LMFDB - Embedded newform 91.8.c.a.64.7

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			64.7
Character	$\chi$	$=$	91.64
Dual form			91.8.c.a.64.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.7532i q^{2} -30.0870 q^{3} -187.174 q^{4} -248.659i q^{5} +534.138i q^{6} -343.000i q^{7} +1050.53i q^{8} -1281.77 q^{9} +O(q^{10})$	\(q-17.7532i q^{2} -30.0870 q^{3} -187.174 q^{4} -248.659i q^{5} +534.138i q^{6} -343.000i q^{7} +1050.53i q^{8} -1281.77 q^{9} -4414.48 q^{10} +3008.56i q^{11} +5631.51 q^{12} +(-1529.81 + 7772.27i) q^{13} -6089.33 q^{14} +7481.39i q^{15} -5308.05 q^{16} -19445.0 q^{17} +22755.5i q^{18} -9364.72i q^{19} +46542.6i q^{20} +10319.8i q^{21} +53411.3 q^{22} +40569.3 q^{23} -31607.4i q^{24} +16293.8 q^{25} +(137982. + 27158.9i) q^{26} +104365. q^{27} +64200.8i q^{28} -33157.9 q^{29} +132818. q^{30} -51745.8i q^{31} +228703. i q^{32} -90518.3i q^{33} +345210. i q^{34} -85290.0 q^{35} +239916. q^{36} -162216. i q^{37} -166253. q^{38} +(46027.3 - 233844. i) q^{39} +261224. q^{40} -207700. i q^{41} +183209. q^{42} +275270. q^{43} -563125. i q^{44} +318725. i q^{45} -720233. i q^{46} +16486.2i q^{47} +159703. q^{48} -117649. q^{49} -289266. i q^{50} +585042. q^{51} +(286341. - 1.45477e6i) q^{52} -1.48377e6 q^{53} -1.85281e6i q^{54} +748104. q^{55} +360333. q^{56} +281756. i q^{57} +588657. i q^{58} +720092. i q^{59} -1.40033e6i q^{60} +2.19367e6 q^{61} -918651. q^{62} +439649. i q^{63} +3.38077e6 q^{64} +(1.93264e6 + 380401. i) q^{65} -1.60698e6 q^{66} -2.16177e6i q^{67} +3.63961e6 q^{68} -1.22061e6 q^{69} +1.51417e6i q^{70} +3.78738e6i q^{71} -1.34655e6i q^{72} +5.84204e6i q^{73} -2.87984e6 q^{74} -490230. q^{75} +1.75284e6i q^{76} +1.03193e6 q^{77} +(-4.15147e6 - 817130. i) q^{78} -2.25288e6 q^{79} +1.31989e6i q^{80} -336780. q^{81} -3.68733e6 q^{82} +6.48960e6i q^{83} -1.93161e6i q^{84} +4.83518e6i q^{85} -4.88692e6i q^{86} +997619. q^{87} -3.16059e6 q^{88} -3.93379e6i q^{89} +5.65837e6 q^{90} +(2.66589e6 + 524724. i) q^{91} -7.59354e6 q^{92} +1.55687e6i q^{93} +292683. q^{94} -2.32862e6 q^{95} -6.88097e6i q^{96} +1.25389e7i q^{97} +2.08864e6i q^{98} -3.85629e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	17.7532i		−	1.56917i	−0.620020	−	0.784586i	$-0.712876\pi$
$2$		−	17.7532i		−	1.56917i	0.620020	−	0.784586i	$-0.287124\pi$
$3$	−30.0870			−0.643360			−0.321680	−	0.946848i	$-0.604247\pi$
$3$	−30.0870			−0.643360			−0.321680	+	0.946848i	$0.604247\pi$
$4$	−187.174			−1.46230
$5$		−	248.659i		−	0.889629i	−0.895623	−	0.444815i	$-0.853270\pi$
$5$		−	248.659i		−	0.889629i	0.895623	−	0.444815i	$-0.146730\pi$
$6$			534.138i			1.00954i
$7$		−	343.000i		−	0.377964i
$7$		−	343.000i		−	0.377964i
$8$			1050.53i			0.725429i
$9$	−1281.77			−0.586088
$10$	−4414.48			−1.39598
$11$			3008.56i			0.681528i	0.940149	+	0.340764i	$0.110686\pi$
$11$			3008.56i			0.681528i	−0.940149	+	0.340764i	$0.889314\pi$
$12$	5631.51			0.940785
$13$	−1529.81	+	7772.27i	−0.193124	+	0.981174i
$13$	−1529.81	+	7772.27i	−0.193124	+	0.981174i
$14$	−6089.33			−0.593091
$15$			7481.39i			0.572352i
$16$	−5308.05			−0.323978
$17$	−19445.0			−0.959925			−0.479962	−	0.877289i	$-0.659350\pi$
$17$	−19445.0			−0.959925			−0.479962	+	0.877289i	$0.659350\pi$
$18$			22755.5i			0.919673i
$19$		−	9364.72i		−	0.313226i	−0.987660	−	0.156613i	$-0.949943\pi$
$19$		−	9364.72i		−	0.313226i	0.987660	−	0.156613i	$-0.0500575\pi$
$20$			46542.6i			1.30091i
$21$			10319.8i			0.243167i
$22$	53411.3			1.06943
$23$	40569.3			0.695265			0.347632	−	0.937631i	$-0.386986\pi$
$23$	40569.3			0.695265			0.347632	+	0.937631i	$0.386986\pi$
$24$		−	31607.4i		−	0.466712i
$25$	16293.8			0.208560
$26$	137982.	+	27158.9i	1.53963	+	0.303044i
$27$	104365.			1.02043
$28$			64200.8i			0.552698i
$29$	−33157.9			−0.252461			−0.126230	−	0.992001i	$-0.540288\pi$
$29$	−33157.9			−0.252461			−0.126230	+	0.992001i	$0.540288\pi$
$30$	132818.			0.898118
$31$		−	51745.8i		−	0.311967i	−0.987760	−	0.155984i	$-0.950145\pi$
$31$		−	51745.8i		−	0.311967i	0.987760	−	0.155984i	$-0.0498547\pi$
$32$			228703.i			1.23381i
$33$		−	90518.3i		−	0.438468i
$34$			345210.i			1.50629i
$35$	−85290.0			−0.336248
$36$	239916.			0.857037
$37$		−	162216.i		−	0.526486i	−0.964730	−	0.263243i	$-0.915208\pi$
$37$		−	162216.i		−	0.526486i	0.964730	−	0.263243i	$-0.0847921\pi$
$38$	−166253.			−0.491505
$39$	46027.3	−	233844.i	0.124248	−	0.631248i
$40$	261224.			0.645363
$41$		−	207700.i		−	0.470644i	−0.971917	−	0.235322i	$-0.924386\pi$
$41$		−	207700.i		−	0.470644i	0.971917	−	0.235322i	$-0.0756145\pi$
$42$	183209.			0.381571
$43$	275270.			0.527983			0.263991	−	0.964525i	$-0.414961\pi$
$43$	275270.			0.527983			0.263991	+	0.964525i	$0.414961\pi$
$44$		−	563125.i		−	0.996598i
$45$			318725.i			0.521401i
$46$		−	720233.i		−	1.09099i
$47$			16486.2i			0.0231622i	0.999933	+	0.0115811i	$0.00368646\pi$
$47$			16486.2i			0.0231622i	−0.999933	+	0.0115811i	$0.996314\pi$
$48$	159703.			0.208434
$49$	−117649.			−0.142857
$50$		−	289266.i		−	0.327267i
$51$	585042.			0.617577
$52$	286341.	−	1.45477e6i	0.282405	−	1.43477i
$53$	−1.48377e6			−1.36899			−0.684495	−	0.729017i	$-0.739977\pi$
$53$	−1.48377e6			−1.36899			−0.684495	+	0.729017i	$0.739977\pi$
$54$		−	1.85281e6i		−	1.60122i
$55$	748104.			0.606307
$56$	360333.			0.274186
$57$			281756.i			0.201517i
$58$			588657.i			0.396154i
$59$			720092.i			0.456464i	0.973607	+	0.228232i	$0.0732944\pi$
$59$			720092.i			0.456464i	−0.973607	+	0.228232i	$0.926706\pi$
$60$		−	1.40033e6i		−	0.836950i
$61$	2.19367e6			1.23742			0.618710	−	0.785620i	$-0.287656\pi$
$61$	2.19367e6			1.23742			0.618710	+	0.785620i	$0.287656\pi$
$62$	−918651.			−0.489530
$63$			439649.i			0.221521i
$64$	3.38077e6			1.61208
$65$	1.93264e6	+	380401.i	0.872881	+	0.171808i
$66$	−1.60698e6			−0.688031
$67$		−	2.16177e6i		−	0.878106i	−0.898461	−	0.439053i	$-0.855314\pi$
$67$		−	2.16177e6i		−	0.878106i	0.898461	−	0.439053i	$-0.144686\pi$
$68$	3.63961e6			1.40370
$69$	−1.22061e6			−0.447305
$70$			1.51417e6i			0.527631i
$71$			3.78738e6i			1.25584i	0.778278	+	0.627920i	$0.216093\pi$
$71$			3.78738e6i			1.25584i	−0.778278	+	0.627920i	$0.783907\pi$
$72$		−	1.34655e6i		−	0.425165i
$73$			5.84204e6i			1.75766i	0.477136	+	0.878830i	$0.341675\pi$
$73$			5.84204e6i			1.75766i	−0.477136	+	0.878830i	$0.658325\pi$
$74$	−2.87984e6			−0.826147
$75$	−490230.			−0.134179
$76$			1.75284e6i			0.458030i
$77$	1.03193e6			0.257593
$78$	−4.15147e6	−	817130.i	−0.990537	−	0.194966i
$79$	−2.25288e6			−0.514095			−0.257047	−	0.966399i	$-0.582750\pi$
$79$	−2.25288e6			−0.514095			−0.257047	+	0.966399i	$0.582750\pi$
$80$			1.31989e6i			0.288220i
$81$	−336780.			−0.0704123
$82$	−3.68733e6			−0.738521
$83$			6.48960e6i			1.24579i	0.782306	+	0.622895i	$0.214043\pi$
$83$			6.48960e6i			1.24579i	−0.782306	+	0.622895i	$0.785957\pi$
$84$		−	1.93161e6i		−	0.355583i
$85$			4.83518e6i			0.853977i
$86$		−	4.88692e6i		−	0.828496i
$87$	997619.			0.162423
$88$	−3.16059e6			−0.494400
$89$		−	3.93379e6i		−	0.591489i	−0.955267	−	0.295744i	$-0.904432\pi$
$89$		−	3.93379e6i		−	0.591489i	0.955267	−	0.295744i	$-0.0955677\pi$
$90$	5.65837e6			0.818168
$91$	2.66589e6	+	524724.i	0.370849	+	0.0729939i
$92$	−7.59354e6			−1.01669
$93$			1.55687e6i			0.200707i
$94$	292683.			0.0363454
$95$	−2.32862e6			−0.278655
$96$		−	6.88097e6i		−	0.793781i
$97$			1.25389e7i			1.39495i	0.716611	+	0.697473i	$0.245692\pi$
$97$			1.25389e7i			1.39495i	−0.716611	+	0.697473i	$0.754308\pi$
$98$			2.08864e6i			0.224167i
$99$		−	3.85629e6i		−	0.399435i
$100$	−3.04978e6			−0.304978
$101$	−3.36494e6			−0.324977			−0.162489	−	0.986710i	$-0.551952\pi$
$101$	−3.36494e6			−0.324977			−0.162489	+	0.986710i	$0.551952\pi$
$102$		−	1.03863e7i		−	0.969084i
$103$	8.47701e6			0.764386			0.382193	−	0.924083i	$-0.375169\pi$
$103$	8.47701e6			0.764386			0.382193	+	0.924083i	$0.375169\pi$
$104$	−8.16503e6	−	1.60712e6i	−0.711772	−	0.140098i
$105$	2.56612e6			0.216329
$106$			2.63416e7i			2.14818i
$107$	−4.92696e6			−0.388808			−0.194404	−	0.980922i	$-0.562277\pi$
$107$	−4.92696e6			−0.388808			−0.194404	+	0.980922i	$0.562277\pi$
$108$	−1.95344e7			−1.49217
$109$			3.80004e6i			0.281058i	0.990077	+	0.140529i	$0.0448803\pi$
$109$			3.80004e6i			0.281058i	−0.990077	+	0.140529i	$0.955120\pi$
$110$		−	1.32812e7i		−	0.951400i
$111$			4.88058e6i			0.338720i
$112$			1.82066e6i			0.122452i
$113$	−2.38368e7			−1.55408			−0.777041	−	0.629450i	$-0.783280\pi$
$113$	−2.38368e7			−1.55408			−0.777041	+	0.629450i	$0.783280\pi$
$114$	5.00206e6			0.316214
$115$		−	1.00879e7i		−	0.618528i
$116$	6.20630e6			0.369173
$117$	1.96087e6	−	9.96230e6i	0.113188	−	0.575055i
$118$	1.27839e7			0.716270
$119$			6.66964e6i			0.362817i
$120$	−7.85945e6			−0.415200
$121$	1.04358e7			0.535520
$122$		−	3.89446e7i		−	1.94172i
$123$			6.24905e6i			0.302793i
$124$			9.68549e6i			0.456190i
$125$		−	2.34781e7i		−	1.07517i
$126$	7.80515e6			0.347604
$127$	−3.40799e7			−1.47634			−0.738169	−	0.674616i	$-0.764309\pi$
$127$	−3.40799e7			−1.47634			−0.738169	+	0.674616i	$0.764309\pi$
$128$		−	3.07453e7i		−	1.29582i
$129$	−8.28205e6			−0.339683
$130$	6.75331e6	−	3.43105e7i	0.269597	−	1.36970i
$131$	−3.31447e7			−1.28815			−0.644073	−	0.764964i	$-0.722757\pi$
$131$	−3.31447e7			−1.28815			−0.644073	+	0.764964i	$0.722757\pi$
$132$			1.69427e7i			0.641171i
$133$	−3.21210e6			−0.118388
$134$	−3.83782e7			−1.37790
$135$		−	2.59513e7i		−	0.907800i
$136$		−	2.04276e7i		−	0.696357i
$137$			2.88881e7i			0.959834i	0.877314	+	0.479917i	$0.159333\pi$
$137$			2.88881e7i			0.959834i	−0.877314	+	0.479917i	$0.840667\pi$
$138$			2.16696e7i			0.701899i
$139$	8.55947e6			0.270331			0.135165	−	0.990823i	$-0.456843\pi$
$139$	8.55947e6			0.270331			0.135165	+	0.990823i	$0.456843\pi$
$140$	1.59641e7			0.491696
$141$		−	496021.i		−	0.0149016i
$142$	6.72379e7			1.97063
$143$	−2.33833e7	−	4.60251e6i	−0.668698	−	0.131619i
$144$	6.80373e6			0.189880
$145$			8.24500e6i			0.224596i
$146$	1.03715e8			2.75807
$147$	3.53970e6			0.0919085
$148$			3.03626e7i			0.769881i
$149$			6.97311e7i			1.72693i	0.504408	+	0.863465i	$0.331711\pi$
$149$			6.97311e7i			1.72693i	−0.504408	+	0.863465i	$0.668289\pi$
$150$			8.70312e6i			0.210550i
$151$			3.67595e7i			0.868860i	0.900706	+	0.434430i	$0.143050\pi$
$151$			3.67595e7i			0.868860i	−0.900706	+	0.434430i	$0.856950\pi$
$152$	9.83795e6			0.227223
$153$	2.49241e7			0.562601
$154$		−	1.83201e7i		−	0.404208i
$155$	−1.28670e7			−0.277535
$156$	−8.61514e6	+	4.37696e7i	−0.181688	+	0.923074i
$157$	1.98051e7			0.408439			0.204220	−	0.978925i	$-0.434534\pi$
$157$	1.98051e7			0.408439			0.204220	+	0.978925i	$0.434534\pi$
$158$			3.99957e7i			0.806703i
$159$	4.46421e7			0.880753
$160$	5.68690e7			1.09763
$161$		−	1.39153e7i		−	0.262785i
$162$			5.97891e6i			0.110489i
$163$			6.69715e7i			1.21125i	0.795750	+	0.605625i	$0.207077\pi$
$163$			6.69715e7i			1.21125i	−0.795750	+	0.605625i	$0.792923\pi$
$164$			3.88761e7i			0.688223i
$165$	−2.25082e7			−0.390073
$166$	1.15211e8			1.95486
$167$		−	1.01218e8i		−	1.68171i	−0.541259	−	0.840856i	$-0.682052\pi$
$167$		−	1.01218e8i		−	1.68171i	0.541259	−	0.840856i	$-0.317948\pi$
$168$	−1.08413e7			−0.176400
$169$	−5.80679e7	−	2.37802e7i	−0.925407	−	0.378976i
$170$	8.58396e7			1.34004
$171$			1.20035e7i			0.183578i
$172$	−5.15236e7			−0.772070
$173$	4.37596e7			0.642558			0.321279	−	0.946985i	$-0.395887\pi$
$173$	4.37596e7			0.642558			0.321279	+	0.946985i	$0.395887\pi$
$174$		−	1.77109e7i		−	0.254870i
$175$		−	5.58876e6i		−	0.0788283i
$176$		−	1.59696e7i		−	0.220800i
$177$		−	2.16654e7i		−	0.293670i
$178$	−6.98372e7			−0.928148
$179$	−2.41841e7			−0.315169			−0.157585	−	0.987505i	$-0.550371\pi$
$179$	−2.41841e7			−0.315169			−0.157585	+	0.987505i	$0.550371\pi$
$180$		−	5.96571e7i		−	0.762445i
$181$	3.37834e7			0.423475			0.211738	−	0.977327i	$-0.432088\pi$
$181$	3.37834e7			0.423475			0.211738	+	0.977327i	$0.432088\pi$
$182$	9.31551e6	−	4.73279e7i	0.114540	−	0.581926i
$183$	−6.60009e7			−0.796106
$184$			4.26194e7i			0.504365i
$185$	−4.03364e7			−0.468377
$186$	2.76394e7			0.314944
$187$		−	5.85014e7i		−	0.654215i
$188$		−	3.08580e6i		−	0.0338701i
$189$		−	3.57972e7i		−	0.385685i
$190$			4.13404e7i			0.437257i
$191$	−1.02022e8			−1.05944			−0.529721	−	0.848172i	$-0.677703\pi$
$191$	−1.02022e8			−1.05944			−0.529721	+	0.848172i	$0.677703\pi$
$192$	−1.01717e8			−1.03714
$193$			7.79730e7i			0.780717i	0.920663	+	0.390359i	$0.127649\pi$
$193$			7.79730e7i			0.780717i	−0.920663	+	0.390359i	$0.872351\pi$
$194$	2.22605e8			2.18891
$195$	−5.81474e7	−	1.14451e7i	−0.561577	−	0.110535i
$196$	2.20209e7			0.208900
$197$		−	6.49328e7i		−	0.605107i	−0.953132	−	0.302554i	$-0.902161\pi$
$197$		−	6.49328e7i		−	0.605107i	0.953132	−	0.302554i	$-0.0978391\pi$
$198$	−6.84613e7			−0.626783
$199$	6.31006e7			0.567607			0.283803	−	0.958882i	$-0.408404\pi$
$199$	6.31006e7			0.567607			0.283803	+	0.958882i	$0.408404\pi$
$200$			1.71171e7i			0.151296i
$201$			6.50410e7i			0.564938i
$202$			5.97384e7i			0.509945i
$203$			1.13731e7i			0.0954211i
$204$	−1.09505e8			−0.903083
$205$	−5.16464e7			−0.418699
$206$		−	1.50494e8i		−	1.19945i
$207$	−5.20007e7			−0.407486
$208$	8.12030e6	−	4.12556e7i	0.0625678	−	0.317879i
$209$	2.81743e7			0.213472
$210$		−	4.55567e7i		−	0.339457i
$211$	−2.04547e8			−1.49901			−0.749505	−	0.661999i	$-0.769708\pi$
$211$	−2.04547e8			−1.49901			−0.749505	+	0.661999i	$0.769708\pi$
$212$	2.77723e8			2.00188
$213$		−	1.13951e8i		−	0.807957i
$214$			8.74691e7i			0.610107i
$215$		−	6.84484e7i		−	0.469709i
$216$			1.09639e8i			0.740246i
$217$	−1.77488e7			−0.117913
$218$	6.74628e7			0.441028
$219$		−	1.75769e8i		−	1.13081i
$220$	−1.40026e8			−0.886603
$221$	2.97472e7	−	1.51132e8i	0.185384	−	0.941854i
$222$	8.66457e7			0.531510
$223$		−	6.62828e7i		−	0.400252i	−0.979770	−	0.200126i	$-0.935865\pi$
$223$		−	6.62828e7i		−	0.400252i	0.979770	−	0.200126i	$-0.0641352\pi$
$224$	7.84451e7			0.466335
$225$	−2.08849e7			−0.122235
$226$			4.23179e8i			2.43862i
$227$		−	1.09550e8i		−	0.621618i	−0.950472	−	0.310809i	$-0.899400\pi$
$227$		−	1.09550e8i		−	0.621618i	0.950472	−	0.310809i	$-0.100600\pi$
$228$		−	5.27375e7i		−	0.294678i
$229$		−	4.79659e7i		−	0.263942i	−0.991254	−	0.131971i	$-0.957869\pi$
$229$		−	4.79659e7i		−	0.263942i	0.991254	−	0.131971i	$-0.0421306\pi$
$230$	−1.79092e8			−0.970576
$231$	−3.10478e7			−0.165725
$232$		−	3.48334e7i		−	0.183142i
$233$	1.04579e8			0.541623			0.270812	−	0.962632i	$-0.412708\pi$
$233$	1.04579e8			0.541623			0.270812	+	0.962632i	$0.412708\pi$
$234$	−1.76862e8	−	3.48116e7i	−0.902360	−	0.177611i
$235$	4.09945e6			0.0206057
$236$		−	1.34783e8i		−	0.667487i
$237$	6.77823e7			0.330748
$238$	1.18407e8			0.569323
$239$			2.62112e8i			1.24192i	0.783841	+	0.620962i	$0.213258\pi$
$239$			2.62112e8i			1.24192i	−0.783841	+	0.620962i	$0.786742\pi$
$240$		−	3.97116e7i		−	0.185429i
$241$			7.89441e7i			0.363296i	0.983364	+	0.181648i	$0.0581431\pi$
$241$			7.89441e7i			0.363296i	−0.983364	+	0.181648i	$0.941857\pi$
$242$		−	1.85268e8i		−	0.840323i
$243$	−2.18113e8			−0.975125
$244$	−4.10599e8			−1.80948
$245$			2.92545e7i			0.127090i
$246$	1.10940e8			0.475135
$247$	7.27851e7	+	1.43262e7i	0.307329	+	0.0604913i
$248$	5.43607e7			0.226310
$249$		−	1.95252e8i		−	0.801491i
$250$	−4.16810e8			−1.68713
$251$	3.66629e8			1.46342			0.731710	−	0.681616i	$-0.238722\pi$
$251$	3.66629e8			1.46342			0.731710	+	0.681616i	$0.238722\pi$
$252$		−	8.22910e7i		−	0.323930i
$253$			1.22055e8i			0.473842i
$254$			6.05026e8i			2.31663i
$255$		−	1.45476e8i		−	0.549414i
$256$	−1.13088e8			−0.421286
$257$	−9.76935e7			−0.359004			−0.179502	−	0.983758i	$-0.557449\pi$
$257$	−9.76935e7			−0.359004			−0.179502	+	0.983758i	$0.557449\pi$
$258$			1.47032e8i			0.533021i
$259$	−5.56400e7			−0.198993
$260$	−3.61742e8	−	7.12013e7i	−1.27641	−	0.251236i
$261$	4.25009e7			0.147964
$262$			5.88423e8i			2.02132i
$263$	−5.44820e8			−1.84675			−0.923375	−	0.383899i	$-0.874581\pi$
$263$	−5.44820e8			−1.84675			−0.923375	+	0.383899i	$0.874581\pi$
$264$	9.50925e7			0.318077
$265$			3.68952e8i			1.21789i
$266$			5.70249e7i			0.185771i
$267$			1.18356e8i			0.380540i
$268$			4.04628e8i			1.28406i
$269$	2.13039e8			0.667308			0.333654	−	0.942696i	$-0.391718\pi$
$269$	2.13039e8			0.667308			0.333654	+	0.942696i	$0.391718\pi$
$270$	−4.60717e8			−1.42449
$271$			4.93003e8i			1.50472i	0.658750	+	0.752362i	$0.271086\pi$
$271$			4.93003e8i			1.50472i	−0.658750	+	0.752362i	$0.728914\pi$
$272$	1.03215e8			0.310994
$273$	−8.02085e7	−	1.57874e7i	−0.238589	−	0.0469613i
$274$	5.12854e8			1.50615
$275$			4.90207e7i			0.142140i
$276$	2.28466e8			0.654095
$277$	1.53522e8			0.434001			0.217001	−	0.976171i	$-0.430373\pi$
$277$	1.53522e8			0.434001			0.217001	+	0.976171i	$0.430373\pi$
$278$		−	1.51958e8i		−	0.424195i
$279$			6.63264e7i			0.182840i
$280$		−	8.96000e7i		−	0.243924i
$281$		−	1.16767e8i		−	0.313942i	−0.987603	−	0.156971i	$-0.949827\pi$
$281$		−	1.16767e8i		−	0.313942i	0.987603	−	0.156971i	$-0.0501729\pi$
$282$	−8.80594e6			−0.0233832
$283$	−4.09297e8			−1.07346			−0.536730	−	0.843754i	$-0.680341\pi$
$283$	−4.09297e8			−1.07346			−0.536730	+	0.843754i	$0.680341\pi$
$284$		−	7.08900e8i		−	1.83641i
$285$	7.00611e7			0.179275
$286$	−8.17092e7	+	4.15127e8i	−0.206533	+	1.04930i
$287$	−7.12410e7			−0.177887
$288$		−	2.93146e8i		−	0.723119i
$289$	−3.22298e7			−0.0785445
$290$	1.46375e8			0.352430
$291$		−	3.77257e8i		−	0.897453i
$292$		−	1.09348e9i		−	2.57023i
$293$			2.07177e8i			0.481178i	0.970627	+	0.240589i	$0.0773406\pi$
$293$			2.07177e8i			0.481178i	−0.970627	+	0.240589i	$0.922659\pi$
$294$		−	6.28408e7i		−	0.144220i
$295$	1.79057e8			0.406083
$296$	1.70413e8			0.381928
$297$			3.13988e8i			0.695448i
$298$	1.23795e9			2.70985
$299$	−6.20633e7	+	3.15316e8i	−0.134272	+	0.682176i
$300$	9.17585e7			0.196210
$301$		−	9.44177e7i		−	0.199559i
$302$	6.52596e8			1.36339
$303$	1.01241e8			0.209077
$304$			4.97084e7i			0.101478i
$305$		−	5.45476e8i		−	1.10084i
$306$		−	4.42482e8i		−	0.882817i
$307$			3.36771e8i			0.664278i	0.943230	+	0.332139i	$0.107770\pi$
$307$			3.36771e8i			0.664278i	−0.943230	+	0.332139i	$0.892230\pi$
$308$	−1.93152e8			−0.376679
$309$	−2.55047e8			−0.491775
$310$			2.28431e8i			0.435500i
$311$	9.45337e8			1.78207			0.891036	−	0.453933i	$-0.149980\pi$
$311$	9.45337e8			1.78207			0.891036	+	0.453933i	$0.149980\pi$
$312$	2.45661e8	+	4.83532e7i	0.457926	+	0.0901331i
$313$	−6.16363e8			−1.13614			−0.568069	−	0.822981i	$-0.692309\pi$
$313$	−6.16363e8			−1.13614			−0.568069	+	0.822981i	$0.692309\pi$
$314$		−	3.51602e8i		−	0.640911i
$315$	1.09323e8			0.197071
$316$	4.21682e8			0.751761
$317$		−	1.10327e8i		−	0.194524i	−0.995259	−	0.0972622i	$-0.968991\pi$
$317$		−	1.10327e8i		−	0.194524i	0.995259	−	0.0972622i	$-0.0310085\pi$
$318$		−	7.92537e8i		−	1.38205i
$319$		−	9.97572e7i		−	0.172059i
$320$		−	8.40658e8i		−	1.43415i
$321$	1.48237e8			0.250144
$322$	−2.47040e8			−0.412355
$323$			1.82097e8i			0.300673i
$324$	6.30366e7			0.102964
$325$	−2.49263e7	+	1.26640e8i	−0.0402779	+	0.204634i
$326$	1.18896e9			1.90066
$327$		−	1.14332e8i		−	0.180821i
$328$	2.18196e8			0.341419
$329$	5.65478e6			0.00875448
$330$			3.99591e8i			0.612092i
$331$		−	3.50848e8i		−	0.531766i	−0.964005	−	0.265883i	$-0.914336\pi$
$331$		−	3.50848e8i		−	0.531766i	0.964005	−	0.265883i	$-0.0856636\pi$
$332$		−	1.21469e9i		−	1.82172i
$333$			2.07924e8i			0.308567i
$334$	−1.79694e9			−2.63889
$335$	−5.37543e8			−0.781189
$336$		−	5.47782e7i		−	0.0787807i
$337$	9.81221e8			1.39657			0.698284	−	0.715821i	$-0.253947\pi$
$337$	9.81221e8			1.39657			0.698284	+	0.715821i	$0.253947\pi$
$338$	−4.22173e8	+	1.03089e9i	−0.594678	+	1.45212i
$339$	7.17178e8			0.999834
$340$		−	9.05022e8i		−	1.24877i
$341$	1.55680e8			0.212614
$342$	2.13099e8			0.288065
$343$			4.03536e7i			0.0539949i
$344$			2.89181e8i			0.383014i
$345$			3.03515e8i			0.397936i
$346$		−	7.76871e8i		−	1.00828i
$347$	−1.33594e9			−1.71646			−0.858229	−	0.513267i	$-0.828435\pi$
$347$	−1.33594e9			−1.71646			−0.858229	+	0.513267i	$0.828435\pi$
$348$	−1.86729e8			−0.237511
$349$			3.17366e8i			0.399643i	0.979832	+	0.199821i	$0.0640362\pi$
$349$			3.17366e8i			0.399643i	−0.979832	+	0.199821i	$0.935964\pi$
$350$	−9.92181e7			−0.123695
$351$	−1.59658e8	+	8.11152e8i	−0.197068	+	1.00122i
$352$	−6.88065e8			−0.840873
$353$		−	9.80903e8i		−	1.18690i	−0.804870	−	0.593451i	$-0.797765\pi$
$353$		−	9.80903e8i		−	1.18690i	0.804870	−	0.593451i	$-0.202235\pi$
$354$	−3.84629e8			−0.460819
$355$	9.41765e8			1.11723
$356$			7.36306e8i			0.864934i
$357$		−	2.00669e8i		−	0.233422i
$358$			4.29343e8i			0.494555i
$359$			1.00161e9i			1.14253i	0.820764	+	0.571267i	$0.193548\pi$
$359$			1.00161e9i			1.14253i	−0.820764	+	0.571267i	$0.806452\pi$
$360$	−3.34831e8			−0.378240
$361$	8.06174e8			0.901890
$362$		−	5.99761e8i		−	0.664505i
$363$	−3.13980e8			−0.344532
$364$	−4.98986e8	−	9.82150e7i	−0.542293	−	0.106739i
$365$	1.45268e9			1.56366
$366$			1.17172e9i			1.24923i
$367$	−4.94144e7			−0.0521822			−0.0260911	−	0.999660i	$-0.508306\pi$
$367$	−4.94144e7			−0.0521822			−0.0260911	+	0.999660i	$0.508306\pi$
$368$	−2.15344e8			−0.225250
$369$			2.66224e8i			0.275839i
$370$			7.16098e8i			0.734965i
$371$			5.08932e8i			0.517430i
$372$		−	2.91407e8i		−	0.293494i
$373$	−1.35583e9			−1.35277			−0.676385	−	0.736548i	$-0.736455\pi$
$373$	−1.35583e9			−1.35277			−0.676385	+	0.736548i	$0.736455\pi$
$374$	−1.03858e9			−1.02658
$375$			7.06384e8i			0.691721i
$376$	−1.73194e7			−0.0168025
$377$	5.07252e7	−	2.57712e8i	0.0487561	−	0.247708i
$378$	−6.35512e8			−0.605205
$379$		−	1.18903e9i		−	1.12191i	−0.827848	−	0.560953i	$-0.810435\pi$
$379$		−	1.18903e9i		−	1.12191i	0.827848	−	0.560953i	$-0.189565\pi$
$380$	4.35858e8			0.407477
$381$	1.02536e9			0.949816
$382$			1.81121e9i			1.66245i
$383$			1.27361e9i			1.15836i	0.815201	+	0.579178i	$0.196626\pi$
$383$			1.27361e9i			1.15836i	−0.815201	+	0.579178i	$0.803374\pi$
$384$			9.25033e8i			0.833677i
$385$		−	2.56600e8i		−	0.229162i
$386$	1.38427e9			1.22508
$387$	−3.52835e8			−0.309445
$388$		−	2.34696e9i		−	2.03983i
$389$	2.73085e8			0.235220			0.117610	−	0.993060i	$-0.462477\pi$
$389$	2.73085e8			0.235220			0.117610	+	0.993060i	$0.462477\pi$
$390$	−2.03187e8	+	1.03230e9i	−0.173448	+	0.881210i
$391$	−7.88871e8			−0.667402
$392$		−	1.23594e8i		−	0.103633i
$393$	9.97224e8			0.828741
$394$	−1.15276e9			−0.949517
$395$			5.60199e8i			0.457354i
$396$			7.21799e8i			0.584095i
$397$		−	9.55534e8i		−	0.766442i	−0.923657	−	0.383221i	$-0.874815\pi$
$397$		−	9.55534e8i		−	0.766442i	0.923657	−	0.383221i	$-0.125185\pi$
$398$		−	1.12023e9i		−	0.890673i
$399$	9.66423e7			0.0761662
$400$	−8.64881e7			−0.0675688
$401$			2.03935e8i			0.157938i	0.996877	+	0.0789691i	$0.0251629\pi$
$401$			2.03935e8i			0.157938i	−0.996877	+	0.0789691i	$0.974837\pi$
$402$	1.15468e9			0.886485
$403$	4.02182e8	+	7.91611e7i	0.306094	+	0.0602482i
$404$	6.29832e8			0.475215
$405$			8.37433e7i			0.0626409i
$406$	2.01909e8			0.149732
$407$	4.88035e8			0.358815
$408$			6.14606e8i			0.448008i
$409$		−	1.31042e9i		−	0.947066i	−0.880776	−	0.473533i	$-0.842978\pi$
$409$		−	1.31042e9i		−	0.947066i	0.880776	−	0.473533i	$-0.157022\pi$
$410$			9.16886e8i			0.657010i
$411$		−	8.69154e8i		−	0.617519i
$412$	−1.58668e9			−1.11776
$413$	2.46992e8			0.172527
$414$			9.23177e8i			0.639416i
$415$	1.61370e9			1.10829
$416$	−1.77754e9	−	3.49872e8i	−1.21058	−	0.238277i
$417$	−2.57529e8			−0.173920
$418$		−	5.00182e8i		−	0.334974i
$419$	1.02742e9			0.682334			0.341167	−	0.940003i	$-0.389178\pi$
$419$	1.02742e9			0.682334			0.341167	+	0.940003i	$0.389178\pi$
$420$	−4.80311e8			−0.316337
$421$			7.05220e8i			0.460614i	0.973118	+	0.230307i	$0.0739731\pi$
$421$			7.05220e8i			0.460614i	−0.973118	+	0.230307i	$0.926027\pi$
$422$			3.63135e9i			2.35220i
$423$		−	2.11317e7i		−	0.0135751i
$424$		−	1.55875e9i		−	0.993106i
$425$	−3.16833e8			−0.200202
$426$	−2.02298e9			−1.26782
$427$		−	7.52429e8i		−	0.467701i
$428$	9.22201e8			0.568555
$429$	7.03533e8	+	1.38476e8i	0.430213	+	0.0846785i
$430$	−1.21518e9			−0.737054
$431$			1.63454e9i			0.983387i	0.870768	+	0.491693i	$0.163622\pi$
$431$			1.63454e9i			0.983387i	−0.870768	+	0.491693i	$0.836378\pi$
$432$	−5.53974e8			−0.330595
$433$	2.83569e8			0.167861			0.0839307	−	0.996472i	$-0.473253\pi$
$433$	2.83569e8			0.167861			0.0839307	+	0.996472i	$0.473253\pi$
$434$			3.15097e8i			0.185025i
$435$		−	2.48067e8i		−	0.144496i
$436$		−	7.11271e8i		−	0.410991i
$437$		−	3.79920e8i		−	0.217775i
$438$	−3.12046e9			−1.77443
$439$	−1.85222e9			−1.04488			−0.522441	−	0.852676i	$-0.674978\pi$
$439$	−1.85222e9			−1.04488			−0.522441	+	0.852676i	$0.674978\pi$
$440$			7.85908e8i			0.439833i
$441$	1.50800e8			0.0837269
$442$	−2.68307e9	−	5.28106e8i	−1.47793	−	0.290900i
$443$	−1.44574e9			−0.790088			−0.395044	−	0.918662i	$-0.629271\pi$
$443$	−1.44574e9			−0.790088			−0.395044	+	0.918662i	$0.629271\pi$
$444$		−	9.13520e8i		−	0.495311i
$445$	−9.78173e8			−0.526206
$446$	−1.17673e9			−0.628064
$447$		−	2.09800e9i		−	1.11104i
$448$		−	1.15960e9i		−	0.609307i
$449$		−	2.65686e9i		−	1.38518i	−0.721331	−	0.692591i	$-0.756469\pi$
$449$		−	2.65686e9i		−	1.38518i	0.721331	−	0.692591i	$-0.243531\pi$
$450$			3.70774e8i			0.191807i
$451$	6.24876e8			0.320757
$452$	4.46165e9			2.27253
$453$		−	1.10598e9i		−	0.558989i
$454$	−1.94487e9			−0.975426
$455$	1.30477e8	−	6.62897e8i	0.0649375	−	0.329918i
$456$	−2.95994e8			−0.146186
$457$		−	1.30928e9i		−	0.641693i	−0.947131	−	0.320846i	$-0.896033\pi$
$457$		−	1.30928e9i		−	0.641693i	0.947131	−	0.320846i	$-0.103967\pi$
$458$	−8.51546e8			−0.414170
$459$	−2.02938e9			−0.979532
$460$			1.88820e9i			0.904473i
$461$			1.53709e9i			0.730711i	0.930868	+	0.365356i	$0.119053\pi$
$461$			1.53709e9i			0.730711i	−0.930868	+	0.365356i	$0.880947\pi$
$462$			5.51196e8i			0.260051i
$463$		−	1.09131e9i		−	0.510991i	−0.966810	−	0.255495i	$-0.917761\pi$
$463$		−	1.09131e9i		−	0.510991i	0.966810	−	0.255495i	$-0.0822385\pi$
$464$	1.76004e8			0.0817916
$465$	3.87130e8			0.178555
$466$		−	1.85660e9i		−	0.849900i
$467$	1.51431e8			0.0688028			0.0344014	−	0.999408i	$-0.489048\pi$
$467$	1.51431e8			0.0688028			0.0344014	+	0.999408i	$0.489048\pi$
$468$	−3.67025e8	+	1.86469e9i	−0.165514	+	0.840903i
$469$	−7.41486e8			−0.331893
$470$		−	7.27782e7i		−	0.0323340i
$471$	−5.95874e8			−0.262773
$472$	−7.56481e8			−0.331132
$473$			8.28166e8i			0.359835i
$474$		−	1.20335e9i		−	0.519000i
$475$		−	1.52587e8i		−	0.0653264i
$476$		−	1.24839e9i		−	0.530548i
$477$	1.90186e9			0.802349
$478$	4.65332e9			1.94879
$479$		−	4.08321e9i		−	1.69757i	−0.528740	−	0.848784i	$-0.677335\pi$
$479$		−	4.08321e9i		−	1.69757i	0.528740	−	0.848784i	$-0.322665\pi$
$480$	−1.71102e9			−0.706171
$481$	1.26078e9	+	2.48159e8i	0.516575	+	0.101677i
$482$	1.40151e9			0.570073
$483$			4.18668e8i			0.169065i
$484$	−1.95331e9			−0.783091
$485$	3.11790e9			1.24099
$486$			3.87220e9i			1.53014i
$487$		−	2.33930e9i		−	0.917770i	−0.888496	−	0.458885i	$-0.848249\pi$
$487$		−	2.33930e9i		−	0.917770i	0.888496	−	0.458885i	$-0.151751\pi$
$488$			2.30452e9i			0.897660i
$489$		−	2.01497e9i		−	0.779269i
$490$	5.19359e8			0.199426
$491$	5.51381e8			0.210216			0.105108	−	0.994461i	$-0.466481\pi$
$491$	5.51381e8			0.210216			0.105108	+	0.994461i	$0.466481\pi$
$492$		−	1.16966e9i		−	0.442775i
$493$	6.44755e8			0.242343
$494$	2.54336e8	−	1.29217e9i	0.0949212	−	0.482252i
$495$	−9.58901e8			−0.355349
$496$			2.74669e8i			0.101070i
$497$	1.29907e9			0.474663
$498$	−3.46634e9			−1.25768
$499$		−	1.41074e9i		−	0.508270i	−0.967169	−	0.254135i	$-0.918209\pi$
$499$		−	1.41074e9i		−	0.508270i	0.967169	−	0.254135i	$-0.0817907\pi$
$500$			4.39449e9i			1.57222i
$501$			3.04535e9i			1.08195i
$502$		−	6.50883e9i		−	2.29636i
$503$	3.57013e9			1.25082			0.625412	−	0.780295i	$-0.284931\pi$
$503$	3.57013e9			1.25082			0.625412	+	0.780295i	$0.284931\pi$
$504$	−4.61866e8			−0.160697
$505$			8.36723e8i			0.289109i
$506$	2.16686e9			0.743540
$507$	1.74709e9	+	7.15473e8i	0.595369	+	0.243818i
$508$	6.37889e9			2.15885
$509$			4.26753e9i			1.43438i	0.696877	+	0.717191i	$0.254572\pi$
$509$			4.26753e9i			1.43438i	−0.696877	+	0.717191i	$0.745428\pi$
$510$	−2.58265e9			−0.862126
$511$	2.00382e9			0.664333
$512$		−	1.92773e9i		−	0.634748i
$513$		−	9.77348e8i		−	0.319623i
$514$			1.73437e9i			0.563340i
$515$		−	2.10788e9i		−	0.680020i
$516$	1.55019e9			0.496719
$517$	−4.95998e7			−0.0157857
$518$			9.87786e8i			0.312254i
$519$	−1.31659e9			−0.413396
$520$	−3.99624e8	+	2.03031e9i	−0.124635	+	0.633213i
$521$	−4.08890e9			−1.26670			−0.633351	−	0.773865i	$-0.718321\pi$
$521$	−4.08890e9			−1.26670			−0.633351	+	0.773865i	$0.718321\pi$
$522$		−	7.54525e8i		−	0.232181i
$523$	−1.55065e9			−0.473978			−0.236989	−	0.971512i	$-0.576161\pi$
$523$	−1.55065e9			−0.473978			−0.236989	+	0.971512i	$0.576161\pi$
$524$	6.20385e9			1.88366
$525$			1.68149e8i			0.0507150i
$526$			9.67228e9i			2.89787i
$527$			1.00620e9i			0.299465i
$528$			4.80476e8i			0.142054i
$529$	−1.75896e9			−0.516607
$530$	6.55006e9			1.91108
$531$		−	9.22997e8i		−	0.267528i
$532$	6.01223e8			0.173119
$533$	1.61430e9	+	3.17741e8i	0.461784	+	0.0908925i
$534$	2.10119e9			0.597133
$535$			1.22513e9i			0.345895i
$536$	2.27101e9			0.637004
$537$	7.27625e8			0.202767
$538$		−	3.78212e9i		−	1.04712i
$539$		−	3.53953e8i		−	0.0973611i
$540$			4.85741e9i			1.32748i
$541$			4.99231e9i			1.35554i	0.735275	+	0.677769i	$0.237053\pi$
$541$			4.99231e9i			1.35554i	−0.735275	+	0.677769i	$0.762947\pi$
$542$	8.75236e9			2.36117
$543$	−1.01644e9			−0.272447
$544$		−	4.44713e9i		−	1.18436i
$545$	9.44915e8			0.250037
$546$	−2.80275e8	+	1.42395e9i	−0.0736904	+	0.374388i
$547$	−5.93129e9			−1.54951			−0.774753	−	0.632263i	$-0.782126\pi$
$547$	−5.93129e9			−1.54951			−0.774753	+	0.632263i	$0.782126\pi$
$548$		−	5.40711e9i		−	1.40357i
$549$	−2.81179e9			−0.725237
$550$	8.70272e8			0.223041
$551$			3.10514e8i			0.0790771i
$552$		−	1.28229e9i		−	0.324488i
$553$			7.72738e8i			0.194310i
$554$		−	2.72550e9i		−	0.681022i
$555$	1.21360e9			0.301335
$556$	−1.60212e9			−0.395305
$557$		−	6.16717e9i		−	1.51214i	−0.654490	−	0.756071i	$-0.727117\pi$
$557$		−	6.16717e9i		−	1.51214i	0.654490	−	0.756071i	$-0.272883\pi$
$558$	1.17750e9			0.286908
$559$	−4.21111e8	+	2.13948e9i	−0.101966	+	0.518043i
$560$	4.52724e8			0.108937
$561$			1.76013e9i			0.420896i
$562$	−2.07299e9			−0.492629
$563$	−9.66921e8			−0.228356			−0.114178	−	0.993460i	$-0.536423\pi$
$563$	−9.66921e8			−0.228356			−0.114178	+	0.993460i	$0.536423\pi$
$564$			9.28425e7i			0.0217906i
$565$			5.92724e9i			1.38256i
$566$			7.26631e9i			1.68444i
$567$			1.15516e8i			0.0266134i
$568$	−3.97876e9			−0.911022
$569$	−4.89789e9			−1.11459			−0.557296	−	0.830314i	$-0.688161\pi$
$569$	−4.89789e9			−1.11459			−0.557296	+	0.830314i	$0.688161\pi$
$570$		−	1.24381e9i		−	0.281313i
$571$	−8.19414e9			−1.84195			−0.920974	−	0.389625i	$-0.872605\pi$
$571$	−8.19414e9			−1.84195			−0.920974	+	0.389625i	$0.872605\pi$
$572$	4.37676e9	+	8.61473e8i	0.977837	+	0.192467i
$573$	3.06953e9			0.681602
$574$			1.26475e9i			0.279135i
$575$	6.61027e8			0.145005
$576$	−4.33338e9			−0.944819
$577$			5.25365e9i			1.13853i	0.822153	+	0.569266i	$0.192773\pi$
$577$			5.25365e9i			1.13853i	−0.822153	+	0.569266i	$0.807227\pi$
$578$			5.72181e8i			0.123250i
$579$		−	2.34597e9i		−	0.502282i
$580$		−	1.54325e9i		−	0.328427i
$581$	2.22593e9			0.470864
$582$	−6.69750e9			−1.40826
$583$		−	4.46400e9i		−	0.933005i
$584$	−6.13726e9			−1.27506
$585$	−2.47722e9	−	4.87588e8i	−0.511585	−	0.100695i
$586$	3.67805e9			0.755051
$587$			3.38299e9i			0.690347i	0.938539	+	0.345173i	$0.112180\pi$
$587$			3.38299e9i			0.690347i	−0.938539	+	0.345173i	$0.887820\pi$
$588$	−6.62542e8			−0.134398
$589$	−4.84585e8			−0.0977161
$590$		−	3.17883e9i		−	0.637215i
$591$			1.95363e9i			0.389302i
$592$			8.61049e8i			0.170570i
$593$		−	6.42408e9i		−	1.26508i	−0.774526	−	0.632542i	$-0.782011\pi$
$593$		−	6.42408e9i		−	1.26508i	0.774526	−	0.632542i	$-0.217989\pi$
$594$	5.57427e9			1.09128
$595$	1.65847e9			0.322773
$596$		−	1.30519e10i		−	2.52529i
$597$	−1.89850e9			−0.365175
$598$	5.59785e9	+	1.10182e9i	1.07045	+	0.210696i
$599$	−9.16752e8			−0.174284			−0.0871421	−	0.996196i	$-0.527773\pi$
$599$	−9.16752e8			−0.174284			−0.0871421	+	0.996196i	$0.527773\pi$
$600$		−	5.15003e8i		−	0.0973375i
$601$	9.04890e9			1.70034			0.850169	−	0.526510i	$-0.176500\pi$
$601$	9.04890e9			1.70034			0.850169	+	0.526510i	$0.176500\pi$
$602$	−1.67621e9			−0.313142
$603$			2.77090e9i			0.514648i
$604$		−	6.88043e9i		−	1.27053i
$605$		−	2.59495e9i		−	0.476414i
$606$		−	1.79735e9i		−	0.328078i
$607$	−1.88906e8			−0.0342835			−0.0171417	−	0.999853i	$-0.505457\pi$
$607$	−1.88906e8			−0.0342835			−0.0171417	+	0.999853i	$0.505457\pi$
$608$	2.14174e9			0.386459
$609$		−	3.42183e8i		−	0.0613901i
$610$	−9.68391e9			−1.72741
$611$	−1.28136e8	−	2.52208e7i	−0.0227261	−	0.00447316i
$612$	−4.66516e9			−0.822691
$613$		−	3.86836e9i		−	0.678290i	−0.940734	−	0.339145i	$-0.889862\pi$
$613$		−	3.86836e9i		−	0.678290i	0.940734	−	0.339145i	$-0.110138\pi$
$614$	5.97874e9			1.04237
$615$	1.55388e9			0.269374
$616$			1.08408e9i			0.186866i
$617$		−	4.21767e9i		−	0.722893i	−0.932393	−	0.361447i	$-0.882283\pi$
$617$		−	4.21767e9i		−	0.722893i	0.932393	−	0.361447i	$-0.117717\pi$
$618$			4.52790e9i			0.771679i
$619$			8.50568e8i			0.144142i	0.997399	+	0.0720712i	$0.0229609\pi$
$619$			8.50568e8i			0.144142i	−0.997399	+	0.0720712i	$0.977039\pi$
$620$	2.40838e9			0.405840
$621$	4.23401e9			0.709466
$622$		−	1.67827e10i		−	2.79638i
$623$	−1.34929e9			−0.223562
$624$	−2.44315e8	+	1.24126e9i	−0.0402536	+	0.204510i
$625$	−4.56508e9			−0.747942
$626$			1.09424e10i			1.78280i
$627$	−8.47678e8			−0.137339
$628$	−3.70700e9			−0.597261
$629$			3.15429e9i			0.505387i
$630$		−	1.94082e9i		−	0.309238i
$631$		−	1.67982e9i		−	0.266170i	−0.991105	−	0.133085i	$-0.957512\pi$
$631$		−	1.67982e9i		−	0.266170i	0.991105	−	0.133085i	$-0.0424884\pi$
$632$		−	2.36673e9i		−	0.372939i
$633$	6.15419e9			0.964402
$634$	−1.95865e9			−0.305242
$635$			8.47427e9i			1.31339i
$636$	−8.35585e9			−1.28793
$637$	1.79981e8	−	9.14400e8i	0.0275891	−	0.140168i
$638$	−1.77101e9			−0.269990
$639$		−	4.85456e9i		−	0.736033i
$640$	−7.64510e9			−1.15280
$641$	−1.11173e10			−1.66724			−0.833618	−	0.552341i	$-0.813735\pi$
$641$	−1.11173e10			−1.66724			−0.833618	+	0.552341i	$0.813735\pi$
$642$		−	2.63168e9i		−	0.392518i
$643$			8.88050e8i			0.131734i	0.997828	+	0.0658672i	$0.0209814\pi$
$643$			8.88050e8i			0.131734i	−0.997828	+	0.0658672i	$0.979019\pi$
$644$			2.60458e9i			0.384271i
$645$			2.05940e9i			0.302192i
$646$	3.23280e9			0.471808
$647$	−8.02462e9			−1.16482			−0.582411	−	0.812895i	$-0.697891\pi$
$647$	−8.02462e9			−1.16482			−0.582411	+	0.812895i	$0.697891\pi$
$648$		−	3.53799e8i		−	0.0510792i
$649$	−2.16644e9			−0.311093
$650$	2.24825e9	+	4.42521e8i	0.321106	+	0.0632030i
$651$	5.34007e8			0.0758602
$652$		−	1.25354e10i		−	1.77121i
$653$	1.46156e9			0.205409			0.102705	−	0.994712i	$-0.467250\pi$
$653$	1.46156e9			0.205409			0.102705	+	0.994712i	$0.467250\pi$
$654$	−2.02975e9			−0.283740
$655$			8.24173e9i			1.14597i
$656$			1.10248e9i			0.152478i
$657$		−	7.48818e9i		−	1.03014i
$658$		−	1.00390e8i		−	0.0137373i
$659$	−9.02281e9			−1.22813			−0.614063	−	0.789257i	$-0.710466\pi$
$659$	−9.02281e9			−1.22813			−0.614063	+	0.789257i	$0.710466\pi$
$660$	4.21295e9			0.570405
$661$			9.85664e9i			1.32747i	0.747969	+	0.663734i	$0.231029\pi$
$661$			9.85664e9i			1.32747i	−0.747969	+	0.663734i	$0.768971\pi$
$662$	−6.22866e9			−0.834433
$663$	−8.95002e8	+	4.54710e9i	−0.119269	+	0.605951i
$664$	−6.81754e9			−0.903732
$665$			7.98717e8i			0.105322i
$666$	3.69131e9			0.484195
$667$	−1.34519e9			−0.175527
$668$			1.89455e10i			2.45917i
$669$			1.99425e9i			0.257506i
$670$			9.54307e9i			1.22582i
$671$			6.59978e9i			0.843336i
$672$	−2.36017e9			−0.300021
$673$	1.40587e10			1.77784			0.888922	−	0.458058i	$-0.151455\pi$
$673$	1.40587e10			1.77784			0.888922	+	0.458058i	$0.151455\pi$
$674$		−	1.74198e10i		−	2.19146i
$675$	1.70050e9			0.212820
$676$	1.08688e10	+	4.45104e9i	1.35322	+	0.554177i
$677$	−4.70763e9			−0.583099			−0.291549	−	0.956556i	$-0.594171\pi$
$677$	−4.70763e9			−0.583099			−0.291549	+	0.956556i	$0.594171\pi$
$678$		−	1.27322e10i		−	1.56891i
$679$	4.30084e9			0.527240
$680$	−5.07952e9			−0.619500
$681$			3.29604e9i			0.399924i
$682$		−	2.76381e9i		−	0.333628i
$683$			2.57350e9i			0.309066i	0.987988	+	0.154533i	$0.0493873\pi$
$683$			2.57350e9i			0.309066i	−0.987988	+	0.154533i	$0.950613\pi$
$684$		−	2.24674e9i		−	0.268446i
$685$	7.18327e9			0.853897
$686$	7.16404e8			0.0847273
$687$			1.44315e9i			0.169810i
$688$	−1.46115e9			−0.171055
$689$	2.26988e9	−	1.15322e10i	0.264384	−	1.34322i
$690$	5.38834e9			0.624430
$691$			1.06996e10i			1.23366i	0.787098	+	0.616829i	$0.211583\pi$
$691$			1.06996e10i			1.23366i	−0.787098	+	0.616829i	$0.788417\pi$
$692$	−8.19068e9			−0.939612
$693$	−1.32271e9			−0.150972
$694$			2.37171e10i			2.69342i
$695$		−	2.12839e9i		−	0.240494i
$696$			1.04803e9i			0.117826i
$697$			4.03873e9i			0.451783i
$698$	5.63426e9			0.627108
$699$	−3.14645e9			−0.348458
$700$			1.04607e9i			0.115271i
$701$	−1.07839e10			−1.18239			−0.591196	−	0.806528i	$-0.701344\pi$
$701$	−1.07839e10			−1.18239			−0.591196	+	0.806528i	$0.701344\pi$
$702$	1.44005e10	+	2.83444e9i	1.57108	+	0.309234i
$703$	−1.51911e9			−0.164909
$704$			1.01712e10i			1.09867i
$705$	−1.23340e8			−0.0132569
$706$	−1.74141e10			−1.86245
$707$			1.15418e9i			0.122830i
$708$			4.05521e9i			0.429434i
$709$			8.51873e9i			0.897662i	0.893617	+	0.448831i	$0.148160\pi$
$709$			8.51873e9i			0.897662i	−0.893617	+	0.448831i	$0.851840\pi$
$710$		−	1.67193e10i		−	1.75313i
$711$	2.88769e9			0.301305
$712$	4.13258e9			0.429083
$713$		−	2.09929e9i		−	0.216900i
$714$	−3.56251e9			−0.366279
$715$	−1.14446e9	+	5.81447e9i	−0.117092	+	0.594893i
$716$	4.52664e9			0.460872
$717$		−	7.88616e9i		−	0.799003i
$718$	1.77818e10			1.79283
$719$	−1.81990e10			−1.82598			−0.912990	−	0.407982i	$-0.866233\pi$
$719$	−1.81990e10			−1.82598			−0.912990	+	0.407982i	$0.866233\pi$
$720$		−	1.69181e9i		−	0.168922i
$721$		−	2.90761e9i		−	0.288911i
$722$		−	1.43121e10i		−	1.41522i
$723$		−	2.37519e9i		−	0.233730i
$724$	−6.32338e9			−0.619248
$725$	−5.40266e8			−0.0526532
$726$			5.57414e9i			0.540630i
$727$	−1.12911e9			−0.108985			−0.0544925	−	0.998514i	$-0.517354\pi$
$727$	−1.12911e9			−0.108985			−0.0544925	+	0.998514i	$0.517354\pi$
$728$	−5.51241e8	+	2.80061e9i	−0.0529519	+	0.269025i
$729$	7.29890e9			0.697768
$730$		−	2.57896e10i		−	2.45366i
$731$	−5.35264e9			−0.506824
$732$	1.23537e10			1.16415
$733$			5.01893e9i			0.470704i	0.971910	+	0.235352i	$0.0756242\pi$
$733$			5.01893e9i			0.470704i	−0.971910	+	0.235352i	$0.924376\pi$
$734$			8.77261e8i			0.0818828i
$735$		−	8.80178e8i		−	0.0817645i
$736$			9.27832e9i			0.857821i
$737$	6.50379e9			0.598454
$738$	4.72632e9			0.432839
$739$			1.89127e10i			1.72384i	0.507042	+	0.861921i	$0.330739\pi$
$739$			1.89127e10i			1.72384i	−0.507042	+	0.861921i	$0.669261\pi$
$740$	7.54994e9			0.684909
$741$	−2.18988e9	−	4.31033e8i	−0.197723	−	0.0389176i
$742$	9.03516e9			0.811936
$743$		−	1.71191e10i		−	1.53116i	−0.643341	−	0.765580i	$-0.722452\pi$
$743$		−	1.71191e10i		−	1.53116i	0.643341	−	0.765580i	$-0.277548\pi$
$744$	−1.63555e9			−0.145599
$745$	1.73393e10			1.53633
$746$			2.40703e10i			2.12273i
$747$		−	8.31820e9i		−	0.730142i
$748$			1.09500e10i			0.956660i
$749$			1.68995e9i			0.146956i
$750$	1.25405e10			1.08543
$751$	−1.12691e10			−0.970846			−0.485423	−	0.874279i	$-0.661334\pi$
$751$	−1.12691e10			−0.970846			−0.485423	+	0.874279i	$0.661334\pi$
$752$		−	8.75098e7i		−	0.00750403i
$753$	−1.10308e10			−0.941506
$754$	−4.57520e9	−	9.00532e8i	−0.388696	−	0.0765067i
$755$	9.14056e9			0.772963
$756$			6.70031e9i			0.563987i
$757$	2.27433e10			1.90554			0.952769	−	0.303697i	$-0.0982210\pi$
$757$	2.27433e10			1.90554			0.952769	+	0.303697i	$0.0982210\pi$
$758$	−2.11091e10			−1.76046
$759$		−	3.67226e9i		−	0.304851i
$760$		−	2.44629e9i		−	0.202144i
$761$			3.25611e9i			0.267826i	0.990993	+	0.133913i	$0.0427542\pi$
$761$			3.25611e9i			0.267826i	−0.990993	+	0.133913i	$0.957246\pi$
$762$		−	1.82034e10i		−	1.49042i
$763$	1.30342e9			0.106230
$764$	1.90959e10			1.54922
$765$		−	6.19761e9i		−	0.500506i
$766$	2.26106e10			1.81766
$767$	−5.59675e9	−	1.10160e9i	−0.447870	−	0.0881539i
$768$	3.40247e9			0.271038
$769$		−	6.76968e9i		−	0.536817i	−0.963305	−	0.268408i	$-0.913502\pi$
$769$		−	6.76968e9i		−	0.536817i	0.963305	−	0.268408i	$-0.0864977\pi$
$770$	−4.55545e9			−0.359595
$771$	2.93930e9			0.230969
$772$		−	1.45946e10i		−	1.14164i
$773$		−	2.26346e10i		−	1.76256i	−0.472590	−	0.881282i	$-0.656681\pi$
$773$		−	2.26346e10i		−	1.76256i	0.472590	−	0.881282i	$-0.343319\pi$
$774$			6.26393e9i			0.485572i
$775$		−	8.43133e8i		−	0.0650639i
$776$	−1.31725e10			−1.01193
$777$	1.67404e9			0.128024
$778$		−	4.84812e9i		−	0.369101i
$779$	−1.94505e9			−0.147418
$780$	1.08837e10	+	2.14223e9i	0.821194	+	0.161635i
$781$	−1.13945e10			−0.855890
$782$			1.40049e10i			1.04727i
$783$	−3.46052e9			−0.257617
$784$	6.24487e8			0.0462825
$785$		−	4.92470e9i		−	0.363359i
$786$		−	1.77039e10i		−	1.30044i
$787$			7.67337e9i			0.561145i	0.959833	+	0.280572i	$0.0905242\pi$
$787$			7.67337e9i			0.561145i	−0.959833	+	0.280572i	$0.909476\pi$
$788$			1.21538e10i			0.884849i
$789$	1.63920e10			1.18812
$790$	9.94529e9			0.717667
$791$			8.17603e9i			0.587388i
$792$	4.05116e9			0.289762
$793$	−3.35590e9	+	1.70498e10i	−0.238975	+	1.21412i
$794$	−1.69637e10			−1.20268
$795$		−	1.11006e10i		−	0.783544i
$796$	−1.18108e10			−0.830012
$797$	−6.84487e9			−0.478918			−0.239459	−	0.970906i	$-0.576970\pi$
$797$	−6.84487e9			−0.478918			−0.239459	+	0.970906i	$0.576970\pi$
$798$		−	1.71571e9i		−	0.119518i
$799$		−	3.20575e8i		−	0.0222339i
$800$			3.72643e9i			0.257323i
$801$			5.04224e9i			0.346665i
$802$	3.62050e9			0.247832
$803$	−1.75761e10			−1.19789
$804$		−	1.21740e10i		−	0.826109i
$805$	−3.46016e9			−0.233781
$806$	1.40536e9	−	7.14000e9i	0.0945399	−	0.480314i
$807$	−6.40970e9			−0.429319
$808$		−	3.53499e9i		−	0.235748i
$809$	1.92035e10			1.27514			0.637572	−	0.770391i	$-0.279939\pi$
$809$	1.92035e10			1.27514			0.637572	+	0.770391i	$0.279939\pi$
$810$	1.48671e9			0.0982943
$811$		−	1.62498e10i		−	1.06973i	−0.844937	−	0.534866i	$-0.820362\pi$
$811$		−	1.62498e10i		−	1.06973i	0.844937	−	0.534866i	$-0.179638\pi$
$812$		−	2.12876e9i		−	0.139534i
$813$		−	1.48330e10i		−	0.968079i
$814$		−	8.66416e9i		−	0.563042i
$815$	1.66531e10			1.07756
$816$	−3.10543e9			−0.200081
$817$		−	2.57783e9i		−	0.165378i
$818$	−2.32642e10			−1.48611
$819$	−3.41707e9	−	6.72579e8i	−0.217350	−	0.0427809i
$820$	9.66688e9			0.612263
$821$		−	1.62324e10i		−	1.02372i	−0.859069	−	0.511859i	$-0.828957\pi$
$821$		−	1.62324e10i		−	1.02372i	0.859069	−	0.511859i	$-0.171043\pi$
$822$	−1.54302e10			−0.968993
$823$	−2.97067e9			−0.185761			−0.0928806	−	0.995677i	$-0.529608\pi$
$823$	−2.97067e9			−0.185761			−0.0928806	+	0.995677i	$0.529608\pi$
$824$			8.90538e9i			0.554507i
$825$		−	1.47488e9i		−	0.0914469i
$826$		−	4.38488e9i		−	0.270725i
$827$		−	2.26730e10i		−	1.39393i	−0.717107	−	0.696963i	$-0.754534\pi$
$827$		−	2.26730e10i		−	1.39393i	0.717107	−	0.696963i	$-0.245466\pi$
$828$	9.73321e9			0.595868
$829$	2.01422e10			1.22791			0.613955	−	0.789341i	$-0.289578\pi$
$829$	2.01422e10			1.22791			0.613955	+	0.789341i	$0.289578\pi$
$830$		−	2.86482e10i		−	1.73910i
$831$	−4.61900e9			−0.279219
$832$	−5.17193e9	+	2.62762e10i	−0.311330	+	1.58173i
$833$	2.28769e9			0.137132
$834$			4.57194e9i			0.272910i
$835$	−2.51688e10			−1.49610
$836$	−5.27350e9			−0.312160
$837$		−	5.40044e9i		−	0.318339i
$838$		−	1.82399e10i		−	1.07070i
$839$			1.62188e10i			0.948098i	0.880499	+	0.474049i	$0.157208\pi$
$839$			1.62188e10i			0.948098i	−0.880499	+	0.474049i	$0.842792\pi$
$840$			2.69579e9i			0.156931i
$841$	−1.61504e10			−0.936264
$842$	1.25199e10			0.722783
$843$			3.51318e9i			0.201978i
$844$	3.82860e10			2.19200
$845$	−5.91315e9	+	1.44391e10i	−0.337148	+	0.823268i
$846$	−3.75154e8			−0.0213016
$847$		−	3.57947e9i		−	0.202407i
$848$	7.87592e9			0.443522
$849$	1.23145e10			0.690621
$850$			5.62478e9i			0.314151i
$851$		−	6.58098e9i		−	0.366047i
$852$			2.13286e10i			1.18148i
$853$			8.08009e9i			0.445754i	0.974847	+	0.222877i	$0.0715448\pi$
$853$			8.08009e9i			0.445754i	−0.974847	+	0.222877i	$0.928455\pi$
$854$	−1.33580e10			−0.733903
$855$	2.98477e9			0.163316
$856$		−	5.17594e9i		−	0.282053i
$857$	2.49987e10			1.35670			0.678352	−	0.734737i	$-0.262694\pi$
$857$	2.49987e10			1.35670			0.678352	+	0.734737i	$0.262694\pi$
$858$	2.45838e9	−	1.24899e10i	0.132875	−	0.675078i
$859$	−3.15642e10			−1.69910			−0.849549	−	0.527509i	$-0.823126\pi$
$859$	−3.15642e10			−1.69910			−0.849549	+	0.527509i	$0.823126\pi$
$860$			1.28118e10i			0.686856i
$861$	2.14343e9			0.114445
$862$	2.90182e10			1.54310
$863$			3.38019e9i			0.179021i	0.995986	+	0.0895104i	$0.0285302\pi$
$863$			3.38019e9i			0.179021i	−0.995986	+	0.0895104i	$0.971470\pi$
$864$			2.38686e10i			1.25901i
$865$		−	1.08812e10i		−	0.571638i
$866$		−	5.03424e9i		−	0.263403i
$867$	9.69698e8			0.0505324
$868$	3.32212e9			0.172424
$869$		−	6.77792e9i		−	0.350370i
$870$	−4.40397e9			−0.226739
$871$	1.68018e10	+	3.30709e9i	0.861575	+	0.169583i
$872$	−3.99207e9			−0.203888
$873$		−	1.60720e10i		−	0.817562i
$874$	−6.74478e9			−0.341726
$875$	−8.05298e9			−0.406376
$876$			3.28995e10i			1.65358i
$877$			2.00317e10i			1.00281i	0.865213	+	0.501405i	$0.167183\pi$
$877$			2.00317e10i			1.00281i	−0.865213	+	0.501405i	$0.832817\pi$
$878$			3.28828e10i			1.63960i
$879$		−	6.23334e9i		−	0.309571i
$880$	−3.97097e9			−0.196430
$881$	2.90133e10			1.42949			0.714746	−	0.699384i	$-0.246542\pi$
$881$	2.90133e10			1.42949			0.714746	+	0.699384i	$0.246542\pi$
$882$		−	2.67717e9i		−	0.131382i
$883$	−6.65737e9			−0.325417			−0.162708	−	0.986674i	$-0.552023\pi$
$883$	−6.65737e9			−0.325417			−0.162708	+	0.986674i	$0.552023\pi$
$884$	−5.56791e9	+	2.82880e10i	−0.271087	+	1.37727i
$885$	−5.38729e9			−0.261258
$886$			2.56664e10i			1.23978i
$887$	−1.67209e9			−0.0804504			−0.0402252	−	0.999191i	$-0.512808\pi$
$887$	−1.67209e9			−0.0804504			−0.0402252	+	0.999191i	$0.512808\pi$
$888$	−5.12721e9			−0.245717
$889$			1.16894e10i			0.558003i
$890$			1.73657e10i			0.825707i
$891$		−	1.01322e9i		−	0.0479880i
$892$			1.24064e10i			0.585289i
$893$	1.54389e8			0.00725498
$894$	−3.72461e10			−1.74341
$895$			6.01358e9i			0.280384i
$896$	−1.05456e10			−0.489773
$897$	1.86730e9	−	9.48689e9i	0.0863852	−	0.438884i
$898$	−4.71677e10			−2.17359
$899$			1.71578e9i			0.0787594i
$900$	3.90913e9			0.178744
$901$	2.88519e10			1.31413
$902$		−	1.10935e10i		−	0.503323i
$903$			2.84074e9i			0.128388i
$904$		−	2.50414e10i		−	1.12738i
$905$		−	8.40054e9i		−	0.376736i
$906$	−1.96346e10			−0.877150
$907$	−1.32698e10			−0.590525			−0.295262	−	0.955416i	$-0.595407\pi$
$907$	−1.32698e10			−0.590525			−0.295262	+	0.955416i	$0.595407\pi$
$908$			2.05051e10i			0.908993i
$909$	4.31310e9			0.190465
$910$	−1.17685e10	−	2.31639e9i	−0.517698	−	0.101898i
$911$	3.79146e9			0.166147			0.0830735	−	0.996543i	$-0.473526\pi$
$911$	3.79146e9			0.166147			0.0830735	+	0.996543i	$0.473526\pi$
$912$		−	1.49557e9i		−	0.0652869i
$913$	−1.95243e10			−0.849040
$914$	−2.32439e10			−1.00693
$915$			1.64117e10i			0.708239i
$916$			8.97799e9i			0.385962i
$917$			1.13686e10i			0.486873i
$918$			3.60278e10i			1.53705i
$919$	9.72099e9			0.413149			0.206574	−	0.978431i	$-0.433768\pi$
$919$	9.72099e9			0.413149			0.206574	+	0.978431i	$0.433768\pi$
$920$	1.05977e10			0.448698
$921$		−	1.01324e10i		−	0.427370i
$922$	2.72882e10			1.14661
$923$	−2.94365e10	−	5.79396e9i	−1.23220	−	0.242532i
$924$	5.81135e9			0.242340
$925$		−	2.64311e9i		−	0.109804i
$926$	−1.93741e10			−0.801832
$927$	−1.08656e10			−0.447997
$928$		−	7.58330e9i		−	0.311487i
$929$		−	4.04453e10i		−	1.65506i	−0.561424	−	0.827529i	$-0.689746\pi$
$929$		−	4.04453e10i		−	1.65506i	0.561424	−	0.827529i	$-0.310254\pi$
$930$		−	6.87278e9i		−	0.280183i
$931$			1.10175e9i			0.0447465i
$932$	−1.95744e10			−0.792016
$933$	−2.84423e10			−1.14651
$934$		−	2.68838e9i		−	0.107963i
$935$	−1.45469e10			−0.582009
$936$	1.04657e10	+	2.05996e9i	0.417161	+	0.0821095i
$937$	3.42893e10			1.36166			0.680832	−	0.732440i	$-0.261619\pi$
$937$	3.42893e10			1.36166			0.680832	+	0.732440i	$0.261619\pi$
$938$			1.31637e10i			0.520797i
$939$	1.85445e10			0.730945
$940$	−7.67313e8			−0.0301318
$941$		−	7.00628e8i		−	0.0274109i	−0.999906	−	0.0137055i	$-0.995637\pi$
$941$		−	7.00628e8i		−	0.0274109i	0.999906	−	0.0137055i	$-0.00436272\pi$
$942$			1.05786e10i			0.412336i
$943$		−	8.42623e9i		−	0.327222i
$944$		−	3.82229e9i		−	0.147884i
$945$	−8.90128e9			−0.343116
$946$	1.47026e10			0.564643
$947$			3.27145e10i			1.25174i	0.779927	+	0.625871i	$0.215256\pi$
$947$			3.27145e10i			1.25174i	−0.779927	+	0.625871i	$0.784744\pi$
$948$	−1.26871e10			−0.483653
$949$	−4.54059e10	−	8.93721e9i	−1.72457	−	0.339446i
$950$	−2.70889e9			−0.102508
$951$			3.31940e9i			0.125149i
$952$	−7.00668e9			−0.263198
$953$	2.16209e10			0.809188			0.404594	−	0.914496i	$-0.367413\pi$
$953$	2.16209e10			0.809188			0.404594	+	0.914496i	$0.367413\pi$
$954$		−	3.37640e10i		−	1.25902i
$955$			2.53687e10i			0.942510i
$956$		−	4.90607e10i		−	1.81607i
$957$			3.00139e9i			0.110696i
$958$	−7.24898e10			−2.66378
$959$	9.90860e9			0.362783
$960$			2.52928e10i			0.922674i
$961$	2.48350e10			0.902676
$962$	4.40561e9	−	2.23829e10i	0.159549	−	0.810595i
$963$	6.31525e9			0.227876
$964$		−	1.47763e10i		−	0.531247i
$965$	1.93887e10			0.694549
$966$	7.43268e9			0.265293
$967$			8.15548e9i			0.290039i	0.989429	+	0.145020i	$0.0463246\pi$
$967$			8.15548e9i			0.290039i	−0.989429	+	0.145020i	$0.953675\pi$
$968$			1.09631e10i			0.388482i
$969$		−	5.47875e9i		−	0.193441i
$970$		−	5.53526e10i		−	1.94732i
$971$	6.32625e9			0.221758			0.110879	−	0.993834i	$-0.464633\pi$
$971$	6.32625e9			0.221758			0.110879	+	0.993834i	$0.464633\pi$
$972$	4.08252e10			1.42593
$973$		−	2.93590e9i		−	0.102175i
$974$	−4.15299e10			−1.44014
$975$	7.49958e8	−	3.81020e9i	0.0259132	−	0.131653i
$976$	−1.16441e10			−0.400896
$977$			2.97975e10i			1.02223i	0.859512	+	0.511116i	$0.170768\pi$
$977$			2.97975e10i			1.02223i	−0.859512	+	0.511116i	$0.829232\pi$
$978$	−3.57721e10			−1.22281
$979$	1.18350e10			0.403116
$980$		−	5.47569e9i		−	0.185844i
$981$		−	4.87080e9i		−	0.164725i
$982$		−	9.78875e9i		−	0.329866i
$983$		−	3.96628e10i		−	1.33182i	−0.746032	−	0.665910i	$-0.768043\pi$
$983$		−	3.96628e10i		−	1.33182i	0.746032	−	0.665910i	$-0.231957\pi$
$984$	−6.56484e9			−0.219655
$985$	−1.61461e10			−0.538321
$986$		−	1.14464e10i		−	0.380278i
$987$	−1.70135e8			−0.00563228
$988$	−1.36235e10	−	2.68150e9i	−0.449407	−	0.0884564i
$989$	1.11675e10			0.367088
$990$			1.70235e10i			0.557604i
$991$	4.71795e10			1.53991			0.769955	−	0.638098i	$-0.220279\pi$
$991$	4.71795e10			1.53991			0.769955	+	0.638098i	$0.220279\pi$
$992$	1.18344e10			0.384907
$993$			1.05559e10i			0.342117i
$994$		−	2.30626e10i		−	0.744827i
$995$		−	1.56905e10i		−	0.504959i
$996$			3.65462e10i			1.17202i
$997$	4.86288e10			1.55403			0.777017	−	0.629480i	$-0.216732\pi$
$997$	4.86288e10			1.55403			0.777017	+	0.629480i	$0.216732\pi$
$998$	−2.50450e10			−0.797562
$999$		−	1.69296e10i		−	0.537240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.c.a.64.7	✓	50
13.12	even	2	inner	91.8.c.a.64.44	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.c.a.64.7	✓	50	1.1	even	1	trivial
91.8.c.a.64.44	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)

\(f(q)\)	\(=\)	\(q-17.7532i q^{2} -30.0870 q^{3} -187.174 q^{4} -248.659i q^{5} +534.138i q^{6} -343.000i q^{7} +1050.53i q^{8} -1281.77 q^{9} +O(q^{10})\)	\(q-17.7532i q^{2} -30.0870 q^{3} -187.174 q^{4} -248.659i q^{5} +534.138i q^{6} -343.000i q^{7} +1050.53i q^{8} -1281.77 q^{9} -4414.48 q^{10} +3008.56i q^{11} +5631.51 q^{12} +(-1529.81 + 7772.27i) q^{13} -6089.33 q^{14} +7481.39i q^{15} -5308.05 q^{16} -19445.0 q^{17} +22755.5i q^{18} -9364.72i q^{19} +46542.6i q^{20} +10319.8i q^{21} +53411.3 q^{22} +40569.3 q^{23} -31607.4i q^{24} +16293.8 q^{25} +(137982. + 27158.9i) q^{26} +104365. q^{27} +64200.8i q^{28} -33157.9 q^{29} +132818. q^{30} -51745.8i q^{31} +228703. i q^{32} -90518.3i q^{33} +345210. i q^{34} -85290.0 q^{35} +239916. q^{36} -162216. i q^{37} -166253. q^{38} +(46027.3 - 233844. i) q^{39} +261224. q^{40} -207700. i q^{41} +183209. q^{42} +275270. q^{43} -563125. i q^{44} +318725. i q^{45} -720233. i q^{46} +16486.2i q^{47} +159703. q^{48} -117649. q^{49} -289266. i q^{50} +585042. q^{51} +(286341. - 1.45477e6i) q^{52} -1.48377e6 q^{53} -1.85281e6i q^{54} +748104. q^{55} +360333. q^{56} +281756. i q^{57} +588657. i q^{58} +720092. i q^{59} -1.40033e6i q^{60} +2.19367e6 q^{61} -918651. q^{62} +439649. i q^{63} +3.38077e6 q^{64} +(1.93264e6 + 380401. i) q^{65} -1.60698e6 q^{66} -2.16177e6i q^{67} +3.63961e6 q^{68} -1.22061e6 q^{69} +1.51417e6i q^{70} +3.78738e6i q^{71} -1.34655e6i q^{72} +5.84204e6i q^{73} -2.87984e6 q^{74} -490230. q^{75} +1.75284e6i q^{76} +1.03193e6 q^{77} +(-4.15147e6 - 817130. i) q^{78} -2.25288e6 q^{79} +1.31989e6i q^{80} -336780. q^{81} -3.68733e6 q^{82} +6.48960e6i q^{83} -1.93161e6i q^{84} +4.83518e6i q^{85} -4.88692e6i q^{86} +997619. q^{87} -3.16059e6 q^{88} -3.93379e6i q^{89} +5.65837e6 q^{90} +(2.66589e6 + 524724. i) q^{91} -7.59354e6 q^{92} +1.55687e6i q^{93} +292683. q^{94} -2.32862e6 q^{95} -6.88097e6i q^{96} +1.25389e7i q^{97} +2.08864e6i q^{98} -3.85629e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 3328 q^{4} + 40514 q^{9}+O(q^{10}) \) 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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