LMFDB - Embedded newform 324.6.e.d.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,6,Mod(109,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("324.109");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	324.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:	$51.9643576194$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	324.109
Dual form			324.6.e.d.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(27.0000 - 46.7654i) q^{5} +(44.0000 + 76.2102i) q^{7} +O(q^{10})$	$q+(27.0000 - 46.7654i) q^{5} +(44.0000 + 76.2102i) q^{7} +(270.000 + 467.654i) q^{11} +(209.000 - 361.999i) q^{13} -594.000 q^{17} +836.000 q^{19} +(-2052.00 + 3554.17i) q^{23} +(104.500 + 180.999i) q^{25} +(-297.000 - 514.419i) q^{29} +(-2128.00 + 3685.80i) q^{31} +4752.00 q^{35} -298.000 q^{37} +(8613.00 - 14918.2i) q^{41} +(6050.00 + 10478.9i) q^{43} +(-648.000 - 1122.37i) q^{47} +(4531.50 - 7848.79i) q^{49} -19494.0 q^{53} +29160.0 q^{55} +(-3834.00 + 6640.68i) q^{59} +(17369.0 + 30084.0i) q^{61} +(-11286.0 - 19547.9i) q^{65} +(-10906.0 + 18889.7i) q^{67} +46872.0 q^{71} +67562.0 q^{73} +(-23760.0 + 41153.5i) q^{77} +(38456.0 + 66607.7i) q^{79} +(33858.0 + 58643.8i) q^{83} +(-16038.0 + 27778.6i) q^{85} -29754.0 q^{89} +36784.0 q^{91} +(22572.0 - 39095.9i) q^{95} +(61199.0 + 106000. i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 54 q^{5} + 88 q^{7}+O(q^{10}) $ 2 * q + 54 * q^5 + 88 * q^7	$ 2 q + 54 q^{5} + 88 q^{7} + 540 q^{11} + 418 q^{13} - 1188 q^{17} + 1672 q^{19} - 4104 q^{23} + 209 q^{25} - 594 q^{29} - 4256 q^{31} + 9504 q^{35} - 596 q^{37} + 17226 q^{41} + 12100 q^{43} - 1296 q^{47} + 9063 q^{49} - 38988 q^{53} + 58320 q^{55} - 7668 q^{59} + 34738 q^{61} - 22572 q^{65} - 21812 q^{67} + 93744 q^{71} + 135124 q^{73} - 47520 q^{77} + 76912 q^{79} + 67716 q^{83} - 32076 q^{85} - 59508 q^{89} + 73568 q^{91} + 45144 q^{95} + 122398 q^{97}+O(q^{100}) $ 2 * q + 54 * q^5 + 88 * q^7 + 540 * q^11 + 418 * q^13 - 1188 * q^17 + 1672 * q^19 - 4104 * q^23 + 209 * q^25 - 594 * q^29 - 4256 * q^31 + 9504 * q^35 - 596 * q^37 + 17226 * q^41 + 12100 * q^43 - 1296 * q^47 + 9063 * q^49 - 38988 * q^53 + 58320 * q^55 - 7668 * q^59 + 34738 * q^61 - 22572 * q^65 - 21812 * q^67 + 93744 * q^71 + 135124 * q^73 - 47520 * q^77 + 76912 * q^79 + 67716 * q^83 - 32076 * q^85 - 59508 * q^89 + 73568 * q^91 + 45144 * q^95 + 122398 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	27.0000	−	46.7654i	0.482991	−	0.836564i	−0.516819	−	0.856095i	$-0.672884\pi$
$5$	27.0000	−	46.7654i	0.482991	−	0.836564i	0.999809	+	0.0195305i	$0.00621716\pi$
$6$		0			0
$7$	44.0000	+	76.2102i	0.339397	+	0.587852i	0.984319	−	0.176396i	$-0.0564438\pi$
$7$	44.0000	+	76.2102i	0.339397	+	0.587852i	−0.644923	+	0.764248i	$0.723110\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	270.000	+	467.654i	0.672794	+	1.16531i	0.977108	+	0.212742i	$0.0682393\pi$
$11$	270.000	+	467.654i	0.672794	+	1.16531i	−0.304315	+	0.952572i	$0.598427\pi$
$12$		0			0
$13$	209.000	−	361.999i	0.342995	−	0.594085i	−0.641992	−	0.766711i	$-0.721892\pi$
$13$	209.000	−	361.999i	0.342995	−	0.594085i	0.984987	+	0.172626i	$0.0552252\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−594.000			−0.498499			−0.249249	−	0.968439i	$-0.580184\pi$
$17$	−594.000			−0.498499			−0.249249	+	0.968439i	$0.580184\pi$
$18$		0			0
$19$	836.000			0.531279			0.265639	−	0.964072i	$-0.414417\pi$
$19$	836.000			0.531279			0.265639	+	0.964072i	$0.414417\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2052.00	+	3554.17i	−0.808831	+	1.40094i	0.104843	+	0.994489i	$0.466566\pi$
$23$	−2052.00	+	3554.17i	−0.808831	+	1.40094i	−0.913674	+	0.406448i	$0.866767\pi$
$24$		0			0
$25$	104.500	+	180.999i	0.0334400	+	0.0579198i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−297.000	−	514.419i	−0.0655785	−	0.113585i	0.831372	−	0.555716i	$-0.187556\pi$
$29$	−297.000	−	514.419i	−0.0655785	−	0.113585i	−0.896950	+	0.442131i	$0.854223\pi$
$30$		0			0
$31$	−2128.00	+	3685.80i	−0.397711	+	0.688855i	−0.993443	−	0.114328i	$-0.963529\pi$
$31$	−2128.00	+	3685.80i	−0.397711	+	0.688855i	0.595732	+	0.803183i	$0.296862\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4752.00			0.655702
$36$		0			0
$37$	−298.000			−0.0357859			−0.0178930	−	0.999840i	$-0.505696\pi$
$37$	−298.000			−0.0357859			−0.0178930	+	0.999840i	$0.505696\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8613.00	−	14918.2i	0.800193	−	1.38598i	−0.119296	−	0.992859i	$-0.538064\pi$
$41$	8613.00	−	14918.2i	0.800193	−	1.38598i	0.919489	−	0.393116i	$-0.128603\pi$
$42$		0			0
$43$	6050.00	+	10478.9i	0.498981	+	0.864261i	0.999999	−	0.00117594i	$-0.000374313\pi$
$43$	6050.00	+	10478.9i	0.498981	+	0.864261i	−0.501018	+	0.865437i	$0.667041\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−648.000	−	1122.37i	−0.0427888	−	0.0741124i	0.843838	−	0.536598i	$-0.180291\pi$
$47$	−648.000	−	1122.37i	−0.0427888	−	0.0741124i	−0.886627	+	0.462486i	$0.846958\pi$
$48$		0			0
$49$	4531.50	−	7848.79i	0.269620	−	0.466995i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−19494.0			−0.953260			−0.476630	−	0.879104i	$-0.658142\pi$
$53$	−19494.0			−0.953260			−0.476630	+	0.879104i	$0.658142\pi$
$54$		0			0
$55$	29160.0			1.29981
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3834.00	+	6640.68i	−0.143391	+	0.248361i	−0.928772	−	0.370653i	$-0.879134\pi$
$59$	−3834.00	+	6640.68i	−0.143391	+	0.248361i	0.785380	+	0.619013i	$0.212467\pi$
$60$		0			0
$61$	17369.0	+	30084.0i	0.597655	+	1.03517i	0.993166	+	0.116707i	$0.0372339\pi$
$61$	17369.0	+	30084.0i	0.597655	+	1.03517i	−0.395512	+	0.918461i	$0.629433\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11286.0	−	19547.9i	−0.331327	−	0.573875i
$66$		0			0
$67$	−10906.0	+	18889.7i	−0.296810	+	0.514090i	−0.975404	−	0.220423i	$-0.929256\pi$
$67$	−10906.0	+	18889.7i	−0.296810	+	0.514090i	0.678594	+	0.734513i	$0.262589\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	46872.0			1.10349			0.551744	−	0.834014i	$-0.313963\pi$
$71$	46872.0			1.10349			0.551744	+	0.834014i	$0.313963\pi$
$72$		0			0
$73$	67562.0			1.48387			0.741934	−	0.670473i	$-0.233909\pi$
$73$	67562.0			1.48387			0.741934	+	0.670473i	$0.233909\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−23760.0	+	41153.5i	−0.456688	+	0.791007i
$78$		0			0
$79$	38456.0	+	66607.7i	0.693260	+	1.20076i	0.970764	+	0.240037i	$0.0771597\pi$
$79$	38456.0	+	66607.7i	0.693260	+	1.20076i	−0.277503	+	0.960725i	$0.589507\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	33858.0	+	58643.8i	0.539468	+	0.934387i	0.998933	+	0.0461905i	$0.0147081\pi$
$83$	33858.0	+	58643.8i	0.539468	+	0.934387i	−0.459464	+	0.888196i	$0.651959\pi$
$84$		0			0
$85$	−16038.0	+	27778.6i	−0.240770	+	0.417026i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−29754.0			−0.398172			−0.199086	−	0.979982i	$-0.563797\pi$
$89$	−29754.0			−0.398172			−0.199086	+	0.979982i	$0.563797\pi$
$90$		0			0
$91$	36784.0			0.465646
$92$		0			0
$93$		0			0
$94$		0			0
$95$	22572.0	−	39095.9i	0.256603	−	0.444449i
$96$		0			0
$97$	61199.0	+	106000.i	0.660412	+	1.14387i	0.980507	+	0.196482i	$0.0629517\pi$
$97$	61199.0	+	106000.i	0.660412	+	1.14387i	−0.320095	+	0.947385i	$0.603715\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5643.00	+	9773.96i	0.0550436	+	0.0953383i	0.892234	−	0.451573i	$-0.149137\pi$
$101$	5643.00	+	9773.96i	0.0550436	+	0.0953383i	−0.837191	+	0.546911i	$0.815804\pi$
$102$		0			0
$103$	13628.0	−	23604.4i	0.126572	−	0.219230i	−0.795774	−	0.605594i	$-0.792936\pi$
$103$	13628.0	−	23604.4i	0.126572	−	0.219230i	0.922346	+	0.386364i	$0.126269\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−122364.			−1.03322			−0.516612	−	0.856220i	$-0.672807\pi$
$107$	−122364.			−1.03322			−0.516612	+	0.856220i	$0.672807\pi$
$108$		0			0
$109$	99902.0			0.805393			0.402697	−	0.915334i	$-0.368073\pi$
$109$	99902.0			0.805393			0.402697	+	0.915334i	$0.368073\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14823.0	+	25674.2i	−0.109204	+	0.189148i	−0.915448	−	0.402436i	$-0.868164\pi$
$113$	−14823.0	+	25674.2i	−0.109204	+	0.189148i	0.806244	+	0.591583i	$0.201497\pi$
$114$		0			0
$115$	110808.	+	191925.i	0.781316	+	1.35328i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−26136.0	−	45268.9i	−0.169189	−	0.293044i
$120$		0			0
$121$	−65274.5	+	113059.i	−0.405303	+	0.702006i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	180036.			1.03059
$126$		0			0
$127$	336512.			1.85136			0.925681	−	0.378305i	$-0.123493\pi$
$127$	336512.			1.85136			0.925681	+	0.378305i	$0.123493\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	50490.0	−	87451.2i	0.257056	−	0.445233i	−0.708396	−	0.705815i	$-0.750581\pi$
$131$	50490.0	−	87451.2i	0.257056	−	0.445233i	0.965452	+	0.260582i	$0.0839143\pi$
$132$		0			0
$133$	36784.0	+	63711.8i	0.180314	+	0.312313i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−158571.	−	274653.i	−0.721809	−	1.25021i	−0.960274	−	0.279059i	$-0.909978\pi$
$137$	−158571.	−	274653.i	−0.721809	−	1.25021i	0.238465	−	0.971151i	$-0.423356\pi$
$138$		0			0
$139$	74162.0	−	128452.i	0.325570	−	0.563904i	−0.656058	−	0.754711i	$-0.727777\pi$
$139$	74162.0	−	128452.i	0.325570	−	0.563904i	0.981628	+	0.190807i	$0.0611105\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	225720.			0.923060
$144$		0			0
$145$	−32076.0			−0.126695
$146$		0			0
$147$		0			0
$148$		0			0
$149$	98307.0	−	170273.i	0.362759	−	0.628318i	−0.625654	−	0.780100i	$-0.715168\pi$
$149$	98307.0	−	170273.i	0.362759	−	0.628318i	0.988414	+	0.151782i	$0.0485013\pi$
$150$		0			0
$151$	−37180.0	−	64397.6i	−0.132699	−	0.229841i	0.792017	−	0.610499i	$-0.209031\pi$
$151$	−37180.0	−	64397.6i	−0.132699	−	0.229841i	−0.924716	+	0.380658i	$0.875698\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	114912.	+	199033.i	0.384181	+	0.665421i
$156$		0			0
$157$	−60439.0	+	104683.i	−0.195690	+	0.338945i	−0.947126	−	0.320861i	$-0.896028\pi$
$157$	−60439.0	+	104683.i	−0.195690	+	0.338945i	0.751437	+	0.659805i	$0.229361\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−361152.			−1.09806
$162$		0			0
$163$	−111340.			−0.328233			−0.164116	−	0.986441i	$-0.552477\pi$
$163$	−111340.			−0.328233			−0.164116	+	0.986441i	$0.552477\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−245916.	+	425939.i	−0.682332	+	1.18183i	0.291936	+	0.956438i	$0.405701\pi$
$167$	−245916.	+	425939.i	−0.682332	+	1.18183i	−0.974267	+	0.225395i	$0.927633\pi$
$168$		0			0
$169$	98284.5	+	170234.i	0.264709	+	0.458489i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	353727.	+	612673.i	0.898572	+	1.55637i	0.829320	+	0.558773i	$0.188728\pi$
$173$	353727.	+	612673.i	0.898572	+	1.55637i	0.0692518	+	0.997599i	$0.477939\pi$
$174$		0			0
$175$	−9196.00	+	15927.9i	−0.0226988	+	0.0393156i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−493668.			−1.15160			−0.575801	−	0.817590i	$-0.695310\pi$
$179$	−493668.			−1.15160			−0.575801	+	0.817590i	$0.695310\pi$
$180$		0			0
$181$	−559450.			−1.26930			−0.634651	−	0.772799i	$-0.718856\pi$
$181$	−559450.			−1.26930			−0.634651	+	0.772799i	$0.718856\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8046.00	+	13936.1i	−0.0172843	+	0.0299372i
$186$		0			0
$187$	−160380.	−	277786.i	−0.335387	−	0.580907i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−362016.	−	627030.i	−0.718033	−	1.24367i	−0.961778	−	0.273830i	$-0.911709\pi$
$191$	−362016.	−	627030.i	−0.718033	−	1.24367i	0.243745	−	0.969839i	$-0.421624\pi$
$192$		0			0
$193$	−3553.00	+	6153.98i	−0.00686597	+	0.0118922i	−0.869438	−	0.494042i	$-0.835519\pi$
$193$	−3553.00	+	6153.98i	−0.00686597	+	0.0118922i	0.862572	+	0.505934i	$0.168852\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	530442.			0.973806			0.486903	−	0.873456i	$-0.338127\pi$
$197$	530442.			0.973806			0.486903	+	0.873456i	$0.338127\pi$
$198$		0			0
$199$	56168.0			0.100544			0.0502720	−	0.998736i	$-0.483991\pi$
$199$	56168.0			0.100544			0.0502720	+	0.998736i	$0.483991\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	26136.0	−	45268.9i	0.0445142	−	0.0771009i
$204$		0			0
$205$	−465102.	−	805580.i	−0.772972	−	1.33883i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	225720.	+	390959.i	0.357441	+	0.619106i
$210$		0			0
$211$	169598.	−	293752.i	0.262249	−	0.454229i	−0.704590	−	0.709615i	$-0.748869\pi$
$211$	169598.	−	293752.i	0.262249	−	0.454229i	0.966839	+	0.255385i	$0.0822023\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	653400.			0.964013
$216$		0			0
$217$	−374528.			−0.539927
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−124146.	+	215027.i	−0.170983	+	0.296151i
$222$		0			0
$223$	−389680.	−	674946.i	−0.524742	−	0.908880i	−0.999585	−	0.0288094i	$-0.990828\pi$
$223$	−389680.	−	674946.i	−0.524742	−	0.908880i	0.474843	−	0.880071i	$-0.342505\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−372438.	−	645082.i	−0.479722	−	0.830902i	0.520008	−	0.854162i	$-0.325929\pi$
$227$	−372438.	−	645082.i	−0.479722	−	0.830902i	−0.999729	+	0.0232592i	$0.992596\pi$
$228$		0			0
$229$	136373.	−	236205.i	0.171846	−	0.297646i	−0.767219	−	0.641385i	$-0.778360\pi$
$229$	136373.	−	236205.i	0.171846	−	0.297646i	0.939065	+	0.343739i	$0.111693\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	153846.			0.185651			0.0928253	−	0.995682i	$-0.470410\pi$
$233$	153846.			0.185651			0.0928253	+	0.995682i	$0.470410\pi$
$234$		0			0
$235$	−69984.0			−0.0826664
$236$		0			0
$237$		0			0
$238$		0			0
$239$	577368.	−	1.00003e6i	0.653820	−	1.13245i	−0.328369	−	0.944550i	$-0.606499\pi$
$239$	577368.	−	1.00003e6i	0.653820	−	1.13245i	0.982188	−	0.187899i	$-0.0601678\pi$
$240$		0			0
$241$	−328537.	−	569043.i	−0.364369	−	0.631106i	0.624306	−	0.781180i	$-0.285382\pi$
$241$	−328537.	−	569043.i	−0.364369	−	0.631106i	−0.988675	+	0.150074i	$0.952049\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−244701.	−	423835.i	−0.260448	−	0.451109i
$246$		0			0
$247$	174724.	−	302631.i	0.182226	−	0.315625i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.34190e6			−1.34442			−0.672211	−	0.740359i	$-0.734655\pi$
$251$	−1.34190e6			−1.34442			−0.672211	+	0.740359i	$0.734655\pi$
$252$		0			0
$253$	−2.21616e6			−2.17671
$254$		0			0
$255$		0			0
$256$		0			0
$257$	66177.0	−	114622.i	0.0624992	−	0.108252i	−0.833083	−	0.553148i	$-0.813426\pi$
$257$	66177.0	−	114622.i	0.0624992	−	0.108252i	0.895582	+	0.444897i	$0.146760\pi$
$258$		0			0
$259$	−13112.0	−	22710.7i	−0.0121456	−	0.0210368i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	471636.	+	816898.i	0.420453	+	0.728246i	0.995984	−	0.0895341i	$-0.0285378\pi$
$263$	471636.	+	816898.i	0.420453	+	0.728246i	−0.575531	+	0.817780i	$0.695204\pi$
$264$		0			0
$265$	−526338.	+	911644.i	−0.460416	+	0.797463i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−967518.			−0.815227			−0.407613	−	0.913155i	$-0.633639\pi$
$269$	−967518.			−0.815227			−0.407613	+	0.913155i	$0.633639\pi$
$270$		0			0
$271$	−518320.			−0.428721			−0.214360	−	0.976755i	$-0.568767\pi$
$271$	−518320.			−0.428721			−0.214360	+	0.976755i	$0.568767\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−56430.0	+	97739.6i	−0.0449965	+	0.0779361i
$276$		0			0
$277$	−1.11136e6	−	1.92494e6i	−0.870275	−	1.50736i	−0.861712	−	0.507397i	$-0.830608\pi$
$277$	−1.11136e6	−	1.92494e6i	−0.870275	−	1.50736i	−0.00856270	−	0.999963i	$-0.502726\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−98307.0	−	170273.i	−0.0742709	−	0.128641i	0.826498	−	0.562940i	$-0.190330\pi$
$281$	−98307.0	−	170273.i	−0.0742709	−	0.128641i	−0.900769	+	0.434299i	$0.856996\pi$
$282$		0			0
$283$	776138.	−	1.34431e6i	0.576067	−	0.997777i	−0.419858	−	0.907590i	$-0.637920\pi$
$283$	776138.	−	1.34431e6i	0.576067	−	0.997777i	0.995925	−	0.0901872i	$-0.0287465\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.51589e6			1.08633
$288$		0			0
$289$	−1.06702e6			−0.751499
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−536085.	+	928526.i	−0.364808	+	0.631866i	−0.988745	−	0.149608i	$-0.952199\pi$
$293$	−536085.	+	928526.i	−0.364808	+	0.631866i	0.623937	+	0.781475i	$0.285532\pi$
$294$		0			0
$295$	207036.	+	358597.i	0.138513	+	0.239912i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	857736.	+	1.48564e6i	0.554850	+	0.961029i
$300$		0			0
$301$	−532400.	+	922144.i	−0.338705	+	0.586655i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.87585e6			1.15465
$306$		0			0
$307$	1.58589e6			0.960346			0.480173	−	0.877174i	$-0.340574\pi$
$307$	1.58589e6			0.960346			0.480173	+	0.877174i	$0.340574\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−365364.	+	632829.i	−0.214203	+	0.371010i	−0.953026	−	0.302890i	$-0.902049\pi$
$311$	−365364.	+	632829.i	−0.214203	+	0.371010i	0.738823	+	0.673900i	$0.235382\pi$
$312$		0			0
$313$	−292429.	−	506502.i	−0.168717	−	0.292227i	0.769252	−	0.638946i	$-0.220629\pi$
$313$	−292429.	−	506502.i	−0.168717	−	0.292227i	−0.937969	+	0.346719i	$0.887296\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.24143e6	−	2.15023e6i	−0.693865	−	1.20181i	−0.970562	−	0.240852i	$-0.922573\pi$
$317$	−1.24143e6	−	2.15023e6i	−0.693865	−	1.20181i	0.276696	−	0.960957i	$-0.410760\pi$
$318$		0			0
$319$	160380.	−	277786.i	0.0882416	−	0.152839i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−496584.			−0.264842
$324$		0			0
$325$	87362.0			0.0458790
$326$		0			0
$327$		0			0
$328$		0			0
$329$	57024.0	−	98768.5i	0.0290448	−	0.0503070i
$330$		0			0
$331$	−188974.	−	327313.i	−0.0948052	−	0.164207i	0.814722	−	0.579852i	$-0.196889\pi$
$331$	−188974.	−	327313.i	−0.0948052	−	0.164207i	−0.909527	+	0.415644i	$0.863556\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	588924.	+	1.02005e6i	0.286713	+	0.496601i
$336$		0			0
$337$	−319561.	+	553496.i	−0.153278	+	0.265485i	−0.932431	−	0.361349i	$-0.882316\pi$
$337$	−319561.	+	553496.i	−0.153278	+	0.265485i	0.779153	+	0.626834i	$0.215650\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.29824e6			−1.07031
$342$		0			0
$343$	2.27656e6			1.04483
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.45233e6	+	2.51551e6i	−0.647503	+	1.12151i	0.336215	+	0.941785i	$0.390853\pi$
$347$	−1.45233e6	+	2.51551e6i	−0.647503	+	1.12151i	−0.983717	+	0.179722i	$0.942480\pi$
$348$		0			0
$349$	1.99579e6	+	3.45680e6i	0.877102	+	1.51919i	0.854506	+	0.519441i	$0.173860\pi$
$349$	1.99579e6	+	3.45680e6i	0.877102	+	1.51919i	0.0225958	+	0.999745i	$0.492807\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	714609.	+	1.23774e6i	0.305233	+	0.528679i	0.977313	−	0.211799i	$-0.0679323\pi$
$353$	714609.	+	1.23774e6i	0.305233	+	0.528679i	−0.672080	+	0.740478i	$0.734599\pi$
$354$		0			0
$355$	1.26554e6	−	2.19199e6i	0.532974	−	0.923139i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.16186e6			−0.475794			−0.237897	−	0.971290i	$-0.576458\pi$
$359$	−1.16186e6			−0.475794			−0.237897	+	0.971290i	$0.576458\pi$
$360$		0			0
$361$	−1.77720e6			−0.717743
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.82417e6	−	3.15956e6i	0.716695	−	1.24135i
$366$		0			0
$367$	544616.	+	943303.i	0.211069	+	0.365583i	0.952049	−	0.305944i	$-0.0989721\pi$
$367$	544616.	+	943303.i	0.211069	+	0.365583i	−0.740980	+	0.671527i	$0.765639\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−857736.	−	1.48564e6i	−0.323533	−	0.560376i
$372$		0			0
$373$	−1.75288e6	+	3.03608e6i	−0.652350	+	1.12990i	0.330201	+	0.943911i	$0.392884\pi$
$373$	−1.75288e6	+	3.03608e6i	−0.652350	+	1.12990i	−0.982551	+	0.185993i	$0.940450\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−248292.			−0.0899724
$378$		0			0
$379$	4.04385e6			1.44610			0.723048	−	0.690798i	$-0.242740\pi$
$379$	4.04385e6			1.44610			0.723048	+	0.690798i	$0.242740\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.59373e6	−	4.49247e6i	0.903499	−	1.56491i	0.0805786	−	0.996748i	$-0.474323\pi$
$383$	2.59373e6	−	4.49247e6i	0.903499	−	1.56491i	0.822920	−	0.568157i	$-0.192343\pi$
$384$		0			0
$385$	1.28304e6	+	2.22229e6i	0.441152	+	0.764098i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−475173.	−	823024.i	−0.159213	−	0.275765i	0.775372	−	0.631504i	$-0.217562\pi$
$389$	−475173.	−	823024.i	−0.159213	−	0.275765i	−0.934585	+	0.355740i	$0.884229\pi$
$390$		0			0
$391$	1.21889e6	−	2.11118e6i	0.403201	−	0.698365i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.15325e6			1.33935
$396$		0			0
$397$	−520738.			−0.165822			−0.0829112	−	0.996557i	$-0.526422\pi$
$397$	−520738.			−0.165822			−0.0829112	+	0.996557i	$0.526422\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	382185.	−	661964.i	0.118690	−	0.205576i	−0.800559	−	0.599254i	$-0.795464\pi$
$401$	382185.	−	661964.i	0.118690	−	0.205576i	0.919249	+	0.393677i	$0.128797\pi$
$402$		0			0
$403$	889504.	+	1.54067e6i	0.272826	+	0.472548i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−80460.0	−	139361.i	−0.0240765	−	0.0417018i
$408$		0			0
$409$	−1.32025e6	+	2.28675e6i	−0.390255	+	0.675942i	−0.992483	−	0.122382i	$-0.960947\pi$
$409$	−1.32025e6	+	2.28675e6i	−0.390255	+	0.675942i	0.602228	+	0.798324i	$0.294280\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−674784.			−0.194666
$414$		0			0
$415$	3.65666e6			1.04223
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.49010e6	+	4.31298e6i	−0.692918	+	1.20017i	0.277959	+	0.960593i	$0.410342\pi$
$419$	−2.49010e6	+	4.31298e6i	−0.692918	+	1.20017i	−0.970877	+	0.239577i	$0.922991\pi$
$420$		0			0
$421$	118997.	+	206109.i	0.0327213	+	0.0566750i	0.881922	−	0.471395i	$-0.156249\pi$
$421$	118997.	+	206109.i	0.0327213	+	0.0566750i	−0.849201	+	0.528070i	$0.822916\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−62073.0	−	107514.i	−0.0166698	−	0.0288729i
$426$		0			0
$427$	−1.52847e6	+	2.64739e6i	−0.405684	+	0.702665i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.88238e6			1.00671			0.503356	−	0.864079i	$-0.332098\pi$
$431$	3.88238e6			1.00671			0.503356	+	0.864079i	$0.332098\pi$
$432$		0			0
$433$	−66958.0			−0.0171626			−0.00858129	−	0.999963i	$-0.502732\pi$
$433$	−66958.0			−0.0171626			−0.00858129	+	0.999963i	$0.502732\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.71547e6	+	2.97128e6i	−0.429715	+	0.744287i
$438$		0			0
$439$	3.25068e6	+	5.63034e6i	0.805031	+	1.39435i	0.916270	+	0.400560i	$0.131184\pi$
$439$	3.25068e6	+	5.63034e6i	0.805031	+	1.39435i	−0.111240	+	0.993794i	$0.535482\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.30380e6	−	3.99030e6i	−0.557745	−	0.966043i	−0.997684	−	0.0680154i	$-0.978333\pi$
$443$	−2.30380e6	−	3.99030e6i	−0.557745	−	0.966043i	0.439939	−	0.898028i	$-0.355000\pi$
$444$		0			0
$445$	−803358.	+	1.39146e6i	−0.192313	+	0.333096i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.77671e6			−0.884092			−0.442046	−	0.896992i	$-0.645747\pi$
$449$	−3.77671e6			−0.884092			−0.442046	+	0.896992i	$0.645747\pi$
$450$		0			0
$451$	9.30204e6			2.15346
$452$		0			0
$453$		0			0
$454$		0			0
$455$	993168.	−	1.72022e6i	0.224902	−	0.389543i
$456$		0			0
$457$	1.59035e6	+	2.75456e6i	0.356206	+	0.616967i	0.987324	−	0.158720i	$-0.0507368\pi$
$457$	1.59035e6	+	2.75456e6i	0.356206	+	0.616967i	−0.631117	+	0.775687i	$0.717403\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.34274e6	+	5.78979e6i	0.732571	+	1.26885i	0.955781	+	0.294080i	$0.0950131\pi$
$461$	3.34274e6	+	5.78979e6i	0.732571	+	1.26885i	−0.223210	+	0.974770i	$0.571654\pi$
$462$		0			0
$463$	2.17561e6	−	3.76826e6i	0.471659	−	0.816937i	−0.527815	−	0.849359i	$-0.676989\pi$
$463$	2.17561e6	−	3.76826e6i	0.471659	−	0.816937i	0.999474	+	0.0324218i	$0.0103220\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.07994e6			−1.50223			−0.751117	−	0.660170i	$-0.770484\pi$
$467$	−7.07994e6			−1.50223			−0.751117	+	0.660170i	$0.770484\pi$
$468$		0			0
$469$	−1.91946e6			−0.402945
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.26700e6	+	5.65861e6i	−0.671423	+	1.16294i
$474$		0			0
$475$	87362.0	+	151315.i	0.0177660	+	0.0307715i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.61093e6	+	2.79021e6i	0.320802	+	0.555646i	0.980654	−	0.195750i	$-0.0627142\pi$
$479$	1.61093e6	+	2.79021e6i	0.320802	+	0.555646i	−0.659852	+	0.751396i	$0.729381\pi$
$480$		0			0
$481$	−62282.0	+	107876.i	−0.0122744	+	0.0212599i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.60949e6			1.27589
$486$		0			0
$487$	2.29710e6			0.438891			0.219446	−	0.975625i	$-0.429575\pi$
$487$	2.29710e6			0.438891			0.219446	+	0.975625i	$0.429575\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.41075e6	−	2.44349e6i	0.264087	−	0.457411i	−0.703237	−	0.710955i	$-0.748263\pi$
$491$	1.41075e6	−	2.44349e6i	0.264087	−	0.457411i	0.967324	+	0.253544i	$0.0815962\pi$
$492$		0			0
$493$	176418.	+	305565.i	0.0326908	+	0.0566221i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.06237e6	+	3.57213e6i	0.374520	+	0.648688i
$498$		0			0
$499$	2.06814e6	−	3.58213e6i	0.371817	−	0.644006i	−0.618028	−	0.786156i	$-0.712068\pi$
$499$	2.06814e6	−	3.58213e6i	0.371817	−	0.644006i	0.989845	+	0.142150i	$0.0454016\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−8.33263e6			−1.46846			−0.734230	−	0.678901i	$-0.762457\pi$
$503$	−8.33263e6			−1.46846			−0.734230	+	0.678901i	$0.762457\pi$
$504$		0			0
$505$	609444.			0.106342
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.17050e6	−	3.75942e6i	0.371335	−	0.643171i	−0.618436	−	0.785835i	$-0.712233\pi$
$509$	2.17050e6	−	3.75942e6i	0.371335	−	0.643171i	0.989771	+	0.142664i	$0.0455668\pi$
$510$		0			0
$511$	2.97273e6	+	5.14892e6i	0.503620	+	0.872295i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−735912.	−	1.27464e6i	−0.122267	−	0.211772i
$516$		0			0
$517$	349920.	−	606079.i	0.0575761	−	0.0997248i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.74185e6			1.08814			0.544070	−	0.839040i	$-0.316883\pi$
$521$	6.74185e6			1.08814			0.544070	+	0.839040i	$0.316883\pi$
$522$		0			0
$523$	−7.72196e6			−1.23445			−0.617224	−	0.786787i	$-0.711743\pi$
$523$	−7.72196e6			−1.23445			−0.617224	+	0.786787i	$0.711743\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.26403e6	−	2.18937e6i	0.198258	−	0.343394i
$528$		0			0
$529$	−5.20324e6	−	9.01227e6i	−0.808415	−	1.40022i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.60023e6	−	6.23579e6i	−0.548925	−	0.950765i
$534$		0			0
$535$	−3.30383e6	+	5.72240e6i	−0.499037	+	0.864358i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.89402e6			0.725594
$540$		0			0
$541$	−682066.			−0.100192			−0.0500960	−	0.998744i	$-0.515953\pi$
$541$	−682066.			−0.100192			−0.0500960	+	0.998744i	$0.515953\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.69735e6	−	4.67195e6i	0.388997	−	0.673763i
$546$		0			0
$547$	−1.07886e6	−	1.86864e6i	−0.154169	−	0.267028i	0.778587	−	0.627536i	$-0.215937\pi$
$547$	−1.07886e6	−	1.86864e6i	−0.154169	−	0.267028i	−0.932756	+	0.360508i	$0.882603\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−248292.	−	430054.i	−0.0348404	−	0.0603454i
$552$		0			0
$553$	−3.38413e6	+	5.86148e6i	−0.470581	+	0.815069i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.67597e6			0.365463			0.182731	−	0.983163i	$-0.441506\pi$
$557$	2.67597e6			0.365463			0.182731	+	0.983163i	$0.441506\pi$
$558$		0			0
$559$	5.05780e6			0.684592
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.77665e6	+	3.07725e6i	−0.236228	+	0.409159i	−0.959629	−	0.281269i	$-0.909245\pi$
$563$	−1.77665e6	+	3.07725e6i	−0.236228	+	0.409159i	0.723401	+	0.690428i	$0.242578\pi$
$564$		0			0
$565$	800442.	+	1.38641e6i	0.105489	+	0.182713i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.46123e6	−	1.11912e7i	−0.836633	−	1.44909i	−0.892694	−	0.450663i	$-0.851188\pi$
$569$	−6.46123e6	−	1.11912e7i	−0.836633	−	1.44909i	0.0560613	−	0.998427i	$-0.482146\pi$
$570$		0			0
$571$	3.04179e6	−	5.26853e6i	0.390426	−	0.676237i	−0.602080	−	0.798436i	$-0.705661\pi$
$571$	3.04179e6	−	5.26853e6i	0.390426	−	0.676237i	0.992506	+	0.122199i	$0.0389945\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−857736.			−0.108189
$576$		0			0
$577$	−1.58241e7			−1.97869			−0.989347	−	0.145579i	$-0.953495\pi$
$577$	−1.58241e7			−1.97869			−0.989347	+	0.145579i	$0.953495\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.97950e6	+	5.16065e6i	−0.366188	+	0.634256i
$582$		0			0
$583$	−5.26338e6	−	9.11644e6i	−0.641347	−	1.11085i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.30110e6	+	3.98563e6i	0.275639	+	0.477421i	0.970296	−	0.241920i	$-0.0777772\pi$
$587$	2.30110e6	+	3.98563e6i	0.275639	+	0.477421i	−0.694657	+	0.719341i	$0.744444\pi$
$588$		0			0
$589$	−1.77901e6	+	3.08133e6i	−0.211295	+	0.365974i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8.61122e6			−1.00561			−0.502803	−	0.864401i	$-0.667698\pi$
$593$	−8.61122e6			−1.00561			−0.502803	+	0.864401i	$0.667698\pi$
$594$		0			0
$595$	−2.82269e6			−0.326867
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.99114e6	+	6.91286e6i	−0.454496	+	0.787210i	−0.998659	−	0.0517695i	$-0.983514\pi$
$599$	−3.99114e6	+	6.91286e6i	−0.454496	+	0.787210i	0.544163	+	0.838979i	$0.316847\pi$
$600$		0			0
$601$	−5.08700e6	−	8.81095e6i	−0.574481	−	0.995031i	−0.996098	−	0.0882567i	$-0.971870\pi$
$601$	−5.08700e6	−	8.81095e6i	−0.574481	−	0.995031i	0.421616	−	0.906774i	$-0.361463\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.52482e6	+	6.10517e6i	0.391515	+	0.678125i
$606$		0			0
$607$	4.97922e6	−	8.62426e6i	0.548516	−	0.950057i	−0.449861	−	0.893099i	$-0.648526\pi$
$607$	4.97922e6	−	8.62426e6i	0.548516	−	0.950057i	0.998377	−	0.0569587i	$-0.0181403\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−541728.			−0.0587054
$612$		0			0
$613$	4.19586e6			0.450993			0.225497	−	0.974244i	$-0.427600\pi$
$613$	4.19586e6			0.450993			0.225497	+	0.974244i	$0.427600\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.56276e6	−	7.90293e6i	0.482519	−	0.835747i	−0.517280	−	0.855816i	$-0.673055\pi$
$617$	4.56276e6	−	7.90293e6i	0.482519	−	0.835747i	0.999799	+	0.0200690i	$0.00638860\pi$
$618$		0			0
$619$	−3.22867e6	−	5.59222e6i	−0.338686	−	0.586621i	0.645500	−	0.763760i	$-0.276649\pi$
$619$	−3.22867e6	−	5.59222e6i	−0.338686	−	0.586621i	−0.984186	+	0.177139i	$0.943316\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.30918e6	−	2.26756e6i	−0.135138	−	0.234066i
$624$		0			0
$625$	4.53441e6	−	7.85383e6i	0.464324	−	0.804232i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	177012.			0.0178392
$630$		0			0
$631$	−1.40514e7			−1.40490			−0.702450	−	0.711733i	$-0.747910\pi$
$631$	−1.40514e7			−1.40490			−0.702450	+	0.711733i	$0.747910\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.08582e6	−	1.57371e7i	0.894190	−	1.54878i
$636$		0			0
$637$	−1.89417e6	−	3.28079e6i	−0.184957	−	0.320354i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.23584e6	+	7.33669e6i	0.407188	+	0.705270i	0.994573	−	0.104037i	$-0.0331762\pi$
$641$	4.23584e6	+	7.33669e6i	0.407188	+	0.705270i	−0.587386	+	0.809307i	$0.699843\pi$
$642$		0			0
$643$	−244282.	+	423109.i	−0.0233004	+	0.0403575i	−0.877441	−	0.479685i	$-0.840751\pi$
$643$	−244282.	+	423109.i	−0.0233004	+	0.0403575i	0.854140	+	0.520043i	$0.174084\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.48119e6			−0.233023			−0.116512	−	0.993189i	$-0.537171\pi$
$647$	−2.48119e6			−0.233023			−0.116512	+	0.993189i	$0.537171\pi$
$648$		0			0
$649$	−4.14072e6			−0.385891
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.64565e6	+	4.58240e6i	−0.242800	+	0.420543i	−0.961511	−	0.274767i	$-0.911399\pi$
$653$	−2.64565e6	+	4.58240e6i	−0.242800	+	0.420543i	0.718711	+	0.695309i	$0.244733\pi$
$654$		0			0
$655$	−2.72646e6	−	4.72237e6i	−0.248311	−	0.430087i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.36234e6	+	4.09169e6i	0.211899	+	0.367019i	0.952309	−	0.305136i	$-0.0987019\pi$
$659$	2.36234e6	+	4.09169e6i	0.211899	+	0.367019i	−0.740410	+	0.672156i	$0.765369\pi$
$660$		0			0
$661$	3.08710e6	−	5.34702e6i	0.274819	−	0.476001i	−0.695270	−	0.718748i	$-0.744715\pi$
$661$	3.08710e6	−	5.34702e6i	0.274819	−	0.476001i	0.970090	+	0.242747i	$0.0780486\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.97267e6			0.348360
$666$		0			0
$667$	2.43778e6			0.212168
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.37926e6	+	1.62454e7i	−0.804197	+	1.39291i
$672$		0			0
$673$	4.70462e6	+	8.14865e6i	0.400394	+	0.693502i	0.993773	−	0.111421i	$-0.0355401\pi$
$673$	4.70462e6	+	8.14865e6i	0.400394	+	0.693502i	−0.593380	+	0.804923i	$0.702207\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.50430e6	+	1.29978e7i	0.629272	+	1.08993i	0.987698	+	0.156373i	$0.0499802\pi$
$677$	7.50430e6	+	1.29978e7i	0.629272	+	1.08993i	−0.358426	+	0.933558i	$0.616686\pi$
$678$		0			0
$679$	−5.38551e6	+	9.32798e6i	−0.448283	+	0.776449i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.29707e7			1.06393			0.531963	−	0.846768i	$-0.321455\pi$
$683$	1.29707e7			1.06393			0.531963	+	0.846768i	$0.321455\pi$
$684$		0			0
$685$	−1.71257e7			−1.39451
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.07425e6	+	7.05680e6i	−0.326963	+	0.566317i
$690$		0			0
$691$	−1.13278e7	−	1.96203e7i	−0.902506	−	1.56319i	−0.824230	−	0.566255i	$-0.808392\pi$
$691$	−1.13278e7	−	1.96203e7i	−0.902506	−	1.56319i	−0.0782761	−	0.996932i	$-0.524942\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.00475e6	−	6.93643e6i	−0.314495	−	0.544721i
$696$		0			0
$697$	−5.11612e6	+	8.86138e6i	−0.398895	+	0.690907i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.90169e7			−1.46166			−0.730828	−	0.682562i	$-0.760866\pi$
$701$	−1.90169e7			−1.46166			−0.730828	+	0.682562i	$0.760866\pi$
$702$		0			0
$703$	−249128.			−0.0190123
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−496584.	+	860109.i	−0.0373632	+	0.0647150i
$708$		0			0
$709$	−7.56556e6	−	1.31039e7i	−0.565231	−	0.979008i	−0.997028	−	0.0770376i	$-0.975454\pi$
$709$	−7.56556e6	−	1.31039e7i	−0.565231	−	0.979008i	0.431798	−	0.901971i	$-0.357879\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−8.73331e6	−	1.51265e7i	−0.643362	−	1.11434i
$714$		0			0
$715$	6.09444e6	−	1.05559e7i	0.445829	−	0.772199i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.50323e7			1.08443			0.542217	−	0.840238i	$-0.317585\pi$
$719$	1.50323e7			1.08443			0.542217	+	0.840238i	$0.317585\pi$
$720$		0			0
$721$	2.39853e6			0.171833
$722$		0			0
$723$		0			0
$724$		0			0
$725$	62073.0	−	107514.i	0.00438589	−	0.00759658i
$726$		0			0
$727$	3.70615e6	+	6.41924e6i	0.260068	+	0.450451i	0.966260	−	0.257570i	$-0.0829217\pi$
$727$	3.70615e6	+	6.41924e6i	0.260068	+	0.450451i	−0.706192	+	0.708021i	$0.749588\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.59370e6	−	6.22447e6i	−0.248742	−	0.430833i
$732$		0			0
$733$	1.38964e6	−	2.40693e6i	0.0955306	−	0.165464i	−0.814299	−	0.580445i	$-0.802879\pi$
$733$	1.38964e6	−	2.40693e6i	0.0955306	−	0.165464i	0.909830	+	0.414981i	$0.136212\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.17785e7			−0.798768
$738$		0			0
$739$	−1.21046e7			−0.815342			−0.407671	−	0.913129i	$-0.633659\pi$
$739$	−1.21046e7			−0.815342			−0.407671	+	0.913129i	$0.633659\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	2.23463e6	−	3.87049e6i	0.148502	−	0.257214i	−0.782172	−	0.623063i	$-0.785888\pi$
$743$	2.23463e6	−	3.87049e6i	0.148502	−	0.257214i	0.930674	+	0.365849i	$0.119221\pi$
$744$		0			0
$745$	−5.30858e6	−	9.19473e6i	−0.350419	−	0.606943i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.38402e6	−	9.32539e6i	−0.350673	−	0.607383i
$750$		0			0
$751$	−1.44231e7	+	2.49816e7i	−0.933168	+	1.61629i	−0.155298	+	0.987868i	$0.549634\pi$
$751$	−1.44231e7	+	2.49816e7i	−0.933168	+	1.61629i	−0.777869	+	0.628426i	$0.783700\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−4.01544e6			−0.256369
$756$		0			0
$757$	9.60868e6			0.609430			0.304715	−	0.952444i	$-0.401439\pi$
$757$	9.60868e6			0.609430			0.304715	+	0.952444i	$0.401439\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.27294e6	−	3.93685e6i	0.142274	−	0.246426i	−0.786078	−	0.618127i	$-0.787892\pi$
$761$	2.27294e6	−	3.93685e6i	0.142274	−	0.246426i	0.928353	+	0.371700i	$0.121225\pi$
$762$		0			0
$763$	4.39569e6	+	7.61355e6i	0.273348	+	0.473452i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.60261e6	+	2.77581e6i	0.0983649	+	0.170373i
$768$		0			0
$769$	1.07962e7	−	1.86995e7i	0.658345	−	1.14029i	−0.322699	−	0.946502i	$-0.604590\pi$
$769$	1.07962e7	−	1.86995e7i	0.658345	−	1.14029i	0.981044	−	0.193785i	$-0.0620765\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.48400e7			0.893276			0.446638	−	0.894715i	$-0.352621\pi$
$773$	1.48400e7			0.893276			0.446638	+	0.894715i	$0.352621\pi$
$774$		0			0
$775$	−889504.			−0.0531978
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.20047e6	−	1.24716e7i	0.425125	−	0.736339i
$780$		0			0
$781$	1.26554e7	+	2.19199e7i	0.742420	+	1.28591i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3.26371e6	+	5.65290e6i	0.189033	+	0.327414i
$786$		0			0
$787$	1.24393e7	−	2.15454e7i	0.715909	−	1.23999i	−0.246699	−	0.969092i	$-0.579346\pi$
$787$	1.24393e7	−	2.15454e7i	0.715909	−	1.23999i	0.962608	−	0.270898i	$-0.0873208\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.60885e6			−0.148254
$792$		0			0
$793$	1.45205e7			0.819970
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.58040e7	−	2.73733e7i	0.881294	−	1.52645i	0.0313914	−	0.999507i	$-0.490006\pi$
$797$	1.58040e7	−	2.73733e7i	0.881294	−	1.52645i	0.849903	−	0.526939i	$-0.176661\pi$
$798$		0			0
$799$	384912.	+	666687.i	0.0213302	+	0.0369450i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.82417e7	+	3.15956e7i	0.998338	+	1.72917i
$804$		0			0
$805$	−9.75110e6	+	1.68894e7i	−0.530352	+	0.918596i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.10009e6			0.166534			0.0832669	−	0.996527i	$-0.473465\pi$
$809$	3.10009e6			0.166534			0.0832669	+	0.996527i	$0.473465\pi$
$810$		0			0
$811$	1.87180e6			0.0999328			0.0499664	−	0.998751i	$-0.484089\pi$
$811$	1.87180e6			0.0999328			0.0499664	+	0.998751i	$0.484089\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.00618e6	+	5.20686e6i	−0.158533	+	0.274588i
$816$		0			0
$817$	5.05780e6	+	8.76037e6i	0.265098	+	0.459163i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.00092e7	−	1.73364e7i	−0.518252	−	0.897640i	−0.999775	−	0.0212059i	$-0.993249\pi$
$821$	−1.00092e7	−	1.73364e7i	−0.518252	−	0.897640i	0.481523	−	0.876434i	$-0.340084\pi$
$822$		0			0
$823$	−7.65588e6	+	1.32604e7i	−0.394000	+	0.682427i	−0.992973	−	0.118342i	$-0.962242\pi$
$823$	−7.65588e6	+	1.32604e7i	−0.394000	+	0.682427i	0.598973	+	0.800769i	$0.295576\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.59310e6			−0.487748			−0.243874	−	0.969807i	$-0.578418\pi$
$827$	−9.59310e6			−0.487748			−0.243874	+	0.969807i	$0.578418\pi$
$828$		0			0
$829$	2.52209e7			1.27460			0.637302	−	0.770615i	$-0.280051\pi$
$829$	2.52209e7			1.27460			0.637302	+	0.770615i	$0.280051\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.69171e6	+	4.66218e6i	−0.134405	+	0.232797i
$834$		0			0
$835$	1.32795e7	+	2.30007e7i	0.659120	+	1.14163i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.88116e6	−	1.53826e7i	−0.435577	−	0.754442i	0.561765	−	0.827297i	$-0.310122\pi$
$839$	−8.88116e6	−	1.53826e7i	−0.435577	−	0.754442i	−0.997343	+	0.0728549i	$0.976789\pi$
$840$		0			0
$841$	1.00792e7	−	1.74576e7i	0.491399	−	0.851128i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.06147e7			0.511407
$846$		0			0
$847$	−1.14883e7			−0.550234
$848$		0			0
$849$		0			0
$850$		0			0
$851$	611496.	−	1.05914e6i	0.0289447	−	0.0501338i
$852$		0			0
$853$	243485.	+	421728.i	0.0114578	+	0.0198454i	0.871697	−	0.490044i	$-0.163019\pi$
$853$	243485.	+	421728.i	0.0114578	+	0.0198454i	−0.860240	+	0.509890i	$0.829686\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−963171.	−	1.66826e6i	−0.0447972	−	0.0775911i	0.842757	−	0.538294i	$-0.180931\pi$
$857$	−963171.	−	1.66826e6i	−0.0447972	−	0.0775911i	−0.887555	+	0.460702i	$0.847598\pi$
$858$		0			0
$859$	−1.11769e7	+	1.93590e7i	−0.516820	+	0.895158i	0.482989	+	0.875626i	$0.339551\pi$
$859$	−1.11769e7	+	1.93590e7i	−0.516820	+	0.895158i	−0.999809	+	0.0195320i	$0.993782\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.85838e7			−0.849390			−0.424695	−	0.905337i	$-0.639619\pi$
$863$	−1.85838e7			−0.849390			−0.424695	+	0.905337i	$0.639619\pi$
$864$		0			0
$865$	3.82025e7			1.73601
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.07662e7	+	3.59682e7i	−0.932843	+	1.61573i
$870$		0			0
$871$	4.55871e6	+	7.89591e6i	0.203609	+	0.352661i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	7.92158e6	+	1.37206e7i	0.349778	+	0.605832i
$876$		0			0
$877$	1.45524e7	−	2.52055e7i	0.638905	−	1.10662i	−0.346769	−	0.937951i	$-0.612721\pi$
$877$	1.45524e7	−	2.52055e7i	0.638905	−	1.10662i	0.985673	−	0.168665i	$-0.0539456\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	3.14696e6			0.136600			0.0683001	−	0.997665i	$-0.478242\pi$
$881$	3.14696e6			0.136600			0.0683001	+	0.997665i	$0.478242\pi$
$882$		0			0
$883$	1.59995e7			0.690566			0.345283	−	0.938499i	$-0.387783\pi$
$883$	1.59995e7			0.690566			0.345283	+	0.938499i	$0.387783\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.72937e7	+	2.99536e7i	−0.738039	+	1.27832i	0.215338	+	0.976540i	$0.430915\pi$
$887$	−1.72937e7	+	2.99536e7i	−0.738039	+	1.27832i	−0.953377	+	0.301781i	$0.902419\pi$
$888$		0			0
$889$	1.48065e7	+	2.56457e7i	0.628346	+	1.08833i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−541728.	−	938300.i	−0.0227328	−	0.0393743i
$894$		0			0
$895$	−1.33290e7	+	2.30866e7i	−0.556213	+	0.963389i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.52806e6			0.104325
$900$		0			0
$901$	1.15794e7			0.475199
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.51052e7	+	2.61629e7i	−0.613061	+	1.06185i
$906$		0			0
$907$	−8.71982e6	−	1.51032e7i	−0.351957	−	0.609607i	0.634635	−	0.772812i	$-0.281150\pi$
$907$	−8.71982e6	−	1.51032e7i	−0.351957	−	0.609607i	−0.986592	+	0.163205i	$0.947817\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.29794e6	−	2.24810e6i	−0.0518155	−	0.0897471i	0.838954	−	0.544202i	$-0.183167\pi$
$911$	−1.29794e6	−	2.24810e6i	−0.0518155	−	0.0897471i	−0.890770	+	0.454455i	$0.849834\pi$
$912$		0			0
$913$	−1.82833e7	+	3.16676e7i	−0.725902	+	1.25730i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.88624e6			0.348975
$918$		0			0
$919$	−1.76411e7			−0.689028			−0.344514	−	0.938781i	$-0.611956\pi$
$919$	−1.76411e7			−0.689028			−0.344514	+	0.938781i	$0.611956\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	9.79625e6	−	1.69676e7i	0.378491	−	0.655566i
$924$		0			0
$925$	−31141.0	−	53937.8i	−0.00119668	−	0.00207271i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.98392e7	+	3.43626e7i	0.754199	+	1.30631i	0.945772	+	0.324833i	$0.105308\pi$
$929$	1.98392e7	+	3.43626e7i	0.754199	+	1.30631i	−0.191573	+	0.981478i	$0.561359\pi$
$930$		0			0
$931$	3.78833e6	−	6.56159e6i	0.143243	−	0.248105i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.73210e7			−0.647955
$936$		0			0
$937$	3.93413e7			1.46386			0.731930	−	0.681380i	$-0.238620\pi$
$937$	3.93413e7			1.46386			0.731930	+	0.681380i	$0.238620\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.31253e7	−	4.00542e7i	0.851361	−	1.47460i	−0.0286202	−	0.999590i	$-0.509111\pi$
$941$	2.31253e7	−	4.00542e7i	0.851361	−	1.47460i	0.879981	−	0.475009i	$-0.157555\pi$
$942$		0			0
$943$	3.53478e7	+	6.12241e7i	1.29444	+	2.24204i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.89512e7	−	3.28245e7i	−0.686693	−	1.18939i	−0.972901	−	0.231220i	$-0.925728\pi$
$947$	−1.89512e7	−	3.28245e7i	−0.686693	−	1.18939i	0.286208	−	0.958167i	$-0.407605\pi$
$948$		0			0
$949$	1.41205e7	−	2.44574e7i	0.508960	−	0.881544i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.66462e7			0.950394			0.475197	−	0.879879i	$-0.342377\pi$
$953$	2.66462e7			0.950394			0.475197	+	0.879879i	$0.342377\pi$
$954$		0			0
$955$	−3.90977e7			−1.38721
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.39542e7	−	2.41695e7i	0.489959	−	0.848634i
$960$		0			0
$961$	5.25781e6	+	9.10679e6i	0.183652	+	0.318095i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	191862.	+	332315.i	0.00663240	+	0.0114877i
$966$		0			0
$967$	−2.04895e7	+	3.54889e7i	−0.704637	+	1.22047i	0.262185	+	0.965018i	$0.415557\pi$
$967$	−2.04895e7	+	3.54889e7i	−0.704637	+	1.22047i	−0.966822	+	0.255450i	$0.917776\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.72034e7			0.925922			0.462961	−	0.886379i	$-0.346787\pi$
$971$	2.72034e7			0.925922			0.462961	+	0.886379i	$0.346787\pi$
$972$		0			0
$973$	1.30525e7			0.441990
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.26778e7	−	2.19585e7i	0.424919	−	0.735982i	−0.571494	−	0.820607i	$-0.693636\pi$
$977$	1.26778e7	−	2.19585e7i	0.424919	−	0.735982i	0.996413	+	0.0846247i	$0.0269691\pi$
$978$		0			0
$979$	−8.03358e6	−	1.39146e7i	−0.267887	−	0.463995i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.95696e6	+	1.03178e7i	0.196626	+	0.340566i	0.947432	−	0.319956i	$-0.103668\pi$
$983$	5.95696e6	+	1.03178e7i	0.196626	+	0.340566i	−0.750806	+	0.660522i	$0.770335\pi$
$984$		0			0
$985$	1.43219e7	−	2.48063e7i	0.470339	−	0.814651i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.96584e7			−1.61437
$990$		0			0
$991$	2.91931e7			0.944268			0.472134	−	0.881527i	$-0.343484\pi$
$991$	2.91931e7			0.944268			0.472134	+	0.881527i	$0.343484\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.51654e6	−	2.62672e6i	0.0485618	−	0.0841116i
$996$		0			0
$997$	8.65004e6	+	1.49823e7i	0.275601	+	0.477354i	0.970286	−	0.241959i	$-0.0777900\pi$
$997$	8.65004e6	+	1.49823e7i	0.275601	+	0.477354i	−0.694686	+	0.719313i	$0.744457\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.6.e.d.109.1		2
3.2	odd	2		324.6.e.a.109.1		2
9.2	odd	6		324.6.e.a.217.1		2
9.4	even	3		36.6.a.a.1.1		1
9.5	odd	6		4.6.a.a.1.1	✓	1
9.7	even	3	inner	324.6.e.d.217.1		2
36.23	even	6		16.6.a.b.1.1		1
36.31	odd	6		144.6.a.c.1.1		1
45.4	even	6		900.6.a.h.1.1		1
45.13	odd	12		900.6.d.a.649.2		2
45.14	odd	6		100.6.a.b.1.1		1
45.22	odd	12		900.6.d.a.649.1		2
45.23	even	12		100.6.c.b.49.1		2
45.32	even	12		100.6.c.b.49.2		2
63.5	even	6		196.6.e.d.165.1		2
63.23	odd	6		196.6.e.g.165.1		2
63.32	odd	6		196.6.e.g.177.1		2
63.41	even	6		196.6.a.e.1.1		1
63.59	even	6		196.6.e.d.177.1		2
72.5	odd	6		64.6.a.f.1.1		1
72.13	even	6		576.6.a.bc.1.1		1
72.59	even	6		64.6.a.b.1.1		1
72.67	odd	6		576.6.a.bd.1.1		1
99.32	even	6		484.6.a.a.1.1		1
117.5	even	12		676.6.d.a.337.1		2
117.77	odd	6		676.6.a.a.1.1		1
117.86	even	12		676.6.d.a.337.2		2
144.5	odd	12		256.6.b.g.129.2		2
144.59	even	12		256.6.b.c.129.1		2
144.77	odd	12		256.6.b.g.129.1		2
144.131	even	12		256.6.b.c.129.2		2
180.23	odd	12		400.6.c.f.49.2		2
180.59	even	6		400.6.a.d.1.1		1
180.167	odd	12		400.6.c.f.49.1		2
252.167	odd	6		784.6.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.6.a.a.1.1	✓	1	9.5	odd	6
16.6.a.b.1.1		1	36.23	even	6
36.6.a.a.1.1		1	9.4	even	3
64.6.a.b.1.1		1	72.59	even	6
64.6.a.f.1.1		1	72.5	odd	6
100.6.a.b.1.1		1	45.14	odd	6
100.6.c.b.49.1		2	45.23	even	12
100.6.c.b.49.2		2	45.32	even	12
144.6.a.c.1.1		1	36.31	odd	6
196.6.a.e.1.1		1	63.41	even	6
196.6.e.d.165.1		2	63.5	even	6
196.6.e.d.177.1		2	63.59	even	6
196.6.e.g.165.1		2	63.23	odd	6
196.6.e.g.177.1		2	63.32	odd	6
256.6.b.c.129.1		2	144.59	even	12
256.6.b.c.129.2		2	144.131	even	12
256.6.b.g.129.1		2	144.77	odd	12
256.6.b.g.129.2		2	144.5	odd	12
324.6.e.a.109.1		2	3.2	odd	2
324.6.e.a.217.1		2	9.2	odd	6
324.6.e.d.109.1		2	1.1	even	1	trivial
324.6.e.d.217.1		2	9.7	even	3	inner
400.6.a.d.1.1		1	180.59	even	6
400.6.c.f.49.1		2	180.167	odd	12
400.6.c.f.49.2		2	180.23	odd	12
484.6.a.a.1.1		1	99.32	even	6
576.6.a.bc.1.1		1	72.13	even	6
576.6.a.bd.1.1		1	72.67	odd	6
676.6.a.a.1.1		1	117.77	odd	6
676.6.d.a.337.1		2	117.5	even	12
676.6.d.a.337.2		2	117.86	even	12
784.6.a.d.1.1		1	252.167	odd	6
900.6.a.h.1.1		1	45.4	even	6
900.6.d.a.649.1		2	45.22	odd	12
900.6.d.a.649.2		2	45.13	odd	12

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	324.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(27.0000 - 46.7654i) q^{5} +(44.0000 + 76.2102i) q^{7} +O(q^{10})\)	\(q+(27.0000 - 46.7654i) q^{5} +(44.0000 + 76.2102i) q^{7} +(270.000 + 467.654i) q^{11} +(209.000 - 361.999i) q^{13} -594.000 q^{17} +836.000 q^{19} +(-2052.00 + 3554.17i) q^{23} +(104.500 + 180.999i) q^{25} +(-297.000 - 514.419i) q^{29} +(-2128.00 + 3685.80i) q^{31} +4752.00 q^{35} -298.000 q^{37} +(8613.00 - 14918.2i) q^{41} +(6050.00 + 10478.9i) q^{43} +(-648.000 - 1122.37i) q^{47} +(4531.50 - 7848.79i) q^{49} -19494.0 q^{53} +29160.0 q^{55} +(-3834.00 + 6640.68i) q^{59} +(17369.0 + 30084.0i) q^{61} +(-11286.0 - 19547.9i) q^{65} +(-10906.0 + 18889.7i) q^{67} +46872.0 q^{71} +67562.0 q^{73} +(-23760.0 + 41153.5i) q^{77} +(38456.0 + 66607.7i) q^{79} +(33858.0 + 58643.8i) q^{83} +(-16038.0 + 27778.6i) q^{85} -29754.0 q^{89} +36784.0 q^{91} +(22572.0 - 39095.9i) q^{95} +(61199.0 + 106000. i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 54 q^{5} + 88 q^{7}+O(q^{10}) \) 2 * q + 54 * q^5 + 88 * q^7	\( 2 q + 54 q^{5} + 88 q^{7} + 540 q^{11} + 418 q^{13} - 1188 q^{17} + 1672 q^{19} - 4104 q^{23} + 209 q^{25} - 594 q^{29} - 4256 q^{31} + 9504 q^{35} - 596 q^{37} + 17226 q^{41} + 12100 q^{43} - 1296 q^{47} + 9063 q^{49} - 38988 q^{53} + 58320 q^{55} - 7668 q^{59} + 34738 q^{61} - 22572 q^{65} - 21812 q^{67} + 93744 q^{71} + 135124 q^{73} - 47520 q^{77} + 76912 q^{79} + 67716 q^{83} - 32076 q^{85} - 59508 q^{89} + 73568 q^{91} + 45144 q^{95} + 122398 q^{97}+O(q^{100}) \) 2 * q + 54 * q^5 + 88 * q^7 + 540 * q^11 + 418 * q^13 - 1188 * q^17 + 1672 * q^19 - 4104 * q^23 + 209 * q^25 - 594 * q^29 - 4256 * q^31 + 9504 * q^35 - 596 * q^37 + 17226 * q^41 + 12100 * q^43 - 1296 * q^47 + 9063 * q^49 - 38988 * q^53 + 58320 * q^55 - 7668 * q^59 + 34738 * q^61 - 22572 * q^65 - 21812 * q^67 + 93744 * q^71 + 135124 * q^73 - 47520 * q^77 + 76912 * q^79 + 67716 * q^83 - 32076 * q^85 - 59508 * q^89 + 73568 * q^91 + 45144 * q^95 + 122398 * q^97

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