LMFDB - Embedded newform 115.7.c.c.114.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,7,Mod(114,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("115.114");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	115.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:	$26.4562196163$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			114.3
Character	$\chi$	$=$	115.114
Dual form			115.7.c.c.114.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.5178i q^{2} +42.9237i q^{3} -176.801 q^{4} +(113.739 - 51.8501i) q^{5} +666.080 q^{6} -624.197 q^{7} +1750.41i q^{8} -1113.45 q^{9} +O(q^{10})$	\(q-15.5178i q^{2} +42.9237i q^{3} -176.801 q^{4} +(113.739 - 51.8501i) q^{5} +666.080 q^{6} -624.197 q^{7} +1750.41i q^{8} -1113.45 q^{9} +(-804.597 - 1764.97i) q^{10} +51.4079i q^{11} -7588.95i q^{12} +262.804i q^{13} +9686.14i q^{14} +(2225.60 + 4882.10i) q^{15} +15847.3 q^{16} +6603.46 q^{17} +17278.2i q^{18} -3565.88i q^{19} +(-20109.1 + 9167.13i) q^{20} -26792.9i q^{21} +797.735 q^{22} +(6555.26 - 10250.1i) q^{23} -75134.3 q^{24} +(10248.1 - 11794.8i) q^{25} +4078.12 q^{26} -16501.9i q^{27} +110358. q^{28} +8301.00 q^{29} +(75759.3 - 34536.3i) q^{30} -11191.6 q^{31} -133887. i q^{32} -2206.62 q^{33} -102471. i q^{34} +(-70995.6 + 32364.6i) q^{35} +196858. q^{36} +57086.6 q^{37} -55334.4 q^{38} -11280.5 q^{39} +(90759.1 + 199090. i) q^{40} -22974.6 q^{41} -415765. q^{42} +69658.4 q^{43} -9088.95i q^{44} +(-126642. + 57732.2i) q^{45} +(-159059. - 101723. i) q^{46} -113704. i q^{47} +680223. i q^{48} +271973. q^{49} +(-183028. - 159028. i) q^{50} +283445. i q^{51} -46463.9i q^{52} +101102. q^{53} -256072. q^{54} +(2665.50 + 5847.08i) q^{55} -1.09260e6i q^{56} +153061. q^{57} -128813. i q^{58} -233754. q^{59} +(-393487. - 863160. i) q^{60} +291283. i q^{61} +173668. i q^{62} +695010. q^{63} -1.06341e6 q^{64} +(13626.4 + 29891.0i) q^{65} +34241.7i q^{66} -146064. q^{67} -1.16750e6 q^{68} +(439972. + 281376. i) q^{69} +(502227. + 1.10169e6i) q^{70} +111615. q^{71} -1.94899e6i q^{72} -618501. i q^{73} -885855. i q^{74} +(506275. + 439888. i) q^{75} +630450. i q^{76} -32088.6i q^{77} +175048. i q^{78} -272812. i q^{79} +(1.80245e6 - 821681. i) q^{80} -103381. q^{81} +356514. i q^{82} +441134. q^{83} +4.73700e6i q^{84} +(751071. - 342390. i) q^{85} -1.08094e6i q^{86} +356310. i q^{87} -89985.1 q^{88} +948476. i q^{89} +(895875. + 1.96520e6i) q^{90} -164041. i q^{91} +(-1.15897e6 + 1.81222e6i) q^{92} -480384. i q^{93} -1.76443e6 q^{94} +(-184891. - 405580. i) q^{95} +5.74694e6 q^{96} +258057. q^{97} -4.22041e6i q^{98} -57239.9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	$ 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) $ 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	15.5178i		−	1.93972i	−0.243664	−	0.969860i	$-0.578349\pi$
$2$		−	15.5178i		−	1.93972i	0.243664	−	0.969860i	$-0.421651\pi$
$3$			42.9237i			1.58977i	0.606762	+	0.794884i	$0.292468\pi$
$3$			42.9237i			1.58977i	−0.606762	+	0.794884i	$0.707532\pi$
$4$	−176.801			−2.76251
$5$	113.739	−	51.8501i	0.909912	−	0.414800i
$5$	113.739	−	51.8501i	0.909912	−	0.414800i
$6$	666.080			3.08370
$7$	−624.197			−1.81982			−0.909908	−	0.414810i	$-0.863848\pi$
$7$	−624.197			−1.81982			−0.909908	+	0.414810i	$0.863848\pi$
$8$			1750.41i			3.41878i
$9$	−1113.45			−1.52736
$10$	−804.597	−	1764.97i	−0.804597	−	1.76497i
$11$			51.4079i			0.0386235i	0.999814	+	0.0193117i	$0.00614750\pi$
$11$			51.4079i			0.0386235i	−0.999814	+	0.0193117i	$0.993852\pi$
$12$		−	7588.95i		−	4.39175i
$13$			262.804i			0.119619i	0.998210	+	0.0598097i	$0.0190494\pi$
$13$			262.804i			0.119619i	−0.998210	+	0.0598097i	$0.980951\pi$
$14$			9686.14i			3.52993i
$15$	2225.60	+	4882.10i	0.659436	+	1.44655i
$16$	15847.3			3.86896
$17$	6603.46			1.34408			0.672040	−	0.740515i	$-0.265418\pi$
$17$	6603.46			1.34408			0.672040	+	0.740515i	$0.265418\pi$
$18$			17278.2i			2.96265i
$19$		−	3565.88i		−	0.519883i	−0.965624	−	0.259942i	$-0.916297\pi$
$19$		−	3565.88i		−	0.519883i	0.965624	−	0.259942i	$-0.0837033\pi$
$20$	−20109.1	+	9167.13i	−2.51364	+	1.14589i
$21$		−	26792.9i		−	2.89308i
$22$	797.735			0.0749187
$23$	6555.26	−	10250.1i	0.538774	−	0.842451i
$23$	6555.26	−	10250.1i	0.538774	−	0.842451i
$24$	−75134.3			−5.43506
$25$	10248.1	−	11794.8i	0.655881	−	0.754864i
$26$	4078.12			0.232028
$27$		−	16501.9i		−	0.838381i
$28$	110358.			5.02726
$29$	8301.00			0.340358			0.170179	−	0.985413i	$-0.445565\pi$
$29$	8301.00			0.340358			0.170179	+	0.985413i	$0.445565\pi$
$30$	75759.3	−	34536.3i	2.80590	−	1.27912i
$31$	−11191.6			−0.375669			−0.187835	−	0.982201i	$-0.560147\pi$
$31$	−11191.6			−0.375669			−0.187835	+	0.982201i	$0.560147\pi$
$32$		−	133887.i		−	4.08592i
$33$	−2206.62			−0.0614024
$34$		−	102471.i		−	2.60714i
$35$	−70995.6	+	32364.6i	−1.65587	+	0.754861i
$36$	196858.			4.21935
$37$	57086.6			1.12701			0.563506	−	0.826112i	$-0.309452\pi$
$37$	57086.6			1.12701			0.563506	+	0.826112i	$0.309452\pi$
$38$	−55334.4			−1.00843
$39$	−11280.5			−0.190167
$40$	90759.1	+	199090.i	1.41811	+	3.11079i
$41$	−22974.6			−0.333347			−0.166673	−	0.986012i	$-0.553303\pi$
$41$	−22974.6			−0.333347			−0.166673	+	0.986012i	$0.553303\pi$
$42$	−415765.			−5.61177
$43$	69658.4			0.876129			0.438065	−	0.898943i	$-0.355664\pi$
$43$	69658.4			0.876129			0.438065	+	0.898943i	$0.355664\pi$
$44$		−	9088.95i		−	0.106698i
$45$	−126642.	+	57732.2i	−1.38976	+	0.633550i
$46$	−159059.	−	101723.i	−1.63412	−	1.04507i
$47$		−	113704.i		−	1.09517i	−0.836749	−	0.547586i	$-0.815547\pi$
$47$		−	113704.i		−	1.09517i	0.836749	−	0.547586i	$-0.184453\pi$
$48$			680223.i			6.15075i
$49$	271973.			2.31173
$50$	−183028.	−	159028.i	−1.46422	−	1.27223i
$51$			283445.i			2.13677i
$52$		−	46463.9i		−	0.330450i
$53$	101102.			0.679096			0.339548	−	0.940589i	$-0.389726\pi$
$53$	101102.			0.679096			0.339548	+	0.940589i	$0.389726\pi$
$54$	−256072.			−1.62622
$55$	2665.50	+	5847.08i	0.0160210	+	0.0351440i
$56$		−	1.09260e6i		−	6.22155i
$57$	153061.			0.826493
$58$		−	128813.i		−	0.660200i
$59$	−233754.			−1.13816			−0.569081	−	0.822282i	$-0.692701\pi$
$59$	−233754.			−1.13816			−0.569081	+	0.822282i	$0.692701\pi$
$60$	−393487.	−	863160.i	−1.82170	−	3.99611i
$61$			291283.i			1.28329i	0.767001	+	0.641646i	$0.221748\pi$
$61$			291283.i			1.28329i	−0.767001	+	0.641646i	$0.778252\pi$
$62$			173668.i			0.728693i
$63$	695010.			2.77952
$64$	−1.06341e6			−4.05657
$65$	13626.4	+	29891.0i	0.0496182	+	0.108843i
$66$			34241.7i			0.119103i
$67$	−146064.			−0.485644			−0.242822	−	0.970071i	$-0.578073\pi$
$67$	−146064.			−0.485644			−0.242822	+	0.970071i	$0.578073\pi$
$68$	−1.16750e6			−3.71303
$69$	439972.	+	281376.i	1.33930	+	0.856525i
$70$	502227.	+	1.10169e6i	1.46422	+	3.21193i
$71$	111615.			0.311850			0.155925	−	0.987769i	$-0.450164\pi$
$71$	111615.			0.311850			0.155925	+	0.987769i	$0.450164\pi$
$72$		−	1.94899e6i		−	5.22171i
$73$		−	618501.i		−	1.58991i	−0.606670	−	0.794953i	$-0.707495\pi$
$73$		−	618501.i		−	1.58991i	0.606670	−	0.794953i	$-0.292505\pi$
$74$		−	885855.i		−	2.18609i
$75$	506275.	+	439888.i	1.20006	+	1.04270i
$76$			630450.i			1.43618i
$77$		−	32088.6i		−	0.0702876i
$78$			175048.i			0.368871i
$79$		−	272812.i		−	0.553327i	−0.960967	−	0.276664i	$-0.910771\pi$
$79$		−	272812.i		−	0.553327i	0.960967	−	0.276664i	$-0.0892287\pi$
$80$	1.80245e6	−	821681.i	3.52041	−	1.60485i
$81$	−103381.			−0.194530
$82$			356514.i			0.646599i
$83$	441134.			0.771500			0.385750	−	0.922603i	$-0.373943\pi$
$83$	441134.			0.771500			0.385750	+	0.922603i	$0.373943\pi$
$84$			4.73700e6i			7.99218i
$85$	751071.	−	342390.i	1.22299	−	0.557525i
$86$		−	1.08094e6i		−	1.69945i
$87$			356310.i			0.541091i
$88$	−89985.1			−0.132045
$89$			948476.i			1.34542i	0.739908	+	0.672708i	$0.234869\pi$
$89$			948476.i			1.34542i	−0.739908	+	0.672708i	$0.765131\pi$
$90$	895875.	+	1.96520e6i	1.22891	+	2.69575i
$91$		−	164041.i		−	0.217685i
$92$	−1.15897e6	+	1.81222e6i	−1.48837	+	2.32728i
$93$		−	480384.i		−	0.597227i
$94$	−1.76443e6			−2.12433
$95$	−184891.	−	405580.i	−0.215648	−	0.473048i
$96$	5.74694e6			6.49566
$97$	258057.			0.282749			0.141374	−	0.989956i	$-0.454848\pi$
$97$	258057.			0.282749			0.141374	+	0.989956i	$0.454848\pi$
$98$		−	4.22041e6i		−	4.48411i
$99$		−	57239.9i		−	0.0589920i
$100$	−1.81188e6	+	2.08532e6i	−1.81188	+	2.08532i
$101$	783518.			0.760475			0.380238	−	0.924889i	$-0.375842\pi$
$101$	783518.			0.760475			0.380238	+	0.924889i	$0.375842\pi$
$102$	4.39843e6			4.14474
$103$	590562.			0.540448			0.270224	−	0.962797i	$-0.412902\pi$
$103$	590562.			0.540448			0.270224	+	0.962797i	$0.412902\pi$
$104$	−460015.			−0.408952
$105$	−1.38921e6	−	3.04739e6i	−1.20005	−	2.63245i
$106$		−	1.56887e6i		−	1.31726i
$107$	1.57085e6			1.28228			0.641139	−	0.767425i	$-0.278462\pi$
$107$	1.57085e6			1.28228			0.641139	+	0.767425i	$0.278462\pi$
$108$			2.91754e6i			2.31604i
$109$		−	1.01724e6i		−	0.785497i	−0.919646	−	0.392749i	$-0.871524\pi$
$109$		−	1.01724e6i		−	0.785497i	0.919646	−	0.392749i	$-0.128476\pi$
$110$	90733.6	−	41362.6i	0.0681695	−	0.0310763i
$111$			2.45037e6i			1.79169i
$112$	−9.89181e6			−7.04079
$113$	−1.44776e6			−1.00337			−0.501685	−	0.865050i	$-0.667286\pi$
$113$	−1.44776e6			−1.00337			−0.501685	+	0.865050i	$0.667286\pi$
$114$		−	2.37516e6i		−	1.60317i
$115$	214121.	−	1.50573e6i	0.140788	−	0.990040i
$116$	−1.46762e6			−0.940244
$117$		−	292618.i		−	0.182702i
$118$			3.62734e6i			2.20771i
$119$	−4.12186e6			−2.44598
$120$	−8.54570e6	+	3.89572e6i	−4.94543	+	2.25447i
$121$	1.76892e6			0.998508
$122$	4.52005e6			2.48922
$123$		−	986154.i		−	0.529943i
$124$	1.97868e6			1.03779
$125$	554055.	−	1.87289e6i	0.283676	−	0.958920i
$126$		−	1.07850e7i		−	5.39148i
$127$			1.80117e6i			0.879313i	0.898166	+	0.439657i	$0.144900\pi$
$127$			1.80117e6i			0.879313i	−0.898166	+	0.439657i	$0.855100\pi$
$128$			7.93290e6i			3.78270i
$129$			2.99000e6i			1.39284i
$130$	463842.	−	211451.i	0.211125	−	0.0962453i
$131$	−353369.			−0.157186			−0.0785931	−	0.996907i	$-0.525043\pi$
$131$	−353369.			−0.157186			−0.0785931	+	0.996907i	$0.525043\pi$
$132$	390131.			0.169625
$133$			2.22581e6i			0.946092i
$134$			2.26658e6i			0.942013i
$135$	−855622.	−	1.87690e6i	−0.347761	−	0.762853i
$136$			1.15588e7i			4.59511i
$137$	2.01923e6			0.785279			0.392640	−	0.919692i	$-0.371562\pi$
$137$	2.01923e6			0.785279			0.392640	+	0.919692i	$0.371562\pi$
$138$	4.36632e6	−	6.82738e6i	1.66142	−	2.59787i
$139$	401861.			0.149634			0.0748172	−	0.997197i	$-0.476163\pi$
$139$	401861.			0.149634			0.0748172	+	0.997197i	$0.476163\pi$
$140$	1.25521e7	−	5.72209e6i	4.57437	−	2.08531i
$141$	4.88060e6			1.74107
$142$		−	1.73201e6i		−	0.604902i
$143$	−13510.2			−0.00462012
$144$	−1.76451e7			−5.90930
$145$	944148.	−	430407.i	0.309696	−	0.141181i
$146$	−9.59774e6			−3.08397
$147$			1.16741e7i			3.67511i
$148$	−1.00929e7			−3.11338
$149$		−	3.54235e6i		−	1.07086i	−0.844579	−	0.535431i	$-0.820149\pi$
$149$		−	3.54235e6i		−	1.07086i	0.844579	−	0.535431i	$-0.179851\pi$
$150$	6.82608e6	−	7.85625e6i	2.02254	−	2.32778i
$151$	−250758.			−0.0728323			−0.0364162	−	0.999337i	$-0.511594\pi$
$151$	−250758.			−0.0728323			−0.0364162	+	0.999337i	$0.511594\pi$
$152$	6.24176e6			1.77737
$153$	−7.35260e6			−2.05289
$154$	−497943.			−0.136338
$155$	−1.27292e6	+	580283.i	−0.341826	+	0.155828i
$156$	1.99440e6			0.525338
$157$	2.90452e6			0.750543			0.375271	−	0.926915i	$-0.377549\pi$
$157$	2.90452e6			0.750543			0.375271	+	0.926915i	$0.377549\pi$
$158$	−4.23343e6			−1.07330
$159$			4.33966e6i			1.07960i
$160$	−6.94207e6	−	1.52282e7i	−1.69484	−	3.71783i
$161$	−4.09177e6	+	6.39808e6i	−0.980469	+	1.53311i
$162$			1.60424e6i			0.377334i
$163$			4.40821e6i			1.01789i	0.860800	+	0.508944i	$0.169964\pi$
$163$			4.40821e6i			1.01789i	−0.860800	+	0.508944i	$0.830036\pi$
$164$	4.06192e6			0.920874
$165$	−250978.	+	114413.i	−0.0558708	+	0.0254697i
$166$		−	6.84541e6i		−	1.49649i
$167$			973879.i			0.209101i	0.994520	+	0.104550i	$0.0333404\pi$
$167$			973879.i			0.209101i	−0.994520	+	0.104550i	$0.966660\pi$
$168$	4.68986e7			9.89081
$169$	4.75774e6			0.985691
$170$	−5.31312e6	−	1.16549e7i	−1.08144	−	2.37227i
$171$			3.97041e6i			0.794049i
$172$	−1.23157e7			−2.42032
$173$		−	2.77829e6i		−	0.536587i	−0.963337	−	0.268293i	$-0.913540\pi$
$173$		−	2.77829e6i		−	0.536587i	0.963337	−	0.268293i	$-0.0864596\pi$
$174$	5.52913e6			1.04956
$175$	−6.39686e6	+	7.36225e6i	−1.19358	+	1.37371i
$176$			814674.i			0.149433i
$177$		−	1.00336e7i		−	1.80941i
$178$	1.47182e7			2.60973
$179$	−4.77836e6			−0.833143			−0.416571	−	0.909103i	$-0.636768\pi$
$179$	−4.77836e6			−0.833143			−0.416571	+	0.909103i	$0.636768\pi$
$180$	2.23905e7	−	1.02071e7i	3.83924	−	1.75019i
$181$		−	6.07866e6i		−	1.02511i	−0.858653	−	0.512557i	$-0.828698\pi$
$181$		−	6.07866e6i		−	1.02511i	0.858653	−	0.512557i	$-0.171302\pi$
$182$	−2.54555e6			−0.422248
$183$	−1.25029e7			−2.04013
$184$	1.79419e7	+	1.14744e7i	2.88015	+	1.84195i
$185$	6.49297e6	−	2.95994e6i	1.02548	−	0.467485i
$186$	−7.45447e6			−1.15845
$187$			339470.i			0.0519130i
$188$			2.01030e7i			3.02543i
$189$			1.03004e7i			1.52570i
$190$	−6.29369e6	+	2.86909e6i	−0.917581	+	0.418296i
$191$			9.65662e6i			1.38588i	0.720996	+	0.692939i	$0.243684\pi$
$191$			9.65662e6i			1.38588i	−0.720996	+	0.692939i	$0.756316\pi$
$192$		−	4.56454e7i		−	6.44901i
$193$		−	1.10865e6i		−	0.154213i	−0.997023	−	0.0771067i	$-0.975432\pi$
$193$		−	1.10865e6i		−	0.154213i	0.997023	−	0.0771067i	$-0.0245682\pi$
$194$		−	4.00447e6i		−	0.548454i
$195$	−1.28303e6	+	584895.i	−0.173035	+	0.0788813i
$196$	−4.80850e7			−6.38618
$197$			8.41897e6i			1.10119i	0.834774	+	0.550593i	$0.185598\pi$
$197$			8.41897e6i			1.10119i	−0.834774	+	0.550593i	$0.814402\pi$
$198$	−888234.			−0.114428
$199$		−	1.25222e7i		−	1.58899i	−0.607273	−	0.794493i	$-0.707737\pi$
$199$		−	1.25222e7i		−	1.58899i	0.607273	−	0.794493i	$-0.292263\pi$
$200$	2.06457e7	+	1.79385e7i	2.58071	+	2.24231i
$201$		−	6.26960e6i		−	0.772061i
$202$		−	1.21584e7i		−	1.47511i
$203$	−5.18146e6			−0.619390
$204$		−	5.01133e7i		−	5.90286i
$205$	−2.61311e6	+	1.19123e6i	−0.303316	+	0.138272i
$206$		−	9.16420e6i		−	1.04832i
$207$	−7.29892e6	+	1.14129e7i	−0.822902	+	1.28673i
$208$			4.16472e6i			0.462802i
$209$	183314.			0.0200797
$210$	−4.72887e7	+	2.15574e7i	−5.10622	+	2.32777i
$211$	7.77074e6			0.827209			0.413604	−	0.910457i	$-0.364270\pi$
$211$	7.77074e6			0.827209			0.413604	+	0.910457i	$0.364270\pi$
$212$	−1.78749e7			−1.87601
$213$			4.79092e6i			0.495769i
$214$		−	2.43760e7i		−	2.48726i
$215$	7.92288e6	−	3.61179e6i	0.797201	−	0.363419i
$216$	2.88851e7			2.86624
$217$	6.98574e6			0.683649
$218$	−1.57853e7			−1.52364
$219$	2.65484e7			2.52758
$220$	−471262.	−	1.03377e6i	−0.0442583	−	0.0970857i
$221$			1.73541e6i			0.160778i
$222$	3.80242e7			3.47537
$223$		−	1.98034e7i		−	1.78577i	−0.450286	−	0.892884i	$-0.648678\pi$
$223$		−	1.98034e7i		−	1.78577i	0.450286	−	0.892884i	$-0.351322\pi$
$224$			8.35721e7i			7.43562i
$225$	−1.14108e7	+	1.31328e7i	−1.00177	+	1.15295i
$226$			2.24660e7i			1.94626i
$227$	−1.43339e7			−1.22542			−0.612711	−	0.790307i	$-0.709921\pi$
$227$	−1.43339e7			−1.22542			−0.612711	+	0.790307i	$0.709921\pi$
$228$	−2.70613e7			−2.28320
$229$			4.10103e6i			0.341497i	0.985315	+	0.170748i	$0.0546185\pi$
$229$			4.10103e6i			0.341497i	−0.985315	+	0.170748i	$0.945381\pi$
$230$	−2.33655e7	−	3.32267e6i	−1.92040	−	0.273089i
$231$	1.37736e6			0.111741
$232$			1.45302e7i			1.16361i
$233$		−	7.92958e6i		−	0.626877i	−0.949608	−	0.313439i	$-0.898519\pi$
$233$		−	7.92958e6i		−	0.626877i	0.949608	−	0.313439i	$-0.101481\pi$
$234$	−4.54077e6			−0.354390
$235$	−5.89557e6	−	1.29326e7i	−0.454278	−	0.996511i
$236$	4.13280e7			3.14418
$237$	1.17101e7			0.879661
$238$			6.39620e7i			4.74451i
$239$	−2.29347e7			−1.67996			−0.839982	−	0.542615i	$-0.817434\pi$
$239$	−2.29347e7			−1.67996			−0.839982	+	0.542615i	$0.817434\pi$
$240$	3.52696e7	+	7.73680e7i	2.55133	+	5.59664i
$241$			1.18944e6i			0.0849748i	0.999097	+	0.0424874i	$0.0135282\pi$
$241$			1.18944e6i			0.0849748i	−0.999097	+	0.0424874i	$0.986472\pi$
$242$		−	2.74496e7i		−	1.93683i
$243$		−	1.64674e7i		−	1.14764i
$244$		−	5.14990e7i		−	3.54511i
$245$	3.09339e7	−	1.41018e7i	2.10347	−	0.958907i
$246$	−1.53029e7			−1.02794
$247$	937126.			0.0621881
$248$		−	1.95899e7i		−	1.28433i
$249$			1.89351e7i			1.22651i
$250$	−2.90631e7	−	8.59770e6i	−1.86004	−	0.550253i
$251$		−	1.98545e7i		−	1.25556i	−0.778391	−	0.627780i	$-0.783964\pi$
$251$		−	1.98545e7i		−	1.25556i	0.778391	−	0.627780i	$-0.216036\pi$
$252$	−1.22878e8			−7.67844
$253$	526935.	+	336992.i	0.0325384	+	0.0208093i
$254$	2.79501e7			1.70562
$255$	1.46966e7	+	3.22388e7i	0.886335	+	1.94428i
$256$	5.50427e7			3.28080
$257$			1.75419e7i			1.03342i	0.856159	+	0.516712i	$0.172844\pi$
$257$			1.75419e7i			1.03342i	−0.856159	+	0.516712i	$0.827156\pi$
$258$	4.63981e7			2.70172
$259$	−3.56333e7			−2.05096
$260$	−2.40916e6	−	5.28476e6i	−0.137071	−	0.300680i
$261$	−9.24272e6			−0.519850
$262$			5.48349e6i			0.304897i
$263$	2.20149e7			1.21018			0.605090	−	0.796157i	$-0.293137\pi$
$263$	2.20149e7			1.21018			0.605090	+	0.796157i	$0.293137\pi$
$264$		−	3.86249e6i		−	0.209921i
$265$	1.14992e7	−	5.24213e6i	0.617918	−	0.281689i
$266$	3.45396e7			1.83515
$267$	−4.07121e7			−2.13890
$268$	2.58242e7			1.34160
$269$	−1.66661e7			−0.856206			−0.428103	−	0.903730i	$-0.640818\pi$
$269$	−1.66661e7			−0.856206			−0.428103	+	0.903730i	$0.640818\pi$
$270$	−2.91254e7	+	1.32773e7i	−1.47972	+	0.674558i
$271$	−3.17047e7			−1.59300			−0.796500	−	0.604639i	$-0.793317\pi$
$271$	−3.17047e7			−1.59300			−0.796500	+	0.604639i	$0.793317\pi$
$272$	1.04647e8			5.20019
$273$	7.04126e6			0.346069
$274$		−	3.13339e7i		−	1.52322i
$275$	606343.	+	526835.i	0.0291555	+	0.0253324i
$276$	−7.77874e7	−	4.97475e7i	−3.69983	−	2.36616i
$277$		−	2.27880e7i		−	1.07218i	−0.844162	−	0.536089i	$-0.819901\pi$
$277$		−	2.27880e7i		−	1.07218i	0.844162	−	0.536089i	$-0.180099\pi$
$278$		−	6.23598e6i		−	0.290249i
$279$	1.24612e7			0.573782
$280$	−5.66515e7	−	1.24272e8i	−2.58070	−	5.66106i
$281$		−	7.78994e6i		−	0.351088i	−0.984472	−	0.175544i	$-0.943832\pi$
$281$		−	7.78994e6i		−	0.351088i	0.984472	−	0.175544i	$-0.0561684\pi$
$282$		−	7.57360e7i		−	3.37719i
$283$	−9.41414e6			−0.415357			−0.207679	−	0.978197i	$-0.566591\pi$
$283$	−9.41414e6			−0.415357			−0.207679	+	0.978197i	$0.566591\pi$
$284$	−1.97336e7			−0.861490
$285$	1.74090e7	−	7.93621e6i	0.752036	−	0.342830i
$286$			209648.i			0.00896173i
$287$	1.43407e7			0.606629
$288$			1.49076e8i			6.24067i
$289$	1.94681e7			0.806549
$290$	−6.67896e6	−	1.46511e7i	−0.273851	−	0.600724i
$291$			1.10768e7i			0.449505i
$292$			1.09351e8i			4.39214i
$293$	3.40721e7			1.35455			0.677277	−	0.735728i	$-0.263160\pi$
$293$	3.40721e7			1.35455			0.677277	+	0.735728i	$0.263160\pi$
$294$	1.81156e8			7.12869
$295$	−2.65870e7	+	1.21202e7i	−1.03563	+	0.472110i
$296$			9.99251e7i			3.85301i
$297$	848325.			0.0323812
$298$	−5.49694e7			−2.07717
$299$	2.69376e6	+	1.72275e6i	0.100773	+	0.0644477i
$300$	−8.95097e7	−	7.77726e7i	−3.31518	−	2.88047i
$301$	−4.34806e7			−1.59439
$302$			3.89120e6i			0.141274i
$303$			3.36315e7i			1.20898i
$304$		−	5.65094e7i		−	2.01141i
$305$	1.51030e7	+	3.31302e7i	0.532310	+	1.16768i
$306$			1.14096e8i			3.98204i
$307$		−	1.00554e7i		−	0.347523i	−0.984788	−	0.173762i	$-0.944408\pi$
$307$		−	1.00554e7i		−	0.347523i	0.984788	−	0.173762i	$-0.0555923\pi$
$308$			5.67329e6i			0.194170i
$309$			2.53491e7i			0.859187i
$310$	9.00469e6	+	1.97528e7i	0.302262	+	0.663047i
$311$	2.97127e6			0.0987782			0.0493891	−	0.998780i	$-0.484273\pi$
$311$	2.97127e6			0.0987782			0.0493891	+	0.998780i	$0.484273\pi$
$312$		−	1.97456e7i		−	0.650139i
$313$	3.56750e7			1.16341			0.581703	−	0.813401i	$-0.302387\pi$
$313$	3.56750e7			1.16341			0.581703	+	0.813401i	$0.302387\pi$
$314$		−	4.50716e7i		−	1.45584i
$315$	7.90497e7	−	3.60363e7i	2.52912	−	1.15294i
$316$			4.82333e7i			1.52857i
$317$		−	1.16809e7i		−	0.366689i	−0.983049	−	0.183344i	$-0.941308\pi$
$317$		−	1.16809e7i		−	0.366689i	0.983049	−	0.183344i	$-0.0586923\pi$
$318$	6.73418e7			2.09413
$319$			426737.i			0.0131458i
$320$	−1.20951e8	+	5.51377e7i	−3.69113	+	1.68267i
$321$			6.74265e7i			2.03852i
$322$	9.92838e7	+	6.34951e7i	2.97379	+	1.90183i
$323$		−	2.35471e7i		−	0.698764i
$324$	1.82779e7			0.537392
$325$	3.09970e6	+	2.69325e6i	0.0902964	+	0.0784561i
$326$	6.84056e7			1.97442
$327$	4.36638e7			1.24876
$328$		−	4.02150e7i		−	1.13964i
$329$			7.09738e7i			1.99301i
$330$	1.77544e6	+	3.89462e6i	0.0494041	+	0.108374i
$331$	1.66756e7			0.459831			0.229915	−	0.973211i	$-0.426155\pi$
$331$	1.66756e7			0.459831			0.229915	+	0.973211i	$0.426155\pi$
$332$	−7.79928e7			−2.13128
$333$	−6.35628e7			−1.72135
$334$	1.51124e7			0.405597
$335$	−1.66132e7	+	7.57342e6i	−0.441894	+	0.201445i
$336$		−	4.24593e8i		−	11.1932i
$337$	−3.26709e7			−0.853635			−0.426817	−	0.904338i	$-0.640365\pi$
$337$	−3.26709e7			−0.853635			−0.426817	+	0.904338i	$0.640365\pi$
$338$		−	7.38295e7i		−	1.91196i
$339$		−	6.21432e7i		−	1.59512i
$340$	−1.32790e8	+	6.05348e7i	−3.37854	+	1.54017i
$341$		−	575334.i		−	0.0145097i
$342$	6.16119e7			1.54023
$343$	−9.63284e7			−2.38711
$344$			1.21931e8i			2.99529i
$345$	6.46314e7	+	9.19086e6i	1.57393	+	0.223820i
$346$	−4.31129e7			−1.04083
$347$			2.23406e7i			0.534696i	0.963600	+	0.267348i	$0.0861473\pi$
$347$			2.23406e7i			0.534696i	−0.963600	+	0.267348i	$0.913853\pi$
$348$		−	6.29959e7i		−	1.49477i
$349$	−1.38244e7			−0.325214			−0.162607	−	0.986691i	$-0.551990\pi$
$349$	−1.38244e7			−0.325214			−0.162607	+	0.986691i	$0.551990\pi$
$350$	1.14246e8	+	9.92649e7i	2.66462	+	2.31522i
$351$	4.33675e6			0.100287
$352$	6.88286e6			0.157812
$353$			1.56162e7i			0.355018i	0.984119	+	0.177509i	$0.0568039\pi$
$353$			1.56162e7i			0.355018i	−0.984119	+	0.177509i	$0.943196\pi$
$354$	−1.55699e8			−3.50975
$355$	1.26949e7	−	5.78723e6i	0.283756	−	0.129356i
$356$		−	1.67691e8i		−	3.71673i
$357$		−	1.76926e8i		−	3.88853i
$358$			7.41494e7i			1.61606i
$359$		−	2.90236e7i		−	0.627289i	−0.949540	−	0.313645i	$-0.898450\pi$
$359$		−	2.90236e7i		−	0.627289i	0.949540	−	0.313645i	$-0.101550\pi$
$360$	−1.01055e8	−	2.21676e8i	−2.16597	−	4.75130i
$361$	3.43304e7			0.729722
$362$	−9.43272e7			−1.98843
$363$			7.59286e7i			1.58740i
$364$			2.90026e7i			0.601358i
$365$	−3.20693e7	−	7.03477e7i	−0.659494	−	1.44668i
$366$			1.94018e8i			3.95729i
$367$	4.09792e7			0.829021			0.414510	−	0.910045i	$-0.363953\pi$
$367$	4.09792e7			0.829021			0.414510	+	0.910045i	$0.363953\pi$
$368$	1.03883e8	−	1.62436e8i	2.08449	−	3.25941i
$369$	2.55809e7			0.509140
$370$	−4.59316e7	−	1.00756e8i	−0.906790	−	1.98915i
$371$	−6.31074e7			−1.23583
$372$			8.49322e7i			1.64985i
$373$	2.55407e7			0.492160			0.246080	−	0.969250i	$-0.420857\pi$
$373$	2.55407e7			0.492160			0.246080	+	0.969250i	$0.420857\pi$
$374$	5.26781e6			0.100697
$375$	8.03914e7	+	2.37821e7i	1.52446	+	0.450980i
$376$	1.99029e8			3.74415
$377$			2.18153e6i			0.0407135i
$378$	1.59839e8			2.95943
$379$			2.06854e7i			0.379967i	0.981787	+	0.189984i	$0.0608435\pi$
$379$			2.06854e7i			0.379967i	−0.981787	+	0.189984i	$0.939156\pi$
$380$	3.26889e7	+	7.17068e7i	0.595729	+	1.30680i
$381$	−7.73129e7			−1.39790
$382$	1.49849e8			2.68821
$383$	2.90102e7			0.516362			0.258181	−	0.966097i	$-0.416877\pi$
$383$	2.90102e7			0.516362			0.258181	+	0.966097i	$0.416877\pi$
$384$	−3.40509e8			−6.01361
$385$	−1.66380e6	−	3.64973e6i	−0.0291553	−	0.0639556i
$386$	−1.72037e7			−0.299131
$387$	−7.75609e7			−1.33817
$388$	−4.56247e7			−0.781097
$389$		−	9.37938e7i		−	1.59340i	−0.604374	−	0.796701i	$-0.706577\pi$
$389$		−	9.37938e7i		−	1.59340i	0.604374	−	0.796701i	$-0.293423\pi$
$390$	9.07626e6	+	1.99098e7i	0.153008	+	0.335640i
$391$	4.32874e7	−	6.76861e7i	0.724154	−	1.13232i
$392$			4.76065e8i			7.90329i
$393$		−	1.51679e7i		−	0.249889i
$394$	1.30644e8			2.13599
$395$	−1.41453e7	−	3.10294e7i	−0.229520	−	0.503479i
$396$			1.01201e7i			0.162966i
$397$		−	2.68066e7i		−	0.428421i	−0.976788	−	0.214210i	$-0.931282\pi$
$397$		−	2.68066e7i		−	0.428421i	0.976788	−	0.214210i	$-0.0687178\pi$
$398$	−1.94316e8			−3.08219
$399$	−9.55401e7			−1.50407
$400$	1.62405e8	−	1.86914e8i	2.53758	−	2.92054i
$401$		−	5.76750e7i		−	0.894446i	−0.894422	−	0.447223i	$-0.852413\pi$
$401$		−	5.76750e7i		−	0.894446i	0.894422	−	0.447223i	$-0.147587\pi$
$402$	−9.72901e7			−1.49758
$403$		−	2.94118e6i		−	0.0449373i
$404$	−1.38527e8			−2.10082
$405$	−1.17585e7	+	5.36032e6i	−0.177005	+	0.0806911i
$406$			8.04046e7i			1.20144i
$407$			2.93470e6i			0.0435291i
$408$	−4.96147e8			−7.30516
$409$	−1.56755e7			−0.229113			−0.114557	−	0.993417i	$-0.536545\pi$
$409$	−1.56755e7			−0.229113			−0.114557	+	0.993417i	$0.536545\pi$
$410$	1.84853e7	+	4.05495e7i	0.268209	+	0.588348i
$411$			8.66729e7i			1.24841i
$412$	−1.04412e8			−1.49299
$413$	1.45909e8			2.07124
$414$	1.77103e8	+	1.13263e8i	2.49589	+	1.59620i
$415$	5.01742e7	−	2.28728e7i	0.701998	−	0.320019i
$416$	3.51861e7			0.488755
$417$			1.72494e7i			0.237884i
$418$		−	2.84462e6i		−	0.0389490i
$419$			7.65092e7i			1.04009i	0.854138	+	0.520046i	$0.174085\pi$
$419$			7.65092e7i			1.04009i	−0.854138	+	0.520046i	$0.825915\pi$
$420$	2.45614e8	+	5.38782e8i	3.31516	+	7.27218i
$421$		−	1.12181e8i		−	1.50339i	−0.659510	−	0.751696i	$-0.729236\pi$
$421$		−	1.12181e8i		−	1.50339i	0.659510	−	0.751696i	$-0.270764\pi$
$422$		−	1.20584e8i		−	1.60455i
$423$			1.26603e8i			1.67272i
$424$			1.76970e8i			2.32168i
$425$	6.76732e7	−	7.78862e7i	0.881556	−	1.01460i
$426$	7.43443e7			0.961654
$427$		−	1.81818e8i		−	2.33535i
$428$	−2.77727e8			−3.54231
$429$		−	579907.i		−	0.00734491i
$430$	−5.60469e7	−	1.22945e8i	−0.704931	−	1.54635i
$431$			2.25949e7i			0.282214i	0.989994	+	0.141107i	$0.0450662\pi$
$431$			2.25949e7i			0.282214i	−0.989994	+	0.141107i	$0.954934\pi$
$432$		−	2.61509e8i		−	3.24366i
$433$	1.43540e8			1.76811			0.884056	−	0.467381i	$-0.154802\pi$
$433$	1.43540e8			1.76811			0.884056	+	0.467381i	$0.154802\pi$
$434$		−	1.08403e8i		−	1.32609i
$435$	1.84747e7	+	4.05264e7i	0.224445	+	0.492345i
$436$			1.79849e8i			2.16995i
$437$	−3.65506e7	−	2.33752e7i	−0.437976	−	0.280099i
$438$		−	4.11971e8i		−	4.90280i
$439$	8.21575e7			0.971077			0.485538	−	0.874215i	$-0.338624\pi$
$439$	8.21575e7			0.971077			0.485538	+	0.874215i	$0.338624\pi$
$440$	−1.02348e7	+	4.66573e6i	−0.120149	+	0.0547724i
$441$	−3.02827e8			−3.53085
$442$	2.69297e7			0.311864
$443$		−	9.35897e7i		−	1.07651i	−0.842783	−	0.538254i	$-0.819084\pi$
$443$		−	9.35897e7i		−	1.07651i	0.842783	−	0.538254i	$-0.180916\pi$
$444$		−	4.33227e8i		−	4.94956i
$445$	4.91786e7	+	1.07879e8i	0.558079	+	1.22421i
$446$	−3.07304e8			−3.46389
$447$	1.52051e8			1.70242
$448$	6.63775e8			7.38222
$449$	5.06404e7			0.559446			0.279723	−	0.960081i	$-0.409757\pi$
$449$	5.06404e7			0.559446			0.279723	+	0.960081i	$0.409757\pi$
$450$	2.03792e8	+	1.77069e8i	2.23640	+	1.94315i
$451$		−	1.18107e6i		−	0.0128750i
$452$	2.55965e8			2.77182
$453$		−	1.07635e7i		−	0.115786i
$454$			2.22429e8i			2.37697i
$455$	−8.50555e6	−	1.86579e7i	−0.0902959	−	0.198074i
$456$			2.67920e8i			2.82560i
$457$	−1.59646e8			−1.67266			−0.836331	−	0.548224i	$-0.815304\pi$
$457$	−1.59646e8			−1.67266			−0.836331	+	0.548224i	$0.815304\pi$
$458$	6.36388e7			0.662408
$459$		−	1.08969e8i		−	1.12685i
$460$	−3.78567e7	+	2.66214e8i	−0.388928	+	2.73500i
$461$	6.15712e7			0.628456			0.314228	−	0.949347i	$-0.398254\pi$
$461$	6.15712e7			0.628456			0.314228	+	0.949347i	$0.398254\pi$
$462$		−	2.13736e7i		−	0.216746i
$463$			1.48994e8i			1.50115i	0.660785	+	0.750576i	$0.270224\pi$
$463$			1.48994e8i			1.50115i	−0.660785	+	0.750576i	$0.729776\pi$
$464$	1.31548e8			1.31683
$465$	−2.49079e7	−	5.46384e7i	−0.247730	−	0.543424i
$466$	−1.23049e8			−1.21597
$467$	4.69749e7			0.461227			0.230614	−	0.973045i	$-0.425927\pi$
$467$	4.69749e7			0.461227			0.230614	+	0.973045i	$0.425927\pi$
$468$			5.17350e7i			0.504716i
$469$	9.11726e7			0.883783
$470$	−2.00685e8	+	9.14860e7i	−1.93295	+	0.881172i
$471$			1.24673e8i			1.19319i
$472$		−	4.09167e8i		−	3.89112i
$473$			3.58099e6i			0.0338392i
$474$		−	1.81714e8i		−	1.70630i
$475$	−4.20586e7	−	3.65436e7i	−0.392441	−	0.340982i
$476$	7.28748e8			6.75704
$477$	−1.12571e8			−1.03722
$478$			3.55895e8i			3.25866i
$479$			5.22536e7i			0.475456i	0.971332	+	0.237728i	$0.0764026\pi$
$479$			5.22536e7i			0.475456i	−0.971332	+	0.237728i	$0.923597\pi$
$480$	6.53652e8	−	2.97979e8i	5.91048	−	2.69440i
$481$			1.50026e7i			0.134812i
$482$	1.84574e7			0.164827
$483$	−2.74629e8	−	1.75634e8i	−2.43728	−	1.55872i
$484$	−3.12746e8			−2.75839
$485$	2.93512e7	−	1.33803e7i	0.257277	−	0.117284i
$486$	−2.55536e8			−2.22610
$487$			1.86381e8i			1.61367i	0.590775	+	0.806836i	$0.298822\pi$
$487$			1.86381e8i			1.61367i	−0.590775	+	0.806836i	$0.701178\pi$
$488$	−5.09866e8			−4.38729
$489$	−1.89217e8			−1.61820
$490$	−2.18828e8	−	4.80025e8i	−1.86001	−	4.08015i
$491$	−5.62410e7			−0.475126			−0.237563	−	0.971372i	$-0.576349\pi$
$491$	−5.62410e7			−0.475126			−0.237563	+	0.971372i	$0.576349\pi$
$492$			1.74353e8i			1.46397i
$493$	5.48154e7			0.457469
$494$		−	1.45421e7i		−	0.120627i
$495$	−2.96789e6	−	6.51041e6i	−0.0244699	−	0.0536775i
$496$	−1.77356e8			−1.45345
$497$	−6.96695e7			−0.567510
$498$	2.93830e8			2.37908
$499$	−1.95781e8			−1.57569			−0.787843	−	0.615876i	$-0.788802\pi$
$499$	−1.95781e8			−1.57569			−0.787843	+	0.615876i	$0.788802\pi$
$500$	−9.79574e7	+	3.31128e8i	−0.783659	+	2.64903i
$501$	−4.18025e7			−0.332422
$502$	−3.08097e8			−2.43544
$503$	2.00788e8			1.57774			0.788869	−	0.614562i	$-0.210667\pi$
$503$	2.00788e8			1.57774			0.788869	+	0.614562i	$0.210667\pi$
$504$			1.21655e9i			9.50255i
$505$	8.91166e7	−	4.06255e7i	0.691966	−	0.315445i
$506$	5.22936e6	−	8.17686e6i	0.0403642	−	0.0631153i
$507$			2.04220e8i			1.56702i
$508$		−	3.18448e8i		−	2.42911i
$509$	3.59165e7			0.272358			0.136179	−	0.990684i	$-0.456518\pi$
$509$	3.59165e7			0.272358			0.136179	+	0.990684i	$0.456518\pi$
$510$	5.00274e8	−	2.28059e8i	3.77135	−	1.71924i
$511$			3.86066e8i			2.89334i
$512$		−	3.46434e8i		−	2.58113i
$513$	−5.88436e7			−0.435860
$514$	2.72212e8			2.00455
$515$	6.71700e7	−	3.06207e7i	0.491761	−	0.224178i
$516$		−	5.28634e8i		−	3.84774i
$517$	5.84529e6			0.0422994
$518$			5.52948e8i			3.97828i
$519$	1.19255e8			0.853048
$520$	−5.23217e7	+	2.38518e7i	−0.372111	+	0.169633i
$521$			1.15913e8i			0.819631i	0.912168	+	0.409816i	$0.134407\pi$
$521$			1.15913e8i			0.819631i	−0.912168	+	0.409816i	$0.865593\pi$
$522$			1.43426e8i			1.00836i
$523$	1.13980e8			0.796750			0.398375	−	0.917223i	$-0.369574\pi$
$523$	1.13980e8			0.796750			0.398375	+	0.917223i	$0.369574\pi$
$524$	6.24758e7			0.434228
$525$	−3.16015e8	−	2.74577e8i	−2.18389	−	1.89752i
$526$		−	3.41622e8i		−	2.34741i
$527$	−7.39031e7			−0.504929
$528$	−3.49688e7			−0.237563
$529$	−6.20931e7	−	1.34384e8i	−0.419446	−	0.907780i
$530$	−8.13461e7	−	1.78442e8i	−0.546398	−	1.19859i
$531$	2.60273e8			1.73838
$532$		−	3.93525e8i		−	2.61359i
$533$		−	6.03780e6i		−	0.0398747i
$534$			6.31761e8i			4.14886i
$535$	1.78666e8	−	8.14484e7i	1.16676	−	0.531889i
$536$		−	2.55672e8i		−	1.66031i
$537$		−	2.05105e8i		−	1.32450i
$538$			2.58621e8i			1.66080i
$539$			1.39815e7i			0.0892871i
$540$	1.51275e8	+	3.31838e8i	0.960693	+	2.10739i
$541$	1.28526e8			0.811706			0.405853	−	0.913938i	$-0.366975\pi$
$541$	1.28526e8			0.811706			0.405853	+	0.913938i	$0.366975\pi$
$542$			4.91986e8i			3.08997i
$543$	2.60919e8			1.62969
$544$		−	8.84120e8i		−	5.49180i
$545$	−5.27441e7	−	1.15700e8i	−0.325825	−	0.714734i
$546$		−	1.09265e8i		−	0.671277i
$547$		−	1.48792e8i		−	0.909115i	−0.890717	−	0.454558i	$-0.849797\pi$
$547$		−	1.48792e8i		−	0.909115i	0.890717	−	0.454558i	$-0.150203\pi$
$548$	−3.57001e8			−2.16934
$549$		−	3.24328e8i		−	1.96005i
$550$	8.17530e6	−	9.40908e6i	0.0491378	−	0.0565535i
$551$		−	2.96004e7i		−	0.176947i
$552$	−4.92525e8	+	7.70134e8i	−2.92827	+	4.57877i
$553$			1.70288e8i			1.00695i
$554$	−3.53618e8			−2.07972
$555$	1.27052e8	+	2.78702e8i	0.743193	+	1.63028i
$556$	−7.10493e7			−0.413367
$557$	8.91331e7			0.515790			0.257895	−	0.966173i	$-0.416971\pi$
$557$	8.91331e7			0.515790			0.257895	+	0.966173i	$0.416971\pi$
$558$		−	1.93370e8i		−	1.11298i
$559$			1.83065e7i			0.104802i
$560$	−1.12509e9	+	5.12891e8i	−6.40651	+	2.92052i
$561$	−1.45713e7			−0.0825296
$562$	−1.20882e8			−0.681011
$563$	−3.21479e8			−1.80147			−0.900735	−	0.434369i	$-0.856971\pi$
$563$	−3.21479e8			−1.80147			−0.900735	+	0.434369i	$0.856971\pi$
$564$	−8.62895e8			−4.80973
$565$	−1.64667e8	+	7.50664e7i	−0.912978	+	0.416198i
$566$			1.46086e8i			0.805676i
$567$	6.45302e7			0.354009
$568$			1.95372e8i			1.06615i
$569$			1.40243e8i			0.761282i	0.924723	+	0.380641i	$0.124297\pi$
$569$			1.40243e8i			0.761282i	−0.924723	+	0.380641i	$0.875703\pi$
$570$	−1.23152e8	−	2.70148e8i	−0.664994	−	1.45874i
$571$		−	2.56875e8i		−	1.37979i	−0.723909	−	0.689895i	$-0.757657\pi$
$571$		−	2.56875e8i		−	1.37979i	0.723909	−	0.689895i	$-0.242343\pi$
$572$	2.38861e6			0.0127631
$573$	−4.14498e8			−2.20322
$574$		−	2.22535e8i		−	1.17669i
$575$	−5.37181e7	−	1.82362e8i	−0.282564	−	0.959248i
$576$	1.18405e9			6.19585
$577$			2.84153e8i			1.47919i	0.673051	+	0.739596i	$0.264983\pi$
$577$			2.84153e8i			1.47919i	−0.673051	+	0.739596i	$0.735017\pi$
$578$		−	3.02102e8i		−	1.56448i
$579$	4.75873e7			0.245163
$580$	−1.66926e8	+	7.60964e7i	−0.855540	+	0.390014i
$581$	−2.75354e8			−1.40399
$582$	1.71887e8			0.871914
$583$			5.19742e6i			0.0262290i
$584$	1.08263e9			5.43554
$585$	−1.51722e7	−	3.32821e7i	−0.0757848	−	0.166243i
$586$		−	5.28723e8i		−	2.62746i
$587$			1.03506e8i			0.511741i	0.966711	+	0.255871i	$0.0823621\pi$
$587$			1.03506e8i			0.511741i	−0.966711	+	0.255871i	$0.917638\pi$
$588$		−	2.06399e9i		−	10.1525i
$589$			3.99077e7i			0.195304i
$590$	1.88078e8	+	4.12571e8i	0.915761	+	2.00883i
$591$	−3.61374e8			−1.75063
$592$	9.04665e8			4.36037
$593$		−	1.88354e8i		−	0.903255i	−0.892207	−	0.451627i	$-0.850844\pi$
$593$		−	1.88354e8i		−	0.903255i	0.892207	−	0.451627i	$-0.149156\pi$
$594$		−	1.31641e7i		−	0.0628104i
$595$	−4.68816e8	+	2.13719e8i	−2.22562	+	1.01459i
$596$			6.26291e8i			2.95827i
$597$	5.37498e8			2.52612
$598$	2.67332e7	−	4.18012e7i	0.125011	−	0.195472i
$599$	2.61634e8			1.21735			0.608674	−	0.793421i	$-0.291702\pi$
$599$	2.61634e8			1.21735			0.608674	+	0.793421i	$0.291702\pi$
$600$	−7.69987e8	+	8.86191e8i	−3.56476	+	4.10273i
$601$	−3.77913e8			−1.74088			−0.870440	−	0.492275i	$-0.836166\pi$
$601$	−3.77913e8			−1.74088			−0.870440	+	0.492275i	$0.836166\pi$
$602$			6.74721e8i			3.09268i
$603$	1.62634e8			0.741754
$604$	4.43342e7			0.201200
$605$	2.01195e8	−	9.17185e7i	0.908555	−	0.414182i
$606$	5.21886e8			2.34508
$607$			1.87899e8i			0.840151i	0.907489	+	0.420076i	$0.137996\pi$
$607$			1.87899e8i			0.840151i	−0.907489	+	0.420076i	$0.862004\pi$
$608$	−4.77426e8			−2.12420
$609$		−	2.22408e8i		−	0.984686i
$610$	5.14107e8	−	2.34365e8i	2.26498	−	1.03253i
$611$	2.98819e7			0.131004
$612$	1.29994e9			5.67114
$613$	−3.35787e8			−1.45775			−0.728874	−	0.684648i	$-0.759956\pi$
$613$	−3.35787e8			−1.45775			−0.728874	+	0.684648i	$0.759956\pi$
$614$	−1.56037e8			−0.674098
$615$	−5.11322e7	−	1.12164e8i	−0.219821	−	0.482202i
$616$	5.61684e7			0.240298
$617$	−4.46839e8			−1.90237			−0.951185	−	0.308620i	$-0.900133\pi$
$617$	−4.46839e8			−1.90237			−0.951185	+	0.308620i	$0.900133\pi$
$618$	3.93362e8			1.66658
$619$		−	1.53780e8i		−	0.648376i	−0.945993	−	0.324188i	$-0.894909\pi$
$619$		−	1.53780e8i		−	0.648376i	0.945993	−	0.324188i	$-0.105091\pi$
$620$	2.25053e8	−	1.02595e8i	0.944299	−	0.430476i
$621$	−1.69146e8	−	1.08174e8i	−0.706294	−	0.451697i
$622$		−	4.61075e7i		−	0.191602i
$623$		−	5.92036e8i		−	2.44841i
$624$	−1.78765e8			−0.735748
$625$	−3.40917e7	−	2.41749e8i	−0.139640	−	0.990202i
$626$		−	5.53597e8i		−	2.25668i
$627$			7.86853e6i			0.0319220i
$628$	−5.13521e8			−2.07338
$629$	3.76969e8			1.51479
$630$	−5.59202e8	−	1.22667e9i	−2.23639	−	4.90577i
$631$			3.96449e8i			1.57797i	0.614410	+	0.788987i	$0.289394\pi$
$631$			3.96449e8i			1.57797i	−0.614410	+	0.788987i	$0.710606\pi$
$632$	4.77534e8			1.89170
$633$			3.33549e8i			1.31507i
$634$	−1.81261e8			−0.711273
$635$	9.33908e7	+	2.04863e8i	0.364739	+	0.800098i
$636$		−	7.67256e8i		−	2.98242i
$637$			7.14755e7i			0.276528i
$638$	6.62200e6			0.0254992
$639$	−1.24277e8			−0.476308
$640$	4.11321e8	+	9.02280e8i	1.56907	+	3.44193i
$641$			1.49151e8i			0.566306i	0.959075	+	0.283153i	$0.0913803\pi$
$641$			1.49151e8i			0.566306i	−0.959075	+	0.283153i	$0.908620\pi$
$642$	1.04631e9			3.95416
$643$	2.09220e8			0.786990			0.393495	−	0.919327i	$-0.371266\pi$
$643$	2.09220e8			0.786990			0.393495	+	0.919327i	$0.371266\pi$
$644$	7.23428e8	−	1.13119e9i	2.70856	−	4.23522i
$645$	1.55032e8	+	3.40080e8i	0.577751	+	1.26736i
$646$	−3.65399e8			−1.35541
$647$		−	3.50361e8i		−	1.29361i	−0.762656	−	0.646804i	$-0.776105\pi$
$647$		−	3.50361e8i		−	1.29361i	0.762656	−	0.646804i	$-0.223895\pi$
$648$		−	1.80960e8i		−	0.665055i
$649$		−	1.20168e7i		−	0.0439598i
$650$	4.17932e7	−	4.81005e7i	0.152183	−	0.175150i
$651$			2.99854e8i			1.08684i
$652$		−	7.79375e8i		−	2.81193i
$653$			1.60598e8i			0.576769i	0.957515	+	0.288384i	$0.0931181\pi$
$653$			1.60598e8i			0.576769i	−0.957515	+	0.288384i	$0.906882\pi$
$654$		−	6.77564e8i		−	2.42224i
$655$	−4.01918e7	+	1.83222e7i	−0.143026	+	0.0652009i
$656$	−3.64084e8			−1.28970
$657$			6.88667e8i			2.42836i
$658$	1.10135e9			3.86589
$659$			1.89902e8i			0.663550i	0.943359	+	0.331775i	$0.107648\pi$
$659$			1.89902e8i			0.663550i	−0.943359	+	0.331775i	$0.892352\pi$
$660$	4.43732e7	−	2.02283e7i	0.154344	−	0.0703604i
$661$			3.58411e8i			1.24101i	0.784201	+	0.620507i	$0.213073\pi$
$661$			3.58411e8i			1.24101i	−0.784201	+	0.620507i	$0.786927\pi$
$662$		−	2.58768e8i		−	0.891942i
$663$	−7.44904e7			−0.255599
$664$			7.72167e8i			2.63759i
$665$	1.15408e8	+	2.53162e8i	0.392439	+	0.860860i
$666$			9.86352e8i			3.33894i
$667$	5.44152e7	−	8.50861e7i	0.183376	−	0.286735i
$668$		−	1.72183e8i		−	0.577643i
$669$	8.50036e8			2.83896
$670$	1.17522e8	+	2.57799e8i	0.390748	+	0.857150i
$671$	−1.49742e7			−0.0495652
$672$	−3.58722e9			−11.8209
$673$			2.20532e8i			0.723479i	0.932279	+	0.361740i	$0.117817\pi$
$673$			2.20532e8i			0.723479i	−0.932279	+	0.361740i	$0.882183\pi$
$674$			5.06980e8i			1.65581i
$675$	−1.94635e8	−	1.69113e8i	−0.632864	−	0.549878i
$676$	−8.41173e8			−2.72298
$677$	3.14189e8			1.01257			0.506285	−	0.862366i	$-0.331018\pi$
$677$	3.14189e8			1.01257			0.506285	+	0.862366i	$0.331018\pi$
$678$	−9.64323e8			−3.09409
$679$	−1.61079e8			−0.514551
$680$	5.99324e8	+	1.31469e9i	1.90605	+	4.18115i
$681$		−	6.15263e8i		−	1.94814i
$682$	−8.92790e6			−0.0281447
$683$			2.83952e8i			0.891214i	0.895229	+	0.445607i	$0.147012\pi$
$683$			2.83952e8i			0.891214i	−0.895229	+	0.445607i	$0.852988\pi$
$684$		−	7.01972e8i		−	2.19357i
$685$	2.29665e8	−	1.04697e8i	0.714535	−	0.325734i
$686$			1.49480e9i			4.63032i
$687$	−1.76032e8			−0.542901
$688$	1.10389e9			3.38971
$689$			2.65699e7i			0.0812330i
$690$	1.42621e8	−	1.00293e9i	0.434148	−	3.05299i
$691$	3.86977e8			1.17287			0.586437	−	0.809995i	$-0.300530\pi$
$691$	3.86977e8			1.17287			0.586437	+	0.809995i	$0.300530\pi$
$692$			4.91204e8i			1.48233i
$693$			3.57289e7i			0.107355i
$694$	3.46676e8			1.03716
$695$	4.57073e7	−	2.08365e7i	0.136154	−	0.0620684i
$696$	−6.23690e8			−1.84987
$697$	−1.51712e8			−0.448044
$698$			2.14523e8i			0.630824i
$699$	3.40367e8			0.996589
$700$	1.13097e9	−	1.30165e9i	3.29729	−	3.79490i
$701$		−	8.24362e6i		−	0.0239312i	−0.999928	−	0.0119656i	$-0.996191\pi$
$701$		−	8.24362e6i		−	0.0239312i	0.999928	−	0.0119656i	$-0.00380885\pi$
$702$		−	6.72966e7i		−	0.194528i
$703$		−	2.03564e8i		−	0.585915i
$704$		−	5.46675e7i		−	0.156679i
$705$	5.55115e8	−	2.53060e8i	1.58422	−	0.722197i
$706$	2.42328e8			0.688635
$707$	−4.89070e8			−1.38393
$708$			1.77395e9i			4.99852i
$709$			1.22613e8i			0.344031i	0.985094	+	0.172015i	$0.0550278\pi$
$709$			1.22613e8i			0.344031i	−0.985094	+	0.172015i	$0.944972\pi$
$710$	−8.98048e7	−	1.96997e8i	−0.250914	−	0.550408i
$711$			3.03761e8i			0.845130i
$712$	−1.66023e9			−4.59968
$713$	−7.33636e7	+	1.14715e8i	−0.202401	+	0.316483i
$714$	−2.74549e9			−7.54267
$715$	−1.53663e6	+	700503.i	−0.00420390	+	0.00191643i
$716$	8.44817e8			2.30157
$717$		−	9.84444e8i		−	2.67075i
$718$	−4.50381e8			−1.21676
$719$	6.30252e8			1.69562			0.847808	−	0.530303i	$-0.177922\pi$
$719$	6.30252e8			1.69562			0.847808	+	0.530303i	$0.177922\pi$
$720$	−2.00693e9	+	9.14898e8i	−5.37694	+	2.45118i
$721$	−3.68627e8			−0.983516
$722$		−	5.32731e8i		−	1.41546i
$723$	−5.10550e7			−0.135090
$724$			1.07471e9i			2.83189i
$725$	8.50699e7	−	9.79083e7i	0.223235	−	0.256924i
$726$	1.17824e9			3.07910
$727$	3.71681e8			0.967313			0.483656	−	0.875258i	$-0.339308\pi$
$727$	3.71681e8			0.967313			0.483656	+	0.875258i	$0.339308\pi$
$728$	2.87140e8			0.744218
$729$	6.31475e8			1.62995
$730$	−1.09164e9	+	4.97644e8i	−2.80615	+	1.27923i
$731$	4.59987e8			1.17759
$732$	2.21053e9			5.63590
$733$	−7.22194e8			−1.83376			−0.916878	−	0.399167i	$-0.869299\pi$
$733$	−7.22194e8			−1.83376			−0.916878	+	0.399167i	$0.869299\pi$
$734$		−	6.35905e8i		−	1.60807i
$735$	6.05302e8	+	1.32780e9i	1.52444	+	3.34403i
$736$	−1.37236e9	−	8.77666e8i	−3.44218	−	2.20138i
$737$		−	7.50883e6i		−	0.0187573i
$738$		−	3.96959e8i		−	0.987589i
$739$	−1.93814e8			−0.480234			−0.240117	−	0.970744i	$-0.577186\pi$
$739$	−1.93814e8			−0.480234			−0.240117	+	0.970744i	$0.577186\pi$
$740$	−1.14796e9	+	5.23320e8i	−2.83291	+	1.29143i
$741$			4.02249e7i			0.0988646i
$742$			9.79285e8i			2.39716i
$743$	1.60398e8			0.391050			0.195525	−	0.980699i	$-0.437359\pi$
$743$	1.60398e8			0.391050			0.195525	+	0.980699i	$0.437359\pi$
$744$	8.40870e8			2.04179
$745$	−1.83671e8	−	4.02904e8i	−0.444194	−	0.974390i
$746$		−	3.96334e8i		−	0.954652i
$747$	−4.91179e8			−1.17836
$748$		−	6.00185e7i		−	0.143410i
$749$	−9.80517e8			−2.33351
$750$	3.69045e8	−	1.24749e9i	0.874774	−	2.95702i
$751$			7.90345e7i			0.186594i	0.995638	+	0.0932968i	$0.0297406\pi$
$751$			7.90345e7i			0.186594i	−0.995638	+	0.0932968i	$0.970259\pi$
$752$		−	1.80190e9i		−	4.23718i
$753$	8.52229e8			1.99605
$754$	3.38525e7			0.0789727
$755$	−2.85210e7	+	1.30018e7i	−0.0662711	+	0.0302109i
$756$		−	1.82112e9i		−	4.21476i
$757$	−2.41113e8			−0.555817			−0.277909	−	0.960607i	$-0.589641\pi$
$757$	−2.41113e8			−0.555817			−0.277909	+	0.960607i	$0.589641\pi$
$758$	3.20991e8			0.737030
$759$	−1.44649e7	+	2.26180e7i	−0.0330820	+	0.0517285i
$760$	7.09932e8	−	3.23636e8i	1.61725	−	0.737252i
$761$	−7.41559e8			−1.68264			−0.841321	−	0.540536i	$-0.818221\pi$
$761$	−7.41559e8			−1.68264			−0.841321	+	0.540536i	$0.818221\pi$
$762$			1.19972e9i			2.71154i
$763$			6.34959e8i			1.42946i
$764$		−	1.70730e9i		−	3.82850i
$765$	−8.36277e8	+	3.81233e8i	−1.86795	+	0.851541i
$766$		−	4.50173e8i		−	1.00160i
$767$		−	6.14315e7i		−	0.136146i
$768$			2.36264e9i			5.21571i
$769$			2.40802e8i			0.529520i	0.964314	+	0.264760i	$0.0852927\pi$
$769$			2.40802e8i			0.529520i	−0.964314	+	0.264760i	$0.914707\pi$
$770$	−5.66356e7	+	2.58184e7i	−0.124056	+	0.0565532i
$771$	−7.52965e8			−1.64290
$772$			1.96010e8i			0.426016i
$773$	4.85380e8			1.05086			0.525428	−	0.850838i	$-0.323905\pi$
$773$	4.85380e8			1.05086			0.525428	+	0.850838i	$0.323905\pi$
$774$			1.20357e9i			2.59567i
$775$	−1.14693e8	+	1.32002e8i	−0.246394	+	0.283579i
$776$			4.51707e8i			0.966656i
$777$		−	1.52951e9i		−	3.26054i
$778$	−1.45547e9			−3.09075
$779$			8.19245e7i			0.173301i
$780$	2.26842e8	−	1.03410e8i	0.478012	−	0.217911i
$781$			5.73787e6i			0.0120447i
$782$	−1.05034e9	−	6.71723e8i	−2.19638	−	1.40466i
$783$		−	1.36982e8i		−	0.285350i
$784$	4.31002e9			8.94399
$785$	3.30357e8	−	1.50600e8i	0.682928	−	0.311326i
$786$	−2.35372e8			−0.484715
$787$	3.49636e8			0.717285			0.358643	−	0.933475i	$-0.383240\pi$
$787$	3.49636e8			0.717285			0.358643	+	0.933475i	$0.383240\pi$
$788$		−	1.48848e9i		−	3.04204i
$789$			9.44962e8i			1.92390i
$790$	−4.81506e8	+	2.19503e8i	−0.976608	+	0.445205i
$791$	9.03687e8			1.82595
$792$	1.00193e8			0.201681
$793$	−7.65502e7			−0.153506
$794$	−4.15979e8			−0.831016
$795$	2.25012e8	+	4.93589e8i	0.447820	+	0.982345i
$796$			2.21393e9i			4.38959i
$797$	4.68057e8			0.924537			0.462268	−	0.886740i	$-0.347036\pi$
$797$	4.68057e8			0.924537			0.462268	+	0.886740i	$0.347036\pi$
$798$			1.48257e9i			2.91747i
$799$		−	7.50841e8i		−	1.47200i
$800$	−1.57917e9	−	1.37210e9i	−3.08431	−	2.67988i
$801$		−	1.05608e9i		−	2.05494i
$802$	−8.94986e8			−1.73497
$803$	3.17958e7			0.0614077
$804$			1.10847e9i			2.13283i
$805$	−1.33653e8	+	9.39870e8i	−0.256208	+	1.80169i
$806$	−4.56406e7			−0.0871658
$807$		−	7.15373e8i		−	1.36117i
$808$			1.37148e9i			2.59990i
$809$	2.93409e8			0.554151			0.277075	−	0.960848i	$-0.410635\pi$
$809$	2.93409e8			0.554151			0.277075	+	0.960848i	$0.410635\pi$
$810$	8.31802e7	+	1.82465e8i	0.156518	+	0.343341i
$811$	4.77199e8			0.894616			0.447308	−	0.894380i	$-0.352383\pi$
$811$	4.77199e8			0.894616			0.447308	+	0.894380i	$0.352383\pi$
$812$	9.16086e8			1.71107
$813$		−	1.36088e9i		−	2.53250i
$814$	4.55399e7			0.0844343
$815$	2.28566e8	+	5.01386e8i	0.422220	+	0.926188i
$816$			4.49183e9i			8.26709i
$817$		−	2.48393e8i		−	0.455485i
$818$			2.43248e8i			0.444415i
$819$			1.82651e8i			0.332484i
$820$	4.61999e8	−	2.10611e8i	0.837914	−	0.381979i
$821$	−3.18940e7			−0.0576340			−0.0288170	−	0.999585i	$-0.509174\pi$
$821$	−3.18940e7			−0.0576340			−0.0288170	+	0.999585i	$0.509174\pi$
$822$	1.34497e9			2.42157
$823$			1.08701e9i			1.95000i	0.222210	+	0.974999i	$0.428673\pi$
$823$			1.08701e9i			1.95000i	−0.222210	+	0.974999i	$0.571327\pi$
$824$			1.03373e9i			1.84767i
$825$	−2.26137e7	+	2.60265e7i	−0.0402726	+	0.0463504i
$826$		−	2.26418e9i		−	4.01763i
$827$	−3.06529e8			−0.541945			−0.270973	−	0.962587i	$-0.587345\pi$
$827$	−3.06529e8			−0.541945			−0.270973	+	0.962587i	$0.587345\pi$
$828$	1.29046e9	−	2.01781e9i	2.27328	−	3.55460i
$829$	−1.48088e8			−0.259930			−0.129965	−	0.991519i	$-0.541487\pi$
$829$	−1.48088e8			−0.259930			−0.129965	+	0.991519i	$0.541487\pi$
$830$	−3.54935e8	−	7.78590e8i	−0.620747	−	1.36168i
$831$	9.78145e8			1.70451
$832$		−	2.79467e8i		−	0.485245i
$833$	1.79596e9			3.10715
$834$	2.67671e8			0.461428
$835$	5.04957e7	+	1.10768e8i	0.0867351	+	0.190263i
$836$	−3.24101e7			−0.0554704
$837$			1.84682e8i			0.314954i
$838$	1.18725e9			2.01749
$839$		−	5.28793e8i		−	0.895364i	−0.894193	−	0.447682i	$-0.852250\pi$
$839$		−	5.28793e8i		−	0.895364i	0.894193	−	0.447682i	$-0.147750\pi$
$840$	5.33420e9	−	2.43170e9i	8.99977	−	4.10271i
$841$	−5.25917e8			−0.884156
$842$	−1.74079e9			−2.91616
$843$	3.34373e8			0.558148
$844$	−1.37387e9			−2.28517
$845$	5.41141e8	−	2.46689e8i	0.896893	−	0.408865i
$846$	1.96460e9			3.24462
$847$	−1.10415e9			−1.81710
$848$	1.60219e9			2.62739
$849$		−	4.04090e8i		−	0.660321i
$850$	−1.20862e9	−	1.05014e9i	−1.96803	−	1.70997i
$851$	3.74217e8	−	5.85143e8i	0.607204	−	0.949452i
$852$		−	8.47038e8i		−	1.36957i
$853$		−	5.66225e7i		−	0.0912309i	−0.998959	−	0.0456154i	$-0.985475\pi$
$853$		−	5.66225e7i		−	0.0912309i	0.998959	−	0.0456154i	$-0.0145249\pi$
$854$	−2.82140e9			−4.52993
$855$	2.05866e8	+	4.51591e8i	0.329372	+	0.722515i
$856$			2.74963e9i			4.38382i
$857$			5.34371e8i			0.848987i	0.905431	+	0.424493i	$0.139548\pi$
$857$			5.34371e8i			0.848987i	−0.905431	+	0.424493i	$0.860452\pi$
$858$	−8.99886e6			−0.0142471
$859$	−1.24433e8			−0.196316			−0.0981582	−	0.995171i	$-0.531295\pi$
$859$	−1.24433e8			−0.196316			−0.0981582	+	0.995171i	$0.531295\pi$
$860$	−1.40077e9	+	6.38568e8i	−2.20228	+	1.00395i
$861$			6.15554e8i			0.964400i
$862$	3.50623e8			0.547417
$863$			5.47222e8i			0.851395i	0.904866	+	0.425697i	$0.139971\pi$
$863$			5.47222e8i			0.851395i	−0.904866	+	0.425697i	$0.860029\pi$
$864$	−2.20939e9			−3.42556
$865$	−1.44055e8	−	3.16001e8i	−0.222576	−	0.488247i
$866$		−	2.22742e9i		−	3.42964i
$867$			8.35645e8i			1.28223i
$868$	−1.23508e9			−1.88859
$869$	1.40247e7			0.0213714
$870$	6.28878e8	−	2.86686e8i	0.955012	−	0.435360i
$871$		−	3.83861e7i		−	0.0580924i
$872$	1.78060e9			2.68544
$873$	−2.87333e8			−0.431860
$874$	−3.62731e8	+	5.67183e8i	−0.543314	+	0.849550i
$875$	−3.45840e8	+	1.16905e9i	−0.516239	+	1.74506i
$876$	−4.69377e9			−6.98248
$877$		−	1.03284e9i		−	1.53121i	−0.643310	−	0.765606i	$-0.722439\pi$
$877$		−	1.03284e9i		−	1.53121i	0.643310	−	0.765606i	$-0.277561\pi$
$878$		−	1.27490e9i		−	1.88362i
$879$			1.46250e9i			2.15343i
$880$	4.22409e7	+	9.26602e7i	0.0619847	+	0.135971i
$881$		−	3.72056e8i		−	0.544103i	−0.962283	−	0.272051i	$-0.912298\pi$
$881$		−	3.72056e8i		−	0.544103i	0.962283	−	0.272051i	$-0.0877021\pi$
$882$			4.69920e9i			6.84885i
$883$			8.87299e8i			1.28881i	0.764686	+	0.644403i	$0.222894\pi$
$883$			8.87299e8i			1.28881i	−0.764686	+	0.644403i	$0.777106\pi$
$884$		−	3.06823e8i		−	0.444151i
$885$	−5.20243e8	−	1.14121e9i	−0.750545	−	1.64641i
$886$	−1.45230e9			−2.08812
$887$		−	1.34528e9i		−	1.92770i	−0.266437	−	0.963852i	$-0.585846\pi$
$887$		−	1.34528e9i		−	1.92770i	0.266437	−	0.963852i	$-0.414154\pi$
$888$	−4.28916e9			−6.12538
$889$		−	1.12428e9i		−	1.60019i
$890$	1.67404e9	−	7.63141e8i	2.37462	−	1.08252i
$891$		−	5.31461e6i		−	0.00751343i
$892$			3.50126e9i			4.93321i
$893$	−4.05455e8			−0.569362
$894$		−	2.35949e9i		−	3.30222i
$895$	−5.43486e8	+	2.47758e8i	−0.758087	+	0.345588i
$896$		−	4.95169e9i		−	6.88382i
$897$	−7.39467e7	+	1.15626e8i	−0.102457	+	0.160206i
$898$		−	7.85826e8i		−	1.08517i
$899$	−9.29012e7			−0.127862
$900$	2.01743e9	−	2.32189e9i	2.76739	−	3.18504i
$901$	6.67621e8			0.912758
$902$	−1.83276e7			−0.0249739
$903$		−	1.86635e9i		−	2.53472i
$904$		−	2.53418e9i		−	3.43030i
$905$	−3.15179e8	−	6.91381e8i	−0.425218	−	0.932764i
$906$	−1.67025e8			−0.224593
$907$	−4.10542e8			−0.550220			−0.275110	−	0.961413i	$-0.588714\pi$
$907$	−4.10542e8			−0.550220			−0.275110	+	0.961413i	$0.588714\pi$
$908$	2.53424e9			3.38524
$909$	−8.72405e8			−1.16152
$910$	−2.89529e8	+	1.31987e8i	−0.384209	+	0.175149i
$911$			6.27667e8i			0.830184i	0.909779	+	0.415092i	$0.136251\pi$
$911$			6.27667e8i			0.830184i	−0.909779	+	0.415092i	$0.863749\pi$
$912$	2.42559e9			3.19767
$913$			2.26777e7i			0.0297980i
$914$			2.47734e9i			3.24450i
$915$	−1.42207e9	+	6.48278e8i	−1.85634	+	0.846249i
$916$		−	7.25066e8i		−	0.943389i
$917$	2.20572e8			0.286050
$918$	−1.69096e9			−2.18577
$919$		−	3.43989e8i		−	0.443199i	−0.975138	−	0.221599i	$-0.928872\pi$
$919$		−	3.43989e8i		−	0.443199i	0.975138	−	0.221599i	$-0.0711277\pi$
$920$	2.63565e9	+	3.74800e8i	3.38473	+	0.481322i
$921$	4.31615e8			0.552482
$922$		−	9.55447e8i		−	1.21903i
$923$			2.93327e7i			0.0373033i
$924$	−2.43519e8			−0.308686
$925$	5.85031e8	−	6.73322e8i	0.739186	−	0.850741i
$926$	2.31205e9			2.91181
$927$	−6.57559e8			−0.825459
$928$		−	1.11140e9i		−	1.39068i
$929$	−6.89273e8			−0.859694			−0.429847	−	0.902902i	$-0.641433\pi$
$929$	−6.89273e8			−0.859694			−0.429847	+	0.902902i	$0.641433\pi$
$930$	−8.47865e8	+	3.86515e8i	−1.05409	+	0.480527i
$931$		−	9.69822e8i		−	1.20183i
$932$			1.40196e9i			1.73176i
$933$			1.27538e8i			0.157034i
$934$		−	7.28944e8i		−	0.894651i
$935$	1.76015e7	+	3.86110e7i	0.0215335	+	0.0472363i
$936$	5.12202e8			0.624617
$937$	−4.41424e8			−0.536583			−0.268291	−	0.963338i	$-0.586459\pi$
$937$	−4.41424e8			−0.536583			−0.268291	+	0.963338i	$0.586459\pi$
$938$		−	1.41479e9i		−	1.71429i
$939$			1.53131e9i			1.84955i
$940$	1.04234e9	+	2.28649e9i	1.25495	+	2.75287i
$941$			9.30663e8i			1.11692i	0.829530	+	0.558462i	$0.188608\pi$
$941$			9.30663e8i			1.11692i	−0.829530	+	0.558462i	$0.811392\pi$
$942$	1.93464e9			2.31445
$943$	−1.50604e8	+	2.35492e8i	−0.179598	+	0.280828i
$944$	−3.70437e9			−4.40350
$945$	5.34077e8	+	1.17156e9i	0.632861	+	1.38825i
$946$	5.55689e7			0.0656385
$947$		−	1.43175e8i		−	0.168584i	−0.996441	−	0.0842922i	$-0.973137\pi$
$947$		−	1.43175e8i		−	0.168584i	0.996441	−	0.0842922i	$-0.0268629\pi$
$948$	−2.07035e9			−2.43007
$949$	1.62544e8			0.190184
$950$	−5.67075e8	+	6.52656e8i	−0.661409	+	0.761226i
$951$	5.01387e8			0.582950
$952$		−	7.21496e9i		−	8.36225i
$953$	4.33891e8			0.501305			0.250653	−	0.968077i	$-0.419355\pi$
$953$	4.33891e8			0.501305			0.250653	+	0.968077i	$0.419355\pi$
$954$			1.74685e9i			2.01192i
$955$	5.00696e8	+	1.09833e9i	0.574863	+	1.26103i
$956$	4.05488e9			4.64092
$957$	−1.83171e7			−0.0208988
$958$	8.10859e8			0.922250
$959$	−1.26040e9			−1.42906
$960$	−2.36672e9	−	5.19166e9i	−2.67505	−	5.86803i
$961$	−7.62253e8			−0.858873
$962$	2.32806e8			0.261498
$963$	−1.74905e9			−1.95850
$964$		−	2.10293e8i		−	0.234744i
$965$	−5.74835e7	−	1.26097e8i	−0.0639678	−	0.140321i
$966$	−2.72545e9	+	4.26163e9i	−3.02347	+	4.72764i
$967$		−	9.38959e8i		−	1.03841i	−0.854651	−	0.519203i	$-0.826229\pi$
$967$		−	9.38959e8i		−	1.03841i	0.854651	−	0.519203i	$-0.173771\pi$
$968$			3.09634e9i			3.41368i
$969$	1.01073e9			1.11087
$970$	−2.07632e8	−	4.55465e8i	−0.227499	−	0.499045i
$971$		−	1.00830e9i		−	1.10136i	−0.834715	−	0.550682i	$-0.814368\pi$
$971$		−	1.00830e9i		−	1.10136i	0.834715	−	0.550682i	$-0.185632\pi$
$972$			2.91144e9i			3.17036i
$973$	−2.50840e8			−0.272307
$974$	2.89222e9			3.13007
$975$	−1.15604e8	+	1.33051e8i	−0.124727	+	0.143550i
$976$			4.61603e9i			4.96500i
$977$	−9.00364e8			−0.965460			−0.482730	−	0.875769i	$-0.660355\pi$
$977$	−9.00364e8			−0.965460			−0.482730	+	0.875769i	$0.660355\pi$
$978$			2.93622e9i			3.13886i
$979$	−4.87591e7			−0.0519646
$980$	−5.46914e9	+	2.49321e9i	−5.81087	+	2.64899i
$981$			1.13264e9i			1.19974i
$982$			8.72734e8i			0.921611i
$983$	−1.15524e9			−1.21622			−0.608112	−	0.793851i	$-0.708073\pi$
$983$	−1.15524e9			−1.21622			−0.608112	+	0.793851i	$0.708073\pi$
$984$	1.72618e9			1.81176
$985$	4.36524e8	+	9.57566e8i	0.456772	+	1.00198i
$986$		−	8.50611e8i		−	0.887361i
$987$	−3.04646e9			−3.16843
$988$	−1.65685e8			−0.171795
$989$	4.56629e8	−	7.14005e8i	0.472035	−	0.738096i
$990$	−1.01027e8	+	4.60550e7i	−0.104119	+	0.0474647i
$991$	−1.58175e8			−0.162524			−0.0812618	−	0.996693i	$-0.525895\pi$
$991$	−1.58175e8			−0.162524			−0.0812618	+	0.996693i	$0.525895\pi$
$992$			1.49841e9i			1.53495i
$993$			7.15779e8i			0.731024i
$994$			1.08111e9i			1.10081i
$995$	−6.49275e8	−	1.42426e9i	−0.659112	−	1.44584i
$996$		−	3.34774e9i		−	3.38824i
$997$			1.03630e9i			1.04568i	0.852430	+	0.522841i	$0.175128\pi$
$997$			1.03630e9i			1.04568i	−0.852430	+	0.522841i	$0.824872\pi$
$998$			3.03809e9i			3.05639i
$999$		−	9.42034e8i		−	0.944866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.7.c.c.114.3	✓	68
5.4	even	2	inner	115.7.c.c.114.66	yes	68
23.22	odd	2	inner	115.7.c.c.114.65	yes	68
115.114	odd	2	inner	115.7.c.c.114.4	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.7.c.c.114.3	✓	68	1.1	even	1	trivial
115.7.c.c.114.4	yes	68	115.114	odd	2	inner
115.7.c.c.114.65	yes	68	23.22	odd	2	inner
115.7.c.c.114.66	yes	68	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-15.5178i q^{2} +42.9237i q^{3} -176.801 q^{4} +(113.739 - 51.8501i) q^{5} +666.080 q^{6} -624.197 q^{7} +1750.41i q^{8} -1113.45 q^{9} +O(q^{10})\)	\(q-15.5178i q^{2} +42.9237i q^{3} -176.801 q^{4} +(113.739 - 51.8501i) q^{5} +666.080 q^{6} -624.197 q^{7} +1750.41i q^{8} -1113.45 q^{9} +(-804.597 - 1764.97i) q^{10} +51.4079i q^{11} -7588.95i q^{12} +262.804i q^{13} +9686.14i q^{14} +(2225.60 + 4882.10i) q^{15} +15847.3 q^{16} +6603.46 q^{17} +17278.2i q^{18} -3565.88i q^{19} +(-20109.1 + 9167.13i) q^{20} -26792.9i q^{21} +797.735 q^{22} +(6555.26 - 10250.1i) q^{23} -75134.3 q^{24} +(10248.1 - 11794.8i) q^{25} +4078.12 q^{26} -16501.9i q^{27} +110358. q^{28} +8301.00 q^{29} +(75759.3 - 34536.3i) q^{30} -11191.6 q^{31} -133887. i q^{32} -2206.62 q^{33} -102471. i q^{34} +(-70995.6 + 32364.6i) q^{35} +196858. q^{36} +57086.6 q^{37} -55334.4 q^{38} -11280.5 q^{39} +(90759.1 + 199090. i) q^{40} -22974.6 q^{41} -415765. q^{42} +69658.4 q^{43} -9088.95i q^{44} +(-126642. + 57732.2i) q^{45} +(-159059. - 101723. i) q^{46} -113704. i q^{47} +680223. i q^{48} +271973. q^{49} +(-183028. - 159028. i) q^{50} +283445. i q^{51} -46463.9i q^{52} +101102. q^{53} -256072. q^{54} +(2665.50 + 5847.08i) q^{55} -1.09260e6i q^{56} +153061. q^{57} -128813. i q^{58} -233754. q^{59} +(-393487. - 863160. i) q^{60} +291283. i q^{61} +173668. i q^{62} +695010. q^{63} -1.06341e6 q^{64} +(13626.4 + 29891.0i) q^{65} +34241.7i q^{66} -146064. q^{67} -1.16750e6 q^{68} +(439972. + 281376. i) q^{69} +(502227. + 1.10169e6i) q^{70} +111615. q^{71} -1.94899e6i q^{72} -618501. i q^{73} -885855. i q^{74} +(506275. + 439888. i) q^{75} +630450. i q^{76} -32088.6i q^{77} +175048. i q^{78} -272812. i q^{79} +(1.80245e6 - 821681. i) q^{80} -103381. q^{81} +356514. i q^{82} +441134. q^{83} +4.73700e6i q^{84} +(751071. - 342390. i) q^{85} -1.08094e6i q^{86} +356310. i q^{87} -89985.1 q^{88} +948476. i q^{89} +(895875. + 1.96520e6i) q^{90} -164041. i q^{91} +(-1.15897e6 + 1.81222e6i) q^{92} -480384. i q^{93} -1.76443e6 q^{94} +(-184891. - 405580. i) q^{95} +5.74694e6 q^{96} +258057. q^{97} -4.22041e6i q^{98} -57239.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9}+O(q^{10}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9	\( 68 q - 2440 q^{4} + 352 q^{6} - 16908 q^{9} + 66968 q^{16} - 30916 q^{24} + 32588 q^{25} - 22072 q^{26} + 103360 q^{29} - 17256 q^{31} - 358168 q^{35} + 451984 q^{36} + 192432 q^{39} - 183552 q^{41} - 397956 q^{46} + 806756 q^{49} - 749960 q^{50} - 1638436 q^{54} - 1752 q^{55} - 505552 q^{59} - 4095100 q^{64} + 1354876 q^{69} + 1196604 q^{70} + 493688 q^{71} + 3178568 q^{75} + 2473820 q^{81} + 3306336 q^{85} - 3770196 q^{94} + 896144 q^{95} + 16928136 q^{96}+O(q^{100}) \) 68 * q - 2440 * q^4 + 352 * q^6 - 16908 * q^9 + 66968 * q^16 - 30916 * q^24 + 32588 * q^25 - 22072 * q^26 + 103360 * q^29 - 17256 * q^31 - 358168 * q^35 + 451984 * q^36 + 192432 * q^39 - 183552 * q^41 - 397956 * q^46 + 806756 * q^49 - 749960 * q^50 - 1638436 * q^54 - 1752 * q^55 - 505552 * q^59 - 4095100 * q^64 + 1354876 * q^69 + 1196604 * q^70 + 493688 * q^71 + 3178568 * q^75 + 2473820 * q^81 + 3306336 * q^85 - 3770196 * q^94 + 896144 * q^95 + 16928136 * q^96

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