LMFDB - Embedded newform 87.7.b.a.59.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,7,Mod(59,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.59"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	87.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$20.0147052749$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.18
Character	$\chi$	$=$	87.59
Dual form			87.7.b.a.59.39

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-7.42129i q^{2} +(-14.8480 + 22.5508i) q^{3} +8.92448 q^{4} +51.0538i q^{5} +(167.356 + 110.191i) q^{6} -600.212 q^{7} -541.194i q^{8} +(-288.074 - 669.667i) q^{9} +378.885 q^{10} -435.717i q^{11} +(-132.511 + 201.254i) q^{12} +3856.92 q^{13} +4454.35i q^{14} +(-1151.30 - 758.047i) q^{15} -3445.19 q^{16} +6036.31i q^{17} +(-4969.79 + 2137.88i) q^{18} +10692.9 q^{19} +455.629i q^{20} +(8911.95 - 13535.2i) q^{21} -3233.58 q^{22} +298.515i q^{23} +(12204.3 + 8035.64i) q^{24} +13018.5 q^{25} -28623.3i q^{26} +(19378.8 + 3446.92i) q^{27} -5356.58 q^{28} +4528.92i q^{29} +(-5625.68 + 8544.15i) q^{30} +27516.4 q^{31} -9068.67i q^{32} +(9825.76 + 6469.52i) q^{33} +44797.2 q^{34} -30643.1i q^{35} +(-2570.91 - 5976.43i) q^{36} +6064.56 q^{37} -79355.3i q^{38} +(-57267.6 + 86976.6i) q^{39} +27630.0 q^{40} -75054.1i q^{41} +(-100449. - 66138.1i) q^{42} -69367.5 q^{43} -3888.55i q^{44} +(34189.1 - 14707.3i) q^{45} +2215.37 q^{46} +28187.6i q^{47} +(51154.1 - 77691.6i) q^{48} +242606. q^{49} -96614.1i q^{50} +(-136123. - 89627.1i) q^{51} +34421.1 q^{52} -138272. i q^{53} +(25580.6 - 143816. i) q^{54} +22245.0 q^{55} +324831. i q^{56} +(-158768. + 241134. i) q^{57} +33610.4 q^{58} +330148. i q^{59} +(-10274.8 - 6765.17i) q^{60} +153145. q^{61} -204207. i q^{62} +(172906. + 401942. i) q^{63} -287793. q^{64} +196911. i q^{65} +(48012.2 - 72919.8i) q^{66} +17464.3 q^{67} +53871.0i q^{68} +(-6731.75 - 4432.35i) q^{69} -227411. q^{70} -472069. i q^{71} +(-362420. + 155904. i) q^{72} +594785. q^{73} -45006.8i q^{74} +(-193299. + 293577. i) q^{75} +95428.8 q^{76} +261523. i q^{77} +(645478. + 424999. i) q^{78} +117250. q^{79} -175890. i q^{80} +(-365467. + 385828. i) q^{81} -556998. q^{82} -233851. i q^{83} +(79534.5 - 120795. i) q^{84} -308177. q^{85} +514796. i q^{86} +(-102131. - 67245.4i) q^{87} -235807. q^{88} -1.22488e6i q^{89} +(-109147. - 253727. i) q^{90} -2.31497e6 q^{91} +2664.10i q^{92} +(-408563. + 620516. i) q^{93} +209188. q^{94} +545915. i q^{95} +(204505. + 134652. i) q^{96} -19188.6 q^{97} -1.80045e6i q^{98} +(-291785. + 125519. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 52 q^{3} - 1924 q^{4} - 160 q^{6} + 160 q^{7} - 1060 q^{9} - 3588 q^{10} - 2166 q^{12} - 1400 q^{13} - 6240 q^{15} + 56588 q^{16} - 5978 q^{18} + 25000 q^{19} + 7520 q^{21} + 20970 q^{22} + 1238 q^{24}+ \cdots + 4793544 q^{99}+O(q^{100}) $ 56 * q + 52 * q^3 - 1924 * q^4 - 160 * q^6 + 160 * q^7 - 1060 * q^9 - 3588 * q^10 - 2166 * q^12 - 1400 * q^13 - 6240 * q^15 + 56588 * q^16 - 5978 * q^18 + 25000 * q^19 + 7520 * q^21 + 20970 * q^22 + 1238 * q^24 - 213304 * q^25 + 25492 * q^27 + 7870 * q^28 + 105092 * q^30 - 78656 * q^31 + 18952 * q^33 - 96642 * q^34 - 40224 * q^36 + 52120 * q^37 - 112096 * q^39 + 343440 * q^40 - 341758 * q^42 - 286760 * q^43 + 68312 * q^45 + 255516 * q^46 + 386086 * q^48 + 1051872 * q^49 - 256656 * q^51 + 58606 * q^52 + 450124 * q^54 - 409632 * q^55 - 1141736 * q^57 + 817806 * q^60 + 309976 * q^61 + 567632 * q^63 - 2844730 * q^64 + 958426 * q^66 + 748696 * q^67 - 1323704 * q^69 - 2123748 * q^70 - 1026242 * q^72 - 333728 * q^73 - 331316 * q^75 + 2846728 * q^76 + 292446 * q^78 - 661184 * q^79 + 1614852 * q^81 + 376908 * q^82 - 1670584 * q^84 + 3342000 * q^85 - 927168 * q^88 + 835882 * q^90 + 2248016 * q^91 + 3960776 * q^93 - 1368294 * q^94 - 5811456 * q^96 - 3057296 * q^97 + 4793544 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	7.42129i		−	0.927661i	−0.885924	−	0.463831i	$-0.846475\pi$
$2$		−	7.42129i		−	0.927661i	0.885924	−	0.463831i	$-0.153525\pi$
$3$	−14.8480	+	22.5508i	−0.549926	+	0.835214i
$3$	−14.8480	+	22.5508i	−0.549926	+	0.835214i
$4$	8.92448			0.139445
$5$			51.0538i			0.408430i	0.978926	+	0.204215i	$0.0654642\pi$
$5$			51.0538i			0.408430i	−0.978926	+	0.204215i	$0.934536\pi$
$6$	167.356	+	110.191i	0.774795	+	0.510145i
$7$	−600.212			−1.74989			−0.874945	−	0.484222i	$-0.839103\pi$
$7$	−600.212			−1.74989			−0.874945	+	0.484222i	$0.839103\pi$
$8$		−	541.194i		−	1.05702i
$9$	−288.074	−	669.667i	−0.395164	−	0.918611i
$10$	378.885			0.378885
$11$		−	435.717i		−	0.327361i	−0.986513	−	0.163680i	$-0.947663\pi$
$11$		−	435.717i		−	0.327361i	0.986513	−	0.163680i	$-0.0523366\pi$
$12$	−132.511	+	201.254i	−0.0766844	+	0.116466i
$13$	3856.92			1.75554			0.877771	−	0.479081i	$-0.159030\pi$
$13$	3856.92			1.75554			0.877771	+	0.479081i	$0.159030\pi$
$14$			4454.35i			1.62330i
$15$	−1151.30	−	758.047i	−0.341127	−	0.224606i
$16$	−3445.19			−0.841110
$17$			6036.31i			1.22864i	0.789057	+	0.614320i	$0.210570\pi$
$17$			6036.31i			1.22864i	−0.789057	+	0.614320i	$0.789430\pi$
$18$	−4969.79	+	2137.88i	−0.852159	+	0.366578i
$19$	10692.9			1.55896			0.779481	−	0.626426i	$-0.215483\pi$
$19$	10692.9			1.55896			0.779481	+	0.626426i	$0.215483\pi$
$20$			455.629i			0.0569536i
$21$	8911.95	−	13535.2i	0.962309	−	1.46153i
$22$	−3233.58			−0.303680
$23$			298.515i			0.0245348i	0.999925	+	0.0122674i	$0.00390494\pi$
$23$			298.515i			0.0245348i	−0.999925	+	0.0122674i	$0.996095\pi$
$24$	12204.3	+	8035.64i	0.882836	+	0.581282i
$25$	13018.5			0.833185
$26$		−	28623.3i		−	1.62855i
$27$	19378.8	+	3446.92i	0.984547	+	0.175122i
$28$	−5356.58			−0.244014
$29$			4528.92i			0.185695i
$29$			4528.92i			0.185695i
$30$	−5625.68	+	8544.15i	−0.208359	+	0.316450i
$31$	27516.4			0.923648			0.461824	−	0.886972i	$-0.347195\pi$
$31$	27516.4			0.923648			0.461824	+	0.886972i	$0.347195\pi$
$32$		−	9068.67i		−	0.276754i
$33$	9825.76	+	6469.52i	0.273416	+	0.180024i
$34$	44797.2			1.13976
$35$		−	30643.1i		−	0.714708i
$36$	−2570.91	−	5976.43i	−0.0551036	−	0.128096i
$37$	6064.56			0.119727			0.0598637	−	0.998207i	$-0.480933\pi$
$37$	6064.56			0.119727			0.0598637	+	0.998207i	$0.480933\pi$
$38$		−	79355.3i		−	1.44619i
$39$	−57267.6	+	86976.6i	−0.965417	+	1.46625i
$40$	27630.0			0.431719
$41$		−	75054.1i		−	1.08899i	−0.838765	−	0.544493i	$-0.816722\pi$
$41$		−	75054.1i		−	1.08899i	0.838765	−	0.544493i	$-0.183278\pi$
$42$	−100449.	−	66138.1i	−1.35581	−	0.892697i
$43$	−69367.5			−0.872470			−0.436235	−	0.899833i	$-0.643688\pi$
$43$	−69367.5			−0.872470			−0.436235	+	0.899833i	$0.643688\pi$
$44$		−	3888.55i		−	0.0456488i
$45$	34189.1	−	14707.3i	0.375189	−	0.161397i
$46$	2215.37			0.0227600
$47$			28187.6i			0.271496i	0.990743	+	0.135748i	$0.0433438\pi$
$47$			28187.6i			0.271496i	−0.990743	+	0.135748i	$0.956656\pi$
$48$	51154.1	−	77691.6i	0.462548	−	0.702507i
$49$	242606.			2.06211
$50$		−	96614.1i		−	0.772913i
$51$	−136123.	−	89627.1i	−1.02618	−	0.675661i
$52$	34421.1			0.244802
$53$		−	138272.i		−	0.928767i	−0.885634	−	0.464384i	$-0.846276\pi$
$53$		−	138272.i		−	0.928767i	0.885634	−	0.464384i	$-0.153724\pi$
$54$	25580.6	−	143816.i	0.162453	−	0.913326i
$55$	22245.0			0.133704
$56$			324831.i			1.84967i
$57$	−158768.	+	241134.i	−0.857313	+	1.30207i
$58$	33610.4			0.172262
$59$			330148.i			1.60751i	0.594962	+	0.803754i	$0.297167\pi$
$59$			330148.i			1.60751i	−0.594962	+	0.803754i	$0.702833\pi$
$60$	−10274.8	−	6765.17i	−0.0475684	−	0.0313203i
$61$	153145.			0.674705			0.337352	−	0.941378i	$-0.390469\pi$
$61$	153145.			0.674705			0.337352	+	0.941378i	$0.390469\pi$
$62$		−	204207.i		−	0.856832i
$63$	172906.	+	401942.i	0.691493	+	1.60747i
$64$	−287793.			−1.09784
$65$			196911.i			0.717016i
$66$	48012.2	−	72919.8i	0.167001	−	0.253637i
$67$	17464.3			0.0580665			0.0290333	−	0.999578i	$-0.490757\pi$
$67$	17464.3			0.0580665			0.0290333	+	0.999578i	$0.490757\pi$
$68$			53871.0i			0.171328i
$69$	−6731.75	−	4432.35i	−0.0204918	−	0.0134923i
$70$	−227411.			−0.663007
$71$		−	472069.i		−	1.31896i	−0.751724	−	0.659478i	$-0.770777\pi$
$71$		−	472069.i		−	1.31896i	0.751724	−	0.659478i	$-0.229223\pi$
$72$	−362420.	+	155904.i	−0.970989	+	0.417695i
$73$	594785.			1.52894			0.764472	−	0.644657i	$-0.223000\pi$
$73$	594785.			1.52894			0.764472	+	0.644657i	$0.223000\pi$
$74$		−	45006.8i		−	0.111067i
$75$	−193299.	+	293577.i	−0.458190	+	0.695887i
$76$	95428.8			0.217390
$77$			261523.i			0.572845i
$78$	645478.	+	424999.i	1.36018	+	0.895580i
$79$	117250.			0.237811			0.118905	−	0.992906i	$-0.462062\pi$
$79$	117250.			0.237811			0.118905	+	0.992906i	$0.462062\pi$
$80$		−	175890.i		−	0.343535i
$81$	−365467.	+	385828.i	−0.687691	+	0.726003i
$82$	−556998.			−1.01021
$83$		−	233851.i		−	0.408983i	−0.978868	−	0.204492i	$-0.934446\pi$
$83$		−	233851.i		−	0.408983i	0.978868	−	0.204492i	$-0.0655541\pi$
$84$	79534.5	−	120795.i	0.134189	−	0.203803i
$85$	−308177.			−0.501814
$86$			514796.i			0.809356i
$87$	−102131.	−	67245.4i	−0.155095	−	0.102119i
$88$	−235807.			−0.346026
$89$		−	1.22488e6i		−	1.73750i	−0.495250	−	0.868751i	$-0.664923\pi$
$89$		−	1.22488e6i		−	1.73750i	0.495250	−	0.868751i	$-0.335077\pi$
$90$	−109147.	−	253727.i	−0.149722	−	0.348048i
$91$	−2.31497e6			−3.07200
$92$			2664.10i			0.00342126i
$93$	−408563.	+	620516.i	−0.507938	+	0.771443i
$94$	209188.			0.251857
$95$			545915.i			0.636728i
$96$	204505.	+	134652.i	0.231149	+	0.152194i
$97$	−19188.6			−0.0210247			−0.0105123	−	0.999945i	$-0.503346\pi$
$97$	−19188.6			−0.0210247			−0.0105123	+	0.999945i	$0.503346\pi$
$98$		−	1.80045e6i		−	1.91294i
$99$	−291785.	+	125519.i	−0.300717	+	0.129361i
$100$	116183.			0.116183
$101$			570642.i			0.553859i	0.960890	+	0.276930i	$0.0893169\pi$
$101$			570642.i			0.553859i	−0.960890	+	0.276930i	$0.910683\pi$
$102$	−665149.	+	1.01021e6i	−0.626784	+	0.951945i
$103$	−485382.			−0.444194			−0.222097	−	0.975025i	$-0.571290\pi$
$103$	−485382.			−0.444194			−0.222097	+	0.975025i	$0.571290\pi$
$104$		−	2.08734e6i		−	1.85564i
$105$	691026.	+	454989.i	0.596934	+	0.393036i
$106$	−1.02616e6			−0.861581
$107$			61780.7i			0.0504315i	0.999682	+	0.0252157i	$0.00802727\pi$
$107$			61780.7i			0.0504315i	−0.999682	+	0.0252157i	$0.991973\pi$
$108$	172946.	+	30762.0i	0.137290	+	0.0244198i
$109$	435769.			0.336493			0.168247	−	0.985745i	$-0.446189\pi$
$109$	435769.			0.336493			0.168247	+	0.985745i	$0.446189\pi$
$110$		−	165087.i		−	0.124032i
$111$	−90046.5	+	136760.i	−0.0658412	+	0.0999980i
$112$	2.06784e6			1.47185
$113$			1.34847e6i			0.934557i	0.884110	+	0.467279i	$0.154766\pi$
$113$			1.34847e6i			0.934557i	−0.884110	+	0.467279i	$0.845234\pi$
$114$	1.78952e6	+	1.17827e6i	1.20788	+	0.795296i
$115$	−15240.3			−0.0100208
$116$			40418.3i			0.0258943i
$117$	−1.11108e6	−	2.58286e6i	−0.693726	−	1.61266i
$118$	2.45012e6			1.49122
$119$		−	3.62307e6i		−	2.14999i
$120$	−410250.	+	623078.i	−0.237413	+	0.360577i
$121$	1.58171e6			0.892835
$122$		−	1.13653e6i		−	0.625897i
$123$	1.69253e6	+	1.11440e6i	0.909537	+	0.598862i
$124$	245570.			0.128798
$125$			1.46236e6i			0.748728i
$126$	2.98293e6	−	1.28318e6i	1.49119	−	0.641471i
$127$	−157123.			−0.0767059			−0.0383529	−	0.999264i	$-0.512211\pi$
$127$	−157123.			−0.0767059			−0.0383529	+	0.999264i	$0.512211\pi$
$128$			1.55540e6i			0.741673i
$129$	1.02997e6	−	1.56429e6i	0.479793	−	0.728699i
$130$	1.46133e6			0.665148
$131$			3.60670e6i			1.60434i	0.597097	+	0.802169i	$0.296321\pi$
$131$			3.60670e6i			1.60434i	−0.597097	+	0.802169i	$0.703679\pi$
$132$	87689.8	+	57737.2i	0.0381265	+	0.0251035i
$133$	−6.41802e6			−2.72801
$134$		−	129607.i		−	0.0538660i
$135$	−175978.	+	989363.i	−0.0715250	+	0.402119i
$136$	3.26681e6			1.29870
$137$			2.13936e6i			0.831998i	0.909365	+	0.415999i	$0.136568\pi$
$137$			2.13936e6i			0.831998i	−0.909365	+	0.415999i	$0.863432\pi$
$138$	−32893.8	+	49958.3i	−0.0125163	+	0.0190095i
$139$	−485864.			−0.180913			−0.0904566	−	0.995900i	$-0.528833\pi$
$139$	−485864.			−0.180913			−0.0904566	+	0.995900i	$0.528833\pi$
$140$		−	273474.i		−	0.0996626i
$141$	−635651.	−	418529.i	−0.226757	−	0.149303i
$142$	−3.50336e6			−1.22354
$143$		−	1.68053e6i		−	0.574695i
$144$	992470.	+	2.30713e6i	0.332376	+	0.772653i
$145$	−231219.			−0.0758436
$146$		−	4.41407e6i		−	1.41834i
$147$	−3.60221e6	+	5.47095e6i	−1.13401	+	1.72231i
$148$	54123.0			0.0166954
$149$		−	6.38081e6i		−	1.92893i	−0.264205	−	0.964466i	$-0.585110\pi$
$149$		−	6.38081e6i		−	1.92893i	0.264205	−	0.964466i	$-0.414890\pi$
$150$	2.17872e6	+	1.43453e6i	0.645547	+	0.425045i
$151$	4.13156e6			1.20001			0.600003	−	0.799998i	$-0.295166\pi$
$151$	4.13156e6			1.20001			0.600003	+	0.799998i	$0.295166\pi$
$152$		−	5.78694e6i		−	1.64785i
$153$	4.04232e6	−	1.73891e6i	1.12864	−	0.485514i
$154$	1.94084e6			0.531406
$155$			1.40482e6i			0.377246i
$156$	−511084.	+	776221.i	−0.134623	+	0.204462i
$157$	700607.			0.181040			0.0905202	−	0.995895i	$-0.471147\pi$
$157$	700607.			0.181040			0.0905202	+	0.995895i	$0.471147\pi$
$158$		−	870145.i		−	0.220608i
$159$	3.11814e6	+	2.05306e6i	0.775719	+	0.510753i
$160$	462990.			0.113035
$161$		−	179173.i		−	0.0429333i
$162$	2.86334e6	+	2.71224e6i	0.673485	+	0.637945i
$163$	−5.01052e6			−1.15696			−0.578482	−	0.815695i	$-0.696355\pi$
$163$	−5.01052e6			−1.15696			−0.578482	+	0.815695i	$0.696355\pi$
$164$		−	669819.i		−	0.151854i
$165$	−330294.	+	501642.i	−0.0735273	+	0.111671i
$166$	−1.73548e6			−0.379398
$167$		−	3.69070e6i		−	0.792427i	−0.918158	−	0.396214i	$-0.870324\pi$
$167$		−	3.69070e6i		−	0.792427i	0.918158	−	0.396214i	$-0.129676\pi$
$168$	−7.32519e6	−	4.82309e6i	−1.54487	−	1.01718i
$169$	1.00491e7			2.08192
$170$			2.28707e6i			0.465514i
$171$	−3.08036e6	−	7.16070e6i	−0.616045	−	1.43208i
$172$	−619069.			−0.121662
$173$			9.47429e6i			1.82982i	0.403657	+	0.914910i	$0.367739\pi$
$173$			9.47429e6i			1.82982i	−0.403657	+	0.914910i	$0.632261\pi$
$174$	−499048.	+	757941.i	−0.0947315	+	0.143876i
$175$	−7.81387e6			−1.45798
$176$			1.50113e6i			0.275346i
$177$	−7.44510e6	−	4.90204e6i	−1.34261	−	0.884009i
$178$	−9.09022e6			−1.61181
$179$		−	7.78036e6i		−	1.35657i	−0.734801	−	0.678283i	$-0.762725\pi$
$179$		−	7.78036e6i		−	1.35657i	0.734801	−	0.678283i	$-0.237275\pi$
$180$	305120.	−	131255.i	0.0523182	−	0.0225060i
$181$	4.54068e6			0.765747			0.382873	−	0.923801i	$-0.374935\pi$
$181$	4.54068e6			0.765747			0.382873	+	0.923801i	$0.374935\pi$
$182$			1.71801e7i			2.84978i
$183$	−2.27390e6	+	3.45354e6i	−0.371037	+	0.563523i
$184$	161555.			0.0259338
$185$			309619.i			0.0489004i
$186$	4.60503e6	+	3.03206e6i	0.715638	+	0.471194i
$187$	2.63012e6			0.402209
$188$			251559.i			0.0378588i
$189$	−1.16314e7	−	2.06888e6i	−1.72285	−	0.306443i
$190$	4.05139e6			0.590668
$191$			1.98531e6i			0.284923i	0.989800	+	0.142461i	$0.0455017\pi$
$191$			1.98531e6i			0.284923i	−0.989800	+	0.142461i	$0.954498\pi$
$192$	4.27315e6	−	6.48996e6i	0.603732	−	0.916934i
$193$	5.25937e6			0.731580			0.365790	−	0.930697i	$-0.380799\pi$
$193$	5.25937e6			0.731580			0.365790	+	0.930697i	$0.380799\pi$
$194$			142404.i			0.0195038i
$195$	−4.44049e6	−	2.92373e6i	−0.598862	−	0.394306i
$196$	2.16513e6			0.287552
$197$			1.26012e7i			1.64821i	0.566438	+	0.824104i	$0.308321\pi$
$197$			1.26012e7i			1.64821i	−0.566438	+	0.824104i	$0.691679\pi$
$198$	931512.	+	2.16542e6i	0.120003	+	0.278964i
$199$	−7.75969e6			−0.984658			−0.492329	−	0.870409i	$-0.663854\pi$
$199$	−7.75969e6			−0.984658			−0.492329	+	0.870409i	$0.663854\pi$
$200$		−	7.04553e6i		−	0.880692i
$201$	−259309.	+	393832.i	−0.0319323	+	0.0484979i
$202$	4.23490e6			0.513794
$203$		−	2.71832e6i		−	0.324946i
$204$	−1.21483e6	−	799876.i	−0.143095	−	0.0942176i
$205$	3.83180e6			0.444775
$206$			3.60216e6i			0.412061i
$207$	199906.	−	85994.6i	0.0225380	−	0.00969527i
$208$	−1.32878e7			−1.47660
$209$		−	4.65909e6i		−	0.510343i
$210$	3.37660e6	−	5.12830e6i	0.364605	−	0.553753i
$211$	−2.64319e6			−0.281372			−0.140686	−	0.990054i	$-0.544931\pi$
$211$	−2.64319e6			−0.281372			−0.140686	+	0.990054i	$0.544931\pi$
$212$		−	1.23401e6i		−	0.129512i
$213$	1.06455e7	+	7.00928e6i	1.10161	+	0.725328i
$214$	458492.			0.0467833
$215$		−	3.54147e6i		−	0.356343i
$216$	1.86545e6	−	1.04877e7i	0.185107	−	1.04068i
$217$	−1.65157e7			−1.61628
$218$		−	3.23396e6i		−	0.312152i
$219$	−8.83136e6	+	1.34129e7i	−0.840805	+	1.27699i
$220$	198525.			0.0186444
$221$			2.32816e7i			2.15693i
$222$	1.01494e6	+	668261.i	0.0927643	+	0.0610783i
$223$	1.23097e7			1.11002			0.555012	−	0.831842i	$-0.312714\pi$
$223$	1.23097e7			1.11002			0.555012	+	0.831842i	$0.312714\pi$
$224$			5.44313e6i			0.484289i
$225$	−3.75030e6	−	8.71807e6i	−0.329244	−	0.765372i
$226$	1.00074e7			0.866952
$227$			1.01820e7i			0.870477i	0.900315	+	0.435239i	$0.143336\pi$
$227$			1.01820e7i			0.870477i	−0.900315	+	0.435239i	$0.856664\pi$
$228$	−1.41693e6	+	2.15199e6i	−0.119548	+	0.181567i
$229$	5.56887e6			0.463725			0.231863	−	0.972749i	$-0.425518\pi$
$229$	5.56887e6			0.463725			0.231863	+	0.972749i	$0.425518\pi$
$230$			113103.i			0.00929588i
$231$	−5.89754e6	−	3.88309e6i	−0.478448	−	0.315022i
$232$	2.45102e6			0.196283
$233$			5.68445e6i			0.449387i	0.974429	+	0.224694i	$0.0721381\pi$
$233$			5.68445e6i			0.449387i	−0.974429	+	0.224694i	$0.927862\pi$
$234$	−1.91681e7	+	8.24565e6i	−1.49600	+	0.643543i
$235$	−1.43908e6			−0.110887
$236$			2.94640e6i			0.224159i
$237$	−1.74093e6	+	2.64408e6i	−0.130778	+	0.198623i
$238$	−2.68878e7			−1.99446
$239$			3.89596e6i			0.285378i	0.989768	+	0.142689i	$0.0455749\pi$
$239$			3.89596e6i			0.285378i	−0.989768	+	0.142689i	$0.954425\pi$
$240$	3.96645e6	+	2.61161e6i	0.286925	+	0.188919i
$241$	−4.55570e6			−0.325465			−0.162732	−	0.986670i	$-0.552031\pi$
$241$	−4.55570e6			−0.325465			−0.162732	+	0.986670i	$0.552031\pi$
$242$		−	1.17383e7i		−	0.828248i
$243$	−3.27426e6	−	1.39703e7i	−0.228189	−	0.973617i
$244$	1.36674e6			0.0940843
$245$			1.23859e7i			0.842231i
$246$	8.27030e6	−	1.25607e7i	0.555541	−	0.843742i
$247$	4.12418e7			2.73682
$248$		−	1.48917e7i		−	0.976313i
$249$	5.27353e6	+	3.47222e6i	0.341589	+	0.224910i
$250$	1.08526e7			0.694566
$251$		−	1.78387e7i		−	1.12808i	−0.825746	−	0.564042i	$-0.809246\pi$
$251$		−	1.78387e7i		−	1.12808i	0.825746	−	0.564042i	$-0.190754\pi$
$252$	1.54309e6	+	3.58713e6i	0.0964253	+	0.224153i
$253$	130068.			0.00803174
$254$			1.16606e6i			0.0711571i
$255$	4.57581e6	−	6.94962e6i	0.275961	−	0.419122i
$256$	−6.87568e6			−0.409823
$257$			1.39928e7i			0.824337i	0.911108	+	0.412169i	$0.135229\pi$
$257$			1.39928e7i			0.824337i	−0.911108	+	0.412169i	$0.864771\pi$
$258$	−1.16090e7	−	7.64368e6i	−0.675985	−	0.445086i
$259$	−3.64002e6			−0.209510
$260$			1.75733e6i			0.0999844i
$261$	3.03287e6	−	1.30467e6i	0.170582	−	0.0733800i
$262$	2.67663e7			1.48828
$263$		−	2.76544e7i		−	1.52019i	−0.649813	−	0.760094i	$-0.725153\pi$
$263$		−	2.76544e7i		−	1.52019i	0.649813	−	0.760094i	$-0.274847\pi$
$264$	3.50127e6	−	5.31764e6i	0.190289	−	0.289006i
$265$	7.05932e6			0.379337
$266$			4.76300e7i			2.53067i
$267$	2.76221e7	+	1.81871e7i	1.45118	+	0.955496i
$268$	155859.			0.00809709
$269$		−	2.85759e6i		−	0.146806i	−0.997302	−	0.0734028i	$-0.976614\pi$
$269$		−	2.85759e6i		−	0.146806i	0.997302	−	0.0734028i	$-0.0233859\pi$
$270$	7.34235e6	+	1.30599e6i	0.373030	+	0.0663509i
$271$	−2.52219e7			−1.26727			−0.633636	−	0.773631i	$-0.718438\pi$
$271$	−2.52219e7			−1.26727			−0.633636	+	0.773631i	$0.718438\pi$
$272$		−	2.07962e7i		−	1.03342i
$273$	3.43727e7	−	5.22044e7i	1.68937	−	2.56578i
$274$	1.58768e7			0.771812
$275$		−	5.67239e6i		−	0.272752i
$276$	−60077.4	−	39556.5i	−0.00285748	−	0.00188144i
$277$	2.74140e7			1.28983			0.644915	−	0.764254i	$-0.276893\pi$
$277$	2.74140e7			1.28983			0.644915	+	0.764254i	$0.276893\pi$
$278$			3.60574e6i			0.167826i
$279$	−7.92676e6	−	1.84268e7i	−0.364992	−	0.848473i
$280$	−1.65839e7			−0.755460
$281$		−	3.36267e7i		−	1.51553i	−0.652527	−	0.757766i	$-0.726291\pi$
$281$		−	3.36267e7i		−	1.51553i	0.652527	−	0.757766i	$-0.273709\pi$
$282$	−3.10602e6	+	4.71735e6i	−0.138502	+	0.210354i
$283$	−2.49158e7			−1.09930			−0.549649	−	0.835396i	$-0.685239\pi$
$283$	−2.49158e7			−1.09930			−0.549649	+	0.835396i	$0.685239\pi$
$284$		−	4.21297e6i		−	0.183922i
$285$	−1.23108e7	−	8.10573e6i	−0.531804	−	0.350153i
$286$	−1.24717e7			−0.533122
$287$			4.50484e7i			1.90561i
$288$	−6.07299e6	+	2.61245e6i	−0.254229	+	0.109363i
$289$	−1.22995e7			−0.509558
$290$			1.71594e6i			0.0703572i
$291$	284913.	−	432719.i	0.0115620	−	0.0175601i
$292$	5.30815e6			0.213204
$293$			1.44908e7i			0.576088i	0.957617	+	0.288044i	$0.0930049\pi$
$293$			1.44908e7i			0.576088i	−0.957617	+	0.288044i	$0.906995\pi$
$294$	4.06015e7	+	2.67330e7i	1.59772	+	1.05198i
$295$	−1.68553e7			−0.656555
$296$		−	3.28210e6i		−	0.126554i
$297$	1.50188e6	−	8.44369e6i	0.0573279	−	0.322302i
$298$	−4.73538e7			−1.78940
$299$			1.15135e6i			0.0430719i
$300$	−1.72509e6	+	2.62003e6i	−0.0638923	+	0.0970380i
$301$	4.16352e7			1.52673
$302$		−	3.06615e7i		−	1.11320i
$303$	−1.28684e7	−	8.47288e6i	−0.462591	−	0.304581i
$304$	−3.68391e7			−1.31126
$305$			7.81864e6i			0.275570i
$306$	−1.29049e7	−	2.99992e7i	−0.450393	−	1.04700i
$307$	−1.52676e7			−0.527663			−0.263831	−	0.964569i	$-0.584986\pi$
$307$	−1.52676e7			−0.527663			−0.263831	+	0.964569i	$0.584986\pi$
$308$			2.33396e6i			0.0798804i
$309$	7.20695e6	−	1.09457e7i	0.244273	−	0.370997i
$310$	1.04255e7			0.349956
$311$			1.72886e7i			0.574749i	0.957818	+	0.287374i	$0.0927824\pi$
$311$			1.72886e7i			0.574749i	−0.957818	+	0.287374i	$0.907218\pi$
$312$	4.70712e7	+	3.09928e7i	1.54986	+	1.02046i
$313$	5.01302e7			1.63481			0.817404	−	0.576065i	$-0.195412\pi$
$313$	5.01302e7			1.63481			0.817404	+	0.576065i	$0.195412\pi$
$314$		−	5.19941e6i		−	0.167944i
$315$	−2.05207e7	+	8.82750e6i	−0.656539	+	0.282427i
$316$	1.04639e6			0.0331615
$317$		−	4.65885e7i		−	1.46252i	−0.682100	−	0.731259i	$-0.738933\pi$
$317$		−	4.65885e7i		−	1.46252i	0.682100	−	0.731259i	$-0.261067\pi$
$318$	1.52364e7	−	2.31406e7i	0.473806	−	0.719604i
$319$	1.97333e6			0.0607894
$320$		−	1.46929e7i		−	0.448393i
$321$	−1.39320e6	−	917319.i	−0.0421210	−	0.0277336i
$322$	−1.32969e6			−0.0398275
$323$			6.45458e7i			1.91541i
$324$	−3.26161e6	+	3.44331e6i	−0.0958952	+	0.101238i
$325$	5.02114e7			1.46269
$326$			3.71845e7i			1.07327i
$327$	−6.47029e6	+	9.82692e6i	−0.185046	+	0.281044i
$328$	−4.06188e7			−1.15108
$329$		−	1.69185e7i		−	0.475089i
$330$	3.72283e6	+	2.45121e6i	0.103593	+	0.0682084i
$331$	5.88714e6			0.162338			0.0811690	−	0.996700i	$-0.474135\pi$
$331$	5.88714e6			0.162338			0.0811690	+	0.996700i	$0.474135\pi$
$332$		−	2.08700e6i		−	0.0570307i
$333$	−1.74704e6	−	4.06123e6i	−0.0473119	−	0.109983i
$334$	−2.73898e7			−0.735104
$335$			891617.i			0.0237161i
$336$	−3.07033e7	+	4.66315e7i	−0.809408	+	1.22931i
$337$	−7.18547e7			−1.87744			−0.938719	−	0.344683i	$-0.887986\pi$
$337$	−7.18547e7			−1.87744			−0.938719	+	0.344683i	$0.887986\pi$
$338$		−	7.45769e7i		−	1.93132i
$339$	−3.04090e7	−	2.00221e7i	−0.780555	−	0.513937i
$340$	−2.75032e6			−0.0699755
$341$		−	1.19894e7i		−	0.302366i
$342$	−5.31416e7	+	2.28602e7i	−1.32848	+	0.571481i
$343$	−7.50006e7			−1.85858
$344$			3.75412e7i			0.922217i
$345$	226289.	−	343681.i	0.00551068	−	0.00836949i
$346$	7.03115e7			1.69745
$347$		−	6.63417e6i		−	0.158781i	−0.996844	−	0.0793905i	$-0.974703\pi$
$347$		−	6.63417e6i		−	0.158781i	0.996844	−	0.0793905i	$-0.0252974\pi$
$348$	−911464.	−	600131.i	−0.0216273	−	0.0142399i
$349$	4.76717e7			1.12146			0.560731	−	0.827998i	$-0.310520\pi$
$349$	4.76717e7			1.12146			0.560731	+	0.827998i	$0.310520\pi$
$350$			5.79890e7i			1.35251i
$351$	7.47427e7	+	1.32945e7i	1.72841	+	0.307433i
$352$	−3.95137e6			−0.0905983
$353$		−	1.03416e7i		−	0.235106i	−0.993067	−	0.117553i	$-0.962495\pi$
$353$		−	1.03416e7i		−	0.235106i	0.993067	−	0.117553i	$-0.0375050\pi$
$354$	−3.63794e7	+	5.52522e7i	−0.820061	+	1.24549i
$355$	2.41009e7			0.538702
$356$		−	1.09315e7i		−	0.242286i
$357$	8.17030e7	+	5.37953e7i	1.79570	+	1.18233i
$358$	−5.77403e7			−1.25843
$359$		−	1.98603e7i		−	0.429242i	−0.976697	−	0.214621i	$-0.931148\pi$
$359$		−	1.98603e7i		−	0.429242i	0.976697	−	0.214621i	$-0.0688517\pi$
$360$	−7.95949e6	−	1.85029e7i	−0.170600	−	0.396581i
$361$	6.72928e7			1.43036
$362$		−	3.36977e7i		−	0.710354i
$363$	−2.34852e7	+	3.56688e7i	−0.490993	+	0.745708i
$364$	−2.06599e7			−0.428376
$365$			3.03660e7i			0.624467i
$366$	2.56297e7	+	1.68753e7i	0.522758	+	0.344197i
$367$	4.00332e7			0.809882			0.404941	−	0.914343i	$-0.367292\pi$
$367$	4.00332e7			0.809882			0.404941	+	0.914343i	$0.367292\pi$
$368$		−	1.02844e6i		−	0.0206365i
$369$	−5.02613e7	+	2.16211e7i	−1.00036	+	0.430328i
$370$	2.29777e6			0.0453629
$371$			8.29926e7i			1.62524i
$372$	−3.64621e6	+	5.53778e6i	−0.0708294	+	0.107574i
$373$	−6.24657e7			−1.20369			−0.601846	−	0.798613i	$-0.705568\pi$
$373$	−6.24657e7			−1.20369			−0.601846	+	0.798613i	$0.705568\pi$
$374$		−	1.95189e7i		−	0.373113i
$375$	−3.29773e7	−	2.17131e7i	−0.625348	−	0.411745i
$376$	1.52549e7			0.286977
$377$			1.74677e7i			0.325996i
$378$	−1.53538e7	+	8.63201e7i	−0.284276	+	1.59822i
$379$	−1.87608e7			−0.344615			−0.172307	−	0.985043i	$-0.555122\pi$
$379$	−1.87608e7			−0.344615			−0.172307	+	0.985043i	$0.555122\pi$
$380$			4.87201e6i			0.0887886i
$381$	2.33296e6	−	3.54325e6i	0.0421825	−	0.0640658i
$382$	1.47335e7			0.264312
$383$			9.88027e6i			0.175862i	0.996127	+	0.0879311i	$0.0280255\pi$
$383$			9.88027e6i			0.175862i	−0.996127	+	0.0879311i	$0.971974\pi$
$384$	−3.50755e7	−	2.30946e7i	−0.619455	−	0.407865i
$385$	−1.33517e7			−0.233967
$386$		−	3.90313e7i		−	0.678658i
$387$	1.99830e7	+	4.64531e7i	0.344768	+	0.801460i
$388$	−171249.			−0.00293179
$389$		−	8.99360e7i		−	1.52786i	−0.645297	−	0.763932i	$-0.723266\pi$
$389$		−	8.99360e7i		−	1.52786i	0.645297	−	0.763932i	$-0.276734\pi$
$390$	−2.16978e7	+	3.29541e7i	−0.365782	+	0.555541i
$391$	−1.80193e6			−0.0301445
$392$		−	1.31297e8i		−	2.17969i
$393$	−8.13338e7	−	5.35522e7i	−1.33996	−	0.882266i
$394$	9.35169e7			1.52898
$395$			5.98605e6i			0.0971291i
$396$	−2.60403e6	+	1.12019e6i	−0.0419335	+	0.0180388i
$397$	−1.52610e7			−0.243900			−0.121950	−	0.992536i	$-0.538915\pi$
$397$	−1.52610e7			−0.243900			−0.121950	+	0.992536i	$0.538915\pi$
$398$			5.75869e7i			0.913429i
$399$	9.52948e7	−	1.44731e8i	1.50020	−	2.27847i
$400$	−4.48512e7			−0.700800
$401$			5.10080e7i			0.791052i	0.918455	+	0.395526i	$0.129438\pi$
$401$			5.10080e7i			0.791052i	−0.918455	+	0.395526i	$0.870562\pi$
$402$	2.92274e6	+	1.92441e6i	0.0449896	+	0.0296223i
$403$	1.06129e8			1.62150
$404$			5.09268e6i			0.0772329i
$405$	−1.96980e7	−	1.86585e7i	−0.296522	−	0.280874i
$406$	−2.01734e7			−0.301440
$407$		−	2.64243e6i		−	0.0391941i
$408$	−4.85056e7	+	7.36692e7i	−0.714186	+	1.08469i
$409$	1.59688e6			0.0233400			0.0116700	−	0.999932i	$-0.496285\pi$
$409$	1.59688e6			0.0233400			0.0116700	+	0.999932i	$0.496285\pi$
$410$		−	2.84369e7i		−	0.412601i
$411$	−4.82442e7	−	3.17652e7i	−0.694896	−	0.457537i
$412$	−4.33179e6			−0.0619406
$413$		−	1.98159e8i		−	2.81296i
$414$	−638191.	−	1.48356e6i	−0.00899393	−	0.0209076i
$415$	1.19390e7			0.167041
$416$		−	3.49772e7i		−	0.485853i
$417$	7.21410e6	−	1.09566e7i	0.0994888	−	0.151101i
$418$	−3.45764e7			−0.473425
$419$		−	4.87381e7i		−	0.662562i	−0.943532	−	0.331281i	$-0.892519\pi$
$419$		−	4.87381e7i		−	0.662562i	0.943532	−	0.331281i	$-0.107481\pi$
$420$	6.16705e6	+	4.06054e6i	0.0832395	+	0.0548070i
$421$	−1.13094e8			−1.51564			−0.757818	−	0.652466i	$-0.773734\pi$
$421$	−1.13094e8			−1.51564			−0.757818	+	0.652466i	$0.773734\pi$
$422$			1.96159e7i			0.261018i
$423$	1.88763e7	−	8.12011e6i	0.249399	−	0.107285i
$424$	−7.48320e7			−0.981725
$425$			7.85838e7i			1.02368i
$426$	5.20179e7	−	7.90035e7i	0.672858	−	1.02192i
$427$	−9.19196e7			−1.18066
$428$			551361.i			0.00703242i
$429$	3.78972e7	+	2.49525e7i	0.479993	+	0.316040i
$430$	−2.62823e7			−0.330566
$431$			9.44033e7i			1.17911i	0.807727	+	0.589556i	$0.200697\pi$
$431$			9.44033e7i			1.17911i	−0.807727	+	0.589556i	$0.799303\pi$
$432$	−6.67637e7	−	1.18753e7i	−0.828112	−	0.147296i
$433$	−1.72744e7			−0.212784			−0.106392	−	0.994324i	$-0.533930\pi$
$433$	−1.72744e7			−0.212784			−0.106392	+	0.994324i	$0.533930\pi$
$434$			1.22568e8i			1.49936i
$435$	3.43313e6	−	5.21416e6i	0.0417084	−	0.0633456i
$436$	3.88901e6			0.0469223
$437$			3.19200e6i			0.0382489i
$438$	9.95407e7	+	6.55401e7i	1.18462	+	0.779982i
$439$	−3.72266e7			−0.440008			−0.220004	−	0.975499i	$-0.570607\pi$
$439$	−3.72266e7			−0.440008			−0.220004	+	0.975499i	$0.570607\pi$
$440$		−	1.20389e7i		−	0.141328i
$441$	−6.98885e7	−	1.62465e8i	−0.814873	−	1.89428i
$442$	1.72779e8			2.00090
$443$			4.93266e7i			0.567375i	0.958917	+	0.283687i	$0.0915578\pi$
$443$			4.93266e7i			0.567375i	−0.958917	+	0.283687i	$0.908442\pi$
$444$	−803618.	+	1.22052e6i	−0.00918123	+	0.0139442i
$445$	6.25350e7			0.709648
$446$		−	9.13538e7i		−	1.02973i
$447$	1.43892e8	+	9.47422e7i	1.61107	+	1.06077i
$448$	1.72737e8			1.92111
$449$		−	8.88290e7i		−	0.981331i	−0.871348	−	0.490666i	$-0.836754\pi$
$449$		−	8.88290e7i		−	0.981331i	0.871348	−	0.490666i	$-0.163246\pi$
$450$	−6.46993e7	+	2.78320e7i	−0.710006	+	0.305427i
$451$	−3.27023e7			−0.356492
$452$			1.20344e7i			0.130319i
$453$	−6.13454e7	+	9.31699e7i	−0.659914	+	1.00226i
$454$	7.55639e7			0.807508
$455$		−	1.18188e8i		−	1.25470i
$456$	1.30500e8	+	8.59245e7i	1.37631	+	0.906196i
$457$	−8.47439e6			−0.0887891			−0.0443946	−	0.999014i	$-0.514136\pi$
$457$	−8.47439e6			−0.0887891			−0.0443946	+	0.999014i	$0.514136\pi$
$458$		−	4.13282e7i		−	0.430180i
$459$	−2.08067e7	+	1.16977e8i	−0.215161	+	1.20965i
$460$	−136012.			−0.00139735
$461$		−	4.03149e7i		−	0.411494i	−0.978605	−	0.205747i	$-0.934038\pi$
$461$		−	4.03149e7i		−	0.411494i	0.978605	−	0.205747i	$-0.0659623\pi$
$462$	−2.88175e7	+	4.37673e7i	−0.292234	+	0.443838i
$463$	1.34370e8			1.35382			0.676909	−	0.736067i	$-0.263319\pi$
$463$	1.34370e8			1.35382			0.676909	+	0.736067i	$0.263319\pi$
$464$		−	1.56030e7i		−	0.156190i
$465$	−3.16797e7	−	2.08587e7i	−0.315081	−	0.207457i
$466$	4.21859e7			0.416879
$467$		−	6.30542e7i		−	0.619104i	−0.950883	−	0.309552i	$-0.899821\pi$
$467$		−	6.30542e7i		−	0.619104i	0.950883	−	0.309552i	$-0.100179\pi$
$468$	−9.91582e6	−	2.30507e7i	−0.0967367	−	0.224877i
$469$	−1.04823e7			−0.101610
$470$			1.06798e7i			0.102866i
$471$	−1.04026e7	+	1.57992e7i	−0.0995588	+	0.151207i
$472$	1.78674e8			1.69917
$473$			3.02246e7i			0.285612i
$474$	1.96224e7	+	1.29199e7i	0.184254	+	0.121318i
$475$	1.39206e8			1.29890
$476$		−	3.23340e7i		−	0.299805i
$477$	−9.25963e7	+	3.98326e7i	−0.853176	+	0.367015i
$478$	2.89130e7			0.264734
$479$		−	4.53517e7i		−	0.412655i	−0.978483	−	0.206328i	$-0.933849\pi$
$479$		−	4.53517e7i		−	0.412655i	0.978483	−	0.206328i	$-0.0661512\pi$
$480$	−6.87447e6	+	1.04408e7i	−0.0621607	+	0.0944081i
$481$	2.33905e7			0.210187
$482$			3.38092e7i			0.301921i
$483$	4.04048e6	+	2.66035e6i	0.0358584	+	0.0236101i
$484$	1.41160e7			0.124501
$485$		−	979654.i		−	0.00858712i
$486$	−1.03678e8	+	2.42992e7i	−0.903186	+	0.211682i
$487$	−4.28077e7			−0.370626			−0.185313	−	0.982680i	$-0.559330\pi$
$487$	−4.28077e7			−0.370626			−0.185313	+	0.982680i	$0.559330\pi$
$488$		−	8.28812e7i		−	0.713176i
$489$	7.43962e7	−	1.12991e8i	0.636244	−	0.966312i
$490$	9.19197e7			0.781304
$491$		−	1.83655e6i		−	0.0155152i	−0.999970	−	0.00775761i	$-0.997531\pi$
$491$		−	1.83655e6i		−	0.0155152i	0.999970	−	0.00775761i	$-0.00246935\pi$
$492$	1.51049e7	+	9.94546e6i	0.126830	+	0.0835083i
$493$	−2.73380e7			−0.228153
$494$		−	3.06067e8i		−	2.53884i
$495$	−6.40822e6	−	1.48968e7i	−0.0528350	−	0.122822i
$496$	−9.47991e7			−0.776889
$497$			2.83342e8i			2.30803i
$498$	2.57684e7	−	3.91364e7i	0.208641	−	0.316878i
$499$	2.44733e7			0.196965			0.0984827	−	0.995139i	$-0.468601\pi$
$499$	2.44733e7			0.196965			0.0984827	+	0.995139i	$0.468601\pi$
$500$			1.30508e7i			0.104406i
$501$	8.32281e7	+	5.47995e7i	0.661846	+	0.435776i
$502$	−1.32386e8			−1.04648
$503$			5.59779e7i			0.439858i	0.975516	+	0.219929i	$0.0705826\pi$
$503$			5.59779e7i			0.439858i	−0.975516	+	0.219929i	$0.929417\pi$
$504$	2.17529e8	−	9.35755e7i	1.69912	−	0.730921i
$505$	−2.91334e7			−0.226213
$506$		−	965274.i		−	0.00745073i
$507$	−1.49208e8	+	2.26614e8i	−1.14490	+	1.73885i
$508$	−1.40224e6			−0.0106963
$509$			2.08152e8i			1.57844i	0.614113	+	0.789218i	$0.289514\pi$
$509$			2.08152e8i			1.57844i	−0.614113	+	0.789218i	$0.710486\pi$
$510$	−5.15751e7	−	3.39584e7i	−0.388803	−	0.255998i
$511$	−3.56997e8			−2.67548
$512$			1.50572e8i			1.12185i
$513$	2.07216e8	+	3.68576e7i	1.53487	+	0.273008i
$514$	1.03845e8			0.764706
$515$		−	2.47806e7i		−	0.181422i
$516$	9.19193e6	−	1.39605e7i	0.0669048	−	0.101613i
$517$	1.22818e7			0.0888772
$518$			2.70136e7i			0.194354i
$519$	−2.13653e8	−	1.40674e8i	−1.52829	−	1.00627i
$520$	1.06567e8			0.757900
$521$			1.64264e8i			1.16153i	0.814072	+	0.580764i	$0.197246\pi$
$521$			1.64264e8i			1.16153i	−0.814072	+	0.580764i	$0.802754\pi$
$522$	−9.68231e6	−	2.25078e7i	−0.0680718	−	0.158242i
$523$	−2.05811e8			−1.43868			−0.719338	−	0.694660i	$-0.755555\pi$
$523$	−2.05811e8			−1.43868			−0.719338	+	0.694660i	$0.755555\pi$
$524$			3.21879e7i			0.223717i
$525$	1.16020e8	−	1.76209e8i	0.801781	−	1.21773i
$526$	−2.05231e8			−1.41022
$527$			1.66098e8i			1.13483i
$528$	−3.38516e7	−	2.22887e7i	−0.229973	−	0.151420i
$529$	1.47947e8			0.999398
$530$		−	5.23892e7i		−	0.351896i
$531$	2.21089e8	−	9.51072e7i	1.47667	−	0.635228i
$532$	−5.72776e7			−0.380408
$533$		−	2.89478e8i		−	1.91176i
$534$	1.34972e8	−	2.04991e8i	0.886377	−	1.34621i
$535$	−3.15414e6			−0.0205977
$536$		−	9.45154e6i		−	0.0613774i
$537$	1.75453e8	+	1.15523e8i	1.13302	+	0.746010i
$538$	−2.12070e7			−0.136186
$539$		−	1.05707e8i		−	0.675055i
$540$	−1.57052e6	+	8.82956e6i	−0.00997380	+	0.0560735i
$541$	−1.70547e8			−1.07709			−0.538546	−	0.842596i	$-0.681026\pi$
$541$	−1.70547e8			−1.07709			−0.538546	+	0.842596i	$0.681026\pi$
$542$			1.87179e8i			1.17560i
$543$	−6.74200e7	+	1.02396e8i	−0.421104	+	0.639562i
$544$	5.47413e7			0.340031
$545$			2.22476e7i			0.137434i
$546$	−3.87424e8	−	2.55090e8i	−2.38017	−	1.56717i
$547$	−2.59357e8			−1.58466			−0.792330	−	0.610093i	$-0.791132\pi$
$547$	−2.59357e8			−1.58466			−0.792330	+	0.610093i	$0.791132\pi$
$548$			1.90927e7i			0.116018i
$549$	−4.41172e7	−	1.02556e8i	−0.266619	−	0.619791i
$550$	−4.20964e7			−0.253021
$551$			4.84274e7i			0.289492i
$552$	−2.39876e6	+	3.64318e6i	−0.0142616	+	0.0216602i
$553$	−7.03748e7			−0.416142
$554$		−	2.03447e8i		−	1.19652i
$555$	−6.98214e6	−	4.59722e6i	−0.0408422	−	0.0268916i
$556$	−4.33608e6			−0.0252274
$557$		−	3.72865e6i		−	0.0215768i	−0.999942	−	0.0107884i	$-0.996566\pi$
$557$		−	3.72865e6i		−	0.0215768i	0.999942	−	0.0107884i	$-0.00343411\pi$
$558$	−1.36751e8	+	5.88268e7i	−0.787095	+	0.338589i
$559$	−2.67545e8			−1.53166
$560$			1.05571e8i			0.601148i
$561$	−3.90521e7	+	5.93113e7i	−0.221185	+	0.335930i
$562$	−2.49553e8			−1.40590
$563$			1.66415e8i			0.932538i	0.884643	+	0.466269i	$0.154402\pi$
$563$			1.66415e8i			0.932538i	−0.884643	+	0.466269i	$0.845598\pi$
$564$	−5.67286e6	−	3.73515e6i	−0.0316202	−	0.0208195i
$565$	−6.88445e7			−0.381702
$566$			1.84907e8i			1.01978i
$567$	2.19358e8	−	2.31579e8i	1.20338	−	1.27043i
$568$	−2.55481e8			−1.39416
$569$		−	1.01456e8i		−	0.550734i	−0.961339	−	0.275367i	$-0.911201\pi$
$569$		−	1.01456e8i		−	0.550734i	0.961339	−	0.275367i	$-0.0887993\pi$
$570$	−6.01550e7	+	9.13619e7i	−0.324823	+	0.493334i
$571$	2.88051e8			1.54725			0.773626	−	0.633642i	$-0.218441\pi$
$571$	2.88051e8			1.54725			0.773626	+	0.633642i	$0.218441\pi$
$572$		−	1.49978e7i		−	0.0801384i
$573$	−4.47702e7	−	2.94778e7i	−0.237971	−	0.156686i
$574$	3.34317e8			1.76776
$575$			3.88622e6i			0.0204420i
$576$	8.29058e7	+	1.92726e8i	0.433828	+	1.00849i
$577$	−1.59495e8			−0.830272			−0.415136	−	0.909759i	$-0.636266\pi$
$577$	−1.59495e8			−0.830272			−0.415136	+	0.909759i	$0.636266\pi$
$578$			9.12781e7i			0.472697i
$579$	−7.80911e7	+	1.18603e8i	−0.402314	+	0.611025i
$580$	−2.06351e6			−0.0105760
$581$			1.40360e8i			0.715676i
$582$	−3.21133e6	−	2.11442e6i	−0.0162898	−	0.0107256i
$583$	−6.02475e7			−0.304042
$584$		−	3.21894e8i		−	1.61612i
$585$	1.31865e8	−	5.67249e7i	0.658659	−	0.283339i
$586$	1.07540e8			0.534414
$587$			3.97580e8i			1.96567i	0.184491	+	0.982834i	$0.440936\pi$
$587$			3.97580e8i			1.96567i	−0.184491	+	0.982834i	$0.559064\pi$
$588$	−3.21479e7	+	4.88254e7i	−0.158132	+	0.240167i
$589$	2.94231e8			1.43993
$590$			1.25088e8i			0.609060i
$591$	−2.84166e8	−	1.87102e8i	−1.37661	−	0.906392i
$592$	−2.08935e7			−0.100704
$593$		−	1.08542e8i		−	0.520516i	−0.965539	−	0.260258i	$-0.916192\pi$
$593$		−	1.08542e8i		−	0.520516i	0.965539	−	0.260258i	$-0.0838077\pi$
$594$	−6.26631e7	−	1.11459e7i	−0.298987	−	0.0531809i
$595$	1.84971e8			0.878120
$596$		−	5.69455e7i		−	0.268980i
$597$	1.15216e8	−	1.74987e8i	0.541489	−	0.822400i
$598$	8.54451e6			0.0399561
$599$			2.18512e8i			1.01671i	0.861149	+	0.508353i	$0.169746\pi$
$599$			2.18512e8i			1.01671i	−0.861149	+	0.508353i	$0.830254\pi$
$600$	1.58882e8	+	1.04612e8i	0.735566	+	0.484315i
$601$	−3.24335e8			−1.49407			−0.747034	−	0.664786i	$-0.768523\pi$
$601$	−3.24335e8			−1.49407			−0.747034	+	0.664786i	$0.768523\pi$
$602$		−	3.08987e8i		−	1.41628i
$603$	−5.03100e6	−	1.16952e7i	−0.0229458	−	0.0533405i
$604$	3.68721e7			0.167335
$605$			8.07524e7i			0.364661i
$606$	−6.28797e7	+	9.55002e7i	−0.282548	+	0.429127i
$607$	−2.33094e8			−1.04223			−0.521117	−	0.853485i	$-0.674484\pi$
$607$	−2.33094e8			−1.04223			−0.521117	+	0.853485i	$0.674484\pi$
$608$		−	9.69706e7i		−	0.431449i
$609$	6.13001e7	+	4.03615e7i	0.271400	+	0.178696i
$610$	5.80244e7			0.255636
$611$			1.08717e8i			0.476623i
$612$	3.60756e7	−	1.55188e7i	0.157384	−	0.0677026i
$613$	1.75311e8			0.761078			0.380539	−	0.924765i	$-0.375739\pi$
$613$	1.75311e8			0.761078			0.380539	+	0.924765i	$0.375739\pi$
$614$			1.13305e8i			0.489492i
$615$	−5.68945e7	+	8.64099e7i	−0.244593	+	0.371483i
$616$	1.41534e8			0.605508
$617$		−	4.00691e7i		−	0.170590i	−0.996356	−	0.0852952i	$-0.972817\pi$
$617$		−	4.00691e7i		−	0.170590i	0.996356	−	0.0852952i	$-0.0271833\pi$
$618$	−8.12315e7	−	5.34849e7i	−0.344159	−	0.226603i
$619$	8.91071e7			0.375699			0.187850	−	0.982198i	$-0.439848\pi$
$619$	8.91071e7			0.375699			0.187850	+	0.982198i	$0.439848\pi$
$620$			1.25373e7i			0.0526051i
$621$	−1.02896e6	+	5.78488e6i	−0.00429658	+	0.0241557i
$622$	1.28303e8			0.533172
$623$			7.35191e8i			3.04044i
$624$	1.97297e8	−	2.99651e8i	0.812022	−	1.23328i
$625$	1.28755e8			0.527381
$626$		−	3.72031e8i		−	1.51655i
$627$	1.05066e8	+	6.91781e7i	0.426246	+	0.280651i
$628$	6.25256e6			0.0252452
$629$			3.66076e7i			0.147102i
$630$	6.55114e7	+	1.52290e8i	0.261996	+	0.609045i
$631$	−1.19235e8			−0.474587			−0.237294	−	0.971438i	$-0.576260\pi$
$631$	−1.19235e8			−0.474587			−0.237294	+	0.971438i	$0.576260\pi$
$632$		−	6.34549e7i		−	0.251370i
$633$	3.92461e7	−	5.96061e7i	0.154734	−	0.235006i
$634$	−3.45747e8			−1.35672
$635$		−	8.02173e6i		−	0.0313290i
$636$	2.78278e7	+	1.83225e7i	0.108170	+	0.0712220i
$637$	9.35712e8			3.62013
$638$		−	1.46446e7i		−	0.0563919i
$639$	−3.16129e8	+	1.35991e8i	−1.21161	+	0.521204i
$640$	−7.94091e7			−0.302922
$641$			2.58040e8i			0.979745i	0.871794	+	0.489873i	$0.162957\pi$
$641$			2.58040e8i			0.979745i	−0.871794	+	0.489873i	$0.837043\pi$
$642$	−6.80769e6	+	1.03394e7i	−0.0257273	+	0.0390740i
$643$	−3.23616e8			−1.21730			−0.608650	−	0.793439i	$-0.708288\pi$
$643$	−3.23616e8			−1.21730			−0.608650	+	0.793439i	$0.708288\pi$
$644$		−	1.59902e6i		−	0.00598683i
$645$	7.98629e7	+	5.25838e7i	0.297623	+	0.195962i
$646$	4.79013e8			1.77685
$647$		−	9.78821e6i		−	0.0361402i	−0.999837	−	0.0180701i	$-0.994248\pi$
$647$		−	9.78821e6i		−	0.0361402i	0.999837	−	0.0180701i	$-0.00575220\pi$
$648$	2.08808e8	+	1.97789e8i	0.767399	+	0.726903i
$649$	1.43851e8			0.526235
$650$		−	3.72633e8i		−	1.35688i
$651$	2.45225e8	−	3.72441e8i	0.888835	−	1.34994i
$652$	−4.47163e7			−0.161333
$653$		−	4.74996e7i		−	0.170589i	−0.996356	−	0.0852944i	$-0.972817\pi$
$653$		−	4.74996e7i		−	0.170589i	0.996356	−	0.0852944i	$-0.0271831\pi$
$654$	7.29284e7	+	4.80179e7i	0.260713	+	0.171660i
$655$	−1.84136e8			−0.655260
$656$			2.58575e8i			0.915958i
$657$	−1.71342e8	−	3.98308e8i	−0.604183	−	1.40450i
$658$	−1.25557e8			−0.440721
$659$			8.26983e7i			0.288962i	0.989508	+	0.144481i	$0.0461512\pi$
$659$			8.26983e7i			0.288962i	−0.989508	+	0.144481i	$0.953849\pi$
$660$	−2.94770e6	+	4.47690e6i	−0.0102530	+	0.0155720i
$661$	7.40018e6			0.0256235			0.0128117	−	0.999918i	$-0.495922\pi$
$661$	7.40018e6			0.0256235			0.0128117	+	0.999918i	$0.495922\pi$
$662$		−	4.36902e7i		−	0.150595i
$663$	−5.25018e8	−	3.45685e8i	−1.80150	−	1.18615i
$664$	−1.26559e8			−0.432303
$665$		−	3.27665e8i		−	1.11420i
$666$	−3.01396e7	+	1.29653e7i	−0.102027	+	0.0438894i
$667$	−1.35195e6			−0.00455600
$668$		−	3.29376e7i		−	0.110500i
$669$	−1.82774e8	+	2.77593e8i	−0.610431	+	0.927108i
$670$	6.61695e6			0.0220005
$671$		−	6.67280e7i		−	0.220872i
$672$	−1.22747e8	−	8.08195e7i	−0.404485	−	0.266323i
$673$	2.83904e8			0.931380			0.465690	−	0.884948i	$-0.345806\pi$
$673$	2.83904e8			0.931380			0.465690	+	0.884948i	$0.345806\pi$
$674$			5.33255e8i			1.74163i
$675$	2.52284e8	+	4.48737e7i	0.820309	+	0.145909i
$676$	8.96826e7			0.290314
$677$		−	1.86630e8i		−	0.601472i	−0.953707	−	0.300736i	$-0.902768\pi$
$677$		−	1.86630e8i		−	0.601472i	0.953707	−	0.300736i	$-0.0972324\pi$
$678$	−1.48590e8	+	2.25674e8i	−0.476759	+	0.724090i
$679$	1.15173e7			0.0367909
$680$			1.66783e8i			0.530427i
$681$	−2.29613e8	−	1.51183e8i	−0.727034	−	0.478698i
$682$	−8.89765e7			−0.280493
$683$			3.66059e6i			0.0114892i	0.999983	+	0.00574458i	$0.00182857\pi$
$683$			3.66059e6i			0.0114892i	−0.999983	+	0.00574458i	$0.998171\pi$
$684$	−2.74906e7	−	6.39056e7i	−0.0859045	−	0.199696i
$685$	−1.09222e8			−0.339813
$686$			5.56601e8i			1.72414i
$687$	−8.26865e7	+	1.25582e8i	−0.255014	+	0.387310i
$688$	2.38984e8			0.733843
$689$		−	5.33305e8i		−	1.63049i
$690$	−2.55056e6	−	1.67935e6i	−0.00776405	−	0.00511204i
$691$	4.80222e8			1.45549			0.727743	−	0.685850i	$-0.240570\pi$
$691$	4.80222e8			1.45549			0.727743	+	0.685850i	$0.240570\pi$
$692$			8.45532e7i			0.255159i
$693$	1.75133e8	−	7.53380e7i	0.526222	−	0.226368i
$694$	−4.92341e7			−0.147295
$695$		−	2.48052e7i		−	0.0738904i
$696$	−3.63928e7	+	5.52725e7i	−0.107941	+	0.163939i
$697$	4.53050e8			1.33797
$698$		−	3.53786e8i		−	1.04034i
$699$	−1.28189e8	−	8.44026e7i	−0.375334	−	0.247129i
$700$	−6.97347e7			−0.203308
$701$		−	4.97056e8i		−	1.44295i	−0.692440	−	0.721475i	$-0.743464\pi$
$701$		−	4.97056e8i		−	1.44295i	0.692440	−	0.721475i	$-0.256536\pi$
$702$	9.86623e7	−	5.54687e8i	0.285194	−	1.60338i
$703$	6.48478e7			0.186651
$704$			1.25396e8i			0.359391i
$705$	2.13675e7	−	3.24524e7i	0.0609798	−	0.0926146i
$706$	−7.67481e7			−0.218099
$707$		−	3.42506e8i		−	0.969193i
$708$	−6.64436e7	−	4.37482e7i	−0.187221	−	0.123271i
$709$	7.79637e7			0.218753			0.109376	−	0.994000i	$-0.465115\pi$
$709$	7.79637e7			0.218753			0.109376	+	0.994000i	$0.465115\pi$
$710$		−	1.78860e8i		−	0.499733i
$711$	−3.37767e7	−	7.85184e7i	−0.0939741	−	0.218455i
$712$	−6.62900e8			−1.83657
$713$			8.21406e6i			0.0226615i
$714$	3.99230e8	−	6.06341e8i	1.09680	−	1.66580i
$715$	8.57973e7			0.234723
$716$		−	6.94357e7i		−	0.189166i
$717$	−8.78568e7	−	5.78471e7i	−0.238352	−	0.156937i
$718$	−1.47389e8			−0.398191
$719$		−	3.91317e8i		−	1.05279i	−0.850240	−	0.526395i	$-0.823543\pi$
$719$		−	3.91317e8i		−	1.05279i	0.850240	−	0.526395i	$-0.176457\pi$
$720$	−1.17788e8	+	5.06694e7i	−0.315575	+	0.135753i
$721$	2.91332e8			0.777290
$722$		−	4.99399e8i		−	1.32689i
$723$	6.76430e7	−	1.02735e8i	0.178982	−	0.271833i
$724$	4.05232e7			0.106780
$725$			5.89598e7i			0.154718i
$726$	2.64709e8	+	1.74291e8i	0.691764	+	0.455475i
$727$	−1.51315e8			−0.393802			−0.196901	−	0.980423i	$-0.563088\pi$
$727$	−1.51315e8			−0.393802			−0.196901	+	0.980423i	$0.563088\pi$
$728$			1.25285e9i			3.24717i
$729$	3.63658e8	+	1.33594e8i	0.938665	+	0.344831i
$730$	2.25355e8			0.579294
$731$		−	4.18724e8i		−	1.07195i
$732$	−2.02934e7	+	3.08211e7i	−0.0517393	+	0.0785805i
$733$	−3.81746e8			−0.969311			−0.484655	−	0.874705i	$-0.661055\pi$
$733$	−3.81746e8			−0.969311			−0.484655	+	0.874705i	$0.661055\pi$
$734$		−	2.97098e8i		−	0.751296i
$735$	−2.79313e8	−	1.83906e8i	−0.703442	−	0.463164i
$736$	2.70714e6			0.00679011
$737$		−	7.60948e6i		−	0.0190087i
$738$	1.60457e8	+	3.73003e8i	0.399199	+	0.927990i
$739$	−2.06461e8			−0.511568			−0.255784	−	0.966734i	$-0.582334\pi$
$739$	−2.06461e8			−0.511568			−0.255784	+	0.966734i	$0.582334\pi$
$740$			2.76319e6i			0.00681891i
$741$	−6.12358e8	+	9.30034e8i	−1.50505	+	2.28583i
$742$	6.15912e8			1.50767
$743$		−	2.59148e8i		−	0.631803i	−0.948792	−	0.315901i	$-0.897693\pi$
$743$		−	2.59148e8i		−	0.631803i	0.948792	−	0.315901i	$-0.102307\pi$
$744$	3.35819e8	+	2.21112e8i	0.815430	+	0.536899i
$745$	3.25765e8			0.787835
$746$			4.63576e8i			1.11662i
$747$	−1.56603e8	+	6.73666e7i	−0.375697	+	0.161615i
$748$	2.34725e7			0.0560860
$749$		−	3.70815e7i		−	0.0882495i
$750$	−1.61139e8	+	2.44734e8i	−0.381960	+	0.580111i
$751$	−5.11966e8			−1.20871			−0.604354	−	0.796716i	$-0.706569\pi$
$751$	−5.11966e8			−1.20871			−0.604354	+	0.796716i	$0.706569\pi$
$752$		−	9.71114e7i		−	0.228358i
$753$	4.02276e8	+	2.64869e8i	0.942191	+	0.620362i
$754$	1.29633e8			0.302414
$755$			2.10932e8i			0.490119i
$756$	−1.03804e8	−	1.84637e7i	−0.240243	−	0.0427320i
$757$	9.23357e7			0.212854			0.106427	−	0.994321i	$-0.466059\pi$
$757$	9.23357e7			0.212854			0.106427	+	0.994321i	$0.466059\pi$
$758$			1.39229e8i			0.319686i
$759$	−1.93125e6	+	2.93314e6i	−0.00441686	+	0.00670822i
$760$	2.95445e8			0.673033
$761$		−	4.39644e8i		−	0.997578i	−0.866723	−	0.498789i	$-0.833778\pi$
$761$		−	4.39644e8i		−	0.997578i	0.866723	−	0.498789i	$-0.166222\pi$
$762$	−2.62954e7	−	1.73136e7i	−0.0594314	−	0.0391311i
$763$	−2.61554e8			−0.588826
$764$			1.77178e7i			0.0397311i
$765$	8.87778e7	+	2.06376e8i	0.198299	+	0.460972i
$766$	7.33244e7			0.163141
$767$			1.27336e9i			2.82204i
$768$	1.02090e8	−	1.55052e8i	0.225372	−	0.342289i
$769$	−4.27609e8			−0.940303			−0.470152	−	0.882586i	$-0.655801\pi$
$769$	−4.27609e8			−0.940303			−0.470152	+	0.882586i	$0.655801\pi$
$770$			9.90871e7i			0.217042i
$771$	−3.15548e8	−	2.07765e8i	−0.688498	−	0.453324i
$772$	4.69372e7			0.102015
$773$			1.41436e8i			0.306212i	0.988210	+	0.153106i	$0.0489275\pi$
$773$			1.41436e8i			0.306212i	−0.988210	+	0.153106i	$0.951072\pi$
$774$	3.44742e8	−	1.48299e8i	0.743483	−	0.319828i
$775$	3.58222e8			0.769569
$776$			1.03848e7i			0.0222235i
$777$	5.40470e7	−	8.20853e7i	0.115215	−	0.174986i
$778$	−6.67441e8			−1.41734
$779$		−	8.02547e8i		−	1.69769i
$780$	−3.96291e7	−	2.60928e7i	−0.0835083	−	0.0549840i
$781$	−2.05689e8			−0.431775
$782$			1.33727e7i			0.0279639i
$783$	−1.56108e7	+	8.77653e7i	−0.0325193	+	0.182826i
$784$	−8.35822e8			−1.73447
$785$			3.57687e7i			0.0739424i
$786$	−3.97426e8	+	6.03601e8i	−0.818444	+	1.24303i
$787$	6.38614e8			1.31013			0.655064	−	0.755573i	$-0.272641\pi$
$787$	6.38614e8			1.31013			0.655064	+	0.755573i	$0.272641\pi$
$788$			1.12459e8i			0.229835i
$789$	6.23629e8	+	4.10613e8i	1.26968	+	0.835991i
$790$	4.44242e7			0.0901029
$791$		−	8.09368e8i		−	1.63537i
$792$	6.79300e7	+	1.57912e8i	0.136737	+	0.317864i
$793$	5.90669e8			1.18447
$794$			1.13256e8i			0.226257i
$795$	−1.04817e8	+	1.59193e8i	−0.208607	+	0.316827i
$796$	−6.92513e7			−0.137306
$797$		−	8.22008e8i		−	1.62368i	−0.583878	−	0.811841i	$-0.698465\pi$
$797$		−	8.22008e8i		−	1.62368i	0.583878	−	0.811841i	$-0.301535\pi$
$798$	−1.07409e9	−	7.07210e8i	−2.11365	−	1.39168i
$799$	−1.70149e8			−0.333571
$800$		−	1.18061e8i		−	0.230587i
$801$	−8.20265e8	+	3.52858e8i	−1.59609	+	0.686597i
$802$	3.78545e8			0.733828
$803$		−	2.59158e8i		−	0.500516i
$804$	−2.31420e6	+	3.51475e6i	−0.00445280	+	0.00676280i
$805$	9.14744e6			0.0175353
$806$		−	7.87611e8i		−	1.50420i
$807$	6.44407e7	+	4.24294e7i	0.122614	+	0.0807321i
$808$	3.08828e8			0.585440
$809$			3.99682e8i			0.754864i	0.926037	+	0.377432i	$0.123193\pi$
$809$			3.99682e8i			0.754864i	−0.926037	+	0.377432i	$0.876807\pi$
$810$	−1.38470e8	+	1.46184e8i	−0.260556	+	0.275072i
$811$	−3.21671e8			−0.603045			−0.301522	−	0.953459i	$-0.597495\pi$
$811$	−3.21671e8			−0.603045			−0.301522	+	0.953459i	$0.597495\pi$
$812$		−	2.42596e7i		−	0.0453122i
$813$	3.74494e8	−	5.68773e8i	0.696905	−	1.05844i
$814$	−1.96102e7			−0.0363588
$815$		−	2.55806e8i		−	0.472540i
$816$	4.68971e8	+	3.08782e8i	0.863128	+	0.568305i
$817$	−7.41741e8			−1.36015
$818$		−	1.18509e7i		−	0.0216516i
$819$	6.66884e8	+	1.55026e9i	1.21394	+	2.82198i
$820$	3.41968e7			0.0620217
$821$			4.69175e8i			0.847823i	0.905704	+	0.423911i	$0.139343\pi$
$821$			4.69175e8i			0.847823i	−0.905704	+	0.423911i	$0.860657\pi$
$822$	−2.35739e8	+	3.58034e8i	−0.424439	+	0.644628i
$823$	−1.46859e8			−0.263451			−0.131726	−	0.991286i	$-0.542052\pi$
$823$	−1.46859e8			−0.263451			−0.131726	+	0.991286i	$0.542052\pi$
$824$			2.62686e8i			0.469521i
$825$	1.27917e8	+	8.42236e7i	0.227806	+	0.149993i
$826$	−1.47060e9			−2.60947
$827$		−	6.58628e8i		−	1.16446i	−0.813025	−	0.582229i	$-0.802181\pi$
$827$		−	6.58628e8i		−	1.16446i	0.813025	−	0.582229i	$-0.197819\pi$
$828$	1.78406e6	−	767457.i	0.00314281	−	0.00135196i
$829$	2.25651e8			0.396072			0.198036	−	0.980195i	$-0.436544\pi$
$829$	2.25651e8			0.396072			0.198036	+	0.980195i	$0.436544\pi$
$830$		−	8.86028e7i		−	0.154958i
$831$	−4.07042e8	+	6.18206e8i	−0.709310	+	1.07728i
$832$	−1.11000e9			−1.92731
$833$			1.46444e9i			2.53360i
$834$	−8.13121e7	−	5.35379e7i	−0.140171	−	0.0922919i
$835$	1.88424e8			0.323651
$836$		−	4.15800e7i		−	0.0711648i
$837$	5.33236e8	+	9.48467e7i	0.909374	+	0.161751i
$838$	−3.61699e8			−0.614633
$839$		−	7.22641e8i		−	1.22359i	−0.791016	−	0.611796i	$-0.790447\pi$
$839$		−	7.22641e8i		−	1.22359i	0.791016	−	0.611796i	$-0.209553\pi$
$840$	2.46237e8	−	3.73979e8i	0.415447	−	0.630971i
$841$	−2.05111e7			−0.0344828
$842$			8.39306e8i			1.40600i
$843$	7.58307e8	+	4.99289e8i	1.26579	+	0.833430i
$844$	−2.35891e7			−0.0392360
$845$			5.13042e8i			0.850321i
$846$	−6.02617e7	−	1.40086e8i	−0.0995245	−	0.231358i
$847$	−9.49363e8			−1.56236
$848$			4.76373e8i			0.781196i
$849$	3.69950e8	−	5.61870e8i	0.604532	−	0.918149i
$850$	5.83193e8			0.949632
$851$			1.81036e6i			0.00293749i
$852$	9.50058e7	+	6.25542e7i	0.153614	+	0.101143i
$853$	−1.28675e8			−0.207323			−0.103662	−	0.994613i	$-0.533056\pi$
$853$	−1.28675e8			−0.207323			−0.103662	+	0.994613i	$0.533056\pi$
$854$			6.82162e8i			1.09525i
$855$	3.65581e8	−	1.57264e8i	0.584905	−	0.251612i
$856$	3.34353e7			0.0533070
$857$		−	2.86617e7i		−	0.0455366i	−0.999741	−	0.0227683i	$-0.992752\pi$
$857$		−	2.86617e7i		−	0.0455366i	0.999741	−	0.0227683i	$-0.00724799\pi$
$858$	1.85179e8	−	2.81246e8i	0.293178	−	0.445271i
$859$	4.16982e8			0.657867			0.328933	−	0.944353i	$-0.393311\pi$
$859$	4.16982e8			0.657867			0.328933	+	0.944353i	$0.393311\pi$
$860$		−	3.16058e7i		−	0.0496903i
$861$	−1.01588e9	−	6.68878e8i	−1.59159	−	1.04794i
$862$	7.00594e8			1.09382
$863$			3.05527e8i			0.475354i	0.971344	+	0.237677i	$0.0763859\pi$
$863$			3.05527e8i			0.475354i	−0.971344	+	0.237677i	$0.923614\pi$
$864$	3.12589e7	−	1.75740e8i	0.0484656	−	0.272477i
$865$	−4.83699e8			−0.747355
$866$			1.28198e8i			0.197391i
$867$	1.82623e8	−	2.77363e8i	0.280219	−	0.425590i
$868$	−1.47394e8			−0.225383
$869$		−	5.10878e7i		−	0.0778498i
$870$	−3.86958e7	−	2.54783e7i	−0.0587633	−	0.0386912i
$871$	6.73583e7			0.101938
$872$		−	2.35835e8i		−	0.355680i
$873$	5.52776e6	+	1.28500e7i	0.00830819	+	0.0193135i
$874$	2.36888e7			0.0354820
$875$		−	8.77727e8i		−	1.31019i
$876$	−7.88154e7	+	1.19703e8i	−0.117246	+	0.178071i
$877$	−7.75901e8			−1.15029			−0.575145	−	0.818051i	$-0.695054\pi$
$877$	−7.75901e8			−1.15029			−0.575145	+	0.818051i	$0.695054\pi$
$878$			2.76269e8i			0.408178i
$879$	−3.26778e8	−	2.15159e8i	−0.481156	−	0.316805i
$880$	−7.66382e7			−0.112460
$881$		−	9.60239e8i		−	1.40427i	−0.712043	−	0.702136i	$-0.752230\pi$
$881$		−	9.60239e8i		−	1.40427i	0.712043	−	0.702136i	$-0.247770\pi$
$882$	−1.20570e9	+	5.18663e8i	−1.75725	+	0.755926i
$883$	7.66285e8			1.11303			0.556517	−	0.830836i	$-0.312138\pi$
$883$	7.66285e8			1.11303			0.556517	+	0.830836i	$0.312138\pi$
$884$			2.07776e8i			0.300773i
$885$	2.50268e8	−	3.80100e8i	0.361056	−	0.548364i
$886$	3.66067e8			0.526331
$887$			2.70708e8i			0.387909i	0.981010	+	0.193955i	$0.0621315\pi$
$887$			2.70708e8i			0.387909i	−0.981010	+	0.193955i	$0.937869\pi$
$888$	7.40139e7	+	4.87326e7i	0.105700	+	0.0695954i
$889$	9.43072e7			0.134227
$890$		−	4.64090e8i		−	0.658313i
$891$	1.68112e8	+	1.59240e8i	0.237665	+	0.225123i
$892$	1.09858e8			0.154787
$893$			3.01407e8i			0.423253i
$894$	7.03109e8	−	1.06787e9i	0.984035	−	1.49453i
$895$	3.97217e8			0.554062
$896$		−	9.33571e8i		−	1.29785i
$897$	−2.59638e7	−	1.70952e7i	−0.0359742	−	0.0236863i
$898$	−6.59225e8			−0.910343
$899$			1.24620e8i			0.171517i
$900$	−3.34695e7	−	7.78043e7i	−0.0459115	−	0.106727i
$901$	8.34654e8			1.14112
$902$			2.42693e8i			0.330703i
$903$	−6.18199e8	+	9.38906e8i	−0.839586	+	1.27514i
$904$	7.29783e8			0.987845
$905$			2.31819e8i			0.312754i
$906$	6.91441e8	+	4.55262e8i	0.929759	+	0.612177i
$907$	−5.17723e8			−0.693865			−0.346933	−	0.937890i	$-0.612777\pi$
$907$	−5.17723e8			−0.693865			−0.346933	+	0.937890i	$0.612777\pi$
$908$			9.08695e7i			0.121384i
$909$	3.82140e8	−	1.64387e8i	0.508781	−	0.218865i
$910$	−8.77109e8			−1.16394
$911$			1.42829e8i			0.188913i	0.995529	+	0.0944564i	$0.0301113\pi$
$911$			1.42829e8i			0.188913i	−0.995529	+	0.0944564i	$0.969889\pi$
$912$	5.46987e8	−	8.30750e8i	0.721095	−	1.09518i
$913$	−1.01893e8			−0.133885
$914$			6.28909e7i			0.0823662i
$915$	−1.76316e8	−	1.16091e8i	−0.230160	−	0.151543i
$916$	4.96993e7			0.0646642
$917$		−	2.16478e9i		−	2.80741i
$918$	8.68118e8	+	1.54412e8i	1.12215	+	0.199597i
$919$	8.91001e8			1.14797			0.573986	−	0.818865i	$-0.305396\pi$
$919$	8.91001e8			1.14797			0.573986	+	0.818865i	$0.305396\pi$
$920$			8.24798e6i			0.0105921i
$921$	2.26694e8	−	3.44297e8i	0.290175	−	0.440711i
$922$	−2.99189e8			−0.381727
$923$		−	1.82073e9i		−	2.31548i
$924$	−5.26325e7	−	3.46546e7i	−0.0667172	−	0.0439283i
$925$	7.89515e7			0.0997551
$926$		−	9.97200e8i		−	1.25588i
$927$	1.39826e8	+	3.25045e8i	0.175529	+	0.408041i
$928$	4.10713e7			0.0513919
$929$			1.30396e9i			1.62636i	0.582009	+	0.813182i	$0.302267\pi$
$929$			1.30396e9i			1.62636i	−0.582009	+	0.813182i	$0.697733\pi$
$930$	−1.54798e8	+	2.35104e8i	−0.192450	+	0.292288i
$931$	2.59416e9			3.21476
$932$			5.07308e7i			0.0626648i
$933$	−3.89871e8	−	2.56701e8i	−0.480038	−	0.316069i
$934$	−4.67943e8			−0.574318
$935$			1.34278e8i			0.164274i
$936$	−1.39782e9	+	6.01310e8i	−1.70461	+	0.733281i
$937$	5.49074e8			0.667439			0.333720	−	0.942672i	$-0.391696\pi$
$937$	5.49074e8			0.667439			0.333720	+	0.942672i	$0.391696\pi$
$938$			7.77919e7i			0.0942596i
$939$	−7.44333e8	+	1.13048e9i	−0.899023	+	1.36541i
$940$	−1.28431e7			−0.0154627
$941$			6.98610e8i			0.838428i	0.907887	+	0.419214i	$0.137694\pi$
$941$			6.98610e8i			0.838428i	−0.907887	+	0.419214i	$0.862306\pi$
$942$	1.17251e8	+	7.72007e7i	0.140269	+	0.0923568i
$943$	2.24048e7			0.0267181
$944$		−	1.13742e9i		−	1.35209i
$945$	1.05624e8	−	5.93828e8i	0.125161	−	0.703664i
$946$	2.24305e8			0.264951
$947$			9.67032e8i			1.13865i	0.822112	+	0.569326i	$0.192796\pi$
$947$			9.67032e8i			1.13865i	−0.822112	+	0.569326i	$0.807204\pi$
$948$	−1.55369e7	+	2.35970e7i	−0.0182364	+	0.0276969i
$949$	2.29404e9			2.68412
$950$		−	1.03309e9i		−	1.20494i
$951$	1.05061e9	+	6.91746e8i	1.22151	+	0.804276i
$952$	−1.96078e9			−2.27258
$953$			1.40157e6i			0.00161933i	1.00000		0.000809664i	$0.000257724\pi$
$953$			1.40157e6i			0.00161933i	−1.00000		0.000809664i	$0.999742\pi$
$954$	2.95609e8	+	6.87184e8i	0.340466	+	0.791458i
$955$	−1.01357e8			−0.116371
$956$			3.47694e7i			0.0397945i
$957$	−2.93000e7	+	4.45001e7i	−0.0334296	+	0.0507721i
$958$	−3.36568e8			−0.382804
$959$		−	1.28407e9i		−	1.45590i
$960$	3.31337e8	+	2.18161e8i	0.374504	+	0.246583i
$961$	−1.30352e8			−0.146875
$962$		−	1.73588e8i		−	0.194982i
$963$	4.13725e7	−	1.77974e7i	0.0463269	−	0.0199287i
$964$	−4.06573e7			−0.0453845
$965$			2.68511e8i			0.298799i
$966$	1.97432e7	−	2.99856e7i	0.0219022	−	0.0332645i
$967$	−1.02482e9			−1.13336			−0.566681	−	0.823937i	$-0.691773\pi$
$967$	−1.02482e9			−1.13336			−0.566681	+	0.823937i	$0.691773\pi$
$968$		−	8.56012e8i		−	0.943743i
$969$	−1.45556e9	−	9.58376e8i	−1.59977	−	1.05333i
$970$	−7.27029e6			−0.00796593
$971$			1.77266e9i			1.93628i	0.250417	+	0.968138i	$0.419432\pi$
$971$			1.77266e9i			1.93628i	−0.250417	+	0.968138i	$0.580568\pi$
$972$	−2.92211e7	−	1.24678e8i	−0.0318198	−	0.135766i
$973$	2.91621e8			0.316578
$974$			3.17689e8i			0.343815i
$975$	−7.45538e8	+	1.13231e9i	−0.804371	+	1.22166i
$976$	−5.27614e8			−0.567501
$977$			1.21143e9i			1.29901i	0.760356	+	0.649507i	$0.225025\pi$
$977$			1.21143e9i			1.29901i	−0.760356	+	0.649507i	$0.774975\pi$
$978$	−8.38539e8	−	5.52115e8i	−0.896410	−	0.590219i
$979$	−5.33703e8			−0.568790
$980$			1.10538e8i			0.117445i
$981$	−1.25534e8	−	2.91820e8i	−0.132970	−	0.309106i
$982$	−1.36295e7			−0.0143929
$983$		−	6.59670e8i		−	0.694490i	−0.937774	−	0.347245i	$-0.887117\pi$
$983$		−	6.59670e8i		−	0.694490i	0.937774	−	0.347245i	$-0.112883\pi$
$984$	6.03107e8	−	9.15985e8i	0.633008	−	0.961397i
$985$	−6.43338e8			−0.673179
$986$			2.02883e8i			0.211649i
$987$	3.81526e8	+	2.51206e8i	0.396801	+	0.261263i
$988$	3.68062e8			0.381636
$989$		−	2.07072e7i		−	0.0214059i
$990$	−1.10553e8	+	4.75572e7i	−0.113937	+	0.0490130i
$991$	1.48885e9			1.52978			0.764890	−	0.644161i	$-0.222793\pi$
$991$	1.48885e9			1.52978			0.764890	+	0.644161i	$0.222793\pi$
$992$		−	2.49537e8i		−	0.255623i
$993$	−8.74122e7	+	1.32759e8i	−0.0892738	+	0.135587i
$994$	2.10276e9			2.14107
$995$		−	3.96162e8i		−	0.402164i
$996$	4.70635e7	+	3.09878e7i	0.0476328	+	0.0313627i
$997$	−1.43861e9			−1.45164			−0.725820	−	0.687885i	$-0.758540\pi$
$997$	−1.43861e9			−1.45164			−0.725820	+	0.687885i	$0.758540\pi$
$998$		−	1.81623e8i		−	0.182717i
$999$	1.17524e8	+	2.09040e7i	0.117877	+	0.0209669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.7.b.a.59.18	✓	56
3.2	odd	2	inner	87.7.b.a.59.39	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.7.b.a.59.18	✓	56	1.1	even	1	trivial
87.7.b.a.59.39	yes	56	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	87.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-7.42129i q^{2} +(-14.8480 + 22.5508i) q^{3} +8.92448 q^{4} +51.0538i q^{5} +(167.356 + 110.191i) q^{6} -600.212 q^{7} -541.194i q^{8} +(-288.074 - 669.667i) q^{9} +378.885 q^{10} -435.717i q^{11} +(-132.511 + 201.254i) q^{12} +3856.92 q^{13} +4454.35i q^{14} +(-1151.30 - 758.047i) q^{15} -3445.19 q^{16} +6036.31i q^{17} +(-4969.79 + 2137.88i) q^{18} +10692.9 q^{19} +455.629i q^{20} +(8911.95 - 13535.2i) q^{21} -3233.58 q^{22} +298.515i q^{23} +(12204.3 + 8035.64i) q^{24} +13018.5 q^{25} -28623.3i q^{26} +(19378.8 + 3446.92i) q^{27} -5356.58 q^{28} +4528.92i q^{29} +(-5625.68 + 8544.15i) q^{30} +27516.4 q^{31} -9068.67i q^{32} +(9825.76 + 6469.52i) q^{33} +44797.2 q^{34} -30643.1i q^{35} +(-2570.91 - 5976.43i) q^{36} +6064.56 q^{37} -79355.3i q^{38} +(-57267.6 + 86976.6i) q^{39} +27630.0 q^{40} -75054.1i q^{41} +(-100449. - 66138.1i) q^{42} -69367.5 q^{43} -3888.55i q^{44} +(34189.1 - 14707.3i) q^{45} +2215.37 q^{46} +28187.6i q^{47} +(51154.1 - 77691.6i) q^{48} +242606. q^{49} -96614.1i q^{50} +(-136123. - 89627.1i) q^{51} +34421.1 q^{52} -138272. i q^{53} +(25580.6 - 143816. i) q^{54} +22245.0 q^{55} +324831. i q^{56} +(-158768. + 241134. i) q^{57} +33610.4 q^{58} +330148. i q^{59} +(-10274.8 - 6765.17i) q^{60} +153145. q^{61} -204207. i q^{62} +(172906. + 401942. i) q^{63} -287793. q^{64} +196911. i q^{65} +(48012.2 - 72919.8i) q^{66} +17464.3 q^{67} +53871.0i q^{68} +(-6731.75 - 4432.35i) q^{69} -227411. q^{70} -472069. i q^{71} +(-362420. + 155904. i) q^{72} +594785. q^{73} -45006.8i q^{74} +(-193299. + 293577. i) q^{75} +95428.8 q^{76} +261523. i q^{77} +(645478. + 424999. i) q^{78} +117250. q^{79} -175890. i q^{80} +(-365467. + 385828. i) q^{81} -556998. q^{82} -233851. i q^{83} +(79534.5 - 120795. i) q^{84} -308177. q^{85} +514796. i q^{86} +(-102131. - 67245.4i) q^{87} -235807. q^{88} -1.22488e6i q^{89} +(-109147. - 253727. i) q^{90} -2.31497e6 q^{91} +2664.10i q^{92} +(-408563. + 620516. i) q^{93} +209188. q^{94} +545915. i q^{95} +(204505. + 134652. i) q^{96} -19188.6 q^{97} -1.80045e6i q^{98} +(-291785. + 125519. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 52 q^{3} - 1924 q^{4} - 160 q^{6} + 160 q^{7} - 1060 q^{9} - 3588 q^{10} - 2166 q^{12} - 1400 q^{13} - 6240 q^{15} + 56588 q^{16} - 5978 q^{18} + 25000 q^{19} + 7520 q^{21} + 20970 q^{22} + 1238 q^{24}+ \cdots + 4793544 q^{99}+O(q^{100}) \) 56 * q + 52 * q^3 - 1924 * q^4 - 160 * q^6 + 160 * q^7 - 1060 * q^9 - 3588 * q^10 - 2166 * q^12 - 1400 * q^13 - 6240 * q^15 + 56588 * q^16 - 5978 * q^18 + 25000 * q^19 + 7520 * q^21 + 20970 * q^22 + 1238 * q^24 - 213304 * q^25 + 25492 * q^27 + 7870 * q^28 + 105092 * q^30 - 78656 * q^31 + 18952 * q^33 - 96642 * q^34 - 40224 * q^36 + 52120 * q^37 - 112096 * q^39 + 343440 * q^40 - 341758 * q^42 - 286760 * q^43 + 68312 * q^45 + 255516 * q^46 + 386086 * q^48 + 1051872 * q^49 - 256656 * q^51 + 58606 * q^52 + 450124 * q^54 - 409632 * q^55 - 1141736 * q^57 + 817806 * q^60 + 309976 * q^61 + 567632 * q^63 - 2844730 * q^64 + 958426 * q^66 + 748696 * q^67 - 1323704 * q^69 - 2123748 * q^70 - 1026242 * q^72 - 333728 * q^73 - 331316 * q^75 + 2846728 * q^76 + 292446 * q^78 - 661184 * q^79 + 1614852 * q^81 + 376908 * q^82 - 1670584 * q^84 + 3342000 * q^85 - 927168 * q^88 + 835882 * q^90 + 2248016 * q^91 + 3960776 * q^93 - 1368294 * q^94 - 5811456 * q^96 - 3057296 * q^97 + 4793544 * q^99

Introduction

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