LMFDB - Embedded newform 891.2.n.b.676.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			676.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	891.676
Dual form			891.2.n.b.460.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.75181 - 1.94558i) q^{2} +(-0.507392 - 4.82751i) q^{4} +(0.413545 + 0.459289i) q^{5} +(-0.913545 - 0.406737i) q^{7} +(-6.04508 - 4.39201i) q^{8} +1.61803 q^{10} +(-1.84894 - 2.75344i) q^{11} +(-0.230909 - 0.0490813i) q^{13} +(-2.39169 + 1.06485i) q^{14} +(-9.63877 + 2.04878i) q^{16} +(0.354102 - 1.08981i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(2.00739 - 2.22943i) q^{20} +(-8.59602 - 1.22622i) q^{22} +(0.118034 - 0.204441i) q^{23} +(0.482716 - 4.59274i) q^{25} +(-0.500000 + 0.363271i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(5.48127 + 2.44042i) q^{29} +(5.95709 + 1.26622i) q^{31} +(-5.42705 + 9.39993i) q^{32} +(-1.50000 - 2.59808i) q^{34} +(-0.190983 - 0.587785i) q^{35} +(5.04508 - 3.66547i) q^{37} +(-14.9913 + 3.18650i) q^{38} +(-0.482716 - 4.59274i) q^{40} +(-0.215659 + 0.0960175i) q^{41} +(3.35410 + 5.80948i) q^{43} +(-12.3541 + 10.3229i) q^{44} +(-0.190983 - 0.587785i) q^{46} +(-1.05471 + 10.0349i) q^{47} +(-4.01478 - 4.45887i) q^{49} +(-8.08990 - 8.98475i) q^{50} +(-0.119779 + 1.13962i) q^{52} +(0.118034 + 0.363271i) q^{53} +(0.500000 - 1.98787i) q^{55} +(3.73607 + 6.47106i) q^{56} +(14.3502 - 6.38910i) q^{58} +(0.771626 + 7.34153i) q^{59} +(11.3096 - 2.40394i) q^{61} +(12.8992 - 9.37181i) q^{62} +(2.69098 + 8.28199i) q^{64} +(-0.0729490 - 0.126351i) q^{65} +(-0.927051 + 1.60570i) q^{67} +(-5.44076 - 1.15647i) q^{68} +(-1.47815 - 0.658114i) q^{70} +(-3.19098 + 9.82084i) q^{71} +(4.61803 - 3.35520i) q^{73} +(1.70656 - 16.2368i) q^{74} +(-14.2082 + 24.6093i) q^{76} +(0.569171 + 3.26742i) q^{77} +(7.36044 - 8.17459i) q^{79} +(-4.92705 - 3.57971i) q^{80} +(-0.190983 + 0.587785i) q^{82} +(1.43997 - 0.306074i) q^{83} +(0.646976 - 0.288052i) q^{85} +(17.1785 + 3.65141i) q^{86} +(-0.916102 + 24.7653i) q^{88} +8.23607 q^{89} +(0.190983 + 0.138757i) q^{91} +(-1.04683 - 0.466079i) q^{92} +(17.6760 + 19.6312i) q^{94} +(-0.378188 - 3.59821i) q^{95} +(5.25542 - 5.83674i) q^{97} -15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 9 q^{4} - 3 q^{5} - q^{7} - 26 q^{8} + 4 q^{10} - 11 q^{11} - 7 q^{13} - 4 q^{14} - q^{16} - 24 q^{17} - 20 q^{19} + 3 q^{20} - 4 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} - 12 q^{28} + 6 q^{29}+ \cdots - 72 q^{98}+O(q^{100}) $ 8 * q - q^2 + 9 * q^4 - 3 * q^5 - q^7 - 26 * q^8 + 4 * q^10 - 11 * q^11 - 7 * q^13 - 4 * q^14 - q^16 - 24 * q^17 - 20 * q^19 + 3 * q^20 - 4 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 - 12 * q^28 + 6 * q^29 + 12 * q^31 - 30 * q^32 - 12 * q^34 - 6 * q^35 + 18 * q^37 - 10 * q^38 + 6 * q^40 - 3 * q^41 - 72 * q^44 - 6 * q^46 + 17 * q^47 - 6 * q^49 + 6 * q^50 - 3 * q^52 - 8 * q^53 + 4 * q^55 + 12 * q^56 + 24 * q^58 - 6 * q^59 + 21 * q^61 + 54 * q^62 + 26 * q^64 - 14 * q^65 + 6 * q^67 - 27 * q^68 - 3 * q^70 - 30 * q^71 + 28 * q^73 - 26 * q^74 - 60 * q^76 + q^77 + 11 * q^79 - 26 * q^80 - 6 * q^82 + 13 * q^83 + 9 * q^85 + 15 * q^86 + 37 * q^88 + 48 * q^89 + 6 * q^91 + 3 * q^92 - 17 * q^94 + 5 * q^95 - 3 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.75181	−	1.94558i	1.23871	−	1.37573i	0.338101	−	0.941110i	$-0.390215\pi$
$2$	1.75181	−	1.94558i	1.23871	−	1.37573i	0.900613	−	0.434622i	$-0.143118\pi$
$3$		0			0
$3$		0			0
$4$	−0.507392	−	4.82751i	−0.253696	−	2.41376i
$5$	0.413545	+	0.459289i	0.184943	+	0.205400i	0.828486	−	0.560010i	$-0.189203\pi$
$5$	0.413545	+	0.459289i	0.184943	+	0.205400i	−0.643543	+	0.765410i	$0.722536\pi$
$6$		0			0
$7$	−0.913545	−	0.406737i	−0.345288	−	0.153732i	0.226764	−	0.973950i	$-0.427186\pi$
$7$	−0.913545	−	0.406737i	−0.345288	−	0.153732i	−0.572051	+	0.820218i	$0.693852\pi$
$8$	−6.04508	−	4.39201i	−2.13726	−	1.55281i
$9$		0			0
$10$	1.61803			0.511667
$11$	−1.84894	−	2.75344i	−0.557477	−	0.830192i
$11$	−1.84894	−	2.75344i	−0.557477	−	0.830192i
$12$		0			0
$13$	−0.230909	−	0.0490813i	−0.0640427	−	0.0136127i	0.175779	−	0.984430i	$-0.443756\pi$
$13$	−0.230909	−	0.0490813i	−0.0640427	−	0.0136127i	−0.239822	+	0.970817i	$0.577089\pi$
$14$	−2.39169	+	1.06485i	−0.639207	+	0.284593i
$15$		0			0
$16$	−9.63877	+	2.04878i	−2.40969	+	0.512196i
$17$	0.354102	−	1.08981i	0.0858823	−	0.264319i	−0.898888	−	0.438178i	$-0.855624\pi$
$17$	0.354102	−	1.08981i	0.0858823	−	0.264319i	0.984770	+	0.173860i	$0.0556239\pi$
$18$		0			0
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.107719	−	0.994181i	$-0.534355\pi$
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.978810	+	0.204772i	$0.934355\pi$
$20$	2.00739	−	2.22943i	0.448866	−	0.498517i
$21$		0			0
$22$	−8.59602	−	1.22622i	−1.83268	−	0.261432i
$23$	0.118034	−	0.204441i	0.0246118	−	0.0426289i	−0.853457	−	0.521163i	$-0.825498\pi$
$23$	0.118034	−	0.204441i	0.0246118	−	0.0426289i	0.878069	+	0.478534i	$0.158832\pi$
$24$		0			0
$25$	0.482716	−	4.59274i	0.0965432	−	0.918547i
$26$	−0.500000	+	0.363271i	−0.0980581	+	0.0712434i
$27$		0			0
$28$	−1.50000	+	4.61653i	−0.283473	+	0.872441i
$29$	5.48127	+	2.44042i	1.01785	+	0.453175i	0.846700	−	0.532071i	$-0.178586\pi$
$29$	5.48127	+	2.44042i	1.01785	+	0.453175i	0.171147	+	0.985246i	$0.445253\pi$
$30$		0			0
$31$	5.95709	+	1.26622i	1.06992	+	0.227419i	0.709023	−	0.705185i	$-0.249136\pi$
$31$	5.95709	+	1.26622i	1.06992	+	0.227419i	0.360901	+	0.932604i	$0.382469\pi$
$32$	−5.42705	+	9.39993i	−0.959376	+	1.66169i
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	−0.190983	−	0.587785i	−0.0322820	−	0.0993538i
$36$		0			0
$37$	5.04508	−	3.66547i	0.829407	−	0.602599i	−0.0899846	−	0.995943i	$-0.528682\pi$
$37$	5.04508	−	3.66547i	0.829407	−	0.602599i	0.919391	+	0.393344i	$0.128682\pi$
$38$	−14.9913	+	3.18650i	−2.43191	+	0.516919i
$39$		0			0
$40$	−0.482716	−	4.59274i	−0.0763241	−	0.726175i
$41$	−0.215659	+	0.0960175i	−0.0336803	+	0.0149954i	−0.423508	−	0.905893i	$-0.639201\pi$
$41$	−0.215659	+	0.0960175i	−0.0336803	+	0.0149954i	0.389827	+	0.920888i	$0.372535\pi$
$42$		0			0
$43$	3.35410	+	5.80948i	0.511496	+	0.885937i	0.999911	+	0.0133254i	$0.00424174\pi$
$43$	3.35410	+	5.80948i	0.511496	+	0.885937i	−0.488415	+	0.872611i	$0.662425\pi$
$44$	−12.3541	+	10.3229i	−1.86245	+	1.55623i
$45$		0			0
$46$	−0.190983	−	0.587785i	−0.0281589	−	0.0866642i
$47$	−1.05471	+	10.0349i	−0.153845	+	1.46374i	0.596457	+	0.802645i	$0.296575\pi$
$47$	−1.05471	+	10.0349i	−0.153845	+	1.46374i	−0.750302	+	0.661095i	$0.770092\pi$
$48$		0			0
$49$	−4.01478	−	4.45887i	−0.573541	−	0.636981i
$50$	−8.08990	−	8.98475i	−1.14409	−	1.27064i
$51$		0			0
$52$	−0.119779	+	1.13962i	−0.0166104	+	0.158037i
$53$	0.118034	+	0.363271i	0.0162132	+	0.0498991i	0.958836	−	0.283961i	$-0.0916486\pi$
$53$	0.118034	+	0.363271i	0.0162132	+	0.0498991i	−0.942623	+	0.333860i	$0.891649\pi$
$54$		0			0
$55$	0.500000	−	1.98787i	0.0674200	−	0.268044i
$56$	3.73607	+	6.47106i	0.499253	+	0.864732i
$57$		0			0
$58$	14.3502	−	6.38910i	1.88427	−	0.838930i
$59$	0.771626	+	7.34153i	0.100457	+	0.955785i	0.922405	+	0.386223i	$0.126221\pi$
$59$	0.771626	+	7.34153i	0.100457	+	0.955785i	−0.821948	+	0.569562i	$0.807113\pi$
$60$		0			0
$61$	11.3096	−	2.40394i	1.44805	−	0.307793i	0.584229	−	0.811589i	$-0.301397\pi$
$61$	11.3096	−	2.40394i	1.44805	−	0.307793i	0.863823	+	0.503796i	$0.168064\pi$
$62$	12.8992	−	9.37181i	1.63820	−	1.19022i
$63$		0			0
$64$	2.69098	+	8.28199i	0.336373	+	1.03525i
$65$	−0.0729490	−	0.126351i	−0.00904821	−	0.0156720i
$66$		0			0
$67$	−0.927051	+	1.60570i	−0.113257	+	0.196167i	−0.917082	−	0.398699i	$-0.869462\pi$
$67$	−0.927051	+	1.60570i	−0.113257	+	0.196167i	0.803824	+	0.594867i	$0.202795\pi$
$68$	−5.44076	−	1.15647i	−0.659789	−	0.140242i
$69$		0			0
$70$	−1.47815	−	0.658114i	−0.176672	−	0.0786596i
$71$	−3.19098	+	9.82084i	−0.378700	+	1.16552i	0.562248	+	0.826968i	$0.309937\pi$
$71$	−3.19098	+	9.82084i	−0.378700	+	1.16552i	−0.940948	+	0.338550i	$0.890063\pi$
$72$		0			0
$73$	4.61803	−	3.35520i	0.540500	−	0.392696i	−0.283771	−	0.958892i	$-0.591585\pi$
$73$	4.61803	−	3.35520i	0.540500	−	0.392696i	0.824271	+	0.566196i	$0.191585\pi$
$74$	1.70656	−	16.2368i	0.198383	−	1.88749i
$75$		0			0
$76$	−14.2082	+	24.6093i	−1.62979	+	2.82288i
$77$	0.569171	+	3.26742i	0.0648630	+	0.372357i
$78$		0			0
$79$	7.36044	−	8.17459i	0.828114	−	0.919714i	−0.169720	−	0.985492i	$-0.554286\pi$
$79$	7.36044	−	8.17459i	0.828114	−	0.919714i	0.997834	+	0.0657787i	$0.0209531\pi$
$80$	−4.92705	−	3.57971i	−0.550861	−	0.400224i
$81$		0			0
$82$	−0.190983	+	0.587785i	−0.0210905	+	0.0649100i
$83$	1.43997	−	0.306074i	0.158057	−	0.0335960i	−0.128204	−	0.991748i	$-0.540921\pi$
$83$	1.43997	−	0.306074i	0.158057	−	0.0335960i	0.286260	+	0.958152i	$0.407588\pi$
$84$		0			0
$85$	0.646976	−	0.288052i	0.0701745	−	0.0312437i
$86$	17.1785	+	3.65141i	1.85241	+	0.393742i
$87$		0			0
$88$	−0.916102	+	24.7653i	−0.0976568	+	2.63999i
$89$	8.23607			0.873021			0.436511	−	0.899699i	$-0.356214\pi$
$89$	8.23607			0.873021			0.436511	+	0.899699i	$0.356214\pi$
$90$		0			0
$91$	0.190983	+	0.138757i	0.0200205	+	0.0145457i
$92$	−1.04683	−	0.466079i	−0.109140	−	0.0485921i
$93$		0			0
$94$	17.6760	+	19.6312i	1.82314	+	2.02481i
$95$	−0.378188	−	3.59821i	−0.0388012	−	0.369169i
$96$		0			0
$97$	5.25542	−	5.83674i	0.533607	−	0.592631i	−0.414711	−	0.909953i	$-0.636117\pi$
$97$	5.25542	−	5.83674i	0.533607	−	0.592631i	0.948318	+	0.317323i	$0.102784\pi$
$98$	−15.7082			−1.58677
$99$		0			0
$100$	−22.4164			−2.24164
$101$	6.84927	−	7.60688i	0.681527	−	0.756913i	−0.298795	−	0.954317i	$-0.596585\pi$
$101$	6.84927	−	7.60688i	0.681527	−	0.756913i	0.980322	+	0.197404i	$0.0632512\pi$
$102$		0			0
$103$	1.14399	+	10.8843i	0.112720	+	1.07246i	0.893934	+	0.448199i	$0.147935\pi$
$103$	1.14399	+	10.8843i	0.112720	+	1.07246i	−0.781213	+	0.624264i	$0.785399\pi$
$104$	1.18030	+	1.31086i	0.115738	+	0.128540i
$105$		0			0
$106$	0.913545	+	0.406737i	0.0887314	+	0.0395058i
$107$	−9.28115	−	6.74315i	−0.897243	−	0.651885i	0.0405134	−	0.999179i	$-0.487101\pi$
$107$	−9.28115	−	6.74315i	−0.897243	−	0.651885i	−0.937756	+	0.347294i	$0.887101\pi$
$108$		0			0
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$	−2.99165	−	4.45515i	−0.285243	−	0.424782i
$111$		0			0
$112$	9.63877	+	2.04878i	0.910778	+	0.193592i
$113$	−12.3074	+	5.47961i	−1.15778	+	0.515478i	−0.893543	−	0.448978i	$-0.851788\pi$
$113$	−12.3074	+	5.47961i	−1.15778	+	0.515478i	−0.264241	+	0.964457i	$0.585121\pi$
$114$		0			0
$115$	0.142710	−	0.0303339i	0.0133078	−	0.00282865i
$116$	9.00000	−	27.6992i	0.835629	−	2.57180i
$117$		0			0
$118$	15.6353	+	11.3597i	1.43934	+	1.04574i
$119$	−0.766755	+	0.851568i	−0.0702884	+	0.0780631i
$120$		0			0
$121$	−4.16282	+	10.1819i	−0.378438	+	0.925627i
$122$	15.1353	−	26.2150i	1.37028	−	2.37340i
$123$		0			0
$124$	3.09010	−	29.4004i	0.277499	−	2.64023i
$125$	4.80902	−	3.49396i	0.430132	−	0.312509i
$126$		0			0
$127$	2.38197	−	7.33094i	0.211365	−	0.650516i	−0.788026	−	0.615641i	$-0.788897\pi$
$127$	2.38197	−	7.33094i	0.211365	−	0.650516i	0.999392	−	0.0348741i	$-0.0111030\pi$
$128$	0.995920	+	0.443412i	0.0880277	+	0.0391925i
$129$		0			0
$130$	−0.373619	−	0.0794152i	−0.0327686	−	0.00696517i
$131$	−5.89919	+	10.2177i	−0.515414	+	0.892724i	0.484426	+	0.874832i	$0.339029\pi$
$131$	−5.89919	+	10.2177i	−0.515414	+	0.892724i	−0.999840	+	0.0178914i	$0.994305\pi$
$132$		0			0
$133$	2.92705	+	5.06980i	0.253808	+	0.439608i
$134$	1.50000	+	4.61653i	0.129580	+	0.398807i
$135$		0			0
$136$	−6.92705	+	5.03280i	−0.593990	+	0.431559i
$137$	9.55057	−	2.03004i	0.815960	−	0.173438i	0.219017	−	0.975721i	$-0.429715\pi$
$137$	9.55057	−	2.03004i	0.815960	−	0.173438i	0.596943	+	0.802283i	$0.296382\pi$
$138$		0			0
$139$	−1.52218	−	14.4825i	−0.129109	−	1.22839i	−0.846755	−	0.531984i	$-0.821447\pi$
$139$	−1.52218	−	14.4825i	−0.129109	−	1.22839i	0.717645	−	0.696409i	$-0.245220\pi$
$140$	−2.74064	+	1.22021i	−0.231626	+	0.103127i
$141$		0			0
$142$	13.5172	+	23.4125i	1.13434	+	1.96473i
$143$	0.291796	+	0.726543i	0.0244012	+	0.0607565i
$144$		0			0
$145$	1.14590	+	3.52671i	0.0951617	+	0.292877i
$146$	1.56210	−	14.8624i	0.129280	−	1.23002i
$147$		0			0
$148$	−20.2549	−	22.4954i	−1.66494	−	1.84911i
$149$	2.83448	+	3.14801i	0.232210	+	0.257895i	0.847977	−	0.530033i	$-0.177820\pi$
$149$	2.83448	+	3.14801i	0.232210	+	0.257895i	−0.615767	+	0.787928i	$0.711154\pi$
$150$		0			0
$151$	−0.110354	+	1.04994i	−0.00898045	+	0.0854433i	−0.998094	−	0.0617103i	$-0.980345\pi$
$151$	−0.110354	+	1.04994i	−0.00898045	+	0.0854433i	0.989114	+	0.147154i	$0.0470112\pi$
$152$	13.5172	+	41.6017i	1.09639	+	3.37435i
$153$		0			0
$154$	7.35410	+	4.61653i	0.592610	+	0.372010i
$155$	1.88197	+	3.25966i	0.151163	+	0.261822i
$156$		0			0
$157$	14.3502	−	6.38910i	1.14527	−	0.509906i	0.255721	−	0.966751i	$-0.417687\pi$
$157$	14.3502	−	6.38910i	1.14527	−	0.509906i	0.889546	+	0.456845i	$0.151021\pi$
$158$	−3.01025	−	28.6406i	−0.239483	−	2.27852i
$159$		0			0
$160$	−6.56161	+	1.39471i	−0.518741	+	0.110262i
$161$	−0.190983	+	0.138757i	−0.0150516	+	0.0109356i
$162$		0			0
$163$	−1.59017	−	4.89404i	−0.124552	−	0.383331i	0.869267	−	0.494342i	$-0.164591\pi$
$163$	−1.59017	−	4.89404i	−0.124552	−	0.383331i	−0.993819	+	0.111011i	$0.964591\pi$
$164$	0.572949	+	0.992377i	0.0447398	+	0.0774916i
$165$		0			0
$166$	1.92705	−	3.33775i	0.149568	−	0.259060i
$167$	11.7715	+	2.50210i	0.910903	+	0.193618i	0.639449	−	0.768833i	$-0.279162\pi$
$167$	11.7715	+	2.50210i	0.910903	+	0.193618i	0.271454	+	0.962452i	$0.412496\pi$
$168$		0			0
$169$	−11.8252	−	5.26491i	−0.909629	−	0.404993i
$170$	0.572949	−	1.76336i	0.0439432	−	0.135243i
$171$		0			0
$172$	26.3435	−	19.1396i	2.00867	−	1.45938i
$173$	−1.88511	+	17.9356i	−0.143322	+	1.36362i	0.652361	+	0.757909i	$0.273779\pi$
$173$	−1.88511	+	17.9356i	−0.143322	+	1.36362i	−0.795683	+	0.605713i	$0.792888\pi$
$174$		0			0
$175$	−2.30902	+	3.99933i	−0.174545	+	0.302321i
$176$	23.4627	+	22.7516i	1.76857	+	1.71497i
$177$		0			0
$178$	14.4280	−	16.0239i	1.08142	−	1.20104i
$179$	−6.89919	−	5.01255i	−0.515669	−	0.374656i	0.299301	−	0.954159i	$-0.403247\pi$
$179$	−6.89919	−	5.01255i	−0.515669	−	0.374656i	−0.814970	+	0.579503i	$0.803247\pi$
$180$		0			0
$181$	0.781153	−	2.40414i	0.0580626	−	0.178698i	−0.917819	−	0.396999i	$-0.870051\pi$
$181$	0.781153	−	2.40414i	0.0580626	−	0.178698i	0.975881	+	0.218301i	$0.0700515\pi$
$182$	0.604528	−	0.128496i	0.0448106	−	0.00952479i
$183$		0			0
$184$	−1.61143	+	0.717456i	−0.118796	+	0.0528915i
$185$	3.76988	+	0.801313i	0.277167	+	0.0589137i
$186$		0			0
$187$	−3.65545	+	1.04001i	−0.267313	+	0.0760528i
$188$	48.9787			3.57214
$189$		0			0
$190$	−7.66312	−	5.56758i	−0.555941	−	0.403915i
$191$	0.748797	+	0.333386i	0.0541810	+	0.0241230i	0.433648	−	0.901082i	$-0.357226\pi$
$191$	0.748797	+	0.333386i	0.0541810	+	0.0241230i	−0.379467	+	0.925205i	$0.623893\pi$
$192$		0			0
$193$	−2.10502	−	2.33786i	−0.151522	−	0.168283i	0.662605	−	0.748969i	$-0.269451\pi$
$193$	−2.10502	−	2.33786i	−0.151522	−	0.168283i	−0.814127	+	0.580686i	$0.802784\pi$
$194$	−2.14935	−	20.4497i	−0.154314	−	1.46820i
$195$		0			0
$196$	−19.4882	+	21.6438i	−1.39201	+	1.54599i
$197$	−13.0344			−0.928666			−0.464333	−	0.885661i	$-0.653706\pi$
$197$	−13.0344			−0.928666			−0.464333	+	0.885661i	$0.653706\pi$
$198$		0			0
$199$	6.70820			0.475532			0.237766	−	0.971322i	$-0.423585\pi$
$199$	6.70820			0.475532			0.237766	+	0.971322i	$0.423585\pi$
$200$	−23.0894	+	25.6434i	−1.63267	+	1.81326i
$201$		0			0
$202$	−2.80119	−	26.6516i	−0.197091	−	1.87520i
$203$	−4.01478	−	4.45887i	−0.281783	−	0.312951i
$204$		0			0
$205$	−0.133284	−	0.0593421i	−0.00930899	−	0.00414463i
$206$	23.1803	+	16.8415i	1.61505	+	1.17340i
$207$		0			0
$208$	2.32624			0.161296
$209$	−0.717727	+	19.4026i	−0.0496462	+	1.34211i
$210$		0			0
$211$	−3.53897	−	0.752232i	−0.243633	−	0.0517858i	0.0844767	−	0.996425i	$-0.473078\pi$
$211$	−3.53897	−	0.752232i	−0.243633	−	0.0517858i	−0.328109	+	0.944640i	$0.606411\pi$
$212$	1.69381	−	0.754131i	0.116331	−	0.0517939i
$213$		0			0
$214$	−29.3781	+	6.24451i	−2.00825	+	0.426866i
$215$	−1.28115	+	3.94298i	−0.0873739	+	0.268909i
$216$		0			0
$217$	−4.92705	−	3.57971i	−0.334470	−	0.243007i
$218$	−21.0217	+	23.3469i	−1.42377	+	1.58125i
$219$		0			0
$220$	−9.85016	−	1.40513i	−0.664098	−	0.0947336i
$221$	−0.135255	+	0.234268i	−0.00909823	+	0.0157586i
$222$		0			0
$223$	−0.750550	+	7.14101i	−0.0502605	+	0.478197i	0.940222	+	0.340561i	$0.110617\pi$
$223$	−0.750550	+	7.14101i	−0.0502605	+	0.478197i	−0.990483	+	0.137636i	$0.956050\pi$
$224$	8.78115	−	6.37988i	0.586715	−	0.426274i
$225$		0			0
$226$	−10.8992	+	33.5442i	−0.725003	+	2.23133i
$227$	−12.0408	−	5.36093i	−0.799179	−	0.355817i	−0.0338254	−	0.999428i	$-0.510769\pi$
$227$	−12.0408	−	5.36093i	−0.799179	−	0.355817i	−0.765353	+	0.643611i	$0.777436\pi$
$228$		0			0
$229$	−0.461819	−	0.0981626i	−0.0305178	−	0.00648677i	0.192627	−	0.981272i	$-0.438299\pi$
$229$	−0.461819	−	0.0981626i	−0.0305178	−	0.00648677i	−0.223145	+	0.974785i	$0.571632\pi$
$230$	0.190983	−	0.330792i	0.0125930	−	0.0218118i
$231$		0			0
$232$	−22.4164	−	38.8264i	−1.47171	−	2.54908i
$233$	1.28115	+	3.94298i	0.0839311	+	0.258313i	0.984211	−	0.176997i	$-0.0566384\pi$
$233$	1.28115	+	3.94298i	0.0839311	+	0.258313i	−0.900280	+	0.435311i	$0.856638\pi$
$234$		0			0
$235$	−5.04508	+	3.66547i	−0.329105	+	0.239109i
$236$	35.0498	−	7.45006i	2.28155	−	0.484958i
$237$		0			0
$238$	0.313585	+	2.98357i	0.0203267	+	0.193396i
$239$	−0.348943	+	0.155360i	−0.0225713	+	0.0100494i	−0.417991	−	0.908451i	$-0.637266\pi$
$239$	−0.348943	+	0.155360i	−0.0225713	+	0.0100494i	0.395420	+	0.918500i	$0.370599\pi$
$240$		0			0
$241$	−4.14590	−	7.18091i	−0.267061	−	0.462563i	0.701041	−	0.713121i	$-0.252719\pi$
$241$	−4.14590	−	7.18091i	−0.267061	−	0.462563i	−0.968101	+	0.250558i	$0.919386\pi$
$242$	12.5172	+	25.9358i	0.804637	+	1.66722i
$243$		0			0
$244$	−17.3435	−	53.3777i	−1.11030	−	3.41716i
$245$	0.387613	−	3.68789i	0.0247637	−	0.235611i
$246$		0			0
$247$	0.924716	+	1.02700i	0.0588383	+	0.0653465i
$248$	−30.4498	−	33.8180i	−1.93357	−	2.14744i
$249$		0			0
$250$	1.62670	−	15.4771i	0.102882	−	0.978855i
$251$	6.79180	+	20.9030i	0.428694	+	1.31939i	0.899412	+	0.437102i	$0.143995\pi$
$251$	6.79180	+	20.9030i	0.428694	+	1.31939i	−0.470718	+	0.882284i	$0.656005\pi$
$252$		0			0
$253$	−0.781153	+	0.0530006i	−0.0491107	+	0.00333212i
$254$	−10.0902	−	17.4767i	−0.633114	−	1.09658i
$255$		0			0
$256$	−13.3033	+	5.92302i	−0.831458	+	0.370189i
$257$	3.10895	+	29.5797i	0.193931	+	1.84513i	0.468376	+	0.883529i	$0.344839\pi$
$257$	3.10895	+	29.5797i	0.193931	+	1.84513i	−0.274445	+	0.961603i	$0.588494\pi$
$258$		0			0
$259$	−6.09979	+	1.29655i	−0.379023	+	0.0805638i
$260$	−0.572949	+	0.416272i	−0.0355328	+	0.0258161i
$261$		0			0
$262$	9.54508	+	29.3768i	0.589697	+	1.81490i
$263$	−7.63525	−	13.2246i	−0.470810	−	0.815467i	0.528633	−	0.848851i	$-0.322705\pi$
$263$	−7.63525	−	13.2246i	−0.470810	−	0.815467i	−0.999443	+	0.0333839i	$0.989372\pi$
$264$		0			0
$265$	−0.118034	+	0.204441i	−0.00725077	+	0.0125587i
$266$	14.9913	+	3.18650i	0.919177	+	0.195377i
$267$		0			0
$268$	8.22191	+	3.66063i	0.502233	+	0.223609i
$269$	7.85410	−	24.1724i	0.478873	−	1.47382i	−0.361789	−	0.932260i	$-0.617834\pi$
$269$	7.85410	−	24.1724i	0.478873	−	1.47382i	0.840662	−	0.541560i	$-0.182166\pi$
$270$		0			0
$271$	−15.0623	+	10.9434i	−0.914970	+	0.664765i	−0.942267	−	0.334863i	$-0.891310\pi$
$271$	−15.0623	+	10.9434i	−0.914970	+	0.664765i	0.0272970	+	0.999627i	$0.491310\pi$
$272$	−1.18031	+	11.2299i	−0.0715671	+	0.680915i
$273$		0			0
$274$	12.7812	−	22.1376i	0.772138	−	1.33738i
$275$	−13.5383	+	7.16258i	−0.816391	+	0.431920i
$276$		0			0
$277$	−19.5485	+	21.7108i	−1.17456	+	1.30448i	−0.231118	+	0.972926i	$0.574238\pi$
$277$	−19.5485	+	21.7108i	−1.17456	+	1.30448i	−0.943437	+	0.331551i	$0.892428\pi$
$278$	−30.8435	−	22.4091i	−1.84987	−	1.34401i
$279$		0			0
$280$	−1.42705	+	4.39201i	−0.0852826	+	0.262473i
$281$	24.2228	−	5.14871i	1.44501	−	0.307146i	0.582353	−	0.812936i	$-0.302132\pi$
$281$	24.2228	−	5.14871i	1.44501	−	0.307146i	0.862657	+	0.505790i	$0.168799\pi$
$282$		0			0
$283$	−5.21470	+	2.32174i	−0.309982	+	0.138013i	−0.555831	−	0.831295i	$-0.687600\pi$
$283$	−5.21470	+	2.32174i	−0.309982	+	0.138013i	0.245849	+	0.969308i	$0.420933\pi$
$284$	49.0293	+	10.4215i	2.90935	+	0.618402i
$285$		0			0
$286$	1.92472	+	0.705050i	0.113811	+	0.0416905i
$287$	0.236068			0.0139347
$288$		0			0
$289$	12.6910	+	9.22054i	0.746528	+	0.542385i
$290$	8.86889	+	3.94868i	0.520799	+	0.231875i
$291$		0			0
$292$	−18.5404	−	20.5912i	−1.08500	−	1.20501i
$293$	−2.26330	−	21.5339i	−0.132223	−	1.25802i	−0.836449	−	0.548045i	$-0.815372\pi$
$293$	−2.26330	−	21.5339i	−0.132223	−	1.25802i	0.704225	−	0.709976i	$-0.251294\pi$
$294$		0			0
$295$	−3.05278	+	3.39045i	−0.177740	+	0.197400i
$296$	−46.5967			−2.70838
$297$		0			0
$298$	11.0902			0.642436
$299$	−0.0372894	+	0.0414140i	−0.00215650	+	0.00239504i
$300$		0			0
$301$	−0.701198	−	6.67146i	−0.0404164	−	0.384536i
$302$	1.84943	+	2.05400i	0.106423	+	0.118195i
$303$		0			0
$304$	52.6996	+	23.4634i	3.02253	+	1.34572i
$305$	5.78115	+	4.20025i	0.331028	+	0.240506i
$306$		0			0
$307$	27.9787			1.59683			0.798415	−	0.602108i	$-0.205672\pi$
$307$	27.9787			1.59683			0.798415	+	0.602108i	$0.205672\pi$
$308$	15.4847	−	4.40554i	0.882324	−	0.251029i
$309$		0			0
$310$	9.63877	+	2.04878i	0.547445	+	0.116363i
$311$	−10.6451	+	4.73949i	−0.603626	+	0.268752i	−0.685711	−	0.727874i	$-0.740509\pi$
$311$	−10.6451	+	4.73949i	−0.603626	+	0.268752i	0.0820850	+	0.996625i	$0.473842\pi$
$312$		0			0
$313$	2.47262	−	0.525572i	0.139761	−	0.0297071i	−0.137500	−	0.990502i	$-0.543907\pi$
$313$	2.47262	−	0.525572i	0.139761	−	0.0297071i	0.277261	+	0.960795i	$0.410573\pi$
$314$	12.7082	−	39.1118i	0.717165	−	2.20721i
$315$		0			0
$316$	−43.1976	−	31.3849i	−2.43005	−	1.76554i
$317$	4.56324	−	5.06800i	0.256297	−	0.284647i	−0.601240	−	0.799068i	$-0.705327\pi$
$317$	4.56324	−	5.06800i	0.256297	−	0.284647i	0.857538	+	0.514421i	$0.171993\pi$
$318$		0			0
$319$	−3.41502	−	19.6045i	−0.191205	−	1.09764i
$320$	−2.69098	+	4.66092i	−0.150431	+	0.260553i
$321$		0			0
$322$	−0.0646021	+	0.614648i	−0.00360014	+	0.0342530i
$323$	−5.42705	+	3.94298i	−0.301969	+	0.219393i
$324$		0			0
$325$	−0.336881	+	1.03681i	−0.0186868	+	0.0575121i
$326$	−12.3074	−	5.47961i	−0.681644	−	0.303488i
$327$		0			0
$328$	1.72539	+	0.366742i	0.0952685	+	0.0202499i
$329$	5.04508	−	8.73834i	0.278145	−	0.481760i
$330$		0			0
$331$	−8.35410	−	14.4697i	−0.459183	−	0.795328i	0.539735	−	0.841835i	$-0.318524\pi$
$331$	−8.35410	−	14.4697i	−0.459183	−	0.795328i	−0.998918	+	0.0465067i	$0.985191\pi$
$332$	−2.20820	−	6.79615i	−0.121191	−	0.372987i
$333$		0			0
$334$	25.4894	−	18.5191i	1.39472	−	1.01332i
$335$	−1.12086	+	0.238246i	−0.0612390	+	0.0130167i
$336$		0			0
$337$	1.90036	+	18.0807i	0.103519	+	0.984921i	0.915795	+	0.401647i	$0.131562\pi$
$337$	1.90036	+	18.0807i	0.103519	+	0.984921i	−0.812275	+	0.583274i	$0.801771\pi$
$338$	−30.9587	+	13.7837i	−1.68393	+	0.749735i
$339$		0			0
$340$	−1.71885	−	2.97713i	−0.0932176	−	0.161458i
$341$	−7.52786	−	18.7436i	−0.407657	−	1.01502i
$342$		0			0
$343$	4.01722	+	12.3637i	0.216910	+	0.667579i
$344$	5.23945	−	49.8500i	0.282492	−	2.68773i
$345$		0			0
$346$	31.5929	+	35.0874i	1.69844	+	1.88631i
$347$	1.02234	+	1.13542i	0.0548821	+	0.0609528i	0.769961	−	0.638091i	$-0.220276\pi$
$347$	1.02234	+	1.13542i	0.0548821	+	0.0609528i	−0.715079	+	0.699044i	$0.753609\pi$
$348$		0			0
$349$	−1.32837	+	12.6386i	−0.0711060	+	0.676528i	0.899675	+	0.436560i	$0.143803\pi$
$349$	−1.32837	+	12.6386i	−0.0711060	+	0.676528i	−0.970781	+	0.239968i	$0.922863\pi$
$350$	3.73607	+	11.4984i	0.199701	+	0.614617i
$351$		0			0
$352$	35.9164	−	2.43690i	1.91435	−	0.129887i
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270130\pi$
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	−0.980352	+	0.197256i	$0.936797\pi$
$354$		0			0
$355$	−5.83022	+	2.59578i	−0.309436	+	0.137770i
$356$	−4.17891	−	39.7597i	−0.221482	−	2.10726i
$357$		0			0
$358$	−21.8384	+	4.64189i	−1.15419	+	0.245331i
$359$	−7.85410	+	5.70634i	−0.414524	+	0.301169i	−0.775431	−	0.631433i	$-0.782467\pi$
$359$	−7.85410	+	5.70634i	−0.414524	+	0.301169i	0.360907	+	0.932602i	$0.382467\pi$
$360$		0			0
$361$	4.71885	+	14.5231i	0.248360	+	0.764375i
$362$	−3.30902	−	5.73139i	−0.173918	−	0.301235i
$363$		0			0
$364$	0.572949	−	0.992377i	0.0300307	−	0.0520147i
$365$	3.45077	+	0.733484i	0.180622	+	0.0383923i
$366$		0			0
$367$	20.2313	+	9.00755i	1.05606	+	0.470190i	0.859943	−	0.510389i	$-0.170499\pi$
$367$	20.2313	+	9.00755i	1.05606	+	0.470190i	0.196121	+	0.980580i	$0.437165\pi$
$368$	−0.718847	+	2.21238i	−0.0374725	+	0.115328i
$369$		0			0
$370$	8.16312	−	5.93085i	0.424380	−	0.308330i
$371$	0.0399263	−	0.379874i	0.00207287	−	0.0197221i
$372$		0			0
$373$	−0.444272	+	0.769502i	−0.0230035	+	0.0398433i	−0.877298	−	0.479946i	$-0.840656\pi$
$373$	−0.444272	+	0.769502i	−0.0230035	+	0.0398433i	0.854294	+	0.519789i	$0.173990\pi$
$374$	−4.38022	+	8.93385i	−0.226496	+	0.461958i
$375$		0			0
$376$	50.4492	−	56.0295i	2.60172	−	2.88950i
$377$	−1.14590	−	0.832544i	−0.0590168	−	0.0428782i
$378$		0			0
$379$	−7.69098	+	23.6704i	−0.395059	+	1.21587i	0.533856	+	0.845575i	$0.320742\pi$
$379$	−7.69098	+	23.6704i	−0.395059	+	1.21587i	−0.928915	+	0.370292i	$0.879258\pi$
$380$	−17.1785	+	3.65141i	−0.881240	+	0.187313i
$381$		0			0
$382$	1.96038	−	0.872815i	0.100302	−	0.0446571i
$383$	−12.4305	−	2.64218i	−0.635169	−	0.135009i	−0.120937	−	0.992660i	$-0.538590\pi$
$383$	−12.4305	−	2.64218i	−0.635169	−	0.135009i	−0.514232	+	0.857651i	$0.671923\pi$
$384$		0			0
$385$	−1.26531	+	1.61264i	−0.0644863	+	0.0821878i
$386$	−8.23607			−0.419205
$387$		0			0
$388$	−30.8435	−	22.4091i	−1.56584	−	1.13765i
$389$	33.5661	+	14.9446i	1.70187	+	0.757720i	0.998919	+	0.0464795i	$0.0148002\pi$
$389$	33.5661	+	14.9446i	1.70187	+	0.757720i	0.702948	+	0.711241i	$0.251866\pi$
$390$		0			0
$391$	−0.181006	−	0.201028i	−0.00915389	−	0.0101664i
$392$	4.68631	+	44.5872i	0.236694	+	2.25199i
$393$		0			0
$394$	−22.8338	+	25.3595i	−1.15035	+	1.27759i
$395$	6.79837			0.342063
$396$		0			0
$397$	−18.7082			−0.938938			−0.469469	−	0.882949i	$-0.655555\pi$
$397$	−18.7082			−0.938938			−0.469469	+	0.882949i	$0.655555\pi$
$398$	11.7515	−	13.0513i	0.589048	−	0.654204i
$399$		0			0
$400$	4.75673	+	45.2573i	0.237837	+	2.26286i
$401$	21.2027	+	23.5480i	1.05881	+	1.17593i	0.983896	+	0.178740i	$0.0572019\pi$
$401$	21.2027	+	23.5480i	1.05881	+	1.17593i	0.0749152	+	0.997190i	$0.476131\pi$
$402$		0			0
$403$	−1.31340	−	0.584763i	−0.0654251	−	0.0291291i
$404$	−40.1976	−	29.2052i	−1.99990	−	1.45301i
$405$		0			0
$406$	−15.7082			−0.779585
$407$	−19.4207	−	7.11407i	−0.962649	−	0.352632i
$408$		0			0
$409$	6.33070	+	1.34563i	0.313033	+	0.0665373i	0.361749	−	0.932275i	$-0.382180\pi$
$409$	6.33070	+	1.34563i	0.313033	+	0.0665373i	−0.0487161	+	0.998813i	$0.515513\pi$
$410$	−0.348943	+	0.155360i	−0.0172331	+	0.00767266i
$411$		0			0
$412$	51.9637	−	11.0452i	2.56007	−	0.544159i
$413$	2.28115	−	7.02067i	0.112248	−	0.345464i
$414$		0			0
$415$	0.736068	+	0.534785i	0.0361322	+	0.0262515i
$416$	1.71452	−	1.90416i	0.0840611	−	0.0933593i
$417$		0			0
$418$	36.4919	+	35.3860i	1.78488	+	1.73078i
$419$	15.7254	−	27.2372i	0.768237	−	1.33063i	−0.170281	−	0.985396i	$-0.554467\pi$
$419$	15.7254	−	27.2372i	0.768237	−	1.33063i	0.938518	−	0.345230i	$-0.112199\pi$
$420$		0			0
$421$	−1.09824	+	10.4490i	−0.0535248	+	0.509254i	0.934611	+	0.355671i	$0.115748\pi$
$421$	−1.09824	+	10.4490i	−0.0535248	+	0.509254i	−0.988136	+	0.153583i	$0.950919\pi$
$422$	−7.66312	+	5.56758i	−0.373035	+	0.271026i
$423$		0			0
$424$	0.881966	−	2.71441i	0.0428321	−	0.131824i
$425$	−4.83430	−	2.15237i	−0.234498	−	0.104405i
$426$		0			0
$427$	−11.3096	−	2.40394i	−0.547312	−	0.116335i
$428$	−27.8435	+	48.2263i	−1.34586	+	2.33111i
$429$		0			0
$430$	5.42705	+	9.39993i	0.261716	+	0.453305i
$431$	1.82624	+	5.62058i	0.0879668	+	0.270734i	0.985357	−	0.170504i	$-0.0545395\pi$
$431$	1.82624	+	5.62058i	0.0879668	+	0.270734i	−0.897390	+	0.441238i	$0.854540\pi$
$432$		0			0
$433$	−28.5623	+	20.7517i	−1.37262	+	0.997264i	−0.375089	+	0.926989i	$0.622388\pi$
$433$	−28.5623	+	20.7517i	−1.37262	+	0.997264i	−0.997528	+	0.0702758i	$0.977612\pi$
$434$	−15.5959	+	3.31500i	−0.748625	+	0.159125i
$435$		0			0
$436$	6.08870	+	57.9301i	0.291596	+	2.77435i
$437$	−1.26249	+	0.562096i	−0.0603930	+	0.0268887i
$438$		0			0
$439$	−11.6459	−	20.1713i	−0.555828	−	0.962723i	−0.997839	−	0.0657130i	$-0.979068\pi$
$439$	−11.6459	−	20.1713i	−0.555828	−	0.962723i	0.442010	−	0.897010i	$-0.354266\pi$
$440$	−11.7533	+	9.82084i	−0.560316	+	0.468190i
$441$		0			0
$442$	0.218847	+	0.673542i	0.0104095	+	0.0320371i
$443$	−3.30276	+	31.4237i	−0.156919	+	1.49298i	0.578674	+	0.815559i	$0.303570\pi$
$443$	−3.30276	+	31.4237i	−0.156919	+	1.49298i	−0.735593	+	0.677424i	$0.763096\pi$
$444$		0			0
$445$	3.40599	+	3.78273i	0.161459	+	0.179319i
$446$	12.5786	+	13.9699i	0.595612	+	0.661495i
$447$		0			0
$448$	0.910255	−	8.66050i	0.0430055	−	0.409170i
$449$	2.79837	+	8.61251i	0.132063	+	0.406449i	0.995122	−	0.0986549i	$-0.0314540\pi$
$449$	2.79837	+	8.61251i	0.132063	+	0.406449i	−0.863058	+	0.505104i	$0.831454\pi$
$450$		0			0
$451$	0.663119	+	0.416272i	0.0312251	+	0.0196015i
$452$	32.6976	+	56.6338i	1.53796	+	2.66383i
$453$		0			0
$454$	−31.5233	+	14.0351i	−1.47946	+	0.658699i
$455$	0.0152505	+	0.145099i	0.000714954	+	0.00680234i
$456$		0			0
$457$	−23.4547	+	4.98545i	−1.09717	+	0.233210i	−0.720718	−	0.693228i	$-0.756188\pi$
$457$	−23.4547	+	4.98545i	−1.09717	+	0.233210i	−0.376447	+	0.926438i	$0.622854\pi$
$458$	−1.00000	+	0.726543i	−0.0467269	+	0.0339491i
$459$		0			0
$460$	−0.218847	−	0.673542i	−0.0102038	−	0.0314041i
$461$	4.63525	+	8.02850i	0.215885	+	0.373924i	0.953546	−	0.301247i	$-0.0974029\pi$
$461$	4.63525	+	8.02850i	0.215885	+	0.373924i	−0.737661	+	0.675172i	$0.764070\pi$
$462$		0			0
$463$	−0.864745	+	1.49778i	−0.0401881	+	0.0696079i	−0.885420	−	0.464792i	$-0.846129\pi$
$463$	−0.864745	+	1.49778i	−0.0401881	+	0.0696079i	0.845232	+	0.534400i	$0.179462\pi$
$464$	−57.8326	−	12.2927i	−2.68481	−	0.570674i
$465$		0			0
$466$	9.91572	+	4.41476i	0.459337	+	0.204510i
$467$	−6.45492	+	19.8662i	−0.298698	+	0.919297i	0.683256	+	0.730179i	$0.260563\pi$
$467$	−6.45492	+	19.8662i	−0.298698	+	0.919297i	−0.981954	+	0.189119i	$0.939437\pi$
$468$		0			0
$469$	1.50000	−	1.08981i	0.0692636	−	0.0503229i
$470$	−1.70656	+	16.2368i	−0.0787176	+	0.748948i
$471$		0			0
$472$	27.5795	−	47.7691i	1.26945	−	2.19875i
$473$	9.79447	−	19.9767i	0.450350	−	0.918529i
$474$		0			0
$475$	−18.0896	+	20.0905i	−0.830007	+	0.921816i
$476$	4.50000	+	3.26944i	0.206257	+	0.149855i
$477$		0			0
$478$	−0.309017	+	0.951057i	−0.0141341	+	0.0435003i
$479$	−27.7618	+	5.90094i	−1.26847	+	0.269621i	−0.792516	−	0.609851i	$-0.791229\pi$
$479$	−27.7618	+	5.90094i	−1.26847	+	0.269621i	−0.475951	+	0.879472i	$0.657896\pi$
$480$		0			0
$481$	−1.34486	+	0.598772i	−0.0613205	+	0.0273016i
$482$	−21.2338	−	4.51339i	−0.967174	−	0.205579i
$483$		0			0
$484$	51.2654	+	14.9298i	2.33024	+	0.678629i
$485$	4.85410			0.220413
$486$		0			0
$487$	10.2812	+	7.46969i	0.465884	+	0.338484i	0.795835	−	0.605514i	$-0.207032\pi$
$487$	10.2812	+	7.46969i	0.465884	+	0.338484i	−0.329951	+	0.943998i	$0.607032\pi$
$488$	−78.9259	−	35.1401i	−3.57281	−	1.59072i
$489$		0			0
$490$	−6.49606	−	7.21460i	−0.293462	−	0.325922i
$491$	−1.87209	−	17.8117i	−0.0844861	−	0.803832i	−0.951934	−	0.306303i	$-0.900908\pi$
$491$	−1.87209	−	17.8117i	−0.0844861	−	0.803832i	0.867448	−	0.497528i	$-0.165759\pi$
$492$		0			0
$493$	4.60053	−	5.10941i	0.207198	−	0.230116i
$494$	3.61803			0.162783
$495$		0			0
$496$	−60.0132			−2.69467
$497$	6.90960	−	7.67389i	0.309938	−	0.344221i
$498$		0			0
$499$	1.89676	+	18.0465i	0.0849108	+	0.807872i	0.951251	+	0.308418i	$0.0997994\pi$
$499$	1.89676	+	18.0465i	0.0849108	+	0.807872i	−0.866340	+	0.499454i	$0.833534\pi$
$500$	−19.3072	−	21.4428i	−0.863443	−	0.958950i
$501$		0			0
$502$	52.5663	+	23.4040i	2.34615	+	1.04457i
$503$	7.00000	+	5.08580i	0.312115	+	0.226765i	0.732803	−	0.680441i	$-0.238212\pi$
$503$	7.00000	+	5.08580i	0.312115	+	0.226765i	−0.420689	+	0.907205i	$0.638212\pi$
$504$		0			0
$505$	6.32624			0.281514
$506$	−1.26531	+	1.61264i	−0.0562500	+	0.0716906i
$507$		0			0
$508$	−36.5988	−	7.77931i	−1.62381	−	0.345151i
$509$	−35.3932	+	15.7581i	−1.56877	+	0.698463i	−0.992886	−	0.119065i	$-0.962010\pi$
$509$	−35.3932	+	15.7581i	−1.56877	+	0.698463i	−0.575888	+	0.817529i	$0.695344\pi$
$510$		0			0
$511$	−5.58347	+	1.18680i	−0.246998	+	0.0525010i
$512$	−12.4549	+	38.3323i	−0.550435	+	1.69406i
$513$		0			0
$514$	62.9959	+	45.7692i	2.77863	+	2.01879i
$515$	−4.52595	+	5.02658i	−0.199437	+	0.221498i
$516$		0			0
$517$	29.5805	−	15.6499i	1.30095	−	0.688281i
$518$	−8.16312	+	14.1389i	−0.358667	+	0.621229i
$519$		0			0
$520$	−0.113954	+	1.08420i	−0.00499720	+	0.0475452i
$521$	7.23607	−	5.25731i	0.317018	−	0.230327i	−0.417884	−	0.908500i	$-0.637228\pi$
$521$	7.23607	−	5.25731i	0.317018	−	0.230327i	0.734902	+	0.678173i	$0.237228\pi$
$522$		0			0
$523$	5.64590	−	17.3763i	0.246878	−	0.759812i	−0.748444	−	0.663198i	$-0.769199\pi$
$523$	5.64590	−	17.3763i	0.246878	−	0.759812i	0.995322	−	0.0966140i	$-0.0308013\pi$
$524$	52.3192	+	23.2940i	2.28558	+	1.01760i
$525$		0			0
$526$	−39.1051	−	8.31204i	−1.70506	−	0.362422i
$527$	3.48936	−	6.04374i	0.151999	−	0.263270i
$528$		0			0
$529$	11.4721	+	19.8703i	0.498789	+	0.863927i
$530$	0.190983	+	0.587785i	0.00829577	+	0.0255318i
$531$		0			0
$532$	22.9894	−	16.7027i	0.996715	−	0.724156i
$533$	0.0545103	−	0.0115865i	0.00236110	−	0.000501868i
$534$		0			0
$535$	−0.741125	−	7.05133i	−0.0320416	−	0.304856i
$536$	12.6564	−	5.63497i	0.546671	−	0.243394i
$537$		0			0
$538$	−33.2705	−	57.6262i	−1.43439	−	2.48444i
$539$	−4.85410	+	19.2986i	−0.209081	+	0.831251i
$540$		0			0
$541$	−2.31559	−	7.12667i	−0.0995552	−	0.306399i	0.888859	−	0.458181i	$-0.151499\pi$
$541$	−2.31559	−	7.12667i	−0.0995552	−	0.306399i	−0.988414	+	0.151782i	$0.951499\pi$
$542$	−5.09499	+	48.4756i	−0.218849	+	2.08221i
$543$		0			0
$544$	8.32244	+	9.24301i	0.356822	+	0.396291i
$545$	−4.96255	−	5.51147i	−0.212572	−	0.236085i
$546$		0			0
$547$	3.21348	−	30.5742i	0.137399	−	1.30726i	−0.680862	−	0.732412i	$-0.738395\pi$
$547$	3.21348	−	30.5742i	0.137399	−	1.30726i	0.818260	−	0.574848i	$-0.194939\pi$
$548$	−14.6459	−	45.0754i	−0.625642	−	1.92553i
$549$		0			0
$550$	−9.78115	+	38.8873i	−0.417070	+	1.65816i
$551$	−17.5623	−	30.4188i	−0.748179	−	1.29588i
$552$		0			0
$553$	−10.0490	+	4.47410i	−0.427327	+	0.190258i
$554$	7.99489	+	76.0663i	0.339670	+	3.23175i
$555$		0			0
$556$	−69.1422	+	14.6966i	−2.93228	+	0.623276i
$557$	30.4443	−	22.1191i	1.28997	−	0.937215i	0.290161	−	0.956978i	$-0.406291\pi$
$557$	30.4443	−	22.1191i	1.28997	−	0.937215i	0.999805	+	0.0197634i	$0.00629130\pi$
$558$		0			0
$559$	−0.489357	−	1.50609i	−0.0206976	−	0.0637006i
$560$	3.04508	+	5.27424i	0.128678	+	0.222877i
$561$		0			0
$562$	32.4164	−	56.1469i	1.36740	−	2.36841i
$563$	39.7096	+	8.44054i	1.67356	+	0.355726i	0.944446	−	0.328666i	$-0.106599\pi$
$563$	39.7096	+	8.44054i	1.67356	+	0.355726i	0.729114	+	0.684392i	$0.239932\pi$
$564$		0			0
$565$	−7.60640	−	3.38659i	−0.320004	−	0.142475i
$566$	−4.61803	+	14.2128i	−0.194110	+	0.597411i
$567$		0			0
$568$	62.4230	−	45.3530i	2.61921	−	1.90297i
$569$	3.57282	−	33.9931i	0.149780	−	1.42506i	−0.618919	−	0.785455i	$-0.712429\pi$
$569$	3.57282	−	33.9931i	0.149780	−	1.42506i	0.768700	−	0.639610i	$-0.220904\pi$
$570$		0			0
$571$	4.54508	−	7.87232i	0.190206	−	0.329446i	−0.755112	−	0.655595i	$-0.772418\pi$
$571$	4.54508	−	7.87232i	0.190206	−	0.329446i	0.945318	+	0.326149i	$0.105751\pi$
$572$	3.35934	−	1.77729i	0.140461	−	0.0743122i
$573$		0			0
$574$	0.413545	−	0.459289i	0.0172611	−	0.0191703i
$575$	−0.881966	−	0.640786i	−0.0367805	−	0.0267226i
$576$		0			0
$577$	9.79837	−	30.1563i	0.407912	−	1.25542i	−0.510528	−	0.859861i	$-0.670550\pi$
$577$	9.79837	−	30.1563i	0.407912	−	1.25542i	0.918439	−	0.395562i	$-0.129450\pi$
$578$	40.1714	−	8.53870i	1.67091	−	0.355163i
$579$		0			0
$580$	16.4438	−	7.32126i	0.682792	−	0.303999i
$581$	−1.43997	−	0.306074i	−0.0597399	−	0.0126981i
$582$		0			0
$583$	0.782006	−	0.996667i	0.0323874	−	0.0412777i
$584$	−42.6525			−1.76497
$585$		0			0
$586$	−45.8607	−	33.3197i	−1.89449	−	1.37643i
$587$	1.94093	+	0.864157i	0.0801107	+	0.0356676i	0.446401	−	0.894833i	$-0.352706\pi$
$587$	1.94093	+	0.864157i	0.0801107	+	0.0356676i	−0.366290	+	0.930501i	$0.619372\pi$
$588$		0			0
$589$	−23.8562	−	26.4950i	−0.982976	−	1.09171i
$590$	1.24852	+	11.8788i	0.0514006	+	0.489044i
$591$		0			0
$592$	−41.1186	+	45.6669i	−1.68997	+	1.87690i
$593$	14.0344			0.576325			0.288163	−	0.957581i	$-0.406956\pi$
$593$	14.0344			0.576325			0.288163	+	0.957581i	$0.406956\pi$
$594$		0			0
$595$	−0.708204			−0.0290335
$596$	13.7589	−	15.2808i	0.563585	−	0.625925i
$597$		0			0
$598$	0.0152505	+	0.145099i	0.000623639	+	0.00593353i
$599$	−8.46616	−	9.40262i	−0.345918	−	0.384181i	0.544931	−	0.838481i	$-0.316556\pi$
$599$	−8.46616	−	9.40262i	−0.345918	−	0.384181i	−0.890849	+	0.454300i	$0.849889\pi$
$600$		0			0
$601$	−6.29300	−	2.80182i	−0.256697	−	0.114289i	0.274354	−	0.961629i	$-0.411536\pi$
$601$	−6.29300	−	2.80182i	−0.256697	−	0.114289i	−0.531051	+	0.847340i	$0.678203\pi$
$602$	−14.2082	−	10.3229i	−0.579083	−	0.420729i
$603$		0			0
$604$	5.12461			0.208517
$605$	−6.39794	+	2.29874i	−0.260113	+	0.0934571i
$606$		0			0
$607$	16.2004	+	3.44350i	0.657553	+	0.139767i	0.524592	−	0.851354i	$-0.324218\pi$
$607$	16.2004	+	3.44350i	0.657553	+	0.139767i	0.132961	+	0.991121i	$0.457551\pi$
$608$	58.0476	−	25.8445i	2.35414	−	1.04813i
$609$		0			0
$610$	18.2994	−	3.88965i	0.740920	−	0.157487i
$611$	0.736068	−	2.26538i	0.0297781	−	0.0916476i
$612$		0			0
$613$	11.5623	+	8.40051i	0.466997	+	0.339293i	0.796270	−	0.604942i	$-0.206804\pi$
$613$	11.5623	+	8.40051i	0.466997	+	0.339293i	−0.329273	+	0.944235i	$0.606804\pi$
$614$	49.0133	−	54.4348i	1.97802	−	2.19681i
$615$		0			0
$616$	10.9099	−	22.2516i	0.439571	−	0.896544i
$617$	5.59017	−	9.68246i	0.225052	−	0.389801i	−0.731283	−	0.682074i	$-0.761078\pi$
$617$	5.59017	−	9.68246i	0.225052	−	0.389801i	0.956335	+	0.292273i	$0.0944115\pi$
$618$		0			0
$619$	−2.52171	+	23.9925i	−0.101356	+	0.964338i	0.819142	+	0.573591i	$0.194450\pi$
$619$	−2.52171	+	23.9925i	−0.101356	+	0.964338i	−0.920498	+	0.390747i	$0.872217\pi$
$620$	14.7812	−	10.7391i	0.593625	−	0.431294i
$621$		0			0
$622$	−9.42705	+	29.0135i	−0.377990	+	1.16333i
$623$	−7.52402	−	3.34991i	−0.301444	−	0.134211i
$624$		0			0
$625$	−18.9921	−	4.03690i	−0.759685	−	0.161476i
$626$	3.30902	−	5.73139i	0.132255	−	0.229072i
$627$		0			0
$628$	−38.1246	−	66.0338i	−1.52134	−	2.63503i
$629$	−2.20820	−	6.79615i	−0.0880469	−	0.270980i
$630$		0			0
$631$	−15.5451	+	11.2942i	−0.618840	+	0.449614i	−0.852516	−	0.522701i	$-0.824924\pi$
$631$	−15.5451	+	11.2942i	−0.618840	+	0.449614i	0.233676	+	0.972314i	$0.424924\pi$
$632$	−80.3974	+	17.0890i	−3.19804	+	0.679763i
$633$		0			0
$634$	−1.86626	−	17.7563i	−0.0741187	−	0.705193i
$635$	4.35207	−	1.93767i	0.172707	−	0.0768939i
$636$		0			0
$637$	0.708204	+	1.22665i	0.0280601	+	0.0486015i
$638$	−44.1246	−	27.6992i	−1.74691	−	1.09662i
$639$		0			0
$640$	0.208204	+	0.640786i	0.00822998	+	0.0253293i
$641$	−2.62264	+	24.9527i	−0.103588	+	0.985573i	0.812055	+	0.583581i	$0.198349\pi$
$641$	−2.62264	+	24.9527i	−0.103588	+	0.985573i	−0.915643	+	0.401992i	$0.868318\pi$
$642$		0			0
$643$	13.9541	+	15.4976i	0.550297	+	0.611166i	0.952557	−	0.304359i	$-0.0984422\pi$
$643$	13.9541	+	15.4976i	0.550297	+	0.611166i	−0.402261	+	0.915525i	$0.631775\pi$
$644$	0.766755	+	0.851568i	0.0302144	+	0.0335565i
$645$		0			0
$646$	−1.83576	+	17.4661i	−0.0722270	+	0.687194i
$647$	−13.9164	−	42.8303i	−0.547110	−	1.68383i	−0.715918	−	0.698184i	$-0.753992\pi$
$647$	−13.9164	−	42.8303i	−0.547110	−	1.68383i	0.168808	−	0.985649i	$-0.446008\pi$
$648$		0			0
$649$	18.7877	−	15.6987i	0.737483	−	0.616227i
$650$	1.42705	+	2.47172i	0.0559735	+	0.0969490i
$651$		0			0
$652$	−22.8192	+	10.1598i	−0.893668	+	0.397887i
$653$	−0.587244	−	5.58726i	−0.0229807	−	0.218646i	−0.999985	−	0.00542814i	$-0.998272\pi$
$653$	−0.587244	−	5.58726i	−0.0229807	−	0.218646i	0.977005	−	0.213218i	$-0.0683945\pi$
$654$		0			0
$655$	−7.13245	+	1.51605i	−0.278688	+	0.0592370i
$656$	1.88197	−	1.36733i	0.0734784	−	0.0533852i
$657$		0			0
$658$	−8.16312	−	25.1235i	−0.318232	−	0.979416i
$659$	−20.5623	−	35.6150i	−0.800994	−	1.38736i	−0.918963	−	0.394345i	$-0.870972\pi$
$659$	−20.5623	−	35.6150i	−0.800994	−	1.38736i	0.117969	−	0.993017i	$-0.462362\pi$
$660$		0			0
$661$	−18.2812	+	31.6639i	−0.711054	+	1.23158i	0.253407	+	0.967360i	$0.418449\pi$
$661$	−18.2812	+	31.6639i	−0.711054	+	1.23158i	−0.964462	+	0.264223i	$0.914885\pi$
$662$	−42.7868	−	9.09461i	−1.66295	−	0.353472i
$663$		0			0
$664$	−10.0490	−	4.47410i	−0.389977	−	0.173629i
$665$	−1.11803	+	3.44095i	−0.0433555	+	0.133435i
$666$		0			0
$667$	1.14590	−	0.832544i	0.0443693	−	0.0322362i
$668$	6.10618	−	58.0964i	0.236255	−	2.24782i
$669$		0			0
$670$	−1.50000	+	2.59808i	−0.0579501	+	0.100372i
$671$	−27.5300	−	26.6956i	−1.06278	−	1.03057i
$672$		0			0
$673$	23.9768	−	26.6290i	0.924239	−	1.02647i	−0.0753313	−	0.997159i	$-0.524001\pi$
$673$	23.9768	−	26.6290i	0.924239	−	1.02647i	0.999570	−	0.0293129i	$-0.00933191\pi$
$674$	38.5066	+	27.9767i	1.48322	+	1.07762i
$675$		0			0
$676$	−19.4164	+	59.7576i	−0.746785	+	2.29837i
$677$	13.2322	−	2.81260i	0.508557	−	0.108097i	0.0535147	−	0.998567i	$-0.482958\pi$
$677$	13.2322	−	2.81260i	0.508557	−	0.108097i	0.455042	+	0.890470i	$0.349624\pi$
$678$		0			0
$679$	−7.17508	+	3.19455i	−0.275354	+	0.122596i
$680$	−5.17616	−	1.10023i	−0.198497	−	0.0421918i
$681$		0			0
$682$	−49.6545	−	18.1891i	−1.90137	−	0.696498i
$683$	−9.06888			−0.347011			−0.173506	−	0.984833i	$-0.555509\pi$
$683$	−9.06888			−0.347011			−0.173506	+	0.984833i	$0.555509\pi$
$684$		0			0
$685$	4.88197	+	3.54696i	0.186530	+	0.135522i
$686$	31.0920	+	13.8431i	1.18710	+	0.528530i
$687$		0			0
$688$	−44.2318	−	49.1243i	−1.68632	−	1.87285i
$689$	−0.00942533	−	0.0896760i	−0.000359076	−	0.00341638i
$690$		0			0
$691$	0.901670	−	1.00141i	0.0343011	−	0.0380953i	−0.725750	−	0.687958i	$-0.758507\pi$
$691$	0.901670	−	1.00141i	0.0343011	−	0.0380953i	0.760051	+	0.649863i	$0.225174\pi$
$692$	87.5410			3.32781
$693$		0			0
$694$	4.00000			0.151838
$695$	6.02218	−	6.68830i	0.228434	−	0.253702i
$696$		0			0
$697$	0.0282760	+	0.269028i	0.00107103	+	0.0101902i
$698$	22.2623	+	24.7248i	0.842641	+	0.935848i
$699$		0			0
$700$	20.4784	+	9.11757i	0.774011	+	0.344612i
$701$	−28.1525	−	20.4540i	−1.06330	−	0.772536i	−0.0886075	−	0.996067i	$-0.528242\pi$
$701$	−28.1525	−	20.4540i	−1.06330	−	0.772536i	−0.974697	+	0.223531i	$0.928242\pi$
$702$		0			0
$703$	−36.5066			−1.37687
$704$	17.8285	−	22.7224i	0.671936	−	0.856382i
$705$		0			0
$706$	−30.7299	−	6.53184i	−1.15653	−	0.245829i
$707$	−9.35111	+	4.16338i	−0.351685	+	0.156580i
$708$		0			0
$709$	−10.9697	+	2.33168i	−0.411976	+	0.0875682i	−0.409237	−	0.912428i	$-0.634205\pi$
$709$	−10.9697	+	2.33168i	−0.411976	+	0.0875682i	−0.00273893	+	0.999996i	$0.500872\pi$
$710$	−5.16312	+	15.8904i	−0.193768	+	0.596358i
$711$		0			0
$712$	−49.7877	−	36.1729i	−1.86587	−	1.35564i
$713$	0.962005	−	1.06841i	0.0360274	−	0.0400125i
$714$		0			0
$715$	−0.213022	+	0.434477i	−0.00796657	+	0.0162485i
$716$	−20.6976	+	35.8492i	−0.773504	+	1.33975i
$717$		0			0
$718$	−2.65674	+	25.2772i	−0.0991486	+	0.943336i
$719$	−31.1353	+	22.6211i	−1.16115	+	0.843624i	−0.989923	−	0.141608i	$-0.954773\pi$
$719$	−31.1353	+	22.6211i	−1.16115	+	0.843624i	−0.171226	+	0.985232i	$0.554773\pi$
$720$		0			0
$721$	3.38197	−	10.4086i	0.125951	−	0.387637i
$722$	36.5224	+	16.2608i	1.35922	+	0.605165i
$723$		0			0
$724$	−12.0024	−	2.55118i	−0.446065	−	0.0948139i
$725$	13.8541	−	23.9960i	0.514528	−	0.891189i
$726$		0			0
$727$	4.57295	+	7.92058i	0.169601	+	0.293758i	0.938280	−	0.345877i	$-0.112419\pi$
$727$	4.57295	+	7.92058i	0.169601	+	0.293758i	−0.768678	+	0.639635i	$0.779085\pi$
$728$	−0.545085	−	1.67760i	−0.0202022	−	0.0621760i
$729$		0			0
$730$	7.47214	−	5.42882i	0.276556	−	0.200930i
$731$	7.51894	−	1.59820i	0.278098	−	0.0591116i
$732$		0			0
$733$	0.0421513	+	0.401043i	0.00155690	+	0.0148129i	0.995273	−	0.0971191i	$-0.0309628\pi$
$733$	0.0421513	+	0.401043i	0.00155690	+	0.0148129i	−0.993716	+	0.111932i	$0.964296\pi$
$734$	52.9662	−	23.5821i	1.95502	−	0.870430i
$735$		0			0
$736$	1.28115	+	2.21902i	0.0472239	+	0.0817942i
$737$	6.13525	−	0.416272i	0.225995	−	0.0153336i
$738$		0			0
$739$	0.927051	+	2.85317i	0.0341021	+	0.104956i	0.966659	−	0.256068i	$-0.0824272\pi$
$739$	0.927051	+	2.85317i	0.0341021	+	0.104956i	−0.932557	+	0.361024i	$0.882427\pi$
$740$	1.95554	−	18.6057i	0.0718871	−	0.683960i
$741$		0			0
$742$	−0.669131	−	0.743145i	−0.0245646	−	0.0272817i
$743$	28.6980	+	31.8724i	1.05283	+	1.16928i	0.985171	+	0.171576i	$0.0548860\pi$
$743$	28.6980	+	31.8724i	1.05283	+	1.16928i	0.0676581	+	0.997709i	$0.478447\pi$
$744$		0			0
$745$	−0.273659	+	2.60369i	−0.0100261	+	0.0953919i
$746$	0.718847	+	2.21238i	0.0263189	+	0.0810011i
$747$		0			0
$748$	6.87539	+	17.1190i	0.251389	+	0.625933i
$749$	5.73607	+	9.93516i	0.209591	+	0.363023i
$750$		0			0
$751$	14.7500	−	6.56713i	0.538236	−	0.239638i	−0.119570	−	0.992826i	$-0.538152\pi$
$751$	14.7500	−	6.56713i	0.538236	−	0.239638i	0.657805	+	0.753188i	$0.271485\pi$
$752$	−10.3932	−	98.8849i	−0.379002	−	3.60596i
$753$		0			0
$754$	−3.62717	+	0.770979i	−0.132094	+	0.0280774i
$755$	−0.527864	+	0.383516i	−0.0192109	+	0.0139576i
$756$		0			0
$757$	1.54508	+	4.75528i	0.0561571	+	0.172834i	0.975201	−	0.221322i	$-0.0710371\pi$
$757$	1.54508	+	4.75528i	0.0561571	+	0.172834i	−0.919044	+	0.394156i	$0.871037\pi$
$758$	32.5795	+	56.4294i	1.18334	+	2.04961i
$759$		0			0
$760$	−13.5172	+	23.4125i	−0.490321	+	0.849261i
$761$	28.6517	+	6.09011i	1.03862	+	0.220766i	0.695501	−	0.718525i	$-0.255182\pi$
$761$	28.6517	+	6.09011i	1.03862	+	0.220766i	0.343122	+	0.939291i	$0.388516\pi$
$762$		0			0
$763$	10.9625	+	4.88084i	0.396871	+	0.176698i
$764$	1.22949	−	3.78398i	0.0444814	−	0.136900i
$765$		0			0
$766$	−26.9164	+	19.5559i	−0.972529	+	0.706584i
$767$	0.182156	−	1.73310i	0.00657728	−	0.0625786i
$768$		0			0
$769$	17.2533	−	29.8836i	0.622170	−	1.07763i	−0.366911	−	0.930256i	$-0.619585\pi$
$769$	17.2533	−	29.8836i	0.622170	−	1.07763i	0.989081	−	0.147373i	$-0.0470819\pi$
$770$	0.920937	+	5.28680i	0.0331883	+	0.190523i
$771$		0			0
$772$	−10.2180	+	11.3482i	−0.367753	+	0.408431i
$773$	21.9894	+	15.9762i	0.790902	+	0.574624i	0.908231	−	0.418469i	$-0.137433\pi$
$773$	21.9894	+	15.9762i	0.790902	+	0.574624i	−0.117329	+	0.993093i	$0.537433\pi$
$774$		0			0
$775$	8.69098	−	26.7481i	0.312189	−	0.960820i
$776$	−57.4045	+	12.2017i	−2.06070	+	0.438015i
$777$		0			0
$778$	87.8771	−	39.1254i	3.15055	−	1.40271i
$779$	1.35177	+	0.287327i	0.0484321	+	0.0102946i
$780$		0			0
$781$	32.9410	−	9.37200i	1.17872	−	0.335357i
$782$	−0.708204			−0.0253253
$783$		0			0
$784$	47.8328	+	34.7526i	1.70831	+	1.24116i
$785$	8.86889	+	3.94868i	0.316544	+	0.140935i
$786$		0			0
$787$	−6.49606	−	7.21460i	−0.231559	−	0.257173i	0.616156	−	0.787624i	$-0.288689\pi$
$787$	−6.49606	−	7.21460i	−0.231559	−	0.257173i	−0.847715	+	0.530451i	$0.822022\pi$
$788$	6.61357	+	62.9239i	0.235599	+	2.24157i
$789$		0			0
$790$	11.9094	−	13.2268i	0.423719	−	0.470587i
$791$	13.4721			0.479014
$792$		0			0
$793$	−2.72949			−0.0969270
$794$	−32.7732	+	36.3983i	−1.16308	+	1.29173i
$795$		0			0
$796$	−3.40369	−	32.3839i	−0.120641	−	1.14782i
$797$	−12.4064	−	13.7787i	−0.439456	−	0.488065i	0.482207	−	0.876057i	$-0.339835\pi$
$797$	−12.4064	−	13.7787i	−0.439456	−	0.488065i	−0.921663	+	0.387992i	$0.873169\pi$
$798$		0			0
$799$	10.5627	+	4.70281i	0.373681	+	0.166374i
$800$	40.5517	+	29.4625i	1.43372	+	1.04166i
$801$		0			0
$802$	82.9574			2.92933
$803$	−17.7768	−	6.51189i	−0.627330	−	0.229800i
$804$		0			0
$805$	−0.142710	−	0.0303339i	−0.00502986	−	0.00106913i
$806$	−3.43852	+	1.53093i	−0.121117	+	0.0539247i
$807$		0			0
$808$	−74.8139	+	15.9022i	−2.63194	+	0.559437i
$809$	−8.37132	+	25.7643i	−0.294320	+	0.905824i	0.689129	+	0.724639i	$0.257993\pi$
$809$	−8.37132	+	25.7643i	−0.294320	+	0.905824i	−0.983449	+	0.181185i	$0.942007\pi$
$810$		0			0
$811$	−29.5795	−	21.4908i	−1.03868	−	0.754644i	−0.0686507	−	0.997641i	$-0.521869\pi$
$811$	−29.5795	−	21.4908i	−1.03868	−	0.754644i	−0.970027	+	0.242997i	$0.921869\pi$
$812$	−19.4882	+	21.6438i	−0.683901	+	0.759549i
$813$		0			0
$814$	−47.8623	+	25.3220i	−1.67757	+	0.887537i
$815$	1.59017	−	2.75426i	0.0557012	−	0.0964773i
$816$		0			0
$817$	4.10489	−	39.0554i	0.143612	−	1.36637i
$818$	13.7082	−	9.95959i	0.479296	−	0.348229i
$819$		0			0
$820$	−0.218847	+	0.673542i	−0.00764247	+	0.0235211i
$821$	−37.0870	−	16.5122i	−1.29434	−	0.576279i	−0.360100	−	0.932914i	$-0.617258\pi$
$821$	−37.0870	−	16.5122i	−1.29434	−	0.576279i	−0.934244	+	0.356634i	$0.883924\pi$
$822$		0			0
$823$	27.2246	+	5.78677i	0.948990	+	0.201714i	0.656306	−	0.754495i	$-0.272118\pi$
$823$	27.2246	+	5.78677i	0.948990	+	0.201714i	0.292684	+	0.956209i	$0.405452\pi$
$824$	40.8885	−	70.8210i	1.42442	−	2.46717i
$825$		0			0
$826$	−9.66312	−	16.7370i	−0.336223	−	0.582355i
$827$	3.29180	+	10.1311i	0.114467	+	0.352293i	0.991835	−	0.127524i	$-0.0407030\pi$
$827$	3.29180	+	10.1311i	0.114467	+	0.352293i	−0.877369	+	0.479817i	$0.840703\pi$
$828$		0			0
$829$	25.3992	−	18.4536i	0.882150	−	0.640920i	−0.0516692	−	0.998664i	$-0.516454\pi$
$829$	25.3992	−	18.4536i	0.882150	−	0.640920i	0.933819	+	0.357745i	$0.116454\pi$
$830$	2.32991	−	0.495239i	0.0808725	−	0.0171900i
$831$		0			0
$832$	−0.214882	−	2.04447i	−0.00744970	−	0.0708791i
$833$	−6.28098	+	2.79647i	−0.217623	+	0.0968920i
$834$		0			0
$835$	3.71885	+	6.44123i	0.128696	+	0.222908i
$836$	94.0304	−	6.37988i	3.25211	−	0.220653i
$837$		0			0
$838$	−25.4443	−	78.3094i	−0.878958	−	2.70515i
$839$	−1.86404	+	17.7351i	−0.0643537	+	0.612285i	0.914053	+	0.405595i	$0.132936\pi$
$839$	−1.86404	+	17.7351i	−0.0643537	+	0.612285i	−0.978407	+	0.206690i	$0.933731\pi$
$840$		0			0
$841$	4.68391	+	5.20201i	0.161514	+	0.179380i
$842$	18.4055	+	20.4414i	0.634295	+	0.704456i
$843$		0			0
$844$	−1.83576	+	17.4661i	−0.0631895	+	0.601208i
$845$	−2.47214	−	7.60845i	−0.0850441	−	0.261739i
$846$		0			0
$847$	7.94427	−	7.60845i	0.272968	−	0.261430i
$848$	−1.88197	−	3.25966i	−0.0646270	−	0.111937i
$849$		0			0
$850$	−12.6564	+	5.63497i	−0.434109	+	0.193278i
$851$	−0.153880	−	1.46407i	−0.00527494	−	0.0501877i
$852$		0			0
$853$	54.6127	−	11.6083i	1.86990	−	0.397460i	0.873849	−	0.486197i	$-0.161616\pi$
$853$	54.6127	−	11.6083i	1.86990	−	0.397460i	0.996055	+	0.0887365i	$0.0282829\pi$
$854$	−24.4894	+	17.7926i	−0.838009	+	0.608849i
$855$		0			0
$856$	26.4894	+	81.5259i	0.905388	+	2.78650i
$857$	13.8820	+	24.0443i	0.474199	+	0.821337i	0.999564	−	0.0295405i	$-0.00940442\pi$
$857$	13.8820	+	24.0443i	0.474199	+	0.821337i	−0.525365	+	0.850877i	$0.676071\pi$
$858$		0			0
$859$	17.2082	−	29.8055i	0.587136	−	1.01695i	−0.407469	−	0.913219i	$-0.633589\pi$
$859$	17.2082	−	29.8055i	0.587136	−	1.01695i	0.994605	−	0.103731i	$-0.0330781\pi$
$860$	19.6848	+	4.18414i	0.671247	+	0.142678i
$861$		0			0
$862$	14.1345	+	6.29308i	0.481423	+	0.214343i
$863$	−0.0344419	+	0.106001i	−0.00117241	+	0.00360832i	−0.951641	−	0.307212i	$-0.900604\pi$
$863$	−0.0344419	+	0.106001i	−0.00117241	+	0.00360832i	0.950469	+	0.310821i	$0.100604\pi$
$864$		0			0
$865$	−9.01722	+	6.55139i	−0.306595	+	0.222754i
$866$	−9.66152	+	91.9232i	−0.328312	+	3.12368i
$867$		0			0
$868$	−14.7812	+	25.6017i	−0.501705	+	0.868979i
$869$	−36.1172	−	5.15213i	−1.22519	−	0.174774i
$870$		0			0
$871$	0.292875	−	0.325270i	0.00992367	−	0.0110214i
$872$	72.5410	+	52.7041i	2.45655	+	1.78479i
$873$		0			0
$874$	−1.11803	+	3.44095i	−0.0378181	+	0.116392i
$875$	−5.81438	+	1.23588i	−0.196562	+	0.0417805i
$876$		0			0
$877$	−52.9347	+	23.5681i	−1.78748	+	0.795837i	−0.809504	+	0.587115i	$0.800264\pi$
$877$	−52.9347	+	23.5681i	−1.78748	+	0.795837i	−0.977975	+	0.208722i	$0.933070\pi$
$878$	−59.6462	−	12.6782i	−2.01296	−	0.427868i
$879$		0			0
$880$	−0.746669	+	20.1850i	−0.0251702	+	0.680436i
$881$	−6.20163			−0.208938			−0.104469	−	0.994528i	$-0.533314\pi$
$881$	−6.20163			−0.208938			−0.104469	+	0.994528i	$0.533314\pi$
$882$		0			0
$883$	−0.854102	−	0.620541i	−0.0287428	−	0.0208829i	0.573321	−	0.819331i	$-0.305655\pi$
$883$	−0.854102	−	0.620541i	−0.0287428	−	0.0208829i	−0.602064	+	0.798448i	$0.705655\pi$
$884$	1.19956	+	0.534079i	0.0403456	+	0.0179630i
$885$		0			0
$886$	55.3514	+	61.4740i	1.85957	+	2.06526i
$887$	−5.69526	−	54.1868i	−0.191228	−	1.81942i	−0.497492	−	0.867469i	$-0.665746\pi$
$887$	−5.69526	−	54.1868i	−0.191228	−	1.81942i	0.306264	−	0.951947i	$-0.400921\pi$
$888$		0			0
$889$	−5.15780	+	5.72831i	−0.172987	+	0.192121i
$890$	13.3262			0.446697
$891$		0			0
$892$	34.8541			1.16700
$893$	39.5248	−	43.8967i	1.32265	−	1.46895i
$894$		0			0
$895$	−0.550918	−	5.24164i	−0.0184152	−	0.175209i
$896$	−0.729466	−	0.810154i	−0.0243698	−	0.0270654i
$897$		0			0
$898$	21.6585	+	9.64300i	0.722754	+	0.321791i
$899$	29.5623	+	21.4783i	0.985958	+	0.716340i
$900$		0			0
$901$	0.437694			0.0145817
$902$	1.97155	−	0.560922i	0.0656453	−	0.0186767i
$903$		0			0
$904$	98.4658	+	20.9296i	3.27493	+	0.696107i
$905$	1.42724	−	0.635447i	0.0474430	−	0.0211230i
$906$		0			0
$907$	41.4687	−	8.81444i	1.37695	−	0.292679i	0.540783	−	0.841162i	$-0.318128\pi$
$907$	41.4687	−	8.81444i	1.37695	−	0.292679i	0.836162	+	0.548483i	$0.184794\pi$
$908$	−19.7705	+	60.8474i	−0.656107	+	2.01929i
$909$		0			0
$910$	0.309017	+	0.224514i	0.0102438	+	0.00744257i
$911$	−25.8263	+	28.6830i	−0.855662	+	0.950309i	−0.999226	−	0.0393318i	$-0.987477\pi$
$911$	−25.8263	+	28.6830i	−0.855662	+	0.950309i	0.143564	+	0.989641i	$0.454144\pi$
$912$		0			0
$913$	−3.50517	−	3.39894i	−0.116004	−	0.112489i
$914$	−31.3885	+	54.3666i	−1.03824	+	1.79829i
$915$		0			0
$916$	−0.239558	+	2.27924i	−0.00791522	+	0.0753083i
$917$	9.54508	−	6.93491i	0.315206	−	0.229011i
$918$		0			0
$919$	7.92705	−	24.3970i	0.261489	−	0.804781i	−0.730992	−	0.682386i	$-0.760942\pi$
$919$	7.92705	−	24.3970i	0.261489	−	0.804781i	0.992481	−	0.122395i	$-0.0390576\pi$
$920$	−0.995920	−	0.443412i	−0.0328345	−	0.0146189i
$921$		0			0
$922$	23.7401	+	5.04612i	0.781840	+	0.166185i
$923$	1.21885	−	2.11111i	0.0401188	−	0.0694879i
$924$		0			0
$925$	−14.3992	−	24.9401i	−0.473442	−	0.820026i
$926$	1.39919	+	4.30625i	0.0459801	+	0.141512i
$927$		0			0
$928$	−52.6869	+	38.2793i	−1.72953	+	1.25658i
$929$	−12.4305	+	2.64218i	−0.407831	+	0.0866873i	−0.407259	−	0.913313i	$-0.633515\pi$
$929$	−12.4305	+	2.64218i	−0.407831	+	0.0866873i	−0.000572170		1.00000i	$0.500182\pi$
$930$		0			0
$931$	3.67152	+	34.9322i	0.120329	+	1.14486i
$932$	18.3847	−	8.18542i	0.602212	−	0.268122i
$933$		0			0
$934$	27.3435	+	47.3603i	0.894705	+	1.54968i
$935$	−1.98936	−	1.24882i	−0.0650589	−	0.0408406i
$936$		0			0
$937$	12.8713	+	39.6139i	0.420488	+	1.29413i	0.907249	+	0.420593i	$0.138178\pi$
$937$	12.8713	+	39.6139i	0.420488	+	1.29413i	−0.486761	+	0.873535i	$0.661822\pi$
$938$	0.507392	−	4.82751i	0.0165669	−	0.157624i
$939$		0			0
$940$	20.2549	+	22.4954i	0.660643	+	0.733718i
$941$	9.66951	+	10.7391i	0.315217	+	0.350084i	0.879844	−	0.475262i	$-0.157647\pi$
$941$	9.66951	+	10.7391i	0.315217	+	0.350084i	−0.564627	+	0.825346i	$0.690980\pi$
$942$		0			0
$943$	−0.00582517	+	0.0554228i	−0.000189694	+	0.00180481i
$944$	−22.4787	−	69.1824i	−0.731620	−	2.25169i
$945$		0			0
$946$	−21.7082	−	54.0512i	−0.705795	−	1.75736i
$947$	−16.1976	−	28.0550i	−0.526350	−	0.911665i	−0.999529	−	0.0306985i	$-0.990227\pi$
$947$	−16.1976	−	28.0550i	−0.526350	−	0.911665i	0.473179	−	0.880966i	$-0.343106\pi$
$948$		0			0
$949$	−1.23102	+	0.548087i	−0.0399607	+	0.0177917i
$950$	7.39822	+	70.3894i	0.240030	+	2.28373i
$951$		0			0
$952$	8.37520	−	1.78020i	0.271442	−	0.0576967i
$953$	9.18034	−	6.66991i	0.297380	−	0.216059i	−0.429082	−	0.903265i	$-0.641163\pi$
$953$	9.18034	−	6.66991i	0.297380	−	0.216059i	0.726463	+	0.687206i	$0.241163\pi$
$954$		0			0
$955$	0.156541	+	0.481784i	0.00506555	+	0.0155902i
$956$	0.927051	+	1.60570i	0.0299830	+	0.0519320i
$957$		0			0
$958$	−37.1525	+	64.3500i	−1.20034	+	2.07905i
$959$	−9.55057	−	2.03004i	−0.308404	−	0.0655533i
$960$		0			0
$961$	5.56365	+	2.47710i	0.179472	+	0.0799063i
$962$	−1.19098	+	3.66547i	−0.0383988	+	0.118179i
$963$		0			0
$964$	−32.5623	+	23.6579i	−1.04876	+	0.761970i
$965$	0.203232	−	1.93362i	0.00654226	−	0.0622455i
$966$		0			0
$967$	−21.9615	+	38.0384i	−0.706234	+	1.22323i	0.260010	+	0.965606i	$0.416274\pi$
$967$	−21.9615	+	38.0384i	−0.706234	+	1.22323i	−0.966244	+	0.257627i	$0.917059\pi$
$968$	69.8836	−	43.2673i	2.24614	−	1.39066i
$969$		0			0
$970$	8.50345	−	9.44404i	0.273029	−	0.303230i
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.110957	−	0.993825i	$-0.535392\pi$
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.979472	+	0.201582i	$0.935392\pi$
$972$		0			0
$973$	−4.50000	+	13.8496i	−0.144263	+	0.443997i
$974$	32.5435	−	6.91733i	1.04276	−	0.221645i
$975$		0			0
$976$	−104.086	+	46.3420i	−3.33171	+	1.48337i
$977$	−0.583707	−	0.124071i	−0.0186745	−	0.00396938i	0.198565	−	0.980088i	$-0.436372\pi$
$977$	−0.583707	−	0.124071i	−0.0186745	−	0.00396938i	−0.217239	+	0.976118i	$0.569705\pi$
$978$		0			0
$979$	−15.2280	−	22.6775i	−0.486690	−	0.724776i
$980$	−18.0000			−0.574989
$981$		0			0
$982$	−37.9336	−	27.5604i	−1.21051	−	0.879488i
$983$	7.41018	+	3.29923i	0.236348	+	0.105229i	0.521493	−	0.853255i	$-0.325375\pi$
$983$	7.41018	+	3.29923i	0.236348	+	0.105229i	−0.285145	+	0.958484i	$0.592042\pi$
$984$		0			0
$985$	−5.39033	−	5.98657i	−0.171750	−	0.190748i
$986$	−1.88151	−	17.9014i	−0.0599196	−	0.570097i
$987$		0			0
$988$	4.48866	−	4.98517i	0.142803	−	0.158599i
$989$	1.58359			0.0503553
$990$		0			0
$991$	3.74265			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$991$	3.74265			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$992$	−44.2318	+	49.1243i	−1.40436	+	1.55970i
$993$		0			0
$994$	−2.82587	−	26.8863i	−0.0896311	−	0.852783i
$995$	2.77415	+	3.08100i	0.0879464	+	0.0976744i
$996$		0			0
$997$	−19.3686	−	8.62348i	−0.613411	−	0.273108i	0.0764231	−	0.997075i	$-0.475650\pi$
$997$	−19.3686	−	8.62348i	−0.613411	−	0.273108i	−0.689834	+	0.723967i	$0.742317\pi$
$998$	38.4336	+	27.9237i	1.21660	+	0.883908i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.b.676.1		8
3.2	odd	2		891.2.n.c.676.1		8
9.2	odd	6		891.2.n.c.379.1		8
9.4	even	3		99.2.f.a.82.1		4
9.5	odd	6		33.2.e.b.16.1	✓	4
9.7	even	3	inner	891.2.n.b.379.1		8
11.9	even	5	inner	891.2.n.b.757.1		8
33.20	odd	10		891.2.n.c.757.1		8
36.23	even	6		528.2.y.b.49.1		4
45.14	odd	6		825.2.n.c.676.1		4
45.23	even	12		825.2.bx.d.49.1		8
45.32	even	12		825.2.bx.d.49.2		8
99.5	odd	30		363.2.e.k.202.1		4
99.14	odd	30		363.2.a.d.1.1		2
99.20	odd	30		891.2.n.c.460.1		8
99.31	even	15		99.2.f.a.64.1		4
99.32	even	6		363.2.e.f.148.1		4
99.41	even	30		363.2.a.i.1.2		2
99.50	even	30		363.2.e.b.202.1		4
99.58	even	15		1089.2.a.t.1.2		2
99.59	odd	30		363.2.e.k.124.1		4
99.68	even	30		363.2.e.f.130.1		4
99.85	odd	30		1089.2.a.l.1.1		2
99.86	odd	30		33.2.e.b.31.1	yes	4
99.95	even	30		363.2.e.b.124.1		4
99.97	even	15	inner	891.2.n.b.460.1		8
396.239	odd	30		5808.2.a.ci.1.1		2
396.311	even	30		5808.2.a.cj.1.1		2
396.383	even	30		528.2.y.b.97.1		4
495.14	odd	30		9075.2.a.cb.1.2		2
495.239	even	30		9075.2.a.u.1.1		2
495.284	odd	30		825.2.n.c.526.1		4
495.383	even	60		825.2.bx.d.724.2		8
495.482	even	60		825.2.bx.d.724.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	9.5	odd	6
33.2.e.b.31.1	yes	4	99.86	odd	30
99.2.f.a.64.1		4	99.31	even	15
99.2.f.a.82.1		4	9.4	even	3
363.2.a.d.1.1		2	99.14	odd	30
363.2.a.i.1.2		2	99.41	even	30
363.2.e.b.124.1		4	99.95	even	30
363.2.e.b.202.1		4	99.50	even	30
363.2.e.f.130.1		4	99.68	even	30
363.2.e.f.148.1		4	99.32	even	6
363.2.e.k.124.1		4	99.59	odd	30
363.2.e.k.202.1		4	99.5	odd	30
528.2.y.b.49.1		4	36.23	even	6
528.2.y.b.97.1		4	396.383	even	30
825.2.n.c.526.1		4	495.284	odd	30
825.2.n.c.676.1		4	45.14	odd	6
825.2.bx.d.49.1		8	45.23	even	12
825.2.bx.d.49.2		8	45.32	even	12
825.2.bx.d.724.1		8	495.482	even	60
825.2.bx.d.724.2		8	495.383	even	60
891.2.n.b.379.1		8	9.7	even	3	inner
891.2.n.b.460.1		8	99.97	even	15	inner
891.2.n.b.676.1		8	1.1	even	1	trivial
891.2.n.b.757.1		8	11.9	even	5	inner
891.2.n.c.379.1		8	9.2	odd	6
891.2.n.c.460.1		8	99.20	odd	30
891.2.n.c.676.1		8	3.2	odd	2
891.2.n.c.757.1		8	33.20	odd	10
1089.2.a.l.1.1		2	99.85	odd	30
1089.2.a.t.1.2		2	99.58	even	15
5808.2.a.ci.1.1		2	396.239	odd	30
5808.2.a.cj.1.1		2	396.311	even	30
9075.2.a.u.1.1		2	495.239	even	30
9075.2.a.cb.1.2		2	495.14	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.75181 - 1.94558i) q^{2} +(-0.507392 - 4.82751i) q^{4} +(0.413545 + 0.459289i) q^{5} +(-0.913545 - 0.406737i) q^{7} +(-6.04508 - 4.39201i) q^{8} +1.61803 q^{10} +(-1.84894 - 2.75344i) q^{11} +(-0.230909 - 0.0490813i) q^{13} +(-2.39169 + 1.06485i) q^{14} +(-9.63877 + 2.04878i) q^{16} +(0.354102 - 1.08981i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(2.00739 - 2.22943i) q^{20} +(-8.59602 - 1.22622i) q^{22} +(0.118034 - 0.204441i) q^{23} +(0.482716 - 4.59274i) q^{25} +(-0.500000 + 0.363271i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(5.48127 + 2.44042i) q^{29} +(5.95709 + 1.26622i) q^{31} +(-5.42705 + 9.39993i) q^{32} +(-1.50000 - 2.59808i) q^{34} +(-0.190983 - 0.587785i) q^{35} +(5.04508 - 3.66547i) q^{37} +(-14.9913 + 3.18650i) q^{38} +(-0.482716 - 4.59274i) q^{40} +(-0.215659 + 0.0960175i) q^{41} +(3.35410 + 5.80948i) q^{43} +(-12.3541 + 10.3229i) q^{44} +(-0.190983 - 0.587785i) q^{46} +(-1.05471 + 10.0349i) q^{47} +(-4.01478 - 4.45887i) q^{49} +(-8.08990 - 8.98475i) q^{50} +(-0.119779 + 1.13962i) q^{52} +(0.118034 + 0.363271i) q^{53} +(0.500000 - 1.98787i) q^{55} +(3.73607 + 6.47106i) q^{56} +(14.3502 - 6.38910i) q^{58} +(0.771626 + 7.34153i) q^{59} +(11.3096 - 2.40394i) q^{61} +(12.8992 - 9.37181i) q^{62} +(2.69098 + 8.28199i) q^{64} +(-0.0729490 - 0.126351i) q^{65} +(-0.927051 + 1.60570i) q^{67} +(-5.44076 - 1.15647i) q^{68} +(-1.47815 - 0.658114i) q^{70} +(-3.19098 + 9.82084i) q^{71} +(4.61803 - 3.35520i) q^{73} +(1.70656 - 16.2368i) q^{74} +(-14.2082 + 24.6093i) q^{76} +(0.569171 + 3.26742i) q^{77} +(7.36044 - 8.17459i) q^{79} +(-4.92705 - 3.57971i) q^{80} +(-0.190983 + 0.587785i) q^{82} +(1.43997 - 0.306074i) q^{83} +(0.646976 - 0.288052i) q^{85} +(17.1785 + 3.65141i) q^{86} +(-0.916102 + 24.7653i) q^{88} +8.23607 q^{89} +(0.190983 + 0.138757i) q^{91} +(-1.04683 - 0.466079i) q^{92} +(17.6760 + 19.6312i) q^{94} +(-0.378188 - 3.59821i) q^{95} +(5.25542 - 5.83674i) q^{97} -15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 9 q^{4} - 3 q^{5} - q^{7} - 26 q^{8} + 4 q^{10} - 11 q^{11} - 7 q^{13} - 4 q^{14} - q^{16} - 24 q^{17} - 20 q^{19} + 3 q^{20} - 4 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} - 12 q^{28} + 6 q^{29}+ \cdots - 72 q^{98}+O(q^{100}) \) 8 * q - q^2 + 9 * q^4 - 3 * q^5 - q^7 - 26 * q^8 + 4 * q^10 - 11 * q^11 - 7 * q^13 - 4 * q^14 - q^16 - 24 * q^17 - 20 * q^19 + 3 * q^20 - 4 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 - 12 * q^28 + 6 * q^29 + 12 * q^31 - 30 * q^32 - 12 * q^34 - 6 * q^35 + 18 * q^37 - 10 * q^38 + 6 * q^40 - 3 * q^41 - 72 * q^44 - 6 * q^46 + 17 * q^47 - 6 * q^49 + 6 * q^50 - 3 * q^52 - 8 * q^53 + 4 * q^55 + 12 * q^56 + 24 * q^58 - 6 * q^59 + 21 * q^61 + 54 * q^62 + 26 * q^64 - 14 * q^65 + 6 * q^67 - 27 * q^68 - 3 * q^70 - 30 * q^71 + 28 * q^73 - 26 * q^74 - 60 * q^76 + q^77 + 11 * q^79 - 26 * q^80 - 6 * q^82 + 13 * q^83 + 9 * q^85 + 15 * q^86 + 37 * q^88 + 48 * q^89 + 6 * q^91 + 3 * q^92 - 17 * q^94 + 5 * q^95 - 3 * q^97 - 72 * q^98

Introduction

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