LMFDB - Embedded newform 304.2.u.f.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(17,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("304.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.u (of order $9$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 34 x^{15} + 204 x^{14} - 267 x^{13} + 1304 x^{12} - 972 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 21x^16 - 34x^15 + 204x^14 - 267x^13 + 1304x^12 - 972x^11 + 4890x^10 - 2547x^9 + 12945x^8 - 2403x^7 + 14457x^6 - 6729x^5 + 8769x^4 - 686x^3 + 132x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			289.2
Root			$0.404662 + 0.700896i$ of defining polynomial
Character	$\chi$	$=$	304.289
Dual form			304.2.u.f.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.140538 - 0.797029i) q^{3} +(-2.64013 + 2.21534i) q^{5} +(2.01284 - 3.48634i) q^{7} +(2.20357 - 0.802035i) q^{9} +O(q^{10})$	\(q+(-0.140538 - 0.797029i) q^{3} +(-2.64013 + 2.21534i) q^{5} +(2.01284 - 3.48634i) q^{7} +(2.20357 - 0.802035i) q^{9} +(-1.26297 - 2.18753i) q^{11} +(0.892594 - 5.06215i) q^{13} +(2.13673 + 1.79293i) q^{15} +(4.64519 + 1.69071i) q^{17} +(4.26250 + 0.911657i) q^{19} +(-3.06159 - 1.11433i) q^{21} +(-4.08548 - 3.42813i) q^{23} +(1.19436 - 6.77352i) q^{25} +(-2.16292 - 3.74628i) q^{27} +(-5.48455 + 1.99621i) q^{29} +(-2.69063 + 4.66031i) q^{31} +(-1.56603 + 1.31406i) q^{33} +(2.40924 + 13.6635i) q^{35} +5.23312 q^{37} -4.16013 q^{39} +(-0.387912 - 2.19996i) q^{41} +(-1.92311 + 1.61368i) q^{43} +(-4.04095 + 6.99913i) q^{45} +(0.138452 - 0.0503924i) q^{47} +(-4.60303 - 7.97267i) q^{49} +(0.694721 - 3.93996i) q^{51} +(5.51409 + 4.62687i) q^{53} +(8.18054 + 2.97747i) q^{55} +(0.127576 - 3.52546i) q^{57} +(4.95898 + 1.80492i) q^{59} +(1.60863 + 1.34980i) q^{61} +(1.63927 - 9.29676i) q^{63} +(8.85779 + 15.3422i) q^{65} +(-4.67313 + 1.70088i) q^{67} +(-2.15815 + 3.73803i) q^{69} +(-3.74525 + 3.14264i) q^{71} +(1.76214 + 9.99360i) q^{73} -5.56655 q^{75} -10.1686 q^{77} +(1.22584 + 6.95208i) q^{79} +(2.70718 - 2.27160i) q^{81} +(5.85181 - 10.1356i) q^{83} +(-16.0094 + 5.82694i) q^{85} +(2.36183 + 4.09080i) q^{87} +(-0.164011 + 0.930152i) q^{89} +(-15.8517 - 13.3012i) q^{91} +(4.09254 + 1.48956i) q^{93} +(-13.2732 + 7.03596i) q^{95} +(-11.2435 - 4.09231i) q^{97} +(-4.53753 - 3.80744i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{7} - 6 q^{9}+O(q^{10}) $ 18 * q + 9 * q^7 - 6 * q^9	$ 18 q + 9 q^{7} - 6 q^{9} + 3 q^{11} + 3 q^{13} - 33 q^{15} + 9 q^{17} + 24 q^{19} - 15 q^{21} - 6 q^{23} + 6 q^{25} + 12 q^{27} - 3 q^{29} + 6 q^{31} - 45 q^{33} + 15 q^{35} + 48 q^{37} - 12 q^{39} - 18 q^{41} + 39 q^{43} - 42 q^{45} + 27 q^{47} - 18 q^{49} - 48 q^{51} + 39 q^{53} + 27 q^{55} - 6 q^{57} - 9 q^{59} - 24 q^{61} - 3 q^{63} + 27 q^{65} - 39 q^{67} - 3 q^{69} + 12 q^{73} - 90 q^{75} + 60 q^{77} - 63 q^{79} - 6 q^{81} + 27 q^{83} - 30 q^{85} - 18 q^{87} + 66 q^{89} - 108 q^{91} + 60 q^{93} + 75 q^{95} - 81 q^{97} - 15 q^{99}+O(q^{100}) $ 18 * q + 9 * q^7 - 6 * q^9 + 3 * q^11 + 3 * q^13 - 33 * q^15 + 9 * q^17 + 24 * q^19 - 15 * q^21 - 6 * q^23 + 6 * q^25 + 12 * q^27 - 3 * q^29 + 6 * q^31 - 45 * q^33 + 15 * q^35 + 48 * q^37 - 12 * q^39 - 18 * q^41 + 39 * q^43 - 42 * q^45 + 27 * q^47 - 18 * q^49 - 48 * q^51 + 39 * q^53 + 27 * q^55 - 6 * q^57 - 9 * q^59 - 24 * q^61 - 3 * q^63 + 27 * q^65 - 39 * q^67 - 3 * q^69 + 12 * q^73 - 90 * q^75 + 60 * q^77 - 63 * q^79 - 6 * q^81 + 27 * q^83 - 30 * q^85 - 18 * q^87 + 66 * q^89 - 108 * q^91 + 60 * q^93 + 75 * q^95 - 81 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.140538	−	0.797029i	−0.0811395	−	0.460165i	−0.998123	−	0.0612400i	$-0.980494\pi$
$3$	−0.140538	−	0.797029i	−0.0811395	−	0.460165i	0.916984	−	0.398925i	$-0.130617\pi$
$4$		0			0
$5$	−2.64013	+	2.21534i	−1.18070	+	0.990728i	−0.180730	+	0.983533i	$0.557846\pi$
$5$	−2.64013	+	2.21534i	−1.18070	+	0.990728i	−0.999974	+	0.00719522i	$0.997710\pi$
$6$		0			0
$7$	2.01284	−	3.48634i	0.760781	−	1.31771i	−0.181668	−	0.983360i	$-0.558150\pi$
$7$	2.01284	−	3.48634i	0.760781	−	1.31771i	0.942449	−	0.334351i	$-0.108517\pi$
$8$		0			0
$9$	2.20357	−	0.802035i	0.734524	−	0.267345i
$10$		0			0
$11$	−1.26297	−	2.18753i	−0.380801	−	0.659566i	0.610376	−	0.792112i	$-0.291018\pi$
$11$	−1.26297	−	2.18753i	−0.380801	−	0.659566i	−0.991177	+	0.132545i	$0.957685\pi$
$12$		0			0
$13$	0.892594	−	5.06215i	0.247561	−	1.40399i	−0.566908	−	0.823781i	$-0.691861\pi$
$13$	0.892594	−	5.06215i	0.247561	−	1.40399i	0.814469	−	0.580207i	$-0.197028\pi$
$14$		0			0
$15$	2.13673	+	1.79293i	0.551700	+	0.462931i
$16$		0			0
$17$	4.64519	+	1.69071i	1.12662	+	0.410057i	0.837065	−	0.547103i	$-0.184270\pi$
$17$	4.64519	+	1.69071i	1.12662	+	0.410057i	0.289558	+	0.957161i	$0.406492\pi$
$18$		0			0
$19$	4.26250	+	0.911657i	0.977884	+	0.209148i
$19$	4.26250	+	0.911657i	0.977884	+	0.209148i
$20$		0			0
$21$	−3.06159	−	1.11433i	−0.668094	−	0.243166i
$22$		0			0
$23$	−4.08548	−	3.42813i	−0.851882	−	0.714814i	0.108321	−	0.994116i	$-0.465453\pi$
$23$	−4.08548	−	3.42813i	−0.851882	−	0.714814i	−0.960203	+	0.279302i	$0.909897\pi$
$24$		0			0
$25$	1.19436	−	6.77352i	0.238871	−	1.35470i
$26$		0			0
$27$	−2.16292	−	3.74628i	−0.416254	−	0.720973i
$28$		0			0
$29$	−5.48455	+	1.99621i	−1.01846	+	0.370687i	−0.796674	−	0.604409i	$-0.793409\pi$
$29$	−5.48455	+	1.99621i	−1.01846	+	0.370687i	−0.221781	+	0.975096i	$0.571187\pi$
$30$		0			0
$31$	−2.69063	+	4.66031i	−0.483251	+	0.837016i	−0.999815	−	0.0192329i	$-0.993878\pi$
$31$	−2.69063	+	4.66031i	−0.483251	+	0.837016i	0.516564	+	0.856249i	$0.327211\pi$
$32$		0			0
$33$	−1.56603	+	1.31406i	−0.272611	+	0.228748i
$34$		0			0
$35$	2.40924	+	13.6635i	0.407237	+	2.30955i
$36$		0			0
$37$	5.23312			0.860319			0.430160	−	0.902753i	$-0.358457\pi$
$37$	5.23312			0.860319			0.430160	+	0.902753i	$0.358457\pi$
$38$		0			0
$39$	−4.16013			−0.666153
$40$		0			0
$41$	−0.387912	−	2.19996i	−0.0605817	−	0.343576i	−1.00000		0.000802188i	$-0.999745\pi$
$41$	−0.387912	−	2.19996i	−0.0605817	−	0.343576i	0.939418	−	0.342774i	$-0.111366\pi$
$42$		0			0
$43$	−1.92311	+	1.61368i	−0.293271	+	0.246084i	−0.777537	−	0.628837i	$-0.783531\pi$
$43$	−1.92311	+	1.61368i	−0.293271	+	0.246084i	0.484266	+	0.874921i	$0.339087\pi$
$44$		0			0
$45$	−4.04095	+	6.99913i	−0.602389	+	1.04337i
$46$		0			0
$47$	0.138452	−	0.0503924i	0.0201953	−	0.00735049i	−0.331903	−	0.943314i	$-0.607691\pi$
$47$	0.138452	−	0.0503924i	0.0201953	−	0.00735049i	0.352098	+	0.935963i	$0.385468\pi$
$48$		0			0
$49$	−4.60303	−	7.97267i	−0.657575	−	1.13895i
$50$		0			0
$51$	0.694721	−	3.93996i	0.0972804	−	0.551704i
$52$		0			0
$53$	5.51409	+	4.62687i	0.757419	+	0.635550i	0.937454	−	0.348110i	$-0.113177\pi$
$53$	5.51409	+	4.62687i	0.757419	+	0.635550i	−0.180035	+	0.983660i	$0.557621\pi$
$54$		0			0
$55$	8.18054	+	2.97747i	1.10306	+	0.401482i
$56$		0			0
$57$	0.127576	−	3.52546i	0.0168978	−	0.466958i
$58$		0			0
$59$	4.95898	+	1.80492i	0.645604	+	0.234981i	0.644009	−	0.765018i	$-0.277270\pi$
$59$	4.95898	+	1.80492i	0.645604	+	0.234981i	0.00159529	+	0.999999i	$0.499492\pi$
$60$		0			0
$61$	1.60863	+	1.34980i	0.205963	+	0.172824i	0.739934	−	0.672679i	$-0.234856\pi$
$61$	1.60863	+	1.34980i	0.205963	+	0.172824i	−0.533971	+	0.845503i	$0.679301\pi$
$62$		0			0
$63$	1.63927	−	9.29676i	0.206529	−	1.17128i
$64$		0			0
$65$	8.85779	+	15.3422i	1.09867	+	1.90296i
$66$		0			0
$67$	−4.67313	+	1.70088i	−0.570914	+	0.207796i	−0.611314	−	0.791388i	$-0.709359\pi$
$67$	−4.67313	+	1.70088i	−0.570914	+	0.207796i	0.0404002	+	0.999184i	$0.487137\pi$
$68$		0			0
$69$	−2.15815	+	3.73803i	−0.259811	+	0.450006i
$70$		0			0
$71$	−3.74525	+	3.14264i	−0.444480	+	0.372963i	−0.837383	−	0.546617i	$-0.815915\pi$
$71$	−3.74525	+	3.14264i	−0.444480	+	0.372963i	0.392903	+	0.919580i	$0.371471\pi$
$72$		0			0
$73$	1.76214	+	9.99360i	0.206243	+	1.16966i	0.895472	+	0.445119i	$0.146839\pi$
$73$	1.76214	+	9.99360i	0.206243	+	1.16966i	−0.689228	+	0.724544i	$0.742050\pi$
$74$		0			0
$75$	−5.56655			−0.642770
$76$		0			0
$77$	−10.1686			−1.15882
$78$		0			0
$79$	1.22584	+	6.95208i	0.137918	+	0.782170i	0.972783	+	0.231717i	$0.0744342\pi$
$79$	1.22584	+	6.95208i	0.137918	+	0.782170i	−0.834866	+	0.550454i	$0.814455\pi$
$80$		0			0
$81$	2.70718	−	2.27160i	0.300798	−	0.252400i
$82$		0			0
$83$	5.85181	−	10.1356i	0.642320	−	1.11253i	−0.342594	−	0.939484i	$-0.611306\pi$
$83$	5.85181	−	10.1356i	0.642320	−	1.11253i	0.984914	−	0.173047i	$-0.0553611\pi$
$84$		0			0
$85$	−16.0094	+	5.82694i	−1.73646	+	0.632021i
$86$		0			0
$87$	2.36183	+	4.09080i	0.253214	+	0.438580i
$88$		0			0
$89$	−0.164011	+	0.930152i	−0.0173851	+	0.0985959i	−0.992266	−	0.124133i	$-0.960385\pi$
$89$	−0.164011	+	0.930152i	−0.0173851	+	0.0985959i	0.974881	+	0.222728i	$0.0714963\pi$
$90$		0			0
$91$	−15.8517	−	13.3012i	−1.66171	−	1.39434i
$92$		0			0
$93$	4.09254	+	1.48956i	0.424376	+	0.154460i
$94$		0			0
$95$	−13.2732	+	7.03596i	−1.36180	+	0.721875i
$96$		0			0
$97$	−11.2435	−	4.09231i	−1.14161	−	0.415512i	−0.299115	−	0.954217i	$-0.596691\pi$
$97$	−11.2435	−	4.09231i	−1.14161	−	0.415512i	−0.842494	+	0.538706i	$0.818913\pi$
$98$		0			0
$99$	−4.53753	−	3.80744i	−0.456039	−	0.382662i
$100$		0			0
$101$	0.988184	−	5.60427i	0.0983280	−	0.557646i	−0.895349	−	0.445366i	$-0.853074\pi$
$101$	0.988184	−	5.60427i	0.0983280	−	0.557646i	0.993677	−	0.112280i	$-0.0358153\pi$
$102$		0			0
$103$	5.62478	+	9.74241i	0.554226	+	0.959948i	0.997963	+	0.0637910i	$0.0203191\pi$
$103$	5.62478	+	9.74241i	0.554226	+	0.959948i	−0.443737	+	0.896157i	$0.646348\pi$
$104$		0			0
$105$	10.5516	−	3.84048i	1.02973	−	0.374792i
$106$		0			0
$107$	−3.73816	+	6.47468i	−0.361381	+	0.625931i	−0.988188	−	0.153244i	$-0.951028\pi$
$107$	−3.73816	+	6.47468i	−0.361381	+	0.625931i	0.626807	+	0.779174i	$0.284361\pi$
$108$		0			0
$109$	−6.80636	+	5.71122i	−0.651931	+	0.547035i	−0.907656	−	0.419714i	$-0.862130\pi$
$109$	−6.80636	+	5.71122i	−0.651931	+	0.547035i	0.255725	+	0.966750i	$0.417686\pi$
$110$		0			0
$111$	−0.735451	−	4.17095i	−0.0698059	−	0.395889i
$112$		0			0
$113$	6.58073			0.619063			0.309531	−	0.950889i	$-0.399828\pi$
$113$	6.58073			0.619063			0.309531	+	0.950889i	$0.399828\pi$
$114$		0			0
$115$	18.3807			1.71401
$116$		0			0
$117$	−2.09313	−	11.8707i	−0.193510	−	1.09745i
$118$		0			0
$119$	15.2444	−	12.7916i	1.39745	−	1.17260i
$120$		0			0
$121$	2.30980	−	4.00069i	0.209982	−	0.363699i
$122$		0			0
$123$	−1.69892	+	0.618355i	−0.153186	+	0.0557552i
$124$		0			0
$125$	3.23624	+	5.60534i	0.289459	+	0.501357i
$126$		0			0
$127$	2.31660	−	13.1381i	0.205565	−	1.16582i	−0.690982	−	0.722872i	$-0.742822\pi$
$127$	2.31660	−	13.1381i	0.205565	−	1.16582i	0.896548	−	0.442947i	$-0.146067\pi$
$128$		0			0
$129$	1.55642	+	1.30599i	0.137035	+	0.114986i
$130$		0			0
$131$	12.1168	+	4.41017i	1.05865	+	0.385318i	0.811922	−	0.583766i	$-0.198421\pi$
$131$	12.1168	+	4.41017i	1.05865	+	0.385318i	0.246731	+	0.969084i	$0.420644\pi$
$132$		0			0
$133$	11.7581	−	13.0255i	1.01955	−	1.12945i
$134$		0			0
$135$	14.0097	+	5.09910i	1.20576	+	0.438861i
$136$		0			0
$137$	−0.0900031	−	0.0755215i	−0.00768948	−	0.00645224i	0.638935	−	0.769261i	$-0.279375\pi$
$137$	−0.0900031	−	0.0755215i	−0.00768948	−	0.00645224i	−0.646624	+	0.762809i	$0.723820\pi$
$138$		0			0
$139$	−2.72461	+	15.4520i	−0.231098	+	1.31062i	0.619579	+	0.784935i	$0.287304\pi$
$139$	−2.72461	+	15.4520i	−0.231098	+	1.31062i	−0.850677	+	0.525689i	$0.823808\pi$
$140$		0			0
$141$	−0.0596219	−	0.103268i	−0.00502107	−	0.00869675i
$142$		0			0
$143$	−12.2009	+	4.44078i	−1.02029	+	0.371357i
$144$		0			0
$145$	10.0577	−	17.4204i	0.835244	−	1.44668i
$146$		0			0
$147$	−5.70756	+	4.78921i	−0.470751	+	0.395007i
$148$		0			0
$149$	−1.57640	−	8.94020i	−0.129144	−	0.732410i	−0.978760	−	0.205009i	$-0.934278\pi$
$149$	−1.57640	−	8.94020i	−0.129144	−	0.732410i	0.849617	−	0.527401i	$-0.176833\pi$
$150$		0			0
$151$	−23.2777			−1.89431			−0.947154	−	0.320778i	$-0.896056\pi$
$151$	−23.2777			−1.89431			−0.947154	+	0.320778i	$0.896056\pi$
$152$		0			0
$153$	11.5920			0.937159
$154$		0			0
$155$	−3.22052	−	18.2645i	−0.258678	−	1.46704i
$156$		0			0
$157$	12.6669	−	10.6288i	1.01093	−	0.848268i	0.0224659	−	0.999748i	$-0.492848\pi$
$157$	12.6669	−	10.6288i	1.01093	−	0.848268i	0.988460	+	0.151480i	$0.0484038\pi$
$158$		0			0
$159$	2.91282	−	5.04514i	0.231001	−	0.400106i
$160$		0			0
$161$	−20.1750	+	7.34311i	−1.59001	+	0.578718i
$162$		0			0
$163$	6.31681	+	10.9410i	0.494770	+	0.856968i	0.999982	−	0.00602806i	$-0.00191880\pi$
$163$	6.31681	+	10.9410i	0.494770	+	0.856968i	−0.505211	+	0.862996i	$0.668585\pi$
$164$		0			0
$165$	1.22346	−	6.93858i	0.0952461	−	0.540167i
$166$		0			0
$167$	15.2997	+	12.8380i	1.18393	+	0.993432i	0.999945	+	0.0105017i	$0.00334287\pi$
$167$	15.2997	+	12.8380i	1.18393	+	0.993432i	0.183981	+	0.982930i	$0.441102\pi$
$168$		0			0
$169$	−12.6126	−	4.59063i	−0.970203	−	0.353125i
$170$		0			0
$171$	10.1239	−	1.40977i	0.774194	−	0.107808i
$172$		0			0
$173$	17.7019	+	6.44298i	1.34585	+	0.489851i	0.911651	−	0.410964i	$-0.134808\pi$
$173$	17.7019	+	6.44298i	1.34585	+	0.489851i	0.434203	+	0.900815i	$0.357030\pi$
$174$		0			0
$175$	−21.2107	−	17.7979i	−1.60338	−	1.34540i
$176$		0			0
$177$	0.741651	−	4.20611i	0.0557459	−	0.316151i
$178$		0			0
$179$	1.17641	+	2.03761i	0.0879292	+	0.152298i	0.906636	−	0.421914i	$-0.138642\pi$
$179$	1.17641	+	2.03761i	0.0879292	+	0.152298i	−0.818706	+	0.574212i	$0.805308\pi$
$180$		0			0
$181$	−8.90819	+	3.24232i	−0.662140	+	0.240999i	−0.651160	−	0.758940i	$-0.725717\pi$
$181$	−8.90819	+	3.24232i	−0.662140	+	0.240999i	−0.0109802	+	0.999940i	$0.503495\pi$
$182$		0			0
$183$	0.849755	−	1.47182i	0.0628157	−	0.108800i
$184$		0			0
$185$	−13.8161	+	11.5931i	−1.01578	+	0.852343i
$186$		0			0
$187$	−2.16826	−	12.2968i	−0.158559	−	0.899233i
$188$		0			0
$189$	−17.4144			−1.26671
$190$		0			0
$191$	−8.06506			−0.583567			−0.291784	−	0.956484i	$-0.594249\pi$
$191$	−8.06506			−0.583567			−0.291784	+	0.956484i	$0.594249\pi$
$192$		0			0
$193$	0.758182	+	4.29986i	0.0545751	+	0.309511i	0.999860	−	0.0167353i	$-0.00532725\pi$
$193$	0.758182	+	4.29986i	0.0545751	+	0.309511i	−0.945285	+	0.326246i	$0.894216\pi$
$194$		0			0
$195$	10.9833	−	9.21607i	0.786530	−	0.659977i
$196$		0			0
$197$	−5.97628	+	10.3512i	−0.425792	+	0.737494i	−0.996494	−	0.0836633i	$-0.973338\pi$
$197$	−5.97628	+	10.3512i	−0.425792	+	0.737494i	0.570702	+	0.821158i	$0.306671\pi$
$198$		0			0
$199$	21.4592	−	7.81051i	1.52120	−	0.553673i	0.559754	−	0.828659i	$-0.310895\pi$
$199$	21.4592	−	7.81051i	1.52120	−	0.553673i	0.961448	+	0.274986i	$0.0886732\pi$
$200$		0			0
$201$	2.01240	+	3.48559i	0.141944	+	0.245854i
$202$		0			0
$203$	−4.08004	+	23.1390i	−0.286362	+	1.62404i
$204$		0			0
$205$	5.89779	+	4.94883i	0.411919	+	0.345641i
$206$		0			0
$207$	−11.7521	−	4.27743i	−0.816830	−	0.297302i
$208$		0			0
$209$	−3.38914	−	10.4758i	−0.234432	−	0.724623i
$210$		0			0
$211$	−2.28987	−	0.833444i	−0.157641	−	0.0573767i	0.261994	−	0.965069i	$-0.415620\pi$
$211$	−2.28987	−	0.833444i	−0.157641	−	0.0573767i	−0.419635	+	0.907693i	$0.637842\pi$
$212$		0			0
$213$	3.03112	+	2.54342i	0.207689	+	0.174272i
$214$		0			0
$215$	1.50242	−	8.52066i	0.102464	−	0.581104i
$216$		0			0
$217$	10.8316	+	18.7609i	0.735297	+	1.27357i
$218$		0			0
$219$	7.71755	−	2.80896i	0.521503	−	0.189812i
$220$		0			0
$221$	12.7049	−	22.0055i	0.854623	−	1.48025i
$222$		0			0
$223$	5.48111	−	4.59920i	0.367042	−	0.307985i	−0.440548	−	0.897729i	$-0.645216\pi$
$223$	5.48111	−	4.59920i	0.367042	−	0.307985i	0.807590	+	0.589744i	$0.200771\pi$
$224$		0			0
$225$	−2.80075	−	15.8839i	−0.186717	−	1.05892i
$226$		0			0
$227$	−15.9444			−1.05827			−0.529134	−	0.848538i	$-0.677483\pi$
$227$	−15.9444			−1.05827			−0.529134	+	0.848538i	$0.677483\pi$
$228$		0			0
$229$	20.4098			1.34872			0.674360	−	0.738403i	$-0.264420\pi$
$229$	20.4098			1.34872			0.674360	+	0.738403i	$0.264420\pi$
$230$		0			0
$231$	1.42908	+	8.10470i	0.0940264	+	0.533250i
$232$		0			0
$233$	−15.5592	+	13.0557i	−1.01932	+	0.855309i	−0.989542	−	0.144247i	$-0.953924\pi$
$233$	−15.5592	+	13.0557i	−1.01932	+	0.855309i	−0.0297761	+	0.999557i	$0.509479\pi$
$234$		0			0
$235$	−0.253896	+	0.439760i	−0.0165623	+	0.0286868i
$236$		0			0
$237$	5.36874	−	1.95406i	0.348737	−	0.126930i
$238$		0			0
$239$	2.09591	+	3.63023i	0.135573	+	0.234820i	0.925816	−	0.377974i	$-0.123379\pi$
$239$	2.09591	+	3.63023i	0.135573	+	0.234820i	−0.790243	+	0.612794i	$0.790046\pi$
$240$		0			0
$241$	−3.22306	+	18.2789i	−0.207615	+	1.17745i	0.685655	+	0.727926i	$0.259516\pi$
$241$	−3.22306	+	18.2789i	−0.207615	+	1.17745i	−0.893271	+	0.449519i	$0.851595\pi$
$242$		0			0
$243$	−12.1323	−	10.1802i	−0.778290	−	0.653063i
$244$		0			0
$245$	29.8148	+	10.8517i	1.90479	+	0.693289i
$246$		0			0
$247$	8.41962	−	20.7637i	0.535728	−	1.32116i
$248$		0			0
$249$	−8.90079	−	3.23962i	−0.564065	−	0.205303i
$250$		0			0
$251$	−6.72610	−	5.64387i	−0.424548	−	0.356238i	0.405342	−	0.914165i	$-0.367152\pi$
$251$	−6.72610	−	5.64387i	−0.424548	−	0.356238i	−0.829890	+	0.557927i	$0.811597\pi$
$252$		0			0
$253$	−2.33929	+	13.2668i	−0.147070	+	0.834075i
$254$		0			0
$255$	6.89417	+	11.9411i	0.431730	+	0.747778i
$256$		0			0
$257$	−11.7145	+	4.26372i	−0.730729	+	0.265964i	−0.680474	−	0.732773i	$-0.738226\pi$
$257$	−11.7145	+	4.26372i	−0.730729	+	0.265964i	−0.0502557	+	0.998736i	$0.516004\pi$
$258$		0			0
$259$	10.5334	−	18.2444i	0.654515	−	1.13365i
$260$		0			0
$261$	−10.4846	+	8.79760i	−0.648979	+	0.544558i
$262$		0			0
$263$	5.05273	+	28.6555i	0.311565	+	1.76697i	0.590867	+	0.806769i	$0.298786\pi$
$263$	5.05273	+	28.6555i	0.311565	+	1.76697i	−0.279302	+	0.960203i	$0.590103\pi$
$264$		0			0
$265$	−24.8080			−1.52394
$266$		0			0
$267$	0.764408			0.0467810
$268$		0			0
$269$	−2.87743	−	16.3187i	−0.175440	−	0.994969i	−0.937635	−	0.347622i	$-0.886989\pi$
$269$	−2.87743	−	16.3187i	−0.175440	−	0.994969i	0.762195	−	0.647347i	$-0.224122\pi$
$270$		0			0
$271$	−2.07222	+	1.73880i	−0.125879	+	0.105625i	−0.703554	−	0.710642i	$-0.748405\pi$
$271$	−2.07222	+	1.73880i	−0.125879	+	0.105625i	0.577675	+	0.816267i	$0.303960\pi$
$272$		0			0
$273$	−8.37365	+	14.5036i	−0.506797	+	0.877797i
$274$		0			0
$275$	−16.3258	+	5.94209i	−0.984480	+	0.358321i
$276$		0			0
$277$	2.42362	+	4.19783i	0.145621	+	0.252223i	0.929604	−	0.368559i	$-0.120149\pi$
$277$	2.42362	+	4.19783i	0.145621	+	0.252223i	−0.783983	+	0.620782i	$0.786815\pi$
$278$		0			0
$279$	−2.19127	+	12.4273i	−0.131188	+	0.744003i
$280$		0			0
$281$	−21.1836	−	17.7752i	−1.26371	−	1.06038i	−0.995277	−	0.0970792i	$-0.969050\pi$
$281$	−21.1836	−	17.7752i	−1.26371	−	1.06038i	−0.268432	−	0.963299i	$-0.586506\pi$
$282$		0			0
$283$	3.32554	+	1.21040i	0.197683	+	0.0719507i	0.438964	−	0.898505i	$-0.355345\pi$
$283$	3.32554	+	1.21040i	0.197683	+	0.0719507i	−0.241281	+	0.970455i	$0.577568\pi$
$284$		0			0
$285$	7.47325	+	9.59030i	0.442677	+	0.568080i
$286$		0			0
$287$	−8.45060	−	3.07577i	−0.498823	−	0.181557i
$288$		0			0
$289$	5.69650	+	4.77993i	0.335088	+	0.281172i
$290$		0			0
$291$	−1.68155	+	9.53655i	−0.0985743	+	0.559043i
$292$		0			0
$293$	5.03558	+	8.72187i	0.294182	+	0.509537i	0.974794	−	0.223106i	$-0.0716196\pi$
$293$	5.03558	+	8.72187i	0.294182	+	0.509537i	−0.680613	+	0.732643i	$0.738286\pi$
$294$		0			0
$295$	−17.0909	+	6.22057i	−0.995069	+	0.362176i
$296$		0			0
$297$	−5.46341	+	9.46291i	−0.317019	+	0.549094i
$298$		0			0
$299$	−21.0004	+	17.6214i	−1.21448	+	1.01907i
$300$		0			0
$301$	1.75493	+	9.95268i	0.101152	+	0.573663i
$302$		0			0
$303$	−4.60564			−0.264587
$304$		0			0
$305$	−7.23724			−0.414403
$306$		0			0
$307$	1.48343	+	8.41294i	0.0846637	+	0.480152i	0.997429	+	0.0716666i	$0.0228318\pi$
$307$	1.48343	+	8.41294i	0.0846637	+	0.480152i	−0.912765	+	0.408485i	$0.866057\pi$
$308$		0			0
$309$	6.97449	−	5.85229i	0.396765	−	0.332925i
$310$		0			0
$311$	−4.35699	+	7.54652i	−0.247062	+	0.427924i	−0.962709	−	0.270538i	$-0.912798\pi$
$311$	−4.35699	+	7.54652i	−0.247062	+	0.427924i	0.715647	+	0.698462i	$0.246132\pi$
$312$		0			0
$313$	31.4169	−	11.4348i	1.77579	−	0.646334i	0.775909	−	0.630844i	$-0.217291\pi$
$313$	31.4169	−	11.4348i	1.77579	−	0.646334i	0.999880	−	0.0154900i	$-0.00493083\pi$
$314$		0			0
$315$	16.2676	+	28.1762i	0.916573	+	1.58755i
$316$		0			0
$317$	3.88906	−	22.0560i	0.218431	−	1.23879i	−0.656420	−	0.754395i	$-0.727930\pi$
$317$	3.88906	−	22.0560i	0.218431	−	1.23879i	0.874852	−	0.484391i	$-0.160959\pi$
$318$		0			0
$319$	11.2936	+	9.47647i	0.632321	+	0.530581i
$320$		0			0
$321$	5.68586	+	2.06948i	0.317354	+	0.115507i
$322$		0			0
$323$	18.2587	+	11.4415i	1.01594	+	0.636620i
$324$		0			0
$325$	−33.2225	−	12.0920i	−1.84285	−	0.670744i
$326$		0			0
$327$	5.50856	+	4.62223i	0.304624	+	0.255610i
$328$		0			0
$329$	0.102996	−	0.584122i	0.00567838	−	0.0322037i
$330$		0			0
$331$	−3.23978	−	5.61146i	−0.178074	−	0.308434i	0.763147	−	0.646225i	$-0.223653\pi$
$331$	−3.23978	−	5.61146i	−0.178074	−	0.308434i	−0.941221	+	0.337792i	$0.890320\pi$
$332$		0			0
$333$	11.5316	−	4.19714i	0.631926	−	0.230002i
$334$		0			0
$335$	8.56968	−	14.8431i	0.468211	−	0.810966i
$336$		0			0
$337$	−5.26978	+	4.42187i	−0.287063	+	0.240875i	−0.774935	−	0.632040i	$-0.782218\pi$
$337$	−5.26978	+	4.42187i	−0.287063	+	0.240875i	0.487872	+	0.872915i	$0.337773\pi$
$338$		0			0
$339$	−0.924841	−	5.24503i	−0.0502305	−	0.284871i
$340$		0			0
$341$	13.5928			0.736090
$342$		0			0
$343$	−8.88084			−0.479521
$344$		0			0
$345$	−2.58318	−	14.6499i	−0.139074	−	0.788726i
$346$		0			0
$347$	4.24297	−	3.56027i	0.227774	−	0.191125i	−0.521757	−	0.853094i	$-0.674723\pi$
$347$	4.24297	−	3.56027i	0.227774	−	0.191125i	0.749532	+	0.661969i	$0.230279\pi$
$348$		0			0
$349$	0.709975	−	1.22971i	0.0380041	−	0.0658250i	−0.846398	−	0.532551i	$-0.821233\pi$
$349$	0.709975	−	1.22971i	0.0380041	−	0.0658250i	0.884402	+	0.466726i	$0.154567\pi$
$350$		0			0
$351$	−20.8949	+	7.60511i	−1.11528	+	0.405931i
$352$		0			0
$353$	9.66793	+	16.7453i	0.514572	+	0.891265i	0.999857	+	0.0169086i	$0.00538244\pi$
$353$	9.66793	+	16.7453i	0.514572	+	0.891265i	−0.485285	+	0.874356i	$0.661284\pi$
$354$		0			0
$355$	2.92597	−	16.5940i	0.155294	−	0.880717i
$356$		0			0
$357$	−12.3377	−	10.3525i	−0.652978	−	0.547914i
$358$		0			0
$359$	19.4151	+	7.06653i	1.02469	+	0.372957i	0.799057	−	0.601255i	$-0.205332\pi$
$359$	19.4151	+	7.06653i	1.02469	+	0.372957i	0.225634	+	0.974212i	$0.427555\pi$
$360$		0			0
$361$	17.3378	+	7.77187i	0.912514	+	0.409046i
$362$		0			0
$363$	−3.51328	−	1.27873i	−0.184399	−	0.0671158i
$364$		0			0
$365$	−26.7915	−	22.4807i	−1.40233	−	1.17669i
$366$		0			0
$367$	1.75251	−	9.93899i	0.0914804	−	0.518811i	−0.904289	−	0.426921i	$-0.859598\pi$
$367$	1.75251	−	9.93899i	0.0914804	−	0.518811i	0.995769	−	0.0918899i	$-0.0292908\pi$
$368$		0			0
$369$	−2.61924	−	4.53665i	−0.136352	−	0.236169i
$370$		0			0
$371$	27.2298	−	9.91084i	1.41370	−	0.514545i
$372$		0			0
$373$	−2.19487	+	3.80163i	−0.113646	+	0.196841i	−0.917238	−	0.398340i	$-0.869586\pi$
$373$	−2.19487	+	3.80163i	−0.113646	+	0.196841i	0.803592	+	0.595181i	$0.202920\pi$
$374$		0			0
$375$	4.01281	−	3.36714i	0.207220	−	0.173879i
$376$		0			0
$377$	5.20966	+	29.5454i	0.268311	+	1.52167i
$378$		0			0
$379$	−29.7063			−1.52591			−0.762954	−	0.646453i	$-0.776252\pi$
$379$	−29.7063			−1.52591			−0.762954	+	0.646453i	$0.776252\pi$
$380$		0			0
$381$	−10.7970			−0.553149
$382$		0			0
$383$	0.242873	+	1.37740i	0.0124102	+	0.0703818i	0.990384	−	0.138346i	$-0.0441787\pi$
$383$	0.242873	+	1.37740i	0.0124102	+	0.0703818i	−0.977974	+	0.208728i	$0.933068\pi$
$384$		0			0
$385$	26.8466	−	22.5269i	1.36823	−	1.14808i
$386$		0			0
$387$	−2.94348	+	5.09826i	−0.149626	+	0.259159i
$388$		0			0
$389$	3.53853	−	1.28792i	0.179411	−	0.0653002i	−0.250753	−	0.968051i	$-0.580678\pi$
$389$	3.53853	−	1.28792i	0.179411	−	0.0653002i	0.430164	+	0.902751i	$0.358456\pi$
$390$		0			0
$391$	−13.1819	−	22.8317i	−0.666636	−	1.15465i
$392$		0			0
$393$	1.81216	−	10.2773i	0.0914114	−	0.518420i
$394$		0			0
$395$	−18.6376	−	15.6388i	−0.937758	−	0.786873i
$396$		0			0
$397$	−9.23858	−	3.36257i	−0.463671	−	0.168762i	0.0996122	−	0.995026i	$-0.468240\pi$
$397$	−9.23858	−	3.36257i	−0.463671	−	0.168762i	−0.563283	+	0.826264i	$0.690462\pi$
$398$		0			0
$399$	−12.0341	−	7.54094i	−0.602460	−	0.377519i
$400$		0			0
$401$	5.05063	+	1.83828i	0.252216	+	0.0917992i	0.465034	−	0.885293i	$-0.346042\pi$
$401$	5.05063	+	1.83828i	0.252216	+	0.0917992i	−0.212818	+	0.977092i	$0.568264\pi$
$402$		0			0
$403$	21.1895	+	17.7801i	1.05553	+	0.885692i
$404$		0			0
$405$	−2.11498	+	11.9946i	−0.105094	+	0.596018i
$406$		0			0
$407$	−6.60929	−	11.4476i	−0.327610	−	0.567438i
$408$		0			0
$409$	−24.1078	+	8.77451i	−1.19205	+	0.433871i	−0.860444	−	0.509546i	$-0.829813\pi$
$409$	−24.1078	+	8.77451i	−1.19205	+	0.433871i	−0.331608	+	0.943417i	$0.607591\pi$
$410$		0			0
$411$	−0.0475440	+	0.0823487i	−0.00234517	+	0.00406196i
$412$		0			0
$413$	16.2742	−	13.6557i	0.800800	−	0.671951i
$414$		0			0
$415$	7.00426	+	39.7231i	0.343826	+	1.94993i
$416$		0			0
$417$	12.6986			0.621854
$418$		0			0
$419$	21.3957			1.04525			0.522623	−	0.852564i	$-0.324953\pi$
$419$	21.3957			1.04525			0.522623	+	0.852564i	$0.324953\pi$
$420$		0			0
$421$	4.24704	+	24.0862i	0.206988	+	1.17389i	0.894281	+	0.447507i	$0.147688\pi$
$421$	4.24704	+	24.0862i	0.206988	+	1.17389i	−0.687293	+	0.726381i	$0.741201\pi$
$422$		0			0
$423$	0.264673	−	0.222087i	0.0128688	−	0.0107982i
$424$		0			0
$425$	17.0001	−	29.4450i	0.824624	−	1.42829i
$426$		0			0
$427$	7.94375	−	2.89129i	0.384425	−	0.139919i
$428$		0			0
$429$	5.25413	+	9.10041i	0.253672	+	0.439372i
$430$		0			0
$431$	7.07014	−	40.0967i	0.340557	−	1.93139i	−0.0227958	−	0.999740i	$-0.507257\pi$
$431$	7.07014	−	40.0967i	0.340557	−	1.93139i	0.363352	−	0.931652i	$-0.381632\pi$
$432$		0			0
$433$	0.400889	+	0.336386i	0.0192655	+	0.0161657i	0.652370	−	0.757901i	$-0.273775\pi$
$433$	0.400889	+	0.336386i	0.0192655	+	0.0161657i	−0.633104	+	0.774067i	$0.718219\pi$
$434$		0			0
$435$	−15.2980	−	5.56803i	−0.733485	−	0.266967i
$436$		0			0
$437$	−14.2891	−	18.3369i	−0.683540	−	0.877175i
$438$		0			0
$439$	−19.8640	−	7.22990i	−0.948057	−	0.345064i	−0.178714	−	0.983901i	$-0.557194\pi$
$439$	−19.8640	−	7.22990i	−0.948057	−	0.345064i	−0.769342	+	0.638837i	$0.779416\pi$
$440$		0			0
$441$	−16.5375	−	13.8766i	−0.787499	−	0.660790i
$442$		0			0
$443$	5.91987	−	33.5732i	0.281261	−	1.59511i	−0.437081	−	0.899422i	$-0.643988\pi$
$443$	5.91987	−	33.5732i	0.281261	−	1.59511i	0.718342	−	0.695690i	$-0.244901\pi$
$444$		0			0
$445$	−1.62759	−	2.81906i	−0.0771550	−	0.133636i
$446$		0			0
$447$	−6.90406	+	2.51287i	−0.326551	+	0.118855i
$448$		0			0
$449$	−13.1273	+	22.7372i	−0.619517	+	1.07304i	0.370057	+	0.929009i	$0.379338\pi$
$449$	−13.1273	+	22.7372i	−0.619517	+	1.07304i	−0.989574	+	0.144026i	$0.953995\pi$
$450$		0			0
$451$	−4.32256	+	3.62706i	−0.203542	+	0.170792i
$452$		0			0
$453$	3.27139	+	18.5530i	0.153703	+	0.871695i
$454$		0			0
$455$	71.3172			3.34340
$456$		0			0
$457$	−4.95693			−0.231875			−0.115938	−	0.993256i	$-0.536987\pi$
$457$	−4.95693			−0.231875			−0.115938	+	0.993256i	$0.536987\pi$
$458$		0			0
$459$	−3.71328	−	21.0590i	−0.173321	−	0.982952i
$460$		0			0
$461$	−6.63550	+	5.56784i	−0.309046	+	0.259320i	−0.784098	−	0.620638i	$-0.786874\pi$
$461$	−6.63550	+	5.56784i	−0.309046	+	0.259320i	0.475052	+	0.879958i	$0.342429\pi$
$462$		0			0
$463$	−2.26791	+	3.92814i	−0.105399	+	0.182556i	−0.913901	−	0.405937i	$-0.866945\pi$
$463$	−2.26791	+	3.92814i	−0.105399	+	0.182556i	0.808502	+	0.588493i	$0.200279\pi$
$464$		0			0
$465$	−14.1047	+	5.13370i	−0.654091	+	0.238070i
$466$		0			0
$467$	−1.64013	−	2.84078i	−0.0758961	−	0.131456i	0.825580	−	0.564286i	$-0.190848\pi$
$467$	−1.64013	−	2.84078i	−0.0758961	−	0.131456i	−0.901476	+	0.432830i	$0.857515\pi$
$468$		0			0
$469$	−3.47641	+	19.7157i	−0.160526	+	0.910387i
$470$		0			0
$471$	−10.2516	−	8.60212i	−0.472369	−	0.396365i
$472$		0			0
$473$	5.95882	+	2.16883i	0.273987	+	0.0997230i
$474$		0			0
$475$	11.2661	−	27.7833i	0.516923	−	1.27478i
$476$		0			0
$477$	15.8616	+	5.77316i	0.726254	+	0.264335i
$478$		0			0
$479$	−16.4975	−	13.8431i	−0.753792	−	0.632507i	0.182711	−	0.983167i	$-0.441513\pi$
$479$	−16.4975	−	13.8431i	−0.753792	−	0.632507i	−0.936503	+	0.350660i	$0.885957\pi$
$480$		0			0
$481$	4.67105	−	26.4908i	0.212982	−	1.20788i
$482$		0			0
$483$	8.68802	+	15.0481i	0.395319	+	0.684712i
$484$		0			0
$485$	38.7503	−	14.1040i	1.75956	−	0.640428i
$486$		0			0
$487$	−18.9874	+	32.8871i	−0.860400	+	1.49026i	0.0111424	+	0.999938i	$0.496453\pi$
$487$	−18.9874	+	32.8871i	−0.860400	+	1.49026i	−0.871543	+	0.490319i	$0.836880\pi$
$488$		0			0
$489$	7.83257	−	6.57231i	0.354201	−	0.297210i
$490$		0			0
$491$	−3.08720	−	17.5084i	−0.139323	−	0.790142i	−0.971751	−	0.236008i	$-0.924161\pi$
$491$	−3.08720	−	17.5084i	−0.139323	−	0.790142i	0.832428	−	0.554134i	$-0.186950\pi$
$492$		0			0
$493$	−28.8518			−1.29942
$494$		0			0
$495$	20.4145			0.917561
$496$		0			0
$497$	3.41772	+	19.3828i	0.153305	+	0.869439i
$498$		0			0
$499$	−10.6818	+	8.96310i	−0.478184	+	0.401244i	−0.849769	−	0.527155i	$-0.823259\pi$
$499$	−10.6818	+	8.96310i	−0.478184	+	0.401244i	0.371586	+	0.928399i	$0.378814\pi$
$500$		0			0
$501$	8.08205	−	13.9985i	0.361079	−	0.625408i
$502$		0			0
$503$	15.4011	−	5.60553i	0.686700	−	0.249938i	0.0249782	−	0.999688i	$-0.492048\pi$
$503$	15.4011	−	5.60553i	0.686700	−	0.249938i	0.661722	+	0.749750i	$0.269826\pi$
$504$		0			0
$505$	9.80640	+	16.9852i	0.436379	+	0.755831i
$506$		0			0
$507$	−1.88631	+	10.6978i	−0.0837740	+	0.475106i
$508$		0			0
$509$	18.1480	+	15.2280i	0.804396	+	0.674969i	0.949263	−	0.314483i	$-0.101831\pi$
$509$	18.1480	+	15.2280i	0.804396	+	0.674969i	−0.144867	+	0.989451i	$0.546275\pi$
$510$		0			0
$511$	38.3880	+	13.9721i	1.69818	+	0.618088i
$512$		0			0
$513$	−5.80410	−	17.9404i	−0.256257	−	0.792086i
$514$		0			0
$515$	−36.4329	−	13.2605i	−1.60542	−	0.584327i
$516$		0			0
$517$	−0.285096	−	0.239224i	−0.0125385	−	0.0105211i
$518$		0			0
$519$	2.64745	−	15.0144i	0.116210	−	0.659061i
$520$		0			0
$521$	−15.1210	−	26.1904i	−0.662465	−	1.14742i	−0.979966	−	0.199164i	$-0.936177\pi$
$521$	−15.1210	−	26.1904i	−0.662465	−	1.14742i	0.317502	−	0.948258i	$-0.397156\pi$
$522$		0			0
$523$	1.49427	−	0.543872i	0.0653401	−	0.0237818i	−0.309143	−	0.951015i	$-0.600042\pi$
$523$	1.49427	−	0.543872i	0.0653401	−	0.0237818i	0.374483	+	0.927234i	$0.377820\pi$
$524$		0			0
$525$	−11.2046	+	19.4069i	−0.489007	+	0.846985i
$526$		0			0
$527$	−20.3777	+	17.0989i	−0.887667	+	0.744841i
$528$		0			0
$529$	0.945210	+	5.36055i	0.0410961	+	0.233067i
$530$		0			0
$531$	12.3751			0.537033
$532$		0			0
$533$	−11.4828			−0.497374
$534$		0			0
$535$	−4.47435	−	25.3753i	−0.193443	−	1.09707i
$536$		0			0
$537$	1.45870	−	1.22400i	0.0629476	−	0.0528193i
$538$		0			0
$539$	−11.6270	+	20.1385i	−0.500810	+	0.867429i
$540$		0			0
$541$	21.9325	−	7.98279i	0.942954	−	0.343207i	0.175622	−	0.984458i	$-0.443806\pi$
$541$	21.9325	−	7.98279i	0.942954	−	0.343207i	0.767332	+	0.641250i	$0.221584\pi$
$542$		0			0
$543$	3.83616	+	6.64442i	0.164625	+	0.285139i
$544$		0			0
$545$	5.31745	−	30.1568i	0.227775	−	1.29177i
$546$		0			0
$547$	30.0193	+	25.1892i	1.28353	+	1.07701i	0.992747	+	0.120224i	$0.0383614\pi$
$547$	30.0193	+	25.1892i	1.28353	+	1.07701i	0.290787	+	0.956788i	$0.406083\pi$
$548$		0			0
$549$	4.62731	+	1.68420i	0.197489	+	0.0718800i
$550$		0			0
$551$	−25.1977	+	3.50882i	−1.07346	+	0.149481i
$552$		0			0
$553$	26.7047	+	9.71972i	1.13560	+	0.413325i
$554$		0			0
$555$	11.1817	+	9.38259i	0.474638	+	0.398269i
$556$		0			0
$557$	5.29866	−	30.0502i	0.224511	−	1.27327i	−0.639106	−	0.769119i	$-0.720695\pi$
$557$	5.29866	−	30.0502i	0.224511	−	1.27327i	0.863617	−	0.504148i	$-0.168193\pi$
$558$		0			0
$559$	6.45214	+	11.1754i	0.272896	+	0.472670i
$560$		0			0
$561$	−9.49620	+	3.45634i	−0.400930	+	0.145927i
$562$		0			0
$563$	9.96179	−	17.2543i	0.419839	−	0.727183i	−0.576084	−	0.817391i	$-0.695420\pi$
$563$	9.96179	−	17.2543i	0.419839	−	0.727183i	0.995923	+	0.0902076i	$0.0287531\pi$
$564$		0			0
$565$	−17.3740	+	14.5785i	−0.730930	+	0.613323i
$566$		0			0
$567$	−2.47043	−	14.0105i	−0.103748	−	0.588386i
$568$		0			0
$569$	−5.35617			−0.224542			−0.112271	−	0.993678i	$-0.535813\pi$
$569$	−5.35617			−0.224542			−0.112271	+	0.993678i	$0.535813\pi$
$570$		0			0
$571$	−35.5473			−1.48761			−0.743805	−	0.668397i	$-0.766981\pi$
$571$	−35.5473			−1.48761			−0.743805	+	0.668397i	$0.766981\pi$
$572$		0			0
$573$	1.13345	+	6.42809i	0.0473504	+	0.268537i
$574$		0			0
$575$	−28.1000	+	23.5787i	−1.17185	+	0.983301i
$576$		0			0
$577$	7.36189	−	12.7512i	0.306480	−	0.530838i	−0.671110	−	0.741358i	$-0.734182\pi$
$577$	7.36189	−	12.7512i	0.306480	−	0.530838i	0.977590	+	0.210520i	$0.0675156\pi$
$578$		0			0
$579$	3.32056	−	1.20859i	0.137998	−	0.0502271i
$580$		0			0
$581$	−23.5575	−	40.8027i	−0.977329	−	1.69278i
$582$		0			0
$583$	3.15729	−	17.9059i	0.130762	−	0.741586i
$584$		0			0
$585$	31.8237	+	26.7033i	1.31575	+	1.10405i
$586$		0			0
$587$	3.25611	+	1.18513i	0.134394	+	0.0489154i	0.408342	−	0.912829i	$-0.366107\pi$
$587$	3.25611	+	1.18513i	0.134394	+	0.0489154i	−0.273948	+	0.961745i	$0.588329\pi$
$588$		0			0
$589$	−15.7174	+	17.4116i	−0.647624	+	0.717433i
$590$		0			0
$591$	9.09012	+	3.30853i	0.373918	+	0.136095i
$592$		0			0
$593$	−27.7344	−	23.2719i	−1.13892	−	0.955664i	−0.139513	−	0.990220i	$-0.544554\pi$
$593$	−27.7344	−	23.2719i	−1.13892	−	0.955664i	−0.999403	+	0.0345561i	$0.988998\pi$
$594$		0			0
$595$	−11.9096	+	67.5428i	−0.488247	+	2.76899i
$596$		0			0
$597$	−9.24103	−	16.0059i	−0.378210	−	0.655080i
$598$		0			0
$599$	−1.29991	+	0.473128i	−0.0531128	+	0.0193315i	−0.368440	−	0.929652i	$-0.620108\pi$
$599$	−1.29991	+	0.473128i	−0.0531128	+	0.0193315i	0.315327	+	0.948983i	$0.397886\pi$
$600$		0			0
$601$	12.9529	−	22.4351i	0.528360	−	0.915146i	−0.471094	−	0.882083i	$-0.656141\pi$
$601$	12.9529	−	22.4351i	0.528360	−	0.915146i	0.999453	−	0.0330627i	$-0.0105261\pi$
$602$		0			0
$603$	−8.93343	+	7.49603i	−0.363797	+	0.305262i
$604$		0			0
$605$	2.76469	+	15.6793i	0.112401	+	0.637455i
$606$		0			0
$607$	48.4162			1.96515			0.982576	−	0.185860i	$-0.0595071\pi$
$607$	48.4162			1.96515			0.982576	+	0.185860i	$0.0595071\pi$
$608$		0			0
$609$	19.0159			0.770563
$610$		0			0
$611$	−0.131513	−	0.745845i	−0.00532043	−	0.0301737i
$612$		0			0
$613$	−19.5109	+	16.3716i	−0.788037	+	0.661242i	−0.945259	−	0.326322i	$-0.894191\pi$
$613$	−19.5109	+	16.3716i	−0.788037	+	0.661242i	0.157221	+	0.987563i	$0.449746\pi$
$614$		0			0
$615$	3.11550	−	5.39621i	0.125629	−	0.217596i
$616$		0			0
$617$	−13.7834	+	5.01675i	−0.554899	+	0.201967i	−0.604222	−	0.796816i	$-0.706516\pi$
$617$	−13.7834	+	5.01675i	−0.554899	+	0.201967i	0.0493226	+	0.998783i	$0.484294\pi$
$618$		0			0
$619$	−5.83971	−	10.1147i	−0.234718	−	0.406543i	0.724473	−	0.689303i	$-0.242083\pi$
$619$	−5.83971	−	10.1147i	−0.234718	−	0.406543i	−0.959191	+	0.282760i	$0.908750\pi$
$620$		0			0
$621$	−4.00617	+	22.7201i	−0.160762	+	0.911728i
$622$		0			0
$623$	2.91269	+	2.44404i	0.116695	+	0.0979184i
$624$		0			0
$625$	11.3543	+	4.13262i	0.454171	+	0.165305i
$626$		0			0
$627$	−7.87318	+	4.17348i	−0.314425	+	0.166673i
$628$		0			0
$629$	24.3088	+	8.84768i	0.969256	+	0.352780i
$630$		0			0
$631$	14.5730	+	12.2282i	0.580142	+	0.486797i	0.884994	−	0.465603i	$-0.154163\pi$
$631$	14.5730	+	12.2282i	0.580142	+	0.486797i	−0.304852	+	0.952400i	$0.598607\pi$
$632$		0			0
$633$	−0.342466	+	1.94222i	−0.0136118	+	0.0771964i
$634$		0			0
$635$	22.9892	+	39.8184i	0.912298	+	1.58015i
$636$		0			0
$637$	−44.4675	+	16.1849i	−1.76187	+	0.641267i
$638$		0			0
$639$	−5.73243	+	9.92886i	−0.226771	+	0.392780i
$640$		0			0
$641$	−9.67545	+	8.11867i	−0.382157	+	0.320668i	−0.813549	−	0.581497i	$-0.802467\pi$
$641$	−9.67545	+	8.11867i	−0.382157	+	0.320668i	0.431391	+	0.902165i	$0.358023\pi$
$642$		0			0
$643$	−6.33513	−	35.9283i	−0.249833	−	1.41687i	−0.808995	−	0.587816i	$-0.799988\pi$
$643$	−6.33513	−	35.9283i	−0.249833	−	1.41687i	0.559162	−	0.829059i	$-0.311123\pi$
$644$		0			0
$645$	−7.00236			−0.275718
$646$		0			0
$647$	−43.4882			−1.70970			−0.854849	−	0.518876i	$-0.826351\pi$
$647$	−43.4882			−1.70970			−0.854849	+	0.518876i	$0.826351\pi$
$648$		0			0
$649$	−2.31473	−	13.1275i	−0.0908612	−	0.515300i
$650$		0			0
$651$	13.4307	−	11.2697i	0.526391	−	0.441695i
$652$		0			0
$653$	1.67607	−	2.90304i	0.0655898	−	0.113605i	−0.831366	−	0.555726i	$-0.812440\pi$
$653$	1.67607	−	2.90304i	0.0655898	−	0.113605i	0.896955	+	0.442121i	$0.145774\pi$
$654$		0			0
$655$	−41.7601	+	15.1994i	−1.63170	+	0.593891i
$656$		0			0
$657$	11.8982	+	20.6083i	0.464194	+	0.804008i
$658$		0			0
$659$	−3.22663	+	18.2991i	−0.125692	+	0.712833i	0.855203	+	0.518293i	$0.173432\pi$
$659$	−3.22663	+	18.2991i	−0.125692	+	0.712833i	−0.980895	+	0.194540i	$0.937679\pi$
$660$		0			0
$661$	−34.7022	−	29.1186i	−1.34976	−	1.13258i	−0.979002	−	0.203853i	$-0.934654\pi$
$661$	−34.7022	−	29.1186i	−1.34976	−	1.13258i	−0.370758	−	0.928730i	$-0.620902\pi$
$662$		0			0
$663$	−19.3246	−	7.03356i	−0.750503	−	0.273161i
$664$		0			0
$665$	−2.18703	+	60.4370i	−0.0848095	+	2.34365i
$666$		0			0
$667$	29.2503	+	10.6462i	1.13258	+	0.412224i
$668$		0			0
$669$	−4.43600	−	3.72224i	−0.171505	−	0.143910i
$670$		0			0
$671$	0.921076	−	5.22368i	0.0355577	−	0.201658i
$672$		0			0
$673$	−15.2205	−	26.3627i	−0.586709	−	1.01621i	−0.994660	−	0.103205i	$-0.967090\pi$
$673$	−15.2205	−	26.3627i	−0.586709	−	1.01621i	0.407951	−	0.913004i	$-0.366243\pi$
$674$		0			0
$675$	−27.9588	+	10.1762i	−1.07614	+	0.391681i
$676$		0			0
$677$	−4.51681	+	7.82335i	−0.173595	+	0.300676i	−0.939674	−	0.342071i	$-0.888872\pi$
$677$	−4.51681	+	7.82335i	−0.173595	+	0.300676i	0.766079	+	0.642746i	$0.222205\pi$
$678$		0			0
$679$	−36.8986	+	30.9616i	−1.41604	+	1.18820i
$680$		0			0
$681$	2.24079	+	12.7082i	0.0858673	+	0.486978i
$682$		0			0
$683$	9.79662			0.374857			0.187429	−	0.982278i	$-0.439985\pi$
$683$	9.79662			0.374857			0.187429	+	0.982278i	$0.439985\pi$
$684$		0			0
$685$	0.404926			0.0154714
$686$		0			0
$687$	−2.86835	−	16.2672i	−0.109434	−	0.620634i
$688$		0			0
$689$	28.3438	−	23.7833i	1.07981	−	0.906070i
$690$		0			0
$691$	−12.0882	+	20.9374i	−0.459856	+	0.796495i	−0.998953	−	0.0457492i	$-0.985432\pi$
$691$	−12.0882	+	20.9374i	−0.459856	+	0.796495i	0.539096	+	0.842244i	$0.318766\pi$
$692$		0			0
$693$	−22.4073	+	8.15560i	−0.851184	+	0.309806i
$694$		0			0
$695$	−27.0381	−	46.8313i	−1.02561	−	1.77641i
$696$		0			0
$697$	1.91757	−	10.8751i	0.0726331	−	0.411923i
$698$		0			0
$699$	12.5925	+	10.5663i	0.476290	+	0.399655i
$700$		0			0
$701$	−5.77009	−	2.10014i	−0.217933	−	0.0793213i	0.230746	−	0.973014i	$-0.425883\pi$
$701$	−5.77009	−	2.10014i	−0.217933	−	0.0793213i	−0.448680	+	0.893693i	$0.648106\pi$
$702$		0			0
$703$	22.3062	+	4.77081i	0.841293	+	0.179934i
$704$		0			0
$705$	0.386184	+	0.140559i	0.0145445	+	0.00529377i
$706$		0			0
$707$	−17.5493	−	14.7256i	−0.660010	−	0.553814i
$708$		0			0
$709$	−4.17275	+	23.6649i	−0.156711	+	0.888752i	0.800494	+	0.599341i	$0.204571\pi$
$709$	−4.17275	+	23.6649i	−0.156711	+	0.888752i	−0.957205	+	0.289411i	$0.906541\pi$
$710$		0			0
$711$	8.27704	+	14.3363i	0.310413	+	0.537652i
$712$		0			0
$713$	26.9687	−	9.81579i	1.00998	−	0.367604i
$714$		0			0
$715$	22.3743	−	38.7534i	0.836752	−	1.44930i
$716$		0			0
$717$	2.59884	−	2.18069i	0.0970556	−	0.0814393i
$718$		0			0
$719$	−1.01040	−	5.73027i	−0.0376816	−	0.213703i	0.960153	−	0.279475i	$-0.0901603\pi$
$719$	−1.01040	−	5.73027i	−0.0376816	−	0.213703i	−0.997835	+	0.0657715i	$0.979049\pi$
$720$		0			0
$721$	45.2871			1.68658
$722$		0			0
$723$	15.0218			0.558665
$724$		0			0
$725$	6.97090	+	39.5339i	0.258893	+	1.46825i
$726$		0			0
$727$	−33.5667	+	28.1658i	−1.24492	+	1.04461i	−0.247796	+	0.968812i	$0.579706\pi$
$727$	−33.5667	+	28.1658i	−1.24492	+	1.04461i	−0.997123	+	0.0757994i	$0.975849\pi$
$728$		0			0
$729$	−1.10793	+	1.91899i	−0.0410345	+	0.0710739i
$730$		0			0
$731$	−11.6615	+	4.24443i	−0.431315	+	0.156986i
$732$		0			0
$733$	0.380554	+	0.659140i	0.0140561	+	0.0243459i	0.872968	−	0.487778i	$-0.162192\pi$
$733$	0.380554	+	0.659140i	0.0140561	+	0.0243459i	−0.858912	+	0.512124i	$0.828859\pi$
$734$		0			0
$735$	4.45901	−	25.2883i	0.164473	−	0.932773i
$736$		0			0
$737$	9.62278	+	8.07447i	0.354460	+	0.297427i
$738$		0			0
$739$	−21.6305	−	7.87287i	−0.795692	−	0.289608i	−0.0879922	−	0.996121i	$-0.528045\pi$
$739$	−21.6305	−	7.87287i	−0.795692	−	0.289608i	−0.707700	+	0.706513i	$0.750267\pi$
$740$		0			0
$741$	−17.7325	−	3.79261i	−0.651420	−	0.139325i
$742$		0			0
$743$	36.1788	+	13.1680i	1.32727	+	0.483088i	0.905782	−	0.423745i	$-0.139285\pi$
$743$	36.1788	+	13.1680i	1.32727	+	0.483088i	0.421491	+	0.906833i	$0.361507\pi$
$744$		0			0
$745$	23.9674	+	20.1111i	0.878099	+	0.736813i
$746$		0			0
$747$	4.76576	−	27.0280i	0.174370	−	0.988901i
$748$		0			0
$749$	15.0486	+	26.0649i	0.549864	+	0.952393i
$750$		0			0
$751$	44.4984	−	16.1961i	1.62377	−	0.591003i	0.639674	−	0.768647i	$-0.279069\pi$
$751$	44.4984	−	16.1961i	1.62377	−	0.591003i	0.984095	+	0.177643i	$0.0568472\pi$
$752$		0			0
$753$	−3.55306	+	6.15407i	−0.129481	+	0.224267i
$754$		0			0
$755$	61.4561	−	51.5678i	2.23662	−	1.87674i
$756$		0			0
$757$	−2.70281	−	15.3284i	−0.0982353	−	0.557120i	−0.993708	−	0.112003i	$-0.964273\pi$
$757$	−2.70281	−	15.3284i	−0.0982353	−	0.557120i	0.895472	−	0.445117i	$-0.146838\pi$
$758$		0			0
$759$	10.9028			0.395745
$760$		0			0
$761$	−17.9648			−0.651225			−0.325612	−	0.945503i	$-0.605570\pi$
$761$	−17.9648			−0.651225			−0.325612	+	0.945503i	$0.605570\pi$
$762$		0			0
$763$	6.21112	+	35.2250i	0.224858	+	1.27523i
$764$		0			0
$765$	−30.6045	+	25.6802i	−1.10651	+	0.928470i
$766$		0			0
$767$	13.5631	−	23.4920i	0.489736	−	0.848248i
$768$		0			0
$769$	37.3210	−	13.5837i	1.34583	−	0.489842i	0.434186	−	0.900823i	$-0.357036\pi$
$769$	37.3210	−	13.5837i	1.34583	−	0.489842i	0.911644	+	0.410982i	$0.134814\pi$
$770$		0			0
$771$	5.04464	+	8.73757i	0.181678	+	0.314676i
$772$		0			0
$773$	−3.44447	+	19.5345i	−0.123889	+	0.702608i	0.858073	+	0.513528i	$0.171662\pi$
$773$	−3.44447	+	19.5345i	−0.123889	+	0.702608i	−0.981962	+	0.189080i	$0.939449\pi$
$774$		0			0
$775$	28.3531	+	23.7911i	1.01847	+	0.854602i
$776$		0			0
$777$	−16.0217	−	5.83141i	−0.574774	−	0.209201i
$778$		0			0
$779$	0.352134	−	9.73097i	0.0126165	−	0.348648i
$780$		0			0
$781$	11.6048	+	4.22380i	0.415252	+	0.151139i
$782$		0			0
$783$	19.3410	+	16.2290i	0.691191	+	0.579978i
$784$		0			0
$785$	−9.89595	+	56.1227i	−0.353202	+	2.00311i
$786$		0			0
$787$	−20.9072	−	36.2123i	−0.745260	−	1.29083i	−0.950073	−	0.312027i	$-0.898992\pi$
$787$	−20.9072	−	36.2123i	−0.745260	−	1.29083i	0.204813	−	0.978801i	$-0.434341\pi$
$788$		0			0
$789$	22.1291	−	8.05435i	0.787819	−	0.286742i
$790$		0			0
$791$	13.2459	−	22.9426i	0.470971	−	0.815746i
$792$		0			0
$793$	8.26872	−	6.93828i	0.293631	−	0.246386i
$794$		0			0
$795$	3.48646	+	19.7727i	0.123652	+	0.701266i
$796$		0			0
$797$	−41.2838			−1.46235			−0.731173	−	0.682192i	$-0.761027\pi$
$797$	−41.2838			−1.46235			−0.731173	+	0.682192i	$0.761027\pi$
$798$		0			0
$799$	0.728334			0.0257666
$800$		0			0
$801$	0.384604	+	2.18120i	0.0135893	+	0.0770689i
$802$		0			0
$803$	19.6358	−	16.4764i	0.692933	−	0.581439i
$804$		0			0
$805$	36.9973	−	64.0812i	1.30398	−	2.25857i
$806$		0			0
$807$	−12.6021	+	4.58679i	−0.443615	+	0.161463i
$808$		0			0
$809$	−21.0183	−	36.4047i	−0.738962	−	1.27992i	−0.952963	−	0.303087i	$-0.901983\pi$
$809$	−21.0183	−	36.4047i	−0.738962	−	1.27992i	0.214001	−	0.976834i	$-0.431351\pi$
$810$		0			0
$811$	−8.04579	+	45.6299i	−0.282526	+	1.60228i	0.431465	+	0.902129i	$0.357997\pi$
$811$	−8.04579	+	45.6299i	−0.282526	+	1.60228i	−0.713991	+	0.700155i	$0.753114\pi$
$812$		0			0
$813$	1.67710	+	1.40726i	0.0588185	+	0.0493546i
$814$		0			0
$815$	−40.9153	−	14.8919i	−1.43320	−	0.521642i
$816$		0			0
$817$	−9.66837	+	5.12509i	−0.338253	+	0.179304i
$818$		0			0
$819$	−45.5984	−	16.5965i	−1.59334	−	0.579927i
$820$		0			0
$821$	−27.1110	−	22.7488i	−0.946179	−	0.793939i	0.0324707	−	0.999473i	$-0.489662\pi$
$821$	−27.1110	−	22.7488i	−0.946179	−	0.793939i	−0.978650	+	0.205534i	$0.934107\pi$
$822$		0			0
$823$	4.78977	−	27.1642i	0.166961	−	0.946883i	−0.780058	−	0.625707i	$-0.784811\pi$
$823$	4.78977	−	27.1642i	0.166961	−	0.946883i	0.947019	−	0.321176i	$-0.104078\pi$
$824$		0			0
$825$	7.03040	+	12.1770i	0.244767	+	0.423949i
$826$		0			0
$827$	−18.6465	+	6.78676i	−0.648402	+	0.235999i	−0.645221	−	0.763996i	$-0.723235\pi$
$827$	−18.6465	+	6.78676i	−0.648402	+	0.235999i	−0.00318075	+	0.999995i	$0.501012\pi$
$828$		0			0
$829$	−4.64864	+	8.05168i	−0.161454	+	0.279646i	−0.935390	−	0.353617i	$-0.884952\pi$
$829$	−4.64864	+	8.05168i	−0.161454	+	0.279646i	0.773936	+	0.633263i	$0.218285\pi$
$830$		0			0
$831$	3.00518	−	2.52165i	0.104249	−	0.0874750i
$832$		0			0
$833$	−7.90243	−	44.8169i	−0.273803	−	1.55281i
$834$		0			0
$835$	−68.8336			−2.38209
$836$		0			0
$837$	23.2784			0.804621
$838$		0			0
$839$	2.38183	+	13.5080i	0.0822298	+	0.466348i	0.997920	+	0.0644636i	$0.0205336\pi$
$839$	2.38183	+	13.5080i	0.0822298	+	0.466348i	−0.915690	+	0.401885i	$0.868355\pi$
$840$		0			0
$841$	3.88013	−	3.25581i	0.133798	−	0.112269i
$842$		0			0
$843$	−11.1902	+	19.3820i	−0.385412	+	0.667553i
$844$		0			0
$845$	43.4688	−	15.8214i	1.49537	−	0.544272i
$846$		0			0
$847$	−9.29849	−	16.1055i	−0.319500	−	0.553390i
$848$		0			0
$849$	0.497358	−	2.82066i	0.0170693	−	0.0968048i
$850$		0			0
$851$	−21.3798	−	17.9398i	−0.732891	−	0.614969i
$852$		0			0
$853$	−27.2169	−	9.90615i	−0.931889	−	0.339180i	−0.168931	−	0.985628i	$-0.554032\pi$
$853$	−27.2169	−	9.90615i	−0.931889	−	0.339180i	−0.762958	+	0.646448i	$0.776254\pi$
$854$		0			0
$855$	−23.6054	+	26.1498i	−0.807286	+	0.894305i
$856$		0			0
$857$	33.0339	+	12.0233i	1.12842	+	0.410710i	0.837717	−	0.546105i	$-0.183890\pi$
$857$	33.0339	+	12.0233i	1.12842	+	0.410710i	0.290699	+	0.956815i	$0.406112\pi$
$858$		0			0
$859$	28.8845	+	24.2369i	0.985525	+	0.826954i	0.984914	−	0.173046i	$-0.0553610\pi$
$859$	28.8845	+	24.2369i	0.985525	+	0.826954i	0.000611293		1.00000i	$0.499805\pi$
$860$		0			0
$861$	−1.26385	+	7.16764i	−0.0430718	+	0.244273i
$862$		0			0
$863$	4.15116	+	7.19001i	0.141307	+	0.244751i	0.927989	−	0.372607i	$-0.121536\pi$
$863$	4.15116	+	7.19001i	0.141307	+	0.244751i	−0.786682	+	0.617358i	$0.788203\pi$
$864$		0			0
$865$	−61.0089	+	22.2054i	−2.07436	+	0.755007i
$866$		0			0
$867$	3.00917	−	5.21203i	0.102197	−	0.177010i
$868$		0			0
$869$	13.6597	−	11.4619i	0.463374	−	0.388817i
$870$		0			0
$871$	4.43891	+	25.1743i	0.150407	+	0.852999i
$872$		0			0
$873$	−28.0581			−0.949624
$874$		0			0
$875$	26.0561			0.880858
$876$		0			0
$877$	−6.90280	−	39.1477i	−0.233091	−	1.32192i	−0.846597	−	0.532235i	$-0.821352\pi$
$877$	−6.90280	−	39.1477i	−0.233091	−	1.32192i	0.613506	−	0.789690i	$-0.289759\pi$
$878$		0			0
$879$	6.24390	−	5.23925i	0.210602	−	0.176716i
$880$		0			0
$881$	−20.4027	+	35.3385i	−0.687384	+	1.19058i	0.285298	+	0.958439i	$0.407907\pi$
$881$	−20.4027	+	35.3385i	−0.687384	+	1.19058i	−0.972681	+	0.232144i	$0.925426\pi$
$882$		0			0
$883$	1.27446	−	0.463866i	0.0428890	−	0.0156103i	−0.320487	−	0.947253i	$-0.603846\pi$
$883$	1.27446	−	0.463866i	0.0428890	−	0.0156103i	0.363376	+	0.931643i	$0.381624\pi$
$884$		0			0
$885$	7.35989	+	12.7477i	0.247400	+	0.428509i
$886$		0			0
$887$	−0.499762	+	2.83429i	−0.0167804	+	0.0951661i	−0.992048	−	0.125862i	$-0.959830\pi$
$887$	−0.499762	+	2.83429i	−0.0167804	+	0.0951661i	0.975267	+	0.221028i	$0.0709414\pi$
$888$		0			0
$889$	−41.1409	−	34.5213i	−1.37982	−	1.15781i
$890$		0			0
$891$	−8.38829	−	3.05309i	−0.281018	−	0.102282i
$892$		0			0
$893$	0.636092	−	0.0885767i	0.0212860	−	0.00296411i
$894$		0			0
$895$	−7.61987	−	2.77340i	−0.254704	−	0.0927047i
$896$		0			0
$897$	16.9961	+	14.2614i	0.567484	+	0.476176i
$898$		0			0
$899$	5.45393	−	30.9308i	0.181899	−	1.03160i
$900$		0			0
$901$	17.7913	+	30.8154i	0.592714	+	1.02661i
$902$		0			0
$903$	7.68594	−	2.79745i	0.255772	−	0.0930935i
$904$		0			0
$905$	16.3360	−	28.2948i	0.543027	−	0.940550i
$906$		0			0
$907$	44.4713	−	37.3159i	1.47665	−	1.23905i	0.566968	−	0.823740i	$-0.308116\pi$
$907$	44.4713	−	37.3159i	1.47665	−	1.23905i	0.909678	−	0.415314i	$-0.136328\pi$
$908$		0			0
$909$	−2.31729	−	13.1420i	−0.0768595	−	0.435892i
$910$		0			0
$911$	7.78240			0.257842			0.128921	−	0.991655i	$-0.458849\pi$
$911$	7.78240			0.257842			0.128921	+	0.991655i	$0.458849\pi$
$912$		0			0
$913$	−29.5627			−0.978383
$914$		0			0
$915$	1.01711	+	5.76829i	0.0336245	+	0.190694i
$916$		0			0
$917$	39.7645	−	33.3664i	1.31314	−	1.10186i
$918$		0			0
$919$	11.8041	−	20.4453i	0.389381	−	0.674428i	−0.602985	−	0.797752i	$-0.706022\pi$
$919$	11.8041	−	20.4453i	0.389381	−	0.674428i	0.992366	+	0.123324i	$0.0393555\pi$
$920$		0			0
$921$	6.49688	−	2.36467i	0.214080	−	0.0779186i
$922$		0			0
$923$	12.5655	+	21.7641i	0.413599	+	0.716375i
$924$		0			0
$925$	6.25020	−	35.4467i	0.205505	−	1.16548i
$926$		0			0
$927$	20.2084	+	16.9568i	0.663730	+	0.556936i
$928$		0			0
$929$	2.76596	+	1.00673i	0.0907481	+	0.0330296i	0.386995	−	0.922082i	$-0.373513\pi$
$929$	2.76596	+	1.00673i	0.0907481	+	0.0330296i	−0.296247	+	0.955111i	$0.595735\pi$
$930$		0			0
$931$	−12.3520	−	38.1799i	−0.404822	−	1.25130i
$932$		0			0
$933$	6.62712	+	2.41207i	0.216962	+	0.0789678i
$934$		0			0
$935$	32.9661	+	27.6618i	1.07811	+	0.904638i
$936$		0			0
$937$	0.331827	−	1.88188i	0.0108403	−	0.0614785i	−0.978908	−	0.204303i	$-0.934507\pi$
$937$	0.331827	−	1.88188i	0.0108403	−	0.0614785i	0.989748	+	0.142824i	$0.0456184\pi$
$938$		0			0
$939$	−13.5292	−	23.4332i	−0.441507	−	0.764713i
$940$		0			0
$941$	14.7725	−	5.37674i	0.481568	−	0.175277i	−0.0898172	−	0.995958i	$-0.528628\pi$
$941$	14.7725	−	5.37674i	0.481568	−	0.175277i	0.571386	+	0.820682i	$0.306406\pi$
$942$		0			0
$943$	−5.95694	+	10.3177i	−0.193985	+	0.335991i
$944$		0			0
$945$	45.9764	−	38.5787i	1.49561	−	1.25497i
$946$		0			0
$947$	−7.73267	−	43.8541i	−0.251278	−	1.42507i	−0.805449	−	0.592665i	$-0.798076\pi$
$947$	−7.73267	−	43.8541i	−0.251278	−	1.42507i	0.554171	−	0.832403i	$-0.313035\pi$
$948$		0			0
$949$	52.1620			1.69325
$950$		0			0
$951$	−18.1258			−0.587769
$952$		0			0
$953$	−8.63883	−	48.9932i	−0.279839	−	1.58705i	−0.723158	−	0.690683i	$-0.757310\pi$
$953$	−8.63883	−	48.9932i	−0.279839	−	1.58705i	0.443319	−	0.896364i	$-0.353801\pi$
$954$		0			0
$955$	21.2928	−	17.8668i	0.689020	−	0.578156i
$956$		0			0
$957$	5.96585	−	10.3331i	0.192848	−	0.334023i
$958$		0			0
$959$	−0.444455	+	0.161768i	−0.0143522	+	0.00522377i
$960$		0			0
$961$	1.02102	+	1.76846i	0.0329362	+	0.0570472i
$962$		0			0
$963$	−3.04438	+	17.2656i	−0.0981039	+	0.556375i
$964$		0			0
$965$	−11.5273	−	9.67259i	−0.371078	−	0.311372i
$966$		0			0
$967$	28.6502	+	10.4278i	0.921327	+	0.335336i	0.758766	−	0.651363i	$-0.225802\pi$
$967$	28.6502	+	10.4278i	0.921327	+	0.335336i	0.162561	+	0.986699i	$0.448025\pi$
$968$		0			0
$969$	6.55313	−	16.1607i	0.210517	−	0.519157i
$970$		0			0
$971$	13.9808	+	5.08860i	0.448666	+	0.163301i	0.556464	−	0.830872i	$-0.312158\pi$
$971$	13.9808	+	5.08860i	0.448666	+	0.163301i	−0.107798	+	0.994173i	$0.534380\pi$
$972$		0			0
$973$	48.3868	+	40.6013i	1.55121	+	1.30162i
$974$		0			0
$975$	−4.96867	+	28.1787i	−0.159125	+	0.902441i
$976$		0			0
$977$	−20.8386	−	36.0936i	−0.666687	−	1.15474i	−0.978825	−	0.204699i	$-0.934378\pi$
$977$	−20.8386	−	36.0936i	−0.666687	−	1.15474i	0.312138	−	0.950037i	$-0.398955\pi$
$978$		0			0
$979$	2.24188	−	0.815977i	0.0716508	−	0.0260787i
$980$		0			0
$981$	−10.4177	+	18.0440i	−0.332612	+	0.576102i
$982$		0			0
$983$	−25.4950	+	21.3928i	−0.813163	+	0.682325i	−0.951361	−	0.308080i	$-0.900314\pi$
$983$	−25.4950	+	21.3928i	−0.813163	+	0.682325i	0.138197	+	0.990405i	$0.455869\pi$
$984$		0			0
$985$	−7.15325	−	40.5681i	−0.227921	−	1.29261i
$986$		0			0
$987$	−0.480037			−0.0152797
$988$		0			0
$989$	13.3887			0.425737
$990$		0			0
$991$	1.66345	+	9.43387i	0.0528411	+	0.299677i	0.999763	−	0.0217881i	$-0.00693592\pi$
$991$	1.66345	+	9.43387i	0.0528411	+	0.299677i	−0.946922	+	0.321465i	$0.895825\pi$
$992$		0			0
$993$	−4.01718	+	3.37082i	−0.127481	+	0.106970i
$994$		0			0
$995$	−39.3523	+	68.1601i	−1.24755	+	2.16082i
$996$		0			0
$997$	−20.2416	+	7.36735i	−0.641059	+	0.233326i	−0.642037	−	0.766673i	$-0.721911\pi$
$997$	−20.2416	+	7.36735i	−0.641059	+	0.233326i	0.000978807		1.00000i	$0.499688\pi$
$998$		0			0
$999$	−11.3188	−	19.6047i	−0.358111	−	0.620267i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.u.f.289.2		18
4.3	odd	2		152.2.q.c.137.2	yes	18
19.5	even	9	inner	304.2.u.f.81.2		18
19.9	even	9		5776.2.a.cd.1.4		9
19.10	odd	18		5776.2.a.ce.1.6		9
76.43	odd	18		152.2.q.c.81.2	✓	18
76.47	odd	18		2888.2.a.y.1.6		9
76.67	even	18		2888.2.a.x.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.q.c.81.2	✓	18	76.43	odd	18
152.2.q.c.137.2	yes	18	4.3	odd	2
304.2.u.f.81.2		18	19.5	even	9	inner
304.2.u.f.289.2		18	1.1	even	1	trivial
2888.2.a.x.1.4		9	76.67	even	18
2888.2.a.y.1.6		9	76.47	odd	18
5776.2.a.cd.1.4		9	19.9	even	9
5776.2.a.ce.1.6		9	19.10	odd	18

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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.140538 - 0.797029i) q^{3} +(-2.64013 + 2.21534i) q^{5} +(2.01284 - 3.48634i) q^{7} +(2.20357 - 0.802035i) q^{9} +O(q^{10})\)	\(q+(-0.140538 - 0.797029i) q^{3} +(-2.64013 + 2.21534i) q^{5} +(2.01284 - 3.48634i) q^{7} +(2.20357 - 0.802035i) q^{9} +(-1.26297 - 2.18753i) q^{11} +(0.892594 - 5.06215i) q^{13} +(2.13673 + 1.79293i) q^{15} +(4.64519 + 1.69071i) q^{17} +(4.26250 + 0.911657i) q^{19} +(-3.06159 - 1.11433i) q^{21} +(-4.08548 - 3.42813i) q^{23} +(1.19436 - 6.77352i) q^{25} +(-2.16292 - 3.74628i) q^{27} +(-5.48455 + 1.99621i) q^{29} +(-2.69063 + 4.66031i) q^{31} +(-1.56603 + 1.31406i) q^{33} +(2.40924 + 13.6635i) q^{35} +5.23312 q^{37} -4.16013 q^{39} +(-0.387912 - 2.19996i) q^{41} +(-1.92311 + 1.61368i) q^{43} +(-4.04095 + 6.99913i) q^{45} +(0.138452 - 0.0503924i) q^{47} +(-4.60303 - 7.97267i) q^{49} +(0.694721 - 3.93996i) q^{51} +(5.51409 + 4.62687i) q^{53} +(8.18054 + 2.97747i) q^{55} +(0.127576 - 3.52546i) q^{57} +(4.95898 + 1.80492i) q^{59} +(1.60863 + 1.34980i) q^{61} +(1.63927 - 9.29676i) q^{63} +(8.85779 + 15.3422i) q^{65} +(-4.67313 + 1.70088i) q^{67} +(-2.15815 + 3.73803i) q^{69} +(-3.74525 + 3.14264i) q^{71} +(1.76214 + 9.99360i) q^{73} -5.56655 q^{75} -10.1686 q^{77} +(1.22584 + 6.95208i) q^{79} +(2.70718 - 2.27160i) q^{81} +(5.85181 - 10.1356i) q^{83} +(-16.0094 + 5.82694i) q^{85} +(2.36183 + 4.09080i) q^{87} +(-0.164011 + 0.930152i) q^{89} +(-15.8517 - 13.3012i) q^{91} +(4.09254 + 1.48956i) q^{93} +(-13.2732 + 7.03596i) q^{95} +(-11.2435 - 4.09231i) q^{97} +(-4.53753 - 3.80744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{7} - 6 q^{9}+O(q^{10}) \) 18 * q + 9 * q^7 - 6 * q^9	\( 18 q + 9 q^{7} - 6 q^{9} + 3 q^{11} + 3 q^{13} - 33 q^{15} + 9 q^{17} + 24 q^{19} - 15 q^{21} - 6 q^{23} + 6 q^{25} + 12 q^{27} - 3 q^{29} + 6 q^{31} - 45 q^{33} + 15 q^{35} + 48 q^{37} - 12 q^{39} - 18 q^{41} + 39 q^{43} - 42 q^{45} + 27 q^{47} - 18 q^{49} - 48 q^{51} + 39 q^{53} + 27 q^{55} - 6 q^{57} - 9 q^{59} - 24 q^{61} - 3 q^{63} + 27 q^{65} - 39 q^{67} - 3 q^{69} + 12 q^{73} - 90 q^{75} + 60 q^{77} - 63 q^{79} - 6 q^{81} + 27 q^{83} - 30 q^{85} - 18 q^{87} + 66 q^{89} - 108 q^{91} + 60 q^{93} + 75 q^{95} - 81 q^{97} - 15 q^{99}+O(q^{100}) \) 18 * q + 9 * q^7 - 6 * q^9 + 3 * q^11 + 3 * q^13 - 33 * q^15 + 9 * q^17 + 24 * q^19 - 15 * q^21 - 6 * q^23 + 6 * q^25 + 12 * q^27 - 3 * q^29 + 6 * q^31 - 45 * q^33 + 15 * q^35 + 48 * q^37 - 12 * q^39 - 18 * q^41 + 39 * q^43 - 42 * q^45 + 27 * q^47 - 18 * q^49 - 48 * q^51 + 39 * q^53 + 27 * q^55 - 6 * q^57 - 9 * q^59 - 24 * q^61 - 3 * q^63 + 27 * q^65 - 39 * q^67 - 3 * q^69 + 12 * q^73 - 90 * q^75 + 60 * q^77 - 63 * q^79 - 6 * q^81 + 27 * q^83 - 30 * q^85 - 18 * q^87 + 66 * q^89 - 108 * q^91 + 60 * q^93 + 75 * q^95 - 81 * q^97 - 15 * q^99

Introduction

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Database

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