LMFDB - Embedded newform 26.6.b.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [26,6,Mod(25,26)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(26, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("26.25");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$N$	$=$	$26 = 2 \cdot 13$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	26.b (of order $2$ , degree $1$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.16997931514$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} + 1$ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			25.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	26.25
Dual form			26.6.b.a.25.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000i q^{2} -13.0000 q^{3} -16.0000 q^{4} -51.0000i q^{5} -52.0000i q^{6} -105.000i q^{7} -64.0000i q^{8} -74.0000 q^{9} +204.000 q^{10} -120.000i q^{11} +208.000 q^{12} +(-598.000 - 117.000i) q^{13} +420.000 q^{14} +663.000i q^{15} +256.000 q^{16} -1101.00 q^{17} -296.000i q^{18} +1170.00i q^{19} +816.000i q^{20} +1365.00i q^{21} +480.000 q^{22} +1050.00 q^{23} +832.000i q^{24} +524.000 q^{25} +(468.000 - 2392.00i) q^{26} +4121.00 q^{27} +1680.00i q^{28} -4104.00 q^{29} -2652.00 q^{30} -9624.00i q^{31} +1024.00i q^{32} +1560.00i q^{33} -4404.00i q^{34} -5355.00 q^{35} +1184.00 q^{36} -8709.00i q^{37} -4680.00 q^{38} +(7774.00 + 1521.00i) q^{39} -3264.00 q^{40} +9480.00i q^{41} -5460.00 q^{42} +9995.00 q^{43} +1920.00i q^{44} +3774.00i q^{45} +4200.00i q^{46} +2943.00i q^{47} -3328.00 q^{48} +5782.00 q^{49} +2096.00i q^{50} +14313.0 q^{51} +(9568.00 + 1872.00i) q^{52} -750.000 q^{53} +16484.0i q^{54} -6120.00 q^{55} -6720.00 q^{56} -15210.0i q^{57} -16416.0i q^{58} +40938.0i q^{59} -10608.0i q^{60} -57920.0 q^{61} +38496.0 q^{62} +7770.00i q^{63} -4096.00 q^{64} +(-5967.00 + 30498.0i) q^{65} -6240.00 q^{66} -22812.0i q^{67} +17616.0 q^{68} -13650.0 q^{69} -21420.0i q^{70} -63741.0i q^{71} +4736.00i q^{72} -58866.0i q^{73} +34836.0 q^{74} -6812.00 q^{75} -18720.0i q^{76} -12600.0 q^{77} +(-6084.00 + 31096.0i) q^{78} +63202.0 q^{79} -13056.0i q^{80} -35591.0 q^{81} -37920.0 q^{82} -55458.0i q^{83} -21840.0i q^{84} +56151.0i q^{85} +39980.0i q^{86} +53352.0 q^{87} -7680.00 q^{88} +104778. i q^{89} -15096.0 q^{90} +(-12285.0 + 62790.0i) q^{91} -16800.0 q^{92} +125112. i q^{93} -11772.0 q^{94} +59670.0 q^{95} -13312.0i q^{96} -160452. i q^{97} +23128.0i q^{98} +8880.00i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 26 q^{3} - 32 q^{4} - 148 q^{9} + 408 q^{10} + 416 q^{12} - 1196 q^{13} + 840 q^{14} + 512 q^{16} - 2202 q^{17} + 960 q^{22} + 2100 q^{23} + 1048 q^{25} + 936 q^{26} + 8242 q^{27} - 8208 q^{29} - 5304 q^{30}+ \cdots + 119340 q^{95}+O(q^{100})$ 2 * q - 26 * q^3 - 32 * q^4 - 148 * q^9 + 408 * q^10 + 416 * q^12 - 1196 * q^13 + 840 * q^14 + 512 * q^16 - 2202 * q^17 + 960 * q^22 + 2100 * q^23 + 1048 * q^25 + 936 * q^26 + 8242 * q^27 - 8208 * q^29 - 5304 * q^30 - 10710 * q^35 + 2368 * q^36 - 9360 * q^38 + 15548 * q^39 - 6528 * q^40 - 10920 * q^42 + 19990 * q^43 - 6656 * q^48 + 11564 * q^49 + 28626 * q^51 + 19136 * q^52 - 1500 * q^53 - 12240 * q^55 - 13440 * q^56 - 115840 * q^61 + 76992 * q^62 - 8192 * q^64 - 11934 * q^65 - 12480 * q^66 + 35232 * q^68 - 27300 * q^69 + 69672 * q^74 - 13624 * q^75 - 25200 * q^77 - 12168 * q^78 + 126404 * q^79 - 71182 * q^81 - 75840 * q^82 + 106704 * q^87 - 15360 * q^88 - 30192 * q^90 - 24570 * q^91 - 33600 * q^92 - 23544 * q^94 + 119340 * q^95

Character values

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

$n$	$15$
$\chi(n)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$			4.00000i			0.707107i
$2$			4.00000i			0.707107i
$3$	−13.0000			−0.833950			−0.416975	−	0.908918i	$-0.636910\pi$
$3$	−13.0000			−0.833950			−0.416975	+	0.908918i	$0.636910\pi$
$4$	−16.0000			−0.500000
$5$		−	51.0000i		−	0.912316i	−0.889899	−	0.456158i	$-0.849225\pi$
$5$		−	51.0000i		−	0.912316i	0.889899	−	0.456158i	$-0.150775\pi$
$6$		−	52.0000i		−	0.589692i
$7$		−	105.000i		−	0.809924i	−0.914334	−	0.404962i	$-0.867285\pi$
$7$		−	105.000i		−	0.809924i	0.914334	−	0.404962i	$-0.132715\pi$
$8$		−	64.0000i		−	0.353553i
$9$	−74.0000			−0.304527
$10$	204.000			0.645105
$11$		−	120.000i		−	0.299020i	−0.988760	−	0.149510i	$-0.952230\pi$
$11$		−	120.000i		−	0.299020i	0.988760	−	0.149510i	$-0.0477695\pi$
$12$	208.000			0.416975
$13$	−598.000	−	117.000i	−0.981393	−	0.192012i
$13$	−598.000	−	117.000i	−0.981393	−	0.192012i
$14$	420.000			0.572703
$15$			663.000i			0.760826i
$16$	256.000			0.250000
$17$	−1101.00			−0.923985			−0.461993	−	0.886884i	$-0.652865\pi$
$17$	−1101.00			−0.923985			−0.461993	+	0.886884i	$0.652865\pi$
$18$		−	296.000i		−	0.215333i
$19$			1170.00i			0.743536i	0.928326	+	0.371768i	$0.121248\pi$
$19$			1170.00i			0.743536i	−0.928326	+	0.371768i	$0.878752\pi$
$20$			816.000i			0.456158i
$21$			1365.00i			0.675436i
$22$	480.000			0.211439
$23$	1050.00			0.413875			0.206938	−	0.978354i	$-0.433650\pi$
$23$	1050.00			0.413875			0.206938	+	0.978354i	$0.433650\pi$
$24$			832.000i			0.294846i
$25$	524.000			0.167680
$26$	468.000	−	2392.00i	0.135773	−	0.693949i
$27$	4121.00			1.08791
$28$			1680.00i			0.404962i
$29$	−4104.00			−0.906176			−0.453088	−	0.891466i	$-0.649678\pi$
$29$	−4104.00			−0.906176			−0.453088	+	0.891466i	$0.649678\pi$
$30$	−2652.00			−0.537985
$31$		−	9624.00i		−	1.79867i	−0.437261	−	0.899335i	$-0.644051\pi$
$31$		−	9624.00i		−	1.79867i	0.437261	−	0.899335i	$-0.355949\pi$
$32$			1024.00i			0.176777i
$33$			1560.00i			0.249367i
$34$		−	4404.00i		−	0.653356i
$35$	−5355.00			−0.738906
$36$	1184.00			0.152263
$37$		−	8709.00i		−	1.04584i	−0.852383	−	0.522918i	$-0.824843\pi$
$37$		−	8709.00i		−	1.04584i	0.852383	−	0.522918i	$-0.175157\pi$
$38$	−4680.00			−0.525759
$39$	7774.00	+	1521.00i	0.818433	+	0.160128i
$40$	−3264.00			−0.322552
$41$			9480.00i			0.880742i	0.897816	+	0.440371i	$0.145153\pi$
$41$			9480.00i			0.880742i	−0.897816	+	0.440371i	$0.854847\pi$
$42$	−5460.00			−0.477606
$43$	9995.00			0.824350			0.412175	−	0.911105i	$-0.364769\pi$
$43$	9995.00			0.824350			0.412175	+	0.911105i	$0.364769\pi$
$44$			1920.00i			0.149510i
$45$			3774.00i			0.277825i
$46$			4200.00i			0.292654i
$47$			2943.00i			0.194333i	0.995268	+	0.0971663i	$0.0309779\pi$
$47$			2943.00i			0.194333i	−0.995268	+	0.0971663i	$0.969022\pi$
$48$	−3328.00			−0.208488
$49$	5782.00			0.344023
$50$			2096.00i			0.118568i
$51$	14313.0			0.770558
$52$	9568.00	+	1872.00i	0.490696	+	0.0960058i
$53$	−750.000			−0.0366751			−0.0183376	−	0.999832i	$-0.505837\pi$
$53$	−750.000			−0.0366751			−0.0183376	+	0.999832i	$0.505837\pi$
$54$			16484.0i			0.769269i
$55$	−6120.00			−0.272800
$56$	−6720.00			−0.286351
$57$		−	15210.0i		−	0.620072i
$58$		−	16416.0i		−	0.640763i
$59$			40938.0i			1.53108i	0.643391	+	0.765538i	$0.277527\pi$
$59$			40938.0i			1.53108i	−0.643391	+	0.765538i	$0.722473\pi$
$60$		−	10608.0i		−	0.380413i
$61$	−57920.0			−1.99298			−0.996492	−	0.0836839i	$-0.973331\pi$
$61$	−57920.0			−1.99298			−0.996492	+	0.0836839i	$0.973331\pi$
$62$	38496.0			1.27185
$63$			7770.00i			0.246643i
$64$	−4096.00			−0.125000
$65$	−5967.00	+	30498.0i	−0.175175	+	0.895340i
$66$	−6240.00			−0.176329
$67$		−	22812.0i		−	0.620835i	−0.950600	−	0.310418i	$-0.899531\pi$
$67$		−	22812.0i		−	0.620835i	0.950600	−	0.310418i	$-0.100469\pi$
$68$	17616.0			0.461993
$69$	−13650.0			−0.345152
$70$		−	21420.0i		−	0.522486i
$71$		−	63741.0i		−	1.50063i	−0.661082	−	0.750314i	$-0.729902\pi$
$71$		−	63741.0i		−	1.50063i	0.661082	−	0.750314i	$-0.270098\pi$
$72$			4736.00i			0.107666i
$73$		−	58866.0i		−	1.29288i	−0.762966	−	0.646439i	$-0.776258\pi$
$73$		−	58866.0i		−	1.29288i	0.762966	−	0.646439i	$-0.223742\pi$
$74$	34836.0			0.739518
$75$	−6812.00			−0.139837
$76$		−	18720.0i		−	0.371768i
$77$	−12600.0			−0.242183
$78$	−6084.00	+	31096.0i	−0.113228	+	0.578719i
$79$	63202.0			1.13937			0.569683	−	0.821865i	$-0.307066\pi$
$79$	63202.0			1.13937			0.569683	+	0.821865i	$0.307066\pi$
$80$		−	13056.0i		−	0.228079i
$81$	−35591.0			−0.602737
$82$	−37920.0			−0.622779
$83$		−	55458.0i		−	0.883627i	−0.897107	−	0.441813i	$-0.854335\pi$
$83$		−	55458.0i		−	0.883627i	0.897107	−	0.441813i	$-0.145665\pi$
$84$		−	21840.0i		−	0.337718i
$85$			56151.0i			0.842966i
$86$			39980.0i			0.582903i
$87$	53352.0			0.755705
$88$	−7680.00			−0.105719
$89$			104778.i			1.40215i	0.713087	+	0.701076i	$0.247297\pi$
$89$			104778.i			1.40215i	−0.713087	+	0.701076i	$0.752703\pi$
$90$	−15096.0			−0.196452
$91$	−12285.0	+	62790.0i	−0.155515	+	0.794853i
$92$	−16800.0			−0.206938
$93$			125112.i			1.50000i
$94$	−11772.0			−0.137414
$95$	59670.0			0.678339
$96$		−	13312.0i		−	0.147423i
$97$		−	160452.i		−	1.73147i	−0.500500	−	0.865737i	$-0.666850\pi$
$97$		−	160452.i		−	1.73147i	0.500500	−	0.865737i	$-0.333150\pi$
$98$			23128.0i			0.243261i
$99$			8880.00i			0.0910594i
$100$	−8384.00			−0.0838400
$101$	−113124.			−1.10345			−0.551723	−	0.834027i	$-0.686030\pi$
$101$	−113124.			−1.10345			−0.551723	+	0.834027i	$0.686030\pi$
$102$			57252.0i			0.544867i
$103$	25046.0			0.232619			0.116310	−	0.993213i	$-0.462894\pi$
$103$	25046.0			0.232619			0.116310	+	0.993213i	$0.462894\pi$
$104$	−7488.00	+	38272.0i	−0.0678864	+	0.346975i
$105$	69615.0			0.616211
$106$		−	3000.00i		−	0.0259332i
$107$	24924.0			0.210455			0.105227	−	0.994448i	$-0.466443\pi$
$107$	24924.0			0.210455			0.105227	+	0.994448i	$0.466443\pi$
$108$	−65936.0			−0.543955
$109$		−	144831.i		−	1.16760i	−0.811896	−	0.583802i	$-0.801565\pi$
$109$		−	144831.i		−	1.16760i	0.811896	−	0.583802i	$-0.198435\pi$
$110$		−	24480.0i		−	0.192899i
$111$			113217.i			0.872176i
$112$		−	26880.0i		−	0.202481i
$113$	100266.			0.738682			0.369341	−	0.929294i	$-0.379583\pi$
$113$	100266.			0.738682			0.369341	+	0.929294i	$0.379583\pi$
$114$	60840.0			0.438457
$115$		−	53550.0i		−	0.377585i
$116$	65664.0			0.453088
$117$	44252.0	+	8658.00i	0.298860	+	0.0584727i
$118$	−163752.			−1.08263
$119$			115605.i			0.748358i
$120$	42432.0			0.268993
$121$	146651.			0.910587
$122$		−	231680.i		−	1.40925i
$123$		−	123240.i		−	0.734495i
$124$			153984.i			0.899335i
$125$		−	186099.i		−	1.06529i
$126$	−31080.0			−0.174403
$127$	−202754.			−1.11548			−0.557738	−	0.830017i	$-0.688331\pi$
$127$	−202754.			−1.11548			−0.557738	+	0.830017i	$0.688331\pi$
$128$		−	16384.0i		−	0.0883883i
$129$	−129935.			−0.687467
$130$	−121992.	−	23868.0i	−0.633101	−	0.123868i
$131$	−303855.			−1.54699			−0.773496	−	0.633801i	$-0.781494\pi$
$131$	−303855.			−1.54699			−0.773496	+	0.633801i	$0.781494\pi$
$132$		−	24960.0i		−	0.124684i
$133$	122850.			0.602207
$134$	91248.0			0.438997
$135$		−	210171.i		−	0.992518i
$136$			70464.0i			0.326678i
$137$			63738.0i			0.290133i	0.989422	+	0.145066i	$0.0463396\pi$
$137$			63738.0i			0.290133i	−0.989422	+	0.145066i	$0.953660\pi$
$138$		−	54600.0i		−	0.244059i
$139$	13841.0			0.0607618			0.0303809	−	0.999538i	$-0.490328\pi$
$139$	13841.0			0.0607618			0.0303809	+	0.999538i	$0.490328\pi$
$140$	85680.0			0.369453
$141$		−	38259.0i		−	0.162064i
$142$	254964.			1.06110
$143$	−14040.0	+	71760.0i	−0.0574152	+	0.293456i
$144$	−18944.0			−0.0761317
$145$			209304.i			0.826718i
$146$	235464.			0.914202
$147$	−75166.0			−0.286898
$148$			139344.i			0.522918i
$149$			276426.i			1.02003i	0.860165	+	0.510015i	$0.170360\pi$
$149$			276426.i			1.02003i	−0.860165	+	0.510015i	$0.829640\pi$
$150$		−	27248.0i		−	0.0988796i
$151$			321333.i			1.14687i	0.819252	+	0.573433i	$0.194389\pi$
$151$			321333.i			1.14687i	−0.819252	+	0.573433i	$0.805611\pi$
$152$	74880.0			0.262880
$153$	81474.0			0.281378
$154$		−	50400.0i		−	0.171249i
$155$	−490824.			−1.64095
$156$	−124384.	−	24336.0i	−0.409216	−	0.0800641i
$157$	339506.			1.09925			0.549627	−	0.835410i	$-0.314770\pi$
$157$	339506.			1.09925			0.549627	+	0.835410i	$0.314770\pi$
$158$			252808.i			0.805653i
$159$	9750.00			0.0305852
$160$	52224.0			0.161276
$161$		−	110250.i		−	0.335208i
$162$		−	142364.i		−	0.426199i
$163$			395718.i			1.16659i	0.812262	+	0.583293i	$0.198236\pi$
$163$			395718.i			1.16659i	−0.812262	+	0.583293i	$0.801764\pi$
$164$		−	151680.i		−	0.440371i
$165$	79560.0			0.227502
$166$	221832.			0.624819
$167$		−	426708.i		−	1.18397i	−0.805950	−	0.591984i	$-0.798345\pi$
$167$		−	426708.i		−	1.18397i	0.805950	−	0.591984i	$-0.201655\pi$
$168$	87360.0			0.238803
$169$	343915.	+	139932.i	0.926263	+	0.376878i
$170$	−224604.			−0.596067
$171$		−	86580.0i		−	0.226427i
$172$	−159920.			−0.412175
$173$	16026.0			0.0407108			0.0203554	−	0.999793i	$-0.493520\pi$
$173$	16026.0			0.0407108			0.0203554	+	0.999793i	$0.493520\pi$
$174$			213408.i			0.534364i
$175$		−	55020.0i		−	0.135808i
$176$		−	30720.0i		−	0.0747549i
$177$		−	532194.i		−	1.27684i
$178$	−419112.			−0.991471
$179$	−690045.			−1.60970			−0.804850	−	0.593479i	$-0.797754\pi$
$179$	−690045.			−1.60970			−0.804850	+	0.593479i	$0.797754\pi$
$180$		−	60384.0i		−	0.138912i
$181$	−96478.0			−0.218893			−0.109446	−	0.993993i	$-0.534908\pi$
$181$	−96478.0			−0.218893			−0.109446	+	0.993993i	$0.534908\pi$
$182$	−251160.	−	49140.0i	−0.562046	−	0.109966i
$183$	752960.			1.66205
$184$		−	67200.0i		−	0.146327i
$185$	−444159.			−0.954134
$186$	−500448.			−1.06066
$187$			132120.i			0.276290i
$188$		−	47088.0i		−	0.0971663i
$189$		−	432705.i		−	0.881125i
$190$			238680.i			0.479658i
$191$	708180.			1.40462			0.702312	−	0.711869i	$-0.252151\pi$
$191$	708180.			1.40462			0.702312	+	0.711869i	$0.252151\pi$
$192$	53248.0			0.104244
$193$			347862.i			0.672224i	0.941822	+	0.336112i	$0.109112\pi$
$193$			347862.i			0.672224i	−0.941822	+	0.336112i	$0.890888\pi$
$194$	641808.			1.22434
$195$	77571.0	−	396474.i	0.146087	−	0.746669i
$196$	−92512.0			−0.172012
$197$		−	899589.i		−	1.65150i	−0.564036	−	0.825750i	$-0.690752\pi$
$197$		−	899589.i		−	1.65150i	0.564036	−	0.825750i	$-0.309248\pi$
$198$	−35520.0			−0.0643887
$199$	143116.			0.256186			0.128093	−	0.991762i	$-0.459114\pi$
$199$	143116.			0.256186			0.128093	+	0.991762i	$0.459114\pi$
$200$		−	33536.0i		−	0.0592838i
$201$			296556.i			0.517746i
$202$		−	452496.i		−	0.780255i
$203$			430920.i			0.733933i
$204$	−229008.			−0.385279
$205$	483480.			0.803515
$206$			100184.i			0.164487i
$207$	−77700.0			−0.126036
$208$	−153088.	−	29952.0i	−0.245348	−	0.0480029i
$209$	140400.			0.222332
$210$			278460.i			0.435727i
$211$	−339731.			−0.525326			−0.262663	−	0.964888i	$-0.584601\pi$
$211$	−339731.			−0.525326			−0.262663	+	0.964888i	$0.584601\pi$
$212$	12000.0			0.0183376
$213$			828633.i			1.25145i
$214$			99696.0i			0.148814i
$215$		−	509745.i		−	0.752068i
$216$		−	263744.i		−	0.384634i
$217$	−1.01052e6			−1.45679
$218$	579324.			0.825620
$219$			765258.i			1.07820i
$220$	97920.0			0.136400
$221$	658398.	+	128817.i	0.906792	+	0.177416i
$222$	−452868.			−0.616722
$223$		−	623757.i		−	0.839950i	−0.907536	−	0.419975i	$-0.862039\pi$
$223$		−	623757.i		−	0.839950i	0.907536	−	0.419975i	$-0.137961\pi$
$224$	107520.			0.143176
$225$	−38776.0			−0.0510630
$226$			401064.i			0.522327i
$227$			177612.i			0.228775i	0.993436	+	0.114387i	$0.0364905\pi$
$227$			177612.i			0.228775i	−0.993436	+	0.114387i	$0.963510\pi$
$228$			243360.i			0.310036i
$229$			1.18705e6i			1.49582i	0.663799	+	0.747911i	$0.268943\pi$
$229$			1.18705e6i			1.49582i	−0.663799	+	0.747911i	$0.731057\pi$
$230$	214200.			0.266993
$231$	163800.			0.201969
$232$			262656.i			0.320381i
$233$	−112317.			−0.135536			−0.0677682	−	0.997701i	$-0.521588\pi$
$233$	−112317.			−0.135536			−0.0677682	+	0.997701i	$0.521588\pi$
$234$	−34632.0	+	177008.i	−0.0413464	+	0.211326i
$235$	150093.			0.177293
$236$		−	655008.i		−	0.765538i
$237$	−821626.			−0.950174
$238$	−462420.			−0.529169
$239$			1.19805e6i			1.35669i	0.734743	+	0.678346i	$0.237303\pi$
$239$			1.19805e6i			1.35669i	−0.734743	+	0.678346i	$0.762697\pi$
$240$			169728.i			0.190207i
$241$		−	1.16629e6i		−	1.29349i	−0.762707	−	0.646744i	$-0.776130\pi$
$241$		−	1.16629e6i		−	1.29349i	0.762707	−	0.646744i	$-0.223870\pi$
$242$			586604.i			0.643882i
$243$	−538720.			−0.585258
$244$	926720.			0.996492
$245$		−	294882.i		−	0.313858i
$246$	492960.			0.519366
$247$	136890.	−	699660.i	0.142767	−	0.729701i
$248$	−615936.			−0.635926
$249$			720954.i			0.736901i
$250$	744396.			0.753276
$251$	648996.			0.650216			0.325108	−	0.945677i	$-0.394599\pi$
$251$	648996.			0.650216			0.325108	+	0.945677i	$0.394599\pi$
$252$		−	124320.i		−	0.123322i
$253$		−	126000.i		−	0.123757i
$254$		−	811016.i		−	0.788760i
$255$		−	729963.i		−	0.702992i
$256$	65536.0			0.0625000
$257$	−945885.			−0.893317			−0.446658	−	0.894705i	$-0.647386\pi$
$257$	−945885.			−0.893317			−0.446658	+	0.894705i	$0.647386\pi$
$258$		−	519740.i		−	0.486113i
$259$	−914445.			−0.847048
$260$	95472.0	−	487968.i	0.0875876	−	0.447670i
$261$	303696.			0.275955
$262$		−	1.21542e6i		−	1.09389i
$263$	1.01222e6			0.902375			0.451188	−	0.892429i	$-0.351000\pi$
$263$	1.01222e6			0.902375			0.451188	+	0.892429i	$0.351000\pi$
$264$	99840.0			0.0881647
$265$			38250.0i			0.0334593i
$266$			491400.i			0.425825i
$267$		−	1.36211e6i		−	1.16933i
$268$			364992.i			0.310418i
$269$	−1.01772e6			−0.857527			−0.428763	−	0.903417i	$-0.641051\pi$
$269$	−1.01772e6			−0.857527			−0.428763	+	0.903417i	$0.641051\pi$
$270$	840684.			0.701816
$271$		−	463461.i		−	0.383345i	−0.981459	−	0.191673i	$-0.938609\pi$
$271$		−	463461.i		−	0.383345i	0.981459	−	0.191673i	$-0.0613912\pi$
$272$	−281856.			−0.230996
$273$	159705.	−	816270.i	0.129692	−	0.662868i
$274$	−254952.			−0.205155
$275$		−	62880.0i		−	0.0501396i
$276$	218400.			0.172576
$277$	332528.			0.260393			0.130196	−	0.991488i	$-0.458439\pi$
$277$	332528.			0.260393			0.130196	+	0.991488i	$0.458439\pi$
$278$			55364.0i			0.0429651i
$279$			712176.i			0.547743i
$280$			342720.i			0.261243i
$281$			49122.0i			0.0371116i	0.999828	+	0.0185558i	$0.00590684\pi$
$281$			49122.0i			0.0371116i	−0.999828	+	0.0185558i	$0.994093\pi$
$282$	153036.			0.114596
$283$	−1.55848e6			−1.15674			−0.578371	−	0.815774i	$-0.696311\pi$
$283$	−1.55848e6			−1.15674			−0.578371	+	0.815774i	$0.696311\pi$
$284$			1.01986e6i			0.750314i
$285$	−775710.			−0.565701
$286$	−287040.	−	56160.0i	−0.207504	−	0.0405987i
$287$	995400.			0.713334
$288$		−	75776.0i		−	0.0538332i
$289$	−207656.			−0.146251
$290$	−837216.			−0.584578
$291$			2.08588e6i			1.44396i
$292$			941856.i			0.646439i
$293$			218463.i			0.148665i	0.997234	+	0.0743325i	$0.0236826\pi$
$293$			218463.i			0.148665i	−0.997234	+	0.0743325i	$0.976317\pi$
$294$		−	300664.i		−	0.202868i
$295$	2.08784e6			1.39682
$296$	−557376.			−0.369759
$297$		−	494520.i		−	0.325306i
$298$	−1.10570e6			−0.721271
$299$	−627900.	−	122850.i	−0.406174	−	0.0794689i
$300$	108992.			0.0699184
$301$		−	1.04948e6i		−	0.667661i
$302$	−1.28533e6			−0.810957
$303$	1.47061e6			0.920220
$304$			299520.i			0.185884i
$305$			2.95392e6i			1.81823i
$306$			325896.i			0.198964i
$307$		−	321102.i		−	0.194445i	−0.995263	−	0.0972226i	$-0.969004\pi$
$307$		−	321102.i		−	0.194445i	0.995263	−	0.0972226i	$-0.0309959\pi$
$308$	201600.			0.121092
$309$	−325598.			−0.193993
$310$		−	1.96330e6i		−	1.16033i
$311$	3.33725e6			1.95654			0.978269	−	0.207340i	$-0.0664805\pi$
$311$	3.33725e6			1.95654			0.978269	+	0.207340i	$0.0664805\pi$
$312$	97344.0	−	497536.i	0.0566139	−	0.289360i
$313$	1.16568e6			0.672538			0.336269	−	0.941766i	$-0.390835\pi$
$313$	1.16568e6			0.672538			0.336269	+	0.941766i	$0.390835\pi$
$314$			1.35802e6i			0.777290i
$315$	396270.			0.225017
$316$	−1.01123e6			−0.569683
$317$		−	73518.0i		−	0.0410909i	−0.999789	−	0.0205454i	$-0.993460\pi$
$317$		−	73518.0i		−	0.0410909i	0.999789	−	0.0205454i	$-0.00654028\pi$
$318$			39000.0i			0.0216270i
$319$			492480.i			0.270964i
$320$			208896.i			0.114039i
$321$	−324012.			−0.175509
$322$	441000.			0.237028
$323$		−	1.28817e6i		−	0.687016i
$324$	569456.			0.301368
$325$	−313352.	−	61308.0i	−0.164560	−	0.0321965i
$326$	−1.58287e6			−0.824901
$327$			1.88280e6i			0.973723i
$328$	606720.			0.311389
$329$	309015.			0.157395
$330$			318240.i			0.160868i
$331$		−	632682.i		−	0.317406i	−0.987326	−	0.158703i	$-0.949269\pi$
$331$		−	632682.i		−	0.317406i	0.987326	−	0.158703i	$-0.0507313\pi$
$332$			887328.i			0.441813i
$333$			644466.i			0.318485i
$334$	1.70683e6			0.837191
$335$	−1.16341e6			−0.566398
$336$			349440.i			0.168859i
$337$	−326843.			−0.156771			−0.0783853	−	0.996923i	$-0.524976\pi$
$337$	−326843.			−0.156771			−0.0783853	+	0.996923i	$0.524976\pi$
$338$	−559728.	+	1.37566e6i	−0.266493	+	0.654967i
$339$	−1.30346e6			−0.616024
$340$		−	898416.i		−	0.421483i
$341$	−1.15488e6			−0.537837
$342$	346320.			0.160108
$343$		−	2.37184e6i		−	1.08856i
$344$		−	639680.i		−	0.291452i
$345$			696150.i			0.314887i
$346$			64104.0i			0.0287869i
$347$	2.96275e6			1.32090			0.660452	−	0.750868i	$-0.270365\pi$
$347$	2.96275e6			1.32090			0.660452	+	0.750868i	$0.270365\pi$
$348$	−853632.			−0.377853
$349$		−	866325.i		−	0.380730i	−0.981713	−	0.190365i	$-0.939033\pi$
$349$		−	866325.i		−	0.380730i	0.981713	−	0.190365i	$-0.0609672\pi$
$350$	220080.			0.0960308
$351$	−2.46436e6	−	482157.i	−1.06767	−	0.208891i
$352$	122880.			0.0528597
$353$		−	1.66291e6i		−	0.710282i	−0.934813	−	0.355141i	$-0.884433\pi$
$353$		−	1.66291e6i		−	0.710282i	0.934813	−	0.355141i	$-0.115567\pi$
$354$	2.12878e6			0.902863
$355$	−3.25079e6			−1.36905
$356$		−	1.67645e6i		−	0.701076i
$357$		−	1.50286e6i		−	0.624093i
$358$		−	2.76018e6i		−	1.13823i
$359$		−	625536.i		−	0.256163i	−0.991764	−	0.128081i	$-0.959118\pi$
$359$		−	625536.i		−	0.256163i	0.991764	−	0.128081i	$-0.0408819\pi$
$360$	241536.			0.0982258
$361$	1.10720e6			0.447155
$362$		−	385912.i		−	0.154781i
$363$	−1.90646e6			−0.759385
$364$	196560.	−	1.00464e6i	0.0777574	−	0.397427i
$365$	−3.00217e6			−1.17951
$366$			3.01184e6i			1.17525i
$367$	1.08327e6			0.419829			0.209914	−	0.977720i	$-0.432681\pi$
$367$	1.08327e6			0.419829			0.209914	+	0.977720i	$0.432681\pi$
$368$	268800.			0.103469
$369$		−	701520.i		−	0.268209i
$370$		−	1.77664e6i		−	0.674674i
$371$			78750.0i			0.0297041i
$372$		−	2.00179e6i		−	0.750001i
$373$	−1.78896e6			−0.665775			−0.332888	−	0.942967i	$-0.608023\pi$
$373$	−1.78896e6			−0.665775			−0.332888	+	0.942967i	$0.608023\pi$
$374$	−528480.			−0.195366
$375$			2.41929e6i			0.888401i
$376$	188352.			0.0687069
$377$	2.45419e6	+	480168.i	0.889314	+	0.173996i
$378$	1.73082e6			0.623049
$379$		−	868614.i		−	0.310620i	−0.987866	−	0.155310i	$-0.950362\pi$
$379$		−	868614.i		−	0.310620i	0.987866	−	0.155310i	$-0.0496376\pi$
$380$	−954720.			−0.339170
$381$	2.63580e6			0.930251
$382$			2.83272e6i			0.993220i
$383$			1.07972e6i			0.376108i	0.982159	+	0.188054i	$0.0602179\pi$
$383$			1.07972e6i			0.376108i	−0.982159	+	0.188054i	$0.939782\pi$
$384$			212992.i			0.0737115i
$385$			642600.i			0.220947i
$386$	−1.39145e6			−0.475334
$387$	−739630.			−0.251037
$388$			2.56723e6i			0.865737i
$389$	1.28822e6			0.431634			0.215817	−	0.976434i	$-0.430759\pi$
$389$	1.28822e6			0.431634			0.215817	+	0.976434i	$0.430759\pi$
$390$	1.58590e6	+	310284.i	0.527975	+	0.103299i
$391$	−1.15605e6			−0.382415
$392$		−	370048.i		−	0.121631i
$393$	3.95012e6			1.29011
$394$	3.59836e6			1.16779
$395$		−	3.22330e6i		−	1.03946i
$396$		−	142080.i		−	0.0455297i
$397$			5.46909e6i			1.74156i	0.491672	+	0.870781i	$0.336386\pi$
$397$			5.46909e6i			1.74156i	−0.491672	+	0.870781i	$0.663614\pi$
$398$			572464.i			0.181151i
$399$	−1.59705e6			−0.502211
$400$	134144.			0.0419200
$401$			1.58612e6i			0.492577i	0.969196	+	0.246289i	$0.0792112\pi$
$401$			1.58612e6i			0.492577i	−0.969196	+	0.246289i	$0.920789\pi$
$402$	−1.18622e6			−0.366102
$403$	−1.12601e6	+	5.75515e6i	−0.345365	+	1.76520i
$404$	1.80998e6			0.551723
$405$			1.81514e6i			0.549886i
$406$	−1.72368e6			−0.518969
$407$	−1.04508e6			−0.312726
$408$		−	916032.i		−	0.272433i
$409$		−	6.44192e6i		−	1.90418i	−0.305825	−	0.952088i	$-0.598932\pi$
$409$		−	6.44192e6i		−	1.90418i	0.305825	−	0.952088i	$-0.401068\pi$
$410$			1.93392e6i			0.568171i
$411$		−	828594.i		−	0.241956i
$412$	−400736.			−0.116310
$413$	4.29849e6			1.24005
$414$		−	310800.i		−	0.0891210i
$415$	−2.82836e6			−0.806147
$416$	119808.	−	612352.i	0.0339432	−	0.173487i
$417$	−179933.			−0.0506723
$418$			561600.i			0.157212i
$419$	−4.30545e6			−1.19807			−0.599037	−	0.800721i	$-0.704450\pi$
$419$	−4.30545e6			−1.19807			−0.599037	+	0.800721i	$0.704450\pi$
$420$	−1.11384e6			−0.308106
$421$		−	1.51346e6i		−	0.416164i	−0.978111	−	0.208082i	$-0.933278\pi$
$421$		−	1.51346e6i		−	0.416164i	0.978111	−	0.208082i	$-0.0667221\pi$
$422$		−	1.35892e6i		−	0.371462i
$423$		−	217782.i		−	0.0591795i
$424$			48000.0i			0.0129666i
$425$	−576924.			−0.154934
$426$	−3.31453e6			−0.884908
$427$			6.08160e6i			1.61417i
$428$	−398784.			−0.105227
$429$	182520.	−	932880.i	0.0478814	−	0.244727i
$430$	2.03898e6			0.531792
$431$			1.43116e6i			0.371105i	0.982634	+	0.185552i	$0.0594074\pi$
$431$			1.43116e6i			0.371105i	−0.982634	+	0.185552i	$0.940593\pi$
$432$	1.05498e6			0.271978
$433$	429613.			0.110118			0.0550589	−	0.998483i	$-0.482465\pi$
$433$	429613.			0.110118			0.0550589	+	0.998483i	$0.482465\pi$
$434$		−	4.04208e6i		−	1.03010i
$435$		−	2.72095e6i		−	0.689442i
$436$			2.31730e6i			0.583802i
$437$			1.22850e6i			0.307731i
$438$	−3.06103e6			−0.762399
$439$	552038.			0.136712			0.0683562	−	0.997661i	$-0.478225\pi$
$439$	552038.			0.136712			0.0683562	+	0.997661i	$0.478225\pi$
$440$			391680.i			0.0964494i
$441$	−427868.			−0.104764
$442$	−515268.	+	2.63359e6i	−0.125452	+	0.641199i
$443$	2.15255e6			0.521128			0.260564	−	0.965457i	$-0.416092\pi$
$443$	2.15255e6			0.521128			0.260564	+	0.965457i	$0.416092\pi$
$444$		−	1.81147e6i		−	0.436088i
$445$	5.34368e6			1.27921
$446$	2.49503e6			0.593934
$447$		−	3.59354e6i		−	0.850655i
$448$			430080.i			0.101240i
$449$		−	1.40429e6i		−	0.328731i	−0.986400	−	0.164365i	$-0.947442\pi$
$449$		−	1.40429e6i		−	0.328731i	0.986400	−	0.164365i	$-0.0525576\pi$
$450$		−	155104.i		−	0.0361070i
$451$	1.13760e6			0.263359
$452$	−1.60426e6			−0.369341
$453$		−	4.17733e6i		−	0.956430i
$454$	−710448.			−0.161768
$455$	3.20229e6	+	626535.i	0.725157	+	0.141879i
$456$	−973440.			−0.219229
$457$			1.32818e6i			0.297485i	0.988876	+	0.148743i	$0.0475226\pi$
$457$			1.32818e6i			0.297485i	−0.988876	+	0.148743i	$0.952477\pi$
$458$	−4.74820e6			−1.05771
$459$	−4.53722e6			−1.00521
$460$			856800.i			0.188793i
$461$		−	5.89070e6i		−	1.29096i	−0.763775	−	0.645482i	$-0.776656\pi$
$461$		−	5.89070e6i		−	1.29096i	0.763775	−	0.645482i	$-0.223344\pi$
$462$			655200.i			0.142813i
$463$		−	2.37139e6i		−	0.514104i	−0.966398	−	0.257052i	$-0.917249\pi$
$463$		−	2.37139e6i		−	0.514104i	0.966398	−	0.257052i	$-0.0827511\pi$
$464$	−1.05062e6			−0.226544
$465$	6.38071e6			1.36847
$466$		−	449268.i		−	0.0958387i
$467$	7.17827e6			1.52310			0.761548	−	0.648108i	$-0.224440\pi$
$467$	7.17827e6			1.52310			0.761548	+	0.648108i	$0.224440\pi$
$468$	−708032.	−	138528.i	−0.149430	−	0.0292363i
$469$	−2.39526e6			−0.502829
$470$			600372.i			0.125365i
$471$	−4.41358e6			−0.916724
$472$	2.62003e6			0.541317
$473$		−	1.19940e6i		−	0.246497i
$474$		−	3.28650e6i		−	0.671875i
$475$			613080.i			0.124676i
$476$		−	1.84968e6i		−	0.374179i
$477$	55500.0			0.0111686
$478$	−4.79221e6			−0.959326
$479$		−	7.25193e6i		−	1.44416i	−0.691810	−	0.722079i	$-0.743186\pi$
$479$		−	7.25193e6i		−	1.44416i	0.691810	−	0.722079i	$-0.256814\pi$
$480$	−678912.			−0.134496
$481$	−1.01895e6	+	5.20798e6i	−0.200813	+	1.02638i
$482$	4.66514e6			0.914634
$483$			1.43325e6i			0.279547i
$484$	−2.34642e6			−0.455294
$485$	−8.18305e6			−1.57965
$486$		−	2.15488e6i		−	0.413840i
$487$			2.53364e6i			0.484087i	0.970265	+	0.242043i	$0.0778176\pi$
$487$			2.53364e6i			0.484087i	−0.970265	+	0.242043i	$0.922182\pi$
$488$			3.70688e6i			0.704626i
$489$		−	5.14433e6i		−	0.972875i
$490$	1.17953e6			0.221931
$491$	8.46186e6			1.58403			0.792013	−	0.610504i	$-0.209033\pi$
$491$	8.46186e6			1.58403			0.792013	+	0.610504i	$0.209033\pi$
$492$			1.97184e6i			0.367248i
$493$	4.51850e6			0.837293
$494$	2.79864e6	+	547560.i	0.515976	+	0.100952i
$495$	452880.			0.0830750
$496$		−	2.46374e6i		−	0.449667i
$497$	−6.69280e6			−1.21539
$498$	−2.88382e6			−0.521068
$499$			1.95383e6i			0.351265i	0.984456	+	0.175633i	$0.0561971\pi$
$499$			1.95383e6i			0.351265i	−0.984456	+	0.175633i	$0.943803\pi$
$500$			2.97758e6i			0.532646i
$501$			5.54720e6i			0.987370i
$502$			2.59598e6i			0.459772i
$503$	119778.			0.0211085			0.0105542	−	0.999944i	$-0.496640\pi$
$503$	119778.			0.0211085			0.0105542	+	0.999944i	$0.496640\pi$
$504$	497280.			0.0872016
$505$			5.76932e6i			1.00669i
$506$	504000.			0.0875093
$507$	−4.47090e6	−	1.81912e6i	−0.772457	−	0.314297i
$508$	3.24406e6			0.557738
$509$			1.03653e7i			1.77332i	0.462420	+	0.886661i	$0.346981\pi$
$509$			1.03653e7i			1.77332i	−0.462420	+	0.886661i	$0.653019\pi$
$510$	2.91985e6			0.497090
$511$	−6.18093e6			−1.04713
$512$			262144.i			0.0441942i
$513$			4.82157e6i			0.808900i
$514$		−	3.78354e6i		−	0.631670i
$515$		−	1.27735e6i		−	0.212222i
$516$	2.07896e6			0.343734
$517$	353160.			0.0581092
$518$		−	3.65778e6i		−	0.598954i
$519$	−208338.			−0.0339508
$520$	1.95187e6	+	381888.i	0.316550	+	0.0619338i
$521$	−1.04899e7			−1.69307			−0.846537	−	0.532330i	$-0.821316\pi$
$521$	−1.04899e7			−1.69307			−0.846537	+	0.532330i	$0.821316\pi$
$522$			1.21478e6i			0.195129i
$523$	4.42662e6			0.707649			0.353824	−	0.935312i	$-0.384881\pi$
$523$	4.42662e6			0.707649			0.353824	+	0.935312i	$0.384881\pi$
$524$	4.86168e6			0.773496
$525$			715260.i			0.113257i
$526$			4.04890e6i			0.638076i
$527$			1.05960e7i			1.66194i
$528$			399360.i			0.0623419i
$529$	−5.33384e6			−0.828707
$530$	−153000.			−0.0236593
$531$		−	3.02941e6i		−	0.466253i
$532$	−1.96560e6			−0.301104
$533$	1.10916e6	−	5.66904e6i	0.169113	−	0.864354i
$534$	5.44846e6			0.826838
$535$		−	1.27112e6i		−	0.192001i
$536$	−1.45997e6			−0.219498
$537$	8.97058e6			1.34241
$538$		−	4.07088e6i		−	0.606363i
$539$		−	693840.i		−	0.102870i
$540$			3.36274e6i			0.496259i
$541$		−	2.26377e6i		−	0.332536i	−0.986081	−	0.166268i	$-0.946828\pi$
$541$		−	2.26377e6i		−	0.332536i	0.986081	−	0.166268i	$-0.0531717\pi$
$542$	1.85384e6			0.271066
$543$	1.25421e6			0.182546
$544$		−	1.12742e6i		−	0.163339i
$545$	−7.38638e6			−1.06522
$546$	3.26508e6	+	638820.i	0.468719	+	0.0917058i
$547$	7.21090e6			1.03044			0.515218	−	0.857059i	$-0.327711\pi$
$547$	7.21090e6			1.03044			0.515218	+	0.857059i	$0.327711\pi$
$548$		−	1.01981e6i		−	0.145066i
$549$	4.28608e6			0.606917
$550$	251520.			0.0354540
$551$		−	4.80168e6i		−	0.673774i
$552$			873600.i			0.122030i
$553$		−	6.63621e6i		−	0.922799i
$554$			1.33011e6i			0.184125i
$555$	5.77407e6			0.795700
$556$	−221456.			−0.0303809
$557$		−	273507.i		−	0.0373534i	−0.999826	−	0.0186767i	$-0.994055\pi$
$557$		−	273507.i		−	0.0373534i	0.999826	−	0.0186767i	$-0.00594533\pi$
$558$	−2.84870e6			−0.387313
$559$	−5.97701e6	−	1.16942e6i	−0.809011	−	0.158285i
$560$	−1.37088e6			−0.184727
$561$		−	1.71756e6i		−	0.230412i
$562$	−196488.			−0.0262419
$563$	−959349.			−0.127557			−0.0637787	−	0.997964i	$-0.520315\pi$
$563$	−959349.			−0.127557			−0.0637787	+	0.997964i	$0.520315\pi$
$564$			612144.i			0.0810319i
$565$		−	5.11357e6i		−	0.673911i
$566$		−	6.23394e6i		−	0.817940i
$567$			3.73706e6i			0.488171i
$568$	−4.07942e6			−0.530552
$569$	−1.19403e7			−1.54609			−0.773044	−	0.634352i	$-0.781267\pi$
$569$	−1.19403e7			−1.54609			−0.773044	+	0.634352i	$0.781267\pi$
$570$		−	3.10284e6i		−	0.400011i
$571$	7.20205e6			0.924413			0.462206	−	0.886772i	$-0.347058\pi$
$571$	7.20205e6			0.924413			0.462206	+	0.886772i	$0.347058\pi$
$572$	224640.	−	1.14816e6i	0.0287076	−	0.146728i
$573$	−9.20634e6			−1.17139
$574$			3.98160e6i			0.504403i
$575$	550200.			0.0693986
$576$	303104.			0.0380658
$577$			1.66990e6i			0.208810i	0.994535	+	0.104405i	$0.0332938\pi$
$577$			1.66990e6i			0.208810i	−0.994535	+	0.104405i	$0.966706\pi$
$578$		−	830624.i		−	0.103415i
$579$		−	4.52221e6i		−	0.560601i
$580$		−	3.34886e6i		−	0.413359i
$581$	−5.82309e6			−0.715671
$582$	−8.34350e6			−1.02104
$583$			90000.0i			0.0109666i
$584$	−3.76742e6			−0.457101
$585$	441558.	−	2.25685e6i	0.0533455	−	0.272655i
$586$	−873852.			−0.105122
$587$		−	8.29913e6i		−	0.994117i	−0.867717	−	0.497059i	$-0.834413\pi$
$587$		−	8.29913e6i		−	0.994117i	0.867717	−	0.497059i	$-0.165587\pi$
$588$	1.20266e6			0.143449
$589$	1.12601e7			1.33738
$590$			8.35135e6i			0.987704i
$591$			1.16947e7i			1.37727i
$592$		−	2.22950e6i		−	0.261459i
$593$			4.48969e6i			0.524300i	0.965027	+	0.262150i	$0.0844315\pi$
$593$			4.48969e6i			0.524300i	−0.965027	+	0.262150i	$0.915568\pi$
$594$	1.97808e6			0.230026
$595$	5.89586e6			0.682738
$596$		−	4.42282e6i		−	0.510015i
$597$	−1.86051e6			−0.213646
$598$	491400.	−	2.51160e6i	0.0561930	−	0.287209i
$599$	1.38261e6			0.157446			0.0787232	−	0.996897i	$-0.474916\pi$
$599$	1.38261e6			0.157446			0.0787232	+	0.996897i	$0.474916\pi$
$600$			435968.i			0.0494398i
$601$	1.04021e7			1.17472			0.587359	−	0.809327i	$-0.300168\pi$
$601$	1.04021e7			1.17472			0.587359	+	0.809327i	$0.300168\pi$
$602$	4.19790e6			0.472107
$603$			1.68809e6i			0.189061i
$604$		−	5.14133e6i		−	0.573433i
$605$		−	7.47920e6i		−	0.830743i
$606$			5.88245e6i			0.650694i
$607$	−4.78668e6			−0.527306			−0.263653	−	0.964618i	$-0.584927\pi$
$607$	−4.78668e6			−0.527306			−0.263653	+	0.964618i	$0.584927\pi$
$608$	−1.19808e6			−0.131440
$609$		−	5.60196e6i		−	0.612064i
$610$	−1.18157e7			−1.28568
$611$	344331.	−	1.75991e6i	0.0373141	−	0.190717i
$612$	−1.30358e6			−0.140689
$613$		−	1.04783e7i		−	1.12627i	−0.826366	−	0.563134i	$-0.809596\pi$
$613$		−	1.04783e7i		−	1.12627i	0.826366	−	0.563134i	$-0.190404\pi$
$614$	1.28441e6			0.137493
$615$	−6.28524e6			−0.670091
$616$			806400.i			0.0856246i
$617$			1.79106e7i			1.89407i	0.321128	+	0.947036i	$0.395938\pi$
$617$			1.79106e7i			1.89407i	−0.321128	+	0.947036i	$0.604062\pi$
$618$		−	1.30239e6i		−	0.137174i
$619$			4.43222e6i			0.464938i	0.972604	+	0.232469i	$0.0746804\pi$
$619$			4.43222e6i			0.464938i	−0.972604	+	0.232469i	$0.925320\pi$
$620$	7.85318e6			0.820477
$621$	4.32705e6			0.450260
$622$			1.33490e7i			1.38348i
$623$	1.10017e7			1.13564
$624$	1.99014e6	+	389376.i	0.204608	+	0.0400320i
$625$	−7.85355e6			−0.804203
$626$			4.66270e6i			0.475556i
$627$	−1.82520e6			−0.185414
$628$	−5.43210e6			−0.549627
$629$			9.58861e6i			0.966338i
$630$			1.58508e6i			0.159111i
$631$		−	1.43291e7i		−	1.43267i	−0.697756	−	0.716335i	$-0.745818\pi$
$631$		−	1.43291e7i		−	1.43267i	0.697756	−	0.716335i	$-0.254182\pi$
$632$		−	4.04493e6i		−	0.402827i
$633$	4.41650e6			0.438096
$634$	294072.			0.0290556
$635$			1.03405e7i			1.01767i
$636$	−156000.			−0.0152926
$637$	−3.45764e6	−	676494.i	−0.337622	−	0.0660565i
$638$	−1.96992e6			−0.191601
$639$			4.71683e6i			0.456981i
$640$	−835584.			−0.0806381
$641$	6.65869e6			0.640094			0.320047	−	0.947402i	$-0.396301\pi$
$641$	6.65869e6			0.640094			0.320047	+	0.947402i	$0.396301\pi$
$642$		−	1.29605e6i		−	0.124103i
$643$		−	1.55224e7i		−	1.48058i	−0.672286	−	0.740291i	$-0.734688\pi$
$643$		−	1.55224e7i		−	1.48058i	0.672286	−	0.740291i	$-0.265312\pi$
$644$			1.76400e6i			0.167604i
$645$			6.62668e6i			0.627187i
$646$	5.15268e6			0.485794
$647$	−2.44454e6			−0.229581			−0.114791	−	0.993390i	$-0.536620\pi$
$647$	−2.44454e6			−0.229581			−0.114791	+	0.993390i	$0.536620\pi$
$648$			2.27782e6i			0.213100i
$649$	4.91256e6			0.457821
$650$	245232.	−	1.25341e6i	0.0227664	−	0.116361i
$651$	1.31368e7			1.21489
$652$		−	6.33149e6i		−	0.583293i
$653$	1.16500e7			1.06916			0.534580	−	0.845118i	$-0.320470\pi$
$653$	1.16500e7			1.06916			0.534580	+	0.845118i	$0.320470\pi$
$654$	−7.53121e6			−0.688526
$655$			1.54966e7i			1.41135i
$656$			2.42688e6i			0.220185i
$657$			4.35608e6i			0.393716i
$658$			1.23606e6i			0.111295i
$659$	1.33185e7			1.19465			0.597326	−	0.801999i	$-0.296230\pi$
$659$	1.33185e7			1.19465			0.597326	+	0.801999i	$0.296230\pi$
$660$	−1.27296e6			−0.113751
$661$			1.35722e7i			1.20822i	0.796900	+	0.604112i	$0.206472\pi$
$661$			1.35722e7i			1.20822i	−0.796900	+	0.604112i	$0.793528\pi$
$662$	2.53073e6			0.224440
$663$	−8.55917e6	−	1.67462e6i	−0.756220	−	0.147956i
$664$	−3.54931e6			−0.312409
$665$		−	6.26535e6i		−	0.549403i
$666$	−2.57786e6			−0.225203
$667$	−4.30920e6			−0.375044
$668$			6.82733e6i			0.591984i
$669$			8.10884e6i			0.700476i
$670$		−	4.65365e6i		−	0.400504i
$671$			6.95040e6i			0.595941i
$672$	−1.39776e6			−0.119401
$673$	−1.58674e7			−1.35042			−0.675209	−	0.737626i	$-0.735947\pi$
$673$	−1.58674e7			−1.35042			−0.675209	+	0.737626i	$0.735947\pi$
$674$		−	1.30737e6i		−	0.110854i
$675$	2.15940e6			0.182421
$676$	−5.50264e6	−	2.23891e6i	−0.463132	−	0.188439i
$677$	−2.24264e7			−1.88056			−0.940281	−	0.340398i	$-0.889438\pi$
$677$	−2.24264e7			−1.88056			−0.940281	+	0.340398i	$0.889438\pi$
$678$		−	5.21383e6i		−	0.435595i
$679$	−1.68475e7			−1.40236
$680$	3.59366e6			0.298034
$681$		−	2.30896e6i		−	0.190787i
$682$		−	4.61952e6i		−	0.380308i
$683$		−	8.11034e6i		−	0.665254i	−0.943059	−	0.332627i	$-0.892065\pi$
$683$		−	8.11034e6i		−	0.665254i	0.943059	−	0.332627i	$-0.107935\pi$
$684$			1.38528e6i			0.113213i
$685$	3.25064e6			0.264693
$686$	9.48738e6			0.769726
$687$		−	1.54316e7i		−	1.24744i
$688$	2.55872e6			0.206088
$689$	448500.	+	87750.0i	0.0359927	+	0.00704205i
$690$	−2.78460e6			−0.222659
$691$		−	2.00020e7i		−	1.59359i	−0.604246	−	0.796797i	$-0.706526\pi$
$691$		−	2.00020e7i		−	1.59359i	0.604246	−	0.796797i	$-0.293474\pi$
$692$	−256416.			−0.0203554
$693$	932400.			0.0737512
$694$			1.18510e7i			0.934020i
$695$		−	705891.i		−	0.0554339i
$696$		−	3.41453e6i		−	0.267182i
$697$		−	1.04375e7i		−	0.813793i
$698$	3.46530e6			0.269217
$699$	1.46012e6			0.113031
$700$			880320.i			0.0679040i
$701$	−2.22272e6			−0.170840			−0.0854200	−	0.996345i	$-0.527223\pi$
$701$	−2.22272e6			−0.170840			−0.0854200	+	0.996345i	$0.527223\pi$
$702$	1.92863e6	−	9.85743e6i	0.147709	−	0.754955i
$703$	1.01895e7			0.777617
$704$			491520.i			0.0373774i
$705$	−1.95121e6			−0.147853
$706$	6.65162e6			0.502245
$707$			1.18780e7i			0.893708i
$708$			8.51510e6i			0.638420i
$709$		−	2.03634e7i		−	1.52137i	−0.649122	−	0.760684i	$-0.724864\pi$
$709$		−	2.03634e7i		−	1.52137i	0.649122	−	0.760684i	$-0.275136\pi$
$710$		−	1.30032e7i		−	0.968062i
$711$	−4.67695e6			−0.346967
$712$	6.70579e6			0.495736
$713$		−	1.01052e7i		−	0.744425i
$714$	6.01146e6			0.441301
$715$	3.65976e6	+	716040.i	0.267724	+	0.0523808i
$716$	1.10407e7			0.804850
$717$		−	1.55747e7i		−	1.13141i
$718$	2.50214e6			0.181135
$719$	−1.98255e7			−1.43022			−0.715108	−	0.699014i	$-0.753623\pi$
$719$	−1.98255e7			−1.43022			−0.715108	+	0.699014i	$0.753623\pi$
$720$			966144.i			0.0694561i
$721$		−	2.62983e6i		−	0.188404i
$722$			4.42880e6i			0.316186i
$723$			1.51617e7i			1.07870i
$724$	1.54365e6			0.109446
$725$	−2.15050e6			−0.151948
$726$		−	7.62585e6i		−	0.536966i
$727$	−9.24667e6			−0.648857			−0.324429	−	0.945910i	$-0.605172\pi$
$727$	−9.24667e6			−0.648857			−0.324429	+	0.945910i	$0.605172\pi$
$728$	4.01856e6	+	786240.i	0.281023	+	0.0549828i
$729$	1.56520e7			1.09081
$730$		−	1.20087e7i		−	0.834041i
$731$	−1.10045e7			−0.761687
$732$	−1.20474e7			−0.831025
$733$			1.48114e7i			1.01821i	0.860704	+	0.509105i	$0.170024\pi$
$733$			1.48114e7i			1.01821i	−0.860704	+	0.509105i	$0.829976\pi$
$734$			4.33309e6i			0.296864i
$735$			3.83347e6i			0.261742i
$736$			1.07520e6i			0.0731635i
$737$	−2.73744e6			−0.185642
$738$	2.80608e6			0.189653
$739$			5.67210e6i			0.382061i	0.981584	+	0.191031i	$0.0611830\pi$
$739$			5.67210e6i			0.382061i	−0.981584	+	0.191031i	$0.938817\pi$
$740$	7.10654e6			0.477067
$741$	−1.77957e6	+	9.09558e6i	−0.119061	+	0.608534i
$742$	−315000.			−0.0210039
$743$			2.75704e7i			1.83219i	0.400960	+	0.916095i	$0.368677\pi$
$743$			2.75704e7i			1.83219i	−0.400960	+	0.916095i	$0.631323\pi$
$744$	8.00717e6			0.530330
$745$	1.40977e7			0.930590
$746$		−	7.15582e6i		−	0.470774i
$747$			4.10389e6i			0.269088i
$748$		−	2.11392e6i		−	0.138145i
$749$		−	2.61702e6i		−	0.170452i
$750$	−9.67715e6			−0.628195
$751$	−4.09636e6			−0.265032			−0.132516	−	0.991181i	$-0.542306\pi$
$751$	−4.09636e6			−0.265032			−0.132516	+	0.991181i	$0.542306\pi$
$752$			753408.i			0.0485831i
$753$	−8.43695e6			−0.542248
$754$	−1.92067e6	+	9.81677e6i	−0.123034	+	0.628840i
$755$	1.63880e7			1.04630
$756$			6.92328e6i			0.440562i
$757$	1.09396e7			0.693844			0.346922	−	0.937894i	$-0.387227\pi$
$757$	1.09396e7			0.693844			0.346922	+	0.937894i	$0.387227\pi$
$758$	3.47446e6			0.219641
$759$			1.63800e6i			0.103207i
$760$		−	3.81888e6i		−	0.239829i
$761$		−	1.36940e6i		−	0.0857172i	−0.999081	−	0.0428586i	$-0.986354\pi$
$761$		−	1.36940e6i		−	0.0857172i	0.999081	−	0.0428586i	$-0.0136465\pi$
$762$			1.05432e7i			0.657787i
$763$	−1.52073e7			−0.945670
$764$	−1.13309e7			−0.702312
$765$		−	4.15517e6i		−	0.256706i
$766$	−4.31886e6			−0.265948
$767$	4.78975e6	−	2.44809e7i	0.293984	−	1.50259i
$768$	−851968.			−0.0521219
$769$			1.08375e7i			0.660867i	0.943829	+	0.330433i	$0.107195\pi$
$769$			1.08375e7i			0.660867i	−0.943829	+	0.330433i	$0.892805\pi$
$770$	−2.57040e6			−0.156233
$771$	1.22965e7			0.744982
$772$		−	5.56579e6i		−	0.336112i
$773$			2.05445e7i			1.23665i	0.785922	+	0.618325i	$0.212188\pi$
$773$			2.05445e7i			1.23665i	−0.785922	+	0.618325i	$0.787812\pi$
$774$		−	2.95852e6i		−	0.177510i
$775$		−	5.04298e6i		−	0.301601i
$776$	−1.02689e7			−0.612168
$777$	1.18878e7			0.706396
$778$			5.15287e6i			0.305211i
$779$	−1.10916e7			−0.654863
$780$	−1.24114e6	+	6.34358e6i	−0.0730437	+	0.373335i
$781$	−7.64892e6			−0.448717
$782$		−	4.62420e6i		−	0.270408i
$783$	−1.69126e7			−0.985838
$784$	1.48019e6			0.0860058
$785$		−	1.73148e7i		−	1.00287i
$786$			1.58005e7i			0.912249i
$787$			1.34637e7i			0.774869i	0.921897	+	0.387435i	$0.126639\pi$
$787$			1.34637e7i			0.774869i	−0.921897	+	0.387435i	$0.873361\pi$
$788$			1.43934e7i			0.825750i
$789$	−1.31589e7			−0.752536
$790$	1.28932e7			0.735010
$791$		−	1.05279e7i		−	0.598276i
$792$	568320.			0.0321944
$793$	3.46362e7	+	6.77664e6i	1.95590	+	0.382676i
$794$	−2.18764e7			−1.23147
$795$		−	497250.i		−	0.0279034i
$796$	−2.28986e6			−0.128093
$797$	2.02451e7			1.12895			0.564475	−	0.825450i	$-0.309079\pi$
$797$	2.02451e7			1.12895			0.564475	+	0.825450i	$0.309079\pi$
$798$		−	6.38820e6i		−	0.355117i
$799$		−	3.24024e6i		−	0.179560i
$800$			536576.i			0.0296419i
$801$		−	7.75357e6i		−	0.426993i
$802$	−6.34447e6			−0.348305
$803$	−7.06392e6			−0.386596
$804$		−	4.74490e6i		−	0.258873i
$805$	−5.62275e6			−0.305815
$806$	−2.30206e7	−	4.50403e6i	−1.24819	−	0.244210i
$807$	1.32304e7			0.715135
$808$			7.23994e6i			0.390127i
$809$	2.48958e7			1.33738			0.668689	−	0.743542i	$-0.266856\pi$
$809$	2.48958e7			1.33738			0.668689	+	0.743542i	$0.266856\pi$
$810$	−7.26056e6			−0.388828
$811$			2.53328e7i			1.35248i	0.736681	+	0.676241i	$0.236392\pi$
$811$			2.53328e7i			1.35248i	−0.736681	+	0.676241i	$0.763608\pi$
$812$		−	6.89472e6i		−	0.366967i
$813$			6.02499e6i			0.319691i
$814$		−	4.18032e6i		−	0.221130i
$815$	2.01816e7			1.06429
$816$	3.66413e6			0.192639
$817$			1.16942e7i			0.612934i
$818$	2.57677e7			1.34646
$819$	909090.	−	4.64646e6i	0.0473584	−	0.242054i
$820$	−7.73568e6			−0.401757
$821$			1.25922e7i			0.651993i	0.945371	+	0.325996i	$0.105700\pi$
$821$			1.25922e7i			0.651993i	−0.945371	+	0.325996i	$0.894300\pi$
$822$	3.31438e6			0.171089
$823$	−3.32776e7			−1.71259			−0.856294	−	0.516490i	$-0.827239\pi$
$823$	−3.32776e7			−1.71259			−0.856294	+	0.516490i	$0.827239\pi$
$824$		−	1.60294e6i		−	0.0822433i
$825$			817440.i			0.0418139i
$826$			1.71940e7i			0.876851i
$827$		−	2.98630e7i		−	1.51834i	−0.650891	−	0.759171i	$-0.725604\pi$
$827$		−	2.98630e7i		−	1.51834i	0.650891	−	0.759171i	$-0.274396\pi$
$828$	1.24320e6			0.0630181
$829$	3.04980e7			1.54129			0.770647	−	0.637262i	$-0.219933\pi$
$829$	3.04980e7			1.54129			0.770647	+	0.637262i	$0.219933\pi$
$830$		−	1.13134e7i		−	0.570032i
$831$	−4.32286e6			−0.217155
$832$	2.44941e6	+	479232.i	0.122674	+	0.0240015i
$833$	−6.36598e6			−0.317872
$834$		−	719732.i		−	0.0358307i
$835$	−2.17621e7			−1.08015
$836$	−2.24640e6			−0.111166
$837$		−	3.96605e7i		−	1.95679i
$838$		−	1.72218e7i		−	0.847167i
$839$			1.46249e7i			0.717278i	0.933476	+	0.358639i	$0.116759\pi$
$839$			1.46249e7i			0.717278i	−0.933476	+	0.358639i	$0.883241\pi$
$840$		−	4.45536e6i		−	0.217864i
$841$	−3.66833e6			−0.178846
$842$	6.05382e6			0.294272
$843$		−	638586.i		−	0.0309493i
$844$	5.43570e6			0.262663
$845$	7.13653e6	−	1.75397e7i	0.343831	−	0.845044i
$846$	871128.			0.0418462
$847$		−	1.53984e7i		−	0.737506i
$848$	−192000.			−0.00916878
$849$	2.02603e7			0.964665
$850$		−	2.30770e6i		−	0.109555i
$851$		−	9.14445e6i		−	0.432846i
$852$		−	1.32581e7i		−	0.625725i
$853$			1.54032e7i			0.724832i	0.932016	+	0.362416i	$0.118048\pi$
$853$			1.54032e7i			0.724832i	−0.932016	+	0.362416i	$0.881952\pi$
$854$	−2.43264e7			−1.14139
$855$	−4.41558e6			−0.206572
$856$		−	1.59514e6i		−	0.0744069i
$857$	−2.59910e7			−1.20884			−0.604422	−	0.796664i	$-0.706596\pi$
$857$	−2.59910e7			−1.20884			−0.604422	+	0.796664i	$0.706596\pi$
$858$	3.73152e6	+	730080.i	0.173048	+	0.0338573i
$859$	1.26690e7			0.585815			0.292908	−	0.956141i	$-0.405377\pi$
$859$	1.26690e7			0.585815			0.292908	+	0.956141i	$0.405377\pi$
$860$			8.15592e6i			0.376034i
$861$	−1.29402e7			−0.594885
$862$	−5.72466e6			−0.262411
$863$		−	3.93618e7i		−	1.79907i	−0.436849	−	0.899535i	$-0.643906\pi$
$863$		−	3.93618e7i		−	1.79907i	0.436849	−	0.899535i	$-0.356094\pi$
$864$			4.21990e6i			0.192317i
$865$		−	817326.i		−	0.0371411i
$866$			1.71845e6i			0.0778651i
$867$	2.69953e6			0.121966
$868$	1.61683e7			0.728393
$869$		−	7.58424e6i		−	0.340693i
$870$	1.08838e7			0.487509
$871$	−2.66900e6	+	1.36416e7i	−0.119208	+	0.609283i
$872$	−9.26918e6			−0.412810
$873$			1.18734e7i			0.527280i
$874$	−4.91400e6			−0.217599
$875$	−1.95404e7			−0.862806
$876$		−	1.22441e7i		−	0.539098i
$877$		−	2.93636e7i		−	1.28917i	−0.764532	−	0.644585i	$-0.777030\pi$
$877$		−	2.93636e7i		−	1.28917i	0.764532	−	0.644585i	$-0.222970\pi$
$878$			2.20815e6i			0.0966702i
$879$		−	2.84002e6i		−	0.123979i
$880$	−1.56672e6			−0.0682001
$881$	−2.47421e7			−1.07398			−0.536990	−	0.843589i	$-0.680439\pi$
$881$	−2.47421e7			−1.07398			−0.536990	+	0.843589i	$0.680439\pi$
$882$		−	1.71147e6i		−	0.0740796i
$883$	1.56178e7			0.674092			0.337046	−	0.941488i	$-0.390572\pi$
$883$	1.56178e7			0.674092			0.337046	+	0.941488i	$0.390572\pi$
$884$	−1.05344e7	−	2.06107e6i	−0.453396	−	0.0887079i
$885$	−2.71419e7			−1.16488
$886$			8.61020e6i			0.368493i
$887$	1.41193e6			0.0602566			0.0301283	−	0.999546i	$-0.490408\pi$
$887$	1.41193e6			0.0602566			0.0301283	+	0.999546i	$0.490408\pi$
$888$	7.24589e6			0.308361
$889$			2.12892e7i			0.903450i
$890$			2.13747e7i			0.904535i
$891$			4.27092e6i			0.180230i
$892$			9.98011e6i			0.419975i
$893$	−3.44331e6			−0.144493
$894$	1.43742e7			0.601504
$895$			3.51923e7i			1.46855i
$896$	−1.72032e6			−0.0715878
$897$	8.16270e6	+	1.59705e6i	0.338729	+	0.0662731i
$898$	5.61715e6			0.232448
$899$			3.94969e7i			1.62991i
$900$	620416.			0.0255315
$901$	825750.			0.0338873
$902$			4.55040e6i			0.186223i
$903$			1.36432e7i			0.556796i
$904$		−	6.41702e6i		−	0.261164i
$905$			4.92038e6i			0.199700i
$906$	1.67093e7			0.676298
$907$	−1.48543e7			−0.599563			−0.299781	−	0.954008i	$-0.596914\pi$
$907$	−1.48543e7			−0.599563			−0.299781	+	0.954008i	$0.596914\pi$
$908$		−	2.84179e6i		−	0.114387i
$909$	8.37118e6			0.336029
$910$	−2.50614e6	+	1.28092e7i	−0.100323	+	0.512764i
$911$	4.29118e7			1.71309			0.856547	−	0.516069i	$-0.172605\pi$
$911$	4.29118e7			1.71309			0.856547	+	0.516069i	$0.172605\pi$
$912$		−	3.89376e6i		−	0.155018i
$913$	−6.65496e6			−0.264222
$914$	−5.31271e6			−0.210354
$915$		−	3.84010e7i		−	1.51631i
$916$		−	1.89928e7i		−	0.747911i
$917$			3.19048e7i			1.25295i
$918$		−	1.81489e7i		−	0.710793i
$919$	4.34706e7			1.69788			0.848939	−	0.528491i	$-0.177242\pi$
$919$	4.34706e7			1.69788			0.848939	+	0.528491i	$0.177242\pi$
$920$	−3.42720e6			−0.133497
$921$			4.17433e6i			0.162158i
$922$	2.35628e7			0.912850
$923$	−7.45770e6	+	3.81171e7i	−0.288138	+	1.47271i
$924$	−2.62080e6			−0.100984
$925$		−	4.56352e6i		−	0.175366i
$926$	9.48557e6			0.363526
$927$	−1.85340e6			−0.0708387
$928$		−	4.20250e6i		−	0.160191i
$929$		−	2.97375e7i		−	1.13049i	−0.824925	−	0.565243i	$-0.808783\pi$
$929$		−	2.97375e7i		−	1.13049i	0.824925	−	0.565243i	$-0.191217\pi$
$930$			2.55228e7i			0.967658i
$931$			6.76494e6i			0.255794i
$932$	1.79707e6			0.0677682
$933$	−4.33843e7			−1.63166
$934$			2.87131e7i			1.07699i
$935$	6.73812e6			0.252063
$936$	554112.	−	2.83213e6i	0.0206732	−	0.105663i
$937$	1.46550e7			0.545303			0.272651	−	0.962113i	$-0.412099\pi$
$937$	1.46550e7			0.545303			0.272651	+	0.962113i	$0.412099\pi$
$938$		−	9.58104e6i		−	0.355554i
$939$	−1.51538e7			−0.560863
$940$	−2.40149e6			−0.0886463
$941$		−	8.80233e6i		−	0.324059i	−0.986786	−	0.162029i	$-0.948196\pi$
$941$		−	8.80233e6i		−	0.324059i	0.986786	−	0.162029i	$-0.0518039\pi$
$942$		−	1.76543e7i		−	0.648222i
$943$			9.95400e6i			0.364518i
$944$			1.04801e7i			0.382769i
$945$	−2.20680e7			−0.803864
$946$	4.79760e6			0.174300
$947$		−	9.00847e6i		−	0.326420i	−0.986591	−	0.163210i	$-0.947815\pi$
$947$		−	9.00847e6i		−	0.326420i	0.986591	−	0.163210i	$-0.0521847\pi$
$948$	1.31460e7			0.475087
$949$	−6.88732e6	+	3.52019e7i	−0.248247	+	1.26882i
$950$	−2.45232e6			−0.0881593
$951$			955734.i			0.0342678i
$952$	7.39872e6			0.264584
$953$	1.31122e7			0.467675			0.233837	−	0.972276i	$-0.424872\pi$
$953$	1.31122e7			0.467675			0.233837	+	0.972276i	$0.424872\pi$
$954$			222000.i			0.00789736i
$955$		−	3.61172e7i		−	1.28146i
$956$		−	1.91688e7i		−	0.678346i
$957$		−	6.40224e6i		−	0.225971i
$958$	2.90077e7			1.02117
$959$	6.69249e6			0.234986
$960$		−	2.71565e6i		−	0.0951033i
$961$	−6.39922e7			−2.23521
$962$	−2.08319e7	−	4.07581e6i	−0.725758	−	0.141996i
$963$	−1.84438e6			−0.0640890
$964$			1.86606e7i			0.646744i
$965$	1.77410e7			0.613280
$966$	−5.73300e6			−0.197669
$967$			1.53210e6i			0.0526892i	0.999653	+	0.0263446i	$0.00838672\pi$
$967$			1.53210e6i			0.0526892i	−0.999653	+	0.0263446i	$0.991613\pi$
$968$		−	9.38566e6i		−	0.321941i
$969$			1.67462e7i			0.572937i
$970$		−	3.27322e7i		−	1.11698i
$971$	2.37514e7			0.808426			0.404213	−	0.914665i	$-0.367545\pi$
$971$	2.37514e7			0.808426			0.404213	+	0.914665i	$0.367545\pi$
$972$	8.61952e6			0.292629
$973$		−	1.45330e6i		−	0.0492124i
$974$	−1.01346e7			−0.342301
$975$	4.07358e6	+	797004.i	0.137235	+	0.0268503i
$976$	−1.48275e7			−0.498246
$977$		−	1.97751e7i		−	0.662798i	−0.943491	−	0.331399i	$-0.892479\pi$
$977$		−	1.97751e7i		−	0.662798i	0.943491	−	0.331399i	$-0.107521\pi$
$978$	2.05773e7			0.687926
$979$	1.25734e7			0.419271
$980$			4.71811e6i			0.156929i
$981$			1.07175e7i			0.355566i
$982$			3.38475e7i			1.12008i
$983$		−	1.57006e7i		−	0.518241i	−0.965845	−	0.259121i	$-0.916567\pi$
$983$		−	1.57006e7i		−	0.518241i	0.965845	−	0.259121i	$-0.0834327\pi$
$984$	−7.88736e6			−0.259683
$985$	−4.58790e7			−1.50669
$986$			1.80740e7i			0.592055i
$987$	−4.01720e6			−0.131259
$988$	−2.19024e6	+	1.11946e7i	−0.0713837	+	0.364850i
$989$	1.04948e7			0.341178
$990$			1.81152e6i			0.0587429i
$991$	1.65835e7			0.536406			0.268203	−	0.963362i	$-0.413570\pi$
$991$	1.65835e7			0.536406			0.268203	+	0.963362i	$0.413570\pi$
$992$	9.85498e6			0.317963
$993$			8.22487e6i			0.264701i
$994$		−	2.67712e7i		−	0.859414i
$995$		−	7.29892e6i		−	0.233723i
$996$		−	1.15353e7i		−	0.368451i
$997$	−2.08432e7			−0.664091			−0.332045	−	0.943263i	$-0.607739\pi$
$997$	−2.08432e7			−0.664091			−0.332045	+	0.943263i	$0.607739\pi$
$998$	−7.81531e6			−0.248382
$999$		−	3.58898e7i		−	1.13778i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.6.b.a.25.2	yes	2
3.2	odd	2		234.6.b.b.181.1		2
4.3	odd	2		208.6.f.b.129.1		2
13.5	odd	4		338.6.a.c.1.1		1
13.8	odd	4		338.6.a.a.1.1		1
13.12	even	2	inner	26.6.b.a.25.1	✓	2
39.38	odd	2		234.6.b.b.181.2		2
52.51	odd	2		208.6.f.b.129.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.b.a.25.1	✓	2	13.12	even	2	inner
26.6.b.a.25.2	yes	2	1.1	even	1	trivial
208.6.f.b.129.1		2	4.3	odd	2
208.6.f.b.129.2		2	52.51	odd	2
234.6.b.b.181.1		2	3.2	odd	2
234.6.b.b.181.2		2	39.38	odd	2
338.6.a.a.1.1		1	13.8	odd	4
338.6.a.c.1.1		1	13.5	odd	4

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Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	26.6.b.a.25.2

Level	$26$
Weight	$6$
Character	26.25
Analytic conductor	$4.170$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$