LMFDB - Embedded newform 78.3.c.a.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(53,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("78.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.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:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.16845963264.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 6x^{6} + 15x^{4} + 8x^{2} + 9 $ x^8 - 6x^6 + 15x^4 + 8*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			53.8
Root			$0.444099 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	78.53
Dual form			78.3.c.a.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(2.93352 + 0.628052i) q^{3} -2.00000 q^{4} +3.99052i q^{5} +(-0.888199 + 4.14863i) q^{6} +0.373294 q^{7} -2.82843i q^{8} +(8.21110 + 3.68481i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(2.93352 + 0.628052i) q^{3} -2.00000 q^{4} +3.99052i q^{5} +(-0.888199 + 4.14863i) q^{6} +0.373294 q^{7} -2.82843i q^{8} +(8.21110 + 3.68481i) q^{9} -5.64344 q^{10} -4.79331i q^{11} +(-5.86704 - 1.25610i) q^{12} -3.60555 q^{13} +0.527917i q^{14} +(-2.50625 + 11.7063i) q^{15} +4.00000 q^{16} -6.00898i q^{17} +(-5.21110 + 11.6123i) q^{18} -3.50861 q^{19} -7.98103i q^{20} +(1.09507 + 0.234448i) q^{21} +6.77876 q^{22} -34.1499i q^{23} +(1.77640 - 8.29725i) q^{24} +9.07578 q^{25} -5.09902i q^{26} +(21.7732 + 15.9665i) q^{27} -0.746587 q^{28} -48.5881i q^{29} +(-16.5552 - 3.54437i) q^{30} +1.30232 q^{31} +5.65685i q^{32} +(3.01045 - 14.0613i) q^{33} +8.49799 q^{34} +1.48963i q^{35} +(-16.4222 - 7.36961i) q^{36} -60.1225 q^{37} -4.96193i q^{38} +(-10.5770 - 2.26447i) q^{39} +11.2869 q^{40} +49.8299i q^{41} +(-0.331559 + 1.54866i) q^{42} +47.7973 q^{43} +9.58662i q^{44} +(-14.7043 + 32.7665i) q^{45} +48.2953 q^{46} +54.0396i q^{47} +(11.7341 + 2.51221i) q^{48} -48.8607 q^{49} +12.8351i q^{50} +(3.77395 - 17.6275i) q^{51} +7.21110 q^{52} +88.2060i q^{53} +(-22.5800 + 30.7920i) q^{54} +19.1278 q^{55} -1.05583i q^{56} +(-10.2926 - 2.20359i) q^{57} +68.7139 q^{58} -61.9608i q^{59} +(5.01250 - 23.4125i) q^{60} -106.659 q^{61} +1.84176i q^{62} +(3.06515 + 1.37551i) q^{63} -8.00000 q^{64} -14.3880i q^{65} +(19.8857 + 4.25741i) q^{66} +72.8589 q^{67} +12.0180i q^{68} +(21.4479 - 100.180i) q^{69} -2.10666 q^{70} +104.009i q^{71} +(10.4222 - 23.2245i) q^{72} -52.3165 q^{73} -85.0260i q^{74} +(26.6240 + 5.70006i) q^{75} +7.01723 q^{76} -1.78931i q^{77} +(3.20245 - 14.9581i) q^{78} -11.4866 q^{79} +15.9621i q^{80} +(53.8444 + 60.5126i) q^{81} -70.4702 q^{82} -75.1101i q^{83} +(-2.19013 - 0.468895i) q^{84} +23.9789 q^{85} +67.5956i q^{86} +(30.5158 - 142.534i) q^{87} -13.5575 q^{88} +54.2621i q^{89} +(-46.3389 - 20.7950i) q^{90} -1.34593 q^{91} +68.2998i q^{92} +(3.82040 + 0.817927i) q^{93} -76.4235 q^{94} -14.0012i q^{95} +(-3.55280 + 16.5945i) q^{96} +21.0461 q^{97} -69.0994i q^{98} +(17.6624 - 39.3584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 16 * q^4 - 8 * q^7 + 8 * q^9	$ 8 q - 16 q^{4} - 8 q^{7} + 8 q^{9} + 16 q^{10} - 56 q^{15} + 32 q^{16} + 16 q^{18} - 24 q^{19} + 88 q^{21} + 8 q^{25} + 16 q^{28} - 64 q^{30} - 72 q^{31} - 56 q^{33} - 112 q^{34} - 16 q^{36} + 96 q^{37} - 32 q^{40} + 80 q^{42} + 208 q^{43} - 16 q^{45} + 32 q^{46} - 24 q^{49} + 112 q^{51} - 176 q^{55} + 40 q^{57} + 176 q^{58} + 112 q^{60} - 272 q^{61} - 216 q^{63} - 64 q^{64} - 64 q^{66} + 264 q^{67} - 240 q^{69} - 32 q^{70} - 32 q^{72} - 416 q^{73} + 128 q^{75} + 48 q^{76} + 160 q^{79} + 200 q^{81} + 176 q^{82} - 176 q^{84} + 464 q^{85} + 384 q^{87} + 16 q^{90} + 104 q^{91} - 264 q^{93} - 384 q^{94} - 16 q^{97} + 416 q^{99}+O(q^{100}) $ 8 * q - 16 * q^4 - 8 * q^7 + 8 * q^9 + 16 * q^10 - 56 * q^15 + 32 * q^16 + 16 * q^18 - 24 * q^19 + 88 * q^21 + 8 * q^25 + 16 * q^28 - 64 * q^30 - 72 * q^31 - 56 * q^33 - 112 * q^34 - 16 * q^36 + 96 * q^37 - 32 * q^40 + 80 * q^42 + 208 * q^43 - 16 * q^45 + 32 * q^46 - 24 * q^49 + 112 * q^51 - 176 * q^55 + 40 * q^57 + 176 * q^58 + 112 * q^60 - 272 * q^61 - 216 * q^63 - 64 * q^64 - 64 * q^66 + 264 * q^67 - 240 * q^69 - 32 * q^70 - 32 * q^72 - 416 * q^73 + 128 * q^75 + 48 * q^76 + 160 * q^79 + 200 * q^81 + 176 * q^82 - 176 * q^84 + 464 * q^85 + 384 * q^87 + 16 * q^90 + 104 * q^91 - 264 * q^93 - 384 * q^94 - 16 * q^97 + 416 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	2.93352	+	0.628052i	0.977841	+	0.209351i
$3$	2.93352	+	0.628052i	0.977841	+	0.209351i
$4$	−2.00000			−0.500000
$5$			3.99052i			0.798103i	0.916928	+	0.399052i	$0.130661\pi$
$5$			3.99052i			0.798103i	−0.916928	+	0.399052i	$0.869339\pi$
$6$	−0.888199	+	4.14863i	−0.148033	+	0.691438i
$7$	0.373294			0.0533277			0.0266638	−	0.999644i	$-0.491512\pi$
$7$	0.373294			0.0533277			0.0266638	+	0.999644i	$0.491512\pi$
$8$		−	2.82843i		−	0.353553i
$9$	8.21110	+	3.68481i	0.912345	+	0.409423i
$10$	−5.64344			−0.564344
$11$		−	4.79331i		−	0.435755i	−0.975976	−	0.217878i	$-0.930087\pi$
$11$		−	4.79331i		−	0.435755i	0.975976	−	0.217878i	$-0.0699134\pi$
$12$	−5.86704	−	1.25610i	−0.488920	−	0.104675i
$13$	−3.60555			−0.277350
$13$	−3.60555			−0.277350
$14$			0.527917i			0.0377084i
$15$	−2.50625	+	11.7063i	−0.167083	+	0.780418i
$16$	4.00000			0.250000
$17$		−	6.00898i		−	0.353470i	−0.984259	−	0.176735i	$-0.943447\pi$
$17$		−	6.00898i		−	0.353470i	0.984259	−	0.176735i	$-0.0565535\pi$
$18$	−5.21110	+	11.6123i	−0.289506	+	0.645125i
$19$	−3.50861			−0.184664			−0.0923320	−	0.995728i	$-0.529432\pi$
$19$	−3.50861			−0.184664			−0.0923320	+	0.995728i	$0.529432\pi$
$20$		−	7.98103i		−	0.399052i
$21$	1.09507	+	0.234448i	0.0521460	+	0.0111642i
$22$	6.77876			0.308126
$23$		−	34.1499i		−	1.48478i	−0.669969	−	0.742389i	$-0.733692\pi$
$23$		−	34.1499i		−	1.48478i	0.669969	−	0.742389i	$-0.266308\pi$
$24$	1.77640	−	8.29725i	0.0740166	−	0.345719i
$25$	9.07578			0.363031
$26$		−	5.09902i		−	0.196116i
$27$	21.7732	+	15.9665i	0.806415	+	0.591350i
$28$	−0.746587			−0.0266638
$29$		−	48.5881i		−	1.67545i	−0.546092	−	0.837725i	$-0.683885\pi$
$29$		−	48.5881i		−	1.67545i	0.546092	−	0.837725i	$-0.316115\pi$
$30$	−16.5552	−	3.54437i	−0.551839	−	0.118146i
$31$	1.30232			0.0420105			0.0210052	−	0.999779i	$-0.493313\pi$
$31$	1.30232			0.0420105			0.0210052	+	0.999779i	$0.493313\pi$
$32$			5.65685i			0.176777i
$33$	3.01045	−	14.0613i	0.0912256	−	0.426099i
$34$	8.49799			0.249941
$35$			1.48963i			0.0425610i
$36$	−16.4222	−	7.36961i	−0.456172	−	0.204711i
$37$	−60.1225			−1.62493			−0.812466	−	0.583009i	$-0.801875\pi$
$37$	−60.1225			−1.62493			−0.812466	+	0.583009i	$0.801875\pi$
$38$		−	4.96193i		−	0.130577i
$39$	−10.5770	−	2.26447i	−0.271204	−	0.0580634i
$40$	11.2869			0.282172
$41$			49.8299i			1.21536i	0.794180	+	0.607682i	$0.207901\pi$
$41$			49.8299i			1.21536i	−0.794180	+	0.607682i	$0.792099\pi$
$42$	−0.331559	+	1.54866i	−0.00789426	+	0.0368728i
$43$	47.7973			1.11156			0.555782	−	0.831328i	$-0.312419\pi$
$43$	47.7973			1.11156			0.555782	+	0.831328i	$0.312419\pi$
$44$			9.58662i			0.217878i
$45$	−14.7043	+	32.7665i	−0.326762	+	0.728145i
$46$	48.2953			1.04990
$47$			54.0396i			1.14978i	0.818231	+	0.574889i	$0.194955\pi$
$47$			54.0396i			1.14978i	−0.818231	+	0.574889i	$0.805045\pi$
$48$	11.7341	+	2.51221i	0.244460	+	0.0523376i
$49$	−48.8607			−0.997156
$50$			12.8351i			0.256702i
$51$	3.77395	−	17.6275i	0.0739990	−	0.345637i
$52$	7.21110			0.138675
$53$			88.2060i			1.66426i	0.554578	+	0.832132i	$0.312880\pi$
$53$			88.2060i			1.66426i	−0.554578	+	0.832132i	$0.687120\pi$
$54$	−22.5800	+	30.7920i	−0.418148	+	0.570221i
$55$	19.1278			0.347778
$56$		−	1.05583i		−	0.0188542i
$57$	−10.2926	−	2.20359i	−0.180572	−	0.0386595i
$58$	68.7139			1.18472
$59$		−	61.9608i		−	1.05018i	−0.851046	−	0.525091i	$-0.824031\pi$
$59$		−	61.9608i		−	1.05018i	0.851046	−	0.525091i	$-0.175969\pi$
$60$	5.01250	−	23.4125i	0.0835417	−	0.390209i
$61$	−106.659			−1.74851			−0.874256	−	0.485466i	$-0.838650\pi$
$61$	−106.659			−1.74851			−0.874256	+	0.485466i	$0.838650\pi$
$62$			1.84176i			0.0297059i
$63$	3.06515	+	1.37551i	0.0486532	+	0.0218336i
$64$	−8.00000			−0.125000
$65$		−	14.3880i		−	0.221354i
$66$	19.8857	+	4.25741i	0.301298	+	0.0645063i
$67$	72.8589			1.08745			0.543723	−	0.839265i	$-0.317014\pi$
$67$	72.8589			1.08745			0.543723	+	0.839265i	$0.317014\pi$
$68$			12.0180i			0.176735i
$69$	21.4479	−	100.180i	0.310839	−	1.45188i
$70$	−2.10666			−0.0300952
$71$			104.009i			1.46491i	0.680814	+	0.732456i	$0.261626\pi$
$71$			104.009i			1.46491i	−0.680814	+	0.732456i	$0.738374\pi$
$72$	10.4222	−	23.2245i	0.144753	−	0.322563i
$73$	−52.3165			−0.716665			−0.358332	−	0.933594i	$-0.616655\pi$
$73$	−52.3165			−0.716665			−0.358332	+	0.933594i	$0.616655\pi$
$74$		−	85.0260i		−	1.14900i
$75$	26.6240	+	5.70006i	0.354987	+	0.0760008i
$76$	7.01723			0.0923320
$77$		−	1.78931i		−	0.0232378i
$78$	3.20245	−	14.9581i	0.0410570	−	0.191770i
$79$	−11.4866			−0.145400			−0.0727001	−	0.997354i	$-0.523162\pi$
$79$	−11.4866			−0.145400			−0.0727001	+	0.997354i	$0.523162\pi$
$80$			15.9621i			0.199526i
$81$	53.8444	+	60.5126i	0.664746	+	0.747070i
$82$	−70.4702			−0.859392
$83$		−	75.1101i		−	0.904941i	−0.891779	−	0.452471i	$-0.850543\pi$
$83$		−	75.1101i		−	0.904941i	0.891779	−	0.452471i	$-0.149457\pi$
$84$	−2.19013	−	0.468895i	−0.0260730	−	0.00558209i
$85$	23.9789			0.282105
$86$			67.5956i			0.785995i
$87$	30.5158	−	142.534i	0.350756	−	1.63832i
$88$	−13.5575			−0.154063
$89$			54.2621i			0.609687i	0.952402	+	0.304843i	$0.0986041\pi$
$89$			54.2621i			0.609687i	−0.952402	+	0.304843i	$0.901396\pi$
$90$	−46.3389	−	20.7950i	−0.514876	−	0.231055i
$91$	−1.34593			−0.0147904
$92$			68.2998i			0.742389i
$93$	3.82040	+	0.817927i	0.0410795	+	0.00879491i
$94$	−76.4235			−0.813016
$95$		−	14.0012i		−	0.147381i
$96$	−3.55280	+	16.5945i	−0.0370083	+	0.172859i
$97$	21.0461			0.216970			0.108485	−	0.994098i	$-0.465400\pi$
$97$	21.0461			0.216970			0.108485	+	0.994098i	$0.465400\pi$
$98$		−	69.0994i		−	0.705096i
$99$	17.6624	−	39.3584i	0.178408	−	0.397559i
$100$	−18.1516			−0.181516
$101$		−	49.3391i		−	0.488506i	−0.969712	−	0.244253i	$-0.921457\pi$
$101$		−	49.3391i		−	0.488506i	0.969712	−	0.244253i	$-0.0785427\pi$
$102$	24.9290	+	5.33717i	0.244402	+	0.0523252i
$103$	40.9246			0.397326			0.198663	−	0.980068i	$-0.436340\pi$
$103$	40.9246			0.397326			0.198663	+	0.980068i	$0.436340\pi$
$104$			10.1980i			0.0980581i
$105$	−0.935567	+	4.36988i	−0.00891016	+	0.0416179i
$106$	−124.742			−1.17681
$107$		−	40.7441i		−	0.380786i	−0.981708	−	0.190393i	$-0.939024\pi$
$107$		−	40.7441i		−	0.380786i	0.981708	−	0.190393i	$-0.0609763\pi$
$108$	−43.5464	−	31.9329i	−0.403207	−	0.295675i
$109$	−58.1780			−0.533743			−0.266871	−	0.963732i	$-0.585990\pi$
$109$	−58.1780			−0.533743			−0.266871	+	0.963732i	$0.585990\pi$
$110$			27.0508i			0.245916i
$111$	−176.371	−	37.7600i	−1.58892	−	0.340180i
$112$	1.49317			0.0133319
$113$		−	153.921i		−	1.36213i	−0.732224	−	0.681064i	$-0.761517\pi$
$113$		−	153.921i		−	1.36213i	0.732224	−	0.681064i	$-0.238483\pi$
$114$	3.11635	−	14.5559i	0.0273364	−	0.127684i
$115$	136.276			1.18501
$116$			97.1761i			0.837725i
$117$	−29.6056	−	13.2858i	−0.253039	−	0.113553i
$118$	87.6258			0.742591
$119$		−	2.24312i		−	0.0188497i
$120$	33.1103	+	7.08874i	0.275919	+	0.0590729i
$121$	98.0242			0.810117
$122$		−	150.839i		−	1.23638i
$123$	−31.2958	+	146.177i	−0.254437	+	1.18843i
$124$	−2.60465			−0.0210052
$125$			135.980i			1.08784i
$126$	−1.94527	+	4.33478i	−0.0154387	+	0.0344030i
$127$	91.0026			0.716556			0.358278	−	0.933615i	$-0.383364\pi$
$127$	91.0026			0.716556			0.358278	+	0.933615i	$0.383364\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	140.214	+	30.0192i	1.08693	+	0.232707i
$130$	20.3477			0.156521
$131$			215.684i			1.64644i	0.567721	+	0.823221i	$0.307825\pi$
$131$			215.684i			1.64644i	−0.567721	+	0.823221i	$0.692175\pi$
$132$	−6.02089	+	28.1226i	−0.0456128	+	0.213050i
$133$	−1.30974			−0.00984770
$134$			103.038i			0.768940i
$135$	−63.7144	+	86.8863i	−0.471958	+	0.643602i
$136$	−16.9960			−0.124970
$137$		−	79.6507i		−	0.581392i	−0.956815	−	0.290696i	$-0.906113\pi$
$137$		−	79.6507i		−	0.581392i	0.956815	−	0.290696i	$-0.0938868\pi$
$138$	141.675	+	30.3319i	1.02663	+	0.219797i
$139$	39.0974			0.281276			0.140638	−	0.990061i	$-0.455085\pi$
$139$	39.0974			0.281276			0.140638	+	0.990061i	$0.455085\pi$
$140$		−	2.97927i		−	0.0212805i
$141$	−33.9396	+	158.526i	−0.240707	+	1.12430i
$142$	−147.091			−1.03585
$143$			17.2825i			0.120857i
$144$	32.8444	+	14.7392i	0.228086	+	0.102356i
$145$	193.891			1.33718
$146$		−	73.9867i		−	0.506759i
$147$	−143.334	−	30.6870i	−0.975060	−	0.208755i
$148$	120.245			0.812466
$149$		−	56.5482i		−	0.379518i	−0.981831	−	0.189759i	$-0.939229\pi$
$149$		−	56.5482i		−	0.379518i	0.981831	−	0.189759i	$-0.0607707\pi$
$150$	−8.06110	+	37.6520i	−0.0537407	+	0.251014i
$151$	−37.5614			−0.248751			−0.124375	−	0.992235i	$-0.539693\pi$
$151$	−37.5614			−0.248751			−0.124375	+	0.992235i	$0.539693\pi$
$152$			9.92386i			0.0652886i
$153$	22.1419	−	49.3404i	0.144719	−	0.322486i
$154$	2.53047			0.0164316
$155$			5.19694i			0.0335287i
$156$	21.1539	+	4.52894i	0.135602	+	0.0290317i
$157$	−82.3650			−0.524618			−0.262309	−	0.964984i	$-0.584484\pi$
$157$	−82.3650			−0.524618			−0.262309	+	0.964984i	$0.584484\pi$
$158$		−	16.2445i		−	0.102814i
$159$	−55.3979	+	258.754i	−0.348415	+	1.62739i
$160$	−22.5738			−0.141086
$161$		−	12.7479i		−	0.0791798i
$162$	−85.5778	+	76.1475i	−0.528258	+	0.470046i
$163$	−259.157			−1.58992			−0.794959	−	0.606663i	$-0.792508\pi$
$163$	−259.157			−1.58992			−0.794959	+	0.606663i	$0.792508\pi$
$164$		−	99.6599i		−	0.607682i
$165$	56.1118	+	12.0132i	0.340071	+	0.0728075i
$166$	106.222			0.639890
$167$		−	198.873i		−	1.19086i	−0.803408	−	0.595429i	$-0.796982\pi$
$167$		−	198.873i		−	1.19086i	0.803408	−	0.595429i	$-0.203018\pi$
$168$	0.663118	−	3.09731i	0.00394713	−	0.0184364i
$169$	13.0000			0.0769231
$170$			33.9114i			0.199479i
$171$	−28.8096	−	12.9286i	−0.168477	−	0.0756056i
$172$	−95.5946			−0.555782
$173$		−	47.1339i		−	0.272450i	−0.990678	−	0.136225i	$-0.956503\pi$
$173$		−	47.1339i		−	0.272450i	0.990678	−	0.136225i	$-0.0434970\pi$
$174$	201.574	+	43.1559i	1.15847	+	0.248022i
$175$	3.38793			0.0193596
$176$		−	19.1732i		−	0.108939i
$177$	38.9146	−	181.763i	0.219856	−	1.02691i
$178$	−76.7382			−0.431114
$179$		−	88.7368i		−	0.495736i	−0.968794	−	0.247868i	$-0.920270\pi$
$179$		−	88.7368i		−	0.495736i	0.968794	−	0.247868i	$-0.0797300\pi$
$180$	29.4086	−	65.5331i	0.163381	−	0.364073i
$181$	2.12167			0.0117219			0.00586097	−	0.999983i	$-0.498134\pi$
$181$	2.12167			0.0117219			0.00586097	+	0.999983i	$0.498134\pi$
$182$		−	1.90343i		−	0.0104584i
$183$	−312.887	−	66.9875i	−1.70977	−	0.366052i
$184$	−96.5906			−0.524949
$185$		−	239.920i		−	1.29686i
$186$	−1.15672	+	5.40286i	−0.00621894	+	0.0290476i
$187$	−28.8029			−0.154026
$188$		−	108.079i		−	0.574889i
$189$	8.12780	+	5.96018i	0.0430042	+	0.0315353i
$190$	19.8007			0.104214
$191$			145.321i			0.760841i	0.924814	+	0.380420i	$0.124221\pi$
$191$			145.321i			0.760841i	−0.924814	+	0.380420i	$0.875779\pi$
$192$	−23.4682	−	5.02441i	−0.122230	−	0.0261688i
$193$	119.689			0.620148			0.310074	−	0.950712i	$-0.399646\pi$
$193$	119.689			0.620148			0.310074	+	0.950712i	$0.399646\pi$
$194$			29.7637i			0.153421i
$195$	9.03641	−	42.2075i	0.0463406	−	0.216449i
$196$	97.7213			0.498578
$197$			67.7201i			0.343757i	0.985118	+	0.171878i	$0.0549836\pi$
$197$			67.7201i			0.343757i	−0.985118	+	0.171878i	$0.945016\pi$
$198$	55.6611	+	24.9784i	0.281117	+	0.126154i
$199$	−21.0351			−0.105704			−0.0528520	−	0.998602i	$-0.516831\pi$
$199$	−21.0351			−0.105704			−0.0528520	+	0.998602i	$0.516831\pi$
$200$		−	25.6702i		−	0.128351i
$201$	213.733	+	45.7591i	1.06335	+	0.227657i
$202$	69.7760			0.345426
$203$		−	18.1376i		−	0.0893479i
$204$	−7.54790	+	35.2550i	−0.0369995	+	0.172818i
$205$	−198.847			−0.969986
$206$			57.8761i			0.280952i
$207$	125.836	−	280.408i	0.607902	−	1.35463i
$208$	−14.4222			−0.0693375
$209$			16.8179i			0.0804683i
$210$	−6.17994	−	1.32309i	−0.0294283	−	0.00630044i
$211$	−96.1961			−0.455906			−0.227953	−	0.973672i	$-0.573203\pi$
$211$	−96.1961			−0.455906			−0.227953	+	0.973672i	$0.573203\pi$
$212$		−	176.412i		−	0.832132i
$213$	−65.3229	+	305.112i	−0.306680	+	1.43245i
$214$	57.6209			0.269257
$215$			190.736i			0.887143i
$216$	45.1600	−	61.5839i	0.209074	−	0.285111i
$217$	0.486149			0.00224032
$218$		−	82.2761i		−	0.377413i
$219$	−153.472	−	32.8575i	−0.700784	−	0.150034i
$220$	−38.2556			−0.173889
$221$			21.6657i			0.0980348i
$222$	53.4007	−	249.426i	0.240544	−	1.12354i
$223$	378.108			1.69555			0.847775	−	0.530355i	$-0.177941\pi$
$223$	378.108			1.69555			0.847775	+	0.530355i	$0.177941\pi$
$224$			2.11167i			0.00942709i
$225$	74.5222	+	33.4425i	0.331210	+	0.148633i
$226$	217.676			0.963170
$227$		−	369.188i		−	1.62638i	−0.581999	−	0.813189i	$-0.697729\pi$
$227$		−	369.188i		−	1.62638i	0.581999	−	0.813189i	$-0.302271\pi$
$228$	20.5852	+	4.40718i	0.0902860	+	0.0193297i
$229$	−340.503			−1.48691			−0.743456	−	0.668785i	$-0.766815\pi$
$229$	−340.503			−1.48691			−0.743456	+	0.668785i	$0.766815\pi$
$230$			192.723i			0.837926i
$231$	1.12378	−	5.24899i	0.00486485	−	0.0227229i
$232$	−137.428			−0.592361
$233$			142.947i			0.613505i	0.951789	+	0.306752i	$0.0992423\pi$
$233$			142.947i			0.613505i	−0.951789	+	0.306752i	$0.900758\pi$
$234$	18.7889	−	41.8686i	0.0802944	−	0.178926i
$235$	−215.646			−0.917642
$236$			123.922i			0.525091i
$237$	−33.6963	−	7.21419i	−0.142178	−	0.0304396i
$238$	3.17224			0.0133288
$239$		−	53.1449i		−	0.222363i	−0.993800	−	0.111182i	$-0.964536\pi$
$239$		−	53.1449i		−	0.222363i	0.993800	−	0.111182i	$-0.0354636\pi$
$240$	−10.0250	+	46.8251i	−0.0417708	+	0.195104i
$241$	411.158			1.70605			0.853025	−	0.521871i	$-0.174766\pi$
$241$	411.158			1.70605			0.853025	+	0.521871i	$0.174766\pi$
$242$			138.627i			0.572839i
$243$	119.949	+	211.332i	0.493616	+	0.869680i
$244$	213.318			0.874256
$245$		−	194.979i		−	0.795834i
$246$	−206.726	−	44.2589i	−0.840349	−	0.179914i
$247$	12.6505			0.0512166
$248$		−	3.68353i		−	0.0148529i
$249$	47.1730	−	220.337i	0.189450	−	0.884889i
$250$	−192.305			−0.769219
$251$			432.085i			1.72146i	0.509066	+	0.860728i	$0.329991\pi$
$251$			432.085i			1.72146i	−0.509066	+	0.860728i	$0.670009\pi$
$252$	−6.13031	−	2.75103i	−0.0243266	−	0.0109168i
$253$	−163.691			−0.647000
$254$			128.697i			0.506682i
$255$	70.3428	+	15.0600i	0.275854	+	0.0590589i
$256$	16.0000			0.0625000
$257$			394.342i			1.53440i	0.641405	+	0.767202i	$0.278352\pi$
$257$			394.342i			1.53440i	−0.641405	+	0.767202i	$0.721648\pi$
$258$	−42.4535	+	198.293i	−0.164548	+	0.768578i
$259$	−22.4433			−0.0866538
$260$			28.7760i			0.110677i
$261$	179.038	−	398.962i	0.685968	−	1.52859i
$262$	−305.023			−1.16421
$263$		−	266.183i		−	1.01210i	−0.862504	−	0.506051i	$-0.831105\pi$
$263$		−	266.183i		−	1.01210i	0.862504	−	0.506051i	$-0.168895\pi$
$264$	−39.7713	−	8.51483i	−0.150649	−	0.0322531i
$265$	−351.987			−1.32825
$266$		−	1.85226i		−	0.00696337i
$267$	−34.0794	+	159.179i	−0.127638	+	0.596176i
$268$	−145.718			−0.543723
$269$			376.113i			1.39819i	0.715028	+	0.699095i	$0.246414\pi$
$269$			376.113i			1.39819i	−0.715028	+	0.699095i	$0.753586\pi$
$270$	−122.876	−	90.1058i	−0.455096	−	0.333725i
$271$	129.556			0.478067			0.239034	−	0.971011i	$-0.423169\pi$
$271$	129.556			0.478067			0.239034	+	0.971011i	$0.423169\pi$
$272$		−	24.0359i		−	0.0883674i
$273$	−3.94831	−	0.845313i	−0.0144627	−	0.00309639i
$274$	112.643			0.411106
$275$		−	43.5030i		−	0.158193i
$276$	−42.8958	+	200.359i	−0.155420	+	0.725939i
$277$	335.738			1.21205			0.606025	−	0.795446i	$-0.292763\pi$
$277$	335.738			1.21205			0.606025	+	0.795446i	$0.292763\pi$
$278$			55.2920i			0.198892i
$279$	10.6935	+	4.79881i	0.0383280	+	0.0172000i
$280$	4.21332			0.0150476
$281$			348.321i			1.23958i	0.784768	+	0.619789i	$0.212782\pi$
$281$			348.321i			1.23958i	−0.784768	+	0.619789i	$0.787218\pi$
$282$	−224.190	−	47.9979i	−0.795000	−	0.170205i
$283$	−79.8481			−0.282149			−0.141074	−	0.989999i	$-0.545056\pi$
$283$	−79.8481			−0.282149			−0.141074	+	0.989999i	$0.545056\pi$
$284$		−	208.018i		−	0.732456i
$285$	8.79347	−	41.0728i	0.0308543	−	0.144115i
$286$	−24.4412			−0.0854587
$287$			18.6012i			0.0648126i
$288$	−20.8444	+	46.4490i	−0.0723764	+	0.161281i
$289$	252.892			0.875059
$290$			274.204i			0.945531i
$291$	61.7393	+	13.2181i	0.212163	+	0.0454229i
$292$	104.633			0.358332
$293$			211.701i			0.722529i	0.932463	+	0.361265i	$0.117655\pi$
$293$			211.701i			0.722529i	−0.932463	+	0.361265i	$0.882345\pi$
$294$	43.3980	−	202.705i	0.147612	−	0.689471i
$295$	247.255			0.838154
$296$			170.052i			0.574500i
$297$	76.5322	−	104.366i	0.257684	−	0.351400i
$298$	79.9713			0.268360
$299$			123.129i			0.411804i
$300$	−53.2480	−	11.4001i	−0.177493	−	0.0380004i
$301$	17.8424			0.0592772
$302$		−	53.1198i		−	0.175893i
$303$	30.9875	−	144.737i	0.102269	−	0.477681i
$304$	−14.0345			−0.0461660
$305$		−	425.625i		−	1.39549i
$306$	69.7778	+	31.3134i	0.228032	+	0.102331i
$307$	457.126			1.48901			0.744505	−	0.667616i	$-0.232685\pi$
$307$	457.126			1.48901			0.744505	+	0.667616i	$0.232685\pi$
$308$			3.57862i			0.0116189i
$309$	120.053	+	25.7027i	0.388521	+	0.0831804i
$310$	−7.34959			−0.0237084
$311$			110.618i			0.355686i	0.984059	+	0.177843i	$0.0569119\pi$
$311$			110.618i			0.355686i	−0.984059	+	0.177843i	$0.943088\pi$
$312$	−6.40489	+	29.9162i	−0.0205285	+	0.0958852i
$313$	101.041			0.322816			0.161408	−	0.986888i	$-0.448397\pi$
$313$	101.041			0.322816			0.161408	+	0.986888i	$0.448397\pi$
$314$		−	116.482i		−	0.370961i
$315$	−5.48901	+	12.2315i	−0.0174254	+	0.0388303i
$316$	22.9732			0.0727001
$317$		−	454.965i		−	1.43522i	−0.696444	−	0.717611i	$-0.745236\pi$
$317$		−	454.965i		−	1.43522i	0.696444	−	0.717611i	$-0.254764\pi$
$318$	−365.934	−	78.3445i	−1.15074	−	0.246366i
$319$	−232.898			−0.730087
$320$		−	31.9241i		−	0.0997629i
$321$	25.5894	−	119.524i	0.0797178	−	0.372348i
$322$	18.0283			0.0559886
$323$			21.0832i			0.0652731i
$324$	−107.689	−	121.025i	−0.332373	−	0.373535i
$325$	−32.7232			−0.100687
$326$		−	366.503i		−	1.12424i
$327$	−170.666	−	36.5388i	−0.521915	−	0.111739i
$328$	140.940			0.429696
$329$			20.1726i			0.0613150i
$330$	−16.9893	+	79.3540i	−0.0514826	+	0.240467i
$331$	−373.285			−1.12775			−0.563874	−	0.825861i	$-0.690690\pi$
$331$	−373.285			−1.12775			−0.563874	+	0.825861i	$0.690690\pi$
$332$			150.220i			0.452471i
$333$	−493.672	−	221.540i	−1.48250	−	0.665284i
$334$	281.249			0.842064
$335$			290.744i			0.867894i
$336$	4.38026	+	0.937791i	0.0130365	+	0.00279104i
$337$	−93.7672			−0.278241			−0.139120	−	0.990275i	$-0.544428\pi$
$337$	−93.7672			−0.278241			−0.139120	+	0.990275i	$0.544428\pi$
$338$			18.3848i			0.0543928i
$339$	96.6700	−	451.529i	0.285162	−	1.33194i
$340$	−47.9579			−0.141053
$341$		−	6.24244i		−	0.0183063i
$342$	18.2838	−	40.7429i	0.0534613	−	0.119131i
$343$	−36.5308			−0.106504
$344$		−	135.191i		−	0.392998i
$345$	399.768	+	85.5882i	1.15875	+	0.248082i
$346$	66.6574			0.192651
$347$		−	56.2406i		−	0.162077i	−0.996711	−	0.0810384i	$-0.974176\pi$
$347$		−	56.2406i		−	0.162077i	0.996711	−	0.0810384i	$-0.0258236\pi$
$348$	−61.0316	+	285.068i	−0.175378	+	0.819162i
$349$	−457.950			−1.31218			−0.656089	−	0.754683i	$-0.727791\pi$
$349$	−457.950			−1.31218			−0.656089	+	0.754683i	$0.727791\pi$
$350$			4.79126i			0.0136893i
$351$	−78.5044	−	57.5679i	−0.223659	−	0.164011i
$352$	27.1151			0.0770314
$353$		−	433.154i		−	1.22707i	−0.789669	−	0.613533i	$-0.789748\pi$
$353$		−	433.154i		−	1.22707i	0.789669	−	0.613533i	$-0.210252\pi$
$354$	257.052	+	55.0335i	0.726136	+	0.155462i
$355$	−415.049			−1.16915
$356$		−	108.524i		−	0.304843i
$357$	1.40879	−	6.58023i	0.00394620	−	0.0184320i
$358$	125.493			0.350538
$359$		−	331.871i		−	0.924431i	−0.886768	−	0.462215i	$-0.847055\pi$
$359$		−	331.871i		−	0.924431i	0.886768	−	0.462215i	$-0.152945\pi$
$360$	92.6778	+	41.5900i	0.257438	+	0.115528i
$361$	−348.690			−0.965899
$362$			3.00050i			0.00828866i
$363$	287.556	+	61.5642i	0.792166	+	0.169598i
$364$	2.69186			0.00739522
$365$		−	208.770i		−	0.571972i
$366$	94.7346	−	442.489i	0.258838	−	1.20899i
$367$	661.515			1.80249			0.901247	−	0.433306i	$-0.142653\pi$
$367$	661.515			1.80249			0.901247	+	0.433306i	$0.142653\pi$
$368$		−	136.600i		−	0.371195i
$369$	−183.614	+	409.159i	−0.497598	+	1.10883i
$370$	339.298			0.917021
$371$			32.9267i			0.0887513i
$372$	−7.64079	−	1.63585i	−0.0205398	−	0.00439745i
$373$	−452.302			−1.21261			−0.606303	−	0.795234i	$-0.707348\pi$
$373$	−452.302			−1.21261			−0.606303	+	0.795234i	$0.707348\pi$
$374$		−	40.7335i		−	0.108913i
$375$	−85.4024	+	398.900i	−0.227740	+	1.06373i
$376$	152.847			0.406508
$377$			175.187i			0.464686i
$378$	−8.42896	+	11.4944i	−0.0222988	+	0.0304086i
$379$	−654.569			−1.72709			−0.863547	−	0.504268i	$-0.831763\pi$
$379$	−654.569			−1.72709			−0.863547	+	0.504268i	$0.831763\pi$
$380$			28.0024i			0.0736904i
$381$	266.958	+	57.1543i	0.700678	+	0.150011i
$382$	−205.514			−0.537996
$383$		−	272.572i		−	0.711676i	−0.934548	−	0.355838i	$-0.884195\pi$
$383$		−	272.572i		−	0.711676i	0.934548	−	0.355838i	$-0.115805\pi$
$384$	7.10559	−	33.1890i	0.0185041	−	0.0864297i
$385$	7.14028			0.0185462
$386$			169.265i			0.438511i
$387$	392.468	+	176.124i	1.01413	+	0.455100i
$388$	−42.0923			−0.108485
$389$			9.24505i			0.0237662i	0.999929	+	0.0118831i	$0.00378260\pi$
$389$			9.24505i			0.0237662i	−0.999929	+	0.0118831i	$0.996217\pi$
$390$	59.6905	+	12.7794i	0.153053	+	0.0327677i
$391$	−205.206			−0.524824
$392$			138.199i			0.352548i
$393$	−135.461	+	632.713i	−0.344683	+	1.60996i
$394$	−95.7706			−0.243073
$395$		−	45.8375i		−	0.116044i
$396$	−35.3248	+	78.7167i	−0.0892041	+	0.198780i
$397$	81.7849			0.206007			0.103004	−	0.994681i	$-0.467155\pi$
$397$	81.7849			0.206007			0.103004	+	0.994681i	$0.467155\pi$
$398$		−	29.7481i		−	0.0747440i
$399$	−3.84216	−	0.822587i	−0.00962948	−	0.00206162i
$400$	36.3031			0.0907578
$401$			301.706i			0.752384i	0.926542	+	0.376192i	$0.122767\pi$
$401$			301.706i			0.752384i	−0.926542	+	0.376192i	$0.877233\pi$
$402$	−64.7132	+	302.264i	−0.160978	+	0.751901i
$403$	−4.69560			−0.0116516
$404$			98.6782i			0.244253i
$405$	−241.477	+	214.867i	−0.596239	+	0.530536i
$406$	25.6505			0.0631785
$407$			288.186i			0.708073i
$408$	−49.8581	−	10.6743i	−0.122201	−	0.0261626i
$409$	−9.59654			−0.0234634			−0.0117317	−	0.999931i	$-0.503734\pi$
$409$	−9.59654			−0.0234634			−0.0117317	+	0.999931i	$0.503734\pi$
$410$		−	281.212i		−	0.685884i
$411$	50.0247	−	233.657i	0.121715	−	0.568509i
$412$	−81.8491			−0.198663
$413$		−	23.1296i		−	0.0560038i
$414$	396.557	+	177.959i	0.957868	+	0.429852i
$415$	299.728			0.722237
$416$		−	20.3961i		−	0.0490290i
$417$	114.693	+	24.5552i	0.275043	+	0.0588853i
$418$	−23.7841			−0.0568997
$419$			178.697i			0.426485i	0.976999	+	0.213243i	$0.0684024\pi$
$419$			178.697i			0.426485i	−0.976999	+	0.213243i	$0.931598\pi$
$420$	1.87113	−	8.73975i	0.00445508	−	0.0208089i
$421$	414.685			0.985001			0.492501	−	0.870312i	$-0.336083\pi$
$421$	414.685			0.985001			0.492501	+	0.870312i	$0.336083\pi$
$422$		−	136.042i		−	0.322374i
$423$	−199.125	+	443.724i	−0.470746	+	1.04899i
$424$	249.484			0.588406
$425$		−	54.5362i		−	0.128321i
$426$	−431.494	−	92.3805i	−1.01290	−	0.216856i
$427$	−39.8152			−0.0932440
$428$			81.4883i			0.190393i
$429$	−10.8543	+	50.6987i	−0.0253014	+	0.118179i
$430$	−269.741			−0.627305
$431$		−	659.696i		−	1.53062i	−0.643663	−	0.765309i	$-0.722586\pi$
$431$		−	659.696i		−	1.53062i	0.643663	−	0.765309i	$-0.277414\pi$
$432$	87.0928	+	63.8658i	0.201604	+	0.147838i
$433$	91.9890			0.212446			0.106223	−	0.994342i	$-0.466124\pi$
$433$	91.9890			0.212446			0.106223	+	0.994342i	$0.466124\pi$
$434$			0.687519i			0.00158415i
$435$	568.785	+	121.774i	1.30755	+	0.279940i
$436$	116.356			0.266871
$437$			119.819i			0.274185i
$438$	46.4675	−	217.042i	0.106090	−	0.495529i
$439$	86.6064			0.197281			0.0986406	−	0.995123i	$-0.468551\pi$
$439$	86.6064			0.197281			0.0986406	+	0.995123i	$0.468551\pi$
$440$		−	54.1015i		−	0.122958i
$441$	−401.200	−	180.042i	−0.909750	−	0.408259i
$442$	−30.6399			−0.0693211
$443$		−	98.9075i		−	0.223267i	−0.993749	−	0.111634i	$-0.964392\pi$
$443$		−	98.9075i		−	0.223267i	0.993749	−	0.111634i	$-0.0356083\pi$
$444$	352.741	+	75.5200i	0.794462	+	0.170090i
$445$	−216.534			−0.486593
$446$			534.725i			1.19894i
$447$	35.5152	−	165.885i	0.0794524	−	0.371108i
$448$	−2.98635			−0.00666596
$449$		−	315.539i		−	0.702760i	−0.936233	−	0.351380i	$-0.885713\pi$
$449$		−	315.539i		−	0.702760i	0.936233	−	0.351380i	$-0.114287\pi$
$450$	−47.2948	+	105.390i	−0.105100	+	0.234201i
$451$	238.850			0.529602
$452$			307.841i			0.681064i
$453$	−110.187	−	23.5905i	−0.243239	−	0.0520761i
$454$	522.111			1.15002
$455$		−	5.37095i		−	0.0118043i
$456$	−6.23270	+	29.1119i	−0.0136682	+	0.0638418i
$457$	122.324			0.267667			0.133834	−	0.991004i	$-0.457271\pi$
$457$	122.324			0.267667			0.133834	+	0.991004i	$0.457271\pi$
$458$		−	481.544i		−	1.05141i
$459$	95.9422	−	130.835i	0.209024	−	0.285043i
$460$	−272.552			−0.592503
$461$			168.888i			0.366352i	0.983080	+	0.183176i	$0.0586379\pi$
$461$			168.888i			0.366352i	−0.983080	+	0.183176i	$0.941362\pi$
$462$	7.42319	+	1.58927i	0.0160675	+	0.00343997i
$463$	574.225			1.24023			0.620113	−	0.784512i	$-0.287087\pi$
$463$	574.225			1.24023			0.620113	+	0.784512i	$0.287087\pi$
$464$		−	194.352i		−	0.418863i
$465$	−3.26395	+	15.2454i	−0.00701925	+	0.0327857i
$466$	−202.157			−0.433813
$467$			505.925i			1.08335i	0.840588	+	0.541675i	$0.182210\pi$
$467$			505.925i			1.08335i	−0.840588	+	0.541675i	$0.817790\pi$
$468$	59.2111	+	26.5715i	0.126519	+	0.0567767i
$469$	27.1978			0.0579909
$470$		−	304.969i		−	0.648871i
$471$	−241.620	−	51.7295i	−0.512993	−	0.109829i
$472$	−175.252			−0.371296
$473$		−	229.107i		−	0.484370i
$474$	10.2024	−	47.6537i	0.0215241	−	0.100535i
$475$	−31.8434			−0.0670388
$476$			4.48623i			0.00942486i
$477$	−325.022	+	724.268i	−0.681388	+	1.51838i
$478$	75.1582			0.157235
$479$			175.654i			0.366710i	0.983047	+	0.183355i	$0.0586959\pi$
$479$			175.654i			0.366710i	−0.983047	+	0.183355i	$0.941304\pi$
$480$	−66.2206	−	14.1775i	−0.137960	−	0.0295364i
$481$	216.775			0.450675
$482$			581.465i			1.20636i
$483$	8.00637	−	37.3964i	0.0165763	−	0.0774252i
$484$	−196.048			−0.405059
$485$			83.9849i			0.173165i
$486$	−298.869	+	169.633i	−0.614957	+	0.349039i
$487$	−760.290			−1.56117			−0.780585	−	0.625049i	$-0.785079\pi$
$487$	−760.290			−1.56117			−0.780585	+	0.625049i	$0.785079\pi$
$488$			301.678i			0.618192i
$489$	−760.242	−	162.764i	−1.55469	−	0.332850i
$490$	275.742			0.562739
$491$		−	642.207i		−	1.30796i	−0.756513	−	0.653979i	$-0.773098\pi$
$491$		−	642.207i		−	1.30796i	0.756513	−	0.653979i	$-0.226902\pi$
$492$	62.5915	−	292.354i	0.127219	−	0.594216i
$493$	−291.965			−0.592221
$494$			17.8905i			0.0362156i
$495$	157.060	+	70.4822i	0.317293	+	0.142388i
$496$	5.20930			0.0105026
$497$			38.8258i			0.0781204i
$498$	311.604	+	66.7127i	0.625711	+	0.133961i
$499$	659.917			1.32248			0.661240	−	0.750175i	$-0.270031\pi$
$499$	659.917			1.32248			0.661240	+	0.750175i	$0.270031\pi$
$500$		−	271.960i		−	0.543920i
$501$	124.903	−	583.399i	0.249307	−	1.16447i
$502$	−611.061			−1.21725
$503$		−	14.8802i		−	0.0295829i	−0.999891	−	0.0147915i	$-0.995292\pi$
$503$		−	14.8802i		−	0.0295829i	0.999891	−	0.0147915i	$-0.00470844\pi$
$504$	3.89054	−	8.66956i	0.00771933	−	0.0172015i
$505$	196.888			0.389878
$506$		−	231.494i		−	0.457498i
$507$	38.1358	+	8.16467i	0.0752185	+	0.0161039i
$508$	−182.005			−0.358278
$509$			516.224i			1.01419i	0.861889	+	0.507096i	$0.169281\pi$
$509$			516.224i			1.01419i	−0.861889	+	0.507096i	$0.830719\pi$
$510$	−21.2981	+	99.4797i	−0.0417609	+	0.195058i
$511$	−19.5294			−0.0382181
$512$			22.6274i			0.0441942i
$513$	−76.3938	−	56.0201i	−0.148916	−	0.109201i
$514$	−557.684			−1.08499
$515$			163.310i			0.317107i
$516$	−280.429	−	60.0383i	−0.543467	−	0.116353i
$517$	259.028			0.501022
$518$		−	31.7397i		−	0.0612735i
$519$	29.6025	−	138.268i	0.0570376	−	0.266413i
$520$	−40.6954			−0.0782605
$521$		−	209.184i		−	0.401505i	−0.979642	−	0.200752i	$-0.935661\pi$
$521$		−	209.184i		−	0.401505i	0.979642	−	0.200752i	$-0.0643386\pi$
$522$	564.217	+	253.197i	1.08088	+	0.485052i
$523$	235.931			0.451111			0.225555	−	0.974230i	$-0.427580\pi$
$523$	235.931			0.451111			0.225555	+	0.974230i	$0.427580\pi$
$524$		−	431.368i		−	0.823221i
$525$	9.93857	+	2.12780i	0.0189306	+	0.00405294i
$526$	376.439			0.715664
$527$		−	7.82564i		−	0.0148494i
$528$	12.0418	−	56.2451i	0.0228064	−	0.106525i
$529$	−637.217			−1.20457
$530$		−	497.785i		−	0.939218i
$531$	228.313	−	508.766i	0.429969	−	0.958129i
$532$	2.61949			0.00492385
$533$		−	179.664i		−	0.337081i
$534$	−225.113	−	48.1956i	−0.421560	−	0.0902539i
$535$	162.590			0.303907
$536$		−	206.076i		−	0.384470i
$537$	55.7313	−	260.311i	0.103783	−	0.484751i
$538$	−531.905			−0.988670
$539$			234.204i			0.434516i
$540$	127.429	−	173.773i	0.235979	−	0.321801i
$541$	462.613			0.855107			0.427553	−	0.903990i	$-0.359376\pi$
$541$	462.613			0.855107			0.427553	+	0.903990i	$0.359376\pi$
$542$			183.220i			0.338045i
$543$	6.22397	+	1.33252i	0.0114622	+	0.00245399i
$544$	33.9919			0.0624852
$545$		−	232.160i		−	0.425982i
$546$	1.19545	−	5.58376i	0.00218947	−	0.0102267i
$547$	795.619			1.45451			0.727256	−	0.686366i	$-0.240795\pi$
$547$	795.619			1.45451			0.727256	+	0.686366i	$0.240795\pi$
$548$			159.301i			0.290696i
$549$	−875.789	−	393.018i	−1.59524	−	0.715880i
$550$	61.5226			0.111859
$551$			170.477i			0.309395i
$552$	−283.351	−	60.6638i	−0.513316	−	0.109898i
$553$	−4.28788			−0.00775386
$554$			474.805i			0.857048i
$555$	150.682	−	703.809i	0.271499	−	1.26813i
$556$	−78.1948			−0.140638
$557$		−	475.910i		−	0.854417i	−0.904153	−	0.427208i	$-0.859497\pi$
$557$		−	475.910i		−	0.854417i	0.904153	−	0.427208i	$-0.140503\pi$
$558$	−6.78654	+	15.1229i	−0.0121623	+	0.0271020i
$559$	−172.336			−0.308293
$560$			5.95854i			0.0106402i
$561$	−84.4940	−	18.0897i	−0.150613	−	0.0322455i
$562$	−492.601			−0.876514
$563$		−	719.510i		−	1.27799i	−0.769210	−	0.638997i	$-0.779350\pi$
$563$		−	719.510i		−	1.27799i	0.769210	−	0.638997i	$-0.220650\pi$
$564$	67.8793	−	317.053i	0.120353	−	0.562150i
$565$	614.222			1.08712
$566$		−	112.922i		−	0.199509i
$567$	20.0998	+	22.5890i	0.0354493	+	0.0398395i
$568$	294.181			0.517925
$569$			207.017i			0.363826i	0.983315	+	0.181913i	$0.0582289\pi$
$569$			207.017i			0.363826i	−0.983315	+	0.181913i	$0.941771\pi$
$570$	58.0857	+	12.4358i	0.101905	+	0.0218173i
$571$	−1063.27			−1.86213			−0.931063	−	0.364859i	$-0.881117\pi$
$571$	−1063.27			−1.86213			−0.931063	+	0.364859i	$0.881117\pi$
$572$		−	34.5650i		−	0.0604284i
$573$	−91.2688	+	426.301i	−0.159282	+	0.743981i
$574$	−26.3061			−0.0458294
$575$		−	309.937i		−	0.539021i
$576$	−65.6888	−	29.4784i	−0.114043	−	0.0511779i
$577$	743.001			1.28770			0.643848	−	0.765153i	$-0.277337\pi$
$577$	743.001			1.28770			0.643848	+	0.765153i	$0.277337\pi$
$578$			357.643i			0.618760i
$579$	351.109	+	75.1706i	0.606406	+	0.129828i
$580$	−387.783			−0.668591
$581$		−	28.0381i		−	0.0482584i
$582$	−18.6932	+	87.3125i	−0.0321188	+	0.150022i
$583$	422.799			0.725212
$584$			147.973i			0.253379i
$585$	53.0170	−	118.141i	0.0906274	−	0.201951i
$586$	−299.391			−0.510905
$587$			1086.64i			1.85118i	0.378533	+	0.925588i	$0.376429\pi$
$587$			1086.64i			1.85118i	−0.378533	+	0.925588i	$0.623571\pi$
$588$	286.668	+	61.3740i	0.487530	+	0.104378i
$589$	−4.56935			−0.00775782
$590$			349.672i			0.592664i
$591$	−42.5317	+	198.658i	−0.0719656	+	0.336139i
$592$	−240.490			−0.406233
$593$		−	84.5815i		−	0.142633i	−0.997454	−	0.0713166i	$-0.977280\pi$
$593$		−	84.5815i		−	0.142633i	0.997454	−	0.0713166i	$-0.0227201\pi$
$594$	147.595	+	108.233i	0.248477	+	0.182210i
$595$	8.95119			0.0150440
$596$			113.096i			0.189759i
$597$	−61.7069	−	13.2111i	−0.103362	−	0.0221292i
$598$	−174.131			−0.291189
$599$			610.440i			1.01910i	0.860442	+	0.509549i	$0.170188\pi$
$599$			610.440i			1.01910i	−0.860442	+	0.509549i	$0.829812\pi$
$600$	16.1222	−	75.3041i	0.0268703	−	0.125507i
$601$	−179.214			−0.298193			−0.149096	−	0.988823i	$-0.547636\pi$
$601$	−179.214			−0.298193			−0.149096	+	0.988823i	$0.547636\pi$
$602$			25.2330i			0.0419153i
$603$	598.252	+	268.471i	0.992125	+	0.445225i
$604$	75.1227			0.124375
$605$			391.167i			0.646557i
$606$	204.690	+	43.8229i	0.337771	+	0.0723151i
$607$	806.466			1.32861			0.664305	−	0.747462i	$-0.268728\pi$
$607$	806.466			1.32861			0.664305	+	0.747462i	$0.268728\pi$
$608$		−	19.8477i		−	0.0326443i
$609$	11.3914	−	53.2071i	0.0187050	−	0.0873680i
$610$	601.925			0.986762
$611$		−	194.842i		−	0.318891i
$612$	−44.2839	+	98.6808i	−0.0723593	+	0.161243i
$613$	625.445			1.02030			0.510151	−	0.860085i	$-0.329590\pi$
$613$	625.445			1.02030			0.510151	+	0.860085i	$0.329590\pi$
$614$			646.474i			1.05289i
$615$	−583.323	−	124.886i	−0.948492	−	0.203067i
$616$	−5.06094			−0.00821581
$617$			1083.44i			1.75598i	0.478676	+	0.877992i	$0.341117\pi$
$617$			1083.44i			1.75598i	−0.478676	+	0.877992i	$0.658883\pi$
$618$	−36.3491	+	169.781i	−0.0588174	+	0.274726i
$619$	358.934			0.579861			0.289931	−	0.957048i	$-0.406368\pi$
$619$	358.934			0.579861			0.289931	+	0.957048i	$0.406368\pi$
$620$		−	10.3939i		−	0.0167643i
$621$	545.253	−	743.553i	0.878024	−	1.19735i
$622$	−156.438			−0.251508
$623$			20.2557i			0.0325132i
$624$	−42.3079	−	9.05789i	−0.0678011	−	0.0145158i
$625$	−315.736			−0.505177
$626$			142.894i			0.228265i
$627$	−10.5625	+	49.3356i	−0.0168461	+	0.0786852i
$628$	164.730			0.262309
$629$			361.275i			0.574364i
$630$	−17.2980	−	7.76264i	−0.0274572	−	0.0123216i
$631$	−1131.53			−1.79323			−0.896613	−	0.442815i	$-0.853980\pi$
$631$	−1131.53			−1.79323			−0.896613	+	0.442815i	$0.853980\pi$
$632$			32.4891i			0.0514068i
$633$	−282.193	−	60.4161i	−0.445803	−	0.0954441i
$634$	643.418			1.01486
$635$			363.147i			0.571886i
$636$	110.796	−	517.508i	0.174207	−	0.813693i
$637$	176.170			0.276561
$638$		−	329.367i		−	0.516249i
$639$	−383.252	+	854.027i	−0.599769	+	1.33651i
$640$	45.1475			0.0705430
$641$			593.464i			0.925841i	0.886400	+	0.462920i	$0.153198\pi$
$641$			593.464i			0.925841i	−0.886400	+	0.462920i	$0.846802\pi$
$642$	169.032	+	36.1889i	0.263290	+	0.0563690i
$643$	−809.095			−1.25831			−0.629156	−	0.777279i	$-0.716600\pi$
$643$	−809.095			−1.25831			−0.629156	+	0.777279i	$0.716600\pi$
$644$			25.4959i			0.0395899i
$645$	−119.792	+	559.528i	−0.185724	+	0.867485i
$646$	−29.8162			−0.0461550
$647$		−	410.483i		−	0.634440i	−0.948352	−	0.317220i	$-0.897251\pi$
$647$		−	410.483i		−	0.634440i	0.948352	−	0.317220i	$-0.102749\pi$
$648$	171.156	−	152.295i	0.264129	−	0.235023i
$649$	−296.997			−0.457623
$650$		−	46.2776i		−	0.0711963i
$651$	1.42613	+	0.305327i	0.00219068	+	0.000469012i
$652$	518.313			0.794959
$653$		−	55.9484i		−	0.0856790i	−0.999082	−	0.0428395i	$-0.986360\pi$
$653$		−	55.9484i		−	0.0856790i	0.999082	−	0.0428395i	$-0.0136404\pi$
$654$	51.6736	−	241.359i	0.0790116	−	0.369050i
$655$	−860.690			−1.31403
$656$			199.320i			0.303841i
$657$	−429.576	−	192.776i	−0.653845	−	0.293419i
$658$	−28.5284			−0.0433563
$659$		−	348.544i		−	0.528899i	−0.964400	−	0.264449i	$-0.914810\pi$
$659$		−	348.544i		−	0.528899i	0.964400	−	0.264449i	$-0.0851902\pi$
$660$	−112.224	−	24.0265i	−0.170036	−	0.0364037i
$661$	677.961			1.02566			0.512829	−	0.858490i	$-0.328597\pi$
$661$	677.961			1.02566			0.512829	+	0.858490i	$0.328597\pi$
$662$		−	527.904i		−	0.797438i
$663$	−13.6072	+	63.5568i	−0.0205236	+	0.0958625i
$664$	−212.444			−0.319945
$665$		−	5.22655i		−	0.00785948i
$666$	313.304	−	698.157i	0.470427	−	1.04828i
$667$	−1659.28			−2.48767
$668$			397.746i			0.595429i
$669$	1109.19	+	237.471i	1.65798	+	0.354964i
$670$	−411.175			−0.613694
$671$			511.250i			0.761923i
$672$	−1.32624	+	6.19462i	−0.00197357	+	0.00921819i
$673$	−588.766			−0.874837			−0.437419	−	0.899258i	$-0.644107\pi$
$673$	−588.766			−0.874837			−0.437419	+	0.899258i	$0.644107\pi$
$674$		−	132.607i		−	0.196746i
$675$	197.609	+	144.908i	0.292754	+	0.214679i
$676$	−26.0000			−0.0384615
$677$			759.531i			1.12191i	0.827847	+	0.560953i	$0.189565\pi$
$677$			759.531i			1.12191i	−0.827847	+	0.560953i	$0.810435\pi$
$678$	638.559	+	136.712i	0.941827	+	0.201640i
$679$	7.85639			0.0115705
$680$		−	67.8227i		−	0.0997393i
$681$	231.869	−	1083.02i	0.340483	−	1.59034i
$682$	8.82815			0.0129445
$683$		−	456.144i		−	0.667854i	−0.942599	−	0.333927i	$-0.891626\pi$
$683$		−	456.144i		−	0.667854i	0.942599	−	0.333927i	$-0.108374\pi$
$684$	57.6192	+	25.8571i	0.0842386	+	0.0378028i
$685$	317.847			0.464011
$686$		−	51.6623i		−	0.0753095i
$687$	−998.873	−	213.853i	−1.45396	−	0.311286i
$688$	191.189			0.277891
$689$		−	318.031i		−	0.461584i
$690$	−121.040	+	565.357i	−0.175420	+	0.819359i
$691$	−1231.45			−1.78213			−0.891063	−	0.453879i	$-0.850040\pi$
$691$	−1231.45			−1.78213			−0.891063	+	0.453879i	$0.850040\pi$
$692$			94.2678i			0.136225i
$693$	6.59327	−	14.6922i	0.00951410	−	0.0212009i
$694$	79.5363			0.114606
$695$			156.019i			0.224487i
$696$	−403.147	−	86.3117i	−0.579235	−	0.124011i
$697$	299.427			0.429594
$698$		−	647.640i		−	0.927850i
$699$	−89.7778	+	419.337i	−0.128438	+	0.599910i
$700$	−6.77586			−0.00967981
$701$		−	1002.31i		−	1.42983i	−0.699214	−	0.714913i	$-0.746466\pi$
$701$		−	1002.31i		−	1.42983i	0.699214	−	0.714913i	$-0.253534\pi$
$702$	81.4133	−	111.022i	0.115973	−	0.158151i
$703$	210.947			0.300066
$704$			38.3465i			0.0544694i
$705$	−632.602	−	135.437i	−0.897307	−	0.192109i
$706$	612.573			0.867667
$707$		−	18.4180i		−	0.0260509i
$708$	−77.8291	+	363.527i	−0.109928	+	0.513456i
$709$	1131.35			1.59570			0.797849	−	0.602857i	$-0.205971\pi$
$709$	1131.35			1.59570			0.797849	+	0.602857i	$0.205971\pi$
$710$		−	586.967i		−	0.826715i
$711$	−94.3178	−	42.3260i	−0.132655	−	0.0595302i
$712$	153.476			0.215557
$713$		−	44.4743i		−	0.0623762i
$714$	9.30585	+	1.99233i	0.0130334	+	0.00279038i
$715$	−68.9662			−0.0964562
$716$			177.474i			0.247868i
$717$	33.3777	−	155.902i	0.0465519	−	0.217436i
$718$	469.336			0.653671
$719$		−	558.755i		−	0.777129i	−0.921422	−	0.388564i	$-0.872971\pi$
$719$		−	558.755i		−	0.777129i	0.921422	−	0.388564i	$-0.127029\pi$
$720$	−58.8171	+	131.066i	−0.0816904	+	0.182036i
$721$	15.2769			0.0211885
$722$		−	493.122i		−	0.682994i
$723$	1206.14	+	258.228i	1.66824	+	0.357162i
$724$	−4.24334			−0.00586097
$725$		−	440.975i		−	0.608241i
$726$	−87.0650	+	406.666i	−0.119924	+	0.560146i
$727$	85.7322			0.117926			0.0589630	−	0.998260i	$-0.481221\pi$
$727$	85.7322			0.117926			0.0589630	+	0.998260i	$0.481221\pi$
$728$			3.80686i			0.00522921i
$729$	219.145	+	695.282i	0.300610	+	0.953747i
$730$	295.245			0.404446
$731$		−	287.213i		−	0.392904i
$732$	625.774	+	133.975i	0.854883	+	0.183026i
$733$	437.921			0.597436			0.298718	−	0.954341i	$-0.403441\pi$
$733$	437.921			0.597436			0.298718	+	0.954341i	$0.403441\pi$
$734$			935.524i			1.27456i
$735$	122.457	−	571.976i	0.166608	−	0.778198i
$736$	193.181			0.262474
$737$		−	349.235i		−	0.473860i
$738$	−578.638	−	259.669i	−0.784062	−	0.351855i
$739$	−108.318			−0.146574			−0.0732868	−	0.997311i	$-0.523349\pi$
$739$	−108.318			−0.146574			−0.0732868	+	0.997311i	$0.523349\pi$
$740$			479.839i			0.648431i
$741$	37.1105	+	7.94516i	0.0500816	+	0.0107222i
$742$	−46.5654			−0.0627567
$743$			552.991i			0.744268i	0.928179	+	0.372134i	$0.121374\pi$
$743$			552.991i			0.744268i	−0.928179	+	0.372134i	$0.878626\pi$
$744$	2.31345	−	10.8057i	0.00310947	−	0.0145238i
$745$	225.657			0.302895
$746$		−	639.651i		−	0.857441i
$747$	276.766	−	616.737i	0.370504	−	0.825619i
$748$	57.6058			0.0770132
$749$		−	15.2095i		−	0.0203065i
$750$	−564.130	−	120.777i	−0.752173	−	0.161036i
$751$	−569.529			−0.758361			−0.379181	−	0.925323i	$-0.623794\pi$
$751$	−569.529			−0.758361			−0.379181	+	0.925323i	$0.623794\pi$
$752$			216.158i			0.287445i
$753$	−271.372	+	1267.53i	−0.360388	+	1.68331i
$754$	−247.751			−0.328583
$755$		−	149.889i		−	0.198529i
$756$	−16.2556	−	11.9204i	−0.0215021	−	0.0157677i
$757$	−512.602			−0.677149			−0.338574	−	0.940940i	$-0.609945\pi$
$757$	−512.602			−0.677149			−0.338574	+	0.940940i	$0.609945\pi$
$758$		−	925.700i		−	1.22124i
$759$	−480.191	−	102.806i	−0.632663	−	0.135450i
$760$	−39.6013			−0.0521070
$761$		−	1223.30i		−	1.60749i	−0.594975	−	0.803745i	$-0.702838\pi$
$761$		−	1223.30i		−	1.60749i	0.594975	−	0.803745i	$-0.297162\pi$
$762$	−80.8284	+	377.536i	−0.106074	+	0.495454i
$763$	−21.7175			−0.0284633
$764$		−	290.641i		−	0.380420i
$765$	196.894	+	88.3578i	0.257377	+	0.115500i
$766$	385.475			0.503231
$767$			223.403i			0.291268i
$768$	46.9364	+	10.0488i	0.0611150	+	0.0130844i
$769$	492.163			0.640003			0.320002	−	0.947417i	$-0.396317\pi$
$769$	492.163			0.640003			0.320002	+	0.947417i	$0.396317\pi$
$770$			10.0979i			0.0131141i
$771$	−247.667	+	1156.81i	−0.321228	+	1.50040i
$772$	−239.377			−0.310074
$773$		−	732.500i		−	0.947607i	−0.880631	−	0.473804i	$-0.842881\pi$
$773$		−	732.500i		−	0.947607i	0.880631	−	0.473804i	$-0.157119\pi$
$774$	−249.077	+	555.034i	−0.321804	+	0.717098i
$775$	11.8196			0.0152511
$776$		−	59.5275i		−	0.0767106i
$777$	−65.8380	−	14.0956i	−0.0847336	−	0.0181410i
$778$	−13.0745			−0.0168052
$779$		−	174.834i		−	0.224434i
$780$	−18.0728	+	84.4151i	−0.0231703	+	0.108224i
$781$	498.546			0.638343
$782$		−	290.206i		−	0.371107i
$783$	775.779	−	1057.92i	0.990778	−	1.35111i
$784$	−195.443			−0.249289
$785$		−	328.679i		−	0.418699i
$786$	−894.792	−	191.570i	−1.13841	−	0.243728i
$787$	118.173			0.150156			0.0750780	−	0.997178i	$-0.476079\pi$
$787$	118.173			0.150156			0.0750780	+	0.997178i	$0.476079\pi$
$788$		−	135.440i		−	0.171878i
$789$	167.177	−	780.853i	0.211884	−	0.989674i
$790$	64.8241			0.0820558
$791$		−	57.4576i		−	0.0726391i
$792$	−111.322	−	49.9569i	−0.140558	−	0.0630768i
$793$	384.565			0.484950
$794$			115.661i			0.145669i
$795$	−1032.56	−	221.066i	−1.29882	−	0.278071i
$796$	42.0702			0.0528520
$797$		−	780.420i		−	0.979197i	−0.871948	−	0.489598i	$-0.837143\pi$
$797$		−	780.420i		−	0.979197i	0.871948	−	0.489598i	$-0.162857\pi$
$798$	1.16331	−	5.43364i	0.00145779	−	0.00680907i
$799$	324.723			0.406412
$800$			51.3404i			0.0641755i
$801$	−199.945	+	445.552i	−0.249620	+	0.556244i
$802$	−426.676			−0.532016
$803$			250.769i			0.312291i
$804$	−427.466	−	91.5182i	−0.531674	−	0.113829i
$805$	50.8709			0.0631937
$806$		−	6.64058i		−	0.00823893i
$807$	−236.219	+	1103.34i	−0.292712	+	1.36721i
$808$	−139.552			−0.172713
$809$			1424.27i			1.76053i	0.474479	+	0.880267i	$0.342636\pi$
$809$			1424.27i			1.76053i	−0.474479	+	0.880267i	$0.657364\pi$
$810$	−303.868	−	341.500i	−0.375145	−	0.421604i
$811$	−804.621			−0.992135			−0.496067	−	0.868284i	$-0.665223\pi$
$811$	−804.621			−0.992135			−0.496067	+	0.868284i	$0.665223\pi$
$812$			36.2752i			0.0446739i
$813$	380.056	+	81.3680i	0.467474	+	0.100084i
$814$	−407.556			−0.500683
$815$		−	1034.17i		−	1.26892i
$816$	15.0958	−	70.5099i	0.0184998	−	0.0864092i
$817$	−167.702			−0.205266
$818$		−	13.5716i		−	0.0165911i
$819$	−11.0516	−	4.95949i	−0.0134940	−	0.00605554i
$820$	397.694			0.484993
$821$		−	84.0907i		−	0.102425i	−0.998688	−	0.0512124i	$-0.983691\pi$
$821$		−	84.0907i		−	0.102425i	0.998688	−	0.0512124i	$-0.0163085\pi$
$822$	330.441	+	70.7457i	0.401996	+	0.0860653i
$823$	185.737			0.225683			0.112842	−	0.993613i	$-0.464005\pi$
$823$	185.737			0.225683			0.112842	+	0.993613i	$0.464005\pi$
$824$		−	115.752i		−	0.140476i
$825$	27.3221	−	127.617i	0.0331177	−	0.154687i
$826$	32.7101			0.0396007
$827$		−	1440.59i		−	1.74195i	−0.491327	−	0.870975i	$-0.663488\pi$
$827$		−	1440.59i		−	1.74195i	0.491327	−	0.870975i	$-0.336512\pi$
$828$	−251.672	+	560.817i	−0.303951	+	0.677315i
$829$	628.270			0.757865			0.378933	−	0.925424i	$-0.376291\pi$
$829$	628.270			0.757865			0.378933	+	0.925424i	$0.376291\pi$
$830$			423.880i			0.510698i
$831$	984.894	+	210.861i	1.18519	+	0.253743i
$832$	28.8444			0.0346688
$833$			293.603i			0.352464i
$834$	−34.7262	+	162.200i	−0.0416382	+	0.194485i
$835$	793.607			0.950427
$836$		−	33.6358i		−	0.0402342i
$837$	28.3558	+	20.7935i	0.0338779	+	0.0248429i
$838$	−252.716			−0.301570
$839$		−	221.365i		−	0.263844i	−0.991260	−	0.131922i	$-0.957885\pi$
$839$		−	221.365i		−	0.263844i	0.991260	−	0.131922i	$-0.0421149\pi$
$840$	12.3599	+	2.64618i	0.0147141	+	0.00315022i
$841$	−1519.80			−1.80713
$842$			586.454i			0.696501i
$843$	−218.764	+	1021.81i	−0.259506	+	1.21211i
$844$	192.392			0.227953
$845$			51.8767i			0.0613926i
$846$	−627.521	−	281.606i	−0.741751	−	0.332867i
$847$	36.5918			0.0432017
$848$			352.824i			0.416066i
$849$	−234.236	−	50.1487i	−0.275896	−	0.0590680i
$850$	77.1259			0.0907363
$851$			2053.18i			2.41266i
$852$	130.646	−	610.224i	0.153340	−	0.716225i
$853$	−1164.32			−1.36497			−0.682483	−	0.730902i	$-0.739100\pi$
$853$	−1164.32			−1.36497			−0.682483	+	0.730902i	$0.739100\pi$
$854$		−	56.3072i		−	0.0659335i
$855$	51.5916	−	114.965i	0.0603411	−	0.134462i
$856$	−115.242			−0.134628
$857$			670.787i			0.782715i	0.920239	+	0.391358i	$0.127994\pi$
$857$			670.787i			0.782715i	−0.920239	+	0.391358i	$0.872006\pi$
$858$	−71.6987	−	15.3503i	−0.0835650	−	0.0178908i
$859$	1050.42			1.22284			0.611420	−	0.791306i	$-0.290599\pi$
$859$	1050.42			1.22284			0.611420	+	0.791306i	$0.290599\pi$
$860$		−	381.472i		−	0.443572i
$861$	−11.6825	+	54.5670i	−0.0135685	+	0.0633764i
$862$	932.951			1.08231
$863$			957.624i			1.10965i	0.831968	+	0.554823i	$0.187214\pi$
$863$			957.624i			1.10965i	−0.831968	+	0.554823i	$0.812786\pi$
$864$	−90.3199	+	123.168i	−0.104537	+	0.142555i
$865$	188.088			0.217443
$866$			130.092i			0.150222i
$867$	741.865	+	158.829i	0.855668	+	0.183194i
$868$	−0.972299			−0.00112016
$869$			55.0589i			0.0633589i
$870$	−172.214	+	804.383i	−0.197947	+	0.924578i
$871$	−262.696			−0.301603
$872$			164.552i			0.188707i
$873$	172.812	+	77.5509i	0.197952	+	0.0888327i
$874$	−169.450			−0.193878
$875$			50.7605i			0.0580120i
$876$	306.943	+	65.7150i	0.350392	+	0.0750171i
$877$	1015.10			1.15747			0.578737	−	0.815514i	$-0.303546\pi$
$877$	1015.10			1.15747			0.578737	+	0.815514i	$0.303546\pi$
$878$			122.480i			0.139499i
$879$	−132.959	+	621.030i	−0.151262	+	0.706518i
$880$	76.5111			0.0869444
$881$		−	27.4680i		−	0.0311782i	−0.999878	−	0.0155891i	$-0.995038\pi$
$881$		−	27.4680i		−	0.0311782i	0.999878	−	0.0155891i	$-0.00496237\pi$
$882$	254.618	−	567.382i	0.288682	−	0.643291i
$883$	−968.487			−1.09681			−0.548407	−	0.836212i	$-0.684766\pi$
$883$	−968.487			−1.09681			−0.548407	+	0.836212i	$0.684766\pi$
$884$		−	43.3314i		−	0.0490174i
$885$	725.329	+	155.289i	0.819581	+	0.175468i
$886$	139.876			0.157874
$887$			944.344i			1.06465i	0.846540	+	0.532325i	$0.178681\pi$
$887$			944.344i			1.06465i	−0.846540	+	0.532325i	$0.821319\pi$
$888$	−106.801	+	498.851i	−0.120272	+	0.561769i
$889$	33.9707			0.0382123
$890$		−	306.225i		−	0.344073i
$891$	290.056	−	258.093i	0.325540	−	0.289667i
$892$	−756.216			−0.847775
$893$		−	189.604i		−	0.212323i
$894$	234.597	+	50.2261i	0.262413	+	0.0561813i
$895$	354.106			0.395649
$896$		−	4.22334i		−	0.00471354i
$897$	−77.3315	+	361.202i	−0.0862113	+	0.402678i
$898$	446.240			0.496926
$899$		−	63.2774i		−	0.0703864i
$900$	−149.044	−	66.8850i	−0.165605	−	0.0743167i
$901$	530.028			0.588267
$902$			337.785i			0.374485i
$903$	52.3412	+	11.2060i	0.0579636	+	0.0124097i
$904$	−435.353			−0.481585
$905$			8.46656i			0.00935532i
$906$	33.3620	−	155.828i	0.0368234	−	0.171996i
$907$	−1174.59			−1.29503			−0.647513	−	0.762054i	$-0.724191\pi$
$907$	−1174.59			−1.29503			−0.647513	+	0.762054i	$0.724191\pi$
$908$			738.376i			0.813189i
$909$	181.805	−	405.128i	0.200006	−	0.445686i
$910$	7.59568			0.00834690
$911$		−	1069.47i		−	1.17395i	−0.809605	−	0.586975i	$-0.800319\pi$
$911$		−	1069.47i		−	1.17395i	0.809605	−	0.586975i	$-0.199681\pi$
$912$	−41.1704	−	8.81436i	−0.0451430	−	0.00966487i
$913$	−360.026			−0.394333
$914$			172.992i			0.189269i
$915$	267.315	−	1248.58i	0.292147	−	1.36457i
$916$	681.006			0.743456
$917$			80.5134i			0.0878009i
$918$	185.028	+	135.683i	0.201556	+	0.147803i
$919$	344.468			0.374830			0.187415	−	0.982281i	$-0.439989\pi$
$919$	344.468			0.374830			0.187415	+	0.982281i	$0.439989\pi$
$920$		−	385.446i		−	0.418963i
$921$	1340.99	+	287.099i	1.45602	+	0.311725i
$922$	−238.844			−0.259050
$923$		−	375.009i		−	0.406294i
$924$	−2.24756	+	10.4980i	−0.00243242	+	0.0113614i
$925$	−545.658			−0.589901
$926$			812.077i			0.876973i
$927$	336.036	+	150.799i	0.362498	+	0.162674i
$928$	274.856			0.296181
$929$		−	380.895i		−	0.410005i	−0.978761	−	0.205003i	$-0.934280\pi$
$929$		−	380.895i		−	0.410005i	0.978761	−	0.205003i	$-0.0657203\pi$
$930$	−21.5602	−	4.61592i	−0.0231830	−	0.00496336i
$931$	171.433			0.184139
$932$		−	285.893i		−	0.306752i
$933$	−69.4741	+	324.502i	−0.0744631	+	0.347804i
$934$	−715.486			−0.766045
$935$		−	114.939i		−	0.122929i
$936$	−37.5778	+	83.7371i	−0.0401472	+	0.0894628i
$937$	−803.158			−0.857159			−0.428579	−	0.903504i	$-0.640986\pi$
$937$	−803.158			−0.857159			−0.428579	+	0.903504i	$0.640986\pi$
$938$			38.4634i			0.0410058i
$939$	296.407	+	63.4592i	0.315663	+	0.0675817i
$940$	431.292			0.458821
$941$			1298.53i			1.37995i	0.723833	+	0.689976i	$0.242379\pi$
$941$			1298.53i			1.37995i	−0.723833	+	0.689976i	$0.757621\pi$
$942$	73.1565	−	341.702i	0.0776609	−	0.362741i
$943$	1701.69			1.80455
$944$		−	247.843i		−	0.262546i
$945$	−23.7842	+	32.4341i	−0.0251684	+	0.0343218i
$946$	324.006			0.342502
$947$		−	111.604i		−	0.117850i	−0.998262	−	0.0589250i	$-0.981233\pi$
$947$		−	111.604i		−	0.117850i	0.998262	−	0.0589250i	$-0.0187673\pi$
$948$	67.3925	+	14.4284i	0.0710891	+	0.0152198i
$949$	188.630			0.198767
$950$		−	45.0334i		−	0.0474036i
$951$	285.742	−	1334.65i	0.300465	−	1.40342i
$952$	−6.34449			−0.00666438
$953$		−	969.562i		−	1.01738i	−0.860950	−	0.508690i	$-0.830130\pi$
$953$		−	969.562i		−	1.01738i	0.860950	−	0.508690i	$-0.169870\pi$
$954$	−1024.27	−	459.650i	−1.07366	−	0.481814i
$955$	−579.904			−0.607229
$956$			106.290i			0.111182i
$957$	−683.210	−	146.272i	−0.713908	−	0.152844i
$958$	−248.413			−0.259303
$959$		−	29.7331i		−	0.0310043i
$960$	20.0500	−	93.6501i	0.0208854	−	0.0975522i
$961$	−959.304			−0.998235
$962$			306.566i			0.318675i
$963$	150.134	−	334.554i	0.155903	−	0.347408i
$964$	−822.316			−0.853025
$965$			477.619i			0.494942i
$966$	52.8865	+	11.3227i	0.0547479	+	0.0117212i
$967$	−18.8423			−0.0194853			−0.00974267	−	0.999953i	$-0.503101\pi$
$967$	−18.8423			−0.0194853			−0.00974267	+	0.999953i	$0.503101\pi$
$968$		−	277.254i		−	0.286420i
$969$	−13.2413	+	61.8481i	−0.0136650	+	0.0638267i
$970$	−118.773			−0.122446
$971$			1145.61i			1.17983i	0.807466	+	0.589915i	$0.200839\pi$
$971$			1145.61i			1.17983i	−0.807466	+	0.589915i	$0.799161\pi$
$972$	−239.897	−	422.664i	−0.246808	−	0.434840i
$973$	14.5948			0.0149998
$974$		−	1075.21i		−	1.10391i
$975$	−95.9942	−	20.5519i	−0.0984556	−	0.0210788i
$976$	−426.637			−0.437128
$977$		−	182.413i		−	0.186707i	−0.995633	−	0.0933536i	$-0.970241\pi$
$977$		−	182.413i		−	0.186707i	0.995633	−	0.0933536i	$-0.0297587\pi$
$978$	230.183	−	1075.14i	0.235361	−	1.09933i
$979$	260.095			0.265674
$980$			389.958i			0.397917i
$981$	−477.705	−	214.375i	−0.486957	−	0.218527i
$982$	908.219			0.924866
$983$		−	700.294i		−	0.712405i	−0.934409	−	0.356203i	$-0.884071\pi$
$983$		−	700.294i		−	0.712405i	0.934409	−	0.356203i	$-0.115929\pi$
$984$	413.452	+	88.5178i	0.420174	+	0.0899571i
$985$	−270.238			−0.274353
$986$		−	412.901i		−	0.418763i
$987$	−12.6695	+	59.1769i	−0.0128363	+	0.0599563i
$988$	−25.3010			−0.0256083
$989$		−	1632.27i		−	1.65043i
$990$	−99.6768	+	222.117i	−0.100684	+	0.224360i
$991$	1176.47			1.18716			0.593578	−	0.804776i	$-0.297715\pi$
$991$	1176.47			1.18716			0.593578	+	0.804776i	$0.297715\pi$
$992$			7.36706i			0.00742647i
$993$	−1095.04	−	234.442i	−1.10276	−	0.236095i
$994$	−54.9080			−0.0552394
$995$		−	83.9409i		−	0.0843627i
$996$	−94.3461	+	440.674i	−0.0947250	+	0.442444i
$997$	−721.900			−0.724072			−0.362036	−	0.932164i	$-0.617918\pi$
$997$	−721.900			−0.724072			−0.362036	+	0.932164i	$0.617918\pi$
$998$			933.264i			0.935134i
$999$	−1309.06	−	959.942i	−1.31037	−	0.960903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.c.a.53.8	yes	8
3.2	odd	2	inner	78.3.c.a.53.4	✓	8
4.3	odd	2		624.3.f.b.209.1		8
12.11	even	2		624.3.f.b.209.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.c.a.53.4	✓	8	3.2	odd	2	inner
78.3.c.a.53.8	yes	8	1.1	even	1	trivial
624.3.f.b.209.1		8	4.3	odd	2
624.3.f.b.209.2		8	12.11	even	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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(2.93352 + 0.628052i) q^{3} -2.00000 q^{4} +3.99052i q^{5} +(-0.888199 + 4.14863i) q^{6} +0.373294 q^{7} -2.82843i q^{8} +(8.21110 + 3.68481i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(2.93352 + 0.628052i) q^{3} -2.00000 q^{4} +3.99052i q^{5} +(-0.888199 + 4.14863i) q^{6} +0.373294 q^{7} -2.82843i q^{8} +(8.21110 + 3.68481i) q^{9} -5.64344 q^{10} -4.79331i q^{11} +(-5.86704 - 1.25610i) q^{12} -3.60555 q^{13} +0.527917i q^{14} +(-2.50625 + 11.7063i) q^{15} +4.00000 q^{16} -6.00898i q^{17} +(-5.21110 + 11.6123i) q^{18} -3.50861 q^{19} -7.98103i q^{20} +(1.09507 + 0.234448i) q^{21} +6.77876 q^{22} -34.1499i q^{23} +(1.77640 - 8.29725i) q^{24} +9.07578 q^{25} -5.09902i q^{26} +(21.7732 + 15.9665i) q^{27} -0.746587 q^{28} -48.5881i q^{29} +(-16.5552 - 3.54437i) q^{30} +1.30232 q^{31} +5.65685i q^{32} +(3.01045 - 14.0613i) q^{33} +8.49799 q^{34} +1.48963i q^{35} +(-16.4222 - 7.36961i) q^{36} -60.1225 q^{37} -4.96193i q^{38} +(-10.5770 - 2.26447i) q^{39} +11.2869 q^{40} +49.8299i q^{41} +(-0.331559 + 1.54866i) q^{42} +47.7973 q^{43} +9.58662i q^{44} +(-14.7043 + 32.7665i) q^{45} +48.2953 q^{46} +54.0396i q^{47} +(11.7341 + 2.51221i) q^{48} -48.8607 q^{49} +12.8351i q^{50} +(3.77395 - 17.6275i) q^{51} +7.21110 q^{52} +88.2060i q^{53} +(-22.5800 + 30.7920i) q^{54} +19.1278 q^{55} -1.05583i q^{56} +(-10.2926 - 2.20359i) q^{57} +68.7139 q^{58} -61.9608i q^{59} +(5.01250 - 23.4125i) q^{60} -106.659 q^{61} +1.84176i q^{62} +(3.06515 + 1.37551i) q^{63} -8.00000 q^{64} -14.3880i q^{65} +(19.8857 + 4.25741i) q^{66} +72.8589 q^{67} +12.0180i q^{68} +(21.4479 - 100.180i) q^{69} -2.10666 q^{70} +104.009i q^{71} +(10.4222 - 23.2245i) q^{72} -52.3165 q^{73} -85.0260i q^{74} +(26.6240 + 5.70006i) q^{75} +7.01723 q^{76} -1.78931i q^{77} +(3.20245 - 14.9581i) q^{78} -11.4866 q^{79} +15.9621i q^{80} +(53.8444 + 60.5126i) q^{81} -70.4702 q^{82} -75.1101i q^{83} +(-2.19013 - 0.468895i) q^{84} +23.9789 q^{85} +67.5956i q^{86} +(30.5158 - 142.534i) q^{87} -13.5575 q^{88} +54.2621i q^{89} +(-46.3389 - 20.7950i) q^{90} -1.34593 q^{91} +68.2998i q^{92} +(3.82040 + 0.817927i) q^{93} -76.4235 q^{94} -14.0012i q^{95} +(-3.55280 + 16.5945i) q^{96} +21.0461 q^{97} -69.0994i q^{98} +(17.6624 - 39.3584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{4} - 8 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 16 * q^4 - 8 * q^7 + 8 * q^9	\( 8 q - 16 q^{4} - 8 q^{7} + 8 q^{9} + 16 q^{10} - 56 q^{15} + 32 q^{16} + 16 q^{18} - 24 q^{19} + 88 q^{21} + 8 q^{25} + 16 q^{28} - 64 q^{30} - 72 q^{31} - 56 q^{33} - 112 q^{34} - 16 q^{36} + 96 q^{37} - 32 q^{40} + 80 q^{42} + 208 q^{43} - 16 q^{45} + 32 q^{46} - 24 q^{49} + 112 q^{51} - 176 q^{55} + 40 q^{57} + 176 q^{58} + 112 q^{60} - 272 q^{61} - 216 q^{63} - 64 q^{64} - 64 q^{66} + 264 q^{67} - 240 q^{69} - 32 q^{70} - 32 q^{72} - 416 q^{73} + 128 q^{75} + 48 q^{76} + 160 q^{79} + 200 q^{81} + 176 q^{82} - 176 q^{84} + 464 q^{85} + 384 q^{87} + 16 q^{90} + 104 q^{91} - 264 q^{93} - 384 q^{94} - 16 q^{97} + 416 q^{99}+O(q^{100}) \) 8 * q - 16 * q^4 - 8 * q^7 + 8 * q^9 + 16 * q^10 - 56 * q^15 + 32 * q^16 + 16 * q^18 - 24 * q^19 + 88 * q^21 + 8 * q^25 + 16 * q^28 - 64 * q^30 - 72 * q^31 - 56 * q^33 - 112 * q^34 - 16 * q^36 + 96 * q^37 - 32 * q^40 + 80 * q^42 + 208 * q^43 - 16 * q^45 + 32 * q^46 - 24 * q^49 + 112 * q^51 - 176 * q^55 + 40 * q^57 + 176 * q^58 + 112 * q^60 - 272 * q^61 - 216 * q^63 - 64 * q^64 - 64 * q^66 + 264 * q^67 - 240 * q^69 - 32 * q^70 - 32 * q^72 - 416 * q^73 + 128 * q^75 + 48 * q^76 + 160 * q^79 + 200 * q^81 + 176 * q^82 - 176 * q^84 + 464 * q^85 + 384 * q^87 + 16 * q^90 + 104 * q^91 - 264 * q^93 - 384 * q^94 - 16 * q^97 + 416 * q^99

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