LMFDB - Embedded newform 784.3.r.n.79.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
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			79.2
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	784.79
Dual form			784.3.r.n.655.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.79129 - 2.18890i) q^{3} +(-2.79129 + 4.83465i) q^{5} +(5.08258 - 8.80328i) q^{9} +O(q^{10})$	\(q+(3.79129 - 2.18890i) q^{3} +(-2.79129 + 4.83465i) q^{5} +(5.08258 - 8.80328i) q^{9} +(-1.58258 + 0.913701i) q^{11} +20.7477 q^{13} +24.4394i q^{15} +(12.5826 + 21.7937i) q^{17} +(-26.5390 - 15.3223i) q^{19} +(2.83485 + 1.63670i) q^{23} +(-3.08258 - 5.33918i) q^{25} -5.10080i q^{27} +53.8258 q^{29} +(25.2523 - 14.5794i) q^{31} +(-4.00000 + 6.92820i) q^{33} +(-8.58258 + 14.8655i) q^{37} +(78.6606 - 45.4147i) q^{39} -7.49545 q^{41} +57.2530i q^{43} +(28.3739 + 49.1450i) q^{45} +(32.2432 + 18.6156i) q^{47} +(95.4083 + 55.0840i) q^{51} +(23.0000 + 39.8372i) q^{53} -10.2016i q^{55} -134.156 q^{57} +(65.0436 - 37.5529i) q^{59} +(14.0436 - 24.3242i) q^{61} +(-57.9129 + 100.308i) q^{65} +(-70.4864 + 40.6953i) q^{67} +14.3303 q^{69} -32.1304i q^{71} +(-22.8258 - 39.5354i) q^{73} +(-23.3739 - 13.4949i) q^{75} +(-9.49545 - 5.48220i) q^{79} +(34.5780 + 59.8909i) q^{81} -143.705i q^{83} -140.486 q^{85} +(204.069 - 117.819i) q^{87} +(29.6606 - 51.3737i) q^{89} +(63.8258 - 110.549i) q^{93} +(148.156 - 85.5379i) q^{95} -17.1652 q^{97} +18.5758i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 2 q^{5} + 2 q^{9}+O(q^{10}) $ 4 * q + 6 * q^3 - 2 * q^5 + 2 * q^9	$ 4 q + 6 q^{3} - 2 q^{5} + 2 q^{9} + 12 q^{11} + 28 q^{13} + 32 q^{17} - 42 q^{19} + 48 q^{23} + 6 q^{25} + 32 q^{29} + 156 q^{31} - 16 q^{33} - 16 q^{37} + 168 q^{39} + 80 q^{41} + 86 q^{45} - 36 q^{47} + 180 q^{51} + 92 q^{53} - 280 q^{57} + 306 q^{59} + 102 q^{61} - 140 q^{65} + 48 q^{67} - 16 q^{69} + 92 q^{73} - 66 q^{75} + 72 q^{79} + 10 q^{81} - 232 q^{85} + 468 q^{87} - 28 q^{89} + 72 q^{93} + 336 q^{95} - 32 q^{97}+O(q^{100}) $ 4 * q + 6 * q^3 - 2 * q^5 + 2 * q^9 + 12 * q^11 + 28 * q^13 + 32 * q^17 - 42 * q^19 + 48 * q^23 + 6 * q^25 + 32 * q^29 + 156 * q^31 - 16 * q^33 - 16 * q^37 + 168 * q^39 + 80 * q^41 + 86 * q^45 - 36 * q^47 + 180 * q^51 + 92 * q^53 - 280 * q^57 + 306 * q^59 + 102 * q^61 - 140 * q^65 + 48 * q^67 - 16 * q^69 + 92 * q^73 - 66 * q^75 + 72 * q^79 + 10 * q^81 - 232 * q^85 + 468 * q^87 - 28 * q^89 + 72 * q^93 + 336 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

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
$3$	3.79129	−	2.18890i	1.26376	−	0.729634i	0.289962	−	0.957038i	$-0.406357\pi$
$3$	3.79129	−	2.18890i	1.26376	−	0.729634i	0.973800	+	0.227404i	$0.0730239\pi$
$4$		0			0
$5$	−2.79129	+	4.83465i	−0.558258	+	0.966930i	0.439385	+	0.898299i	$0.355197\pi$
$5$	−2.79129	+	4.83465i	−0.558258	+	0.966930i	−0.997642	+	0.0686314i	$0.978137\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	5.08258	−	8.80328i	0.564731	−	0.978142i
$10$		0			0
$11$	−1.58258	+	0.913701i	−0.143871	+	0.0830637i	−0.570207	−	0.821501i	$-0.693137\pi$
$11$	−1.58258	+	0.913701i	−0.143871	+	0.0830637i	0.426337	+	0.904564i	$0.359804\pi$
$12$		0			0
$13$	20.7477			1.59598			0.797990	−	0.602671i	$-0.205897\pi$
$13$	20.7477			1.59598			0.797990	+	0.602671i	$0.205897\pi$
$14$		0			0
$15$			24.4394i			1.62929i
$16$		0			0
$17$	12.5826	+	21.7937i	0.740152	+	1.28198i	0.952426	+	0.304770i	$0.0985796\pi$
$17$	12.5826	+	21.7937i	0.740152	+	1.28198i	−0.212274	+	0.977210i	$0.568087\pi$
$18$		0			0
$19$	−26.5390	−	15.3223i	−1.39679	−	0.806437i	−0.402735	−	0.915317i	$-0.631940\pi$
$19$	−26.5390	−	15.3223i	−1.39679	−	0.806437i	−0.994055	+	0.108879i	$0.965274\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.83485	+	1.63670i	0.123254	+	0.0711609i	0.560360	−	0.828249i	$-0.310663\pi$
$23$	2.83485	+	1.63670i	0.123254	+	0.0711609i	−0.437105	+	0.899410i	$0.643996\pi$
$24$		0			0
$25$	−3.08258	−	5.33918i	−0.123303	−	0.213567i
$26$		0			0
$27$		−	5.10080i		−	0.188919i
$28$		0			0
$29$	53.8258			1.85606			0.928030	−	0.372505i	$-0.121501\pi$
$29$	53.8258			1.85606			0.928030	+	0.372505i	$0.121501\pi$
$30$		0			0
$31$	25.2523	−	14.5794i	0.814589	−	0.470303i	−0.0339577	−	0.999423i	$-0.510811\pi$
$31$	25.2523	−	14.5794i	0.814589	−	0.470303i	0.848547	+	0.529120i	$0.177478\pi$
$32$		0			0
$33$	−4.00000	+	6.92820i	−0.121212	+	0.209946i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−8.58258	+	14.8655i	−0.231962	+	0.401769i	−0.958385	−	0.285478i	$-0.907848\pi$
$37$	−8.58258	+	14.8655i	−0.231962	+	0.401769i	0.726424	+	0.687247i	$0.241181\pi$
$38$		0			0
$39$	78.6606	−	45.4147i	2.01694	−	1.16448i
$40$		0			0
$41$	−7.49545			−0.182816			−0.0914080	−	0.995814i	$-0.529137\pi$
$41$	−7.49545			−0.182816			−0.0914080	+	0.995814i	$0.529137\pi$
$42$		0			0
$43$			57.2530i			1.33147i	0.746190	+	0.665733i	$0.231881\pi$
$43$			57.2530i			1.33147i	−0.746190	+	0.665733i	$0.768119\pi$
$44$		0			0
$45$	28.3739	+	49.1450i	0.630530	+	1.09211i
$46$		0			0
$47$	32.2432	+	18.6156i	0.686025	+	0.396077i	0.802121	−	0.597161i	$-0.203705\pi$
$47$	32.2432	+	18.6156i	0.686025	+	0.396077i	−0.116096	+	0.993238i	$0.537038\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	95.4083	+	55.0840i	1.87075	+	1.08008i
$52$		0			0
$53$	23.0000	+	39.8372i	0.433962	+	0.751645i	0.997210	−	0.0746432i	$-0.0237818\pi$
$53$	23.0000	+	39.8372i	0.433962	+	0.751645i	−0.563248	+	0.826288i	$0.690448\pi$
$54$		0			0
$55$		−	10.2016i		−	0.185484i
$56$		0			0
$57$	−134.156			−2.35362
$58$		0			0
$59$	65.0436	−	37.5529i	1.10243	−	0.636490i	0.165574	−	0.986197i	$-0.447052\pi$
$59$	65.0436	−	37.5529i	1.10243	−	0.636490i	0.936859	+	0.349707i	$0.113719\pi$
$60$		0			0
$61$	14.0436	−	24.3242i	0.230222	−	0.398757i	−0.727651	−	0.685947i	$-0.759388\pi$
$61$	14.0436	−	24.3242i	0.230222	−	0.398757i	0.957873	+	0.287191i	$0.0927213\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−57.9129	+	100.308i	−0.890967	+	1.54320i
$66$		0			0
$67$	−70.4864	+	40.6953i	−1.05204	+	0.607393i	−0.923218	−	0.384276i	$-0.874451\pi$
$67$	−70.4864	+	40.6953i	−1.05204	+	0.607393i	−0.128817	+	0.991668i	$0.541118\pi$
$68$		0			0
$69$	14.3303			0.207686
$70$		0			0
$71$		−	32.1304i		−	0.452541i	−0.974064	−	0.226271i	$-0.927347\pi$
$71$		−	32.1304i		−	0.452541i	0.974064	−	0.226271i	$-0.0726533\pi$
$72$		0			0
$73$	−22.8258	−	39.5354i	−0.312682	−	0.541580i	0.666260	−	0.745719i	$-0.267894\pi$
$73$	−22.8258	−	39.5354i	−0.312682	−	0.541580i	−0.978942	+	0.204139i	$0.934561\pi$
$74$		0			0
$75$	−23.3739	−	13.4949i	−0.311652	−	0.179932i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−9.49545	−	5.48220i	−0.120196	−	0.0693950i	0.438697	−	0.898635i	$-0.355440\pi$
$79$	−9.49545	−	5.48220i	−0.120196	−	0.0693950i	−0.558892	+	0.829240i	$0.688774\pi$
$80$		0			0
$81$	34.5780	+	59.8909i	0.426889	+	0.739394i
$82$		0			0
$83$		−	143.705i		−	1.73138i	−0.500579	−	0.865691i	$-0.666880\pi$
$83$		−	143.705i		−	1.73138i	0.500579	−	0.865691i	$-0.333120\pi$
$84$		0			0
$85$	−140.486			−1.65278
$86$		0			0
$87$	204.069	−	117.819i	2.34562	−	1.35424i
$88$		0			0
$89$	29.6606	−	51.3737i	0.333265	−	0.577232i	−0.649885	−	0.760033i	$-0.725183\pi$
$89$	29.6606	−	51.3737i	0.333265	−	0.577232i	0.983150	+	0.182800i	$0.0585162\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	63.8258	−	110.549i	0.686298	−	1.18870i
$94$		0			0
$95$	148.156	−	85.5379i	1.55954	−	0.900399i
$96$		0			0
$97$	−17.1652			−0.176960			−0.0884802	−	0.996078i	$-0.528201\pi$
$97$	−17.1652			−0.176960			−0.0884802	+	0.996078i	$0.528201\pi$
$98$		0			0
$99$			18.5758i			0.187634i
$100$		0			0
$101$	4.37386	+	7.57575i	0.0433056	+	0.0750075i	0.886866	−	0.462027i	$-0.152878\pi$
$101$	4.37386	+	7.57575i	0.0433056	+	0.0750075i	−0.843560	+	0.537035i	$0.819544\pi$
$102$		0			0
$103$	−47.4083	−	27.3712i	−0.460275	−	0.265740i	0.251885	−	0.967757i	$-0.418950\pi$
$103$	−47.4083	−	27.3712i	−0.460275	−	0.265740i	−0.712160	+	0.702017i	$0.752283\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−110.312	−	63.6887i	−1.03095	−	0.595222i	−0.113696	−	0.993516i	$-0.536269\pi$
$107$	−110.312	−	63.6887i	−1.03095	−	0.595222i	−0.917258	+	0.398294i	$0.869602\pi$
$108$		0			0
$109$	24.2523	+	42.0062i	0.222498	+	0.385378i	0.955566	−	0.294778i	$-0.0952456\pi$
$109$	24.2523	+	42.0062i	0.222498	+	0.385378i	−0.733068	+	0.680155i	$0.761912\pi$
$110$		0			0
$111$			75.1456i			0.676988i
$112$		0			0
$113$	−36.5045			−0.323049			−0.161525	−	0.986869i	$-0.551641\pi$
$113$	−36.5045			−0.323049			−0.161525	+	0.986869i	$0.551641\pi$
$114$		0			0
$115$	−15.8258	+	9.13701i	−0.137615	+	0.0794522i
$116$		0			0
$117$	105.452	−	182.648i	0.901298	−	1.56109i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−58.8303	+	101.897i	−0.486201	+	0.842125i
$122$		0			0
$123$	−28.4174	+	16.4068i	−0.231036	+	0.133389i
$124$		0			0
$125$	−105.147			−0.841176
$126$		0			0
$127$			41.9506i			0.330320i	0.986267	+	0.165160i	$0.0528140\pi$
$127$			41.9506i			0.330320i	−0.986267	+	0.165160i	$0.947186\pi$
$128$		0			0
$129$	125.321	+	217.063i	0.971482	+	1.68266i
$130$		0			0
$131$	−41.0436	−	23.6965i	−0.313310	−	0.180889i	0.335097	−	0.942184i	$-0.391231\pi$
$131$	−41.0436	−	23.6965i	−0.313310	−	0.180889i	−0.648407	+	0.761294i	$0.724564\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	24.6606	+	14.2378i	0.182671	+	0.105465i
$136$		0			0
$137$	−76.8258	−	133.066i	−0.560772	−	0.971286i	−0.997429	−	0.0716576i	$-0.977171\pi$
$137$	−76.8258	−	133.066i	−0.560772	−	0.971286i	0.436657	−	0.899628i	$-0.356162\pi$
$138$		0			0
$139$		−	147.439i		−	1.06071i	−0.847775	−	0.530356i	$-0.822058\pi$
$139$		−	147.439i		−	1.06071i	0.847775	−	0.530356i	$-0.177942\pi$
$140$		0			0
$141$	162.991			1.15596
$142$		0			0
$143$	−32.8348	+	18.9572i	−0.229614	+	0.132568i
$144$		0			0
$145$	−150.243	+	260.229i	−1.03616	+	1.79468i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−39.1561	+	67.8203i	−0.262792	+	0.455170i	−0.966983	−	0.254841i	$-0.917977\pi$
$149$	−39.1561	+	67.8203i	−0.262792	+	0.455170i	0.704191	+	0.710011i	$0.251310\pi$
$150$		0			0
$151$	−133.652	+	77.1637i	−0.885109	+	0.511018i	−0.872340	−	0.488900i	$-0.837398\pi$
$151$	−133.652	+	77.1637i	−0.885109	+	0.511018i	−0.0127697	+	0.999918i	$0.504065\pi$
$152$		0			0
$153$	255.808			1.67194
$154$		0			0
$155$			162.781i			1.05020i
$156$		0			0
$157$	−80.7042	−	139.784i	−0.514039	−	0.890342i	−0.999867	−	0.0162877i	$-0.994815\pi$
$157$	−80.7042	−	139.784i	−0.514039	−	0.890342i	0.485828	−	0.874054i	$-0.338518\pi$
$158$		0			0
$159$	174.399	+	100.689i	1.09685	+	0.633267i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	121.060	+	69.8939i	0.742698	+	0.428797i	0.823050	−	0.567969i	$-0.192271\pi$
$163$	121.060	+	69.8939i	0.742698	+	0.428797i	−0.0803512	+	0.996767i	$0.525604\pi$
$164$		0			0
$165$	−22.3303	−	38.6772i	−0.135335	−	0.234407i
$166$		0			0
$167$			115.348i			0.690709i	0.938472	+	0.345355i	$0.112241\pi$
$167$			115.348i			0.690709i	−0.938472	+	0.345355i	$0.887759\pi$
$168$		0			0
$169$	261.468			1.54715
$170$		0			0
$171$	−269.773	+	155.754i	−1.57762	+	0.910840i
$172$		0			0
$173$	−42.8602	+	74.2361i	−0.247747	+	0.429110i	−0.962900	−	0.269857i	$-0.913023\pi$
$173$	−42.8602	+	74.2361i	−0.247747	+	0.429110i	0.715153	+	0.698968i	$0.246357\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	164.399	−	284.748i	0.928809	−	1.60874i
$178$		0			0
$179$	97.6515	−	56.3791i	0.545539	−	0.314967i	−0.201782	−	0.979431i	$-0.564673\pi$
$179$	97.6515	−	56.3791i	0.545539	−	0.314967i	0.747321	+	0.664463i	$0.231340\pi$
$180$		0			0
$181$	−65.9311			−0.364260			−0.182130	−	0.983274i	$-0.558299\pi$
$181$	−65.9311			−0.364260			−0.182130	+	0.983274i	$0.558299\pi$
$182$		0			0
$183$		−	122.960i		−	0.671912i
$184$		0			0
$185$	−47.9129	−	82.9875i	−0.258989	−	0.448581i
$186$		0			0
$187$	−39.8258	−	22.9934i	−0.212972	−	0.122959i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	179.477	+	103.621i	0.939672	+	0.542520i	0.889857	−	0.456239i	$-0.150804\pi$
$191$	179.477	+	103.621i	0.939672	+	0.542520i	0.0498142	+	0.998759i	$0.484137\pi$
$192$		0			0
$193$	−63.5917	−	110.144i	−0.329491	−	0.570694i	0.652920	−	0.757427i	$-0.273544\pi$
$193$	−63.5917	−	110.144i	−0.329491	−	0.570694i	−0.982411	+	0.186732i	$0.940210\pi$
$194$		0			0
$195$			507.062i			2.60032i
$196$		0			0
$197$	227.670			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$197$	227.670			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$198$		0			0
$199$	−148.417	+	85.6888i	−0.745816	+	0.430597i	−0.824180	−	0.566328i	$-0.808364\pi$
$199$	−148.417	+	85.6888i	−0.745816	+	0.430597i	0.0783640	+	0.996925i	$0.475030\pi$
$200$		0			0
$201$	−178.156	+	308.575i	−0.886349	+	1.53520i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	20.9220	−	36.2379i	0.102058	−	0.176770i
$206$		0			0
$207$	28.8167	−	16.6373i	0.139211	−	0.0803735i
$208$		0			0
$209$	56.0000			0.267943
$210$		0			0
$211$		−	149.910i		−	0.710473i	−0.934776	−	0.355237i	$-0.884400\pi$
$211$		−	149.910i		−	0.710473i	0.934776	−	0.355237i	$-0.115600\pi$
$212$		0			0
$213$	−70.3303	−	121.816i	−0.330189	−	0.571904i
$214$		0			0
$215$	−276.798	−	159.810i	−1.28743	−	0.743301i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−173.078	−	99.9266i	−0.790311	−	0.456286i
$220$		0			0
$221$	261.060	+	452.169i	1.18127	+	2.04601i
$222$		0			0
$223$			85.2676i			0.382366i	0.981554	+	0.191183i	$0.0612324\pi$
$223$			85.2676i			0.382366i	−0.981554	+	0.191183i	$0.938768\pi$
$224$		0			0
$225$	−62.6697			−0.278532
$226$		0			0
$227$	−133.809	+	77.2549i	−0.589469	+	0.340330i	−0.764888	−	0.644164i	$-0.777205\pi$
$227$	−133.809	+	77.2549i	−0.589469	+	0.340330i	0.175418	+	0.984494i	$0.443872\pi$
$228$		0			0
$229$	165.278	−	286.269i	0.721736	−	1.25008i	−0.238567	−	0.971126i	$-0.576678\pi$
$229$	165.278	−	286.269i	0.721736	−	1.25008i	0.960303	−	0.278958i	$-0.0899891\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−106.670	+	184.757i	−0.457810	+	0.792950i	−0.998845	−	0.0480501i	$-0.984699\pi$
$233$	−106.670	+	184.757i	−0.457810	+	0.792950i	0.541035	+	0.841000i	$0.318033\pi$
$234$		0			0
$235$	−180.000	+	103.923i	−0.765957	+	0.442226i
$236$		0			0
$237$	−48.0000			−0.202532
$238$		0			0
$239$		−	266.545i		−	1.11525i	−0.830092	−	0.557626i	$-0.811712\pi$
$239$		−	266.545i		−	1.11525i	0.830092	−	0.557626i	$-0.188288\pi$
$240$		0			0
$241$	13.2432	+	22.9379i	0.0549510	+	0.0951779i	0.892192	−	0.451656i	$-0.149166\pi$
$241$	13.2432	+	22.9379i	0.0549510	+	0.0951779i	−0.837241	+	0.546833i	$0.815833\pi$
$242$		0			0
$243$	301.947	+	174.329i	1.24258	+	0.717405i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−550.624	−	317.903i	−2.22925	−	1.28706i
$248$		0			0
$249$	−314.555	−	544.826i	−1.26327	−	2.18806i
$250$		0			0
$251$		−	372.796i		−	1.48524i	−0.669711	−	0.742622i	$-0.733582\pi$
$251$		−	372.796i		−	1.48524i	0.669711	−	0.742622i	$-0.266418\pi$
$252$		0			0
$253$	−5.98182			−0.0236435
$254$		0			0
$255$	−532.624	+	307.511i	−2.08872	+	1.20592i
$256$		0			0
$257$	−103.000	+	178.401i	−0.400778	+	0.694168i	−0.993820	−	0.111003i	$-0.964594\pi$
$257$	−103.000	+	178.401i	−0.400778	+	0.694168i	0.593042	+	0.805172i	$0.297927\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	273.573	−	473.843i	1.04817	−	1.81549i
$262$		0			0
$263$	−403.129	+	232.747i	−1.53281	+	0.884968i	−0.533578	+	0.845751i	$0.679153\pi$
$263$	−403.129	+	232.747i	−1.53281	+	0.884968i	−0.999231	+	0.0392171i	$0.987514\pi$
$264$		0			0
$265$	−256.798			−0.969051
$266$		0			0
$267$		−	259.697i		−	0.972646i
$268$		0			0
$269$	−195.209	−	338.111i	−0.725683	−	1.25692i	−0.958692	−	0.284445i	$-0.908191\pi$
$269$	−195.209	−	338.111i	−0.725683	−	1.25692i	0.233009	−	0.972474i	$-0.425143\pi$
$270$		0			0
$271$	115.652	+	66.7714i	0.426758	+	0.246389i	0.697965	−	0.716132i	$-0.254089\pi$
$271$	115.652	+	66.7714i	0.426758	+	0.246389i	−0.271206	+	0.962521i	$0.587423\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.75682	+	5.63310i	0.0354793	+	0.0204840i
$276$		0			0
$277$	−153.312	−	265.544i	−0.553473	−	0.958644i	−0.998021	−	0.0628885i	$-0.979969\pi$
$277$	−153.312	−	265.544i	−0.553473	−	0.958644i	0.444547	−	0.895755i	$-0.353365\pi$
$278$		0			0
$279$		−	296.404i		−	1.06238i
$280$		0			0
$281$	−112.642			−0.400863			−0.200431	−	0.979708i	$-0.564234\pi$
$281$	−112.642			−0.400863			−0.200431	+	0.979708i	$0.564234\pi$
$282$		0			0
$283$	410.815	−	237.184i	1.45164	−	0.838106i	0.453067	−	0.891476i	$-0.350330\pi$
$283$	410.815	−	237.184i	1.45164	−	0.838106i	0.998575	+	0.0533702i	$0.0169963\pi$
$284$		0			0
$285$	374.468	−	648.598i	1.31392	−	2.27578i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−172.142	+	298.159i	−0.595649	+	1.03169i
$290$		0			0
$291$	−65.0780	+	37.5728i	−0.223636	+	0.129116i
$292$		0			0
$293$	−17.0962			−0.0583489			−0.0291744	−	0.999574i	$-0.509288\pi$
$293$	−17.0962			−0.0583489			−0.0291744	+	0.999574i	$0.509288\pi$
$294$		0			0
$295$			419.284i			1.42130i
$296$		0			0
$297$	4.66061	+	8.07241i	0.0156923	+	0.0271798i
$298$		0			0
$299$	58.8167	+	33.9578i	0.196711	+	0.113571i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	33.1652	+	19.1479i	0.109456	+	0.0631944i
$304$		0			0
$305$	78.3992	+	135.791i	0.257047	+	0.445218i
$306$		0			0
$307$			508.468i			1.65625i	0.560544	+	0.828124i	$0.310592\pi$
$307$			508.468i			1.65625i	−0.560544	+	0.828124i	$0.689408\pi$
$308$		0			0
$309$	−239.652			−0.775571
$310$		0			0
$311$	−27.0273	+	15.6042i	−0.0869044	+	0.0501743i	−0.542822	−	0.839847i	$-0.682644\pi$
$311$	−27.0273	+	15.6042i	−0.0869044	+	0.0501743i	0.455918	+	0.890022i	$0.349311\pi$
$312$		0			0
$313$	−87.5917	+	151.713i	−0.279846	+	0.484707i	−0.971346	−	0.237669i	$-0.923617\pi$
$313$	−87.5917	+	151.713i	−0.279846	+	0.484707i	0.691501	+	0.722376i	$0.256950\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−108.826	+	188.492i	−0.343299	+	0.594611i	−0.985043	−	0.172308i	$-0.944878\pi$
$317$	−108.826	+	188.492i	−0.343299	+	0.594611i	0.641744	+	0.766919i	$0.278211\pi$
$318$		0			0
$319$	−85.1833	+	49.1806i	−0.267032	+	0.154171i
$320$		0			0
$321$	−557.633			−1.73718
$322$		0			0
$323$		−	771.176i		−	2.38754i
$324$		0			0
$325$	−63.9564	−	110.776i	−0.196789	−	0.340849i
$326$		0			0
$327$	183.895	+	106.172i	0.562369	+	0.324684i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−520.886	−	300.733i	−1.57367	−	0.908560i	−0.995713	−	0.0924947i	$-0.970516\pi$
$331$	−520.886	−	300.733i	−1.57367	−	0.908560i	−0.577959	−	0.816066i	$-0.696151\pi$
$332$		0			0
$333$	87.2432	+	151.110i	0.261992	+	0.453783i
$334$		0			0
$335$		−	454.369i		−	1.35633i
$336$		0			0
$337$	−445.477			−1.32189			−0.660946	−	0.750434i	$-0.729845\pi$
$337$	−445.477			−1.32189			−0.660946	+	0.750434i	$0.729845\pi$
$338$		0			0
$339$	−138.399	+	79.9048i	−0.408257	+	0.235707i
$340$		0			0
$341$	−26.6424	+	46.1460i	−0.0781303	+	0.135326i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−40.0000	+	69.2820i	−0.115942	+	0.200817i
$346$		0			0
$347$	350.243	−	202.213i	1.00935	−	0.582746i	0.0983461	−	0.995152i	$-0.468645\pi$
$347$	350.243	−	202.213i	1.00935	−	0.582746i	0.911000	+	0.412406i	$0.135311\pi$
$348$		0			0
$349$	−157.895			−0.452420			−0.226210	−	0.974079i	$-0.572634\pi$
$349$	−157.895			−0.452420			−0.226210	+	0.974079i	$0.572634\pi$
$350$		0			0
$351$		−	105.830i		−	0.301510i
$352$		0			0
$353$	−160.633	−	278.225i	−0.455052	−	0.788173i	0.543639	−	0.839319i	$-0.317046\pi$
$353$	−160.633	−	278.225i	−0.455052	−	0.788173i	−0.998691	+	0.0511459i	$0.983713\pi$
$354$		0			0
$355$	155.339	+	89.6852i	0.437576	+	0.252634i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	150.661	+	86.9839i	0.419667	+	0.242295i	0.694935	−	0.719073i	$-0.255433\pi$
$359$	150.661	+	86.9839i	0.419667	+	0.242295i	−0.275268	+	0.961368i	$0.588766\pi$
$360$		0			0
$361$	289.046	+	500.643i	0.800682	+	1.38682i
$362$		0			0
$363$			515.095i			1.41899i
$364$		0			0
$365$	254.853			0.698227
$366$		0			0
$367$	−240.798	+	139.025i	−0.656127	+	0.378815i	−0.790800	−	0.612075i	$-0.790335\pi$
$367$	−240.798	+	139.025i	−0.656127	+	0.378815i	0.134673	+	0.990890i	$0.457002\pi$
$368$		0			0
$369$	−38.0962	+	65.9846i	−0.103242	+	0.178820i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	171.486	−	297.023i	0.459749	−	0.796309i	−0.539198	−	0.842179i	$-0.681273\pi$
$373$	171.486	−	297.023i	0.459749	−	0.796309i	0.998947	+	0.0458702i	$0.0146061\pi$
$374$		0			0
$375$	−398.642	+	230.156i	−1.06305	+	0.613750i
$376$		0			0
$377$	1116.76			2.96223
$378$		0			0
$379$		−	145.731i		−	0.384515i	−0.981345	−	0.192257i	$-0.938419\pi$
$379$		−	145.731i		−	0.384515i	0.981345	−	0.192257i	$-0.0615808\pi$
$380$		0			0
$381$	91.8258	+	159.047i	0.241012	+	0.417446i
$382$		0			0
$383$	−194.051	−	112.035i	−0.506660	−	0.292520i	0.224800	−	0.974405i	$-0.427827\pi$
$383$	−194.051	−	112.035i	−0.506660	−	0.292520i	−0.731460	+	0.681885i	$0.761161\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	504.014	+	290.993i	1.30236	+	0.751919i
$388$		0			0
$389$	−49.9038	−	86.4359i	−0.128287	−	0.222200i	0.794726	−	0.606969i	$-0.207615\pi$
$389$	−49.9038	−	86.4359i	−0.128287	−	0.222200i	−0.923013	+	0.384768i	$0.874281\pi$
$390$		0			0
$391$			82.3756i			0.210679i
$392$		0			0
$393$	−207.477			−0.527932
$394$		0			0
$395$	53.0091	−	30.6048i	0.134200	−	0.0774805i
$396$		0			0
$397$	−81.6769	+	141.469i	−0.205735	+	0.356344i	−0.950367	−	0.311132i	$-0.899292\pi$
$397$	−81.6769	+	141.469i	−0.205735	+	0.356344i	0.744631	+	0.667476i	$0.232625\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	61.7295	−	106.919i	0.153939	−	0.266630i	−0.778733	−	0.627355i	$-0.784137\pi$
$401$	61.7295	−	106.919i	0.153939	−	0.266630i	0.932672	+	0.360725i	$0.117471\pi$
$402$		0			0
$403$	523.927	−	302.490i	1.30007	−	0.750594i
$404$		0			0
$405$	−386.069			−0.953257
$406$		0			0
$407$		−	31.3676i		−	0.0770703i
$408$		0			0
$409$	3.92197	+	6.79305i	0.00958917	+	0.0166089i	0.870780	−	0.491673i	$-0.163614\pi$
$409$	3.92197	+	6.79305i	0.00958917	+	0.0166089i	−0.861191	+	0.508281i	$0.830281\pi$
$410$		0			0
$411$	−582.537	−	336.328i	−1.41737	−	0.818316i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	694.762	+	401.121i	1.67413	+	0.966557i
$416$		0			0
$417$	−322.730	−	558.984i	−0.773932	−	1.34049i
$418$		0			0
$419$		−	364.565i		−	0.870083i	−0.900410	−	0.435041i	$-0.856734\pi$
$419$		−	364.565i		−	0.870083i	0.900410	−	0.435041i	$-0.143266\pi$
$420$		0			0
$421$	708.570			1.68306			0.841532	−	0.540208i	$-0.181654\pi$
$421$	708.570			1.68306			0.841532	+	0.540208i	$0.181654\pi$
$422$		0			0
$423$	327.757	−	189.230i	0.774839	−	0.447353i
$424$		0			0
$425$	77.5735	−	134.361i	0.182526	−	0.316144i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−82.9909	+	143.744i	−0.193452	+	0.335069i
$430$		0			0
$431$	−70.1015	+	40.4731i	−0.162649	+	0.0939052i	−0.579115	−	0.815246i	$-0.696602\pi$
$431$	−70.1015	+	40.4731i	−0.162649	+	0.0939052i	0.416466	+	0.909151i	$0.363268\pi$
$432$		0			0
$433$	−295.495			−0.682438			−0.341219	−	0.939984i	$-0.610840\pi$
$433$	−295.495			−0.682438			−0.341219	+	0.939984i	$0.610840\pi$
$434$		0			0
$435$			1315.47i			3.02407i
$436$		0			0
$437$	−50.1561	−	86.8728i	−0.114774	−	0.198794i
$438$		0			0
$439$	−10.0182	−	5.78400i	−0.0228205	−	0.0131754i	0.488546	−	0.872538i	$-0.337527\pi$
$439$	−10.0182	−	5.78400i	−0.0228205	−	0.0131754i	−0.511367	+	0.859363i	$0.670861\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	246.523	+	142.330i	0.556485	+	0.321287i	0.751733	−	0.659467i	$-0.229218\pi$
$443$	246.523	+	142.330i	0.556485	+	0.321287i	−0.195249	+	0.980754i	$0.562551\pi$
$444$		0			0
$445$	165.583	+	286.797i	0.372096	+	0.644489i
$446$		0			0
$447$			342.835i			0.766969i
$448$		0			0
$449$	154.624			0.344375			0.172187	−	0.985064i	$-0.444917\pi$
$449$	154.624			0.344375			0.172187	+	0.985064i	$0.444917\pi$
$450$		0			0
$451$	11.8621	−	6.84860i	0.0263018	−	0.0151854i
$452$		0			0
$453$	−337.808	+	585.100i	−0.745712	+	1.29161i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−205.225	+	355.460i	−0.449070	+	0.777812i	−0.998326	−	0.0578422i	$-0.981578\pi$
$457$	−205.225	+	355.460i	−0.449070	+	0.777812i	0.549256	+	0.835654i	$0.314911\pi$
$458$		0			0
$459$	111.165	−	64.1812i	0.242190	−	0.139828i
$460$		0			0
$461$	595.078			1.29084			0.645421	−	0.763827i	$-0.276682\pi$
$461$	595.078			1.29084			0.645421	+	0.763827i	$0.276682\pi$
$462$		0			0
$463$			511.924i			1.10567i	0.833291	+	0.552834i	$0.186454\pi$
$463$			511.924i			1.10567i	−0.833291	+	0.552834i	$0.813546\pi$
$464$		0			0
$465$	356.312	+	617.151i	0.766263	+	1.32721i
$466$		0			0
$467$	316.205	+	182.561i	0.677098	+	0.390923i	0.798761	−	0.601649i	$-0.205489\pi$
$467$	316.205	+	182.561i	0.677098	+	0.390923i	−0.121663	+	0.992572i	$0.538823\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−611.945	−	353.307i	−1.29925	−	0.750121i
$472$		0			0
$473$	−52.3121	−	90.6072i	−0.110596	−	0.191559i
$474$		0			0
$475$			188.929i			0.397745i
$476$		0			0
$477$	467.597			0.980287
$478$		0			0
$479$	175.583	−	101.373i	0.366561	−	0.211634i	−0.305394	−	0.952226i	$-0.598788\pi$
$479$	175.583	−	101.373i	0.366561	−	0.211634i	0.671955	+	0.740592i	$0.265455\pi$
$480$		0			0
$481$	−178.069	+	308.424i	−0.370206	+	0.641215i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	47.9129	−	82.9875i	0.0987894	−	0.171108i
$486$		0			0
$487$	711.111	−	410.560i	1.46019	−	0.843039i	0.461167	−	0.887314i	$-0.347431\pi$
$487$	711.111	−	410.560i	1.46019	−	0.843039i	0.999019	+	0.0442747i	$0.0140977\pi$
$488$		0			0
$489$	611.964			1.25146
$490$		0			0
$491$			316.505i			0.644613i	0.946635	+	0.322307i	$0.104458\pi$
$491$			316.505i			0.644613i	−0.946635	+	0.322307i	$0.895542\pi$
$492$		0			0
$493$	677.267	+	1173.06i	1.37377	+	2.37943i
$494$		0			0
$495$	−89.8076	−	51.8504i	−0.181429	−	0.104748i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−152.780	−	88.2077i	−0.306173	−	0.176769i	0.339040	−	0.940772i	$-0.389898\pi$
$499$	−152.780	−	88.2077i	−0.306173	−	0.176769i	−0.645213	+	0.764003i	$0.723231\pi$
$500$		0			0
$501$	252.486	+	437.319i	0.503965	+	0.872893i
$502$		0			0
$503$		−	883.918i		−	1.75729i	−0.477474	−	0.878646i	$-0.658447\pi$
$503$		−	883.918i		−	1.75729i	0.477474	−	0.878646i	$-0.341553\pi$
$504$		0			0
$505$	−48.8348			−0.0967027
$506$		0			0
$507$	991.301	−	572.328i	1.95523	−	1.12885i
$508$		0			0
$509$	259.608	−	449.654i	0.510035	−	0.883407i	−0.489897	−	0.871780i	$-0.662966\pi$
$509$	259.608	−	449.654i	0.510035	−	0.883407i	0.999932	−	0.0116268i	$-0.00370100\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−78.1561	+	135.370i	−0.152351	+	0.263880i
$514$		0			0
$515$	264.661	−	152.802i	0.513904	−	0.296703i
$516$		0			0
$517$	−68.0364			−0.131598
$518$		0			0
$519$			375.267i			0.723058i
$520$		0			0
$521$	518.702	+	898.419i	0.995590	+	1.72441i	0.579040	+	0.815299i	$0.303428\pi$
$521$	518.702	+	898.419i	0.995590	+	1.72441i	0.416550	+	0.909113i	$0.363239\pi$
$522$		0			0
$523$	455.443	+	262.950i	0.870828	+	0.502773i	0.867623	−	0.497222i	$-0.165647\pi$
$523$	455.443	+	262.950i	0.870828	+	0.502773i	0.00320439	+	0.999995i	$0.498980\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	635.477	+	366.893i	1.20584	+	0.696192i
$528$		0			0
$529$	−259.142	−	448.848i	−0.489872	−	0.848484i
$530$		0			0
$531$		−	763.462i		−	1.43778i
$532$		0			0
$533$	−155.514			−0.291770
$534$		0			0
$535$	615.826	−	355.547i	1.15108	−	0.664574i
$536$		0			0
$537$	246.817	−	427.499i	0.459621	−	0.796088i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	388.111	−	672.227i	0.717395	−	1.24256i	−0.244634	−	0.969616i	$-0.578668\pi$
$541$	388.111	−	672.227i	0.717395	−	1.24256i	0.962029	−	0.272949i	$-0.0879989\pi$
$542$		0			0
$543$	−249.964	+	144.317i	−0.460338	+	0.265776i
$544$		0			0
$545$	−270.780			−0.496845
$546$		0			0
$547$		−	153.041i		−	0.279782i	−0.990167	−	0.139891i	$-0.955325\pi$
$547$		−	153.041i		−	0.279782i	0.990167	−	0.139891i	$-0.0446752\pi$
$548$		0			0
$549$	−142.755	−	247.259i	−0.260027	−	0.450380i
$550$		0			0
$551$	−1428.48	−	824.735i	−2.59253	−	1.49680i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−363.303	−	209.753i	−0.654600	−	0.377934i
$556$		0			0
$557$	−240.789	−	417.059i	−0.432297	−	0.748760i	0.564774	−	0.825246i	$-0.308963\pi$
$557$	−240.789	−	417.059i	−0.432297	−	0.748760i	−0.997071	+	0.0764855i	$0.975630\pi$
$558$		0			0
$559$			1187.87i			2.12499i
$560$		0			0
$561$	−201.321			−0.358861
$562$		0			0
$563$	−424.274	+	244.955i	−0.753595	+	0.435088i	−0.826991	−	0.562215i	$-0.809949\pi$
$563$	−424.274	+	244.955i	−0.753595	+	0.435088i	0.0733965	+	0.997303i	$0.476616\pi$
$564$		0			0
$565$	101.895	−	176.487i	0.180345	−	0.312366i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−48.9492	+	84.7826i	−0.0860268	+	0.149003i	−0.905828	−	0.423645i	$-0.860750\pi$
$569$	−48.9492	+	84.7826i	−0.0860268	+	0.149003i	0.819801	+	0.572648i	$0.194084\pi$
$570$		0			0
$571$	−651.840	+	376.340i	−1.14158	+	0.659089i	−0.946820	−	0.321762i	$-0.895725\pi$
$571$	−651.840	+	376.340i	−1.14158	+	0.659089i	−0.194756	+	0.980852i	$0.562391\pi$
$572$		0			0
$573$	907.267			1.58336
$574$		0			0
$575$		−	20.1810i		−	0.0350974i
$576$		0			0
$577$	−462.267	−	800.669i	−0.801155	−	1.38764i	−0.918856	−	0.394593i	$-0.870886\pi$
$577$	−462.267	−	800.669i	−0.801155	−	1.38764i	0.117701	−	0.993049i	$-0.462448\pi$
$578$		0			0
$579$	−482.189	−	278.392i	−0.832796	−	0.480815i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−72.7985	−	42.0302i	−0.124869	−	0.0720930i
$584$		0			0
$585$	588.693	+	1019.65i	1.00631	+	1.74299i
$586$		0			0
$587$		−	1110.24i		−	1.89138i	−0.325077	−	0.945688i	$-0.605390\pi$
$587$		−	1110.24i		−	1.89138i	0.325077	−	0.945688i	$-0.394610\pi$
$588$		0			0
$589$	−893.561			−1.51708
$590$		0			0
$591$	863.161	−	498.346i	1.46051	−	0.843226i
$592$		0			0
$593$	22.4955	−	38.9633i	0.0379350	−	0.0657053i	−0.846435	−	0.532493i	$-0.821255\pi$
$593$	22.4955	−	38.9633i	0.0379350	−	0.0657053i	0.884370	+	0.466787i	$0.154589\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−375.129	+	649.742i	−0.628356	+	1.08835i
$598$		0			0
$599$	855.964	−	494.191i	1.42899	−	0.825026i	0.431947	−	0.901899i	$-0.357827\pi$
$599$	855.964	−	494.191i	1.42899	−	0.825026i	0.997041	+	0.0768727i	$0.0244935\pi$
$600$		0			0
$601$	−732.570			−1.21892			−0.609459	−	0.792818i	$-0.708613\pi$
$601$	−732.570			−1.21892			−0.609459	+	0.792818i	$0.708613\pi$
$602$		0			0
$603$			827.348i			1.37205i
$604$		0			0
$605$	−328.425	−	568.848i	−0.542851	−	0.940245i
$606$		0			0
$607$	126.330	+	72.9368i	0.208122	+	0.120160i	0.600439	−	0.799671i	$-0.294993\pi$
$607$	126.330	+	72.9368i	0.208122	+	0.120160i	−0.392316	+	0.919830i	$0.628326\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	668.973	+	386.232i	1.09488	+	0.632130i
$612$		0			0
$613$	−50.2886	−	87.1025i	−0.0820369	−	0.142092i	0.822088	−	0.569361i	$-0.192809\pi$
$613$	−50.2886	−	87.1025i	−0.0820369	−	0.142092i	−0.904125	+	0.427269i	$0.859476\pi$
$614$		0			0
$615$		−	183.184i		−	0.297861i
$616$		0			0
$617$	−342.102			−0.554459			−0.277230	−	0.960804i	$-0.589416\pi$
$617$	−342.102			−0.554459			−0.277230	+	0.960804i	$0.589416\pi$
$618$		0			0
$619$	443.512	−	256.062i	0.716497	−	0.413670i	−0.0969649	−	0.995288i	$-0.530913\pi$
$619$	443.512	−	256.062i	0.716497	−	0.413670i	0.813462	+	0.581618i	$0.197580\pi$
$620$		0			0
$621$	8.34849	−	14.4600i	0.0134436	−	0.0232850i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	370.560	−	641.828i	0.592896	−	1.02693i
$626$		0			0
$627$	212.312	−	122.578i	0.338616	−	0.195500i
$628$		0			0
$629$	−431.964			−0.686747
$630$		0			0
$631$		−	530.517i		−	0.840755i	−0.907349	−	0.420378i	$-0.861898\pi$
$631$		−	530.517i		−	0.840755i	0.907349	−	0.420378i	$-0.138102\pi$
$632$		0			0
$633$	−328.138	−	568.351i	−0.518385	−	0.897870i
$634$		0			0
$635$	−202.817	−	117.096i	−0.319396	−	0.184404i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−282.853	−	163.305i	−0.442650	−	0.255564i
$640$		0			0
$641$	527.399	+	913.482i	0.822776	+	1.42509i	0.903607	+	0.428362i	$0.140909\pi$
$641$	527.399	+	913.482i	0.822776	+	1.42509i	−0.0808317	+	0.996728i	$0.525758\pi$
$642$		0			0
$643$			107.316i			0.166899i	0.996512	+	0.0834493i	$0.0265937\pi$
$643$			107.316i			0.166899i	−0.996512	+	0.0834493i	$0.973406\pi$
$644$		0			0
$645$	−1399.23			−2.16935
$646$		0			0
$647$	−175.060	+	101.071i	−0.270572	+	0.156215i	−0.629147	−	0.777286i	$-0.716596\pi$
$647$	−175.060	+	101.071i	−0.270572	+	0.156215i	0.358576	+	0.933501i	$0.383262\pi$
$648$		0			0
$649$	−68.6242	+	118.861i	−0.105738	+	0.183144i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−639.363	+	1107.41i	−0.979116	+	1.69588i	−0.313494	+	0.949590i	$0.601500\pi$
$653$	−639.363	+	1107.41i	−0.979116	+	1.69588i	−0.665622	+	0.746289i	$0.731834\pi$
$654$		0			0
$655$	229.129	−	132.288i	0.349815	−	0.201966i
$656$		0			0
$657$	−464.055			−0.706324
$658$		0			0
$659$		−	835.500i		−	1.26783i	−0.773403	−	0.633915i	$-0.781447\pi$
$659$		−	835.500i		−	1.26783i	0.773403	−	0.633915i	$-0.218553\pi$
$660$		0			0
$661$	499.191	+	864.623i	0.755205	+	1.30805i	0.945272	+	0.326282i	$0.105796\pi$
$661$	499.191	+	864.623i	0.755205	+	1.30805i	−0.190067	+	0.981771i	$0.560871\pi$
$662$		0			0
$663$	1979.51	+	1142.87i	2.98568	+	1.72378i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	152.588	+	88.0966i	0.228767	+	0.132079i
$668$		0			0
$669$	186.642	+	323.274i	0.278987	+	0.483220i
$670$		0			0
$671$			51.3264i			0.0764925i
$672$		0			0
$673$	−572.330			−0.850416			−0.425208	−	0.905096i	$-0.639799\pi$
$673$	−572.330			−0.850416			−0.425208	+	0.905096i	$0.639799\pi$
$674$		0			0
$675$	−27.2341	+	15.7236i	−0.0403468	+	0.0232942i
$676$		0			0
$677$	539.884	−	935.106i	0.797465	−	1.38125i	−0.123797	−	0.992308i	$-0.539507\pi$
$677$	539.884	−	935.106i	0.797465	−	1.38125i	0.921262	−	0.388942i	$-0.127159\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−338.207	+	585.791i	−0.496633	+	0.860193i
$682$		0			0
$683$	−385.129	+	222.354i	−0.563878	+	0.325555i	−0.754701	−	0.656069i	$-0.772218\pi$
$683$	−385.129	+	222.354i	−0.563878	+	0.325555i	0.190822	+	0.981625i	$0.438885\pi$
$684$		0			0
$685$	857.771			1.25222
$686$		0			0
$687$		−	1447.11i		−	2.10641i
$688$		0			0
$689$	477.198	+	826.531i	0.692595	+	1.19961i
$690$		0			0
$691$	185.526	+	107.114i	0.268489	+	0.155012i	0.628201	−	0.778051i	$-0.283792\pi$
$691$	185.526	+	107.114i	0.268489	+	0.155012i	−0.359712	+	0.933064i	$0.617125\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	712.817	+	411.545i	1.02564	+	0.592151i
$696$		0			0
$697$	−94.3121	−	163.353i	−0.135312	−	0.234366i
$698$		0			0
$699$			933.958i			1.33613i
$700$		0			0
$701$	573.477			0.818085			0.409042	−	0.912515i	$-0.365863\pi$
$701$	573.477			0.818085			0.409042	+	0.912515i	$0.365863\pi$
$702$		0			0
$703$	455.546	−	263.010i	0.648003	−	0.374125i
$704$		0			0
$705$	−454.955	+	788.004i	−0.645326	+	1.11774i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	218.408	−	378.294i	0.308051	−	0.533560i	−0.669885	−	0.742465i	$-0.733657\pi$
$709$	218.408	−	378.294i	0.308051	−	0.533560i	0.977936	+	0.208905i	$0.0669898\pi$
$710$		0			0
$711$	−96.5227	+	55.7274i	−0.135756	+	0.0783789i
$712$		0			0
$713$	95.4485			0.133869
$714$		0			0
$715$		−	211.660i		−	0.296028i
$716$		0			0
$717$	−583.441	−	1010.55i	−0.813725	−	1.40941i
$718$		0			0
$719$	1107.92	+	639.660i	1.54092	+	0.889652i	0.998781	+	0.0493653i	$0.0157198\pi$
$719$	1107.92	+	639.660i	1.54092	+	0.889652i	0.542142	+	0.840287i	$0.317613\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	100.417	+	57.9760i	0.138890	+	0.0801881i
$724$		0			0
$725$	−165.922	−	287.385i	−0.228858	−	0.396393i
$726$		0			0
$727$		−	166.834i		−	0.229483i	−0.993395	−	0.114741i	$-0.963396\pi$
$727$		−	166.834i		−	0.229483i	0.993395	−	0.114741i	$-0.0366040\pi$
$728$		0			0
$729$	903.955			1.23999
$730$		0			0
$731$	−1247.75	+	720.391i	−1.70691	+	0.985486i
$732$		0			0
$733$	52.6496	−	91.1918i	0.0718276	−	0.124409i	−0.827875	−	0.560913i	$-0.810450\pi$
$733$	52.6496	−	91.1918i	0.0718276	−	0.124409i	0.899702	+	0.436504i	$0.143784\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	74.3667	−	128.807i	0.100905	−	0.174772i
$738$		0			0
$739$	−778.308	+	449.357i	−1.05319	+	0.608060i	−0.923541	−	0.383500i	$-0.874719\pi$
$739$	−778.308	+	449.357i	−1.05319	+	0.608060i	−0.129650	+	0.991560i	$0.541385\pi$
$740$		0			0
$741$	−2783.43			−3.75632
$742$		0			0
$743$			1154.15i			1.55337i	0.629891	+	0.776683i	$0.283099\pi$
$743$			1154.15i			1.55337i	−0.629891	+	0.776683i	$0.716901\pi$
$744$		0			0
$745$	−218.592	−	378.612i	−0.293412	−	0.508204i
$746$		0			0
$747$	−1265.07	−	730.390i	−1.69354	−	0.977764i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−485.862	−	280.513i	−0.646954	−	0.373519i	0.140335	−	0.990104i	$-0.455182\pi$
$751$	−485.862	−	280.513i	−0.646954	−	0.373519i	−0.787288	+	0.616585i	$0.788516\pi$
$752$		0			0
$753$	−816.014	−	1413.38i	−1.08368	−	1.87700i
$754$		0			0
$755$		−	861.545i		−	1.14112i
$756$		0			0
$757$	−860.120			−1.13622			−0.568111	−	0.822952i	$-0.692325\pi$
$757$	−860.120			−1.13622			−0.568111	+	0.822952i	$0.692325\pi$
$758$		0			0
$759$	−22.6788	+	13.0936i	−0.0298798	+	0.0172511i
$760$		0			0
$761$	668.234	−	1157.42i	0.878100	−	1.52091i	0.0246766	−	0.999695i	$-0.492144\pi$
$761$	668.234	−	1157.42i	0.878100	−	1.52091i	0.853423	−	0.521218i	$-0.174522\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−714.033	+	1236.74i	−0.933376	+	1.61665i
$766$		0			0
$767$	1349.51	−	779.138i	1.75946	−	1.01582i
$768$		0			0
$769$	716.323			0.931499			0.465749	−	0.884917i	$-0.345785\pi$
$769$	716.323			0.931499			0.465749	+	0.884917i	$0.345785\pi$
$770$		0			0
$771$			901.827i			1.16969i
$772$		0			0
$773$	−49.3322	−	85.4459i	−0.0638191	−	0.110538i	0.832350	−	0.554250i	$-0.186995\pi$
$773$	−49.3322	−	85.4459i	−0.0638191	−	0.110538i	−0.896170	+	0.443712i	$0.853661\pi$
$774$		0			0
$775$	−155.684	−	89.8842i	−0.200883	−	0.115980i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	198.922	+	114.848i	0.255356	+	0.147430i
$780$		0			0
$781$	29.3576	+	50.8488i	0.0375897	+	0.0651073i
$782$		0			0
$783$		−	274.555i		−	0.350644i
$784$		0			0
$785$	901.074			1.14787
$786$		0			0
$787$	−583.617	+	336.951i	−0.741572	+	0.428147i	−0.822641	−	0.568562i	$-0.807500\pi$
$787$	−583.617	+	336.951i	−0.741572	+	0.428147i	0.0810687	+	0.996709i	$0.474167\pi$
$788$		0			0
$789$	−1018.92	+	1764.82i	−1.29140	+	2.23678i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	291.372	−	504.671i	0.367430	−	0.636407i
$794$		0			0
$795$	−973.597	+	562.106i	−1.22465	+	0.707052i
$796$		0			0
$797$	1097.76			1.37736			0.688681	−	0.725065i	$-0.258190\pi$
$797$	1097.76			1.37736			0.688681	+	0.725065i	$0.258190\pi$
$798$		0			0
$799$			936.929i			1.17263i
$800$		0			0
$801$	−301.505	−	522.221i	−0.376410	−	0.651962i
$802$		0			0
$803$	72.2470	+	41.7118i	0.0899713	+	0.0519450i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1480.18	−	854.585i	−1.83418	−	1.05897i
$808$		0			0
$809$	170.427	+	295.187i	0.210663	+	0.364879i	0.951922	−	0.306340i	$-0.0991043\pi$
$809$	170.427	+	295.187i	0.210663	+	0.364879i	−0.741259	+	0.671219i	$0.765771\pi$
$810$		0			0
$811$		−	112.655i		−	0.138909i	−0.997585	−	0.0694547i	$-0.977874\pi$
$811$		−	112.655i		−	0.138909i	0.997585	−	0.0694547i	$-0.0221259\pi$
$812$		0			0
$813$	584.624			0.719095
$814$		0			0
$815$	−675.826	+	390.188i	−0.829234	+	0.478759i
$816$		0			0
$817$	877.248	−	1519.44i	1.07374	−	1.85978i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	633.955	−	1098.04i	0.772174	−	1.33744i	−0.164196	−	0.986428i	$-0.552503\pi$
$821$	633.955	−	1098.04i	0.772174	−	1.33744i	0.936369	−	0.351016i	$-0.114164\pi$
$822$		0			0
$823$	−644.036	+	371.835i	−0.782547	+	0.451804i	−0.837332	−	0.546694i	$-0.815886\pi$
$823$	−644.036	+	371.835i	−0.782547	+	0.451804i	0.0547850	+	0.998498i	$0.482553\pi$
$824$		0			0
$825$	49.3212			0.0597833
$826$		0			0
$827$		−	1473.29i		−	1.78149i	−0.454503	−	0.890745i	$-0.650183\pi$
$827$		−	1473.29i		−	1.78149i	0.454503	−	0.890745i	$-0.349817\pi$
$828$		0			0
$829$	−189.920	−	328.951i	−0.229095	−	0.396805i	0.728445	−	0.685104i	$-0.240243\pi$
$829$	−189.920	−	328.951i	−0.229095	−	0.396805i	−0.957540	+	0.288300i	$0.906910\pi$
$830$		0			0
$831$	−1162.50	−	671.170i	−1.39892	−	0.807666i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−557.670	−	321.971i	−0.667868	−	0.385594i
$836$		0			0
$837$	−74.3667	−	128.807i	−0.0888491	−	0.153891i
$838$		0			0
$839$			1080.75i			1.28814i	0.764965	+	0.644072i	$0.222756\pi$
$839$			1080.75i			1.28814i	−0.764965	+	0.644072i	$0.777244\pi$
$840$		0			0
$841$	2056.21			2.44496
$842$		0			0
$843$	−427.060	+	246.563i	−0.506595	+	0.292483i
$844$		0			0
$845$	−729.833	+	1264.11i	−0.863708	+	1.49599i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1038.34	−	1798.47i	1.22302	−	2.11833i
$850$		0			0
$851$	−48.6606	+	28.0942i	−0.0571805	+	0.0330132i
$852$		0			0
$853$	125.372			0.146978			0.0734888	−	0.997296i	$-0.476587\pi$
$853$	125.372			0.146978			0.0734888	+	0.997296i	$0.476587\pi$
$854$		0			0
$855$		−	1739.01i		−	2.03393i
$856$		0			0
$857$	360.858	+	625.025i	0.421072	+	0.729317i	0.996045	−	0.0888550i	$-0.0283208\pi$
$857$	360.858	+	625.025i	0.421072	+	0.729317i	−0.574973	+	0.818172i	$0.694987\pi$
$858$		0			0
$859$	−90.7095	−	52.3711i	−0.105599	−	0.0609676i	0.446270	−	0.894898i	$-0.352752\pi$
$859$	−90.7095	−	52.3711i	−0.105599	−	0.0609676i	−0.551869	+	0.833931i	$0.686085\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−368.065	−	212.503i	−0.426495	−	0.246237i	0.271357	−	0.962479i	$-0.412527\pi$
$863$	−368.065	−	212.503i	−0.426495	−	0.246237i	−0.697852	+	0.716242i	$0.745861\pi$
$864$		0			0
$865$	−239.270	−	414.429i	−0.276613	−	0.479108i
$866$		0			0
$867$			1507.21i			1.73842i
$868$		0			0
$869$	20.0364			0.0230568
$870$		0			0
$871$	−1462.43	+	844.335i	−1.67903	+	0.969386i
$872$		0			0
$873$	−87.2432	+	151.110i	−0.0999349	+	0.173092i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	234.684	−	406.485i	0.267599	−	0.463495i	−0.700642	−	0.713513i	$-0.747103\pi$
$877$	234.684	−	406.485i	0.267599	−	0.463495i	0.968241	+	0.250018i	$0.0804365\pi$
$878$		0			0
$879$	−64.8167	+	37.4219i	−0.0737391	+	0.0425733i
$880$		0			0
$881$	1116.11			1.26687			0.633435	−	0.773796i	$-0.281644\pi$
$881$	1116.11			1.26687			0.633435	+	0.773796i	$0.281644\pi$
$882$		0			0
$883$			271.281i			0.307227i	0.988131	+	0.153613i	$0.0490910\pi$
$883$			271.281i			0.307227i	−0.988131	+	0.153613i	$0.950909\pi$
$884$		0			0
$885$	917.771	+	1589.63i	1.03703	+	1.79619i
$886$		0			0
$887$	−183.096	−	105.711i	−0.206422	−	0.119178i	0.393226	−	0.919442i	$-0.371359\pi$
$887$	−183.096	−	105.711i	−0.206422	−	0.119178i	−0.599647	+	0.800264i	$0.704692\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−109.445	−	63.1879i	−0.122834	−	0.0709180i
$892$		0			0
$893$	−570.468	−	988.080i	−0.638822	−	1.10647i
$894$		0			0
$895$			629.481i			0.703331i
$896$		0			0
$897$	297.321			0.331462
$898$		0			0
$899$	1359.22	−	784.748i	1.51193	−	0.872912i
$900$		0			0
$901$	−578.798	+	1002.51i	−0.642396	+	1.11266i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	184.033	−	318.754i	0.203351	−	0.352214i
$906$		0			0
$907$	−355.321	+	205.145i	−0.391754	+	0.226179i	−0.682920	−	0.730493i	$-0.739290\pi$
$907$	−355.321	+	205.145i	−0.391754	+	0.226179i	0.291166	+	0.956673i	$0.405957\pi$
$908$		0			0
$909$	88.9220			0.0978239
$910$		0			0
$911$		−	608.982i		−	0.668476i	−0.942489	−	0.334238i	$-0.891521\pi$
$911$		−	608.982i		−	0.668476i	0.942489	−	0.334238i	$-0.108479\pi$
$912$		0			0
$913$	131.303	+	227.424i	0.143815	+	0.249095i
$914$		0			0
$915$	594.468	+	343.216i	0.649692	+	0.375100i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	431.230	+	248.971i	0.469239	+	0.270915i	0.715921	−	0.698181i	$-0.246007\pi$
$919$	431.230	+	248.971i	0.469239	+	0.270915i	−0.246682	+	0.969096i	$0.579340\pi$
$920$		0			0
$921$	1112.99	+	1927.75i	1.20846	+	2.09311i
$922$		0			0
$923$		−	666.633i		−	0.722246i
$924$		0			0
$925$	105.826			0.114406
$926$		0			0
$927$	−481.913	+	278.233i	−0.519863	+	0.300143i
$928$		0			0
$929$	−32.7023	+	56.6420i	−0.0352016	+	0.0609709i	−0.883089	−	0.469205i	$-0.844541\pi$
$929$	−32.7023	+	56.6420i	−0.0352016	+	0.0609709i	0.847888	+	0.530176i	$0.177874\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−68.3121	+	118.320i	−0.0732177	+	0.126817i
$934$		0			0
$935$	222.330	−	128.362i	0.237786	−	0.137286i
$936$		0			0
$937$	600.918			0.641321			0.320661	−	0.947194i	$-0.396095\pi$
$937$	600.918			0.641321			0.320661	+	0.947194i	$0.396095\pi$
$938$		0			0
$939$			766.918i			0.816739i
$940$		0			0
$941$	−741.434	−	1284.20i	−0.787921	−	1.36472i	−0.927238	−	0.374472i	$-0.877824\pi$
$941$	−741.434	−	1284.20i	−0.787921	−	1.36472i	0.139317	−	0.990248i	$-0.455509\pi$
$942$		0			0
$943$	−21.2485	−	12.2678i	−0.0225329	−	0.0130093i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−698.766	−	403.433i	−0.737873	−	0.426011i	0.0834223	−	0.996514i	$-0.473415\pi$
$947$	−698.766	−	403.433i	−0.737873	−	0.426011i	−0.821296	+	0.570503i	$0.806748\pi$
$948$		0			0
$949$	−473.583	−	820.269i	−0.499033	−	0.864351i
$950$		0			0
$951$			952.835i			1.00193i
$952$		0			0
$953$	899.945			0.944329			0.472164	−	0.881510i	$-0.343473\pi$
$953$	899.945			0.944329			0.472164	+	0.881510i	$0.343473\pi$
$954$		0			0
$955$	−1001.95	+	578.473i	−1.04916	+	0.605731i
$956$		0			0
$957$	−215.303	+	372.916i	−0.224977	+	0.389672i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−55.3818	+	95.9241i	−0.0576294	+	0.0998170i
$962$		0			0
$963$	−1121.34	+	647.406i	−1.16442	+	0.672280i
$964$		0			0
$965$	710.011			0.735762
$966$		0			0
$967$			1725.92i			1.78482i	0.451228	+	0.892409i	$0.350986\pi$
$967$			1725.92i			1.78482i	−0.451228	+	0.892409i	$0.649014\pi$
$968$		0			0
$969$	−1688.03	−	2923.75i	−1.74203	−	3.01729i
$970$		0			0
$971$	569.802	+	328.975i	0.586820	+	0.338800i	0.763839	−	0.645407i	$-0.223312\pi$
$971$	569.802	+	328.975i	0.586820	+	0.338800i	−0.177019	+	0.984207i	$0.556646\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−484.955	−	279.989i	−0.497389	−	0.287168i
$976$		0			0
$977$	−23.4682	−	40.6481i	−0.0240207	−	0.0416050i	0.853765	−	0.520658i	$-0.174313\pi$
$977$	−23.4682	−	40.6481i	−0.0240207	−	0.0416050i	−0.877786	+	0.479053i	$0.840980\pi$
$978$		0			0
$979$			108.404i			0.110729i
$980$		0			0
$981$	493.056			0.502606
$982$		0			0
$983$	−326.573	+	188.547i	−0.332221	+	0.191808i	−0.656827	−	0.754041i	$-0.728102\pi$
$983$	−326.573	+	188.547i	−0.332221	+	0.191808i	0.324606	+	0.945849i	$0.394768\pi$
$984$		0			0
$985$	−635.492	+	1100.70i	−0.645169	+	1.11747i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−93.7061	+	162.304i	−0.0947483	+	0.164109i
$990$		0			0
$991$	−802.185	+	463.142i	−0.809470	+	0.467348i	−0.846772	−	0.531956i	$-0.821457\pi$
$991$	−802.185	+	463.142i	−0.809470	+	0.467348i	0.0373017	+	0.999304i	$0.488124\pi$
$992$		0			0
$993$	−2633.10			−2.65166
$994$		0			0
$995$		−	956.729i		−	0.961537i
$996$		0			0
$997$	−28.3231	−	49.0571i	−0.0284083	−	0.0492047i	0.851472	−	0.524401i	$-0.175711\pi$
$997$	−28.3231	−	49.0571i	−0.0284083	−	0.0492047i	−0.879880	+	0.475196i	$0.842377\pi$
$998$		0			0
$999$	75.8258	+	43.7780i	0.0759017	+	0.0438218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.3.r.n.79.2		4
4.3	odd	2		784.3.r.i.79.1		4
7.2	even	3		784.3.d.j.687.4		4
7.3	odd	6		784.3.r.o.655.2		4
7.4	even	3		784.3.r.i.655.1		4
7.5	odd	6		112.3.d.b.15.1	✓	4
7.6	odd	2		784.3.r.j.79.1		4
21.5	even	6		1008.3.m.d.127.3		4
28.3	even	6		784.3.r.j.655.1		4
28.11	odd	6	inner	784.3.r.n.655.2		4
28.19	even	6		112.3.d.b.15.4	yes	4
28.23	odd	6		784.3.d.j.687.1		4
28.27	even	2		784.3.r.o.79.2		4
56.5	odd	6		448.3.d.b.127.4		4
56.19	even	6		448.3.d.b.127.1		4
84.47	odd	6		1008.3.m.d.127.4		4
112.5	odd	12		1792.3.g.e.127.1		8
112.19	even	12		1792.3.g.e.127.2		8
112.61	odd	12		1792.3.g.e.127.8		8
112.75	even	12		1792.3.g.e.127.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.d.b.15.1	✓	4	7.5	odd	6
112.3.d.b.15.4	yes	4	28.19	even	6
448.3.d.b.127.1		4	56.19	even	6
448.3.d.b.127.4		4	56.5	odd	6
784.3.d.j.687.1		4	28.23	odd	6
784.3.d.j.687.4		4	7.2	even	3
784.3.r.i.79.1		4	4.3	odd	2
784.3.r.i.655.1		4	7.4	even	3
784.3.r.j.79.1		4	7.6	odd	2
784.3.r.j.655.1		4	28.3	even	6
784.3.r.n.79.2		4	1.1	even	1	trivial
784.3.r.n.655.2		4	28.11	odd	6	inner
784.3.r.o.79.2		4	28.27	even	2
784.3.r.o.655.2		4	7.3	odd	6
1008.3.m.d.127.3		4	21.5	even	6
1008.3.m.d.127.4		4	84.47	odd	6
1792.3.g.e.127.1		8	112.5	odd	12
1792.3.g.e.127.2		8	112.19	even	12
1792.3.g.e.127.7		8	112.75	even	12
1792.3.g.e.127.8		8	112.61	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(3.79129 - 2.18890i) q^{3} +(-2.79129 + 4.83465i) q^{5} +(5.08258 - 8.80328i) q^{9} +O(q^{10})\)	\(q+(3.79129 - 2.18890i) q^{3} +(-2.79129 + 4.83465i) q^{5} +(5.08258 - 8.80328i) q^{9} +(-1.58258 + 0.913701i) q^{11} +20.7477 q^{13} +24.4394i q^{15} +(12.5826 + 21.7937i) q^{17} +(-26.5390 - 15.3223i) q^{19} +(2.83485 + 1.63670i) q^{23} +(-3.08258 - 5.33918i) q^{25} -5.10080i q^{27} +53.8258 q^{29} +(25.2523 - 14.5794i) q^{31} +(-4.00000 + 6.92820i) q^{33} +(-8.58258 + 14.8655i) q^{37} +(78.6606 - 45.4147i) q^{39} -7.49545 q^{41} +57.2530i q^{43} +(28.3739 + 49.1450i) q^{45} +(32.2432 + 18.6156i) q^{47} +(95.4083 + 55.0840i) q^{51} +(23.0000 + 39.8372i) q^{53} -10.2016i q^{55} -134.156 q^{57} +(65.0436 - 37.5529i) q^{59} +(14.0436 - 24.3242i) q^{61} +(-57.9129 + 100.308i) q^{65} +(-70.4864 + 40.6953i) q^{67} +14.3303 q^{69} -32.1304i q^{71} +(-22.8258 - 39.5354i) q^{73} +(-23.3739 - 13.4949i) q^{75} +(-9.49545 - 5.48220i) q^{79} +(34.5780 + 59.8909i) q^{81} -143.705i q^{83} -140.486 q^{85} +(204.069 - 117.819i) q^{87} +(29.6606 - 51.3737i) q^{89} +(63.8258 - 110.549i) q^{93} +(148.156 - 85.5379i) q^{95} -17.1652 q^{97} +18.5758i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 2 q^{5} + 2 q^{9}+O(q^{10}) \) 4 * q + 6 * q^3 - 2 * q^5 + 2 * q^9	\( 4 q + 6 q^{3} - 2 q^{5} + 2 q^{9} + 12 q^{11} + 28 q^{13} + 32 q^{17} - 42 q^{19} + 48 q^{23} + 6 q^{25} + 32 q^{29} + 156 q^{31} - 16 q^{33} - 16 q^{37} + 168 q^{39} + 80 q^{41} + 86 q^{45} - 36 q^{47} + 180 q^{51} + 92 q^{53} - 280 q^{57} + 306 q^{59} + 102 q^{61} - 140 q^{65} + 48 q^{67} - 16 q^{69} + 92 q^{73} - 66 q^{75} + 72 q^{79} + 10 q^{81} - 232 q^{85} + 468 q^{87} - 28 q^{89} + 72 q^{93} + 336 q^{95} - 32 q^{97}+O(q^{100}) \) 4 * q + 6 * q^3 - 2 * q^5 + 2 * q^9 + 12 * q^11 + 28 * q^13 + 32 * q^17 - 42 * q^19 + 48 * q^23 + 6 * q^25 + 32 * q^29 + 156 * q^31 - 16 * q^33 - 16 * q^37 + 168 * q^39 + 80 * q^41 + 86 * q^45 - 36 * q^47 + 180 * q^51 + 92 * q^53 - 280 * q^57 + 306 * q^59 + 102 * q^61 - 140 * q^65 + 48 * q^67 - 16 * q^69 + 92 * q^73 - 66 * q^75 + 72 * q^79 + 10 * q^81 - 232 * q^85 + 468 * q^87 - 28 * q^89 + 72 * q^93 + 336 * q^95 - 32 * q^97

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