LMFDB - Embedded newform 115.7.d.a.91.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(91,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("115.91");

S:= CuspForms(chi, 7);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.4562196163$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.17
Character	$\chi$	$=$	115.91
Dual form			115.7.d.a.91.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.73099 q^{2} +3.68399 q^{3} -18.6938 q^{4} +55.9017i q^{5} -24.7969 q^{6} -614.798i q^{7} +556.611 q^{8} -715.428 q^{9} +O(q^{10})$	\(q-6.73099 q^{2} +3.68399 q^{3} -18.6938 q^{4} +55.9017i q^{5} -24.7969 q^{6} -614.798i q^{7} +556.611 q^{8} -715.428 q^{9} -376.274i q^{10} +1137.22i q^{11} -68.8679 q^{12} +3080.51 q^{13} +4138.19i q^{14} +205.942i q^{15} -2550.14 q^{16} -5826.83i q^{17} +4815.54 q^{18} +7056.38i q^{19} -1045.02i q^{20} -2264.91i q^{21} -7654.60i q^{22} +(2624.68 - 11880.5i) q^{23} +2050.55 q^{24} -3125.00 q^{25} -20734.9 q^{26} -5321.26 q^{27} +11492.9i q^{28} +9273.26 q^{29} -1386.19i q^{30} -8973.78 q^{31} -18458.2 q^{32} +4189.51i q^{33} +39220.3i q^{34} +34368.2 q^{35} +13374.1 q^{36} +10178.0i q^{37} -47496.4i q^{38} +11348.6 q^{39} +31115.5i q^{40} -123306. q^{41} +15245.1i q^{42} +83455.9i q^{43} -21259.0i q^{44} -39993.7i q^{45} +(-17666.7 + 79967.7i) q^{46} -171824. q^{47} -9394.68 q^{48} -260327. q^{49} +21034.3 q^{50} -21466.0i q^{51} -57586.5 q^{52} -123735. i q^{53} +35817.4 q^{54} -63572.5 q^{55} -342203. i q^{56} +25995.7i q^{57} -62418.2 q^{58} -227043. q^{59} -3849.83i q^{60} +282942. i q^{61} +60402.4 q^{62} +439844. i q^{63} +287450. q^{64} +172206. i q^{65} -28199.5i q^{66} -46370.3i q^{67} +108926. i q^{68} +(9669.31 - 43767.8i) q^{69} -231332. q^{70} +77500.2 q^{71} -398215. q^{72} -583730. q^{73} -68507.9i q^{74} -11512.5 q^{75} -131911. i q^{76} +699159. q^{77} -76387.2 q^{78} -33216.2i q^{79} -142557. i q^{80} +501944. q^{81} +829971. q^{82} -268419. i q^{83} +42339.8i q^{84} +325730. q^{85} -561741. i q^{86} +34162.6 q^{87} +632988. i q^{88} +724119. i q^{89} +269197. i q^{90} -1.89389e6i q^{91} +(-49065.3 + 222093. i) q^{92} -33059.3 q^{93} +1.15654e6 q^{94} -394464. q^{95} -67999.8 q^{96} -719067. i q^{97} +1.75226e6 q^{98} -813598. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) $ 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9	$ 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + 4290 q^{12} - 1440 q^{13} + 65400 q^{16} + 4610 q^{18} + 26600 q^{23} + 14940 q^{24} - 150000 q^{25} + 47594 q^{26} + 16080 q^{27} + 131800 q^{29} - 1392 q^{31} - 225040 q^{32} + 5000 q^{35} + 658786 q^{36} - 236320 q^{39} - 351496 q^{41} + 382692 q^{46} + 395680 q^{47} + 1042550 q^{48} - 637848 q^{49} + 62500 q^{50} + 523890 q^{52} - 241250 q^{54} - 402000 q^{55} - 479130 q^{58} - 466312 q^{59} - 1124330 q^{62} + 837582 q^{64} + 1021060 q^{69} - 396000 q^{70} - 114336 q^{71} - 1960750 q^{72} - 498720 q^{73} + 3610400 q^{77} - 1104610 q^{78} + 972888 q^{81} + 124950 q^{82} - 246000 q^{85} - 2090960 q^{87} + 4913480 q^{92} + 3234320 q^{93} - 5550378 q^{94} - 1664000 q^{95} - 776990 q^{96} + 9993220 q^{98}+O(q^{100}) $ 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9 + 4290 * q^12 - 1440 * q^13 + 65400 * q^16 + 4610 * q^18 + 26600 * q^23 + 14940 * q^24 - 150000 * q^25 + 47594 * q^26 + 16080 * q^27 + 131800 * q^29 - 1392 * q^31 - 225040 * q^32 + 5000 * q^35 + 658786 * q^36 - 236320 * q^39 - 351496 * q^41 + 382692 * q^46 + 395680 * q^47 + 1042550 * q^48 - 637848 * q^49 + 62500 * q^50 + 523890 * q^52 - 241250 * q^54 - 402000 * q^55 - 479130 * q^58 - 466312 * q^59 - 1124330 * q^62 + 837582 * q^64 + 1021060 * q^69 - 396000 * q^70 - 114336 * q^71 - 1960750 * q^72 - 498720 * q^73 + 3610400 * q^77 - 1104610 * q^78 + 972888 * q^81 + 124950 * q^82 - 246000 * q^85 - 2090960 * q^87 + 4913480 * q^92 + 3234320 * q^93 - 5550378 * q^94 - 1664000 * q^95 - 776990 * q^96 + 9993220 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−6.73099			−0.841373			−0.420687	−	0.907206i	$-0.638211\pi$
$2$	−6.73099			−0.841373			−0.420687	+	0.907206i	$0.638211\pi$
$3$	3.68399			0.136444			0.0682221	−	0.997670i	$-0.478267\pi$
$3$	3.68399			0.136444			0.0682221	+	0.997670i	$0.478267\pi$
$4$	−18.6938			−0.292091
$5$			55.9017i			0.447214i
$5$			55.9017i			0.447214i
$6$	−24.7969			−0.114801
$7$		−	614.798i		−	1.79241i	−0.443637	−	0.896206i	$-0.646312\pi$
$7$		−	614.798i		−	1.79241i	0.443637	−	0.896206i	$-0.353688\pi$
$8$	556.611			1.08713
$9$	−715.428			−0.981383
$10$		−	376.274i		−	0.376274i
$11$			1137.22i			0.854409i	0.904155	+	0.427205i	$0.140502\pi$
$11$			1137.22i			0.854409i	−0.904155	+	0.427205i	$0.859498\pi$
$12$	−68.8679			−0.0398541
$13$	3080.51			1.40214			0.701072	−	0.713090i	$-0.252705\pi$
$13$	3080.51			1.40214			0.701072	+	0.713090i	$0.252705\pi$
$14$			4138.19i			1.50809i
$15$			205.942i			0.0610197i
$16$	−2550.14			−0.622592
$17$		−	5826.83i		−	1.18600i	−0.805201	−	0.593001i	$-0.797943\pi$
$17$		−	5826.83i		−	1.18600i	0.805201	−	0.593001i	$-0.202057\pi$
$18$	4815.54			0.825709
$19$			7056.38i			1.02878i	0.857557	+	0.514389i	$0.171981\pi$
$19$			7056.38i			1.02878i	−0.857557	+	0.514389i	$0.828019\pi$
$20$		−	1045.02i		−	0.130627i
$21$		−	2264.91i		−	0.244564i
$22$		−	7654.60i		−	0.718877i
$23$	2624.68	−	11880.5i	0.215721	−	0.976455i
$23$	2624.68	−	11880.5i	0.215721	−	0.976455i
$24$	2050.55			0.148333
$25$	−3125.00			−0.200000
$26$	−20734.9			−1.17973
$27$	−5321.26			−0.270348
$28$			11492.9i			0.523548i
$29$	9273.26			0.380223			0.190111	−	0.981763i	$-0.439115\pi$
$29$	9273.26			0.380223			0.190111	+	0.981763i	$0.439115\pi$
$30$		−	1386.19i		−	0.0513403i
$31$	−8973.78			−0.301225			−0.150612	−	0.988593i	$-0.548125\pi$
$31$	−8973.78			−0.301225			−0.150612	+	0.988593i	$0.548125\pi$
$32$	−18458.2			−0.563299
$33$			4189.51i			0.116579i
$34$			39220.3i			0.997871i
$35$	34368.2			0.801591
$36$	13374.1			0.286653
$37$			10178.0i			0.200935i	0.994940	+	0.100468i	$0.0320339\pi$
$37$			10178.0i			0.200935i	−0.994940	+	0.100468i	$0.967966\pi$
$38$		−	47496.4i		−	0.865586i
$39$	11348.6			0.191314
$40$			31115.5i			0.486180i
$41$	−123306.			−1.78909			−0.894546	−	0.446976i	$-0.852501\pi$
$41$	−123306.			−1.78909			−0.894546	+	0.446976i	$0.852501\pi$
$42$			15245.1i			0.205770i
$43$			83455.9i			1.04967i	0.851205	+	0.524834i	$0.175873\pi$
$43$			83455.9i			1.04967i	−0.851205	+	0.524834i	$0.824127\pi$
$44$		−	21259.0i		−	0.249565i
$45$		−	39993.7i		−	0.438888i
$46$	−17666.7	+	79967.7i	−0.181502	+	0.821563i
$47$	−171824.			−1.65497			−0.827484	−	0.561489i	$-0.810229\pi$
$47$	−171824.			−1.65497			−0.827484	+	0.561489i	$0.810229\pi$
$48$	−9394.68			−0.0849490
$49$	−260327.			−2.21274
$50$	21034.3			0.168275
$51$		−	21466.0i		−	0.161823i
$52$	−57586.5			−0.409554
$53$		−	123735.i		−	0.831122i	−0.909565	−	0.415561i	$-0.863585\pi$
$53$		−	123735.i		−	0.831122i	0.909565	−	0.415561i	$-0.136415\pi$
$54$	35817.4			0.227464
$55$	−63572.5			−0.382103
$56$		−	342203.i		−	1.94859i
$57$			25995.7i			0.140371i
$58$	−62418.2			−0.319909
$59$	−227043.			−1.10548			−0.552740	−	0.833353i	$-0.686418\pi$
$59$	−227043.			−1.10548			−0.552740	+	0.833353i	$0.686418\pi$
$60$		−	3849.83i		−	0.0178233i
$61$			282942.i			1.24655i	0.782004	+	0.623273i	$0.214197\pi$
$61$			282942.i			1.24655i	−0.782004	+	0.623273i	$0.785803\pi$
$62$	60402.4			0.253442
$63$			439844.i			1.75904i
$64$	287450.			1.09654
$65$			172206.i			0.627058i
$66$		−	28199.5i		−	0.0980866i
$67$		−	46370.3i		−	0.154176i	−0.997024	−	0.0770878i	$-0.975438\pi$
$67$		−	46370.3i		−	0.154176i	0.997024	−	0.0770878i	$-0.0245622\pi$
$68$			108926.i			0.346421i
$69$	9669.31	−	43767.8i	0.0294339	−	0.133232i
$70$	−231332.			−0.674438
$71$	77500.2			0.216535			0.108267	−	0.994122i	$-0.465470\pi$
$71$	77500.2			0.216535			0.108267	+	0.994122i	$0.465470\pi$
$72$	−398215.			−1.06689
$73$	−583730.			−1.50053			−0.750263	−	0.661140i	$-0.770073\pi$
$73$	−583730.			−1.50053			−0.750263	+	0.661140i	$0.770073\pi$
$74$		−	68507.9i		−	0.169062i
$75$	−11512.5			−0.0272888
$76$		−	131911.i		−	0.300497i
$77$	699159.			1.53145
$78$	−76387.2			−0.160967
$79$		−	33216.2i		−	0.0673704i	−0.999432	−	0.0336852i	$-0.989276\pi$
$79$		−	33216.2i		−	0.0673704i	0.999432	−	0.0336852i	$-0.0107244\pi$
$80$		−	142557.i		−	0.278432i
$81$	501944.			0.944496
$82$	829971.			1.50529
$83$		−	268419.i		−	0.469438i	−0.972063	−	0.234719i	$-0.924583\pi$
$83$		−	268419.i		−	0.469438i	0.972063	−	0.234719i	$-0.0754170\pi$
$84$			42339.8i			0.0714350i
$85$	325730.			0.530397
$86$		−	561741.i		−	0.883162i
$87$	34162.6			0.0518792
$88$			632988.i			0.928855i
$89$			724119.i			1.02716i	0.858040	+	0.513582i	$0.171682\pi$
$89$			724119.i			1.02716i	−0.858040	+	0.513582i	$0.828318\pi$
$90$			269197.i			0.369268i
$91$		−	1.89389e6i		−	2.51322i
$92$	−49065.3	+	222093.i	−0.0630103	+	0.285214i
$93$	−33059.3			−0.0411003
$94$	1.15654e6			1.39245
$95$	−394464.			−0.460083
$96$	−67999.8			−0.0768589
$97$		−	719067.i		−	0.787870i	−0.919138	−	0.393935i	$-0.871114\pi$
$97$		−	719067.i		−	0.787870i	0.919138	−	0.393935i	$-0.128886\pi$
$98$	1.75226e6			1.86174
$99$		−	813598.i		−	0.838503i
$100$	58418.2			0.0584182
$101$	63846.3			0.0619686			0.0309843	−	0.999520i	$-0.490136\pi$
$101$	63846.3			0.0619686			0.0309843	+	0.999520i	$0.490136\pi$
$102$			144487.i			0.136154i
$103$		−	434607.i		−	0.397727i	−0.980027	−	0.198863i	$-0.936275\pi$
$103$		−	434607.i		−	0.397727i	0.980027	−	0.198863i	$-0.0637250\pi$
$104$	1.71465e6			1.52431
$105$	126612.			0.109372
$106$			832858.i			0.699284i
$107$		−	851205.i		−	0.694837i	−0.937710	−	0.347419i	$-0.887058\pi$
$107$		−	851205.i		−	0.694837i	0.937710	−	0.347419i	$-0.112942\pi$
$108$	99474.8			0.0789663
$109$			1.22791e6i			0.948171i	0.880479	+	0.474085i	$0.157221\pi$
$109$			1.22791e6i			0.948171i	−0.880479	+	0.474085i	$0.842779\pi$
$110$	427905.			0.321492
$111$			37495.6i			0.0274165i
$112$			1.56782e6i			1.11594i
$113$			2.48235e6i			1.72039i	0.509963	+	0.860196i	$0.329659\pi$
$113$			2.48235e6i			1.72039i	−0.509963	+	0.860196i	$0.670341\pi$
$114$		−	174976.i		−	0.118104i
$115$	664142.	+	146724.i	0.436684	+	0.0964735i
$116$	−173353.			−0.111060
$117$	−2.20388e6			−1.37604
$118$	1.52822e6			0.930122
$119$	−3.58232e6			−2.12581
$120$			114629.i			0.0663364i
$121$	478295.			0.269985
$122$		−	1.90448e6i		−	1.04881i
$123$	−454259.			−0.244111
$124$	167754.			0.0879850
$125$		−	174693.i		−	0.0894427i
$126$		−	2.96058e6i		−	1.48001i
$127$	1.64333e6			0.802257			0.401129	−	0.916022i	$-0.368618\pi$
$127$	1.64333e6			0.802257			0.401129	+	0.916022i	$0.368618\pi$
$128$	−753502.			−0.359298
$129$			307451.i			0.143221i
$130$		−	1.15911e6i		−	0.527590i
$131$	−4.45076e6			−1.97979			−0.989897	−	0.141790i	$-0.954714\pi$
$131$	−4.45076e6			−1.97979			−0.989897	+	0.141790i	$0.954714\pi$
$132$		−	78317.9i		−	0.0340517i
$133$	4.33825e6			1.84399
$134$			312118.i			0.129719i
$135$		−	297468.i		−	0.120903i
$136$		−	3.24328e6i		−	1.28934i
$137$			1.34744e6i			0.524020i	0.965065	+	0.262010i	$0.0843854\pi$
$137$			1.34744e6i			0.524020i	−0.965065	+	0.262010i	$0.915615\pi$
$138$	−65084.0	+	294600.i	−0.0247649	+	0.112098i
$139$	−545854.			−0.203251			−0.101625	−	0.994823i	$-0.532404\pi$
$139$	−545854.			−0.203251			−0.101625	+	0.994823i	$0.532404\pi$
$140$	−642474.			−0.234138
$141$	−632998.			−0.225811
$142$	−521653.			−0.182187
$143$			3.50321e6i			1.19800i
$144$	1.82444e6			0.611001
$145$			518391.i			0.170041i
$146$	3.92908e6			1.26250
$147$	−959043.			−0.301916
$148$		−	190265.i		−	0.0586914i
$149$		−	2.16644e6i		−	0.654919i	−0.944865	−	0.327459i	$-0.893808\pi$
$149$		−	2.16644e6i		−	0.654919i	0.944865	−	0.327459i	$-0.106192\pi$
$150$	77490.3			0.0229601
$151$	190158.			0.0552311			0.0276156	−	0.999619i	$-0.491209\pi$
$151$	190158.			0.0552311			0.0276156	+	0.999619i	$0.491209\pi$
$152$			3.92766e6i			1.11842i
$153$			4.16868e6i			1.16392i
$154$	−4.70603e6			−1.28852
$155$		−	501650.i		−	0.134712i
$156$	−212148.			−0.0558812
$157$			2.89230e6i			0.747385i	0.927553	+	0.373693i	$0.121909\pi$
$157$			2.89230e6i			0.747385i	−0.927553	+	0.373693i	$0.878091\pi$
$158$			223578.i			0.0566837i
$159$		−	455839.i		−	0.113402i
$160$		−	1.03184e6i		−	0.251915i
$161$	−7.30412e6	−	1.61365e6i	−1.75021	−	0.386662i
$162$	−3.37858e6			−0.794673
$163$	−5.47201e6			−1.26353			−0.631763	−	0.775162i	$-0.717668\pi$
$163$	−5.47201e6			−1.26353			−0.631763	+	0.775162i	$0.717668\pi$
$164$	2.30506e6			0.522578
$165$	−234201.			−0.0521358
$166$			1.80672e6i			0.394973i
$167$	6.78598e6			1.45701			0.728506	−	0.685039i	$-0.240215\pi$
$167$	6.78598e6			1.45701			0.728506	+	0.685039i	$0.240215\pi$
$168$		−	1.26067e6i		−	0.265873i
$169$	4.66274e6			0.966009
$170$	−2.19248e6			−0.446262
$171$		−	5.04834e6i		−	1.00962i
$172$		−	1.56011e6i		−	0.306598i
$173$	−3.19739e6			−0.617528			−0.308764	−	0.951139i	$-0.599915\pi$
$173$	−3.19739e6			−0.617528			−0.308764	+	0.951139i	$0.599915\pi$
$174$	−229948.			−0.0436498
$175$			1.92124e6i			0.358483i
$176$		−	2.90006e6i		−	0.531948i
$177$	−836423.			−0.150836
$178$		−	4.87404e6i		−	0.864229i
$179$	−2.22450e6			−0.387859			−0.193929	−	0.981015i	$-0.562123\pi$
$179$	−2.22450e6			−0.387859			−0.193929	+	0.981015i	$0.562123\pi$
$180$			747634.i			0.128195i
$181$		−	5.51667e6i		−	0.930339i	−0.885222	−	0.465169i	$-0.845993\pi$
$181$		−	5.51667e6i		−	0.930339i	0.885222	−	0.465169i	$-0.154007\pi$
$182$			1.27478e7i			2.11456i
$183$			1.04236e6i			0.170084i
$184$	1.46093e6	−	6.61283e6i	0.234517	−	1.06153i
$185$	−568967.			−0.0898611
$186$	222522.			0.0345807
$187$	6.62638e6			1.01333
$188$	3.21204e6			0.483402
$189$			3.27150e6i			0.484576i
$190$	2.65513e6			0.387102
$191$		−	3.58926e6i		−	0.515115i	−0.966263	−	0.257558i	$-0.917082\pi$
$191$		−	3.58926e6i		−	0.515115i	0.966263	−	0.257558i	$-0.0829177\pi$
$192$	1.05897e6			0.149616
$193$	−1.15474e7			−1.60624			−0.803120	−	0.595817i	$-0.796828\pi$
$193$	−1.15474e7			−1.60624			−0.803120	+	0.595817i	$0.796828\pi$
$194$			4.84003e6i			0.662892i
$195$			634405.i			0.0855584i
$196$	4.86651e6			0.646322
$197$	−4.79424e6			−0.627078			−0.313539	−	0.949575i	$-0.601515\pi$
$197$	−4.79424e6			−0.627078			−0.313539	+	0.949575i	$0.601515\pi$
$198$			5.47632e6i			0.705494i
$199$			6.98314e6i			0.886118i	0.896492	+	0.443059i	$0.146107\pi$
$199$			6.98314e6i			0.886118i	−0.896492	+	0.443059i	$0.853893\pi$
$200$	−1.73941e6			−0.217426
$201$		−	170828.i		−	0.0210364i
$202$	−429748.			−0.0521387
$203$		−	5.70117e6i		−	0.681516i
$204$			401282.i			0.0472671i
$205$		−	6.89302e6i		−	0.800106i
$206$			2.92533e6i			0.334636i
$207$	−1.87777e6	+	8.49966e6i	−0.211705	+	0.958276i
$208$	−7.85572e6			−0.872964
$209$	−8.02465e6			−0.878997
$210$	−852226.			−0.0920231
$211$	2.14933e6			0.228800			0.114400	−	0.993435i	$-0.463505\pi$
$211$	2.14933e6			0.228800			0.114400	+	0.993435i	$0.463505\pi$
$212$			2.31308e6i			0.242763i
$213$	285510.			0.0295449
$214$			5.72945e6i			0.584617i
$215$	−4.66533e6			−0.469426
$216$	−2.96187e6			−0.293904
$217$			5.51706e6i			0.539919i
$218$		−	8.26503e6i		−	0.797765i
$219$	−2.15046e6			−0.204738
$220$	1.18841e6			0.111609
$221$		−	1.79496e7i		−	1.66295i
$222$		−	252383.i		−	0.0230675i
$223$	5.94505e6			0.536094			0.268047	−	0.963406i	$-0.413622\pi$
$223$	5.94505e6			0.536094			0.268047	+	0.963406i	$0.413622\pi$
$224$			1.13480e7i			1.00966i
$225$	2.23571e6			0.196277
$226$		−	1.67087e7i		−	1.44749i
$227$		−	1.02958e7i		−	0.880206i	−0.897947	−	0.440103i	$-0.854942\pi$
$227$		−	1.02958e7i		−	0.880206i	0.897947	−	0.440103i	$-0.145058\pi$
$228$		−	485958.i		−	0.0410010i
$229$			1.83834e7i			1.53080i	0.643555	+	0.765400i	$0.277459\pi$
$229$			1.83834e7i			1.53080i	−0.643555	+	0.765400i	$0.722541\pi$
$230$	−4.47033e6	−	987598.i	−0.367414	−	0.0811702i
$231$	2.57570e6			0.208958
$232$	5.16160e6			0.413352
$233$	−5.71785e6			−0.452028			−0.226014	−	0.974124i	$-0.572569\pi$
$233$	−5.71785e6			−0.452028			−0.226014	+	0.974124i	$0.572569\pi$
$234$	1.48343e7			1.15776
$235$		−	9.60524e6i		−	0.740125i
$236$	4.24429e6			0.322901
$237$		−	122368.i		−	0.00919230i
$238$	2.41126e7			1.78860
$239$	−1.43134e6			−0.104845			−0.0524225	−	0.998625i	$-0.516694\pi$
$239$	−1.43134e6			−0.104845			−0.0524225	+	0.998625i	$0.516694\pi$
$240$		−	525179.i		−	0.0379904i
$241$			4.10248e6i			0.293086i	0.989204	+	0.146543i	$0.0468147\pi$
$241$			4.10248e6i			0.293086i	−0.989204	+	0.146543i	$0.953185\pi$
$242$	−3.21940e6			−0.227158
$243$	5.72836e6			0.399219
$244$		−	5.28927e6i		−	0.364105i
$245$		−	1.45527e7i		−	0.989569i
$246$	3.05761e6			0.205389
$247$			2.17373e7i			1.44249i
$248$	−4.99490e6			−0.327470
$249$		−	988852.i		−	0.0640521i
$250$			1.17585e6i			0.0752547i
$251$			1.57925e7i			0.998686i	0.866404	+	0.499343i	$0.166425\pi$
$251$			1.57925e7i			0.998686i	−0.866404	+	0.499343i	$0.833575\pi$
$252$		−	8.22236e6i		−	0.513801i
$253$	1.35108e7	+	2.98484e6i	0.834292	+	0.184314i
$254$	−1.10612e7			−0.674998
$255$	1.19999e6			0.0723695
$256$	−1.33250e7			−0.794233
$257$	−3.17020e7			−1.86762			−0.933808	−	0.357774i	$-0.883536\pi$
$257$	−3.17020e7			−1.86762			−0.933808	+	0.357774i	$0.883536\pi$
$258$		−	2.06945e6i		−	0.120502i
$259$	6.25740e6			0.360159
$260$		−	3.21919e6i		−	0.183158i
$261$	−6.63435e6			−0.373144
$262$	2.99580e7			1.66575
$263$		−	1.31506e7i		−	0.722898i	−0.932392	−	0.361449i	$-0.882282\pi$
$263$		−	1.31506e7i		−	0.722898i	0.932392	−	0.361449i	$-0.117718\pi$
$264$			2.33193e6i			0.126737i
$265$	6.91700e6			0.371689
$266$	−2.92007e7			−1.55149
$267$			2.66765e6i			0.140151i
$268$			866838.i			0.0450333i
$269$	2.96438e7			1.52292			0.761460	−	0.648212i	$-0.224483\pi$
$269$	2.96438e7			1.52292			0.761460	+	0.648212i	$0.224483\pi$
$270$			2.00225e6i			0.101725i
$271$	−7.03193e6			−0.353319			−0.176659	−	0.984272i	$-0.556529\pi$
$271$	−7.03193e6			−0.353319			−0.176659	+	0.984272i	$0.556529\pi$
$272$			1.48592e7i			0.738396i
$273$		−	6.97708e6i		−	0.342914i
$274$		−	9.06961e6i		−	0.440897i
$275$		−	3.55381e6i		−	0.170882i
$276$	−180756.	+	818187.i	−0.00859739	+	0.0389158i
$277$	3.64930e7			1.71700			0.858501	−	0.512813i	$-0.171396\pi$
$277$	3.64930e7			1.71700			0.858501	+	0.512813i	$0.171396\pi$
$278$	3.67414e6			0.171010
$279$	6.42010e6			0.295617
$280$	1.91297e7			0.871435
$281$			4.70662e6i			0.212124i	0.994360	+	0.106062i	$0.0338242\pi$
$281$			4.70662e6i			0.212124i	−0.994360	+	0.106062i	$0.966176\pi$
$282$	4.26070e6			0.189991
$283$			6.85429e6i			0.302415i	0.988502	+	0.151208i	$0.0483162\pi$
$283$			6.85429e6i			0.302415i	−0.988502	+	0.151208i	$0.951684\pi$
$284$	−1.44878e6			−0.0632479
$285$	−1.45320e6			−0.0627757
$286$		−	2.35801e7i		−	1.00797i
$287$			7.58082e7i			3.20679i
$288$	1.32055e7			0.552812
$289$	−9.81440e6			−0.406603
$290$		−	3.48928e6i		−	0.143068i
$291$		−	2.64904e6i		−	0.107500i
$292$	1.09121e7			0.438290
$293$		−	3.44219e7i		−	1.36846i	−0.729266	−	0.684231i	$-0.760138\pi$
$293$		−	3.44219e7i		−	1.36846i	0.729266	−	0.684231i	$-0.239862\pi$
$294$	6.45531e6			0.254024
$295$		−	1.26921e7i		−	0.494386i
$296$			5.66518e6i			0.218443i
$297$		−	6.05144e6i		−	0.230988i
$298$			1.45823e7i			0.551031i
$299$	8.08536e6	−	3.65981e7i	0.302472	−	1.36913i
$300$	215212.			0.00797083
$301$	5.13085e7			1.88144
$302$	−1.27995e6			−0.0464700
$303$	235209.			0.00845525
$304$		−	1.79947e7i		−	0.640508i
$305$	−1.58170e7			−0.557472
$306$		−	2.80593e7i		−	0.979294i
$307$	−9.53770e6			−0.329631			−0.164816	−	0.986324i	$-0.552703\pi$
$307$	−9.53770e6			−0.329631			−0.164816	+	0.986324i	$0.552703\pi$
$308$	−1.30700e7			−0.447324
$309$		−	1.60109e6i		−	0.0542675i
$310$			3.37660e6i			0.113343i
$311$	3.83309e6			0.127429			0.0637145	−	0.997968i	$-0.479705\pi$
$311$	3.83309e6			0.127429			0.0637145	+	0.997968i	$0.479705\pi$
$312$	6.31675e6			0.207984
$313$		−	4.38613e7i		−	1.43037i	−0.698936	−	0.715184i	$-0.746343\pi$
$313$		−	4.38613e7i		−	1.43037i	0.698936	−	0.715184i	$-0.253657\pi$
$314$		−	1.94680e7i		−	0.628830i
$315$	−2.45880e7			−0.786668
$316$			620939.i			0.0196783i
$317$	−3.90522e7			−1.22594			−0.612969	−	0.790107i	$-0.710025\pi$
$317$	−3.90522e7			−1.22594			−0.612969	+	0.790107i	$0.710025\pi$
$318$			3.06825e6i			0.0954133i
$319$			1.05457e7i			0.324866i
$320$			1.60690e7i			0.490386i
$321$		−	3.13583e6i		−	0.0948065i
$322$	4.91639e7	+	1.08614e7i	1.47258	+	0.325327i
$323$	4.11164e7			1.22013
$324$	−9.38325e6			−0.275879
$325$	−9.62660e6			−0.280429
$326$	3.68320e7			1.06310
$327$			4.52361e6i			0.129372i
$328$	−6.86335e7			−1.94498
$329$			1.05637e8i			2.96639i
$330$	1.57640e6			0.0438657
$331$	9.03304e6			0.249086			0.124543	−	0.992214i	$-0.460253\pi$
$331$	9.03304e6			0.249086			0.124543	+	0.992214i	$0.460253\pi$
$332$			5.01777e6i			0.137119i
$333$		−	7.28162e6i		−	0.197195i
$334$	−4.56763e7			−1.22589
$335$	2.59218e6			0.0689494
$336$			5.77583e6i			0.152264i
$337$		−	6.87681e7i		−	1.79679i	−0.439188	−	0.898395i	$-0.644734\pi$
$337$		−	6.87681e7i		−	1.79679i	0.439188	−	0.898395i	$-0.355266\pi$
$338$	−3.13848e7			−0.812774
$339$			9.14496e6i			0.234738i
$340$	−6.08914e6			−0.154924
$341$		−	1.02051e7i		−	0.257369i
$342$			3.39803e7i			0.849471i
$343$			8.77181e7i			2.17374i
$344$			4.64525e7i			1.14113i
$345$	2.44669e6	+	540531.i	0.0595830	+	0.0131633i
$346$	2.15216e7			0.519572
$347$	−4.42361e7			−1.05874			−0.529369	−	0.848392i	$-0.677571\pi$
$347$	−4.42361e7			−1.05874			−0.529369	+	0.848392i	$0.677571\pi$
$348$	−638630.			−0.0151535
$349$	−3.91763e7			−0.921609			−0.460804	−	0.887502i	$-0.652439\pi$
$349$	−3.91763e7			−0.921609			−0.460804	+	0.887502i	$0.652439\pi$
$350$		−	1.29319e7i		−	0.301618i
$351$	−1.63922e7			−0.379067
$352$		−	2.09910e7i		−	0.481288i
$353$	−6.80059e7			−1.54605			−0.773023	−	0.634378i	$-0.781256\pi$
$353$	−6.80059e7			−1.54605			−0.773023	+	0.634378i	$0.781256\pi$
$354$	5.62995e6			0.126910
$355$			4.33240e6i			0.0968374i
$356$		−	1.35366e7i		−	0.300026i
$357$	−1.31973e7			−0.290054
$358$	1.49731e7			0.326334
$359$		−	3.57516e7i		−	0.772702i	−0.922352	−	0.386351i	$-0.873735\pi$
$359$		−	3.57516e7i		−	0.772702i	0.922352	−	0.386351i	$-0.126265\pi$
$360$		−	2.22609e7i		−	0.477128i
$361$	−2.74665e6			−0.0583825
$362$			3.71326e7i			0.782762i
$363$	1.76204e6			0.0368379
$364$			3.54041e7i			0.734089i
$365$		−	3.26315e7i		−	0.671055i
$366$		−	7.01609e6i		−	0.143104i
$367$		−	5.97233e7i		−	1.20822i	−0.796901	−	0.604110i	$-0.793529\pi$
$367$		−	5.97233e7i		−	1.20822i	0.796901	−	0.604110i	$-0.206471\pi$
$368$	−6.69329e6	+	3.02970e7i	−0.134306	+	0.607933i
$369$	8.82166e7			1.75578
$370$	3.82971e6			0.0756067
$371$	−7.60720e7			−1.48971
$372$	618006.			0.0120050
$373$			6.99150e7i			1.34724i	0.739079	+	0.673619i	$0.235261\pi$
$373$			6.99150e7i			1.34724i	−0.739079	+	0.673619i	$0.764739\pi$
$374$	−4.46021e7			−0.852590
$375$		−	643567.i		−	0.0122039i
$376$	−9.56390e7			−1.79917
$377$	2.85664e7			0.533127
$378$		−	2.20204e7i		−	0.407709i
$379$		−	4.12864e7i		−	0.758384i	−0.925318	−	0.379192i	$-0.876202\pi$
$379$		−	4.12864e7i		−	0.758384i	0.925318	−	0.379192i	$-0.123798\pi$
$380$	7.37404e6			0.134386
$381$	6.05402e6			0.109463
$382$			2.41592e7i			0.433404i
$383$		−	7.36748e7i		−	1.31136i	−0.755038	−	0.655681i	$-0.772381\pi$
$383$		−	7.36748e7i		−	1.31136i	0.755038	−	0.655681i	$-0.227619\pi$
$384$	−2.77590e6			−0.0490241
$385$			3.90842e7i			0.684887i
$386$	7.77251e7			1.35145
$387$		−	5.97067e7i		−	1.03013i
$388$			1.34421e7i			0.230130i
$389$		−	2.05467e7i		−	0.349055i	−0.984652	−	0.174528i	$-0.944160\pi$
$389$		−	2.05467e7i		−	0.349055i	0.984652	−	0.174528i	$-0.0558398\pi$
$390$		−	4.27017e6i		−	0.0719866i
$391$	−6.92258e7	−	1.52936e7i	−1.15808	−	0.255846i
$392$	−1.44901e8			−2.40554
$393$	−1.63966e7			−0.270131
$394$	3.22700e7			0.527606
$395$	1.85684e6			0.0301290
$396$			1.52093e7i			0.244919i
$397$	−1.79681e7			−0.287164			−0.143582	−	0.989638i	$-0.545862\pi$
$397$	−1.79681e7			−0.287164			−0.143582	+	0.989638i	$0.545862\pi$
$398$		−	4.70034e7i		−	0.745556i
$399$	1.59821e7			0.251602
$400$	7.96918e6			0.124518
$401$			2.43718e7i			0.377968i	0.981980	+	0.188984i	$0.0605194\pi$
$401$			2.43718e7i			0.377968i	−0.981980	+	0.188984i	$0.939481\pi$
$402$			1.14984e6i			0.0176994i
$403$	−2.76438e7			−0.422360
$404$	−1.19353e6			−0.0181005
$405$			2.80595e7i			0.422391i
$406$			3.83745e7i			0.573410i
$407$	−1.15746e7			−0.171681
$408$		−	1.19482e7i		−	0.175923i
$409$	−1.13727e8			−1.66224			−0.831122	−	0.556090i	$-0.812301\pi$
$409$	−1.13727e8			−1.66224			−0.831122	+	0.556090i	$0.812301\pi$
$410$			4.63968e7i			0.673188i
$411$			4.96397e6i			0.0714995i
$412$			8.12446e6i			0.116172i
$413$			1.39585e8i			1.98148i
$414$	1.26393e7	−	5.72111e7i	0.178123	−	0.806268i
$415$	1.50051e7			0.209939
$416$	−5.68606e7			−0.789826
$417$	−2.01092e6			−0.0277324
$418$	5.40138e7			0.739564
$419$		−	3.25473e7i		−	0.442459i	−0.975222	−	0.221229i	$-0.928993\pi$
$419$		−	3.25473e7i		−	0.442459i	0.975222	−	0.221229i	$-0.0710069\pi$
$420$	−2.36687e6			−0.0319467
$421$		−	9.07526e6i		−	0.121622i	−0.998149	−	0.0608111i	$-0.980631\pi$
$421$		−	9.07526e6i		−	0.121622i	0.998149	−	0.0608111i	$-0.0193687\pi$
$422$	−1.44671e7			−0.192506
$423$	1.22928e8			1.62416
$424$		−	6.88722e7i		−	0.903539i
$425$			1.82089e7i			0.237201i
$426$	−1.92177e6			−0.0248583
$427$	1.73952e8			2.23433
$428$			1.59123e7i			0.202956i
$429$			1.29058e7i			0.163461i
$430$	3.14023e7			0.394962
$431$			7.24002e7i			0.904291i	0.891944	+	0.452145i	$0.149341\pi$
$431$			7.24002e7i			0.904291i	−0.891944	+	0.452145i	$0.850659\pi$
$432$	1.35699e7			0.168317
$433$			1.40514e8i			1.73084i	0.501050	+	0.865418i	$0.332947\pi$
$433$			1.40514e8i			1.73084i	−0.501050	+	0.865418i	$0.667053\pi$
$434$		−	3.71352e7i		−	0.454273i
$435$			1.90975e6i			0.0232011i
$436$		−	2.29543e7i		−	0.276952i
$437$	8.38335e7	+	1.85208e7i	1.00455	+	0.221929i
$438$	1.44747e7			0.172261
$439$	8.74700e7			1.03387			0.516934	−	0.856025i	$-0.327073\pi$
$439$	8.74700e7			1.03387			0.516934	+	0.856025i	$0.327073\pi$
$440$	−3.53851e7			−0.415396
$441$	1.86245e8			2.17155
$442$			1.20819e8i			1.39916i
$443$	1.00617e8			1.15734			0.578671	−	0.815561i	$-0.303572\pi$
$443$	1.00617e8			1.15734			0.578671	+	0.815561i	$0.303572\pi$
$444$		−	700937.i		−	0.00800811i
$445$	−4.04795e7			−0.459362
$446$	−4.00160e7			−0.451055
$447$		−	7.98114e6i		−	0.0893599i
$448$		−	1.76724e8i		−	1.96545i
$449$	−2.83088e7			−0.312739			−0.156369	−	0.987699i	$-0.549979\pi$
$449$	−2.83088e7			−0.312739			−0.156369	+	0.987699i	$0.549979\pi$
$450$	−1.50486e7			−0.165142
$451$		−	1.40226e8i		−	1.52862i
$452$		−	4.64046e7i		−	0.502511i
$453$	700541.			0.00753597
$454$			6.93012e7i			0.740582i
$455$	1.05872e8			1.12395
$456$			1.44695e7i			0.152601i
$457$		−	1.59566e8i		−	1.67183i	−0.548861	−	0.835913i	$-0.684938\pi$
$457$		−	1.59566e8i		−	1.67183i	0.548861	−	0.835913i	$-0.315062\pi$
$458$		−	1.23738e8i		−	1.28797i
$459$			3.10061e7i			0.320634i
$460$	−1.24153e7	−	2.74284e6i	−0.127551	−	0.0281790i
$461$	−5.26762e7			−0.537665			−0.268833	−	0.963187i	$-0.586638\pi$
$461$	−5.26762e7			−0.537665			−0.268833	+	0.963187i	$0.586638\pi$
$462$	−1.73370e7			−0.175812
$463$	1.83554e8			1.84936			0.924679	−	0.380748i	$-0.124333\pi$
$463$	1.83554e8			1.84936			0.924679	+	0.380748i	$0.124333\pi$
$464$	−2.36481e7			−0.236724
$465$		−	1.84807e6i		−	0.0183806i
$466$	3.84868e7			0.380324
$467$		−	1.84057e8i		−	1.80718i	−0.428398	−	0.903590i	$-0.640922\pi$
$467$		−	1.84057e8i		−	1.80718i	0.428398	−	0.903590i	$-0.359078\pi$
$468$	4.11990e7			0.401929
$469$	−2.85083e7			−0.276346
$470$			6.46528e7i			0.622721i
$471$			1.06552e7i			0.101976i
$472$	−1.26374e8			−1.20180
$473$	−9.49076e7			−0.896845
$474$			823660.i			0.00773416i
$475$		−	2.20512e7i		−	0.205755i
$476$	6.69673e7			0.620929
$477$			8.85235e7i			0.815649i
$478$	9.63430e6			0.0882138
$479$		−	7.33889e7i		−	0.667765i	−0.942615	−	0.333882i	$-0.891641\pi$
$479$		−	7.33889e7i		−	0.667765i	0.942615	−	0.333882i	$-0.108359\pi$
$480$		−	3.80130e6i		−	0.0343723i
$481$			3.13534e7i			0.281741i
$482$		−	2.76137e7i		−	0.246595i
$483$	−2.69083e7	−	5.94467e6i	−0.238806	−	0.0527577i
$484$	−8.94116e6			−0.0788602
$485$	4.01971e7			0.352346
$486$	−3.85575e7			−0.335892
$487$	−6.51218e7			−0.563819			−0.281910	−	0.959441i	$-0.590968\pi$
$487$	−6.51218e7			−0.563819			−0.281910	+	0.959441i	$0.590968\pi$
$488$			1.57489e8i			1.35516i
$489$	−2.01588e7			−0.172401
$490$			9.79542e7i			0.832597i
$491$	1.01474e8			0.857256			0.428628	−	0.903481i	$-0.358997\pi$
$491$	1.01474e8			0.857256			0.428628	+	0.903481i	$0.358997\pi$
$492$	8.49183e6			0.0713027
$493$		−	5.40337e7i		−	0.450945i
$494$		−	1.46313e8i		−	1.21368i
$495$	4.54815e7			0.374990
$496$	2.28844e7			0.187540
$497$		−	4.76470e7i		−	0.388120i
$498$			6.65595e6i			0.0538917i
$499$	7.44524e7			0.599208			0.299604	−	0.954064i	$-0.403146\pi$
$499$	7.44524e7			0.599208			0.299604	+	0.954064i	$0.403146\pi$
$500$			3.26568e6i			0.0261254i
$501$	2.49995e7			0.198801
$502$		−	1.06299e8i		−	0.840268i
$503$			1.73996e8i			1.36721i	0.729851	+	0.683606i	$0.239589\pi$
$503$			1.73996e8i			1.36721i	−0.729851	+	0.683606i	$0.760411\pi$
$504$			2.44822e8i			1.91231i
$505$			3.56912e6i			0.0277132i
$506$	−9.09407e7	−	2.00909e7i	−0.701951	−	0.155077i
$507$	1.71775e7			0.131806
$508$	−3.07201e7			−0.234332
$509$	9.87261e7			0.748650			0.374325	−	0.927298i	$-0.377874\pi$
$509$	9.87261e7			0.748650			0.374325	+	0.927298i	$0.377874\pi$
$510$	−8.07709e6			−0.0608898
$511$			3.58876e8i			2.68956i
$512$	1.37915e8			1.02754
$513$		−	3.75489e7i		−	0.278128i
$514$	2.13386e8			1.57136
$515$	2.42952e7			0.177869
$516$		−	5.74744e6i		−	0.0418336i
$517$		−	1.95401e8i		−	1.41402i
$518$	−4.21185e7			−0.303028
$519$	−1.17791e7			−0.0842581
$520$			9.58516e7i			0.681694i
$521$		−	8.98035e7i		−	0.635009i	−0.948257	−	0.317505i	$-0.897155\pi$
$521$		−	8.98035e7i		−	0.635009i	0.948257	−	0.317505i	$-0.102845\pi$
$522$	4.46557e7			0.313954
$523$		−	1.44419e8i		−	1.00953i	−0.863257	−	0.504765i	$-0.831579\pi$
$523$		−	1.44419e8i		−	1.00953i	0.863257	−	0.504765i	$-0.168421\pi$
$524$	8.32017e7			0.578280
$525$			7.07784e6i			0.0489129i
$526$			8.85163e7i			0.608227i
$527$			5.22887e7i			0.357253i
$528$		−	1.06838e7i		−	0.0725812i
$529$	−1.34258e8	−	6.23652e7i	−0.906929	−	0.421284i
$530$	−4.65582e7			−0.312729
$531$	1.62433e8			1.08490
$532$	−8.10984e7			−0.538614
$533$	−3.79846e8			−2.50857
$534$		−	1.79559e7i		−	0.117919i
$535$	4.75838e7			0.310741
$536$		−	2.58102e7i		−	0.167609i
$537$	−8.19505e6			−0.0529211
$538$	−1.99532e8			−1.28134
$539$		−	2.96049e8i		−	1.89059i
$540$			5.56081e6i			0.0353148i
$541$	1.87860e8			1.18643			0.593214	−	0.805045i	$-0.297859\pi$
$541$	1.87860e8			1.18643			0.593214	+	0.805045i	$0.297859\pi$
$542$	4.73318e7			0.297273
$543$		−	2.03234e7i		−	0.126939i
$544$			1.07553e8i			0.668074i
$545$	−6.86422e7			−0.424035
$546$			4.69626e7i			0.288519i
$547$	−2.62687e8			−1.60501			−0.802503	−	0.596647i	$-0.796499\pi$
$547$	−2.62687e8			−1.60501			−0.802503	+	0.596647i	$0.796499\pi$
$548$		−	2.51888e7i		−	0.153062i
$549$		−	2.02425e8i		−	1.22334i
$550$			2.39206e7i			0.143775i
$551$			6.54356e7i			0.391165i
$552$	5.38204e6	−	2.43616e7i	0.0319985	−	0.144840i
$553$	−2.04213e7			−0.120756
$554$	−2.45634e8			−1.44464
$555$	−2.09607e6			−0.0122610
$556$	1.02041e7			0.0593677
$557$			1.23998e8i			0.717547i	0.933425	+	0.358774i	$0.116805\pi$
$557$			1.23998e8i			0.717547i	−0.933425	+	0.358774i	$0.883195\pi$
$558$	−4.32136e7			−0.248724
$559$			2.57087e8i			1.47179i
$560$	−8.76437e7			−0.499064
$561$	2.44115e7			0.138263
$562$		−	3.16802e7i		−	0.178475i
$563$			1.81006e8i			1.01430i	0.861857	+	0.507152i	$0.169302\pi$
$563$			1.81006e8i			1.01430i	−0.861857	+	0.507152i	$0.830698\pi$
$564$	1.18332e7			0.0659573
$565$	−1.38768e8			−0.769383
$566$		−	4.61362e7i		−	0.254444i
$567$		−	3.08594e8i		−	1.69293i
$568$	4.31375e7			0.235402
$569$			3.67095e8i			1.99270i	0.0853742	+	0.996349i	$0.472791\pi$
$569$			3.67095e8i			1.99270i	−0.0853742	+	0.996349i	$0.527209\pi$
$570$	9.78148e6			0.0528178
$571$			2.60370e8i			1.39857i	0.714845	+	0.699283i	$0.246497\pi$
$571$			2.60370e8i			1.39857i	−0.714845	+	0.699283i	$0.753503\pi$
$572$		−	6.54885e7i		−	0.349926i
$573$		−	1.32228e7i		−	0.0702845i
$574$		−	5.10264e8i		−	2.69811i
$575$	−8.20213e6	+	3.71266e7i	−0.0431443	+	0.195291i
$576$	−2.05650e8			−1.07612
$577$	1.38192e8			0.719377			0.359689	−	0.933072i	$-0.382883\pi$
$577$	1.38192e8			0.719377			0.359689	+	0.933072i	$0.382883\pi$
$578$	6.60606e7			0.342105
$579$	−4.25404e7			−0.219162
$580$		−	9.69071e6i		−	0.0496674i
$581$	−1.65023e8			−0.841427
$582$			1.78306e7i			0.0904478i
$583$	1.40714e8			0.710118
$584$	−3.24910e8			−1.63127
$585$		−	1.23201e8i		−	0.615384i
$586$			2.31694e8i			1.15139i
$587$	3.42395e8			1.69283			0.846415	−	0.532524i	$-0.178756\pi$
$587$	3.42395e8			1.69283			0.846415	+	0.532524i	$0.178756\pi$
$588$	1.79282e7			0.0881870
$589$		−	6.33224e7i		−	0.309893i
$590$			8.54301e7i			0.415963i
$591$	−1.76620e7			−0.0855611
$592$		−	2.59552e7i		−	0.125101i
$593$	6.94822e6			0.0333203			0.0166602	−	0.999861i	$-0.494697\pi$
$593$	6.94822e6			0.0333203			0.0166602	+	0.999861i	$0.494697\pi$
$594$			4.07322e7i			0.194347i
$595$		−	2.00258e8i		−	0.950690i
$596$			4.04990e7i			0.191296i
$597$			2.57259e7i			0.120906i
$598$	−5.44224e7	+	2.46341e8i	−0.254492	+	1.15195i
$599$	−1.16571e8			−0.542386			−0.271193	−	0.962525i	$-0.587418\pi$
$599$	−1.16571e8			−0.542386			−0.271193	+	0.962525i	$0.587418\pi$
$600$	−6.40797e6			−0.0296665
$601$	1.54013e8			0.709470			0.354735	−	0.934967i	$-0.384571\pi$
$601$	1.54013e8			0.709470			0.354735	+	0.934967i	$0.384571\pi$
$602$	−3.45357e8			−1.58299
$603$			3.31746e7i			0.151305i
$604$	−3.55478e6			−0.0161325
$605$			2.67375e7i			0.120741i
$606$	−1.58319e6			−0.00711402
$607$	−8.66118e7			−0.387267			−0.193634	−	0.981074i	$-0.562027\pi$
$607$	−8.66118e7			−0.387267			−0.193634	+	0.981074i	$0.562027\pi$
$608$		−	1.30248e8i		−	0.579509i
$609$		−	2.10031e7i		−	0.0929890i
$610$	1.06464e8			0.469042
$611$	−5.29305e8			−2.32051
$612$		−	7.79286e7i		−	0.339971i
$613$		−	3.84539e8i		−	1.66940i	−0.550708	−	0.834698i	$-0.685642\pi$
$613$		−	3.84539e8i		−	1.66940i	0.550708	−	0.834698i	$-0.314358\pi$
$614$	6.41981e7			0.277343
$615$		−	2.53938e7i		−	0.109170i
$616$	3.89160e8			1.66489
$617$			6.41301e7i			0.273027i	0.990638	+	0.136514i	$0.0435898\pi$
$617$			6.41301e7i			0.273027i	−0.990638	+	0.136514i	$0.956410\pi$
$618$			1.07769e7i			0.0456592i
$619$			2.68331e8i			1.13136i	0.824626	+	0.565678i	$0.191386\pi$
$619$			2.68331e8i			1.13136i	−0.824626	+	0.565678i	$0.808614\pi$
$620$			9.37775e6i			0.0393481i
$621$	−1.39666e7	+	6.32194e7i	−0.0583199	+	0.263983i
$622$	−2.58005e7			−0.107215
$623$	4.45187e8			1.84110
$624$	−2.89404e7			−0.119111
$625$	9.76562e6			0.0400000
$626$			2.95230e8i			1.20347i
$627$	−2.95628e7			−0.119934
$628$		−	5.40682e7i		−	0.218305i
$629$	5.93054e7			0.238310
$630$	1.65501e8			0.661881
$631$		−	3.07692e7i		−	0.122470i	−0.998123	−	0.0612348i	$-0.980496\pi$
$631$		−	3.07692e7i		−	0.122470i	0.998123	−	0.0612348i	$-0.0195038\pi$
$632$		−	1.84885e7i		−	0.0732405i
$633$	7.91811e6			0.0312184
$634$	2.62860e8			1.03147
$635$			9.18649e7i			0.358780i
$636$			8.52137e6i			0.0331237i
$637$	−8.01940e8			−3.10259
$638$		−	7.09831e7i		−	0.273333i
$639$	−5.54459e7			−0.212504
$640$		−	4.21220e7i		−	0.160683i
$641$			3.45736e8i			1.31271i	0.754450	+	0.656357i	$0.227904\pi$
$641$			3.45736e8i			1.31271i	−0.754450	+	0.656357i	$0.772096\pi$
$642$			2.11073e7i			0.0797677i
$643$			3.31853e8i			1.24828i	0.781312	+	0.624141i	$0.214551\pi$
$643$			3.31853e8i			1.24828i	−0.781312	+	0.624141i	$0.785449\pi$
$644$	1.36542e8	+	3.01653e7i	0.511221	+	0.112940i
$645$	−1.71870e7			−0.0640504
$646$	−2.76754e8			−1.02659
$647$	6.78011e7			0.250336			0.125168	−	0.992136i	$-0.460053\pi$
$647$	6.78011e7			0.250336			0.125168	+	0.992136i	$0.460053\pi$
$648$	2.79387e8			1.02679
$649$		−	2.58197e8i		−	0.944533i
$650$	6.47965e7			0.235945
$651$			2.03248e7i			0.0736688i
$652$	1.02293e8			0.369064
$653$	−2.25186e8			−0.808726			−0.404363	−	0.914599i	$-0.632507\pi$
$653$	−2.25186e8			−0.808726			−0.404363	+	0.914599i	$0.632507\pi$
$654$		−	3.04483e7i		−	0.108850i
$655$		−	2.48805e8i		−	0.885391i
$656$	3.14447e8			1.11387
$657$	4.17617e8			1.47259
$658$		−	7.11040e8i		−	2.49584i
$659$		−	2.98768e8i		−	1.04395i	−0.852962	−	0.521973i	$-0.825196\pi$
$659$		−	2.98768e8i		−	1.04395i	0.852962	−	0.521973i	$-0.174804\pi$
$660$	4.37810e6			0.0152284
$661$			2.47990e8i			0.858678i	0.903143	+	0.429339i	$0.141254\pi$
$661$			2.47990e8i			0.858678i	−0.903143	+	0.429339i	$0.858746\pi$
$662$	−6.08012e7			−0.209574
$663$		−	6.61263e7i		−	0.226900i
$664$		−	1.49405e8i		−	0.510341i
$665$			2.42515e8i			0.824659i
$666$			4.90125e7i			0.165914i
$667$	2.43393e7	−	1.10171e8i	0.0820222	−	0.371271i
$668$	−1.26856e8			−0.425580
$669$	2.19015e7			0.0731469
$670$	−1.74479e7			−0.0580122
$671$	−3.21767e8			−1.06506
$672$			4.18061e7i			0.137763i
$673$	−8.58358e7			−0.281594			−0.140797	−	0.990038i	$-0.544966\pi$
$673$	−8.58358e7			−0.281594			−0.140797	+	0.990038i	$0.544966\pi$
$674$			4.62877e8i			1.51177i
$675$	1.66290e7			0.0540696
$676$	−8.71644e7			−0.282162
$677$		−	3.71985e7i		−	0.119884i	−0.998202	−	0.0599418i	$-0.980909\pi$
$677$		−	3.71985e7i		−	0.119884i	0.998202	−	0.0599418i	$-0.0190915\pi$
$678$		−	6.15546e7i		−	0.197502i
$679$	−4.42081e8			−1.41219
$680$	1.81305e8			0.576611
$681$		−	3.79298e7i		−	0.120099i
$682$			6.86907e7i			0.216543i
$683$	1.56757e8			0.492000			0.246000	−	0.969270i	$-0.420884\pi$
$683$	1.56757e8			0.492000			0.246000	+	0.969270i	$0.420884\pi$
$684$			9.43727e7i			0.294902i
$685$	−7.53243e7			−0.234349
$686$		−	5.90429e8i		−	1.82892i
$687$			6.77242e7i			0.208869i
$688$		−	2.12824e8i		−	0.653514i
$689$		−	3.81167e8i		−	1.16535i
$690$	−1.64687e7	−	3.63831e6i	−0.0501315	−	0.0110752i
$691$	2.41353e8			0.731507			0.365753	−	0.930712i	$-0.380811\pi$
$691$	2.41353e8			0.731507			0.365753	+	0.930712i	$0.380811\pi$
$692$	5.97714e7			0.180374
$693$	−5.00198e8			−1.50294
$694$	2.97752e8			0.890793
$695$		−	3.05142e7i		−	0.0908965i
$696$	1.90153e7			0.0563995
$697$			7.18484e8i			2.12187i
$698$	2.63695e8			0.775417
$699$	−2.10645e7			−0.0616766
$700$		−	3.59154e7i		−	0.104710i
$701$			7.73141e7i			0.224442i	0.993683	+	0.112221i	$0.0357965\pi$
$701$			7.73141e7i			0.224442i	−0.993683	+	0.112221i	$0.964203\pi$
$702$	1.10336e8			0.318937
$703$	−7.18198e7			−0.206718
$704$			3.26894e8i			0.936891i
$705$		−	3.53857e7i		−	0.100986i
$706$	4.57746e8			1.30080
$707$		−	3.92525e7i		−	0.111073i
$708$	1.56360e7			0.0440580
$709$			5.56367e7i			0.156107i	0.996949	+	0.0780535i	$0.0248705\pi$
$709$			5.56367e7i			0.156107i	−0.996949	+	0.0780535i	$0.975130\pi$
$710$		−	2.91613e7i		−	0.0814764i
$711$			2.37638e7i			0.0661162i
$712$			4.03053e8i			1.11666i
$713$	−2.35533e7	+	1.06613e8i	−0.0649806	+	0.294132i
$714$	8.88305e7			0.244044
$715$	−1.95836e8			−0.535764
$716$	4.15845e7			0.113290
$717$	−5.27303e6			−0.0143055
$718$			2.40643e8i			0.650130i
$719$	4.23247e8			1.13869			0.569347	−	0.822097i	$-0.307196\pi$
$719$	4.23247e8			1.13869			0.569347	+	0.822097i	$0.307196\pi$
$720$			1.01989e8i			0.273248i
$721$	−2.67195e8			−0.712890
$722$	1.84877e7			0.0491214
$723$			1.51135e7i			0.0399899i
$724$			1.03128e8i			0.271744i
$725$	−2.89789e7			−0.0760446
$726$	−1.18602e7			−0.0309944
$727$		−	3.83180e8i		−	0.997240i	−0.866821	−	0.498620i	$-0.833840\pi$
$727$		−	3.83180e8i		−	0.997240i	0.866821	−	0.498620i	$-0.166160\pi$
$728$		−	1.05416e9i		−	2.73220i
$729$	−3.44814e8			−0.890024
$730$			2.19642e8i			0.564608i
$731$	4.86284e8			1.24491
$732$		−	1.94857e7i		−	0.0496800i
$733$			2.93629e8i			0.745568i	0.927918	+	0.372784i	$0.121597\pi$
$733$			2.93629e8i			0.745568i	−0.927918	+	0.372784i	$0.878403\pi$
$734$			4.01997e8i			1.01656i
$735$		−	5.36121e7i		−	0.135021i
$736$	−4.84468e7	+	2.19293e8i	−0.121516	+	0.550036i
$737$	5.27332e7			0.131729
$738$	−5.93785e8			−1.47727
$739$	4.63263e8			1.14787			0.573937	−	0.818899i	$-0.305415\pi$
$739$	4.63263e8			1.14787			0.573937	+	0.818899i	$0.305415\pi$
$740$	1.06362e7			0.0262476
$741$			8.00799e7i			0.196820i
$742$	5.12039e8			1.25341
$743$		−	9.13264e7i		−	0.222654i	−0.993784	−	0.111327i	$-0.964490\pi$
$743$		−	9.13264e7i		−	0.222654i	0.993784	−	0.111327i	$-0.0355100\pi$
$744$	−1.84012e7			−0.0446815
$745$	1.21108e8			0.292889
$746$		−	4.70597e8i		−	1.13353i
$747$			1.92034e8i			0.460699i
$748$	−1.23872e8			−0.295985
$749$	−5.23319e8			−1.24543
$750$			4.33184e6i			0.0102681i
$751$		−	5.18085e8i		−	1.22315i	−0.791185	−	0.611577i	$-0.790535\pi$
$751$		−	5.18085e8i		−	1.22315i	0.791185	−	0.611577i	$-0.209465\pi$
$752$	4.38174e8			1.03037
$753$			5.81794e7i			0.136265i
$754$	−1.92280e8			−0.448559
$755$			1.06302e7i			0.0247001i
$756$		−	6.11569e7i		−	0.141540i
$757$		−	7.58017e8i		−	1.74740i	−0.486469	−	0.873698i	$-0.661715\pi$
$757$		−	7.58017e8i		−	1.74740i	0.486469	−	0.873698i	$-0.338285\pi$
$758$			2.77898e8i			0.638084i
$759$	4.97735e7	+	1.09961e7i	0.113834	+	0.0251486i
$760$	−2.19563e8			−0.500171
$761$	−6.81646e8			−1.54670			−0.773348	−	0.633982i	$-0.781419\pi$
$761$	−6.81646e8			−1.54670			−0.773348	+	0.633982i	$0.781419\pi$
$762$	−4.07495e7			−0.0920995
$763$	7.54915e8			1.69951
$764$			6.70969e7i			0.150461i
$765$	−2.33036e8			−0.520522
$766$			4.95904e8i			1.10335i
$767$	−6.99407e8			−1.55004
$768$	−4.90893e7			−0.108368
$769$		−	5.34615e8i		−	1.17561i	−0.809003	−	0.587804i	$-0.799993\pi$
$769$		−	5.34615e8i		−	1.17561i	0.809003	−	0.587804i	$-0.200007\pi$
$770$		−	2.63075e8i		−	0.576246i
$771$	−1.16790e8			−0.254825
$772$	2.15864e8			0.469169
$773$		−	2.71048e7i		−	0.0586825i	−0.999569	−	0.0293412i	$-0.990659\pi$
$773$		−	2.71048e7i		−	0.0586825i	0.999569	−	0.0293412i	$-0.00934094\pi$
$774$			4.01885e8i			0.866720i
$775$	2.80431e7			0.0602449
$776$		−	4.00241e8i		−	0.856517i
$777$	2.30522e7			0.0491416
$778$			1.38300e8i			0.293686i
$779$		−	8.70095e8i		−	1.84058i
$780$		−	1.18595e7i		−	0.0249909i
$781$			8.81347e7i			0.185009i
$782$	4.65958e8	+	1.02941e8i	0.974376	+	0.215262i
$783$	−4.93454e7			−0.102793
$784$	6.63869e8			1.37764
$785$	−1.61685e8			−0.334241
$786$	1.10365e8			0.227281
$787$			6.75542e8i			1.38589i	0.720992	+	0.692944i	$0.243687\pi$
$787$			6.75542e8i			1.38589i	−0.720992	+	0.692944i	$0.756313\pi$
$788$	8.96227e7			0.183164
$789$		−	4.84466e7i		−	0.0986353i
$790$	−1.24984e7			−0.0253497
$791$	1.52614e9			3.08365
$792$		−	4.52858e8i		−	0.911562i
$793$			8.71607e8i			1.74784i
$794$	1.20943e8			0.241612
$795$	2.54822e7			0.0507148
$796$		−	1.30542e8i		−	0.258827i
$797$			5.66233e8i			1.11846i	0.829013	+	0.559230i	$0.188903\pi$
$797$			5.66233e8i			1.11846i	−0.829013	+	0.559230i	$0.811097\pi$
$798$	−1.07575e8			−0.211691
$799$			1.00119e9i			1.96280i
$800$	5.76818e7			0.112660
$801$		−	5.18055e8i		−	1.00804i
$802$		−	1.64046e8i		−	0.318012i
$803$		−	6.63828e8i		−	1.28206i
$804$			3.19343e6i			0.00614453i
$805$	9.02057e7	−	4.08313e8i	0.172920	−	0.782718i
$806$	1.86070e8			0.355363
$807$	1.09208e8			0.207794
$808$	3.55375e7			0.0673679
$809$	−1.88073e8			−0.355207			−0.177604	−	0.984102i	$-0.556834\pi$
$809$	−1.88073e8			−0.355207			−0.177604	+	0.984102i	$0.556834\pi$
$810$		−	1.88868e8i		−	0.355389i
$811$	−4.39831e8			−0.824562			−0.412281	−	0.911057i	$-0.635268\pi$
$811$	−4.39831e8			−0.824562			−0.412281	+	0.911057i	$0.635268\pi$
$812$			1.06577e8i			0.199065i
$813$	−2.59056e7			−0.0482083
$814$	7.79084e7			0.144448
$815$		−	3.05895e8i		−	0.565066i
$816$			5.47413e7i			0.100750i
$817$	−5.88897e8			−1.07987
$818$	7.65497e8			1.39857
$819$			1.35494e9i			2.46643i
$820$			1.28857e8i			0.233704i
$821$	−4.87774e7			−0.0881433			−0.0440716	−	0.999028i	$-0.514033\pi$
$821$	−4.87774e7			−0.0881433			−0.0440716	+	0.999028i	$0.514033\pi$
$822$		−	3.34124e7i		−	0.0601578i
$823$	−5.55307e8			−0.996170			−0.498085	−	0.867128i	$-0.665963\pi$
$823$	−5.55307e8			−0.996170			−0.498085	+	0.867128i	$0.665963\pi$
$824$		−	2.41907e8i		−	0.432381i
$825$		−	1.30922e7i		−	0.0233158i
$826$		−	9.39546e8i		−	1.66716i
$827$			2.49373e8i			0.440892i	0.975399	+	0.220446i	$0.0707513\pi$
$827$			2.49373e8i			0.440892i	−0.975399	+	0.220446i	$0.929249\pi$
$828$	3.51027e7	−	1.58891e8i	0.0618372	−	0.279904i
$829$	1.06683e9			1.87254			0.936269	−	0.351284i	$-0.114255\pi$
$829$	1.06683e9			1.87254			0.936269	+	0.351284i	$0.114255\pi$
$830$	−1.00999e8			−0.176637
$831$	1.34440e8			0.234275
$832$	8.85494e8			1.53750
$833$			1.51688e9i			2.62432i
$834$	1.35355e7			0.0233333
$835$			3.79348e8i			0.651596i
$836$	1.50011e8			0.256747
$837$	4.77519e7			0.0814355
$838$			2.19075e8i			0.372273i
$839$		−	1.10471e9i		−	1.87051i	−0.353970	−	0.935257i	$-0.615169\pi$
$839$		−	1.10471e9i		−	1.87051i	0.353970	−	0.935257i	$-0.384831\pi$
$840$	7.04738e7			0.118902
$841$	−5.08830e8			−0.855431
$842$			6.10855e7i			0.102330i
$843$			1.73391e7i			0.0289431i
$844$	−4.01792e7			−0.0668303
$845$			2.60655e8i			0.432012i
$846$	−8.27424e8			−1.36652
$847$		−	2.94055e8i		−	0.483925i
$848$			3.15541e8i			0.517450i
$849$			2.52512e7i			0.0412628i
$850$		−	1.22564e8i		−	0.199574i
$851$	1.20920e8	+	2.67140e7i	0.196204	+	0.0433461i
$852$	−5.33728e6			−0.00862981
$853$	3.60470e8			0.580793			0.290397	−	0.956906i	$-0.406213\pi$
$853$	3.60470e8			0.580793			0.290397	+	0.956906i	$0.406213\pi$
$854$	−1.17087e9			−1.87990
$855$	2.82211e8			0.451518
$856$		−	4.73790e8i		−	0.755379i
$857$	1.82394e8			0.289780			0.144890	−	0.989448i	$-0.453717\pi$
$857$	1.82394e8			0.289780			0.144890	+	0.989448i	$0.453717\pi$
$858$		−	8.68689e7i		−	0.137532i
$859$	4.56365e7			0.0720001			0.0360001	−	0.999352i	$-0.488538\pi$
$859$	4.56365e7			0.0720001			0.0360001	+	0.999352i	$0.488538\pi$
$860$	8.72128e7			0.137115
$861$			2.79277e8i			0.437548i
$862$		−	4.87325e8i		−	0.760846i
$863$	−9.44755e8			−1.46990			−0.734948	−	0.678123i	$-0.762794\pi$
$863$	−9.44755e8			−1.46990			−0.734948	+	0.678123i	$0.762794\pi$
$864$	9.82208e7			0.152287
$865$		−	1.78739e8i		−	0.276167i
$866$		−	9.45798e8i		−	1.45628i
$867$	−3.61562e7			−0.0554786
$868$		−	1.03135e8i		−	0.157705i
$869$	3.77741e7			0.0575619
$870$		−	1.28545e7i		−	0.0195208i
$871$		−	1.42844e8i		−	0.216176i
$872$			6.83467e8i			1.03079i
$873$			5.14441e8i			0.773202i
$874$	−5.64282e8	−	1.24663e8i	−0.845205	−	0.186725i
$875$	−1.07401e8			−0.160318
$876$	4.02003e7			0.0598021
$877$	−7.35873e8			−1.09095			−0.545474	−	0.838128i	$-0.683650\pi$
$877$	−7.35873e8			−1.09095			−0.545474	+	0.838128i	$0.683650\pi$
$878$	−5.88759e8			−0.869869
$879$		−	1.26810e8i		−	0.186719i
$880$	1.62118e8			0.237894
$881$		−	6.81818e8i		−	0.997105i	−0.866860	−	0.498552i	$-0.833865\pi$
$881$		−	6.81818e8i		−	0.997105i	0.866860	−	0.498552i	$-0.166135\pi$
$882$	−1.25361e9			−1.82708
$883$	1.07664e9			1.56383			0.781913	−	0.623388i	$-0.214244\pi$
$883$	1.07664e9			1.56383			0.781913	+	0.623388i	$0.214244\pi$
$884$			3.35547e8i			0.485732i
$885$		−	4.67575e7i		−	0.0674561i
$886$	−6.77254e8			−0.973756
$887$	−1.06413e8			−0.152483			−0.0762417	−	0.997089i	$-0.524292\pi$
$887$	−1.06413e8			−0.152483			−0.0762417	+	0.997089i	$0.524292\pi$
$888$			2.08705e7i			0.0298053i
$889$		−	1.01032e9i		−	1.43798i
$890$	2.72467e8			0.386495
$891$			5.70820e8i			0.806986i
$892$	−1.11136e8			−0.156588
$893$		−	1.21245e9i		−	1.70259i
$894$			5.37210e7i			0.0751850i
$895$		−	1.24353e8i		−	0.173456i
$896$			4.63251e8i			0.644010i
$897$	2.97864e7	−	1.34827e8i	0.0412706	−	0.186810i
$898$	1.90546e8			0.263130
$899$	−8.32162e7			−0.114532
$900$	−4.17940e7			−0.0573306
$901$	−7.20983e8			−0.985713
$902$			9.43859e8i			1.28614i
$903$	1.89020e8			0.256711
$904$			1.38170e9i			1.87029i
$905$	3.08391e8			0.416060
$906$	−4.71533e6			−0.00634056
$907$		−	1.63860e8i		−	0.219610i	−0.993953	−	0.109805i	$-0.964977\pi$
$907$		−	1.63860e8i		−	0.219610i	0.993953	−	0.109805i	$-0.0350226\pi$
$908$			1.92469e8i			0.257100i
$909$	−4.56774e7			−0.0608149
$910$	−7.12621e8			−0.945659
$911$		−	9.29998e8i		−	1.23006i	−0.788503	−	0.615031i	$-0.789143\pi$
$911$		−	9.29998e8i		−	1.23006i	0.788503	−	0.615031i	$-0.210857\pi$
$912$		−	6.62925e7i		−	0.0873936i
$913$	3.05251e8			0.401092
$914$			1.07404e9i			1.40663i
$915$	−5.82696e7			−0.0760639
$916$		−	3.43655e8i		−	0.447133i
$917$			2.73631e9i			3.54861i
$918$		−	2.08702e8i		−	0.269773i
$919$		−	1.48094e9i		−	1.90806i	−0.299717	−	0.954028i	$-0.596892\pi$
$919$		−	1.48094e9i		−	1.90806i	0.299717	−	0.954028i	$-0.403108\pi$
$920$	3.69669e8	+	8.16683e7i	0.474733	+	0.104879i
$921$	−3.51368e7			−0.0449763
$922$	3.54563e8			0.452377
$923$	2.38740e8			0.303613
$924$	−4.81497e7			−0.0610348
$925$		−	3.18062e7i		−	0.0401871i
$926$	−1.23550e9			−1.55600
$927$			3.10930e8i			0.390322i
$928$	−1.71167e8			−0.214179
$929$	−5.66780e8			−0.706915			−0.353457	−	0.935451i	$-0.614994\pi$
$929$	−5.66780e8			−0.706915			−0.353457	+	0.935451i	$0.614994\pi$
$930$			1.24394e7i			0.0154650i
$931$		−	1.83697e9i		−	2.27642i
$932$	1.06888e8			0.132033
$933$	1.41211e7			0.0173870
$934$			1.23888e9i			1.52051i
$935$			3.70426e8i			0.453176i
$936$	−1.22671e9			−1.49594
$937$			5.52878e8i			0.672064i	0.941851	+	0.336032i	$0.109085\pi$
$937$			5.52878e8i			0.672064i	−0.941851	+	0.336032i	$0.890915\pi$
$938$	1.91889e8			0.232510
$939$		−	1.61585e8i		−	0.195166i
$940$			1.79559e8i			0.216184i
$941$		−	5.59629e8i		−	0.671632i	−0.941928	−	0.335816i	$-0.890988\pi$
$941$		−	5.59629e8i		−	0.671632i	0.941928	−	0.335816i	$-0.109012\pi$
$942$		−	7.17201e7i		−	0.0858002i
$943$	−3.23639e8	+	1.46494e9i	−0.385945	+	1.74697i
$944$	5.78989e8			0.688263
$945$	−1.82882e8			−0.216709
$946$	6.38822e8			0.754582
$947$	5.55928e8			0.654589			0.327294	−	0.944922i	$-0.393863\pi$
$947$	5.55928e8			0.654589			0.327294	+	0.944922i	$0.393863\pi$
$948$			2.28753e6i			0.00268499i
$949$	−1.79819e9			−2.10395
$950$			1.48426e8i			0.173117i
$951$	−1.43868e8			−0.167272
$952$	−1.99396e9			−2.31103
$953$		−	1.34042e8i		−	0.154868i	−0.996997	−	0.0774340i	$-0.975327\pi$
$953$		−	1.34042e8i		−	0.154868i	0.996997	−	0.0774340i	$-0.0246727\pi$
$954$		−	5.95850e8i		−	0.686265i
$955$	2.00646e8			0.230367
$956$	2.67571e7			0.0306243
$957$			3.88504e7i			0.0443261i
$958$			4.93979e8i			0.561840i
$959$	8.28404e8			0.939261
$960$			5.91980e7i			0.0669103i
$961$	−8.06975e8			−0.909264
$962$		−	2.11039e8i		−	0.237049i
$963$			6.08976e8i			0.681901i
$964$		−	7.66910e7i		−	0.0856078i
$965$		−	6.45517e8i		−	0.718333i
$966$	1.81120e8	+	4.00135e7i	0.200925	+	0.0443890i
$967$	1.35689e9			1.50060			0.750301	−	0.661096i	$-0.229908\pi$
$967$	1.35689e9			1.50060			0.750301	+	0.661096i	$0.229908\pi$
$968$	2.66224e8			0.293509
$969$	1.51472e8			0.166480
$970$	−2.70566e8			−0.296455
$971$			1.56611e9i			1.71067i	0.518078	+	0.855333i	$0.326648\pi$
$971$			1.56611e9i			1.71067i	−0.518078	+	0.855333i	$0.673352\pi$
$972$	−1.07085e8			−0.116608
$973$			3.35590e8i			0.364309i
$974$	4.38334e8			0.474382
$975$	−3.54643e7			−0.0382629
$976$		−	7.21541e8i		−	0.776089i
$977$		−	6.11863e8i		−	0.656100i	−0.944660	−	0.328050i	$-0.893608\pi$
$977$		−	6.11863e8i		−	0.656100i	0.944660	−	0.328050i	$-0.106392\pi$
$978$	1.35689e8			0.145053
$979$	−8.23482e8			−0.877619
$980$			2.72046e8i			0.289044i
$981$		−	8.78480e8i		−	0.930518i
$982$	−6.83020e8			−0.721272
$983$		−	9.64077e8i		−	1.01496i	−0.861662	−	0.507482i	$-0.830576\pi$
$983$		−	9.64077e8i		−	1.01496i	0.861662	−	0.507482i	$-0.169424\pi$
$984$	−2.52845e8			−0.265381
$985$		−	2.68006e8i		−	0.280438i
$986$			3.63700e8i			0.379413i
$987$			3.89166e8i			0.404746i
$988$		−	4.06353e8i		−	0.421340i
$989$	9.91500e8	+	2.19045e8i	1.02495	+	0.226436i
$990$	−3.06136e8			−0.315506
$991$	−6.25232e8			−0.642421			−0.321211	−	0.947008i	$-0.604090\pi$
$991$	−6.25232e8			−0.642421			−0.321211	+	0.947008i	$0.604090\pi$
$992$	1.65640e8			0.169679
$993$	3.32776e7			0.0339864
$994$			3.20711e8i			0.326554i
$995$	−3.90370e8			−0.396284
$996$			1.84854e7i			0.0187090i
$997$	1.30697e9			1.31881			0.659404	−	0.751789i	$-0.270809\pi$
$997$	1.30697e9			1.31881			0.659404	+	0.751789i	$0.270809\pi$
$998$	−5.01138e8			−0.504157
$999$		−	5.41597e7i		−	0.0543225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.d.a.91.17	✓	48
23.22	odd	2	inner	115.7.d.a.91.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.d.a.91.17	✓	48	1.1	even	1	trivial
115.7.d.a.91.18	yes	48	23.22	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-6.73099 q^{2} +3.68399 q^{3} -18.6938 q^{4} +55.9017i q^{5} -24.7969 q^{6} -614.798i q^{7} +556.611 q^{8} -715.428 q^{9} +O(q^{10})\)	\(q-6.73099 q^{2} +3.68399 q^{3} -18.6938 q^{4} +55.9017i q^{5} -24.7969 q^{6} -614.798i q^{7} +556.611 q^{8} -715.428 q^{9} -376.274i q^{10} +1137.22i q^{11} -68.8679 q^{12} +3080.51 q^{13} +4138.19i q^{14} +205.942i q^{15} -2550.14 q^{16} -5826.83i q^{17} +4815.54 q^{18} +7056.38i q^{19} -1045.02i q^{20} -2264.91i q^{21} -7654.60i q^{22} +(2624.68 - 11880.5i) q^{23} +2050.55 q^{24} -3125.00 q^{25} -20734.9 q^{26} -5321.26 q^{27} +11492.9i q^{28} +9273.26 q^{29} -1386.19i q^{30} -8973.78 q^{31} -18458.2 q^{32} +4189.51i q^{33} +39220.3i q^{34} +34368.2 q^{35} +13374.1 q^{36} +10178.0i q^{37} -47496.4i q^{38} +11348.6 q^{39} +31115.5i q^{40} -123306. q^{41} +15245.1i q^{42} +83455.9i q^{43} -21259.0i q^{44} -39993.7i q^{45} +(-17666.7 + 79967.7i) q^{46} -171824. q^{47} -9394.68 q^{48} -260327. q^{49} +21034.3 q^{50} -21466.0i q^{51} -57586.5 q^{52} -123735. i q^{53} +35817.4 q^{54} -63572.5 q^{55} -342203. i q^{56} +25995.7i q^{57} -62418.2 q^{58} -227043. q^{59} -3849.83i q^{60} +282942. i q^{61} +60402.4 q^{62} +439844. i q^{63} +287450. q^{64} +172206. i q^{65} -28199.5i q^{66} -46370.3i q^{67} +108926. i q^{68} +(9669.31 - 43767.8i) q^{69} -231332. q^{70} +77500.2 q^{71} -398215. q^{72} -583730. q^{73} -68507.9i q^{74} -11512.5 q^{75} -131911. i q^{76} +699159. q^{77} -76387.2 q^{78} -33216.2i q^{79} -142557. i q^{80} +501944. q^{81} +829971. q^{82} -268419. i q^{83} +42339.8i q^{84} +325730. q^{85} -561741. i q^{86} +34162.6 q^{87} +632988. i q^{88} +724119. i q^{89} +269197. i q^{90} -1.89389e6i q^{91} +(-49065.3 + 222093. i) q^{92} -33059.3 q^{93} +1.15654e6 q^{94} -394464. q^{95} -67999.8 q^{96} -719067. i q^{97} +1.75226e6 q^{98} -813598. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) \) 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9} + 4290 q^{12} - 1440 q^{13} + 65400 q^{16} + 4610 q^{18} + 26600 q^{23} + 14940 q^{24} - 150000 q^{25} + 47594 q^{26} + 16080 q^{27} + 131800 q^{29} - 1392 q^{31} - 225040 q^{32} + 5000 q^{35} + 658786 q^{36} - 236320 q^{39} - 351496 q^{41} + 382692 q^{46} + 395680 q^{47} + 1042550 q^{48} - 637848 q^{49} + 62500 q^{50} + 523890 q^{52} - 241250 q^{54} - 402000 q^{55} - 479130 q^{58} - 466312 q^{59} - 1124330 q^{62} + 837582 q^{64} + 1021060 q^{69} - 396000 q^{70} - 114336 q^{71} - 1960750 q^{72} - 498720 q^{73} + 3610400 q^{77} - 1104610 q^{78} + 972888 q^{81} + 124950 q^{82} - 246000 q^{85} - 2090960 q^{87} + 4913480 q^{92} + 3234320 q^{93} - 5550378 q^{94} - 1664000 q^{95} - 776990 q^{96} + 9993220 q^{98}+O(q^{100}) \) 48 * q - 20 * q^2 + 1584 * q^4 + 410 * q^6 - 1210 * q^8 + 12896 * q^9 + 4290 * q^12 - 1440 * q^13 + 65400 * q^16 + 4610 * q^18 + 26600 * q^23 + 14940 * q^24 - 150000 * q^25 + 47594 * q^26 + 16080 * q^27 + 131800 * q^29 - 1392 * q^31 - 225040 * q^32 + 5000 * q^35 + 658786 * q^36 - 236320 * q^39 - 351496 * q^41 + 382692 * q^46 + 395680 * q^47 + 1042550 * q^48 - 637848 * q^49 + 62500 * q^50 + 523890 * q^52 - 241250 * q^54 - 402000 * q^55 - 479130 * q^58 - 466312 * q^59 - 1124330 * q^62 + 837582 * q^64 + 1021060 * q^69 - 396000 * q^70 - 114336 * q^71 - 1960750 * q^72 - 498720 * q^73 + 3610400 * q^77 - 1104610 * q^78 + 972888 * q^81 + 124950 * q^82 - 246000 * q^85 - 2090960 * q^87 + 4913480 * q^92 + 3234320 * q^93 - 5550378 * q^94 - 1664000 * q^95 - 776990 * q^96 + 9993220 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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