LMFDB - Embedded newform 225.2.h.d.136.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
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} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.1
Root			$0.623865 - 1.92006i$ of defining polynomial
Character	$\chi$	$=$	225.136
Dual form			225.2.h.d.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63330 + 1.18666i) q^{2} +(0.641469 - 1.97424i) q^{4} +(2.07079 + 0.843702i) q^{5} +1.01887 q^{7} +(0.0473123 + 0.145612i) q^{8} +O(q^{10})$	\(q+(-1.63330 + 1.18666i) q^{2} +(0.641469 - 1.97424i) q^{4} +(2.07079 + 0.843702i) q^{5} +1.01887 q^{7} +(0.0473123 + 0.145612i) q^{8} +(-4.38341 + 1.07931i) q^{10} +(3.85061 - 2.79763i) q^{11} +(0.0840060 + 0.0610339i) q^{13} +(-1.66412 + 1.20905i) q^{14} +(3.10871 + 2.25861i) q^{16} +(1.80397 + 5.55204i) q^{17} +(-0.223853 - 0.688949i) q^{19} +(2.99402 - 3.54702i) q^{20} +(-2.96936 + 9.13874i) q^{22} +(-7.33901 + 5.33210i) q^{23} +(3.57633 + 3.49426i) q^{25} -0.209634 q^{26} +(0.653574 - 2.01149i) q^{28} +(1.23251 - 3.79326i) q^{29} +(0.329605 + 1.01442i) q^{31} -8.06387 q^{32} +(-9.53482 - 6.92745i) q^{34} +(2.10987 + 0.859623i) q^{35} +(-3.25727 - 2.36655i) q^{37} +(1.18317 + 0.859623i) q^{38} +(-0.0248796 + 0.341450i) q^{40} +(5.83282 + 4.23780i) q^{41} +8.62791 q^{43} +(-3.05314 - 9.39661i) q^{44} +(5.65940 - 17.4179i) q^{46} +(2.53331 - 7.79673i) q^{47} -5.96190 q^{49} +(-9.98773 - 1.46327i) q^{50} +(0.174383 - 0.126697i) q^{52} +(1.34954 - 4.15345i) q^{53} +(10.3342 - 2.54454i) q^{55} +(0.0482051 + 0.148360i) q^{56} +(2.48827 + 7.65810i) q^{58} +(-3.97458 - 2.88770i) q^{59} +(-5.63428 + 4.09354i) q^{61} +(-1.74212 - 1.26572i) q^{62} +(6.95331 - 5.05187i) q^{64} +(0.122464 + 0.197264i) q^{65} +(-3.06544 - 9.43446i) q^{67} +12.1183 q^{68} +(-4.46613 + 1.09967i) q^{70} +(3.33323 - 10.2586i) q^{71} +(-6.98275 + 5.07326i) q^{73} +8.12840 q^{74} -1.50375 q^{76} +(3.92327 - 2.85042i) q^{77} +(0.767263 - 2.36139i) q^{79} +(4.53188 + 7.29992i) q^{80} -14.5556 q^{82} +(-1.31142 - 4.03614i) q^{83} +(-0.948634 + 13.0191i) q^{85} +(-14.0920 + 10.2384i) q^{86} +(0.589550 + 0.428333i) q^{88} +(-14.8659 + 10.8007i) q^{89} +(0.0855912 + 0.0621857i) q^{91} +(5.81910 + 17.9093i) q^{92} +(5.11443 + 15.7406i) q^{94} +(0.117715 - 1.61553i) q^{95} +(2.07003 - 6.37090i) q^{97} +(9.73758 - 7.07477i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.63330	+	1.18666i	−1.15492	+	0.839097i	−0.989127	−	0.147064i	$-0.953018\pi$
$2$	−1.63330	+	1.18666i	−1.15492	+	0.839097i	−0.165791	+	0.986161i	$0.553018\pi$
$3$		0			0
$3$		0			0
$4$	0.641469	−	1.97424i	0.320735	−	0.987119i
$5$	2.07079	+	0.843702i	0.926085	+	0.377315i
$5$	2.07079	+	0.843702i	0.926085	+	0.377315i
$6$		0			0
$7$	1.01887			0.385097			0.192548	−	0.981287i	$-0.438325\pi$
$7$	1.01887			0.385097			0.192548	+	0.981287i	$0.438325\pi$
$8$	0.0473123	+	0.145612i	0.0167274	+	0.0514817i
$9$		0			0
$10$	−4.38341	+	1.07931i	−1.38616	+	0.341307i
$11$	3.85061	−	2.79763i	1.16100	−	0.843517i	0.171097	−	0.985254i	$-0.445269\pi$
$11$	3.85061	−	2.79763i	1.16100	−	0.843517i	0.989904	+	0.141737i	$0.0452688\pi$
$12$		0			0
$13$	0.0840060	+	0.0610339i	0.0232991	+	0.0169278i	0.599374	−	0.800469i	$-0.295416\pi$
$13$	0.0840060	+	0.0610339i	0.0232991	+	0.0169278i	−0.576075	+	0.817397i	$0.695416\pi$
$14$	−1.66412	+	1.20905i	−0.444755	+	0.323134i
$15$		0			0
$16$	3.10871	+	2.25861i	0.777177	+	0.564652i
$17$	1.80397	+	5.55204i	0.437527	+	1.34657i	0.890475	+	0.455032i	$0.150372\pi$
$17$	1.80397	+	5.55204i	0.437527	+	1.34657i	−0.452949	+	0.891537i	$0.649628\pi$
$18$		0			0
$19$	−0.223853	−	0.688949i	−0.0513554	−	0.158056i	0.922090	−	0.386976i	$-0.126480\pi$
$19$	−0.223853	−	0.688949i	−0.0513554	−	0.158056i	−0.973445	+	0.228920i	$0.926480\pi$
$20$	2.99402	−	3.54702i	0.669482	−	0.793138i
$21$		0			0
$22$	−2.96936	+	9.13874i	−0.633069	+	1.94839i
$23$	−7.33901	+	5.33210i	−1.53029	+	1.11182i	−0.574212	+	0.818707i	$0.694692\pi$
$23$	−7.33901	+	5.33210i	−1.53029	+	1.11182i	−0.956077	+	0.293114i	$0.905308\pi$
$24$		0			0
$25$	3.57633	+	3.49426i	0.715267	+	0.698852i
$26$	−0.209634			−0.0411126
$27$		0			0
$28$	0.653574	−	2.01149i	0.123514	−	0.380136i
$29$	1.23251	−	3.79326i	0.228871	−	0.704391i	−0.769005	−	0.639243i	$-0.779248\pi$
$29$	1.23251	−	3.79326i	0.228871	−	0.704391i	0.997876	−	0.0651484i	$-0.0207521\pi$
$30$		0			0
$31$	0.329605	+	1.01442i	0.0591988	+	0.182195i	0.976283	−	0.216498i	$-0.0694636\pi$
$31$	0.329605	+	1.01442i	0.0591988	+	0.182195i	−0.917084	+	0.398694i	$0.869464\pi$
$32$	−8.06387			−1.42550
$33$		0			0
$34$	−9.53482	−	6.92745i	−1.63521	−	1.18805i
$35$	2.10987	+	0.859623i	0.356632	+	0.145303i
$36$		0			0
$37$	−3.25727	−	2.36655i	−0.535493	−	0.389058i	0.286916	−	0.957956i	$-0.407370\pi$
$37$	−3.25727	−	2.36655i	−0.535493	−	0.389058i	−0.822408	+	0.568898i	$0.807370\pi$
$38$	1.18317	+	0.859623i	0.191935	+	0.139449i
$39$		0			0
$40$	−0.0248796	+	0.341450i	−0.00393381	+	0.0539880i
$41$	5.83282	+	4.23780i	0.910934	+	0.661832i	0.941251	−	0.337708i	$-0.109652\pi$
$41$	5.83282	+	4.23780i	0.910934	+	0.661832i	−0.0303167	+	0.999540i	$0.509652\pi$
$42$		0			0
$43$	8.62791			1.31574			0.657872	−	0.753130i	$-0.271457\pi$
$43$	8.62791			1.31574			0.657872	+	0.753130i	$0.271457\pi$
$44$	−3.05314	−	9.39661i	−0.460279	−	1.41659i
$45$		0			0
$46$	5.65940	−	17.4179i	0.834434	−	2.56812i
$47$	2.53331	−	7.79673i	0.369522	−	1.13727i	−0.577579	−	0.816335i	$-0.696003\pi$
$47$	2.53331	−	7.79673i	0.369522	−	1.13727i	0.947101	−	0.320936i	$-0.103997\pi$
$48$		0			0
$49$	−5.96190			−0.851700
$50$	−9.98773	−	1.46327i	−1.41248	−	0.206938i
$51$		0			0
$52$	0.174383	−	0.126697i	0.0241825	−	0.0175696i
$53$	1.34954	−	4.15345i	0.185373	−	0.570520i	−0.814581	−	0.580049i	$-0.803033\pi$
$53$	1.34954	−	4.15345i	0.185373	−	0.570520i	0.999955	+	0.00952922i	$0.00303329\pi$
$54$		0			0
$55$	10.3342	−	2.54454i	1.39346	−	0.343105i
$56$	0.0482051	+	0.148360i	0.00644168	+	0.0198254i
$57$		0			0
$58$	2.48827	+	7.65810i	0.326726	+	1.00556i
$59$	−3.97458	−	2.88770i	−0.517446	−	0.375947i	0.298195	−	0.954505i	$-0.403616\pi$
$59$	−3.97458	−	2.88770i	−0.517446	−	0.375947i	−0.815641	+	0.578558i	$0.803616\pi$
$60$		0			0
$61$	−5.63428	+	4.09354i	−0.721396	+	0.524125i	−0.886830	−	0.462096i	$-0.847097\pi$
$61$	−5.63428	+	4.09354i	−0.721396	+	0.524125i	0.165434	+	0.986221i	$0.447097\pi$
$62$	−1.74212	−	1.26572i	−0.221249	−	0.160747i
$63$		0			0
$64$	6.95331	−	5.05187i	0.869163	−	0.631484i
$65$	0.122464	+	0.197264i	0.0151898	+	0.0244676i
$66$		0			0
$67$	−3.06544	−	9.43446i	−0.374503	−	1.15260i	−0.943813	−	0.330480i	$-0.892790\pi$
$67$	−3.06544	−	9.43446i	−0.374503	−	1.15260i	0.569310	−	0.822123i	$-0.307210\pi$
$68$	12.1183			1.46955
$69$		0			0
$70$	−4.46613	+	1.09967i	−0.533804	+	0.131436i
$71$	3.33323	−	10.2586i	0.395582	−	1.21748i	−0.532925	−	0.846162i	$-0.678907\pi$
$71$	3.33323	−	10.2586i	0.395582	−	1.21748i	0.928507	−	0.371314i	$-0.121093\pi$
$72$		0			0
$73$	−6.98275	+	5.07326i	−0.817269	+	0.593781i	−0.915929	−	0.401341i	$-0.868544\pi$
$73$	−6.98275	+	5.07326i	−0.817269	+	0.593781i	0.0986599	+	0.995121i	$0.468544\pi$
$74$	8.12840			0.944907
$75$		0			0
$76$	−1.50375			−0.172491
$77$	3.92327	−	2.85042i	0.447098	−	0.324836i
$78$		0			0
$79$	0.767263	−	2.36139i	0.0863238	−	0.265677i	−0.898572	−	0.438826i	$-0.855394\pi$
$79$	0.767263	−	2.36139i	0.0863238	−	0.265677i	0.984896	+	0.173149i	$0.0553943\pi$
$80$	4.53188	+	7.29992i	0.506680	+	0.816156i
$81$		0			0
$82$	−14.5556			−1.60740
$83$	−1.31142	−	4.03614i	−0.143947	−	0.443024i	0.852927	−	0.522030i	$-0.174825\pi$
$83$	−1.31142	−	4.03614i	−0.143947	−	0.443024i	−0.996874	+	0.0790064i	$0.974825\pi$
$84$		0			0
$85$	−0.948634	+	13.0191i	−0.102894	+	1.41212i
$86$	−14.0920	+	10.2384i	−1.51958	+	1.10404i
$87$		0			0
$88$	0.589550	+	0.428333i	0.0628463	+	0.0456605i
$89$	−14.8659	+	10.8007i	−1.57578	+	1.14487i	−0.654434	+	0.756120i	$0.727093\pi$
$89$	−14.8659	+	10.8007i	−1.57578	+	1.14487i	−0.921344	+	0.388749i	$0.872907\pi$
$90$		0			0
$91$	0.0855912	+	0.0621857i	0.00897240	+	0.00651883i
$92$	5.81910	+	17.9093i	0.606683	+	1.86718i
$93$		0			0
$94$	5.11443	+	15.7406i	0.527513	+	1.62352i
$95$	0.117715	−	1.61553i	0.0120773	−	0.165750i
$96$		0			0
$97$	2.07003	−	6.37090i	0.210180	−	0.646867i	−0.789281	−	0.614032i	$-0.789546\pi$
$97$	2.07003	−	6.37090i	0.210180	−	0.646867i	0.999461	−	0.0328349i	$-0.0104535\pi$
$98$	9.73758	−	7.07477i	0.983644	−	0.714659i
$99$		0			0
$100$	9.19261	−	4.81908i	0.919261	−	0.481908i
$101$	−5.66147			−0.563337			−0.281669	−	0.959512i	$-0.590888\pi$
$101$	−5.66147			−0.563337			−0.281669	+	0.959512i	$0.590888\pi$
$102$		0			0
$103$	0.183707	−	0.565393i	0.0181012	−	0.0557098i	−0.941598	−	0.336739i	$-0.890676\pi$
$103$	0.183707	−	0.565393i	0.0181012	−	0.0557098i	0.959699	+	0.281030i	$0.0906759\pi$
$104$	−0.00491278	+	0.0151200i	−0.000481737	+	0.00148263i
$105$		0			0
$106$	2.72454	+	8.38527i	0.264631	+	0.814450i
$107$	−1.38651			−0.134039			−0.0670193	−	0.997752i	$-0.521349\pi$
$107$	−1.38651			−0.134039			−0.0670193	+	0.997752i	$0.521349\pi$
$108$		0			0
$109$	7.16528	+	5.20588i	0.686309	+	0.498633i	0.875445	−	0.483318i	$-0.160569\pi$
$109$	7.16528	+	5.20588i	0.686309	+	0.498633i	−0.189136	+	0.981951i	$0.560569\pi$
$110$	−13.8593	+	16.4191i	−1.32143	+	1.56550i
$111$		0			0
$112$	3.16737	+	2.30123i	0.299288	+	0.217446i
$113$	5.33173	+	3.87373i	0.501567	+	0.364410i	0.809615	−	0.586961i	$-0.199676\pi$
$113$	5.33173	+	3.87373i	0.501567	+	0.364410i	−0.308048	+	0.951371i	$0.599676\pi$
$114$		0			0
$115$	−19.6963	+	4.84972i	−1.83668	+	0.452239i
$116$	−6.69819	−	4.86652i	−0.621911	−	0.451845i
$117$		0			0
$118$	9.91841			0.913064
$119$	1.83801	+	5.65681i	0.168490	+	0.518559i
$120$		0			0
$121$	3.60125	−	11.0835i	0.327387	−	1.00759i
$122$	4.34482	−	13.3720i	0.393361	−	1.21064i
$123$		0			0
$124$	2.21414			0.198836
$125$	4.45772	+	10.2532i	0.398710	+	0.917077i
$126$		0			0
$127$	5.89890	−	4.28580i	0.523443	−	0.380303i	−0.294457	−	0.955665i	$-0.595139\pi$
$127$	5.89890	−	4.28580i	0.523443	−	0.380303i	0.817899	+	0.575362i	$0.195139\pi$
$128$	−0.378226	+	1.16406i	−0.0334308	+	0.102889i
$129$		0			0
$130$	−0.434107	−	0.176868i	−0.0380737	−	0.0155124i
$131$	2.95230	+	9.08626i	0.257944	+	0.793870i	0.993235	+	0.116119i	$0.0370454\pi$
$131$	2.95230	+	9.08626i	0.257944	+	0.793870i	−0.735291	+	0.677751i	$0.762955\pi$
$132$		0			0
$133$	−0.228077	−	0.701950i	−0.0197768	−	0.0608668i
$134$	16.2023	+	11.7717i	1.39967	+	1.01692i
$135$		0			0
$136$	−0.723096	+	0.525360i	−0.0620050	+	0.0450493i
$137$	−5.01578	−	3.64418i	−0.428527	−	0.311343i	0.352533	−	0.935799i	$-0.385320\pi$
$137$	−5.01578	−	3.64418i	−0.428527	−	0.311343i	−0.781060	+	0.624457i	$0.785320\pi$
$138$		0			0
$139$	0.733399	−	0.532846i	0.0622061	−	0.0451954i	−0.556248	−	0.831017i	$-0.687759\pi$
$139$	0.733399	−	0.532846i	0.0622061	−	0.0451954i	0.618454	+	0.785821i	$0.287759\pi$
$140$	3.05051	−	3.61396i	0.257816	−	0.305435i
$141$		0			0
$142$	6.72937	+	20.7109i	0.564716	+	1.73802i
$143$	0.494225			0.0413291
$144$		0			0
$145$	5.75264	−	6.81518i	0.477731	−	0.565970i
$146$	5.38468	−	16.5723i	0.445639	−	1.37154i
$147$		0			0
$148$	−6.76157	+	4.91257i	−0.555798	+	0.403811i
$149$	4.89808			0.401267			0.200633	−	0.979666i	$-0.435700\pi$
$149$	4.89808			0.401267			0.200633	+	0.979666i	$0.435700\pi$
$150$		0			0
$151$	−10.2626			−0.835161			−0.417581	−	0.908640i	$-0.637122\pi$
$151$	−10.2626			−0.835161			−0.417581	+	0.908640i	$0.637122\pi$
$152$	0.0897285	−	0.0651916i	0.00727794	−	0.00528773i
$153$		0			0
$154$	−3.02539	+	9.31119i	−0.243793	+	0.750317i
$155$	−0.173326	+	2.37874i	−0.0139219	+	0.191065i
$156$		0			0
$157$	−8.89537			−0.709928			−0.354964	−	0.934880i	$-0.615507\pi$
$157$	−8.89537			−0.709928			−0.354964	+	0.934880i	$0.615507\pi$
$158$	1.54900	+	4.76734i	0.123232	+	0.379269i
$159$		0			0
$160$	−16.6986	−	6.80350i	−1.32014	−	0.537864i
$161$	−7.47750	+	5.43272i	−0.589310	+	0.428159i
$162$		0			0
$163$	−9.52946	−	6.92356i	−0.746405	−	0.542295i	0.148305	−	0.988942i	$-0.452618\pi$
$163$	−9.52946	−	6.92356i	−0.746405	−	0.542295i	−0.894710	+	0.446647i	$0.852618\pi$
$164$	12.1080	−	8.79697i	0.945476	−	0.686928i
$165$		0			0
$166$	6.93148	+	5.03602i	0.537987	+	0.390871i
$167$	−5.36954	−	16.5258i	−0.415508	−	1.27880i	−0.911796	−	0.410644i	$-0.865304\pi$
$167$	−5.36954	−	16.5258i	−0.415508	−	1.27880i	0.496288	−	0.868158i	$-0.334696\pi$
$168$		0			0
$169$	−4.01389	−	12.3535i	−0.308761	−	0.950268i
$170$	−13.8999	−	22.3898i	−1.06607	−	1.71722i
$171$		0			0
$172$	5.53454	−	17.0336i	0.422004	−	1.29880i
$173$	−10.4845	+	7.61744i	−0.797123	+	0.579144i	−0.910069	−	0.414458i	$-0.863971\pi$
$173$	−10.4845	+	7.61744i	−0.797123	+	0.579144i	0.112946	+	0.993601i	$0.463971\pi$
$174$		0			0
$175$	3.64382	+	3.56020i	0.275447	+	0.269126i
$176$	18.2892			1.37860
$177$		0			0
$178$	11.4636	−	35.2815i	0.859237	−	2.64446i
$179$	−0.339600	+	1.04518i	−0.0253829	+	0.0781206i	−0.962946	−	0.269696i	$-0.913077\pi$
$179$	−0.339600	+	1.04518i	−0.0253829	+	0.0781206i	0.937563	+	0.347817i	$0.113077\pi$
$180$		0			0
$181$	−4.62898	−	14.2465i	−0.344069	−	1.05894i	−0.962080	−	0.272767i	$-0.912061\pi$
$181$	−4.62898	−	14.2465i	−0.344069	−	1.05894i	0.618011	−	0.786170i	$-0.287939\pi$
$182$	−0.213590			−0.0158323
$183$		0			0
$184$	−1.12365	−	0.816376i	−0.0828363	−	0.0601841i
$185$	−4.74847	−	7.64879i	−0.349114	−	0.562350i
$186$		0			0
$187$	22.4789	+	16.3319i	1.64382	+	1.19431i
$188$	−13.7676	−	10.0027i	−1.00410	−	0.729524i
$189$		0			0
$190$	1.72483	+	2.77834i	0.125132	+	0.201562i
$191$	−10.3072	−	7.48861i	−0.745802	−	0.541857i	0.148721	−	0.988879i	$-0.452484\pi$
$191$	−10.3072	−	7.48861i	−0.745802	−	0.541857i	−0.894523	+	0.447022i	$0.852484\pi$
$192$		0			0
$193$	−4.38386			−0.315557			−0.157779	−	0.987475i	$-0.550433\pi$
$193$	−4.38386			−0.315557			−0.157779	+	0.987475i	$0.550433\pi$
$194$	4.17913	+	12.8620i	0.300044	+	0.923440i
$195$		0			0
$196$	−3.82438	+	11.7702i	−0.273170	+	0.840730i
$197$	−0.995545	+	3.06397i	−0.0709296	+	0.218299i	−0.980237	−	0.197826i	$-0.936612\pi$
$197$	−0.995545	+	3.06397i	−0.0709296	+	0.218299i	0.909308	+	0.416125i	$0.136612\pi$
$198$		0			0
$199$	−2.70518			−0.191765			−0.0958825	−	0.995393i	$-0.530567\pi$
$199$	−2.70518			−0.191765			−0.0958825	+	0.995393i	$0.530567\pi$
$200$	−0.339602	+	0.686080i	−0.0240135	+	0.0485132i
$201$		0			0
$202$	9.24688	−	6.71825i	0.650608	−	0.472694i
$203$	1.25576	−	3.86484i	0.0881373	−	0.271259i
$204$		0			0
$205$	8.50311	+	13.6967i	0.593883	+	0.956622i
$206$	0.370881	+	1.14145i	0.0258405	+	0.0795289i
$207$		0			0
$208$	0.123298	+	0.379473i	0.00854920	+	0.0263117i
$209$	−2.78940	−	2.02661i	−0.192947	−	0.140184i
$210$		0			0
$211$	−21.3932	+	15.5431i	−1.47277	+	1.07003i	−0.492970	+	0.870046i	$0.664089\pi$
$211$	−21.3932	+	15.5431i	−1.47277	+	1.07003i	−0.979799	+	0.199983i	$0.935911\pi$
$212$	−7.33421	−	5.32862i	−0.503716	−	0.365971i
$213$		0			0
$214$	2.26458	−	1.64531i	0.154804	−	0.112471i
$215$	17.8666	+	7.27939i	1.21849	+	0.496450i
$216$		0			0
$217$	0.335825	+	1.03356i	0.0227973	+	0.0701628i
$218$	−17.8807			−1.21103
$219$		0			0
$220$	1.60552	−	22.0343i	0.108244	−	1.48555i
$221$	−0.187319	+	0.576508i	−0.0126004	+	0.0387802i
$222$		0			0
$223$	6.49839	−	4.72136i	0.435164	−	0.316165i	−0.348546	−	0.937292i	$-0.613325\pi$
$223$	6.49839	−	4.72136i	0.435164	−	0.316165i	0.783711	+	0.621126i	$0.213325\pi$
$224$	−8.21604			−0.548957
$225$		0			0
$226$	−13.3051			−0.885044
$227$	13.3145	−	9.67356i	0.883715	−	0.642056i	−0.0505168	−	0.998723i	$-0.516087\pi$
$227$	13.3145	−	9.67356i	0.883715	−	0.642056i	0.934232	+	0.356667i	$0.116087\pi$
$228$		0			0
$229$	0.126476	−	0.389253i	0.00835776	−	0.0257226i	−0.946791	−	0.321850i	$-0.895695\pi$
$229$	0.126476	−	0.389253i	0.00835776	−	0.0257226i	0.955148	+	0.296127i	$0.0956953\pi$
$230$	26.4149	−	31.2938i	1.74175	−	2.06346i
$231$		0			0
$232$	0.610658			0.0400917
$233$	5.70571	+	17.5604i	0.373794	+	1.15042i	0.944289	+	0.329118i	$0.106751\pi$
$233$	5.70571	+	17.5604i	0.373794	+	1.15042i	−0.570495	+	0.821301i	$0.693249\pi$
$234$		0			0
$235$	11.8241	−	14.0080i	0.771318	−	0.913783i
$236$	−8.25058	+	5.99440i	−0.537067	+	0.390202i
$237$		0			0
$238$	−9.71475	−	7.05818i	−0.629714	−	0.457514i
$239$	−3.73509	+	2.71370i	−0.241603	+	0.175535i	−0.701997	−	0.712180i	$-0.747708\pi$
$239$	−3.73509	+	2.71370i	−0.241603	+	0.175535i	0.460394	+	0.887715i	$0.347708\pi$
$240$		0			0
$241$	23.6251	+	17.1646i	1.52183	+	1.10567i	0.960573	+	0.278028i	$0.0896807\pi$
$241$	23.6251	+	17.1646i	1.52183	+	1.10567i	0.561253	+	0.827644i	$0.310319\pi$
$242$	7.27047	+	22.3762i	0.467363	+	1.43840i
$243$		0			0
$244$	4.46742	+	13.7493i	0.285997	+	0.880208i
$245$	−12.3458	−	5.03007i	−0.788747	−	0.321359i
$246$		0			0
$247$	0.0232443	−	0.0715385i	0.00147900	−	0.00455189i
$248$	−0.132118	+	0.0959892i	−0.00838949	+	0.00609532i
$249$		0			0
$250$	−19.4479	−	11.4568i	−1.22999	−	0.724592i
$251$	−0.389664			−0.0245954			−0.0122977	−	0.999924i	$-0.503915\pi$
$251$	−0.389664			−0.0245954			−0.0122977	+	0.999924i	$0.503915\pi$
$252$		0			0
$253$	−13.3424	+	41.0637i	−0.838829	+	2.58165i
$254$	−4.54888	+	14.0000i	−0.285422	+	0.878438i
$255$		0			0
$256$	4.54826	+	13.9981i	0.284266	+	0.874882i
$257$	−8.03324			−0.501100			−0.250550	−	0.968104i	$-0.580611\pi$
$257$	−8.03324			−0.501100			−0.250550	+	0.968104i	$0.580611\pi$
$258$		0			0
$259$	−3.31874	−	2.41121i	−0.206216	−	0.149825i
$260$	0.468004	−	0.115235i	0.0290244	−	0.00714655i
$261$		0			0
$262$	−15.6043	−	11.3372i	−0.964038	−	0.700415i
$263$	−19.5888	−	14.2321i	−1.20790	−	0.877590i	−0.212860	−	0.977083i	$-0.568278\pi$
$263$	−19.5888	−	14.2321i	−1.20790	−	0.877590i	−0.995038	+	0.0994928i	$0.968278\pi$
$264$		0			0
$265$	6.29888	−	7.46231i	0.386937	−	0.458406i
$266$	1.20550	+	0.875844i	0.0739137	+	0.0537015i
$267$		0			0
$268$	−20.5923			−1.25787
$269$	−8.15998	−	25.1138i	−0.497523	−	1.53122i	−0.812988	−	0.582281i	$-0.802161\pi$
$269$	−8.15998	−	25.1138i	−0.497523	−	1.53122i	0.315465	−	0.948937i	$-0.397839\pi$
$270$		0			0
$271$	−3.21648	+	9.89932i	−0.195387	+	0.601341i	0.804584	+	0.593838i	$0.202388\pi$
$271$	−3.21648	+	9.89932i	−0.195387	+	0.601341i	−0.999972	+	0.00750242i	$0.997612\pi$
$272$	−6.93188	+	21.3341i	−0.420307	+	1.29357i
$273$		0			0
$274$	12.5167			0.756160
$275$	23.5467	+	3.44976i	1.41992	+	0.208028i
$276$		0			0
$277$	19.8376	−	14.4129i	1.19193	−	0.865987i	0.198462	−	0.980109i	$-0.436405\pi$
$277$	19.8376	−	14.4129i	1.19193	−	0.865987i	0.993467	+	0.114122i	$0.0364054\pi$
$278$	−0.565553	+	1.74059i	−0.0339196	+	0.104394i
$279$		0			0
$280$	−0.0253491	+	0.347893i	−0.00151490	+	0.0207906i
$281$	4.45690	+	13.7169i	0.265876	+	0.818283i	0.991490	+	0.130181i	$0.0415558\pi$
$281$	4.45690	+	13.7169i	0.265876	+	0.818283i	−0.725614	+	0.688102i	$0.758444\pi$
$282$		0			0
$283$	0.664155	+	2.04406i	0.0394799	+	0.121507i	0.968854	−	0.247633i	$-0.0796526\pi$
$283$	0.664155	+	2.04406i	0.0394799	+	0.121507i	−0.929374	+	0.369139i	$0.879653\pi$
$284$	−18.1148	−	13.1612i	−1.07492	−	0.780974i
$285$		0			0
$286$	−0.807217	+	0.586478i	−0.0477317	+	0.0346791i
$287$	5.94289	+	4.31776i	0.350798	+	0.254870i
$288$		0			0
$289$	−13.8176	+	10.0391i	−0.812800	+	0.590534i
$290$	−1.30848	+	17.9577i	−0.0768366	+	1.05451i
$291$		0			0
$292$	5.53662	+	17.0400i	0.324006	+	0.997188i
$293$	9.02970			0.527521			0.263760	−	0.964588i	$-0.415037\pi$
$293$	9.02970			0.527521			0.263760	+	0.964588i	$0.415037\pi$
$294$		0			0
$295$	−5.79416	−	9.33318i	−0.337349	−	0.543399i
$296$	0.190489	−	0.586266i	0.0110720	−	0.0340760i
$297$		0			0
$298$	−8.00004	+	5.81237i	−0.463430	+	0.336702i
$299$	−0.941960			−0.0544750
$300$		0			0
$301$	8.79072			0.506689
$302$	16.7620	−	12.1783i	0.964543	−	0.700781i
$303$		0			0
$304$	0.860173	−	2.64734i	0.0493343	−	0.151835i
$305$	−15.1211	+	3.72321i	−0.865834	+	0.213190i
$306$		0			0
$307$	5.03454			0.287336			0.143668	−	0.989626i	$-0.454110\pi$
$307$	5.03454			0.287336			0.143668	+	0.989626i	$0.454110\pi$
$308$	−3.11076	−	9.57393i	−0.177252	−	0.545525i
$309$		0			0
$310$	−2.53967	−	4.09088i	−0.144243	−	0.232346i
$311$	−3.95737	+	2.87520i	−0.224402	+	0.163038i	−0.694306	−	0.719680i	$-0.744289\pi$
$311$	−3.95737	+	2.87520i	−0.224402	+	0.163038i	0.469904	+	0.882718i	$0.344289\pi$
$312$		0			0
$313$	2.56686	+	1.86494i	0.145088	+	0.105412i	0.657961	−	0.753052i	$-0.271419\pi$
$313$	2.56686	+	1.86494i	0.145088	+	0.105412i	−0.512874	+	0.858464i	$0.671419\pi$
$314$	14.5288	−	10.5558i	0.819908	−	0.595698i
$315$		0			0
$316$	−4.16978	−	3.02952i	−0.234568	−	0.170424i
$317$	6.17888	+	19.0166i	0.347041	+	1.06808i	0.960482	+	0.278341i	$0.0897846\pi$
$317$	6.17888	+	19.0166i	0.347041	+	1.06808i	−0.613442	+	0.789740i	$0.710215\pi$
$318$		0			0
$319$	−5.86625	−	18.0545i	−0.328447	−	1.01086i
$320$	18.6611	−	4.59484i	1.04319	−	0.256860i
$321$		0			0
$322$	5.76620	−	17.7465i	0.321338	−	0.988976i
$323$	3.42125	−	2.48569i	0.190364	−	0.138307i
$324$		0			0
$325$	0.0871652	+	0.511816i	0.00483505	+	0.0283905i
$326$	23.7804			1.31707
$327$		0			0
$328$	−0.341111	+	1.04983i	−0.0188347	+	0.0579672i
$329$	2.58112	−	7.94386i	0.142302	−	0.437959i
$330$		0			0
$331$	1.85943	+	5.72274i	0.102204	+	0.314550i	0.989064	−	0.147487i	$-0.0471186\pi$
$331$	1.85943	+	5.72274i	0.102204	+	0.314550i	−0.886860	+	0.462037i	$0.847119\pi$
$332$	−8.80954			−0.483486
$333$		0			0
$334$	28.3806	+	20.6197i	1.55292	+	1.12826i
$335$	1.61199	−	22.1231i	0.0880725	−	1.20871i
$336$		0			0
$337$	−18.4566	−	13.4095i	−1.00540	−	0.730463i	−0.0421575	−	0.999111i	$-0.513423\pi$
$337$	−18.4566	−	13.4095i	−1.00540	−	0.730463i	−0.963238	+	0.268648i	$0.913423\pi$
$338$	21.2153	+	15.4138i	1.15396	+	0.838401i
$339$		0			0
$340$	25.0943	+	10.2242i	1.36093	+	0.554485i
$341$	4.10715	+	2.98402i	0.222415	+	0.161594i
$342$		0			0
$343$	−13.2065			−0.713084
$344$	0.408206	+	1.25633i	0.0220090	+	0.0677368i
$345$		0			0
$346$	8.08502	−	24.8831i	0.434654	−	1.33773i
$347$	−3.02549	+	9.31149i	−0.162417	+	0.499867i	−0.998837	−	0.0482222i	$-0.984644\pi$
$347$	−3.02549	+	9.31149i	−0.162417	+	0.499867i	0.836420	+	0.548089i	$0.184644\pi$
$348$		0			0
$349$	−1.28648			−0.0688639			−0.0344320	−	0.999407i	$-0.510962\pi$
$349$	−1.28648			−0.0688639			−0.0344320	+	0.999407i	$0.510962\pi$
$350$	−10.1762	−	1.49089i	−0.543941	−	0.0796912i
$351$		0			0
$352$	−31.0508	+	22.5597i	−1.65501	+	1.20244i
$353$	−0.359765	+	1.10724i	−0.0191484	+	0.0589326i	−0.960174	−	0.279402i	$-0.909864\pi$
$353$	−0.359765	+	1.10724i	−0.0191484	+	0.0589326i	0.941026	+	0.338335i	$0.109864\pi$
$354$		0			0
$355$	15.5577	−	18.4312i	0.825715	−	0.978228i
$356$	11.7871	+	36.2770i	0.624716	+	1.92268i
$357$		0			0
$358$	−0.685609	−	2.11009i	−0.0362356	−	0.111522i
$359$	15.4121	+	11.1975i	0.813418	+	0.590983i	0.914820	−	0.403863i	$-0.132333\pi$
$359$	15.4121	+	11.1975i	0.813418	+	0.590983i	−0.101402	+	0.994846i	$0.532333\pi$
$360$		0			0
$361$	14.9468	−	10.8595i	0.786673	−	0.571551i
$362$	24.4663	+	17.7758i	1.28592	+	0.934277i
$363$		0			0
$364$	0.177673	−	0.129087i	0.00931262	−	0.00676602i
$365$	−18.7401	+	4.61430i	−0.980903	+	0.241523i
$366$		0			0
$367$	5.18204	+	15.9487i	0.270500	+	0.832514i	0.990375	+	0.138410i	$0.0441992\pi$
$367$	5.18204	+	15.9487i	0.270500	+	0.832514i	−0.719875	+	0.694104i	$0.755801\pi$
$368$	−34.8580			−1.81710
$369$		0			0
$370$	16.8322	+	6.85795i	0.875065	+	0.356528i
$371$	1.37500	−	4.23183i	0.0713866	−	0.219705i
$372$		0			0
$373$	13.7954	−	10.0229i	0.714297	−	0.518967i	−0.170260	−	0.985399i	$-0.554461\pi$
$373$	13.7954	−	10.0229i	0.714297	−	0.518967i	0.884557	+	0.466432i	$0.154461\pi$
$374$	−56.0953			−2.90062
$375$		0			0
$376$	1.25516			0.0647298
$377$	0.335056	−	0.243432i	0.0172562	−	0.0125374i
$378$		0			0
$379$	0.514857	−	1.58457i	0.0264464	−	0.0813938i	−0.936962	−	0.349431i	$-0.886375\pi$
$379$	0.514857	−	1.58457i	0.0264464	−	0.0813938i	0.963409	+	0.268037i	$0.0863750\pi$
$380$	−3.11394	−	1.26871i	−0.159742	−	0.0650836i
$381$		0			0
$382$	25.7212			1.31601
$383$	−0.943618	−	2.90416i	−0.0482166	−	0.148396i	0.924049	−	0.382273i	$-0.124859\pi$
$383$	−0.943618	−	2.90416i	−0.0482166	−	0.148396i	−0.972266	+	0.233877i	$0.924859\pi$
$384$		0			0
$385$	10.5292	−	2.59255i	0.536616	−	0.132129i
$386$	7.16016	−	5.20216i	0.364443	−	0.264783i
$387$		0			0
$388$	−11.2498	−	8.17347i	−0.571123	−	0.414945i
$389$	22.8730	−	16.6182i	1.15971	−	0.842575i	0.169965	−	0.985450i	$-0.445635\pi$
$389$	22.8730	−	16.6182i	1.15971	−	0.842575i	0.989741	+	0.142875i	$0.0456347\pi$
$390$		0			0
$391$	−42.8434	−	31.1276i	−2.16669	−	1.57419i
$392$	−0.282071	−	0.868127i	−0.0142468	−	0.0438470i
$393$		0			0
$394$	−2.00988	−	6.18576i	−0.101256	−	0.311634i
$395$	3.58115	−	4.24260i	0.180187	−	0.213468i
$396$		0			0
$397$	−6.32814	+	19.4760i	−0.317600	+	0.977472i	0.657071	+	0.753829i	$0.271795\pi$
$397$	−6.32814	+	19.4760i	−0.317600	+	0.977472i	−0.974671	+	0.223644i	$0.928205\pi$
$398$	4.41837	−	3.21013i	0.221473	−	0.160909i
$399$		0			0
$400$	3.22561	+	18.9402i	0.161281	+	0.947008i
$401$	−25.5952			−1.27816			−0.639081	−	0.769139i	$-0.720685\pi$
$401$	−25.5952			−1.27816			−0.639081	+	0.769139i	$0.720685\pi$
$402$		0			0
$403$	−0.0342253	+	0.105335i	−0.00170488	+	0.00524709i
$404$	−3.63166	+	11.1771i	−0.180682	+	0.556081i
$405$		0			0
$406$	2.53522	+	7.80262i	0.125821	+	0.387237i
$407$	−19.1632			−0.949885
$408$		0			0
$409$	9.74072	+	7.07705i	0.481648	+	0.349938i	0.801963	−	0.597373i	$-0.203789\pi$
$409$	9.74072	+	7.07705i	0.481648	+	0.349938i	−0.320316	+	0.947311i	$0.603789\pi$
$410$	−30.1415	−	12.2806i	−1.48858	−	0.606495i
$411$		0			0
$412$	−0.998377	−	0.725364i	−0.0491865	−	0.0357361i
$413$	−4.04958	−	2.94219i	−0.199267	−	0.144776i
$414$		0			0
$415$	0.689623	−	9.46444i	0.0338523	−	0.464591i
$416$	−0.677414	−	0.492170i	−0.0332129	−	0.0241306i
$417$		0			0
$418$	6.96083			0.340465
$419$	10.6934	+	32.9108i	0.522405	+	1.60780i	0.769390	+	0.638779i	$0.220560\pi$
$419$	10.6934	+	32.9108i	0.522405	+	1.60780i	−0.246985	+	0.969019i	$0.579440\pi$
$420$		0			0
$421$	−4.62056	+	14.2206i	−0.225193	+	0.693071i	0.773079	+	0.634309i	$0.218715\pi$
$421$	−4.62056	+	14.2206i	−0.225193	+	0.693071i	−0.998272	+	0.0587622i	$0.981285\pi$
$422$	16.4972	−	50.7730i	0.803069	−	2.47159i
$423$		0			0
$424$	0.668643			0.0324722
$425$	−12.9487	+	26.1595i	−0.628103	+	1.26892i
$426$		0			0
$427$	−5.74060	+	4.17079i	−0.277807	+	0.201839i
$428$	−0.889401	+	2.73729i	−0.0429908	+	0.132312i
$429$		0			0
$430$	−37.8197	+	9.31217i	−1.82383	+	0.449073i
$431$	−1.48670	−	4.57560i	−0.0716119	−	0.220399i	0.908845	−	0.417135i	$-0.136966\pi$
$431$	−1.48670	−	4.57560i	−0.0716119	−	0.220399i	−0.980456	+	0.196736i	$0.936966\pi$
$432$		0			0
$433$	3.19632	+	9.83725i	0.153605	+	0.472748i	0.998017	−	0.0629466i	$-0.0200498\pi$
$433$	3.19632	+	9.83725i	0.153605	+	0.472748i	−0.844412	+	0.535695i	$0.820050\pi$
$434$	−1.77499	−	1.28961i	−0.0852024	−	0.0619032i
$435$		0			0
$436$	14.8739	−	10.8066i	0.712333	−	0.517540i
$437$	5.31641	+	3.86260i	0.254318	+	0.184773i
$438$		0			0
$439$	−24.8886	+	18.0826i	−1.18787	+	0.863037i	−0.993037	−	0.117800i	$-0.962416\pi$
$439$	−24.8886	+	18.0826i	−1.18787	+	0.863037i	−0.194831	+	0.980837i	$0.562416\pi$
$440$	0.859449	+	1.38439i	0.0409726	+	0.0659984i
$441$		0			0
$442$	−0.378173	−	1.16390i	−0.0179878	−	0.0553609i
$443$	17.7545			0.843543			0.421772	−	0.906702i	$-0.361408\pi$
$443$	17.7545			0.843543			0.421772	+	0.906702i	$0.361408\pi$
$444$		0			0
$445$	−39.8966	+	9.82356i	−1.89128	+	0.465682i
$446$	−5.01117	+	15.4228i	−0.237286	+	0.730290i
$447$		0			0
$448$	7.08452	−	5.14720i	0.334712	−	0.243183i
$449$	37.2184			1.75645			0.878223	−	0.478251i	$-0.158729\pi$
$449$	37.2184			1.75645			0.878223	+	0.478251i	$0.158729\pi$
$450$		0			0
$451$	34.3157			1.61586
$452$	11.0678	−	8.04124i	0.520586	−	0.378228i
$453$		0			0
$454$	−10.2673	+	31.5996i	−0.481870	+	1.48304i
$455$	0.124775	+	0.200987i	0.00584955	+	0.00942241i
$456$		0			0
$457$	−27.6987			−1.29569			−0.647846	−	0.761772i	$-0.724330\pi$
$457$	−27.6987			−1.29569			−0.647846	+	0.761772i	$0.724330\pi$
$458$	0.255338	+	0.785851i	0.0119312	+	0.0367204i
$459$		0			0
$460$	−3.06003	+	41.9960i	−0.142674	+	1.95808i
$461$	7.94246	−	5.77053i	0.369917	−	0.268760i	−0.387259	−	0.921971i	$-0.626578\pi$
$461$	7.94246	−	5.77053i	0.369917	−	0.268760i	0.757177	+	0.653210i	$0.226578\pi$
$462$		0			0
$463$	3.01546	+	2.19086i	0.140140	+	0.101818i	0.655647	−	0.755068i	$-0.272396\pi$
$463$	3.01546	+	2.19086i	0.140140	+	0.101818i	−0.515506	+	0.856886i	$0.672396\pi$
$464$	12.3990	−	9.00840i	0.575609	−	0.418204i
$465$		0			0
$466$	−30.1574	−	21.9106i	−1.39701	−	1.01499i
$467$	2.19379	+	6.75179i	0.101516	+	0.312436i	0.988897	−	0.148602i	$-0.0474773\pi$
$467$	2.19379	+	6.75179i	0.101516	+	0.312436i	−0.887381	+	0.461038i	$0.847477\pi$
$468$		0			0
$469$	−3.12329	−	9.61249i	−0.144220	−	0.443864i
$470$	−2.68947	+	36.9105i	−0.124056	+	1.70255i
$471$		0			0
$472$	0.232438	−	0.715372i	0.0106988	−	0.0329277i
$473$	33.2227	−	24.1377i	1.52758	−	1.10985i
$474$		0			0
$475$	1.60679	−	3.24611i	0.0737247	−	0.148942i
$476$	12.3469			0.565920
$477$		0			0
$478$	2.88027	−	8.86457i	0.131741	−	0.405456i
$479$	8.79003	−	27.0529i	0.401627	−	1.23608i	−0.522053	−	0.852913i	$-0.674834\pi$
$479$	8.79003	−	27.0529i	0.401627	−	1.23608i	0.923679	−	0.383166i	$-0.125166\pi$
$480$		0			0
$481$	−0.129191	−	0.397609i	−0.00589060	−	0.0181294i
$482$	−58.9555			−2.68535
$483$		0			0
$484$	−19.5714	−	14.2195i	−0.889610	−	0.646340i
$485$	9.66174	−	11.4463i	0.438717	−	0.519750i
$486$		0			0
$487$	11.9236	+	8.66301i	0.540310	+	0.392558i	0.824200	−	0.566298i	$-0.191625\pi$
$487$	11.9236	+	8.66301i	0.540310	+	0.392558i	−0.283890	+	0.958857i	$0.591625\pi$
$488$	−0.862641	−	0.626746i	−0.0390499	−	0.0283714i
$489$		0			0
$490$	26.1335	−	6.43473i	1.18059	−	0.290691i
$491$	−22.9772	−	16.6939i	−1.03695	−	0.753387i	−0.0672603	−	0.997735i	$-0.521426\pi$
$491$	−22.9772	−	16.6939i	−1.03695	−	0.753387i	−0.969687	+	0.244349i	$0.921426\pi$
$492$		0			0
$493$	23.2838			1.04865
$494$	0.0469272	+	0.144427i	0.00211135	+	0.00649808i
$495$		0			0
$496$	−1.26653	+	3.89799i	−0.0568690	+	0.175025i
$497$	3.39613	−	10.4522i	0.152337	−	0.468846i
$498$		0			0
$499$	26.3842			1.18112			0.590559	−	0.806995i	$-0.298907\pi$
$499$	26.3842			1.18112			0.590559	+	0.806995i	$0.298907\pi$
$500$	23.1018	−	2.22347i	1.03314	−	0.0994366i
$501$		0			0
$502$	0.636439	−	0.462400i	0.0284057	−	0.0206379i
$503$	−5.14796	+	15.8438i	−0.229536	+	0.706440i	0.768263	+	0.640134i	$0.221121\pi$
$503$	−5.14796	+	15.8438i	−0.229536	+	0.706440i	−0.997799	+	0.0663060i	$0.978879\pi$
$504$		0			0
$505$	−11.7237	−	4.77659i	−0.521698	−	0.212556i
$506$	−26.9366	−	82.9022i	−1.19748	−	3.68545i
$507$		0			0
$508$	−4.67723	−	14.3950i	−0.207519	−	0.638677i
$509$	−25.7073	−	18.6774i	−1.13946	−	0.827863i	−0.152413	−	0.988317i	$-0.548704\pi$
$509$	−25.7073	−	18.6774i	−1.13946	−	0.827863i	−0.987043	+	0.160454i	$0.948704\pi$
$510$		0			0
$511$	−7.11452	+	5.16900i	−0.314728	+	0.228663i
$512$	−26.0201	−	18.9047i	−1.14994	−	0.835479i
$513$		0			0
$514$	13.1207	−	9.53274i	0.578729	−	0.420471i
$515$	0.857442	−	1.01581i	0.0377834	−	0.0447621i
$516$		0			0
$517$	−12.0576	−	37.1094i	−0.530292	−	1.63207i
$518$	8.28179			0.363881
$519$		0			0
$520$	−0.0229301	+	0.0271653i	−0.00100555	+	0.00119128i
$521$	0.183050	−	0.563371i	0.00801958	−	0.0246817i	−0.946967	−	0.321332i	$-0.895870\pi$
$521$	0.183050	−	0.563371i	0.00801958	−	0.0246817i	0.954986	+	0.296650i	$0.0958695\pi$
$522$		0			0
$523$	13.9392	−	10.1274i	0.609518	−	0.442840i	−0.239727	−	0.970840i	$-0.577058\pi$
$523$	13.9392	−	10.1274i	0.609518	−	0.442840i	0.849244	+	0.528000i	$0.177058\pi$
$524$	19.8323			0.866376
$525$		0			0
$526$	48.8832			2.13141
$527$	−5.03751	+	3.65997i	−0.219437	+	0.159431i
$528$		0			0
$529$	18.3224	−	56.3904i	0.796625	−	2.45176i
$530$	−1.43273	+	19.6628i	−0.0622336	+	0.854099i
$531$		0			0
$532$	−1.53212			−0.0664259
$533$	0.231343	+	0.712001i	0.0100206	+	0.0308402i
$534$		0			0
$535$	−2.87116	−	1.16980i	−0.124131	−	0.0505748i
$536$	1.22874	−	0.892732i	0.0530735	−	0.0385602i
$537$		0			0
$538$	43.1293	+	31.3353i	1.85944	+	1.35096i
$539$	−22.9569	+	16.6792i	−0.988826	+	0.718424i
$540$		0			0
$541$	−11.9726	−	8.69863i	−0.514744	−	0.373983i	0.299876	−	0.953978i	$-0.403055\pi$
$541$	−11.9726	−	8.69863i	−0.514744	−	0.373983i	−0.814620	+	0.579995i	$0.803055\pi$
$542$	−6.49366	−	19.9854i	−0.278927	−	0.858448i
$543$		0			0
$544$	−14.5470	−	44.7710i	−0.623696	−	1.91954i
$545$	10.4456	+	16.8256i	0.447439	+	0.720731i
$546$		0			0
$547$	2.01110	−	6.18953i	0.0859884	−	0.264645i	−0.898812	−	0.438334i	$-0.855569\pi$
$547$	2.01110	−	6.18953i	0.0859884	−	0.264645i	0.984801	+	0.173689i	$0.0555687\pi$
$548$	−10.4119	+	7.56472i	−0.444776	+	0.323149i
$549$		0			0
$550$	−42.5525	+	22.3075i	−1.81445	+	0.951194i
$551$	−2.88927			−0.123087
$552$		0			0
$553$	0.781741	−	2.40595i	0.0332430	−	0.102311i
$554$	−15.2976	+	47.0812i	−0.649933	+	2.00029i
$555$		0			0
$556$	−0.581512	−	1.78971i	−0.0246616	−	0.0759006i
$557$	6.67224			0.282712			0.141356	−	0.989959i	$-0.454854\pi$
$557$	6.67224			0.282712			0.141356	+	0.989959i	$0.454854\pi$
$558$		0			0
$559$	0.724796	+	0.526595i	0.0306556	+	0.0222726i
$560$	4.61740	+	7.43768i	0.195121	+	0.314299i
$561$		0			0
$562$	−23.5568	−	17.1150i	−0.993684	−	0.721953i
$563$	16.2340	+	11.7947i	0.684181	+	0.497087i	0.874742	−	0.484589i	$-0.161031\pi$
$563$	16.2340	+	11.7947i	0.684181	+	0.497087i	−0.190561	+	0.981675i	$0.561031\pi$
$564$		0			0
$565$	7.77262	+	12.5201i	0.326997	+	0.526724i
$566$	−3.51037	−	2.55043i	−0.147552	−	0.107203i
$567$		0			0
$568$	1.65149			0.0692949
$569$	6.67287	+	20.5370i	0.279741	+	0.860955i	0.987926	+	0.154927i	$0.0495144\pi$
$569$	6.67287	+	20.5370i	0.279741	+	0.860955i	−0.708185	+	0.706027i	$0.750486\pi$
$570$		0			0
$571$	−8.13758	+	25.0449i	−0.340547	+	1.04810i	0.623377	+	0.781921i	$0.285760\pi$
$571$	−8.13758	+	25.0449i	−0.340547	+	1.04810i	−0.963925	+	0.266176i	$0.914240\pi$
$572$	0.317030	−	0.975717i	0.0132557	−	0.0407968i
$573$		0			0
$574$	−14.8303			−0.619003
$575$	−44.8785	−	6.57502i	−1.87156	−	0.274197i
$576$		0			0
$577$	7.42872	−	5.39728i	0.309262	−	0.224692i	−0.422318	−	0.906448i	$-0.638783\pi$
$577$	7.42872	−	5.39728i	0.309262	−	0.224692i	0.731580	+	0.681756i	$0.238783\pi$
$578$	10.6553	−	32.7937i	0.443202	−	1.36404i
$579$		0			0
$580$	−9.76465	−	15.7288i	−0.405455	−	0.653103i
$581$	−1.33617	−	4.11230i	−0.0554336	−	0.170607i
$582$		0			0
$583$	−6.42327	−	19.7688i	−0.266025	−	0.818740i
$584$	−1.06910	−	0.776746i	−0.0442397	−	0.0321420i
$585$		0			0
$586$	−14.7482	+	10.7152i	−0.609243	+	0.442641i
$587$	32.3422	+	23.4980i	1.33491	+	0.969865i	0.999615	+	0.0277503i	$0.00883434\pi$
$587$	32.3422	+	23.4980i	1.33491	+	0.969865i	0.335290	+	0.942115i	$0.391166\pi$
$588$		0			0
$589$	0.625101	−	0.454163i	0.0257568	−	0.0187134i
$590$	20.5389	+	8.36819i	0.845575	+	0.344513i
$591$		0			0
$592$	−4.78081	−	14.7138i	−0.196490	−	0.604734i
$593$	41.6331			1.70967			0.854834	−	0.518902i	$-0.173659\pi$
$593$	41.6331			1.70967			0.854834	+	0.518902i	$0.173659\pi$
$594$		0			0
$595$	−0.966535	+	13.2648i	−0.0396241	+	0.543804i
$596$	3.14197	−	9.66999i	0.128700	−	0.396098i
$597$		0			0
$598$	1.53850	−	1.11779i	0.0629141	−	0.0457098i
$599$	−39.0726			−1.59646			−0.798232	−	0.602350i	$-0.794231\pi$
$599$	−39.0726			−1.59646			−0.798232	+	0.602350i	$0.794231\pi$
$600$		0			0
$601$	5.46965			0.223112			0.111556	−	0.993758i	$-0.464417\pi$
$601$	5.46965			0.223112			0.111556	+	0.993758i	$0.464417\pi$
$602$	−14.3579	+	10.4316i	−0.585184	+	0.425161i
$603$		0			0
$604$	−6.58316	+	20.2609i	−0.267865	+	0.824404i
$605$	16.8086	−	19.9132i	0.683368	−	0.809589i
$606$		0			0
$607$	42.3108			1.71734			0.858671	−	0.512527i	$-0.171291\pi$
$607$	42.3108			1.71734			0.858671	+	0.512527i	$0.171291\pi$
$608$	1.80512	+	5.55560i	0.0732074	+	0.225309i
$609$		0			0
$610$	20.2792	−	24.0248i	0.821079	−	0.972736i
$611$	0.688679	−	0.500355i	0.0278610	−	0.0202422i
$612$		0			0
$613$	27.5118	+	19.9885i	1.11119	+	0.807327i	0.982851	−	0.184403i	$-0.0590353\pi$
$613$	27.5118	+	19.9885i	1.11119	+	0.807327i	0.128340	+	0.991730i	$0.459035\pi$
$614$	−8.22292	+	5.97430i	−0.331850	+	0.241103i
$615$		0			0
$616$	0.600675	+	0.436416i	0.0242019	+	0.0175837i
$617$	−7.20543	−	22.1760i	−0.290080	−	0.892773i	−0.984830	−	0.173522i	$-0.944485\pi$
$617$	−7.20543	−	22.1760i	−0.290080	−	0.892773i	0.694750	−	0.719251i	$-0.255515\pi$
$618$		0			0
$619$	10.9082	+	33.5721i	0.438439	+	1.34938i	0.889521	+	0.456893i	$0.151038\pi$
$619$	10.9082	+	33.5721i	0.438439	+	1.34938i	−0.451083	+	0.892482i	$0.648962\pi$
$620$	4.58502	+	1.86807i	0.184139	+	0.0750237i
$621$		0			0
$622$	3.05169	−	9.39213i	0.122362	−	0.376590i
$623$	−15.1464	+	11.0045i	−0.606827	+	0.440885i
$624$		0			0
$625$	0.580320	+	24.9933i	0.0232128	+	0.999731i
$626$	−6.40551			−0.256016
$627$		0			0
$628$	−5.70610	+	17.5616i	−0.227698	+	0.700783i
$629$	7.26316	−	22.3537i	0.289601	−	0.891301i
$630$		0			0
$631$	−1.08290	−	3.33282i	−0.0431095	−	0.132677i	0.927185	−	0.374603i	$-0.122221\pi$
$631$	−1.08290	−	3.33282i	−0.0431095	−	0.132677i	−0.970295	+	0.241926i	$0.922221\pi$
$632$	0.380149			0.0151215
$633$		0			0
$634$	−32.6583	−	23.7276i	−1.29703	−	0.942345i
$635$	15.8313	−	3.89808i	0.628247	−	0.154690i
$636$		0			0
$637$	−0.500836	−	0.363878i	−0.0198438	−	0.0144174i
$638$	31.0059	+	22.5271i	1.22753	+	0.891856i
$639$		0			0
$640$	−1.76535	+	2.09141i	−0.0697815	+	0.0826704i
$641$	−7.51448	−	5.45959i	−0.296804	−	0.215641i	0.429409	−	0.903110i	$-0.358722\pi$
$641$	−7.51448	−	5.45959i	−0.296804	−	0.215641i	−0.726214	+	0.687469i	$0.758722\pi$
$642$		0			0
$643$	−0.0291680			−0.00115028			−0.000575138	−	1.00000i	$-0.500183\pi$
$643$	−0.0291680			−0.00115028			−0.000575138		1.00000i	$0.500183\pi$
$644$	5.92891	+	18.2473i	0.233632	+	0.719044i
$645$		0			0
$646$	−2.63826	+	8.11974i	−0.103801	+	0.319467i
$647$	0.260841	−	0.802787i	0.0102547	−	0.0315608i	−0.945798	−	0.324755i	$-0.894718\pi$
$647$	0.260841	−	0.802787i	0.0102547	−	0.0315608i	0.956053	+	0.293194i	$0.0947182\pi$
$648$		0			0
$649$	−23.3833			−0.917874
$650$	−0.749720	−	0.732514i	−0.0294064	−	0.0287316i
$651$		0			0
$652$	−19.7816	+	14.3722i	−0.774708	+	0.562858i
$653$	−11.7646	+	36.2077i	−0.460385	+	1.41692i	0.404311	+	0.914622i	$0.367511\pi$
$653$	−11.7646	+	36.2077i	−0.460385	+	1.41692i	−0.864695	+	0.502297i	$0.832489\pi$
$654$		0			0
$655$	−1.55250	+	21.3066i	−0.0606611	+	0.832517i
$656$	8.56103	+	26.3481i	0.334252	+	1.02872i
$657$		0			0
$658$	5.21094	+	16.0376i	0.203144	+	0.625212i
$659$	30.6086	+	22.2385i	1.19234	+	0.866287i	0.993510	−	0.113746i	$-0.0362851\pi$
$659$	30.6086	+	22.2385i	1.19234	+	0.866287i	0.198832	+	0.980034i	$0.436285\pi$
$660$		0			0
$661$	15.0165	−	10.9101i	0.584074	−	0.424355i	−0.256116	−	0.966646i	$-0.582443\pi$
$661$	15.0165	−	10.9101i	0.584074	−	0.424355i	0.840191	+	0.542291i	$0.182443\pi$
$662$	−9.82797	−	7.14044i	−0.381975	−	0.277521i
$663$		0			0
$664$	0.525665	−	0.381918i	0.0203998	−	0.0148213i
$665$	0.119937	−	1.64602i	0.00465094	−	0.0638299i
$666$		0			0
$667$	11.1807	+	34.4106i	0.432918	+	1.33239i
$668$	−36.0702			−1.39560
$669$		0			0
$670$	23.6198	+	38.0465i	0.912511	+	1.46987i
$671$	−10.2432	+	31.5253i	−0.395433	+	1.21702i
$672$		0			0
$673$	−14.6923	+	10.6746i	−0.566347	+	0.411475i	−0.833776	−	0.552102i	$-0.813826\pi$
$673$	−14.6923	+	10.6746i	−0.566347	+	0.411475i	0.267429	+	0.963578i	$0.413826\pi$
$674$	46.0578			1.77408
$675$		0			0
$676$	−26.9635			−1.03706
$677$	−4.56538	+	3.31695i	−0.175462	+	0.127481i	−0.672050	−	0.740506i	$-0.734586\pi$
$677$	−4.56538	+	3.31695i	−0.175462	+	0.127481i	0.496588	+	0.867986i	$0.334586\pi$
$678$		0			0
$679$	2.10909	−	6.49112i	0.0809396	−	0.249106i
$680$	−1.94063	+	0.477832i	−0.0744196	+	0.0183240i
$681$		0			0
$682$	−10.2492			−0.392464
$683$	−9.40859	−	28.9567i	−0.360010	−	1.10800i	−0.953047	−	0.302821i	$-0.902071\pi$
$683$	−9.40859	−	28.9567i	−0.360010	−	1.10800i	0.593038	−	0.805175i	$-0.297929\pi$
$684$		0			0
$685$	−7.31202	−	11.7781i	−0.279378	−	0.450020i
$686$	21.5702	−	15.6717i	0.823553	−	0.598346i
$687$		0			0
$688$	26.8216	+	19.4871i	1.02257	+	0.742937i
$689$	0.366871	−	0.266547i	0.0139767	−	0.0101546i
$690$		0			0
$691$	7.46294	+	5.42214i	0.283904	+	0.206268i	0.720618	−	0.693332i	$-0.243858\pi$
$691$	7.46294	+	5.42214i	0.283904	+	0.206268i	−0.436715	+	0.899600i	$0.643858\pi$
$692$	8.31316	+	25.5853i	0.316019	+	0.972607i
$693$		0			0
$694$	−6.10806	−	18.7987i	−0.231859	−	0.713588i
$695$	1.96828	−	0.484640i	0.0746610	−	0.0183835i
$696$		0			0
$697$	−13.0062	+	40.0290i	−0.492645	+	1.51620i
$698$	2.10121	−	1.52662i	0.0795322	−	0.0577835i
$699$		0			0
$700$	9.36607	−	4.91001i	0.354004	−	0.185581i
$701$	19.9822			0.754717			0.377358	−	0.926067i	$-0.376832\pi$
$701$	19.9822			0.754717			0.377358	+	0.926067i	$0.376832\pi$
$702$		0			0
$703$	−0.901281	+	2.77386i	−0.0339924	+	0.104618i
$704$	12.6412	−	38.9056i	0.476432	−	1.46631i
$705$		0			0
$706$	−0.726319	−	2.23538i	−0.0273354	−	0.0841296i
$707$	−5.76830			−0.216939
$708$		0			0
$709$	21.7026	+	15.7679i	0.815059	+	0.592175i	0.915293	−	0.402789i	$-0.131959\pi$
$709$	21.7026	+	15.7679i	0.815059	+	0.592175i	−0.100234	+	0.994964i	$0.531959\pi$
$710$	−3.53870	+	48.5654i	−0.132805	+	1.82263i
$711$		0			0
$712$	−2.27605	−	1.65365i	−0.0852985	−	0.0619730i
$713$	−7.82797	−	5.68735i	−0.293160	−	0.212993i
$714$		0			0
$715$	1.02343	+	0.416978i	0.0382743	+	0.0155941i
$716$	1.84560	+	1.34090i	0.0689732	+	0.0501120i
$717$		0			0
$718$	−38.4602			−1.43532
$719$	−11.9968	−	36.9223i	−0.447404	−	1.37697i	−0.879825	−	0.475297i	$-0.842341\pi$
$719$	−11.9968	−	36.9223i	−0.447404	−	1.37697i	0.432421	−	0.901672i	$-0.357659\pi$
$720$		0			0
$721$	0.187174	−	0.576062i	0.00697072	−	0.0214537i
$722$	−11.5261	+	35.4736i	−0.428956	+	1.32019i
$723$		0			0
$724$	−31.0954			−1.15565
$725$	17.6625	−	9.25928i	0.655968	−	0.343881i
$726$		0			0
$727$	−23.9278	+	17.3846i	−0.887434	+	0.644759i	−0.935208	−	0.354099i	$-0.884787\pi$
$727$	−23.9278	+	17.3846i	−0.887434	+	0.644759i	0.0477734	+	0.998858i	$0.484787\pi$
$728$	−0.00500548	+	0.0154053i	−0.000185515	+	0.000570958i
$729$		0			0
$730$	25.1326	−	29.7747i	0.930201	−	1.10201i
$731$	15.5645	+	47.9025i	0.575673	+	1.77174i
$732$		0			0
$733$	−15.1042	−	46.4859i	−0.557886	−	1.71700i	−0.688197	−	0.725524i	$-0.741598\pi$
$733$	−15.1042	−	46.4859i	−0.557886	−	1.71700i	0.130311	−	0.991473i	$-0.458402\pi$
$734$	−27.3895	−	19.8997i	−1.01097	−	0.734510i
$735$		0			0
$736$	59.1808	−	42.9974i	2.18143	−	1.58490i
$737$	−38.1979	−	27.7524i	−1.40704	−	1.02227i
$738$		0			0
$739$	−17.6045	+	12.7904i	−0.647590	+	0.470502i	−0.862450	−	0.506143i	$-0.831071\pi$
$739$	−17.6045	+	12.7904i	−0.647590	+	0.470502i	0.214859	+	0.976645i	$0.431071\pi$
$740$	−18.1465	+	4.46814i	−0.667080	+	0.164252i
$741$		0			0
$742$	2.77595	+	8.54351i	0.101908	+	0.313642i
$743$	9.75724			0.357959			0.178979	−	0.983853i	$-0.442720\pi$
$743$	9.75724			0.357959			0.178979	+	0.983853i	$0.442720\pi$
$744$		0			0
$745$	10.1429	+	4.13252i	0.371607	+	0.151404i
$746$	−10.6382	+	32.7409i	−0.389491	+	1.19873i
$747$		0			0
$748$	46.6626	−	33.9024i	1.70615	−	1.23959i
$749$	−1.41267			−0.0516178
$750$		0			0
$751$	−17.6413			−0.643741			−0.321871	−	0.946784i	$-0.604312\pi$
$751$	−17.6413			−0.643741			−0.321871	+	0.946784i	$0.604312\pi$
$752$	25.4851	−	18.5160i	0.929346	−	0.675209i
$753$		0			0
$754$	−0.258375	+	0.795196i	−0.00940945	+	0.0289593i
$755$	−21.2517	−	8.65861i	−0.773430	−	0.315119i
$756$		0			0
$757$	−44.2551			−1.60848			−0.804240	−	0.594305i	$-0.797427\pi$
$757$	−44.2551			−1.60848			−0.804240	+	0.594305i	$0.797427\pi$
$758$	1.03943	+	3.19904i	0.0377538	+	0.116194i
$759$		0			0
$760$	0.240811	−	0.0592939i	0.00873514	−	0.00215081i
$761$	32.2600	−	23.4382i	1.16942	−	0.849636i	0.178483	−	0.983943i	$-0.442881\pi$
$761$	32.2600	−	23.4382i	1.16942	−	0.849636i	0.990940	+	0.134307i	$0.0428809\pi$
$762$		0			0
$763$	7.30049	+	5.30412i	0.264295	+	0.192022i
$764$	−21.3960	+	15.5451i	−0.774082	+	0.562403i
$765$		0			0
$766$	4.98747	+	3.62361i	0.180205	+	0.130926i
$767$	−0.157641	−	0.485169i	−0.00569208	−	0.0175184i
$768$		0			0
$769$	10.8980	+	33.5407i	0.392993	+	1.20951i	0.930514	+	0.366257i	$0.119361\pi$
$769$	10.8980	+	33.5407i	0.392993	+	1.20951i	−0.537521	+	0.843250i	$0.680639\pi$
$770$	−14.1208	+	16.7290i	−0.508879	+	0.602871i
$771$		0			0
$772$	−2.81211	+	8.65479i	−0.101210	+	0.311493i
$773$	−18.8029	+	13.6611i	−0.676295	+	0.491357i	−0.872126	−	0.489281i	$-0.837259\pi$
$773$	−18.8029	+	13.6611i	−0.676295	+	0.491357i	0.195832	+	0.980638i	$0.437259\pi$
$774$		0			0
$775$	−2.36587	+	4.77963i	−0.0849845	+	0.171689i
$776$	1.02562			0.0368176
$777$		0			0
$778$	−17.6383	+	54.2850i	−0.632362	+	1.94621i
$779$	1.61393	−	4.96717i	0.0578250	−	0.177967i
$780$		0			0
$781$	−15.8649	−	48.8272i	−0.567691	−	1.74717i
$782$	106.914			3.82324
$783$		0			0
$784$	−18.5338	−	13.4656i	−0.661922	−	0.480914i
$785$	−18.4204	−	7.50504i	−0.657453	−	0.267866i
$786$		0			0
$787$	−5.52636	−	4.01513i	−0.196993	−	0.143124i	0.484916	−	0.874561i	$-0.338850\pi$
$787$	−5.52636	−	4.01513i	−0.196993	−	0.143124i	−0.681909	+	0.731437i	$0.738850\pi$
$788$	5.41040	+	3.93089i	0.192738	+	0.140032i
$789$		0			0
$790$	−0.814558	+	11.1791i	−0.0289807	+	0.397733i
$791$	5.43235	+	3.94683i	0.193152	+	0.140333i
$792$		0			0
$793$	−0.723159			−0.0256801
$794$	−12.7757	−	39.3195i	−0.453392	−	1.39540i
$795$		0			0
$796$	−1.73529	+	5.34067i	−0.0615056	+	0.189295i
$797$	−16.6649	+	51.2892i	−0.590301	+	1.81676i	−0.0134488	+	0.999910i	$0.504281\pi$
$797$	−16.6649	+	51.2892i	−0.590301	+	1.81676i	−0.576852	+	0.816849i	$0.695719\pi$
$798$		0			0
$799$	47.8578			1.69309
$800$	−28.8391	−	28.1772i	−1.01962	−	0.996216i
$801$		0			0
$802$	41.8046	−	30.3728i	1.47617	−	1.07250i
$803$	−12.6947	+	39.0703i	−0.447987	+	1.37876i
$804$		0			0
$805$	−20.0679	+	4.94124i	−0.707301	+	0.174156i
$806$	−0.0690964	−	0.212657i	−0.00243382	−	0.00749052i
$807$		0			0
$808$	−0.267857	−	0.824380i	−0.00942318	−	0.0290016i
$809$	−14.8943	−	10.8214i	−0.523656	−	0.380459i	0.294323	−	0.955706i	$-0.404906\pi$
$809$	−14.8943	−	10.8214i	−0.523656	−	0.380459i	−0.817980	+	0.575247i	$0.804906\pi$
$810$		0			0
$811$	9.53916	−	6.93060i	0.334965	−	0.243366i	−0.407569	−	0.913174i	$-0.633624\pi$
$811$	9.53916	−	6.93060i	0.334965	−	0.243366i	0.742534	+	0.669808i	$0.233624\pi$
$812$	−6.82459	−	4.95835i	−0.239496	−	0.174004i
$813$		0			0
$814$	31.2993	−	22.7403i	1.09704	−	0.797046i
$815$	−13.8921	−	22.3773i	−0.486618	−	0.783841i
$816$		0			0
$817$	−1.93139	−	5.94419i	−0.0675706	−	0.207961i
$818$	−24.3076			−0.849895
$819$		0			0
$820$	32.4951	−	8.00113i	1.13478	−	0.279412i
$821$	3.80899	−	11.7229i	0.132935	−	0.409130i	−0.862329	−	0.506349i	$-0.830995\pi$
$821$	3.80899	−	11.7229i	0.132935	−	0.409130i	0.995263	+	0.0972189i	$0.0309947\pi$
$822$		0			0
$823$	−2.28023	+	1.65668i	−0.0794839	+	0.0577484i	−0.626818	−	0.779166i	$-0.715643\pi$
$823$	−2.28023	+	1.65668i	−0.0794839	+	0.0577484i	0.547334	+	0.836914i	$0.315643\pi$
$824$	0.0910197			0.00317082
$825$		0			0
$826$	10.1056			0.351618
$827$	−30.2776	+	21.9979i	−1.05285	+	0.764943i	−0.972753	−	0.231844i	$-0.925524\pi$
$827$	−30.2776	+	21.9979i	−1.05285	+	0.764943i	−0.0801008	+	0.996787i	$0.525524\pi$
$828$		0			0
$829$	9.56205	−	29.4289i	0.332104	−	1.02211i	−0.636028	−	0.771666i	$-0.719424\pi$
$829$	9.56205	−	29.4289i	0.332104	−	1.02211i	0.968131	−	0.250443i	$-0.0805764\pi$
$830$	10.1047	+	16.2766i	0.350741	+	0.564970i
$831$		0			0
$832$	0.892455			0.0309403
$833$	−10.7551	−	33.1008i	−0.372642	−	1.14687i
$834$		0			0
$835$	2.82363	−	38.7517i	0.0977156	−	1.34106i
$836$	−5.79033	+	4.20692i	−0.200263	+	0.145499i
$837$		0			0
$838$	−56.5195	−	41.0638i	−1.95243	−	1.41853i
$839$	−21.5988	+	15.6924i	−0.745672	+	0.541762i	−0.894482	−	0.447103i	$-0.852456\pi$
$839$	−21.5988	+	15.6924i	−0.745672	+	0.541762i	0.148810	+	0.988866i	$0.452456\pi$
$840$		0			0
$841$	10.5917	+	7.69534i	0.365232	+	0.265356i
$842$	−9.32832	−	28.7096i	−0.321475	−	0.989399i
$843$		0			0
$844$	16.9627	+	52.2057i	0.583879	+	1.79699i
$845$	2.11074	−	28.9680i	0.0726117	−	0.996529i
$846$		0			0
$847$	3.66921	−	11.2927i	0.126076	−	0.388021i
$848$	13.5763	−	9.86378i	0.466213	−	0.338724i
$849$		0			0
$850$	−9.89339	−	58.0920i	−0.339341	−	1.99254i
$851$	36.5239			1.25202
$852$		0			0
$853$	9.04183	−	27.8279i	0.309586	−	0.952808i	−0.668340	−	0.743856i	$-0.732995\pi$
$853$	9.04183	−	27.8279i	0.309586	−	0.952808i	0.977926	−	0.208952i	$-0.0670053\pi$
$854$	4.42681	−	13.6243i	0.151482	−	0.466214i
$855$		0			0
$856$	−0.0655988	−	0.201892i	−0.00224212	−	0.00690054i
$857$	33.5284			1.14531			0.572654	−	0.819797i	$-0.305914\pi$
$857$	33.5284			1.14531			0.572654	+	0.819797i	$0.305914\pi$
$858$		0			0
$859$	20.8923	+	15.1792i	0.712837	+	0.517906i	0.884088	−	0.467321i	$-0.154781\pi$
$859$	20.8923	+	15.1792i	0.712837	+	0.517906i	−0.171251	+	0.985227i	$0.554781\pi$
$860$	25.8321	−	30.6034i	0.880867	−	1.04357i
$861$		0			0
$862$	7.85792	+	5.70911i	0.267642	+	0.194453i
$863$	−23.3713	−	16.9803i	−0.795569	−	0.578015i	0.114042	−	0.993476i	$-0.463620\pi$
$863$	−23.3713	−	16.9803i	−0.795569	−	0.578015i	−0.909611	+	0.415461i	$0.863620\pi$
$864$		0			0
$865$	−28.1381	+	6.92831i	−0.956723	+	0.235570i
$866$	−16.8940	−	12.2742i	−0.574083	−	0.417096i
$867$		0			0
$868$	2.25592			0.0765710
$869$	−3.65187	−	11.2393i	−0.123881	−	0.381267i
$870$		0			0
$871$	0.318307	−	0.979647i	0.0107854	−	0.0331941i
$872$	−0.419034	+	1.28965i	−0.0141903	+	0.0436732i
$873$		0			0
$874$	−13.2669			−0.448759
$875$	4.54184	+	10.4467i	0.153542	+	0.353163i
$876$		0			0
$877$	12.2165	−	8.87581i	0.412522	−	0.299715i	−0.362100	−	0.932139i	$-0.617940\pi$
$877$	12.2165	−	8.87581i	0.412522	−	0.299715i	0.774622	+	0.632425i	$0.217940\pi$
$878$	19.1926	−	59.0688i	0.647719	−	1.99347i
$879$		0			0
$880$	37.8730	+	15.4306i	1.27670	+	0.520166i
$881$	−11.3167	−	34.8292i	−0.381269	−	1.17342i	−0.939151	−	0.343505i	$-0.888386\pi$
$881$	−11.3167	−	34.8292i	−0.381269	−	1.17342i	0.557882	−	0.829920i	$-0.311614\pi$
$882$		0			0
$883$	−10.6753	−	32.8551i	−0.359251	−	1.10566i	−0.953503	−	0.301383i	$-0.902552\pi$
$883$	−10.6753	−	32.8551i	−0.359251	−	1.10566i	0.594252	−	0.804279i	$-0.297448\pi$
$884$	1.01801	+	0.739625i	0.0342392	+	0.0248763i
$885$		0			0
$886$	−28.9985	+	21.0686i	−0.974223	+	0.707814i
$887$	26.7267	+	19.4181i	0.897394	+	0.651995i	0.937795	−	0.347189i	$-0.112864\pi$
$887$	26.7267	+	19.4181i	0.897394	+	0.651995i	−0.0404016	+	0.999184i	$0.512864\pi$
$888$		0			0
$889$	6.01021	−	4.36668i	0.201576	−	0.146454i
$890$	53.5059	−	63.3886i	1.79352	−	2.12479i
$891$		0			0
$892$	−5.15257	−	15.8580i	−0.172521	−	0.530964i
$893$	−5.93864			−0.198729
$894$		0			0
$895$	−1.58506	+	1.87783i	−0.0529828	+	0.0627690i
$896$	−0.385364	+	1.18603i	−0.0128741	+	0.0396224i
$897$		0			0
$898$	−60.7889	+	44.1657i	−2.02855	+	1.47383i
$899$	4.25420			0.141886
$900$		0			0
$901$	25.4947			0.849350
$902$	−56.0478	+	40.7211i	−1.86619	+	1.35587i
$903$		0			0
$904$	−0.311806	+	0.959641i	−0.0103705	+	0.0319172i
$905$	2.43419	−	33.4071i	0.0809153	−	1.11049i
$906$		0			0
$907$	−44.2708			−1.46999			−0.734994	−	0.678074i	$-0.762815\pi$
$907$	−44.2708			−1.46999			−0.734994	+	0.678074i	$0.762815\pi$
$908$	−10.5571	−	32.4913i	−0.350348	−	1.07826i
$909$		0			0
$910$	−0.442299	−	0.180206i	−0.0146621	−	0.00597377i
$911$	−31.4581	+	22.8556i	−1.04225	+	0.757241i	−0.970724	−	0.240197i	$-0.922788\pi$
$911$	−31.4581	+	22.8556i	−1.04225	+	0.757241i	−0.0715293	+	0.997439i	$0.522788\pi$
$912$		0			0
$913$	−16.3414	−	11.8727i	−0.540821	−	0.392930i
$914$	45.2403	−	32.8690i	1.49642	−	1.08721i
$915$		0			0
$916$	−0.687348	−	0.499387i	−0.0227106	−	0.0165002i
$917$	3.00802	+	9.25772i	0.0993334	+	0.305717i
$918$		0			0
$919$	−8.81634	−	27.1339i	−0.290824	−	0.895065i	−0.984592	−	0.174866i	$-0.944051\pi$
$919$	−8.81634	−	27.1339i	−0.290824	−	0.895065i	0.693768	−	0.720198i	$-0.255949\pi$
$920$	−1.63805	−	2.63857i	−0.0540051	−	0.0869909i
$921$		0			0
$922$	−6.12474	+	18.8500i	−0.201708	+	0.620793i
$923$	0.906137	−	0.658347i	0.0298259	−	0.0216698i
$924$		0			0
$925$	−3.37977	−	19.8453i	−0.111126	−	0.652510i
$926$	−7.52497			−0.247286
$927$		0			0
$928$	−9.93877	+	30.5884i	−0.326256	+	1.00411i
$929$	−11.2447	+	34.6076i	−0.368926	+	1.13544i	0.578559	+	0.815640i	$0.303615\pi$
$929$	−11.2447	+	34.6076i	−0.368926	+	1.13544i	−0.947486	+	0.319798i	$0.896385\pi$
$930$		0			0
$931$	1.33459	+	4.10745i	0.0437395	+	0.134616i
$932$	38.3284			1.25549
$933$		0			0
$934$	−11.5952	−	8.42441i	−0.379407	−	0.275655i
$935$	32.7699	+	52.7855i	1.07169	+	1.72627i
$936$		0			0
$937$	38.2951	+	27.8230i	1.25105	+	0.908939i	0.998282	−	0.0585890i	$-0.0186602\pi$
$937$	38.2951	+	27.8230i	1.25105	+	0.908939i	0.252765	+	0.967528i	$0.418660\pi$
$938$	16.5080	+	11.9938i	0.539007	+	0.391611i
$939$		0			0
$940$	−20.0704	−	32.3293i	−0.654625	−	1.05446i
$941$	42.8175	+	31.1087i	1.39581	+	1.01412i	0.995199	+	0.0978679i	$0.0312023\pi$
$941$	42.8175	+	31.1087i	1.39581	+	1.01412i	0.400611	+	0.916248i	$0.368798\pi$
$942$		0			0
$943$	−65.4035			−2.12983
$944$	−5.83362	−	17.9540i	−0.189868	−	0.584354i
$945$		0			0
$946$	−25.6193	+	78.8482i	−0.832957	+	2.56358i
$947$	−5.85061	+	18.0063i	−0.190119	+	0.585127i	−0.999999	−	0.00146915i	$-0.999532\pi$
$947$	−5.85061	+	18.0063i	−0.190119	+	0.585127i	0.809880	+	0.586596i	$0.199532\pi$
$948$		0			0
$949$	−0.896234			−0.0290930
$950$	1.22766	+	7.20860i	0.0398307	+	0.233878i
$951$		0			0
$952$	−0.736741	+	0.535274i	−0.0238779	+	0.0173483i
$953$	3.53822	−	10.8895i	0.114614	−	0.352746i	−0.877252	−	0.480030i	$-0.840626\pi$
$953$	3.53822	−	10.8895i	0.114614	−	0.352746i	0.991866	+	0.127284i	$0.0406258\pi$
$954$		0			0
$955$	−15.0259	−	24.2035i	−0.486225	−	0.783208i
$956$	2.96155	+	9.11471i	0.0957833	+	0.294791i
$957$		0			0
$958$	17.7459	+	54.6163i	0.573345	+	1.76457i
$959$	−5.11043	−	3.71294i	−0.165024	−	0.119897i
$960$		0			0
$961$	24.1591	−	17.5526i	0.779326	−	0.566214i
$962$	0.682835	+	0.496108i	0.0220155	+	0.0159952i
$963$		0			0
$964$	49.0419	−	35.6310i	1.57953	−	1.14760i
$965$	−9.07805	−	3.69867i	−0.292233	−	0.119065i
$966$		0			0
$967$	−11.4313	−	35.1821i	−0.367607	−	1.13138i	−0.948332	−	0.317279i	$-0.897231\pi$
$967$	−11.4313	−	35.1821i	−0.367607	−	1.13138i	0.580725	−	0.814100i	$-0.302769\pi$
$968$	1.78428			0.0573490
$969$		0			0
$970$	−2.19763	+	30.1605i	−0.0705617	+	0.968395i
$971$	9.36004	−	28.8072i	0.300378	−	0.924468i	−0.680984	−	0.732298i	$-0.738448\pi$
$971$	9.36004	−	28.8072i	0.300378	−	0.924468i	0.981362	−	0.192170i	$-0.0615524\pi$
$972$		0			0
$973$	0.747239	−	0.542901i	0.0239554	−	0.0174046i
$974$	−29.7549			−0.953408
$975$		0			0
$976$	−26.7610			−0.856600
$977$	13.4629	−	9.78136i	0.430716	−	0.312934i	−0.351219	−	0.936293i	$-0.614233\pi$
$977$	13.4629	−	9.78136i	0.430716	−	0.312934i	0.781935	+	0.623360i	$0.214233\pi$
$978$		0			0
$979$	−27.0263	+	83.1783i	−0.863763	+	2.65839i
$980$	−17.8500	+	21.1470i	−0.570198	+	0.675516i
$981$		0			0
$982$	57.3388			1.82975
$983$	−8.09305	−	24.9078i	−0.258128	−	0.794437i	−0.993197	−	0.116445i	$-0.962850\pi$
$983$	−8.09305	−	24.9078i	−0.258128	−	0.794437i	0.735069	−	0.677992i	$-0.237150\pi$
$984$		0			0
$985$	−4.64664	+	5.50490i	−0.148054	+	0.175401i
$986$	−38.0294	+	27.6300i	−1.21110	+	0.879917i
$987$		0			0
$988$	−0.126324	−	0.0917795i	−0.00401889	−	0.00291990i
$989$	−63.3203	+	46.0049i	−2.01347	+	1.46287i
$990$		0			0
$991$	20.0938	+	14.5990i	0.638300	+	0.463752i	0.859266	−	0.511530i	$-0.170921\pi$
$991$	20.0938	+	14.5990i	0.638300	+	0.463752i	−0.220966	+	0.975282i	$0.570921\pi$
$992$	−2.65789	−	8.18016i	−0.0843882	−	0.259720i
$993$		0			0
$994$	6.85635	+	21.1017i	0.217470	+	0.669305i
$995$	−5.60185	−	2.28236i	−0.177591	−	0.0723558i
$996$		0			0
$997$	7.75208	−	23.8585i	0.245511	−	0.755605i	−0.750041	−	0.661391i	$-0.769966\pi$
$997$	7.75208	−	23.8585i	0.245511	−	0.755605i	0.995552	−	0.0942136i	$-0.0300337\pi$
$998$	−43.0933	+	31.3091i	−1.36409	+	0.991072i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.d.136.1		12
3.2	odd	2		75.2.g.c.61.3	yes	12
15.2	even	4		375.2.i.d.199.5		24
15.8	even	4		375.2.i.d.199.2		24
15.14	odd	2		375.2.g.c.301.1		12
25.4	even	10		5625.2.a.q.1.2		6
25.16	even	5	inner	225.2.h.d.91.1		12
25.21	even	5		5625.2.a.p.1.5		6
75.29	odd	10		1875.2.a.k.1.5		6
75.38	even	20		375.2.i.d.49.5		24
75.41	odd	10		75.2.g.c.16.3	✓	12
75.47	even	20		1875.2.b.f.1249.4		12
75.53	even	20		1875.2.b.f.1249.9		12
75.59	odd	10		375.2.g.c.76.1		12
75.62	even	20		375.2.i.d.49.2		24
75.71	odd	10		1875.2.a.j.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.3	✓	12	75.41	odd	10
75.2.g.c.61.3	yes	12	3.2	odd	2
225.2.h.d.91.1		12	25.16	even	5	inner
225.2.h.d.136.1		12	1.1	even	1	trivial
375.2.g.c.76.1		12	75.59	odd	10
375.2.g.c.301.1		12	15.14	odd	2
375.2.i.d.49.2		24	75.62	even	20
375.2.i.d.49.5		24	75.38	even	20
375.2.i.d.199.2		24	15.8	even	4
375.2.i.d.199.5		24	15.2	even	4
1875.2.a.j.1.2		6	75.71	odd	10
1875.2.a.k.1.5		6	75.29	odd	10
1875.2.b.f.1249.4		12	75.47	even	20
1875.2.b.f.1249.9		12	75.53	even	20
5625.2.a.p.1.5		6	25.21	even	5
5625.2.a.q.1.2		6	25.4	even	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.63330 + 1.18666i) q^{2} +(0.641469 - 1.97424i) q^{4} +(2.07079 + 0.843702i) q^{5} +1.01887 q^{7} +(0.0473123 + 0.145612i) q^{8} +O(q^{10})\)	\(q+(-1.63330 + 1.18666i) q^{2} +(0.641469 - 1.97424i) q^{4} +(2.07079 + 0.843702i) q^{5} +1.01887 q^{7} +(0.0473123 + 0.145612i) q^{8} +(-4.38341 + 1.07931i) q^{10} +(3.85061 - 2.79763i) q^{11} +(0.0840060 + 0.0610339i) q^{13} +(-1.66412 + 1.20905i) q^{14} +(3.10871 + 2.25861i) q^{16} +(1.80397 + 5.55204i) q^{17} +(-0.223853 - 0.688949i) q^{19} +(2.99402 - 3.54702i) q^{20} +(-2.96936 + 9.13874i) q^{22} +(-7.33901 + 5.33210i) q^{23} +(3.57633 + 3.49426i) q^{25} -0.209634 q^{26} +(0.653574 - 2.01149i) q^{28} +(1.23251 - 3.79326i) q^{29} +(0.329605 + 1.01442i) q^{31} -8.06387 q^{32} +(-9.53482 - 6.92745i) q^{34} +(2.10987 + 0.859623i) q^{35} +(-3.25727 - 2.36655i) q^{37} +(1.18317 + 0.859623i) q^{38} +(-0.0248796 + 0.341450i) q^{40} +(5.83282 + 4.23780i) q^{41} +8.62791 q^{43} +(-3.05314 - 9.39661i) q^{44} +(5.65940 - 17.4179i) q^{46} +(2.53331 - 7.79673i) q^{47} -5.96190 q^{49} +(-9.98773 - 1.46327i) q^{50} +(0.174383 - 0.126697i) q^{52} +(1.34954 - 4.15345i) q^{53} +(10.3342 - 2.54454i) q^{55} +(0.0482051 + 0.148360i) q^{56} +(2.48827 + 7.65810i) q^{58} +(-3.97458 - 2.88770i) q^{59} +(-5.63428 + 4.09354i) q^{61} +(-1.74212 - 1.26572i) q^{62} +(6.95331 - 5.05187i) q^{64} +(0.122464 + 0.197264i) q^{65} +(-3.06544 - 9.43446i) q^{67} +12.1183 q^{68} +(-4.46613 + 1.09967i) q^{70} +(3.33323 - 10.2586i) q^{71} +(-6.98275 + 5.07326i) q^{73} +8.12840 q^{74} -1.50375 q^{76} +(3.92327 - 2.85042i) q^{77} +(0.767263 - 2.36139i) q^{79} +(4.53188 + 7.29992i) q^{80} -14.5556 q^{82} +(-1.31142 - 4.03614i) q^{83} +(-0.948634 + 13.0191i) q^{85} +(-14.0920 + 10.2384i) q^{86} +(0.589550 + 0.428333i) q^{88} +(-14.8659 + 10.8007i) q^{89} +(0.0855912 + 0.0621857i) q^{91} +(5.81910 + 17.9093i) q^{92} +(5.11443 + 15.7406i) q^{94} +(0.117715 - 1.61553i) q^{95} +(2.07003 - 6.37090i) q^{97} +(9.73758 - 7.07477i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

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