LMFDB - Embedded newform 115.7.d.a.91.6

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			91.6
Character	$\chi$	$=$	115.91
Dual form			115.7.d.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-12.7662 q^{2} +22.2634 q^{3} +98.9763 q^{4} -55.9017i q^{5} -284.219 q^{6} -111.835i q^{7} -446.515 q^{8} -233.341 q^{9} +O(q^{10})$	\(q-12.7662 q^{2} +22.2634 q^{3} +98.9763 q^{4} -55.9017i q^{5} -284.219 q^{6} -111.835i q^{7} -446.515 q^{8} -233.341 q^{9} +713.653i q^{10} +1300.62i q^{11} +2203.55 q^{12} +2224.37 q^{13} +1427.71i q^{14} -1244.56i q^{15} -634.172 q^{16} +6993.98i q^{17} +2978.89 q^{18} -2699.58i q^{19} -5532.94i q^{20} -2489.82i q^{21} -16604.0i q^{22} +(-9106.69 - 8068.72i) q^{23} -9940.95 q^{24} -3125.00 q^{25} -28396.8 q^{26} -21425.0 q^{27} -11069.0i q^{28} +35047.9 q^{29} +15888.3i q^{30} -25512.7 q^{31} +36673.0 q^{32} +28956.3i q^{33} -89286.6i q^{34} -6251.75 q^{35} -23095.3 q^{36} -8970.01i q^{37} +34463.4i q^{38} +49522.0 q^{39} +24961.0i q^{40} +70822.9 q^{41} +31785.6i q^{42} +137360. i q^{43} +128731. i q^{44} +13044.2i q^{45} +(116258. + 103007. i) q^{46} +38983.3 q^{47} -14118.8 q^{48} +105142. q^{49} +39894.4 q^{50} +155710. i q^{51} +220160. q^{52} +175231. i q^{53} +273516. q^{54} +72707.1 q^{55} +49935.9i q^{56} -60101.7i q^{57} -447429. q^{58} +181554. q^{59} -123182. i q^{60} +285415. i q^{61} +325700. q^{62} +26095.7i q^{63} -427588. q^{64} -124346. i q^{65} -369662. i q^{66} -182861. i q^{67} +692238. i q^{68} +(-202746. - 179637. i) q^{69} +79811.2 q^{70} +276035. q^{71} +104191. q^{72} -43439.8 q^{73} +114513. i q^{74} -69573.1 q^{75} -267194. i q^{76} +145455. q^{77} -632209. q^{78} -146080. i q^{79} +35451.3i q^{80} -306887. q^{81} -904140. q^{82} +446305. i q^{83} -246433. i q^{84} +390975. q^{85} -1.75357e6i q^{86} +780285. q^{87} -580748. i q^{88} +1.03283e6i q^{89} -166525. i q^{90} -248762. i q^{91} +(-901346. - 798612. i) q^{92} -567998. q^{93} -497669. q^{94} -150911. q^{95} +816464. q^{96} +781880. i q^{97} -1.34227e6 q^{98} -303489. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−12.7662			−1.59578			−0.797889	−	0.602805i	$-0.794050\pi$
$2$	−12.7662			−1.59578			−0.797889	+	0.602805i	$0.794050\pi$
$3$	22.2634			0.824570			0.412285	−	0.911055i	$-0.364731\pi$
$3$	22.2634			0.824570			0.412285	+	0.911055i	$0.364731\pi$
$4$	98.9763			1.54651
$5$		−	55.9017i		−	0.447214i
$5$		−	55.9017i		−	0.447214i
$6$	−284.219			−1.31583
$7$		−	111.835i		−	0.326049i	−0.986622	−	0.163024i	$-0.947875\pi$
$7$		−	111.835i		−	0.326049i	0.986622	−	0.163024i	$-0.0521249\pi$
$8$	−446.515			−0.872100
$9$	−233.341			−0.320084
$10$			713.653i			0.713653i
$11$			1300.62i			0.977178i	0.872514	+	0.488589i	$0.162488\pi$
$11$			1300.62i			0.977178i	−0.872514	+	0.488589i	$0.837512\pi$
$12$	2203.55			1.27520
$13$	2224.37			1.01246			0.506229	−	0.862399i	$-0.331039\pi$
$13$	2224.37			1.01246			0.506229	+	0.862399i	$0.331039\pi$
$14$			1427.71i			0.520301i
$15$		−	1244.56i		−	0.368759i
$16$	−634.172			−0.154827
$17$			6993.98i			1.42357i	0.702400	+	0.711783i	$0.252112\pi$
$17$			6993.98i			1.42357i	−0.702400	+	0.711783i	$0.747888\pi$
$18$	2978.89			0.510783
$19$		−	2699.58i		−	0.393582i	−0.980446	−	0.196791i	$-0.936948\pi$
$19$		−	2699.58i		−	0.393582i	0.980446	−	0.196791i	$-0.0630520\pi$
$20$		−	5532.94i		−	0.691618i
$21$		−	2489.82i		−	0.268850i
$22$		−	16604.0i		−	1.55936i
$23$	−9106.69	−	8068.72i	−0.748474	−	0.663164i
$23$	−9106.69	−	8068.72i	−0.748474	−	0.663164i
$24$	−9940.95			−0.719108
$25$	−3125.00			−0.200000
$26$	−28396.8			−1.61566
$27$	−21425.0			−1.08850
$28$		−	11069.0i		−	0.504236i
$29$	35047.9			1.43704			0.718519	−	0.695508i	$-0.244821\pi$
$29$	35047.9			1.43704			0.718519	+	0.695508i	$0.244821\pi$
$30$			15888.3i			0.588457i
$31$	−25512.7			−0.856388			−0.428194	−	0.903687i	$-0.640850\pi$
$31$	−25512.7			−0.856388			−0.428194	+	0.903687i	$0.640850\pi$
$32$	36673.0			1.11917
$33$			28956.3i			0.805751i
$34$		−	89286.6i		−	2.27169i
$35$	−6251.75			−0.145813
$36$	−23095.3			−0.495012
$37$		−	8970.01i		−	0.177087i	−0.996072	−	0.0885437i	$-0.971779\pi$
$37$		−	8970.01i		−	0.177087i	0.996072	−	0.0885437i	$-0.0282213\pi$
$38$			34463.4i			0.628068i
$39$	49522.0			0.834842
$40$			24961.0i			0.390015i
$41$	70822.9			1.02759			0.513797	−	0.857912i	$-0.328238\pi$
$41$	70822.9			1.02759			0.513797	+	0.857912i	$0.328238\pi$
$42$			31785.6i			0.429025i
$43$			137360.i			1.72765i	0.503791	+	0.863826i	$0.331938\pi$
$43$			137360.i			1.72765i	−0.503791	+	0.863826i	$0.668062\pi$
$44$			128731.i			1.51121i
$45$			13044.2i			0.143146i
$46$	116258.	+	103007.i	1.19440	+	1.05826i
$47$	38983.3			0.375478			0.187739	−	0.982219i	$-0.439884\pi$
$47$	38983.3			0.375478			0.187739	+	0.982219i	$0.439884\pi$
$48$	−14118.8			−0.127666
$49$	105142.			0.893692
$50$	39894.4			0.319155
$51$			155710.i			1.17383i
$52$	220160.			1.56577
$53$			175231.i			1.17702i	0.808489	+	0.588511i	$0.200286\pi$
$53$			175231.i			1.17702i	−0.808489	+	0.588511i	$0.799714\pi$
$54$	273516.			1.73701
$55$	72707.1			0.437007
$56$			49935.9i			0.284347i
$57$		−	60101.7i		−	0.324536i
$58$	−447429.			−2.29319
$59$	181554.			0.883993			0.441996	−	0.897017i	$-0.354270\pi$
$59$	181554.			0.883993			0.441996	+	0.897017i	$0.354270\pi$
$60$		−	123182.i		−	0.570288i
$61$			285415.i			1.25744i	0.777632	+	0.628720i	$0.216421\pi$
$61$			285415.i			1.25744i	−0.777632	+	0.628720i	$0.783579\pi$
$62$	325700.			1.36660
$63$			26095.7i			0.104363i
$64$	−427588.			−1.63112
$65$		−	124346.i		−	0.452785i
$66$		−	369662.i		−	1.28580i
$67$		−	182861.i		−	0.607992i	−0.952673	−	0.303996i	$-0.901679\pi$
$67$		−	182861.i		−	0.607992i	0.952673	−	0.303996i	$-0.0983209\pi$
$68$			692238.i			2.20155i
$69$	−202746.	−	179637.i	−0.617169	−	0.546825i
$70$	79811.2			0.232686
$71$	276035.			0.771240			0.385620	−	0.922658i	$-0.373988\pi$
$71$	276035.			0.771240			0.385620	+	0.922658i	$0.373988\pi$
$72$	104191.			0.279146
$73$	−43439.8			−0.111666			−0.0558328	−	0.998440i	$-0.517781\pi$
$73$	−43439.8			−0.111666			−0.0558328	+	0.998440i	$0.517781\pi$
$74$			114513.i			0.282592i
$75$	−69573.1			−0.164914
$76$		−	267194.i		−	0.608676i
$77$	145455.			0.318608
$78$	−632209.			−1.33222
$79$		−	146080.i		−	0.296284i	−0.988966	−	0.148142i	$-0.952671\pi$
$79$		−	146080.i		−	0.296284i	0.988966	−	0.148142i	$-0.0473293\pi$
$80$			35451.3i			0.0692408i
$81$	−306887.			−0.577462
$82$	−904140.			−1.63981
$83$			446305.i			0.780544i	0.920700	+	0.390272i	$0.127619\pi$
$83$			446305.i			0.780544i	−0.920700	+	0.390272i	$0.872381\pi$
$84$		−	246433.i		−	0.415778i
$85$	390975.			0.636638
$86$		−	1.75357e6i		−	2.75695i
$87$	780285.			1.18494
$88$		−	580748.i		−	0.852197i
$89$			1.03283e6i			1.46506i	0.680732	+	0.732532i	$0.261662\pi$
$89$			1.03283e6i			1.46506i	−0.680732	+	0.732532i	$0.738338\pi$
$90$		−	166525.i		−	0.228429i
$91$		−	248762.i		−	0.330111i
$92$	−901346.	−	798612.i	−1.15752	−	1.02559i
$93$	−567998.			−0.706152
$94$	−497669.			−0.599179
$95$	−150911.			−0.176015
$96$	816464.			0.922834
$97$			781880.i			0.856692i	0.903615	+	0.428346i	$0.140904\pi$
$97$			781880.i			0.856692i	−0.903615	+	0.428346i	$0.859096\pi$
$98$	−1.34227e6			−1.42613
$99$		−	303489.i		−	0.312779i
$100$	−309301.			−0.309301
$101$	1.61517e6			1.56767			0.783835	−	0.620969i	$-0.213261\pi$
$101$	1.61517e6			1.56767			0.783835	+	0.620969i	$0.213261\pi$
$102$		−	1.98782e6i		−	1.87317i
$103$		−	197781.i		−	0.180997i	−0.995897	−	0.0904986i	$-0.971154\pi$
$103$		−	197781.i		−	0.180997i	0.995897	−	0.0904986i	$-0.0288461\pi$
$104$	−993215.			−0.882965
$105$	−139185.			−0.120233
$106$		−	2.23704e6i		−	1.87826i
$107$			1.73536e6i			1.41657i	0.705925	+	0.708287i	$0.250532\pi$
$107$			1.73536e6i			1.41657i	−0.705925	+	0.708287i	$0.749468\pi$
$108$	−2.12057e6			−1.68337
$109$		−	2.09013e6i		−	1.61396i	−0.590577	−	0.806981i	$-0.701100\pi$
$109$		−	2.09013e6i		−	1.61396i	0.590577	−	0.806981i	$-0.298900\pi$
$110$	−928194.			−0.697366
$111$		−	199703.i		−	0.146021i
$112$			70922.5i			0.0504812i
$113$			1.87686e6i			1.30076i	0.759610	+	0.650379i	$0.225390\pi$
$113$			1.87686e6i			1.30076i	−0.759610	+	0.650379i	$0.774610\pi$
$114$			767272.i			0.517886i
$115$	−451055.	+	509079.i	−0.296576	+	0.334728i
$116$	3.46891e6			2.22239
$117$	−519038.			−0.324072
$118$	−2.31775e6			−1.41066
$119$	782169.			0.464152
$120$			555716.i			0.321595i
$121$	79939.4			0.0451237
$122$		−	3.64367e6i		−	2.00660i
$123$	1.57676e6			0.847324
$124$	−2.52515e6			−1.32441
$125$			174693.i			0.0894427i
$126$		−	333143.i		−	0.166540i
$127$	2.33025e6			1.13761			0.568803	−	0.822474i	$-0.307407\pi$
$127$	2.33025e6			1.13761			0.568803	+	0.822474i	$0.307407\pi$
$128$	3.11161e6			1.48373
$129$			3.05811e6i			1.42457i
$130$			1.58743e6i			0.722544i
$131$	865543.			0.385012			0.192506	−	0.981296i	$-0.438338\pi$
$131$	865543.			0.385012			0.192506	+	0.981296i	$0.438338\pi$
$132$			2.86599e6i			1.24610i
$133$	−301906.			−0.128327
$134$			2.33445e6i			0.970220i
$135$			1.19769e6i			0.486793i
$136$		−	3.12292e6i		−	1.24149i
$137$			1.86630e6i			0.725805i	0.931827	+	0.362903i	$0.118214\pi$
$137$			1.86630e6i			0.725805i	−0.931827	+	0.362903i	$0.881786\pi$
$138$	2.58830e6	+	2.29328e6i	0.984865	+	0.872611i
$139$	−82442.4			−0.0306977			−0.0153489	−	0.999882i	$-0.504886\pi$
$139$	−82442.4			−0.0306977			−0.0153489	+	0.999882i	$0.504886\pi$
$140$	−618775.			−0.225501
$141$	867900.			0.309608
$142$	−3.52393e6			−1.23073
$143$			2.89307e6i			0.989351i
$144$	147979.			0.0495578
$145$		−	1.95924e6i		−	0.642663i
$146$	554562.			0.178193
$147$	2.34082e6			0.736912
$148$		−	887818.i		−	0.273867i
$149$		−	3.39753e6i		−	1.02708i	−0.858066	−	0.513540i	$-0.828334\pi$
$149$		−	3.39753e6i		−	1.02708i	0.858066	−	0.513540i	$-0.171666\pi$
$150$	888185.			0.263166
$151$	−1.07743e6			−0.312937			−0.156469	−	0.987683i	$-0.550011\pi$
$151$	−1.07743e6			−0.312937			−0.156469	+	0.987683i	$0.550011\pi$
$152$			1.20540e6i			0.343243i
$153$		−	1.63198e6i		−	0.455661i
$154$	−1.85691e6			−0.508427
$155$			1.42620e6i			0.382988i
$156$	4.90151e6			1.29109
$157$		−	7.72434e6i		−	1.99601i	−0.0631406	−	0.998005i	$-0.520112\pi$
$157$		−	7.72434e6i		−	1.99601i	0.0631406	−	0.998005i	$-0.479888\pi$
$158$			1.86489e6i			0.472804i
$159$			3.90125e6i			0.970537i
$160$		−	2.05008e6i		−	0.500508i
$161$	−902363.	+	1.01844e6i	−0.216224	+	0.244039i
$162$	3.91778e6			0.921500
$163$	−4.84826e6			−1.11950			−0.559748	−	0.828663i	$-0.689102\pi$
$163$	−4.84826e6			−1.11950			−0.559748	+	0.828663i	$0.689102\pi$
$164$	7.00979e6			1.58918
$165$	1.61871e6			0.360343
$166$		−	5.69762e6i		−	1.24557i
$167$	−2.09586e6			−0.450000			−0.225000	−	0.974359i	$-0.572238\pi$
$167$	−2.09586e6			−0.450000			−0.225000	+	0.974359i	$0.572238\pi$
$168$			1.11174e6i			0.234464i
$169$	121014.			0.0250711
$170$	−4.99127e6			−1.01593
$171$			629923.i			0.125979i
$172$			1.35954e7i			2.67182i
$173$	−7.02331e6			−1.35645			−0.678225	−	0.734855i	$-0.737250\pi$
$173$	−7.02331e6			−1.35645			−0.678225	+	0.734855i	$0.737250\pi$
$174$	−9.96129e6			−1.89090
$175$			349483.i			0.0652097i
$176$		−	824819.i		−	0.151294i
$177$	4.04200e6			0.728914
$178$		−	1.31853e7i		−	2.33792i
$179$	4.30303e6			0.750265			0.375133	−	0.926971i	$-0.377597\pi$
$179$	4.30303e6			0.750265			0.375133	+	0.926971i	$0.377597\pi$
$180$			1.29107e6i			0.221376i
$181$			3.54900e6i			0.598508i	0.954174	+	0.299254i	$0.0967378\pi$
$181$			3.54900e6i			0.598508i	−0.954174	+	0.299254i	$0.903262\pi$
$182$			3.17575e6i			0.526783i
$183$			6.35431e6i			1.03685i
$184$	4.06627e6	+	3.60281e6i	0.652745	+	0.578345i
$185$	−501439.			−0.0791959
$186$	7.25119e6			1.12686
$187$	−9.09653e6			−1.39108
$188$	3.85842e6			0.580679
$189$			2.39606e6i			0.354905i
$190$	1.92656e6			0.280881
$191$		−	1.18346e7i		−	1.69845i	−0.528030	−	0.849226i	$-0.677069\pi$
$191$		−	1.18346e7i		−	1.69845i	0.528030	−	0.849226i	$-0.322931\pi$
$192$	−9.51956e6			−1.34497
$193$	951154.			0.132306			0.0661529	−	0.997809i	$-0.478927\pi$
$193$	951154.			0.132306			0.0661529	+	0.997809i	$0.478927\pi$
$194$		−	9.98164e6i		−	1.36709i
$195$		−	2.76837e6i		−	0.373353i
$196$	1.04066e7			1.38210
$197$	876366.			0.114627			0.0573135	−	0.998356i	$-0.481747\pi$
$197$	876366.			0.114627			0.0573135	+	0.998356i	$0.481747\pi$
$198$			3.87441e6i			0.499126i
$199$		−	7.82981e6i		−	0.993556i	−0.867878	−	0.496778i	$-0.834516\pi$
$199$		−	7.82981e6i		−	0.993556i	0.867878	−	0.496778i	$-0.165484\pi$
$200$	1.39536e6			0.174420
$201$		−	4.07112e6i		−	0.501332i
$202$	−2.06196e7			−2.50165
$203$		−	3.91957e6i		−	0.468544i
$204$			1.54116e7i			1.81533i
$205$		−	3.95912e6i		−	0.459554i
$206$			2.52491e6i			0.288831i
$207$	2.12497e6	+	1.88277e6i	0.239575	+	0.212268i
$208$	−1.41063e6			−0.156756
$209$	3.51113e6			0.384599
$210$	1.77687e6			0.191866
$211$	−2.90405e6			−0.309141			−0.154571	−	0.987982i	$-0.549399\pi$
$211$	−2.90405e6			−0.309141			−0.154571	+	0.987982i	$0.549399\pi$
$212$			1.73438e7i			1.82027i
$213$	6.14548e6			0.635942
$214$		−	2.21540e7i		−	2.26054i
$215$	7.67868e6			0.772629
$216$	9.56658e6			0.949283
$217$			2.85320e6i			0.279224i
$218$			2.66830e7i			2.57553i
$219$	−967117.			−0.0920761
$220$	7.19628e6			0.675834
$221$			1.55572e7i			1.44130i
$222$			2.54945e6i			0.233017i
$223$	1.12783e7			1.01702			0.508510	−	0.861056i	$-0.330196\pi$
$223$	1.12783e7			1.01702			0.508510	+	0.861056i	$0.330196\pi$
$224$		−	4.10131e6i		−	0.364904i
$225$	729192.			0.0640169
$226$		−	2.39604e7i		−	2.07572i
$227$			1.52598e7i			1.30458i	0.757968	+	0.652292i	$0.226192\pi$
$227$			1.52598e7i			1.30458i	−0.757968	+	0.652292i	$0.773808\pi$
$228$		−	5.94865e6i		−	0.501896i
$229$			7.50731e6i			0.625141i	0.949895	+	0.312570i	$0.101190\pi$
$229$			7.50731e6i			0.625141i	−0.949895	+	0.312570i	$0.898810\pi$
$230$	5.75827e6	−	6.49902e6i	0.473269	−	0.534151i
$231$	3.23832e6			0.262714
$232$	−1.56494e7			−1.25324
$233$	−1.44004e7			−1.13843			−0.569214	−	0.822189i	$-0.692753\pi$
$233$	−1.44004e7			−1.13843			−0.569214	+	0.822189i	$0.692753\pi$
$234$	6.62615e6			0.517147
$235$		−	2.17923e6i		−	0.167919i
$236$	1.79695e7			1.36710
$237$		−	3.25223e6i		−	0.244307i
$238$	−9.98534e6			−0.740683
$239$	1.28498e7			0.941246			0.470623	−	0.882334i	$-0.344029\pi$
$239$	1.28498e7			0.941246			0.470623	+	0.882334i	$0.344029\pi$
$240$			789266.i			0.0570939i
$241$			1.92762e7i			1.37712i	0.725180	+	0.688559i	$0.241756\pi$
$241$			1.92762e7i			1.37712i	−0.725180	+	0.688559i	$0.758244\pi$
$242$	−1.02052e6			−0.0720074
$243$	8.78647e6			0.612344
$244$			2.82493e7i			1.94464i
$245$		−	5.87762e6i		−	0.399671i
$246$	−2.01292e7			−1.35214
$247$		−	6.00486e6i		−	0.398485i
$248$	1.13918e7			0.746856
$249$			9.93625e6i			0.643613i
$250$		−	2.23017e6i		−	0.142731i
$251$			2.75905e6i			0.174477i	0.996187	+	0.0872386i	$0.0278043\pi$
$251$			2.75905e6i			0.174477i	−0.996187	+	0.0872386i	$0.972196\pi$
$252$			2.58285e6i			0.161398i
$253$	1.04944e7	−	1.18444e7i	0.648029	−	0.731392i
$254$	−2.97485e7			−1.81536
$255$	8.70443e6			0.524952
$256$	−1.23579e7			−0.736588
$257$	−1.38945e7			−0.818547			−0.409273	−	0.912412i	$-0.634218\pi$
$257$	−1.38945e7			−0.818547			−0.409273	+	0.912412i	$0.634218\pi$
$258$		−	3.90405e7i		−	2.27330i
$259$	−1.00316e6			−0.0577391
$260$		−	1.23073e7i		−	0.700234i
$261$	−8.17813e6			−0.459973
$262$	−1.10497e7			−0.614394
$263$		−	5.61875e6i		−	0.308867i	−0.988003	−	0.154434i	$-0.950645\pi$
$263$		−	5.61875e6i		−	0.308867i	0.988003	−	0.154434i	$-0.0493553\pi$
$264$		−	1.29294e7i		−	0.702696i
$265$	9.79574e6			0.526380
$266$	3.85420e6			0.204781
$267$			2.29942e7i			1.20805i
$268$		−	1.80990e7i		−	0.940263i
$269$	−2.48084e7			−1.27450			−0.637252	−	0.770655i	$-0.719929\pi$
$269$	−2.48084e7			−1.27450			−0.637252	+	0.770655i	$0.719929\pi$
$270$		−	1.52900e7i		−	0.776813i
$271$	−2.07424e7			−1.04220			−0.521100	−	0.853496i	$-0.674478\pi$
$271$	−2.07424e7			−1.04220			−0.521100	+	0.853496i	$0.674478\pi$
$272$		−	4.43538e6i		−	0.220407i
$273$		−	5.53828e6i		−	0.272199i
$274$		−	2.38256e7i		−	1.15822i
$275$		−	4.06445e6i		−	0.195436i
$276$	−2.00670e7	−	1.77798e7i	−0.954456	−	0.845668i
$277$	−2.82795e6			−0.133055			−0.0665277	−	0.997785i	$-0.521192\pi$
$277$	−2.82795e6			−0.133055			−0.0665277	+	0.997785i	$0.521192\pi$
$278$	1.05248e6			0.0489867
$279$	5.95316e6			0.274116
$280$	2.79150e6			0.127164
$281$		−	1.19100e7i		−	0.536774i	−0.963311	−	0.268387i	$-0.913509\pi$
$281$		−	1.19100e7i		−	0.536774i	0.963311	−	0.268387i	$-0.0864907\pi$
$282$	−1.10798e7			−0.494065
$283$			7.71594e6i			0.340432i	0.985407	+	0.170216i	$0.0544465\pi$
$283$			7.71594e6i			0.340432i	−0.985407	+	0.170216i	$0.945554\pi$
$284$	2.73210e7			1.19273
$285$	−3.35979e6			−0.145137
$286$		−	3.69335e7i		−	1.57878i
$287$		−	7.92045e6i		−	0.335046i
$288$	−8.55732e6			−0.358229
$289$	−2.47781e7			−1.02654
$290$			2.50120e7i			1.02555i
$291$			1.74073e7i			0.706402i
$292$	−4.29951e6			−0.172691
$293$		−	1.72720e7i		−	0.686656i	−0.939216	−	0.343328i	$-0.888446\pi$
$293$		−	1.72720e7i		−	0.686656i	0.939216	−	0.343328i	$-0.111554\pi$
$294$	−2.98834e7			−1.17595
$295$		−	1.01491e7i		−	0.395333i
$296$			4.00525e6i			0.154438i
$297$		−	2.78658e7i		−	1.06366i
$298$			4.33736e7i			1.63899i
$299$	−2.02566e7	−	1.79478e7i	−0.757799	−	0.671426i
$300$	−6.88609e6			−0.255040
$301$	1.53617e7			0.563299
$302$	1.37547e7			0.499378
$303$	3.59592e7			1.29265
$304$			1.71200e6i			0.0609371i
$305$	1.59552e7			0.562345
$306$			2.08343e7i			0.727133i
$307$	1.95875e7			0.676961			0.338480	−	0.940973i	$-0.390087\pi$
$307$	1.95875e7			0.676961			0.338480	+	0.940973i	$0.390087\pi$
$308$	1.43966e7			0.492728
$309$		−	4.40327e6i		−	0.149245i
$310$		−	1.82072e7i		−	0.611164i
$311$	−1.06971e7			−0.355619			−0.177809	−	0.984065i	$-0.556901\pi$
$311$	−1.06971e7			−0.355619			−0.177809	+	0.984065i	$0.556901\pi$
$312$	−2.21123e7			−0.728066
$313$			7.10575e6i			0.231727i	0.993265	+	0.115864i	$0.0369635\pi$
$313$			7.10575e6i			0.231727i	−0.993265	+	0.115864i	$0.963036\pi$
$314$			9.86106e7i			3.18519i
$315$	1.45879e6			0.0466726
$316$		−	1.44584e7i		−	0.458205i
$317$	4.35289e7			1.36647			0.683235	−	0.730199i	$-0.260573\pi$
$317$	4.35289e7			1.36647			0.683235	+	0.730199i	$0.260573\pi$
$318$		−	4.98042e7i		−	1.54876i
$319$			4.55841e7i			1.40424i
$320$			2.39029e7i			0.729459i
$321$			3.86351e7i			1.16806i
$322$	1.15198e7	−	1.30017e7i	0.345045	−	0.389432i
$323$	1.88808e7			0.560289
$324$	−3.03745e7			−0.893047
$325$	−6.95116e6			−0.202492
$326$	6.18939e7			1.78647
$327$		−	4.65334e7i		−	1.33083i
$328$	−3.16235e7			−0.896166
$329$		−	4.35968e6i		−	0.122424i
$330$	−2.06648e7			−0.575027
$331$	−3.99394e7			−1.10133			−0.550665	−	0.834727i	$-0.685626\pi$
$331$	−3.99394e7			−1.10133			−0.550665	+	0.834727i	$0.685626\pi$
$332$			4.41736e7i			1.20711i
$333$			2.09307e6i			0.0566829i
$334$	2.67562e7			0.718099
$335$	−1.02223e7			−0.271902
$336$			1.57897e6i			0.0416253i
$337$		−	7.87413e6i		−	0.205737i	−0.994695	−	0.102869i	$-0.967198\pi$
$337$		−	7.87413e6i		−	0.205737i	0.994695	−	0.102869i	$-0.0328021\pi$
$338$	−1.54489e6			−0.0400080
$339$			4.17853e7i			1.07257i
$340$	3.86973e7			0.984563
$341$		−	3.31824e7i		−	0.836843i
$342$		−	8.04173e6i		−	0.201035i
$343$		−	2.49158e7i		−	0.617436i
$344$		−	6.13335e7i		−	1.50669i
$345$	−1.00420e7	+	1.13338e7i	−0.244548	+	0.276007i
$346$	8.96611e7			2.16459
$347$	−2.77850e7			−0.665000			−0.332500	−	0.943103i	$-0.607892\pi$
$347$	−2.77850e7			−0.665000			−0.332500	+	0.943103i	$0.607892\pi$
$348$	7.72297e7			1.83251
$349$	−8.11360e7			−1.90870			−0.954349	−	0.298694i	$-0.903449\pi$
$349$	−8.11360e7			−1.90870			−0.954349	+	0.298694i	$0.903449\pi$
$350$		−	4.46158e6i		−	0.104060i
$351$	−4.76571e7			−1.10206
$352$			4.76977e7i			1.09363i
$353$	2.10955e7			0.479585			0.239792	−	0.970824i	$-0.422921\pi$
$353$	2.10955e7			0.479585			0.239792	+	0.970824i	$0.422921\pi$
$354$	−5.16010e7			−1.16318
$355$		−	1.54308e7i		−	0.344909i
$356$			1.02225e8i			2.26573i
$357$	1.74137e7			0.382725
$358$	−5.49334e7			−1.19726
$359$			5.11460e7i			1.10542i	0.833373	+	0.552712i	$0.186407\pi$
$359$			5.11460e7i			1.10542i	−0.833373	+	0.552712i	$0.813593\pi$
$360$		−	5.82443e6i		−	0.124838i
$361$	3.97582e7			0.845094
$362$		−	4.53073e7i		−	0.955085i
$363$	1.77972e6			0.0372076
$364$		−	2.46215e7i		−	0.510518i
$365$			2.42836e6i			0.0499384i
$366$		−	8.11205e7i		−	1.65458i
$367$			4.49780e7i			0.909917i	0.890513	+	0.454959i	$0.150346\pi$
$367$			4.49780e7i			0.909917i	−0.890513	+	0.454959i	$0.849654\pi$
$368$	5.77521e6	+	5.11695e6i	0.115884	+	0.102676i
$369$	−1.65259e7			−0.328917
$370$	6.40148e6			0.126379
$371$	1.95970e7			0.383766
$372$	−5.62184e7			−1.09207
$373$		−	4.13709e7i		−	0.797203i	−0.917124	−	0.398602i	$-0.869496\pi$
$373$		−	4.13709e7i		−	0.797203i	0.917124	−	0.398602i	$-0.130504\pi$
$374$	1.16128e8			2.21985
$375$			3.88925e6i			0.0737518i
$376$	−1.74066e7			−0.327455
$377$	7.79595e7			1.45494
$378$		−	3.05886e7i		−	0.566349i
$379$		−	2.12185e6i		−	0.0389760i	−0.999810	−	0.0194880i	$-0.993796\pi$
$379$		−	2.12185e6i		−	0.0389760i	0.999810	−	0.0194880i	$-0.00620362\pi$
$380$	−1.49366e7			−0.272208
$381$	5.18793e7			0.938035
$382$			1.51083e8i			2.71035i
$383$			7.96327e7i			1.41741i	0.705506	+	0.708704i	$0.250720\pi$
$383$			7.96327e7i			1.41741i	−0.705506	+	0.708704i	$0.749280\pi$
$384$	6.92750e7			1.22344
$385$		−	8.13117e6i		−	0.142486i
$386$	−1.21426e7			−0.211131
$387$		−	3.20519e7i		−	0.552994i
$388$			7.73876e7i			1.32488i
$389$			3.83129e7i			0.650873i	0.945564	+	0.325437i	$0.105511\pi$
$389$			3.83129e7i			0.650873i	−0.945564	+	0.325437i	$0.894489\pi$
$390$			3.53416e7i			0.595788i
$391$	5.64324e7	−	6.36919e7i	0.944057	−	1.06550i
$392$	−4.69475e7			−0.779389
$393$	1.92699e7			0.317470
$394$	−1.11879e7			−0.182919
$395$	−8.16610e6			−0.132502
$396$		−	3.00383e7i		−	0.483715i
$397$	−3.59557e7			−0.574641			−0.287320	−	0.957835i	$-0.592764\pi$
$397$	−3.59557e7			−0.574641			−0.287320	+	0.957835i	$0.592764\pi$
$398$			9.99571e7i			1.58549i
$399$	−6.72146e6			−0.105814
$400$	1.98179e6			0.0309654
$401$			6.23377e6i			0.0966757i	0.998831	+	0.0483379i	$0.0153924\pi$
$401$			6.23377e6i			0.0966757i	−0.998831	+	0.0483379i	$0.984608\pi$
$402$			5.19728e7i			0.800014i
$403$	−5.67496e7			−0.867057
$404$	1.59864e8			2.42441
$405$			1.71555e7i			0.258249i
$406$			5.00381e7i			0.747692i
$407$	1.16666e7			0.173046
$408$		−	6.95267e7i		−	1.02370i
$409$	6.82266e7			0.997204			0.498602	−	0.866831i	$-0.333847\pi$
$409$	6.82266e7			0.997204			0.498602	+	0.866831i	$0.333847\pi$
$410$			5.05430e7i			0.733346i
$411$			4.15502e7i			0.598477i
$412$		−	1.95756e7i		−	0.279913i
$413$		−	2.03040e7i		−	0.288225i
$414$	−2.71278e7	−	2.40358e7i	−0.382308	−	0.338733i
$415$	2.49492e7			0.349070
$416$	8.15742e7			1.13311
$417$	−1.83545e6			−0.0253124
$418$	−4.48239e7			−0.613735
$419$		−	6.85476e7i		−	0.931858i	−0.884822	−	0.465929i	$-0.845720\pi$
$419$		−	6.85476e7i		−	0.931858i	0.884822	−	0.465929i	$-0.154280\pi$
$420$	−1.37760e7			−0.185942
$421$		−	3.45987e7i		−	0.463675i	−0.972754	−	0.231838i	$-0.925526\pi$
$421$		−	3.45987e7i		−	0.463675i	0.972754	−	0.231838i	$-0.0744738\pi$
$422$	3.70738e7			0.493321
$423$	−9.09641e6			−0.120185
$424$		−	7.82435e7i		−	1.02648i
$425$		−	2.18562e7i		−	0.284713i
$426$	−7.84546e7			−1.01482
$427$	3.19193e7			0.409987
$428$			1.71760e8i			2.19074i
$429$			6.44095e7i			0.815789i
$430$	−9.80277e7			−1.23294
$431$			9.72814e6i			0.121506i	0.998153	+	0.0607530i	$0.0193502\pi$
$431$			9.72814e6i			0.121506i	−0.998153	+	0.0607530i	$0.980650\pi$
$432$	1.35871e7			0.168530
$433$			8.40491e7i			1.03531i	0.855590	+	0.517654i	$0.173194\pi$
$433$			8.40491e7i			1.03531i	−0.855590	+	0.517654i	$0.826806\pi$
$434$		−	3.64246e7i		−	0.445580i
$435$		−	4.36193e7i		−	0.529920i
$436$		−	2.06873e8i		−	2.49600i
$437$	−2.17821e7	+	2.45842e7i	−0.261009	+	0.294586i
$438$	1.23464e7			0.146933
$439$	−9.99992e7			−1.18196			−0.590980	−	0.806686i	$-0.701259\pi$
$439$	−9.99992e7			−1.18196			−0.590980	+	0.806686i	$0.701259\pi$
$440$	−3.24648e7			−0.381114
$441$	−2.45340e7			−0.286057
$442$		−	1.98606e8i		−	2.29999i
$443$	−1.51145e8			−1.73853			−0.869267	−	0.494343i	$-0.835409\pi$
$443$	−1.51145e8			−1.73853			−0.869267	+	0.494343i	$0.835409\pi$
$444$		−	1.97658e7i		−	0.225822i
$445$	5.77367e7			0.655197
$446$	−1.43981e8			−1.62294
$447$		−	7.56404e7i		−	0.846899i
$448$			4.78192e7i			0.531824i
$449$	1.34836e8			1.48960			0.744798	−	0.667291i	$-0.232546\pi$
$449$	1.34836e8			1.48960			0.744798	+	0.667291i	$0.232546\pi$
$450$	−9.30903e6			−0.102157
$451$			9.21139e7i			1.00414i
$452$			1.85765e8i			2.01163i
$453$	−2.39872e7			−0.258039
$454$		−	1.94810e8i		−	2.08182i
$455$	−1.39062e7			−0.147630
$456$			2.68363e7i			0.283028i
$457$		−	1.12013e8i		−	1.17360i	−0.809732	−	0.586800i	$-0.800388\pi$
$457$		−	1.12013e8i		−	1.17360i	0.809732	−	0.586800i	$-0.199612\pi$
$458$		−	9.58399e7i		−	0.997585i
$459$		−	1.49846e8i		−	1.54955i
$460$	−4.46438e7	+	5.03868e7i	−0.458656	+	0.517658i
$461$	−9.08745e7			−0.927554			−0.463777	−	0.885952i	$-0.653506\pi$
$461$	−9.08745e7			−0.927554			−0.463777	+	0.885952i	$0.653506\pi$
$462$	−4.13411e7			−0.419233
$463$	−1.37280e8			−1.38313			−0.691567	−	0.722313i	$-0.743079\pi$
$463$	−1.37280e8			−1.38313			−0.691567	+	0.722313i	$0.743079\pi$
$464$	−2.22264e7			−0.222492
$465$			3.17521e7i			0.315801i
$466$	1.83838e8			1.81668
$467$		−	1.32638e8i		−	1.30232i	−0.758940	−	0.651160i	$-0.774283\pi$
$467$		−	1.32638e8i		−	1.30232i	0.758940	−	0.651160i	$-0.225717\pi$
$468$	−5.13725e7			−0.501179
$469$	−2.04503e7			−0.198235
$470$			2.78205e7i			0.267961i
$471$		−	1.71970e8i		−	1.64585i
$472$	−8.10664e7			−0.770930
$473$	−1.78654e8			−1.68822
$474$			4.15187e7i			0.389860i
$475$			8.43617e6i			0.0787163i
$476$	7.74162e7			0.717813
$477$		−	4.08888e7i		−	0.376746i
$478$	−1.64044e8			−1.50202
$479$		−	1.71367e8i		−	1.55926i	−0.626238	−	0.779632i	$-0.715406\pi$
$479$		−	1.71367e8i		−	1.55926i	0.626238	−	0.779632i	$-0.284594\pi$
$480$		−	4.56418e7i		−	0.412704i
$481$		−	1.99526e7i		−	0.179294i
$482$		−	2.46085e8i		−	2.19757i
$483$	−2.00896e7	+	2.26740e7i	−0.178292	+	0.201227i
$484$	7.91210e6			0.0697840
$485$	4.37084e7			0.383124
$486$	−1.12170e8			−0.977165
$487$	2.06163e8			1.78494			0.892470	−	0.451107i	$-0.148971\pi$
$487$	2.06163e8			1.78494			0.892470	+	0.451107i	$0.148971\pi$
$488$		−	1.27442e8i		−	1.09661i
$489$	−1.07939e8			−0.923103
$490$			7.50349e7i			0.637786i
$491$	−1.84006e8			−1.55449			−0.777243	−	0.629200i	$-0.783383\pi$
$491$	−1.84006e8			−1.55449			−0.777243	+	0.629200i	$0.783383\pi$
$492$	1.56062e8			1.31039
$493$			2.45124e8i			2.04572i
$494$			7.66593e7i			0.635893i
$495$	−1.69656e7			−0.139879
$496$	1.61794e7			0.132592
$497$		−	3.08703e7i		−	0.251462i
$498$		−	1.26848e8i		−	1.02706i
$499$	3.98940e7			0.321075			0.160537	−	0.987030i	$-0.448677\pi$
$499$	3.98940e7			0.321075			0.160537	+	0.987030i	$0.448677\pi$
$500$			1.72905e7i			0.138324i
$501$	−4.66609e7			−0.371056
$502$		−	3.52227e7i		−	0.278427i
$503$		−	4.39784e7i		−	0.345570i	−0.984960	−	0.172785i	$-0.944723\pi$
$503$		−	4.39784e7i		−	0.345570i	0.984960	−	0.172785i	$-0.0552766\pi$
$504$		−	1.16521e7i		−	0.0910151i
$505$		−	9.02909e7i		−	0.701084i
$506$	−1.33973e8	+	1.51208e8i	−1.03411	+	1.16714i
$507$	2.69417e6			0.0206729
$508$	2.30640e8			1.75931
$509$	1.40205e8			1.06319			0.531594	−	0.846999i	$-0.321593\pi$
$509$	1.40205e8			1.06319			0.531594	+	0.846999i	$0.321593\pi$
$510$	−1.11123e8			−0.837707
$511$			4.85808e6i			0.0364084i
$512$	−4.13797e7			−0.308303
$513$			5.78384e7i			0.428414i
$514$	1.77380e8			1.30622
$515$	−1.10563e7			−0.0809444
$516$			3.02680e8i			2.20310i
$517$			5.07025e7i			0.366909i
$518$	1.28065e7			0.0921388
$519$	−1.56363e8			−1.11849
$520$			5.55224e7i			0.394874i
$521$			2.56574e8i			1.81426i	0.420853	+	0.907129i	$0.361731\pi$
$521$			2.56574e8i			1.81426i	−0.420853	+	0.907129i	$0.638269\pi$
$522$	1.04404e8			0.734015
$523$		−	1.07414e8i		−	0.750856i	−0.926852	−	0.375428i	$-0.877496\pi$
$523$		−	1.07414e8i		−	0.750856i	0.926852	−	0.375428i	$-0.122504\pi$
$524$	8.56682e7			0.595423
$525$			7.78069e6i			0.0537700i
$526$			7.17301e7i			0.492884i
$527$		−	1.78435e8i		−	1.21912i
$528$		−	1.83633e7i		−	0.124752i
$529$	1.78275e7	+	1.46959e8i	0.120427	+	0.992722i
$530$	−1.25055e8			−0.839985
$531$	−4.23640e7			−0.282952
$532$	−2.98816e7			−0.198458
$533$	1.57536e8			1.04040
$534$		−	2.93549e8i		−	1.92778i
$535$	9.70098e7			0.633511
$536$			8.16505e7i			0.530230i
$537$	9.58000e7			0.618646
$538$	3.16709e8			2.03383
$539$			1.36750e8i			0.873296i
$540$			1.18543e8i			0.752828i
$541$	1.04543e8			0.660240			0.330120	−	0.943939i	$-0.392911\pi$
$541$	1.04543e8			0.660240			0.330120	+	0.943939i	$0.392911\pi$
$542$	2.64802e8			1.66312
$543$			7.90127e7i			0.493512i
$544$			2.56490e8i			1.59321i
$545$	−1.16842e8			−0.721786
$546$			7.07029e7i			0.434369i
$547$	−6.93396e7			−0.423662			−0.211831	−	0.977306i	$-0.567943\pi$
$547$	−6.93396e7			−0.423662			−0.211831	+	0.977306i	$0.567943\pi$
$548$			1.84720e8i			1.12246i
$549$		−	6.65992e7i		−	0.402487i
$550$			5.18876e7i			0.311872i
$551$		−	9.46145e7i		−	0.565591i
$552$	9.05291e7	+	8.02107e7i	0.538234	+	0.476886i
$553$	−1.63368e7			−0.0966031
$554$	3.61022e7			0.212327
$555$	−1.11637e7			−0.0653026
$556$	−8.15984e6			−0.0474742
$557$			2.24108e8i			1.29686i	0.761276	+	0.648428i	$0.224573\pi$
$557$			2.24108e8i			1.29686i	−0.761276	+	0.648428i	$0.775427\pi$
$558$	−7.59994e7			−0.437429
$559$			3.05540e8i			1.74917i
$560$	3.96469e6			0.0225759
$561$	−2.02520e8			−1.14704
$562$			1.52045e8i			0.856572i
$563$		−	2.82218e8i		−	1.58146i	−0.612163	−	0.790731i	$-0.709700\pi$
$563$		−	2.82218e8i		−	1.58146i	0.612163	−	0.790731i	$-0.290300\pi$
$564$	8.59015e7			0.478810
$565$	1.04920e8			0.581717
$566$		−	9.85034e7i		−	0.543253i
$567$			3.43206e7i			0.188281i
$568$	−1.23254e8			−0.672599
$569$		−	2.62605e8i		−	1.42550i	−0.701420	−	0.712748i	$-0.747450\pi$
$569$		−	2.62605e8i		−	1.42550i	0.701420	−	0.712748i	$-0.252550\pi$
$570$	4.28918e7			0.231606
$571$		−	1.26825e8i		−	0.681232i	−0.940203	−	0.340616i	$-0.889364\pi$
$571$		−	1.26825e8i		−	0.681232i	0.940203	−	0.340616i	$-0.110636\pi$
$572$			2.86345e8i			1.53004i
$573$		−	2.63478e8i		−	1.40049i
$574$			1.01114e8i			0.534659i
$575$	2.84584e7	+	2.52147e7i	0.149695	+	0.132633i
$576$	9.97740e7			0.522096
$577$	−9.87595e7			−0.514104			−0.257052	−	0.966398i	$-0.582751\pi$
$577$	−9.87595e7			−0.514104			−0.257052	+	0.966398i	$0.582751\pi$
$578$	3.16323e8			1.63813
$579$	2.11759e7			0.109095
$580$		−	1.93918e8i		−	0.993881i
$581$	4.99124e7			0.254495
$582$		−	2.22225e8i		−	1.12726i
$583$	−2.27910e8			−1.15016
$584$	1.93965e7			0.0973836
$585$			2.90151e7i			0.144929i
$586$			2.20498e8i			1.09575i
$587$	4.91671e7			0.243086			0.121543	−	0.992586i	$-0.461216\pi$
$587$	4.91671e7			0.243086			0.121543	+	0.992586i	$0.461216\pi$
$588$	2.31685e8			1.13964
$589$			6.88734e7i			0.337059i
$590$			1.29566e8i			0.630864i
$591$	1.95109e7			0.0945179
$592$			5.68853e6i			0.0274179i
$593$	8.27371e7			0.396767			0.198384	−	0.980124i	$-0.436431\pi$
$593$	8.27371e7			0.396767			0.198384	+	0.980124i	$0.436431\pi$
$594$			3.55741e8i			1.69736i
$595$		−	4.37246e7i		−	0.207575i
$596$		−	3.36275e8i		−	1.58838i
$597$		−	1.74318e8i		−	0.819256i
$598$	2.58601e8	+	2.29126e8i	1.20928	+	1.07145i
$599$	−2.53310e8			−1.17862			−0.589308	−	0.807909i	$-0.700599\pi$
$599$	−2.53310e8			−1.17862			−0.589308	+	0.807909i	$0.700599\pi$
$600$	3.10655e7			0.143822
$601$	−18325.8			−8.44190e−5			−4.22095e−5	−	1.00000i	$-0.500013\pi$
$601$	−18325.8			−8.44190e−5			−4.22095e−5		1.00000i	$0.500013\pi$
$602$	−1.96110e8			−0.898899
$603$			4.26692e7i			0.194609i
$604$	−1.06640e8			−0.483959
$605$		−	4.46875e6i		−	0.0201799i
$606$	−4.59063e8			−2.06279
$607$	2.29246e8			1.02503			0.512515	−	0.858678i	$-0.328714\pi$
$607$	2.29246e8			1.02503			0.512515	+	0.858678i	$0.328714\pi$
$608$		−	9.90014e7i		−	0.440485i
$609$		−	8.72630e7i		−	0.386347i
$610$	−2.03687e8			−0.897377
$611$	8.67132e7			0.380156
$612$		−	1.61528e8i		−	0.704682i
$613$			4.47197e8i			1.94141i	0.240272	+	0.970706i	$0.422763\pi$
$613$			4.47197e8i			1.94141i	−0.240272	+	0.970706i	$0.577237\pi$
$614$	−2.50058e8			−1.08028
$615$		−	8.81434e7i		−	0.378935i
$616$	−6.49478e7			−0.277858
$617$		−	1.87627e8i		−	0.798804i	−0.916776	−	0.399402i	$-0.869218\pi$
$617$		−	1.87627e8i		−	0.798804i	0.916776	−	0.399402i	$-0.130782\pi$
$618$			5.62131e7i			0.238162i
$619$		−	3.28707e8i		−	1.38592i	−0.720978	−	0.692958i	$-0.756307\pi$
$619$		−	3.28707e8i		−	1.38592i	0.720978	−	0.692958i	$-0.243693\pi$
$620$			1.41160e8i			0.592294i
$621$	1.95111e8	+	1.72872e8i	0.814716	+	0.721855i
$622$	1.36561e8			0.567488
$623$	1.15506e8			0.477682
$624$	−3.14055e7			−0.129256
$625$	9.76562e6			0.0400000
$626$		−	9.07136e7i		−	0.369785i
$627$	7.81697e7			0.317129
$628$		−	7.64527e8i		−	3.08684i
$629$	6.27360e7			0.252095
$630$	−1.86233e7			−0.0744791
$631$			1.04377e8i			0.415448i	0.978187	+	0.207724i	$0.0666057\pi$
$631$			1.04377e8i			0.415448i	−0.978187	+	0.207724i	$0.933394\pi$
$632$			6.52268e7i			0.258390i
$633$	−6.46541e7			−0.254909
$634$	−5.55699e8			−2.18058
$635$		−	1.30265e8i		−	0.508753i
$636$			3.86131e8i			1.50094i
$637$	2.33875e8			0.904826
$638$		−	5.81937e8i		−	2.24086i
$639$	−6.44105e7			−0.246862
$640$		−	1.73944e8i		−	0.663545i
$641$			2.24696e8i			0.853143i	0.904454	+	0.426572i	$0.140279\pi$
$641$			2.24696e8i			0.853143i	−0.904454	+	0.426572i	$0.859721\pi$
$642$		−	4.93224e8i		−	1.86397i
$643$			2.96545e7i			0.111547i	0.998443	+	0.0557735i	$0.0177625\pi$
$643$			2.96545e7i			0.111547i	−0.998443	+	0.0557735i	$0.982238\pi$
$644$	−8.93125e7	+	1.00802e8i	−0.334391	+	0.377408i
$645$	1.70953e8			0.637087
$646$	−2.41036e8			−0.894096
$647$	−1.83343e8			−0.676941			−0.338470	−	0.940977i	$-0.609909\pi$
$647$	−1.83343e8			−0.676941			−0.338470	+	0.940977i	$0.609909\pi$
$648$	1.37030e8			0.503605
$649$			2.36133e8i			0.863818i
$650$	8.87400e7			0.323131
$651$			6.35219e7i			0.230240i
$652$	−4.79863e8			−1.73131
$653$	−166098.			−0.000596519			−0.000298259	−	1.00000i	$-0.500095\pi$
$653$	−166098.			−0.000596519			−0.000298259		1.00000i	$0.500095\pi$
$654$			5.94055e8i			2.12370i
$655$		−	4.83853e7i		−	0.172183i
$656$	−4.49139e7			−0.159100
$657$	1.01363e7			0.0357424
$658$			5.56566e7i			0.195362i
$659$		−	1.79273e8i		−	0.626409i	−0.949686	−	0.313204i	$-0.898597\pi$
$659$		−	1.79273e8i		−	0.626409i	0.949686	−	0.313204i	$-0.101403\pi$
$660$	1.60214e8			0.557272
$661$		−	3.52289e8i		−	1.21982i	−0.792472	−	0.609908i	$-0.791206\pi$
$661$		−	3.52289e8i		−	1.21982i	0.792472	−	0.609908i	$-0.208794\pi$
$662$	5.09875e8			1.75748
$663$			3.46356e8i			1.18845i
$664$		−	1.99282e8i		−	0.680712i
$665$			1.68771e7i			0.0573895i
$666$		−	2.67206e7i		−	0.0904533i
$667$	−3.19170e8	−	2.82792e8i	−1.07559	−	0.952991i
$668$	−2.07440e8			−0.695927
$669$	2.51094e8			0.838605
$670$	1.30500e8			0.433895
$671$	−3.71218e8			−1.22874
$672$		−	9.13091e7i		−	0.300889i
$673$	−1.74699e7			−0.0573120			−0.0286560	−	0.999589i	$-0.509123\pi$
$673$	−1.74699e7			−0.0573120			−0.0286560	+	0.999589i	$0.509123\pi$
$674$			1.00523e8i			0.328311i
$675$	6.69531e7			0.217700
$676$	1.19775e7			0.0387726
$677$			6.06815e8i			1.95565i	0.209433	+	0.977823i	$0.432838\pi$
$677$			6.06815e8i			1.95565i	−0.209433	+	0.977823i	$0.567162\pi$
$678$		−	5.33440e8i		−	1.71158i
$679$	8.74413e7			0.279323
$680$	−1.74576e8			−0.555212
$681$			3.39735e8i			1.07572i
$682$			4.23613e8i			1.33542i
$683$	−1.82863e8			−0.573935			−0.286968	−	0.957940i	$-0.592647\pi$
$683$	−1.82863e8			−0.573935			−0.286968	+	0.957940i	$0.592647\pi$
$684$			6.23475e7i			0.194828i
$685$	1.04329e8			0.324590
$686$			3.18080e8i			0.985290i
$687$			1.67138e8i			0.515472i
$688$		−	8.71101e7i		−	0.267487i
$689$			3.89780e8i			1.19169i
$690$	1.28199e8	−	1.44690e8i	0.390244	−	0.440445i
$691$	4.95717e8			1.50245			0.751224	−	0.660047i	$-0.229464\pi$
$691$	4.95717e8			1.50245			0.751224	+	0.660047i	$0.229464\pi$
$692$	−6.95142e8			−2.09776
$693$	−3.39407e7			−0.101981
$694$	3.54709e8			1.06119
$695$			4.60867e6i			0.0137284i
$696$	−3.48409e8			−1.03338
$697$			4.95333e8i			1.46285i
$698$	1.03580e9			3.04586
$699$	−3.20601e8			−0.938714
$700$			3.45906e7i			0.100847i
$701$			7.04418e7i			0.204492i	0.994759	+	0.102246i	$0.0326029\pi$
$701$			7.04418e7i			0.204492i	−0.994759	+	0.102246i	$0.967397\pi$
$702$	6.08401e8			1.75865
$703$	−2.42152e7			−0.0696983
$704$		−	5.56131e8i		−	1.59389i
$705$		−	4.85171e7i		−	0.138461i
$706$	−2.69310e8			−0.765311
$707$		−	1.80632e8i		−	0.511137i
$708$	4.00062e8			1.12727
$709$		−	3.20962e8i		−	0.900564i	−0.892886	−	0.450282i	$-0.851323\pi$
$709$		−	3.20962e8i		−	0.900564i	0.892886	−	0.450282i	$-0.148677\pi$
$710$			1.96994e8i			0.550398i
$711$			3.40865e7i			0.0948360i
$712$		−	4.61172e8i		−	1.27768i
$713$	2.32336e8	+	2.05854e8i	0.640984	+	0.567926i
$714$	−2.22308e8			−0.610745
$715$	1.61727e8			0.442451
$716$	4.25898e8			1.16029
$717$	2.86080e8			0.776123
$718$		−	6.52941e8i		−	1.76401i
$719$	4.15362e8			1.11748			0.558741	−	0.829342i	$-0.311285\pi$
$719$	4.15362e8			1.11748			0.558741	+	0.829342i	$0.311285\pi$
$720$		−	8.27226e6i		−	0.0221629i
$721$	−2.21187e7			−0.0590139
$722$	−5.07561e8			−1.34858
$723$			4.29155e8i			1.13553i
$724$			3.51267e8i			0.925595i
$725$	−1.09525e8			−0.287407
$726$	−2.27203e7			−0.0593751
$727$		−	6.10148e8i		−	1.58793i	−0.607963	−	0.793966i	$-0.708013\pi$
$727$		−	6.10148e8i		−	1.58793i	0.607963	−	0.793966i	$-0.291987\pi$
$728$			1.11076e8i			0.287890i
$729$	4.19337e8			1.08238
$730$		−	3.10010e7i		−	0.0796905i
$731$	−9.60695e8			−2.45942
$732$			6.28926e8i			1.60349i
$733$			1.71703e8i			0.435980i	0.975951	+	0.217990i	$0.0699501\pi$
$733$			1.71703e8i			0.435980i	−0.975951	+	0.217990i	$0.930050\pi$
$734$		−	5.74199e8i		−	1.45203i
$735$		−	1.30856e8i		−	0.329557i
$736$	−3.33969e8	−	2.95904e8i	−0.837670	−	0.742193i
$737$	2.37834e8			0.594116
$738$	2.10973e8			0.524878
$739$	6.41482e8			1.58947			0.794733	−	0.606959i	$-0.207611\pi$
$739$	6.41482e8			1.58947			0.794733	+	0.606959i	$0.207611\pi$
$740$	−4.96306e7			−0.122477
$741$		−	1.33688e8i		−	0.328579i
$742$	−2.50179e8			−0.612406
$743$			4.67416e8i			1.13956i	0.821798	+	0.569779i	$0.192971\pi$
$743$			4.67416e8i			1.13956i	−0.821798	+	0.569779i	$0.807029\pi$
$744$	2.53620e8			0.615835
$745$	−1.89927e8			−0.459324
$746$			5.28150e8i			1.27216i
$747$		−	1.04141e8i		−	0.249840i
$748$	−9.00341e8			−2.15131
$749$	1.94074e8			0.461872
$750$		−	4.96511e7i		−	0.117691i
$751$			4.67104e8i			1.10279i	0.834243	+	0.551396i	$0.185905\pi$
$751$			4.67104e8i			1.10279i	−0.834243	+	0.551396i	$0.814095\pi$
$752$	−2.47221e7			−0.0581342
$753$			6.14259e7i			0.143869i
$754$	−9.95248e8			−2.32176
$755$			6.02300e7i			0.139950i
$756$			2.37153e8i			0.548862i
$757$			5.24867e8i			1.20993i	0.796251	+	0.604966i	$0.206814\pi$
$757$			5.24867e8i			1.20993i	−0.796251	+	0.604966i	$0.793186\pi$
$758$			2.70880e7i			0.0621971i
$759$	2.33640e8	−	2.63696e8i	0.534345	−	0.603084i
$760$	6.73840e7			0.153503
$761$	3.55642e8			0.806972			0.403486	−	0.914986i	$-0.367798\pi$
$761$	3.55642e8			0.806972			0.403486	+	0.914986i	$0.367798\pi$
$762$	−6.62302e8			−1.49690
$763$	−2.33749e8			−0.526231
$764$		−	1.17134e9i		−	2.62666i
$765$	−9.12307e7			−0.203778
$766$		−	1.01661e9i		−	2.26187i
$767$	4.03842e8			0.895005
$768$	−2.75128e8			−0.607368
$769$		−	5.30836e7i		−	0.116730i	−0.998295	−	0.0583648i	$-0.981411\pi$
$769$		−	5.30836e7i		−	0.116730i	0.998295	−	0.0583648i	$-0.0185887\pi$
$770$			1.03804e8i			0.227375i
$771$	−3.09339e8			−0.674949
$772$	9.41417e7			0.204612
$773$		−	7.10550e8i		−	1.53835i	−0.639036	−	0.769177i	$-0.720666\pi$
$773$		−	7.10550e8i		−	1.53835i	0.639036	−	0.769177i	$-0.279334\pi$
$774$			4.09181e8i			0.882455i
$775$	7.97271e7			0.171278
$776$		−	3.49121e8i		−	0.747121i
$777$	−2.23337e7			−0.0476099
$778$		−	4.89111e8i		−	1.03865i
$779$		−	1.91192e8i		−	0.404442i
$780$		−	2.74003e8i		−	0.577392i
$781$			3.59018e8i			0.753639i
$782$	−7.20428e8	+	8.13105e8i	−1.50650	+	1.70030i
$783$	−7.50901e8			−1.56422
$784$	−6.66781e7			−0.138368
$785$	−4.31804e8			−0.892642
$786$	−2.46004e8			−0.506611
$787$		−	5.96861e8i		−	1.22447i	−0.790675	−	0.612237i	$-0.790270\pi$
$787$		−	5.96861e8i		−	1.22447i	0.790675	−	0.612237i	$-0.209730\pi$
$788$	8.67394e7			0.177271
$789$		−	1.25092e8i		−	0.254683i
$790$	1.04250e8			0.211444
$791$	2.09898e8			0.424110
$792$			1.35513e8i			0.272775i
$793$			6.34869e8i			1.27311i
$794$	4.59019e8			0.916999
$795$	2.18086e8			0.434037
$796$		−	7.74966e8i		−	1.53654i
$797$			2.04326e8i			0.403597i	0.979427	+	0.201798i	$0.0646786\pi$
$797$			2.04326e8i			0.403597i	−0.979427	+	0.201798i	$0.935321\pi$
$798$	8.58076e7			0.168856
$799$			2.72648e8i			0.534517i
$800$	−1.14603e8			−0.223834
$801$		−	2.41001e8i		−	0.468944i
$802$		−	7.95816e7i		−	0.154273i
$803$		−	5.64988e7i		−	0.109117i
$804$		−	4.02944e8i		−	0.775312i
$805$	5.69327e7	+	5.04436e7i	0.109138	+	0.0966982i
$806$	7.24478e8			1.38363
$807$	−5.52318e8			−1.05092
$808$	−7.21199e8			−1.36717
$809$	8.15631e8			1.54045			0.770226	−	0.637771i	$-0.220143\pi$
$809$	8.15631e8			1.54045			0.770226	+	0.637771i	$0.220143\pi$
$810$		−	2.19011e8i		−	0.412107i
$811$	6.49009e8			1.21671			0.608357	−	0.793664i	$-0.291829\pi$
$811$	6.49009e8			1.21671			0.608357	+	0.793664i	$0.291829\pi$
$812$		−	3.87945e8i		−	0.724606i
$813$	−4.61796e8			−0.859366
$814$	−1.48938e8			−0.276143
$815$			2.71026e8i			0.500654i
$816$		−	9.87467e7i		−	0.181741i
$817$	3.70815e8			0.679972
$818$	−8.70996e8			−1.59132
$819$			5.80464e7i			0.105663i
$820$		−	3.91859e8i		−	0.710703i
$821$	8.04621e8			1.45399			0.726996	−	0.686642i	$-0.240916\pi$
$821$	8.04621e8			1.45399			0.726996	+	0.686642i	$0.240916\pi$
$822$		−	5.30439e8i		−	0.955036i
$823$	6.46700e8			1.16012			0.580061	−	0.814573i	$-0.303029\pi$
$823$	6.46700e8			1.16012			0.580061	+	0.814573i	$0.303029\pi$
$824$			8.83121e7i			0.157848i
$825$		−	9.04884e7i		−	0.161150i
$826$			2.59205e8i			0.459942i
$827$			8.71144e8i			1.54019i	0.637931	+	0.770093i	$0.279790\pi$
$827$			8.71144e8i			1.54019i	−0.637931	+	0.770093i	$0.720210\pi$
$828$	2.10321e8	+	1.86349e8i	0.370504	+	0.328274i
$829$	1.04437e8			0.183312			0.0916560	−	0.995791i	$-0.470784\pi$
$829$	1.04437e8			0.183312			0.0916560	+	0.995791i	$0.470784\pi$
$830$	−3.18507e8			−0.557037
$831$	−6.29598e7			−0.109714
$832$	−9.51114e8			−1.65144
$833$			7.35361e8i			1.27223i
$834$	2.34317e7			0.0403930
$835$			1.17162e8i			0.201246i
$836$	3.47519e8			0.594784
$837$	5.46608e8			0.932180
$838$			8.75093e8i			1.48704i
$839$			1.51530e8i			0.256573i	0.991737	+	0.128287i	$0.0409477\pi$
$839$			1.51530e8i			0.256573i	−0.991737	+	0.128287i	$0.959052\pi$
$840$	6.21483e7			0.104856
$841$	6.33532e8			1.06508
$842$			4.41695e8i			0.739923i
$843$		−	2.65156e8i		−	0.442608i
$844$	−2.87432e8			−0.478089
$845$		−	6.76487e6i		−	0.0112122i
$846$	1.16127e8			0.191788
$847$		−	8.94000e6i		−	0.0147125i
$848$		−	1.11127e8i		−	0.182235i
$849$			1.71783e8i			0.280710i
$850$			2.79021e8i			0.454339i
$851$	−7.23764e7	+	8.16870e7i	−0.117438	+	0.132545i
$852$	6.08257e8			0.983487
$853$	7.68836e8			1.23876			0.619379	−	0.785092i	$-0.287384\pi$
$853$	7.68836e8			1.23876			0.619379	+	0.785092i	$0.287384\pi$
$854$	−4.07489e8			−0.654248
$855$	3.52138e7			0.0563396
$856$		−	7.74867e8i		−	1.23539i
$857$	−9.74767e8			−1.54867			−0.774334	−	0.632777i	$-0.781915\pi$
$857$	−9.74767e8			−1.54867			−0.774334	+	0.632777i	$0.781915\pi$
$858$		−	8.22266e8i		−	1.30182i
$859$	−8.50418e8			−1.34169			−0.670846	−	0.741596i	$-0.734069\pi$
$859$	−8.50418e8			−1.34169			−0.670846	+	0.741596i	$0.734069\pi$
$860$	7.60007e8			1.19487
$861$		−	1.76336e8i		−	0.276269i
$862$		−	1.24192e8i		−	0.193897i
$863$	−8.97745e8			−1.39676			−0.698378	−	0.715729i	$-0.746095\pi$
$863$	−8.97745e8			−1.39676			−0.698378	+	0.715729i	$0.746095\pi$
$864$	−7.85718e8			−1.21822
$865$			3.92615e8i			0.606623i
$866$		−	1.07299e9i		−	1.65212i
$867$	−5.51645e8			−0.846452
$868$			2.82399e8i			0.431822i
$869$	1.89995e8			0.289522
$870$			5.56853e8i			0.845635i
$871$		−	4.06752e8i		−	0.615566i
$872$			9.33275e8i			1.40754i
$873$		−	1.82445e8i		−	0.274214i
$874$	2.78075e8	−	3.13847e8i	0.416512	−	0.470093i
$875$	1.95367e7			0.0291627
$876$	−9.57217e7			−0.142396
$877$	−9.50582e8			−1.40926			−0.704629	−	0.709576i	$-0.748887\pi$
$877$	−9.50582e8			−1.40926			−0.704629	+	0.709576i	$0.748887\pi$
$878$	1.27661e9			1.88615
$879$		−	3.84533e8i		−	0.566196i
$880$	−4.61088e7			−0.0676606
$881$		−	1.15056e9i		−	1.68260i	−0.540566	−	0.841302i	$-0.681790\pi$
$881$		−	1.15056e9i		−	1.68260i	0.540566	−	0.841302i	$-0.318210\pi$
$882$	3.13206e8			0.456483
$883$	3.54216e7			0.0514501			0.0257250	−	0.999669i	$-0.491811\pi$
$883$	3.54216e7			0.0514501			0.0257250	+	0.999669i	$0.491811\pi$
$884$			1.53979e9i			2.22898i
$885$		−	2.25954e8i		−	0.325980i
$886$	1.92955e9			2.77431
$887$	2.44826e8			0.350822			0.175411	−	0.984495i	$-0.443875\pi$
$887$	2.44826e8			0.350822			0.175411	+	0.984495i	$0.443875\pi$
$888$			8.91704e7i			0.127345i
$889$		−	2.60603e8i		−	0.370915i
$890$	−7.37079e8			−1.04555
$891$		−	3.99144e8i		−	0.564283i
$892$	1.11629e9			1.57283
$893$		−	1.05238e8i		−	0.147781i
$894$			9.65642e8i			1.35146i
$895$		−	2.40547e8i		−	0.335529i
$896$		−	3.47986e8i		−	0.483769i
$897$	−4.50981e8	−	3.99579e8i	−0.624858	−	0.553637i
$898$	−1.72135e9			−2.37706
$899$	−8.94165e8			−1.23066
$900$	7.21728e7			0.0990024
$901$	−1.22556e9			−1.67557
$902$		−	1.17595e9i		−	1.60239i
$903$	3.42003e8			0.464479
$904$		−	8.38047e8i		−	1.13439i
$905$	1.98395e8			0.267661
$906$	3.06226e8			0.411772
$907$		−	2.19877e8i		−	0.294685i	−0.989086	−	0.147343i	$-0.952928\pi$
$907$		−	2.19877e8i		−	0.294685i	0.989086	−	0.147343i	$-0.0470720\pi$
$908$			1.51036e9i			2.01754i
$909$	−3.76887e8			−0.501787
$910$	1.77530e8			0.235585
$911$		−	4.00377e7i		−	0.0529558i	−0.999649	−	0.0264779i	$-0.991571\pi$
$911$		−	4.00377e7i		−	0.0529558i	0.999649	−	0.0264779i	$-0.00842917\pi$
$912$			3.81148e7i			0.0502469i
$913$	−5.80474e8			−0.762730
$914$			1.42998e9i			1.87280i
$915$	3.55217e8			0.463692
$916$			7.43046e8i			0.966783i
$917$		−	9.67977e7i		−	0.125533i
$918$			1.91296e9i			2.47274i
$919$		−	9.55985e7i		−	0.123170i	−0.998102	−	0.0615850i	$-0.980384\pi$
$919$		−	9.55985e7i		−	0.123170i	0.998102	−	0.0615850i	$-0.0196155\pi$
$920$	2.01403e8	−	2.27312e8i	0.258644	−	0.291916i
$921$	4.36084e8			0.558202
$922$	1.16012e9			1.48017
$923$	6.14005e8			0.780848
$924$	3.20517e8			0.406289
$925$			2.80313e7i			0.0354175i
$926$	1.75255e9			2.20717
$927$			4.61504e7i			0.0579344i
$928$	1.28531e9			1.60829
$929$	6.80901e8			0.849253			0.424626	−	0.905369i	$-0.360405\pi$
$929$	6.80901e8			0.849253			0.424626	+	0.905369i	$0.360405\pi$
$930$		−	4.05354e8i		−	0.503948i
$931$		−	2.83839e8i		−	0.351741i
$932$	−1.42530e9			−1.76059
$933$	−2.38153e8			−0.293232
$934$			1.69329e9i			2.07821i
$935$			5.08511e8i			0.622108i
$936$	2.31758e8			0.282623
$937$			3.16140e8i			0.384292i	0.981366	+	0.192146i	$0.0615447\pi$
$937$			3.16140e8i			0.384292i	−0.981366	+	0.192146i	$0.938455\pi$
$938$	2.61072e8			0.316339
$939$			1.58198e8i			0.191075i
$940$		−	2.15692e8i		−	0.259687i
$941$			6.80761e8i			0.817007i	0.912757	+	0.408504i	$0.133949\pi$
$941$			6.80761e8i			0.817007i	−0.912757	+	0.408504i	$0.866051\pi$
$942$			2.19541e9i			2.62641i
$943$	−6.44961e8	−	5.71449e8i	−0.769128	−	0.681464i
$944$	−1.15136e8			−0.136866
$945$	1.33944e8			0.158718
$946$	2.28074e9			2.69403
$947$	−1.31424e7			−0.0154748			−0.00773742	−	0.999970i	$-0.502463\pi$
$947$	−1.31424e7			−0.0154748			−0.00773742	+	0.999970i	$0.502463\pi$
$948$		−	3.21894e8i		−	0.377822i
$949$	−9.66262e7			−0.113057
$950$		−	1.07698e8i		−	0.125614i
$951$	9.69101e8			1.12675
$952$	−3.49251e8			−0.404787
$953$		−	1.44397e9i		−	1.66832i	−0.551524	−	0.834159i	$-0.685953\pi$
$953$		−	1.44397e9i		−	1.66832i	0.551524	−	0.834159i	$-0.314047\pi$
$954$			5.21995e8i			0.601203i
$955$	−6.61574e8			−0.759570
$956$	1.27183e9			1.45564
$957$			1.01486e9i			1.15789i
$958$			2.18770e9i			2.48824i
$959$	2.08717e8			0.236648
$960$			5.32160e8i			0.601490i
$961$	−2.36608e8			−0.266599
$962$			2.54719e8i			0.286113i
$963$		−	4.04932e8i		−	0.453423i
$964$			1.90789e9i			2.12972i
$965$		−	5.31711e7i		−	0.0591690i
$966$	2.56469e8	−	2.89461e8i	0.284514	−	0.321114i
$967$	1.20301e9			1.33042			0.665212	−	0.746654i	$-0.268341\pi$
$967$	1.20301e9			1.33042			0.665212	+	0.746654i	$0.268341\pi$
$968$	−3.56942e7			−0.0393524
$969$	4.20350e8			0.461997
$970$	−5.57991e8			−0.611381
$971$		−	5.41032e8i		−	0.590969i	−0.955347	−	0.295485i	$-0.904519\pi$
$971$		−	5.41032e8i		−	0.590969i	0.955347	−	0.295485i	$-0.0954811\pi$
$972$	8.69653e8			0.946994
$973$			9.21992e6i			0.0100090i
$974$	−2.63192e9			−2.84837
$975$	−1.54756e8			−0.166968
$976$		−	1.81002e8i		−	0.194686i
$977$			2.17150e8i			0.232850i	0.993199	+	0.116425i	$0.0371435\pi$
$977$			2.17150e8i			0.232850i	−0.993199	+	0.116425i	$0.962856\pi$
$978$	1.37797e9			1.47307
$979$	−1.34332e9			−1.43163
$980$		−	5.81745e8i		−	0.618094i
$981$			4.87714e8i			0.516604i
$982$	2.34906e9			2.48061
$983$		−	4.24551e8i		−	0.446961i	−0.974708	−	0.223480i	$-0.928258\pi$
$983$		−	4.24551e8i		−	0.446961i	0.974708	−	0.223480i	$-0.0717418\pi$
$984$	−7.04046e8			−0.738951
$985$		−	4.89903e7i		−	0.0512627i
$986$		−	3.12931e9i		−	3.26451i
$987$		−	9.70613e7i		−	0.100947i
$988$		−	5.94339e8i		−	0.616259i
$989$	1.10832e9	−	1.25090e9i	1.14572	−	1.29310i
$990$	2.16586e8			0.223216
$991$	−1.08093e9			−1.11065			−0.555324	−	0.831634i	$-0.687406\pi$
$991$	−1.08093e9			−1.11065			−0.555324	+	0.831634i	$0.687406\pi$
$992$	−9.35625e8			−0.958444
$993$	−8.89186e8			−0.908123
$994$			3.94097e8i			0.401277i
$995$	−4.37700e8			−0.444332
$996$			9.83454e8i			0.995350i
$997$	−4.62455e8			−0.466642			−0.233321	−	0.972400i	$-0.574959\pi$
$997$	−4.62455e8			−0.466642			−0.233321	+	0.972400i	$0.574959\pi$
$998$	−5.09295e8			−0.512364
$999$			1.92182e8i			0.192760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.d.a.91.6	yes	48
23.22	odd	2	inner	115.7.d.a.91.5	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.d.a.91.5	✓	48	23.22	odd	2	inner
115.7.d.a.91.6	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-12.7662 q^{2} +22.2634 q^{3} +98.9763 q^{4} -55.9017i q^{5} -284.219 q^{6} -111.835i q^{7} -446.515 q^{8} -233.341 q^{9} +O(q^{10})\)	\(q-12.7662 q^{2} +22.2634 q^{3} +98.9763 q^{4} -55.9017i q^{5} -284.219 q^{6} -111.835i q^{7} -446.515 q^{8} -233.341 q^{9} +713.653i q^{10} +1300.62i q^{11} +2203.55 q^{12} +2224.37 q^{13} +1427.71i q^{14} -1244.56i q^{15} -634.172 q^{16} +6993.98i q^{17} +2978.89 q^{18} -2699.58i q^{19} -5532.94i q^{20} -2489.82i q^{21} -16604.0i q^{22} +(-9106.69 - 8068.72i) q^{23} -9940.95 q^{24} -3125.00 q^{25} -28396.8 q^{26} -21425.0 q^{27} -11069.0i q^{28} +35047.9 q^{29} +15888.3i q^{30} -25512.7 q^{31} +36673.0 q^{32} +28956.3i q^{33} -89286.6i q^{34} -6251.75 q^{35} -23095.3 q^{36} -8970.01i q^{37} +34463.4i q^{38} +49522.0 q^{39} +24961.0i q^{40} +70822.9 q^{41} +31785.6i q^{42} +137360. i q^{43} +128731. i q^{44} +13044.2i q^{45} +(116258. + 103007. i) q^{46} +38983.3 q^{47} -14118.8 q^{48} +105142. q^{49} +39894.4 q^{50} +155710. i q^{51} +220160. q^{52} +175231. i q^{53} +273516. q^{54} +72707.1 q^{55} +49935.9i q^{56} -60101.7i q^{57} -447429. q^{58} +181554. q^{59} -123182. i q^{60} +285415. i q^{61} +325700. q^{62} +26095.7i q^{63} -427588. q^{64} -124346. i q^{65} -369662. i q^{66} -182861. i q^{67} +692238. i q^{68} +(-202746. - 179637. i) q^{69} +79811.2 q^{70} +276035. q^{71} +104191. q^{72} -43439.8 q^{73} +114513. i q^{74} -69573.1 q^{75} -267194. i q^{76} +145455. q^{77} -632209. q^{78} -146080. i q^{79} +35451.3i q^{80} -306887. q^{81} -904140. q^{82} +446305. i q^{83} -246433. i q^{84} +390975. q^{85} -1.75357e6i q^{86} +780285. q^{87} -580748. i q^{88} +1.03283e6i q^{89} -166525. i q^{90} -248762. i q^{91} +(-901346. - 798612. i) q^{92} -567998. q^{93} -497669. q^{94} -150911. q^{95} +816464. q^{96} +781880. i q^{97} -1.34227e6 q^{98} -303489. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 20 q^{2} + 1584 q^{4} + 410 q^{6} - 1210 q^{8} + 12896 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

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