LMFDB - Embedded newform 891.2.n.b.460.1

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			460.1
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	891.460
Dual form			891.2.n.b.676.1

$q$-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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

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

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	0.900613	+	0.434622i	$0.143118\pi$
$2$	1.75181	+	1.94558i	1.23871	+	1.37573i	0.338101	+	0.941110i	$0.390215\pi$
$3$		0			0
$3$		0			0
$4$	−0.507392	+	4.82751i	−0.253696	+	2.41376i
$5$	0.413545	−	0.459289i	0.184943	−	0.205400i	−0.643543	−	0.765410i	$-0.722536\pi$
$5$	0.413545	−	0.459289i	0.184943	−	0.205400i	0.828486	+	0.560010i	$0.189203\pi$
$6$		0			0
$7$	−0.913545	+	0.406737i	−0.345288	+	0.153732i	−0.572051	−	0.820218i	$-0.693852\pi$
$7$	−0.913545	+	0.406737i	−0.345288	+	0.153732i	0.226764	+	0.973950i	$0.427186\pi$
$8$	−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	−0.239822	−	0.970817i	$-0.577089\pi$
$13$	−0.230909	+	0.0490813i	−0.0640427	+	0.0136127i	0.175779	+	0.984430i	$0.443756\pi$
$14$	−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	0.984770	−	0.173860i	$-0.0556239\pi$
$17$	0.354102	+	1.08981i	0.0858823	+	0.264319i	−0.898888	+	0.438178i	$0.855624\pi$
$18$		0			0
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.978810	−	0.204772i	$-0.934355\pi$
$19$	−4.73607	+	3.44095i	−1.08653	+	0.789409i	−0.107719	+	0.994181i	$0.534355\pi$
$20$	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	0.878069	−	0.478534i	$-0.158832\pi$
$23$	0.118034	+	0.204441i	0.0246118	+	0.0426289i	−0.853457	+	0.521163i	$0.825498\pi$
$24$		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	0.171147	−	0.985246i	$-0.445253\pi$
$29$	5.48127	−	2.44042i	1.01785	−	0.453175i	0.846700	+	0.532071i	$0.178586\pi$
$30$		0			0
$31$	5.95709	−	1.26622i	1.06992	−	0.227419i	0.360901	−	0.932604i	$-0.382469\pi$
$31$	5.95709	−	1.26622i	1.06992	−	0.227419i	0.709023	+	0.705185i	$0.249136\pi$
$32$	−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	0.919391	−	0.393344i	$-0.128682\pi$
$37$	5.04508	+	3.66547i	0.829407	+	0.602599i	−0.0899846	+	0.995943i	$0.528682\pi$
$38$	−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	0.389827	−	0.920888i	$-0.372535\pi$
$41$	−0.215659	−	0.0960175i	−0.0336803	−	0.0149954i	−0.423508	+	0.905893i	$0.639201\pi$
$42$		0			0
$43$	3.35410	−	5.80948i	0.511496	−	0.885937i	−0.488415	−	0.872611i	$-0.662425\pi$
$43$	3.35410	−	5.80948i	0.511496	−	0.885937i	0.999911	−	0.0133254i	$-0.00424174\pi$
$44$	−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	−0.750302	−	0.661095i	$-0.770092\pi$
$47$	−1.05471	−	10.0349i	−0.153845	−	1.46374i	0.596457	−	0.802645i	$-0.296575\pi$
$48$		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	−0.942623	−	0.333860i	$-0.891649\pi$
$53$	0.118034	−	0.363271i	0.0162132	−	0.0498991i	0.958836	+	0.283961i	$0.0916486\pi$
$54$		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	−0.821948	−	0.569562i	$-0.807113\pi$
$59$	0.771626	−	7.34153i	0.100457	−	0.955785i	0.922405	−	0.386223i	$-0.126221\pi$
$60$		0			0
$61$	11.3096	+	2.40394i	1.44805	+	0.307793i	0.863823	−	0.503796i	$-0.168064\pi$
$61$	11.3096	+	2.40394i	1.44805	+	0.307793i	0.584229	+	0.811589i	$0.301397\pi$
$62$	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	0.803824	−	0.594867i	$-0.202795\pi$
$67$	−0.927051	−	1.60570i	−0.113257	−	0.196167i	−0.917082	+	0.398699i	$0.869462\pi$
$68$	−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	−0.940948	−	0.338550i	$-0.890063\pi$
$71$	−3.19098	−	9.82084i	−0.378700	−	1.16552i	0.562248	−	0.826968i	$-0.309937\pi$
$72$		0			0
$73$	4.61803	+	3.35520i	0.540500	+	0.392696i	0.824271	−	0.566196i	$-0.191585\pi$
$73$	4.61803	+	3.35520i	0.540500	+	0.392696i	−0.283771	+	0.958892i	$0.591585\pi$
$74$	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	0.997834	−	0.0657787i	$-0.0209531\pi$
$79$	7.36044	+	8.17459i	0.828114	+	0.919714i	−0.169720	+	0.985492i	$0.554286\pi$
$80$	−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	0.286260	−	0.958152i	$-0.407588\pi$
$83$	1.43997	+	0.306074i	0.158057	+	0.0335960i	−0.128204	+	0.991748i	$0.540921\pi$
$84$		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	0.948318	−	0.317323i	$-0.102784\pi$
$97$	5.25542	+	5.83674i	0.533607	+	0.592631i	−0.414711	+	0.909953i	$0.636117\pi$
$98$	−15.7082			−1.58677
$99$		0			0
$100$	−22.4164			−2.24164
$101$	6.84927	+	7.60688i	0.681527	+	0.756913i	0.980322	−	0.197404i	$-0.0632512\pi$
$101$	6.84927	+	7.60688i	0.681527	+	0.756913i	−0.298795	+	0.954317i	$0.596585\pi$
$102$		0			0
$103$	1.14399	−	10.8843i	0.112720	−	1.07246i	−0.781213	−	0.624264i	$-0.785399\pi$
$103$	1.14399	−	10.8843i	0.112720	−	1.07246i	0.893934	−	0.448199i	$-0.147935\pi$
$104$	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	−0.937756	−	0.347294i	$-0.887101\pi$
$107$	−9.28115	+	6.74315i	−0.897243	+	0.651885i	0.0405134	+	0.999179i	$0.487101\pi$
$108$		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	−0.264241	−	0.964457i	$-0.585121\pi$
$113$	−12.3074	−	5.47961i	−1.15778	−	0.515478i	−0.893543	+	0.448978i	$0.851788\pi$
$114$		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	0.999392	+	0.0348741i	$0.0111030\pi$
$127$	2.38197	+	7.33094i	0.211365	+	0.650516i	−0.788026	+	0.615641i	$0.788897\pi$
$128$	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	−0.999840	−	0.0178914i	$-0.994305\pi$
$131$	−5.89919	−	10.2177i	−0.515414	−	0.892724i	0.484426	−	0.874832i	$-0.339029\pi$
$132$		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	0.596943	−	0.802283i	$-0.296382\pi$
$137$	9.55057	+	2.03004i	0.815960	+	0.173438i	0.219017	+	0.975721i	$0.429715\pi$
$138$		0			0
$139$	−1.52218	+	14.4825i	−0.129109	+	1.22839i	0.717645	+	0.696409i	$0.245220\pi$
$139$	−1.52218	+	14.4825i	−0.129109	+	1.22839i	−0.846755	+	0.531984i	$0.821447\pi$
$140$	−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	−0.615767	−	0.787928i	$-0.711154\pi$
$149$	2.83448	−	3.14801i	0.232210	−	0.257895i	0.847977	+	0.530033i	$0.177820\pi$
$150$		0			0
$151$	−0.110354	−	1.04994i	−0.00898045	−	0.0854433i	0.989114	−	0.147154i	$-0.0470112\pi$
$151$	−0.110354	−	1.04994i	−0.00898045	−	0.0854433i	−0.998094	+	0.0617103i	$0.980345\pi$
$152$	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	0.889546	−	0.456845i	$-0.151021\pi$
$157$	14.3502	+	6.38910i	1.14527	+	0.509906i	0.255721	+	0.966751i	$0.417687\pi$
$158$	−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	−0.993819	−	0.111011i	$-0.964591\pi$
$163$	−1.59017	+	4.89404i	−0.124552	+	0.383331i	0.869267	+	0.494342i	$0.164591\pi$
$164$	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	0.271454	−	0.962452i	$-0.412496\pi$
$167$	11.7715	−	2.50210i	0.910903	−	0.193618i	0.639449	+	0.768833i	$0.279162\pi$
$168$		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	−0.795683	−	0.605713i	$-0.792888\pi$
$173$	−1.88511	−	17.9356i	−0.143322	−	1.36362i	0.652361	−	0.757909i	$-0.273779\pi$
$174$		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	−0.814970	−	0.579503i	$-0.803247\pi$
$179$	−6.89919	+	5.01255i	−0.515669	+	0.374656i	0.299301	+	0.954159i	$0.403247\pi$
$180$		0			0
$181$	0.781153	+	2.40414i	0.0580626	+	0.178698i	0.975881	−	0.218301i	$-0.0700515\pi$
$181$	0.781153	+	2.40414i	0.0580626	+	0.178698i	−0.917819	+	0.396999i	$0.870051\pi$
$182$	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	−0.379467	−	0.925205i	$-0.623893\pi$
$191$	0.748797	−	0.333386i	0.0541810	−	0.0241230i	0.433648	+	0.901082i	$0.357226\pi$
$192$		0			0
$193$	−2.10502	+	2.33786i	−0.151522	+	0.168283i	−0.814127	−	0.580686i	$-0.802784\pi$
$193$	−2.10502	+	2.33786i	−0.151522	+	0.168283i	0.662605	+	0.748969i	$0.269451\pi$
$194$	−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	−0.328109	−	0.944640i	$-0.606411\pi$
$211$	−3.53897	+	0.752232i	−0.243633	+	0.0517858i	0.0844767	+	0.996425i	$0.473078\pi$
$212$	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	−0.990483	−	0.137636i	$-0.956050\pi$
$223$	−0.750550	−	7.14101i	−0.0502605	−	0.478197i	0.940222	−	0.340561i	$-0.110617\pi$
$224$	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	−0.765353	−	0.643611i	$-0.777436\pi$
$227$	−12.0408	+	5.36093i	−0.799179	+	0.355817i	−0.0338254	+	0.999428i	$0.510769\pi$
$228$		0			0
$229$	−0.461819	+	0.0981626i	−0.0305178	+	0.00648677i	−0.223145	−	0.974785i	$-0.571632\pi$
$229$	−0.461819	+	0.0981626i	−0.0305178	+	0.00648677i	0.192627	+	0.981272i	$0.438299\pi$
$230$	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	−0.900280	−	0.435311i	$-0.856638\pi$
$233$	1.28115	−	3.94298i	0.0839311	−	0.258313i	0.984211	+	0.176997i	$0.0566384\pi$
$234$		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	0.395420	−	0.918500i	$-0.370599\pi$
$239$	−0.348943	−	0.155360i	−0.0225713	−	0.0100494i	−0.417991	+	0.908451i	$0.637266\pi$
$240$		0			0
$241$	−4.14590	+	7.18091i	−0.267061	+	0.462563i	−0.968101	−	0.250558i	$-0.919386\pi$
$241$	−4.14590	+	7.18091i	−0.267061	+	0.462563i	0.701041	+	0.713121i	$0.252719\pi$
$242$	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	−0.470718	−	0.882284i	$-0.656005\pi$
$251$	6.79180	−	20.9030i	0.428694	−	1.31939i	0.899412	−	0.437102i	$-0.143995\pi$
$252$		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	−0.274445	−	0.961603i	$-0.588494\pi$
$257$	3.10895	−	29.5797i	0.193931	−	1.84513i	0.468376	−	0.883529i	$-0.344839\pi$
$258$		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	−0.999443	−	0.0333839i	$-0.989372\pi$
$263$	−7.63525	+	13.2246i	−0.470810	+	0.815467i	0.528633	+	0.848851i	$0.322705\pi$
$264$		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	0.840662	+	0.541560i	$0.182166\pi$
$269$	7.85410	+	24.1724i	0.478873	+	1.47382i	−0.361789	+	0.932260i	$0.617834\pi$
$270$		0			0
$271$	−15.0623	−	10.9434i	−0.914970	−	0.664765i	0.0272970	−	0.999627i	$-0.491310\pi$
$271$	−15.0623	−	10.9434i	−0.914970	−	0.664765i	−0.942267	+	0.334863i	$0.891310\pi$
$272$	−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	−0.943437	−	0.331551i	$-0.892428\pi$
$277$	−19.5485	−	21.7108i	−1.17456	−	1.30448i	−0.231118	−	0.972926i	$-0.574238\pi$
$278$	−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	0.862657	−	0.505790i	$-0.168799\pi$
$281$	24.2228	+	5.14871i	1.44501	+	0.307146i	0.582353	+	0.812936i	$0.302132\pi$
$282$		0			0
$283$	−5.21470	−	2.32174i	−0.309982	−	0.138013i	0.245849	−	0.969308i	$-0.420933\pi$
$283$	−5.21470	−	2.32174i	−0.309982	−	0.138013i	−0.555831	+	0.831295i	$0.687600\pi$
$284$	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	0.704225	+	0.709976i	$0.251294\pi$
$293$	−2.26330	+	21.5339i	−0.132223	+	1.25802i	−0.836449	+	0.548045i	$0.815372\pi$
$294$		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	0.0820850	−	0.996625i	$-0.473842\pi$
$311$	−10.6451	−	4.73949i	−0.603626	−	0.268752i	−0.685711	+	0.727874i	$0.740509\pi$
$312$		0			0
$313$	2.47262	+	0.525572i	0.139761	+	0.0297071i	0.277261	−	0.960795i	$-0.410573\pi$
$313$	2.47262	+	0.525572i	0.139761	+	0.0297071i	−0.137500	+	0.990502i	$0.543907\pi$
$314$	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	0.857538	−	0.514421i	$-0.171993\pi$
$317$	4.56324	+	5.06800i	0.256297	+	0.284647i	−0.601240	+	0.799068i	$0.705327\pi$
$318$		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	−0.998918	−	0.0465067i	$-0.985191\pi$
$331$	−8.35410	+	14.4697i	−0.459183	+	0.795328i	0.539735	+	0.841835i	$0.318524\pi$
$332$	−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	−0.812275	−	0.583274i	$-0.801771\pi$
$337$	1.90036	−	18.0807i	0.103519	−	0.984921i	0.915795	−	0.401647i	$-0.131562\pi$
$338$	−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	−0.715079	−	0.699044i	$-0.753609\pi$
$347$	1.02234	−	1.13542i	0.0548821	−	0.0609528i	0.769961	+	0.638091i	$0.220276\pi$
$348$		0			0
$349$	−1.32837	−	12.6386i	−0.0711060	−	0.676528i	−0.970781	−	0.239968i	$-0.922863\pi$
$349$	−1.32837	−	12.6386i	−0.0711060	−	0.676528i	0.899675	−	0.436560i	$-0.143803\pi$
$350$	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	−0.980352	−	0.197256i	$-0.936797\pi$
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270130\pi$
$354$		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	0.360907	−	0.932602i	$-0.382467\pi$
$359$	−7.85410	−	5.70634i	−0.414524	−	0.301169i	−0.775431	+	0.631433i	$0.782467\pi$
$360$		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	0.196121	−	0.980580i	$-0.437165\pi$
$367$	20.2313	−	9.00755i	1.05606	−	0.470190i	0.859943	+	0.510389i	$0.170499\pi$
$368$	−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	0.854294	−	0.519789i	$-0.173990\pi$
$373$	−0.444272	−	0.769502i	−0.0230035	−	0.0398433i	−0.877298	+	0.479946i	$0.840656\pi$
$374$	−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	−0.928915	−	0.370292i	$-0.879258\pi$
$379$	−7.69098	−	23.6704i	−0.395059	−	1.21587i	0.533856	−	0.845575i	$-0.320742\pi$
$380$	−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	−0.514232	−	0.857651i	$-0.671923\pi$
$383$	−12.4305	+	2.64218i	−0.635169	+	0.135009i	−0.120937	+	0.992660i	$0.538590\pi$
$384$		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	0.702948	−	0.711241i	$-0.251866\pi$
$389$	33.5661	−	14.9446i	1.70187	−	0.757720i	0.998919	−	0.0464795i	$-0.0148002\pi$
$390$		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	0.0749152	−	0.997190i	$-0.476131\pi$
$401$	21.2027	−	23.5480i	1.05881	−	1.17593i	0.983896	−	0.178740i	$-0.0572019\pi$
$402$		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	−0.0487161	−	0.998813i	$-0.515513\pi$
$409$	6.33070	−	1.34563i	0.313033	−	0.0665373i	0.361749	+	0.932275i	$0.382180\pi$
$410$	−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	0.938518	+	0.345230i	$0.112199\pi$
$419$	15.7254	+	27.2372i	0.768237	+	1.33063i	−0.170281	+	0.985396i	$0.554467\pi$
$420$		0			0
$421$	−1.09824	−	10.4490i	−0.0535248	−	0.509254i	−0.988136	−	0.153583i	$-0.950919\pi$
$421$	−1.09824	−	10.4490i	−0.0535248	−	0.509254i	0.934611	−	0.355671i	$-0.115748\pi$
$422$	−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	−0.897390	−	0.441238i	$-0.854540\pi$
$431$	1.82624	−	5.62058i	0.0879668	−	0.270734i	0.985357	+	0.170504i	$0.0545395\pi$
$432$		0			0
$433$	−28.5623	−	20.7517i	−1.37262	−	0.997264i	−0.997528	−	0.0702758i	$-0.977612\pi$
$433$	−28.5623	−	20.7517i	−1.37262	−	0.997264i	−0.375089	−	0.926989i	$-0.622388\pi$
$434$	−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	0.442010	+	0.897010i	$0.354266\pi$
$439$	−11.6459	+	20.1713i	−0.555828	+	0.962723i	−0.997839	+	0.0657130i	$0.979068\pi$
$440$	−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	−0.735593	−	0.677424i	$-0.763096\pi$
$443$	−3.30276	−	31.4237i	−0.156919	−	1.49298i	0.578674	−	0.815559i	$-0.303570\pi$
$444$		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	−0.863058	−	0.505104i	$-0.831454\pi$
$449$	2.79837	−	8.61251i	0.132063	−	0.406449i	0.995122	+	0.0986549i	$0.0314540\pi$
$450$		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	−0.376447	−	0.926438i	$-0.622854\pi$
$457$	−23.4547	−	4.98545i	−1.09717	−	0.233210i	−0.720718	+	0.693228i	$0.756188\pi$
$458$	−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	−0.737661	−	0.675172i	$-0.764070\pi$
$461$	4.63525	−	8.02850i	0.215885	−	0.373924i	0.953546	+	0.301247i	$0.0974029\pi$
$462$		0			0
$463$	−0.864745	−	1.49778i	−0.0401881	−	0.0696079i	0.845232	−	0.534400i	$-0.179462\pi$
$463$	−0.864745	−	1.49778i	−0.0401881	−	0.0696079i	−0.885420	+	0.464792i	$0.846129\pi$
$464$	−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	−0.981954	−	0.189119i	$-0.939437\pi$
$467$	−6.45492	−	19.8662i	−0.298698	−	0.919297i	0.683256	−	0.730179i	$-0.260563\pi$
$468$		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	−0.475951	−	0.879472i	$-0.657896\pi$
$479$	−27.7618	−	5.90094i	−1.26847	−	0.269621i	−0.792516	+	0.609851i	$0.791229\pi$
$480$		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	−0.329951	−	0.943998i	$-0.607032\pi$
$487$	10.2812	−	7.46969i	0.465884	−	0.338484i	0.795835	+	0.605514i	$0.207032\pi$
$488$	−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	0.867448	+	0.497528i	$0.165759\pi$
$491$	−1.87209	+	17.8117i	−0.0844861	+	0.803832i	−0.951934	+	0.306303i	$0.900908\pi$
$492$		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	−0.866340	−	0.499454i	$-0.833534\pi$
$499$	1.89676	−	18.0465i	0.0849108	−	0.807872i	0.951251	−	0.308418i	$-0.0997994\pi$
$500$	−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	−0.420689	−	0.907205i	$-0.638212\pi$
$503$	7.00000	−	5.08580i	0.312115	−	0.226765i	0.732803	+	0.680441i	$0.238212\pi$
$504$		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	−0.575888	−	0.817529i	$-0.695344\pi$
$509$	−35.3932	−	15.7581i	−1.56877	−	0.698463i	−0.992886	+	0.119065i	$0.962010\pi$
$510$		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	0.734902	−	0.678173i	$-0.237228\pi$
$521$	7.23607	+	5.25731i	0.317018	+	0.230327i	−0.417884	+	0.908500i	$0.637228\pi$
$522$		0			0
$523$	5.64590	+	17.3763i	0.246878	+	0.759812i	0.995322	+	0.0966140i	$0.0308013\pi$
$523$	5.64590	+	17.3763i	0.246878	+	0.759812i	−0.748444	+	0.663198i	$0.769199\pi$
$524$	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	−0.988414	−	0.151782i	$-0.951499\pi$
$541$	−2.31559	+	7.12667i	−0.0995552	+	0.306399i	0.888859	+	0.458181i	$0.151499\pi$
$542$	−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	0.818260	+	0.574848i	$0.194939\pi$
$547$	3.21348	+	30.5742i	0.137399	+	1.30726i	−0.680862	+	0.732412i	$0.738395\pi$
$548$	−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	0.999805	−	0.0197634i	$-0.00629130\pi$
$557$	30.4443	+	22.1191i	1.28997	+	0.937215i	0.290161	+	0.956978i	$0.406291\pi$
$558$		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	0.729114	−	0.684392i	$-0.239932\pi$
$563$	39.7096	−	8.44054i	1.67356	−	0.355726i	0.944446	+	0.328666i	$0.106599\pi$
$564$		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	0.768700	+	0.639610i	$0.220904\pi$
$569$	3.57282	+	33.9931i	0.149780	+	1.42506i	−0.618919	+	0.785455i	$0.712429\pi$
$570$		0			0
$571$	4.54508	+	7.87232i	0.190206	+	0.329446i	0.945318	−	0.326149i	$-0.105751\pi$
$571$	4.54508	+	7.87232i	0.190206	+	0.329446i	−0.755112	+	0.655595i	$0.772418\pi$
$572$	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	0.918439	+	0.395562i	$0.129450\pi$
$577$	9.79837	+	30.1563i	0.407912	+	1.25542i	−0.510528	+	0.859861i	$0.670550\pi$
$578$	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	−0.366290	−	0.930501i	$-0.619372\pi$
$587$	1.94093	−	0.864157i	0.0801107	−	0.0356676i	0.446401	+	0.894833i	$0.352706\pi$
$588$		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	−0.890849	−	0.454300i	$-0.849889\pi$
$599$	−8.46616	+	9.40262i	−0.345918	+	0.384181i	0.544931	+	0.838481i	$0.316556\pi$
$600$		0			0
$601$	−6.29300	+	2.80182i	−0.256697	+	0.114289i	−0.531051	−	0.847340i	$-0.678203\pi$
$601$	−6.29300	+	2.80182i	−0.256697	+	0.114289i	0.274354	+	0.961629i	$0.411536\pi$
$602$	−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	0.132961	−	0.991121i	$-0.457551\pi$
$607$	16.2004	−	3.44350i	0.657553	−	0.139767i	0.524592	+	0.851354i	$0.324218\pi$
$608$	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	−0.329273	−	0.944235i	$-0.606804\pi$
$613$	11.5623	−	8.40051i	0.466997	−	0.339293i	0.796270	+	0.604942i	$0.206804\pi$
$614$	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	0.956335	−	0.292273i	$-0.0944115\pi$
$617$	5.59017	+	9.68246i	0.225052	+	0.389801i	−0.731283	+	0.682074i	$0.761078\pi$
$618$		0			0
$619$	−2.52171	−	23.9925i	−0.101356	−	0.964338i	−0.920498	−	0.390747i	$-0.872217\pi$
$619$	−2.52171	−	23.9925i	−0.101356	−	0.964338i	0.819142	−	0.573591i	$-0.194450\pi$
$620$	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	0.233676	−	0.972314i	$-0.424924\pi$
$631$	−15.5451	−	11.2942i	−0.618840	−	0.449614i	−0.852516	+	0.522701i	$0.824924\pi$
$632$	−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	−0.915643	−	0.401992i	$-0.868318\pi$
$641$	−2.62264	−	24.9527i	−0.103588	−	0.985573i	0.812055	−	0.583581i	$-0.198349\pi$
$642$		0			0
$643$	13.9541	−	15.4976i	0.550297	−	0.611166i	−0.402261	−	0.915525i	$-0.631775\pi$
$643$	13.9541	−	15.4976i	0.550297	−	0.611166i	0.952557	+	0.304359i	$0.0984422\pi$
$644$	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	0.168808	+	0.985649i	$0.446008\pi$
$647$	−13.9164	+	42.8303i	−0.547110	+	1.68383i	−0.715918	+	0.698184i	$0.753992\pi$
$648$		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	0.977005	+	0.213218i	$0.0683945\pi$
$653$	−0.587244	+	5.58726i	−0.0229807	+	0.218646i	−0.999985	+	0.00542814i	$0.998272\pi$
$654$		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	0.117969	+	0.993017i	$0.462362\pi$
$659$	−20.5623	+	35.6150i	−0.800994	+	1.38736i	−0.918963	+	0.394345i	$0.870972\pi$
$660$		0			0
$661$	−18.2812	−	31.6639i	−0.711054	−	1.23158i	−0.964462	−	0.264223i	$-0.914885\pi$
$661$	−18.2812	−	31.6639i	−0.711054	−	1.23158i	0.253407	−	0.967360i	$-0.418449\pi$
$662$	−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	0.999570	+	0.0293129i	$0.00933191\pi$
$673$	23.9768	+	26.6290i	0.924239	+	1.02647i	−0.0753313	+	0.997159i	$0.524001\pi$
$674$	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	0.455042	−	0.890470i	$-0.349624\pi$
$677$	13.2322	+	2.81260i	0.508557	+	0.108097i	0.0535147	+	0.998567i	$0.482958\pi$
$678$		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	0.760051	−	0.649863i	$-0.225174\pi$
$691$	0.901670	+	1.00141i	0.0343011	+	0.0380953i	−0.725750	+	0.687958i	$0.758507\pi$
$692$	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	−0.974697	−	0.223531i	$-0.928242\pi$
$701$	−28.1525	+	20.4540i	−1.06330	+	0.772536i	−0.0886075	+	0.996067i	$0.528242\pi$
$702$		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	−0.00273893	−	0.999996i	$-0.500872\pi$
$709$	−10.9697	−	2.33168i	−0.411976	−	0.0875682i	−0.409237	+	0.912428i	$0.634205\pi$
$710$	−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	−0.171226	−	0.985232i	$-0.554773\pi$
$719$	−31.1353	−	22.6211i	−1.16115	−	0.843624i	−0.989923	+	0.141608i	$0.954773\pi$
$720$		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	−0.768678	−	0.639635i	$-0.779085\pi$
$727$	4.57295	−	7.92058i	0.169601	−	0.293758i	0.938280	+	0.345877i	$0.112419\pi$
$728$	−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	−0.993716	−	0.111932i	$-0.964296\pi$
$733$	0.0421513	−	0.401043i	0.00155690	−	0.0148129i	0.995273	+	0.0971191i	$0.0309628\pi$
$734$	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	−0.932557	−	0.361024i	$-0.882427\pi$
$739$	0.927051	−	2.85317i	0.0341021	−	0.104956i	0.966659	+	0.256068i	$0.0824272\pi$
$740$	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	0.0676581	−	0.997709i	$-0.478447\pi$
$743$	28.6980	−	31.8724i	1.05283	−	1.16928i	0.985171	−	0.171576i	$-0.0548860\pi$
$744$		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	0.657805	−	0.753188i	$-0.271485\pi$
$751$	14.7500	+	6.56713i	0.538236	+	0.239638i	−0.119570	+	0.992826i	$0.538152\pi$
$752$	−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	−0.919044	−	0.394156i	$-0.871037\pi$
$757$	1.54508	−	4.75528i	0.0561571	−	0.172834i	0.975201	+	0.221322i	$0.0710371\pi$
$758$	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	0.343122	−	0.939291i	$-0.388516\pi$
$761$	28.6517	−	6.09011i	1.03862	−	0.220766i	0.695501	+	0.718525i	$0.255182\pi$
$762$		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	0.989081	+	0.147373i	$0.0470819\pi$
$769$	17.2533	+	29.8836i	0.622170	+	1.07763i	−0.366911	+	0.930256i	$0.619585\pi$
$770$	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	−0.117329	−	0.993093i	$-0.537433\pi$
$773$	21.9894	−	15.9762i	0.790902	−	0.574624i	0.908231	+	0.418469i	$0.137433\pi$
$774$		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	−0.847715	−	0.530451i	$-0.822022\pi$
$787$	−6.49606	+	7.21460i	−0.231559	+	0.257173i	0.616156	+	0.787624i	$0.288689\pi$
$788$	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	−0.921663	−	0.387992i	$-0.873169\pi$
$797$	−12.4064	+	13.7787i	−0.439456	+	0.488065i	0.482207	+	0.876057i	$0.339835\pi$
$798$		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	−0.983449	−	0.181185i	$-0.942007\pi$
$809$	−8.37132	−	25.7643i	−0.294320	−	0.905824i	0.689129	−	0.724639i	$-0.257993\pi$
$810$		0			0
$811$	−29.5795	+	21.4908i	−1.03868	+	0.754644i	−0.970027	−	0.242997i	$-0.921869\pi$
$811$	−29.5795	+	21.4908i	−1.03868	+	0.754644i	−0.0686507	+	0.997641i	$0.521869\pi$
$812$	−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	−0.934244	−	0.356634i	$-0.883924\pi$
$821$	−37.0870	+	16.5122i	−1.29434	+	0.576279i	−0.360100	+	0.932914i	$0.617258\pi$
$822$		0			0
$823$	27.2246	−	5.78677i	0.948990	−	0.201714i	0.292684	−	0.956209i	$-0.405452\pi$
$823$	27.2246	−	5.78677i	0.948990	−	0.201714i	0.656306	+	0.754495i	$0.272118\pi$
$824$	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	−0.877369	−	0.479817i	$-0.840703\pi$
$827$	3.29180	−	10.1311i	0.114467	−	0.352293i	0.991835	+	0.127524i	$0.0407030\pi$
$828$		0			0
$829$	25.3992	+	18.4536i	0.882150	+	0.640920i	0.933819	−	0.357745i	$-0.116454\pi$
$829$	25.3992	+	18.4536i	0.882150	+	0.640920i	−0.0516692	+	0.998664i	$0.516454\pi$
$830$	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	−0.978407	−	0.206690i	$-0.933731\pi$
$839$	−1.86404	−	17.7351i	−0.0643537	−	0.612285i	0.914053	−	0.405595i	$-0.132936\pi$
$840$		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	0.996055	−	0.0887365i	$-0.0282829\pi$
$853$	54.6127	+	11.6083i	1.86990	+	0.397460i	0.873849	+	0.486197i	$0.161616\pi$
$854$	−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	−0.525365	−	0.850877i	$-0.676071\pi$
$857$	13.8820	−	24.0443i	0.474199	−	0.821337i	0.999564	+	0.0295405i	$0.00940442\pi$
$858$		0			0
$859$	17.2082	+	29.8055i	0.587136	+	1.01695i	0.994605	+	0.103731i	$0.0330781\pi$
$859$	17.2082	+	29.8055i	0.587136	+	1.01695i	−0.407469	+	0.913219i	$0.633589\pi$
$860$	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	0.950469	−	0.310821i	$-0.100604\pi$
$863$	−0.0344419	−	0.106001i	−0.00117241	−	0.00360832i	−0.951641	+	0.307212i	$0.900604\pi$
$864$		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	−0.977975	−	0.208722i	$-0.933070\pi$
$877$	−52.9347	−	23.5681i	−1.78748	−	0.795837i	−0.809504	−	0.587115i	$-0.800264\pi$
$878$	−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	−0.602064	−	0.798448i	$-0.705655\pi$
$883$	−0.854102	+	0.620541i	−0.0287428	+	0.0208829i	0.573321	+	0.819331i	$0.305655\pi$
$884$	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	0.306264	+	0.951947i	$0.400921\pi$
$887$	−5.69526	+	54.1868i	−0.191228	+	1.81942i	−0.497492	+	0.867469i	$0.665746\pi$
$888$		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	0.836162	−	0.548483i	$-0.184794\pi$
$907$	41.4687	+	8.81444i	1.37695	+	0.292679i	0.540783	+	0.841162i	$0.318128\pi$
$908$	−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	0.143564	−	0.989641i	$-0.454144\pi$
$911$	−25.8263	−	28.6830i	−0.855662	−	0.950309i	−0.999226	+	0.0393318i	$0.987477\pi$
$912$		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	0.992481	+	0.122395i	$0.0390576\pi$
$919$	7.92705	+	24.3970i	0.261489	+	0.804781i	−0.730992	+	0.682386i	$0.760942\pi$
$920$	−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	−0.000572170	−	1.00000i	$-0.500182\pi$
$929$	−12.4305	−	2.64218i	−0.407831	−	0.0866873i	−0.407259	+	0.913313i	$0.633515\pi$
$930$		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	−0.486761	−	0.873535i	$-0.661822\pi$
$937$	12.8713	−	39.6139i	0.420488	−	1.29413i	0.907249	−	0.420593i	$-0.138178\pi$
$938$	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	−0.564627	−	0.825346i	$-0.690980\pi$
$941$	9.66951	−	10.7391i	0.315217	−	0.350084i	0.879844	+	0.475262i	$0.157647\pi$
$942$		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	0.473179	+	0.880966i	$0.343106\pi$
$947$	−16.1976	+	28.0550i	−0.526350	+	0.911665i	−0.999529	+	0.0306985i	$0.990227\pi$
$948$		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	0.726463	−	0.687206i	$-0.241163\pi$
$953$	9.18034	+	6.66991i	0.297380	+	0.216059i	−0.429082	+	0.903265i	$0.641163\pi$
$954$		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	−0.966244	−	0.257627i	$-0.917059\pi$
$967$	−21.9615	−	38.0384i	−0.706234	−	1.22323i	0.260010	−	0.965606i	$-0.416274\pi$
$968$	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	−0.979472	−	0.201582i	$-0.935392\pi$
$971$	−33.9787	+	24.6870i	−1.09043	+	0.792243i	−0.110957	+	0.993825i	$0.535392\pi$
$972$		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	−0.217239	−	0.976118i	$-0.569705\pi$
$977$	−0.583707	+	0.124071i	−0.0186745	+	0.00396938i	0.198565	+	0.980088i	$0.436372\pi$
$978$		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	−0.285145	−	0.958484i	$-0.592042\pi$
$983$	7.41018	−	3.29923i	0.236348	−	0.105229i	0.521493	+	0.853255i	$0.325375\pi$
$984$		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	−0.689834	−	0.723967i	$-0.742317\pi$
$997$	−19.3686	+	8.62348i	−0.613411	+	0.273108i	0.0764231	+	0.997075i	$0.475650\pi$
$998$	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.460.1		8
3.2	odd	2		891.2.n.c.460.1		8
9.2	odd	6		33.2.e.b.31.1	yes	4
9.4	even	3	inner	891.2.n.b.757.1		8
9.5	odd	6		891.2.n.c.757.1		8
9.7	even	3		99.2.f.a.64.1		4
11.5	even	5	inner	891.2.n.b.379.1		8
33.5	odd	10		891.2.n.c.379.1		8
36.11	even	6		528.2.y.b.97.1		4
45.2	even	12		825.2.bx.d.724.1		8
45.29	odd	6		825.2.n.c.526.1		4
45.38	even	12		825.2.bx.d.724.2		8
99.2	even	30		363.2.e.b.124.1		4
99.5	odd	30		891.2.n.c.676.1		8
99.7	odd	30		1089.2.a.l.1.1		2
99.16	even	15		99.2.f.a.82.1		4
99.20	odd	30		363.2.e.k.124.1		4
99.29	even	30		363.2.a.i.1.2		2
99.38	odd	30		33.2.e.b.16.1	✓	4
99.47	odd	30		363.2.e.k.202.1		4
99.49	even	15	inner	891.2.n.b.676.1		8
99.65	even	6		363.2.e.f.130.1		4
99.70	even	15		1089.2.a.t.1.2		2
99.74	even	30		363.2.e.b.202.1		4
99.83	even	30		363.2.e.f.148.1		4
99.92	odd	30		363.2.a.d.1.1		2
396.191	even	30		5808.2.a.cj.1.1		2
396.227	odd	30		5808.2.a.ci.1.1		2
396.335	even	30		528.2.y.b.49.1		4
495.29	even	30		9075.2.a.u.1.1		2
495.38	even	60		825.2.bx.d.49.1		8
495.137	even	60		825.2.bx.d.49.2		8
495.389	odd	30		9075.2.a.cb.1.2		2
495.434	odd	30		825.2.n.c.676.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	99.38	odd	30
33.2.e.b.31.1	yes	4	9.2	odd	6
99.2.f.a.64.1		4	9.7	even	3
99.2.f.a.82.1		4	99.16	even	15
363.2.a.d.1.1		2	99.92	odd	30
363.2.a.i.1.2		2	99.29	even	30
363.2.e.b.124.1		4	99.2	even	30
363.2.e.b.202.1		4	99.74	even	30
363.2.e.f.130.1		4	99.65	even	6
363.2.e.f.148.1		4	99.83	even	30
363.2.e.k.124.1		4	99.20	odd	30
363.2.e.k.202.1		4	99.47	odd	30
528.2.y.b.49.1		4	396.335	even	30
528.2.y.b.97.1		4	36.11	even	6
825.2.n.c.526.1		4	45.29	odd	6
825.2.n.c.676.1		4	495.434	odd	30
825.2.bx.d.49.1		8	495.38	even	60
825.2.bx.d.49.2		8	495.137	even	60
825.2.bx.d.724.1		8	45.2	even	12
825.2.bx.d.724.2		8	45.38	even	12
891.2.n.b.379.1		8	11.5	even	5	inner
891.2.n.b.460.1		8	1.1	even	1	trivial
891.2.n.b.676.1		8	99.49	even	15	inner
891.2.n.b.757.1		8	9.4	even	3	inner
891.2.n.c.379.1		8	33.5	odd	10
891.2.n.c.460.1		8	3.2	odd	2
891.2.n.c.676.1		8	99.5	odd	30
891.2.n.c.757.1		8	9.5	odd	6
1089.2.a.l.1.1		2	99.7	odd	30
1089.2.a.t.1.2		2	99.70	even	15
5808.2.a.ci.1.1		2	396.227	odd	30
5808.2.a.cj.1.1		2	396.191	even	30
9075.2.a.u.1.1		2	495.29	even	30
9075.2.a.cb.1.2		2	495.389	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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