LMFDB - Embedded newform 2646.2.e.p.2125.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1549,2646)]

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([2, 2]))

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

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

chi := DirichletCharacter("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.e (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2125.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	2646.2125
Dual form			2646.2.e.p.1549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.794182 + 1.37556i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.794182 + 1.37556i) q^{5} +1.00000 q^{8} +(-0.794182 + 1.37556i) q^{10} +(-0.794182 - 1.37556i) q^{11} +(-2.40545 - 4.16635i) q^{13} +1.00000 q^{16} +(-2.69963 + 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +(-0.794182 + 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} +(0.150186 - 0.260130i) q^{23} +(1.23855 + 2.14523i) q^{25} +(-2.40545 - 4.16635i) q^{26} +(-4.13781 + 7.16689i) q^{29} +2.71201 q^{31} +1.00000 q^{32} +(-2.69963 + 4.67589i) q^{34} +(0.500000 + 0.866025i) q^{37} +(3.54944 + 6.14781i) q^{38} +(-0.794182 + 1.37556i) q^{40} +(2.93818 + 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} +(-0.794182 - 1.37556i) q^{44} +(0.150186 - 0.260130i) q^{46} +2.66621 q^{47} +(1.23855 + 2.14523i) q^{50} +(-2.40545 - 4.16635i) q^{52} +(-2.44437 + 4.23377i) q^{53} +2.52290 q^{55} +(-4.13781 + 7.16689i) q^{58} +6.47710 q^{59} +4.47710 q^{61} +2.71201 q^{62} +1.00000 q^{64} +7.64145 q^{65} -10.0531 q^{67} +(-2.69963 + 4.67589i) q^{68} -12.7207 q^{71} +(-8.02654 + 13.9024i) q^{73} +(0.500000 + 0.866025i) q^{74} +(3.54944 + 6.14781i) q^{76} +8.38688 q^{79} +(-0.794182 + 1.37556i) q^{80} +(2.93818 + 5.08907i) q^{82} +(1.18292 - 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(-0.833104 + 1.44298i) q^{86} +(-0.794182 - 1.37556i) q^{88} +(1.60507 + 2.78007i) q^{89} +(0.150186 - 0.260130i) q^{92} +2.66621 q^{94} -11.2756 q^{95} +(-0.712008 + 1.23323i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8	$ 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8} + q^{10} + q^{11} - 8 q^{13} + 6 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 8 q^{26} + 5 q^{29} + 40 q^{31} + 6 q^{32} - 4 q^{34} + 3 q^{37} + 3 q^{38} + q^{40} - 6 q^{43} + q^{44} + 7 q^{46} + 18 q^{47} + 2 q^{50} - 8 q^{52} - 15 q^{53} + 26 q^{55} + 5 q^{58} + 28 q^{59} + 16 q^{61} + 40 q^{62} + 6 q^{64} - 24 q^{65} - 2 q^{67} - 4 q^{68} - 14 q^{71} - 19 q^{73} + 3 q^{74} + 3 q^{76} - 10 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} - 9 q^{89} + 7 q^{92} + 18 q^{94} - 8 q^{95} - 28 q^{97}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8 + q^10 + q^11 - 8 * q^13 + 6 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 + 7 * q^23 + 2 * q^25 - 8 * q^26 + 5 * q^29 + 40 * q^31 + 6 * q^32 - 4 * q^34 + 3 * q^37 + 3 * q^38 + q^40 - 6 * q^43 + q^44 + 7 * q^46 + 18 * q^47 + 2 * q^50 - 8 * q^52 - 15 * q^53 + 26 * q^55 + 5 * q^58 + 28 * q^59 + 16 * q^61 + 40 * q^62 + 6 * q^64 - 24 * q^65 - 2 * q^67 - 4 * q^68 - 14 * q^71 - 19 * q^73 + 3 * q^74 + 3 * q^76 - 10 * q^79 + q^80 + 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 - 9 * q^89 + 7 * q^92 + 18 * q^94 - 8 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.794182	+	1.37556i	−0.355169	+	0.615171i	−0.987147	−	0.159816i	$-0.948910\pi$
$5$	−0.794182	+	1.37556i	−0.355169	+	0.615171i	0.631978	+	0.774986i	$0.282243\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.794182	+	1.37556i	−0.251142	+	0.434991i
$11$	−0.794182	−	1.37556i	−0.239455	−	0.414748i	0.721103	−	0.692828i	$-0.243635\pi$
$11$	−0.794182	−	1.37556i	−0.239455	−	0.414748i	−0.960558	+	0.278080i	$0.910302\pi$
$12$		0			0
$13$	−2.40545	−	4.16635i	−0.667151	−	1.15554i	−0.978697	−	0.205308i	$-0.934180\pi$
$13$	−2.40545	−	4.16635i	−0.667151	−	1.15554i	0.311547	−	0.950231i	$-0.399153\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−2.69963	+	4.67589i	−0.654756	+	1.13407i	0.327199	+	0.944955i	$0.393895\pi$
$17$	−2.69963	+	4.67589i	−0.654756	+	1.13407i	−0.981955	+	0.189115i	$0.939438\pi$
$18$		0			0
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	0.909831	+	0.414979i	$0.136211\pi$
$19$	3.54944	+	6.14781i	0.814298	+	1.41041i	−0.0955331	+	0.995426i	$0.530456\pi$
$20$	−0.794182	+	1.37556i	−0.177584	+	0.307585i
$21$		0			0
$22$	−0.794182	−	1.37556i	−0.169320	−	0.293271i
$23$	0.150186	−	0.260130i	0.0313159	−	0.0542408i	−0.849943	−	0.526875i	$-0.823364\pi$
$23$	0.150186	−	0.260130i	0.0313159	−	0.0542408i	0.881259	+	0.472634i	$0.156697\pi$
$24$		0			0
$25$	1.23855	+	2.14523i	0.247710	+	0.429046i
$26$	−2.40545	−	4.16635i	−0.471747	−	0.817089i
$27$		0			0
$28$		0			0
$29$	−4.13781	+	7.16689i	−0.768371	+	1.33086i	0.170074	+	0.985431i	$0.445599\pi$
$29$	−4.13781	+	7.16689i	−0.768371	+	1.33086i	−0.938446	+	0.345427i	$0.887734\pi$
$30$		0			0
$31$	2.71201			0.487091			0.243545	−	0.969889i	$-0.421689\pi$
$31$	2.71201			0.487091			0.243545	+	0.969889i	$0.421689\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−2.69963	+	4.67589i	−0.462982	+	0.801909i
$35$		0			0
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	3.54944	+	6.14781i	0.575796	+	0.997307i
$39$		0			0
$40$	−0.794182	+	1.37556i	−0.125571	+	0.217496i
$41$	2.93818	+	5.08907i	0.458866	+	0.794780i	0.998901	−	0.0468628i	$-0.0149223\pi$
$41$	2.93818	+	5.08907i	0.458866	+	0.794780i	−0.540035	+	0.841643i	$0.681589\pi$
$42$		0			0
$43$	−0.833104	+	1.44298i	−0.127047	+	0.220052i	−0.922531	−	0.385922i	$-0.873883\pi$
$43$	−0.833104	+	1.44298i	−0.127047	+	0.220052i	0.795484	+	0.605974i	$0.207217\pi$
$44$	−0.794182	−	1.37556i	−0.119727	−	0.207374i
$45$		0			0
$46$	0.150186	−	0.260130i	0.0221437	−	0.0383540i
$47$	2.66621			0.388906			0.194453	−	0.980912i	$-0.437707\pi$
$47$	2.66621			0.388906			0.194453	+	0.980912i	$0.437707\pi$
$48$		0			0
$49$		0			0
$50$	1.23855	+	2.14523i	0.175157	+	0.303382i
$51$		0			0
$52$	−2.40545	−	4.16635i	−0.333575	−	0.577769i
$53$	−2.44437	+	4.23377i	−0.335760	+	0.581553i	−0.983630	−	0.180197i	$-0.942326\pi$
$53$	−2.44437	+	4.23377i	−0.335760	+	0.581553i	0.647871	+	0.761750i	$0.275660\pi$
$54$		0			0
$55$	2.52290			0.340188
$56$		0			0
$57$		0			0
$58$	−4.13781	+	7.16689i	−0.543321	+	0.941059i
$59$	6.47710			0.843247			0.421623	−	0.906771i	$-0.361460\pi$
$59$	6.47710			0.843247			0.421623	+	0.906771i	$0.361460\pi$
$60$		0			0
$61$	4.47710			0.573234			0.286617	−	0.958045i	$-0.407469\pi$
$61$	4.47710			0.573234			0.286617	+	0.958045i	$0.407469\pi$
$62$	2.71201			0.344425
$63$		0			0
$64$	1.00000			0.125000
$65$	7.64145			0.947805
$66$		0			0
$67$	−10.0531			−1.22818			−0.614090	−	0.789236i	$-0.710477\pi$
$67$	−10.0531			−1.22818			−0.614090	+	0.789236i	$0.710477\pi$
$68$	−2.69963	+	4.67589i	−0.327378	+	0.567035i
$69$		0			0
$70$		0			0
$71$	−12.7207			−1.50967			−0.754833	−	0.655917i	$-0.772282\pi$
$71$	−12.7207			−1.50967			−0.754833	+	0.655917i	$0.772282\pi$
$72$		0			0
$73$	−8.02654	+	13.9024i	−0.939436	+	1.62715i	−0.172909	+	0.984938i	$0.555317\pi$
$73$	−8.02654	+	13.9024i	−0.939436	+	1.62715i	−0.766527	+	0.642213i	$0.778017\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$		0			0
$76$	3.54944	+	6.14781i	0.407149	+	0.705203i
$77$		0			0
$78$		0			0
$79$	8.38688			0.943597			0.471799	−	0.881706i	$-0.343605\pi$
$79$	8.38688			0.943597			0.471799	+	0.881706i	$0.343605\pi$
$80$	−0.794182	+	1.37556i	−0.0887922	+	0.153793i
$81$		0			0
$82$	2.93818	+	5.08907i	0.324467	+	0.561994i
$83$	1.18292	−	2.04887i	0.129842	−	0.224893i	−0.793773	−	0.608214i	$-0.791886\pi$
$83$	1.18292	−	2.04887i	0.129842	−	0.224893i	0.923615	+	0.383321i	$0.125220\pi$
$84$		0			0
$85$	−4.28799	−	7.42702i	−0.465098	−	0.805573i
$86$	−0.833104	+	1.44298i	−0.0898359	+	0.155600i
$87$		0			0
$88$	−0.794182	−	1.37556i	−0.0846601	−	0.146636i
$89$	1.60507	+	2.78007i	0.170138	+	0.294687i	0.938468	−	0.345367i	$-0.112245\pi$
$89$	1.60507	+	2.78007i	0.170138	+	0.294687i	−0.768330	+	0.640054i	$0.778912\pi$
$90$		0			0
$91$		0			0
$92$	0.150186	−	0.260130i	0.0156580	−	0.0271204i
$93$		0			0
$94$	2.66621			0.274998
$95$	−11.2756			−1.15685
$96$		0			0
$97$	−0.712008	+	1.23323i	−0.0722934	+	0.125216i	−0.899906	−	0.436084i	$-0.856365\pi$
$97$	−0.712008	+	1.23323i	−0.0722934	+	0.125216i	0.827613	+	0.561300i	$0.189698\pi$
$98$		0			0
$99$		0			0
$100$	1.23855	+	2.14523i	0.123855	+	0.214523i
$101$	−6.01671	−	10.4212i	−0.598685	−	1.03695i	−0.993015	−	0.117984i	$-0.962357\pi$
$101$	−6.01671	−	10.4212i	−0.598685	−	1.03695i	0.394330	−	0.918969i	$-0.370977\pi$
$102$		0			0
$103$	−3.04944	+	5.28179i	−0.300470	+	0.520430i	−0.976243	−	0.216680i	$-0.930477\pi$
$103$	−3.04944	+	5.28179i	−0.300470	+	0.520430i	0.675772	+	0.737111i	$0.263810\pi$
$104$	−2.40545	−	4.16635i	−0.235873	−	0.408545i
$105$		0			0
$106$	−2.44437	+	4.23377i	−0.237418	+	0.411220i
$107$	1.54325	+	2.67299i	0.149192	+	0.258408i	0.930929	−	0.365200i	$-0.118999\pi$
$107$	1.54325	+	2.67299i	0.149192	+	0.258408i	−0.781737	+	0.623608i	$0.785666\pi$
$108$		0			0
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	−0.806023	−	0.591884i	$-0.798384\pi$
$109$	1.14400	−	1.98146i	0.109575	−	0.189789i	0.915598	+	0.402095i	$0.131718\pi$
$110$	2.52290			0.240549
$111$		0			0
$112$		0			0
$113$	9.73236	+	16.8569i	0.915543	+	1.58577i	0.806104	+	0.591774i	$0.201572\pi$
$113$	9.73236	+	16.8569i	0.915543	+	1.58577i	0.109440	+	0.993993i	$0.465094\pi$
$114$		0			0
$115$	0.238550	+	0.413181i	0.0222449	+	0.0385293i
$116$	−4.13781	+	7.16689i	−0.384186	+	0.665429i
$117$		0			0
$118$	6.47710			0.596265
$119$		0			0
$120$		0			0
$121$	4.23855	−	7.34138i	0.385323	−	0.667399i
$122$	4.47710			0.405338
$123$		0			0
$124$	2.71201			0.243545
$125$	−11.8764			−1.06225
$126$		0			0
$127$	−13.4400			−1.19260			−0.596302	−	0.802760i	$-0.703364\pi$
$127$	−13.4400			−1.19260			−0.596302	+	0.802760i	$0.703364\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	7.64145			0.670199
$131$	1.58836	−	2.75113i	0.138776	−	0.240367i	−0.788258	−	0.615345i	$-0.789017\pi$
$131$	1.58836	−	2.75113i	0.138776	−	0.240367i	0.927034	+	0.374978i	$0.122350\pi$
$132$		0			0
$133$		0			0
$134$	−10.0531			−0.868454
$135$		0			0
$136$	−2.69963	+	4.67589i	−0.231491	+	0.400955i
$137$	−10.6316	−	18.4145i	−0.908320	−	1.57326i	−0.816397	−	0.577491i	$-0.804032\pi$
$137$	−10.6316	−	18.4145i	−0.908320	−	1.57326i	−0.0919231	−	0.995766i	$-0.529301\pi$
$138$		0			0
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	−0.998013	−	0.0630092i	$-0.979930\pi$
$139$	−6.52654	−	11.3043i	−0.553574	−	0.958818i	0.444439	−	0.895809i	$-0.353403\pi$
$140$		0			0
$141$		0			0
$142$	−12.7207			−1.06749
$143$	−3.82072	+	6.61769i	−0.319505	+	0.553399i
$144$		0			0
$145$	−6.57234	−	11.3836i	−0.545803	−	0.945359i
$146$	−8.02654	+	13.9024i	−0.664281	+	1.15057i
$147$		0			0
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	2.60439	−	4.51093i	0.213360	−	0.369550i	−0.739404	−	0.673262i	$-0.764893\pi$
$149$	2.60439	−	4.51093i	0.213360	−	0.369550i	0.952764	+	0.303712i	$0.0982261\pi$
$150$		0			0
$151$	0.261450	+	0.452845i	0.0212765	+	0.0368520i	0.876468	−	0.481461i	$-0.159894\pi$
$151$	0.261450	+	0.452845i	0.0212765	+	0.0368520i	−0.855191	+	0.518313i	$0.826560\pi$
$152$	3.54944	+	6.14781i	0.287898	+	0.498654i
$153$		0			0
$154$		0			0
$155$	−2.15383	+	3.73054i	−0.173000	+	0.299644i
$156$		0			0
$157$	−8.86398			−0.707422			−0.353711	−	0.935355i	$-0.615080\pi$
$157$	−8.86398			−0.707422			−0.353711	+	0.935355i	$0.615080\pi$
$158$	8.38688			0.667224
$159$		0			0
$160$	−0.794182	+	1.37556i	−0.0627856	+	0.108748i
$161$		0			0
$162$		0			0
$163$	10.9814	+	19.0204i	0.860132	+	1.48979i	0.871801	+	0.489860i	$0.162952\pi$
$163$	10.9814	+	19.0204i	0.860132	+	1.48979i	−0.0116689	+	0.999932i	$0.503714\pi$
$164$	2.93818	+	5.08907i	0.229433	+	0.397390i
$165$		0			0
$166$	1.18292	−	2.04887i	0.0918122	−	0.159023i
$167$	1.65019	+	2.85821i	0.127695	+	0.221175i	0.922783	−	0.385319i	$-0.125909\pi$
$167$	1.65019	+	2.85821i	0.127695	+	0.221175i	−0.795088	+	0.606494i	$0.792575\pi$
$168$		0			0
$169$	−5.07234	+	8.78555i	−0.390180	+	0.675812i
$170$	−4.28799	−	7.42702i	−0.328874	−	0.569626i
$171$		0			0
$172$	−0.833104	+	1.44298i	−0.0635236	+	0.110026i
$173$	19.1075			1.45272			0.726360	−	0.687315i	$-0.241211\pi$
$173$	19.1075			1.45272			0.726360	+	0.687315i	$0.241211\pi$
$174$		0			0
$175$		0			0
$176$	−0.794182	−	1.37556i	−0.0598637	−	0.103687i
$177$		0			0
$178$	1.60507	+	2.78007i	0.120305	+	0.208375i
$179$	8.03706	−	13.9206i	0.600718	−	1.04047i	−0.391994	−	0.919968i	$-0.628215\pi$
$179$	8.03706	−	13.9206i	0.600718	−	1.04047i	0.992712	−	0.120507i	$-0.0384520\pi$
$180$		0			0
$181$	−8.05308			−0.598581			−0.299291	−	0.954162i	$-0.596750\pi$
$181$	−8.05308			−0.598581			−0.299291	+	0.954162i	$0.596750\pi$
$182$		0			0
$183$		0			0
$184$	0.150186	−	0.260130i	0.0110719	−	0.0191770i
$185$	−1.58836			−0.116779
$186$		0			0
$187$	8.57598			0.627138
$188$	2.66621			0.194453
$189$		0			0
$190$	−11.2756			−0.818019
$191$	23.9629			1.73389			0.866946	−	0.498402i	$-0.166080\pi$
$191$	23.9629			1.73389			0.866946	+	0.498402i	$0.166080\pi$
$192$		0			0
$193$	9.76509			0.702907			0.351453	−	0.936205i	$-0.385688\pi$
$193$	9.76509			0.702907			0.351453	+	0.936205i	$0.385688\pi$
$194$	−0.712008	+	1.23323i	−0.0511192	+	0.0885410i
$195$		0			0
$196$		0			0
$197$	18.2436			1.29980			0.649900	−	0.760020i	$-0.274811\pi$
$197$	18.2436			1.29980			0.649900	+	0.760020i	$0.274811\pi$
$198$		0			0
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	0.343601	+	0.939116i	$0.388353\pi$
$199$	−9.04944	+	15.6741i	−0.641498	+	1.11111i	−0.985098	+	0.171991i	$0.944980\pi$
$200$	1.23855	+	2.14523i	0.0875787	+	0.151691i
$201$		0			0
$202$	−6.01671	−	10.4212i	−0.423334	−	0.733236i
$203$		0			0
$204$		0			0
$205$	−9.33379			−0.651900
$206$	−3.04944	+	5.28179i	−0.212465	+	0.368000i
$207$		0			0
$208$	−2.40545	−	4.16635i	−0.166788	−	0.288885i
$209$	5.63781	−	9.76497i	0.389975	−	0.675457i
$210$		0			0
$211$	0.166208	+	0.287880i	0.0114422	+	0.0198185i	0.871690	−	0.490058i	$-0.163024\pi$
$211$	0.166208	+	0.287880i	0.0114422	+	0.0198185i	−0.860248	+	0.509877i	$0.829691\pi$
$212$	−2.44437	+	4.23377i	−0.167880	+	0.290776i
$213$		0			0
$214$	1.54325	+	2.67299i	0.105495	+	0.182722i
$215$	−1.32327	−	2.29197i	−0.0902464	−	0.156311i
$216$		0			0
$217$		0			0
$218$	1.14400	−	1.98146i	0.0774812	−	0.134201i
$219$		0			0
$220$	2.52290			0.170094
$221$	25.9752			1.74728
$222$		0			0
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	−0.952348	−	0.305013i	$-0.901339\pi$
$223$	−3.16621	+	5.48403i	−0.212025	+	0.367238i	0.740323	+	0.672251i	$0.234672\pi$
$224$		0			0
$225$		0			0
$226$	9.73236	+	16.8569i	0.647387	+	1.12131i
$227$	11.6545	+	20.1862i	0.773537	+	1.33981i	0.935613	+	0.353028i	$0.114848\pi$
$227$	11.6545	+	20.1862i	0.773537	+	1.33981i	−0.162075	+	0.986778i	$0.551819\pi$
$228$		0			0
$229$	−2.47710	+	4.29046i	−0.163691	+	0.283522i	−0.936190	−	0.351495i	$-0.885673\pi$
$229$	−2.47710	+	4.29046i	−0.163691	+	0.283522i	0.772498	+	0.635017i	$0.219007\pi$
$230$	0.238550	+	0.413181i	0.0157295	+	0.0272443i
$231$		0			0
$232$	−4.13781	+	7.16689i	−0.271660	+	0.470529i
$233$	7.13781	+	12.3630i	0.467613	+	0.809930i	0.999315	−	0.0370017i	$-0.0117807\pi$
$233$	7.13781	+	12.3630i	0.467613	+	0.809930i	−0.531702	+	0.846932i	$0.678447\pi$
$234$		0			0
$235$	−2.11745	+	3.66754i	−0.138127	+	0.239244i
$236$	6.47710			0.421623
$237$		0			0
$238$		0			0
$239$	−2.48762	−	4.30868i	−0.160911	−	0.278706i	0.774285	−	0.632837i	$-0.218110\pi$
$239$	−2.48762	−	4.30868i	−0.160911	−	0.278706i	−0.935196	+	0.354132i	$0.884776\pi$
$240$		0			0
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	0.577107	−	0.816668i	$-0.304181\pi$
$241$	−6.50000	−	11.2583i	−0.418702	−	0.725213i	−0.995809	+	0.0914555i	$0.970848\pi$
$242$	4.23855	−	7.34138i	0.272464	−	0.471922i
$243$		0			0
$244$	4.47710			0.286617
$245$		0			0
$246$		0			0
$247$	17.0760	−	29.5765i	1.08652	−	1.88191i
$248$	2.71201			0.172213
$249$		0			0
$250$	−11.8764			−0.751127
$251$	2.43268			0.153549			0.0767746	−	0.997048i	$-0.475538\pi$
$251$	2.43268			0.153549			0.0767746	+	0.997048i	$0.475538\pi$
$252$		0			0
$253$	−0.477100			−0.0299950
$254$	−13.4400			−0.843298
$255$		0			0
$256$	1.00000			0.0625000
$257$	0.493810	−	0.855304i	0.0308030	−	0.0533524i	−0.850213	−	0.526439i	$-0.823527\pi$
$257$	0.493810	−	0.855304i	0.0308030	−	0.0533524i	0.881016	+	0.473087i	$0.156860\pi$
$258$		0			0
$259$		0			0
$260$	7.64145			0.473902
$261$		0			0
$262$	1.58836	−	2.75113i	0.0981295	−	0.169965i
$263$	8.59269	+	14.8830i	0.529848	+	0.917724i	0.999394	+	0.0348158i	$0.0110845\pi$
$263$	8.59269	+	14.8830i	0.529848	+	0.917724i	−0.469545	+	0.882908i	$0.655582\pi$
$264$		0			0
$265$	−3.88255	−	6.72477i	−0.238503	−	0.413099i
$266$		0			0
$267$		0			0
$268$	−10.0531			−0.614090
$269$	11.4523	−	19.8360i	0.698262	−	1.20942i	−0.270807	−	0.962634i	$-0.587291\pi$
$269$	11.4523	−	19.8360i	0.698262	−	1.20942i	0.969069	−	0.246791i	$-0.0793761\pi$
$270$		0			0
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	0.571021	−	0.820936i	$-0.306548\pi$
$271$	−7.00364	−	12.1307i	−0.425441	−	0.736885i	−0.996462	+	0.0840504i	$0.973214\pi$
$272$	−2.69963	+	4.67589i	−0.163689	+	0.283518i
$273$		0			0
$274$	−10.6316	−	18.4145i	−0.642279	−	1.11246i
$275$	1.96727	−	3.40741i	0.118631	−	0.205474i
$276$		0			0
$277$	−14.1476	−	24.5044i	−0.850049	−	1.47233i	−0.881163	−	0.472813i	$-0.843239\pi$
$277$	−14.1476	−	24.5044i	−0.850049	−	1.47233i	0.0311139	−	0.999516i	$-0.490095\pi$
$278$	−6.52654	−	11.3043i	−0.391436	−	0.677987i
$279$		0			0
$280$		0			0
$281$	8.79782	−	15.2383i	0.524834	−	0.909039i	−0.474748	−	0.880122i	$-0.657461\pi$
$281$	8.79782	−	15.2383i	0.524834	−	0.909039i	0.999582	−	0.0289175i	$-0.00920600\pi$
$282$		0			0
$283$	18.5229			1.10107			0.550536	−	0.834811i	$-0.314423\pi$
$283$	18.5229			1.10107			0.550536	+	0.834811i	$0.314423\pi$
$284$	−12.7207			−0.754833
$285$		0			0
$286$	−3.82072	+	6.61769i	−0.225924	+	0.391312i
$287$		0			0
$288$		0			0
$289$	−6.07598	−	10.5239i	−0.357411	−	0.619054i
$290$	−6.57234	−	11.3836i	−0.385941	−	0.668470i
$291$		0			0
$292$	−8.02654	+	13.9024i	−0.469718	+	0.813575i
$293$	−7.04256	−	12.1981i	−0.411431	−	0.712619i	0.583616	−	0.812030i	$-0.301638\pi$
$293$	−7.04256	−	12.1981i	−0.411431	−	0.712619i	−0.995046	+	0.0994108i	$0.968304\pi$
$294$		0			0
$295$	−5.14400	+	8.90966i	−0.299495	+	0.518741i
$296$	0.500000	+	0.866025i	0.0290619	+	0.0503367i
$297$		0			0
$298$	2.60439	−	4.51093i	0.150868	−	0.261311i
$299$	−1.44506			−0.0835698
$300$		0			0
$301$		0			0
$302$	0.261450	+	0.452845i	0.0150448	+	0.0260583i
$303$		0			0
$304$	3.54944	+	6.14781i	0.203574	+	0.352601i
$305$	−3.55563	+	6.15854i	−0.203595	+	0.352637i
$306$		0			0
$307$	5.85532			0.334180			0.167090	−	0.985942i	$-0.446563\pi$
$307$	5.85532			0.334180			0.167090	+	0.985942i	$0.446563\pi$
$308$		0			0
$309$		0			0
$310$	−2.15383	+	3.73054i	−0.122329	+	0.211880i
$311$	0.810892			0.0459815			0.0229907	−	0.999736i	$-0.492681\pi$
$311$	0.810892			0.0459815			0.0229907	+	0.999736i	$0.492681\pi$
$312$		0			0
$313$	−10.5760			−0.597790			−0.298895	−	0.954286i	$-0.596618\pi$
$313$	−10.5760			−0.597790			−0.298895	+	0.954286i	$0.596618\pi$
$314$	−8.86398			−0.500223
$315$		0			0
$316$	8.38688			0.471799
$317$	−12.1964			−0.685018			−0.342509	−	0.939515i	$-0.611277\pi$
$317$	−12.1964			−0.685018			−0.342509	+	0.939515i	$0.611277\pi$
$318$		0			0
$319$	13.1447			0.735961
$320$	−0.794182	+	1.37556i	−0.0443961	+	0.0768963i
$321$		0			0
$322$		0			0
$323$	−38.3287			−2.13267
$324$		0			0
$325$	5.95853	−	10.3205i	0.330520	−	0.572477i
$326$	10.9814	+	19.0204i	0.608205	+	1.05344i
$327$		0			0
$328$	2.93818	+	5.08907i	0.162234	+	0.280997i
$329$		0			0
$330$		0			0
$331$	−15.6662			−0.861093			−0.430546	−	0.902568i	$-0.641679\pi$
$331$	−15.6662			−0.861093			−0.430546	+	0.902568i	$0.641679\pi$
$332$	1.18292	−	2.04887i	0.0649211	−	0.112447i
$333$		0			0
$334$	1.65019	+	2.85821i	0.0902942	+	0.156394i
$335$	7.98398	−	13.8287i	0.436211	−	0.755540i
$336$		0			0
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	0.728200	−	0.685364i	$-0.240357\pi$
$337$	−4.21201	−	7.29541i	−0.229443	−	0.397406i	−0.957643	+	0.287958i	$0.907024\pi$
$338$	−5.07234	+	8.78555i	−0.275899	+	0.477871i
$339$		0			0
$340$	−4.28799	−	7.42702i	−0.232549	−	0.402787i
$341$	−2.15383	−	3.73054i	−0.116636	−	0.202020i
$342$		0			0
$343$		0			0
$344$	−0.833104	+	1.44298i	−0.0449179	+	0.0778002i
$345$		0			0
$346$	19.1075			1.02723
$347$	−0.567323			−0.0304555			−0.0152277	−	0.999884i	$-0.504847\pi$
$347$	−0.567323			−0.0304555			−0.0152277	+	0.999884i	$0.504847\pi$
$348$		0			0
$349$	0.00364189	−	0.00630794i	0.000194946	−	0.000337656i	−0.865928	−	0.500169i	$-0.833271\pi$
$349$	0.00364189	−	0.00630794i	0.000194946	−	0.000337656i	0.866123	+	0.499831i	$0.166605\pi$
$350$		0			0
$351$		0			0
$352$	−0.794182	−	1.37556i	−0.0423300	−	0.0733178i
$353$	−3.32691	−	5.76238i	−0.177074	−	0.306701i	0.763803	−	0.645449i	$-0.223330\pi$
$353$	−3.32691	−	5.76238i	−0.177074	−	0.306701i	−0.940877	+	0.338748i	$0.889996\pi$
$354$		0			0
$355$	10.1025	−	17.4981i	0.536186	−	0.928702i
$356$	1.60507	+	2.78007i	0.0850688	+	0.147343i
$357$		0			0
$358$	8.03706	−	13.9206i	0.424772	−	0.735727i
$359$	0.398568	+	0.690339i	0.0210356	+	0.0364347i	0.876352	−	0.481672i	$-0.159970\pi$
$359$	0.398568	+	0.690339i	0.0210356	+	0.0364347i	−0.855316	+	0.518107i	$0.826637\pi$
$360$		0			0
$361$	−15.6971	+	27.1881i	−0.826162	+	1.43095i
$362$	−8.05308			−0.423261
$363$		0			0
$364$		0			0
$365$	−12.7491	−	22.0820i	−0.667317	−	1.15583i
$366$		0			0
$367$	−7.71634	−	13.3651i	−0.402790	−	0.697652i	0.591272	−	0.806472i	$-0.298626\pi$
$367$	−7.71634	−	13.3651i	−0.402790	−	0.697652i	−0.994061	+	0.108820i	$0.965293\pi$
$368$	0.150186	−	0.260130i	0.00782898	−	0.0135602i
$369$		0			0
$370$	−1.58836			−0.0825751
$371$		0			0
$372$		0			0
$373$	−5.12110	+	8.87000i	−0.265160	+	0.459271i	−0.967606	−	0.252467i	$-0.918758\pi$
$373$	−5.12110	+	8.87000i	−0.265160	+	0.459271i	0.702445	+	0.711738i	$0.252092\pi$
$374$	8.57598			0.443454
$375$		0			0
$376$	2.66621			0.137499
$377$	39.8131			2.05048
$378$		0			0
$379$	25.0087			1.28461			0.642304	−	0.766450i	$-0.277979\pi$
$379$	25.0087			1.28461			0.642304	+	0.766450i	$0.277979\pi$
$380$	−11.2756			−0.578427
$381$		0			0
$382$	23.9629			1.22605
$383$	3.13348	−	5.42734i	0.160113	−	0.277324i	−0.774796	−	0.632211i	$-0.782147\pi$
$383$	3.13348	−	5.42734i	0.160113	−	0.277324i	0.934909	+	0.354887i	$0.115481\pi$
$384$		0			0
$385$		0			0
$386$	9.76509			0.497030
$387$		0			0
$388$	−0.712008	+	1.23323i	−0.0361467	+	0.0626080i
$389$	−10.8171	−	18.7357i	−0.548448	−	0.949940i	−0.998381	−	0.0568774i	$-0.981886\pi$
$389$	−10.8171	−	18.7357i	−0.548448	−	0.949940i	0.449933	−	0.893062i	$-0.351448\pi$
$390$		0			0
$391$	0.810892	+	1.40451i	0.0410086	+	0.0710290i
$392$		0			0
$393$		0			0
$394$	18.2436			0.919098
$395$	−6.66071	+	11.5367i	−0.335137	+	0.580473i
$396$		0			0
$397$	−2.05308	−	3.55605i	−0.103041	−	0.178473i	0.809895	−	0.586575i	$-0.199524\pi$
$397$	−2.05308	−	3.55605i	−0.103041	−	0.178473i	−0.912936	+	0.408102i	$0.866191\pi$
$398$	−9.04944	+	15.6741i	−0.453608	+	0.785671i
$399$		0			0
$400$	1.23855	+	2.14523i	0.0619275	+	0.107262i
$401$	8.37085	−	14.4987i	0.418021	−	0.724033i	−0.577720	−	0.816235i	$-0.696057\pi$
$401$	8.37085	−	14.4987i	0.418021	−	0.724033i	0.995740	+	0.0922024i	$0.0293907\pi$
$402$		0			0
$403$	−6.52359	−	11.2992i	−0.324963	−	0.562853i
$404$	−6.01671	−	10.4212i	−0.299343	−	0.518476i
$405$		0			0
$406$		0			0
$407$	0.794182	−	1.37556i	0.0393661	−	0.0681842i
$408$		0			0
$409$	8.76509			0.433406			0.216703	−	0.976238i	$-0.430470\pi$
$409$	8.76509			0.433406			0.216703	+	0.976238i	$0.430470\pi$
$410$	−9.33379			−0.460963
$411$		0			0
$412$	−3.04944	+	5.28179i	−0.150235	+	0.260215i
$413$		0			0
$414$		0			0
$415$	1.87890	+	3.25436i	0.0922318	+	0.159750i
$416$	−2.40545	−	4.16635i	−0.117937	−	0.204272i
$417$		0			0
$418$	5.63781	−	9.76497i	0.275754	−	0.477620i
$419$	−0.210149	−	0.363988i	−0.0102664	−	0.0177820i	0.860847	−	0.508865i	$-0.169935\pi$
$419$	−0.210149	−	0.363988i	−0.0102664	−	0.0177820i	−0.871113	+	0.491083i	$0.836601\pi$
$420$		0			0
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	−0.774710	−	0.632316i	$-0.782104\pi$
$421$	3.28799	−	5.69497i	0.160247	−	0.277556i	0.934957	+	0.354761i	$0.115438\pi$
$422$	0.166208	+	0.287880i	0.00809086	+	0.0140138i
$423$		0			0
$424$	−2.44437	+	4.23377i	−0.118709	+	0.205610i
$425$	−13.3745			−0.648758
$426$		0			0
$427$		0			0
$428$	1.54325	+	2.67299i	0.0745959	+	0.129204i
$429$		0			0
$430$	−1.32327	−	2.29197i	−0.0638138	−	0.110529i
$431$	−11.0439	+	19.1287i	−0.531968	+	0.921395i	0.467336	+	0.884080i	$0.345214\pi$
$431$	−11.0439	+	19.1287i	−0.531968	+	0.921395i	−0.999304	+	0.0373155i	$0.988119\pi$
$432$		0			0
$433$	9.43268			0.453306			0.226653	−	0.973976i	$-0.427222\pi$
$433$	9.43268			0.453306			0.226653	+	0.973976i	$0.427222\pi$
$434$		0			0
$435$		0			0
$436$	1.14400	−	1.98146i	0.0547875	−	0.0948947i
$437$	2.13231			0.102002
$438$		0			0
$439$	31.2064			1.48940			0.744701	−	0.667398i	$-0.232592\pi$
$439$	31.2064			1.48940			0.744701	+	0.667398i	$0.232592\pi$
$440$	2.52290			0.120275
$441$		0			0
$442$	25.9752			1.23552
$443$	−13.0545			−0.620236			−0.310118	−	0.950698i	$-0.600369\pi$
$443$	−13.0545			−0.620236			−0.310118	+	0.950698i	$0.600369\pi$
$444$		0			0
$445$	−5.09888			−0.241710
$446$	−3.16621	+	5.48403i	−0.149924	+	0.259676i
$447$		0			0
$448$		0			0
$449$	9.91706			0.468015			0.234008	−	0.972235i	$-0.424816\pi$
$449$	9.91706			0.468015			0.234008	+	0.972235i	$0.424816\pi$
$450$		0			0
$451$	4.66690	−	8.08330i	0.219756	−	0.380628i
$452$	9.73236	+	16.8569i	0.457772	+	0.792884i
$453$		0			0
$454$	11.6545	+	20.1862i	0.546974	+	0.947386i
$455$		0			0
$456$		0			0
$457$	−24.5229			−1.14713			−0.573566	−	0.819159i	$-0.694441\pi$
$457$	−24.5229			−1.14713			−0.573566	+	0.819159i	$0.694441\pi$
$458$	−2.47710	+	4.29046i	−0.115747	+	0.200480i
$459$		0			0
$460$	0.238550	+	0.413181i	0.0111224	+	0.0192646i
$461$	1.75526	−	3.04020i	0.0817506	−	0.141596i	−0.822251	−	0.569125i	$-0.807282\pi$
$461$	1.75526	−	3.04020i	0.0817506	−	0.141596i	0.904002	+	0.427528i	$0.140616\pi$
$462$		0			0
$463$	8.69413	+	15.0587i	0.404050	+	0.699836i	0.994210	−	0.107451i	$-0.0342687\pi$
$463$	8.69413	+	15.0587i	0.404050	+	0.699836i	−0.590160	+	0.807286i	$0.700935\pi$
$464$	−4.13781	+	7.16689i	−0.192093	+	0.332715i
$465$		0			0
$466$	7.13781	+	12.3630i	0.330652	+	0.572707i
$467$	6.69894	+	11.6029i	0.309990	+	0.536918i	0.978360	−	0.206911i	$-0.0663410\pi$
$467$	6.69894	+	11.6029i	0.309990	+	0.536918i	−0.668370	+	0.743829i	$0.733008\pi$
$468$		0			0
$469$		0			0
$470$	−2.11745	+	3.66754i	−0.0976709	+	0.169171i
$471$		0			0
$472$	6.47710			0.298133
$473$	2.64654			0.121688
$474$		0			0
$475$	−8.79232	+	15.2287i	−0.403419	+	0.698743i
$476$		0			0
$477$		0			0
$478$	−2.48762	−	4.30868i	−0.113781	−	0.197075i
$479$	−10.4029	−	18.0183i	−0.475321	−	0.823279i	0.524280	−	0.851546i	$-0.324335\pi$
$479$	−10.4029	−	18.0183i	−0.475321	−	0.823279i	−0.999600	+	0.0282667i	$0.991001\pi$
$480$		0			0
$481$	2.40545	−	4.16635i	0.109679	−	0.189969i
$482$	−6.50000	−	11.2583i	−0.296067	−	0.512803i
$483$		0			0
$484$	4.23855	−	7.34138i	0.192661	−	0.333699i
$485$	−1.13093	−	1.95882i	−0.0513528	−	0.0889456i
$486$		0			0
$487$	16.2472	−	28.1410i	0.736231	−	1.27519i	−0.217950	−	0.975960i	$-0.569937\pi$
$487$	16.2472	−	28.1410i	0.736231	−	1.27519i	0.954181	−	0.299230i	$-0.0967298\pi$
$488$	4.47710			0.202669
$489$		0			0
$490$		0			0
$491$	9.66071	+	16.7328i	0.435982	+	0.755142i	0.997375	−	0.0724067i	$-0.0230679\pi$
$491$	9.66071	+	16.7328i	0.435982	+	0.755142i	−0.561394	+	0.827549i	$0.689735\pi$
$492$		0			0
$493$	−22.3411	−	38.6959i	−1.00619	−	1.74277i
$494$	17.0760	−	29.5765i	0.768285	−	1.33071i
$495$		0			0
$496$	2.71201			0.121773
$497$		0			0
$498$		0			0
$499$	5.57530	−	9.65670i	0.249585	−	0.432293i	−0.713826	−	0.700323i	$-0.753039\pi$
$499$	5.57530	−	9.65670i	0.249585	−	0.432293i	0.963411	+	0.268030i	$0.0863726\pi$
$500$	−11.8764			−0.531127
$501$		0			0
$502$	2.43268			0.108576
$503$	−40.7651			−1.81763			−0.908813	−	0.417204i	$-0.863010\pi$
$503$	−40.7651			−1.81763			−0.908813	+	0.417204i	$0.863010\pi$
$504$		0			0
$505$	19.1135			0.850537
$506$	−0.477100			−0.0212097
$507$		0			0
$508$	−13.4400			−0.596302
$509$	−0.722528	+	1.25146i	−0.0320255	+	0.0554698i	−0.881594	−	0.472009i	$-0.843529\pi$
$509$	−0.722528	+	1.25146i	−0.0320255	+	0.0554698i	0.849568	+	0.527478i	$0.176862\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	0.493810	−	0.855304i	0.0217810	−	0.0377259i
$515$	−4.84362	−	8.38940i	−0.213436	−	0.369681i
$516$		0			0
$517$	−2.11745	−	3.66754i	−0.0931255	−	0.161298i
$518$		0			0
$519$		0			0
$520$	7.64145			0.335100
$521$	9.64214	−	16.7007i	0.422430	−	0.731670i	−0.573747	−	0.819033i	$-0.694511\pi$
$521$	9.64214	−	16.7007i	0.422430	−	0.731670i	0.996177	+	0.0873630i	$0.0278440\pi$
$522$		0			0
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	0.918173	+	0.396180i	$0.129665\pi$
$523$	18.3454	+	31.7752i	0.802189	+	1.38943i	−0.115984	+	0.993251i	$0.537002\pi$
$524$	1.58836	−	2.75113i	0.0693880	−	0.120184i
$525$		0			0
$526$	8.59269	+	14.8830i	0.374659	+	0.648929i
$527$	−7.32141	+	12.6811i	−0.318926	+	0.552396i
$528$		0			0
$529$	11.4549	+	19.8404i	0.498039	+	0.862628i
$530$	−3.88255	−	6.72477i	−0.168647	−	0.292105i
$531$		0			0
$532$		0			0
$533$	14.1353	−	24.4830i	0.612266	−	1.06048i
$534$		0			0
$535$	−4.90249			−0.211953
$536$	−10.0531			−0.434227
$537$		0			0
$538$	11.4523	−	19.8360i	0.493745	−	0.855192i
$539$		0			0
$540$		0			0
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	0.828967	−	0.559298i	$-0.188929\pi$
$541$	−1.62543	−	2.81532i	−0.0698825	−	0.121040i	−0.898849	+	0.438258i	$0.855596\pi$
$542$	−7.00364	−	12.1307i	−0.300832	−	0.521057i
$543$		0			0
$544$	−2.69963	+	4.67589i	−0.115746	+	0.200477i
$545$	1.81708	+	3.14728i	0.0778352	+	0.134815i
$546$		0			0
$547$	−2.95853	+	5.12432i	−0.126498	+	0.219100i	−0.922317	−	0.386433i	$-0.873707\pi$
$547$	−2.95853	+	5.12432i	−0.126498	+	0.219100i	0.795820	+	0.605534i	$0.207040\pi$
$548$	−10.6316	−	18.4145i	−0.454160	−	0.786628i
$549$		0			0
$550$	1.96727	−	3.40741i	0.0838846	−	0.145292i
$551$	−58.7476			−2.50273
$552$		0			0
$553$		0			0
$554$	−14.1476	−	24.5044i	−0.601076	−	1.04109i
$555$		0			0
$556$	−6.52654	−	11.3043i	−0.276787	−	0.479409i
$557$	−12.8040	+	22.1772i	−0.542523	+	0.939678i	0.456235	+	0.889859i	$0.349198\pi$
$557$	−12.8040	+	22.1772i	−0.542523	+	0.939678i	−0.998758	+	0.0498188i	$0.984136\pi$
$558$		0			0
$559$	8.01594			0.339038
$560$		0			0
$561$		0			0
$562$	8.79782	−	15.2383i	0.371114	−	0.642788i
$563$	−46.6377			−1.96555			−0.982773	−	0.184817i	$-0.940831\pi$
$563$	−46.6377			−1.96555			−0.982773	+	0.184817i	$0.940831\pi$
$564$		0			0
$565$	−30.9171			−1.30069
$566$	18.5229			0.778576
$567$		0			0
$568$	−12.7207			−0.533747
$569$	−31.1978			−1.30788			−0.653939	−	0.756547i	$-0.726885\pi$
$569$	−31.1978			−1.30788			−0.653939	+	0.756547i	$0.726885\pi$
$570$		0			0
$571$	−15.6762			−0.656030			−0.328015	−	0.944672i	$-0.606380\pi$
$571$	−15.6762			−0.656030			−0.328015	+	0.944672i	$0.606380\pi$
$572$	−3.82072	+	6.61769i	−0.159752	+	0.276699i
$573$		0			0
$574$		0			0
$575$	0.744051			0.0310291
$576$		0			0
$577$	−6.99567	+	12.1169i	−0.291234	+	0.504431i	−0.974102	−	0.226110i	$-0.927399\pi$
$577$	−6.99567	+	12.1169i	−0.291234	+	0.504431i	0.682868	+	0.730542i	$0.260732\pi$
$578$	−6.07598	−	10.5239i	−0.252728	−	0.437737i
$579$		0			0
$580$	−6.57234	−	11.3836i	−0.272902	−	0.472680i
$581$		0			0
$582$		0			0
$583$	7.76509			0.321597
$584$	−8.02654	+	13.9024i	−0.332141	+	0.575285i
$585$		0			0
$586$	−7.04256	−	12.1981i	−0.290926	−	0.503898i
$587$	1.44801	−	2.50803i	0.0597658	−	0.103517i	−0.834594	−	0.550865i	$-0.814298\pi$
$587$	1.44801	−	2.50803i	0.0597658	−	0.103517i	0.894360	+	0.447348i	$0.147631\pi$
$588$		0			0
$589$	9.62612	+	16.6729i	0.396637	+	0.686996i
$590$	−5.14400	+	8.90966i	−0.211775	+	0.366805i
$591$		0			0
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−2.04394	−	3.54021i	−0.0839346	−	0.145379i	0.821002	−	0.570925i	$-0.193415\pi$
$593$	−2.04394	−	3.54021i	−0.0839346	−	0.145379i	−0.904937	+	0.425546i	$0.860082\pi$
$594$		0			0
$595$		0			0
$596$	2.60439	−	4.51093i	0.106680	−	0.184775i
$597$		0			0
$598$	−1.44506			−0.0590928
$599$	19.7651			0.807580			0.403790	−	0.914852i	$-0.367693\pi$
$599$	19.7651			0.807580			0.403790	+	0.914852i	$0.367693\pi$
$600$		0			0
$601$	13.4320	−	23.2649i	0.547902	−	0.948994i	−0.450516	−	0.892768i	$-0.648760\pi$
$601$	13.4320	−	23.2649i	0.547902	−	0.948994i	0.998418	−	0.0562261i	$-0.0179068\pi$
$602$		0			0
$603$		0			0
$604$	0.261450	+	0.452845i	0.0106383	+	0.0184260i
$605$	6.73236	+	11.6608i	0.273709	+	0.474079i
$606$		0			0
$607$	−7.62110	+	13.2001i	−0.309331	+	0.535777i	−0.978216	−	0.207589i	$-0.933438\pi$
$607$	−7.62110	+	13.2001i	−0.309331	+	0.535777i	0.668885	+	0.743366i	$0.266772\pi$
$608$	3.54944	+	6.14781i	0.143949	+	0.249327i
$609$		0			0
$610$	−3.55563	+	6.15854i	−0.143963	+	0.249352i
$611$	−6.41342	−	11.1084i	−0.259459	−	0.449396i
$612$		0			0
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	−0.892189	−	0.451662i	$-0.850831\pi$
$613$	−1.36033	+	2.35617i	−0.0549434	+	0.0951648i	0.837246	+	0.546827i	$0.184165\pi$
$614$	5.85532			0.236301
$615$		0			0
$616$		0			0
$617$	9.21812	+	15.9663i	0.371108	+	0.642777i	0.989736	−	0.142906i	$-0.0456448\pi$
$617$	9.21812	+	15.9663i	0.371108	+	0.642777i	−0.618629	+	0.785684i	$0.712311\pi$
$618$		0			0
$619$	0.0537728	+	0.0931373i	0.00216131	+	0.00374350i	0.867104	−	0.498127i	$-0.165979\pi$
$619$	0.0537728	+	0.0931373i	0.00216131	+	0.00374350i	−0.864943	+	0.501871i	$0.832645\pi$
$620$	−2.15383	+	3.73054i	−0.0864998	+	0.149822i
$621$		0			0
$622$	0.810892			0.0325138
$623$		0			0
$624$		0			0
$625$	3.23924	−	5.61053i	0.129570	−	0.224421i
$626$	−10.5760			−0.422701
$627$		0			0
$628$	−8.86398			−0.353711
$629$	−5.39926			−0.215282
$630$		0			0
$631$	35.7266			1.42225			0.711126	−	0.703064i	$-0.248185\pi$
$631$	35.7266			1.42225			0.711126	+	0.703064i	$0.248185\pi$
$632$	8.38688			0.333612
$633$		0			0
$634$	−12.1964			−0.484381
$635$	10.6738	−	18.4875i	0.423576	−	0.733655i
$636$		0			0
$637$		0			0
$638$	13.1447			0.520403
$639$		0			0
$640$	−0.794182	+	1.37556i	−0.0313928	+	0.0543739i
$641$	8.65638	+	14.9933i	0.341906	+	0.592199i	0.984787	−	0.173767i	$-0.0555941\pi$
$641$	8.65638	+	14.9933i	0.341906	+	0.592199i	−0.642880	+	0.765967i	$0.722261\pi$
$642$		0			0
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	−0.996451	−	0.0841700i	$-0.973176\pi$
$643$	−14.4821	−	25.0838i	−0.571119	−	0.989207i	0.425332	−	0.905037i	$-0.360157\pi$
$644$		0			0
$645$		0			0
$646$	−38.3287			−1.50802
$647$	1.27816	−	2.21384i	0.0502497	−	0.0870350i	−0.839807	−	0.542886i	$-0.817332\pi$
$647$	1.27816	−	2.21384i	0.0502497	−	0.0870350i	0.890056	+	0.455851i	$0.150665\pi$
$648$		0			0
$649$	−5.14400	−	8.90966i	−0.201920	−	0.349735i
$650$	5.95853	−	10.3205i	0.233713	−	0.404802i
$651$		0			0
$652$	10.9814	+	19.0204i	0.430066	+	0.744896i
$653$	14.9883	−	25.9605i	0.586538	−	1.01591i	−0.408144	−	0.912918i	$-0.633824\pi$
$653$	14.9883	−	25.9605i	0.586538	−	1.01591i	0.994682	−	0.102996i	$-0.0328428\pi$
$654$		0			0
$655$	2.52290	+	4.36979i	0.0985779	+	0.170742i
$656$	2.93818	+	5.08907i	0.114717	+	0.198695i
$657$		0			0
$658$		0			0
$659$	7.63162	−	13.2183i	0.297286	−	0.514914i	−0.678228	−	0.734851i	$-0.737252\pi$
$659$	7.63162	−	13.2183i	0.297286	−	0.514914i	0.975514	+	0.219937i	$0.0705853\pi$
$660$		0			0
$661$	27.2522			1.05999			0.529994	−	0.848001i	$-0.322194\pi$
$661$	27.2522			1.05999			0.529994	+	0.848001i	$0.322194\pi$
$662$	−15.6662			−0.608884
$663$		0			0
$664$	1.18292	−	2.04887i	0.0459061	−	0.0795117i
$665$		0			0
$666$		0			0
$667$	1.24288	+	2.15273i	0.0481245	+	0.0833541i
$668$	1.65019	+	2.85821i	0.0638476	+	0.110587i
$669$		0			0
$670$	7.98398	−	13.8287i	0.308448	−	0.534248i
$671$	−3.55563	−	6.15854i	−0.137264	−	0.237748i
$672$		0			0
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.0620280	−	0.998074i	$-0.480243\pi$
$673$	23.2280	−	40.2320i	0.895372	−	1.55083i	0.833344	−	0.552755i	$-0.186423\pi$
$674$	−4.21201	−	7.29541i	−0.162240	−	0.281009i
$675$		0			0
$676$	−5.07234	+	8.78555i	−0.195090	+	0.337906i
$677$	5.09888			0.195966			0.0979830	−	0.995188i	$-0.468761\pi$
$677$	5.09888			0.195966			0.0979830	+	0.995188i	$0.468761\pi$
$678$		0			0
$679$		0			0
$680$	−4.28799	−	7.42702i	−0.164437	−	0.284813i
$681$		0			0
$682$	−2.15383	−	3.73054i	−0.0824743	−	0.142850i
$683$	7.77197	−	13.4614i	0.297386	−	0.515088i	−0.678151	−	0.734923i	$-0.737218\pi$
$683$	7.77197	−	13.4614i	0.297386	−	0.515088i	0.975537	+	0.219835i	$0.0705518\pi$
$684$		0			0
$685$	33.7738			1.29043
$686$		0			0
$687$		0			0
$688$	−0.833104	+	1.44298i	−0.0317618	+	0.0550130i
$689$	23.5192			0.896009
$690$		0			0
$691$	−23.2967			−0.886246			−0.443123	−	0.896461i	$-0.646130\pi$
$691$	−23.2967			−0.886246			−0.443123	+	0.896461i	$0.646130\pi$
$692$	19.1075			0.726360
$693$		0			0
$694$	−0.567323			−0.0215353
$695$	20.7330			0.786449
$696$		0			0
$697$	−31.7280			−1.20178
$698$	0.00364189	−	0.00630794i	0.000137848	−	0.000238759i
$699$		0			0
$700$		0			0
$701$	45.6464			1.72404			0.862020	−	0.506874i	$-0.169199\pi$
$701$	45.6464			1.72404			0.862020	+	0.506874i	$0.169199\pi$
$702$		0			0
$703$	−3.54944	+	6.14781i	−0.133870	+	0.231869i
$704$	−0.794182	−	1.37556i	−0.0299319	−	0.0518435i
$705$		0			0
$706$	−3.32691	−	5.76238i	−0.125210	−	0.216870i
$707$		0			0
$708$		0			0
$709$	18.0014			0.676056			0.338028	−	0.941136i	$-0.390240\pi$
$709$	18.0014			0.676056			0.338028	+	0.941136i	$0.390240\pi$
$710$	10.1025	−	17.4981i	0.379141	−	0.656692i
$711$		0			0
$712$	1.60507	+	2.78007i	0.0601527	+	0.104188i
$713$	0.407305	−	0.705474i	0.0152537	−	0.0264202i
$714$		0			0
$715$	−6.06870	−	10.5113i	−0.226957	−	0.393100i
$716$	8.03706	−	13.9206i	0.300359	−	0.520237i
$717$		0			0
$718$	0.398568	+	0.690339i	0.0148744	+	0.0257632i
$719$	18.4389	+	31.9371i	0.687654	+	1.19105i	0.972595	+	0.232506i	$0.0746926\pi$
$719$	18.4389	+	31.9371i	0.687654	+	1.19105i	−0.284941	+	0.958545i	$0.591974\pi$
$720$		0			0
$721$		0			0
$722$	−15.6971	+	27.1881i	−0.584185	+	1.01184i
$723$		0			0
$724$	−8.05308			−0.299291
$725$	−20.4995			−0.761333
$726$		0			0
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	0.431692	+	0.902021i	$0.357917\pi$
$727$	−15.2429	+	26.4014i	−0.565327	+	0.979175i	−0.997019	+	0.0771543i	$0.975417\pi$
$728$		0			0
$729$		0			0
$730$	−12.7491	−	22.0820i	−0.471864	−	0.817293i
$731$	−4.49814	−	7.79101i	−0.166370	−	0.288161i
$732$		0			0
$733$	3.07530	−	5.32657i	0.113589	−	0.196741i	−0.803626	−	0.595135i	$-0.797099\pi$
$733$	3.07530	−	5.32657i	0.113589	−	0.196741i	0.917215	+	0.398393i	$0.130432\pi$
$734$	−7.71634	−	13.3651i	−0.284815	−	0.493314i
$735$		0			0
$736$	0.150186	−	0.260130i	0.00553593	−	0.00958851i
$737$	7.98398	+	13.8287i	0.294094	+	0.509385i
$738$		0			0
$739$	−20.3912	+	35.3186i	−0.750103	+	1.29922i	0.197670	+	0.980269i	$0.436663\pi$
$739$	−20.3912	+	35.3186i	−0.750103	+	1.29922i	−0.947772	+	0.318947i	$0.896671\pi$
$740$	−1.58836			−0.0583894
$741$		0			0
$742$		0			0
$743$	−7.25271	−	12.5621i	−0.266076	−	0.460858i	0.701769	−	0.712405i	$-0.252394\pi$
$743$	−7.25271	−	12.5621i	−0.266076	−	0.460858i	−0.967845	+	0.251547i	$0.919061\pi$
$744$		0			0
$745$	4.13671	+	7.16500i	0.151557	+	0.262505i
$746$	−5.12110	+	8.87000i	−0.187497	+	0.324754i
$747$		0			0
$748$	8.57598			0.313569
$749$		0			0
$750$		0			0
$751$	−2.09455	+	3.62787i	−0.0764314	+	0.132383i	−0.901708	−	0.432346i	$-0.857686\pi$
$751$	−2.09455	+	3.62787i	−0.0764314	+	0.132383i	0.825276	+	0.564729i	$0.191019\pi$
$752$	2.66621			0.0972266
$753$		0			0
$754$	39.8131			1.44991
$755$	−0.830556			−0.0302270
$756$		0			0
$757$	2.38688			0.0867525			0.0433763	−	0.999059i	$-0.486189\pi$
$757$	2.38688			0.0867525			0.0433763	+	0.999059i	$0.486189\pi$
$758$	25.0087			0.908355
$759$		0			0
$760$	−11.2756			−0.409009
$761$	−1.81708	+	3.14728i	−0.0658692	+	0.114089i	−0.897079	−	0.441870i	$-0.854315\pi$
$761$	−1.81708	+	3.14728i	−0.0658692	+	0.114089i	0.831210	+	0.555959i	$0.187649\pi$
$762$		0			0
$763$		0			0
$764$	23.9629			0.866946
$765$		0			0
$766$	3.13348	−	5.42734i	0.113217	−	0.196098i
$767$	−15.5803	−	26.9859i	−0.562573	−	0.974404i
$768$		0			0
$769$	19.9672	+	34.5842i	0.720035	+	1.24714i	0.960985	+	0.276600i	$0.0892078\pi$
$769$	19.9672	+	34.5842i	0.720035	+	1.24714i	−0.240950	+	0.970538i	$0.577459\pi$
$770$		0			0
$771$		0			0
$772$	9.76509			0.351453
$773$	18.0698	−	31.2978i	0.649925	−	1.12570i	−0.333215	−	0.942851i	$-0.608133\pi$
$773$	18.0698	−	31.2978i	0.649925	−	1.12570i	0.983140	−	0.182853i	$-0.0585332\pi$
$774$		0			0
$775$	3.35896	+	5.81788i	0.120657	+	0.208985i
$776$	−0.712008	+	1.23323i	−0.0255596	+	0.0442705i
$777$		0			0
$778$	−10.8171	−	18.7357i	−0.387811	−	0.671709i
$779$	−20.8578	+	36.1267i	−0.747308	+	1.29438i
$780$		0			0
$781$	10.1025	+	17.4981i	0.361497	+	0.626131i
$782$	0.810892	+	1.40451i	0.0289974	+	0.0502251i
$783$		0			0
$784$		0			0
$785$	7.03961	−	12.1930i	0.251254	−	0.435186i
$786$		0			0
$787$	44.6377			1.59116			0.795582	−	0.605846i	$-0.207165\pi$
$787$	44.6377			1.59116			0.795582	+	0.605846i	$0.207165\pi$
$788$	18.2436			0.649900
$789$		0			0
$790$	−6.66071	+	11.5367i	−0.236977	+	0.410457i
$791$		0			0
$792$		0			0
$793$	−10.7694	−	18.6532i	−0.382433	−	0.662394i
$794$	−2.05308	−	3.55605i	−0.0728612	−	0.126199i
$795$		0			0
$796$	−9.04944	+	15.6741i	−0.320749	+	0.555554i
$797$	26.2836	+	45.5245i	0.931012	+	1.61256i	0.781595	+	0.623786i	$0.214407\pi$
$797$	26.2836	+	45.5245i	0.931012	+	1.61256i	0.149418	+	0.988774i	$0.452260\pi$
$798$		0			0
$799$	−7.19777	+	12.4669i	−0.254639	+	0.441047i
$800$	1.23855	+	2.14523i	0.0437894	+	0.0758454i
$801$		0			0
$802$	8.37085	−	14.4987i	0.295585	−	0.511969i
$803$	25.4981			0.899810
$804$		0			0
$805$		0			0
$806$	−6.52359	−	11.2992i	−0.229784	−	0.397997i
$807$		0			0
$808$	−6.01671	−	10.4212i	−0.211667	−	0.366618i
$809$	−7.40290	+	12.8222i	−0.260272	+	0.450804i	−0.966314	−	0.257365i	$-0.917146\pi$
$809$	−7.40290	+	12.8222i	−0.260272	+	0.450804i	0.706042	+	0.708170i	$0.250479\pi$
$810$		0			0
$811$	−27.0704			−0.950571			−0.475285	−	0.879832i	$-0.657655\pi$
$811$	−27.0704			−0.950571			−0.475285	+	0.879832i	$0.657655\pi$
$812$		0			0
$813$		0			0
$814$	0.794182	−	1.37556i	0.0278361	−	0.0482135i
$815$	−34.8850			−1.22197
$816$		0			0
$817$	−11.8282			−0.413817
$818$	8.76509			0.306464
$819$		0			0
$820$	−9.33379			−0.325950
$821$	−43.8182			−1.52926			−0.764632	−	0.644467i	$-0.777079\pi$
$821$	−43.8182			−1.52926			−0.764632	+	0.644467i	$0.777079\pi$
$822$		0			0
$823$	31.3425			1.09253			0.546265	−	0.837613i	$-0.316049\pi$
$823$	31.3425			1.09253			0.546265	+	0.837613i	$0.316049\pi$
$824$	−3.04944	+	5.28179i	−0.106232	+	0.184000i
$825$		0			0
$826$		0			0
$827$	14.7665			0.513480			0.256740	−	0.966480i	$-0.417352\pi$
$827$	14.7665			0.513480			0.256740	+	0.966480i	$0.417352\pi$
$828$		0			0
$829$	15.0036	−	25.9871i	0.521098	−	0.902568i	−0.478601	−	0.878033i	$-0.658856\pi$
$829$	15.0036	−	25.9871i	0.521098	−	0.902568i	0.999699	−	0.0245357i	$-0.00781074\pi$
$830$	1.87890	+	3.25436i	0.0652177	+	0.112960i
$831$		0			0
$832$	−2.40545	−	4.16635i	−0.0833938	−	0.144442i
$833$		0			0
$834$		0			0
$835$	−5.24219			−0.181414
$836$	5.63781	−	9.76497i	0.194988	−	0.337728i
$837$		0			0
$838$	−0.210149	−	0.363988i	−0.00725946	−	0.0125738i
$839$	18.0167	−	31.2059i	0.622006	−	1.07735i	−0.367106	−	0.930179i	$-0.619651\pi$
$839$	18.0167	−	31.2059i	0.622006	−	1.07735i	0.989112	−	0.147167i	$-0.0470154\pi$
$840$		0			0
$841$	−19.7429	−	34.1957i	−0.680789	−	1.17916i
$842$	3.28799	−	5.69497i	0.113312	−	0.196262i
$843$		0			0
$844$	0.166208	+	0.287880i	0.00572110	+	0.00990923i
$845$	−8.05673	−	13.9547i	−0.277160	−	0.480055i
$846$		0			0
$847$		0			0
$848$	−2.44437	+	4.23377i	−0.0839399	+	0.145388i
$849$		0			0
$850$	−13.3745			−0.458741
$851$	0.300372			0.0102966
$852$		0			0
$853$	12.2658	−	21.2450i	0.419972	−	0.727413i	−0.575964	−	0.817475i	$-0.695373\pi$
$853$	12.2658	−	21.2450i	0.419972	−	0.727413i	0.995936	+	0.0900617i	$0.0287064\pi$
$854$		0			0
$855$		0			0
$856$	1.54325	+	2.67299i	0.0527473	+	0.0913610i
$857$	−14.5240	−	25.1563i	−0.496130	−	0.859323i	0.503860	−	0.863785i	$-0.331913\pi$
$857$	−14.5240	−	25.1563i	−0.496130	−	0.859323i	−0.999990	+	0.00446273i	$0.998579\pi$
$858$		0			0
$859$	12.6476	−	21.9064i	0.431532	−	0.747435i	−0.565474	−	0.824766i	$-0.691307\pi$
$859$	12.6476	−	21.9064i	0.431532	−	0.747435i	0.997005	+	0.0773313i	$0.0246399\pi$
$860$	−1.32327	−	2.29197i	−0.0451232	−	0.0781557i
$861$		0			0
$862$	−11.0439	+	19.1287i	−0.376158	+	0.651525i
$863$	1.34981	+	2.33795i	0.0459482	+	0.0795846i	0.888085	−	0.459680i	$-0.152036\pi$
$863$	1.34981	+	2.33795i	0.0459482	+	0.0795846i	−0.842137	+	0.539264i	$0.818702\pi$
$864$		0			0
$865$	−15.1749	+	26.2836i	−0.515961	+	0.893671i
$866$	9.43268			0.320535
$867$		0			0
$868$		0			0
$869$	−6.66071	−	11.5367i	−0.225949	−	0.391355i
$870$		0			0
$871$	24.1822	+	41.8847i	0.819381	+	1.41921i
$872$	1.14400	−	1.98146i	0.0387406	−	0.0671007i
$873$		0			0
$874$	2.13231			0.0721263
$875$		0			0
$876$		0			0
$877$	5.54580	−	9.60561i	0.187268	−	0.324358i	−0.757070	−	0.653334i	$-0.773370\pi$
$877$	5.54580	−	9.60561i	0.187268	−	0.324358i	0.944339	+	0.328975i	$0.106703\pi$
$878$	31.2064			1.05317
$879$		0			0
$880$	2.52290			0.0850469
$881$	−40.3942			−1.36091			−0.680457	−	0.732788i	$-0.738219\pi$
$881$	−40.3942			−1.36091			−0.680457	+	0.732788i	$0.738219\pi$
$882$		0			0
$883$	−33.2581			−1.11923			−0.559613	−	0.828754i	$-0.689050\pi$
$883$	−33.2581			−1.11923			−0.559613	+	0.828754i	$0.689050\pi$
$884$	25.9752			0.873642
$885$		0			0
$886$	−13.0545			−0.438573
$887$	−20.2836	+	35.1322i	−0.681056	+	1.17962i	0.293603	+	0.955928i	$0.405146\pi$
$887$	−20.2836	+	35.1322i	−0.681056	+	1.17962i	−0.974659	+	0.223696i	$0.928188\pi$
$888$		0			0
$889$		0			0
$890$	−5.09888			−0.170915
$891$		0			0
$892$	−3.16621	+	5.48403i	−0.106012	+	0.183619i
$893$	9.46355	+	16.3913i	0.316686	+	0.548516i
$894$		0			0
$895$	12.7658	+	22.1110i	0.426713	+	0.739089i
$896$		0			0
$897$		0			0
$898$	9.91706			0.330937
$899$	−11.2218	+	19.4367i	−0.374267	+	0.648249i
$900$		0			0
$901$	−13.1978	−	22.8592i	−0.439681	−	0.761551i
$902$	4.66690	−	8.08330i	0.155391	−	0.269144i
$903$		0			0
$904$	9.73236	+	16.8569i	0.323693	+	0.560654i
$905$	6.39561	−	11.0775i	0.212597	−	0.368230i
$906$		0			0
$907$	−15.0567	−	26.0790i	−0.499950	−	0.865939i	0.500050	−	0.865997i	$-0.333315\pi$
$907$	−15.0567	−	26.0790i	−0.499950	−	0.865939i	−1.00000		5.72941e-5i	$0.999982\pi$
$908$	11.6545	+	20.1862i	0.386769	+	0.669903i
$909$		0			0
$910$		0			0
$911$	−14.6113	+	25.3075i	−0.484093	+	0.838473i	−0.999833	−	0.0182717i	$-0.994184\pi$
$911$	−14.6113	+	25.3075i	−0.484093	+	0.838473i	0.515740	+	0.856745i	$0.327517\pi$
$912$		0			0
$913$	−3.75781			−0.124365
$914$	−24.5229			−0.811145
$915$		0			0
$916$	−2.47710	+	4.29046i	−0.0818457	+	0.141761i
$917$		0			0
$918$		0			0
$919$	−5.52359	−	9.56714i	−0.182206	−	0.315591i	0.760425	−	0.649426i	$-0.224991\pi$
$919$	−5.52359	−	9.56714i	−0.182206	−	0.315591i	−0.942632	+	0.333835i	$0.891657\pi$
$920$	0.238550	+	0.413181i	0.00786476	+	0.0136222i
$921$		0			0
$922$	1.75526	−	3.04020i	0.0578064	−	0.100124i
$923$	30.5989	+	52.9988i	1.00717	+	1.74448i
$924$		0			0
$925$	−1.23855	+	2.14523i	−0.0407233	+	0.0705348i
$926$	8.69413	+	15.0587i	0.285707	+	0.494859i
$927$		0			0
$928$	−4.13781	+	7.16689i	−0.135830	+	0.235265i
$929$	−42.3338			−1.38893			−0.694463	−	0.719528i	$-0.744358\pi$
$929$	−42.3338			−1.38893			−0.694463	+	0.719528i	$0.744358\pi$
$930$		0			0
$931$		0			0
$932$	7.13781	+	12.3630i	0.233807	+	0.404965i
$933$		0			0
$934$	6.69894	+	11.6029i	0.219196	+	0.379659i
$935$	−6.81089	+	11.7968i	−0.222740	+	0.385797i
$936$		0			0
$937$	11.7651			0.384349			0.192174	−	0.981361i	$-0.438446\pi$
$937$	11.7651			0.384349			0.192174	+	0.981361i	$0.438446\pi$
$938$		0			0
$939$		0			0
$940$	−2.11745	+	3.66754i	−0.0690637	+	0.119622i
$941$	14.5760			0.475164			0.237582	−	0.971368i	$-0.423645\pi$
$941$	14.5760			0.475164			0.237582	+	0.971368i	$0.423645\pi$
$942$		0			0
$943$	1.76509			0.0574793
$944$	6.47710			0.210812
$945$		0			0
$946$	2.64654			0.0860466
$947$	−6.24357			−0.202889			−0.101444	−	0.994841i	$-0.532346\pi$
$947$	−6.24357			−0.202889			−0.101444	+	0.994841i	$0.532346\pi$
$948$		0			0
$949$	77.2297			2.50698
$950$	−8.79232	+	15.2287i	−0.285261	+	0.494086i
$951$		0			0
$952$		0			0
$953$	−28.0173			−0.907570			−0.453785	−	0.891111i	$-0.649927\pi$
$953$	−28.0173			−0.907570			−0.453785	+	0.891111i	$0.649927\pi$
$954$		0			0
$955$	−19.0309	+	32.9624i	−0.615825	+	1.06664i
$956$	−2.48762	−	4.30868i	−0.0804554	−	0.139353i
$957$		0			0
$958$	−10.4029	−	18.0183i	−0.336102	−	0.582146i
$959$		0			0
$960$		0			0
$961$	−23.6450			−0.762742
$962$	2.40545	−	4.16635i	0.0775547	−	0.134329i
$963$		0			0
$964$	−6.50000	−	11.2583i	−0.209351	−	0.362606i
$965$	−7.75526	+	13.4325i	−0.249651	+	0.432408i
$966$		0			0
$967$	15.7837	+	27.3381i	0.507568	+	0.879134i	0.999962	+	0.00876132i	$0.00278885\pi$
$967$	15.7837	+	27.3381i	0.507568	+	0.879134i	−0.492393	+	0.870373i	$0.663878\pi$
$968$	4.23855	−	7.34138i	0.136232	−	0.235961i
$969$		0			0
$970$	−1.13093	−	1.95882i	−0.0363119	−	0.0628941i
$971$	2.82141	+	4.88683i	0.0905434	+	0.156826i	0.907740	−	0.419533i	$-0.137806\pi$
$971$	2.82141	+	4.88683i	0.0905434	+	0.156826i	−0.817196	+	0.576359i	$0.804473\pi$
$972$		0			0
$973$		0			0
$974$	16.2472	−	28.1410i	0.520594	−	0.901696i
$975$		0			0
$976$	4.47710			0.143308
$977$	−6.49304			−0.207731			−0.103865	−	0.994591i	$-0.533121\pi$
$977$	−6.49304			−0.207731			−0.103865	+	0.994591i	$0.533121\pi$
$978$		0			0
$979$	2.54944	−	4.41576i	0.0814805	−	0.141128i
$980$		0			0
$981$		0			0
$982$	9.66071	+	16.7328i	0.308286	+	0.533966i
$983$	15.1531	+	26.2460i	0.483310	+	0.837118i	0.999816	−	0.0191658i	$-0.00610104\pi$
$983$	15.1531	+	26.2460i	0.483310	+	0.837118i	−0.516506	+	0.856283i	$0.672768\pi$
$984$		0			0
$985$	−14.4887	+	25.0952i	−0.461649	+	0.799599i
$986$	−22.3411	−	38.6959i	−0.711485	−	1.23233i
$987$		0			0
$988$	17.0760	−	29.5765i	0.543259	−	0.940953i
$989$	0.250241	+	0.433430i	0.00795720	+	0.0137823i
$990$		0			0
$991$	11.1669	−	19.3416i	0.354728	−	0.614407i	−0.632343	−	0.774688i	$-0.717907\pi$
$991$	11.1669	−	19.3416i	0.354728	−	0.614407i	0.987071	+	0.160281i	$0.0512401\pi$
$992$	2.71201			0.0861063
$993$		0			0
$994$		0			0
$995$	−14.3738	−	24.8962i	−0.455680	−	0.789262i
$996$		0			0
$997$	−4.38255	−	7.59079i	−0.138797	−	0.240403i	0.788245	−	0.615362i	$-0.210990\pi$
$997$	−4.38255	−	7.59079i	−0.138797	−	0.240403i	−0.927041	+	0.374959i	$0.877657\pi$
$998$	5.57530	−	9.65670i	0.176483	−	0.305677i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.p.2125.1		6
3.2	odd	2		882.2.e.o.655.3		6
7.2	even	3		2646.2.h.o.667.3		6
7.3	odd	6		2646.2.f.l.883.3		6
7.4	even	3		2646.2.f.m.883.1		6
7.5	odd	6		378.2.h.c.289.1		6
7.6	odd	2		378.2.e.d.235.3		6
9.4	even	3		2646.2.h.o.361.3		6
9.5	odd	6		882.2.h.p.67.1		6
21.2	odd	6		882.2.h.p.79.1		6
21.5	even	6		126.2.h.d.79.3	yes	6
21.11	odd	6		882.2.f.o.295.1		6
21.17	even	6		882.2.f.n.295.3		6
21.20	even	2		126.2.e.c.25.1	✓	6
28.19	even	6		3024.2.t.h.289.1		6
28.27	even	2		3024.2.q.g.2881.3		6
63.4	even	3		2646.2.f.m.1765.1		6
63.5	even	6		126.2.e.c.121.1	yes	6
63.11	odd	6		7938.2.a.bw.1.1		3
63.13	odd	6		378.2.h.c.361.1		6
63.20	even	6		1134.2.g.m.487.1		6
63.23	odd	6		882.2.e.o.373.3		6
63.25	even	3		7938.2.a.bz.1.3		3
63.31	odd	6		2646.2.f.l.1765.3		6
63.32	odd	6		882.2.f.o.589.1		6
63.34	odd	6		1134.2.g.l.487.3		6
63.38	even	6		7938.2.a.bv.1.3		3
63.40	odd	6		378.2.e.d.37.3		6
63.41	even	6		126.2.h.d.67.3	yes	6
63.47	even	6		1134.2.g.m.163.1		6
63.52	odd	6		7938.2.a.ca.1.1		3
63.58	even	3	inner	2646.2.e.p.1549.1		6
63.59	even	6		882.2.f.n.589.3		6
63.61	odd	6		1134.2.g.l.163.3		6
84.47	odd	6		1008.2.t.h.961.1		6
84.83	odd	2		1008.2.q.g.529.3		6
252.103	even	6		3024.2.q.g.2305.3		6
252.131	odd	6		1008.2.q.g.625.3		6
252.139	even	6		3024.2.t.h.1873.1		6
252.167	odd	6		1008.2.t.h.193.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.1	✓	6	21.20	even	2
126.2.e.c.121.1	yes	6	63.5	even	6
126.2.h.d.67.3	yes	6	63.41	even	6
126.2.h.d.79.3	yes	6	21.5	even	6
378.2.e.d.37.3		6	63.40	odd	6
378.2.e.d.235.3		6	7.6	odd	2
378.2.h.c.289.1		6	7.5	odd	6
378.2.h.c.361.1		6	63.13	odd	6
882.2.e.o.373.3		6	63.23	odd	6
882.2.e.o.655.3		6	3.2	odd	2
882.2.f.n.295.3		6	21.17	even	6
882.2.f.n.589.3		6	63.59	even	6
882.2.f.o.295.1		6	21.11	odd	6
882.2.f.o.589.1		6	63.32	odd	6
882.2.h.p.67.1		6	9.5	odd	6
882.2.h.p.79.1		6	21.2	odd	6
1008.2.q.g.529.3		6	84.83	odd	2
1008.2.q.g.625.3		6	252.131	odd	6
1008.2.t.h.193.1		6	252.167	odd	6
1008.2.t.h.961.1		6	84.47	odd	6
1134.2.g.l.163.3		6	63.61	odd	6
1134.2.g.l.487.3		6	63.34	odd	6
1134.2.g.m.163.1		6	63.47	even	6
1134.2.g.m.487.1		6	63.20	even	6
2646.2.e.p.1549.1		6	63.58	even	3	inner
2646.2.e.p.2125.1		6	1.1	even	1	trivial
2646.2.f.l.883.3		6	7.3	odd	6
2646.2.f.l.1765.3		6	63.31	odd	6
2646.2.f.m.883.1		6	7.4	even	3
2646.2.f.m.1765.1		6	63.4	even	3
2646.2.h.o.361.3		6	9.4	even	3
2646.2.h.o.667.3		6	7.2	even	3
3024.2.q.g.2305.3		6	252.103	even	6
3024.2.q.g.2881.3		6	28.27	even	2
3024.2.t.h.289.1		6	28.19	even	6
3024.2.t.h.1873.1		6	252.139	even	6
7938.2.a.bv.1.3		3	63.38	even	6
7938.2.a.bw.1.1		3	63.11	odd	6
7938.2.a.bz.1.3		3	63.25	even	3
7938.2.a.ca.1.1		3	63.52	odd	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.794182 + 1.37556i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.794182 + 1.37556i) q^{5} +1.00000 q^{8} +(-0.794182 + 1.37556i) q^{10} +(-0.794182 - 1.37556i) q^{11} +(-2.40545 - 4.16635i) q^{13} +1.00000 q^{16} +(-2.69963 + 4.67589i) q^{17} +(3.54944 + 6.14781i) q^{19} +(-0.794182 + 1.37556i) q^{20} +(-0.794182 - 1.37556i) q^{22} +(0.150186 - 0.260130i) q^{23} +(1.23855 + 2.14523i) q^{25} +(-2.40545 - 4.16635i) q^{26} +(-4.13781 + 7.16689i) q^{29} +2.71201 q^{31} +1.00000 q^{32} +(-2.69963 + 4.67589i) q^{34} +(0.500000 + 0.866025i) q^{37} +(3.54944 + 6.14781i) q^{38} +(-0.794182 + 1.37556i) q^{40} +(2.93818 + 5.08907i) q^{41} +(-0.833104 + 1.44298i) q^{43} +(-0.794182 - 1.37556i) q^{44} +(0.150186 - 0.260130i) q^{46} +2.66621 q^{47} +(1.23855 + 2.14523i) q^{50} +(-2.40545 - 4.16635i) q^{52} +(-2.44437 + 4.23377i) q^{53} +2.52290 q^{55} +(-4.13781 + 7.16689i) q^{58} +6.47710 q^{59} +4.47710 q^{61} +2.71201 q^{62} +1.00000 q^{64} +7.64145 q^{65} -10.0531 q^{67} +(-2.69963 + 4.67589i) q^{68} -12.7207 q^{71} +(-8.02654 + 13.9024i) q^{73} +(0.500000 + 0.866025i) q^{74} +(3.54944 + 6.14781i) q^{76} +8.38688 q^{79} +(-0.794182 + 1.37556i) q^{80} +(2.93818 + 5.08907i) q^{82} +(1.18292 - 2.04887i) q^{83} +(-4.28799 - 7.42702i) q^{85} +(-0.833104 + 1.44298i) q^{86} +(-0.794182 - 1.37556i) q^{88} +(1.60507 + 2.78007i) q^{89} +(0.150186 - 0.260130i) q^{92} +2.66621 q^{94} -11.2756 q^{95} +(-0.712008 + 1.23323i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8	\( 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8} + q^{10} + q^{11} - 8 q^{13} + 6 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 8 q^{26} + 5 q^{29} + 40 q^{31} + 6 q^{32} - 4 q^{34} + 3 q^{37} + 3 q^{38} + q^{40} - 6 q^{43} + q^{44} + 7 q^{46} + 18 q^{47} + 2 q^{50} - 8 q^{52} - 15 q^{53} + 26 q^{55} + 5 q^{58} + 28 q^{59} + 16 q^{61} + 40 q^{62} + 6 q^{64} - 24 q^{65} - 2 q^{67} - 4 q^{68} - 14 q^{71} - 19 q^{73} + 3 q^{74} + 3 q^{76} - 10 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} - 9 q^{89} + 7 q^{92} + 18 q^{94} - 8 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8 + q^10 + q^11 - 8 * q^13 + 6 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 + 7 * q^23 + 2 * q^25 - 8 * q^26 + 5 * q^29 + 40 * q^31 + 6 * q^32 - 4 * q^34 + 3 * q^37 + 3 * q^38 + q^40 - 6 * q^43 + q^44 + 7 * q^46 + 18 * q^47 + 2 * q^50 - 8 * q^52 - 15 * q^53 + 26 * q^55 + 5 * q^58 + 28 * q^59 + 16 * q^61 + 40 * q^62 + 6 * q^64 - 24 * q^65 - 2 * q^67 - 4 * q^68 - 14 * q^71 - 19 * q^73 + 3 * q^74 + 3 * q^76 - 10 * q^79 + q^80 + 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 - 9 * q^89 + 7 * q^92 + 18 * q^94 - 8 * q^95 - 28 * q^97

Introduction

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