LMFDB - Embedded newform 399.2.ci.b.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [399,2,Mod(17,399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(399, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 3, 10]))

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

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

chi := DirichletCharacter("399.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.ci (of order $18$, degree $6$, 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:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	399.17
Dual form			399.2.ci.b.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.858572 - 2.35891i) q^{2} +(0.919907 - 1.46757i) q^{3} +(-3.29521 + 2.76501i) q^{4} +(-3.13043 - 2.62674i) q^{5} +(-4.25167 - 0.909959i) q^{6} +(1.76041 + 1.97509i) q^{7} +(5.00361 + 2.88883i) q^{8} +(-1.30754 - 2.70006i) q^{9} +(-3.50854 + 9.63963i) q^{10} +(-2.83500 + 1.63679i) q^{11} +(1.02656 + 7.37951i) q^{12} +(-1.14920 - 1.36956i) q^{13} +(3.14761 - 5.84839i) q^{14} +(-6.73463 + 2.17777i) q^{15} +(1.02461 - 5.81084i) q^{16} +(1.91207 + 1.60442i) q^{17} +(-5.24658 + 5.40256i) q^{18} +(-2.95921 - 3.20048i) q^{19} +17.5784 q^{20} +(4.51799 - 0.766630i) q^{21} +(6.29508 + 5.28220i) q^{22} +(5.45691 - 0.962200i) q^{23} +(8.84243 - 4.68570i) q^{24} +(2.03157 + 11.5216i) q^{25} +(-2.24400 + 3.88672i) q^{26} +(-5.16535 - 0.564896i) q^{27} +(-11.2620 - 1.64078i) q^{28} +(-6.98417 + 1.23150i) q^{29} +(10.9193 + 14.0166i) q^{30} -7.26574i q^{31} +(-3.20715 + 0.565506i) q^{32} +(-0.205832 + 5.66626i) q^{33} +(2.14302 - 5.88791i) q^{34} +(-0.322789 - 10.8070i) q^{35} +(11.7743 + 5.28191i) q^{36} +(-1.36448 - 2.36335i) q^{37} +(-5.00895 + 9.72834i) q^{38} +(-3.06709 + 0.426663i) q^{39} +(-8.07521 - 22.1864i) q^{40} +(-3.39108 - 2.84545i) q^{41} +(-5.68743 - 9.99932i) q^{42} +(3.60172 - 1.31092i) q^{43} +(4.81618 - 13.2324i) q^{44} +(-2.99920 + 11.8869i) q^{45} +(-6.95489 - 12.0462i) q^{46} +(-4.51956 + 3.79236i) q^{47} +(-7.58529 - 6.84912i) q^{48} +(-0.801931 + 6.95391i) q^{49} +(25.4341 - 14.6844i) q^{50} +(4.11353 - 1.33019i) q^{51} +(7.57370 + 1.33545i) q^{52} +(-0.210323 - 0.250653i) q^{53} +(3.10229 + 12.6696i) q^{54} +(13.1742 + 2.32296i) q^{55} +(3.10269 + 14.9681i) q^{56} +(-7.41914 + 1.39870i) q^{57} +(8.90140 + 15.4177i) q^{58} +(-4.07006 - 3.41519i) q^{59} +(16.1705 - 25.7975i) q^{60} +(3.06112 - 0.539758i) q^{61} +(-17.1392 + 6.23816i) q^{62} +(3.03105 - 7.33572i) q^{63} +(-1.81294 - 3.14010i) q^{64} +7.30596i q^{65} +(13.5429 - 4.37936i) q^{66} +(-6.95509 - 2.53144i) q^{67} -10.7369 q^{68} +(3.60775 - 8.89354i) q^{69} +(-25.2155 + 10.0400i) q^{70} +(-1.57076 - 4.31564i) q^{71} +(1.25761 - 17.2873i) q^{72} +(-1.52724 - 4.19607i) q^{73} +(-4.40341 + 5.24778i) q^{74} +(18.7776 + 7.61732i) q^{75} +(18.6006 + 2.36403i) q^{76} +(-8.22356 - 2.71796i) q^{77} +(3.63977 + 6.86866i) q^{78} +(-1.27767 + 7.24605i) q^{79} +(-18.4710 + 15.4990i) q^{80} +(-5.58067 + 7.06088i) q^{81} +(-3.80067 + 10.4423i) q^{82} +(1.64914 + 2.85639i) q^{83} +(-12.7680 + 15.0185i) q^{84} +(-1.77121 - 10.0450i) q^{85} +(-6.18466 - 7.37060i) q^{86} +(-4.61748 + 11.3826i) q^{87} -18.9136 q^{88} +(6.28426 + 2.28728i) q^{89} +(30.6151 - 3.13093i) q^{90} +(0.681944 - 4.68075i) q^{91} +(-15.3211 + 18.2590i) q^{92} +(-10.6630 - 6.68381i) q^{93} +(12.8262 + 7.40521i) q^{94} +(0.856739 + 17.7919i) q^{95} +(-2.12036 + 5.22694i) q^{96} +(-6.96973 - 1.22895i) q^{97} +(17.0921 - 4.07875i) q^{98} +(8.12631 + 5.51451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 9 q^{3} - 6 q^{4} - 6 q^{7} - 3 q^{9} - 18 q^{10} - 27 q^{12} - 36 q^{13} - 15 q^{15} + 6 q^{16} - 18 q^{18} - 72 q^{19} + 12 q^{21} - 9 q^{24} + 18 q^{25} + 27 q^{27} - 108 q^{28} - 6 q^{30} - 9 q^{33}+ \cdots - 24 q^{99}+O(q^{100}) $ 288 * q - 9 * q^3 - 6 * q^4 - 6 * q^7 - 3 * q^9 - 18 * q^10 - 27 * q^12 - 36 * q^13 - 15 * q^15 + 6 * q^16 - 18 * q^18 - 72 * q^19 + 12 * q^21 - 9 * q^24 + 18 * q^25 + 27 * q^27 - 108 * q^28 - 6 * q^30 - 9 * q^33 + 36 * q^34 - 84 * q^36 - 24 * q^39 - 144 * q^40 + 39 * q^42 + 12 * q^43 - 6 * q^46 + 63 * q^48 - 30 * q^49 - 3 * q^51 + 90 * q^52 + 9 * q^54 - 90 * q^55 - 66 * q^57 + 24 * q^58 + 42 * q^60 + 54 * q^61 + 60 * q^63 + 54 * q^64 - 27 * q^66 + 102 * q^67 + 60 * q^70 - 39 * q^72 + 36 * q^73 - 63 * q^75 - 87 * q^78 + 6 * q^79 + 45 * q^81 - 18 * q^82 - 117 * q^84 + 36 * q^85 - 9 * q^87 - 204 * q^88 + 144 * q^90 - 198 * q^91 - 60 * q^93 - 180 * q^94 - 243 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.858572	−	2.35891i	−0.607102	−	1.66800i	−0.736526	−	0.676410i	$-0.763535\pi$
$2$	−0.858572	−	2.35891i	−0.607102	−	1.66800i	0.129424	−	0.991589i	$-0.458687\pi$
$3$	0.919907	−	1.46757i	0.531109	−	0.847304i
$3$	0.919907	−	1.46757i	0.531109	−	0.847304i
$4$	−3.29521	+	2.76501i	−1.64760	+	1.38250i
$5$	−3.13043	−	2.62674i	−1.39997	−	1.17471i	−0.961113	−	0.276156i	$-0.910939\pi$
$5$	−3.13043	−	2.62674i	−1.39997	−	1.17471i	−0.438856	−	0.898557i	$-0.644616\pi$
$6$	−4.25167	−	0.909959i	−1.73574	−	0.371489i
$7$	1.76041	+	1.97509i	0.665371	+	0.746512i
$7$	1.76041	+	1.97509i	0.665371	+	0.746512i
$8$	5.00361	+	2.88883i	1.76904	+	1.02136i
$9$	−1.30754	−	2.70006i	−0.435847	−	0.900021i
$10$	−3.50854	+	9.63963i	−1.10950	+	3.04832i
$11$	−2.83500	+	1.63679i	−0.854785	+	0.493510i	−0.862262	−	0.506462i	$-0.830953\pi$
$11$	−2.83500	+	1.63679i	−0.854785	+	0.493510i	0.00747750	+	0.999972i	$0.497620\pi$
$12$	1.02656	+	7.37951i	0.296344	+	2.13028i
$13$	−1.14920	−	1.36956i	−0.318730	−	0.379848i	0.582762	−	0.812643i	$-0.301972\pi$
$13$	−1.14920	−	1.36956i	−0.318730	−	0.379848i	−0.901493	+	0.432795i	$0.857528\pi$
$14$	3.14761	−	5.84839i	0.841234	−	1.56305i
$15$	−6.73463	+	2.17777i	−1.73887	+	0.562298i
$16$	1.02461	−	5.81084i	0.256152	−	1.45271i
$17$	1.91207	+	1.60442i	0.463746	+	0.389129i	0.844507	−	0.535545i	$-0.179894\pi$
$17$	1.91207	+	1.60442i	0.463746	+	0.389129i	−0.380761	+	0.924673i	$0.624338\pi$
$18$	−5.24658	+	5.40256i	−1.23663	+	1.27340i
$19$	−2.95921	−	3.20048i	−0.678888	−	0.734241i
$19$	−2.95921	−	3.20048i	−0.678888	−	0.734241i
$20$	17.5784			3.93064
$21$	4.51799	−	0.766630i	0.985907	−	0.167292i
$22$	6.29508	+	5.28220i	1.34212	+	1.12617i
$23$	5.45691	−	0.962200i	1.13784	−	0.200633i	0.427181	−	0.904166i	$-0.359507\pi$
$23$	5.45691	−	0.962200i	1.13784	−	0.200633i	0.710662	+	0.703533i	$0.248395\pi$
$24$	8.84243	−	4.68570i	1.80495	−	0.956464i
$25$	2.03157	+	11.5216i	0.406313	+	2.30432i
$26$	−2.24400	+	3.88672i	−0.440084	+	0.762249i
$27$	−5.16535	−	0.564896i	−0.994073	−	0.108714i
$28$	−11.2620	−	1.64078i	−2.12832	−	0.310078i
$29$	−6.98417	+	1.23150i	−1.29693	+	0.228683i	−0.779153	−	0.626834i	$-0.784351\pi$
$29$	−6.98417	+	1.23150i	−1.29693	+	0.228683i	−0.517775	+	0.855517i	$0.673239\pi$
$30$	10.9193	+	14.0166i	1.99359	+	2.55907i
$31$		−	7.26574i		−	1.30496i	−0.757804	−	0.652482i	$-0.773728\pi$
$31$		−	7.26574i		−	1.30496i	0.757804	−	0.652482i	$-0.226272\pi$
$32$	−3.20715	+	0.565506i	−0.566949	+	0.0999684i
$33$	−0.205832	+	5.66626i	−0.0358307	+	0.986370i
$34$	2.14302	−	5.88791i	0.367526	−	1.00977i
$35$	−0.322789	−	10.8070i	−0.0545613	−	1.82671i
$36$	11.7743	+	5.28191i	1.96238	+	0.880318i
$37$	−1.36448	−	2.36335i	−0.224319	−	0.388532i	0.731796	−	0.681524i	$-0.238682\pi$
$37$	−1.36448	−	2.36335i	−0.224319	−	0.388532i	−0.956115	+	0.292992i	$0.905349\pi$
$38$	−5.00895	+	9.72834i	−0.812559	+	1.57814i
$39$	−3.06709	+	0.426663i	−0.491127	+	0.0683208i
$40$	−8.07521	−	22.1864i	−1.27680	−	3.50798i
$41$	−3.39108	−	2.84545i	−0.529598	−	0.444385i	0.338365	−	0.941015i	$-0.390126\pi$
$41$	−3.39108	−	2.84545i	−0.529598	−	0.444385i	−0.867962	+	0.496630i	$0.834571\pi$
$42$	−5.68743	−	9.99932i	−0.877590	−	1.54293i
$43$	3.60172	−	1.31092i	0.549257	−	0.199913i	−0.0524596	−	0.998623i	$-0.516706\pi$
$43$	3.60172	−	1.31092i	0.549257	−	0.199913i	0.601716	+	0.798710i	$0.294484\pi$
$44$	4.81618	−	13.2324i	0.726067	−	1.99485i
$45$	−2.99920	+	11.8869i	−0.447094	+	1.77200i
$46$	−6.95489	−	12.0462i	−1.02544	−	1.77612i
$47$	−4.51956	+	3.79236i	−0.659246	+	0.553173i	−0.909861	−	0.414914i	$-0.863812\pi$
$47$	−4.51956	+	3.79236i	−0.659246	+	0.553173i	0.250615	+	0.968087i	$0.419367\pi$
$48$	−7.58529	−	6.84912i	−1.09484	−	0.988585i
$49$	−0.801931	+	6.95391i	−0.114562	+	0.993416i
$50$	25.4341	−	14.6844i	3.59692	−	2.07668i
$51$	4.11353	−	1.33019i	0.576010	−	0.186264i
$52$	7.57370	+	1.33545i	1.05028	+	0.185193i
$53$	−0.210323	−	0.250653i	−0.0288901	−	0.0344299i	0.751406	−	0.659840i	$-0.229376\pi$
$53$	−0.210323	−	0.250653i	−0.0288901	−	0.0344299i	−0.780296	+	0.625410i	$0.784932\pi$
$54$	3.10229	+	12.6696i	0.422168	+	1.72411i
$55$	13.1742	+	2.32296i	1.77641	+	0.313228i
$56$	3.10269	+	14.9681i	0.414615	+	2.00019i
$57$	−7.41914	+	1.39870i	−0.982689	+	0.185263i
$58$	8.90140	+	15.4177i	1.16881	+	2.02444i
$59$	−4.07006	−	3.41519i	−0.529877	−	0.444619i	0.338182	−	0.941081i	$-0.390188\pi$
$59$	−4.07006	−	3.41519i	−0.529877	−	0.444619i	−0.868059	+	0.496461i	$0.834632\pi$
$60$	16.1705	−	25.7975i	2.08760	−	3.33044i
$61$	3.06112	−	0.539758i	0.391936	−	0.0691089i	0.0257927	−	0.999667i	$-0.491789\pi$
$61$	3.06112	−	0.539758i	0.391936	−	0.0691089i	0.366144	+	0.930558i	$0.380678\pi$
$62$	−17.1392	+	6.23816i	−2.17668	+	0.792247i
$63$	3.03105	−	7.33572i	0.381877	−	0.924213i
$64$	−1.81294	−	3.14010i	−0.226617	−	0.392513i
$65$			7.30596i			0.906192i
$66$	13.5429	−	4.37936i	1.66702	−	0.539062i
$67$	−6.95509	−	2.53144i	−0.849699	−	0.309265i	−0.119781	−	0.992800i	$-0.538219\pi$
$67$	−6.95509	−	2.53144i	−0.849699	−	0.309265i	−0.729918	+	0.683535i	$0.760442\pi$
$68$	−10.7369			−1.30204
$69$	3.60775	−	8.89354i	0.434322	−	1.07066i
$70$	−25.2155	+	10.0400i	−3.01383	+	1.20001i
$71$	−1.57076	−	4.31564i	−0.186415	−	0.512172i	0.810917	−	0.585161i	$-0.198968\pi$
$71$	−1.57076	−	4.31564i	−0.186415	−	0.512172i	−0.997333	+	0.0729888i	$0.976746\pi$
$72$	1.25761	−	17.2873i	0.148211	−	2.03733i
$73$	−1.52724	−	4.19607i	−0.178750	−	0.491112i	0.817666	−	0.575692i	$-0.195267\pi$
$73$	−1.52724	−	4.19607i	−0.178750	−	0.491112i	−0.996417	+	0.0845800i	$0.973045\pi$
$74$	−4.40341	+	5.24778i	−0.511886	+	0.610042i
$75$	18.7776	+	7.61732i	2.16825	+	0.879572i
$76$	18.6006	+	2.36403i	2.13363	+	0.271173i
$77$	−8.22356	−	2.71796i	−0.937161	−	0.309740i
$78$	3.63977	+	6.86866i	0.412123	+	0.777722i
$79$	−1.27767	+	7.24605i	−0.143750	+	0.815244i	0.824613	+	0.565697i	$0.191393\pi$
$79$	−1.27767	+	7.24605i	−0.143750	+	0.815244i	−0.968363	+	0.249547i	$0.919718\pi$
$80$	−18.4710	+	15.4990i	−2.06512	+	1.73284i
$81$	−5.58067	+	7.06088i	−0.620075	+	0.784543i
$82$	−3.80067	+	10.4423i	−0.419714	+	1.15316i
$83$	1.64914	+	2.85639i	0.181016	+	0.313530i	0.942227	−	0.334975i	$-0.108728\pi$
$83$	1.64914	+	2.85639i	0.181016	+	0.313530i	−0.761211	+	0.648505i	$0.775395\pi$
$84$	−12.7680	+	15.0185i	−1.39310	+	1.63865i
$85$	−1.77121	−	10.0450i	−0.192115	−	1.08954i
$86$	−6.18466	−	7.37060i	−0.666909	−	0.794792i
$87$	−4.61748	+	11.3826i	−0.495046	+	1.22035i
$88$	−18.9136			−2.01620
$89$	6.28426	+	2.28728i	0.666131	+	0.242452i	0.652881	−	0.757461i	$-0.273560\pi$
$89$	6.28426	+	2.28728i	0.666131	+	0.242452i	0.0132496	+	0.999912i	$0.495782\pi$
$90$	30.6151	−	3.13093i	3.22712	−	0.330029i
$91$	0.681944	−	4.68075i	0.0714872	−	0.490676i
$92$	−15.3211	+	18.2590i	−1.59734	+	1.90364i
$93$	−10.6630	−	6.68381i	−1.10570	−	0.693078i
$94$	12.8262	+	7.40521i	1.32292	+	0.763789i
$95$	0.856739	+	17.7919i	0.0878996	+	1.82541i
$96$	−2.12036	+	5.22694i	−0.216408	+	0.533472i
$97$	−6.96973	−	1.22895i	−0.707669	−	0.124781i	−0.191782	−	0.981438i	$-0.561427\pi$
$97$	−6.96973	−	1.22895i	−0.707669	−	0.124781i	−0.515887	+	0.856656i	$0.672538\pi$
$98$	17.0921	−	4.07875i	1.72657	−	0.412016i
$99$	8.12631	+	5.51451i	0.816725	+	0.554229i
$100$	−38.5517	−	32.3487i	−3.85517	−	3.23487i
$101$	−0.189865	−	1.07678i	−0.0188923	−	0.107143i	0.973903	−	0.226963i	$-0.0728796\pi$
$101$	−0.189865	−	1.07678i	−0.0188923	−	0.107143i	−0.992796	+	0.119819i	$0.961768\pi$
$102$	−6.66955	−	8.56138i	−0.660384	−	0.847703i
$103$		−	18.7189i		−	1.84443i	−0.386676	−	0.922216i	$-0.626377\pi$
$103$		−	18.7189i		−	1.84443i	0.386676	−	0.922216i	$-0.373623\pi$
$104$	−1.79370	−	10.1726i	−0.175887	−	0.997505i
$105$	−16.1570	−	9.46771i	−1.57676	−	0.923954i
$106$	−0.410690	+	0.711337i	−0.0398898	+	0.0690911i
$107$	−8.41625	−	4.85912i	−0.813629	−	0.469749i	0.0345852	−	0.999402i	$-0.488989\pi$
$107$	−8.41625	−	4.85912i	−0.813629	−	0.469749i	−0.848215	+	0.529653i	$0.822322\pi$
$108$	18.5829	−	12.4208i	1.78814	−	1.19519i
$109$	−1.33681	+	7.58142i	−0.128043	+	0.726168i	0.851411	+	0.524500i	$0.175748\pi$
$109$	−1.33681	+	7.58142i	−0.128043	+	0.726168i	−0.979454	+	0.201669i	$0.935364\pi$
$110$	−5.83132	−	33.0711i	−0.555995	−	3.15320i
$111$	−4.72358	−	0.171588i	−0.448342	−	0.0162864i
$112$	13.2806	−	8.20576i	1.25490	−	0.775371i
$113$		−	7.07825i		−	0.665866i	−0.942951	−	0.332933i	$-0.891962\pi$
$113$		−	7.07825i		−	0.665866i	0.942951	−	0.332933i	$-0.108038\pi$
$114$	9.66927	+	16.3002i	0.905610	+	1.52665i
$115$	−19.6099	−	11.3218i	−1.82863	−	1.05576i
$116$	19.6092	−	23.3693i	1.82067	−	2.16979i
$117$	−2.19528	+	4.89367i	−0.202954	+	0.452420i
$118$	−4.56167	+	12.5331i	−0.419936	+	1.15376i
$119$	0.197160	+	6.60094i	0.0180737	+	0.605107i
$120$	−39.9887	−	8.55852i	−3.65045	−	0.781283i
$121$	−0.141846	+	0.245685i	−0.0128951	+	0.0223350i
$122$	−3.90143	−	6.75748i	−0.353219	−	0.611793i
$123$	−7.29539	+	2.35910i	−0.657803	+	0.212713i
$124$	20.0898	+	23.9421i	1.80412	+	2.15006i
$125$	13.6883	−	23.7089i	1.22432	−	2.12059i
$126$	−19.9066	−	0.851730i	−1.77343	−	0.0758781i
$127$	−2.46392	+	2.06747i	−0.218637	+	0.183458i	−0.745527	−	0.666475i	$-0.767802\pi$
$127$	−2.46392	+	2.06747i	−0.218637	+	0.183458i	0.526890	+	0.849933i	$0.323358\pi$
$128$	−10.0373	+	11.9620i	−0.887180	+	1.05730i
$129$	1.38938	−	6.49170i	0.122328	−	0.571563i
$130$	17.2341	−	6.27269i	1.51153	−	0.550151i
$131$	5.71715	−	2.08087i	0.499510	−	0.181807i	−0.0799636	−	0.996798i	$-0.525480\pi$
$131$	5.71715	−	2.08087i	0.499510	−	0.181807i	0.579474	+	0.814991i	$0.303258\pi$
$132$	−14.9890	−	19.2406i	−1.30463	−	1.67468i
$133$	1.11182	−	11.4788i	0.0964073	−	0.995342i
$134$			18.5798i			1.60505i
$135$	14.6859	+	15.3364i	1.26396	+	1.31995i
$136$	4.93236	+	13.5515i	0.422946	+	1.16204i
$137$	−8.90273	−	10.6099i	−0.760611	−	0.906461i	0.237275	−	0.971443i	$-0.423746\pi$
$137$	−8.90273	−	10.6099i	−0.760611	−	0.906461i	−0.997886	+	0.0649811i	$0.979301\pi$
$138$	−24.0766	−	0.874601i	−2.04953	−	0.0744510i
$139$	1.33842	+	1.59507i	0.113524	+	0.135292i	0.819814	−	0.572630i	$-0.194077\pi$
$139$	1.33842	+	1.59507i	0.113524	+	0.135292i	−0.706290	+	0.707923i	$0.749633\pi$
$140$	30.9451	+	34.7188i	2.61534	+	2.93427i
$141$	1.40799	+	10.1214i	0.118574	+	0.852376i
$142$	−8.83157	+	7.41057i	−0.741129	+	0.621881i
$143$	5.49966	+	2.00171i	0.459905	+	0.167392i
$144$	−17.0293	+	4.83140i	−1.41911	+	0.402617i
$145$	25.0982	+	14.4905i	2.08430	+	1.20337i
$146$	−8.58688	+	7.20525i	−0.710655	+	0.596311i
$147$	9.46767	+	7.57385i	0.780880	+	0.624680i
$148$	11.0309	+	4.01492i	0.906735	+	0.330025i
$149$	−5.24708	−	0.925201i	−0.429857	−	0.0757954i	−0.0454663	−	0.998966i	$-0.514477\pi$
$149$	−5.24708	−	0.925201i	−0.429857	−	0.0757954i	−0.384391	+	0.923170i	$0.625588\pi$
$150$	1.84661	−	50.8347i	0.150775	−	4.15063i
$151$	3.86241	−	6.68990i	0.314319	−	0.544416i	−0.664974	−	0.746867i	$-0.731557\pi$
$151$	3.86241	−	6.68990i	0.314319	−	0.544416i	0.979292	+	0.202451i	$0.0648906\pi$
$152$	−5.56104	−	24.5626i	−0.451060	−	1.99229i
$153$	1.83192	−	7.26056i	0.148102	−	0.586981i
$154$	0.649108	+	21.7322i	0.0523066	+	1.75123i
$155$	−19.0852	+	22.7448i	−1.53296	+	1.82691i
$156$	8.92697	−	9.88646i	0.714729	−	0.791551i
$157$	11.1348	+	1.96337i	0.888657	+	0.156694i	0.599298	−	0.800526i	$-0.295447\pi$
$157$	11.1348	+	1.96337i	0.888657	+	0.156694i	0.289360	+	0.957220i	$0.406558\pi$
$158$	18.1897	−	3.20734i	1.44710	−	0.255162i
$159$	−0.561330	+	0.0780867i	−0.0445164	+	0.00619267i
$160$	11.5252	+	6.65406i	0.911145	+	0.526050i
$161$	11.5068	+	9.08400i	0.906863	+	0.715919i
$162$	21.4474	+	7.10202i	1.68507	+	0.557987i
$163$	3.22234			0.252393			0.126197	−	0.992005i	$-0.459723\pi$
$163$	3.22234			0.252393			0.126197	+	0.992005i	$0.459723\pi$
$164$	19.0420			1.48693
$165$	15.5281	−	17.1972i	1.20886	−	1.33880i
$166$	5.32206	−	6.34258i	0.413072	−	0.492280i
$167$	5.27869	+	1.92129i	0.408477	+	0.148674i	0.538083	−	0.842892i	$-0.319149\pi$
$167$	5.27869	+	1.92129i	0.408477	+	0.148674i	−0.129605	+	0.991566i	$0.541371\pi$
$168$	24.8209	+	9.21582i	1.91498	+	0.711016i
$169$	1.70238	−	9.65470i	0.130953	−	0.742669i
$170$	−22.1746	+	12.8025i	−1.70071	+	0.981907i
$171$	−4.77222	+	12.1748i	−0.364941	+	0.931031i
$172$	−8.24370	+	14.2785i	−0.628577	+	1.08873i
$173$	18.7111	−	6.81029i	1.42258	−	0.517777i	0.487784	−	0.872964i	$-0.337805\pi$
$173$	18.7111	−	6.81029i	1.42258	−	0.517777i	0.934795	+	0.355188i	$0.115583\pi$
$174$	30.8150	+	1.11938i	2.33608	+	0.0848601i
$175$	−19.1797	+	24.2952i	−1.44985	+	1.83654i
$176$	6.60635	+	18.1508i	0.497972	+	1.36817i
$177$	−8.75611	+	2.83146i	−0.658150	+	0.212825i
$178$		−	16.7878i		−	1.25830i
$179$	−14.8198	+	8.55622i	−1.10768	+	0.639522i	−0.938229	−	0.346016i	$-0.887534\pi$
$179$	−14.8198	+	8.55622i	−1.10768	+	0.639522i	−0.169455	+	0.985538i	$0.554201\pi$
$180$	−22.9844	−	47.4627i	−1.71316	−	3.53766i
$181$	5.61350	−	0.989812i	0.417248	−	0.0735722i	0.0389172	−	0.999242i	$-0.487609\pi$
$181$	5.61350	−	0.989812i	0.417248	−	0.0735722i	0.378331	+	0.925670i	$0.376498\pi$
$182$	−11.6270	+	2.41012i	−0.861848	+	0.178650i
$183$	2.02381	−	4.98894i	0.149605	−	0.368793i
$184$	30.0838	+	10.9496i	2.21781	+	0.807217i
$185$	−1.93649	+	10.9824i	−0.142374	+	0.807442i
$186$	−6.61152	+	30.8915i	−0.484780	+	2.26508i
$187$	−8.04682	−	1.41887i	−0.588442	−	0.103758i
$188$	4.40698	−	24.9932i	0.321412	−	1.82282i
$189$	−7.97741	−	11.1965i	−0.580271	−	0.814423i
$190$	41.2340	−	17.2966i	2.99143	−	1.25483i
$191$	21.9806	−	12.6905i	1.59046	−	0.918251i	0.597230	−	0.802070i	$-0.296268\pi$
$191$	21.9806	−	12.6905i	1.59046	−	0.918251i	0.993228	−	0.116181i	$-0.0370652\pi$
$192$	−6.27606	−	0.227983i	−0.452936	−	0.0164533i
$193$	14.7816	−	5.38007i	1.06400	−	0.387266i	0.250073	−	0.968227i	$-0.419545\pi$
$193$	14.7816	−	5.38007i	1.06400	−	0.387266i	0.813931	+	0.580961i	$0.197323\pi$
$194$	3.08503	+	17.4961i	0.221492	+	1.25615i
$195$	10.7220	+	6.72080i	0.767820	+	0.481287i
$196$	−16.5851	−	25.1319i	−1.18465	−	1.79514i
$197$	12.9700	−	7.48821i	0.924072	−	0.533513i	0.0391399	−	0.999234i	$-0.487538\pi$
$197$	12.9700	−	7.48821i	0.924072	−	0.533513i	0.884932	+	0.465721i	$0.154205\pi$
$198$	6.03120	−	23.9038i	0.428619	−	1.69877i
$199$	4.18311	−	11.4930i	0.296533	−	0.814718i	−0.698540	−	0.715571i	$-0.746166\pi$
$199$	4.18311	−	11.4930i	0.296533	−	0.814718i	0.995073	−	0.0991467i	$-0.0316113\pi$
$200$	−23.1188	+	63.5183i	−1.63474	+	4.49142i
$201$	−10.1131	+	7.87840i	−0.713324	+	0.555700i
$202$	−2.37700	+	1.37236i	−0.167245	+	0.0965592i
$203$	−14.7273	−	11.6264i	−1.03365	−	0.816013i
$204$	−9.87696	+	15.7572i	−0.691526	+	1.10322i
$205$	3.14126	+	17.8150i	0.219395	+	1.24425i
$206$	−44.1562	+	16.0716i	−3.07651	+	1.11976i
$207$	−9.73313	−	13.4759i	−0.676499	−	0.936638i
$208$	−9.13578	+	5.27455i	−0.633453	+	0.365724i
$209$	13.6279	+	4.22978i	0.942659	+	0.292580i
$210$	−8.46153	+	46.2415i	−0.583901	+	3.19097i
$211$	1.56313	−	8.86496i	0.107610	−	0.610289i	−0.882535	−	0.470246i	$-0.844165\pi$
$211$	1.56313	−	8.86496i	0.107610	−	0.610289i	0.990146	−	0.140042i	$-0.0447239\pi$
$212$	1.38612	+	0.244410i	0.0951989	+	0.0167861i
$213$	−7.77847	−	1.66478i	−0.532972	−	0.114069i
$214$	−4.23627	+	24.0251i	−0.289585	+	1.64232i
$215$	−14.7183	−	5.35704i	−1.00378	−	0.365347i
$216$	−24.2135	−	17.7484i	−1.64752	−	1.20762i
$217$	14.3505	−	12.7907i	0.974172	−	0.868286i
$218$	19.0316	−	3.35579i	1.28898	−	0.227283i
$219$	−7.56295	−	1.61865i	−0.511057	−	0.109378i
$220$	−49.8346	+	28.7720i	−3.35985	+	1.93981i
$221$		−	4.46250i		−	0.300180i
$222$	3.65077	+	11.2898i	0.245024	+	0.757721i
$223$	0.505646	+	1.38925i	0.0338605	+	0.0930311i	0.955471	−	0.295085i	$-0.0953481\pi$
$223$	0.505646	+	1.38925i	0.0338605	+	0.0930311i	−0.921610	+	0.388116i	$0.873126\pi$
$224$	−6.76281	−	5.33887i	−0.451859	−	0.356718i
$225$	28.4526	−	20.5503i	1.89684	−	1.37002i
$226$	−16.6969	+	6.07719i	−1.11066	+	0.404248i
$227$	10.8504	−	18.7935i	0.720168	−	1.24737i	−0.240764	−	0.970584i	$-0.577398\pi$
$227$	10.8504	−	18.7935i	0.720168	−	1.24737i	0.960932	−	0.276784i	$-0.0892686\pi$
$228$	20.5802	−	25.1230i	1.36296	−	1.66381i
$229$	17.7233	−	10.2326i	1.17119	−	0.676187i	0.217230	−	0.976120i	$-0.430298\pi$
$229$	17.7233	−	10.2326i	1.17119	−	0.676187i	0.953960	+	0.299934i	$0.0969646\pi$
$230$	−9.87051	+	55.9785i	−0.650842	+	3.69111i
$231$	−11.5537	+	9.56840i	−0.760178	+	0.629554i
$232$	−38.5036	−	14.0142i	−2.52789	−	0.920076i
$233$	−11.0729	+	13.1961i	−0.725408	+	0.864508i	−0.995144	−	0.0984263i	$-0.968619\pi$
$233$	−11.0729	+	13.1961i	−0.725408	+	0.864508i	0.269736	+	0.962934i	$0.413064\pi$
$234$	13.4285	+	0.976893i	0.877849	+	0.0638615i
$235$	24.1097			1.57274
$236$	22.8547			1.48771
$237$	9.45877	+	8.54078i	0.614413	+	0.554783i
$238$	15.4017	−	6.13246i	0.998346	−	0.397509i
$239$	2.33543	+	1.34836i	0.151066	+	0.0872182i	0.573628	−	0.819116i	$-0.305536\pi$
$239$	2.33543	+	1.34836i	0.151066	+	0.0872182i	−0.422561	+	0.906334i	$0.638869\pi$
$240$	5.75432	+	41.3652i	0.371440	+	2.67011i
$241$	1.92188	−	0.338879i	0.123799	−	0.0218291i	−0.111405	−	0.993775i	$-0.535535\pi$
$241$	1.92188	−	0.338879i	0.123799	−	0.0218291i	0.235204	+	0.971946i	$0.424424\pi$
$242$	0.701334	+	0.123664i	0.0450835	+	0.00794943i
$243$	5.22866	+	14.6854i	0.335418	+	0.942069i
$244$	−8.59459	+	10.2426i	−0.550212	+	0.655717i
$245$	20.7765	−	19.6622i	1.32736	−	1.25617i
$246$	11.8285	+	15.1837i	0.754159	+	0.968076i
$247$	−0.982544	+	7.73081i	−0.0625178	+	0.491900i
$248$	20.9895	−	36.3549i	1.33283	−	2.30854i
$249$	5.70902	+	0.207385i	0.361794	+	0.0131425i
$250$	−67.6794	−	11.9337i	−4.28042	−	0.754754i
$251$	−17.5543	−	6.38926i	−1.10802	−	0.403286i	−0.277753	−	0.960652i	$-0.589590\pi$
$251$	−17.5543	−	6.38926i	−1.10802	−	0.403286i	−0.830267	+	0.557366i	$0.811812\pi$
$252$	10.2954	+	32.5536i	0.648547	+	2.05068i
$253$	−13.8954	+	11.6596i	−0.873597	+	0.733035i
$254$	6.99242	+	4.03708i	0.438744	+	0.253309i
$255$	−16.3712	−	6.64112i	−1.02520	−	0.415883i
$256$	30.0205	+	10.9266i	1.87628	+	0.682912i
$257$	−0.132098	+	0.110844i	−0.00824006	+	0.00691423i	−0.646898	−	0.762576i	$-0.723934\pi$
$257$	−0.132098	+	0.110844i	−0.00824006	+	0.00691423i	0.638658	+	0.769490i	$0.279490\pi$
$258$	−16.5062	+	2.29618i	−1.02763	+	0.142954i
$259$	2.26577	−	6.85541i	0.140788	−	0.425975i
$260$	−20.2010	−	24.0746i	−1.25281	−	1.49305i
$261$	12.4572	+	17.2475i	0.771082	+	1.06759i
$262$	−9.81717	−	11.6997i	−0.606507	−	0.722807i
$263$	4.01329	+	11.0264i	0.247470	+	0.679918i	0.999777	+	0.0211055i	$0.00671857\pi$
$263$	4.01329	+	11.0264i	0.247470	+	0.679918i	−0.752307	+	0.658812i	$0.771059\pi$
$264$	−17.3988	+	27.7571i	−1.07082	+	1.70833i
$265$			1.33712i			0.0821384i
$266$	−28.0321	+	7.23273i	−1.71876	+	0.443467i
$267$	9.13770	−	7.11852i	0.559218	−	0.435647i
$268$	29.9179	−	10.8892i	1.82753	−	0.665165i
$269$	17.2073	−	6.26295i	1.04915	−	0.381859i	0.240807	−	0.970573i	$-0.422588\pi$
$269$	17.2073	−	6.26295i	1.04915	−	0.381859i	0.808341	+	0.588714i	$0.200366\pi$
$270$	23.5682	−	47.8101i	1.43432	−	2.90963i
$271$	5.94060	−	7.07973i	0.360866	−	0.430063i	−0.554812	−	0.831976i	$-0.687210\pi$
$271$	5.94060	−	7.07973i	0.360866	−	0.430063i	0.915678	+	0.401912i	$0.131654\pi$
$272$	11.2821	−	9.46685i	0.684081	−	0.574012i
$273$	−6.24202	−	5.30666i	−0.377784	−	0.321174i
$274$	−17.3840	+	30.1100i	−1.05021	+	1.81901i
$275$	−24.6179	−	29.3384i	−1.48451	−	1.76918i
$276$	12.7024	+	39.2815i	0.764596	+	2.36447i
$277$	−10.5106	−	18.2049i	−0.631519	−	1.09382i	−0.987241	−	0.159232i	$-0.949098\pi$
$277$	−10.5106	−	18.2049i	−0.631519	−	1.09382i	0.355722	−	0.934592i	$-0.384235\pi$
$278$	2.61349	−	4.52670i	0.156747	−	0.271494i
$279$	−19.6179	+	9.50025i	−1.17450	+	0.568765i
$280$	29.6045	−	55.0064i	1.76921	−	3.28726i
$281$	−2.95782	+	8.12653i	−0.176448	+	0.484788i	−0.996116	−	0.0880515i	$-0.971936\pi$
$281$	−2.95782	+	8.12653i	−0.176448	+	0.484788i	0.819667	+	0.572840i	$0.194158\pi$
$282$	22.6666	−	12.0113i	1.34978	−	0.715261i
$283$	−14.4895	+	17.2679i	−0.861312	+	1.02647i	0.138038	+	0.990427i	$0.455920\pi$
$283$	−14.4895	+	17.2679i	−0.861312	+	1.02647i	−0.999350	+	0.0360447i	$0.988524\pi$
$284$	17.1088	+	9.87774i	1.01522	+	0.586136i
$285$	26.8991	+	15.1096i	1.59336	+	0.895016i
$286$		−	14.6918i		−	0.868745i
$287$	−0.349666	−	11.7068i	−0.0206401	−	0.691032i
$288$	5.72038	+	7.92007i	0.337076	+	0.466695i
$289$	−1.87016	−	10.6062i	−0.110009	−	0.623894i
$290$	12.6330	−	71.6456i	0.741838	−	4.20717i
$291$	−8.21509	+	9.09807i	−0.481577	+	0.533338i
$292$	16.6347	+	9.60407i	0.973474	+	0.562036i
$293$	10.9443	−	18.9560i	0.639371	−	1.10742i	−0.346200	−	0.938161i	$-0.612528\pi$
$293$	10.9443	−	18.9560i	0.639371	−	1.10742i	0.985571	−	0.169262i	$-0.0541384\pi$
$294$	9.73733	−	28.8361i	0.567892	−	1.68175i
$295$	3.77022	+	21.3820i	0.219511	+	1.24491i
$296$		−	15.7670i		−	0.916438i
$297$	15.5684	−	6.85311i	0.903370	−	0.397658i
$298$	2.32253	+	13.1717i	0.134540	+	0.763017i
$299$	−7.58886	−	6.36781i	−0.438875	−	0.368260i
$300$	−82.9381	+	26.8196i	−4.78843	+	1.54843i
$301$	8.92966	+	4.80595i	0.514697	+	0.277010i
$302$	−19.0970	−	3.36732i	−1.09891	−	0.193767i
$303$	−1.75491	−	0.711895i	−0.100817	−	0.0408973i
$304$	−21.6295	+	13.9162i	−1.24054	+	0.798151i
$305$	−11.0004	−	6.35109i	−0.629882	−	0.363662i
$306$	−18.6998	+	1.91238i	−1.06900	+	0.109324i
$307$	−19.6955	+	23.4722i	−1.12408	+	1.33963i	−0.190326	+	0.981721i	$0.560954\pi$
$307$	−19.6955	+	23.4722i	−1.12408	+	1.33963i	−0.933757	+	0.357908i	$0.883490\pi$
$308$	34.6135	−	13.7820i	1.97229	−	0.785300i
$309$	−27.4714	−	17.2197i	−1.56279	−	0.979594i
$310$	70.0390	+	25.4921i	3.97795	+	1.44785i
$311$	11.8875			0.674076			0.337038	−	0.941491i	$-0.390575\pi$
$311$	11.8875			0.674076			0.337038	+	0.941491i	$0.390575\pi$
$312$	−16.5791	−	6.72545i	−0.938605	−	0.380754i
$313$	−4.32568	−	5.15514i	−0.244502	−	0.291386i	0.629811	−	0.776748i	$-0.283132\pi$
$313$	−4.32568	−	5.15514i	−0.244502	−	0.291386i	−0.874313	+	0.485362i	$0.838688\pi$
$314$	−4.92865	−	27.9518i	−0.278140	−	1.57741i
$315$	−28.7575	+	15.0021i	−1.62030	+	0.845274i
$316$	−15.8252	−	27.4100i	−0.890236	−	1.54193i
$317$	−5.05778	+	13.8961i	−0.284073	+	0.780485i	0.712793	+	0.701375i	$0.247430\pi$
$317$	−5.05778	+	13.8961i	−0.284073	+	0.780485i	−0.996866	+	0.0791101i	$0.974792\pi$
$318$	0.666141	+	1.25708i	0.0373553	+	0.0704937i
$319$	17.7844	−	14.9229i	0.995737	−	0.835522i
$320$	−2.57296	+	14.5920i	−0.143833	+	0.815716i
$321$	−14.8733	+	7.88152i	−0.830146	+	0.439903i
$322$	11.5489	−	34.9428i	0.643594	−	1.94728i
$323$	−0.523299	−	10.8674i	−0.0291171	−	0.604676i
$324$	−1.13391	−	38.6977i	−0.0629951	−	2.14987i
$325$	13.4448	−	16.0229i	0.745786	−	0.888793i
$326$	−2.76661	−	7.60120i	−0.153228	−	0.420992i
$327$	9.89655	+	8.93607i	0.547280	+	0.494166i
$328$	−8.74759	−	24.0338i	−0.483005	−	1.32704i
$329$	−15.4465	−	2.25042i	−0.851594	−	0.124070i
$330$	−53.8985	−	21.8644i	−2.96702	−	1.20360i
$331$	−7.73956			−0.425405			−0.212702	−	0.977117i	$-0.568226\pi$
$331$	−7.73956			−0.425405			−0.212702	+	0.977117i	$0.568226\pi$
$332$	−13.3322	−	4.85252i	−0.731699	−	0.266317i
$333$	−4.59707	+	6.77435i	−0.251918	+	0.371232i
$334$		−	14.1015i		−	0.771600i
$335$	15.1229	+	26.1937i	0.826254	+	1.43111i
$336$	0.174409	−	27.0388i	0.00951481	−	1.47509i
$337$	−23.8257	+	8.67184i	−1.29787	+	0.472385i	−0.896302	−	0.443445i	$-0.853756\pi$
$337$	−23.8257	+	8.67184i	−1.29787	+	0.472385i	−0.401566	+	0.915830i	$0.631534\pi$
$338$	−24.2362	+	4.27349i	−1.31827	+	0.232447i
$339$	−10.3878	−	6.51134i	−0.564191	−	0.353647i
$340$	33.6111	+	28.2030i	1.82282	+	1.52953i
$341$	11.8925	+	20.5984i	0.644014	+	1.11546i
$342$	32.8165	+	0.804287i	1.77451	+	0.0434909i
$343$	−15.1463	+	10.6578i	−0.817823	+	0.575469i
$344$	21.8086	+	3.84544i	1.17584	+	0.207332i
$345$	−34.6548	+	18.3640i	−1.86575	+	0.988682i
$346$	−32.1297	−	38.2906i	−1.72730	−	2.05852i
$347$	30.7718	+	5.42590i	1.65192	+	0.291278i	0.920526	−	0.390680i	$-0.127760\pi$
$347$	30.7718	+	5.42590i	1.65192	+	0.291278i	0.731391	+	0.681958i	$0.238871\pi$
$348$	−16.2575	−	50.2755i	−0.871496	−	2.69505i
$349$	−20.5544	+	11.8671i	−1.10025	+	0.635232i	−0.936288	−	0.351234i	$-0.885762\pi$
$349$	−20.5544	+	11.8671i	−1.10025	+	0.635232i	−0.163966	+	0.986466i	$0.552429\pi$
$350$	73.7773	+	24.3840i	3.94356	+	1.30338i
$351$	5.16236	+	7.72345i	0.275546	+	0.412247i
$352$	8.16665	−	6.85263i	0.435284	−	0.365247i
$353$	15.3692	+	26.6203i	0.818021	+	1.41685i	0.907139	+	0.420832i	$0.138262\pi$
$353$	15.3692	+	26.6203i	0.818021	+	1.41685i	−0.0891180	+	0.996021i	$0.528405\pi$
$354$	14.1969	+	18.2239i	0.754556	+	0.968587i
$355$	−6.41889	+	17.6358i	−0.340679	+	0.936009i
$356$	−27.0323	+	9.83896i	−1.43271	+	0.521464i
$357$	9.86873	+	5.78291i	0.522309	+	0.306064i
$358$	32.9072	+	27.6124i	1.73920	+	1.45936i
$359$	6.61601	+	18.1773i	0.349180	+	0.959363i	0.982629	+	0.185579i	$0.0594161\pi$
$359$	6.61601	+	18.1773i	0.349180	+	0.959363i	−0.633450	+	0.773784i	$0.718362\pi$
$360$	−49.3461	+	50.8132i	−2.60077	+	2.67809i
$361$	−1.48620	+	18.9418i	−0.0782208	+	0.996936i
$362$	−7.15447	−	12.3919i	−0.376031	−	0.651304i
$363$	0.230075	+	0.434178i	0.0120758	+	0.0227884i
$364$	10.6952	+	17.3096i	0.560579	+	0.907271i
$365$	−6.24105	+	17.1471i	−0.326671	+	0.897522i
$366$	−13.5060	−	0.490618i	−0.705972	−	0.0256450i
$367$	−21.0951	+	3.71964i	−1.10116	+	0.194164i	−0.694553	−	0.719441i	$-0.744398\pi$
$367$	−21.0951	+	3.71964i	−1.10116	+	0.194164i	−0.406603	+	0.913605i	$0.633287\pi$
$368$		−	32.6951i		−	1.70435i
$369$	−3.24893	+	12.8767i	−0.169132	+	0.670333i
$370$	27.5691	−	4.86117i	1.43325	−	0.252720i
$371$	0.124808	−	0.856658i	0.00647968	−	0.0444755i
$372$	53.6176	−	7.45874i	2.77994	−	0.386718i
$373$	7.76334	−	13.4465i	0.401970	−	0.696233i	−0.591993	−	0.805943i	$-0.701659\pi$
$373$	7.76334	−	13.4465i	0.401970	−	0.696233i	0.993964	+	0.109710i	$0.0349921\pi$
$374$	3.56179	+	20.1999i	0.184176	+	1.04451i
$375$	−22.2025	−	41.8986i	−1.14653	−	2.16363i
$376$	−33.5696	+	5.91923i	−1.73122	+	0.305261i
$377$	9.71281	+	8.15002i	0.500235	+	0.419747i
$378$	−19.5622	+	28.4309i	−1.00617	+	1.46233i
$379$	3.06692			0.157537			0.0787685	−	0.996893i	$-0.474901\pi$
$379$	3.06692			0.157537			0.0787685	+	0.996893i	$0.474901\pi$
$380$	−52.0180	−	56.2592i	−2.66847	−	2.88604i
$381$	0.767590	+	5.51786i	0.0393248	+	0.282689i
$382$	−48.8076	−	40.9544i	−2.49721	−	2.09541i
$383$	2.81902	−	15.9875i	0.144045	−	0.816922i	−0.824083	−	0.566469i	$-0.808309\pi$
$383$	2.81902	−	15.9875i	0.144045	−	0.816922i	0.968129	−	0.250453i	$-0.0805797\pi$
$384$	8.32170	+	25.7344i	0.424665	+	1.31325i
$385$	18.6039	+	30.1095i	0.948141	+	1.53452i
$386$	−25.3822	−	30.2493i	−1.29192	−	1.53965i
$387$	−8.24895	−	8.01078i	−0.419318	−	0.407211i
$388$	26.3648	−	15.2217i	1.33847	−	0.772765i
$389$	0.290403	−	0.797875i	0.0147240	−	0.0404539i	−0.932113	−	0.362168i	$-0.882037\pi$
$389$	0.290403	−	0.797875i	0.0147240	−	0.0404539i	0.946837	+	0.321714i	$0.104259\pi$
$390$	6.64812	−	31.0625i	0.336641	−	1.57291i
$391$	11.9778	+	6.91537i	0.605742	+	0.349725i
$392$	−24.1012	+	32.4780i	−1.21730	+	1.64039i
$393$	2.20542	−	10.3045i	0.111249	−	0.519796i
$394$	−28.7996	−	24.1658i	−1.45091	−	1.21745i
$395$	23.0331	−	19.3271i	1.15892	−	0.972452i
$396$	−42.0255	+	4.29785i	−2.11186	+	0.215975i
$397$	−0.984899	−	2.70599i	−0.0494307	−	0.135810i	0.912521	−	0.409031i	$-0.134133\pi$
$397$	−0.984899	−	2.70599i	−0.0494307	−	0.135810i	−0.961951	+	0.273221i	$0.911911\pi$
$398$	−30.7024			−1.53897
$399$	−15.8233	−	12.1912i	−0.792154	−	0.610321i
$400$	69.0316			3.45158
$401$	1.38384	+	3.80208i	0.0691058	+	0.189867i	0.969438	−	0.245337i	$-0.0788986\pi$
$401$	1.38384	+	3.80208i	0.0691058	+	0.189867i	−0.900332	+	0.435204i	$0.856676\pi$
$402$	27.2672	+	17.0917i	1.35997	+	0.852457i
$403$	−9.95088	+	8.34978i	−0.495688	+	0.415932i
$404$	3.60294	+	3.02323i	0.179253	+	0.150411i
$405$	36.0170	−	7.44459i	1.78970	−	0.369925i
$406$	−14.7812	+	44.7224i	−0.733576	+	2.21954i
$407$	7.73659	+	4.46672i	0.383489	+	0.221407i
$408$	24.4252	+	5.22757i	1.20923	+	0.258803i
$409$	4.87787	−	13.4018i	0.241195	−	0.662679i	−0.758741	−	0.651392i	$-0.774185\pi$
$409$	4.87787	−	13.4018i	0.241195	−	0.662679i	0.999936	−	0.0112862i	$-0.00359257\pi$
$410$	39.3268	−	22.7054i	1.94221	−	1.12134i
$411$	−23.7604	+	3.30532i	−1.17202	+	0.163039i
$412$	51.7580	+	61.6828i	2.54993	+	3.03889i
$413$	−0.419678	−	14.0508i	−0.0206510	−	0.691397i
$414$	−23.4317	+	34.5295i	−1.15161	+	1.69703i
$415$	2.34049	−	13.2736i	0.114890	−	0.651574i
$416$	4.46015	+	3.74251i	0.218677	+	0.183491i
$417$	3.57211	−	0.496917i	0.174927	−	0.0243341i
$418$	−1.72285	−	35.7784i	−0.0842672	−	1.74998i
$419$	−34.1484			−1.66826			−0.834130	−	0.551568i	$-0.814030\pi$
$419$	−34.1484			−1.66826			−0.834130	+	0.551568i	$0.814030\pi$
$420$	79.4189	−	13.4761i	3.87525	−	0.657566i
$421$	−6.51592	−	5.46751i	−0.317567	−	0.266470i	0.470044	−	0.882643i	$-0.344238\pi$
$421$	−6.51592	−	5.46751i	−0.317567	−	0.266470i	−0.787611	+	0.616173i	$0.788682\pi$
$422$	−22.2537	+	3.92392i	−1.08329	+	0.191014i
$423$	16.1491	+	7.24443i	0.785197	+	0.352236i
$424$	−0.328278	−	1.86176i	−0.0159426	−	0.0904150i
$425$	−14.6009	+	25.2896i	−0.708250	+	1.22672i
$426$	2.75132	+	19.7780i	0.133302	+	0.958248i
$427$	6.45489	+	5.09578i	0.312374	+	0.246602i
$428$	41.1688	−	7.25917i	1.98997	−	0.350885i
$429$	7.99684	−	6.22977i	0.386091	−	0.300776i
$430$			39.3186i			1.89611i
$431$	14.1609	−	2.49694i	0.682104	−	0.120273i	0.178150	−	0.984003i	$-0.442989\pi$
$431$	14.1609	−	2.49694i	0.682104	−	0.120273i	0.503955	+	0.863730i	$0.331878\pi$
$432$	−8.57498	+	29.4363i	−0.412564	+	1.41625i
$433$	9.35717	−	25.7086i	0.449677	−	1.23548i	−0.483273	−	0.875470i	$-0.660552\pi$
$433$	9.35717	−	25.7086i	0.449677	−	1.23548i	0.932949	−	0.360007i	$-0.117226\pi$
$434$	−42.4929	−	22.8697i	−2.03972	−	1.09778i
$435$	44.3539	−	23.5036i	2.12661	−	1.12691i
$436$	−16.5576	−	28.6786i	−0.792966	−	1.37346i
$437$	−19.2276	−	14.6174i	−0.919782	−	0.699245i
$438$	2.67509	+	19.2300i	0.127821	+	0.918847i
$439$	9.20897	+	25.3014i	0.439520	+	1.20757i	0.939805	+	0.341711i	$0.111006\pi$
$439$	9.20897	+	25.3014i	0.439520	+	1.20757i	−0.500285	+	0.865861i	$0.666771\pi$
$440$	59.2077	+	49.6812i	2.82262	+	2.36846i
$441$	19.8246	−	6.92726i	0.944027	−	0.329870i
$442$	−10.5266	+	3.83138i	−0.500700	+	0.182240i
$443$	−11.7693	+	32.3359i	−0.559176	+	1.53632i	0.261661	+	0.965160i	$0.415730\pi$
$443$	−11.7693	+	32.3359i	−0.559176	+	1.53632i	−0.820837	+	0.571163i	$0.806492\pi$
$444$	16.0396	−	12.4953i	0.761206	−	0.593001i
$445$	−13.6643	−	23.6673i	−0.647751	−	1.12194i
$446$	2.84298	−	2.38554i	0.134619	−	0.112959i
$447$	−6.18462	+	6.84937i	−0.292523	+	0.323964i
$448$	3.01046	−	9.10857i	0.142231	−	0.430339i
$449$	−18.2172	+	10.5177i	−0.859724	+	0.496362i	−0.863920	−	0.503629i	$-0.831998\pi$
$449$	−18.2172	+	10.5177i	−0.859724	+	0.496362i	0.00419561	+	0.999991i	$0.498664\pi$
$450$	−72.9049	−	49.4732i	−3.43677	−	2.33219i
$451$	14.2711	+	2.51638i	0.672001	+	0.118492i
$452$	19.5714	+	23.3243i	0.920562	+	1.09708i
$453$	−6.26485	−	11.8225i	−0.294348	−	0.555468i
$454$	−53.6480	−	9.45958i	−2.51782	−	0.443960i
$455$	−14.4299	+	12.8615i	−0.676484	+	0.602955i
$456$	−41.1631	−	14.4341i	−1.92764	−	0.675939i
$457$	12.8446	+	22.2476i	0.600846	+	1.04070i	0.992693	+	0.120666i	$0.0385030\pi$
$457$	12.8446	+	22.2476i	0.600846	+	1.04070i	−0.391847	+	0.920031i	$0.628164\pi$
$458$	−39.3544	−	33.0223i	−1.83891	−	1.54303i
$459$	−8.97020	−	9.36752i	−0.418693	−	0.437238i
$460$	95.9234	−	16.9139i	4.47245	−	0.788614i
$461$	−8.38726	+	3.05271i	−0.390634	+	0.142179i	−0.529867	−	0.848080i	$-0.677758\pi$
$461$	−8.38726	+	3.05271i	−0.390634	+	0.142179i	0.139234	+	0.990260i	$0.455536\pi$
$462$	32.4907	+	19.0390i	1.51160	+	0.885773i
$463$	−1.47312	−	2.55152i	−0.0684618	−	0.118579i	0.829763	−	0.558116i	$-0.188476\pi$
$463$	−1.47312	−	2.55152i	−0.0684618	−	0.118579i	−0.898224	+	0.439537i	$0.855142\pi$
$464$			41.8457i			1.94264i
$465$	15.8231	+	48.9321i	0.733779	+	2.26917i
$466$	40.6353	+	14.7901i	1.88240	+	0.685136i
$467$	−26.0250			−1.20429			−0.602146	−	0.798386i	$-0.705687\pi$
$467$	−26.0250			−1.20429			−0.602146	+	0.798386i	$0.705687\pi$
$468$	−6.29713	−	22.1956i	−0.291085	−	1.02599i
$469$	−7.24396	−	18.1933i	−0.334495	−	0.840087i
$470$	−20.6999	−	56.8725i	−0.954815	−	2.62333i
$471$	13.1244	−	14.5351i	0.604741	−	0.669741i
$472$	−10.4991	−	28.8460i	−0.483259	−	1.32774i
$473$	−8.06517	+	9.61170i	−0.370837	+	0.441946i
$474$	12.0259	−	29.6452i	0.552366	−	1.36165i
$475$	30.8628	−	40.5967i	1.41608	−	1.86271i
$476$	−18.9013	−	21.2063i	−0.866341	−	0.971990i
$477$	−0.401774	+	0.895625i	−0.0183960	+	0.0410079i
$478$	1.17552	−	6.66672i	0.0537672	−	0.304929i
$479$	−5.34265	+	4.48302i	−0.244112	+	0.204834i	−0.756632	−	0.653841i	$-0.773156\pi$
$479$	−5.34265	+	4.48302i	−0.244112	+	0.204834i	0.512520	+	0.858675i	$0.328712\pi$
$480$	20.3674	−	10.7929i	0.929641	−	0.492627i
$481$	−1.66869	+	4.58469i	−0.0760858	+	0.209044i
$482$	−2.44945	−	4.24257i	−0.111569	−	0.193244i
$483$	23.9166	−	8.53064i	1.08824	−	0.388158i
$484$	−0.211908	−	1.20179i	−0.00963219	−	0.0546268i
$485$	18.5901	+	22.1548i	0.844133	+	1.00600i
$486$	30.1523	−	24.9424i	1.36774	−	1.13141i
$487$	−26.8873			−1.21838			−0.609190	−	0.793025i	$-0.708505\pi$
$487$	−26.8873			−1.21838			−0.609190	+	0.793025i	$0.708505\pi$
$488$	16.8759	+	6.14233i	0.763937	+	0.278050i
$489$	2.96426	−	4.72902i	0.134048	−	0.213854i
$490$	−64.2195	−	32.1284i	−2.90114	−	1.45141i
$491$	3.79708	−	4.52519i	0.171360	−	0.204219i	−0.673529	−	0.739161i	$-0.735222\pi$
$491$	3.79708	−	4.52519i	0.171360	−	0.204219i	0.844889	+	0.534942i	$0.179667\pi$
$492$	17.5169	−	27.9455i	0.789722	−	1.25988i
$493$	−15.3301	−	8.85083i	−0.690432	−	0.398621i
$494$	19.0798	−	4.31972i	0.858443	−	0.194354i
$495$	−10.9536	−	38.6085i	−0.492329	−	1.73532i
$496$	−42.2200	−	7.44453i	−1.89574	−	0.334269i
$497$	5.75857	−	10.6997i	0.258307	−	0.479946i
$498$	−4.41240	−	13.6451i	−0.197724	−	0.611451i
$499$	13.7450	+	11.5334i	0.615309	+	0.516305i	0.896325	−	0.443398i	$-0.146227\pi$
$499$	13.7450	+	11.5334i	0.615309	+	0.516305i	−0.281016	+	0.959703i	$0.590671\pi$
$500$	20.4493	+	115.974i	0.914522	+	5.18651i
$501$	7.67553	−	5.97946i	0.342917	−	0.267142i
$502$			46.8947i			2.09301i
$503$	−5.14112	−	29.1567i	−0.229231	−	1.30003i	−0.854429	−	0.519568i	$-0.826093\pi$
$503$	−5.14112	−	29.1567i	−0.229231	−	1.30003i	0.625198	−	0.780467i	$-0.285018\pi$
$504$	36.3579	−	27.9488i	1.61951	−	1.24494i
$505$	−2.23405	+	3.86950i	−0.0994141	+	0.172190i
$506$	39.4342	+	22.7674i	1.75306	+	1.01213i
$507$	−12.6029	−	11.3798i	−0.559716	−	0.505395i
$508$	2.40254	−	13.6255i	0.106596	−	0.604534i
$509$	−4.75472	−	26.9654i	−0.210749	−	1.19522i	−0.888132	−	0.459588i	$-0.847997\pi$
$509$	−4.75472	−	26.9654i	−0.210749	−	1.19522i	0.677383	−	0.735631i	$-0.263114\pi$
$510$	−1.60996	+	44.3199i	−0.0712902	+	1.96252i
$511$	5.59902	−	10.4032i	0.247686	−	0.460211i
$512$		−	48.9664i		−	2.16403i
$513$	13.4774	+	18.2033i	0.595042	+	0.803694i
$514$	0.374886	+	0.216440i	0.0165355	+	0.00954677i
$515$	−49.1698	+	58.5982i	−2.16668	+	2.58215i
$516$	13.3713	+	25.2331i	0.588639	+	1.11083i
$517$	6.60566	−	18.1489i	0.290517	−	0.798188i
$518$	−18.1166	+	0.541116i	−0.795998	+	0.0237753i
$519$	7.21790	−	33.7248i	0.316830	−	1.48035i
$520$	−21.1057	+	36.5561i	−0.925546	+	1.60309i
$521$	20.4465	+	35.4143i	0.895776	+	1.55153i	0.832841	+	0.553513i	$0.186713\pi$
$521$	20.4465	+	35.4143i	0.895776	+	1.55153i	0.0629356	+	0.998018i	$0.479954\pi$
$522$	29.9898	−	44.1936i	1.31262	−	1.93430i
$523$	−1.46088	−	1.74101i	−0.0638799	−	0.0761291i	0.733158	−	0.680058i	$-0.238045\pi$
$523$	−1.46088	−	1.74101i	−0.0638799	−	0.0761291i	−0.797038	+	0.603929i	$0.793601\pi$
$524$	−13.0856	+	22.6649i	−0.571646	+	0.990120i
$525$	18.0114	+	50.4970i	0.786082	+	2.20387i
$526$	22.5646	−	18.9339i	0.983863	−	0.825559i
$527$	11.6573	−	13.8926i	0.507799	−	0.605172i
$528$	32.7149	+	7.00175i	1.42373	+	0.304712i
$529$	7.23907	−	2.63481i	0.314742	−	0.114557i
$530$	3.15413	−	1.14801i	0.137007	−	0.0498664i
$531$	−3.89945	+	15.4549i	−0.169222	+	0.670686i
$532$	28.0754	+	40.8994i	1.21722	+	1.77321i
$533$			7.91428i			0.342806i
$534$	−24.6373	−	15.4432i	−1.06616	−	0.668293i
$535$	13.5828	+	37.3184i	0.587235	+	1.61342i
$536$	−27.4876	−	32.7584i	−1.18728	−	1.41495i
$537$	−1.07597	+	29.6201i	−0.0464317	+	1.27820i
$538$	−29.5474	−	35.2132i	−1.27388	−	1.51815i
$539$	−9.10861	−	21.0269i	−0.392336	−	0.905694i
$540$	−90.7984	−	9.92995i	−3.90734	−	0.427317i
$541$	31.6295	−	26.5403i	1.35986	−	1.14106i	0.383835	−	0.923402i	$-0.374603\pi$
$541$	31.6295	−	26.5403i	1.35986	−	1.14106i	0.976025	−	0.217656i	$-0.0698412\pi$
$542$	−21.8009	−	7.93487i	−0.936427	−	0.340832i
$543$	3.71128	−	9.14876i	0.159266	−	0.392611i
$544$	−7.03961	−	4.06432i	−0.301821	−	0.174256i
$545$	24.0992	−	20.2216i	1.03230	−	0.866199i
$546$	−7.15870	+	19.2805i	−0.306364	+	0.825129i
$547$	33.4032	+	12.1578i	1.42822	+	0.519829i	0.936420	−	0.350881i	$-0.114118\pi$
$547$	33.4032	+	12.1578i	1.42822	+	0.519829i	0.491798	+	0.870709i	$0.336340\pi$
$548$	58.6727	+	10.3456i	2.50637	+	0.441941i
$549$	−5.45992	−	7.55946i	−0.233024	−	0.322630i
$550$	−48.0704	+	83.2605i	−2.04973	+	3.55024i
$551$	24.6090	+	18.7085i	1.04838	+	0.797008i
$552$	43.7437	−	34.0776i	1.86186	−	1.45044i
$553$	−16.5608	+	10.2325i	−0.704237	+	0.435130i
$554$	−33.9195	+	40.4236i	−1.44110	+	1.71744i
$555$	14.3361	+	12.9447i	0.608533	+	0.549474i
$556$	−8.82077	−	1.55534i	−0.374084	−	0.0659611i
$557$	14.4366	−	2.54556i	0.611697	−	0.107859i	0.140787	−	0.990040i	$-0.455037\pi$
$557$	14.4366	−	2.54556i	0.611697	−	0.107859i	0.470910	+	0.882181i	$0.343926\pi$
$558$	39.2536	+	38.1203i	1.66174	+	1.61376i
$559$	−5.93447	−	3.42627i	−0.251001	−	0.144916i
$560$	−63.1284	−	9.19725i	−2.66766	−	0.388655i
$561$	−9.48463	+	10.5041i	−0.400441	+	0.443482i
$562$	21.7092			0.915748
$563$	−17.8785			−0.753488			−0.376744	−	0.926318i	$-0.622956\pi$
$563$	−17.8785			−0.753488			−0.376744	+	0.926318i	$0.622956\pi$
$564$	−32.6254	−	29.4590i	−1.37378	−	1.24045i
$565$	−18.5927	+	22.1579i	−0.782201	+	0.932191i
$566$	53.1737	+	19.3536i	2.23506	+	0.813495i
$567$	−23.7701	+	1.40772i	−0.998251	+	0.0591186i
$568$	4.60767	−	26.1314i	0.193334	−	1.09645i
$569$	24.3149	−	14.0382i	1.01933	−	0.588513i	0.105423	−	0.994427i	$-0.466380\pi$
$569$	24.3149	−	14.0382i	1.01933	−	0.588513i	0.913911	+	0.405915i	$0.133047\pi$
$570$	12.5474	−	76.4251i	0.525551	−	3.20110i
$571$	−4.53603	+	7.85663i	−0.189827	+	0.328790i	−0.945192	−	0.326514i	$-0.894126\pi$
$571$	−4.53603	+	7.85663i	−0.189827	+	0.328790i	0.755366	+	0.655304i	$0.227459\pi$
$572$	−23.6573	+	8.61055i	−0.989161	+	0.360025i
$573$	1.59587	−	43.9321i	0.0666685	−	1.83529i
$574$	−27.3151	+	10.8760i	−1.14011	+	0.453955i
$575$	22.1721	+	60.9174i	0.924642	+	2.54043i
$576$	−6.10798	+	9.00086i	−0.254499	+	0.375036i
$577$			20.4114i			0.849736i	0.905255	+	0.424868i	$0.139680\pi$
$577$			20.4114i			0.849736i	−0.905255	+	0.424868i	$0.860320\pi$
$578$	−23.4134	+	13.5177i	−0.973868	+	0.562263i
$579$	5.70207	−	26.6423i	0.236970	−	1.10721i
$580$	−122.770	+	21.6477i	−5.09776	+	0.898872i
$581$	−2.73846	+	8.28560i	−0.113611	+	0.343745i
$582$	28.5147	+	11.5673i	1.18197	+	0.479479i
$583$	1.00653	+	0.366348i	0.0416863	+	0.0151726i
$584$	4.48001	−	25.4074i	0.185384	−	1.05137i
$585$	19.7265	−	9.55283i	0.815592	−	0.394961i
$586$	−54.1119	−	9.54139i	−2.23534	−	0.394151i
$587$	7.41612	−	42.0589i	0.306096	−	1.73596i	−0.312205	−	0.950015i	$-0.601067\pi$
$587$	7.41612	−	42.0589i	0.306096	−	1.73596i	0.618301	−	0.785942i	$-0.287821\pi$
$588$	−52.1397	+	1.22078i	−2.15020	+	0.0503442i
$589$	−23.2539	+	21.5008i	−0.958159	+	0.885926i
$590$	47.2011	−	27.2516i	1.94324	−	1.12193i
$591$	0.941669	−	25.9228i	0.0387351	−	1.06632i
$592$	−15.1311	+	5.50726i	−0.621883	+	0.226347i
$593$	1.11928	+	6.34778i	0.0459635	+	0.260672i	0.999127	−	0.0417846i	$-0.0133043\pi$
$593$	1.11928	+	6.34778i	0.0459635	+	0.260672i	−0.953163	+	0.302457i	$0.902193\pi$
$594$	−29.5324	−	30.8405i	−1.21173	−	1.26540i
$595$	16.7217	−	21.1816i	0.685525	−	0.868362i
$596$	19.8484	−	11.4595i	0.813022	−	0.469398i
$597$	−13.0188	−	16.7115i	−0.532822	−	0.683957i
$598$	−8.50549	+	23.3686i	−0.347815	+	0.955615i
$599$	−1.50519	+	4.13548i	−0.0615004	+	0.168971i	−0.966637	−	0.256150i	$-0.917546\pi$
$599$	−1.50519	+	4.13548i	−0.0615004	+	0.168971i	0.905137	+	0.425120i	$0.139768\pi$
$600$	71.9506	+	92.3595i	2.93737	+	3.77056i
$601$	29.1023	−	16.8022i	1.18711	−	0.685376i	0.229459	−	0.973318i	$-0.426304\pi$
$601$	29.1023	−	16.8022i	1.18711	−	0.685376i	0.957648	+	0.287942i	$0.0929711\pi$
$602$	3.67003	−	25.1905i	0.149579	−	1.02669i
$603$	2.25900	+	22.0891i	0.0919936	+	0.899539i
$604$	5.77016	+	32.7242i	0.234784	+	1.33153i
$605$	1.08939	−	0.396506i	0.0442900	−	0.0161203i
$606$	−0.172580	+	4.75087i	−0.00701056	+	0.192991i
$607$	−31.5510	+	18.2160i	−1.28061	+	0.739363i	−0.976961	−	0.213419i	$-0.931540\pi$
$607$	−31.5510	+	18.2160i	−1.28061	+	0.739363i	−0.303654	+	0.952782i	$0.598207\pi$
$608$	11.3005	+	8.59097i	0.458296	+	0.348410i
$609$	−30.6103	+	10.9182i	−1.24039	+	0.442427i
$610$	−5.53699	+	31.4018i	−0.224186	+	1.27142i
$611$	10.3877	+	1.83164i	0.420243	+	0.0741002i
$612$	14.0389	+	28.9903i	0.567491	+	1.17186i
$613$	−1.32611	+	7.52076i	−0.0535612	+	0.303761i	−0.999806	−	0.0196902i	$-0.993732\pi$
$613$	−1.32611	+	7.52076i	−0.0535612	+	0.303761i	0.946245	+	0.323451i	$0.104843\pi$
$614$	72.2788	+	26.3073i	2.91693	+	1.06168i
$615$	29.0344	+	11.7781i	1.17078	+	0.474938i
$616$	−33.2957	−	37.3561i	−1.34152	−	1.50512i
$617$	−39.2498	+	6.92080i	−1.58014	+	0.278621i	−0.893733	−	0.448599i	$-0.851923\pi$
$617$	−39.2498	+	6.92080i	−1.58014	+	0.278621i	−0.686404	+	0.727220i	$0.740812\pi$
$618$	−17.0335	+	79.5868i	−0.685186	+	3.20145i
$619$	3.92535	−	2.26630i	0.157773	−	0.0910905i	−0.419035	−	0.907970i	$-0.637631\pi$
$619$	3.92535	−	2.26630i	0.157773	−	0.0910905i	0.576808	+	0.816880i	$0.304298\pi$
$620$		−	127.720i		−	5.12935i
$621$	−28.7304	+	1.88752i	−1.15291	+	0.0757435i
$622$	−10.2062	−	28.0414i	−0.409233	−	1.12436i
$623$	6.54528	+	16.4385i	0.262231	+	0.658595i
$624$	−0.663293	+	18.2595i	−0.0265530	+	0.730966i
$625$	−50.1584	+	18.2562i	−2.00634	+	0.730247i
$626$	−8.44659	+	14.6299i	−0.337594	+	0.584729i
$627$	18.7439	−	16.1089i	0.748559	−	0.643327i
$628$	−42.1204	+	24.3182i	−1.68079	+	0.970402i
$629$	1.18282	−	6.70808i	0.0471620	−	0.267469i
$630$	60.0790	+	54.9558i	2.39360	+	2.18949i
$631$	−43.5840	−	15.8633i	−1.73505	−	0.631507i	−0.736082	−	0.676893i	$-0.763326\pi$
$631$	−43.5840	−	15.8633i	−1.73505	−	0.631507i	−0.998970	+	0.0453857i	$0.985548\pi$
$632$	−27.3256	+	32.5654i	−1.08695	+	1.29538i
$633$	−11.5720	−	10.4489i	−0.459947	−	0.415308i
$634$	37.1222			1.47431
$635$	13.1438			0.521597
$636$	1.63379	−	1.80939i	0.0647839	−	0.0717471i
$637$	10.4454	−	6.89313i	0.413861	−	0.273116i
$638$	−50.4710	−	29.1394i	−1.99816	−	1.15364i
$639$	−9.59865	+	9.88403i	−0.379717	+	0.391006i
$640$	62.8420	−	11.0807i	2.48405	−	0.438005i
$641$	4.62322	+	0.815198i	0.182606	+	0.0321984i	0.264203	−	0.964467i	$-0.414891\pi$
$641$	4.62322	+	0.815198i	0.182606	+	0.0321984i	−0.0815972	+	0.996665i	$0.526002\pi$
$642$	31.3615	+	28.3179i	1.23774	+	1.11762i
$643$	−9.91878	+	11.8207i	−0.391158	+	0.466164i	−0.925303	−	0.379229i	$-0.876189\pi$
$643$	−9.91878	+	11.8207i	−0.391158	+	0.466164i	0.534145	+	0.845393i	$0.320634\pi$
$644$	−63.0346	+	1.88275i	−2.48391	+	0.0741908i
$645$	−21.4014	+	16.6723i	−0.842677	+	0.656470i
$646$	−25.1858	+	10.5648i	−0.990923	+	0.415668i
$647$	−21.4008	+	37.0673i	−0.841353	+	1.45727i	0.0473974	+	0.998876i	$0.484907\pi$
$647$	−21.4008	+	37.0673i	−0.841353	+	1.45727i	−0.888751	+	0.458391i	$0.848426\pi$
$648$	−48.3212	+	19.2082i	−1.89824	+	0.754571i
$649$	17.1286	+	3.02023i	0.672355	+	0.118554i
$650$	−49.3400	−	17.9583i	−1.93527	−	0.704382i
$651$	−5.57013	−	32.8266i	−0.218311	−	1.28657i
$652$	−10.6183	+	8.90980i	−0.415844	+	0.348935i
$653$	−8.79779	−	5.07941i	−0.344284	−	0.198772i	0.317881	−	0.948131i	$-0.397029\pi$
$653$	−8.79779	−	5.07941i	−0.344284	−	0.198772i	−0.662165	+	0.749358i	$0.730362\pi$
$654$	12.5825	−	31.0173i	0.492013	−	1.21287i
$655$	−23.3630	−	8.50345i	−0.912869	−	0.332257i
$656$	−20.0090	+	16.7895i	−0.781220	+	0.655522i
$657$	−9.33271	+	9.61018i	−0.364104	+	0.374929i
$658$	7.95341	+	38.3690i	0.310056	+	1.49578i
$659$	25.8630	+	30.8224i	1.00748	+	1.20067i	0.979579	+	0.201059i	$0.0644382\pi$
$659$	25.8630	+	30.8224i	1.00748	+	1.20067i	0.0279020	+	0.999611i	$0.491117\pi$
$660$	−3.61818	+	99.6036i	−0.140838	+	3.87706i
$661$	−3.62937	−	4.32531i	−0.141166	−	0.168235i	0.690829	−	0.723018i	$-0.257246\pi$
$661$	−3.62937	−	4.32531i	−0.141166	−	0.168235i	−0.831995	+	0.554783i	$0.812801\pi$
$662$	6.64497	+	18.2569i	0.258264	+	0.709575i
$663$	−6.54904	−	4.10509i	−0.254344	−	0.159428i
$664$			19.0563i			0.739529i
$665$	−33.6324	+	33.0132i	−1.30421	+	1.28020i
$666$	19.9270	+	5.02780i	0.772154	+	0.194823i
$667$	−36.9270	+	13.4403i	−1.42982	+	0.520412i
$668$	−22.7067	+	8.26458i	−0.878550	+	0.319766i
$669$	2.50397	+	0.535910i	0.0968092	+	0.0207195i
$670$	48.8043	−	58.1628i	1.88548	−	2.24702i
$671$	−7.79481	+	6.54062i	−0.300915	+	0.252498i
$672$	−14.0563	+	5.01365i	−0.542235	+	0.193406i
$673$	18.7403	−	32.4592i	0.722386	−	1.25121i	−0.237655	−	0.971350i	$-0.576379\pi$
$673$	18.7403	−	32.4592i	0.722386	−	1.25121i	0.960041	−	0.279860i	$-0.0902879\pi$
$674$	40.9121	+	48.7572i	1.57588	+	1.87806i
$675$	−3.98526	−	60.6607i	−0.153393	−	2.33483i
$676$	21.0856	+	36.5214i	0.810985	+	1.40467i
$677$	−16.5658	+	28.6928i	−0.636675	+	1.10275i	0.349483	+	0.936943i	$0.386357\pi$
$677$	−16.5658	+	28.6928i	−0.636675	+	1.10275i	−0.986158	+	0.165810i	$0.946976\pi$
$678$	−6.44092	+	30.0944i	−0.247362	+	1.15577i
$679$	−9.84228	−	15.9293i	−0.377712	−	0.611310i
$680$	20.1560	−	55.3781i	0.772947	−	2.12365i
$681$	−17.5994	−	33.2121i	−0.674411	−	1.27269i
$682$	38.3791	−	45.7384i	1.46961	−	1.75141i
$683$	−0.790161	−	0.456199i	−0.0302347	−	0.0174560i	0.484806	−	0.874621i	$-0.338890\pi$
$683$	−0.790161	−	0.456199i	−0.0302347	−	0.0174560i	−0.515041	+	0.857165i	$0.672223\pi$
$684$	−17.9380	−	53.3137i	−0.685875	−	2.03850i
$685$			56.5985i			2.16252i
$686$	38.1450	+	26.5782i	1.45638	+	1.01476i
$687$	1.28678	−	35.4233i	0.0490937	−	1.35148i
$688$	−3.92718	−	22.2722i	−0.149723	−	0.849118i
$689$	−0.101582	+	0.576101i	−0.00386997	+	0.0219477i
$690$	73.0725	+	65.9807i	2.78182	+	2.51184i
$691$	1.78436	+	1.03020i	0.0678803	+	0.0391907i	0.533556	−	0.845765i	$-0.320855\pi$
$691$	1.78436	+	1.03020i	0.0678803	+	0.0391907i	−0.465676	+	0.884955i	$0.654189\pi$
$692$	−42.8265	+	74.1777i	−1.62802	+	2.81981i
$693$	3.41398	+	25.7580i	0.129686	+	0.978464i
$694$	−13.6206	−	77.2464i	−0.517032	−	2.93223i
$695$		−	8.50895i		−	0.322763i
$696$	−55.9866	+	43.6151i	−2.12217	+	1.65323i
$697$	−1.91869	−	10.8814i	−0.0726755	−	0.412163i
$698$	45.6409	+	38.2972i	1.72753	+	1.44957i
$699$	9.18028	+	28.3895i	0.347230	+	1.07379i
$700$	−3.97520	−	133.090i	−0.150248	−	5.03032i
$701$	−5.04790	−	0.890080i	−0.190656	−	0.0336179i	0.0775045	−	0.996992i	$-0.475305\pi$
$701$	−5.04790	−	0.890080i	−0.190656	−	0.0336179i	−0.268161	+	0.963374i	$0.586416\pi$
$702$	13.7866	−	18.8087i	0.520343	−	0.709887i
$703$	−3.52608	+	11.3606i	−0.132989	+	0.428474i
$704$	10.2794	+	5.93479i	0.387418	+	0.223676i
$705$	22.1787	−	35.3827i	0.835298	−	1.33259i
$706$	49.5991	−	59.1099i	1.86669	−	2.22463i
$707$	1.79249	−	2.27057i	0.0674134	−	0.0853934i
$708$	21.0242	−	33.5410i	0.790138	−	1.26055i
$709$	23.6017	+	8.59033i	0.886382	+	0.322617i	0.744782	−	0.667307i	$-0.232553\pi$
$709$	23.6017	+	8.59033i	0.886382	+	0.322617i	0.141599	+	0.989924i	$0.454775\pi$
$710$	47.1122			1.76809
$711$	21.2354	−	6.02471i	0.796390	−	0.225944i
$712$	24.8364	+	29.5989i	0.930783	+	1.10926i
$713$	−6.99109	−	39.6484i	−0.261818	−	1.48485i
$714$	5.16832	−	28.2445i	0.193420	−	1.05702i
$715$	−11.9583	−	20.7124i	−0.447215	−	0.774600i
$716$	25.1763	−	69.1714i	0.940883	−	2.58506i
$717$	4.12720	−	2.18704i	0.154133	−	0.0816767i
$718$	37.1983	−	31.2131i	1.38823	−	1.16486i
$719$	6.50517	−	36.8926i	0.242602	−	1.37586i	−0.583395	−	0.812189i	$-0.698276\pi$
$719$	6.50517	−	36.8926i	0.242602	−	1.37586i	0.825997	−	0.563675i	$-0.190613\pi$
$720$	65.9999	+	29.6073i	2.45967	+	1.10340i
$721$	36.9715	−	32.9530i	1.37689	−	1.22723i
$722$	45.9579	−	12.7571i	1.71038	−	0.474770i
$723$	1.27062	−	3.13223i	0.0472548	−	0.116489i
$724$	−15.7608	+	18.7830i	−0.585746	+	0.698065i
$725$	−28.3776	−	77.9668i	−1.05392	−	2.89562i
$726$	0.826649	−	0.915499i	0.0306798	−	0.0339774i
$727$	1.11287	+	3.05760i	0.0412742	+	0.113400i	0.958618	−	0.284697i	$-0.0918930\pi$
$727$	1.11287	+	3.05760i	0.0412742	+	0.113400i	−0.917343	+	0.398097i	$0.869671\pi$
$728$	16.9341	−	21.4506i	0.627619	−	0.795013i
$729$	26.3618	+	5.83578i	0.976362	+	0.216140i
$730$	45.8069			1.69539
$731$	8.99000	+	3.27209i	0.332507	+	0.121023i
$732$	7.12558	+	22.0355i	0.263369	+	0.814454i
$733$		−	46.3282i		−	1.71117i	−0.517662	−	0.855585i	$-0.673198\pi$
$733$		−	46.3282i		−	1.71117i	0.517662	−	0.855585i	$-0.326802\pi$
$734$	26.8860	+	46.5678i	0.992379	+	1.71885i
$735$	−9.74332	−	48.5785i	−0.359388	−	1.79184i
$736$	−16.9570	+	6.17183i	−0.625042	+	0.227497i
$737$	23.8611	−	4.20736i	0.878935	−	0.154980i
$738$	33.1643	−	3.39163i	1.22080	−	0.124848i
$739$	−35.2784	−	29.6021i	−1.29774	−	1.08893i	−0.990531	−	0.137287i	$-0.956162\pi$
$739$	−35.2784	−	29.6021i	−1.29774	−	1.08893i	−0.307206	−	0.951643i	$-0.599394\pi$
$740$	−23.9853	−	41.5437i	−0.881716	−	1.52718i
$741$	10.4417	+	8.55358i	0.383585	+	0.314224i
$742$	−2.12793	+	0.441093i	−0.0781189	+	0.0161930i
$743$	13.4066	+	2.36394i	0.491840	+	0.0867246i	0.414067	−	0.910247i	$-0.364108\pi$
$743$	13.4066	+	2.36394i	0.491840	+	0.0867246i	0.0777729	+	0.996971i	$0.475219\pi$
$744$	−34.0450	−	64.2468i	−1.24815	−	2.35540i
$745$	13.9953	+	16.6790i	0.512749	+	0.611070i
$746$	−38.3844	−	6.76821i	−1.40535	−	0.247802i
$747$	5.55612	−	8.18762i	0.203288	−	0.299569i
$748$	30.4391	−	17.5740i	1.11297	−	0.642571i
$749$	−5.21884	−	25.1769i	−0.190692	−	0.919942i
$750$	−79.7724	+	88.3466i	−2.91288	+	3.22596i
$751$	12.9606	−	10.8752i	0.472938	−	0.396842i	−0.374927	−	0.927054i	$-0.622332\pi$
$751$	12.9606	−	10.8752i	0.472938	−	0.396842i	0.847865	+	0.530213i	$0.177888\pi$
$752$	17.4060	+	30.1481i	0.634733	+	1.09939i
$753$	−25.5251	+	19.8847i	−0.930185	+	0.724640i
$754$	10.8860	−	29.9090i	0.396444	−	1.08922i
$755$	−29.6636	+	10.7967i	−1.07957	+	0.392931i
$756$	57.2455	+	14.8371i	2.08200	+	0.539620i
$757$	38.6225	+	32.4081i	1.40376	+	1.17789i	0.959402	+	0.282041i	$0.0910114\pi$
$757$	38.6225	+	32.4081i	1.40376	+	1.17789i	0.444355	+	0.895851i	$0.353433\pi$
$758$	−2.63317	−	7.23457i	−0.0956410	−	0.262771i
$759$	4.32887	+	31.1183i	0.157128	+	1.12952i
$760$	−47.1112	+	91.4988i	−1.70890	+	3.31901i
$761$	6.95990	+	12.0549i	0.252296	+	0.436990i	0.964158	−	0.265330i	$-0.0854810\pi$
$761$	6.95990	+	12.0549i	0.252296	+	0.436990i	−0.711862	+	0.702320i	$0.752148\pi$
$762$	12.3571	−	6.54815i	0.447650	−	0.237215i
$763$	−17.3273	+	10.7061i	−0.627290	+	0.387586i
$764$	−37.3412	+	102.594i	−1.35096	+	3.71173i
$765$	−24.8063	+	17.9167i	−0.896873	+	0.647778i
$766$	−40.1333	+	7.07659i	−1.45008	+	0.255687i
$767$			9.49893i			0.342986i
$768$	43.6517	−	34.0059i	1.57514	−	1.22708i
$769$	−22.4606	+	3.96041i	−0.809950	+	0.142816i	−0.563261	−	0.826279i	$-0.690454\pi$
$769$	−22.4606	+	3.96041i	−0.809950	+	0.142816i	−0.246689	+	0.969095i	$0.579343\pi$
$770$	55.0527	−	69.7360i	1.98396	−	2.51311i
$771$	0.0411529	+	0.295830i	0.00148209	+	0.0106540i
$772$	−33.8326	+	58.5997i	−1.21766	+	2.10905i
$773$	−1.06737	−	6.05335i	−0.0383906	−	0.217724i	0.959577	−	0.281446i	$-0.0908140\pi$
$773$	−1.06737	−	6.05335i	−0.0383906	−	0.217724i	−0.997968	+	0.0637221i	$0.979703\pi$
$774$	−11.8144	+	26.3363i	−0.424659	+	0.946640i
$775$	83.7128	−	14.7608i	3.00705	−	0.530224i
$776$	−31.3236	−	26.2836i	−1.12445	−	0.943526i
$777$	−7.97652	−	9.63153i	−0.286156	−	0.345529i
$778$	−2.13144			−0.0764160
$779$	0.928075	+	19.2734i	0.0332518	+	0.690540i
$780$	−53.9144	+	7.50003i	−1.93044	+	0.268544i
$781$	11.5169	+	9.66382i	0.412107	+	0.345799i
$782$	6.02894	−	34.1918i	0.215594	−	1.22270i
$783$	36.7714	−	2.41579i	1.31410	−	0.0863333i
$784$	39.5864	+	11.7849i	1.41380	+	0.420890i
$785$	−29.6995	−	35.3945i	−1.06002	−	1.26328i
$786$	−26.2010	+	3.64482i	−0.934558	+	0.130006i
$787$	−20.1837	+	11.6531i	−0.719473	+	0.415388i	−0.814559	−	0.580081i	$-0.803021\pi$
$787$	−20.1837	+	11.6531i	−0.719473	+	0.415388i	0.0950857	+	0.995469i	$0.469687\pi$
$788$	−22.0338	+	60.5373i	−0.784920	+	2.15655i
$789$	19.8739	+	4.25349i	0.707530	+	0.151428i
$790$	−65.3665	−	37.7393i	−2.32563	−	1.34271i
$791$	13.9802	−	12.4606i	0.497077	−	0.443048i
$792$	24.7304	+	51.0680i	0.878755	+	1.81462i
$793$	−4.25707	−	3.57210i	−0.151173	−	0.126849i
$794$	−5.53757	+	4.64657i	−0.196521	+	0.164901i
$795$	1.96231	+	1.23002i	0.0695961	+	0.0436244i
$796$	17.9940	+	49.4382i	0.637781	+	1.75229i
$797$	48.9359			1.73340			0.866699	−	0.498832i	$-0.166238\pi$
$797$	48.9359			1.73340			0.866699	+	0.498832i	$0.166238\pi$
$798$	−15.1724	+	47.7926i	−0.537097	+	1.69184i
$799$	−14.7263			−0.520978
$800$	−13.0311	−	35.8025i	−0.460717	−	1.26581i
$801$	−2.04112	−	19.9586i	−0.0721193	−	0.705203i
$802$	7.78062	−	6.52871i	0.274743	−	0.230537i
$803$	11.1978	+	9.39608i	0.395162	+	0.331580i
$804$	11.5410	−	53.9238i	0.407019	−	1.90175i
$805$	−12.1599	−	58.6622i	−0.428581	−	2.06757i
$806$	28.2399	+	16.3043i	0.994708	+	0.574295i
$807$	6.63780	−	31.0143i	0.233662	−	1.09176i
$808$	2.16062	−	5.93626i	0.0760104	−	0.208837i
$809$	4.99484	−	2.88377i	0.175609	−	0.101388i	−0.409619	−	0.912257i	$-0.634338\pi$
$809$	4.99484	−	2.88377i	0.175609	−	0.101388i	0.585228	+	0.810869i	$0.301005\pi$
$810$	−48.4843	−	78.5690i	−1.70356	−	2.76063i
$811$	−11.1542	−	13.2930i	−0.391676	−	0.466782i	0.533787	−	0.845619i	$-0.320768\pi$
$811$	−11.1542	−	13.2930i	−0.391676	−	0.466782i	−0.925463	+	0.378837i	$0.876324\pi$
$812$	80.6766	−	2.40969i	2.83119	−	0.0845636i
$813$	−4.92522	−	15.2310i	−0.172735	−	0.534173i
$814$	3.89417	−	22.0849i	0.136490	−	0.774076i
$815$	−10.0873	−	8.46425i	−0.353343	−	0.296490i
$816$	−3.51476	−	25.2660i	−0.123041	−	0.884487i
$817$	−14.8538	−	7.64796i	−0.519668	−	0.267568i
$818$	−35.8017			−1.25178
$819$	−13.5300	+	4.27898i	−0.472776	+	0.149520i
$820$	−59.6096	−	50.0184i	−2.08166	−	1.74672i
$821$	−3.21192	+	0.566348i	−0.112097	+	0.0197657i	−0.229415	−	0.973329i	$-0.573681\pi$
$821$	−3.21192	+	0.566348i	−0.112097	+	0.0197657i	0.117318	+	0.993094i	$0.462570\pi$
$822$	28.1970	+	53.2108i	0.983482	+	1.85594i
$823$	4.88500	+	27.7042i	0.170280	+	0.965707i	0.943452	+	0.331510i	$0.107558\pi$
$823$	4.88500	+	27.7042i	0.170280	+	0.965707i	−0.773171	+	0.634197i	$0.781331\pi$
$824$	54.0759	−	93.6622i	1.88382	−	3.26288i
$825$	−65.7025	+	9.13988i	−2.28747	+	0.318210i
$826$	−32.7843	+	13.0536i	−1.14071	+	0.454194i
$827$	−14.8981	+	2.62693i	−0.518057	+	0.0913474i	−0.426562	−	0.904458i	$-0.640276\pi$
$827$	−14.8981	+	2.62693i	−0.518057	+	0.0913474i	−0.0914946	+	0.995806i	$0.529164\pi$
$828$	69.3336	+	17.4936i	2.40951	+	0.607946i
$829$			34.3877i			1.19433i	0.802117	+	0.597167i	$0.203707\pi$
$829$			34.3877i			1.19433i	−0.802117	+	0.597167i	$0.796293\pi$
$830$	−33.3206	+	5.87532i	−1.15657	+	0.203935i
$831$	−36.3857	−	1.32174i	−1.26221	−	0.0458507i
$832$	−2.21714	+	6.09153i	−0.0768654	+	0.211186i
$833$	−12.6903	+	12.0098i	−0.439694	+	0.416113i
$834$	−4.23910	−	7.99964i	−0.146788	−	0.277005i
$835$	−11.4778	−	19.8802i	−0.397207	−	0.687982i
$836$	−56.6020	+	23.7432i	−1.95762	+	0.821174i
$837$	−4.10439	+	37.5301i	−0.141868	+	1.29723i
$838$	29.3189	+	80.5530i	1.01280	+	2.78266i
$839$	12.9208	+	10.8418i	0.446075	+	0.374301i	0.837977	−	0.545706i	$-0.183738\pi$
$839$	12.9208	+	10.8418i	0.446075	+	0.374301i	−0.391902	+	0.920007i	$0.628183\pi$
$840$	−53.4925	−	94.0476i	−1.84567	−	3.24495i
$841$	20.0110	−	7.28340i	0.690033	−	0.251152i
$842$	−7.30295	+	20.0647i	−0.251676	+	0.691475i
$843$	9.20536	+	11.8165i	0.317049	+	0.406981i
$844$	19.3608	+	33.5339i	0.666427	+	1.15429i
$845$	−30.6896	+	25.7516i	−1.05575	+	0.885882i
$846$	3.22375	−	44.3141i	0.110835	−	1.52355i
$847$	−0.734957	+	0.152347i	−0.0252534	+	0.00523471i
$848$	−1.67201	+	0.965333i	−0.0574169	+	0.0331497i
$849$	12.0129	+	37.1493i	0.412283	+	1.27496i
$850$	72.1917	+	12.7293i	2.47616	+	0.436613i
$851$	−9.71984	−	11.5837i	−0.333192	−	0.397083i
$852$	30.2348	−	16.0217i	1.03583	−	0.548896i
$853$	23.6016	+	4.16160i	0.808104	+	0.142491i	0.562412	−	0.826857i	$-0.309874\pi$
$853$	23.6016	+	4.16160i	0.808104	+	0.142491i	0.245692	+	0.969348i	$0.420985\pi$
$854$	6.47849	−	19.6016i	0.221689	−	0.670752i
$855$	46.9191	−	25.5769i	1.60460	−	0.874713i
$856$	−28.0744	−	48.6263i	−0.959563	−	1.66201i
$857$	−19.8798	−	16.6811i	−0.679082	−	0.569817i	0.236656	−	0.971593i	$-0.423948\pi$
$857$	−19.8798	−	16.6811i	−0.679082	−	0.569817i	−0.915738	+	0.401776i	$0.868393\pi$
$858$	−21.5613	−	13.5151i	−0.736091	−	0.461398i
$859$	27.5338	−	4.85495i	0.939442	−	0.165649i	0.317098	−	0.948393i	$-0.397292\pi$
$859$	27.5338	−	4.85495i	0.939442	−	0.165649i	0.622344	+	0.782744i	$0.286181\pi$
$860$	63.3122	−	23.0438i	2.15893	−	0.785786i
$861$	−17.5023	−	10.2560i	−0.596476	−	0.349525i
$862$	−18.0482	−	31.2603i	−0.614723	−	1.06473i
$863$		−	43.8853i		−	1.49387i	−0.664896	−	0.746936i	$-0.731524\pi$
$863$		−	43.8853i		−	1.49387i	0.664896	−	0.746936i	$-0.268476\pi$
$864$	16.8855	−	1.10934i	0.574456	−	0.0377404i
$865$	−76.4626	−	27.8301i	−2.59981	−	0.946252i
$866$	−68.6780			−2.33377
$867$	−17.2857	−	7.01213i	−0.587055	−	0.238144i
$868$	−11.9215	+	81.8270i	−0.404641	+	2.77739i
$869$	−8.23805	−	22.6338i	−0.279457	−	0.767801i
$870$	−93.5238	−	84.4472i	−3.17076	−	2.86303i
$871$	4.52581	+	12.4346i	0.153351	+	0.421329i
$872$	−28.5903	+	34.0726i	−0.968191	+	1.15384i
$873$	5.79496	+	20.4256i	0.196130	+	0.691302i
$874$	−17.9728	+	57.9062i	−0.607938	+	1.95871i
$875$	70.9241	−	14.7017i	2.39767	−	0.497007i
$876$	29.3971	−	15.5778i	0.993235	−	0.526326i
$877$	3.79204	−	21.5057i	0.128048	−	0.726196i	−0.851403	−	0.524513i	$-0.824248\pi$
$877$	3.79204	−	21.5057i	0.128048	−	0.726196i	0.979451	−	0.201684i	$-0.0646413\pi$
$878$	51.7772	−	43.4462i	1.74740	−	1.46624i
$879$	−17.7516	−	33.4993i	−0.598748	−	1.12990i
$880$	26.9967	−	74.1729i	0.910059	−	2.50037i
$881$	13.1118	+	22.7103i	0.441748	+	0.765130i	0.997819	−	0.0660046i	$-0.0210252\pi$
$881$	13.1118	+	22.7103i	0.441748	+	0.765130i	−0.556071	+	0.831135i	$0.687692\pi$
$882$	−33.3616	−	40.8167i	−1.12334	−	1.37437i
$883$	8.11944	+	46.0476i	0.273241	+	1.54963i	0.744495	+	0.667628i	$0.232690\pi$
$883$	8.11944	+	46.0476i	0.273241	+	1.54963i	−0.471254	+	0.881997i	$0.656199\pi$
$884$	12.3388	+	14.7049i	0.415000	+	0.494578i
$885$	34.8479	+	14.1364i	1.17140	+	0.475189i
$886$	86.3821			2.90206
$887$	28.1885	+	10.2598i	0.946479	+	0.344490i	0.768721	−	0.639584i	$-0.220893\pi$
$887$	28.1885	+	10.2598i	0.946479	+	0.344490i	0.177758	+	0.984074i	$0.443116\pi$
$888$	−23.1392	−	14.5042i	−0.776502	−	0.486728i
$889$	−8.42093	−	1.22686i	−0.282429	−	0.0411474i
$890$	−44.0971	+	52.5529i	−1.47814	+	1.76158i
$891$	4.26405	−	29.1520i	0.142851	−	0.976629i
$892$	−5.50749	−	3.17975i	−0.184405	−	0.106466i
$893$	25.5117	+	3.24240i	0.853717	+	0.108503i
$894$	21.4670	+	8.70828i	0.717963	+	0.291248i
$895$	68.8672	+	12.1431i	2.30198	+	0.405901i
$896$	−41.2957	+	1.23344i	−1.37959	+	0.0412064i
$897$	−16.3263	+	5.27941i	−0.545119	+	0.176274i
$898$	40.4511	+	33.9425i	1.34987	+	1.13268i
$899$	8.94774	+	50.7451i	0.298424	+	1.69245i
$900$	−36.9356	+	146.389i	−1.23119	+	4.87964i
$901$		−	0.816714i		−	0.0272087i
$902$	−6.31687	−	35.8247i	−0.210329	−	1.19283i
$903$	15.2675	−	8.68390i	0.508072	−	0.288982i
$904$	20.4479	−	35.4168i	0.680087	−	1.17794i
$905$	−20.1726	−	11.6467i	−0.670561	−	0.387149i
$906$	−22.5093	+	24.9286i	−0.747820	+	0.828198i
$907$	−8.91714	+	50.5716i	−0.296089	+	1.67920i	0.366655	+	0.930357i	$0.380503\pi$
$907$	−8.91714	+	50.5716i	−0.296089	+	1.67920i	−0.662744	+	0.748846i	$0.730608\pi$
$908$	16.2097	+	91.9299i	0.537939	+	3.05080i
$909$	−2.65911	+	1.92058i	−0.0881971	+	0.0637015i
$910$	42.7281	+	22.9963i	1.41642	+	0.762319i
$911$		−	44.3218i		−	1.46845i	−0.678908	−	0.734223i	$-0.737546\pi$
$911$		−	44.3218i		−	1.46845i	0.678908	−	0.734223i	$-0.262454\pi$
$912$	0.525926	+	44.5446i	0.0174151	+	1.47502i
$913$	−9.35061	−	5.39858i	−0.309460	−	0.178667i
$914$	41.4519	−	49.4004i	1.37111	−	1.63402i
$915$	−19.4400	+	10.3015i	−0.642668	+	0.340557i
$916$	−30.1089	+	82.7235i	−0.994826	+	2.73326i
$917$	14.1744	+	7.62868i	0.468081	+	0.251921i
$918$	−14.3955	+	29.2026i	−0.475124	+	0.963828i
$919$	25.4391	−	44.0619i	0.839160	−	1.45347i	−0.0514385	−	0.998676i	$-0.516381\pi$
$919$	25.4391	−	44.0619i	0.839160	−	1.45347i	0.890598	−	0.454791i	$-0.150286\pi$
$920$	−65.4134	−	113.299i	−2.15662	−	3.73537i
$921$	16.3291	+	50.4969i	0.538063	+	1.66393i
$922$	14.4021	+	17.1638i	0.474309	+	0.565260i
$923$	−4.10541	+	7.11078i	−0.135131	+	0.234054i
$924$	11.6152	−	63.4759i	0.382111	−	2.08821i
$925$	24.4574	−	20.5222i	0.804156	−	0.674767i
$926$	−4.75402	+	5.66562i	−0.156227	+	0.186184i
$927$	−50.5423	+	24.4758i	−1.66003	+	0.803890i
$928$	21.7028	−	7.89919i	0.712431	−	0.259304i
$929$	50.6811	−	18.4464i	1.66279	−	0.605207i	0.671995	−	0.740556i	$-0.265438\pi$
$929$	50.6811	−	18.4464i	1.66279	−	0.605207i	0.990798	+	0.135349i	$0.0432156\pi$
$930$	101.841	−	79.3369i	3.33949	−	2.60156i
$931$	24.6290	−	18.0115i	0.807182	−	0.590303i
$932$		−	74.1006i		−	2.42725i
$933$	10.9354	−	17.4457i	0.358008	−	0.571147i
$934$	22.3443	+	61.3905i	0.731128	+	2.00876i
$935$	21.4630	+	25.5786i	0.701914	+	0.836509i
$936$	−25.1213	+	18.1442i	−0.821115	+	0.593061i
$937$	−26.9289	−	32.0927i	−0.879730	−	1.04842i	−0.998459	−	0.0554945i	$-0.982326\pi$
$937$	−26.9289	−	32.0927i	−0.879730	−	1.04842i	0.118729	−	0.992927i	$-0.462118\pi$
$938$	−36.6968	+	32.7081i	−1.19819	+	1.06796i
$939$	−11.5448	+	1.60599i	−0.376749	+	0.0524096i
$940$	−79.4464	+	66.6635i	−2.59126	+	2.17432i
$941$	−13.2275	−	4.81443i	−0.431205	−	0.156946i	0.117294	−	0.993097i	$-0.462578\pi$
$941$	−13.2275	−	4.81443i	−0.431205	−	0.156946i	−0.548499	+	0.836152i	$0.684800\pi$
$942$	−45.5552	−	18.4799i	−1.48427	−	0.602107i
$943$	−21.2427	−	12.2645i	−0.691757	−	0.399386i
$944$	−24.0153	+	20.1512i	−0.781632	+	0.655867i
$945$	−4.43751	+	56.0043i	−0.144352	+	1.82182i
$946$	29.5976	+	10.7727i	0.962302	+	0.350249i
$947$	21.6330	+	3.81448i	0.702979	+	0.123954i	0.513701	−	0.857969i	$-0.328274\pi$
$947$	21.6330	+	3.81448i	0.702979	+	0.123954i	0.189278	+	0.981924i	$0.439385\pi$
$948$	−54.7839	−	1.99007i	−1.77930	−	0.0646345i
$949$	−3.99167	+	6.91377i	−0.129575	+	0.224430i
$950$	−122.262	−	37.9473i	−3.96670	−	1.23117i
$951$	15.7409	+	20.2058i	0.510434	+	0.655219i
$952$	−18.0825	+	33.5981i	−0.586057	+	1.08892i
$953$	33.2347	−	39.6075i	1.07658	−	1.28301i	0.119608	−	0.992821i	$-0.461836\pi$
$953$	33.2347	−	39.6075i	1.07658	−	1.28301i	0.956968	−	0.290193i	$-0.0937195\pi$
$954$	2.45765	+	0.178788i	0.0795693	+	0.00578848i
$955$	−102.143	−	18.0106i	−3.30527	−	0.582809i
$956$	−11.4239	+	2.01435i	−0.369477	+	0.0651487i
$957$	−5.54043	−	39.8276i	−0.179097	−	1.28744i
$958$	15.1621	+	8.75382i	0.489864	+	0.282823i
$959$	5.28296	−	36.2613i	0.170596	−	1.17094i
$960$	19.0479	+	17.1993i	0.614768	+	0.555104i
$961$	−21.7909			−0.702933
$962$	12.2476			0.394877
$963$	−2.11535	+	29.0779i	−0.0681662	+	0.937022i
$964$	−5.39598	+	6.43068i	−0.173793	+	0.207118i
$965$	−60.4048	−	21.9855i	−1.94450	−	0.707740i
$966$	−40.6571	−	49.0929i	−1.30812	−	1.57954i
$967$	−0.786440	+	4.46012i	−0.0252902	+	0.143428i	−0.994838	−	0.101473i	$-0.967644\pi$
$967$	−0.786440	+	4.46012i	−0.0252902	+	0.143428i	0.969548	+	0.244901i	$0.0787555\pi$
$968$	−1.41949	+	0.819542i	−0.0456241	+	0.0263411i
$969$	−16.4300	−	9.22899i	−0.527809	−	0.296478i
$970$	36.3002	−	62.8738i	1.16553	−	2.01876i
$971$	−17.7032	+	6.44343i	−0.568122	+	0.206780i	−0.610080	−	0.792340i	$-0.708863\pi$
$971$	−17.7032	+	6.44343i	−0.568122	+	0.206780i	0.0419577	+	0.999119i	$0.486641\pi$
$972$	−57.8348	−	33.9342i	−1.85505	−	1.08844i
$973$	−0.794233	+	5.45148i	−0.0254619	+	0.174766i
$974$	23.0847	+	63.4246i	0.739681	+	2.03226i
$975$	−11.1468	−	34.4709i	−0.356984	−	1.10395i
$976$		−	18.3407i		−	0.587072i
$977$	11.8426	−	6.83735i	0.378880	−	0.218746i	−0.298451	−	0.954425i	$-0.596470\pi$
$977$	11.8426	−	6.83735i	0.378880	−	0.218746i	0.677331	+	0.735679i	$0.263137\pi$
$978$	−13.7003	−	2.93220i	−0.438089	−	0.0937614i
$979$	−21.5597	+	3.80156i	−0.689051	+	0.121498i
$980$	−14.0966	+	122.238i	−0.450300	+	3.90476i
$981$	22.2182	−	6.30355i	0.709374	−	0.201257i
$982$	−13.9346	−	5.07177i	−0.444670	−	0.161847i
$983$	−1.58428	+	8.98492i	−0.0505308	+	0.286574i	−0.999593	−	0.0285131i	$-0.990923\pi$
$983$	−1.58428	+	8.98492i	−0.0505308	+	0.286574i	0.949063	+	0.315088i	$0.102034\pi$
$984$	−43.3183	−	9.27115i	−1.38094	−	0.295553i
$985$	−60.2711	−	10.6274i	−1.92040	−	0.338618i
$986$	−7.71630	+	43.7613i	−0.245737	+	1.39364i
$987$	−17.5120	+	20.5987i	−0.557414	+	0.655664i
$988$	−18.1381	−	28.1914i	−0.577048	−	0.896887i
$989$	18.3929	−	10.6191i	0.584859	−	0.337669i
$990$	−81.6693	+	58.9867i	−2.59562	+	1.87472i
$991$	15.4782	−	5.63362i	0.491682	−	0.178958i	−0.0842669	−	0.996443i	$-0.526855\pi$
$991$	15.4782	−	5.63362i	0.491682	−	0.178958i	0.575949	+	0.817485i	$0.304633\pi$
$992$	4.10882	+	23.3023i	0.130455	+	0.739848i
$993$	−7.11968	+	11.3584i	−0.225936	+	0.360447i
$994$	−30.1837	−	4.39749i	−0.957368	−	0.139480i
$995$	−43.2841	+	24.9901i	−1.37220	+	0.792238i
$996$	−19.3858	+	15.1021i	−0.614263	+	0.478528i
$997$	8.30115	−	22.8072i	0.262900	−	0.722312i	−0.736069	−	0.676907i	$-0.763320\pi$
$997$	8.30115	−	22.8072i	0.262900	−	0.722312i	0.998969	−	0.0454051i	$-0.0144579\pi$
$998$	15.4052	−	42.3253i	0.487642	−	1.33978i
$999$	5.71297	+	12.9783i	0.180750	+	0.410615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.ci.b.17.4	yes	288
3.2	odd	2	inner	399.2.ci.b.17.45	yes	288
7.5	odd	6		399.2.cb.b.131.4	✓	288
19.9	even	9		399.2.cb.b.332.45	yes	288
21.5	even	6		399.2.cb.b.131.45	yes	288
57.47	odd	18		399.2.cb.b.332.4	yes	288
133.47	odd	18	inner	399.2.ci.b.47.45	yes	288
399.47	even	18	inner	399.2.ci.b.47.4	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.cb.b.131.4	✓	288	7.5	odd	6
399.2.cb.b.131.45	yes	288	21.5	even	6
399.2.cb.b.332.4	yes	288	57.47	odd	18
399.2.cb.b.332.45	yes	288	19.9	even	9
399.2.ci.b.17.4	yes	288	1.1	even	1	trivial
399.2.ci.b.17.45	yes	288	3.2	odd	2	inner
399.2.ci.b.47.4	yes	288	399.47	even	18	inner
399.2.ci.b.47.45	yes	288	133.47	odd	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.858572 - 2.35891i) q^{2} +(0.919907 - 1.46757i) q^{3} +(-3.29521 + 2.76501i) q^{4} +(-3.13043 - 2.62674i) q^{5} +(-4.25167 - 0.909959i) q^{6} +(1.76041 + 1.97509i) q^{7} +(5.00361 + 2.88883i) q^{8} +(-1.30754 - 2.70006i) q^{9} +(-3.50854 + 9.63963i) q^{10} +(-2.83500 + 1.63679i) q^{11} +(1.02656 + 7.37951i) q^{12} +(-1.14920 - 1.36956i) q^{13} +(3.14761 - 5.84839i) q^{14} +(-6.73463 + 2.17777i) q^{15} +(1.02461 - 5.81084i) q^{16} +(1.91207 + 1.60442i) q^{17} +(-5.24658 + 5.40256i) q^{18} +(-2.95921 - 3.20048i) q^{19} +17.5784 q^{20} +(4.51799 - 0.766630i) q^{21} +(6.29508 + 5.28220i) q^{22} +(5.45691 - 0.962200i) q^{23} +(8.84243 - 4.68570i) q^{24} +(2.03157 + 11.5216i) q^{25} +(-2.24400 + 3.88672i) q^{26} +(-5.16535 - 0.564896i) q^{27} +(-11.2620 - 1.64078i) q^{28} +(-6.98417 + 1.23150i) q^{29} +(10.9193 + 14.0166i) q^{30} -7.26574i q^{31} +(-3.20715 + 0.565506i) q^{32} +(-0.205832 + 5.66626i) q^{33} +(2.14302 - 5.88791i) q^{34} +(-0.322789 - 10.8070i) q^{35} +(11.7743 + 5.28191i) q^{36} +(-1.36448 - 2.36335i) q^{37} +(-5.00895 + 9.72834i) q^{38} +(-3.06709 + 0.426663i) q^{39} +(-8.07521 - 22.1864i) q^{40} +(-3.39108 - 2.84545i) q^{41} +(-5.68743 - 9.99932i) q^{42} +(3.60172 - 1.31092i) q^{43} +(4.81618 - 13.2324i) q^{44} +(-2.99920 + 11.8869i) q^{45} +(-6.95489 - 12.0462i) q^{46} +(-4.51956 + 3.79236i) q^{47} +(-7.58529 - 6.84912i) q^{48} +(-0.801931 + 6.95391i) q^{49} +(25.4341 - 14.6844i) q^{50} +(4.11353 - 1.33019i) q^{51} +(7.57370 + 1.33545i) q^{52} +(-0.210323 - 0.250653i) q^{53} +(3.10229 + 12.6696i) q^{54} +(13.1742 + 2.32296i) q^{55} +(3.10269 + 14.9681i) q^{56} +(-7.41914 + 1.39870i) q^{57} +(8.90140 + 15.4177i) q^{58} +(-4.07006 - 3.41519i) q^{59} +(16.1705 - 25.7975i) q^{60} +(3.06112 - 0.539758i) q^{61} +(-17.1392 + 6.23816i) q^{62} +(3.03105 - 7.33572i) q^{63} +(-1.81294 - 3.14010i) q^{64} +7.30596i q^{65} +(13.5429 - 4.37936i) q^{66} +(-6.95509 - 2.53144i) q^{67} -10.7369 q^{68} +(3.60775 - 8.89354i) q^{69} +(-25.2155 + 10.0400i) q^{70} +(-1.57076 - 4.31564i) q^{71} +(1.25761 - 17.2873i) q^{72} +(-1.52724 - 4.19607i) q^{73} +(-4.40341 + 5.24778i) q^{74} +(18.7776 + 7.61732i) q^{75} +(18.6006 + 2.36403i) q^{76} +(-8.22356 - 2.71796i) q^{77} +(3.63977 + 6.86866i) q^{78} +(-1.27767 + 7.24605i) q^{79} +(-18.4710 + 15.4990i) q^{80} +(-5.58067 + 7.06088i) q^{81} +(-3.80067 + 10.4423i) q^{82} +(1.64914 + 2.85639i) q^{83} +(-12.7680 + 15.0185i) q^{84} +(-1.77121 - 10.0450i) q^{85} +(-6.18466 - 7.37060i) q^{86} +(-4.61748 + 11.3826i) q^{87} -18.9136 q^{88} +(6.28426 + 2.28728i) q^{89} +(30.6151 - 3.13093i) q^{90} +(0.681944 - 4.68075i) q^{91} +(-15.3211 + 18.2590i) q^{92} +(-10.6630 - 6.68381i) q^{93} +(12.8262 + 7.40521i) q^{94} +(0.856739 + 17.7919i) q^{95} +(-2.12036 + 5.22694i) q^{96} +(-6.96973 - 1.22895i) q^{97} +(17.0921 - 4.07875i) q^{98} +(8.12631 + 5.51451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 9 q^{3} - 6 q^{4} - 6 q^{7} - 3 q^{9} - 18 q^{10} - 27 q^{12} - 36 q^{13} - 15 q^{15} + 6 q^{16} - 18 q^{18} - 72 q^{19} + 12 q^{21} - 9 q^{24} + 18 q^{25} + 27 q^{27} - 108 q^{28} - 6 q^{30} - 9 q^{33}+ \cdots - 24 q^{99}+O(q^{100}) \) 288 * q - 9 * q^3 - 6 * q^4 - 6 * q^7 - 3 * q^9 - 18 * q^10 - 27 * q^12 - 36 * q^13 - 15 * q^15 + 6 * q^16 - 18 * q^18 - 72 * q^19 + 12 * q^21 - 9 * q^24 + 18 * q^25 + 27 * q^27 - 108 * q^28 - 6 * q^30 - 9 * q^33 + 36 * q^34 - 84 * q^36 - 24 * q^39 - 144 * q^40 + 39 * q^42 + 12 * q^43 - 6 * q^46 + 63 * q^48 - 30 * q^49 - 3 * q^51 + 90 * q^52 + 9 * q^54 - 90 * q^55 - 66 * q^57 + 24 * q^58 + 42 * q^60 + 54 * q^61 + 60 * q^63 + 54 * q^64 - 27 * q^66 + 102 * q^67 + 60 * q^70 - 39 * q^72 + 36 * q^73 - 63 * q^75 - 87 * q^78 + 6 * q^79 + 45 * q^81 - 18 * q^82 - 117 * q^84 + 36 * q^85 - 9 * q^87 - 204 * q^88 + 144 * q^90 - 198 * q^91 - 60 * q^93 - 180 * q^94 - 243 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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