LMFDB - Embedded newform 103.7.b.b.102.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [103,7,Mod(102,103)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(103, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("103.102");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 103 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	103.b (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:	$23.6955706128$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			102.2
Character	$\chi$	$=$	103.102
Dual form			103.7.b.b.102.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.4764 q^{2} -40.9460i q^{3} +175.520 q^{4} +131.999i q^{5} +633.698i q^{6} +19.5425 q^{7} -1725.94 q^{8} -947.573 q^{9} +O(q^{10})$	\(q-15.4764 q^{2} -40.9460i q^{3} +175.520 q^{4} +131.999i q^{5} +633.698i q^{6} +19.5425 q^{7} -1725.94 q^{8} -947.573 q^{9} -2042.88i q^{10} +1625.11i q^{11} -7186.85i q^{12} -559.880 q^{13} -302.448 q^{14} +5404.84 q^{15} +15478.1 q^{16} +925.444 q^{17} +14665.1 q^{18} -11995.7 q^{19} +23168.6i q^{20} -800.187i q^{21} -25150.9i q^{22} +15240.2 q^{23} +70670.3i q^{24} -1798.82 q^{25} +8664.95 q^{26} +8949.71i q^{27} +3430.11 q^{28} +23080.3 q^{29} -83647.7 q^{30} -41245.7i q^{31} -129086. q^{32} +66541.6 q^{33} -14322.6 q^{34} +2579.60i q^{35} -166318. q^{36} -53616.1i q^{37} +185650. q^{38} +22924.8i q^{39} -227823. i q^{40} -25274.4 q^{41} +12384.0i q^{42} -29030.8i q^{43} +285239. i q^{44} -125079. i q^{45} -235864. q^{46} -191707. i q^{47} -633766. i q^{48} -117267. q^{49} +27839.3 q^{50} -37893.2i q^{51} -98270.3 q^{52} +137178. i q^{53} -138510. i q^{54} -214513. q^{55} -33729.1 q^{56} +491174. i q^{57} -357201. q^{58} -339384. q^{59} +948660. q^{60} +390795. q^{61} +638337. i q^{62} -18517.9 q^{63} +1.00719e6 q^{64} -73903.8i q^{65} -1.02983e6 q^{66} +205709. i q^{67} +162434. q^{68} -624024. i q^{69} -39923.0i q^{70} -332887. i q^{71} +1.63545e6 q^{72} -139428. i q^{73} +829786. i q^{74} +73654.3i q^{75} -2.10548e6 q^{76} +31758.6i q^{77} -354795. i q^{78} -327094. q^{79} +2.04310e6i q^{80} -324327. q^{81} +391158. q^{82} +599362. q^{83} -140449. i q^{84} +122158. i q^{85} +449294. i q^{86} -945045. i q^{87} -2.80483e6i q^{88} -1.21502e6i q^{89} +1.93578e6i q^{90} -10941.5 q^{91} +2.67496e6 q^{92} -1.68885e6 q^{93} +2.96694e6i q^{94} -1.58342e6i q^{95} +5.28555e6i q^{96} -532486. q^{97} +1.81488e6 q^{98} -1.53991e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 2 q^{2} + 1278 q^{4} - 810 q^{7} - 1096 q^{8} - 17938 q^{9}+O(q^{10}) $ 46 * q - 2 * q^2 + 1278 * q^4 - 810 * q^7 - 1096 * q^8 - 17938 * q^9	$ 46 q - 2 q^{2} + 1278 q^{4} - 810 q^{7} - 1096 q^{8} - 17938 q^{9} + 2822 q^{13} - 6690 q^{14} + 4488 q^{15} + 36822 q^{16} + 478 q^{17} - 21436 q^{18} - 4650 q^{19} + 14246 q^{23} - 178082 q^{25} + 107000 q^{26} - 107086 q^{28} - 16666 q^{29} + 128416 q^{30} - 264566 q^{32} + 2280 q^{33} + 2840 q^{34} - 852564 q^{36} - 127366 q^{38} - 272394 q^{41} + 31656 q^{46} - 214532 q^{49} + 536876 q^{50} + 334070 q^{52} + 307608 q^{55} - 1074240 q^{56} + 31640 q^{58} + 183558 q^{59} + 215010 q^{60} + 118358 q^{61} + 132158 q^{63} + 1507580 q^{64} - 3093882 q^{66} - 350686 q^{68} - 1888056 q^{72} - 553676 q^{76} - 1485538 q^{79} + 3422742 q^{81} + 4547424 q^{82} + 3191126 q^{83} + 2101612 q^{91} + 2758828 q^{92} - 9030976 q^{93} - 1466602 q^{97} + 11212176 q^{98}+O(q^{100}) $ 46 * q - 2 * q^2 + 1278 * q^4 - 810 * q^7 - 1096 * q^8 - 17938 * q^9 + 2822 * q^13 - 6690 * q^14 + 4488 * q^15 + 36822 * q^16 + 478 * q^17 - 21436 * q^18 - 4650 * q^19 + 14246 * q^23 - 178082 * q^25 + 107000 * q^26 - 107086 * q^28 - 16666 * q^29 + 128416 * q^30 - 264566 * q^32 + 2280 * q^33 + 2840 * q^34 - 852564 * q^36 - 127366 * q^38 - 272394 * q^41 + 31656 * q^46 - 214532 * q^49 + 536876 * q^50 + 334070 * q^52 + 307608 * q^55 - 1074240 * q^56 + 31640 * q^58 + 183558 * q^59 + 215010 * q^60 + 118358 * q^61 + 132158 * q^63 + 1507580 * q^64 - 3093882 * q^66 - 350686 * q^68 - 1888056 * q^72 - 553676 * q^76 - 1485538 * q^79 + 3422742 * q^81 + 4547424 * q^82 + 3191126 * q^83 + 2101612 * q^91 + 2758828 * q^92 - 9030976 * q^93 - 1466602 * q^97 + 11212176 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/103\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	−15.4764			−1.93456			−0.967278	−	0.253719i	$-0.918346\pi$
$2$	−15.4764			−1.93456			−0.967278	+	0.253719i	$0.918346\pi$
$3$		−	40.9460i		−	1.51652i	−0.651954	−	0.758259i	$-0.726050\pi$
$3$		−	40.9460i		−	1.51652i	0.651954	−	0.758259i	$-0.273950\pi$
$4$	175.520			2.74251
$5$			131.999i			1.05599i	0.849246	+	0.527997i	$0.177057\pi$
$5$			131.999i			1.05599i	−0.849246	+	0.527997i	$0.822943\pi$
$6$			633.698i			2.93379i
$7$	19.5425			0.0569752			0.0284876	−	0.999594i	$-0.490931\pi$
$7$	19.5425			0.0569752			0.0284876	+	0.999594i	$0.490931\pi$
$8$	−1725.94			−3.37097
$9$	−947.573			−1.29983
$10$		−	2042.88i		−	2.04288i
$11$			1625.11i			1.22097i	0.792029	+	0.610483i	$0.209025\pi$
$11$			1625.11i			1.22097i	−0.792029	+	0.610483i	$0.790975\pi$
$12$		−	7186.85i		−	4.15906i
$13$	−559.880			−0.254838			−0.127419	−	0.991849i	$-0.540669\pi$
$13$	−559.880			−0.254838			−0.127419	+	0.991849i	$0.540669\pi$
$14$	−302.448			−0.110222
$15$	5404.84			1.60143
$16$	15478.1			3.77883
$17$	925.444			0.188366			0.0941831	−	0.995555i	$-0.469976\pi$
$17$	925.444			0.188366			0.0941831	+	0.995555i	$0.469976\pi$
$18$	14665.1			2.51459
$19$	−11995.7			−1.74889			−0.874446	−	0.485123i	$-0.838775\pi$
$19$	−11995.7			−1.74889			−0.874446	+	0.485123i	$0.838775\pi$
$20$			23168.6i			2.89607i
$21$		−	800.187i		−	0.0864039i
$22$		−	25150.9i		−	2.36203i
$23$	15240.2			1.25258			0.626292	−	0.779589i	$-0.284572\pi$
$23$	15240.2			1.25258			0.626292	+	0.779589i	$0.284572\pi$
$24$			70670.3i			5.11214i
$25$	−1798.82			−0.115124
$26$	8664.95			0.492999
$27$			8949.71i			0.454692i
$28$	3430.11			0.156255
$29$	23080.3			0.946340			0.473170	−	0.880971i	$-0.343110\pi$
$29$	23080.3			0.946340			0.473170	+	0.880971i	$0.343110\pi$
$30$	−83647.7			−3.09806
$31$		−	41245.7i		−	1.38450i	−0.721656	−	0.692252i	$-0.756619\pi$
$31$		−	41245.7i		−	1.38450i	0.721656	−	0.692252i	$-0.243381\pi$
$32$	−129086.			−3.93939
$33$	66541.6			1.85162
$34$	−14322.6			−0.364405
$35$			2579.60i			0.0601655i
$36$	−166318.			−3.56478
$37$		−	53616.1i		−	1.05850i	−0.848467	−	0.529249i	$-0.822474\pi$
$37$		−	53616.1i		−	1.05850i	0.848467	−	0.529249i	$-0.177526\pi$
$38$	185650.			3.38333
$39$			22924.8i			0.386467i
$40$		−	227823.i		−	3.55973i
$41$	−25274.4			−0.366716			−0.183358	−	0.983046i	$-0.558697\pi$
$41$	−25274.4			−0.366716			−0.183358	+	0.983046i	$0.558697\pi$
$42$			12384.0i			0.167153i
$43$		−	29030.8i		−	0.365135i	−0.983193	−	0.182568i	$-0.941559\pi$
$43$		−	29030.8i		−	0.365135i	0.983193	−	0.182568i	$-0.0584409\pi$
$44$			285239.i			3.34851i
$45$		−	125079.i		−	1.37261i
$46$	−235864.			−2.42319
$47$		−	191707.i		−	1.84648i	−0.384228	−	0.923238i	$-0.625532\pi$
$47$		−	191707.i		−	1.84648i	0.384228	−	0.923238i	$-0.374468\pi$
$48$		−	633766.i		−	5.73067i
$49$	−117267.			−0.996754
$50$	27839.3			0.222714
$51$		−	37893.2i		−	0.285661i
$52$	−98270.3			−0.698896
$53$			137178.i			0.921416i	0.887552	+	0.460708i	$0.152404\pi$
$53$			137178.i			0.921416i	−0.887552	+	0.460708i	$0.847596\pi$
$54$		−	138510.i		−	0.879627i
$55$	−214513.			−1.28933
$56$	−33729.1			−0.192062
$57$			491174.i			2.65223i
$58$	−357201.			−1.83075
$59$	−339384.			−1.65248			−0.826239	−	0.563320i	$-0.809524\pi$
$59$	−339384.			−1.65248			−0.826239	+	0.563320i	$0.809524\pi$
$60$	948660.			4.39194
$61$	390795.			1.72171			0.860854	−	0.508852i	$-0.169930\pi$
$61$	390795.			1.72171			0.860854	+	0.508852i	$0.169930\pi$
$62$			638337.i			2.67840i
$63$	−18517.9			−0.0740579
$64$	1.00719e6			3.84213
$65$		−	73903.8i		−	0.269108i
$66$	−1.02983e6			−3.58206
$67$			205709.i			0.683957i	0.939708	+	0.341979i	$0.111097\pi$
$67$			205709.i			0.683957i	−0.939708	+	0.341979i	$0.888903\pi$
$68$	162434.			0.516596
$69$		−	624024.i		−	1.89956i
$70$		−	39923.0i		−	0.116393i
$71$		−	332887.i		−	0.930085i	−0.885288	−	0.465042i	$-0.846039\pi$
$71$		−	332887.i		−	0.930085i	0.885288	−	0.465042i	$-0.153961\pi$
$72$	1.63545e6			4.38168
$73$		−	139428.i		−	0.358411i	−0.983812	−	0.179206i	$-0.942647\pi$
$73$		−	139428.i		−	0.358411i	0.983812	−	0.179206i	$-0.0573527\pi$
$74$			829786.i			2.04772i
$75$			73654.3i			0.174588i
$76$	−2.10548e6			−4.79635
$77$			31758.6i			0.0695648i
$78$		−	354795.i		−	0.747642i
$79$	−327094.			−0.663423			−0.331712	−	0.943381i	$-0.607626\pi$
$79$	−327094.			−0.663423			−0.331712	+	0.943381i	$0.607626\pi$
$80$			2.04310e6i			3.99043i
$81$	−324327.			−0.610278
$82$	391158.			0.709432
$83$	599362.			1.04823			0.524113	−	0.851649i	$-0.324397\pi$
$83$	599362.			1.04823			0.524113	+	0.851649i	$0.324397\pi$
$84$		−	140449.i		−	0.236963i
$85$			122158.i			0.198914i
$86$			449294.i			0.706375i
$87$		−	945045.i		−	1.43514i
$88$		−	2.80483e6i		−	4.11585i
$89$		−	1.21502e6i		−	1.72351i	−0.507323	−	0.861756i	$-0.669365\pi$
$89$		−	1.21502e6i		−	1.72351i	0.507323	−	0.861756i	$-0.330635\pi$
$90$			1.93578e6i			2.65539i
$91$	−10941.5			−0.0145195
$92$	2.67496e6			3.43522
$93$	−1.68885e6			−2.09962
$94$			2.96694e6i			3.57211i
$95$		−	1.58342e6i		−	1.84682i
$96$			5.28555e6i			5.97415i
$97$	−532486.			−0.583436			−0.291718	−	0.956504i	$-0.594227\pi$
$97$	−532486.			−0.583436			−0.291718	+	0.956504i	$0.594227\pi$
$98$	1.81488e6			1.92828
$99$		−	1.53991e6i		−	1.58704i
$100$	−315729.			−0.315729
$101$			1.30006e6i			1.26182i	0.775855	+	0.630911i	$0.217319\pi$
$101$			1.30006e6i			1.26182i	−0.775855	+	0.630911i	$0.782681\pi$
$102$			586452.i			0.552627i
$103$	766728.	−	778576.i	0.701665	−	0.712507i
$103$	766728.	−	778576.i	0.701665	−	0.712507i
$104$	966319.			0.859054
$105$	105624.			0.0912420
$106$		−	2.12302e6i		−	1.78253i
$107$	206169.			0.168296			0.0841478	−	0.996453i	$-0.473183\pi$
$107$	206169.			0.168296			0.0841478	+	0.996453i	$0.473183\pi$
$108$			1.57086e6i			1.24700i
$109$		−	8890.56i		−	0.00686514i	−0.999994	−	0.00343257i	$-0.998907\pi$
$109$		−	8890.56i		−	0.00686514i	0.999994	−	0.00343257i	$-0.00109262\pi$
$110$	3.31990e6			2.49429
$111$	−2.19536e6			−1.60523
$112$	302481.			0.215300
$113$		−	227147.i		−	0.157424i	−0.996897	−	0.0787122i	$-0.974919\pi$
$113$		−	227147.i		−	0.157424i	0.996897	−	0.0787122i	$-0.0250808\pi$
$114$		−	7.60162e6i		−	5.13088i
$115$			2.01169e6i			1.32272i
$116$	4.05106e6			2.59534
$117$	530527.			0.331246
$118$	5.25246e6			3.19681
$119$	18085.5			0.0107322
$120$	−9.32843e6			−5.39839
$121$	−869410.			−0.490759
$122$	−6.04812e6			−3.33074
$123$			1.03489e6i			0.556131i
$124$		−	7.23947e6i		−	3.79701i
$125$			1.82505e6i			0.934424i
$126$	286592.			0.143269
$127$		−	2.76033e6i		−	1.34756i	−0.738930	−	0.673782i	$-0.764668\pi$
$127$		−	2.76033e6i		−	1.34756i	0.738930	−	0.673782i	$-0.235332\pi$
$128$	−7.32626e6			−3.49343
$129$	−1.18870e6			−0.553734
$130$			1.14377e6i			0.520604i
$131$	484466.			0.215501			0.107750	−	0.994178i	$-0.465635\pi$
$131$	484466.			0.215501			0.107750	+	0.994178i	$0.465635\pi$
$132$	1.16794e7			5.07807
$133$	−234425.			−0.0996435
$134$		−	3.18364e6i		−	1.32315i
$135$	−1.18136e6			−0.480152
$136$	−1.59726e6			−0.634978
$137$	−2.59659e6			−1.00982			−0.504908	−	0.863173i	$-0.668473\pi$
$137$	−2.59659e6			−1.00982			−0.504908	+	0.863173i	$0.668473\pi$
$138$			9.65768e6i			3.67481i
$139$	854924.			0.318334			0.159167	−	0.987252i	$-0.449119\pi$
$139$	854924.			0.318334			0.159167	+	0.987252i	$0.449119\pi$
$140$			452772.i			0.165004i
$141$	−7.84962e6			−2.80021
$142$			5.15192e6i			1.79930i
$143$		−	909865.i		−	0.311149i
$144$	−1.46666e7			−4.91183
$145$			3.04658e6i			0.999329i
$146$			2.15785e6i			0.693366i
$147$			4.80162e6i			1.51159i
$148$		−	9.41071e6i		−	2.90294i
$149$	−2.50343e6			−0.756791			−0.378396	−	0.925644i	$-0.623524\pi$
$149$	−2.50343e6			−0.756791			−0.378396	+	0.925644i	$0.623524\pi$
$150$		−	1.13991e6i		−	0.337750i
$151$		−	2.23356e6i		−	0.648734i	−0.945931	−	0.324367i	$-0.894849\pi$
$151$		−	2.23356e6i		−	0.648734i	0.945931	−	0.324367i	$-0.105151\pi$
$152$	2.07038e7			5.89547
$153$	−876926.			−0.244843
$154$		−	491511.i		−	0.134577i
$155$	5.44441e6			1.46203
$156$			4.02378e6i			1.05989i
$157$		−	6.86921e6i		−	1.77504i	−0.460770	−	0.887519i	$-0.652427\pi$
$157$		−	6.86921e6i		−	1.77504i	0.460770	−	0.887519i	$-0.347573\pi$
$158$	5.06225e6			1.28343
$159$	5.61687e6			1.39734
$160$		−	1.70392e7i		−	4.15997i
$161$	297831.			0.0713662
$162$	5.01942e6			1.18062
$163$	2.37651e6			0.548753			0.274376	−	0.961622i	$-0.411529\pi$
$163$	2.37651e6			0.548753			0.274376	+	0.961622i	$0.411529\pi$
$164$	−4.43617e6			−1.00572
$165$			8.78344e6i			1.95530i
$166$	−9.27600e6			−2.02785
$167$	−2.13203e6			−0.457766			−0.228883	−	0.973454i	$-0.573507\pi$
$167$	−2.13203e6			−0.457766			−0.228883	+	0.973454i	$0.573507\pi$
$168$			1.38107e6i			0.291265i
$169$	−4.51334e6			−0.935057
$170$		−	1.89057e6i		−	0.384810i
$171$	1.13668e7			2.27326
$172$		−	5.09550e6i		−	1.00139i
$173$			4.48071e6i			0.865384i	0.901542	+	0.432692i	$0.142436\pi$
$173$			4.48071e6i			0.865384i	−0.901542	+	0.432692i	$0.857564\pi$
$174$			1.46259e7i			2.77636i
$175$	−35153.3			−0.00655922
$176$			2.51536e7i			4.61383i
$177$			1.38964e7i			2.50601i
$178$			1.88042e7i			3.33423i
$179$	−1.20916e6			−0.210827			−0.105413	−	0.994429i	$-0.533617\pi$
$179$	−1.20916e6			−0.210827			−0.105413	+	0.994429i	$0.533617\pi$
$180$		−	2.19539e7i		−	3.76439i
$181$		−	7.89543e6i		−	1.33150i	−0.746177	−	0.665748i	$-0.768113\pi$
$181$		−	7.89543e6i		−	1.33150i	0.746177	−	0.665748i	$-0.231887\pi$
$182$	169335.			0.0280887
$183$		−	1.60015e7i		−	2.61100i
$184$	−2.63036e7			−4.22243
$185$	7.07729e6			1.11777
$186$	2.61374e7			4.06184
$187$			1.50394e6i			0.229989i
$188$		−	3.36484e7i		−	5.06397i
$189$			174900.i			0.0259062i
$190$			2.45057e7i			3.57278i
$191$			3.52024e6i			0.505210i	0.967570	+	0.252605i	$0.0812873\pi$
$191$			3.52024e6i			0.505210i	−0.967570	+	0.252605i	$0.918713\pi$
$192$		−	4.12405e7i		−	5.82666i
$193$			4.11146e6i			0.571905i	0.958244	+	0.285953i	$0.0923100\pi$
$193$			4.11146e6i			0.571905i	−0.958244	+	0.285953i	$0.907690\pi$
$194$	8.24099e6			1.12869
$195$	−3.02606e6			−0.408107
$196$	−2.05828e7			−2.73360
$197$		−	2.00236e6i		−	0.261905i	−0.991389	−	0.130953i	$-0.958196\pi$
$197$		−	2.00236e6i		−	0.261905i	0.991389	−	0.130953i	$-0.0418036\pi$
$198$			2.38323e7i			3.07023i
$199$		−	4.98162e6i		−	0.632137i	−0.948736	−	0.316068i	$-0.897637\pi$
$199$		−	4.98162e6i		−	0.632137i	0.948736	−	0.316068i	$-0.102363\pi$
$200$	3.10465e6			0.388081
$201$	8.42296e6			1.03723
$202$		−	2.01203e7i		−	2.44107i
$203$	451046.			0.0539179
$204$		−	6.65103e6i		−	0.783427i
$205$		−	3.33620e6i		−	0.387250i
$206$	−1.18662e7	+	1.20496e7i	−1.35741	+	1.37838i
$207$	−1.44412e7			−1.62814
$208$	−8.66588e6			−0.962992
$209$		−	1.94942e7i		−	2.13534i
$210$	−1.63469e6			−0.176513
$211$		−	9.58723e6i		−	1.02058i	−0.860003	−	0.510288i	$-0.829539\pi$
$211$		−	9.58723e6i		−	1.02058i	0.860003	−	0.510288i	$-0.170461\pi$
$212$			2.40775e7i			2.52699i
$213$	−1.36304e7			−1.41049
$214$	−3.19077e6			−0.325577
$215$	3.83205e6			0.385581
$216$		−	1.54466e7i		−	1.53276i
$217$		−	806044.i		−	0.0788823i
$218$			137594.i			0.0132810i
$219$	−5.70902e6			−0.543537
$220$	−3.76514e7			−3.53601
$221$	−518137.			−0.0480030
$222$	3.39764e7			3.10541
$223$	1.55438e7			1.40166			0.700831	−	0.713327i	$-0.252813\pi$
$223$	1.55438e7			1.40166			0.700831	+	0.713327i	$0.252813\pi$
$224$	−2.52266e6			−0.224447
$225$	1.70451e6			0.149641
$226$			3.51543e6i			0.304546i
$227$		−	1.07570e7i		−	0.919627i	−0.888015	−	0.459814i	$-0.847916\pi$
$227$		−	1.07570e7i		−	0.919627i	0.888015	−	0.459814i	$-0.152084\pi$
$228$			8.62110e7i			7.27375i
$229$	1.77622e7			1.47907			0.739537	−	0.673116i	$-0.235044\pi$
$229$	1.77622e7			1.47907			0.739537	+	0.673116i	$0.235044\pi$
$230$		−	3.11339e7i		−	2.55888i
$231$	1.30039e6			0.105496
$232$	−3.98352e7			−3.19009
$233$			6.74016e6i			0.532847i	0.963856	+	0.266423i	$0.0858419\pi$
$233$			6.74016e6i			0.532847i	−0.963856	+	0.266423i	$0.914158\pi$
$234$	−8.21068e6			−0.640813
$235$	2.53052e7			1.94987
$236$	−5.95688e7			−4.53193
$237$			1.33932e7i			1.00609i
$238$	−279899.			−0.0207621
$239$	3.53754e6			0.259124			0.129562	−	0.991571i	$-0.458643\pi$
$239$	3.53754e6			0.259124			0.129562	+	0.991571i	$0.458643\pi$
$240$	8.36567e7			6.05155
$241$			1.48695e7i			1.06229i	0.847280	+	0.531147i	$0.178239\pi$
$241$			1.48695e7i			1.06229i	−0.847280	+	0.531147i	$0.821761\pi$
$242$	1.34554e7			0.949402
$243$			1.98042e7i			1.38019i
$244$	6.85925e7			4.72179
$245$		−	1.54792e7i		−	1.05257i
$246$		−	1.60163e7i		−	1.07587i
$247$	6.71612e6			0.445685
$248$			7.11876e7i			4.66713i
$249$		−	2.45415e7i		−	1.58965i
$250$		−	2.82452e7i		−	1.80770i
$251$		−	2.11133e6i		−	0.133517i	−0.997769	−	0.0667583i	$-0.978734\pi$
$251$		−	2.11133e6i		−	0.133517i	0.997769	−	0.0667583i	$-0.0212656\pi$
$252$	−3.25028e6			−0.203104
$253$			2.47669e7i			1.52936i
$254$			4.27201e7i			2.60694i
$255$	5.00188e6			0.301656
$256$	4.89241e7			2.91610
$257$		−	4.02536e6i		−	0.237140i	−0.992946	−	0.118570i	$-0.962169\pi$
$257$		−	4.02536e6i		−	0.237140i	0.992946	−	0.118570i	$-0.0378311\pi$
$258$	1.83968e7			1.07123
$259$		−	1.04779e6i		−	0.0603081i
$260$		−	1.29716e7i		−	0.738030i
$261$	−2.18703e7			−1.23008
$262$	−7.49781e6			−0.416899
$263$		−	2.83454e7i		−	1.55817i	−0.626916	−	0.779087i	$-0.715683\pi$
$263$		−	2.83454e7i		−	1.55817i	0.626916	−	0.779087i	$-0.284317\pi$
$264$	−1.14847e8			−6.24176
$265$	−1.81074e7			−0.973010
$266$	3.62806e6			0.192766
$267$	−4.97503e7			−2.61374
$268$			3.61061e7i			1.87576i
$269$	1.53485e7			0.788515			0.394257	−	0.919000i	$-0.371002\pi$
$269$	1.53485e7			0.788515			0.394257	+	0.919000i	$0.371002\pi$
$270$	1.82832e7			0.928882
$271$			3.80537e7i			1.91200i	0.293361	+	0.956002i	$0.405226\pi$
$271$			3.80537e7i			1.91200i	−0.293361	+	0.956002i	$0.594774\pi$
$272$	1.43241e7			0.711805
$273$			448008.i			0.0220190i
$274$	4.01860e7			1.95354
$275$		−	2.92327e6i		−	0.140563i
$276$		−	1.09529e8i		−	5.20957i
$277$		−	2.83045e7i		−	1.33173i	−0.746073	−	0.665864i	$-0.768063\pi$
$277$		−	2.83045e7i		−	1.33173i	0.746073	−	0.665864i	$-0.231937\pi$
$278$	−1.32312e7			−0.615835
$279$			3.90834e7i			1.79961i
$280$		−	4.45222e6i		−	0.202816i
$281$			3.19916e6i			0.144184i	0.997398	+	0.0720919i	$0.0229675\pi$
$281$			3.19916e6i			0.144184i	−0.997398	+	0.0720919i	$0.977033\pi$
$282$	1.21484e8			5.41717
$283$		−	8.62664e6i		−	0.380612i	−0.981725	−	0.190306i	$-0.939052\pi$
$283$		−	8.62664e6i		−	0.380612i	0.981725	−	0.190306i	$-0.0609480\pi$
$284$		−	5.84285e7i		−	2.55076i
$285$	−6.48346e7			−2.80074
$286$			1.40815e7i			0.601935i
$287$	−493925.			−0.0208937
$288$	1.22318e8			5.12052
$289$	−2.32811e7			−0.964518
$290$		−	4.71502e7i		−	1.93326i
$291$			2.18032e7i			0.884791i
$292$		−	2.44725e7i		−	0.982945i
$293$			5.64168e6i			0.224288i	0.993692	+	0.112144i	$0.0357718\pi$
$293$			5.64168e6i			0.224288i	−0.993692	+	0.112144i	$0.964228\pi$
$294$		−	7.43120e7i		−	2.92426i
$295$		−	4.47985e7i		−	1.74501i
$296$			9.25381e7i			3.56817i
$297$	−1.45442e7			−0.555164
$298$	3.87441e7			1.46405
$299$	−8.53267e6			−0.319206
$300$			1.29278e7i			0.478808i
$301$		−	567335.i		−	0.0208037i
$302$			3.45676e7i			1.25501i
$303$	5.32321e7			1.91358
$304$	−1.85670e8			−6.60877
$305$			5.15847e7i			1.81811i
$306$	1.35717e7			0.473663
$307$		−	1.08146e7i		−	0.373761i	−0.982383	−	0.186880i	$-0.940162\pi$
$307$		−	1.08146e7i		−	0.373761i	0.982383	−	0.186880i	$-0.0598376\pi$
$308$			5.57429e6i			0.190782i
$309$	−3.18795e7	−	3.13944e7i	−1.08053	−	1.06409i
$310$	−8.42601e7			−2.82837
$311$	−1.23626e7			−0.410988			−0.205494	−	0.978658i	$-0.565880\pi$
$311$	−1.23626e7			−0.410988			−0.205494	+	0.978658i	$0.565880\pi$
$312$		−	3.95669e7i		−	1.30277i
$313$	3.81095e7			1.24280			0.621399	−	0.783494i	$-0.286565\pi$
$313$	3.81095e7			1.24280			0.621399	+	0.783494i	$0.286565\pi$
$314$			1.06311e8i			3.43391i
$315$		−	2.44436e6i		−	0.0782047i
$316$	−5.74116e7			−1.81944
$317$	6.55721e6			0.205845			0.102923	−	0.994689i	$-0.467181\pi$
$317$	6.55721e6			0.205845			0.102923	+	0.994689i	$0.467181\pi$
$318$	−8.69293e7			−2.70324
$319$			3.75079e7i			1.15545i
$320$			1.32949e8i			4.05727i
$321$		−	8.44180e6i		−	0.255223i
$322$	−4.60937e6			−0.138062
$323$	−1.11013e7			−0.329432
$324$	−5.69259e7			−1.67369
$325$	1.00712e6			0.0293381
$326$	−3.67799e7			−1.06159
$327$	−364033.			−0.0104111
$328$	4.36221e7			1.23619
$329$		−	3.74643e6i		−	0.105203i
$330$		−	1.35936e8i		−	3.78263i
$331$		−	4.23928e7i		−	1.16898i	−0.811400	−	0.584492i	$-0.801294\pi$
$331$		−	4.23928e7i		−	1.16898i	0.811400	−	0.584492i	$-0.198706\pi$
$332$	1.05200e8			2.87477
$333$			5.08052e7i			1.37586i
$334$	3.29962e7			0.885574
$335$	−2.71534e7			−0.722255
$336$		−	1.23854e7i		−	0.326506i
$337$	−5.85872e7			−1.53078			−0.765391	−	0.643566i	$-0.777454\pi$
$337$	−5.85872e7			−1.53078			−0.765391	+	0.643566i	$0.777454\pi$
$338$	6.98505e7			1.80892
$339$	−9.30076e6			−0.238737
$340$			2.14412e7i			0.545522i
$341$	6.70287e7			1.69043
$342$	−1.75917e8			−4.39774
$343$	−4.59085e6			−0.113765
$344$			5.01054e7i			1.23086i
$345$	8.23708e7			2.00593
$346$		−	6.93455e7i		−	1.67413i
$347$	−4.24894e7			−1.01693			−0.508466	−	0.861082i	$-0.669787\pi$
$347$	−4.24894e7			−1.01693			−0.508466	+	0.861082i	$0.669787\pi$
$348$		−	1.65875e8i		−	3.93588i
$349$			2.11713e6i			0.0498047i	0.999690	+	0.0249023i	$0.00792748\pi$
$349$			2.11713e6i			0.0498047i	−0.999690	+	0.0249023i	$0.992073\pi$
$350$	544049.			0.0126892
$351$		−	5.01076e6i		−	0.115873i
$352$		−	2.09778e8i		−	4.80986i
$353$		−	3.61248e7i		−	0.821262i	−0.911802	−	0.410631i	$-0.865308\pi$
$353$		−	3.61248e7i		−	0.821262i	0.911802	−	0.410631i	$-0.134692\pi$
$354$		−	2.15067e8i		−	4.84802i
$355$	4.39409e7			0.982164
$356$		−	2.13261e8i		−	4.72674i
$357$		−	740528.i		−	0.0162756i
$358$	1.87135e7			0.407856
$359$	−6.99281e7			−1.51136			−0.755681	−	0.654940i	$-0.772694\pi$
$359$	−6.99281e7			−1.51136			−0.755681	+	0.654940i	$0.772694\pi$
$360$			2.15879e8i			4.62703i
$361$	9.68497e7			2.05862
$362$			1.22193e8i			2.57585i
$363$			3.55989e7i			0.744246i
$364$	−1.92045e6			−0.0398197
$365$	1.84044e7			0.378480
$366$			2.47646e8i			5.05113i
$367$	5.77902e7			1.16911			0.584556	−	0.811353i	$-0.301269\pi$
$367$	5.77902e7			1.16911			0.584556	+	0.811353i	$0.301269\pi$
$368$	2.35889e8			4.73330
$369$	2.39494e7			0.476667
$370$	−1.09531e8			−2.16238
$371$			2.68079e6i			0.0524979i
$372$	−2.96427e8			−5.75823
$373$	2.42475e7			0.467241			0.233620	−	0.972328i	$-0.424943\pi$
$373$	2.42475e7			0.467241			0.233620	+	0.972328i	$0.424943\pi$
$374$		−	2.32757e7i		−	0.444926i
$375$	7.47283e7			1.41707
$376$			3.30874e8i			6.22443i
$377$	−1.29222e7			−0.241164
$378$		−	2.70682e6i		−	0.0501169i
$379$		−	9.04885e7i		−	1.66217i	−0.556144	−	0.831086i	$-0.687720\pi$
$379$		−	9.04885e7i		−	1.66217i	0.556144	−	0.831086i	$-0.312280\pi$
$380$		−	2.77922e8i		−	5.06492i
$381$	−1.13024e8			−2.04361
$382$		−	5.44807e7i		−	0.977356i
$383$		−	6.02831e7i		−	1.07300i	−0.843901	−	0.536499i	$-0.819746\pi$
$383$		−	6.02831e7i		−	1.07300i	0.843901	−	0.536499i	$-0.180254\pi$
$384$			2.99981e8i			5.29785i
$385$	−4.19212e6			−0.0734601
$386$		−	6.36308e7i		−	1.10638i
$387$			2.75088e7i			0.474613i
$388$	−9.34622e7			−1.60008
$389$			6.02555e7i			1.02364i	0.859092	+	0.511821i	$0.171029\pi$
$389$			6.02555e7i			1.02364i	−0.859092	+	0.511821i	$0.828971\pi$
$390$	4.68327e7			0.789506
$391$	1.41039e7			0.235944
$392$	2.02396e8			3.36003
$393$		−	1.98369e7i		−	0.326811i
$394$			3.09895e7i			0.506670i
$395$		−	4.31761e7i		−	0.700571i
$396$		−	2.70285e8i		−	4.35248i
$397$		−	9.88474e7i		−	1.57977i	−0.613255	−	0.789885i	$-0.710140\pi$
$397$		−	9.88474e7i		−	1.57977i	0.613255	−	0.789885i	$-0.289860\pi$
$398$			7.70977e7i			1.22290i
$399$			9.59876e6i			0.151111i
$400$	−2.78422e7			−0.435035
$401$	−4.82124e7			−0.747698			−0.373849	−	0.927490i	$-0.621962\pi$
$401$	−4.82124e7			−0.747698			−0.373849	+	0.927490i	$0.621962\pi$
$402$	−1.30357e8			−2.00659
$403$			2.30927e7i			0.352825i
$404$			2.28187e8i			3.46056i
$405$		−	4.28109e7i		−	0.644450i
$406$	−6.98059e6			−0.104307
$407$	8.71318e7			1.29239
$408$			6.54013e7i			0.962956i
$409$	7.25539e7			1.06045			0.530226	−	0.847856i	$-0.322107\pi$
$409$	7.25539e7			1.06045			0.530226	+	0.847856i	$0.322107\pi$
$410$			5.16326e7i			0.749156i
$411$			1.06320e8i			1.53140i
$412$	1.34576e8	−	1.36656e8i	1.92432	−	1.95405i
$413$	−6.63241e6			−0.0941502
$414$	2.23498e8			3.14973
$415$			7.91154e7i			1.10692i
$416$	7.22726e7			1.00391
$417$		−	3.50057e7i		−	0.482759i
$418$			3.01701e8i			4.13093i
$419$	−1.13944e7			−0.154900			−0.0774498	−	0.996996i	$-0.524678\pi$
$419$	−1.13944e7			−0.154900			−0.0774498	+	0.996996i	$0.524678\pi$
$420$	1.85392e7			0.250232
$421$	−1.32298e8			−1.77299			−0.886495	−	0.462738i	$-0.846867\pi$
$421$	−1.32298e8			−1.77299			−0.886495	+	0.462738i	$0.846867\pi$
$422$			1.48376e8i			1.97436i
$423$			1.81656e8i			2.40010i
$424$		−	2.36760e8i		−	3.10607i
$425$	−1.66470e6			−0.0216855
$426$	2.10950e8			2.72867
$427$	7.63711e6			0.0980946
$428$	3.61869e7			0.461552
$429$	−3.72553e7			−0.471863
$430$	−5.93065e7			−0.745928
$431$	6.07890e7			0.759265			0.379633	−	0.925137i	$-0.376050\pi$
$431$	6.07890e7			0.759265			0.379633	+	0.925137i	$0.376050\pi$
$432$			1.38524e8i			1.71821i
$433$			6.31799e7i			0.778243i	0.921186	+	0.389122i	$0.127221\pi$
$433$			6.31799e7i			0.778243i	−0.921186	+	0.389122i	$0.872779\pi$
$434$			1.24747e7i			0.152602i
$435$	1.24745e8			1.51550
$436$		−	1.56047e6i		−	0.0188277i
$437$	−1.82816e8			−2.19063
$438$	8.83553e7			1.05150
$439$			7.40084e7i			0.874757i	0.899277	+	0.437379i	$0.144093\pi$
$439$			7.40084e7i			0.874757i	−0.899277	+	0.437379i	$0.855907\pi$
$440$	3.70236e8			4.34631
$441$	1.11119e8			1.29561
$442$	8.01892e6			0.0928644
$443$			9.90006e7i			1.13875i	0.822080	+	0.569373i	$0.192814\pi$
$443$			9.90006e7i			1.13875i	−0.822080	+	0.569373i	$0.807186\pi$
$444$	−3.85331e8			−4.40235
$445$	1.60382e8			1.82002
$446$	−2.40563e8			−2.71159
$447$			1.02505e8i			1.14769i
$448$	1.96830e7			0.218906
$449$		−	4.18818e7i		−	0.462686i	−0.972872	−	0.231343i	$-0.925688\pi$
$449$		−	4.18818e7i		−	0.462686i	0.972872	−	0.231343i	$-0.0743120\pi$
$450$	−2.63798e7			−0.289490
$451$		−	4.10736e7i		−	0.447747i
$452$		−	3.98689e7i		−	0.431737i
$453$	−9.14553e7			−0.983817
$454$			1.66479e8i			1.77907i
$455$		−	1.44426e6i		−	0.0153325i
$456$		−	8.47736e8i		−	8.94059i
$457$			8.44078e7i			0.884370i	0.896924	+	0.442185i	$0.145797\pi$
$457$			8.44078e7i			0.884370i	−0.896924	+	0.442185i	$0.854203\pi$
$458$	−2.74896e8			−2.86135
$459$			8.28245e6i			0.0856487i
$460$			3.53093e8i			3.62757i
$461$	2.58793e7			0.264149			0.132075	−	0.991240i	$-0.457836\pi$
$461$	2.58793e7			0.264149			0.132075	+	0.991240i	$0.457836\pi$
$462$	−2.01254e7			−0.204088
$463$			2.67148e7i			0.269159i	0.990903	+	0.134580i	$0.0429684\pi$
$463$			2.67148e7i			0.269159i	−0.990903	+	0.134580i	$0.957032\pi$
$464$	3.57239e8			3.57606
$465$		−	2.22927e8i		−	2.21719i
$466$		−	1.04314e8i		−	1.03082i
$467$	9.43349e7			0.926236			0.463118	−	0.886297i	$-0.346731\pi$
$467$	9.43349e7			0.926236			0.463118	+	0.886297i	$0.346731\pi$
$468$	9.31184e7			0.908443
$469$			4.02007e6i			0.0389686i
$470$	−3.91634e8			−3.77213
$471$	−2.81267e8			−2.69188
$472$	5.85756e8			5.57046
$473$	4.71782e7			0.445818
$474$		−	2.07279e8i		−	1.94634i
$475$	2.15780e7			0.201340
$476$	3.17437e6			0.0294331
$477$		−	1.29986e8i		−	1.19768i
$478$	−5.47485e7			−0.501290
$479$			2.45547e7i			0.223424i	0.993741	+	0.111712i	$0.0356333\pi$
$479$			2.45547e7i			0.223424i	−0.993741	+	0.111712i	$0.964367\pi$
$480$	−6.97688e8			−6.30867
$481$			3.00186e7i			0.269746i
$482$		−	2.30127e8i		−	2.05507i
$483$		−	1.21950e7i		−	0.108228i
$484$	−1.52599e8			−1.34591
$485$		−	7.02878e7i		−	0.616105i
$486$		−	3.06499e8i		−	2.67005i
$487$			1.36235e8i			1.17951i	0.807582	+	0.589756i	$0.200776\pi$
$487$			1.36235e8i			1.17951i	−0.807582	+	0.589756i	$0.799224\pi$
$488$	−6.74488e8			−5.80383
$489$		−	9.73085e7i		−	0.832194i
$490$			2.39563e8i			2.03625i
$491$	6.81773e7			0.575964			0.287982	−	0.957636i	$-0.407016\pi$
$491$	6.81773e7			0.575964			0.287982	+	0.957636i	$0.407016\pi$
$492$			1.81643e8i			1.52519i
$493$	2.13595e7			0.178259
$494$	−1.03942e8			−0.862202
$495$	2.03267e8			1.67591
$496$		−	6.38406e8i		−	5.23181i
$497$		−	6.50545e6i		−	0.0529918i
$498$			3.79815e8i			3.07527i
$499$			4.92236e7i			0.396161i	0.980186	+	0.198081i	$0.0634708\pi$
$499$			4.92236e7i			0.396161i	−0.980186	+	0.198081i	$0.936529\pi$
$500$			3.20333e8i			2.56266i
$501$			8.72980e7i			0.694210i
$502$			3.26759e7i			0.258295i
$503$	−2.30742e8			−1.81310			−0.906551	−	0.422095i	$-0.861295\pi$
$503$	−2.30742e8			−1.81310			−0.906551	+	0.422095i	$0.861295\pi$
$504$	3.19608e7			0.249647
$505$	−1.71607e8			−1.33248
$506$		−	3.83304e8i		−	2.95864i
$507$			1.84803e8i			1.41803i
$508$		−	4.84494e8i		−	3.69570i
$509$	1.55030e8			1.17561			0.587803	−	0.809004i	$-0.299993\pi$
$509$	1.55030e8			1.17561			0.587803	+	0.809004i	$0.299993\pi$
$510$	−7.74113e7			−0.583571
$511$		−	2.72477e6i		−	0.0204205i
$512$	−2.88291e8			−2.14794
$513$		−	1.07358e8i		−	0.795208i
$514$			6.22983e7i			0.458761i
$515$	1.02771e8	+	1.01208e8i	0.752403	+	0.740954i
$516$	−2.08640e8			−1.51862
$517$	3.11544e8			2.25449
$518$			1.62161e7i			0.116669i
$519$	1.83467e8			1.31237
$520$			1.27553e8i			0.907156i
$521$			5.48195e7i			0.387634i	0.981038	+	0.193817i	$0.0620868\pi$
$521$			5.48195e7i			0.387634i	−0.981038	+	0.193817i	$0.937913\pi$
$522$	3.38474e8			2.37965
$523$	6.61511e7			0.462415			0.231207	−	0.972904i	$-0.425732\pi$
$523$	6.61511e7			0.462415			0.231207	+	0.972904i	$0.425732\pi$
$524$	8.50336e7			0.591013
$525$			1.43939e6i			0.00994718i
$526$			4.38687e8i			3.01438i
$527$		−	3.81706e7i		−	0.260794i
$528$	1.02994e9			6.99695
$529$	8.42272e7			0.568965
$530$	2.80238e8			1.88234
$531$	3.21591e8			2.14793
$532$	−4.11463e7			−0.273273
$533$	1.41506e7			0.0934532
$534$	7.69958e8			5.05642
$535$			2.72142e7i			0.177719i
$536$		−	3.55041e8i		−	2.30560i
$537$			4.95103e7i			0.319722i
$538$	−2.37541e8			−1.52543
$539$		−	1.90572e8i		−	1.21700i
$540$	−2.07352e8			−1.31682
$541$	−2.48050e7			−0.156656			−0.0783279	−	0.996928i	$-0.524958\pi$
$541$	−2.48050e7			−0.156656			−0.0783279	+	0.996928i	$0.524958\pi$
$542$		−	5.88936e8i		−	3.69888i
$543$	−3.23286e8			−2.01924
$544$	−1.19462e8			−0.742048
$545$	1.17355e6			0.00724955
$546$		−	6.93358e6i		−	0.0425970i
$547$	4.86051e7			0.296975			0.148487	−	0.988914i	$-0.452560\pi$
$547$	4.86051e7			0.296975			0.148487	+	0.988914i	$0.452560\pi$
$548$	−4.55755e8			−2.76942
$549$	−3.70307e8			−2.23792
$550$			4.52418e7i			0.271927i
$551$	−2.76863e8			−1.65505
$552$			1.07703e9i			6.40339i
$553$	−6.39222e6			−0.0377987
$554$			4.38053e8i			2.57630i
$555$		−	2.89786e8i		−	1.69511i
$556$	1.50057e8			0.873033
$557$			1.11738e8i			0.646601i	0.946296	+	0.323301i	$0.104793\pi$
$557$			1.11738e8i			0.646601i	−0.946296	+	0.323301i	$0.895207\pi$
$558$		−	6.04872e8i		−	3.48145i
$559$			1.62538e7i			0.0930505i
$560$			3.99272e7i			0.227355i
$561$	6.15805e7			0.348782
$562$		−	4.95115e7i		−	0.278932i
$563$		−	9.82192e7i		−	0.550391i	−0.961388	−	0.275195i	$-0.911257\pi$
$563$		−	9.82192e7i		−	0.550391i	0.961388	−	0.275195i	$-0.0887426\pi$
$564$	−1.37777e9			−7.67961
$565$	2.99833e7			0.166239
$566$			1.33510e8i			0.736315i
$567$	−6.33815e6			−0.0347707
$568$			5.74544e8i			3.13529i
$569$		−	2.47105e8i		−	1.34136i	−0.741749	−	0.670678i	$-0.766003\pi$
$569$		−	2.47105e8i		−	1.34136i	0.741749	−	0.670678i	$-0.233997\pi$
$570$	1.00341e9			5.41818
$571$	9.62697e7			0.517108			0.258554	−	0.965997i	$-0.416754\pi$
$571$	9.62697e7			0.517108			0.258554	+	0.965997i	$0.416754\pi$
$572$		−	1.59700e8i		−	0.853328i
$573$	1.44140e8			0.766159
$574$	7.64420e6			0.0404200
$575$	−2.74143e7			−0.144203
$576$	−9.54388e8			−4.99410
$577$			2.90175e7i			0.151054i	0.997144	+	0.0755271i	$0.0240639\pi$
$577$			2.90175e7i			0.151054i	−0.997144	+	0.0755271i	$0.975936\pi$
$578$	3.60309e8			1.86591
$579$	1.68348e8			0.867305
$580$			5.34737e8i			2.74067i
$581$	1.17130e7			0.0597229
$582$		−	3.37436e8i		−	1.71168i
$583$	−2.22928e8			−1.12502
$584$			2.40644e8i			1.20819i
$585$			7.00293e7i			0.349794i
$586$		−	8.73132e7i		−	0.433897i
$587$	−1.78835e8			−0.884177			−0.442089	−	0.896971i	$-0.645762\pi$
$587$	−1.78835e8			−0.884177			−0.442089	+	0.896971i	$0.645762\pi$
$588$			8.42781e8i			4.14556i
$589$			4.94769e8i			2.42135i
$590$			6.93321e8i			3.37581i
$591$	−8.19887e7			−0.397184
$592$		−	8.29875e8i		−	3.99989i
$593$		−	3.00511e8i		−	1.44111i	−0.693399	−	0.720554i	$-0.743888\pi$
$593$		−	3.00511e8i		−	1.44111i	0.693399	−	0.720554i	$-0.256112\pi$
$594$	2.25093e8			1.07400
$595$			2.38727e6i			0.0113332i
$596$	−4.39402e8			−2.07550
$597$	−2.03977e8			−0.958647
$598$	1.32055e8			0.617522
$599$		−	4.00970e7i		−	0.186566i	−0.995640	−	0.0932829i	$-0.970264\pi$
$599$		−	4.00970e7i		−	0.186566i	0.995640	−	0.0932829i	$-0.0297361\pi$
$600$		−	1.27123e8i		−	0.588531i
$601$			5.73697e7i			0.264277i	0.991231	+	0.132138i	$0.0421844\pi$
$601$			5.73697e7i			0.264277i	−0.991231	+	0.132138i	$0.957816\pi$
$602$			8.78032e6i			0.0402458i
$603$		−	1.94924e8i		−	0.889026i
$604$		−	3.92035e8i		−	1.77916i
$605$		−	1.14762e8i		−	0.518239i
$606$	−8.23844e8			−3.70192
$607$	−1.68814e8			−0.754817			−0.377408	−	0.926047i	$-0.623185\pi$
$607$	−1.68814e8			−0.754817			−0.377408	+	0.926047i	$0.623185\pi$
$608$	1.54847e9			6.88956
$609$		−	1.84685e7i		−	0.0817674i
$610$		−	7.98347e8i		−	3.51724i
$611$			1.07333e8i			0.470553i
$612$	−1.53918e8			−0.671485
$613$	−2.67211e8			−1.16004			−0.580020	−	0.814602i	$-0.696955\pi$
$613$	−2.67211e8			−1.16004			−0.580020	+	0.814602i	$0.696955\pi$
$614$			1.67371e8i			0.723061i
$615$	−1.36604e8			−0.587271
$616$		−	5.48135e7i		−	0.234501i
$617$		−	1.84915e8i		−	0.787258i	−0.919269	−	0.393629i	$-0.871219\pi$
$617$		−	1.84915e8i		−	0.787258i	0.919269	−	0.393629i	$-0.128781\pi$
$618$	4.93382e8	+	4.85874e8i	2.09034	+	2.05854i
$619$	2.51001e8			1.05829			0.529144	−	0.848532i	$-0.322513\pi$
$619$	2.51001e8			1.05829			0.529144	+	0.848532i	$0.322513\pi$
$620$	9.55605e8			4.00962
$621$			1.36395e8i			0.569540i
$622$	1.91329e8			0.795080
$623$		−	2.37446e7i		−	0.0981975i
$624$			3.54833e8i			1.46039i
$625$	−2.69011e8			−1.10187
$626$	−5.89800e8			−2.40426
$627$	−7.98210e8			−3.23828
$628$		−	1.20569e9i		−	4.86805i
$629$		−	4.96187e7i		−	0.199385i
$630$			3.78299e7i			0.151291i
$631$	4.97065e6			0.0197845			0.00989225	−	0.999951i	$-0.496851\pi$
$631$	4.97065e6			0.0197845			0.00989225	+	0.999951i	$0.496851\pi$
$632$	5.64544e8			2.23638
$633$	−3.92558e8			−1.54772
$634$	−1.01482e8			−0.398219
$635$	3.64361e8			1.42302
$636$	9.85876e8			3.83222
$637$	6.56555e7			0.254011
$638$		−	5.80489e8i		−	2.23528i
$639$			3.15435e8i			1.20895i
$640$		−	9.67061e8i		−	3.68904i
$641$	−3.36436e8			−1.27740			−0.638702	−	0.769454i	$-0.720528\pi$
$641$	−3.36436e8			−1.27740			−0.638702	+	0.769454i	$0.720528\pi$
$642$			1.30649e8i			0.493743i
$643$	−4.78392e8			−1.79949			−0.899747	−	0.436411i	$-0.856249\pi$
$643$	−4.78392e8			−1.79949			−0.899747	+	0.436411i	$0.856249\pi$
$644$	5.22754e7			0.195722
$645$		−	1.56907e8i		−	0.584740i
$646$	1.71809e8			0.637305
$647$	1.53527e8			0.566855			0.283428	−	0.958994i	$-0.408528\pi$
$647$	1.53527e8			0.566855			0.283428	+	0.958994i	$0.408528\pi$
$648$	5.59768e8			2.05723
$649$		−	5.51535e8i		−	2.01762i
$650$	−1.55866e7			−0.0567561
$651$	−3.30043e7			−0.119626
$652$	4.17126e8			1.50496
$653$			1.35151e8i			0.485379i	0.970104	+	0.242689i	$0.0780296\pi$
$653$			1.35151e8i			0.485379i	−0.970104	+	0.242689i	$0.921970\pi$
$654$	5.63393e6			0.0201409
$655$			6.39491e7i			0.227568i
$656$	−3.91200e8			−1.38576
$657$			1.32118e8i			0.465872i
$658$			5.79814e7i			0.203522i
$659$	2.99977e8			1.04817			0.524085	−	0.851666i	$-0.324407\pi$
$659$	2.99977e8			1.04817			0.524085	+	0.851666i	$0.324407\pi$
$660$			1.54167e9i			5.36242i
$661$			3.24295e8i			1.12289i	0.827515	+	0.561443i	$0.189754\pi$
$661$			3.24295e8i			1.12289i	−0.827515	+	0.561443i	$0.810246\pi$
$662$			6.56090e8i			2.26146i
$663$			2.12156e7i			0.0727974i
$664$	−1.03446e9			−3.53354
$665$		−	3.09439e7i		−	0.105223i
$666$		−	7.86284e8i		−	2.66168i
$667$	3.51748e8			1.18537
$668$	−3.74214e8			−1.25543
$669$		−	6.36457e8i		−	2.12565i
$670$	4.20239e8			1.39724
$671$			6.35083e8i			2.10215i
$672$			1.03293e8i			0.340378i
$673$	1.23362e8			0.404702			0.202351	−	0.979313i	$-0.435142\pi$
$673$	1.23362e8			0.404702			0.202351	+	0.979313i	$0.435142\pi$
$674$	9.06722e8			2.96138
$675$		−	1.60989e7i		−	0.0523461i
$676$	−7.92184e8			−2.56440
$677$	−2.84716e8			−0.917585			−0.458793	−	0.888543i	$-0.651718\pi$
$677$	−2.84716e8			−0.917585			−0.458793	+	0.888543i	$0.651718\pi$
$678$	1.43943e8			0.461850
$679$	−1.04061e7			−0.0332414
$680$		−	2.10837e8i		−	0.670533i
$681$	−4.40454e8			−1.39463
$682$	−1.03737e9			−3.27024
$683$		−	7.78553e7i		−	0.244358i	−0.992508	−	0.122179i	$-0.961012\pi$
$683$		−	7.78553e7i		−	0.244358i	0.992508	−	0.122179i	$-0.0389882\pi$
$684$	1.99510e9			6.23442
$685$		−	3.42748e8i		−	1.06636i
$686$	7.10500e7			0.220086
$687$		−	7.27290e8i		−	2.24304i
$688$		−	4.49342e8i		−	1.37979i
$689$		−	7.68030e7i		−	0.234812i
$690$	−1.27481e9			−3.88058
$691$		−	6.64386e7i		−	0.201366i	−0.994919	−	0.100683i	$-0.967897\pi$
$691$		−	6.64386e7i		−	0.201366i	0.994919	−	0.100683i	$-0.0321028\pi$
$692$			7.86456e8i			2.37332i
$693$		−	3.00936e7i		−	0.0904222i
$694$	6.57584e8			1.96731
$695$			1.12849e8i			0.336159i
$696$			1.63109e9i			4.83782i
$697$	−2.33900e7			−0.0690769
$698$		−	3.27656e7i		−	0.0963499i
$699$	2.75982e8			0.808072
$700$	−6.17013e6			−0.0179887
$701$	−2.06032e8			−0.598109			−0.299055	−	0.954236i	$-0.596671\pi$
$701$	−2.06032e8			−0.598109			−0.299055	+	0.954236i	$0.596671\pi$
$702$			7.75488e7i			0.224163i
$703$			6.43160e8i			1.85120i
$704$			1.63679e9i			4.69111i
$705$		−	1.03614e9i		−	2.95701i
$706$			5.59084e8i			1.58878i
$707$			2.54064e7i			0.0718926i
$708$			2.43910e9i			6.87275i
$709$	4.60969e7			0.129340			0.0646701	−	0.997907i	$-0.479401\pi$
$709$	4.60969e7			0.129340			0.0646701	+	0.997907i	$0.479401\pi$
$710$	−6.80049e8			−1.90005
$711$	3.09945e8			0.862335
$712$			2.09706e9i			5.80992i
$713$		−	6.28592e8i		−	1.73421i
$714$			1.14607e7i			0.0314860i
$715$	1.20101e8			0.328572
$716$	−2.12232e8			−0.578193
$717$		−	1.44848e8i		−	0.392966i
$718$	1.08224e9			2.92381
$719$			5.05587e7i			0.136022i	0.997685	+	0.0680110i	$0.0216653\pi$
$719$			5.05587e7i			0.136022i	−0.997685	+	0.0680110i	$0.978335\pi$
$720$		−	1.93599e9i		−	5.18686i
$721$	1.49838e7	−	1.52153e7i	0.0399775	−	0.0405952i
$722$	−1.49889e9			−3.98252
$723$	6.08846e8			1.61099
$724$		−	1.38581e9i		−	3.65164i
$725$	−4.15172e7			−0.108947
$726$		−	5.50944e8i		−	1.43978i
$727$		−	3.51457e8i		−	0.914679i	−0.889292	−	0.457339i	$-0.848802\pi$
$727$		−	3.51457e8i		−	0.914679i	0.889292	−	0.457339i	$-0.151198\pi$
$728$	1.88843e7			0.0489448
$729$	5.74469e8			1.48280
$730$	−2.84835e8			−0.732191
$731$		−	2.68664e7i		−	0.0687792i
$732$		−	2.80859e9i		−	7.16068i
$733$			5.35984e8i			1.36094i	0.732775	+	0.680471i	$0.238225\pi$
$733$			5.35984e8i			1.36094i	−0.732775	+	0.680471i	$0.761775\pi$
$734$	−8.94388e8			−2.26171
$735$	−6.33810e8			−1.59624
$736$	−1.96729e9			−4.93441
$737$	−3.34299e8			−0.835089
$738$	−3.70651e8			−0.922138
$739$	−1.60052e8			−0.396577			−0.198289	−	0.980144i	$-0.563538\pi$
$739$	−1.60052e8			−0.396577			−0.198289	+	0.980144i	$0.563538\pi$
$740$	1.24221e9			3.06548
$741$		−	2.74998e8i		−	0.675889i
$742$		−	4.14892e7i		−	0.101560i
$743$			1.06654e8i			0.260023i	0.991512	+	0.130012i	$0.0415015\pi$
$743$			1.06654e8i			0.260023i	−0.991512	+	0.130012i	$0.958499\pi$
$744$	2.91485e9			7.07778
$745$		−	3.30451e8i		−	0.799167i
$746$	−3.75265e8			−0.903903
$747$	−5.67940e8			−1.36251
$748$			2.63973e8i			0.630746i
$749$	4.02906e6			0.00958867
$750$	−1.15653e9			−2.74140
$751$	4.77999e8			1.12851			0.564257	−	0.825599i	$-0.309163\pi$
$751$	4.77999e8			1.12851			0.564257	+	0.825599i	$0.309163\pi$
$752$		−	2.96726e9i		−	6.97753i
$753$	−8.64505e7			−0.202480
$754$	1.99990e8			0.466545
$755$	2.94828e8			0.685060
$756$			3.06984e7i			0.0710478i
$757$	−2.65145e8			−0.611218			−0.305609	−	0.952157i	$-0.598860\pi$
$757$	−2.65145e8			−0.611218			−0.305609	+	0.952157i	$0.598860\pi$
$758$			1.40044e9i			3.21556i
$759$	1.01411e9			2.31931
$760$			2.73288e9i			6.22558i
$761$			1.60277e8i			0.363678i	0.983328	+	0.181839i	$0.0582049\pi$
$761$			1.60277e8i			0.363678i	−0.983328	+	0.181839i	$0.941795\pi$
$762$	1.74922e9			3.95347
$763$		−	173744.i		−	0.000391143i
$764$			6.17873e8i			1.38554i
$765$		−	1.15754e8i		−	0.258553i
$766$			9.32968e8i			2.07578i
$767$	1.90014e8			0.421115
$768$		−	2.00325e9i		−	4.42232i
$769$		−	2.13795e8i		−	0.470131i	−0.971980	−	0.235066i	$-0.924470\pi$
$769$		−	2.13795e8i		−	0.470131i	0.971980	−	0.235066i	$-0.0755305\pi$
$770$	6.48791e7			0.142113
$771$	−1.64822e8			−0.359628
$772$			7.21645e8i			1.56845i
$773$	−8.18893e7			−0.177292			−0.0886459	−	0.996063i	$-0.528254\pi$
$773$	−8.18893e7			−0.177292			−0.0886459	+	0.996063i	$0.528254\pi$
$774$		−	4.25739e8i		−	0.918165i
$775$			7.41935e7i			0.159390i
$776$	9.19039e8			1.96675
$777$	−4.29029e7			−0.0914583
$778$		−	9.32541e8i		−	1.98029i
$779$	3.03183e8			0.641346
$780$	−5.31136e8			−1.11924
$781$	5.40978e8			1.13560
$782$	−2.18279e8			−0.456448
$783$			2.06562e8i			0.430293i
$784$	−1.81507e9			−3.76657
$785$	9.06731e8			1.87443
$786$			3.07005e8i			0.632234i
$787$	7.46529e8			1.53152			0.765759	−	0.643127i	$-0.222363\pi$
$787$	7.46529e8			1.53152			0.765759	+	0.643127i	$0.222363\pi$
$788$		−	3.51455e8i		−	0.718276i
$789$	−1.16063e9			−2.36300
$790$			6.68213e8i			1.35529i
$791$		−	4.43902e6i		−	0.00896928i
$792$			2.65779e9i			5.34989i
$793$	−2.18798e8			−0.438757
$794$			1.52981e9i			3.05615i
$795$			7.41424e8i			1.47559i
$796$		−	8.74375e8i		−	1.73364i
$797$	−5.54196e8			−1.09468			−0.547342	−	0.836909i	$-0.684360\pi$
$797$	−5.54196e8			−1.09468			−0.547342	+	0.836909i	$0.684360\pi$
$798$		−	1.48555e8i		−	0.292333i
$799$		−	1.77414e8i		−	0.347814i
$800$	2.32202e8			0.453519
$801$			1.15132e9i			2.24027i
$802$	7.46157e8			1.44646
$803$	2.26585e8			0.437608
$804$	1.47840e9			2.84462
$805$			3.93135e7i			0.0753623i
$806$		−	3.57392e8i		−	0.682559i
$807$		−	6.28461e8i		−	1.19580i
$808$		−	2.24382e9i		−	4.25357i
$809$			8.97479e7i			0.169504i	0.996402	+	0.0847518i	$0.0270097\pi$
$809$			8.97479e7i			0.169504i	−0.996402	+	0.0847518i	$0.972990\pi$
$810$			6.62560e8i			1.24672i
$811$		−	6.39806e8i		−	1.19946i	−0.800202	−	0.599730i	$-0.795275\pi$
$811$		−	6.39806e8i		−	1.19946i	0.800202	−	0.599730i	$-0.204725\pi$
$812$	7.91678e7			0.147870
$813$	1.55815e9			2.89959
$814$	−1.34849e9			−2.50020
$815$			3.13698e8i			0.579480i
$816$		−	5.86515e8i		−	1.07946i
$817$			3.48244e8i			0.638582i
$818$	−1.12288e9			−2.05150
$819$	1.03678e7			0.0188728
$820$		−	5.85572e8i		−	1.06203i
$821$	5.11833e8			0.924908			0.462454	−	0.886643i	$-0.346969\pi$
$821$	5.11833e8			0.924908			0.462454	+	0.886643i	$0.346969\pi$
$822$		−	1.64546e9i		−	2.96258i
$823$			2.38989e8i			0.428725i	0.976754	+	0.214362i	$0.0687674\pi$
$823$			2.38989e8i			0.428725i	−0.976754	+	0.214362i	$0.931233\pi$
$824$	−1.32333e9	+	1.34377e9i	−2.36529	+	2.40184i
$825$	−1.19696e8			−0.213166
$826$	1.02646e8			0.182139
$827$			1.88266e8i			0.332856i	0.986054	+	0.166428i	$0.0532233\pi$
$827$			1.88266e8i			0.332856i	−0.986054	+	0.166428i	$0.946777\pi$
$828$	−2.53472e9			−4.46519
$829$			6.76369e8i			1.18719i	0.804764	+	0.593595i	$0.202292\pi$
$829$			6.76369e8i			1.18719i	−0.804764	+	0.593595i	$0.797708\pi$
$830$		−	1.22443e9i		−	2.14140i
$831$	−1.15895e9			−2.01959
$832$	−5.63907e8			−0.979123
$833$	−1.08524e8			−0.187755
$834$			5.41764e8i			0.933925i
$835$		−	2.81426e8i		−	0.483398i
$836$		−	3.42163e9i		−	5.85618i
$837$	3.69137e8			0.629523
$838$	1.76345e8			0.299662
$839$	−1.07709e8			−0.182375			−0.0911874	−	0.995834i	$-0.529066\pi$
$839$	−1.07709e8			−0.182375			−0.0911874	+	0.995834i	$0.529066\pi$
$840$	−1.82301e8			−0.307575
$841$	−6.21241e7			−0.104441
$842$	2.04750e9			3.42995
$843$	1.30993e8			0.218657
$844$		−	1.68275e9i		−	2.79894i
$845$		−	5.95758e8i		−	0.987415i
$846$		−	2.81139e9i		−	4.64313i
$847$	−1.69904e7			−0.0279611
$848$			2.12325e9i			3.48188i
$849$	−3.53226e8			−0.577205
$850$	2.57637e7			0.0419518
$851$		−	8.17119e8i		−	1.32586i
$852$	−2.39241e9			−3.86828
$853$	3.35331e8			0.540290			0.270145	−	0.962820i	$-0.412928\pi$
$853$	3.35331e8			0.540290			0.270145	+	0.962820i	$0.412928\pi$
$854$	−1.18195e8			−0.189770
$855$			1.50040e9i			2.40055i
$856$	−3.55836e8			−0.567320
$857$	−3.41471e8			−0.542515			−0.271258	−	0.962507i	$-0.587440\pi$
$857$	−3.41471e8			−0.542515			−0.271258	+	0.962507i	$0.587440\pi$
$858$	5.76580e8			0.912846
$859$			9.78921e8i			1.54443i	0.635361	+	0.772215i	$0.280851\pi$
$859$			9.78921e8i			1.54443i	−0.635361	+	0.772215i	$0.719149\pi$
$860$	6.72603e8			1.05746
$861$			2.02242e7i			0.0316857i
$862$	−9.40798e8			−1.46884
$863$			8.55414e8i			1.33090i	0.746444	+	0.665448i	$0.231760\pi$
$863$			8.55414e8i			1.33090i	−0.746444	+	0.665448i	$0.768240\pi$
$864$		−	1.15528e9i		−	1.79121i
$865$	−5.91451e8			−0.913841
$866$		−	9.77801e8i		−	1.50556i
$867$			9.53268e8i			1.46271i
$868$		−	1.41477e8i		−	0.216335i
$869$		−	5.31562e8i		−	0.810018i
$870$	−1.93061e9			−2.93182
$871$		−	1.15172e8i		−	0.174299i
$872$			1.53446e7i			0.0231422i
$873$	5.04570e8			0.758365
$874$	2.82934e9			4.23790
$875$			3.56660e7i			0.0532390i
$876$	−1.00205e9			−1.49065
$877$			4.71601e8i			0.699159i	0.936907	+	0.349580i	$0.113676\pi$
$877$			4.71601e8i			0.699159i	−0.936907	+	0.349580i	$0.886324\pi$
$878$		−	1.14539e9i		−	1.69227i
$879$	2.31004e8			0.340137
$880$	−3.32025e9			−4.87218
$881$			8.93342e8i			1.30644i	0.757168	+	0.653221i	$0.226583\pi$
$881$			8.93342e8i			1.30644i	−0.757168	+	0.653221i	$0.773417\pi$
$882$	−1.71973e9			−2.50642
$883$	3.85308e8			0.559663			0.279831	−	0.960049i	$-0.409721\pi$
$883$	3.85308e8			0.559663			0.279831	+	0.960049i	$0.409721\pi$
$884$	−9.09437e7			−0.131648
$885$	−1.83432e9			−2.64633
$886$		−	1.53218e9i		−	2.20297i
$887$	7.91501e8			1.13418			0.567088	−	0.823657i	$-0.308070\pi$
$887$	7.91501e8			1.13418			0.567088	+	0.823657i	$0.308070\pi$
$888$	3.78906e9			5.41119
$889$		−	5.39437e7i		−	0.0767778i
$890$	−2.48215e9			−3.52093
$891$		−	5.27065e8i		−	0.745129i
$892$	2.72826e9			3.84407
$893$			2.29965e9i			3.22929i
$894$		−	1.58642e9i		−	2.22026i
$895$		−	1.59608e8i		−	0.222632i
$896$	−1.43173e8			−0.199039
$897$			3.49379e8i			0.484082i
$898$			6.48182e8i			0.895092i
$899$		−	9.51963e8i		−	1.31021i
$900$	2.99176e8			0.410393
$901$			1.26950e8i			0.173564i
$902$			6.35673e8i			0.866192i
$903$	−2.32301e7			−0.0315491
$904$			3.92042e8i			0.530673i
$905$	1.04219e9			1.40605
$906$	1.41540e9			1.90325
$907$	−1.06365e9			−1.42553			−0.712763	−	0.701405i	$-0.752556\pi$
$907$	−1.06365e9			−1.42553			−0.712763	+	0.701405i	$0.752556\pi$
$908$		−	1.88807e9i		−	2.52208i
$909$		−	1.23190e9i		−	1.64015i
$910$			2.23521e7i			0.0296615i
$911$			1.24626e9i			1.64837i	0.566322	+	0.824184i	$0.308366\pi$
$911$			1.24626e9i			1.64837i	−0.566322	+	0.824184i	$0.691634\pi$
$912$			7.60243e9i			10.0223i
$913$			9.74028e8i			1.27985i
$914$		−	1.30633e9i		−	1.71086i
$915$	2.11218e9			2.75720
$916$	3.11763e9			4.05637
$917$	9.46767e6			0.0122782
$918$		−	1.28183e8i		−	0.165692i
$919$			1.09276e9i			1.40792i	0.710240	+	0.703960i	$0.248587\pi$
$919$			1.09276e9i			1.40792i	−0.710240	+	0.703960i	$0.751413\pi$
$920$		−	3.47206e9i		−	4.45886i
$921$	−4.42812e8			−0.566815
$922$	−4.00519e8			−0.511011
$923$			1.86377e8i			0.237021i
$924$	2.28245e8			0.289324
$925$			9.64454e7i			0.121859i
$926$		−	4.13450e8i		−	0.520703i
$927$	−7.26531e8	+	7.37758e8i	−0.912043	+	0.926136i
$928$	−2.97934e9			−3.72800
$929$	−2.34655e8			−0.292673			−0.146336	−	0.989235i	$-0.546748\pi$
$929$	−2.34655e8			−0.292673			−0.146336	+	0.989235i	$0.546748\pi$
$930$			3.45011e9i			4.28928i
$931$	1.40670e9			1.74321
$932$			1.18304e9i			1.46134i
$933$			5.06200e8i			0.623271i
$934$	−1.45997e9			−1.79185
$935$	−1.98520e8			−0.242867
$936$	−9.15658e8			−1.11662
$937$		−	6.40828e8i		−	0.778974i	−0.921032	−	0.389487i	$-0.872652\pi$
$937$		−	6.40828e8i		−	0.778974i	0.921032	−	0.389487i	$-0.127348\pi$
$938$		−	6.22163e7i		−	0.0753869i
$939$		−	1.56043e9i		−	1.88472i
$940$	4.44157e9			5.34753
$941$	−1.19436e9			−1.43339			−0.716697	−	0.697384i	$-0.754347\pi$
$941$	−1.19436e9			−1.43339			−0.716697	+	0.697384i	$0.754347\pi$
$942$	4.35301e9			5.20759
$943$	−3.85186e8			−0.459342
$944$	−5.25302e9			−6.24444
$945$	−2.30866e7			−0.0273568
$946$	−7.30151e8			−0.862460
$947$		−	1.59695e9i		−	1.88036i	−0.340677	−	0.940180i	$-0.610656\pi$
$947$		−	1.59695e9i		−	1.88036i	0.340677	−	0.940180i	$-0.389344\pi$
$948$			2.35077e9i			2.75922i
$949$			7.80630e7i			0.0913369i
$950$	−3.33950e8			−0.389503
$951$		−	2.68491e8i		−	0.312168i
$952$	−3.12144e7			−0.0361780
$953$	−1.35778e9			−1.56874			−0.784369	−	0.620294i	$-0.787013\pi$
$953$	−1.35778e9			−1.56874			−0.784369	+	0.620294i	$0.787013\pi$
$954$			2.01172e9i			2.31698i
$955$	−4.64669e8			−0.533499
$956$	6.20910e8			0.710649
$957$	1.53580e9			1.75226
$958$		−	3.80020e8i		−	0.432225i
$959$	−5.07439e7			−0.0575344
$960$	5.44371e9			6.15292
$961$	−8.13707e8			−0.916849
$962$		−	4.64581e8i		−	0.521838i
$963$	−1.95361e8			−0.218755
$964$			2.60990e9i			2.91335i
$965$	−5.42710e8			−0.603929
$966$			1.88735e8i			0.209373i
$967$		−	7.65338e8i		−	0.846397i	−0.906037	−	0.423198i	$-0.860907\pi$
$967$		−	7.65338e8i		−	0.846397i	0.906037	−	0.423198i	$-0.139093\pi$
$968$	1.50055e9			1.65434
$969$			4.54554e8i			0.499590i
$970$			1.08781e9i			1.19189i
$971$		−	2.71476e8i		−	0.296533i	−0.988947	−	0.148267i	$-0.952631\pi$
$971$		−	2.71476e8i		−	0.296533i	0.988947	−	0.148267i	$-0.0473694\pi$
$972$			3.47604e9i			3.78518i
$973$	1.67073e7			0.0181371
$974$		−	2.10844e9i		−	2.28183i
$975$		−	4.12375e7i		−	0.0444917i
$976$	6.04876e9			6.50605
$977$	9.62285e7			0.103186			0.0515929	−	0.998668i	$-0.483570\pi$
$977$	9.62285e7			0.103186			0.0515929	+	0.998668i	$0.483570\pi$
$978$			1.50599e9i			1.60992i
$979$	1.97454e9			2.10435
$980$		−	2.71691e9i		−	2.88667i
$981$			8.42446e6i			0.00892349i
$982$	−1.05514e9			−1.11423
$983$	6.70371e8			0.705756			0.352878	−	0.935669i	$-0.385203\pi$
$983$	6.70371e8			0.705756			0.352878	+	0.935669i	$0.385203\pi$
$984$		−	1.78615e9i		−	1.87470i
$985$	2.64310e8			0.276570
$986$	−3.30569e8			−0.344851
$987$	−1.53401e8			−0.159543
$988$	1.17882e9			1.22229
$989$		−	4.42435e8i		−	0.457363i
$990$	−3.14585e9			−3.24214
$991$	−1.27928e8			−0.131446			−0.0657228	−	0.997838i	$-0.520935\pi$
$991$	−1.27928e8			−0.131446			−0.0657228	+	0.997838i	$0.520935\pi$
$992$			5.32424e9i			5.45409i
$993$	−1.73582e9			−1.77278
$994$			1.00681e8i			0.102515i
$995$	6.57570e8			0.667533
$996$		−	4.30753e9i		−	4.35964i
$997$		−	1.08716e9i		−	1.09700i	−0.836151	−	0.548500i	$-0.815199\pi$
$997$		−	1.08716e9i		−	1.09700i	0.836151	−	0.548500i	$-0.184801\pi$
$998$		−	7.61807e8i		−	0.766396i
$999$	4.79848e8			0.481291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	103.7.b.b.102.2	yes	46
103.102	odd	2	inner	103.7.b.b.102.1	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
103.7.b.b.102.1	✓	46	103.102	odd	2	inner
103.7.b.b.102.2	yes	46	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:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	103.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-15.4764 q^{2} -40.9460i q^{3} +175.520 q^{4} +131.999i q^{5} +633.698i q^{6} +19.5425 q^{7} -1725.94 q^{8} -947.573 q^{9} +O(q^{10})\)	\(q-15.4764 q^{2} -40.9460i q^{3} +175.520 q^{4} +131.999i q^{5} +633.698i q^{6} +19.5425 q^{7} -1725.94 q^{8} -947.573 q^{9} -2042.88i q^{10} +1625.11i q^{11} -7186.85i q^{12} -559.880 q^{13} -302.448 q^{14} +5404.84 q^{15} +15478.1 q^{16} +925.444 q^{17} +14665.1 q^{18} -11995.7 q^{19} +23168.6i q^{20} -800.187i q^{21} -25150.9i q^{22} +15240.2 q^{23} +70670.3i q^{24} -1798.82 q^{25} +8664.95 q^{26} +8949.71i q^{27} +3430.11 q^{28} +23080.3 q^{29} -83647.7 q^{30} -41245.7i q^{31} -129086. q^{32} +66541.6 q^{33} -14322.6 q^{34} +2579.60i q^{35} -166318. q^{36} -53616.1i q^{37} +185650. q^{38} +22924.8i q^{39} -227823. i q^{40} -25274.4 q^{41} +12384.0i q^{42} -29030.8i q^{43} +285239. i q^{44} -125079. i q^{45} -235864. q^{46} -191707. i q^{47} -633766. i q^{48} -117267. q^{49} +27839.3 q^{50} -37893.2i q^{51} -98270.3 q^{52} +137178. i q^{53} -138510. i q^{54} -214513. q^{55} -33729.1 q^{56} +491174. i q^{57} -357201. q^{58} -339384. q^{59} +948660. q^{60} +390795. q^{61} +638337. i q^{62} -18517.9 q^{63} +1.00719e6 q^{64} -73903.8i q^{65} -1.02983e6 q^{66} +205709. i q^{67} +162434. q^{68} -624024. i q^{69} -39923.0i q^{70} -332887. i q^{71} +1.63545e6 q^{72} -139428. i q^{73} +829786. i q^{74} +73654.3i q^{75} -2.10548e6 q^{76} +31758.6i q^{77} -354795. i q^{78} -327094. q^{79} +2.04310e6i q^{80} -324327. q^{81} +391158. q^{82} +599362. q^{83} -140449. i q^{84} +122158. i q^{85} +449294. i q^{86} -945045. i q^{87} -2.80483e6i q^{88} -1.21502e6i q^{89} +1.93578e6i q^{90} -10941.5 q^{91} +2.67496e6 q^{92} -1.68885e6 q^{93} +2.96694e6i q^{94} -1.58342e6i q^{95} +5.28555e6i q^{96} -532486. q^{97} +1.81488e6 q^{98} -1.53991e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 2 q^{2} + 1278 q^{4} - 810 q^{7} - 1096 q^{8} - 17938 q^{9}+O(q^{10}) \) 46 * q - 2 * q^2 + 1278 * q^4 - 810 * q^7 - 1096 * q^8 - 17938 * q^9	\( 46 q - 2 q^{2} + 1278 q^{4} - 810 q^{7} - 1096 q^{8} - 17938 q^{9} + 2822 q^{13} - 6690 q^{14} + 4488 q^{15} + 36822 q^{16} + 478 q^{17} - 21436 q^{18} - 4650 q^{19} + 14246 q^{23} - 178082 q^{25} + 107000 q^{26} - 107086 q^{28} - 16666 q^{29} + 128416 q^{30} - 264566 q^{32} + 2280 q^{33} + 2840 q^{34} - 852564 q^{36} - 127366 q^{38} - 272394 q^{41} + 31656 q^{46} - 214532 q^{49} + 536876 q^{50} + 334070 q^{52} + 307608 q^{55} - 1074240 q^{56} + 31640 q^{58} + 183558 q^{59} + 215010 q^{60} + 118358 q^{61} + 132158 q^{63} + 1507580 q^{64} - 3093882 q^{66} - 350686 q^{68} - 1888056 q^{72} - 553676 q^{76} - 1485538 q^{79} + 3422742 q^{81} + 4547424 q^{82} + 3191126 q^{83} + 2101612 q^{91} + 2758828 q^{92} - 9030976 q^{93} - 1466602 q^{97} + 11212176 q^{98}+O(q^{100}) \) 46 * q - 2 * q^2 + 1278 * q^4 - 810 * q^7 - 1096 * q^8 - 17938 * q^9 + 2822 * q^13 - 6690 * q^14 + 4488 * q^15 + 36822 * q^16 + 478 * q^17 - 21436 * q^18 - 4650 * q^19 + 14246 * q^23 - 178082 * q^25 + 107000 * q^26 - 107086 * q^28 - 16666 * q^29 + 128416 * q^30 - 264566 * q^32 + 2280 * q^33 + 2840 * q^34 - 852564 * q^36 - 127366 * q^38 - 272394 * q^41 + 31656 * q^46 - 214532 * q^49 + 536876 * q^50 + 334070 * q^52 + 307608 * q^55 - 1074240 * q^56 + 31640 * q^58 + 183558 * q^59 + 215010 * q^60 + 118358 * q^61 + 132158 * q^63 + 1507580 * q^64 - 3093882 * q^66 - 350686 * q^68 - 1888056 * q^72 - 553676 * q^76 - 1485538 * q^79 + 3422742 * q^81 + 4547424 * q^82 + 3191126 * q^83 + 2101612 * q^91 + 2758828 * q^92 - 9030976 * q^93 - 1466602 * q^97 + 11212176 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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