LMFDB - Embedded newform 91.8.c.a.64.10

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			64.10
Character	$\chi$	$=$	91.64
Dual form			91.8.c.a.64.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.4646i q^{2} -2.30214 q^{3} -111.152 q^{4} +85.0277i q^{5} +35.6015i q^{6} +343.000i q^{7} -260.539i q^{8} -2181.70 q^{9} +O(q^{10})$	\(q-15.4646i q^{2} -2.30214 q^{3} -111.152 q^{4} +85.0277i q^{5} +35.6015i q^{6} +343.000i q^{7} -260.539i q^{8} -2181.70 q^{9} +1314.92 q^{10} +5966.96i q^{11} +255.888 q^{12} +(6658.47 - 4291.07i) q^{13} +5304.34 q^{14} -195.745i q^{15} -18256.6 q^{16} +18892.7 q^{17} +33739.0i q^{18} +16025.8i q^{19} -9451.04i q^{20} -789.633i q^{21} +92276.4 q^{22} +77812.5 q^{23} +599.797i q^{24} +70895.3 q^{25} +(-66359.5 - 102970. i) q^{26} +10057.3 q^{27} -38125.3i q^{28} +99977.8 q^{29} -3027.11 q^{30} -106857. i q^{31} +248982. i q^{32} -13736.8i q^{33} -292167. i q^{34} -29164.5 q^{35} +242501. q^{36} +113839. i q^{37} +247832. q^{38} +(-15328.7 + 9878.63i) q^{39} +22153.1 q^{40} +60438.2i q^{41} -12211.3 q^{42} -647559. q^{43} -663243. i q^{44} -185505. i q^{45} -1.20334e6i q^{46} +151997. i q^{47} +42029.3 q^{48} -117649. q^{49} -1.09636e6i q^{50} -43493.5 q^{51} +(-740106. + 476963. i) q^{52} +881391. q^{53} -155532. i q^{54} -507357. q^{55} +89365.0 q^{56} -36893.6i q^{57} -1.54611e6i q^{58} -2.30742e6i q^{59} +21757.6i q^{60} +2.92390e6 q^{61} -1.65249e6 q^{62} -748323. i q^{63} +1.51354e6 q^{64} +(364860. + 566154. i) q^{65} -212433. q^{66} +2.10213e6i q^{67} -2.09997e6 q^{68} -179135. q^{69} +451016. i q^{70} -2.09712e6i q^{71} +568419. i q^{72} +2.45591e6i q^{73} +1.76047e6 q^{74} -163211. q^{75} -1.78131e6i q^{76} -2.04667e6 q^{77} +(152769. + 237052. i) q^{78} +4.18892e6 q^{79} -1.55232e6i q^{80} +4.74822e6 q^{81} +934649. q^{82} +9.52469e6i q^{83} +87769.6i q^{84} +1.60640e6i q^{85} +1.00142e7i q^{86} -230163. q^{87} +1.55463e6 q^{88} +9.73207e6i q^{89} -2.86875e6 q^{90} +(1.47184e6 + 2.28386e6i) q^{91} -8.64905e6 q^{92} +245999. i q^{93} +2.35056e6 q^{94} -1.36264e6 q^{95} -573190. i q^{96} -3.39327e6i q^{97} +1.81939e6i q^{98} -1.30181e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	15.4646i		−	1.36689i	−0.730004	−	0.683443i	$-0.760482\pi$
$2$		−	15.4646i		−	1.36689i	0.730004	−	0.683443i	$-0.239518\pi$
$3$	−2.30214			−0.0492274			−0.0246137	−	0.999697i	$-0.507836\pi$
$3$	−2.30214			−0.0492274			−0.0246137	+	0.999697i	$0.507836\pi$
$4$	−111.152			−0.868379
$5$			85.0277i			0.304204i	0.988365	+	0.152102i	$0.0486043\pi$
$5$			85.0277i			0.304204i	−0.988365	+	0.152102i	$0.951396\pi$
$6$			35.6015i			0.0672882i
$7$			343.000i			0.377964i
$7$			343.000i			0.377964i
$8$		−	260.539i		−	0.179911i
$9$	−2181.70			−0.997577
$10$	1314.92			0.415813
$11$			5966.96i			1.35170i	0.737041	+	0.675848i	$0.236222\pi$
$11$			5966.96i			1.35170i	−0.737041	+	0.675848i	$0.763778\pi$
$12$	255.888			0.0427480
$13$	6658.47	−	4291.07i	0.840568	−	0.541706i
$13$	6658.47	−	4291.07i	0.840568	−	0.541706i
$14$	5304.34			0.516635
$15$		−	195.745i		−	0.0149752i
$16$	−18256.6			−1.11430
$17$	18892.7			0.932658			0.466329	−	0.884611i	$-0.345576\pi$
$17$	18892.7			0.932658			0.466329	+	0.884611i	$0.345576\pi$
$18$			33739.0i			1.36357i
$19$			16025.8i			0.536022i	0.963416	+	0.268011i	$0.0863663\pi$
$19$			16025.8i			0.536022i	−0.963416	+	0.268011i	$0.913634\pi$
$20$		−	9451.04i		−	0.264165i
$21$		−	789.633i		−	0.0186062i
$22$	92276.4			1.84761
$23$	77812.5			1.33353			0.666764	−	0.745269i	$-0.267679\pi$
$23$	77812.5			1.33353			0.666764	+	0.745269i	$0.267679\pi$
$24$			599.797i			0.00885656i
$25$	70895.3			0.907460
$26$	−66359.5	−	102970.i	−0.740451	−	1.14896i
$27$	10057.3			0.0983354
$28$		−	38125.3i		−	0.328216i
$29$	99977.8			0.761221			0.380610	−	0.924735i	$-0.375714\pi$
$29$	99977.8			0.761221			0.380610	+	0.924735i	$0.375714\pi$
$30$	−3027.11			−0.0204694
$31$		−	106857.i		−	0.644224i	−0.946702	−	0.322112i	$-0.895607\pi$
$31$		−	106857.i		−	0.644224i	0.946702	−	0.322112i	$-0.104393\pi$
$32$			248982.i			1.34321i
$33$		−	13736.8i		−	0.0665404i
$34$		−	292167.i		−	1.27484i
$35$	−29164.5			−0.114978
$36$	242501.			0.866274
$37$			113839.i			0.369475i	0.982788	+	0.184737i	$0.0591435\pi$
$37$			113839.i			0.369475i	−0.982788	+	0.184737i	$0.940857\pi$
$38$	247832.			0.732681
$39$	−15328.7	+	9878.63i	−0.0413789	+	0.0266668i
$40$	22153.1			0.0547298
$41$			60438.2i			0.136952i	0.997653	+	0.0684759i	$0.0218136\pi$
$41$			60438.2i			0.136952i	−0.997653	+	0.0684759i	$0.978186\pi$
$42$	−12211.3			−0.0254326
$43$	−647559.			−1.24205			−0.621026	−	0.783790i	$-0.713284\pi$
$43$	−647559.			−1.24205			−0.621026	+	0.783790i	$0.713284\pi$
$44$		−	663243.i		−	1.17378i
$45$		−	185505.i		−	0.303467i
$46$		−	1.20334e6i		−	1.82278i
$47$			151997.i			0.213546i	0.994283	+	0.106773i	$0.0340518\pi$
$47$			151997.i			0.213546i	−0.994283	+	0.106773i	$0.965948\pi$
$48$	42029.3			0.0548539
$49$	−117649.			−0.142857
$50$		−	1.09636e6i		−	1.24039i
$51$	−43493.5			−0.0459123
$52$	−740106.	+	476963.i	−0.729931	+	0.470406i
$53$	881391.			0.813210			0.406605	−	0.913604i	$-0.366712\pi$
$53$	881391.			0.813210			0.406605	+	0.913604i	$0.366712\pi$
$54$		−	155532.i		−	0.134413i
$55$	−507357.			−0.411192
$56$	89365.0			0.0680001
$57$		−	36893.6i		−	0.0263869i
$58$		−	1.54611e6i		−	1.04050i
$59$		−	2.30742e6i		−	1.46267i	−0.682020	−	0.731333i	$-0.738898\pi$
$59$		−	2.30742e6i		−	1.46267i	0.682020	−	0.731333i	$-0.261102\pi$
$60$			21757.6i			0.0130041i
$61$	2.92390e6			1.64933			0.824665	−	0.565621i	$-0.191364\pi$
$61$	2.92390e6			1.64933			0.824665	+	0.565621i	$0.191364\pi$
$62$	−1.65249e6			−0.880580
$63$		−	748323.i		−	0.377049i
$64$	1.51354e6			0.721714
$65$	364860.	+	566154.i	0.164789	+	0.255704i
$66$	−212433.			−0.0909532
$67$			2.10213e6i			0.853883i	0.904279	+	0.426941i	$0.140409\pi$
$67$			2.10213e6i			0.853883i	−0.904279	+	0.426941i	$0.859591\pi$
$68$	−2.09997e6			−0.809900
$69$	−179135.			−0.0656460
$70$			451016.i			0.157162i
$71$		−	2.09712e6i		−	0.695375i	−0.937611	−	0.347687i	$-0.886967\pi$
$71$		−	2.09712e6i		−	0.695375i	0.937611	−	0.347687i	$-0.113033\pi$
$72$			568419.i			0.179475i
$73$			2.45591e6i			0.738895i	0.929252	+	0.369447i	$0.120453\pi$
$73$			2.45591e6i			0.738895i	−0.929252	+	0.369447i	$0.879547\pi$
$74$	1.76047e6			0.505030
$75$	−163211.			−0.0446719
$76$		−	1.78131e6i		−	0.465470i
$77$	−2.04667e6			−0.510893
$78$	152769.	+	237052.i	0.0364505	+	0.0565603i
$79$	4.18892e6			0.955888			0.477944	−	0.878390i	$-0.341382\pi$
$79$	4.18892e6			0.955888			0.477944	+	0.878390i	$0.341382\pi$
$80$		−	1.55232e6i		−	0.338974i
$81$	4.74822e6			0.992736
$82$	934649.			0.187198
$83$			9.52469e6i			1.82843i	0.405232	+	0.914214i	$0.367191\pi$
$83$			9.52469e6i			1.82843i	−0.405232	+	0.914214i	$0.632809\pi$
$84$			87769.6i			0.0161572i
$85$			1.60640e6i			0.283719i
$86$			1.00142e7i			1.69774i
$87$	−230163.			−0.0374729
$88$	1.55463e6			0.243185
$89$			9.73207e6i			1.46332i	0.681668	+	0.731662i	$0.261255\pi$
$89$			9.73207e6i			1.46332i	−0.681668	+	0.731662i	$0.738745\pi$
$90$	−2.86875e6			−0.414805
$91$	1.47184e6	+	2.28386e6i	0.204746	+	0.317705i
$92$	−8.64905e6			−1.15801
$93$			245999.i			0.0317134i
$94$	2.35056e6			0.291893
$95$	−1.36264e6			−0.163060
$96$		−	573190.i		−	0.0661225i
$97$		−	3.39327e6i		−	0.377501i	−0.982025	−	0.188750i	$-0.939556\pi$
$97$		−	3.39327e6i		−	0.377501i	0.982025	−	0.188750i	$-0.0604437\pi$
$98$			1.81939e6i			0.195270i
$99$		−	1.30181e7i		−	1.34842i
$100$	−7.88019e6			−0.788019
$101$	−1.85255e6			−0.178915			−0.0894574	−	0.995991i	$-0.528513\pi$
$101$	−1.85255e6			−0.178915			−0.0894574	+	0.995991i	$0.528513\pi$
$102$			672608.i			0.0627569i
$103$	6.88997e6			0.621280			0.310640	−	0.950528i	$-0.399457\pi$
$103$	6.88997e6			0.621280			0.310640	+	0.950528i	$0.399457\pi$
$104$	−1.11799e6	−	1.73479e6i	−0.0974591	−	0.151228i
$105$	67140.6			0.00566008
$106$		−	1.36303e7i		−	1.11157i
$107$	−4.70694e6			−0.371446			−0.185723	−	0.982602i	$-0.559463\pi$
$107$	−4.70694e6			−0.371446			−0.185723	+	0.982602i	$0.559463\pi$
$108$	−1.11790e6			−0.0853924
$109$			2.16754e7i			1.60315i	0.597895	+	0.801574i	$0.296004\pi$
$109$			2.16754e7i			1.60315i	−0.597895	+	0.801574i	$0.703996\pi$
$110$			7.84605e6i			0.562052i
$111$		−	262073.i		−	0.0181883i
$112$		−	6.26203e6i		−	0.421165i
$113$	5.03574e6			0.328314			0.164157	−	0.986434i	$-0.447510\pi$
$113$	5.03574e6			0.328314			0.164157	+	0.986434i	$0.447510\pi$
$114$	−570543.			−0.0360679
$115$			6.61622e6i			0.405665i
$116$	−1.11128e7			−0.661028
$117$	−1.45268e7	+	9.36183e6i	−0.838531	+	0.540394i
$118$	−3.56833e7			−1.99930
$119$			6.48019e6i			0.352512i
$120$	−50999.4			−0.00269420
$121$	−1.61175e7			−0.827081
$122$		−	4.52168e7i		−	2.25445i
$123$		−	139137.i		−	0.00674178i
$124$			1.18774e7i			0.559430i
$125$			1.26708e7i			0.580257i
$126$	−1.15725e7			−0.515383
$127$	3.32450e7			1.44017			0.720084	−	0.693887i	$-0.244103\pi$
$127$	3.32450e7			1.44017			0.720084	+	0.693887i	$0.244103\pi$
$128$			8.46341e6i			0.356706i
$129$	1.49077e6			0.0611429
$130$	8.75532e6	−	5.64239e6i	0.349519	−	0.225248i
$131$	−4.34316e7			−1.68794			−0.843968	−	0.536394i	$-0.819786\pi$
$131$	−4.34316e7			−1.68794			−0.843968	+	0.536394i	$0.819786\pi$
$132$			1.52687e6i			0.0577823i
$133$	−5.49685e6			−0.202597
$134$	3.25086e7			1.16716
$135$			855152.i			0.0299141i
$136$		−	4.92229e6i		−	0.167796i
$137$		−	2.83956e7i		−	0.943471i	−0.881740	−	0.471735i	$-0.843628\pi$
$137$		−	2.83956e7i		−	0.943471i	0.881740	−	0.471735i	$-0.156372\pi$
$138$			2.77024e6i			0.0897307i
$139$	1.71362e7			0.541207			0.270604	−	0.962691i	$-0.412777\pi$
$139$	1.71362e7			0.541207			0.270604	+	0.962691i	$0.412777\pi$
$140$	3.24171e6			0.0998448
$141$		−	349917.i		−	0.0105123i
$142$	−3.24310e7			−0.950498
$143$	2.56047e7	+	3.97308e7i	0.732222	+	1.13619i
$144$	3.98305e7			1.11160
$145$			8.50088e6i			0.231567i
$146$	3.79796e7			1.00999
$147$	270844.			0.00703248
$148$		−	1.26535e7i		−	0.320844i
$149$		−	4.01768e7i		−	0.995000i	−0.867464	−	0.497500i	$-0.834251\pi$
$149$		−	4.01768e7i		−	0.995000i	0.867464	−	0.497500i	$-0.165749\pi$
$150$			2.52398e6i			0.0610614i
$151$		−	3.51416e7i		−	0.830620i	−0.909680	−	0.415310i	$-0.863673\pi$
$151$		−	3.51416e7i		−	0.830620i	0.909680	−	0.415310i	$-0.136327\pi$
$152$	4.17535e6			0.0964364
$153$	−4.12182e7			−0.930398
$154$			3.16508e7i			0.698333i
$155$	9.08579e6			0.195976
$156$	1.70382e6	−	1.09803e6i	0.0359326	−	0.0231569i
$157$	6.58352e7			1.35772			0.678858	−	0.734269i	$-0.262475\pi$
$157$	6.58352e7			1.35772			0.678858	+	0.734269i	$0.262475\pi$
$158$		−	6.47798e7i		−	1.30659i
$159$	−2.02908e6			−0.0400322
$160$	−2.11703e7			−0.408609
$161$			2.66897e7i			0.504026i
$162$		−	7.34292e7i		−	1.35696i
$163$			4.75660e7i			0.860279i	0.902762	+	0.430140i	$0.141536\pi$
$163$			4.75660e7i			0.860279i	−0.902762	+	0.430140i	$0.858464\pi$
$164$		−	6.71785e6i		−	0.118926i
$165$	1.16800e6			0.0202419
$166$	1.47295e8			2.49925
$167$			7.94907e7i			1.32071i	0.750952	+	0.660357i	$0.229595\pi$
$167$			7.94907e7i			1.32071i	−0.750952	+	0.660357i	$0.770405\pi$
$168$	−205730.			−0.00334747
$169$	2.59219e7	−	5.71439e7i	0.413109	−	0.910682i
$170$	2.48423e7			0.387811
$171$		−	3.49635e7i		−	0.534723i
$172$	7.19778e7			1.07857
$173$	−9.23250e7			−1.35568			−0.677841	−	0.735208i	$-0.737084\pi$
$173$	−9.23250e7			−1.35568			−0.677841	+	0.735208i	$0.737084\pi$
$174$			3.55936e6i			0.0512212i
$175$			2.43171e7i			0.342988i
$176$		−	1.08937e8i		−	1.50619i
$177$			5.31200e6i			0.0720032i
$178$	1.50502e8			2.00020
$179$	−1.03755e8			−1.35215			−0.676074	−	0.736834i	$-0.736320\pi$
$179$	−1.03755e8			−1.35215			−0.676074	+	0.736834i	$0.736320\pi$
$180$			2.06193e7i			0.263524i
$181$	1.01023e7			0.126632			0.0633161	−	0.997994i	$-0.479832\pi$
$181$	1.01023e7			0.126632			0.0633161	+	0.997994i	$0.479832\pi$
$182$	3.53188e7	−	2.27613e7i	0.434266	−	0.279864i
$183$	−6.73121e6			−0.0811922
$184$		−	2.02732e7i		−	0.239917i
$185$	−9.67946e6			−0.112396
$186$	3.80427e6			0.0433487
$187$			1.12732e8i			1.26067i
$188$		−	1.68948e7i		−	0.185439i
$189$			3.44967e6i			0.0371673i
$190$			2.10726e7i			0.222885i
$191$	−1.33288e7			−0.138412			−0.0692061	−	0.997602i	$-0.522047\pi$
$191$	−1.33288e7			−0.138412			−0.0692061	+	0.997602i	$0.522047\pi$
$192$	−3.48438e6			−0.0355281
$193$			5.04799e7i			0.505438i	0.967540	+	0.252719i	$0.0813248\pi$
$193$			5.04799e7i			0.505438i	−0.967540	+	0.252719i	$0.918675\pi$
$194$	−5.24755e7			−0.516001
$195$	−839957.	−	1.30336e6i	−0.00811215	−	0.0125876i
$196$	1.30770e7			0.124054
$197$		−	1.32179e8i		−	1.23177i	−0.787835	−	0.615887i	$-0.788798\pi$
$197$		−	1.32179e8i		−	1.23177i	0.787835	−	0.615887i	$-0.211202\pi$
$198$	−2.01319e8			−1.84314
$199$	−6.85130e7			−0.616293			−0.308146	−	0.951339i	$-0.599709\pi$
$199$	−6.85130e7			−0.616293			−0.308146	+	0.951339i	$0.599709\pi$
$200$		−	1.84710e7i		−	0.163262i
$201$		−	4.83940e6i		−	0.0420344i
$202$			2.86489e7i			0.244556i
$203$			3.42924e7i			0.287714i
$204$	4.83441e6			0.0398693
$205$	−5.13892e6			−0.0416613
$206$		−	1.06550e8i		−	0.849219i
$207$	−1.69764e8			−1.33030
$208$	−1.21561e8	+	7.83405e7i	−0.936642	+	0.603622i
$209$	−9.56254e7			−0.724538
$210$		−	1.03830e6i		−	0.00773669i
$211$	−1.69003e7			−0.123853			−0.0619265	−	0.998081i	$-0.519724\pi$
$211$	−1.69003e7			−0.123853			−0.0619265	+	0.998081i	$0.519724\pi$
$212$	−9.79688e7			−0.706175
$213$			4.82785e6i			0.0342315i
$214$			7.27907e7i			0.507724i
$215$		−	5.50604e7i		−	0.377837i
$216$		−	2.62033e6i		−	0.0176917i
$217$	3.66519e7			0.243494
$218$	3.35200e8			2.19132
$219$		−	5.65384e6i		−	0.0363738i
$220$	5.63940e7			0.357070
$221$	1.25796e8	−	8.10698e7i	0.783962	−	0.505227i
$222$	−4.05284e6			−0.0248613
$223$			8.53148e7i			0.515178i	0.966255	+	0.257589i	$0.0829281\pi$
$223$			8.53148e7i			0.515178i	−0.966255	+	0.257589i	$0.917072\pi$
$224$	−8.54008e7			−0.507684
$225$	−1.54672e8			−0.905261
$226$		−	7.78755e7i		−	0.448768i
$227$		−	2.73948e8i		−	1.55445i	−0.629222	−	0.777225i	$-0.716627\pi$
$227$		−	2.73948e8i		−	1.55445i	0.629222	−	0.777225i	$-0.283373\pi$
$228$			4.10081e6i			0.0229138i
$229$			9.34384e7i			0.514163i	0.966390	+	0.257082i	$0.0827609\pi$
$229$			9.34384e7i			0.514163i	−0.966390	+	0.257082i	$0.917239\pi$
$230$	1.02317e8			0.554498
$231$	4.71171e6			0.0251499
$232$		−	2.60482e7i		−	0.136952i
$233$	−3.64876e8			−1.88973			−0.944865	−	0.327461i	$-0.893807\pi$
$233$	−3.64876e8			−1.88973			−0.944865	+	0.327461i	$0.893807\pi$
$234$	1.44777e8	+	2.24650e8i	0.738657	+	1.14618i
$235$	−1.29239e7			−0.0649617
$236$			2.56476e8i			1.27015i
$237$	−9.64346e6			−0.0470559
$238$	1.00213e8			0.481843
$239$		−	7.25061e7i		−	0.343543i	−0.985137	−	0.171772i	$-0.945051\pi$
$239$		−	7.25061e7i		−	0.343543i	0.985137	−	0.171772i	$-0.0549491\pi$
$240$			3.57365e6i			0.0166868i
$241$			2.16691e8i			0.997199i	0.866833	+	0.498599i	$0.166152\pi$
$241$			2.16691e8i			0.997199i	−0.866833	+	0.498599i	$0.833848\pi$
$242$			2.49249e8i			1.13053i
$243$	−3.29265e7			−0.147205
$244$	−3.24998e8			−1.43224
$245$		−	1.00034e7i		−	0.0434578i
$246$	−2.15169e6			−0.00921524
$247$	6.87679e7	+	1.06707e8i	0.290366	+	0.450562i
$248$	−2.78404e7			−0.115903
$249$		−	2.19271e7i		−	0.0900087i
$250$	1.95949e8			0.793146
$251$	−4.15820e8			−1.65977			−0.829884	−	0.557935i	$-0.811594\pi$
$251$	−4.15820e8			−1.65977			−0.829884	+	0.557935i	$0.811594\pi$
$252$			8.31780e7i			0.327421i
$253$			4.64304e8i			1.80252i
$254$		−	5.14119e8i		−	1.96855i
$255$		−	3.69815e6i		−	0.0139667i
$256$	3.24616e8			1.20929
$257$	4.58949e8			1.68655			0.843274	−	0.537483i	$-0.180625\pi$
$257$	4.58949e8			1.68655			0.843274	+	0.537483i	$0.180625\pi$
$258$		−	2.30541e7i		−	0.0835755i
$259$	−3.90468e7			−0.139648
$260$	−4.05551e7	−	6.29295e7i	−0.143100	−	0.222048i
$261$	−2.18122e8			−0.759376
$262$			6.71650e8i			2.30722i
$263$	5.29560e8			1.79502			0.897512	−	0.440990i	$-0.145373\pi$
$263$	5.29560e8			1.79502			0.897512	+	0.440990i	$0.145373\pi$
$264$	−3.57897e6			−0.0119714
$265$			7.49426e7i			0.247382i
$266$			8.50064e7i			0.276927i
$267$		−	2.24046e7i		−	0.0720355i
$268$		−	2.33657e8i		−	0.741494i
$269$	3.00658e8			0.941760			0.470880	−	0.882197i	$-0.343936\pi$
$269$	3.00658e8			0.941760			0.470880	+	0.882197i	$0.343936\pi$
$270$	1.32246e7			0.0408891
$271$			7.06296e7i			0.215573i	0.994174	+	0.107786i	$0.0343763\pi$
$271$			7.06296e7i			0.215573i	−0.994174	+	0.107786i	$0.965624\pi$
$272$	−3.44917e8			−1.03926
$273$	−3.38837e6	−	5.25775e6i	−0.0100791	−	0.0156398i
$274$	−4.39125e8			−1.28962
$275$			4.23030e8i			1.22661i
$276$	1.99113e7			0.0570056
$277$	1.75140e8			0.495116			0.247558	−	0.968873i	$-0.420372\pi$
$277$	1.75140e8			0.495116			0.247558	+	0.968873i	$0.420372\pi$
$278$		−	2.65004e8i		−	0.739769i
$279$			2.33130e8i			0.642662i
$280$			7.59850e6i			0.0206859i
$281$			1.60535e8i			0.431617i	0.976436	+	0.215808i	$0.0692386\pi$
$281$			1.60535e8i			0.431617i	−0.976436	+	0.215808i	$0.930761\pi$
$282$	−5.41132e6			−0.0143691
$283$	−1.29728e8			−0.340237			−0.170118	−	0.985424i	$-0.554415\pi$
$283$	−1.29728e8			−0.340237			−0.170118	+	0.985424i	$0.554415\pi$
$284$			2.33100e8i			0.603849i
$285$	3.13698e6			0.00802702
$286$	6.14420e8	−	3.95965e8i	1.55305	−	1.00086i
$287$	−2.07303e7			−0.0517629
$288$		−	5.43204e8i		−	1.33995i
$289$	−5.34051e7			−0.130149
$290$	1.31462e8			0.316525
$291$			7.81178e6i			0.0185834i
$292$		−	2.72981e8i		−	0.641640i
$293$		−	3.81629e8i		−	0.886349i	−0.896435	−	0.443174i	$-0.853852\pi$
$293$		−	3.81629e8i		−	0.886349i	0.896435	−	0.443174i	$-0.146148\pi$
$294$		−	4.18848e6i		−	0.00961260i
$295$	1.96195e8			0.444949
$296$	2.96595e7			0.0664727
$297$			6.00118e7i			0.132920i
$298$	−6.21316e8			−1.36005
$299$	5.18112e8	−	3.33899e8i	1.12092	−	0.722380i
$300$	1.81413e7			0.0387921
$301$		−	2.22113e8i		−	0.469451i
$302$	−5.43450e8			−1.13536
$303$	4.26483e6			0.00880750
$304$		−	2.92577e8i		−	0.597287i
$305$			2.48612e8i			0.501733i
$306$			6.37421e8i			1.27175i
$307$		−	4.52612e8i		−	0.892775i	−0.894840	−	0.446388i	$-0.852710\pi$
$307$		−	4.52612e8i		−	0.892775i	0.894840	−	0.446388i	$-0.147290\pi$
$308$	2.27492e8			0.443649
$309$	−1.58617e7			−0.0305840
$310$		−	1.40508e8i		−	0.267876i
$311$	−2.78783e8			−0.525539			−0.262770	−	0.964859i	$-0.584636\pi$
$311$	−2.78783e8			−0.525539			−0.262770	+	0.964859i	$0.584636\pi$
$312$	2.57377e6	+	3.99373e6i	0.00479766	+	0.00744454i
$313$	−5.64579e7			−0.104068			−0.0520342	−	0.998645i	$-0.516570\pi$
$313$	−5.64579e7			−0.104068			−0.0520342	+	0.998645i	$0.516570\pi$
$314$		−	1.01811e9i		−	1.85584i
$315$	6.36282e7			0.114700
$316$	−4.65609e8			−0.830073
$317$		−	1.01759e9i		−	1.79417i	−0.441856	−	0.897086i	$-0.645680\pi$
$317$		−	1.01759e9i		−	1.79417i	0.441856	−	0.897086i	$-0.354320\pi$
$318$			3.13788e7i			0.0547195i
$319$			5.96564e8i			1.02894i
$320$			1.28693e8i			0.219548i
$321$	1.08360e7			0.0182853
$322$	4.12744e8			0.688946
$323$			3.02770e8i			0.499925i
$324$	−5.27777e8			−0.862071
$325$	4.72054e8	−	3.04217e8i	0.762781	−	0.491577i
$326$	7.35586e8			1.17590
$327$		−	4.98996e7i		−	0.0789188i
$328$	1.57465e7			0.0246392
$329$	−5.21349e7			−0.0807129
$330$		−	1.80627e7i		−	0.0276683i
$331$		−	9.08428e8i		−	1.37687i	−0.725298	−	0.688435i	$-0.758298\pi$
$331$		−	9.08428e8i		−	1.37687i	0.725298	−	0.688435i	$-0.241702\pi$
$332$		−	1.05869e9i		−	1.58777i
$333$		−	2.48362e8i		−	0.368579i
$334$	1.22929e9			1.80527
$335$	−1.78739e8			−0.259755
$336$			1.44160e7i			0.0207328i
$337$	−1.14832e9			−1.63439			−0.817197	−	0.576359i	$-0.804473\pi$
$337$	−1.14832e9			−1.63439			−0.817197	+	0.576359i	$0.804473\pi$
$338$	−8.83706e8	−	4.00871e8i	−1.24480	−	0.564673i
$339$	−1.15930e7			−0.0161620
$340$		−	1.78555e8i		−	0.246375i
$341$	6.37611e8			0.870794
$342$	−5.40695e8			−0.730905
$343$		−	4.03536e7i		−	0.0539949i
$344$			1.68715e8i			0.223459i
$345$		−	1.52314e7i		−	0.0199698i
$346$			1.42777e9i			1.85306i
$347$	3.91718e8			0.503292			0.251646	−	0.967819i	$-0.419028\pi$
$347$	3.91718e8			0.503292			0.251646	+	0.967819i	$0.419028\pi$
$348$	2.55831e7			0.0325407
$349$		−	6.30910e7i		−	0.0794471i	−0.999211	−	0.0397236i	$-0.987352\pi$
$349$		−	6.30910e7i		−	0.0794471i	0.999211	−	0.0397236i	$-0.0126477\pi$
$350$	3.76053e8			0.468825
$351$	6.69665e7	−	4.31568e7i	0.0826576	−	0.0532689i
$352$	−1.48567e9			−1.81561
$353$			1.59863e9i			1.93436i	0.254097	+	0.967179i	$0.418222\pi$
$353$			1.59863e9i			1.93436i	−0.254097	+	0.967179i	$0.581778\pi$
$354$	8.21478e7			0.0984202
$355$	1.78313e8			0.211536
$356$		−	1.08174e9i		−	1.27072i
$357$		−	1.49183e7i		−	0.0173532i
$358$			1.60453e9i			1.84823i
$359$		−	2.35789e8i		−	0.268963i	−0.990916	−	0.134482i	$-0.957063\pi$
$359$		−	2.35789e8i		−	0.268963i	0.990916	−	0.134482i	$-0.0429369\pi$
$360$	−4.83313e7			−0.0545972
$361$	6.37045e8			0.712681
$362$		−	1.56227e8i		−	0.173092i
$363$	3.71046e7			0.0407150
$364$	−1.63598e8	−	2.53856e8i	−0.177797	−	0.275888i
$365$	−2.08820e8			−0.224775
$366$			1.04095e8i			0.110981i
$367$	−1.22992e8			−0.129881			−0.0649403	−	0.997889i	$-0.520686\pi$
$367$	−1.22992e8			−0.129881			−0.0649403	+	0.997889i	$0.520686\pi$
$368$	−1.42060e9			−1.48595
$369$		−	1.31858e8i		−	0.136620i
$370$			1.49689e8i			0.153632i
$371$			3.02317e8i			0.307365i
$372$		−	2.73434e7i		−	0.0275393i
$373$	8.50511e8			0.848592			0.424296	−	0.905524i	$-0.360522\pi$
$373$	8.50511e8			0.848592			0.424296	+	0.905524i	$0.360522\pi$
$374$	1.74335e9			1.72319
$375$		−	2.91700e7i		−	0.0285645i
$376$	3.96012e7			0.0384194
$377$	6.65699e8	−	4.29012e8i	0.639858	−	0.412358i
$378$	5.33476e7			0.0508035
$379$			1.02740e9i			0.969395i	0.874682	+	0.484697i	$0.161070\pi$
$379$			1.02740e9i			0.969395i	−0.874682	+	0.484697i	$0.838930\pi$
$380$	1.51460e8			0.141598
$381$	−7.65345e7			−0.0708957
$382$			2.06124e8i			0.189194i
$383$			2.57581e8i			0.234270i	0.993116	+	0.117135i	$0.0373711\pi$
$383$			2.57581e8i			0.234270i	−0.993116	+	0.117135i	$0.962629\pi$
$384$		−	1.94839e7i		−	0.0175597i
$385$		−	1.74023e8i		−	0.155416i
$386$	7.80649e8			0.690876
$387$	1.41278e9			1.23904
$388$			3.77171e8i			0.327814i
$389$	3.51092e8			0.302411			0.151206	−	0.988502i	$-0.451684\pi$
$389$	3.51092e8			0.302411			0.151206	+	0.988502i	$0.451684\pi$
$390$	−2.01559e7	+	1.29896e7i	−0.0172059	+	0.0110884i
$391$	1.47009e9			1.24373
$392$			3.06522e7i			0.0257016i
$393$	9.99853e7			0.0830926
$394$	−2.04409e9			−1.68369
$395$			3.56174e8i			0.290785i
$396$			1.44700e9i			1.17094i
$397$		−	2.29198e9i		−	1.83841i	−0.393776	−	0.919207i	$-0.628831\pi$
$397$		−	2.29198e9i		−	1.83841i	0.393776	−	0.919207i	$-0.371169\pi$
$398$			1.05952e9i			0.842402i
$399$	1.26545e7			0.00997332
$400$	−1.29431e9			−1.01118
$401$		−	1.02804e9i		−	0.796164i	−0.917350	−	0.398082i	$-0.869676\pi$
$401$		−	1.02804e9i		−	0.796164i	0.917350	−	0.398082i	$-0.130324\pi$
$402$	−7.48391e7			−0.0574563
$403$	−4.58530e8	−	7.11503e8i	−0.348980	−	0.541514i
$404$	2.05916e8			0.155366
$405$			4.03731e8i			0.301994i
$406$	5.30317e8			0.393273
$407$	−6.79273e8			−0.499417
$408$			1.13318e7i			0.00826014i
$409$			1.03655e9i			0.749136i	0.927199	+	0.374568i	$0.122209\pi$
$409$			1.03655e9i			0.749136i	−0.927199	+	0.374568i	$0.877791\pi$
$410$			7.94711e7i			0.0569463i
$411$			6.53704e7i			0.0464446i
$412$	−7.65837e8			−0.539506
$413$	7.91446e8			0.552836
$414$			2.62532e9i			1.81836i
$415$	−8.09863e8			−0.556215
$416$	1.06840e9	+	1.65784e9i	0.727623	+	1.12906i
$417$	−3.94499e7			−0.0266422
$418$			1.47880e9i			0.990361i
$419$	−2.12570e9			−1.41174			−0.705868	−	0.708344i	$-0.749443\pi$
$419$	−2.12570e9			−1.41174			−0.705868	+	0.708344i	$0.749443\pi$
$420$	−7.46285e6			−0.00491510
$421$		−	1.83604e8i		−	0.119921i	−0.998201	−	0.0599604i	$-0.980903\pi$
$421$		−	1.83604e8i		−	0.119921i	0.998201	−	0.0599604i	$-0.0190974\pi$
$422$			2.61356e8i			0.169293i
$423$		−	3.31611e8i		−	0.213029i
$424$		−	2.29637e8i		−	0.146306i
$425$	1.33940e9			0.846350
$426$	7.46606e7			0.0467905
$427$			1.00290e9i			0.623388i
$428$	5.23188e8			0.322556
$429$	−5.89454e7	−	9.14658e7i	−0.0360454	−	0.0559317i
$430$	−8.51485e8			−0.516461
$431$		−	3.79393e7i		−	0.0228254i	−0.999935	−	0.0114127i	$-0.996367\pi$
$431$		−	3.79393e7i		−	0.0228254i	0.999935	−	0.0114127i	$-0.00363286\pi$
$432$	−1.83613e8			−0.109575
$433$	4.79633e8			0.283923			0.141962	−	0.989872i	$-0.454659\pi$
$433$	4.79633e8			0.283923			0.141962	+	0.989872i	$0.454659\pi$
$434$		−	5.66806e8i		−	0.332828i
$435$		−	1.95702e7i		−	0.0113994i
$436$		−	2.40927e9i		−	1.39214i
$437$			1.24701e9i			0.714799i
$438$	−8.74341e7			−0.0497189
$439$	−1.99118e9			−1.12327			−0.561637	−	0.827384i	$-0.689828\pi$
$439$	−1.99118e9			−1.12327			−0.561637	+	0.827384i	$0.689828\pi$
$440$			1.32186e8i			0.0739780i
$441$	2.56675e8			0.142511
$442$	−1.25371e9	−	1.94539e9i	−0.690588	−	1.07159i
$443$	−2.56188e9			−1.40006			−0.700028	−	0.714115i	$-0.746829\pi$
$443$	−2.56188e9			−1.40006			−0.700028	+	0.714115i	$0.746829\pi$
$444$			2.91300e7i			0.0157943i
$445$	−8.27495e8			−0.445149
$446$	1.31936e9			0.704190
$447$			9.24924e7i			0.0489812i
$448$			5.19145e8i			0.272782i
$449$		−	4.26454e8i		−	0.222336i	−0.993802	−	0.111168i	$-0.964541\pi$
$449$		−	4.26454e8i		−	0.222336i	0.993802	−	0.111168i	$-0.0354592\pi$
$450$			2.39194e9i			1.23739i
$451$	−3.60632e8			−0.185117
$452$	−5.59735e8			−0.285101
$453$			8.09008e7i			0.0408892i
$454$	−4.23648e9			−2.12476
$455$	−1.94191e8	+	1.25147e8i	−0.0966471	+	0.0622845i
$456$	−9.61223e6			−0.00474731
$457$		−	2.70225e9i		−	1.32440i	−0.749327	−	0.662200i	$-0.769623\pi$
$457$		−	2.70225e9i		−	1.32440i	0.749327	−	0.662200i	$-0.230377\pi$
$458$	1.44498e9			0.702803
$459$	1.90010e8			0.0917133
$460$		−	7.35409e8i		−	0.352271i
$461$		−	2.18076e9i		−	1.03670i	−0.855168	−	0.518351i	$-0.826546\pi$
$461$		−	2.18076e9i		−	1.03670i	0.855168	−	0.518351i	$-0.173454\pi$
$462$		−	7.28645e7i		−	0.0343771i
$463$			3.46183e6i			0.00162096i	1.00000		0.000810481i	$0.000257984\pi$
$463$			3.46183e6i			0.00162096i	−1.00000		0.000810481i	$0.999742\pi$
$464$	−1.82526e9			−0.848226
$465$	−2.09167e7			−0.00964736
$466$			5.64265e9i			2.58305i
$467$	−1.98918e9			−0.903785			−0.451892	−	0.892072i	$-0.649251\pi$
$467$	−1.98918e9			−0.903785			−0.451892	+	0.892072i	$0.649251\pi$
$468$	1.61469e9	−	1.04059e9i	0.728162	−	0.469266i
$469$	−7.21032e8			−0.322737
$470$			1.99863e8i			0.0887952i
$471$	−1.51562e8			−0.0668368
$472$	−6.01175e8			−0.263150
$473$		−	3.86396e9i		−	1.67888i
$474$			1.49132e8i			0.0643200i
$475$			1.13615e9i			0.486418i
$476$		−	7.20289e8i		−	0.306114i
$477$	−1.92293e9			−0.811240
$478$	−1.12127e9			−0.469585
$479$		−	1.32046e9i		−	0.548973i	−0.961591	−	0.274486i	$-0.911492\pi$
$479$		−	1.32046e9i		−	0.548973i	0.961591	−	0.274486i	$-0.0885078\pi$
$480$	4.87370e7			0.0201147
$481$	4.88491e8	+	7.57993e8i	0.200147	+	0.310569i
$482$	3.35103e9			1.36306
$483$		−	6.14433e7i		−	0.0248119i
$484$	1.79150e9			0.718219
$485$	2.88522e8			0.114837
$486$			5.09193e8i			0.201213i
$487$		−	3.80409e9i		−	1.49245i	−0.665695	−	0.746224i	$-0.731865\pi$
$487$		−	3.80409e9i		−	1.49245i	0.665695	−	0.746224i	$-0.268135\pi$
$488$		−	7.61791e8i		−	0.296733i
$489$		−	1.09503e8i		−	0.0423493i
$490$	−1.54698e8			−0.0594018
$491$	4.16851e9			1.58926			0.794632	−	0.607092i	$-0.207664\pi$
$491$	4.16851e9			1.58926			0.794632	+	0.607092i	$0.207664\pi$
$492$			1.54654e7i			0.00585442i
$493$	1.88885e9			0.709959
$494$	1.65018e9	−	1.06346e9i	0.615868	−	0.396898i
$495$	1.10690e9			0.410195
$496$			1.95085e9i			0.717856i
$497$	7.19312e8			0.262827
$498$	−3.39094e8			−0.123032
$499$			1.64932e9i			0.594229i	0.954842	+	0.297115i	$0.0960244\pi$
$499$			1.64932e9i			0.594229i	−0.954842	+	0.297115i	$0.903976\pi$
$500$		−	1.40840e9i		−	0.503883i
$501$		−	1.82998e8i		−	0.0650153i
$502$			6.43048e9i			2.26872i
$503$	−1.61351e9			−0.565307			−0.282653	−	0.959222i	$-0.591215\pi$
$503$	−1.61351e9			−0.565307			−0.282653	+	0.959222i	$0.591215\pi$
$504$	−1.94968e8			−0.0678353
$505$		−	1.57518e8i		−	0.0544266i
$506$	7.18026e9			2.46384
$507$	−5.96759e7	+	1.31553e8i	−0.0203362	+	0.0448305i
$508$	−3.69526e9			−1.25061
$509$		−	3.04468e9i		−	1.02336i	−0.859176	−	0.511681i	$-0.829023\pi$
$509$		−	3.04468e9i		−	1.02336i	0.859176	−	0.511681i	$-0.170977\pi$
$510$	−5.71903e7			−0.0190909
$511$	−8.42377e8			−0.279276
$512$		−	3.93673e9i		−	1.29626i
$513$			1.61177e8i			0.0527099i
$514$		−	7.09745e9i		−	2.30532i
$515$			5.85838e8i			0.188996i
$516$	−1.65703e8			−0.0530952
$517$	−9.06959e8			−0.288649
$518$			6.03841e8i			0.190883i
$519$	2.12545e8			0.0667367
$520$	1.47506e8	−	9.50604e7i	0.0460041	−	0.0296475i
$521$	1.68738e9			0.522734			0.261367	−	0.965239i	$-0.415827\pi$
$521$	1.68738e9			0.522734			0.261367	+	0.965239i	$0.415827\pi$
$522$			3.37315e9i			1.03798i
$523$	7.77668e8			0.237705			0.118852	−	0.992912i	$-0.462078\pi$
$523$	7.77668e8			0.237705			0.118852	+	0.992912i	$0.462078\pi$
$524$	4.82752e9			1.46577
$525$		−	5.59812e7i		−	0.0168844i
$526$		−	8.18941e9i		−	2.45359i
$527$		−	2.01881e9i		−	0.600840i
$528$			2.50787e8i			0.0741458i
$529$	2.64996e9			0.778295
$530$	1.15895e9			0.338143
$531$			5.03411e9i			1.45912i
$532$	6.10989e8			0.175931
$533$	2.59344e8	+	4.02426e8i	0.0741877	+	0.115117i
$534$	−3.46476e8			−0.0984644
$535$		−	4.00220e8i		−	0.112995i
$536$	5.47689e8			0.153623
$537$	2.38859e8			0.0665627
$538$		−	4.64955e9i		−	1.28728i
$539$		−	7.02007e8i		−	0.193099i
$540$		−	9.50523e7i		−	0.0259767i
$541$			4.08850e9i			1.11013i	0.831807	+	0.555065i	$0.187307\pi$
$541$			4.08850e9i			1.11013i	−0.831807	+	0.555065i	$0.812693\pi$
$542$	1.09226e9			0.294664
$543$	−2.32568e7			−0.00623377
$544$			4.70394e9i			1.25275i
$545$	−1.84301e9			−0.487685
$546$	−8.13087e7	+	5.23996e7i	−0.0213778	+	0.0137770i
$547$	1.76459e8			0.0460986			0.0230493	−	0.999734i	$-0.492663\pi$
$547$	1.76459e8			0.0460986			0.0230493	+	0.999734i	$0.492663\pi$
$548$			3.15624e9i			0.819290i
$549$	−6.37907e9			−1.64533
$550$	6.54196e9			1.67664
$551$			1.60222e9i			0.408031i
$552$			4.66717e7i			0.0118105i
$553$			1.43680e9i			0.361292i
$554$		−	2.70847e9i		−	0.676767i
$555$	2.22834e7			0.00553295
$556$	−1.90473e9			−0.469973
$557$		−	6.57296e8i		−	0.161164i	−0.996748	−	0.0805819i	$-0.974322\pi$
$557$		−	6.57296e8i		−	0.161164i	0.996748	−	0.0805819i	$-0.0256779\pi$
$558$	3.60525e9			0.878447
$559$	−4.31175e9	+	2.77872e9i	−1.04403	+	0.672827i
$560$	5.32446e8			0.128120
$561$		−	2.59524e8i		−	0.0620594i
$562$	2.48261e9			0.589971
$563$	3.20481e9			0.756873			0.378436	−	0.925627i	$-0.376462\pi$
$563$	3.20481e9			0.756873			0.378436	+	0.925627i	$0.376462\pi$
$564$			3.88942e7i			0.00912867i
$565$			4.28178e8i			0.0998744i
$566$			2.00619e9i			0.465065i
$567$			1.62864e9i			0.375219i
$568$	−5.46382e8			−0.125106
$569$	−2.10522e9			−0.479077			−0.239538	−	0.970887i	$-0.576996\pi$
$569$	−2.10522e9			−0.479077			−0.239538	+	0.970887i	$0.576996\pi$
$570$		−	4.85119e7i		−	0.0109720i
$571$	3.90593e9			0.878008			0.439004	−	0.898485i	$-0.355331\pi$
$571$	3.90593e9			0.878008			0.439004	+	0.898485i	$0.355331\pi$
$572$	−2.84602e9	−	4.41618e9i	−0.635846	−	0.986645i
$573$	3.06847e7			0.00681367
$574$			3.20585e8i			0.0707540i
$575$	5.51654e9			1.21012
$576$	−3.30210e9			−0.719965
$577$		−	1.87841e9i		−	0.407076i	−0.979067	−	0.203538i	$-0.934756\pi$
$577$		−	1.87841e9i		−	0.407076i	0.979067	−	0.203538i	$-0.0652441\pi$
$578$			8.25887e8i			0.177899i
$579$		−	1.16212e8i		−	0.0248814i
$580$		−	9.44894e8i		−	0.201088i
$581$	−3.26697e9			−0.691081
$582$	1.20806e8			0.0254014
$583$			5.25923e9i			1.09921i
$584$	6.39862e8			0.132936
$585$	−7.96015e8	−	1.23518e9i	−0.164390	−	0.255085i
$586$	−5.90172e9			−1.21154
$587$		−	2.11715e9i		−	0.432034i	−0.976390	−	0.216017i	$-0.930693\pi$
$587$		−	2.11715e9i		−	0.432034i	0.976390	−	0.216017i	$-0.0693067\pi$
$588$	−3.01050e7			−0.00610686
$589$	1.71247e9			0.345318
$590$		−	3.03407e9i		−	0.608195i
$591$			3.04294e8i			0.0606370i
$592$		−	2.07832e9i		−	0.411705i
$593$		−	1.36944e9i		−	0.269682i	−0.990867	−	0.134841i	$-0.956948\pi$
$593$		−	1.36944e9i		−	0.269682i	0.990867	−	0.134841i	$-0.0430524\pi$
$594$	9.28055e8			0.181686
$595$	−5.50996e8			−0.107236
$596$			4.46575e9i			0.864037i
$597$	1.57726e8			0.0303385
$598$	−5.16360e9	−	8.01238e9i	−0.987412	−	1.53217i
$599$	6.01178e9			1.14290			0.571451	−	0.820636i	$-0.306381\pi$
$599$	6.01178e9			1.14290			0.571451	+	0.820636i	$0.306381\pi$
$600$			4.25228e7i			0.00803697i
$601$	−2.42753e9			−0.456146			−0.228073	−	0.973644i	$-0.573242\pi$
$601$	−2.42753e9			−0.456146			−0.228073	+	0.973644i	$0.573242\pi$
$602$	−3.43487e9			−0.641687
$603$		−	4.58622e9i		−	0.851814i
$604$			3.90608e9i			0.721293i
$605$		−	1.37043e9i		−	0.251601i
$606$		−	6.59537e7i		−	0.0120389i
$607$	−9.80893e9			−1.78017			−0.890085	−	0.455795i	$-0.849355\pi$
$607$	−9.80893e9			−1.78017			−0.890085	+	0.455795i	$0.849355\pi$
$608$	−3.99013e9			−0.719988
$609$		−	7.89457e7i		−	0.0141634i
$610$	3.84468e9			0.685812
$611$	6.52229e8	+	1.01207e9i	0.115679	+	0.179500i
$612$	4.58150e9			0.807938
$613$		−	6.25492e9i		−	1.09676i	−0.836231	−	0.548378i	$-0.815246\pi$
$613$		−	6.25492e9i		−	1.09676i	0.836231	−	0.548378i	$-0.184754\pi$
$614$	−6.99945e9			−1.22032
$615$	1.18305e7			0.00205088
$616$			5.33238e8i			0.0919154i
$617$			3.47329e9i			0.595310i	0.954673	+	0.297655i	$0.0962046\pi$
$617$			3.47329e9i			0.595310i	−0.954673	+	0.297655i	$0.903795\pi$
$618$			2.45293e8i			0.0418048i
$619$			3.78514e9i			0.641453i	0.947172	+	0.320726i	$0.103927\pi$
$619$			3.78514e9i			0.641453i	−0.947172	+	0.320726i	$0.896073\pi$
$620$	−1.00991e9			−0.170181
$621$	7.82587e8			0.131133
$622$			4.31126e9i			0.718353i
$623$	−3.33810e9			−0.553084
$624$	2.79851e8	−	1.80351e8i	0.0461084	−	0.0297147i
$625$	4.46132e9			0.730943
$626$			8.73096e8i			0.142250i
$627$	2.20143e8			0.0356671
$628$	−7.31774e9			−1.17901
$629$			2.15072e9i			0.344594i
$630$		−	9.83981e8i		−	0.156782i
$631$			1.26267e9i			0.200072i	0.994984	+	0.100036i	$0.0318959\pi$
$631$			1.26267e9i			0.200072i	−0.994984	+	0.100036i	$0.968104\pi$
$632$		−	1.09138e9i		−	0.171975i
$633$	3.89068e7			0.00609695
$634$	−1.57365e10			−2.45243
$635$			2.82675e9i			0.438105i
$636$	2.25537e8			0.0347631
$637$	−7.83362e8	+	5.04840e8i	−0.120081	+	0.0773866i
$638$	9.22559e9			1.40644
$639$			4.57529e9i			0.693690i
$640$	−7.19624e8			−0.108511
$641$	4.77618e9			0.716271			0.358135	−	0.933670i	$-0.383413\pi$
$641$	4.77618e9			0.716271			0.358135	+	0.933670i	$0.383413\pi$
$642$		−	1.67574e8i		−	0.0249939i
$643$			1.08083e10i			1.60331i	0.597785	+	0.801656i	$0.296047\pi$
$643$			1.08083e10i			1.60331i	−0.597785	+	0.801656i	$0.703953\pi$
$644$		−	2.96662e9i		−	0.437685i
$645$			1.26757e8i			0.0185999i
$646$	4.68221e9			0.683340
$647$	−1.04711e10			−1.51995			−0.759973	−	0.649954i	$-0.774788\pi$
$647$	−1.04711e10			−1.51995			−0.759973	+	0.649954i	$0.774788\pi$
$648$		−	1.23710e9i		−	0.178604i
$649$	1.37683e10			1.97708
$650$	−4.70458e9	−	7.30011e9i	−0.671930	−	1.04264i
$651$	−8.43777e7			−0.0119865
$652$		−	5.28707e9i		−	0.747048i
$653$	−2.55515e9			−0.359104			−0.179552	−	0.983749i	$-0.557465\pi$
$653$	−2.55515e9			−0.359104			−0.179552	+	0.983749i	$0.557465\pi$
$654$	−7.71676e8			−0.107873
$655$		−	3.69288e9i		−	0.513477i
$656$		−	1.10340e9i		−	0.152605i
$657$		−	5.35806e9i		−	0.737104i
$658$			8.06243e8i			0.110325i
$659$	−1.10017e10			−1.49748			−0.748741	−	0.662863i	$-0.769341\pi$
$659$	−1.10017e10			−1.49748			−0.748741	+	0.662863i	$0.769341\pi$
$660$	−1.29827e8			−0.0175776
$661$			1.33720e10i			1.80091i	0.434949	+	0.900455i	$0.356766\pi$
$661$			1.33720e10i			1.80091i	−0.434949	+	0.900455i	$0.643234\pi$
$662$	−1.40484e10			−1.88202
$663$	−2.89600e8	+	1.86634e8i	−0.0385924	+	0.0248710i
$664$	2.48156e9			0.328955
$665$		−	4.67384e8i		−	0.0616309i
$666$	−3.84081e9			−0.503806
$667$	7.77952e9			1.01511
$668$		−	8.83559e9i		−	1.14688i
$669$		−	1.96406e8i		−	0.0253609i
$670$			2.76413e9i			0.355055i
$671$			1.74468e10i			2.22939i
$672$	1.96604e8			0.0249920
$673$	2.80135e9			0.354254			0.177127	−	0.984188i	$-0.443320\pi$
$673$	2.80135e9			0.354254			0.177127	+	0.984188i	$0.443320\pi$
$674$			1.77582e10i			2.23403i
$675$	7.13018e8			0.0892355
$676$	−2.88129e9	+	6.35169e9i	−0.358735	+	0.790817i
$677$	−6.76863e9			−0.838379			−0.419190	−	0.907899i	$-0.637686\pi$
$677$	−6.76863e9			−0.838379			−0.419190	+	0.907899i	$0.637686\pi$
$678$			1.79280e8i			0.0220916i
$679$	1.16389e9			0.142682
$680$	4.18531e8			0.0510442
$681$			6.30665e8i			0.0765215i
$682$		−	9.86037e9i		−	1.19028i
$683$			4.46941e9i			0.536757i	0.963314	+	0.268379i	$0.0864878\pi$
$683$			4.46941e9i			0.536757i	−0.963314	+	0.268379i	$0.913512\pi$
$684$			3.88628e9i			0.464342i
$685$	2.41441e9			0.287008
$686$	−6.24051e8			−0.0738049
$687$		−	2.15108e8i		−	0.0253109i
$688$	1.18223e10			1.38401
$689$	5.86871e9	−	3.78211e9i	0.683559	−	0.440521i
$690$	−2.35547e8			−0.0272965
$691$			1.32628e10i			1.52920i	0.644507	+	0.764598i	$0.277063\pi$
$691$			1.32628e10i			1.52920i	−0.644507	+	0.764598i	$0.722937\pi$
$692$	1.02622e10			1.17725
$693$	4.46522e9			0.509655
$694$		−	6.05774e9i		−	0.687943i
$695$			1.45705e9i			0.164637i
$696$			5.99664e7i			0.00674180i
$697$			1.14184e9i			0.127729i
$698$	−9.75674e8			−0.108595
$699$	8.39994e8			0.0930264
$700$		−	2.70290e9i		−	0.297843i
$701$	1.06759e10			1.17056			0.585279	−	0.810832i	$-0.300985\pi$
$701$	1.06759e10			1.17056			0.585279	+	0.810832i	$0.300985\pi$
$702$	−6.67400e8	−	1.03561e9i	−0.0728126	−	0.112984i
$703$	−1.82436e9			−0.198046
$704$			9.03125e9i			0.975537i
$705$	2.97527e7			0.00319789
$706$	2.47221e10			2.64405
$707$		−	6.35426e8i		−	0.0676234i
$708$		−	5.90442e8i		−	0.0625261i
$709$		−	6.28944e9i		−	0.662751i	−0.943499	−	0.331376i	$-0.892487\pi$
$709$		−	6.28944e9i		−	0.662751i	0.943499	−	0.331376i	$-0.107513\pi$
$710$		−	2.75753e9i		−	0.289146i
$711$	−9.13896e9			−0.953572
$712$	2.53559e9			0.263268
$713$		−	8.31480e9i		−	0.859090i
$714$	−2.30705e8			−0.0237199
$715$	−3.37822e9	+	2.17710e9i	−0.345634	+	0.222745i
$716$	1.15326e10			1.17418
$717$			1.66919e8i			0.0169117i
$718$	−3.64637e9			−0.367642
$719$	−4.92354e9			−0.494000			−0.247000	−	0.969016i	$-0.579445\pi$
$719$	−4.92354e9			−0.494000			−0.247000	+	0.969016i	$0.579445\pi$
$720$			3.38670e9i			0.338152i
$721$			2.36326e9i			0.234822i
$722$		−	9.85162e9i		−	0.974154i
$723$		−	4.98853e8i		−	0.0490895i
$724$	−1.12289e9			−0.109965
$725$	7.08796e9			0.690777
$726$		−	5.73806e8i		−	0.0556528i
$727$	4.33161e9			0.418099			0.209050	−	0.977905i	$-0.432963\pi$
$727$	4.33161e9			0.418099			0.209050	+	0.977905i	$0.432963\pi$
$728$	5.95034e8	−	3.83472e8i	0.0571587	−	0.0368361i
$729$	−1.03086e10			−0.985489
$730$			3.22931e9i			0.307242i
$731$	−1.22341e10			−1.15841
$732$	7.48191e8			0.0705056
$733$		−	1.12362e10i		−	1.05380i	−0.849928	−	0.526898i	$-0.823355\pi$
$733$		−	1.12362e10i		−	1.05380i	0.849928	−	0.526898i	$-0.176645\pi$
$734$			1.90201e9i			0.177532i
$735$			2.30292e7i			0.00213931i
$736$			1.93739e10i			1.79120i
$737$	−1.25433e10			−1.15419
$738$	−2.03912e9			−0.186744
$739$		−	7.17167e9i		−	0.653679i	−0.945080	−	0.326840i	$-0.894016\pi$
$739$		−	7.17167e9i		−	0.653679i	0.945080	−	0.326840i	$-0.105984\pi$
$740$	1.07590e9			0.0976021
$741$	−1.58313e8	−	2.45655e8i	−0.0142940	−	0.0221800i
$742$	4.67520e9			0.420133
$743$			1.92500e10i			1.72175i	0.508819	+	0.860873i	$0.330082\pi$
$743$			1.92500e10i			1.72175i	−0.508819	+	0.860873i	$0.669918\pi$
$744$	6.40925e7			0.00570561
$745$	3.41614e9			0.302683
$746$		−	1.31528e10i		−	1.15993i
$747$		−	2.07800e10i		−	1.82400i
$748$		−	1.25304e10i		−	1.09474i
$749$		−	1.61448e9i		−	0.140393i
$750$	−4.51101e8			−0.0390445
$751$	9.87101e9			0.850397			0.425199	−	0.905100i	$-0.360204\pi$
$751$	9.87101e9			0.850397			0.425199	+	0.905100i	$0.360204\pi$
$752$		−	2.77495e9i		−	0.237954i
$753$	9.57275e8			0.0817061
$754$	−6.63448e9	−	1.02947e10i	−0.563647	−	0.874613i
$755$	2.98801e9			0.252678
$756$		−	3.83439e8i		−	0.0322753i
$757$	1.74545e10			1.46242			0.731210	−	0.682152i	$-0.238956\pi$
$757$	1.74545e10			1.46242			0.731210	+	0.682152i	$0.238956\pi$
$758$	1.58882e10			1.32505
$759$		−	1.06889e9i		−	0.0887335i
$760$			3.55021e8i			0.0293363i
$761$		−	1.58032e10i		−	1.29987i	−0.759992	−	0.649933i	$-0.774797\pi$
$761$		−	1.58032e10i		−	1.29987i	0.759992	−	0.649933i	$-0.225203\pi$
$762$			1.18357e9i			0.0969064i
$763$	−7.43465e9			−0.605933
$764$	1.48153e9			0.120194
$765$		−	3.50469e9i		−	0.283031i
$766$	3.98337e9			0.320221
$767$	−9.90132e9	−	1.53639e10i	−0.792336	−	1.22947i
$768$	−7.47311e8			−0.0595302
$769$			1.90499e10i			1.51060i	0.655376	+	0.755302i	$0.272510\pi$
$769$			1.90499e10i			1.51060i	−0.655376	+	0.755302i	$0.727490\pi$
$770$	−2.69119e9			−0.212436
$771$	−1.05656e9			−0.0830244
$772$		−	5.61096e9i		−	0.438911i
$773$			1.35399e10i			1.05436i	0.849754	+	0.527179i	$0.176750\pi$
$773$			1.35399e10i			1.05436i	−0.849754	+	0.527179i	$0.823250\pi$
$774$		−	2.18480e10i		−	1.69363i
$775$		−	7.57565e9i		−	0.584607i
$776$	−8.84082e8			−0.0679167
$777$	8.98910e7			0.00687452
$778$		−	5.42949e9i		−	0.413362i
$779$	−9.68570e8			−0.0734091
$780$	9.33633e7	+	1.44872e8i	0.00704442	+	0.0109308i
$781$	1.25134e10			0.939935
$782$		−	2.27342e10i		−	1.70003i
$783$	1.00551e9			0.0748550
$784$	2.14788e9			0.159185
$785$			5.59781e9i			0.413023i
$786$		−	1.54623e9i		−	0.113578i
$787$			2.57905e10i			1.88603i	0.332755	+	0.943013i	$0.392022\pi$
$787$			2.57905e10i			1.88603i	−0.332755	+	0.943013i	$0.607978\pi$
$788$			1.46920e10i			1.06965i
$789$	−1.21912e9			−0.0883643
$790$	5.50807e9			0.397470
$791$			1.72726e9i			0.124091i
$792$	−3.39173e9			−0.242596
$793$	1.94687e10	−	1.25466e10i	1.38637	−	0.893453i
$794$	−3.54444e10			−2.51290
$795$		−	1.72528e8i		−	0.0121780i
$796$	7.61539e9			0.535176
$797$	−2.77333e10			−1.94043			−0.970214	−	0.242248i	$-0.922115\pi$
$797$	−2.77333e10			−1.94043			−0.970214	+	0.242248i	$0.922115\pi$
$798$		−	1.95696e8i		−	0.0136324i
$799$			2.87163e9i			0.199166i
$800$			1.76516e10i			1.21891i
$801$		−	2.12325e10i		−	1.45978i
$802$	−1.58981e10			−1.08827
$803$	−1.46543e10			−0.998760
$804$			5.37911e8i			0.0365018i
$805$	−2.26936e9			−0.153327
$806$	−1.10031e10	+	7.09097e9i	−0.740188	+	0.477016i
$807$	−6.92157e8			−0.0463604
$808$			4.82664e8i			0.0321888i
$809$	2.05781e9			0.136642			0.0683211	−	0.997663i	$-0.478236\pi$
$809$	2.05781e9			0.136642			0.0683211	+	0.997663i	$0.478236\pi$
$810$	6.24351e9			0.412792
$811$		−	1.67235e10i		−	1.10091i	−0.834863	−	0.550457i	$-0.814453\pi$
$811$		−	1.67235e10i		−	1.10091i	0.834863	−	0.550457i	$-0.185547\pi$
$812$		−	3.81168e9i		−	0.249845i
$813$		−	1.62599e8i		−	0.0106121i
$814$			1.05046e10i			0.682647i
$815$	−4.04442e9			−0.261701
$816$	7.94046e8			0.0511599
$817$		−	1.03777e10i		−	0.665767i
$818$	1.60299e10			1.02398
$819$	−3.21111e9	−	4.98269e9i	−0.204250	−	0.316935i
$820$	5.71203e8			0.0361778
$821$		−	1.53885e10i		−	0.970502i	−0.874375	−	0.485251i	$-0.838728\pi$
$821$		−	1.53885e10i		−	0.970502i	0.874375	−	0.485251i	$-0.161272\pi$
$822$	1.01092e9			0.0634845
$823$	−1.33147e10			−0.832592			−0.416296	−	0.909229i	$-0.636672\pi$
$823$	−1.33147e10			−0.832592			−0.416296	+	0.909229i	$0.636672\pi$
$824$		−	1.79511e9i		−	0.111775i
$825$		−	9.73872e8i		−	0.0603827i
$826$		−	1.22394e10i		−	0.755664i
$827$			2.20985e10i			1.35861i	0.733858	+	0.679303i	$0.237718\pi$
$827$			2.20985e10i			1.35861i	−0.733858	+	0.679303i	$0.762282\pi$
$828$	1.88696e10			1.15520
$829$	−7.34592e9			−0.447822			−0.223911	−	0.974610i	$-0.571882\pi$
$829$	−7.34592e9			−0.447822			−0.223911	+	0.974610i	$0.571882\pi$
$830$			1.25242e10i			0.760283i
$831$	−4.03197e8			−0.0243733
$832$	1.00779e10	−	6.49472e9i	0.606649	−	0.390957i
$833$	−2.22271e9			−0.133237
$834$			6.10076e8i			0.0364169i
$835$	−6.75891e9			−0.401767
$836$	1.06290e10			0.629173
$837$		−	1.07470e9i		−	0.0633500i
$838$			3.28730e10i			1.92968i
$839$		−	2.83301e9i		−	0.165608i	−0.996566	−	0.0828040i	$-0.973612\pi$
$839$		−	2.83301e9i		−	0.165608i	0.996566	−	0.0828040i	$-0.0263876\pi$
$840$		−	1.74928e7i		−	0.00101831i
$841$	−7.25431e9			−0.420543
$842$	−2.83935e9			−0.163918
$843$		−	3.69574e8i		−	0.0212473i
$844$	1.87851e9			0.107551
$845$	4.85882e9	+	2.20408e9i	0.277033	+	0.125669i
$846$	−5.12822e9			−0.291186
$847$		−	5.52829e9i		−	0.312607i
$848$	−1.60912e10			−0.906158
$849$	2.98652e8			0.0167490
$850$		−	2.07133e10i		−	1.15686i
$851$			8.85809e9i			0.492705i
$852$		−	5.36628e8i		−	0.0297259i
$853$		−	2.71629e10i		−	1.49849i	−0.662292	−	0.749246i	$-0.730416\pi$
$853$		−	2.71629e10i		−	1.49849i	0.662292	−	0.749246i	$-0.269584\pi$
$854$	1.55094e10			0.852101
$855$	2.97287e9			0.162665
$856$			1.22634e9i			0.0668273i
$857$	2.41182e10			1.30892			0.654459	−	0.756097i	$-0.272896\pi$
$857$	2.41182e10			1.30892			0.654459	+	0.756097i	$0.272896\pi$
$858$	−1.41448e9	+	9.11564e8i	−0.0764523	+	0.0492699i
$859$	1.33069e10			0.716312			0.358156	−	0.933662i	$-0.383406\pi$
$859$	1.33069e10			0.716312			0.358156	+	0.933662i	$0.383406\pi$
$860$			6.12010e9i			0.328106i
$861$	4.77239e7			0.00254815
$862$	−5.86714e8			−0.0311998
$863$		−	1.16187e10i		−	0.615344i	−0.951492	−	0.307672i	$-0.900450\pi$
$863$		−	1.16187e10i		−	0.615344i	0.951492	−	0.307672i	$-0.0995500\pi$
$864$			2.50410e9i			0.132085i
$865$		−	7.85018e9i		−	0.412405i
$866$		−	7.41730e9i		−	0.388091i
$867$	1.22946e8			0.00640689
$868$	−4.07395e9			−0.211445
$869$			2.49951e10i			1.29207i
$870$	−3.02644e8			−0.0155817
$871$	9.02040e9	+	1.39970e10i	0.462554	+	0.717747i
$872$	5.64729e9			0.288425
$873$			7.40311e9i			0.376586i
$874$	1.92844e10			0.977050
$875$	−4.34610e9			−0.219317
$876$			6.28438e8i			0.0315863i
$877$		−	1.28281e10i		−	0.642188i	−0.947047	−	0.321094i	$-0.895949\pi$
$877$		−	1.28281e10i		−	0.642188i	0.947047	−	0.321094i	$-0.104051\pi$
$878$			3.07928e10i			1.53539i
$879$			8.78562e8i			0.0436326i
$880$	9.26263e9			0.458190
$881$	4.44034e9			0.218776			0.109388	−	0.993999i	$-0.465111\pi$
$881$	4.44034e9			0.218776			0.109388	+	0.993999i	$0.465111\pi$
$882$		−	3.96936e9i		−	0.194796i
$883$	−3.19204e10			−1.56029			−0.780145	−	0.625598i	$-0.784855\pi$
$883$	−3.19204e10			−1.56029			−0.780145	+	0.625598i	$0.784855\pi$
$884$	−1.39826e10	+	9.01111e9i	−0.680776	+	0.438728i
$885$	−4.51667e8			−0.0219037
$886$			3.96183e10i			1.91372i
$887$	−3.06589e9			−0.147511			−0.0737554	−	0.997276i	$-0.523498\pi$
$887$	−3.06589e9			−0.147511			−0.0737554	+	0.997276i	$0.523498\pi$
$888$	−6.82803e7			−0.00327228
$889$			1.14030e10i			0.544333i
$890$			1.27968e10i			0.608468i
$891$			2.83325e10i			1.34188i
$892$		−	9.48295e9i		−	0.447370i
$893$	−2.43587e9			−0.114465
$894$	1.43035e9			0.0669518
$895$		−	8.82206e9i		−	0.411329i
$896$	−2.90295e9			−0.134822
$897$	−1.19276e9	+	7.68681e8i	−0.0551800	+	0.0355609i
$898$	−6.59493e9			−0.303909
$899$		−	1.06833e10i		−	0.490396i
$900$	1.71922e10			0.786109
$901$	1.66518e10			0.758447
$902$			5.57702e9i			0.253034i
$903$			5.11334e8i			0.0231099i
$904$		−	1.31201e9i		−	0.0590674i
$905$			8.58973e8i			0.0385220i
$906$	1.25109e9			0.0558910
$907$	3.65519e10			1.62662			0.813308	−	0.581834i	$-0.197665\pi$
$907$	3.65519e10			1.62662			0.813308	+	0.581834i	$0.197665\pi$
$908$			3.04499e10i			1.34985i
$909$	4.04172e9			0.178481
$910$	1.93534e9	+	3.00308e9i	0.0851359	+	0.132106i
$911$	2.78467e10			1.22028			0.610139	−	0.792294i	$-0.291114\pi$
$911$	2.78467e10			1.22028			0.610139	+	0.792294i	$0.291114\pi$
$912$			6.73553e8i			0.0294029i
$913$	−5.68335e10			−2.47148
$914$	−4.17891e10			−1.81031
$915$		−	5.72339e8i		−	0.0246990i
$916$		−	1.03859e10i		−	0.446488i
$917$		−	1.48970e10i		−	0.637980i
$918$		−	2.93842e9i		−	0.125362i
$919$	2.49559e10			1.06064			0.530321	−	0.847797i	$-0.322072\pi$
$919$	2.49559e10			1.06064			0.530321	+	0.847797i	$0.322072\pi$
$920$	1.72379e9			0.0729837
$921$			1.04198e9i			0.0439490i
$922$	−3.37244e10			−1.41705
$923$	−8.99889e9	−	1.39636e10i	−0.376689	−	0.584510i
$924$	−5.23718e8			−0.0218396
$925$			8.07065e9i			0.335284i
$926$	5.35357e7			0.00221567
$927$	−1.50319e10			−0.619774
$928$			2.48927e10i			1.02248i
$929$		−	1.73364e10i		−	0.709423i	−0.934976	−	0.354711i	$-0.884579\pi$
$929$		−	1.73364e10i		−	0.709423i	0.934976	−	0.354711i	$-0.115421\pi$
$930$			3.23468e8i			0.0131868i
$931$		−	1.88542e9i		−	0.0765745i
$932$	4.05569e10			1.64100
$933$	6.41797e8			0.0258709
$934$			3.07618e10i			1.23537i
$935$	−9.58533e9			−0.383501
$936$	2.43913e9	+	3.78480e9i	0.0972229	+	0.150861i
$937$	1.84059e10			0.730919			0.365459	−	0.930827i	$-0.380912\pi$
$937$	1.84059e10			0.730919			0.365459	+	0.930827i	$0.380912\pi$
$938$			1.11504e10i			0.441145i
$939$	1.29974e8			0.00512302
$940$	1.43653e9			0.0564113
$941$		−	2.72816e10i		−	1.06735i	−0.845691	−	0.533673i	$-0.820811\pi$
$941$		−	2.72816e10i		−	1.06735i	0.845691	−	0.533673i	$-0.179189\pi$
$942$			2.34383e9i			0.0913584i
$943$			4.70284e9i			0.182629i
$944$			4.21258e10i			1.62984i
$945$	−2.93317e8			−0.0113065
$946$	−5.97544e10			−2.29483
$947$			1.45374e10i			0.556238i	0.960547	+	0.278119i	$0.0897110\pi$
$947$			1.45374e10i			0.556238i	−0.960547	+	0.278119i	$0.910289\pi$
$948$	1.07189e9			0.0408623
$949$	1.05385e10	+	1.63526e10i	0.400264	+	0.621091i
$950$	1.75701e10			0.664878
$951$			2.34262e9i			0.0883223i
$952$	1.68835e9			0.0634208
$953$	7.43119e9			0.278121			0.139060	−	0.990284i	$-0.455592\pi$
$953$	7.43119e9			0.278121			0.139060	+	0.990284i	$0.455592\pi$
$954$			2.97373e10i			1.10887i
$955$		−	1.13332e9i		−	0.0421056i
$956$			8.05923e9i			0.298326i
$957$		−	1.37337e9i		−	0.0506519i
$958$	−2.04203e10			−0.750383
$959$	9.73968e9			0.356598
$960$		−	2.96269e8i		−	0.0108078i
$961$	1.60942e10			0.584976
$962$	1.17220e10	−	7.55429e9i	0.424512	−	0.273578i
$963$	1.02691e10			0.370546
$964$		−	2.40858e10i		−	0.865946i
$965$	−4.29219e9			−0.153756
$966$	−9.50193e8			−0.0339150
$967$			3.00507e10i			1.06872i	0.845258	+	0.534358i	$0.179447\pi$
$967$			3.00507e10i			1.06872i	−0.845258	+	0.534358i	$0.820553\pi$
$968$			4.19924e9i			0.148801i
$969$		−	6.97019e8i		−	0.0246100i
$970$		−	4.46187e9i		−	0.156970i
$971$	−1.13184e10			−0.396751			−0.198376	−	0.980126i	$-0.563567\pi$
$971$	−1.13184e10			−0.396751			−0.198376	+	0.980126i	$0.563567\pi$
$972$	3.65986e9			0.127830
$973$			5.87773e9i			0.204557i
$974$	−5.88285e10			−2.04001
$975$	−1.08673e9	+	7.00348e8i	−0.0375497	+	0.0241990i
$976$	−5.33805e10			−1.83784
$977$		−	3.46586e10i		−	1.18900i	−0.804097	−	0.594498i	$-0.797351\pi$
$977$		−	3.46586e10i		−	1.18900i	0.804097	−	0.594498i	$-0.202649\pi$
$978$	−1.69342e9			−0.0578867
$979$	−5.80709e10			−1.97797
$980$			1.11191e9i			0.0377378i
$981$		−	4.72892e10i		−	1.59926i
$982$		−	6.44642e10i		−	2.17234i
$983$			3.88001e10i			1.30285i	0.758712	+	0.651427i	$0.225829\pi$
$983$			3.88001e10i			1.30285i	−0.758712	+	0.651427i	$0.774171\pi$
$984$	−3.62506e7			−0.00121292
$985$	1.12389e10			0.374711
$986$		−	2.92102e10i		−	0.970433i
$987$	1.20022e8			0.00397328
$988$	−7.64372e9	−	1.18608e10i	−0.252148	−	0.391259i
$989$	−5.03882e10			−1.65631
$990$		−	1.71177e10i		−	0.560690i
$991$	3.06280e10			0.999680			0.499840	−	0.866118i	$-0.333392\pi$
$991$	3.06280e10			0.999680			0.499840	+	0.866118i	$0.333392\pi$
$992$	2.66054e10			0.865325
$993$			2.09133e9i			0.0677797i
$994$		−	1.11238e10i		−	0.359255i
$995$		−	5.82550e9i		−	0.187479i
$996$			2.43726e9i			0.0781616i
$997$	5.43059e10			1.73546			0.867729	−	0.497038i	$-0.165579\pi$
$997$	5.43059e10			1.73546			0.867729	+	0.497038i	$0.165579\pi$
$998$	2.55061e10			0.812244
$999$			1.14492e9i			0.0363325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.c.a.64.10	✓	50
13.12	even	2	inner	91.8.c.a.64.41	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.c.a.64.10	✓	50	1.1	even	1	trivial
91.8.c.a.64.41	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)

\(f(q)\)	\(=\)	\(q-15.4646i q^{2} -2.30214 q^{3} -111.152 q^{4} +85.0277i q^{5} +35.6015i q^{6} +343.000i q^{7} -260.539i q^{8} -2181.70 q^{9} +O(q^{10})\)	\(q-15.4646i q^{2} -2.30214 q^{3} -111.152 q^{4} +85.0277i q^{5} +35.6015i q^{6} +343.000i q^{7} -260.539i q^{8} -2181.70 q^{9} +1314.92 q^{10} +5966.96i q^{11} +255.888 q^{12} +(6658.47 - 4291.07i) q^{13} +5304.34 q^{14} -195.745i q^{15} -18256.6 q^{16} +18892.7 q^{17} +33739.0i q^{18} +16025.8i q^{19} -9451.04i q^{20} -789.633i q^{21} +92276.4 q^{22} +77812.5 q^{23} +599.797i q^{24} +70895.3 q^{25} +(-66359.5 - 102970. i) q^{26} +10057.3 q^{27} -38125.3i q^{28} +99977.8 q^{29} -3027.11 q^{30} -106857. i q^{31} +248982. i q^{32} -13736.8i q^{33} -292167. i q^{34} -29164.5 q^{35} +242501. q^{36} +113839. i q^{37} +247832. q^{38} +(-15328.7 + 9878.63i) q^{39} +22153.1 q^{40} +60438.2i q^{41} -12211.3 q^{42} -647559. q^{43} -663243. i q^{44} -185505. i q^{45} -1.20334e6i q^{46} +151997. i q^{47} +42029.3 q^{48} -117649. q^{49} -1.09636e6i q^{50} -43493.5 q^{51} +(-740106. + 476963. i) q^{52} +881391. q^{53} -155532. i q^{54} -507357. q^{55} +89365.0 q^{56} -36893.6i q^{57} -1.54611e6i q^{58} -2.30742e6i q^{59} +21757.6i q^{60} +2.92390e6 q^{61} -1.65249e6 q^{62} -748323. i q^{63} +1.51354e6 q^{64} +(364860. + 566154. i) q^{65} -212433. q^{66} +2.10213e6i q^{67} -2.09997e6 q^{68} -179135. q^{69} +451016. i q^{70} -2.09712e6i q^{71} +568419. i q^{72} +2.45591e6i q^{73} +1.76047e6 q^{74} -163211. q^{75} -1.78131e6i q^{76} -2.04667e6 q^{77} +(152769. + 237052. i) q^{78} +4.18892e6 q^{79} -1.55232e6i q^{80} +4.74822e6 q^{81} +934649. q^{82} +9.52469e6i q^{83} +87769.6i q^{84} +1.60640e6i q^{85} +1.00142e7i q^{86} -230163. q^{87} +1.55463e6 q^{88} +9.73207e6i q^{89} -2.86875e6 q^{90} +(1.47184e6 + 2.28386e6i) q^{91} -8.64905e6 q^{92} +245999. i q^{93} +2.35056e6 q^{94} -1.36264e6 q^{95} -573190. i q^{96} -3.39327e6i q^{97} +1.81939e6i q^{98} -1.30181e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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