LMFDB - Embedded newform 784.3.r.p.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,3,Mod(79,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("784.79");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	784.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.3624527258$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.259470000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 14x^{4} - x^{3} + 176x^{2} - 91x + 49 $ x^6 - x^5 + 14x^4 - x^3 + 176x^2 - 91*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.1
Root			$0.264167 + 0.457551i$ of defining polynomial
Character	$\chi$	$=$	784.79
Dual form			784.3.r.p.655.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.86043 + 2.80617i) q^{3} +(-0.0283339 + 0.0490758i) q^{5} +(11.2492 - 19.4842i) q^{9} +(-9.27543 + 5.35517i) q^{11} +12.3851 q^{13} -0.318039i q^{15} +(9.74920 + 16.8861i) q^{17} +(-5.55457 - 3.20693i) q^{19} +(25.0230 + 14.4470i) q^{23} +(12.4984 + 21.6479i) q^{25} +75.7576i q^{27} -34.4984 q^{29} +(25.1663 - 14.5298i) q^{31} +(30.0551 - 52.0569i) q^{33} +(10.0509 - 17.4086i) q^{37} +(-60.1967 + 34.7546i) q^{39} -1.27493 q^{41} +35.9132i q^{43} +(0.637467 + 1.10413i) q^{45} +(-17.1737 - 9.91525i) q^{47} +(-94.7706 - 54.7158i) q^{51} +(-26.4475 - 45.8085i) q^{53} -0.606932i q^{55} +35.9968 q^{57} +(-63.5256 + 36.6765i) q^{59} +(-11.7193 + 20.2983i) q^{61} +(-0.350917 + 0.607806i) q^{65} +(-13.4261 + 7.75157i) q^{67} -162.164 q^{69} -37.6397i q^{71} +(-36.7717 - 63.6905i) q^{73} +(-121.495 - 70.1453i) q^{75} +(-18.0787 - 10.4377i) q^{79} +(-111.346 - 192.857i) q^{81} +50.4931i q^{83} -1.10493 q^{85} +(167.677 - 96.8084i) q^{87} +(-69.0519 + 119.601i) q^{89} +(-81.5460 + 141.242i) q^{93} +(0.314765 - 0.181730i) q^{95} -143.149 q^{97} +240.966i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + q^{5} + 14 q^{9} - 33 q^{11} - 28 q^{13} + 5 q^{17} - 63 q^{19} - 33 q^{23} - 32 q^{25} - 100 q^{29} + 69 q^{31} + 71 q^{33} + 15 q^{37} - 246 q^{39} - 124 q^{41} + 62 q^{45} - 171 q^{47}+ \cdots - 124 q^{97}+O(q^{100}) $ 6 * q - 3 * q^3 + q^5 + 14 * q^9 - 33 * q^11 - 28 * q^13 + 5 * q^17 - 63 * q^19 - 33 * q^23 - 32 * q^25 - 100 * q^29 + 69 * q^31 + 71 * q^33 + 15 * q^37 - 246 * q^39 - 124 * q^41 + 62 * q^45 - 171 * q^47 - 225 * q^51 - 97 * q^53 + 2 * q^57 - 27 * q^59 + 89 * q^61 + 142 * q^65 - 309 * q^67 - 538 * q^69 - 123 * q^73 - 408 * q^75 - 201 * q^79 - 203 * q^81 - 130 * q^85 + 270 * q^87 - 91 * q^89 - 123 * q^93 - 321 * q^95 - 124 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.86043	+	2.80617i	−1.62014	+	0.935391i	−0.633264	+	0.773936i	$0.718285\pi$
$3$	−4.86043	+	2.80617i	−1.62014	+	0.935391i	−0.986880	+	0.161454i	$0.948382\pi$
$4$		0			0
$5$	−0.0283339	+	0.0490758i	−0.00566678	+	0.00981515i	−0.868845	−	0.495084i	$-0.835137\pi$
$5$	−0.0283339	+	0.0490758i	−0.00566678	+	0.00981515i	0.863178	+	0.504900i	$0.168470\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	11.2492	−	19.4842i	1.24991	−	2.16491i
$10$		0			0
$11$	−9.27543	+	5.35517i	−0.843221	+	0.486834i	−0.858358	−	0.513052i	$-0.828515\pi$
$11$	−9.27543	+	5.35517i	−0.843221	+	0.486834i	0.0151369	+	0.999885i	$0.495182\pi$
$12$		0			0
$13$	12.3851			0.952697			0.476348	−	0.879257i	$-0.341960\pi$
$13$	12.3851			0.952697			0.476348	+	0.879257i	$0.341960\pi$
$14$		0			0
$15$		−	0.318039i		−	0.0212026i
$16$		0			0
$17$	9.74920	+	16.8861i	0.573482	+	0.993300i	0.996205	+	0.0870411i	$0.0277412\pi$
$17$	9.74920	+	16.8861i	0.573482	+	0.993300i	−0.422723	+	0.906259i	$0.638926\pi$
$18$		0			0
$19$	−5.55457	−	3.20693i	−0.292346	−	0.168786i	0.346654	−	0.937993i	$-0.387318\pi$
$19$	−5.55457	−	3.20693i	−0.292346	−	0.168786i	−0.638999	+	0.769207i	$0.720651\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	25.0230	+	14.4470i	1.08796	+	0.628133i	0.933032	−	0.359794i	$-0.117153\pi$
$23$	25.0230	+	14.4470i	1.08796	+	0.628133i	0.154926	+	0.987926i	$0.450486\pi$
$24$		0			0
$25$	12.4984	+	21.6479i	0.499936	+	0.865914i
$26$		0			0
$27$			75.7576i			2.80584i
$28$		0			0
$29$	−34.4984			−1.18960			−0.594800	−	0.803874i	$-0.702769\pi$
$29$	−34.4984			−1.18960			−0.594800	+	0.803874i	$0.702769\pi$
$30$		0			0
$31$	25.1663	−	14.5298i	0.811816	−	0.468702i	−0.0357701	−	0.999360i	$-0.511388\pi$
$31$	25.1663	−	14.5298i	0.811816	−	0.468702i	0.847586	+	0.530658i	$0.178055\pi$
$32$		0			0
$33$	30.0551	−	52.0569i	0.910759	−	1.57748i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	10.0509	−	17.4086i	0.271645	−	0.470503i	−0.697638	−	0.716450i	$-0.745766\pi$
$37$	10.0509	−	17.4086i	0.271645	−	0.470503i	0.969283	+	0.245947i	$0.0790991\pi$
$38$		0			0
$39$	−60.1967	+	34.7546i	−1.54351	+	0.891144i
$40$		0			0
$41$	−1.27493			−0.0310960			−0.0155480	−	0.999879i	$-0.504949\pi$
$41$	−1.27493			−0.0310960			−0.0155480	+	0.999879i	$0.504949\pi$
$42$		0			0
$43$			35.9132i			0.835190i	0.908633	+	0.417595i	$0.137127\pi$
$43$			35.9132i			0.835190i	−0.908633	+	0.417595i	$0.862873\pi$
$44$		0			0
$45$	0.637467	+	1.10413i	0.0141659	+	0.0245361i
$46$		0			0
$47$	−17.1737	−	9.91525i	−0.365398	−	0.210963i	0.306048	−	0.952016i	$-0.400993\pi$
$47$	−17.1737	−	9.91525i	−0.365398	−	0.210963i	−0.671446	+	0.741053i	$0.734327\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−94.7706	−	54.7158i	−1.85825	−	1.07286i
$52$		0			0
$53$	−26.4475	−	45.8085i	−0.499010	−	0.864311i	0.500989	−	0.865453i	$-0.332970\pi$
$53$	−26.4475	−	45.8085i	−0.499010	−	0.864311i	−0.999999	+	0.00114268i	$0.999636\pi$
$54$		0			0
$55$		−	0.606932i		−	0.0110351i
$56$		0			0
$57$	35.9968			0.631523
$58$		0			0
$59$	−63.5256	+	36.6765i	−1.07671	+	0.621636i	−0.930006	−	0.367545i	$-0.880198\pi$
$59$	−63.5256	+	36.6765i	−1.07671	+	0.621636i	−0.146700	+	0.989181i	$0.546865\pi$
$60$		0			0
$61$	−11.7193	+	20.2983i	−0.192119	+	0.332760i	−0.945952	−	0.324306i	$-0.894869\pi$
$61$	−11.7193	+	20.2983i	−0.192119	+	0.332760i	0.753833	+	0.657066i	$0.228203\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.350917	+	0.607806i	−0.00539872	+	0.00935086i
$66$		0			0
$67$	−13.4261	+	7.75157i	−0.200390	+	0.115695i	−0.596837	−	0.802362i	$-0.703576\pi$
$67$	−13.4261	+	7.75157i	−0.200390	+	0.115695i	0.396447	+	0.918057i	$0.370243\pi$
$68$		0			0
$69$	−162.164			−2.35020
$70$		0			0
$71$		−	37.6397i		−	0.530136i	−0.964230	−	0.265068i	$-0.914606\pi$
$71$		−	37.6397i		−	0.530136i	0.964230	−	0.265068i	$-0.0853944\pi$
$72$		0			0
$73$	−36.7717	−	63.6905i	−0.503722	−	0.872473i	−0.999991	−	0.00430341i	$-0.998630\pi$
$73$	−36.7717	−	63.6905i	−0.503722	−	0.872473i	0.496269	−	0.868169i	$-0.334703\pi$
$74$		0			0
$75$	−121.495	−	70.1453i	−1.61994	−	0.935270i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−18.0787	−	10.4377i	−0.228844	−	0.132123i	0.381195	−	0.924495i	$-0.375513\pi$
$79$	−18.0787	−	10.4377i	−0.228844	−	0.132123i	−0.610039	+	0.792372i	$0.708846\pi$
$80$		0			0
$81$	−111.346	−	192.857i	−1.37464	−	2.38095i
$82$		0			0
$83$			50.4931i			0.608350i	0.952616	+	0.304175i	$0.0983808\pi$
$83$			50.4931i			0.608350i	−0.952616	+	0.304175i	$0.901619\pi$
$84$		0			0
$85$	−1.10493			−0.0129992
$86$		0			0
$87$	167.677	−	96.8084i	1.92732	−	1.11274i
$88$		0			0
$89$	−69.0519	+	119.601i	−0.775863	+	1.34383i	0.158444	+	0.987368i	$0.449352\pi$
$89$	−69.0519	+	119.601i	−0.775863	+	1.34383i	−0.934308	+	0.356467i	$0.883981\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−81.5460	+	141.242i	−0.876839	+	1.51873i
$94$		0			0
$95$	0.314765	−	0.181730i	0.00331332	−	0.00191294i
$96$		0			0
$97$	−143.149			−1.47576			−0.737880	−	0.674932i	$-0.764173\pi$
$97$	−143.149			−1.47576			−0.737880	+	0.674932i	$0.764173\pi$
$98$		0			0
$99$			240.966i			2.43400i
$100$		0			0
$101$	61.6401	+	106.764i	0.610298	+	1.05707i	0.991190	+	0.132447i	$0.0422835\pi$
$101$	61.6401	+	106.764i	0.610298	+	1.05707i	−0.380892	+	0.924619i	$0.624383\pi$
$102$		0			0
$103$	−36.2896	−	20.9518i	−0.352326	−	0.203415i	0.313383	−	0.949627i	$-0.398538\pi$
$103$	−36.2896	−	20.9518i	−0.352326	−	0.203415i	−0.665709	+	0.746211i	$0.731871\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−58.7706	−	33.9312i	−0.549258	−	0.317114i	0.199565	−	0.979885i	$-0.436047\pi$
$107$	−58.7706	−	33.9312i	−0.549258	−	0.317114i	−0.748823	+	0.662770i	$0.769381\pi$
$108$		0			0
$109$	46.1951	+	80.0123i	0.423808	+	0.734058i	0.996308	−	0.0858470i	$-0.0273596\pi$
$109$	46.1951	+	80.0123i	0.423808	+	0.734058i	−0.572500	+	0.819905i	$0.694026\pi$
$110$		0			0
$111$			112.818i			1.01638i
$112$		0			0
$113$	−95.2853			−0.843233			−0.421616	−	0.906774i	$-0.638537\pi$
$113$	−95.2853			−0.843233			−0.421616	+	0.906774i	$0.638537\pi$
$114$		0			0
$115$	−1.41800	+	0.818682i	−0.0123304	+	0.00711898i
$116$		0			0
$117$	139.322	−	241.313i	1.19079	−	2.06250i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.14427	+	5.44603i	−0.0259857	+	0.0450085i
$122$		0			0
$123$	6.19673	−	3.57768i	0.0503799	−	0.0290869i
$124$		0			0
$125$	−2.83321			−0.0226657
$126$		0			0
$127$		−	218.682i		−	1.72190i	−0.508688	−	0.860951i	$-0.669869\pi$
$127$		−	218.682i		−	1.72190i	0.508688	−	0.860951i	$-0.330131\pi$
$128$		0			0
$129$	−100.779	−	174.554i	−0.781229	−	1.35313i
$130$		0			0
$131$	38.8678	+	22.4404i	0.296701	+	0.171300i	0.640960	−	0.767574i	$-0.278536\pi$
$131$	38.8678	+	22.4404i	0.296701	+	0.171300i	−0.344259	+	0.938875i	$0.611870\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.71786	−	2.14651i	−0.0275397	−	0.0159001i
$136$		0			0
$137$	51.3461	+	88.9341i	0.374789	+	0.649154i	0.990295	−	0.138978i	$-0.0443818\pi$
$137$	51.3461	+	88.9341i	0.374789	+	0.649154i	−0.615506	+	0.788132i	$0.711048\pi$
$138$		0			0
$139$		−	47.2870i		−	0.340194i	−0.985427	−	0.170097i	$-0.945592\pi$
$139$		−	47.2870i		−	0.340194i	0.985427	−	0.170097i	$-0.0544081\pi$
$140$		0			0
$141$	111.296			0.789330
$142$		0			0
$143$	−114.877	+	66.3241i	−0.803334	+	0.463805i
$144$		0			0
$145$	0.977474	−	1.69303i	0.00674120	−	0.0116761i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	62.7920	−	108.759i	0.421423	−	0.729926i	−0.574656	−	0.818395i	$-0.694864\pi$
$149$	62.7920	−	108.759i	0.421423	−	0.729926i	0.996079	+	0.0884691i	$0.0281974\pi$
$150$		0			0
$151$	−161.705	+	93.3606i	−1.07090	+	0.618282i	−0.928426	−	0.371517i	$-0.878838\pi$
$151$	−161.705	+	93.3606i	−1.07090	+	0.618282i	−0.142470	+	0.989799i	$0.545504\pi$
$152$		0			0
$153$	438.683			2.86721
$154$		0			0
$155$			1.64674i			0.0106241i
$156$		0			0
$157$	88.6059	+	153.470i	0.564369	+	0.977516i	0.997108	+	0.0759965i	$0.0242138\pi$
$157$	88.6059	+	153.470i	0.564369	+	0.977516i	−0.432739	+	0.901519i	$0.642453\pi$
$158$		0			0
$159$	257.093	+	148.433i	1.61694	+	0.933539i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	45.8656	+	26.4805i	0.281384	+	0.162457i	0.634050	−	0.773292i	$-0.281391\pi$
$163$	45.8656	+	26.4805i	0.281384	+	0.162457i	−0.352666	+	0.935749i	$0.614725\pi$
$164$		0			0
$165$	1.70315	+	2.94995i	0.0103221	+	0.0178785i
$166$		0			0
$167$		−	97.7964i		−	0.585607i	−0.956173	−	0.292803i	$-0.905412\pi$
$167$		−	97.7964i		−	0.585607i	0.956173	−	0.292803i	$-0.0945882\pi$
$168$		0			0
$169$	−15.6103			−0.0923688
$170$		0			0
$171$	−124.969	+	72.1508i	−0.730812	+	0.421934i
$172$		0			0
$173$	−102.323	+	177.228i	−0.591460	+	1.02444i	0.402576	+	0.915387i	$0.368115\pi$
$173$	−102.323	+	177.228i	−0.591460	+	1.02444i	−0.994036	+	0.109052i	$0.965218\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	205.841	−	356.528i	1.16295	−	2.01428i
$178$		0			0
$179$	−50.9606	+	29.4221i	−0.284696	+	0.164369i	−0.635548	−	0.772062i	$-0.719226\pi$
$179$	−50.9606	+	29.4221i	−0.284696	+	0.164369i	0.350851	+	0.936431i	$0.385892\pi$
$180$		0			0
$181$	47.5570			0.262746			0.131373	−	0.991333i	$-0.458061\pi$
$181$	47.5570			0.262746			0.131373	+	0.991333i	$0.458061\pi$
$182$		0			0
$183$		−	131.545i		−	0.718825i
$184$		0			0
$185$	0.569560	+	0.986507i	0.00307870	+	0.00533247i
$186$		0			0
$187$	−180.856	−	104.417i	−0.967144	−	0.558381i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	260.164	+	150.206i	1.36212	+	0.786418i	0.989905	−	0.141731i	$-0.0452667\pi$
$191$	260.164	+	150.206i	1.36212	+	0.786418i	0.372210	+	0.928148i	$0.378600\pi$
$192$		0			0
$193$	129.051	+	223.523i	0.668659	+	1.15815i	0.978279	+	0.207291i	$0.0664646\pi$
$193$	129.051	+	223.523i	0.668659	+	1.15815i	−0.309621	+	0.950860i	$0.600202\pi$
$194$		0			0
$195$		−	3.93893i		−	0.0201997i
$196$		0			0
$197$	−290.892			−1.47661			−0.738306	−	0.674466i	$-0.764374\pi$
$197$	−290.892			−1.47661			−0.738306	+	0.674466i	$0.764374\pi$
$198$		0			0
$199$	−50.5323	+	29.1749i	−0.253931	+	0.146607i	−0.621563	−	0.783364i	$-0.713502\pi$
$199$	−50.5323	+	29.1749i	−0.253931	+	0.146607i	0.367632	+	0.929971i	$0.380169\pi$
$200$		0			0
$201$	43.5045	−	75.3520i	0.216440	−	0.374885i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.0361239	−	0.0625684i	0.000176214	−	0.000305212i
$206$		0			0
$207$	562.978	−	325.035i	2.71970	−	1.57022i
$208$		0			0
$209$	68.6947			0.328683
$210$		0			0
$211$			18.1272i			0.0859109i	0.999077	+	0.0429555i	$0.0136774\pi$
$211$			18.1272i			0.0859109i	−0.999077	+	0.0429555i	$0.986323\pi$
$212$		0			0
$213$	105.623	+	182.945i	0.495884	+	0.858897i
$214$		0			0
$215$	−1.76247	−	1.01756i	−0.00819752	−	0.00473284i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	357.453	+	206.376i	1.63220	+	0.942354i
$220$		0			0
$221$	120.744	+	209.135i	0.546355	+	0.946314i
$222$		0			0
$223$			6.84423i			0.0306916i	0.999882	+	0.0153458i	$0.00488491\pi$
$223$			6.84423i			0.0306916i	−0.999882	+	0.0153458i	$0.995115\pi$
$224$		0			0
$225$	562.388			2.49950
$226$		0			0
$227$	202.411	−	116.862i	0.891680	−	0.514812i	0.0171883	−	0.999852i	$-0.494529\pi$
$227$	202.411	−	116.862i	0.891680	−	0.514812i	0.874492	+	0.485041i	$0.161195\pi$
$228$		0			0
$229$	−82.3020	+	142.551i	−0.359398	+	0.622495i	−0.987860	−	0.155345i	$-0.950351\pi$
$229$	−82.3020	+	142.551i	−0.359398	+	0.622495i	0.628463	+	0.777840i	$0.283684\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.95906	−	5.12524i	0.0126998	−	0.0219967i	−0.859606	−	0.510958i	$-0.829291\pi$
$233$	2.95906	−	5.12524i	0.0126998	−	0.0219967i	0.872305	+	0.488961i	$0.162624\pi$
$234$		0			0
$235$	0.973196	−	0.561875i	0.00414126	−	0.00239096i
$236$		0			0
$237$	117.160			0.494348
$238$		0			0
$239$			401.405i			1.67952i	0.542960	+	0.839759i	$0.317304\pi$
$239$			401.405i			1.67952i	−0.542960	+	0.839759i	$0.682696\pi$
$240$		0			0
$241$	77.8104	+	134.771i	0.322865	+	0.559218i	0.981078	−	0.193614i	$-0.0620208\pi$
$241$	77.8104	+	134.771i	0.322865	+	0.559218i	−0.658213	+	0.752831i	$0.728688\pi$
$242$		0			0
$243$	491.908	+	284.003i	2.02431	+	1.16874i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−68.7936	−	39.7180i	−0.278517	−	0.160802i
$248$		0			0
$249$	−141.692	−	245.418i	−0.569045	−	0.985615i
$250$		0			0
$251$		−	348.371i		−	1.38793i	−0.720008	−	0.693966i	$-0.755862\pi$
$251$		−	348.371i		−	1.38793i	0.720008	−	0.693966i	$-0.244138\pi$
$252$		0			0
$253$	−309.466			−1.22318
$254$		0			0
$255$	5.37044	−	3.10063i	0.0210606	−	0.0121593i
$256$		0			0
$257$	6.97266	−	12.0770i	0.0271310	−	0.0469922i	−0.852141	−	0.523312i	$-0.824696\pi$
$257$	6.97266	−	12.0770i	0.0271310	−	0.0469922i	0.879272	+	0.476320i	$0.158030\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−388.079	+	672.173i	−1.48689	+	2.57538i
$262$		0			0
$263$	−315.758	+	182.303i	−1.20060	+	0.693167i	−0.960689	−	0.277627i	$-0.910452\pi$
$263$	−315.758	+	182.303i	−1.20060	+	0.693167i	−0.239912	+	0.970795i	$0.577119\pi$
$264$		0			0
$265$	2.99745			0.0113111
$266$		0			0
$267$		−	775.085i		−	2.90294i
$268$		0			0
$269$	−215.715	−	373.629i	−0.801914	−	1.38896i	−0.918355	−	0.395758i	$-0.870482\pi$
$269$	−215.715	−	373.629i	−0.801914	−	1.38896i	0.116441	−	0.993198i	$-0.462851\pi$
$270$		0			0
$271$	−90.8182	−	52.4339i	−0.335122	−	0.193483i	0.322991	−	0.946402i	$-0.395312\pi$
$271$	−90.8182	−	52.4339i	−0.335122	−	0.193483i	−0.658113	+	0.752919i	$0.728645\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−231.856	−	133.862i	−0.843113	−	0.486771i
$276$		0			0
$277$	80.3458	+	139.163i	0.290057	+	0.502394i	0.973823	−	0.227308i	$-0.0729924\pi$
$277$	80.3458	+	139.163i	0.290057	+	0.502394i	−0.683766	+	0.729701i	$0.739659\pi$
$278$		0			0
$279$		−	653.793i		−	2.34334i
$280$		0			0
$281$	138.683			0.493532			0.246766	−	0.969075i	$-0.420632\pi$
$281$	138.683			0.493532			0.246766	+	0.969075i	$0.420632\pi$
$282$		0			0
$283$	−72.5211	+	41.8701i	−0.256258	+	0.147951i	−0.622627	−	0.782519i	$-0.713934\pi$
$283$	−72.5211	+	41.8701i	−0.256258	+	0.147951i	0.366368	+	0.930470i	$0.380601\pi$
$284$		0			0
$285$	−1.01993	+	1.76657i	−0.00357870	+	0.00619849i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−45.5937	+	78.9706i	−0.157764	+	0.273255i
$290$		0			0
$291$	695.765	−	401.700i	2.39094	−	1.38041i
$292$		0			0
$293$	−261.928			−0.893952			−0.446976	−	0.894546i	$-0.647499\pi$
$293$	−261.928			−0.893952			−0.446976	+	0.894546i	$0.647499\pi$
$294$		0			0
$295$		−	4.15676i		−	0.0140907i
$296$		0			0
$297$	−405.695	−	702.684i	−1.36598	−	2.36594i
$298$		0			0
$299$	309.912	+	178.928i	1.03649	+	0.598420i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−599.195	−	345.945i	−1.97754	−	1.14173i
$304$		0			0
$305$	−0.664105	−	1.15026i	−0.00217739	−	0.00377135i
$306$		0			0
$307$		−	248.186i		−	0.808424i	−0.914665	−	0.404212i	$-0.867546\pi$
$307$		−	248.186i		−	0.808424i	0.914665	−	0.404212i	$-0.132454\pi$
$308$		0			0
$309$	235.177			0.761091
$310$		0			0
$311$	−484.498	+	279.725i	−1.55787	+	0.899437i	−0.560409	+	0.828216i	$0.689356\pi$
$311$	−484.498	+	279.725i	−1.55787	+	0.899437i	−0.997461	+	0.0712208i	$0.977311\pi$
$312$		0			0
$313$	−145.542	+	252.086i	−0.464990	+	0.805386i	−0.999201	−	0.0399649i	$-0.987275\pi$
$313$	−145.542	+	252.086i	−0.464990	+	0.805386i	0.534211	+	0.845351i	$0.320609\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−239.444	+	414.730i	−0.755345	+	1.30830i	0.189858	+	0.981812i	$0.439197\pi$
$317$	−239.444	+	414.730i	−0.755345	+	1.30830i	−0.945203	+	0.326484i	$0.894136\pi$
$318$		0			0
$319$	319.987	−	184.745i	1.00310	−	0.579137i
$320$		0			0
$321$	380.867			1.18650
$322$		0			0
$323$		−	125.060i		−	0.387183i
$324$		0			0
$325$	154.793	+	268.110i	0.476287	+	0.824954i
$326$		0			0
$327$	−449.057	−	259.263i	−1.37326	−	0.792853i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−18.6199	−	10.7502i	−0.0562535	−	0.0324780i	0.471609	−	0.881808i	$-0.343673\pi$
$331$	−18.6199	−	10.7502i	−0.0562535	−	0.0324780i	−0.527863	+	0.849330i	$0.677007\pi$
$332$		0			0
$333$	−226.128	−	391.666i	−0.679064	−	1.17617i
$334$		0			0
$335$		−	0.878529i		−	0.00262248i
$336$		0			0
$337$	−108.466			−0.321858			−0.160929	−	0.986966i	$-0.551449\pi$
$337$	−108.466			−0.321858			−0.160929	+	0.986966i	$0.551449\pi$
$338$		0			0
$339$	463.128	−	267.387i	1.36616	−	0.788752i
$340$		0			0
$341$	−155.619	+	269.540i	−0.456360	+	0.790439i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.59473	−	7.95830i	0.0133180	−	0.0230675i
$346$		0			0
$347$	−419.892	+	242.425i	−1.21006	+	0.698631i	−0.962773	−	0.270310i	$-0.912874\pi$
$347$	−419.892	+	242.425i	−1.21006	+	0.698631i	−0.247291	+	0.968941i	$0.579540\pi$
$348$		0			0
$349$	−539.969			−1.54719			−0.773595	−	0.633680i	$-0.781543\pi$
$349$	−539.969			−1.54719			−0.773595	+	0.633680i	$0.781543\pi$
$350$		0			0
$351$			938.263i			2.67311i
$352$		0			0
$353$	−137.761	−	238.609i	−0.390257	−	0.675945i	0.602226	−	0.798326i	$-0.294281\pi$
$353$	−137.761	−	238.609i	−0.390257	−	0.675945i	−0.992483	+	0.122380i	$0.960947\pi$
$354$		0			0
$355$	1.84719	+	1.06648i	0.00520337	+	0.00300416i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	395.233	+	228.188i	1.10093	+	0.635621i	0.936465	−	0.350762i	$-0.114077\pi$
$359$	395.233	+	228.188i	1.10093	+	0.635621i	0.164463	+	0.986383i	$0.447411\pi$
$360$		0			0
$361$	−159.931	−	277.009i	−0.443023	−	0.767338i
$362$		0			0
$363$		−	35.2934i		−	0.0972270i
$364$		0			0
$365$	4.16755			0.0114179
$366$		0			0
$367$	348.742	−	201.347i	0.950252	−	0.548628i	0.0570928	−	0.998369i	$-0.481817\pi$
$367$	348.742	−	201.347i	0.950252	−	0.548628i	0.893159	+	0.449741i	$0.148484\pi$
$368$		0			0
$369$	−14.3420	+	24.8411i	−0.0388672	+	0.0673199i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	174.648	−	302.499i	0.468225	−	0.810989i	−0.531116	−	0.847299i	$-0.678227\pi$
$373$	174.648	−	302.499i	0.468225	−	0.810989i	0.999341	+	0.0363104i	$0.0115605\pi$
$374$		0			0
$375$	13.7706	−	7.95047i	0.0367216	−	0.0212012i
$376$		0			0
$377$	−427.265			−1.13333
$378$		0			0
$379$		−	559.255i		−	1.47561i	−0.675016	−	0.737803i	$-0.735863\pi$
$379$		−	559.255i		−	1.47561i	0.675016	−	0.737803i	$-0.264137\pi$
$380$		0			0
$381$	613.658	+	1062.89i	1.61065	+	2.78973i
$382$		0			0
$383$	334.500	+	193.123i	0.873367	+	0.504239i	0.868466	−	0.495749i	$-0.165106\pi$
$383$	334.500	+	193.123i	0.873367	+	0.504239i	0.00490157	+	0.999988i	$0.498440\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	699.739	+	403.994i	1.80811	+	1.04391i
$388$		0			0
$389$	276.097	+	478.214i	0.709761	+	1.22934i	0.964946	+	0.262450i	$0.0845306\pi$
$389$	276.097	+	478.214i	0.709761	+	1.22934i	−0.255184	+	0.966892i	$0.582136\pi$
$390$		0			0
$391$			563.388i			1.44089i
$392$		0			0
$393$	−251.886			−0.640931
$394$		0			0
$395$	1.02448	−	0.591484i	0.00259362	−	0.00149743i
$396$		0			0
$397$	259.204	−	448.955i	0.652907	−	1.13087i	−0.329507	−	0.944153i	$-0.606883\pi$
$397$	259.204	−	448.955i	0.652907	−	1.13087i	0.982414	−	0.186715i	$-0.0597841\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−23.9526	+	41.4872i	−0.0597323	+	0.103459i	−0.894345	−	0.447378i	$-0.852358\pi$
$401$	−23.9526	+	41.4872i	−0.0597323	+	0.103459i	0.834613	+	0.550837i	$0.185691\pi$
$402$		0			0
$403$	311.686	−	179.952i	0.773415	−	0.446531i
$404$		0			0
$405$	12.6195			0.0311592
$406$		0			0
$407$			215.296i			0.528984i
$408$		0			0
$409$	−4.92883	−	8.53699i	−0.0120509	−	0.0208728i	0.859937	−	0.510400i	$-0.170503\pi$
$409$	−4.92883	−	8.53699i	−0.0120509	−	0.0208728i	−0.871988	+	0.489527i	$0.837169\pi$
$410$		0			0
$411$	−499.128	−	288.172i	−1.21442	−	0.701148i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.47799	−	1.43067i	−0.00597105	−	0.00344739i
$416$		0			0
$417$	132.695	+	229.835i	0.318214	+	0.551164i
$418$		0			0
$419$			256.169i			0.611381i	0.952131	+	0.305691i	$0.0988873\pi$
$419$			256.169i			0.611381i	−0.952131	+	0.305691i	$0.901113\pi$
$420$		0			0
$421$	765.070			1.81727			0.908634	−	0.417593i	$-0.137126\pi$
$421$	765.070			1.81727			0.908634	+	0.417593i	$0.137126\pi$
$422$		0			0
$423$	−386.381	+	223.077i	−0.913430	+	0.527369i
$424$		0			0
$425$	−243.699	+	422.098i	−0.573409	+	0.993173i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	372.234	−	644.728i	0.867678	−	1.50286i
$430$		0			0
$431$	−123.619	+	71.3715i	−0.286819	+	0.165595i	−0.636507	−	0.771271i	$-0.719621\pi$
$431$	−123.619	+	71.3715i	−0.286819	+	0.165595i	0.349687	+	0.936866i	$0.386288\pi$
$432$		0			0
$433$	849.228			1.96126			0.980632	−	0.195858i	$-0.0627492\pi$
$433$	849.228			1.96126			0.980632	+	0.195858i	$0.0627492\pi$
$434$		0			0
$435$			10.9718i			0.0252226i
$436$		0			0
$437$	−92.6614	−	160.494i	−0.212040	−	0.367264i
$438$		0			0
$439$	−390.669	−	225.553i	−0.889906	−	0.513788i	−0.0159945	−	0.999872i	$-0.505091\pi$
$439$	−390.669	−	225.553i	−0.889906	−	0.513788i	−0.873912	+	0.486084i	$0.838425\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−143.183	−	82.6669i	−0.323213	−	0.186607i	0.329611	−	0.944117i	$-0.393082\pi$
$443$	−143.183	−	82.6669i	−0.323213	−	0.186607i	−0.652824	+	0.757510i	$0.726416\pi$
$444$		0			0
$445$	−3.91302	−	6.77754i	−0.00879329	−	0.0152304i
$446$		0			0
$447$			704.821i			1.57678i
$448$		0			0
$449$	−386.892			−0.861676			−0.430838	−	0.902429i	$-0.641782\pi$
$449$	−386.892			−0.861676			−0.430838	+	0.902429i	$0.641782\pi$
$450$		0			0
$451$	11.8256	−	6.82749i	0.0262208	−	0.0151386i
$452$		0			0
$453$	523.972	−	907.546i	1.15667	−	2.00341i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	399.176	−	691.393i	0.873471	−	1.51290i	0.0150879	−	0.999886i	$-0.495197\pi$
$457$	399.176	−	691.393i	0.873471	−	1.51290i	0.858383	−	0.513010i	$-0.171469\pi$
$458$		0			0
$459$	−1279.25	+	738.576i	−2.78704	+	1.60910i
$460$		0			0
$461$	541.733			1.17513			0.587563	−	0.809178i	$-0.300087\pi$
$461$	541.733			1.17513			0.587563	+	0.809178i	$0.300087\pi$
$462$		0			0
$463$		−	432.093i		−	0.933246i	−0.884456	−	0.466623i	$-0.845470\pi$
$463$		−	432.093i		−	0.933246i	0.884456	−	0.466623i	$-0.154530\pi$
$464$		0			0
$465$	−4.62103	−	8.00387i	−0.00993771	−	0.0172126i
$466$		0			0
$467$	776.486	+	448.305i	1.66271	+	0.959967i	0.971412	+	0.237398i	$0.0762946\pi$
$467$	776.486	+	448.305i	1.66271	+	0.959967i	0.691299	+	0.722569i	$0.257039\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−861.326	−	497.287i	−1.82872	−	1.05581i
$472$		0			0
$473$	−192.321	−	333.110i	−0.406599	−	0.704250i
$474$		0			0
$475$		−	160.326i		−	0.337528i
$476$		0			0
$477$	−1190.05			−2.49487
$478$		0			0
$479$	−357.755	+	206.550i	−0.746879	+	0.431211i	−0.824565	−	0.565767i	$-0.808580\pi$
$479$	−357.755	+	206.550i	−0.746879	+	0.431211i	0.0776861	+	0.996978i	$0.475247\pi$
$480$		0			0
$481$	124.480	−	215.607i	0.258795	−	0.448246i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.05596	−	7.02513i	0.00836281	−	0.0144848i
$486$		0			0
$487$	−543.562	+	313.826i	−1.11614	+	0.644406i	−0.940414	−	0.340032i	$-0.889562\pi$
$487$	−543.562	+	313.826i	−1.11614	+	0.644406i	−0.175730	+	0.984438i	$0.556229\pi$
$488$		0			0
$489$	−297.236			−0.607844
$490$		0			0
$491$			857.281i			1.74599i	0.487730	+	0.872995i	$0.337825\pi$
$491$			857.281i			1.74599i	−0.487730	+	0.872995i	$0.662175\pi$
$492$		0			0
$493$	−336.332	−	582.544i	−0.682214	−	1.18163i
$494$		0			0
$495$	−11.8256	−	6.82749i	−0.0238900	−	0.0137929i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−267.708	−	154.561i	−0.536489	−	0.309742i	0.207166	−	0.978306i	$-0.433576\pi$
$499$	−267.708	−	154.561i	−0.536489	−	0.309742i	−0.743655	+	0.668564i	$0.766909\pi$
$500$		0			0
$501$	274.433	+	475.333i	0.547771	+	0.948768i
$502$		0			0
$503$			78.0463i			0.155162i	0.996986	+	0.0775808i	$0.0247196\pi$
$503$			78.0463i			0.155162i	−0.996986	+	0.0775808i	$0.975280\pi$
$504$		0			0
$505$	−6.98601			−0.0138337
$506$		0			0
$507$	75.8729	−	43.8052i	0.149651	−	0.0864009i
$508$		0			0
$509$	42.9408	−	74.3756i	0.0843630	−	0.146121i	−0.820757	−	0.571278i	$-0.806448\pi$
$509$	42.9408	−	74.3756i	0.0843630	−	0.146121i	0.905120	+	0.425157i	$0.139781\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	242.949	−	420.801i	0.473586	−	0.820274i
$514$		0			0
$515$	2.05645	−	1.18729i	0.00399310	−	0.00230542i
$516$		0			0
$517$	212.391			0.410815
$518$		0			0
$519$		−	1148.54i		−	2.21298i
$520$		0			0
$521$	201.036	+	348.204i	0.385865	+	0.668338i	0.991889	−	0.127108i	$-0.0405696\pi$
$521$	201.036	+	348.204i	0.385865	+	0.668338i	−0.606024	+	0.795447i	$0.707236\pi$
$522$		0			0
$523$	−705.791	−	407.488i	−1.34950	−	0.779137i	−0.361325	−	0.932440i	$-0.617676\pi$
$523$	−705.791	−	407.488i	−1.34950	−	0.779137i	−0.988179	+	0.153303i	$0.951009\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	490.702	+	283.307i	0.931124	+	0.537585i
$528$		0			0
$529$	152.934	+	264.890i	0.289101	+	0.500738i
$530$		0			0
$531$			1650.33i			3.10796i
$532$		0			0
$533$	−15.7901			−0.0296250
$534$		0			0
$535$	3.33040	−	1.92281i	0.00622505	−	0.00359403i
$536$		0			0
$537$	165.127	−	286.009i	0.307499	−	0.532604i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−365.478	+	633.026i	−0.675560	+	1.17010i	0.300745	+	0.953705i	$0.402765\pi$
$541$	−365.478	+	633.026i	−0.675560	+	1.17010i	−0.976305	+	0.216399i	$0.930569\pi$
$542$		0			0
$543$	−231.148	+	133.453i	−0.425686	+	0.245770i
$544$		0			0
$545$	−5.23555			−0.00960652
$546$		0			0
$547$			712.083i			1.30180i	0.759165	+	0.650899i	$0.225608\pi$
$547$			712.083i			1.30180i	−0.759165	+	0.650899i	$0.774392\pi$
$548$		0			0
$549$	263.664	+	456.680i	0.480263	+	0.831840i
$550$		0			0
$551$	191.624	+	110.634i	0.347774	+	0.200788i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−5.53662	−	3.19657i	−0.00997588	−	0.00575958i
$556$		0			0
$557$	−444.573	−	770.022i	−0.798155	−	1.38245i	−0.920816	−	0.389997i	$-0.872476\pi$
$557$	−444.573	−	770.022i	−0.798155	−	1.38245i	0.122661	−	0.992449i	$-0.460857\pi$
$558$		0			0
$559$			444.787i			0.795683i
$560$		0			0
$561$	1172.05			2.08922
$562$		0			0
$563$	−143.972	+	83.1225i	−0.255724	+	0.147642i	−0.622382	−	0.782713i	$-0.713835\pi$
$563$	−143.972	+	83.1225i	−0.255724	+	0.147642i	0.366659	+	0.930356i	$0.380502\pi$
$564$		0			0
$565$	2.69980	−	4.67620i	0.00477842	−	0.00827646i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.79174	−	6.56749i	0.00666387	−	0.0115422i	−0.862674	−	0.505760i	$-0.831212\pi$
$569$	3.79174	−	6.56749i	0.00666387	−	0.0115422i	0.869338	+	0.494218i	$0.164545\pi$
$570$		0			0
$571$	157.899	−	91.1631i	0.276531	−	0.159655i	−0.355321	−	0.934744i	$-0.615628\pi$
$571$	157.899	−	91.1631i	0.276531	−	0.159655i	0.631852	+	0.775089i	$0.282295\pi$
$572$		0			0
$573$	−1686.01			−2.94243
$574$		0			0
$575$			722.260i			1.25610i
$576$		0			0
$577$	191.393	+	331.503i	0.331704	+	0.574528i	0.982846	−	0.184428i	$-0.0590432\pi$
$577$	191.393	+	331.503i	0.331704	+	0.574528i	−0.651142	+	0.758956i	$0.725710\pi$
$578$		0			0
$579$	−1254.49	−	724.279i	−2.16665	−	1.25091i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	490.625	+	283.262i	0.841551	+	0.485870i
$584$		0			0
$585$	7.89507	+	13.6747i	0.0134958	+	0.0233755i
$586$		0			0
$587$		−	496.707i		−	0.846178i	−0.906088	−	0.423089i	$-0.860946\pi$
$587$		−	496.707i		−	0.846178i	0.906088	−	0.423089i	$-0.139054\pi$
$588$		0			0
$589$	−186.384			−0.316441
$590$		0			0
$591$	1413.86	−	816.294i	2.39232	−	1.38121i
$592$		0			0
$593$	302.253	−	523.518i	0.509702	−	0.882829i	−0.490235	−	0.871590i	$-0.663089\pi$
$593$	302.253	−	523.518i	0.509702	−	0.882829i	0.999937	−	0.0112392i	$-0.00357761\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	163.739	−	283.605i	0.274270	−	0.475050i
$598$		0			0
$599$	470.558	−	271.677i	0.785573	−	0.453551i	−0.0528286	−	0.998604i	$-0.516824\pi$
$599$	470.558	−	271.677i	0.785573	−	0.453551i	0.838402	+	0.545053i	$0.183490\pi$
$600$		0			0
$601$	−590.129			−0.981912			−0.490956	−	0.871184i	$-0.663352\pi$
$601$	−590.129			−0.981912			−0.490956	+	0.871184i	$0.663352\pi$
$602$		0			0
$603$			348.796i			0.578434i
$604$		0			0
$605$	−0.178179	−	0.308614i	−0.000294510	−	0.000510107i
$606$		0			0
$607$	602.616	+	347.920i	0.992777	+	0.573180i	0.906103	−	0.423057i	$-0.139043\pi$
$607$	602.616	+	347.920i	0.992777	+	0.573180i	0.0866738	+	0.996237i	$0.472376\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−212.697	−	122.801i	−0.348114	−	0.200983i
$612$		0			0
$613$	−360.291	−	624.042i	−0.587750	−	1.01801i	−0.994526	−	0.104486i	$-0.966680\pi$
$613$	−360.291	−	624.042i	−0.587750	−	1.01801i	0.406776	−	0.913528i	$-0.366653\pi$
$614$		0			0
$615$			0.405479i			0.000659315i
$616$		0			0
$617$	−950.880			−1.54113			−0.770567	−	0.637359i	$-0.780027\pi$
$617$	−950.880			−1.54113			−0.770567	+	0.637359i	$0.780027\pi$
$618$		0			0
$619$	686.615	−	396.418i	1.10923	−	0.640416i	0.170603	−	0.985340i	$-0.445429\pi$
$619$	686.615	−	396.418i	1.10923	−	0.640416i	0.938631	+	0.344924i	$0.112095\pi$
$620$		0			0
$621$	−1094.47	+	1895.68i	−1.76244	+	3.05263i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−312.380	+	541.057i	−0.499807	+	0.865692i
$626$		0			0
$627$	−333.886	+	192.769i	−0.532513	+	0.307447i
$628$		0			0
$629$	391.951			0.623134
$630$		0			0
$631$			50.5874i			0.0801702i	0.999196	+	0.0400851i	$0.0127629\pi$
$631$			50.5874i			0.0801702i	−0.999196	+	0.0400851i	$0.987237\pi$
$632$		0			0
$633$	−50.8681	−	88.1061i	−0.0803603	−	0.139188i
$634$		0			0
$635$	10.7320	+	6.19610i	0.0169007	+	0.00975764i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−733.378	−	423.416i	−1.14770	−	0.662623i
$640$		0			0
$641$	−564.039	−	976.943i	−0.879935	−	1.52409i	−0.851411	−	0.524500i	$-0.824252\pi$
$641$	−564.039	−	976.943i	−0.879935	−	1.52409i	−0.0285246	−	0.999593i	$-0.509081\pi$
$642$		0			0
$643$		−	500.619i		−	0.778567i	−0.921118	−	0.389284i	$-0.872723\pi$
$643$		−	500.619i		−	0.778567i	0.921118	−	0.389284i	$-0.127277\pi$
$644$		0			0
$645$	11.4218			0.0177082
$646$		0			0
$647$	−230.843	+	133.277i	−0.356790	+	0.205993i	−0.667672	−	0.744456i	$-0.732709\pi$
$647$	−230.843	+	133.277i	−0.356790	+	0.205993i	0.310882	+	0.950449i	$0.399376\pi$
$648$		0			0
$649$	392.818	−	680.381i	0.605267	−	1.04835i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−51.0514	+	88.4237i	−0.0781798	+	0.135411i	−0.902465	−	0.430764i	$-0.858244\pi$
$653$	−51.0514	+	88.4237i	−0.0781798	+	0.135411i	0.824285	+	0.566175i	$0.191578\pi$
$654$		0			0
$655$	−2.20256	+	1.27165i	−0.00336268	+	0.00194144i
$656$		0			0
$657$	−1654.61			−2.51843
$658$		0			0
$659$			303.615i			0.460721i	0.973105	+	0.230361i	$0.0739906\pi$
$659$			303.615i			0.460721i	−0.973105	+	0.230361i	$0.926009\pi$
$660$		0			0
$661$	−81.8366	−	141.745i	−0.123807	−	0.214440i	0.797459	−	0.603373i	$-0.206177\pi$
$661$	−81.8366	−	141.745i	−0.123807	−	0.214440i	−0.921266	+	0.388933i	$0.872844\pi$
$662$		0			0
$663$	−1173.74	−	677.659i	−1.77035	−	1.02211i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−863.254	−	498.400i	−1.29423	−	0.747226i
$668$		0			0
$669$	−19.2061	−	33.2659i	−0.0287086	−	0.0497248i
$670$		0			0
$671$		−	251.035i		−	0.374120i
$672$		0			0
$673$	1181.37			1.75538			0.877690	−	0.479229i	$-0.159084\pi$
$673$	1181.37			1.75538			0.877690	+	0.479229i	$0.159084\pi$
$674$		0			0
$675$	−1639.99	+	946.849i	−2.42961	+	1.40274i
$676$		0			0
$677$	−342.239	+	592.775i	−0.505523	+	0.875591i	0.494457	+	0.869202i	$0.335367\pi$
$677$	−342.239	+	592.775i	−0.505523	+	0.875591i	−0.999980	+	0.00638867i	$0.997966\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−655.871	+	1136.00i	−0.963100	+	1.66814i
$682$		0			0
$683$	355.939	−	205.502i	0.521141	−	0.300881i	−0.216260	−	0.976336i	$-0.569386\pi$
$683$	355.939	−	205.502i	0.521141	−	0.300881i	0.737401	+	0.675455i	$0.236053\pi$
$684$		0			0
$685$	−5.81934			−0.00849539
$686$		0			0
$687$		−	923.815i		−	1.34471i
$688$		0			0
$689$	−327.554	−	567.341i	−0.475405	−	0.823426i
$690$		0			0
$691$	−140.238	−	80.9666i	−0.202950	−	0.117173i	0.395081	−	0.918646i	$-0.370717\pi$
$691$	−140.238	−	80.9666i	−0.202950	−	0.117173i	−0.598031	+	0.801473i	$0.704050\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.32064	+	1.33982i	0.00333906	+	0.00192781i
$696$		0			0
$697$	−12.4296	−	21.5287i	−0.0178330	−	0.0308876i
$698$		0			0
$699$			33.2145i			0.0475172i
$700$		0			0
$701$	448.323			0.639548			0.319774	−	0.947494i	$-0.396393\pi$
$701$	448.323			0.639548			0.319774	+	0.947494i	$0.396393\pi$
$702$		0			0
$703$	−111.656	+	64.4648i	−0.158828	+	0.0916996i
$704$		0			0
$705$	−3.15344	+	5.46191i	−0.00447296	+	0.00774739i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−100.350	+	173.811i	−0.141537	+	0.245149i	−0.928076	−	0.372392i	$-0.878538\pi$
$709$	−100.350	+	173.811i	−0.141537	+	0.245149i	0.786539	+	0.617541i	$0.211871\pi$
$710$		0			0
$711$	−406.742	+	234.832i	−0.572070	+	0.330285i
$712$		0			0
$713$	839.649			1.17763
$714$		0			0
$715$		−	7.51688i		−	0.0105131i
$716$		0			0
$717$	−1126.41	−	1951.00i	−1.57100	−	2.72106i
$718$		0			0
$719$	567.356	+	327.563i	0.789090	+	0.455581i	0.839642	−	0.543140i	$-0.182765\pi$
$719$	567.356	+	327.563i	0.789090	+	0.455581i	−0.0505522	+	0.998721i	$0.516098\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−756.384	−	436.698i	−1.04617	−	0.604009i
$724$		0			0
$725$	−431.175	−	746.816i	−0.594724	−	1.03009i
$726$		0			0
$727$		−	341.027i		−	0.469088i	−0.972106	−	0.234544i	$-0.924640\pi$
$727$		−	341.027i		−	0.469088i	0.972106	−	0.234544i	$-0.0753596\pi$
$728$		0			0
$729$	−1183.62			−1.62362
$730$		0			0
$731$	−606.434	+	350.125i	−0.829595	+	0.478967i
$732$		0			0
$733$	297.395	−	515.104i	0.405724	−	0.702734i	−0.588682	−	0.808365i	$-0.700353\pi$
$733$	297.395	−	515.104i	0.405724	−	0.702734i	0.994405	+	0.105631i	$0.0336862\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	83.0220	−	143.798i	0.112649	−	0.195113i
$738$		0			0
$739$	1107.39	−	639.354i	1.49850	−	0.865162i	0.498505	−	0.866887i	$-0.333882\pi$
$739$	1107.39	−	639.354i	1.49850	−	0.865162i	0.999999	+	0.00172511i	$0.000549120\pi$
$740$		0			0
$741$	445.822			0.601650
$742$		0			0
$743$		−	544.059i		−	0.732246i	−0.930566	−	0.366123i	$-0.880685\pi$
$743$		−	544.059i		−	0.732246i	0.930566	−	0.366123i	$-0.119315\pi$
$744$		0			0
$745$	3.55829	+	6.16313i	0.00477622	+	0.00827266i
$746$		0			0
$747$	983.816	+	568.006i	1.31702	+	0.760383i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	34.3675	+	19.8421i	0.0457623	+	0.0264209i	0.522707	−	0.852513i	$-0.324922\pi$
$751$	34.3675	+	19.8421i	0.0457623	+	0.0264209i	−0.476944	+	0.878934i	$0.658256\pi$
$752$		0			0
$753$	977.588	+	1693.23i	1.29826	+	2.24865i
$754$		0			0
$755$		−	10.5811i		−	0.0140147i
$756$		0			0
$757$	−47.2200			−0.0623777			−0.0311889	−	0.999514i	$-0.509929\pi$
$757$	−47.2200			−0.0623777			−0.0311889	+	0.999514i	$0.509929\pi$
$758$		0			0
$759$	1504.14	−	868.414i	1.98174	−	1.14416i
$760$		0			0
$761$	−421.703	+	730.411i	−0.554143	+	0.959804i	0.443827	+	0.896113i	$0.353621\pi$
$761$	−421.703	+	730.411i	−0.554143	+	0.959804i	−0.997970	+	0.0636913i	$0.979713\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−12.4296	+	21.5287i	−0.0162478	+	0.0281421i
$766$		0			0
$767$	−786.769	+	454.241i	−1.02577	+	0.592231i
$768$		0			0
$769$	−343.976			−0.447304			−0.223652	−	0.974669i	$-0.571798\pi$
$769$	−343.976			−0.447304			−0.223652	+	0.974669i	$0.571798\pi$
$770$		0			0
$771$			78.2659i			0.101512i
$772$		0			0
$773$	188.558	+	326.593i	0.243931	+	0.422500i	0.961830	−	0.273646i	$-0.0882298\pi$
$773$	188.558	+	326.593i	0.243931	+	0.422500i	−0.717900	+	0.696146i	$0.754896\pi$
$774$		0			0
$775$	629.077	+	363.198i	0.811712	+	0.468642i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.08171	+	4.08863i	0.00909077	+	0.00524856i
$780$		0			0
$781$	201.567	+	349.124i	0.258088	+	0.447022i
$782$		0			0
$783$		−	2613.52i		−	3.33782i
$784$		0			0
$785$	−10.0422			−0.0127926
$786$		0			0
$787$	662.278	−	382.367i	0.841523	−	0.485853i	−0.0162588	−	0.999868i	$-0.505176\pi$
$787$	662.278	−	382.367i	0.841523	−	0.485853i	0.857782	+	0.514014i	$0.171842\pi$
$788$		0			0
$789$	1023.15	−	1772.14i	1.29676	−	2.24606i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−145.144	+	251.396i	−0.183031	+	0.317019i
$794$		0			0
$795$	−14.5689	+	8.41135i	−0.0183256	+	0.0105803i
$796$		0			0
$797$	1306.69			1.63951			0.819753	−	0.572717i	$-0.194111\pi$
$797$	1306.69			1.63951			0.819753	+	0.572717i	$0.194111\pi$
$798$		0			0
$799$		−	386.663i		−	0.483933i
$800$		0			0
$801$	1553.56	+	2690.84i	1.93952	+	3.35935i
$802$		0			0
$803$	682.147	+	393.838i	0.849498	+	0.490458i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2096.93	+	1210.67i	2.59843	+	1.50021i
$808$		0			0
$809$	−235.592	−	408.056i	−0.291213	−	0.504396i	0.682884	−	0.730527i	$-0.260726\pi$
$809$	−235.592	−	408.056i	−0.291213	−	0.504396i	−0.974097	+	0.226131i	$0.927392\pi$
$810$		0			0
$811$			1563.73i			1.92815i	0.265632	+	0.964074i	$0.414419\pi$
$811$			1563.73i			1.92815i	−0.265632	+	0.964074i	$0.585581\pi$
$812$		0			0
$813$	588.554			0.723929
$814$		0			0
$815$	−2.59910	+	1.50059i	−0.00318908	+	0.00184122i
$816$		0			0
$817$	115.171	−	199.482i	0.140968	−	0.244164i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	126.365	−	218.871i	0.153916	−	0.266591i	−0.778748	−	0.627337i	$-0.784145\pi$
$821$	126.365	−	218.871i	0.153916	−	0.266591i	0.932664	+	0.360746i	$0.117478\pi$
$822$		0			0
$823$	218.597	−	126.207i	0.265610	−	0.153350i	−0.361281	−	0.932457i	$-0.617661\pi$
$823$	218.597	−	126.207i	0.265610	−	0.153350i	0.626891	+	0.779107i	$0.284327\pi$
$824$		0			0
$825$	1502.56			1.82128
$826$		0			0
$827$			1045.75i			1.26451i	0.774760	+	0.632256i	$0.217871\pi$
$827$			1045.75i			1.26451i	−0.774760	+	0.632256i	$0.782129\pi$
$828$		0			0
$829$	221.059	+	382.886i	0.266658	+	0.461865i	0.967997	−	0.250963i	$-0.0807472\pi$
$829$	221.059	+	382.886i	0.266658	+	0.461865i	−0.701339	+	0.712828i	$0.747414\pi$
$830$		0			0
$831$	−781.031	−	450.928i	−0.939868	−	0.542633i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	4.79943	+	2.77095i	0.00574782	+	0.00331851i
$836$		0			0
$837$	1100.74	+	1906.54i	1.31510	+	2.27782i
$838$		0			0
$839$			1532.20i			1.82622i	0.407714	+	0.913110i	$0.366326\pi$
$839$			1532.20i			1.82622i	−0.407714	+	0.913110i	$0.633674\pi$
$840$		0			0
$841$	349.139			0.415148
$842$		0			0
$843$	−674.057	+	389.167i	−0.799593	+	0.461645i
$844$		0			0
$845$	0.442301	−	0.766088i	0.000523433	−	0.000906613i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	234.989	−	407.013i	0.276784	−	0.479403i
$850$		0			0
$851$	503.006	−	290.411i	0.591076	−	0.341258i
$852$		0			0
$853$	−725.264			−0.850251			−0.425125	−	0.905134i	$-0.639770\pi$
$853$	−725.264			−0.850251			−0.425125	+	0.905134i	$0.639770\pi$
$854$		0			0
$855$		−	8.17725i		−	0.00956404i
$856$		0			0
$857$	−472.823	−	818.954i	−0.551719	−	0.955606i	−0.998151	−	0.0607878i	$-0.980639\pi$
$857$	−472.823	−	818.954i	−0.551719	−	0.955606i	0.446432	−	0.894818i	$-0.352695\pi$
$858$		0			0
$859$	−427.861	−	247.025i	−0.498092	−	0.287573i	0.229834	−	0.973230i	$-0.426182\pi$
$859$	−427.861	−	247.025i	−0.498092	−	0.287573i	−0.727925	+	0.685657i	$0.759515\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1198.21	+	691.788i	1.38843	+	0.801609i	0.993138	−	0.116948i	$-0.0373111\pi$
$863$	1198.21	+	691.788i	1.38843	+	0.801609i	0.395289	+	0.918557i	$0.370644\pi$
$864$		0			0
$865$	−5.79840	−	10.0431i	−0.00670335	−	0.0116105i
$866$		0			0
$867$		−	511.775i		−	0.590282i
$868$		0			0
$869$	223.584			0.257288
$870$		0			0
$871$	−166.283	+	96.0037i	−0.190911	+	0.110222i
$872$		0			0
$873$	−1610.31	+	2789.14i	−1.84457	+	3.19489i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	686.052	−	1188.28i	0.782272	−	1.35493i	−0.148344	−	0.988936i	$-0.547394\pi$
$877$	686.052	−	1188.28i	0.782272	−	1.35493i	0.930615	−	0.365998i	$-0.119272\pi$
$878$		0			0
$879$	1273.08	−	735.014i	1.44833	−	0.836194i
$880$		0			0
$881$	−927.004			−1.05222			−0.526109	−	0.850417i	$-0.676350\pi$
$881$	−927.004			−1.05222			−0.526109	+	0.850417i	$0.676350\pi$
$882$		0			0
$883$		−	1144.18i		−	1.29578i	−0.761733	−	0.647891i	$-0.775651\pi$
$883$		−	1144.18i		−	1.29578i	0.761733	−	0.647891i	$-0.224349\pi$
$884$		0			0
$885$	11.6646	+	20.2036i	0.0131803	+	0.0228290i
$886$		0			0
$887$	1402.29	+	809.611i	1.58093	+	0.912752i	0.994723	+	0.102592i	$0.0327138\pi$
$887$	1402.29	+	809.611i	1.58093	+	0.912752i	0.586209	+	0.810160i	$0.300620\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2065.57	+	1192.56i	2.31826	+	1.33845i
$892$		0			0
$893$	63.5950	+	110.150i	0.0712150	+	0.123348i
$894$		0			0
$895$		−	3.33458i		−	0.00372578i
$896$		0			0
$897$	−2008.41			−2.23903
$898$		0			0
$899$	−868.197	+	501.254i	−0.965736	+	0.557568i
$900$		0			0
$901$	515.684	−	893.192i	0.572347	−	0.991334i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.34748	+	2.33390i	−0.00148892	+	0.00257889i
$906$		0			0
$907$	425.263	−	245.526i	0.468868	−	0.270701i	−0.246898	−	0.969041i	$-0.579411\pi$
$907$	425.263	−	245.526i	0.468868	−	0.270701i	0.715766	+	0.698341i	$0.246078\pi$
$908$		0			0
$909$	2773.60			3.05127
$910$		0			0
$911$			551.167i			0.605013i	0.953147	+	0.302506i	$0.0978234\pi$
$911$			551.167i			0.605013i	−0.953147	+	0.302506i	$0.902177\pi$
$912$		0			0
$913$	−270.399	−	468.345i	−0.296165	−	0.512974i
$914$		0			0
$915$	6.45567	+	3.72718i	0.00705538	+	0.00407342i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−254.106	−	146.708i	−0.276503	−	0.159639i	0.355336	−	0.934739i	$-0.384366\pi$
$919$	−254.106	−	146.708i	−0.276503	−	0.159639i	−0.631839	+	0.775099i	$0.717700\pi$
$920$		0			0
$921$	696.453	+	1206.29i	0.756192	+	1.30976i
$922$		0			0
$923$		−	466.169i		−	0.505059i
$924$		0			0
$925$	502.478			0.543220
$926$		0			0
$927$	−816.457	+	471.381i	−0.880751	+	0.508502i
$928$		0			0
$929$	526.411	−	911.771i	0.566643	−	0.981454i	−0.430252	−	0.902709i	$-0.641575\pi$
$929$	526.411	−	911.771i	0.566643	−	0.981454i	0.996895	−	0.0787454i	$-0.0250914\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1569.91	−	2719.17i	1.68265	−	2.91443i
$934$		0			0
$935$	10.2487	−	5.91710i	0.0109612	−	0.00632844i
$936$		0			0
$937$	1323.90			1.41292			0.706459	−	0.707754i	$-0.250292\pi$
$937$	1323.90			1.41292			0.706459	+	0.707754i	$0.250292\pi$
$938$		0			0
$939$		−	1633.66i		−	1.73979i
$940$		0			0
$941$	82.1275	+	142.249i	0.0872768	+	0.151168i	0.906359	−	0.422508i	$-0.138850\pi$
$941$	82.1275	+	142.249i	0.0872768	+	0.151168i	−0.819082	+	0.573676i	$0.805517\pi$
$942$		0			0
$943$	−31.9027	−	18.4190i	−0.0338311	−	0.0195324i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−198.482	−	114.593i	−0.209590	−	0.121007i	0.391531	−	0.920165i	$-0.371946\pi$
$947$	−198.482	−	114.593i	−0.209590	−	0.121007i	−0.601121	+	0.799158i	$0.705279\pi$
$948$		0			0
$949$	−455.420	−	788.810i	−0.479895	−	0.831202i
$950$		0			0
$951$		−	2687.69i		−	2.82617i
$952$		0			0
$953$	203.077			0.213092			0.106546	−	0.994308i	$-0.466021\pi$
$953$	203.077			0.213092			0.106546	+	0.994308i	$0.466021\pi$
$954$		0			0
$955$	−14.7429	+	8.51183i	−0.0154376	+	0.00891291i
$956$		0			0
$957$	−1036.85	+	1795.88i	−1.08344	+	1.87657i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−58.2717	+	100.930i	−0.0606365	+	0.105025i
$962$		0			0
$963$	−1322.24	+	763.398i	−1.37305	+	0.792729i
$964$		0			0
$965$	−14.6261			−0.0151566
$966$		0			0
$967$			483.181i			0.499670i	0.968288	+	0.249835i	$0.0803764\pi$
$967$			483.181i			0.499670i	−0.968288	+	0.249835i	$0.919624\pi$
$968$		0			0
$969$	350.940	+	607.846i	0.362167	+	0.627292i
$970$		0			0
$971$	108.752	+	62.7881i	0.112000	+	0.0646633i	0.554954	−	0.831881i	$-0.312736\pi$
$971$	108.752	+	62.7881i	0.112000	+	0.0646633i	−0.442953	+	0.896545i	$0.646069\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1504.72	−	868.753i	−1.54331	−	0.891029i
$976$		0			0
$977$	−176.354	−	305.454i	−0.180505	−	0.312644i	0.761547	−	0.648109i	$-0.224440\pi$
$977$	−176.354	−	305.454i	−0.180505	−	0.312644i	−0.942053	+	0.335465i	$0.891107\pi$
$978$		0			0
$979$		−	1479.14i		−	1.51087i
$980$		0			0
$981$	2078.63			2.11889
$982$		0			0
$983$	−458.984	+	264.994i	−0.466921	+	0.269577i	−0.714950	−	0.699176i	$-0.753551\pi$
$983$	−458.984	+	264.994i	−0.466921	+	0.269577i	0.248029	+	0.968753i	$0.420217\pi$
$984$		0			0
$985$	8.24212	−	14.2758i	0.00836763	−	0.0144932i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−518.839	+	898.656i	−0.524610	+	0.908651i
$990$		0			0
$991$	−249.779	+	144.210i	−0.252047	+	0.145520i	−0.620701	−	0.784047i	$-0.713152\pi$
$991$	−249.779	+	144.210i	−0.252047	+	0.145520i	0.368654	+	0.929567i	$0.379819\pi$
$992$		0			0
$993$	120.668			0.121518
$994$		0			0
$995$		−	3.30655i		−	0.00332316i
$996$		0			0
$997$	221.355	+	383.398i	0.222021	+	0.384551i	0.955421	−	0.295245i	$-0.0954014\pi$
$997$	221.355	+	383.398i	0.222021	+	0.384551i	−0.733401	+	0.679797i	$0.762068\pi$
$998$		0			0
$999$	1318.83	+	761.429i	1.32015	+	0.762191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.3.r.p.79.1		6
4.3	odd	2		784.3.r.q.79.3		6
7.2	even	3		784.3.d.k.687.1		6
7.3	odd	6		112.3.r.b.95.1	yes	6
7.4	even	3		784.3.r.q.655.3		6
7.5	odd	6		784.3.d.l.687.6		6
7.6	odd	2		112.3.r.c.79.3	yes	6
21.17	even	6		1008.3.cd.j.991.2		6
21.20	even	2		1008.3.cd.k.415.2		6
28.3	even	6		112.3.r.c.95.3	yes	6
28.11	odd	6	inner	784.3.r.p.655.1		6
28.19	even	6		784.3.d.l.687.1		6
28.23	odd	6		784.3.d.k.687.6		6
28.27	even	2		112.3.r.b.79.1	✓	6
56.3	even	6		448.3.r.d.319.1		6
56.13	odd	2		448.3.r.d.191.1		6
56.27	even	2		448.3.r.e.191.3		6
56.45	odd	6		448.3.r.e.319.3		6
84.59	odd	6		1008.3.cd.k.991.2		6
84.83	odd	2		1008.3.cd.j.415.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.r.b.79.1	✓	6	28.27	even	2
112.3.r.b.95.1	yes	6	7.3	odd	6
112.3.r.c.79.3	yes	6	7.6	odd	2
112.3.r.c.95.3	yes	6	28.3	even	6
448.3.r.d.191.1		6	56.13	odd	2
448.3.r.d.319.1		6	56.3	even	6
448.3.r.e.191.3		6	56.27	even	2
448.3.r.e.319.3		6	56.45	odd	6
784.3.d.k.687.1		6	7.2	even	3
784.3.d.k.687.6		6	28.23	odd	6
784.3.d.l.687.1		6	28.19	even	6
784.3.d.l.687.6		6	7.5	odd	6
784.3.r.p.79.1		6	1.1	even	1	trivial
784.3.r.p.655.1		6	28.11	odd	6	inner
784.3.r.q.79.3		6	4.3	odd	2
784.3.r.q.655.3		6	7.4	even	3
1008.3.cd.j.415.2		6	84.83	odd	2
1008.3.cd.j.991.2		6	21.17	even	6
1008.3.cd.k.415.2		6	21.20	even	2
1008.3.cd.k.991.2		6	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	784.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.86043 + 2.80617i) q^{3} +(-0.0283339 + 0.0490758i) q^{5} +(11.2492 - 19.4842i) q^{9} +(-9.27543 + 5.35517i) q^{11} +12.3851 q^{13} -0.318039i q^{15} +(9.74920 + 16.8861i) q^{17} +(-5.55457 - 3.20693i) q^{19} +(25.0230 + 14.4470i) q^{23} +(12.4984 + 21.6479i) q^{25} +75.7576i q^{27} -34.4984 q^{29} +(25.1663 - 14.5298i) q^{31} +(30.0551 - 52.0569i) q^{33} +(10.0509 - 17.4086i) q^{37} +(-60.1967 + 34.7546i) q^{39} -1.27493 q^{41} +35.9132i q^{43} +(0.637467 + 1.10413i) q^{45} +(-17.1737 - 9.91525i) q^{47} +(-94.7706 - 54.7158i) q^{51} +(-26.4475 - 45.8085i) q^{53} -0.606932i q^{55} +35.9968 q^{57} +(-63.5256 + 36.6765i) q^{59} +(-11.7193 + 20.2983i) q^{61} +(-0.350917 + 0.607806i) q^{65} +(-13.4261 + 7.75157i) q^{67} -162.164 q^{69} -37.6397i q^{71} +(-36.7717 - 63.6905i) q^{73} +(-121.495 - 70.1453i) q^{75} +(-18.0787 - 10.4377i) q^{79} +(-111.346 - 192.857i) q^{81} +50.4931i q^{83} -1.10493 q^{85} +(167.677 - 96.8084i) q^{87} +(-69.0519 + 119.601i) q^{89} +(-81.5460 + 141.242i) q^{93} +(0.314765 - 0.181730i) q^{95} -143.149 q^{97} +240.966i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + q^{5} + 14 q^{9} - 33 q^{11} - 28 q^{13} + 5 q^{17} - 63 q^{19} - 33 q^{23} - 32 q^{25} - 100 q^{29} + 69 q^{31} + 71 q^{33} + 15 q^{37} - 246 q^{39} - 124 q^{41} + 62 q^{45} - 171 q^{47}+ \cdots - 124 q^{97}+O(q^{100}) \) 6 * q - 3 * q^3 + q^5 + 14 * q^9 - 33 * q^11 - 28 * q^13 + 5 * q^17 - 63 * q^19 - 33 * q^23 - 32 * q^25 - 100 * q^29 + 69 * q^31 + 71 * q^33 + 15 * q^37 - 246 * q^39 - 124 * q^41 + 62 * q^45 - 171 * q^47 - 225 * q^51 - 97 * q^53 + 2 * q^57 - 27 * q^59 + 89 * q^61 + 142 * q^65 - 309 * q^67 - 538 * q^69 - 123 * q^73 - 408 * q^75 - 201 * q^79 - 203 * q^81 - 130 * q^85 + 270 * q^87 - 91 * q^89 - 123 * q^93 - 321 * q^95 - 124 * q^97

Introduction

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