LMFDB - Embedded newform 26.8.e.a.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,8,Mod(17,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.17"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	26.e (of order $6$, degree $2$, 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:	$8.12201066259$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22180 x^{14} + 184473654 x^{12} + 707524481236 x^{10} + \cdots + 18\!\cdots\!76 $ x^16 + 22180x^14 + 184473654x^12 + 707524481236x^10 + 1235305573179121x^8 + 834592841081820432x^6 + 142296444753813668448x^4 + 5907885179463590558976*x^2 + 18970385728293762437376
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{34}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$-69.7232i$ of defining polynomial
Character	$\chi$	$=$	26.23
Dual form			26.8.e.a.17.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.92820 + 4.00000i) q^{2} +(-34.8616 - 60.3821i) q^{3} +(32.0000 - 55.4256i) q^{4} -226.832i q^{5} +(483.056 + 278.893i) q^{6} +(-154.640 - 89.2812i) q^{7} +512.000i q^{8} +(-1337.16 + 2316.03i) q^{9} +(907.328 + 1571.54i) q^{10} +(-762.215 + 440.065i) q^{11} -4462.28 q^{12} +(-7466.71 + 2645.15i) q^{13} +1428.50 q^{14} +(-13696.6 + 7907.72i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-5090.76 + 8817.45i) q^{17} -21394.6i q^{18} +(9791.36 + 5653.04i) q^{19} +(-12572.3 - 7258.62i) q^{20} +12449.9i q^{21} +(3520.52 - 6097.72i) q^{22} +(46052.4 + 79765.1i) q^{23} +(30915.6 - 17849.1i) q^{24} +26672.3 q^{25} +(41150.3 - 48192.9i) q^{26} +33977.8 q^{27} +(-9896.93 + 5714.00i) q^{28} +(-79316.7 - 137381. i) q^{29} +(63261.8 - 109573. i) q^{30} -195692. i q^{31} +(28377.9 + 16384.0i) q^{32} +(53144.1 + 30682.7i) q^{33} -81452.1i q^{34} +(-20251.8 + 35077.2i) q^{35} +(85578.4 + 148226. i) q^{36} +(-447631. + 258440. i) q^{37} -90448.7 q^{38} +(420021. + 358641. i) q^{39} +116138. q^{40} +(-563499. + 325336. i) q^{41} +(-49799.8 - 86255.7i) q^{42} +(346040. - 599359. i) q^{43} +56328.3i q^{44} +(525350. + 303311. i) q^{45} +(-638121. - 368419. i) q^{46} +523680. i q^{47} +(-142793. + 247325. i) q^{48} +(-395829. - 685596. i) q^{49} +(-184791. + 106689. i) q^{50} +709887. q^{51} +(-92325.8 + 498492. i) q^{52} -1.07679e6 q^{53} +(-235405. + 135911. i) q^{54} +(99820.8 + 172895. i) q^{55} +(45712.0 - 79175.4i) q^{56} -788296. i q^{57} +(1.09904e6 + 634533. i) q^{58} +(-1.80955e6 - 1.04475e6i) q^{59} +1.01219e6i q^{60} +(743353. - 1.28753e6i) q^{61} +(782769. + 1.35579e6i) q^{62} +(413556. - 238767. i) q^{63} -262144. q^{64} +(600003. + 1.69369e6i) q^{65} -490924. q^{66} +(-686834. + 396544. i) q^{67} +(325808. + 564317. i) q^{68} +(3.21092e6 - 5.56148e6i) q^{69} -324029. i q^{70} +(4.33418e6 + 2.50234e6i) q^{71} +(-1.18581e6 - 684627. i) q^{72} -2.74028e6i q^{73} +(2.06752e6 - 3.58104e6i) q^{74} +(-929839. - 1.61053e6i) q^{75} +(626647. - 361795. i) q^{76} +157158. q^{77} +(-4.34455e6 - 804656. i) q^{78} -2.95721e6 q^{79} +(-804627. + 464552. i) q^{80} +(1.73985e6 + 3.01351e6i) q^{81} +(2.60269e6 - 4.50799e6i) q^{82} +6.23432e6i q^{83} +(690046. + 398398. i) q^{84} +(2.00008e6 + 1.15475e6i) q^{85} +5.53664e6i q^{86} +(-5.53021e6 + 9.57861e6i) q^{87} +(-225313. - 390254. i) q^{88} +(-2.70251e6 + 1.56029e6i) q^{89} -4.85298e6 q^{90} +(1.39081e6 + 257592. i) q^{91} +5.89471e6 q^{92} +(-1.18163e7 + 6.82214e6i) q^{93} +(-2.09472e6 - 3.62816e6i) q^{94} +(1.28229e6 - 2.22099e6i) q^{95} -2.28469e6i q^{96} +(-5.04686e6 - 2.91380e6i) q^{97} +(5.48477e6 + 3.16663e6i) q^{98} -2.35375e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 512 q^{4} + 2520 q^{7} - 4684 q^{9} + 2432 q^{10} - 8496 q^{11} - 3620 q^{13} + 34560 q^{14} + 51648 q^{15} - 32768 q^{16} + 41520 q^{17} - 54432 q^{19} - 16128 q^{20} - 17280 q^{22} - 7560 q^{23}+ \cdots + 19031040 q^{98}+O(q^{100}) $ 16 * q + 512 * q^4 + 2520 * q^7 - 4684 * q^9 + 2432 * q^10 - 8496 * q^11 - 3620 * q^13 + 34560 * q^14 + 51648 * q^15 - 32768 * q^16 + 41520 * q^17 - 54432 * q^19 - 16128 * q^20 - 17280 * q^22 - 7560 * q^23 - 273960 * q^25 + 51072 * q^26 + 133920 * q^27 + 161280 * q^28 - 346056 * q^29 + 170368 * q^30 + 486300 * q^33 - 283248 * q^35 + 299776 * q^36 - 68280 * q^37 - 1059840 * q^38 - 1122680 * q^39 + 311296 * q^40 - 1288008 * q^41 + 408320 * q^42 + 285360 * q^43 + 5743980 * q^45 - 188928 * q^46 - 2131660 * q^49 + 85248 * q^50 + 957280 * q^51 + 354560 * q^52 + 3666600 * q^53 - 4074624 * q^54 - 1091472 * q^55 + 1105920 * q^56 + 3504000 * q^58 + 1799280 * q^59 - 4626000 * q^61 - 2770560 * q^62 - 8609760 * q^63 - 4194304 * q^64 - 11518020 * q^65 + 7941120 * q^66 - 7094400 * q^67 - 2657280 * q^68 + 18027316 * q^69 + 25958520 * q^71 + 4423680 * q^72 - 1142400 * q^74 - 10898032 * q^75 - 3483648 * q^76 - 20577480 * q^77 - 22023040 * q^78 + 34143488 * q^79 - 1032192 * q^80 - 15745864 * q^81 + 12202240 * q^82 + 17311488 * q^84 + 7123932 * q^85 - 10460440 * q^87 + 1105920 * q^88 + 10609452 * q^89 + 4070656 * q^90 - 38683952 * q^91 - 967680 * q^92 - 52747080 * q^93 - 14303616 * q^94 + 33837504 * q^95 + 83706300 * q^97 + 19031040 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−6.92820	+	4.00000i	−0.612372	+	0.353553i
$2$	−6.92820	+	4.00000i	−0.612372	+	0.353553i
$3$	−34.8616	−	60.3821i	−0.745458	−	1.29117i	−0.949981	−	0.312309i	$-0.898898\pi$
$3$	−34.8616	−	60.3821i	−0.745458	−	1.29117i	0.204523	−	0.978862i	$-0.434436\pi$
$4$	32.0000	−	55.4256i	0.250000	−	0.433013i
$5$		−	226.832i		−	0.811538i	−0.913976	−	0.405769i	$-0.867004\pi$
$5$		−	226.832i		−	0.811538i	0.913976	−	0.405769i	$-0.132996\pi$
$6$	483.056	+	278.893i	0.912995	+	0.527118i
$7$	−154.640	−	89.2812i	−0.170403	−	0.0983823i	0.412373	−	0.911015i	$-0.364700\pi$
$7$	−154.640	−	89.2812i	−0.170403	−	0.0983823i	−0.582776	+	0.812633i	$0.698033\pi$
$8$			512.000i			0.353553i
$9$	−1337.16	+	2316.03i	−0.611414	+	1.05900i
$10$	907.328	+	1571.54i	0.286922	+	0.496964i
$11$	−762.215	+	440.065i	−0.172664	+	0.0996879i	−0.583842	−	0.811868i	$-0.698451\pi$
$11$	−762.215	+	440.065i	−0.172664	+	0.0996879i	0.411177	+	0.911555i	$0.365118\pi$
$12$	−4462.28			−0.745458
$13$	−7466.71	+	2645.15i	−0.942600	+	0.333924i
$13$	−7466.71	+	2645.15i	−0.942600	+	0.333924i
$14$	1428.50			0.139134
$15$	−13696.6	+	7907.72i	−1.04783	+	0.604967i
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−5090.76	+	8817.45i	−0.251311	+	0.435283i	−0.963887	−	0.266312i	$-0.914195\pi$
$17$	−5090.76	+	8817.45i	−0.251311	+	0.435283i	0.712576	+	0.701595i	$0.247528\pi$
$18$		−	21394.6i		−	0.864670i
$19$	9791.36	+	5653.04i	0.327495	+	0.189080i	0.654729	−	0.755864i	$-0.272783\pi$
$19$	9791.36	+	5653.04i	0.327495	+	0.189080i	−0.327233	+	0.944944i	$0.606116\pi$
$20$	−12572.3	−	7258.62i	−0.351406	−	0.202885i
$21$			12449.9i			0.293359i
$22$	3520.52	−	6097.72i	0.0704900	−	0.122092i
$23$	46052.4	+	79765.1i	0.789232	+	1.36699i	0.926438	+	0.376448i	$0.122855\pi$
$23$	46052.4	+	79765.1i	0.789232	+	1.36699i	−0.137206	+	0.990543i	$0.543812\pi$
$24$	30915.6	−	17849.1i	0.456498	−	0.263559i
$25$	26672.3			0.341405
$26$	41150.3	−	48192.9i	0.459162	−	0.537745i
$27$	33977.8			0.332217
$28$	−9896.93	+	5714.00i	−0.0852015	+	0.0491911i
$29$	−79316.7	−	137381.i	−0.603909	−	1.04600i	−0.992223	−	0.124474i	$-0.960276\pi$
$29$	−79316.7	−	137381.i	−0.603909	−	1.04600i	0.388314	−	0.921527i	$-0.373058\pi$
$30$	63261.8	−	109573.i	0.427777	−	0.740931i
$31$		−	195692.i		−	1.17980i	−0.807477	−	0.589899i	$-0.799168\pi$
$31$		−	195692.i		−	1.17980i	0.807477	−	0.589899i	$-0.200832\pi$
$32$	28377.9	+	16384.0i	0.153093	+	0.0883883i
$33$	53144.1	+	30682.7i	0.257428	+	0.148626i
$34$		−	81452.1i		−	0.355407i
$35$	−20251.8	+	35077.2i	−0.0798410	+	0.138289i
$36$	85578.4	+	148226.i	0.305707	+	0.529500i
$37$	−447631.	+	258440.i	−1.45283	+	0.838790i	−0.998641	−	0.0521175i	$-0.983403\pi$
$37$	−447631.	+	258440.i	−1.45283	+	0.838790i	−0.454185	+	0.890907i	$0.650070\pi$
$38$	−90448.7			−0.267399
$39$	420021.	+	358641.i	1.13382	+	0.968131i
$40$	116138.			0.286922
$41$	−563499.	+	325336.i	−1.27688	+	0.737206i	−0.976273	−	0.216542i	$-0.930522\pi$
$41$	−563499.	+	325336.i	−1.27688	+	0.737206i	−0.300606	+	0.953749i	$0.597189\pi$
$42$	−49799.8	−	86255.7i	−0.103718	−	0.179645i
$43$	346040.	−	599359.i	0.663723	−	1.14960i	−0.315907	−	0.948790i	$-0.602309\pi$
$43$	346040.	−	599359.i	0.663723	−	1.14960i	0.979630	−	0.200812i	$-0.0643580\pi$
$44$			56328.3i			0.0996879i
$45$	525350.	+	303311.i	0.859419	+	0.496186i
$46$	−638121.	−	368419.i	−0.966608	−	0.558071i
$47$			523680.i			0.735738i	0.929878	+	0.367869i	$0.119913\pi$
$47$			523680.i			0.735738i	−0.929878	+	0.367869i	$0.880087\pi$
$48$	−142793.	+	247325.i	−0.186364	+	0.322793i
$49$	−395829.	−	685596.i	−0.480642	−	0.832496i
$50$	−184791.	+	106689.i	−0.209067	+	0.120705i
$51$	709887.			0.749366
$52$	−92325.8	+	498492.i	−0.0910566	+	0.491639i
$53$	−1.07679e6			−0.993492			−0.496746	−	0.867896i	$-0.665472\pi$
$53$	−1.07679e6			−0.993492			−0.496746	+	0.867896i	$0.665472\pi$
$54$	−235405.	+	135911.i	−0.203441	+	0.117456i
$55$	99820.8	+	172895.i	0.0809006	+	0.140124i
$56$	45712.0	−	79175.4i	0.0347834	−	0.0602466i
$57$		−	788296.i		−	0.563803i
$58$	1.09904e6	+	634533.i	0.739635	+	0.427028i
$59$	−1.80955e6	−	1.04475e6i	−1.14707	−	0.662260i	−0.198897	−	0.980020i	$-0.563736\pi$
$59$	−1.80955e6	−	1.04475e6i	−1.14707	−	0.662260i	−0.948171	+	0.317761i	$0.897069\pi$
$60$			1.01219e6i			0.604967i
$61$	743353.	−	1.28753e6i	0.419315	−	0.726275i	−0.576555	−	0.817058i	$-0.695604\pi$
$61$	743353.	−	1.28753e6i	0.419315	−	0.726275i	0.995871	+	0.0907826i	$0.0289368\pi$
$62$	782769.	+	1.35579e6i	0.417121	+	0.722475i
$63$	413556.	−	238767.i	0.208374	−	0.120305i
$64$	−262144.			−0.125000
$65$	600003.	+	1.69369e6i	0.270992	+	0.764956i
$66$	−490924.			−0.210189
$67$	−686834.	+	396544.i	−0.278991	+	0.161076i	−0.632967	−	0.774179i	$-0.718163\pi$
$67$	−686834.	+	396544.i	−0.278991	+	0.161076i	0.353976	+	0.935255i	$0.384830\pi$
$68$	325808.	+	564317.i	0.125655	+	0.217641i
$69$	3.21092e6	−	5.56148e6i	1.17668	−	2.03807i
$70$		−	324029.i		−	0.112912i
$71$	4.33418e6	+	2.50234e6i	1.43715	+	0.829740i	0.997651	−	0.0685019i	$-0.0218219\pi$
$71$	4.33418e6	+	2.50234e6i	1.43715	+	0.829740i	0.439501	+	0.898242i	$0.355155\pi$
$72$	−1.18581e6	−	684627.i	−0.374413	−	0.216167i
$73$		−	2.74028e6i		−	0.824450i	−0.911082	−	0.412225i	$-0.864752\pi$
$73$		−	2.74028e6i		−	0.824450i	0.911082	−	0.412225i	$-0.135248\pi$
$74$	2.06752e6	−	3.58104e6i	0.593114	−	1.02730i
$75$	−929839.	−	1.61053e6i	−0.254503	−	0.440812i
$76$	626647.	−	361795.i	0.163748	−	0.0945398i
$77$	157158.			0.0392301
$78$	−4.34455e6	−	804656.i	−1.03661	−	0.191990i
$79$	−2.95721e6			−0.674819			−0.337409	−	0.941358i	$-0.609551\pi$
$79$	−2.95721e6			−0.674819			−0.337409	+	0.941358i	$0.609551\pi$
$80$	−804627.	+	464552.i	−0.175703	+	0.101442i
$81$	1.73985e6	+	3.01351e6i	0.363760	+	0.630051i
$82$	2.60269e6	−	4.50799e6i	0.521284	−	0.902890i
$83$			6.23432e6i			1.19678i	0.801203	+	0.598392i	$0.204194\pi$
$83$			6.23432e6i			1.19678i	−0.801203	+	0.598392i	$0.795806\pi$
$84$	690046.	+	398398.i	0.127028	+	0.0733398i
$85$	2.00008e6	+	1.15475e6i	0.353249	+	0.203948i
$86$			5.53664e6i			0.938646i
$87$	−5.53021e6	+	9.57861e6i	−0.900377	+	1.55950i
$88$	−225313.	−	390254.i	−0.0352450	−	0.0610461i
$89$	−2.70251e6	+	1.56029e6i	−0.406352	+	0.234607i	−0.689221	−	0.724551i	$-0.742047\pi$
$89$	−2.70251e6	+	1.56029e6i	−0.406352	+	0.234607i	0.282869	+	0.959158i	$0.408714\pi$
$90$	−4.85298e6			−0.701713
$91$	1.39081e6	+	257592.i	0.193474	+	0.0358334i
$92$	5.89471e6			0.789232
$93$	−1.18163e7	+	6.82214e6i	−1.52332	+	0.879489i
$94$	−2.09472e6	−	3.62816e6i	−0.260123	−	0.450546i
$95$	1.28229e6	−	2.22099e6i	0.153445	−	0.265775i
$96$		−	2.28469e6i		−	0.263559i
$97$	−5.04686e6	−	2.91380e6i	−0.561462	−	0.324160i	0.192270	−	0.981342i	$-0.438415\pi$
$97$	−5.04686e6	−	2.91380e6i	−0.561462	−	0.324160i	−0.753732	+	0.657182i	$0.771748\pi$
$98$	5.48477e6	+	3.16663e6i	0.588664	+	0.339865i
$99$		−	2.35375e6i		−	0.243802i
$100$	853513.	−	1.47833e6i	0.0853513	−	0.147833i
$101$	−5.88075e6	−	1.01858e7i	−0.567947	−	0.983714i	−0.996769	−	0.0803245i	$-0.974404\pi$
$101$	−5.88075e6	−	1.01858e7i	−0.567947	−	0.983714i	0.428821	−	0.903389i	$-0.358929\pi$
$102$	−4.91824e6	+	2.83955e6i	−0.458891	+	0.264941i
$103$	−7.76395e6			−0.700087			−0.350044	−	0.936733i	$-0.613833\pi$
$103$	−7.76395e6			−0.700087			−0.350044	+	0.936733i	$0.613833\pi$
$104$	−1.35431e6	−	3.82295e6i	−0.118060	−	0.333259i
$105$	2.82404e6			0.238072
$106$	7.46020e6	−	4.30715e6i	0.608387	−	0.351252i
$107$	4.33599e6	+	7.51015e6i	0.342172	+	0.592660i	0.984836	−	0.173489i	$-0.0555041\pi$
$107$	4.33599e6	+	7.51015e6i	0.342172	+	0.592660i	−0.642664	+	0.766148i	$0.722171\pi$
$108$	1.08729e6	−	1.88324e6i	0.0830543	−	0.143854i
$109$		−	1.48382e7i		−	1.09746i	−0.835999	−	0.548731i	$-0.815111\pi$
$109$		−	1.48382e7i		−	1.09746i	0.835999	−	0.548731i	$-0.184889\pi$
$110$	−1.38316e6	−	798566.i	−0.0990825	−	0.0572053i
$111$	3.12102e7	+	1.80192e7i	2.16604	+	1.25056i
$112$			731391.i			0.0491911i
$113$	−6.26843e6	+	1.08572e7i	−0.408681	+	0.707856i	−0.994742	−	0.102411i	$-0.967344\pi$
$113$	−6.26843e6	+	1.08572e7i	−0.408681	+	0.707856i	0.586062	+	0.810267i	$0.300678\pi$
$114$	3.15319e6	+	5.46148e6i	0.199335	+	0.345258i
$115$	1.80933e7	−	1.04462e7i	1.10937	−	0.640492i
$116$	−1.01525e7			−0.603909
$117$	3.85795e6	−	2.08301e7i	0.222693	−	1.20238i
$118$	1.67159e7			0.936577
$119$	1.57446e6	−	909017.i	0.0856482	−	0.0494490i
$120$	−4.04875e6	−	7.01265e6i	−0.213888	−	0.370465i
$121$	−9.35627e6	+	1.62055e7i	−0.480125	+	0.831600i
$122$			1.18936e7i			0.593001i
$123$	3.92890e7	+	2.26835e7i	1.90372	+	1.09911i
$124$	−1.08464e7	−	6.26215e6i	−0.510867	−	0.294949i
$125$		−	2.37714e7i		−	1.08860i
$126$	−1.91013e6	+	3.30845e6i	−0.0850682	+	0.147342i
$127$	−1.73675e7	−	3.00813e7i	−0.752356	−	1.30312i	−0.946678	−	0.322181i	$-0.895584\pi$
$127$	−1.73675e7	−	3.00813e7i	−0.752356	−	1.30312i	0.194322	−	0.980938i	$-0.437749\pi$
$128$	1.81619e6	−	1.04858e6i	0.0765466	−	0.0441942i
$129$	−4.82541e7			−1.97911
$130$	−1.09317e7	−	9.33420e6i	−0.436401	−	0.372628i
$131$	−8.14415e6			−0.316516			−0.158258	−	0.987398i	$-0.550588\pi$
$131$	−8.14415e6			−0.316516			−0.158258	+	0.987398i	$0.550588\pi$
$132$	3.40122e6	−	1.96369e6i	0.128714	−	0.0743131i
$133$	−1.00942e6	−	1.74837e6i	−0.0372042	−	0.0644395i
$134$	3.17235e6	−	5.49467e6i	0.113898	−	0.197276i
$135$		−	7.70725e6i		−	0.269607i
$136$	−4.51453e6	−	2.60647e6i	−0.153896	−	0.0888518i
$137$	2.13418e7	+	1.23217e7i	0.709101	+	0.409400i	0.810728	−	0.585423i	$-0.199072\pi$
$137$	2.13418e7	+	1.23217e7i	0.709101	+	0.409400i	−0.101627	+	0.994823i	$0.532405\pi$
$138$			5.13747e7i			1.66407i
$139$	2.24507e7	−	3.88858e7i	0.709053	−	1.22812i	−0.256155	−	0.966636i	$-0.582456\pi$
$139$	2.24507e7	−	3.88858e7i	0.709053	−	1.22812i	0.965209	−	0.261481i	$-0.0842108\pi$
$140$	1.29612e6	+	2.24494e6i	0.0399205	+	0.0691443i
$141$	3.16209e7	−	1.82563e7i	0.949964	−	0.548462i
$142$	−4.00374e7			−1.17343
$143$	4.52720e6	−	5.30201e6i	0.129465	−	0.151623i
$144$	1.09540e7			0.305707
$145$	−3.11623e7	+	1.79916e7i	−0.848870	+	0.490095i
$146$	1.09611e7	+	1.89852e7i	0.291487	+	0.504871i
$147$	−2.75985e7	+	4.78020e7i	−0.716596	+	1.24118i
$148$			3.30803e7i			0.838790i
$149$	−1.06442e7	−	6.14542e6i	−0.263609	−	0.152195i	0.362371	−	0.932034i	$-0.381967\pi$
$149$	−1.06442e7	−	6.14542e6i	−0.263609	−	0.152195i	−0.625980	+	0.779839i	$0.715301\pi$
$150$	1.28842e7	+	7.43871e6i	0.311701	+	0.179961i
$151$			3.27158e7i			0.773283i	0.922230	+	0.386642i	$0.126365\pi$
$151$			3.27158e7i			0.773283i	−0.922230	+	0.386642i	$0.873635\pi$
$152$	−2.89436e6	+	5.01318e6i	−0.0668497	+	0.115787i
$153$	−1.36143e7	−	2.35807e7i	−0.307310	−	0.532276i
$154$	−1.08882e6	+	628632.i	−0.0240234	+	0.0138699i
$155$	−4.43892e7			−0.957451
$156$	3.33186e7	−	1.18034e7i	0.702668	−	0.248926i
$157$	−1.60558e7			−0.331117			−0.165559	−	0.986200i	$-0.552943\pi$
$157$	−1.60558e7			−0.331117			−0.165559	+	0.986200i	$0.552943\pi$
$158$	2.04881e7	−	1.18288e7i	0.413240	−	0.238585i
$159$	3.75385e7	+	6.50186e7i	0.740606	+	1.28277i
$160$	3.71641e6	−	6.43702e6i	0.0717305	−	0.124241i
$161$		−	1.64464e7i		−	0.310586i
$162$	−2.41081e7	−	1.39188e7i	−0.445513	−	0.257217i
$163$	−1.88846e7	−	1.09030e7i	−0.341548	−	0.197193i	0.319408	−	0.947617i	$-0.396516\pi$
$163$	−1.88846e7	−	1.09030e7i	−0.341548	−	0.197193i	−0.660956	+	0.750424i	$0.729849\pi$
$164$			4.16431e7i			0.737206i
$165$	6.95982e6	−	1.20548e7i	0.120616	−	0.208913i
$166$	−2.49373e7	−	4.31927e7i	−0.423127	−	0.732878i
$167$	7.64637e6	−	4.41464e6i	0.127042	−	0.0733478i	−0.435132	−	0.900367i	$-0.643298\pi$
$167$	7.64637e6	−	4.41464e6i	0.127042	−	0.0733478i	0.562174	+	0.827019i	$0.309965\pi$
$168$	−6.37437e6			−0.103718
$169$	4.87549e7	−	3.95011e7i	0.776989	−	0.629514i
$170$	−1.84759e7			−0.288426
$171$	−2.61853e7	+	1.51181e7i	−0.400471	+	0.231212i
$172$	−2.21466e7	−	3.83590e7i	−0.331862	−	0.574801i
$173$	3.97127e7	−	6.87844e7i	0.583133	−	1.01002i	−0.411972	−	0.911196i	$-0.635160\pi$
$173$	3.97127e7	−	6.87844e7i	0.583133	−	1.01002i	0.995105	−	0.0988198i	$-0.0315067\pi$
$174$		−	8.84834e7i		−	1.27333i
$175$	−4.12459e6	−	2.38133e6i	−0.0581765	−	0.0335882i
$176$	3.12203e6	+	1.80251e6i	0.0431661	+	0.0249220i
$177$			1.45686e8i			1.97475i
$178$	1.24824e7	−	2.16201e7i	0.165892	−	0.287334i
$179$	−9.22201e6	−	1.59730e7i	−0.120182	−	0.208162i	0.799657	−	0.600457i	$-0.205015\pi$
$179$	−9.22201e6	−	1.59730e7i	−0.120182	−	0.208162i	−0.919839	+	0.392295i	$0.871681\pi$
$180$	3.36224e7	−	1.94119e7i	0.429710	−	0.248093i
$181$	8.95446e7			1.12244			0.561222	−	0.827666i	$-0.310332\pi$
$181$	8.95446e7			1.12244			0.561222	+	0.827666i	$0.310332\pi$
$182$	−1.06662e7	+	3.77859e6i	−0.131147	+	0.0464600i
$183$	−1.03658e8			−1.25033
$184$	−4.08397e7	+	2.35788e7i	−0.483304	+	0.279036i
$185$	5.86224e7	+	1.01537e8i	0.680710	+	1.17902i
$186$	5.45771e7	−	9.45304e7i	0.621893	−	1.07715i
$187$		−	8.96105e6i		−	0.100211i
$188$	2.90253e7	+	1.67578e7i	0.318584	+	0.183935i
$189$	−5.25431e6	−	3.03358e6i	−0.0566108	−	0.0326843i
$190$			2.05166e7i			0.217005i
$191$	1.96790e7	−	3.40850e7i	0.204356	−	0.353954i	−0.745572	−	0.666425i	$-0.767823\pi$
$191$	1.96790e7	−	3.40850e7i	0.204356	−	0.353954i	0.949927	+	0.312471i	$0.101157\pi$
$192$	9.13876e6	+	1.58288e7i	0.0931822	+	0.161396i
$193$	−3.23971e6	+	1.87044e6i	−0.0324381	+	0.0187281i	−0.516131	−	0.856509i	$-0.672628\pi$
$193$	−3.23971e6	+	1.87044e6i	−0.0324381	+	0.0187281i	0.483693	+	0.875238i	$0.339295\pi$
$194$	4.66209e7			0.458431
$195$	8.13513e7	−	9.52741e7i	0.785675	−	0.920140i
$196$	−5.06661e7			−0.480642
$197$	−1.31060e8	+	7.56674e7i	−1.22134	+	0.705143i	−0.965204	−	0.261498i	$-0.915784\pi$
$197$	−1.31060e8	+	7.56674e7i	−1.22134	+	0.705143i	−0.256139	+	0.966640i	$0.582450\pi$
$198$	9.41501e6	+	1.63073e7i	0.0861971	+	0.149298i
$199$	8.18051e7	−	1.41691e8i	0.735859	−	1.27455i	−0.218486	−	0.975840i	$-0.570112\pi$
$199$	8.18051e7	−	1.41691e8i	0.735859	−	1.27455i	0.954345	−	0.298705i	$-0.0965548\pi$
$200$			1.36562e7i			0.120705i
$201$	4.78883e7	+	2.76483e7i	0.415952	+	0.240150i
$202$	8.14861e7	+	4.70460e7i	0.695591	+	0.401600i
$203$			2.83259e7i			0.237656i
$204$	2.27164e7	−	3.93460e7i	0.187341	−	0.324485i
$205$	7.37967e7	+	1.27820e8i	0.598271	+	1.03624i
$206$	5.37902e7	−	3.10558e7i	0.428714	−	0.247518i
$207$	−2.46318e8			−1.93019
$208$	2.46748e7	+	2.10689e7i	0.190122	+	0.162338i
$209$	−9.95082e6			−0.0753958
$210$	−1.95655e7	+	1.12962e7i	−0.145789	+	0.0841712i
$211$	6.37605e7	+	1.10436e8i	0.467265	+	0.809326i	0.999301	−	0.0373956i	$-0.0119062\pi$
$211$	6.37605e7	+	1.10436e8i	0.467265	+	0.809326i	−0.532036	+	0.846722i	$0.678573\pi$
$212$	−3.44572e7	+	5.96816e7i	−0.248373	+	0.430195i
$213$		−	3.48942e8i		−	2.47414i
$214$	−6.00812e7	−	3.46879e7i	−0.419074	−	0.241952i
$215$	−1.35954e8	−	7.84930e7i	−0.932946	−	0.538637i
$216$			1.73966e7i			0.117456i
$217$	−1.74716e7	+	3.02617e7i	−0.116071	+	0.201041i
$218$	5.93530e7	+	1.02802e8i	0.388012	+	0.672056i
$219$	−1.65464e8	+	9.55304e7i	−1.06451	+	0.614593i
$220$	1.27771e7			0.0809006
$221$	1.46877e7	−	7.93031e7i	0.0915340	−	0.494216i
$222$	−2.88308e8			−1.76856
$223$	7.36730e6	−	4.25351e6i	0.0444879	−	0.0256851i	−0.477591	−	0.878582i	$-0.658490\pi$
$223$	7.36730e6	−	4.25351e6i	0.0444879	−	0.0256851i	0.522079	+	0.852897i	$0.325157\pi$
$224$	−2.92557e6	−	5.06723e6i	−0.0173917	−	0.0301233i
$225$	−3.56652e7	+	6.17739e7i	−0.208740	+	0.361548i
$226$		−	1.00295e8i		−	0.577962i
$227$	8.08933e7	+	4.67037e7i	0.459010	+	0.265009i	0.711628	−	0.702557i	$-0.247958\pi$
$227$	8.08933e7	+	4.67037e7i	0.459010	+	0.265009i	−0.252618	+	0.967566i	$0.581292\pi$
$228$	−4.36918e7	−	2.52255e7i	−0.244134	−	0.140951i
$229$			3.51301e8i			1.93310i	0.256474	+	0.966551i	$0.417439\pi$
$229$			3.51301e8i			1.93310i	−0.256474	+	0.966551i	$0.582561\pi$
$230$	−8.35692e7	+	1.44746e8i	−0.452896	+	0.784440i
$231$	−5.47878e6	−	9.48953e6i	−0.0292444	−	0.0506527i
$232$	7.03388e7	−	4.06101e7i	0.369817	−	0.213514i
$233$	−1.12428e7			−0.0582274			−0.0291137	−	0.999576i	$-0.509268\pi$
$233$	−1.12428e7			−0.0582274			−0.0291137	+	0.999576i	$0.509268\pi$
$234$	5.65918e7	+	1.59747e8i	0.288734	+	0.815038i
$235$	1.18787e8			0.597080
$236$	−1.15811e8	+	6.68637e7i	−0.573534	+	0.331130i
$237$	1.03093e8	+	1.78562e8i	0.503049	+	0.871306i
$238$	−7.27214e6	+	1.25957e7i	−0.0349657	+	0.0605624i
$239$			5.94300e7i			0.281587i	0.990039	+	0.140794i	$0.0449654\pi$
$239$			5.94300e7i			0.281587i	−0.990039	+	0.140794i	$0.955035\pi$
$240$	5.61012e7	+	3.23900e7i	0.261959	+	0.151242i
$241$	−3.47888e7	−	2.00853e7i	−0.160096	−	0.0924312i	0.417812	−	0.908534i	$-0.362797\pi$
$241$	−3.47888e7	−	2.00853e7i	−0.160096	−	0.0924312i	−0.577907	+	0.816102i	$0.696130\pi$
$242$		−	1.49700e8i		−	0.678999i
$243$	1.58463e8	−	2.74466e8i	0.708444	−	1.22706i
$244$	−4.75746e7	−	8.24016e7i	−0.209658	−	0.363138i
$245$	−1.55515e8	+	8.97867e7i	−0.675603	+	0.390059i
$246$	−3.62936e8			−1.55438
$247$	−8.80623e7	−	1.63100e7i	−0.371835	−	0.0688678i
$248$	1.00194e8			0.417121
$249$	3.76441e8	−	2.17338e8i	1.54525	−	0.892152i
$250$	9.50855e7	+	1.64693e8i	0.384879	+	0.666630i
$251$	1.81995e8	−	3.15225e8i	0.726444	−	1.25824i	−0.231934	−	0.972732i	$-0.574505\pi$
$251$	1.81995e8	−	3.15225e8i	0.726444	−	1.25824i	0.958377	−	0.285505i	$-0.0921615\pi$
$252$		−	3.05621e7i		−	0.120305i
$253$	−7.02036e7	−	4.05321e7i	−0.272545	−	0.157354i
$254$	2.40651e8	+	1.38940e8i	0.921444	+	0.531996i
$255$		−	1.61025e8i		−	0.608139i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−2.57245e8	−	4.45562e8i	−0.945325	−	1.63735i	−0.755098	−	0.655612i	$-0.772411\pi$
$257$	−2.57245e8	−	4.45562e8i	−0.945325	−	1.63735i	−0.190227	−	0.981740i	$-0.560922\pi$
$258$	3.34314e8	−	1.93016e8i	1.21195	−	0.699721i
$259$	9.22952e7			0.330088
$260$	1.13074e8	+	2.09424e7i	0.398984	+	0.0738959i
$261$	4.24237e8			1.47695
$262$	5.64243e7	−	3.25766e7i	0.193826	−	0.111905i
$263$	−2.58989e8	−	4.48581e8i	−0.877881	−	1.52053i	−0.853662	−	0.520827i	$-0.825624\pi$
$263$	−2.58989e8	−	4.48581e8i	−0.877881	−	1.52053i	−0.0242186	−	0.999707i	$-0.507710\pi$
$264$	−1.57096e7	+	2.72098e7i	−0.0525473	+	0.0910146i
$265$			2.44250e8i			0.806257i
$266$	1.39869e7	+	8.07537e6i	0.0455656	+	0.0263073i
$267$	1.88428e8	+	1.08789e8i	0.605836	+	0.349780i
$268$			5.07576e7i			0.161076i
$269$	8.19954e6	−	1.42020e7i	0.0256836	−	0.0444854i	−0.852898	−	0.522078i	$-0.825157\pi$
$269$	8.19954e6	−	1.42020e7i	0.0256836	−	0.0444854i	0.878582	+	0.477592i	$0.158490\pi$
$270$	3.08290e7	+	5.33974e7i	0.0953204	+	0.165100i
$271$	−2.52866e8	+	1.45992e8i	−0.771787	+	0.445592i	−0.833512	−	0.552502i	$-0.813673\pi$
$271$	−2.52866e8	+	1.45992e8i	−0.771787	+	0.445592i	0.0617244	+	0.998093i	$0.480340\pi$
$272$	4.17035e7			0.125655
$273$	−3.29319e7	−	9.29600e7i	−0.0979597	−	0.276520i
$274$	−1.97147e8			−0.578979
$275$	−2.03300e7	+	1.17375e7i	−0.0589486	+	0.0340340i
$276$	−2.05499e8	−	3.55935e8i	−0.588339	−	1.01903i
$277$	−3.06025e8	+	5.30051e8i	−0.865122	+	1.49844i	0.00180331	+	0.999998i	$0.499426\pi$
$277$	−3.06025e8	+	5.30051e8i	−0.865122	+	1.49844i	−0.866926	+	0.498437i	$0.833907\pi$
$278$			3.59212e8i			1.00275i
$279$	4.53229e8	+	2.61672e8i	1.24941	+	0.721344i
$280$	−1.79595e7	−	1.03689e7i	−0.0488924	−	0.0282281i
$281$			5.99258e6i			0.0161117i	0.999968	+	0.00805586i	$0.00256429\pi$
$281$			5.99258e6i			0.0161117i	−0.999968	+	0.00805586i	$0.997436\pi$
$282$	−1.46051e8	+	2.52967e8i	−0.387821	+	0.671726i
$283$	−1.16811e8	−	2.02323e8i	−0.306360	−	0.530631i	0.671203	−	0.741274i	$-0.265778\pi$
$283$	−1.16811e8	−	2.02323e8i	−0.306360	−	0.530631i	−0.977563	+	0.210642i	$0.932445\pi$
$284$	2.77388e8	−	1.60150e8i	0.718576	−	0.414870i
$285$	−1.78811e8			−0.457548
$286$	−1.01573e7	+	5.48422e7i	−0.0256743	+	0.138622i
$287$	1.16186e8			0.290112
$288$	−7.58918e7	+	4.38161e7i	−0.187206	+	0.108084i
$289$	1.53338e8	+	2.65589e8i	0.373686	+	0.647243i
$290$	1.43932e8	−	2.49298e8i	0.346550	−	0.600242i
$291$			4.06320e8i			0.966590i
$292$	−1.51882e8	−	8.76889e7i	−0.356997	−	0.206113i
$293$	−2.52687e7	−	1.45889e7i	−0.0586875	−	0.0338833i	0.470369	−	0.882470i	$-0.344121\pi$
$293$	−2.52687e7	−	1.45889e7i	−0.0586875	−	0.0338833i	−0.529057	+	0.848586i	$0.677454\pi$
$294$		−	4.41576e8i		−	1.01342i
$295$	−2.36982e8	+	4.10464e8i	−0.537449	+	0.930890i
$296$	−1.32321e8	−	2.29187e8i	−0.296557	−	0.513652i
$297$	−2.58984e7	+	1.49524e7i	−0.0573621	+	0.0331180i
$298$	9.83267e7			0.215236
$299$	−5.54850e8	−	4.73767e8i	−1.20040	−	1.02498i
$300$	−1.19019e8			−0.254503
$301$	−1.07023e8	+	6.17897e7i	−0.226201	+	0.130597i
$302$	−1.30863e8	−	2.26662e8i	−0.273397	−	0.473537i
$303$	−4.10025e8	+	7.10184e8i	−0.846761	+	1.46663i
$304$		−	4.63097e7i		−	0.0945398i
$305$	−2.92052e8	−	1.68616e8i	−0.589400	−	0.340291i
$306$	1.88646e8	+	1.08915e8i	0.376376	+	0.217301i
$307$		−	2.78271e8i		−	0.548888i	−0.961603	−	0.274444i	$-0.911506\pi$
$307$		−	2.78271e8i		−	0.548888i	0.961603	−	0.274444i	$-0.0884938\pi$
$308$	5.02906e6	−	8.71058e6i	0.00980752	−	0.0169871i
$309$	2.70664e8	+	4.68803e8i	0.521885	+	0.903932i
$310$	3.07538e8	−	1.77557e8i	0.586317	−	0.338510i
$311$	1.22355e8			0.230655			0.115327	−	0.993328i	$-0.463208\pi$
$311$	1.22355e8			0.230655			0.115327	+	0.993328i	$0.463208\pi$
$312$	−1.83624e8	+	2.15051e8i	−0.342286	+	0.400866i
$313$	5.93289e8			1.09361			0.546804	−	0.837261i	$-0.315844\pi$
$313$	5.93289e8			1.09361			0.546804	+	0.837261i	$0.315844\pi$
$314$	1.11238e8	−	6.42230e7i	0.202767	−	0.117068i
$315$	−5.41599e7	−	9.38077e7i	−0.0976318	−	0.169103i
$316$	−9.46307e7	+	1.63905e8i	−0.168705	+	0.292205i
$317$			4.86395e8i			0.857594i	0.903401	+	0.428797i	$0.141062\pi$
$317$			4.86395e8i			0.857594i	−0.903401	+	0.428797i	$0.858938\pi$
$318$	−5.20149e8	−	3.00308e8i	−0.907054	−	0.523688i
$319$	1.20913e8	+	6.98090e7i	0.208547	+	0.120405i
$320$			5.94626e7i			0.101442i
$321$	3.02319e8	−	5.23632e8i	0.510150	−	0.883605i
$322$	6.57858e7	+	1.13944e8i	0.109809	+	0.190194i
$323$	−9.96908e7	+	5.75565e7i	−0.164606	+	0.0950355i
$324$	2.22701e8			0.363760
$325$	−1.99154e8	+	7.05521e7i	−0.321809	+	0.114003i
$326$	1.74449e8			0.278873
$327$	−8.95963e8	+	5.17285e8i	−1.41701	+	0.818112i
$328$	−1.66572e8	−	2.88512e8i	−0.260642	−	0.451445i
$329$	4.67548e7	−	8.09816e7i	0.0723836	−	0.125372i
$330$			1.11357e8i			0.170577i
$331$	3.35527e8	+	1.93717e8i	0.508545	+	0.293609i	0.732235	−	0.681052i	$-0.238477\pi$
$331$	3.35527e8	+	1.93717e8i	0.508545	+	0.293609i	−0.223690	+	0.974660i	$0.571810\pi$
$332$	3.45541e8	+	1.99498e8i	0.518223	+	0.299196i
$333$		−	1.38230e9i		−	2.05139i
$334$	−3.53171e7	+	6.11710e7i	−0.0518647	+	0.0898324i
$335$	8.99488e7	+	1.55796e8i	0.130719	+	0.226412i
$336$	4.41629e7	−	2.54975e7i	0.0635141	−	0.0366699i
$337$	7.84207e8			1.11616			0.558079	−	0.829788i	$-0.311539\pi$
$337$	7.84207e8			1.11616			0.558079	+	0.829788i	$0.311539\pi$
$338$	−1.79780e8	+	4.68691e8i	−0.253240	+	0.660204i
$339$	8.74110e8			1.21862
$340$	1.28005e8	−	7.39037e7i	0.176624	−	0.101974i
$341$	8.61173e7	+	1.49159e8i	0.117612	+	0.203709i
$342$	1.20945e8	−	2.09482e8i	0.163491	−	0.283175i
$343$			2.88414e8i			0.385911i
$344$	3.06872e8	+	1.77173e8i	0.406446	+	0.234662i
$345$	−1.26152e9	−	7.28339e8i	−1.65397	−	0.954920i
$346$			6.35403e8i			0.824675i
$347$	−2.63084e8	+	4.55676e8i	−0.338020	+	0.585467i	−0.984060	−	0.177836i	$-0.943090\pi$
$347$	−2.63084e8	+	4.55676e8i	−0.338020	+	0.585467i	0.646041	+	0.763303i	$0.276424\pi$
$348$	3.53934e8	+	6.13031e8i	0.450189	+	0.779749i
$349$	−5.22169e7	+	3.01474e7i	−0.0657539	+	0.0379631i	−0.532517	−	0.846420i	$-0.678754\pi$
$349$	−5.22169e7	+	3.01474e7i	−0.0657539	+	0.0379631i	0.466763	+	0.884383i	$0.345420\pi$
$350$	3.81013e7			0.0475009
$351$	−2.53702e8	+	8.98762e7i	−0.313148	+	0.110935i
$352$	−2.88401e7			−0.0352450
$353$	4.16560e8	−	2.40501e8i	0.504042	−	0.291009i	−0.226339	−	0.974048i	$-0.572676\pi$
$353$	4.16560e8	−	2.40501e8i	0.504042	−	0.291009i	0.730381	+	0.683040i	$0.239343\pi$
$354$	−5.82744e8	−	1.00934e9i	−0.698178	−	1.20928i
$355$	5.67611e8	−	9.83130e8i	0.673366	−	1.16630i
$356$			1.99718e8i			0.234607i
$357$	−1.09777e8	−	6.33796e7i	−0.127694	−	0.0737243i
$358$	1.27784e8	+	7.37761e7i	0.147193	+	0.0849816i
$359$		−	1.69698e9i		−	1.93574i	−0.251453	−	0.967869i	$-0.580909\pi$
$359$		−	1.69698e9i		−	1.93574i	0.251453	−	0.967869i	$-0.419091\pi$
$360$	−1.55295e8	+	2.68979e8i	−0.175428	+	0.303851i
$361$	−3.83022e8	−	6.63414e8i	−0.428498	−	0.742180i
$362$	−6.20383e8	+	3.58178e8i	−0.687353	+	0.396844i
$363$	1.30470e9			1.43165
$364$	5.87831e7	−	6.88436e7i	0.0638848	−	0.0748184i
$365$	−6.21582e8			−0.669073
$366$	7.18163e8	−	4.14632e8i	0.765666	−	0.442057i
$367$	5.87011e7	+	1.01673e8i	0.0619890	+	0.107368i	0.895354	−	0.445354i	$-0.146922\pi$
$367$	5.87011e7	+	1.01673e8i	0.0619890	+	0.107368i	−0.833365	+	0.552722i	$0.813589\pi$
$368$	1.88631e8	−	3.26718e8i	0.197308	−	0.341748i
$369$		−	1.74011e9i		−	1.80295i
$370$	−8.12295e8	−	4.68979e8i	−0.833696	−	0.481335i
$371$	1.66514e8	+	9.61368e7i	0.169294	+	0.0977420i
$372$			8.73234e8i			0.879489i
$373$	1.70210e8	−	2.94812e8i	0.169826	−	0.294147i	−0.768533	−	0.639811i	$-0.779013\pi$
$373$	1.70210e8	−	2.94812e8i	0.169826	−	0.294147i	0.938359	+	0.345664i	$0.112346\pi$
$374$	3.58442e7	+	6.20840e7i	0.0354298	+	0.0613662i
$375$	−1.43536e9	+	8.28708e8i	−1.40557	+	0.811507i
$376$	−2.68124e8			−0.260123
$377$	9.55626e8	+	8.15976e8i	0.918530	+	0.784301i
$378$	4.85372e7			0.0462225
$379$	1.37316e9	−	7.92793e8i	1.29564	−	0.748036i	0.315990	−	0.948763i	$-0.397664\pi$
$379$	1.37316e9	−	7.92793e8i	1.29564	−	0.748036i	0.979647	+	0.200726i	$0.0643302\pi$
$380$	−8.20666e7	−	1.42144e8i	−0.0767227	−	0.132888i
$381$	−1.21092e9	+	2.09737e9i	−1.12170	+	1.94284i
$382$			3.14864e8i			0.289002i
$383$	1.17380e9	+	6.77692e8i	1.06757	+	0.616364i	0.927517	−	0.373780i	$-0.121939\pi$
$383$	1.17380e9	+	6.77692e8i	1.06757	+	0.616364i	0.140056	+	0.990144i	$0.455272\pi$
$384$	−1.26630e8	−	7.31101e7i	−0.114124	−	0.0658898i
$385$		−	3.56485e7i		−	0.0318367i
$386$	1.49636e7	−	2.59176e7i	0.0132428	−	0.0229372i
$387$	9.25424e8	+	1.60288e9i	0.811619	+	1.40577i
$388$	−3.22999e8	+	1.86484e8i	−0.280731	+	0.162080i
$389$	1.20573e9			1.03855			0.519275	−	0.854607i	$-0.326202\pi$
$389$	1.20573e9			1.03855			0.519275	+	0.854607i	$0.326202\pi$
$390$	−1.82522e8	+	9.85483e8i	−0.155807	+	0.841246i
$391$	−9.37766e8			−0.793370
$392$	3.51025e8	−	2.02665e8i	0.294332	−	0.169933i
$393$	2.83918e8	+	4.91760e8i	0.235949	+	0.408676i
$394$	6.05339e8	−	1.04848e9i	0.498611	−	0.863620i
$395$			6.70789e8i			0.547642i
$396$	−1.30458e8	−	7.53201e7i	−0.105569	−	0.0609505i
$397$	−1.91356e9	−	1.10479e9i	−1.53488	−	0.886163i	−0.999127	−	0.0417879i	$-0.986695\pi$
$397$	−1.91356e9	−	1.10479e9i	−1.53488	−	0.886163i	−0.535753	−	0.844375i	$-0.679972\pi$
$398$			1.30888e9i			1.04066i
$399$	−7.03800e7	+	1.21902e8i	−0.0554682	+	0.0960738i
$400$	−5.46248e7	−	9.46130e7i	−0.0426757	−	0.0739164i
$401$	−1.42835e9	+	8.24656e8i	−1.10619	+	0.638657i	−0.937839	−	0.347071i	$-0.887176\pi$
$401$	−1.42835e9	+	8.24656e8i	−1.10619	+	0.638657i	−0.168347	+	0.985728i	$0.553843\pi$
$402$	−4.42373e8			−0.339623
$403$	5.17634e8	+	1.46118e9i	0.393963	+	1.11208i
$404$	−7.52736e8			−0.567947
$405$	6.83561e8	−	3.94654e8i	0.511311	−	0.295205i
$406$	−1.13304e8	−	1.96248e8i	−0.0840240	−	0.145534i
$407$	2.27460e8	−	3.93973e8i	0.167234	−	0.289658i
$408$			3.63462e8i			0.264941i
$409$	−1.80735e9	−	1.04348e9i	−1.30620	−	0.754138i	−0.324744	−	0.945802i	$-0.605278\pi$
$409$	−1.80735e9	−	1.04348e9i	−1.30620	−	0.754138i	−0.981461	+	0.191664i	$0.938612\pi$
$410$	−1.02256e9	−	5.90373e8i	−0.732730	−	0.423042i
$411$		−	1.71821e9i		−	1.22076i
$412$	−2.48446e8	+	4.30322e8i	−0.175022	+	0.303147i
$413$	1.86552e8	+	3.23118e8i	0.130309	+	0.225702i
$414$	1.70654e9	−	9.85272e8i	1.18200	−	0.682425i
$415$	1.41414e9			0.971237
$416$	−2.55228e8	−	4.72708e7i	−0.173821	−	0.0321934i
$417$	−3.13068e9			−2.11428
$418$	6.89413e7	−	3.98033e7i	0.0461703	−	0.0266564i
$419$	2.16651e8	+	3.75251e8i	0.143884	+	0.249214i	0.928956	−	0.370190i	$-0.120707\pi$
$419$	2.16651e8	+	3.75251e8i	0.143884	+	0.249214i	−0.785072	+	0.619405i	$0.787374\pi$
$420$	9.03694e7	−	1.56524e8i	0.0595181	−	0.103088i
$421$		−	2.20780e9i		−	1.44203i	−0.692922	−	0.721013i	$-0.743677\pi$
$421$		−	2.20780e9i		−	1.44203i	0.692922	−	0.721013i	$-0.256323\pi$
$422$	−8.83491e8	−	5.10084e8i	−0.572280	−	0.330406i
$423$	−1.21286e9	−	7.00245e8i	−0.779147	−	0.449841i
$424$		−	5.51315e8i		−	0.351252i
$425$	−1.35782e8	+	2.35181e8i	−0.0857988	+	0.148608i
$426$	1.39577e9	+	2.41754e9i	0.874742	+	1.51510i
$427$	−2.29904e8	+	1.32735e8i	−0.142905	+	0.0825064i
$428$	5.55006e8			0.342172
$429$	−4.77971e8	−	8.85252e7i	−0.292282	−	0.0541335i
$430$	1.25589e9			0.761748
$431$	−2.38463e9	+	1.37676e9i	−1.43466	+	0.828303i	−0.997472	−	0.0710652i	$-0.977360\pi$
$431$	−2.38463e9	+	1.37676e9i	−1.43466	+	0.828303i	−0.437192	+	0.899368i	$0.644027\pi$
$432$	−6.95865e7	−	1.20527e8i	−0.0415271	−	0.0719271i
$433$	−1.01907e9	+	1.76508e9i	−0.603248	+	1.04486i	0.389077	+	0.921205i	$0.372794\pi$
$433$	−1.01907e9	+	1.76508e9i	−0.603248	+	1.04486i	−0.992326	+	0.123652i	$0.960539\pi$
$434$		−	2.79546e8i		−	0.164149i
$435$	2.17273e9	+	1.25443e9i	1.26559	+	0.730691i
$436$	−8.22419e8	−	4.74824e8i	−0.475215	−	0.274366i
$437$			1.04134e9i			0.596911i
$438$	7.64244e8	−	1.32371e9i	0.434583	−	0.752719i
$439$	−1.20861e9	−	2.09338e9i	−0.681806	−	1.18092i	−0.974429	−	0.224694i	$-0.927862\pi$
$439$	−1.20861e9	−	2.09338e9i	−0.681806	−	1.18092i	0.292624	−	0.956228i	$-0.405472\pi$
$440$	−8.85221e7	+	5.11082e7i	−0.0495413	+	0.0286027i
$441$	2.11715e9			1.17548
$442$	2.15453e8	+	6.08179e8i	0.118679	+	0.335007i
$443$	2.45177e9			1.33988			0.669941	−	0.742415i	$-0.266320\pi$
$443$	2.45177e9			1.33988			0.669941	+	0.742415i	$0.266320\pi$
$444$	1.99746e9	−	1.15323e9i	1.08302	−	0.625282i
$445$	3.53925e8	+	6.13015e8i	0.190393	+	0.329770i
$446$	−3.40281e7	+	5.89384e7i	−0.0181621	+	0.0314577i
$447$			8.56957e8i			0.453819i
$448$	4.05378e7	+	2.34045e7i	0.0213004	+	0.0122978i
$449$	2.43087e9	+	1.40347e9i	1.26736	+	0.731711i	0.974488	−	0.224441i	$-0.0720555\pi$
$449$	2.43087e9	+	1.40347e9i	1.26736	+	0.731711i	0.292873	+	0.956151i	$0.405389\pi$
$450$		−	5.70643e8i		−	0.295203i
$451$	2.86338e8	−	4.95952e8i	0.146981	−	0.254579i
$452$	4.01179e8	+	6.94863e8i	0.204340	+	0.353928i
$453$	1.97545e9	−	1.14053e9i	0.998440	−	0.576450i
$454$	−7.47260e8			−0.374780
$455$	5.84301e7	−	3.15480e8i	0.0290802	−	0.157012i
$456$	4.03608e8			0.199335
$457$	1.13462e8	−	6.55075e7i	0.0556090	−	0.0321059i	−0.471938	−	0.881632i	$-0.656445\pi$
$457$	1.13462e8	−	6.55075e7i	0.0556090	−	0.0321059i	0.527547	+	0.849526i	$0.323112\pi$
$458$	−1.40520e9	−	2.43388e9i	−0.683455	−	1.18378i
$459$	−1.72973e8	+	2.99597e8i	−0.0834897	+	0.144608i
$460$		−	1.33711e9i		−	0.640492i
$461$	−1.54398e9	−	8.91418e8i	−0.733987	−	0.423768i	0.0858917	−	0.996304i	$-0.472626\pi$
$461$	−1.54398e9	−	8.91418e8i	−0.733987	−	0.423768i	−0.819879	+	0.572537i	$0.805959\pi$
$462$	7.59162e7	+	4.38302e7i	0.0358169	+	0.0206789i
$463$		−	1.77948e9i		−	0.833221i	−0.909085	−	0.416611i	$-0.863218\pi$
$463$		−	1.77948e9i		−	0.833221i	0.909085	−	0.416611i	$-0.136782\pi$
$464$	−3.24881e8	+	5.62711e8i	−0.150977	+	0.261500i
$465$	1.54748e9	+	2.68031e9i	0.713739	+	1.23623i
$466$	7.78921e7	−	4.49710e7i	0.0356568	−	0.0205865i
$467$	4.43694e8			0.201592			0.100796	−	0.994907i	$-0.467861\pi$
$467$	4.43694e8			0.201592			0.100796	+	0.994907i	$0.467861\pi$
$468$	−1.03107e9	−	8.80393e8i	−0.464972	−	0.397024i
$469$	1.41616e8			0.0633879
$470$	−8.22983e8	+	4.75149e8i	−0.365635	+	0.211100i
$471$	5.59729e8	+	9.69480e8i	0.246834	+	0.427529i
$472$	5.34910e8	−	9.26491e8i	0.234144	−	0.405550i
$473$			6.09121e8i			0.264661i
$474$	−1.42850e9	−	8.24744e8i	−0.616106	−	0.355709i
$475$	2.61158e8	+	1.50780e8i	0.111809	+	0.0645528i
$476$		−	1.16354e8i		−	0.0494490i
$477$	1.43984e9	−	2.49387e9i	0.607435	−	1.05211i
$478$	−2.37720e8	−	4.11743e8i	−0.0995561	−	0.172436i
$479$	−1.77489e9	+	1.02473e9i	−0.737900	+	0.426027i	−0.821305	−	0.570489i	$-0.806754\pi$
$479$	−1.77489e9	+	1.02473e9i	−0.737900	+	0.426027i	0.0834055	+	0.996516i	$0.473420\pi$
$480$	−5.18240e8			−0.213888
$481$	2.65872e9	−	3.11374e9i	1.08934	−	1.27578i
$482$	3.21365e8			0.130717
$483$	−9.93070e8	+	5.73349e8i	−0.401019	+	0.231529i
$484$	5.98801e8	+	1.03715e9i	0.240062	+	0.415800i
$485$	−6.60944e8	+	1.14479e9i	−0.263068	+	0.455648i
$486$			2.53541e9i			1.00189i
$487$	−2.95096e9	−	1.70374e9i	−1.15774	−	0.668423i	−0.206980	−	0.978345i	$-0.566364\pi$
$487$	−2.95096e9	−	1.70374e9i	−1.15774	−	0.668423i	−0.950762	+	0.309923i	$0.899697\pi$
$488$	6.59213e8	+	3.80597e8i	0.256777	+	0.148250i
$489$			1.52039e9i			0.587996i
$490$	7.18294e8	−	1.24412e9i	0.275814	−	0.477723i
$491$	−1.89288e9	−	3.27857e9i	−0.721670	−	1.24997i	−0.960330	−	0.278866i	$-0.910041\pi$
$491$	−1.89288e9	−	3.27857e9i	−0.721670	−	1.24997i	0.238660	−	0.971103i	$-0.423292\pi$
$492$	2.51449e9	−	1.45174e9i	0.951859	−	0.549556i
$493$	1.61513e9			0.607075
$494$	6.75354e8	−	2.39250e8i	0.252050	−	0.0892910i
$495$	−5.33906e8			−0.197855
$496$	−6.94167e8	+	4.00778e8i	−0.255434	+	0.147475i
$497$	−4.46824e8	−	7.73921e8i	−0.163263	−	0.282781i
$498$	−1.73871e9	+	3.01153e9i	−0.630847	+	1.09266i
$499$			3.07456e9i			1.10772i	0.832609	+	0.553861i	$0.186846\pi$
$499$			3.07456e9i			1.10772i	−0.832609	+	0.553861i	$0.813154\pi$
$500$	−1.31754e9	−	7.60684e8i	−0.471378	−	0.272151i
$501$	−5.33130e8	−	3.07802e8i	−0.189409	−	0.109355i
$502$			2.91192e9i			1.02735i
$503$	−1.74726e9	+	3.02635e9i	−0.612168	+	1.06031i	0.378706	+	0.925517i	$0.376369\pi$
$503$	−1.74726e9	+	3.02635e9i	−0.612168	+	1.06031i	−0.990874	+	0.134789i	$0.956964\pi$
$504$	1.22249e8	+	2.11741e8i	0.0425341	+	0.0736712i
$505$	−2.31046e9	+	1.33394e9i	−0.798322	+	0.460911i
$506$	6.48513e8			0.222532
$507$	−4.08483e9	−	1.56685e9i	−1.39202	−	0.533950i
$508$	−2.22304e9			−0.752356
$509$	2.35781e9	−	1.36129e9i	0.792497	−	0.457548i	−0.0483440	−	0.998831i	$-0.515394\pi$
$509$	2.35781e9	−	1.36129e9i	0.792497	−	0.457548i	0.840841	+	0.541283i	$0.182061\pi$
$510$	6.44100e8	+	1.11561e9i	0.215010	+	0.372408i
$511$	−2.44655e8	+	4.23755e8i	−0.0811113	+	0.140489i
$512$		−	1.34218e8i		−	0.0441942i
$513$	3.32689e8	+	1.92078e8i	0.108800	+	0.0628155i
$514$	3.56449e9	+	2.05796e9i	1.15778	+	0.668446i
$515$			1.76111e9i			0.568148i
$516$	−1.54413e9	+	2.67451e9i	−0.494777	+	0.856980i
$517$	−2.30453e8	−	3.99157e8i	−0.0733442	−	0.127036i
$518$	−6.39440e8	+	3.69181e8i	−0.202137	+	0.116704i
$519$	−5.53779e9			−1.73880
$520$	−8.67168e8	+	3.07202e8i	−0.270453	+	0.0958103i
$521$	3.75722e9			1.16395			0.581975	−	0.813206i	$-0.302280\pi$
$521$	3.75722e9			1.16395			0.581975	+	0.813206i	$0.302280\pi$
$522$	−2.93920e9	+	1.69695e9i	−0.904446	+	0.522182i
$523$	−2.03887e9	−	3.53143e9i	−0.623210	−	1.07943i	−0.988884	−	0.148689i	$-0.952495\pi$
$523$	−2.03887e9	−	3.53143e9i	−0.623210	−	1.07943i	0.365674	−	0.930743i	$-0.380839\pi$
$524$	−2.60613e8	+	4.51394e8i	−0.0791291	+	0.137056i
$525$			3.32068e8i			0.100154i
$526$	3.58865e9	+	2.07191e9i	1.07518	+	0.620755i
$527$	1.72551e9	+	9.96221e8i	0.513546	+	0.296496i
$528$		−	2.51353e8i		−	0.0743131i
$529$	−2.53923e9	+	4.39808e9i	−0.745775	+	1.29172i
$530$	−9.76999e8	−	1.69221e9i	−0.285055	−	0.493730i
$531$	4.83933e9	−	2.79399e9i	1.40267	−	0.809830i
$532$	−1.29206e8			−0.0372042
$533$	3.34692e9	−	3.91973e9i	0.957415	−	1.12127i
$534$	−1.74062e9			−0.494663
$535$	1.70354e9	−	9.83540e8i	0.480966	−	0.277686i
$536$	−2.03031e8	−	3.51659e8i	−0.0569488	−	0.0986382i
$537$	−6.42988e8	+	1.11369e9i	−0.179181	+	0.310351i
$538$			1.31193e8i			0.0363222i
$539$	6.03414e8	+	3.48381e8i	0.165980	+	0.0958283i
$540$	−4.27179e8	−	2.46632e8i	−0.116743	−	0.0674017i
$541$			7.00434e7i			0.0190185i	0.999955	+	0.00950926i	$0.00302694\pi$
$541$			7.00434e7i			0.0190185i	−0.999955	+	0.00950926i	$0.996973\pi$
$542$	1.16794e9	−	2.02293e9i	0.315081	−	0.545736i
$543$	−3.12167e9	−	5.40689e9i	−0.836734	−	1.44927i
$544$	−2.88930e8	+	1.66814e8i	−0.0769479	+	0.0444259i
$545$	−3.36579e9			−0.890633
$546$	5.99999e8	+	5.12318e8i	0.157753	+	0.134699i
$547$	6.87329e9			1.79560			0.897799	−	0.440405i	$-0.145165\pi$
$547$	6.87329e9			1.79560			0.897799	+	0.440405i	$0.145165\pi$
$548$	1.36587e9	−	7.88587e8i	0.354551	−	0.204700i
$549$	1.98797e9	+	3.44326e9i	0.512750	+	0.888110i
$550$	9.39003e7	−	1.62640e8i	0.0240657	−	0.0416829i
$551$		−	1.79352e9i		−	0.456748i
$552$	2.84748e9	+	1.64399e9i	0.720565	+	0.416019i
$553$	4.57301e8	+	2.64023e8i	0.114991	+	0.0663902i
$554$		−	4.89640e9i		−	1.22347i
$555$	4.08734e9	−	7.07948e9i	1.01488	−	1.75783i
$556$	−1.43685e9	−	2.48869e9i	−0.354527	−	0.614058i
$557$	7.42705e8	−	4.28801e8i	0.182105	−	0.105139i	−0.406176	−	0.913795i	$-0.633138\pi$
$557$	7.42705e8	−	4.28801e8i	0.182105	−	0.105139i	0.588282	+	0.808656i	$0.299805\pi$
$558$	−4.18675e9			−1.02014
$559$	−9.98388e8	+	5.39057e9i	−0.241745	+	1.30525i
$560$	1.65903e8			0.0399205
$561$	−5.41087e8	+	3.12397e8i	−0.129389	+	0.0747027i
$562$	−2.39703e7	−	4.15178e7i	−0.00569635	−	0.00986637i
$563$	2.31984e9	−	4.01808e9i	0.547871	−	0.948940i	−0.450549	−	0.892752i	$-0.648772\pi$
$563$	2.31984e9	−	4.01808e9i	0.547871	−	0.948940i	0.998420	−	0.0561888i	$-0.0178949\pi$
$564$		−	2.33681e9i		−	0.548462i
$565$	2.46277e9	+	1.42188e9i	0.574452	+	0.331660i
$566$	1.61858e9	+	9.34490e8i	0.375213	+	0.216629i
$567$		−	6.21345e8i		−	0.143150i
$568$	−1.28120e9	+	2.21910e9i	−0.293357	+	0.508110i
$569$	2.82835e9	+	4.89884e9i	0.643635	+	1.11481i	0.984615	+	0.174738i	$0.0559079\pi$
$569$	2.82835e9	+	4.89884e9i	0.643635	+	1.11481i	−0.340980	+	0.940071i	$0.610759\pi$
$570$	1.23884e9	−	7.15243e8i	0.280190	−	0.161768i
$571$	−6.69059e9			−1.50397			−0.751983	−	0.659182i	$-0.770902\pi$
$571$	−6.69059e9			−1.50397			−0.751983	+	0.659182i	$0.770902\pi$
$572$	−1.48997e8	−	4.20587e8i	−0.0332882	−	0.0939658i
$573$	−2.74417e9			−0.609353
$574$	−8.04958e8	+	4.64743e8i	−0.177657	+	0.102570i
$575$	1.22832e9	+	2.12752e9i	0.269448	+	0.466698i
$576$	3.50529e8	−	6.07134e8i	0.0764267	−	0.132375i
$577$			3.61605e8i			0.0783644i	0.999232	+	0.0391822i	$0.0124753\pi$
$577$			3.61605e8i			0.0783644i	−0.999232	+	0.0391822i	$0.987525\pi$
$578$	−2.12471e9	−	1.22670e9i	−0.457670	−	0.264236i
$579$	2.25883e8	+	1.30413e8i	0.0483624	+	0.0279220i
$580$			2.30292e9i			0.490095i
$581$	5.56608e8	−	9.64073e8i	0.117742	−	0.203936i
$582$	−1.62528e9	−	2.81506e9i	−0.341741	−	0.591913i
$583$	8.20743e8	−	4.73856e8i	0.171541	−	0.0990391i
$584$	1.40302e9			0.291487
$585$	−4.72494e9	−	8.75107e8i	−0.975777	−	0.180724i
$586$	2.33422e8			0.0479182
$587$	8.36022e8	−	4.82677e8i	0.170602	−	0.0984971i	−0.412268	−	0.911063i	$-0.635263\pi$
$587$	8.36022e8	−	4.82677e8i	0.170602	−	0.0984971i	0.582870	+	0.812566i	$0.301930\pi$
$588$	1.76630e9	+	3.05933e9i	0.358298	+	0.620590i
$589$	1.10626e9	−	1.91609e9i	0.223076	−	0.386378i
$590$		−	3.79171e9i		−	0.760068i
$591$	9.13790e9	+	5.27577e9i	1.82092	+	1.05131i
$592$	1.83349e9	+	1.05857e9i	0.363207	+	0.209697i
$593$			4.97419e9i			0.979560i	0.871846	+	0.489780i	$0.162923\pi$
$593$			4.97419e9i			0.979560i	−0.871846	+	0.489780i	$0.837077\pi$
$594$	1.19619e8	−	2.07187e8i	0.0234180	−	0.0405611i
$595$	−2.06194e8	−	3.57139e8i	−0.0401298	−	0.0695068i
$596$	−6.81228e8	+	3.93307e8i	−0.131805	+	0.0760974i
$597$	−1.14074e10			−2.19421
$598$	5.73918e9	+	1.06296e9i	1.09748	+	0.203264i
$599$	−5.55418e9			−1.05591			−0.527954	−	0.849273i	$-0.677041\pi$
$599$	−5.55418e9			−1.05591			−0.527954	+	0.849273i	$0.677041\pi$
$600$	8.24590e8	−	4.76077e8i	0.155851	−	0.0899805i
$601$	5.43311e8	+	9.41043e8i	0.102091	+	0.176827i	0.912546	−	0.408974i	$-0.134113\pi$
$601$	5.43311e8	+	9.41043e8i	0.102091	+	0.176827i	−0.810455	+	0.585801i	$0.800780\pi$
$602$	4.94318e8	−	8.56184e8i	0.0923461	−	0.159948i
$603$		−	2.12097e9i		−	0.393935i
$604$	1.81329e9	+	1.04691e9i	0.334841	+	0.193321i
$605$	3.67593e9	+	2.12230e9i	0.674876	+	0.389640i
$606$		−	6.56040e9i		−	1.19750i
$607$	−1.41161e9	+	2.44499e9i	−0.256186	+	0.443727i	−0.965217	−	0.261450i	$-0.915799\pi$
$607$	−1.41161e9	+	2.44499e9i	−0.256186	+	0.443727i	0.709031	+	0.705177i	$0.249133\pi$
$608$	1.85239e8	+	3.20843e8i	0.0334249	+	0.0578936i
$609$	1.71038e9	−	9.87488e8i	0.306854	−	0.177162i
$610$	2.69786e9			0.481243
$611$	−1.38521e9	−	3.91017e9i	−0.245681	−	0.693507i
$612$	−1.74263e9			−0.307310
$613$	−2.97386e9	+	1.71696e9i	−0.521445	+	0.301056i	−0.737526	−	0.675319i	$-0.764006\pi$
$613$	−2.97386e9	+	1.71696e9i	−0.521445	+	0.301056i	0.216081	+	0.976376i	$0.430673\pi$
$614$	1.11308e9	+	1.92792e9i	0.194061	+	0.336124i
$615$	5.14534e9	−	8.91199e9i	0.891972	−	1.54494i
$616$			8.04649e7i			0.0138699i
$617$	−4.79676e9	−	2.76941e9i	−0.822149	−	0.474668i	0.0290082	−	0.999579i	$-0.490765\pi$
$617$	−4.79676e9	−	2.76941e9i	−0.822149	−	0.474668i	−0.851157	+	0.524911i	$0.824098\pi$
$618$	−3.75042e9	−	2.16531e9i	−0.639177	−	0.369029i
$619$			1.06724e10i			1.80862i	0.426881	+	0.904308i	$0.359612\pi$
$619$			1.06724e10i			1.80862i	−0.426881	+	0.904308i	$0.640388\pi$
$620$	−1.42046e9	+	2.46030e9i	−0.239363	+	0.414588i
$621$	1.56476e9	+	2.71024e9i	0.262196	+	0.454137i
$622$	−8.47704e8	+	4.89422e8i	−0.141246	+	0.0815487i
$623$	5.57220e8			0.0923248
$624$	4.11984e8	−	2.22441e9i	0.0678788	−	0.366496i
$625$	−3.30833e9			−0.542037
$626$	−4.11043e9	+	2.37316e9i	−0.669695	+	0.386649i
$627$	3.46902e8	+	6.00851e8i	0.0562044	+	0.0973488i
$628$	−5.13784e8	+	8.89901e8i	−0.0827794	+	0.143378i
$629$		−	5.26261e9i		−	0.843187i
$630$	7.50462e8	+	4.33279e8i	0.119574	+	0.0690361i
$631$	−4.72434e9	−	2.72760e9i	−0.748580	−	0.432193i	0.0766004	−	0.997062i	$-0.475593\pi$
$631$	−4.72434e9	−	2.72760e9i	−0.748580	−	0.432193i	−0.825181	+	0.564869i	$0.808927\pi$
$632$		−	1.51409e9i		−	0.238585i
$633$	4.44558e9	−	7.69998e9i	0.696652	−	1.20664i
$634$	−1.94558e9	−	3.36984e9i	−0.303205	−	0.525167i
$635$	−6.82341e9	+	3.93950e9i	−1.05753	+	0.610566i
$636$	4.80493e9			0.740606
$637$	4.76904e9	+	4.07212e9i	0.731044	+	0.624213i
$638$	−1.11694e9			−0.170278
$639$	−1.15910e10	+	6.69207e9i	−1.75739	+	1.01463i
$640$	−2.37850e8	−	4.11969e8i	−0.0358653	−	0.0621205i
$641$	2.93577e9	−	5.08490e9i	0.440270	−	0.762570i	−0.557439	−	0.830218i	$-0.688216\pi$
$641$	2.93577e9	−	5.08490e9i	0.440270	−	0.762570i	0.997709	+	0.0676479i	$0.0215495\pi$
$642$			4.83710e9i			0.721460i
$643$	7.14991e9	+	4.12800e9i	1.06063	+	0.612352i	0.925605	−	0.378491i	$-0.123557\pi$
$643$	7.14991e9	+	4.12800e9i	1.06063	+	0.612352i	0.135020	+	0.990843i	$0.456890\pi$
$644$	−9.11555e8	−	5.26286e8i	−0.134488	−	0.0776464i
$645$			1.09456e10i			1.60612i
$646$	4.60452e8	−	7.97526e8i	0.0672002	−	0.116394i
$647$	1.13186e9	+	1.96045e9i	0.164297	+	0.284570i	0.936405	−	0.350920i	$-0.114131\pi$
$647$	1.13186e9	+	1.96045e9i	0.164297	+	0.284570i	−0.772109	+	0.635491i	$0.780798\pi$
$648$	−1.54292e9	+	8.90805e8i	−0.222757	+	0.128609i
$649$	1.83902e9			0.264077
$650$	1.09757e9	−	1.28542e9i	0.156760	−	0.183589i
$651$	2.43635e9			0.346104
$652$	−1.20862e9	+	6.97795e8i	−0.170774	+	0.0985965i
$653$	−2.40293e9	−	4.16200e9i	−0.337711	−	0.584933i	0.646291	−	0.763091i	$-0.276319\pi$
$653$	−2.40293e9	−	4.16200e9i	−0.337711	−	0.584933i	−0.984002	+	0.178158i	$0.942986\pi$
$654$	4.13828e9	−	7.16771e9i	0.578492	−	1.00198i
$655$			1.84735e9i			0.256865i
$656$	2.30809e9	+	1.33258e9i	0.319220	+	0.184302i
$657$	6.34657e9	+	3.66419e9i	0.873093	+	0.504080i
$658$			7.48076e8i			0.102366i
$659$	−6.83424e9	+	1.18373e10i	−0.930232	+	1.61121i	−0.147310	+	0.989090i	$0.547061\pi$
$659$	−6.83424e9	+	1.18373e10i	−0.930232	+	1.61121i	−0.782922	+	0.622119i	$0.786272\pi$
$660$	−4.45429e8	−	7.71505e8i	−0.0603079	−	0.104456i
$661$	−8.73698e9	+	5.04430e9i	−1.17667	+	0.679353i	−0.955243	−	0.295822i	$-0.904406\pi$
$661$	−8.73698e9	+	5.04430e9i	−1.17667	+	0.679353i	−0.221432	+	0.975176i	$0.571073\pi$
$662$	−3.09947e9			−0.415225
$663$	−5.30052e9	+	1.87776e9i	−0.706352	+	0.250231i
$664$	−3.19197e9			−0.423127
$665$	−3.96586e8	+	2.28969e8i	−0.0522951	+	0.0301926i
$666$	5.52921e9	+	9.57687e9i	0.725276	+	1.25621i
$667$	7.30545e9	−	1.26534e10i	0.953249	−	1.65108i
$668$		−	5.65073e8i		−	0.0733478i
$669$	−5.13672e8	−	2.96569e8i	−0.0663276	−	0.0382943i
$670$	−1.24637e9	−	7.19591e8i	−0.160097	−	0.0924323i
$671$			1.30849e9i			0.167203i
$672$	−2.03980e8	+	3.53303e8i	−0.0259295	+	0.0449113i
$673$	−8.84367e8	−	1.53177e9i	−0.111836	−	0.193705i	0.804675	−	0.593716i	$-0.202340\pi$
$673$	−8.84367e8	−	1.53177e9i	−0.111836	−	0.193705i	−0.916510	+	0.400011i	$0.869006\pi$
$674$	−5.43314e9	+	3.13683e9i	−0.683505	+	0.394622i
$675$	9.06265e8			0.113421
$676$	−6.29214e8	−	3.96631e9i	−0.0783402	−	0.493825i
$677$	5.56373e6			0.000689138			0.000344569	−	1.00000i	$-0.499890\pi$
$677$	5.56373e6			0.000689138			0.000344569		1.00000i	$0.499890\pi$
$678$	−6.05601e9	+	3.49644e9i	−0.746247	+	0.430846i
$679$	5.20296e8	+	9.01179e8i	0.0637832	+	0.110476i
$680$	−5.91230e8	+	1.02404e9i	−0.0721066	+	0.124892i
$681$		−	6.51267e9i		−	0.790213i
$682$	−1.19328e9	−	6.88938e8i	−0.144044	−	0.0831639i
$683$	−2.88892e9	−	1.66792e9i	−0.346947	−	0.200310i	0.316393	−	0.948628i	$-0.397528\pi$
$683$	−2.88892e9	−	1.66792e9i	−0.346947	−	0.200310i	−0.663340	+	0.748318i	$0.730862\pi$
$684$			1.93511e9i			0.231212i
$685$	2.79495e9	−	4.84099e9i	0.332244	−	0.575463i
$686$	−1.15366e9	−	1.99819e9i	−0.136440	−	0.236321i
$687$	2.12123e10	−	1.22469e10i	2.49596	−	1.44105i
$688$	−2.83476e9			−0.331862
$689$	8.04006e9	−	2.84826e9i	0.936466	−	0.331751i
$690$	1.16534e10			1.35046
$691$	2.34131e9	−	1.35175e9i	0.269951	−	0.155856i	−0.358914	−	0.933371i	$-0.616853\pi$
$691$	2.34131e9	−	1.35175e9i	0.269951	−	0.155856i	0.628865	+	0.777514i	$0.283520\pi$
$692$	−2.54161e9	−	4.40220e9i	−0.291567	−	0.505008i
$693$	−2.10146e8	+	3.63983e8i	−0.0239858	+	0.0415446i
$694$		−	4.20935e9i		−	0.478032i
$695$	−8.82055e9	−	5.09254e9i	−0.996664	−	0.575424i
$696$	−4.90425e9	−	2.83147e9i	−0.551366	−	0.318331i
$697$		−	6.62483e9i		−	0.741071i
$698$	2.41179e8	−	4.17735e8i	0.0268439	−	0.0464951i
$699$	3.91941e8	+	6.78861e8i	0.0434060	+	0.0751815i
$700$	−2.63974e8	+	1.52405e8i	−0.0290883	+	0.0167941i
$701$	6.28610e9			0.689236			0.344618	−	0.938743i	$-0.388008\pi$
$701$	6.28610e9			0.689236			0.344618	+	0.938743i	$0.388008\pi$
$702$	1.39820e9	−	1.63749e9i	0.152541	−	0.178648i
$703$	−5.84388e9			−0.634392
$704$	1.99810e8	−	1.15360e8i	0.0215831	−	0.0124610i
$705$	−4.14112e9	−	7.17262e9i	−0.445098	−	0.770932i
$706$	−1.92401e9	+	3.33248e9i	−0.205774	+	0.356411i
$707$			2.10016e9i			0.223504i
$708$	8.07474e9	+	4.66195e9i	0.855090	+	0.493687i
$709$	−6.55765e9	−	3.78606e9i	−0.691013	−	0.398957i	0.112978	−	0.993597i	$-0.463961\pi$
$709$	−6.55765e9	−	3.78606e9i	−0.691013	−	0.398957i	−0.803991	+	0.594641i	$0.797294\pi$
$710$			9.08177e9i			0.952283i
$711$	3.95427e9	−	6.84899e9i	0.412594	−	0.714633i
$712$	−7.98871e8	−	1.38369e9i	−0.0829462	−	0.143667i
$713$	1.56094e10	−	9.01209e9i	1.61277	−	0.931134i
$714$	1.01407e9			0.104262
$715$	−1.20266e9	−	1.02691e9i	−0.123048	−	0.105066i
$716$	−1.18042e9			−0.120182
$717$	3.58851e9	−	2.07182e9i	0.363577	−	0.209911i
$718$	6.78793e9	+	1.17570e10i	0.684387	+	1.18539i
$719$	−3.06478e9	+	5.30836e9i	−0.307503	+	0.532610i	−0.977815	−	0.209469i	$-0.932827\pi$
$719$	−3.06478e9	+	5.30836e9i	−0.307503	+	0.532610i	0.670313	+	0.742079i	$0.266160\pi$
$720$		−	2.48472e9i		−	0.248093i
$721$	1.20061e9	+	6.93174e8i	0.119297	+	0.0688762i
$722$	5.30731e9	+	3.06418e9i	0.524800	+	0.302994i
$723$			2.80082e9i			0.275614i
$724$	2.86543e9	−	4.96307e9i	0.280611	−	0.486032i
$725$	−2.11556e9	−	3.66425e9i	−0.206178	−	0.357110i
$726$	−9.03921e9	+	5.21879e9i	−0.876703	+	0.506165i
$727$	9.74159e9			0.940285			0.470143	−	0.882590i	$-0.344203\pi$
$727$	9.74159e9			0.940285			0.470143	+	0.882590i	$0.344203\pi$
$728$	−1.31887e8	+	7.12095e8i	−0.0126690	+	0.0684034i
$729$	−1.44870e10			−1.38494
$730$	4.30645e9	−	2.48633e9i	0.409722	−	0.236553i
$731$	3.52321e9	+	6.10238e9i	0.333601	+	0.577815i
$732$	−3.31705e9	+	5.74530e9i	−0.312582	+	0.541407i
$733$			4.34921e9i			0.407893i	0.978982	+	0.203947i	$0.0653769\pi$
$733$			4.34921e9i			0.407893i	−0.978982	+	0.203947i	$0.934623\pi$
$734$	−8.13386e8	−	4.69609e8i	−0.0759207	−	0.0438329i
$735$	1.08430e10	+	6.26022e9i	1.00727	+	0.581545i
$736$			3.01809e9i			0.279036i
$737$	3.49010e8	−	6.04503e8i	0.0321146	−	0.0556240i
$738$	6.96044e9	+	1.20558e10i	0.637440	+	1.10408i
$739$	2.77290e9	−	1.60093e9i	0.252742	−	0.145921i	−0.368277	−	0.929716i	$-0.620052\pi$
$739$	2.77290e9	−	1.60093e9i	0.252742	−	0.145921i	0.621019	+	0.783795i	$0.286719\pi$
$740$	7.50366e9			0.680710
$741$	2.08516e9	+	5.88598e9i	0.188268	+	0.531441i
$742$	−1.53819e9			−0.138228
$743$	−8.45322e9	+	4.88047e9i	−0.756069	+	0.436517i	−0.827883	−	0.560901i	$-0.810455\pi$
$743$	−8.45322e9	+	4.88047e9i	−0.756069	+	0.436517i	0.0718135	+	0.997418i	$0.477121\pi$
$744$	−3.49294e9	−	6.04994e9i	−0.310946	−	0.538575i
$745$	−1.39398e9	+	2.41444e9i	−0.123512	+	0.213929i
$746$			2.72336e9i			0.240170i
$747$	−1.44389e10	−	8.33630e9i	−1.26739	−	0.731731i
$748$	−4.96672e8	−	2.86754e8i	−0.0433924	−	0.0250526i
$749$		−	1.54849e9i		−	0.134655i
$750$	6.62966e9	−	1.14829e10i	0.573822	−	0.993888i
$751$	2.79021e9	+	4.83279e9i	0.240379	+	0.416349i	0.960822	−	0.277165i	$-0.0893948\pi$
$751$	2.79021e9	+	4.83279e9i	0.240379	+	0.416349i	−0.720443	+	0.693514i	$0.756062\pi$
$752$	1.85762e9	−	1.07250e9i	0.159292	−	0.0919673i
$753$	−2.53786e10			−2.16613
$754$	−9.88468e9	−	1.83074e9i	−0.839775	−	0.155535i
$755$	7.42099e9			0.627549
$756$	−3.36276e8	+	1.94149e8i	−0.0283054	+	0.0163421i
$757$	−1.82897e9	−	3.16787e9i	−0.153240	−	0.265419i	0.779177	−	0.626804i	$-0.215637\pi$
$757$	−1.82897e9	−	3.16787e9i	−0.153240	−	0.265419i	−0.932417	+	0.361385i	$0.882304\pi$
$758$	−6.34235e9	+	1.09853e10i	−0.528942	+	0.916154i
$759$			5.65205e9i			0.469202i
$760$	1.13715e9	+	6.56533e8i	0.0939657	+	0.0542511i
$761$	−4.62008e9	−	2.66740e9i	−0.380017	−	0.219403i	0.297809	−	0.954626i	$-0.403744\pi$
$761$	−4.62008e9	−	2.66740e9i	−0.380017	−	0.219403i	−0.677826	+	0.735223i	$0.737078\pi$
$762$		−	1.93746e10i		−	1.58632i
$763$	−1.32478e9	+	2.29458e9i	−0.107971	+	0.187011i
$764$	−1.25946e9	−	2.18144e9i	−0.102178	−	0.176977i
$765$	−5.34886e9	+	3.08816e9i	−0.431962	+	0.249394i
$766$	−1.08431e10			−0.871670
$767$	1.62749e10	+	3.01428e9i	1.30237	+	0.241212i
$768$	1.16976e9			0.0931822
$769$	1.76106e10	−	1.01675e10i	1.39647	−	0.806252i	0.402448	−	0.915443i	$-0.368159\pi$
$769$	1.76106e10	−	1.01675e10i	1.39647	−	0.806252i	0.994021	+	0.109191i	$0.0348260\pi$
$770$	1.42594e8	+	2.46980e8i	0.0112560	+	0.0194959i
$771$	−1.79360e10	+	3.10660e10i	−1.40940	+	2.44115i
$772$			2.39417e8i			0.0187281i
$773$	−2.16196e9	−	1.24821e9i	−0.168352	−	0.0971982i	0.413456	−	0.910524i	$-0.364321\pi$
$773$	−2.16196e9	−	1.24821e9i	−0.168352	−	0.0971982i	−0.581809	+	0.813326i	$0.697655\pi$
$774$	−1.28230e10	−	7.40339e9i	−0.994026	−	0.573901i
$775$		−	5.21956e9i		−	0.402789i
$776$	1.49187e9	−	2.58399e9i	0.114608	−	0.198507i
$777$	−3.21756e9	−	5.57297e9i	−0.246067	−	0.426200i
$778$	−8.35357e9	+	4.82293e9i	−0.635980	+	0.367183i
$779$	−7.35656e9			−0.557563
$780$	−2.67739e9	−	7.55772e9i	−0.202013	−	0.570242i
$781$	−4.40477e9			−0.330860
$782$	6.49703e9	−	3.75106e9i	0.485838	−	0.280499i
$783$	−2.69501e9	−	4.66789e9i	−0.200629	−	0.347499i
$784$	−1.62132e9	+	2.80820e9i	−0.120160	+	0.208124i
$785$			3.64196e9i			0.268715i
$786$	−3.93408e9	−	2.27134e9i	−0.288978	−	0.166841i
$787$	1.12179e10	+	6.47665e9i	0.820351	+	0.473630i	0.850538	−	0.525914i	$-0.176277\pi$
$787$	1.12179e10	+	6.47665e9i	0.820351	+	0.473630i	−0.0301864	+	0.999544i	$0.509610\pi$
$788$			9.68543e9i			0.705143i
$789$	−1.80575e10	+	3.12765e10i	−1.30885	+	2.26699i
$790$	−2.68316e9	−	4.64737e9i	−0.193621	−	0.335361i
$791$	1.93869e9	−	1.11931e9i	0.139281	−	0.0804138i
$792$	1.20512e9			0.0861971
$793$	−2.14471e9	+	1.15799e10i	−0.152726	+	0.824607i
$794$	1.76767e10			1.25322
$795$	1.47483e10	−	8.51494e9i	1.04102	−	0.601030i
$796$	−5.23553e9	−	9.06820e9i	−0.367930	−	0.637273i
$797$	−3.77934e9	+	6.54601e9i	−0.264431	+	0.458007i	−0.967414	−	0.253199i	$-0.918517\pi$
$797$	−3.77934e9	+	6.54601e9i	−0.264431	+	0.458007i	0.702984	+	0.711206i	$0.251851\pi$
$798$		−	1.12608e9i		−	0.0784439i
$799$	−4.61752e9	−	2.66593e9i	−0.320254	−	0.184899i
$800$	7.56904e8	+	4.36999e8i	0.0522668	+	0.0301763i
$801$		−	8.34547e9i		−	0.573769i
$802$	6.59725e9	−	1.14268e10i	0.451599	−	0.782192i
$803$	1.20590e9	+	2.08868e9i	0.0821877	+	0.142353i
$804$	3.06485e9	−	1.76949e9i	0.207976	−	0.120075i
$805$	−3.73058e9			−0.252052
$806$	−9.43098e9	−	8.05279e9i	−0.634431	−	0.541718i
$807$	−1.14340e9			−0.0765843
$808$	5.21511e9	−	3.01095e9i	0.347795	−	0.200800i
$809$	−6.59467e9	−	1.14223e10i	−0.437898	−	0.758462i	0.559629	−	0.828743i	$-0.310944\pi$
$809$	−6.59467e9	−	1.14223e10i	−0.437898	−	0.758462i	−0.997527	+	0.0702814i	$0.977610\pi$
$810$	−3.15723e9	+	5.46849e9i	−0.208742	+	0.361551i
$811$			8.98563e9i			0.591528i	0.955261	+	0.295764i	$0.0955743\pi$
$811$			8.98563e9i			0.591528i	−0.955261	+	0.295764i	$0.904426\pi$
$812$	1.56998e9	+	9.06430e8i	0.102908	+	0.0594139i
$813$	1.76306e10	+	1.01790e10i	1.15067	+	0.664339i
$814$			3.63937e9i			0.236505i
$815$	−2.47316e9	+	4.28364e9i	−0.160030	+	0.277180i
$816$	−1.45385e9	−	2.51814e9i	−0.0936707	−	0.162242i
$817$	6.77641e9	−	3.91236e9i	0.434733	−	0.250993i
$818$	1.66956e10			1.06651
$819$	−2.45633e9	+	2.87672e9i	−0.156240	+	0.182980i
$820$	9.44597e9			0.598271
$821$	4.61205e8	−	2.66277e8i	0.0290866	−	0.0167931i	−0.485386	−	0.874300i	$-0.661321\pi$
$821$	4.61205e8	−	2.66277e8i	0.0290866	−	0.0167931i	0.514473	+	0.857507i	$0.327988\pi$
$822$	6.87285e9	+	1.19041e10i	0.431604	+	0.747560i
$823$	5.92544e9	−	1.02632e10i	0.370528	−	0.641774i	−0.619119	−	0.785298i	$-0.712510\pi$
$823$	5.92544e9	−	1.02632e10i	0.370528	−	0.641774i	0.989647	+	0.143524i	$0.0458433\pi$
$824$		−	3.97514e9i		−	0.247518i
$825$	1.41747e9	+	8.18379e8i	0.0878873	+	0.0507418i
$826$	−2.58494e9	−	1.49242e9i	−0.159596	−	0.0921425i
$827$		−	8.52069e9i		−	0.523848i	−0.965088	−	0.261924i	$-0.915643\pi$
$827$		−	8.52069e9i		−	0.523848i	0.965088	−	0.261924i	$-0.0843570\pi$
$828$	−7.88218e9	+	1.36523e10i	−0.482547	+	0.835797i
$829$	−5.69598e9	−	9.86572e9i	−0.347238	−	0.601434i	0.638520	−	0.769606i	$-0.279547\pi$
$829$	−5.69598e9	−	9.86572e9i	−0.347238	−	0.601434i	−0.985758	+	0.168171i	$0.946214\pi$
$830$	−9.79747e9	+	5.65657e9i	−0.594759	+	0.343384i
$831$	4.26741e10			2.57965
$832$	1.95735e9	−	6.93409e8i	0.117825	−	0.0417405i
$833$	8.06028e9			0.483162
$834$	2.16900e10	−	1.25227e10i	1.29472	−	0.747510i
$835$	−1.00138e9	−	1.73444e9i	−0.0595246	−	0.103100i
$836$	−3.18426e8	+	5.51531e8i	−0.0188489	+	0.0326473i
$837$		−	6.64919e9i		−	0.391949i
$838$	−3.00201e9	−	1.73321e9i	−0.176221	−	0.101741i
$839$	1.19762e10	+	6.91447e9i	0.700088	+	0.404196i	0.807380	−	0.590032i	$-0.200885\pi$
$839$	1.19762e10	+	6.91447e9i	0.700088	+	0.404196i	−0.107292	+	0.994228i	$0.534218\pi$
$840$			1.44591e9i			0.0841712i
$841$	−3.95733e9	+	6.85430e9i	−0.229412	+	0.397354i
$842$	8.83121e9	+	1.52961e10i	0.509833	+	0.883056i
$843$	3.61844e8	−	2.08911e8i	0.0208030	−	0.0120106i
$844$	8.16134e9			0.467265
$845$	−8.96010e9	−	1.10592e10i	−0.510875	−	0.630557i
$846$	1.12039e10			0.636171
$847$	2.89370e9	−	1.67068e9i	0.163629	−	0.0944715i
$848$	2.20526e9	+	3.81962e9i	0.124187	+	0.215097i
$849$	−8.14446e9	+	1.41066e10i	−0.456757	+	0.791126i
$850$		−	2.17251e9i		−	0.121338i
$851$	−4.12289e10	−	2.38035e10i	−2.29323	−	1.32400i
$852$	−1.93403e10	−	1.11662e10i	−1.07134	−	0.618536i
$853$		−	1.88342e10i		−	1.03902i	−0.854463	−	0.519512i	$-0.826114\pi$
$853$		−	1.88342e10i		−	1.03902i	0.854463	−	0.519512i	$-0.173886\pi$
$854$	1.06188e9	−	1.83923e9i	0.0583408	−	0.101049i
$855$	3.42926e9	+	5.93965e9i	0.187637	+	0.324997i
$856$	−3.84520e9	+	2.22002e9i	−0.209537	+	0.120976i
$857$	9.32532e9			0.506094			0.253047	−	0.967454i	$-0.418567\pi$
$857$	9.32532e9			0.506094			0.253047	+	0.967454i	$0.418567\pi$
$858$	3.66558e9	−	1.29856e9i	0.198124	−	0.0701872i
$859$	−2.41498e10			−1.29998			−0.649990	−	0.759943i	$-0.725227\pi$
$859$	−2.41498e10			−1.29998			−0.649990	+	0.759943i	$0.725227\pi$
$860$	−8.70104e9	+	5.02355e9i	−0.466473	+	0.269318i
$861$	−4.05042e9	−	7.01553e9i	−0.216266	−	0.374584i
$862$	1.10141e10	−	1.90770e10i	0.585699	−	1.01446i
$863$		−	7.60254e9i		−	0.402644i	−0.979525	−	0.201322i	$-0.935476\pi$
$863$		−	7.60254e9i		−	0.402644i	0.979525	−	0.201322i	$-0.0645237\pi$
$864$	9.64219e8	+	5.56692e8i	0.0508601	+	0.0293641i
$865$	−1.56025e10	−	9.00810e9i	−0.819667	−	0.473235i
$866$		−	1.63051e10i		−	0.853122i
$867$	1.06912e10	−	1.85177e10i	0.557134	−	0.964984i
$868$	1.11818e9	+	1.93675e9i	0.0580356	+	0.100521i
$869$	2.25403e9	−	1.30136e9i	0.116517	−	0.0672713i
$870$	−2.00709e10			−1.03335
$871$	4.07947e9	−	4.77765e9i	0.209190	−	0.244992i
$872$	7.59718e9			0.388012
$873$	1.34969e10	−	7.79246e9i	0.686571	−	0.396392i
$874$	−4.16538e9	−	7.21465e9i	−0.211040	−	0.365532i
$875$	−2.12234e9	+	3.67599e9i	−0.107099	+	0.185501i
$876$			1.22279e10i			0.614593i
$877$	−4.73367e9	−	2.73298e9i	−0.236973	−	0.136817i	0.376812	−	0.926290i	$-0.377020\pi$
$877$	−4.73367e9	−	2.73298e9i	−0.236973	−	0.136817i	−0.613785	+	0.789473i	$0.710354\pi$
$878$	1.67470e10	+	9.66889e9i	0.835038	+	0.482109i
$879$			2.03437e9i			0.101034i
$880$	4.08866e8	−	7.08176e8i	0.0202251	−	0.0350310i
$881$	1.35522e10	+	2.34731e10i	0.667718	+	1.15652i	0.978541	+	0.206054i	$0.0660623\pi$
$881$	1.35522e10	+	2.34731e10i	0.667718	+	1.15652i	−0.310822	+	0.950468i	$0.600604\pi$
$882$	−1.46681e10	+	8.46860e9i	−0.719834	+	0.415596i
$883$	1.42158e10			0.694879			0.347439	−	0.937702i	$-0.387051\pi$
$883$	1.42158e10			0.694879			0.347439	+	0.937702i	$0.387051\pi$
$884$	−3.92542e9	−	3.35178e9i	−0.191118	−	0.163189i
$885$	3.30462e10			1.60258
$886$	−1.69863e10	+	9.80707e9i	−0.820506	+	0.473720i
$887$	−1.76905e9	−	3.06408e9i	−0.0851151	−	0.147424i	0.820325	−	0.571897i	$-0.193792\pi$
$887$	−1.76905e9	−	3.06408e9i	−0.0851151	−	0.147424i	−0.905440	+	0.424474i	$0.860459\pi$
$888$	−9.22585e9	+	1.59796e10i	−0.442141	+	0.765811i
$889$			6.20235e9i			0.296074i
$890$	−4.90412e9	−	2.83140e9i	−0.233183	−	0.134628i
$891$	−2.65228e9	−	1.53130e9i	−0.125617	−	0.0725250i
$892$		−	5.44450e8i		−	0.0256851i
$893$	−2.96039e9	+	5.12754e9i	−0.139113	+	0.240951i
$894$	−3.42783e9	−	5.93717e9i	−0.160449	−	0.277906i
$895$	−3.62318e9	+	2.09185e9i	−0.168931	+	0.0975325i
$896$	−3.74472e8			−0.0173917
$897$	−9.26408e9	+	5.00193e10i	−0.428577	+	2.31400i
$898$	−2.24554e10			−1.03480
$899$	−2.68843e10	+	1.55217e10i	−1.23407	+	0.712490i
$900$	2.28257e9	+	3.95353e9i	0.104370	+	0.180774i
$901$	5.48166e9	−	9.49451e9i	0.249675	−	0.432450i
$902$			4.58141e9i			0.207863i
$903$	7.46198e9	+	4.30818e9i	0.337246	+	0.194709i
$904$	−5.55890e9	−	3.20943e9i	−0.250265	−	0.144490i
$905$		−	2.03116e10i		−	0.910906i
$906$	−9.12421e9	+	1.58036e10i	−0.407611	+	0.706004i
$907$	1.56883e10	+	2.71730e10i	0.698154	+	1.20924i	0.969106	+	0.246645i	$0.0793281\pi$
$907$	1.56883e10	+	2.71730e10i	0.698154	+	1.20924i	−0.270952	+	0.962593i	$0.587339\pi$
$908$	5.17717e9	−	2.98904e9i	0.229505	−	0.132505i
$909$	3.14541e10			1.38900
$910$	8.57104e8	+	2.41943e9i	0.0377041	+	0.106431i
$911$	−2.69642e10			−1.18161			−0.590803	−	0.806816i	$-0.701189\pi$
$911$	−2.69642e10			−1.18161			−0.590803	+	0.806816i	$0.701189\pi$
$912$	−2.79628e9	+	1.61443e9i	−0.122067	+	0.0704754i
$913$	−2.74351e9	−	4.75189e9i	−0.119305	−	0.206642i
$914$	−5.24060e8	+	9.07699e8i	−0.0227023	+	0.0393215i
$915$			2.35129e10i			1.01469i
$916$	1.94711e10	+	1.12416e10i	0.837058	+	0.483276i
$917$	1.25941e9	+	7.27119e8i	0.0539353	+	0.0311396i
$918$		−	2.76756e9i		−	0.118072i
$919$	9.42533e9	−	1.63252e10i	0.400583	−	0.693830i	−0.593213	−	0.805045i	$-0.702141\pi$
$919$	9.42533e9	−	1.63252e10i	0.400583	−	0.693830i	0.993796	+	0.111215i	$0.0354743\pi$
$920$	5.34843e9	+	9.26375e9i	0.226448	+	0.392220i
$921$	−1.68026e10	+	9.70097e9i	−0.708708	+	0.409173i
$922$	1.42627e10			0.599298
$923$	−3.89811e10	−	7.21970e9i	−1.63173	−	0.302213i
$924$	−7.01284e8			−0.0292444
$925$	−1.19393e10	+	6.89318e9i	−0.496003	+	0.286367i
$926$	7.11793e9	+	1.23286e10i	0.294588	+	0.510242i
$927$	1.03817e10	−	1.79816e10i	0.428043	−	0.741392i
$928$		−	5.19810e9i		−	0.213514i
$929$	3.92193e10	+	2.26433e10i	1.60489	+	0.926582i	0.990490	+	0.137585i	$0.0439341\pi$
$929$	3.92193e10	+	2.26433e10i	1.60489	+	0.926582i	0.614397	+	0.788997i	$0.289399\pi$
$930$	−2.14425e10	−	1.23798e10i	−0.874148	−	0.504690i
$931$		−	8.95056e9i		−	0.363518i
$932$	−3.59768e8	+	6.23137e8i	−0.0145568	+	0.0252132i
$933$	−4.26551e9	−	7.38807e9i	−0.171943	−	0.297814i
$934$	−3.07400e9	+	1.77477e9i	−0.123450	+	0.0712737i
$935$	−2.03265e9			−0.0813247
$936$	1.06650e10	+	1.97527e9i	0.425105	+	0.0787338i
$937$	−6.38092e9			−0.253393			−0.126697	−	0.991942i	$-0.540437\pi$
$937$	−6.38092e9			−0.253393			−0.126697	+	0.991942i	$0.540437\pi$
$938$	−9.81142e8	+	5.66463e8i	−0.0388170	+	0.0224110i
$939$	−2.06830e10	−	3.58240e10i	−0.815238	−	1.41203i
$940$	3.80119e9	−	6.58386e9i	0.149270	−	0.258543i
$941$		−	1.19504e10i		−	0.467538i	−0.972292	−	0.233769i	$-0.924894\pi$
$941$		−	1.19504e10i		−	0.467538i	0.972292	−	0.233769i	$-0.0751060\pi$
$942$	−7.75584e9	−	4.47784e9i	−0.302309	−	0.174538i
$943$	−5.19010e10	−	2.99650e10i	−2.01551	−	1.16365i
$944$			8.55855e9i			0.331130i
$945$	−6.88112e8	+	1.19184e9i	−0.0265245	+	0.0459418i
$946$	−2.43648e9	−	4.22011e9i	−0.0935717	−	0.162071i
$947$	1.72652e10	−	9.96805e9i	0.660611	−	0.381404i	−0.131898	−	0.991263i	$-0.542107\pi$
$947$	1.72652e10	−	9.96805e9i	0.660611	−	0.381404i	0.792510	+	0.609859i	$0.208774\pi$
$948$	1.31959e10			0.503049
$949$	7.24843e9	+	2.04608e10i	0.275304	+	0.777127i
$950$	−2.41247e9			−0.0912914
$951$	2.93695e10	−	1.69565e10i	1.10730	−	0.639300i
$952$	4.65417e8	+	8.06126e8i	0.0174829	+	0.0302812i
$953$	1.75720e10	−	3.04356e10i	0.657652	−	1.13909i	−0.323570	−	0.946204i	$-0.604883\pi$
$953$	1.75720e10	−	3.04356e10i	0.657652	−	1.13909i	0.981222	−	0.192882i	$-0.0617834\pi$
$954$			2.30374e10i			0.859042i
$955$	−7.73157e9	−	4.46383e9i	−0.287247	−	0.165842i
$956$	3.29394e9	+	1.90176e9i	0.121931	+	0.0703968i
$957$		−	9.73461e9i		−	0.359027i
$958$	8.19787e9	−	1.41991e10i	0.301246	−	0.521774i
$959$	−2.20019e9	−	3.81083e9i	−0.0805553	−	0.139526i
$960$	3.59048e9	−	2.07296e9i	0.130979	−	0.0756209i
$961$	−1.07828e10			−0.391922
$962$	−5.96516e9	+	3.22075e10i	−0.216028	+	1.16639i
$963$	−2.31917e10			−0.836835
$964$	−2.22648e9	+	1.28546e9i	−0.0800478	+	0.0462156i
$965$	4.24277e8	+	7.34868e8i	0.0151986	+	0.0263247i
$966$	4.58680e9	−	7.94456e9i	0.163715	−	0.283563i
$967$			8.28494e9i			0.294643i	0.989089	+	0.147322i	$0.0470653\pi$
$967$			8.28494e9i			0.294643i	−0.989089	+	0.147322i	$0.952935\pi$
$968$	−8.29723e9	−	4.79041e9i	−0.294015	−	0.169750i
$969$	6.95076e9	+	4.01302e9i	0.245414	+	0.141690i
$970$		−	1.05751e10i		−	0.372035i
$971$	−4.69131e9	+	8.12558e9i	−0.164447	+	0.284831i	−0.936459	−	0.350777i	$-0.885917\pi$
$971$	−4.69131e9	+	8.12558e9i	−0.164447	+	0.284831i	0.772012	+	0.635608i	$0.219251\pi$
$972$	−1.01416e10	−	1.75658e10i	−0.354222	−	0.613530i
$973$	−6.94355e9	+	4.00886e9i	−0.241650	+	0.139517i
$974$	2.72598e10			0.945292
$975$	1.12029e10	+	9.56578e9i	0.387093	+	0.330525i
$976$	−6.08955e9			−0.209658
$977$	−3.03629e10	+	1.75300e10i	−1.04163	+	0.601383i	−0.920294	−	0.391228i	$-0.872050\pi$
$977$	−3.03629e10	+	1.75300e10i	−1.04163	+	0.601383i	−0.121333	+	0.992612i	$0.538717\pi$
$978$	−6.08156e9	−	1.05336e10i	−0.207888	−	0.360072i
$979$	1.37326e9	−	2.37856e9i	0.0467750	−	0.0810167i
$980$			1.14927e10i			0.390059i
$981$	3.43658e10	+	1.98411e10i	1.16221	+	0.671004i
$982$	2.62286e10	+	1.51431e10i	0.883862	+	0.510298i
$983$			4.57533e9i			0.153633i	0.997045	+	0.0768167i	$0.0244756\pi$
$983$			4.57533e9i			0.153633i	−0.997045	+	0.0768167i	$0.975524\pi$
$984$	−1.16139e10	+	2.01159e10i	−0.388595	+	0.673066i
$985$	1.71638e10	+	2.97285e10i	0.572250	+	0.991167i
$986$	−1.11899e10	+	6.46051e9i	−0.371756	+	0.214634i
$987$	−6.51978e9			−0.215836
$988$	−3.72199e9	+	4.35899e9i	−0.122779	+	0.143793i
$989$	6.37439e10			2.09533
$990$	3.69901e9	−	2.13562e9i	0.121161	−	0.0699523i
$991$	2.48276e10	+	4.30026e10i	0.810357	+	1.40358i	0.912614	+	0.408821i	$0.134060\pi$
$991$	2.48276e10	+	4.30026e10i	0.810357	+	1.40358i	−0.102258	+	0.994758i	$0.532607\pi$
$992$	3.20622e9	−	5.55334e9i	0.104280	−	0.180619i
$993$		−	2.70131e10i		−	0.875491i
$994$	6.19137e9	+	3.57459e9i	0.199956	+	0.115445i
$995$	−3.21400e10	−	1.85560e10i	−1.03434	−	0.597178i
$996$		−	2.78193e10i		−	0.892152i
$997$	6.78662e9	−	1.17548e10i	0.216880	−	0.375648i	−0.736972	−	0.675923i	$-0.763745\pi$
$997$	6.78662e9	−	1.17548e10i	0.216880	−	0.375648i	0.953853	+	0.300275i	$0.0970785\pi$
$998$	−1.22982e10	−	2.13012e10i	−0.391639	−	0.678338i
$999$	−1.52095e10	+	8.78121e9i	−0.482654	+	0.278660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.8.e.a.23.1	yes	16
3.2	odd	2		234.8.l.c.127.7		16
4.3	odd	2		208.8.w.b.49.7		16
13.2	odd	12		338.8.a.m.1.7		8
13.3	even	3		338.8.b.i.337.7		16
13.4	even	6	inner	26.8.e.a.17.1	✓	16
13.10	even	6		338.8.b.i.337.15		16
13.11	odd	12		338.8.a.n.1.7		8
39.17	odd	6		234.8.l.c.199.6		16
52.43	odd	6		208.8.w.b.17.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.e.a.17.1	✓	16	13.4	even	6	inner
26.8.e.a.23.1	yes	16	1.1	even	1	trivial
208.8.w.b.17.7		16	52.43	odd	6
208.8.w.b.49.7		16	4.3	odd	2
234.8.l.c.127.7		16	3.2	odd	2
234.8.l.c.199.6		16	39.17	odd	6
338.8.a.m.1.7		8	13.2	odd	12
338.8.a.n.1.7		8	13.11	odd	12
338.8.b.i.337.7		16	13.3	even	3
338.8.b.i.337.15		16	13.10	even	6

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	26.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.92820 + 4.00000i) q^{2} +(-34.8616 - 60.3821i) q^{3} +(32.0000 - 55.4256i) q^{4} -226.832i q^{5} +(483.056 + 278.893i) q^{6} +(-154.640 - 89.2812i) q^{7} +512.000i q^{8} +(-1337.16 + 2316.03i) q^{9} +(907.328 + 1571.54i) q^{10} +(-762.215 + 440.065i) q^{11} -4462.28 q^{12} +(-7466.71 + 2645.15i) q^{13} +1428.50 q^{14} +(-13696.6 + 7907.72i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-5090.76 + 8817.45i) q^{17} -21394.6i q^{18} +(9791.36 + 5653.04i) q^{19} +(-12572.3 - 7258.62i) q^{20} +12449.9i q^{21} +(3520.52 - 6097.72i) q^{22} +(46052.4 + 79765.1i) q^{23} +(30915.6 - 17849.1i) q^{24} +26672.3 q^{25} +(41150.3 - 48192.9i) q^{26} +33977.8 q^{27} +(-9896.93 + 5714.00i) q^{28} +(-79316.7 - 137381. i) q^{29} +(63261.8 - 109573. i) q^{30} -195692. i q^{31} +(28377.9 + 16384.0i) q^{32} +(53144.1 + 30682.7i) q^{33} -81452.1i q^{34} +(-20251.8 + 35077.2i) q^{35} +(85578.4 + 148226. i) q^{36} +(-447631. + 258440. i) q^{37} -90448.7 q^{38} +(420021. + 358641. i) q^{39} +116138. q^{40} +(-563499. + 325336. i) q^{41} +(-49799.8 - 86255.7i) q^{42} +(346040. - 599359. i) q^{43} +56328.3i q^{44} +(525350. + 303311. i) q^{45} +(-638121. - 368419. i) q^{46} +523680. i q^{47} +(-142793. + 247325. i) q^{48} +(-395829. - 685596. i) q^{49} +(-184791. + 106689. i) q^{50} +709887. q^{51} +(-92325.8 + 498492. i) q^{52} -1.07679e6 q^{53} +(-235405. + 135911. i) q^{54} +(99820.8 + 172895. i) q^{55} +(45712.0 - 79175.4i) q^{56} -788296. i q^{57} +(1.09904e6 + 634533. i) q^{58} +(-1.80955e6 - 1.04475e6i) q^{59} +1.01219e6i q^{60} +(743353. - 1.28753e6i) q^{61} +(782769. + 1.35579e6i) q^{62} +(413556. - 238767. i) q^{63} -262144. q^{64} +(600003. + 1.69369e6i) q^{65} -490924. q^{66} +(-686834. + 396544. i) q^{67} +(325808. + 564317. i) q^{68} +(3.21092e6 - 5.56148e6i) q^{69} -324029. i q^{70} +(4.33418e6 + 2.50234e6i) q^{71} +(-1.18581e6 - 684627. i) q^{72} -2.74028e6i q^{73} +(2.06752e6 - 3.58104e6i) q^{74} +(-929839. - 1.61053e6i) q^{75} +(626647. - 361795. i) q^{76} +157158. q^{77} +(-4.34455e6 - 804656. i) q^{78} -2.95721e6 q^{79} +(-804627. + 464552. i) q^{80} +(1.73985e6 + 3.01351e6i) q^{81} +(2.60269e6 - 4.50799e6i) q^{82} +6.23432e6i q^{83} +(690046. + 398398. i) q^{84} +(2.00008e6 + 1.15475e6i) q^{85} +5.53664e6i q^{86} +(-5.53021e6 + 9.57861e6i) q^{87} +(-225313. - 390254. i) q^{88} +(-2.70251e6 + 1.56029e6i) q^{89} -4.85298e6 q^{90} +(1.39081e6 + 257592. i) q^{91} +5.89471e6 q^{92} +(-1.18163e7 + 6.82214e6i) q^{93} +(-2.09472e6 - 3.62816e6i) q^{94} +(1.28229e6 - 2.22099e6i) q^{95} -2.28469e6i q^{96} +(-5.04686e6 - 2.91380e6i) q^{97} +(5.48477e6 + 3.16663e6i) q^{98} -2.35375e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 512 q^{4} + 2520 q^{7} - 4684 q^{9} + 2432 q^{10} - 8496 q^{11} - 3620 q^{13} + 34560 q^{14} + 51648 q^{15} - 32768 q^{16} + 41520 q^{17} - 54432 q^{19} - 16128 q^{20} - 17280 q^{22} - 7560 q^{23}+ \cdots + 19031040 q^{98}+O(q^{100}) \) 16 * q + 512 * q^4 + 2520 * q^7 - 4684 * q^9 + 2432 * q^10 - 8496 * q^11 - 3620 * q^13 + 34560 * q^14 + 51648 * q^15 - 32768 * q^16 + 41520 * q^17 - 54432 * q^19 - 16128 * q^20 - 17280 * q^22 - 7560 * q^23 - 273960 * q^25 + 51072 * q^26 + 133920 * q^27 + 161280 * q^28 - 346056 * q^29 + 170368 * q^30 + 486300 * q^33 - 283248 * q^35 + 299776 * q^36 - 68280 * q^37 - 1059840 * q^38 - 1122680 * q^39 + 311296 * q^40 - 1288008 * q^41 + 408320 * q^42 + 285360 * q^43 + 5743980 * q^45 - 188928 * q^46 - 2131660 * q^49 + 85248 * q^50 + 957280 * q^51 + 354560 * q^52 + 3666600 * q^53 - 4074624 * q^54 - 1091472 * q^55 + 1105920 * q^56 + 3504000 * q^58 + 1799280 * q^59 - 4626000 * q^61 - 2770560 * q^62 - 8609760 * q^63 - 4194304 * q^64 - 11518020 * q^65 + 7941120 * q^66 - 7094400 * q^67 - 2657280 * q^68 + 18027316 * q^69 + 25958520 * q^71 + 4423680 * q^72 - 1142400 * q^74 - 10898032 * q^75 - 3483648 * q^76 - 20577480 * q^77 - 22023040 * q^78 + 34143488 * q^79 - 1032192 * q^80 - 15745864 * q^81 + 12202240 * q^82 + 17311488 * q^84 + 7123932 * q^85 - 10460440 * q^87 + 1105920 * q^88 + 10609452 * q^89 + 4070656 * q^90 - 38683952 * q^91 - 967680 * q^92 - 52747080 * q^93 - 14303616 * q^94 + 33837504 * q^95 + 83706300 * q^97 + 19031040 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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