LMFDB - Embedded newform 26.8.e.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,8,Mod(17,26)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			23.4
Root			$50.2253i$ of defining polynomial
Character	$\chi$	$=$	26.23
Dual form			26.8.e.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.92820 + 4.00000i) q^{2} +(25.1127 + 43.4964i) q^{3} +(32.0000 - 55.4256i) q^{4} -469.361i q^{5} +(-347.971 - 200.901i) q^{6} +(64.3718 + 37.1651i) q^{7} +512.000i q^{8} +(-167.792 + 290.624i) q^{9} +(1877.44 + 3251.83i) q^{10} +(2926.79 - 1689.78i) q^{11} +3214.42 q^{12} +(5470.00 - 5729.54i) q^{13} -594.641 q^{14} +(20415.5 - 11786.9i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-4589.65 + 7949.50i) q^{17} -2684.67i q^{18} +(40877.8 + 23600.8i) q^{19} +(-26014.6 - 15019.6i) q^{20} +3733.25i q^{21} +(-13518.3 + 23414.3i) q^{22} +(-21052.4 - 36463.9i) q^{23} +(-22270.2 + 12857.7i) q^{24} -142175. q^{25} +(-14979.1 + 61575.4i) q^{26} +92988.0 q^{27} +(4119.79 - 2378.56i) q^{28} +(-82803.7 - 143420. i) q^{29} +(-94295.3 + 163324. i) q^{30} -107861. i q^{31} +(28377.9 + 16384.0i) q^{32} +(146999. + 84869.8i) q^{33} -73434.4i q^{34} +(17443.8 - 30213.6i) q^{35} +(10738.7 + 18599.9i) q^{36} +(-228730. + 132058. i) q^{37} -377613. q^{38} +(386581. + 94041.1i) q^{39} +240313. q^{40} +(384584. - 222040. i) q^{41} +(-14933.0 - 25864.7i) q^{42} +(-308598. + 534508. i) q^{43} -216292. i q^{44} +(136408. + 78754.9i) q^{45} +(291711. + 168419. i) q^{46} -281242. i q^{47} +(102861. - 178161. i) q^{48} +(-409009. - 708424. i) q^{49} +(985016. - 568699. i) q^{50} -461033. q^{51} +(-142524. - 486523. i) q^{52} +1.57574e6 q^{53} +(-644240. + 371952. i) q^{54} +(-793118. - 1.37372e6i) q^{55} +(-19028.5 + 32958.3i) q^{56} +2.37072e6i q^{57} +(1.14736e6 + 662430. i) q^{58} +(1.46781e6 + 847438. i) q^{59} -1.50872e6i q^{60} +(-1.64761e6 + 2.85375e6i) q^{61} +(431444. + 747283. i) q^{62} +(-21602.1 + 12472.0i) q^{63} -262144. q^{64} +(-2.68922e6 - 2.56740e6i) q^{65} -1.35792e6 q^{66} +(-2.11527e6 + 1.22125e6i) q^{67} +(293737. + 508768. i) q^{68} +(1.05737e6 - 1.83141e6i) q^{69} +279101. i q^{70} +(-2.46302e6 - 1.42202e6i) q^{71} +(-148799. - 85909.4i) q^{72} +3.94991e6i q^{73} +(1.05646e6 - 1.82984e6i) q^{74} +(-3.57039e6 - 6.18410e6i) q^{75} +(2.61618e6 - 1.51045e6i) q^{76} +251203. q^{77} +(-3.05447e6 + 894787. i) q^{78} +3.64110e6 q^{79} +(-1.66494e6 + 961252. i) q^{80} +(2.70214e6 + 4.68024e6i) q^{81} +(-1.77632e6 + 3.07667e6i) q^{82} +5.97315e6i q^{83} +(206918. + 119464. i) q^{84} +(3.73119e6 + 2.15420e6i) q^{85} -4.93757e6i q^{86} +(4.15884e6 - 7.20333e6i) q^{87} +(865168. + 1.49852e6i) q^{88} +(-1.28990e6 + 744724. i) q^{89} -1.26008e6 q^{90} +(565052. - 165528. i) q^{91} -2.69471e6 q^{92} +(4.69156e6 - 2.70868e6i) q^{93} +(1.12497e6 + 1.94850e6i) q^{94} +(1.10773e7 - 1.91865e7i) q^{95} +1.64578e6i q^{96} +(1.20731e7 + 6.97042e6i) q^{97} +(5.66740e6 + 3.27207e6i) q^{98} +1.13413e6i 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
$3$	25.1127	+	43.4964i	0.536993	+	0.930099i	0.999064	+	0.0432559i	$0.0137731\pi$
$3$	25.1127	+	43.4964i	0.536993	+	0.930099i	−0.462071	+	0.886843i	$0.652894\pi$
$4$	32.0000	−	55.4256i	0.250000	−	0.433013i
$5$		−	469.361i		−	1.67924i	−0.543176	−	0.839619i	$-0.682778\pi$
$5$		−	469.361i		−	1.67924i	0.543176	−	0.839619i	$-0.317222\pi$
$6$	−347.971	−	200.901i	−0.657679	−	0.379711i
$7$	64.3718	+	37.1651i	0.0709336	+	0.0409536i	0.535047	−	0.844822i	$-0.320294\pi$
$7$	64.3718	+	37.1651i	0.0709336	+	0.0409536i	−0.464114	+	0.885776i	$0.653627\pi$
$8$			512.000i			0.353553i
$9$	−167.792	+	290.624i	−0.0767223	+	0.132887i
$10$	1877.44	+	3251.83i	0.593700	+	1.02832i
$11$	2926.79	−	1689.78i	0.663005	−	0.382786i	−0.130416	−	0.991459i	$-0.541631\pi$
$11$	2926.79	−	1689.78i	0.663005	−	0.382786i	0.793421	+	0.608673i	$0.208298\pi$
$12$	3214.42			0.536993
$13$	5470.00	−	5729.54i	0.690534	−	0.723300i
$13$	5470.00	−	5729.54i	0.690534	−	0.723300i
$14$	−594.641			−0.0579171
$15$	20415.5	−	11786.9i	1.56186	−	0.901738i
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−4589.65	+	7949.50i	−0.226573	+	0.392436i	−0.956790	−	0.290779i	$-0.906086\pi$
$17$	−4589.65	+	7949.50i	−0.226573	+	0.392436i	0.730217	+	0.683215i	$0.239419\pi$
$18$		−	2684.67i		−	0.108502i
$19$	40877.8	+	23600.8i	1.36726	+	0.789387i	0.990577	−	0.136957i	$-0.0437321\pi$
$19$	40877.8	+	23600.8i	1.36726	+	0.789387i	0.376681	+	0.926343i	$0.377065\pi$
$20$	−26014.6	−	15019.6i	−0.727131	−	0.419809i
$21$			3733.25i			0.0879671i
$22$	−13518.3	+	23414.3i	−0.270671	+	0.468815i
$23$	−21052.4	−	36463.9i	−0.360790	−	0.624907i	0.627301	−	0.778777i	$-0.284160\pi$
$23$	−21052.4	−	36463.9i	−0.360790	−	0.624907i	−0.988091	+	0.153870i	$0.950826\pi$
$24$	−22270.2	+	12857.7i	−0.328840	+	0.189856i
$25$	−142175.			−1.81984
$26$	−14979.1	+	61575.4i	−0.167139	+	0.687070i
$27$	92988.0			0.909188
$28$	4119.79	−	2378.56i	0.0354668	−	0.0204768i
$29$	−82803.7	−	143420.i	−0.630459	−	1.09199i	−0.987458	−	0.157882i	$-0.949533\pi$
$29$	−82803.7	−	143420.i	−0.630459	−	1.09199i	0.356999	−	0.934105i	$-0.383800\pi$
$30$	−94295.3	+	163324.i	−0.637625	+	1.10440i
$31$		−	107861.i		−	0.650277i	−0.945666	−	0.325138i	$-0.894589\pi$
$31$		−	107861.i		−	0.650277i	0.945666	−	0.325138i	$-0.105411\pi$
$32$	28377.9	+	16384.0i	0.153093	+	0.0883883i
$33$	146999.	+	84869.8i	0.712058	+	0.411107i
$34$		−	73434.4i		−	0.320423i
$35$	17443.8	−	30213.6i	0.0687708	−	0.119114i
$36$	10738.7	+	18599.9i	0.0383612	+	0.0664435i
$37$	−228730.	+	132058.i	−0.742365	+	0.428605i	−0.822929	−	0.568145i	$-0.807661\pi$
$37$	−228730.	+	132058.i	−0.742365	+	0.428605i	0.0805633	+	0.996749i	$0.474328\pi$
$38$	−377613.			−1.11636
$39$	386581.	+	94041.1i	1.04355	+	0.253858i
$40$	240313.			0.593700
$41$	384584.	−	222040.i	0.871460	−	0.503138i	0.00362686	−	0.999993i	$-0.498846\pi$
$41$	384584.	−	222040.i	0.871460	−	0.503138i	0.867833	+	0.496856i	$0.165512\pi$
$42$	−14933.0	−	25864.7i	−0.0311010	−	0.0538686i
$43$	−308598.	+	534508.i	−0.591907	+	1.02521i	0.402068	+	0.915610i	$0.368291\pi$
$43$	−308598.	+	534508.i	−0.591907	+	1.02521i	−0.993975	+	0.109604i	$0.965042\pi$
$44$		−	216292.i		−	0.382786i
$45$	136408.	+	78754.9i	0.223149	+	0.128835i
$46$	291711.	+	168419.i	0.441876	+	0.255117i
$47$		−	281242.i		−	0.395128i	−0.980290	−	0.197564i	$-0.936697\pi$
$47$		−	281242.i		−	0.395128i	0.980290	−	0.197564i	$-0.0633030\pi$
$48$	102861.	−	178161.i	0.134248	−	0.232525i
$49$	−409009.	−	708424.i	−0.496646	−	0.860215i
$50$	985016.	−	568699.i	1.11442	−	0.643410i
$51$	−461033.			−0.486672
$52$	−142524.	−	486523.i	−0.140564	−	0.479835i
$53$	1.57574e6			1.45385			0.726924	−	0.686718i	$-0.240949\pi$
$53$	1.57574e6			1.45385			0.726924	+	0.686718i	$0.240949\pi$
$54$	−644240.	+	371952.i	−0.556762	+	0.321447i
$55$	−793118.	−	1.37372e6i	−0.642789	−	1.11334i
$56$	−19028.5	+	32958.3i	−0.0144793	+	0.0250788i
$57$			2.37072e6i			1.69558i
$58$	1.14736e6	+	662430.i	0.772151	+	0.445802i
$59$	1.46781e6	+	847438.i	0.930436	+	0.537188i	0.886950	−	0.461866i	$-0.152820\pi$
$59$	1.46781e6	+	847438.i	0.930436	+	0.537188i	0.0434869	+	0.999054i	$0.486153\pi$
$60$		−	1.50872e6i		−	0.901738i
$61$	−1.64761e6	+	2.85375e6i	−0.929395	+	1.60976i	−0.145059	+	0.989423i	$0.546337\pi$
$61$	−1.64761e6	+	2.85375e6i	−0.929395	+	1.60976i	−0.784336	+	0.620336i	$0.786996\pi$
$62$	431444.	+	747283.i	0.229908	+	0.398212i
$63$	−21602.1	+	12472.0i	−0.0108844	+	0.00628410i
$64$	−262144.			−0.125000
$65$	−2.68922e6	−	2.56740e6i	−1.21459	−	1.15957i
$66$	−1.35792e6			−0.581393
$67$	−2.11527e6	+	1.22125e6i	−0.859219	+	0.496071i	−0.863751	−	0.503919i	$-0.831891\pi$
$67$	−2.11527e6	+	1.22125e6i	−0.859219	+	0.496071i	0.00453136	+	0.999990i	$0.498558\pi$
$68$	293737.	+	508768.i	0.113286	+	0.196218i
$69$	1.05737e6	−	1.83141e6i	0.387483	−	0.671141i
$70$			279101.i			0.0972565i
$71$	−2.46302e6	−	1.42202e6i	−0.816701	−	0.471523i	0.0325765	−	0.999469i	$-0.489629\pi$
$71$	−2.46302e6	−	1.42202e6i	−0.816701	−	0.471523i	−0.849278	+	0.527947i	$0.822962\pi$
$72$	−148799.	−	85909.4i	−0.0469826	−	0.0271254i
$73$			3.94991e6i			1.18839i	0.804323	+	0.594193i	$0.202528\pi$
$73$			3.94991e6i			1.18839i	−0.804323	+	0.594193i	$0.797472\pi$
$74$	1.05646e6	−	1.82984e6i	0.303069	−	0.524932i
$75$	−3.57039e6	−	6.18410e6i	−0.977240	−	1.69263i
$76$	2.61618e6	−	1.51045e6i	0.683629	−	0.394693i
$77$	251203.			0.0627058
$78$	−3.05447e6	+	894787.i	−0.728795	+	0.213495i
$79$	3.64110e6			0.830880			0.415440	−	0.909621i	$-0.363628\pi$
$79$	3.64110e6			0.830880			0.415440	+	0.909621i	$0.363628\pi$
$80$	−1.66494e6	+	961252.i	−0.363566	+	0.209905i
$81$	2.70214e6	+	4.68024e6i	0.564950	+	0.978522i
$82$	−1.77632e6	+	3.07667e6i	−0.355772	+	0.616215i
$83$			5.97315e6i			1.14665i	0.819329	+	0.573324i	$0.194346\pi$
$83$			5.97315e6i			1.14665i	−0.819329	+	0.573324i	$0.805654\pi$
$84$	206918.	+	119464.i	0.0380909	+	0.0219918i
$85$	3.73119e6	+	2.15420e6i	0.658993	+	0.380470i
$86$		−	4.93757e6i		−	0.837083i
$87$	4.15884e6	−	7.20333e6i	0.677104	−	1.17278i
$88$	865168.	+	1.49852e6i	0.135335	+	0.234408i
$89$	−1.28990e6	+	744724.i	−0.193950	+	0.111977i	−0.593831	−	0.804590i	$-0.702385\pi$
$89$	−1.28990e6	+	744724.i	−0.193950	+	0.111977i	0.399880	+	0.916567i	$0.369052\pi$
$90$	−1.26008e6			−0.182200
$91$	565052.	−	165528.i	0.0786038	−	0.0230264i
$92$	−2.69471e6			−0.360790
$93$	4.69156e6	−	2.70868e6i	0.604822	−	0.349194i
$94$	1.12497e6	+	1.94850e6i	0.139699	+	0.241965i
$95$	1.10773e7	−	1.91865e7i	1.32557	−	2.29595i
$96$			1.64578e6i			0.189856i
$97$	1.20731e7	+	6.97042e6i	1.34313	+	0.775457i	0.987266	−	0.159080i	$-0.0508526\pi$
$97$	1.20731e7	+	6.97042e6i	1.34313	+	0.775457i	0.355866	+	0.934537i	$0.384186\pi$
$98$	5.66740e6	+	3.27207e6i	0.608264	+	0.351181i
$99$			1.13413e6i			0.117473i
$100$	−4.54960e6	+	7.88013e6i	−0.454960	+	0.788013i
$101$	−1.00902e6	−	1.74767e6i	−0.0974485	−	0.168786i	0.813179	−	0.582013i	$-0.197735\pi$
$101$	−1.00902e6	−	1.74767e6i	−0.0974485	−	0.168786i	−0.910628	+	0.413227i	$0.864401\pi$
$102$	3.19413e6	−	1.84413e6i	0.298025	−	0.172065i
$103$	−1.67184e7			−1.50753			−0.753763	−	0.657147i	$-0.771763\pi$
$103$	−1.67184e7			−1.50753			−0.753763	+	0.657147i	$0.771763\pi$
$104$	2.93353e6	+	2.80064e6i	0.255725	+	0.244141i
$105$	1.75224e6			0.147718
$106$	−1.09170e7	+	6.30296e6i	−0.890296	+	0.514013i
$107$	−2.27240e6	−	3.93592e6i	−0.179326	−	0.310601i	0.762324	−	0.647195i	$-0.224058\pi$
$107$	−2.27240e6	−	3.93592e6i	−0.179326	−	0.310601i	−0.941650	+	0.336594i	$0.890725\pi$
$108$	2.97562e6	−	5.15392e6i	0.227297	−	0.393690i
$109$		−	1.28345e7i		−	0.949265i	−0.880184	−	0.474632i	$-0.842581\pi$
$109$		−	1.28345e7i		−	0.949265i	0.880184	−	0.474632i	$-0.157419\pi$
$110$	1.09898e7	+	6.34494e6i	0.787252	+	0.454520i
$111$	−1.14881e7	−	6.63263e6i	−0.797290	−	0.460315i
$112$		−	304456.i		−	0.0204768i
$113$	−7.89884e6	+	1.36812e7i	−0.514978	+	0.891968i	0.484871	+	0.874586i	$0.338867\pi$
$113$	−7.89884e6	+	1.36812e7i	−0.514978	+	0.891968i	−0.999849	+	0.0173821i	$0.994467\pi$
$114$	−9.48288e6	−	1.64248e7i	−0.599478	−	1.03833i
$115$	−1.71147e7	+	9.88119e6i	−1.04937	+	0.605853i
$116$	−1.05989e7			−0.630459
$117$	747321.	+	2.55108e6i	0.0431377	+	0.147256i
$118$	−1.35590e7			−0.759698
$119$	−590887.	+	341149.i	−0.0321433	+	0.0185579i
$120$	6.03490e6	+	1.04527e7i	0.318813	+	0.552200i
$121$	−4.03286e6	+	6.98512e6i	−0.206949	+	0.358447i
$122$		−	2.63618e7i		−	1.31436i
$123$	1.93158e7	+	1.11520e7i	0.935935	+	0.540363i
$124$	−5.97826e6	−	3.45155e6i	−0.281578	−	0.162569i
$125$			3.00625e7i			1.37670i
$126$	99775.8	−	172817.i	0.00444353	−	0.00769642i
$127$	1.38226e7	+	2.39414e7i	0.598793	+	1.03714i	0.993000	+	0.118118i	$0.0376861\pi$
$127$	1.38226e7	+	2.39414e7i	0.598793	+	1.03714i	−0.394207	+	0.919022i	$0.628981\pi$
$128$	1.81619e6	−	1.04858e6i	0.0765466	−	0.0441942i
$129$	−3.09989e7			−1.27140
$130$	2.89011e7	+	7.03059e6i	1.15375	+	0.280666i
$131$	−9.74162e6			−0.378601			−0.189300	−	0.981919i	$-0.560622\pi$
$131$	−9.74162e6			−0.378601			−0.189300	+	0.981919i	$0.560622\pi$
$132$	9.40793e6	−	5.43167e6i	0.356029	−	0.205553i
$133$	1.75425e6	+	3.03845e6i	0.0646564	+	0.111988i
$134$	9.77002e6	−	1.69222e7i	0.350775	−	0.607560i
$135$		−	4.36450e7i		−	1.52674i
$136$	−4.07015e6	−	2.34990e6i	−0.138747	−	0.0801056i
$137$	2.47332e6	+	1.42797e6i	0.0821785	+	0.0474458i	0.540526	−	0.841327i	$-0.318225\pi$
$137$	2.47332e6	+	1.42797e6i	0.0821785	+	0.0474458i	−0.458348	+	0.888773i	$0.651559\pi$
$138$			1.69178e7i			0.547984i
$139$	2.24368e7	−	3.88616e7i	0.708612	−	1.22735i	−0.256760	−	0.966475i	$-0.582655\pi$
$139$	2.24368e7	−	3.88616e7i	0.708612	−	1.22735i	0.965372	−	0.260877i	$-0.0840118\pi$
$140$	−1.11641e6	−	1.93367e6i	−0.0343854	−	0.0595572i
$141$	1.22330e7	−	7.06273e6i	0.367508	−	0.212181i
$142$	2.27524e7			0.666834
$143$	6.32784e6	−	2.60123e7i	0.180959	−	0.743878i
$144$	1.37455e6			0.0383612
$145$	−6.73159e7	+	3.88648e7i	−1.83371	+	1.05869i
$146$	−1.57996e7	−	2.73658e7i	−0.420158	−	0.727734i
$147$	2.05426e7	−	3.55808e7i	0.533390	−	0.923859i
$148$			1.69034e7i			0.428605i
$149$	2.11798e7	+	1.22282e7i	0.524531	+	0.302838i	0.738786	−	0.673940i	$-0.235399\pi$
$149$	2.11798e7	+	1.22282e7i	0.524531	+	0.302838i	−0.214256	+	0.976778i	$0.568733\pi$
$150$	4.94728e7	+	2.85631e7i	1.19687	+	0.691013i
$151$			5.94949e7i			1.40624i	0.711069	+	0.703122i	$0.248211\pi$
$151$			5.94949e7i			1.40624i	−0.711069	+	0.703122i	$0.751789\pi$
$152$	−1.20836e7	+	2.09295e7i	−0.279090	+	0.483399i
$153$	−1.54021e6	−	2.66772e6i	−0.0347664	−	0.0602172i
$154$	−1.74039e6	+	1.00481e6i	−0.0383993	+	0.0221699i
$155$	−5.06257e7			−1.09197
$156$	1.75829e7	−	1.84172e7i	0.370812	−	0.388407i
$157$	4.61680e7			0.952122			0.476061	−	0.879412i	$-0.342064\pi$
$157$	4.61680e7			0.952122			0.476061	+	0.879412i	$0.342064\pi$
$158$	−2.52263e7	+	1.45644e7i	−0.508808	+	0.293760i
$159$	3.95710e7	+	6.85390e7i	0.780706	+	1.35222i
$160$	7.69001e6	−	1.33195e7i	0.148425	−	0.257080i
$161$		−	3.12966e6i		−	0.0591026i
$162$	−3.74419e7	−	2.16171e7i	−0.691919	−	0.399480i
$163$	−8.58326e6	−	4.95554e6i	−0.155237	−	0.0896262i	0.420369	−	0.907353i	$-0.361901\pi$
$163$	−8.58326e6	−	4.95554e6i	−0.155237	−	0.0896262i	−0.575606	+	0.817727i	$0.695234\pi$
$164$		−	2.84211e7i		−	0.503138i
$165$	3.98346e7	−	6.89956e7i	0.690346	−	1.19571i
$166$	−2.38926e7	−	4.13832e7i	−0.405401	−	0.702175i
$167$	5.08074e7	−	2.93337e7i	0.844150	−	0.487370i	−0.0145226	−	0.999895i	$-0.504623\pi$
$167$	5.08074e7	−	2.93337e7i	0.844150	−	0.487370i	0.858673	+	0.512524i	$0.171290\pi$
$168$	−1.91143e6			−0.0311010
$169$	−2.90681e6	−	6.26812e7i	−0.0463248	−	0.998926i
$170$	−3.44672e7			−0.538066
$171$	−1.37179e7	+	7.92005e6i	−0.209798	+	0.121127i
$172$	1.97503e7	+	3.42085e7i	0.295954	+	0.512607i
$173$	3.14153e6	−	5.44129e6i	0.0461296	−	0.0798989i	−0.842039	−	0.539417i	$-0.818645\pi$
$173$	3.14153e6	−	5.44129e6i	0.0461296	−	0.0798989i	0.888168	+	0.459518i	$0.151978\pi$
$174$			6.65415e7i			0.957569i
$175$	−9.15205e6	−	5.28394e6i	−0.129088	−	0.0745289i
$176$	−1.19881e7	−	6.92135e6i	−0.165751	−	0.0956965i
$177$			8.51257e7i			1.15386i
$178$	5.95779e6	−	1.03192e7i	0.0791799	−	0.137144i
$179$	−2.66019e7	−	4.60759e7i	−0.346679	−	0.600465i	0.638979	−	0.769225i	$-0.279357\pi$
$179$	−2.66019e7	−	4.60759e7i	−0.346679	−	0.600465i	−0.985657	+	0.168759i	$0.946024\pi$
$180$	8.73008e6	−	5.04031e6i	0.111574	−	0.0644175i
$181$	−3.34020e7			−0.418695			−0.209347	−	0.977841i	$-0.567134\pi$
$181$	−3.34020e7			−0.418695			−0.209347	+	0.977841i	$0.567134\pi$
$182$	−3.25268e6	+	3.40702e6i	−0.0399937	+	0.0418914i
$183$	−1.65504e8			−1.99631
$184$	1.86695e7	−	1.07788e7i	0.220938	−	0.127559i
$185$	6.19827e7	+	1.07357e8i	0.719729	+	1.24661i
$186$	−2.16694e7	+	3.75325e7i	−0.246917	+	0.427674i
$187$			3.10220e7i			0.346916i
$188$	−1.55880e7	−	8.99974e6i	−0.171095	−	0.0987819i
$189$	5.98580e6	+	3.45590e6i	0.0644920	+	0.0372345i
$190$			1.77237e8i			1.87464i
$191$	−1.59471e7	+	2.76212e7i	−0.165602	+	0.286831i	−0.936869	−	0.349681i	$-0.886290\pi$
$191$	−1.59471e7	+	2.76212e7i	−0.165602	+	0.286831i	0.771267	+	0.636512i	$0.219623\pi$
$192$	−6.58313e6	−	1.14023e7i	−0.0671241	−	0.116262i
$193$	1.33692e8	−	7.71874e7i	1.33862	−	0.772851i	0.352015	−	0.935994i	$-0.385497\pi$
$193$	1.33692e8	−	7.71874e7i	1.33862	−	0.772851i	0.986602	+	0.163143i	$0.0521633\pi$
$194$	−1.11527e8			−1.09666
$195$	4.41392e7	−	1.81446e8i	0.426288	−	1.75237i
$196$	−5.23532e7			−0.496646
$197$	1.48984e7	−	8.60161e6i	0.138838	−	0.0801582i	−0.428972	−	0.903318i	$-0.641124\pi$
$197$	1.48984e7	−	8.60161e6i	0.138838	−	0.0801582i	0.567810	+	0.823160i	$0.307791\pi$
$198$	−4.53650e6	−	7.85745e6i	−0.0415330	−	0.0719372i
$199$	−1.05808e8	+	1.83264e8i	−0.951769	+	1.64851i	−0.210175	+	0.977664i	$0.567403\pi$
$199$	−1.05808e8	+	1.83264e8i	−0.951769	+	1.64851i	−0.741594	+	0.670849i	$0.765930\pi$
$200$		−	7.27935e7i		−	0.643410i
$201$	−1.06240e8	−	6.13378e7i	−0.922789	−	0.532773i
$202$	1.39814e7	+	8.07216e6i	0.119350	+	0.0689065i
$203$		−	1.23096e7i		−	0.103278i
$204$	−1.47531e7	+	2.55530e7i	−0.121668	+	0.210735i
$205$	−1.04217e8	−	1.80509e8i	−0.844888	−	1.46339i
$206$	1.15829e8	−	6.68736e7i	0.923167	−	0.532991i
$207$	1.41297e7			0.110723
$208$	−3.15266e7	−	7.66928e6i	−0.242916	−	0.0590926i
$209$	1.59521e8			1.20867
$210$	−1.21399e7	+	7.00898e6i	−0.0904582	+	0.0522260i
$211$	2.35499e7	+	4.07897e7i	0.172584	+	0.298925i	0.939323	−	0.343035i	$-0.111455\pi$
$211$	2.35499e7	+	4.07897e7i	0.172584	+	0.298925i	−0.766738	+	0.641960i	$0.778122\pi$
$212$	5.04237e7	−	8.73363e7i	0.363462	−	0.629534i
$213$		−	1.42843e8i		−	1.01282i
$214$	3.14874e7	+	1.81792e7i	0.219628	+	0.126802i
$215$	2.50877e8	+	1.44844e8i	1.72158	+	0.993953i
$216$			4.76099e7i			0.321447i
$217$	4.00866e6	−	6.94320e6i	0.0266312	−	0.0461265i
$218$	5.13381e7	+	8.89203e7i	0.335616	+	0.581304i
$219$	−1.71807e8	+	9.91928e7i	−1.10532	+	0.638154i
$220$	−1.01519e8			−0.642789
$221$	2.04417e7	+	6.97803e7i	0.127392	+	0.434871i
$222$	1.06122e8			0.650984
$223$	1.46451e8	−	8.45534e7i	0.884351	−	0.510580i	0.0122607	−	0.999925i	$-0.496097\pi$
$223$	1.46451e8	−	8.45534e7i	0.884351	−	0.510580i	0.872091	+	0.489344i	$0.162764\pi$
$224$	1.21782e6	+	2.10933e6i	0.00723964	+	0.0125394i
$225$	2.38558e7	−	4.13194e7i	0.139622	−	0.241833i
$226$		−	1.26381e8i		−	0.728289i
$227$	2.75344e8	+	1.58970e8i	1.56237	+	0.902036i	0.997017	+	0.0771881i	$0.0245942\pi$
$227$	2.75344e8	+	1.58970e8i	1.56237	+	0.902036i	0.565355	+	0.824848i	$0.308739\pi$
$228$	1.31399e8	+	7.58630e7i	0.734207	+	0.423895i
$229$		−	1.16369e8i		−	0.640345i	−0.947359	−	0.320173i	$-0.896259\pi$
$229$		−	1.16369e8i		−	0.640345i	0.947359	−	0.320173i	$-0.103741\pi$
$230$	7.90495e7	−	1.36918e8i	0.428402	−	0.742015i
$231$	6.30839e6	+	1.09264e7i	0.0336726	+	0.0583226i
$232$	7.34312e7	−	4.23955e7i	0.386076	−	0.222901i
$233$	−3.60170e8			−1.86536			−0.932679	−	0.360707i	$-0.882535\pi$
$233$	−3.60170e8			−1.86536			−0.932679	+	0.360707i	$0.882535\pi$
$234$	−1.53819e7	−	1.46851e7i	−0.0784793	−	0.0749242i
$235$	−1.32004e8			−0.663513
$236$	9.39396e7	−	5.42361e7i	0.465218	−	0.268594i
$237$	9.14378e7	+	1.58375e8i	0.446177	+	0.772800i
$238$	2.72919e6	−	4.72710e6i	0.0131224	−	0.0227287i
$239$			1.23549e8i			0.585394i	0.956205	+	0.292697i	$0.0945527\pi$
$239$			1.23549e8i			0.585394i	−0.956205	+	0.292697i	$0.905447\pi$
$240$	−8.36220e7	−	4.82792e7i	−0.390464	−	0.225435i
$241$	−2.01715e7	−	1.16460e7i	−0.0928280	−	0.0535943i	0.452867	−	0.891578i	$-0.350401\pi$
$241$	−2.01715e7	−	1.16460e7i	−0.0928280	−	0.0535943i	−0.545695	+	0.837984i	$0.683734\pi$
$242$		−	6.45258e7i		−	0.292671i
$243$	−3.40333e7	+	5.89475e7i	−0.152154	+	0.263538i
$244$	1.05447e8	+	1.82640e8i	0.464697	+	0.804880i
$245$	−3.32507e8	+	1.91973e8i	−1.44451	+	0.833986i
$246$	−1.78432e8			−0.764188
$247$	3.58824e8	−	1.05115e8i	1.51510	−	0.443839i
$248$	5.52248e7			0.229908
$249$	−2.59810e8	+	1.50002e8i	−1.06649	+	0.615741i
$250$	−1.20250e8	−	2.08279e8i	−0.486738	−	0.843055i
$251$	1.65291e7	−	2.86293e7i	0.0659769	−	0.114275i	−0.831150	−	0.556048i	$-0.812317\pi$
$251$	1.65291e7	−	2.86293e7i	0.0659769	−	0.114275i	0.897127	+	0.441773i	$0.145650\pi$
$252$			1.59641e6i			0.00628410i
$253$	−1.23232e8	−	7.11480e7i	−0.478412	−	0.276211i
$254$	−1.91532e8	−	1.10581e8i	−0.733368	−	0.423410i
$255$			2.16391e8i			0.817238i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−1.32117e8	−	2.28834e8i	−0.485505	−	0.840919i	0.514356	−	0.857577i	$-0.328031\pi$
$257$	−1.32117e8	−	2.28834e8i	−0.485505	−	0.840919i	−0.999861	+	0.0166574i	$0.994698\pi$
$258$	2.14767e8	−	1.23996e8i	0.778570	−	0.449508i
$259$	−1.96317e7			−0.0702116
$260$	−2.28355e8	+	6.68951e7i	−0.805757	+	0.236041i
$261$	5.55751e7			0.193481
$262$	6.74919e7	−	3.89665e7i	0.231845	−	0.133856i
$263$	−4.04021e7	−	6.99785e7i	−0.136949	−	0.237202i	0.789391	−	0.613890i	$-0.210396\pi$
$263$	−4.04021e7	−	6.99785e7i	−0.136949	−	0.237202i	−0.926340	+	0.376688i	$0.877063\pi$
$264$	−4.34534e7	+	7.52634e7i	−0.145348	+	0.251750i
$265$		−	7.39591e8i		−	2.44136i
$266$	−2.43076e7	−	1.40340e7i	−0.0791876	−	0.0457190i
$267$	−6.47856e7	−	3.74040e7i	−0.208300	−	0.120262i
$268$			1.56320e8i			0.496071i
$269$	−2.58417e8	+	4.47591e8i	−0.809445	+	1.40200i	0.103803	+	0.994598i	$0.466899\pi$
$269$	−2.58417e8	+	4.47591e8i	−0.809445	+	1.40200i	−0.913249	+	0.407403i	$0.866435\pi$
$270$	1.74580e8	+	3.02381e8i	0.539785	+	0.934935i
$271$	−1.37813e8	+	7.95666e7i	−0.420629	+	0.242850i	−0.695346	−	0.718675i	$-0.744749\pi$
$271$	−1.37813e8	+	7.95666e7i	−0.420629	+	0.242850i	0.274718	+	0.961525i	$0.411416\pi$
$272$	3.75984e7			0.113286
$273$	2.13898e7	+	2.04209e7i	0.0636265	+	0.0607443i
$274$	−2.28476e7			−0.0670985
$275$	−4.16116e8	+	2.40245e8i	−1.20656	+	0.696609i
$276$	−6.76714e7	−	1.17210e8i	−0.193742	−	0.335571i
$277$	1.07125e8	−	1.85545e8i	0.302838	−	0.524530i	−0.673940	−	0.738786i	$-0.735399\pi$
$277$	1.07125e8	−	1.85545e8i	0.302838	−	0.524530i	0.976778	+	0.214256i	$0.0687327\pi$
$278$			3.58988e8i			1.00213i
$279$	3.13470e7	+	1.80982e7i	0.0864133	+	0.0498908i
$280$	1.54694e7	+	8.93124e6i	0.0421133	+	0.0243141i
$281$		−	3.43238e8i		−	0.922833i	−0.887184	−	0.461416i	$-0.847341\pi$
$281$		−	3.43238e8i		−	0.922833i	0.887184	−	0.461416i	$-0.152659\pi$
$282$	−5.65019e7	+	9.78641e7i	−0.150034	+	0.259867i
$283$	4.02846e7	+	6.97750e7i	0.105654	+	0.182998i	0.914005	−	0.405702i	$-0.132973\pi$
$283$	4.02846e7	+	6.97750e7i	0.105654	+	0.182998i	−0.808351	+	0.588701i	$0.799640\pi$
$284$	−1.57633e8	+	9.10095e7i	−0.408351	+	0.235761i
$285$	1.11272e9			2.84728
$286$	6.02085e7	+	2.05530e8i	0.152187	+	0.519509i
$287$	3.30084e7			0.0824211
$288$	−9.52316e6	+	5.49820e6i	−0.0234913	+	0.0135627i
$289$	1.63040e8	+	2.82393e8i	0.397329	+	0.688195i
$290$	3.10919e8	−	5.38527e8i	0.748607	−	1.29663i
$291$			7.00183e8i			1.66566i
$292$	2.18926e8	+	1.26397e8i	0.514586	+	0.297096i
$293$	−3.64956e8	−	2.10707e8i	−0.847625	−	0.489377i	0.0122236	−	0.999925i	$-0.496109\pi$
$293$	−3.64956e8	−	2.10707e8i	−0.847625	−	0.489377i	−0.859849	+	0.510549i	$0.829442\pi$
$294$			3.28682e8i			0.754328i
$295$	3.97755e8	−	6.88931e8i	0.902066	−	1.56242i
$296$	−6.76134e7	−	1.17110e8i	−0.151535	−	0.262466i
$297$	2.72156e8	−	1.57129e8i	0.602796	−	0.348025i
$298$	−1.95651e8			−0.428277
$299$	−3.24078e8	−	7.88365e7i	−0.701133	−	0.170560i
$300$	−4.57010e8			−0.977240
$301$	−3.97300e7	+	2.29381e7i	−0.0839723	+	0.0484814i
$302$	−2.37980e8	−	4.12193e8i	−0.497182	−	0.861145i
$303$	5.06784e7	−	8.77775e7i	0.104658	−	0.181273i
$304$		−	1.93338e8i		−	0.394693i
$305$	1.33944e9	+	7.73325e8i	2.70317	+	1.56067i
$306$	2.13418e7	+	1.23217e7i	0.0425800	+	0.0245836i
$307$		−	8.05591e8i		−	1.58902i	−0.607248	−	0.794512i	$-0.707727\pi$
$307$		−	8.05591e8i		−	1.58902i	0.607248	−	0.794512i	$-0.292273\pi$
$308$	8.03851e6	−	1.39231e7i	0.0156765	−	0.0271524i
$309$	−4.19844e8	−	7.27191e8i	−0.809530	−	1.40215i
$310$	3.50745e8	−	2.02503e8i	0.668692	−	0.386069i
$311$	4.44406e8			0.837758			0.418879	−	0.908042i	$-0.362423\pi$
$311$	4.44406e8			0.837758			0.418879	+	0.908042i	$0.362423\pi$
$312$	−4.81490e7	+	1.97929e8i	−0.0897525	+	0.368951i
$313$	4.53945e8			0.836755			0.418377	−	0.908273i	$-0.362599\pi$
$313$	4.53945e8			0.836755			0.418377	+	0.908273i	$0.362599\pi$
$314$	−3.19862e8	+	1.84672e8i	−0.583053	+	0.336626i
$315$	5.85386e6	+	1.01392e7i	0.0105525	+	0.0182775i
$316$	1.16515e8	−	2.01810e8i	0.207720	−	0.359782i
$317$			6.82323e8i			1.20305i	0.798855	+	0.601524i	$0.205439\pi$
$317$			6.82323e8i			1.20305i	−0.798855	+	0.601524i	$0.794561\pi$
$318$	−5.48312e8	−	3.16568e8i	−0.956165	−	0.552042i
$319$	−4.84698e8	−	2.79840e8i	−0.835995	−	0.482662i
$320$			1.23040e8i			0.209905i
$321$	1.14132e8	−	1.97683e8i	0.192593	−	0.333581i
$322$	1.25186e7	+	2.16829e7i	0.0208959	+	0.0361928i
$323$	−3.75230e8	+	2.16639e8i	−0.619567	+	0.357707i
$324$	3.45874e8			0.564950
$325$	−7.77696e8	+	8.14597e8i	−1.25666	+	1.31629i
$326$	7.92887e7			0.126751
$327$	5.58256e8	−	3.22309e8i	0.882910	−	0.509748i
$328$	1.13684e8	+	1.96907e8i	0.177886	+	0.308108i
$329$	1.04524e7	−	1.81040e7i	0.0161819	−	0.0280278i
$330$			6.37354e8i			0.976296i
$331$	−8.80479e8	−	5.08345e8i	−1.33451	−	0.770478i	−0.348520	−	0.937301i	$-0.613316\pi$
$331$	−8.80479e8	−	5.08345e8i	−1.33451	−	0.770478i	−0.985987	+	0.166823i	$0.946649\pi$
$332$	3.31065e8	+	1.91141e8i	0.496513	+	0.286662i
$333$		−	8.86326e7i		−	0.131534i
$334$	−2.34670e8	+	4.06460e8i	−0.344623	+	0.596904i
$335$	5.73208e8	+	9.92826e8i	0.833020	+	1.44283i
$336$	1.32427e7	−	7.64570e6i	0.0190454	−	0.0109959i
$337$	3.52031e8			0.501044			0.250522	−	0.968111i	$-0.419398\pi$
$337$	3.52031e8			0.501044			0.250522	+	0.968111i	$0.419398\pi$
$338$	2.70864e8	+	4.22641e8i	0.381542	+	0.595337i
$339$	−7.93443e8			−1.10616
$340$	2.38796e8	−	1.37869e8i	0.329497	−	0.190235i
$341$	−1.82261e8	−	3.15686e8i	−0.248917	−	0.431137i
$342$	6.33604e7	−	1.09743e8i	0.0856498	−	0.148350i
$343$		−	1.22017e8i		−	0.163265i
$344$	−2.73668e8	−	1.58002e8i	−0.362468	−	0.209271i
$345$	−8.59593e8	−	4.96286e8i	−1.12701	−	0.650677i
$346$			5.02645e7i			0.0652372i
$347$	3.04896e8	−	5.28095e8i	0.391740	−	0.678514i	−0.600939	−	0.799295i	$-0.705207\pi$
$347$	3.04896e8	−	5.28095e8i	0.391740	−	0.678514i	0.992679	+	0.120781i	$0.0385398\pi$
$348$	−2.66166e8	−	4.61013e8i	−0.338552	−	0.586389i
$349$	−6.42715e8	+	3.71072e8i	−0.809337	+	0.467271i	−0.846726	−	0.532030i	$-0.821429\pi$
$349$	−6.42715e8	+	3.71072e8i	−0.809337	+	0.467271i	0.0373883	+	0.999301i	$0.488096\pi$
$350$	8.45430e7			0.105400
$351$	5.08644e8	−	5.32779e8i	0.627826	−	0.657615i
$352$	1.10742e8			0.135335
$353$	−9.41104e8	+	5.43346e8i	−1.13874	+	0.657454i	−0.946119	−	0.323819i	$-0.895033\pi$
$353$	−9.41104e8	+	5.43346e8i	−1.13874	+	0.657454i	−0.192624	+	0.981273i	$0.561700\pi$
$354$	−3.40503e8	−	5.89768e8i	−0.407952	−	0.706594i
$355$	−6.67442e8	+	1.15604e9i	−0.791798	+	1.37143i
$356$			9.53246e7i			0.111977i
$357$	−2.96775e7	−	1.71343e7i	−0.0345214	−	0.0199310i
$358$	3.68607e8	+	2.12815e8i	0.424593	+	0.245139i
$359$		−	1.56901e9i		−	1.78976i	−0.446302	−	0.894882i	$-0.647259\pi$
$359$		−	1.56901e9i		−	1.78976i	0.446302	−	0.894882i	$-0.352741\pi$
$360$	−4.03225e7	+	6.98406e7i	−0.0455500	+	0.0788950i
$361$	6.67063e8	+	1.15539e9i	0.746262	+	1.29256i
$362$	2.31416e8	−	1.33608e8i	0.256397	−	0.148031i
$363$	−4.05103e8			−0.444521
$364$	8.90717e6	−	3.66153e7i	0.00968021	−	0.0397931i
$365$	1.85393e9			1.99558
$366$	1.14664e9	−	6.62015e8i	1.22249	−	0.705803i
$367$	2.69422e8	+	4.66653e8i	0.284513	+	0.492791i	0.972491	−	0.232940i	$-0.0748347\pi$
$367$	2.69422e8	+	4.66653e8i	0.284513	+	0.492791i	−0.687978	+	0.725732i	$0.741501\pi$
$368$	−8.62308e7	+	1.49356e8i	−0.0901976	+	0.156227i
$369$			1.49026e8i			0.154408i
$370$	−8.58857e8	−	4.95861e8i	−0.881485	−	0.508925i
$371$	1.01433e8	+	5.85624e7i	0.103127	+	0.0595402i
$372$		−	3.46711e8i		−	0.349194i
$373$	−7.04483e8	+	1.22020e9i	−0.702894	+	1.21745i	0.264552	+	0.964371i	$0.414776\pi$
$373$	−7.04483e8	+	1.22020e9i	−0.702894	+	1.21745i	−0.967446	+	0.253077i	$0.918558\pi$
$374$	−1.24088e8	−	2.14927e8i	−0.122653	−	0.212442i
$375$	−1.30761e9	+	7.54950e8i	−1.28047	+	0.739280i
$376$	1.43996e8			0.139699
$377$	−1.27467e9	−	3.10081e8i	−1.22519	−	0.298044i
$378$	−5.52945e7			−0.0526575
$379$	1.37512e9	−	7.93925e8i	1.29749	−	0.749104i	0.317517	−	0.948253i	$-0.397151\pi$
$379$	1.37512e9	−	7.93925e8i	1.29749	−	0.749104i	0.979969	+	0.199149i	$0.0638176\pi$
$380$	−7.08948e8	−	1.22793e9i	−0.662784	−	1.14798i
$381$	−6.94244e8	+	1.20247e9i	−0.643095	+	1.11387i
$382$		−	2.55154e8i		−	0.234197i
$383$	8.74416e8	+	5.04845e8i	0.795285	+	0.459158i	0.841820	−	0.539759i	$-0.181485\pi$
$383$	8.74416e8	+	5.04845e8i	0.795285	+	0.459158i	−0.0465351	+	0.998917i	$0.514818\pi$
$384$	9.12186e7	+	5.26651e7i	0.0822099	+	0.0474639i
$385$		−	1.17905e8i		−	0.105298i
$386$	−6.17499e8	+	1.06954e9i	−0.546488	+	0.946545i
$387$	−1.03560e8	−	1.79372e8i	−0.0908250	−	0.157313i
$388$	7.72680e8	−	4.46107e8i	0.671566	−	0.387729i
$389$	−6.14149e8			−0.528993			−0.264497	−	0.964387i	$-0.585206\pi$
$389$	−6.14149e8			−0.528993			−0.264497	+	0.964387i	$0.585206\pi$
$390$	4.19978e8	+	1.43365e9i	0.358510	+	1.22382i
$391$	3.86493e8			0.326981
$392$	3.62713e8	−	2.09413e8i	0.304132	−	0.175591i
$393$	−2.44638e8	−	4.23726e8i	−0.203306	−	0.352136i
$394$	−6.88129e7	+	1.19187e8i	−0.0566804	+	0.0981734i
$395$		−	1.70899e9i		−	1.39524i
$396$	6.28596e7	+	3.62920e7i	0.0508673	+	0.0293682i
$397$	2.26743e8	+	1.30910e8i	0.181873	+	0.105004i	0.588172	−	0.808736i	$-0.299848\pi$
$397$	2.26743e8	+	1.30910e8i	0.181873	+	0.105004i	−0.406300	+	0.913740i	$0.633181\pi$
$398$		−	1.69292e9i		−	1.34600i
$399$	−8.81079e7	+	1.52607e8i	−0.0694400	+	0.120274i
$400$	2.91174e8	+	5.04328e8i	0.227480	+	0.394007i
$401$	7.19925e6	−	4.15649e6i	0.00557547	−	0.00321900i	−0.497210	−	0.867630i	$-0.665642\pi$
$401$	7.19925e6	−	4.15649e6i	0.00557547	−	0.00321900i	0.502785	+	0.864411i	$0.332309\pi$
$402$	9.81405e8			0.753454
$403$	−6.17994e8	−	5.89999e8i	−0.470345	−	0.449039i
$404$	−1.29155e8			−0.0974485
$405$	2.19672e9	−	1.26828e9i	1.64317	−	0.948685i
$406$	4.92385e7	+	8.52835e7i	0.0365143	+	0.0632447i
$407$	−4.46297e8	+	7.73009e8i	−0.328128	+	0.568334i
$408$		−	2.36049e8i		−	0.172065i
$409$	−1.36216e8	−	7.86441e7i	−0.0984454	−	0.0568375i	0.449969	−	0.893044i	$-0.351435\pi$
$409$	−1.36216e8	−	7.86441e7i	−0.0984454	−	0.0568375i	−0.548414	+	0.836207i	$0.684768\pi$
$410$	1.44407e9	+	8.33734e8i	1.03477	+	0.597426i
$411$			1.43441e8i			0.101912i
$412$	−5.34989e8	+	9.26628e8i	−0.376881	+	0.652777i
$413$	6.29902e7	+	1.09102e8i	0.0439995	+	0.0762094i
$414$	−9.78934e7	+	5.65188e7i	−0.0678035	+	0.0391464i
$415$	2.80356e9			1.92549
$416$	2.49100e8	−	7.29721e7i	0.169647	−	0.0496970i
$417$	2.25379e9			1.52208
$418$	−1.10519e9	+	6.38084e8i	−0.740153	+	0.427328i
$419$	−4.85746e8	−	8.41336e8i	−0.322597	−	0.558754i	0.658426	−	0.752645i	$-0.271222\pi$
$419$	−4.85746e8	−	8.41336e8i	−0.322597	−	0.558754i	−0.981023	+	0.193891i	$0.937889\pi$
$420$	5.60718e7	−	9.71192e7i	0.0369294	−	0.0639636i
$421$			4.85973e8i			0.317413i	0.987326	+	0.158707i	$0.0507324\pi$
$421$			4.85973e8i			0.317413i	−0.987326	+	0.158707i	$0.949268\pi$
$422$	−3.26317e8	−	1.88399e8i	−0.211372	−	0.122035i
$423$	8.17356e7	+	4.71901e7i	0.0525073	+	0.0303151i
$424$			8.06779e8i			0.514013i
$425$	6.52533e8	−	1.13022e9i	0.412326	−	0.714170i
$426$	5.71373e8	+	9.89646e8i	0.358085	+	0.620221i
$427$	−2.12119e8	+	1.22467e8i	−0.131851	+	0.0761241i
$428$	−2.90868e8			−0.179326
$429$	1.29035e9	−	3.77999e8i	0.789054	−	0.231148i
$430$	−2.31750e9			−1.40566
$431$	2.39621e8	−	1.38345e8i	0.144163	−	0.0832328i	−0.426183	−	0.904637i	$-0.640142\pi$
$431$	2.39621e8	−	1.38345e8i	0.144163	−	0.0832328i	0.570347	+	0.821404i	$0.306809\pi$
$432$	−1.90439e8	−	3.29851e8i	−0.113649	−	0.196845i
$433$	−1.17994e9	+	2.04371e9i	−0.698476	+	1.20980i	0.270519	+	0.962715i	$0.412805\pi$
$433$	−1.17994e9	+	2.04371e9i	−0.698476	+	1.20980i	−0.968995	+	0.247081i	$0.920529\pi$
$434$			6.41385e7i			0.0376621i
$435$	−3.38096e9	−	1.95200e9i	−1.96937	−	1.13702i
$436$	−7.11362e8	−	4.10705e8i	−0.411044	−	0.237316i
$437$		−	1.98742e9i		−	1.13921i
$438$	7.93542e8	−	1.37446e9i	0.451243	−	0.781576i
$439$	5.02423e8	+	8.70222e8i	0.283428	+	0.490912i	0.972227	−	0.234041i	$-0.0751948\pi$
$439$	5.02423e8	+	8.70222e8i	0.283428	+	0.490912i	−0.688798	+	0.724953i	$0.741862\pi$
$440$	7.03345e8	−	4.06076e8i	0.393626	−	0.227260i
$441$	2.74513e8			0.152415
$442$	−4.20745e8	−	4.01686e8i	−0.231762	−	0.221263i
$443$	−9.97546e8			−0.545155			−0.272578	−	0.962134i	$-0.587876\pi$
$443$	−9.97546e8			−0.545155			−0.272578	+	0.962134i	$0.587876\pi$
$444$	−7.35236e8	+	4.24488e8i	−0.398645	+	0.230158i
$445$	3.49544e8	+	6.05429e8i	0.188037	+	0.325689i
$446$	−6.76427e8	+	1.17161e9i	−0.361035	+	0.625331i
$447$			1.22833e9i			0.650487i
$448$	−1.68747e7	−	9.74260e6i	−0.00886671	−	0.00511920i
$449$	1.25644e7	+	7.25408e6i	0.00655060	+	0.00378199i	0.503272	−	0.864128i	$-0.332129\pi$
$449$	1.25644e7	+	7.25408e6i	0.00655060	+	0.00378199i	−0.496721	+	0.867910i	$0.665463\pi$
$450$			3.81692e8i			0.197456i
$451$	7.50397e8	−	1.29973e9i	0.385188	−	0.667166i
$452$	5.05525e8	+	8.75596e8i	0.257489	+	0.445984i
$453$	−2.58782e9	+	1.49408e9i	−1.30795	+	0.755143i
$454$	−2.54351e9			−1.27567
$455$	−7.76925e7	−	2.65213e8i	−0.0386669	−	0.131994i
$456$	−1.21381e9			−0.599478
$457$	−6.28752e8	+	3.63010e8i	−0.308157	+	0.177915i	−0.646102	−	0.763251i	$-0.723602\pi$
$457$	−6.28752e8	+	3.63010e8i	−0.308157	+	0.177915i	0.337944	+	0.941166i	$0.390268\pi$
$458$	4.65477e8	+	8.06230e8i	0.226396	+	0.392130i
$459$	−4.26782e8	+	7.39208e8i	−0.205997	+	0.356798i
$460$			1.26479e9i			0.605853i
$461$	−1.36362e9	−	7.87284e8i	−0.648244	−	0.374264i	0.139539	−	0.990217i	$-0.455438\pi$
$461$	−1.36362e9	−	7.87284e8i	−0.648244	−	0.374264i	−0.787783	+	0.615953i	$0.788771\pi$
$462$	−8.74116e7	−	5.04671e7i	−0.0412403	−	0.0238101i
$463$			2.40145e9i			1.12445i	0.826984	+	0.562225i	$0.190054\pi$
$463$			2.40145e9i			1.12445i	−0.826984	+	0.562225i	$0.809946\pi$
$464$	−3.39164e8	+	5.87449e8i	−0.157615	+	0.272997i
$465$	−1.27135e9	−	2.20204e9i	−0.586380	−	1.01564i
$466$	2.49533e9	−	1.44068e9i	1.14229	−	0.659504i
$467$	2.88669e9			1.31157			0.655784	−	0.754948i	$-0.272338\pi$
$467$	2.88669e9			1.31157			0.655784	+	0.754948i	$0.272338\pi$
$468$	1.65310e8	+	4.02138e7i	0.0745482	+	0.0181349i
$469$	−1.81552e8			−0.0812634
$470$	9.14551e8	−	5.28016e8i	0.406317	−	0.234587i
$471$	1.15940e9	+	2.00814e9i	0.511283	+	0.885567i
$472$	−4.33888e8	+	7.51517e8i	−0.189925	+	0.328959i
$473$			2.08585e9i			0.906296i
$474$	−1.26700e9	−	7.31503e8i	−0.546452	−	0.315494i
$475$	−5.81180e9	−	3.35545e9i	−2.48819	−	1.43656i
$476$			4.36671e7i			0.0185579i
$477$	−2.64396e8	+	4.57947e8i	−0.111543	+	0.193197i
$478$	−4.94198e8	−	8.55975e8i	−0.206968	−	0.358479i
$479$	1.36402e9	−	7.87515e8i	0.567081	−	0.327404i	−0.188902	−	0.981996i	$-0.560493\pi$
$479$	1.36402e9	−	7.87515e8i	0.567081	−	0.327404i	0.755983	+	0.654592i	$0.227159\pi$
$480$	7.72467e8			0.318813
$481$	−4.94525e8	+	2.03287e9i	−0.202619	+	0.832919i
$482$	1.86336e8			0.0757937
$483$	1.36129e8	−	7.85941e7i	0.0549712	−	0.0317377i
$484$	2.58103e8	+	4.47048e8i	0.103475	+	0.179224i
$485$	3.27165e9	−	5.66666e9i	1.30218	−	2.25544i
$486$		−	5.44533e8i		−	0.215178i
$487$	1.70387e9	+	9.83730e8i	0.668475	+	0.385944i	0.795499	−	0.605955i	$-0.207209\pi$
$487$	1.70387e9	+	9.83730e8i	0.668475	+	0.385944i	−0.127023	+	0.991900i	$0.540542\pi$
$488$	−1.46112e9	−	8.43577e8i	−0.569136	−	0.328591i
$489$		−	4.97788e8i		−	0.192514i
$490$	1.53578e9	−	2.66005e9i	0.589717	−	1.02142i
$491$	−3.80549e8	−	6.59129e8i	−0.145086	−	0.251296i	0.784319	−	0.620358i	$-0.213012\pi$
$491$	−3.80549e8	−	6.59129e8i	−0.145086	−	0.251296i	−0.929405	+	0.369062i	$0.879679\pi$
$492$	1.23621e9	−	7.13729e8i	0.467968	−	0.270181i
$493$	1.52016e9			0.571380
$494$	−2.06554e9	+	2.16355e9i	−0.770886	+	0.807464i
$495$	5.32314e8			0.197265
$496$	−3.82609e8	+	2.20899e8i	−0.140789	+	0.0812846i
$497$	−1.05699e8	−	1.83076e8i	−0.0386211	−	0.0668936i
$498$	1.20001e9	−	2.07848e9i	0.435395	−	0.754126i
$499$			5.96355e8i			0.214859i	0.994213	+	0.107429i	$0.0342620\pi$
$499$			5.96355e8i			0.214859i	−0.994213	+	0.107429i	$0.965738\pi$
$500$	1.66623e9	+	9.62001e8i	0.596130	+	0.344176i
$501$	2.55182e9	+	1.47329e9i	0.906605	+	0.523429i
$502$			2.64466e8i			0.0933055i
$503$	2.42561e8	−	4.20128e8i	0.0849832	−	0.147195i	−0.820401	−	0.571789i	$-0.806250\pi$
$503$	2.42561e8	−	4.20128e8i	0.0849832	−	0.147195i	0.905384	+	0.424594i	$0.139583\pi$
$504$	−6.38565e6	−	1.10603e7i	−0.00222177	−	0.00384821i
$505$	−8.20290e8	+	4.73595e8i	−0.283431	+	0.163639i
$506$	1.13837e9			0.390621
$507$	2.65341e9	−	1.70053e9i	0.904224	−	0.579503i
$508$	1.76929e9			0.598793
$509$	−1.92665e9	+	1.11235e9i	−0.647576	+	0.373878i	−0.787527	−	0.616280i	$-0.788639\pi$
$509$	−1.92665e9	+	1.11235e9i	−0.647576	+	0.373878i	0.139951	+	0.990158i	$0.455305\pi$
$510$	−8.65564e8	−	1.49920e9i	−0.288937	−	0.500454i
$511$	−1.46799e8	+	2.54263e8i	−0.0486686	+	0.0842965i
$512$		−	1.34218e8i		−	0.0441942i
$513$	3.80115e9	+	2.19459e9i	1.24309	+	0.717701i
$514$	1.83067e9	+	1.05694e9i	0.594620	+	0.343304i
$515$			7.84697e9i			2.53149i
$516$	−9.91964e8	+	1.71813e9i	−0.317850	+	0.550532i
$517$	−4.75237e8	−	8.23135e8i	−0.151249	−	0.261972i
$518$	1.36012e8	−	7.85268e7i	0.0429956	−	0.0248235i
$519$	3.15569e8			0.0990851
$520$	1.31451e9	−	1.37688e9i	0.409970	−	0.429423i
$521$	−5.35828e9			−1.65994			−0.829972	−	0.557805i	$-0.811644\pi$
$521$	−5.35828e9			−1.65994			−0.829972	+	0.557805i	$0.811644\pi$
$522$	−3.85036e8	+	2.22300e8i	−0.118482	+	0.0684059i
$523$	3.99109e8	+	6.91277e8i	0.121993	+	0.211299i	0.920554	−	0.390616i	$-0.127738\pi$
$523$	3.99109e8	+	6.91277e8i	0.121993	+	0.211299i	−0.798560	+	0.601915i	$0.794405\pi$
$524$	−3.11732e8	+	5.39935e8i	−0.0946502	+	0.163939i
$525$		−	5.30775e8i		−	0.160086i
$526$	5.59828e8	+	3.23217e8i	0.167727	+	0.0968375i
$527$	8.57441e8	+	4.95044e8i	0.255192	+	0.147335i
$528$		−	6.95254e8i		−	0.205553i
$529$	8.16003e8	−	1.41336e9i	0.239661	−	0.415105i
$530$	2.95836e9	+	5.12404e9i	0.863149	+	1.49502i
$531$	−4.92572e8	+	2.84386e8i	−0.142770	+	0.0824286i
$532$	2.24544e8			0.0646564
$533$	8.31486e8	−	3.41804e9i	0.237854	−	0.977761i
$534$	5.98464e8			0.170076
$535$	−1.84737e9	+	1.06658e9i	−0.521573	+	0.301130i
$536$	−6.25281e8	−	1.08302e9i	−0.175387	−	0.303780i
$537$	1.33609e9	−	2.31417e9i	0.372328	−	0.644891i
$538$		−	4.13467e9i		−	1.14473i
$539$	−2.39417e9	−	1.38227e9i	−0.658557	−	0.380218i
$540$	−2.41905e9	−	1.39664e9i	−0.661099	−	0.381686i
$541$		−	3.89614e9i		−	1.05790i	−0.848654	−	0.528949i	$-0.822586\pi$
$541$		−	3.89614e9i		−	1.05790i	0.848654	−	0.528949i	$-0.177414\pi$
$542$	6.36533e8	−	1.10251e9i	0.171721	−	0.297429i
$543$	−8.38814e8	−	1.45287e9i	−0.224836	−	0.389428i
$544$	−2.60489e8	+	1.50394e8i	−0.0693735	+	0.0400528i
$545$	−6.02403e9			−1.59404
$546$	−2.29877e8	−	5.59207e7i	−0.0604395	−	0.0147027i
$547$	−2.21748e8			−0.0579300			−0.0289650	−	0.999580i	$-0.509221\pi$
$547$	−2.21748e8			−0.0579300			−0.0289650	+	0.999580i	$0.509221\pi$
$548$	1.58293e8	−	9.13902e7i	0.0410893	−	0.0237229i
$549$	−5.52911e8	−	9.57670e8i	−0.142611	−	0.247009i
$550$	1.92196e9	−	3.32893e9i	0.492577	−	0.853168i
$551$		−	7.81695e9i		−	1.99070i
$552$	9.37682e8	+	5.41371e8i	0.237284	+	0.136996i
$553$	2.34384e8	+	1.35322e8i	0.0589374	+	0.0340275i
$554$			1.71399e9i			0.428277i
$555$	−3.11310e9	+	5.39205e9i	−0.772979	+	1.33884i
$556$	−1.43595e9	−	2.48715e9i	−0.354306	−	0.613676i
$557$	−1.24412e9	+	7.18292e8i	−0.305048	+	0.176120i	−0.644708	−	0.764429i	$-0.723021\pi$
$557$	−1.24412e9	+	7.18292e8i	−0.305048	+	0.176120i	0.339660	+	0.940548i	$0.389688\pi$
$558$	−2.89571e8			−0.0705562
$559$	1.37445e9	+	4.69188e9i	0.332804	+	1.13607i
$560$	−1.42900e8			−0.0343854
$561$	−1.34935e9	+	7.79045e8i	−0.322666	+	0.186291i
$562$	1.37295e9	+	2.37802e9i	0.326271	+	0.565117i
$563$	−2.93914e9	+	5.09074e9i	−0.694130	+	1.20227i	0.276344	+	0.961059i	$0.410877\pi$
$563$	−2.93914e9	+	5.09074e9i	−0.694130	+	1.20227i	−0.970473	+	0.241209i	$0.922456\pi$
$564$		−	9.04030e8i		−	0.212181i
$565$	6.42142e9	+	3.70741e9i	1.49783	+	0.864770i
$566$	−5.58200e8	−	3.22277e8i	−0.129399	−	0.0747088i
$567$			4.01700e8i			0.0925468i
$568$	7.28076e8	−	1.26106e9i	0.166708	−	0.288747i
$569$	1.49786e9	+	2.59437e9i	0.340862	+	0.590390i	0.984593	−	0.174862i	$-0.0559478\pi$
$569$	1.49786e9	+	2.59437e9i	0.340862	+	0.590390i	−0.643731	+	0.765252i	$0.722614\pi$
$570$	−7.70917e9	+	4.45089e9i	−1.74360	+	1.00667i
$571$	−5.32432e9			−1.19685			−0.598423	−	0.801181i	$-0.704206\pi$
$571$	−5.32432e9			−1.19685			−0.598423	+	0.801181i	$0.704206\pi$
$572$	−1.23925e9	−	1.18312e9i	−0.276869	−	0.264327i
$573$	−1.60190e9			−0.355708
$574$	−2.28689e8	+	1.32034e8i	−0.0504724	+	0.0291403i
$575$	2.99313e9	+	5.18425e9i	0.656580	+	1.13723i
$576$	4.39856e7	−	7.61853e7i	0.00959029	−	0.0166109i
$577$		−	2.16008e9i		−	0.468118i	−0.972222	−	0.234059i	$-0.924799\pi$
$577$		−	2.16008e9i		−	0.468118i	0.972222	−	0.234059i	$-0.0752009\pi$
$578$	−2.25914e9	−	1.30432e9i	−0.486627	−	0.280954i
$579$	6.71475e9	+	3.87676e9i	1.43766	+	0.830031i
$580$			4.97470e9i			1.05869i
$581$	−2.21992e8	+	3.84502e8i	−0.0469593	+	0.0813359i
$582$	−2.80073e9	−	4.85101e9i	−0.588900	−	1.02000i
$583$	4.61186e9	−	2.66266e9i	0.963908	−	0.556513i
$584$	−2.02235e9			−0.420158
$585$	1.19738e9	−	3.50764e8i	0.247278	−	0.0724384i
$586$	3.37132e9			0.692083
$587$	−4.55850e9	+	2.63185e9i	−0.930227	+	0.537067i	−0.886883	−	0.461994i	$-0.847134\pi$
$587$	−4.55850e9	+	2.63185e9i	−0.930227	+	0.537067i	−0.0433434	+	0.999060i	$0.513801\pi$
$588$	−1.31473e9	−	2.27717e9i	−0.266695	−	0.461929i
$589$	2.54561e9	−	4.40912e9i	0.513320	−	0.889096i
$590$			6.36407e9i			1.27571i
$591$	7.48278e8	+	4.32019e8i	0.149110	+	0.0860888i
$592$	9.36879e8	+	5.40908e8i	0.185591	+	0.107151i
$593$		−	6.23434e9i		−	1.22772i	−0.789415	−	0.613859i	$-0.789616\pi$
$593$		−	6.23434e9i		−	1.22772i	0.789415	−	0.613859i	$-0.210384\pi$
$594$	−1.25704e9	+	2.17725e9i	−0.246091	+	0.426241i
$595$	1.60122e8	+	2.77340e8i	0.0311632	+	0.0539762i
$596$	1.35551e9	−	7.82604e8i	0.262265	−	0.151419i
$597$	−1.06285e10			−2.04437
$598$	2.56062e9	−	7.50117e8i	0.489657	−	0.143442i
$599$	3.87748e9			0.737149			0.368575	−	0.929598i	$-0.379846\pi$
$599$	3.87748e9			0.737149			0.368575	+	0.929598i	$0.379846\pi$
$600$	3.16626e9	−	1.82804e9i	0.598435	−	0.345506i
$601$	−3.87101e9	−	6.70479e9i	−0.727385	−	1.25987i	−0.957985	−	0.286819i	$-0.907402\pi$
$601$	−3.87101e9	−	6.70479e9i	−0.727385	−	1.25987i	0.230600	−	0.973049i	$-0.425931\pi$
$602$	1.83505e8	−	3.17840e8i	0.0342815	−	0.0593774i
$603$		−	8.19664e8i		−	0.152239i
$604$	3.29754e9	+	1.90384e9i	0.608921	+	0.351561i
$605$	3.27854e9	+	1.89287e9i	0.601918	+	0.347517i
$606$			8.10854e8i			0.148009i
$607$	7.39619e8	−	1.28106e9i	0.134229	−	0.232492i	−0.791073	−	0.611721i	$-0.790477\pi$
$607$	7.39619e8	−	1.28106e9i	0.134229	−	0.232492i	0.925303	+	0.379229i	$0.123811\pi$
$608$	7.73352e8	+	1.33949e9i	0.139545	+	0.241699i
$609$	5.35424e8	−	3.09127e8i	0.0960589	−	0.0554596i
$610$	−1.23732e10			−2.20713
$611$	−1.61139e9	−	1.53839e9i	−0.285796	−	0.272849i
$612$	−1.97147e8			−0.0347664
$613$	−2.65542e8	+	1.53311e8i	−0.0465609	+	0.0268820i	−0.523100	−	0.852271i	$-0.675224\pi$
$613$	−2.65542e8	+	1.53311e8i	−0.0465609	+	0.0268820i	0.476539	+	0.879153i	$0.341891\pi$
$614$	3.22237e9	+	5.58130e9i	0.561805	+	0.973075i
$615$	5.23432e9	−	9.06611e9i	0.907397	−	1.57166i
$616$			1.28616e8i			0.0221699i
$617$	3.53172e9	+	2.03904e9i	0.605325	+	0.349484i	0.771133	−	0.636674i	$-0.219690\pi$
$617$	3.53172e9	+	2.03904e9i	0.605325	+	0.349484i	−0.165809	+	0.986158i	$0.553023\pi$
$618$	5.81752e9	+	3.35875e9i	0.991468	+	0.572424i
$619$		−	8.66187e9i		−	1.46789i	−0.679208	−	0.733946i	$-0.737676\pi$
$619$		−	8.66187e9i		−	1.46789i	0.679208	−	0.733946i	$-0.262324\pi$
$620$	−1.62002e9	+	2.80596e9i	−0.272992	+	0.472837i
$621$	−1.95762e9	−	3.39070e9i	−0.328026	−	0.568158i
$622$	−3.07893e9	+	1.77762e9i	−0.513020	+	0.296192i
$623$	−1.10711e8			−0.0183435
$624$	−4.58131e8	−	1.56389e9i	−0.0754820	−	0.257668i
$625$	3.00277e9			0.491973
$626$	−3.14502e9	+	1.81578e9i	−0.512405	+	0.295837i
$627$	4.00600e9	+	6.93859e9i	0.649044	+	1.12418i
$628$	1.47738e9	−	2.55889e9i	0.238030	−	0.412281i
$629$		−	2.42439e9i		−	0.388441i
$630$	−8.11135e7	−	4.68309e7i	−0.0129241	−	0.00746175i
$631$	5.94670e8	+	3.43333e8i	0.0942266	+	0.0544017i	0.546373	−	0.837542i	$-0.316008\pi$
$631$	5.94670e8	+	3.43333e8i	0.0942266	+	0.0544017i	−0.452146	+	0.891944i	$0.649342\pi$
$632$			1.86425e9i			0.293760i
$633$	−1.18280e9	+	2.04867e9i	−0.185353	+	0.321041i
$634$	−2.72929e9	−	4.72727e9i	−0.425341	−	0.736713i
$635$	1.12372e10	−	6.48779e9i	1.74160	−	1.00552i
$636$	5.06509e9			0.780706
$637$	−6.29623e9	−	1.53164e9i	−0.965144	−	0.234785i
$638$	4.47745e9			0.682587
$639$	8.26548e8	−	4.77207e8i	0.125318	−	0.0723526i
$640$	−4.92161e8	−	8.52448e8i	−0.0742125	−	0.128540i
$641$	−2.49684e9	+	4.32466e9i	−0.374445	+	0.648558i	−0.990244	−	0.139346i	$-0.955500\pi$
$641$	−2.49684e9	+	4.32466e9i	−0.374445	+	0.648558i	0.615799	+	0.787903i	$0.288833\pi$
$642$			1.82612e9i			0.272368i
$643$	−1.76995e9	−	1.02188e9i	−0.262557	−	0.151587i	0.362944	−	0.931811i	$-0.381772\pi$
$643$	−1.76995e9	−	1.02188e9i	−0.262557	−	0.151587i	−0.625500	+	0.780224i	$0.715105\pi$
$644$	−1.73463e8	−	1.00149e8i	−0.0255922	−	0.0147756i
$645$			1.45497e10i			2.13498i
$646$	1.73311e9	−	3.00184e9i	0.252937	−	0.438100i
$647$	−2.19517e9	−	3.80215e9i	−0.318642	−	0.551904i	0.661563	−	0.749890i	$-0.269893\pi$
$647$	−2.19517e9	−	3.80215e9i	−0.318642	−	0.551904i	−0.980205	+	0.197985i	$0.936560\pi$
$648$	−2.39628e9	+	1.38349e9i	−0.345960	+	0.199740i
$649$	5.72794e9			0.822512
$650$	2.12965e9	−	8.75448e9i	0.304166	−	1.25036i
$651$	4.02672e8			0.0572029
$652$	−5.49328e8	+	3.17155e8i	−0.0776185	+	0.0448131i
$653$	7.64503e8	+	1.32416e9i	0.107444	+	0.186099i	0.914734	−	0.404056i	$-0.132400\pi$
$653$	7.64503e8	+	1.32416e9i	0.107444	+	0.186099i	−0.807290	+	0.590155i	$0.799067\pi$
$654$	−2.57847e9	+	4.46605e9i	−0.360446	+	0.624312i
$655$			4.57234e9i			0.635761i
$656$	−1.57526e9	−	9.09474e8i	−0.217865	−	0.125784i
$657$	−1.14794e9	−	6.62762e8i	−0.157921	−	0.0911757i
$658$			1.67238e8i			0.0228846i
$659$	3.30987e9	−	5.73287e9i	0.450518	−	0.780320i	−0.547900	−	0.836544i	$-0.684573\pi$
$659$	3.30987e9	−	5.73287e9i	0.450518	−	0.780320i	0.998418	+	0.0562235i	$0.0179060\pi$
$660$	−2.54941e9	−	4.41572e9i	−0.345173	−	0.597857i
$661$	1.02805e10	−	5.93546e9i	1.38455	−	0.799372i	0.391859	−	0.920025i	$-0.371832\pi$
$661$	1.02805e10	−	5.93546e9i	1.38455	−	0.799372i	0.992695	+	0.120653i	$0.0384988\pi$
$662$	8.13351e9			1.08962
$663$	−2.52185e9	+	2.64151e9i	−0.336064	+	0.352010i
$664$	−3.05825e9			−0.405401
$665$	1.42613e9	−	8.23378e8i	0.188055	−	0.108573i
$666$	3.54531e8	+	6.14065e8i	0.0465044	+	0.0805479i
$667$	−3.48644e9	+	6.03869e9i	−0.454927	+	0.787956i
$668$		−	3.75471e9i		−	0.487370i
$669$	7.35554e9	+	4.24672e9i	0.949780	+	0.548356i
$670$	−7.94261e9	−	4.58567e9i	−1.02024	−	0.589034i
$671$			1.11364e10i			1.42304i
$672$	−6.11656e7	+	1.05942e8i	−0.00777526	+	0.0134671i
$673$	−5.07802e8	−	8.79539e8i	−0.0642158	−	0.111225i	0.832130	−	0.554581i	$-0.187121\pi$
$673$	−5.07802e8	−	8.79539e8i	−0.0642158	−	0.111225i	−0.896346	+	0.443356i	$0.853788\pi$
$674$	−2.43894e9	+	1.40812e9i	−0.306825	+	0.177146i
$675$	−1.32206e10			−1.65458
$676$	−3.56716e9	−	1.84469e9i	−0.444129	−	0.229672i
$677$	−1.52605e10			−1.89020			−0.945099	−	0.326785i	$-0.894035\pi$
$677$	−1.52605e10			−1.89020			−0.945099	+	0.326785i	$0.894035\pi$
$678$	5.49714e9	−	3.17377e9i	0.677380	−	0.391086i
$679$	5.18112e8	+	8.97397e8i	0.0635155	+	0.110012i
$680$	−1.10295e9	+	1.91037e9i	−0.134516	+	0.232989i
$681$			1.59686e10i			1.93755i
$682$	2.52549e9	+	1.45809e9i	0.304860	+	0.176011i
$683$	1.02242e10	+	5.90295e9i	1.22788	+	0.708918i	0.966587	−	0.256340i	$-0.0825167\pi$
$683$	1.02242e10	+	5.90295e9i	1.22788	+	0.708918i	0.261296	+	0.965259i	$0.415850\pi$
$684$			1.01377e9i			0.121127i
$685$	6.70235e8	−	1.16088e9i	0.0796728	−	0.137997i
$686$	4.88070e8	+	8.45361e8i	0.0577228	+	0.0999788i
$687$	5.06164e9	−	2.92234e9i	0.595584	−	0.343861i
$688$	2.52804e9			0.295954
$689$	8.61929e9	−	9.02827e9i	1.00393	−	1.05157i
$690$	7.94058e9			0.920196
$691$	−1.95302e9	+	1.12758e9i	−0.225182	+	0.130009i	−0.608348	−	0.793671i	$-0.708167\pi$
$691$	−1.95302e9	+	1.12758e9i	−0.225182	+	0.130009i	0.383165	+	0.923680i	$0.374834\pi$
$692$	−2.01058e8	−	3.48243e8i	−0.0230648	−	0.0399494i
$693$	−4.21498e7	+	7.30057e7i	−0.00481094	+	0.00833279i
$694$			4.87833e9i			0.554004i
$695$	−1.82401e10	−	1.05310e10i	−2.06102	−	1.18993i
$696$	3.68810e9	+	2.12933e9i	0.414640	+	0.239392i
$697$			4.07633e9i			0.455990i
$698$	2.96857e9	−	5.14172e9i	0.330411	−	0.572288i
$699$	−9.04484e9	−	1.56661e10i	−1.00168	−	1.73497i
$700$	−5.85731e8	+	3.38172e8i	−0.0645439	+	0.0372644i
$701$	−1.12762e10			−1.23637			−0.618187	−	0.786031i	$-0.712132\pi$
$701$	−1.12762e10			−1.23637			−0.618187	+	0.786031i	$0.712132\pi$
$702$	−1.39287e9	+	5.72578e9i	−0.151961	+	0.624675i
$703$	−1.24667e10			−1.35334
$704$	−7.67240e8	+	4.42966e8i	−0.0828756	+	0.0478483i
$705$	−3.31497e9	−	5.74170e9i	−0.356302	−	0.617133i
$706$	4.34677e9	−	7.52883e9i	0.464890	−	0.805213i
$707$		−	1.50001e8i		−	0.0159634i
$708$	4.71815e9	+	2.72402e9i	0.499638	+	0.288466i
$709$	6.54595e9	+	3.77931e9i	0.689780	+	0.398245i	0.803530	−	0.595265i	$-0.202953\pi$
$709$	6.54595e9	+	3.77931e9i	0.689780	+	0.398245i	−0.113749	+	0.993509i	$0.536286\pi$
$710$		−	1.06791e10i		−	1.11977i
$711$	−6.10947e8	+	1.05819e9i	−0.0637470	+	0.110413i
$712$	−3.81299e8	−	6.60428e8i	−0.0395900	−	0.0685718i
$713$	−3.93303e9	+	2.27074e9i	−0.406363	+	0.234614i
$714$	2.74149e8			0.0281866
$715$	−1.22091e10	−	2.97004e9i	−1.24915	−	0.303873i
$716$	−3.40504e9			−0.346679
$717$	−5.37396e9	+	3.10265e9i	−0.544474	+	0.314352i
$718$	6.27605e9	+	1.08704e10i	0.632777	+	1.09600i
$719$	1.23044e9	−	2.13118e9i	0.123455	−	0.213831i	−0.797673	−	0.603090i	$-0.793936\pi$
$719$	1.23044e9	−	2.13118e9i	0.123455	−	0.213831i	0.921128	+	0.389260i	$0.127269\pi$
$720$		−	6.45160e8i		−	0.0644175i
$721$	−1.07619e9	−	6.21340e8i	−0.106934	−	0.0617385i
$722$	−9.24310e9	−	5.33650e9i	−0.913981	−	0.527687i
$723$		−	1.16985e9i		−	0.115119i
$724$	−1.06886e9	+	1.85133e9i	−0.104674	+	0.181300i
$725$	1.17726e10	+	2.03908e10i	1.14733	+	1.98724i
$726$	2.80664e9	−	1.62041e9i	0.272213	−	0.157162i
$727$	1.00899e10			0.973902			0.486951	−	0.873429i	$-0.338109\pi$
$727$	1.00899e10			0.973902			0.486951	+	0.873429i	$0.338109\pi$
$728$	8.47504e7	+	2.89307e8i	0.00814108	+	0.0277906i
$729$	8.40048e9			0.803078
$730$	−1.28444e10	+	7.41574e9i	−1.22204	+	0.705544i
$731$	−2.83271e9	−	4.90640e9i	−0.268220	−	0.464571i
$732$	−5.29612e9	+	9.17314e9i	−0.499078	+	0.864429i
$733$		−	8.44259e8i		−	0.0791793i	−0.999216	−	0.0395897i	$-0.987395\pi$
$733$		−	8.44259e8i		−	0.0791793i	0.999216	−	0.0395897i	$-0.0126051\pi$
$734$	−3.73322e9	−	2.15538e9i	−0.348456	−	0.201181i
$735$	−1.67003e10	−	9.64190e9i	−1.55138	−	0.895689i
$736$		−	1.37969e9i		−	0.127559i
$737$	−4.12730e9	+	7.14869e9i	−0.379778	+	0.657795i
$738$	−5.96102e8	−	1.03248e9i	−0.0545913	−	0.0945549i
$739$	−6.39606e9	+	3.69277e9i	−0.582984	+	0.336586i	−0.762318	−	0.647202i	$-0.775939\pi$
$739$	−6.39606e9	+	3.69277e9i	−0.582984	+	0.336586i	0.179334	+	0.983788i	$0.442606\pi$
$740$	7.93378e9			0.719729
$741$	1.35831e10	+	1.29678e10i	1.22641	+	1.17086i
$742$	−9.36999e8			−0.0842026
$743$	−1.15376e10	+	6.66123e9i	−1.03194	+	0.595791i	−0.917540	−	0.397644i	$-0.869828\pi$
$743$	−1.15376e10	+	6.66123e9i	−1.03194	+	0.595791i	−0.114400	+	0.993435i	$0.536495\pi$
$744$	1.38684e9	+	2.40208e9i	0.123459	+	0.213837i
$745$	5.73944e9	−	9.94099e9i	0.508537	−	0.880811i
$746$		−	1.12717e10i		−	0.994042i
$747$	−1.73594e9	−	1.00224e9i	−0.152374	−	0.0879734i
$748$	1.71941e9	+	9.92704e8i	0.150219	+	0.0867290i
$749$		−	3.37816e8i		−	0.0293761i
$750$	6.03960e9	−	1.04609e10i	0.522750	−	0.905429i
$751$	6.71361e9	+	1.16283e10i	0.578384	+	1.00179i	0.995665	+	0.0930132i	$0.0296499\pi$
$751$	6.71361e9	+	1.16283e10i	0.578384	+	1.00179i	−0.417281	+	0.908778i	$0.637017\pi$
$752$	−9.97632e8	+	5.75983e8i	−0.0855477	+	0.0493910i
$753$	1.66036e9			0.141716
$754$	1.00715e10	−	2.95037e9i	0.855645	−	0.250655i
$755$	2.79246e10			2.36142
$756$	3.83091e8	−	2.21178e8i	0.0322460	−	0.0186172i
$757$	−2.20189e9	−	3.81378e9i	−0.184484	−	0.319536i	0.758918	−	0.651186i	$-0.225728\pi$
$757$	−2.20189e9	−	3.81378e9i	−0.184484	−	0.319536i	−0.943403	+	0.331650i	$0.892395\pi$
$758$	−6.35140e9	+	1.10009e10i	−0.529697	+	0.917461i
$759$		−	7.14687e9i		−	0.593293i
$760$	9.82347e9	+	5.67158e9i	0.811741	+	0.468659i
$761$	6.51209e9	+	3.75976e9i	0.535642	+	0.309253i	0.743311	−	0.668946i	$-0.233254\pi$
$761$	6.51209e9	+	3.75976e9i	0.535642	+	0.309253i	−0.207669	+	0.978199i	$0.566588\pi$
$762$		−	1.11079e10i		−	0.909473i
$763$	4.76996e8	−	8.26182e8i	0.0388758	−	0.0673348i
$764$	1.02062e9	+	1.76776e9i	0.0828010	+	0.143416i
$765$	−1.25212e9	+	7.22915e8i	−0.101119	+	0.0583811i
$766$	−8.07751e9			−0.649347
$767$	1.28843e10	−	3.77438e9i	1.03105	−	0.302038i
$768$	−8.42641e8			−0.0671241
$769$	1.97283e10	−	1.13902e10i	1.56440	−	0.903208i	0.567599	−	0.823305i	$-0.307872\pi$
$769$	1.97283e10	−	1.13902e10i	1.56440	−	0.903208i	0.996803	−	0.0799025i	$-0.0254609\pi$
$770$	4.71620e8	+	8.16870e8i	0.0372285	+	0.0644816i
$771$	6.63563e9	−	1.14933e10i	0.521425	−	0.903135i
$772$		−	9.87999e9i		−	0.772851i
$773$	−1.25609e10	−	7.25204e9i	−0.978122	−	0.564719i	−0.0764191	−	0.997076i	$-0.524349\pi$
$773$	−1.25609e10	−	7.25204e9i	−0.978122	−	0.564719i	−0.901703	+	0.432357i	$0.857682\pi$
$774$	1.43497e9	+	8.28483e8i	0.111237	+	0.0642230i
$775$			1.53351e10i			1.18340i
$776$	−3.56886e9	+	6.18144e9i	−0.274166	+	0.474869i
$777$	−4.93004e8	−	8.53908e8i	−0.0377031	−	0.0653037i
$778$	4.25495e9	−	2.45660e9i	0.323941	−	0.187027i
$779$	2.09613e10			1.58868
$780$	−8.64430e9	−	8.25272e9i	−0.652227	−	0.622681i
$781$	−9.61164e9			−0.721969
$782$	−2.67770e9	+	1.54597e9i	−0.200234	+	0.115605i
$783$	−7.69975e9	−	1.33364e10i	−0.573206	−	0.992821i
$784$	−1.67530e9	+	2.90171e9i	−0.124161	+	0.215054i
$785$		−	2.16695e10i		−	1.59884i
$786$	3.38980e9	+	1.95710e9i	0.248998	+	0.143759i
$787$	−7.41960e9	−	4.28371e9i	−0.542586	−	0.313262i	0.203540	−	0.979067i	$-0.434755\pi$
$787$	−7.41960e9	−	4.28371e9i	−0.542586	−	0.313262i	−0.746126	+	0.665804i	$0.768089\pi$
$788$		−	1.10101e9i		−	0.0801582i
$789$	2.02921e9	−	3.51469e9i	0.147081	−	0.254752i
$790$	6.83597e9	+	1.18402e10i	0.493294	+	0.854409i
$791$	−1.01692e9	+	5.87121e8i	−0.0730585	+	0.0421804i
$792$	−5.80672e8			−0.0415330
$793$	7.33824e9	+	2.50500e10i	0.522559	+	1.78383i
$794$	−2.09456e9			−0.148498
$795$	3.21695e10	−	1.85731e10i	2.27070	−	1.31099i
$796$	6.77169e9	+	1.17289e10i	0.475885	+	0.824256i
$797$	−8.46996e9	+	1.46704e10i	−0.592621	+	1.02645i	0.401257	+	0.915966i	$0.368573\pi$
$797$	−8.46996e9	+	1.46704e10i	−0.592621	+	1.02645i	−0.993878	+	0.110484i	$0.964760\pi$
$798$		−	1.40973e9i		−	0.0982030i
$799$	2.23573e9	+	1.29080e9i	0.155062	+	0.0895253i
$800$	−4.03463e9	−	2.32939e9i	−0.278605	−	0.160853i
$801$		−	4.99834e8i		−	0.0343646i
$802$	−3.32519e7	+	5.75940e7i	−0.00227618	+	0.00394245i
$803$	6.67449e9	+	1.15606e10i	0.454897	+	0.787906i
$804$	−6.79937e9	+	3.92562e9i	−0.461395	+	0.266386i
$805$	−1.46894e9			−0.0992473
$806$	6.64158e9	+	1.61566e9i	0.446785	+	0.108687i
$807$	−2.59581e10			−1.73866
$808$	8.94809e8	−	5.16618e8i	0.0596748	−	0.0344532i
$809$	−4.69798e8	−	8.13714e8i	−0.0311955	−	0.0540321i	0.850006	−	0.526773i	$-0.176598\pi$
$809$	−4.69798e8	−	8.13714e8i	−0.0311955	−	0.0540321i	−0.881202	+	0.472741i	$0.843265\pi$
$810$	−1.01462e10	+	1.75738e10i	−0.670821	+	1.16190i
$811$			8.49475e9i			0.559213i	0.960115	+	0.279607i	$0.0902041\pi$
$811$			8.49475e9i			0.559213i	−0.960115	+	0.279607i	$0.909796\pi$
$812$	−6.82268e8	−	3.93908e8i	−0.0447207	−	0.0258195i
$813$	−6.92172e9	−	3.99626e9i	−0.451749	−	0.260817i
$814$		−	7.14075e9i		−	0.464043i
$815$	−2.32594e9	+	4.02865e9i	−0.150504	+	0.260680i
$816$	9.44196e8	+	1.63540e9i	0.0608340	+	0.105368i
$817$	−2.52296e10	+	1.45663e10i	−1.61858	+	0.934487i
$818$	1.25831e9			0.0803803
$819$	−4.67047e7	+	1.91992e8i	−0.00297075	+	0.0122121i
$820$	−1.33397e10			−0.844888
$821$	9.50583e9	−	5.48819e9i	0.599499	−	0.346121i	−0.169345	−	0.985557i	$-0.554165\pi$
$821$	9.50583e9	−	5.48819e9i	0.599499	−	0.346121i	0.768845	+	0.639436i	$0.220832\pi$
$822$	−5.73763e8	−	9.93787e8i	−0.0360314	−	0.0624082i
$823$	7.58620e9	−	1.31397e10i	0.474379	−	0.821648i	−0.525191	−	0.850984i	$-0.676006\pi$
$823$	7.58620e9	−	1.31397e10i	0.474379	−	0.821648i	0.999570	+	0.0293366i	$0.00933947\pi$
$824$		−	8.55982e9i		−	0.532991i
$825$	−2.08995e10	−	1.20664e10i	−1.29583	−	0.748148i
$826$	−8.72818e8	−	5.03922e8i	−0.0538882	−	0.0311123i
$827$			1.08176e10i			0.665062i	0.943092	+	0.332531i	$0.107903\pi$
$827$			1.08176e10i			0.665062i	−0.943092	+	0.332531i	$0.892097\pi$
$828$	4.52150e8	−	7.83147e8i	0.0276807	−	0.0479443i
$829$	2.83648e9	+	4.91293e9i	0.172918	+	0.299502i	0.939439	−	0.342717i	$-0.111347\pi$
$829$	2.83648e9	+	4.91293e9i	0.172918	+	0.299502i	−0.766521	+	0.642219i	$0.778014\pi$
$830$	−1.94236e10	+	1.12142e10i	−1.17912	+	0.680764i
$831$	1.07607e10			0.650486
$832$	−1.43393e9	+	1.50197e9i	−0.0863168	+	0.0904125i
$833$	7.50883e9			0.450106
$834$	−1.56147e10	+	9.01516e9i	−0.932079	+	0.538136i
$835$	−1.37681e10	−	2.38470e10i	−0.818410	−	1.41753i
$836$	5.10467e9	−	8.84155e9i	0.302166	−	0.523367i
$837$		−	1.00298e10i		−	0.591224i
$838$	6.73069e9	+	3.88597e9i	0.395099	+	0.228110i
$839$	−8.48728e9	−	4.90013e9i	−0.496137	−	0.286445i	0.230980	−	0.972959i	$-0.425807\pi$
$839$	−8.48728e9	−	4.90013e9i	−0.496137	−	0.286445i	−0.727117	+	0.686514i	$0.759140\pi$
$840$			8.97149e8i			0.0522260i
$841$	−5.08797e9	+	8.81262e9i	−0.294957	+	0.510880i
$842$	−1.94389e9	−	3.36692e9i	−0.112222	−	0.194375i
$843$	1.49296e10	−	8.61961e9i	0.858325	−	0.495554i
$844$	3.01439e9			0.172584
$845$	−2.94201e10	+	1.36434e9i	−1.67743	+	0.0777903i
$846$	−7.55041e8			−0.0428720
$847$	−5.19205e8	+	2.99763e8i	−0.0293594	+	0.0169506i
$848$	−3.22711e9	−	5.58953e9i	−0.181731	−	0.314767i
$849$	−2.02331e9	+	3.50447e9i	−0.113471	+	0.196538i
$850$			1.04405e10i			0.583117i
$851$	9.63066e9	+	5.56026e9i	0.535676	+	0.309273i
$852$	−7.91717e9	−	4.57098e9i	−0.438562	−	0.253204i
$853$		−	1.09563e10i		−	0.604424i	−0.953241	−	0.302212i	$-0.902275\pi$
$853$		−	1.09563e10i		−	0.604424i	0.953241	−	0.302212i	$-0.0977251\pi$
$854$	9.79737e8	−	1.69695e9i	0.0538278	−	0.0932326i
$855$	3.71736e9	+	6.43866e9i	0.203401	+	0.352301i
$856$	2.01519e9	−	1.16347e9i	0.109814	−	0.0634012i
$857$	4.83453e9			0.262374			0.131187	−	0.991358i	$-0.458121\pi$
$857$	4.83453e9			0.262374			0.131187	+	0.991358i	$0.458121\pi$
$858$	−7.42780e9	+	7.78025e9i	−0.401472	+	0.420521i
$859$	−4.19822e9			−0.225990			−0.112995	−	0.993596i	$-0.536044\pi$
$859$	−4.19822e9			−0.225990			−0.112995	+	0.993596i	$0.536044\pi$
$860$	1.60561e10	−	9.27001e9i	0.860788	−	0.496976i
$861$	8.28930e8	+	1.43575e9i	0.0442595	+	0.0766598i
$862$	−1.10676e9	+	1.91697e9i	−0.0588545	+	0.101939i
$863$			1.58890e10i			0.841510i	0.907174	+	0.420755i	$0.138235\pi$
$863$			1.58890e10i			0.841510i	−0.907174	+	0.420755i	$0.861765\pi$
$864$	2.63881e9	+	1.52352e9i	0.139190	+	0.0803616i
$865$	−2.55393e9	−	1.47451e9i	−0.134169	−	0.0774626i
$866$		−	1.88790e10i		−	0.987794i
$867$	−8.18872e9	+	1.41833e10i	−0.426726	+	0.739111i
$868$	−2.56554e8	−	4.44365e8i	−0.0133156	−	0.0230633i
$869$	1.06567e10	−	6.15267e9i	0.550878	−	0.318049i
$870$	3.12320e10			1.60799
$871$	−4.57330e9	+	1.87998e10i	−0.234513	+	0.964027i
$872$	6.57128e9			0.335616
$873$	−4.05154e9	+	2.33916e9i	−0.206096	+	0.118990i
$874$	7.94968e9	+	1.37692e10i	0.402772	+	0.697622i
$875$	−1.11728e9	+	1.93518e9i	−0.0563809	+	0.0976546i
$876$			1.26967e10i			0.638154i
$877$	−7.52789e9	−	4.34623e9i	−0.376855	−	0.217578i	0.299594	−	0.954067i	$-0.403149\pi$
$877$	−7.52789e9	−	4.34623e9i	−0.376855	−	0.217578i	−0.676449	+	0.736489i	$0.736482\pi$
$878$	−6.96177e9	−	4.01938e9i	−0.347127	−	0.200414i
$879$		−	2.11657e10i		−	1.05117i
$880$	−3.24861e9	+	5.62676e9i	−0.160697	+	0.278336i
$881$	−3.97881e9	−	6.89150e9i	−0.196037	−	0.339546i	0.751203	−	0.660071i	$-0.229474\pi$
$881$	−3.97881e9	−	6.89150e9i	−0.196037	−	0.339546i	−0.947240	+	0.320525i	$0.896141\pi$
$882$	−1.90188e9	+	1.09805e9i	−0.0933349	+	0.0538869i
$883$	2.25480e8			0.0110216			0.00551080	−	0.999985i	$-0.498246\pi$
$883$	2.25480e8			0.0110216			0.00551080	+	0.999985i	$0.498246\pi$
$884$	4.52175e9	+	1.09998e9i	0.220153	+	0.0535551i
$885$	3.99547e10			1.93761
$886$	6.91120e9	−	3.99019e9i	0.333838	−	0.192741i
$887$	1.14024e9	+	1.97496e9i	0.0548611	+	0.0950222i	0.892152	−	0.451736i	$-0.149195\pi$
$887$	1.14024e9	+	1.97496e9i	0.0548611	+	0.0950222i	−0.837291	+	0.546758i	$0.815862\pi$
$888$	3.39591e9	−	5.88188e9i	0.162746	−	0.281884i
$889$			2.05487e9i			0.0980908i
$890$	−4.84343e9	−	2.79635e9i	−0.230297	−	0.132962i
$891$	1.58172e10	+	9.13204e9i	0.749129	+	0.432510i
$892$		−	1.08228e10i		−	0.510580i
$893$	6.63754e9	−	1.14966e10i	0.311909	−	0.540241i
$894$	−4.91332e9	−	8.51012e9i	−0.229982	−	0.398340i
$895$	−2.16262e10	+	1.24859e10i	−1.00832	+	0.582156i
$896$	1.55882e8			0.00723964
$897$	−4.70936e9	−	1.60760e10i	−0.217865	−	0.743713i
$898$	−1.16065e8			−0.00534854
$899$	−1.54694e10	+	8.93129e9i	−0.710094	+	0.409973i
$900$	−1.52677e9	−	2.64444e9i	−0.0698111	−	0.120916i
$901$	−7.23209e9	+	1.25263e10i	−0.329403	+	0.570542i
$902$			1.20063e10i			0.544739i
$903$	−1.99545e9	−	1.15208e9i	−0.0901850	−	0.0520683i
$904$	−7.00477e9	−	4.04420e9i	−0.315358	−	0.182072i
$905$			1.56776e10i			0.703088i
$906$	1.19526e10	−	2.07025e10i	0.533966	−	0.924857i
$907$	−1.00273e9	−	1.73678e9i	−0.0446231	−	0.0772894i	0.842851	−	0.538147i	$-0.180875\pi$
$907$	−1.00273e9	−	1.73678e9i	−0.0446231	−	0.0772894i	−0.887474	+	0.460857i	$0.847542\pi$
$908$	1.76220e10	−	1.01741e10i	0.781186	−	0.451018i
$909$	6.77221e8			0.0299059
$910$	1.59912e9	+	1.52668e9i	0.0703456	+	0.0671590i
$911$	−2.82977e10			−1.24004			−0.620022	−	0.784584i	$-0.712876\pi$
$911$	−2.82977e10			−1.24004			−0.620022	+	0.784584i	$0.712876\pi$
$912$	8.40951e9	−	4.85523e9i	0.367104	−	0.211947i
$913$	1.00933e10	+	1.74821e10i	0.438921	+	0.760233i
$914$	2.90408e9	−	5.03002e9i	0.125805	−	0.217900i
$915$			7.76810e10i			3.35228i
$916$	−6.44984e9	−	3.72382e9i	−0.277278	−	0.160086i
$917$	−6.27085e8	−	3.62048e8i	−0.0268555	−	0.0155051i
$918$		−	6.82851e9i		−	0.291324i
$919$	1.59245e10	−	2.75820e10i	0.676802	−	1.17226i	−0.299137	−	0.954210i	$-0.596699\pi$
$919$	1.59245e10	−	2.75820e10i	0.676802	−	1.17226i	0.975939	−	0.218045i	$-0.0699679\pi$
$920$	−5.05917e9	−	8.76274e9i	−0.214201	−	0.371007i
$921$	3.50403e10	−	2.02305e10i	1.47795	−	0.853294i
$922$	1.25965e10			0.529289
$923$	−2.16202e10	+	6.33350e9i	−0.905012	+	0.265117i
$924$	8.07473e8			0.0336726
$925$	3.25197e10	−	1.87753e10i	1.35099	−	0.779992i
$926$	−9.60580e9	−	1.66377e10i	−0.397553	−	0.688582i
$927$	2.80521e9	−	4.85877e9i	0.115661	−	0.200330i
$928$		−	5.42662e9i		−	0.222901i
$929$	−2.32073e10	−	1.33988e10i	−0.949665	−	0.548289i	−0.0566883	−	0.998392i	$-0.518054\pi$
$929$	−2.32073e10	−	1.33988e10i	−0.949665	−	0.548289i	−0.892977	+	0.450102i	$0.851387\pi$
$930$	1.76163e10	+	1.01708e10i	0.718165	+	0.414633i
$931$		−	3.86118e10i		−	1.56818i
$932$	−1.15255e10	+	1.99627e10i	−0.466340	+	0.807724i
$933$	1.11602e10	+	1.93301e10i	0.449870	+	0.779197i
$934$	−1.99996e10	+	1.15468e10i	−0.803168	+	0.463710i
$935$	1.45605e10			0.582554
$936$	−1.30615e9	+	3.82629e8i	−0.0520629	+	0.0152515i
$937$	−6.16082e9			−0.244653			−0.122326	−	0.992490i	$-0.539035\pi$
$937$	−6.16082e9			−0.244653			−0.122326	+	0.992490i	$0.539035\pi$
$938$	1.25783e9	−	7.26206e8i	0.0497635	−	0.0287310i
$939$	1.13998e10	+	1.97450e10i	0.449331	+	0.778264i
$940$	−4.22413e9	+	7.31640e9i	−0.165878	+	0.287310i
$941$		−	7.68185e9i		−	0.300540i	−0.988645	−	0.150270i	$-0.951986\pi$
$941$		−	7.68185e9i		−	0.300540i	0.988645	−	0.150270i	$-0.0480143\pi$
$942$	−1.60651e10	−	9.27522e9i	−0.626191	−	0.361531i
$943$	−1.61928e10	−	9.34894e9i	−0.628829	−	0.363054i
$944$		−	6.94222e9i		−	0.268594i
$945$	1.62207e9	−	2.80950e9i	0.0625255	−	0.108297i
$946$	−8.34341e9	−	1.44512e10i	−0.320424	−	0.554990i
$947$	2.89463e10	−	1.67121e10i	1.10756	−	0.639451i	0.169365	−	0.985553i	$-0.445828\pi$
$947$	2.89463e10	−	1.67121e10i	1.10756	−	0.639451i	0.938197	+	0.346102i	$0.112495\pi$
$948$	1.17040e10			0.446177
$949$	2.26312e10	+	2.16060e10i	0.859559	+	0.820621i
$950$	5.36871e10			2.03160
$951$	−2.96786e10	+	1.71350e10i	−1.11895	+	0.646028i
$952$	−1.74668e8	−	3.02534e8i	−0.00656122	−	0.0113644i
$953$	−1.24555e10	+	2.15736e10i	−0.466162	+	0.807416i	−0.999253	−	0.0386419i	$-0.987697\pi$
$953$	−1.24555e10	+	2.15736e10i	−0.466162	+	0.807416i	0.533091	+	0.846058i	$0.321030\pi$
$954$		−	4.23034e9i		−	0.157745i
$955$	1.29643e10	+	7.48496e9i	0.481657	+	0.278085i
$956$	6.84780e9	+	3.95358e9i	0.253483	+	0.146348i
$957$		−	2.81101e10i		−	1.03674i
$958$	−6.30012e9	+	1.09121e10i	−0.231510	+	0.400987i
$959$	1.06141e8	+	1.83842e8i	0.00388615	+	0.00673101i
$960$	−5.35181e9	+	3.08987e9i	−0.195232	+	0.112717i
$961$	1.58786e10			0.577140
$962$	−4.70533e9	−	1.60623e10i	−0.170403	−	0.581693i
$963$	1.52516e9			0.0550331
$964$	−1.29098e9	+	7.45346e8i	−0.0464140	+	0.0267971i
$965$	−3.62288e10	−	6.27501e10i	−1.29780	−	2.24786i
$966$	−6.28753e8	+	1.08903e9i	−0.0224419	+	0.0388705i
$967$			7.88858e9i			0.280547i	0.990113	+	0.140274i	$0.0447982\pi$
$967$			7.88858e9i			0.280547i	−0.990113	+	0.140274i	$0.955202\pi$
$968$	−3.57638e9	−	2.06482e9i	−0.126730	−	0.0731677i
$969$	−1.88460e10	−	1.08808e10i	−0.665406	−	0.384172i
$970$			5.23463e10i			1.84156i
$971$	−1.61821e10	+	2.80282e10i	−0.567241	+	0.982491i	0.429596	+	0.903021i	$0.358656\pi$
$971$	−1.61821e10	+	2.80282e10i	−0.567241	+	0.982491i	−0.996837	+	0.0794697i	$0.974677\pi$
$972$	2.17813e9	+	3.77264e9i	0.0760768	+	0.131769i
$973$	2.88859e9	−	1.66773e9i	0.100529	−	0.0580404i
$974$	−1.57397e10			−0.545808
$975$	−5.49621e10	−	1.33703e10i	−1.89910	−	0.461981i
$976$	1.34972e10			0.464697
$977$	−1.42381e10	+	8.22037e9i	−0.488451	+	0.282007i	−0.723932	−	0.689872i	$-0.757667\pi$
$977$	−1.42381e10	+	8.22037e9i	−0.488451	+	0.282007i	0.235481	+	0.971879i	$0.424334\pi$
$978$	1.99115e9	+	3.44877e9i	0.0680641	+	0.117891i
$979$	−2.51684e9	+	4.35930e9i	−0.0857268	+	0.148483i
$980$			2.45725e10i			0.833986i
$981$	3.73002e9	+	2.15353e9i	0.126145	+	0.0728298i
$982$	5.27303e9	+	3.04439e9i	0.177693	+	0.102591i
$983$		−	5.12228e10i		−	1.71999i	−0.510301	−	0.859996i	$-0.670466\pi$
$983$		−	5.12228e10i		−	1.71999i	0.510301	−	0.859996i	$-0.329534\pi$
$984$	−5.70983e9	+	9.88971e9i	−0.191047	+	0.330903i
$985$	−4.03726e9	−	6.99274e9i	−0.134605	−	0.233142i
$986$	−1.05320e10	+	6.08064e9i	−0.349897	+	0.202013i
$987$	1.04995e9			0.0347582
$988$	5.65630e9	−	2.32517e10i	0.186588	−	0.767018i
$989$	2.59870e10			0.854217
$990$	−3.68798e9	+	2.12926e9i	−0.120800	+	0.0697437i
$991$	−1.27794e10	−	2.21346e10i	−0.417113	−	0.722460i	0.578535	−	0.815657i	$-0.303625\pi$
$991$	−1.27794e10	−	2.21346e10i	−0.417113	−	0.722460i	−0.995648	+	0.0931974i	$0.970291\pi$
$992$	1.76719e9	−	3.06087e9i	0.0574769	−	0.0995529i
$993$		−	5.10635e10i		−	1.65496i
$994$	1.46461e9	+	8.45593e8i	0.0473009	+	0.0273092i
$995$	8.60172e10	+	4.96620e10i	2.76824	+	1.59825i
$996$			1.92002e10i			0.615741i
$997$	−1.70676e10	+	2.95620e10i	−0.545432	+	0.944715i	0.453148	+	0.891435i	$0.350301\pi$
$997$	−1.70676e10	+	2.95620e10i	−0.545432	+	0.944715i	−0.998580	+	0.0532799i	$0.983032\pi$
$998$	−2.38542e9	−	4.13167e9i	−0.0759641	−	0.131574i
$999$	−2.12692e10	+	1.22798e10i	−0.674950	+	0.389682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.8.e.a.23.4	yes	16
3.2	odd	2		234.8.l.c.127.8		16
4.3	odd	2		208.8.w.b.49.2		16
13.2	odd	12		338.8.a.m.1.2		8
13.3	even	3		338.8.b.i.337.2		16
13.4	even	6	inner	26.8.e.a.17.4	✓	16
13.10	even	6		338.8.b.i.337.10		16
13.11	odd	12		338.8.a.n.1.2		8
39.17	odd	6		234.8.l.c.199.5		16
52.43	odd	6		208.8.w.b.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.e.a.17.4	✓	16	13.4	even	6	inner
26.8.e.a.23.4	yes	16	1.1	even	1	trivial
208.8.w.b.17.2		16	52.43	odd	6
208.8.w.b.49.2		16	4.3	odd	2
234.8.l.c.127.8		16	3.2	odd	2
234.8.l.c.199.5		16	39.17	odd	6
338.8.a.m.1.2		8	13.2	odd	12
338.8.a.n.1.2		8	13.11	odd	12
338.8.b.i.337.2		16	13.3	even	3
338.8.b.i.337.10		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 $\F_{q}$

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} +(25.1127 + 43.4964i) q^{3} +(32.0000 - 55.4256i) q^{4} -469.361i q^{5} +(-347.971 - 200.901i) q^{6} +(64.3718 + 37.1651i) q^{7} +512.000i q^{8} +(-167.792 + 290.624i) q^{9} +(1877.44 + 3251.83i) q^{10} +(2926.79 - 1689.78i) q^{11} +3214.42 q^{12} +(5470.00 - 5729.54i) q^{13} -594.641 q^{14} +(20415.5 - 11786.9i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(-4589.65 + 7949.50i) q^{17} -2684.67i q^{18} +(40877.8 + 23600.8i) q^{19} +(-26014.6 - 15019.6i) q^{20} +3733.25i q^{21} +(-13518.3 + 23414.3i) q^{22} +(-21052.4 - 36463.9i) q^{23} +(-22270.2 + 12857.7i) q^{24} -142175. q^{25} +(-14979.1 + 61575.4i) q^{26} +92988.0 q^{27} +(4119.79 - 2378.56i) q^{28} +(-82803.7 - 143420. i) q^{29} +(-94295.3 + 163324. i) q^{30} -107861. i q^{31} +(28377.9 + 16384.0i) q^{32} +(146999. + 84869.8i) q^{33} -73434.4i q^{34} +(17443.8 - 30213.6i) q^{35} +(10738.7 + 18599.9i) q^{36} +(-228730. + 132058. i) q^{37} -377613. q^{38} +(386581. + 94041.1i) q^{39} +240313. q^{40} +(384584. - 222040. i) q^{41} +(-14933.0 - 25864.7i) q^{42} +(-308598. + 534508. i) q^{43} -216292. i q^{44} +(136408. + 78754.9i) q^{45} +(291711. + 168419. i) q^{46} -281242. i q^{47} +(102861. - 178161. i) q^{48} +(-409009. - 708424. i) q^{49} +(985016. - 568699. i) q^{50} -461033. q^{51} +(-142524. - 486523. i) q^{52} +1.57574e6 q^{53} +(-644240. + 371952. i) q^{54} +(-793118. - 1.37372e6i) q^{55} +(-19028.5 + 32958.3i) q^{56} +2.37072e6i q^{57} +(1.14736e6 + 662430. i) q^{58} +(1.46781e6 + 847438. i) q^{59} -1.50872e6i q^{60} +(-1.64761e6 + 2.85375e6i) q^{61} +(431444. + 747283. i) q^{62} +(-21602.1 + 12472.0i) q^{63} -262144. q^{64} +(-2.68922e6 - 2.56740e6i) q^{65} -1.35792e6 q^{66} +(-2.11527e6 + 1.22125e6i) q^{67} +(293737. + 508768. i) q^{68} +(1.05737e6 - 1.83141e6i) q^{69} +279101. i q^{70} +(-2.46302e6 - 1.42202e6i) q^{71} +(-148799. - 85909.4i) q^{72} +3.94991e6i q^{73} +(1.05646e6 - 1.82984e6i) q^{74} +(-3.57039e6 - 6.18410e6i) q^{75} +(2.61618e6 - 1.51045e6i) q^{76} +251203. q^{77} +(-3.05447e6 + 894787. i) q^{78} +3.64110e6 q^{79} +(-1.66494e6 + 961252. i) q^{80} +(2.70214e6 + 4.68024e6i) q^{81} +(-1.77632e6 + 3.07667e6i) q^{82} +5.97315e6i q^{83} +(206918. + 119464. i) q^{84} +(3.73119e6 + 2.15420e6i) q^{85} -4.93757e6i q^{86} +(4.15884e6 - 7.20333e6i) q^{87} +(865168. + 1.49852e6i) q^{88} +(-1.28990e6 + 744724. i) q^{89} -1.26008e6 q^{90} +(565052. - 165528. i) q^{91} -2.69471e6 q^{92} +(4.69156e6 - 2.70868e6i) q^{93} +(1.12497e6 + 1.94850e6i) q^{94} +(1.10773e7 - 1.91865e7i) q^{95} +1.64578e6i q^{96} +(1.20731e7 + 6.97042e6i) q^{97} +(5.66740e6 + 3.27207e6i) q^{98} +1.13413e6i 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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