LMFDB - Embedded newform 75.9.c.f.26.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(26,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.26");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 1634x^{8} + 776307x^{6} + 148116566x^{4} + 10575941812x^{2} + 105274575720 $ x^10 + 1634x^8 + 776307x^6 + 148116566x^4 + 10575941812x^2 + 105274575720
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3^{11}\cdot 5^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			26.4
Root			$-13.7835i$ of defining polynomial
Character	$\chi$	$=$	75.26
Dual form			75.9.c.f.26.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.2639i q^{2} +(77.7167 - 22.8278i) q^{3} -8.51375 q^{4} +(-371.269 - 1263.98i) q^{6} -569.895 q^{7} -4025.09i q^{8} +(5518.78 - 3548.20i) q^{9} +O(q^{10})$	\(q-16.2639i q^{2} +(77.7167 - 22.8278i) q^{3} -8.51375 q^{4} +(-371.269 - 1263.98i) q^{6} -569.895 q^{7} -4025.09i q^{8} +(5518.78 - 3548.20i) q^{9} +6582.70i q^{11} +(-661.661 + 194.350i) q^{12} -28214.2 q^{13} +9268.70i q^{14} -67643.0 q^{16} -151139. i q^{17} +(-57707.6 - 89756.8i) q^{18} +41572.9 q^{19} +(-44290.4 + 13009.4i) q^{21} +107060. q^{22} -173241. i q^{23} +(-91883.9 - 312817. i) q^{24} +458873. i q^{26} +(347904. - 401737. i) q^{27} +4851.94 q^{28} -783419. i q^{29} -215271. q^{31} +69716.1i q^{32} +(150269. + 511586. i) q^{33} -2.45811e6 q^{34} +(-46985.6 + 30208.5i) q^{36} +2.71385e6 q^{37} -676137. i q^{38} +(-2.19272e6 + 644068. i) q^{39} -676092. i q^{41} +(211584. + 720333. i) q^{42} -4.21531e6 q^{43} -56043.5i q^{44} -2.81758e6 q^{46} +8.87092e6i q^{47} +(-5.25700e6 + 1.54414e6i) q^{48} -5.44002e6 q^{49} +(-3.45018e6 - 1.17461e7i) q^{51} +240209. q^{52} -6.53406e6i q^{53} +(-6.53379e6 - 5.65827e6i) q^{54} +2.29387e6i q^{56} +(3.23091e6 - 949019. i) q^{57} -1.27414e7 q^{58} +1.54958e7i q^{59} -8.68344e6 q^{61} +3.50114e6i q^{62} +(-3.14512e6 + 2.02210e6i) q^{63} -1.61828e7 q^{64} +(8.32037e6 - 2.44395e6i) q^{66} +2.87523e7 q^{67} +1.28676e6i q^{68} +(-3.95472e6 - 1.34638e7i) q^{69} +3.73955e7i q^{71} +(-1.42818e7 - 2.22136e7i) q^{72} +3.75089e7 q^{73} -4.41378e7i q^{74} -353942. q^{76} -3.75145e6i q^{77} +(1.04751e7 + 3.56621e7i) q^{78} +4.22725e7 q^{79} +(1.78672e7 - 3.91635e7i) q^{81} -1.09959e7 q^{82} -7.28474e7i q^{83} +(377077. - 110759. i) q^{84} +6.85572e7i q^{86} +(-1.78837e7 - 6.08847e7i) q^{87} +2.64959e7 q^{88} +5.99236e7i q^{89} +1.60791e7 q^{91} +1.47494e6i q^{92} +(-1.67302e7 + 4.91416e6i) q^{93} +1.44276e8 q^{94} +(1.59146e6 + 5.41811e6i) q^{96} -1.15177e7 q^{97} +8.84758e7i q^{98} +(2.33568e7 + 3.63285e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 25 q^{3} - 1554 q^{4} + 2257 q^{6} - 1960 q^{7} - 11207 q^{9}+O(q^{10}) $ 10 * q + 25 * q^3 - 1554 * q^4 + 2257 * q^6 - 1960 * q^7 - 11207 * q^9	$ 10 q + 25 q^{3} - 1554 q^{4} + 2257 q^{6} - 1960 q^{7} - 11207 q^{9} + 5915 q^{12} + 16920 q^{13} + 44634 q^{16} + 224875 q^{18} - 143934 q^{19} + 673428 q^{21} - 818990 q^{22} - 1016859 q^{24} + 260830 q^{27} - 3810100 q^{28} - 3014060 q^{31} + 4677515 q^{33} + 4977146 q^{34} + 4500527 q^{36} - 3016760 q^{37} - 7513282 q^{39} + 4001760 q^{42} - 11747340 q^{43} - 13938636 q^{46} + 14748755 q^{48} + 8953546 q^{49} + 6209287 q^{51} + 38918320 q^{52} - 8886272 q^{54} - 14759525 q^{57} + 48407900 q^{58} + 1520220 q^{61} - 74748240 q^{63} - 4536998 q^{64} + 10465295 q^{66} + 16269290 q^{67} + 11394978 q^{69} - 172231185 q^{72} + 52090170 q^{73} - 29529046 q^{76} - 198205810 q^{78} + 8549896 q^{79} + 22612945 q^{81} + 295714190 q^{82} - 136883292 q^{84} - 318901610 q^{87} + 310673250 q^{88} - 107224264 q^{91} - 79679130 q^{93} + 356118596 q^{94} + 525424001 q^{96} + 402167800 q^{97} - 382421335 q^{99}+O(q^{100}) $ 10 * q + 25 * q^3 - 1554 * q^4 + 2257 * q^6 - 1960 * q^7 - 11207 * q^9 + 5915 * q^12 + 16920 * q^13 + 44634 * q^16 + 224875 * q^18 - 143934 * q^19 + 673428 * q^21 - 818990 * q^22 - 1016859 * q^24 + 260830 * q^27 - 3810100 * q^28 - 3014060 * q^31 + 4677515 * q^33 + 4977146 * q^34 + 4500527 * q^36 - 3016760 * q^37 - 7513282 * q^39 + 4001760 * q^42 - 11747340 * q^43 - 13938636 * q^46 + 14748755 * q^48 + 8953546 * q^49 + 6209287 * q^51 + 38918320 * q^52 - 8886272 * q^54 - 14759525 * q^57 + 48407900 * q^58 + 1520220 * q^61 - 74748240 * q^63 - 4536998 * q^64 + 10465295 * q^66 + 16269290 * q^67 + 11394978 * q^69 - 172231185 * q^72 + 52090170 * q^73 - 29529046 * q^76 - 198205810 * q^78 + 8549896 * q^79 + 22612945 * q^81 + 295714190 * q^82 - 136883292 * q^84 - 318901610 * q^87 + 310673250 * q^88 - 107224264 * q^91 - 79679130 * q^93 + 356118596 * q^94 + 525424001 * q^96 + 402167800 * q^97 - 382421335 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	16.2639i		−	1.01649i	−0.861212	−	0.508246i	$-0.830294\pi$
$2$		−	16.2639i		−	1.01649i	0.861212	−	0.508246i	$-0.169706\pi$
$3$	77.7167	−	22.8278i	0.959466	−	0.281825i
$3$	77.7167	−	22.8278i	0.959466	−	0.281825i
$4$	−8.51375			−0.0332569
$5$		0			0
$5$		0			0
$6$	−371.269	−	1263.98i	−0.286473	−	0.975290i
$7$	−569.895			−0.237357			−0.118679	−	0.992933i	$-0.537866\pi$
$7$	−569.895			−0.237357			−0.118679	+	0.992933i	$0.537866\pi$
$8$		−	4025.09i		−	0.982687i
$9$	5518.78	−	3548.20i	0.841150	−	0.540802i
$10$		0			0
$11$			6582.70i			0.449607i	0.974404	+	0.224804i	$0.0721741\pi$
$11$			6582.70i			0.449607i	−0.974404	+	0.224804i	$0.927826\pi$
$12$	−661.661	+	194.350i	−0.0319088	+	0.00937260i
$13$	−28214.2			−0.987858			−0.493929	−	0.869502i	$-0.664440\pi$
$13$	−28214.2			−0.987858			−0.493929	+	0.869502i	$0.664440\pi$
$14$			9268.70i			0.241272i
$15$		0			0
$16$	−67643.0			−1.03215
$17$		−	151139.i		−	1.80960i	−0.425840	−	0.904798i	$-0.640021\pi$
$17$		−	151139.i		−	1.80960i	0.425840	−	0.904798i	$-0.359979\pi$
$18$	−57707.6	−	89756.8i	−0.549721	−	0.855022i
$19$	41572.9			0.319004			0.159502	−	0.987198i	$-0.449011\pi$
$19$	41572.9			0.319004			0.159502	+	0.987198i	$0.449011\pi$
$20$		0			0
$21$	−44290.4	+	13009.4i	−0.227736	+	0.0668931i
$22$	107060.			0.457022
$23$		−	173241.i		−	0.619071i	−0.950888	−	0.309536i	$-0.899826\pi$
$23$		−	173241.i		−	0.619071i	0.950888	−	0.309536i	$-0.100174\pi$
$24$	−91883.9	−	312817.i	−0.276945	−	0.942855i
$25$		0			0
$26$			458873.i			1.00415i
$27$	347904.	−	401737.i	0.654643	−	0.755938i
$28$	4851.94			0.00789375
$29$		−	783419.i		−	1.10765i	−0.832634	−	0.553824i	$-0.813168\pi$
$29$		−	783419.i		−	1.10765i	0.832634	−	0.553824i	$-0.186832\pi$
$30$		0			0
$31$	−215271.			−0.233098			−0.116549	−	0.993185i	$-0.537183\pi$
$31$	−215271.			−0.233098			−0.116549	+	0.993185i	$0.537183\pi$
$32$			69716.1i			0.0664864i
$33$	150269.	+	511586.i	0.126710	+	0.431383i
$34$	−2.45811e6			−1.83944
$35$		0			0
$36$	−46985.6	+	30208.5i	−0.0279740	+	0.0179854i
$37$	2.71385e6			1.44804			0.724018	−	0.689781i	$-0.242293\pi$
$37$	2.71385e6			1.44804			0.724018	+	0.689781i	$0.242293\pi$
$38$		−	676137.i		−	0.324265i
$39$	−2.19272e6	+	644068.i	−0.947816	+	0.278403i
$40$		0			0
$41$		−	676092.i		−	0.239260i	−0.992819	−	0.119630i	$-0.961829\pi$
$41$		−	676092.i		−	0.239260i	0.992819	−	0.119630i	$-0.0381709\pi$
$42$	211584.	+	720333.i	0.0679963	+	0.231492i
$43$	−4.21531e6			−1.23298			−0.616489	−	0.787364i	$-0.711445\pi$
$43$	−4.21531e6			−1.23298			−0.616489	+	0.787364i	$0.711445\pi$
$44$		−	56043.5i		−	0.0149525i
$45$		0			0
$46$	−2.81758e6			−0.629281
$47$			8.87092e6i			1.81793i	0.416872	+	0.908965i	$0.363126\pi$
$47$			8.87092e6i			1.81793i	−0.416872	+	0.908965i	$0.636874\pi$
$48$	−5.25700e6	+	1.54414e6i	−0.990314	+	0.290886i
$49$	−5.44002e6			−0.943662
$50$		0			0
$51$	−3.45018e6	−	1.17461e7i	−0.509989	−	1.73625i
$52$	240209.			0.0328531
$53$		−	6.53406e6i		−	0.828094i	−0.910255	−	0.414047i	$-0.864115\pi$
$53$		−	6.53406e6i		−	0.828094i	0.910255	−	0.414047i	$-0.135885\pi$
$54$	−6.53379e6	−	5.65827e6i	−0.768405	−	0.665440i
$55$		0			0
$56$			2.29387e6i			0.233248i
$57$	3.23091e6	−	949019.i	0.306074	−	0.0899032i
$58$	−1.27414e7			−1.12592
$59$			1.54958e7i			1.27881i	0.768871	+	0.639403i	$0.220819\pi$
$59$			1.54958e7i			1.27881i	−0.768871	+	0.639403i	$0.779181\pi$
$60$		0			0
$61$	−8.68344e6			−0.627152			−0.313576	−	0.949563i	$-0.601527\pi$
$61$	−8.68344e6			−0.627152			−0.313576	+	0.949563i	$0.601527\pi$
$62$			3.50114e6i			0.236942i
$63$	−3.14512e6	+	2.02210e6i	−0.199653	+	0.128363i
$64$	−1.61828e7			−0.964568
$65$		0			0
$66$	8.32037e6	−	2.44395e6i	0.438497	−	0.128800i
$67$	2.87523e7			1.42684			0.713418	−	0.700739i	$-0.247146\pi$
$67$	2.87523e7			1.42684			0.713418	+	0.700739i	$0.247146\pi$
$68$			1.28676e6i			0.0601815i
$69$	−3.95472e6	−	1.34638e7i	−0.174470	−	0.593978i
$70$		0			0
$71$			3.73955e7i			1.47159i	0.677207	+	0.735793i	$0.263190\pi$
$71$			3.73955e7i			1.47159i	−0.677207	+	0.735793i	$0.736810\pi$
$72$	−1.42818e7	−	2.22136e7i	−0.531439	−	0.826587i
$73$	3.75089e7			1.32082			0.660408	−	0.750907i	$-0.270383\pi$
$73$	3.75089e7			1.32082			0.660408	+	0.750907i	$0.270383\pi$
$74$		−	4.41378e7i		−	1.47192i
$75$		0			0
$76$	−353942.			−0.0106091
$77$		−	3.75145e6i		−	0.106718i
$78$	1.04751e7	+	3.56621e7i	0.282994	+	0.963448i
$79$	4.22725e7			1.08530			0.542649	−	0.839959i	$-0.317421\pi$
$79$	4.22725e7			1.08530			0.542649	+	0.839959i	$0.317421\pi$
$80$		0			0
$81$	1.78672e7	−	3.91635e7i	0.415066	−	0.909791i
$82$	−1.09959e7			−0.243206
$83$		−	7.28474e7i		−	1.53498i	−0.641064	−	0.767488i	$-0.721507\pi$
$83$		−	7.28474e7i		−	1.53498i	0.641064	−	0.767488i	$-0.278493\pi$
$84$	377077.	−	110759.i	0.00757379	−	0.00222465i
$85$		0			0
$86$			6.85572e7i			1.25331i
$87$	−1.78837e7	−	6.08847e7i	−0.312163	−	1.06275i
$88$	2.64959e7			0.441823
$89$			5.99236e7i			0.955077i	0.878611	+	0.477538i	$0.158471\pi$
$89$			5.99236e7i			0.955077i	−0.878611	+	0.477538i	$0.841529\pi$
$90$		0			0
$91$	1.60791e7			0.234475
$92$			1.47494e6i			0.0205884i
$93$	−1.67302e7	+	4.91416e6i	−0.223650	+	0.0656928i
$94$	1.44276e8			1.84791
$95$		0			0
$96$	1.59146e6	+	5.41811e6i	0.0187375	+	0.0637915i
$97$	−1.15177e7			−0.130100			−0.0650500	−	0.997882i	$-0.520721\pi$
$97$	−1.15177e7			−0.130100			−0.0650500	+	0.997882i	$0.520721\pi$
$98$			8.84758e7i			0.959225i
$99$	2.33568e7	+	3.63285e7i	0.243149	+	0.378187i
$100$		0			0
$101$		−	9.81566e7i		−	0.943266i	−0.881795	−	0.471633i	$-0.843665\pi$
$101$		−	9.81566e7i		−	0.943266i	0.881795	−	0.471633i	$-0.156335\pi$
$102$	−1.91036e8	+	5.61133e7i	−1.76488	+	0.518400i
$103$	1.66920e7			0.148306			0.0741529	−	0.997247i	$-0.476375\pi$
$103$	1.66920e7			0.148306			0.0741529	+	0.997247i	$0.476375\pi$
$104$			1.13565e8i			0.970755i
$105$		0			0
$106$	−1.06269e8			−0.841751
$107$			4.28172e7i			0.326651i	0.986572	+	0.163325i	$0.0522220\pi$
$107$			4.28172e7i			0.326651i	−0.986572	+	0.163325i	$0.947778\pi$
$108$	−2.96197e6	+	3.42029e6i	−0.0217714	+	0.0251401i
$109$	1.49703e8			1.06053			0.530266	−	0.847831i	$-0.322092\pi$
$109$	1.49703e8			1.06053			0.530266	+	0.847831i	$0.322092\pi$
$110$		0			0
$111$	2.10912e8	−	6.19513e7i	1.38934	−	0.408092i
$112$	3.85494e7			0.244988
$113$		−	1.27819e7i		−	0.0783937i	−0.999232	−	0.0391969i	$-0.987520\pi$
$113$		−	1.27819e7i		−	0.0783937i	0.999232	−	0.0391969i	$-0.0124799\pi$
$114$	−1.54347e7	−	5.25472e7i	−0.0913860	−	0.311122i
$115$		0			0
$116$			6.66983e6i			0.0368369i
$117$	−1.55708e8	+	1.00110e8i	−0.830937	+	0.534236i
$118$	2.52021e8			1.29990
$119$			8.61335e7i			0.429521i
$120$		0			0
$121$	1.71027e8			0.797853
$122$			1.41226e8i			0.637495i
$123$	−1.54337e7	−	5.25437e7i	−0.0674295	−	0.229562i
$124$	1.83276e6			0.00775211
$125$		0			0
$126$	3.28872e7	+	5.11519e7i	0.130480	+	0.202946i
$127$	2.68115e8			1.03064			0.515320	−	0.856998i	$-0.327673\pi$
$127$	2.68115e8			1.03064			0.515320	+	0.856998i	$0.327673\pi$
$128$			2.81042e8i			1.04696i
$129$	−3.27600e8	+	9.62261e7i	−1.18300	+	0.347484i
$130$		0			0
$131$			5.50651e6i			0.0186978i	0.999956	+	0.00934892i	$0.00297590\pi$
$131$			5.50651e6i			0.0186978i	−0.999956	+	0.00934892i	$0.997024\pi$
$132$	−1.27935e6	−	4.35552e6i	−0.00421399	−	0.0143464i
$133$	−2.36922e7			−0.0757179
$134$		−	4.67624e8i		−	1.45037i
$135$		0			0
$136$	−6.08349e8			−1.77827
$137$		−	5.57045e8i		−	1.58128i	−0.612283	−	0.790639i	$-0.709749\pi$
$137$		−	5.57045e8i		−	1.58128i	0.612283	−	0.790639i	$-0.290251\pi$
$138$	−2.18973e8	+	6.43191e7i	−0.603774	+	0.177347i
$139$	−3.34413e7			−0.0895827			−0.0447914	−	0.998996i	$-0.514262\pi$
$139$	−3.34413e7			−0.0895827			−0.0447914	+	0.998996i	$0.514262\pi$
$140$		0			0
$141$	2.02504e8	+	6.89419e8i	0.512338	+	1.74424i
$142$	6.08195e8			1.49586
$143$		−	1.85726e8i		−	0.444148i
$144$	−3.73307e8	+	2.40011e8i	−0.868193	+	0.558190i
$145$		0			0
$146$		−	6.10040e8i		−	1.34260i
$147$	−4.22781e8	+	1.24184e8i	−0.905411	+	0.265947i
$148$	−2.31051e7			−0.0481571
$149$		−	4.46572e8i		−	0.906037i	−0.891501	−	0.453019i	$-0.850347\pi$
$149$		−	4.46572e8i		−	0.906037i	0.891501	−	0.453019i	$-0.149653\pi$
$150$		0			0
$151$	−2.41495e8			−0.464515			−0.232257	−	0.972654i	$-0.574611\pi$
$151$	−2.41495e8			−0.464515			−0.232257	+	0.972654i	$0.574611\pi$
$152$		−	1.67335e8i		−	0.313481i
$153$	−5.36273e8	−	8.34105e8i	−0.978634	−	1.52214i
$154$	−6.10130e7			−0.108478
$155$		0			0
$156$	1.86683e7	−	5.48344e6i	0.0315214	−	0.00925880i
$157$	1.12488e9			1.85143			0.925713	−	0.378226i	$-0.123466\pi$
$157$	1.12488e9			1.85143			0.925713	+	0.378226i	$0.123466\pi$
$158$		−	6.87514e8i		−	1.10320i
$159$	−1.49158e8	−	5.07806e8i	−0.233377	−	0.794528i
$160$		0			0
$161$			9.87294e7i			0.146941i
$162$	−6.36951e8	−	2.90590e8i	−0.924796	−	0.421911i
$163$	−1.05083e9			−1.48861			−0.744307	−	0.667838i	$-0.767220\pi$
$163$	−1.05083e9			−1.48861			−0.744307	+	0.667838i	$0.767220\pi$
$164$			5.75609e6i			0.00795705i
$165$		0			0
$166$	−1.18478e9			−1.56029
$167$			1.52565e8i			0.196150i	0.995179	+	0.0980751i	$0.0312685\pi$
$167$			1.52565e8i			0.196150i	−0.995179	+	0.0980751i	$0.968731\pi$
$168$	5.23641e7	+	1.78272e8i	0.0657350	+	0.223793i
$169$	−1.96888e7			−0.0241364
$170$		0			0
$171$	2.29432e8	−	1.47509e8i	0.268330	−	0.172518i
$172$	3.58881e7			0.0410050
$173$			1.48867e9i			1.66193i	0.556321	+	0.830967i	$0.312212\pi$
$173$			1.48867e9i			1.66193i	−0.556321	+	0.830967i	$0.687788\pi$
$174$	−9.90222e8	+	2.90859e8i	−1.08028	+	0.317311i
$175$		0			0
$176$		−	4.45274e8i		−	0.464063i
$177$	3.53734e8	+	1.20428e9i	0.360399	+	1.22697i
$178$	9.74591e8			0.970828
$179$			6.73543e8i			0.656074i	0.944665	+	0.328037i	$0.106387\pi$
$179$			6.73543e8i			0.656074i	−0.944665	+	0.328037i	$0.893613\pi$
$180$		0			0
$181$	9.31938e8			0.868306			0.434153	−	0.900839i	$-0.357048\pi$
$181$	9.31938e8			0.868306			0.434153	+	0.900839i	$0.357048\pi$
$182$		−	2.61509e8i		−	0.238342i
$183$	−6.74849e8	+	1.98224e8i	−0.601731	+	0.176747i
$184$	−6.97312e8			−0.608353
$185$		0			0
$186$	7.99233e7	+	2.72097e8i	0.0667762	+	0.227338i
$187$	9.94905e8			0.813608
$188$		−	7.55248e7i		−	0.0604586i
$189$	−1.98269e8	+	2.28947e8i	−0.155384	+	0.179427i
$190$		0			0
$191$		−	6.44104e7i		−	0.0483974i	−0.999707	−	0.0241987i	$-0.992297\pi$
$191$		−	6.44104e7i		−	0.0483974i	0.999707	−	0.0241987i	$-0.00770344\pi$
$192$	−1.25767e9	+	3.69417e8i	−0.925470	+	0.271839i
$193$	9.15124e8			0.659554			0.329777	−	0.944059i	$-0.393026\pi$
$193$	9.15124e8			0.659554			0.329777	+	0.944059i	$0.393026\pi$
$194$			1.87322e8i			0.132246i
$195$		0			0
$196$	4.63150e7			0.0313832
$197$			1.99042e9i			1.32154i	0.750589	+	0.660769i	$0.229770\pi$
$197$			1.99042e9i			1.32154i	−0.750589	+	0.660769i	$0.770230\pi$
$198$	5.90842e8	−	3.79872e8i	0.384424	−	0.247159i
$199$	2.33793e9			1.49080			0.745400	−	0.666618i	$-0.232259\pi$
$199$	2.33793e9			1.49080			0.745400	+	0.666618i	$0.232259\pi$
$200$		0			0
$201$	2.23454e9	−	6.56352e8i	1.36900	−	0.402117i
$202$	−1.59641e9			−0.958823
$203$			4.46466e8i			0.262908i
$204$	2.93740e7	+	1.00003e8i	0.0169606	+	0.0577421i
$205$		0			0
$206$		−	2.71476e8i		−	0.150752i
$207$	−6.14696e8	−	9.56082e8i	−0.334795	−	0.520732i
$208$	1.90850e9			1.01962
$209$			2.73662e8i			0.143427i
$210$		0			0
$211$	−3.72705e7			−0.0188034			−0.00940168	−	0.999956i	$-0.502993\pi$
$211$	−3.72705e7			−0.0188034			−0.00940168	+	0.999956i	$0.502993\pi$
$212$			5.56294e7i			0.0275398i
$213$	8.53656e8	+	2.90625e9i	0.414729	+	1.41194i
$214$	6.96374e8			0.332038
$215$		0			0
$216$	−1.61702e9	−	1.40034e9i	−0.742851	−	0.643309i
$217$	1.22682e8			0.0553275
$218$		−	2.43475e9i		−	1.07802i
$219$	2.91507e9	−	8.56245e8i	1.26728	−	0.372239i
$220$		0			0
$221$			4.26428e9i			1.78762i
$222$	−1.00757e9	−	3.43024e9i	−0.414823	−	1.41225i
$223$	−2.51046e9			−1.01516			−0.507578	−	0.861606i	$-0.669459\pi$
$223$	−2.51046e9			−1.01516			−0.507578	+	0.861606i	$0.669459\pi$
$224$		−	3.97308e7i		−	0.0157810i
$225$		0			0
$226$	−2.07883e8			−0.0796866
$227$		−	1.11767e9i		−	0.420930i	−0.977601	−	0.210465i	$-0.932502\pi$
$227$		−	1.11767e9i		−	0.420930i	0.977601	−	0.210465i	$-0.0674979\pi$
$228$	−2.75072e7	+	8.07971e6i	−0.0101790	+	0.00298990i
$229$	3.29155e9			1.19690			0.598450	−	0.801160i	$-0.295783\pi$
$229$	3.29155e9			1.19690			0.598450	+	0.801160i	$0.295783\pi$
$230$		0			0
$231$	−8.56372e7	−	2.91550e8i	−0.0300756	−	0.102392i
$232$	−3.15333e9			−1.08847
$233$		−	1.74654e9i		−	0.592591i	−0.955096	−	0.296296i	$-0.904249\pi$
$233$		−	1.74654e9i		−	0.592591i	0.955096	−	0.296296i	$-0.0957514\pi$
$234$	1.62817e9	+	2.53242e9i	0.543047	+	0.844641i
$235$		0			0
$236$		−	1.31927e8i		−	0.0425291i
$237$	3.28528e9	−	9.64988e8i	1.04131	−	0.305864i
$238$	1.40086e9			0.436605
$239$			3.20404e9i			0.981988i	0.871163	+	0.490994i	$0.163366\pi$
$239$			3.20404e9i			0.981988i	−0.871163	+	0.490994i	$0.836634\pi$
$240$		0			0
$241$	2.32540e9			0.689334			0.344667	−	0.938725i	$-0.387992\pi$
$241$	2.32540e9			0.689334			0.344667	+	0.938725i	$0.387992\pi$
$242$		−	2.78156e9i		−	0.811012i
$243$	4.94565e8	−	3.45153e9i	0.141840	−	0.989890i
$244$	7.39287e7			0.0208571
$245$		0			0
$246$	−8.54564e8	+	2.51012e8i	−0.233348	+	0.0685415i
$247$	−1.17295e9			−0.315131
$248$			8.66484e8i			0.229062i
$249$	−1.66294e9	−	5.66146e9i	−0.432594	−	1.47276i
$250$		0			0
$251$			3.38503e9i			0.852840i	0.904525	+	0.426420i	$0.140225\pi$
$251$			3.38503e9i			0.852840i	−0.904525	+	0.426420i	$0.859775\pi$
$252$	2.67768e7	−	1.72157e7i	0.00663983	−	0.00426896i
$253$	1.14040e9			0.278339
$254$		−	4.36059e9i		−	1.04764i
$255$		0			0
$256$	4.28043e8			0.0996614
$257$		−	9.71066e8i		−	0.222595i	−0.993787	−	0.111298i	$-0.964499\pi$
$257$		−	9.71066e8i		−	0.222595i	0.993787	−	0.111298i	$-0.0355007\pi$
$258$	1.56501e9	+	5.32804e9i	0.353214	+	1.20251i
$259$	−1.54661e9			−0.343702
$260$		0			0
$261$	−2.77973e9	−	4.32352e9i	−0.599019	−	0.931698i
$262$	8.95573e7			0.0190062
$263$			2.06605e8i			0.0431835i	0.999767	+	0.0215918i	$0.00687341\pi$
$263$			2.06605e8i			0.0431835i	−0.999767	+	0.0215918i	$0.993127\pi$
$264$	2.05918e9	−	6.04844e8i	0.423914	−	0.124517i
$265$		0			0
$266$			3.85327e8i			0.0769667i
$267$	1.36792e9	+	4.65707e9i	0.269164	+	0.916363i
$268$	−2.44790e8			−0.0474520
$269$			3.12793e9i			0.597376i	0.954351	+	0.298688i	$0.0965489\pi$
$269$			3.12793e9i			0.597376i	−0.954351	+	0.298688i	$0.903451\pi$
$270$		0			0
$271$	4.61051e9			0.854814			0.427407	−	0.904059i	$-0.359427\pi$
$271$	4.61051e9			0.854814			0.427407	+	0.904059i	$0.359427\pi$
$272$			1.02235e10i			1.86778i
$273$	1.24962e9	−	3.67051e8i	0.224971	−	0.0660809i
$274$	−9.05972e9			−1.60736
$275$		0			0
$276$	3.36695e7	+	1.14627e8i	0.00580231	+	0.0197538i
$277$	−1.77445e9			−0.301401			−0.150700	−	0.988579i	$-0.548153\pi$
$277$	−1.77445e9			−0.301401			−0.150700	+	0.988579i	$0.548153\pi$
$278$			5.43886e8i			0.0910602i
$279$	−1.18803e9	+	7.63825e8i	−0.196070	+	0.126060i
$280$		0			0
$281$			7.80582e7i			0.0125197i	0.999980	+	0.00625984i	$0.00199258\pi$
$281$			7.80582e7i			0.0125197i	−0.999980	+	0.00625984i	$0.998007\pi$
$282$	1.12126e10	−	3.29349e9i	1.77301	−	0.520787i
$283$	−8.12145e9			−1.26616			−0.633079	−	0.774088i	$-0.718209\pi$
$283$	−8.12145e9			−1.26616			−0.633079	+	0.774088i	$0.718209\pi$
$284$		−	3.18376e8i		−	0.0489403i
$285$		0			0
$286$	−3.02062e9			−0.451473
$287$			3.85301e8i			0.0567902i
$288$	2.47367e8	+	3.84748e8i	0.0359560	+	0.0559250i
$289$	−1.58673e10			−2.27464
$290$		0			0
$291$	−8.95115e8	+	2.62923e8i	−0.124826	+	0.0366654i
$292$	−3.19341e8			−0.0439262
$293$			2.52625e9i			0.342773i	0.985204	+	0.171386i	$0.0548246\pi$
$293$			2.52625e9i			0.342773i	−0.985204	+	0.171386i	$0.945175\pi$
$294$	2.01971e9	+	6.87605e9i	0.270333	+	0.920344i
$295$		0			0
$296$		−	1.09235e10i		−	1.42297i
$297$	2.64451e9	+	2.29015e9i	0.339875	+	0.294332i
$298$	−7.26299e9			−0.920980
$299$			4.88787e9i			0.611554i
$300$		0			0
$301$	2.40228e9			0.292656
$302$			3.92764e9i			0.472176i
$303$	−2.24070e9	−	7.62841e9i	−0.265836	−	0.905032i
$304$	−2.81212e9			−0.329260
$305$		0			0
$306$	−1.35658e10	+	8.72188e9i	−1.54725	+	0.994774i
$307$	−1.03150e10			−1.16123			−0.580613	−	0.814180i	$-0.697187\pi$
$307$	−1.03150e10			−1.16123			−0.580613	+	0.814180i	$0.697187\pi$
$308$			3.19389e7i			0.00354909i
$309$	1.29724e9	−	3.81040e8i	0.142294	−	0.0417962i
$310$		0			0
$311$		−	1.72354e10i		−	1.84239i	−0.389106	−	0.921193i	$-0.627216\pi$
$311$		−	1.72354e10i		−	1.84239i	0.389106	−	0.921193i	$-0.372784\pi$
$312$	2.59243e9	+	8.82587e9i	0.273583	+	0.931407i
$313$	−5.42800e9			−0.565539			−0.282770	−	0.959188i	$-0.591253\pi$
$313$	−5.42800e9			−0.565539			−0.282770	+	0.959188i	$0.591253\pi$
$314$		−	1.82949e10i		−	1.88196i
$315$		0			0
$316$	−3.59897e8			−0.0360936
$317$		−	1.16981e10i		−	1.15845i	−0.815167	−	0.579226i	$-0.803355\pi$
$317$		−	1.16981e10i		−	1.15845i	0.815167	−	0.579226i	$-0.196645\pi$
$318$	−8.25889e9	+	2.42589e9i	−0.807632	+	0.237226i
$319$	5.15701e9			0.498007
$320$		0			0
$321$	9.77423e8	+	3.32761e9i	0.0920582	+	0.313410i
$322$	1.60572e9			0.149364
$323$		−	6.28331e9i		−	0.577269i
$324$	−1.52117e8	+	3.33429e8i	−0.0138038	+	0.0302568i
$325$		0			0
$326$			1.70906e10i			1.51316i
$327$	1.16344e10	−	3.41738e9i	1.01754	−	0.298884i
$328$	−2.72133e9			−0.235118
$329$		−	5.05549e9i		−	0.431499i
$330$		0			0
$331$	−6.03632e9			−0.502875			−0.251438	−	0.967873i	$-0.580903\pi$
$331$	−6.03632e9			−0.502875			−0.251438	+	0.967873i	$0.580903\pi$
$332$			6.20205e8i			0.0510485i
$333$	1.49772e10	−	9.62930e9i	1.21801	−	0.783101i
$334$	2.48130e9			0.199385
$335$		0			0
$336$	2.99593e9	−	8.79998e8i	0.235058	−	0.0690438i
$337$	−1.35475e9			−0.105037			−0.0525183	−	0.998620i	$-0.516725\pi$
$337$	−1.35475e9			−0.105037			−0.0525183	+	0.998620i	$0.516725\pi$
$338$			3.20216e8i			0.0245345i
$339$	−2.91782e8	−	9.93367e8i	−0.0220933	−	0.0752161i
$340$		0			0
$341$		−	1.41706e9i		−	0.104803i
$342$	−2.39907e9	−	3.73146e9i	−0.175363	−	0.272756i
$343$	6.38557e9			0.461342
$344$			1.69670e10i			1.21163i
$345$		0			0
$346$	2.42115e10			1.68934
$347$		−	2.47345e10i		−	1.70602i	−0.521891	−	0.853012i	$-0.674773\pi$
$347$		−	2.47345e10i		−	1.70602i	0.521891	−	0.853012i	$-0.325227\pi$
$348$	1.52258e8	+	5.18358e8i	0.0103815	+	0.0353437i
$349$	−9.08306e9			−0.612253			−0.306126	−	0.951991i	$-0.599033\pi$
$349$	−9.08306e9			−0.612253			−0.306126	+	0.951991i	$0.599033\pi$
$350$		0			0
$351$	−9.81584e9	+	1.13347e10i	−0.646694	+	0.746760i
$352$	−4.58920e8			−0.0298928
$353$			1.66294e10i			1.07097i	0.844545	+	0.535485i	$0.179871\pi$
$353$			1.66294e10i			1.07097i	−0.844545	+	0.535485i	$0.820129\pi$
$354$	1.95863e10	−	5.75309e9i	1.24721	−	0.366343i
$355$		0			0
$356$		−	5.10175e8i		−	0.0317628i
$357$	1.96624e9	+	6.69401e9i	0.121050	+	0.412111i
$358$	1.09544e10			0.666894
$359$		−	6.51832e9i		−	0.392426i	−0.980561	−	0.196213i	$-0.937136\pi$
$359$		−	6.51832e9i		−	0.392426i	0.980561	−	0.196213i	$-0.0628644\pi$
$360$		0			0
$361$	−1.52553e10			−0.898236
$362$		−	1.51569e10i		−	0.882626i
$363$	1.32917e10	−	3.90417e9i	0.765513	−	0.224855i
$364$	−1.36894e8			−0.00779791
$365$		0			0
$366$	3.22389e9	+	1.09757e10i	0.179662	+	0.611655i
$367$	−1.72068e10			−0.948498			−0.474249	−	0.880391i	$-0.657280\pi$
$367$	−1.72068e10			−0.948498			−0.474249	+	0.880391i	$0.657280\pi$
$368$			1.17186e10i			0.638975i
$369$	−2.39891e9	−	3.73121e9i	−0.129393	−	0.201254i
$370$		0			0
$371$			3.72373e9i			0.196554i
$372$	1.42436e8	−	4.18380e7i	0.00743789	−	0.00218474i
$373$	1.47580e10			0.762418			0.381209	−	0.924489i	$-0.375508\pi$
$373$	1.47580e10			0.762418			0.381209	+	0.924489i	$0.375508\pi$
$374$		−	1.61810e10i		−	0.827026i
$375$		0			0
$376$	3.57062e10			1.78646
$377$			2.21035e10i			1.09420i
$378$	3.72357e9	+	3.22462e9i	0.182387	+	0.157947i
$379$	3.28781e10			1.59349			0.796746	−	0.604315i	$-0.206553\pi$
$379$	3.28781e10			1.59349			0.796746	+	0.604315i	$0.206553\pi$
$380$		0			0
$381$	2.08370e10	−	6.12048e9i	0.988863	−	0.290460i
$382$	−1.04756e9			−0.0491956
$383$			1.11696e10i			0.519089i	0.965731	+	0.259544i	$0.0835724\pi$
$383$			1.11696e10i			0.519089i	−0.965731	+	0.259544i	$0.916428\pi$
$384$	6.41557e9	+	2.18417e10i	0.295060	+	1.00452i
$385$		0			0
$386$		−	1.48835e10i		−	0.670432i
$387$	−2.32634e10	+	1.49568e10i	−1.03712	+	0.666797i
$388$	9.80585e7			0.00432672
$389$			3.14195e10i			1.37215i	0.727533	+	0.686073i	$0.240667\pi$
$389$			3.14195e10i			1.37215i	−0.727533	+	0.686073i	$0.759333\pi$
$390$		0			0
$391$	−2.61836e10			−1.12027
$392$			2.18966e10i			0.927324i
$393$	1.25702e8	+	4.27948e8i	0.00526951	+	0.0179399i
$394$	3.23719e10			1.34333
$395$		0			0
$396$	−1.98854e8	−	3.09292e8i	−0.00808636	−	0.0125773i
$397$	−8.73430e9			−0.351614			−0.175807	−	0.984425i	$-0.556253\pi$
$397$	−8.73430e9			−0.351614			−0.175807	+	0.984425i	$0.556253\pi$
$398$		−	3.80238e10i		−	1.51539i
$399$	−1.84128e9	+	5.40841e8i	−0.0726488	+	0.0213392i
$400$		0			0
$401$		−	1.27867e9i		−	0.0494516i	−0.999694	−	0.0247258i	$-0.992129\pi$
$401$		−	1.27867e9i		−	0.0494516i	0.999694	−	0.0247258i	$-0.00787127\pi$
$402$	−1.06748e10	−	3.63422e10i	−0.408749	−	1.39158i
$403$	6.07370e9			0.230268
$404$			8.35682e8i			0.0313701i
$405$		0			0
$406$	7.26127e9			0.267244
$407$			1.78645e10i			0.651047i
$408$	−4.72789e10	+	1.38873e10i	−1.70619	+	0.501160i
$409$	1.02810e10			0.367401			0.183701	−	0.982982i	$-0.441192\pi$
$409$	1.02810e10			0.367401			0.183701	+	0.982982i	$0.441192\pi$
$410$		0			0
$411$	−1.27161e10	−	4.32917e10i	−0.445643	−	1.51718i
$412$	−1.42111e8			−0.00493219
$413$		−	8.83095e9i		−	0.303534i
$414$	−1.55496e10	+	9.99734e9i	−0.529320	+	0.340317i
$415$		0			0
$416$		−	1.96698e9i		−	0.0656792i
$417$	−2.59895e9	+	7.63392e8i	−0.0859516	+	0.0252466i
$418$	4.45081e9			0.145792
$419$			3.60565e10i			1.16984i	0.811090	+	0.584922i	$0.198875\pi$
$419$			3.60565e10i			1.16984i	−0.811090	+	0.584922i	$0.801125\pi$
$420$		0			0
$421$	−3.63986e10			−1.15866			−0.579331	−	0.815092i	$-0.696686\pi$
$421$	−3.63986e10			−1.15866			−0.579331	+	0.815092i	$0.696686\pi$
$422$			6.06163e8i			0.0191135i
$423$	3.14758e10	+	4.89567e10i	0.983141	+	1.52915i
$424$	−2.63002e10			−0.813757
$425$		0			0
$426$	4.72670e10	−	1.38838e10i	1.43522	−	0.421569i
$427$	4.94865e9			0.148859
$428$		−	3.64535e8i		−	0.0108634i
$429$	−4.23971e9	−	1.44340e10i	−0.125172	−	0.426145i
$430$		0			0
$431$			3.03555e10i			0.879686i	0.898075	+	0.439843i	$0.144966\pi$
$431$			3.03555e10i			0.879686i	−0.898075	+	0.439843i	$0.855034\pi$
$432$	−2.35333e10	+	2.71747e10i	−0.675690	+	0.780242i
$433$	−3.45811e10			−0.983757			−0.491878	−	0.870664i	$-0.663690\pi$
$433$	−3.45811e10			−0.983757			−0.491878	+	0.870664i	$0.663690\pi$
$434$		−	1.99528e9i		−	0.0562400i
$435$		0			0
$436$	−1.27453e9			−0.0352700
$437$		−	7.20216e9i		−	0.197486i
$438$	−1.39259e10	−	4.74103e10i	−0.378378	−	1.28818i
$439$	−1.76997e9			−0.0476549			−0.0238275	−	0.999716i	$-0.507585\pi$
$439$	−1.76997e9			−0.0476549			−0.0238275	+	0.999716i	$0.507585\pi$
$440$		0			0
$441$	−3.00223e10	+	1.93023e10i	−0.793761	+	0.510334i
$442$	6.93537e10			1.81711
$443$			3.19676e10i			0.830033i	0.909814	+	0.415017i	$0.136224\pi$
$443$			3.19676e10i			0.830033i	−0.909814	+	0.415017i	$0.863776\pi$
$444$	−1.79565e9	+	5.27438e8i	−0.0462051	+	0.0135719i
$445$		0			0
$446$			4.08297e10i			1.03190i
$447$	−1.01942e10	−	3.47061e10i	−0.255344	−	0.869312i
$448$	9.22247e9			0.228947
$449$		−	8.00746e10i		−	1.97020i	−0.171994	−	0.985098i	$-0.555021\pi$
$449$		−	8.00746e10i		−	1.97020i	0.171994	−	0.985098i	$-0.444979\pi$
$450$		0			0
$451$	4.45051e9			0.107573
$452$			1.08822e8i			0.00260713i
$453$	−1.87682e10	+	5.51279e9i	−0.445686	+	0.130912i
$454$	−1.81777e10			−0.427873
$455$		0			0
$456$	−3.81988e9	−	1.30047e10i	−0.0883468	−	0.300775i
$457$	5.45219e10			1.24999			0.624994	−	0.780629i	$-0.285101\pi$
$457$	5.45219e10			1.24999			0.624994	+	0.780629i	$0.285101\pi$
$458$		−	5.35333e10i		−	1.21664i
$459$	−6.07182e10	−	5.25820e10i	−1.36794	−	1.18464i
$460$		0			0
$461$		−	3.66539e8i		−	0.00811552i	−0.999992	−	0.00405776i	$-0.998708\pi$
$461$		−	3.66539e8i		−	0.00811552i	0.999992	−	0.00405776i	$-0.00129163\pi$
$462$	−4.74174e9	+	1.39279e9i	−0.104081	+	0.0305716i
$463$	3.22822e10			0.702488			0.351244	−	0.936284i	$-0.385759\pi$
$463$	3.22822e10			0.702488			0.351244	+	0.936284i	$0.385759\pi$
$464$			5.29928e10i			1.14326i
$465$		0			0
$466$	−2.84055e10			−0.602365
$467$			2.11777e10i			0.445258i	0.974903	+	0.222629i	$0.0714638\pi$
$467$			2.11777e10i			0.445258i	−0.974903	+	0.222629i	$0.928536\pi$
$468$	1.32566e9	−	8.52310e8i	0.0276343	−	0.0177670i
$469$	−1.63858e10			−0.338670
$470$		0			0
$471$	8.74218e10	−	2.56785e10i	1.77638	−	0.521778i
$472$	6.23718e10			1.25667
$473$		−	2.77481e10i		−	0.554356i
$474$	−1.56944e10	−	5.34314e10i	−0.310908	−	1.05848i
$475$		0			0
$476$		−	7.33319e8i		−	0.0142845i
$477$	−2.31842e10	−	3.60601e10i	−0.447835	−	0.696551i
$478$	5.21101e10			0.998184
$479$		−	4.69016e10i		−	0.890934i	−0.895298	−	0.445467i	$-0.853038\pi$
$479$		−	4.69016e10i		−	0.890934i	0.895298	−	0.445467i	$-0.146962\pi$
$480$		0			0
$481$	−7.65692e10			−1.43045
$482$		−	3.78201e10i		−	0.700703i
$483$	2.25377e9	+	7.67293e9i	0.0414116	+	0.140985i
$484$	−1.45608e9			−0.0265341
$485$		0			0
$486$	−5.61353e10	−	8.04354e9i	−1.00622	−	0.144179i
$487$	1.34767e10			0.239590			0.119795	−	0.992799i	$-0.461776\pi$
$487$	1.34767e10			0.239590			0.119795	+	0.992799i	$0.461776\pi$
$488$			3.49516e10i			0.616294i
$489$	−8.16671e10	+	2.39881e10i	−1.42827	+	0.419528i
$490$		0			0
$491$			8.27160e10i			1.42319i	0.702589	+	0.711596i	$0.252027\pi$
$491$			8.27160e10i			1.42319i	−0.702589	+	0.711596i	$0.747973\pi$
$492$	1.31399e8	+	4.47344e8i	0.00224249	+	0.00763451i
$493$	−1.18405e11			−2.00440
$494$			1.90767e10i			0.320328i
$495$		0			0
$496$	1.45616e10			0.240592
$497$		−	2.13115e10i		−	0.349291i
$498$	−9.20773e10	+	2.70459e10i	−1.49705	+	0.439728i
$499$	1.96950e10			0.317653			0.158827	−	0.987307i	$-0.449229\pi$
$499$	1.96950e10			0.317653			0.158827	+	0.987307i	$0.449229\pi$
$500$		0			0
$501$	3.48272e9	+	1.18569e10i	0.0552800	+	0.188199i
$502$	5.50537e10			0.866906
$503$		−	5.14640e10i		−	0.803955i	−0.915649	−	0.401978i	$-0.868323\pi$
$503$		−	5.14640e10i		−	0.803955i	0.915649	−	0.401978i	$-0.131677\pi$
$504$	8.13914e9	+	1.26594e10i	0.126141	+	0.196196i
$505$		0			0
$506$		−	1.85473e10i		−	0.282929i
$507$	−1.53015e9	+	4.49452e8i	−0.0231580	+	0.00680223i
$508$	−2.28267e9			−0.0342758
$509$			7.84617e8i			0.0116893i	0.999983	+	0.00584463i	$0.00186041\pi$
$509$			7.84617e8i			0.0116893i	−0.999983	+	0.00584463i	$0.998140\pi$
$510$		0			0
$511$	−2.13761e10			−0.313505
$512$			6.49851e10i			0.945657i
$513$	1.44634e10	−	1.67014e10i	0.208834	−	0.241147i
$514$	−1.57933e10			−0.226267
$515$		0			0
$516$	2.78910e9	−	8.19246e8i	0.0393429	−	0.0115562i
$517$	−5.83946e10			−0.817355
$518$			2.51539e10i			0.349370i
$519$	3.39830e10	+	1.15695e11i	0.468374	+	1.59457i
$520$		0			0
$521$		−	1.39001e11i		−	1.88654i	−0.332024	−	0.943271i	$-0.607731\pi$
$521$		−	1.39001e11i		−	1.88654i	0.332024	−	0.943271i	$-0.392269\pi$
$522$	−7.03172e10	+	4.52092e10i	−0.947064	+	0.608898i
$523$	9.91022e9			0.132457			0.0662287	−	0.997804i	$-0.478903\pi$
$523$	9.91022e9			0.132457			0.0662287	+	0.997804i	$0.478903\pi$
$524$		−	4.68811e7i		−	0.000621831i
$525$		0			0
$526$	3.36020e9			0.0438957
$527$			3.25359e10i			0.421814i
$528$	−1.01646e10	−	3.46052e10i	−0.130784	−	0.445252i
$529$	4.82984e10			0.616751
$530$		0			0
$531$	5.49821e10	+	8.55178e10i	0.691582	+	1.07567i
$532$	2.01710e8			0.00251814
$533$			1.90754e10i			0.236355i
$534$	7.57420e10	−	2.22478e10i	0.931477	−	0.273603i
$535$		0			0
$536$		−	1.15731e11i		−	1.40213i
$537$	1.53755e10	+	5.23455e10i	0.184898	+	0.629481i
$538$	5.08722e10			0.607228
$539$		−	3.58100e10i		−	0.424277i
$540$		0			0
$541$	−2.74155e10			−0.320042			−0.160021	−	0.987114i	$-0.551156\pi$
$541$	−2.74155e10			−0.320042			−0.160021	+	0.987114i	$0.551156\pi$
$542$		−	7.49848e10i		−	0.868912i
$543$	7.24272e10	−	2.12741e10i	0.833110	−	0.244710i
$544$	1.05368e10			0.120314
$545$		0			0
$546$	−5.96967e9	−	2.03236e10i	−0.0671707	−	0.228681i
$547$	−8.62303e10			−0.963187			−0.481594	−	0.876395i	$-0.659942\pi$
$547$	−8.62303e10			−0.963187			−0.481594	+	0.876395i	$0.659942\pi$
$548$			4.74255e9i			0.0525883i
$549$	−4.79220e10	+	3.08106e10i	−0.527528	+	0.339165i
$550$		0			0
$551$		−	3.25690e10i		−	0.353344i
$552$	−5.41928e10	+	1.59181e10i	−0.583694	+	0.171449i
$553$	−2.40909e10			−0.257603
$554$			2.88594e10i			0.306372i
$555$		0			0
$556$	2.84711e8			0.00297924
$557$			6.87189e10i			0.713929i	0.934118	+	0.356965i	$0.116188\pi$
$557$			6.87189e10i			0.713929i	−0.934118	+	0.356965i	$0.883812\pi$
$558$	1.24228e10	+	1.93220e10i	0.128139	+	0.199304i
$559$	1.18932e11			1.21801
$560$		0			0
$561$	7.73208e10	−	2.27115e10i	0.780629	−	0.229295i
$562$	1.26953e9			0.0127262
$563$			9.04024e10i			0.899801i	0.893079	+	0.449901i	$0.148541\pi$
$563$			9.04024e10i			0.899801i	−0.893079	+	0.449901i	$0.851459\pi$
$564$	−1.72407e9	−	5.86954e9i	−0.0170387	−	0.0580080i
$565$		0			0
$566$			1.32086e11i			1.28704i
$567$	−1.01824e10	+	2.23191e10i	−0.0985188	+	0.215946i
$568$	1.50520e11			1.44611
$569$			1.77922e11i			1.69739i	0.528886	+	0.848693i	$0.322610\pi$
$569$			1.77922e11i			1.69739i	−0.528886	+	0.848693i	$0.677390\pi$
$570$		0			0
$571$	1.96988e11			1.85309			0.926543	−	0.376189i	$-0.122766\pi$
$571$	1.96988e11			1.85309			0.926543	+	0.376189i	$0.122766\pi$
$572$			1.58122e9i			0.0147710i
$573$	−1.47035e9	−	5.00576e9i	−0.0136396	−	0.0464357i
$574$	6.26650e9			0.0577268
$575$		0			0
$576$	−8.93092e10	+	5.74197e10i	−0.811346	+	0.521641i
$577$	2.39252e10			0.215850			0.107925	−	0.994159i	$-0.465579\pi$
$577$	2.39252e10			0.215850			0.107925	+	0.994159i	$0.465579\pi$
$578$			2.58064e11i			2.31215i
$579$	7.11204e10	−	2.08903e10i	0.632820	−	0.185879i
$580$		0			0
$581$			4.15153e10i			0.364337i
$582$	4.27614e9	+	1.45580e10i	0.0372701	+	0.126885i
$583$	4.30118e10			0.372317
$584$		−	1.50976e11i		−	1.29795i
$585$		0			0
$586$	4.10866e10			0.348426
$587$		−	2.02670e11i		−	1.70701i	−0.521085	−	0.853505i	$-0.674472\pi$
$587$		−	2.02670e11i		−	1.70701i	0.521085	−	0.853505i	$-0.325528\pi$
$588$	3.59945e9	−	1.05727e9i	0.0301111	−	0.00884456i
$589$	−8.94945e9			−0.0743593
$590$		0			0
$591$	4.54369e10	+	1.54689e11i	0.372442	+	1.26797i
$592$	−1.83573e11			−1.49459
$593$		−	1.89947e11i		−	1.53608i	−0.640403	−	0.768039i	$-0.721233\pi$
$593$		−	1.89947e11i		−	1.53608i	0.640403	−	0.768039i	$-0.278767\pi$
$594$	3.72467e10	−	4.30100e10i	0.299187	−	0.345481i
$595$		0			0
$596$			3.80200e9i			0.0301320i
$597$	1.81696e11	−	5.33698e10i	1.43037	−	0.420144i
$598$	7.94958e10			0.621640
$599$		−	3.15053e10i		−	0.244724i	−0.992486	−	0.122362i	$-0.960953\pi$
$599$		−	3.15053e10i		−	0.244724i	0.992486	−	0.122362i	$-0.0390469\pi$
$600$		0			0
$601$	2.47794e10			0.189930			0.0949649	−	0.995481i	$-0.469726\pi$
$601$	2.47794e10			0.189930			0.0949649	+	0.995481i	$0.469726\pi$
$602$		−	3.90704e10i		−	0.297483i
$603$	1.58678e11	−	1.02019e11i	1.20018	−	0.771636i
$604$	2.05603e9			0.0154483
$605$		0			0
$606$	−1.24068e11	+	3.64425e10i	−0.919958	+	0.270220i
$607$	6.54251e10			0.481936			0.240968	−	0.970533i	$-0.422535\pi$
$607$	6.54251e10			0.481936			0.240968	+	0.970533i	$0.422535\pi$
$608$			2.89830e9i			0.0212094i
$609$	1.01918e10	+	3.46979e10i	0.0740940	+	0.252252i
$610$		0			0
$611$		−	2.50286e11i		−	1.79586i
$612$	4.56570e9	+	7.10137e9i	0.0325463	+	0.0506216i
$613$	−1.70377e11			−1.20661			−0.603307	−	0.797509i	$-0.706151\pi$
$613$	−1.70377e11			−1.20661			−0.603307	+	0.797509i	$0.706151\pi$
$614$			1.67762e11i			1.18038i
$615$		0			0
$616$	−1.50999e10			−0.104870
$617$		−	8.96664e10i		−	0.618713i	−0.950946	−	0.309356i	$-0.899886\pi$
$617$		−	8.96664e10i		−	0.618713i	0.950946	−	0.309356i	$-0.100114\pi$
$618$	−6.19720e9	−	2.10982e10i	−0.0424856	−	0.144641i
$619$	1.34052e11			0.913085			0.456542	−	0.889702i	$-0.349088\pi$
$619$	1.34052e11			0.913085			0.456542	+	0.889702i	$0.349088\pi$
$620$		0			0
$621$	−6.95974e10	−	6.02714e10i	−0.467979	−	0.405271i
$622$	−2.80315e11			−1.87277
$623$		−	3.41502e10i		−	0.226694i
$624$	1.48322e11	−	4.35667e10i	0.978289	−	0.287354i
$625$		0			0
$626$			8.82804e10i			0.574867i
$627$	6.24711e9	+	2.12681e10i	0.0404212	+	0.137613i
$628$	−9.57693e9			−0.0615726
$629$		−	4.10170e11i		−	2.62036i
$630$		0			0
$631$	−3.60073e9			−0.0227130			−0.0113565	−	0.999936i	$-0.503615\pi$
$631$	−3.60073e9			−0.0227130			−0.0113565	+	0.999936i	$0.503615\pi$
$632$		−	1.70150e11i		−	1.06651i
$633$	−2.89654e9	+	8.50804e8i	−0.0180412	+	0.00529925i
$634$	−1.90256e11			−1.17756
$635$		0			0
$636$	1.26990e9	+	4.32333e9i	0.00776140	+	0.0264235i
$637$	1.53486e11			0.932204
$638$		−	8.38730e10i		−	0.506220i
$639$	1.32687e11	+	2.06377e11i	0.795837	+	1.23782i
$640$		0			0
$641$			1.77443e11i			1.05106i	0.850775	+	0.525530i	$0.176133\pi$
$641$			1.77443e11i			1.05106i	−0.850775	+	0.525530i	$0.823867\pi$
$642$	5.41199e10	−	1.58967e10i	0.318579	−	0.0935764i
$643$	−1.47027e11			−0.860110			−0.430055	−	0.902803i	$-0.641506\pi$
$643$	−1.47027e11			−0.860110			−0.430055	+	0.902803i	$0.641506\pi$
$644$		−	8.40558e8i		−	0.00488680i
$645$		0			0
$646$	−1.02191e11			−0.586789
$647$			2.73529e11i			1.56094i	0.625192	+	0.780471i	$0.285021\pi$
$647$			2.73529e11i			1.56094i	−0.625192	+	0.780471i	$0.714979\pi$
$648$	−1.57637e11	−	7.19171e10i	−0.894040	−	0.407880i
$649$	−1.02004e11			−0.574961
$650$		0			0
$651$	9.53443e9	−	2.80055e9i	0.0530849	−	0.0155927i
$652$	8.94651e9			0.0495066
$653$		−	1.23992e11i		−	0.681933i	−0.940075	−	0.340967i	$-0.889246\pi$
$653$		−	1.23992e11i		−	0.681933i	0.940075	−	0.340967i	$-0.110754\pi$
$654$	−5.55799e10	−	1.89221e11i	−0.303813	−	1.03433i
$655$		0			0
$656$			4.57329e10i			0.246953i
$657$	2.07003e11	−	1.33089e11i	1.11100	−	0.714301i
$658$	−8.22219e10			−0.438615
$659$			2.37796e11i			1.26085i	0.776251	+	0.630424i	$0.217119\pi$
$659$			2.37796e11i			1.26085i	−0.776251	+	0.630424i	$0.782881\pi$
$660$		0			0
$661$	8.33114e10			0.436414			0.218207	−	0.975903i	$-0.429979\pi$
$661$	8.33114e10			0.436414			0.218207	+	0.975903i	$0.429979\pi$
$662$			9.81740e10i			0.511169i
$663$	9.73441e10	+	3.31406e11i	0.503797	+	1.71517i
$664$	−2.93217e11			−1.50840
$665$		0			0
$666$	−1.56610e11	−	2.43587e11i	−0.796016	−	1.23810i
$667$	−1.35721e11			−0.685713
$668$		−	1.29890e9i		−	0.00652334i
$669$	−1.95104e11	+	5.73082e10i	−0.974008	+	0.286096i
$670$		0			0
$671$		−	5.71605e10i		−	0.281972i
$672$	−9.06967e8	−	3.08775e9i	−0.00444748	−	0.0151414i
$673$	−3.96318e11			−1.93189			−0.965947	−	0.258742i	$-0.916692\pi$
$673$	−3.96318e11			−1.93189			−0.965947	+	0.258742i	$0.916692\pi$
$674$			2.20335e10i			0.106769i
$675$		0			0
$676$	1.67626e8			0.000802700
$677$			3.22020e11i			1.53295i	0.642275	+	0.766474i	$0.277991\pi$
$677$			3.22020e11i			1.53295i	−0.642275	+	0.766474i	$0.722009\pi$
$678$	−1.61560e10	+	4.74551e9i	−0.0764566	+	0.0224577i
$679$	6.56385e9			0.0308802
$680$		0			0
$681$	−2.55140e10	−	8.68617e10i	−0.118629	−	0.403868i
$682$	−2.30470e10			−0.106531
$683$		−	3.92810e10i		−	0.180510i	−0.995919	−	0.0902548i	$-0.971232\pi$
$683$		−	3.92810e10i		−	0.180510i	0.995919	−	0.0902548i	$-0.0287681\pi$
$684$	−1.95333e9	+	1.25586e9i	−0.00892382	+	0.00573741i
$685$		0			0
$686$		−	1.03854e11i		−	0.468951i
$687$	2.55808e11	−	7.51387e10i	1.14839	−	0.337316i
$688$	2.85136e11			1.27262
$689$			1.84353e11i			0.818039i
$690$		0			0
$691$	3.54272e10			0.155391			0.0776954	−	0.996977i	$-0.475244\pi$
$691$	3.54272e10			0.155391			0.0776954	+	0.996977i	$0.475244\pi$
$692$		−	1.26742e10i		−	0.0552707i
$693$	−1.33109e10	−	2.07034e10i	−0.0577131	−	0.0897654i
$694$	−4.02279e11			−1.73416
$695$		0			0
$696$	−2.45066e11	+	7.19835e10i	−1.04435	+	0.306758i
$697$	−1.02184e11			−0.432965
$698$			1.47726e11i			0.622350i
$699$	−3.98697e10	−	1.35736e11i	−0.167007	−	0.568571i
$700$		0			0
$701$		−	3.64764e9i		−	0.0151057i	−0.999971	−	0.00755284i	$-0.997596\pi$
$701$		−	3.64764e9i		−	0.0151057i	0.999971	−	0.00755284i	$-0.00240417\pi$
$702$	1.84346e11	+	1.59644e11i	0.759075	+	0.657360i
$703$	1.12823e11			0.461929
$704$		−	1.06526e11i		−	0.433677i
$705$		0			0
$706$	2.70458e11			1.08863
$707$			5.59389e10i			0.223891i
$708$	−3.01161e9	−	1.02529e10i	−0.0119857	−	0.0408052i
$709$	−2.79311e11			−1.10536			−0.552678	−	0.833395i	$-0.686394\pi$
$709$	−2.79311e11			−1.10536			−0.552678	+	0.833395i	$0.686394\pi$
$710$		0			0
$711$	2.33293e11	−	1.49991e11i	0.912899	−	0.586932i
$712$	2.41198e11			0.938541
$713$			3.72939e10i			0.144304i
$714$	1.08871e11	−	3.19787e10i	0.418907	−	0.123046i
$715$		0			0
$716$		−	5.73438e9i		−	0.0218190i
$717$	7.31412e10	+	2.49008e11i	0.276749	+	0.942184i
$718$	−1.06013e11			−0.398898
$719$		−	1.75259e11i		−	0.655789i	−0.944714	−	0.327895i	$-0.893661\pi$
$719$		−	1.75259e11i		−	0.655789i	0.944714	−	0.327895i	$-0.106339\pi$
$720$		0			0
$721$	−9.51265e9			−0.0352015
$722$			2.48110e11i			0.913050i
$723$	1.80723e11	−	5.30838e10i	0.661393	−	0.194271i
$724$	−7.93429e9			−0.0288771
$725$		0			0
$726$	−6.34969e10	−	2.16174e11i	−0.228563	−	0.778138i
$727$	−3.76305e11			−1.34711			−0.673555	−	0.739137i	$-0.735233\pi$
$727$	−3.76305e11			−1.34711			−0.673555	+	0.739137i	$0.735233\pi$
$728$		−	6.47199e10i		−	0.230416i
$729$	−4.03549e10	−	2.79532e11i	−0.142885	−	0.989739i
$730$		0			0
$731$			6.37098e11i			2.23119i
$732$	5.74550e9	−	1.68763e9i	0.0200117	−	0.00587804i
$733$	−2.94004e11			−1.01845			−0.509223	−	0.860635i	$-0.670067\pi$
$733$	−2.94004e11			−1.01845			−0.509223	+	0.860635i	$0.670067\pi$
$734$			2.79850e11i			0.964141i
$735$		0			0
$736$	1.20777e10			0.0411598
$737$			1.89268e11i			0.641515i
$738$	−6.06839e10	+	3.90156e10i	−0.204573	+	0.131527i
$739$	2.57966e11			0.864939			0.432470	−	0.901649i	$-0.357642\pi$
$739$	2.57966e11			0.864939			0.432470	+	0.901649i	$0.357642\pi$
$740$		0			0
$741$	−9.11577e10	+	2.67758e10i	−0.302357	+	0.0888117i
$742$	6.05622e10			0.199796
$743$			8.70436e10i			0.285615i	0.989750	+	0.142808i	$0.0456130\pi$
$743$			8.70436e10i			0.285615i	−0.989750	+	0.142808i	$0.954387\pi$
$744$	1.97799e10	+	6.73403e10i	0.0645555	+	0.219778i
$745$		0			0
$746$		−	2.40023e11i		−	0.774992i
$747$	−2.58477e11	−	4.02029e11i	−0.830118	−	1.29114i
$748$	−8.47038e9			−0.0270580
$749$		−	2.44013e10i		−	0.0775328i
$750$		0			0
$751$	−3.07477e11			−0.966613			−0.483306	−	0.875451i	$-0.660564\pi$
$751$	−3.07477e11			−0.966613			−0.483306	+	0.875451i	$0.660564\pi$
$752$		−	6.00056e11i		−	1.87638i
$753$	7.72728e10	+	2.63074e11i	0.240351	+	0.818271i
$754$	3.59489e11			1.11225
$755$		0			0
$756$	1.68801e9	−	1.94920e9i	0.00516759	−	0.00596719i
$757$	3.68112e11			1.12098			0.560488	−	0.828163i	$-0.310614\pi$
$757$	3.68112e11			1.12098			0.560488	+	0.828163i	$0.310614\pi$
$758$		−	5.34725e11i		−	1.61977i
$759$	8.86279e10	−	2.60327e10i	0.267057	−	0.0784428i
$760$		0			0
$761$			1.79849e11i			0.536252i	0.963384	+	0.268126i	$0.0864043\pi$
$761$			1.79849e11i			0.536252i	−0.963384	+	0.268126i	$0.913596\pi$
$762$	−9.95427e10	−	3.38891e11i	−0.295250	−	1.00517i
$763$	−8.53148e10			−0.251725
$764$			5.48374e8i			0.00160955i
$765$		0			0
$766$	1.81661e11			0.527650
$767$		−	4.37201e11i		−	1.26328i
$768$	3.32661e10	−	9.77127e9i	0.0956218	−	0.0280871i
$769$	−4.66289e11			−1.33337			−0.666684	−	0.745341i	$-0.732287\pi$
$769$	−4.66289e11			−1.33337			−0.666684	+	0.745341i	$0.732287\pi$
$770$		0			0
$771$	−2.21673e10	−	7.54681e10i	−0.0627329	−	0.213573i
$772$	−7.79114e9			−0.0219347
$773$		−	3.85685e10i		−	0.108023i	−0.998540	−	0.0540114i	$-0.982799\pi$
$773$		−	3.85685e10i		−	0.108023i	0.998540	−	0.0540114i	$-0.0172007\pi$
$774$	2.43255e11	+	3.78352e11i	0.677794	+	1.05422i
$775$		0			0
$776$			4.63596e10i			0.127848i
$777$	−1.20197e11	+	3.53057e10i	−0.329770	+	0.0968636i
$778$	5.11002e11			1.39478
$779$		−	2.81072e10i		−	0.0763250i
$780$		0			0
$781$	−2.46163e11			−0.661636
$782$			4.25847e11i			1.13875i
$783$	−3.14728e11	−	2.72555e11i	−0.837314	−	0.725114i
$784$	3.67980e11			0.974001
$785$		0			0
$786$	6.96010e9	−	2.04439e9i	0.0182358	−	0.00535642i
$787$	−5.13745e11			−1.33921			−0.669605	−	0.742717i	$-0.733537\pi$
$787$	−5.13745e11			−1.33921			−0.669605	+	0.742717i	$0.733537\pi$
$788$		−	1.69459e10i		−	0.0439502i
$789$	4.71634e9	+	1.60567e10i	0.0121702	+	0.0414331i
$790$		0			0
$791$			7.28433e9i			0.0186073i
$792$	1.46225e11	−	9.40130e10i	0.371640	−	0.238939i
$793$	2.44996e11			0.619537
$794$			1.42054e11i			0.357413i
$795$		0			0
$796$	−1.99046e10			−0.0495793
$797$		−	5.20760e11i		−	1.29064i	−0.763914	−	0.645318i	$-0.776725\pi$
$797$		−	5.20760e11i		−	1.29064i	0.763914	−	0.645318i	$-0.223275\pi$
$798$	8.79617e9	+	2.99464e10i	0.0216911	+	0.0738469i
$799$	1.34074e12			3.28972
$800$		0			0
$801$	2.12621e11	+	3.30706e11i	0.516508	+	0.803362i
$802$	−2.07961e10			−0.0502672
$803$			2.46910e11i			0.593849i
$804$	−1.90243e10	+	5.58802e9i	−0.0455286	+	0.0133732i
$805$		0			0
$806$		−	9.87820e10i		−	0.234066i
$807$	7.14037e10	+	2.43092e11i	0.168355	+	0.573162i
$808$	−3.95089e11			−0.926935
$809$		−	7.88009e11i		−	1.83966i	−0.392320	−	0.919829i	$-0.628327\pi$
$809$		−	7.88009e11i		−	1.83966i	0.392320	−	0.919829i	$-0.371673\pi$
$810$		0			0
$811$	5.15883e11			1.19253			0.596263	−	0.802789i	$-0.296651\pi$
$811$	5.15883e11			1.19253			0.596263	+	0.802789i	$0.296651\pi$
$812$		−	3.80110e9i		−	0.00874350i
$813$	3.58314e11	−	1.05248e11i	0.820165	−	0.240908i
$814$	2.90546e11			0.661785
$815$		0			0
$816$	2.33381e11	+	7.94539e11i	0.526386	+	1.79207i
$817$	−1.75243e11			−0.393325
$818$		−	1.67208e11i		−	0.373461i
$819$	8.87372e10	−	5.70520e10i	0.197229	−	0.126805i
$820$		0			0
$821$		−	5.32514e11i		−	1.17208i	−0.810281	−	0.586041i	$-0.800686\pi$
$821$		−	5.32514e11i		−	1.17208i	0.810281	−	0.586041i	$-0.199314\pi$
$822$	−7.04092e11	+	2.06813e11i	−1.54220	+	0.452993i
$823$	6.35863e11			1.38600			0.693002	−	0.720936i	$-0.256288\pi$
$823$	6.35863e11			1.38600			0.693002	+	0.720936i	$0.256288\pi$
$824$		−	6.71865e10i		−	0.145738i
$825$		0			0
$826$	−1.43626e11			−0.308540
$827$		−	1.67343e10i		−	0.0357756i	−0.999840	−	0.0178878i	$-0.994306\pi$
$827$		−	1.67343e10i		−	0.0357756i	0.999840	−	0.0178878i	$-0.00569416\pi$
$828$	5.23337e9	+	8.13985e9i	0.0111342	+	0.0173179i
$829$	−5.88172e11			−1.24534			−0.622668	−	0.782486i	$-0.713951\pi$
$829$	−5.88172e11			−1.24534			−0.622668	+	0.782486i	$0.713951\pi$
$830$		0			0
$831$	−1.37904e11	+	4.05068e10i	−0.289184	+	0.0849422i
$832$	4.56584e11			0.952856
$833$			8.22201e11i			1.70765i
$834$	1.24157e10	+	4.22690e10i	0.0256630	+	0.0873691i
$835$		0			0
$836$		−	2.32989e9i		−	0.00476992i
$837$	−7.48937e10	+	8.64822e10i	−0.152596	+	0.176208i
$838$	5.86419e11			1.18914
$839$			9.03790e11i			1.82398i	0.410215	+	0.911989i	$0.365454\pi$
$839$			9.03790e11i			1.82398i	−0.410215	+	0.911989i	$0.634546\pi$
$840$		0			0
$841$	−1.13498e11			−0.226885
$842$			5.91983e11i			1.17777i
$843$	1.78190e9	+	6.06643e9i	0.00352836	+	0.0120122i
$844$	3.17312e8			0.000625341
$845$		0			0
$846$	7.96225e11	−	5.11919e11i	1.55437	−	0.999355i
$847$	−9.74673e10			−0.189376
$848$			4.41984e11i			0.854718i
$849$	−6.31172e11	+	1.85395e11i	−1.21483	+	0.356834i
$850$		0			0
$851$		−	4.70152e11i		−	0.896437i
$852$	−7.26782e9	−	2.47431e10i	−0.0137926	−	0.0469566i
$853$	2.17472e11			0.410779			0.205389	−	0.978680i	$-0.434154\pi$
$853$	2.17472e11			0.410779			0.205389	+	0.978680i	$0.434154\pi$
$854$		−	8.04842e10i		−	0.151314i
$855$		0			0
$856$	1.72343e11			0.320995
$857$		−	5.72821e10i		−	0.106193i	−0.998589	−	0.0530964i	$-0.983091\pi$
$857$		−	5.72821e10i		−	0.106193i	0.998589	−	0.0530964i	$-0.0169091\pi$
$858$	−2.34753e11	+	6.89541e10i	−0.433173	+	0.127236i
$859$	2.59635e11			0.476860			0.238430	−	0.971160i	$-0.423367\pi$
$859$	2.59635e11			0.476860			0.238430	+	0.971160i	$0.423367\pi$
$860$		0			0
$861$	8.79558e9	+	2.99444e10i	0.0160049	+	0.0544882i
$862$	4.93697e11			0.894194
$863$		−	9.75428e10i		−	0.175854i	−0.996127	−	0.0879270i	$-0.971976\pi$
$863$		−	9.75428e10i		−	0.175854i	0.996127	−	0.0879270i	$-0.0280242\pi$
$864$	2.80075e10	+	2.42545e10i	0.0502596	+	0.0435249i
$865$		0			0
$866$			5.62424e11i			0.999982i
$867$	−1.23316e12	+	3.62216e11i	−2.18244	+	0.641050i
$868$	−1.04448e9			−0.00184002
$869$			2.78267e11i			0.487958i
$870$		0			0
$871$	−8.11224e11			−1.40951
$872$		−	6.02566e11i		−	1.04217i
$873$	−6.35634e10	+	4.08670e10i	−0.109434	+	0.0703584i
$874$	−1.17135e11			−0.200743
$875$		0			0
$876$	−2.48182e10	+	7.28986e9i	−0.0421457	+	0.0123795i
$877$	9.16421e11			1.54916			0.774580	−	0.632476i	$-0.217961\pi$
$877$	9.16421e11			1.54916			0.774580	+	0.632476i	$0.217961\pi$
$878$			2.87866e10i			0.0484409i
$879$	5.76688e10	+	1.96332e11i	0.0966018	+	0.328879i
$880$		0			0
$881$		−	5.22036e11i		−	0.866557i	−0.901260	−	0.433279i	$-0.857357\pi$
$881$		−	5.22036e11i		−	0.866557i	0.901260	−	0.433279i	$-0.142643\pi$
$882$	3.13930e11	+	4.88279e11i	0.518751	+	0.806852i
$883$	−2.66487e11			−0.438363			−0.219181	−	0.975684i	$-0.570339\pi$
$883$	−2.66487e11			−0.438363			−0.219181	+	0.975684i	$0.570339\pi$
$884$		−	3.63050e10i		−	0.0594508i
$885$		0			0
$886$	5.19917e11			0.843722
$887$			4.32506e11i			0.698710i	0.936990	+	0.349355i	$0.113599\pi$
$887$			4.32506e11i			0.698710i	−0.936990	+	0.349355i	$0.886401\pi$
$888$	−2.49359e11	−	8.48938e11i	−0.401027	−	1.36529i
$889$	−1.52797e11			−0.244630
$890$		0			0
$891$	2.57802e11	+	1.17615e11i	0.409049	+	0.186617i
$892$	2.13734e10			0.0337609
$893$			3.68790e11i			0.579927i
$894$	−5.64456e11	+	1.65798e11i	−0.883649	+	0.259555i
$895$		0			0
$896$		−	1.60164e11i		−	0.248504i
$897$	1.11579e11	+	3.79870e11i	0.172351	+	0.586766i
$898$	−1.30232e12			−2.00269
$899$			1.68647e11i			0.258191i
$900$		0			0
$901$	−9.87554e11			−1.49852
$902$		−	7.23826e10i		−	0.109347i
$903$	1.86697e11	−	5.48388e10i	0.280794	−	0.0824777i
$904$	−5.14482e10			−0.0770365
$905$		0			0
$906$	8.96593e10	+	3.05243e11i	0.133071	+	0.453037i
$907$	−1.46416e10			−0.0216352			−0.0108176	−	0.999941i	$-0.503443\pi$
$907$	−1.46416e10			−0.0216352			−0.0108176	+	0.999941i	$0.503443\pi$
$908$			9.51557e9i			0.0139988i
$909$	−3.48280e11	−	5.41705e11i	−0.510120	−	0.793428i
$910$		0			0
$911$		−	4.82789e11i		−	0.700944i	−0.936573	−	0.350472i	$-0.886021\pi$
$911$		−	4.82789e11i		−	0.700944i	0.936573	−	0.350472i	$-0.113979\pi$
$912$	−2.18549e11	+	6.41945e10i	−0.315914	+	0.0927937i
$913$	4.79532e11			0.690136
$914$		−	8.86737e11i		−	1.27060i
$915$		0			0
$916$	−2.80234e10			−0.0398051
$917$		−	3.13813e9i		−	0.00443807i
$918$	−8.55187e11	+	9.87513e11i	−1.20418	+	1.39050i
$919$	2.79672e11			0.392090			0.196045	−	0.980595i	$-0.437190\pi$
$919$	2.79672e11			0.392090			0.196045	+	0.980595i	$0.437190\pi$
$920$		0			0
$921$	−8.01650e11	+	2.35469e11i	−1.11416	+	0.327262i
$922$	−5.96134e9			−0.00824936
$923$		−	1.05508e12i		−	1.45372i
$924$	7.29094e8	+	2.48219e9i	0.00100022	+	0.00340523i
$925$		0			0
$926$		−	5.25034e11i		−	0.714074i
$927$	9.21193e10	−	5.92264e10i	0.124747	−	0.0802041i
$928$	5.46169e10			0.0736436
$929$		−	9.95357e10i		−	0.133634i	−0.997765	−	0.0668169i	$-0.978716\pi$
$929$		−	9.95357e10i		−	0.133634i	0.997765	−	0.0668169i	$-0.0212843\pi$
$930$		0			0
$931$	−2.26158e11			−0.301032
$932$			1.48696e10i			0.0197077i
$933$	−3.93447e11	−	1.33948e12i	−0.519230	−	1.76771i
$934$	3.44432e11			0.452601
$935$		0			0
$936$	4.02951e11	+	6.26739e11i	0.524987	+	0.816551i
$937$	8.34167e11			1.08217			0.541084	−	0.840968i	$-0.318014\pi$
$937$	8.34167e11			1.08217			0.541084	+	0.840968i	$0.318014\pi$
$938$			2.66497e11i			0.344255i
$939$	−4.21847e11	+	1.23909e11i	−0.542616	+	0.159383i
$940$		0			0
$941$			2.45126e11i			0.312630i	0.987707	+	0.156315i	$0.0499615\pi$
$941$			2.45126e11i			0.312630i	−0.987707	+	0.156315i	$0.950039\pi$
$942$	−4.17632e11	−	1.42182e12i	−0.530383	−	1.80568i
$943$	−1.17127e11			−0.148119
$944$		−	1.04818e12i		−	1.31992i
$945$		0			0
$946$	−4.51292e11			−0.563498
$947$		−	1.34423e12i		−	1.67137i	−0.549209	−	0.835685i	$-0.685071\pi$
$947$		−	1.34423e12i		−	1.67137i	0.549209	−	0.835685i	$-0.314929\pi$
$948$	−2.79701e10	+	8.21567e9i	−0.0346306	+	0.0101721i
$949$	−1.05828e12			−1.30478
$950$		0			0
$951$	−2.67042e11	−	9.09137e11i	−0.326480	−	1.11149i
$952$	3.46695e11			0.422085
$953$		−	1.02998e12i		−	1.24870i	−0.781144	−	0.624351i	$-0.785363\pi$
$953$		−	1.02998e12i		−	1.24870i	0.781144	−	0.624351i	$-0.214637\pi$
$954$	−5.86477e11	+	3.77065e11i	−0.708039	+	0.455221i
$955$		0			0
$956$		−	2.72784e10i		−	0.0326578i
$957$	4.00786e11	−	1.17723e11i	0.477820	−	0.140351i
$958$	−7.62802e11			−0.905628
$959$			3.17457e11i			0.375328i
$960$		0			0
$961$	−8.06549e11			−0.945665
$962$			1.24531e12i			1.45405i
$963$	1.51924e11	+	2.36299e11i	0.176653	+	0.274762i
$964$	−1.97979e10			−0.0229251
$965$		0			0
$966$	1.24792e11	−	3.66551e10i	0.143310	−	0.0420946i
$967$	8.83788e11			1.01075			0.505373	−	0.862901i	$-0.331355\pi$
$967$	8.83788e11			1.01075			0.505373	+	0.862901i	$0.331355\pi$
$968$		−	6.88398e11i		−	0.784040i
$969$	−1.43434e11	−	4.88318e11i	−0.162689	−	0.553870i
$970$		0			0
$971$			1.36295e12i			1.53321i	0.642117	+	0.766607i	$0.278057\pi$
$971$			1.36295e12i			1.53321i	−0.642117	+	0.766607i	$0.721943\pi$
$972$	−4.21060e9	+	2.93855e10i	−0.00471714	+	0.0329206i
$973$	1.90580e10			0.0212631
$974$		−	2.19184e11i		−	0.243541i
$975$		0			0
$976$	5.87374e11			0.647315
$977$			8.27099e10i			0.0907777i	0.998969	+	0.0453888i	$0.0144527\pi$
$977$			8.27099e10i			0.0907777i	−0.998969	+	0.0453888i	$0.985547\pi$
$978$	3.90140e11	+	1.32822e12i	0.426447	+	1.45183i
$979$	−3.94459e11			−0.429409
$980$		0			0
$981$	8.26177e11	−	5.31176e11i	0.892066	−	0.573538i
$982$	1.34528e12			1.44666
$983$			1.05894e12i			1.13412i	0.823678	+	0.567058i	$0.191918\pi$
$983$			1.05894e12i			1.13412i	−0.823678	+	0.567058i	$0.808082\pi$
$984$	−2.11493e11	+	6.21220e10i	−0.225588	+	0.0662621i
$985$		0			0
$986$			1.92573e12i			2.03745i
$987$	−1.15406e11	−	3.92896e11i	−0.121607	−	0.414008i
$988$	9.98619e9			0.0104803
$989$			7.30266e11i			0.763301i
$990$		0			0
$991$	1.36731e11			0.141766			0.0708828	−	0.997485i	$-0.477418\pi$
$991$	1.36731e11			0.141766			0.0708828	+	0.997485i	$0.477418\pi$
$992$		−	1.50078e10i		−	0.0154979i
$993$	−4.69123e11	+	1.37796e11i	−0.482492	+	0.141723i
$994$	−3.46607e11			−0.355052
$995$		0			0
$996$	1.41579e10	+	4.82003e10i	0.0143867	+	0.0489793i
$997$	−1.12309e12			−1.13667			−0.568334	−	0.822798i	$-0.692412\pi$
$997$	−1.12309e12			−1.13667			−0.568334	+	0.822798i	$0.692412\pi$
$998$		−	3.20317e11i		−	0.322892i
$999$	9.44160e11	−	1.09025e12i	0.947947	−	1.09463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.c.f.26.4	yes	10
3.2	odd	2	inner	75.9.c.f.26.7	yes	10
5.2	odd	4		75.9.d.d.74.13		20
5.3	odd	4		75.9.d.d.74.8		20
5.4	even	2		75.9.c.e.26.7	yes	10
15.2	even	4		75.9.d.d.74.7		20
15.8	even	4		75.9.d.d.74.14		20
15.14	odd	2		75.9.c.e.26.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.c.e.26.4	✓	10	15.14	odd	2
75.9.c.e.26.7	yes	10	5.4	even	2
75.9.c.f.26.4	yes	10	1.1	even	1	trivial
75.9.c.f.26.7	yes	10	3.2	odd	2	inner
75.9.d.d.74.7		20	15.2	even	4
75.9.d.d.74.8		20	5.3	odd	4
75.9.d.d.74.13		20	5.2	odd	4
75.9.d.d.74.14		20	15.8	even	4

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-16.2639i q^{2} +(77.7167 - 22.8278i) q^{3} -8.51375 q^{4} +(-371.269 - 1263.98i) q^{6} -569.895 q^{7} -4025.09i q^{8} +(5518.78 - 3548.20i) q^{9} +O(q^{10})\)	\(q-16.2639i q^{2} +(77.7167 - 22.8278i) q^{3} -8.51375 q^{4} +(-371.269 - 1263.98i) q^{6} -569.895 q^{7} -4025.09i q^{8} +(5518.78 - 3548.20i) q^{9} +6582.70i q^{11} +(-661.661 + 194.350i) q^{12} -28214.2 q^{13} +9268.70i q^{14} -67643.0 q^{16} -151139. i q^{17} +(-57707.6 - 89756.8i) q^{18} +41572.9 q^{19} +(-44290.4 + 13009.4i) q^{21} +107060. q^{22} -173241. i q^{23} +(-91883.9 - 312817. i) q^{24} +458873. i q^{26} +(347904. - 401737. i) q^{27} +4851.94 q^{28} -783419. i q^{29} -215271. q^{31} +69716.1i q^{32} +(150269. + 511586. i) q^{33} -2.45811e6 q^{34} +(-46985.6 + 30208.5i) q^{36} +2.71385e6 q^{37} -676137. i q^{38} +(-2.19272e6 + 644068. i) q^{39} -676092. i q^{41} +(211584. + 720333. i) q^{42} -4.21531e6 q^{43} -56043.5i q^{44} -2.81758e6 q^{46} +8.87092e6i q^{47} +(-5.25700e6 + 1.54414e6i) q^{48} -5.44002e6 q^{49} +(-3.45018e6 - 1.17461e7i) q^{51} +240209. q^{52} -6.53406e6i q^{53} +(-6.53379e6 - 5.65827e6i) q^{54} +2.29387e6i q^{56} +(3.23091e6 - 949019. i) q^{57} -1.27414e7 q^{58} +1.54958e7i q^{59} -8.68344e6 q^{61} +3.50114e6i q^{62} +(-3.14512e6 + 2.02210e6i) q^{63} -1.61828e7 q^{64} +(8.32037e6 - 2.44395e6i) q^{66} +2.87523e7 q^{67} +1.28676e6i q^{68} +(-3.95472e6 - 1.34638e7i) q^{69} +3.73955e7i q^{71} +(-1.42818e7 - 2.22136e7i) q^{72} +3.75089e7 q^{73} -4.41378e7i q^{74} -353942. q^{76} -3.75145e6i q^{77} +(1.04751e7 + 3.56621e7i) q^{78} +4.22725e7 q^{79} +(1.78672e7 - 3.91635e7i) q^{81} -1.09959e7 q^{82} -7.28474e7i q^{83} +(377077. - 110759. i) q^{84} +6.85572e7i q^{86} +(-1.78837e7 - 6.08847e7i) q^{87} +2.64959e7 q^{88} +5.99236e7i q^{89} +1.60791e7 q^{91} +1.47494e6i q^{92} +(-1.67302e7 + 4.91416e6i) q^{93} +1.44276e8 q^{94} +(1.59146e6 + 5.41811e6i) q^{96} -1.15177e7 q^{97} +8.84758e7i q^{98} +(2.33568e7 + 3.63285e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 25 q^{3} - 1554 q^{4} + 2257 q^{6} - 1960 q^{7} - 11207 q^{9}+O(q^{10}) \) 10 * q + 25 * q^3 - 1554 * q^4 + 2257 * q^6 - 1960 * q^7 - 11207 * q^9	\( 10 q + 25 q^{3} - 1554 q^{4} + 2257 q^{6} - 1960 q^{7} - 11207 q^{9} + 5915 q^{12} + 16920 q^{13} + 44634 q^{16} + 224875 q^{18} - 143934 q^{19} + 673428 q^{21} - 818990 q^{22} - 1016859 q^{24} + 260830 q^{27} - 3810100 q^{28} - 3014060 q^{31} + 4677515 q^{33} + 4977146 q^{34} + 4500527 q^{36} - 3016760 q^{37} - 7513282 q^{39} + 4001760 q^{42} - 11747340 q^{43} - 13938636 q^{46} + 14748755 q^{48} + 8953546 q^{49} + 6209287 q^{51} + 38918320 q^{52} - 8886272 q^{54} - 14759525 q^{57} + 48407900 q^{58} + 1520220 q^{61} - 74748240 q^{63} - 4536998 q^{64} + 10465295 q^{66} + 16269290 q^{67} + 11394978 q^{69} - 172231185 q^{72} + 52090170 q^{73} - 29529046 q^{76} - 198205810 q^{78} + 8549896 q^{79} + 22612945 q^{81} + 295714190 q^{82} - 136883292 q^{84} - 318901610 q^{87} + 310673250 q^{88} - 107224264 q^{91} - 79679130 q^{93} + 356118596 q^{94} + 525424001 q^{96} + 402167800 q^{97} - 382421335 q^{99}+O(q^{100}) \) 10 * q + 25 * q^3 - 1554 * q^4 + 2257 * q^6 - 1960 * q^7 - 11207 * q^9 + 5915 * q^12 + 16920 * q^13 + 44634 * q^16 + 224875 * q^18 - 143934 * q^19 + 673428 * q^21 - 818990 * q^22 - 1016859 * q^24 + 260830 * q^27 - 3810100 * q^28 - 3014060 * q^31 + 4677515 * q^33 + 4977146 * q^34 + 4500527 * q^36 - 3016760 * q^37 - 7513282 * q^39 + 4001760 * q^42 - 11747340 * q^43 - 13938636 * q^46 + 14748755 * q^48 + 8953546 * q^49 + 6209287 * q^51 + 38918320 * q^52 - 8886272 * q^54 - 14759525 * q^57 + 48407900 * q^58 + 1520220 * q^61 - 74748240 * q^63 - 4536998 * q^64 + 10465295 * q^66 + 16269290 * q^67 + 11394978 * q^69 - 172231185 * q^72 + 52090170 * q^73 - 29529046 * q^76 - 198205810 * q^78 + 8549896 * q^79 + 22612945 * q^81 + 295714190 * q^82 - 136883292 * q^84 - 318901610 * q^87 + 310673250 * q^88 - 107224264 * q^91 - 79679130 * q^93 + 356118596 * q^94 + 525424001 * q^96 + 402167800 * q^97 - 382421335 * q^99

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