LMFDB - Embedded newform 128.3.f.a.95.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(31,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("128.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.f (of order $4$, 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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			95.3
Root			$1.40680 - 0.144584i$ of defining polynomial
Character	$\chi$	$=$	128.95
Dual form			128.3.f.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10278 - 2.10278i) q^{3} +(4.62721 - 4.62721i) q^{5} -3.04888 q^{7} +0.156674i q^{9} +O(q^{10})$	\(q+(2.10278 - 2.10278i) q^{3} +(4.62721 - 4.62721i) q^{5} -3.04888 q^{7} +0.156674i q^{9} +(-9.15165 - 9.15165i) q^{11} +(5.78389 + 5.78389i) q^{13} -19.4600i q^{15} +17.6655 q^{17} +(-1.15165 + 1.15165i) q^{19} +(-6.41110 + 6.41110i) q^{21} +3.45998 q^{23} -17.8222i q^{25} +(19.2544 + 19.2544i) q^{27} +(-12.1950 - 12.1950i) q^{29} +38.5089i q^{31} -38.4877 q^{33} +(-14.1078 + 14.1078i) q^{35} +(0.0972356 - 0.0972356i) q^{37} +24.3244 q^{39} +51.5266i q^{41} +(-1.70172 - 1.70172i) q^{43} +(0.724965 + 0.724965i) q^{45} +24.1533i q^{47} -39.7044 q^{49} +(37.1466 - 37.1466i) q^{51} +(-27.0383 + 27.0383i) q^{53} -84.6933 q^{55} +4.84333i q^{57} +(19.5939 + 19.5939i) q^{59} +(-16.7250 - 16.7250i) q^{61} -0.477680i q^{63} +53.5266 q^{65} +(-75.8560 + 75.8560i) q^{67} +(7.27555 - 7.27555i) q^{69} +134.749 q^{71} -112.210i q^{73} +(-37.4761 - 37.4761i) q^{75} +(27.9022 + 27.9022i) q^{77} -135.915i q^{79} +79.5654 q^{81} +(74.9250 - 74.9250i) q^{83} +(81.7422 - 81.7422i) q^{85} -51.2866 q^{87} +31.4278i q^{89} +(-17.6344 - 17.6344i) q^{91} +(80.9755 + 80.9755i) q^{93} +10.6579i q^{95} +31.5456 q^{97} +(1.43383 - 1.43383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) $ 6 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	$ 6 q - 2 q^{3} + 2 q^{5} + 4 q^{7} - 18 q^{11} + 2 q^{13} - 4 q^{17} + 30 q^{19} + 20 q^{21} - 60 q^{23} + 64 q^{27} + 18 q^{29} - 4 q^{33} - 100 q^{35} - 46 q^{37} + 196 q^{39} - 114 q^{43} - 66 q^{45} - 46 q^{49} + 156 q^{51} - 78 q^{53} - 252 q^{55} + 206 q^{59} - 30 q^{61} + 12 q^{65} - 226 q^{67} + 116 q^{69} + 260 q^{71} - 238 q^{75} + 212 q^{77} + 86 q^{81} + 318 q^{83} + 212 q^{85} - 444 q^{87} + 188 q^{91} + 32 q^{93} - 4 q^{97} - 226 q^{99}+O(q^{100}) $ 6 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 - 18 * q^11 + 2 * q^13 - 4 * q^17 + 30 * q^19 + 20 * q^21 - 60 * q^23 + 64 * q^27 + 18 * q^29 - 4 * q^33 - 100 * q^35 - 46 * q^37 + 196 * q^39 - 114 * q^43 - 66 * q^45 - 46 * q^49 + 156 * q^51 - 78 * q^53 - 252 * q^55 + 206 * q^59 - 30 * q^61 + 12 * q^65 - 226 * q^67 + 116 * q^69 + 260 * q^71 - 238 * q^75 + 212 * q^77 + 86 * q^81 + 318 * q^83 + 212 * q^85 - 444 * q^87 + 188 * q^91 + 32 * q^93 - 4 * q^97 - 226 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	2.10278	−	2.10278i	0.700925	−	0.700925i	−0.263684	−	0.964609i	$-0.584938\pi$
$3$	2.10278	−	2.10278i	0.700925	−	0.700925i	0.964609	+	0.263684i	$0.0849376\pi$
$4$		0			0
$5$	4.62721	−	4.62721i	0.925443	−	0.925443i	−0.0719646	−	0.997407i	$-0.522927\pi$
$5$	4.62721	−	4.62721i	0.925443	−	0.925443i	0.997407	+	0.0719646i	$0.0229269\pi$
$6$		0			0
$7$	−3.04888			−0.435554			−0.217777	−	0.975999i	$-0.569881\pi$
$7$	−3.04888			−0.435554			−0.217777	+	0.975999i	$0.569881\pi$
$8$		0			0
$9$			0.156674i			0.0174082i
$10$		0			0
$11$	−9.15165	−	9.15165i	−0.831968	−	0.831968i	0.155818	−	0.987786i	$-0.450199\pi$
$11$	−9.15165	−	9.15165i	−0.831968	−	0.831968i	−0.987786	+	0.155818i	$0.950199\pi$
$12$		0			0
$13$	5.78389	+	5.78389i	0.444914	+	0.444914i	0.893660	−	0.448745i	$-0.148129\pi$
$13$	5.78389	+	5.78389i	0.444914	+	0.444914i	−0.448745	+	0.893660i	$0.648129\pi$
$14$		0			0
$15$		−	19.4600i		−	1.29733i
$16$		0			0
$17$	17.6655			1.03915			0.519574	−	0.854425i	$-0.326091\pi$
$17$	17.6655			1.03915			0.519574	+	0.854425i	$0.326091\pi$
$18$		0			0
$19$	−1.15165	+	1.15165i	−0.0606132	+	0.0606132i	−0.736764	−	0.676150i	$-0.763647\pi$
$19$	−1.15165	+	1.15165i	−0.0606132	+	0.0606132i	0.676150	+	0.736764i	$0.263647\pi$
$20$		0			0
$21$	−6.41110	+	6.41110i	−0.305290	+	0.305290i
$22$		0			0
$23$	3.45998			0.150434			0.0752169	−	0.997167i	$-0.476035\pi$
$23$	3.45998			0.150434			0.0752169	+	0.997167i	$0.476035\pi$
$24$		0			0
$25$		−	17.8222i		−	0.712888i
$26$		0			0
$27$	19.2544	+	19.2544i	0.713127	+	0.713127i
$28$		0			0
$29$	−12.1950	−	12.1950i	−0.420517	−	0.420517i	0.464865	−	0.885382i	$-0.346103\pi$
$29$	−12.1950	−	12.1950i	−0.420517	−	0.420517i	−0.885382	+	0.464865i	$0.846103\pi$
$30$		0			0
$31$			38.5089i			1.24222i	0.783723	+	0.621111i	$0.213318\pi$
$31$			38.5089i			1.24222i	−0.783723	+	0.621111i	$0.786682\pi$
$32$		0			0
$33$	−38.4877			−1.16629
$34$		0			0
$35$	−14.1078	+	14.1078i	−0.403080	+	0.403080i
$36$		0			0
$37$	0.0972356	−	0.0972356i	0.00262799	−	0.00262799i	−0.705792	−	0.708420i	$-0.749408\pi$
$37$	0.0972356	−	0.0972356i	0.00262799	−	0.00262799i	0.708420	+	0.705792i	$0.249408\pi$
$38$		0			0
$39$	24.3244			0.623703
$40$		0			0
$41$			51.5266i			1.25675i	0.777912	+	0.628373i	$0.216279\pi$
$41$			51.5266i			1.25675i	−0.777912	+	0.628373i	$0.783721\pi$
$42$		0			0
$43$	−1.70172	−	1.70172i	−0.0395749	−	0.0395749i	0.687042	−	0.726617i	$-0.258909\pi$
$43$	−1.70172	−	1.70172i	−0.0395749	−	0.0395749i	−0.726617	+	0.687042i	$0.758909\pi$
$44$		0			0
$45$	0.724965	+	0.724965i	0.0161103	+	0.0161103i
$46$		0			0
$47$			24.1533i			0.513899i	0.966425	+	0.256949i	$0.0827174\pi$
$47$			24.1533i			0.513899i	−0.966425	+	0.256949i	$0.917283\pi$
$48$		0			0
$49$	−39.7044			−0.810293
$50$		0			0
$51$	37.1466	−	37.1466i	0.728365	−	0.728365i
$52$		0			0
$53$	−27.0383	+	27.0383i	−0.510157	+	0.510157i	−0.914574	−	0.404418i	$-0.867474\pi$
$53$	−27.0383	+	27.0383i	−0.510157	+	0.510157i	0.404418	+	0.914574i	$0.367474\pi$
$54$		0			0
$55$	−84.6933			−1.53988
$56$		0			0
$57$			4.84333i			0.0849706i
$58$		0			0
$59$	19.5939	+	19.5939i	0.332100	+	0.332100i	0.853384	−	0.521283i	$-0.174547\pi$
$59$	19.5939	+	19.5939i	0.332100	+	0.332100i	−0.521283	+	0.853384i	$0.674547\pi$
$60$		0			0
$61$	−16.7250	−	16.7250i	−0.274180	−	0.274180i	0.556601	−	0.830780i	$-0.312105\pi$
$61$	−16.7250	−	16.7250i	−0.274180	−	0.274180i	−0.830780	+	0.556601i	$0.812105\pi$
$62$		0			0
$63$		−	0.477680i		−	0.00758222i
$64$		0			0
$65$	53.5266			0.823485
$66$		0			0
$67$	−75.8560	+	75.8560i	−1.13218	+	1.13218i	−0.142365	+	0.989814i	$0.545471\pi$
$67$	−75.8560	+	75.8560i	−1.13218	+	1.13218i	−0.989814	+	0.142365i	$0.954529\pi$
$68$		0			0
$69$	7.27555	−	7.27555i	0.105443	−	0.105443i
$70$		0			0
$71$	134.749			1.89787			0.948935	−	0.315471i	$-0.102163\pi$
$71$	134.749			1.89787			0.948935	+	0.315471i	$0.102163\pi$
$72$		0			0
$73$		−	112.210i		−	1.53712i	−0.639777	−	0.768560i	$-0.720974\pi$
$73$		−	112.210i		−	1.53712i	0.639777	−	0.768560i	$-0.279026\pi$
$74$		0			0
$75$	−37.4761	−	37.4761i	−0.499681	−	0.499681i
$76$		0			0
$77$	27.9022	+	27.9022i	0.362367	+	0.362367i
$78$		0			0
$79$		−	135.915i		−	1.72045i	−0.509915	−	0.860225i	$-0.670323\pi$
$79$		−	135.915i		−	1.72045i	0.509915	−	0.860225i	$-0.329677\pi$
$80$		0			0
$81$	79.5654			0.982289
$82$		0			0
$83$	74.9250	−	74.9250i	0.902711	−	0.902711i	−0.0929594	−	0.995670i	$-0.529633\pi$
$83$	74.9250	−	74.9250i	0.902711	−	0.902711i	0.995670	+	0.0929594i	$0.0296327\pi$
$84$		0			0
$85$	81.7422	−	81.7422i	0.961672	−	0.961672i
$86$		0			0
$87$	−51.2866			−0.589501
$88$		0			0
$89$			31.4278i			0.353121i	0.984290	+	0.176561i	$0.0564971\pi$
$89$			31.4278i			0.353121i	−0.984290	+	0.176561i	$0.943503\pi$
$90$		0			0
$91$	−17.6344	−	17.6344i	−0.193784	−	0.193784i
$92$		0			0
$93$	80.9755	+	80.9755i	0.870704	+	0.870704i
$94$		0			0
$95$			10.6579i			0.112188i
$96$		0			0
$97$	31.5456			0.325213			0.162606	−	0.986691i	$-0.448010\pi$
$97$	31.5456			0.325213			0.162606	+	0.986691i	$0.448010\pi$
$98$		0			0
$99$	1.43383	−	1.43383i	0.0144831	−	0.0144831i
$100$		0			0
$101$	−27.4695	+	27.4695i	−0.271975	+	0.271975i	−0.829895	−	0.557920i	$-0.811600\pi$
$101$	−27.4695	+	27.4695i	−0.271975	+	0.271975i	0.557920	+	0.829895i	$0.311600\pi$
$102$		0			0
$103$	−102.882			−0.998854			−0.499427	−	0.866356i	$-0.666456\pi$
$103$	−102.882			−0.998854			−0.499427	+	0.866356i	$0.666456\pi$
$104$		0			0
$105$			59.3311i			0.565058i
$106$		0			0
$107$	−79.6605	−	79.6605i	−0.744491	−	0.744491i	0.228948	−	0.973439i	$-0.426471\pi$
$107$	−79.6605	−	79.6605i	−0.744491	−	0.744491i	−0.973439	+	0.228948i	$0.926471\pi$
$108$		0			0
$109$	−125.408	−	125.408i	−1.15053	−	1.15053i	−0.986446	−	0.164088i	$-0.947532\pi$
$109$	−125.408	−	125.408i	−1.15053	−	1.15053i	−0.164088	−	0.986446i	$-0.552468\pi$
$110$		0			0
$111$		−	0.408929i		−	0.00368405i
$112$		0			0
$113$	−96.6199			−0.855043			−0.427521	−	0.904005i	$-0.640613\pi$
$113$	−96.6199			−0.855043			−0.427521	+	0.904005i	$0.640613\pi$
$114$		0			0
$115$	16.0100	−	16.0100i	0.139218	−	0.139218i
$116$		0			0
$117$	−0.906186	+	0.906186i	−0.00774518	+	0.00774518i
$118$		0			0
$119$	−53.8600			−0.452605
$120$		0			0
$121$			46.5054i			0.384342i
$122$		0			0
$123$	108.349	+	108.349i	0.880884	+	0.880884i
$124$		0			0
$125$	33.2132	+	33.2132i	0.265706	+	0.265706i
$126$		0			0
$127$			196.309i			1.54574i	0.634566	+	0.772868i	$0.281179\pi$
$127$			196.309i			1.54574i	−0.634566	+	0.772868i	$0.718821\pi$
$128$		0			0
$129$	−7.15667			−0.0554781
$130$		0			0
$131$	17.9437	−	17.9437i	0.136975	−	0.136975i	−0.635295	−	0.772270i	$-0.719121\pi$
$131$	17.9437	−	17.9437i	0.136975	−	0.136975i	0.772270	+	0.635295i	$0.219121\pi$
$132$		0			0
$133$	3.51124	−	3.51124i	0.0264003	−	0.0264003i
$134$		0			0
$135$	178.189			1.31992
$136$		0			0
$137$		−	51.7200i		−	0.377518i	−0.982023	−	0.188759i	$-0.939553\pi$
$137$		−	51.7200i		−	0.377518i	0.982023	−	0.188759i	$-0.0604465\pi$
$138$		0			0
$139$	−17.4640	−	17.4640i	−0.125640	−	0.125640i	0.641491	−	0.767131i	$-0.278316\pi$
$139$	−17.4640	−	17.4640i	−0.125640	−	0.125640i	−0.767131	+	0.641491i	$0.778316\pi$
$140$		0			0
$141$	50.7889	+	50.7889i	0.360205	+	0.360205i
$142$		0			0
$143$		−	105.864i		−	0.740309i
$144$		0			0
$145$	−112.858			−0.778328
$146$		0			0
$147$	−83.4893	+	83.4893i	−0.567955	+	0.567955i
$148$		0			0
$149$	−11.9170	+	11.9170i	−0.0799802	+	0.0799802i	−0.745965	−	0.665985i	$-0.768011\pi$
$149$	−11.9170	+	11.9170i	−0.0799802	+	0.0799802i	0.665985	+	0.745965i	$0.268011\pi$
$150$		0			0
$151$	132.548			0.877805			0.438902	−	0.898535i	$-0.355367\pi$
$151$	132.548			0.877805			0.438902	+	0.898535i	$0.355367\pi$
$152$		0			0
$153$			2.76773i			0.0180898i
$154$		0			0
$155$	178.189	+	178.189i	1.14960	+	1.14960i
$156$		0			0
$157$	−106.091	−	106.091i	−0.675742	−	0.675742i	0.283292	−	0.959034i	$-0.408573\pi$
$157$	−106.091	−	106.091i	−0.675742	−	0.675742i	−0.959034	+	0.283292i	$0.908573\pi$
$158$		0			0
$159$			113.711i			0.715163i
$160$		0			0
$161$	−10.5490			−0.0655220
$162$		0			0
$163$	−105.577	+	105.577i	−0.647712	+	0.647712i	−0.952440	−	0.304728i	$-0.901435\pi$
$163$	−105.577	+	105.577i	−0.647712	+	0.647712i	0.304728	+	0.952440i	$0.401435\pi$
$164$		0			0
$165$	−178.091	+	178.091i	−1.07934	+	1.07934i
$166$		0			0
$167$	−111.591			−0.668210			−0.334105	−	0.942536i	$-0.608434\pi$
$167$	−111.591			−0.668210			−0.334105	+	0.942536i	$0.608434\pi$
$168$		0			0
$169$		−	102.093i		−	0.604102i
$170$		0			0
$171$	−0.180434	−	0.180434i	−0.00105517	−	0.00105517i
$172$		0			0
$173$	−14.5363	−	14.5363i	−0.0840249	−	0.0840249i	0.663845	−	0.747870i	$-0.268923\pi$
$173$	−14.5363	−	14.5363i	−0.0840249	−	0.0840249i	−0.747870	+	0.663845i	$0.768923\pi$
$174$		0			0
$175$			54.3377i			0.310501i
$176$		0			0
$177$	82.4032			0.465555
$178$		0			0
$179$	−19.7371	+	19.7371i	−0.110263	+	0.110263i	−0.760086	−	0.649823i	$-0.774843\pi$
$179$	−19.7371	+	19.7371i	−0.110263	+	0.110263i	0.649823	+	0.760086i	$0.274843\pi$
$180$		0			0
$181$	−168.153	+	168.153i	−0.929021	+	0.929021i	−0.997643	−	0.0686221i	$-0.978140\pi$
$181$	−168.153	+	168.153i	−0.929021	+	0.929021i	0.0686221	+	0.997643i	$0.478140\pi$
$182$		0			0
$183$	−70.3377			−0.384359
$184$		0			0
$185$		−	0.899859i		−	0.00486410i
$186$		0			0
$187$	−161.669	−	161.669i	−0.864539	−	0.864539i
$188$		0			0
$189$	−58.7044	−	58.7044i	−0.310605	−	0.310605i
$190$		0			0
$191$		−	196.309i		−	1.02779i	−0.857852	−	0.513897i	$-0.828201\pi$
$191$		−	196.309i		−	1.02779i	0.857852	−	0.513897i	$-0.171799\pi$
$192$		0			0
$193$	−40.3699			−0.209170			−0.104585	−	0.994516i	$-0.533351\pi$
$193$	−40.3699			−0.209170			−0.104585	+	0.994516i	$0.533351\pi$
$194$		0			0
$195$	112.554	−	112.554i	0.577202	−	0.577202i
$196$		0			0
$197$	230.578	−	230.578i	1.17045	−	1.17045i	0.188344	−	0.982103i	$-0.439688\pi$
$197$	230.578	−	230.578i	1.17045	−	1.17045i	0.982103	−	0.188344i	$-0.0603121\pi$
$198$		0			0
$199$	−61.5598			−0.309346			−0.154673	−	0.987966i	$-0.549432\pi$
$199$	−61.5598			−0.309346			−0.154673	+	0.987966i	$0.549432\pi$
$200$		0			0
$201$			319.016i			1.58715i
$202$		0			0
$203$	37.1810	+	37.1810i	0.183158	+	0.183158i
$204$		0			0
$205$	238.424	+	238.424i	1.16305	+	1.16305i
$206$		0			0
$207$			0.542089i			0.00261879i
$208$		0			0
$209$	21.0790			0.100857
$210$		0			0
$211$	151.149	−	151.149i	0.716346	−	0.716346i	−0.251509	−	0.967855i	$-0.580927\pi$
$211$	151.149	−	151.149i	0.716346	−	0.716346i	0.967855	+	0.251509i	$0.0809267\pi$
$212$		0			0
$213$	283.346	−	283.346i	1.33026	−	1.33026i
$214$		0			0
$215$	−15.7485			−0.0732486
$216$		0			0
$217$		−	117.409i		−	0.541054i
$218$		0			0
$219$	−235.952	−	235.952i	−1.07741	−	1.07741i
$220$		0			0
$221$	102.175	+	102.175i	0.462332	+	0.462332i
$222$		0			0
$223$		−	115.527i		−	0.518056i	−0.965870	−	0.259028i	$-0.916598\pi$
$223$		−	115.527i		−	0.518056i	0.965870	−	0.259028i	$-0.0834022\pi$
$224$		0			0
$225$	2.79228			0.0124101
$226$		0			0
$227$	25.2363	−	25.2363i	0.111173	−	0.111173i	−0.649332	−	0.760505i	$-0.724951\pi$
$227$	25.2363	−	25.2363i	0.111173	−	0.111173i	0.760505	+	0.649332i	$0.224951\pi$
$228$		0			0
$229$	155.318	−	155.318i	0.678244	−	0.678244i	−0.281359	−	0.959603i	$-0.590785\pi$
$229$	155.318	−	155.318i	0.678244	−	0.678244i	0.959603	+	0.281359i	$0.0907851\pi$
$230$		0			0
$231$	117.344			0.507984
$232$		0			0
$233$		−	119.738i		−	0.513899i	−0.966425	−	0.256949i	$-0.917283\pi$
$233$		−	119.738i		−	0.513899i	0.966425	−	0.256949i	$-0.0827174\pi$
$234$		0			0
$235$	111.762	+	111.762i	0.475584	+	0.475584i
$236$		0			0
$237$	−285.800	−	285.800i	−1.20591	−	1.20591i
$238$		0			0
$239$			245.409i			1.02681i	0.858145	+	0.513407i	$0.171617\pi$
$239$			245.409i			1.02681i	−0.858145	+	0.513407i	$0.828383\pi$
$240$		0			0
$241$	431.216			1.78928			0.894639	−	0.446790i	$-0.147433\pi$
$241$	431.216			1.78928			0.894639	+	0.446790i	$0.147433\pi$
$242$		0			0
$243$	−5.98173	+	5.98173i	−0.0246162	+	0.0246162i
$244$		0			0
$245$	−183.721	+	183.721i	−0.749880	+	0.749880i
$246$		0			0
$247$	−13.3220			−0.0539354
$248$		0			0
$249$		−	315.101i		−	1.26546i
$250$		0			0
$251$	−24.0171	−	24.0171i	−0.0956858	−	0.0956858i	0.657643	−	0.753329i	$-0.271553\pi$
$251$	−24.0171	−	24.0171i	−0.0956858	−	0.0956858i	−0.753329	+	0.657643i	$0.771553\pi$
$252$		0			0
$253$	−31.6645	−	31.6645i	−0.125156	−	0.125156i
$254$		0			0
$255$		−	343.771i		−	1.34812i
$256$		0			0
$257$	−100.860			−0.392450			−0.196225	−	0.980559i	$-0.562868\pi$
$257$	−100.860			−0.392450			−0.196225	+	0.980559i	$0.562868\pi$
$258$		0			0
$259$	−0.296459	+	0.296459i	−0.00114463	+	0.00114463i
$260$		0			0
$261$	1.91064	−	1.91064i	0.00732046	−	0.00732046i
$262$		0			0
$263$	−216.776			−0.824242			−0.412121	−	0.911129i	$-0.635212\pi$
$263$	−216.776			−0.824242			−0.412121	+	0.911129i	$0.635212\pi$
$264$		0			0
$265$			250.224i			0.944242i
$266$		0			0
$267$	66.0855	+	66.0855i	0.247511	+	0.247511i
$268$		0			0
$269$	256.778	+	256.778i	0.954567	+	0.954567i	0.999012	−	0.0444453i	$-0.0141520\pi$
$269$	256.778	+	256.778i	0.954567	+	0.954567i	−0.0444453	+	0.999012i	$0.514152\pi$
$270$		0			0
$271$			12.8603i			0.0474551i	0.999718	+	0.0237275i	$0.00755342\pi$
$271$			12.8603i			0.0474551i	−0.999718	+	0.0237275i	$0.992447\pi$
$272$		0			0
$273$	−74.1622			−0.271656
$274$		0			0
$275$	−163.103	+	163.103i	−0.593100	+	0.593100i
$276$		0			0
$277$	−77.1023	+	77.1023i	−0.278348	+	0.278348i	−0.832449	−	0.554102i	$-0.813062\pi$
$277$	−77.1023	+	77.1023i	−0.278348	+	0.278348i	0.554102	+	0.832449i	$0.313062\pi$
$278$		0			0
$279$	−6.03334			−0.0216249
$280$		0			0
$281$			189.034i			0.672719i	0.941734	+	0.336360i	$0.109196\pi$
$281$			189.034i			0.672719i	−0.941734	+	0.336360i	$0.890804\pi$
$282$		0			0
$283$	−69.4317	−	69.4317i	−0.245342	−	0.245342i	0.573714	−	0.819056i	$-0.305502\pi$
$283$	−69.4317	−	69.4317i	−0.245342	−	0.245342i	−0.819056	+	0.573714i	$0.805502\pi$
$284$		0			0
$285$	22.4111	+	22.4111i	0.0786354	+	0.0786354i
$286$		0			0
$287$		−	157.098i		−	0.547380i
$288$		0			0
$289$	23.0708			0.0798298
$290$		0			0
$291$	66.3333	−	66.3333i	0.227950	−	0.227950i
$292$		0			0
$293$	−239.919	+	239.919i	−0.818837	+	0.818837i	−0.985939	−	0.167103i	$-0.946559\pi$
$293$	−239.919	+	239.919i	−0.818837	+	0.818837i	0.167103	+	0.985939i	$0.446559\pi$
$294$		0			0
$295$	181.331			0.614680
$296$		0			0
$297$		−	352.420i		−	1.18660i
$298$		0			0
$299$	20.0121	+	20.0121i	0.0669301	+	0.0669301i
$300$		0			0
$301$	5.18834	+	5.18834i	0.0172370	+	0.0172370i
$302$		0			0
$303$			115.524i			0.381269i
$304$		0			0
$305$	−154.780			−0.507475
$306$		0			0
$307$	−231.185	+	231.185i	−0.753046	+	0.753046i	−0.975046	−	0.222001i	$-0.928741\pi$
$307$	−231.185	+	231.185i	−0.753046	+	0.753046i	0.222001	+	0.975046i	$0.428741\pi$
$308$		0			0
$309$	−216.338	+	216.338i	−0.700122	+	0.700122i
$310$		0			0
$311$	513.328			1.65057			0.825287	−	0.564714i	$-0.191013\pi$
$311$	513.328			1.65057			0.825287	+	0.564714i	$0.191013\pi$
$312$		0			0
$313$			345.242i			1.10301i	0.834172	+	0.551504i	$0.185946\pi$
$313$			345.242i			1.10301i	−0.834172	+	0.551504i	$0.814054\pi$
$314$		0			0
$315$	−2.21033	−	2.21033i	−0.00701691	−	0.00701691i
$316$		0			0
$317$	−345.632	−	345.632i	−1.09032	−	1.09032i	−0.995494	−	0.0948290i	$-0.969770\pi$
$317$	−345.632	−	345.632i	−1.09032	−	1.09032i	−0.0948290	−	0.995494i	$-0.530230\pi$
$318$		0			0
$319$			223.209i			0.699713i
$320$		0			0
$321$	−335.016			−1.04366
$322$		0			0
$323$	−20.3445	+	20.3445i	−0.0629861	+	0.0629861i
$324$		0			0
$325$	103.082	−	103.082i	0.317174	−	0.317174i
$326$		0			0
$327$	−527.410			−1.61288
$328$		0			0
$329$		−	73.6403i		−	0.223831i
$330$		0			0
$331$	425.968	+	425.968i	1.28691	+	1.28691i	0.936652	+	0.350261i	$0.113907\pi$
$331$	425.968	+	425.968i	1.28691	+	1.28691i	0.350261	+	0.936652i	$0.386093\pi$
$332$		0			0
$333$	0.0152343	+	0.0152343i	4.57487e−5	+	4.57487e-5i
$334$		0			0
$335$			702.004i			2.09553i
$336$		0			0
$337$	−467.297			−1.38664			−0.693319	−	0.720631i	$-0.743852\pi$
$337$	−467.297			−1.38664			−0.693319	+	0.720631i	$0.743852\pi$
$338$		0			0
$339$	−203.170	+	203.170i	−0.599321	+	0.599321i
$340$		0			0
$341$	352.420	−	352.420i	1.03349	−	1.03349i
$342$		0			0
$343$	270.449			0.788480
$344$		0			0
$345$		−	67.3311i		−	0.195162i
$346$		0			0
$347$	−22.0463	−	22.0463i	−0.0635341	−	0.0635341i	0.674626	−	0.738160i	$-0.264305\pi$
$347$	−22.0463	−	22.0463i	−0.0635341	−	0.0635341i	−0.738160	+	0.674626i	$0.764305\pi$
$348$		0			0
$349$	158.622	+	158.622i	0.454506	+	0.454506i	0.896847	−	0.442341i	$-0.145852\pi$
$349$	158.622	+	158.622i	0.454506	+	0.454506i	−0.442341	+	0.896847i	$0.645852\pi$
$350$		0			0
$351$			222.731i			0.634561i
$352$		0			0
$353$	404.451			1.14575			0.572877	−	0.819642i	$-0.305827\pi$
$353$	404.451			1.14575			0.572877	+	0.819642i	$0.305827\pi$
$354$		0			0
$355$	623.511	−	623.511i	1.75637	−	1.75637i
$356$		0			0
$357$	−113.255	+	113.255i	−0.317242	+	0.317242i
$358$		0			0
$359$	−423.833			−1.18059			−0.590297	−	0.807186i	$-0.700989\pi$
$359$	−423.833			−1.18059			−0.590297	+	0.807186i	$0.700989\pi$
$360$		0			0
$361$			358.347i			0.992652i
$362$		0			0
$363$	97.7905	+	97.7905i	0.269395	+	0.269395i
$364$		0			0
$365$	−519.219	−	519.219i	−1.42252	−	1.42252i
$366$		0			0
$367$		−	477.144i		−	1.30012i	−0.759883	−	0.650059i	$-0.774744\pi$
$367$		−	477.144i		−	1.30012i	0.759883	−	0.650059i	$-0.225256\pi$
$368$		0			0
$369$	−8.07288			−0.0218777
$370$		0			0
$371$	82.4365	−	82.4365i	0.222201	−	0.222201i
$372$		0			0
$373$	−112.221	+	112.221i	−0.300860	+	0.300860i	−0.841350	−	0.540490i	$-0.818239\pi$
$373$	−112.221	+	112.221i	−0.300860	+	0.300860i	0.540490	+	0.841350i	$0.318239\pi$
$374$		0			0
$375$	139.680			0.372479
$376$		0			0
$377$		−	141.069i		−	0.374188i
$378$		0			0
$379$	52.2069	+	52.2069i	0.137749	+	0.137749i	0.772619	−	0.634870i	$-0.218946\pi$
$379$	52.2069	+	52.2069i	0.137749	+	0.137749i	−0.634870	+	0.772619i	$0.718946\pi$
$380$		0			0
$381$	412.793	+	412.793i	1.08345	+	1.08345i
$382$		0			0
$383$		−	74.8407i		−	0.195406i	−0.995216	−	0.0977032i	$-0.968850\pi$
$383$		−	74.8407i		−	0.195406i	0.995216	−	0.0977032i	$-0.0311496\pi$
$384$		0			0
$385$	258.219			0.670699
$386$		0			0
$387$	0.266616	−	0.266616i	0.000688930	−	0.000688930i
$388$		0			0
$389$	57.0441	−	57.0441i	0.146643	−	0.146643i	−0.629974	−	0.776617i	$-0.716934\pi$
$389$	57.0441	−	57.0441i	0.146643	−	0.146643i	0.776617	+	0.629974i	$0.216934\pi$
$390$		0			0
$391$	61.1223			0.156323
$392$		0			0
$393$		−	75.4632i		−	0.192018i
$394$		0			0
$395$	−628.910	−	628.910i	−1.59218	−	1.59218i
$396$		0			0
$397$	355.874	+	355.874i	0.896407	+	0.896407i	0.995116	−	0.0987089i	$-0.0314713\pi$
$397$	355.874	+	355.874i	0.896407	+	0.896407i	−0.0987089	+	0.995116i	$0.531471\pi$
$398$		0			0
$399$		−	14.7667i		−	0.0370093i
$400$		0			0
$401$	113.892			0.284019			0.142010	−	0.989865i	$-0.454644\pi$
$401$	113.892			0.284019			0.142010	+	0.989865i	$0.454644\pi$
$402$		0			0
$403$	−222.731	+	222.731i	−0.552682	+	0.552682i
$404$		0			0
$405$	368.166	−	368.166i	0.909052	−	0.909052i
$406$		0			0
$407$	−1.77973			−0.00437281
$408$		0			0
$409$			139.909i			0.342077i	0.985264	+	0.171038i	$0.0547122\pi$
$409$			139.909i			0.342077i	−0.985264	+	0.171038i	$0.945288\pi$
$410$		0			0
$411$	−108.756	−	108.756i	−0.264612	−	0.264612i
$412$		0			0
$413$	−59.7394	−	59.7394i	−0.144648	−	0.144648i
$414$		0			0
$415$		−	693.388i		−	1.67081i
$416$		0			0
$417$	−73.4456			−0.176129
$418$		0			0
$419$	−370.978	+	370.978i	−0.885389	+	0.885389i	−0.994076	−	0.108687i	$-0.965335\pi$
$419$	−370.978	+	370.978i	−0.885389	+	0.885389i	0.108687	+	0.994076i	$0.465335\pi$
$420$		0			0
$421$	−465.112	+	465.112i	−1.10478	+	1.10478i	−0.110955	+	0.993825i	$0.535391\pi$
$421$	−465.112	+	465.112i	−1.10478	+	1.10478i	−0.993825	+	0.110955i	$0.964609\pi$
$422$		0			0
$423$	−3.78419			−0.00894608
$424$		0			0
$425$		−	314.839i		−	0.740797i
$426$		0			0
$427$	50.9923	+	50.9923i	0.119420	+	0.119420i
$428$		0			0
$429$	−222.609	−	222.609i	−0.518901	−	0.518901i
$430$		0			0
$431$		−	409.924i		−	0.951099i	−0.879689	−	0.475549i	$-0.842249\pi$
$431$		−	409.924i		−	0.951099i	0.879689	−	0.475549i	$-0.157751\pi$
$432$		0			0
$433$	−20.6859			−0.0477735			−0.0238868	−	0.999715i	$-0.507604\pi$
$433$	−20.6859			−0.0477735			−0.0238868	+	0.999715i	$0.507604\pi$
$434$		0			0
$435$	−237.314	+	237.314i	−0.545550	+	0.545550i
$436$		0			0
$437$	−3.98468	+	3.98468i	−0.00911827	+	0.00911827i
$438$		0			0
$439$	63.2889			0.144166			0.0720830	−	0.997399i	$-0.477035\pi$
$439$	63.2889			0.144166			0.0720830	+	0.997399i	$0.477035\pi$
$440$		0			0
$441$		−	6.22065i		−	0.0141058i
$442$		0			0
$443$	−297.084	−	297.084i	−0.670619	−	0.670619i	0.287240	−	0.957859i	$-0.407262\pi$
$443$	−297.084	−	297.084i	−0.670619	−	0.670619i	−0.957859	+	0.287240i	$0.907262\pi$
$444$		0			0
$445$	145.423	+	145.423i	0.326793	+	0.326793i
$446$		0			0
$447$			50.1177i			0.112120i
$448$		0			0
$449$	364.701			0.812251			0.406126	−	0.913817i	$-0.366880\pi$
$449$	364.701			0.812251			0.406126	+	0.913817i	$0.366880\pi$
$450$		0			0
$451$	471.553	−	471.553i	1.04557	−	1.04557i
$452$		0			0
$453$	278.720	−	278.720i	0.615275	−	0.615275i
$454$		0			0
$455$	−163.196			−0.358672
$456$		0			0
$457$		−	640.046i		−	1.40054i	−0.713879	−	0.700269i	$-0.753064\pi$
$457$		−	640.046i		−	1.40054i	0.713879	−	0.700269i	$-0.246936\pi$
$458$		0			0
$459$	340.140	+	340.140i	0.741045	+	0.741045i
$460$		0			0
$461$	239.416	+	239.416i	0.519341	+	0.519341i	0.917372	−	0.398031i	$-0.130306\pi$
$461$	239.416	+	239.416i	0.519341	+	0.519341i	−0.398031	+	0.917372i	$0.630306\pi$
$462$		0			0
$463$			479.413i			1.03545i	0.855548	+	0.517724i	$0.173221\pi$
$463$			479.413i			1.03545i	−0.855548	+	0.517724i	$0.826779\pi$
$464$		0			0
$465$	749.381			1.61157
$466$		0			0
$467$	403.375	−	403.375i	0.863758	−	0.863758i	−0.128015	−	0.991772i	$-0.540860\pi$
$467$	403.375	−	403.375i	0.863758	−	0.863758i	0.991772	+	0.128015i	$0.0408605\pi$
$468$		0			0
$469$	231.276	−	231.276i	0.493125	−	0.493125i
$470$		0			0
$471$	−446.173			−0.947288
$472$		0			0
$473$			31.1471i			0.0658501i
$474$		0			0
$475$	20.5250	+	20.5250i	0.0432104	+	0.0432104i
$476$		0			0
$477$	−4.23621	−	4.23621i	−0.00888093	−	0.00888093i
$478$		0			0
$479$		−	460.611i		−	0.961609i	−0.876828	−	0.480805i	$-0.840345\pi$
$479$		−	460.611i		−	0.961609i	0.876828	−	0.480805i	$-0.159655\pi$
$480$		0			0
$481$	1.12480			0.00233846
$482$		0			0
$483$	−22.1823	+	22.1823i	−0.0459260	+	0.0459260i
$484$		0			0
$485$	145.968	−	145.968i	0.300966	−	0.300966i
$486$		0			0
$487$	575.128			1.18096			0.590481	−	0.807052i	$-0.298938\pi$
$487$	575.128			1.18096			0.590481	+	0.807052i	$0.298938\pi$
$488$		0			0
$489$			444.010i			0.907995i
$490$		0			0
$491$	271.375	+	271.375i	0.552699	+	0.552699i	0.927219	−	0.374520i	$-0.122192\pi$
$491$	271.375	+	271.375i	0.552699	+	0.552699i	−0.374520	+	0.927219i	$0.622192\pi$
$492$		0			0
$493$	−215.431	−	215.431i	−0.436979	−	0.436979i
$494$		0			0
$495$		−	13.2693i		−	0.0268066i
$496$		0			0
$497$	−410.832			−0.826624
$498$		0			0
$499$	268.082	−	268.082i	0.537239	−	0.537239i	−0.385478	−	0.922717i	$-0.625963\pi$
$499$	268.082	−	268.082i	0.537239	−	0.537239i	0.922717	+	0.385478i	$0.125963\pi$
$500$		0			0
$501$	−234.651	+	234.651i	−0.468365	+	0.468365i
$502$		0			0
$503$	368.002			0.731615			0.365807	−	0.930691i	$-0.380793\pi$
$503$	368.002			0.731615			0.365807	+	0.930691i	$0.380793\pi$
$504$		0			0
$505$			254.215i			0.503395i
$506$		0			0
$507$	−214.679	−	214.679i	−0.423430	−	0.423430i
$508$		0			0
$509$	−297.809	−	297.809i	−0.585087	−	0.585087i	0.351210	−	0.936297i	$-0.385770\pi$
$509$	−297.809	−	297.809i	−0.585087	−	0.585087i	−0.936297	+	0.351210i	$0.885770\pi$
$510$		0			0
$511$			342.114i			0.669498i
$512$		0			0
$513$	−44.3488			−0.0864498
$514$		0			0
$515$	−476.057	+	476.057i	−0.924382	+	0.924382i
$516$		0			0
$517$	221.042	−	221.042i	0.427548	−	0.427548i
$518$		0			0
$519$	−61.1332			−0.117790
$520$		0			0
$521$			95.5605i			0.183418i	0.995786	+	0.0917088i	$0.0292329\pi$
$521$			95.5605i			0.183418i	−0.995786	+	0.0917088i	$0.970767\pi$
$522$		0			0
$523$	−250.389	−	250.389i	−0.478756	−	0.478756i	0.425978	−	0.904734i	$-0.359930\pi$
$523$	−250.389	−	250.389i	−0.478756	−	0.478756i	−0.904734	+	0.425978i	$0.859930\pi$
$524$		0			0
$525$	114.260	+	114.260i	0.217638	+	0.217638i
$526$		0			0
$527$			680.279i			1.29085i
$528$		0			0
$529$	−517.029			−0.977370
$530$		0			0
$531$	−3.06986	+	3.06986i	−0.00578128	+	0.00578128i
$532$		0			0
$533$	−298.024	+	298.024i	−0.559144	+	0.559144i
$534$		0			0
$535$	−737.212			−1.37797
$536$		0			0
$537$			83.0055i			0.154573i
$538$		0			0
$539$	363.360	+	363.360i	0.674138	+	0.674138i
$540$		0			0
$541$	81.7015	+	81.7015i	0.151019	+	0.151019i	0.778573	−	0.627554i	$-0.215944\pi$
$541$	81.7015	+	81.7015i	0.151019	+	0.151019i	−0.627554	+	0.778573i	$0.715944\pi$
$542$		0			0
$543$			707.175i			1.30235i
$544$		0			0
$545$	−1160.58			−2.12951
$546$		0			0
$547$	−381.162	+	381.162i	−0.696823	+	0.696823i	−0.963724	−	0.266901i	$-0.914000\pi$
$547$	−381.162	+	381.162i	−0.696823	+	0.696823i	0.266901	+	0.963724i	$0.414000\pi$
$548$		0			0
$549$	2.62037	−	2.62037i	0.00477299	−	0.00477299i
$550$		0			0
$551$	28.0887			0.0509777
$552$		0			0
$553$			414.389i			0.749348i
$554$		0			0
$555$	−1.89220	−	1.89220i	−0.00340937	−	0.00340937i
$556$		0			0
$557$	63.7634	+	63.7634i	0.114476	+	0.114476i	0.762025	−	0.647548i	$-0.224206\pi$
$557$	63.7634	+	63.7634i	0.114476	+	0.114476i	−0.647548	+	0.762025i	$0.724206\pi$
$558$		0			0
$559$		−	19.6851i		−	0.0352149i
$560$		0			0
$561$	−679.906			−1.21195
$562$		0			0
$563$	333.679	−	333.679i	0.592681	−	0.592681i	−0.345674	−	0.938355i	$-0.612350\pi$
$563$	333.679	−	333.679i	0.592681	−	0.592681i	0.938355	+	0.345674i	$0.112350\pi$
$564$		0			0
$565$	−447.081	+	447.081i	−0.791293	+	0.791293i
$566$		0			0
$567$	−242.585			−0.427839
$568$		0			0
$569$			93.3114i			0.163992i	0.996633	+	0.0819960i	$0.0261295\pi$
$569$			93.3114i			0.163992i	−0.996633	+	0.0819960i	$0.973871\pi$
$570$		0			0
$571$	196.999	+	196.999i	0.345007	+	0.345007i	0.858246	−	0.513239i	$-0.171555\pi$
$571$	196.999	+	196.999i	0.345007	+	0.345007i	−0.513239	+	0.858246i	$0.671555\pi$
$572$		0			0
$573$	−412.793	−	412.793i	−0.720406	−	0.720406i
$574$		0			0
$575$		−	61.6644i		−	0.107242i
$576$		0			0
$577$	370.057			0.641347			0.320673	−	0.947190i	$-0.396091\pi$
$577$	370.057			0.641347			0.320673	+	0.947190i	$0.396091\pi$
$578$		0			0
$579$	−84.8888	+	84.8888i	−0.146613	+	0.146613i
$580$		0			0
$581$	−228.437	+	228.437i	−0.393179	+	0.393179i
$582$		0			0
$583$	494.890			0.848869
$584$		0			0
$585$			8.38623i			0.0143354i
$586$		0			0
$587$	328.063	+	328.063i	0.558880	+	0.558880i	0.928989	−	0.370108i	$-0.120679\pi$
$587$	328.063	+	328.063i	0.558880	+	0.558880i	−0.370108	+	0.928989i	$0.620679\pi$
$588$		0			0
$589$	−44.3488	−	44.3488i	−0.0752950	−	0.0752950i
$590$		0			0
$591$		−	969.708i		−	1.64079i
$592$		0			0
$593$	1088.78			1.83605			0.918024	−	0.396525i	$-0.129784\pi$
$593$	1088.78			1.83605			0.918024	+	0.396525i	$0.129784\pi$
$594$		0			0
$595$	−249.222	+	249.222i	−0.418860	+	0.418860i
$596$		0			0
$597$	−129.446	+	129.446i	−0.216828	+	0.216828i
$598$		0			0
$599$	350.354			0.584899			0.292449	−	0.956281i	$-0.405530\pi$
$599$	350.354			0.584899			0.292449	+	0.956281i	$0.405530\pi$
$600$		0			0
$601$		−	1021.45i		−	1.69958i	−0.527123	−	0.849789i	$-0.676729\pi$
$601$		−	1021.45i		−	1.69958i	0.527123	−	0.849789i	$-0.323271\pi$
$602$		0			0
$603$	−11.8847	−	11.8847i	−0.0197093	−	0.0197093i
$604$		0			0
$605$	215.191	+	215.191i	0.355687	+	0.355687i
$606$		0			0
$607$			394.204i			0.649431i	0.945812	+	0.324715i	$0.105268\pi$
$607$			394.204i			0.649431i	−0.945812	+	0.324715i	$0.894732\pi$
$608$		0			0
$609$	156.367			0.256760
$610$		0			0
$611$	−139.700	+	139.700i	−0.228641	+	0.228641i
$612$		0			0
$613$	−157.606	+	157.606i	−0.257106	+	0.257106i	−0.823876	−	0.566770i	$-0.808193\pi$
$613$	−157.606	+	157.606i	−0.257106	+	0.257106i	0.566770	+	0.823876i	$0.308193\pi$
$614$		0			0
$615$	1002.71			1.63042
$616$		0			0
$617$			609.080i			0.987164i	0.869699	+	0.493582i	$0.164313\pi$
$617$			609.080i			0.987164i	−0.869699	+	0.493582i	$0.835687\pi$
$618$		0			0
$619$	−497.519	−	497.519i	−0.803747	−	0.803747i	0.179932	−	0.983679i	$-0.442412\pi$
$619$	−497.519	−	497.519i	−0.803747	−	0.803747i	−0.983679	+	0.179932i	$0.942412\pi$
$620$		0			0
$621$	66.6199	+	66.6199i	0.107278	+	0.107278i
$622$		0			0
$623$		−	95.8194i		−	0.153803i
$624$		0			0
$625$	752.924			1.20468
$626$		0			0
$627$	44.3244	−	44.3244i	0.0706929	−	0.0706929i
$628$		0			0
$629$	1.71772	−	1.71772i	0.00273087	−	0.00273087i
$630$		0			0
$631$	−668.065			−1.05874			−0.529370	−	0.848391i	$-0.677572\pi$
$631$	−668.065			−1.05874			−0.529370	+	0.848391i	$0.677572\pi$
$632$		0			0
$633$		−	635.665i		−	1.00421i
$634$		0			0
$635$	908.362	+	908.362i	1.43049	+	1.43049i
$636$		0			0
$637$	−229.646	−	229.646i	−0.360511	−	0.360511i
$638$		0			0
$639$			21.1117i			0.0330386i
$640$		0			0
$641$	−419.792			−0.654902			−0.327451	−	0.944868i	$-0.606190\pi$
$641$	−419.792			−0.654902			−0.327451	+	0.944868i	$0.606190\pi$
$642$		0			0
$643$	−138.767	+	138.767i	−0.215813	+	0.215813i	−0.806731	−	0.590919i	$-0.798765\pi$
$643$	−138.767	+	138.767i	−0.215813	+	0.215813i	0.590919	+	0.806731i	$0.298765\pi$
$644$		0			0
$645$	−33.1155	+	33.1155i	−0.0513418	+	0.0513418i
$646$		0			0
$647$	−647.036			−1.00006			−0.500028	−	0.866009i	$-0.666677\pi$
$647$	−647.036			−1.00006			−0.500028	+	0.866009i	$0.666677\pi$
$648$		0			0
$649$		−	358.633i		−	0.552594i
$650$		0			0
$651$	−246.884	−	246.884i	−0.379238	−	0.379238i
$652$		0			0
$653$	452.293	+	452.293i	0.692639	+	0.692639i	0.962812	−	0.270173i	$-0.0870808\pi$
$653$	452.293	+	452.293i	0.692639	+	0.692639i	−0.270173	+	0.962812i	$0.587081\pi$
$654$		0			0
$655$		−	166.059i		−	0.253525i
$656$		0			0
$657$	17.5804			0.0267586
$658$		0			0
$659$	382.858	−	382.858i	0.580969	−	0.580969i	−0.354201	−	0.935169i	$-0.615247\pi$
$659$	382.858	−	382.858i	0.580969	−	0.580969i	0.935169	+	0.354201i	$0.115247\pi$
$660$		0			0
$661$	841.606	−	841.606i	1.27323	−	1.27323i	0.328849	−	0.944383i	$-0.393339\pi$
$661$	841.606	−	841.606i	1.27323	−	1.27323i	0.944383	−	0.328849i	$-0.106661\pi$
$662$		0			0
$663$	429.704			0.648120
$664$		0			0
$665$		−	32.4945i		−	0.0488639i
$666$		0			0
$667$	−42.1944	−	42.1944i	−0.0632599	−	0.0632599i
$668$		0			0
$669$	−242.926	−	242.926i	−0.363119	−	0.363119i
$670$		0			0
$671$			306.122i			0.456218i
$672$		0			0
$673$	−506.103			−0.752010			−0.376005	−	0.926618i	$-0.622703\pi$
$673$	−506.103			−0.752010			−0.376005	+	0.926618i	$0.622703\pi$
$674$		0			0
$675$	343.156	−	343.156i	0.508380	−	0.508380i
$676$		0			0
$677$	430.816	−	430.816i	0.636361	−	0.636361i	−0.313295	−	0.949656i	$-0.601433\pi$
$677$	430.816	−	430.816i	0.636361	−	0.636361i	0.949656	+	0.313295i	$0.101433\pi$
$678$		0			0
$679$	−96.1787			−0.141648
$680$		0			0
$681$		−	106.132i		−	0.155848i
$682$		0			0
$683$	−910.083	−	910.083i	−1.33248	−	1.33248i	−0.903146	−	0.429333i	$-0.858749\pi$
$683$	−910.083	−	910.083i	−1.33248	−	1.33248i	−0.429333	−	0.903146i	$-0.641251\pi$
$684$		0			0
$685$	−239.319	−	239.319i	−0.349371	−	0.349371i
$686$		0			0
$687$		−	653.197i		−	0.950796i
$688$		0			0
$689$	−312.773			−0.453952
$690$		0			0
$691$	−601.836	+	601.836i	−0.870964	+	0.870964i	−0.992577	−	0.121614i	$-0.961193\pi$
$691$	−601.836	+	601.836i	−0.870964	+	0.870964i	0.121614	+	0.992577i	$0.461193\pi$
$692$		0			0
$693$	−4.37156	+	4.37156i	−0.00630817	+	0.00630817i
$694$		0			0
$695$	−161.619			−0.232545
$696$		0			0
$697$			910.244i			1.30595i
$698$		0			0
$699$	−251.783	−	251.783i	−0.360204	−	0.360204i
$700$		0			0
$701$	555.343	+	555.343i	0.792215	+	0.792215i	0.981854	−	0.189639i	$-0.0607317\pi$
$701$	555.343	+	555.343i	0.792215	+	0.792215i	−0.189639	+	0.981854i	$0.560732\pi$
$702$		0			0
$703$			0.223963i			0.000318582i
$704$		0			0
$705$	470.022			0.666697
$706$		0			0
$707$	83.7511	−	83.7511i	0.118460	−	0.118460i
$708$		0			0
$709$	412.979	−	412.979i	0.582480	−	0.582480i	−0.353104	−	0.935584i	$-0.614874\pi$
$709$	412.979	−	412.979i	0.582480	−	0.582480i	0.935584	+	0.353104i	$0.114874\pi$
$710$		0			0
$711$	21.2945			0.0299500
$712$		0			0
$713$			133.240i			0.186872i
$714$		0			0
$715$	−489.856	−	489.856i	−0.685114	−	0.685114i
$716$		0			0
$717$	516.039	+	516.039i	0.719720	+	0.719720i
$718$		0			0
$719$		−	1173.98i		−	1.63279i	−0.577495	−	0.816394i	$-0.695970\pi$
$719$		−	1173.98i		−	1.63279i	0.577495	−	0.816394i	$-0.304030\pi$
$720$		0			0
$721$	313.674			0.435054
$722$		0			0
$723$	906.750	−	906.750i	1.25415	−	1.25415i
$724$		0			0
$725$	−217.342	+	217.342i	−0.299781	+	0.299781i
$726$		0			0
$727$	−678.813			−0.933718			−0.466859	−	0.884332i	$-0.654614\pi$
$727$	−678.813			−0.933718			−0.466859	+	0.884332i	$0.654614\pi$
$728$		0			0
$729$			741.245i			1.01680i
$730$		0			0
$731$	−30.0618	−	30.0618i	−0.0411242	−	0.0411242i
$732$		0			0
$733$	−336.854	−	336.854i	−0.459556	−	0.459556i	0.438954	−	0.898510i	$-0.355349\pi$
$733$	−336.854	−	336.854i	−0.459556	−	0.459556i	−0.898510	+	0.438954i	$0.855349\pi$
$734$		0			0
$735$			772.646i			1.05122i
$736$		0			0
$737$	1388.42			1.88387
$738$		0			0
$739$	178.478	−	178.478i	0.241513	−	0.241513i	−0.575963	−	0.817476i	$-0.695373\pi$
$739$	178.478	−	178.478i	0.241513	−	0.241513i	0.817476	+	0.575963i	$0.195373\pi$
$740$		0			0
$741$	−28.0133	+	28.0133i	−0.0378047	+	0.0378047i
$742$		0			0
$743$	−795.320			−1.07042			−0.535208	−	0.844720i	$-0.679767\pi$
$743$	−795.320			−1.07042			−0.535208	+	0.844720i	$0.679767\pi$
$744$		0			0
$745$			110.285i			0.148034i
$746$		0			0
$747$	11.7388	+	11.7388i	0.0157146	+	0.0157146i
$748$		0			0
$749$	242.875	+	242.875i	0.324266	+	0.324266i
$750$		0			0
$751$		−	102.850i		−	0.136951i	−0.997653	−	0.0684755i	$-0.978186\pi$
$751$		−	102.850i		−	0.136951i	0.997653	−	0.0684755i	$-0.0218135\pi$
$752$		0			0
$753$	−101.005			−0.134137
$754$		0			0
$755$	613.330	−	613.330i	0.812358	−	0.812358i
$756$		0			0
$757$	−48.6324	+	48.6324i	−0.0642436	+	0.0642436i	−0.738499	−	0.674255i	$-0.764465\pi$
$757$	−48.6324	+	48.6324i	−0.0642436	+	0.0642436i	0.674255	+	0.738499i	$0.264465\pi$
$758$		0			0
$759$	−133.167			−0.175450
$760$		0			0
$761$		−	947.802i		−	1.24547i	−0.782433	−	0.622734i	$-0.786022\pi$
$761$		−	947.802i		−	1.24547i	0.782433	−	0.622734i	$-0.213978\pi$
$762$		0			0
$763$	382.354	+	382.354i	0.501119	+	0.501119i
$764$		0			0
$765$	12.8069	+	12.8069i	0.0167410	+	0.0167410i
$766$		0			0
$767$			226.658i			0.295512i
$768$		0			0
$769$	−183.427			−0.238527			−0.119263	−	0.992863i	$-0.538053\pi$
$769$	−183.427			−0.238527			−0.119263	+	0.992863i	$0.538053\pi$
$770$		0			0
$771$	−212.085	+	212.085i	−0.275078	+	0.275078i
$772$		0			0
$773$	178.338	−	178.338i	0.230710	−	0.230710i	−0.582279	−	0.812989i	$-0.697839\pi$
$773$	178.338	−	178.338i	0.230710	−	0.230710i	0.812989	+	0.582279i	$0.197839\pi$
$774$		0			0
$775$	686.312			0.885564
$776$		0			0
$777$			1.24677i			0.00160460i
$778$		0			0
$779$	−59.3406	−	59.3406i	−0.0761754	−	0.0761754i
$780$		0			0
$781$	−1233.17	−	1233.17i	−1.57897	−	1.57897i
$782$		0			0
$783$		−	469.615i		−	0.599764i
$784$		0			0
$785$	−981.815			−1.25072
$786$		0			0
$787$	−480.981	+	480.981i	−0.611158	+	0.611158i	−0.943248	−	0.332090i	$-0.892246\pi$
$787$	−480.981	+	480.981i	−0.611158	+	0.611158i	0.332090	+	0.943248i	$0.392246\pi$
$788$		0			0
$789$	−455.831	+	455.831i	−0.577732	+	0.577732i
$790$		0			0
$791$	294.582			0.372417
$792$		0			0
$793$		−	193.471i		−	0.243973i
$794$		0			0
$795$	526.165	+	526.165i	0.661843	+	0.661843i
$796$		0			0
$797$	558.478	+	558.478i	0.700725	+	0.700725i	0.964566	−	0.263841i	$-0.0849894\pi$
$797$	558.478	+	558.478i	0.700725	+	0.700725i	−0.263841	+	0.964566i	$0.584989\pi$
$798$		0			0
$799$			426.680i			0.534017i
$800$		0			0
$801$	−4.92392			−0.00614722
$802$		0			0
$803$	−1026.90	+	1026.90i	−1.27884	+	1.27884i
$804$		0			0
$805$	−48.8126	+	48.8126i	−0.0606368	+	0.0606368i
$806$		0			0
$807$	1079.89			1.33816
$808$		0			0
$809$		−	1152.43i		−	1.42451i	−0.701918	−	0.712257i	$-0.747673\pi$
$809$		−	1152.43i		−	1.42451i	0.701918	−	0.712257i	$-0.252327\pi$
$810$		0			0
$811$	364.890	+	364.890i	0.449926	+	0.449926i	0.895330	−	0.445404i	$-0.146940\pi$
$811$	364.890	+	364.890i	0.449926	+	0.449926i	−0.445404	+	0.895330i	$0.646940\pi$
$812$		0			0
$813$	27.0424	+	27.0424i	0.0332624	+	0.0332624i
$814$		0			0
$815$			977.055i			1.19884i
$816$		0			0
$817$	3.91958			0.00479753
$818$		0			0
$819$	2.76285	−	2.76285i	0.00337344	−	0.00337344i
$820$		0			0
$821$	618.975	−	618.975i	0.753928	−	0.753928i	−0.221282	−	0.975210i	$-0.571024\pi$
$821$	618.975	−	618.975i	0.753928	−	0.753928i	0.975210	+	0.221282i	$0.0710240\pi$
$822$		0			0
$823$	−626.066			−0.760712			−0.380356	−	0.924840i	$-0.624199\pi$
$823$	−626.066			−0.760712			−0.380356	+	0.924840i	$0.624199\pi$
$824$		0			0
$825$			685.936i			0.831438i
$826$		0			0
$827$	375.666	+	375.666i	0.454252	+	0.454252i	0.896763	−	0.442511i	$-0.145912\pi$
$827$	375.666	+	375.666i	0.454252	+	0.454252i	−0.442511	+	0.896763i	$0.645912\pi$
$828$		0			0
$829$	299.648	+	299.648i	0.361457	+	0.361457i	0.864349	−	0.502892i	$-0.167731\pi$
$829$	299.648	+	299.648i	0.361457	+	0.361457i	−0.502892	+	0.864349i	$0.667731\pi$
$830$		0			0
$831$			324.258i			0.390202i
$832$		0			0
$833$	−701.398			−0.842015
$834$		0			0
$835$	−516.356	+	516.356i	−0.618390	+	0.618390i
$836$		0			0
$837$	−741.466	+	741.466i	−0.885861	+	0.885861i
$838$		0			0
$839$	1477.80			1.76138			0.880689	−	0.473694i	$-0.157080\pi$
$839$	1477.80			1.76138			0.880689	+	0.473694i	$0.157080\pi$
$840$		0			0
$841$		−	543.565i		−	0.646331i
$842$		0			0
$843$	397.496	+	397.496i	0.471526	+	0.471526i
$844$		0			0
$845$	−472.407	−	472.407i	−0.559062	−	0.559062i
$846$		0			0
$847$		−	141.789i		−	0.167402i
$848$		0			0
$849$	−291.998			−0.343932
$850$		0			0
$851$	0.336433	−	0.336433i	0.000395338	−	0.000395338i
$852$		0			0
$853$	−404.051	+	404.051i	−0.473682	+	0.473682i	−0.903104	−	0.429422i	$-0.858717\pi$
$853$	−404.051	+	404.051i	−0.473682	+	0.473682i	0.429422	+	0.903104i	$0.358717\pi$
$854$		0			0
$855$	−1.66981			−0.00195300
$856$		0			0
$857$			892.363i			1.04126i	0.853781	+	0.520632i	$0.174304\pi$
$857$			892.363i			1.04126i	−0.853781	+	0.520632i	$0.825696\pi$
$858$		0			0
$859$	−378.424	−	378.424i	−0.440540	−	0.440540i	0.451654	−	0.892193i	$-0.350834\pi$
$859$	−378.424	−	378.424i	−0.440540	−	0.440540i	−0.892193	+	0.451654i	$0.850834\pi$
$860$		0			0
$861$	−330.342	−	330.342i	−0.383672	−	0.383672i
$862$		0			0
$863$		−	1457.30i		−	1.68865i	−0.535833	−	0.844324i	$-0.680002\pi$
$863$		−	1457.30i		−	1.68865i	0.535833	−	0.844324i	$-0.319998\pi$
$864$		0			0
$865$	−134.525			−0.155520
$866$		0			0
$867$	48.5127	−	48.5127i	0.0559547	−	0.0559547i
$868$		0			0
$869$	−1243.85	+	1243.85i	−1.43136	+	1.43136i
$870$		0			0
$871$	−877.485			−1.00745
$872$		0			0
$873$			4.94238i			0.00566138i
$874$		0			0
$875$	−101.263	−	101.263i	−0.115729	−	0.115729i
$876$		0			0
$877$	571.322	+	571.322i	0.651450	+	0.651450i	0.953342	−	0.301892i	$-0.0976181\pi$
$877$	571.322	+	571.322i	0.651450	+	0.651450i	−0.301892	+	0.953342i	$0.597618\pi$
$878$		0			0
$879$			1008.99i			1.14789i
$880$		0			0
$881$	994.662			1.12901			0.564507	−	0.825428i	$-0.309066\pi$
$881$	994.662			1.12901			0.564507	+	0.825428i	$0.309066\pi$
$882$		0			0
$883$	74.0725	−	74.0725i	0.0838873	−	0.0838873i	−0.663918	−	0.747805i	$-0.731108\pi$
$883$	74.0725	−	74.0725i	0.0838873	−	0.0838873i	0.747805	+	0.663918i	$0.231108\pi$
$884$		0			0
$885$	381.297	−	381.297i	0.430844	−	0.430844i
$886$		0			0
$887$	522.759			0.589356			0.294678	−	0.955597i	$-0.404788\pi$
$887$	522.759			0.589356			0.294678	+	0.955597i	$0.404788\pi$
$888$		0			0
$889$		−	598.520i		−	0.673251i
$890$		0			0
$891$	−728.155	−	728.155i	−0.817233	−	0.817233i
$892$		0			0
$893$	−27.8161	−	27.8161i	−0.0311491	−	0.0311491i
$894$		0			0
$895$			182.656i			0.204085i
$896$		0			0
$897$	84.1619			0.0938260
$898$		0			0
$899$	469.615	−	469.615i	0.522375	−	0.522375i
$900$		0			0
$901$	−477.646	+	477.646i	−0.530129	+	0.530129i
$902$		0			0
$903$	21.8198			0.0241637
$904$		0			0
$905$			1556.16i			1.71951i
$906$		0			0
$907$	442.760	+	442.760i	0.488159	+	0.488159i	0.907725	−	0.419566i	$-0.137818\pi$
$907$	442.760	+	442.760i	0.488159	+	0.488159i	−0.419566	+	0.907725i	$0.637818\pi$
$908$		0			0
$909$	−4.30376	−	4.30376i	−0.00473461	−	0.00473461i
$910$		0			0
$911$			835.738i			0.917385i	0.888595	+	0.458692i	$0.151682\pi$
$911$			835.738i			0.917385i	−0.888595	+	0.458692i	$0.848318\pi$
$912$		0			0
$913$	−1371.37			−1.50205
$914$		0			0
$915$	−325.467	+	325.467i	−0.355702	+	0.355702i
$916$		0			0
$917$	−54.7082	+	54.7082i	−0.0596599	+	0.0596599i
$918$		0			0
$919$	−776.423			−0.844856			−0.422428	−	0.906396i	$-0.638822\pi$
$919$	−776.423			−0.844856			−0.422428	+	0.906396i	$0.638822\pi$
$920$		0			0
$921$			972.260i			1.05566i
$922$		0			0
$923$	779.372	+	779.372i	0.844390	+	0.844390i
$924$		0			0
$925$	−1.73295	−	1.73295i	−0.00187346	−	0.00187346i
$926$		0			0
$927$		−	16.1189i		−	0.0173883i
$928$		0			0
$929$	−144.945			−0.156022			−0.0780112	−	0.996952i	$-0.524857\pi$
$929$	−144.945			−0.156022			−0.0780112	+	0.996952i	$0.524857\pi$
$930$		0			0
$931$	45.7256	−	45.7256i	0.0491145	−	0.0491145i
$932$		0			0
$933$	1079.41	−	1079.41i	1.15693	−	1.15693i
$934$		0			0
$935$	−1496.15			−1.60016
$936$		0			0
$937$		−	851.499i		−	0.908750i	−0.890811	−	0.454375i	$-0.849863\pi$
$937$		−	851.499i		−	0.908750i	0.890811	−	0.454375i	$-0.150137\pi$
$938$		0			0
$939$	725.966	+	725.966i	0.773127	+	0.773127i
$940$		0			0
$941$	−1251.60	−	1251.60i	−1.33008	−	1.33008i	−0.905297	−	0.424778i	$-0.860352\pi$
$941$	−1251.60	−	1251.60i	−1.33008	−	1.33008i	−0.424778	−	0.905297i	$-0.639648\pi$
$942$		0			0
$943$			178.281i			0.189057i
$944$		0			0
$945$	−543.275			−0.574894
$946$		0			0
$947$	919.818	−	919.818i	0.971296	−	0.971296i	−0.0283032	−	0.999599i	$-0.509010\pi$
$947$	919.818	−	919.818i	0.971296	−	0.971296i	0.999599	+	0.0283032i	$0.00901039\pi$
$948$		0			0
$949$	649.009	−	649.009i	0.683887	−	0.683887i
$950$		0			0
$951$	−1453.57			−1.52847
$952$		0			0
$953$			489.450i			0.513589i	0.966466	+	0.256794i	$0.0826663\pi$
$953$			489.450i			0.513589i	−0.966466	+	0.256794i	$0.917334\pi$
$954$		0			0
$955$	−908.362	−	908.362i	−0.951164	−	0.951164i
$956$		0			0
$957$	469.357	+	469.357i	0.490447	+	0.490447i
$958$		0			0
$959$			157.688i			0.164429i
$960$		0			0
$961$	−521.932			−0.543113
$962$		0			0
$963$	12.4807	−	12.4807i	0.0129603	−	0.0129603i
$964$		0			0
$965$	−186.800	+	186.800i	−0.193575	+	0.193575i
$966$		0			0
$967$	1368.49			1.41519			0.707594	−	0.706619i	$-0.249780\pi$
$967$	1368.49			1.41519			0.707594	+	0.706619i	$0.249780\pi$
$968$		0			0
$969$			85.5599i			0.0882971i
$970$		0			0
$971$	−1013.79	−	1013.79i	−1.04407	−	1.04407i	−0.998983	−	0.0450900i	$-0.985643\pi$
$971$	−1013.79	−	1013.79i	−1.04407	−	1.04407i	−0.0450900	−	0.998983i	$-0.514357\pi$
$972$		0			0
$973$	53.2455	+	53.2455i	0.0547230	+	0.0547230i
$974$		0			0
$975$		−	433.515i		−	0.444631i
$976$		0			0
$977$	−5.19534			−0.00531765			−0.00265882	−	0.999996i	$-0.500846\pi$
$977$	−5.19534			−0.00531765			−0.00265882	+	0.999996i	$0.500846\pi$
$978$		0			0
$979$	287.616	−	287.616i	0.293785	−	0.293785i
$980$		0			0
$981$	19.6482	−	19.6482i	0.0200288	−	0.0200288i
$982$		0			0
$983$	1591.90			1.61943			0.809714	−	0.586825i	$-0.199622\pi$
$983$	1591.90			1.61943			0.809714	+	0.586825i	$0.199622\pi$
$984$		0			0
$985$		−	2133.87i		−	2.16636i
$986$		0			0
$987$	−154.849	−	154.849i	−0.156888	−	0.156888i
$988$		0			0
$989$	−5.88792	−	5.88792i	−0.00595340	−	0.00595340i
$990$		0			0
$991$			622.896i			0.628553i	0.949331	+	0.314277i	$0.101762\pi$
$991$			622.896i			0.628553i	−0.949331	+	0.314277i	$0.898238\pi$
$992$		0			0
$993$	1791.43			1.80406
$994$		0			0
$995$	−284.850	+	284.850i	−0.286282	+	0.286282i
$996$		0			0
$997$	635.503	−	635.503i	0.637415	−	0.637415i	−0.312502	−	0.949917i	$-0.601167\pi$
$997$	635.503	−	635.503i	0.637415	−	0.637415i	0.949917	+	0.312502i	$0.101167\pi$
$998$		0			0
$999$	3.74443			0.00374818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.f.a.95.3		6
3.2	odd	2		1152.3.m.b.991.1		6
4.3	odd	2		128.3.f.b.95.1		6
8.3	odd	2		16.3.f.a.3.1	✓	6
8.5	even	2		64.3.f.a.47.1		6
12.11	even	2		1152.3.m.a.991.1		6
16.3	odd	4		64.3.f.a.15.1		6
16.5	even	4		128.3.f.b.31.1		6
16.11	odd	4	inner	128.3.f.a.31.3		6
16.13	even	4		16.3.f.a.11.1	yes	6
24.5	odd	2		576.3.m.a.559.3		6
24.11	even	2		144.3.m.a.19.3		6
32.3	odd	8		1024.3.d.k.511.4		12
32.5	even	8		1024.3.c.j.1023.10		12
32.11	odd	8		1024.3.c.j.1023.9		12
32.13	even	8		1024.3.d.k.511.3		12
32.19	odd	8		1024.3.d.k.511.9		12
32.21	even	8		1024.3.c.j.1023.3		12
32.27	odd	8		1024.3.c.j.1023.4		12
32.29	even	8		1024.3.d.k.511.10		12
40.3	even	4		400.3.k.c.99.2		6
40.19	odd	2		400.3.r.c.51.3		6
40.27	even	4		400.3.k.d.99.2		6
48.5	odd	4		1152.3.m.a.415.1		6
48.11	even	4		1152.3.m.b.415.1		6
48.29	odd	4		144.3.m.a.91.3		6
48.35	even	4		576.3.m.a.271.3		6
80.13	odd	4		400.3.k.d.299.2		6
80.29	even	4		400.3.r.c.251.3		6
80.77	odd	4		400.3.k.c.299.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.1	✓	6	8.3	odd	2
16.3.f.a.11.1	yes	6	16.13	even	4
64.3.f.a.15.1		6	16.3	odd	4
64.3.f.a.47.1		6	8.5	even	2
128.3.f.a.31.3		6	16.11	odd	4	inner
128.3.f.a.95.3		6	1.1	even	1	trivial
128.3.f.b.31.1		6	16.5	even	4
128.3.f.b.95.1		6	4.3	odd	2
144.3.m.a.19.3		6	24.11	even	2
144.3.m.a.91.3		6	48.29	odd	4
400.3.k.c.99.2		6	40.3	even	4
400.3.k.c.299.2		6	80.77	odd	4
400.3.k.d.99.2		6	40.27	even	4
400.3.k.d.299.2		6	80.13	odd	4
400.3.r.c.51.3		6	40.19	odd	2
400.3.r.c.251.3		6	80.29	even	4
576.3.m.a.271.3		6	48.35	even	4
576.3.m.a.559.3		6	24.5	odd	2
1024.3.c.j.1023.3		12	32.21	even	8
1024.3.c.j.1023.4		12	32.27	odd	8
1024.3.c.j.1023.9		12	32.11	odd	8
1024.3.c.j.1023.10		12	32.5	even	8
1024.3.d.k.511.3		12	32.13	even	8
1024.3.d.k.511.4		12	32.3	odd	8
1024.3.d.k.511.9		12	32.19	odd	8
1024.3.d.k.511.10		12	32.29	even	8
1152.3.m.a.415.1		6	48.5	odd	4
1152.3.m.a.991.1		6	12.11	even	2
1152.3.m.b.415.1		6	48.11	even	4
1152.3.m.b.991.1		6	3.2	odd	2

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.10278 - 2.10278i) q^{3} +(4.62721 - 4.62721i) q^{5} -3.04888 q^{7} +0.156674i q^{9} +O(q^{10})\)	\(q+(2.10278 - 2.10278i) q^{3} +(4.62721 - 4.62721i) q^{5} -3.04888 q^{7} +0.156674i q^{9} +(-9.15165 - 9.15165i) q^{11} +(5.78389 + 5.78389i) q^{13} -19.4600i q^{15} +17.6655 q^{17} +(-1.15165 + 1.15165i) q^{19} +(-6.41110 + 6.41110i) q^{21} +3.45998 q^{23} -17.8222i q^{25} +(19.2544 + 19.2544i) q^{27} +(-12.1950 - 12.1950i) q^{29} +38.5089i q^{31} -38.4877 q^{33} +(-14.1078 + 14.1078i) q^{35} +(0.0972356 - 0.0972356i) q^{37} +24.3244 q^{39} +51.5266i q^{41} +(-1.70172 - 1.70172i) q^{43} +(0.724965 + 0.724965i) q^{45} +24.1533i q^{47} -39.7044 q^{49} +(37.1466 - 37.1466i) q^{51} +(-27.0383 + 27.0383i) q^{53} -84.6933 q^{55} +4.84333i q^{57} +(19.5939 + 19.5939i) q^{59} +(-16.7250 - 16.7250i) q^{61} -0.477680i q^{63} +53.5266 q^{65} +(-75.8560 + 75.8560i) q^{67} +(7.27555 - 7.27555i) q^{69} +134.749 q^{71} -112.210i q^{73} +(-37.4761 - 37.4761i) q^{75} +(27.9022 + 27.9022i) q^{77} -135.915i q^{79} +79.5654 q^{81} +(74.9250 - 74.9250i) q^{83} +(81.7422 - 81.7422i) q^{85} -51.2866 q^{87} +31.4278i q^{89} +(-17.6344 - 17.6344i) q^{91} +(80.9755 + 80.9755i) q^{93} +10.6579i q^{95} +31.5456 q^{97} +(1.43383 - 1.43383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{3} + 2 q^{5} + 4 q^{7}+O(q^{10}) \) 6 * q - 2 * q^3 + 2 * q^5 + 4 * q^7	\( 6 q - 2 q^{3} + 2 q^{5} + 4 q^{7} - 18 q^{11} + 2 q^{13} - 4 q^{17} + 30 q^{19} + 20 q^{21} - 60 q^{23} + 64 q^{27} + 18 q^{29} - 4 q^{33} - 100 q^{35} - 46 q^{37} + 196 q^{39} - 114 q^{43} - 66 q^{45} - 46 q^{49} + 156 q^{51} - 78 q^{53} - 252 q^{55} + 206 q^{59} - 30 q^{61} + 12 q^{65} - 226 q^{67} + 116 q^{69} + 260 q^{71} - 238 q^{75} + 212 q^{77} + 86 q^{81} + 318 q^{83} + 212 q^{85} - 444 q^{87} + 188 q^{91} + 32 q^{93} - 4 q^{97} - 226 q^{99}+O(q^{100}) \) 6 * q - 2 * q^3 + 2 * q^5 + 4 * q^7 - 18 * q^11 + 2 * q^13 - 4 * q^17 + 30 * q^19 + 20 * q^21 - 60 * q^23 + 64 * q^27 + 18 * q^29 - 4 * q^33 - 100 * q^35 - 46 * q^37 + 196 * q^39 - 114 * q^43 - 66 * q^45 - 46 * q^49 + 156 * q^51 - 78 * q^53 - 252 * q^55 + 206 * q^59 - 30 * q^61 + 12 * q^65 - 226 * q^67 + 116 * q^69 + 260 * q^71 - 238 * q^75 + 212 * q^77 + 86 * q^81 + 318 * q^83 + 212 * q^85 - 444 * q^87 + 188 * q^91 + 32 * q^93 - 4 * q^97 - 226 * q^99

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