LMFDB - Embedded newform 26.8.e.a.17.3

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			17.3
Root			$-32.3527i$ of defining polynomial
Character	$\chi$	$=$	26.17
Dual form			26.8.e.a.23.3

$q$-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} +(16.1763 - 28.0182i) q^{3} +(32.0000 + 55.4256i) q^{4} -211.408i q^{5} +(-224.146 + 129.411i) q^{6} +(635.796 - 367.077i) q^{7} -512.000i q^{8} +(570.153 + 987.534i) q^{9} +(-845.633 + 1464.68i) q^{10} +(-7445.38 - 4298.59i) q^{11} +2070.57 q^{12} +(-6928.10 - 3840.57i) q^{13} -5873.23 q^{14} +(-5923.28 - 3419.81i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-8168.98 - 14149.1i) q^{17} -9122.45i q^{18} +(3033.16 - 1751.20i) q^{19} +(11717.4 - 6765.06i) q^{20} -23751.8i q^{21} +(34388.7 + 59563.0i) q^{22} +(-32638.2 + 56531.0i) q^{23} +(-14345.3 - 8282.28i) q^{24} +33431.5 q^{25} +(32637.0 + 54320.7i) q^{26} +107647. q^{27} +(40690.9 + 23492.9i) q^{28} +(56295.7 - 97507.0i) q^{29} +(27358.5 + 47386.3i) q^{30} -176071. i q^{31} +(28377.9 - 16384.0i) q^{32} +(-240878. + 139071. i) q^{33} +130704. i q^{34} +(-77603.1 - 134412. i) q^{35} +(-36489.8 + 63202.2i) q^{36} +(432385. + 249638. i) q^{37} -28019.1 q^{38} +(-219677. + 131987. i) q^{39} -108241. q^{40} +(-250415. - 144577. i) q^{41} +(-95007.3 + 164557. i) q^{42} +(-201010. - 348160. i) q^{43} -550219. i q^{44} +(208773. - 120535. i) q^{45} +(452248. - 261106. i) q^{46} -64966.5i q^{47} +(66258.2 + 114763. i) q^{48} +(-142281. + 246438. i) q^{49} +(-231621. - 133726. i) q^{50} -528576. q^{51} +(-8832.82 - 506892. i) q^{52} +263903. q^{53} +(-745801. - 430589. i) q^{54} +(-908757. + 1.57401e6i) q^{55} +(-187943. - 325527. i) q^{56} -113312. i q^{57} +(-780056. + 450366. i) q^{58} +(2.22659e6 - 1.28552e6i) q^{59} -437736. i q^{60} +(269475. + 466745. i) q^{61} +(-704284. + 1.21986e6i) q^{62} +(725002. + 418580. i) q^{63} -262144. q^{64} +(-811929. + 1.46466e6i) q^{65} +2.22513e6 q^{66} +(771672. + 445525. i) q^{67} +(522815. - 905541. i) q^{68} +(1.05593e6 + 1.82893e6i) q^{69} +1.24165e6i q^{70} +(3.42530e6 - 1.97760e6i) q^{71} +(505617. - 291918. i) q^{72} +2.77895e6i q^{73} +(-1.99710e6 - 3.45908e6i) q^{74} +(540800. - 936692. i) q^{75} +(194122. + 112077. i) q^{76} -6.31165e6 q^{77} +(2.04991e6 - 35720.7i) q^{78} +4.53826e6 q^{79} +(749916. + 432964. i) q^{80} +(494411. - 856345. i) q^{81} +(1.15662e6 + 2.00332e6i) q^{82} -2.61022e6i q^{83} +(1.31646e6 - 760058. i) q^{84} +(-2.99123e6 + 1.72699e6i) q^{85} +3.21616e6i q^{86} +(-1.82131e6 - 3.15461e6i) q^{87} +(-2.20088e6 + 3.81203e6i) q^{88} +(-6.82257e6 - 3.93901e6i) q^{89} -1.92856e6 q^{90} +(-5.81464e6 + 101323. i) q^{91} -4.17769e6 q^{92} +(-4.93320e6 - 2.84818e6i) q^{93} +(-259866. + 450101. i) q^{94} +(-370217. - 641235. i) q^{95} -1.06013e6i q^{96} +(7.91553e6 - 4.57003e6i) q^{97} +(1.97150e6 - 1.13825e6i) q^{98} -9.80341e6i 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 $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$3$	16.1763	−	28.0182i	0.345904	−	0.599123i	−0.639614	−	0.768697i	$-0.720906\pi$
$3$	16.1763	−	28.0182i	0.345904	−	0.599123i	0.985518	+	0.169573i	$0.0542390\pi$
$4$	32.0000	+	55.4256i	0.250000	+	0.433013i
$5$		−	211.408i		−	0.756357i	−0.925733	−	0.378179i	$-0.876551\pi$
$5$		−	211.408i		−	0.756357i	0.925733	−	0.378179i	$-0.123449\pi$
$6$	−224.146	+	129.411i	−0.423644	+	0.244591i
$7$	635.796	−	367.077i	0.700607	−	0.404496i	−0.106967	−	0.994263i	$-0.534114\pi$
$7$	635.796	−	367.077i	0.700607	−	0.404496i	0.807573	+	0.589767i	$0.200780\pi$
$8$		−	512.000i		−	0.353553i
$9$	570.153	+	987.534i	0.260701	+	0.451547i
$10$	−845.633	+	1464.68i	−0.267413	+	0.463172i
$11$	−7445.38	−	4298.59i	−1.68660	−	0.973759i	−0.957091	−	0.289789i	$-0.906415\pi$
$11$	−7445.38	−	4298.59i	−1.68660	−	0.973759i	−0.729510	−	0.683970i	$-0.760252\pi$
$12$	2070.57			0.345904
$13$	−6928.10	−	3840.57i	−0.874605	−	0.484836i
$13$	−6928.10	−	3840.57i	−0.874605	−	0.484836i
$14$	−5873.23			−0.572043
$15$	−5923.28	−	3419.81i	−0.453151	−	0.261627i
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−8168.98	−	14149.1i	−0.403271	−	0.698485i	0.590848	−	0.806783i	$-0.298793\pi$
$17$	−8168.98	−	14149.1i	−0.403271	−	0.698485i	−0.994118	+	0.108298i	$0.965460\pi$
$18$		−	9122.45i		−	0.368687i
$19$	3033.16	−	1751.20i	0.101451	−	0.0585730i	−0.448416	−	0.893825i	$-0.648012\pi$
$19$	3033.16	−	1751.20i	0.101451	−	0.0585730i	0.549867	+	0.835252i	$0.314678\pi$
$20$	11717.4	−	6765.06i	0.327512	−	0.189089i
$21$		−	23751.8i		−	0.559666i
$22$	34388.7	+	59563.0i	0.688552	+	1.19261i
$23$	−32638.2	+	56531.0i	−0.559344	+	0.968812i	0.438207	+	0.898874i	$0.355614\pi$
$23$	−32638.2	+	56531.0i	−0.559344	+	0.968812i	−0.997551	+	0.0699383i	$0.977720\pi$
$24$	−14345.3	−	8282.28i	−0.211822	−	0.122296i
$25$	33431.5			0.427924
$26$	32637.0	+	54320.7i	0.364169	+	0.606120i
$27$	107647.			1.05252
$28$	40690.9	+	23492.9i	0.350303	+	0.202248i
$29$	56295.7	−	97507.0i	0.428630	−	0.742408i	−0.568122	−	0.822944i	$-0.692330\pi$
$29$	56295.7	−	97507.0i	0.428630	−	0.742408i	0.996752	+	0.0805360i	$0.0256632\pi$
$30$	27358.5	+	47386.3i	0.184998	+	0.320426i
$31$		−	176071.i		−	1.06150i	−0.847527	−	0.530752i	$-0.821909\pi$
$31$		−	176071.i		−	1.06150i	0.847527	−	0.530752i	$-0.178091\pi$
$32$	28377.9	−	16384.0i	0.153093	−	0.0883883i
$33$	−240878.	+	139071.i	−1.16680	+	0.673654i
$34$			130704.i			0.570311i
$35$	−77603.1	−	134412.i	−0.305943	−	0.529909i
$36$	−36489.8	+	63202.2i	−0.130350	+	0.225774i
$37$	432385.	+	249638.i	1.40335	+	0.810222i	0.994734	−	0.102486i	$-0.0326798\pi$
$37$	432385.	+	249638.i	1.40335	+	0.810222i	0.408611	+	0.912708i	$0.366013\pi$
$38$	−28019.1			−0.0828347
$39$	−219677.	+	131987.i	−0.593006	+	0.356290i
$40$	−108241.			−0.267413
$41$	−250415.	−	144577.i	−0.567436	−	0.327610i	0.188688	−	0.982037i	$-0.439576\pi$
$41$	−250415.	−	144577.i	−0.567436	−	0.327610i	−0.756125	+	0.654427i	$0.772910\pi$
$42$	−95007.3	+	164557.i	−0.197872	+	0.342724i
$43$	−201010.	−	348160.i	−0.385548	−	0.667788i	0.606297	−	0.795238i	$-0.292654\pi$
$43$	−201010.	−	348160.i	−0.385548	−	0.667788i	−0.991845	+	0.127450i	$0.959321\pi$
$44$		−	550219.i		−	0.973759i
$45$	208773.	−	120535.i	0.341531	−	0.197183i
$46$	452248.	−	261106.i	0.685054	−	0.395516i
$47$		−	64966.5i		−	0.0912739i	−0.998958	−	0.0456370i	$-0.985468\pi$
$47$		−	64966.5i		−	0.0912739i	0.998958	−	0.0456370i	$-0.0145317\pi$
$48$	66258.2	+	114763.i	0.0864760	+	0.149781i
$49$	−142281.	+	246438.i	−0.172767	+	0.299241i
$50$	−231621.	−	133726.i	−0.262049	−	0.151294i
$51$	−528576.			−0.557971
$52$	−8832.82	−	506892.i	−0.00871140	−	0.499924i
$53$	263903.			0.243489			0.121744	−	0.992561i	$-0.461151\pi$
$53$	263903.			0.243489			0.121744	+	0.992561i	$0.461151\pi$
$54$	−745801.	−	430589.i	−0.644533	−	0.372121i
$55$	−908757.	+	1.57401e6i	−0.736510	+	1.27567i
$56$	−187943.	−	325527.i	−0.143011	−	0.247702i
$57$		−	113312.i		−	0.0810425i
$58$	−780056.	+	450366.i	−0.524962	+	0.303087i
$59$	2.22659e6	−	1.28552e6i	1.41143	−	0.814887i	0.415903	−	0.909409i	$-0.363466\pi$
$59$	2.22659e6	−	1.28552e6i	1.41143	−	0.814887i	0.995523	+	0.0945221i	$0.0301323\pi$
$60$		−	437736.i		−	0.261627i
$61$	269475.	+	466745.i	0.152007	+	0.263285i	0.931965	−	0.362547i	$-0.118093\pi$
$61$	269475.	+	466745.i	0.152007	+	0.263285i	−0.779958	+	0.625832i	$0.784760\pi$
$62$	−704284.	+	1.21986e6i	−0.375299	+	0.650036i
$63$	725002.	+	418580.i	0.365298	+	0.210905i
$64$	−262144.			−0.125000
$65$	−811929.	+	1.46466e6i	−0.366709	+	0.661514i
$66$	2.22513e6			0.952691
$67$	771672.	+	445525.i	0.313452	+	0.180972i	0.648470	−	0.761240i	$-0.275409\pi$
$67$	771672.	+	445525.i	0.313452	+	0.180972i	−0.335018	+	0.942212i	$0.608742\pi$
$68$	522815.	−	905541.i	0.201635	−	0.349243i
$69$	1.05593e6	+	1.82893e6i	0.386959	+	0.670232i
$70$			1.24165e6i			0.432669i
$71$	3.42530e6	−	1.97760e6i	1.13578	−	0.655744i	0.190399	−	0.981707i	$-0.439022\pi$
$71$	3.42530e6	−	1.97760e6i	1.13578	−	0.655744i	0.945382	+	0.325963i	$0.105689\pi$
$72$	505617.	−	291918.i	0.159646	−	0.0921717i
$73$			2.77895e6i			0.836087i	0.908427	+	0.418043i	$0.137284\pi$
$73$			2.77895e6i			0.836087i	−0.908427	+	0.418043i	$0.862716\pi$
$74$	−1.99710e6	−	3.45908e6i	−0.572914	−	0.992315i
$75$	540800.	−	936692.i	0.148021	−	0.256379i
$76$	194122.	+	112077.i	0.0507257	+	0.0292865i
$77$	−6.31165e6			−1.57553
$78$	2.04991e6	−	35720.7i	0.489108	−	0.00852292i
$79$	4.53826e6			1.03561			0.517803	−	0.855500i	$-0.326750\pi$
$79$	4.53826e6			1.03561			0.517803	+	0.855500i	$0.326750\pi$
$80$	749916.	+	432964.i	0.163756	+	0.0945447i
$81$	494411.	−	856345.i	0.103369	−	0.179040i
$82$	1.15662e6	+	2.00332e6i	0.231655	+	0.401238i
$83$		−	2.61022e6i		−	0.501076i	−0.968107	−	0.250538i	$-0.919393\pi$
$83$		−	2.61022e6i		−	0.501076i	0.968107	−	0.250538i	$-0.0806074\pi$
$84$	1.31646e6	−	760058.i	0.242343	−	0.139917i
$85$	−2.99123e6	+	1.72699e6i	−0.528304	+	0.305017i
$86$			3.21616e6i			0.545247i
$87$	−1.82131e6	−	3.15461e6i	−0.296529	−	0.513604i
$88$	−2.20088e6	+	3.81203e6i	−0.344276	+	0.596303i
$89$	−6.82257e6	−	3.93901e6i	−1.02585	−	0.592274i	−0.110056	−	0.993925i	$-0.535103\pi$
$89$	−6.82257e6	−	3.93901e6i	−1.02585	−	0.592274i	−0.915793	+	0.401652i	$0.868436\pi$
$90$	−1.92856e6			−0.278859
$91$	−5.81464e6	+	101323.i	−0.808868	+	0.0140949i
$92$	−4.17769e6			−0.559344
$93$	−4.93320e6	−	2.84818e6i	−0.635972	−	0.367179i
$94$	−259866.	+	450101.i	−0.0322702	+	0.0558936i
$95$	−370217.	−	641235.i	−0.0443021	−	0.0767335i
$96$		−	1.06013e6i		−	0.122296i
$97$	7.91553e6	−	4.57003e6i	0.880600	−	0.508415i	0.00974386	−	0.999953i	$-0.496898\pi$
$97$	7.91553e6	−	4.57003e6i	0.880600	−	0.508415i	0.870856	+	0.491538i	$0.163565\pi$
$98$	1.97150e6	−	1.13825e6i	0.211595	−	0.122164i
$99$		−	9.80341e6i		−	1.01544i
$100$	1.06981e6	+	1.85296e6i	0.106981	+	0.185296i
$101$	−2.87415e6	+	4.97817e6i	−0.277578	+	0.480779i	−0.970782	−	0.239962i	$-0.922865\pi$
$101$	−2.87415e6	+	4.97817e6i	−0.277578	+	0.480779i	0.693205	+	0.720741i	$0.256198\pi$
$102$	3.66208e6	+	2.11430e6i	0.341686	+	0.197273i
$103$	−9.21760e6			−0.831166			−0.415583	−	0.909555i	$-0.636422\pi$
$103$	−9.21760e6			−0.831166			−0.415583	+	0.909555i	$0.636422\pi$
$104$	−1.96637e6	+	3.54718e6i	−0.171415	+	0.309220i
$105$	−5.02133e6			−0.423308
$106$	−1.82837e6	−	1.05561e6i	−0.149106	−	0.0860863i
$107$	8.35748e6	−	1.44756e7i	0.659526	−	1.14233i	−0.321212	−	0.947007i	$-0.604090\pi$
$107$	8.35748e6	−	1.44756e7i	0.659526	−	1.14233i	0.980738	−	0.195325i	$-0.0625763\pi$
$108$	3.44471e6	+	5.96641e6i	0.263129	+	0.455754i
$109$			1.42886e7i			1.05681i	0.848993	+	0.528403i	$0.177209\pi$
$109$			1.42886e7i			1.05681i	−0.848993	+	0.528403i	$0.822791\pi$
$110$	1.25921e7	−	7.27006e6i	0.902037	−	0.520791i
$111$	1.39888e7	−	8.07644e6i	0.970846	−	0.560518i
$112$			3.00709e6i			0.202248i
$113$	1.09827e7	+	1.90225e7i	0.716032	+	1.24020i	0.962560	+	0.271069i	$0.0873770\pi$
$113$	1.09827e7	+	1.90225e7i	0.716032	+	1.24020i	−0.246528	+	0.969136i	$0.579290\pi$
$114$	−453247.	+	785046.i	−0.0286528	+	0.0496282i
$115$	1.19511e7	+	6.89999e6i	0.732768	+	0.423064i
$116$	7.20585e6			0.428630
$117$	−157377.	−	9.03144e6i	−0.00908428	−	0.521323i
$118$	−2.05683e7			−1.15242
$119$	−1.03876e7	−	5.99728e6i	−0.565068	−	0.326242i
$120$	−1.75094e6	+	3.03272e6i	−0.0924991	+	0.160213i
$121$	2.72122e7	+	4.71328e7i	1.39641	+	2.41866i
$122$		−	4.31161e6i		−	0.214971i
$123$	−8.10159e6	+	4.67746e6i	−0.392557	+	0.226643i
$124$	9.75885e6	−	5.63427e6i	0.459645	−	0.265376i
$125$		−	2.35840e7i		−	1.08002i
$126$	−3.34864e6	−	5.80001e6i	−0.149132	−	0.258305i
$127$	−1.07006e7	+	1.85339e7i	−0.463546	+	0.802886i	−0.999135	−	0.0415933i	$-0.986757\pi$
$127$	−1.07006e7	+	1.85339e7i	−0.463546	+	0.802886i	0.535588	+	0.844479i	$0.320090\pi$
$128$	1.81619e6	+	1.04858e6i	0.0765466	+	0.0441942i
$129$	−1.30064e7			−0.533450
$130$	1.14838e7	−	6.89972e6i	0.458443	−	0.275442i
$131$	2.79550e7			1.08645			0.543226	−	0.839587i	$-0.317203\pi$
$131$	2.79550e7			1.08645			0.543226	+	0.839587i	$0.317203\pi$
$132$	−1.54162e7	−	8.90053e6i	−0.583402	−	0.336827i
$133$	1.28565e6	−	2.22681e6i	0.0473850	−	0.0820732i
$134$	−3.56420e6	−	6.17337e6i	−0.127966	−	0.221644i
$135$		−	2.27575e7i		−	0.796079i
$136$	−7.24433e6	+	4.18252e6i	−0.246952	+	0.142578i
$137$	−3.87791e7	+	2.23891e7i	−1.28848	+	0.743902i	−0.978382	−	0.206804i	$-0.933694\pi$
$137$	−3.87791e7	+	2.23891e7i	−1.28848	+	0.743902i	−0.310093	+	0.950706i	$0.600360\pi$
$138$		−	1.68949e7i		−	0.547242i
$139$	−1.19723e7	−	2.07367e7i	−0.378117	−	0.654918i	0.612671	−	0.790338i	$-0.290095\pi$
$139$	−1.19723e7	−	2.07367e7i	−0.378117	−	0.654918i	−0.990788	+	0.135420i	$0.956762\pi$
$140$	4.96660e6	−	8.60240e6i	0.152972	−	0.264955i
$141$	−1.82024e6	−	1.05092e6i	−0.0546843	−	0.0315720i
$142$	−3.16416e7			−0.927362
$143$	3.50732e7	+	5.83756e7i	1.00300	+	1.66938i
$144$	−4.67069e6			−0.130350
$145$	−2.06138e7	−	1.19014e7i	−0.561526	−	0.324197i
$146$	1.11158e7	−	1.92532e7i	0.295601	−	0.511997i
$147$	4.60316e6	+	7.97291e6i	0.119521	+	0.207017i
$148$			3.19536e7i			0.810222i
$149$	3.40494e7	−	1.96584e7i	0.843253	−	0.486852i	−0.0151156	−	0.999886i	$-0.504812\pi$
$149$	3.40494e7	−	1.96584e7i	0.843253	−	0.486852i	0.858369	+	0.513033i	$0.171478\pi$
$150$	−7.49354e6	+	4.32640e6i	−0.181287	+	0.104666i
$151$		−	5.45163e7i		−	1.28857i	−0.764786	−	0.644284i	$-0.777155\pi$
$151$		−	5.45163e7i		−	1.28857i	0.764786	−	0.644284i	$-0.222845\pi$
$152$	−896612.	−	1.55298e6i	−0.0207087	−	0.0358685i
$153$	9.31513e6	−	1.61343e7i	0.210266	−	0.364191i
$154$	4.37284e7	+	2.52466e7i	0.964808	+	0.557032i
$155$	−3.72229e7			−0.802877
$156$	−1.43451e7	−	7.95218e6i	−0.302529	−	0.167707i
$157$	−6.58173e7			−1.35735			−0.678674	−	0.734440i	$-0.737445\pi$
$157$	−6.58173e7			−1.35735			−0.678674	+	0.734440i	$0.737445\pi$
$158$	−3.14420e7	−	1.81531e7i	−0.634177	−	0.366142i
$159$	4.26898e6	−	7.39409e6i	0.0842237	−	0.145880i
$160$	−3.46371e6	−	5.99933e6i	−0.0668532	−	0.115793i
$161$			4.79229e7i			0.905009i
$162$	−6.85076e6	+	3.95529e6i	−0.126601	+	0.0730930i
$163$	5.64786e7	−	3.26079e7i	1.02147	−	0.589748i	0.106944	−	0.994265i	$-0.465894\pi$
$163$	5.64786e7	−	3.26079e7i	1.02147	−	0.589748i	0.914531	+	0.404517i	$0.132560\pi$
$164$		−	1.85059e7i		−	0.327610i
$165$	2.94007e7	+	5.09235e7i	0.509523	+	0.882520i
$166$	−1.04409e7	+	1.80841e7i	−0.177157	+	0.306845i
$167$	−5.48034e7	−	3.16407e7i	−0.910541	−	0.525701i	−0.0299360	−	0.999552i	$-0.509530\pi$
$167$	−5.48034e7	−	3.16407e7i	−0.910541	−	0.525701i	−0.880605	+	0.473851i	$0.842864\pi$
$168$	−1.21609e7			−0.197872
$169$	3.32485e7	+	5.32157e7i	0.529869	+	0.848079i
$170$	2.76318e7			0.431359
$171$	3.45873e6	+	1.99690e6i	0.0528969	+	0.0305401i
$172$	1.28646e7	−	2.22822e7i	0.192774	−	0.333894i
$173$	−3.84579e7	−	6.66111e7i	−0.564709	−	0.978104i	−0.997077	−	0.0764069i	$-0.975655\pi$
$173$	−3.84579e7	−	6.66111e7i	−0.564709	−	0.978104i	0.432368	−	0.901697i	$-0.357678\pi$
$174$			2.91410e7i			0.419356i
$175$	2.12556e7	−	1.22719e7i	0.299806	−	0.173093i
$176$	3.04963e7	−	1.76070e7i	0.421650	−	0.243440i
$177$		−	8.31801e7i		−	1.12749i
$178$	3.15121e7	+	5.45806e7i	0.418801	+	0.725384i
$179$	−4.32366e7	+	7.48880e7i	−0.563464	+	0.975948i	0.433727	+	0.901044i	$0.357198\pi$
$179$	−4.32366e7	+	7.48880e7i	−0.563464	+	0.975948i	−0.997191	+	0.0749036i	$0.976135\pi$
$180$	1.33615e7	+	7.71424e6i	0.170766	+	0.0985915i
$181$	−8.42468e7			−1.05603			−0.528017	−	0.849234i	$-0.677064\pi$
$181$	−8.42468e7			−1.05603			−0.528017	+	0.849234i	$0.677064\pi$
$182$	4.06903e7	+	2.25566e7i	0.500312	+	0.277347i
$183$	1.74365e7			0.210320
$184$	2.89439e7	+	1.67108e7i	0.342527	+	0.197758i
$185$	5.27755e7	−	9.14098e7i	0.612817	−	1.06143i
$186$	2.27855e7	+	3.94656e7i	0.259635	+	0.449700i
$187$			1.40460e8i			1.57075i
$188$	3.60081e6	−	2.07893e6i	0.0395228	−	0.0228185i
$189$	6.84416e7	−	3.95148e7i	0.737401	−	0.425739i
$190$			5.92348e6i			0.0626526i
$191$	1.60963e7	+	2.78796e7i	0.167151	+	0.289514i	0.937417	−	0.348209i	$-0.113210\pi$
$191$	1.60963e7	+	2.78796e7i	0.167151	+	0.289514i	−0.770266	+	0.637723i	$0.779877\pi$
$192$	−4.24053e6	+	7.34481e6i	−0.0432380	+	0.0748904i
$193$	7.67729e7	+	4.43249e7i	0.768701	+	0.443810i	0.832411	−	0.554159i	$-0.186960\pi$
$193$	7.67729e7	+	4.43249e7i	0.768701	+	0.443810i	−0.0637099	+	0.997968i	$0.520293\pi$
$194$	−7.31205e7			−0.719007
$195$	2.79030e7	+	4.64416e7i	0.269482	+	0.448524i
$196$	−1.82119e7			−0.172767
$197$	7.69162e6	+	4.44076e6i	0.0716780	+	0.0413833i	0.535411	−	0.844592i	$-0.320157\pi$
$197$	7.69162e6	+	4.44076e6i	0.0716780	+	0.0413833i	−0.463733	+	0.885975i	$0.653490\pi$
$198$	−3.92137e7	+	6.79200e7i	−0.359012	+	0.621827i
$199$	−3.95228e7	−	6.84555e7i	−0.355519	−	0.615776i	0.631688	−	0.775223i	$-0.282362\pi$
$199$	−3.95228e7	−	6.84555e7i	−0.355519	−	0.615776i	−0.987207	+	0.159447i	$0.949029\pi$
$200$		−	1.71170e7i		−	0.151294i
$201$	2.49656e7	−	1.44139e7i	0.216848	−	0.125198i
$202$	3.98254e7	−	2.29932e7i	0.339962	−	0.196277i
$203$		−	8.26594e7i		−	0.693515i
$204$	−1.69144e7	−	2.92967e7i	−0.139493	−	0.241609i
$205$	−3.05648e7	+	5.29398e7i	−0.247790	+	0.429185i
$206$	6.38614e7	+	3.68704e7i	0.508983	+	0.293862i
$207$	−7.44351e7			−0.583286
$208$	2.78122e7	−	1.67101e7i	0.214296	−	0.128753i
$209$	−3.01107e7			−0.228144
$210$	3.47888e7	+	2.00853e7i	0.259222	+	0.149662i
$211$	1.08770e8	−	1.88395e8i	0.797114	−	1.38064i	−0.124373	−	0.992235i	$-0.539692\pi$
$211$	1.08770e8	−	1.88395e8i	0.797114	−	1.38064i	0.921488	−	0.388407i	$-0.126975\pi$
$212$	8.44490e6	+	1.46270e7i	0.0608722	+	0.105434i
$213$		−	1.27961e8i		−	0.907297i
$214$	−1.15805e8	+	6.68598e7i	−0.807751	+	0.466355i
$215$	−7.36038e7	+	4.24952e7i	−0.505086	+	0.291612i
$216$		−	5.51154e7i		−	0.372121i
$217$	−6.46316e7	−	1.11945e8i	−0.429374	−	0.743698i
$218$	5.71542e7	−	9.89940e7i	0.373638	−	0.647159i
$219$	7.78614e7	+	4.49533e7i	0.500919	+	0.289206i
$220$	−1.16321e8			−0.736510
$221$	2.25485e6	+	1.29400e8i	0.0140522	+	0.806419i
$222$	−1.29223e8			−0.792692
$223$	−1.08999e8	−	6.29308e7i	−0.658198	−	0.380011i	0.133392	−	0.991063i	$-0.457413\pi$
$223$	−1.08999e8	−	6.29308e7i	−0.658198	−	0.380011i	−0.791590	+	0.611052i	$0.790746\pi$
$224$	1.20284e7	−	2.08338e7i	0.0715054	−	0.123851i
$225$	1.90611e7	+	3.30148e7i	0.111560	+	0.193228i
$226$		−	1.75722e8i		−	1.01262i
$227$	−2.28753e8	+	1.32070e8i	−1.29800	+	0.749402i	−0.980059	−	0.198708i	$-0.936326\pi$
$227$	−2.28753e8	+	1.32070e8i	−1.29800	+	0.749402i	−0.317943	+	0.948110i	$0.602992\pi$
$228$	6.28037e6	−	3.62597e6i	0.0350924	−	0.0202606i
$229$			6.38112e7i			0.351134i	0.984467	+	0.175567i	$0.0561759\pi$
$229$			6.38112e7i			0.351134i	−0.984467	+	0.175567i	$0.943824\pi$
$230$	−5.51999e7	−	9.56090e7i	−0.299151	−	0.518145i
$231$	−1.02099e8	+	1.76841e8i	−0.544980	+	0.943934i
$232$	−4.99236e7	−	2.88234e7i	−0.262481	−	0.151543i
$233$	−1.58319e8			−0.819947			−0.409974	−	0.912097i	$-0.634462\pi$
$233$	−1.58319e8			−0.819947			−0.409974	+	0.912097i	$0.634462\pi$
$234$	−3.50354e7	+	6.32012e7i	−0.178752	+	0.322455i
$235$	−1.37344e7			−0.0690357
$236$	1.42502e8	+	8.22734e7i	0.705713	+	0.407443i
$237$	7.34124e7	−	1.27154e8i	0.358220	−	0.620456i
$238$	4.79783e7	+	8.31008e7i	0.230688	+	0.399564i
$239$			2.79618e8i			1.32487i	0.749120	+	0.662434i	$0.230477\pi$
$239$			2.79618e8i			1.32487i	−0.749120	+	0.662434i	$0.769523\pi$
$240$	2.42618e7	−	1.40075e7i	0.113288	−	0.0654067i
$241$	1.95982e8	−	1.13150e8i	0.901895	−	0.520710i	0.0240807	−	0.999710i	$-0.492334\pi$
$241$	1.95982e8	−	1.13150e8i	0.901895	−	0.520710i	0.877815	+	0.479000i	$0.159001\pi$
$242$		−	4.35395e8i		−	1.97483i
$243$	1.01717e8	+	1.76178e8i	0.454747	+	0.787646i
$244$	−1.72464e7	+	2.98717e7i	−0.0760037	+	0.131642i
$245$	5.20989e7	+	3.00793e7i	0.226333	+	0.130673i
$246$	7.48393e7			0.320521
$247$	−2.77396e7	+	483375.i	−0.117128	+	0.00204101i
$248$	−9.01484e7			−0.375299
$249$	−7.31336e7	−	4.22237e7i	−0.300206	−	0.173324i
$250$	−9.43359e7	+	1.63395e8i	−0.381845	+	0.661375i
$251$	1.08219e8	+	1.87441e8i	0.431962	+	0.748181i	0.997042	−	0.0768554i	$-0.0244880\pi$
$251$	1.08219e8	+	1.87441e8i	0.431962	+	0.748181i	−0.565080	+	0.825036i	$0.691155\pi$
$252$			5.35782e7i			0.210905i
$253$	4.86008e8	−	2.80597e8i	1.88678	−	1.08933i
$254$	1.48271e8	−	8.56044e7i	0.567726	−	0.327777i
$255$			1.11745e8i			0.422026i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	1.21788e8	−	2.10943e8i	0.447547	−	0.775174i	−0.550679	−	0.834717i	$-0.685631\pi$
$257$	1.21788e8	−	2.10943e8i	0.447547	−	0.775174i	0.998226	+	0.0595432i	$0.0189644\pi$
$258$	9.01111e7	+	5.20257e7i	0.326670	+	0.188603i
$259$	3.66545e8			1.31093
$260$	−1.07161e8	+	1.86733e6i	−0.378121	+	0.00658893i
$261$	1.28389e8			0.446977
$262$	−1.93678e8	−	1.11820e8i	−0.665313	−	0.384119i
$263$	2.52252e6	−	4.36913e6i	0.00855045	−	0.0148098i	−0.861719	−	0.507387i	$-0.830612\pi$
$263$	2.52252e6	−	4.36913e6i	0.00855045	−	0.0148098i	0.870269	+	0.492577i	$0.163945\pi$
$264$	7.12042e7	+	1.23329e8i	0.238173	+	0.412527i
$265$		−	5.57913e7i		−	0.184164i
$266$	−1.78144e7	+	1.02852e7i	−0.0580345	+	0.0335063i
$267$	−2.20728e8	+	1.27438e8i	−0.709690	+	0.409740i
$268$			5.70272e7i			0.180972i
$269$	2.32684e8	+	4.03021e8i	0.728844	+	1.26239i	0.957372	+	0.288857i	$0.0932752\pi$
$269$	2.32684e8	+	4.03021e8i	0.728844	+	1.26239i	−0.228529	+	0.973537i	$0.573391\pi$
$270$	−9.10300e7	+	1.57669e8i	−0.281457	+	0.487497i
$271$	−2.87325e8	−	1.65887e8i	−0.876962	−	0.506314i	−0.00730633	−	0.999973i	$-0.502326\pi$
$271$	−2.87325e8	−	1.65887e8i	−0.876962	−	0.506314i	−0.869655	+	0.493659i	$0.835659\pi$
$272$	6.69203e7			0.201635
$273$	−9.12206e7	+	1.64555e8i	−0.271346	+	0.489487i
$274$	3.58226e8			1.05204
$275$	−2.48910e8	−	1.43708e8i	−0.721736	−	0.416695i
$276$	−6.75797e7	+	1.17051e8i	−0.193479	+	0.335116i
$277$	−2.04267e8	−	3.53801e8i	−0.577456	−	1.00018i	−0.995770	−	0.0918807i	$-0.970712\pi$
$277$	−2.04267e8	−	3.53801e8i	−0.577456	−	1.00018i	0.418314	−	0.908302i	$-0.362621\pi$
$278$			1.91557e8i			0.534739i
$279$	1.73876e8	−	1.00387e8i	0.479320	−	0.276735i
$280$	−6.88192e7	+	3.97328e7i	−0.187351	+	0.108167i
$281$			6.26412e8i			1.68418i	0.539339	+	0.842089i	$0.318674\pi$
$281$			6.26412e8i			1.68418i	−0.539339	+	0.842089i	$0.681326\pi$
$282$	8.40735e6	+	1.45620e7i	0.0223248	+	0.0386677i
$283$	−1.37435e7	+	2.38045e7i	−0.0360450	+	0.0624318i	−0.883485	−	0.468459i	$-0.844809\pi$
$283$	−1.37435e7	+	2.38045e7i	−0.0360450	+	0.0624318i	0.847440	+	0.530891i	$0.178143\pi$
$284$	2.19219e8	+	1.26566e8i	0.567891	+	0.327872i
$285$	−2.39550e7			−0.0612971
$286$	−9.49217e6	−	5.44731e8i	−0.0239930	−	1.37689i
$287$	−2.12284e8			−0.530066
$288$	3.23595e7	+	1.86828e7i	0.0798230	+	0.0460859i
$289$	7.17049e7	−	1.24197e8i	0.174746	−	0.302669i
$290$	9.52110e7	+	1.64910e8i	0.229242	+	0.397059i
$291$		−	2.95705e8i		−	0.703451i
$292$	−1.54025e8	+	8.89265e7i	−0.362036	+	0.209022i
$293$	−1.60266e8	+	9.25295e7i	−0.372224	+	0.214904i	−0.674430	−	0.738339i	$-0.735610\pi$
$293$	−1.60266e8	+	9.25295e7i	−0.372224	+	0.214904i	0.302206	+	0.953243i	$0.402277\pi$
$294$		−	7.36506e7i		−	0.169029i
$295$	−2.71770e8	−	4.70719e8i	−0.616346	−	1.06754i
$296$	1.27814e8	−	2.21381e8i	0.286457	−	0.496158i
$297$	−8.01474e8	−	4.62731e8i	−1.77518	−	1.02490i
$298$	−3.14535e8			−0.688513
$299$	4.43232e8	−	2.66303e8i	0.958920	−	0.576139i
$300$	6.92223e7			0.148021
$301$	−2.55603e8	−	1.47572e8i	−0.540235	−	0.311905i
$302$	−2.18065e8	+	3.77700e8i	−0.455578	+	0.789083i
$303$	9.29864e7	+	1.61057e8i	0.192030	+	0.332606i
$304$			1.43458e7i			0.0292865i
$305$	9.86738e7	−	5.69693e7i	0.199137	−	0.114972i
$306$	−1.29074e8	+	7.45211e7i	−0.257522	+	0.148681i
$307$		−	2.08464e7i		−	0.0411194i	−0.999789	−	0.0205597i	$-0.993455\pi$
$307$		−	2.08464e7i		−	0.0411194i	0.999789	−	0.0205597i	$-0.00654481\pi$
$308$	−2.01973e8	−	3.49827e8i	−0.393881	−	0.682222i
$309$	−1.49107e8	+	2.58261e8i	−0.287504	+	0.497971i
$310$	2.57888e8	+	1.48891e8i	0.491660	+	0.283860i
$311$	7.13088e7			0.134426			0.0672128	−	0.997739i	$-0.478589\pi$
$311$	7.13088e7			0.134426			0.0672128	+	0.997739i	$0.478589\pi$
$312$	6.75771e7	+	1.12475e8i	0.125967	+	0.209659i
$313$	3.19037e8			0.588080			0.294040	−	0.955793i	$-0.405000\pi$
$313$	3.19037e8			0.588080			0.294040	+	0.955793i	$0.405000\pi$
$314$	4.55995e8	+	2.63269e8i	0.831202	+	0.479895i
$315$	8.84912e7	−	1.53271e8i	0.159519	−	0.276296i
$316$	1.45224e8	+	2.51536e8i	0.258902	+	0.448431i
$317$		−	3.53993e8i		−	0.624147i	−0.950058	−	0.312074i	$-0.898976\pi$
$317$		−	3.53993e8i		−	0.624147i	0.950058	−	0.312074i	$-0.101024\pi$
$318$	−5.91527e7	+	3.41518e7i	−0.103153	+	0.0595551i
$319$	−8.38285e8	+	4.83984e8i	−1.44585	+	0.834764i
$320$			5.54194e7i			0.0945447i
$321$	−2.70387e8	−	4.68323e8i	−0.456265	−	0.790275i
$322$	1.91692e8	−	3.32020e8i	0.319969	−	0.554202i
$323$	−4.95556e7	−	2.86110e7i	−0.0818247	−	0.0472415i
$324$	6.32846e7			0.103369
$325$	−2.31617e8	−	1.28396e8i	−0.374264	−	0.207473i
$326$	−5.21727e8			−0.834030
$327$	4.00340e8	+	2.31136e8i	0.633157	+	0.365554i
$328$	−7.40236e7	+	1.28213e8i	−0.115827	+	0.200619i
$329$	−2.38477e7	−	4.13054e7i	−0.0369199	−	0.0639471i
$330$		−	4.70411e8i		−	0.720575i
$331$	8.73685e8	−	5.04422e8i	1.32421	−	0.764533i	0.339813	−	0.940493i	$-0.389636\pi$
$331$	8.73685e8	−	5.04422e8i	1.32421	−	0.764533i	0.984397	+	0.175960i	$0.0563028\pi$
$332$	1.44673e8	−	8.35269e7i	0.216972	−	0.125269i
$333$			5.69327e8i			0.844903i
$334$	2.53126e8	+	4.38427e8i	0.371727	+	0.643850i
$335$	9.41877e7	−	1.63138e8i	0.136879	−	0.237082i
$336$	8.42534e7	+	4.86437e7i	0.121171	+	0.0699583i
$337$	6.85528e8			0.975709			0.487855	−	0.872925i	$-0.337780\pi$
$337$	6.85528e8			0.975709			0.487855	+	0.872925i	$0.337780\pi$
$338$	−1.74894e7	−	5.01683e8i	−0.0246358	−	0.706677i
$339$	7.10636e8			0.990714
$340$	−1.91439e8	−	1.10527e8i	−0.264152	−	0.152508i
$341$	−7.56857e8	+	1.31091e9i	−1.03365	+	1.79033i
$342$	−1.59752e7	−	2.76699e7i	−0.0215951	−	0.0374038i
$343$			8.13519e8i			1.08852i
$344$	−1.78258e8	+	1.02917e8i	−0.236099	+	0.136312i
$345$	3.86651e8	−	2.23233e8i	0.506935	−	0.292679i
$346$			6.15327e8i			0.798619i
$347$	2.49148e8	+	4.31537e8i	0.320114	+	0.554453i	0.980511	−	0.196463i	$-0.0629456\pi$
$347$	2.49148e8	+	4.31537e8i	0.320114	+	0.554453i	−0.660398	+	0.750916i	$0.729612\pi$
$348$	1.16564e8	−	2.01895e8i	0.148265	−	0.256802i
$349$	−2.43339e8	−	1.40492e8i	−0.306424	−	0.176914i	0.338901	−	0.940822i	$-0.389945\pi$
$349$	−2.43339e8	−	1.40492e8i	−0.306424	−	0.176914i	−0.645325	+	0.763908i	$0.723278\pi$
$350$	−1.96351e8			−0.244791
$351$	−7.45790e8	−	4.13427e8i	−0.920538	−	0.510298i
$352$	−2.81712e8			−0.344276
$353$	5.71431e8	+	3.29916e8i	0.691437	+	0.399201i	0.804150	−	0.594426i	$-0.202621\pi$
$353$	5.71431e8	+	3.29916e8i	0.691437	+	0.399201i	−0.112713	+	0.993628i	$0.535954\pi$
$354$	−3.32720e8	+	5.76288e8i	−0.398628	+	0.690444i
$355$	−4.18081e8	−	7.24137e8i	−0.495976	−	0.859056i
$356$		−	5.04194e8i		−	0.592274i
$357$	−3.36066e8	+	1.94028e8i	−0.390919	+	0.225697i
$358$	5.99104e8	−	3.45893e8i	0.690099	−	0.398429i
$359$		−	3.72973e7i		−	0.0425448i	−0.999774	−	0.0212724i	$-0.993228\pi$
$359$		−	3.72973e7i		−	0.0425448i	0.999774	−	0.0212724i	$-0.00677172\pi$
$360$	−6.17139e7	−	1.06892e8i	−0.0697147	−	0.120749i
$361$	−4.40802e8	+	7.63492e8i	−0.493138	+	0.854141i
$362$	5.83679e8	+	3.36987e8i	0.646687	+	0.373365i
$363$	1.76077e9			1.93210
$364$	−1.91684e8	−	3.19038e8i	−0.208320	−	0.346727i
$365$	5.87494e8			0.632380
$366$	−1.20804e8	−	6.97459e7i	−0.128794	−	0.0743593i
$367$	3.60243e8	−	6.23959e8i	0.380421	−	0.658908i	−0.610702	−	0.791861i	$-0.709113\pi$
$367$	3.60243e8	−	6.23959e8i	0.380421	−	0.658908i	0.991122	+	0.132953i	$0.0424459\pi$
$368$	−1.33686e8	−	2.31551e8i	−0.139836	−	0.242203i
$369$		−	3.29725e8i		−	0.341632i
$370$	−7.31278e8	+	4.22204e8i	−0.750545	+	0.433327i
$371$	1.67788e8	−	9.68727e7i	0.170590	−	0.0984901i
$372$		−	3.64567e8i		−	0.367179i
$373$	1.45502e8	+	2.52017e8i	0.145174	+	0.251449i	0.929438	−	0.368979i	$-0.120292\pi$
$373$	1.45502e8	+	2.52017e8i	0.145174	+	0.251449i	−0.784264	+	0.620427i	$0.786959\pi$
$374$	5.61841e8	−	9.73138e8i	0.555345	−	0.961886i
$375$	−6.60781e8	−	3.81502e8i	−0.647065	−	0.373583i
$376$	−3.32628e7			−0.0322702
$377$	−7.64505e8	+	4.59330e8i	−0.734828	+	0.441499i
$378$	−6.32236e8			−0.602086
$379$	9.12613e8	+	5.26897e8i	0.861092	+	0.497152i	0.864378	−	0.502843i	$-0.167713\pi$
$379$	9.12613e8	+	5.26897e8i	0.861092	+	0.497152i	−0.00328585	+	0.999995i	$0.501046\pi$
$380$	2.36939e7	−	4.10391e7i	0.0221510	−	0.0383667i
$381$	3.46191e8	+	5.99621e8i	0.320685	+	0.555443i
$382$		−	2.57541e8i		−	0.236387i
$383$	−1.61663e9	+	9.33363e8i	−1.47033	+	0.848896i	−0.999445	−	0.0332976i	$-0.989399\pi$
$383$	−1.61663e9	+	9.33363e8i	−1.47033	+	0.848896i	−0.470886	+	0.882194i	$0.656066\pi$
$384$	5.87585e7	−	3.39242e7i	0.0529555	−	0.0305739i
$385$			1.33433e9i			1.19166i
$386$	−3.54599e8	−	6.14183e8i	−0.313821	−	0.543554i
$387$	2.29213e8	−	3.97008e8i	0.201025	−	0.348186i
$388$	5.06594e8	+	2.92482e8i	0.440300	+	0.254207i
$389$	1.47943e9			1.27430			0.637151	−	0.770739i	$-0.280113\pi$
$389$	1.47943e9			1.27430			0.637151	+	0.770739i	$0.280113\pi$
$390$	−7.55164e6	−	4.33369e8i	−0.00644637	−	0.369940i
$391$	1.06648e9			0.902268
$392$	1.26176e8	+	7.28478e7i	0.105798	+	0.0610822i
$393$	4.52210e8	−	7.83250e8i	0.375808	−	0.650919i
$394$	−3.55261e7	−	6.15329e7i	−0.0292624	−	0.0506840i
$395$		−	9.59426e8i		−	0.783289i
$396$	5.43360e8	−	3.13709e8i	0.439698	−	0.253860i
$397$	−1.94946e9	+	1.12552e9i	−1.56368	+	0.902789i	−0.566796	+	0.823858i	$0.691817\pi$
$397$	−1.94946e9	+	1.12552e9i	−1.56368	+	0.902789i	−0.996880	+	0.0789312i	$0.974849\pi$
$398$			6.32365e8i			0.502779i
$399$	−4.15941e7	−	7.20431e7i	−0.0327813	−	0.0567789i
$400$	−6.84678e7	+	1.18590e8i	−0.0534905	+	0.0926482i
$401$	−1.62628e9	−	9.38935e8i	−1.25948	−	0.727161i	−0.286506	−	0.958078i	$-0.592494\pi$
$401$	−1.62628e9	−	9.38935e8i	−1.25948	−	0.727161i	−0.972973	+	0.230918i	$0.925827\pi$
$402$	−2.30623e8			−0.177056
$403$	−6.76214e8	+	1.21984e9i	−0.514655	+	0.928398i
$404$	−3.67891e8			−0.277578
$405$	−1.81038e8	−	1.04523e8i	−0.135419	−	0.0781839i
$406$	−3.30637e8	+	5.72681e8i	−0.245195	+	0.424690i
$407$	−2.14618e9	−	3.71729e9i	−1.57792	−	2.73304i
$408$			2.70631e8i			0.197273i
$409$	−5.51529e8	+	3.18426e8i	−0.398600	+	0.230132i	−0.685880	−	0.727715i	$-0.740582\pi$
$409$	−5.51529e8	+	3.18426e8i	−0.398600	+	0.230132i	0.287280	+	0.957847i	$0.407249\pi$
$410$	4.23519e8	−	2.44519e8i	0.303479	−	0.175214i
$411$			1.44870e9i			1.02927i
$412$	−2.94963e8	−	5.10891e8i	−0.207792	−	0.359905i
$413$	9.43770e8	−	1.63466e9i	0.659236	−	1.14183i
$414$	5.15702e8	+	2.97740e8i	0.357188	+	0.206223i
$415$	−5.51821e8			−0.378992
$416$	−2.59529e8	+	4.52241e6i	−0.176750	+	0.00307994i
$417$	−7.74673e8			−0.523169
$418$	2.08613e8	+	1.20443e8i	0.139709	+	0.0806610i
$419$	7.77149e8	−	1.34606e9i	0.516125	−	0.893955i	−0.483699	−	0.875234i	$-0.660707\pi$
$419$	7.77149e8	−	1.34606e9i	0.516125	−	0.893955i	0.999825	−	0.0187211i	$-0.00595945\pi$
$420$	−1.60683e8	−	2.78310e8i	−0.105827	−	0.183298i
$421$		−	9.46533e8i		−	0.618228i	−0.951025	−	0.309114i	$-0.899968\pi$
$421$		−	9.46533e8i		−	0.618228i	0.951025	−	0.309114i	$-0.100032\pi$
$422$	−1.50716e9	+	8.70160e8i	−0.976262	+	0.563645i
$423$	6.41566e7	−	3.70408e7i	0.0412145	−	0.0237952i
$424$		−	1.35118e8i		−	0.0860863i
$425$	−2.73102e8	−	4.73026e8i	−0.172569	−	0.298898i
$426$	−5.11845e8	+	8.86541e8i	−0.320778	+	0.555604i
$427$	3.42663e8	+	1.97836e8i	0.212995	+	0.122973i
$428$	1.06976e9			0.659526
$429$	2.20293e9	−	3.83871e7i	1.34710	−	0.0234739i
$430$	6.79923e8			0.412401
$431$	−4.49874e7	−	2.59735e7i	−0.0270658	−	0.0156264i	0.486406	−	0.873733i	$-0.338308\pi$
$431$	−4.49874e7	−	2.59735e7i	−0.0270658	−	0.0156264i	−0.513472	+	0.858106i	$0.671641\pi$
$432$	−2.20461e8	+	3.81850e8i	−0.131565	+	0.227877i
$433$	7.84073e8	+	1.35806e9i	0.464140	+	0.803914i	0.999162	−	0.0409237i	$-0.0130301\pi$
$433$	7.84073e8	+	1.35806e9i	0.464140	+	0.803914i	−0.535022	+	0.844838i	$0.679697\pi$
$434$			1.03411e9i			0.607226i
$435$	−6.66911e8	+	3.85041e8i	−0.388468	+	0.224282i
$436$	−7.91952e8	+	4.57234e8i	−0.457611	+	0.264202i
$437$			2.28624e8i			0.131050i
$438$	−3.59626e8	−	6.22891e8i	−0.204499	−	0.354203i
$439$	4.29729e8	−	7.44312e8i	0.242420	−	0.419884i	−0.718983	−	0.695028i	$-0.755392\pi$
$439$	4.29729e8	−	7.44312e8i	0.242420	−	0.419884i	0.961403	+	0.275144i	$0.0887255\pi$
$440$	8.05895e8	+	4.65284e8i	0.451018	+	0.260396i
$441$	−3.24487e8			−0.180162
$442$	5.01977e8	−	9.05527e8i	0.276507	−	0.498797i
$443$	3.13741e8			0.171458			0.0857292	−	0.996318i	$-0.472678\pi$
$443$	3.13741e8			0.171458			0.0857292	+	0.996318i	$0.472678\pi$
$444$	8.95284e8	+	5.16892e8i	0.485423	+	0.280259i
$445$	−8.32740e8	+	1.44235e9i	−0.447971	+	0.775908i
$446$	5.03446e8	+	8.71995e8i	0.268708	+	0.465417i
$447$		−	1.27201e9i		−	0.673617i
$448$	−1.66670e8	+	9.62270e7i	−0.0875759	+	0.0505619i
$449$	−7.07915e7	+	4.08715e7i	−0.0369079	+	0.0213088i	−0.518340	−	0.855174i	$-0.673450\pi$
$449$	−7.07915e7	+	4.08715e7i	−0.0369079	+	0.0213088i	0.481433	+	0.876483i	$0.340117\pi$
$450$		−	3.04978e8i		−	0.157770i
$451$	1.24296e9	+	2.15286e9i	0.638026	+	1.10509i
$452$	−7.02890e8	+	1.21744e9i	−0.358016	+	0.620102i
$453$	−1.52745e9	−	8.81874e8i	−0.772011	−	0.445721i
$454$	2.11313e9			1.05981
$455$	2.14204e7	+	1.22926e9i	0.0106608	+	0.611793i
$456$	−5.80156e7			−0.0286528
$457$	1.68781e9	+	9.74458e8i	0.827213	+	0.477592i	0.852897	−	0.522079i	$-0.174843\pi$
$457$	1.68781e9	+	9.74458e8i	0.827213	+	0.477592i	−0.0256846	+	0.999670i	$0.508177\pi$
$458$	2.55245e8	−	4.42097e8i	0.124145	−	0.215025i
$459$	−8.79367e8	−	1.52311e9i	−0.424449	−	0.735168i
$460$			8.83199e8i			0.423064i
$461$	2.99997e9	−	1.73204e9i	1.42615	−	0.823386i	0.429333	−	0.903146i	$-0.358749\pi$
$461$	2.99997e9	−	1.73204e9i	1.42615	−	0.823386i	0.996814	+	0.0797602i	$0.0254155\pi$
$462$	1.41473e9	−	8.16794e8i	0.667462	−	0.385359i
$463$		−	1.13332e9i		−	0.530665i	−0.964157	−	0.265332i	$-0.914518\pi$
$463$		−	1.13332e9i		−	0.530665i	0.964157	−	0.265332i	$-0.0854817\pi$
$464$	2.30587e8	+	3.99389e8i	0.107157	+	0.185602i
$465$	−6.02129e8	+	1.04292e9i	−0.277718	+	0.481022i
$466$	1.09686e9	+	6.33274e8i	0.502113	+	0.289895i
$467$	2.08755e9			0.948479			0.474239	−	0.880396i	$-0.342723\pi$
$467$	2.08755e9			0.948479			0.474239	+	0.880396i	$0.342723\pi$
$468$	4.95537e8	−	2.97729e8i	0.223468	−	0.134264i
$469$	6.54167e8			0.292809
$470$	9.51551e7	+	5.49378e7i	0.0422756	+	0.0244078i
$471$	−1.06468e9	+	1.84408e9i	−0.469512	+	0.813218i
$472$	−6.58187e8	−	1.14001e9i	−0.288106	−	0.499014i
$473$			3.45624e9i			1.50172i
$474$	−1.01723e9	+	5.87299e8i	−0.438729	+	0.253300i
$475$	1.01403e8	−	5.85452e7i	0.0434134	−	0.0250648i
$476$		−	7.67652e8i		−	0.326242i
$477$	1.50465e8	+	2.60613e8i	0.0634777	+	0.109947i
$478$	1.11847e9	−	1.93725e9i	0.468412	−	0.811313i
$479$	−1.60014e8	−	9.23844e7i	−0.0665250	−	0.0384082i	0.466369	−	0.884590i	$-0.345562\pi$
$479$	−1.60014e8	−	9.23844e7i	−0.0665250	−	0.0384082i	−0.532894	+	0.846182i	$0.678895\pi$
$480$	−2.24121e8			−0.0924991
$481$	−2.03685e9	−	3.39012e9i	−0.834549	−	1.38902i
$482$	−1.81040e9			−0.736394
$483$	1.34271e9	+	7.75217e8i	0.542212	+	0.313046i
$484$	−1.74158e9	+	3.01650e9i	−0.698207	+	1.20933i
$485$	−9.66142e8	−	1.67341e9i	−0.384543	−	0.666048i
$486$		−	1.62747e9i		−	0.643110i
$487$	−1.97464e9	+	1.14006e9i	−0.774704	+	0.447275i	−0.834550	−	0.550932i	$-0.814272\pi$
$487$	−1.97464e9	+	1.14006e9i	−0.774704	+	0.447275i	0.0598463	+	0.998208i	$0.480939\pi$
$488$	2.38973e8	−	1.37971e8i	0.0930851	−	0.0537427i
$489$		−	2.10991e9i		−	0.815985i
$490$	−2.40635e8	−	4.16791e8i	−0.0924000	−	0.160041i
$491$	9.75730e8	−	1.69001e9i	0.372001	−	0.644325i	−0.617872	−	0.786279i	$-0.712005\pi$
$491$	9.75730e8	−	1.69001e9i	0.372001	−	0.644325i	0.989873	+	0.141953i	$0.0453383\pi$
$492$	−5.18502e8	−	2.99357e8i	−0.196278	−	0.113321i
$493$	−1.83951e9			−0.691415
$494$	1.94119e8	+	1.07610e8i	0.0724477	+	0.0401612i
$495$	−2.07252e9			−0.768035
$496$	6.24566e8	+	3.60593e8i	0.229823	+	0.132688i
$497$	1.45186e9	−	2.51470e9i	0.530491	−	0.918837i
$498$	3.37790e8	+	5.85069e8i	0.122559	+	0.212278i
$499$			3.18870e9i			1.14885i	0.818559	+	0.574423i	$0.194773\pi$
$499$			3.18870e9i			1.14885i	−0.818559	+	0.574423i	$0.805227\pi$
$500$	1.30716e9	−	7.54687e8i	0.467663	−	0.270005i
$501$	−1.77303e9	+	1.02366e9i	−0.629920	+	0.363684i
$502$		−	1.73151e9i		−	0.610887i
$503$	8.88123e8	+	1.53827e9i	0.311161	+	0.538947i	0.978614	−	0.205705i	$-0.0659489\pi$
$503$	8.88123e8	+	1.53827e9i	0.311161	+	0.538947i	−0.667453	+	0.744652i	$0.732616\pi$
$504$	2.14313e8	−	3.71201e8i	0.0745661	−	0.129152i
$505$	1.05243e9	+	6.07619e8i	0.363640	+	0.209948i
$506$	−4.48955e9			−1.54055
$507$	2.02885e9	−	7.07286e7i	0.691388	−	0.0241028i
$508$	−1.36967e9			−0.463546
$509$	−5.11200e9	−	2.95142e9i	−1.71822	−	0.992015i	−0.922169	−	0.386787i	$-0.873585\pi$
$509$	−5.11200e9	−	2.95142e9i	−1.71822	−	0.992015i	−0.796052	−	0.605228i	$-0.793082\pi$
$510$	4.46981e8	−	7.74195e8i	0.149209	−	0.258437i
$511$	1.02009e9	+	1.76685e9i	0.338193	+	0.585768i
$512$			1.34218e8i			0.0441942i
$513$	3.26511e8	−	1.88511e8i	0.106779	−	0.0616491i
$514$	−1.68754e9	+	9.74304e8i	−0.548131	+	0.316463i
$515$			1.94868e9i			0.628658i
$516$	−4.16205e8	−	7.20889e8i	−0.133362	−	0.230991i
$517$	−2.79264e8	+	4.83700e8i	−0.0888788	+	0.153943i
$518$	−2.53950e9	−	1.46618e9i	−0.802774	−	0.463482i
$519$	−2.48843e9			−0.781340
$520$	7.49904e8	+	4.15708e8i	0.233881	+	0.129651i
$521$	2.84267e9			0.880633			0.440317	−	0.897843i	$-0.354866\pi$
$521$	2.84267e9			0.880633			0.440317	+	0.897843i	$0.354866\pi$
$522$	−8.89503e8	−	5.13555e8i	−0.273716	−	0.158030i
$523$	1.53452e9	−	2.65787e9i	0.469048	−	0.812415i	−0.530326	−	0.847794i	$-0.677930\pi$
$523$	1.53452e9	−	2.65787e9i	0.469048	−	0.812415i	0.999374	+	0.0353788i	$0.0112638\pi$
$524$	8.94561e8	+	1.54943e9i	0.271613	+	0.470448i
$525$		−	7.94060e8i		−	0.239495i
$526$	−3.49530e7	+	2.01801e7i	−0.0104721	+	0.00604608i
$527$	−2.49124e9	+	1.43832e9i	−0.741445	+	0.428074i
$528$		−	1.13927e9i		−	0.336827i
$529$	−4.28094e8	−	7.41480e8i	−0.125731	−	0.217773i
$530$	−2.23165e8	+	3.86533e8i	−0.0651120	+	0.112777i
$531$	2.53899e9	+	1.46589e9i	0.735920	+	0.424884i
$532$	1.64563e8			0.0473850
$533$	1.17964e9	+	1.96338e9i	0.337446	+	0.561642i
$534$	2.03900e9			0.579459
$535$	−3.06026e9	−	1.76684e9i	−0.864012	−	0.498837i
$536$	2.28109e8	−	3.95096e8i	0.0639831	−	0.110822i
$537$	1.39882e9	+	2.42283e9i	0.389809	+	0.675168i
$538$		−	3.72295e9i		−	1.03074i
$539$	2.11867e9	−	1.22321e9i	0.582777	−	0.336466i
$540$	1.26135e9	−	7.28240e8i	0.344712	−	0.199020i
$541$		−	2.24439e9i		−	0.609407i	−0.952447	−	0.304703i	$-0.901443\pi$
$541$		−	2.24439e9i		−	0.609407i	0.952447	−	0.304703i	$-0.0985573\pi$
$542$	1.32710e9	+	2.29860e9i	0.358018	+	0.620106i
$543$	−1.36280e9	+	2.36044e9i	−0.365287	+	0.632695i
$544$	−4.63637e8	−	2.67681e8i	−0.123476	−	0.0712888i
$545$	3.02072e9			0.799323
$546$	1.29021e9	−	7.75187e8i	0.339225	−	0.203813i
$547$	−3.05066e9			−0.796963			−0.398481	−	0.917176i	$-0.630463\pi$
$547$	−3.05066e9			−0.796963			−0.398481	+	0.917176i	$0.630463\pi$
$548$	−2.48187e9	−	1.43291e9i	−0.644238	−	0.371951i
$549$	−3.07284e8	+	5.32232e8i	−0.0792569	+	0.137277i
$550$	1.14967e9	+	1.99128e9i	0.294648	+	0.510345i
$551$		−	3.94339e8i		−	0.100424i
$552$	9.36412e8	−	5.40638e8i	0.236963	−	0.136811i
$553$	2.88541e9	−	1.66589e9i	0.725553	−	0.418898i
$554$			3.26827e9i			0.816646i
$555$	−1.70743e9	−	2.95735e9i	−0.423952	−	0.734306i
$556$	7.66229e8	−	1.32715e9i	0.189059	−	0.327459i
$557$	1.71586e9	+	9.90653e8i	0.420716	+	0.242901i	0.695384	−	0.718639i	$-0.255234\pi$
$557$	1.71586e9	+	9.90653e8i	0.420716	+	0.242901i	−0.274668	+	0.961539i	$0.588568\pi$
$558$	−1.60620e9			−0.391363
$559$	5.54839e7	+	3.18408e9i	0.0134346	+	0.770978i
$560$	6.35724e8			0.152972
$561$	3.93545e9	+	2.27213e9i	0.941075	+	0.543330i
$562$	2.50565e9	−	4.33991e9i	0.595447	−	1.03134i
$563$	3.19492e9	+	5.53376e9i	0.754537	+	1.30690i	0.945604	+	0.325320i	$0.105472\pi$
$563$	3.19492e9	+	5.53376e9i	0.754537	+	1.30690i	−0.191067	+	0.981577i	$0.561195\pi$
$564$		−	1.34518e8i		−	0.0315720i
$565$	4.02152e9	−	2.32182e9i	0.938037	−	0.541576i
$566$	1.90436e8	−	1.09948e8i	0.0441460	−	0.0254877i
$567$		−	7.25947e8i		−	0.167249i
$568$	−1.01253e9	−	1.75375e9i	−0.231840	−	0.401559i
$569$	−1.97808e9	+	3.42613e9i	−0.450143	+	0.779671i	−0.998395	−	0.0566429i	$-0.981960\pi$
$569$	−1.97808e9	+	3.42613e9i	−0.450143	+	0.779671i	0.548251	+	0.836314i	$0.315294\pi$
$570$	1.65965e8	+	9.58201e7i	0.0375366	+	0.0216718i
$571$	−1.72462e9			−0.387675			−0.193837	−	0.981034i	$-0.562093\pi$
$571$	−1.72462e9			−0.387675			−0.193837	+	0.981034i	$0.562093\pi$
$572$	−2.11316e9	+	3.81197e9i	−0.472113	+	0.851655i
$573$	1.04152e9			0.231273
$574$	1.47075e9	+	8.49135e8i	0.324598	+	0.187407i
$575$	−1.09115e9	+	1.88992e9i	−0.239357	+	0.414578i
$576$	−1.49462e8	−	2.58876e8i	−0.0325876	−	0.0564434i
$577$			1.44292e9i			0.312698i	0.987702	+	0.156349i	$0.0499725\pi$
$577$			1.44292e9i			0.312698i	−0.987702	+	0.156349i	$0.950027\pi$
$578$	−9.93573e8	+	5.73640e8i	−0.214019	+	0.123564i
$579$	2.48381e9	−	1.43403e9i	0.531794	−	0.307031i
$580$		−	1.52338e9i		−	0.324197i
$581$	−9.58150e8	−	1.65956e9i	−0.202683	−	0.351057i
$582$	−1.18282e9	+	2.04871e9i	−0.248707	+	0.430774i
$583$	−1.96486e9	−	1.13441e9i	−0.410668	−	0.237099i
$584$	1.42282e9			0.295601
$585$	−1.90932e9	+	3.32708e7i	−0.394306	+	0.00687096i
$586$	1.48047e9			0.303919
$587$	−4.68617e9	−	2.70556e9i	−0.956280	−	0.552108i	−0.0612537	−	0.998122i	$-0.519510\pi$
$587$	−4.68617e9	−	2.70556e9i	−0.956280	−	0.552108i	−0.895026	+	0.446014i	$0.852843\pi$
$588$	−2.94602e8	+	5.10266e8i	−0.0597607	+	0.103509i
$589$	−3.08335e8	−	5.34052e8i	−0.0621755	−	0.107691i
$590$			4.34832e9i			0.871644i
$591$	2.48844e8	−	1.43670e8i	0.0495874	−	0.0286293i
$592$	−1.77105e9	+	1.02252e9i	−0.350836	+	0.202556i
$593$			1.30921e9i			0.257820i	0.991656	+	0.128910i	$0.0411478\pi$
$593$			1.30921e9i			0.257820i	−0.991656	+	0.128910i	$0.958852\pi$
$594$	3.70185e9	+	6.41179e9i	0.724713	+	1.25524i
$595$	−1.26788e9	+	2.19602e9i	−0.246756	+	0.427393i
$596$	2.17916e9	+	1.25814e9i	0.421626	+	0.243426i
$597$	−2.55734e9			−0.491901
$598$	−4.13602e9	+	7.20719e7i	−0.790912	+	0.0137820i
$599$	−5.82086e9			−1.10661			−0.553303	−	0.832980i	$-0.686633\pi$
$599$	−5.82086e9			−1.10661			−0.553303	+	0.832980i	$0.686633\pi$
$600$	−4.79586e8	−	2.76889e8i	−0.0906437	−	0.0523332i
$601$	4.65256e9	−	8.05847e9i	0.874241	−	1.51423i	0.0166722	−	0.999861i	$-0.494693\pi$
$601$	4.65256e9	−	8.05847e9i	0.874241	−	1.51423i	0.857569	−	0.514369i	$-0.171974\pi$
$602$	1.18058e9	+	2.04482e9i	0.220550	+	0.382004i
$603$			1.01607e9i			0.188718i
$604$	3.02160e9	−	1.74452e9i	0.557966	−	0.322142i
$605$	9.96427e9	−	5.75287e9i	1.82937	−	1.05619i
$606$		−	1.48778e9i		−	0.271572i
$607$	1.77466e9	+	3.07379e9i	0.322072	+	0.557846i	0.980915	−	0.194435i	$-0.0622872\pi$
$607$	1.77466e9	+	3.07379e9i	0.322072	+	0.557846i	−0.658843	+	0.752280i	$0.728954\pi$
$608$	5.73832e7	−	9.93906e7i	0.0103543	−	0.0179342i
$609$	−2.31597e9	−	1.33712e9i	−0.415501	−	0.239890i
$610$	−9.11509e8			−0.162595
$611$	−2.49509e8	+	4.50094e8i	−0.0442528	+	0.0798287i
$612$	1.19234e9			0.210266
$613$	−5.38574e9	−	3.10946e9i	−0.944352	−	0.545222i	−0.0530301	−	0.998593i	$-0.516888\pi$
$613$	−5.38574e9	−	3.10946e9i	−0.944352	−	0.545222i	−0.891322	+	0.453371i	$0.850221\pi$
$614$	−8.33855e7	+	1.44428e8i	−0.0145379	+	0.0251804i
$615$	9.88853e8	+	1.71274e9i	0.171423	+	0.296913i
$616$			3.23156e9i			0.557032i
$617$	2.81896e9	−	1.62753e9i	0.483159	−	0.278952i	−0.238573	−	0.971125i	$-0.576680\pi$
$617$	2.81896e9	−	1.62753e9i	0.483159	−	0.278952i	0.721732	+	0.692172i	$0.243346\pi$
$618$	2.06609e9	−	1.19286e9i	0.352119	−	0.203296i
$619$		−	8.80728e9i		−	1.49254i	−0.665646	−	0.746268i	$-0.731844\pi$
$619$		−	8.80728e9i		−	1.49254i	0.665646	−	0.746268i	$-0.268156\pi$
$620$	−1.19113e9	−	2.06310e9i	−0.200719	−	0.347656i
$621$	−3.51341e9	+	6.08541e9i	−0.588720	+	1.01969i
$622$	−4.94042e8	−	2.85235e8i	−0.0823185	−	0.0475266i
$623$	−5.78368e9			−0.958289
$624$	−1.82890e7	−	1.04956e9i	−0.00301331	−	0.172926i
$625$	−2.37401e9			−0.388957
$626$	−2.21036e9	−	1.27615e9i	−0.360124	−	0.207918i
$627$	−4.87080e8	+	8.43648e8i	−0.0789158	+	0.136686i
$628$	−2.10615e9	−	3.64796e9i	−0.339337	−	0.587749i
$629$		−	8.15714e9i		−	1.30695i
$630$	−1.22617e9	+	7.07930e8i	−0.195370	+	0.112797i
$631$	4.23686e9	−	2.44615e9i	0.671338	−	0.387597i	−0.125246	−	0.992126i	$-0.539972\pi$
$631$	4.23686e9	−	2.44615e9i	0.671338	−	0.387597i	0.796583	+	0.604529i	$0.206639\pi$
$632$		−	2.32359e9i		−	0.366142i
$633$	−3.51900e9	−	6.09508e9i	−0.551450	−	0.955139i
$634$	−1.41597e9	+	2.45253e9i	−0.220669	+	0.382211i
$635$	3.91822e9	+	2.26219e9i	0.607269	+	0.350607i
$636$	5.46430e8			0.0842237
$637$	1.93220e9	−	1.16090e9i	0.296185	−	0.177954i
$638$	7.74375e9			1.18053
$639$	3.90589e9	+	2.25507e9i	0.592199	+	0.341906i
$640$	2.21678e8	−	3.83957e8i	0.0334266	−	0.0578965i
$641$	1.45291e9	+	2.51651e9i	0.217889	+	0.377395i	0.954162	−	0.299289i	$-0.0967496\pi$
$641$	1.45291e9	+	2.51651e9i	0.217889	+	0.377395i	−0.736273	+	0.676684i	$0.763416\pi$
$642$			4.32618e9i			0.645257i
$643$	−3.26011e8	+	1.88222e8i	−0.0483608	+	0.0279211i	−0.523985	−	0.851727i	$-0.675555\pi$
$643$	−3.26011e8	+	1.88222e8i	−0.0483608	+	0.0279211i	0.475625	+	0.879648i	$0.342222\pi$
$644$	−2.65616e9	+	1.53353e9i	−0.391880	+	0.226252i
$645$			2.74966e9i			0.403479i
$646$	2.28888e8	+	3.96445e8i	0.0334048	+	0.0578588i
$647$	1.69765e9	−	2.94042e9i	0.246425	−	0.426820i	−0.716106	−	0.697991i	$-0.754077\pi$
$647$	1.69765e9	−	2.94042e9i	0.246425	−	0.426820i	0.962531	+	0.271171i	$0.0874108\pi$
$648$	−4.38449e8	−	2.53138e8i	−0.0633004	−	0.0365465i
$649$	−2.21037e10			−3.17401
$650$	1.09110e9	+	1.81602e9i	0.155837	+	0.259373i
$651$	−4.18201e9			−0.594089
$652$	3.61463e9	+	2.08691e9i	0.510737	+	0.294874i
$653$	−6.46268e9	+	1.11937e10i	−0.908273	+	1.57317i	−0.0918103	+	0.995777i	$0.529265\pi$
$653$	−6.46268e9	+	1.11937e10i	−0.908273	+	1.57317i	−0.816463	+	0.577398i	$0.804068\pi$
$654$	−1.84909e9	−	3.20272e9i	−0.258485	−	0.447710i
$655$		−	5.90993e9i		−	0.821746i
$656$	1.02570e9	−	5.92188e8i	0.141859	−	0.0819024i
$657$	−2.74431e9	+	1.58443e9i	−0.377533	+	0.217969i
$658$			3.81563e8i			0.0522126i
$659$	−2.50007e9	−	4.33024e9i	−0.340293	−	0.589405i	0.644194	−	0.764862i	$-0.277193\pi$
$659$	−2.50007e9	−	4.33024e9i	−0.340293	−	0.589405i	−0.984487	+	0.175457i	$0.943860\pi$
$660$	−1.88165e9	+	3.25911e9i	−0.254762	+	0.441260i
$661$	1.10755e10	+	6.39445e9i	1.49162	+	0.861189i	0.999954	−	0.00959383i	$-0.00305386\pi$
$661$	1.10755e10	+	6.39445e9i	1.49162	+	0.861189i	0.491668	+	0.870782i	$0.336387\pi$
$662$	−8.07076e9			−1.08121
$663$	3.66203e9	+	2.03004e9i	0.488005	+	0.270524i
$664$	−1.33643e9			−0.177157
$665$	−4.70765e8	−	2.71796e8i	−0.0620767	−	0.0358400i
$666$	2.27731e9	−	3.94441e9i	0.298718	−	0.517395i
$667$	3.67478e9	+	6.36491e9i	0.479503	+	0.830523i
$668$		−	4.05002e9i		−	0.525701i
$669$	−3.52642e9	+	2.03598e9i	−0.455347	+	0.262895i
$670$	−1.30510e9	+	7.53501e8i	−0.167642	+	0.0967881i
$671$		−	4.63346e9i		−	0.592074i
$672$	−3.89150e8	−	6.74027e8i	−0.0494680	−	0.0856811i
$673$	1.96087e9	−	3.39633e9i	0.247969	−	0.429494i	−0.714993	−	0.699131i	$-0.753570\pi$
$673$	1.96087e9	−	3.39633e9i	0.247969	−	0.429494i	0.962962	+	0.269637i	$0.0869037\pi$
$674$	−4.74948e9	−	2.74211e9i	−0.597498	−	0.344965i
$675$	3.59881e9			0.450397
$676$	−1.88556e9	+	3.54572e9i	−0.234762	+	0.441460i
$677$	1.10745e10			1.37171			0.685855	−	0.727739i	$-0.259429\pi$
$677$	1.10745e10			1.37171			0.685855	+	0.727739i	$0.259429\pi$
$678$	−4.92343e9	−	2.84254e9i	−0.606686	−	0.350270i
$679$	3.35510e9	−	5.81121e9i	0.411303	−	0.712398i
$680$	8.84219e8	+	1.53151e9i	0.107840	+	0.186784i
$681$			8.54565e9i			1.03688i
$682$	1.04873e10	−	6.05486e9i	1.26596	−	0.730901i
$683$	2.30202e9	−	1.32907e9i	0.276463	−	0.159616i	−0.355358	−	0.934730i	$-0.615641\pi$
$683$	2.30202e9	−	1.32907e9i	0.276463	−	0.159616i	0.631821	+	0.775114i	$0.282308\pi$
$684$			2.55603e8i			0.0305401i
$685$	4.73325e9	+	8.19823e9i	0.562655	+	0.974548i
$686$	3.25408e9	−	5.63622e9i	0.384852	−	0.666582i
$687$	1.78788e9	+	1.03223e9i	0.210373	+	0.121459i
$688$	1.64667e9			0.192774
$689$	−1.82835e9	−	1.01354e9i	−0.212957	−	0.118052i
$690$	−3.57173e9			−0.413910
$691$	2.79991e9	+	1.61653e9i	0.322828	+	0.186385i	0.652653	−	0.757657i	$-0.273656\pi$
$691$	2.79991e9	+	1.61653e9i	0.322828	+	0.186385i	−0.329824	+	0.944042i	$0.606989\pi$
$692$	2.46131e9	−	4.26311e9i	0.282354	−	0.489052i
$693$	−3.59861e9	−	6.23297e9i	−0.410741	−	0.711424i
$694$		−	3.98637e9i		−	0.452709i
$695$	−4.38390e9	+	2.53105e9i	−0.495352	+	0.285992i
$696$	−1.61516e9	+	9.32513e8i	−0.181586	+	0.104839i
$697$			4.72419e9i			0.528461i
$698$	1.12394e9	+	1.94671e9i	0.125097	+	0.216675i
$699$	−2.56101e9	+	4.43580e9i	−0.283623	+	0.491249i
$700$	1.36036e9	+	7.85404e8i	0.149903	+	0.0865466i
$701$	−1.01439e10			−1.11223			−0.556114	−	0.831106i	$-0.687708\pi$
$701$	−1.01439e10			−1.11223			−0.556114	+	0.831106i	$0.687708\pi$
$702$	3.51328e9	+	5.84747e9i	0.383294	+	0.637952i
$703$	1.74866e9			0.189828
$704$	1.95176e9	+	1.12685e9i	0.210825	+	0.121720i
$705$	−2.22173e8	+	3.84815e8i	−0.0238797	+	0.0413609i
$706$	−2.63933e9	−	4.57145e9i	−0.282278	−	0.488920i
$707$			4.22013e9i			0.449116i
$708$	4.61031e9	−	2.66176e9i	0.488218	−	0.281873i
$709$	−2.29529e8	+	1.32519e8i	−0.0241867	+	0.0139642i	−0.512045	−	0.858959i	$-0.671112\pi$
$709$	−2.29529e8	+	1.32519e8i	−0.0241867	+	0.0139642i	0.487858	+	0.872923i	$0.337778\pi$
$710$			6.68929e9i			0.701417i
$711$	2.58750e9	+	4.48169e9i	0.269984	+	0.467625i
$712$	−2.01678e9	+	3.49316e9i	−0.209400	+	0.362692i
$713$	9.95348e9	+	5.74664e9i	1.02840	+	0.593746i
$714$	3.10445e9			0.319184
$715$	1.23411e10	−	7.41477e9i	1.26265	−	0.758624i
$716$	−5.53429e9			−0.563464
$717$	7.83440e9	+	4.52319e9i	0.793759	+	0.458277i
$718$	−1.49189e8	+	2.58403e8i	−0.0150419	+	0.0260533i
$719$	1.30879e9	+	2.26689e9i	0.131317	+	0.227447i	0.924184	−	0.381947i	$-0.124746\pi$
$719$	1.30879e9	+	2.26689e9i	0.131317	+	0.227447i	−0.792868	+	0.609394i	$0.791413\pi$
$720$			9.87423e8i			0.0985915i
$721$	−5.86051e9	+	3.38357e9i	−0.582321	+	0.336203i
$722$	6.10794e9	−	3.52642e9i	0.603969	−	0.348702i
$723$		−	7.32142e9i		−	0.720462i
$724$	−2.69590e9	−	4.66943e9i	−0.264009	−	0.457276i
$725$	1.88205e9	−	3.25981e9i	0.183421	−	0.317694i
$726$	−1.21990e10	−	7.04308e9i	−1.18316	−	0.683101i
$727$	1.98815e10			1.91902			0.959509	−	0.281676i	$-0.0908904\pi$
$727$	1.98815e10			1.91902			0.959509	+	0.281676i	$0.0908904\pi$
$728$	5.18772e7	+	2.97709e9i	0.00498329	+	0.285978i
$729$	8.74416e9			0.835934
$730$	−4.07028e9	−	2.34998e9i	−0.387252	−	0.223580i
$731$	−3.28409e9	+	5.68822e9i	−0.310960	+	0.538599i
$732$	5.57968e8	+	9.66428e8i	0.0525800	+	0.0910711i
$733$			1.77576e10i			1.66541i	0.553720	+	0.832703i	$0.313208\pi$
$733$			1.77576e10i			1.66541i	−0.553720	+	0.832703i	$0.686792\pi$
$734$	−4.99167e9	+	2.88194e9i	−0.465918	+	0.268998i
$735$	1.68554e9	−	9.73146e8i	0.156579	−	0.0904008i
$736$			2.13898e9i			0.197758i
$737$	−3.83026e9	−	6.63420e9i	−0.352445	−	0.610453i
$738$	−1.31890e9	+	2.28440e9i	−0.120785	+	0.209206i
$739$	−9.78135e9	−	5.64727e9i	−0.891545	−	0.514734i	−0.0170975	−	0.999854i	$-0.505443\pi$
$739$	−9.78135e9	−	5.64727e9i	−0.891545	−	0.514734i	−0.874448	+	0.485120i	$0.838776\pi$
$740$	6.75526e9			0.612817
$741$	−4.35182e8	+	7.85034e8i	−0.0392923	+	0.0708802i
$742$	−1.54996e9			−0.139286
$743$	−6.78319e9	−	3.91628e9i	−0.606699	−	0.350278i	0.164974	−	0.986298i	$-0.447246\pi$
$743$	−6.78319e9	−	3.91628e9i	−0.606699	−	0.350278i	−0.771672	+	0.636020i	$0.780579\pi$
$744$	−1.45827e9	+	2.52580e9i	−0.129817	+	0.224850i
$745$	−4.15596e9	−	7.19833e9i	−0.368234	−	0.637800i
$746$		−	2.32803e9i		−	0.205307i
$747$	2.57768e9	−	1.48822e9i	0.226259	−	0.130631i
$748$	−7.78510e9	+	4.49473e9i	−0.680156	+	0.392688i
$749$		−	1.22713e10i		−	1.06710i
$750$	3.05202e9	+	5.28625e9i	0.264163	+	0.457544i
$751$	−1.17937e9	+	2.04273e9i	−0.101604	+	0.175983i	−0.912346	−	0.409421i	$-0.865731\pi$
$751$	−1.17937e9	+	2.04273e9i	−0.101604	+	0.175983i	0.810742	+	0.585404i	$0.199064\pi$
$752$	2.30452e8	+	1.33051e8i	0.0197614	+	0.0114092i
$753$	7.00235e9			0.597670
$754$	7.13397e9	−	1.24312e8i	0.606082	−	0.0105612i
$755$	−1.15252e10			−0.974618
$756$	4.38026e9	+	2.52895e9i	0.368701	+	0.212869i
$757$	−6.42271e9	+	1.11245e10i	−0.538125	+	0.932059i	0.460880	+	0.887462i	$0.347534\pi$
$757$	−6.42271e9	+	1.11245e10i	−0.538125	+	0.932059i	−0.999005	+	0.0445970i	$0.985800\pi$
$758$	−4.21518e9	−	7.30091e9i	−0.351539	−	0.608884i
$759$		−	1.81561e10i		−	1.50722i
$760$	−3.28312e8	+	1.89551e8i	−0.0271294	+	0.0156632i
$761$	8.56209e8	−	4.94332e8i	0.0704261	−	0.0406605i	−0.464373	−	0.885639i	$-0.653720\pi$
$761$	8.56209e8	−	4.94332e8i	0.0704261	−	0.0406605i	0.534800	+	0.844979i	$0.320387\pi$
$762$		−	5.53906e9i		−	0.453517i
$763$	5.24500e9	+	9.08460e9i	0.427474	+	0.740406i
$764$	−1.03016e9	+	1.78430e9i	−0.0835756	+	0.144757i
$765$	−3.41092e9	−	1.96930e9i	−0.275459	−	0.159036i
$766$	1.49338e10			1.20052
$767$	−2.03632e10	+	3.54837e8i	−1.62953	+	0.0283952i
$768$	−5.42787e8			−0.0432380
$769$	−1.15938e10	−	6.69371e9i	−0.919359	−	0.530792i	−0.0359285	−	0.999354i	$-0.511439\pi$
$769$	−1.15938e10	−	6.69371e9i	−0.919359	−	0.530792i	−0.883431	+	0.468562i	$0.844772\pi$
$770$	5.33734e9	−	9.24454e9i	0.421315	−	0.729740i
$771$	−3.94016e9	−	6.82457e9i	−0.309616	−	0.536271i
$772$			5.67358e9i			0.443810i
$773$	−9.24800e9	+	5.33934e9i	−0.720145	+	0.415776i	−0.814806	−	0.579734i	$-0.803157\pi$
$773$	−9.24800e9	+	5.33934e9i	−0.720145	+	0.415776i	0.0946613	+	0.995510i	$0.469823\pi$
$774$	−3.17607e9	+	1.83370e9i	−0.246205	+	0.142146i
$775$		−	5.88633e9i		−	0.454243i
$776$	−2.33986e9	−	4.05275e9i	−0.179752	−	0.311339i
$777$	5.92935e9	−	1.02699e10i	0.453454	−	0.785406i
$778$	−1.02498e10	−	5.91774e9i	−0.780347	−	0.450534i
$779$	−1.01273e9			−0.0767562
$780$	−1.68116e9	+	3.03267e9i	−0.126846	+	0.228820i
$781$	−3.40036e10			−2.55415
$782$	−7.38881e9	−	4.26593e9i	−0.552524	−	0.319000i
$783$	6.06007e9	−	1.04964e10i	0.451140	−	0.781398i
$784$	−5.82782e8	−	1.00941e9i	−0.0431917	−	0.0748102i
$785$			1.39143e10i			1.02664i
$786$	−6.26600e9	+	3.61768e9i	−0.460269	+	0.265736i
$787$	−1.33997e10	+	7.73632e9i	−0.979903	+	0.565748i	−0.902241	−	0.431232i	$-0.858079\pi$
$787$	−1.33997e10	+	7.73632e9i	−0.979903	+	0.565748i	−0.0776624	+	0.996980i	$0.524746\pi$
$788$			5.68417e8i			0.0413833i
$789$	−8.16101e7	−	1.41353e8i	−0.00591527	−	0.0102455i
$790$	−3.83771e9	+	6.64710e9i	−0.276934	+	0.479664i
$791$	1.39654e10	+	8.06295e9i	1.00331	+	0.579264i
$792$	−5.01935e9			−0.359012
$793$	−7.43821e7	−	4.26859e9i	−0.00529679	−	0.303969i
$794$	1.80083e10			1.27674
$795$	−1.56317e9	−	9.02498e8i	−0.110337	−	0.0637032i
$796$	2.52946e9	−	4.38115e9i	0.177759	−	0.307888i
$797$	9.15716e9	+	1.58607e10i	0.640703	+	1.10973i	0.985276	+	0.170971i	$0.0546904\pi$
$797$	9.15716e9	+	1.58607e10i	0.640703	+	1.10973i	−0.344573	+	0.938760i	$0.611976\pi$
$798$			6.65505e8i			0.0463598i
$799$	−9.19216e8	+	5.30710e8i	−0.0637535	+	0.0368081i
$800$	9.48718e8	−	5.47742e8i	0.0655122	−	0.0378235i
$801$		−	8.98336e9i		−	0.617625i
$802$	7.51148e9	+	1.30103e10i	0.514180	+	0.890586i
$803$	1.19456e10	−	2.06904e10i	0.814147	−	1.41014i
$804$	1.59780e9	+	9.22490e8i	0.108424	+	0.0625988i
$805$	1.01313e10			0.684510
$806$	9.56429e9	−	5.74642e9i	0.643399	−	0.386567i
$807$	1.50559e10			1.00844
$808$	2.54882e9	+	1.47156e9i	0.169981	+	0.0981385i
$809$	−3.03106e9	+	5.24995e9i	−0.201268	+	0.348606i	−0.948937	−	0.315465i	$-0.897840\pi$
$809$	−3.03106e9	+	5.24995e9i	−0.201268	+	0.348606i	0.747669	+	0.664071i	$0.231173\pi$
$810$	8.36181e8	+	1.44831e9i	0.0552844	+	0.0957554i
$811$		−	2.18462e10i		−	1.43815i	−0.694933	−	0.719074i	$-0.744566\pi$
$811$		−	2.18462e10i		−	1.43815i	0.694933	−	0.719074i	$-0.255434\pi$
$812$	4.58145e9	−	2.64510e9i	0.300301	−	0.173379i
$813$	−9.29572e9	+	5.36689e9i	−0.606689	+	0.350272i
$814$			3.43389e10i			2.23152i
$815$	−6.89359e9	−	1.19400e10i	−0.446060	−	0.772599i
$816$	1.08252e9	−	1.87499e9i	0.0697464	−	0.120804i
$817$	−1.21939e9	−	7.04016e8i	−0.0782287	−	0.0451653i
$818$	5.09481e9			0.325455
$819$	−3.41529e9	−	5.68438e9i	−0.217237	−	0.361568i
$820$	−3.91230e9			−0.247790
$821$	2.26398e10	+	1.30711e10i	1.42782	+	0.824350i	0.996948	−	0.0780644i	$-0.0248740\pi$
$821$	2.26398e10	+	1.30711e10i	1.42782	+	0.824350i	0.430868	+	0.902415i	$0.358207\pi$
$822$	5.79479e9	−	1.00369e10i	0.363903	−	0.630299i
$823$	4.08115e9	+	7.06876e9i	0.255202	+	0.442022i	0.964950	−	0.262433i	$-0.0845248\pi$
$823$	4.08115e9	+	7.06876e9i	0.255202	+	0.442022i	−0.709749	+	0.704455i	$0.751191\pi$
$824$			4.71941e9i			0.293862i
$825$	−8.05291e9	+	4.64935e9i	−0.499303	+	0.288273i
$826$	−1.30773e10	+	7.55016e9i	−0.807396	+	0.466150i
$827$			2.10648e10i			1.29505i	0.762042	+	0.647527i	$0.224197\pi$
$827$			2.10648e10i			1.29505i	−0.762042	+	0.647527i	$0.775803\pi$
$828$	−2.38192e9	−	4.12561e9i	−0.145822	−	0.252570i
$829$	1.44410e10	−	2.50126e10i	0.880353	−	1.52482i	0.0294044	−	0.999568i	$-0.490639\pi$
$829$	1.44410e10	−	2.50126e10i	0.880353	−	1.52482i	0.850949	−	0.525249i	$-0.176028\pi$
$830$	3.82313e9	+	2.20729e9i	0.232084	+	0.133994i
$831$	−1.32172e10			−0.798977
$832$	1.81616e9	+	1.00678e9i	0.109326	+	0.0606044i
$833$	4.64915e9			0.278687
$834$	5.36709e9	+	3.09869e9i	0.320374	+	0.184968i
$835$	−6.68911e9	+	1.15859e10i	−0.397618	+	0.688695i
$836$	−9.63542e8	−	1.66890e9i	−0.0570360	−	0.0987892i
$837$		−	1.89535e10i		−	1.11725i
$838$	−1.07685e10	+	6.21719e9i	−0.632122	+	0.364956i
$839$	1.02477e10	−	5.91652e9i	0.599046	−	0.345859i	−0.169620	−	0.985509i	$-0.554254\pi$
$839$	1.02477e10	−	5.91652e9i	0.599046	−	0.345859i	0.768666	+	0.639650i	$0.220921\pi$
$840$			2.57092e9i			0.149662i
$841$	2.28653e9	+	3.96038e9i	0.132553	+	0.229589i
$842$	−3.78613e9	+	6.55777e9i	−0.218576	+	0.378586i
$843$	1.75509e10	+	1.01330e10i	1.00903	+	0.582564i
$844$	1.39226e10			0.797114
$845$	1.12502e10	−	7.02901e9i	0.641451	−	0.400770i
$846$	−5.92653e8			−0.0336515
$847$	3.46027e10	+	1.99779e10i	1.95667	+	1.12969i
$848$	−5.40473e8	+	9.36127e8i	−0.0304361	+	0.0527168i
$849$	4.44639e8	+	7.70138e8i	0.0249362	+	0.0431908i
$850$			4.36962e9i			0.244049i
$851$	−2.82246e10	+	1.62955e10i	−1.56991	+	0.906386i
$852$	7.09233e9	−	4.09476e9i	0.392871	−	0.226824i
$853$			4.54152e9i			0.250542i	0.992123	+	0.125271i	$0.0399800\pi$
$853$			4.54152e9i			0.250542i	−0.992123	+	0.125271i	$0.960020\pi$
$854$	−1.58269e9	−	2.74130e9i	−0.0869548	−	0.150610i
$855$	4.22161e8	−	7.31204e8i	0.0230992	−	0.0400090i
$856$	−7.41149e9	−	4.27903e9i	−0.403876	−	0.233178i
$857$	2.71958e10			1.47594			0.737971	−	0.674833i	$-0.235784\pi$
$857$	2.71958e10			1.47594			0.737971	+	0.674833i	$0.235784\pi$
$858$	−1.54159e10	−	8.54579e9i	−0.833229	−	0.461898i
$859$	−1.24708e10			−0.671304			−0.335652	−	0.941986i	$-0.608957\pi$
$859$	−1.24708e10			−0.671304			−0.335652	+	0.941986i	$0.608957\pi$
$860$	−4.71064e9	−	2.71969e9i	−0.252543	−	0.145806i
$861$	−3.43397e9	+	5.94781e9i	−0.183352	+	0.317575i
$862$	2.07788e8	+	3.59899e8i	0.0110496	+	0.0191384i
$863$			3.88024e9i			0.205504i	0.994707	+	0.102752i	$0.0327648\pi$
$863$			3.88024e9i			0.205504i	−0.994707	+	0.102752i	$0.967235\pi$
$864$	3.05480e9	−	1.76369e9i	0.161133	−	0.0930303i
$865$	−1.40821e10	+	8.13032e9i	−0.739796	+	0.427121i
$866$		−	1.25452e10i		−	0.656393i
$867$	−2.31984e9	−	4.01809e9i	−0.120890	−	0.209388i
$868$	4.13642e9	−	7.16449e9i	0.214687	−	0.371849i
$869$	−3.37891e10	−	1.95081e10i	−1.74665	−	1.00843i
$870$	6.16066e9			0.317183
$871$	−3.63514e9	−	6.05030e9i	−0.186405	−	0.310251i
$872$	7.31574e9			0.373638
$873$	9.02612e9	+	5.21123e9i	0.459147	+	0.265088i
$874$	9.14495e8	−	1.58395e9i	0.0463331	−	0.0802512i
$875$	−8.65713e9	−	1.49946e10i	−0.436863	−	0.756670i
$876$			5.75402e9i			0.289206i
$877$	2.70830e10	−	1.56364e10i	1.35581	−	0.782777i	0.366754	−	0.930318i	$-0.380469\pi$
$877$	2.70830e10	−	1.56364e10i	1.35581	−	0.782777i	0.989056	+	0.147541i	$0.0471358\pi$
$878$	−5.95449e9	+	3.43783e9i	−0.296903	+	0.171417i
$879$			5.98715e9i			0.297344i
$880$	−3.72227e9	−	6.44716e9i	−0.184127	−	0.318918i
$881$	4.00303e9	−	6.93345e9i	0.197230	−	0.341612i	−0.750399	−	0.660985i	$-0.770139\pi$
$881$	4.00303e9	−	6.93345e9i	0.197230	−	0.341612i	0.947629	+	0.319372i	$0.103472\pi$
$882$	2.24811e9	+	1.29795e9i	0.110326	+	0.0636968i
$883$	5.19038e9			0.253709			0.126855	−	0.991921i	$-0.459512\pi$
$883$	5.19038e9			0.253709			0.126855	+	0.991921i	$0.459512\pi$
$884$	−7.09991e9	+	4.26577e9i	−0.345676	+	0.207689i
$885$	−1.75850e10			−0.852785
$886$	−2.17366e9	−	1.25497e9i	−0.104996	−	0.0606197i
$887$	−1.30177e10	+	2.25474e10i	−0.626329	+	1.08483i	0.361954	+	0.932196i	$0.382110\pi$
$887$	−1.30177e10	+	2.25474e10i	−0.626329	+	1.08483i	−0.988282	+	0.152637i	$0.951224\pi$
$888$	−4.13514e9	−	7.16227e9i	−0.198173	−	0.343246i
$889$			1.57117e10i			0.750010i
$890$	1.15388e10	−	6.66192e9i	0.548650	−	0.316763i
$891$	−7.36215e9	+	4.25054e9i	−0.348685	+	0.201313i
$892$		−	8.05514e9i		−	0.380011i
$893$	−1.13769e8	−	1.97054e8i	−0.00534618	−	0.00925986i
$894$	−5.08802e9	+	8.81271e9i	−0.238159	+	0.412504i
$895$	1.58319e10	+	9.14058e9i	0.738165	+	0.426180i
$896$	1.53963e9			0.0715054
$897$	−2.91465e8	−	1.67264e10i	−0.0134838	−	0.773800i
$898$	6.53944e8			0.0301351
$899$	−1.71682e10	−	9.91204e9i	−0.788070	−	0.454992i
$900$	−1.21991e9	+	2.11295e9i	−0.0557801	+	0.0966139i
$901$	−2.15582e9	−	3.73399e9i	−0.0981918	−	0.170073i
$902$		−	1.98873e10i		−	0.902304i
$903$	−8.26942e9	+	4.77435e9i	−0.373739	+	0.215778i
$904$	9.73952e9	−	5.62312e9i	0.438478	−	0.253156i
$905$			1.78105e10i			0.798740i
$906$	7.05499e9	+	1.22196e10i	0.315172	+	0.545894i
$907$	−1.83101e10	+	3.17140e10i	−0.814826	+	1.41132i	0.0946274	+	0.995513i	$0.469834\pi$
$907$	−1.83101e10	+	3.17140e10i	−0.814826	+	1.41132i	−0.909453	+	0.415807i	$0.863499\pi$
$908$	−1.46402e10	−	8.45250e9i	−0.649001	−	0.374701i
$909$	−6.55482e9			−0.289459
$910$	4.76865e9	−	8.60226e9i	0.209773	−	0.378415i
$911$	3.91136e10			1.71401			0.857006	−	0.515306i	$-0.172322\pi$
$911$	3.91136e10			1.71401			0.857006	+	0.515306i	$0.172322\pi$
$912$	4.01944e8	+	2.32062e8i	0.0175462	+	0.0101303i
$913$	−1.12202e10	+	1.94340e10i	−0.487927	+	0.845114i
$914$	−7.79567e9	−	1.35025e10i	−0.337708	−	0.584928i
$915$		−	3.68622e9i		−	0.159077i
$916$	−3.53678e9	+	2.04196e9i	−0.152046	+	0.0877835i
$917$	1.77737e10	−	1.02616e10i	0.761176	−	0.439465i
$918$			1.40699e10i			0.600262i
$919$	−6.48209e9	−	1.12273e10i	−0.275493	−	0.477168i	0.694766	−	0.719235i	$-0.255508\pi$
$919$	−6.48209e9	−	1.12273e10i	−0.275493	−	0.477168i	−0.970259	+	0.242068i	$0.922174\pi$
$920$	3.53279e9	−	6.11898e9i	0.149576	−	0.259073i
$921$	−5.84078e8	−	3.37218e8i	−0.0246356	−	0.0142233i
$922$	−2.77126e10			−1.16444
$923$	−3.13259e10	+	5.45868e8i	−1.31129	+	0.0228498i
$924$	−1.30687e10			−0.544980
$925$	1.44553e10	+	8.34577e9i	0.600525	+	0.346713i
$926$	−4.53329e9	+	7.85189e9i	−0.187618	+	0.324965i
$927$	−5.25544e9	−	9.10270e9i	−0.216686	−	0.375311i
$928$		−	3.68939e9i		−	0.151543i
$929$	−5.10464e9	+	2.94716e9i	−0.208886	+	0.120601i	−0.600794	−	0.799404i	$-0.705149\pi$
$929$	−5.10464e9	+	2.94716e9i	−0.208886	+	0.120601i	0.391907	+	0.920005i	$0.371815\pi$
$930$	8.34335e9	−	4.81703e9i	0.340134	−	0.196376i
$931$			9.96646e8i			0.0404778i
$932$	−5.06619e9	−	8.77490e9i	−0.204987	−	0.355048i
$933$	1.15351e9	−	1.99795e9i	0.0464983	−	0.0805374i
$934$	−1.44630e10	−	8.35020e9i	−0.580822	−	0.335338i
$935$	2.96945e10			1.18805
$936$	−4.62410e9	+	8.05770e7i	−0.184315	+	0.00321178i
$937$	2.40381e10			0.954577			0.477288	−	0.878747i	$-0.341620\pi$
$937$	2.40381e10			0.954577			0.477288	+	0.878747i	$0.341620\pi$
$938$	−4.53220e9	−	2.61667e9i	−0.179308	−	0.103524i
$939$	5.16085e9	−	8.93886e9i	0.203419	−	0.352332i
$940$	−4.39502e8	−	7.61240e8i	−0.0172589	−	0.0298933i
$941$			5.30161e9i			0.207417i	0.994608	+	0.103708i	$0.0330709\pi$
$941$			5.30161e9i			0.207417i	−0.994608	+	0.103708i	$0.966929\pi$
$942$	1.47527e10	−	8.51745e9i	0.575032	−	0.331995i
$943$	1.63462e10	−	9.43749e9i	0.634784	−	0.366493i
$944$			1.05310e10i			0.407443i
$945$	−8.35375e9	−	1.44691e10i	−0.322011	−	0.557739i
$946$	1.38250e10	−	2.39455e10i	0.530939	−	0.919614i
$947$	−2.49066e10	−	1.43798e10i	−0.952991	−	0.550210i	−0.0589823	−	0.998259i	$-0.518786\pi$
$947$	−2.49066e10	−	1.43798e10i	−0.952991	−	0.550210i	−0.894009	+	0.448049i	$0.852119\pi$
$948$	9.39679e9			0.358220
$949$	1.06728e10	−	1.92529e10i	0.405365	−	0.731246i
$950$	−9.36723e8			−0.0354469
$951$	−9.91825e9	−	5.72630e9i	−0.373941	−	0.215895i
$952$	−3.07061e9	+	5.31845e9i	−0.115344	+	0.199782i
$953$	−1.73485e10	−	3.00485e10i	−0.649288	−	1.12460i	−0.983293	−	0.182028i	$-0.941734\pi$
$953$	−1.73485e10	−	3.00485e10i	−0.649288	−	1.12460i	0.334006	−	0.942571i	$-0.391600\pi$
$954$		−	2.40744e9i		−	0.0897711i
$955$	5.89398e9	−	3.40289e9i	0.218976	−	0.126426i
$956$	−1.54980e10	+	8.94778e9i	−0.573685	+	0.331217i
$957$			3.13163e10i			1.15499i
$958$	7.39075e8	+	1.28012e9i	0.0271587	+	0.0470403i
$959$	−1.64371e10	+	2.84698e10i	−0.601810	+	1.04237i
$960$	1.55275e9	+	8.96482e8i	0.0566439	+	0.0327034i
$961$	−3.48839e9			−0.126792
$962$	5.51251e8	+	3.16349e10i	0.0199635	+	1.14565i
$963$	1.90602e10			0.687756
$964$	1.25428e10	+	7.24161e9i	0.450948	+	0.260355i
$965$	9.37064e9	−	1.62304e10i	0.335679	−	0.581413i
$966$	−6.20173e9	−	1.07417e10i	−0.221357	−	0.383402i
$967$		−	2.32799e10i		−	0.827921i	−0.910295	−	0.413960i	$-0.864145\pi$
$967$		−	2.32799e10i		−	0.827921i	0.910295	−	0.413960i	$-0.135855\pi$
$968$	2.41320e10	−	1.39326e10i	0.855125	−	0.493707i
$969$	−1.60326e9	+	9.25641e8i	−0.0566070	+	0.0326820i
$970$			1.54583e10i			0.543826i
$971$	1.04009e9	+	1.80150e9i	0.0364591	+	0.0631489i	0.883679	−	0.468093i	$-0.155059\pi$
$971$	1.04009e9	+	1.80150e9i	0.0364591	+	0.0631489i	−0.847220	+	0.531242i	$0.821725\pi$
$972$	−6.50987e9	+	1.12754e10i	−0.227374	+	0.393823i
$973$	−1.52239e10	−	8.78952e9i	−0.529823	−	0.305894i
$974$	1.82409e10			0.632543
$975$	−7.34415e9	+	4.41251e9i	−0.253761	+	0.152465i
$976$	−2.20754e9			−0.0760037
$977$	−8.50985e9	−	4.91316e9i	−0.291938	−	0.168551i	0.346877	−	0.937910i	$-0.387242\pi$
$977$	−8.50985e9	−	4.91316e9i	−0.291938	−	0.168551i	−0.638816	+	0.769360i	$0.720575\pi$
$978$	−8.43963e9	+	1.46179e10i	−0.288494	+	0.499687i
$979$	3.38644e10	+	5.86549e10i	1.15346	+	1.99786i
$980$			3.85015e9i			0.130673i
$981$	−1.41104e10	+	8.14666e9i	−0.477198	+	0.275511i
$982$	−1.35201e10	+	7.80584e9i	−0.455607	+	0.263045i
$983$			3.81722e10i			1.28177i	0.767637	+	0.640885i	$0.221432\pi$
$983$			3.81722e10i			1.28177i	−0.767637	+	0.640885i	$0.778568\pi$
$984$	2.39486e9	+	4.14802e9i	0.0801303	+	0.138790i
$985$	9.38813e8	−	1.62607e9i	0.0313006	−	0.0542142i
$986$	1.27445e10	+	7.35805e9i	0.423403	+	0.244452i
$987$	−1.54307e9			−0.0510830
$988$	−9.14459e8	−	1.52202e9i	−0.0301658	−	0.0502077i
$989$	2.62424e10			0.862615
$990$	1.43589e10	+	8.29009e9i	0.470324	+	0.271541i
$991$	−6.66158e9	+	1.15382e10i	−0.217430	+	0.376600i	−0.954022	−	0.299738i	$-0.903101\pi$
$991$	−6.66158e9	+	1.15382e10i	−0.217430	+	0.376600i	0.736592	+	0.676338i	$0.236434\pi$
$992$	−2.88475e9	−	4.99653e9i	−0.0938246	−	0.162509i
$993$		−	3.26388e10i		−	1.05782i
$994$	−2.01176e10	+	1.16149e10i	−0.649716	+	0.375114i
$995$	−1.44721e10	+	8.35545e9i	−0.465747	+	0.268899i
$996$		−	5.40464e9i		−	0.173324i
$997$	−1.91796e10	−	3.32200e10i	−0.612923	−	1.06161i	−0.990745	−	0.135736i	$-0.956660\pi$
$997$	−1.91796e10	−	3.32200e10i	−0.612923	−	1.06161i	0.377822	−	0.925878i	$-0.376673\pi$
$998$	1.27548e10	−	2.20919e10i	0.406178	−	0.703521i
$999$	4.65450e10	+	2.68728e10i	1.47705	+	0.852773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.8.e.a.17.3	✓	16
3.2	odd	2		234.8.l.c.199.7		16
4.3	odd	2		208.8.w.b.17.3		16
13.4	even	6		338.8.b.i.337.3		16
13.6	odd	12		338.8.a.n.1.3		8
13.7	odd	12		338.8.a.m.1.3		8
13.9	even	3		338.8.b.i.337.11		16
13.10	even	6	inner	26.8.e.a.23.3	yes	16
39.23	odd	6		234.8.l.c.127.6		16
52.23	odd	6		208.8.w.b.49.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.e.a.17.3	✓	16	1.1	even	1	trivial
26.8.e.a.23.3	yes	16	13.10	even	6	inner
208.8.w.b.17.3		16	4.3	odd	2
208.8.w.b.49.3		16	52.23	odd	6
234.8.l.c.127.6		16	39.23	odd	6
234.8.l.c.199.7		16	3.2	odd	2
338.8.a.m.1.3		8	13.7	odd	12
338.8.a.n.1.3		8	13.6	odd	12
338.8.b.i.337.3		16	13.4	even	6
338.8.b.i.337.11		16	13.9	even	3

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} +(16.1763 - 28.0182i) q^{3} +(32.0000 + 55.4256i) q^{4} -211.408i q^{5} +(-224.146 + 129.411i) q^{6} +(635.796 - 367.077i) q^{7} -512.000i q^{8} +(570.153 + 987.534i) q^{9} +(-845.633 + 1464.68i) q^{10} +(-7445.38 - 4298.59i) q^{11} +2070.57 q^{12} +(-6928.10 - 3840.57i) q^{13} -5873.23 q^{14} +(-5923.28 - 3419.81i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-8168.98 - 14149.1i) q^{17} -9122.45i q^{18} +(3033.16 - 1751.20i) q^{19} +(11717.4 - 6765.06i) q^{20} -23751.8i q^{21} +(34388.7 + 59563.0i) q^{22} +(-32638.2 + 56531.0i) q^{23} +(-14345.3 - 8282.28i) q^{24} +33431.5 q^{25} +(32637.0 + 54320.7i) q^{26} +107647. q^{27} +(40690.9 + 23492.9i) q^{28} +(56295.7 - 97507.0i) q^{29} +(27358.5 + 47386.3i) q^{30} -176071. i q^{31} +(28377.9 - 16384.0i) q^{32} +(-240878. + 139071. i) q^{33} +130704. i q^{34} +(-77603.1 - 134412. i) q^{35} +(-36489.8 + 63202.2i) q^{36} +(432385. + 249638. i) q^{37} -28019.1 q^{38} +(-219677. + 131987. i) q^{39} -108241. q^{40} +(-250415. - 144577. i) q^{41} +(-95007.3 + 164557. i) q^{42} +(-201010. - 348160. i) q^{43} -550219. i q^{44} +(208773. - 120535. i) q^{45} +(452248. - 261106. i) q^{46} -64966.5i q^{47} +(66258.2 + 114763. i) q^{48} +(-142281. + 246438. i) q^{49} +(-231621. - 133726. i) q^{50} -528576. q^{51} +(-8832.82 - 506892. i) q^{52} +263903. q^{53} +(-745801. - 430589. i) q^{54} +(-908757. + 1.57401e6i) q^{55} +(-187943. - 325527. i) q^{56} -113312. i q^{57} +(-780056. + 450366. i) q^{58} +(2.22659e6 - 1.28552e6i) q^{59} -437736. i q^{60} +(269475. + 466745. i) q^{61} +(-704284. + 1.21986e6i) q^{62} +(725002. + 418580. i) q^{63} -262144. q^{64} +(-811929. + 1.46466e6i) q^{65} +2.22513e6 q^{66} +(771672. + 445525. i) q^{67} +(522815. - 905541. i) q^{68} +(1.05593e6 + 1.82893e6i) q^{69} +1.24165e6i q^{70} +(3.42530e6 - 1.97760e6i) q^{71} +(505617. - 291918. i) q^{72} +2.77895e6i q^{73} +(-1.99710e6 - 3.45908e6i) q^{74} +(540800. - 936692. i) q^{75} +(194122. + 112077. i) q^{76} -6.31165e6 q^{77} +(2.04991e6 - 35720.7i) q^{78} +4.53826e6 q^{79} +(749916. + 432964. i) q^{80} +(494411. - 856345. i) q^{81} +(1.15662e6 + 2.00332e6i) q^{82} -2.61022e6i q^{83} +(1.31646e6 - 760058. i) q^{84} +(-2.99123e6 + 1.72699e6i) q^{85} +3.21616e6i q^{86} +(-1.82131e6 - 3.15461e6i) q^{87} +(-2.20088e6 + 3.81203e6i) q^{88} +(-6.82257e6 - 3.93901e6i) q^{89} -1.92856e6 q^{90} +(-5.81464e6 + 101323. i) q^{91} -4.17769e6 q^{92} +(-4.93320e6 - 2.84818e6i) q^{93} +(-259866. + 450101. i) q^{94} +(-370217. - 641235. i) q^{95} -1.06013e6i q^{96} +(7.91553e6 - 4.57003e6i) q^{97} +(1.97150e6 - 1.13825e6i) q^{98} -9.80341e6i 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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