075	−	8.04649i	−0.861188	−	0.313447i	−0.126595	−	0.991955i	$-0.540405\pi$
$659$	−22.1075	−	8.04649i	−0.861188	−	0.313447i	−0.734593	+	0.678508i	$0.762627\pi$
$660$		0			0
$661$	−3.70008	−	20.9842i	−0.143916	−	0.816190i	−0.968231	−	0.250058i	$-0.919550\pi$
$661$	−3.70008	−	20.9842i	−0.143916	−	0.816190i	0.824315	−	0.566132i	$-0.191561\pi$
$662$	14.5048	+	39.8516i	0.563745	+	1.54888i
$663$	−1.21016	+	1.44221i	−0.0469985	+	0.0560107i
$664$	3.42503			0.132917
$665$		0			0
$666$	30.4660			1.18054
$667$	−2.53928	+	3.02619i	−0.0983212	+	0.117175i
$668$	0.864785	+	2.37598i	0.0334595	+	0.0919293i
$669$	0.619026	+	3.51067i	0.0239329	+	0.135730i
$670$		0			0
$671$	42.7070	+	15.5441i	1.64868	+	0.600072i
$672$	−1.05072	+	0.606633i	−0.0405324	+	0.0234014i
$673$	6.70824	+	3.87301i	0.258584	+	0.149293i	0.623688	−	0.781673i	$-0.285633\pi$
$673$	6.70824	+	3.87301i	0.258584	+	0.149293i	−0.365105	+	0.930967i	$0.618967\pi$
$674$	17.8919	−	15.0130i	0.689168	−	0.578281i
$675$		0			0
$676$	3.86372	−	6.69216i	0.148605	−	0.257391i
$677$	−2.86781	+	1.65573i	−0.110219	+	0.0636348i	−0.554096	−	0.832453i	$-0.686936\pi$
$677$	−2.86781	+	1.65573i	−0.110219	+	0.0636348i	0.443877	+	0.896088i	$0.353603\pi$
$678$	−1.82588	+	5.01656i	−0.0701224	+	0.192660i
$679$	3.48911	−	19.7877i	0.133900	−	0.759384i
$680$		0			0
$681$	−2.30796	+	0.840030i	−0.0884414	+	0.0321900i
$682$	−31.1328	+	37.1027i	−1.19214	+	1.42073i
$683$			4.09964i			0.156868i	0.996919	+	0.0784342i	$0.0249920\pi$
$683$			4.09964i			0.156868i	−0.996919	+	0.0784342i	$0.975008\pi$
$684$	−9.96891	+	13.5752i	−0.381171	+	0.519060i
$685$		0			0
$686$	−19.1967	−	16.1079i	−0.732933	−	0.615004i
$687$	−0.527200	−	1.44847i	−0.0201139	−	0.0552626i
$688$	41.1516	−	7.25613i	1.56889	−	0.276637i
$689$	1.56881	−	8.89717i	0.0597670	−	0.338955i
$690$		0			0
$691$	11.4219	+	19.7832i	0.434508	+	0.752590i	0.997255	−	0.0740389i	$-0.0235889\pi$
$691$	11.4219	+	19.7832i	0.434508	+	0.752590i	−0.562747	+	0.826629i	$0.690256\pi$
$692$	13.5844	+	7.84294i	0.516400	+	0.298144i
$693$	−6.78046	−	8.08064i	−0.257568	−	0.306958i
$694$	45.1459	−	37.8819i	1.71372	−	1.43798i
$695$		0			0
$696$	0.253132	+	0.438437i	0.00959494	+	0.0166189i
$697$	1.22601	−	3.36843i	0.0464383	−	0.127588i
$698$	−21.6671	−	3.82050i	−0.820113	−	0.144608i
$699$	−0.483469	−	2.74189i	−0.0182865	−	0.103708i
$700$		0			0
$701$	−33.0796	−	27.7571i	−1.24940	−	1.04837i	−0.996729	−	0.0808184i	$-0.974247\pi$
$701$	−33.0796	−	27.7571i	−1.24940	−	1.04837i	−0.252671	−	0.967552i	$-0.581309\pi$
$702$		−	5.10457i		−	0.192660i
$703$	−24.5677	+	1.59233i	−0.926590	+	0.0600557i
$704$	−5.88442			−0.221778
$705$		0			0
$706$	39.4354	−	14.3533i	1.48417	−	0.540194i
$707$	−19.9984	+	3.52625i	−0.752116	+	0.132618i
$708$	0.337514	+	0.0595128i	0.0126845	+	0.00223663i
$709$	11.7936	+	4.29251i	0.442917	+	0.161209i	0.553845	−	0.832620i	$-0.313160\pi$
$709$	11.7936	+	4.29251i	0.442917	+	0.161209i	−0.110928	+	0.993828i	$0.535382\pi$
$710$		0			0
$711$	−9.75270	+	16.8922i	−0.365755	+	0.633506i
$712$	−0.644297	−	0.767843i	−0.0241461	−	0.0287761i
$713$	9.07791	+	10.8186i	0.339970	+	0.405161i
$714$	−0.690870	+	1.19662i	−0.0258552	+	0.0447825i
$715$		0			0
$716$	22.3951	+	8.15114i	0.836943	+	0.304622i
$717$	−2.41295	−	0.425467i	−0.0901131	−	0.0158894i
$718$	−11.5348	+	2.03390i	−0.430476	+	0.0759045i
$719$	21.1132	−	7.68458i	0.787390	−	0.286587i	0.0831393	−	0.996538i	$-0.473505\pi$
$719$	21.1132	−	7.68458i	0.787390	−	0.286587i	0.704251	+	0.709951i	$0.251283\pi$
$720$		0			0
$721$	−12.4992			−0.465495
$722$	18.5917	−	29.0898i	0.691913	−	1.08261i
$723$		−	2.15655i		−	0.0802031i
$724$	25.5761	+	21.4609i	0.950527	+	0.797587i
$725$		0			0
$726$	−0.00239712	−	0.0135947i	−8.89653e−5	−	0.000504547i
$727$	29.1373	+	5.13769i	1.08064	+	0.190546i	0.685499	−	0.728073i	$-0.259584\pi$
$727$	29.1373	+	5.13769i	1.08064	+	0.190546i	0.395143	+	0.918620i	$0.370695\pi$
$728$	1.23827	−	3.40211i	0.0458932	−	0.126091i
$729$	−12.6605	−	21.9286i	−0.468907	−	0.812170i
$730$		0			0
$731$	26.0820	−	21.8854i	0.964678	−	0.809461i
$732$	2.03437	+	2.42447i	0.0751926	+	0.0896111i
$733$	40.5570	+	23.4156i	1.49801	+	0.864876i	0.999997	−	0.00229524i	$-0.000730598\pi$
$733$	40.5570	+	23.4156i	1.49801	+	0.864876i	0.498011	+	0.867171i	$0.334064\pi$
$734$	−7.83027	−	13.5624i	−0.289021	−	0.500598i
$735$		0			0
$736$	−1.94351	+	11.0222i	−0.0716386	+	0.406283i
$737$	41.9208	−	7.39178i	1.54417	−	0.272280i
$738$	1.65333	+	4.54249i	0.0608600	+	0.167212i
$739$	−29.8695	−	25.0635i	−1.09877	−	0.921976i	−0.101427	−	0.994843i	$-0.532341\pi$
$739$	−29.8695	−	25.0635i	−1.09877	−	0.921976i	−0.997342	+	0.0728667i	$0.976785\pi$
$740$		0			0
$741$	0.132696	+	2.04734i	0.00487470	+	0.0752110i
$742$		−	6.63061i		−	0.243417i
$743$	7.80001	−	9.29569i	0.286155	−	0.341026i	−0.603749	−	0.797174i	$-0.706327\pi$
$743$	7.80001	−	9.29569i	0.286155	−	0.341026i	0.889904	+	0.456149i	$0.150772\pi$
$744$	1.70074	−	0.619019i	0.0623522	−	0.0226943i
$745$		0			0
$746$	−2.99930	+	17.0099i	−0.109812	+	0.622776i
$747$	−2.74026	+	7.52881i	−0.100261	+	0.275465i
$748$	−14.9244	+	8.61662i	−0.545691	+	0.315055i
$749$	6.11650	−	10.5941i	0.223492	−	0.387099i
$750$		0			0
$751$	−4.07011	+	3.41523i	−0.148521	+	0.124624i	−0.714021	−	0.700125i	$-0.753128\pi$
$751$	−4.07011	+	3.41523i	−0.148521	+	0.124624i	0.565500	+	0.824748i	$0.308683\pi$
$752$	−26.7673	−	15.4541i	−0.976101	−	0.563552i
$753$	−0.672265	+	0.388132i	−0.0244987	+	0.0141443i
$754$	10.2213	+	3.72027i	0.372239	+	0.135484i
$755$		0			0
$756$	−0.256466	−	1.45449i	−0.00932759	−	0.0528994i
$757$	7.26590	+	19.9629i	0.264084	+	0.725564i	0.998882	+	0.0472781i	$0.0150547\pi$
$757$	7.26590	+	19.9629i	0.264084	+	0.725564i	−0.734798	+	0.678286i	$0.762723\pi$
$758$	−13.2722	+	15.8172i	−0.482067	+	0.574505i
$759$	1.02814			0.0373191
$760$		0			0
$761$	37.4718			1.35835			0.679176	−	0.733975i	$-0.262337\pi$
$761$	37.4718			1.35835			0.679176	+	0.733975i	$0.262337\pi$
$762$	2.01129	−	2.39696i	0.0728613	−	0.0868327i
$763$	−4.67651	−	12.8486i	−0.169301	−	0.465151i
$764$	−2.08425	−	11.8204i	−0.0754057	−	0.427647i
$765$		0			0
$766$	4.66627	+	1.69838i	0.168599	+	0.0613650i
$767$	−3.42190	+	1.97563i	−0.123558	+	0.0713360i
$768$	3.20217	+	1.84877i	0.115548	+	0.0667119i
$769$	2.29530	−	1.92599i	0.0827707	−	0.0694529i	−0.600464	−	0.799652i	$-0.705017\pi$
$769$	2.29530	−	1.92599i	0.0827707	−	0.0694529i	0.683234	+	0.730199i	$0.260573\pi$
$770$		0			0
$771$	−2.05072	+	3.55196i	−0.0738550	+	0.127921i
$772$	13.5286	−	7.81074i	0.486905	−	0.281115i
$773$	−5.42954	+	14.9175i	−0.195287	+	0.536547i	−0.998228	−	0.0595125i	$-0.981045\pi$
$773$	−5.42954	+	14.9175i	−0.195287	+	0.536547i	0.802941	+	0.596059i	$0.203268\pi$
$774$	−7.97305	+	45.2174i	−0.286585	+	1.62531i
$775$		0			0
$776$	−22.3215	+	8.12438i	−0.801297	+	0.291648i
$777$	0.690212	−	0.822563i	0.0247612	−	0.0295093i
$778$			40.2536i			1.44316i
$779$	−1.57066	−	3.57664i	−0.0562747	−	0.128147i
$780$		0			0
$781$	−27.9595	−	23.4608i	−1.00047	−	0.839493i
$782$	4.35951	+	11.9777i	0.155896	+	0.428320i
$783$	−2.34489	+	0.413467i	−0.0837995	+	0.0147761i
$784$	−4.98484	+	28.2704i	−0.178030	+	1.00966i
$785$		0			0
$786$	−2.37978	−	4.12190i	−0.0848840	−	0.147023i
$787$	−4.20037	−	2.42508i	−0.149727	−	0.0864449i	0.423265	−	0.906006i	$-0.360884\pi$
$787$	−4.20037	−	2.42508i	−0.149727	−	0.0864449i	−0.572992	+	0.819561i	$0.694217\pi$
$788$	22.5032	+	26.8183i	0.801643	+	0.955361i
$789$	−4.34255	+	3.64383i	−0.154599	+	0.129724i
$790$		0			0
$791$	−8.90405	−	15.4223i	−0.316592	−	0.548353i
$792$	−4.26518	+	11.7185i	−0.151556	+	0.416398i
$793$	−35.9345	−	6.33622i	−1.27607	−	0.225006i
$794$	−5.35152	−	30.3500i	−0.189918	−	1.07708i
$795$		0			0
$796$	−4.56051	−	3.82673i	−0.161643	−	0.135635i
$797$			42.7169i			1.51311i	0.653930	+	0.756555i	$0.273119\pi$
$797$			42.7169i			1.51311i	−0.653930	+	0.756555i	$0.726881\pi$
$798$	0.356833	+	1.46286i	0.0126318	+	0.0517847i
$799$	−25.1840			−0.890947
$800$		0			0
$801$	2.20333	−	0.801948i	0.0778510	−	0.0283354i
$802$	−11.8443	+	2.08847i	−0.418236	+	0.0737463i
$803$	−8.51035	−	1.50060i	−0.300324	−	0.0529552i
$804$	2.78557	+	1.01387i	0.0982396	+	0.0357563i
$805$		0			0
$806$	19.4432	−	33.6766i	0.684858	−	1.18621i
$807$	0.431131	+	0.513802i	0.0151765	+	0.0180867i
$808$	15.4314	+	18.3904i	0.542873	+	0.646971i
$809$	7.67860	−	13.2997i	0.269965	−	0.467593i	−0.698887	−	0.715232i	$-0.746321\pi$
$809$	7.67860	−	13.2997i	0.269965	−	0.467593i	0.968853	+	0.247638i	$0.0796545\pi$
$810$		0			0
$811$	26.8518	+	9.77325i	0.942894	+	0.343185i	0.767308	−	0.641279i	$-0.221596\pi$
$811$	26.8518	+	9.77325i	0.942894	+	0.343185i	0.175586	+	0.984464i	$0.443818\pi$
$812$	3.09938	+	0.546504i	0.108767	+	0.0191785i
$813$	2.91938	−	0.514766i	0.102387	−	0.0180536i
$814$	31.9222	−	11.6187i	1.11887	−	0.407237i
$815$		0			0
$816$	3.47758			0.121740
$817$	4.06614	−	36.8799i	0.142256	−	1.29027i
$818$		−	64.9843i		−	2.27212i
$819$	6.48773	+	5.44385i	0.226699	+	0.190223i
$820$		0			0
$821$	−0.156048	−	0.884994i	−0.00544612	−	0.0308865i	0.981964	−	0.189070i	$-0.0605473\pi$
$821$	−0.156048	−	0.884994i	−0.00544612	−	0.0308865i	−0.987410	+	0.158184i	$0.949436\pi$
$822$	1.13972	+	0.200963i	0.0397521	+	0.00700937i
$823$	12.5556	−	34.4963i	0.437661	−	1.20246i	−0.503348	−	0.864084i	$-0.667899\pi$
$823$	12.5556	−	34.4963i	0.437661	−	1.20246i	0.941009	−	0.338381i	$-0.109879\pi$
$824$	7.38833	+	12.7970i	0.257385	+	0.445803i
$825$		0			0
$826$	−2.22149	+	1.86405i	−0.0772954	+	0.0648585i
$827$	−27.2274	−	32.4484i	−0.946791	−	1.12834i	−0.991599	−	0.129346i	$-0.958712\pi$
$827$	−27.2274	−	32.4484i	−0.946791	−	1.12834i	0.0448083	−	0.998996i	$-0.485732\pi$
$828$	−5.86856	−	3.38822i	−0.203947	−	0.117749i
$829$	12.1944	+	21.1213i	0.423530	+	0.733575i	0.996282	−	0.0861537i	$-0.0274576\pi$
$829$	12.1944	+	21.1213i	0.423530	+	0.733575i	−0.572752	+	0.819729i	$0.694124\pi$
$830$		0			0
$831$	0.356414	−	2.02132i	0.0123639	−	0.0701189i
$832$	4.65267	−	0.820391i	0.161302	−	0.0284420i
$833$	7.99991	+	21.9796i	0.277180	+	0.761547i
$834$	1.44327	+	1.21104i	0.0499762	+	0.0419350i
$835$		0			0
$836$	−5.26827	+	18.0258i	−0.182207	+	0.623437i
$837$			8.51230i			0.294228i
$838$	−34.6512	+	41.2957i	−1.19701	+	1.42654i
$839$	−22.0649	+	8.03097i	−0.761765	+	0.277260i	−0.693548	−	0.720411i	$-0.743953\pi$
$839$	−22.0649	+	8.03097i	−0.761765	+	0.277260i	−0.0682173	+	0.997670i	$0.521731\pi$
$840$		0			0
$841$	−4.15474	+	23.5627i	−0.143267	+	0.812507i
$842$	7.67286	−	21.0810i	0.264424	−	0.726500i
$843$	0.391273	−	0.225901i	0.0134761	−	0.00778045i
$844$	−10.1280	+	17.5421i	−0.348619	+	0.603826i
$845$		0			0
$846$	26.0164	−	21.8303i	0.894461	−	0.750542i
$847$	0.0398792	+	0.0230243i	0.00137027	+	0.000791124i
$848$	−14.4522	+	8.34399i	−0.496291	+	0.286534i
$849$	−0.0863560	−	0.0314310i	−0.00296373	−	0.00107871i
$850$		0			0
$851$	−1.72006	−	9.75497i	−0.0589630	−	0.334396i
$852$	−0.869315	−	2.38842i	−0.0297822	−	0.0818260i
$853$	3.75372	−	4.47350i	0.128525	−	0.153170i	−0.697944	−	0.716152i	$-0.745902\pi$
$853$	3.75372	−	4.47350i	0.128525	−	0.153170i	0.826469	+	0.562982i	$0.190346\pi$
$854$	−26.7801			−0.916397
$855$		0			0
$856$	−14.4619			−0.494299
$857$	17.3558	−	20.6838i	0.592862	−	0.706546i	−0.383291	−	0.923628i	$-0.625209\pi$
$857$	17.3558	−	20.6838i	0.592862	−	0.706546i	0.976153	+	0.217082i	$0.0696538\pi$
$858$	−0.968242	−	2.66022i	−0.0330552	−	0.0908185i
$859$	0.553337	+	3.13813i	0.0188796	+	0.107072i	0.992791	−	0.119856i	$-0.0382432\pi$
$859$	0.553337	+	3.13813i	0.0188796	+	0.107072i	−0.973912	+	0.226927i	$0.927132\pi$
$860$		0			0
$861$	0.160101	+	0.0582719i	0.00545622	+	0.00198590i
$862$	−26.8558	+	15.5052i	−0.914712	+	0.528109i
$863$	7.29344	+	4.21087i	0.248272	+	0.143340i	0.618973	−	0.785413i	$-0.287549\pi$
$863$	7.29344	+	4.21087i	0.248272	+	0.143340i	−0.370701	+	0.928752i	$0.620883\pi$
$864$	−5.16771	+	4.33622i	−0.175809	+	0.147521i
$865$		0			0
$866$	2.54399	−	4.40632i	0.0864483	−	0.149733i
$867$	−0.153491	+	0.0886182i	−0.00521283	+	0.00300963i
$868$	3.84814	−	10.5727i	0.130614	−	0.358860i
$869$	−3.77673	+	21.4189i	−0.128117	+	0.726587i
$870$		0			0
$871$	−32.1152	+	11.6890i	−1.08818	+	0.396066i
$872$	−10.3904	+	12.3828i	−0.351863	+	0.419334i
$873$		−	55.5667i		−	1.88065i
$874$	12.4534	+	6.15259i	0.421243	+	0.208115i
$875$		0			0
$876$	−0.460999	−	0.386824i	−0.0155757	−	0.0130696i
$877$	14.2999	+	39.2887i	0.482874	+	1.32669i	0.907018	+	0.421091i	$0.138353\pi$
$877$	14.2999	+	39.2887i	0.482874	+	1.32669i	−0.424144	+	0.905595i	$0.639425\pi$
$878$	37.9627	−	6.69384i	1.28118	−	0.225906i
$879$	−0.0356874	+	0.202393i	−0.00120371	+	0.00682656i
$880$		0			0
$881$	13.9233	+	24.1158i	0.469087	+	0.812482i	0.999376	−	0.0353351i	$-0.0112498\pi$
$881$	13.9233	+	24.1158i	0.469087	+	0.812482i	−0.530289	+	0.847817i	$0.677917\pi$
$882$	−27.3169	−	15.7714i	−0.919807	−	0.531051i
$883$	−18.0558	−	21.5180i	−0.607625	−	0.724139i	0.371265	−	0.928527i	$-0.378924\pi$
$883$	−18.0558	−	21.5180i	−0.607625	−	0.724139i	−0.978890	+	0.204388i	$0.934480\pi$
$884$	10.5991	−	8.89367i	0.356485	−	0.299127i
$885$		0			0
$886$	−20.6950	−	35.8447i	−0.695261	−	1.20423i
$887$	0.0384300	−	0.105586i	0.00129035	−	0.00354522i	−0.939046	−	0.343792i	$-0.888288\pi$
$887$	0.0384300	−	0.105586i	0.00129035	−	0.00354522i	0.940336	+	0.340247i	$0.110511\pi$
$888$	−1.25014	−	0.220434i	−0.0419521	−	0.00739728i
$889$	1.81249	+	10.2791i	0.0607888	+	0.344751i
$890$		0			0
$891$	−22.1082	−	18.5510i	−0.740652	−	0.621481i
$892$		−	26.1986i		−	0.877195i
$893$	−19.8386	+	18.9637i	−0.663872	+	0.634595i
$894$	−3.23948			−0.108344
$895$		0			0
$896$	−9.61658	+	3.50015i	−0.321268	+	0.116932i
$897$	−0.812926	+	0.143341i	−0.0271428	+	0.00478601i
$898$	53.2706	+	9.39304i	1.77766	+	0.313450i
$899$	−17.0449	−	6.20385i	−0.568481	−	0.206910i
$900$		0			0
$901$	−6.79870	+	11.7757i	−0.226497	+	0.392305i
$902$	3.46471	+	4.12908i	0.115362	+	0.137483i
$903$	1.04021	+	1.23967i	0.0346160	+	0.0412537i
$904$	−10.5264	+	18.2323i	−0.350104	+	0.606398i
$905$		0			0
$906$	0.643053	+	0.234052i	0.0213640	+	0.00777586i
$907$	35.5251	+	6.26402i	1.17959	+	0.207994i	0.728857	−	0.684666i	$-0.240052\pi$
$907$	35.5251	+	6.26402i	1.17959	+	0.207994i	0.450733	+	0.892659i	$0.351163\pi$
$908$	17.7760	−	3.13439i	0.589918	−	0.104019i
$909$	−52.7714	+	19.2072i	−1.75032	+	0.637063i
$910$		0			0
$911$	−51.0528			−1.69145			−0.845727	−	0.533615i	$-0.820833\pi$
$911$	−51.0528			−1.69145			−0.845727	+	0.533615i	$0.820833\pi$
$912$	2.73944	−	2.61863i	0.0907119	−	0.0867115i
$913$			8.93370i			0.295662i
$914$	51.1761	+	42.9419i	1.69276	+	1.42039i
$915$		0			0
$916$	1.96713	+	11.1562i	0.0649960	+	0.368610i
$917$	15.6356	+	2.75699i	0.516335	+	0.0910437i
$918$	−2.62764	+	7.21939i	−0.0867251	+	0.238275i
$919$	20.6112	+	35.6996i	0.679900	+	1.17762i	0.975011	+	0.222159i	$0.0713103\pi$
$919$	20.6112	+	35.6996i	0.679900	+	1.17762i	−0.295110	+	0.955463i	$0.595356\pi$
$920$		0			0
$921$	−2.03115	+	1.70434i	−0.0669287	+	0.0561598i
$922$	−30.0515	−	35.8140i	−0.989695	−	1.17947i
$923$	25.3777	+	14.6518i	0.835318	+	0.482271i
$924$	−0.409546	−	0.709355i	−0.0134731	−	0.0233361i
$925$		0			0
$926$	−11.2228	+	63.6475i	−0.368803	+	2.09159i
$927$	−34.0411	+	6.00237i	−1.11806	+	0.197144i
$928$	−4.91653	−	13.5081i	−0.161393	−	0.443424i
$929$	−9.91750	−	8.32177i	−0.325383	−	0.273029i	0.465433	−	0.885083i	$-0.345899\pi$
$929$	−9.91750	−	8.32177i	−0.325383	−	0.273029i	−0.790815	+	0.612055i	$0.790343\pi$
$930$		0			0
$931$	22.8526	+	11.2903i	0.748963	+	0.370025i
$932$			20.4616i			0.670241i
$933$	1.27573	−	1.52036i	0.0417656	−	0.0497743i
$934$	−12.1497	+	4.42212i	−0.397549	+	0.144696i
$935$		0			0
$936$	1.73861	−	9.86015i	0.0568283	−	0.322289i
$937$	10.6297	−	29.2049i	0.347258	−	0.954082i	−0.635972	−	0.771712i	$-0.719401\pi$
$937$	10.6297	−	29.2049i	0.347258	−	0.954082i	0.983230	−	0.182370i	$-0.0583770\pi$
$938$	−21.7225	+	12.5415i	−0.709263	+	0.409493i
$939$	1.20646	−	2.08964i	0.0393712	−	0.0681929i
$940$		0			0
$941$	1.29987	−	1.09072i	0.0423745	−	0.0355564i	−0.621354	−	0.783530i	$-0.713417\pi$
$941$	1.29987	−	1.09072i	0.0423745	−	0.0355564i	0.663729	+	0.747973i	$0.268973\pi$
$942$	3.21883	+	1.85839i	0.104875	+	0.0605498i
$943$	1.36112	−	0.785845i	0.0443243	−	0.0255906i
$944$	6.85844	+	2.49627i	0.223223	+	0.0812466i
$945$		0			0
$946$	8.89029	+	50.4193i	0.289048	+	1.63927i
$947$	16.1177	+	44.2831i	0.523756	+	1.43901i	0.866309	+	0.499509i	$0.166486\pi$
$947$	16.1177	+	44.2831i	0.523756	+	1.43901i	−0.342553	+	0.939499i	$0.611291\pi$
$948$	−0.973563	+	1.16025i	−0.0316198	+	0.0376831i
$949$	6.93813			0.225221
$950$		0			0
$951$	−1.53815			−0.0498779
$952$	−3.50256	+	4.17418i	−0.113518	+	0.135286i
$953$	17.6855	+	48.5905i	0.572889	+	1.57400i	0.799917	+	0.600111i	$0.204877\pi$
$953$	17.6855	+	48.5905i	0.572889	+	1.57400i	−0.227028	+	0.973888i	$0.572901\pi$
$954$	−3.18415	−	18.0582i	−0.103091	−	0.584656i
$955$		0			0
$956$	16.9208	+	6.15868i	0.547259	+	0.199186i
$957$	−1.14360	+	0.660258i	−0.0369674	+	0.0213431i
$958$	−13.8676	−	8.00649i	−0.448043	−	0.258678i
$959$	−2.95731	+	2.48147i	−0.0954964	+	0.0801310i
$960$		0			0
$961$	−16.9232	+	29.3118i	−0.545909	+	0.945541i
$962$	−23.6203	+	13.6372i	−0.761548	+	0.439680i
$963$	11.5706	−	31.7898i	0.372856	−	1.02441i
$964$	−2.75214	+	15.6082i	−0.0886405	+	0.502705i
$965$		0			0
$966$	−0.569296	+	0.207207i	−0.0183168	+	0.00666677i
$967$	7.44284	−	8.87003i	0.239346	−	0.285241i	−0.632978	−	0.774170i	$-0.718168\pi$
$967$	7.44284	−	8.87003i	0.239346	−	0.285241i	0.872324	+	0.488929i	$0.162612\pi$
$968$		−	0.0544390i		−	0.00174973i
$969$	0.866223	−	2.96386i	0.0278271	−	0.0952128i
$970$		0			0
$971$	−45.4143	−	38.1071i	−1.45742	−	1.22292i	−0.926937	−	0.375218i	$-0.877568\pi$
$971$	−45.4143	−	38.1071i	−1.45742	−	1.22292i	−0.530478	−	0.847698i	$-0.677988\pi$
$972$	−2.09910	−	5.76722i	−0.0673286	−	0.184984i
$973$	−6.18930	+	1.09134i	−0.198420	+	0.0349868i
$974$	1.50916	−	8.55889i	0.0483567	−	0.274245i
$975$		0			0
$976$	33.7002	+	58.3705i	1.07872	+	1.86839i
$977$	−19.0420	−	10.9939i	−0.609209	−	0.351727i	0.163447	−	0.986552i	$-0.447739\pi$
$977$	−19.0420	−	10.9939i	−0.609209	−	0.351727i	−0.772656	+	0.634825i	$0.781072\pi$
$978$	−3.81254	−	4.54361i	−0.121912	−	0.145288i
$979$	2.00281	−	1.68056i	0.0640101	−	0.0537108i
$980$		0			0
$981$	−18.9065	−	32.7469i	−0.603636	−	1.04553i
$982$	6.25869	−	17.1956i	0.199723	−	0.548734i
$983$	−19.4068	−	3.42195i	−0.618982	−	0.109143i	−0.144641	−	0.989484i	$-0.546203\pi$
$983$	−19.4068	−	3.42195i	−0.618982	−	0.109143i	−0.474341	+	0.880341i	$0.657314\pi$
$984$	−0.0349761	−	0.198359i	−0.00111500	−	0.00632346i
$985$		0			0
$986$	−12.5410	−	10.5231i	−0.399386	−	0.335125i
$987$		−	1.19699i		−	0.0381007i
$988$	1.65237	−	14.9871i	0.0525690	−	0.476802i
$989$	14.9284			0.474695
$990$		0			0
$991$	43.9295	−	15.9890i	1.39547	−	0.507909i	0.468638	−	0.883390i	$-0.344745\pi$
$991$	43.9295	−	15.9890i	1.39547	−	0.507909i	0.926830	+	0.375482i	$0.122523\pi$
$992$	−50.6097	+	8.92386i	−1.60686	+	0.283333i
$993$	4.07080	+	0.717792i	0.129183	+	0.0227785i
$994$	20.2097	+	7.35575i	0.641014	+	0.233310i
$995$		0			0
$996$	−0.311065	+	0.538781i	−0.00985649	+	0.0170719i
$997$	7.46351	+	8.89467i	0.236372	+	0.281697i	0.871170	−	0.490981i	$-0.163361\pi$
$997$	7.46351	+	8.89467i	0.236372	+	0.281697i	−0.634799	+	0.772678i	$0.718917\pi$
$998$	2.24497	+	2.67545i	0.0710632	+	0.0846898i
$999$	2.98520	−	5.17051i	0.0944474	−	0.163588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.c.149.1		36
5.2	odd	4		475.2.l.b.301.1		18
5.3	odd	4		95.2.k.b.16.3	yes	18
5.4	even	2	inner	475.2.u.c.149.6		36
15.8	even	4		855.2.bs.b.586.1		18
19.6	even	9	inner	475.2.u.c.424.6		36
95.33	even	36		1805.2.a.u.1.2		9
95.43	odd	36		1805.2.a.t.1.8		9
95.44	even	18	inner	475.2.u.c.424.1		36
95.52	even	36		9025.2.a.cd.1.8		9
95.62	odd	36		9025.2.a.ce.1.2		9
95.63	odd	36		95.2.k.b.6.3	✓	18
95.82	odd	36		475.2.l.b.101.1		18
285.158	even	36		855.2.bs.b.766.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.6.3	✓	18	95.63	odd	36
95.2.k.b.16.3	yes	18	5.3	odd	4
475.2.l.b.101.1		18	95.82	odd	36
475.2.l.b.301.1		18	5.2	odd	4
475.2.u.c.149.1		36	1.1	even	1	trivial
475.2.u.c.149.6		36	5.4	even	2	inner
475.2.u.c.424.1		36	95.44	even	18	inner
475.2.u.c.424.6		36	19.6	even	9	inner
855.2.bs.b.586.1		18	15.8	even	4
855.2.bs.b.766.1		18	285.158	even	36
1805.2.a.t.1.8		9	95.43	odd	36
1805.2.a.u.1.2		9	95.33	even	36
9025.2.a.cd.1.8		9	95.52	even	36
9025.2.a.ce.1.2		9	95.62	odd	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.16796 + 1.39192i) q^{2} +(0.0605732 + 0.166424i) q^{3} +(-0.226016 - 1.28180i) q^{4} +(-0.302396 - 0.110063i) q^{6} +(0.929646 - 0.536732i) q^{7} +(-1.09903 - 0.634528i) q^{8} +(2.27411 - 1.90820i) q^{9} +O(q^{10})\)	\(q+(-1.16796 + 1.39192i) q^{2} +(0.0605732 + 0.166424i) q^{3} +(-0.226016 - 1.28180i) q^{4} +(-0.302396 - 0.110063i) q^{6} +(0.929646 - 0.536732i) q^{7} +(-1.09903 - 0.634528i) q^{8} +(2.27411 - 1.90820i) q^{9} +(1.65508 - 2.86668i) q^{11} +(0.199631 - 0.115257i) q^{12} +(-0.908963 + 2.49736i) q^{13} +(-0.338702 + 1.92087i) q^{14} +(4.61300 - 1.67899i) q^{16} +(2.57109 - 3.06411i) q^{17} +5.39408i q^{18} +(-0.281925 - 4.34977i) q^{19} +(0.145636 + 0.122203i) q^{21} +(2.05712 + 5.65190i) q^{22} +(1.72714 - 0.304541i) q^{23} +(0.0390283 - 0.221341i) q^{24} +(-2.41449 - 4.18202i) q^{26} +(0.915450 + 0.528535i) q^{27} +(-0.898098 - 1.07031i) q^{28} +(-1.72552 + 1.44789i) q^{29} +(4.02636 + 6.97386i) q^{31} +(-2.18269 + 5.99689i) q^{32} +(0.577336 + 0.101800i) q^{33} +(1.26206 + 7.15751i) q^{34} +(-2.95992 - 2.48367i) q^{36} -5.64805i q^{37} +(6.38382 + 4.68794i) q^{38} -0.470678 q^{39} +(0.842126 - 0.306509i) q^{41} +(-0.340195 + 0.0599856i) q^{42} +(8.38279 + 1.47811i) q^{43} +(-4.04858 - 1.47356i) q^{44} +(-1.59333 + 2.75973i) q^{46} +(-4.04709 - 4.82313i) q^{47} +(0.558849 + 0.666010i) q^{48} +(-2.92384 + 5.06424i) q^{49} +(0.665679 + 0.242287i) q^{51} +(3.40655 + 0.600667i) q^{52} +(-3.34778 + 0.590304i) q^{53} +(-1.80489 + 0.656926i) q^{54} -1.36228 q^{56} +(0.706828 - 0.310399i) q^{57} -4.09287i q^{58} +(1.13893 + 0.955673i) q^{59} +(2.38416 + 13.5212i) q^{61} +(-14.4097 - 2.54082i) q^{62} +(1.08992 - 2.99454i) q^{63} +(-0.888845 - 1.53952i) q^{64} +(-0.816002 + 0.684707i) q^{66} +(8.26605 + 9.85110i) q^{67} +(-4.50868 - 2.60309i) q^{68} +(0.155301 + 0.268989i) q^{69} +(1.91469 - 10.8587i) q^{71} +(-3.71013 + 0.654195i) q^{72} +(-0.892893 - 2.45320i) q^{73} +(7.86164 + 6.59670i) q^{74} +(-5.51182 + 1.34449i) q^{76} -3.55333i q^{77} +(0.549733 - 0.655146i) q^{78} +(-6.17425 + 2.24724i) q^{79} +(1.51398 - 8.58623i) q^{81} +(-0.556934 + 1.53016i) q^{82} +(-2.33730 + 1.34944i) q^{83} +(0.123724 - 0.214297i) q^{84} +(-11.8482 + 9.94180i) q^{86} +(-0.345483 - 0.199465i) q^{87} +(-3.63797 + 2.10038i) q^{88} +(0.742205 + 0.270140i) q^{89} +(0.495396 + 2.80953i) q^{91} +(-0.780722 - 2.14502i) q^{92} +(-0.916725 + 1.09251i) q^{93} +11.4403 q^{94} -1.13024 q^{96} +(12.0317 - 14.3388i) q^{97} +(-3.63409 - 9.98458i) q^{98} +(-1.70638 - 9.67734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) \) 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9	\( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9 - 48 * q^14 + 42 * q^16 + 24 * q^19 + 6 * q^21 - 42 * q^24 - 42 * q^26 + 18 * q^29 + 60 * q^31 - 48 * q^34 - 42 * q^36 - 24 * q^39 - 12 * q^41 + 60 * q^44 + 42 * q^46 + 6 * q^49 + 54 * q^51 - 60 * q^54 - 144 * q^56 - 36 * q^59 + 12 * q^61 + 48 * q^64 - 66 * q^66 - 54 * q^69 + 48 * q^71 + 78 * q^74 + 54 * q^76 - 18 * q^79 + 30 * q^81 + 24 * q^84 - 66 * q^86 + 12 * q^89 - 12 * q^91 + 132 * q^94 - 36 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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