LMFDB - Embedded newform 64.3.f.a.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,3,Mod(15,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, 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("64.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	64.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:	$1.74387369191$
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			47.1
Root			$1.40680 + 0.144584i$ of defining polynomial
Character	$\chi$	$=$	64.47
Dual form			64.3.f.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10278 + 2.10278i) q^{3} +(-4.62721 + 4.62721i) q^{5} -3.04888 q^{7} +0.156674i q^{9} +O(q^{10})$	\(q+(-2.10278 + 2.10278i) q^{3} +(-4.62721 + 4.62721i) q^{5} -3.04888 q^{7} +0.156674i q^{9} +(9.15165 + 9.15165i) q^{11} +(-5.78389 - 5.78389i) q^{13} -19.4600i q^{15} +17.6655 q^{17} +(1.15165 - 1.15165i) q^{19} +(6.41110 - 6.41110i) q^{21} +3.45998 q^{23} -17.8222i q^{25} +(-19.2544 - 19.2544i) q^{27} +(12.1950 + 12.1950i) q^{29} +38.5089i q^{31} -38.4877 q^{33} +(14.1078 - 14.1078i) q^{35} +(-0.0972356 + 0.0972356i) q^{37} +24.3244 q^{39} +51.5266i q^{41} +(1.70172 + 1.70172i) q^{43} +(-0.724965 - 0.724965i) q^{45} +24.1533i q^{47} -39.7044 q^{49} +(-37.1466 + 37.1466i) q^{51} +(27.0383 - 27.0383i) q^{53} -84.6933 q^{55} +4.84333i q^{57} +(-19.5939 - 19.5939i) q^{59} +(16.7250 + 16.7250i) q^{61} -0.477680i q^{63} +53.5266 q^{65} +(75.8560 - 75.8560i) q^{67} +(-7.27555 + 7.27555i) q^{69} +134.749 q^{71} -112.210i q^{73} +(37.4761 + 37.4761i) q^{75} +(-27.9022 - 27.9022i) q^{77} -135.915i q^{79} +79.5654 q^{81} +(-74.9250 + 74.9250i) q^{83} +(-81.7422 + 81.7422i) q^{85} -51.2866 q^{87} +31.4278i q^{89} +(17.6344 + 17.6344i) q^{91} +(-80.9755 - 80.9755i) q^{93} +10.6579i q^{95} +31.5456 q^{97} +(-1.43383 + 1.43383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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	−0.964609	−	0.263684i	$-0.915062\pi$
$3$	−2.10278	+	2.10278i	−0.700925	+	0.700925i	0.263684	+	0.964609i	$0.415062\pi$
$4$		0			0
$5$	−4.62721	+	4.62721i	−0.925443	+	0.925443i	−0.997407	−	0.0719646i	$-0.977073\pi$
$5$	−4.62721	+	4.62721i	−0.925443	+	0.925443i	0.0719646	+	0.997407i	$0.477073\pi$
$6$		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	0.987786	−	0.155818i	$-0.0498012\pi$
$11$	9.15165	+	9.15165i	0.831968	+	0.831968i	−0.155818	+	0.987786i	$0.549801\pi$
$12$		0			0
$13$	−5.78389	−	5.78389i	−0.444914	−	0.444914i	0.448745	−	0.893660i	$-0.351871\pi$
$13$	−5.78389	−	5.78389i	−0.444914	−	0.444914i	−0.893660	+	0.448745i	$0.851871\pi$
$14$		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	−0.676150	−	0.736764i	$-0.736353\pi$
$19$	1.15165	−	1.15165i	0.0606132	−	0.0606132i	0.736764	+	0.676150i	$0.236353\pi$
$20$		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	0.885382	−	0.464865i	$-0.153897\pi$
$29$	12.1950	+	12.1950i	0.420517	+	0.420517i	−0.464865	+	0.885382i	$0.653897\pi$
$30$		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	−0.708420	−	0.705792i	$-0.750592\pi$
$37$	−0.0972356	+	0.0972356i	−0.00262799	+	0.00262799i	0.705792	+	0.708420i	$0.250592\pi$
$38$		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	0.726617	−	0.687042i	$-0.241091\pi$
$43$	1.70172	+	1.70172i	0.0395749	+	0.0395749i	−0.687042	+	0.726617i	$0.741091\pi$
$44$		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	−0.404418	−	0.914574i	$-0.632526\pi$
$53$	27.0383	−	27.0383i	0.510157	−	0.510157i	0.914574	+	0.404418i	$0.132526\pi$
$54$		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	0.521283	−	0.853384i	$-0.325453\pi$
$59$	−19.5939	−	19.5939i	−0.332100	−	0.332100i	−0.853384	+	0.521283i	$0.825453\pi$
$60$		0			0
$61$	16.7250	+	16.7250i	0.274180	+	0.274180i	0.830780	−	0.556601i	$-0.187895\pi$
$61$	16.7250	+	16.7250i	0.274180	+	0.274180i	−0.556601	+	0.830780i	$0.687895\pi$
$62$		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	$-0.454529\pi$
$67$	75.8560	−	75.8560i	1.13218	−	1.13218i	0.989814	−	0.142365i	$-0.0454707\pi$
$68$		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	−0.995670	−	0.0929594i	$-0.970367\pi$
$83$	−74.9250	+	74.9250i	−0.902711	+	0.902711i	0.0929594	+	0.995670i	$0.470367\pi$
$84$		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	−0.557920	−	0.829895i	$-0.688400\pi$
$101$	27.4695	−	27.4695i	0.271975	−	0.271975i	0.829895	+	0.557920i	$0.188400\pi$
$102$		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	0.973439	−	0.228948i	$-0.0735286\pi$
$107$	79.6605	+	79.6605i	0.744491	+	0.744491i	−0.228948	+	0.973439i	$0.573529\pi$
$108$		0			0
$109$	125.408	+	125.408i	1.15053	+	1.15053i	0.986446	+	0.164088i	$0.0524682\pi$
$109$	125.408	+	125.408i	1.15053	+	1.15053i	0.164088	+	0.986446i	$0.447532\pi$
$110$		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	−0.772270	−	0.635295i	$-0.780879\pi$
$131$	−17.9437	+	17.9437i	−0.136975	+	0.136975i	0.635295	+	0.772270i	$0.280879\pi$
$132$		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	0.767131	−	0.641491i	$-0.221684\pi$
$139$	17.4640	+	17.4640i	0.125640	+	0.125640i	−0.641491	+	0.767131i	$0.721684\pi$
$140$		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	−0.665985	−	0.745965i	$-0.731989\pi$
$149$	11.9170	−	11.9170i	0.0799802	−	0.0799802i	0.745965	+	0.665985i	$0.231989\pi$
$150$		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	0.959034	−	0.283292i	$-0.0914266\pi$
$157$	106.091	+	106.091i	0.675742	+	0.675742i	−0.283292	+	0.959034i	$0.591427\pi$
$158$		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	−0.304728	−	0.952440i	$-0.598565\pi$
$163$	105.577	−	105.577i	0.647712	−	0.647712i	0.952440	+	0.304728i	$0.0985654\pi$
$164$		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	0.747870	−	0.663845i	$-0.231077\pi$
$173$	14.5363	+	14.5363i	0.0840249	+	0.0840249i	−0.663845	+	0.747870i	$0.731077\pi$
$174$		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	−0.649823	−	0.760086i	$-0.725157\pi$
$179$	19.7371	−	19.7371i	0.110263	−	0.110263i	0.760086	+	0.649823i	$0.225157\pi$
$180$		0			0
$181$	168.153	−	168.153i	0.929021	−	0.929021i	−0.0686221	−	0.997643i	$-0.521860\pi$
$181$	168.153	−	168.153i	0.929021	−	0.929021i	0.997643	+	0.0686221i	$0.0218603\pi$
$182$		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	$0.560312\pi$
$197$	−230.578	+	230.578i	−1.17045	+	1.17045i	−0.982103	+	0.188344i	$0.939688\pi$
$198$		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	−0.967855	−	0.251509i	$-0.919073\pi$
$211$	−151.149	+	151.149i	−0.716346	+	0.716346i	0.251509	+	0.967855i	$0.419073\pi$
$212$		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	−0.760505	−	0.649332i	$-0.775049\pi$
$227$	−25.2363	+	25.2363i	−0.111173	+	0.111173i	0.649332	+	0.760505i	$0.275049\pi$
$228$		0			0
$229$	−155.318	+	155.318i	−0.678244	+	0.678244i	−0.959603	−	0.281359i	$-0.909215\pi$
$229$	−155.318	+	155.318i	−0.678244	+	0.678244i	0.281359	+	0.959603i	$0.409215\pi$
$230$		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	0.753329	−	0.657643i	$-0.228447\pi$
$251$	24.0171	+	24.0171i	0.0956858	+	0.0956858i	−0.657643	+	0.753329i	$0.728447\pi$
$252$		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	0.0444453	−	0.999012i	$-0.485848\pi$
$269$	−256.778	−	256.778i	−0.954567	−	0.954567i	−0.999012	+	0.0444453i	$0.985848\pi$
$270$		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	−0.554102	−	0.832449i	$-0.686938\pi$
$277$	77.1023	−	77.1023i	0.278348	−	0.278348i	0.832449	+	0.554102i	$0.186938\pi$
$278$		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	0.819056	−	0.573714i	$-0.194498\pi$
$283$	69.4317	+	69.4317i	0.245342	+	0.245342i	−0.573714	+	0.819056i	$0.694498\pi$
$284$		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	−0.167103	−	0.985939i	$-0.553441\pi$
$293$	239.919	−	239.919i	0.818837	−	0.818837i	0.985939	+	0.167103i	$0.0534412\pi$
$294$		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	−0.222001	−	0.975046i	$-0.571259\pi$
$307$	231.185	−	231.185i	0.753046	−	0.753046i	0.975046	+	0.222001i	$0.0712588\pi$
$308$		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	$0.0302304\pi$
$317$	345.632	+	345.632i	1.09032	+	1.09032i	0.0948290	+	0.995494i	$0.469770\pi$
$318$		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	$-0.886093\pi$
$331$	−425.968	−	425.968i	−1.28691	−	1.28691i	−0.350261	−	0.936652i	$-0.613907\pi$
$332$		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	0.738160	−	0.674626i	$-0.235695\pi$
$347$	22.0463	+	22.0463i	0.0635341	+	0.0635341i	−0.674626	+	0.738160i	$0.735695\pi$
$348$		0			0
$349$	−158.622	−	158.622i	−0.454506	−	0.454506i	0.442341	−	0.896847i	$-0.354148\pi$
$349$	−158.622	−	158.622i	−0.454506	−	0.454506i	−0.896847	+	0.442341i	$0.854148\pi$
$350$		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	−0.540490	−	0.841350i	$-0.681761\pi$
$373$	112.221	−	112.221i	0.300860	−	0.300860i	0.841350	+	0.540490i	$0.181761\pi$
$374$		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	0.634870	−	0.772619i	$-0.281054\pi$
$379$	−52.2069	−	52.2069i	−0.137749	−	0.137749i	−0.772619	+	0.634870i	$0.781054\pi$
$380$		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	−0.776617	−	0.629974i	$-0.783066\pi$
$389$	−57.0441	+	57.0441i	−0.146643	+	0.146643i	0.629974	+	0.776617i	$0.283066\pi$
$390$		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	0.0987089	−	0.995116i	$-0.468529\pi$
$397$	−355.874	−	355.874i	−0.896407	−	0.896407i	−0.995116	+	0.0987089i	$0.968529\pi$
$398$		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	−0.108687	−	0.994076i	$-0.534665\pi$
$419$	370.978	−	370.978i	0.885389	−	0.885389i	0.994076	+	0.108687i	$0.0346647\pi$
$420$		0			0
$421$	465.112	−	465.112i	1.10478	−	1.10478i	0.110955	−	0.993825i	$-0.464609\pi$
$421$	465.112	−	465.112i	1.10478	−	1.10478i	0.993825	−	0.110955i	$-0.0353908\pi$
$422$		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	0.957859	−	0.287240i	$-0.0927377\pi$
$443$	297.084	+	297.084i	0.670619	+	0.670619i	−0.287240	+	0.957859i	$0.592738\pi$
$444$		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	0.398031	−	0.917372i	$-0.369694\pi$
$461$	−239.416	−	239.416i	−0.519341	−	0.519341i	−0.917372	+	0.398031i	$0.869694\pi$
$462$		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	−0.991772	−	0.128015i	$-0.959140\pi$
$467$	−403.375	+	403.375i	−0.863758	+	0.863758i	0.128015	+	0.991772i	$0.459140\pi$
$468$		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	0.374520	−	0.927219i	$-0.377808\pi$
$491$	−271.375	−	271.375i	−0.552699	−	0.552699i	−0.927219	+	0.374520i	$0.877808\pi$
$492$		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	−0.922717	−	0.385478i	$-0.874037\pi$
$499$	−268.082	+	268.082i	−0.537239	+	0.537239i	0.385478	+	0.922717i	$0.374037\pi$
$500$		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	0.936297	−	0.351210i	$-0.114230\pi$
$509$	297.809	+	297.809i	0.585087	+	0.585087i	−0.351210	+	0.936297i	$0.614230\pi$
$510$		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	0.904734	−	0.425978i	$-0.140070\pi$
$523$	250.389	+	250.389i	0.478756	+	0.478756i	−0.425978	+	0.904734i	$0.640070\pi$
$524$		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	0.627554	−	0.778573i	$-0.284056\pi$
$541$	−81.7015	−	81.7015i	−0.151019	−	0.151019i	−0.778573	+	0.627554i	$0.784056\pi$
$542$		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	−0.266901	−	0.963724i	$-0.586000\pi$
$547$	381.162	−	381.162i	0.696823	−	0.696823i	0.963724	+	0.266901i	$0.0859996\pi$
$548$		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	0.647548	−	0.762025i	$-0.275794\pi$
$557$	−63.7634	−	63.7634i	−0.114476	−	0.114476i	−0.762025	+	0.647548i	$0.775794\pi$
$558$		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	−0.938355	−	0.345674i	$-0.887650\pi$
$563$	−333.679	+	333.679i	−0.592681	+	0.592681i	0.345674	+	0.938355i	$0.387650\pi$
$564$		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	0.513239	−	0.858246i	$-0.328445\pi$
$571$	−196.999	−	196.999i	−0.345007	−	0.345007i	−0.858246	+	0.513239i	$0.828445\pi$
$572$		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	0.370108	−	0.928989i	$-0.379321\pi$
$587$	−328.063	−	328.063i	−0.558880	−	0.558880i	−0.928989	+	0.370108i	$0.879321\pi$
$588$		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	−0.566770	−	0.823876i	$-0.691807\pi$
$613$	157.606	−	157.606i	0.257106	−	0.257106i	0.823876	+	0.566770i	$0.191807\pi$
$614$		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	0.983679	−	0.179932i	$-0.0575878\pi$
$619$	497.519	+	497.519i	0.803747	+	0.803747i	−0.179932	+	0.983679i	$0.557588\pi$
$620$		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	−0.590919	−	0.806731i	$-0.701235\pi$
$643$	138.767	−	138.767i	0.215813	−	0.215813i	0.806731	+	0.590919i	$0.201235\pi$
$644$		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	0.270173	−	0.962812i	$-0.412919\pi$
$653$	−452.293	−	452.293i	−0.692639	−	0.692639i	−0.962812	+	0.270173i	$0.912919\pi$
$654$		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	−0.935169	−	0.354201i	$-0.884753\pi$
$659$	−382.858	+	382.858i	−0.580969	+	0.580969i	0.354201	+	0.935169i	$0.384753\pi$
$660$		0			0
$661$	−841.606	+	841.606i	−1.27323	+	1.27323i	−0.328849	+	0.944383i	$0.606661\pi$
$661$	−841.606	+	841.606i	−1.27323	+	1.27323i	−0.944383	+	0.328849i	$0.893339\pi$
$662$		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	−0.949656	−	0.313295i	$-0.898567\pi$
$677$	−430.816	+	430.816i	−0.636361	+	0.636361i	0.313295	+	0.949656i	$0.398567\pi$
$678$		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	$0.141251\pi$
$683$	910.083	+	910.083i	1.33248	+	1.33248i	0.429333	+	0.903146i	$0.358749\pi$
$684$		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	−0.121614	−	0.992577i	$-0.538807\pi$
$691$	601.836	−	601.836i	0.870964	−	0.870964i	0.992577	+	0.121614i	$0.0388070\pi$
$692$		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	0.189639	−	0.981854i	$-0.439268\pi$
$701$	−555.343	−	555.343i	−0.792215	−	0.792215i	−0.981854	+	0.189639i	$0.939268\pi$
$702$		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	−0.935584	−	0.353104i	$-0.885126\pi$
$709$	−412.979	+	412.979i	−0.582480	+	0.582480i	0.353104	+	0.935584i	$0.385126\pi$
$710$		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	0.898510	−	0.438954i	$-0.144651\pi$
$733$	336.854	+	336.854i	0.459556	+	0.459556i	−0.438954	+	0.898510i	$0.644651\pi$
$734$		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	−0.817476	−	0.575963i	$-0.804627\pi$
$739$	−178.478	+	178.478i	−0.241513	+	0.241513i	0.575963	+	0.817476i	$0.304627\pi$
$740$		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	−0.674255	−	0.738499i	$-0.735535\pi$
$757$	48.6324	−	48.6324i	0.0642436	−	0.0642436i	0.738499	+	0.674255i	$0.235535\pi$
$758$		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	−0.812989	−	0.582279i	$-0.802161\pi$
$773$	−178.338	+	178.338i	−0.230710	+	0.230710i	0.582279	+	0.812989i	$0.302161\pi$
$774$		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	−0.332090	−	0.943248i	$-0.607754\pi$
$787$	480.981	−	480.981i	0.611158	−	0.611158i	0.943248	+	0.332090i	$0.107754\pi$
$788$		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	0.263841	−	0.964566i	$-0.415011\pi$
$797$	−558.478	−	558.478i	−0.700725	−	0.700725i	−0.964566	+	0.263841i	$0.915011\pi$
$798$		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	0.445404	−	0.895330i	$-0.353060\pi$
$811$	−364.890	−	364.890i	−0.449926	−	0.449926i	−0.895330	+	0.445404i	$0.853060\pi$
$812$		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	−0.975210	−	0.221282i	$-0.928976\pi$
$821$	−618.975	+	618.975i	−0.753928	+	0.753928i	0.221282	+	0.975210i	$0.428976\pi$
$822$		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	0.442511	−	0.896763i	$-0.354088\pi$
$827$	−375.666	−	375.666i	−0.454252	−	0.454252i	−0.896763	+	0.442511i	$0.854088\pi$
$828$		0			0
$829$	−299.648	−	299.648i	−0.361457	−	0.361457i	0.502892	−	0.864349i	$-0.332269\pi$
$829$	−299.648	−	299.648i	−0.361457	−	0.361457i	−0.864349	+	0.502892i	$0.832269\pi$
$830$		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	−0.429422	−	0.903104i	$-0.641283\pi$
$853$	404.051	−	404.051i	0.473682	−	0.473682i	0.903104	+	0.429422i	$0.141283\pi$
$854$		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	0.892193	−	0.451654i	$-0.149166\pi$
$859$	378.424	+	378.424i	0.440540	+	0.440540i	−0.451654	+	0.892193i	$0.649166\pi$
$860$		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	0.301892	−	0.953342i	$-0.402382\pi$
$877$	−571.322	−	571.322i	−0.651450	−	0.651450i	−0.953342	+	0.301892i	$0.902382\pi$
$878$		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	−0.747805	−	0.663918i	$-0.768892\pi$
$883$	−74.0725	+	74.0725i	−0.0838873	+	0.0838873i	0.663918	+	0.747805i	$0.268892\pi$
$884$		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	0.419566	−	0.907725i	$-0.362182\pi$
$907$	−442.760	−	442.760i	−0.488159	−	0.488159i	−0.907725	+	0.419566i	$0.862182\pi$
$908$		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	$0.139648\pi$
$941$	1251.60	+	1251.60i	1.33008	+	1.33008i	0.424778	+	0.905297i	$0.360352\pi$
$942$		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	−0.999599	−	0.0283032i	$-0.990990\pi$
$947$	−919.818	+	919.818i	−0.971296	+	0.971296i	0.0283032	+	0.999599i	$0.490990\pi$
$948$		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	$0.0143575\pi$
$971$	1013.79	+	1013.79i	1.04407	+	1.04407i	0.0450900	+	0.998983i	$0.485643\pi$
$972$		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	−0.949917	−	0.312502i	$-0.898833\pi$
$997$	−635.503	+	635.503i	−0.637415	+	0.637415i	0.312502	+	0.949917i	$0.398833\pi$
$998$		0			0
$999$	3.74443			0.00374818

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.3.f.a.3.1	✓	6	4.3	odd	2
16.3.f.a.11.1	yes	6	16.5	even	4
64.3.f.a.15.1		6	16.11	odd	4	inner
64.3.f.a.47.1		6	1.1	even	1	trivial
128.3.f.a.31.3		6	16.3	odd	4
128.3.f.a.95.3		6	8.5	even	2
128.3.f.b.31.1		6	16.13	even	4
128.3.f.b.95.1		6	8.3	odd	2
144.3.m.a.19.3		6	12.11	even	2
144.3.m.a.91.3		6	48.5	odd	4
400.3.k.c.99.2		6	20.3	even	4
400.3.k.c.299.2		6	80.37	odd	4
400.3.k.d.99.2		6	20.7	even	4
400.3.k.d.299.2		6	80.53	odd	4
400.3.r.c.51.3		6	20.19	odd	2
400.3.r.c.251.3		6	80.69	even	4
576.3.m.a.271.3		6	48.11	even	4
576.3.m.a.559.3		6	3.2	odd	2
1024.3.c.j.1023.3		12	32.5	even	8
1024.3.c.j.1023.4		12	32.11	odd	8
1024.3.c.j.1023.9		12	32.27	odd	8
1024.3.c.j.1023.10		12	32.21	even	8
1024.3.d.k.511.3		12	32.29	even	8
1024.3.d.k.511.4		12	32.19	odd	8
1024.3.d.k.511.9		12	32.3	odd	8
1024.3.d.k.511.10		12	32.13	even	8
1152.3.m.a.415.1		6	48.29	odd	4
1152.3.m.a.991.1		6	24.11	even	2
1152.3.m.b.415.1		6	48.35	even	4
1152.3.m.b.991.1		6	24.5	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	64.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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more