LMFDB - Embedded newform 2646.2.l.c.521.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(521,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2646.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.l (of order $6$, degree $2$, 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:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.5
Character	$\chi$	$=$	2646.521
Dual form			2646.2.l.c.1097.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(-0.474556 + 0.821956i) q^{5} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.474556 + 0.821956i) q^{5} +1.00000i q^{8} +(0.821956 + 0.474556i) q^{10} +(1.51873 - 0.876838i) q^{11} +(-0.720756 + 0.416129i) q^{13} +1.00000 q^{16} +(2.73638 - 4.73955i) q^{17} +(-3.21232 + 1.85463i) q^{19} +(0.474556 - 0.821956i) q^{20} +(-0.876838 - 1.51873i) q^{22} +(-0.888998 - 0.513263i) q^{23} +(2.04959 + 3.55000i) q^{25} +(0.416129 + 0.720756i) q^{26} +(6.58867 + 3.80397i) q^{29} +11.0016i q^{31} -1.00000i q^{32} +(-4.73955 - 2.73638i) q^{34} +(-2.19830 - 3.80756i) q^{37} +(1.85463 + 3.21232i) q^{38} +(-0.821956 - 0.474556i) q^{40} +(-4.05647 - 7.02601i) q^{41} +(3.08463 - 5.34273i) q^{43} +(-1.51873 + 0.876838i) q^{44} +(-0.513263 + 0.888998i) q^{46} -6.80125 q^{47} +(3.55000 - 2.04959i) q^{50} +(0.720756 - 0.416129i) q^{52} +(-1.88177 - 1.08644i) q^{53} +1.66444i q^{55} +(3.80397 - 6.58867i) q^{58} +10.8659 q^{59} +1.09663i q^{61} +11.0016 q^{62} -1.00000 q^{64} -0.789907i q^{65} +14.4481 q^{67} +(-2.73638 + 4.73955i) q^{68} +11.0131i q^{71} +(3.16204 + 1.82561i) q^{73} +(-3.80756 + 2.19830i) q^{74} +(3.21232 - 1.85463i) q^{76} +9.84819 q^{79} +(-0.474556 + 0.821956i) q^{80} +(-7.02601 + 4.05647i) q^{82} +(-2.41103 + 4.17603i) q^{83} +(2.59713 + 4.49837i) q^{85} +(-5.34273 - 3.08463i) q^{86} +(0.876838 + 1.51873i) q^{88} +(2.15943 + 3.74024i) q^{89} +(0.888998 + 0.513263i) q^{92} +6.80125i q^{94} -3.52051i q^{95} +(3.90396 + 2.25395i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} + 48 q^{11} + 48 q^{16} + 48 q^{23} - 24 q^{25} - 48 q^{44} + 48 q^{50} - 96 q^{53} - 48 q^{64} - 96 q^{79} + 48 q^{85} + 96 q^{86} - 48 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 + 48 * q^11 + 48 * q^16 + 48 * q^23 - 24 * q^25 - 48 * q^44 + 48 * q^50 - 96 * q^53 - 48 * q^64 - 96 * q^79 + 48 * q^85 + 96 * q^86 - 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.474556	+	0.821956i	−0.212228	+	0.367590i	−0.952412	−	0.304815i	$-0.901405\pi$
$5$	−0.474556	+	0.821956i	−0.212228	+	0.367590i	0.740183	+	0.672405i	$0.234739\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.821956	+	0.474556i	0.259925	+	0.150068i
$11$	1.51873	−	0.876838i	0.457914	−	0.264377i	−0.253253	−	0.967400i	$-0.581500\pi$
$11$	1.51873	−	0.876838i	0.457914	−	0.264377i	0.711167	+	0.703024i	$0.248167\pi$
$12$		0			0
$13$	−0.720756	+	0.416129i	−0.199902	+	0.115413i	−0.596610	−	0.802532i	$-0.703486\pi$
$13$	−0.720756	+	0.416129i	−0.199902	+	0.115413i	0.396708	+	0.917945i	$0.370153\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	2.73638	−	4.73955i	0.663670	−	1.14951i	−0.315975	−	0.948768i	$-0.602331\pi$
$17$	2.73638	−	4.73955i	0.663670	−	1.14951i	0.979644	−	0.200742i	$-0.0643352\pi$
$18$		0			0
$19$	−3.21232	+	1.85463i	−0.736957	+	0.425482i	−0.820962	−	0.570983i	$-0.806562\pi$
$19$	−3.21232	+	1.85463i	−0.736957	+	0.425482i	0.0840051	+	0.996465i	$0.473229\pi$
$20$	0.474556	−	0.821956i	0.106114	−	0.183795i
$21$		0			0
$22$	−0.876838	−	1.51873i	−0.186942	−	0.323794i
$23$	−0.888998	−	0.513263i	−0.185369	−	0.107023i	0.404444	−	0.914563i	$-0.367465\pi$
$23$	−0.888998	−	0.513263i	−0.185369	−	0.107023i	−0.589813	+	0.807540i	$0.700798\pi$
$24$		0			0
$25$	2.04959	+	3.55000i	0.409918	+	0.710000i
$26$	0.416129	+	0.720756i	0.0816096	+	0.141352i
$27$		0			0
$28$		0			0
$29$	6.58867	+	3.80397i	1.22348	+	0.706379i	0.965659	−	0.259812i	$-0.0836607\pi$
$29$	6.58867	+	3.80397i	1.22348	+	0.706379i	0.257826	+	0.966191i	$0.416994\pi$
$30$		0			0
$31$			11.0016i			1.97595i	0.154602	+	0.987977i	$0.450591\pi$
$31$			11.0016i			1.97595i	−0.154602	+	0.987977i	$0.549409\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−4.73955	−	2.73638i	−0.812826	−	0.469285i
$35$		0			0
$36$		0			0
$37$	−2.19830	−	3.80756i	−0.361398	−	0.625959i	0.626794	−	0.779185i	$-0.284367\pi$
$37$	−2.19830	−	3.80756i	−0.361398	−	0.625959i	−0.988191	+	0.153226i	$0.951034\pi$
$38$	1.85463	+	3.21232i	0.300861	+	0.521107i
$39$		0			0
$40$	−0.821956	−	0.474556i	−0.129963	−	0.0750340i
$41$	−4.05647	−	7.02601i	−0.633514	−	1.09728i	−0.986828	−	0.161774i	$-0.948278\pi$
$41$	−4.05647	−	7.02601i	−0.633514	−	1.09728i	0.353314	−	0.935505i	$-0.385055\pi$
$42$		0			0
$43$	3.08463	−	5.34273i	0.470401	−	0.814759i	−0.529026	−	0.848606i	$-0.677443\pi$
$43$	3.08463	−	5.34273i	0.470401	−	0.814759i	0.999427	+	0.0338470i	$0.0107759\pi$
$44$	−1.51873	+	0.876838i	−0.228957	+	0.132188i
$45$		0			0
$46$	−0.513263	+	0.888998i	−0.0756766	+	0.131076i
$47$	−6.80125			−0.992064			−0.496032	−	0.868304i	$-0.665210\pi$
$47$	−6.80125			−0.992064			−0.496032	+	0.868304i	$0.665210\pi$
$48$		0			0
$49$		0			0
$50$	3.55000	−	2.04959i	0.502046	−	0.289856i
$51$		0			0
$52$	0.720756	−	0.416129i	0.0999509	−	0.0577067i
$53$	−1.88177	−	1.08644i	−0.258480	−	0.149234i	0.365161	−	0.930944i	$-0.381014\pi$
$53$	−1.88177	−	1.08644i	−0.258480	−	0.149234i	−0.623641	+	0.781711i	$0.714347\pi$
$54$		0			0
$55$			1.66444i			0.224433i
$56$		0			0
$57$		0			0
$58$	3.80397	−	6.58867i	0.499486	−	0.865134i
$59$	10.8659			1.41462			0.707311	−	0.706902i	$-0.249908\pi$
$59$	10.8659			1.41462			0.707311	+	0.706902i	$0.249908\pi$
$60$		0			0
$61$			1.09663i			0.140409i	0.997533	+	0.0702043i	$0.0223651\pi$
$61$			1.09663i			0.140409i	−0.997533	+	0.0702043i	$0.977635\pi$
$62$	11.0016			1.39721
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	0.789907i		−	0.0979759i
$66$		0			0
$67$	14.4481			1.76512			0.882559	−	0.470202i	$-0.155819\pi$
$67$	14.4481			1.76512			0.882559	+	0.470202i	$0.155819\pi$
$68$	−2.73638	+	4.73955i	−0.331835	+	0.574755i
$69$		0			0
$70$		0			0
$71$			11.0131i			1.30701i	0.756922	+	0.653505i	$0.226702\pi$
$71$			11.0131i			1.30701i	−0.756922	+	0.653505i	$0.773298\pi$
$72$		0			0
$73$	3.16204	+	1.82561i	0.370089	+	0.213671i	0.673497	−	0.739190i	$-0.264791\pi$
$73$	3.16204	+	1.82561i	0.370089	+	0.213671i	−0.303408	+	0.952861i	$0.598125\pi$
$74$	−3.80756	+	2.19830i	−0.442620	+	0.255547i
$75$		0			0
$76$	3.21232	−	1.85463i	0.368478	−	0.212741i
$77$		0			0
$78$		0			0
$79$	9.84819			1.10801			0.554004	−	0.832514i	$-0.313099\pi$
$79$	9.84819			1.10801			0.554004	+	0.832514i	$0.313099\pi$
$80$	−0.474556	+	0.821956i	−0.0530570	+	0.0918975i
$81$		0			0
$82$	−7.02601	+	4.05647i	−0.775893	+	0.447962i
$83$	−2.41103	+	4.17603i	−0.264645	+	0.458379i	−0.967471	−	0.252983i	$-0.918588\pi$
$83$	−2.41103	+	4.17603i	−0.264645	+	0.458379i	0.702825	+	0.711363i	$0.251922\pi$
$84$		0			0
$85$	2.59713	+	4.49837i	0.281699	+	0.487916i
$86$	−5.34273	−	3.08463i	−0.576121	−	0.332624i
$87$		0			0
$88$	0.876838	+	1.51873i	0.0934712	+	0.161897i
$89$	2.15943	+	3.74024i	0.228899	+	0.396465i	0.957482	−	0.288493i	$-0.0931541\pi$
$89$	2.15943	+	3.74024i	0.228899	+	0.396465i	−0.728583	+	0.684957i	$0.759821\pi$
$90$		0			0
$91$		0			0
$92$	0.888998	+	0.513263i	0.0926845	+	0.0535114i
$93$		0			0
$94$			6.80125i			0.701495i
$95$		−	3.52051i		−	0.361197i
$96$		0			0
$97$	3.90396	+	2.25395i	0.396387	+	0.228854i	0.684924	−	0.728615i	$-0.259836\pi$
$97$	3.90396	+	2.25395i	0.396387	+	0.228854i	−0.288537	+	0.957469i	$0.593169\pi$
$98$		0			0
$99$		0			0
$100$	−2.04959	−	3.55000i	−0.204959	−	0.355000i
$101$	6.33624	+	10.9747i	0.630480	+	1.09202i	0.987454	+	0.157909i	$0.0504751\pi$
$101$	6.33624	+	10.9747i	0.630480	+	1.09202i	−0.356974	+	0.934114i	$0.616192\pi$
$102$		0			0
$103$	7.33341	+	4.23394i	0.722582	+	0.417183i	0.815702	−	0.578472i	$-0.196351\pi$
$103$	7.33341	+	4.23394i	0.722582	+	0.417183i	−0.0931202	+	0.995655i	$0.529684\pi$
$104$	−0.416129	−	0.720756i	−0.0408048	−	0.0706760i
$105$		0			0
$106$	−1.08644	+	1.88177i	−0.105524	+	0.182773i
$107$	1.28657	−	0.742804i	0.124378	−	0.0718096i	−0.436520	−	0.899694i	$-0.643789\pi$
$107$	1.28657	−	0.742804i	0.124378	−	0.0718096i	0.560898	+	0.827885i	$0.310456\pi$
$108$		0			0
$109$	7.60276	−	13.1684i	0.728213	−	1.26130i	−0.229425	−	0.973326i	$-0.573685\pi$
$109$	7.60276	−	13.1684i	0.728213	−	1.26130i	0.957638	−	0.287975i	$-0.0929820\pi$
$110$	1.66444			0.158698
$111$		0			0
$112$		0			0
$113$	17.0031	−	9.81676i	1.59952	−	0.923483i	0.607941	−	0.793982i	$-0.291996\pi$
$113$	17.0031	−	9.81676i	1.59952	−	0.923483i	0.991579	−	0.129501i	$-0.0413376\pi$
$114$		0			0
$115$	0.843760	−	0.487145i	0.0786810	−	0.0454265i
$116$	−6.58867	−	3.80397i	−0.611742	−	0.353190i
$117$		0			0
$118$		−	10.8659i		−	1.00029i
$119$		0			0
$120$		0			0
$121$	−3.96231	+	6.86292i	−0.360210	+	0.623902i
$122$	1.09663			0.0992838
$123$		0			0
$124$		−	11.0016i		−	0.987977i
$125$	−8.63615			−0.772441
$126$		0			0
$127$	18.7051			1.65981			0.829903	−	0.557907i	$-0.188395\pi$
$127$	18.7051			1.65981			0.829903	+	0.557907i	$0.188395\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−0.789907			−0.0692794
$131$	3.32193	−	5.75375i	0.290238	−	0.502707i	−0.683628	−	0.729831i	$-0.739599\pi$
$131$	3.32193	−	5.75375i	0.290238	−	0.502707i	0.973866	+	0.227124i	$0.0729321\pi$
$132$		0			0
$133$		0			0
$134$		−	14.4481i		−	1.24813i
$135$		0			0
$136$	4.73955	+	2.73638i	0.406413	+	0.234643i
$137$	17.6798	−	10.2074i	1.51049	−	0.872080i	0.510562	−	0.859841i	$-0.329437\pi$
$137$	17.6798	−	10.2074i	1.51049	−	0.872080i	0.999925	−	0.0122395i	$-0.00389606\pi$
$138$		0			0
$139$	10.9829	−	6.34099i	0.931559	−	0.537836i	0.0442550	−	0.999020i	$-0.485909\pi$
$139$	10.9829	−	6.34099i	0.931559	−	0.537836i	0.887304	+	0.461184i	$0.152575\pi$
$140$		0			0
$141$		0			0
$142$	11.0131			0.924196
$143$	−0.729755	+	1.26397i	−0.0610252	+	0.105699i
$144$		0			0
$145$	−6.25339	+	3.61040i	−0.519316	+	0.299827i
$146$	1.82561	−	3.16204i	0.151088	−	0.261693i
$147$		0			0
$148$	2.19830	+	3.80756i	0.180699	+	0.312979i
$149$	−17.1827	−	9.92046i	−1.40767	−	0.812716i	−0.412503	−	0.910956i	$-0.635345\pi$
$149$	−17.1827	−	9.92046i	−1.40767	−	0.812716i	−0.995163	+	0.0982404i	$0.968679\pi$
$150$		0			0
$151$	−0.872422	−	1.51108i	−0.0709967	−	0.122970i	0.828342	−	0.560223i	$-0.189285\pi$
$151$	−0.872422	−	1.51108i	−0.0709967	−	0.122970i	−0.899338	+	0.437253i	$0.855951\pi$
$152$	−1.85463	−	3.21232i	−0.150431	−	0.260553i
$153$		0			0
$154$		0			0
$155$	−9.04287	−	5.22090i	−0.726341	−	0.419353i
$156$		0			0
$157$			9.49564i			0.757835i	0.925431	+	0.378917i	$0.123704\pi$
$157$			9.49564i			0.757835i	−0.925431	+	0.378917i	$0.876296\pi$
$158$		−	9.84819i		−	0.783480i
$159$		0			0
$160$	0.821956	+	0.474556i	0.0649813	+	0.0375170i
$161$		0			0
$162$		0			0
$163$	−5.92061	−	10.2548i	−0.463738	−	0.803217i	0.535406	−	0.844595i	$-0.320159\pi$
$163$	−5.92061	−	10.2548i	−0.463738	−	0.803217i	−0.999144	+	0.0413777i	$0.986825\pi$
$164$	4.05647	+	7.02601i	0.316757	+	0.548639i
$165$		0			0
$166$	4.17603	+	2.41103i	0.324123	+	0.187133i
$167$	−1.73229	−	3.00041i	−0.134048	−	0.232179i	0.791185	−	0.611577i	$-0.209464\pi$
$167$	−1.73229	−	3.00041i	−0.134048	−	0.232179i	−0.925234	+	0.379398i	$0.876131\pi$
$168$		0			0
$169$	−6.15367	+	10.6585i	−0.473359	+	0.819883i
$170$	4.49837	−	2.59713i	0.345009	−	0.199191i
$171$		0			0
$172$	−3.08463	+	5.34273i	−0.235201	+	0.407379i
$173$	−3.09982			−0.235675			−0.117838	−	0.993033i	$-0.537596\pi$
$173$	−3.09982			−0.235675			−0.117838	+	0.993033i	$0.537596\pi$
$174$		0			0
$175$		0			0
$176$	1.51873	−	0.876838i	0.114478	−	0.0660941i
$177$		0			0
$178$	3.74024	−	2.15943i	0.280343	−	0.161856i
$179$	−0.500470	−	0.288947i	−0.0374069	−	0.0215969i	0.481180	−	0.876622i	$-0.340208\pi$
$179$	−0.500470	−	0.288947i	−0.0374069	−	0.0215969i	−0.518587	+	0.855025i	$0.673542\pi$
$180$		0			0
$181$			26.0581i			1.93688i	0.249238	+	0.968442i	$0.419820\pi$
$181$			26.0581i			1.93688i	−0.249238	+	0.968442i	$0.580180\pi$
$182$		0			0
$183$		0			0
$184$	0.513263	−	0.888998i	0.0378383	−	0.0655378i
$185$	4.17286			0.306795
$186$		0			0
$187$		−	9.59745i		−	0.701835i
$188$	6.80125			0.496032
$189$		0			0
$190$	−3.52051			−0.255405
$191$		−	1.77964i		−	0.128770i	−0.997925	−	0.0643852i	$-0.979491\pi$
$191$		−	1.77964i		−	0.128770i	0.997925	−	0.0643852i	$-0.0205086\pi$
$192$		0			0
$193$	−1.48335			−0.106774			−0.0533871	−	0.998574i	$-0.517002\pi$
$193$	−1.48335			−0.106774			−0.0533871	+	0.998574i	$0.517002\pi$
$194$	2.25395	−	3.90396i	0.161824	−	0.280288i
$195$		0			0
$196$		0			0
$197$		−	2.44809i		−	0.174419i	−0.996190	−	0.0872096i	$-0.972205\pi$
$197$		−	2.44809i		−	0.174419i	0.996190	−	0.0872096i	$-0.0277950\pi$
$198$		0			0
$199$	−9.47403	−	5.46984i	−0.671596	−	0.387746i	0.125085	−	0.992146i	$-0.460080\pi$
$199$	−9.47403	−	5.46984i	−0.671596	−	0.387746i	−0.796681	+	0.604400i	$0.793413\pi$
$200$	−3.55000	+	2.04959i	−0.251023	+	0.144928i
$201$		0			0
$202$	10.9747	−	6.33624i	0.772177	−	0.445816i
$203$		0			0
$204$		0			0
$205$	7.70010			0.537798
$206$	4.23394	−	7.33341i	0.294993	−	0.510943i
$207$		0			0
$208$	−0.720756	+	0.416129i	−0.0499755	+	0.0288534i
$209$	−3.25243	+	5.63337i	−0.224975	+	0.389668i
$210$		0			0
$211$	12.7481	+	22.0804i	0.877617	+	1.52008i	0.853949	+	0.520357i	$0.174201\pi$
$211$	12.7481	+	22.0804i	0.877617	+	1.52008i	0.0236678	+	0.999720i	$0.492466\pi$
$212$	1.88177	+	1.08644i	0.129240	+	0.0746169i
$213$		0			0
$214$	−0.742804	−	1.28657i	−0.0507770	−	0.0879484i
$215$	2.92766	+	5.07085i	0.199665	+	0.345829i
$216$		0			0
$217$		0			0
$218$	−13.1684	−	7.60276i	−0.891875	−	0.514924i
$219$		0			0
$220$		−	1.66444i		−	0.112216i
$221$			4.55475i			0.306385i
$222$		0			0
$223$	−13.3108	−	7.68501i	−0.891359	−	0.514626i	−0.0169720	−	0.999856i	$-0.505403\pi$
$223$	−13.3108	−	7.68501i	−0.891359	−	0.514626i	−0.874387	+	0.485230i	$0.838736\pi$
$224$		0			0
$225$		0			0
$226$	−9.81676	−	17.0031i	−0.653001	−	1.13103i
$227$	4.17388	+	7.22937i	0.277030	+	0.479830i	0.970645	−	0.240515i	$-0.0773165\pi$
$227$	4.17388	+	7.22937i	0.277030	+	0.479830i	−0.693615	+	0.720346i	$0.743983\pi$
$228$		0			0
$229$	11.3671	+	6.56281i	0.751161	+	0.433683i	0.826113	−	0.563504i	$-0.190547\pi$
$229$	11.3671	+	6.56281i	0.751161	+	0.433683i	−0.0749523	+	0.997187i	$0.523880\pi$
$230$	−0.487145	−	0.843760i	−0.0321214	−	0.0556359i
$231$		0			0
$232$	−3.80397	+	6.58867i	−0.249743	+	0.432567i
$233$	−9.84350	+	5.68315i	−0.644869	+	0.372315i	−0.786488	−	0.617606i	$-0.788103\pi$
$233$	−9.84350	+	5.68315i	−0.644869	+	0.372315i	0.141619	+	0.989921i	$0.454769\pi$
$234$		0			0
$235$	3.22758	−	5.59033i	0.210544	−	0.364673i
$236$	−10.8659			−0.707311
$237$		0			0
$238$		0			0
$239$	−4.67039	+	2.69645i	−0.302102	+	0.174419i	−0.643387	−	0.765541i	$-0.722471\pi$
$239$	−4.67039	+	2.69645i	−0.302102	+	0.174419i	0.341285	+	0.939960i	$0.389138\pi$
$240$		0			0
$241$	12.1233	−	6.99936i	0.780928	−	0.450869i	−0.0558314	−	0.998440i	$-0.517781\pi$
$241$	12.1233	−	6.99936i	0.780928	−	0.450869i	0.836759	+	0.547572i	$0.184448\pi$
$242$	6.86292	+	3.96231i	0.441165	+	0.254707i
$243$		0			0
$244$		−	1.09663i		−	0.0702043i
$245$		0			0
$246$		0			0
$247$	1.54353	−	2.67348i	0.0982127	−	0.170109i
$248$	−11.0016			−0.698605
$249$		0			0
$250$			8.63615i			0.546198i
$251$	−16.5094			−1.04207			−0.521033	−	0.853536i	$-0.674453\pi$
$251$	−16.5094			−1.04207			−0.521033	+	0.853536i	$0.674453\pi$
$252$		0			0
$253$	−1.80019			−0.113177
$254$		−	18.7051i		−	1.17366i
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.06000	−	5.30007i	0.190878	−	0.330610i	−0.754664	−	0.656112i	$-0.772200\pi$
$257$	3.06000	−	5.30007i	0.190878	−	0.330610i	0.945541	+	0.325502i	$0.105533\pi$
$258$		0			0
$259$		0			0
$260$			0.789907i			0.0489879i
$261$		0			0
$262$	−5.75375	−	3.32193i	−0.355468	−	0.205229i
$263$	14.1668	−	8.17923i	0.873565	−	0.504353i	0.00503369	−	0.999987i	$-0.498398\pi$
$263$	14.1668	−	8.17923i	0.873565	−	0.504353i	0.868531	+	0.495634i	$0.165064\pi$
$264$		0			0
$265$	1.78601	−	1.03115i	0.109714	−	0.0633432i
$266$		0			0
$267$		0			0
$268$	−14.4481			−0.882559
$269$	2.65845	−	4.60457i	0.162088	−	0.280745i	−0.773529	−	0.633761i	$-0.781510\pi$
$269$	2.65845	−	4.60457i	0.162088	−	0.280745i	0.935617	+	0.353015i	$0.114844\pi$
$270$		0			0
$271$	14.2825	−	8.24602i	0.867601	−	0.500910i	0.00105086	−	0.999999i	$-0.499666\pi$
$271$	14.2825	−	8.24602i	0.867601	−	0.500910i	0.866550	+	0.499090i	$0.166332\pi$
$272$	2.73638	−	4.73955i	0.165917	−	0.287377i
$273$		0			0
$274$	−10.2074	−	17.6798i	−0.616654	−	1.06808i
$275$	6.22554	+	3.59432i	0.375414	+	0.216746i
$276$		0			0
$277$	−7.31402	−	12.6682i	−0.439457	−	0.761161i	0.558191	−	0.829713i	$-0.311496\pi$
$277$	−7.31402	−	12.6682i	−0.439457	−	0.761161i	−0.997648	+	0.0685513i	$0.978162\pi$
$278$	−6.34099	−	10.9829i	−0.380308	−	0.658712i
$279$		0			0
$280$		0			0
$281$	−3.62307	−	2.09178i	−0.216134	−	0.124785i	0.388025	−	0.921649i	$-0.373158\pi$
$281$	−3.62307	−	2.09178i	−0.216134	−	0.124785i	−0.604159	+	0.796864i	$0.706491\pi$
$282$		0			0
$283$			9.70591i			0.576957i	0.957486	+	0.288478i	$0.0931493\pi$
$283$			9.70591i			0.576957i	−0.957486	+	0.288478i	$0.906851\pi$
$284$		−	11.0131i		−	0.653505i
$285$		0			0
$286$	1.26397	+	0.729755i	0.0747403	+	0.0431513i
$287$		0			0
$288$		0			0
$289$	−6.47555	−	11.2160i	−0.380915	−	0.659764i
$290$	3.61040	+	6.25339i	0.212010	+	0.367212i
$291$		0			0
$292$	−3.16204	−	1.82561i	−0.185045	−	0.106836i
$293$	−1.01377	−	1.75591i	−0.0592253	−	0.102581i	0.834893	−	0.550413i	$-0.185530\pi$
$293$	−1.01377	−	1.75591i	−0.0592253	−	0.102581i	−0.894118	+	0.447832i	$0.852196\pi$
$294$		0			0
$295$	−5.15650	+	8.93131i	−0.300223	+	0.520001i
$296$	3.80756	−	2.19830i	0.221310	−	0.127773i
$297$		0			0
$298$	−9.92046	+	17.1827i	−0.574677	+	0.995370i
$299$	0.854335			0.0494075
$300$		0			0
$301$		0			0
$302$	−1.51108	+	0.872422i	−0.0869528	+	0.0502022i
$303$		0			0
$304$	−3.21232	+	1.85463i	−0.184239	+	0.106371i
$305$	−0.901378	−	0.520411i	−0.0516128	−	0.0297986i
$306$		0			0
$307$			9.79004i			0.558747i	0.960183	+	0.279374i	$0.0901268\pi$
$307$			9.79004i			0.558747i	−0.960183	+	0.279374i	$0.909873\pi$
$308$		0			0
$309$		0			0
$310$	−5.22090	+	9.04287i	−0.296527	+	0.513600i
$311$	−13.7039			−0.777076			−0.388538	−	0.921433i	$-0.627020\pi$
$311$	−13.7039			−0.777076			−0.388538	+	0.921433i	$0.627020\pi$
$312$		0			0
$313$		−	18.8585i		−	1.06595i	−0.846132	−	0.532974i	$-0.821074\pi$
$313$		−	18.8585i		−	1.06595i	0.846132	−	0.532974i	$-0.178926\pi$
$314$	9.49564			0.535870
$315$		0			0
$316$	−9.84819			−0.554004
$317$			7.86426i			0.441701i	0.975308	+	0.220850i	$0.0708832\pi$
$317$			7.86426i			0.441701i	−0.975308	+	0.220850i	$0.929117\pi$
$318$		0			0
$319$	13.3419			0.747000
$320$	0.474556	−	0.821956i	0.0265285	−	0.0459487i
$321$		0			0
$322$		0			0
$323$			20.2999i			1.12952i
$324$		0			0
$325$	−2.95451	−	1.70579i	−0.163887	−	0.0946202i
$326$	−10.2548	+	5.92061i	−0.567960	+	0.327912i
$327$		0			0
$328$	7.02601	−	4.05647i	0.387947	−	0.223981i
$329$		0			0
$330$		0			0
$331$	22.7350			1.24963			0.624813	−	0.780774i	$-0.285175\pi$
$331$	22.7350			1.24963			0.624813	+	0.780774i	$0.285175\pi$
$332$	2.41103	−	4.17603i	0.132323	−	0.229190i
$333$		0			0
$334$	−3.00041	+	1.73229i	−0.164175	+	0.0947866i
$335$	−6.85644	+	11.8757i	−0.374608	+	0.648839i
$336$		0			0
$337$	−10.0639	−	17.4312i	−0.548217	−	0.949539i	−0.998397	−	0.0566014i	$-0.981974\pi$
$337$	−10.0639	−	17.4312i	−0.548217	−	0.949539i	0.450180	−	0.892938i	$-0.351360\pi$
$338$	10.6585	+	6.15367i	0.579745	+	0.334716i
$339$		0			0
$340$	−2.59713	−	4.49837i	−0.140849	−	0.243958i
$341$	9.64666	+	16.7085i	0.522396	+	0.904816i
$342$		0			0
$343$		0			0
$344$	5.34273	+	3.08463i	0.288061	+	0.166312i
$345$		0			0
$346$			3.09982i			0.166647i
$347$			22.6395i			1.21535i	0.794185	+	0.607677i	$0.207898\pi$
$347$			22.6395i			1.21535i	−0.794185	+	0.607677i	$0.792102\pi$
$348$		0			0
$349$	−13.3378	−	7.70058i	−0.713955	−	0.412202i	0.0985684	−	0.995130i	$-0.468574\pi$
$349$	−13.3378	−	7.70058i	−0.713955	−	0.412202i	−0.812524	+	0.582928i	$0.801907\pi$
$350$		0			0
$351$		0			0
$352$	−0.876838	−	1.51873i	−0.0467356	−	0.0809485i
$353$	−15.6132	−	27.0429i	−0.831009	−	1.43935i	−0.897239	−	0.441545i	$-0.854430\pi$
$353$	−15.6132	−	27.0429i	−0.831009	−	1.43935i	0.0662300	−	0.997804i	$-0.478903\pi$
$354$		0			0
$355$	−9.05225	−	5.22632i	−0.480444	−	0.277384i
$356$	−2.15943	−	3.74024i	−0.114449	−	0.198232i
$357$		0			0
$358$	−0.288947	+	0.500470i	−0.0152713	+	0.0264507i
$359$	−1.39179	+	0.803552i	−0.0734560	+	0.0424098i	−0.536278	−	0.844041i	$-0.680170\pi$
$359$	−1.39179	+	0.803552i	−0.0734560	+	0.0424098i	0.462822	+	0.886451i	$0.346837\pi$
$360$		0			0
$361$	−2.62067	+	4.53913i	−0.137930	+	0.238902i
$362$	26.0581			1.36958
$363$		0			0
$364$		0			0
$365$	−3.00114	+	1.73271i	−0.157087	+	0.0906941i
$366$		0			0
$367$	−16.1877	+	9.34599i	−0.844992	+	0.487856i	−0.858958	−	0.512046i	$-0.828888\pi$
$367$	−16.1877	+	9.34599i	−0.844992	+	0.487856i	0.0139659	+	0.999902i	$0.495554\pi$
$368$	−0.888998	−	0.513263i	−0.0463422	−	0.0267557i
$369$		0			0
$370$		−	4.17286i		−	0.216937i
$371$		0			0
$372$		0			0
$373$	−18.7682	+	32.5075i	−0.971781	+	1.68317i	−0.281609	+	0.959529i	$0.590868\pi$
$373$	−18.7682	+	32.5075i	−0.971781	+	1.68317i	−0.690173	+	0.723645i	$0.742465\pi$
$374$	−9.59745			−0.496272
$375$		0			0
$376$		−	6.80125i		−	0.350748i
$377$	−6.33177			−0.326103
$378$		0			0
$379$	−8.63192			−0.443392			−0.221696	−	0.975116i	$-0.571159\pi$
$379$	−8.63192			−0.443392			−0.221696	+	0.975116i	$0.571159\pi$
$380$			3.52051i			0.180599i
$381$		0			0
$382$	−1.77964			−0.0910545
$383$	4.19997	−	7.27456i	0.214608	−	0.371713i	−0.738543	−	0.674206i	$-0.764486\pi$
$383$	4.19997	−	7.27456i	0.214608	−	0.371713i	0.953151	+	0.302494i	$0.0978191\pi$
$384$		0			0
$385$		0			0
$386$			1.48335i			0.0755007i
$387$		0			0
$388$	−3.90396	−	2.25395i	−0.198193	−	0.114427i
$389$	−12.3475	+	7.12883i	−0.626043	+	0.361446i	−0.779218	−	0.626753i	$-0.784383\pi$
$389$	−12.3475	+	7.12883i	−0.626043	+	0.361446i	0.153175	+	0.988199i	$0.451050\pi$
$390$		0			0
$391$	−4.86527	+	2.80897i	−0.246047	+	0.142056i
$392$		0			0
$393$		0			0
$394$	−2.44809			−0.123333
$395$	−4.67352	+	8.09477i	−0.235150	+	0.407292i
$396$		0			0
$397$	−22.2162	+	12.8265i	−1.11500	+	0.643744i	−0.940119	−	0.340846i	$-0.889287\pi$
$397$	−22.2162	+	12.8265i	−1.11500	+	0.643744i	−0.174879	+	0.984590i	$0.555953\pi$
$398$	−5.46984	+	9.47403i	−0.274178	+	0.474890i
$399$		0			0
$400$	2.04959	+	3.55000i	0.102480	+	0.177500i
$401$	−22.5981	−	13.0470i	−1.12849	−	0.651536i	−0.184938	−	0.982750i	$-0.559209\pi$
$401$	−22.5981	−	13.0470i	−1.12849	−	0.651536i	−0.943556	+	0.331214i	$0.892542\pi$
$402$		0			0
$403$	−4.57810	−	7.92951i	−0.228052	−	0.394997i
$404$	−6.33624	−	10.9747i	−0.315240	−	0.546011i
$405$		0			0
$406$		0			0
$407$	−6.67722	−	3.85510i	−0.330978	−	0.191090i
$408$		0			0
$409$		−	30.8308i		−	1.52448i	−0.647292	−	0.762242i	$-0.724099\pi$
$409$		−	30.8308i		−	1.52448i	0.647292	−	0.762242i	$-0.275901\pi$
$410$		−	7.70010i		−	0.380281i
$411$		0			0
$412$	−7.33341	−	4.23394i	−0.361291	−	0.208591i
$413$		0			0
$414$		0			0
$415$	−2.28834	−	3.96353i	−0.112330	−	0.194562i
$416$	0.416129	+	0.720756i	0.0204024	+	0.0353380i
$417$		0			0
$418$	5.63337	+	3.25243i	0.275537	+	0.159081i
$419$	13.9168	+	24.1047i	0.679883	+	1.17759i	0.975016	+	0.222135i	$0.0713026\pi$
$419$	13.9168	+	24.1047i	0.679883	+	1.17759i	−0.295133	+	0.955456i	$0.595364\pi$
$420$		0			0
$421$	7.39960	−	12.8165i	0.360634	−	0.624637i	−0.627431	−	0.778672i	$-0.715894\pi$
$421$	7.39960	−	12.8165i	0.360634	−	0.624637i	0.988065	+	0.154035i	$0.0492269\pi$
$422$	22.0804	−	12.7481i	1.07486	−	0.620569i
$423$		0			0
$424$	1.08644	−	1.88177i	0.0527621	−	0.0913866i
$425$	22.4339			1.08820
$426$		0			0
$427$		0			0
$428$	−1.28657	+	0.742804i	−0.0621889	+	0.0359048i
$429$		0			0
$430$	5.07085	−	2.92766i	0.244538	−	0.141184i
$431$	24.7338	+	14.2801i	1.19139	+	0.687847i	0.958621	−	0.284686i	$-0.0918892\pi$
$431$	24.7338	+	14.2801i	1.19139	+	0.687847i	0.232765	+	0.972533i	$0.425223\pi$
$432$		0			0
$433$			18.0220i			0.866080i	0.901375	+	0.433040i	$0.142559\pi$
$433$			18.0220i			0.866080i	−0.901375	+	0.433040i	$0.857441\pi$
$434$		0			0
$435$		0			0
$436$	−7.60276	+	13.1684i	−0.364106	+	0.630651i
$437$	3.80766			0.182145
$438$		0			0
$439$		−	24.5104i		−	1.16982i	−0.811099	−	0.584909i	$-0.801130\pi$
$439$		−	24.5104i		−	1.16982i	0.811099	−	0.584909i	$-0.198870\pi$
$440$	−1.66444			−0.0793489
$441$		0			0
$442$	4.55475			0.216647
$443$			10.5547i			0.501469i	0.968056	+	0.250734i	$0.0806720\pi$
$443$			10.5547i			0.501469i	−0.968056	+	0.250734i	$0.919328\pi$
$444$		0			0
$445$	−4.09908			−0.194315
$446$	−7.68501	+	13.3108i	−0.363896	+	0.630286i
$447$		0			0
$448$		0			0
$449$			17.2540i			0.814267i	0.913369	+	0.407133i	$0.133472\pi$
$449$			17.2540i			0.814267i	−0.913369	+	0.407133i	$0.866528\pi$
$450$		0			0
$451$	−12.3213	−	7.11373i	−0.580190	−	0.334973i
$452$	−17.0031	+	9.81676i	−0.799760	+	0.461742i
$453$		0			0
$454$	7.22937	−	4.17388i	0.339291	−	0.195890i
$455$		0			0
$456$		0			0
$457$	1.37536			0.0643368			0.0321684	−	0.999482i	$-0.489759\pi$
$457$	1.37536			0.0643368			0.0321684	+	0.999482i	$0.489759\pi$
$458$	6.56281	−	11.3671i	0.306660	−	0.531151i
$459$		0			0
$460$	−0.843760	+	0.487145i	−0.0393405	+	0.0227132i
$461$	18.7031	−	32.3947i	0.871088	−	1.50877i	0.0102165	−	0.999948i	$-0.496748\pi$
$461$	18.7031	−	32.3947i	0.871088	−	1.50877i	0.860872	−	0.508822i	$-0.169919\pi$
$462$		0			0
$463$	−5.18312	−	8.97742i	−0.240880	−	0.417216i	0.720085	−	0.693886i	$-0.244103\pi$
$463$	−5.18312	−	8.97742i	−0.240880	−	0.417216i	−0.960965	+	0.276669i	$0.910769\pi$
$464$	6.58867	+	3.80397i	0.305871	+	0.176595i
$465$		0			0
$466$	5.68315	+	9.84350i	0.263267	+	0.455991i
$467$	18.1423	+	31.4234i	0.839527	+	1.45410i	0.890291	+	0.455393i	$0.150501\pi$
$467$	18.1423	+	31.4234i	0.839527	+	1.45410i	−0.0507637	+	0.998711i	$0.516166\pi$
$468$		0			0
$469$		0			0
$470$	−5.59033	−	3.22758i	−0.257862	−	0.148877i
$471$		0			0
$472$			10.8659i			0.500145i
$473$		−	10.8189i		−	0.497452i
$474$		0			0
$475$	−13.1679	−	7.60248i	−0.604184	−	0.348826i
$476$		0			0
$477$		0			0
$478$	2.69645	+	4.67039i	0.123333	+	0.213619i
$479$	−11.5975	−	20.0875i	−0.529905	−	0.917822i	−0.999391	−	0.0348822i	$-0.988894\pi$
$479$	−11.5975	−	20.0875i	−0.529905	−	0.917822i	0.469487	−	0.882939i	$-0.344439\pi$
$480$		0			0
$481$	3.16887	+	1.82955i	0.144488	+	0.0834202i
$482$	−6.99936	−	12.1233i	−0.318812	−	0.552199i
$483$		0			0
$484$	3.96231	−	6.86292i	0.180105	−	0.311951i
$485$	−3.70529	+	2.13925i	−0.168249	+	0.0971385i
$486$		0			0
$487$	−14.3695	+	24.8887i	−0.651144	+	1.12781i	0.331701	+	0.943384i	$0.392377\pi$
$487$	−14.3695	+	24.8887i	−0.651144	+	1.12781i	−0.982846	+	0.184430i	$0.940956\pi$
$488$	−1.09663			−0.0496419
$489$		0			0
$490$		0			0
$491$	−21.0143	+	12.1326i	−0.948364	+	0.547538i	−0.892572	−	0.450904i	$-0.851102\pi$
$491$	−21.0143	+	12.1326i	−0.948364	+	0.547538i	−0.0557919	+	0.998442i	$0.517768\pi$
$492$		0			0
$493$	36.0582	−	20.8182i	1.62398	−	0.937605i
$494$	−2.67348	−	1.54353i	−0.120285	−	0.0694468i
$495$		0			0
$496$			11.0016i			0.493988i
$497$		0			0
$498$		0			0
$499$	−13.2911	+	23.0209i	−0.594992	+	1.03056i	0.398556	+	0.917144i	$0.369511\pi$
$499$	−13.2911	+	23.0209i	−0.594992	+	1.03056i	−0.993548	+	0.113412i	$0.963822\pi$
$500$	8.63615			0.386221
$501$		0			0
$502$			16.5094i			0.736852i
$503$	33.9478			1.51366			0.756829	−	0.653613i	$-0.226748\pi$
$503$	33.9478			1.51366			0.756829	+	0.653613i	$0.226748\pi$
$504$		0			0
$505$	−12.0276			−0.535222
$506$			1.80019i			0.0800284i
$507$		0			0
$508$	−18.7051			−0.829903
$509$	5.70574	−	9.88263i	0.252902	−	0.438040i	−0.711421	−	0.702766i	$-0.751948\pi$
$509$	5.70574	−	9.88263i	0.252902	−	0.438040i	0.964324	+	0.264726i	$0.0852815\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−5.30007	−	3.06000i	−0.233776	−	0.134971i
$515$	−6.96023	+	4.01849i	−0.306704	+	0.177076i
$516$		0			0
$517$	−10.3292	+	5.96359i	−0.454280	+	0.262278i
$518$		0			0
$519$		0			0
$520$	0.789907			0.0346397
$521$	−9.24387	+	16.0108i	−0.404981	+	0.701448i	−0.994319	−	0.106439i	$-0.966055\pi$
$521$	−9.24387	+	16.0108i	−0.404981	+	0.701448i	0.589338	+	0.807887i	$0.299389\pi$
$522$		0			0
$523$	−0.133147	+	0.0768726i	−0.00582212	+	0.00336140i	−0.502908	−	0.864340i	$-0.667737\pi$
$523$	−0.133147	+	0.0768726i	−0.00582212	+	0.00336140i	0.497086	+	0.867701i	$0.334403\pi$
$524$	−3.32193	+	5.75375i	−0.145119	+	0.251354i
$525$		0			0
$526$	−8.17923	−	14.1668i	−0.356631	−	0.617704i
$527$	52.1428	+	30.1047i	2.27138	+	1.31138i
$528$		0			0
$529$	−10.9731	−	19.0060i	−0.477092	−	0.826348i
$530$	−1.03115	−	1.78601i	−0.0447904	−	0.0775792i
$531$		0			0
$532$		0			0
$533$	5.84746	+	3.37603i	0.253281	+	0.146232i
$534$		0			0
$535$			1.41001i			0.0609600i
$536$			14.4481i			0.624063i
$537$		0			0
$538$	−4.60457	−	2.65845i	−0.198517	−	0.114614i
$539$		0			0
$540$		0			0
$541$	17.9635	+	31.1136i	0.772309	+	1.33768i	0.936294	+	0.351216i	$0.114232\pi$
$541$	17.9635	+	31.1136i	0.772309	+	1.33768i	−0.163985	+	0.986463i	$0.552435\pi$
$542$	−8.24602	−	14.2825i	−0.354197	−	0.613487i
$543$		0			0
$544$	−4.73955	−	2.73638i	−0.203206	−	0.117321i
$545$	7.21588	+	12.4983i	0.309094	+	0.535367i
$546$		0			0
$547$	10.2216	−	17.7043i	0.437044	−	0.756983i	−0.560416	−	0.828211i	$-0.689359\pi$
$547$	10.2216	−	17.7043i	0.437044	−	0.756983i	0.997460	+	0.0712286i	$0.0226920\pi$
$548$	−17.6798	+	10.2074i	−0.755244	+	0.436040i
$549$		0			0
$550$	3.59432	−	6.22554i	0.153262	−	0.265458i
$551$	−28.2199			−1.20221
$552$		0			0
$553$		0			0
$554$	−12.6682	+	7.31402i	−0.538222	+	0.310743i
$555$		0			0
$556$	−10.9829	+	6.34099i	−0.465780	+	0.268918i
$557$	−18.8181	−	10.8646i	−0.797348	−	0.460349i	0.0451952	−	0.998978i	$-0.485609\pi$
$557$	−18.8181	−	10.8646i	−0.797348	−	0.460349i	−0.842543	+	0.538629i	$0.818942\pi$
$558$		0			0
$559$			5.13441i			0.217162i
$560$		0			0
$561$		0			0
$562$	−2.09178	+	3.62307i	−0.0882365	+	0.152830i
$563$	−20.8519			−0.878805			−0.439402	−	0.898290i	$-0.644810\pi$
$563$	−20.8519			−0.878805			−0.439402	+	0.898290i	$0.644810\pi$
$564$		0			0
$565$			18.6344i			0.783957i
$566$	9.70591			0.407970
$567$		0			0
$568$	−11.0131			−0.462098
$569$			11.6914i			0.490128i	0.969507	+	0.245064i	$0.0788090\pi$
$569$			11.6914i			0.490128i	−0.969507	+	0.245064i	$0.921191\pi$
$570$		0			0
$571$	13.5544			0.567235			0.283617	−	0.958938i	$-0.408465\pi$
$571$	13.5544			0.567235			0.283617	+	0.958938i	$0.408465\pi$
$572$	0.729755	−	1.26397i	0.0305126	−	0.0528494i
$573$		0			0
$574$		0			0
$575$		−	4.20792i		−	0.175483i
$576$		0			0
$577$	−20.0748	−	11.5902i	−0.835727	−	0.482507i	0.0200828	−	0.999798i	$-0.493607\pi$
$577$	−20.0748	−	11.5902i	−0.835727	−	0.482507i	−0.855809	+	0.517291i	$0.826940\pi$
$578$	−11.2160	+	6.47555i	−0.466523	+	0.269347i
$579$		0			0
$580$	6.25339	−	3.61040i	0.259658	−	0.149914i
$581$		0			0
$582$		0			0
$583$	−3.81052			−0.157816
$584$	−1.82561	+	3.16204i	−0.0755442	+	0.130846i
$585$		0			0
$586$	−1.75591	+	1.01377i	−0.0725358	+	0.0418786i
$587$	−4.22194	+	7.31262i	−0.174258	+	0.301824i	−0.939904	−	0.341438i	$-0.889086\pi$
$587$	−4.22194	+	7.31262i	−0.174258	+	0.301824i	0.765646	+	0.643262i	$0.222419\pi$
$588$		0			0
$589$	−20.4040	−	35.3408i	−0.840733	−	1.45619i
$590$	8.93131	+	5.15650i	0.367696	+	0.212290i
$591$		0			0
$592$	−2.19830	−	3.80756i	−0.0903494	−	0.156490i
$593$	−16.3255	−	28.2765i	−0.670407	−	1.16118i	−0.977789	−	0.209592i	$-0.932786\pi$
$593$	−16.3255	−	28.2765i	−0.670407	−	1.16118i	0.307382	−	0.951586i	$-0.400547\pi$
$594$		0			0
$595$		0			0
$596$	17.1827	+	9.92046i	0.703833	+	0.406358i
$597$		0			0
$598$		−	0.854335i		−	0.0349364i
$599$			47.9900i			1.96082i	0.196974	+	0.980409i	$0.436888\pi$
$599$			47.9900i			1.96082i	−0.196974	+	0.980409i	$0.563112\pi$
$600$		0			0
$601$	−20.1783	−	11.6499i	−0.823090	−	0.475211i	0.0283909	−	0.999597i	$-0.490962\pi$
$601$	−20.1783	−	11.6499i	−0.823090	−	0.475211i	−0.851481	+	0.524386i	$0.824295\pi$
$602$		0			0
$603$		0			0
$604$	0.872422	+	1.51108i	0.0354983	+	0.0614849i
$605$	−3.76068	−	6.51369i	−0.152893	−	0.264819i
$606$		0			0
$607$	21.3385	+	12.3198i	0.866101	+	0.500044i	0.866051	−	0.499956i	$-0.166651\pi$
$607$	21.3385	+	12.3198i	0.866101	+	0.500044i	5.03773e−5		1.00000i	$0.499984\pi$
$608$	1.85463	+	3.21232i	0.0752153	+	0.130277i
$609$		0			0
$610$	−0.520411	+	0.901378i	−0.0210708	+	0.0364957i
$611$	4.90204	−	2.83020i	0.198315	−	0.114497i
$612$		0			0
$613$	−17.2009	+	29.7928i	−0.694736	+	1.20332i	0.275533	+	0.961291i	$0.411146\pi$
$613$	−17.2009	+	29.7928i	−0.694736	+	1.20332i	−0.970270	+	0.242027i	$0.922188\pi$
$614$	9.79004			0.395094
$615$		0			0
$616$		0			0
$617$	22.4321	−	12.9512i	0.903083	−	0.521395i	0.0248838	−	0.999690i	$-0.492078\pi$
$617$	22.4321	−	12.9512i	0.903083	−	0.521395i	0.878199	+	0.478295i	$0.158745\pi$
$618$		0			0
$619$	−10.1907	+	5.88361i	−0.409599	+	0.236482i	−0.690618	−	0.723220i	$-0.742661\pi$
$619$	−10.1907	+	5.88361i	−0.409599	+	0.236482i	0.281018	+	0.959702i	$0.409328\pi$
$620$	9.04287	+	5.22090i	0.363170	+	0.209676i
$621$		0			0
$622$			13.7039i			0.549476i
$623$		0			0
$624$		0			0
$625$	−6.14962	+	10.6515i	−0.245985	+	0.426058i
$626$	−18.8585			−0.753739
$627$		0			0
$628$		−	9.49564i		−	0.378917i
$629$	−24.0615			−0.959394
$630$		0			0
$631$	16.4353			0.654277			0.327139	−	0.944976i	$-0.393916\pi$
$631$	16.4353			0.654277			0.327139	+	0.944976i	$0.393916\pi$
$632$			9.84819i			0.391740i
$633$		0			0
$634$	7.86426			0.312329
$635$	−8.87661	+	15.3747i	−0.352258	+	0.610128i
$636$		0			0
$637$		0			0
$638$		−	13.3419i		−	0.528209i
$639$		0			0
$640$	−0.821956	−	0.474556i	−0.0324907	−	0.0187585i
$641$	13.4048	−	7.73929i	0.529460	−	0.305684i	−0.211337	−	0.977413i	$-0.567782\pi$
$641$	13.4048	−	7.73929i	0.529460	−	0.305684i	0.740796	+	0.671730i	$0.234448\pi$
$642$		0			0
$643$	3.28185	−	1.89478i	0.129423	−	0.0747226i	−0.433890	−	0.900966i	$-0.642860\pi$
$643$	3.28185	−	1.89478i	0.129423	−	0.0747226i	0.563314	+	0.826243i	$0.309526\pi$
$644$		0			0
$645$		0			0
$646$	20.2999			0.798690
$647$	−11.0730	+	19.1789i	−0.435323	+	0.754002i	−0.997322	−	0.0731360i	$-0.976699\pi$
$647$	−11.0730	+	19.1789i	−0.435323	+	0.754002i	0.561999	+	0.827138i	$0.310033\pi$
$648$		0			0
$649$	16.5024	−	9.52765i	0.647775	−	0.373993i
$650$	−1.70579	+	2.95451i	−0.0669066	+	0.115886i
$651$		0			0
$652$	5.92061	+	10.2548i	0.231869	+	0.401609i
$653$	6.54842	+	3.78073i	0.256259	+	0.147951i	0.622627	−	0.782519i	$-0.286065\pi$
$653$	6.54842	+	3.78073i	0.256259	+	0.147951i	−0.366368	+	0.930470i	$0.619399\pi$
$654$		0			0
$655$	3.15289	+	5.46096i	0.123193	+	0.213377i
$656$	−4.05647	−	7.02601i	−0.158379	−	0.274320i
$657$		0			0
$658$		0			0
$659$	12.2514	+	7.07334i	0.477246	+	0.275538i	0.719268	−	0.694733i	$-0.244477\pi$
$659$	12.2514	+	7.07334i	0.477246	+	0.275538i	−0.242022	+	0.970271i	$0.577811\pi$
$660$		0			0
$661$		−	22.9586i		−	0.892985i	−0.894787	−	0.446492i	$-0.852673\pi$
$661$		−	22.9586i		−	0.892985i	0.894787	−	0.446492i	$-0.147327\pi$
$662$		−	22.7350i		−	0.883620i
$663$		0			0
$664$	−4.17603	−	2.41103i	−0.162062	−	0.0935663i
$665$		0			0
$666$		0			0
$667$	−3.90488	−	6.76344i	−0.151197	−	0.261882i
$668$	1.73229	+	3.00041i	0.0670242	+	0.116089i
$669$		0			0
$670$	11.8757	+	6.85644i	0.458799	+	0.264888i
$671$	0.961563	+	1.66548i	0.0371207	+	0.0642950i
$672$		0			0
$673$	−1.86542	+	3.23100i	−0.0719066	+	0.124546i	−0.899737	−	0.436433i	$-0.856242\pi$
$673$	−1.86542	+	3.23100i	−0.0719066	+	0.124546i	0.827830	+	0.560979i	$0.189575\pi$
$674$	−17.4312	+	10.0639i	−0.671426	+	0.387648i
$675$		0			0
$676$	6.15367	−	10.6585i	0.236680	−	0.409941i
$677$	−47.5314			−1.82678			−0.913390	−	0.407087i	$-0.866545\pi$
$677$	−47.5314			−1.82678			−0.913390	+	0.407087i	$0.866545\pi$
$678$		0			0
$679$		0			0
$680$	−4.49837	+	2.59713i	−0.172505	+	0.0995955i
$681$		0			0
$682$	16.7085	−	9.64666i	0.639802	−	0.369390i
$683$	−28.5275	−	16.4704i	−1.09158	−	0.630222i	−0.157580	−	0.987506i	$-0.550369\pi$
$683$	−28.5275	−	16.4704i	−1.09158	−	0.630222i	−0.933996	+	0.357284i	$0.883703\pi$
$684$		0			0
$685$			19.3760i			0.740320i
$686$		0			0
$687$		0			0
$688$	3.08463	−	5.34273i	0.117600	−	0.203690i
$689$	1.80839			0.0688943
$690$		0			0
$691$			7.93611i			0.301904i	0.988541	+	0.150952i	$0.0482339\pi$
$691$			7.93611i			0.301904i	−0.988541	+	0.150952i	$0.951766\pi$
$692$	3.09982			0.117838
$693$		0			0
$694$	22.6395			0.859385
$695$			12.0366i			0.456576i
$696$		0			0
$697$	−44.4002			−1.68178
$698$	−7.70058	+	13.3378i	−0.291471	+	0.504843i
$699$		0			0
$700$		0			0
$701$		−	25.1838i		−	0.951180i	−0.879667	−	0.475590i	$-0.842235\pi$
$701$		−	25.1838i		−	0.951180i	0.879667	−	0.475590i	$-0.157765\pi$
$702$		0			0
$703$	14.1233	+	8.15406i	0.532669	+	0.307536i
$704$	−1.51873	+	0.876838i	−0.0572392	+	0.0330471i
$705$		0			0
$706$	−27.0429	+	15.6132i	−1.01777	+	0.587612i
$707$		0			0
$708$		0			0
$709$	21.5021			0.807530			0.403765	−	0.914863i	$-0.367701\pi$
$709$	21.5021			0.807530			0.403765	+	0.914863i	$0.367701\pi$
$710$	−5.22632	+	9.05225i	−0.196140	+	0.339725i
$711$		0			0
$712$	−3.74024	+	2.15943i	−0.140171	+	0.0809280i
$713$	5.64674	−	9.78044i	0.211472	−	0.366280i
$714$		0			0
$715$	−0.692620	−	1.19965i	−0.0259025	−	0.0448645i
$716$	0.500470	+	0.288947i	0.0187035	+	0.0107984i
$717$		0			0
$718$	0.803552	+	1.39179i	0.0299883	+	0.0519412i
$719$	−8.30671	−	14.3876i	−0.309788	−	0.536569i	0.668528	−	0.743687i	$-0.266925\pi$
$719$	−8.30671	−	14.3876i	−0.309788	−	0.536569i	−0.978316	+	0.207119i	$0.933591\pi$
$720$		0			0
$721$		0			0
$722$	4.53913	+	2.62067i	0.168929	+	0.0975312i
$723$		0			0
$724$		−	26.0581i		−	0.968442i
$725$			31.1863i			1.15823i
$726$		0			0
$727$	39.4866	+	22.7976i	1.46448	+	0.845517i	0.999213	−	0.0396542i	$-0.0126256\pi$
$727$	39.4866	+	22.7976i	1.46448	+	0.845517i	0.465265	+	0.885171i	$0.345959\pi$
$728$		0			0
$729$		0			0
$730$	1.73271	+	3.00114i	0.0641304	+	0.111077i
$731$	−16.8814	−	29.2395i	−0.624382	−	1.08146i
$732$		0			0
$733$	14.3262	+	8.27123i	0.529150	+	0.305505i	0.740670	−	0.671869i	$-0.234508\pi$
$733$	14.3262	+	8.27123i	0.529150	+	0.305505i	−0.211520	+	0.977374i	$0.567841\pi$
$734$	9.34599	+	16.1877i	0.344967	+	0.597500i
$735$		0			0
$736$	−0.513263	+	0.888998i	−0.0189191	+	0.0327689i
$737$	21.9427	−	12.6686i	0.808271	−	0.466656i
$738$		0			0
$739$	7.75506	−	13.4322i	0.285274	−	0.494110i	−0.687401	−	0.726278i	$-0.741249\pi$
$739$	7.75506	−	13.4322i	0.285274	−	0.494110i	0.972676	+	0.232168i	$0.0745819\pi$
$740$	−4.17286			−0.153397
$741$		0			0
$742$		0			0
$743$	−36.0654	+	20.8224i	−1.32311	+	0.763899i	−0.984224	−	0.176928i	$-0.943384\pi$
$743$	−36.0654	+	20.8224i	−1.32311	+	0.763899i	−0.338888	+	0.940827i	$0.610051\pi$
$744$		0			0
$745$	16.3084	−	9.41564i	0.597492	−	0.344962i
$746$	32.5075	+	18.7682i	1.19018	+	0.687153i
$747$		0			0
$748$			9.59745i			0.350917i
$749$		0			0
$750$		0			0
$751$	6.21569	−	10.7659i	0.226814	−	0.392853i	−0.730048	−	0.683395i	$-0.760503\pi$
$751$	6.21569	−	10.7659i	0.226814	−	0.392853i	0.956862	+	0.290543i	$0.0938359\pi$
$752$	−6.80125			−0.248016
$753$		0			0
$754$			6.33177i			0.230589i
$755$	1.65605			0.0602699
$756$		0			0
$757$	24.8661			0.903775			0.451887	−	0.892075i	$-0.350751\pi$
$757$	24.8661			0.903775			0.451887	+	0.892075i	$0.350751\pi$
$758$			8.63192i			0.313526i
$759$		0			0
$760$	3.52051			0.127702
$761$	5.68277	−	9.84285i	0.206000	−	0.356803i	−0.744451	−	0.667678i	$-0.767289\pi$
$761$	5.68277	−	9.84285i	0.206000	−	0.356803i	0.950451	+	0.310874i	$0.100622\pi$
$762$		0			0
$763$		0			0
$764$			1.77964i			0.0643852i
$765$		0			0
$766$	−7.27456	−	4.19997i	−0.262841	−	0.151751i
$767$	−7.83169	+	4.52163i	−0.282786	+	0.163266i
$768$		0			0
$769$	29.8857	−	17.2545i	1.07771	−	0.622214i	0.147429	−	0.989073i	$-0.452900\pi$
$769$	29.8857	−	17.2545i	1.07771	−	0.622214i	0.930277	+	0.366859i	$0.119567\pi$
$770$		0			0
$771$		0			0
$772$	1.48335			0.0533871
$773$	10.6262	−	18.4051i	0.382197	−	0.661984i	−0.609179	−	0.793033i	$-0.708501\pi$
$773$	10.6262	−	18.4051i	0.382197	−	0.661984i	0.991376	+	0.131048i	$0.0418344\pi$
$774$		0			0
$775$	−39.0558	+	22.5489i	−1.40293	+	0.809980i
$776$	−2.25395	+	3.90396i	−0.0809121	+	0.140144i
$777$		0			0
$778$	7.12883	+	12.3475i	0.255581	+	0.442679i
$779$	26.0614	+	15.0465i	0.933745	+	0.539098i
$780$		0			0
$781$	9.65667	+	16.7258i	0.345543	+	0.598498i
$782$	2.80897	+	4.86527i	0.100448	+	0.173982i
$783$		0			0
$784$		0			0
$785$	−7.80500	−	4.50622i	−0.278572	−	0.160834i
$786$		0			0
$787$		−	11.9663i		−	0.426551i	−0.976992	−	0.213276i	$-0.931587\pi$
$787$		−	11.9663i		−	0.426551i	0.976992	−	0.213276i	$-0.0684132\pi$
$788$			2.44809i			0.0872096i
$789$		0			0
$790$	8.09477	+	4.67352i	0.287999	+	0.166276i
$791$		0			0
$792$		0			0
$793$	−0.456338	−	0.790400i	−0.0162050	−	0.0280679i
$794$	12.8265	+	22.2162i	0.455196	+	0.788422i
$795$		0			0
$796$	9.47403	+	5.46984i	0.335798	+	0.193873i
$797$	2.86820	+	4.96786i	0.101597	+	0.175971i	0.912343	−	0.409427i	$-0.134272\pi$
$797$	2.86820	+	4.96786i	0.101597	+	0.175971i	−0.810746	+	0.585398i	$0.800938\pi$
$798$		0			0
$799$	−18.6108	+	32.2348i	−0.658403	+	1.14039i
$800$	3.55000	−	2.04959i	0.125511	−	0.0724640i
$801$		0			0
$802$	−13.0470	+	22.5981i	−0.460706	+	0.797966i
$803$	6.40305			0.225959
$804$		0			0
$805$		0			0
$806$	−7.92951	+	4.57810i	−0.279305	+	0.161257i
$807$		0			0
$808$	−10.9747	+	6.33624i	−0.386088	+	0.222908i
$809$	−27.5185	−	15.8878i	−0.967500	−	0.558586i	−0.0690269	−	0.997615i	$-0.521989\pi$
$809$	−27.5185	−	15.8878i	−0.967500	−	0.558586i	−0.898473	+	0.439028i	$0.855323\pi$
$810$		0			0
$811$		−	41.2541i		−	1.44863i	−0.689471	−	0.724314i	$-0.742157\pi$
$811$		−	41.2541i		−	1.44863i	0.689471	−	0.724314i	$-0.257843\pi$
$812$		0			0
$813$		0			0
$814$	−3.85510	+	6.67722i	−0.135121	+	0.234037i
$815$	11.2386			0.393673
$816$		0			0
$817$			22.8834i			0.800589i
$818$	−30.8308			−1.07797
$819$		0			0
$820$	−7.70010			−0.268899
$821$			13.5045i			0.471309i	0.971837	+	0.235655i	$0.0757234\pi$
$821$			13.5045i			0.471309i	−0.971837	+	0.235655i	$0.924277\pi$
$822$		0			0
$823$	−18.9133			−0.659277			−0.329638	−	0.944107i	$-0.606927\pi$
$823$	−18.9133			−0.659277			−0.329638	+	0.944107i	$0.606927\pi$
$824$	−4.23394	+	7.33341i	−0.147496	+	0.255471i
$825$		0			0
$826$		0			0
$827$		−	33.8495i		−	1.17706i	−0.808475	−	0.588531i	$-0.799707\pi$
$827$		−	33.8495i		−	1.17706i	0.808475	−	0.588531i	$-0.200293\pi$
$828$		0			0
$829$	−21.8963	−	12.6418i	−0.760489	−	0.439068i	0.0689825	−	0.997618i	$-0.478025\pi$
$829$	−21.8963	−	12.6418i	−0.760489	−	0.439068i	−0.829471	+	0.558550i	$0.811358\pi$
$830$	−3.96353	+	2.28834i	−0.137576	+	0.0794296i
$831$		0			0
$832$	0.720756	−	0.416129i	0.0249877	−	0.0144267i
$833$		0			0
$834$		0			0
$835$	3.28827			0.113795
$836$	3.25243	−	5.63337i	0.112487	−	0.194834i
$837$		0			0
$838$	24.1047	−	13.9168i	0.832683	−	0.480750i
$839$	1.28248	−	2.22133i	0.0442763	−	0.0766888i	−0.843038	−	0.537854i	$-0.819235\pi$
$839$	1.28248	−	2.22133i	0.0442763	−	0.0766888i	0.887314	+	0.461165i	$0.152568\pi$
$840$		0			0
$841$	14.4404	+	25.0114i	0.497943	+	0.862463i
$842$	−12.8165	−	7.39960i	−0.441685	−	0.255007i
$843$		0			0
$844$	−12.7481	−	22.0804i	−0.438808	−	0.760038i
$845$	−5.84053	−	10.1161i	−0.200920	−	0.348004i
$846$		0			0
$847$		0			0
$848$	−1.88177	−	1.08644i	−0.0646201	−	0.0373084i
$849$		0			0
$850$		−	22.4339i		−	0.769475i
$851$			4.51322i			0.154711i
$852$		0			0
$853$	1.98108	+	1.14378i	0.0678310	+	0.0391622i	0.533532	−	0.845780i	$-0.320864\pi$
$853$	1.98108	+	1.14378i	0.0678310	+	0.0391622i	−0.465701	+	0.884942i	$0.654198\pi$
$854$		0			0
$855$		0			0
$856$	0.742804	+	1.28657i	0.0253885	+	0.0439742i
$857$	10.3313	+	17.8943i	0.352911	+	0.611259i	0.986758	−	0.162199i	$-0.0518586\pi$
$857$	10.3313	+	17.8943i	0.352911	+	0.611259i	−0.633847	+	0.773458i	$0.718525\pi$
$858$		0			0
$859$	−14.3879	−	8.30688i	−0.490910	−	0.283427i	0.234042	−	0.972226i	$-0.424805\pi$
$859$	−14.3879	−	8.30688i	−0.490910	−	0.283427i	−0.724952	+	0.688800i	$0.758138\pi$
$860$	−2.92766	−	5.07085i	−0.0998323	−	0.172915i
$861$		0			0
$862$	14.2801	−	24.7338i	0.486381	−	0.842437i
$863$	5.54125	−	3.19924i	0.188626	−	0.108904i	−0.402713	−	0.915326i	$-0.631933\pi$
$863$	5.54125	−	3.19924i	0.188626	−	0.108904i	0.591339	+	0.806423i	$0.298599\pi$
$864$		0			0
$865$	1.47104	−	2.54792i	0.0500169	−	0.0866318i
$866$	18.0220			0.612411
$867$		0			0
$868$		0			0
$869$	14.9567	−	8.63526i	0.507372	−	0.292931i
$870$		0			0
$871$	−10.4136	+	6.01228i	−0.352850	+	0.203718i
$872$	13.1684	+	7.60276i	0.445937	+	0.257462i
$873$		0			0
$874$		−	3.80766i		−	0.128796i
$875$		0			0
$876$		0			0
$877$	−5.08369	+	8.80522i	−0.171664	+	0.297331i	−0.939002	−	0.343912i	$-0.888248\pi$
$877$	−5.08369	+	8.80522i	−0.171664	+	0.297331i	0.767338	+	0.641243i	$0.221581\pi$
$878$	−24.5104			−0.827187
$879$		0			0
$880$			1.66444i			0.0561081i
$881$	−47.2933			−1.59335			−0.796675	−	0.604407i	$-0.793410\pi$
$881$	−47.2933			−1.59335			−0.796675	+	0.604407i	$0.793410\pi$
$882$		0			0
$883$	−16.5706			−0.557645			−0.278822	−	0.960343i	$-0.589944\pi$
$883$	−16.5706			−0.557645			−0.278822	+	0.960343i	$0.589944\pi$
$884$		−	4.55475i		−	0.153193i
$885$		0			0
$886$	10.5547			0.354592
$887$	11.3965	−	19.7393i	0.382656	−	0.662780i	−0.608785	−	0.793335i	$-0.708343\pi$
$887$	11.3965	−	19.7393i	0.382656	−	0.662780i	0.991441	+	0.130556i	$0.0416761\pi$
$888$		0			0
$889$		0			0
$890$			4.09908i			0.137402i
$891$		0			0
$892$	13.3108	+	7.68501i	0.445679	+	0.257313i
$893$	21.8478	−	12.6138i	0.731108	−	0.422105i
$894$		0			0
$895$	0.475003	−	0.274243i	0.0158776	−	0.00916694i
$896$		0			0
$897$		0			0
$898$	17.2540			0.575774
$899$	−41.8499	+	72.4862i	−1.39577	+	2.41755i
$900$		0			0
$901$	−10.2985	+	5.94581i	−0.343091	+	0.198084i
$902$	−7.11373	+	12.3213i	−0.236861	+	0.410256i
$903$		0			0
$904$	9.81676	+	17.0031i	0.326501	+	0.565516i
$905$	−21.4186	−	12.3660i	−0.711979	−	0.411061i
$906$		0			0
$907$	24.0653	+	41.6824i	0.799077	+	1.38404i	0.920218	+	0.391406i	$0.128011\pi$
$907$	24.0653	+	41.6824i	0.799077	+	1.38404i	−0.121142	+	0.992635i	$0.538656\pi$
$908$	−4.17388	−	7.22937i	−0.138515	−	0.239915i
$909$		0			0
$910$		0			0
$911$	−20.5958	−	11.8910i	−0.682368	−	0.393966i	0.118378	−	0.992969i	$-0.462230\pi$
$911$	−20.5958	−	11.8910i	−0.682368	−	0.393966i	−0.800747	+	0.599003i	$0.795564\pi$
$912$		0			0
$913$			8.45635i			0.279864i
$914$		−	1.37536i		−	0.0454930i
$915$		0			0
$916$	−11.3671	−	6.56281i	−0.375580	−	0.216841i
$917$		0			0
$918$		0			0
$919$	−10.9692	−	18.9992i	−0.361841	−	0.626727i	0.626423	−	0.779483i	$-0.284518\pi$
$919$	−10.9692	−	18.9992i	−0.361841	−	0.626727i	−0.988264	+	0.152757i	$0.951185\pi$
$920$	0.487145	+	0.843760i	0.0160607	+	0.0278179i
$921$		0			0
$922$	−32.3947	−	18.7031i	−1.06686	−	0.615953i
$923$	−4.58286	−	7.93774i	−0.150847	−	0.261274i
$924$		0			0
$925$	9.01122	−	15.6079i	0.296287	−	0.513184i
$926$	−8.97742	+	5.18312i	−0.295016	+	0.170328i
$927$		0			0
$928$	3.80397	−	6.58867i	0.124871	−	0.216284i
$929$	50.4538			1.65534			0.827668	−	0.561217i	$-0.189667\pi$
$929$	50.4538			1.65534			0.827668	+	0.561217i	$0.189667\pi$
$930$		0			0
$931$		0			0
$932$	9.84350	−	5.68315i	0.322435	−	0.186158i
$933$		0			0
$934$	31.4234	−	18.1423i	1.02821	−	0.593635i
$935$	7.88868	+	4.55453i	0.257987	+	0.148949i
$936$		0			0
$937$		−	42.6251i		−	1.39250i	−0.717799	−	0.696250i	$-0.754850\pi$
$937$		−	42.6251i		−	1.39250i	0.717799	−	0.696250i	$-0.245150\pi$
$938$		0			0
$939$		0			0
$940$	−3.22758	+	5.59033i	−0.105272	+	0.182336i
$941$	55.0404			1.79427			0.897133	−	0.441761i	$-0.145646\pi$
$941$	55.0404			1.79427			0.897133	+	0.441761i	$0.145646\pi$
$942$		0			0
$943$			8.32815i			0.271202i
$944$	10.8659			0.353656
$945$		0			0
$946$	−10.8189			−0.351752
$947$		−	25.6884i		−	0.834760i	−0.908732	−	0.417380i	$-0.862948\pi$
$947$		−	25.6884i		−	0.834760i	0.908732	−	0.417380i	$-0.137052\pi$
$948$		0			0
$949$	−3.03875			−0.0986421
$950$	−7.60248	+	13.1679i	−0.246657	+	0.427223i
$951$		0			0
$952$		0			0
$953$		−	17.3463i		−	0.561903i	−0.959722	−	0.280952i	$-0.909350\pi$
$953$		−	17.3463i		−	0.561903i	0.959722	−	0.280952i	$-0.0906500\pi$
$954$		0			0
$955$	1.46279	+	0.844541i	0.0473347	+	0.0273287i
$956$	4.67039	−	2.69645i	0.151051	−	0.0872094i
$957$		0			0
$958$	−20.0875	+	11.5975i	−0.648998	+	0.374699i
$959$		0			0
$960$		0			0
$961$	−90.0362			−2.90439
$962$	1.82955	−	3.16887i	0.0589870	−	0.102169i
$963$		0			0
$964$	−12.1233	+	6.99936i	−0.390464	+	0.225434i
$965$	0.703935	−	1.21925i	0.0226605	−	0.0392491i
$966$		0			0
$967$	2.61334	+	4.52644i	0.0840393	+	0.145560i	0.904981	−	0.425451i	$-0.139885\pi$
$967$	2.61334	+	4.52644i	0.0840393	+	0.145560i	−0.820942	+	0.571011i	$0.806551\pi$
$968$	−6.86292	−	3.96231i	−0.220583	−	0.127353i
$969$		0			0
$970$	2.13925	+	3.70529i	0.0686873	+	0.118970i
$971$	−14.2195	−	24.6289i	−0.456326	−	0.790379i	0.542438	−	0.840096i	$-0.317501\pi$
$971$	−14.2195	−	24.6289i	−0.456326	−	0.790379i	−0.998763	+	0.0497167i	$0.984168\pi$
$972$		0			0
$973$		0			0
$974$	24.8887	+	14.3695i	0.797485	+	0.460428i
$975$		0			0
$976$			1.09663i			0.0351021i
$977$		−	24.3217i		−	0.778119i	−0.921213	−	0.389059i	$-0.872800\pi$
$977$		−	24.3217i		−	0.778119i	0.921213	−	0.389059i	$-0.127200\pi$
$978$		0			0
$979$	6.55917	+	3.78694i	0.209632	+	0.121031i
$980$		0			0
$981$		0			0
$982$	12.1326	+	21.0143i	0.387168	+	0.670595i
$983$	−13.4186	−	23.2417i	−0.427987	−	0.741295i	0.568707	−	0.822540i	$-0.307444\pi$
$983$	−13.4186	−	23.2417i	−0.427987	−	0.741295i	−0.996694	+	0.0812449i	$0.974110\pi$
$984$		0			0
$985$	2.01222	+	1.16176i	0.0641147	+	0.0370166i
$986$	−20.8182	−	36.0582i	−0.662987	−	1.14833i
$987$		0			0
$988$	−1.54353	+	2.67348i	−0.0491063	+	0.0850547i
$989$	−5.48446	+	3.16645i	−0.174396	+	0.100687i
$990$		0			0
$991$	−3.51093	+	6.08111i	−0.111528	+	0.193173i	−0.916387	−	0.400294i	$-0.868908\pi$
$991$	−3.51093	+	6.08111i	−0.111528	+	0.193173i	0.804858	+	0.593467i	$0.202241\pi$
$992$	11.0016			0.349303
$993$		0			0
$994$		0			0
$995$	8.99193	−	5.19149i	0.285063	−	0.164581i
$996$		0			0
$997$	9.60463	−	5.54524i	0.304182	−	0.175619i	−0.340138	−	0.940375i	$-0.610474\pi$
$997$	9.60463	−	5.54524i	0.304182	−	0.175619i	0.644320	+	0.764756i	$0.277141\pi$
$998$	23.0209	+	13.2911i	0.728713	+	0.420723i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.l.c.521.5		48
3.2	odd	2		882.2.l.c.227.19		48
7.2	even	3		2646.2.t.c.1979.8		48
7.3	odd	6		2646.2.m.c.1763.16		48
7.4	even	3		2646.2.m.c.1763.15		48
7.5	odd	6		2646.2.t.c.1979.7		48
7.6	odd	2	inner	2646.2.l.c.521.6		48
9.4	even	3		882.2.t.c.815.24		48
9.5	odd	6		2646.2.t.c.2285.7		48
21.2	odd	6		882.2.t.c.803.13		48
21.5	even	6		882.2.t.c.803.24		48
21.11	odd	6		882.2.m.c.587.10	yes	48
21.17	even	6		882.2.m.c.587.3	yes	48
21.20	even	2		882.2.l.c.227.18		48
63.4	even	3		882.2.m.c.293.3	✓	48
63.5	even	6	inner	2646.2.l.c.1097.5		48
63.13	odd	6		882.2.t.c.815.13		48
63.23	odd	6	inner	2646.2.l.c.1097.6		48
63.31	odd	6		882.2.m.c.293.10	yes	48
63.32	odd	6		2646.2.m.c.881.16		48
63.40	odd	6		882.2.l.c.509.7		48
63.41	even	6		2646.2.t.c.2285.8		48
63.58	even	3		882.2.l.c.509.6		48
63.59	even	6		2646.2.m.c.881.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.18		48	21.20	even	2
882.2.l.c.227.19		48	3.2	odd	2
882.2.l.c.509.6		48	63.58	even	3
882.2.l.c.509.7		48	63.40	odd	6
882.2.m.c.293.3	✓	48	63.4	even	3
882.2.m.c.293.10	yes	48	63.31	odd	6
882.2.m.c.587.3	yes	48	21.17	even	6
882.2.m.c.587.10	yes	48	21.11	odd	6
882.2.t.c.803.13		48	21.2	odd	6
882.2.t.c.803.24		48	21.5	even	6
882.2.t.c.815.13		48	63.13	odd	6
882.2.t.c.815.24		48	9.4	even	3
2646.2.l.c.521.5		48	1.1	even	1	trivial
2646.2.l.c.521.6		48	7.6	odd	2	inner
2646.2.l.c.1097.5		48	63.5	even	6	inner
2646.2.l.c.1097.6		48	63.23	odd	6	inner
2646.2.m.c.881.15		48	63.59	even	6
2646.2.m.c.881.16		48	63.32	odd	6
2646.2.m.c.1763.15		48	7.4	even	3
2646.2.m.c.1763.16		48	7.3	odd	6
2646.2.t.c.1979.7		48	7.5	odd	6
2646.2.t.c.1979.8		48	7.2	even	3
2646.2.t.c.2285.7		48	9.5	odd	6
2646.2.t.c.2285.8		48	63.41	even	6

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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.474556 + 0.821956i) q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.474556 + 0.821956i) q^{5} +1.00000i q^{8} +(0.821956 + 0.474556i) q^{10} +(1.51873 - 0.876838i) q^{11} +(-0.720756 + 0.416129i) q^{13} +1.00000 q^{16} +(2.73638 - 4.73955i) q^{17} +(-3.21232 + 1.85463i) q^{19} +(0.474556 - 0.821956i) q^{20} +(-0.876838 - 1.51873i) q^{22} +(-0.888998 - 0.513263i) q^{23} +(2.04959 + 3.55000i) q^{25} +(0.416129 + 0.720756i) q^{26} +(6.58867 + 3.80397i) q^{29} +11.0016i q^{31} -1.00000i q^{32} +(-4.73955 - 2.73638i) q^{34} +(-2.19830 - 3.80756i) q^{37} +(1.85463 + 3.21232i) q^{38} +(-0.821956 - 0.474556i) q^{40} +(-4.05647 - 7.02601i) q^{41} +(3.08463 - 5.34273i) q^{43} +(-1.51873 + 0.876838i) q^{44} +(-0.513263 + 0.888998i) q^{46} -6.80125 q^{47} +(3.55000 - 2.04959i) q^{50} +(0.720756 - 0.416129i) q^{52} +(-1.88177 - 1.08644i) q^{53} +1.66444i q^{55} +(3.80397 - 6.58867i) q^{58} +10.8659 q^{59} +1.09663i q^{61} +11.0016 q^{62} -1.00000 q^{64} -0.789907i q^{65} +14.4481 q^{67} +(-2.73638 + 4.73955i) q^{68} +11.0131i q^{71} +(3.16204 + 1.82561i) q^{73} +(-3.80756 + 2.19830i) q^{74} +(3.21232 - 1.85463i) q^{76} +9.84819 q^{79} +(-0.474556 + 0.821956i) q^{80} +(-7.02601 + 4.05647i) q^{82} +(-2.41103 + 4.17603i) q^{83} +(2.59713 + 4.49837i) q^{85} +(-5.34273 - 3.08463i) q^{86} +(0.876838 + 1.51873i) q^{88} +(2.15943 + 3.74024i) q^{89} +(0.888998 + 0.513263i) q^{92} +6.80125i q^{94} -3.52051i q^{95} +(3.90396 + 2.25395i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} + 48 q^{11} + 48 q^{16} + 48 q^{23} - 24 q^{25} - 48 q^{44} + 48 q^{50} - 96 q^{53} - 48 q^{64} - 96 q^{79} + 48 q^{85} + 96 q^{86} - 48 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 + 48 * q^11 + 48 * q^16 + 48 * q^23 - 24 * q^25 - 48 * q^44 + 48 * q^50 - 96 * q^53 - 48 * q^64 - 96 * q^79 + 48 * q^85 + 96 * q^86 - 48 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more