LMFDB - Embedded newform 891.2.n.c.379.1

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			379.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	891.379
Dual form			891.2.n.c.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.56082 + 0.544320i) q^{2} +(4.43444 + 1.97434i) q^{4} +(0.604528 - 0.128496i) q^{5} +(0.104528 + 0.994522i) q^{7} +(6.04508 + 4.39201i) q^{8} +1.61803 q^{10} +(1.46007 - 2.97795i) q^{11} +(0.157960 - 0.175433i) q^{13} +(-0.273659 + 2.60369i) q^{14} +(6.59368 + 7.32302i) q^{16} +(-0.354102 + 1.08981i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(2.93444 + 0.623735i) q^{20} +(5.35995 - 6.83126i) q^{22} +(-0.118034 - 0.204441i) q^{23} +(-4.21878 + 1.87832i) q^{25} +(0.500000 - 0.363271i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(0.627171 + 5.96713i) q^{29} +(-4.07512 + 4.52588i) q^{31} +(5.42705 + 9.39993i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(0.190983 + 0.587785i) q^{35} +(5.04508 - 3.66547i) q^{37} +(-10.2553 - 11.3896i) q^{38} +(4.21878 + 1.87832i) q^{40} +(-0.0246758 + 0.234775i) q^{41} +(3.35410 - 5.80948i) q^{43} +(12.3541 - 10.3229i) q^{44} +(-0.190983 - 0.587785i) q^{46} +(-9.21783 + 4.10404i) q^{47} +(5.86889 - 1.24747i) q^{49} +(-11.8260 + 2.51369i) q^{50} +(1.04683 - 0.466079i) q^{52} +(-0.118034 - 0.363271i) q^{53} +(0.500000 - 1.98787i) q^{55} +(-3.73607 + 6.47106i) q^{56} +(-1.64195 + 15.6222i) q^{58} +(6.74376 + 3.00252i) q^{59} +(-7.73669 - 8.59247i) q^{61} +(-12.8992 + 9.37181i) q^{62} +(2.69098 + 8.28199i) q^{64} +(0.0729490 - 0.126351i) q^{65} +(-0.927051 - 1.60570i) q^{67} +(-3.72191 + 4.13360i) q^{68} +(0.169131 + 1.60917i) q^{70} +(3.19098 - 9.82084i) q^{71} +(4.61803 - 3.35520i) q^{73} +(14.9148 - 6.64048i) q^{74} +(-14.2082 - 24.6093i) q^{76} +(3.11426 + 1.14079i) q^{77} +(-10.7596 - 2.28703i) q^{79} +(4.92705 + 3.57971i) q^{80} +(-0.190983 + 0.587785i) q^{82} +(0.985051 + 1.09401i) q^{83} +(-0.0740275 + 0.704324i) q^{85} +(11.7515 - 13.0513i) q^{86} +(21.9055 - 11.5893i) q^{88} -8.23607 q^{89} +(0.190983 + 0.138757i) q^{91} +(-0.119779 - 1.13962i) q^{92} +(-25.8391 + 5.49228i) q^{94} +(-3.30524 - 1.47159i) q^{95} +(-7.68247 - 1.63296i) q^{97} +15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.56082	+	0.544320i	1.81078	+	0.384892i	0.984076	−	0.177750i	$-0.0568820\pi$
$2$	2.56082	+	0.544320i	1.81078	+	0.384892i	0.826700	+	0.562643i	$0.190215\pi$
$3$		0			0
$3$		0			0
$4$	4.43444	+	1.97434i	2.21722	+	0.987171i
$5$	0.604528	−	0.128496i	0.270353	−	0.0574654i	−0.0707401	−	0.997495i	$-0.522536\pi$
$5$	0.604528	−	0.128496i	0.270353	−	0.0574654i	0.341093	+	0.940029i	$0.389203\pi$
$6$		0			0
$7$	0.104528	+	0.994522i	0.0395080	+	0.375894i	0.996355	+	0.0853021i	$0.0271855\pi$
$7$	0.104528	+	0.994522i	0.0395080	+	0.375894i	−0.956847	+	0.290592i	$0.906148\pi$
$8$	6.04508	+	4.39201i	2.13726	+	1.55281i
$9$		0			0
$10$	1.61803			0.511667
$11$	1.46007	−	2.97795i	0.440229	−	0.897886i
$11$	1.46007	−	2.97795i	0.440229	−	0.897886i
$12$		0			0
$13$	0.157960	−	0.175433i	0.0438103	−	0.0486563i	−0.720841	−	0.693100i	$-0.756244\pi$
$13$	0.157960	−	0.175433i	0.0438103	−	0.0486563i	0.764652	+	0.644444i	$0.222911\pi$
$14$	−0.273659	+	2.60369i	−0.0731385	+	0.695866i
$15$		0			0
$16$	6.59368	+	7.32302i	1.64842	+	1.83076i
$17$	−0.354102	+	1.08981i	−0.0858823	+	0.264319i	−0.984770	−	0.173860i	$-0.944376\pi$
$17$	−0.354102	+	1.08981i	−0.0858823	+	0.264319i	0.898888	+	0.438178i	$0.144376\pi$
$18$		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	$0.934355\pi$
$20$	2.93444	+	0.623735i	0.656161	+	0.139471i
$21$		0			0
$22$	5.35995	−	6.83126i	1.14274	−	1.45643i
$23$	−0.118034	−	0.204441i	−0.0246118	−	0.0426289i	0.853457	−	0.521163i	$-0.174502\pi$
$23$	−0.118034	−	0.204441i	−0.0246118	−	0.0426289i	−0.878069	+	0.478534i	$0.841168\pi$
$24$		0			0
$25$	−4.21878	+	1.87832i	−0.843757	+	0.375665i
$26$	0.500000	−	0.363271i	0.0980581	−	0.0712434i
$27$		0			0
$28$	−1.50000	+	4.61653i	−0.283473	+	0.872441i
$29$	0.627171	+	5.96713i	0.116463	+	1.10807i	0.884137	+	0.467228i	$0.154747\pi$
$29$	0.627171	+	5.96713i	0.116463	+	1.10807i	−0.767674	+	0.640840i	$0.778586\pi$
$30$		0			0
$31$	−4.07512	+	4.52588i	−0.731913	+	0.812872i	−0.988109	−	0.153753i	$-0.950864\pi$
$31$	−4.07512	+	4.52588i	−0.731913	+	0.812872i	0.256196	+	0.966625i	$0.417531\pi$
$32$	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	$0.128682\pi$
$38$	−10.2553	−	11.3896i	−1.66362	−	1.84764i
$39$		0			0
$40$	4.21878	+	1.87832i	0.667048	+	0.296989i
$41$	−0.0246758	+	0.234775i	−0.00385372	+	0.0366657i	−0.996280	−	0.0861779i	$-0.972535\pi$
$41$	−0.0246758	+	0.234775i	−0.00385372	+	0.0366657i	0.992426	+	0.122844i	$0.0392013\pi$
$42$		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
$47$	−9.21783	+	4.10404i	−1.34456	+	0.598636i	−0.947676	−	0.319233i	$-0.896575\pi$
$47$	−9.21783	+	4.10404i	−1.34456	+	0.598636i	−0.396882	+	0.917869i	$0.629908\pi$
$48$		0			0
$49$	5.86889	−	1.24747i	0.838412	−	0.178210i
$50$	−11.8260	+	2.51369i	−1.67244	+	0.355489i
$51$		0			0
$52$	1.04683	−	0.466079i	0.145169	−	0.0646335i
$53$	−0.118034	−	0.363271i	−0.0162132	−	0.0498991i	0.942623	−	0.333860i	$-0.108351\pi$
$53$	−0.118034	−	0.363271i	−0.0162132	−	0.0498991i	−0.958836	+	0.283961i	$0.908351\pi$
$54$		0			0
$55$	0.500000	−	1.98787i	0.0674200	−	0.268044i
$56$	−3.73607	+	6.47106i	−0.499253	+	0.864732i
$57$		0			0
$58$	−1.64195	+	15.6222i	−0.215599	+	2.05129i
$59$	6.74376	+	3.00252i	0.877963	+	0.390894i	0.795682	−	0.605715i	$-0.207113\pi$
$59$	6.74376	+	3.00252i	0.877963	+	0.390894i	0.0822812	+	0.996609i	$0.473779\pi$
$60$		0			0
$61$	−7.73669	−	8.59247i	−0.990582	−	1.10015i	−0.994971	−	0.100162i	$-0.968064\pi$
$61$	−7.73669	−	8.59247i	−0.990582	−	1.10015i	0.00438910	−	0.999990i	$-0.498603\pi$
$62$	−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	$0.869462\pi$
$68$	−3.72191	+	4.13360i	−0.451348	+	0.501272i
$69$		0			0
$70$	0.169131	+	1.60917i	0.0202150	+	0.192333i
$71$	3.19098	−	9.82084i	0.378700	−	1.16552i	−0.562248	−	0.826968i	$-0.690063\pi$
$71$	3.19098	−	9.82084i	0.378700	−	1.16552i	0.940948	−	0.338550i	$-0.109937\pi$
$72$		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	$0.191585\pi$
$74$	14.9148	−	6.64048i	1.73381	−	0.771940i
$75$		0			0
$76$	−14.2082	−	24.6093i	−1.62979	−	2.82288i
$77$	3.11426	+	1.14079i	0.354902	+	0.130006i
$78$		0			0
$79$	−10.7596	−	2.28703i	−1.21055	−	0.257311i	−0.441951	−	0.897039i	$-0.645714\pi$
$79$	−10.7596	−	2.28703i	−1.21055	−	0.257311i	−0.768601	+	0.639728i	$0.779047\pi$
$80$	4.92705	+	3.57971i	0.550861	+	0.400224i
$81$		0			0
$82$	−0.190983	+	0.587785i	−0.0210905	+	0.0649100i
$83$	0.985051	+	1.09401i	0.108123	+	0.120083i	0.794777	−	0.606901i	$-0.207588\pi$
$83$	0.985051	+	1.09401i	0.108123	+	0.120083i	−0.686654	+	0.726985i	$0.740921\pi$
$84$		0			0
$85$	−0.0740275	+	0.704324i	−0.00802941	+	0.0763947i
$86$	11.7515	−	13.0513i	1.26719	−	1.40736i
$87$		0			0
$88$	21.9055	−	11.5893i	2.33513	−	1.23542i
$89$	−8.23607			−0.873021			−0.436511	−	0.899699i	$-0.643786\pi$
$89$	−8.23607			−0.873021			−0.436511	+	0.899699i	$0.643786\pi$
$90$		0			0
$91$	0.190983	+	0.138757i	0.0200205	+	0.0145457i
$92$	−0.119779	−	1.13962i	−0.0124878	−	0.118814i
$93$		0			0
$94$	−25.8391	+	5.49228i	−2.66510	+	0.566485i
$95$	−3.30524	−	1.47159i	−0.339110	−	0.150982i
$96$		0			0
$97$	−7.68247	−	1.63296i	−0.780037	−	0.165802i	−0.199349	−	0.979928i	$-0.563883\pi$
$97$	−7.68247	−	1.63296i	−0.780037	−	0.165802i	−0.580687	+	0.814127i	$0.697216\pi$
$98$	15.7082			1.58677
$99$		0			0
$100$	−22.4164			−2.24164
$101$	10.0124	+	2.12820i	0.996270	+	0.211764i	0.677066	−	0.735922i	$-0.263251\pi$
$101$	10.0124	+	2.12820i	0.996270	+	0.211764i	0.319204	+	0.947686i	$0.396585\pi$
$102$		0			0
$103$	−9.99809	−	4.45144i	−0.985141	−	0.438613i	−0.150022	−	0.988683i	$-0.547935\pi$
$103$	−9.99809	−	4.45144i	−0.985141	−	0.438613i	−0.835119	+	0.550070i	$0.814601\pi$
$104$	1.72539	−	0.366742i	0.169188	−	0.0359620i
$105$		0			0
$106$	−0.104528	−	0.994522i	−0.0101527	−	0.0965965i
$107$	9.28115	+	6.74315i	0.897243	+	0.651885i	0.937756	−	0.347294i	$-0.112899\pi$
$107$	9.28115	+	6.74315i	0.897243	+	0.651885i	−0.0405134	+	0.999179i	$0.512899\pi$
$108$		0			0
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$	2.36245	−	4.81842i	0.225251	−	0.459419i
$111$		0			0
$112$	−6.59368	+	7.32302i	−0.623044	+	0.691961i
$113$	−1.40822	+	13.3983i	−0.132474	+	1.26041i	0.703124	+	0.711068i	$0.251788\pi$
$113$	−1.40822	+	13.3983i	−0.132474	+	1.26041i	−0.835598	+	0.549342i	$0.814879\pi$
$114$		0			0
$115$	−0.0976248	−	0.108423i	−0.00910356	−	0.0101105i
$116$	−9.00000	+	27.6992i	−0.835629	+	2.57180i
$117$		0			0
$118$	15.6353	+	11.3597i	1.43934	+	1.04574i
$119$	−1.12086	−	0.238246i	−0.102749	−	0.0218399i
$120$		0			0
$121$	−6.73637	−	8.69605i	−0.612397	−	0.790550i
$122$	−15.1353	−	26.2150i	−1.37028	−	2.37340i
$123$		0			0
$124$	−27.0065	+	12.0241i	−2.42526	+	1.07979i
$125$	−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	$-0.0111030\pi$
$128$	0.113954	+	1.08420i	0.0100722	+	0.0958305i
$129$		0			0
$130$	0.255585	−	0.283856i	0.0224163	−	0.0248958i
$131$	5.89919	+	10.2177i	0.515414	+	0.892724i	0.999840	+	0.0178914i	$0.00569531\pi$
$131$	5.89919	+	10.2177i	0.515414	+	0.892724i	−0.484426	+	0.874832i	$0.660971\pi$
$132$		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
$137$	6.53335	+	7.25602i	0.558181	+	0.619923i	0.954508	−	0.298187i	$-0.0963817\pi$
$137$	6.53335	+	7.25602i	0.558181	+	0.619923i	−0.396326	+	0.918110i	$0.629715\pi$
$138$		0			0
$139$	13.3033	+	5.92302i	1.12837	+	0.502384i	0.884089	−	0.467319i	$-0.154780\pi$
$139$	13.3033	+	5.92302i	1.12837	+	0.502384i	0.244285	+	0.969703i	$0.421447\pi$
$140$	−0.313585	+	2.98357i	−0.0265028	+	0.252157i
$141$		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
$146$	13.6523	−	6.07838i	1.12987	−	0.503051i
$147$		0			0
$148$	29.6090	−	6.29359i	2.43385	−	0.517330i
$149$	4.14350	−	0.880728i	0.339449	−	0.0721521i	−0.0350335	−	0.999386i	$-0.511154\pi$
$149$	4.14350	−	0.880728i	0.339449	−	0.0721521i	0.374482	+	0.927234i	$0.377820\pi$
$150$		0			0
$151$	0.964456	−	0.429403i	0.0784863	−	0.0349443i	−0.367118	−	0.930174i	$-0.619655\pi$
$151$	0.964456	−	0.429403i	0.0784863	−	0.0349443i	0.445604	+	0.895230i	$0.352989\pi$
$152$	−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
$157$	−1.64195	+	15.6222i	−0.131042	+	1.24678i	0.709370	+	0.704836i	$0.248979\pi$
$157$	−1.64195	+	15.6222i	−0.131042	+	1.24678i	−0.840412	+	0.541947i	$0.817687\pi$
$158$	−26.3086	−	11.7134i	−2.09300	−	0.931864i
$159$		0			0
$160$	4.48866	+	4.98517i	0.354860	+	0.394112i
$161$	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
$167$	8.05261	−	8.94333i	0.623130	−	0.692056i	−0.346104	−	0.938196i	$-0.612496\pi$
$167$	8.05261	−	8.94333i	0.623130	−	0.692056i	0.969234	+	0.246140i	$0.0791623\pi$
$168$		0			0
$169$	1.35304	+	12.8734i	0.104080	+	0.990259i
$170$	−0.572949	+	1.76336i	−0.0439432	+	0.135243i
$171$		0			0
$172$	26.3435	−	19.1396i	2.00867	−	1.45938i
$173$	−16.4753	+	7.33527i	−1.25259	+	0.557690i	−0.922405	−	0.386225i	$-0.873779\pi$
$173$	−16.4753	+	7.33527i	−1.25259	+	0.557690i	−0.330188	+	0.943915i	$0.607112\pi$
$174$		0			0
$175$	−2.30902	−	3.99933i	−0.174545	−	0.302321i
$176$	31.4349	−	8.94350i	2.36949	−	0.674141i
$177$		0			0
$178$	−21.0911	−	4.48306i	−1.58085	−	0.336019i
$179$	6.89919	+	5.01255i	0.515669	+	0.374656i	0.814970	−	0.579503i	$-0.196753\pi$
$179$	6.89919	+	5.01255i	0.515669	+	0.374656i	−0.299301	+	0.954159i	$0.596753\pi$
$180$		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	$0.0700515\pi$
$182$	0.413545	+	0.459289i	0.0306540	+	0.0340447i
$183$		0			0
$184$	0.184381	−	1.75427i	0.0135928	−	0.129326i
$185$	2.57890	−	2.86416i	0.189604	−	0.210577i
$186$		0			0
$187$	2.72840	+	2.64571i	0.199520	+	0.193473i
$188$	−48.9787			−3.57214
$189$		0			0
$190$	−7.66312	−	5.56758i	−0.555941	−	0.403915i
$191$	0.0856778	+	0.815170i	0.00619943	+	0.0589836i	0.997184	−	0.0749907i	$-0.0238927\pi$
$191$	0.0856778	+	0.815170i	0.00619943	+	0.0589836i	−0.990985	+	0.133974i	$0.957226\pi$
$192$		0			0
$193$	3.07715	−	0.654069i	0.221498	−	0.0470809i	−0.0958256	−	0.995398i	$-0.530549\pi$
$193$	3.07715	−	0.654069i	0.221498	−	0.0470809i	0.317324	+	0.948317i	$0.397216\pi$
$194$	−18.7846	−	8.36344i	−1.34866	−	0.600460i
$195$		0			0
$196$	28.4882	+	6.05535i	2.03487	+	0.432525i
$197$	13.0344			0.928666			0.464333	−	0.885661i	$-0.346294\pi$
$197$	13.0344			0.928666			0.464333	+	0.885661i	$0.346294\pi$
$198$		0			0
$199$	6.70820			0.475532			0.237766	−	0.971322i	$-0.423585\pi$
$199$	6.70820			0.475532			0.237766	+	0.971322i	$0.423585\pi$
$200$	−33.7525	−	7.17432i	−2.38666	−	0.507301i
$201$		0			0
$202$	24.4815	+	10.8999i	1.72251	+	0.766913i
$203$	−5.86889	+	1.24747i	−0.411915	+	0.0875552i
$204$		0			0
$205$	0.0152505	+	0.145099i	0.00106514	+	0.0101341i
$206$	−23.1803	−	16.8415i	−1.61505	−	1.17340i
$207$		0			0
$208$	2.32624			0.161296
$209$	−17.1620	+	9.07973i	−1.18712	+	0.628058i
$210$		0			0
$211$	2.42094	−	2.68872i	0.166664	−	0.185099i	−0.654027	−	0.756471i	$-0.726922\pi$
$211$	2.42094	−	2.68872i	0.166664	−	0.185099i	0.820691	+	0.571372i	$0.193589\pi$
$212$	0.193806	−	1.84395i	0.0133107	−	0.126643i
$213$		0			0
$214$	20.0970	+	22.3199i	1.37380	+	1.52576i
$215$	1.28115	−	3.94298i	0.0873739	−	0.268909i
$216$		0			0
$217$	−4.92705	−	3.57971i	−0.334470	−	0.243007i
$218$	−30.7299	−	6.53184i	−2.08129	−	0.442392i
$219$		0			0
$220$	6.14195	−	7.82792i	0.414090	−	0.527759i
$221$	0.135255	+	0.234268i	0.00909823	+	0.0157586i
$222$		0			0
$223$	6.55957	−	2.92051i	0.439261	−	0.195572i	−0.175177	−	0.984537i	$-0.556050\pi$
$223$	6.55957	−	2.92051i	0.439261	−	0.195572i	0.614438	+	0.788965i	$0.289383\pi$
$224$	−8.78115	+	6.37988i	−0.586715	+	0.426274i
$225$		0			0
$226$	−10.8992	+	33.5442i	−0.725003	+	2.23133i
$227$	−1.37772	−	13.1081i	−0.0914425	−	0.870018i	−0.940060	−	0.341010i	$-0.889231\pi$
$227$	−1.37772	−	13.1081i	−0.0914425	−	0.870018i	0.848617	−	0.529008i	$-0.177436\pi$
$228$		0			0
$229$	0.315921	−	0.350865i	0.0208766	−	0.0231858i	−0.732616	−	0.680642i	$-0.761701\pi$
$229$	0.315921	−	0.350865i	0.0208766	−	0.0231858i	0.753493	+	0.657456i	$0.228368\pi$
$230$	−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	$-0.143362\pi$
$233$	−1.28115	−	3.94298i	−0.0839311	−	0.258313i	−0.984211	+	0.176997i	$0.943362\pi$
$234$		0			0
$235$	−5.04508	+	3.66547i	−0.329105	+	0.239109i
$236$	23.9768	+	26.6290i	1.56076	+	1.73340i
$237$		0			0
$238$	−2.74064	−	1.22021i	−0.177649	−	0.0790945i
$239$	−0.0399263	+	0.379874i	−0.00258262	+	0.0245720i	−0.995737	−	0.0922345i	$-0.970599\pi$
$239$	−0.0399263	+	0.379874i	−0.00258262	+	0.0245720i	0.993155	+	0.116806i	$0.0372657\pi$
$240$		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
$245$	3.38761	−	1.50826i	0.216427	−	0.0963594i
$246$		0			0
$247$	−1.35177	+	0.287327i	−0.0860109	+	0.0182822i
$248$	−44.5121	+	9.46135i	−2.82652	+	0.600796i
$249$		0			0
$250$	−14.2169	+	6.32976i	−0.899154	+	0.400329i
$251$	−6.79180	−	20.9030i	−0.428694	−	1.31939i	−0.899412	−	0.437102i	$-0.856005\pi$
$251$	−6.79180	−	20.9030i	−0.428694	−	1.31939i	0.470718	−	0.882284i	$-0.343995\pi$
$252$		0			0
$253$	−0.781153	+	0.0530006i	−0.0491107	+	0.00333212i
$254$	10.0902	−	17.4767i	0.633114	−	1.09658i
$255$		0			0
$256$	1.52218	−	14.4825i	0.0951360	−	0.905158i
$257$	27.1713	+	12.0974i	1.69490	+	0.754617i	0.999347	+	0.0361387i	$0.0115058\pi$
$257$	27.1713	+	12.0974i	1.69490	+	0.754617i	0.695550	+	0.718478i	$0.255161\pi$
$258$		0			0
$259$	4.17274	+	4.63430i	0.259282	+	0.287961i
$260$	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	$-0.677295\pi$
$263$	7.63525	−	13.2246i	0.470810	−	0.815467i	0.999443	+	0.0333839i	$0.0106284\pi$
$264$		0			0
$265$	−0.118034	−	0.204441i	−0.00725077	−	0.0125587i
$266$	10.2553	−	11.3896i	0.628790	−	0.698342i
$267$		0			0
$268$	−0.940756	−	8.95070i	−0.0574658	−	0.546751i
$269$	−7.85410	+	24.1724i	−0.478873	+	1.47382i	0.361789	+	0.932260i	$0.382166\pi$
$269$	−7.85410	+	24.1724i	−0.478873	+	1.47382i	−0.840662	+	0.541560i	$0.817834\pi$
$270$		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	$0.491310\pi$
$272$	−10.3156	+	4.59279i	−0.625473	+	0.278479i
$273$		0			0
$274$	12.7812	+	22.1376i	0.772138	+	1.33738i
$275$	−0.566182	+	15.3058i	−0.0341421	+	0.922976i
$276$		0			0
$277$	28.5764	+	6.07409i	1.71699	+	0.364957i	0.958138	−	0.286308i	$-0.0924282\pi$
$277$	28.5764	+	6.07409i	1.71699	+	0.364957i	0.758850	+	0.651265i	$0.225762\pi$
$278$	30.8435	+	22.4091i	1.84987	+	1.34401i
$279$		0			0
$280$	−1.42705	+	4.39201i	−0.0852826	+	0.262473i
$281$	16.5703	+	18.4032i	0.988502	+	1.09784i	0.995200	+	0.0978646i	$0.0312012\pi$
$281$	16.5703	+	18.4032i	0.988502	+	1.09784i	−0.00669823	+	0.999978i	$0.502132\pi$
$282$		0			0
$283$	0.596670	−	5.67693i	0.0354683	−	0.337459i	−0.962370	−	0.271742i	$-0.912400\pi$
$283$	0.596670	−	5.67693i	0.0354683	−	0.337459i	0.997838	−	0.0657162i	$-0.0209332\pi$
$284$	33.5399	−	37.2498i	1.99023	−	2.21037i
$285$		0			0
$286$	−0.351767	−	2.01938i	−0.0208004	−	0.119408i
$287$	−0.236068			−0.0139347
$288$		0			0
$289$	12.6910	+	9.22054i	0.746528	+	0.542385i
$290$	1.01478	+	9.65502i	0.0595901	+	0.566962i
$291$		0			0
$292$	27.1027	−	5.76086i	1.58607	−	0.337129i
$293$	−19.7805	−	8.80686i	−1.15559	−	0.514502i	−0.262745	−	0.964865i	$-0.584628\pi$
$293$	−19.7805	−	8.80686i	−1.15559	−	0.514502i	−0.892845	+	0.450363i	$0.851294\pi$
$294$		0			0
$295$	4.46261	+	0.948557i	0.259823	+	0.0552271i
$296$	46.5967			2.70838
$297$		0			0
$298$	11.0902			0.642436
$299$	−0.0545103	−	0.0115865i	−0.00315241	−	0.000670066i
$300$		0			0
$301$	6.12825	+	2.72847i	0.353226	+	0.157267i
$302$	2.70353	−	0.574654i	0.155571	−	0.0330676i
$303$		0			0
$304$	−6.02992	−	57.3709i	−0.345840	−	3.29045i
$305$	−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	$0.205672\pi$
$308$	11.5577	+	11.2074i	0.658559	+	0.638600i
$309$		0			0
$310$	−6.59368	+	7.32302i	−0.374496	+	0.415920i
$311$	−1.21802	+	11.5886i	−0.0690673	+	0.657132i	0.904145	+	0.427225i	$0.140509\pi$
$311$	−1.21802	+	11.5886i	−0.0690673	+	0.657132i	−0.973213	+	0.229907i	$0.926158\pi$
$312$		0			0
$313$	−1.69147	−	1.87857i	−0.0956076	−	0.106183i	0.693442	−	0.720512i	$-0.256093\pi$
$313$	−1.69147	−	1.87857i	−0.0956076	−	0.106183i	−0.789050	+	0.614329i	$0.789427\pi$
$314$	−12.7082	+	39.1118i	−0.717165	+	2.20721i
$315$		0			0
$316$	−43.1976	−	31.3849i	−2.43005	−	1.76554i
$317$	6.67063	+	1.41789i	0.374660	+	0.0796365i	0.391393	−	0.920224i	$-0.371993\pi$
$317$	6.67063	+	1.41789i	0.374660	+	0.0796365i	−0.0167331	+	0.999860i	$0.505327\pi$
$318$		0			0
$319$	18.6855	+	6.84477i	1.04619	+	0.383233i
$320$	2.69098	+	4.66092i	0.150431	+	0.260553i
$321$		0			0
$322$	0.564602	−	0.251377i	0.0314640	−	0.0140087i
$323$	5.42705	−	3.94298i	0.301969	−	0.219393i
$324$		0			0
$325$	−0.336881	+	1.03681i	−0.0186868	+	0.0575121i
$326$	−1.40822	−	13.3983i	−0.0779942	−	0.742065i
$327$		0			0
$328$	−1.18030	+	1.31086i	−0.0651712	+	0.0723800i
$329$	−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
$335$	−0.766755	−	0.851568i	−0.0418923	−	0.0465261i
$336$		0			0
$337$	−16.6086	−	7.39461i	−0.904726	−	0.402810i	−0.0989927	−	0.995088i	$-0.531562\pi$
$337$	−16.6086	−	7.39461i	−0.904726	−	0.402810i	−0.805734	+	0.592278i	$0.798229\pi$
$338$	−3.54232	+	33.7029i	−0.192677	+	1.83320i
$339$		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
$344$	45.7911	−	20.3875i	2.46889	−	1.09922i
$345$		0			0
$346$	−46.1830	+	9.81651i	−2.48281	+	0.527739i
$347$	1.49448	−	0.317661i	0.0802277	−	0.0170529i	−0.167623	−	0.985851i	$-0.553609\pi$
$347$	1.49448	−	0.317661i	0.0802277	−	0.0170529i	0.247851	+	0.968798i	$0.420276\pi$
$348$		0			0
$349$	11.6095	−	5.16889i	0.621443	−	0.276684i	−0.0717650	−	0.997422i	$-0.522863\pi$
$349$	11.6095	−	5.16889i	0.621443	−	0.276684i	0.693208	+	0.720737i	$0.256197\pi$
$350$	−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	$-0.729870\pi$
$353$	6.00000	−	10.3923i	0.319348	−	0.553127i	0.980352	+	0.197256i	$0.0632029\pi$
$354$		0			0
$355$	0.667097	−	6.34700i	0.0354058	−	0.336864i
$356$	−36.5224	−	16.2608i	−1.93568	−	0.861821i
$357$		0			0
$358$	14.9392	+	16.5916i	0.789560	+	0.876895i
$359$	7.85410	−	5.70634i	0.414524	−	0.301169i	−0.360907	−	0.932602i	$-0.617533\pi$
$359$	7.85410	−	5.70634i	0.414524	−	0.301169i	0.775431	+	0.631433i	$0.217533\pi$
$360$		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
$365$	2.36060	−	2.62171i	0.123560	−	0.137227i
$366$		0			0
$367$	−2.31488	−	22.0246i	−0.120836	−	1.14967i	−0.871982	−	0.489538i	$-0.837165\pi$
$367$	−2.31488	−	22.0246i	−0.120836	−	1.14967i	0.751146	−	0.660136i	$-0.229501\pi$
$368$	0.718847	−	2.21238i	0.0374725	−	0.115328i
$369$		0			0
$370$	8.16312	−	5.93085i	0.424380	−	0.308330i
$371$	0.348943	−	0.155360i	0.0181162	−	0.00806587i
$372$		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	$0.840656\pi$
$374$	5.54683	+	8.26031i	0.286820	+	0.427130i
$375$		0			0
$376$	−73.7476	−	15.6755i	−3.80324	−	0.808404i
$377$	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	$0.879258\pi$
$380$	−11.7515	−	13.0513i	−0.602838	−	0.669519i
$381$		0			0
$382$	−0.224307	+	2.13414i	−0.0114766	+	0.109192i
$383$	−8.50345	+	9.44404i	−0.434506	+	0.482568i	−0.920137	−	0.391596i	$-0.871923\pi$
$383$	−8.50345	+	9.44404i	−0.434506	+	0.482568i	0.485631	+	0.874164i	$0.338590\pi$
$384$		0			0
$385$	2.02924	+	0.289472i	0.103420	+	0.0147529i
$386$	8.23607			0.419205
$387$		0			0
$388$	−30.8435	−	22.4091i	−1.56584	−	1.13765i
$389$	3.84065	+	36.5414i	0.194729	+	1.85272i	0.459207	+	0.888329i	$0.348134\pi$
$389$	3.84065	+	36.5414i	0.194729	+	1.85272i	−0.264478	+	0.964392i	$0.585200\pi$
$390$		0			0
$391$	0.264599	−	0.0562422i	0.0133813	−	0.00284429i
$392$	40.9568	+	18.2351i	2.06863	+	0.921014i
$393$		0			0
$394$	33.3789	+	7.09491i	1.68161	+	0.357436i
$395$	−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	$0.655555\pi$
$398$	17.1785	+	3.65141i	0.861082	+	0.183029i
$399$		0			0
$400$	−41.5723	−	18.5092i	−2.07862	−	0.925460i
$401$	30.9945	−	6.58808i	1.54779	−	0.328993i	0.646741	−	0.762710i	$-0.276131\pi$
$401$	30.9945	−	6.58808i	1.54779	−	0.328993i	0.901049	+	0.433716i	$0.142798\pi$
$402$		0			0
$403$	0.150280	+	1.42982i	0.00748598	+	0.0712243i
$404$	40.1976	+	29.2052i	1.99990	+	1.45301i
$405$		0			0
$406$	−15.7082			−0.779585
$407$	−3.54939	−	20.3759i	−0.175937	−	1.00999i
$408$		0			0
$409$	−4.33070	+	4.80973i	−0.214140	+	0.237826i	−0.840639	−	0.541596i	$-0.817820\pi$
$409$	−4.33070	+	4.80973i	−0.214140	+	0.237826i	0.626500	+	0.779422i	$0.284487\pi$
$410$	−0.0399263	+	0.379874i	−0.00197182	+	0.0187606i
$411$		0			0
$412$	−35.5473	−	39.4793i	−1.75129	−	1.94500i
$413$	−2.28115	+	7.02067i	−0.112248	+	0.345464i
$414$		0			0
$415$	0.736068	+	0.534785i	0.0361322	+	0.0262515i
$416$	2.50631	+	0.532733i	0.122882	+	0.0261194i
$417$		0			0
$418$	−48.8911	+	13.9100i	−2.39134	+	0.680358i
$419$	−15.7254	−	27.2372i	−0.768237	−	1.33063i	−0.938518	−	0.345230i	$-0.887801\pi$
$419$	−15.7254	−	27.2372i	−0.768237	−	1.33063i	0.170281	−	0.985396i	$-0.445533\pi$
$420$		0			0
$421$	9.59824	−	4.27341i	0.467789	−	0.208273i	−0.159285	−	0.987233i	$-0.550919\pi$
$421$	9.59824	−	4.27341i	0.467789	−	0.208273i	0.627074	+	0.778959i	$0.284252\pi$
$422$	7.66312	−	5.56758i	0.373035	−	0.271026i
$423$		0			0
$424$	0.881966	−	2.71441i	0.0428321	−	0.131824i
$425$	−0.553143	−	5.26281i	−0.0268314	−	0.255284i
$426$		0			0
$427$	7.73669	−	8.59247i	0.374405	−	0.415819i
$428$	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	$-0.145460\pi$
$431$	−1.82624	−	5.62058i	−0.0879668	−	0.270734i	−0.985357	+	0.170504i	$0.945460\pi$
$432$		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	$0.977612\pi$
$434$	−10.6688	−	11.8489i	−0.512119	−	0.568766i
$435$		0			0
$436$	−53.2133	−	23.6921i	−2.54846	−	1.13465i
$437$	−0.144455	+	1.37440i	−0.00691021	+	0.0657463i
$438$		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
$443$	−28.8651	+	12.8516i	−1.37142	+	0.610596i	−0.954463	−	0.298330i	$-0.903570\pi$
$443$	−28.8651	+	12.8516i	−1.37142	+	0.610596i	−0.416958	+	0.908926i	$0.636904\pi$
$444$		0			0
$445$	−4.97894	+	1.05831i	−0.236024	+	0.0501685i
$446$	18.3876	−	3.90840i	0.870677	−	0.185068i
$447$		0			0
$448$	−7.95534	+	3.54195i	−0.375854	+	0.167341i
$449$	−2.79837	−	8.61251i	−0.132063	−	0.406449i	0.863058	−	0.505104i	$-0.168546\pi$
$449$	−2.79837	−	8.61251i	−0.132063	−	0.406449i	−0.995122	+	0.0986549i	$0.968546\pi$
$450$		0			0
$451$	0.663119	+	0.416272i	0.0312251	+	0.0196015i
$452$	−32.6976	+	56.6338i	−1.53796	+	2.66383i
$453$		0			0
$454$	3.60692	−	34.3175i	0.169281	−	1.61060i
$455$	0.133284	+	0.0593421i	0.00624847	+	0.00278200i
$456$		0			0
$457$	16.0449	+	17.8197i	0.750548	+	0.833568i	0.990543	−	0.137206i	$-0.0438122\pi$
$457$	16.0449	+	17.8197i	0.750548	+	0.833568i	−0.239994	+	0.970774i	$0.577146\pi$
$458$	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	$-0.902597\pi$
$461$	−4.63525	+	8.02850i	−0.215885	+	0.373924i	0.737661	+	0.675172i	$0.235930\pi$
$462$		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	$0.846129\pi$
$464$	−39.5621	+	43.9381i	−1.83662	+	2.03978i
$465$		0			0
$466$	−1.13456	−	10.7946i	−0.0525576	−	0.500052i
$467$	6.45492	−	19.8662i	0.298698	−	0.919297i	−0.683256	−	0.730179i	$-0.739437\pi$
$467$	6.45492	−	19.8662i	0.298698	−	0.919297i	0.981954	−	0.189119i	$-0.0605631\pi$
$468$		0			0
$469$	1.50000	−	1.08981i	0.0692636	−	0.0503229i
$470$	−14.9148	+	6.64048i	−0.687967	+	0.306302i
$471$		0			0
$472$	27.5795	+	47.7691i	1.26945	+	2.19875i
$473$	−12.4031	−	18.4706i	−0.570295	−	0.849279i
$474$		0			0
$475$	26.4437	+	5.62078i	1.21332	+	0.257899i
$476$	−4.50000	−	3.26944i	−0.206257	−	0.149855i
$477$		0			0
$478$	−0.309017	+	0.951057i	−0.0141341	+	0.0435003i
$479$	−18.9912	−	21.0919i	−0.867732	−	0.963714i	0.131888	−	0.991265i	$-0.457896\pi$
$479$	−18.9912	−	21.0919i	−0.867732	−	0.963714i	−0.999620	+	0.0275505i	$0.991229\pi$
$480$		0			0
$481$	0.153880	−	1.46407i	0.00701633	−	0.0667559i
$482$	−14.5256	+	16.1323i	−0.661624	+	0.734808i
$483$		0			0
$484$	−12.7031	−	51.8620i	−0.577412	−	2.35737i
$485$	−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	$0.607032\pi$
$488$	−9.03075	−	85.9218i	−0.408803	−	3.88950i
$489$		0			0
$490$	9.49606	−	2.01845i	0.428988	−	0.0911842i
$491$	−16.3614	−	7.28458i	−0.738382	−	0.328749i	0.00285189	−	0.999996i	$-0.499092\pi$
$491$	−16.3614	−	7.28458i	−0.738382	−	0.328749i	−0.741234	+	0.671247i	$0.765759\pi$
$492$		0			0
$493$	−6.72514	−	1.42947i	−0.302885	−	0.0643803i
$494$	−3.61803			−0.162783
$495$		0			0
$496$	−60.0132			−2.69467
$497$	10.1006	+	2.14695i	0.453073	+	0.0963037i
$498$		0			0
$499$	−16.5771	−	7.38060i	−0.742093	−	0.330401i	0.000630054	−	1.00000i	$-0.499799\pi$
$499$	−16.5771	−	7.38060i	−0.742093	−	0.330401i	−0.742723	+	0.669599i	$0.766466\pi$
$500$	−28.2236	+	5.99911i	−1.26220	+	0.268288i
$501$		0			0
$502$	−6.01467	−	57.2258i	−0.268448	−	2.55411i
$503$	−7.00000	−	5.08580i	−0.312115	−	0.226765i	0.420689	−	0.907205i	$-0.361788\pi$
$503$	−7.00000	−	5.08580i	−0.312115	−	0.226765i	−0.732803	+	0.680441i	$0.761788\pi$
$504$		0			0
$505$	6.32624			0.281514
$506$	−2.02924	−	0.289472i	−0.0902109	−	0.0128686i
$507$		0			0
$508$	25.0365	−	27.8058i	1.11081	−	1.23368i
$509$	−4.04971	+	38.5304i	−0.179500	+	1.70783i	0.420056	+	0.907498i	$0.362010\pi$
$509$	−4.04971	+	38.5304i	−0.179500	+	1.70783i	−0.599557	+	0.800332i	$0.704656\pi$
$510$		0			0
$511$	3.81953	+	4.24202i	0.168966	+	0.187656i
$512$	12.4549	−	38.3323i	0.550435	−	1.69406i
$513$		0			0
$514$	62.9959	+	45.7692i	2.77863	+	2.01879i
$515$	−6.61612	−	1.40630i	−0.291541	−	0.0619690i
$516$		0			0
$517$	−1.23708	+	33.4424i	−0.0544067	+	1.47080i
$518$	8.16312	+	14.1389i	0.358667	+	0.621229i
$519$		0			0
$520$	0.995920	−	0.443412i	0.0436740	−	0.0194449i
$521$	−7.23607	+	5.25731i	−0.317018	+	0.230327i	−0.734902	−	0.678173i	$-0.762772\pi$
$521$	−7.23607	+	5.25731i	−0.317018	+	0.230327i	0.417884	+	0.908500i	$0.362772\pi$
$522$		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	$-0.0308013\pi$
$524$	5.98640	+	56.9568i	0.261517	+	2.48817i
$525$		0			0
$526$	26.7510	−	29.7100i	1.16640	−	1.29542i
$527$	−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
$533$	0.0372894	+	0.0414140i	0.00161518	+	0.00179384i
$534$		0			0
$535$	6.47719	+	2.88383i	0.280033	+	0.124679i
$536$	1.44815	−	13.7782i	0.0625505	−	0.595128i
$537$		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	$0.951499\pi$
$542$	−44.5286	+	19.8254i	−1.91267	+	0.851575i
$543$		0			0
$544$	−12.1659	+	2.58594i	−0.521609	+	0.110871i
$545$	−7.25434	+	1.54196i	−0.310742	+	0.0660502i
$546$		0			0
$547$	−28.0848	+	12.5042i	−1.20082	+	0.534639i	−0.906963	−	0.421210i	$-0.861605\pi$
$547$	−28.0848	+	12.5042i	−1.20082	+	0.534639i	−0.293857	+	0.955850i	$0.594939\pi$
$548$	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
$553$	1.14981	−	10.9397i	0.0488950	−	0.465205i
$554$	69.8728	+	31.1094i	2.96861	+	1.32171i
$555$		0			0
$556$	47.2988	+	52.5306i	2.00592	+	2.22779i
$557$	−30.4443	+	22.1191i	−1.28997	+	0.937215i	−0.999805	−	0.0197634i	$-0.993709\pi$
$557$	−30.4443	+	22.1191i	−1.28997	+	0.937215i	−0.290161	+	0.956978i	$0.593709\pi$
$558$		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
$563$	27.1645	−	30.1693i	1.14485	−	1.27148i	0.187590	−	0.982247i	$-0.439932\pi$
$563$	27.1645	−	30.1693i	1.14485	−	1.27148i	0.957258	−	0.289235i	$-0.0934011\pi$
$564$		0			0
$565$	0.870329	+	8.28063i	0.0366150	+	0.348369i
$566$	4.61803	−	14.2128i	0.194110	−	0.597411i
$567$		0			0
$568$	62.4230	−	45.3530i	2.61921	−	1.90297i
$569$	31.2253	−	13.9024i	1.30903	−	0.582819i	0.370764	−	0.928727i	$-0.379096\pi$
$569$	31.2253	−	13.9024i	1.30903	−	0.582819i	0.938268	+	0.345908i	$0.112429\pi$
$570$		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	$0.772418\pi$
$572$	0.140490	−	3.79792i	0.00587417	−	0.158799i
$573$		0			0
$574$	−0.604528	−	0.128496i	−0.0252325	−	0.00536334i
$575$	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	$-0.129450\pi$
$578$	27.4804	+	30.5201i	1.14304	+	1.26947i
$579$		0			0
$580$	−1.88151	+	17.9014i	−0.0781255	+	0.743315i
$581$	−0.985051	+	1.09401i	−0.0408668	+	0.0453872i
$582$		0			0
$583$	−1.25414	−	0.178904i	−0.0519413	−	0.00740943i
$584$	42.6525			1.76497
$585$		0			0
$586$	−45.8607	−	33.3197i	−1.89449	−	1.37643i
$587$	0.222082	+	2.11297i	0.00916632	+	0.0872117i	0.998149	−	0.0608221i	$-0.0193722\pi$
$587$	0.222082	+	2.11297i	0.00916632	+	0.0872117i	−0.988982	+	0.148034i	$0.952706\pi$
$588$		0			0
$589$	34.8734	−	7.41257i	1.43693	−	0.305429i
$590$	10.9116	+	4.85817i	0.449225	+	0.200008i
$591$		0			0
$592$	60.1080	+	12.7764i	2.47042	+	0.525105i
$593$	−14.0344			−0.576325			−0.288163	−	0.957581i	$-0.593044\pi$
$593$	−14.0344			−0.576325			−0.288163	+	0.957581i	$0.593044\pi$
$594$		0			0
$595$	−0.708204			−0.0290335
$596$	20.1130	+	4.27514i	0.823859	+	0.175117i
$597$		0			0
$598$	−0.133284	−	0.0593421i	−0.00545041	−	0.00242668i
$599$	−12.3760	+	2.63060i	−0.505669	+	0.107483i	−0.453681	−	0.891164i	$-0.649889\pi$
$599$	−12.3760	+	2.63060i	−0.505669	+	0.107483i	−0.0519886	+	0.998648i	$0.516556\pi$
$600$		0			0
$601$	0.720049	+	6.85081i	0.0293714	+	0.279450i	0.999343	+	0.0362334i	$0.0115360\pi$
$601$	0.720049	+	6.85081i	0.0293714	+	0.279450i	−0.969972	+	0.243217i	$0.921797\pi$
$602$	14.2082	+	10.3229i	0.579083	+	0.420729i
$603$		0			0
$604$	5.12461			0.208517
$605$	−5.18974	−	4.39141i	−0.210993	−	0.178536i
$606$		0			0
$607$	−11.0823	+	12.3082i	−0.449819	+	0.499574i	−0.924817	−	0.380413i	$-0.875782\pi$
$607$	−11.0823	+	12.3082i	−0.449819	+	0.499574i	0.474998	+	0.879987i	$0.342449\pi$
$608$	6.64185	−	63.1929i	0.269362	−	2.56281i
$609$		0			0
$610$	−12.5182	−	13.9029i	−0.506848	−	0.562912i
$611$	−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	$0.606804\pi$
$614$	71.6486	+	15.2294i	2.89150	+	0.614607i
$615$		0			0
$616$	13.8156	+	20.5740i	0.556645	+	0.828952i
$617$	−5.59017	−	9.68246i	−0.225052	−	0.389801i	0.731283	−	0.682074i	$-0.238922\pi$
$617$	−5.59017	−	9.68246i	−0.225052	−	0.389801i	−0.956335	+	0.292273i	$0.905588\pi$
$618$		0			0
$619$	22.0389	−	9.81236i	0.885819	−	0.394392i	0.0871733	−	0.996193i	$-0.472217\pi$
$619$	22.0389	−	9.81236i	0.885819	−	0.394392i	0.798646	+	0.601801i	$0.205550\pi$
$620$	−14.7812	+	10.7391i	−0.593625	+	0.431294i
$621$		0			0
$622$	−9.42705	+	29.0135i	−0.377990	+	1.16333i
$623$	−0.860904	−	8.19095i	−0.0344914	−	0.328163i
$624$		0			0
$625$	12.9921	−	14.4292i	0.519685	−	0.577168i
$626$	−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	$0.424924\pi$
$632$	−54.9982	−	61.0817i	−2.18771	−	2.42970i
$633$		0			0
$634$	16.3105	+	7.26192i	0.647774	+	0.288408i
$635$	0.497966	−	4.73783i	0.0197612	−	0.188015i
$636$		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
$641$	−22.9210	+	10.2051i	−0.905325	+	0.403077i	−0.805957	−	0.591974i	$-0.798349\pi$
$641$	−22.9210	+	10.2051i	−0.905325	+	0.403077i	−0.0993683	+	0.995051i	$0.531682\pi$
$642$		0			0
$643$	−20.3984	+	4.33581i	−0.804434	+	0.170988i	−0.591738	−	0.806131i	$-0.701558\pi$
$643$	−20.3984	+	4.33581i	−0.804434	+	0.170988i	−0.212696	+	0.977118i	$0.568225\pi$
$644$	1.12086	−	0.238246i	0.0441680	−	0.00938819i
$645$		0			0
$646$	16.0440	−	7.14323i	0.631241	−	0.281047i
$647$	13.9164	+	42.8303i	0.547110	+	1.68383i	0.715918	+	0.698184i	$0.246008\pi$
$647$	13.9164	+	42.8303i	0.547110	+	1.68383i	−0.168808	+	0.985649i	$0.553992\pi$
$648$		0			0
$649$	18.7877	−	15.6987i	0.737483	−	0.616227i
$650$	−1.42705	+	2.47172i	−0.0559735	+	0.0969490i
$651$		0			0
$652$	2.61099	−	24.8419i	0.102254	−	0.972883i
$653$	−5.13233	−	2.28506i	−0.200844	−	0.0894213i	0.303850	−	0.952720i	$-0.401728\pi$
$653$	−5.13233	−	2.28506i	−0.200844	−	0.0894213i	−0.504694	+	0.863299i	$0.668395\pi$
$654$		0			0
$655$	4.87916	+	5.41886i	0.190645	+	0.211732i
$656$	−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	$-0.537638\pi$
$659$	20.5623	−	35.6150i	0.800994	−	1.38736i	0.918963	−	0.394345i	$-0.129028\pi$
$660$		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	$-0.418449\pi$
$662$	−29.2695	+	32.5071i	−1.13759	+	1.26343i
$663$		0			0
$664$	1.14981	+	10.9397i	0.0446214	+	0.424544i
$665$	1.11803	−	3.44095i	0.0433555	−	0.133435i
$666$		0			0
$667$	1.14590	−	0.832544i	0.0443693	−	0.0322362i
$668$	53.3660	−	23.7601i	2.06479	−	0.919306i
$669$		0			0
$670$	−1.50000	−	2.59808i	−0.0579501	−	0.100372i
$671$	−36.8841	+	10.4938i	−1.42389	+	0.405110i
$672$		0			0
$673$	−35.0498	−	7.45006i	−1.35107	−	0.287179i	−0.525171	−	0.850997i	$-0.675999\pi$
$673$	−35.0498	−	7.45006i	−1.35107	−	0.287179i	−0.825899	+	0.563818i	$0.809332\pi$
$674$	−38.5066	−	27.9767i	−1.48322	−	1.07762i
$675$		0			0
$676$	−19.4164	+	59.7576i	−0.746785	+	2.29837i
$677$	9.05191	+	10.0532i	0.347893	+	0.386374i	0.891542	−	0.452938i	$-0.149624\pi$
$677$	9.05191	+	10.0532i	0.347893	+	0.386374i	−0.543649	+	0.839313i	$0.682958\pi$
$678$		0			0
$679$	0.820977	−	7.81108i	0.0315062	−	0.299762i
$680$	−3.54090	+	3.93257i	−0.135787	+	0.150807i
$681$		0			0
$682$	9.07501	+	52.0967i	0.347500	+	1.99488i
$683$	9.06888			0.347011			0.173506	−	0.984833i	$-0.444491\pi$
$683$	9.06888			0.347011			0.173506	+	0.984833i	$0.444491\pi$
$684$		0			0
$685$	4.88197	+	3.54696i	0.186530	+	0.135522i
$686$	3.55757	+	33.8480i	0.135829	+	1.29232i
$687$		0			0
$688$	64.6588	−	13.7437i	2.46509	−	0.523972i
$689$	−0.0823743	−	0.0366754i	−0.00313821	−	0.00139722i
$690$		0			0
$691$	−1.31808	−	0.280166i	−0.0501420	−	0.0106580i	0.182772	−	0.983155i	$-0.441493\pi$
$691$	−1.31808	−	0.280166i	−0.0501420	−	0.0106580i	−0.232914	+	0.972497i	$0.574826\pi$
$692$	−87.5410			−3.32781
$693$		0			0
$694$	4.00000			0.151838
$695$	8.80333	+	1.87121i	0.333929	+	0.0709789i
$696$		0			0
$697$	−0.247123	−	0.110026i	−0.00936045	−	0.00416754i
$698$	32.5435	−	6.91733i	1.23179	−	0.261825i
$699$		0			0
$700$	−2.34315	−	22.2936i	−0.0885628	−	0.842619i
$701$	28.1525	+	20.4540i	1.06330	+	0.772536i	0.974697	−	0.223531i	$-0.0717583\pi$
$701$	28.1525	+	20.4540i	1.06330	+	0.772536i	0.0886075	+	0.996067i	$0.471758\pi$
$702$		0			0
$703$	−36.5066			−1.37687
$704$	28.5924	+	4.07871i	1.07762	+	0.153722i
$705$		0			0
$706$	21.0217	−	23.3469i	0.791161	−	0.878674i
$707$	−1.06996	+	10.1800i	−0.0402400	+	0.382858i
$708$		0			0
$709$	7.50415	+	8.33421i	0.281824	+	0.312998i	0.867392	−	0.497626i	$-0.165795\pi$
$709$	7.50415	+	8.33421i	0.281824	+	0.312998i	−0.585567	+	0.810624i	$0.699128\pi$
$710$	5.16312	−	15.8904i	0.193768	−	0.596358i
$711$		0			0
$712$	−49.7877	−	36.1729i	−1.86587	−	1.35564i
$713$	1.40628	+	0.298913i	0.0526655	+	0.0111944i
$714$		0			0
$715$	−0.269757	−	0.401721i	−0.0100883	−	0.0150235i
$716$	20.6976	+	35.8492i	0.773504	+	1.33975i
$717$		0			0
$718$	23.2190	−	10.3378i	0.866527	−	0.385803i
$719$	31.1353	−	22.6211i	1.16115	−	0.843624i	0.171226	−	0.985232i	$-0.445227\pi$
$719$	31.1353	−	22.6211i	1.16115	−	0.843624i	0.989923	+	0.141608i	$0.0452271\pi$
$720$		0			0
$721$	3.38197	−	10.4086i	0.125951	−	0.387637i
$722$	4.17891	+	39.7597i	0.155523	+	1.47970i
$723$		0			0
$724$	8.21057	−	9.11877i	0.305144	−	0.338896i
$725$	−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
$731$	5.14355	+	5.71249i	0.190241	+	0.211284i
$732$		0			0
$733$	−0.368389	−	0.164017i	−0.0136068	−	0.00605812i	0.399922	−	0.916549i	$-0.369037\pi$
$733$	−0.368389	−	0.164017i	−0.0136068	−	0.00605812i	−0.413529	+	0.910491i	$0.635704\pi$
$734$	6.06043	−	57.6611i	0.223694	−	2.12831i
$735$		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	$0.882427\pi$
$740$	17.0908	−	7.60931i	0.628270	−	0.279724i
$741$		0			0
$742$	0.978148	−	0.207912i	0.0359089	−	0.00763268i
$743$	41.9513	−	8.91703i	1.53904	−	0.327134i	0.641175	−	0.767395i	$-0.278447\pi$
$743$	41.9513	−	8.91703i	1.53904	−	0.327134i	0.897870	+	0.440261i	$0.145114\pi$
$744$		0			0
$745$	2.39169	−	1.06485i	0.0876249	−	0.0390131i
$746$	−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
$751$	−1.68771	+	16.0574i	−0.0615853	+	0.585945i	0.919597	+	0.392862i	$0.128515\pi$
$751$	−1.68771	+	16.0574i	−0.0615853	+	0.585945i	−0.981183	+	0.193082i	$0.938152\pi$
$752$	−90.8334	−	40.4416i	−3.31235	−	1.47476i
$753$		0			0
$754$	2.48127	+	2.75573i	0.0903626	+	0.100358i
$755$	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
$761$	19.6000	−	21.7680i	0.710501	−	0.789091i	−0.274510	−	0.961584i	$-0.588516\pi$
$761$	19.6000	−	21.7680i	0.710501	−	0.789091i	0.985011	+	0.172493i	$0.0551823\pi$
$762$		0			0
$763$	−1.25434	−	11.9343i	−0.0454102	−	0.432049i
$764$	−1.22949	+	3.78398i	−0.0444814	+	0.136900i
$765$		0			0
$766$	−26.9164	+	19.5559i	−0.972529	+	0.706584i
$767$	1.59199	−	0.708798i	0.0574833	−	0.0255932i
$768$		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	$0.619585\pi$
$770$	5.03897	+	1.84584i	0.181592	+	0.0665196i
$771$		0			0
$772$	14.9368	+	3.17492i	0.537588	+	0.114268i
$773$	−21.9894	−	15.9762i	−0.790902	−	0.574624i	0.117329	−	0.993093i	$-0.462567\pi$
$773$	−21.9894	−	15.9762i	−0.790902	−	0.574624i	−0.908231	+	0.418469i	$0.862567\pi$
$774$		0			0
$775$	8.69098	−	26.7481i	0.312189	−	0.960820i
$776$	−39.2692	−	43.6129i	−1.40968	−	1.56561i
$777$		0			0
$778$	−10.0550	+	95.6665i	−0.360488	+	3.42981i
$779$	0.924716	−	1.02700i	0.0331314	−	0.0367961i
$780$		0			0
$781$	−24.5869	−	23.8417i	−0.879788	−	0.853124i
$782$	0.708204			0.0253253
$783$		0			0
$784$	47.8328	+	34.7526i	1.70831	+	1.24116i
$785$	1.01478	+	9.65502i	0.0362192	+	0.344602i
$786$		0			0
$787$	9.49606	−	2.01845i	0.338498	−	0.0719499i	−0.0355267	−	0.999369i	$-0.511311\pi$
$787$	9.49606	−	2.01845i	0.338498	−	0.0719499i	0.374025	+	0.927419i	$0.377978\pi$
$788$	57.8005	+	25.7344i	2.05906	+	0.916751i
$789$		0			0
$790$	−17.4094	−	3.70049i	−0.619400	−	0.131658i
$791$	−13.4721			−0.479014
$792$		0			0
$793$	−2.72949			−0.0969270
$794$	−47.9084	−	10.1832i	−1.70021	−	0.361390i
$795$		0			0
$796$	29.7471	+	13.2443i	1.05436	+	0.469431i
$797$	−18.1359	+	3.85489i	−0.642405	+	0.136547i	−0.517585	−	0.855632i	$-0.673169\pi$
$797$	−18.1359	+	3.85489i	−0.642405	+	0.136547i	−0.124820	+	0.992179i	$0.539835\pi$
$798$		0			0
$799$	−1.20859	−	11.4990i	−0.0427568	−	0.406804i
$800$	−40.5517	−	29.4625i	−1.43372	−	1.04166i
$801$		0			0
$802$	82.9574			2.92933
$803$	−3.24894	−	18.6511i	−0.114653	−	0.658183i
$804$		0			0
$805$	0.0976248	−	0.108423i	0.00344082	−	0.00382142i
$806$	−0.393438	+	3.74331i	−0.0138583	+	0.131853i
$807$		0			0
$808$	51.1786	+	56.8396i	1.80046	+	1.99961i
$809$	8.37132	−	25.7643i	0.294320	−	0.905824i	−0.689129	−	0.724639i	$-0.742007\pi$
$809$	8.37132	−	25.7643i	0.294320	−	0.905824i	0.983449	−	0.181185i	$-0.0579933\pi$
$810$		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	$0.921869\pi$
$812$	−28.4882	−	6.05535i	−0.999739	−	0.212501i
$813$		0			0
$814$	2.00164	−	54.1110i	0.0701573	−	1.89659i
$815$	−1.59017	−	2.75426i	−0.0557012	−	0.0964773i
$816$		0			0
$817$	−35.8754	+	15.9728i	−1.25512	+	0.558816i
$818$	−13.7082	+	9.95959i	−0.479296	+	0.348229i
$819$		0			0
$820$	−0.218847	+	0.673542i	−0.00764247	+	0.0235211i
$821$	−4.24352	−	40.3744i	−0.148100	−	1.40907i	−0.775976	−	0.630762i	$-0.782742\pi$
$821$	−4.24352	−	40.3744i	−0.148100	−	1.40907i	0.627877	−	0.778313i	$-0.283924\pi$
$822$		0			0
$823$	−18.6238	+	20.6838i	−0.649184	+	0.720992i	−0.974444	−	0.224633i	$-0.927882\pi$
$823$	−18.6238	+	20.6838i	−0.649184	+	0.720992i	0.325259	+	0.945625i	$0.394548\pi$
$824$	−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	$-0.159297\pi$
$827$	−3.29180	−	10.1311i	−0.114467	−	0.352293i	−0.991835	+	0.127524i	$0.959297\pi$
$828$		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	$0.116454\pi$
$830$	1.59385	+	1.77015i	0.0553232	+	0.0614427i
$831$		0			0
$832$	1.87800	+	0.836140i	0.0651080	+	0.0289879i
$833$	−0.718674	+	6.83772i	−0.0249006	+	0.236913i
$834$		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
$839$	−16.2911	+	7.25326i	−0.562431	+	0.250410i	−0.668202	−	0.743980i	$-0.732936\pi$
$839$	−16.2911	+	7.25326i	−0.562431	+	0.250410i	0.105771	+	0.994391i	$0.466269\pi$
$840$		0			0
$841$	−6.84703	+	1.45538i	−0.236105	+	0.0501856i
$842$	26.9055	−	5.71894i	0.927225	−	0.197088i
$843$		0			0
$844$	16.0440	−	7.14323i	0.552256	−	0.245880i
$845$	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
$850$	1.44815	−	13.7782i	0.0496711	−	0.472589i
$851$	−1.34486	−	0.598772i	−0.0461013	−	0.0205256i
$852$		0			0
$853$	−37.3594	−	41.4919i	−1.27916	−	1.42065i	−0.857984	−	0.513677i	$-0.828283\pi$
$853$	−37.3594	−	41.4919i	−1.27916	−	1.42065i	−0.421180	−	0.906977i	$-0.638384\pi$
$854$	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	$-0.990596\pi$
$857$	−13.8820	+	24.0443i	−0.474199	+	0.821337i	0.525365	+	0.850877i	$0.323929\pi$
$858$		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	$0.633589\pi$
$860$	13.4660	−	14.9555i	0.459187	−	0.509978i
$861$		0			0
$862$	−1.61728	−	15.3874i	−0.0550847	−	0.524096i
$863$	0.0344419	−	0.106001i	0.00117241	−	0.00360832i	−0.950469	−	0.310821i	$-0.899396\pi$
$863$	0.0344419	−	0.106001i	0.00117241	−	0.00360832i	0.951641	+	0.307212i	$0.0993962\pi$
$864$		0			0
$865$	−9.01722	+	6.55139i	−0.306595	+	0.222754i
$866$	−84.4386	+	37.5945i	−2.86934	+	1.27751i
$867$		0			0
$868$	−14.7812	−	25.6017i	−0.501705	−	0.868979i
$869$	−22.5205	+	28.7024i	−0.763956	+	0.973662i
$870$		0			0
$871$	−0.428129	−	0.0910017i	−0.0145066	−	0.00308348i
$872$	−72.5410	−	52.7041i	−2.45655	−	1.78479i
$873$		0			0
$874$	−1.11803	+	3.44095i	−0.0378181	+	0.116392i
$875$	−3.97749	−	4.41745i	−0.134464	−	0.149337i
$876$		0			0
$877$	6.05683	−	57.6268i	0.204524	−	1.94592i	−0.103704	−	0.994608i	$-0.533070\pi$
$877$	6.05683	−	57.6268i	0.204524	−	1.94592i	0.308229	−	0.951312i	$-0.400264\pi$
$878$	−40.8027	+	45.3160i	−1.37703	+	1.52934i
$879$		0			0
$880$	17.8541	−	9.44587i	0.601860	−	0.318420i
$881$	6.20163			0.208938			0.104469	−	0.994528i	$-0.466686\pi$
$881$	6.20163			0.208938			0.104469	+	0.994528i	$0.466686\pi$
$882$		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	$0.705655\pi$
$884$	0.137254	+	1.30589i	0.00461637	+	0.0439218i
$885$		0			0
$886$	−80.9137	+	17.1987i	−2.71835	+	0.577803i
$887$	−49.7748	−	22.1612i	−1.67127	−	0.744099i	−0.999996	−	0.00289349i	$-0.999079\pi$
$887$	−49.7748	−	22.1612i	−1.67127	−	0.744099i	−0.671278	−	0.741206i	$-0.734254\pi$
$888$		0			0
$889$	7.53976	+	1.60263i	0.252875	+	0.0537503i
$890$	−13.3262			−0.446697
$891$		0			0
$892$	34.8541			1.16700
$893$	57.7781	+	12.2811i	1.93347	+	0.410972i
$894$		0			0
$895$	4.81485	+	2.14371i	0.160943	+	0.0716563i
$896$	−1.06635	+	0.226659i	−0.0356242	+	0.00757215i
$897$		0			0
$898$	−2.47818	−	23.5783i	−0.0826980	−	0.786819i
$899$	−29.5623	−	21.4783i	−0.985958	−	0.716340i
$900$		0			0
$901$	0.437694			0.0145817
$902$	1.47155	+	1.42695i	0.0489971	+	0.0475122i
$903$		0			0
$904$	−67.3585	+	74.8091i	−2.24031	+	2.48812i
$905$	0.163305	−	1.55375i	0.00542846	−	0.0516483i
$906$		0			0
$907$	−28.3679	−	31.5057i	−0.941940	−	1.04613i	−0.998859	−	0.0477513i	$-0.984794\pi$
$907$	−28.3679	−	31.5057i	−0.941940	−	1.04613i	0.0569195	−	0.998379i	$-0.481872\pi$
$908$	19.7705	−	60.8474i	0.656107	−	2.01929i
$909$		0			0
$910$	0.309017	+	0.224514i	0.0102438	+	0.00744257i
$911$	−37.7533	−	8.02472i	−1.25082	−	0.265871i	−0.465551	−	0.885021i	$-0.654144\pi$
$911$	−37.7533	−	8.02472i	−1.25082	−	0.265871i	−0.785272	+	0.619150i	$0.787477\pi$
$912$		0			0
$913$	4.69615	−	1.33610i	0.155420	−	0.0442184i
$914$	31.3885	+	54.3666i	1.03824	+	1.79829i
$915$		0			0
$916$	2.09366	−	0.932157i	0.0691765	−	0.0307993i
$917$	−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	$-0.0390576\pi$
$920$	−0.113954	−	1.08420i	−0.00375695	−	0.0357449i
$921$		0			0
$922$	−16.2401	+	18.0365i	−0.534841	+	0.594001i
$923$	−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
$929$	−8.50345	−	9.44404i	−0.278989	−	0.309849i	0.587322	−	0.809353i	$-0.300182\pi$
$929$	−8.50345	−	9.44404i	−0.278989	−	0.309849i	−0.866311	+	0.499504i	$0.833515\pi$
$930$		0			0
$931$	−32.0879	−	14.2865i	−1.05164	−	0.468220i
$932$	2.10359	−	20.0144i	0.0689055	−	0.655592i
$933$		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	$0.661822\pi$
$938$	4.43444	−	1.97434i	0.144790	−	0.0644645i
$939$		0			0
$940$	−29.6090	+	6.29359i	−0.965740	+	0.205274i
$941$	14.1351	−	3.00450i	0.460790	−	0.0979439i	0.0283330	−	0.999599i	$-0.490980\pi$
$941$	14.1351	−	3.00450i	0.460790	−	0.0979439i	0.432457	+	0.901655i	$0.357647\pi$
$942$		0			0
$943$	0.0509101	−	0.0226667i	0.00165786	−	0.000738128i
$944$	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	$-0.656894\pi$
$947$	16.1976	−	28.0550i	0.526350	−	0.911665i	0.999529	−	0.0306985i	$-0.00977316\pi$
$948$		0			0
$949$	0.140855	−	1.34014i	0.00457233	−	0.0435029i
$950$	64.6581	+	28.7876i	2.09779	+	0.933994i
$951$		0			0
$952$	−5.72930	−	6.36303i	−0.185688	−	0.206227i
$953$	−9.18034	+	6.66991i	−0.297380	+	0.216059i	−0.726463	−	0.687206i	$-0.758837\pi$
$953$	−9.18034	+	6.66991i	−0.297380	+	0.216059i	0.429082	+	0.903265i	$0.358837\pi$
$954$		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
$959$	−6.53335	+	7.25602i	−0.210973	+	0.234309i
$960$		0			0
$961$	−0.636596	−	6.05681i	−0.0205354	−	0.195381i
$962$	1.19098	−	3.66547i	0.0383988	−	0.118179i
$963$		0			0
$964$	−32.5623	+	23.6579i	−1.04876	+	0.761970i
$965$	1.77618	−	0.790807i	0.0571773	−	0.0254570i
$966$		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	$-0.416274\pi$
$968$	−2.52877	−	82.1546i	−0.0812777	−	2.64055i
$969$		0			0
$970$	−12.4305	−	2.64218i	−0.399119	−	0.0848354i
$971$	33.9787	+	24.6870i	1.09043	+	0.792243i	0.979472	−	0.201582i	$-0.0646083\pi$
$971$	33.9787	+	24.6870i	1.09043	+	0.792243i	0.110957	+	0.993825i	$0.464608\pi$
$972$		0			0
$973$	−4.50000	+	13.8496i	−0.144263	+	0.443997i
$974$	22.2623	+	24.7248i	0.713331	+	0.792234i
$975$		0			0
$976$	11.9096	−	113.312i	0.381216	−	3.62703i
$977$	−0.399302	+	0.443470i	−0.0127748	+	0.0141879i	−0.749498	−	0.662006i	$-0.769705\pi$
$977$	−0.399302	+	0.443470i	−0.0127748	+	0.0141879i	0.736724	+	0.676194i	$0.236372\pi$
$978$		0			0
$979$	−12.0253	+	24.5266i	−0.384329	+	0.783873i
$980$	18.0000			0.574989
$981$		0			0
$982$	−37.9336	−	27.5604i	−1.21051	−	0.879488i
$983$	0.847878	+	8.06702i	0.0270431	+	0.257298i	0.999687	+	0.0249988i	$0.00795819\pi$
$983$	0.847878	+	8.06702i	0.0270431	+	0.257298i	−0.972644	+	0.232299i	$0.925375\pi$
$984$		0			0
$985$	7.87969	−	1.67488i	0.251068	−	0.0533661i
$986$	−16.4438	−	7.32126i	−0.523678	−	0.233156i
$987$		0			0
$988$	−6.56161	−	1.39471i	−0.208753	−	0.0443718i
$989$	−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	$0.481067\pi$
$992$	−64.6588	−	13.7437i	−2.05292	−	0.436361i
$993$		0			0
$994$	24.6972	+	10.9959i	0.783347	+	0.348769i
$995$	4.05530	−	0.861981i	0.128562	−	0.0273266i
$996$		0			0
$997$	2.21617	+	21.0855i	0.0701869	+	0.667784i	0.971891	+	0.235431i	$0.0756500\pi$
$997$	2.21617	+	21.0855i	0.0701869	+	0.667784i	−0.901704	+	0.432353i	$0.857683\pi$
$998$	−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.c.379.1		8
3.2	odd	2		891.2.n.b.379.1		8
9.2	odd	6		99.2.f.a.82.1		4
9.4	even	3	inner	891.2.n.c.676.1		8
9.5	odd	6		891.2.n.b.676.1		8
9.7	even	3		33.2.e.b.16.1	✓	4
11.9	even	5	inner	891.2.n.c.460.1		8
33.20	odd	10		891.2.n.b.460.1		8
36.7	odd	6		528.2.y.b.49.1		4
45.7	odd	12		825.2.bx.d.49.2		8
45.34	even	6		825.2.n.c.676.1		4
45.43	odd	12		825.2.bx.d.49.1		8
99.7	odd	30		363.2.e.b.124.1		4
99.16	even	15		363.2.e.k.202.1		4
99.20	odd	30		99.2.f.a.64.1		4
99.25	even	15		363.2.a.d.1.1		2
99.31	even	15	inner	891.2.n.c.757.1		8
99.43	odd	6		363.2.e.f.148.1		4
99.47	odd	30		1089.2.a.t.1.2		2
99.52	odd	30		363.2.a.i.1.2		2
99.61	odd	30		363.2.e.b.202.1		4
99.70	even	15		363.2.e.k.124.1		4
99.74	even	30		1089.2.a.l.1.1		2
99.79	odd	30		363.2.e.f.130.1		4
99.86	odd	30		891.2.n.b.757.1		8
99.97	even	15		33.2.e.b.31.1	yes	4
396.151	even	30		5808.2.a.ci.1.1		2
396.223	odd	30		5808.2.a.cj.1.1		2
396.295	odd	30		528.2.y.b.97.1		4
495.97	odd	60		825.2.bx.d.724.1		8
495.124	even	30		9075.2.a.cb.1.2		2
495.349	odd	30		9075.2.a.u.1.1		2
495.394	even	30		825.2.n.c.526.1		4
495.493	odd	60		825.2.bx.d.724.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	9.7	even	3
33.2.e.b.31.1	yes	4	99.97	even	15
99.2.f.a.64.1		4	99.20	odd	30
99.2.f.a.82.1		4	9.2	odd	6
363.2.a.d.1.1		2	99.25	even	15
363.2.a.i.1.2		2	99.52	odd	30
363.2.e.b.124.1		4	99.7	odd	30
363.2.e.b.202.1		4	99.61	odd	30
363.2.e.f.130.1		4	99.79	odd	30
363.2.e.f.148.1		4	99.43	odd	6
363.2.e.k.124.1		4	99.70	even	15
363.2.e.k.202.1		4	99.16	even	15
528.2.y.b.49.1		4	36.7	odd	6
528.2.y.b.97.1		4	396.295	odd	30
825.2.n.c.526.1		4	495.394	even	30
825.2.n.c.676.1		4	45.34	even	6
825.2.bx.d.49.1		8	45.43	odd	12
825.2.bx.d.49.2		8	45.7	odd	12
825.2.bx.d.724.1		8	495.97	odd	60
825.2.bx.d.724.2		8	495.493	odd	60
891.2.n.b.379.1		8	3.2	odd	2
891.2.n.b.460.1		8	33.20	odd	10
891.2.n.b.676.1		8	9.5	odd	6
891.2.n.b.757.1		8	99.86	odd	30
891.2.n.c.379.1		8	1.1	even	1	trivial
891.2.n.c.460.1		8	11.9	even	5	inner
891.2.n.c.676.1		8	9.4	even	3	inner
891.2.n.c.757.1		8	99.31	even	15	inner
1089.2.a.l.1.1		2	99.74	even	30
1089.2.a.t.1.2		2	99.47	odd	30
5808.2.a.ci.1.1		2	396.151	even	30
5808.2.a.cj.1.1		2	396.223	odd	30
9075.2.a.u.1.1		2	495.349	odd	30
9075.2.a.cb.1.2		2	495.124	even	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)

\(f(q)\)	\(=\)	\(q+(2.56082 + 0.544320i) q^{2} +(4.43444 + 1.97434i) q^{4} +(0.604528 - 0.128496i) q^{5} +(0.104528 + 0.994522i) q^{7} +(6.04508 + 4.39201i) q^{8} +1.61803 q^{10} +(1.46007 - 2.97795i) q^{11} +(0.157960 - 0.175433i) q^{13} +(-0.273659 + 2.60369i) q^{14} +(6.59368 + 7.32302i) q^{16} +(-0.354102 + 1.08981i) q^{17} +(-4.73607 - 3.44095i) q^{19} +(2.93444 + 0.623735i) q^{20} +(5.35995 - 6.83126i) q^{22} +(-0.118034 - 0.204441i) q^{23} +(-4.21878 + 1.87832i) q^{25} +(0.500000 - 0.363271i) q^{26} +(-1.50000 + 4.61653i) q^{28} +(0.627171 + 5.96713i) q^{29} +(-4.07512 + 4.52588i) q^{31} +(5.42705 + 9.39993i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(0.190983 + 0.587785i) q^{35} +(5.04508 - 3.66547i) q^{37} +(-10.2553 - 11.3896i) q^{38} +(4.21878 + 1.87832i) q^{40} +(-0.0246758 + 0.234775i) q^{41} +(3.35410 - 5.80948i) q^{43} +(12.3541 - 10.3229i) q^{44} +(-0.190983 - 0.587785i) q^{46} +(-9.21783 + 4.10404i) q^{47} +(5.86889 - 1.24747i) q^{49} +(-11.8260 + 2.51369i) q^{50} +(1.04683 - 0.466079i) q^{52} +(-0.118034 - 0.363271i) q^{53} +(0.500000 - 1.98787i) q^{55} +(-3.73607 + 6.47106i) q^{56} +(-1.64195 + 15.6222i) q^{58} +(6.74376 + 3.00252i) q^{59} +(-7.73669 - 8.59247i) q^{61} +(-12.8992 + 9.37181i) q^{62} +(2.69098 + 8.28199i) q^{64} +(0.0729490 - 0.126351i) q^{65} +(-0.927051 - 1.60570i) q^{67} +(-3.72191 + 4.13360i) q^{68} +(0.169131 + 1.60917i) q^{70} +(3.19098 - 9.82084i) q^{71} +(4.61803 - 3.35520i) q^{73} +(14.9148 - 6.64048i) q^{74} +(-14.2082 - 24.6093i) q^{76} +(3.11426 + 1.14079i) q^{77} +(-10.7596 - 2.28703i) q^{79} +(4.92705 + 3.57971i) q^{80} +(-0.190983 + 0.587785i) q^{82} +(0.985051 + 1.09401i) q^{83} +(-0.0740275 + 0.704324i) q^{85} +(11.7515 - 13.0513i) q^{86} +(21.9055 - 11.5893i) q^{88} -8.23607 q^{89} +(0.190983 + 0.138757i) q^{91} +(-0.119779 - 1.13962i) q^{92} +(-25.8391 + 5.49228i) q^{94} +(-3.30524 - 1.47159i) q^{95} +(-7.68247 - 1.63296i) q^{97} +15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 9 q^{4} + 3 q^{5} - q^{7} + 26 q^{8} + 4 q^{10} + 11 q^{11} - 7 q^{13} + 4 q^{14} - q^{16} + 24 q^{17} - 20 q^{19} - 3 q^{20} - 4 q^{22} + 8 q^{23} - 6 q^{25} + 4 q^{26} - 12 q^{28} - 6 q^{29}+ \cdots + 72 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more