LMFDB - Embedded newform 177.9.c.a.58.75

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,9,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	177.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$72.1060139808$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.75
Character	$\chi$	$=$	177.58
Dual form			177.9.c.a.58.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+28.5404i q^{2} -46.7654 q^{3} -558.553 q^{4} +1019.37 q^{5} -1334.70i q^{6} +1132.75 q^{7} -8634.97i q^{8} +2187.00 q^{9} +O(q^{10})$	\(q+28.5404i q^{2} -46.7654 q^{3} -558.553 q^{4} +1019.37 q^{5} -1334.70i q^{6} +1132.75 q^{7} -8634.97i q^{8} +2187.00 q^{9} +29093.1i q^{10} -4608.39i q^{11} +26120.9 q^{12} +8985.26i q^{13} +32329.1i q^{14} -47671.0 q^{15} +103456. q^{16} -141765. q^{17} +62417.8i q^{18} +37622.4 q^{19} -569370. q^{20} -52973.4 q^{21} +131525. q^{22} -368411. i q^{23} +403817. i q^{24} +648482. q^{25} -256443. q^{26} -102276. q^{27} -632700. q^{28} +1.07625e6 q^{29} -1.36055e6i q^{30} -1.36196e6i q^{31} +742110. i q^{32} +215513. i q^{33} -4.04601e6i q^{34} +1.15468e6 q^{35} -1.22155e6 q^{36} -454793. i q^{37} +1.07376e6i q^{38} -420199. i q^{39} -8.80219e6i q^{40} -2.19561e6 q^{41} -1.51188e6i q^{42} +155344. i q^{43} +2.57403e6i q^{44} +2.22935e6 q^{45} +1.05146e7 q^{46} -4.12397e6i q^{47} -4.83814e6 q^{48} -4.48168e6 q^{49} +1.85079e7i q^{50} +6.62967e6 q^{51} -5.01874e6i q^{52} -8.47567e6 q^{53} -2.91899e6i q^{54} -4.69764e6i q^{55} -9.78124e6i q^{56} -1.75943e6 q^{57} +3.07167e7i q^{58} +(8.59574e6 - 8.54071e6i) q^{59} +2.66268e7 q^{60} -1.90458e7i q^{61} +3.88709e7 q^{62} +2.47732e6 q^{63} +5.30453e6 q^{64} +9.15927e6i q^{65} -6.15083e6 q^{66} -1.59131e6i q^{67} +7.91830e7 q^{68} +1.72289e7i q^{69} +3.29551e7i q^{70} +2.82229e7 q^{71} -1.88847e7i q^{72} -3.05689e7i q^{73} +1.29800e7 q^{74} -3.03265e7 q^{75} -2.10141e7 q^{76} -5.22015e6i q^{77} +1.19926e7 q^{78} -4.78817e6 q^{79} +1.05459e8 q^{80} +4.78297e6 q^{81} -6.26636e7i q^{82} +6.63663e7i q^{83} +2.95884e7 q^{84} -1.44510e8 q^{85} -4.43357e6 q^{86} -5.03314e7 q^{87} -3.97933e7 q^{88} -8.43518e7i q^{89} +6.36266e7i q^{90} +1.01780e7i q^{91} +2.05777e8i q^{92} +6.36926e7i q^{93} +1.17700e8 q^{94} +3.83510e7 q^{95} -3.47051e7i q^{96} +1.27671e8i q^{97} -1.27909e8i q^{98} -1.00786e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	$ 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) $ 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			28.5404i			1.78377i	0.452259	+	0.891887i	$0.350618\pi$
$2$			28.5404i			1.78377i	−0.452259	+	0.891887i	$0.649382\pi$
$3$	−46.7654			−0.577350
$3$	−46.7654			−0.577350
$4$	−558.553			−2.18185
$5$	1019.37			1.63099			0.815493	−	0.578767i	$-0.196466\pi$
$5$	1019.37			1.63099			0.815493	+	0.578767i	$0.196466\pi$
$6$		−	1334.70i		−	1.02986i
$7$	1132.75			0.471782			0.235891	−	0.971780i	$-0.424199\pi$
$7$	1132.75			0.471782			0.235891	+	0.971780i	$0.424199\pi$
$8$		−	8634.97i		−	2.10815i
$9$	2187.00			0.333333
$10$			29093.1i			2.90931i
$11$		−	4608.39i		−	0.314760i	−0.987538	−	0.157380i	$-0.949695\pi$
$11$		−	4608.39i		−	0.314760i	0.987538	−	0.157380i	$-0.0503047\pi$
$12$	26120.9			1.25969
$13$			8985.26i			0.314599i	0.987551	+	0.157299i	$0.0502788\pi$
$13$			8985.26i			0.314599i	−0.987551	+	0.157299i	$0.949721\pi$
$14$			32329.1i			0.841552i
$15$	−47671.0			−0.941650
$16$	103456.			1.57861
$17$	−141765.			−1.69735			−0.848676	−	0.528913i	$-0.822600\pi$
$17$	−141765.			−1.69735			−0.848676	+	0.528913i	$0.822600\pi$
$18$			62417.8i			0.594591i
$19$	37622.4			0.288690			0.144345	−	0.989527i	$-0.453892\pi$
$19$	37622.4			0.288690			0.144345	+	0.989527i	$0.453892\pi$
$20$	−569370.			−3.55856
$21$	−52973.4			−0.272383
$22$	131525.			0.561460
$23$		−	368411.i		−	1.31650i	−0.752800	−	0.658250i	$-0.771297\pi$
$23$		−	368411.i		−	1.31650i	0.752800	−	0.658250i	$-0.228703\pi$
$24$			403817.i			1.21714i
$25$	648482.			1.66011
$26$	−256443.			−0.561173
$27$	−102276.			−0.192450
$28$	−632700.			−1.02936
$29$	1.07625e6			1.52168			0.760839	−	0.648940i	$-0.224788\pi$
$29$	1.07625e6			1.52168			0.760839	+	0.648940i	$0.224788\pi$
$30$		−	1.36055e6i		−	1.67969i
$31$		−	1.36196e6i		−	1.47475i	−0.675485	−	0.737374i	$-0.736066\pi$
$31$		−	1.36196e6i		−	1.47475i	0.675485	−	0.737374i	$-0.263934\pi$
$32$			742110.i			0.707732i
$33$			215513.i			0.181727i
$34$		−	4.04601e6i		−	3.02769i
$35$	1.15468e6			0.769469
$36$	−1.22155e6			−0.727282
$37$		−	454793.i		−	0.242665i	−0.992612	−	0.121332i	$-0.961283\pi$
$37$		−	454793.i		−	0.242665i	0.992612	−	0.121332i	$-0.0387167\pi$
$38$			1.07376e6i			0.514958i
$39$		−	420199.i		−	0.181634i
$40$		−	8.80219e6i		−	3.43835i
$41$	−2.19561e6			−0.776999			−0.388500	−	0.921449i	$-0.627006\pi$
$41$	−2.19561e6			−0.776999			−0.388500	+	0.921449i	$0.627006\pi$
$42$		−	1.51188e6i		−	0.485870i
$43$			155344.i			0.0454381i	0.999742	+	0.0227190i	$0.00723232\pi$
$43$			155344.i			0.0454381i	−0.999742	+	0.0227190i	$0.992768\pi$
$44$			2.57403e6i			0.686757i
$45$	2.22935e6			0.543662
$46$	1.05146e7			2.34834
$47$		−	4.12397e6i		−	0.845131i	−0.906332	−	0.422566i	$-0.861130\pi$
$47$		−	4.12397e6i		−	0.845131i	0.906332	−	0.422566i	$-0.138870\pi$
$48$	−4.83814e6			−0.911409
$49$	−4.48168e6			−0.777422
$50$			1.85079e7i			2.96126i
$51$	6.62967e6			0.979967
$52$		−	5.01874e6i		−	0.686407i
$53$	−8.47567e6			−1.07416			−0.537082	−	0.843530i	$-0.680474\pi$
$53$	−8.47567e6			−1.07416			−0.537082	+	0.843530i	$0.680474\pi$
$54$		−	2.91899e6i		−	0.343287i
$55$		−	4.69764e6i		−	0.513368i
$56$		−	9.78124e6i		−	0.994585i
$57$	−1.75943e6			−0.166675
$58$			3.07167e7i			2.71433i
$59$	8.59574e6	−	8.54071e6i	0.709374	−	0.704833i
$59$	8.59574e6	−	8.54071e6i	0.709374	−	0.704833i
$60$	2.66268e7			2.05454
$61$		−	1.90458e7i		−	1.37556i	−0.725918	−	0.687781i	$-0.758585\pi$
$61$		−	1.90458e7i		−	1.37556i	0.725918	−	0.687781i	$-0.241415\pi$
$62$	3.88709e7			2.63062
$63$	2.47732e6			0.157261
$64$	5.30453e6			0.316175
$65$			9.15927e6i			0.513106i
$66$	−6.15083e6			−0.324159
$67$		−	1.59131e6i		−	0.0789686i	−0.999220	−	0.0394843i	$-0.987428\pi$
$67$		−	1.59131e6i		−	0.0789686i	0.999220	−	0.0394843i	$-0.0125715\pi$
$68$	7.91830e7			3.70336
$69$			1.72289e7i			0.760081i
$70$			3.29551e7i			1.37256i
$71$	2.82229e7			1.11063			0.555314	−	0.831641i	$-0.312598\pi$
$71$	2.82229e7			1.11063			0.555314	+	0.831641i	$0.312598\pi$
$72$		−	1.88847e7i		−	0.702715i
$73$		−	3.05689e7i		−	1.07644i	−0.842806	−	0.538218i	$-0.819098\pi$
$73$		−	3.05689e7i		−	1.07644i	0.842806	−	0.538218i	$-0.180902\pi$
$74$	1.29800e7			0.432859
$75$	−3.03265e7			−0.958467
$76$	−2.10141e7			−0.629878
$77$		−	5.22015e6i		−	0.148498i
$78$	1.19926e7			0.323993
$79$	−4.78817e6			−0.122931			−0.0614655	−	0.998109i	$-0.519577\pi$
$79$	−4.78817e6			−0.122931			−0.0614655	+	0.998109i	$0.519577\pi$
$80$	1.05459e8			2.57469
$81$	4.78297e6			0.111111
$82$		−	6.26636e7i		−	1.38599i
$83$			6.63663e7i			1.39841i	0.714920	+	0.699206i	$0.246463\pi$
$83$			6.63663e7i			1.39841i	−0.714920	+	0.699206i	$0.753537\pi$
$84$	2.95884e7			0.594299
$85$	−1.44510e8			−2.76836
$86$	−4.43357e6			−0.0810512
$87$	−5.03314e7			−0.878542
$88$	−3.97933e7			−0.663559
$89$		−	8.43518e7i		−	1.34442i	−0.740361	−	0.672209i	$-0.765346\pi$
$89$		−	8.43518e7i		−	1.34442i	0.740361	−	0.672209i	$-0.234654\pi$
$90$			6.36266e7i			0.969769i
$91$			1.01780e7i			0.148422i
$92$			2.05777e8i			2.87240i
$93$			6.36926e7i			0.851446i
$94$	1.17700e8			1.50752
$95$	3.83510e7			0.470850
$96$		−	3.47051e7i		−	0.408609i
$97$			1.27671e8i			1.44214i	0.692864	+	0.721068i	$0.256349\pi$
$97$			1.27671e8i			1.44214i	−0.692864	+	0.721068i	$0.743651\pi$
$98$		−	1.27909e8i		−	1.38674i
$99$		−	1.00786e7i		−	0.104920i
$100$	−3.62211e8			−3.62211
$101$			3.20910e7i			0.308388i	0.988041	+	0.154194i	$0.0492781\pi$
$101$			3.20910e7i			0.308388i	−0.988041	+	0.154194i	$0.950722\pi$
$102$			1.89213e8i			1.74804i
$103$		−	1.23245e8i		−	1.09502i	−0.836800	−	0.547509i	$-0.815576\pi$
$103$		−	1.23245e8i		−	1.09502i	0.836800	−	0.547509i	$-0.184424\pi$
$104$	7.75874e7			0.663221
$105$	−5.39993e7			−0.444253
$106$		−	2.41899e8i		−	1.91607i
$107$	−5.92387e7			−0.451929			−0.225965	−	0.974136i	$-0.572553\pi$
$107$	−5.92387e7			−0.451929			−0.225965	+	0.974136i	$0.572553\pi$
$108$	5.71265e7			0.419897
$109$			6.91512e7i			0.489885i	0.969538	+	0.244942i	$0.0787690\pi$
$109$			6.91512e7i			0.489885i	−0.969538	+	0.244942i	$0.921231\pi$
$110$	1.34072e8			0.915732
$111$			2.12686e7i			0.140103i
$112$	1.17189e8			0.744758
$113$		−	7.29000e7i		−	0.447109i	−0.974691	−	0.223555i	$-0.928234\pi$
$113$		−	7.29000e7i		−	0.447109i	0.974691	−	0.223555i	$-0.0717661\pi$
$114$		−	5.02147e7i		−	0.297311i
$115$		−	3.75545e8i		−	2.14719i
$116$	−6.01145e8			−3.32007
$117$			1.96508e7i			0.104866i
$118$	2.43755e8	+	2.45325e8i	1.25726	+	1.26536i
$119$	−1.60584e8			−0.800780
$120$			4.11638e8i			1.98514i
$121$	1.93122e8			0.900926
$122$	5.43575e8			2.45369
$123$	1.02679e8			0.448601
$124$			7.60727e8i			3.21767i
$125$	2.62850e8			1.07663
$126$			7.07036e7i			0.280517i
$127$	−5.75493e7			−0.221221			−0.110610	−	0.993864i	$-0.535281\pi$
$127$	−5.75493e7			−0.221221			−0.110610	+	0.993864i	$0.535281\pi$
$128$			3.41374e8i			1.27172i
$129$		−	7.26471e6i		−	0.0262337i
$130$	−2.61409e8			−0.915265
$131$			4.64228e8i			1.57633i	0.615466	+	0.788164i	$0.288968\pi$
$131$			4.64228e8i			1.57633i	−0.615466	+	0.788164i	$0.711032\pi$
$132$		−	1.20376e8i		−	0.396499i
$133$	4.26167e7			0.136199
$134$	4.54165e7			0.140862
$135$	−1.04257e8			−0.313883
$136$			1.22413e9i			3.57827i
$137$	−1.42176e8			−0.403595			−0.201797	−	0.979427i	$-0.564678\pi$
$137$	−1.42176e8			−0.403595			−0.201797	+	0.979427i	$0.564678\pi$
$138$	−4.91718e8			−1.35581
$139$	−5.03971e6			−0.0135004			−0.00675020	−	0.999977i	$-0.502149\pi$
$139$	−5.03971e6			−0.0135004			−0.00675020	+	0.999977i	$0.502149\pi$
$140$	−6.44952e8			−1.67886
$141$			1.92859e8i			0.487937i
$142$			8.05493e8i			1.98111i
$143$	4.14076e7			0.0990230
$144$	2.26257e8			0.526202
$145$	1.09710e9			2.48184
$146$	8.72448e8			1.92012
$147$	2.09588e8			0.448845
$148$			2.54026e8i			0.529458i
$149$		−	9.48159e7i		−	0.192369i	−0.995364	−	0.0961847i	$-0.969336\pi$
$149$		−	9.48159e7i		−	0.192369i	0.995364	−	0.0961847i	$-0.0306639\pi$
$150$		−	8.65529e8i		−	1.70969i
$151$			3.28428e8i			0.631732i	0.948804	+	0.315866i	$0.102295\pi$
$151$			3.28428e8i			0.631732i	−0.948804	+	0.315866i	$0.897705\pi$
$152$		−	3.24868e8i		−	0.608601i
$153$	−3.10039e8			−0.565784
$154$	1.48985e8			0.264886
$155$		−	1.38834e9i		−	2.40529i
$156$			2.34703e8i			0.396297i
$157$		−	1.00364e9i		−	1.65188i	−0.563760	−	0.825939i	$-0.690646\pi$
$157$		−	1.00364e9i		−	1.65188i	0.563760	−	0.825939i	$-0.309354\pi$
$158$		−	1.36656e8i		−	0.219281i
$159$	3.96368e8			0.620169
$160$			7.56482e8i			1.15430i
$161$		−	4.17316e8i		−	0.621101i
$162$			1.36508e8i			0.198197i
$163$	2.53012e8			0.358419			0.179209	−	0.983811i	$-0.442646\pi$
$163$	2.53012e8			0.358419			0.179209	+	0.983811i	$0.442646\pi$
$164$	1.22637e9			1.69529
$165$			2.19687e8i			0.296393i
$166$	−1.89412e9			−2.49445
$167$	1.03285e9			1.32792			0.663959	−	0.747769i	$-0.268875\pi$
$167$	1.03285e9			1.32792			0.663959	+	0.747769i	$0.268875\pi$
$168$			4.57423e8i			0.574224i
$169$	7.34996e8			0.901027
$170$		−	4.12437e9i		−	4.93812i
$171$	8.22802e7			0.0962301
$172$		−	8.67677e7i		−	0.0991389i
$173$		−	3.04295e8i		−	0.339711i	−0.985469	−	0.169856i	$-0.945670\pi$
$173$		−	3.04295e8i		−	0.339711i	0.985469	−	0.169856i	$-0.0543301\pi$
$174$		−	1.43648e9i		−	1.56712i
$175$	7.34566e8			0.783211
$176$		−	4.76764e8i		−	0.496882i
$177$	−4.01983e8	+	3.99410e8i	−0.409557	+	0.406935i
$178$	2.40743e9			2.39814
$179$		−	1.71863e9i		−	1.67406i	−0.547157	−	0.837030i	$-0.684290\pi$
$179$		−	1.71863e9i		−	1.67406i	0.547157	−	0.837030i	$-0.315710\pi$
$180$	−1.24521e9			−1.18619
$181$	−9.08307e8			−0.846288			−0.423144	−	0.906062i	$-0.639074\pi$
$181$	−9.08307e8			−0.846288			−0.423144	+	0.906062i	$0.639074\pi$
$182$	−2.90485e8			−0.264751
$183$			8.90685e8i			0.794181i
$184$	−3.18121e9			−2.77537
$185$		−	4.63601e8i		−	0.395783i
$186$	−1.81781e9			−1.51879
$187$			6.53307e8i			0.534258i
$188$			2.30345e9i			1.84395i
$189$	−1.15853e8			−0.0907945
$190$			1.09455e9i			0.839889i
$191$			1.61997e9i			1.21723i	0.793464	+	0.608617i	$0.208275\pi$
$191$			1.61997e9i			1.21723i	−0.793464	+	0.608617i	$0.791725\pi$
$192$	−2.48068e8			−0.182544
$193$	2.18095e9			1.57187			0.785934	−	0.618311i	$-0.212183\pi$
$193$	2.18095e9			1.57187			0.785934	+	0.618311i	$0.212183\pi$
$194$	−3.64379e9			−2.57244
$195$		−	4.28337e8i		−	0.296242i
$196$	2.50326e9			1.69622
$197$	−2.14024e8			−0.142101			−0.0710505	−	0.997473i	$-0.522635\pi$
$197$	−2.14024e8			−0.142101			−0.0710505	+	0.997473i	$0.522635\pi$
$198$	2.87646e8			0.187153
$199$	1.13469e9			0.723543			0.361772	−	0.932267i	$-0.382172\pi$
$199$	1.13469e9			0.723543			0.361772	+	0.932267i	$0.382172\pi$
$200$		−	5.59962e9i		−	3.49976i
$201$			7.44180e7i			0.0455925i
$202$	−9.15888e8			−0.550094
$203$	1.21913e9			0.717900
$204$	−3.70302e9			−2.13814
$205$	−2.23813e9			−1.26727
$206$	3.51747e9			1.95326
$207$		−	8.05714e8i		−	0.438833i
$208$			9.29576e8i			0.496628i
$209$		−	1.73379e8i		−	0.0908680i
$210$		−	1.54116e9i		−	0.792447i
$211$			1.95172e9i			0.984663i	0.870408	+	0.492332i	$0.163855\pi$
$211$			1.95172e9i			0.984663i	−0.870408	+	0.492332i	$0.836145\pi$
$212$	4.73411e9			2.34366
$213$	−1.31986e9			−0.641222
$214$		−	1.69069e9i		−	0.806139i
$215$			1.58352e8i			0.0741088i
$216$			8.83149e8i			0.405713i
$217$		−	1.54276e9i		−	0.695759i
$218$	−1.97360e9			−0.873843
$219$			1.42957e9i			0.621481i
$220$			2.62388e9i			1.12009i
$221$		−	1.27379e9i		−	0.533985i
$222$	−6.07013e8			−0.249911
$223$	1.32438e9			0.535543			0.267772	−	0.963482i	$-0.413713\pi$
$223$	1.32438e9			0.535543			0.267772	+	0.963482i	$0.413713\pi$
$224$			8.40624e8i			0.333895i
$225$	1.41823e9			0.553371
$226$	2.08059e9			0.797542
$227$			1.82424e9i			0.687036i	0.939146	+	0.343518i	$0.111619\pi$
$227$			1.82424e9i			0.687036i	−0.939146	+	0.343518i	$0.888381\pi$
$228$	9.82732e8			0.363660
$229$			1.80199e9i			0.655255i	0.944807	+	0.327628i	$0.106249\pi$
$229$			1.80199e9i			0.655255i	−0.944807	+	0.327628i	$0.893751\pi$
$230$	1.07182e10			3.83010
$231$			2.44122e8i			0.0857353i
$232$		−	9.29342e9i		−	3.20792i
$233$		−	3.16225e9i		−	1.07293i	−0.843921	−	0.536467i	$-0.819759\pi$
$233$		−	3.16225e9i		−	1.07293i	0.843921	−	0.536467i	$-0.180241\pi$
$234$	−5.60840e8			−0.187058
$235$		−	4.20383e9i		−	1.37840i
$236$	−4.80117e9	+	4.77044e9i	−1.54774	+	1.53784i
$237$	2.23921e8			0.0709743
$238$		−	4.58311e9i		−	1.42841i
$239$	5.10702e9			1.56522			0.782612	−	0.622510i	$-0.213887\pi$
$239$	5.10702e9			1.56522			0.782612	+	0.622510i	$0.213887\pi$
$240$	−4.93183e9			−1.48650
$241$	−2.02026e8			−0.0598880			−0.0299440	−	0.999552i	$-0.509533\pi$
$241$	−2.02026e8			−0.0598880			−0.0299440	+	0.999552i	$0.509533\pi$
$242$			5.51176e9i			1.60705i
$243$	−2.23677e8			−0.0641500
$244$			1.06381e10i			3.00127i
$245$	−4.56847e9			−1.26796
$246$			2.93049e9i			0.800202i
$247$			3.38047e8i			0.0908217i
$248$	−1.17605e10			−3.10898
$249$		−	3.10364e9i		−	0.807373i
$250$			7.50184e9i			1.92047i
$251$	2.06222e9			0.519565			0.259782	−	0.965667i	$-0.416349\pi$
$251$	2.06222e9			0.519565			0.259782	+	0.965667i	$0.416349\pi$
$252$	−1.38371e9			−0.343119
$253$	−1.69778e9			−0.414381
$254$		−	1.64248e9i		−	0.394607i
$255$	6.75806e9			1.59831
$256$	−8.38497e9			−1.95228
$257$	−1.00844e9			−0.231163			−0.115581	−	0.993298i	$-0.536873\pi$
$257$	−1.00844e9			−0.231163			−0.115581	+	0.993298i	$0.536873\pi$
$258$	2.07337e8			0.0467949
$259$		−	5.15166e8i		−	0.114485i
$260$		−	5.11593e9i		−	1.11952i
$261$	2.35377e9			0.507226
$262$	−1.32492e10			−2.81181
$263$	−7.21830e9			−1.50873			−0.754366	−	0.656454i	$-0.772055\pi$
$263$	−7.21830e9			−1.50873			−0.754366	+	0.656454i	$0.772055\pi$
$264$	1.86095e9			0.383106
$265$	−8.63981e9			−1.75195
$266$			1.21630e9i			0.242948i
$267$			3.94474e9i			0.776200i
$268$			8.88828e8i			0.172297i
$269$		−	6.48688e9i		−	1.23887i	−0.785047	−	0.619437i	$-0.787361\pi$
$269$		−	6.48688e9i		−	1.23887i	0.785047	−	0.619437i	$-0.212639\pi$
$270$		−	2.97552e9i		−	0.559897i
$271$	−8.97992e9			−1.66493			−0.832464	−	0.554079i	$-0.813070\pi$
$271$	−8.97992e9			−1.66493			−0.832464	+	0.554079i	$0.813070\pi$
$272$	−1.46663e10			−2.67945
$273$		−	4.75980e8i		−	0.0856915i
$274$		−	4.05777e9i		−	0.719921i
$275$		−	2.98846e9i		−	0.522536i
$276$		−	9.62323e9i		−	1.65838i
$277$	−1.27542e9			−0.216638			−0.108319	−	0.994116i	$-0.534547\pi$
$277$	−1.27542e9			−0.216638			−0.108319	+	0.994116i	$0.534547\pi$
$278$		−	1.43835e8i		−	0.0240816i
$279$		−	2.97861e9i		−	0.491583i
$280$		−	9.97066e9i		−	1.62215i
$281$	3.69474e9			0.592595			0.296298	−	0.955096i	$-0.404248\pi$
$281$	3.69474e9			0.592595			0.296298	+	0.955096i	$0.404248\pi$
$282$	−5.50427e9			−0.870368
$283$			1.45323e9i			0.226562i	0.993563	+	0.113281i	$0.0361361\pi$
$283$			1.45323e9i			0.226562i	−0.993563	+	0.113281i	$0.963864\pi$
$284$	−1.57640e10			−2.42322
$285$	−1.79350e9			−0.271845
$286$			1.18179e9i			0.176635i
$287$	−2.48708e9			−0.366574
$288$			1.62300e9i			0.235911i
$289$	1.31214e10			1.88100
$290$			3.13116e10i			4.42703i
$291$		−	5.97060e9i		−	0.832618i
$292$			1.70743e10i			2.34862i
$293$	8.50585e9			1.15411			0.577055	−	0.816705i	$-0.304202\pi$
$293$	8.50585e9			1.15411			0.577055	+	0.816705i	$0.304202\pi$
$294$			5.98171e9i			0.800637i
$295$	8.76220e9	−	8.70611e9i	1.15698	−	1.14957i
$296$	−3.92712e9			−0.511573
$297$			4.71328e8i			0.0605755i
$298$	2.70608e9			0.343143
$299$	3.31027e9			0.414169
$300$	1.69389e10			2.09123
$301$			1.75965e8i			0.0214369i
$302$	−9.37347e9			−1.12687
$303$		−	1.50075e9i		−	0.178048i
$304$	3.89225e9			0.455729
$305$		−	1.94147e10i		−	2.24352i
$306$		−	8.84863e9i		−	1.00923i
$307$	−5.58937e9			−0.629230			−0.314615	−	0.949219i	$-0.601875\pi$
$307$	−5.58937e9			−0.629230			−0.314615	+	0.949219i	$0.601875\pi$
$308$			2.91573e9i			0.324000i
$309$			5.76361e9i			0.632209i
$310$	3.96236e10			4.29050
$311$	−3.30025e9			−0.352781			−0.176391	−	0.984320i	$-0.556442\pi$
$311$	−3.30025e9			−0.352781			−0.176391	+	0.984320i	$0.556442\pi$
$312$	−3.62840e9			−0.382911
$313$		−	1.37415e10i		−	1.43171i	−0.698247	−	0.715857i	$-0.746036\pi$
$313$		−	1.37415e10i		−	1.43171i	0.698247	−	0.715857i	$-0.253964\pi$
$314$	2.86442e10			2.94658
$315$	2.52530e9			0.256490
$316$	2.67445e9			0.268217
$317$	−8.87944e9			−0.879323			−0.439661	−	0.898164i	$-0.644902\pi$
$317$	−8.87944e9			−0.879323			−0.439661	+	0.898164i	$0.644902\pi$
$318$			1.13125e10i			1.10624i
$319$		−	4.95981e9i		−	0.478963i
$320$	5.40726e9			0.515676
$321$	2.77032e9			0.260921
$322$	1.19104e10			1.10790
$323$	−5.33352e9			−0.490009
$324$	−2.67154e9			−0.242427
$325$			5.82678e9i			0.522270i
$326$			7.22106e9i			0.639338i
$327$		−	3.23388e9i		−	0.282835i
$328$			1.89590e10i			1.63803i
$329$		−	4.67142e9i		−	0.398718i
$330$	−6.26995e9			−0.528698
$331$	−2.05246e10			−1.70987			−0.854934	−	0.518736i	$-0.826403\pi$
$331$	−2.05246e10			−1.70987			−0.854934	+	0.518736i	$0.826403\pi$
$332$		−	3.70691e10i		−	3.05112i
$333$		−	9.94633e8i		−	0.0808883i
$334$			2.94779e10i			2.36870i
$335$		−	1.62212e9i		−	0.128797i
$336$	−5.48039e9			−0.429986
$337$			9.56605e9i			0.741674i	0.928698	+	0.370837i	$0.120929\pi$
$337$			9.56605e9i			0.741674i	−0.928698	+	0.370837i	$0.879071\pi$
$338$			2.09771e10i			1.60723i
$339$			3.40920e9i			0.258139i
$340$	8.07164e10			6.04013
$341$	−6.27645e9			−0.464191
$342$			2.34831e9i			0.171653i
$343$	−1.16067e10			−0.838555
$344$	1.34139e9			0.0957901
$345$			1.75625e10i			1.23968i
$346$	8.68468e9			0.605968
$347$			2.43628e9i			0.168039i	0.996464	+	0.0840194i	$0.0267758\pi$
$347$			2.43628e9i			0.168039i	−0.996464	+	0.0840194i	$0.973224\pi$
$348$	2.81128e10			1.91684
$349$		−	9.35066e8i		−	0.0630290i	−0.999503	−	0.0315145i	$-0.989967\pi$
$349$		−	9.35066e8i		−	0.0630290i	0.999503	−	0.0315145i	$-0.0100330\pi$
$350$			2.09648e10i			1.39707i
$351$		−	9.18975e8i		−	0.0605446i
$352$	3.41994e9			0.222765
$353$		−	3.18010e9i		−	0.204806i	−0.994743	−	0.102403i	$-0.967347\pi$
$353$		−	3.18010e9i		−	0.204806i	0.994743	−	0.102403i	$-0.0326531\pi$
$354$	−1.13993e10	−	1.14727e10i	−0.725880	−	0.730557i
$355$	2.87695e10			1.81142
$356$			4.71149e10i			2.93331i
$357$	7.50975e9			0.462330
$358$	4.90504e10			2.98614
$359$	5.00991e9			0.301615			0.150807	−	0.988563i	$-0.451813\pi$
$359$	5.00991e9			0.301615			0.150807	+	0.988563i	$0.451813\pi$
$360$		−	1.92504e10i		−	1.14612i
$361$	−1.55681e10			−0.916658
$362$		−	2.59234e10i		−	1.50959i
$363$	−9.03140e9			−0.520150
$364$		−	5.68497e9i		−	0.323834i
$365$		−	3.11609e10i		−	1.75565i
$366$	−2.54205e10			−1.41664
$367$		−	4.69877e9i		−	0.259012i	−0.991579	−	0.129506i	$-0.958661\pi$
$367$		−	4.69877e9i		−	0.259012i	0.991579	−	0.129506i	$-0.0413391\pi$
$368$		−	3.81141e10i		−	2.07824i
$369$	−4.80181e9			−0.259000
$370$	1.32313e10			0.705987
$371$	−9.60080e9			−0.506771
$372$		−	3.55757e10i		−	1.85772i
$373$	−2.30261e10			−1.18955			−0.594777	−	0.803890i	$-0.702760\pi$
$373$	−2.30261e10			−1.18955			−0.594777	+	0.803890i	$0.702760\pi$
$374$	−1.86456e10			−0.952995
$375$	−1.22923e10			−0.621595
$376$	−3.56103e10			−1.78166
$377$			9.67043e9i			0.478719i
$378$		−	3.30648e9i		−	0.161957i
$379$	2.29516e10			1.11239			0.556194	−	0.831052i	$-0.312261\pi$
$379$	2.29516e10			1.11239			0.556194	+	0.831052i	$0.312261\pi$
$380$	−2.14211e10			−1.02732
$381$	2.69132e9			0.127722
$382$	−4.62346e10			−2.17127
$383$	3.54785e10			1.64881			0.824403	−	0.566003i	$-0.191511\pi$
$383$	3.54785e10			1.64881			0.824403	+	0.566003i	$0.191511\pi$
$384$		−	1.59645e10i		−	0.734225i
$385$		−	5.32124e9i		−	0.242198i
$386$			6.22450e10i			2.80385i
$387$			3.39737e8i			0.0151460i
$388$		−	7.13111e10i		−	3.14652i
$389$	−3.93579e10			−1.71883			−0.859415	−	0.511278i	$-0.829172\pi$
$389$	−3.93579e10			−1.71883			−0.859415	+	0.511278i	$0.829172\pi$
$390$	1.22249e10			0.528429
$391$			5.22276e10i			2.23456i
$392$			3.86992e10i			1.63892i
$393$		−	2.17098e10i		−	0.910093i
$394$		−	6.10832e9i		−	0.253476i
$395$	−4.88090e9			−0.200499
$396$			5.62941e9i			0.228919i
$397$		−	3.54396e10i		−	1.42668i	−0.700818	−	0.713340i	$-0.747182\pi$
$397$		−	3.54396e10i		−	1.42668i	0.700818	−	0.713340i	$-0.252818\pi$
$398$			3.23844e10i			1.29064i
$399$	−1.99299e9			−0.0786344
$400$	6.70891e10			2.62067
$401$		−	9.00839e9i		−	0.348393i	−0.984711	−	0.174197i	$-0.944267\pi$
$401$		−	9.00839e9i		−	0.348393i	0.984711	−	0.174197i	$-0.0557328\pi$
$402$	−2.12392e9			−0.0813268
$403$	1.22376e10			0.463954
$404$		−	1.79245e10i		−	0.672855i
$405$	4.87560e9			0.181221
$406$			3.47943e10i			1.28057i
$407$	−2.09587e9			−0.0763811
$408$		−	5.72470e10i		−	2.06591i
$409$			1.89660e10i			0.677772i	0.940827	+	0.338886i	$0.110050\pi$
$409$			1.89660e10i			0.677772i	−0.940827	+	0.338886i	$0.889950\pi$
$410$		−	6.38772e10i		−	2.26053i
$411$	6.64893e9			0.233015
$412$			6.88390e10i			2.38916i
$413$	9.73681e9	−	9.67448e9i	0.334670	−	0.332527i
$414$	2.29954e10			0.782779
$415$			6.76515e10i			2.28079i
$416$	−6.66806e9			−0.222652
$417$	2.35684e8			0.00779445
$418$	4.94830e9			0.162088
$419$			3.49441e9i			0.113375i	0.998392	+	0.0566876i	$0.0180539\pi$
$419$			3.49441e9i			0.113375i	−0.998392	+	0.0566876i	$0.981946\pi$
$420$	3.01614e10			0.969292
$421$			2.84577e10i			0.905881i	0.891541	+	0.452941i	$0.149625\pi$
$421$			2.84577e10i			0.905881i	−0.891541	+	0.452941i	$0.850375\pi$
$422$	−5.57028e10			−1.75642
$423$		−	9.01912e9i		−	0.281710i
$424$			7.31872e10i			2.26450i
$425$	−9.19317e10			−2.81780
$426$		−	3.76692e10i		−	1.14379i
$427$		−	2.15741e10i		−	0.648965i
$428$	3.30879e10			0.986040
$429$	−1.93644e9			−0.0571710
$430$	−4.51943e9			−0.132193
$431$			5.38709e9i			0.156115i	0.996949	+	0.0780575i	$0.0248718\pi$
$431$			5.38709e9i			0.156115i	−0.996949	+	0.0780575i	$0.975128\pi$
$432$	−1.05810e10			−0.303803
$433$	−1.33819e10			−0.380686			−0.190343	−	0.981718i	$-0.560960\pi$
$433$	−1.33819e10			−0.380686			−0.190343	+	0.981718i	$0.560960\pi$
$434$	4.40309e10			1.24108
$435$	−5.13061e10			−1.43289
$436$		−	3.86246e10i		−	1.06885i
$437$		−	1.38605e10i		−	0.380061i
$438$	−4.08003e10			−1.10858
$439$	4.83699e10			1.30232			0.651159	−	0.758941i	$-0.274283\pi$
$439$	4.83699e10			1.30232			0.651159	+	0.758941i	$0.274283\pi$
$440$	−4.05640e10			−1.08226
$441$	−9.80144e9			−0.259141
$442$	3.63545e10			0.952508
$443$			4.24323e10i			1.10175i	0.834589	+	0.550873i	$0.185705\pi$
$443$			4.24323e10i			1.10175i	−0.834589	+	0.550873i	$0.814295\pi$
$444$		−	1.18796e10i		−	0.305682i
$445$		−	8.59854e10i		−	2.19273i
$446$			3.77984e10i			0.955288i
$447$			4.43410e9i			0.111065i
$448$	6.00870e9			0.149166
$449$	6.76235e9			0.166384			0.0831921	−	0.996534i	$-0.473488\pi$
$449$	6.76235e9			0.166384			0.0831921	+	0.996534i	$0.473488\pi$
$450$			4.04768e10i			0.987088i
$451$			1.01183e10i			0.244568i
$452$			4.07185e10i			0.975524i
$453$		−	1.53591e10i		−	0.364731i
$454$	−5.20646e10			−1.22552
$455$			1.03751e10i			0.242074i
$456$			1.51926e10i			0.351376i
$457$		−	6.09387e10i		−	1.39710i	−0.715560	−	0.698551i	$-0.753828\pi$
$457$		−	6.09387e10i		−	1.39710i	0.715560	−	0.698551i	$-0.246172\pi$
$458$	−5.14295e10			−1.16883
$459$	1.44991e10			0.326656
$460$			2.09762e11i			4.68484i
$461$	−2.44762e10			−0.541927			−0.270964	−	0.962590i	$-0.587342\pi$
$461$	−2.44762e10			−0.541927			−0.270964	+	0.962590i	$0.587342\pi$
$462$	−6.96734e9			−0.152932
$463$		−	3.15779e10i		−	0.687163i	−0.939123	−	0.343581i	$-0.888360\pi$
$463$		−	3.15779e10i		−	0.687163i	0.939123	−	0.343581i	$-0.111640\pi$
$464$	1.11345e11			2.40213
$465$			6.49261e10i			1.38870i
$466$	9.02519e10			1.91387
$467$			7.82070e10i			1.64429i	0.569280	+	0.822144i	$0.307222\pi$
$467$			7.82070e10i			1.64429i	−0.569280	+	0.822144i	$0.692778\pi$
$468$		−	1.09760e10i		−	0.228802i
$469$		−	1.80255e9i		−	0.0372560i
$470$	1.19979e11			2.45875
$471$			4.69354e10i			0.953712i
$472$	−7.37487e10	−	7.42239e10i	−1.48589	−	1.49546i
$473$	7.15885e8			0.0143021
$474$			6.39078e9i			0.126602i
$475$	2.43974e10			0.479258
$476$	8.96944e10			1.74718
$477$	−1.85363e10			−0.358055
$478$			1.45756e11i			2.79200i
$479$	9.23414e8			0.0175410			0.00877050	−	0.999962i	$-0.497208\pi$
$479$	9.23414e8			0.0175410			0.00877050	+	0.999962i	$0.497208\pi$
$480$		−	3.53772e10i		−	0.666435i
$481$	4.08643e9			0.0763421
$482$		−	5.76591e9i		−	0.106827i
$483$			1.95160e10i			0.358593i
$484$	−1.07869e11			−1.96568
$485$			1.30144e11i			2.35210i
$486$		−	6.38383e9i		−	0.114429i
$487$	−1.08429e10			−0.192766			−0.0963829	−	0.995344i	$-0.530727\pi$
$487$	−1.08429e10			−0.192766			−0.0963829	+	0.995344i	$0.530727\pi$
$488$	−1.64460e11			−2.89989
$489$	−1.18322e10			−0.206933
$490$		−	1.30386e11i		−	2.26176i
$491$	8.23576e10			1.41703			0.708513	−	0.705698i	$-0.249366\pi$
$491$	8.23576e10			1.41703			0.708513	+	0.705698i	$0.249366\pi$
$492$	−5.73515e10			−0.978778
$493$	−1.52575e11			−2.58282
$494$	−9.64799e9			−0.162005
$495$		−	1.02737e10i		−	0.171123i
$496$		−	1.40902e11i		−	2.32805i
$497$	3.19695e10			0.523974
$498$	8.85791e10			1.44017
$499$	−5.20239e10			−0.839075			−0.419538	−	0.907738i	$-0.637808\pi$
$499$	−5.20239e10			−0.839075			−0.419538	+	0.907738i	$0.637808\pi$
$500$	−1.46816e11			−2.34905
$501$	−4.83016e10			−0.766674
$502$			5.88564e10i			0.926785i
$503$		−	9.39091e10i		−	1.46702i	−0.679680	−	0.733509i	$-0.737881\pi$
$503$		−	9.39091e10i		−	1.46702i	0.679680	−	0.733509i	$-0.262119\pi$
$504$		−	2.13916e10i		−	0.331528i
$505$			3.27124e10i			0.502976i
$506$		−	4.84553e10i		−	0.739161i
$507$	−3.43724e10			−0.520208
$508$	3.21443e10			0.482669
$509$		−	1.17018e11i		−	1.74334i	−0.490095	−	0.871669i	$-0.663038\pi$
$509$		−	1.17018e11i		−	1.74334i	0.490095	−	0.871669i	$-0.336962\pi$
$510$			1.92878e11i			2.85102i
$511$		−	3.46269e10i		−	0.507843i
$512$		−	1.51918e11i		−	2.21070i
$513$	−3.84786e9			−0.0555585
$514$		−	2.87813e10i		−	0.412342i
$515$		−	1.25632e11i		−	1.78596i
$516$			4.05772e9i			0.0572379i
$517$	−1.90049e10			−0.266013
$518$	1.47030e10			0.204215
$519$			1.42304e10i			0.196132i
$520$	7.90900e10			1.08170
$521$	9.93682e10			1.34864			0.674321	−	0.738438i	$-0.264436\pi$
$521$	9.93682e10			1.34864			0.674321	+	0.738438i	$0.264436\pi$
$522$			6.71774e10i			0.904776i
$523$	−5.39431e10			−0.720990			−0.360495	−	0.932761i	$-0.617392\pi$
$523$	−5.39431e10			−0.720990			−0.360495	+	0.932761i	$0.617392\pi$
$524$		−	2.59296e11i		−	3.43930i
$525$	−3.43523e10			−0.452187
$526$		−	2.06013e11i		−	2.69123i
$527$			1.93078e11i			2.50317i
$528$			2.22961e10i			0.286875i
$529$	−5.74154e10			−0.733172
$530$		−	2.46583e11i		−	3.12507i
$531$	1.87989e10	−	1.86785e10i	0.236458	−	0.234944i
$532$	−2.38037e10			−0.297165
$533$		−	1.97282e10i		−	0.244443i
$534$	−1.12584e11			−1.38457
$535$	−6.03859e10			−0.737090
$536$	−1.37409e10			−0.166477
$537$			8.03725e10i			0.966519i
$538$	1.85138e11			2.20987
$539$			2.06534e10i			0.244701i
$540$	5.82328e10			0.684845
$541$			1.11202e11i			1.29815i	0.760725	+	0.649075i	$0.224844\pi$
$541$			1.11202e11i			1.29815i	−0.760725	+	0.649075i	$0.775156\pi$
$542$		−	2.56290e11i		−	2.96985i
$543$	4.24773e10			0.488605
$544$		−	1.05205e11i		−	1.20127i
$545$			7.04904e10i			0.798995i
$546$	1.35846e10			0.152854
$547$	−1.12537e11			−1.25703			−0.628516	−	0.777797i	$-0.716337\pi$
$547$	−1.12537e11			−1.25703			−0.628516	+	0.777797i	$0.716337\pi$
$548$	7.94130e10			0.880581
$549$		−	4.16532e10i		−	0.458521i
$550$	8.52917e10			0.932086
$551$	4.04913e10			0.439294
$552$	1.48771e11			1.60236
$553$	−5.42380e9			−0.0579966
$554$		−	3.64009e10i		−	0.386432i
$555$			2.16805e10i			0.228505i
$556$	2.81494e9			0.0294558
$557$	4.45807e10			0.463155			0.231578	−	0.972816i	$-0.425611\pi$
$557$	4.45807e10			0.463155			0.231578	+	0.972816i	$0.425611\pi$
$558$	8.50106e10			0.876872
$559$	−1.39580e9			−0.0142948
$560$	1.19459e11			1.21469
$561$		−	3.05521e10i		−	0.308454i
$562$			1.05449e11i			1.05706i
$563$		−	3.41893e10i		−	0.340296i	−0.985419	−	0.170148i	$-0.945575\pi$
$563$		−	3.41893e10i		−	0.340296i	0.985419	−	0.170148i	$-0.0544246\pi$
$564$		−	1.07722e11i		−	1.06460i
$565$		−	7.43118e10i		−	0.729229i
$566$	−4.14756e10			−0.404136
$567$	5.41790e9			0.0524202
$568$		−	2.43704e11i		−	2.34137i
$569$		−	1.30593e11i		−	1.24586i	−0.782277	−	0.622930i	$-0.785942\pi$
$569$		−	1.30593e11i		−	1.24586i	0.782277	−	0.622930i	$-0.214058\pi$
$570$		−	5.11871e10i		−	0.484910i
$571$			1.69505e11i			1.59455i	0.603616	+	0.797275i	$0.293726\pi$
$571$			1.69505e11i			1.59455i	−0.603616	+	0.797275i	$0.706274\pi$
$572$	−2.31283e10			−0.216053
$573$		−	7.57586e10i		−	0.702770i
$574$		−	7.09821e10i		−	0.653885i
$575$		−	2.38908e11i		−	2.18554i
$576$	1.16010e10			0.105392
$577$	−2.04372e11			−1.84382			−0.921909	−	0.387407i	$-0.873371\pi$
$577$	−2.04372e11			−1.84382			−0.921909	+	0.387407i	$0.873371\pi$
$578$			3.74490e11i			3.35528i
$579$	−1.01993e11			−0.907518
$580$	−6.12786e11			−5.41498
$581$			7.51763e10i			0.659745i
$582$	1.70403e11			1.48520
$583$			3.90593e10i			0.338104i
$584$	−2.63961e11			−2.26928
$585$			2.00313e10i			0.171035i
$586$			2.42760e11i			2.05867i
$587$		−	2.15948e11i		−	1.81885i	−0.415868	−	0.909425i	$-0.636522\pi$
$587$		−	2.15948e11i		−	1.81885i	0.415868	−	0.909425i	$-0.363478\pi$
$588$	−1.17066e11			−0.979310
$589$		−	5.12402e10i		−	0.425745i
$590$	2.48476e11	+	2.50076e11i	2.05057	+	2.06379i
$591$	1.00089e10			0.0820421
$592$		−	4.70509e10i		−	0.383073i
$593$	−8.98244e10			−0.726400			−0.363200	−	0.931711i	$-0.618316\pi$
$593$	−8.98244e10			−0.726400			−0.363200	+	0.931711i	$0.618316\pi$
$594$	−1.34519e10			−0.108053
$595$	−1.63693e11			−1.30606
$596$			5.29597e10i			0.419720i
$597$	−5.30641e10			−0.417738
$598$			9.44762e10i			0.738784i
$599$	1.85353e11			1.43977			0.719885	−	0.694094i	$-0.244195\pi$
$599$	1.85353e11			1.43977			0.719885	+	0.694094i	$0.244195\pi$
$600$			2.61868e11i			2.02059i
$601$		−	6.21320e10i		−	0.476231i	−0.971237	−	0.238116i	$-0.923470\pi$
$601$		−	6.21320e10i		−	0.476231i	0.971237	−	0.238116i	$-0.0765297\pi$
$602$	−5.02212e9			−0.0382385
$603$		−	3.48019e9i		−	0.0263229i
$604$		−	1.83445e11i		−	1.37834i
$605$	1.96862e11			1.46940
$606$	4.28318e10			0.317597
$607$	1.27832e10			0.0941638			0.0470819	−	0.998891i	$-0.485008\pi$
$607$	1.27832e10			0.0941638			0.0470819	+	0.998891i	$0.485008\pi$
$608$			2.79200e10i			0.204315i
$609$	−5.70128e10			−0.414480
$610$	5.54101e11			4.00193
$611$	3.70550e10			0.265877
$612$	1.73173e11			1.23445
$613$		−	2.61394e11i		−	1.85120i	−0.378501	−	0.925601i	$-0.623560\pi$
$613$		−	2.61394e11i		−	1.85120i	0.378501	−	0.925601i	$-0.376440\pi$
$614$		−	1.59523e11i		−	1.12240i
$615$	1.04667e11			0.731661
$616$	−4.50758e10			−0.313055
$617$	−6.95322e10			−0.479783			−0.239892	−	0.970800i	$-0.577112\pi$
$617$	−6.95322e10			−0.479783			−0.239892	+	0.970800i	$0.577112\pi$
$618$	−1.64496e11			−1.12772
$619$	1.25236e11			0.853034			0.426517	−	0.904480i	$-0.359740\pi$
$619$	1.25236e11			0.853034			0.426517	+	0.904480i	$0.359740\pi$
$620$			7.75459e11i			5.24798i
$621$			3.76795e10i			0.253360i
$622$		−	9.41904e10i		−	0.629282i
$623$		−	9.55494e10i		−	0.634272i
$624$		−	4.34720e10i		−	0.286728i
$625$	1.46274e10			0.0958622
$626$	3.92187e11			2.55385
$627$			8.10813e9i			0.0524627i
$628$			5.60584e11i			3.60414i
$629$			6.44735e10i			0.411888i
$630$			7.20729e10i			0.457520i
$631$	2.29719e11			1.44904			0.724519	−	0.689255i	$-0.242062\pi$
$631$	2.29719e11			1.44904			0.724519	+	0.689255i	$0.242062\pi$
$632$			4.13457e10i			0.259157i
$633$		−	9.12729e10i		−	0.568496i
$634$		−	2.53422e11i		−	1.56851i
$635$	−5.86638e10			−0.360807
$636$	−2.21392e11			−1.35311
$637$		−	4.02691e10i		−	0.244576i
$638$	1.41555e11			0.854361
$639$	6.17236e10			0.370209
$640$			3.47985e11i			2.07415i
$641$	2.02783e11			1.20115			0.600577	−	0.799567i	$-0.294938\pi$
$641$	2.02783e11			1.20115			0.600577	+	0.799567i	$0.294938\pi$
$642$			7.90659e10i			0.465425i
$643$	−5.69766e10			−0.333313			−0.166657	−	0.986015i	$-0.553297\pi$
$643$	−5.69766e10			−0.333313			−0.166657	+	0.986015i	$0.553297\pi$
$644$			2.33093e11i			1.35515i
$645$		−	7.40540e9i		−	0.0427868i
$646$		−	1.52221e11i		−	0.874065i
$647$	−3.14802e11			−1.79647			−0.898237	−	0.439512i	$-0.855151\pi$
$647$	−3.14802e11			−1.79647			−0.898237	+	0.439512i	$0.855151\pi$
$648$		−	4.13008e10i		−	0.234238i
$649$	−3.93590e10	−	3.96125e10i	−0.221853	−	0.223282i
$650$	−1.66298e11			−0.931611
$651$			7.21477e10i			0.401697i
$652$	−1.41321e11			−0.782015
$653$	3.29760e11			1.81361			0.906807	−	0.421546i	$-0.138512\pi$
$653$	3.29760e11			1.81361			0.906807	+	0.421546i	$0.138512\pi$
$654$	9.22962e10			0.504513
$655$			4.73218e11i			2.57097i
$656$	−2.27149e11			−1.22658
$657$		−	6.68542e10i		−	0.358812i
$658$	1.33324e11			0.711222
$659$		−	1.81204e11i		−	0.960785i	−0.877053	−	0.480393i	$-0.840494\pi$
$659$		−	1.81204e11i		−	0.960785i	0.877053	−	0.480393i	$-0.159506\pi$
$660$		−	1.22707e11i		−	0.646685i
$661$	2.36523e11			1.23899			0.619494	−	0.785001i	$-0.287338\pi$
$661$	2.36523e11			1.23899			0.619494	+	0.785001i	$0.287338\pi$
$662$		−	5.85780e11i		−	3.05002i
$663$			5.95693e10i			0.308297i
$664$	5.73070e11			2.94806
$665$	4.34420e10			0.222138
$666$	2.83872e10			0.144286
$667$		−	3.96504e11i		−	2.00329i
$668$	−5.76901e11			−2.89731
$669$	−6.19353e10			−0.309196
$670$	4.62960e10			0.229744
$671$	−8.77706e10			−0.432971
$672$		−	3.93121e10i		−	0.192774i
$673$			3.76786e11i			1.83668i	0.395790	+	0.918341i	$0.370471\pi$
$673$			3.76786e11i			1.83668i	−0.395790	+	0.918341i	$0.629529\pi$
$674$	−2.73019e11			−1.32298
$675$	−6.63240e10			−0.319489
$676$	−4.10534e11			−1.96590
$677$	3.19535e11			1.52112			0.760559	−	0.649268i	$-0.224925\pi$
$677$	3.19535e11			1.52112			0.760559	+	0.649268i	$0.224925\pi$
$678$	−9.72997e10			−0.460461
$679$			1.44619e11i			0.680374i
$680$			1.24784e12i			5.83610i
$681$		−	8.53114e10i		−	0.396660i
$682$		−	1.79132e11i		−	0.828011i
$683$		−	1.91834e11i		−	0.881540i	−0.897620	−	0.440770i	$-0.854705\pi$
$683$		−	1.91834e11i		−	0.881540i	0.897620	−	0.440770i	$-0.145295\pi$
$684$	−4.59578e10			−0.209959
$685$	−1.44930e11			−0.658257
$686$		−	3.31259e11i		−	1.49579i
$687$		−	8.42707e10i		−	0.378312i
$688$			1.60712e10i			0.0717289i
$689$		−	7.61561e10i		−	0.337931i
$690$	−5.01241e11			−2.21131
$691$			4.73092e10i			0.207508i	0.994603	+	0.103754i	$0.0330854\pi$
$691$			4.73092e10i			0.207508i	−0.994603	+	0.103754i	$0.966915\pi$
$692$			1.69965e11i			0.741198i
$693$		−	1.14165e10i		−	0.0494993i
$694$	−6.95324e10			−0.299743
$695$	−5.13731e9			−0.0220189
$696$			4.34610e11i			1.85209i
$697$	3.11260e11			1.31884
$698$	2.66871e10			0.112430
$699$			1.47884e11i			0.619459i
$700$	−4.10294e11			−1.70885
$701$		−	1.75140e11i		−	0.725292i	−0.931927	−	0.362646i	$-0.881873\pi$
$701$		−	1.75140e11i		−	0.725292i	0.931927	−	0.362646i	$-0.118127\pi$
$702$	2.62279e10			0.107998
$703$		−	1.71104e10i		−	0.0700550i
$704$		−	2.44454e10i		−	0.0995191i
$705$			1.96594e11i			0.795818i
$706$	9.07613e10			0.365327
$707$			3.63510e10i			0.145492i
$708$	2.24529e11	−	2.23091e11i	0.893591	−	0.887870i
$709$	−4.53463e11			−1.79456			−0.897278	−	0.441467i	$-0.854458\pi$
$709$	−4.53463e11			−1.79456			−0.897278	+	0.441467i	$0.854458\pi$
$710$			8.21092e11i			3.23116i
$711$	−1.04717e10			−0.0409770
$712$	−7.28375e11			−2.83423
$713$	−5.01761e11			−1.94151
$714$			2.14331e11i			0.824693i
$715$	4.22095e10			0.161505
$716$			9.59947e11i			3.65254i
$717$	−2.38832e11			−0.903682
$718$			1.42985e11i			0.538012i
$719$		−	1.80912e11i		−	0.676942i	−0.940977	−	0.338471i	$-0.890090\pi$
$719$		−	1.80912e11i		−	0.676942i	0.940977	−	0.338471i	$-0.109910\pi$
$720$	2.30639e11			0.858229
$721$		−	1.39606e11i		−	0.516610i
$722$		−	4.44320e11i		−	1.63511i
$723$	9.44784e9			0.0345764
$724$	5.07337e11			1.84647
$725$	6.97931e11			2.52616
$726$		−	2.57760e11i		−	0.927830i
$727$	−2.99841e11			−1.07338			−0.536691	−	0.843779i	$-0.680326\pi$
$727$	−2.99841e11			−1.07338			−0.536691	+	0.843779i	$0.680326\pi$
$728$	8.78870e10			0.312895
$729$	1.04604e10			0.0370370
$730$	8.89343e11			3.13168
$731$		−	2.20222e10i		−	0.0771244i
$732$		−	4.97494e11i		−	1.73278i
$733$	−2.19804e11			−0.761410			−0.380705	−	0.924696i	$-0.624319\pi$
$733$	−2.19804e11			−0.761410			−0.380705	+	0.924696i	$0.624319\pi$
$734$	1.34105e11			0.462018
$735$	2.13646e11			0.732059
$736$	2.73401e11			0.931729
$737$	−7.33337e9			−0.0248561
$738$		−	1.37045e11i		−	0.461997i
$739$		−	7.66573e10i		−	0.257025i	−0.991708	−	0.128513i	$-0.958980\pi$
$739$		−	7.66573e10i		−	0.257025i	0.991708	−	0.128513i	$-0.0410203\pi$
$740$			2.58945e11i			0.863537i
$741$		−	1.58089e10i		−	0.0524359i
$742$		−	2.74011e11i		−	0.903965i
$743$	1.01874e10			0.0334280			0.0167140	−	0.999860i	$-0.494680\pi$
$743$	1.01874e10			0.0334280			0.0167140	+	0.999860i	$0.494680\pi$
$744$	5.49983e11			1.79497
$745$		−	9.66521e10i		−	0.313752i
$746$		−	6.57172e11i		−	2.12190i
$747$			1.45143e11i			0.466137i
$748$		−	3.64906e11i		−	1.16567i
$749$	−6.71025e10			−0.213212
$750$		−	3.50826e11i		−	1.10878i
$751$			2.54136e11i			0.798925i	0.916750	+	0.399462i	$0.130803\pi$
$751$			2.54136e11i			0.798925i	−0.916750	+	0.399462i	$0.869197\pi$
$752$		−	4.26648e11i		−	1.33413i
$753$	−9.64403e10			−0.299971
$754$	−2.75998e11			−0.853925
$755$			3.34789e11i			1.03035i
$756$	6.47099e10			0.198100
$757$	8.96205e10			0.272913			0.136456	−	0.990646i	$-0.456429\pi$
$757$	8.96205e10			0.272913			0.136456	+	0.990646i	$0.456429\pi$
$758$			6.55047e11i			1.98425i
$759$	7.93974e10			0.239243
$760$		−	3.31160e11i		−	0.992620i
$761$	1.56648e11			0.467075			0.233537	−	0.972348i	$-0.424970\pi$
$761$	1.56648e11			0.467075			0.233537	+	0.972348i	$0.424970\pi$
$762$			7.68111e10i			0.227827i
$763$			7.83309e10i			0.231119i
$764$		−	9.04840e11i		−	2.65582i
$765$	−3.16043e11			−0.922785
$766$			1.01257e12i			2.94110i
$767$	7.67405e10	+	7.72349e10i	0.221740	+	0.223168i
$768$	3.92126e11			1.12715
$769$			6.55610e11i			1.87474i	0.348339	+	0.937369i	$0.386746\pi$
$769$			6.55610e11i			1.87474i	−0.348339	+	0.937369i	$0.613254\pi$
$770$	1.51870e11			0.432026
$771$	4.71601e10			0.133462
$772$	−1.21817e12			−3.42957
$773$			4.84858e11i			1.35799i	0.734143	+	0.678995i	$0.237584\pi$
$773$			4.84858e11i			1.35799i	−0.734143	+	0.678995i	$0.762416\pi$
$774$	−9.69621e9			−0.0270171
$775$		−	8.83206e11i		−	2.44825i
$776$	1.10244e12			3.04023
$777$			2.40919e10i			0.0660979i
$778$		−	1.12329e12i		−	3.06600i
$779$	−8.26043e10			−0.224312
$780$			2.39249e11i			0.646355i
$781$		−	1.30062e11i		−	0.349581i
$782$	−1.49059e12			−3.98595
$783$	−1.10075e11			−0.292847
$784$	−4.63655e11			−1.22724
$785$		−	1.02307e12i		−	2.69419i
$786$	6.19606e11			1.62340
$787$	4.69906e11			1.22493			0.612465	−	0.790497i	$-0.290178\pi$
$787$	4.69906e11			1.22493			0.612465	+	0.790497i	$0.290178\pi$
$788$	1.19544e11			0.310043
$789$	3.37566e11			0.871066
$790$		−	1.39303e11i		−	0.357644i
$791$		−	8.25773e10i		−	0.210938i
$792$	−8.70280e10			−0.221186
$793$	1.71132e11			0.432750
$794$	1.01146e12			2.54487
$795$	4.04044e11			1.01149
$796$	−6.33783e11			−1.57866
$797$			3.73312e11i			0.925207i	0.886565	+	0.462604i	$0.153085\pi$
$797$			3.73312e11i			0.925207i	−0.886565	+	0.462604i	$0.846915\pi$
$798$		−	5.68806e10i		−	0.140266i
$799$			5.84633e11i			1.43449i
$800$			4.81245e11i			1.17491i
$801$		−	1.84477e11i		−	0.448139i
$802$	2.57103e11			0.621455
$803$	−1.40874e11			−0.338819
$804$		−	4.15664e10i		−	0.0994759i
$805$		−	4.25398e11i		−	1.01301i
$806$			3.49265e11i			0.827589i
$807$			3.03362e11i			0.715264i
$808$	2.77104e11			0.650127
$809$			5.58022e11i			1.30274i	0.758761	+	0.651369i	$0.225805\pi$
$809$			5.58022e11i			1.30274i	−0.758761	+	0.651369i	$0.774195\pi$
$810$			1.39151e11i			0.323256i
$811$		−	4.59672e11i		−	1.06259i	−0.847188	−	0.531293i	$-0.821706\pi$
$811$		−	4.59672e11i		−	1.06259i	0.847188	−	0.531293i	$-0.178294\pi$
$812$	−6.80946e11			−1.56635
$813$	4.19949e11			0.961246
$814$		−	5.98168e10i		−	0.136247i
$815$	2.57912e11			0.584576
$816$	6.85877e11			1.54698
$817$			5.84441e9i			0.0131175i
$818$	−5.41298e11			−1.20899
$819$			2.22594e10i			0.0494740i
$820$	1.25012e12			2.76500
$821$			1.70661e11i			0.375632i	0.982204	+	0.187816i	$0.0601408\pi$
$821$			1.70661e11i			0.375632i	−0.982204	+	0.187816i	$0.939859\pi$
$822$			1.89763e11i			0.415647i
$823$		−	7.80683e11i		−	1.70167i	−0.525434	−	0.850835i	$-0.676097\pi$
$823$		−	7.80683e11i		−	1.70167i	0.525434	−	0.850835i	$-0.323903\pi$
$824$	−1.06422e12			−2.30846
$825$			1.39756e11i			0.301687i
$826$	2.76113e11	+	2.77892e11i	0.593153	+	0.596975i
$827$	1.62553e11			0.347514			0.173757	−	0.984789i	$-0.444409\pi$
$827$	1.62553e11			0.347514			0.173757	+	0.984789i	$0.444409\pi$
$828$			4.50034e11i			0.957467i
$829$	−7.77703e11			−1.64663			−0.823315	−	0.567585i	$-0.807878\pi$
$829$	−7.77703e11			−1.64663			−0.823315	+	0.567585i	$0.807878\pi$
$830$	−1.93080e12			−4.06841
$831$	5.96454e10			0.125076
$832$			4.76626e10i			0.0994683i
$833$	6.35344e11			1.31956
$834$			6.72651e9i			0.0139035i
$835$	1.05285e12			2.16581
$836$			9.68413e10i			0.198260i
$837$			1.39296e11i			0.283815i
$838$	−9.97319e10			−0.202236
$839$			2.75011e11i			0.555012i	0.960724	+	0.277506i	$0.0895078\pi$
$839$			2.75011e11i			0.555012i	−0.960724	+	0.277506i	$0.910492\pi$
$840$			4.66282e11i			0.936551i
$841$	6.58077e11			1.31551
$842$	−8.12193e11			−1.61589
$843$	−1.72786e11			−0.342135
$844$		−	1.09014e12i		−	2.14838i
$845$	7.49230e11			1.46956
$846$	2.57409e11			0.502507
$847$	2.18758e11			0.425041
$848$	−8.76856e11			−1.69568
$849$		−	6.79607e10i		−	0.130806i
$850$		−	2.62376e12i		−	5.02631i
$851$	−1.67551e11			−0.319468
$852$	7.37209e11			1.39905
$853$	2.82978e9			0.00534512			0.00267256	−	0.999996i	$-0.499149\pi$
$853$	2.82978e9			0.00534512			0.00267256	+	0.999996i	$0.499149\pi$
$854$	6.15733e11			1.15761
$855$	8.38736e10			0.156950
$856$			5.11524e11i			0.952732i
$857$		−	4.40031e11i		−	0.815755i	−0.913037	−	0.407878i	$-0.866269\pi$
$857$		−	4.40031e11i		−	0.815755i	0.913037	−	0.407878i	$-0.133731\pi$
$858$		−	5.52668e10i		−	0.101980i
$859$			5.69549e11i			1.04606i	0.852313	+	0.523032i	$0.175199\pi$
$859$			5.69549e11i			1.04606i	−0.852313	+	0.523032i	$0.824801\pi$
$860$		−	8.84480e10i		−	0.161694i
$861$	1.16309e11			0.211642
$862$	−1.53749e11			−0.278474
$863$			1.21360e11i			0.218792i	0.993998	+	0.109396i	$0.0348916\pi$
$863$			1.21360e11i			0.218792i	−0.993998	+	0.109396i	$0.965108\pi$
$864$		−	7.59000e10i		−	0.136203i
$865$		−	3.10187e11i		−	0.554064i
$866$		−	3.81925e11i		−	0.679057i
$867$	−6.13628e11			−1.08600
$868$			8.61712e11i			1.51804i
$869$			2.20658e10i			0.0386937i
$870$		−	1.46430e12i		−	2.55595i
$871$	1.42983e10			0.0248434
$872$	5.97118e11			1.03275
$873$			2.79217e11i			0.480712i
$874$	3.95584e11			0.677942
$875$	2.97743e11			0.507937
$876$		−	7.98488e11i		−	1.35598i
$877$	−9.59287e11			−1.62162			−0.810812	−	0.585307i	$-0.800974\pi$
$877$	−9.59287e11			−1.62162			−0.810812	+	0.585307i	$0.800974\pi$
$878$			1.38049e12i			2.32304i
$879$	−3.97779e11			−0.666326
$880$		−	4.85997e11i		−	0.810407i
$881$			5.21952e11i			0.866417i	0.901294	+	0.433208i	$0.142619\pi$
$881$			5.21952e11i			0.866417i	−0.901294	+	0.433208i	$0.857381\pi$
$882$		−	2.79737e11i		−	0.462248i
$883$	1.53484e11			0.252476			0.126238	−	0.992000i	$-0.459710\pi$
$883$	1.53484e11			0.252476			0.126238	+	0.992000i	$0.459710\pi$
$884$			7.11480e11i			1.16507i
$885$	−4.09768e11	+	4.07144e11i	−0.667982	+	0.663705i
$886$	−1.21103e12			−1.96526
$887$		−	7.35931e11i		−	1.18889i	−0.804135	−	0.594447i	$-0.797371\pi$
$887$		−	7.35931e11i		−	1.18889i	0.804135	−	0.594447i	$-0.202629\pi$
$888$	1.83653e11			0.295357
$889$	−6.51889e10			−0.104368
$890$	2.45405e12			3.91133
$891$		−	2.20418e10i		−	0.0349733i
$892$	−7.39738e11			−1.16847
$893$		−	1.55154e11i		−	0.243981i
$894$	−1.26551e11			−0.198114
$895$		−	1.75192e12i		−	2.73037i
$896$			3.86690e11i			0.599972i
$897$	−1.54806e11			−0.239121
$898$			1.93000e11i			0.296792i
$899$		−	1.46582e12i		−	2.24409i
$900$	−7.92156e11			−1.20737
$901$	1.20155e12			1.82324
$902$	−2.88779e11			−0.436254
$903$		−	8.22909e9i		−	0.0123766i
$904$	−6.29489e11			−0.942572
$905$	−9.25897e11			−1.38028
$906$	4.38354e11			0.650597
$907$	−1.79463e11			−0.265183			−0.132591	−	0.991171i	$-0.542330\pi$
$907$	−1.79463e11			−0.265183			−0.132591	+	0.991171i	$0.542330\pi$
$908$		−	1.01894e12i		−	1.49901i
$909$			7.01829e10i			0.102796i
$910$	−2.96110e11			−0.431806
$911$	−8.80249e11			−1.27800			−0.639001	−	0.769206i	$-0.720652\pi$
$911$	−8.80249e11			−1.27800			−0.639001	+	0.769206i	$0.720652\pi$
$912$	−1.82022e11			−0.263115
$913$	3.05842e11			0.440163
$914$	1.73921e12			2.49211
$915$			9.07933e11i			1.29530i
$916$		−	1.00651e12i		−	1.42967i
$917$			5.25854e11i			0.743683i
$918$			4.13809e11i			0.582679i
$919$			3.61438e11i			0.506725i	0.967371	+	0.253362i	$0.0815365\pi$
$919$			3.61438e11i			0.506725i	−0.967371	+	0.253362i	$0.918464\pi$
$920$	−3.24282e12			−4.52659
$921$	2.61389e11			0.363286
$922$		−	6.98561e11i		−	0.966675i
$923$			2.53590e11i			0.349403i
$924$		−	1.36355e11i		−	0.187061i
$925$		−	2.94925e11i		−	0.402851i
$926$	9.01246e11			1.22574
$927$		−	2.69537e11i		−	0.365006i
$928$			7.98700e11i			1.07694i
$929$		−	1.46626e12i		−	1.96855i	−0.176633	−	0.984277i	$-0.556521\pi$
$929$		−	1.46626e12i		−	1.96855i	0.176633	−	0.984277i	$-0.443479\pi$
$930$	−1.85301e12			−2.47712
$931$	−1.68612e11			−0.224434
$932$			1.76629e12i			2.34098i
$933$	1.54338e11			0.203678
$934$	−2.23206e12			−2.93304
$935$			6.65959e11i			0.871367i
$936$	1.69684e11			0.221074
$937$			5.76825e11i			0.748317i	0.927365	+	0.374159i	$0.122068\pi$
$937$			5.76825e11i			0.748317i	−0.927365	+	0.374159i	$0.877932\pi$
$938$	5.14454e10			0.0664562
$939$			6.42626e11i			0.826600i
$940$			2.34806e12i			3.00745i
$941$			6.17055e11i			0.786984i	0.919328	+	0.393492i	$0.128733\pi$
$941$			6.17055e11i			0.786984i	−0.919328	+	0.393492i	$0.871267\pi$
$942$	−1.33956e12			−1.70121
$943$			8.08887e11i			1.02292i
$944$	8.89277e11	−	8.83585e11i	1.11982	−	1.11265i
$945$	−1.18096e11			−0.148084
$946$			2.04316e10i			0.0255116i
$947$	−1.59497e11			−0.198313			−0.0991567	−	0.995072i	$-0.531615\pi$
$947$	−1.59497e11			−0.198313			−0.0991567	+	0.995072i	$0.531615\pi$
$948$	−1.25072e11			−0.154855
$949$	2.74670e11			0.338646
$950$			6.96312e11i			0.854888i
$951$	4.15250e11			0.507677
$952$			1.38663e12i			1.68816i
$953$	−1.34340e12			−1.62868			−0.814338	−	0.580391i	$-0.802900\pi$
$953$	−1.34340e12			−1.62868			−0.814338	+	0.580391i	$0.802900\pi$
$954$		−	5.29033e11i		−	0.638689i
$955$			1.65134e12i			1.98529i
$956$	−2.85254e12			−3.41508
$957$			2.31947e11i			0.276529i
$958$			2.63546e10i			0.0312892i
$959$	−1.61050e11			−0.190409
$960$	−2.52873e11			−0.297726
$961$	−1.00205e12			−1.17488
$962$			1.16628e11i			0.136177i
$963$	−1.29555e11			−0.150643
$964$	1.12842e11			0.130666
$965$	2.22318e12			2.56369
$966$	−5.56993e11			−0.639648
$967$			1.00762e12i			1.15237i	0.817321	+	0.576183i	$0.195458\pi$
$967$			1.00762e12i			1.15237i	−0.817321	+	0.576183i	$0.804542\pi$
$968$		−	1.66760e12i		−	1.89928i
$969$	2.49424e11			0.282907
$970$	−3.71435e12			−4.19562
$971$	−7.88132e11			−0.886588			−0.443294	−	0.896376i	$-0.646190\pi$
$971$	−7.88132e11			−0.886588			−0.443294	+	0.896376i	$0.646190\pi$
$972$	1.24936e11			0.139966
$973$	−5.70872e9			−0.00636924
$974$		−	3.09461e11i		−	0.343850i
$975$		−	2.72491e11i		−	0.301533i
$976$		−	1.97040e12i		−	2.17147i
$977$		−	1.44942e12i		−	1.59080i	−0.606084	−	0.795401i	$-0.707260\pi$
$977$		−	1.44942e12i		−	1.59080i	0.606084	−	0.795401i	$-0.292740\pi$
$978$		−	3.37695e11i		−	0.369122i
$979$	−3.88727e11			−0.423169
$980$	2.55173e12			2.76650
$981$			1.51234e11i			0.163295i
$982$			2.35052e12i			2.52765i
$983$		−	1.13455e12i		−	1.21509i	−0.794286	−	0.607545i	$-0.792155\pi$
$983$		−	1.13455e12i		−	1.21509i	0.794286	−	0.607545i	$-0.207845\pi$
$984$		−	8.86627e11i		−	0.945715i
$985$	−2.18169e11			−0.231765
$986$		−	4.35454e12i		−	4.60717i
$987$			2.18461e11i			0.230200i
$988$		−	1.88817e11i		−	0.198159i
$989$	5.72303e10			0.0598192
$990$	2.93216e11			0.305244
$991$			1.88620e12i			1.95566i	0.209397	+	0.977831i	$0.432850\pi$
$991$			1.88620e12i			1.95566i	−0.209397	+	0.977831i	$0.567150\pi$
$992$	1.01073e12			1.04373
$993$	9.59841e11			0.987193
$994$			9.12421e11i			0.934651i
$995$	1.15666e12			1.18009
$996$			1.73355e12i			1.76156i
$997$	−5.37257e11			−0.543753			−0.271877	−	0.962332i	$-0.587644\pi$
$997$	−5.37257e11			−0.543753			−0.271877	+	0.962332i	$0.587644\pi$
$998$		−	1.48478e12i		−	1.49672i
$999$			4.65144e10i			0.0467009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.9.c.a.58.75	yes	80
59.58	odd	2	inner	177.9.c.a.58.6	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.9.c.a.58.6	✓	80	59.58	odd	2	inner
177.9.c.a.58.75	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+28.5404i q^{2} -46.7654 q^{3} -558.553 q^{4} +1019.37 q^{5} -1334.70i q^{6} +1132.75 q^{7} -8634.97i q^{8} +2187.00 q^{9} +O(q^{10})\)	\(q+28.5404i q^{2} -46.7654 q^{3} -558.553 q^{4} +1019.37 q^{5} -1334.70i q^{6} +1132.75 q^{7} -8634.97i q^{8} +2187.00 q^{9} +29093.1i q^{10} -4608.39i q^{11} +26120.9 q^{12} +8985.26i q^{13} +32329.1i q^{14} -47671.0 q^{15} +103456. q^{16} -141765. q^{17} +62417.8i q^{18} +37622.4 q^{19} -569370. q^{20} -52973.4 q^{21} +131525. q^{22} -368411. i q^{23} +403817. i q^{24} +648482. q^{25} -256443. q^{26} -102276. q^{27} -632700. q^{28} +1.07625e6 q^{29} -1.36055e6i q^{30} -1.36196e6i q^{31} +742110. i q^{32} +215513. i q^{33} -4.04601e6i q^{34} +1.15468e6 q^{35} -1.22155e6 q^{36} -454793. i q^{37} +1.07376e6i q^{38} -420199. i q^{39} -8.80219e6i q^{40} -2.19561e6 q^{41} -1.51188e6i q^{42} +155344. i q^{43} +2.57403e6i q^{44} +2.22935e6 q^{45} +1.05146e7 q^{46} -4.12397e6i q^{47} -4.83814e6 q^{48} -4.48168e6 q^{49} +1.85079e7i q^{50} +6.62967e6 q^{51} -5.01874e6i q^{52} -8.47567e6 q^{53} -2.91899e6i q^{54} -4.69764e6i q^{55} -9.78124e6i q^{56} -1.75943e6 q^{57} +3.07167e7i q^{58} +(8.59574e6 - 8.54071e6i) q^{59} +2.66268e7 q^{60} -1.90458e7i q^{61} +3.88709e7 q^{62} +2.47732e6 q^{63} +5.30453e6 q^{64} +9.15927e6i q^{65} -6.15083e6 q^{66} -1.59131e6i q^{67} +7.91830e7 q^{68} +1.72289e7i q^{69} +3.29551e7i q^{70} +2.82229e7 q^{71} -1.88847e7i q^{72} -3.05689e7i q^{73} +1.29800e7 q^{74} -3.03265e7 q^{75} -2.10141e7 q^{76} -5.22015e6i q^{77} +1.19926e7 q^{78} -4.78817e6 q^{79} +1.05459e8 q^{80} +4.78297e6 q^{81} -6.26636e7i q^{82} +6.63663e7i q^{83} +2.95884e7 q^{84} -1.44510e8 q^{85} -4.43357e6 q^{86} -5.03314e7 q^{87} -3.97933e7 q^{88} -8.43518e7i q^{89} +6.36266e7i q^{90} +1.01780e7i q^{91} +2.05777e8i q^{92} +6.36926e7i q^{93} +1.17700e8 q^{94} +3.83510e7 q^{95} -3.47051e7i q^{96} +1.27671e8i q^{97} -1.27909e8i q^{98} -1.00786e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9}+O(q^{10}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9	\( 80 q - 10240 q^{4} + 160 q^{7} + 174960 q^{9} - 22680 q^{12} - 59616 q^{15} + 1199848 q^{16} - 10608 q^{17} - 27516 q^{19} - 146436 q^{20} - 974696 q^{22} + 5718040 q^{25} - 797484 q^{26} - 3133000 q^{28} + 1725924 q^{29} + 4318800 q^{35} - 22394880 q^{36} - 732180 q^{41} + 22752084 q^{46} + 8703936 q^{48} + 55899176 q^{49} - 10373832 q^{51} - 39265944 q^{53} - 11408040 q^{57} - 33575112 q^{59} - 18034488 q^{60} + 13038600 q^{62} + 349920 q^{63} - 241654260 q^{64} - 35711928 q^{66} + 36772608 q^{68} - 235272660 q^{71} - 63050712 q^{74} + 74363184 q^{75} + 9454680 q^{76} - 10865988 q^{78} + 17252580 q^{79} + 318203976 q^{80} + 382637520 q^{81} - 20743128 q^{84} - 27245820 q^{85} + 105666984 q^{86} + 29437992 q^{87} + 82079788 q^{88} + 121215992 q^{94} - 690837276 q^{95}+O(q^{100}) \) 80 * q - 10240 * q^4 + 160 * q^7 + 174960 * q^9 - 22680 * q^12 - 59616 * q^15 + 1199848 * q^16 - 10608 * q^17 - 27516 * q^19 - 146436 * q^20 - 974696 * q^22 + 5718040 * q^25 - 797484 * q^26 - 3133000 * q^28 + 1725924 * q^29 + 4318800 * q^35 - 22394880 * q^36 - 732180 * q^41 + 22752084 * q^46 + 8703936 * q^48 + 55899176 * q^49 - 10373832 * q^51 - 39265944 * q^53 - 11408040 * q^57 - 33575112 * q^59 - 18034488 * q^60 + 13038600 * q^62 + 349920 * q^63 - 241654260 * q^64 - 35711928 * q^66 + 36772608 * q^68 - 235272660 * q^71 - 63050712 * q^74 + 74363184 * q^75 + 9454680 * q^76 - 10865988 * q^78 + 17252580 * q^79 + 318203976 * q^80 + 382637520 * q^81 - 20743128 * q^84 - 27245820 * q^85 + 105666984 * q^86 + 29437992 * q^87 + 82079788 * q^88 + 121215992 * q^94 - 690837276 * q^95

Introduction

L-functions

Modular forms

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Database

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