LMFDB - Embedded newform 91.8.c.a.64.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(64,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("91.64");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			64.18
Character	$\chi$	$=$	91.64
Dual form			91.8.c.a.64.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.36017i q^{2} -8.01801 q^{3} +58.1075 q^{4} -455.948i q^{5} +67.0319i q^{6} -343.000i q^{7} -1555.89i q^{8} -2122.71 q^{9} +O(q^{10})$	\(q-8.36017i q^{2} -8.01801 q^{3} +58.1075 q^{4} -455.948i q^{5} +67.0319i q^{6} -343.000i q^{7} -1555.89i q^{8} -2122.71 q^{9} -3811.80 q^{10} +2672.84i q^{11} -465.906 q^{12} +(3682.90 - 7013.18i) q^{13} -2867.54 q^{14} +3655.79i q^{15} -5569.76 q^{16} +15196.7 q^{17} +17746.2i q^{18} -14298.1i q^{19} -26494.0i q^{20} +2750.18i q^{21} +22345.4 q^{22} -28703.8 q^{23} +12475.1i q^{24} -129764. q^{25} +(-58631.4 - 30789.7i) q^{26} +34555.3 q^{27} -19930.9i q^{28} -17248.3 q^{29} +30563.1 q^{30} +200820. i q^{31} -152590. i q^{32} -21430.8i q^{33} -127047. i q^{34} -156390. q^{35} -123345. q^{36} +64106.6i q^{37} -119535. q^{38} +(-29529.5 + 56231.8i) q^{39} -709405. q^{40} -197614. i q^{41} +22991.9 q^{42} -311942. q^{43} +155312. i q^{44} +967846. i q^{45} +239969. i q^{46} +1.26009e6i q^{47} +44658.4 q^{48} -117649. q^{49} +1.08485e6i q^{50} -121848. q^{51} +(214004. - 407519. i) q^{52} +370143. q^{53} -288888. i q^{54} +1.21868e6 q^{55} -533671. q^{56} +114643. i q^{57} +144199. i q^{58} -249875. i q^{59} +212429. i q^{60} -2.84414e6 q^{61} +1.67889e6 q^{62} +728090. i q^{63} -1.98861e6 q^{64} +(-3.19765e6 - 1.67921e6i) q^{65} -179165. q^{66} -4.08931e6i q^{67} +883045. q^{68} +230147. q^{69} +1.30745e6i q^{70} +2.40390e6i q^{71} +3.30271e6i q^{72} -5.39520e6i q^{73} +535942. q^{74} +1.04045e6 q^{75} -830829. i q^{76} +916783. q^{77} +(470107. + 246872. i) q^{78} -3.85634e6 q^{79} +2.53952e6i q^{80} +4.36531e6 q^{81} -1.65209e6 q^{82} +3.90020e6i q^{83} +159806. i q^{84} -6.92893e6i q^{85} +2.60789e6i q^{86} +138297. q^{87} +4.15864e6 q^{88} -2.76512e6i q^{89} +8.09136e6 q^{90} +(-2.40552e6 - 1.26324e6i) q^{91} -1.66790e6 q^{92} -1.61018e6i q^{93} +1.05346e7 q^{94} -6.51921e6 q^{95} +1.22347e6i q^{96} -5.17027e6i q^{97} +983566. i q^{98} -5.67366e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) $ 50 * q - 3328 * q^4 + 40514 * q^9	$ 50 q - 3328 q^{4} + 40514 q^{9} + 5320 q^{10} + 8700 q^{12} + 17044 q^{13} + 10976 q^{14} + 228808 q^{16} + 33664 q^{17} + 70228 q^{22} - 75042 q^{23} - 664772 q^{25} + 78276 q^{26} - 661404 q^{27} + 135778 q^{29} + 994888 q^{30} + 372498 q^{35} - 3549604 q^{36} + 338468 q^{38} - 973080 q^{39} + 79316 q^{40} + 296352 q^{42} - 53618 q^{43} + 1400384 q^{48} - 5882450 q^{49} - 2182360 q^{51} - 6982340 q^{52} + 2841746 q^{53} + 6871356 q^{55} - 2107392 q^{56} + 1773716 q^{61} - 6969608 q^{62} - 9449120 q^{64} - 7901430 q^{65} - 11755548 q^{66} + 11829980 q^{68} + 3564460 q^{69} + 45595884 q^{74} - 7220964 q^{75} + 186592 q^{77} - 8093012 q^{78} - 21257822 q^{79} + 53034530 q^{81} + 10907568 q^{82} + 14135000 q^{87} - 51594780 q^{88} - 61226356 q^{90} - 8096858 q^{91} - 11200212 q^{92} + 80667028 q^{94} + 30430066 q^{95}+O(q^{100}) $ 50 * q - 3328 * q^4 + 40514 * q^9 + 5320 * q^10 + 8700 * q^12 + 17044 * q^13 + 10976 * q^14 + 228808 * q^16 + 33664 * q^17 + 70228 * q^22 - 75042 * q^23 - 664772 * q^25 + 78276 * q^26 - 661404 * q^27 + 135778 * q^29 + 994888 * q^30 + 372498 * q^35 - 3549604 * q^36 + 338468 * q^38 - 973080 * q^39 + 79316 * q^40 + 296352 * q^42 - 53618 * q^43 + 1400384 * q^48 - 5882450 * q^49 - 2182360 * q^51 - 6982340 * q^52 + 2841746 * q^53 + 6871356 * q^55 - 2107392 * q^56 + 1773716 * q^61 - 6969608 * q^62 - 9449120 * q^64 - 7901430 * q^65 - 11755548 * q^66 + 11829980 * q^68 + 3564460 * q^69 + 45595884 * q^74 - 7220964 * q^75 + 186592 * q^77 - 8093012 * q^78 - 21257822 * q^79 + 53034530 * q^81 + 10907568 * q^82 + 14135000 * q^87 - 51594780 * q^88 - 61226356 * q^90 - 8096858 * q^91 - 11200212 * q^92 + 80667028 * q^94 + 30430066 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	8.36017i		−	0.738942i	−0.929242	−	0.369471i	$-0.879539\pi$
$2$		−	8.36017i		−	0.738942i	0.929242	−	0.369471i	$-0.120461\pi$
$3$	−8.01801			−0.171452			−0.0857259	−	0.996319i	$-0.527321\pi$
$3$	−8.01801			−0.171452			−0.0857259	+	0.996319i	$0.527321\pi$
$4$	58.1075			0.453965
$5$		−	455.948i		−	1.63125i	−0.578581	−	0.815625i	$-0.696393\pi$
$5$		−	455.948i		−	1.63125i	0.578581	−	0.815625i	$-0.303607\pi$
$6$			67.0319i			0.126693i
$7$		−	343.000i		−	0.377964i
$7$		−	343.000i		−	0.377964i
$8$		−	1555.89i		−	1.07440i
$9$	−2122.71			−0.970604
$10$	−3811.80			−1.20540
$11$			2672.84i			0.605478i	0.953074	+	0.302739i	$0.0979010\pi$
$11$			2672.84i			0.605478i	−0.953074	+	0.302739i	$0.902099\pi$
$12$	−465.906			−0.0778331
$13$	3682.90	−	7013.18i	0.464931	−	0.885347i
$13$	3682.90	−	7013.18i	0.464931	−	0.885347i
$14$	−2867.54			−0.279294
$15$			3655.79i			0.279681i
$16$	−5569.76			−0.339951
$17$	15196.7			0.750204			0.375102	−	0.926984i	$-0.377608\pi$
$17$	15196.7			0.750204			0.375102	+	0.926984i	$0.377608\pi$
$18$			17746.2i			0.717220i
$19$		−	14298.1i		−	0.478236i	−0.970991	−	0.239118i	$-0.923142\pi$
$19$		−	14298.1i		−	0.478236i	0.970991	−	0.239118i	$-0.0768583\pi$
$20$		−	26494.0i		−	0.740530i
$21$			2750.18i			0.0648027i
$22$	22345.4			0.447413
$23$	−28703.8			−0.491917			−0.245958	−	0.969280i	$-0.579103\pi$
$23$	−28703.8			−0.491917			−0.245958	+	0.969280i	$0.579103\pi$
$24$			12475.1i			0.184207i
$25$	−129764.			−1.66097
$26$	−58631.4	−	30789.7i	−0.654220	−	0.343557i
$27$	34555.3			0.337864
$28$		−	19930.9i		−	0.171583i
$29$	−17248.3			−0.131327			−0.0656635	−	0.997842i	$-0.520916\pi$
$29$	−17248.3			−0.131327			−0.0656635	+	0.997842i	$0.520916\pi$
$30$	30563.1			0.206668
$31$			200820.i			1.21072i	0.795954	+	0.605358i	$0.206970\pi$
$31$			200820.i			1.21072i	−0.795954	+	0.605358i	$0.793030\pi$
$32$		−	152590.i		−	0.823191i
$33$		−	21430.8i		−	0.103810i
$34$		−	127047.i		−	0.554357i
$35$	−156390.			−0.616554
$36$	−123345.			−0.440620
$37$			64106.6i			0.208064i	0.994574	+	0.104032i	$0.0331744\pi$
$37$			64106.6i			0.208064i	−0.994574	+	0.104032i	$0.966826\pi$
$38$	−119535.			−0.353389
$39$	−29529.5	+	56231.8i	−0.0797132	+	0.151794i
$40$	−709405.			−1.75261
$41$		−	197614.i		−	0.447790i	−0.974613	−	0.223895i	$-0.928123\pi$
$41$		−	197614.i		−	0.447790i	0.974613	−	0.223895i	$-0.0718772\pi$
$42$	22991.9			0.0478854
$43$	−311942.			−0.598321			−0.299160	−	0.954203i	$-0.596707\pi$
$43$	−311942.			−0.598321			−0.299160	+	0.954203i	$0.596707\pi$
$44$			155312.i			0.274866i
$45$			967846.i			1.58330i
$46$			239969.i			0.363498i
$47$			1.26009e6i			1.77035i	0.465257	+	0.885176i	$0.345962\pi$
$47$			1.26009e6i			1.77035i	−0.465257	+	0.885176i	$0.654038\pi$
$48$	44658.4			0.0582852
$49$	−117649.			−0.142857
$50$			1.08485e6i			1.22736i
$51$	−121848.			−0.128624
$52$	214004.	−	407519.i	0.211062	−	0.401916i
$53$	370143.			0.341510			0.170755	−	0.985313i	$-0.445379\pi$
$53$	370143.			0.341510			0.170755	+	0.985313i	$0.445379\pi$
$54$		−	288888.i		−	0.249662i
$55$	1.21868e6			0.987685
$56$	−533671.			−0.406083
$57$			114643.i			0.0819944i
$58$			144199.i			0.0970431i
$59$		−	249875.i		−	0.158395i	−0.996859	−	0.0791974i	$-0.974764\pi$
$59$		−	249875.i		−	0.158395i	0.996859	−	0.0791974i	$-0.0252358\pi$
$60$			212429.i			0.126965i
$61$	−2.84414e6			−1.60434			−0.802169	−	0.597097i	$-0.796321\pi$
$61$	−2.84414e6			−1.60434			−0.802169	+	0.597097i	$0.796321\pi$
$62$	1.67889e6			0.894648
$63$			728090.i			0.366854i
$64$	−1.98861e6			−0.948242
$65$	−3.19765e6	−	1.67921e6i	−1.44422	−	0.758418i
$66$	−179165.			−0.0767097
$67$		−	4.08931e6i		−	1.66107i	−0.556966	−	0.830535i	$-0.688035\pi$
$67$		−	4.08931e6i		−	1.66107i	0.556966	−	0.830535i	$-0.311965\pi$
$68$	883045.			0.340566
$69$	230147.			0.0843400
$70$			1.30745e6i			0.455598i
$71$			2.40390e6i			0.797099i	0.917147	+	0.398550i	$0.130486\pi$
$71$			2.40390e6i			0.797099i	−0.917147	+	0.398550i	$0.869514\pi$
$72$			3.30271e6i			1.04281i
$73$		−	5.39520e6i		−	1.62322i	−0.584198	−	0.811611i	$-0.698591\pi$
$73$		−	5.39520e6i		−	1.62322i	0.584198	−	0.811611i	$-0.301409\pi$
$74$	535942.			0.153747
$75$	1.04045e6			0.284777
$76$		−	830829.i		−	0.217102i
$77$	916783.			0.228849
$78$	470107.	+	246872.i	0.112167	+	0.0589034i
$79$	−3.85634e6			−0.879995			−0.439997	−	0.897999i	$-0.645021\pi$
$79$	−3.85634e6			−0.879995			−0.439997	+	0.897999i	$0.645021\pi$
$80$			2.53952e6i			0.554545i
$81$	4.36531e6			0.912677
$82$	−1.65209e6			−0.330891
$83$			3.90020e6i			0.748709i	0.927286	+	0.374355i	$0.122136\pi$
$83$			3.90020e6i			0.748709i	−0.927286	+	0.374355i	$0.877864\pi$
$84$			159806.i			0.0294181i
$85$		−	6.92893e6i		−	1.22377i
$86$			2.60789e6i			0.442124i
$87$	138297.			0.0225163
$88$	4.15864e6			0.650523
$89$		−	2.76512e6i		−	0.415766i	−0.978154	−	0.207883i	$-0.933343\pi$
$89$		−	2.76512e6i		−	0.415766i	0.978154	−	0.207883i	$-0.0666573\pi$
$90$	8.09136e6			1.16997
$91$	−2.40552e6	−	1.26324e6i	−0.334630	−	0.175727i
$92$	−1.66790e6			−0.223313
$93$		−	1.61018e6i		−	0.207579i
$94$	1.05346e7			1.30819
$95$	−6.51921e6			−0.780122
$96$			1.22347e6i			0.141138i
$97$		−	5.17027e6i		−	0.575191i	−0.957752	−	0.287595i	$-0.907144\pi$
$97$		−	5.17027e6i		−	0.575191i	0.957752	−	0.287595i	$-0.0928558\pi$
$98$			983566.i			0.105563i
$99$		−	5.67366e6i		−	0.587679i
$100$	−7.54024e6			−0.754024
$101$	9.13338e6			0.882078			0.441039	−	0.897488i	$-0.354610\pi$
$101$	9.13338e6			0.882078			0.441039	+	0.897488i	$0.354610\pi$
$102$			1.01867e6i			0.0950455i
$103$	1.38250e7			1.24662			0.623310	−	0.781975i	$-0.285787\pi$
$103$	1.38250e7			1.24662			0.623310	+	0.781975i	$0.285787\pi$
$104$	−1.09118e7	−	5.73019e6i	−0.951213	−	0.499520i
$105$	1.25394e6			0.105709
$106$		−	3.09446e6i		−	0.252356i
$107$	7.04161e6			0.555685			0.277843	−	0.960627i	$-0.410381\pi$
$107$	7.04161e6			0.555685			0.277843	+	0.960627i	$0.410381\pi$
$108$	2.00792e6			0.153378
$109$		−	2.26170e7i		−	1.67280i	−0.548123	−	0.836398i	$-0.684658\pi$
$109$		−	2.26170e7i		−	1.67280i	0.548123	−	0.836398i	$-0.315342\pi$
$110$		−	1.01883e7i		−	0.729842i
$111$		−	514007.i		−	0.0356729i
$112$			1.91043e6i			0.128489i
$113$	2.69297e7			1.75573			0.877863	−	0.478912i	$-0.158969\pi$
$113$	2.69297e7			1.75573			0.877863	+	0.478912i	$0.158969\pi$
$114$	958432.			0.0605891
$115$			1.30874e7i			0.802439i
$116$	−1.00226e6			−0.0596179
$117$	−7.81774e6	+	1.48870e7i	−0.451264	+	0.859322i
$118$	−2.08900e6			−0.117045
$119$		−	5.21248e6i		−	0.283550i
$120$	5.68802e6			0.300488
$121$	1.23431e7			0.633397
$122$			2.37775e7i			1.18551i
$123$			1.58447e6i			0.0767743i
$124$			1.16692e7i			0.549622i
$125$			2.35445e7i			1.07821i
$126$	6.08696e6			0.271084
$127$	3.65994e7			1.58548			0.792740	−	0.609560i	$-0.208654\pi$
$127$	3.65994e7			1.58548			0.792740	+	0.609560i	$0.208654\pi$
$128$		−	2.90641e6i		−	0.122496i
$129$	2.50115e6			0.102583
$130$	−1.40385e7	+	2.67329e7i	−0.560427	+	1.06720i
$131$	−2.23401e7			−0.868233			−0.434117	−	0.900857i	$-0.642939\pi$
$131$	−2.23401e7			−0.868233			−0.434117	+	0.900857i	$0.642939\pi$
$132$		−	1.24529e6i		−	0.0471262i
$133$	−4.90426e6			−0.180756
$134$	−3.41873e7			−1.22743
$135$		−	1.57554e7i		−	0.551140i
$136$		−	2.36445e7i		−	0.806016i
$137$			1.17908e7i			0.391761i	0.980628	+	0.195880i	$0.0627564\pi$
$137$			1.17908e7i			0.391761i	−0.980628	+	0.195880i	$0.937244\pi$
$138$		−	1.92407e6i		−	0.0623224i
$139$	−3.28708e7			−1.03815			−0.519073	−	0.854730i	$-0.673723\pi$
$139$	−3.28708e7			−1.03815			−0.519073	+	0.854730i	$0.673723\pi$
$140$	−9.08744e6			−0.279894
$141$		−	1.01034e7i		−	0.303530i
$142$	2.00970e7			0.589010
$143$	1.87451e7	+	9.84380e6i	0.536058	+	0.281505i
$144$	1.18230e7			0.329958
$145$			7.86434e6i			0.214227i
$146$	−4.51049e7			−1.19947
$147$	943310.			0.0244931
$148$			3.72507e6i			0.0944537i
$149$		−	4.64892e7i		−	1.15133i	−0.817686	−	0.575665i	$-0.804743\pi$
$149$		−	4.64892e7i		−	1.15133i	0.817686	−	0.575665i	$-0.195257\pi$
$150$		−	8.69831e6i		−	0.210434i
$151$		−	631935.i		−	0.0149366i	−0.999972	−	0.00746832i	$-0.997623\pi$
$151$		−	631935.i		−	0.0149366i	0.999972	−	0.00746832i	$-0.00237726\pi$
$152$	−2.22464e7			−0.513814
$153$	−3.22583e7			−0.728151
$154$		−	7.66447e6i		−	0.169106i
$155$	9.15637e7			1.97498
$156$	−1.71589e6	+	3.26749e6i	−0.0361870	+	0.0689093i
$157$	−9.17953e7			−1.89309			−0.946546	−	0.322568i	$-0.895454\pi$
$157$	−9.17953e7			−1.89309			−0.946546	+	0.322568i	$0.895454\pi$
$158$			3.22396e7i			0.650265i
$159$	−2.96781e6			−0.0585525
$160$	−6.95731e7			−1.34283
$161$			9.84540e6i			0.185927i
$162$		−	3.64947e7i		−	0.674415i
$163$		−	1.97531e7i		−	0.357256i	−0.983917	−	0.178628i	$-0.942834\pi$
$163$		−	1.97531e7i		−	0.357256i	0.983917	−	0.178628i	$-0.0571658\pi$
$164$		−	1.14829e7i		−	0.203281i
$165$	−9.77134e6			−0.169340
$166$	3.26063e7			0.553253
$167$			8.92967e6i			0.148364i	0.997245	+	0.0741819i	$0.0236345\pi$
$167$			8.92967e6i			0.148364i	−0.997245	+	0.0741819i	$0.976365\pi$
$168$	4.27897e6			0.0696237
$169$	−3.56210e7	−	5.16577e7i	−0.567679	−	0.823250i
$170$	−5.79270e7			−0.904295
$171$			3.03508e7i			0.464178i
$172$	−1.81262e7			−0.271617
$173$	3.32223e6			0.0487830			0.0243915	−	0.999702i	$-0.492235\pi$
$173$	3.32223e6			0.0487830			0.0243915	+	0.999702i	$0.492235\pi$
$174$		−	1.15619e6i		−	0.0166382i
$175$			4.45089e7i			0.627789i
$176$		−	1.48871e7i		−	0.205833i
$177$			2.00350e6i			0.0271571i
$178$	−2.31169e7			−0.307227
$179$	4.17946e7			0.544671			0.272335	−	0.962202i	$-0.412204\pi$
$179$	4.17946e7			0.544671			0.272335	+	0.962202i	$0.412204\pi$
$180$			5.62391e7i			0.718761i
$181$	2.81590e7			0.352974			0.176487	−	0.984303i	$-0.443527\pi$
$181$	2.81590e7			0.352974			0.176487	+	0.984303i	$0.443527\pi$
$182$	−1.05609e7	+	2.01106e7i	−0.129852	+	0.247272i
$183$	2.28043e7			0.275067
$184$			4.46600e7i			0.528513i
$185$	2.92293e7			0.339404
$186$	−1.34614e7			−0.153389
$187$			4.06184e7i			0.454232i
$188$			7.32208e7i			0.803677i
$189$		−	1.18525e7i		−	0.127700i
$190$			5.45017e7i			0.576465i
$191$	−9.68572e7			−1.00581			−0.502904	−	0.864342i	$-0.667735\pi$
$191$	−9.68572e7			−1.00581			−0.502904	+	0.864342i	$0.667735\pi$
$192$	1.59447e7			0.162578
$193$		−	2.93983e7i		−	0.294355i	−0.989110	−	0.147177i	$-0.952981\pi$
$193$		−	2.93983e7i		−	0.294355i	0.989110	−	0.147177i	$-0.0470188\pi$
$194$	−4.32243e7			−0.425032
$195$	2.56388e7	+	1.34639e7i	0.247614	+	0.130032i
$196$	−6.83629e6			−0.0648521
$197$		−	1.45110e8i		−	1.35228i	−0.736774	−	0.676139i	$-0.763652\pi$
$197$		−	1.45110e8i		−	1.35228i	0.736774	−	0.676139i	$-0.236348\pi$
$198$	−4.74328e7			−0.434261
$199$	2.19974e8			1.97872			0.989362	−	0.145472i	$-0.0464701\pi$
$199$	2.19974e8			1.97872			0.989362	+	0.145472i	$0.0464701\pi$
$200$			2.01898e8i			1.78454i
$201$			3.27881e7i			0.284794i
$202$		−	7.63567e7i		−	0.651804i
$203$			5.91618e6i			0.0496370i
$204$	−7.08026e6			−0.0583907
$205$	−9.01017e7			−0.730457
$206$		−	1.15579e8i		−	0.921180i
$207$	6.09298e7			0.477457
$208$	−2.05129e7	+	3.90617e7i	−0.158054	+	0.300975i
$209$	3.82166e7			0.289561
$210$		−	1.04831e7i		−	0.0781131i
$211$	−3.88060e7			−0.284388			−0.142194	−	0.989839i	$-0.545416\pi$
$211$	−3.88060e7			−0.284388			−0.142194	+	0.989839i	$0.545416\pi$
$212$	2.15081e7			0.155034
$213$		−	1.92745e7i		−	0.136664i
$214$		−	5.88691e7i		−	0.410619i
$215$			1.42229e8i			0.976010i
$216$		−	5.37643e7i		−	0.362999i
$217$	6.88814e7			0.457607
$218$	−1.89082e8			−1.23610
$219$			4.32588e7i			0.278304i
$220$	7.08142e7			0.448374
$221$	5.59681e7	−	1.06578e8i	0.348793	−	0.664191i
$222$	−4.29719e6			−0.0263602
$223$		−	3.04493e8i		−	1.83869i	−0.393447	−	0.919347i	$-0.628717\pi$
$223$		−	3.04493e8i		−	1.83869i	0.393447	−	0.919347i	$-0.371283\pi$
$224$	−5.23383e7			−0.311137
$225$	2.75451e8			1.61215
$226$		−	2.25137e8i		−	1.29738i
$227$			5.83415e7i			0.331045i	0.986206	+	0.165522i	$0.0529310\pi$
$227$			5.83415e7i			0.331045i	−0.986206	+	0.165522i	$0.947069\pi$
$228$			6.66160e6i			0.0372226i
$229$			5.34993e7i			0.294391i	0.989107	+	0.147195i	$0.0470246\pi$
$229$			5.34993e7i			0.294391i	−0.989107	+	0.147195i	$0.952975\pi$
$230$	1.09413e8			0.592956
$231$	−7.35077e6			−0.0392366
$232$			2.68365e7i			0.141097i
$233$	−2.06229e8			−1.06808			−0.534041	−	0.845458i	$-0.679327\pi$
$233$	−2.06229e8			−1.06808			−0.534041	+	0.845458i	$0.679327\pi$
$234$	1.24458e8	+	6.53576e7i	0.634989	+	0.333458i
$235$	5.74536e8			2.88788
$236$		−	1.45196e7i		−	0.0719057i
$237$	3.09201e7			0.150877
$238$	−4.35773e7			−0.209527
$239$			2.20261e8i			1.04362i	0.853060	+	0.521812i	$0.174744\pi$
$239$			2.20261e8i			1.04362i	−0.853060	+	0.521812i	$0.825256\pi$
$240$		−	2.03619e7i		−	0.0950777i
$241$			2.47042e8i			1.13687i	0.822728	+	0.568435i	$0.192451\pi$
$241$			2.47042e8i			1.13687i	−0.822728	+	0.568435i	$0.807549\pi$
$242$		−	1.03191e8i		−	0.468043i
$243$	−1.10573e8			−0.494344
$244$	−1.65266e8			−0.728313
$245$			5.36418e7i			0.233036i
$246$	1.32464e7			0.0567318
$247$	−1.00276e8	−	5.26587e7i	−0.423405	−	0.222347i
$248$	3.12455e8			1.30079
$249$		−	3.12718e7i		−	0.128368i
$250$	1.96836e8			0.796738
$251$	2.38950e8			0.953783			0.476891	−	0.878962i	$-0.341763\pi$
$251$	2.38950e8			0.953783			0.476891	+	0.878962i	$0.341763\pi$
$252$			4.23075e7i			0.166539i
$253$		−	7.67205e7i		−	0.297845i
$254$		−	3.05977e8i		−	1.17158i
$255$			5.55562e7i			0.209817i
$256$	−2.78840e8			−1.03876
$257$	1.25424e8			0.460908			0.230454	−	0.973083i	$-0.425979\pi$
$257$	1.25424e8			0.460908			0.230454	+	0.973083i	$0.425979\pi$
$258$		−	2.09101e7i		−	0.0758030i
$259$	2.19886e7			0.0786408
$260$	−1.85807e8	−	9.75748e7i	−0.655626	−	0.344295i
$261$	3.66132e7			0.127467
$262$			1.86767e8i			0.641574i
$263$	−5.66197e7			−0.191921			−0.0959604	−	0.995385i	$-0.530592\pi$
$263$	−5.66197e7			−0.191921			−0.0959604	+	0.995385i	$0.530592\pi$
$264$	−3.33440e7			−0.111533
$265$		−	1.68766e8i		−	0.557088i
$266$			4.10005e7i			0.133568i
$267$			2.21707e7i			0.0712838i
$268$		−	2.37620e8i		−	0.754068i
$269$	−9.92351e7			−0.310837			−0.155418	−	0.987849i	$-0.549673\pi$
$269$	−9.92351e7			−0.310837			−0.155418	+	0.987849i	$0.549673\pi$
$270$	−1.31718e8			−0.407260
$271$		−	3.29084e8i		−	1.00442i	−0.864746	−	0.502209i	$-0.832521\pi$
$271$		−	3.29084e8i		−	1.00442i	0.864746	−	0.502209i	$-0.167479\pi$
$272$	−8.46422e7			−0.255033
$273$	1.92875e7	+	1.01286e7i	0.0573729	+	0.0301288i
$274$	9.85730e7			0.289488
$275$		−	3.46837e8i		−	1.00568i
$276$	1.33733e7			0.0382874
$277$	1.30406e8			0.368654			0.184327	−	0.982865i	$-0.440989\pi$
$277$	1.30406e8			0.368654			0.184327	+	0.982865i	$0.440989\pi$
$278$			2.74805e8i			0.767129i
$279$		−	4.26284e8i		−	1.17513i
$280$			2.43326e8i			0.662423i
$281$		−	3.72567e8i		−	1.00169i	−0.865538	−	0.500843i	$-0.833023\pi$
$281$		−	3.72567e8i		−	1.00169i	0.865538	−	0.500843i	$-0.166977\pi$
$282$	−8.44663e7			−0.224291
$283$	−7.06392e8			−1.85265			−0.926325	−	0.376724i	$-0.877050\pi$
$283$	−7.06392e8			−1.85265			−0.926325	+	0.376724i	$0.877050\pi$
$284$			1.39685e8i			0.361855i
$285$	5.22711e7			0.133753
$286$	8.22959e7	−	1.56712e8i	0.208016	−	0.396116i
$287$	−6.77816e7			−0.169249
$288$			3.23904e8i			0.798993i
$289$	−1.79398e8			−0.437194
$290$	6.57473e7			0.158301
$291$			4.14552e7i			0.0986174i
$292$		−	3.13502e8i		−	0.736886i
$293$			3.61211e8i			0.838927i	0.907772	+	0.419463i	$0.137782\pi$
$293$			3.61211e8i			0.838927i	−0.907772	+	0.419463i	$0.862218\pi$
$294$		−	7.88624e6i		−	0.0180990i
$295$	−1.13930e8			−0.258382
$296$	9.97429e7			0.223543
$297$			9.23607e7i			0.204569i
$298$	−3.88657e8			−0.850766
$299$	−1.05713e8	+	2.01305e8i	−0.228707	+	0.435517i
$300$	6.04577e7			0.129279
$301$			1.06996e8i			0.226144i
$302$	−5.28308e6			−0.0110373
$303$	−7.32315e7			−0.151234
$304$			7.96372e7i			0.162577i
$305$			1.29678e9i			2.61708i
$306$			2.69685e8i			0.538061i
$307$		−	7.04717e6i		−	0.0139005i	−0.999976	−	0.00695025i	$-0.997788\pi$
$307$		−	7.04717e6i		−	0.0139005i	0.999976	−	0.00695025i	$-0.00221235\pi$
$308$	5.32720e7			0.103889
$309$	−1.10849e8			−0.213735
$310$		−	7.65488e8i		−	1.45939i
$311$	2.83836e8			0.535064			0.267532	−	0.963549i	$-0.413792\pi$
$311$	2.83836e8			0.535064			0.267532	+	0.963549i	$0.413792\pi$
$312$	8.74905e7	+	4.59447e7i	0.163087	+	0.0856435i
$313$	7.38948e8			1.36210			0.681050	−	0.732237i	$-0.261524\pi$
$313$	7.38948e8			1.36210			0.681050	+	0.732237i	$0.261524\pi$
$314$			7.67425e8i			1.39889i
$315$	3.31971e8			0.598430
$316$	−2.24082e8			−0.399487
$317$		−	6.35611e8i		−	1.12069i	−0.828260	−	0.560343i	$-0.810669\pi$
$317$		−	6.35611e8i		−	1.12069i	0.828260	−	0.560343i	$-0.189331\pi$
$318$			2.48114e7i			0.0432669i
$319$		−	4.61020e7i		−	0.0795156i
$320$			9.06702e8i			1.54682i
$321$	−5.64597e7			−0.0952732
$322$	8.23092e7			0.137389
$323$		−	2.17285e8i		−	0.358774i
$324$	2.53657e8			0.414323
$325$	−4.77907e8	+	9.10056e8i	−0.772238	+	1.47054i
$326$	−1.65140e8			−0.263991
$327$			1.81343e8i			0.286804i
$328$	−3.07466e8			−0.481103
$329$	4.32211e8			0.669130
$330$			8.16901e7i			0.125133i
$331$		−	3.27799e8i		−	0.496832i	−0.968653	−	0.248416i	$-0.920090\pi$
$331$		−	3.27799e8i		−	0.496832i	0.968653	−	0.248416i	$-0.0799100\pi$
$332$			2.26631e8i			0.339888i
$333$		−	1.36080e8i		−	0.201948i
$334$	7.46536e7			0.109632
$335$	−1.86451e9			−2.70962
$336$		−	1.53178e7i		−	0.0220297i
$337$	−3.43062e7			−0.0488278			−0.0244139	−	0.999702i	$-0.507772\pi$
$337$	−3.43062e7			−0.0488278			−0.0244139	+	0.999702i	$0.507772\pi$
$338$	−4.31868e8	+	2.97798e8i	−0.608334	+	0.419482i
$339$	−2.15922e8			−0.301022
$340$		−	4.02623e8i		−	0.555548i
$341$	−5.36760e8			−0.733061
$342$	2.53738e8			0.343000
$343$			4.03536e7i			0.0539949i
$344$			4.85347e8i			0.642833i
$345$		−	1.04935e8i		−	0.137580i
$346$		−	2.77744e7i		−	0.0360478i
$347$	−1.50703e9			−1.93629			−0.968144	−	0.250393i	$-0.919440\pi$
$347$	−1.50703e9			−1.93629			−0.968144	+	0.250393i	$0.919440\pi$
$348$	8.03611e6			0.0102216
$349$		−	6.70004e8i		−	0.843701i	−0.906666	−	0.421850i	$-0.861381\pi$
$349$		−	6.70004e8i		−	0.843701i	0.906666	−	0.421850i	$-0.138619\pi$
$350$	3.72102e8			0.463900
$351$	1.27264e8	−	2.42343e8i	0.157083	−	0.299127i
$352$	4.07848e8			0.498424
$353$			1.03475e9i			1.25205i	0.779802	+	0.626026i	$0.215320\pi$
$353$			1.03475e9i			1.25205i	−0.779802	+	0.626026i	$0.784680\pi$
$354$	1.67496e7			0.0200675
$355$	1.09605e9			1.30027
$356$		−	1.60674e8i		−	0.188743i
$357$			4.17937e7i			0.0486152i
$358$		−	3.49410e8i		−	0.402480i
$359$		−	9.67506e8i		−	1.10363i	−0.833967	−	0.551814i	$-0.813936\pi$
$359$		−	9.67506e8i		−	1.10363i	0.833967	−	0.551814i	$-0.186064\pi$
$360$	1.50586e9			1.70109
$361$	6.89435e8			0.771290
$362$		−	2.35414e8i		−	0.260827i
$363$	−9.89671e7			−0.108597
$364$	−1.39779e8	−	7.34034e7i	−0.151910	−	0.0797740i
$365$	−2.45993e9			−2.64788
$366$		−	1.90648e8i		−	0.203258i
$367$	1.52572e8			0.161118			0.0805589	−	0.996750i	$-0.474329\pi$
$367$	1.52572e8			0.161118			0.0805589	+	0.996750i	$0.474329\pi$
$368$	1.59873e8			0.167228
$369$			4.19477e8i			0.434627i
$370$		−	2.44362e8i		−	0.250800i
$371$		−	1.26959e8i		−	0.129079i
$372$		−	9.35635e7i		−	0.0942337i
$373$	−1.16787e9			−1.16523			−0.582617	−	0.812747i	$-0.697971\pi$
$373$	−1.16787e9			−1.16523			−0.582617	+	0.812747i	$0.697971\pi$
$374$	3.39577e8			0.335651
$375$		−	1.88780e8i		−	0.184862i
$376$	1.96056e9			1.90206
$377$	−6.35239e7	+	1.20966e8i	−0.0610580	+	0.116270i
$378$	−9.90887e7			−0.0943632
$379$		−	1.13519e9i		−	1.07110i	−0.844502	−	0.535552i	$-0.820103\pi$
$379$		−	1.13519e9i		−	1.07110i	0.844502	−	0.535552i	$-0.179897\pi$
$380$	−3.78815e8			−0.354148
$381$	−2.93454e8			−0.271833
$382$			8.09743e8i			0.743234i
$383$		−	6.94602e8i		−	0.631743i	−0.948802	−	0.315872i	$-0.897703\pi$
$383$		−	6.94602e8i		−	0.631743i	0.948802	−	0.315872i	$-0.102297\pi$
$384$			2.33036e7i			0.0210021i
$385$		−	4.18006e8i		−	0.373310i
$386$	−2.45775e8			−0.217511
$387$	6.62162e8			0.580733
$388$		−	3.00431e8i		−	0.261116i
$389$	1.01841e9			0.877205			0.438602	−	0.898681i	$-0.355474\pi$
$389$	1.01841e9			0.877205			0.438602	+	0.898681i	$0.355474\pi$
$390$	1.12561e8	−	2.14344e8i	0.0960862	−	0.182973i
$391$	−4.36204e8			−0.369038
$392$			1.83049e8i			0.153485i
$393$	1.79123e8			0.148860
$394$	−1.21315e9			−0.999255
$395$			1.75829e9i			1.43549i
$396$		−	3.29682e8i		−	0.266786i
$397$			1.33547e9i			1.07120i	0.844473	+	0.535598i	$0.179914\pi$
$397$			1.33547e9i			1.07120i	−0.844473	+	0.535598i	$0.820086\pi$
$398$		−	1.83902e9i		−	1.46216i
$399$	3.93224e7			0.0309910
$400$	7.22752e8			0.564650
$401$		−	1.59231e9i		−	1.23317i	−0.787289	−	0.616584i	$-0.788516\pi$
$401$		−	1.59231e9i		−	1.23317i	0.787289	−	0.616584i	$-0.211484\pi$
$402$	2.74114e8			0.210446
$403$	1.40839e9	+	7.39602e8i	1.07190	+	0.562899i
$404$	5.30718e8			0.400432
$405$		−	1.99035e9i		−	1.48880i
$406$	4.94603e7			0.0366788
$407$	−1.71347e8			−0.125978
$408$			1.89582e8i			0.138193i
$409$			1.87636e9i			1.35608i	0.735026	+	0.678039i	$0.237170\pi$
$409$			1.87636e9i			1.35608i	−0.735026	+	0.678039i	$0.762830\pi$
$410$			7.53266e8i			0.539765i
$411$		−	9.45386e7i		−	0.0671681i
$412$	8.03335e8			0.565922
$413$	−8.57072e7			−0.0598676
$414$		−	5.09384e8i		−	0.352813i
$415$	1.77829e9			1.22133
$416$	−1.07014e9	−	5.61973e8i	−0.728810	−	0.382727i
$417$	2.63558e8			0.177992
$418$		−	3.19498e8i		−	0.213969i
$419$	1.39790e9			0.928380			0.464190	−	0.885736i	$-0.346345\pi$
$419$	1.39790e9			0.928380			0.464190	+	0.885736i	$0.346345\pi$
$420$	7.28632e7			0.0479883
$421$			2.08334e9i			1.36073i	0.732872	+	0.680367i	$0.238180\pi$
$421$			2.08334e9i			1.36073i	−0.732872	+	0.680367i	$0.761820\pi$
$422$			3.24425e8i			0.210146i
$423$		−	2.67481e9i		−	1.71831i
$424$		−	5.75902e8i		−	0.366917i
$425$	−1.97199e9			−1.24607
$426$	−1.61138e8			−0.100987
$427$			9.75538e8i			0.606383i
$428$	4.09170e8			0.252261
$429$	−1.50298e8	−	7.89276e7i	−0.0919081	−	0.0482646i
$430$	1.18906e9			0.721215
$431$			6.58249e8i			0.396022i	0.980200	+	0.198011i	$0.0634482\pi$
$431$			6.58249e8i			0.396022i	−0.980200	+	0.198011i	$0.936552\pi$
$432$	−1.92465e8			−0.114857
$433$	2.38480e9			1.41171			0.705854	−	0.708357i	$-0.250563\pi$
$433$	2.38480e9			1.41171			0.705854	+	0.708357i	$0.250563\pi$
$434$		−	5.75861e8i		−	0.338145i
$435$		−	6.30564e7i		−	0.0367296i
$436$		−	1.31422e9i		−	0.759390i
$437$			4.10411e8i			0.235252i
$438$	3.61651e8			0.205651
$439$	3.24140e9			1.82855			0.914276	−	0.405092i	$-0.132760\pi$
$439$	3.24140e9			1.82855			0.914276	+	0.405092i	$0.132760\pi$
$440$		−	1.89613e9i		−	1.06116i
$441$	2.49735e8			0.138658
$442$	−8.91007e8	−	4.67903e8i	−0.490798	−	0.257738i
$443$	−2.68326e9			−1.46639			−0.733194	−	0.680019i	$-0.761971\pi$
$443$	−2.68326e9			−1.46639			−0.733194	+	0.680019i	$0.761971\pi$
$444$		−	2.98677e7i		−	0.0161943i
$445$	−1.26075e9			−0.678217
$446$	−2.54561e9			−1.35869
$447$			3.72750e8i			0.197398i
$448$			6.82092e8i			0.358402i
$449$			2.30645e9i			1.20249i	0.799065	+	0.601244i	$0.205328\pi$
$449$			2.30645e9i			1.20249i	−0.799065	+	0.601244i	$0.794672\pi$
$450$		−	2.30282e9i		−	1.19128i
$451$	5.28190e8			0.271127
$452$	1.56482e9			0.797038
$453$			5.06685e6i			0.00256091i
$454$	4.87745e8			0.244623
$455$	−5.75970e8	+	1.09679e9i	−0.286655	+	0.545865i
$456$	1.78371e8			0.0880944
$457$		−	2.83712e6i		−	0.00139050i	−1.00000		0.000695249i	$-0.999779\pi$
$457$		−	2.83712e6i		−	0.00139050i	1.00000		0.000695249i	$-0.000221305\pi$
$458$	4.47264e8			0.217538
$459$	5.25128e8			0.253467
$460$			7.60478e8i			0.364279i
$461$		−	5.94593e8i		−	0.282661i	−0.989962	−	0.141331i	$-0.954862\pi$
$461$		−	5.94593e8i		−	0.282661i	0.989962	−	0.141331i	$-0.0451381\pi$
$462$			6.14537e7i			0.0289936i
$463$			2.76963e9i			1.29684i	0.761281	+	0.648422i	$0.224571\pi$
$463$			2.76963e9i			1.29684i	−0.761281	+	0.648422i	$0.775429\pi$
$464$	9.60691e7			0.0446448
$465$	−7.34158e8			−0.338614
$466$			1.72411e9i			0.789251i
$467$	−3.52202e8			−0.160023			−0.0800115	−	0.996794i	$-0.525496\pi$
$467$	−3.52202e8			−0.160023			−0.0800115	+	0.996794i	$0.525496\pi$
$468$	−4.54269e8	+	8.65044e8i	−0.204858	+	0.390102i
$469$	−1.40263e9			−0.627826
$470$		−	4.80322e9i		−	2.13398i
$471$	7.36016e8			0.324574
$472$	−3.88779e8			−0.170179
$473$		−	8.33770e8i		−	0.362270i
$474$		−	2.58498e8i		−	0.111489i
$475$			1.85538e9i			0.794338i
$476$		−	3.02884e8i		−	0.128722i
$477$	−7.85706e8			−0.331471
$478$	1.84142e9			0.771178
$479$		−	1.11047e9i		−	0.461672i	−0.972993	−	0.230836i	$-0.925854\pi$
$479$		−	1.11047e9i		−	0.461672i	0.972993	−	0.230836i	$-0.0741461\pi$
$480$	5.57837e8			0.230231
$481$	4.49591e8	+	2.36098e8i	0.184209	+	0.0967353i
$482$	2.06531e9			0.840081
$483$		−	7.89404e7i		−	0.0318775i
$484$	7.17227e8			0.287540
$485$	−2.35737e9			−0.938279
$486$			9.24413e8i			0.365291i
$487$			1.49203e9i			0.585364i	0.956210	+	0.292682i	$0.0945477\pi$
$487$			1.49203e9i			0.585364i	−0.956210	+	0.292682i	$0.905452\pi$
$488$			4.42516e9i			1.72369i
$489$			1.58381e8i			0.0612521i
$490$	4.48455e8			0.172200
$491$	−6.67337e8			−0.254425			−0.127213	−	0.991875i	$-0.540603\pi$
$491$	−6.67337e8			−0.254425			−0.127213	+	0.991875i	$0.540603\pi$
$492$			9.20696e7i			0.0348528i
$493$	−2.62119e8			−0.0985221
$494$	−4.40236e8	+	8.38321e8i	−0.164301	+	0.312871i
$495$	−2.58690e9			−0.958652
$496$		−	1.11852e9i		−	0.411584i
$497$	8.24538e8			0.301275
$498$	−2.61438e8			−0.0948562
$499$			2.05637e9i			0.740882i	0.928856	+	0.370441i	$0.120793\pi$
$499$			2.05637e9i			0.740882i	−0.928856	+	0.370441i	$0.879207\pi$
$500$			1.36811e9i			0.489471i
$501$		−	7.15982e7i		−	0.0254372i
$502$		−	1.99767e9i		−	0.704790i
$503$	1.92840e9			0.675632			0.337816	−	0.941212i	$-0.390312\pi$
$503$	1.92840e9			0.675632			0.337816	+	0.941212i	$0.390312\pi$
$504$	1.13283e9			0.394146
$505$		−	4.16435e9i		−	1.43889i
$506$	−6.41397e8			−0.220090
$507$	2.85609e8	+	4.14192e8i	0.0973295	+	0.141148i
$508$	2.12670e9			0.719752
$509$			4.05353e9i			1.36245i	0.732073	+	0.681226i	$0.238553\pi$
$509$			4.05353e9i			1.36245i	−0.732073	+	0.681226i	$0.761447\pi$
$510$	4.64459e8			0.155043
$511$	−1.85056e9			−0.613520
$512$			1.95913e9i			0.645087i
$513$		−	4.94077e8i		−	0.161578i
$514$		−	1.04857e9i		−	0.340584i
$515$		−	6.30347e9i		−	2.03355i
$516$	1.45336e8			0.0465691
$517$	−3.36802e9			−1.07191
$518$		−	1.83828e8i		−	0.0581110i
$519$	−2.66376e7			−0.00836392
$520$	−2.61267e9	+	4.97519e9i	−0.814841	+	1.55167i
$521$	−9.78566e8			−0.303150			−0.151575	−	0.988446i	$-0.548435\pi$
$521$	−9.78566e8			−0.303150			−0.151575	+	0.988446i	$0.548435\pi$
$522$		−	3.06093e8i		−	0.0941904i
$523$	2.50883e8			0.0766858			0.0383429	−	0.999265i	$-0.487792\pi$
$523$	2.50883e8			0.0766858			0.0383429	+	0.999265i	$0.487792\pi$
$524$	−1.29813e9			−0.394147
$525$		−	3.56873e8i		−	0.107636i
$526$			4.73350e8i			0.141818i
$527$			3.05182e9i			0.908283i
$528$			1.19365e8i			0.0352904i
$529$	−2.58092e9			−0.758018
$530$	−1.41091e9			−0.411656
$531$			5.30413e8i			0.153739i
$532$	−2.84975e8			−0.0820569
$533$	−1.38590e9	−	7.27793e8i	−0.396449	−	0.208191i
$534$	1.85351e8			0.0526746
$535$		−	3.21061e9i		−	0.906461i
$536$	−6.36252e9			−1.78465
$537$	−3.35109e8			−0.0933848
$538$			8.29623e8i			0.229690i
$539$		−	3.14457e8i		−	0.0864968i
$540$		−	9.15508e8i		−	0.250198i
$541$		−	5.18527e9i		−	1.40793i	−0.710235	−	0.703964i	$-0.751411\pi$
$541$		−	5.18527e9i		−	1.40793i	0.710235	−	0.703964i	$-0.248589\pi$
$542$	−2.75120e9			−0.742207
$543$	−2.25779e8			−0.0605179
$544$		−	2.31887e9i		−	0.617562i
$545$	−1.03122e10			−2.72875
$546$	8.46771e7	−	1.61247e8i	0.0222634	−	0.0423952i
$547$	2.72277e9			0.711304			0.355652	−	0.934618i	$-0.384259\pi$
$547$	2.72277e9			0.711304			0.355652	+	0.934618i	$0.384259\pi$
$548$			6.85133e8i			0.177846i
$549$	6.03728e9			1.55718
$550$	−2.89962e9			−0.743141
$551$			2.46619e8i			0.0628053i
$552$		−	3.58084e8i		−	0.0906145i
$553$			1.32272e9i			0.332607i
$554$		−	1.09022e9i		−	0.272414i
$555$	−2.34361e8			−0.0581914
$556$	−1.91004e9			−0.471281
$557$		−	1.60971e9i		−	0.394688i	−0.980334	−	0.197344i	$-0.936768\pi$
$557$		−	1.60971e9i		−	0.394688i	0.980334	−	0.197344i	$-0.0632316\pi$
$558$	−3.56381e9			−0.868349
$559$	−1.14885e9	+	2.18771e9i	−0.278178	+	0.529721i
$560$	8.71056e8			0.209598
$561$		−	3.25679e8i		−	0.0778789i
$562$	−3.11472e9			−0.740188
$563$	6.52084e9			1.54001			0.770006	−	0.638037i	$-0.220253\pi$
$563$	6.52084e9			1.54001			0.770006	+	0.638037i	$0.220253\pi$
$564$		−	5.87084e8i		−	0.137792i
$565$		−	1.22785e10i		−	2.86403i
$566$			5.90556e9i			1.36900i
$567$		−	1.49730e9i		−	0.344959i
$568$	3.74021e9			0.856400
$569$	1.37450e9			0.312788			0.156394	−	0.987695i	$-0.450013\pi$
$569$	1.37450e9			0.312788			0.156394	+	0.987695i	$0.450013\pi$
$570$		−	4.36995e8i		−	0.0988359i
$571$	−8.38105e8			−0.188396			−0.0941981	−	0.995553i	$-0.530029\pi$
$571$	−8.38105e8			−0.188396			−0.0941981	+	0.995553i	$0.530029\pi$
$572$	1.08923e9	+	5.71998e8i	0.243351	+	0.127793i
$573$	7.76602e8			0.172448
$574$			5.66666e8i			0.125065i
$575$	3.72471e9			0.817061
$576$	4.22124e9			0.920368
$577$			7.39362e9i			1.60229i	0.598469	+	0.801146i	$0.295776\pi$
$577$			7.39362e9i			1.60229i	−0.598469	+	0.801146i	$0.704224\pi$
$578$			1.49979e9i			0.323061i
$579$			2.35716e8i			0.0504677i
$580$			4.56977e8i			0.0972516i
$581$	1.33777e9			0.282986
$582$	3.46573e8			0.0728726
$583$			9.89332e8i			0.206777i
$584$	−8.39435e9			−1.74398
$585$	6.78768e9	+	3.56448e9i	1.40177	+	0.736124i
$586$	3.01978e9			0.619918
$587$			7.16306e9i			1.46172i	0.682525	+	0.730862i	$0.260882\pi$
$587$			7.16306e9i			1.46172i	−0.682525	+	0.730862i	$0.739118\pi$
$588$	5.48134e7			0.0111190
$589$	2.87136e9			0.579007
$590$			9.52475e8i			0.190929i
$591$			1.16349e9i			0.231851i
$592$		−	3.57058e8i		−	0.0707316i
$593$			5.56281e9i			1.09548i	0.836650	+	0.547738i	$0.184511\pi$
$593$			5.56281e9i			1.09548i	−0.836650	+	0.547738i	$0.815489\pi$
$594$	7.72151e8			0.151165
$595$	−2.37662e9			−0.462542
$596$		−	2.70137e9i		−	0.522663i
$597$	−1.76375e9			−0.339256
$598$	1.68294e9	+	8.83781e8i	0.321822	+	0.169001i
$599$	2.74503e9			0.521858			0.260929	−	0.965358i	$-0.415971\pi$
$599$	2.74503e9			0.521858			0.260929	+	0.965358i	$0.415971\pi$
$600$		−	1.61882e9i		−	0.305963i
$601$	−5.93627e9			−1.11546			−0.557728	−	0.830023i	$-0.688327\pi$
$601$	−5.93627e9			−1.11546			−0.557728	+	0.830023i	$0.688327\pi$
$602$	8.94505e8			0.167107
$603$			8.68042e9i			1.61224i
$604$		−	3.67201e7i		−	0.00678071i
$605$		−	5.62782e9i		−	1.03323i
$606$			6.12228e8i			0.111753i
$607$	3.85660e9			0.699913			0.349956	−	0.936766i	$-0.386196\pi$
$607$	3.85660e9			0.699913			0.349956	+	0.936766i	$0.386196\pi$
$608$	−2.18175e9			−0.393680
$609$		−	4.74360e7i		−	0.00851034i
$610$	1.08413e10			1.93387
$611$	8.83725e9	+	4.64079e9i	1.56738	+	0.823091i
$612$	−1.87445e9			−0.330555
$613$		−	5.10682e9i		−	0.895445i	−0.894172	−	0.447723i	$-0.852235\pi$
$613$		−	5.10682e9i		−	0.895445i	0.894172	−	0.447723i	$-0.147765\pi$
$614$	−5.89156e7			−0.0102717
$615$	7.22436e8			0.125238
$616$		−	1.42641e9i		−	0.245874i
$617$			7.89344e9i			1.35291i	0.736485	+	0.676454i	$0.236484\pi$
$617$			7.89344e9i			1.35291i	−0.736485	+	0.676454i	$0.763516\pi$
$618$			9.26715e8i			0.157938i
$619$		−	8.14995e9i		−	1.38114i	−0.723265	−	0.690570i	$-0.757360\pi$
$619$		−	8.14995e9i		−	1.38114i	0.723265	−	0.690570i	$-0.242640\pi$
$620$	5.32054e9			0.896571
$621$	−9.91868e8			−0.166201
$622$		−	2.37292e9i		−	0.395381i
$623$	−9.48435e8			−0.157145
$624$	1.64472e8	−	3.13197e8i	0.0270986	−	0.0516026i
$625$	5.97302e8			0.0978619
$626$		−	6.17774e9i		−	1.00651i
$627$	−3.06421e8			−0.0496458
$628$	−5.33400e9			−0.859397
$629$			9.74212e8i			0.156090i
$630$		−	2.77534e9i		−	0.442205i
$631$		−	8.98853e9i		−	1.42425i	−0.702053	−	0.712125i	$-0.747733\pi$
$631$		−	8.98853e9i		−	1.42425i	0.702053	−	0.712125i	$-0.252267\pi$
$632$			6.00004e9i			0.945462i
$633$	3.11147e8			0.0487588
$634$	−5.31382e9			−0.828122
$635$		−	1.66874e10i		−	2.58631i
$636$	−1.72452e8			−0.0265808
$637$	−4.33290e8	+	8.25094e8i	−0.0664187	+	0.126478i
$638$	−3.85421e8			−0.0587574
$639$		−	5.10279e9i		−	0.773668i
$640$	−1.32517e9			−0.199821
$641$	−3.30874e8			−0.0496203			−0.0248101	−	0.999692i	$-0.507898\pi$
$641$	−3.30874e8			−0.0496203			−0.0248101	+	0.999692i	$0.507898\pi$
$642$			4.72013e8i			0.0704013i
$643$		−	5.45857e9i		−	0.809731i	−0.914376	−	0.404865i	$-0.867318\pi$
$643$		−	5.45857e9i		−	0.809731i	0.914376	−	0.404865i	$-0.132682\pi$
$644$			5.72091e8i			0.0844044i
$645$		−	1.14040e9i		−	0.167339i
$646$	−1.81654e9			−0.265113
$647$	2.31166e9			0.335551			0.167775	−	0.985825i	$-0.446342\pi$
$647$	2.31166e9			0.335551			0.167775	+	0.985825i	$0.446342\pi$
$648$		−	6.79194e9i		−	0.980576i
$649$	6.67876e8			0.0959046
$650$	7.60823e9	+	3.99538e9i	1.08664	+	0.570639i
$651$	−5.52292e8			−0.0784576
$652$		−	1.14780e9i		−	0.162181i
$653$	1.33688e10			1.87887			0.939435	−	0.342728i	$-0.111351\pi$
$653$	1.33688e10			1.87887			0.939435	+	0.342728i	$0.111351\pi$
$654$	1.51606e9			0.211931
$655$			1.01859e10i			1.41631i
$656$			1.10066e9i			0.152227i
$657$			1.14525e10i			1.57551i
$658$		−	3.61336e9i		−	0.494448i
$659$	9.68372e9			1.31808			0.659042	−	0.752106i	$-0.270962\pi$
$659$	9.68372e9			1.31808			0.659042	+	0.752106i	$0.270962\pi$
$660$	−5.67788e8			−0.0768746
$661$		−	8.46016e9i		−	1.13939i	−0.821855	−	0.569696i	$-0.807061\pi$
$661$		−	8.46016e9i		−	1.13939i	0.821855	−	0.569696i	$-0.192939\pi$
$662$	−2.74045e9			−0.367130
$663$	−4.48753e8	+	8.54540e8i	−0.0598012	+	0.113877i
$664$	6.06828e9			0.804410
$665$			2.23609e9i			0.294858i
$666$	−1.13765e9			−0.149228
$667$	4.95092e8			0.0646020
$668$			5.18881e8i			0.0673519i
$669$			2.44142e9i			0.315248i
$670$			1.55876e10i			2.00225i
$671$		−	7.60191e9i		−	0.971391i
$672$	4.19649e8			0.0533450
$673$	5.08905e9			0.643552			0.321776	−	0.946816i	$-0.395720\pi$
$673$	5.08905e9			0.643552			0.321776	+	0.946816i	$0.395720\pi$
$674$			2.86805e8i			0.0360809i
$675$	−4.48402e9			−0.561183
$676$	−2.06985e9	−	3.00170e9i	−0.257706	−	0.373727i
$677$	−1.21592e10			−1.50607			−0.753036	−	0.657979i	$-0.771411\pi$
$677$	−1.21592e10			−1.50607			−0.753036	+	0.657979i	$0.771411\pi$
$678$			1.80515e9i			0.222438i
$679$	−1.77340e9			−0.217402
$680$	−1.07807e10			−1.31481
$681$		−	4.67782e8i		−	0.0567582i
$682$			4.48741e9i			0.541690i
$683$		−	1.07548e10i		−	1.29160i	−0.763506	−	0.645801i	$-0.776524\pi$
$683$		−	1.07548e10i		−	1.29160i	0.763506	−	0.645801i	$-0.223476\pi$
$684$			1.76361e9i			0.210720i
$685$	5.37599e9			0.639059
$686$	3.37363e8			0.0398991
$687$		−	4.28958e8i		−	0.0504738i
$688$	1.73744e9			0.203400
$689$	1.36320e9	−	2.59588e9i	0.158779	−	0.302355i
$690$	−8.77276e8			−0.101663
$691$		−	7.43901e9i		−	0.857713i	−0.903373	−	0.428856i	$-0.858917\pi$
$691$		−	7.43901e9i		−	0.857713i	0.903373	−	0.428856i	$-0.141083\pi$
$692$	1.93046e8			0.0221457
$693$	−1.94607e9			−0.222122
$694$			1.25991e10i			1.43080i
$695$			1.49874e10i			1.69347i
$696$		−	2.15175e8i		−	0.0241914i
$697$		−	3.00309e9i		−	0.335934i
$698$	−5.60135e9			−0.623446
$699$	1.65355e9			0.183125
$700$			2.58630e9i			0.284994i
$701$	−1.48234e10			−1.62530			−0.812650	−	0.582751i	$-0.801976\pi$
$701$	−1.48234e10			−1.62530			−0.812650	+	0.582751i	$0.801976\pi$
$702$	−2.02603e9	−	1.06395e9i	−0.221037	−	0.116075i
$703$	9.16606e8			0.0995036
$704$		−	5.31522e9i		−	0.574139i
$705$	−4.60663e9			−0.495133
$706$	8.65066e9			0.925194
$707$		−	3.13275e9i		−	0.333394i
$708$			1.16418e8i			0.0123284i
$709$			8.30565e9i			0.875210i	0.899167	+	0.437605i	$0.144173\pi$
$709$			8.30565e9i			0.875210i	−0.899167	+	0.437605i	$0.855827\pi$
$710$		−	9.16321e9i		−	0.960823i
$711$	8.18589e9			0.854126
$712$	−4.30222e9			−0.446697
$713$		−	5.76431e9i		−	0.595571i
$714$	3.49403e8			0.0359238
$715$	4.48826e9	−	8.54679e9i	0.459205	−	0.874444i
$716$	2.42858e9			0.247261
$717$		−	1.76605e9i		−	0.178931i
$718$	−8.08852e9			−0.815517
$719$	1.10800e10			1.11170			0.555851	−	0.831282i	$-0.312393\pi$
$719$	1.10800e10			1.11170			0.555851	+	0.831282i	$0.312393\pi$
$720$		−	5.39067e9i		−	0.538244i
$721$		−	4.74197e9i		−	0.471178i
$722$		−	5.76379e9i		−	0.569939i
$723$		−	1.98078e9i		−	0.194918i
$724$	1.63625e9			0.160238
$725$	2.23821e9			0.218131
$726$			8.27382e8i			0.0802469i
$727$	1.20204e10			1.16025			0.580123	−	0.814529i	$-0.303004\pi$
$727$	1.20204e10			1.16025			0.580123	+	0.814529i	$0.303004\pi$
$728$	−1.96546e9	+	3.74273e9i	−0.188801	+	0.359525i
$729$	−8.66034e9			−0.827921
$730$			2.05655e10i			1.95663i
$731$	−4.74050e9			−0.448863
$732$	1.32510e9			0.124871
$733$		−	3.40751e9i		−	0.319575i	−0.987151	−	0.159788i	$-0.948919\pi$
$733$		−	3.40751e9i		−	0.319575i	0.987151	−	0.159788i	$-0.0510810\pi$
$734$		−	1.27553e9i		−	0.119057i
$735$		−	4.30101e8i		−	0.0399544i
$736$			4.37991e9i			0.404942i
$737$	1.09301e10			1.00574
$738$	3.50690e9			0.321164
$739$		−	3.52419e9i		−	0.321221i	−0.987018	−	0.160610i	$-0.948654\pi$
$739$		−	3.52419e9i		−	0.321221i	0.987018	−	0.160610i	$-0.0513462\pi$
$740$	1.69844e9			0.154078
$741$	8.04010e8	+	4.22217e8i	0.0725935	+	0.0381217i
$742$	−1.06140e9			−0.0953817
$743$		−	1.32406e10i		−	1.18426i	−0.805843	−	0.592129i	$-0.798287\pi$
$743$		−	1.32406e10i		−	1.18426i	0.805843	−	0.592129i	$-0.201713\pi$
$744$	−2.50526e9			−0.223022
$745$	−2.11966e10			−1.87811
$746$			9.76358e9i			0.861040i
$747$		−	8.27900e9i		−	0.726701i
$748$			2.36024e9i			0.206205i
$749$		−	2.41527e9i		−	0.210029i
$750$	−1.57824e9			−0.136602
$751$	−1.90255e9			−0.163907			−0.0819533	−	0.996636i	$-0.526116\pi$
$751$	−1.90255e9			−0.163907			−0.0819533	+	0.996636i	$0.526116\pi$
$752$		−	7.01841e9i		−	0.601833i
$753$	−1.91590e9			−0.163528
$754$	1.01129e9	+	5.31071e8i	0.0859168	+	0.0451183i
$755$	−2.88129e8			−0.0243654
$756$		−	6.88717e8i		−	0.0579715i
$757$	−1.21454e10			−1.01760			−0.508798	−	0.860886i	$-0.669910\pi$
$757$	−1.21454e10			−1.01760			−0.508798	+	0.860886i	$0.669910\pi$
$758$	−9.49040e9			−0.791484
$759$			6.15146e8i			0.0510660i
$760$			1.01432e10i			0.838160i
$761$			1.36699e10i			1.12439i	0.827003	+	0.562197i	$0.190044\pi$
$761$			1.36699e10i			1.12439i	−0.827003	+	0.562197i	$0.809956\pi$
$762$			2.45333e9i			0.200869i
$763$	−7.75764e9			−0.632257
$764$	−5.62813e9			−0.456601
$765$			1.47081e10i			1.18780i
$766$	−5.80700e9			−0.466822
$767$	−1.75242e9	−	9.20266e8i	−0.140234	−	0.0736426i
$768$	2.23574e9			0.178097
$769$			4.57340e9i			0.362658i	0.983422	+	0.181329i	$0.0580399\pi$
$769$			4.57340e9i			0.362658i	−0.983422	+	0.181329i	$0.941960\pi$
$770$	−3.49460e9			−0.275854
$771$	−1.00565e9			−0.0790235
$772$		−	1.70826e9i		−	0.133627i
$773$			8.27376e8i			0.0644280i	0.999481	+	0.0322140i	$0.0102558\pi$
$773$			8.27376e8i			0.0644280i	−0.999481	+	0.0322140i	$0.989744\pi$
$774$		−	5.53579e9i		−	0.429128i
$775$		−	2.60592e10i		−	2.01097i
$776$	−8.04437e9			−0.617982
$777$	−1.76304e8			−0.0134831
$778$		−	8.51412e9i		−	0.648203i
$779$	−2.82551e9			−0.214149
$780$	1.48980e9	+	7.82355e8i	0.112408	+	0.0590300i
$781$	−6.42524e9			−0.482626
$782$			3.64674e9i			0.272698i
$783$	−5.96021e8			−0.0443706
$784$	6.55277e8			0.0485644
$785$			4.18539e10i			3.08811i
$786$		−	1.49750e9i		−	0.109999i
$787$			1.88492e10i			1.37842i	0.724561	+	0.689211i	$0.242043\pi$
$787$			1.88492e10i			1.37842i	−0.724561	+	0.689211i	$0.757957\pi$
$788$		−	8.43199e9i		−	0.613887i
$789$	4.53977e8			0.0329052
$790$	1.46996e10			1.06074
$791$		−	9.23688e9i		−	0.663602i
$792$	−8.82760e9			−0.631400
$793$	−1.04747e10	+	1.99464e10i	−0.745906	+	1.42040i
$794$	1.11648e10			0.791551
$795$			1.35317e9i			0.0955138i
$796$	1.27821e10			0.898271
$797$	−1.49574e10			−1.04653			−0.523264	−	0.852171i	$-0.675286\pi$
$797$	−1.49574e10			−1.04653			−0.523264	+	0.852171i	$0.675286\pi$
$798$		−	3.28742e8i		−	0.0229005i
$799$			1.91493e10i			1.32812i
$800$			1.98006e10i			1.36730i
$801$			5.86955e9i			0.403544i
$802$	−1.33120e10			−0.911240
$803$	1.44205e10			0.982825
$804$			1.90523e9i			0.129286i
$805$	4.48899e9			0.303293
$806$	6.18320e9	−	1.17744e10i	0.415950	−	0.792074i
$807$	7.95668e8			0.0532935
$808$		−	1.42105e10i		−	0.947700i
$809$	2.93851e10			1.95122			0.975612	−	0.219504i	$-0.0704440\pi$
$809$	2.93851e10			1.95122			0.975612	+	0.219504i	$0.0704440\pi$
$810$	−1.66397e10			−1.10014
$811$		−	1.84343e10i		−	1.21354i	−0.794877	−	0.606770i	$-0.792465\pi$
$811$		−	1.84343e10i		−	1.21354i	0.794877	−	0.606770i	$-0.207535\pi$
$812$			3.43774e8i			0.0225334i
$813$			2.63860e9i			0.172209i
$814$			1.43249e9i			0.0930905i
$815$	−9.00640e9			−0.582773
$816$	6.78662e8			0.0437258
$817$			4.46019e9i			0.286138i
$818$	1.56867e10			1.00206
$819$	5.10623e9	+	2.68148e9i	0.324793	+	0.170562i
$820$	−5.23558e9			−0.331602
$821$		−	9.80011e9i		−	0.618059i	−0.951052	−	0.309029i	$-0.899996\pi$
$821$		−	9.80011e9i		−	0.618059i	0.951052	−	0.309029i	$-0.100004\pi$
$822$	−7.90359e8			−0.0496333
$823$	−4.88004e9			−0.305158			−0.152579	−	0.988291i	$-0.548758\pi$
$823$	−4.88004e9			−0.305158			−0.152579	+	0.988291i	$0.548758\pi$
$824$		−	2.15102e10i		−	1.33936i
$825$			2.78094e9i			0.172426i
$826$			7.16527e8i			0.0442387i
$827$			2.79819e10i			1.72032i	0.510027	+	0.860158i	$0.329635\pi$
$827$			2.79819e10i			1.72032i	−0.510027	+	0.860158i	$0.670365\pi$
$828$	3.54048e9			0.216748
$829$	7.29357e8			0.0444631			0.0222315	−	0.999753i	$-0.492923\pi$
$829$	7.29357e8			0.0444631			0.0222315	+	0.999753i	$0.492923\pi$
$830$		−	1.48668e10i		−	0.902493i
$831$	−1.04560e9			−0.0632064
$832$	−7.32384e9	+	1.39465e10i	−0.440867	+	0.839523i
$833$	−1.78788e9			−0.107172
$834$		−	2.20339e9i		−	0.131526i
$835$	4.07147e9			0.242018
$836$	2.22067e9			0.131451
$837$			6.93941e9i			0.409057i
$838$		−	1.16867e10i		−	0.686019i
$839$			1.44574e10i			0.845129i	0.906333	+	0.422564i	$0.138870\pi$
$839$			1.44574e10i			0.845129i	−0.906333	+	0.422564i	$0.861130\pi$
$840$		−	1.95099e9i		−	0.113574i
$841$	−1.69524e10			−0.982753
$842$	1.74171e10			1.00550
$843$			2.98724e9i			0.171741i
$844$	−2.25492e9			−0.129102
$845$	−2.35532e10	+	1.62413e10i	−1.34293	+	0.926025i
$846$	−2.23619e10			−1.26973
$847$		−	4.23369e9i		−	0.239401i
$848$	−2.06161e9			−0.116097
$849$	5.66386e9			0.317640
$850$			1.64861e10i			0.920773i
$851$		−	1.84010e9i		−	0.102350i
$852$		−	1.11999e9i		−	0.0620407i
$853$			4.75542e9i			0.262342i	0.991360	+	0.131171i	$0.0418737\pi$
$853$			4.75542e9i			0.262342i	−0.991360	+	0.131171i	$0.958126\pi$
$854$	8.15567e9			0.448082
$855$	1.38384e10			0.757190
$856$		−	1.09560e10i		−	0.597026i
$857$	1.31971e10			0.716217			0.358109	−	0.933680i	$-0.383422\pi$
$857$	1.31971e10			0.716217			0.358109	+	0.933680i	$0.383422\pi$
$858$	−6.59849e8	+	1.25652e9i	−0.0356647	+	0.0679147i
$859$	1.38332e10			0.744641			0.372320	−	0.928104i	$-0.378562\pi$
$859$	1.38332e10			0.744641			0.372320	+	0.928104i	$0.378562\pi$
$860$			8.26459e9i			0.443074i
$861$	5.43473e8			0.0290180
$862$	5.50307e9			0.292637
$863$		−	1.83196e10i		−	0.970238i	−0.874448	−	0.485119i	$-0.838776\pi$
$863$		−	1.83196e10i		−	0.970238i	0.874448	−	0.485119i	$-0.161224\pi$
$864$		−	5.27279e9i		−	0.278126i
$865$		−	1.51476e9i		−	0.0795772i
$866$		−	1.99374e10i		−	1.04317i
$867$	1.43841e9			0.0749577
$868$	4.00253e9			0.207738
$869$		−	1.03074e10i		−	0.532817i
$870$	−5.27162e8			−0.0271411
$871$	−2.86791e10	−	1.50605e10i	−1.47062	−	0.772283i
$872$	−3.51896e10			−1.79724
$873$			1.09750e10i			0.558282i
$874$	3.43111e9			0.173838
$875$	8.07578e9			0.407527
$876$			2.51366e9i			0.126340i
$877$		−	3.39492e10i		−	1.69954i	−0.527156	−	0.849768i	$-0.676742\pi$
$877$		−	3.39492e10i		−	1.69954i	0.527156	−	0.849768i	$-0.323258\pi$
$878$		−	2.70987e10i		−	1.35119i
$879$		−	2.89619e9i		−	0.143835i
$880$	−6.78773e9			−0.335765
$881$	2.63362e10			1.29759			0.648794	−	0.760964i	$-0.275274\pi$
$881$	2.63362e10			1.29759			0.648794	+	0.760964i	$0.275274\pi$
$882$		−	2.08783e9i		−	0.102460i
$883$	2.77014e10			1.35406			0.677031	−	0.735954i	$-0.263266\pi$
$883$	2.77014e10			1.35406			0.677031	+	0.735954i	$0.263266\pi$
$884$	3.25217e9	−	6.19296e9i	0.158340	−	0.301519i
$885$	9.13492e8			0.0443000
$886$			2.24325e10i			1.08358i
$887$	1.47023e10			0.707382			0.353691	−	0.935362i	$-0.384926\pi$
$887$	1.47023e10			0.707382			0.353691	+	0.935362i	$0.384926\pi$
$888$	−7.99739e8			−0.0383268
$889$		−	1.25536e10i		−	0.599255i
$890$			1.05401e10i			0.501163i
$891$			1.16678e10i			0.552606i
$892$		−	1.76933e10i		−	0.834703i
$893$	1.80170e10			0.846646
$894$	3.11626e9			0.145865
$895$		−	1.90562e10i		−	0.888494i
$896$	−9.96897e8			−0.0462991
$897$	8.47609e8	−	1.61406e9i	0.0392123	−	0.0746702i
$898$	1.92823e10			0.888569
$899$		−	3.46382e9i		−	0.159000i
$900$	1.60058e10			0.731859
$901$	5.62497e9			0.256202
$902$		−	4.41576e9i		−	0.200347i
$903$		−	8.57895e8i		−	0.0387728i
$904$		−	4.18997e10i		−	1.88634i
$905$		−	1.28390e10i		−	0.575788i
$906$	4.23598e7			0.00189237
$907$	−3.58213e10			−1.59410			−0.797050	−	0.603913i	$-0.793607\pi$
$907$	−3.58213e10			−1.59410			−0.797050	+	0.603913i	$0.793607\pi$
$908$			3.39008e9i			0.150283i
$909$	−1.93875e10			−0.856148
$910$	9.16938e9	+	4.81521e9i	0.403362	+	0.211821i
$911$	4.64485e9			0.203543			0.101772	−	0.994808i	$-0.467549\pi$
$911$	4.64485e9			0.203543			0.101772	+	0.994808i	$0.467549\pi$
$912$		−	6.38532e8i		−	0.0278741i
$913$	−1.04246e10			−0.453327
$914$	−2.37188e7			−0.00102750
$915$		−	1.03976e10i		−	0.448702i
$916$			3.10871e9i			0.133643i
$917$			7.66267e9i			0.328161i
$918$		−	4.39016e9i		−	0.187297i
$919$	1.05920e10			0.450166			0.225083	−	0.974340i	$-0.427735\pi$
$919$	1.05920e10			0.450166			0.225083	+	0.974340i	$0.427735\pi$
$920$	2.03626e10			0.862137
$921$			5.65042e7i			0.00238327i
$922$	−4.97090e9			−0.208870
$923$	1.68590e10	+	8.85333e9i	0.705710	+	0.370596i
$924$	−4.27135e8			−0.0178120
$925$		−	8.31871e9i		−	0.345589i
$926$	2.31546e10			0.958292
$927$	−2.93464e10			−1.20998
$928$			2.63192e9i			0.108107i
$929$		−	2.49946e10i		−	1.02280i	−0.859343	−	0.511400i	$-0.829127\pi$
$929$		−	2.49946e10i		−	1.02280i	0.859343	−	0.511400i	$-0.170873\pi$
$930$			6.13769e9i			0.250216i
$931$			1.68216e9i			0.0683194i
$932$	−1.19835e10			−0.484872
$933$	−2.27580e9			−0.0917377
$934$			2.94447e9i			0.118248i
$935$	1.85199e10			0.740965
$936$	2.31625e10	+	1.21635e10i	0.923251	+	0.484836i
$937$	−1.53893e10			−0.611125			−0.305563	−	0.952172i	$-0.598845\pi$
$937$	−1.53893e10			−0.611125			−0.305563	+	0.952172i	$0.598845\pi$
$938$			1.17263e10i			0.463927i
$939$	−5.92489e9			−0.233534
$940$	3.33849e10			1.31100
$941$			2.08170e10i			0.814433i	0.913332	+	0.407216i	$0.133501\pi$
$941$			2.08170e10i			0.814433i	−0.913332	+	0.407216i	$0.866499\pi$
$942$		−	6.15322e9i		−	0.239841i
$943$			5.67227e9i			0.220275i
$944$			1.39174e9i			0.0538465i
$945$	−5.40411e9			−0.208311
$946$	−6.97046e9			−0.267696
$947$			8.60328e9i			0.329184i	0.986362	+	0.164592i	$0.0526308\pi$
$947$			8.60328e9i			0.329184i	−0.986362	+	0.164592i	$0.947369\pi$
$948$	1.79669e9			0.0684927
$949$	−3.78376e10	−	1.98700e10i	−1.43711	−	0.754686i
$950$	1.55113e10			0.586969
$951$			5.09633e9i			0.192144i
$952$	−8.11006e9			−0.304645
$953$	3.33562e10			1.24839			0.624197	−	0.781267i	$-0.285426\pi$
$953$	3.33562e10			1.24839			0.624197	+	0.781267i	$0.285426\pi$
$954$			6.56864e9i			0.244938i
$955$			4.41618e10i			1.64072i
$956$			1.27988e10i			0.473769i
$957$			3.69646e8i			0.0136331i
$958$	−9.28375e9			−0.341149
$959$	4.04424e9			0.148072
$960$		−	7.26994e9i		−	0.265205i
$961$	−1.28162e10			−0.465831
$962$	1.97382e9	−	3.75866e9i	0.0714818	−	0.136120i
$963$	−1.49473e10			−0.539350
$964$			1.43550e10i			0.516099i
$965$	−1.34041e10			−0.480166
$966$	−6.59956e8			−0.0235556
$967$			4.03128e10i			1.43367i	0.697242	+	0.716836i	$0.254410\pi$
$967$			4.03128e10i			1.43367i	−0.697242	+	0.716836i	$0.745590\pi$
$968$		−	1.92045e10i		−	0.680519i
$969$			1.74219e9i			0.0615125i
$970$			1.97080e10i			0.693334i
$971$	3.76794e10			1.32080			0.660400	−	0.750914i	$-0.270387\pi$
$971$	3.76794e10			1.32080			0.660400	+	0.750914i	$0.270387\pi$
$972$	−6.42515e9			−0.224415
$973$			1.12747e10i			0.392382i
$974$	1.24736e10			0.432550
$975$	3.83186e9	−	7.29684e9i	0.132402	−	0.252126i
$976$	1.58411e10			0.545396
$977$		−	3.21536e10i		−	1.10306i	−0.834155	−	0.551529i	$-0.814044\pi$
$977$		−	3.21536e10i		−	1.10306i	0.834155	−	0.551529i	$-0.185956\pi$
$978$	1.32409e9			0.0452618
$979$	7.39071e9			0.251737
$980$			3.11699e9i			0.105790i
$981$			4.80094e10i			1.62362i
$982$			5.57905e9i			0.188005i
$983$			2.28786e10i			0.768231i	0.923285	+	0.384116i	$0.125494\pi$
$983$			2.28786e10i			0.768231i	−0.923285	+	0.384116i	$0.874506\pi$
$984$	2.46526e9			0.0824860
$985$	−6.61627e10			−2.20590
$986$			2.19136e9i			0.0728021i
$987$	−3.46547e9			−0.114724
$988$	−5.82676e9	−	3.05986e9i	−0.192211	−	0.100938i
$989$	8.95391e9			0.294324
$990$			2.16269e10i			0.708388i
$991$	2.63256e10			0.859253			0.429626	−	0.903007i	$-0.358645\pi$
$991$	2.63256e10			0.859253			0.429626	+	0.903007i	$0.358645\pi$
$992$	3.06432e10			0.996650
$993$			2.62829e9i			0.0851827i
$994$		−	6.89328e9i		−	0.222625i
$995$		−	1.00297e11i		−	3.22779i
$996$		−	1.81713e9i		−	0.0582744i
$997$	−2.46804e10			−0.788712			−0.394356	−	0.918958i	$-0.629032\pi$
$997$	−2.46804e10			−0.788712			−0.394356	+	0.918958i	$0.629032\pi$
$998$	1.71916e10			0.547469
$999$			2.21522e9i			0.0702972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.c.a.64.18	✓	50
13.12	even	2	inner	91.8.c.a.64.33	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.c.a.64.18	✓	50	1.1	even	1	trivial
91.8.c.a.64.33	yes	50	13.12	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.36017i q^{2} -8.01801 q^{3} +58.1075 q^{4} -455.948i q^{5} +67.0319i q^{6} -343.000i q^{7} -1555.89i q^{8} -2122.71 q^{9} +O(q^{10})\)	\(q-8.36017i q^{2} -8.01801 q^{3} +58.1075 q^{4} -455.948i q^{5} +67.0319i q^{6} -343.000i q^{7} -1555.89i q^{8} -2122.71 q^{9} -3811.80 q^{10} +2672.84i q^{11} -465.906 q^{12} +(3682.90 - 7013.18i) q^{13} -2867.54 q^{14} +3655.79i q^{15} -5569.76 q^{16} +15196.7 q^{17} +17746.2i q^{18} -14298.1i q^{19} -26494.0i q^{20} +2750.18i q^{21} +22345.4 q^{22} -28703.8 q^{23} +12475.1i q^{24} -129764. q^{25} +(-58631.4 - 30789.7i) q^{26} +34555.3 q^{27} -19930.9i q^{28} -17248.3 q^{29} +30563.1 q^{30} +200820. i q^{31} -152590. i q^{32} -21430.8i q^{33} -127047. i q^{34} -156390. q^{35} -123345. q^{36} +64106.6i q^{37} -119535. q^{38} +(-29529.5 + 56231.8i) q^{39} -709405. q^{40} -197614. i q^{41} +22991.9 q^{42} -311942. q^{43} +155312. i q^{44} +967846. i q^{45} +239969. i q^{46} +1.26009e6i q^{47} +44658.4 q^{48} -117649. q^{49} +1.08485e6i q^{50} -121848. q^{51} +(214004. - 407519. i) q^{52} +370143. q^{53} -288888. i q^{54} +1.21868e6 q^{55} -533671. q^{56} +114643. i q^{57} +144199. i q^{58} -249875. i q^{59} +212429. i q^{60} -2.84414e6 q^{61} +1.67889e6 q^{62} +728090. i q^{63} -1.98861e6 q^{64} +(-3.19765e6 - 1.67921e6i) q^{65} -179165. q^{66} -4.08931e6i q^{67} +883045. q^{68} +230147. q^{69} +1.30745e6i q^{70} +2.40390e6i q^{71} +3.30271e6i q^{72} -5.39520e6i q^{73} +535942. q^{74} +1.04045e6 q^{75} -830829. i q^{76} +916783. q^{77} +(470107. + 246872. i) q^{78} -3.85634e6 q^{79} +2.53952e6i q^{80} +4.36531e6 q^{81} -1.65209e6 q^{82} +3.90020e6i q^{83} +159806. i q^{84} -6.92893e6i q^{85} +2.60789e6i q^{86} +138297. q^{87} +4.15864e6 q^{88} -2.76512e6i q^{89} +8.09136e6 q^{90} +(-2.40552e6 - 1.26324e6i) q^{91} -1.66790e6 q^{92} -1.61018e6i q^{93} +1.05346e7 q^{94} -6.51921e6 q^{95} +1.22347e6i q^{96} -5.17027e6i q^{97} +983566. i q^{98} -5.67366e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) \) 50 * q - 3328 * q^4 + 40514 * q^9	\( 50 q - 3328 q^{4} + 40514 q^{9} + 5320 q^{10} + 8700 q^{12} + 17044 q^{13} + 10976 q^{14} + 228808 q^{16} + 33664 q^{17} + 70228 q^{22} - 75042 q^{23} - 664772 q^{25} + 78276 q^{26} - 661404 q^{27} + 135778 q^{29} + 994888 q^{30} + 372498 q^{35} - 3549604 q^{36} + 338468 q^{38} - 973080 q^{39} + 79316 q^{40} + 296352 q^{42} - 53618 q^{43} + 1400384 q^{48} - 5882450 q^{49} - 2182360 q^{51} - 6982340 q^{52} + 2841746 q^{53} + 6871356 q^{55} - 2107392 q^{56} + 1773716 q^{61} - 6969608 q^{62} - 9449120 q^{64} - 7901430 q^{65} - 11755548 q^{66} + 11829980 q^{68} + 3564460 q^{69} + 45595884 q^{74} - 7220964 q^{75} + 186592 q^{77} - 8093012 q^{78} - 21257822 q^{79} + 53034530 q^{81} + 10907568 q^{82} + 14135000 q^{87} - 51594780 q^{88} - 61226356 q^{90} - 8096858 q^{91} - 11200212 q^{92} + 80667028 q^{94} + 30430066 q^{95}+O(q^{100}) \) 50 * q - 3328 * q^4 + 40514 * q^9 + 5320 * q^10 + 8700 * q^12 + 17044 * q^13 + 10976 * q^14 + 228808 * q^16 + 33664 * q^17 + 70228 * q^22 - 75042 * q^23 - 664772 * q^25 + 78276 * q^26 - 661404 * q^27 + 135778 * q^29 + 994888 * q^30 + 372498 * q^35 - 3549604 * q^36 + 338468 * q^38 - 973080 * q^39 + 79316 * q^40 + 296352 * q^42 - 53618 * q^43 + 1400384 * q^48 - 5882450 * q^49 - 2182360 * q^51 - 6982340 * q^52 + 2841746 * q^53 + 6871356 * q^55 - 2107392 * q^56 + 1773716 * q^61 - 6969608 * q^62 - 9449120 * q^64 - 7901430 * q^65 - 11755548 * q^66 + 11829980 * q^68 + 3564460 * q^69 + 45595884 * q^74 - 7220964 * q^75 + 186592 * q^77 - 8093012 * q^78 - 21257822 * q^79 + 53034530 * q^81 + 10907568 * q^82 + 14135000 * q^87 - 51594780 * q^88 - 61226356 * q^90 - 8096858 * q^91 - 11200212 * q^92 + 80667028 * q^94 + 30430066 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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