LMFDB - Embedded newform 3234.2.e.b.2155.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (of order $2$, degree $1$, 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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.5
Root			$0.500000 + 0.0286340i$ of defining polynomial
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.b.2155.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +0.837391i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +0.837391i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +0.837391 q^{10} +(0.697189 + 3.24252i) q^{11} -1.00000i q^{12} +2.59370 q^{13} -0.837391 q^{15} +1.00000 q^{16} +5.97372 q^{17} +1.00000i q^{18} -3.11181 q^{19} -0.837391i q^{20} +(3.24252 - 0.697189i) q^{22} +2.86511 q^{23} -1.00000 q^{24} +4.29878 q^{25} -2.59370i q^{26} -1.00000i q^{27} +5.38769i q^{29} +0.837391i q^{30} +1.05470i q^{31} -1.00000i q^{32} +(-3.24252 + 0.697189i) q^{33} -5.97372i q^{34} +1.00000 q^{36} -10.9893 q^{37} +3.11181i q^{38} +2.59370i q^{39} -0.837391 q^{40} -11.2350 q^{41} -1.27527i q^{43} +(-0.697189 - 3.24252i) q^{44} -0.837391i q^{45} -2.86511i q^{46} -12.2437i q^{47} +1.00000i q^{48} -4.29878i q^{50} +5.97372i q^{51} -2.59370 q^{52} +5.17461 q^{53} -1.00000 q^{54} +(-2.71526 + 0.583820i) q^{55} -3.11181i q^{57} +5.38769 q^{58} +9.68506i q^{59} +0.837391 q^{60} +4.07048 q^{61} +1.05470 q^{62} -1.00000 q^{64} +2.17195i q^{65} +(0.697189 + 3.24252i) q^{66} +13.0383 q^{67} -5.97372 q^{68} +2.86511i q^{69} +14.0795 q^{71} -1.00000i q^{72} -9.91318 q^{73} +10.9893i q^{74} +4.29878i q^{75} +3.11181 q^{76} +2.59370 q^{78} +13.5121i q^{79} +0.837391i q^{80} +1.00000 q^{81} +11.2350i q^{82} +2.99287 q^{83} +5.00234i q^{85} -1.27527 q^{86} -5.38769 q^{87} +(-3.24252 + 0.697189i) q^{88} +8.40678i q^{89} -0.837391 q^{90} -2.86511 q^{92} -1.05470 q^{93} -12.2437 q^{94} -2.60580i q^{95} +1.00000 q^{96} +0.786131i q^{97} +(-0.697189 - 3.24252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9	$ 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9} + 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} - 20 q^{19} + 2 q^{22} + 8 q^{23} - 16 q^{24} - 20 q^{25} - 2 q^{33} + 16 q^{36} - 28 q^{37} - 4 q^{40} - 32 q^{41} - 8 q^{44} - 16 q^{54} + 14 q^{55} + 4 q^{60} + 56 q^{61} + 8 q^{62} - 16 q^{64} + 8 q^{66} + 32 q^{67} - 56 q^{71} - 88 q^{73} + 20 q^{76} + 16 q^{81} - 8 q^{83} + 24 q^{86} - 2 q^{88} - 4 q^{90} - 8 q^{92} - 8 q^{93} + 28 q^{94} + 16 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9 + 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 - 20 * q^19 + 2 * q^22 + 8 * q^23 - 16 * q^24 - 20 * q^25 - 2 * q^33 + 16 * q^36 - 28 * q^37 - 4 * q^40 - 32 * q^41 - 8 * q^44 - 16 * q^54 + 14 * q^55 + 4 * q^60 + 56 * q^61 + 8 * q^62 - 16 * q^64 + 8 * q^66 + 32 * q^67 - 56 * q^71 - 88 * q^73 + 20 * q^76 + 16 * q^81 - 8 * q^83 + 24 * q^86 - 2 * q^88 - 4 * q^90 - 8 * q^92 - 8 * q^93 + 28 * q^94 + 16 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.00000			−0.500000
$5$			0.837391i			0.374493i	0.982313	+	0.187246i	$0.0599563\pi$
$5$			0.837391i			0.374493i	−0.982313	+	0.187246i	$0.940044\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	0.837391			0.264806
$11$	0.697189	+	3.24252i	0.210210	+	0.977656i
$11$	0.697189	+	3.24252i	0.210210	+	0.977656i
$12$		−	1.00000i		−	0.288675i
$13$	2.59370			0.719364			0.359682	−	0.933075i	$-0.382885\pi$
$13$	2.59370			0.719364			0.359682	+	0.933075i	$0.382885\pi$
$14$		0			0
$15$	−0.837391			−0.216214
$16$	1.00000			0.250000
$17$	5.97372			1.44884			0.724420	−	0.689359i	$-0.242108\pi$
$17$	5.97372			1.44884			0.724420	+	0.689359i	$0.242108\pi$
$18$			1.00000i			0.235702i
$19$	−3.11181			−0.713898			−0.356949	−	0.934124i	$-0.616183\pi$
$19$	−3.11181			−0.713898			−0.356949	+	0.934124i	$0.616183\pi$
$20$		−	0.837391i		−	0.187246i
$21$		0			0
$22$	3.24252	−	0.697189i	0.691307	−	0.148641i
$23$	2.86511			0.597418			0.298709	−	0.954344i	$-0.403444\pi$
$23$	2.86511			0.597418			0.298709	+	0.954344i	$0.403444\pi$
$24$	−1.00000			−0.204124
$25$	4.29878			0.859755
$26$		−	2.59370i		−	0.508667i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$			5.38769i			1.00047i	0.865890	+	0.500234i	$0.166753\pi$
$29$			5.38769i			1.00047i	−0.865890	+	0.500234i	$0.833247\pi$
$30$			0.837391i			0.152886i
$31$			1.05470i			0.189430i	0.995504	+	0.0947151i	$0.0301940\pi$
$31$			1.05470i			0.189430i	−0.995504	+	0.0947151i	$0.969806\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−3.24252	+	0.697189i	−0.564450	+	0.121365i
$34$		−	5.97372i		−	1.02448i
$35$		0			0
$36$	1.00000			0.166667
$37$	−10.9893			−1.80664			−0.903319	−	0.428970i	$-0.858877\pi$
$37$	−10.9893			−1.80664			−0.903319	+	0.428970i	$0.858877\pi$
$38$			3.11181i			0.504802i
$39$			2.59370i			0.415325i
$40$	−0.837391			−0.132403
$41$	−11.2350			−1.75461			−0.877304	−	0.479934i	$-0.840661\pi$
$41$	−11.2350			−1.75461			−0.877304	+	0.479934i	$0.840661\pi$
$42$		0			0
$43$		−	1.27527i		−	0.194478i	−0.995261	−	0.0972388i	$-0.968999\pi$
$43$		−	1.27527i		−	0.194478i	0.995261	−	0.0972388i	$-0.0310010\pi$
$44$	−0.697189	−	3.24252i	−0.105105	−	0.488828i
$45$		−	0.837391i		−	0.124831i
$46$		−	2.86511i		−	0.422438i
$47$		−	12.2437i		−	1.78593i	−0.450128	−	0.892964i	$-0.648622\pi$
$47$		−	12.2437i		−	1.78593i	0.450128	−	0.892964i	$-0.351378\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$		−	4.29878i		−	0.607939i
$51$			5.97372i			0.836488i
$52$	−2.59370			−0.359682
$53$	5.17461			0.710787			0.355394	−	0.934717i	$-0.384347\pi$
$53$	5.17461			0.710787			0.355394	+	0.934717i	$0.384347\pi$
$54$	−1.00000			−0.136083
$55$	−2.71526	+	0.583820i	−0.366125	+	0.0787223i
$56$		0			0
$57$		−	3.11181i		−	0.412169i
$58$	5.38769			0.707438
$59$			9.68506i			1.26089i	0.776235	+	0.630444i	$0.217127\pi$
$59$			9.68506i			1.26089i	−0.776235	+	0.630444i	$0.782873\pi$
$60$	0.837391			0.108107
$61$	4.07048			0.521172			0.260586	−	0.965451i	$-0.416084\pi$
$61$	4.07048			0.521172			0.260586	+	0.965451i	$0.416084\pi$
$62$	1.05470			0.133947
$63$		0			0
$64$	−1.00000			−0.125000
$65$			2.17195i			0.269397i
$66$	0.697189	+	3.24252i	0.0858180	+	0.399126i
$67$	13.0383			1.59288			0.796442	−	0.604715i	$-0.206713\pi$
$67$	13.0383			1.59288			0.796442	+	0.604715i	$0.206713\pi$
$68$	−5.97372			−0.724420
$69$			2.86511i			0.344919i
$70$		0			0
$71$	14.0795			1.67093			0.835467	−	0.549541i	$-0.185197\pi$
$71$	14.0795			1.67093			0.835467	+	0.549541i	$0.185197\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−9.91318			−1.16025			−0.580125	−	0.814527i	$-0.696996\pi$
$73$	−9.91318			−1.16025			−0.580125	+	0.814527i	$0.696996\pi$
$74$			10.9893i			1.27749i
$75$			4.29878i			0.496380i
$76$	3.11181			0.356949
$77$		0			0
$78$	2.59370			0.293679
$79$			13.5121i			1.52023i	0.649791	+	0.760113i	$0.274856\pi$
$79$			13.5121i			1.52023i	−0.649791	+	0.760113i	$0.725144\pi$
$80$			0.837391i			0.0936232i
$81$	1.00000			0.111111
$82$			11.2350i			1.24070i
$83$	2.99287			0.328510			0.164255	−	0.986418i	$-0.447478\pi$
$83$	2.99287			0.328510			0.164255	+	0.986418i	$0.447478\pi$
$84$		0			0
$85$			5.00234i			0.542580i
$86$	−1.27527			−0.137516
$87$	−5.38769			−0.577621
$88$	−3.24252	+	0.697189i	−0.345654	+	0.0743206i
$89$			8.40678i			0.891117i	0.895253	+	0.445559i	$0.146995\pi$
$89$			8.40678i			0.891117i	−0.895253	+	0.445559i	$0.853005\pi$
$90$	−0.837391			−0.0882688
$91$		0			0
$92$	−2.86511			−0.298709
$93$	−1.05470			−0.109368
$94$	−12.2437			−1.26284
$95$		−	2.60580i		−	0.267350i
$96$	1.00000			0.102062
$97$			0.786131i			0.0798195i	0.999203	+	0.0399097i	$0.0127070\pi$
$97$			0.786131i			0.0798195i	−0.999203	+	0.0399097i	$0.987293\pi$
$98$		0			0
$99$	−0.697189	−	3.24252i	−0.0700701	−	0.325885i
$100$	−4.29878			−0.429878
$101$	−6.72227			−0.668891			−0.334445	−	0.942415i	$-0.608549\pi$
$101$	−6.72227			−0.668891			−0.334445	+	0.942415i	$0.608549\pi$
$102$	5.97372			0.591486
$103$		−	4.07143i		−	0.401170i	−0.979676	−	0.200585i	$-0.935716\pi$
$103$		−	4.07143i		−	0.401170i	0.979676	−	0.200585i	$-0.0642842\pi$
$104$			2.59370i			0.254334i
$105$		0			0
$106$		−	5.17461i		−	0.502602i
$107$			0.241883i			0.0233837i	0.999932	+	0.0116919i	$0.00372172\pi$
$107$			0.241883i			0.0233837i	−0.999932	+	0.0116919i	$0.996278\pi$
$108$			1.00000i			0.0962250i
$109$			17.5252i			1.67861i	0.543662	+	0.839304i	$0.317037\pi$
$109$			17.5252i			1.67861i	−0.543662	+	0.839304i	$0.682963\pi$
$110$	0.583820	+	2.71526i	0.0556651	+	0.258890i
$111$		−	10.9893i		−	1.04306i
$112$		0			0
$113$	8.08949			0.760995			0.380498	−	0.924782i	$-0.375753\pi$
$113$	8.08949			0.760995			0.380498	+	0.924782i	$0.375753\pi$
$114$	−3.11181			−0.291448
$115$			2.39922i			0.223729i
$116$		−	5.38769i		−	0.500234i
$117$	−2.59370			−0.239788
$118$	9.68506			0.891582
$119$		0			0
$120$		−	0.837391i		−	0.0764430i
$121$	−10.0279	+	4.52130i	−0.911623	+	0.411027i
$122$		−	4.07048i		−	0.368524i
$123$		−	11.2350i		−	1.01302i
$124$		−	1.05470i		−	0.0947151i
$125$			7.78672i			0.696465i
$126$		0			0
$127$			12.1313i			1.07648i	0.842791	+	0.538241i	$0.180911\pi$
$127$			12.1313i			1.07648i	−0.842791	+	0.538241i	$0.819089\pi$
$128$			1.00000i			0.0883883i
$129$	1.27527			0.112282
$130$	2.17195			0.190492
$131$	2.04449			0.178628			0.0893139	−	0.996004i	$-0.471533\pi$
$131$	2.04449			0.178628			0.0893139	+	0.996004i	$0.471533\pi$
$132$	3.24252	−	0.697189i	0.282225	−	0.0606825i
$133$		0			0
$134$		−	13.0383i		−	1.12634i
$135$	0.837391			0.0720712
$136$			5.97372i			0.512242i
$137$	−13.2111			−1.12870			−0.564351	−	0.825535i	$-0.690874\pi$
$137$	−13.2111			−1.12870			−0.564351	+	0.825535i	$0.690874\pi$
$138$	2.86511			0.243895
$139$	6.16293			0.522733			0.261367	−	0.965240i	$-0.415827\pi$
$139$	6.16293			0.522733			0.261367	+	0.965240i	$0.415827\pi$
$140$		0			0
$141$	12.2437			1.03111
$142$		−	14.0795i		−	1.18153i
$143$	1.80830	+	8.41014i	0.151218	+	0.703291i
$144$	−1.00000			−0.0833333
$145$	−4.51160			−0.374668
$146$			9.91318i			0.820421i
$147$		0			0
$148$	10.9893			0.903319
$149$			4.39696i			0.360213i	0.983647	+	0.180107i	$0.0576443\pi$
$149$			4.39696i			0.360213i	−0.983647	+	0.180107i	$0.942356\pi$
$150$	4.29878			0.350994
$151$			10.2407i			0.833380i	0.909049	+	0.416690i	$0.136810\pi$
$151$			10.2407i			0.833380i	−0.909049	+	0.416690i	$0.863190\pi$
$152$		−	3.11181i		−	0.252401i
$153$	−5.97372			−0.482947
$154$		0			0
$155$	−0.883199			−0.0709402
$156$		−	2.59370i		−	0.207663i
$157$			15.9861i			1.27583i	0.770107	+	0.637914i	$0.220203\pi$
$157$			15.9861i			1.27583i	−0.770107	+	0.637914i	$0.779797\pi$
$158$	13.5121			1.07496
$159$			5.17461i			0.410373i
$160$	0.837391			0.0662016
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−0.523852			−0.0410313			−0.0205156	−	0.999790i	$-0.506531\pi$
$163$	−0.523852			−0.0410313			−0.0205156	+	0.999790i	$0.506531\pi$
$164$	11.2350			0.877304
$165$	−0.583820	−	2.71526i	−0.0454503	−	0.211383i
$166$		−	2.99287i		−	0.232292i
$167$	−17.0544			−1.31971			−0.659855	−	0.751393i	$-0.729382\pi$
$167$	−17.0544			−1.31971			−0.659855	+	0.751393i	$0.729382\pi$
$168$		0			0
$169$	−6.27269			−0.482515
$170$	5.00234			0.383662
$171$	3.11181			0.237966
$172$			1.27527i			0.0972388i
$173$	−7.23663			−0.550191			−0.275095	−	0.961417i	$-0.588709\pi$
$173$	−7.23663			−0.550191			−0.275095	+	0.961417i	$0.588709\pi$
$174$			5.38769i			0.408440i
$175$		0			0
$176$	0.697189	+	3.24252i	0.0525526	+	0.244414i
$177$	−9.68506			−0.727974
$178$	8.40678			0.630115
$179$	8.06636			0.602908			0.301454	−	0.953481i	$-0.402528\pi$
$179$	8.06636			0.602908			0.301454	+	0.953481i	$0.402528\pi$
$180$			0.837391i			0.0624155i
$181$		−	5.61056i		−	0.417030i	−0.978019	−	0.208515i	$-0.933137\pi$
$181$		−	5.61056i		−	0.417030i	0.978019	−	0.208515i	$-0.0668630\pi$
$182$		0			0
$183$			4.07048i			0.300899i
$184$			2.86511i			0.211219i
$185$		−	9.20238i		−	0.676573i
$186$			1.05470i			0.0773345i
$187$	4.16481	+	19.3699i	0.304561	+	1.41647i
$188$			12.2437i			0.892964i
$189$		0			0
$190$	−2.60580			−0.189045
$191$	11.7841			0.852668			0.426334	−	0.904566i	$-0.359805\pi$
$191$	11.7841			0.852668			0.426334	+	0.904566i	$0.359805\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	18.0976i		−	1.30270i	−0.758779	−	0.651348i	$-0.774204\pi$
$193$		−	18.0976i		−	1.30270i	0.758779	−	0.651348i	$-0.225796\pi$
$194$	0.786131			0.0564409
$195$	−2.17195			−0.155536
$196$		0			0
$197$		−	6.23110i		−	0.443948i	−0.975053	−	0.221974i	$-0.928750\pi$
$197$		−	6.23110i		−	0.443948i	0.975053	−	0.221974i	$-0.0712500\pi$
$198$	−3.24252	+	0.697189i	−0.230436	+	0.0495471i
$199$			18.2669i			1.29491i	0.762106	+	0.647453i	$0.224166\pi$
$199$			18.2669i			1.29491i	−0.762106	+	0.647453i	$0.775834\pi$
$200$			4.29878i			0.303969i
$201$			13.0383i			0.919652i
$202$			6.72227i			0.472977i
$203$		0			0
$204$		−	5.97372i		−	0.418244i
$205$		−	9.40808i		−	0.657088i
$206$	−4.07143			−0.283670
$207$	−2.86511			−0.199139
$208$	2.59370			0.179841
$209$	−2.16952	−	10.0901i	−0.150069	−	0.697947i
$210$		0			0
$211$			10.2446i			0.705269i	0.935761	+	0.352635i	$0.114714\pi$
$211$			10.2446i			0.705269i	−0.935761	+	0.352635i	$0.885286\pi$
$212$	−5.17461			−0.355394
$213$			14.0795i			0.964714i
$214$	0.241883			0.0165348
$215$	1.06790			0.0728304
$216$	1.00000			0.0680414
$217$		0			0
$218$	17.5252			1.18696
$219$		−	9.91318i		−	0.669871i
$220$	2.71526	−	0.583820i	0.183063	−	0.0393612i
$221$	15.4941			1.04224
$222$	−10.9893			−0.737557
$223$			15.6665i			1.04911i	0.851377	+	0.524554i	$0.175768\pi$
$223$			15.6665i			1.04911i	−0.851377	+	0.524554i	$0.824232\pi$
$224$		0			0
$225$	−4.29878			−0.286585
$226$		−	8.08949i		−	0.538105i
$227$	−15.7205			−1.04341			−0.521703	−	0.853127i	$-0.674703\pi$
$227$	−15.7205			−1.04341			−0.521703	+	0.853127i	$0.674703\pi$
$228$			3.11181i			0.206085i
$229$		−	2.50417i		−	0.165480i	−0.996571	−	0.0827400i	$-0.973633\pi$
$229$		−	2.50417i		−	0.165480i	0.996571	−	0.0827400i	$-0.0263671\pi$
$230$	2.39922			0.158200
$231$		0			0
$232$	−5.38769			−0.353719
$233$		−	0.0553161i		−	0.00362388i	−0.999998	−	0.00181194i	$-0.999423\pi$
$233$		−	0.0553161i		−	0.00362388i	0.999998	−	0.00181194i	$-0.000576759\pi$
$234$			2.59370i			0.169556i
$235$	10.2528			0.668817
$236$		−	9.68506i		−	0.630444i
$237$	−13.5121			−0.877702
$238$		0			0
$239$			5.74465i			0.371591i	0.982588	+	0.185795i	$0.0594861\pi$
$239$			5.74465i			0.371591i	−0.982588	+	0.185795i	$0.940514\pi$
$240$	−0.837391			−0.0540534
$241$	7.34245			0.472969			0.236484	−	0.971635i	$-0.424005\pi$
$241$	7.34245			0.472969			0.236484	+	0.971635i	$0.424005\pi$
$242$	4.52130	+	10.0279i	0.290640	+	0.644615i
$243$			1.00000i			0.0641500i
$244$	−4.07048			−0.260586
$245$		0			0
$246$	−11.2350			−0.716316
$247$	−8.07111			−0.513553
$248$	−1.05470			−0.0669737
$249$			2.99287i			0.189665i
$250$	7.78672			0.492475
$251$			4.20803i			0.265608i	0.991142	+	0.132804i	$0.0423981\pi$
$251$			4.20803i			0.265608i	−0.991142	+	0.132804i	$0.957602\pi$
$252$		0			0
$253$	1.99753	+	9.29019i	0.125583	+	0.584069i
$254$	12.1313			0.761188
$255$	−5.00234			−0.313259
$256$	1.00000			0.0625000
$257$		−	24.6466i		−	1.53741i	−0.639602	−	0.768706i	$-0.720901\pi$
$257$		−	24.6466i		−	1.53741i	0.639602	−	0.768706i	$-0.279099\pi$
$258$		−	1.27527i		−	0.0793951i
$259$		0			0
$260$		−	2.17195i		−	0.134698i
$261$		−	5.38769i		−	0.333489i
$262$		−	2.04449i		−	0.126309i
$263$		−	30.3837i		−	1.87354i	−0.349950	−	0.936768i	$-0.613802\pi$
$263$		−	30.3837i		−	1.87354i	0.349950	−	0.936768i	$-0.386198\pi$
$264$	−0.697189	−	3.24252i	−0.0429090	−	0.199563i
$265$			4.33317i			0.266185i
$266$		0			0
$267$	−8.40678			−0.514487
$268$	−13.0383			−0.796442
$269$		−	19.9737i		−	1.21782i	−0.793240	−	0.608910i	$-0.791607\pi$
$269$		−	19.9737i		−	1.21782i	0.793240	−	0.608910i	$-0.208393\pi$
$270$		−	0.837391i		−	0.0509620i
$271$	1.61528			0.0981212			0.0490606	−	0.998796i	$-0.484377\pi$
$271$	1.61528			0.0981212			0.0490606	+	0.998796i	$0.484377\pi$
$272$	5.97372			0.362210
$273$		0			0
$274$			13.2111i			0.798113i
$275$	2.99706	+	13.9389i	0.180729	+	0.840545i
$276$		−	2.86511i		−	0.172460i
$277$			5.18071i			0.311279i	0.987814	+	0.155639i	$0.0497438\pi$
$277$			5.18071i			0.311279i	−0.987814	+	0.155639i	$0.950256\pi$
$278$		−	6.16293i		−	0.369628i
$279$		−	1.05470i		−	0.0631434i
$280$		0			0
$281$			25.1883i			1.50261i	0.659956	+	0.751304i	$0.270575\pi$
$281$			25.1883i			1.50261i	−0.659956	+	0.751304i	$0.729425\pi$
$282$		−	12.2437i		−	0.729102i
$283$	23.0334			1.36920			0.684598	−	0.728921i	$-0.259978\pi$
$283$	23.0334			1.36920			0.684598	+	0.728921i	$0.259978\pi$
$284$	−14.0795			−0.835467
$285$	2.60580			0.154354
$286$	8.41014	−	1.80830i	0.497302	−	0.106927i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	18.6853			1.09914
$290$			4.51160i			0.264930i
$291$	−0.786131			−0.0460838
$292$	9.91318			0.580125
$293$	−4.18076			−0.244242			−0.122121	−	0.992515i	$-0.538970\pi$
$293$	−4.18076			−0.244242			−0.122121	+	0.992515i	$0.538970\pi$
$294$		0			0
$295$	−8.11019			−0.472194
$296$		−	10.9893i		−	0.638743i
$297$	3.24252	−	0.697189i	0.188150	−	0.0404550i
$298$	4.39696			0.254709
$299$	7.43126			0.429761
$300$		−	4.29878i		−	0.248190i
$301$		0			0
$302$	10.2407			0.589288
$303$		−	6.72227i		−	0.386184i
$304$	−3.11181			−0.178474
$305$			3.40859i			0.195175i
$306$			5.97372i			0.341495i
$307$	10.0657			0.574478			0.287239	−	0.957859i	$-0.407263\pi$
$307$	10.0657			0.574478			0.287239	+	0.957859i	$0.407263\pi$
$308$		0			0
$309$	4.07143			0.231615
$310$			0.883199i			0.0501623i
$311$		−	1.42972i		−	0.0810718i	−0.999178	−	0.0405359i	$-0.987093\pi$
$311$		−	1.42972i		−	0.0810718i	0.999178	−	0.0405359i	$-0.0129065\pi$
$312$	−2.59370			−0.146840
$313$			30.3930i			1.71792i	0.512046	+	0.858958i	$0.328888\pi$
$313$			30.3930i			1.71792i	−0.512046	+	0.858958i	$0.671112\pi$
$314$	15.9861			0.902147
$315$		0			0
$316$		−	13.5121i		−	0.760113i
$317$	10.8522			0.609521			0.304760	−	0.952429i	$-0.401424\pi$
$317$	10.8522			0.609521			0.304760	+	0.952429i	$0.401424\pi$
$318$	5.17461			0.290178
$319$	−17.4697	+	3.75624i	−0.978114	+	0.210309i
$320$		−	0.837391i		−	0.0468116i
$321$	−0.241883			−0.0135006
$322$		0			0
$323$	−18.5891			−1.03432
$324$	−1.00000			−0.0555556
$325$	11.1498			0.618477
$326$			0.523852i			0.0290135i
$327$	−17.5252			−0.969145
$328$		−	11.2350i		−	0.620348i
$329$		0			0
$330$	−2.71526	+	0.583820i	−0.149470	+	0.0321382i
$331$	−12.9149			−0.709870			−0.354935	−	0.934891i	$-0.615497\pi$
$331$	−12.9149			−0.709870			−0.354935	+	0.934891i	$0.615497\pi$
$332$	−2.99287			−0.164255
$333$	10.9893			0.602212
$334$			17.0544i			0.933175i
$335$			10.9182i			0.596523i
$336$		0			0
$337$			16.4809i			0.897772i	0.893589	+	0.448886i	$0.148179\pi$
$337$			16.4809i			0.897772i	−0.893589	+	0.448886i	$0.851821\pi$
$338$			6.27269i			0.341190i
$339$			8.08949i			0.439361i
$340$		−	5.00234i		−	0.271290i
$341$	−3.41989	+	0.735327i	−0.185198	+	0.0398202i
$342$		−	3.11181i		−	0.168267i
$343$		0			0
$344$	1.27527			0.0687582
$345$	−2.39922			−0.129170
$346$			7.23663i			0.389044i
$347$		−	11.4633i		−	0.615380i	−0.951487	−	0.307690i	$-0.900444\pi$
$347$		−	11.4633i		−	0.615380i	0.951487	−	0.307690i	$-0.0995560\pi$
$348$	5.38769			0.288810
$349$	−20.9561			−1.12176			−0.560878	−	0.827899i	$-0.689536\pi$
$349$	−20.9561			−1.12176			−0.560878	+	0.827899i	$0.689536\pi$
$350$		0			0
$351$		−	2.59370i		−	0.138442i
$352$	3.24252	−	0.697189i	0.172827	−	0.0371603i
$353$		−	19.9221i		−	1.06035i	−0.847890	−	0.530173i	$-0.822127\pi$
$353$		−	19.9221i		−	1.06035i	0.847890	−	0.530173i	$-0.177873\pi$
$354$			9.68506i			0.514755i
$355$			11.7901i			0.625753i
$356$		−	8.40678i		−	0.445559i
$357$		0			0
$358$		−	8.06636i		−	0.426321i
$359$		−	3.91431i		−	0.206589i	−0.994651	−	0.103295i	$-0.967062\pi$
$359$		−	3.91431i		−	0.206589i	0.994651	−	0.103295i	$-0.0329384\pi$
$360$	0.837391			0.0441344
$361$	−9.31665			−0.490350
$362$	−5.61056			−0.294885
$363$	−4.52130	−	10.0279i	−0.237307	−	0.526326i
$364$		0			0
$365$		−	8.30121i		−	0.434505i
$366$	4.07048			0.212768
$367$		−	12.0920i		−	0.631198i	−0.948893	−	0.315599i	$-0.897795\pi$
$367$		−	12.0920i		−	0.631198i	0.948893	−	0.315599i	$-0.102205\pi$
$368$	2.86511			0.149354
$369$	11.2350			0.584870
$370$	−9.20238			−0.478409
$371$		0			0
$372$	1.05470			0.0546838
$373$			17.6936i			0.916141i	0.888916	+	0.458070i	$0.151459\pi$
$373$			17.6936i			0.916141i	−0.888916	+	0.458070i	$0.848541\pi$
$374$	19.3699	−	4.16481i	1.00159	−	0.215357i
$375$	−7.78672			−0.402104
$376$	12.2437			0.631421
$377$			13.9741i			0.719701i
$378$		0			0
$379$	19.6577			1.00975			0.504874	−	0.863193i	$-0.331539\pi$
$379$	19.6577			1.00975			0.504874	+	0.863193i	$0.331539\pi$
$380$			2.60580i			0.133675i
$381$	−12.1313			−0.621507
$382$		−	11.7841i		−	0.602928i
$383$			1.37345i			0.0701800i	0.999384	+	0.0350900i	$0.0111718\pi$
$383$			1.37345i			0.0701800i	−0.999384	+	0.0350900i	$0.988828\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−18.0976			−0.921145
$387$			1.27527i			0.0648258i
$388$		−	0.786131i		−	0.0399097i
$389$	31.3793			1.59099			0.795496	−	0.605959i	$-0.207210\pi$
$389$	31.3793			1.59099			0.795496	+	0.605959i	$0.207210\pi$
$390$			2.17195i			0.109981i
$391$	17.1154			0.865562
$392$		0			0
$393$			2.04449i			0.103131i
$394$	−6.23110			−0.313918
$395$	−11.3149			−0.569313
$396$	0.697189	+	3.24252i	0.0350351	+	0.162943i
$397$		−	35.2719i		−	1.77025i	−0.465357	−	0.885123i	$-0.654074\pi$
$397$		−	35.2719i		−	1.77025i	0.465357	−	0.885123i	$-0.345926\pi$
$398$	18.2669			0.915636
$399$		0			0
$400$	4.29878			0.214939
$401$	8.96618			0.447750			0.223875	−	0.974618i	$-0.428129\pi$
$401$	8.96618			0.447750			0.223875	+	0.974618i	$0.428129\pi$
$402$	13.0383			0.650292
$403$			2.73559i			0.136269i
$404$	6.72227			0.334445
$405$			0.837391i			0.0416103i
$406$		0			0
$407$	−7.66165	−	35.6332i	−0.379774	−	1.76627i
$408$	−5.97372			−0.295743
$409$	−35.9524			−1.77773			−0.888867	−	0.458166i	$-0.848506\pi$
$409$	−35.9524			−1.77773			−0.888867	+	0.458166i	$0.848506\pi$
$410$	−9.40808			−0.464632
$411$		−	13.2111i		−	0.651657i
$412$			4.07143i			0.200585i
$413$		0			0
$414$			2.86511i			0.140813i
$415$			2.50620i			0.123025i
$416$		−	2.59370i		−	0.127167i
$417$			6.16293i			0.301800i
$418$	−10.0901	+	2.16952i	−0.493523	+	0.106115i
$419$		−	0.724634i		−	0.0354007i	−0.999843	−	0.0177004i	$-0.994366\pi$
$419$		−	0.724634i		−	0.0354007i	0.999843	−	0.0177004i	$-0.00563449\pi$
$420$		0			0
$421$	3.71423			0.181021			0.0905103	−	0.995896i	$-0.471150\pi$
$421$	3.71423			0.181021			0.0905103	+	0.995896i	$0.471150\pi$
$422$	10.2446			0.498701
$423$			12.2437i			0.595309i
$424$			5.17461i			0.251301i
$425$	25.6797			1.24565
$426$	14.0795			0.682156
$427$		0			0
$428$		−	0.241883i		−	0.0116919i
$429$	−8.41014	+	1.80830i	−0.406045	+	0.0873057i
$430$		−	1.06790i		−	0.0514989i
$431$		−	4.08478i		−	0.196757i	−0.995149	−	0.0983784i	$-0.968634\pi$
$431$		−	4.08478i		−	0.196757i	0.995149	−	0.0983784i	$-0.0313656\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	30.3109i		−	1.45665i	−0.685232	−	0.728325i	$-0.740299\pi$
$433$		−	30.3109i		−	1.45665i	0.685232	−	0.728325i	$-0.259701\pi$
$434$		0			0
$435$		−	4.51160i		−	0.216315i
$436$		−	17.5252i		−	0.839304i
$437$	−8.91569			−0.426495
$438$	−9.91318			−0.473670
$439$	12.6102			0.601854			0.300927	−	0.953647i	$-0.402704\pi$
$439$	12.6102			0.601854			0.300927	+	0.953647i	$0.402704\pi$
$440$	−0.583820	−	2.71526i	−0.0278325	−	0.129445i
$441$		0			0
$442$		−	15.4941i		−	0.736978i
$443$	15.2372			0.723940			0.361970	−	0.932190i	$-0.382104\pi$
$443$	15.2372			0.723940			0.361970	+	0.932190i	$0.382104\pi$
$444$			10.9893i			0.521531i
$445$	−7.03977			−0.333717
$446$	15.6665			0.741831
$447$	−4.39696			−0.207969
$448$		0			0
$449$	32.2780			1.52329			0.761647	−	0.647993i	$-0.224391\pi$
$449$	32.2780			1.52329			0.761647	+	0.647993i	$0.224391\pi$
$450$			4.29878i			0.202646i
$451$	−7.83291	−	36.4296i	−0.368837	−	1.71540i
$452$	−8.08949			−0.380498
$453$	−10.2407			−0.481152
$454$			15.7205i			0.737799i
$455$		0			0
$456$	3.11181			0.145724
$457$		−	30.3447i		−	1.41947i	−0.704471	−	0.709733i	$-0.748816\pi$
$457$		−	30.3447i		−	1.41947i	0.704471	−	0.709733i	$-0.251184\pi$
$458$	−2.50417			−0.117012
$459$		−	5.97372i		−	0.278829i
$460$		−	2.39922i		−	0.111864i
$461$	4.81402			0.224211			0.112106	−	0.993696i	$-0.464240\pi$
$461$	4.81402			0.224211			0.112106	+	0.993696i	$0.464240\pi$
$462$		0			0
$463$	−33.1197			−1.53920			−0.769600	−	0.638526i	$-0.779545\pi$
$463$	−33.1197			−1.53920			−0.769600	+	0.638526i	$0.779545\pi$
$464$			5.38769i			0.250117i
$465$		−	0.883199i		−	0.0409574i
$466$	−0.0553161			−0.00256247
$467$		−	14.3866i		−	0.665730i	−0.942974	−	0.332865i	$-0.891985\pi$
$467$		−	14.3866i		−	0.665730i	0.942974	−	0.332865i	$-0.108015\pi$
$468$	2.59370			0.119894
$469$		0			0
$470$		−	10.2528i		−	0.472925i
$471$	−15.9861			−0.736600
$472$	−9.68506			−0.445791
$473$	4.13510	−	0.889107i	0.190132	−	0.0408812i
$474$			13.5121i			0.620629i
$475$	−13.3770			−0.613777
$476$		0			0
$477$	−5.17461			−0.236929
$478$	5.74465			0.262754
$479$	6.47208			0.295717			0.147859	−	0.989009i	$-0.452762\pi$
$479$	6.47208			0.295717			0.147859	+	0.989009i	$0.452762\pi$
$480$			0.837391i			0.0382215i
$481$	−28.5031			−1.29963
$482$		−	7.34245i		−	0.334440i
$483$		0			0
$484$	10.0279	−	4.52130i	0.455812	−	0.205514i
$485$	−0.658299			−0.0298918
$486$	1.00000			0.0453609
$487$	−5.28096			−0.239303			−0.119652	−	0.992816i	$-0.538178\pi$
$487$	−5.28096			−0.239303			−0.119652	+	0.992816i	$0.538178\pi$
$488$			4.07048i			0.184262i
$489$		−	0.523852i		−	0.0236894i
$490$		0			0
$491$			11.3633i			0.512820i	0.966568	+	0.256410i	$0.0825398\pi$
$491$			11.3633i			0.512820i	−0.966568	+	0.256410i	$0.917460\pi$
$492$			11.2350i			0.506512i
$493$			32.1845i			1.44952i
$494$			8.07111i			0.363137i
$495$	2.71526	−	0.583820i	0.122042	−	0.0262408i
$496$			1.05470i			0.0473575i
$497$		0			0
$498$	2.99287			0.134114
$499$	−29.1721			−1.30592			−0.652961	−	0.757392i	$-0.726473\pi$
$499$	−29.1721			−1.30592			−0.652961	+	0.757392i	$0.726473\pi$
$500$		−	7.78672i		−	0.348232i
$501$		−	17.0544i		−	0.761934i
$502$	4.20803			0.187813
$503$	22.4317			1.00018			0.500090	−	0.865973i	$-0.333300\pi$
$503$	22.4317			1.00018			0.500090	+	0.865973i	$0.333300\pi$
$504$		0			0
$505$		−	5.62917i		−	0.250495i
$506$	9.29019	−	1.99753i	0.412999	−	0.0888009i
$507$		−	6.27269i		−	0.278580i
$508$		−	12.1313i		−	0.538241i
$509$		−	27.3682i		−	1.21307i	−0.795055	−	0.606537i	$-0.792558\pi$
$509$		−	27.3682i		−	1.21307i	0.795055	−	0.606537i	$-0.207442\pi$
$510$			5.00234i			0.221507i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			3.11181i			0.137390i
$514$	−24.6466			−1.08711
$515$	3.40938			0.150235
$516$	−1.27527			−0.0561408
$517$	39.7005	−	8.53618i	1.74602	−	0.375421i
$518$		0			0
$519$		−	7.23663i		−	0.317653i
$520$	−2.17195			−0.0952461
$521$		−	34.9911i		−	1.53299i	−0.642252	−	0.766493i	$-0.722000\pi$
$521$		−	34.9911i		−	1.53299i	0.642252	−	0.766493i	$-0.278000\pi$
$522$	−5.38769			−0.235813
$523$	38.2448			1.67233			0.836165	−	0.548479i	$-0.184793\pi$
$523$	38.2448			1.67233			0.836165	+	0.548479i	$0.184793\pi$
$524$	−2.04449			−0.0893139
$525$		0			0
$526$	−30.3837			−1.32479
$527$			6.30050i			0.274454i
$528$	−3.24252	+	0.697189i	−0.141113	+	0.0303413i
$529$	−14.7911			−0.643092
$530$	4.33317			0.188221
$531$		−	9.68506i		−	0.420296i
$532$		0			0
$533$	−29.1402			−1.26220
$534$			8.40678i			0.363797i
$535$	−0.202551			−0.00875704
$536$			13.0383i			0.563169i
$537$			8.06636i			0.348089i
$538$	−19.9737			−0.861128
$539$		0			0
$540$	−0.837391			−0.0360356
$541$		−	3.15324i		−	0.135568i	−0.997700	−	0.0677842i	$-0.978407\pi$
$541$		−	3.15324i		−	0.135568i	0.997700	−	0.0677842i	$-0.0215929\pi$
$542$		−	1.61528i		−	0.0693821i
$543$	5.61056			0.240772
$544$		−	5.97372i		−	0.256121i
$545$	−14.6754			−0.628627
$546$		0			0
$547$			20.6313i			0.882131i	0.897475	+	0.441065i	$0.145399\pi$
$547$			20.6313i			0.882131i	−0.897475	+	0.441065i	$0.854601\pi$
$548$	13.2111			0.564351
$549$	−4.07048			−0.173724
$550$	13.9389	−	2.99706i	0.594355	−	0.127795i
$551$		−	16.7655i		−	0.714232i
$552$	−2.86511			−0.121947
$553$		0			0
$554$	5.18071			0.220107
$555$	9.20238			0.390619
$556$	−6.16293			−0.261367
$557$			1.27071i			0.0538415i	0.999638	+	0.0269208i	$0.00857018\pi$
$557$			1.27071i			0.0538415i	−0.999638	+	0.0269208i	$0.991430\pi$
$558$	−1.05470			−0.0446491
$559$		−	3.30769i		−	0.139900i
$560$		0			0
$561$	−19.3699	+	4.16481i	−0.817798	+	0.175839i
$562$	25.1883			1.06250
$563$	40.3458			1.70037			0.850187	−	0.526481i	$-0.176489\pi$
$563$	40.3458			1.70037			0.850187	+	0.526481i	$0.176489\pi$
$564$	−12.2437			−0.515553
$565$			6.77407i			0.284987i
$566$		−	23.0334i		−	0.968168i
$567$		0			0
$568$			14.0795i			0.590764i
$569$			2.78095i			0.116583i	0.998300	+	0.0582917i	$0.0185653\pi$
$569$			2.78095i			0.116583i	−0.998300	+	0.0582917i	$0.981435\pi$
$570$		−	2.60580i		−	0.109145i
$571$		−	38.1829i		−	1.59791i	−0.601393	−	0.798953i	$-0.705388\pi$
$571$		−	38.1829i		−	1.59791i	0.601393	−	0.798953i	$-0.294612\pi$
$572$	−1.80830	−	8.41014i	−0.0756089	−	0.351645i
$573$			11.7841i			0.492288i
$574$		0			0
$575$	12.3165			0.513633
$576$	1.00000			0.0416667
$577$		−	6.84536i		−	0.284976i	−0.989797	−	0.142488i	$-0.954490\pi$
$577$		−	6.84536i		−	0.284976i	0.989797	−	0.142488i	$-0.0455103\pi$
$578$		−	18.6853i		−	0.777208i
$579$	18.0976			0.752112
$580$	4.51160			0.187334
$581$		0			0
$582$			0.786131i			0.0325862i
$583$	3.60768	+	16.7788i	0.149415	+	0.694905i
$584$		−	9.91318i		−	0.410210i
$585$		−	2.17195i		−	0.0897989i
$586$			4.18076i			0.172705i
$587$		−	22.7050i		−	0.937135i	−0.883428	−	0.468568i	$-0.844770\pi$
$587$		−	22.7050i		−	0.937135i	0.883428	−	0.468568i	$-0.155230\pi$
$588$		0			0
$589$		−	3.28203i		−	0.135234i
$590$			8.11019i			0.333891i
$591$	6.23110			0.256313
$592$	−10.9893			−0.451659
$593$	10.1112			0.415215			0.207608	−	0.978212i	$-0.433432\pi$
$593$	10.1112			0.415215			0.207608	+	0.978212i	$0.433432\pi$
$594$	−0.697189	−	3.24252i	−0.0286060	−	0.133042i
$595$		0			0
$596$		−	4.39696i		−	0.180107i
$597$	−18.2669			−0.747614
$598$		−	7.43126i		−	0.303887i
$599$	−2.90438			−0.118670			−0.0593349	−	0.998238i	$-0.518898\pi$
$599$	−2.90438			−0.118670			−0.0593349	+	0.998238i	$0.518898\pi$
$600$	−4.29878			−0.175497
$601$	−8.68237			−0.354161			−0.177081	−	0.984196i	$-0.556665\pi$
$601$	−8.68237			−0.354161			−0.177081	+	0.984196i	$0.556665\pi$
$602$		0			0
$603$	−13.0383			−0.530961
$604$		−	10.2407i		−	0.416690i
$605$	−3.78610	−	8.39724i	−0.153927	−	0.341396i
$606$	−6.72227			−0.273074
$607$	−23.4682			−0.952544			−0.476272	−	0.879298i	$-0.658012\pi$
$607$	−23.4682			−0.952544			−0.476272	+	0.879298i	$0.658012\pi$
$608$			3.11181i			0.126200i
$609$		0			0
$610$	3.40859			0.138010
$611$		−	31.7566i		−	1.28473i
$612$	5.97372			0.241473
$613$			30.9799i			1.25127i	0.780117	+	0.625633i	$0.215159\pi$
$613$			30.9799i			1.25127i	−0.780117	+	0.625633i	$0.784841\pi$
$614$		−	10.0657i		−	0.406217i
$615$	9.40808			0.379370
$616$		0			0
$617$	7.35346			0.296039			0.148020	−	0.988984i	$-0.452710\pi$
$617$	7.35346			0.296039			0.148020	+	0.988984i	$0.452710\pi$
$618$		−	4.07143i		−	0.163777i
$619$			3.65678i			0.146978i	0.997296	+	0.0734892i	$0.0234134\pi$
$619$			3.65678i			0.146978i	−0.997296	+	0.0734892i	$0.976587\pi$
$620$	0.883199			0.0354701
$621$		−	2.86511i		−	0.114973i
$622$	−1.42972			−0.0573264
$623$		0			0
$624$			2.59370i			0.103831i
$625$	14.9733			0.598934
$626$	30.3930			1.21475
$627$	10.0901	−	2.16952i	0.402960	−	0.0866422i
$628$		−	15.9861i		−	0.637914i
$629$	−65.6473			−2.61753
$630$		0			0
$631$	22.5757			0.898724			0.449362	−	0.893350i	$-0.351651\pi$
$631$	22.5757			0.898724			0.449362	+	0.893350i	$0.351651\pi$
$632$	−13.5121			−0.537481
$633$	−10.2446			−0.407187
$634$		−	10.8522i		−	0.430996i
$635$	−10.1587			−0.403135
$636$		−	5.17461i		−	0.205187i
$637$		0			0
$638$	3.75624	+	17.4697i	0.148711	+	0.691631i
$639$	−14.0795			−0.556978
$640$	−0.837391			−0.0331008
$641$	−44.5605			−1.76003			−0.880017	−	0.474943i	$-0.842469\pi$
$641$	−44.5605			−1.76003			−0.880017	+	0.474943i	$0.842469\pi$
$642$			0.241883i			0.00954637i
$643$			14.8587i			0.585968i	0.956117	+	0.292984i	$0.0946483\pi$
$643$			14.8587i			0.585968i	−0.956117	+	0.292984i	$0.905352\pi$
$644$		0			0
$645$			1.06790i			0.0420487i
$646$			18.5891i			0.731377i
$647$		−	47.9408i		−	1.88475i	−0.334565	−	0.942373i	$-0.608589\pi$
$647$		−	47.9408i		−	1.88475i	0.334565	−	0.942373i	$-0.391411\pi$
$648$			1.00000i			0.0392837i
$649$	−31.4040	+	6.75232i	−1.23271	+	0.265052i
$650$		−	11.1498i		−	0.437329i
$651$		0			0
$652$	0.523852			0.0205156
$653$	25.8319			1.01088			0.505440	−	0.862862i	$-0.331330\pi$
$653$	25.8319			1.01088			0.505440	+	0.862862i	$0.331330\pi$
$654$			17.5252i			0.685289i
$655$			1.71204i			0.0668948i
$656$	−11.2350			−0.438652
$657$	9.91318			0.386750
$658$		0			0
$659$			28.7951i			1.12170i	0.827918	+	0.560850i	$0.189525\pi$
$659$			28.7951i			1.12170i	−0.827918	+	0.560850i	$0.810475\pi$
$660$	0.583820	+	2.71526i	0.0227252	+	0.105691i
$661$			26.6354i			1.03600i	0.855381	+	0.517999i	$0.173323\pi$
$661$			26.6354i			1.03600i	−0.855381	+	0.517999i	$0.826677\pi$
$662$			12.9149i			0.501954i
$663$			15.4941i			0.601740i
$664$			2.99287i			0.116146i
$665$		0			0
$666$		−	10.9893i		−	0.425829i
$667$			15.4363i			0.597697i
$668$	17.0544			0.659855
$669$	−15.6665			−0.605703
$670$	10.9182			0.421806
$671$	2.83790	+	13.1986i	0.109556	+	0.509527i
$672$		0			0
$673$		−	12.3054i		−	0.474337i	−0.971469	−	0.237168i	$-0.923781\pi$
$673$		−	12.3054i		−	0.474337i	0.971469	−	0.237168i	$-0.0762193\pi$
$674$	16.4809			0.634820
$675$		−	4.29878i		−	0.165460i
$676$	6.27269			0.241257
$677$	−11.4608			−0.440476			−0.220238	−	0.975446i	$-0.570683\pi$
$677$	−11.4608			−0.440476			−0.220238	+	0.975446i	$0.570683\pi$
$678$	8.08949			0.310675
$679$		0			0
$680$	−5.00234			−0.191831
$681$		−	15.7205i		−	0.602411i
$682$	0.735327	+	3.41989i	0.0281571	+	0.130954i
$683$	−7.56002			−0.289276			−0.144638	−	0.989485i	$-0.546202\pi$
$683$	−7.56002			−0.289276			−0.144638	+	0.989485i	$0.546202\pi$
$684$	−3.11181			−0.118983
$685$		−	11.0629i		−	0.422691i
$686$		0			0
$687$	2.50417			0.0955399
$688$		−	1.27527i		−	0.0486194i
$689$	13.4214			0.511315
$690$			2.39922i			0.0913368i
$691$		−	19.0094i		−	0.723152i	−0.932343	−	0.361576i	$-0.882239\pi$
$691$		−	19.0094i		−	0.723152i	0.932343	−	0.361576i	$-0.117761\pi$
$692$	7.23663			0.275095
$693$		0			0
$694$	−11.4633			−0.435140
$695$			5.16079i			0.195760i
$696$		−	5.38769i		−	0.204220i
$697$	−67.1146			−2.54215
$698$			20.9561i			0.793201i
$699$	0.0553161			0.00209225
$700$		0			0
$701$			32.6349i			1.23260i	0.787510	+	0.616302i	$0.211370\pi$
$701$			32.6349i			1.23260i	−0.787510	+	0.616302i	$0.788630\pi$
$702$	−2.59370			−0.0978931
$703$	34.1967			1.28975
$704$	−0.697189	−	3.24252i	−0.0262763	−	0.122207i
$705$			10.2528i			0.386142i
$706$	−19.9221			−0.749778
$707$		0			0
$708$	9.68506			0.363987
$709$	15.1506			0.568994			0.284497	−	0.958677i	$-0.408173\pi$
$709$	15.1506			0.568994			0.284497	+	0.958677i	$0.408173\pi$
$710$	11.7901			0.442474
$711$		−	13.5121i		−	0.506742i
$712$	−8.40678			−0.315057
$713$			3.02184i			0.113169i
$714$		0			0
$715$	−7.04258	+	1.51426i	−0.263377	+	0.0566300i
$716$	−8.06636			−0.301454
$717$	−5.74465			−0.214538
$718$	−3.91431			−0.146081
$719$			5.15470i			0.192238i	0.995370	+	0.0961189i	$0.0306429\pi$
$719$			5.15470i			0.192238i	−0.995370	+	0.0961189i	$0.969357\pi$
$720$		−	0.837391i		−	0.0312077i
$721$		0			0
$722$			9.31665i			0.346730i
$723$			7.34245i			0.273069i
$724$			5.61056i			0.208515i
$725$			23.1605i			0.860158i
$726$	−10.0279	+	4.52130i	−0.372169	+	0.167801i
$727$		−	24.1329i		−	0.895041i	−0.894274	−	0.447520i	$-0.852307\pi$
$727$		−	24.1329i		−	0.895041i	0.894274	−	0.447520i	$-0.147693\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−8.30121			−0.307242
$731$		−	7.61813i		−	0.281767i
$732$		−	4.07048i		−	0.150449i
$733$	−52.1041			−1.92451			−0.962254	−	0.272153i	$-0.912264\pi$
$733$	−52.1041			−1.92451			−0.962254	+	0.272153i	$0.912264\pi$
$734$	−12.0920			−0.446324
$735$		0			0
$736$		−	2.86511i		−	0.105609i
$737$	9.09017	+	42.2770i	0.334841	+	1.55729i
$738$		−	11.2350i		−	0.413565i
$739$			5.54673i			0.204040i	0.994782	+	0.102020i	$0.0325305\pi$
$739$			5.54673i			0.204040i	−0.994782	+	0.102020i	$0.967469\pi$
$740$			9.20238i			0.338286i
$741$		−	8.07111i		−	0.296500i
$742$		0			0
$743$		−	18.2750i		−	0.670443i	−0.942139	−	0.335222i	$-0.891189\pi$
$743$		−	18.2750i		−	0.670443i	0.942139	−	0.335222i	$-0.108811\pi$
$744$		−	1.05470i		−	0.0386673i
$745$	−3.68198			−0.134897
$746$	17.6936			0.647809
$747$	−2.99287			−0.109503
$748$	−4.16481	−	19.3699i	−0.152281	−	0.708234i
$749$		0			0
$750$			7.78672i			0.284331i
$751$	−14.7153			−0.536968			−0.268484	−	0.963284i	$-0.586523\pi$
$751$	−14.7153			−0.536968			−0.268484	+	0.963284i	$0.586523\pi$
$752$		−	12.2437i		−	0.446482i
$753$	−4.20803			−0.153349
$754$	13.9741			0.508906
$755$	−8.57551			−0.312095
$756$		0			0
$757$	−46.8890			−1.70421			−0.852105	−	0.523371i	$-0.824674\pi$
$757$	−46.8890			−1.70421			−0.852105	+	0.523371i	$0.824674\pi$
$758$		−	19.6577i		−	0.713999i
$759$	−9.29019	+	1.99753i	−0.337212	+	0.0725056i
$760$	2.60580			0.0945224
$761$	−37.0413			−1.34275			−0.671373	−	0.741120i	$-0.734295\pi$
$761$	−37.0413			−1.34275			−0.671373	+	0.741120i	$0.734295\pi$
$762$			12.1313i			0.439472i
$763$		0			0
$764$	−11.7841			−0.426334
$765$		−	5.00234i		−	0.180860i
$766$	1.37345			0.0496248
$767$			25.1202i			0.907038i
$768$			1.00000i			0.0360844i
$769$	−10.3666			−0.373830			−0.186915	−	0.982376i	$-0.559849\pi$
$769$	−10.3666			−0.373830			−0.186915	+	0.982376i	$0.559849\pi$
$770$		0			0
$771$	24.6466			0.887625
$772$			18.0976i			0.651348i
$773$			21.6146i			0.777423i	0.921359	+	0.388712i	$0.127080\pi$
$773$			21.6146i			0.777423i	−0.921359	+	0.388712i	$0.872920\pi$
$774$	1.27527			0.0458388
$775$			4.53393i			0.162864i
$776$	−0.786131			−0.0282204
$777$		0			0
$778$		−	31.3793i		−	1.12500i
$779$	34.9611			1.25261
$780$	2.17195			0.0777682
$781$	9.81610	+	45.6532i	0.351248	+	1.63360i
$782$		−	17.1154i		−	0.612045i
$783$	5.38769			0.192540
$784$		0			0
$785$	−13.3866			−0.477789
$786$	2.04449			0.0729245
$787$	48.6910			1.73565			0.867824	−	0.496871i	$-0.165518\pi$
$787$	48.6910			1.73565			0.867824	+	0.496871i	$0.165518\pi$
$788$			6.23110i			0.221974i
$789$	30.3837			1.08169
$790$			11.3149i			0.402565i
$791$		0			0
$792$	3.24252	−	0.697189i	0.115218	−	0.0247735i
$793$	10.5576			0.374913
$794$	−35.2719			−1.25175
$795$	−4.33317			−0.153682
$796$		−	18.2669i		−	0.647453i
$797$			36.0374i			1.27651i	0.769825	+	0.638255i	$0.220343\pi$
$797$			36.0374i			1.27651i	−0.769825	+	0.638255i	$0.779657\pi$
$798$		0			0
$799$		−	73.1405i		−	2.58752i
$800$		−	4.29878i		−	0.151985i
$801$		−	8.40678i		−	0.297039i
$802$		−	8.96618i		−	0.316607i
$803$	−6.91136	−	32.1437i	−0.243897	−	1.13433i
$804$		−	13.0383i		−	0.459826i
$805$		0			0
$806$	2.73559			0.0963569
$807$	19.9737			0.703108
$808$		−	6.72227i		−	0.236489i
$809$		−	29.9102i		−	1.05159i	−0.850613	−	0.525793i	$-0.823769\pi$
$809$		−	29.9102i		−	1.05159i	0.850613	−	0.525793i	$-0.176231\pi$
$810$	0.837391			0.0294229
$811$	18.1295			0.636611			0.318306	−	0.947988i	$-0.396886\pi$
$811$	18.1295			0.636611			0.318306	+	0.947988i	$0.396886\pi$
$812$		0			0
$813$			1.61528i			0.0566503i
$814$	−35.6332	+	7.66165i	−1.24894	+	0.268541i
$815$		−	0.438669i		−	0.0153659i
$816$			5.97372i			0.209122i
$817$			3.96841i			0.138837i
$818$			35.9524i			1.25705i
$819$		0			0
$820$			9.40808i			0.328544i
$821$		−	19.4780i		−	0.679786i	−0.940464	−	0.339893i	$-0.889609\pi$
$821$		−	19.4780i		−	0.679786i	0.940464	−	0.339893i	$-0.110391\pi$
$822$	−13.2111			−0.460791
$823$	28.1862			0.982510			0.491255	−	0.871016i	$-0.336538\pi$
$823$	28.1862			0.982510			0.491255	+	0.871016i	$0.336538\pi$
$824$	4.07143			0.141835
$825$	−13.9389	+	2.99706i	−0.485289	+	0.104344i
$826$		0			0
$827$		−	25.7981i		−	0.897089i	−0.893761	−	0.448544i	$-0.851943\pi$
$827$		−	25.7981i		−	0.897089i	0.893761	−	0.448544i	$-0.148057\pi$
$828$	2.86511			0.0995696
$829$		−	36.9176i		−	1.28220i	−0.767457	−	0.641100i	$-0.778478\pi$
$829$		−	36.9176i		−	1.28220i	0.767457	−	0.641100i	$-0.221522\pi$
$830$	2.50620			0.0869915
$831$	−5.18071			−0.179717
$832$	−2.59370			−0.0899205
$833$		0			0
$834$	6.16293			0.213405
$835$		−	14.2812i		−	0.494222i
$836$	2.16952	+	10.0901i	0.0750344	+	0.348973i
$837$	1.05470			0.0364559
$838$	−0.724634			−0.0250321
$839$			6.71611i			0.231866i	0.993257	+	0.115933i	$0.0369858\pi$
$839$			6.71611i			0.231866i	−0.993257	+	0.115933i	$0.963014\pi$
$840$		0			0
$841$	−0.0271771			−0.000937142
$842$		−	3.71423i		−	0.128001i
$843$	−25.1883			−0.867531
$844$		−	10.2446i		−	0.352635i
$845$		−	5.25270i		−	0.180698i
$846$	12.2437			0.420947
$847$		0			0
$848$	5.17461			0.177697
$849$			23.0334i			0.790506i
$850$		−	25.6797i		−	0.880806i
$851$	−31.4857			−1.07932
$852$		−	14.0795i		−	0.482357i
$853$	39.8993			1.36613			0.683063	−	0.730360i	$-0.260648\pi$
$853$	39.8993			1.36613			0.683063	+	0.730360i	$0.260648\pi$
$854$		0			0
$855$			2.60580i			0.0891165i
$856$	−0.241883			−0.00826740
$857$	−15.7093			−0.536621			−0.268310	−	0.963332i	$-0.586465\pi$
$857$	−15.7093			−0.536621			−0.268310	+	0.963332i	$0.586465\pi$
$858$	1.80830	+	8.41014i	0.0617344	+	0.287117i
$859$			19.2809i			0.657854i	0.944355	+	0.328927i	$0.106687\pi$
$859$			19.2809i			0.657854i	−0.944355	+	0.328927i	$0.893313\pi$
$860$	−1.06790			−0.0364152
$861$		0			0
$862$	−4.08478			−0.139128
$863$	38.1522			1.29872			0.649358	−	0.760483i	$-0.275038\pi$
$863$	38.1522			1.29872			0.649358	+	0.760483i	$0.275038\pi$
$864$	−1.00000			−0.0340207
$865$		−	6.05989i		−	0.206042i
$866$	−30.3109			−1.03001
$867$			18.6853i			0.634587i
$868$		0			0
$869$	−43.8131	+	9.42046i	−1.48626	+	0.319567i
$870$	−4.51160			−0.152958
$871$	33.8175			1.14586
$872$	−17.5252			−0.593478
$873$		−	0.786131i		−	0.0266065i
$874$			8.91569i			0.301578i
$875$		0			0
$876$			9.91318i			0.334935i
$877$			9.15113i			0.309012i	0.987992	+	0.154506i	$0.0493785\pi$
$877$			9.15113i			0.309012i	−0.987992	+	0.154506i	$0.950621\pi$
$878$		−	12.6102i		−	0.425575i
$879$		−	4.18076i		−	0.141013i
$880$	−2.71526	+	0.583820i	−0.0915313	+	0.0196806i
$881$		−	47.7019i		−	1.60712i	−0.595225	−	0.803559i	$-0.702937\pi$
$881$		−	47.7019i		−	1.60712i	0.595225	−	0.803559i	$-0.297063\pi$
$882$		0			0
$883$	43.7932			1.47376			0.736879	−	0.676025i	$-0.236299\pi$
$883$	43.7932			1.47376			0.736879	+	0.676025i	$0.236299\pi$
$884$	−15.4941			−0.521122
$885$		−	8.11019i		−	0.272621i
$886$		−	15.2372i		−	0.511903i
$887$	50.5792			1.69828			0.849142	−	0.528165i	$-0.177120\pi$
$887$	50.5792			1.69828			0.849142	+	0.528165i	$0.177120\pi$
$888$	10.9893			0.368778
$889$		0			0
$890$			7.03977i			0.235974i
$891$	0.697189	+	3.24252i	0.0233567	+	0.108628i
$892$		−	15.6665i		−	0.524554i
$893$			38.1001i			1.27497i
$894$			4.39696i			0.147056i
$895$			6.75470i			0.225785i
$896$		0			0
$897$			7.43126i			0.248123i
$898$		−	32.2780i		−	1.07713i
$899$	−5.68241			−0.189519
$900$	4.29878			0.143293
$901$	30.9117			1.02982
$902$	−36.4296	+	7.83291i	−1.21297	+	0.260807i
$903$		0			0
$904$			8.08949i			0.269053i
$905$	4.69824			0.156175
$906$			10.2407i			0.340226i
$907$	−57.8688			−1.92150			−0.960752	−	0.277410i	$-0.910524\pi$
$907$	−57.8688			−1.92150			−0.960752	+	0.277410i	$0.910524\pi$
$908$	15.7205			0.521703
$909$	6.72227			0.222964
$910$		0			0
$911$	25.4860			0.844389			0.422195	−	0.906505i	$-0.361260\pi$
$911$	25.4860			0.844389			0.422195	+	0.906505i	$0.361260\pi$
$912$		−	3.11181i		−	0.103042i
$913$	2.08659	+	9.70443i	0.0690562	+	0.321170i
$914$	−30.3447			−1.00371
$915$	−3.40859			−0.112684
$916$			2.50417i			0.0827400i
$917$		0			0
$918$	−5.97372			−0.197162
$919$			12.9898i			0.428494i	0.976779	+	0.214247i	$0.0687298\pi$
$919$			12.9898i			0.428494i	−0.976779	+	0.214247i	$0.931270\pi$
$920$	−2.39922			−0.0791000
$921$			10.0657i			0.331675i
$922$		−	4.81402i		−	0.158541i
$923$	36.5182			1.20201
$924$		0			0
$925$	−47.2407			−1.55327
$926$			33.1197i			1.08838i
$927$			4.07143i			0.133723i
$928$	5.38769			0.176860
$929$		−	21.8047i		−	0.715389i	−0.933839	−	0.357695i	$-0.883563\pi$
$929$		−	21.8047i		−	0.715389i	0.933839	−	0.357695i	$-0.116437\pi$
$930$	−0.883199			−0.0289612
$931$		0			0
$932$			0.0553161i			0.00181194i
$933$	1.42972			0.0468068
$934$	−14.3866			−0.470742
$935$	−16.2202	+	3.48758i	−0.530457	+	0.114056i
$936$		−	2.59370i		−	0.0847779i
$937$	31.2647			1.02137			0.510686	−	0.859767i	$-0.329391\pi$
$937$	31.2647			1.02137			0.510686	+	0.859767i	$0.329391\pi$
$938$		0			0
$939$	−30.3930			−0.991839
$940$	−10.2528			−0.334409
$941$	−18.7756			−0.612066			−0.306033	−	0.952021i	$-0.599002\pi$
$941$	−18.7756			−0.612066			−0.306033	+	0.952021i	$0.599002\pi$
$942$			15.9861i			0.520855i
$943$	−32.1895			−1.04823
$944$			9.68506i			0.315222i
$945$		0			0
$946$	−0.889107	−	4.13510i	−0.0289074	−	0.134444i
$947$	−39.5459			−1.28507			−0.642534	−	0.766257i	$-0.722117\pi$
$947$	−39.5459			−1.28507			−0.642534	+	0.766257i	$0.722117\pi$
$948$	13.5121			0.438851
$949$	−25.7119			−0.834643
$950$			13.3770i			0.434006i
$951$			10.8522i			0.351907i
$952$		0			0
$953$		−	2.98673i		−	0.0967495i	−0.998829	−	0.0483748i	$-0.984596\pi$
$953$		−	2.98673i		−	0.0967495i	0.998829	−	0.0483748i	$-0.0154042\pi$
$954$			5.17461i			0.167534i
$955$			9.86792i			0.319318i
$956$		−	5.74465i		−	0.185795i
$957$	−3.75624	−	17.4697i	−0.121422	−	0.564714i
$958$		−	6.47208i		−	0.209104i
$959$		0			0
$960$	0.837391			0.0270267
$961$	29.8876			0.964116
$962$			28.5031i			0.918977i
$963$		−	0.241883i		−	0.00779458i
$964$	−7.34245			−0.236484
$965$	15.1548			0.487850
$966$		0			0
$967$			3.61655i			0.116300i	0.998308	+	0.0581502i	$0.0185202\pi$
$967$			3.61655i			0.116300i	−0.998308	+	0.0581502i	$0.981480\pi$
$968$	−4.52130	−	10.0279i	−0.145320	−	0.322307i
$969$		−	18.5891i		−	0.597167i
$970$			0.658299i			0.0211367i
$971$			27.6549i			0.887488i	0.896154	+	0.443744i	$0.146350\pi$
$971$			27.6549i			0.887488i	−0.896154	+	0.443744i	$0.853650\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$			5.28096i			0.169213i
$975$			11.1498i			0.357078i
$976$	4.07048			0.130293
$977$	34.8349			1.11447			0.557234	−	0.830356i	$-0.311863\pi$
$977$	34.8349			1.11447			0.557234	+	0.830356i	$0.311863\pi$
$978$	−0.523852			−0.0167509
$979$	−27.2591	+	5.86112i	−0.871206	+	0.187322i
$980$		0			0
$981$		−	17.5252i		−	0.559536i
$982$	11.3633			0.362619
$983$		−	22.2764i		−	0.710507i	−0.934770	−	0.355254i	$-0.884395\pi$
$983$		−	22.2764i		−	0.710507i	0.934770	−	0.355254i	$-0.115605\pi$
$984$	11.2350			0.358158
$985$	5.21787			0.166255
$986$	32.1845			1.02496
$987$		0			0
$988$	8.07111			0.256776
$989$		−	3.65381i		−	0.116184i
$990$	−0.583820	−	2.71526i	−0.0185550	−	0.0862965i
$991$	54.6176			1.73499			0.867493	−	0.497449i	$-0.165730\pi$
$991$	54.6176			1.73499			0.867493	+	0.497449i	$0.165730\pi$
$992$	1.05470			0.0334868
$993$		−	12.9149i		−	0.409843i
$994$		0			0
$995$	−15.2965			−0.484933
$996$		−	2.99287i		−	0.0948326i
$997$	−16.9182			−0.535806			−0.267903	−	0.963446i	$-0.586331\pi$
$997$	−16.9182			−0.535806			−0.267903	+	0.963446i	$0.586331\pi$
$998$			29.1721i			0.923426i
$999$			10.9893i			0.347688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.b.2155.5		16
7.2	even	3		462.2.p.b.241.2	yes	16
7.3	odd	6		462.2.p.a.439.6	yes	16
7.6	odd	2		3234.2.e.a.2155.4		16
11.10	odd	2		3234.2.e.a.2155.13		16
21.2	odd	6		1386.2.bk.b.703.7		16
21.17	even	6		1386.2.bk.a.901.3		16
77.10	even	6		462.2.p.b.439.2	yes	16
77.65	odd	6		462.2.p.a.241.6	✓	16
77.76	even	2	inner	3234.2.e.b.2155.12		16
231.65	even	6		1386.2.bk.a.703.3		16
231.164	odd	6		1386.2.bk.b.901.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.6	✓	16	77.65	odd	6
462.2.p.a.439.6	yes	16	7.3	odd	6
462.2.p.b.241.2	yes	16	7.2	even	3
462.2.p.b.439.2	yes	16	77.10	even	6
1386.2.bk.a.703.3		16	231.65	even	6
1386.2.bk.a.901.3		16	21.17	even	6
1386.2.bk.b.703.7		16	21.2	odd	6
1386.2.bk.b.901.7		16	231.164	odd	6
3234.2.e.a.2155.4		16	7.6	odd	2
3234.2.e.a.2155.13		16	11.10	odd	2
3234.2.e.b.2155.5		16	1.1	even	1	trivial
3234.2.e.b.2155.12		16	77.76	even	2	inner

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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +0.837391i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +0.837391i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +0.837391 q^{10} +(0.697189 + 3.24252i) q^{11} -1.00000i q^{12} +2.59370 q^{13} -0.837391 q^{15} +1.00000 q^{16} +5.97372 q^{17} +1.00000i q^{18} -3.11181 q^{19} -0.837391i q^{20} +(3.24252 - 0.697189i) q^{22} +2.86511 q^{23} -1.00000 q^{24} +4.29878 q^{25} -2.59370i q^{26} -1.00000i q^{27} +5.38769i q^{29} +0.837391i q^{30} +1.05470i q^{31} -1.00000i q^{32} +(-3.24252 + 0.697189i) q^{33} -5.97372i q^{34} +1.00000 q^{36} -10.9893 q^{37} +3.11181i q^{38} +2.59370i q^{39} -0.837391 q^{40} -11.2350 q^{41} -1.27527i q^{43} +(-0.697189 - 3.24252i) q^{44} -0.837391i q^{45} -2.86511i q^{46} -12.2437i q^{47} +1.00000i q^{48} -4.29878i q^{50} +5.97372i q^{51} -2.59370 q^{52} +5.17461 q^{53} -1.00000 q^{54} +(-2.71526 + 0.583820i) q^{55} -3.11181i q^{57} +5.38769 q^{58} +9.68506i q^{59} +0.837391 q^{60} +4.07048 q^{61} +1.05470 q^{62} -1.00000 q^{64} +2.17195i q^{65} +(0.697189 + 3.24252i) q^{66} +13.0383 q^{67} -5.97372 q^{68} +2.86511i q^{69} +14.0795 q^{71} -1.00000i q^{72} -9.91318 q^{73} +10.9893i q^{74} +4.29878i q^{75} +3.11181 q^{76} +2.59370 q^{78} +13.5121i q^{79} +0.837391i q^{80} +1.00000 q^{81} +11.2350i q^{82} +2.99287 q^{83} +5.00234i q^{85} -1.27527 q^{86} -5.38769 q^{87} +(-3.24252 + 0.697189i) q^{88} +8.40678i q^{89} -0.837391 q^{90} -2.86511 q^{92} -1.05470 q^{93} -12.2437 q^{94} -2.60580i q^{95} +1.00000 q^{96} +0.786131i q^{97} +(-0.697189 - 3.24252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9	\( 16 q - 16 q^{4} + 16 q^{6} - 16 q^{9} + 4 q^{10} + 8 q^{11} - 4 q^{15} + 16 q^{16} - 20 q^{19} + 2 q^{22} + 8 q^{23} - 16 q^{24} - 20 q^{25} - 2 q^{33} + 16 q^{36} - 28 q^{37} - 4 q^{40} - 32 q^{41} - 8 q^{44} - 16 q^{54} + 14 q^{55} + 4 q^{60} + 56 q^{61} + 8 q^{62} - 16 q^{64} + 8 q^{66} + 32 q^{67} - 56 q^{71} - 88 q^{73} + 20 q^{76} + 16 q^{81} - 8 q^{83} + 24 q^{86} - 2 q^{88} - 4 q^{90} - 8 q^{92} - 8 q^{93} + 28 q^{94} + 16 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^6 - 16 * q^9 + 4 * q^10 + 8 * q^11 - 4 * q^15 + 16 * q^16 - 20 * q^19 + 2 * q^22 + 8 * q^23 - 16 * q^24 - 20 * q^25 - 2 * q^33 + 16 * q^36 - 28 * q^37 - 4 * q^40 - 32 * q^41 - 8 * q^44 - 16 * q^54 + 14 * q^55 + 4 * q^60 + 56 * q^61 + 8 * q^62 - 16 * q^64 + 8 * q^66 + 32 * q^67 - 56 * q^71 - 88 * q^73 + 20 * q^76 + 16 * q^81 - 8 * q^83 + 24 * q^86 - 2 * q^88 - 4 * q^90 - 8 * q^92 - 8 * q^93 + 28 * q^94 + 16 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more