LMFDB - Embedded newform 177.3.c.a.58.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.c (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:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 $ x^20 + 60x^18 + 1522x^16 + 21286x^14 + 179593x^12 + 941588x^10 + 3057025x^8 + 5962230x^6 + 6517782x^4 + 3428244*x^2 + 570861
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.3
Root			$-3.07256i$ of defining polynomial
Character	$\chi$	$=$	177.58
Dual form			177.3.c.a.58.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.07256i q^{2} +1.73205 q^{3} -5.44061 q^{4} -6.03179 q^{5} -5.32183i q^{6} -9.30133 q^{7} +4.42637i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-3.07256i q^{2} +1.73205 q^{3} -5.44061 q^{4} -6.03179 q^{5} -5.32183i q^{6} -9.30133 q^{7} +4.42637i q^{8} +3.00000 q^{9} +18.5330i q^{10} +12.6629i q^{11} -9.42342 q^{12} -16.7819i q^{13} +28.5789i q^{14} -10.4474 q^{15} -8.16217 q^{16} +14.0828 q^{17} -9.21767i q^{18} -37.4075 q^{19} +32.8166 q^{20} -16.1104 q^{21} +38.9074 q^{22} -27.8025i q^{23} +7.66670i q^{24} +11.3824 q^{25} -51.5635 q^{26} +5.19615 q^{27} +50.6050 q^{28} +39.1159 q^{29} +32.1001i q^{30} -0.257147i q^{31} +42.7842i q^{32} +21.9327i q^{33} -43.2703i q^{34} +56.1036 q^{35} -16.3218 q^{36} -54.7014i q^{37} +114.937i q^{38} -29.0672i q^{39} -26.6989i q^{40} -11.3202 q^{41} +49.5001i q^{42} -7.36421i q^{43} -68.8937i q^{44} -18.0954 q^{45} -85.4249 q^{46} -28.7287i q^{47} -14.1373 q^{48} +37.5148 q^{49} -34.9732i q^{50} +24.3922 q^{51} +91.3041i q^{52} -47.3053 q^{53} -15.9655i q^{54} -76.3796i q^{55} -41.1711i q^{56} -64.7917 q^{57} -120.186i q^{58} +(-28.6844 - 51.5578i) q^{59} +56.8401 q^{60} +84.0505i q^{61} -0.790099 q^{62} -27.9040 q^{63} +98.8084 q^{64} +101.225i q^{65} +67.3895 q^{66} +81.5123i q^{67} -76.6193 q^{68} -48.1554i q^{69} -172.382i q^{70} -6.96917 q^{71} +13.2791i q^{72} -131.681i q^{73} -168.073 q^{74} +19.7150 q^{75} +203.520 q^{76} -117.781i q^{77} -89.3106 q^{78} +51.9880 q^{79} +49.2325 q^{80} +9.00000 q^{81} +34.7820i q^{82} -16.5553i q^{83} +87.6504 q^{84} -84.9447 q^{85} -22.6270 q^{86} +67.7508 q^{87} -56.0505 q^{88} -69.2544i q^{89} +55.5990i q^{90} +156.094i q^{91} +151.263i q^{92} -0.445392i q^{93} -88.2705 q^{94} +225.634 q^{95} +74.1045i q^{96} +110.495i q^{97} -115.266i q^{98} +37.9886i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9}+O(q^{10}) $ 20 * q - 40 * q^4 - 8 * q^7 + 60 * q^9	$ 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9} - 24 q^{12} + 24 q^{15} - 8 q^{16} + 16 q^{17} - 60 q^{19} - 164 q^{20} + 40 q^{22} + 100 q^{25} - 156 q^{26} + 200 q^{28} - 60 q^{29} - 32 q^{35} - 120 q^{36} + 28 q^{41} + 180 q^{46} - 96 q^{48} + 284 q^{49} - 24 q^{51} - 8 q^{53} + 24 q^{57} - 152 q^{59} - 72 q^{60} - 8 q^{62} - 24 q^{63} + 204 q^{64} - 120 q^{66} + 384 q^{68} + 92 q^{71} + 104 q^{74} + 240 q^{75} + 120 q^{76} - 468 q^{78} - 420 q^{79} + 376 q^{80} + 180 q^{81} + 168 q^{84} - 348 q^{85} + 232 q^{86} + 144 q^{87} - 212 q^{88} + 152 q^{94} + 788 q^{95}+O(q^{100}) $ 20 * q - 40 * q^4 - 8 * q^7 + 60 * q^9 - 24 * q^12 + 24 * q^15 - 8 * q^16 + 16 * q^17 - 60 * q^19 - 164 * q^20 + 40 * q^22 + 100 * q^25 - 156 * q^26 + 200 * q^28 - 60 * q^29 - 32 * q^35 - 120 * q^36 + 28 * q^41 + 180 * q^46 - 96 * q^48 + 284 * q^49 - 24 * q^51 - 8 * q^53 + 24 * q^57 - 152 * q^59 - 72 * q^60 - 8 * q^62 - 24 * q^63 + 204 * q^64 - 120 * q^66 + 384 * q^68 + 92 * q^71 + 104 * q^74 + 240 * q^75 + 120 * q^76 - 468 * q^78 - 420 * q^79 + 376 * q^80 + 180 * q^81 + 168 * q^84 - 348 * q^85 + 232 * q^86 + 144 * q^87 - 212 * q^88 + 152 * q^94 + 788 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.07256i		−	1.53628i	−0.640282	−	0.768140i	$-0.721183\pi$
$2$		−	3.07256i		−	1.53628i	0.640282	−	0.768140i	$-0.278817\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	−5.44061			−1.36015
$5$	−6.03179			−1.20636			−0.603179	−	0.797606i	$-0.706099\pi$
$5$	−6.03179			−1.20636			−0.603179	+	0.797606i	$0.706099\pi$
$6$		−	5.32183i		−	0.886971i
$7$	−9.30133			−1.32876			−0.664381	−	0.747394i	$-0.731305\pi$
$7$	−9.30133			−1.32876			−0.664381	+	0.747394i	$0.731305\pi$
$8$			4.42637i			0.553296i
$9$	3.00000			0.333333
$10$			18.5330i			1.85330i
$11$			12.6629i			1.15117i	0.817742	+	0.575584i	$0.195225\pi$
$11$			12.6629i			1.15117i	−0.817742	+	0.575584i	$0.804775\pi$
$12$	−9.42342			−0.785285
$13$		−	16.7819i		−	1.29092i	−0.763795	−	0.645459i	$-0.776666\pi$
$13$		−	16.7819i		−	1.29092i	0.763795	−	0.645459i	$-0.223334\pi$
$14$			28.5789i			2.04135i
$15$	−10.4474			−0.696491
$16$	−8.16217			−0.510136
$17$	14.0828			0.828402			0.414201	−	0.910185i	$-0.364061\pi$
$17$	14.0828			0.828402			0.414201	+	0.910185i	$0.364061\pi$
$18$		−	9.21767i		−	0.512093i
$19$	−37.4075			−1.96882			−0.984408	−	0.175902i	$-0.943716\pi$
$19$	−37.4075			−1.96882			−0.984408	+	0.175902i	$0.943716\pi$
$20$	32.8166			1.64083
$21$	−16.1104			−0.767161
$22$	38.9074			1.76852
$23$		−	27.8025i		−	1.20881i	−0.796679	−	0.604403i	$-0.793412\pi$
$23$		−	27.8025i		−	1.20881i	0.796679	−	0.604403i	$-0.206588\pi$
$24$			7.66670i			0.319446i
$25$	11.3824			0.455298
$26$	−51.5635			−1.98321
$27$	5.19615			0.192450
$28$	50.6050			1.80732
$29$	39.1159			1.34882			0.674412	−	0.738355i	$-0.264397\pi$
$29$	39.1159			1.34882			0.674412	+	0.738355i	$0.264397\pi$
$30$			32.1001i			1.07000i
$31$		−	0.257147i		−	0.00829506i	−0.999991	−	0.00414753i	$-0.998680\pi$
$31$		−	0.257147i		−	0.00829506i	0.999991	−	0.00414753i	$-0.00132020\pi$
$32$			42.7842i			1.33701i
$33$			21.9327i			0.664627i
$34$		−	43.2703i		−	1.27266i
$35$	56.1036			1.60296
$36$	−16.3218			−0.453385
$37$		−	54.7014i		−	1.47842i	−0.673477	−	0.739208i	$-0.735200\pi$
$37$		−	54.7014i		−	1.47842i	0.673477	−	0.739208i	$-0.264800\pi$
$38$			114.937i			3.02465i
$39$		−	29.0672i		−	0.745312i
$40$		−	26.6989i		−	0.667473i
$41$	−11.3202			−0.276102			−0.138051	−	0.990425i	$-0.544084\pi$
$41$	−11.3202			−0.276102			−0.138051	+	0.990425i	$0.544084\pi$
$42$			49.5001i			1.17857i
$43$		−	7.36421i		−	0.171261i	−0.996327	−	0.0856303i	$-0.972710\pi$
$43$		−	7.36421i		−	0.171261i	0.996327	−	0.0856303i	$-0.0272904\pi$
$44$		−	68.8937i		−	1.56577i
$45$	−18.0954			−0.402119
$46$	−85.4249			−1.85706
$47$		−	28.7287i		−	0.611248i	−0.952152	−	0.305624i	$-0.901135\pi$
$47$		−	28.7287i		−	0.611248i	0.952152	−	0.305624i	$-0.0988651\pi$
$48$	−14.1373			−0.294527
$49$	37.5148			0.765608
$50$		−	34.9732i		−	0.699464i
$51$	24.3922			0.478278
$52$			91.3041i			1.75585i
$53$	−47.3053			−0.892552			−0.446276	−	0.894895i	$-0.647250\pi$
$53$	−47.3053			−0.892552			−0.446276	+	0.894895i	$0.647250\pi$
$54$		−	15.9655i		−	0.295657i
$55$		−	76.3796i		−	1.38872i
$56$		−	41.1711i		−	0.735199i
$57$	−64.7917			−1.13670
$58$		−	120.186i		−	2.07217i
$59$	−28.6844	−	51.5578i	−0.486176	−	0.873861i
$59$	−28.6844	−	51.5578i	−0.486176	−	0.873861i
$60$	56.8401			0.947334
$61$			84.0505i			1.37788i	0.724820	+	0.688938i	$0.241923\pi$
$61$			84.0505i			1.37788i	−0.724820	+	0.688938i	$0.758077\pi$
$62$	−0.790099			−0.0127435
$63$	−27.9040			−0.442921
$64$	98.8084			1.54388
$65$			101.225i			1.55731i
$66$	67.3895			1.02105
$67$			81.5123i			1.21660i	0.793707	+	0.608300i	$0.208148\pi$
$67$			81.5123i			1.21660i	−0.793707	+	0.608300i	$0.791852\pi$
$68$	−76.6193			−1.12675
$69$		−	48.1554i		−	0.697905i
$70$		−	172.382i		−	2.46260i
$71$	−6.96917			−0.0981573			−0.0490787	−	0.998795i	$-0.515628\pi$
$71$	−6.96917			−0.0981573			−0.0490787	+	0.998795i	$0.515628\pi$
$72$			13.2791i			0.184432i
$73$		−	131.681i		−	1.80385i	−0.431896	−	0.901923i	$-0.642155\pi$
$73$		−	131.681i		−	1.80385i	0.431896	−	0.901923i	$-0.357845\pi$
$74$	−168.073			−2.27126
$75$	19.7150			0.262866
$76$	203.520			2.67789
$77$		−	117.781i		−	1.52963i
$78$	−89.3106			−1.14501
$79$	51.9880			0.658076			0.329038	−	0.944317i	$-0.393276\pi$
$79$	51.9880			0.658076			0.329038	+	0.944317i	$0.393276\pi$
$80$	49.2325			0.615406
$81$	9.00000			0.111111
$82$			34.7820i			0.424170i
$83$		−	16.5553i		−	0.199461i	−0.995014	−	0.0997305i	$-0.968202\pi$
$83$		−	16.5553i		−	0.199461i	0.995014	−	0.0997305i	$-0.0317981\pi$
$84$	87.6504			1.04346
$85$	−84.9447			−0.999349
$86$	−22.6270			−0.263104
$87$	67.7508			0.778744
$88$	−56.0505			−0.636937
$89$		−	69.2544i		−	0.778139i	−0.921208	−	0.389070i	$-0.872797\pi$
$89$		−	69.2544i		−	0.778139i	0.921208	−	0.389070i	$-0.127203\pi$
$90$			55.5990i			0.617767i
$91$			156.094i			1.71532i
$92$			151.263i			1.64416i
$93$		−	0.445392i		−	0.00478916i
$94$	−88.2705			−0.939048
$95$	225.634			2.37509
$96$			74.1045i			0.771922i
$97$			110.495i			1.13912i	0.821949	+	0.569560i	$0.192887\pi$
$97$			110.495i			1.13912i	−0.821949	+	0.569560i	$0.807113\pi$
$98$		−	115.266i		−	1.17619i
$99$			37.9886i			0.383723i
$100$	−61.9275			−0.619275
$101$			159.617i			1.58037i	0.612868	+	0.790186i	$0.290016\pi$
$101$			159.617i			1.58037i	−0.612868	+	0.790186i	$0.709984\pi$
$102$		−	74.9464i		−	0.734769i
$103$			26.7475i			0.259684i	0.991535	+	0.129842i	$0.0414470\pi$
$103$			26.7475i			0.259684i	−0.991535	+	0.129842i	$0.958553\pi$
$104$	74.2831			0.714260
$105$	97.1744			0.925470
$106$			145.348i			1.37121i
$107$	−35.3863			−0.330713			−0.165356	−	0.986234i	$-0.552877\pi$
$107$	−35.3863			−0.330713			−0.165356	+	0.986234i	$0.552877\pi$
$108$	−28.2703			−0.261762
$109$		−	68.2150i		−	0.625826i	−0.949782	−	0.312913i	$-0.898695\pi$
$109$		−	68.2150i		−	0.625826i	0.949782	−	0.312913i	$-0.101305\pi$
$110$	−234.681			−2.13346
$111$		−	94.7456i		−	0.853564i
$112$	75.9191			0.677849
$113$			120.908i			1.06998i	0.844858	+	0.534990i	$0.179685\pi$
$113$			120.908i			1.06998i	−0.844858	+	0.534990i	$0.820315\pi$
$114$			199.076i			1.74628i
$115$			167.699i			1.45825i
$116$	−212.815			−1.83461
$117$		−	50.3458i		−	0.430306i
$118$	−158.414	+	88.1345i	−1.34249	+	0.746902i
$119$	−130.989			−1.10075
$120$		−	46.2439i		−	0.385366i
$121$	−39.3479			−0.325189
$122$	258.250			2.11680
$123$	−19.6072			−0.159408
$124$			1.39904i			0.0112826i
$125$	82.1382			0.657105
$126$			85.7367i			0.680450i
$127$	−158.088			−1.24479			−0.622393	−	0.782705i	$-0.713839\pi$
$127$	−158.088			−1.24479			−0.622393	+	0.782705i	$0.713839\pi$
$128$		−	132.458i		−	1.03482i
$129$		−	12.7552i		−	0.0988774i
$130$	311.020			2.39246
$131$		−	130.513i		−	0.996282i	−0.867096	−	0.498141i	$-0.834016\pi$
$131$		−	130.513i		−	0.996282i	0.867096	−	0.498141i	$-0.165984\pi$
$132$		−	119.327i		−	0.903995i
$133$	347.939			2.61609
$134$	250.451			1.86904
$135$	−31.3421			−0.232164
$136$			62.3359i			0.458352i
$137$	208.921			1.52497			0.762487	−	0.647004i	$-0.223978\pi$
$137$	208.921			1.52497			0.762487	+	0.647004i	$0.223978\pi$
$138$	−147.960			−1.07218
$139$	−73.8315			−0.531162			−0.265581	−	0.964089i	$-0.585564\pi$
$139$	−73.8315			−0.531162			−0.265581	+	0.964089i	$0.585564\pi$
$140$	−305.238			−2.18027
$141$		−	49.7595i		−	0.352904i
$142$			21.4132i			0.150797i
$143$	212.507			1.48606
$144$	−24.4865			−0.170045
$145$	−235.939			−1.62716
$146$	−404.597			−2.77121
$147$	64.9775			0.442024
$148$			297.609i			2.01087i
$149$		−	66.3172i		−	0.445082i	−0.974923	−	0.222541i	$-0.928565\pi$
$149$		−	66.3172i		−	0.445082i	0.974923	−	0.222541i	$-0.0714351\pi$
$150$		−	60.5754i		−	0.403836i
$151$		−	103.185i		−	0.683347i	−0.939819	−	0.341673i	$-0.889006\pi$
$151$		−	103.185i		−	0.683347i	0.939819	−	0.341673i	$-0.110994\pi$
$152$		−	165.579i		−	1.08934i
$153$	42.2485			0.276134
$154$	−361.890			−2.34994
$155$			1.55106i			0.0100068i
$156$			158.143i			1.01374i
$157$		−	251.051i		−	1.59905i	−0.600630	−	0.799527i	$-0.705084\pi$
$157$		−	251.051i		−	1.59905i	0.600630	−	0.799527i	$-0.294916\pi$
$158$		−	159.736i		−	1.01099i
$159$	−81.9351			−0.515315
$160$		−	258.065i		−	1.61291i
$161$			258.601i			1.60622i
$162$		−	27.6530i		−	0.170698i
$163$	−96.4209			−0.591539			−0.295770	−	0.955259i	$-0.595576\pi$
$163$	−96.4209			−0.591539			−0.295770	+	0.955259i	$0.595576\pi$
$164$	61.5888			0.375542
$165$		−	132.293i		−	0.801778i
$166$	−50.8670			−0.306428
$167$	78.3907			0.469405			0.234703	−	0.972067i	$-0.424588\pi$
$167$	78.3907			0.469405			0.234703	+	0.972067i	$0.424588\pi$
$168$		−	71.3105i		−	0.424467i
$169$	−112.633			−0.666470
$170$			260.997i			1.53528i
$171$	−112.222			−0.656272
$172$			40.0658i			0.232941i
$173$		−	52.2561i		−	0.302058i	−0.988529	−	0.151029i	$-0.951741\pi$
$173$		−	52.2561i		−	0.302058i	0.988529	−	0.151029i	$-0.0482587\pi$
$174$		−	208.168i		−	1.19637i
$175$	−105.872			−0.604982
$176$		−	103.356i		−	0.587252i
$177$	−49.6828	−	89.3007i	−0.280694	−	0.504524i
$178$	−212.788			−1.19544
$179$			117.505i			0.656453i	0.944599	+	0.328226i	$0.106451\pi$
$179$			117.505i			0.656453i	−0.944599	+	0.328226i	$0.893549\pi$
$180$	98.4499			0.546944
$181$	160.180			0.884972			0.442486	−	0.896776i	$-0.354097\pi$
$181$	160.180			0.884972			0.442486	+	0.896776i	$0.354097\pi$
$182$	479.609			2.63521
$183$			145.580i			0.795517i
$184$	123.064			0.668828
$185$			329.947i			1.78350i
$186$	−1.36849			−0.00735748
$187$			178.329i			0.953630i
$188$			156.302i			0.831391i
$189$	−48.3311			−0.255720
$190$		−	693.274i		−	3.64881i
$191$			14.2938i			0.0748369i	0.999300	+	0.0374184i	$0.0119134\pi$
$191$			14.2938i			0.0748369i	−0.999300	+	0.0374184i	$0.988087\pi$
$192$	171.141			0.891360
$193$	71.9463			0.372779			0.186389	−	0.982476i	$-0.440321\pi$
$193$	71.9463			0.372779			0.186389	+	0.982476i	$0.440321\pi$
$194$	339.501			1.75001
$195$			175.327i			0.899113i
$196$	−204.103			−1.04134
$197$	−44.5489			−0.226137			−0.113068	−	0.993587i	$-0.536068\pi$
$197$	−44.5489			−0.226137			−0.113068	+	0.993587i	$0.536068\pi$
$198$	116.722			0.589505
$199$	−125.217			−0.629233			−0.314617	−	0.949219i	$-0.601876\pi$
$199$	−125.217			−0.629233			−0.314617	+	0.949219i	$0.601876\pi$
$200$			50.3829i			0.251915i
$201$			141.183i			0.702405i
$202$	490.434			2.42789
$203$	−363.830			−1.79227
$204$	−132.708			−0.650532
$205$	68.2810			0.333078
$206$	82.1831			0.398947
$207$		−	83.4076i		−	0.402935i
$208$			136.977i			0.658544i
$209$		−	473.686i		−	2.26644i
$210$		−	298.574i		−	1.42178i
$211$			106.781i			0.506071i	0.967457	+	0.253035i	$0.0814289\pi$
$211$			106.781i			0.506071i	−0.967457	+	0.253035i	$0.918571\pi$
$212$	257.370			1.21401
$213$	−12.0710			−0.0566711
$214$			108.726i			0.508067i
$215$			44.4193i			0.206602i
$216$			23.0001i			0.106482i
$217$			2.39181i			0.0110222i
$218$	−209.595			−0.961443
$219$		−	228.078i		−	1.04145i
$220$			415.552i			1.88887i
$221$		−	236.337i		−	1.06940i
$222$	−291.111			−1.31131
$223$	−37.6647			−0.168900			−0.0844501	−	0.996428i	$-0.526913\pi$
$223$	−37.6647			−0.168900			−0.0844501	+	0.996428i	$0.526913\pi$
$224$		−	397.950i		−	1.77656i
$225$	34.1473			0.151766
$226$	371.496			1.64379
$227$			189.636i			0.835399i	0.908585	+	0.417699i	$0.137163\pi$
$227$			189.636i			0.835399i	−0.908585	+	0.417699i	$0.862837\pi$
$228$	352.507			1.54608
$229$		−	206.938i		−	0.903658i	−0.892104	−	0.451829i	$-0.850772\pi$
$229$		−	206.938i		−	0.903658i	0.892104	−	0.451829i	$-0.149228\pi$
$230$	515.265			2.24028
$231$		−	204.003i		−	0.883131i
$232$			173.142i			0.746300i
$233$		−	213.272i		−	0.915330i	−0.889125	−	0.457665i	$-0.848686\pi$
$233$		−	213.272i		−	0.915330i	0.889125	−	0.457665i	$-0.151314\pi$
$234$	−154.690			−0.661070
$235$			173.285i			0.737384i
$236$	156.061	+	280.506i	0.661274	+	1.18858i
$237$	90.0458			0.379940
$238$			402.472i			1.69106i
$239$	−142.148			−0.594760			−0.297380	−	0.954759i	$-0.596113\pi$
$239$	−142.148			−0.594760			−0.297380	+	0.954759i	$0.596113\pi$
$240$	85.2732			0.355305
$241$	−391.267			−1.62351			−0.811756	−	0.583996i	$-0.801488\pi$
$241$	−391.267			−1.62351			−0.811756	+	0.583996i	$0.801488\pi$
$242$			120.899i			0.499581i
$243$	15.5885			0.0641500
$244$		−	457.286i		−	1.87412i
$245$	−226.281			−0.923596
$246$			60.2441i			0.244895i
$247$			627.770i			2.54158i
$248$	1.13823			0.00458963
$249$		−	28.6745i		−	0.115159i
$250$		−	252.374i		−	1.00950i
$251$	135.007			0.537877			0.268938	−	0.963157i	$-0.413327\pi$
$251$	135.007			0.537877			0.268938	+	0.963157i	$0.413327\pi$
$252$	151.815			0.602440
$253$	352.060			1.39154
$254$			485.734i			1.91234i
$255$	−147.128			−0.576974
$256$	−11.7500			−0.0458983
$257$	−133.333			−0.518807			−0.259403	−	0.965769i	$-0.583526\pi$
$257$	−133.333			−0.518807			−0.259403	+	0.965769i	$0.583526\pi$
$258$	−39.1910			−0.151903
$259$			508.796i			1.96446i
$260$		−	550.727i		−	2.11818i
$261$	117.348			0.449608
$262$	−401.009			−1.53057
$263$	272.345			1.03553			0.517765	−	0.855523i	$-0.326764\pi$
$263$	272.345			1.03553			0.517765	+	0.855523i	$0.326764\pi$
$264$	−97.0823			−0.367736
$265$	285.335			1.07674
$266$		−	1069.06i		−	4.01904i
$267$		−	119.952i		−	0.449259i
$268$		−	443.477i		−	1.65476i
$269$		−	275.151i		−	1.02287i	−0.859323	−	0.511434i	$-0.829114\pi$
$269$		−	275.151i		−	1.02287i	0.859323	−	0.511434i	$-0.170886\pi$
$270$			96.3004i			0.356668i
$271$	−142.359			−0.525308			−0.262654	−	0.964890i	$-0.584598\pi$
$271$	−142.359			−0.525308			−0.262654	+	0.964890i	$0.584598\pi$
$272$	−114.947			−0.422598
$273$			270.363i			0.990342i
$274$		−	641.923i		−	2.34278i
$275$			144.134i			0.524124i
$276$			261.995i			0.949257i
$277$	−282.049			−1.01823			−0.509114	−	0.860699i	$-0.670027\pi$
$277$	−282.049			−1.01823			−0.509114	+	0.860699i	$0.670027\pi$
$278$			226.852i			0.816013i
$279$		−	0.771441i		−	0.00276502i
$280$			248.336i			0.886913i
$281$	−273.179			−0.972168			−0.486084	−	0.873912i	$-0.661575\pi$
$281$	−273.179			−0.972168			−0.486084	+	0.873912i	$0.661575\pi$
$282$	−152.889			−0.542159
$283$		−	240.930i		−	0.851343i	−0.904878	−	0.425671i	$-0.860038\pi$
$283$		−	240.930i		−	0.851343i	0.904878	−	0.425671i	$-0.139962\pi$
$284$	37.9166			0.133509
$285$	390.810			1.37126
$286$		−	652.941i		−	2.28301i
$287$	105.293			0.366874
$288$			128.353i			0.445669i
$289$	−90.6737			−0.313750
$290$			724.936i			2.49978i
$291$			191.382i			0.657672i
$292$			716.424i			2.45351i
$293$	−321.271			−1.09649			−0.548245	−	0.836318i	$-0.684704\pi$
$293$	−321.271			−1.09649			−0.548245	+	0.836318i	$0.684704\pi$
$294$		−	199.647i		−	0.679072i
$295$	173.018	+	310.986i	0.586502	+	1.05419i
$296$	242.129			0.818002
$297$			65.7981i			0.221542i
$298$	−203.763			−0.683770
$299$	−466.581			−1.56047
$300$	−107.262			−0.357539
$301$			68.4969i			0.227565i
$302$	−317.043			−1.04981
$303$			276.466i			0.912428i
$304$	305.326			1.00436
$305$		−	506.974i		−	1.66221i
$306$		−	129.811i		−	0.424219i
$307$	−569.638			−1.85550			−0.927750	−	0.373203i	$-0.878259\pi$
$307$	−569.638			−1.85550			−0.927750	+	0.373203i	$0.878259\pi$
$308$			640.803i			2.08053i
$309$			46.3280i			0.149929i
$310$	4.76571			0.0153733
$311$	−357.447			−1.14935			−0.574673	−	0.818383i	$-0.694871\pi$
$311$	−357.447			−1.14935			−0.574673	+	0.818383i	$0.694871\pi$
$312$	128.662			0.412378
$313$		−	540.979i		−	1.72837i	−0.503176	−	0.864184i	$-0.667835\pi$
$313$		−	540.979i		−	1.72837i	0.503176	−	0.864184i	$-0.332165\pi$
$314$	−771.370			−2.45659
$315$	168.311			0.534320
$316$	−282.847			−0.895084
$317$	431.328			1.36066			0.680328	−	0.732908i	$-0.261837\pi$
$317$	431.328			1.36066			0.680328	+	0.732908i	$0.261837\pi$
$318$			251.750i			0.791668i
$319$			495.319i			1.55272i
$320$	−595.991			−1.86247
$321$	−61.2908			−0.190937
$322$	794.566			2.46760
$323$	−526.804			−1.63097
$324$	−48.9655			−0.151128
$325$		−	191.019i		−	0.587752i
$326$			296.259i			0.908770i
$327$		−	118.152i		−	0.361321i
$328$		−	50.1074i		−	0.152766i
$329$			267.215i			0.812203i
$330$	−406.479			−1.23176
$331$	241.399			0.729301			0.364650	−	0.931145i	$-0.381189\pi$
$331$	241.399			0.729301			0.364650	+	0.931145i	$0.381189\pi$
$332$			90.0708i			0.271297i
$333$		−	164.104i		−	0.492805i
$334$		−	240.860i		−	0.721138i
$335$		−	491.664i		−	1.46766i
$336$	131.496			0.391356
$337$			122.088i			0.362278i	0.983457	+	0.181139i	$0.0579784\pi$
$337$			122.088i			0.362278i	−0.983457	+	0.181139i	$0.942022\pi$
$338$			346.073i			1.02388i
$339$			209.419i			0.617754i
$340$	462.151			1.35927
$341$	3.25621			0.00954901
$342$			344.810i			1.00822i
$343$	106.828			0.311452
$344$	32.5967			0.0947579
$345$			290.463i			0.841922i
$346$	−160.560			−0.464046
$347$			403.930i			1.16406i	0.813166	+	0.582032i	$0.197742\pi$
$347$			403.930i			1.16406i	−0.813166	+	0.582032i	$0.802258\pi$
$348$	−368.606			−1.05921
$349$		−	449.445i		−	1.28781i	−0.765106	−	0.643904i	$-0.777314\pi$
$349$		−	449.445i		−	1.28781i	0.765106	−	0.643904i	$-0.222686\pi$
$350$			325.298i			0.929422i
$351$		−	87.2015i		−	0.248437i
$352$	−541.771			−1.53912
$353$		−	213.176i		−	0.603899i	−0.953324	−	0.301950i	$-0.902363\pi$
$353$		−	213.176i		−	0.603899i	0.953324	−	0.301950i	$-0.0976374\pi$
$354$	−274.382	+	152.653i	−0.775089	+	0.431224i
$355$	42.0365			0.118413
$356$			376.786i			1.05839i
$357$	−226.880			−0.635518
$358$	361.041			1.00849
$359$	405.372			1.12917			0.564585	−	0.825375i	$-0.309036\pi$
$359$	405.372			1.12917			0.564585	+	0.825375i	$0.309036\pi$
$360$		−	80.0968i		−	0.222491i
$361$	1038.32			2.87623
$362$		−	492.162i		−	1.35956i
$363$	−68.1525			−0.187748
$364$		−	849.249i		−	2.33310i
$365$			794.270i			2.17608i
$366$	447.302			1.22214
$367$		−	541.192i		−	1.47464i	−0.675546	−	0.737318i	$-0.736092\pi$
$367$		−	541.192i		−	1.47464i	0.675546	−	0.737318i	$-0.263908\pi$
$368$			226.929i			0.616655i
$369$	−33.9606			−0.0920341
$370$	1013.78			2.73995
$371$	440.002			1.18599
$372$			2.42320i			0.00651399i
$373$	−107.068			−0.287046			−0.143523	−	0.989647i	$-0.545843\pi$
$373$	−107.068			−0.287046			−0.143523	+	0.989647i	$0.545843\pi$
$374$	547.926			1.46504
$375$	142.268			0.379380
$376$	127.164			0.338201
$377$		−	656.441i		−	1.74122i
$378$			148.500i			0.392858i
$379$	−204.702			−0.540112			−0.270056	−	0.962845i	$-0.587042\pi$
$379$	−204.702			−0.540112			−0.270056	+	0.962845i	$0.587042\pi$
$380$	−1227.59			−3.23049
$381$	−273.816			−0.718678
$382$	43.9187			0.114970
$383$	−4.98048			−0.0130039			−0.00650193	−	0.999979i	$-0.502070\pi$
$383$	−4.98048			−0.0130039			−0.00650193	+	0.999979i	$0.502070\pi$
$384$		−	229.423i		−	0.597456i
$385$			710.432i			1.84528i
$386$		−	221.059i		−	0.572692i
$387$		−	22.0926i		−	0.0570869i
$388$		−	601.159i		−	1.54938i
$389$	138.904			0.357079			0.178539	−	0.983933i	$-0.442863\pi$
$389$	138.904			0.357079			0.178539	+	0.983933i	$0.442863\pi$
$390$	538.702			1.38129
$391$		−	391.539i		−	1.00138i
$392$			166.054i			0.423608i
$393$		−	226.055i		−	0.575204i
$394$			136.879i			0.347409i
$395$	−313.580			−0.793874
$396$		−	206.681i		−	0.521922i
$397$			266.530i			0.671359i	0.941976	+	0.335679i	$0.108966\pi$
$397$			266.530i			0.671359i	−0.941976	+	0.335679i	$0.891034\pi$
$398$			384.738i			0.966678i
$399$	602.649			1.51040
$400$	−92.9055			−0.232264
$401$		−	515.725i		−	1.28610i	−0.765825	−	0.643049i	$-0.777669\pi$
$401$		−	515.725i		−	1.28610i	0.765825	−	0.643049i	$-0.222331\pi$
$402$	433.794			1.07909
$403$	−4.31542			−0.0107082
$404$		−	868.417i		−	2.14955i
$405$	−54.2861			−0.134040
$406$			1117.89i			2.75342i
$407$	692.676			1.70191
$408$			107.969i			0.264630i
$409$		−	53.2453i		−	0.130184i	−0.997879	−	0.0650920i	$-0.979266\pi$
$409$		−	53.2453i		−	0.130184i	0.997879	−	0.0650920i	$-0.0207341\pi$
$410$		−	209.797i		−	0.511701i
$411$	361.862			0.880444
$412$		−	145.523i		−	0.353210i
$413$	266.803	+	479.556i	0.646012	+	1.16115i
$414$	−256.275			−0.619021
$415$			99.8578i			0.240621i
$416$	718.002			1.72597
$417$	−127.880			−0.306667
$418$	−1455.43			−3.48188
$419$			275.166i			0.656721i	0.944553	+	0.328360i	$0.106496\pi$
$419$			275.166i			0.656721i	−0.944553	+	0.328360i	$0.893504\pi$
$420$	−528.688			−1.25878
$421$			508.314i			1.20740i	0.797213	+	0.603699i	$0.206307\pi$
$421$			508.314i			1.20740i	−0.797213	+	0.603699i	$0.793693\pi$
$422$	328.091			0.777466
$423$		−	86.1860i		−	0.203749i
$424$		−	209.391i		−	0.493846i
$425$	160.297			0.377170
$426$			37.0887i			0.0870627i
$427$		−	781.781i		−	1.83087i
$428$	192.523			0.449820
$429$	368.073			0.857980
$430$	136.481			0.317398
$431$		−	331.069i		−	0.768141i	−0.923304	−	0.384070i	$-0.874522\pi$
$431$		−	331.069i		−	0.768141i	0.923304	−	0.384070i	$-0.125478\pi$
$432$	−42.4119			−0.0981757
$433$	216.406			0.499783			0.249891	−	0.968274i	$-0.419605\pi$
$433$	216.406			0.499783			0.249891	+	0.968274i	$0.419605\pi$
$434$	7.34897			0.0169331
$435$	−408.658			−0.939444
$436$			371.132i			0.851219i
$437$			1040.02i			2.37992i
$438$	−700.782			−1.59996
$439$	594.843			1.35500			0.677498	−	0.735525i	$-0.263064\pi$
$439$	594.843			1.35500			0.677498	+	0.735525i	$0.263064\pi$
$440$	338.085			0.768374
$441$	112.544			0.255203
$442$	−726.160			−1.64290
$443$			101.223i			0.228495i	0.993452	+	0.114247i	$0.0364456\pi$
$443$			101.223i			0.228495i	−0.993452	+	0.114247i	$0.963554\pi$
$444$			515.474i			1.16098i
$445$			417.728i			0.938714i
$446$			115.727i			0.259478i
$447$		−	114.865i		−	0.256968i
$448$	−919.049			−2.05145
$449$	612.041			1.36312			0.681561	−	0.731762i	$-0.261302\pi$
$449$	612.041			1.36312			0.681561	+	0.731762i	$0.261302\pi$
$450$		−	104.920i		−	0.233155i
$451$		−	143.346i		−	0.317840i
$452$		−	657.813i		−	1.45534i
$453$		−	178.722i		−	0.394530i
$454$	582.666			1.28341
$455$		−	941.528i		−	2.06929i
$456$		−	286.792i		−	0.628930i
$457$			406.851i			0.890264i	0.895465	+	0.445132i	$0.146843\pi$
$457$			406.851i			0.890264i	−0.895465	+	0.445132i	$0.853157\pi$
$458$	−635.828			−1.38827
$459$	73.1766			0.159426
$460$		−	912.385i		−	1.98345i
$461$	−852.748			−1.84978			−0.924889	−	0.380236i	$-0.875843\pi$
$461$	−852.748			−1.84978			−0.924889	+	0.380236i	$0.875843\pi$
$462$	−626.812			−1.35674
$463$		−	727.640i		−	1.57158i	−0.618495	−	0.785788i	$-0.712257\pi$
$463$		−	727.640i		−	1.57158i	0.618495	−	0.785788i	$-0.287743\pi$
$464$	−319.271			−0.688084
$465$			2.68651i			0.00577743i
$466$	−655.290			−1.40620
$467$			24.1720i			0.0517602i	0.999665	+	0.0258801i	$0.00823880\pi$
$467$			24.1720i			0.0517602i	−0.999665	+	0.0258801i	$0.991761\pi$
$468$			273.912i			0.585282i
$469$		−	758.173i		−	1.61657i
$470$	532.429			1.13283
$471$		−	434.834i		−	0.923214i
$472$	228.214	−	126.968i	0.483504	−	0.268999i
$473$	93.2519			0.197150
$474$		−	276.671i		−	0.583694i
$475$	−425.789			−0.896397
$476$	712.661			1.49719
$477$	−141.916			−0.297517
$478$			436.757i			0.913717i
$479$	−540.528			−1.12845			−0.564225	−	0.825621i	$-0.690825\pi$
$479$	−540.528			−1.12845			−0.564225	+	0.825621i	$0.690825\pi$
$480$		−	446.982i		−	0.931213i
$481$	−917.996			−1.90851
$482$			1202.19i			2.49417i
$483$			447.909i			0.927349i
$484$	214.077			0.442307
$485$		−	666.481i		−	1.37419i
$486$		−	47.8964i		−	0.0985524i
$487$	−564.800			−1.15975			−0.579877	−	0.814704i	$-0.696899\pi$
$487$	−564.800			−1.15975			−0.579877	+	0.814704i	$0.696899\pi$
$488$	−372.038			−0.762374
$489$	−167.006			−0.341525
$490$			695.262i			1.41890i
$491$	8.09712			0.0164911			0.00824554	−	0.999966i	$-0.497375\pi$
$491$	8.09712			0.0164911			0.00824554	+	0.999966i	$0.497375\pi$
$492$	106.675			0.216819
$493$	550.863			1.11737
$494$	1928.86			3.90458
$495$		−	229.139i		−	0.462907i
$496$			2.09888i			0.00423161i
$497$	64.8226			0.130428
$498$	−88.1042			−0.176916
$499$	719.073			1.44103			0.720514	−	0.693440i	$-0.243906\pi$
$499$	719.073			1.44103			0.720514	+	0.693440i	$0.243906\pi$
$500$	−446.882			−0.893764
$501$	135.777			0.271011
$502$		−	414.817i		−	0.826329i
$503$			524.427i			1.04260i	0.853374	+	0.521299i	$0.174552\pi$
$503$			524.427i			1.04260i	−0.853374	+	0.521299i	$0.825448\pi$
$504$		−	123.513i		−	0.245066i
$505$		−	962.778i		−	1.90649i
$506$		−	1081.72i		−	2.13779i
$507$	−195.087			−0.384787
$508$	860.095			1.69310
$509$		−	749.520i		−	1.47253i	−0.676691	−	0.736267i	$-0.736587\pi$
$509$		−	749.520i		−	1.47253i	0.676691	−	0.736267i	$-0.263413\pi$
$510$			452.061i			0.886394i
$511$			1224.81i			2.39688i
$512$		−	493.728i		−	0.964312i
$513$	−194.375			−0.378899
$514$			409.674i			0.797032i
$515$		−	161.335i		−	0.313272i
$516$			69.3960i			0.134488i
$517$	363.787			0.703650
$518$	1563.31			3.01796
$519$		−	90.5102i		−	0.174393i
$520$	−448.060			−0.861653
$521$	−191.543			−0.367646			−0.183823	−	0.982959i	$-0.558847\pi$
$521$	−191.543			−0.367646			−0.183823	+	0.982959i	$0.558847\pi$
$522$		−	360.558i		−	0.690724i
$523$	985.876			1.88504			0.942520	−	0.334149i	$-0.108449\pi$
$523$	985.876			1.88504			0.942520	+	0.334149i	$0.108449\pi$
$524$			710.071i			1.35510i
$525$	−183.375			−0.349287
$526$		−	836.795i		−	1.59086i
$527$		−	3.62136i		−	0.00687165i
$528$		−	179.019i		−	0.339050i
$529$	−243.981			−0.461212
$530$		−	876.709i		−	1.65417i
$531$	−86.0532	−	154.673i	−0.162059	−	0.291287i
$532$	−1893.00			−3.55828
$533$			189.975i			0.356426i
$534$	−368.560			−0.690187
$535$	213.443			0.398958
$536$	−360.804			−0.673141
$537$			203.525i			0.379003i
$538$	−845.419			−1.57141
$539$			475.044i			0.881343i
$540$	170.520			0.315778
$541$			239.083i			0.441928i	0.975282	+	0.220964i	$0.0709204\pi$
$541$			239.083i			0.441928i	−0.975282	+	0.220964i	$0.929080\pi$
$542$			437.405i			0.807020i
$543$	277.440			0.510939
$544$			602.523i			1.10758i
$545$			411.458i			0.754969i
$546$	830.707			1.52144
$547$	106.125			0.194013			0.0970065	−	0.995284i	$-0.469073\pi$
$547$	106.125			0.194013			0.0970065	+	0.995284i	$0.469073\pi$
$548$	−1136.66			−2.07420
$549$			252.151i			0.459292i
$550$	442.861			0.805201
$551$	−1463.23			−2.65559
$552$	213.154			0.386148
$553$	−483.557			−0.874426
$554$			866.613i			1.56428i
$555$			571.485i			1.02970i
$556$	401.689			0.722462
$557$	8.64276			0.0155166			0.00775831	−	0.999970i	$-0.497530\pi$
$557$	8.64276			0.0155166			0.00775831	+	0.999970i	$0.497530\pi$
$558$	−2.37030			−0.00424784
$559$	−123.586			−0.221084
$560$	−457.928			−0.817728
$561$			308.875i			0.550579i
$562$			839.359i			1.49352i
$563$			327.402i			0.581530i	0.956794	+	0.290765i	$0.0939099\pi$
$563$			327.402i			0.581530i	−0.956794	+	0.290765i	$0.906090\pi$
$564$			270.722i			0.480004i
$565$		−	729.290i		−	1.29078i
$566$	−740.272			−1.30790
$567$	−83.7120			−0.147640
$568$		−	30.8481i		−	0.0543101i
$569$			616.454i			1.08340i	0.840572	+	0.541700i	$0.182219\pi$
$569$			616.454i			1.08340i	−0.840572	+	0.541700i	$0.817781\pi$
$570$		−	1200.79i		−	2.10664i
$571$		−	518.165i		−	0.907470i	−0.891137	−	0.453735i	$-0.850091\pi$
$571$		−	518.165i		−	0.907470i	0.891137	−	0.453735i	$-0.149909\pi$
$572$	−1156.17			−2.02128
$573$			24.7577i			0.0432071i
$574$		−	323.519i		−	0.563621i
$575$		−	316.461i		−	0.550367i
$576$	296.425			0.514627
$577$	787.940			1.36558			0.682790	−	0.730614i	$-0.260766\pi$
$577$	787.940			1.36558			0.682790	+	0.730614i	$0.260766\pi$
$578$			278.600i			0.482007i
$579$	124.615			0.215224
$580$	1283.65			2.21319
$581$			153.986i			0.265036i
$582$	588.034			1.01037
$583$		−	599.020i		−	1.02748i
$584$	582.868			0.998062
$585$			303.675i			0.519103i
$586$			987.125i			1.68451i
$587$			782.879i			1.33370i	0.745194	+	0.666848i	$0.232357\pi$
$587$			782.879i			1.33370i	−0.745194	+	0.666848i	$0.767643\pi$
$588$	−353.517			−0.601220
$589$			9.61922i			0.0163314i
$590$	955.521	−	531.608i	1.61953	−	0.901031i
$591$	−77.1610			−0.130560
$592$			446.482i			0.754193i
$593$	1037.25			1.74916			0.874580	−	0.484881i	$-0.161137\pi$
$593$	1037.25			1.74916			0.874580	+	0.484881i	$0.161137\pi$
$594$	202.169			0.340351
$595$	790.098			1.32790
$596$			360.806i			0.605380i
$597$	−216.883			−0.363288
$598$			1433.60i			2.39732i
$599$	673.671			1.12466			0.562330	−	0.826913i	$-0.309905\pi$
$599$	673.671			1.12466			0.562330	+	0.826913i	$0.309905\pi$
$600$			87.2658i			0.145443i
$601$		−	962.944i		−	1.60224i	−0.598506	−	0.801118i	$-0.704239\pi$
$601$		−	962.944i		−	1.60224i	0.598506	−	0.801118i	$-0.295761\pi$
$602$	210.461			0.349603
$603$			244.537i			0.405534i
$604$			561.392i			0.929457i
$605$	237.338			0.392294
$606$	849.457			1.40174
$607$	−790.355			−1.30207			−0.651034	−	0.759049i	$-0.725664\pi$
$607$	−790.355			−1.30207			−0.651034	+	0.759049i	$0.725664\pi$
$608$		−	1600.45i		−	2.63232i
$609$	−630.172			−1.03477
$610$	−1557.71			−2.55362
$611$	−482.123			−0.789071
$612$	−229.858			−0.375585
$613$			953.011i			1.55467i	0.629088	+	0.777334i	$0.283428\pi$
$613$			953.011i			1.55467i	−0.629088	+	0.777334i	$0.716572\pi$
$614$			1750.25i			2.85056i
$615$	118.266			0.192303
$616$	521.344			0.846338
$617$	419.167			0.679364			0.339682	−	0.940540i	$-0.389681\pi$
$617$	419.167			0.679364			0.339682	+	0.940540i	$0.389681\pi$
$618$	142.345			0.230332
$619$	−209.634			−0.338666			−0.169333	−	0.985559i	$-0.554161\pi$
$619$	−209.634			−0.338666			−0.169333	+	0.985559i	$0.554161\pi$
$620$		−	8.43869i		−	0.0136108i
$621$		−	144.466i		−	0.232635i
$622$			1098.28i			1.76572i
$623$			644.158i			1.03396i
$624$			237.251i			0.380210i
$625$	−780.001			−1.24800
$626$	−1662.19			−2.65526
$627$		−	820.448i		−	1.30853i
$628$			1365.87i			2.17496i
$629$		−	770.351i		−	1.22472i
$630$		−	517.145i		−	0.820865i
$631$	−612.575			−0.970800			−0.485400	−	0.874292i	$-0.661326\pi$
$631$	−612.575			−0.970800			−0.485400	+	0.874292i	$0.661326\pi$
$632$			230.118i			0.364111i
$633$			184.950i			0.292180i
$634$		−	1325.28i		−	2.09035i
$635$	953.552			1.50166
$636$	445.777			0.700908
$637$		−	629.571i		−	0.988337i
$638$	1521.90			2.38542
$639$	−20.9075			−0.0327191
$640$			798.955i			1.24837i
$641$	198.748			0.310060			0.155030	−	0.987910i	$-0.450453\pi$
$641$	198.748			0.310060			0.155030	+	0.987910i	$0.450453\pi$
$642$			188.320i			0.293333i
$643$	−157.384			−0.244766			−0.122383	−	0.992483i	$-0.539054\pi$
$643$	−157.384			−0.244766			−0.122383	+	0.992483i	$0.539054\pi$
$644$		−	1406.95i		−	2.18470i
$645$			76.9365i			0.119281i
$646$			1618.63i			2.50563i
$647$	1214.33			1.87686			0.938430	−	0.345470i	$-0.112280\pi$
$647$	1214.33			1.87686			0.938430	+	0.345470i	$0.112280\pi$
$648$			39.8373i			0.0614774i
$649$	652.869	−	363.226i	1.00596	−	0.559671i
$650$	−586.918			−0.902951
$651$			4.14273i			0.00636365i
$652$	524.589			0.804584
$653$	−404.646			−0.619673			−0.309836	−	0.950790i	$-0.600274\pi$
$653$	−404.646			−0.619673			−0.309836	+	0.950790i	$0.600274\pi$
$654$	−363.028			−0.555089
$655$			787.226i			1.20187i
$656$	92.3974			0.140850
$657$		−	395.042i		−	0.601282i
$658$	821.033			1.24777
$659$		−	1245.68i		−	1.89025i	−0.326703	−	0.945127i	$-0.605938\pi$
$659$		−	1245.68i		−	1.89025i	0.326703	−	0.945127i	$-0.394062\pi$
$660$			719.757i			1.09054i
$661$	96.3638			0.145785			0.0728924	−	0.997340i	$-0.476777\pi$
$661$	96.3638			0.145785			0.0728924	+	0.997340i	$0.476777\pi$
$662$		−	741.711i		−	1.12041i
$663$		−	409.348i		−	0.617418i
$664$	73.2797			0.110361
$665$	−2098.70			−3.15593
$666$	−504.220			−0.757087
$667$		−	1087.52i		−	1.63047i
$668$	−426.493			−0.638463
$669$	−65.2372			−0.0975146
$670$	−1510.67			−2.25473
$671$	−1064.32			−1.58617
$672$		−	689.270i		−	1.02570i
$673$		−	786.566i		−	1.16875i	−0.811485	−	0.584373i	$-0.801340\pi$
$673$		−	786.566i		−	1.16875i	0.811485	−	0.584373i	$-0.198660\pi$
$674$	375.122			0.556561
$675$	59.1449			0.0876221
$676$	612.795			0.906502
$677$	−797.643			−1.17820			−0.589101	−	0.808059i	$-0.700518\pi$
$677$	−797.643			−1.17820			−0.589101	+	0.808059i	$0.700518\pi$
$678$	643.451			0.949042
$679$		−	1027.75i		−	1.51362i
$680$		−	375.997i		−	0.552936i
$681$			328.458i			0.482318i
$682$		−	10.0049i		−	0.0146700i
$683$			743.492i			1.08857i	0.838901	+	0.544284i	$0.183199\pi$
$683$			743.492i			1.08857i	−0.838901	+	0.544284i	$0.816801\pi$
$684$	610.559			0.892630
$685$	−1260.17			−1.83966
$686$		−	328.235i		−	0.478477i
$687$		−	358.427i		−	0.521727i
$688$			60.1079i			0.0873662i
$689$			793.874i			1.15221i
$690$	892.465			1.29343
$691$			652.050i			0.943632i	0.881697	+	0.471816i	$0.156401\pi$
$691$			652.050i			0.943632i	−0.881697	+	0.471816i	$0.843599\pi$
$692$			284.305i			0.410845i
$693$		−	353.344i		−	0.509876i
$694$	1241.10			1.78833
$695$	445.336			0.640771
$696$			299.890i			0.430877i
$697$	−159.420			−0.228724
$698$	−1380.95			−1.97843
$699$		−	369.398i		−	0.528466i
$700$	576.008			0.822869
$701$		−	24.8059i		−	0.0353864i	−0.999843	−	0.0176932i	$-0.994368\pi$
$701$		−	24.8059i		−	0.0353864i	0.999843	−	0.0176932i	$-0.00563221\pi$
$702$	−267.932			−0.381669
$703$			2046.24i			2.91073i
$704$			1251.20i			1.77727i
$705$			300.139i			0.425729i
$706$	−654.997			−0.927758
$707$		−	1484.66i		−	2.09994i
$708$	270.305	+	485.851i	0.381787	+	0.686230i
$709$	521.844			0.736028			0.368014	−	0.929820i	$-0.380038\pi$
$709$	521.844			0.736028			0.368014	+	0.929820i	$0.380038\pi$
$710$		−	129.160i		−	0.181915i
$711$	155.964			0.219359
$712$	306.546			0.430542
$713$	−7.14934			−0.0100271
$714$			697.102i			0.976333i
$715$	−1281.80			−1.79272
$716$		−	639.299i		−	0.892876i
$717$	−246.207			−0.343385
$718$		−	1245.53i		−	1.73472i
$719$		−	997.450i		−	1.38727i	−0.720325	−	0.693637i	$-0.756007\pi$
$719$		−	997.450i		−	1.38727i	0.720325	−	0.693637i	$-0.243993\pi$
$720$	147.697			0.205135
$721$		−	248.787i		−	0.345058i
$722$		−	3190.30i		−	4.41870i
$723$	−677.693			−0.937335
$724$	−871.477			−1.20370
$725$	445.235			0.614117
$726$			209.403i			0.288433i
$727$	−570.949			−0.785349			−0.392675	−	0.919677i	$-0.628450\pi$
$727$	−570.949			−0.785349			−0.392675	+	0.919677i	$0.628450\pi$
$728$	−690.932			−0.949082
$729$	27.0000			0.0370370
$730$	2440.44			3.34307
$731$		−	103.709i		−	0.141873i
$732$		−	792.043i		−	1.08203i
$733$	−337.572			−0.460535			−0.230268	−	0.973127i	$-0.573960\pi$
$733$	−337.572			−0.460535			−0.230268	+	0.973127i	$0.573960\pi$
$734$	−1662.84			−2.26545
$735$	−391.930			−0.533239
$736$	1189.51			1.61618
$737$	−1032.18			−1.40051
$738$			104.346i			0.141390i
$739$			1041.04i			1.40872i	0.709843	+	0.704360i	$0.248766\pi$
$739$			1041.04i			1.40872i	−0.709843	+	0.704360i	$0.751234\pi$
$740$		−	1795.12i		−	2.42583i
$741$			1087.33i			1.46738i
$742$		−	1351.93i		−	1.82201i
$743$	955.497			1.28600			0.643000	−	0.765867i	$-0.277690\pi$
$743$	955.497			1.28600			0.643000	+	0.765867i	$0.277690\pi$
$744$	1.97147			0.00264982
$745$			400.011i			0.536928i
$746$			328.974i			0.440983i
$747$		−	49.6658i		−	0.0664870i
$748$		−	970.219i		−	1.29708i
$749$	329.140			0.439439
$750$		−	437.125i		−	0.582834i
$751$			450.913i			0.600416i	0.953874	+	0.300208i	$0.0970561\pi$
$751$			450.913i			0.600416i	−0.953874	+	0.300208i	$0.902944\pi$
$752$			234.488i			0.311820i
$753$	233.839			0.310543
$754$	−2016.95			−2.67500
$755$			622.392i			0.824360i
$756$	262.951			0.347819
$757$	410.015			0.541632			0.270816	−	0.962631i	$-0.412707\pi$
$757$	410.015			0.541632			0.270816	+	0.962631i	$0.412707\pi$
$758$			628.960i			0.829763i
$759$	609.785			0.803406
$760$			998.740i			1.31413i
$761$	1469.25			1.93068			0.965339	−	0.260998i	$-0.0840517\pi$
$761$	1469.25			1.93068			0.965339	+	0.260998i	$0.0840517\pi$
$762$			841.316i			1.10409i
$763$			634.490i			0.831573i
$764$		−	77.7673i		−	0.101790i
$765$	−254.834			−0.333116
$766$			15.3028i			0.0199776i
$767$	−865.240	+	481.380i	−1.12808	+	0.627614i
$768$	−20.3515			−0.0264994
$769$			469.742i			0.610848i	0.952216	+	0.305424i	$0.0987982\pi$
$769$			469.742i			0.610848i	−0.952216	+	0.305424i	$0.901202\pi$
$770$	2182.84			2.83486
$771$	−230.940			−0.299533
$772$	−391.432			−0.507037
$773$			373.454i			0.483122i	0.970386	+	0.241561i	$0.0776595\pi$
$773$			373.454i			0.483122i	−0.970386	+	0.241561i	$0.922341\pi$
$774$	−67.8809			−0.0877014
$775$		−	2.92696i		−	0.00377672i
$776$	−489.091			−0.630271
$777$			881.260i			1.13418i
$778$		−	426.789i		−	0.548572i
$779$	423.460			0.543594
$780$		−	953.886i		−	1.22293i
$781$		−	88.2496i		−	0.112996i
$782$	−1203.03			−1.53840
$783$	203.252			0.259581
$784$	−306.202			−0.390564
$785$			1514.29i			1.92903i
$786$	−694.567			−0.883674
$787$	−97.7362			−0.124188			−0.0620942	−	0.998070i	$-0.519778\pi$
$787$	−97.7362			−0.124188			−0.0620942	+	0.998070i	$0.519778\pi$
$788$	242.374			0.307581
$789$	471.715			0.597864
$790$			963.494i			1.21961i
$791$		−	1124.60i		−	1.42175i
$792$	−168.151			−0.212312
$793$	1410.53			1.77873
$794$	818.927			1.03139
$795$	494.215			0.621654
$796$	681.260			0.855854
$797$		−	66.2564i		−	0.0831323i	−0.999136	−	0.0415661i	$-0.986765\pi$
$797$		−	66.2564i		−	0.0831323i	0.999136	−	0.0415661i	$-0.0132347\pi$
$798$		−	1851.67i		−	2.32039i
$799$		−	404.581i		−	0.506359i
$800$			486.989i			0.608737i
$801$		−	207.763i		−	0.259380i
$802$	−1584.60			−1.97580
$803$	1667.45			2.07653
$804$		−	768.124i		−	0.955378i
$805$		−	1559.82i		−	1.93767i
$806$			13.2594i			0.0164509i
$807$		−	476.576i		−	0.590553i
$808$	−706.526			−0.874414
$809$		−	884.904i		−	1.09382i	−0.837190	−	0.546912i	$-0.815803\pi$
$809$		−	884.904i		−	1.09382i	0.837190	−	0.546912i	$-0.184197\pi$
$810$			166.797i			0.205922i
$811$			29.8964i			0.0368637i	0.999830	+	0.0184318i	$0.00586737\pi$
$811$			29.8964i			0.0368637i	−0.999830	+	0.0184318i	$0.994133\pi$
$812$	1979.46			2.43776
$813$	−246.572			−0.303287
$814$		−	2128.29i		−	2.61460i
$815$	581.590			0.713608
$816$	−199.093			−0.243987
$817$			275.477i			0.337181i
$818$	−163.599			−0.199999
$819$			468.283i			0.571774i
$820$	−371.491			−0.453037
$821$			1374.88i			1.67464i	0.546710	+	0.837322i	$0.315880\pi$
$821$			1374.88i			1.67464i	−0.546710	+	0.837322i	$0.684120\pi$
$822$		−	1111.84i		−	1.35261i
$823$		−	434.163i		−	0.527537i	−0.964586	−	0.263768i	$-0.915035\pi$
$823$		−	434.163i		−	0.527537i	0.964586	−	0.263768i	$-0.0849654\pi$
$824$	−118.394			−0.143682
$825$			249.648i			0.302603i
$826$	1473.46	−	819.768i	1.78385	−	0.992455i
$827$	−186.426			−0.225424			−0.112712	−	0.993628i	$-0.535954\pi$
$827$	−186.426			−0.225424			−0.112712	+	0.993628i	$0.535954\pi$
$828$			453.789i			0.548054i
$829$	−394.103			−0.475396			−0.237698	−	0.971339i	$-0.576393\pi$
$829$	−394.103			−0.475396			−0.237698	+	0.971339i	$0.576393\pi$
$830$	306.819			0.369661
$831$	−488.524			−0.587874
$832$		−	1658.20i		−	1.99302i
$833$	528.314			0.634231
$834$			392.919i			0.471125i
$835$	−472.836			−0.566270
$836$			2577.14i			3.08270i
$837$		−	1.33617i		−	0.00159639i
$838$	845.463			1.00891
$839$			249.235i			0.297062i	0.988908	+	0.148531i	$0.0474545\pi$
$839$			249.235i			0.297062i	−0.988908	+	0.148531i	$0.952545\pi$
$840$			430.130i			0.512059i
$841$	689.056			0.819329
$842$	1561.83			1.85490
$843$	−473.160			−0.561281
$844$		−	580.954i		−	0.688334i
$845$	679.381			0.804001
$846$	−264.811			−0.313016
$847$	365.988			0.432099
$848$	386.114			0.455323
$849$		−	417.303i		−	0.491523i
$850$		−	492.522i		−	0.579438i
$851$	−1520.84			−1.78712
$852$	65.6734			0.0770815
$853$	−493.294			−0.578305			−0.289152	−	0.957283i	$-0.593373\pi$
$853$	−493.294			−0.578305			−0.289152	+	0.957283i	$0.593373\pi$
$854$	−2402.07			−2.81273
$855$	676.902			0.791698
$856$		−	156.633i		−	0.182982i
$857$		−	570.888i		−	0.666147i	−0.942901	−	0.333074i	$-0.891914\pi$
$857$		−	570.888i		−	0.666147i	0.942901	−	0.333074i	$-0.108086\pi$
$858$		−	1130.93i		−	1.31810i
$859$			930.308i			1.08301i	0.840697	+	0.541506i	$0.182146\pi$
$859$			930.308i			1.08301i	−0.840697	+	0.541506i	$0.817854\pi$
$860$		−	241.668i		−	0.281010i
$861$	182.373			0.211815
$862$	−1017.23			−1.18008
$863$			1021.24i			1.18336i	0.806175	+	0.591678i	$0.201534\pi$
$863$			1021.24i			1.18336i	−0.806175	+	0.591678i	$0.798466\pi$
$864$			222.313i			0.257307i
$865$			315.197i			0.364390i
$866$		−	664.920i		−	0.767806i
$867$	−157.051			−0.181144
$868$		−	13.0129i		−	0.0149918i
$869$			658.316i			0.757556i
$870$			1255.63i			1.44325i
$871$	1367.93			1.57053
$872$	301.945			0.346267
$873$			331.484i			0.379707i
$874$	3195.53			3.65622
$875$	−763.994			−0.873137
$876$			1240.88i			1.41653i
$877$	68.6160			0.0782394			0.0391197	−	0.999235i	$-0.487545\pi$
$877$	68.6160			0.0782394			0.0391197	+	0.999235i	$0.487545\pi$
$878$		−	1827.69i		−	2.08165i
$879$	−556.459			−0.633059
$880$			623.424i			0.708436i
$881$			1053.01i			1.19524i	0.801779	+	0.597621i	$0.203887\pi$
$881$			1053.01i			1.19524i	−0.801779	+	0.597621i	$0.796113\pi$
$882$		−	345.799i		−	0.392062i
$883$	439.558			0.497801			0.248901	−	0.968529i	$-0.419931\pi$
$883$	439.558			0.497801			0.248901	+	0.968529i	$0.419931\pi$
$884$			1285.82i			1.45455i
$885$	299.676	+	538.643i	0.338617	+	0.608636i
$886$	311.014			0.351032
$887$		−	992.568i		−	1.11902i	−0.828825	−	0.559509i	$-0.810990\pi$
$887$		−	992.568i		−	1.11902i	0.828825	−	0.559509i	$-0.189010\pi$
$888$	419.379			0.472274
$889$	1470.43			1.65402
$890$	1283.49			1.44213
$891$			113.966i			0.127908i
$892$	204.919			0.229730
$893$			1074.67i			1.20343i
$894$	−352.929			−0.394775
$895$		−	708.765i		−	0.791916i
$896$			1232.03i			1.37503i
$897$	−808.141			−0.900938
$898$		−	1880.53i		−	2.09413i
$899$		−	10.0585i		−	0.0111886i
$900$	−185.782			−0.206425
$901$	−666.192			−0.739392
$902$	−440.439			−0.488291
$903$			118.640i			0.131384i
$904$	−535.183			−0.592017
$905$	−966.171			−1.06759
$906$	−549.135			−0.606109
$907$	−42.7354			−0.0471174			−0.0235587	−	0.999722i	$-0.507500\pi$
$907$	−42.7354			−0.0471174			−0.0235587	+	0.999722i	$0.507500\pi$
$908$		−	1031.73i		−	1.13627i
$909$			478.852i			0.526790i
$910$	−2892.90			−3.17901
$911$	1660.26			1.82246			0.911228	−	0.411903i	$-0.135136\pi$
$911$	1660.26			1.82246			0.911228	+	0.411903i	$0.135136\pi$
$912$	528.841			0.579869
$913$	209.637			0.229613
$914$	1250.07			1.36769
$915$		−	878.105i		−	0.959678i
$916$			1125.87i			1.22911i
$917$			1213.94i			1.32382i
$918$		−	224.839i		−	0.244923i
$919$			254.602i			0.277043i	0.990359	+	0.138521i	$0.0442350\pi$
$919$			254.602i			0.277043i	−0.990359	+	0.138521i	$0.955765\pi$
$920$	−742.298			−0.806846
$921$	−986.642			−1.07127
$922$			2620.12i			2.84178i
$923$			116.956i			0.126713i
$924$			1109.90i			1.20119i
$925$		−	622.636i		−	0.673120i
$926$	−2235.72			−2.41438
$927$			80.2424i			0.0865614i
$928$			1673.55i			1.80339i
$929$			1601.04i			1.72340i	0.507421	+	0.861698i	$0.330599\pi$
$929$			1601.04i			1.72340i	−0.507421	+	0.861698i	$0.669401\pi$
$930$	8.25445			0.00887575
$931$	−1403.33			−1.50734
$932$			1160.33i			1.24499i
$933$	−619.116			−0.663575
$934$	74.2699			0.0795180
$935$		−	1075.64i		−	1.15042i
$936$	222.849			0.238087
$937$		−	1268.15i		−	1.35341i	−0.736253	−	0.676706i	$-0.763407\pi$
$937$		−	1268.15i		−	1.35341i	0.736253	−	0.676706i	$-0.236593\pi$
$938$	−2329.53			−2.48351
$939$		−	937.003i		−	0.997874i
$940$		−	942.778i		−	1.00295i
$941$		−	506.877i		−	0.538658i	−0.963048	−	0.269329i	$-0.913198\pi$
$941$		−	506.877i		−	0.538658i	0.963048	−	0.269329i	$-0.0868019\pi$
$942$	−1336.05			−1.41831
$943$			314.730i			0.333754i
$944$	234.127	+	420.824i	0.248016	+	0.445788i
$945$	291.523			0.308490
$946$		−	286.522i		−	0.302877i
$947$	1500.28			1.58425			0.792124	−	0.610360i	$-0.208975\pi$
$947$	1500.28			1.58425			0.792124	+	0.610360i	$0.208975\pi$
$948$	−489.905			−0.516777
$949$	−2209.86			−2.32862
$950$			1308.26i			1.37712i
$951$	747.082			0.785575
$952$		−	579.807i		−	0.609040i
$953$	−707.162			−0.742038			−0.371019	−	0.928625i	$-0.620991\pi$
$953$	−707.162			−0.742038			−0.371019	+	0.928625i	$0.620991\pi$
$954$			436.044i			0.457070i
$955$		−	86.2174i		−	0.0902800i
$956$	773.370			0.808965
$957$			857.918i			0.896466i
$958$			1660.80i			1.73361i
$959$	−1943.25			−2.02633
$960$	−1032.29			−1.07530
$961$	960.934			0.999931
$962$			2820.60i			2.93201i
$963$	−106.159			−0.110238
$964$	2128.73			2.20823
$965$	−433.965			−0.449705
$966$	1376.23			1.42467
$967$		−	613.039i		−	0.633960i	−0.948432	−	0.316980i	$-0.897331\pi$
$967$		−	613.039i		−	0.633960i	0.948432	−	0.316980i	$-0.102669\pi$
$968$		−	174.168i		−	0.179926i
$969$	−912.451			−0.941641
$970$	−2047.80			−2.11113
$971$	975.116			1.00424			0.502119	−	0.864798i	$-0.332554\pi$
$971$	975.116			1.00424			0.502119	+	0.864798i	$0.332554\pi$
$972$	−84.8108			−0.0872539
$973$	686.732			0.705788
$974$			1735.38i			1.78171i
$975$		−	330.855i		−	0.339339i
$976$		−	686.034i		−	0.702904i
$977$		−	791.601i		−	0.810236i	−0.914264	−	0.405118i	$-0.867230\pi$
$977$		−	791.601i		−	0.810236i	0.914264	−	0.405118i	$-0.132770\pi$
$978$			513.135i			0.524678i
$979$	876.958			0.895769
$980$	1231.11			1.25623
$981$		−	204.645i		−	0.208609i
$982$		−	24.8789i		−	0.0253349i
$983$		−	429.642i		−	0.437073i	−0.975829	−	0.218536i	$-0.929872\pi$
$983$		−	429.642i		−	0.437073i	0.975829	−	0.218536i	$-0.0701282\pi$
$984$		−	86.7885i		−	0.0881997i
$985$	268.710			0.272802
$986$		−	1692.56i		−	1.71659i
$987$			462.830i			0.468926i
$988$		−	3415.46i		−	3.45694i
$989$	−204.744			−0.207021
$990$	−704.043			−0.711154
$991$		−	543.830i		−	0.548769i	−0.961620	−	0.274384i	$-0.911526\pi$
$991$		−	543.830i		−	0.548769i	0.961620	−	0.274384i	$-0.0884741\pi$
$992$	11.0018			0.0110906
$993$	418.115			0.421062
$994$		−	199.171i		−	0.200373i
$995$	755.285			0.759080
$996$			156.007i			0.156634i
$997$	−827.466			−0.829956			−0.414978	−	0.909832i	$-0.636211\pi$
$997$	−827.466			−0.829956			−0.414978	+	0.909832i	$0.636211\pi$
$998$		−	2209.39i		−	2.21382i
$999$		−	284.237i		−	0.284521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.c.a.58.3	✓	20
3.2	odd	2		531.3.c.c.235.18		20
59.58	odd	2	inner	177.3.c.a.58.18	yes	20
177.176	even	2		531.3.c.c.235.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.c.a.58.3	✓	20	1.1	even	1	trivial
177.3.c.a.58.18	yes	20	59.58	odd	2	inner
531.3.c.c.235.3		20	177.176	even	2
531.3.c.c.235.18		20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.07256i q^{2} +1.73205 q^{3} -5.44061 q^{4} -6.03179 q^{5} -5.32183i q^{6} -9.30133 q^{7} +4.42637i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-3.07256i q^{2} +1.73205 q^{3} -5.44061 q^{4} -6.03179 q^{5} -5.32183i q^{6} -9.30133 q^{7} +4.42637i q^{8} +3.00000 q^{9} +18.5330i q^{10} +12.6629i q^{11} -9.42342 q^{12} -16.7819i q^{13} +28.5789i q^{14} -10.4474 q^{15} -8.16217 q^{16} +14.0828 q^{17} -9.21767i q^{18} -37.4075 q^{19} +32.8166 q^{20} -16.1104 q^{21} +38.9074 q^{22} -27.8025i q^{23} +7.66670i q^{24} +11.3824 q^{25} -51.5635 q^{26} +5.19615 q^{27} +50.6050 q^{28} +39.1159 q^{29} +32.1001i q^{30} -0.257147i q^{31} +42.7842i q^{32} +21.9327i q^{33} -43.2703i q^{34} +56.1036 q^{35} -16.3218 q^{36} -54.7014i q^{37} +114.937i q^{38} -29.0672i q^{39} -26.6989i q^{40} -11.3202 q^{41} +49.5001i q^{42} -7.36421i q^{43} -68.8937i q^{44} -18.0954 q^{45} -85.4249 q^{46} -28.7287i q^{47} -14.1373 q^{48} +37.5148 q^{49} -34.9732i q^{50} +24.3922 q^{51} +91.3041i q^{52} -47.3053 q^{53} -15.9655i q^{54} -76.3796i q^{55} -41.1711i q^{56} -64.7917 q^{57} -120.186i q^{58} +(-28.6844 - 51.5578i) q^{59} +56.8401 q^{60} +84.0505i q^{61} -0.790099 q^{62} -27.9040 q^{63} +98.8084 q^{64} +101.225i q^{65} +67.3895 q^{66} +81.5123i q^{67} -76.6193 q^{68} -48.1554i q^{69} -172.382i q^{70} -6.96917 q^{71} +13.2791i q^{72} -131.681i q^{73} -168.073 q^{74} +19.7150 q^{75} +203.520 q^{76} -117.781i q^{77} -89.3106 q^{78} +51.9880 q^{79} +49.2325 q^{80} +9.00000 q^{81} +34.7820i q^{82} -16.5553i q^{83} +87.6504 q^{84} -84.9447 q^{85} -22.6270 q^{86} +67.7508 q^{87} -56.0505 q^{88} -69.2544i q^{89} +55.5990i q^{90} +156.094i q^{91} +151.263i q^{92} -0.445392i q^{93} -88.2705 q^{94} +225.634 q^{95} +74.1045i q^{96} +110.495i q^{97} -115.266i q^{98} +37.9886i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9}+O(q^{10}) \) 20 * q - 40 * q^4 - 8 * q^7 + 60 * q^9	\( 20 q - 40 q^{4} - 8 q^{7} + 60 q^{9} - 24 q^{12} + 24 q^{15} - 8 q^{16} + 16 q^{17} - 60 q^{19} - 164 q^{20} + 40 q^{22} + 100 q^{25} - 156 q^{26} + 200 q^{28} - 60 q^{29} - 32 q^{35} - 120 q^{36} + 28 q^{41} + 180 q^{46} - 96 q^{48} + 284 q^{49} - 24 q^{51} - 8 q^{53} + 24 q^{57} - 152 q^{59} - 72 q^{60} - 8 q^{62} - 24 q^{63} + 204 q^{64} - 120 q^{66} + 384 q^{68} + 92 q^{71} + 104 q^{74} + 240 q^{75} + 120 q^{76} - 468 q^{78} - 420 q^{79} + 376 q^{80} + 180 q^{81} + 168 q^{84} - 348 q^{85} + 232 q^{86} + 144 q^{87} - 212 q^{88} + 152 q^{94} + 788 q^{95}+O(q^{100}) \) 20 * q - 40 * q^4 - 8 * q^7 + 60 * q^9 - 24 * q^12 + 24 * q^15 - 8 * q^16 + 16 * q^17 - 60 * q^19 - 164 * q^20 + 40 * q^22 + 100 * q^25 - 156 * q^26 + 200 * q^28 - 60 * q^29 - 32 * q^35 - 120 * q^36 + 28 * q^41 + 180 * q^46 - 96 * q^48 + 284 * q^49 - 24 * q^51 - 8 * q^53 + 24 * q^57 - 152 * q^59 - 72 * q^60 - 8 * q^62 - 24 * q^63 + 204 * q^64 - 120 * q^66 + 384 * q^68 + 92 * q^71 + 104 * q^74 + 240 * q^75 + 120 * q^76 - 468 * q^78 - 420 * q^79 + 376 * q^80 + 180 * q^81 + 168 * q^84 - 348 * q^85 + 232 * q^86 + 144 * q^87 - 212 * q^88 + 152 * q^94 + 788 * q^95

Introduction

L-functions

Modular forms

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