LMFDB - Embedded newform 126.4.g.e.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, 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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{193})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 49x^{2} + 48x + 2304 $ x^4 - x^3 + 49x^2 + 48x + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$-3.22311 + 5.58259i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.4.g.e.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.72311 + 2.98452i) q^{5} +(15.3924 - 10.2992i) q^{7} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.72311 + 2.98452i) q^{5} +(15.3924 - 10.2992i) q^{7} +8.00000 q^{8} +(-3.44622 - 5.96903i) q^{10} +(18.0618 + 31.2839i) q^{11} +10.2311 q^{13} +(2.44622 + 36.9597i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(59.2311 + 102.591i) q^{17} +(19.3307 - 33.4817i) q^{19} +13.7849 q^{20} -72.2471 q^{22} +(-18.1236 + 31.3909i) q^{23} +(56.5618 + 97.9679i) q^{25} +(-10.2311 + 17.7208i) q^{26} +(-66.4622 - 32.7227i) q^{28} +12.1236 q^{29} +(72.7471 + 126.002i) q^{31} +(-16.0000 - 27.7128i) q^{32} -236.924 q^{34} +(4.21511 + 63.6856i) q^{35} +(0.685331 - 1.18703i) q^{37} +(38.6613 + 66.9634i) q^{38} +(-13.7849 + 23.8761i) q^{40} -168.000 q^{41} +299.371 q^{43} +(72.2471 - 125.136i) q^{44} +(-36.2471 - 62.7818i) q^{46} +(251.355 - 435.359i) q^{47} +(130.855 - 317.058i) q^{49} -226.247 q^{50} +(-20.4622 - 35.4416i) q^{52} +(-312.556 - 541.363i) q^{53} -124.490 q^{55} +(123.140 - 82.3933i) q^{56} +(-12.1236 + 20.9986i) q^{58} +(-21.1098 - 36.5632i) q^{59} +(219.586 - 380.334i) q^{61} -290.988 q^{62} +64.0000 q^{64} +(-17.6293 + 30.5349i) q^{65} +(381.809 + 661.312i) q^{67} +(236.924 - 410.365i) q^{68} +(-114.522 - 56.3848i) q^{70} -1020.49 q^{71} +(-289.642 - 501.674i) q^{73} +(1.37066 + 2.37406i) q^{74} -154.645 q^{76} +(600.213 + 295.515i) q^{77} +(-471.365 + 816.428i) q^{79} +(-27.5698 - 47.7523i) q^{80} +(168.000 - 290.985i) q^{82} +474.714 q^{83} -408.247 q^{85} +(-299.371 + 518.525i) q^{86} +(144.494 + 250.271i) q^{88} +(410.952 - 711.790i) q^{89} +(157.482 - 105.372i) q^{91} +144.988 q^{92} +(502.709 + 870.718i) q^{94} +(66.6178 + 115.385i) q^{95} -1108.16 q^{97} +(418.307 + 543.705i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 8 q^{4} + 7 q^{5} + 6 q^{7} + 32 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 8 * q^4 + 7 * q^5 + 6 * q^7 + 32 * q^8	$ 4 q - 4 q^{2} - 8 q^{4} + 7 q^{5} + 6 q^{7} + 32 q^{8} + 14 q^{10} - 25 q^{11} - 98 q^{13} - 18 q^{14} - 32 q^{16} + 98 q^{17} + 119 q^{19} - 56 q^{20} + 100 q^{22} + 122 q^{23} + 129 q^{25} + 98 q^{26} + 12 q^{28} - 146 q^{29} - 98 q^{31} - 64 q^{32} - 392 q^{34} + 128 q^{35} - 289 q^{37} + 238 q^{38} + 56 q^{40} - 672 q^{41} + 614 q^{43} - 100 q^{44} + 244 q^{46} + 672 q^{47} + 190 q^{49} - 516 q^{50} + 196 q^{52} - 375 q^{53} - 1526 q^{55} + 48 q^{56} + 146 q^{58} + 763 q^{59} + 406 q^{61} + 392 q^{62} + 256 q^{64} - 654 q^{65} + 1041 q^{67} + 392 q^{68} - 986 q^{70} - 3304 q^{71} + 189 q^{73} - 578 q^{74} - 952 q^{76} + 3415 q^{77} - 524 q^{79} + 112 q^{80} + 672 q^{82} - 574 q^{83} - 1244 q^{85} - 614 q^{86} - 200 q^{88} + 2394 q^{89} + 1783 q^{91} - 976 q^{92} + 1344 q^{94} - 706 q^{95} - 126 q^{97} + 2090 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 8 * q^4 + 7 * q^5 + 6 * q^7 + 32 * q^8 + 14 * q^10 - 25 * q^11 - 98 * q^13 - 18 * q^14 - 32 * q^16 + 98 * q^17 + 119 * q^19 - 56 * q^20 + 100 * q^22 + 122 * q^23 + 129 * q^25 + 98 * q^26 + 12 * q^28 - 146 * q^29 - 98 * q^31 - 64 * q^32 - 392 * q^34 + 128 * q^35 - 289 * q^37 + 238 * q^38 + 56 * q^40 - 672 * q^41 + 614 * q^43 - 100 * q^44 + 244 * q^46 + 672 * q^47 + 190 * q^49 - 516 * q^50 + 196 * q^52 - 375 * q^53 - 1526 * q^55 + 48 * q^56 + 146 * q^58 + 763 * q^59 + 406 * q^61 + 392 * q^62 + 256 * q^64 - 654 * q^65 + 1041 * q^67 + 392 * q^68 - 986 * q^70 - 3304 * q^71 + 189 * q^73 - 578 * q^74 - 952 * q^76 + 3415 * q^77 - 524 * q^79 + 112 * q^80 + 672 * q^82 - 574 * q^83 - 1244 * q^85 - 614 * q^86 - 200 * q^88 + 2394 * q^89 + 1783 * q^91 - 976 * q^92 + 1344 * q^94 - 706 * q^95 - 126 * q^97 + 2090 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−1.72311	+	2.98452i	−0.154120	+	0.266943i	−0.932738	−	0.360554i	$-0.882587\pi$
$5$	−1.72311	+	2.98452i	−0.154120	+	0.266943i	0.778618	+	0.627498i	$0.215921\pi$
$6$		0			0
$7$	15.3924	−	10.2992i	0.831114	−	0.556102i
$7$	15.3924	−	10.2992i	0.831114	−	0.556102i
$8$	8.00000			0.353553
$9$		0			0
$10$	−3.44622	−	5.96903i	−0.108979	−	0.188757i
$11$	18.0618	+	31.2839i	0.495076	+	0.857496i	0.999984	−	0.00567700i	$-0.00180706\pi$
$11$	18.0618	+	31.2839i	0.495076	+	0.857496i	−0.504908	+	0.863173i	$0.668474\pi$
$12$		0			0
$13$	10.2311			0.218277			0.109138	−	0.994027i	$-0.465191\pi$
$13$	10.2311			0.218277			0.109138	+	0.994027i	$0.465191\pi$
$14$	2.44622	+	36.9597i	0.0466986	+	0.705563i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	59.2311	+	102.591i	0.845038	+	1.46365i	0.885588	+	0.464472i	$0.153756\pi$
$17$	59.2311	+	102.591i	0.845038	+	1.46365i	−0.0405493	+	0.999178i	$0.512911\pi$
$18$		0			0
$19$	19.3307	−	33.4817i	0.233408	−	0.404275i	−0.725401	−	0.688327i	$-0.758345\pi$
$19$	19.3307	−	33.4817i	0.233408	−	0.404275i	0.958809	+	0.284052i	$0.0916788\pi$
$20$	13.7849			0.154120
$21$		0			0
$22$	−72.2471			−0.700143
$23$	−18.1236	+	31.3909i	−0.164305	+	0.284585i	−0.936408	−	0.350912i	$-0.885872\pi$
$23$	−18.1236	+	31.3909i	−0.164305	+	0.284585i	0.772103	+	0.635497i	$0.219205\pi$
$24$		0			0
$25$	56.5618	+	97.9679i	0.452494	+	0.783743i
$26$	−10.2311	+	17.7208i	−0.0771725	+	0.133667i
$27$		0			0
$28$	−66.4622	−	32.7227i	−0.448578	−	0.220857i
$29$	12.1236			0.0776306			0.0388153	−	0.999246i	$-0.487642\pi$
$29$	12.1236			0.0776306			0.0388153	+	0.999246i	$0.487642\pi$
$30$		0			0
$31$	72.7471	+	126.002i	0.421476	+	0.730018i	0.996084	−	0.0884105i	$-0.0281787\pi$
$31$	72.7471	+	126.002i	0.421476	+	0.730018i	−0.574608	+	0.818429i	$0.694845\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−236.924			−1.19506
$35$	4.21511	+	63.6856i	0.0203567	+	0.307567i
$36$		0			0
$37$	0.685331	−	1.18703i	0.00304507	−	0.00527422i	−0.864499	−	0.502635i	$-0.832364\pi$
$37$	0.685331	−	1.18703i	0.00304507	−	0.00527422i	0.867544	+	0.497361i	$0.165697\pi$
$38$	38.6613	+	66.9634i	0.165045	+	0.285866i
$39$		0			0
$40$	−13.7849	+	23.8761i	−0.0544896	+	0.0943787i
$41$	−168.000			−0.639932			−0.319966	−	0.947429i	$-0.603671\pi$
$41$	−168.000			−0.639932			−0.319966	+	0.947429i	$0.603671\pi$
$42$		0			0
$43$	299.371			1.06171			0.530856	−	0.847462i	$-0.321871\pi$
$43$	299.371			1.06171			0.530856	+	0.847462i	$0.321871\pi$
$44$	72.2471	−	125.136i	0.247538	−	0.428748i
$45$		0			0
$46$	−36.2471	−	62.7818i	−0.116181	−	0.201232i
$47$	251.355	−	435.359i	0.780082	−	1.35114i	−0.151812	−	0.988409i	$-0.548511\pi$
$47$	251.355	−	435.359i	0.780082	−	1.35114i	0.931894	−	0.362732i	$-0.118156\pi$
$48$		0			0
$49$	130.855	−	317.058i	0.381500	−	0.924369i
$50$	−226.247			−0.639923
$51$		0			0
$52$	−20.4622	−	35.4416i	−0.0545692	−	0.0945167i
$53$	−312.556	−	541.363i	−0.810054	−	1.40305i	−0.912825	−	0.408350i	$-0.866104\pi$
$53$	−312.556	−	541.363i	−0.810054	−	1.40305i	0.102771	−	0.994705i	$-0.467229\pi$
$54$		0			0
$55$	−124.490			−0.305204
$56$	123.140	−	82.3933i	0.293843	−	0.196612i
$57$		0			0
$58$	−12.1236	+	20.9986i	−0.0274466	+	0.0475388i
$59$	−21.1098	−	36.5632i	−0.0465806	−	0.0806800i	0.841795	−	0.539797i	$-0.181499\pi$
$59$	−21.1098	−	36.5632i	−0.0465806	−	0.0806800i	−0.888376	+	0.459117i	$0.848166\pi$
$60$		0			0
$61$	219.586	−	380.334i	0.460903	−	0.798307i	−0.538103	−	0.842879i	$-0.680859\pi$
$61$	219.586	−	380.334i	0.460903	−	0.798307i	0.999006	+	0.0445717i	$0.0141923\pi$
$62$	−290.988			−0.596058
$63$		0			0
$64$	64.0000			0.125000
$65$	−17.6293	+	30.5349i	−0.0336408	+	0.0582675i
$66$		0			0
$67$	381.809	+	661.312i	0.696200	+	1.20585i	0.969775	+	0.244003i	$0.0784605\pi$
$67$	381.809	+	661.312i	0.696200	+	1.20585i	−0.273575	+	0.961851i	$0.588206\pi$
$68$	236.924	−	410.365i	0.422519	−	0.731825i
$69$		0			0
$70$	−114.522	−	56.3848i	−0.195542	−	0.0962753i
$71$	−1020.49			−1.70578			−0.852890	−	0.522091i	$-0.825152\pi$
$71$	−1020.49			−1.70578			−0.852890	+	0.522091i	$0.825152\pi$
$72$		0			0
$73$	−289.642	−	501.674i	−0.464384	−	0.804336i	0.534790	−	0.844985i	$-0.320391\pi$
$73$	−289.642	−	501.674i	−0.464384	−	0.804336i	−0.999173	+	0.0406491i	$0.987057\pi$
$74$	1.37066	+	2.37406i	0.00215319	+	0.00372944i
$75$		0			0
$76$	−154.645			−0.233408
$77$	600.213	+	295.515i	0.888320	+	0.437364i
$78$		0			0
$79$	−471.365	+	816.428i	−0.671300	+	1.16273i	0.306236	+	0.951956i	$0.400930\pi$
$79$	−471.365	+	816.428i	−0.671300	+	1.16273i	−0.977536	+	0.210770i	$0.932403\pi$
$80$	−27.5698	−	47.7523i	−0.0385299	−	0.0667358i
$81$		0			0
$82$	168.000	−	290.985i	0.226250	−	0.391876i
$83$	474.714			0.627790			0.313895	−	0.949458i	$-0.398366\pi$
$83$	474.714			0.627790			0.313895	+	0.949458i	$0.398366\pi$
$84$		0			0
$85$	−408.247			−0.520948
$86$	−299.371	+	518.525i	−0.375372	+	0.650163i
$87$		0			0
$88$	144.494	+	250.271i	0.175036	+	0.303171i
$89$	410.952	−	711.790i	0.489447	−	0.847748i	−0.510479	−	0.859890i	$-0.670532\pi$
$89$	410.952	−	711.790i	0.489447	−	0.847748i	0.999926	+	0.0121424i	$0.00386515\pi$
$90$		0			0
$91$	157.482	−	105.372i	0.181413	−	0.121384i
$92$	144.988			0.164305
$93$		0			0
$94$	502.709	+	870.718i	0.551601	+	0.955401i
$95$	66.6178	+	115.385i	0.0719457	+	0.124614i
$96$		0			0
$97$	−1108.16			−1.15997			−0.579985	−	0.814627i	$-0.696942\pi$
$97$	−1108.16			−1.15997			−0.579985	+	0.814627i	$0.696942\pi$
$98$	418.307	+	543.705i	0.431177	+	0.560434i
$99$		0			0
$100$	226.247	−	391.871i	0.226247	−	0.391871i
$101$	942.961	+	1633.26i	0.928991	+	1.60906i	0.785013	+	0.619479i	$0.212656\pi$
$101$	942.961	+	1633.26i	0.928991	+	1.60906i	0.143978	+	0.989581i	$0.454011\pi$
$102$		0			0
$103$	−241.072	+	417.549i	−0.230617	+	0.399440i	−0.957990	−	0.286802i	$-0.907408\pi$
$103$	−241.072	+	417.549i	−0.230617	+	0.399440i	0.727373	+	0.686242i	$0.240741\pi$
$104$	81.8489			0.0771725
$105$		0			0
$106$	1250.22			1.14559
$107$	−865.297	+	1498.74i	−0.781789	+	1.35410i	0.149109	+	0.988821i	$0.452359\pi$
$107$	−865.297	+	1498.74i	−0.781789	+	1.35410i	−0.930898	+	0.365278i	$0.880974\pi$
$108$		0			0
$109$	−574.415	−	994.916i	−0.504761	−	0.874272i	−0.999985	−	0.00550668i	$-0.998247\pi$
$109$	−574.415	−	994.916i	−0.504761	−	0.874272i	0.495223	−	0.868766i	$-0.335086\pi$
$110$	124.490	−	215.623i	0.107906	−	0.186898i
$111$		0			0
$112$	19.5698	+	295.677i	0.0165104	+	0.249454i
$113$	−1331.51			−1.10847			−0.554237	−	0.832359i	$-0.686990\pi$
$113$	−1331.51			−1.10847			−0.554237	+	0.832359i	$0.686990\pi$
$114$		0			0
$115$	−62.4578	−	108.180i	−0.0506454	−	0.0877204i
$116$	−24.2471	−	41.9972i	−0.0194077	−	0.0336150i
$117$		0			0
$118$	84.4391			0.0658750
$119$	1968.32	+	969.100i	1.51626	+	0.746532i
$120$		0			0
$121$	13.0444	−	22.5936i	0.00980047	−	0.0169749i
$122$	439.172	+	760.667i	0.325908	+	0.564488i
$123$		0			0
$124$	290.988	−	504.007i	0.210738	−	0.365009i
$125$	−820.627			−0.587193
$126$		0			0
$127$	−830.236			−0.580090			−0.290045	−	0.957013i	$-0.593670\pi$
$127$	−830.236			−0.580090			−0.290045	+	0.957013i	$0.593670\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−35.2587	−	61.0698i	−0.0237876	−	0.0412014i
$131$	986.245	−	1708.23i	0.657776	−	1.13930i	−0.323414	−	0.946257i	$-0.604831\pi$
$131$	986.245	−	1708.23i	0.657776	−	1.13930i	0.981190	−	0.193044i	$-0.0618359\pi$
$132$		0			0
$133$	−47.2871	−	714.455i	−0.0308294	−	0.465798i
$134$	−1527.24			−0.984575
$135$		0			0
$136$	473.849	+	820.730i	0.298766	+	0.517478i
$137$	−34.3938	−	59.5718i	−0.0214486	−	0.0371501i	0.855102	−	0.518460i	$-0.173494\pi$
$137$	−34.3938	−	59.5718i	−0.0214486	−	0.0371501i	−0.876550	+	0.481310i	$0.840161\pi$
$138$		0			0
$139$	1864.48			1.13772			0.568860	−	0.822435i	$-0.307385\pi$
$139$	1864.48			1.13772			0.568860	+	0.822435i	$0.307385\pi$
$140$	212.183	−	141.973i	0.128091	−	0.0857063i
$141$		0			0
$142$	1020.49	−	1767.55i	0.603084	−	1.04457i
$143$	184.792	+	320.069i	0.108064	+	0.187172i
$144$		0			0
$145$	−20.8902	+	36.1829i	−0.0119644	+	0.0207230i
$146$	1158.57			0.656738
$147$		0			0
$148$	−5.48265			−0.00304507
$149$	−10.1467	+	17.5746i	−0.00557885	+	0.00966286i	−0.868801	−	0.495161i	$-0.835109\pi$
$149$	−10.1467	+	17.5746i	−0.00557885	+	0.00966286i	0.863222	+	0.504824i	$0.168442\pi$
$150$		0			0
$151$	790.162	+	1368.60i	0.425844	+	0.737584i	0.996499	−	0.0836063i	$-0.0266438\pi$
$151$	790.162	+	1368.60i	0.425844	+	0.737584i	−0.570655	+	0.821190i	$0.693310\pi$
$152$	154.645	−	267.854i	0.0825223	−	0.142933i
$153$		0			0
$154$	−1112.06	+	744.084i	−0.581898	+	0.389351i
$155$	−501.405			−0.259831
$156$		0			0
$157$	−1692.18	−	2930.93i	−0.860193	−	1.48990i	−0.871742	−	0.489965i	$-0.837009\pi$
$157$	−1692.18	−	2930.93i	−0.860193	−	1.48990i	0.0115487	−	0.999933i	$-0.496324\pi$
$158$	−942.730	−	1632.86i	−0.474681	−	0.822171i
$159$		0			0
$160$	110.279			0.0544896
$161$	44.3342	+	669.840i	0.0217020	+	0.327893i
$162$		0			0
$163$	−785.853	+	1361.14i	−0.377624	+	0.654065i	−0.990716	−	0.135947i	$-0.956592\pi$
$163$	−785.853	+	1361.14i	−0.377624	+	0.654065i	0.613092	+	0.790012i	$0.289926\pi$
$164$	336.000	+	581.969i	0.159983	+	0.277098i
$165$		0			0
$166$	−474.714	+	822.228i	−0.221957	+	0.384442i
$167$	−2473.92			−1.14633			−0.573167	−	0.819439i	$-0.694285\pi$
$167$	−2473.92			−1.14633			−0.573167	+	0.819439i	$0.694285\pi$
$168$		0			0
$169$	−2092.32			−0.952355
$170$	408.247	−	707.105i	0.184183	−	0.319014i
$171$		0			0
$172$	−598.741	−	1037.05i	−0.265428	−	0.459735i
$173$	2075.67	−	3595.17i	0.912198	−	1.57997i	0.101246	−	0.994861i	$-0.467717\pi$
$173$	2075.67	−	3595.17i	0.912198	−	1.57997i	0.810952	−	0.585112i	$-0.198950\pi$
$174$		0			0
$175$	1879.61	+	925.426i	0.811915	+	0.399747i
$176$	−577.977			−0.247538
$177$		0			0
$178$	821.904	+	1423.58i	0.346092	+	0.599448i
$179$	−2108.97	−	3652.84i	−0.880623	−	1.52528i	−0.850650	−	0.525733i	$-0.823791\pi$
$179$	−2108.97	−	3652.84i	−0.880623	−	1.52528i	−0.0299728	−	0.999551i	$-0.509542\pi$
$180$		0			0
$181$	3504.65			1.43922			0.719609	−	0.694380i	$-0.244321\pi$
$181$	3504.65			1.43922			0.719609	+	0.694380i	$0.244321\pi$
$182$	25.0276	+	378.138i	0.0101932	+	0.154008i
$183$		0			0
$184$	−144.988	+	251.127i	−0.0580907	+	0.100616i
$185$	2.36180	+	4.09076i	0.000938612	+	0.00162572i
$186$		0			0
$187$	−2139.64	+	3705.96i	−0.836716	+	1.44923i
$188$	−2010.84			−0.780082
$189$		0			0
$190$	−266.471			−0.101747
$191$	991.483	−	1717.30i	0.375608	−	0.650572i	−0.614810	−	0.788676i	$-0.710767\pi$
$191$	991.483	−	1717.30i	0.375608	−	0.650572i	0.990418	+	0.138103i	$0.0441005\pi$
$192$		0			0
$193$	−1055.87	−	1828.82i	−0.393799	−	0.682080i	0.599148	−	0.800638i	$-0.295506\pi$
$193$	−1055.87	−	1828.82i	−0.393799	−	0.682080i	−0.992947	+	0.118558i	$0.962173\pi$
$194$	1108.16	−	1919.40i	0.410111	−	0.710333i
$195$		0			0
$196$	−1360.03	+	180.823i	−0.495638	+	0.0658976i
$197$	−3932.65			−1.42228			−0.711141	−	0.703049i	$-0.751821\pi$
$197$	−3932.65			−1.42228			−0.711141	+	0.703049i	$0.751821\pi$
$198$		0			0
$199$	276.352	+	478.656i	0.0984426	+	0.170508i	0.911040	−	0.412318i	$-0.135281\pi$
$199$	276.352	+	478.656i	0.0984426	+	0.170508i	−0.812598	+	0.582825i	$0.801947\pi$
$200$	452.494	+	783.743i	0.159981	+	0.277095i
$201$		0			0
$202$	−3771.84			−1.31379
$203$	186.611	−	124.862i	0.0645199	−	0.0431706i
$204$		0			0
$205$	289.483	−	501.399i	0.0986261	−	0.170825i
$206$	−482.144	−	835.098i	−0.163071	−	0.282447i
$207$		0			0
$208$	−81.8489	+	141.766i	−0.0272846	+	0.0472583i
$209$	1396.58			0.462219
$210$		0			0
$211$	1720.90			0.561476			0.280738	−	0.959784i	$-0.409421\pi$
$211$	1720.90			0.561476			0.280738	+	0.959784i	$0.409421\pi$
$212$	−1250.22	+	2165.45i	−0.405027	+	0.701527i
$213$		0			0
$214$	−1730.59	−	2997.48i	−0.552808	−	0.957492i
$215$	−515.849	+	893.476i	−0.163631	+	0.283417i
$216$		0			0
$217$	2417.47	+	1190.24i	0.756260	+	0.372344i
$218$	2297.66			0.713840
$219$		0			0
$220$	248.980	+	431.245i	0.0763009	+	0.132157i
$221$	606.000	+	1049.62i	0.184452	+	0.319481i
$222$		0			0
$223$	4788.43			1.43793			0.718963	−	0.695049i	$-0.244617\pi$
$223$	4788.43			1.43793			0.718963	+	0.695049i	$0.244617\pi$
$224$	−531.698	−	261.781i	−0.158596	−	0.0780848i
$225$		0			0
$226$	1331.51	−	2306.24i	0.391905	−	0.678799i
$227$	2043.80	+	3539.96i	0.597584	+	1.03505i	0.993177	+	0.116619i	$0.0372058\pi$
$227$	2043.80	+	3539.96i	0.597584	+	1.03505i	−0.395593	+	0.918426i	$0.629461\pi$
$228$		0			0
$229$	2033.30	−	3521.79i	0.586745	−	1.01627i	−0.407911	−	0.913022i	$-0.633743\pi$
$229$	2033.30	−	3521.79i	0.586745	−	1.01627i	0.994655	−	0.103250i	$-0.0329242\pi$
$230$	249.831			0.0716234
$231$		0			0
$232$	96.9884			0.0274466
$233$	89.1351	−	154.387i	0.0250620	−	0.0434086i	−0.853222	−	0.521547i	$-0.825355\pi$
$233$	89.1351	−	154.387i	0.0250620	−	0.0434086i	0.878284	+	0.478139i	$0.158688\pi$
$234$		0			0
$235$	866.224	+	1500.34i	0.240452	+	0.416475i
$236$	−84.4391	+	146.253i	−0.0232903	+	0.0403400i
$237$		0			0
$238$	−3646.85	+	2440.12i	−0.993235	+	0.664578i
$239$	2118.67			0.573412			0.286706	−	0.958019i	$-0.407440\pi$
$239$	2118.67			0.573412			0.286706	+	0.958019i	$0.407440\pi$
$240$		0			0
$241$	−1199.15	−	2076.99i	−0.320516	−	0.555149i	0.660079	−	0.751196i	$-0.270523\pi$
$241$	−1199.15	−	2076.99i	−0.320516	−	0.555149i	−0.980595	+	0.196047i	$0.937189\pi$
$242$	26.0888	+	45.1872i	0.00692998	+	0.0120031i
$243$		0			0
$244$	−1756.69			−0.460903
$245$	720.789	+	936.865i	0.187957	+	0.244302i
$246$		0			0
$247$	197.774	−	342.555i	0.0509477	−	0.0882439i
$248$	581.977	+	1008.01i	0.149014	+	0.258100i
$249$		0			0
$250$	820.627	−	1421.37i	0.207604	−	0.359581i
$251$	1550.76			0.389973			0.194986	−	0.980806i	$-0.437534\pi$
$251$	1550.76			0.389973			0.194986	+	0.980806i	$0.437534\pi$
$252$		0			0
$253$	−1309.37			−0.325374
$254$	830.236	−	1438.01i	0.205093	−	0.355231i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2697.72	+	4672.59i	−0.654783	+	1.13412i	0.327166	+	0.944967i	$0.393907\pi$
$257$	−2697.72	+	4672.59i	−0.654783	+	1.13412i	−0.981948	+	0.189150i	$0.939427\pi$
$258$		0			0
$259$	−1.67647	−	25.3296i	−0.000402204	−	0.00607685i
$260$	141.035			0.0336408
$261$		0			0
$262$	1972.49	+	3416.45i	0.465118	+	0.805607i
$263$	1790.97	+	3102.04i	0.419907	+	0.727301i	0.995930	−	0.0901330i	$-0.0287292\pi$
$263$	1790.97	+	3102.04i	0.419907	+	0.727301i	−0.576022	+	0.817434i	$0.695396\pi$
$264$		0			0
$265$	2154.27			0.499381
$266$	1284.76	+	632.551i	0.296141	+	0.145805i
$267$		0			0
$268$	1527.24	−	2645.25i	0.348100	−	0.602927i
$269$	−587.774	−	1018.05i	−0.133224	−	0.230750i	0.791694	−	0.610918i	$-0.209200\pi$
$269$	−587.774	−	1018.05i	−0.133224	−	0.230750i	−0.924918	+	0.380168i	$0.875866\pi$
$270$		0			0
$271$	−129.664	+	224.584i	−0.0290646	+	0.0503413i	−0.880192	−	0.474618i	$-0.842586\pi$
$271$	−129.664	+	224.584i	−0.0290646	+	0.0503413i	0.851127	+	0.524959i	$0.175920\pi$
$272$	−1895.40			−0.422519
$273$		0			0
$274$	137.575			0.0303329
$275$	−2043.21	+	3538.95i	−0.448038	+	0.776024i
$276$		0			0
$277$	649.461	+	1124.90i	0.140875	+	0.244003i	0.927826	−	0.373012i	$-0.121675\pi$
$277$	649.461	+	1124.90i	0.140875	+	0.244003i	−0.786951	+	0.617015i	$0.788342\pi$
$278$	−1864.48	+	3229.37i	−0.402245	+	0.696708i
$279$		0			0
$280$	33.7209	+	509.485i	0.00719717	+	0.108741i
$281$	4524.25			0.960477			0.480238	−	0.877138i	$-0.340550\pi$
$281$	4524.25			0.960477			0.480238	+	0.877138i	$0.340550\pi$
$282$		0			0
$283$	−3239.03	−	5610.16i	−0.680354	−	1.17841i	−0.974873	−	0.222762i	$-0.928493\pi$
$283$	−3239.03	−	5610.16i	−0.680354	−	1.17841i	0.294519	−	0.955646i	$-0.404840\pi$
$284$	2040.99	+	3535.10i	0.426445	+	0.738624i
$285$		0			0
$286$	−739.168			−0.152825
$287$	−2585.93	+	1730.26i	−0.531856	+	0.355867i
$288$		0			0
$289$	−4560.15	+	7898.41i	−0.928180	+	1.60766i
$290$	−41.7805	−	72.3659i	−0.00846011	−	0.0146533i
$291$		0			0
$292$	−1158.57	+	2006.70i	−0.232192	+	0.402168i
$293$	2890.91			0.576413			0.288207	−	0.957568i	$-0.406941\pi$
$293$	2890.91			0.576413			0.288207	+	0.957568i	$0.406941\pi$
$294$		0			0
$295$	145.498			0.0287160
$296$	5.48265	−	9.49622i	0.00107660	−	0.00186472i
$297$		0			0
$298$	−20.2934	−	35.1492i	−0.00394485	−	0.00683267i
$299$	−185.424	+	321.164i	−0.0358641	+	0.0621184i
$300$		0			0
$301$	4608.05	−	3083.27i	0.882403	−	0.590420i
$302$	−3160.65			−0.602235
$303$		0			0
$304$	309.291	+	535.707i	0.0583521	+	0.101069i
$305$	756.741	+	1310.71i	0.142068	+	0.246070i
$306$		0			0
$307$	−3137.42			−0.583264			−0.291632	−	0.956531i	$-0.594198\pi$
$307$	−3137.42			−0.583264			−0.291632	+	0.956531i	$0.594198\pi$
$308$	−176.732	−	2670.23i	−0.0326957	−	0.493995i
$309$		0			0
$310$	501.405	−	868.460i	0.0918642	−	0.159114i
$311$	−3957.47	−	6854.55i	−0.721568	−	1.24979i	−0.960371	−	0.278725i	$-0.910088\pi$
$311$	−3957.47	−	6854.55i	−0.721568	−	1.24979i	0.238803	−	0.971068i	$-0.423245\pi$
$312$		0			0
$313$	−3808.30	+	6596.18i	−0.687726	+	1.19118i	0.284846	+	0.958573i	$0.408057\pi$
$313$	−3808.30	+	6596.18i	−0.687726	+	1.19118i	−0.972572	+	0.232602i	$0.925276\pi$
$314$	6768.70			1.21650
$315$		0			0
$316$	3770.92			0.671300
$317$	−995.745	+	1724.68i	−0.176425	+	0.305577i	−0.940653	−	0.339369i	$-0.889787\pi$
$317$	−995.745	+	1724.68i	−0.176425	+	0.305577i	0.764229	+	0.644945i	$0.223120\pi$
$318$		0			0
$319$	218.973	+	379.272i	0.0384330	+	0.0665679i
$320$	−110.279	+	191.009i	−0.0192650	+	0.0333679i
$321$		0			0
$322$	−1204.53	−	593.051i	−0.208466	−	0.102638i
$323$	4579.91			0.788956
$324$		0			0
$325$	578.690	+	1002.32i	0.0987690	+	0.171073i
$326$	−1571.71	−	2722.28i	−0.267021	−	0.462494i
$327$		0			0
$328$	−1344.00			−0.226250
$329$	−614.869	−	9289.98i	−0.103036	−	1.55676i
$330$		0			0
$331$	−1424.31	+	2466.99i	−0.236518	+	0.409661i	−0.959713	−	0.280983i	$-0.909340\pi$
$331$	−1424.31	+	2466.99i	−0.236518	+	0.409661i	0.723195	+	0.690644i	$0.242673\pi$
$332$	−949.428	−	1644.46i	−0.156948	−	0.271841i
$333$		0			0
$334$	2473.92	−	4284.96i	0.405290	−	0.701983i
$335$	−2631.60			−0.429192
$336$		0			0
$337$	−5813.87			−0.939768			−0.469884	−	0.882728i	$-0.655704\pi$
$337$	−5813.87			−0.939768			−0.469884	+	0.882728i	$0.655704\pi$
$338$	2092.32	−	3624.01i	0.336708	−	0.583196i
$339$		0			0
$340$	816.494	+	1414.21i	0.130237	+	0.225577i
$341$	−2627.88	+	4551.63i	−0.417325	+	0.722828i
$342$		0			0
$343$	−1251.26	−	6228.00i	−0.196973	−	0.980409i
$344$	2394.97			0.375372
$345$		0			0
$346$	4151.34	+	7190.33i	0.645022	+	1.11721i
$347$	1717.55	+	2974.89i	0.265715	+	0.460231i	0.967751	−	0.251910i	$-0.0810587\pi$
$347$	1717.55	+	2974.89i	0.265715	+	0.460231i	−0.702036	+	0.712142i	$0.747725\pi$
$348$		0			0
$349$	−3034.99			−0.465499			−0.232750	−	0.972537i	$-0.574772\pi$
$349$	−3034.99			−0.465499			−0.232750	+	0.972537i	$0.574772\pi$
$350$	−3482.50	+	2330.15i	−0.531849	+	0.355863i
$351$		0			0
$352$	577.977	−	1001.09i	0.0875178	−	0.151585i
$353$	−4110.22	−	7119.11i	−0.619730	−	1.07340i	−0.989535	−	0.144295i	$-0.953909\pi$
$353$	−4110.22	−	7119.11i	−0.619730	−	1.07340i	0.369804	−	0.929110i	$-0.379425\pi$
$354$		0			0
$355$	1758.42	−	3045.68i	0.262894	−	0.455346i
$356$	−3287.62			−0.489447
$357$		0			0
$358$	8435.86			1.24539
$359$	4950.80	−	8575.03i	0.727836	−	1.26065i	−0.229961	−	0.973200i	$-0.573860\pi$
$359$	4950.80	−	8575.03i	0.727836	−	1.26065i	0.957796	−	0.287448i	$-0.0928070\pi$
$360$		0			0
$361$	2682.15	+	4645.62i	0.391041	+	0.677303i
$362$	−3504.65	+	6070.23i	−0.508840	+	0.881337i
$363$		0			0
$364$	−679.982	−	334.789i	−0.0979142	−	0.0482080i
$365$	1996.34			0.286283
$366$		0			0
$367$	−5514.01	−	9550.55i	−0.784276	−	1.35841i	−0.929431	−	0.368997i	$-0.879701\pi$
$367$	−5514.01	−	9550.55i	−0.784276	−	1.35841i	0.145155	−	0.989409i	$-0.453632\pi$
$368$	−289.977	−	502.255i	−0.0410763	−	0.0711463i
$369$		0			0
$370$	−9.44721			−0.00132740
$371$	−10386.6	−	5113.83i	−1.45349	−	0.715625i
$372$		0			0
$373$	1373.19	−	2378.43i	0.190619	−	0.330162i	−0.754836	−	0.655913i	$-0.772284\pi$
$373$	1373.19	−	2378.43i	0.190619	−	0.330162i	0.945456	+	0.325751i	$0.105617\pi$
$374$	−4279.28	−	7411.92i	−0.591647	−	1.02476i
$375$		0			0
$376$	2010.84	−	3482.87i	0.275801	−	0.477701i
$377$	124.037			0.0169450
$378$		0			0
$379$	−4184.22			−0.567095			−0.283547	−	0.958958i	$-0.591511\pi$
$379$	−4184.22			−0.567095			−0.283547	+	0.958958i	$0.591511\pi$
$380$	266.471	−	461.541i	0.0359728	−	0.0623068i
$381$		0			0
$382$	1982.97	+	3434.60i	0.265595	+	0.460024i
$383$	−1530.29	+	2650.54i	−0.204162	+	0.353619i	−0.949865	−	0.312659i	$-0.898780\pi$
$383$	−1530.29	+	2650.54i	−0.204162	+	0.353619i	0.745703	+	0.666278i	$0.232114\pi$
$384$		0			0
$385$	−1916.20	+	1282.14i	−0.253659	+	0.169724i
$386$	4223.48			0.556916
$387$		0			0
$388$	2216.33	+	3838.79i	0.289992	+	0.502282i
$389$	−2459.81	−	4260.51i	−0.320610	−	0.555312i	0.660004	−	0.751262i	$-0.270554\pi$
$389$	−2459.81	−	4260.51i	−0.320610	−	0.555312i	−0.980614	+	0.195950i	$0.937221\pi$
$390$		0			0
$391$	−4293.91			−0.555377
$392$	1046.84	−	2536.47i	0.134881	−	0.326814i
$393$		0			0
$394$	3932.65	−	6811.55i	0.502853	−	0.870967i
$395$	−1624.43	−	2813.59i	−0.206921	−	0.358398i
$396$		0			0
$397$	6586.63	−	11408.4i	0.832678	−	1.44224i	−0.0632286	−	0.997999i	$-0.520140\pi$
$397$	6586.63	−	11408.4i	0.832678	−	1.44224i	0.895907	−	0.444242i	$-0.146527\pi$
$398$	−1105.41			−0.139219
$399$		0			0
$400$	−1809.98			−0.226247
$401$	1331.19	−	2305.69i	0.165777	−	0.287134i	−0.771154	−	0.636648i	$-0.780320\pi$
$401$	1331.19	−	2305.69i	0.165777	−	0.287134i	0.936931	+	0.349515i	$0.113654\pi$
$402$		0			0
$403$	744.284	+	1289.14i	0.0919985	+	0.159346i
$404$	3771.84	−	6533.02i	0.464496	−	0.804530i
$405$		0			0
$406$	29.6569	+	448.082i	0.00362524	+	0.0547733i
$407$	49.5132			0.00603016
$408$		0			0
$409$	6496.09	+	11251.6i	0.785357	+	1.36028i	0.928786	+	0.370617i	$0.120854\pi$
$409$	6496.09	+	11251.6i	0.785357	+	1.36028i	−0.143429	+	0.989661i	$0.545813\pi$
$410$	578.965	+	1002.80i	0.0697392	+	0.120792i
$411$		0			0
$412$	1928.58			0.230617
$413$	−701.501	−	345.384i	−0.0835802	−	0.0411507i
$414$		0			0
$415$	−817.984	+	1416.79i	−0.0967549	+	0.167584i
$416$	−163.698	−	283.533i	−0.0192931	−	0.0334167i
$417$		0			0
$418$	−1396.58	+	2418.96i	−0.163419	+	0.283050i
$419$	7236.96			0.843791			0.421896	−	0.906644i	$-0.361365\pi$
$419$	7236.96			0.843791			0.421896	+	0.906644i	$0.361365\pi$
$420$		0			0
$421$	3706.07			0.429032			0.214516	−	0.976720i	$-0.431183\pi$
$421$	3706.07			0.429032			0.214516	+	0.976720i	$0.431183\pi$
$422$	−1720.90	+	2980.68i	−0.198512	+	0.343832i
$423$		0			0
$424$	−2500.45	−	4330.90i	−0.286397	−	0.496055i
$425$	−6700.43	+	11605.5i	−0.764750	+	1.32459i
$426$		0			0
$427$	−537.156	−	8115.81i	−0.0608777	−	0.919793i
$428$	6922.38			0.781789
$429$		0			0
$430$	−1031.70	−	1786.95i	−0.115704	−	0.200406i
$431$	3191.19	+	5527.30i	0.356645	+	0.617728i	0.987398	−	0.158256i	$-0.0505871\pi$
$431$	3191.19	+	5527.30i	0.356645	+	0.617728i	−0.630753	+	0.775984i	$0.717254\pi$
$432$		0			0
$433$	−7275.62			−0.807492			−0.403746	−	0.914871i	$-0.632292\pi$
$433$	−7275.62			−0.807492			−0.403746	+	0.914871i	$0.632292\pi$
$434$	−4479.02	+	2996.94i	−0.495392	+	0.331469i
$435$		0			0
$436$	−2297.66	+	3979.66i	−0.252381	+	0.437136i
$437$	700.681	+	1213.61i	0.0767005	+	0.132849i
$438$		0			0
$439$	−4880.18	+	8452.72i	−0.530566	+	0.918967i	0.468798	+	0.883305i	$0.344687\pi$
$439$	−4880.18	+	8452.72i	−0.530566	+	0.918967i	−0.999364	+	0.0356614i	$0.988646\pi$
$440$	−995.918			−0.107906
$441$		0			0
$442$	−2424.00			−0.260855
$443$	2866.58	−	4965.06i	0.307439	−	0.532499i	−0.670363	−	0.742034i	$-0.733861\pi$
$443$	2866.58	−	4965.06i	0.307439	−	0.532499i	0.977801	+	0.209534i	$0.0671948\pi$
$444$		0			0
$445$	1416.23	+	2452.99i	0.150867	+	0.261309i
$446$	−4788.43	+	8293.81i	−0.508383	+	0.880546i
$447$		0			0
$448$	985.116	−	659.146i	0.103889	−	0.0695128i
$449$	16628.4			1.74775			0.873877	−	0.486147i	$-0.161598\pi$
$449$	16628.4			1.74775			0.873877	+	0.486147i	$0.161598\pi$
$450$		0			0
$451$	−3034.38	−	5255.70i	−0.316814	−	0.548739i
$452$	2663.01	+	4612.47i	0.277118	+	0.479983i
$453$		0			0
$454$	−8175.18			−0.845111
$455$	43.1253	+	651.574i	0.00444339	+	0.0671347i
$456$		0			0
$457$	−8559.65	+	14825.8i	−0.876157	+	1.51755i	−0.0206311	+	0.999787i	$0.506568\pi$
$457$	−8559.65	+	14825.8i	−0.876157	+	1.51755i	−0.855526	+	0.517761i	$0.826766\pi$
$458$	4066.61	+	7043.57i	0.414891	+	0.718613i
$459$		0			0
$460$	−249.831	+	432.720i	−0.0253227	+	0.0438602i
$461$	−6956.95			−0.702858			−0.351429	−	0.936215i	$-0.614304\pi$
$461$	−6956.95			−0.702858			−0.351429	+	0.936215i	$0.614304\pi$
$462$		0			0
$463$	6594.47			0.661924			0.330962	−	0.943644i	$-0.392627\pi$
$463$	6594.47			0.661924			0.330962	+	0.943644i	$0.392627\pi$
$464$	−96.9884	+	167.989i	−0.00970383	+	0.0168075i
$465$		0			0
$466$	178.270	+	308.773i	0.0177215	+	0.0306945i
$467$	−7232.91	+	12527.8i	−0.716700	+	1.24136i	0.245600	+	0.969371i	$0.421015\pi$
$467$	−7232.91	+	12527.8i	−0.716700	+	1.24136i	−0.962300	+	0.271990i	$0.912318\pi$
$468$		0			0
$469$	12687.9	+	6246.90i	1.24920	+	0.615043i
$470$	−3464.90			−0.340050
$471$		0			0
$472$	−168.878	−	292.506i	−0.0164687	−	0.0285247i
$473$	5407.17	+	9365.49i	0.525627	+	0.910413i
$474$		0			0
$475$	4373.51			0.422464
$476$	−579.570	−	8756.65i	−0.0558079	−	0.843194i
$477$		0			0
$478$	−2118.67	+	3669.65i	−0.202732	+	0.351142i
$479$	2037.74	+	3529.46i	0.194377	+	0.336671i	0.946696	−	0.322128i	$-0.104398\pi$
$479$	2037.74	+	3529.46i	0.194377	+	0.336671i	−0.752319	+	0.658799i	$0.771065\pi$
$480$		0			0
$481$	7.01170	−	12.1446i	0.000664669	−	0.00115124i
$482$	4796.61			0.453277
$483$		0			0
$484$	−104.355			−0.00980047
$485$	1909.49	−	3307.33i	0.178774	−	0.309646i
$486$		0			0
$487$	−2189.40	−	3792.14i	−0.203719	−	0.352851i	0.746005	−	0.665940i	$-0.231969\pi$
$487$	−2189.40	−	3792.14i	−0.203719	−	0.352851i	−0.949724	+	0.313089i	$0.898636\pi$
$488$	1756.69	−	3042.67i	0.162954	−	0.282244i
$489$		0			0
$490$	−2343.49	+	311.578i	−0.216057	+	0.0287259i
$491$	6612.37			0.607764			0.303882	−	0.952710i	$-0.401717\pi$
$491$	6612.37			0.607764			0.303882	+	0.952710i	$0.401717\pi$
$492$		0			0
$493$	718.092	+	1243.77i	0.0656008	+	0.113624i
$494$	395.548	+	685.110i	0.0360254	+	0.0623979i
$495$		0			0
$496$	−2327.91			−0.210738
$497$	−15707.9	+	10510.2i	−1.41770	+	0.948588i
$498$		0			0
$499$	5728.21	−	9921.56i	0.513888	−	0.890080i	−0.485982	−	0.873969i	$-0.661538\pi$
$499$	5728.21	−	9921.56i	0.513888	−	0.890080i	0.999870	−	0.0161114i	$-0.00512863\pi$
$500$	1641.25	+	2842.73i	0.146798	+	0.254262i
$501$		0			0
$502$	−1550.76	+	2686.00i	−0.137876	+	0.238808i
$503$	7697.10			0.682300			0.341150	−	0.940009i	$-0.389184\pi$
$503$	7697.10			0.682300			0.341150	+	0.940009i	$0.389184\pi$
$504$		0			0
$505$	−6499.30			−0.572704
$506$	1309.37	−	2267.90i	0.115037	−	0.199250i
$507$		0			0
$508$	1660.47	+	2876.02i	0.145023	+	0.251187i
$509$	2311.98	−	4004.47i	0.201330	−	0.348713i	−0.747627	−	0.664118i	$-0.768807\pi$
$509$	2311.98	−	4004.47i	0.201330	−	0.348713i	0.948957	+	0.315405i	$0.102140\pi$
$510$		0			0
$511$	−9625.12	−	4738.93i	−0.833249	−	0.410250i
$512$	512.000			0.0441942
$513$		0			0
$514$	−5395.44	−	9345.18i	−0.463001	−	0.801942i
$515$	−830.788	−	1438.97i	−0.0710852	−	0.123123i
$516$		0			0
$517$	18159.6			1.54480
$518$	45.5486	+	22.4259i	0.00386350	+	0.00190219i
$519$		0			0
$520$	−141.035	+	244.279i	−0.0118938	+	0.0206007i
$521$	1743.35	+	3019.57i	0.146598	+	0.253915i	0.929968	−	0.367641i	$-0.119834\pi$
$521$	1743.35	+	3019.57i	0.146598	+	0.253915i	−0.783370	+	0.621556i	$0.786501\pi$
$522$		0			0
$523$	2207.57	−	3823.62i	0.184570	−	0.319685i	−0.758862	−	0.651252i	$-0.774244\pi$
$523$	2207.57	−	3823.62i	0.184570	−	0.319685i	0.943432	+	0.331567i	$0.107577\pi$
$524$	−7889.96			−0.657776
$525$		0			0
$526$	−7163.86			−0.593839
$527$	−8617.78	+	14926.4i	−0.712327	+	1.23379i
$528$		0			0
$529$	5426.57	+	9399.10i	0.446008	+	0.772508i
$530$	−2154.27	+	3731.31i	−0.176558	+	0.305807i
$531$		0			0
$532$	−2380.37	+	1592.72i	−0.193989	+	0.129799i
$533$	−1718.83			−0.139682
$534$		0			0
$535$	−2982.01	−	5164.99i	−0.240978	−	0.417387i
$536$	3054.47	+	5290.50i	0.246144	+	0.426334i
$537$		0			0
$538$	2351.10			0.188407
$539$	12282.3	−	1632.99i	0.981514	−	0.130497i
$540$		0			0
$541$	5402.24	−	9356.96i	0.429317	−	0.743599i	−0.567496	−	0.823376i	$-0.692088\pi$
$541$	5402.24	−	9356.96i	0.429317	−	0.743599i	0.996813	+	0.0797775i	$0.0254210\pi$
$542$	−259.327	−	449.168i	−0.0205518	−	0.0355967i
$543$		0			0
$544$	1895.40	−	3282.92i	0.149383	−	0.258739i
$545$	3959.12			0.311175
$546$		0			0
$547$	18783.4			1.46823			0.734113	−	0.679027i	$-0.237598\pi$
$547$	18783.4			1.46823			0.734113	+	0.679027i	$0.237598\pi$
$548$	−137.575	+	238.287i	−0.0107243	+	0.0185750i
$549$		0			0
$550$	−4086.42	−	7077.90i	−0.316810	−	0.548732i
$551$	234.356	−	405.917i	0.0181196	−	0.0313841i
$552$		0			0
$553$	1153.06	+	17421.5i	0.0886677	+	1.33967i
$554$	−2597.85			−0.199227
$555$		0			0
$556$	−3728.96	−	6458.74i	−0.284430	−	0.492647i
$557$	725.568	+	1256.72i	0.0551944	+	0.0955995i	0.892302	−	0.451438i	$-0.149089\pi$
$557$	725.568	+	1256.72i	0.0551944	+	0.0955995i	−0.837108	+	0.547038i	$0.815755\pi$
$558$		0			0
$559$	3062.89			0.231747
$560$	−916.174	−	451.078i	−0.0691347	−	0.0340385i
$561$		0			0
$562$	−4524.25	+	7836.23i	−0.339580	+	0.588169i
$563$	−8390.55	−	14532.9i	−0.628098	−	1.08790i	−0.987933	−	0.154882i	$-0.950500\pi$
$563$	−8390.55	−	14532.9i	−0.628098	−	1.08790i	0.359835	−	0.933016i	$-0.382833\pi$
$564$		0			0
$565$	2294.33	−	3973.90i	0.170838	−	0.295900i
$566$	12956.1			0.962165
$567$		0			0
$568$	−8163.95			−0.603084
$569$	7361.42	−	12750.4i	0.542367	−	0.939407i	−0.456401	−	0.889774i	$-0.650862\pi$
$569$	7361.42	−	12750.4i	0.542367	−	0.939407i	0.998768	−	0.0496328i	$-0.0158051\pi$
$570$		0			0
$571$	−4858.56	−	8415.27i	−0.356085	−	0.616757i	0.631218	−	0.775605i	$-0.282555\pi$
$571$	−4858.56	−	8415.27i	−0.356085	−	0.616757i	−0.987303	+	0.158849i	$0.949222\pi$
$572$	739.168	−	1280.28i	0.0540318	−	0.0935858i
$573$		0			0
$574$	−410.965	−	6209.22i	−0.0298839	−	0.451512i
$575$	−4100.40			−0.297389
$576$		0			0
$577$	10094.4	+	17484.1i	0.728313	+	1.26148i	0.957596	+	0.288116i	$0.0930288\pi$
$577$	10094.4	+	17484.1i	0.728313	+	1.26148i	−0.229282	+	0.973360i	$0.573638\pi$
$578$	−9120.30	−	15796.8i	−0.656322	−	1.13678i
$579$		0			0
$580$	167.122			0.0119644
$581$	7307.00	−	4889.15i	0.521765	−	0.349116i
$582$		0			0
$583$	11290.6	−	19556.0i	0.802076	−	1.38924i
$584$	−2317.13	−	4013.39i	−0.164184	−	0.284376i
$585$		0			0
$586$	−2890.91	+	5007.21i	−0.203793	+	0.352979i
$587$	−21720.8			−1.52728			−0.763641	−	0.645641i	$-0.776590\pi$
$587$	−21720.8			−1.52728			−0.763641	+	0.645641i	$0.776590\pi$
$588$		0			0
$589$	5625.00			0.393504
$590$	−145.498	+	252.010i	−0.0101526	+	0.0175849i
$591$		0			0
$592$	10.9653	+	18.9924i	0.000761268	+	0.00131856i
$593$	9762.14	−	16908.5i	0.676025	−	1.17091i	−0.300143	−	0.953894i	$-0.597034\pi$
$593$	9762.14	−	16908.5i	0.676025	−	1.17091i	0.976168	−	0.217016i	$-0.0696322\pi$
$594$		0			0
$595$	−6283.92	+	4204.60i	−0.432967	+	0.289701i
$596$	81.1735			0.00557885
$597$		0			0
$598$	−370.848	−	642.328i	−0.0253597	−	0.0439243i
$599$	−5799.34	−	10044.7i	−0.395583	−	0.685171i	0.597592	−	0.801800i	$-0.296124\pi$
$599$	−5799.34	−	10044.7i	−0.395583	−	0.685171i	−0.993175	+	0.116630i	$0.962791\pi$
$600$		0			0
$601$	−9335.68			−0.633628			−0.316814	−	0.948488i	$-0.602613\pi$
$601$	−9335.68			−0.633628			−0.316814	+	0.948488i	$0.602613\pi$
$602$	732.327	+	11064.6i	0.0495804	+	0.749104i
$603$		0			0
$604$	3160.65	−	5474.40i	0.212922	−	0.368792i
$605$	44.9540	+	77.8626i	0.00302089	+	0.00523234i
$606$		0			0
$607$	−7575.45	+	13121.1i	−0.506553	+	0.877376i	0.493418	+	0.869792i	$0.335747\pi$
$607$	−7575.45	+	13121.1i	−0.506553	+	0.877376i	−0.999971	+	0.00758385i	$0.997586\pi$
$608$	−1237.16			−0.0825223
$609$		0			0
$610$	−3026.97			−0.200915
$611$	2571.64	−	4454.21i	0.170274	−	0.294923i
$612$		0			0
$613$	−12396.7	−	21471.7i	−0.816798	−	1.41474i	−0.908029	−	0.418906i	$-0.862414\pi$
$613$	−12396.7	−	21471.7i	−0.816798	−	1.41474i	0.0912312	−	0.995830i	$-0.470920\pi$
$614$	3137.42	−	5434.17i	0.206215	−	0.357175i
$615$		0			0
$616$	4801.70	+	2364.12i	0.314068	+	0.154632i
$617$	−25194.6			−1.64391			−0.821957	−	0.569550i	$-0.807118\pi$
$617$	−25194.6			−1.64391			−0.821957	+	0.569550i	$0.807118\pi$
$618$		0			0
$619$	3023.24	+	5236.40i	0.196307	+	0.340014i	0.947328	−	0.320264i	$-0.103772\pi$
$619$	3023.24	+	5236.40i	0.196307	+	0.340014i	−0.751021	+	0.660278i	$0.770438\pi$
$620$	1002.81	+	1736.92i	0.0649578	+	0.112510i
$621$		0			0
$622$	15829.9			1.02045
$623$	−1005.28	−	15188.6i	−0.0646480	−	0.976758i
$624$		0			0
$625$	−5656.19	+	9796.81i	−0.361996	+	0.626996i
$626$	−7616.61	−	13192.4i	−0.486295	−	0.842288i
$627$		0			0
$628$	−6768.70	+	11723.7i	−0.430097	+	0.744949i
$629$	162.372			0.0102928
$630$		0			0
$631$	−6537.14			−0.412424			−0.206212	−	0.978507i	$-0.566114\pi$
$631$	−6537.14			−0.412424			−0.206212	+	0.978507i	$0.566114\pi$
$632$	−3770.92	+	6531.42i	−0.237340	+	0.411086i
$633$		0			0
$634$	−1991.49	−	3449.36i	−0.124751	−	0.216075i
$635$	1430.59	−	2477.85i	0.0894034	−	0.154851i
$636$		0			0
$637$	1338.79	−	3243.86i	0.0832727	−	0.201768i
$638$	−875.892			−0.0543525
$639$		0			0
$640$	−220.558	−	382.018i	−0.0136224	−	0.0235947i
$641$	−4623.39	−	8007.95i	−0.284888	−	0.493440i	0.687694	−	0.726000i	$-0.258623\pi$
$641$	−4623.39	−	8007.95i	−0.284888	−	0.493440i	−0.972582	+	0.232561i	$0.925290\pi$
$642$		0			0
$643$	−157.563			−0.00966355			−0.00483178	−	0.999988i	$-0.501538\pi$
$643$	−157.563			−0.00966355			−0.00483178	+	0.999988i	$0.501538\pi$
$644$	2231.73	−	1493.26i	0.136556	−	0.0913706i
$645$		0			0
$646$	−4579.91	+	7932.63i	−0.278938	+	0.483135i
$647$	6353.00	+	11003.7i	0.386031	+	0.668625i	0.991912	−	0.126930i	$-0.0405124\pi$
$647$	6353.00	+	11003.7i	0.386031	+	0.668625i	−0.605881	+	0.795556i	$0.707179\pi$
$648$		0			0
$649$	762.560	−	1320.79i	0.0461219	−	0.0798854i
$650$	−2314.76			−0.139680
$651$		0			0
$652$	6286.83			0.377624
$653$	−8552.41	+	14813.2i	−0.512529	+	0.887727i	0.487365	+	0.873198i	$0.337958\pi$
$653$	−8552.41	+	14813.2i	−0.512529	+	0.887727i	−0.999894	+	0.0145285i	$0.995375\pi$
$654$		0			0
$655$	3398.82	+	5886.93i	0.202752	+	0.351178i
$656$	1344.00	−	2327.88i	0.0799914	−	0.138549i
$657$		0			0
$658$	16705.6	+	8225.00i	0.989744	+	0.487301i
$659$	−12518.0			−0.739956			−0.369978	−	0.929040i	$-0.620635\pi$
$659$	−12518.0			−0.739956			−0.369978	+	0.929040i	$0.620635\pi$
$660$		0			0
$661$	2390.24	+	4140.01i	0.140650	+	0.243613i	0.927741	−	0.373223i	$-0.121748\pi$
$661$	2390.24	+	4140.01i	0.140650	+	0.243613i	−0.787092	+	0.616836i	$0.788414\pi$
$662$	−2848.63	−	4933.97i	−0.167243	−	0.289674i
$663$		0			0
$664$	3797.71			0.221957
$665$	2213.78	+	1089.96i	0.129093	+	0.0635589i
$666$		0			0
$667$	−219.722	+	380.569i	−0.0127551	+	0.0220925i
$668$	4947.84	+	8569.92i	0.286584	+	0.496377i
$669$		0			0
$670$	2631.60	−	4558.06i	0.151742	−	0.262826i
$671$	15864.4			0.912727
$672$		0			0
$673$	−28447.0			−1.62935			−0.814673	−	0.579920i	$-0.803084\pi$
$673$	−28447.0			−1.62935			−0.814673	+	0.579920i	$0.803084\pi$
$674$	5813.87	−	10069.9i	0.332258	−	0.575488i
$675$		0			0
$676$	4184.65	+	7248.02i	0.238089	+	0.412382i
$677$	7939.27	−	13751.2i	0.450710	−	0.780653i	−0.547720	−	0.836662i	$-0.684504\pi$
$677$	7939.27	−	13751.2i	0.450710	−	0.780653i	0.998430	+	0.0560084i	$0.0178374\pi$
$678$		0			0
$679$	−17057.4	+	11413.2i	−0.964067	+	0.645062i
$680$	−3265.98			−0.184183
$681$		0			0
$682$	−5255.77	−	9103.26i	−0.295093	−	0.511117i
$683$	−1219.23	−	2111.76i	−0.0683052	−	0.118308i	0.829850	−	0.557986i	$-0.188426\pi$
$683$	−1219.23	−	2111.76i	−0.0683052	−	0.118308i	−0.898155	+	0.439678i	$0.855092\pi$
$684$		0			0
$685$	237.057			0.0132226
$686$	12038.5	+	4060.75i	0.670016	+	0.226006i
$687$		0			0
$688$	−2394.97	+	4148.20i	−0.132714	+	0.229867i
$689$	−3197.79	−	5538.74i	−0.176816	−	0.306254i
$690$		0			0
$691$	−11243.5	+	19474.3i	−0.618990	+	1.07212i	0.370681	+	0.928760i	$0.379124\pi$
$691$	−11243.5	+	19474.3i	−0.618990	+	1.07212i	−0.989670	+	0.143361i	$0.954209\pi$
$692$	−16605.4			−0.912198
$693$		0			0
$694$	−6870.21			−0.375777
$695$	−3212.70	+	5564.56i	−0.175345	+	0.303706i
$696$		0			0
$697$	−9950.83	−	17235.3i	−0.540767	−	0.936635i
$698$	3034.99	−	5256.75i	0.164579	−	0.285059i
$699$		0			0
$700$	−553.451	−	8362.01i	−0.0298835	−	0.451506i
$701$	3916.29			0.211008			0.105504	−	0.994419i	$-0.466354\pi$
$701$	3916.29			0.211008			0.105504	+	0.994419i	$0.466354\pi$
$702$		0			0
$703$	−26.4958	−	45.8921i	−0.00142149	−	0.00246210i
$704$	1155.95	+	2002.17i	0.0618844	+	0.107187i
$705$		0			0
$706$	16440.9			0.876431
$707$	31335.6	+	15428.1i	1.66690	+	0.820698i
$708$		0			0
$709$	11455.2	−	19840.9i	0.606780	−	1.05097i	−0.384987	−	0.922922i	$-0.625794\pi$
$709$	11455.2	−	19840.9i	0.606780	−	1.05097i	0.991767	−	0.128053i	$-0.0408726\pi$
$710$	3516.85	+	6091.36i	0.185894	+	0.321979i
$711$		0			0
$712$	3287.62	−	5694.32i	0.173046	−	0.299724i
$713$	−5273.74			−0.277003
$714$		0			0
$715$	−1273.67			−0.0666189
$716$	−8435.86	+	14611.3i	−0.440311	+	0.762642i
$717$		0			0
$718$	9901.59	+	17150.1i	0.514658	+	0.891413i
$719$	10236.4	−	17729.9i	0.530949	−	0.919630i	−0.468399	−	0.883517i	$-0.655169\pi$
$719$	10236.4	−	17729.9i	0.530949	−	0.919630i	0.999348	−	0.0361132i	$-0.0114977\pi$
$720$		0			0
$721$	589.716	+	8909.94i	0.0304607	+	0.460227i
$722$	−10728.6			−0.553016
$723$		0			0
$724$	−7009.29	−	12140.5i	−0.359804	−	0.623199i
$725$	685.730	+	1187.72i	0.0351274	+	0.0608424i
$726$		0			0
$727$	11208.5			0.571802			0.285901	−	0.958259i	$-0.407707\pi$
$727$	11208.5			0.571802			0.285901	+	0.958259i	$0.407707\pi$
$728$	1259.85	−	842.975i	0.0641392	−	0.0429158i
$729$		0			0
$730$	−1996.34	+	3457.76i	−0.101216	+	0.175312i
$731$	17732.1	+	30712.8i	0.897187	+	1.55397i
$732$		0			0
$733$	17719.0	−	30690.2i	0.892860	−	1.54648i	0.0564289	−	0.998407i	$-0.482029\pi$
$733$	17719.0	−	30690.2i	0.892860	−	1.54648i	0.836431	−	0.548072i	$-0.184638\pi$
$734$	22056.1			1.10913
$735$		0			0
$736$	1159.91			0.0580907
$737$	−13792.3	+	23889.0i	−0.689343	+	1.19398i
$738$		0			0
$739$	8967.69	+	15532.5i	0.446389	+	0.773169i	0.998148	−	0.0608348i	$-0.0193763\pi$
$739$	8967.69	+	15532.5i	0.446389	+	0.773169i	−0.551758	+	0.834004i	$0.686043\pi$
$740$	9.44721	−	16.3630i	0.000469306	−	0.000812862i
$741$		0			0
$742$	19244.0	−	12876.3i	0.952115	−	0.637065i
$743$	−19031.0			−0.939676			−0.469838	−	0.882753i	$-0.655688\pi$
$743$	−19031.0			−0.939676			−0.469838	+	0.882753i	$0.655688\pi$
$744$		0			0
$745$	−34.9677	−	60.5659i	−0.00171962	−	0.00297847i
$746$	2746.37	+	4756.86i	0.134788	+	0.233460i
$747$		0			0
$748$	17117.1			0.836716
$749$	2116.71	+	31981.1i	0.103262	+	1.56016i
$750$		0			0
$751$	1364.07	−	2362.63i	0.0662790	−	0.114799i	−0.830982	−	0.556300i	$-0.812221\pi$
$751$	1364.07	−	2362.63i	0.0662790	−	0.114799i	0.897261	+	0.441501i	$0.145554\pi$
$752$	4021.67	+	6965.74i	0.195020	+	0.337785i
$753$		0			0
$754$	−124.037	+	214.839i	−0.00599095	+	0.0103766i
$755$	−5446.15			−0.262524
$756$		0			0
$757$	−6617.58			−0.317728			−0.158864	−	0.987300i	$-0.550783\pi$
$757$	−6617.58			−0.317728			−0.158864	+	0.987300i	$0.550783\pi$
$758$	4184.22	−	7247.28i	0.200498	−	0.347273i
$759$		0			0
$760$	532.942	+	923.083i	0.0254366	+	0.0440575i
$761$	−300.054	+	519.709i	−0.0142930	+	0.0247562i	−0.873083	−	0.487571i	$-0.837883\pi$
$761$	−300.054	+	519.709i	−0.0142930	+	0.0247562i	0.858790	+	0.512327i	$0.171216\pi$
$762$		0			0
$763$	−19088.5	−	9398.20i	−0.905699	−	0.445921i
$764$	−7931.86			−0.375608
$765$		0			0
$766$	−3060.58	−	5301.08i	−0.144364	−	0.250047i
$767$	−215.976	−	374.082i	−0.0101675	−	0.0176106i
$768$		0			0
$769$	−28329.2			−1.32845			−0.664223	−	0.747534i	$-0.731238\pi$
$769$	−28329.2			−1.32845			−0.664223	+	0.747534i	$0.731238\pi$
$770$	−304.530	−	4601.10i	−0.0142526	−	0.215340i
$771$		0			0
$772$	−4223.48	+	7315.29i	−0.196900	+	0.341040i
$773$	11918.5	+	20643.5i	0.554565	+	0.960536i	0.997937	+	0.0641977i	$0.0204488\pi$
$773$	11918.5	+	20643.5i	0.554565	+	0.960536i	−0.443372	+	0.896338i	$0.646218\pi$
$774$		0			0
$775$	−8229.41	+	14253.8i	−0.381431	+	0.660658i
$776$	−8865.32			−0.410111
$777$		0			0
$778$	9839.23			0.453411
$779$	−3247.55	+	5624.93i	−0.149365	+	0.258708i
$780$		0			0
$781$	−18431.9	−	31925.1i	−0.844490	−	1.46270i
$782$	4293.91	−	7437.28i	0.196356	−	0.340098i
$783$		0			0
$784$	3346.45	+	4349.64i	0.152444	+	0.198143i
$785$	11663.2			0.530291
$786$		0			0
$787$	268.455	+	464.977i	0.0121593	+	0.0210606i	0.872041	−	0.489433i	$-0.162796\pi$
$787$	268.455	+	464.977i	0.0121593	+	0.0210606i	−0.859882	+	0.510493i	$0.829463\pi$
$788$	7865.30	+	13623.1i	0.355571	+	0.615866i
$789$		0			0
$790$	6497.71			0.292631
$791$	−20495.1	+	13713.4i	−0.921268	+	0.616425i
$792$		0			0
$793$	2246.61	−	3891.24i	0.100604	−	0.174252i
$794$	13173.3	+	22816.7i	0.588792	+	1.01982i
$795$		0			0
$796$	1105.41	−	1914.62i	0.0492213	−	0.0852538i
$797$	8857.47			0.393661			0.196830	−	0.980438i	$-0.436935\pi$
$797$	8857.47			0.393661			0.196830	+	0.980438i	$0.436935\pi$
$798$		0			0
$799$	59552.1			2.63680
$800$	1809.98	−	3134.97i	0.0799904	−	0.138547i
$801$		0			0
$802$	2662.38	+	4611.37i	0.117222	+	0.203034i
$803$	10462.9	−	18122.3i	0.459810	−	0.796414i
$804$		0			0
$805$	−2075.54	−	1021.89i	−0.0908736	−	0.0447416i
$806$	−2977.13			−0.130106
$807$		0			0
$808$	7543.69	+	13066.0i	0.328448	+	0.568889i
$809$	−10916.5	−	18907.9i	−0.474416	−	0.821713i	0.525155	−	0.851007i	$-0.324007\pi$
$809$	−10916.5	−	18907.9i	−0.474416	−	0.821713i	−0.999571	+	0.0292939i	$0.990674\pi$
$810$		0			0
$811$	−37942.3			−1.64283			−0.821415	−	0.570330i	$-0.806815\pi$
$811$	−37942.3			−1.64283			−0.821415	+	0.570330i	$0.806815\pi$
$812$	−805.758	−	396.715i	−0.0348234	−	0.0171453i
$813$		0			0
$814$	−49.5132	+	85.7593i	−0.00213199	+	0.00369271i
$815$	−2708.22	−	4690.78i	−0.116399	−	0.201609i
$816$		0			0
$817$	5787.03	−	10023.4i	0.247812	−	0.429224i
$818$	−25984.4			−1.11066
$819$		0			0
$820$	−2315.86			−0.0986261
$821$	9038.66	−	15655.4i	0.384228	−	0.665503i	−0.607434	−	0.794370i	$-0.707801\pi$
$821$	9038.66	−	15655.4i	0.384228	−	0.665503i	0.991662	+	0.128868i	$0.0411343\pi$
$822$		0			0
$823$	2451.37	+	4245.90i	0.103827	+	0.179833i	0.913258	−	0.407381i	$-0.133558\pi$
$823$	2451.37	+	4245.90i	0.103827	+	0.179833i	−0.809431	+	0.587214i	$0.800225\pi$
$824$	−1928.58	+	3340.39i	−0.0815353	+	0.141223i
$825$		0			0
$826$	1299.72	−	869.652i	0.0547496	−	0.0366332i
$827$	−19578.9			−0.823247			−0.411623	−	0.911354i	$-0.635038\pi$
$827$	−19578.9			−0.823247			−0.411623	+	0.911354i	$0.635038\pi$
$828$		0			0
$829$	18965.1	+	32848.5i	0.794554	+	1.37621i	0.923122	+	0.384507i	$0.125629\pi$
$829$	18965.1	+	32848.5i	0.794554	+	1.37621i	−0.128568	+	0.991701i	$0.541038\pi$
$830$	−1635.97	−	2833.58i	−0.0684160	−	0.118500i
$831$		0			0
$832$	654.791			0.0272846
$833$	40278.1	−	5355.17i	1.67533	−	0.222744i
$834$		0			0
$835$	4262.84	−	7383.46i	0.176673	−	0.306006i
$836$	−2793.17	−	4837.91i	−0.115555	−	0.200147i
$837$		0			0
$838$	−7236.96	+	12534.8i	−0.298325	+	0.516715i
$839$	5954.22			0.245009			0.122504	−	0.992468i	$-0.460907\pi$
$839$	5954.22			0.245009			0.122504	+	0.992468i	$0.460907\pi$
$840$		0			0
$841$	−24242.0			−0.993973
$842$	−3706.07	+	6419.09i	−0.151686	+	0.262728i
$843$		0			0
$844$	−3441.79	−	5961.36i	−0.140369	−	0.243126i
$845$	3605.31	−	6244.58i	0.146777	−	0.254225i
$846$		0			0
$847$	−31.9096	−	482.117i	−0.00129448	−	0.0195581i
$848$	10001.8			0.405027
$849$		0			0
$850$	−13400.9	−	23211.0i	−0.540760	−	0.936624i
$851$	24.8413	+	43.0263i	0.00100064	+	0.00173317i
$852$		0			0
$853$	−26196.2			−1.05151			−0.525757	−	0.850635i	$-0.676218\pi$
$853$	−26196.2			−1.05151			−0.525757	+	0.850635i	$0.676218\pi$
$854$	14594.2	+	7185.43i	0.584780	+	0.287916i
$855$		0			0
$856$	−6922.38	+	11989.9i	−0.276404	+	0.478746i
$857$	18438.6	+	31936.6i	0.734949	+	1.27297i	0.954746	+	0.297423i	$0.0961272\pi$
$857$	18438.6	+	31936.6i	0.734949	+	1.27297i	−0.219797	+	0.975546i	$0.570539\pi$
$858$		0			0
$859$	−17239.1	+	29859.0i	−0.684740	+	1.18600i	0.288779	+	0.957396i	$0.406751\pi$
$859$	−17239.1	+	29859.0i	−0.684740	+	1.18600i	−0.973519	+	0.228608i	$0.926583\pi$
$860$	4126.79			0.163631
$861$		0			0
$862$	−12764.8			−0.504373
$863$	839.846	−	1454.66i	0.0331271	−	0.0573778i	−0.848987	−	0.528414i	$-0.822787\pi$
$863$	839.846	−	1454.66i	0.0331271	−	0.0573778i	0.882114	+	0.471037i	$0.156120\pi$
$864$		0			0
$865$	7153.22	+	12389.7i	0.281175	+	0.487010i
$866$	7275.62	−	12601.7i	0.285492	−	0.494486i
$867$		0			0
$868$	−711.822	−	10754.8i	−0.0278350	−	0.420556i
$869$	−34054.7			−1.32938
$870$		0			0
$871$	3906.33	+	6765.96i	0.151964	+	0.263210i
$872$	−4595.32	−	7959.33i	−0.178460	−	0.309102i
$873$		0			0
$874$	−2802.72			−0.108471
$875$	−12631.4	+	8451.76i	−0.488024	+	0.326539i
$876$		0			0
$877$	−1251.91	+	2168.37i	−0.0482030	+	0.0834901i	−0.889120	−	0.457674i	$-0.848683\pi$
$877$	−1251.91	+	2168.37i	−0.0482030	+	0.0834901i	0.840917	+	0.541164i	$0.182016\pi$
$878$	−9760.36	−	16905.4i	−0.375167	−	0.649808i
$879$		0			0
$880$	995.918	−	1724.98i	0.0381505	−	0.0660785i
$881$	−34886.0			−1.33410			−0.667048	−	0.745014i	$-0.732443\pi$
$881$	−34886.0			−1.33410			−0.667048	+	0.745014i	$0.732443\pi$
$882$		0			0
$883$	35334.0			1.34664			0.673320	−	0.739351i	$-0.264868\pi$
$883$	35334.0			1.34664			0.673320	+	0.739351i	$0.264868\pi$
$884$	2424.00	−	4198.49i	0.0922262	−	0.159740i
$885$		0			0
$886$	5733.16	+	9930.12i	0.217392	+	0.376534i
$887$	13326.4	−	23082.0i	0.504460	−	0.873750i	−0.495527	−	0.868593i	$-0.665025\pi$
$887$	13326.4	−	23082.0i	0.504460	−	0.873750i	0.999987	−	0.00515772i	$-0.00164176\pi$
$888$		0			0
$889$	−12779.4	+	8550.73i	−0.482121	+	0.322590i
$890$	−5664.93			−0.213358
$891$		0			0
$892$	−9576.87	−	16587.6i	−0.359481	−	0.622640i
$893$	−9717.71	−	16831.6i	−0.364155	−	0.630735i
$894$		0			0
$895$	14535.9			0.542885
$896$	156.558	+	2365.42i	0.00583732	+	0.0881954i
$897$		0			0
$898$	−16628.4	+	28801.2i	−0.617924	+	1.07028i
$899$	881.953	+	1527.59i	0.0327195	+	0.0566718i
$900$		0			0
$901$	37026.1	−	64131.0i	1.36905	−	2.37127i
$902$	12137.5			0.448043
$903$		0			0
$904$	−10652.0			−0.391905
$905$	−6038.90	+	10459.7i	−0.221812	+	0.384189i
$906$		0			0
$907$	23027.5	+	39884.8i	0.843016	+	1.46015i	0.887333	+	0.461130i	$0.152556\pi$
$907$	23027.5	+	39884.8i	0.843016	+	1.46015i	−0.0443164	+	0.999018i	$0.514111\pi$
$908$	8175.18	−	14159.8i	0.298792	−	0.517523i
$909$		0			0
$910$	−1171.68	−	576.879i	−0.0426824	−	0.0210147i
$911$	14227.1			0.517416			0.258708	−	0.965956i	$-0.416703\pi$
$911$	14227.1			0.517416			0.258708	+	0.965956i	$0.416703\pi$
$912$		0			0
$913$	8574.17	+	14850.9i	0.310804	+	0.538328i
$914$	−17119.3	−	29651.5i	−0.619536	−	1.07307i
$915$		0			0
$916$	−16266.4			−0.586745
$917$	−2412.57	−	36451.3i	−0.0868814	−	1.31268i
$918$		0			0
$919$	−3343.47	+	5791.07i	−0.120012	+	0.207867i	−0.919772	−	0.392453i	$-0.871627\pi$
$919$	−3343.47	+	5791.07i	−0.120012	+	0.207867i	0.799760	+	0.600320i	$0.204960\pi$
$920$	−499.662	−	865.441i	−0.0179058	−	0.0310138i
$921$		0			0
$922$	6956.95	−	12049.8i	0.248498	−	0.430411i
$923$	−10440.8			−0.372332
$924$		0			0
$925$	155.054			0.00551151
$926$	−6594.47	+	11422.0i	−0.234026	+	0.405344i
$927$		0			0
$928$	−193.977	−	335.978i	−0.00686164	−	0.0118847i
$929$	6769.82	−	11725.7i	0.239086	−	0.414109i	−0.721366	−	0.692554i	$-0.756486\pi$
$929$	6769.82	−	11725.7i	0.239086	−	0.414109i	0.960452	+	0.278445i	$0.0898189\pi$
$930$		0			0
$931$	−8086.15	−	10510.2i	−0.284654	−	0.369987i
$932$	−713.081			−0.0250620
$933$		0			0
$934$	−14465.8	−	25055.5i	−0.506784	−	0.877775i
$935$	−7373.67	−	12771.6i	−0.257909	−	0.446711i
$936$		0			0
$937$	−12017.0			−0.418974			−0.209487	−	0.977811i	$-0.567179\pi$
$937$	−12017.0			−0.418974			−0.209487	+	0.977811i	$0.567179\pi$
$938$	−23507.9	+	15729.2i	−0.818294	+	0.547524i
$939$		0			0
$940$	3464.90	−	6001.38i	0.120226	−	0.208238i
$941$	−27619.7	−	47838.8i	−0.956831	−	1.65728i	−0.730122	−	0.683316i	$-0.760537\pi$
$941$	−27619.7	−	47838.8i	−0.956831	−	1.65728i	−0.226708	−	0.973963i	$-0.572796\pi$
$942$		0			0
$943$	3044.76	−	5273.67i	0.105144	−	0.182115i
$944$	675.513			0.0232903
$945$		0			0
$946$	−21628.7			−0.743349
$947$	23994.9	−	41560.4i	0.823368	−	1.42611i	−0.0797929	−	0.996811i	$-0.525426\pi$
$947$	23994.9	−	41560.4i	0.823368	−	1.42611i	0.903161	−	0.429303i	$-0.141241\pi$
$948$		0			0
$949$	−2963.36	−	5132.68i	−0.101364	−	0.175568i
$950$	−4373.51	+	7575.14i	−0.149363	+	0.258705i
$951$		0			0
$952$	15746.5	+	7752.80i	0.536080	+	0.263939i
$953$	−19900.0			−0.676415			−0.338207	−	0.941072i	$-0.609821\pi$
$953$	−19900.0			−0.676415			−0.338207	+	0.941072i	$0.609821\pi$
$954$		0			0
$955$	3416.87	+	5918.19i	0.115777	+	0.200532i
$956$	−4237.34	−	7339.29i	−0.143353	−	0.248295i
$957$		0			0
$958$	−8150.94			−0.274890
$959$	−1142.94	−	562.729i	−0.0384855	−	0.0189483i
$960$		0			0
$961$	4311.22	−	7467.25i	0.144715	−	0.250654i
$962$	14.0234	+	24.2892i	0.000469992	+	0.000814050i
$963$		0			0
$964$	−4796.61	+	8307.98i	−0.160258	+	0.277575i
$965$	7277.53			0.242769
$966$		0			0
$967$	−423.293			−0.0140767			−0.00703836	−	0.999975i	$-0.502240\pi$
$967$	−423.293			−0.0140767			−0.00703836	+	0.999975i	$0.502240\pi$
$968$	104.355	−	180.749i	0.00346499	−	0.00600154i
$969$		0			0
$970$	3818.98	+	6614.67i	0.126412	+	0.218953i
$971$	−872.300	+	1510.87i	−0.0288295	+	0.0499342i	−0.880080	−	0.474825i	$-0.842511\pi$
$971$	−872.300	+	1510.87i	−0.0288295	+	0.0499342i	0.851251	+	0.524759i	$0.175845\pi$
$972$		0			0
$973$	28698.9	−	19202.6i	0.945574	−	0.632688i
$974$	8757.58			0.288102
$975$		0			0
$976$	3513.37	+	6085.34i	0.115226	+	0.199577i
$977$	1830.67	+	3170.82i	0.0599472	+	0.103832i	0.894441	−	0.447185i	$-0.147573\pi$
$977$	1830.67	+	3170.82i	0.0599472	+	0.103832i	−0.834494	+	0.551017i	$0.814240\pi$
$978$		0			0
$979$	29690.1			0.969254
$980$	1803.82	−	4370.62i	0.0587968	−	0.142463i
$981$		0			0
$982$	−6612.37	+	11453.0i	−0.214877	+	0.372178i
$983$	13597.1	+	23550.8i	0.441179	+	0.764144i	0.997777	−	0.0666376i	$-0.0212271\pi$
$983$	13597.1	+	23550.8i	0.441179	+	0.764144i	−0.556598	+	0.830782i	$0.687894\pi$
$984$		0			0
$985$	6776.39	−	11737.1i	0.219202	−	0.379669i
$986$	−2872.37			−0.0927736
$987$		0			0
$988$	−1582.19			−0.0509477
$989$	−5425.66	+	9397.52i	−0.174445	+	0.302147i
$990$		0			0
$991$	6769.84	+	11725.7i	0.217004	+	0.375862i	0.953891	−	0.300154i	$-0.0970381\pi$
$991$	6769.84	+	11725.7i	0.217004	+	0.375862i	−0.736886	+	0.676016i	$0.763705\pi$
$992$	2327.91	−	4032.05i	0.0745072	−	0.129050i
$993$		0			0
$994$	−2496.36	−	37717.1i	−0.0796575	−	1.20354i
$995$	−1904.74			−0.0606878
$996$		0			0
$997$	−11431.9	−	19800.6i	−0.363142	−	0.628980i	0.625335	−	0.780357i	$-0.284963\pi$
$997$	−11431.9	−	19800.6i	−0.363142	−	0.628980i	−0.988476	+	0.151377i	$0.951629\pi$
$998$	11456.4	+	19843.1i	0.363374	+	0.629382i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.g.e.37.1	✓	4
3.2	odd	2		126.4.g.f.37.2	yes	4
7.2	even	3		882.4.a.bd.1.2		2
7.3	odd	6		882.4.g.z.361.2		4
7.4	even	3	inner	126.4.g.e.109.1	yes	4
7.5	odd	6		882.4.a.bh.1.1		2
7.6	odd	2		882.4.g.z.667.2		4
21.2	odd	6		882.4.a.ba.1.1		2
21.5	even	6		882.4.a.u.1.2		2
21.11	odd	6		126.4.g.f.109.2	yes	4
21.17	even	6		882.4.g.bj.361.1		4
21.20	even	2		882.4.g.bj.667.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.g.e.37.1	✓	4	1.1	even	1	trivial
126.4.g.e.109.1	yes	4	7.4	even	3	inner
126.4.g.f.37.2	yes	4	3.2	odd	2
126.4.g.f.109.2	yes	4	21.11	odd	6
882.4.a.u.1.2		2	21.5	even	6
882.4.a.ba.1.1		2	21.2	odd	6
882.4.a.bd.1.2		2	7.2	even	3
882.4.a.bh.1.1		2	7.5	odd	6
882.4.g.z.361.2		4	7.3	odd	6
882.4.g.z.667.2		4	7.6	odd	2
882.4.g.bj.361.1		4	21.17	even	6
882.4.g.bj.667.1		4	21.20	even	2

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.72311 + 2.98452i) q^{5} +(15.3924 - 10.2992i) q^{7} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-1.72311 + 2.98452i) q^{5} +(15.3924 - 10.2992i) q^{7} +8.00000 q^{8} +(-3.44622 - 5.96903i) q^{10} +(18.0618 + 31.2839i) q^{11} +10.2311 q^{13} +(2.44622 + 36.9597i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(59.2311 + 102.591i) q^{17} +(19.3307 - 33.4817i) q^{19} +13.7849 q^{20} -72.2471 q^{22} +(-18.1236 + 31.3909i) q^{23} +(56.5618 + 97.9679i) q^{25} +(-10.2311 + 17.7208i) q^{26} +(-66.4622 - 32.7227i) q^{28} +12.1236 q^{29} +(72.7471 + 126.002i) q^{31} +(-16.0000 - 27.7128i) q^{32} -236.924 q^{34} +(4.21511 + 63.6856i) q^{35} +(0.685331 - 1.18703i) q^{37} +(38.6613 + 66.9634i) q^{38} +(-13.7849 + 23.8761i) q^{40} -168.000 q^{41} +299.371 q^{43} +(72.2471 - 125.136i) q^{44} +(-36.2471 - 62.7818i) q^{46} +(251.355 - 435.359i) q^{47} +(130.855 - 317.058i) q^{49} -226.247 q^{50} +(-20.4622 - 35.4416i) q^{52} +(-312.556 - 541.363i) q^{53} -124.490 q^{55} +(123.140 - 82.3933i) q^{56} +(-12.1236 + 20.9986i) q^{58} +(-21.1098 - 36.5632i) q^{59} +(219.586 - 380.334i) q^{61} -290.988 q^{62} +64.0000 q^{64} +(-17.6293 + 30.5349i) q^{65} +(381.809 + 661.312i) q^{67} +(236.924 - 410.365i) q^{68} +(-114.522 - 56.3848i) q^{70} -1020.49 q^{71} +(-289.642 - 501.674i) q^{73} +(1.37066 + 2.37406i) q^{74} -154.645 q^{76} +(600.213 + 295.515i) q^{77} +(-471.365 + 816.428i) q^{79} +(-27.5698 - 47.7523i) q^{80} +(168.000 - 290.985i) q^{82} +474.714 q^{83} -408.247 q^{85} +(-299.371 + 518.525i) q^{86} +(144.494 + 250.271i) q^{88} +(410.952 - 711.790i) q^{89} +(157.482 - 105.372i) q^{91} +144.988 q^{92} +(502.709 + 870.718i) q^{94} +(66.6178 + 115.385i) q^{95} -1108.16 q^{97} +(418.307 + 543.705i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{4} + 7 q^{5} + 6 q^{7} + 32 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 8 * q^4 + 7 * q^5 + 6 * q^7 + 32 * q^8	\( 4 q - 4 q^{2} - 8 q^{4} + 7 q^{5} + 6 q^{7} + 32 q^{8} + 14 q^{10} - 25 q^{11} - 98 q^{13} - 18 q^{14} - 32 q^{16} + 98 q^{17} + 119 q^{19} - 56 q^{20} + 100 q^{22} + 122 q^{23} + 129 q^{25} + 98 q^{26} + 12 q^{28} - 146 q^{29} - 98 q^{31} - 64 q^{32} - 392 q^{34} + 128 q^{35} - 289 q^{37} + 238 q^{38} + 56 q^{40} - 672 q^{41} + 614 q^{43} - 100 q^{44} + 244 q^{46} + 672 q^{47} + 190 q^{49} - 516 q^{50} + 196 q^{52} - 375 q^{53} - 1526 q^{55} + 48 q^{56} + 146 q^{58} + 763 q^{59} + 406 q^{61} + 392 q^{62} + 256 q^{64} - 654 q^{65} + 1041 q^{67} + 392 q^{68} - 986 q^{70} - 3304 q^{71} + 189 q^{73} - 578 q^{74} - 952 q^{76} + 3415 q^{77} - 524 q^{79} + 112 q^{80} + 672 q^{82} - 574 q^{83} - 1244 q^{85} - 614 q^{86} - 200 q^{88} + 2394 q^{89} + 1783 q^{91} - 976 q^{92} + 1344 q^{94} - 706 q^{95} - 126 q^{97} + 2090 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 8 * q^4 + 7 * q^5 + 6 * q^7 + 32 * q^8 + 14 * q^10 - 25 * q^11 - 98 * q^13 - 18 * q^14 - 32 * q^16 + 98 * q^17 + 119 * q^19 - 56 * q^20 + 100 * q^22 + 122 * q^23 + 129 * q^25 + 98 * q^26 + 12 * q^28 - 146 * q^29 - 98 * q^31 - 64 * q^32 - 392 * q^34 + 128 * q^35 - 289 * q^37 + 238 * q^38 + 56 * q^40 - 672 * q^41 + 614 * q^43 - 100 * q^44 + 244 * q^46 + 672 * q^47 + 190 * q^49 - 516 * q^50 + 196 * q^52 - 375 * q^53 - 1526 * q^55 + 48 * q^56 + 146 * q^58 + 763 * q^59 + 406 * q^61 + 392 * q^62 + 256 * q^64 - 654 * q^65 + 1041 * q^67 + 392 * q^68 - 986 * q^70 - 3304 * q^71 + 189 * q^73 - 578 * q^74 - 952 * q^76 + 3415 * q^77 - 524 * q^79 + 112 * q^80 + 672 * q^82 - 574 * q^83 - 1244 * q^85 - 614 * q^86 - 200 * q^88 + 2394 * q^89 + 1783 * q^91 - 976 * q^92 + 1344 * q^94 - 706 * q^95 - 126 * q^97 + 2090 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more