LMFDB - Embedded newform 79.3.b.b.78.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [79,3,Mod(78,79)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(79, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("79.78");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 79 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	79.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.15259408845$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 77x^{6} + 2073x^{4} + 23519x^{2} + 95938 $ x^8 + 77x^6 + 2073x^4 + 23519*x^2 + 95938
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			78.1
Root			$5.79987i$ of defining polynomial
Character	$\chi$	$=$	79.78
Dual form			79.3.b.b.78.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.17284 q^{2} -5.79987i q^{3} +6.06689 q^{4} +6.39881 q^{5} +18.4021i q^{6} -7.72499i q^{7} -6.55790 q^{8} -24.6385 q^{9} +O(q^{10})$	\(q-3.17284 q^{2} -5.79987i q^{3} +6.06689 q^{4} +6.39881 q^{5} +18.4021i q^{6} -7.72499i q^{7} -6.55790 q^{8} -24.6385 q^{9} -20.3024 q^{10} +5.61527 q^{11} -35.1872i q^{12} +0.716990 q^{13} +24.5101i q^{14} -37.1123i q^{15} -3.46041 q^{16} +16.7851i q^{17} +78.1741 q^{18} -18.2852 q^{19} +38.8209 q^{20} -44.8040 q^{21} -17.8163 q^{22} +22.8948 q^{23} +38.0350i q^{24} +15.9448 q^{25} -2.27489 q^{26} +90.7016i q^{27} -46.8667i q^{28} -8.44567i q^{29} +117.751i q^{30} +32.3616 q^{31} +37.2109 q^{32} -32.5679i q^{33} -53.2565i q^{34} -49.4308i q^{35} -149.479 q^{36} -57.3597i q^{37} +58.0159 q^{38} -4.15845i q^{39} -41.9628 q^{40} +57.1558i q^{41} +142.156 q^{42} -8.33947i q^{43} +34.0672 q^{44} -157.657 q^{45} -72.6414 q^{46} -14.5253i q^{47} +20.0699i q^{48} -10.6755 q^{49} -50.5903 q^{50} +97.3517 q^{51} +4.34990 q^{52} -13.5739i q^{53} -287.781i q^{54} +35.9311 q^{55} +50.6597i q^{56} +106.052i q^{57} +26.7967i q^{58} -76.3337i q^{59} -225.156i q^{60} +51.8236i q^{61} -102.678 q^{62} +190.333i q^{63} -104.223 q^{64} +4.58789 q^{65} +103.332i q^{66} +42.1742 q^{67} +101.834i q^{68} -132.787i q^{69} +156.836i q^{70} +74.6532i q^{71} +161.577 q^{72} -5.85752 q^{73} +181.993i q^{74} -92.4779i q^{75} -110.934 q^{76} -43.3779i q^{77} +13.1941i q^{78} +(59.1180 - 52.4028i) q^{79} -22.1425 q^{80} +304.311 q^{81} -181.346i q^{82} -40.6315 q^{83} -271.821 q^{84} +107.405i q^{85} +26.4598i q^{86} -48.9838 q^{87} -36.8244 q^{88} +12.2414 q^{89} +500.221 q^{90} -5.53874i q^{91} +138.900 q^{92} -187.693i q^{93} +46.0865i q^{94} -117.004 q^{95} -215.819i q^{96} +127.711 q^{97} +33.8717 q^{98} -138.352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 8 q^{8} - 82 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 8 * q^8 - 82 * q^9	$ 8 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 8 q^{8} - 82 q^{9} - 22 q^{10} + 28 q^{11} - 30 q^{13} - 40 q^{16} + 122 q^{18} - 32 q^{19} + 106 q^{20} - 2 q^{21} + 60 q^{22} + 60 q^{23} - 50 q^{25} + 62 q^{26} + 36 q^{31} + 4 q^{32} - 322 q^{36} + 284 q^{38} - 166 q^{40} + 238 q^{42} + 192 q^{44} - 260 q^{45} - 236 q^{46} - 294 q^{49} - 258 q^{50} + 236 q^{51} + 30 q^{52} + 140 q^{55} - 388 q^{62} - 208 q^{64} + 194 q^{65} + 132 q^{67} + 322 q^{72} + 384 q^{73} - 308 q^{76} + 210 q^{79} + 6 q^{80} + 56 q^{81} + 96 q^{83} - 246 q^{84} - 8 q^{87} - 232 q^{88} + 102 q^{89} + 908 q^{90} - 68 q^{92} - 12 q^{95} + 470 q^{97} + 498 q^{98} - 524 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 8 * q^8 - 82 * q^9 - 22 * q^10 + 28 * q^11 - 30 * q^13 - 40 * q^16 + 122 * q^18 - 32 * q^19 + 106 * q^20 - 2 * q^21 + 60 * q^22 + 60 * q^23 - 50 * q^25 + 62 * q^26 + 36 * q^31 + 4 * q^32 - 322 * q^36 + 284 * q^38 - 166 * q^40 + 238 * q^42 + 192 * q^44 - 260 * q^45 - 236 * q^46 - 294 * q^49 - 258 * q^50 + 236 * q^51 + 30 * q^52 + 140 * q^55 - 388 * q^62 - 208 * q^64 + 194 * q^65 + 132 * q^67 + 322 * q^72 + 384 * q^73 - 308 * q^76 + 210 * q^79 + 6 * q^80 + 56 * q^81 + 96 * q^83 - 246 * q^84 - 8 * q^87 - 232 * q^88 + 102 * q^89 + 908 * q^90 - 68 * q^92 - 12 * q^95 + 470 * q^97 + 498 * q^98 - 524 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/79\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	−3.17284			−1.58642			−0.793209	−	0.608949i	$-0.791591\pi$
$2$	−3.17284			−1.58642			−0.793209	+	0.608949i	$0.791591\pi$
$3$		−	5.79987i		−	1.93329i	−0.256117	−	0.966646i	$-0.582443\pi$
$3$		−	5.79987i		−	1.93329i	0.256117	−	0.966646i	$-0.417557\pi$
$4$	6.06689			1.51672
$5$	6.39881			1.27976			0.639881	−	0.768474i	$-0.278983\pi$
$5$	6.39881			1.27976			0.639881	+	0.768474i	$0.278983\pi$
$6$			18.4021i			3.06701i
$7$		−	7.72499i		−	1.10357i	−0.833986	−	0.551785i	$-0.813947\pi$
$7$		−	7.72499i		−	1.10357i	0.833986	−	0.551785i	$-0.186053\pi$
$8$	−6.55790			−0.819738
$9$	−24.6385			−2.73762
$10$	−20.3024			−2.03024
$11$	5.61527			0.510479			0.255240	−	0.966878i	$-0.417846\pi$
$11$	5.61527			0.510479			0.255240	+	0.966878i	$0.417846\pi$
$12$		−	35.1872i		−	2.93227i
$13$	0.716990			0.0551531			0.0275765	−	0.999620i	$-0.491221\pi$
$13$	0.716990			0.0551531			0.0275765	+	0.999620i	$0.491221\pi$
$14$			24.5101i			1.75072i
$15$		−	37.1123i		−	2.47415i
$16$	−3.46041			−0.216276
$17$			16.7851i			0.987361i	0.869643	+	0.493681i	$0.164349\pi$
$17$			16.7851i			0.987361i	−0.869643	+	0.493681i	$0.835651\pi$
$18$	78.1741			4.34300
$19$	−18.2852			−0.962379			−0.481189	−	0.876617i	$-0.659795\pi$
$19$	−18.2852			−0.962379			−0.481189	+	0.876617i	$0.659795\pi$
$20$	38.8209			1.94104
$21$	−44.8040			−2.13352
$22$	−17.8163			−0.809833
$23$	22.8948			0.995425			0.497713	−	0.867342i	$-0.334173\pi$
$23$	22.8948			0.995425			0.497713	+	0.867342i	$0.334173\pi$
$24$			38.0350i			1.58479i
$25$	15.9448			0.637793
$26$	−2.27489			−0.0874958
$27$			90.7016i			3.35932i
$28$		−	46.8667i		−	1.67381i
$29$		−	8.44567i		−	0.291230i	−0.989341	−	0.145615i	$-0.953484\pi$
$29$		−	8.44567i		−	0.291230i	0.989341	−	0.145615i	$-0.0465161\pi$
$30$			117.751i			3.92504i
$31$	32.3616			1.04392			0.521961	−	0.852969i	$-0.325200\pi$
$31$	32.3616			1.04392			0.521961	+	0.852969i	$0.325200\pi$
$32$	37.2109			1.16284
$33$		−	32.5679i		−	0.986905i
$34$		−	53.2565i		−	1.56637i
$35$		−	49.4308i		−	1.41231i
$36$	−149.479			−4.15220
$37$		−	57.3597i		−	1.55026i	−0.631800	−	0.775132i	$-0.717683\pi$
$37$		−	57.3597i		−	1.55026i	0.631800	−	0.775132i	$-0.282317\pi$
$38$	58.0159			1.52674
$39$		−	4.15845i		−	0.106627i
$40$	−41.9628			−1.04907
$41$			57.1558i			1.39404i	0.717050	+	0.697022i	$0.245492\pi$
$41$			57.1558i			1.39404i	−0.717050	+	0.697022i	$0.754508\pi$
$42$	142.156			3.38466
$43$		−	8.33947i		−	0.193941i	−0.995287	−	0.0969706i	$-0.969085\pi$
$43$		−	8.33947i		−	0.193941i	0.995287	−	0.0969706i	$-0.0309153\pi$
$44$	34.0672			0.774255
$45$	−157.657			−3.50350
$46$	−72.6414			−1.57916
$47$		−	14.5253i		−	0.309050i	−0.987989	−	0.154525i	$-0.950615\pi$
$47$		−	14.5253i		−	0.309050i	0.987989	−	0.154525i	$-0.0493847\pi$
$48$			20.0699i			0.418124i
$49$	−10.6755			−0.217868
$50$	−50.5903			−1.01181
$51$	97.3517			1.90886
$52$	4.34990			0.0836519
$53$		−	13.5739i		−	0.256111i	−0.991767	−	0.128056i	$-0.959126\pi$
$53$		−	13.5739i		−	0.256111i	0.991767	−	0.128056i	$-0.0408736\pi$
$54$		−	287.781i		−	5.32928i
$55$	35.9311			0.653292
$56$			50.6597i			0.904638i
$57$			106.052i			1.86056i
$58$			26.7967i			0.462013i
$59$		−	76.3337i		−	1.29379i	−0.762578	−	0.646896i	$-0.776067\pi$
$59$		−	76.3337i		−	1.29379i	0.762578	−	0.646896i	$-0.223933\pi$
$60$		−	225.156i		−	3.75261i
$61$			51.8236i			0.849567i	0.905295	+	0.424784i	$0.139650\pi$
$61$			51.8236i			0.849567i	−0.905295	+	0.424784i	$0.860350\pi$
$62$	−102.678			−1.65610
$63$			190.333i			3.02115i
$64$	−104.223			−1.62848
$65$	4.58789			0.0705829
$66$			103.332i			1.56564i
$67$	42.1742			0.629466			0.314733	−	0.949180i	$-0.398085\pi$
$67$	42.1742			0.629466			0.314733	+	0.949180i	$0.398085\pi$
$68$			101.834i			1.49755i
$69$		−	132.787i		−	1.92445i
$70$			156.836i			2.24051i
$71$			74.6532i			1.05145i	0.850654	+	0.525727i	$0.176206\pi$
$71$			74.6532i			1.05145i	−0.850654	+	0.525727i	$0.823794\pi$
$72$	161.577			2.24413
$73$	−5.85752			−0.0802401			−0.0401200	−	0.999195i	$-0.512774\pi$
$73$	−5.85752			−0.0802401			−0.0401200	+	0.999195i	$0.512774\pi$
$74$			181.993i			2.45937i
$75$		−	92.4779i		−	1.23304i
$76$	−110.934			−1.45966
$77$		−	43.3779i		−	0.563350i
$78$			13.1941i			0.169155i
$79$	59.1180	−	52.4028i	0.748330	−	0.663327i
$79$	59.1180	−	52.4028i	0.748330	−	0.663327i
$80$	−22.1425			−0.276781
$81$	304.311			3.75692
$82$		−	181.346i		−	2.21154i
$83$	−40.6315			−0.489536			−0.244768	−	0.969582i	$-0.578712\pi$
$83$	−40.6315			−0.489536			−0.244768	+	0.969582i	$0.578712\pi$
$84$	−271.821			−3.23596
$85$			107.405i			1.26359i
$86$			26.4598i			0.307672i
$87$	−48.9838			−0.563033
$88$	−36.8244			−0.418459
$89$	12.2414			0.137544			0.0687721	−	0.997632i	$-0.478092\pi$
$89$	12.2414			0.137544			0.0687721	+	0.997632i	$0.478092\pi$
$90$	500.221			5.55801
$91$		−	5.53874i		−	0.0608653i
$92$	138.900			1.50978
$93$		−	187.693i		−	2.01821i
$94$			46.0865i			0.490282i
$95$	−117.004			−1.23162
$96$		−	215.819i		−	2.24811i
$97$	127.711			1.31661			0.658303	−	0.752753i	$-0.271275\pi$
$97$	127.711			1.31661			0.658303	+	0.752753i	$0.271275\pi$
$98$	33.8717			0.345629
$99$	−138.352			−1.39750
$100$	96.7355			0.967355
$101$	79.5433			0.787558			0.393779	−	0.919205i	$-0.371168\pi$
$101$	79.5433			0.787558			0.393779	+	0.919205i	$0.371168\pi$
$102$	−308.881			−3.02825
$103$			14.4901i			0.140681i	0.997523	+	0.0703403i	$0.0224085\pi$
$103$			14.4901i			0.140681i	−0.997523	+	0.0703403i	$0.977591\pi$
$104$	−4.70195			−0.0452111
$105$	−286.692			−2.73040
$106$			43.0678i			0.406300i
$107$			21.2636i			0.198726i	0.995051	+	0.0993628i	$0.0316804\pi$
$107$			21.2636i			0.198726i	−0.995051	+	0.0993628i	$0.968320\pi$
$108$			550.276i			5.09515i
$109$			142.231i			1.30487i	0.757844	+	0.652436i	$0.226253\pi$
$109$			142.231i			1.30487i	−0.757844	+	0.652436i	$0.773747\pi$
$110$	−114.003			−1.03639
$111$	−332.679			−2.99711
$112$			26.7316i			0.238675i
$113$		−	154.641i		−	1.36851i	−0.729244	−	0.684254i	$-0.760128\pi$
$113$		−	154.641i		−	1.36851i	0.729244	−	0.684254i	$-0.239872\pi$
$114$		−	336.485i		−	2.95162i
$115$	146.499			1.27391
$116$		−	51.2390i		−	0.441715i
$117$	−17.6656			−0.150988
$118$			242.194i			2.05250i
$119$	129.665			1.08962
$120$			243.379i			2.02816i
$121$	−89.4687			−0.739411
$122$		−	164.428i		−	1.34777i
$123$	331.496			2.69509
$124$	196.334			1.58334
$125$	−57.9424			−0.463539
$126$		−	603.894i		−	4.79281i
$127$		−	73.6366i		−	0.579816i	−0.957055	−	0.289908i	$-0.906375\pi$
$127$		−	73.6366i		−	0.579816i	0.957055	−	0.289908i	$-0.0936247\pi$
$128$	181.837			1.42060
$129$	−48.3679			−0.374945
$130$	−14.5566			−0.111974
$131$	−37.2976			−0.284714			−0.142357	−	0.989815i	$-0.545468\pi$
$131$	−37.2976			−0.284714			−0.142357	+	0.989815i	$0.545468\pi$
$132$		−	197.586i		−	1.49686i
$133$			141.253i			1.06205i
$134$	−133.812			−0.998597
$135$			580.382i			4.29913i
$136$		−	110.075i		−	0.809377i
$137$			153.111i			1.11760i	0.829304	+	0.558798i	$0.188737\pi$
$137$			153.111i			1.11760i	−0.829304	+	0.558798i	$0.811263\pi$
$138$			421.311i			3.05298i
$139$			57.1969i			0.411488i	0.978606	+	0.205744i	$0.0659615\pi$
$139$			57.1969i			0.411488i	−0.978606	+	0.205744i	$0.934039\pi$
$140$		−	299.891i		−	2.14208i
$141$	−84.2452			−0.597484
$142$		−	236.862i		−	1.66804i
$143$	4.02609			0.0281545
$144$	85.2594			0.592079
$145$		−	54.0423i		−	0.372706i
$146$	18.5850			0.127294
$147$			61.9167i			0.421202i
$148$		−	347.995i		−	2.35132i
$149$			17.0300i			0.114295i	0.998366	+	0.0571477i	$0.0182006\pi$
$149$			17.0300i			0.114295i	−0.998366	+	0.0571477i	$0.981799\pi$
$150$			293.417i			1.95612i
$151$	−91.2949			−0.604602			−0.302301	−	0.953213i	$-0.597755\pi$
$151$	−91.2949			−0.604602			−0.302301	+	0.953213i	$0.597755\pi$
$152$	119.913			0.788898
$153$		−	413.561i		−	2.70302i
$154$			137.631i			0.893708i
$155$	207.076			1.33597
$156$		−	25.2289i		−	0.161724i
$157$		−	199.776i		−	1.27246i	−0.771499	−	0.636231i	$-0.780493\pi$
$157$		−	199.776i		−	1.27246i	0.771499	−	0.636231i	$-0.219507\pi$
$158$	−187.572	+	166.266i	−1.18716	+	1.05231i
$159$	−78.7269			−0.495138
$160$	238.106			1.48816
$161$		−	176.862i		−	1.09852i
$162$	−965.528			−5.96005
$163$	−208.549			−1.27944			−0.639721	−	0.768607i	$-0.720950\pi$
$163$	−208.549			−1.27944			−0.639721	+	0.768607i	$0.720950\pi$
$164$			346.758i			2.11438i
$165$		−	208.396i		−	1.26300i
$166$	128.917			0.776608
$167$	157.415			0.942606			0.471303	−	0.881971i	$-0.343784\pi$
$167$	157.415			0.942606			0.471303	+	0.881971i	$0.343784\pi$
$168$	293.820			1.74893
$169$	−168.486			−0.996958
$170$		−	340.779i		−	2.00458i
$171$	450.521			2.63462
$172$		−	50.5946i		−	0.294155i
$173$			115.266i			0.666278i	0.942878	+	0.333139i	$0.108108\pi$
$173$			115.266i			0.666278i	−0.942878	+	0.333139i	$0.891892\pi$
$174$	155.418			0.893205
$175$		−	123.174i		−	0.703849i
$176$	−19.4311			−0.110404
$177$	−442.726			−2.50128
$178$	−38.8401			−0.218203
$179$	−24.6611			−0.137772			−0.0688858	−	0.997625i	$-0.521944\pi$
$179$	−24.6611			−0.137772			−0.0688858	+	0.997625i	$0.521944\pi$
$180$	−956.490			−5.31383
$181$	173.834			0.960407			0.480203	−	0.877157i	$-0.340563\pi$
$181$	173.834			0.960407			0.480203	+	0.877157i	$0.340563\pi$
$182$			17.5735i			0.0965578i
$183$	300.570			1.64246
$184$	−150.142			−0.815988
$185$		−	367.034i		−	1.98397i
$186$			595.520i			3.20172i
$187$			94.2531i			0.504027i
$188$		−	88.1237i		−	0.468743i
$189$	700.669			3.70724
$190$	371.233			1.95386
$191$			367.616i			1.92469i	0.271826	+	0.962347i	$0.412373\pi$
$191$			367.616i			1.92469i	−0.271826	+	0.962347i	$0.587627\pi$
$192$			604.477i			3.14832i
$193$			84.0672i			0.435581i	0.975996	+	0.217791i	$0.0698850\pi$
$193$			84.0672i			0.435581i	−0.975996	+	0.217791i	$0.930115\pi$
$194$	−405.205			−2.08869
$195$		−	26.6092i		−	0.136457i
$196$	−64.7672			−0.330445
$197$			258.392i			1.31163i	0.754920	+	0.655817i	$0.227676\pi$
$197$			258.392i			1.31163i	−0.754920	+	0.655817i	$0.772324\pi$
$198$	438.968			2.21701
$199$			16.1270i			0.0810400i	0.999179	+	0.0405200i	$0.0129015\pi$
$199$			16.1270i			0.0810400i	−0.999179	+	0.0405200i	$0.987099\pi$
$200$	−104.565			−0.522823
$201$		−	244.605i		−	1.21694i
$202$	−252.378			−1.24940
$203$	−65.2428			−0.321393
$204$	590.622			2.89521
$205$			365.729i			1.78405i
$206$		−	45.9747i		−	0.223178i
$207$	−564.094			−2.72509
$208$	−2.48108			−0.0119283
$209$	−102.676			−0.491274
$210$	909.628			4.33156
$211$		−	110.640i		−	0.524361i	−0.965019	−	0.262181i	$-0.915558\pi$
$211$		−	110.640i		−	0.524361i	0.965019	−	0.262181i	$-0.0844417\pi$
$212$		−	82.3514i		−	0.388450i
$213$	432.979			2.03277
$214$		−	67.4661i		−	0.315262i
$215$		−	53.3627i		−	0.248199i
$216$		−	594.812i		−	2.75376i
$217$		−	249.993i		−	1.15204i
$218$		−	451.276i		−	2.07007i
$219$			33.9729i			0.155127i
$220$	217.990			0.990863
$221$			12.0348i			0.0544560i
$222$	1055.54			4.75467
$223$	−75.5373			−0.338732			−0.169366	−	0.985553i	$-0.554172\pi$
$223$	−75.5373			−0.338732			−0.169366	+	0.985553i	$0.554172\pi$
$224$		−	287.454i		−	1.28328i
$225$	−392.857			−1.74603
$226$			490.652i			2.17102i
$227$			38.8968i			0.171352i	0.996323	+	0.0856758i	$0.0273049\pi$
$227$			38.8968i			0.171352i	−0.996323	+	0.0856758i	$0.972695\pi$
$228$			643.405i			2.82195i
$229$			100.672i			0.439617i	0.975543	+	0.219809i	$0.0705433\pi$
$229$			100.672i			0.439617i	−0.975543	+	0.219809i	$0.929457\pi$
$230$	−464.819			−2.02095
$231$	−251.587			−1.08912
$232$			55.3859i			0.238732i
$233$			437.608i			1.87815i	0.343715	+	0.939074i	$0.388315\pi$
$233$			437.608i			1.87815i	−0.343715	+	0.939074i	$0.611685\pi$
$234$	56.0500			0.239530
$235$		−	92.9450i		−	0.395511i
$236$		−	463.108i		−	1.96232i
$237$	−303.930	−	342.877i	−1.28240	−	1.44674i
$238$	−411.406			−1.72860
$239$	−139.108			−0.582041			−0.291020	−	0.956717i	$-0.593995\pi$
$239$	−139.108			−0.582041			−0.291020	+	0.956717i	$0.593995\pi$
$240$			128.424i			0.535099i
$241$	−23.6947			−0.0983184			−0.0491592	−	0.998791i	$-0.515654\pi$
$241$	−23.6947			−0.0983184			−0.0491592	+	0.998791i	$0.515654\pi$
$242$	283.870			1.17302
$243$		−	948.650i		−	3.90391i
$244$			314.408i			1.28856i
$245$	−68.3107			−0.278819
$246$	−1051.78			−4.27554
$247$	−13.1103			−0.0530782
$248$	−212.224			−0.855743
$249$			235.657i			0.946415i
$250$	183.842			0.735367
$251$			220.942i			0.880246i	0.897937	+	0.440123i	$0.145065\pi$
$251$			220.942i			0.880246i	−0.897937	+	0.440123i	$0.854935\pi$
$252$			1154.73i			4.58225i
$253$	128.560			0.508144
$254$			233.637i			0.919830i
$255$	622.936			2.44288
$256$	−160.050			−0.625195
$257$	−87.3207			−0.339769			−0.169885	−	0.985464i	$-0.554339\pi$
$257$	−87.3207			−0.339769			−0.169885	+	0.985464i	$0.554339\pi$
$258$	153.463			0.594819
$259$	−443.104			−1.71082
$260$	27.8342			0.107055
$261$			208.089i			0.797276i
$262$	118.339			0.451676
$263$	−208.424			−0.792486			−0.396243	−	0.918146i	$-0.629686\pi$
$263$	−208.424			−0.792486			−0.396243	+	0.918146i	$0.629686\pi$
$264$			213.577i			0.809003i
$265$		−	86.8569i		−	0.327762i
$266$		−	448.173i		−	1.68486i
$267$		−	70.9988i		−	0.265913i
$268$	255.866			0.954726
$269$	−242.999			−0.903343			−0.451671	−	0.892184i	$-0.649172\pi$
$269$	−242.999			−0.903343			−0.451671	+	0.892184i	$0.649172\pi$
$270$		−	1841.46i		−	6.82022i
$271$			220.990i			0.815461i	0.913102	+	0.407731i	$0.133680\pi$
$271$			220.990i			0.815461i	−0.913102	+	0.407731i	$0.866320\pi$
$272$		−	58.0835i		−	0.213542i
$273$	−32.1240			−0.117670
$274$		−	485.795i		−	1.77297i
$275$	89.5345			0.325580
$276$		−	805.603i		−	2.91885i
$277$	−320.138			−1.15573			−0.577866	−	0.816132i	$-0.696114\pi$
$277$	−320.138			−1.15573			−0.577866	+	0.816132i	$0.696114\pi$
$278$		−	181.476i		−	0.652793i
$279$	−797.343			−2.85786
$280$			324.162i			1.15772i
$281$	452.010			1.60858			0.804288	−	0.594240i	$-0.202547\pi$
$281$	452.010			1.60858			0.804288	+	0.594240i	$0.202547\pi$
$282$	267.296			0.947859
$283$	524.657			1.85391			0.926956	−	0.375169i	$-0.122415\pi$
$283$	524.657			1.85391			0.926956	+	0.375169i	$0.122415\pi$
$284$			452.913i			1.59476i
$285$			678.606i			2.38107i
$286$	−12.7741			−0.0446648
$287$	441.528			1.53843
$288$	−916.823			−3.18341
$289$	7.25891			0.0251173
$290$			171.467i			0.591267i
$291$		−	740.706i		−	2.54538i
$292$	−35.5370			−0.121702
$293$		−	301.999i		−	1.03071i	−0.856976	−	0.515357i	$-0.827659\pi$
$293$		−	301.999i		−	1.03071i	0.856976	−	0.515357i	$-0.172341\pi$
$294$		−	196.451i		−	0.668202i
$295$		−	488.445i		−	1.65575i
$296$			376.160i			1.27081i
$297$			509.314i			1.71486i
$298$		−	54.0334i		−	0.181320i
$299$	16.4153			0.0549008
$300$		−	561.053i		−	1.87018i
$301$	−64.4224			−0.214028
$302$	289.664			0.959152
$303$		−	461.341i		−	1.52258i
$304$	63.2743			0.208139
$305$			331.610i			1.08724i
$306$			1312.16i			4.28811i
$307$		−	433.723i		−	1.41278i	−0.707824	−	0.706389i	$-0.750323\pi$
$307$		−	433.723i		−	1.41278i	0.707824	−	0.706389i	$-0.249677\pi$
$308$		−	263.169i		−	0.854445i
$309$	84.0407			0.271976
$310$	−657.018			−2.11941
$311$		−	148.313i		−	0.476892i	−0.971156	−	0.238446i	$-0.923362\pi$
$311$		−	148.313i		−	0.476892i	0.971156	−	0.238446i	$-0.0766380\pi$
$312$			27.2707i			0.0874062i
$313$	−346.053			−1.10560			−0.552800	−	0.833314i	$-0.686441\pi$
$313$	−346.053			−1.10560			−0.552800	+	0.833314i	$0.686441\pi$
$314$			633.858i			2.01866i
$315$			1217.90i			3.86636i
$316$	358.663	−	317.922i	1.13501	−	1.00608i
$317$	305.178			0.962706			0.481353	−	0.876527i	$-0.340145\pi$
$317$	305.178			0.962706			0.481353	+	0.876527i	$0.340145\pi$
$318$	249.788			0.785496
$319$		−	47.4247i		−	0.148667i
$320$	−666.900			−2.08406
$321$	123.326			0.384195
$322$			561.154i			1.74272i
$323$		−	306.920i		−	0.950216i
$324$	1846.22			5.69821
$325$	11.4323			0.0351762
$326$	661.692			2.02973
$327$	824.922			2.52270
$328$		−	374.822i		−	1.14275i
$329$	−112.208			−0.341058
$330$			661.205i			2.00365i
$331$		−	581.155i		−	1.75575i	−0.478885	−	0.877877i	$-0.658959\pi$
$331$		−	581.155i		−	1.75575i	0.478885	−	0.877877i	$-0.341041\pi$
$332$	−246.507			−0.742490
$333$			1413.26i			4.24403i
$334$	−499.453			−1.49537
$335$	269.865			0.805567
$336$	155.040			0.461429
$337$	108.777			0.322779			0.161390	−	0.986891i	$-0.448402\pi$
$337$	108.777			0.322779			0.161390	+	0.986891i	$0.448402\pi$
$338$	534.578			1.58159
$339$	−896.900			−2.64572
$340$			651.614i			1.91651i
$341$	181.719			0.532901
$342$	−1429.43			−4.17961
$343$		−	296.056i		−	0.863138i
$344$			54.6894i			0.158981i
$345$		−	849.678i		−	2.46284i
$346$		−	365.720i		−	1.05700i
$347$	−229.092			−0.660208			−0.330104	−	0.943945i	$-0.607084\pi$
$347$	−229.092			−0.660208			−0.330104	+	0.943945i	$0.607084\pi$
$348$	−297.180			−0.853964
$349$			295.437i			0.846523i	0.906007	+	0.423262i	$0.139115\pi$
$349$			295.437i			0.846523i	−0.906007	+	0.423262i	$0.860885\pi$
$350$			390.810i			1.11660i
$351$			65.0321i			0.185277i
$352$	208.949			0.593606
$353$			298.377i			0.845260i	0.906302	+	0.422630i	$0.138893\pi$
$353$			298.377i			0.845260i	−0.906302	+	0.422630i	$0.861107\pi$
$354$	1404.70			3.96807
$355$			477.692i			1.34561i
$356$	74.2674			0.208616
$357$		−	752.041i		−	2.10656i
$358$	78.2457			0.218563
$359$			13.3730i			0.0372507i	0.999827	+	0.0186253i	$0.00592897\pi$
$359$			13.3730i			0.0372507i	−0.999827	+	0.0186253i	$0.994071\pi$
$360$	1033.90			2.87195
$361$	−26.6516			−0.0738271
$362$	−551.546			−1.52361
$363$			518.907i			1.42950i
$364$		−	33.6029i		−	0.0923158i
$365$	−37.4812			−0.102688
$366$	−953.661			−2.60563
$367$	432.610			1.17877			0.589387	−	0.807851i	$-0.299369\pi$
$367$	432.610			1.17877			0.589387	+	0.807851i	$0.299369\pi$
$368$	−79.2253			−0.215286
$369$		−	1408.24i		−	3.81636i
$370$			1164.54i			3.14741i
$371$	−104.858			−0.282637
$372$		−	1138.71i		−	3.06106i
$373$			38.5002i			0.103218i	0.998667	+	0.0516088i	$0.0164349\pi$
$373$			38.5002i			0.103218i	−0.998667	+	0.0516088i	$0.983565\pi$
$374$		−	299.050i		−	0.799598i
$375$			336.059i			0.896157i
$376$			95.2558i			0.253340i
$377$		−	6.05546i		−	0.0160622i
$378$	−2223.11			−5.88124
$379$			638.332i			1.68425i	0.539280	+	0.842127i	$0.318697\pi$
$379$			638.332i			1.68425i	−0.539280	+	0.842127i	$0.681303\pi$
$380$	−709.848			−1.86802
$381$	−427.083			−1.12095
$382$		−	1166.39i		−	3.05337i
$383$	−671.350			−1.75287			−0.876436	−	0.481519i	$-0.840085\pi$
$383$	−671.350			−1.75287			−0.876436	+	0.481519i	$0.840085\pi$
$384$		−	1054.63i		−	2.74644i
$385$		−	277.567i		−	0.720954i
$386$		−	266.731i		−	0.691014i
$387$			205.472i			0.530936i
$388$	774.807			1.99693
$389$	587.616			1.51058			0.755290	−	0.655391i	$-0.227496\pi$
$389$	587.616			1.51058			0.755290	+	0.655391i	$0.227496\pi$
$390$			84.4265i			0.216478i
$391$			384.292i			0.982845i
$392$	70.0090			0.178594
$393$			216.321i			0.550436i
$394$		−	819.835i		−	2.08080i
$395$	378.285	−	335.316i	0.957685	−	0.848901i
$396$	−839.367			−2.11961
$397$	−159.890			−0.402746			−0.201373	−	0.979515i	$-0.564540\pi$
$397$	−159.890			−0.402746			−0.201373	+	0.979515i	$0.564540\pi$
$398$		−	51.1682i		−	0.128563i
$399$	819.250			2.05326
$400$	−55.1756			−0.137939
$401$			606.954i			1.51360i	0.653646	+	0.756800i	$0.273239\pi$
$401$			606.954i			1.51360i	−0.653646	+	0.756800i	$0.726761\pi$
$402$			776.092i			1.93058i
$403$	23.2030			0.0575756
$404$	482.581			1.19451
$405$	1947.23			4.80797
$406$	207.005			0.509864
$407$		−	322.090i		−	0.791377i
$408$	−638.423			−1.56476
$409$			621.424i			1.51937i	0.650289	+	0.759687i	$0.274648\pi$
$409$			621.424i			1.51937i	−0.650289	+	0.759687i	$0.725352\pi$
$410$		−	1160.40i		−	2.83024i
$411$	888.022			2.16064
$412$			87.9098i			0.213373i
$413$	−589.678			−1.42779
$414$	1789.78			4.32314
$415$	−259.993			−0.626490
$416$	26.6799			0.0641343
$417$	331.735			0.795527
$418$	325.775			0.779366
$419$		−	470.576i		−	1.12309i	−0.827445	−	0.561547i	$-0.810207\pi$
$419$		−	470.576i		−	1.12309i	0.827445	−	0.561547i	$-0.189793\pi$
$420$	−1739.33			−4.14126
$421$	582.850			1.38444			0.692221	−	0.721685i	$-0.256632\pi$
$421$	582.850			1.38444			0.692221	+	0.721685i	$0.256632\pi$
$422$			351.043i			0.831856i
$423$			357.883i			0.846060i
$424$			89.0163i			0.209944i
$425$			267.636i			0.629732i
$426$	−1373.77			−3.22482
$427$	400.337			0.937557
$428$			129.004i			0.301412i
$429$		−	23.3508i		−	0.0544308i
$430$			169.311i			0.393747i
$431$	−254.224			−0.589847			−0.294924	−	0.955521i	$-0.595294\pi$
$431$	−254.224			−0.589847			−0.294924	+	0.955521i	$0.595294\pi$
$432$		−	313.865i		−	0.726538i
$433$	−271.088			−0.626069			−0.313034	−	0.949742i	$-0.601346\pi$
$433$	−271.088			−0.626069			−0.313034	+	0.949742i	$0.601346\pi$
$434$			793.187i			1.82762i
$435$	−313.439			−0.720548
$436$			862.900i			1.97913i
$437$	−418.636			−0.957976
$438$		−	107.790i		−	0.246097i
$439$	−757.230			−1.72490			−0.862449	−	0.506144i	$-0.831070\pi$
$439$	−757.230			−1.72490			−0.862449	+	0.506144i	$0.831070\pi$
$440$	−235.632			−0.535528
$441$	263.029			0.596438
$442$		−	38.1844i		−	0.0863900i
$443$			86.1383i			0.194443i	0.995263	+	0.0972216i	$0.0309956\pi$
$443$			86.1383i			0.194443i	−0.995263	+	0.0972216i	$0.969004\pi$
$444$	−2018.33			−4.54579
$445$	78.3307			0.176024
$446$	239.668			0.537371
$447$	98.7719			0.220966
$448$			805.118i			1.79714i
$449$			452.485i			1.00776i	0.863773	+	0.503881i	$0.168095\pi$
$449$			452.485i			1.00776i	−0.863773	+	0.503881i	$0.831905\pi$
$450$	1246.47			2.76994
$451$			320.945i			0.711630i
$452$		−	938.192i		−	2.07565i
$453$			529.499i			1.16887i
$454$		−	123.413i		−	0.271835i
$455$		−	35.4414i		−	0.0778932i
$456$		−	695.478i		−	1.52517i
$457$	−772.113			−1.68952			−0.844762	−	0.535142i	$-0.820258\pi$
$457$	−772.113			−1.68952			−0.844762	+	0.535142i	$0.820258\pi$
$458$		−	319.417i		−	0.697417i
$459$	−1522.44			−3.31686
$460$	888.796			1.93217
$461$			99.6878i			0.216242i	0.994138	+	0.108121i	$0.0344835\pi$
$461$			99.6878i			0.216242i	−0.994138	+	0.108121i	$0.965517\pi$
$462$	798.243			1.72780
$463$		−	611.798i		−	1.32138i	−0.750660	−	0.660689i	$-0.770264\pi$
$463$		−	611.798i		−	1.32138i	0.750660	−	0.660689i	$-0.229736\pi$
$464$			29.2255i			0.0629860i
$465$		−	1201.01i		−	2.58283i
$466$		−	1388.46i		−	2.97953i
$467$	594.094			1.27215			0.636075	−	0.771628i	$-0.280557\pi$
$467$	594.094			1.27215			0.636075	+	0.771628i	$0.280557\pi$
$468$	−107.175			−0.229007
$469$		−	325.796i		−	0.694660i
$470$			294.899i			0.627445i
$471$	−1158.68			−2.46004
$472$			500.589i			1.06057i
$473$		−	46.8284i		−	0.0990029i
$474$	964.319	+	1087.89i	2.03443	+	2.29513i
$475$	−291.554			−0.613798
$476$	786.664			1.65266
$477$			334.441i			0.701134i
$478$	441.366			0.923360
$479$	7.66178			0.0159954			0.00799768	−	0.999968i	$-0.497454\pi$
$479$	7.66178			0.0159954			0.00799768	+	0.999968i	$0.497454\pi$
$480$		−	1380.98i		−	2.87705i
$481$		−	41.1264i		−	0.0855018i
$482$	75.1795			0.155974
$483$	−1025.78			−2.12376
$484$	−542.797			−1.12148
$485$	817.197			1.68494
$486$			3009.91i			6.19323i
$487$	672.701			1.38132			0.690659	−	0.723181i	$-0.257321\pi$
$487$	672.701			1.38132			0.690659	+	0.723181i	$0.257321\pi$
$488$		−	339.854i		−	0.696422i
$489$			1209.56i			2.47353i
$490$	216.739			0.442324
$491$		−	729.442i		−	1.48563i	−0.669499	−	0.742813i	$-0.733491\pi$
$491$		−	729.442i		−	1.48563i	0.669499	−	0.742813i	$-0.266509\pi$
$492$	2011.15			4.08771
$493$	141.762			0.287549
$494$	41.5968			0.0842041
$495$	−885.289			−1.78846
$496$	−111.984			−0.225775
$497$	576.695			1.16035
$498$		−	747.702i		−	1.50141i
$499$	−15.1978			−0.0304565			−0.0152282	−	0.999884i	$-0.504847\pi$
$499$	−15.1978			−0.0304565			−0.0152282	+	0.999884i	$0.504847\pi$
$500$	−351.530			−0.703061
$501$		−	912.989i		−	1.82233i
$502$		−	701.012i		−	1.39644i
$503$		−	452.158i		−	0.898922i	−0.893300	−	0.449461i	$-0.851616\pi$
$503$		−	452.158i		−	0.898922i	0.893300	−	0.449461i	$-0.148384\pi$
$504$		−	1248.18i		−	2.47655i
$505$	508.983			1.00789
$506$	−407.901			−0.806129
$507$			977.197i			1.92741i
$508$		−	446.745i		−	0.879420i
$509$			804.806i			1.58115i	0.612364	+	0.790576i	$0.290219\pi$
$509$			804.806i			1.58115i	−0.612364	+	0.790576i	$0.709781\pi$
$510$	−1976.47			−3.87544
$511$			45.2493i			0.0885506i
$512$	−219.537			−0.428783
$513$		−	1658.50i		−	3.23294i
$514$	277.054			0.539016
$515$			92.7194i			0.180038i
$516$	−293.443			−0.568687
$517$		−	81.5637i		−	0.157764i
$518$	1405.90			2.71408
$519$	668.529			1.28811
$520$	−30.0869			−0.0578594
$521$		−	771.747i		−	1.48128i	−0.671902	−	0.740640i	$-0.734522\pi$
$521$		−	771.747i		−	1.48128i	0.671902	−	0.740640i	$-0.265478\pi$
$522$		−	660.233i		−	1.26481i
$523$	−79.5893			−0.152178			−0.0760892	−	0.997101i	$-0.524243\pi$
$523$	−79.5893			−0.152178			−0.0760892	+	0.997101i	$0.524243\pi$
$524$	−226.280			−0.431833
$525$	−714.391			−1.36075
$526$	661.295			1.25721
$527$			543.194i			1.03073i
$528$			112.698i			0.213443i
$529$	−4.82887			−0.00912830
$530$			275.583i			0.519967i
$531$			1880.75i			3.54191i
$532$			856.966i			1.61084i
$533$			40.9801i			0.0768858i
$534$			225.267i			0.421849i
$535$			136.062i			0.254322i
$536$	−276.575			−0.515997
$537$			143.031i			0.266353i
$538$	770.996			1.43308
$539$	−59.9459			−0.111217
$540$			3521.12i			6.52059i
$541$	−464.467			−0.858533			−0.429267	−	0.903178i	$-0.641228\pi$
$541$	−464.467			−0.858533			−0.429267	+	0.903178i	$0.641228\pi$
$542$		−	701.165i		−	1.29366i
$543$		−	1008.21i		−	1.85675i
$544$			624.591i			1.14814i
$545$			910.110i			1.66993i
$546$	101.924			0.186674
$547$	−678.614			−1.24061			−0.620306	−	0.784360i	$-0.712991\pi$
$547$	−678.614			−1.24061			−0.620306	+	0.784360i	$0.712991\pi$
$548$			928.905i			1.69508i
$549$		−	1276.86i		−	2.32579i
$550$	−284.078			−0.516506
$551$			154.431i			0.280274i
$552$			870.803i			1.57754i
$553$	−404.811	−	456.687i	−0.732028	−	0.825835i
$554$	1015.74			1.83347
$555$	−2128.75			−3.83559
$556$			347.007i			0.624114i
$557$	−429.371			−0.770864			−0.385432	−	0.922736i	$-0.625948\pi$
$557$	−429.371			−0.770864			−0.385432	+	0.922736i	$0.625948\pi$
$558$	2529.84			4.53376
$559$		−	5.97932i		−	0.0106965i
$560$			171.051i			0.305448i
$561$	546.656			0.974432
$562$	−1434.15			−2.55187
$563$	500.284			0.888604			0.444302	−	0.895877i	$-0.353452\pi$
$563$	500.284			0.888604			0.444302	+	0.895877i	$0.353452\pi$
$564$	−511.106			−0.906217
$565$		−	989.521i		−	1.75136i
$566$	−1664.65			−2.94108
$567$		−	2350.80i		−	4.14603i
$568$		−	489.568i		−	0.861916i
$569$	−694.114			−1.21988			−0.609942	−	0.792446i	$-0.708807\pi$
$569$	−694.114			−1.21988			−0.609942	+	0.792446i	$0.708807\pi$
$570$		−	2153.11i		−	3.77738i
$571$	276.562			0.484347			0.242174	−	0.970233i	$-0.422140\pi$
$571$	276.562			0.484347			0.242174	+	0.970233i	$0.422140\pi$
$572$	24.4259			0.0427026
$573$	2132.13			3.72099
$574$	−1400.90			−2.44059
$575$	365.053			0.634875
$576$	2567.89			4.45814
$577$		−	541.450i		−	0.938388i	−0.883095	−	0.469194i	$-0.844545\pi$
$577$		−	541.450i		−	0.938388i	0.883095	−	0.469194i	$-0.155455\pi$
$578$	−23.0313			−0.0398466
$579$	487.579			0.842105
$580$		−	327.869i		−	0.565291i
$581$			313.878i			0.540237i
$582$			2350.14i			4.03804i
$583$		−	76.2211i		−	0.130739i
$584$	38.4131			0.0657758
$585$	−113.039			−0.193229
$586$			958.194i			1.63514i
$587$			495.305i			0.843790i	0.906645	+	0.421895i	$0.138635\pi$
$587$			495.305i			0.843790i	−0.906645	+	0.421895i	$0.861365\pi$
$588$			375.642i			0.638846i
$589$	−591.738			−1.00465
$590$			1549.76i			2.62671i
$591$	1498.64			2.53577
$592$			198.488i			0.335284i
$593$	−625.616			−1.05500			−0.527501	−	0.849554i	$-0.676871\pi$
$593$	−625.616			−1.05500			−0.527501	+	0.849554i	$0.676871\pi$
$594$		−	1615.97i		−	2.72049i
$595$	829.703			1.39446
$596$			103.319i			0.173354i
$597$	93.5344			0.156674
$598$	−52.0832			−0.0870956
$599$	242.107			0.404186			0.202093	−	0.979366i	$-0.435226\pi$
$599$	242.107			0.404186			0.202093	+	0.979366i	$0.435226\pi$
$600$			606.461i			1.01077i
$601$		−	724.534i		−	1.20555i	−0.797912	−	0.602773i	$-0.794062\pi$
$601$		−	724.534i		−	1.20555i	0.797912	−	0.602773i	$-0.205938\pi$
$602$	204.402			0.339538
$603$	−1039.11			−1.72324
$604$	−553.876			−0.917013
$605$	−572.494			−0.946271
$606$			1463.76i			2.41545i
$607$			111.969i			0.184462i	0.995738	+	0.0922311i	$0.0293999\pi$
$607$			111.969i			0.184462i	−0.995738	+	0.0922311i	$0.970600\pi$
$608$	−680.409			−1.11909
$609$			378.400i			0.621346i
$610$		−	1052.14i		−	1.72482i
$611$		−	10.4145i		−	0.0170451i
$612$		−	2509.03i		−	4.09972i
$613$			237.743i			0.387835i	0.981018	+	0.193917i	$0.0621194\pi$
$613$			237.743i			0.387835i	−0.981018	+	0.193917i	$0.937881\pi$
$614$			1376.13i			2.24126i
$615$	2121.18			3.44908
$616$			284.468i			0.461799i
$617$	−162.306			−0.263056			−0.131528	−	0.991312i	$-0.541988\pi$
$617$	−162.306			−0.263056			−0.131528	+	0.991312i	$0.541988\pi$
$618$	−266.647			−0.431468
$619$		−	109.480i		−	0.176865i	−0.996082	−	0.0884327i	$-0.971814\pi$
$619$		−	109.480i		−	0.176865i	0.996082	−	0.0884327i	$-0.0281858\pi$
$620$	1256.31			2.02630
$621$			2076.59i			3.34395i
$622$			470.574i			0.756550i
$623$		−	94.5650i		−	0.151790i
$624$			14.3899i			0.0230608i
$625$	−769.383			−1.23101
$626$	1097.97			1.75394
$627$			595.510i			0.949776i
$628$		−	1212.02i		−	1.92997i
$629$	962.792			1.53067
$630$		−	3864.21i		−	6.13366i
$631$			493.710i			0.782425i	0.920300	+	0.391213i	$0.127944\pi$
$631$			493.710i			0.782425i	−0.920300	+	0.391213i	$0.872056\pi$
$632$	−387.690	+	343.653i	−0.613434	+	0.543754i
$633$	−641.700			−1.01374
$634$	−968.280			−1.52725
$635$		−	471.187i		−	0.742027i
$636$	−477.627			−0.750987
$637$	−7.65424			−0.0120161
$638$			150.471i			0.235848i
$639$		−	1839.34i		−	2.87847i
$640$	1163.54			1.81804
$641$	907.125			1.41517			0.707586	−	0.706628i	$-0.249784\pi$
$641$	907.125			1.41517			0.707586	+	0.706628i	$0.249784\pi$
$642$	−391.295			−0.609493
$643$	−968.751			−1.50661			−0.753306	−	0.657671i	$-0.771542\pi$
$643$	−968.751			−1.50661			−0.753306	+	0.657671i	$0.771542\pi$
$644$		−	1073.00i		−	1.66615i
$645$	−309.497			−0.479840
$646$			973.806i			1.50744i
$647$		−	811.942i		−	1.25493i	−0.778643	−	0.627467i	$-0.784092\pi$
$647$		−	811.942i		−	1.25493i	0.778643	−	0.627467i	$-0.215908\pi$
$648$	−1995.64			−3.07969
$649$		−	428.635i		−	0.660454i
$650$	−36.2727			−0.0558042
$651$	−1449.93			−2.22723
$652$	−1265.24			−1.94056
$653$	348.523			0.533726			0.266863	−	0.963735i	$-0.414013\pi$
$653$	348.523			0.533726			0.266863	+	0.963735i	$0.414013\pi$
$654$	−2617.34			−4.00205
$655$	−238.660			−0.364367
$656$		−	197.782i		−	0.301498i
$657$	144.321			0.219666
$658$	356.018			0.541061
$659$		−	89.1660i		−	0.135305i	−0.997709	−	0.0676525i	$-0.978449\pi$
$659$		−	89.1660i		−	0.135305i	0.997709	−	0.0676525i	$-0.0215509\pi$
$660$		−	1264.31i		−	1.91563i
$661$		−	98.1421i		−	0.148475i	−0.997241	−	0.0742376i	$-0.976348\pi$
$661$		−	98.1421i		−	0.148475i	0.997241	−	0.0742376i	$-0.0236523\pi$
$662$			1843.91i			2.78536i
$663$	69.8002			0.105279
$664$	266.457			0.401291
$665$			903.852i			1.35918i
$666$		−	4484.04i		−	6.73280i
$667$		−	193.362i		−	0.289898i
$668$	955.021			1.42967
$669$			438.107i			0.654868i
$670$	−856.238			−1.27797
$671$			291.004i			0.433686i
$672$	−1667.20			−2.48095
$673$			349.410i			0.519183i	0.965718	+	0.259592i	$0.0835880\pi$
$673$			349.410i			0.519183i	−0.965718	+	0.259592i	$0.916412\pi$
$674$	−345.131			−0.512063
$675$			1446.22i			2.14255i
$676$	−1022.19			−1.51211
$677$	−561.067			−0.828755			−0.414378	−	0.910105i	$-0.636001\pi$
$677$	−561.067			−0.828755			−0.414378	+	0.910105i	$0.636001\pi$
$678$	2845.72			4.19722
$679$		−	986.565i		−	1.45297i
$680$		−	704.352i		−	1.03581i
$681$	225.597			0.331273
$682$	−576.565			−0.845404
$683$	−341.339			−0.499764			−0.249882	−	0.968276i	$-0.580392\pi$
$683$	−341.339			−0.499764			−0.249882	+	0.968276i	$0.580392\pi$
$684$	2733.26			3.99599
$685$			979.727i			1.43026i
$686$			939.338i			1.36930i
$687$	583.887			0.849908
$688$			28.8580i			0.0419447i
$689$		−	9.73235i		−	0.0141253i
$690$			2695.89i			3.90709i
$691$			566.537i			0.819879i	0.912113	+	0.409940i	$0.134450\pi$
$691$			566.537i			0.819879i	−0.912113	+	0.409940i	$0.865550\pi$
$692$			699.306i			1.01056i
$693$			1068.77i			1.54223i
$694$	726.872			1.04737
$695$			365.992i			0.526608i
$696$	321.231			0.461539
$697$	−959.368			−1.37642
$698$		−	937.372i		−	1.34294i
$699$	2538.07			3.63101
$700$		−	747.281i		−	1.06754i
$701$		−	845.646i		−	1.20634i	−0.797612	−	0.603171i	$-0.793904\pi$
$701$		−	845.646i		−	1.20634i	0.797612	−	0.603171i	$-0.206096\pi$
$702$		−	206.336i		−	0.293926i
$703$			1048.83i			1.49194i
$704$	−585.238			−0.831303
$705$	−539.069			−0.764637
$706$		−	946.700i		−	1.34094i
$707$		−	614.472i		−	0.869125i
$708$	−2685.97			−3.79374
$709$			6.44178i			0.00908572i	0.999990	+	0.00454286i	$0.00144604\pi$
$709$			6.44178i			0.00908572i	−0.999990	+	0.00454286i	$0.998554\pi$
$710$		−	1515.64i		−	2.13470i
$711$	−1456.58	+	1291.13i	−2.04864	+	1.81593i
$712$	−80.2781			−0.112750
$713$	740.912			1.03915
$714$			2386.10i			3.34188i
$715$	25.7622			0.0360311
$716$	−149.616			−0.208961
$717$			806.807i			1.12525i
$718$		−	42.4303i		−	0.0590951i
$719$	50.0547			0.0696171			0.0348085	−	0.999394i	$-0.488918\pi$
$719$	50.0547			0.0696171			0.0348085	+	0.999394i	$0.488918\pi$
$720$	545.559			0.757721
$721$	111.936			0.155251
$722$	84.5611			0.117121
$723$			137.427i			0.190078i
$724$	1054.63			1.45667
$725$		−	134.665i		−	0.185744i
$726$		−	1646.41i		−	2.26778i
$727$	538.942			0.741323			0.370661	−	0.928768i	$-0.379131\pi$
$727$	538.942			0.741323			0.370661	+	0.928768i	$0.379131\pi$
$728$			36.3225i			0.0498936i
$729$	−2763.25			−3.79047
$730$	118.922			0.162906
$731$	139.979			0.191490
$732$	1823.53			2.49116
$733$	639.757			0.872792			0.436396	−	0.899755i	$-0.356255\pi$
$733$	639.757			0.872792			0.436396	+	0.899755i	$0.356255\pi$
$734$	−1372.60			−1.87003
$735$			396.193i			0.539039i
$736$	851.936			1.15752
$737$	236.820			0.321329
$738$			4468.10i			6.05434i
$739$		−	1128.63i		−	1.52724i	−0.645667	−	0.763619i	$-0.723421\pi$
$739$		−	1128.63i		−	1.52724i	0.645667	−	0.763619i	$-0.276579\pi$
$740$		−	2226.76i		−	3.00913i
$741$			76.0381i			0.102616i
$742$	332.698			0.448380
$743$	−779.477			−1.04909			−0.524547	−	0.851381i	$-0.675765\pi$
$743$	−779.477			−1.04909			−0.524547	+	0.851381i	$0.675765\pi$
$744$			1230.87i			1.65440i
$745$			108.972i			0.146271i
$746$		−	122.155i		−	0.163746i
$747$	1001.10			1.34016
$748$			571.823i			0.764470i
$749$	164.261			0.219308
$750$		−	1066.26i		−	1.42168i
$751$	988.929			1.31682			0.658408	−	0.752661i	$-0.271230\pi$
$751$	988.929			1.31682			0.658408	+	0.752661i	$0.271230\pi$
$752$			50.2636i			0.0668400i
$753$	1281.43			1.70177
$754$			19.2130i			0.0254814i
$755$	−584.179			−0.773747
$756$	4250.88			5.62286
$757$	−132.217			−0.174659			−0.0873295	−	0.996179i	$-0.527833\pi$
$757$	−132.217			−0.174659			−0.0873295	+	0.996179i	$0.527833\pi$
$758$		−	2025.32i		−	2.67193i
$759$		−	745.634i		−	0.982390i
$760$	767.298			1.00960
$761$	100.415			0.131952			0.0659758	−	0.997821i	$-0.478984\pi$
$761$	100.415			0.131952			0.0659758	+	0.997821i	$0.478984\pi$
$762$	1355.06			1.77830
$763$	1098.73			1.44002
$764$			2230.29i			2.91923i
$765$		−	2646.30i		−	3.45922i
$766$	2130.08			2.78079
$767$		−	54.7305i		−	0.0713566i
$768$			928.269i			1.20868i
$769$		−	414.587i		−	0.539125i	−0.962983	−	0.269563i	$-0.913121\pi$
$769$		−	414.587i		−	0.539125i	0.962983	−	0.269563i	$-0.0868791\pi$
$770$			880.676i			1.14373i
$771$			506.449i			0.656873i
$772$			510.026i			0.660656i
$773$	−1145.11			−1.48139			−0.740694	−	0.671843i	$-0.765503\pi$
$773$	−1145.11			−1.48139			−0.740694	+	0.671843i	$0.765503\pi$
$774$		−	651.930i		−	0.842287i
$775$	516.000			0.665806
$776$	−837.515			−1.07927
$777$			2569.95i			3.30752i
$778$	−1864.41			−2.39641
$779$		−	1045.10i		−	1.34160i
$780$		−	161.435i		−	0.206968i
$781$			419.198i			0.536745i
$782$		−	1219.30i		−	1.55920i
$783$	766.036			0.978334
$784$	36.9417			0.0471195
$785$		−	1278.33i		−	1.62845i
$786$		−	686.352i		−	0.873221i
$787$	798.997			1.01524			0.507622	−	0.861580i	$-0.330525\pi$
$787$	798.997			1.01524			0.507622	+	0.861580i	$0.330525\pi$
$788$			1567.64i			1.98938i
$789$			1208.83i			1.53211i
$790$	−1200.24	+	1063.90i	−1.51929	+	1.34671i
$791$	−1194.60			−1.51024
$792$	907.299			1.14558
$793$			37.1570i			0.0468563i
$794$	507.305			0.638923
$795$	−503.759			−0.633659
$796$			97.8405i			0.122915i
$797$		−	369.855i		−	0.464060i	−0.972709	−	0.232030i	$-0.925463\pi$
$797$		−	369.855i		−	0.464060i	0.972709	−	0.232030i	$-0.0745367\pi$
$798$	−2599.35			−3.25732
$799$	243.810			0.305144
$800$	593.321			0.741652
$801$	−301.611			−0.376543
$802$		−	1925.77i		−	2.40120i
$803$	−32.8916			−0.0409609
$804$		−	1483.99i		−	1.84576i
$805$		−	1131.71i		−	1.40585i
$806$	−73.6192			−0.0913389
$807$			1409.36i			1.74642i
$808$	−521.637			−0.645591
$809$	1209.25			1.49475			0.747374	−	0.664404i	$-0.231315\pi$
$809$	1209.25			1.49475			0.747374	+	0.664404i	$0.231315\pi$
$810$	−6178.24			−7.62745
$811$	1049.68			1.29431			0.647153	−	0.762360i	$-0.275960\pi$
$811$	1049.68			1.29431			0.647153	+	0.762360i	$0.275960\pi$
$812$	−395.821			−0.487464
$813$	1281.71			1.57652
$814$			1021.94i			1.25546i
$815$	−1334.47			−1.63738
$816$	−336.877			−0.412839
$817$			152.489i			0.186645i
$818$		−	1971.68i		−	2.41036i
$819$			136.467i			0.166626i
$820$			2218.84i			2.70590i
$821$	−207.870			−0.253192			−0.126596	−	0.991954i	$-0.540405\pi$
$821$	−207.870			−0.253192			−0.126596	+	0.991954i	$0.540405\pi$
$822$	−2817.55			−3.42768
$823$			1305.11i			1.58580i	0.609351	+	0.792901i	$0.291430\pi$
$823$			1305.11i			1.58580i	−0.609351	+	0.792901i	$0.708570\pi$
$824$		−	95.0246i		−	0.115321i
$825$		−	519.289i		−	0.629441i
$826$	1870.95			2.26507
$827$		−	343.902i		−	0.415843i	−0.978146	−	0.207921i	$-0.933330\pi$
$827$		−	343.902i		−	0.415843i	0.978146	−	0.207921i	$-0.0666698\pi$
$828$	−3422.30			−4.13321
$829$		−	27.5538i		−	0.0332374i	−0.999862	−	0.0166187i	$-0.994710\pi$
$829$		−	27.5538i		−	0.0332374i	0.999862	−	0.0166187i	$-0.00529014\pi$
$830$	824.916			0.993874
$831$			1856.76i			2.23437i
$832$	−74.7265			−0.0898155
$833$		−	179.190i		−	0.215114i
$834$	−1052.54			−1.26204
$835$	1007.27			1.20631
$836$	−622.926			−0.745127
$837$			2935.25i			3.50687i
$838$			1493.06i			1.78170i
$839$	−458.048			−0.545945			−0.272972	−	0.962022i	$-0.588007\pi$
$839$	−458.048			−0.545945			−0.272972	+	0.962022i	$0.588007\pi$
$840$	1880.10			2.23821
$841$	769.671			0.915185
$842$	−1849.29			−2.19630
$843$		−	2621.60i		−	3.10984i
$844$		−	671.242i		−	0.795311i
$845$	−1078.11			−1.27587
$846$		−	1135.51i		−	1.34220i
$847$			691.145i			0.815992i
$848$			46.9713i			0.0553906i
$849$		−	3042.95i		−	3.58415i
$850$		−	849.165i		−	0.999018i
$851$		−	1313.24i		−	1.54317i
$852$	2626.84			3.08314
$853$			633.466i			0.742633i	0.928506	+	0.371317i	$0.121094\pi$
$853$			633.466i			0.742633i	−0.928506	+	0.371317i	$0.878906\pi$
$854$	−1270.20			−1.48736
$855$	2882.80			3.37169
$856$		−	139.445i		−	0.162903i
$857$	1187.28			1.38539			0.692695	−	0.721230i	$-0.256423\pi$
$857$	1187.28			1.38539			0.692695	+	0.721230i	$0.256423\pi$
$858$			74.0884i			0.0863501i
$859$		−	646.718i		−	0.752873i	−0.926442	−	0.376436i	$-0.877149\pi$
$859$		−	646.718i		−	0.752873i	0.926442	−	0.376436i	$-0.122851\pi$
$860$		−	323.746i		−	0.376449i
$861$		−	2560.81i		−	2.97422i
$862$	806.612			0.935744
$863$	−394.999			−0.457704			−0.228852	−	0.973461i	$-0.573497\pi$
$863$	−394.999			−0.457704			−0.228852	+	0.973461i	$0.573497\pi$
$864$			3375.09i			3.90635i
$865$			737.566i			0.852678i
$866$	860.117			0.993207
$867$		−	42.1007i		−	0.0485591i
$868$		−	1516.68i		−	1.74733i
$869$	331.964	−	294.256i	0.382007	−	0.338615i
$870$	994.489			1.14309
$871$	30.2385			0.0347170
$872$		−	932.737i		−	1.06965i
$873$	−3146.61			−3.60436
$874$	1328.26			1.51975
$875$			447.605i			0.511548i
$876$			206.110i			0.235285i
$877$	732.466			0.835195			0.417597	−	0.908632i	$-0.362872\pi$
$877$	732.466			0.835195			0.417597	+	0.908632i	$0.362872\pi$
$878$	2402.57			2.73641
$879$	−1751.56			−1.99267
$880$	−124.336			−0.141291
$881$		−	418.869i		−	0.475447i	−0.971333	−	0.237724i	$-0.923599\pi$
$881$		−	418.869i		−	0.475447i	0.971333	−	0.237724i	$-0.0764012\pi$
$882$	−834.549			−0.946200
$883$			723.914i			0.819835i	0.912123	+	0.409918i	$0.134443\pi$
$883$			723.914i			0.819835i	−0.912123	+	0.409918i	$0.865557\pi$
$884$			73.0137i			0.0825947i
$885$	−2832.92			−3.20104
$886$		−	273.303i		−	0.308468i
$887$	−1611.13			−1.81638			−0.908191	−	0.418556i	$-0.862536\pi$
$887$	−1611.13			−1.81638			−0.908191	+	0.418556i	$0.862536\pi$
$888$	2181.68			2.45684
$889$	−568.842			−0.639868
$890$	−248.530			−0.279248
$891$	1708.79			1.91783
$892$	−458.277			−0.513763
$893$			265.599i			0.297423i
$894$	−313.387			−0.350545
$895$	−157.802			−0.176315
$896$		−	1404.69i		−	1.56774i
$897$		−	95.2069i		−	0.106139i
$898$		−	1435.66i		−	1.59873i
$899$		−	273.316i		−	0.304022i
$900$	−2383.42			−2.64824
$901$	227.840			0.252874
$902$		−	1018.31i		−	1.12894i
$903$			373.642i			0.413778i
$904$			1014.12i			1.12182i
$905$	1112.33			1.22909
$906$		−	1680.01i		−	1.85432i
$907$	413.826			0.456258			0.228129	−	0.973631i	$-0.426739\pi$
$907$	413.826			0.456258			0.228129	+	0.973631i	$0.426739\pi$
$908$			235.983i			0.259893i
$909$	−1959.83			−2.15603
$910$			112.450i			0.123571i
$911$	−882.425			−0.968633			−0.484317	−	0.874893i	$-0.660932\pi$
$911$	−882.425			−0.968633			−0.484317	+	0.874893i	$0.660932\pi$
$912$		−	366.983i		−	0.402393i
$913$	−228.157			−0.249898
$914$	2449.79			2.68029
$915$	1923.29			2.10196
$916$			610.768i			0.666777i
$917$			288.124i			0.314202i
$918$	4830.45			5.26193
$919$	−379.413			−0.412854			−0.206427	−	0.978462i	$-0.566184\pi$
$919$	−379.413			−0.412854			−0.206427	+	0.978462i	$0.566184\pi$
$920$	−960.729			−1.04427
$921$	−2515.54			−2.73131
$922$		−	316.293i		−	0.343051i
$923$			53.5256i			0.0579909i
$924$	−1526.35			−1.65189
$925$		−	914.591i		−	0.988747i
$926$			1941.13i			2.09626i
$927$		−	357.015i		−	0.385129i
$928$		−	314.271i		−	0.338654i
$929$		−	457.682i		−	0.492661i	−0.969186	−	0.246330i	$-0.920775\pi$
$929$		−	457.682i		−	0.492661i	0.969186	−	0.246330i	$-0.0792248\pi$
$930$			3810.62i			4.09744i
$931$	195.204			0.209671
$932$			2654.92i			2.84863i
$933$	−860.199			−0.921971
$934$	−1884.96			−2.01816
$935$			603.108i			0.645036i
$936$	115.849			0.123771
$937$		−	1483.01i		−	1.58272i	−0.611352	−	0.791359i	$-0.709374\pi$
$937$		−	1483.01i		−	1.58272i	0.611352	−	0.791359i	$-0.290626\pi$
$938$			1033.70i			1.10202i
$939$			2007.06i			2.13745i
$940$		−	563.887i		−	0.599880i
$941$	−127.076			−0.135044			−0.0675218	−	0.997718i	$-0.521509\pi$
$941$	−127.076			−0.135044			−0.0675218	+	0.997718i	$0.521509\pi$
$942$	3676.30			3.90265
$943$			1308.57i			1.38767i
$944$			264.146i			0.279816i
$945$	4483.45			4.74439
$946$			148.579i			0.157060i
$947$		−	1154.67i		−	1.21929i	−0.792674	−	0.609645i	$-0.791312\pi$
$947$		−	1154.67i		−	1.21929i	0.792674	−	0.609645i	$-0.208688\pi$
$948$	−1843.91	−	2080.20i	−1.94505	−	2.19430i
$949$	−4.19979			−0.00442549
$950$	925.054			0.973741
$951$		−	1769.99i		−	1.86119i
$952$	−850.331			−0.893205
$953$	604.411			0.634219			0.317110	−	0.948389i	$-0.397288\pi$
$953$	604.411			0.634219			0.317110	+	0.948389i	$0.397288\pi$
$954$		−	1061.13i		−	1.11229i
$955$			2352.31i			2.46315i
$956$	−843.951			−0.882794
$957$	−275.058			−0.287416
$958$	−24.3096			−0.0253753
$959$	1182.78			1.23335
$960$			3867.94i			4.02910i
$961$	86.2736			0.0897749
$962$			130.487i			0.135642i
$963$		−	523.905i		−	0.544034i
$964$	−143.753			−0.149122
$965$			537.930i			0.557441i
$966$	3254.62			3.36918
$967$	−1822.30			−1.88449			−0.942243	−	0.334931i	$-0.891287\pi$
$967$	−1822.30			−1.88449			−0.942243	+	0.334931i	$0.891287\pi$
$968$	586.727			0.606123
$969$	−1780.10			−1.83704
$970$	−2592.83			−2.67302
$971$	−1015.49			−1.04581			−0.522907	−	0.852389i	$-0.675153\pi$
$971$	−1015.49			−1.04581			−0.522907	+	0.852389i	$0.675153\pi$
$972$		−	5755.36i		−	5.92115i
$973$	441.846			0.454106
$974$	−2134.37			−2.19135
$975$		−	66.3058i		−	0.0680059i
$976$		−	179.331i		−	0.183741i
$977$			1808.32i			1.85089i	0.378883	+	0.925445i	$0.376308\pi$
$977$			1808.32i			1.85089i	−0.378883	+	0.925445i	$0.623692\pi$
$978$		−	3837.73i		−	3.92406i
$979$	68.7390			0.0702134
$980$	−414.433			−0.422891
$981$		−	3504.37i		−	3.57224i
$982$			2314.40i			2.35682i
$983$			1529.34i			1.55579i	0.628397	+	0.777893i	$0.283711\pi$
$983$			1529.34i			1.55579i	−0.628397	+	0.777893i	$0.716289\pi$
$984$	−2173.92			−2.20927
$985$			1653.40i			1.67858i
$986$	−449.787			−0.456174
$987$			650.793i			0.659365i
$988$	−79.5388			−0.0805048
$989$		−	190.930i		−	0.193054i
$990$	2808.88			2.83725
$991$		−	477.812i		−	0.482151i	−0.970506	−	0.241076i	$-0.922500\pi$
$991$		−	477.812i		−	0.482151i	0.970506	−	0.241076i	$-0.0775002\pi$
$992$	1204.21			1.21392
$993$	−3370.63			−3.39439
$994$	−1829.76			−1.84080
$995$			103.193i			0.103712i
$996$			1429.71i			1.43545i
$997$	1538.67			1.54330			0.771649	−	0.636048i	$-0.219432\pi$
$997$	1538.67			1.54330			0.771649	+	0.636048i	$0.219432\pi$
$998$	48.2201			0.0483167
$999$	5202.62			5.20783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	79.3.b.b.78.1	✓	8
3.2	odd	2		711.3.d.b.631.7		8
4.3	odd	2		1264.3.e.b.1105.8		8
79.78	odd	2	inner	79.3.b.b.78.2	yes	8
237.236	even	2		711.3.d.b.631.8		8
316.315	even	2		1264.3.e.b.1105.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
79.3.b.b.78.1	✓	8	1.1	even	1	trivial
79.3.b.b.78.2	yes	8	79.78	odd	2	inner
711.3.d.b.631.7		8	3.2	odd	2
711.3.d.b.631.8		8	237.236	even	2
1264.3.e.b.1105.1		8	316.315	even	2
1264.3.e.b.1105.8		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 79 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	79.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.17284 q^{2} -5.79987i q^{3} +6.06689 q^{4} +6.39881 q^{5} +18.4021i q^{6} -7.72499i q^{7} -6.55790 q^{8} -24.6385 q^{9} +O(q^{10})\)	\(q-3.17284 q^{2} -5.79987i q^{3} +6.06689 q^{4} +6.39881 q^{5} +18.4021i q^{6} -7.72499i q^{7} -6.55790 q^{8} -24.6385 q^{9} -20.3024 q^{10} +5.61527 q^{11} -35.1872i q^{12} +0.716990 q^{13} +24.5101i q^{14} -37.1123i q^{15} -3.46041 q^{16} +16.7851i q^{17} +78.1741 q^{18} -18.2852 q^{19} +38.8209 q^{20} -44.8040 q^{21} -17.8163 q^{22} +22.8948 q^{23} +38.0350i q^{24} +15.9448 q^{25} -2.27489 q^{26} +90.7016i q^{27} -46.8667i q^{28} -8.44567i q^{29} +117.751i q^{30} +32.3616 q^{31} +37.2109 q^{32} -32.5679i q^{33} -53.2565i q^{34} -49.4308i q^{35} -149.479 q^{36} -57.3597i q^{37} +58.0159 q^{38} -4.15845i q^{39} -41.9628 q^{40} +57.1558i q^{41} +142.156 q^{42} -8.33947i q^{43} +34.0672 q^{44} -157.657 q^{45} -72.6414 q^{46} -14.5253i q^{47} +20.0699i q^{48} -10.6755 q^{49} -50.5903 q^{50} +97.3517 q^{51} +4.34990 q^{52} -13.5739i q^{53} -287.781i q^{54} +35.9311 q^{55} +50.6597i q^{56} +106.052i q^{57} +26.7967i q^{58} -76.3337i q^{59} -225.156i q^{60} +51.8236i q^{61} -102.678 q^{62} +190.333i q^{63} -104.223 q^{64} +4.58789 q^{65} +103.332i q^{66} +42.1742 q^{67} +101.834i q^{68} -132.787i q^{69} +156.836i q^{70} +74.6532i q^{71} +161.577 q^{72} -5.85752 q^{73} +181.993i q^{74} -92.4779i q^{75} -110.934 q^{76} -43.3779i q^{77} +13.1941i q^{78} +(59.1180 - 52.4028i) q^{79} -22.1425 q^{80} +304.311 q^{81} -181.346i q^{82} -40.6315 q^{83} -271.821 q^{84} +107.405i q^{85} +26.4598i q^{86} -48.9838 q^{87} -36.8244 q^{88} +12.2414 q^{89} +500.221 q^{90} -5.53874i q^{91} +138.900 q^{92} -187.693i q^{93} +46.0865i q^{94} -117.004 q^{95} -215.819i q^{96} +127.711 q^{97} +33.8717 q^{98} -138.352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 8 q^{8} - 82 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 8 * q^8 - 82 * q^9	\( 8 q - 4 q^{2} + 8 q^{4} - 2 q^{5} - 8 q^{8} - 82 q^{9} - 22 q^{10} + 28 q^{11} - 30 q^{13} - 40 q^{16} + 122 q^{18} - 32 q^{19} + 106 q^{20} - 2 q^{21} + 60 q^{22} + 60 q^{23} - 50 q^{25} + 62 q^{26} + 36 q^{31} + 4 q^{32} - 322 q^{36} + 284 q^{38} - 166 q^{40} + 238 q^{42} + 192 q^{44} - 260 q^{45} - 236 q^{46} - 294 q^{49} - 258 q^{50} + 236 q^{51} + 30 q^{52} + 140 q^{55} - 388 q^{62} - 208 q^{64} + 194 q^{65} + 132 q^{67} + 322 q^{72} + 384 q^{73} - 308 q^{76} + 210 q^{79} + 6 q^{80} + 56 q^{81} + 96 q^{83} - 246 q^{84} - 8 q^{87} - 232 q^{88} + 102 q^{89} + 908 q^{90} - 68 q^{92} - 12 q^{95} + 470 q^{97} + 498 q^{98} - 524 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 - 8 * q^8 - 82 * q^9 - 22 * q^10 + 28 * q^11 - 30 * q^13 - 40 * q^16 + 122 * q^18 - 32 * q^19 + 106 * q^20 - 2 * q^21 + 60 * q^22 + 60 * q^23 - 50 * q^25 + 62 * q^26 + 36 * q^31 + 4 * q^32 - 322 * q^36 + 284 * q^38 - 166 * q^40 + 238 * q^42 + 192 * q^44 - 260 * q^45 - 236 * q^46 - 294 * q^49 - 258 * q^50 + 236 * q^51 + 30 * q^52 + 140 * q^55 - 388 * q^62 - 208 * q^64 + 194 * q^65 + 132 * q^67 + 322 * q^72 + 384 * q^73 - 308 * q^76 + 210 * q^79 + 6 * q^80 + 56 * q^81 + 96 * q^83 - 246 * q^84 - 8 * q^87 - 232 * q^88 + 102 * q^89 + 908 * q^90 - 68 * q^92 - 12 * q^95 + 470 * q^97 + 498 * q^98 - 524 * q^99

Introduction

L-functions

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