LMFDB - Embedded newform 1920.2.w.i.1663.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(127,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))

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

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

chi := DirichletCharacter("1920.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.w (of order $4$, degree $2$, 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 71x^{8} + 158x^{6} + 149x^{4} + 52x^{2} + 4 $ x^12 + 14x^10 + 71x^8 + 158x^6 + 149x^4 + 52*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1663.2
Root			$-2.02068i$ of defining polynomial
Character	$\chi$	$=$	1920.1663
Dual form			1920.2.w.i.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(-0.118826 + 2.23291i) q^{5} +(2.68963 + 2.68963i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.118826 + 2.23291i) q^{5} +(2.68963 + 2.68963i) q^{7} -1.00000i q^{9} +5.80372i q^{11} +(2.15781 + 2.15781i) q^{13} +(-1.49488 - 1.66293i) q^{15} +(-3.88356 + 3.88356i) q^{17} +4.64163 q^{19} -3.80372 q^{21} +(2.62003 - 2.62003i) q^{23} +(-4.97176 - 0.530656i) q^{25} +(0.707107 + 0.707107i) q^{27} +5.95301i q^{29} -6.89027i q^{31} +(-4.10385 - 4.10385i) q^{33} +(-6.32530 + 5.68611i) q^{35} +(1.49571 - 1.49571i) q^{37} -3.05160 q^{39} +11.3588 q^{41} +(6.04137 - 6.04137i) q^{43} +(2.23291 + 0.118826i) q^{45} +(-2.98740 - 2.98740i) q^{47} +7.46825i q^{49} -5.49218i q^{51} +(-6.19205 - 6.19205i) q^{53} +(-12.9592 - 0.689633i) q^{55} +(-3.28213 + 3.28213i) q^{57} +8.84328 q^{59} -10.0998 q^{61} +(2.68963 - 2.68963i) q^{63} +(-5.07460 + 4.56179i) q^{65} +(4.10321 + 4.10321i) q^{67} +3.70528i q^{69} -2.74097i q^{71} +(-0.673989 - 0.673989i) q^{73} +(3.89080 - 3.14034i) q^{75} +(-15.6099 + 15.6099i) q^{77} +9.89871 q^{79} -1.00000 q^{81} +(-2.42445 + 2.42445i) q^{83} +(-8.21016 - 9.13310i) q^{85} +(-4.20941 - 4.20941i) q^{87} -11.5557i q^{89} +11.6074i q^{91} +(4.87215 + 4.87215i) q^{93} +(-0.551547 + 10.3643i) q^{95} +(-6.48719 + 6.48719i) q^{97} +5.80372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) $ 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	−0.118826	+	2.23291i	−0.0531406	+	0.998587i
$5$	−0.118826	+	2.23291i	−0.0531406	+	0.998587i
$6$		0			0
$7$	2.68963	+	2.68963i	1.01659	+	1.01659i	0.999860	+	0.0167255i	$0.00532415\pi$
$7$	2.68963	+	2.68963i	1.01659	+	1.01659i	0.0167255	+	0.999860i	$0.494676\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			5.80372i			1.74989i	0.484226	+	0.874943i	$0.339101\pi$
$11$			5.80372i			1.74989i	−0.484226	+	0.874943i	$0.660899\pi$
$12$		0			0
$13$	2.15781	+	2.15781i	0.598469	+	0.598469i	0.939905	−	0.341436i	$-0.110913\pi$
$13$	2.15781	+	2.15781i	0.598469	+	0.598469i	−0.341436	+	0.939905i	$0.610913\pi$
$14$		0			0
$15$	−1.49488	−	1.66293i	−0.385977	−	0.429366i
$16$		0			0
$17$	−3.88356	+	3.88356i	−0.941901	+	0.941901i	−0.998403	−	0.0565014i	$-0.982005\pi$
$17$	−3.88356	+	3.88356i	−0.941901	+	0.941901i	0.0565014	+	0.998403i	$0.482005\pi$
$18$		0			0
$19$	4.64163			1.06486			0.532431	−	0.846473i	$-0.321278\pi$
$19$	4.64163			1.06486			0.532431	+	0.846473i	$0.321278\pi$
$20$		0			0
$21$	−3.80372			−0.830039
$22$		0			0
$23$	2.62003	−	2.62003i	0.546313	−	0.546313i	−0.379059	−	0.925372i	$-0.623752\pi$
$23$	2.62003	−	2.62003i	0.546313	−	0.546313i	0.925372	+	0.379059i	$0.123752\pi$
$24$		0			0
$25$	−4.97176	−	0.530656i	−0.994352	−	0.106131i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$			5.95301i			1.10545i	0.833365	+	0.552723i	$0.186411\pi$
$29$			5.95301i			1.10545i	−0.833365	+	0.552723i	$0.813589\pi$
$30$		0			0
$31$		−	6.89027i		−	1.23753i	−0.785577	−	0.618764i	$-0.787634\pi$
$31$		−	6.89027i		−	1.23753i	0.785577	−	0.618764i	$-0.212366\pi$
$32$		0			0
$33$	−4.10385	−	4.10385i	−0.714388	−	0.714388i
$34$		0			0
$35$	−6.32530	+	5.68611i	−1.06917	+	0.961127i
$36$		0			0
$37$	1.49571	−	1.49571i	0.245893	−	0.245893i	−0.573390	−	0.819283i	$-0.694372\pi$
$37$	1.49571	−	1.49571i	0.245893	−	0.245893i	0.819283	+	0.573390i	$0.194372\pi$
$38$		0			0
$39$	−3.05160			−0.488648
$40$		0			0
$41$	11.3588			1.77395			0.886973	−	0.461822i	$-0.152804\pi$
$41$	11.3588			1.77395			0.886973	+	0.461822i	$0.152804\pi$
$42$		0			0
$43$	6.04137	−	6.04137i	0.921300	−	0.921300i	−0.0758215	−	0.997121i	$-0.524158\pi$
$43$	6.04137	−	6.04137i	0.921300	−	0.921300i	0.997121	+	0.0758215i	$0.0241579\pi$
$44$		0			0
$45$	2.23291	+	0.118826i	0.332862	+	0.0177135i
$46$		0			0
$47$	−2.98740	−	2.98740i	−0.435758	−	0.435758i	0.454824	−	0.890581i	$-0.349702\pi$
$47$	−2.98740	−	2.98740i	−0.435758	−	0.435758i	−0.890581	+	0.454824i	$0.849702\pi$
$48$		0			0
$49$			7.46825i			1.06689i
$50$		0			0
$51$		−	5.49218i		−	0.769059i
$52$		0			0
$53$	−6.19205	−	6.19205i	−0.850543	−	0.850543i	0.139657	−	0.990200i	$-0.455400\pi$
$53$	−6.19205	−	6.19205i	−0.850543	−	0.850543i	−0.990200	+	0.139657i	$0.955400\pi$
$54$		0			0
$55$	−12.9592	−	0.689633i	−1.74741	−	0.0929901i
$56$		0			0
$57$	−3.28213	+	3.28213i	−0.434728	+	0.434728i
$58$		0			0
$59$	8.84328			1.15130			0.575648	−	0.817697i	$-0.304750\pi$
$59$	8.84328			1.15130			0.575648	+	0.817697i	$0.304750\pi$
$60$		0			0
$61$	−10.0998			−1.29314			−0.646571	−	0.762854i	$-0.723798\pi$
$61$	−10.0998			−1.29314			−0.646571	+	0.762854i	$0.723798\pi$
$62$		0			0
$63$	2.68963	−	2.68963i	0.338862	−	0.338862i
$64$		0			0
$65$	−5.07460	+	4.56179i	−0.629426	+	0.565820i
$66$		0			0
$67$	4.10321	+	4.10321i	0.501287	+	0.501287i	0.911838	−	0.410551i	$-0.134664\pi$
$67$	4.10321	+	4.10321i	0.501287	+	0.501287i	−0.410551	+	0.911838i	$0.634664\pi$
$68$		0			0
$69$			3.70528i			0.446063i
$70$		0			0
$71$		−	2.74097i		−	0.325294i	−0.986684	−	0.162647i	$-0.947997\pi$
$71$		−	2.74097i		−	0.325294i	0.986684	−	0.162647i	$-0.0520031\pi$
$72$		0			0
$73$	−0.673989	−	0.673989i	−0.0788845	−	0.0788845i	0.666564	−	0.745448i	$-0.267764\pi$
$73$	−0.673989	−	0.673989i	−0.0788845	−	0.0788845i	−0.745448	+	0.666564i	$0.767764\pi$
$74$		0			0
$75$	3.89080	−	3.14034i	0.449270	−	0.362615i
$76$		0			0
$77$	−15.6099	+	15.6099i	−1.77891	+	1.77891i
$78$		0			0
$79$	9.89871			1.11369			0.556846	−	0.830616i	$-0.312011\pi$
$79$	9.89871			1.11369			0.556846	+	0.830616i	$0.312011\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−2.42445	+	2.42445i	−0.266118	+	0.266118i	−0.827534	−	0.561416i	$-0.810257\pi$
$83$	−2.42445	+	2.42445i	−0.266118	+	0.266118i	0.561416	+	0.827534i	$0.310257\pi$
$84$		0			0
$85$	−8.21016	−	9.13310i	−0.890517	−	0.990624i
$86$		0			0
$87$	−4.20941	−	4.20941i	−0.451296	−	0.451296i
$88$		0			0
$89$		−	11.5557i		−	1.22490i	−0.790510	−	0.612449i	$-0.790184\pi$
$89$		−	11.5557i		−	1.22490i	0.790510	−	0.612449i	$-0.209816\pi$
$90$		0			0
$91$			11.6074i			1.21679i
$92$		0			0
$93$	4.87215	+	4.87215i	0.505219	+	0.505219i
$94$		0			0
$95$	−0.551547	+	10.3643i	−0.0565875	+	1.06336i
$96$		0			0
$97$	−6.48719	+	6.48719i	−0.658675	+	0.658675i	−0.955066	−	0.296392i	$-0.904217\pi$
$97$	−6.48719	+	6.48719i	−0.658675	+	0.658675i	0.296392	+	0.955066i	$0.404217\pi$
$98$		0			0
$99$	5.80372			0.583295
$100$		0			0
$101$	−5.13800			−0.511250			−0.255625	−	0.966776i	$-0.582281\pi$
$101$	−5.13800			−0.511250			−0.255625	+	0.966776i	$0.582281\pi$
$102$		0			0
$103$	7.01564	−	7.01564i	0.691272	−	0.691272i	−0.271240	−	0.962512i	$-0.587434\pi$
$103$	7.01564	−	7.01564i	0.691272	−	0.691272i	0.962512	+	0.271240i	$0.0874337\pi$
$104$		0			0
$105$	0.451981	−	8.49335i	0.0441088	−	0.828866i
$106$		0			0
$107$	−3.70051	−	3.70051i	−0.357742	−	0.357742i	0.505238	−	0.862980i	$-0.331405\pi$
$107$	−3.70051	−	3.70051i	−0.357742	−	0.357742i	−0.862980	+	0.505238i	$0.831405\pi$
$108$		0			0
$109$		−	3.18155i		−	0.304737i	−0.988324	−	0.152369i	$-0.951310\pi$
$109$		−	3.18155i		−	0.304737i	0.988324	−	0.152369i	$-0.0486901\pi$
$110$		0			0
$111$			2.11525i			0.200771i
$112$		0			0
$113$	4.07894	+	4.07894i	0.383714	+	0.383714i	0.872438	−	0.488724i	$-0.162538\pi$
$113$	4.07894	+	4.07894i	0.383714	+	0.383714i	−0.488724	+	0.872438i	$0.662538\pi$
$114$		0			0
$115$	5.53895	+	6.16161i	0.516510	+	0.574573i
$116$		0			0
$117$	2.15781	−	2.15781i	0.199490	−	0.199490i
$118$		0			0
$119$	−20.8907			−1.91505
$120$		0			0
$121$	−22.6831			−2.06210
$122$		0			0
$123$	−8.03188	+	8.03188i	−0.724210	+	0.724210i
$124$		0			0
$125$	1.77568	−	11.0384i	0.158822	−	0.987307i
$126$		0			0
$127$	−10.7239	−	10.7239i	−0.951596	−	0.951596i	0.0472851	−	0.998881i	$-0.484943\pi$
$127$	−10.7239	−	10.7239i	−0.951596	−	0.951596i	−0.998881	+	0.0472851i	$0.984943\pi$
$128$		0			0
$129$			8.54378i			0.752238i
$130$		0			0
$131$			16.5429i			1.44536i	0.691184	+	0.722679i	$0.257090\pi$
$131$			16.5429i			1.44536i	−0.691184	+	0.722679i	$0.742910\pi$
$132$		0			0
$133$	12.4843	+	12.4843i	1.08252	+	1.08252i
$134$		0			0
$135$	−1.66293	+	1.49488i	−0.143122	+	0.128659i
$136$		0			0
$137$	−7.77563	+	7.77563i	−0.664317	+	0.664317i	−0.956395	−	0.292078i	$-0.905653\pi$
$137$	−7.77563	+	7.77563i	−0.664317	+	0.664317i	0.292078	+	0.956395i	$0.405653\pi$
$138$		0			0
$139$	−7.26439			−0.616157			−0.308079	−	0.951361i	$-0.599686\pi$
$139$	−7.26439			−0.616157			−0.308079	+	0.951361i	$0.599686\pi$
$140$		0			0
$141$	4.22483			0.355795
$142$		0			0
$143$	−12.5233	+	12.5233i	−1.04725	+	1.04725i
$144$		0			0
$145$	−13.2925	−	0.707373i	−1.10388	−	0.0587441i
$146$		0			0
$147$	−5.28085	−	5.28085i	−0.435557	−	0.435557i
$148$		0			0
$149$		−	17.2086i		−	1.40978i	−0.709315	−	0.704892i	$-0.750996\pi$
$149$		−	17.2086i		−	1.40978i	0.709315	−	0.704892i	$-0.249004\pi$
$150$		0			0
$151$		−	3.16118i		−	0.257253i	−0.991693	−	0.128627i	$-0.958943\pi$
$151$		−	3.16118i		−	0.257253i	0.991693	−	0.128627i	$-0.0410569\pi$
$152$		0			0
$153$	3.88356	+	3.88356i	0.313967	+	0.313967i
$154$		0			0
$155$	15.3853	+	0.818743i	1.23578	+	0.0657631i
$156$		0			0
$157$	−9.31225	+	9.31225i	−0.743198	+	0.743198i	−0.973192	−	0.229994i	$-0.926129\pi$
$157$	−9.31225	+	9.31225i	−0.743198	+	0.743198i	0.229994	+	0.973192i	$0.426129\pi$
$158$		0			0
$159$	8.75688			0.694466
$160$		0			0
$161$	14.0938			1.11075
$162$		0			0
$163$	−3.95863	+	3.95863i	−0.310064	+	0.310064i	−0.844934	−	0.534870i	$-0.820361\pi$
$163$	−3.95863	+	3.95863i	−0.310064	+	0.310064i	0.534870	+	0.844934i	$0.320361\pi$
$164$		0			0
$165$	9.65116	−	8.67587i	0.751342	−	0.675416i
$166$		0			0
$167$	4.10722	+	4.10722i	0.317826	+	0.317826i	0.847932	−	0.530106i	$-0.177848\pi$
$167$	4.10722	+	4.10722i	0.317826	+	0.317826i	−0.530106	+	0.847932i	$0.677848\pi$
$168$		0			0
$169$		−	3.68772i		−	0.283670i
$170$		0			0
$171$		−	4.64163i		−	0.354954i
$172$		0			0
$173$	1.07091	+	1.07091i	0.0814196	+	0.0814196i	0.746644	−	0.665224i	$-0.231664\pi$
$173$	1.07091	+	1.07091i	0.0814196	+	0.0814196i	−0.665224	+	0.746644i	$0.731664\pi$
$174$		0			0
$175$	−11.9449	−	14.7995i	−0.902953	−	1.11874i
$176$		0			0
$177$	−6.25314	+	6.25314i	−0.470015	+	0.470015i
$178$		0			0
$179$	4.93726			0.369028			0.184514	−	0.982830i	$-0.440929\pi$
$179$	4.93726			0.369028			0.184514	+	0.982830i	$0.440929\pi$
$180$		0			0
$181$	24.4648			1.81845			0.909227	−	0.416300i	$-0.136673\pi$
$181$	24.4648			1.81845			0.909227	+	0.416300i	$0.136673\pi$
$182$		0			0
$183$	7.14161	−	7.14161i	0.527923	−	0.527923i
$184$		0			0
$185$	3.16205	+	3.51751i	0.232478	+	0.258612i
$186$		0			0
$187$	−22.5391	−	22.5391i	−1.64822	−	1.64822i
$188$		0			0
$189$			3.80372i			0.276680i
$190$		0			0
$191$		−	1.37724i		−	0.0996537i	−0.998758	−	0.0498269i	$-0.984133\pi$
$191$		−	1.37724i		−	0.0996537i	0.998758	−	0.0498269i	$-0.0158670\pi$
$192$		0			0
$193$	12.6175	+	12.6175i	0.908228	+	0.908228i	0.996129	−	0.0879009i	$-0.0280159\pi$
$193$	12.6175	+	12.6175i	0.908228	+	0.908228i	−0.0879009	+	0.996129i	$0.528016\pi$
$194$		0			0
$195$	0.362610	−	6.81395i	0.0259671	−	0.487957i
$196$		0			0
$197$	−7.09945	+	7.09945i	−0.505815	+	0.505815i	−0.913239	−	0.407424i	$-0.866427\pi$
$197$	−7.09945	+	7.09945i	−0.505815	+	0.505815i	0.407424	+	0.913239i	$0.366427\pi$
$198$		0			0
$199$	15.2096			1.07818			0.539092	−	0.842247i	$-0.318768\pi$
$199$	15.2096			1.07818			0.539092	+	0.842247i	$0.318768\pi$
$200$		0			0
$201$	−5.80281			−0.409299
$202$		0			0
$203$	−16.0114	+	16.0114i	−1.12378	+	1.12378i
$204$		0			0
$205$	−1.34972	+	25.3631i	−0.0942686	+	1.77144i
$206$		0			0
$207$	−2.62003	−	2.62003i	−0.182104	−	0.182104i
$208$		0			0
$209$			26.9387i			1.86339i
$210$		0			0
$211$		−	6.76711i		−	0.465867i	−0.972493	−	0.232934i	$-0.925167\pi$
$211$		−	6.76711i		−	0.465867i	0.972493	−	0.232934i	$-0.0748325\pi$
$212$		0			0
$213$	1.93816	+	1.93816i	0.132801	+	0.132801i
$214$		0			0
$215$	12.7719	+	14.2077i	0.871040	+	0.968957i
$216$		0			0
$217$	18.5323	−	18.5323i	1.25805	−	1.25805i
$218$		0			0
$219$	0.953165			0.0644089
$220$		0			0
$221$	−16.7600			−1.12740
$222$		0			0
$223$	−1.95433	+	1.95433i	−0.130872	+	0.130872i	−0.769508	−	0.638637i	$-0.779499\pi$
$223$	−1.95433	+	1.95433i	−0.130872	+	0.130872i	0.638637	+	0.769508i	$0.279499\pi$
$224$		0			0
$225$	−0.530656	+	4.97176i	−0.0353770	+	0.331451i
$226$		0			0
$227$	4.59995	+	4.59995i	0.305309	+	0.305309i	0.843087	−	0.537777i	$-0.180736\pi$
$227$	4.59995	+	4.59995i	0.305309	+	0.305309i	−0.537777	+	0.843087i	$0.680736\pi$
$228$		0			0
$229$		−	22.5952i		−	1.49313i	−0.665310	−	0.746567i	$-0.731701\pi$
$229$		−	22.5952i		−	1.49313i	0.665310	−	0.746567i	$-0.268299\pi$
$230$		0			0
$231$		−	22.0757i		−	1.45247i
$232$		0			0
$233$	−10.1427	−	10.1427i	−0.664470	−	0.664470i	0.291960	−	0.956430i	$-0.405693\pi$
$233$	−10.1427	−	10.1427i	−0.664470	−	0.664470i	−0.956430	+	0.291960i	$0.905693\pi$
$234$		0			0
$235$	7.02558	−	6.31562i	0.458298	−	0.411986i
$236$		0			0
$237$	−6.99945	+	6.99945i	−0.454663	+	0.454663i
$238$		0			0
$239$	0.912267			0.0590096			0.0295048	−	0.999565i	$-0.490607\pi$
$239$	0.912267			0.0590096			0.0295048	+	0.999565i	$0.490607\pi$
$240$		0			0
$241$	4.00000			0.257663			0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000			0.257663			0.128831	+	0.991667i	$0.458877\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−16.6759	−	0.887423i	−1.06539	−	0.0566954i
$246$		0			0
$247$	10.0158	+	10.0158i	0.637287	+	0.637287i
$248$		0			0
$249$		−	3.42869i		−	0.217284i
$250$		0			0
$251$			22.1023i			1.39508i	0.716543	+	0.697542i	$0.245723\pi$
$251$			22.1023i			1.39508i	−0.716543	+	0.697542i	$0.754277\pi$
$252$		0			0
$253$	15.2059	+	15.2059i	0.955986	+	0.955986i
$254$		0			0
$255$	12.2635	+	0.652614i	0.767972	+	0.0408683i
$256$		0			0
$257$	15.3590	−	15.3590i	0.958067	−	0.958067i	−0.0410889	−	0.999155i	$-0.513083\pi$
$257$	15.3590	−	15.3590i	0.958067	−	0.958067i	0.999155	+	0.0410889i	$0.0130827\pi$
$258$		0			0
$259$	8.04581			0.499942
$260$		0			0
$261$	5.95301			0.368482
$262$		0			0
$263$	−3.19982	+	3.19982i	−0.197309	+	0.197309i	−0.798845	−	0.601536i	$-0.794556\pi$
$263$	−3.19982	+	3.19982i	−0.197309	+	0.197309i	0.601536	+	0.798845i	$0.294556\pi$
$264$		0			0
$265$	14.5621	−	13.0905i	0.894540	−	0.804143i
$266$		0			0
$267$	8.17109	+	8.17109i	0.500063	+	0.500063i
$268$		0			0
$269$		−	16.6668i		−	1.01619i	−0.861301	−	0.508095i	$-0.830350\pi$
$269$		−	16.6668i		−	1.01619i	0.861301	−	0.508095i	$-0.169650\pi$
$270$		0			0
$271$		−	15.7144i		−	0.954579i	−0.878746	−	0.477290i	$-0.841619\pi$
$271$		−	15.7144i		−	0.954579i	0.878746	−	0.477290i	$-0.158381\pi$
$272$		0			0
$273$	−8.20769	−	8.20769i	−0.496752	−	0.496752i
$274$		0			0
$275$	3.07977	−	28.8547i	0.185717	−	1.74000i
$276$		0			0
$277$	−12.5594	+	12.5594i	−0.754618	+	0.754618i	−0.975337	−	0.220719i	$-0.929160\pi$
$277$	−12.5594	+	12.5594i	−0.754618	+	0.754618i	0.220719	+	0.975337i	$0.429160\pi$
$278$		0			0
$279$	−6.89027			−0.412509
$280$		0			0
$281$	26.3984			1.57479			0.787397	−	0.616446i	$-0.211428\pi$
$281$	26.3984			1.57479			0.787397	+	0.616446i	$0.211428\pi$
$282$		0			0
$283$	−0.122182	+	0.122182i	−0.00726295	+	0.00726295i	−0.710729	−	0.703466i	$-0.751635\pi$
$283$	−0.122182	+	0.122182i	−0.00726295	+	0.00726295i	0.703466	+	0.710729i	$0.251635\pi$
$284$		0			0
$285$	−6.93869	−	7.71869i	−0.411012	−	0.457216i
$286$		0			0
$287$	30.5510	+	30.5510i	1.80337	+	1.80337i
$288$		0			0
$289$		−	13.1640i		−	0.774356i
$290$		0			0
$291$		−	9.17427i		−	0.537806i
$292$		0			0
$293$	−18.3646	−	18.3646i	−1.07287	−	1.07287i	−0.997127	−	0.0757424i	$-0.975867\pi$
$293$	−18.3646	−	18.3646i	−1.07287	−	1.07287i	−0.0757424	−	0.997127i	$-0.524133\pi$
$294$		0			0
$295$	−1.05081	+	19.7462i	−0.0611806	+	1.14967i
$296$		0			0
$297$	−4.10385	+	4.10385i	−0.238129	+	0.238129i
$298$		0			0
$299$	11.3070			0.653903
$300$		0			0
$301$	32.4981			1.87316
$302$		0			0
$303$	3.63311	−	3.63311i	0.208717	−	0.208717i
$304$		0			0
$305$	1.20012	−	22.5519i	0.0687184	−	1.29132i
$306$		0			0
$307$	−15.4902	−	15.4902i	−0.884073	−	0.884073i	0.109872	−	0.993946i	$-0.464956\pi$
$307$	−15.4902	−	15.4902i	−0.884073	−	0.884073i	−0.993946	+	0.109872i	$0.964956\pi$
$308$		0			0
$309$			9.92162i			0.564421i
$310$		0			0
$311$		−	10.1515i		−	0.575640i	−0.957684	−	0.287820i	$-0.907069\pi$
$311$		−	10.1515i		−	0.575640i	0.957684	−	0.287820i	$-0.0929305\pi$
$312$		0			0
$313$	12.7908	+	12.7908i	0.722978	+	0.722978i	0.969211	−	0.246233i	$-0.0791927\pi$
$313$	12.7908	+	12.7908i	0.722978	+	0.722978i	−0.246233	+	0.969211i	$0.579193\pi$
$314$		0			0
$315$	5.68611	+	6.32530i	0.320376	+	0.356390i
$316$		0			0
$317$	−2.11880	+	2.11880i	−0.119004	+	0.119004i	−0.764101	−	0.645097i	$-0.776817\pi$
$317$	−2.11880	+	2.11880i	−0.119004	+	0.119004i	0.645097	+	0.764101i	$0.276817\pi$
$318$		0			0
$319$	−34.5496			−1.93440
$320$		0			0
$321$	5.23331			0.292095
$322$		0			0
$323$	−18.0260	+	18.0260i	−1.00300	+	1.00300i
$324$		0			0
$325$	−9.58306	−	11.8732i	−0.531572	−	0.658605i
$326$		0			0
$327$	2.24970	+	2.24970i	0.124408	+	0.124408i
$328$		0			0
$329$		−	16.0700i		−	0.885970i
$330$		0			0
$331$		−	22.6761i		−	1.24639i	−0.782065	−	0.623196i	$-0.785834\pi$
$331$		−	22.6761i		−	1.24639i	0.782065	−	0.623196i	$-0.214166\pi$
$332$		0			0
$333$	−1.49571	−	1.49571i	−0.0819643	−	0.0819643i
$334$		0			0
$335$	−9.64965	+	8.67452i	−0.527217	+	0.473940i
$336$		0			0
$337$	−14.2885	+	14.2885i	−0.778343	+	0.778343i	−0.979549	−	0.201206i	$-0.935514\pi$
$337$	−14.2885	+	14.2885i	−0.778343	+	0.778343i	0.201206	+	0.979549i	$0.435514\pi$
$338$		0			0
$339$	−5.76849			−0.313301
$340$		0			0
$341$	39.9891			2.16553
$342$		0			0
$343$	−1.25942	+	1.25942i	−0.0680023	+	0.0680023i
$344$		0			0
$345$	−8.27354	−	0.440284i	−0.445433	−	0.0237041i
$346$		0			0
$347$	−1.50798	−	1.50798i	−0.0809524	−	0.0809524i	0.665471	−	0.746424i	$-0.268231\pi$
$347$	−1.50798	−	1.50798i	−0.0809524	−	0.0809524i	−0.746424	+	0.665471i	$0.768231\pi$
$348$		0			0
$349$		−	21.8565i		−	1.16995i	−0.811050	−	0.584976i	$-0.801104\pi$
$349$		−	21.8565i		−	1.16995i	0.811050	−	0.584976i	$-0.198896\pi$
$350$		0			0
$351$			3.05160i			0.162883i
$352$		0			0
$353$	15.3384	+	15.3384i	0.816378	+	0.816378i	0.985581	−	0.169203i	$-0.0541193\pi$
$353$	15.3384	+	15.3384i	0.816378	+	0.816378i	−0.169203	+	0.985581i	$0.554119\pi$
$354$		0			0
$355$	6.12034	+	0.325699i	0.324834	+	0.0172863i
$356$		0			0
$357$	14.7719	−	14.7719i	0.781814	−	0.781814i
$358$		0			0
$359$	8.22111			0.433894			0.216947	−	0.976183i	$-0.430390\pi$
$359$	8.22111			0.433894			0.216947	+	0.976183i	$0.430390\pi$
$360$		0			0
$361$	2.54473			0.133933
$362$		0			0
$363$	16.0394	−	16.0394i	0.841849	−	0.841849i
$364$		0			0
$365$	1.58504	−	1.42487i	0.0829650	−	0.0745810i
$366$		0			0
$367$	23.8887	+	23.8887i	1.24698	+	1.24698i	0.957046	+	0.289936i	$0.0936341\pi$
$367$	23.8887	+	23.8887i	1.24698	+	1.24698i	0.289936	+	0.957046i	$0.406366\pi$
$368$		0			0
$369$		−	11.3588i		−	0.591315i
$370$		0			0
$371$		−	33.3087i		−	1.72930i
$372$		0			0
$373$	−10.5595	−	10.5595i	−0.546750	−	0.546750i	0.378749	−	0.925499i	$-0.376354\pi$
$373$	−10.5595	−	10.5595i	−0.546750	−	0.546750i	−0.925499	+	0.378749i	$0.876354\pi$
$374$		0			0
$375$	6.54975	+	9.06095i	0.338228	+	0.467905i
$376$		0			0
$377$	−12.8455	+	12.8455i	−0.661575	+	0.661575i
$378$		0			0
$379$	6.56369			0.337154			0.168577	−	0.985688i	$-0.446083\pi$
$379$	6.56369			0.337154			0.168577	+	0.985688i	$0.446083\pi$
$380$		0			0
$381$	15.1659			0.776975
$382$		0			0
$383$	9.18512	−	9.18512i	0.469338	−	0.469338i	−0.432362	−	0.901700i	$-0.642320\pi$
$383$	9.18512	−	9.18512i	0.469338	−	0.469338i	0.901700	+	0.432362i	$0.142320\pi$
$384$		0			0
$385$	−33.0005	−	36.7103i	−1.68186	−	1.87093i
$386$		0			0
$387$	−6.04137	−	6.04137i	−0.307100	−	0.307100i
$388$		0			0
$389$			22.3585i			1.13362i	0.823849	+	0.566810i	$0.191823\pi$
$389$			22.3585i			1.13362i	−0.823849	+	0.566810i	$0.808177\pi$
$390$		0			0
$391$			20.3500i			1.02915i
$392$		0			0
$393$	−11.6976	−	11.6976i	−0.590065	−	0.590065i
$394$		0			0
$395$	−1.17623	+	22.1029i	−0.0591823	+	1.11212i
$396$		0			0
$397$	5.77102	−	5.77102i	0.289639	−	0.289639i	−0.547299	−	0.836937i	$-0.684344\pi$
$397$	5.77102	−	5.77102i	0.289639	−	0.289639i	0.836937	+	0.547299i	$0.184344\pi$
$398$		0			0
$399$	−17.6554			−0.883877
$400$		0			0
$401$	4.18780			0.209129			0.104564	−	0.994518i	$-0.466655\pi$
$401$	4.18780			0.209129			0.104564	+	0.994518i	$0.466655\pi$
$402$		0			0
$403$	14.8679	−	14.8679i	0.740622	−	0.740622i
$404$		0			0
$405$	0.118826	−	2.23291i	0.00590452	−	0.110954i
$406$		0			0
$407$	8.68066	+	8.68066i	0.430284	+	0.430284i
$408$		0			0
$409$		−	33.1651i		−	1.63991i	−0.572430	−	0.819953i	$-0.693999\pi$
$409$		−	33.1651i		−	1.63991i	0.572430	−	0.819953i	$-0.306001\pi$
$410$		0			0
$411$		−	10.9964i		−	0.542413i
$412$		0			0
$413$	23.7852	+	23.7852i	1.17039	+	1.17039i
$414$		0			0
$415$	−5.12549	−	5.70166i	−0.251600	−	0.279884i
$416$		0			0
$417$	5.13670	−	5.13670i	0.251545	−	0.251545i
$418$		0			0
$419$	−22.0479			−1.07711			−0.538555	−	0.842591i	$-0.681029\pi$
$419$	−22.0479			−1.07711			−0.538555	+	0.842591i	$0.681029\pi$
$420$		0			0
$421$	3.71970			0.181287			0.0906434	−	0.995883i	$-0.471108\pi$
$421$	3.71970			0.181287			0.0906434	+	0.995883i	$0.471108\pi$
$422$		0			0
$423$	−2.98740	+	2.98740i	−0.145253	+	0.145253i
$424$		0			0
$425$	21.3690	−	17.2473i	1.03655	−	0.836616i
$426$		0			0
$427$	−27.1647	−	27.1647i	−1.31459	−	1.31459i
$428$		0			0
$429$		−	17.7106i		−	0.855078i
$430$		0			0
$431$			12.9149i			0.622090i	0.950395	+	0.311045i	$0.100679\pi$
$431$			12.9149i			0.622090i	−0.950395	+	0.311045i	$0.899321\pi$
$432$		0			0
$433$	0.521393	+	0.521393i	0.0250565	+	0.0250565i	0.719524	−	0.694468i	$-0.244360\pi$
$433$	0.521393	+	0.521393i	0.0250565	+	0.0250565i	−0.694468	+	0.719524i	$0.744360\pi$
$434$		0			0
$435$	9.89942	−	8.89905i	0.474641	−	0.426677i
$436$		0			0
$437$	12.1612	−	12.1612i	0.581749	−	0.581749i
$438$		0			0
$439$	12.7544			0.608733			0.304367	−	0.952555i	$-0.401555\pi$
$439$	12.7544			0.608733			0.304367	+	0.952555i	$0.401555\pi$
$440$		0			0
$441$	7.46825			0.355631
$442$		0			0
$443$	−17.5846	+	17.5846i	−0.835471	+	0.835471i	−0.988259	−	0.152788i	$-0.951175\pi$
$443$	−17.5846	+	17.5846i	−0.835471	+	0.835471i	0.152788	+	0.988259i	$0.451175\pi$
$444$		0			0
$445$	25.8028	+	1.37312i	1.22317	+	0.0650919i
$446$		0			0
$447$	12.1683	+	12.1683i	0.575542	+	0.575542i
$448$		0			0
$449$			12.1662i			0.574160i	0.957907	+	0.287080i	$0.0926845\pi$
$449$			12.1662i			0.574160i	−0.957907	+	0.287080i	$0.907316\pi$
$450$		0			0
$451$			65.9232i			3.10420i
$452$		0			0
$453$	2.23529	+	2.23529i	0.105023	+	0.105023i
$454$		0			0
$455$	−25.9183	−	1.37927i	−1.21507	−	0.0646610i
$456$		0			0
$457$	−21.1370	+	21.1370i	−0.988745	+	0.988745i	−0.999937	−	0.0111921i	$-0.996437\pi$
$457$	−21.1370	+	21.1370i	−0.988745	+	0.988745i	0.0111921	+	0.999937i	$0.496437\pi$
$458$		0			0
$459$	−5.49218			−0.256353
$460$		0			0
$461$	−26.5966			−1.23873			−0.619363	−	0.785105i	$-0.712609\pi$
$461$	−26.5966			−1.23873			−0.619363	+	0.785105i	$0.712609\pi$
$462$		0			0
$463$	15.2232	−	15.2232i	0.707484	−	0.707484i	−0.258522	−	0.966005i	$-0.583235\pi$
$463$	15.2232	−	15.2232i	0.707484	−	0.707484i	0.966005	+	0.258522i	$0.0832354\pi$
$464$		0			0
$465$	−11.4580	+	10.3001i	−0.531353	+	0.477657i
$466$		0			0
$467$	2.32014	+	2.32014i	0.107363	+	0.107363i	0.758748	−	0.651385i	$-0.225812\pi$
$467$	2.32014	+	2.32014i	0.107363	+	0.107363i	−0.651385	+	0.758748i	$0.725812\pi$
$468$		0			0
$469$			22.0722i			1.01920i
$470$		0			0
$471$		−	13.1695i		−	0.606819i
$472$		0			0
$473$	35.0624	+	35.0624i	1.61217	+	1.61217i
$474$		0			0
$475$	−23.0771	−	2.46311i	−1.05885	−	0.113015i
$476$		0			0
$477$	−6.19205	+	6.19205i	−0.283514	+	0.283514i
$478$		0			0
$479$	−1.39194			−0.0635993			−0.0317996	−	0.999494i	$-0.510124\pi$
$479$	−1.39194			−0.0635993			−0.0317996	+	0.999494i	$0.510124\pi$
$480$		0			0
$481$	6.45490			0.294318
$482$		0			0
$483$	−9.96583	+	9.96583i	−0.453461	+	0.453461i
$484$		0			0
$485$	−13.7145	−	15.2562i	−0.622741	−	0.692746i
$486$		0			0
$487$	4.00720	+	4.00720i	0.181583	+	0.181583i	0.792045	−	0.610462i	$-0.209016\pi$
$487$	4.00720	+	4.00720i	0.181583	+	0.181583i	−0.610462	+	0.792045i	$0.709016\pi$
$488$		0			0
$489$		−	5.59835i		−	0.253166i
$490$		0			0
$491$		−	21.1445i		−	0.954239i	−0.878838	−	0.477119i	$-0.841681\pi$
$491$		−	21.1445i		−	0.954239i	0.878838	−	0.477119i	$-0.158319\pi$
$492$		0			0
$493$	−23.1189	−	23.1189i	−1.04122	−	1.04122i
$494$		0			0
$495$	−0.689633	+	12.9592i	−0.0309967	+	0.582471i
$496$		0			0
$497$	7.37221	−	7.37221i	0.330689	−	0.330689i
$498$		0			0
$499$	23.1641			1.03697			0.518485	−	0.855087i	$-0.326496\pi$
$499$	23.1641			1.03697			0.518485	+	0.855087i	$0.326496\pi$
$500$		0			0
$501$	−5.80848			−0.259504
$502$		0			0
$503$	−6.10016	+	6.10016i	−0.271993	+	0.271993i	−0.829902	−	0.557909i	$-0.811604\pi$
$503$	−6.10016	+	6.10016i	−0.271993	+	0.271993i	0.557909	+	0.829902i	$0.311604\pi$
$504$		0			0
$505$	0.610528	−	11.4727i	0.0271682	−	0.510528i
$506$		0			0
$507$	2.60761	+	2.60761i	0.115808	+	0.115808i
$508$		0			0
$509$			3.76702i			0.166970i	0.996509	+	0.0834851i	$0.0266051\pi$
$509$			3.76702i			0.166970i	−0.996509	+	0.0834851i	$0.973395\pi$
$510$		0			0
$511$		−	3.62557i		−	0.160386i
$512$		0			0
$513$	3.28213	+	3.28213i	0.144909	+	0.144909i
$514$		0			0
$515$	14.8316	+	16.4989i	0.653561	+	0.727030i
$516$		0			0
$517$	17.3380	−	17.3380i	0.762526	−	0.762526i
$518$		0			0
$519$	−1.51449			−0.0664788
$520$		0			0
$521$	27.4355			1.20197			0.600986	−	0.799260i	$-0.294775\pi$
$521$	27.4355			1.20197			0.600986	+	0.799260i	$0.294775\pi$
$522$		0			0
$523$	23.0461	−	23.0461i	1.00774	−	1.00774i	0.00776561	−	0.999970i	$-0.497528\pi$
$523$	23.0461	−	23.0461i	1.00774	−	1.00774i	0.999970	−	0.00776561i	$-0.00247190\pi$
$524$		0			0
$525$	18.9112	+	2.01846i	0.825351	+	0.0880929i
$526$		0			0
$527$	26.7587	+	26.7587i	1.16563	+	1.16563i
$528$		0			0
$529$			9.27093i			0.403084i
$530$		0			0
$531$		−	8.84328i		−	0.383765i
$532$		0			0
$533$	24.5101	+	24.5101i	1.06165	+	1.06165i
$534$		0			0
$535$	8.70261	−	7.82318i	0.376247	−	0.338226i
$536$		0			0
$537$	−3.49117	+	3.49117i	−0.150655	+	0.150655i
$538$		0			0
$539$	−43.3436			−1.86694
$540$		0			0
$541$	16.0627			0.690590			0.345295	−	0.938494i	$-0.387779\pi$
$541$	16.0627			0.690590			0.345295	+	0.938494i	$0.387779\pi$
$542$		0			0
$543$	−17.2992	+	17.2992i	−0.742381	+	0.742381i
$544$		0			0
$545$	7.10411	+	0.378051i	0.304307	+	0.0161939i
$546$		0			0
$547$	8.74219	+	8.74219i	0.373789	+	0.373789i	0.868855	−	0.495066i	$-0.164856\pi$
$547$	8.74219	+	8.74219i	0.373789	+	0.373789i	−0.495066	+	0.868855i	$0.664856\pi$
$548$		0			0
$549$			10.0998i			0.431048i
$550$		0			0
$551$			27.6317i			1.17715i
$552$		0			0
$553$	26.6239	+	26.6239i	1.13216	+	1.13216i
$554$		0			0
$555$	−4.72316	−	0.251347i	−0.200487	−	0.0106691i
$556$		0			0
$557$	−2.10460	+	2.10460i	−0.0891746	+	0.0891746i	−0.750287	−	0.661112i	$-0.770085\pi$
$557$	−2.10460	+	2.10460i	−0.0891746	+	0.0891746i	0.661112	+	0.750287i	$0.270085\pi$
$558$		0			0
$559$	26.0722			1.10274
$560$		0			0
$561$	31.8751			1.34577
$562$		0			0
$563$	4.03931	−	4.03931i	0.170237	−	0.170237i	−0.616847	−	0.787083i	$-0.711590\pi$
$563$	4.03931	−	4.03931i	0.170237	−	0.170237i	0.787083	+	0.616847i	$0.211590\pi$
$564$		0			0
$565$	−9.59258	+	8.62321i	−0.403563	+	0.362781i
$566$		0			0
$567$	−2.68963	−	2.68963i	−0.112954	−	0.112954i
$568$		0			0
$569$		−	29.0811i		−	1.21915i	−0.792730	−	0.609573i	$-0.791341\pi$
$569$		−	29.0811i		−	1.21915i	0.792730	−	0.609573i	$-0.208659\pi$
$570$		0			0
$571$		−	0.0150628i		−	0.000630360i	−1.00000		0.000315180i	$-0.999900\pi$
$571$		−	0.0150628i		−	0.000630360i	1.00000		0.000315180i	$-0.000100325\pi$
$572$		0			0
$573$	0.973857	+	0.973857i	0.0406835	+	0.0406835i
$574$		0			0
$575$	−14.4165	+	11.6358i	−0.601209	+	0.485247i
$576$		0			0
$577$	19.1488	−	19.1488i	0.797174	−	0.797174i	−0.185475	−	0.982649i	$-0.559382\pi$
$577$	19.1488	−	19.1488i	0.797174	−	0.797174i	0.982649	+	0.185475i	$0.0593824\pi$
$578$		0			0
$579$	−17.8439			−0.741565
$580$		0			0
$581$	−13.0418			−0.541063
$582$		0			0
$583$	35.9369	−	35.9369i	1.48835	−	1.48835i
$584$		0			0
$585$	4.56179	+	5.07460i	0.188607	+	0.209809i
$586$		0			0
$587$	−12.2928	−	12.2928i	−0.507379	−	0.507379i	0.406342	−	0.913721i	$-0.366804\pi$
$587$	−12.2928	−	12.2928i	−0.507379	−	0.507379i	−0.913721	+	0.406342i	$0.866804\pi$
$588$		0			0
$589$		−	31.9821i		−	1.31780i
$590$		0			0
$591$		−	10.0401i		−	0.412996i
$592$		0			0
$593$	−9.80097	−	9.80097i	−0.402478	−	0.402478i	0.476628	−	0.879105i	$-0.341859\pi$
$593$	−9.80097	−	9.80097i	−0.402478	−	0.402478i	−0.879105	+	0.476628i	$0.841859\pi$
$594$		0			0
$595$	2.48236	−	46.6470i	0.101767	−	1.91234i
$596$		0			0
$597$	−10.7548	+	10.7548i	−0.440166	+	0.440166i
$598$		0			0
$599$	5.51181			0.225206			0.112603	−	0.993640i	$-0.464081\pi$
$599$	5.51181			0.225206			0.112603	+	0.993640i	$0.464081\pi$
$600$		0			0
$601$	−22.5167			−0.918476			−0.459238	−	0.888313i	$-0.651877\pi$
$601$	−22.5167			−0.918476			−0.459238	+	0.888313i	$0.651877\pi$
$602$		0			0
$603$	4.10321	−	4.10321i	0.167096	−	0.167096i
$604$		0			0
$605$	2.69535	−	50.6493i	0.109581	−	2.05919i
$606$		0			0
$607$	−21.4758	−	21.4758i	−0.871677	−	0.871677i	0.120978	−	0.992655i	$-0.461397\pi$
$607$	−21.4758	−	21.4758i	−0.871677	−	0.871677i	−0.992655	+	0.120978i	$0.961397\pi$
$608$		0			0
$609$		−	22.6436i		−	0.917563i
$610$		0			0
$611$		−	12.8925i		−	0.521575i
$612$		0			0
$613$	−11.5608	−	11.5608i	−0.466936	−	0.466936i	0.433985	−	0.900920i	$-0.357107\pi$
$613$	−11.5608	−	11.5608i	−0.466936	−	0.466936i	−0.900920	+	0.433985i	$0.857107\pi$
$614$		0			0
$615$	−16.9801	−	18.8889i	−0.684702	−	0.761672i
$616$		0			0
$617$	−14.1179	+	14.1179i	−0.568364	+	0.568364i	−0.931670	−	0.363306i	$-0.881648\pi$
$617$	−14.1179	+	14.1179i	−0.568364	+	0.568364i	0.363306	+	0.931670i	$0.381648\pi$
$618$		0			0
$619$	−3.95735			−0.159059			−0.0795297	−	0.996832i	$-0.525342\pi$
$619$	−3.95735			−0.159059			−0.0795297	+	0.996832i	$0.525342\pi$
$620$		0			0
$621$	3.70528			0.148688
$622$		0			0
$623$	31.0805	−	31.0805i	1.24521	−	1.24521i
$624$		0			0
$625$	24.4368	+	5.27659i	0.977472	+	0.211063i
$626$		0			0
$627$	−19.0485	−	19.0485i	−0.760725	−	0.760725i
$628$		0			0
$629$			11.6173i			0.463213i
$630$		0			0
$631$			17.0654i			0.679363i	0.940541	+	0.339681i	$0.110319\pi$
$631$			17.0654i			0.679363i	−0.940541	+	0.339681i	$0.889681\pi$
$632$		0			0
$633$	4.78507	+	4.78507i	0.190190	+	0.190190i
$634$		0			0
$635$	25.2199	−	22.6713i	1.00082	−	0.899683i
$636$		0			0
$637$	−16.1151	+	16.1151i	−0.638502	+	0.638502i
$638$		0			0
$639$	−2.74097			−0.108431
$640$		0			0
$641$	−0.0287123			−0.00113407			−0.000567034	−	1.00000i	$-0.500180\pi$
$641$	−0.0287123			−0.00113407			−0.000567034		1.00000i	$0.500180\pi$
$642$		0			0
$643$	−30.3038	+	30.3038i	−1.19507	+	1.19507i	−0.219440	+	0.975626i	$0.570423\pi$
$643$	−30.3038	+	30.3038i	−1.19507	+	1.19507i	−0.975626	+	0.219440i	$0.929577\pi$
$644$		0			0
$645$	−19.0775	−	1.01522i	−0.751175	−	0.0399744i
$646$		0			0
$647$	−34.4599	−	34.4599i	−1.35476	−	1.35476i	−0.880252	−	0.474507i	$-0.842626\pi$
$647$	−34.4599	−	34.4599i	−1.35476	−	1.35476i	−0.474507	−	0.880252i	$-0.657374\pi$
$648$		0			0
$649$			51.3239i			2.01464i
$650$		0			0
$651$			26.2086i			1.02720i
$652$		0			0
$653$	17.3425	+	17.3425i	0.678663	+	0.678663i	0.959698	−	0.281035i	$-0.0906777\pi$
$653$	17.3425	+	17.3425i	0.678663	+	0.678663i	−0.281035	+	0.959698i	$0.590678\pi$
$654$		0			0
$655$	−36.9387	−	1.96573i	−1.44332	−	0.0768073i
$656$		0			0
$657$	−0.673989	+	0.673989i	−0.0262948	+	0.0262948i
$658$		0			0
$659$	−21.6781			−0.844458			−0.422229	−	0.906489i	$-0.638752\pi$
$659$	−21.6781			−0.844458			−0.422229	+	0.906489i	$0.638752\pi$
$660$		0			0
$661$	24.3118			0.945619			0.472810	−	0.881165i	$-0.343240\pi$
$661$	24.3118			0.945619			0.472810	+	0.881165i	$0.343240\pi$
$662$		0			0
$663$	11.8511	−	11.8511i	0.460258	−	0.460258i
$664$		0			0
$665$	−29.3597	+	26.3928i	−1.13852	+	1.02347i
$666$		0			0
$667$	15.5970	+	15.5970i	0.603920	+	0.603920i
$668$		0			0
$669$		−	2.76384i		−	0.106856i
$670$		0			0
$671$		−	58.6162i		−	2.26285i
$672$		0			0
$673$	−11.5868	−	11.5868i	−0.446636	−	0.446636i	0.447598	−	0.894235i	$-0.352279\pi$
$673$	−11.5868	−	11.5868i	−0.446636	−	0.446636i	−0.894235	+	0.447598i	$0.852279\pi$
$674$		0			0
$675$	−3.14034	−	3.89080i	−0.120872	−	0.149757i
$676$		0			0
$677$	5.46873	−	5.46873i	0.210181	−	0.210181i	−0.594164	−	0.804344i	$-0.702517\pi$
$677$	5.46873	−	5.46873i	0.210181	−	0.210181i	0.804344	+	0.594164i	$0.202517\pi$
$678$		0			0
$679$	−34.8963			−1.33920
$680$		0			0
$681$	−6.50531			−0.249284
$682$		0			0
$683$	10.0494	−	10.0494i	0.384531	−	0.384531i	−0.488200	−	0.872732i	$-0.662347\pi$
$683$	10.0494	−	10.0494i	0.384531	−	0.384531i	0.872732	+	0.488200i	$0.162347\pi$
$684$		0			0
$685$	−16.4383	−	18.2862i	−0.628076	−	0.698681i
$686$		0			0
$687$	15.9772	+	15.9772i	0.609570	+	0.609570i
$688$		0			0
$689$		−	26.7225i		−	1.01805i
$690$		0			0
$691$			48.6568i			1.85099i	0.378757	+	0.925496i	$0.376352\pi$
$691$			48.6568i			1.85099i	−0.378757	+	0.925496i	$0.623648\pi$
$692$		0			0
$693$	15.6099	+	15.6099i	0.592970	+	0.592970i
$694$		0			0
$695$	0.863199	−	16.2207i	0.0327430	−	0.615287i
$696$		0			0
$697$	−44.1125	+	44.1125i	−1.67088	+	1.67088i
$698$		0			0
$699$	14.3439			0.542538
$700$		0			0
$701$	−6.75669			−0.255196			−0.127598	−	0.991826i	$-0.540727\pi$
$701$	−6.75669			−0.255196			−0.127598	+	0.991826i	$0.540727\pi$
$702$		0			0
$703$	6.94252	−	6.94252i	0.261842	−	0.261842i
$704$		0			0
$705$	−0.502020	+	9.43365i	−0.0189072	+	0.355292i
$706$		0			0
$707$	−13.8193	−	13.8193i	−0.519729	−	0.519729i
$708$		0			0
$709$			31.1296i			1.16910i	0.811359	+	0.584549i	$0.198728\pi$
$709$			31.1296i			1.16910i	−0.811359	+	0.584549i	$0.801272\pi$
$710$		0			0
$711$		−	9.89871i		−	0.371231i
$712$		0			0
$713$	−18.0527	−	18.0527i	−0.676078	−	0.676078i
$714$		0			0
$715$	−26.4753	−	29.4515i	−0.990121	−	1.10142i
$716$		0			0
$717$	−0.645070	+	0.645070i	−0.0240906	+	0.0240906i
$718$		0			0
$719$	−12.6923			−0.473344			−0.236672	−	0.971590i	$-0.576057\pi$
$719$	−12.6923			−0.473344			−0.236672	+	0.971590i	$0.576057\pi$
$720$		0			0
$721$	37.7390			1.40547
$722$		0			0
$723$	−2.82843	+	2.82843i	−0.105190	+	0.105190i
$724$		0			0
$725$	3.15900	−	29.5969i	0.117322	−	1.09920i
$726$		0			0
$727$	31.6059	+	31.6059i	1.17220	+	1.17220i	0.981684	+	0.190515i	$0.0610158\pi$
$727$	31.6059	+	31.6059i	1.17220	+	1.17220i	0.190515	+	0.981684i	$0.438984\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			46.9240i			1.73555i
$732$		0			0
$733$	−9.20040	−	9.20040i	−0.339824	−	0.339824i	0.516477	−	0.856301i	$-0.327243\pi$
$733$	−9.20040	−	9.20040i	−0.339824	−	0.339824i	−0.856301	+	0.516477i	$0.827243\pi$
$734$		0			0
$735$	12.4192	−	11.1642i	0.458088	−	0.411796i
$736$		0			0
$737$	−23.8138	+	23.8138i	−0.877194	+	0.877194i
$738$		0			0
$739$	22.9272			0.843389			0.421695	−	0.906738i	$-0.361435\pi$
$739$	22.9272			0.843389			0.421695	+	0.906738i	$0.361435\pi$
$740$		0			0
$741$	−14.1644			−0.520343
$742$		0			0
$743$	−26.1819	+	26.1819i	−0.960522	+	0.960522i	−0.999250	−	0.0387279i	$-0.987669\pi$
$743$	−26.1819	+	26.1819i	−0.960522	+	0.960522i	0.0387279	+	0.999250i	$0.487669\pi$
$744$		0			0
$745$	38.4252	+	2.04483i	1.40779	+	0.0749168i
$746$		0			0
$747$	2.42445	+	2.42445i	0.0887060	+	0.0887060i
$748$		0			0
$749$		−	19.9060i		−	0.727350i
$750$		0			0
$751$			40.7010i			1.48520i	0.669734	+	0.742601i	$0.266408\pi$
$751$			40.7010i			1.48520i	−0.669734	+	0.742601i	$0.733592\pi$
$752$		0			0
$753$	−15.6287	−	15.6287i	−0.569541	−	0.569541i
$754$		0			0
$755$	7.05863	+	0.375631i	0.256890	+	0.0136706i
$756$		0			0
$757$	−7.49681	+	7.49681i	−0.272476	+	0.272476i	−0.830096	−	0.557620i	$-0.811715\pi$
$757$	−7.49681	+	7.49681i	−0.272476	+	0.272476i	0.557620	+	0.830096i	$0.311715\pi$
$758$		0			0
$759$	−21.5044			−0.780559
$760$		0			0
$761$	−48.3651			−1.75323			−0.876617	−	0.481188i	$-0.840205\pi$
$761$	−48.3651			−1.75323			−0.876617	+	0.481188i	$0.840205\pi$
$762$		0			0
$763$	8.55720	−	8.55720i	0.309791	−	0.309791i
$764$		0			0
$765$	−9.13310	+	8.21016i	−0.330208	+	0.296839i
$766$		0			0
$767$	19.0821	+	19.0821i	0.689015	+	0.689015i
$768$		0			0
$769$			38.3210i			1.38189i	0.722907	+	0.690946i	$0.242806\pi$
$769$			38.3210i			1.38189i	−0.722907	+	0.690946i	$0.757194\pi$
$770$		0			0
$771$			21.7209i			0.782258i
$772$		0			0
$773$	7.77146	+	7.77146i	0.279520	+	0.279520i	0.832917	−	0.553397i	$-0.186669\pi$
$773$	7.77146	+	7.77146i	0.279520	+	0.279520i	−0.553397	+	0.832917i	$0.686669\pi$
$774$		0			0
$775$	−3.65636	+	34.2568i	−0.131340	+	1.23054i
$776$		0			0
$777$	−5.68925	+	5.68925i	−0.204101	+	0.204101i
$778$		0			0
$779$	52.7233			1.88901
$780$		0			0
$781$	15.9078			0.569227
$782$		0			0
$783$	−4.20941	+	4.20941i	−0.150432	+	0.150432i
$784$		0			0
$785$	−19.6869	−	21.8999i	−0.702654	−	0.781642i
$786$		0			0
$787$	−34.1905	−	34.1905i	−1.21876	−	1.21876i	−0.968066	−	0.250694i	$-0.919341\pi$
$787$	−34.1905	−	34.1905i	−1.21876	−	1.21876i	−0.250694	−	0.968066i	$-0.580659\pi$
$788$		0			0
$789$		−	4.52522i		−	0.161102i
$790$		0			0
$791$			21.9417i			0.780157i
$792$		0			0
$793$	−21.7934	−	21.7934i	−0.773905	−	0.773905i
$794$		0			0
$795$	−1.04055	+	19.5533i	−0.0369044	+	0.693484i
$796$		0			0
$797$	0.579272	−	0.579272i	0.0205189	−	0.0205189i	−0.696773	−	0.717292i	$-0.745381\pi$
$797$	0.579272	−	0.579272i	0.0205189	−	0.0205189i	0.717292	+	0.696773i	$0.245381\pi$
$798$		0			0
$799$	23.2035			0.820881
$800$		0			0
$801$	−11.5557			−0.408300
$802$		0			0
$803$	3.91164	−	3.91164i	0.138039	−	0.138039i
$804$		0			0
$805$	−1.67471	+	31.4702i	−0.0590259	+	1.10918i
$806$		0			0
$807$	11.7852	+	11.7852i	0.414858	+	0.414858i
$808$		0			0
$809$		−	32.0703i		−	1.12753i	−0.825935	−	0.563766i	$-0.809352\pi$
$809$		−	32.0703i		−	1.12753i	0.825935	−	0.563766i	$-0.190648\pi$
$810$		0			0
$811$			22.0227i			0.773322i	0.922222	+	0.386661i	$0.126372\pi$
$811$			22.0227i			0.773322i	−0.922222	+	0.386661i	$0.873628\pi$
$812$		0			0
$813$	11.1117	+	11.1117i	0.389705	+	0.389705i
$814$		0			0
$815$	−8.36888	−	9.30965i	−0.293149	−	0.326103i
$816$		0			0
$817$	28.0418	−	28.0418i	0.981058	−	0.981058i
$818$		0			0
$819$	11.6074			0.405596
$820$		0			0
$821$	−19.5956			−0.683890			−0.341945	−	0.939720i	$-0.611086\pi$
$821$	−19.5956			−0.683890			−0.341945	+	0.939720i	$0.611086\pi$
$822$		0			0
$823$	−27.2779	+	27.2779i	−0.950848	+	0.950848i	−0.998847	−	0.0479991i	$-0.984716\pi$
$823$	−27.2779	+	27.2779i	−0.950848	+	0.950848i	0.0479991	+	0.998847i	$0.484716\pi$
$824$		0			0
$825$	18.2256	+	22.5811i	0.634534	+	0.786172i
$826$		0			0
$827$	29.8352	+	29.8352i	1.03747	+	1.03747i	0.999270	+	0.0382002i	$0.0121624\pi$
$827$	29.8352	+	29.8352i	1.03747	+	1.03747i	0.0382002	+	0.999270i	$0.487838\pi$
$828$		0			0
$829$		−	30.0389i		−	1.04330i	−0.853161	−	0.521648i	$-0.825318\pi$
$829$		−	30.0389i		−	1.04330i	0.853161	−	0.521648i	$-0.174682\pi$
$830$		0			0
$831$		−	17.7616i		−	0.616143i
$832$		0			0
$833$	−29.0034	−	29.0034i	−1.00491	−	1.00491i
$834$		0			0
$835$	−9.65909	+	8.68300i	−0.334266	+	0.300488i
$836$		0			0
$837$	4.87215	−	4.87215i	0.168406	−	0.168406i
$838$		0			0
$839$	−12.2765			−0.423830			−0.211915	−	0.977288i	$-0.567970\pi$
$839$	−12.2765			−0.423830			−0.211915	+	0.977288i	$0.567970\pi$
$840$		0			0
$841$	−6.43831			−0.222011
$842$		0			0
$843$	−18.6665	+	18.6665i	−0.642907	+	0.642907i
$844$		0			0
$845$	8.23433	+	0.438197i	0.283270	+	0.0150744i
$846$		0			0
$847$	−61.0092	−	61.0092i	−2.09630	−	2.09630i
$848$		0			0
$849$		−	0.172791i		−	0.00593017i
$850$		0			0
$851$		−	7.83759i		−	0.268669i
$852$		0			0
$853$	15.3263	+	15.3263i	0.524762	+	0.524762i	0.919006	−	0.394244i	$-0.128993\pi$
$853$	15.3263	+	15.3263i	0.524762	+	0.524762i	−0.394244	+	0.919006i	$0.628993\pi$
$854$		0			0
$855$	10.3643	+	0.551547i	0.354453	+	0.0188625i
$856$		0			0
$857$	−3.09750	+	3.09750i	−0.105809	+	0.105809i	−0.758029	−	0.652221i	$-0.773838\pi$
$857$	−3.09750	+	3.09750i	−0.105809	+	0.105809i	0.652221	+	0.758029i	$0.273838\pi$
$858$		0			0
$859$	21.0380			0.717809			0.358904	−	0.933374i	$-0.383150\pi$
$859$	21.0380			0.717809			0.358904	+	0.933374i	$0.383150\pi$
$860$		0			0
$861$	−43.2056			−1.47244
$862$		0			0
$863$	−25.3036	+	25.3036i	−0.861343	+	0.861343i	−0.991494	−	0.130151i	$-0.958454\pi$
$863$	−25.3036	+	25.3036i	−0.861343	+	0.861343i	0.130151	+	0.991494i	$0.458454\pi$
$864$		0			0
$865$	−2.51849	+	2.26399i	−0.0856313	+	0.0769779i
$866$		0			0
$867$	9.30839	+	9.30839i	0.316129	+	0.316129i
$868$		0			0
$869$			57.4493i			1.94883i
$870$		0			0
$871$			17.7079i			0.600009i
$872$		0			0
$873$	6.48719	+	6.48719i	0.219558	+	0.219558i
$874$		0			0
$875$	34.4653	−	24.9134i	1.16514	−	0.842227i
$876$		0			0
$877$	−40.0472	+	40.0472i	−1.35230	+	1.35230i	−0.469215	+	0.883084i	$0.655463\pi$
$877$	−40.0472	+	40.0472i	−1.35230	+	1.35230i	−0.883084	+	0.469215i	$0.844537\pi$
$878$		0			0
$879$	25.9714			0.875995
$880$		0			0
$881$	5.03824			0.169743			0.0848713	−	0.996392i	$-0.472952\pi$
$881$	5.03824			0.169743			0.0848713	+	0.996392i	$0.472952\pi$
$882$		0			0
$883$	8.99198	−	8.99198i	0.302604	−	0.302604i	−0.539428	−	0.842032i	$-0.681359\pi$
$883$	8.99198	−	8.99198i	0.302604	−	0.302604i	0.842032	+	0.539428i	$0.181359\pi$
$884$		0			0
$885$	−13.2197	−	14.7057i	−0.444374	−	0.494328i
$886$		0			0
$887$	−27.1468	−	27.1468i	−0.911500	−	0.911500i	0.0848907	−	0.996390i	$-0.472946\pi$
$887$	−27.1468	−	27.1468i	−0.911500	−	0.911500i	−0.996390	+	0.0848907i	$0.972946\pi$
$888$		0			0
$889$		−	57.6870i		−	1.93476i
$890$		0			0
$891$		−	5.80372i		−	0.194432i
$892$		0			0
$893$	−13.8664	−	13.8664i	−0.464022	−	0.464022i
$894$		0			0
$895$	−0.586675	+	11.0244i	−0.0196104	+	0.368507i
$896$		0			0
$897$	−7.99528	+	7.99528i	−0.266955	+	0.266955i
$898$		0			0
$899$	41.0178			1.36802
$900$		0			0
$901$	48.0944			1.60226
$902$		0			0
$903$	−22.9796	+	22.9796i	−0.764715	+	0.764715i
$904$		0			0
$905$	−2.90706	+	54.6277i	−0.0966339	+	1.81589i
$906$		0			0
$907$	34.6231	+	34.6231i	1.14964	+	1.14964i	0.986623	+	0.163017i	$0.0521226\pi$
$907$	34.6231	+	34.6231i	1.14964	+	1.14964i	0.163017	+	0.986623i	$0.447877\pi$
$908$		0			0
$909$			5.13800i			0.170417i
$910$		0			0
$911$			16.7555i			0.555135i	0.960706	+	0.277567i	$0.0895281\pi$
$911$			16.7555i			0.555135i	−0.960706	+	0.277567i	$0.910472\pi$
$912$		0			0
$913$	−14.0708	−	14.0708i	−0.465676	−	0.465676i
$914$		0			0
$915$	15.0980	+	16.7952i	0.499123	+	0.555232i
$916$		0			0
$917$	−44.4943	+	44.4943i	−1.46933	+	1.46933i
$918$		0			0
$919$	40.7555			1.34440			0.672199	−	0.740370i	$-0.265350\pi$
$919$	40.7555			1.34440			0.672199	+	0.740370i	$0.265350\pi$
$920$		0			0
$921$	21.9065			0.721843
$922$		0			0
$923$	5.91450	−	5.91450i	0.194678	−	0.194678i
$924$		0			0
$925$	−8.23001	+	6.64260i	−0.270601	+	0.218407i
$926$		0			0
$927$	−7.01564	−	7.01564i	−0.230424	−	0.230424i
$928$		0			0
$929$		−	25.5892i		−	0.839555i	−0.907627	−	0.419777i	$-0.862108\pi$
$929$		−	25.5892i		−	0.839555i	0.907627	−	0.419777i	$-0.137892\pi$
$930$		0			0
$931$			34.6648i			1.13609i
$932$		0			0
$933$	7.17821	+	7.17821i	0.235004	+	0.235004i
$934$		0			0
$935$	53.0059	−	47.6494i	1.73348	−	1.55830i
$936$		0			0
$937$	−16.5528	+	16.5528i	−0.540755	+	0.540755i	−0.923750	−	0.382995i	$-0.874893\pi$
$937$	−16.5528	+	16.5528i	−0.540755	+	0.540755i	0.382995	+	0.923750i	$0.374893\pi$
$938$		0			0
$939$	−18.0889			−0.590309
$940$		0			0
$941$	−15.4535			−0.503771			−0.251886	−	0.967757i	$-0.581051\pi$
$941$	−15.4535			−0.503771			−0.251886	+	0.967757i	$0.581051\pi$
$942$		0			0
$943$	29.7603	−	29.7603i	0.969130	−	0.969130i
$944$		0			0
$945$	−8.49335	−	0.451981i	−0.276289	−	0.0147029i
$946$		0			0
$947$	−15.7978	−	15.7978i	−0.513359	−	0.513359i	0.402195	−	0.915554i	$-0.368247\pi$
$947$	−15.7978	−	15.7978i	−0.513359	−	0.513359i	−0.915554	+	0.402195i	$0.868247\pi$
$948$		0			0
$949$		−	2.90868i		−	0.0944198i
$950$		0			0
$951$		−	2.99644i		−	0.0971662i
$952$		0			0
$953$	31.9855	+	31.9855i	1.03611	+	1.03611i	0.999323	+	0.0367887i	$0.0117129\pi$
$953$	31.9855	+	31.9855i	1.03611	+	1.03611i	0.0367887	+	0.999323i	$0.488287\pi$
$954$		0			0
$955$	3.07526	+	0.163652i	0.0995129	+	0.00529566i
$956$		0			0
$957$	24.4302	−	24.4302i	0.789717	−	0.789717i
$958$		0			0
$959$	−41.8272			−1.35067
$960$		0			0
$961$	−16.4758			−0.531477
$962$		0			0
$963$	−3.70051	+	3.70051i	−0.119247	+	0.119247i
$964$		0			0
$965$	−29.6730	+	26.6745i	−0.955209	+	0.858681i
$966$		0			0
$967$	−11.9438	−	11.9438i	−0.384088	−	0.384088i	0.488485	−	0.872573i	$-0.337550\pi$
$967$	−11.9438	−	11.9438i	−0.384088	−	0.384088i	−0.872573	+	0.488485i	$0.837550\pi$
$968$		0			0
$969$		−	25.4927i		−	0.818942i
$970$		0			0
$971$		−	0.800817i		−	0.0256995i	−0.999917	−	0.0128497i	$-0.995910\pi$
$971$		−	0.800817i		−	0.0256995i	0.999917	−	0.0128497i	$-0.00409031\pi$
$972$		0			0
$973$	−19.5385	−	19.5385i	−0.626377	−	0.626377i
$974$		0			0
$975$	15.1718	+	1.61935i	0.485888	+	0.0518607i
$976$		0			0
$977$	18.0673	−	18.0673i	0.578025	−	0.578025i	−0.356333	−	0.934359i	$-0.615973\pi$
$977$	18.0673	−	18.0673i	0.578025	−	0.578025i	0.934359	+	0.356333i	$0.115973\pi$
$978$		0			0
$979$	67.0658			2.14343
$980$		0			0
$981$	−3.18155			−0.101579
$982$		0			0
$983$	42.1597	−	42.1597i	1.34469	−	1.34469i	0.453358	−	0.891328i	$-0.350226\pi$
$983$	42.1597	−	42.1597i	1.34469	−	1.34469i	0.891328	−	0.453358i	$-0.149774\pi$
$984$		0			0
$985$	−15.0088	−	16.6960i	−0.478221	−	0.531980i
$986$		0			0
$987$	11.3632	+	11.3632i	0.361696	+	0.361696i
$988$		0			0
$989$		−	31.6571i		−	1.00664i
$990$		0			0
$991$		−	5.73069i		−	0.182042i	−0.995849	−	0.0910208i	$-0.970987\pi$
$991$		−	5.73069i		−	0.182042i	0.995849	−	0.0910208i	$-0.0290130\pi$
$992$		0			0
$993$	16.0344	+	16.0344i	0.508838	+	0.508838i
$994$		0			0
$995$	−1.80730	+	33.9617i	−0.0572954	+	1.07666i
$996$		0			0
$997$	−19.8537	+	19.8537i	−0.628772	+	0.628772i	−0.947759	−	0.318987i	$-0.896657\pi$
$997$	−19.8537	+	19.8537i	−0.628772	+	0.628772i	0.318987	+	0.947759i	$0.396657\pi$
$998$		0			0
$999$	2.11525			0.0669236

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.w.i.1663.2	yes	12
4.3	odd	2		1920.2.w.j.1663.5	yes	12
5.2	odd	4		1920.2.w.j.127.5	yes	12
8.3	odd	2		1920.2.w.l.1663.2	yes	12
8.5	even	2		1920.2.w.k.1663.5	yes	12
20.7	even	4	inner	1920.2.w.i.127.2	✓	12
40.27	even	4		1920.2.w.k.127.5	yes	12
40.37	odd	4		1920.2.w.l.127.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.w.i.127.2	✓	12	20.7	even	4	inner
1920.2.w.i.1663.2	yes	12	1.1	even	1	trivial
1920.2.w.j.127.5	yes	12	5.2	odd	4
1920.2.w.j.1663.5	yes	12	4.3	odd	2
1920.2.w.k.127.5	yes	12	40.27	even	4
1920.2.w.k.1663.5	yes	12	8.5	even	2
1920.2.w.l.127.2	yes	12	40.37	odd	4
1920.2.w.l.1663.2	yes	12	8.3	odd	2

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.118826 + 2.23291i) q^{5} +(2.68963 + 2.68963i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(-0.118826 + 2.23291i) q^{5} +(2.68963 + 2.68963i) q^{7} -1.00000i q^{9} +5.80372i q^{11} +(2.15781 + 2.15781i) q^{13} +(-1.49488 - 1.66293i) q^{15} +(-3.88356 + 3.88356i) q^{17} +4.64163 q^{19} -3.80372 q^{21} +(2.62003 - 2.62003i) q^{23} +(-4.97176 - 0.530656i) q^{25} +(0.707107 + 0.707107i) q^{27} +5.95301i q^{29} -6.89027i q^{31} +(-4.10385 - 4.10385i) q^{33} +(-6.32530 + 5.68611i) q^{35} +(1.49571 - 1.49571i) q^{37} -3.05160 q^{39} +11.3588 q^{41} +(6.04137 - 6.04137i) q^{43} +(2.23291 + 0.118826i) q^{45} +(-2.98740 - 2.98740i) q^{47} +7.46825i q^{49} -5.49218i q^{51} +(-6.19205 - 6.19205i) q^{53} +(-12.9592 - 0.689633i) q^{55} +(-3.28213 + 3.28213i) q^{57} +8.84328 q^{59} -10.0998 q^{61} +(2.68963 - 2.68963i) q^{63} +(-5.07460 + 4.56179i) q^{65} +(4.10321 + 4.10321i) q^{67} +3.70528i q^{69} -2.74097i q^{71} +(-0.673989 - 0.673989i) q^{73} +(3.89080 - 3.14034i) q^{75} +(-15.6099 + 15.6099i) q^{77} +9.89871 q^{79} -1.00000 q^{81} +(-2.42445 + 2.42445i) q^{83} +(-8.21016 - 9.13310i) q^{85} +(-4.20941 - 4.20941i) q^{87} -11.5557i q^{89} +11.6074i q^{91} +(4.87215 + 4.87215i) q^{93} +(-0.551547 + 10.3643i) q^{95} +(-6.48719 + 6.48719i) q^{97} +5.80372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 4 q^{13} - 4 q^{15} - 20 q^{17} + 8 q^{19} + 8 q^{21} - 4 q^{25} + 8 q^{35} - 20 q^{37} - 8 q^{39} + 16 q^{41} + 16 q^{43} + 4 q^{45} + 40 q^{47} + 4 q^{53} - 24 q^{55} - 16 q^{57} + 16 q^{61} - 12 q^{65} - 8 q^{67} + 4 q^{73} + 16 q^{75} - 48 q^{77} - 16 q^{79} - 12 q^{81} - 40 q^{83} - 28 q^{85} + 8 q^{87} + 16 q^{93} - 72 q^{95} - 52 q^{97} + 16 q^{99}+O(q^{100}) \) 12 * q - 4 * q^13 - 4 * q^15 - 20 * q^17 + 8 * q^19 + 8 * q^21 - 4 * q^25 + 8 * q^35 - 20 * q^37 - 8 * q^39 + 16 * q^41 + 16 * q^43 + 4 * q^45 + 40 * q^47 + 4 * q^53 - 24 * q^55 - 16 * q^57 + 16 * q^61 - 12 * q^65 - 8 * q^67 + 4 * q^73 + 16 * q^75 - 48 * q^77 - 16 * q^79 - 12 * q^81 - 40 * q^83 - 28 * q^85 + 8 * q^87 + 16 * q^93 - 72 * q^95 - 52 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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