LMFDB - Embedded newform 98.4.c.c.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,4,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not 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:	$5.78218718056$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.4.c.c.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} -4.00000 q^{6} +8.00000 q^{8} +(11.5000 - 19.9186i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} -4.00000 q^{6} +8.00000 q^{8} +(11.5000 - 19.9186i) q^{9} +(12.0000 + 20.7846i) q^{10} +(-24.0000 - 41.5692i) q^{11} +(4.00000 - 6.92820i) q^{12} +56.0000 q^{13} +24.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(57.0000 + 98.7269i) q^{17} +(23.0000 + 39.8372i) q^{18} +(-1.00000 + 1.73205i) q^{19} -48.0000 q^{20} +96.0000 q^{22} +(60.0000 - 103.923i) q^{23} +(8.00000 + 13.8564i) q^{24} +(-9.50000 - 16.4545i) q^{25} +(-56.0000 + 96.9948i) q^{26} +100.000 q^{27} -54.0000 q^{29} +(-24.0000 + 41.5692i) q^{30} +(-118.000 - 204.382i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(48.0000 - 83.1384i) q^{33} -228.000 q^{34} -92.0000 q^{36} +(-73.0000 + 126.440i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(56.0000 + 96.9948i) q^{39} +(48.0000 - 83.1384i) q^{40} +126.000 q^{41} -376.000 q^{43} +(-96.0000 + 166.277i) q^{44} +(-138.000 - 239.023i) q^{45} +(120.000 + 207.846i) q^{46} +(6.00000 - 10.3923i) q^{47} -32.0000 q^{48} +38.0000 q^{50} +(-114.000 + 197.454i) q^{51} +(-112.000 - 193.990i) q^{52} +(-87.0000 - 150.688i) q^{53} +(-100.000 + 173.205i) q^{54} -576.000 q^{55} -4.00000 q^{57} +(54.0000 - 93.5307i) q^{58} +(-69.0000 - 119.512i) q^{59} +(-48.0000 - 83.1384i) q^{60} +(-190.000 + 329.090i) q^{61} +472.000 q^{62} +64.0000 q^{64} +(336.000 - 581.969i) q^{65} +(96.0000 + 166.277i) q^{66} +(242.000 + 419.156i) q^{67} +(228.000 - 394.908i) q^{68} +240.000 q^{69} +576.000 q^{71} +(92.0000 - 159.349i) q^{72} +(575.000 + 995.929i) q^{73} +(-146.000 - 252.879i) q^{74} +(19.0000 - 32.9090i) q^{75} +8.00000 q^{76} -224.000 q^{78} +(-388.000 + 672.036i) q^{79} +(96.0000 + 166.277i) q^{80} +(-210.500 - 364.597i) q^{81} +(-126.000 + 218.238i) q^{82} +378.000 q^{83} +1368.00 q^{85} +(376.000 - 651.251i) q^{86} +(-54.0000 - 93.5307i) q^{87} +(-192.000 - 332.554i) q^{88} +(195.000 - 337.750i) q^{89} +552.000 q^{90} -480.000 q^{92} +(236.000 - 408.764i) q^{93} +(12.0000 + 20.7846i) q^{94} +(12.0000 + 20.7846i) q^{95} +(32.0000 - 55.4256i) q^{96} -1330.00 q^{97} -1104.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 12 q^{5} - 8 q^{6} + 16 q^{8} + 23 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 + 12 * q^5 - 8 * q^6 + 16 * q^8 + 23 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 12 q^{5} - 8 q^{6} + 16 q^{8} + 23 q^{9} + 24 q^{10} - 48 q^{11} + 8 q^{12} + 112 q^{13} + 48 q^{15} - 16 q^{16} + 114 q^{17} + 46 q^{18} - 2 q^{19} - 96 q^{20} + 192 q^{22} + 120 q^{23} + 16 q^{24} - 19 q^{25} - 112 q^{26} + 200 q^{27} - 108 q^{29} - 48 q^{30} - 236 q^{31} - 32 q^{32} + 96 q^{33} - 456 q^{34} - 184 q^{36} - 146 q^{37} - 4 q^{38} + 112 q^{39} + 96 q^{40} + 252 q^{41} - 752 q^{43} - 192 q^{44} - 276 q^{45} + 240 q^{46} + 12 q^{47} - 64 q^{48} + 76 q^{50} - 228 q^{51} - 224 q^{52} - 174 q^{53} - 200 q^{54} - 1152 q^{55} - 8 q^{57} + 108 q^{58} - 138 q^{59} - 96 q^{60} - 380 q^{61} + 944 q^{62} + 128 q^{64} + 672 q^{65} + 192 q^{66} + 484 q^{67} + 456 q^{68} + 480 q^{69} + 1152 q^{71} + 184 q^{72} + 1150 q^{73} - 292 q^{74} + 38 q^{75} + 16 q^{76} - 448 q^{78} - 776 q^{79} + 192 q^{80} - 421 q^{81} - 252 q^{82} + 756 q^{83} + 2736 q^{85} + 752 q^{86} - 108 q^{87} - 384 q^{88} + 390 q^{89} + 1104 q^{90} - 960 q^{92} + 472 q^{93} + 24 q^{94} + 24 q^{95} + 64 q^{96} - 2660 q^{97} - 2208 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 + 12 * q^5 - 8 * q^6 + 16 * q^8 + 23 * q^9 + 24 * q^10 - 48 * q^11 + 8 * q^12 + 112 * q^13 + 48 * q^15 - 16 * q^16 + 114 * q^17 + 46 * q^18 - 2 * q^19 - 96 * q^20 + 192 * q^22 + 120 * q^23 + 16 * q^24 - 19 * q^25 - 112 * q^26 + 200 * q^27 - 108 * q^29 - 48 * q^30 - 236 * q^31 - 32 * q^32 + 96 * q^33 - 456 * q^34 - 184 * q^36 - 146 * q^37 - 4 * q^38 + 112 * q^39 + 96 * q^40 + 252 * q^41 - 752 * q^43 - 192 * q^44 - 276 * q^45 + 240 * q^46 + 12 * q^47 - 64 * q^48 + 76 * q^50 - 228 * q^51 - 224 * q^52 - 174 * q^53 - 200 * q^54 - 1152 * q^55 - 8 * q^57 + 108 * q^58 - 138 * q^59 - 96 * q^60 - 380 * q^61 + 944 * q^62 + 128 * q^64 + 672 * q^65 + 192 * q^66 + 484 * q^67 + 456 * q^68 + 480 * q^69 + 1152 * q^71 + 184 * q^72 + 1150 * q^73 - 292 * q^74 + 38 * q^75 + 16 * q^76 - 448 * q^78 - 776 * q^79 + 192 * q^80 - 421 * q^81 - 252 * q^82 + 756 * q^83 + 2736 * q^85 + 752 * q^86 - 108 * q^87 - 384 * q^88 + 390 * q^89 + 1104 * q^90 - 960 * q^92 + 472 * q^93 + 24 * q^94 + 24 * q^95 + 64 * q^96 - 2660 * q^97 - 2208 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

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
$3$	1.00000	+	1.73205i	0.192450	+	0.333333i	0.946062	−	0.323987i	$-0.105023\pi$
$3$	1.00000	+	1.73205i	0.192450	+	0.333333i	−0.753612	+	0.657320i	$0.771690\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	6.00000	−	10.3923i	0.536656	−	0.929516i	−0.462425	−	0.886658i	$-0.653021\pi$
$5$	6.00000	−	10.3923i	0.536656	−	0.929516i	0.999081	−	0.0428575i	$-0.0136462\pi$
$6$	−4.00000			−0.272166
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	11.5000	−	19.9186i	0.425926	−	0.737725i
$10$	12.0000	+	20.7846i	0.379473	+	0.657267i
$11$	−24.0000	−	41.5692i	−0.657843	−	1.13942i	−0.981173	−	0.193131i	$-0.938136\pi$
$11$	−24.0000	−	41.5692i	−0.657843	−	1.13942i	0.323330	−	0.946286i	$-0.395198\pi$
$12$	4.00000	−	6.92820i	0.0962250	−	0.166667i
$13$	56.0000			1.19474			0.597369	−	0.801966i	$-0.296213\pi$
$13$	56.0000			1.19474			0.597369	+	0.801966i	$0.296213\pi$
$14$		0			0
$15$	24.0000			0.413118
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	57.0000	+	98.7269i	0.813208	+	1.40852i	0.910608	+	0.413272i	$0.135614\pi$
$17$	57.0000	+	98.7269i	0.813208	+	1.40852i	−0.0974001	+	0.995245i	$0.531053\pi$
$18$	23.0000	+	39.8372i	0.301175	+	0.521651i
$19$	−1.00000	+	1.73205i	−0.0120745	+	0.0209137i	−0.872000	−	0.489507i	$-0.837177\pi$
$19$	−1.00000	+	1.73205i	−0.0120745	+	0.0209137i	0.859925	+	0.510420i	$0.170510\pi$
$20$	−48.0000			−0.536656
$21$		0			0
$22$	96.0000			0.930330
$23$	60.0000	−	103.923i	0.543951	−	0.942150i	−0.454721	−	0.890634i	$-0.650261\pi$
$23$	60.0000	−	103.923i	0.543951	−	0.942150i	0.998672	−	0.0515165i	$-0.0164055\pi$
$24$	8.00000	+	13.8564i	0.0680414	+	0.117851i
$25$	−9.50000	−	16.4545i	−0.0760000	−	0.131636i
$26$	−56.0000	+	96.9948i	−0.422404	+	0.731625i
$27$	100.000			0.712778
$28$		0			0
$29$	−54.0000			−0.345778			−0.172889	−	0.984941i	$-0.555310\pi$
$29$	−54.0000			−0.345778			−0.172889	+	0.984941i	$0.555310\pi$
$30$	−24.0000	+	41.5692i	−0.146059	+	0.252982i
$31$	−118.000	−	204.382i	−0.683659	−	1.18413i	−0.973856	−	0.227165i	$-0.927054\pi$
$31$	−118.000	−	204.382i	−0.683659	−	1.18413i	0.290197	−	0.956967i	$-0.406279\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	48.0000	−	83.1384i	0.253204	−	0.438562i
$34$	−228.000			−1.15005
$35$		0			0
$36$	−92.0000			−0.425926
$37$	−73.0000	+	126.440i	−0.324355	+	0.561799i	−0.981382	−	0.192068i	$-0.938480\pi$
$37$	−73.0000	+	126.440i	−0.324355	+	0.561799i	0.657027	+	0.753867i	$0.271814\pi$
$38$	−2.00000	−	3.46410i	−0.00853797	−	0.0147882i
$39$	56.0000	+	96.9948i	0.229928	+	0.398246i
$40$	48.0000	−	83.1384i	0.189737	−	0.328634i
$41$	126.000			0.479949			0.239974	−	0.970779i	$-0.422861\pi$
$41$	126.000			0.479949			0.239974	+	0.970779i	$0.422861\pi$
$42$		0			0
$43$	−376.000			−1.33348			−0.666738	−	0.745292i	$-0.732310\pi$
$43$	−376.000			−1.33348			−0.666738	+	0.745292i	$0.732310\pi$
$44$	−96.0000	+	166.277i	−0.328921	+	0.569709i
$45$	−138.000	−	239.023i	−0.457152	−	0.791810i
$46$	120.000	+	207.846i	0.384631	+	0.666201i
$47$	6.00000	−	10.3923i	0.0186211	−	0.0322526i	−0.856565	−	0.516040i	$-0.827406\pi$
$47$	6.00000	−	10.3923i	0.0186211	−	0.0322526i	0.875186	+	0.483787i	$0.160739\pi$
$48$	−32.0000			−0.0962250
$49$		0			0
$50$	38.0000			0.107480
$51$	−114.000	+	197.454i	−0.313004	+	0.542138i
$52$	−112.000	−	193.990i	−0.298685	−	0.517337i
$53$	−87.0000	−	150.688i	−0.225479	−	0.390540i	0.730984	−	0.682394i	$-0.239061\pi$
$53$	−87.0000	−	150.688i	−0.225479	−	0.390540i	−0.956463	+	0.291854i	$0.905728\pi$
$54$	−100.000	+	173.205i	−0.252005	+	0.436486i
$55$	−576.000			−1.41214
$56$		0			0
$57$	−4.00000			−0.00929496
$58$	54.0000	−	93.5307i	0.122251	−	0.211745i
$59$	−69.0000	−	119.512i	−0.152255	−	0.263713i	0.779801	−	0.626027i	$-0.215320\pi$
$59$	−69.0000	−	119.512i	−0.152255	−	0.263713i	−0.932056	+	0.362314i	$0.881987\pi$
$60$	−48.0000	−	83.1384i	−0.103280	−	0.178885i
$61$	−190.000	+	329.090i	−0.398803	+	0.690748i	−0.993579	−	0.113144i	$-0.963908\pi$
$61$	−190.000	+	329.090i	−0.398803	+	0.690748i	0.594775	+	0.803892i	$0.297241\pi$
$62$	472.000			0.966840
$63$		0			0
$64$	64.0000			0.125000
$65$	336.000	−	581.969i	0.641164	−	1.11053i
$66$	96.0000	+	166.277i	0.179042	+	0.310110i
$67$	242.000	+	419.156i	0.441269	+	0.764300i	0.997784	−	0.0665376i	$-0.0211952\pi$
$67$	242.000	+	419.156i	0.441269	+	0.764300i	−0.556515	+	0.830837i	$0.687862\pi$
$68$	228.000	−	394.908i	0.406604	−	0.704259i
$69$	240.000			0.418733
$70$		0			0
$71$	576.000			0.962798			0.481399	−	0.876502i	$-0.340129\pi$
$71$	576.000			0.962798			0.481399	+	0.876502i	$0.340129\pi$
$72$	92.0000	−	159.349i	0.150588	−	0.260825i
$73$	575.000	+	995.929i	0.921899	+	1.59678i	0.796473	+	0.604674i	$0.206696\pi$
$73$	575.000	+	995.929i	0.921899	+	1.59678i	0.125426	+	0.992103i	$0.459970\pi$
$74$	−146.000	−	252.879i	−0.229353	−	0.397252i
$75$	19.0000	−	32.9090i	0.0292524	−	0.0506667i
$76$	8.00000			0.0120745
$77$		0			0
$78$	−224.000			−0.325167
$79$	−388.000	+	672.036i	−0.552575	+	0.957088i	0.445513	+	0.895275i	$0.353021\pi$
$79$	−388.000	+	672.036i	−0.552575	+	0.957088i	−0.998088	+	0.0618122i	$0.980312\pi$
$80$	96.0000	+	166.277i	0.134164	+	0.232379i
$81$	−210.500	−	364.597i	−0.288752	−	0.500133i
$82$	−126.000	+	218.238i	−0.169687	+	0.293907i
$83$	378.000			0.499890			0.249945	−	0.968260i	$-0.419587\pi$
$83$	378.000			0.499890			0.249945	+	0.968260i	$0.419587\pi$
$84$		0			0
$85$	1368.00			1.74565
$86$	376.000	−	651.251i	0.471455	−	0.816584i
$87$	−54.0000	−	93.5307i	−0.0665449	−	0.115259i
$88$	−192.000	−	332.554i	−0.232583	−	0.402845i
$89$	195.000	−	337.750i	0.232247	−	0.402263i	−0.726222	−	0.687460i	$-0.758726\pi$
$89$	195.000	−	337.750i	0.232247	−	0.402263i	0.958469	+	0.285197i	$0.0920590\pi$
$90$	552.000			0.646510
$91$		0			0
$92$	−480.000			−0.543951
$93$	236.000	−	408.764i	0.263140	−	0.455773i
$94$	12.0000	+	20.7846i	0.0131671	+	0.0228061i
$95$	12.0000	+	20.7846i	0.0129597	+	0.0224469i
$96$	32.0000	−	55.4256i	0.0340207	−	0.0589256i
$97$	−1330.00			−1.39218			−0.696088	−	0.717957i	$-0.745078\pi$
$97$	−1330.00			−1.39218			−0.696088	+	0.717957i	$0.745078\pi$
$98$		0			0
$99$	−1104.00			−1.12077
$100$	−38.0000	+	65.8179i	−0.0380000	+	0.0658179i
$101$	750.000	+	1299.04i	0.738889	+	1.27979i	0.952996	+	0.302983i	$0.0979826\pi$
$101$	750.000	+	1299.04i	0.738889	+	1.27979i	−0.214107	+	0.976810i	$0.568684\pi$
$102$	−228.000	−	394.908i	−0.221327	−	0.383350i
$103$	−190.000	+	329.090i	−0.181760	+	0.314817i	−0.942480	−	0.334263i	$-0.891513\pi$
$103$	−190.000	+	329.090i	−0.181760	+	0.314817i	0.760720	+	0.649080i	$0.224846\pi$
$104$	448.000			0.422404
$105$		0			0
$106$	348.000			0.318875
$107$	−318.000	+	550.792i	−0.287310	+	0.497636i	−0.973167	−	0.230101i	$-0.926094\pi$
$107$	−318.000	+	550.792i	−0.287310	+	0.497636i	0.685856	+	0.727737i	$0.259428\pi$
$108$	−200.000	−	346.410i	−0.178195	−	0.308642i
$109$	−73.0000	−	126.440i	−0.0641480	−	0.111108i	0.832168	−	0.554524i	$-0.187100\pi$
$109$	−73.0000	−	126.440i	−0.0641480	−	0.111108i	−0.896316	+	0.443416i	$0.853766\pi$
$110$	576.000	−	997.661i	0.499268	−	0.864757i
$111$	−292.000			−0.249688
$112$		0			0
$113$	198.000			0.164834			0.0824171	−	0.996598i	$-0.473736\pi$
$113$	198.000			0.164834			0.0824171	+	0.996598i	$0.473736\pi$
$114$	4.00000	−	6.92820i	0.00328627	−	0.00569198i
$115$	−720.000	−	1247.08i	−0.583829	−	1.01122i
$116$	108.000	+	187.061i	0.0864444	+	0.149726i
$117$	644.000	−	1115.44i	0.508870	−	0.881389i
$118$	276.000			0.215321
$119$		0			0
$120$	192.000			0.146059
$121$	−486.500	+	842.643i	−0.365515	+	0.633090i
$122$	−380.000	−	658.179i	−0.281997	−	0.488432i
$123$	126.000	+	218.238i	0.0923662	+	0.159983i
$124$	−472.000	+	817.528i	−0.341829	+	0.592066i
$125$	1272.00			0.910169
$126$		0			0
$127$	−376.000			−0.262713			−0.131357	−	0.991335i	$-0.541933\pi$
$127$	−376.000			−0.262713			−0.131357	+	0.991335i	$0.541933\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−376.000	−	651.251i	−0.256628	−	0.444492i
$130$	672.000	+	1163.94i	0.453372	+	0.785263i
$131$	−1065.00	+	1844.63i	−0.710301	+	1.23028i	0.254443	+	0.967088i	$0.418108\pi$
$131$	−1065.00	+	1844.63i	−0.710301	+	1.23028i	−0.964744	+	0.263190i	$0.915225\pi$
$132$	−384.000			−0.253204
$133$		0			0
$134$	−968.000			−0.624048
$135$	600.000	−	1039.23i	0.382517	−	0.662539i
$136$	456.000	+	789.815i	0.287512	+	0.497986i
$137$	39.0000	+	67.5500i	0.0243211	+	0.0421254i	0.877930	−	0.478789i	$-0.158924\pi$
$137$	39.0000	+	67.5500i	0.0243211	+	0.0421254i	−0.853609	+	0.520915i	$0.825591\pi$
$138$	−240.000	+	415.692i	−0.148045	+	0.256421i
$139$	−2338.00			−1.42667			−0.713333	−	0.700825i	$-0.752815\pi$
$139$	−2338.00			−1.42667			−0.713333	+	0.700825i	$0.752815\pi$
$140$		0			0
$141$	24.0000			0.0143345
$142$	−576.000	+	997.661i	−0.340400	+	0.589591i
$143$	−1344.00	−	2327.88i	−0.785951	−	1.36131i
$144$	184.000	+	318.697i	0.106481	+	0.184431i
$145$	−324.000	+	561.184i	−0.185564	+	0.321406i
$146$	−2300.00			−1.30376
$147$		0			0
$148$	584.000			0.324355
$149$	501.000	−	867.757i	0.275460	−	0.477110i	−0.694791	−	0.719212i	$-0.744503\pi$
$149$	501.000	−	867.757i	0.275460	−	0.477110i	0.970251	+	0.242101i	$0.0778366\pi$
$150$	38.0000	+	65.8179i	0.0206846	+	0.0358267i
$151$	1376.00	+	2383.30i	0.741571	+	1.28444i	0.951780	+	0.306783i	$0.0992525\pi$
$151$	1376.00	+	2383.30i	0.741571	+	1.28444i	−0.210208	+	0.977657i	$0.567414\pi$
$152$	−8.00000	+	13.8564i	−0.00426898	+	0.00739410i
$153$	2622.00			1.38546
$154$		0			0
$155$	−2832.00			−1.46756
$156$	224.000	−	387.979i	0.114964	−	0.199123i
$157$	260.000	+	450.333i	0.132167	+	0.228920i	0.924512	−	0.381154i	$-0.124473\pi$
$157$	260.000	+	450.333i	0.132167	+	0.228920i	−0.792345	+	0.610074i	$0.791140\pi$
$158$	−776.000	−	1344.07i	−0.390729	−	0.676763i
$159$	174.000	−	301.377i	0.0867868	−	0.150319i
$160$	−384.000			−0.189737
$161$		0			0
$162$	842.000			0.408357
$163$	−640.000	+	1108.51i	−0.307538	+	0.532671i	−0.977823	−	0.209432i	$-0.932838\pi$
$163$	−640.000	+	1108.51i	−0.307538	+	0.532671i	0.670285	+	0.742104i	$0.266172\pi$
$164$	−252.000	−	436.477i	−0.119987	−	0.207824i
$165$	−576.000	−	997.661i	−0.271767	−	0.470714i
$166$	−378.000	+	654.715i	−0.176738	+	0.306119i
$167$	1764.00			0.817380			0.408690	−	0.912673i	$-0.365986\pi$
$167$	1764.00			0.817380			0.408690	+	0.912673i	$0.365986\pi$
$168$		0			0
$169$	939.000			0.427401
$170$	−1368.00	+	2369.45i	−0.617181	+	1.06899i
$171$	23.0000	+	39.8372i	0.0102857	+	0.0178153i
$172$	752.000	+	1302.50i	0.333369	+	0.577412i
$173$	384.000	−	665.108i	0.168757	−	0.292296i	−0.769226	−	0.638977i	$-0.779358\pi$
$173$	384.000	−	665.108i	0.168757	−	0.292296i	0.937983	+	0.346681i	$0.112691\pi$
$174$	216.000			0.0941087
$175$		0			0
$176$	768.000			0.328921
$177$	138.000	−	239.023i	0.0586029	−	0.101503i
$178$	390.000	+	675.500i	0.164223	+	0.284443i
$179$	−906.000	−	1569.24i	−0.378311	−	0.655253i	0.612506	−	0.790466i	$-0.290162\pi$
$179$	−906.000	−	1569.24i	−0.378311	−	0.655253i	−0.990817	+	0.135213i	$0.956828\pi$
$180$	−552.000	+	956.092i	−0.228576	+	0.395905i
$181$	−448.000			−0.183976			−0.0919878	−	0.995760i	$-0.529322\pi$
$181$	−448.000			−0.183976			−0.0919878	+	0.995760i	$0.529322\pi$
$182$		0			0
$183$	−760.000			−0.306999
$184$	480.000	−	831.384i	0.192316	−	0.333100i
$185$	876.000	+	1517.28i	0.348134	+	0.602986i
$186$	472.000	+	817.528i	0.186068	+	0.322280i
$187$	2736.00	−	4738.89i	1.06993	−	1.85317i
$188$	−48.0000			−0.0186211
$189$		0			0
$190$	−48.0000			−0.0183278
$191$	1068.00	−	1849.83i	0.404596	−	0.700780i	−0.589679	−	0.807638i	$-0.700746\pi$
$191$	1068.00	−	1849.83i	0.404596	−	0.700780i	0.994274	+	0.106858i	$0.0340789\pi$
$192$	64.0000	+	110.851i	0.0240563	+	0.0416667i
$193$	−2215.00	−	3836.49i	−0.826110	−	1.43086i	−0.901068	−	0.433677i	$-0.857216\pi$
$193$	−2215.00	−	3836.49i	−0.826110	−	1.43086i	0.0749584	−	0.997187i	$-0.476118\pi$
$194$	1330.00	−	2303.63i	0.492208	−	0.852530i
$195$	1344.00			0.493568
$196$		0			0
$197$	198.000			0.0716087			0.0358044	−	0.999359i	$-0.488601\pi$
$197$	198.000			0.0716087			0.0358044	+	0.999359i	$0.488601\pi$
$198$	1104.00	−	1912.18i	0.396252	−	0.686328i
$199$	1142.00	+	1978.00i	0.406805	+	0.704607i	0.994530	−	0.104454i	$-0.0333094\pi$
$199$	1142.00	+	1978.00i	0.406805	+	0.704607i	−0.587725	+	0.809061i	$0.699976\pi$
$200$	−76.0000	−	131.636i	−0.0268701	−	0.0465403i
$201$	−484.000	+	838.313i	−0.169844	+	0.294179i
$202$	−3000.00			−1.04495
$203$		0			0
$204$	912.000			0.313004
$205$	756.000	−	1309.43i	0.257567	−	0.446120i
$206$	−380.000	−	658.179i	−0.128524	−	0.222609i
$207$	−1380.00	−	2390.23i	−0.463365	−	0.802572i
$208$	−448.000	+	775.959i	−0.149342	+	0.258669i
$209$	96.0000			0.0317725
$210$		0			0
$211$	4412.00			1.43950			0.719750	−	0.694233i	$-0.244256\pi$
$211$	4412.00			1.43950			0.719750	+	0.694233i	$0.244256\pi$
$212$	−348.000	+	602.754i	−0.112739	+	0.195270i
$213$	576.000	+	997.661i	0.185290	+	0.320933i
$214$	−636.000	−	1101.58i	−0.203159	−	0.351882i
$215$	−2256.00	+	3907.51i	−0.715618	+	1.23949i
$216$	800.000			0.252005
$217$		0			0
$218$	292.000			0.0907190
$219$	−1150.00	+	1991.86i	−0.354839	+	0.614600i
$220$	1152.00	+	1995.32i	0.353036	+	0.611476i
$221$	3192.00	+	5528.71i	0.971571	+	1.68281i
$222$	292.000	−	505.759i	0.0882782	−	0.152902i
$223$	2072.00			0.622204			0.311102	−	0.950377i	$-0.399302\pi$
$223$	2072.00			0.622204			0.311102	+	0.950377i	$0.399302\pi$
$224$		0			0
$225$	−437.000			−0.129481
$226$	−198.000	+	342.946i	−0.0582777	+	0.100940i
$227$	183.000	+	316.965i	0.0535072	+	0.0926772i	0.891538	−	0.452945i	$-0.149627\pi$
$227$	183.000	+	316.965i	0.0535072	+	0.0926772i	−0.838031	+	0.545622i	$0.816293\pi$
$228$	8.00000	+	13.8564i	0.00232374	+	0.00402484i
$229$	188.000	−	325.626i	0.0542506	−	0.0939648i	−0.837625	−	0.546246i	$-0.816056\pi$
$229$	188.000	−	325.626i	0.0542506	−	0.0939648i	0.891875	+	0.452281i	$0.149390\pi$
$230$	2880.00			0.825659
$231$		0			0
$232$	−432.000			−0.122251
$233$	1131.00	−	1958.95i	0.318001	−	0.550794i	−0.662070	−	0.749442i	$-0.730322\pi$
$233$	1131.00	−	1958.95i	0.318001	−	0.550794i	0.980071	+	0.198648i	$0.0636551\pi$
$234$	1288.00	+	2230.88i	0.359826	+	0.623236i
$235$	−72.0000	−	124.708i	−0.0199862	−	0.0346172i
$236$	−276.000	+	478.046i	−0.0761274	+	0.131857i
$237$	−1552.00			−0.425372
$238$		0			0
$239$	2592.00			0.701517			0.350758	−	0.936466i	$-0.385924\pi$
$239$	2592.00			0.701517			0.350758	+	0.936466i	$0.385924\pi$
$240$	−192.000	+	332.554i	−0.0516398	+	0.0894427i
$241$	−55.0000	−	95.2628i	−0.0147007	−	0.0254623i	0.858581	−	0.512677i	$-0.171346\pi$
$241$	−55.0000	−	95.2628i	−0.0147007	−	0.0254623i	−0.873282	+	0.487215i	$0.838013\pi$
$242$	−973.000	−	1685.29i	−0.258458	−	0.447662i
$243$	1771.00	−	3067.46i	0.467530	−	0.809785i
$244$	1520.00			0.398803
$245$		0			0
$246$	−504.000			−0.130625
$247$	−56.0000	+	96.9948i	−0.0144259	+	0.0249864i
$248$	−944.000	−	1635.06i	−0.241710	−	0.418654i
$249$	378.000	+	654.715i	0.0962039	+	0.166630i
$250$	−1272.00	+	2203.17i	−0.321793	+	0.557362i
$251$	−1890.00			−0.475282			−0.237641	−	0.971353i	$-0.576374\pi$
$251$	−1890.00			−0.475282			−0.237641	+	0.971353i	$0.576374\pi$
$252$		0			0
$253$	−5760.00			−1.43134
$254$	376.000	−	651.251i	0.0928832	−	0.160878i
$255$	1368.00	+	2369.45i	0.335951	+	0.581884i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−1065.00	+	1844.63i	−0.258494	+	0.447724i	−0.965839	−	0.259144i	$-0.916559\pi$
$257$	−1065.00	+	1844.63i	−0.258494	+	0.447724i	0.707345	+	0.706869i	$0.249893\pi$
$258$	1504.00			0.362926
$259$		0			0
$260$	−2688.00			−0.641164
$261$	−621.000	+	1075.60i	−0.147276	+	0.255089i
$262$	−2130.00	−	3689.27i	−0.502259	−	0.869938i
$263$	2496.00	+	4323.20i	0.585209	+	1.01361i	0.994849	+	0.101365i	$0.0323208\pi$
$263$	2496.00	+	4323.20i	0.585209	+	1.01361i	−0.409640	+	0.912247i	$0.634346\pi$
$264$	384.000	−	665.108i	0.0895211	−	0.155055i
$265$	−2088.00			−0.484018
$266$		0			0
$267$	780.000			0.178784
$268$	968.000	−	1676.63i	0.220634	−	0.382150i
$269$	−3408.00	−	5902.83i	−0.772451	−	1.33793i	−0.936216	−	0.351426i	$-0.885697\pi$
$269$	−3408.00	−	5902.83i	−0.772451	−	1.33793i	0.163764	−	0.986499i	$-0.447636\pi$
$270$	1200.00	+	2078.46i	0.270480	+	0.468486i
$271$	−4096.00	+	7094.48i	−0.918134	+	1.59025i	−0.115887	+	0.993262i	$0.536971\pi$
$271$	−4096.00	+	7094.48i	−0.918134	+	1.59025i	−0.802247	+	0.596992i	$0.796362\pi$
$272$	−1824.00			−0.406604
$273$		0			0
$274$	−156.000			−0.0343953
$275$	−456.000	+	789.815i	−0.0999921	+	0.173191i
$276$	−480.000	−	831.384i	−0.104683	−	0.181317i
$277$	−1207.00	−	2090.59i	−0.261811	−	0.453470i	0.704912	−	0.709294i	$-0.250986\pi$
$277$	−1207.00	−	2090.59i	−0.261811	−	0.453470i	−0.966723	+	0.255825i	$0.917653\pi$
$278$	2338.00	−	4049.53i	0.504403	−	0.873651i
$279$	−5428.00			−1.16475
$280$		0			0
$281$	1962.00			0.416524			0.208262	−	0.978073i	$-0.433219\pi$
$281$	1962.00			0.416524			0.208262	+	0.978073i	$0.433219\pi$
$282$	−24.0000	+	41.5692i	−0.00506801	+	0.00877805i
$283$	−2701.00	−	4678.27i	−0.567342	−	0.982665i	−0.996828	−	0.0795914i	$-0.974638\pi$
$283$	−2701.00	−	4678.27i	−0.567342	−	0.982665i	0.429486	−	0.903074i	$-0.358695\pi$
$284$	−1152.00	−	1995.32i	−0.240699	−	0.416904i
$285$	−24.0000	+	41.5692i	−0.00498820	+	0.00863982i
$286$	5376.00			1.11150
$287$		0			0
$288$	−736.000			−0.150588
$289$	−4041.50	+	7000.08i	−0.822613	+	1.42481i
$290$	−648.000	−	1122.37i	−0.131213	−	0.227268i
$291$	−1330.00	−	2303.63i	−0.267924	−	0.464059i
$292$	2300.00	−	3983.72i	0.460950	−	0.798388i
$293$	−4788.00			−0.954669			−0.477334	−	0.878722i	$-0.658397\pi$
$293$	−4788.00			−0.954669			−0.477334	+	0.878722i	$0.658397\pi$
$294$		0			0
$295$	−1656.00			−0.326834
$296$	−584.000	+	1011.52i	−0.114677	+	0.198626i
$297$	−2400.00	−	4156.92i	−0.468896	−	0.812152i
$298$	1002.00	+	1735.51i	0.194780	+	0.337368i
$299$	3360.00	−	5819.69i	0.649879	−	1.12562i
$300$	−152.000			−0.0292524
$301$		0			0
$302$	−5504.00			−1.04874
$303$	−1500.00	+	2598.08i	−0.284399	+	0.492593i
$304$	−16.0000	−	27.7128i	−0.00301863	−	0.00522842i
$305$	2280.00	+	3949.08i	0.428041	+	0.741388i
$306$	−2622.00	+	4541.44i	−0.489836	+	0.848421i
$307$	−574.000			−0.106710			−0.0533549	−	0.998576i	$-0.516991\pi$
$307$	−574.000			−0.106710			−0.0533549	+	0.998576i	$0.516991\pi$
$308$		0			0
$309$	−760.000			−0.139919
$310$	2832.00	−	4905.17i	0.518861	−	0.898693i
$311$	4404.00	+	7627.95i	0.802984	+	1.39081i	0.917644	+	0.397404i	$0.130089\pi$
$311$	4404.00	+	7627.95i	0.802984	+	1.39081i	−0.114660	+	0.993405i	$0.536578\pi$
$312$	448.000	+	775.959i	0.0812917	+	0.140801i
$313$	1385.00	−	2398.89i	0.250111	−	0.433205i	−0.713445	−	0.700711i	$-0.752866\pi$
$313$	1385.00	−	2398.89i	0.250111	−	0.433205i	0.963556	+	0.267506i	$0.0861995\pi$
$314$	−1040.00			−0.186913
$315$		0			0
$316$	3104.00			0.552575
$317$	−3783.00	+	6552.35i	−0.670266	+	1.16094i	0.307562	+	0.951528i	$0.400487\pi$
$317$	−3783.00	+	6552.35i	−0.670266	+	1.16094i	−0.977828	+	0.209407i	$0.932847\pi$
$318$	348.000	+	602.754i	0.0613675	+	0.106292i
$319$	1296.00	+	2244.74i	0.227467	+	0.393985i
$320$	384.000	−	665.108i	0.0670820	−	0.116190i
$321$	−1272.00			−0.221172
$322$		0			0
$323$	−228.000			−0.0392763
$324$	−842.000	+	1458.39i	−0.144376	+	0.250066i
$325$	−532.000	−	921.451i	−0.0908002	−	0.157270i
$326$	−1280.00	−	2217.03i	−0.217462	−	0.376655i
$327$	146.000	−	252.879i	0.0246906	−	0.0427653i
$328$	1008.00			0.169687
$329$		0			0
$330$	2304.00			0.384336
$331$	5660.00	−	9803.41i	0.939884	−	1.62793i	0.174201	−	0.984710i	$-0.444266\pi$
$331$	5660.00	−	9803.41i	0.939884	−	1.62793i	0.765684	−	0.643217i	$-0.222401\pi$
$332$	−756.000	−	1309.43i	−0.124973	−	0.216459i
$333$	1679.00	+	2908.11i	0.276302	+	0.478569i
$334$	−1764.00	+	3055.34i	−0.288987	+	0.500541i
$335$	5808.00			0.947239
$336$		0			0
$337$	−4786.00			−0.773620			−0.386810	−	0.922159i	$-0.626423\pi$
$337$	−4786.00			−0.773620			−0.386810	+	0.922159i	$0.626423\pi$
$338$	−939.000	+	1626.40i	−0.151109	+	0.261729i
$339$	198.000	+	342.946i	0.0317224	+	0.0549448i
$340$	−2736.00	−	4738.89i	−0.436413	−	0.755890i
$341$	−5664.00	+	9810.34i	−0.899480	+	1.55795i
$342$	−92.0000			−0.0145462
$343$		0			0
$344$	−3008.00			−0.471455
$345$	1440.00	−	2494.15i	0.224716	−	0.389219i
$346$	768.000	+	1330.22i	0.119329	+	0.206684i
$347$	−6324.00	−	10953.5i	−0.978358	−	1.69457i	−0.668378	−	0.743822i	$-0.733011\pi$
$347$	−6324.00	−	10953.5i	−0.978358	−	1.69457i	−0.309980	−	0.950743i	$-0.600322\pi$
$348$	−216.000	+	374.123i	−0.0332725	+	0.0576296i
$349$	9632.00			1.47733			0.738666	−	0.674071i	$-0.235456\pi$
$349$	9632.00			1.47733			0.738666	+	0.674071i	$0.235456\pi$
$350$		0			0
$351$	5600.00			0.851584
$352$	−768.000	+	1330.22i	−0.116291	+	0.201422i
$353$	1695.00	+	2935.83i	0.255569	+	0.442658i	0.965050	−	0.262066i	$-0.0844040\pi$
$353$	1695.00	+	2935.83i	0.255569	+	0.442658i	−0.709481	+	0.704724i	$0.751071\pi$
$354$	276.000	+	478.046i	0.0414385	+	0.0717736i
$355$	3456.00	−	5985.97i	0.516691	−	0.894936i
$356$	−1560.00			−0.232247
$357$		0			0
$358$	3624.00			0.535012
$359$	5352.00	−	9269.94i	0.786818	−	1.36281i	−0.141089	−	0.989997i	$-0.545060\pi$
$359$	5352.00	−	9269.94i	0.786818	−	1.36281i	0.927907	−	0.372812i	$-0.121606\pi$
$360$	−1104.00	−	1912.18i	−0.161628	−	0.279947i
$361$	3427.50	+	5936.60i	0.499708	+	0.865520i
$362$	448.000	−	775.959i	0.0650452	−	0.112662i
$363$	−1946.00			−0.281373
$364$		0			0
$365$	13800.0			1.97897
$366$	760.000	−	1316.36i	0.108541	−	0.187998i
$367$	4292.00	+	7433.96i	0.610465	+	1.05736i	0.991162	+	0.132656i	$0.0423507\pi$
$367$	4292.00	+	7433.96i	0.610465	+	1.05736i	−0.380697	+	0.924700i	$0.624316\pi$
$368$	960.000	+	1662.77i	0.135988	+	0.235538i
$369$	1449.00	−	2509.74i	0.204423	−	0.354070i
$370$	−3504.00			−0.492336
$371$		0			0
$372$	−1888.00			−0.263140
$373$	1061.00	−	1837.71i	0.147283	−	0.255101i	−0.782939	−	0.622098i	$-0.786281\pi$
$373$	1061.00	−	1837.71i	0.147283	−	0.255101i	0.930222	+	0.366997i	$0.119614\pi$
$374$	5472.00	+	9477.78i	0.756552	+	1.31039i
$375$	1272.00	+	2203.17i	0.175162	+	0.303390i
$376$	48.0000	−	83.1384i	0.00658354	−	0.0114030i
$377$	−3024.00			−0.413114
$378$		0			0
$379$	−4912.00			−0.665732			−0.332866	−	0.942974i	$-0.608016\pi$
$379$	−4912.00			−0.665732			−0.332866	+	0.942974i	$0.608016\pi$
$380$	48.0000	−	83.1384i	0.00647986	−	0.0112235i
$381$	−376.000	−	651.251i	−0.0505592	−	0.0875711i
$382$	2136.00	+	3699.66i	0.286092	+	0.495526i
$383$	−4530.00	+	7846.19i	−0.604366	+	1.04679i	0.387785	+	0.921750i	$0.373240\pi$
$383$	−4530.00	+	7846.19i	−0.604366	+	1.04679i	−0.992151	+	0.125043i	$0.960093\pi$
$384$	−256.000			−0.0340207
$385$		0			0
$386$	8860.00			1.16830
$387$	−4324.00	+	7489.39i	−0.567962	+	0.983739i
$388$	2660.00	+	4607.26i	0.348044	+	0.602830i
$389$	−4497.00	−	7789.03i	−0.586136	−	1.01522i	−0.994733	−	0.102502i	$-0.967315\pi$
$389$	−4497.00	−	7789.03i	−0.586136	−	1.01522i	0.408597	−	0.912715i	$-0.366018\pi$
$390$	−1344.00	+	2327.88i	−0.174503	+	0.302248i
$391$	13680.0			1.76938
$392$		0			0
$393$	−4260.00			−0.546790
$394$	−198.000	+	342.946i	−0.0253175	+	0.0438512i
$395$	4656.00	+	8064.43i	0.593086	+	1.02725i
$396$	2208.00	+	3824.37i	0.280192	+	0.485307i
$397$	6488.00	−	11237.5i	0.820210	−	1.42065i	−0.0853156	−	0.996354i	$-0.527190\pi$
$397$	6488.00	−	11237.5i	0.820210	−	1.42065i	0.905526	−	0.424291i	$-0.139477\pi$
$398$	−4568.00			−0.575309
$399$		0			0
$400$	304.000			0.0380000
$401$	1761.00	−	3050.14i	0.219302	−	0.379842i	−0.735293	−	0.677750i	$-0.762955\pi$
$401$	1761.00	−	3050.14i	0.219302	−	0.379842i	0.954595	+	0.297907i	$0.0962886\pi$
$402$	−968.000	−	1676.63i	−0.120098	−	0.208016i
$403$	−6608.00	−	11445.4i	−0.816794	−	1.41473i
$404$	3000.00	−	5196.15i	0.369445	−	0.639897i
$405$	−5052.00			−0.619842
$406$		0			0
$407$	7008.00			0.853498
$408$	−912.000	+	1579.63i	−0.110664	+	0.191675i
$409$	−6355.00	−	11007.2i	−0.768300	−	1.33073i	−0.938484	−	0.345322i	$-0.887770\pi$
$409$	−6355.00	−	11007.2i	−0.768300	−	1.33073i	0.170185	−	0.985412i	$-0.445564\pi$
$410$	1512.00	+	2618.86i	0.182128	+	0.315454i
$411$	−78.0000	+	135.100i	−0.00936121	+	0.0162141i
$412$	1520.00			0.181760
$413$		0			0
$414$	5520.00			0.655298
$415$	2268.00	−	3928.29i	0.268269	−	0.464656i
$416$	−896.000	−	1551.92i	−0.105601	−	0.182906i
$417$	−2338.00	−	4049.53i	−0.274562	−	0.475555i
$418$	−96.0000	+	166.277i	−0.0112333	+	0.0194566i
$419$	1638.00			0.190982			0.0954911	−	0.995430i	$-0.469558\pi$
$419$	1638.00			0.190982			0.0954911	+	0.995430i	$0.469558\pi$
$420$		0			0
$421$	−12850.0			−1.48758			−0.743789	−	0.668414i	$-0.766973\pi$
$421$	−12850.0			−1.48758			−0.743789	+	0.668414i	$0.766973\pi$
$422$	−4412.00	+	7641.81i	−0.508940	+	0.881510i
$423$	−138.000	−	239.023i	−0.0158624	−	0.0274745i
$424$	−696.000	−	1205.51i	−0.0797187	−	0.138077i
$425$	1083.00	−	1875.81i	0.123608	−	0.214095i
$426$	−2304.00			−0.262040
$427$		0			0
$428$	2544.00			0.287310
$429$	2688.00	−	4655.75i	0.302513	−	0.523967i
$430$	−4512.00	−	7815.01i	−0.506019	−	0.876450i
$431$	4008.00	+	6942.06i	0.447932	+	0.775840i	0.998251	−	0.0591136i	$-0.0188274\pi$
$431$	4008.00	+	6942.06i	0.447932	+	0.775840i	−0.550320	+	0.834954i	$0.685494\pi$
$432$	−800.000	+	1385.64i	−0.0890973	+	0.154321i
$433$	2198.00			0.243947			0.121974	−	0.992533i	$-0.461078\pi$
$433$	2198.00			0.243947			0.121974	+	0.992533i	$0.461078\pi$
$434$		0			0
$435$	−1296.00			−0.142847
$436$	−292.000	+	505.759i	−0.0320740	+	0.0555538i
$437$	120.000	+	207.846i	0.0131359	+	0.0227520i
$438$	−2300.00	−	3983.72i	−0.250909	−	0.434588i
$439$	188.000	−	325.626i	0.0204391	−	0.0354015i	−0.855625	−	0.517596i	$-0.826827\pi$
$439$	188.000	−	325.626i	0.0204391	−	0.0354015i	0.876064	+	0.482195i	$0.160160\pi$
$440$	−4608.00			−0.499268
$441$		0			0
$442$	−12768.0			−1.37401
$443$	−3594.00	+	6224.99i	−0.385454	+	0.667626i	−0.991832	−	0.127551i	$-0.959288\pi$
$443$	−3594.00	+	6224.99i	−0.385454	+	0.667626i	0.606378	+	0.795176i	$0.292622\pi$
$444$	584.000	+	1011.52i	0.0624221	+	0.108118i
$445$	−2340.00	−	4053.00i	−0.249273	−	0.431754i
$446$	−2072.00	+	3588.81i	−0.219982	+	0.381020i
$447$	2004.00			0.212049
$448$		0			0
$449$	−14670.0			−1.54192			−0.770958	−	0.636886i	$-0.780222\pi$
$449$	−14670.0			−1.54192			−0.770958	+	0.636886i	$0.780222\pi$
$450$	437.000	−	756.906i	0.0457786	−	0.0792909i
$451$	−3024.00	−	5237.72i	−0.315731	−	0.546862i
$452$	−396.000	−	685.892i	−0.0412086	−	0.0713753i
$453$	−2752.00	+	4766.60i	−0.285431	+	0.494381i
$454$	−732.000			−0.0756706
$455$		0			0
$456$	−32.0000			−0.00328627
$457$	2573.00	−	4456.57i	0.263370	−	0.456169i	−0.703766	−	0.710432i	$-0.748499\pi$
$457$	2573.00	−	4456.57i	0.263370	−	0.456169i	0.967135	+	0.254263i	$0.0818328\pi$
$458$	376.000	+	651.251i	0.0383610	+	0.0664432i
$459$	5700.00	+	9872.69i	0.579637	+	1.00396i
$460$	−2880.00	+	4988.31i	−0.291915	+	0.505611i
$461$	−1512.00			−0.152757			−0.0763784	−	0.997079i	$-0.524336\pi$
$461$	−1512.00			−0.152757			−0.0763784	+	0.997079i	$0.524336\pi$
$462$		0			0
$463$	7184.00			0.721099			0.360549	−	0.932740i	$-0.382589\pi$
$463$	7184.00			0.721099			0.360549	+	0.932740i	$0.382589\pi$
$464$	432.000	−	748.246i	0.0432222	−	0.0748630i
$465$	−2832.00	−	4905.17i	−0.282432	−	0.489186i
$466$	2262.00	+	3917.90i	0.224861	+	0.389470i
$467$	8259.00	−	14305.0i	0.818375	−	1.41747i	−0.0885046	−	0.996076i	$-0.528209\pi$
$467$	8259.00	−	14305.0i	0.818375	−	1.41747i	0.906879	−	0.421391i	$-0.138458\pi$
$468$	−5152.00			−0.508870
$469$		0			0
$470$	288.000			0.0282648
$471$	−520.000	+	900.666i	−0.0508712	+	0.0881115i
$472$	−552.000	−	956.092i	−0.0538302	−	0.0932367i
$473$	9024.00	+	15630.0i	0.877218	+	1.51939i
$474$	1552.00	−	2688.14i	0.150392	−	0.260486i
$475$	38.0000			0.00367065
$476$		0			0
$477$	−4002.00			−0.384149
$478$	−2592.00	+	4489.48i	−0.248024	+	0.429590i
$479$	−5046.00	−	8739.93i	−0.481331	−	0.833690i	0.518439	−	0.855114i	$-0.326513\pi$
$479$	−5046.00	−	8739.93i	−0.481331	−	0.833690i	−0.999770	+	0.0214244i	$0.993180\pi$
$480$	−384.000	−	665.108i	−0.0365148	−	0.0632456i
$481$	−4088.00	+	7080.62i	−0.387519	+	0.671203i
$482$	220.000			0.0207899
$483$		0			0
$484$	3892.00			0.365515
$485$	−7980.00	+	13821.8i	−0.747120	+	1.29405i
$486$	3542.00	+	6134.92i	0.330593	+	0.572605i
$487$	−3916.00	−	6782.71i	−0.364376	−	0.631117i	0.624300	−	0.781185i	$-0.285384\pi$
$487$	−3916.00	−	6782.71i	−0.364376	−	0.631117i	−0.988676	+	0.150068i	$0.952051\pi$
$488$	−1520.00	+	2632.72i	−0.140998	+	0.244216i
$489$	−2560.00			−0.236743
$490$		0			0
$491$	−6732.00			−0.618759			−0.309380	−	0.950939i	$-0.600121\pi$
$491$	−6732.00			−0.618759			−0.309380	+	0.950939i	$0.600121\pi$
$492$	504.000	−	872.954i	0.0461831	−	0.0799914i
$493$	−3078.00	−	5331.25i	−0.281189	−	0.487034i
$494$	−112.000	−	193.990i	−0.0102006	−	0.0176680i
$495$	−6624.00	+	11473.1i	−0.601468	+	1.04177i
$496$	3776.00			0.341829
$497$		0			0
$498$	−1512.00			−0.136053
$499$	−9334.00	+	16167.0i	−0.837369	+	1.45037i	0.0547176	+	0.998502i	$0.482574\pi$
$499$	−9334.00	+	16167.0i	−0.837369	+	1.45037i	−0.892087	+	0.451864i	$0.850759\pi$
$500$	−2544.00	−	4406.34i	−0.227542	−	0.394115i
$501$	1764.00	+	3055.34i	0.157305	+	0.272460i
$502$	1890.00	−	3273.58i	0.168038	−	0.291049i
$503$	−6048.00			−0.536117			−0.268059	−	0.963403i	$-0.586382\pi$
$503$	−6048.00			−0.536117			−0.268059	+	0.963403i	$0.586382\pi$
$504$		0			0
$505$	18000.0			1.58612
$506$	5760.00	−	9976.61i	0.506054	−	0.876511i
$507$	939.000	+	1626.40i	0.0822534	+	0.142467i
$508$	752.000	+	1302.50i	0.0656784	+	0.113758i
$509$	−5664.00	+	9810.34i	−0.493227	+	0.854294i	−0.999970	−	0.00780356i	$-0.997516\pi$
$509$	−5664.00	+	9810.34i	−0.493227	+	0.854294i	0.506743	+	0.862097i	$0.330849\pi$
$510$	−5472.00			−0.475106
$511$		0			0
$512$	512.000			0.0441942
$513$	−100.000	+	173.205i	−0.00860645	+	0.0149068i
$514$	−2130.00	−	3689.27i	−0.182783	−	0.316589i
$515$	2280.00	+	3949.08i	0.195085	+	0.337897i
$516$	−1504.00	+	2605.00i	−0.128314	+	0.222246i
$517$	−576.000			−0.0489989
$518$		0			0
$519$	1536.00			0.129909
$520$	2688.00	−	4655.75i	0.226686	−	0.392631i
$521$	2073.00	+	3590.54i	0.174318	+	0.301928i	0.939925	−	0.341381i	$-0.110895\pi$
$521$	2073.00	+	3590.54i	0.174318	+	0.301928i	−0.765607	+	0.643309i	$0.777561\pi$
$522$	−1242.00	−	2151.21i	−0.104140	−	0.180375i
$523$	503.000	−	871.222i	0.0420548	−	0.0728410i	−0.844232	−	0.535978i	$-0.819943\pi$
$523$	503.000	−	871.222i	0.0420548	−	0.0728410i	0.886287	+	0.463137i	$0.153276\pi$
$524$	8520.00			0.710301
$525$		0			0
$526$	−9984.00			−0.827610
$527$	13452.0	−	23299.5i	1.11191	−	1.92589i
$528$	768.000	+	1330.22i	0.0633010	+	0.109640i
$529$	−1116.50	−	1933.83i	−0.0917646	−	0.158941i
$530$	2088.00	−	3616.52i	0.171126	−	0.296399i
$531$	−3174.00			−0.259397
$532$		0			0
$533$	7056.00			0.573413
$534$	−780.000	+	1351.00i	−0.0632096	+	0.109482i
$535$	3816.00	+	6609.51i	0.308374	+	0.534119i
$536$	1936.00	+	3353.25i	0.156012	+	0.270221i
$537$	1812.00	−	3138.48i	0.145612	−	0.252207i
$538$	13632.0			1.09241
$539$		0			0
$540$	−4800.00			−0.382517
$541$	7361.00	−	12749.6i	0.584980	−	1.01321i	−0.409898	−	0.912131i	$-0.634436\pi$
$541$	7361.00	−	12749.6i	0.584980	−	1.01321i	0.994878	−	0.101084i	$-0.0322309\pi$
$542$	−8192.00	−	14189.0i	−0.649219	−	1.12448i
$543$	−448.000	−	775.959i	−0.0354061	−	0.0613252i
$544$	1824.00	−	3159.26i	0.143756	−	0.248993i
$545$	−1752.00			−0.137702
$546$		0			0
$547$	−13480.0			−1.05368			−0.526840	−	0.849964i	$-0.676623\pi$
$547$	−13480.0			−1.05368			−0.526840	+	0.849964i	$0.676623\pi$
$548$	156.000	−	270.200i	0.0121606	−	0.0210627i
$549$	4370.00	+	7569.06i	0.339721	+	0.588415i
$550$	−912.000	−	1579.63i	−0.0707051	−	0.122465i
$551$	54.0000	−	93.5307i	0.00417509	−	0.00723148i
$552$	1920.00			0.148045
$553$		0			0
$554$	4828.00			0.370256
$555$	−1752.00	+	3034.55i	−0.133997	+	0.232089i
$556$	4676.00	+	8099.07i	0.356666	+	0.617764i
$557$	−3111.00	−	5388.41i	−0.236656	−	0.409900i	0.723097	−	0.690747i	$-0.242718\pi$
$557$	−3111.00	−	5388.41i	−0.236656	−	0.409900i	−0.959753	+	0.280847i	$0.909385\pi$
$558$	5428.00	−	9401.57i	0.411802	−	0.713262i
$559$	−21056.0			−1.59316
$560$		0			0
$561$	10944.0			0.823629
$562$	−1962.00	+	3398.28i	−0.147263	+	0.255068i
$563$	−2463.00	−	4266.04i	−0.184375	−	0.319347i	0.758991	−	0.651101i	$-0.225693\pi$
$563$	−2463.00	−	4266.04i	−0.184375	−	0.319347i	−0.943366	+	0.331755i	$0.892359\pi$
$564$	−48.0000	−	83.1384i	−0.00358363	−	0.00620702i
$565$	1188.00	−	2057.68i	0.0884594	−	0.153216i
$566$	10804.0			0.802343
$567$		0			0
$568$	4608.00			0.340400
$569$	−11091.0	+	19210.2i	−0.817151	+	1.41535i	0.0906221	+	0.995885i	$0.471114\pi$
$569$	−11091.0	+	19210.2i	−0.817151	+	1.41535i	−0.907773	+	0.419462i	$0.862219\pi$
$570$	−48.0000	−	83.1384i	−0.00352719	−	0.00610927i
$571$	−1648.00	−	2854.42i	−0.120782	−	0.209201i	0.799294	−	0.600940i	$-0.205207\pi$
$571$	−1648.00	−	2854.42i	−0.120782	−	0.209201i	−0.920076	+	0.391739i	$0.871874\pi$
$572$	−5376.00	+	9311.51i	−0.392975	+	0.680653i
$573$	4272.00			0.311458
$574$		0			0
$575$	−2280.00			−0.165361
$576$	736.000	−	1274.79i	0.0532407	−	0.0922157i
$577$	12167.0	+	21073.9i	0.877849	+	1.52048i	0.853697	+	0.520771i	$0.174355\pi$
$577$	12167.0	+	21073.9i	0.877849	+	1.52048i	0.0241523	+	0.999708i	$0.492311\pi$
$578$	−8083.00	−	14000.2i	−0.581676	−	1.00749i
$579$	4430.00	−	7672.99i	0.317970	−	0.550740i
$580$	2592.00			0.185564
$581$		0			0
$582$	5320.00			0.378902
$583$	−4176.00	+	7233.04i	−0.296659	+	0.513829i
$584$	4600.00	+	7967.43i	0.325941	+	0.564546i
$585$	−7728.00	−	13385.3i	−0.546177	−	0.946006i
$586$	4788.00	−	8293.06i	0.337526	−	0.584613i
$587$	1638.00			0.115175			0.0575873	−	0.998340i	$-0.481659\pi$
$587$	1638.00			0.115175			0.0575873	+	0.998340i	$0.481659\pi$
$588$		0			0
$589$	472.000			0.0330194
$590$	1656.00	−	2868.28i	0.115553	−	0.200144i
$591$	198.000	+	342.946i	0.0137811	+	0.0238696i
$592$	−1168.00	−	2023.04i	−0.0810887	−	0.140450i
$593$	3723.00	−	6448.43i	0.257817	−	0.446552i	−0.707840	−	0.706373i	$-0.750330\pi$
$593$	3723.00	−	6448.43i	0.257817	−	0.446552i	0.965657	+	0.259821i	$0.0836636\pi$
$594$	9600.00			0.663119
$595$		0			0
$596$	−4008.00			−0.275460
$597$	−2284.00	+	3956.00i	−0.156579	+	0.271203i
$598$	6720.00	+	11639.4i	0.459534	+	0.795936i
$599$	3252.00	+	5632.63i	0.221825	+	0.384212i	0.955362	−	0.295437i	$-0.0954653\pi$
$599$	3252.00	+	5632.63i	0.221825	+	0.384212i	−0.733537	+	0.679649i	$0.762132\pi$
$600$	152.000	−	263.272i	0.0103423	−	0.0179134i
$601$	16058.0			1.08988			0.544941	−	0.838474i	$-0.316552\pi$
$601$	16058.0			1.08988			0.544941	+	0.838474i	$0.316552\pi$
$602$		0			0
$603$	11132.0			0.751791
$604$	5504.00	−	9533.21i	0.370786	−	0.642220i
$605$	5838.00	+	10111.7i	0.392311	+	0.679503i
$606$	−3000.00	−	5196.15i	−0.201100	−	0.348316i
$607$	−5104.00	+	8840.39i	−0.341293	+	0.591137i	−0.984673	−	0.174410i	$-0.944198\pi$
$607$	−5104.00	+	8840.39i	−0.341293	+	0.591137i	0.643380	+	0.765547i	$0.277532\pi$
$608$	64.0000			0.00426898
$609$		0			0
$610$	−9120.00			−0.605341
$611$	336.000	−	581.969i	0.0222473	−	0.0385335i
$612$	−5244.00	−	9082.87i	−0.346366	−	0.599924i
$613$	7487.00	+	12967.9i	0.493307	+	0.854432i	0.999970	−	0.00771145i	$-0.00245465\pi$
$613$	7487.00	+	12967.9i	0.493307	+	0.854432i	−0.506663	+	0.862144i	$0.669121\pi$
$614$	574.000	−	994.197i	0.0377276	−	0.0653461i
$615$	3024.00			0.198276
$616$		0			0
$617$	7254.00			0.473314			0.236657	−	0.971593i	$-0.423948\pi$
$617$	7254.00			0.473314			0.236657	+	0.971593i	$0.423948\pi$
$618$	760.000	−	1316.36i	0.0494687	−	0.0856824i
$619$	−6229.00	−	10788.9i	−0.404466	−	0.700556i	0.589793	−	0.807555i	$-0.299209\pi$
$619$	−6229.00	−	10788.9i	−0.404466	−	0.700556i	−0.994259	+	0.106998i	$0.965876\pi$
$620$	5664.00	+	9810.34i	0.366890	+	0.635472i
$621$	6000.00	−	10392.3i	0.387716	−	0.671544i
$622$	−17616.0			−1.13559
$623$		0			0
$624$	−1792.00			−0.114964
$625$	8819.50	−	15275.8i	0.564448	−	0.977653i
$626$	2770.00	+	4797.78i	0.176855	+	0.306322i
$627$	96.0000	+	166.277i	0.00611463	+	0.0105908i
$628$	1040.00	−	1801.33i	0.0660836	−	0.114460i
$629$	−16644.0			−1.05507
$630$		0			0
$631$	28352.0			1.78871			0.894354	−	0.447359i	$-0.147635\pi$
$631$	28352.0			1.78871			0.894354	+	0.447359i	$0.147635\pi$
$632$	−3104.00	+	5376.29i	−0.195365	+	0.338382i
$633$	4412.00	+	7641.81i	0.277032	+	0.479834i
$634$	−7566.00	−	13104.7i	−0.473950	−	0.820905i
$635$	−2256.00	+	3907.51i	−0.140987	+	0.244196i
$636$	−1392.00			−0.0867868
$637$		0			0
$638$	−5184.00			−0.321687
$639$	6624.00	−	11473.1i	0.410080	−	0.710280i
$640$	768.000	+	1330.22i	0.0474342	+	0.0821584i
$641$	−13695.0	−	23720.4i	−0.843869	−	1.46162i	−0.886600	−	0.462537i	$-0.846939\pi$
$641$	−13695.0	−	23720.4i	−0.843869	−	1.46162i	0.0427309	−	0.999087i	$-0.486394\pi$
$642$	1272.00	−	2203.17i	0.0781960	−	0.135439i
$643$	−21490.0			−1.31801			−0.659007	−	0.752137i	$-0.729023\pi$
$643$	−21490.0			−1.31801			−0.659007	+	0.752137i	$0.729023\pi$
$644$		0			0
$645$	−9024.00			−0.550883
$646$	228.000	−	394.908i	0.0138863	−	0.0240518i
$647$	−8826.00	−	15287.1i	−0.536300	−	0.928898i	−0.999099	−	0.0424353i	$-0.986488\pi$
$647$	−8826.00	−	15287.1i	−0.536300	−	0.928898i	0.462800	−	0.886463i	$-0.346845\pi$
$648$	−1684.00	−	2916.77i	−0.102089	−	0.176824i
$649$	−3312.00	+	5736.55i	−0.200320	+	0.346964i
$650$	2128.00			0.128411
$651$		0			0
$652$	5120.00			0.307538
$653$	2391.00	−	4141.33i	0.143288	−	0.248182i	−0.785445	−	0.618932i	$-0.787566\pi$
$653$	2391.00	−	4141.33i	0.143288	−	0.248182i	0.928733	+	0.370749i	$0.120899\pi$
$654$	292.000	+	505.759i	0.0174589	+	0.0302397i
$655$	12780.0	+	22135.6i	0.762375	+	1.32047i
$656$	−1008.00	+	1745.91i	−0.0599936	+	0.103912i
$657$	26450.0			1.57064
$658$		0			0
$659$	−27144.0			−1.60452			−0.802261	−	0.596973i	$-0.796370\pi$
$659$	−27144.0			−1.60452			−0.802261	+	0.596973i	$0.796370\pi$
$660$	−2304.00	+	3990.65i	−0.135883	+	0.235357i
$661$	5930.00	+	10271.1i	0.348941	+	0.604384i	0.986062	−	0.166380i	$-0.0532079\pi$
$661$	5930.00	+	10271.1i	0.348941	+	0.604384i	−0.637120	+	0.770764i	$0.719875\pi$
$662$	11320.0	+	19606.8i	0.664599	+	1.15112i
$663$	−6384.00	+	11057.4i	−0.373958	+	0.647714i
$664$	3024.00			0.176738
$665$		0			0
$666$	−6716.00			−0.390750
$667$	−3240.00	+	5611.84i	−0.188086	+	0.325774i
$668$	−3528.00	−	6110.68i	−0.204345	−	0.353936i
$669$	2072.00	+	3588.81i	0.119743	+	0.207401i
$670$	−5808.00	+	10059.8i	−0.334899	+	0.580063i
$671$	18240.0			1.04940
$672$		0			0
$673$	5546.00			0.317656			0.158828	−	0.987306i	$-0.449228\pi$
$673$	5546.00			0.317656			0.158828	+	0.987306i	$0.449228\pi$
$674$	4786.00	−	8289.60i	0.273516	−	0.473744i
$675$	−950.000	−	1645.45i	−0.0541711	−	0.0938272i
$676$	−1878.00	−	3252.79i	−0.106850	−	0.185070i
$677$	7440.00	−	12886.5i	0.422367	−	0.731561i	−0.573804	−	0.818993i	$-0.694533\pi$
$677$	7440.00	−	12886.5i	0.422367	−	0.731561i	0.996170	+	0.0874320i	$0.0278660\pi$
$678$	−792.000			−0.0448622
$679$		0			0
$680$	10944.0			0.617181
$681$	−366.000	+	633.931i	−0.0205949	+	0.0356715i
$682$	−11328.0	−	19620.7i	−0.636029	−	1.10163i
$683$	−10482.0	−	18155.4i	−0.587237	−	1.01712i	−0.994593	−	0.103854i	$-0.966882\pi$
$683$	−10482.0	−	18155.4i	−0.587237	−	1.01712i	0.407356	−	0.913269i	$-0.366451\pi$
$684$	92.0000	−	159.349i	0.00514285	−	0.00890767i
$685$	936.000			0.0522084
$686$		0			0
$687$	752.000			0.0417621
$688$	3008.00	−	5210.01i	0.166684	−	0.288706i
$689$	−4872.00	−	8438.55i	−0.269388	−	0.466594i
$690$	2880.00	+	4988.31i	0.158898	+	0.275220i
$691$	−6553.00	+	11350.1i	−0.360764	+	0.624861i	−0.988087	−	0.153898i	$-0.950817\pi$
$691$	−6553.00	+	11350.1i	−0.360764	+	0.624861i	0.627323	+	0.778759i	$0.284151\pi$
$692$	−3072.00			−0.168757
$693$		0			0
$694$	25296.0			1.38361
$695$	−14028.0	+	24297.2i	−0.765629	+	1.32611i
$696$	−432.000	−	748.246i	−0.0235272	−	0.0407503i
$697$	7182.00	+	12439.6i	0.390298	+	0.676016i
$698$	−9632.00	+	16683.1i	−0.522316	+	0.904678i
$699$	4524.00			0.244797
$700$		0			0
$701$	−4590.00			−0.247307			−0.123653	−	0.992325i	$-0.539461\pi$
$701$	−4590.00			−0.247307			−0.123653	+	0.992325i	$0.539461\pi$
$702$	−5600.00	+	9699.48i	−0.301080	+	0.521486i
$703$	−146.000	−	252.879i	−0.00783285	−	0.0135669i
$704$	−1536.00	−	2660.43i	−0.0822304	−	0.142427i
$705$	144.000	−	249.415i	0.00769270	−	0.0133241i
$706$	−6780.00			−0.361429
$707$		0			0
$708$	−1104.00			−0.0586029
$709$	431.000	−	746.514i	0.0228301	−	0.0395429i	−0.854385	−	0.519641i	$-0.826066\pi$
$709$	431.000	−	746.514i	0.0228301	−	0.0395429i	0.877215	+	0.480098i	$0.159399\pi$
$710$	6912.00	+	11971.9i	0.365356	+	0.632815i
$711$	8924.00	+	15456.8i	0.470712	+	0.815297i
$712$	1560.00	−	2702.00i	0.0821116	−	0.142221i
$713$	−28320.0			−1.48751
$714$		0			0
$715$	−32256.0			−1.68714
$716$	−3624.00	+	6276.95i	−0.189155	+	0.327627i
$717$	2592.00	+	4489.48i	0.135007	+	0.233839i
$718$	10704.0	+	18539.9i	0.556365	+	0.963652i
$719$	1770.00	−	3065.73i	0.0918079	−	0.159016i	−0.816464	−	0.577396i	$-0.804069\pi$
$719$	1770.00	−	3065.73i	0.0918079	−	0.159016i	0.908272	+	0.418380i	$0.137402\pi$
$720$	4416.00			0.228576
$721$		0			0
$722$	−13710.0			−0.706694
$723$	110.000	−	190.526i	0.00565829	−	0.00980045i
$724$	896.000	+	1551.92i	0.0459939	+	0.0796638i
$725$	513.000	+	888.542i	0.0262791	+	0.0455167i
$726$	1946.00	−	3370.57i	0.0994805	−	0.172305i
$727$	−4228.00			−0.215692			−0.107846	−	0.994168i	$-0.534395\pi$
$727$	−4228.00			−0.215692			−0.107846	+	0.994168i	$0.534395\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$	−13800.0	+	23902.3i	−0.699672	+	1.21187i
$731$	−21432.0	−	37121.3i	−1.08439	−	1.87822i
$732$	1520.00	+	2632.72i	0.0767497	+	0.132934i
$733$	−2710.00	+	4693.86i	−0.136557	+	0.236523i	−0.926191	−	0.377054i	$-0.876937\pi$
$733$	−2710.00	+	4693.86i	−0.136557	+	0.236523i	0.789634	+	0.613578i	$0.210270\pi$
$734$	−17168.0			−0.863328
$735$		0			0
$736$	−3840.00			−0.192316
$737$	11616.0	−	20119.5i	0.580571	−	1.00558i
$738$	2898.00	+	5019.48i	0.144549	+	0.250365i
$739$	−640.000	−	1108.51i	−0.0318576	−	0.0551790i	0.849657	−	0.527336i	$-0.176809\pi$
$739$	−640.000	−	1108.51i	−0.0318576	−	0.0551790i	−0.881515	+	0.472157i	$0.843476\pi$
$740$	3504.00	−	6069.11i	0.174067	−	0.301493i
$741$	−224.000			−0.0111051
$742$		0			0
$743$	−35712.0			−1.76332			−0.881660	−	0.471886i	$-0.843573\pi$
$743$	−35712.0			−1.76332			−0.881660	+	0.471886i	$0.843573\pi$
$744$	1888.00	−	3270.11i	0.0930342	−	0.161140i
$745$	−6012.00	−	10413.1i	−0.295655	−	0.512089i
$746$	2122.00	+	3675.41i	0.104145	+	0.180384i
$747$	4347.00	−	7529.22i	0.212916	−	0.368782i
$748$	−21888.0			−1.06993
$749$		0			0
$750$	−5088.00			−0.247717
$751$	−12232.0	+	21186.4i	−0.594344	+	1.02943i	0.399296	+	0.916822i	$0.369255\pi$
$751$	−12232.0	+	21186.4i	−0.594344	+	1.02943i	−0.993639	+	0.112611i	$0.964079\pi$
$752$	96.0000	+	166.277i	0.00465527	+	0.00806316i
$753$	−1890.00	−	3273.58i	−0.0914680	−	0.158427i
$754$	3024.00	−	5237.72i	0.146058	−	0.252980i
$755$	33024.0			1.59188
$756$		0			0
$757$	30242.0			1.45200			0.726000	−	0.687695i	$-0.241377\pi$
$757$	30242.0			1.45200			0.726000	+	0.687695i	$0.241377\pi$
$758$	4912.00	−	8507.83i	0.235372	−	0.407676i
$759$	−5760.00	−	9976.61i	−0.275461	−	0.477112i
$760$	96.0000	+	166.277i	0.00458196	+	0.00793618i
$761$	1077.00	−	1865.42i	0.0513025	−	0.0888586i	−0.839234	−	0.543771i	$-0.816996\pi$
$761$	1077.00	−	1865.42i	0.0513025	−	0.0888586i	0.890536	+	0.454912i	$0.150329\pi$
$762$	1504.00			0.0715015
$763$		0			0
$764$	−8544.00			−0.404596
$765$	15732.0	−	27248.6i	0.743519	−	1.28781i
$766$	−9060.00	−	15692.4i	−0.427351	−	0.740194i
$767$	−3864.00	−	6692.64i	−0.181905	−	0.315068i
$768$	256.000	−	443.405i	0.0120281	−	0.0208333i
$769$	10262.0			0.481219			0.240609	−	0.970622i	$-0.422653\pi$
$769$	10262.0			0.481219			0.240609	+	0.970622i	$0.422653\pi$
$770$		0			0
$771$	−4260.00			−0.198989
$772$	−8860.00	+	15346.0i	−0.413055	+	0.715432i
$773$	−4542.00	−	7866.97i	−0.211338	−	0.366048i	0.740795	−	0.671731i	$-0.234449\pi$
$773$	−4542.00	−	7866.97i	−0.211338	−	0.366048i	−0.952134	+	0.305682i	$0.901115\pi$
$774$	−8648.00	−	14978.8i	−0.401610	−	0.695608i
$775$	−2242.00	+	3883.26i	−0.103916	+	0.179988i
$776$	−10640.0			−0.492208
$777$		0			0
$778$	17988.0			0.828922
$779$	−126.000	+	218.238i	−0.00579515	+	0.0100375i
$780$	−2688.00	−	4655.75i	−0.123392	−	0.213721i
$781$	−13824.0	−	23943.9i	−0.633370	−	1.09703i
$782$	−13680.0	+	23694.5i	−0.625570	+	1.08352i
$783$	−5400.00			−0.246463
$784$		0			0
$785$	6240.00			0.283714
$786$	4260.00	−	7378.54i	0.193320	−	0.334839i
$787$	9899.00	+	17145.6i	0.448362	+	0.776587i	0.998280	−	0.0586327i	$-0.0186741\pi$
$787$	9899.00	+	17145.6i	0.448362	+	0.776587i	−0.549917	+	0.835219i	$0.685341\pi$
$788$	−396.000	−	685.892i	−0.0179022	−	0.0310075i
$789$	−4992.00	+	8646.40i	−0.225247	+	0.390139i
$790$	−18624.0			−0.838750
$791$		0			0
$792$	−8832.00			−0.396252
$793$	−10640.0	+	18429.0i	−0.476466	+	0.825263i
$794$	12976.0	+	22475.1i	0.579976	+	1.00455i
$795$	−2088.00	−	3616.52i	−0.0931493	−	0.161339i
$796$	4568.00	−	7912.01i	0.203403	−	0.352304i
$797$	30240.0			1.34398			0.671992	−	0.740558i	$-0.265439\pi$
$797$	30240.0			1.34398			0.671992	+	0.740558i	$0.265439\pi$
$798$		0			0
$799$	1368.00			0.0605712
$800$	−304.000	+	526.543i	−0.0134350	+	0.0232702i
$801$	−4485.00	−	7768.25i	−0.197840	−	0.342669i
$802$	3522.00	+	6100.28i	0.155070	+	0.268589i
$803$	27600.0	−	47804.6i	1.21293	−	2.10086i
$804$	3872.00			0.169844
$805$		0			0
$806$	26432.0			1.15512
$807$	6816.00	−	11805.7i	0.297317	−	0.514968i
$808$	6000.00	+	10392.3i	0.261237	+	0.452475i
$809$	1173.00	+	2031.70i	0.0509771	+	0.0882949i	0.890388	−	0.455202i	$-0.150433\pi$
$809$	1173.00	+	2031.70i	0.0509771	+	0.0882949i	−0.839411	+	0.543497i	$0.817100\pi$
$810$	5052.00	−	8750.32i	0.219147	−	0.379574i
$811$	−29806.0			−1.29054			−0.645271	−	0.763953i	$-0.723256\pi$
$811$	−29806.0			−1.29054			−0.645271	+	0.763953i	$0.723256\pi$
$812$		0			0
$813$	−16384.0			−0.706780
$814$	−7008.00	+	12138.2i	−0.301757	+	0.522659i
$815$	7680.00	+	13302.2i	0.330084	+	0.571723i
$816$	−1824.00	−	3159.26i	−0.0782509	−	0.135535i
$817$	376.000	−	651.251i	0.0161011	−	0.0278879i
$818$	25420.0			1.08654
$819$		0			0
$820$	−6048.00			−0.257567
$821$	753.000	−	1304.23i	0.0320096	−	0.0554423i	−0.849577	−	0.527465i	$-0.823143\pi$
$821$	753.000	−	1304.23i	0.0320096	−	0.0554423i	0.881586	+	0.472023i	$0.156476\pi$
$822$	−156.000	−	270.200i	−0.00661937	−	0.0114651i
$823$	10196.0	+	17660.0i	0.431847	+	0.747981i	0.997032	−	0.0769828i	$-0.0245286\pi$
$823$	10196.0	+	17660.0i	0.431847	+	0.747981i	−0.565185	+	0.824964i	$0.691195\pi$
$824$	−1520.00	+	2632.72i	−0.0642618	+	0.111305i
$825$	−1824.00			−0.0769740
$826$		0			0
$827$	36108.0			1.51826			0.759128	−	0.650941i	$-0.225626\pi$
$827$	36108.0			1.51826			0.759128	+	0.650941i	$0.225626\pi$
$828$	−5520.00	+	9560.92i	−0.231683	+	0.401286i
$829$	6938.00	+	12017.0i	0.290672	+	0.503458i	0.973969	−	0.226683i	$-0.0727880\pi$
$829$	6938.00	+	12017.0i	0.290672	+	0.503458i	−0.683297	+	0.730140i	$0.739455\pi$
$830$	4536.00	+	7856.58i	0.189695	+	0.328561i
$831$	2414.00	−	4181.17i	0.100771	−	0.174541i
$832$	3584.00			0.149342
$833$		0			0
$834$	9352.00			0.388289
$835$	10584.0	−	18332.0i	0.438652	−	0.759768i
$836$	−192.000	−	332.554i	−0.00794313	−	0.0137579i
$837$	−11800.0	−	20438.2i	−0.487297	−	0.844023i
$838$	−1638.00	+	2837.10i	−0.0675224	+	0.116952i
$839$	23436.0			0.964363			0.482182	−	0.876071i	$-0.339845\pi$
$839$	23436.0			0.964363			0.482182	+	0.876071i	$0.339845\pi$
$840$		0			0
$841$	−21473.0			−0.880438
$842$	12850.0	−	22256.9i	0.525939	−	0.910952i
$843$	1962.00	+	3398.28i	0.0801600	+	0.138841i
$844$	−8824.00	−	15283.6i	−0.359875	−	0.623322i
$845$	5634.00	−	9758.37i	0.229367	−	0.397276i
$846$	552.000			0.0224328
$847$		0			0
$848$	2784.00			0.112739
$849$	5402.00	−	9356.54i	0.218370	−	0.378228i
$850$	2166.00	+	3751.62i	0.0874037	+	0.151388i
$851$	8760.00	+	15172.8i	0.352866	+	0.611182i
$852$	2304.00	−	3990.65i	0.0926452	−	0.160466i
$853$	8120.00			0.325936			0.162968	−	0.986631i	$-0.447893\pi$
$853$	8120.00			0.325936			0.162968	+	0.986631i	$0.447893\pi$
$854$		0			0
$855$	552.000			0.0220795
$856$	−2544.00	+	4406.34i	−0.101580	+	0.175941i
$857$	25005.0	+	43309.9i	0.996680	+	1.72630i	0.568853	+	0.822439i	$0.307387\pi$
$857$	25005.0	+	43309.9i	0.996680	+	1.72630i	0.427826	+	0.903861i	$0.359279\pi$
$858$	5376.00	+	9311.51i	0.213909	+	0.370501i
$859$	−17263.0	+	29900.4i	−0.685688	+	1.18765i	0.287532	+	0.957771i	$0.407165\pi$
$859$	−17263.0	+	29900.4i	−0.685688	+	1.18765i	−0.973220	+	0.229875i	$0.926168\pi$
$860$	18048.0			0.715618
$861$		0			0
$862$	−16032.0			−0.633471
$863$	8628.00	−	14944.1i	0.340325	−	0.589460i	−0.644168	−	0.764884i	$-0.722796\pi$
$863$	8628.00	−	14944.1i	0.340325	−	0.589460i	0.984493	+	0.175424i	$0.0561296\pi$
$864$	−1600.00	−	2771.28i	−0.0630013	−	0.109121i
$865$	−4608.00	−	7981.29i	−0.181129	−	0.313725i
$866$	−2198.00	+	3807.05i	−0.0862484	+	0.149387i
$867$	−16166.0			−0.633248
$868$		0			0
$869$	37248.0			1.45403
$870$	1296.00	−	2244.74i	0.0505040	−	0.0874756i
$871$	13552.0	+	23472.8i	0.527201	+	0.913139i
$872$	−584.000	−	1011.52i	−0.0226797	−	0.0392825i
$873$	−15295.0	+	26491.7i	−0.592964	+	1.02704i
$874$	−480.000			−0.0185769
$875$		0			0
$876$	9200.00			0.354839
$877$	−4357.00	+	7546.55i	−0.167760	+	0.290569i	−0.937632	−	0.347630i	$-0.886987\pi$
$877$	−4357.00	+	7546.55i	−0.167760	+	0.290569i	0.769872	+	0.638198i	$0.220320\pi$
$878$	376.000	+	651.251i	0.0144526	+	0.0250326i
$879$	−4788.00	−	8293.06i	−0.183726	−	0.318223i
$880$	4608.00	−	7981.29i	0.176518	−	0.305738i
$881$	−22806.0			−0.872138			−0.436069	−	0.899913i	$-0.643630\pi$
$881$	−22806.0			−0.872138			−0.436069	+	0.899913i	$0.643630\pi$
$882$		0			0
$883$	40196.0			1.53194			0.765970	−	0.642876i	$-0.222259\pi$
$883$	40196.0			1.53194			0.765970	+	0.642876i	$0.222259\pi$
$884$	12768.0	−	22114.8i	0.485785	−	0.841405i
$885$	−1656.00	−	2868.28i	−0.0628992	−	0.108945i
$886$	−7188.00	−	12450.0i	−0.272557	−	0.472083i
$887$	−20406.0	+	35344.2i	−0.772454	+	1.33793i	0.163761	+	0.986500i	$0.447637\pi$
$887$	−20406.0	+	35344.2i	−0.772454	+	1.33793i	−0.936215	+	0.351429i	$0.885696\pi$
$888$	−2336.00			−0.0882782
$889$		0			0
$890$	9360.00			0.352526
$891$	−10104.0	+	17500.6i	−0.379907	+	0.658017i
$892$	−4144.00	−	7177.62i	−0.155551	−	0.269422i
$893$	12.0000	+	20.7846i	0.000449681	+	0.000778869i
$894$	−2004.00	+	3471.03i	−0.0749707	+	0.129853i
$895$	−21744.0			−0.812091
$896$		0			0
$897$	13440.0			0.500277
$898$	14670.0	−	25409.2i	0.545149	−	0.944227i
$899$	6372.00	+	11036.6i	0.236394	+	0.409446i
$900$	874.000	+	1513.81i	0.0323704	+	0.0560671i
$901$	9918.00	−	17178.5i	0.366722	−	0.635181i
$902$	12096.0			0.446511
$903$		0			0
$904$	1584.00			0.0582777
$905$	−2688.00	+	4655.75i	−0.0987317	+	0.171008i
$906$	−5504.00	−	9533.21i	−0.201830	−	0.349580i
$907$	6794.00	+	11767.6i	0.248722	+	0.430800i	0.963172	−	0.268888i	$-0.0866560\pi$
$907$	6794.00	+	11767.6i	0.248722	+	0.430800i	−0.714449	+	0.699687i	$0.753323\pi$
$908$	732.000	−	1267.86i	0.0267536	−	0.0463386i
$909$	34500.0			1.25885
$910$		0			0
$911$	−47304.0			−1.72036			−0.860182	−	0.509987i	$-0.829650\pi$
$911$	−47304.0			−1.72036			−0.860182	+	0.509987i	$0.829650\pi$
$912$	32.0000	−	55.4256i	0.00116187	−	0.00201242i
$913$	−9072.00	−	15713.2i	−0.328849	−	0.569584i
$914$	5146.00	+	8913.13i	0.186230	+	0.322560i
$915$	−4560.00	+	7898.15i	−0.164753	+	0.285360i
$916$	−1504.00			−0.0542506
$917$		0			0
$918$	−22800.0			−0.819730
$919$	−892.000	+	1544.99i	−0.0320178	+	0.0554565i	−0.881590	−	0.472015i	$-0.843527\pi$
$919$	−892.000	+	1544.99i	−0.0320178	+	0.0554565i	0.849572	+	0.527472i	$0.176860\pi$
$920$	−5760.00	−	9976.61i	−0.206415	−	0.357521i
$921$	−574.000	−	994.197i	−0.0205363	−	0.0355699i
$922$	1512.00	−	2618.86i	0.0540077	−	0.0935440i
$923$	32256.0			1.15029
$924$		0			0
$925$	2774.00			0.0986038
$926$	−7184.00	+	12443.1i	−0.254947	+	0.441581i
$927$	4370.00	+	7569.06i	0.154832	+	0.268178i
$928$	864.000	+	1496.49i	0.0305627	+	0.0529362i
$929$	17961.0	−	31109.4i	0.634318	−	1.09867i	−0.352341	−	0.935872i	$-0.614614\pi$
$929$	17961.0	−	31109.4i	0.634318	−	1.09867i	0.986659	−	0.162799i	$-0.0520523\pi$
$930$	11328.0			0.399419
$931$		0			0
$932$	−9048.00			−0.318001
$933$	−8808.00	+	15255.9i	−0.309069	+	0.535322i
$934$	16518.0	+	28610.0i	0.578678	+	1.00230i
$935$	−32832.0	−	56866.7i	−1.14836	−	1.98903i
$936$	5152.00	−	8923.53i	0.179913	−	0.311618i
$937$	−26782.0			−0.933756			−0.466878	−	0.884322i	$-0.654621\pi$
$937$	−26782.0			−0.933756			−0.466878	+	0.884322i	$0.654621\pi$
$938$		0			0
$939$	5540.00			0.192536
$940$	−288.000	+	498.831i	−0.00999311	+	0.0173086i
$941$	−2022.00	−	3502.21i	−0.0700482	−	0.121327i	0.828874	−	0.559435i	$-0.188982\pi$
$941$	−2022.00	−	3502.21i	−0.0700482	−	0.121327i	−0.898922	+	0.438108i	$0.855649\pi$
$942$	−1040.00	−	1801.33i	−0.0359714	−	0.0623042i
$943$	7560.00	−	13094.3i	0.261068	−	0.452184i
$944$	2208.00			0.0761274
$945$		0			0
$946$	−36096.0			−1.24057
$947$	1068.00	−	1849.83i	0.0366477	−	0.0634756i	−0.847120	−	0.531402i	$-0.821665\pi$
$947$	1068.00	−	1849.83i	0.0366477	−	0.0634756i	0.883767	+	0.467926i	$0.154999\pi$
$948$	3104.00	+	5376.29i	0.106343	+	0.184192i
$949$	32200.0	+	55772.0i	1.10143	+	1.90773i
$950$	−38.0000	+	65.8179i	−0.00129777	+	0.00224781i
$951$	−15132.0			−0.515971
$952$		0			0
$953$	−15174.0			−0.515776			−0.257888	−	0.966175i	$-0.583026\pi$
$953$	−15174.0			−0.515776			−0.257888	+	0.966175i	$0.583026\pi$
$954$	4002.00	−	6931.67i	0.135817	−	0.235242i
$955$	−12816.0	−	22198.0i	−0.434258	−	0.752156i
$956$	−5184.00	−	8978.95i	−0.175379	−	0.303766i
$957$	−2592.00	+	4489.48i	−0.0875522	+	0.151645i
$958$	20184.0			0.680705
$959$		0			0
$960$	1536.00			0.0516398
$961$	−12952.5	+	22434.4i	−0.434779	+	0.753059i
$962$	−8176.00	−	14161.2i	−0.274017	−	0.474612i
$963$	7314.00	+	12668.2i	0.244746	+	0.423912i
$964$	−220.000	+	381.051i	−0.00735033	+	0.0127312i
$965$	−53160.0			−1.77335
$966$		0			0
$967$	25832.0			0.859050			0.429525	−	0.903055i	$-0.358681\pi$
$967$	25832.0			0.859050			0.429525	+	0.903055i	$0.358681\pi$
$968$	−3892.00	+	6741.14i	−0.129229	+	0.223831i
$969$	−228.000	−	394.908i	−0.00755874	−	0.0130921i
$970$	−15960.0	−	27643.5i	−0.528294	−	0.915031i
$971$	18843.0	−	32637.0i	0.622761	−	1.07865i	−0.366209	−	0.930533i	$-0.619344\pi$
$971$	18843.0	−	32637.0i	0.622761	−	1.07865i	0.988969	−	0.148120i	$-0.0473223\pi$
$972$	−14168.0			−0.467530
$973$		0			0
$974$	15664.0			0.515305
$975$	1064.00	−	1842.90i	0.0349490	−	0.0605334i
$976$	−3040.00	−	5265.43i	−0.0997008	−	0.172687i
$977$	27003.0	+	46770.6i	0.884240	+	1.53155i	0.846582	+	0.532258i	$0.178656\pi$
$977$	27003.0	+	46770.6i	0.884240	+	1.53155i	0.0376578	+	0.999291i	$0.488010\pi$
$978$	2560.00	−	4434.05i	0.0837012	−	0.144975i
$979$	−18720.0			−0.611127
$980$		0			0
$981$	−3358.00			−0.109289
$982$	6732.00	−	11660.2i	0.218765	−	0.378911i
$983$	−16638.0	−	28817.9i	−0.539847	−	0.935043i	−0.998912	−	0.0466399i	$-0.985149\pi$
$983$	−16638.0	−	28817.9i	−0.539847	−	0.935043i	0.459065	−	0.888403i	$-0.348185\pi$
$984$	1008.00	+	1745.91i	0.0326564	+	0.0565625i
$985$	1188.00	−	2057.68i	0.0384293	−	0.0665614i
$986$	12312.0			0.397661
$987$		0			0
$988$	448.000			0.0144259
$989$	−22560.0	+	39075.1i	−0.725345	+	1.25633i
$990$	−13248.0	−	22946.2i	−0.425302	−	0.736645i
$991$	1880.00	+	3256.26i	0.0602625	+	0.104378i	0.894583	−	0.446902i	$-0.147473\pi$
$991$	1880.00	+	3256.26i	0.0602625	+	0.104378i	−0.834320	+	0.551280i	$0.814140\pi$
$992$	−3776.00	+	6540.22i	−0.120855	+	0.209327i
$993$	22640.0			0.723523
$994$		0			0
$995$	27408.0			0.873258
$996$	1512.00	−	2618.86i	0.0481020	−	0.0833150i
$997$	−18262.0	−	31630.7i	−0.580104	−	1.00477i	−0.995466	−	0.0951132i	$-0.969679\pi$
$997$	−18262.0	−	31630.7i	−0.580104	−	1.00477i	0.415363	−	0.909656i	$-0.363655\pi$
$998$	−18668.0	−	32333.9i	−0.592109	−	1.02556i
$999$	−7300.00	+	12644.0i	−0.231193	+	0.400438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.4.c.c.79.1		2
3.2	odd	2		882.4.g.p.667.1		2
7.2	even	3		14.4.a.b.1.1	✓	1
7.3	odd	6		98.4.c.b.67.1		2
7.4	even	3	inner	98.4.c.c.67.1		2
7.5	odd	6		98.4.a.e.1.1		1
7.6	odd	2		98.4.c.b.79.1		2
21.2	odd	6		126.4.a.d.1.1		1
21.5	even	6		882.4.a.b.1.1		1
21.11	odd	6		882.4.g.p.361.1		2
21.17	even	6		882.4.g.v.361.1		2
21.20	even	2		882.4.g.v.667.1		2
28.19	even	6		784.4.a.h.1.1		1
28.23	odd	6		112.4.a.e.1.1		1
35.2	odd	12		350.4.c.g.99.2		2
35.9	even	6		350.4.a.f.1.1		1
35.19	odd	6		2450.4.a.i.1.1		1
35.23	odd	12		350.4.c.g.99.1		2
56.37	even	6		448.4.a.k.1.1		1
56.51	odd	6		448.4.a.g.1.1		1
77.65	odd	6		1694.4.a.b.1.1		1
84.23	even	6		1008.4.a.r.1.1		1
91.51	even	6		2366.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.a.b.1.1	✓	1	7.2	even	3
98.4.a.e.1.1		1	7.5	odd	6
98.4.c.b.67.1		2	7.3	odd	6
98.4.c.b.79.1		2	7.6	odd	2
98.4.c.c.67.1		2	7.4	even	3	inner
98.4.c.c.79.1		2	1.1	even	1	trivial
112.4.a.e.1.1		1	28.23	odd	6
126.4.a.d.1.1		1	21.2	odd	6
350.4.a.f.1.1		1	35.9	even	6
350.4.c.g.99.1		2	35.23	odd	12
350.4.c.g.99.2		2	35.2	odd	12
448.4.a.g.1.1		1	56.51	odd	6
448.4.a.k.1.1		1	56.37	even	6
784.4.a.h.1.1		1	28.19	even	6
882.4.a.b.1.1		1	21.5	even	6
882.4.g.p.361.1		2	21.11	odd	6
882.4.g.p.667.1		2	3.2	odd	2
882.4.g.v.361.1		2	21.17	even	6
882.4.g.v.667.1		2	21.20	even	2
1008.4.a.r.1.1		1	84.23	even	6
1694.4.a.b.1.1		1	77.65	odd	6
2366.4.a.c.1.1		1	91.51	even	6
2450.4.a.i.1.1		1	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} -4.00000 q^{6} +8.00000 q^{8} +(11.5000 - 19.9186i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.00000 - 10.3923i) q^{5} -4.00000 q^{6} +8.00000 q^{8} +(11.5000 - 19.9186i) q^{9} +(12.0000 + 20.7846i) q^{10} +(-24.0000 - 41.5692i) q^{11} +(4.00000 - 6.92820i) q^{12} +56.0000 q^{13} +24.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(57.0000 + 98.7269i) q^{17} +(23.0000 + 39.8372i) q^{18} +(-1.00000 + 1.73205i) q^{19} -48.0000 q^{20} +96.0000 q^{22} +(60.0000 - 103.923i) q^{23} +(8.00000 + 13.8564i) q^{24} +(-9.50000 - 16.4545i) q^{25} +(-56.0000 + 96.9948i) q^{26} +100.000 q^{27} -54.0000 q^{29} +(-24.0000 + 41.5692i) q^{30} +(-118.000 - 204.382i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(48.0000 - 83.1384i) q^{33} -228.000 q^{34} -92.0000 q^{36} +(-73.0000 + 126.440i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(56.0000 + 96.9948i) q^{39} +(48.0000 - 83.1384i) q^{40} +126.000 q^{41} -376.000 q^{43} +(-96.0000 + 166.277i) q^{44} +(-138.000 - 239.023i) q^{45} +(120.000 + 207.846i) q^{46} +(6.00000 - 10.3923i) q^{47} -32.0000 q^{48} +38.0000 q^{50} +(-114.000 + 197.454i) q^{51} +(-112.000 - 193.990i) q^{52} +(-87.0000 - 150.688i) q^{53} +(-100.000 + 173.205i) q^{54} -576.000 q^{55} -4.00000 q^{57} +(54.0000 - 93.5307i) q^{58} +(-69.0000 - 119.512i) q^{59} +(-48.0000 - 83.1384i) q^{60} +(-190.000 + 329.090i) q^{61} +472.000 q^{62} +64.0000 q^{64} +(336.000 - 581.969i) q^{65} +(96.0000 + 166.277i) q^{66} +(242.000 + 419.156i) q^{67} +(228.000 - 394.908i) q^{68} +240.000 q^{69} +576.000 q^{71} +(92.0000 - 159.349i) q^{72} +(575.000 + 995.929i) q^{73} +(-146.000 - 252.879i) q^{74} +(19.0000 - 32.9090i) q^{75} +8.00000 q^{76} -224.000 q^{78} +(-388.000 + 672.036i) q^{79} +(96.0000 + 166.277i) q^{80} +(-210.500 - 364.597i) q^{81} +(-126.000 + 218.238i) q^{82} +378.000 q^{83} +1368.00 q^{85} +(376.000 - 651.251i) q^{86} +(-54.0000 - 93.5307i) q^{87} +(-192.000 - 332.554i) q^{88} +(195.000 - 337.750i) q^{89} +552.000 q^{90} -480.000 q^{92} +(236.000 - 408.764i) q^{93} +(12.0000 + 20.7846i) q^{94} +(12.0000 + 20.7846i) q^{95} +(32.0000 - 55.4256i) q^{96} -1330.00 q^{97} -1104.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 12 q^{5} - 8 q^{6} + 16 q^{8} + 23 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 + 12 * q^5 - 8 * q^6 + 16 * q^8 + 23 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} - 4 q^{4} + 12 q^{5} - 8 q^{6} + 16 q^{8} + 23 q^{9} + 24 q^{10} - 48 q^{11} + 8 q^{12} + 112 q^{13} + 48 q^{15} - 16 q^{16} + 114 q^{17} + 46 q^{18} - 2 q^{19} - 96 q^{20} + 192 q^{22} + 120 q^{23} + 16 q^{24} - 19 q^{25} - 112 q^{26} + 200 q^{27} - 108 q^{29} - 48 q^{30} - 236 q^{31} - 32 q^{32} + 96 q^{33} - 456 q^{34} - 184 q^{36} - 146 q^{37} - 4 q^{38} + 112 q^{39} + 96 q^{40} + 252 q^{41} - 752 q^{43} - 192 q^{44} - 276 q^{45} + 240 q^{46} + 12 q^{47} - 64 q^{48} + 76 q^{50} - 228 q^{51} - 224 q^{52} - 174 q^{53} - 200 q^{54} - 1152 q^{55} - 8 q^{57} + 108 q^{58} - 138 q^{59} - 96 q^{60} - 380 q^{61} + 944 q^{62} + 128 q^{64} + 672 q^{65} + 192 q^{66} + 484 q^{67} + 456 q^{68} + 480 q^{69} + 1152 q^{71} + 184 q^{72} + 1150 q^{73} - 292 q^{74} + 38 q^{75} + 16 q^{76} - 448 q^{78} - 776 q^{79} + 192 q^{80} - 421 q^{81} - 252 q^{82} + 756 q^{83} + 2736 q^{85} + 752 q^{86} - 108 q^{87} - 384 q^{88} + 390 q^{89} + 1104 q^{90} - 960 q^{92} + 472 q^{93} + 24 q^{94} + 24 q^{95} + 64 q^{96} - 2660 q^{97} - 2208 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 - 4 * q^4 + 12 * q^5 - 8 * q^6 + 16 * q^8 + 23 * q^9 + 24 * q^10 - 48 * q^11 + 8 * q^12 + 112 * q^13 + 48 * q^15 - 16 * q^16 + 114 * q^17 + 46 * q^18 - 2 * q^19 - 96 * q^20 + 192 * q^22 + 120 * q^23 + 16 * q^24 - 19 * q^25 - 112 * q^26 + 200 * q^27 - 108 * q^29 - 48 * q^30 - 236 * q^31 - 32 * q^32 + 96 * q^33 - 456 * q^34 - 184 * q^36 - 146 * q^37 - 4 * q^38 + 112 * q^39 + 96 * q^40 + 252 * q^41 - 752 * q^43 - 192 * q^44 - 276 * q^45 + 240 * q^46 + 12 * q^47 - 64 * q^48 + 76 * q^50 - 228 * q^51 - 224 * q^52 - 174 * q^53 - 200 * q^54 - 1152 * q^55 - 8 * q^57 + 108 * q^58 - 138 * q^59 - 96 * q^60 - 380 * q^61 + 944 * q^62 + 128 * q^64 + 672 * q^65 + 192 * q^66 + 484 * q^67 + 456 * q^68 + 480 * q^69 + 1152 * q^71 + 184 * q^72 + 1150 * q^73 - 292 * q^74 + 38 * q^75 + 16 * q^76 - 448 * q^78 - 776 * q^79 + 192 * q^80 - 421 * q^81 - 252 * q^82 + 756 * q^83 + 2736 * q^85 + 752 * q^86 - 108 * q^87 - 384 * q^88 + 390 * q^89 + 1104 * q^90 - 960 * q^92 + 472 * q^93 + 24 * q^94 + 24 * q^95 + 64 * q^96 - 2660 * q^97 - 2208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more