LMFDB - Embedded newform 115.7.c.c.114.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	115.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:	$26.4562196163$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.17
Character	$\chi$	$=$	115.114
Dual form			115.7.c.c.114.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0499926i q^{2} +38.9668i q^{3} +63.9975 q^{4} +(95.0255 + 81.2106i) q^{5} +1.94805 q^{6} -273.692 q^{7} -6.39893i q^{8} -789.409 q^{9} +O(q^{10})$	\(q-0.0499926i q^{2} +38.9668i q^{3} +63.9975 q^{4} +(95.0255 + 81.2106i) q^{5} +1.94805 q^{6} -273.692 q^{7} -6.39893i q^{8} -789.409 q^{9} +(4.05993 - 4.75057i) q^{10} +242.304i q^{11} +2493.78i q^{12} +3670.46i q^{13} +13.6826i q^{14} +(-3164.51 + 3702.84i) q^{15} +4095.52 q^{16} -5119.28 q^{17} +39.4646i q^{18} -6778.31i q^{19} +(6081.39 + 5197.27i) q^{20} -10664.9i q^{21} +12.1134 q^{22} +(11478.8 - 4034.10i) q^{23} +249.346 q^{24} +(2434.68 + 15434.1i) q^{25} +183.496 q^{26} -2353.96i q^{27} -17515.6 q^{28} -8879.57 q^{29} +(185.114 + 158.202i) q^{30} -13097.7 q^{31} -614.277i q^{32} -9441.79 q^{33} +255.926i q^{34} +(-26007.7 - 22226.7i) q^{35} -50520.2 q^{36} +26655.0 q^{37} -338.865 q^{38} -143026. q^{39} +(519.661 - 608.061i) q^{40} +15621.1 q^{41} -533.166 q^{42} -12013.8 q^{43} +15506.8i q^{44} +(-75014.0 - 64108.4i) q^{45} +(-201.675 - 573.853i) q^{46} +79285.9i q^{47} +159589. i q^{48} -42741.5 q^{49} +(771.593 - 121.716i) q^{50} -199482. i q^{51} +234900. i q^{52} -117940. q^{53} -117.680 q^{54} +(-19677.6 + 23025.0i) q^{55} +1751.34i q^{56} +264129. q^{57} +443.913i q^{58} -139779. q^{59} +(-202521. + 236972. i) q^{60} -364167. i q^{61} +654.785i q^{62} +216055. q^{63} +262083. q^{64} +(-298080. + 348787. i) q^{65} +472.020i q^{66} +122330. q^{67} -327621. q^{68} +(157196. + 447290. i) q^{69} +(-1111.17 + 1300.19i) q^{70} +461792. q^{71} +5051.37i q^{72} -115836. i q^{73} -1332.55i q^{74} +(-601419. + 94871.6i) q^{75} -433795. i q^{76} -66316.7i q^{77} +7150.24i q^{78} +110461. i q^{79} +(389179. + 332600. i) q^{80} -483753. q^{81} -780.938i q^{82} +251740. q^{83} -682528. i q^{84} +(-486462. - 415740. i) q^{85} +600.603i q^{86} -346008. i q^{87} +1550.48 q^{88} +428905. i q^{89} +(-3204.94 + 3750.14i) q^{90} -1.00458e6i q^{91} +(734612. - 258173. i) q^{92} -510373. i q^{93} +3963.71 q^{94} +(550470. - 644112. i) q^{95} +23936.4 q^{96} -727617. q^{97} +2136.76i q^{98} -191277. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	0.0499926i		−	0.00624907i	−0.999995	−	0.00312454i	$-0.999005\pi$
$2$		−	0.0499926i		−	0.00624907i	0.999995	−	0.00312454i	$-0.000994573\pi$
$3$			38.9668i			1.44321i	0.692303	+	0.721607i	$0.256596\pi$
$3$			38.9668i			1.44321i	−0.692303	+	0.721607i	$0.743404\pi$
$4$	63.9975			0.999961
$5$	95.0255	+	81.2106i	0.760204	+	0.649685i
$5$	95.0255	+	81.2106i	0.760204	+	0.649685i
$6$	1.94805			0.00901875
$7$	−273.692			−0.797937			−0.398969	−	0.916965i	$-0.630632\pi$
$7$	−273.692			−0.797937			−0.398969	+	0.916965i	$0.630632\pi$
$8$		−	6.39893i		−	0.0124979i
$9$	−789.409			−1.08287
$10$	4.05993	−	4.75057i	0.00405993	−	0.00475057i
$11$			242.304i			0.182046i	0.995849	+	0.0910232i	$0.0290137\pi$
$11$			242.304i			0.182046i	−0.995849	+	0.0910232i	$0.970986\pi$
$12$			2493.78i			1.44316i
$13$			3670.46i			1.67067i	0.549742	+	0.835335i	$0.314726\pi$
$13$			3670.46i			1.67067i	−0.549742	+	0.835335i	$0.685274\pi$
$14$			13.6826i			0.00498637i
$15$	−3164.51	+	3702.84i	−0.937634	+	1.09714i
$16$	4095.52			0.999883
$17$	−5119.28			−1.04199			−0.520993	−	0.853561i	$-0.674438\pi$
$17$	−5119.28			−1.04199			−0.520993	+	0.853561i	$0.674438\pi$
$18$			39.4646i			0.00676691i
$19$		−	6778.31i		−	0.988235i	−0.869395	−	0.494118i	$-0.835491\pi$
$19$		−	6778.31i		−	0.988235i	0.869395	−	0.494118i	$-0.164509\pi$
$20$	6081.39	+	5197.27i	0.760174	+	0.649659i
$21$		−	10664.9i		−	1.15159i
$22$	12.1134			0.00113762
$23$	11478.8	−	4034.10i	0.943434	−	0.331561i
$23$	11478.8	−	4034.10i	0.943434	−	0.331561i
$24$	249.346			0.0180371
$25$	2434.68	+	15434.1i	0.155820	+	0.987786i
$26$	183.496			0.0104401
$27$		−	2353.96i		−	0.119594i
$28$	−17515.6			−0.797906
$29$	−8879.57			−0.364081			−0.182040	−	0.983291i	$-0.558270\pi$
$29$	−8879.57			−0.364081			−0.182040	+	0.983291i	$0.558270\pi$
$30$	185.114	+	158.202i	0.00685609	+	0.00585934i
$31$	−13097.7			−0.439651			−0.219826	−	0.975539i	$-0.570549\pi$
$31$	−13097.7			−0.439651			−0.219826	+	0.975539i	$0.570549\pi$
$32$		−	614.277i		−	0.0187462i
$33$	−9441.79			−0.262732
$34$			255.926i			0.00651145i
$35$	−26007.7	−	22226.7i	−0.606595	−	0.518407i
$36$	−50520.2			−1.08282
$37$	26655.0			0.526226			0.263113	−	0.964765i	$-0.415251\pi$
$37$	26655.0			0.526226			0.263113	+	0.964765i	$0.415251\pi$
$38$	−338.865			−0.00617555
$39$	−143026.			−2.41113
$40$	519.661	−	608.061i	0.00811970	−	0.00950095i
$41$	15621.1			0.226652			0.113326	−	0.993558i	$-0.463850\pi$
$41$	15621.1			0.226652			0.113326	+	0.993558i	$0.463850\pi$
$42$	−533.166			−0.00719639
$43$	−12013.8			−0.151104			−0.0755521	−	0.997142i	$-0.524072\pi$
$43$	−12013.8			−0.151104			−0.0755521	+	0.997142i	$0.524072\pi$
$44$			15506.8i			0.182039i
$45$	−75014.0	−	64108.4i	−0.823199	−	0.703522i
$46$	−201.675	−	573.853i	−0.00207195	−	0.00589559i
$47$			79285.9i			0.763664i	0.924232	+	0.381832i	$0.124707\pi$
$47$			79285.9i			0.763664i	−0.924232	+	0.381832i	$0.875293\pi$
$48$			159589.i			1.44304i
$49$	−42741.5			−0.363297
$50$	771.593	−	121.716i	0.00617274	−	0.000973728i
$51$		−	199482.i		−	1.50381i
$52$			234900.i			1.67060i
$53$	−117940.			−0.792200			−0.396100	−	0.918207i	$-0.629637\pi$
$53$	−117940.			−0.792200			−0.396100	+	0.918207i	$0.629637\pi$
$54$	−117.680			−0.000747349
$55$	−19677.6	+	23025.0i	−0.118273	+	0.138392i
$56$			1751.34i			0.00997254i
$57$	264129.			1.42623
$58$			443.913i			0.00227517i
$59$	−139779.			−0.680589			−0.340294	−	0.940319i	$-0.610527\pi$
$59$	−139779.			−0.680589			−0.340294	+	0.940319i	$0.610527\pi$
$60$	−202521.	+	236972.i	−0.937597	+	1.09709i
$61$		−	364167.i		−	1.60439i	−0.597060	−	0.802196i	$-0.703665\pi$
$61$		−	364167.i		−	1.60439i	0.597060	−	0.802196i	$-0.296335\pi$
$62$			654.785i			0.00274741i
$63$	216055.			0.864059
$64$	262083.			0.999766
$65$	−298080.	+	348787.i	−1.08541	+	1.27005i
$66$			472.020i			0.00164183i
$67$	122330.			0.406732			0.203366	−	0.979103i	$-0.434812\pi$
$67$	122330.			0.406732			0.203366	+	0.979103i	$0.434812\pi$
$68$	−327621.			−1.04195
$69$	157196.	+	447290.i	0.478514	+	1.36158i
$70$	−1111.17	+	1300.19i	−0.00323957	+	0.00379065i
$71$	461792.			1.29024			0.645121	−	0.764080i	$-0.276807\pi$
$71$	461792.			1.29024			0.645121	+	0.764080i	$0.276807\pi$
$72$			5051.37i			0.0135336i
$73$		−	115836.i		−	0.297765i	−0.988855	−	0.148882i	$-0.952432\pi$
$73$		−	115836.i		−	0.297765i	0.988855	−	0.148882i	$-0.0475676\pi$
$74$		−	1332.55i		−	0.00328843i
$75$	−601419.	+	94871.6i	−1.42559	+	0.224881i
$76$		−	433795.i		−	0.988197i
$77$		−	66316.7i		−	0.145261i
$78$			7150.24i			0.0150673i
$79$			110461.i			0.224041i	0.993706	+	0.112021i	$0.0357323\pi$
$79$			110461.i			0.224041i	−0.993706	+	0.112021i	$0.964268\pi$
$80$	389179.	+	332600.i	0.760115	+	0.649609i
$81$	−483753.			−0.910267
$82$		−	780.938i		−	0.00141636i
$83$	251740.			0.440270			0.220135	−	0.975469i	$-0.429350\pi$
$83$	251740.			0.440270			0.220135	+	0.975469i	$0.429350\pi$
$84$		−	682528.i		−	1.15155i
$85$	−486462.	−	415740.i	−0.792122	−	0.676963i
$86$			600.603i			0.000944261i
$87$		−	346008.i		−	0.525446i
$88$	1550.48			0.00227520
$89$			428905.i			0.608403i	0.952608	+	0.304202i	$0.0983897\pi$
$89$			428905.i			0.608403i	−0.952608	+	0.304202i	$0.901610\pi$
$90$	−3204.94	+	3750.14i	−0.00439636	+	0.00514423i
$91$		−	1.00458e6i		−	1.33309i
$92$	734612.	−	258173.i	0.943397	−	0.331548i
$93$		−	510373.i		−	0.634511i
$94$	3963.71			0.00477219
$95$	550470.	−	644112.i	0.642041	−	0.751260i
$96$	23936.4			0.0270548
$97$	−727617.			−0.797237			−0.398618	−	0.917117i	$-0.630510\pi$
$97$	−727617.			−0.797237			−0.398618	+	0.917117i	$0.630510\pi$
$98$			2136.76i			0.00227027i
$99$		−	191277.i		−	0.197132i
$100$	155813.	+	987747.i	0.155813	+	0.987747i
$101$	1.43516e6			1.39296			0.696478	−	0.717578i	$-0.254749\pi$
$101$	1.43516e6			1.39296			0.696478	+	0.717578i	$0.254749\pi$
$102$	−9972.61			−0.00939741
$103$	987945.			0.904109			0.452055	−	0.891990i	$-0.350691\pi$
$103$	987945.			0.904109			0.452055	+	0.891990i	$0.350691\pi$
$104$	23487.0			0.0208799
$105$	866104.	−	1.01344e6i	0.748173	−	0.875446i
$106$			5896.15i			0.00495052i
$107$	−1.58629e6			−1.29488			−0.647442	−	0.762114i	$-0.724161\pi$
$107$	−1.58629e6			−1.29488			−0.647442	+	0.762114i	$0.724161\pi$
$108$		−	150647.i		−	0.119589i
$109$			2.33325e6i			1.80170i	0.434131	+	0.900850i	$0.357056\pi$
$109$			2.33325e6i			1.80170i	−0.434131	+	0.900850i	$0.642944\pi$
$110$	1151.08	+	983.735i	0.000864824	+	0.000739095i
$111$			1.03866e6i			0.759457i
$112$	−1.12091e6			−0.797844
$113$	2.49865e6			1.73169			0.865847	−	0.500310i	$-0.166780\pi$
$113$	2.49865e6			1.73169			0.865847	+	0.500310i	$0.166780\pi$
$114$		−	13204.5i		−	0.00891265i
$115$	1.41839e6	+	548854.i	0.932612	+	0.360880i
$116$	−568270.			−0.364067
$117$		−	2.89750e6i		−	1.80911i
$118$			6987.89i			0.00425305i
$119$	1.40111e6			0.831439
$120$	23694.2	+	20249.5i	0.0137119	+	0.0117185i
$121$	1.71285e6			0.966859
$122$	−18205.6			−0.0100260
$123$			608703.i			0.327107i
$124$	−838217.			−0.439634
$125$	−1.02206e6	+	1.66436e6i	−0.523295	+	0.852152i
$126$		−	10801.2i		−	0.00539957i
$127$			1.78708e6i			0.872434i	0.899842	+	0.436217i	$0.143682\pi$
$127$			1.78708e6i			0.872434i	−0.899842	+	0.436217i	$0.856318\pi$
$128$		−	52415.9i		−	0.0249939i
$129$		−	468140.i		−	0.218076i
$130$	17436.8	+	14901.8i	0.00793663	+	0.00678280i
$131$	4.16712e6			1.85363			0.926813	−	0.375524i	$-0.122537\pi$
$131$	4.16712e6			1.85363			0.926813	+	0.375524i	$0.122537\pi$
$132$	−604251.			−0.262721
$133$			1.85517e6i			0.788549i
$134$		−	6115.58i		−	0.00254170i
$135$	191166.	−	223686.i	0.0776981	−	0.0909154i
$136$			32757.9i			0.0130226i
$137$	1.52099e6			0.591515			0.295758	−	0.955263i	$-0.404428\pi$
$137$	1.52099e6			0.591515			0.295758	+	0.955263i	$0.404428\pi$
$138$	22361.2	−	7858.64i	0.00850859	−	0.00299027i
$139$	2.21822e6			0.825963			0.412982	−	0.910739i	$-0.364487\pi$
$139$	2.21822e6			0.825963			0.412982	+	0.910739i	$0.364487\pi$
$140$	−1.66443e6	−	1.42245e6i	−0.606571	−	0.518387i
$141$	−3.08952e6			−1.10213
$142$		−	23086.2i		−	0.00806282i
$143$	−889366.			−0.304139
$144$	−3.23304e6			−1.08274
$145$	−843785.	−	721115.i	−0.276776	−	0.236538i
$146$	−5790.92			−0.00186076
$147$		−	1.66550e6i		−	0.524315i
$148$	1.70585e6			0.526206
$149$		−	3.80088e6i		−	1.14902i	−0.818499	−	0.574508i	$-0.805194\pi$
$149$		−	3.80088e6i		−	1.14902i	0.818499	−	0.574508i	$-0.194806\pi$
$150$	4742.88	+	30066.5i	0.00140530	+	0.00890859i
$151$	358833.			0.104223			0.0521113	−	0.998641i	$-0.483405\pi$
$151$	358833.			0.104223			0.0521113	+	0.998641i	$0.483405\pi$
$152$	−43373.9			−0.0123509
$153$	4.04121e6			1.12833
$154$	−3315.34			−0.000907750
$155$	−1.24461e6	−	1.06367e6i	−0.334225	−	0.285635i
$156$	−9.15331e6			−2.41104
$157$	−5.76792e6			−1.49046			−0.745229	−	0.666808i	$-0.767660\pi$
$157$	−5.76792e6			−1.49046			−0.745229	+	0.666808i	$0.767660\pi$
$158$	5522.23			0.00140005
$159$		−	4.59576e6i		−	1.14331i
$160$	49885.8	−	58372.0i	0.0121791	−	0.0142510i
$161$	−3.14165e6	+	1.10410e6i	−0.752801	+	0.264565i
$162$			24184.1i			0.00568833i
$163$			497854.i			0.114958i	0.998347	+	0.0574790i	$0.0183062\pi$
$163$			497854.i			0.114958i	−0.998347	+	0.0574790i	$0.981694\pi$
$164$	999710.			0.226643
$165$	−897211.	−	766773.i	−0.199730	−	0.170693i
$166$		−	12585.2i		−	0.00275128i
$167$			6.49481e6i			1.39449i	0.716831	+	0.697247i	$0.245592\pi$
$167$			6.49481e6i			1.39449i	−0.716831	+	0.697247i	$0.754408\pi$
$168$	−68244.0			−0.0143925
$169$	−8.64548e6			−1.79114
$170$	−20783.9	+	24319.5i	−0.00423039	+	0.00495003i
$171$			5.35086e6i			1.07013i
$172$	−768856.			−0.151098
$173$			2.74052e6i			0.529291i	0.964346	+	0.264645i	$0.0852549\pi$
$173$			2.74052e6i			0.529291i	−0.964346	+	0.264645i	$0.914745\pi$
$174$	−17297.8			−0.00328355
$175$	−666353.	−	4.22421e6i	−0.124334	−	0.788191i
$176$			992359.i			0.182025i
$177$		−	5.44672e6i		−	0.982235i
$178$	21442.1			0.00380196
$179$	7.64370e6			1.33274			0.666369	−	0.745622i	$-0.267848\pi$
$179$	7.64370e6			1.33274			0.666369	+	0.745622i	$0.267848\pi$
$180$	−4.80071e6	−	4.10278e6i	−0.823167	−	0.703494i
$181$			6.05322e6i			1.02082i	0.859930	+	0.510411i	$0.170507\pi$
$181$			6.05322e6i			1.02082i	−0.859930	+	0.510411i	$0.829493\pi$
$182$	−50221.4			−0.00833057
$183$	1.41904e7			2.31548
$184$	−25813.9	−	73451.7i	−0.00414382	−	0.0117909i
$185$	2.53290e6	+	2.16466e6i	0.400039	+	0.341881i
$186$	−25514.9			−0.00396510
$187$		−	1.24042e6i		−	0.189690i
$188$			5.07410e6i			0.763634i
$189$			644261.i			0.0954281i
$190$	−32200.8	−	27519.4i	−0.00469468	−	0.00401216i
$191$			6.19579e6i			0.889194i	0.895731	+	0.444597i	$0.146653\pi$
$191$			6.19579e6i			0.889194i	−0.895731	+	0.444597i	$0.853347\pi$
$192$			1.02125e7i			1.44288i
$193$		−	3.91985e6i		−	0.545252i	−0.962120	−	0.272626i	$-0.912108\pi$
$193$		−	3.91985e6i		−	0.545252i	0.962120	−	0.272626i	$-0.0878921\pi$
$194$			36375.4i			0.00498199i
$195$	−1.35911e7	−	1.16152e7i	−1.83295	−	1.56648i
$196$	−2.73535e6			−0.363282
$197$		−	7.32270e6i		−	0.957794i	−0.877871	−	0.478897i	$-0.841037\pi$
$197$		−	7.32270e6i		−	0.957794i	0.877871	−	0.478897i	$-0.158963\pi$
$198$	−9562.42			−0.00123189
$199$			1.21278e7i			1.53894i	0.638682	+	0.769471i	$0.279480\pi$
$199$			1.21278e7i			1.53894i	−0.638682	+	0.769471i	$0.720520\pi$
$200$	98762.0	−	15579.3i	0.0123452	−	0.00194742i
$201$			4.76680e6i			0.587001i
$202$		−	71747.5i		−	0.00870468i
$203$	2.43027e6			0.290514
$204$		−	1.27663e7i		−	1.50375i
$205$	1.48440e6	+	1.26860e6i	0.172302	+	0.147252i
$206$		−	49389.9i		−	0.00564985i
$207$	−9.06144e6	+	3.18456e6i	−1.02161	+	0.359036i
$208$			1.50324e7i			1.67047i
$209$	1.64241e6			0.179905
$210$	−50664.4	−	43298.8i	−0.00547073	−	0.00467539i
$211$	1.69614e6			0.180557			0.0902785	−	0.995917i	$-0.471224\pi$
$211$	1.69614e6			0.180557			0.0902785	+	0.995917i	$0.471224\pi$
$212$	−7.54789e6			−0.792169
$213$			1.79945e7i			1.86210i
$214$			79302.7i			0.00809183i
$215$	−1.14162e6	−	975651.i	−0.114870	−	0.0981701i
$216$	−15062.8			−0.00149467
$217$	3.58473e6			0.350814
$218$	116645.			0.0112590
$219$	4.51374e6			0.429739
$220$	−1.25932e6	+	1.47354e6i	−0.118268	+	0.138387i
$221$		−	1.87901e7i		−	1.74081i
$222$	51925.2			0.00474590
$223$		−	4.84477e6i		−	0.436877i	−0.975851	−	0.218438i	$-0.929904\pi$
$223$		−	4.84477e6i		−	0.436877i	0.975851	−	0.218438i	$-0.0700963\pi$
$224$			168123.i			0.0149583i
$225$	−1.92196e6	−	1.21839e7i	−0.168732	−	1.06964i
$226$		−	124914.i		−	0.0108215i
$227$	9.20933e6			0.787318			0.393659	−	0.919256i	$-0.371209\pi$
$227$	9.20933e6			0.787318			0.393659	+	0.919256i	$0.371209\pi$
$228$	1.69036e7			1.42618
$229$			1.20553e7i			1.00385i	0.864910	+	0.501926i	$0.167375\pi$
$229$			1.20553e7i			1.00385i	−0.864910	+	0.501926i	$0.832625\pi$
$230$	27438.6	−	70908.8i	0.00225517	−	0.00582796i
$231$	2.58415e6			0.209643
$232$			56819.7i			0.00455025i
$233$		−	1.66052e7i		−	1.31273i	−0.754441	−	0.656367i	$-0.772092\pi$
$233$		−	1.66052e7i		−	1.31273i	0.754441	−	0.656367i	$-0.227908\pi$
$234$	−144853.			−0.0113053
$235$	−6.43885e6	+	7.53418e6i	−0.496141	+	0.580540i
$236$	−8.94548e6			−0.680562
$237$	−4.30431e6			−0.323339
$238$		−	70045.0i		−	0.00519573i
$239$	−1.89952e6			−0.139139			−0.0695696	−	0.997577i	$-0.522163\pi$
$239$	−1.89952e6			−0.139139			−0.0695696	+	0.997577i	$0.522163\pi$
$240$	−1.29603e7	+	1.51650e7i	−0.937524	+	1.09701i
$241$		−	1.42080e7i		−	1.01504i	−0.861641	−	0.507518i	$-0.830563\pi$
$241$		−	1.42080e7i		−	1.01504i	0.861641	−	0.507518i	$-0.169437\pi$
$242$		−	85629.8i		−	0.00604197i
$243$		−	2.05663e7i		−	1.43330i
$244$		−	2.33058e7i		−	1.60433i
$245$	−4.06153e6	−	3.47106e6i	−0.276179	−	0.236028i
$246$	30430.6			0.00204412
$247$	2.48795e7			1.65101
$248$			83810.9i			0.00549472i
$249$			9.80951e6i			0.635403i
$250$	83205.6	+	51095.4i	0.00532516	+	0.00327011i
$251$			1.82680e7i			1.15523i	0.816308	+	0.577617i	$0.196017\pi$
$251$			1.82680e7i			1.15523i	−0.816308	+	0.577617i	$0.803983\pi$
$252$	1.38270e7			0.864025
$253$	977478.	+	2.78134e6i	0.0603595	+	0.171749i
$254$	89340.7			0.00545190
$255$	1.62000e7	−	1.89559e7i	0.977002	−	1.14320i
$256$	1.67707e7			0.999610
$257$		−	1.66413e7i		−	0.980368i	−0.871619	−	0.490184i	$-0.836930\pi$
$257$		−	1.66413e7i		−	0.980368i	0.871619	−	0.490184i	$-0.163070\pi$
$258$	−23403.6			−0.00136277
$259$	−7.29526e6			−0.419896
$260$	−1.90764e7	+	2.23215e7i	−1.08537	+	1.27000i
$261$	7.00961e6			0.394251
$262$		−	208325.i		−	0.0115834i
$263$	2.35711e7			1.29572			0.647861	−	0.761759i	$-0.275664\pi$
$263$	2.35711e7			1.29572			0.647861	+	0.761759i	$0.275664\pi$
$264$			60417.3i			0.00328360i
$265$	−1.12073e7	−	9.57801e6i	−0.602234	−	0.514680i
$266$	92744.8			0.00492770
$267$	−1.67131e7			−0.878056
$268$	7.82880e6			0.406716
$269$	−2.23646e7			−1.14896			−0.574479	−	0.818519i	$-0.694795\pi$
$269$	−2.23646e7			−1.14896			−0.574479	+	0.818519i	$0.694795\pi$
$270$	−11182.6	−	9556.90i	−0.000568137	−	0.000485541i
$271$	2.47493e7			1.24353			0.621764	−	0.783205i	$-0.286416\pi$
$271$	2.47493e7			1.24353			0.621764	+	0.783205i	$0.286416\pi$
$272$	−2.09661e7			−1.04186
$273$	3.91451e7			1.92393
$274$		−	76038.4i		−	0.00369642i
$275$	−3.73975e6	+	589932.i	−0.179823	+	0.0283664i
$276$	1.00602e7	+	2.86255e7i	0.478495	+	1.36152i
$277$		−	2.41469e7i		−	1.13612i	−0.822989	−	0.568058i	$-0.807695\pi$
$277$		−	2.41469e7i		−	1.13612i	0.822989	−	0.568058i	$-0.192305\pi$
$278$		−	110895.i		−	0.00516151i
$279$	1.03394e7			0.476083
$280$	−142227.	+	166422.i	−0.00647901	+	0.00758116i
$281$		−	3.36563e7i		−	1.51687i	−0.651749	−	0.758434i	$-0.725965\pi$
$281$		−	3.36563e7i		−	1.51687i	0.651749	−	0.758434i	$-0.274035\pi$
$282$			154453.i			0.00688729i
$283$	−3.84160e7			−1.69493			−0.847466	−	0.530850i	$-0.821873\pi$
$283$	−3.84160e7			−1.69493			−0.847466	+	0.530850i	$0.821873\pi$
$284$	2.95535e7			1.29019
$285$	2.50990e7	+	2.14500e7i	1.08423	+	0.926603i
$286$			44461.7i			0.00190059i
$287$	−4.27537e6			−0.180854
$288$			484916.i			0.0202997i
$289$	2.06945e6			0.0857356
$290$	−36050.4	+	42183.0i	−0.00147814	+	0.00172959i
$291$		−	2.83529e7i		−	1.15058i
$292$		−	7.41319e6i		−	0.297753i
$293$	3.66623e7			1.45753			0.728764	−	0.684765i	$-0.240095\pi$
$293$	3.66623e7			1.45753			0.728764	+	0.684765i	$0.240095\pi$
$294$	−83262.5			−0.00327648
$295$	−1.32825e7	−	1.13515e7i	−0.517386	−	0.442168i
$296$		−	170563.i		−	0.00657673i
$297$	570373.			0.0217716
$298$	−190016.			−0.00718028
$299$	1.48070e7	+	4.21323e7i	0.553929	+	1.57617i
$300$	−3.84893e7	+	6.07155e6i	−1.42553	+	0.224872i
$301$	3.28810e6			0.120572
$302$		−	17939.0i		−	0.000651294i
$303$			5.59237e7i			2.01033i
$304$		−	2.77607e7i		−	0.988119i
$305$	2.95742e7	−	3.46051e7i	1.04235	−	1.21967i
$306$		−	202030.i		−	0.00705103i
$307$			3.74473e7i			1.29421i	0.762400	+	0.647106i	$0.224021\pi$
$307$			3.74473e7i			1.29421i	−0.762400	+	0.647106i	$0.775979\pi$
$308$		−	4.24410e6i		−	0.145256i
$309$			3.84970e7i			1.30482i
$310$	−53175.5	+	62221.3i	−0.00178495	+	0.00208859i
$311$	1.43449e6			0.0476887			0.0238444	−	0.999716i	$-0.492409\pi$
$311$	1.43449e6			0.0476887			0.0238444	+	0.999716i	$0.492409\pi$
$312$			915213.i			0.0301341i
$313$	2.29301e7			0.747778			0.373889	−	0.927473i	$-0.378024\pi$
$313$	2.29301e7			0.747778			0.373889	+	0.927473i	$0.378024\pi$
$314$			288353.i			0.00931399i
$315$	2.05308e7	+	1.75460e7i	0.656861	+	0.561366i
$316$			7.06923e6i			0.224032i
$317$			217347.i			0.00682301i	0.999994	+	0.00341151i	$0.00108592\pi$
$317$			217347.i			0.00682301i	−0.999994	+	0.00341151i	$0.998914\pi$
$318$	−229754.			−0.00714465
$319$		−	2.15155e6i		−	0.0662796i
$320$	2.49045e7	+	2.12839e7i	0.760026	+	0.649532i
$321$		−	6.18126e7i		−	1.86880i
$322$	55197.0	+	157059.i	0.00165329	+	0.00470431i
$323$			3.47000e7i			1.02973i
$324$	−3.09590e7			−0.910232
$325$	−5.66504e7	+	8.93640e6i	−1.65026	+	0.260323i
$326$	24889.0			0.000718381
$327$	−9.09194e7			−2.60024
$328$		−	99958.1i		−	0.00283267i
$329$		−	2.16999e7i		−	0.609356i
$330$	−38333.0	+	44853.9i	−0.00106667	+	0.00124813i
$331$	−5.24148e7			−1.44534			−0.722670	−	0.691193i	$-0.757085\pi$
$331$	−5.24148e7			−1.44534			−0.722670	+	0.691193i	$0.757085\pi$
$332$	1.61108e7			0.440252
$333$	−2.10417e7			−0.569833
$334$	324692.			0.00871430
$335$	1.16244e7	+	9.93448e6i	0.309199	+	0.264247i
$336$		−	4.36784e7i		−	1.15146i
$337$	−6.87525e7			−1.79638			−0.898192	−	0.439604i	$-0.855119\pi$
$337$	−6.87525e7			−1.79638			−0.898192	+	0.439604i	$0.855119\pi$
$338$			432210.i			0.0111929i
$339$			9.73645e7i			2.49920i
$340$	−3.11323e7	−	2.66063e7i	−0.792091	−	0.676936i
$341$		−	3.17361e6i		−	0.0800369i
$342$	267503.			0.00668730
$343$	4.38977e7			1.08782
$344$			76875.7i			0.00188848i
$345$	−2.13871e7	+	5.52699e7i	−0.520828	+	1.34596i
$346$	137006.			0.00330758
$347$		−	5.59687e7i		−	1.33954i	−0.742567	−	0.669771i	$-0.766392\pi$
$347$		−	5.59687e7i		−	1.33954i	0.742567	−	0.669771i	$-0.233608\pi$
$348$		−	2.21437e7i		−	0.525426i
$349$	−2.91358e7			−0.685410			−0.342705	−	0.939443i	$-0.611343\pi$
$349$	−2.91358e7			−0.685410			−0.342705	+	0.939443i	$0.611343\pi$
$350$	−211179.	+	33312.7i	−0.00492546	+	0.000776973i
$351$	8.64011e6			0.199801
$352$	148842.			0.00341268
$353$		−	8.62683e7i		−	1.96122i	−0.195958	−	0.980612i	$-0.562782\pi$
$353$		−	8.62683e7i		−	1.96122i	0.195958	−	0.980612i	$-0.437218\pi$
$354$	−272296.			−0.00613806
$355$	4.38820e7	+	3.75024e7i	0.980847	+	0.838251i
$356$			2.74489e7i			0.608380i
$357$			5.45966e7i			1.19994i
$358$		−	382128.i		−	0.00832837i
$359$		−	4.61290e7i		−	0.996990i	−0.866893	−	0.498495i	$-0.833886\pi$
$359$		−	4.61290e7i		−	0.996990i	0.866893	−	0.498495i	$-0.166114\pi$
$360$	−410225.	+	480009.i	−0.00879254	+	0.0102883i
$361$	1.10045e6			0.0233911
$362$	302616.			0.00637920
$363$			6.67442e7i			1.39538i
$364$		−	6.42904e7i		−	1.33304i
$365$	9.40708e6	−	1.10073e7i	0.193453	−	0.226362i
$366$		−	709415.i		−	0.0144696i
$367$	5.88784e7			1.19113			0.595564	−	0.803308i	$-0.296929\pi$
$367$	5.88784e7			1.19113			0.595564	+	0.803308i	$0.296929\pi$
$368$	4.70115e7	−	1.65218e7i	0.943323	−	0.331522i
$369$	−1.23314e7			−0.245434
$370$	108217.	−	126626.i	0.00213644	−	0.00249988i
$371$	3.22794e7			0.632126
$372$		−	3.26626e7i		−	0.634486i
$373$	−4.61085e7			−0.888494			−0.444247	−	0.895904i	$-0.646529\pi$
$373$	−4.61085e7			−0.888494			−0.444247	+	0.895904i	$0.646529\pi$
$374$	−62011.8			−0.00118539
$375$	−6.48547e7	−	3.98264e7i	−1.22984	−	0.755226i
$376$	507345.			0.00954420
$377$		−	3.25921e7i		−	0.608259i
$378$	32208.3			0.000596337
$379$		−	9.86364e7i		−	1.81184i	−0.423451	−	0.905919i	$-0.639181\pi$
$379$		−	9.86364e7i		−	1.81184i	0.423451	−	0.905919i	$-0.360819\pi$
$380$	3.52287e7	−	4.12215e7i	0.642016	−	0.751231i
$381$	−6.96367e7			−1.25911
$382$	309744.			0.00555664
$383$	−4.46022e6			−0.0793889			−0.0396945	−	0.999212i	$-0.512638\pi$
$383$	−4.46022e6			−0.0793889			−0.0396945	+	0.999212i	$0.512638\pi$
$384$	2.04248e6			0.0360715
$385$	5.38562e6	−	6.30177e6i	0.0943742	−	0.110428i
$386$	−195963.			−0.00340732
$387$	9.48384e6			0.163626
$388$	−4.65656e7			−0.797206
$389$			1.10203e7i			0.187216i	0.995609	+	0.0936079i	$0.0298400\pi$
$389$			1.10203e7i			0.187216i	−0.995609	+	0.0936079i	$0.970160\pi$
$390$	−580675.	+	679455.i	−0.00978903	+	0.0114543i
$391$	−5.87630e7	+	2.06517e7i	−0.983045	+	0.345482i
$392$			273500.i			0.00454044i
$393$			1.62379e8i			2.67518i
$394$	−366081.			−0.00598533
$395$	−8.97061e6	+	1.04966e7i	−0.145556	+	0.170317i
$396$		−	1.22412e7i		−	0.197124i
$397$			6.53323e7i			1.04413i	0.852904	+	0.522067i	$0.174839\pi$
$397$			6.53323e7i			1.04413i	−0.852904	+	0.522067i	$0.825161\pi$
$398$	606299.			0.00961696
$399$	−7.22900e7			−1.13805
$400$	9.97128e6	+	6.32109e7i	0.155801	+	0.987670i
$401$			8.22615e7i			1.27574i	0.770142	+	0.637872i	$0.220185\pi$
$401$			8.22615e7i			1.27574i	−0.770142	+	0.637872i	$0.779815\pi$
$402$	238305.			0.00366821
$403$		−	4.80744e7i		−	0.734512i
$404$	9.18469e7			1.39290
$405$	−4.59689e7	−	3.92859e7i	−0.691988	−	0.591387i
$406$		−	121495.i		−	0.00181544i
$407$			6.45859e6i			0.0957976i
$408$	−1.27647e6			−0.0187945
$409$	−8.15374e6			−0.119176			−0.0595878	−	0.998223i	$-0.518979\pi$
$409$	−8.15374e6			−0.119176			−0.0595878	+	0.998223i	$0.518979\pi$
$410$	63420.4	−	74209.0i	0.000920190	−	0.00107673i
$411$			5.92682e7i			0.853683i
$412$	6.32260e7			0.904074
$413$	3.82563e7			0.543067
$414$	159204.	+	453005.i	0.00224364	+	0.00638413i
$415$	2.39218e7	+	2.04440e7i	0.334695	+	0.286036i
$416$	2.25468e6			0.0313188
$417$			8.64370e7i			1.19204i
$418$		−	82108.2i		−	0.00112424i
$419$			4.11012e7i			0.558744i	0.960183	+	0.279372i	$0.0901262\pi$
$419$			4.11012e7i			0.558744i	−0.960183	+	0.279372i	$0.909874\pi$
$420$	5.54285e7	−	6.48575e7i	0.748144	−	0.875412i
$421$		−	8.11904e6i		−	0.108807i	−0.998519	−	0.0544037i	$-0.982674\pi$
$421$		−	8.11904e6i		−	0.108807i	0.998519	−	0.0544037i	$-0.0173258\pi$
$422$		−	84794.4i		−	0.00112831i
$423$		−	6.25890e7i		−	0.826946i
$424$			754692.i			0.00990084i
$425$	−1.24638e7	−	7.90117e7i	−0.162362	−	1.02926i
$426$	899594.			0.0116364
$427$			9.96697e7i			1.28020i
$428$	−1.01519e8			−1.29483
$429$		−	3.46557e7i		−	0.438938i
$430$	−48775.3	+	57072.6i	−0.000613472	+	0.000717831i
$431$			1.08174e8i			1.35111i	0.737312	+	0.675553i	$0.236095\pi$
$431$			1.08174e8i			1.35111i	−0.737312	+	0.675553i	$0.763905\pi$
$432$		−	9.64069e6i		−	0.119579i
$433$	−1.35098e8			−1.66412			−0.832062	−	0.554683i	$-0.812839\pi$
$433$	−1.35098e8			−1.66412			−0.832062	+	0.554683i	$0.812839\pi$
$434$		−	179210.i		−	0.00219226i
$435$	2.80995e7	−	3.28796e7i	0.341375	−	0.399446i
$436$			1.49322e8i			1.80163i
$437$	−2.73444e7	−	7.78065e7i	−0.327660	−	0.932334i
$438$		−	225654.i		−	0.00268547i
$439$	−8.68021e6			−0.102597			−0.0512987	−	0.998683i	$-0.516336\pi$
$439$	−8.68021e6			−0.102597			−0.0512987	+	0.998683i	$0.516336\pi$
$440$	147335.	+	125916.i	0.00172961	+	0.00147816i
$441$	3.37405e7			0.393402
$442$	−939366.			−0.0108785
$443$		−	7.40093e7i		−	0.851285i	−0.904891	−	0.425643i	$-0.860048\pi$
$443$		−	7.40093e7i		−	0.851285i	0.904891	−	0.425643i	$-0.139952\pi$
$444$			6.64715e7i			0.759428i
$445$	−3.48317e7	+	4.07569e7i	−0.395270	+	0.462510i
$446$	−242203.			−0.00273007
$447$	1.48108e8			1.65827
$448$	−7.17300e7			−0.797750
$449$	9.67598e7			1.06895			0.534473	−	0.845185i	$-0.320510\pi$
$449$	9.67598e7			1.06895			0.534473	+	0.845185i	$0.320510\pi$
$450$	−609103.	+	96083.7i	−0.00668426	+	0.00105442i
$451$			3.78504e6i			0.0412612i
$452$	1.59908e8			1.73163
$453$			1.39826e7i			0.150415i
$454$		−	460398.i		−	0.00492001i
$455$	8.15823e7	−	9.54604e7i	0.866088	−	1.01342i
$456$		−	1.69014e6i		−	0.0178249i
$457$	−7.92424e7			−0.830250			−0.415125	−	0.909764i	$-0.636262\pi$
$457$	−7.92424e7			−0.830250			−0.415125	+	0.909764i	$0.636262\pi$
$458$	602673.			0.00627315
$459$			1.20506e7i			0.124615i
$460$	9.07732e7	+	3.51253e7i	0.932576	+	0.360866i
$461$	3.90939e7			0.399030			0.199515	−	0.979895i	$-0.436063\pi$
$461$	3.90939e7			0.399030			0.199515	+	0.979895i	$0.436063\pi$
$462$		−	129188.i		−	0.00131008i
$463$		−	3.87235e7i		−	0.390150i	−0.980788	−	0.195075i	$-0.937505\pi$
$463$		−	3.87235e7i		−	0.390150i	0.980788	−	0.195075i	$-0.0624950\pi$
$464$	−3.63664e7			−0.364038
$465$	4.14477e7	−	4.84985e7i	0.412232	−	0.482358i
$466$	−830138.			−0.00820338
$467$	6.98991e7			0.686311			0.343155	−	0.939279i	$-0.388504\pi$
$467$	6.98991e7			0.686311			0.343155	+	0.939279i	$0.388504\pi$
$468$		−	1.85433e8i		−	1.80904i
$469$	−3.34807e7			−0.324546
$470$	376653.	+	321895.i	0.00362784	+	0.00310042i
$471$		−	2.24757e8i		−	2.15105i
$472$			894433.i			0.00850593i
$473$		−	2.91100e6i		−	0.0275080i
$474$			215184.i			0.00202057i
$475$	1.04617e8	−	1.65030e7i	0.976165	−	0.153986i
$476$	8.96674e7			0.831407
$477$	9.31033e7			0.857847
$478$			94961.8i			0.000869491i
$479$		−	6.42153e7i		−	0.584294i	−0.956373	−	0.292147i	$-0.905630\pi$
$479$		−	6.42153e7i		−	0.584294i	0.956373	−	0.292147i	$-0.0943697\pi$
$480$	2.27457e6	+	1.94389e6i	0.0205672	+	0.0175771i
$481$			9.78360e7i			0.879151i
$482$	−710293.			−0.00634303
$483$	−4.30234e7	−	1.22420e8i	−0.381824	−	1.08645i
$484$	1.09618e8			0.966821
$485$	−6.91421e7	−	5.90902e7i	−0.606062	−	0.517953i
$486$	−1.02816e6			−0.00895682
$487$		−	1.81770e8i		−	1.57375i	−0.617112	−	0.786875i	$-0.711697\pi$
$487$		−	1.81770e8i		−	1.57375i	0.617112	−	0.786875i	$-0.288303\pi$
$488$	−2.33028e6			−0.0200515
$489$	−1.93998e7			−0.165909
$490$	−173527.	+	203046.i	−0.00147496	+	0.00172587i
$491$	2.17455e8			1.83706			0.918532	−	0.395346i	$-0.129375\pi$
$491$	2.17455e8			1.83706			0.918532	+	0.395346i	$0.129375\pi$
$492$			3.89555e7i			0.327094i
$493$	4.54570e7			0.379367
$494$		−	1.24379e6i		−	0.0103173i
$495$	1.55337e7	−	1.81762e7i	0.128074	−	0.149860i
$496$	−5.36417e7			−0.439600
$497$	−1.26389e8			−1.02953
$498$	490403.			0.00397068
$499$	−1.27767e8			−1.02829			−0.514145	−	0.857703i	$-0.671891\pi$
$499$	−1.27767e8			−1.02829			−0.514145	+	0.857703i	$0.671891\pi$
$500$	−6.54093e7	+	1.06515e8i	−0.523274	+	0.852119i
$501$	−2.53082e8			−2.01255
$502$	913264.			0.00721914
$503$	−3.52231e7			−0.276773			−0.138387	−	0.990378i	$-0.544192\pi$
$503$	−3.52231e7			−0.276773			−0.138387	+	0.990378i	$0.544192\pi$
$504$		−	1.38252e6i		−	0.0107989i
$505$	1.36377e8	+	1.16550e8i	1.05893	+	0.904982i
$506$	139047.	−	48866.7i	0.00107327	−	0.000377191i
$507$		−	3.36886e8i		−	2.58499i
$508$			1.14369e8i			0.872400i
$509$	7.49631e7			0.568453			0.284226	−	0.958757i	$-0.408263\pi$
$509$	7.49631e7			0.568453			0.284226	+	0.958757i	$0.408263\pi$
$510$	−947652.	−	809882.i	−0.00714395	−	0.00610536i
$511$			3.17033e7i			0.237598i
$512$		−	4.19303e6i		−	0.0312405i
$513$	−1.59559e7			−0.118187
$514$	−831944.			−0.00612639
$515$	9.38799e7	+	8.02316e7i	0.687307	+	0.587386i
$516$		−	2.99598e7i		−	0.218067i
$517$	−1.92113e7			−0.139022
$518$			364709.i			0.00262396i
$519$	−1.06789e8			−0.763879
$520$	2.23186e6	+	1.90739e6i	0.0158730	+	0.0135653i
$521$			5.42215e7i			0.383406i	0.981453	+	0.191703i	$0.0614010\pi$
$521$			5.42215e7i			0.383406i	−0.981453	+	0.191703i	$0.938599\pi$
$522$		−	350429.i		−	0.00246370i
$523$	−1.83961e8			−1.28594			−0.642970	−	0.765891i	$-0.722298\pi$
$523$	−1.83961e8			−1.28594			−0.642970	+	0.765891i	$0.722298\pi$
$524$	2.66685e8			1.85355
$525$	1.64604e8	−	2.59656e7i	1.13753	−	0.179441i
$526$		−	1.17838e6i		−	0.00809706i
$527$	6.70505e7			0.458111
$528$	−3.86690e7			−0.262701
$529$	1.15488e8	−	9.26130e7i	0.780134	−	0.625612i
$530$	−478829.	+	560284.i	−0.00321628	+	0.00376340i
$531$	1.10343e8			0.736986
$532$			1.18726e8i			0.788519i
$533$			5.73366e7i			0.378661i
$534$			835529.i			0.00548704i
$535$	−1.50738e8	−	1.28823e8i	−0.984376	−	0.841267i
$536$		−	782779.i		−	0.00508329i
$537$			2.97850e8i			1.92343i
$538$			1.11806e6i			0.00717993i
$539$		−	1.03564e7i		−	0.0661368i
$540$	1.22342e7	−	1.43153e7i	0.0776950	−	0.0909119i
$541$	−2.37686e8			−1.50111			−0.750554	−	0.660809i	$-0.770213\pi$
$541$	−2.37686e8			−1.50111			−0.750554	+	0.660809i	$0.770213\pi$
$542$		−	1.23728e6i		−	0.00777089i
$543$	−2.35874e8			−1.47327
$544$			3.14465e6i			0.0195333i
$545$	−1.89485e8	+	2.21718e8i	−1.17054	+	1.36966i
$546$		−	1.95697e6i		−	0.0120228i
$547$			2.07699e8i			1.26903i	0.772909	+	0.634517i	$0.218801\pi$
$547$			2.07699e8i			1.26903i	−0.772909	+	0.634517i	$0.781199\pi$
$548$	9.73398e7			0.591492
$549$			2.87477e8i			1.73734i
$550$	29492.2	+	186960.i	0.000177264	+	0.00112373i
$551$			6.01884e7i			0.359798i
$552$	2.86218e6	−	1.00589e6i	0.0170169	−	0.00598042i
$553$		−	3.02323e7i		−	0.178771i
$554$	−1.20717e6			−0.00709967
$555$	−8.43500e7	+	9.86989e7i	−0.493408	+	0.577342i
$556$	1.41961e8			0.825931
$557$	−1.41522e8			−0.818949			−0.409475	−	0.912321i	$-0.634288\pi$
$557$	−1.41522e8			−0.818949			−0.409475	+	0.912321i	$0.634288\pi$
$558$		−	516894.i		−	0.00297508i
$559$		−	4.40963e7i		−	0.252445i
$560$	−1.06515e8	−	9.10300e7i	−0.606524	−	0.518347i
$561$	4.83352e7			0.273763
$562$	−1.68257e6			−0.00947902
$563$	4.85721e7			0.272183			0.136092	−	0.990696i	$-0.456546\pi$
$563$	4.85721e7			0.272183			0.136092	+	0.990696i	$0.456546\pi$
$564$	−1.97721e8			−1.10209
$565$	2.37436e8	+	2.02917e8i	1.31644	+	1.12505i
$566$			1.92051e6i			0.0105918i
$567$	1.32400e8			0.726336
$568$		−	2.95497e6i		−	0.0161253i
$569$		−	1.81262e8i		−	0.983944i	−0.870611	−	0.491972i	$-0.836276\pi$
$569$		−	1.81262e8i		−	0.983944i	0.870611	−	0.491972i	$-0.163724\pi$
$570$	1.07234e6	−	1.25476e6i	0.00579041	−	0.00677543i
$571$		−	3.14462e8i		−	1.68912i	−0.535462	−	0.844559i	$-0.679863\pi$
$571$		−	3.14462e8i		−	1.68912i	0.535462	−	0.844559i	$-0.320137\pi$
$572$	−5.69172e7			−0.304127
$573$	−2.41430e8			−1.28330
$574$			213737.i			0.00113017i
$575$	9.02101e7	+	1.67343e8i	0.474517	+	0.880246i
$576$	−2.06890e8			−1.08261
$577$			2.68584e7i			0.139814i	0.997553	+	0.0699072i	$0.0222703\pi$
$577$			2.68584e7i			0.139814i	−0.997553	+	0.0699072i	$0.977730\pi$
$578$		−	103457.i		−	0.000535768i
$579$	1.52744e8			0.786915
$580$	−5.40001e7	−	4.61495e7i	−0.276765	−	0.236529i
$581$	−6.88994e7			−0.351307
$582$	−1.41743e6			−0.00719008
$583$		−	2.85774e7i		−	0.144217i
$584$	−741224.			−0.00372144
$585$	2.35307e8	−	2.75336e8i	1.17535	−	1.37529i
$586$		−	1.83284e6i		−	0.00910820i
$587$			1.18436e8i			0.585558i	0.956180	+	0.292779i	$0.0945800\pi$
$587$			1.18436e8i			0.585558i	−0.956180	+	0.292779i	$0.905420\pi$
$588$		−	1.06588e8i		−	0.524294i
$589$			8.87799e7i			0.434479i
$590$	−567491.	+	664028.i	−0.00276314	+	0.00323318i
$591$	2.85342e8			1.38230
$592$	1.09166e8			0.526165
$593$			1.10661e8i			0.530679i	0.964155	+	0.265340i	$0.0854841\pi$
$593$			1.10661e8i			0.530679i	−0.964155	+	0.265340i	$0.914516\pi$
$594$		−	28514.4i		−	0.000136052i
$595$	1.33141e8	+	1.13785e8i	0.632063	+	0.540174i
$596$		−	2.43247e8i		−	1.14897i
$597$	−4.72581e8			−2.22102
$598$	2.10630e6	−	740241.i	0.00984958	−	0.00346154i
$599$	−1.03711e8			−0.482551			−0.241276	−	0.970457i	$-0.577566\pi$
$599$	−1.03711e8			−0.482551			−0.241276	+	0.970457i	$0.577566\pi$
$600$	607077.	+	3.84844e6i	0.00281054	+	0.0178168i
$601$	2.36329e8			1.08866			0.544331	−	0.838870i	$-0.316783\pi$
$601$	2.36329e8			1.08866			0.544331	+	0.838870i	$0.316783\pi$
$602$		−	164380.i		−	0.000753461i
$603$	−9.65683e7			−0.440436
$604$	2.29644e7			0.104218
$605$	1.62764e8	+	1.39102e8i	0.735010	+	0.628154i
$606$	2.79577e6			0.0125627
$607$		−	2.14980e8i		−	0.961239i	−0.876929	−	0.480619i	$-0.840412\pi$
$607$		−	2.14980e8i		−	0.961239i	0.876929	−	0.480619i	$-0.159588\pi$
$608$	−4.16376e6			−0.0185257
$609$			9.46998e7i			0.419273i
$610$	−1.73000e6	−	1.47849e6i	−0.00762178	−	0.00651372i
$611$	−2.91016e8			−1.27583
$612$	2.58627e8			1.12829
$613$	−4.36609e7			−0.189544			−0.0947722	−	0.995499i	$-0.530212\pi$
$613$	−4.36609e7			−0.189544			−0.0947722	+	0.995499i	$0.530212\pi$
$614$	1.87209e6			0.00808762
$615$	−4.94331e7	+	5.78423e7i	−0.212517	+	0.248668i
$616$	−424355.			−0.00181546
$617$	2.79752e8			1.19102			0.595509	−	0.803349i	$-0.296951\pi$
$617$	2.79752e8			1.19102			0.595509	+	0.803349i	$0.296951\pi$
$618$	1.92457e6			0.00815394
$619$			3.23205e8i			1.36272i	0.731948	+	0.681360i	$0.238611\pi$
$619$			3.23205e8i			1.36272i	−0.731948	+	0.681360i	$0.761389\pi$
$620$	−7.96520e7	−	6.80721e7i	−0.334212	−	0.285624i
$621$	−9.49612e6	−	2.70205e7i	−0.0396526	−	0.112829i
$622$		−	71713.8i		−	0.000298010i
$623$		−	1.17388e8i		−	0.485468i
$624$	−5.85766e8			−2.41085
$625$	−2.32285e8	+	7.51544e7i	−0.951441	+	0.307833i
$626$		−	1.14633e6i		−	0.00467292i
$627$			6.39993e7i			0.259641i
$628$	−3.69132e8			−1.49040
$629$	−1.36454e8			−0.548321
$630$	877169.	−	1.02639e6i	0.00350802	−	0.00410477i
$631$		−	4.78637e8i		−	1.90510i	−0.304380	−	0.952551i	$-0.598449\pi$
$631$		−	4.78637e8i		−	1.90510i	0.304380	−	0.952551i	$-0.401551\pi$
$632$	706832.			0.00280004
$633$			6.60931e7i			0.260582i
$634$	10865.7			4.26375e−5
$635$	−1.45130e8	+	1.69818e8i	−0.566807	+	0.663227i
$636$		−	2.94117e8i		−	1.14327i
$637$		−	1.56881e8i		−	0.606948i
$638$	−107562.			−0.000414186
$639$	−3.64543e8			−1.39716
$640$	4.25673e6	−	4.98085e6i	0.0162381	−	0.0190004i
$641$		−	2.22887e8i		−	0.846272i	−0.906066	−	0.423136i	$-0.860929\pi$
$641$		−	2.22887e8i		−	0.846272i	0.906066	−	0.423136i	$-0.139071\pi$
$642$	−3.09017e6			−0.0116782
$643$	−2.01608e8			−0.758359			−0.379179	−	0.925323i	$-0.623794\pi$
$643$	−2.01608e8			−0.758359			−0.379179	+	0.925323i	$0.623794\pi$
$644$	−2.01058e8	+	7.06599e7i	−0.752771	+	0.264555i
$645$	3.80180e7	−	4.44853e7i	0.141680	−	0.165782i
$646$	1.73474e6			0.00643484
$647$		−	1.42016e8i		−	0.524352i	−0.965020	−	0.262176i	$-0.915560\pi$
$647$		−	1.42016e8i		−	0.524352i	0.965020	−	0.262176i	$-0.0844401\pi$
$648$			3.09550e6i			0.0113764i
$649$		−	3.38689e7i		−	0.123899i
$650$	446754.	+	2.83210e6i	0.00162678	+	0.0103126i
$651$			1.39685e8i			0.506300i
$652$			3.18614e7i			0.114954i
$653$		−	9.47697e7i		−	0.340353i	−0.985414	−	0.170177i	$-0.945566\pi$
$653$		−	9.47697e7i		−	0.340353i	0.985414	−	0.170177i	$-0.0544339\pi$
$654$			4.54529e6i			0.0162491i
$655$	3.95982e8	+	3.38414e8i	1.40913	+	1.20427i
$656$	6.39764e7			0.226625
$657$			9.14417e7i			0.322440i
$658$	−1.08484e6			−0.00380791
$659$		−	3.42287e8i		−	1.19601i	−0.801494	−	0.598003i	$-0.795961\pi$
$659$		−	3.42287e8i		−	1.19601i	0.801494	−	0.598003i	$-0.204039\pi$
$660$	−5.74192e7	−	4.90716e7i	−0.199722	−	0.170686i
$661$		−	6.23686e7i		−	0.215954i	−0.994153	−	0.107977i	$-0.965563\pi$
$661$		−	6.23686e7i		−	0.215954i	0.994153	−	0.107977i	$-0.0344373\pi$
$662$			2.62035e6i			0.00903203i
$663$	7.32190e8			2.51237
$664$		−	1.61087e6i		−	0.00550245i
$665$	−1.50660e8	+	1.76288e8i	−0.512309	+	0.599458i
$666$			1.05193e6i			0.00356093i
$667$	−1.01926e8	+	3.58211e7i	−0.343486	+	0.120715i
$668$			4.15651e8i			1.39444i
$669$	1.88785e8			0.630506
$670$	496650.	−	581136.i	0.00165130	−	0.00193221i
$671$	8.82389e7			0.292074
$672$	−6.55121e6			−0.0215881
$673$			3.42894e8i			1.12490i	0.826831	+	0.562450i	$0.190141\pi$
$673$			3.42894e8i			1.12490i	−0.826831	+	0.562450i	$0.809859\pi$
$674$			3.43712e6i			0.0112257i
$675$	3.63314e7	−	5.73114e6i	0.118133	−	0.0186350i
$676$	−5.53289e8			−1.79107
$677$	−2.13434e7			−0.0687857			−0.0343928	−	0.999408i	$-0.510950\pi$
$677$	−2.13434e7			−0.0687857			−0.0343928	+	0.999408i	$0.510950\pi$
$678$	4.86750e6			0.0156177
$679$	1.99143e8			0.636145
$680$	−2.66029e6	+	3.11283e6i	−0.00846061	+	0.00989986i
$681$			3.58858e8i			1.13627i
$682$	−158657.			−0.000500156
$683$		−	3.62289e8i		−	1.13708i	−0.822654	−	0.568542i	$-0.807508\pi$
$683$		−	3.62289e8i		−	1.13708i	0.822654	−	0.568542i	$-0.192492\pi$
$684$			3.42442e8i			1.07008i
$685$	1.44533e8	+	1.23521e8i	0.449672	+	0.384298i
$686$		−	2.19456e6i		−	0.00679790i
$687$	−4.69754e8			−1.44877
$688$	−4.92029e7			−0.151086
$689$		−	4.32896e8i		−	1.32350i
$690$	2.76309e6	+	1.06919e6i	0.00841099	+	0.00325469i
$691$	5.52715e8			1.67520			0.837601	−	0.546283i	$-0.183958\pi$
$691$	5.52715e8			1.67520			0.837601	+	0.546283i	$0.183958\pi$
$692$			1.75386e8i			0.529270i
$693$			5.23510e7i			0.157299i
$694$	−2.79802e6			−0.00837090
$695$	2.10788e8	+	1.80143e8i	0.627900	+	0.536616i
$696$	−2.21408e6			−0.00656698
$697$	−7.99687e7			−0.236168
$698$			1.45657e6i			0.00428318i
$699$	6.47052e8			1.89456
$700$	−4.26450e7	−	2.70339e8i	−0.124329	−	0.788160i
$701$			5.70839e8i			1.65714i	0.559885	+	0.828571i	$0.310845\pi$
$701$			5.70839e8i			1.65714i	−0.559885	+	0.828571i	$0.689155\pi$
$702$		−	431942.i		−	0.00124857i
$703$		−	1.80675e8i		−	0.520036i
$704$			6.35036e7i			0.182004i
$705$	−2.93583e8	−	2.50901e8i	−0.837844	−	0.716037i
$706$	−4.31278e6			−0.0122558
$707$	−3.92793e8			−1.11149
$708$		−	3.48577e8i		−	0.982196i
$709$		−	5.06264e8i		−	1.42049i	−0.703954	−	0.710245i	$-0.748584\pi$
$709$		−	5.06264e8i		−	1.42049i	0.703954	−	0.710245i	$-0.251416\pi$
$710$	1.87484e6	−	2.19377e6i	0.00523829	−	0.00612938i
$711$		−	8.71990e7i		−	0.242607i
$712$	2.74453e6			0.00760377
$713$	−1.50345e8	+	5.28373e7i	−0.414782	+	0.145771i
$714$	2.72943e6			0.00749854
$715$	−8.45124e7	−	7.22259e7i	−0.231208	−	0.197595i
$716$	4.89178e8			1.33269
$717$		−	7.40181e7i		−	0.200808i
$718$	−2.30611e6			−0.00623027
$719$	2.34601e8			0.631164			0.315582	−	0.948898i	$-0.397800\pi$
$719$	2.34601e8			0.631164			0.315582	+	0.948898i	$0.397800\pi$
$720$	−3.07221e8	−	2.62557e8i	−0.823102	−	0.703439i
$721$	−2.70393e8			−0.721422
$722$		−	55014.5i		−	0.000146172i
$723$	5.53639e8			1.46491
$724$			3.87391e8i			1.02078i
$725$	−2.16189e7	−	1.37049e8i	−0.0567309	−	0.359634i
$726$	3.33672e6			0.00871986
$727$	5.42009e8			1.41060			0.705299	−	0.708910i	$-0.250813\pi$
$727$	5.42009e8			1.41060			0.705299	+	0.708910i	$0.250813\pi$
$728$	−6.42822e6			−0.0166608
$729$	4.48748e8			1.15830
$730$	−550285.	−	470284.i	−0.00141455	−	0.00120890i
$731$	6.15022e7			0.157448
$732$	9.08150e8			2.31539
$733$	−1.73456e8			−0.440430			−0.220215	−	0.975451i	$-0.570676\pi$
$733$	−1.73456e8			−0.440430			−0.220215	+	0.975451i	$0.570676\pi$
$734$		−	2.94349e6i		−	0.00744344i
$735$	1.35256e8	−	1.58265e8i	0.340639	−	0.398586i
$736$	−2.47806e6	−	7.05114e6i	−0.00621553	−	0.0176858i
$737$			2.96410e7i			0.0740440i
$738$			616480.i			0.00153373i
$739$	1.33441e8			0.330640			0.165320	−	0.986240i	$-0.447134\pi$
$739$	1.33441e8			0.330640			0.165320	+	0.986240i	$0.447134\pi$
$740$	1.62099e8	+	1.38533e8i	0.400024	+	0.341868i
$741$			9.69474e8i			2.38277i
$742$		−	1.61373e6i		−	0.00395020i
$743$	3.12017e7			0.0760698			0.0380349	−	0.999276i	$-0.487890\pi$
$743$	3.12017e7			0.0760698			0.0380349	+	0.999276i	$0.487890\pi$
$744$	−3.26584e6			−0.00793005
$745$	3.08672e8	−	3.61181e8i	0.746498	−	0.873486i
$746$			2.30508e6i			0.00555226i
$747$	−1.98726e8			−0.476753
$748$		−	7.93838e7i		−	0.189682i
$749$	4.34155e8			1.03324
$750$	−1.99102e6	+	3.24225e6i	−0.00471946	+	0.00768534i
$751$			2.66791e8i			0.629872i	0.949113	+	0.314936i	$0.101983\pi$
$751$			2.66791e8i			0.629872i	−0.949113	+	0.314936i	$0.898017\pi$
$752$			3.24717e8i			0.763575i
$753$	−7.11845e8			−1.66725
$754$	−1.62936e6			−0.00380105
$755$	3.40983e7	+	2.91410e7i	0.0792303	+	0.0677118i
$756$			4.12311e7i			0.0954244i
$757$	3.15295e8			0.726824			0.363412	−	0.931629i	$-0.381612\pi$
$757$	3.15295e8			0.726824			0.363412	+	0.931629i	$0.381612\pi$
$758$	−4.93109e6			−0.0113223
$759$	−1.08380e8	+	3.80892e7i	−0.247870	+	0.0871117i
$760$	−4.12162e6	−	3.52242e6i	−0.00938918	−	0.00802417i
$761$	−3.17422e8			−0.720251			−0.360125	−	0.932904i	$-0.617266\pi$
$761$	−3.17422e8			−0.720251			−0.360125	+	0.932904i	$0.617266\pi$
$762$			3.48132e6i			0.00786826i
$763$		−	6.38594e8i		−	1.43764i
$764$			3.96515e8i			0.889159i
$765$	3.84018e8	+	3.28189e8i	0.857762	+	0.733060i
$766$			222978.i			0.000496107i
$767$		−	5.13052e8i		−	1.13704i
$768$			6.53499e8i			1.44265i
$769$		−	8.26143e8i		−	1.81667i	−0.418243	−	0.908335i	$-0.637354\pi$
$769$		−	8.26143e8i		−	1.81667i	0.418243	−	0.908335i	$-0.362646\pi$
$770$	−315042.	−	269241.i	−0.000690075	−	0.000589751i
$771$	6.48459e8			1.41488
$772$		−	2.50860e8i		−	0.545231i
$773$	3.97143e8			0.859822			0.429911	−	0.902871i	$-0.358545\pi$
$773$	3.97143e8			0.859822			0.429911	+	0.902871i	$0.358545\pi$
$774$		−	474121.i		−	0.00102251i
$775$	−3.18886e7	−	2.02151e8i	−0.0685063	−	0.434281i
$776$			4.65596e6i			0.00996379i
$777$		−	2.84273e8i		−	0.605999i
$778$	550931.			0.00116993
$779$		−	1.05884e8i		−	0.223985i
$780$	−8.69797e8	−	7.43346e8i	−1.83288	−	1.56642i
$781$			1.11894e8i			0.234884i
$782$	1.03243e6	+	2.93771e6i	0.00215894	+	0.00614312i
$783$			2.09021e7i			0.0435417i
$784$	−1.75049e8			−0.363254
$785$	−5.48099e8	−	4.68416e8i	−1.13305	−	0.968328i
$786$	8.11775e6			0.0167174
$787$	−2.96400e8			−0.608070			−0.304035	−	0.952661i	$-0.598334\pi$
$787$	−2.96400e8			−0.608070			−0.304035	+	0.952661i	$0.598334\pi$
$788$		−	4.68634e8i		−	0.957757i
$789$			9.18488e8i			1.87000i
$790$	524753.	+	448464.i	0.00106432	+	0.000909591i
$791$	−6.83863e8			−1.38178
$792$	−1.22397e6			−0.00246373
$793$	1.33666e9			2.68041
$794$	3.26613e6			0.00652487
$795$	3.73224e8	−	4.36714e8i	0.742794	−	0.869152i
$796$			7.76148e8i			1.53888i
$797$	6.42411e8			1.26893			0.634465	−	0.772951i	$-0.281220\pi$
$797$	6.42411e8			1.26893			0.634465	+	0.772951i	$0.281220\pi$
$798$			3.61396e6i			0.00711173i
$799$		−	4.05887e8i		−	0.795728i
$800$	9.48084e6	−	1.49557e6i	0.0185173	−	0.00292103i
$801$		−	3.38582e8i		−	0.658819i
$802$	4.11247e6			0.00797222
$803$	2.80674e7			0.0542070
$804$			3.05063e8i			0.586978i
$805$	−3.88202e8	−	1.50217e8i	−0.744166	−	0.287960i
$806$	−2.40336e6			−0.00459002
$807$		−	8.71477e8i		−	1.65819i
$808$		−	9.18351e6i		−	0.0174090i
$809$	−7.31889e8			−1.38229			−0.691146	−	0.722715i	$-0.742894\pi$
$809$	−7.31889e8			−1.38229			−0.691146	+	0.722715i	$0.742894\pi$
$810$	−1.96400e6	+	2.29810e6i	−0.00369562	+	0.00432429i
$811$	−6.15012e8			−1.15298			−0.576489	−	0.817105i	$-0.695578\pi$
$811$	−6.15012e8			−1.15298			−0.576489	+	0.817105i	$0.695578\pi$
$812$	1.55531e8			0.290502
$813$			9.64401e8i			1.79468i
$814$	322882.			0.000598646
$815$	−4.04310e7	+	4.73088e7i	−0.0746865	+	0.0873916i
$816$		−	8.16982e8i		−	1.50363i
$817$			8.14335e7i			0.149326i
$818$			407627.i			0.000744737i
$819$			7.93023e8i			1.44356i
$820$	9.49979e7	+	8.11870e7i	0.172295	+	0.147247i
$821$	−7.84110e8			−1.41693			−0.708463	−	0.705748i	$-0.750611\pi$
$821$	−7.84110e8			−1.41693			−0.708463	+	0.705748i	$0.750611\pi$
$822$	2.96297e6			0.00533473
$823$		−	5.00871e8i		−	0.898518i	−0.893402	−	0.449259i	$-0.851688\pi$
$823$		−	5.00871e8i		−	0.898518i	0.893402	−	0.449259i	$-0.148312\pi$
$824$		−	6.32179e6i		−	0.0112995i
$825$	−2.29877e7	−	1.45726e8i	−0.0409387	−	0.259523i
$826$		−	1.91253e6i		−	0.00339366i
$827$	−5.28892e8			−0.935084			−0.467542	−	0.883971i	$-0.654860\pi$
$827$	−5.28892e8			−0.935084			−0.467542	+	0.883971i	$0.654860\pi$
$828$	−5.79909e8	+	2.03804e8i	−1.02157	+	0.359022i
$829$	−5.57387e8			−0.978348			−0.489174	−	0.872186i	$-0.662702\pi$
$829$	−5.57387e8			−0.978348			−0.489174	+	0.872186i	$0.662702\pi$
$830$	1.02205e6	−	1.19591e6i	0.00178746	−	0.00209153i
$831$	9.40928e8			1.63966
$832$			9.61964e8i			1.67028i
$833$	2.18806e8			0.378550
$834$	4.32121e6			0.00744916
$835$	−5.27447e8	+	6.17172e8i	−0.905982	+	1.06010i
$836$	1.05110e8			0.179898
$837$			3.08313e7i			0.0525794i
$838$	2.05476e6			0.00349163
$839$		−	5.96060e8i		−	1.00926i	−0.863335	−	0.504632i	$-0.831628\pi$
$839$		−	5.96060e8i		−	1.00926i	0.863335	−	0.504632i	$-0.168372\pi$
$840$	−6.48492e6	−	5.54213e6i	−0.0109412	−	0.00935059i
$841$	−5.15977e8			−0.867445
$842$	−405892.			−0.000679946
$843$	1.31148e9			2.18917
$844$	1.08549e8			0.180550
$845$	−8.21540e8	−	7.02104e8i	−1.36163	−	1.16367i
$846$	−3.12899e6			−0.00516765
$847$	−4.68794e8			−0.771493
$848$	−4.83027e8			−0.792107
$849$		−	1.49695e9i		−	2.44615i
$850$	−3.95000e6	+	623098.i	−0.00643192	+	0.00101461i
$851$	3.05966e8	−	1.07529e8i	0.496460	−	0.174476i
$852$			1.15161e9i			1.86202i
$853$		−	2.41514e8i		−	0.389131i	−0.980890	−	0.194565i	$-0.937670\pi$
$853$		−	2.41514e8i		−	0.389131i	0.980890	−	0.194565i	$-0.0623296\pi$
$854$	4.98274e6			0.00800009
$855$	−4.34546e8	+	5.08468e8i	−0.695245	+	0.813514i
$856$			1.01505e7i			0.0161833i
$857$			5.35063e8i			0.850085i	0.905173	+	0.425043i	$0.139741\pi$
$857$			5.35063e8i			0.850085i	−0.905173	+	0.425043i	$0.860259\pi$
$858$	−1.73253e6			−0.00274296
$859$	9.70068e8			1.53046			0.765231	−	0.643755i	$-0.222625\pi$
$859$	9.70068e8			1.53046			0.765231	+	0.643755i	$0.222625\pi$
$860$	−7.30609e7	−	6.24392e7i	−0.114865	−	0.0981662i
$861$		−	1.66597e8i		−	0.261011i
$862$	5.40787e6			0.00844315
$863$			4.36688e8i			0.679421i	0.940530	+	0.339711i	$0.110329\pi$
$863$			4.36688e8i			0.679421i	−0.940530	+	0.339711i	$0.889671\pi$
$864$	−1.44598e6			−0.00224193
$865$	−2.22559e8	+	2.60419e8i	−0.343872	+	0.402369i
$866$			6.75390e6i			0.0103992i
$867$			8.06397e7i			0.123735i
$868$	2.29414e8			0.350800
$869$	−2.67651e7			−0.0407859
$870$	−1.64374e6	−	1.40477e6i	−0.00249617	−	0.00213327i
$871$			4.49007e8i			0.679514i
$872$	1.49303e7			0.0225175
$873$	5.74387e8			0.863301
$874$	−3.88975e6	+	1.36702e6i	−0.00582623	+	0.00204757i
$875$	2.79730e8	−	4.55522e8i	0.417556	−	0.679963i
$876$	2.88868e8			0.429722
$877$		−	1.14541e9i		−	1.69809i	−0.528319	−	0.849046i	$-0.677177\pi$
$877$		−	1.14541e9i		−	1.69809i	0.528319	−	0.849046i	$-0.322823\pi$
$878$			433946.i			0.000641139i
$879$			1.42861e9i			2.10352i
$880$	−8.05901e7	+	9.42994e7i	−0.118259	+	0.138376i
$881$			1.15946e9i			1.69562i	0.530299	+	0.847811i	$0.322080\pi$
$881$			1.15946e9i			1.69562i	−0.530299	+	0.847811i	$0.677920\pi$
$882$		−	1.68678e6i		−	0.00245839i
$883$			1.17453e9i			1.70601i	0.521900	+	0.853007i	$0.325223\pi$
$883$			1.17453e9i			1.70601i	−0.521900	+	0.853007i	$0.674777\pi$
$884$		−	1.20252e9i		−	1.74075i
$885$	4.42331e8	−	5.17577e8i	0.638143	−	0.746699i
$886$	−3.69992e6			−0.00531974
$887$		−	3.87732e8i		−	0.555598i	−0.960639	−	0.277799i	$-0.910395\pi$
$887$		−	3.87732e8i		−	0.555598i	0.960639	−	0.277799i	$-0.0896050\pi$
$888$	6.64629e6			0.00949162
$889$		−	4.89110e8i		−	0.696147i
$890$	2.03755e6	+	1.74133e6i	0.00289026	+	0.00247007i
$891$		−	1.17215e8i		−	0.165711i
$892$		−	3.10053e8i		−	0.436860i
$893$	5.37424e8			0.754680
$894$		−	7.40431e6i		−	0.0103627i
$895$	7.26346e8	+	6.20750e8i	1.01315	+	0.865859i
$896$			1.43458e7i			0.0199435i
$897$	−1.64176e9	+	5.76982e8i	−2.27474	+	0.799438i
$898$		−	4.83727e6i		−	0.00667993i
$899$	1.16301e8			0.160069
$900$	−1.23001e8	−	7.79737e8i	−0.168725	−	1.06960i
$901$	6.03770e8			0.825462
$902$	189224.			0.000257844
$903$			1.28126e8i			0.174011i
$904$		−	1.59887e7i		−	0.0216425i
$905$	−4.91585e8	+	5.75210e8i	−0.663213	+	0.776033i
$906$	699024.			0.000939957
$907$	−7.33932e8			−0.983635			−0.491817	−	0.870698i	$-0.663667\pi$
$907$	−7.33932e8			−0.983635			−0.491817	+	0.870698i	$0.663667\pi$
$908$	5.89374e8			0.787288
$909$	−1.13293e9			−1.50838
$910$	−4.77231e6	−	4.07851e6i	−0.00633293	−	0.00541224i
$911$		−	7.75309e8i		−	1.02546i	−0.858549	−	0.512731i	$-0.828634\pi$
$911$		−	7.75309e8i		−	1.02546i	0.858549	−	0.512731i	$-0.171366\pi$
$912$	1.08174e9			1.42607
$913$			6.09976e7i			0.0801495i
$914$			3.96153e6i			0.00518829i
$915$	1.34845e9	+	1.15241e9i	1.76024	+	1.50433i
$916$			7.71506e8i			1.00381i
$917$	−1.14051e9			−1.47908
$918$	602439.			0.000778727
$919$			2.32445e7i			0.0299485i	0.999888	+	0.0149742i	$0.00476662\pi$
$919$			2.32445e7i			0.0299485i	−0.999888	+	0.0149742i	$0.995233\pi$
$920$	3.51208e6	−	9.07615e6i	0.00451025	−	0.0116557i
$921$	−1.45920e9			−1.86782
$922$		−	1.95440e6i		−	0.00249357i
$923$			1.69499e9i			2.15557i
$924$	1.65379e8			0.209635
$925$	6.48963e7	+	4.11396e8i	0.0819964	+	0.519799i
$926$	−1.93589e6			−0.00243807
$927$	−7.79893e8			−0.979030
$928$			5.45451e6i			0.00682515i
$929$	−2.30858e8			−0.287937			−0.143968	−	0.989582i	$-0.545986\pi$
$929$	−2.30858e8			−0.287937			−0.143968	+	0.989582i	$0.545986\pi$
$930$	−2.42456e6	−	2.07208e6i	−0.00301429	−	0.00257607i
$931$			2.89715e8i			0.359022i
$932$		−	1.06269e9i		−	1.31268i
$933$			5.58974e7i			0.0688250i
$934$		−	3.49444e6i		−	0.00428881i
$935$	1.00735e8	−	1.17871e8i	0.123239	−	0.144203i
$936$	−1.85409e7			−0.0226101
$937$	−1.36086e9			−1.65422			−0.827112	−	0.562037i	$-0.810018\pi$
$937$	−1.36086e9			−1.65422			−0.827112	+	0.562037i	$0.810018\pi$
$938$			1.67379e6i			0.00202811i
$939$			8.93511e8i			1.07920i
$940$	−4.12071e8	+	4.82169e8i	−0.496121	+	0.580518i
$941$		−	1.04159e9i		−	1.25005i	−0.780603	−	0.625027i	$-0.785088\pi$
$941$		−	1.04159e9i		−	1.25005i	0.780603	−	0.625027i	$-0.214912\pi$
$942$	−1.12362e7			−0.0134421
$943$	1.79311e8	−	6.30171e7i	0.213831	−	0.0751490i
$944$	−5.72466e8			−0.680509
$945$	−5.23208e7	+	6.12212e7i	−0.0619982	+	0.0725448i
$946$	−145528.			−0.000171899
$947$			1.43050e9i			1.68437i	0.539192	+	0.842183i	$0.318730\pi$
$947$			1.43050e9i			1.68437i	−0.539192	+	0.842183i	$0.681270\pi$
$948$	−2.75465e8			−0.323327
$949$	4.25170e8			0.497467
$950$	−825028.	−	5.23009e6i	−0.000962272	−	0.00610012i
$951$	−8.46932e6			−0.00984707
$952$		−	8.96558e6i		−	0.0103912i
$953$	5.23432e8			0.604757			0.302379	−	0.953188i	$-0.402219\pi$
$953$	5.23432e8			0.604757			0.302379	+	0.953188i	$0.402219\pi$
$954$		−	4.65447e6i		−	0.00536075i
$955$	−5.03164e8	+	5.88758e8i	−0.577696	+	0.675969i
$956$	−1.21564e8			−0.139134
$957$	8.38390e7			0.0956556
$958$	−3.21029e6			−0.00365130
$959$	−4.16285e8			−0.471992
$960$	−8.29364e8	+	9.70449e8i	−0.937414	+	1.09688i
$961$	−7.15955e8			−0.806707
$962$	4.89107e6			0.00549388
$963$	1.25223e9			1.40219
$964$		−	9.09275e8i		−	1.01500i
$965$	3.18333e8	−	3.72485e8i	0.354242	−	0.414503i
$966$	−6.12009e6	+	2.15085e6i	−0.00678932	+	0.00238604i
$967$		−	1.91748e8i		−	0.212057i	−0.994363	−	0.106028i	$-0.966187\pi$
$967$		−	1.91748e8i		−	0.212057i	0.994363	−	0.106028i	$-0.0338135\pi$
$968$		−	1.09604e7i		−	0.0120837i
$969$	−1.35215e9			−1.48612
$970$	−2.95407e6	+	3.45659e6i	−0.00323672	+	0.00378733i
$971$			5.43084e8i			0.593212i	0.955000	+	0.296606i	$0.0958547\pi$
$971$			5.43084e8i			0.593212i	−0.955000	+	0.296606i	$0.904145\pi$
$972$		−	1.31619e9i		−	1.43325i
$973$	−6.07111e8			−0.659067
$974$	−9.08716e6			−0.00983448
$975$	−3.48223e8	−	2.20748e9i	−0.375702	−	2.38168i
$976$		−	1.49145e9i		−	1.60420i
$977$	1.08675e9			1.16533			0.582664	−	0.812713i	$-0.302011\pi$
$977$	1.08675e9			1.16533			0.582664	+	0.812713i	$0.302011\pi$
$978$			969845.i			0.00103678i
$979$	−1.03925e8			−0.110758
$980$	−2.59928e8	−	2.22139e8i	−0.276169	−	0.236019i
$981$		−	1.84189e9i		−	1.95100i
$982$		−	1.08711e7i		−	0.0114800i
$983$	−1.52089e9			−1.60116			−0.800582	−	0.599223i	$-0.795476\pi$
$983$	−1.52089e9			−1.60116			−0.800582	+	0.599223i	$0.795476\pi$
$984$	3.89505e6			0.00408815
$985$	5.94680e8	−	6.95843e8i	0.622264	−	0.728119i
$986$		−	2.27251e6i		−	0.00237069i
$987$	8.45577e8			0.879431
$988$	1.59223e9			1.65095
$989$	−1.37904e8	+	4.84651e7i	−0.142557	+	0.0501003i
$990$	−908674.	−	776570.i	−0.000936488	−	0.000800341i
$991$	1.27801e9			1.31315			0.656575	−	0.754260i	$-0.272004\pi$
$991$	1.27801e9			1.31315			0.656575	+	0.754260i	$0.272004\pi$
$992$			8.04559e6i			0.00824181i
$993$		−	2.04244e9i		−	2.08593i
$994$			6.31851e6i			0.00643362i
$995$	−9.84905e8	+	1.15245e9i	−0.999827	+	1.16991i
$996$			6.27784e8i			0.635378i
$997$		−	1.37512e9i		−	1.38757i	−0.720181	−	0.693786i	$-0.755941\pi$
$997$		−	1.37512e9i		−	1.38757i	0.720181	−	0.693786i	$-0.244059\pi$
$998$			6.38739e6i			0.00642586i
$999$		−	6.27447e7i		−	0.0629333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.c.c.114.17	✓	68
5.4	even	2	inner	115.7.c.c.114.52	yes	68
23.22	odd	2	inner	115.7.c.c.114.51	yes	68
115.114	odd	2	inner	115.7.c.c.114.18	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.c.c.114.17	✓	68	1.1	even	1	trivial
115.7.c.c.114.18	yes	68	115.114	odd	2	inner
115.7.c.c.114.51	yes	68	23.22	odd	2	inner
115.7.c.c.114.52	yes	68	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	115.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.0499926i q^{2} +38.9668i q^{3} +63.9975 q^{4} +(95.0255 + 81.2106i) q^{5} +1.94805 q^{6} -273.692 q^{7} -6.39893i q^{8} -789.409 q^{9} +O(q^{10})\)	\(q-0.0499926i q^{2} +38.9668i q^{3} +63.9975 q^{4} +(95.0255 + 81.2106i) q^{5} +1.94805 q^{6} -273.692 q^{7} -6.39893i q^{8} -789.409 q^{9} +(4.05993 - 4.75057i) q^{10} +242.304i q^{11} +2493.78i q^{12} +3670.46i q^{13} +13.6826i q^{14} +(-3164.51 + 3702.84i) q^{15} +4095.52 q^{16} -5119.28 q^{17} +39.4646i q^{18} -6778.31i q^{19} +(6081.39 + 5197.27i) q^{20} -10664.9i q^{21} +12.1134 q^{22} +(11478.8 - 4034.10i) q^{23} +249.346 q^{24} +(2434.68 + 15434.1i) q^{25} +183.496 q^{26} -2353.96i q^{27} -17515.6 q^{28} -8879.57 q^{29} +(185.114 + 158.202i) q^{30} -13097.7 q^{31} -614.277i q^{32} -9441.79 q^{33} +255.926i q^{34} +(-26007.7 - 22226.7i) q^{35} -50520.2 q^{36} +26655.0 q^{37} -338.865 q^{38} -143026. q^{39} +(519.661 - 608.061i) q^{40} +15621.1 q^{41} -533.166 q^{42} -12013.8 q^{43} +15506.8i q^{44} +(-75014.0 - 64108.4i) q^{45} +(-201.675 - 573.853i) q^{46} +79285.9i q^{47} +159589. i q^{48} -42741.5 q^{49} +(771.593 - 121.716i) q^{50} -199482. i q^{51} +234900. i q^{52} -117940. q^{53} -117.680 q^{54} +(-19677.6 + 23025.0i) q^{55} +1751.34i q^{56} +264129. q^{57} +443.913i q^{58} -139779. q^{59} +(-202521. + 236972. i) q^{60} -364167. i q^{61} +654.785i q^{62} +216055. q^{63} +262083. q^{64} +(-298080. + 348787. i) q^{65} +472.020i q^{66} +122330. q^{67} -327621. q^{68} +(157196. + 447290. i) q^{69} +(-1111.17 + 1300.19i) q^{70} +461792. q^{71} +5051.37i q^{72} -115836. i q^{73} -1332.55i q^{74} +(-601419. + 94871.6i) q^{75} -433795. i q^{76} -66316.7i q^{77} +7150.24i q^{78} +110461. i q^{79} +(389179. + 332600. i) q^{80} -483753. q^{81} -780.938i q^{82} +251740. q^{83} -682528. i q^{84} +(-486462. - 415740. i) q^{85} +600.603i q^{86} -346008. i q^{87} +1550.48 q^{88} +428905. i q^{89} +(-3204.94 + 3750.14i) q^{90} -1.00458e6i q^{91} +(734612. - 258173. i) q^{92} -510373. i q^{93} +3963.71 q^{94} +(550470. - 644112. i) q^{95} +23936.4 q^{96} -727617. q^{97} +2136.76i q^{98} -191277. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

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