LMFDB - Embedded newform 98.3.d.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,3,Mod(19,98)]

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([5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("98.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, 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:	$2.67030659073$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.3.d.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(3.62132 - 2.09077i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-2.74264 - 1.58346i) q^{5} -5.91359i q^{6} -2.82843 q^{8} +(4.24264 - 7.34847i) q^{9} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(3.62132 - 2.09077i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-2.74264 - 1.58346i) q^{5} -5.91359i q^{6} -2.82843 q^{8} +(4.24264 - 7.34847i) q^{9} +(-3.87868 + 2.23936i) q^{10} +(6.62132 + 11.4685i) q^{11} +(-7.24264 - 4.18154i) q^{12} +5.49333i q^{13} -13.2426 q^{15} +(-2.00000 + 3.46410i) q^{16} +(11.7426 - 6.77962i) q^{17} +(-6.00000 - 10.3923i) q^{18} +(0.621320 + 0.358719i) q^{19} +6.33386i q^{20} +18.7279 q^{22} +(1.13604 - 1.96768i) q^{23} +(-10.2426 + 5.91359i) q^{24} +(-7.48528 - 12.9649i) q^{25} +(6.72792 + 3.88437i) q^{26} +2.15232i q^{27} +20.4853 q^{29} +(-9.36396 + 16.2189i) q^{30} +(-21.3198 + 12.3090i) q^{31} +(2.82843 + 4.89898i) q^{32} +(47.9558 + 27.6873i) q^{33} -19.1757i q^{34} -16.9706 q^{36} +(-32.4706 + 56.2407i) q^{37} +(0.878680 - 0.507306i) q^{38} +(11.4853 + 19.8931i) q^{39} +(7.75736 + 4.47871i) q^{40} +21.0308i q^{41} +6.48528 q^{43} +(13.2426 - 22.9369i) q^{44} +(-23.2721 + 13.4361i) q^{45} +(-1.60660 - 2.78272i) q^{46} +(-41.3787 - 23.8900i) q^{47} +16.7262i q^{48} -21.1716 q^{50} +(28.3492 - 49.1023i) q^{51} +(9.51472 - 5.49333i) q^{52} +(-11.0147 - 19.0781i) q^{53} +(2.63604 + 1.52192i) q^{54} -41.9385i q^{55} +3.00000 q^{57} +(14.4853 - 25.0892i) q^{58} +(72.5330 - 41.8770i) q^{59} +(13.2426 + 22.9369i) q^{60} +(-57.3823 - 33.1297i) q^{61} +34.8151i q^{62} +8.00000 q^{64} +(8.69848 - 15.0662i) q^{65} +(67.8198 - 39.1558i) q^{66} +(-46.3198 - 80.2283i) q^{67} +(-23.4853 - 13.5592i) q^{68} -9.50079i q^{69} -48.4264 q^{71} +(-12.0000 + 20.7846i) q^{72} +(-113.441 + 65.4953i) q^{73} +(45.9203 + 79.5363i) q^{74} +(-54.2132 - 31.3000i) q^{75} -1.43488i q^{76} +32.4853 q^{78} +(38.1066 - 66.0026i) q^{79} +(10.9706 - 6.33386i) q^{80} +(42.6838 + 73.9305i) q^{81} +(25.7574 + 14.8710i) q^{82} -107.981i q^{83} -42.9411 q^{85} +(4.58579 - 7.94282i) q^{86} +(74.1838 - 42.8300i) q^{87} +(-18.7279 - 32.4377i) q^{88} +(145.412 + 83.9535i) q^{89} +38.0031i q^{90} -4.54416 q^{92} +(-51.4706 + 89.1496i) q^{93} +(-58.5183 + 33.7856i) q^{94} +(-1.13604 - 1.96768i) q^{95} +(20.4853 + 11.8272i) q^{96} -25.5816i q^{97} +112.368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 4 q^{4} + 6 q^{5}+O(q^{10}) $ 4 * q + 6 * q^3 - 4 * q^4 + 6 * q^5	$ 4 q + 6 q^{3} - 4 q^{4} + 6 q^{5} - 24 q^{10} + 18 q^{11} - 12 q^{12} - 36 q^{15} - 8 q^{16} + 30 q^{17} - 24 q^{18} - 6 q^{19} + 24 q^{22} + 30 q^{23} - 24 q^{24} + 4 q^{25} - 24 q^{26} + 48 q^{29} - 12 q^{30} + 42 q^{31} + 90 q^{33} - 62 q^{37} + 12 q^{38} + 12 q^{39} + 48 q^{40} - 8 q^{43} + 36 q^{44} - 144 q^{45} + 36 q^{46} - 174 q^{47} - 96 q^{50} + 54 q^{51} + 72 q^{52} - 78 q^{53} + 36 q^{54} + 12 q^{57} + 24 q^{58} + 78 q^{59} + 36 q^{60} + 42 q^{61} + 32 q^{64} - 84 q^{65} + 144 q^{66} - 58 q^{67} - 60 q^{68} - 24 q^{71} - 48 q^{72} - 318 q^{73} + 96 q^{74} - 132 q^{75} + 96 q^{78} + 110 q^{79} - 24 q^{80} + 18 q^{81} + 120 q^{82} - 36 q^{85} + 24 q^{86} + 144 q^{87} - 24 q^{88} + 378 q^{89} - 120 q^{92} - 138 q^{93} + 12 q^{94} - 30 q^{95} + 48 q^{96} + 144 q^{99}+O(q^{100}) $ 4 * q + 6 * q^3 - 4 * q^4 + 6 * q^5 - 24 * q^10 + 18 * q^11 - 12 * q^12 - 36 * q^15 - 8 * q^16 + 30 * q^17 - 24 * q^18 - 6 * q^19 + 24 * q^22 + 30 * q^23 - 24 * q^24 + 4 * q^25 - 24 * q^26 + 48 * q^29 - 12 * q^30 + 42 * q^31 + 90 * q^33 - 62 * q^37 + 12 * q^38 + 12 * q^39 + 48 * q^40 - 8 * q^43 + 36 * q^44 - 144 * q^45 + 36 * q^46 - 174 * q^47 - 96 * q^50 + 54 * q^51 + 72 * q^52 - 78 * q^53 + 36 * q^54 + 12 * q^57 + 24 * q^58 + 78 * q^59 + 36 * q^60 + 42 * q^61 + 32 * q^64 - 84 * q^65 + 144 * q^66 - 58 * q^67 - 60 * q^68 - 24 * q^71 - 48 * q^72 - 318 * q^73 + 96 * q^74 - 132 * q^75 + 96 * q^78 + 110 * q^79 - 24 * q^80 + 18 * q^81 + 120 * q^82 - 36 * q^85 + 24 * q^86 + 144 * q^87 - 24 * q^88 + 378 * q^89 - 120 * q^92 - 138 * q^93 + 12 * q^94 - 30 * q^95 + 48 * q^96 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$	3.62132	−	2.09077i	1.20711	−	0.696923i	0.244981	−	0.969528i	$-0.421218\pi$
$3$	3.62132	−	2.09077i	1.20711	−	0.696923i	0.962126	+	0.272605i	$0.0878851\pi$
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−2.74264	−	1.58346i	−0.548528	−	0.316693i	0.200000	−	0.979796i	$-0.435906\pi$
$5$	−2.74264	−	1.58346i	−0.548528	−	0.316693i	−0.748528	+	0.663103i	$0.769239\pi$
$6$		−	5.91359i		−	0.985599i
$7$		0			0
$7$		0			0
$8$	−2.82843			−0.353553
$9$	4.24264	−	7.34847i	0.471405	−	0.816497i
$10$	−3.87868	+	2.23936i	−0.387868	+	0.223936i
$11$	6.62132	+	11.4685i	0.601938	+	1.04259i	0.992527	+	0.122022i	$0.0389380\pi$
$11$	6.62132	+	11.4685i	0.601938	+	1.04259i	−0.390589	+	0.920565i	$0.627729\pi$
$12$	−7.24264	−	4.18154i	−0.603553	−	0.348462i
$13$			5.49333i			0.422563i	0.977425	+	0.211282i	$0.0677638\pi$
$13$			5.49333i			0.422563i	−0.977425	+	0.211282i	$0.932236\pi$
$14$		0			0
$15$	−13.2426			−0.882843
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	11.7426	−	6.77962i	0.690744	−	0.398801i	−0.113147	−	0.993578i	$-0.536093\pi$
$17$	11.7426	−	6.77962i	0.690744	−	0.398801i	0.803891	+	0.594777i	$0.202760\pi$
$18$	−6.00000	−	10.3923i	−0.333333	−	0.577350i
$19$	0.621320	+	0.358719i	0.0327011	+	0.0188800i	0.516261	−	0.856431i	$-0.327323\pi$
$19$	0.621320	+	0.358719i	0.0327011	+	0.0188800i	−0.483560	+	0.875311i	$0.660657\pi$
$20$			6.33386i			0.316693i
$21$		0			0
$22$	18.7279			0.851269
$23$	1.13604	−	1.96768i	0.0493930	−	0.0855512i	−0.840272	−	0.542165i	$-0.817605\pi$
$23$	1.13604	−	1.96768i	0.0493930	−	0.0855512i	0.889665	+	0.456614i	$0.150938\pi$
$24$	−10.2426	+	5.91359i	−0.426777	+	0.246400i
$25$	−7.48528	−	12.9649i	−0.299411	−	0.518596i
$26$	6.72792	+	3.88437i	0.258766	+	0.149399i
$27$			2.15232i			0.0797154i
$28$		0			0
$29$	20.4853			0.706389			0.353195	−	0.935550i	$-0.385095\pi$
$29$	20.4853			0.706389			0.353195	+	0.935550i	$0.385095\pi$
$30$	−9.36396	+	16.2189i	−0.312132	+	0.540629i
$31$	−21.3198	+	12.3090i	−0.687736	+	0.397064i	−0.802763	−	0.596298i	$-0.796638\pi$
$31$	−21.3198	+	12.3090i	−0.687736	+	0.397064i	0.115028	+	0.993362i	$0.463304\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$	47.9558	+	27.6873i	1.45321	+	0.839010i
$34$		−	19.1757i		−	0.563990i
$35$		0			0
$36$	−16.9706			−0.471405
$37$	−32.4706	+	56.2407i	−0.877583	+	1.52002i	−0.0235970	+	0.999722i	$0.507512\pi$
$37$	−32.4706	+	56.2407i	−0.877583	+	1.52002i	−0.853986	+	0.520296i	$0.825821\pi$
$38$	0.878680	−	0.507306i	0.0231231	−	0.0133502i
$39$	11.4853	+	19.8931i	0.294494	+	0.510079i
$40$	7.75736	+	4.47871i	0.193934	+	0.111968i
$41$			21.0308i			0.512946i	0.966551	+	0.256473i	$0.0825605\pi$
$41$			21.0308i			0.512946i	−0.966551	+	0.256473i	$0.917439\pi$
$42$		0			0
$43$	6.48528			0.150820			0.0754102	−	0.997153i	$-0.475973\pi$
$43$	6.48528			0.150820			0.0754102	+	0.997153i	$0.475973\pi$
$44$	13.2426	−	22.9369i	0.300969	−	0.521294i
$45$	−23.2721	+	13.4361i	−0.517157	+	0.298581i
$46$	−1.60660	−	2.78272i	−0.0349261	−	0.0604938i
$47$	−41.3787	−	23.8900i	−0.880397	−	0.508298i	−0.00960801	−	0.999954i	$-0.503058\pi$
$47$	−41.3787	−	23.8900i	−0.880397	−	0.508298i	−0.870789	+	0.491656i	$0.836392\pi$
$48$			16.7262i			0.348462i
$49$		0			0
$50$	−21.1716			−0.423431
$51$	28.3492	−	49.1023i	0.555867	−	0.962791i
$52$	9.51472	−	5.49333i	0.182975	−	0.105641i
$53$	−11.0147	−	19.0781i	−0.207825	−	0.359963i	0.743204	−	0.669065i	$-0.233305\pi$
$53$	−11.0147	−	19.0781i	−0.207825	−	0.359963i	−0.951029	+	0.309101i	$0.899972\pi$
$54$	2.63604	+	1.52192i	0.0488155	+	0.0281837i
$55$		−	41.9385i		−	0.762518i
$56$		0			0
$57$	3.00000			0.0526316
$58$	14.4853	−	25.0892i	0.249746	−	0.432573i
$59$	72.5330	−	41.8770i	1.22937	−	0.709779i	0.262474	−	0.964939i	$-0.415462\pi$
$59$	72.5330	−	41.8770i	1.22937	−	0.709779i	0.966899	+	0.255160i	$0.0821282\pi$
$60$	13.2426	+	22.9369i	0.220711	+	0.382282i
$61$	−57.3823	−	33.1297i	−0.940693	−	0.543109i	−0.0505153	−	0.998723i	$-0.516086\pi$
$61$	−57.3823	−	33.1297i	−0.940693	−	0.543109i	−0.890177	+	0.455614i	$0.849420\pi$
$62$			34.8151i			0.561534i
$63$		0			0
$64$	8.00000			0.125000
$65$	8.69848	−	15.0662i	0.133823	−	0.231788i
$66$	67.8198	−	39.1558i	1.02757	−	0.593269i
$67$	−46.3198	−	80.2283i	−0.691340	−	1.19744i	−0.971399	−	0.237454i	$-0.923687\pi$
$67$	−46.3198	−	80.2283i	−0.691340	−	1.19744i	0.280058	−	0.959983i	$-0.409646\pi$
$68$	−23.4853	−	13.5592i	−0.345372	−	0.199400i
$69$		−	9.50079i		−	0.137693i
$70$		0			0
$71$	−48.4264			−0.682062			−0.341031	−	0.940052i	$-0.610776\pi$
$71$	−48.4264			−0.682062			−0.341031	+	0.940052i	$0.610776\pi$
$72$	−12.0000	+	20.7846i	−0.166667	+	0.288675i
$73$	−113.441	+	65.4953i	−1.55399	+	0.897195i	−0.556177	+	0.831064i	$0.687732\pi$
$73$	−113.441	+	65.4953i	−1.55399	+	0.897195i	−0.997811	+	0.0661316i	$0.978934\pi$
$74$	45.9203	+	79.5363i	0.620545	+	1.07482i
$75$	−54.2132	−	31.3000i	−0.722843	−	0.417333i
$76$		−	1.43488i		−	0.0188800i
$77$		0			0
$78$	32.4853			0.416478
$79$	38.1066	−	66.0026i	0.482362	−	0.835476i	−0.517433	−	0.855724i	$-0.673112\pi$
$79$	38.1066	−	66.0026i	0.482362	−	0.835476i	0.999795	+	0.0202482i	$0.00644564\pi$
$80$	10.9706	−	6.33386i	0.137132	−	0.0791732i
$81$	42.6838	+	73.9305i	0.526960	+	0.912722i
$82$	25.7574	+	14.8710i	0.314114	+	0.181354i
$83$		−	107.981i		−	1.30098i	−0.759514	−	0.650491i	$-0.774563\pi$
$83$		−	107.981i		−	1.30098i	0.759514	−	0.650491i	$-0.225437\pi$
$84$		0			0
$85$	−42.9411			−0.505190
$86$	4.58579	−	7.94282i	0.0533231	−	0.0923583i
$87$	74.1838	−	42.8300i	0.852687	−	0.492299i
$88$	−18.7279	−	32.4377i	−0.212817	−	0.368610i
$89$	145.412	+	83.9535i	1.63384	+	0.943297i	0.982894	+	0.184173i	$0.0589606\pi$
$89$	145.412	+	83.9535i	1.63384	+	0.943297i	0.650945	+	0.759125i	$0.274373\pi$
$90$			38.0031i			0.422257i
$91$		0			0
$92$	−4.54416			−0.0493930
$93$	−51.4706	+	89.1496i	−0.553447	+	0.958598i
$94$	−58.5183	+	33.7856i	−0.622535	+	0.359421i
$95$	−1.13604	−	1.96768i	−0.0119583	−	0.0207124i
$96$	20.4853	+	11.8272i	0.213388	+	0.123200i
$97$		−	25.5816i		−	0.263728i	−0.991268	−	0.131864i	$-0.957904\pi$
$97$		−	25.5816i		−	0.263728i	0.991268	−	0.131864i	$-0.0420962\pi$
$98$		0			0
$99$	112.368			1.13503
$100$	−14.9706	+	25.9298i	−0.149706	+	0.259298i
$101$	−24.6838	+	14.2512i	−0.244394	+	0.141101i	−0.617194	−	0.786811i	$-0.711731\pi$
$101$	−24.6838	+	14.2512i	−0.244394	+	0.141101i	0.372801	+	0.927911i	$0.378397\pi$
$102$	−40.0919	−	69.4412i	−0.393058	−	0.680796i
$103$	−48.9228	−	28.2456i	−0.474979	−	0.274229i	0.243343	−	0.969940i	$-0.421756\pi$
$103$	−48.9228	−	28.2456i	−0.474979	−	0.274229i	−0.718322	+	0.695711i	$0.755089\pi$
$104$		−	15.5375i		−	0.149399i
$105$		0			0
$106$	−31.1543			−0.293909
$107$	−23.8051	+	41.2316i	−0.222477	+	0.385342i	−0.955560	−	0.294798i	$-0.904748\pi$
$107$	−23.8051	+	41.2316i	−0.222477	+	0.385342i	0.733082	+	0.680140i	$0.238081\pi$
$108$	3.72792	−	2.15232i	0.0345178	−	0.0199289i
$109$	−37.6543	−	65.2192i	−0.345453	−	0.598341i	0.639983	−	0.768389i	$-0.278941\pi$
$109$	−37.6543	−	65.2192i	−0.345453	−	0.598341i	−0.985436	+	0.170047i	$0.945608\pi$
$110$	−51.3640	−	29.6550i	−0.466945	−	0.269591i
$111$			271.554i			2.44643i
$112$		0			0
$113$	85.4558			0.756246			0.378123	−	0.925755i	$-0.376570\pi$
$113$	85.4558			0.756246			0.378123	+	0.925755i	$0.376570\pi$
$114$	2.12132	−	3.67423i	0.0186081	−	0.0322301i
$115$	−6.23149	+	3.59775i	−0.0541869	+	0.0312848i
$116$	−20.4853	−	35.4815i	−0.176597	−	0.305875i
$117$	40.3675	+	23.3062i	0.345022	+	0.199198i
$118$		−	118.446i		−	1.00378i
$119$		0			0
$120$	37.4558			0.312132
$121$	−27.1838	+	47.0837i	−0.224659	+	0.389121i
$122$	−81.1508	+	46.8524i	−0.665170	+	0.384036i
$123$	43.9706	+	76.1592i	0.357484	+	0.619181i
$124$	42.6396	+	24.6180i	0.343868	+	0.198532i
$125$			126.584i			1.01267i
$126$		0			0
$127$	−60.6619			−0.477653			−0.238826	−	0.971062i	$-0.576763\pi$
$127$	−60.6619			−0.477653			−0.238826	+	0.971062i	$0.576763\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$	23.4853	−	13.5592i	0.182056	−	0.105110i
$130$	−12.3015	−	21.3068i	−0.0946270	−	0.163899i
$131$	115.136	+	66.4738i	0.878901	+	0.507434i	0.870296	−	0.492529i	$-0.163928\pi$
$131$	115.136	+	66.4738i	0.878901	+	0.507434i	0.00860515	+	0.999963i	$0.497261\pi$
$132$		−	110.749i		−	0.839010i
$133$		0			0
$134$	−131.012			−0.977703
$135$	3.40812	−	5.90303i	0.0252453	−	0.0437262i
$136$	−33.2132	+	19.1757i	−0.244215	+	0.140997i
$137$	58.7132	+	101.694i	0.428564	+	0.742294i	0.996746	−	0.0806089i	$-0.0256865\pi$
$137$	58.7132	+	101.694i	0.428564	+	0.742294i	−0.568182	+	0.822903i	$0.692353\pi$
$138$	−11.6360	−	6.71807i	−0.0843191	−	0.0486817i
$139$		−	68.5857i		−	0.493422i	−0.969089	−	0.246711i	$-0.920650\pi$
$139$		−	68.5857i		−	0.493422i	0.969089	−	0.246711i	$-0.0793499\pi$
$140$		0			0
$141$	−199.794			−1.41698
$142$	−34.2426	+	59.3100i	−0.241145	+	0.417676i
$143$	−63.0000	+	36.3731i	−0.440559	+	0.254357i
$144$	16.9706	+	29.3939i	0.117851	+	0.204124i
$145$	−56.1838	−	32.4377i	−0.387474	−	0.223708i
$146$			185.249i			1.26883i
$147$		0			0
$148$	129.882			0.877583
$149$	13.1985	−	22.8604i	0.0885804	−	0.153426i	−0.818331	−	0.574747i	$-0.805100\pi$
$149$	13.1985	−	22.8604i	0.0885804	−	0.153426i	0.906911	+	0.421322i	$0.138434\pi$
$150$	−76.6690	+	44.2649i	−0.511127	+	0.295099i
$151$	67.1066	+	116.232i	0.444415	+	0.769749i	0.998011	−	0.0630363i	$-0.0200784\pi$
$151$	67.1066	+	116.232i	0.444415	+	0.769749i	−0.553597	+	0.832785i	$0.686745\pi$
$152$	−1.75736	−	1.01461i	−0.0115616	−	0.00667508i
$153$		−	115.054i		−	0.751986i
$154$		0			0
$155$	77.9634			0.502990
$156$	22.9706	−	39.7862i	0.147247	−	0.255040i
$157$	196.323	−	113.347i	1.25047	−	0.721958i	0.279265	−	0.960214i	$-0.409909\pi$
$157$	196.323	−	113.347i	1.25047	−	0.721958i	0.971202	+	0.238256i	$0.0765759\pi$
$158$	−53.8909	−	93.3417i	−0.341081	−	0.590770i
$159$	−79.7756	−	46.0585i	−0.501734	−	0.289676i
$160$		−	17.9149i		−	0.111968i
$161$		0			0
$162$	120.728			0.745234
$163$	45.9889	−	79.6550i	0.282140	−	0.488681i	−0.689771	−	0.724027i	$-0.742289\pi$
$163$	45.9889	−	79.6550i	0.282140	−	0.488681i	0.971912	+	0.235346i	$0.0756223\pi$
$164$	36.4264	−	21.0308i	0.222112	−	0.128237i
$165$	−87.6838	−	151.873i	−0.531417	−	0.920441i
$166$	−132.250	−	76.3544i	−0.796685	−	0.459967i
$167$		−	203.482i		−	1.21845i	−0.792996	−	0.609227i	$-0.791480\pi$
$167$		−	203.482i		−	1.21845i	0.792996	−	0.609227i	$-0.208520\pi$
$168$		0			0
$169$	138.823			0.821440
$170$	−30.3640	+	52.5919i	−0.178612	+	0.309364i
$171$	5.27208	−	3.04384i	0.0308309	−	0.0178002i
$172$	−6.48528	−	11.2328i	−0.0377051	−	0.0653072i
$173$	−61.3234	−	35.4051i	−0.354470	−	0.204654i	0.312182	−	0.950022i	$-0.398940\pi$
$173$	−61.3234	−	35.4051i	−0.354470	−	0.204654i	−0.666652	+	0.745369i	$0.732273\pi$
$174$		−	121.142i		−	0.696216i
$175$		0			0
$176$	−52.9706			−0.300969
$177$	175.110	−	303.300i	0.989323	−	1.71356i
$178$	205.643	−	118.728i	1.15530	−	0.667012i
$179$	−54.4081	−	94.2376i	−0.303956	−	0.526467i	0.673072	−	0.739577i	$-0.264974\pi$
$179$	−54.4081	−	94.2376i	−0.303956	−	0.526467i	−0.977028	+	0.213109i	$0.931641\pi$
$180$	46.5442	+	26.8723i	0.258579	+	0.149290i
$181$			99.6607i			0.550611i	0.961357	+	0.275306i	$0.0887791\pi$
$181$			99.6607i			0.550611i	−0.961357	+	0.275306i	$0.911221\pi$
$182$		0			0
$183$	−277.066			−1.51402
$184$	−3.21320	+	5.56543i	−0.0174631	+	0.0302469i
$185$	178.110	−	102.832i	0.962758	−	0.555848i
$186$	72.7904	+	126.077i	0.391346	+	0.677831i
$187$	155.504	+	89.7800i	0.831570	+	0.480107i
$188$			95.5600i			0.508298i
$189$		0			0
$190$	−3.21320			−0.0169116
$191$	−34.9523	+	60.5391i	−0.182996	+	0.316959i	−0.942899	−	0.333077i	$-0.891913\pi$
$191$	−34.9523	+	60.5391i	−0.182996	+	0.316959i	0.759903	+	0.650036i	$0.225246\pi$
$192$	28.9706	−	16.7262i	0.150888	−	0.0871154i
$193$	16.1690	+	28.0056i	0.0837774	+	0.145107i	0.904870	−	0.425689i	$-0.139968\pi$
$193$	16.1690	+	28.0056i	0.0837774	+	0.145107i	−0.821092	+	0.570796i	$0.806635\pi$
$194$	−31.3310	−	18.0889i	−0.161500	−	0.0932419i
$195$		−	72.7461i		−	0.373057i
$196$		0			0
$197$	277.103			1.40661			0.703306	−	0.710887i	$-0.251706\pi$
$197$	277.103			1.40661			0.703306	+	0.710887i	$0.251706\pi$
$198$	79.4558	−	137.622i	0.401292	−	0.695058i
$199$	−145.011	+	83.7222i	−0.728699	+	0.420715i	−0.817946	−	0.575295i	$-0.804887\pi$
$199$	−145.011	+	83.7222i	−0.728699	+	0.420715i	0.0892469	+	0.996010i	$0.471554\pi$
$200$	21.1716	+	36.6702i	0.105858	+	0.183351i
$201$	−335.478	−	193.688i	−1.66904	−	0.963623i
$202$			40.3084i			0.199547i
$203$		0			0
$204$	−113.397			−0.555867
$205$	33.3015	−	57.6799i	0.162446	−	0.281365i
$206$	−69.1873	+	39.9453i	−0.335861	+	0.193909i
$207$	−9.63961	−	16.6963i	−0.0465682	−	0.0806584i
$208$	−19.0294	−	10.9867i	−0.0914877	−	0.0528204i
$209$			9.50079i			0.0454583i
$210$		0			0
$211$	−128.073			−0.606982			−0.303491	−	0.952834i	$-0.598152\pi$
$211$	−128.073			−0.606982			−0.303491	+	0.952834i	$0.598152\pi$
$212$	−22.0294	+	38.1561i	−0.103912	+	0.179982i
$213$	−175.368	+	101.248i	−0.823322	+	0.475345i
$214$	33.6655	+	58.3103i	0.157315	+	0.272478i
$215$	−17.7868	−	10.2692i	−0.0827293	−	0.0477638i
$216$		−	6.08767i		−	0.0281837i
$217$		0			0
$218$	−106.503			−0.488544
$219$	−273.871	+	474.359i	−1.25055	+	2.16602i
$220$	−72.6396	+	41.9385i	−0.330180	+	0.190630i
$221$	37.2426	+	64.5061i	0.168519	+	0.291883i
$222$	332.584	+	192.018i	1.49813	+	0.864944i
$223$			417.169i			1.87071i	0.353705	+	0.935357i	$0.384922\pi$
$223$			417.169i			1.87071i	−0.353705	+	0.935357i	$0.615078\pi$
$224$		0			0
$225$	−127.029			−0.564575
$226$	60.4264	−	104.662i	0.267373	−	0.463104i
$227$	−201.143	+	116.130i	−0.886093	+	0.511586i	−0.872663	−	0.488324i	$-0.837609\pi$
$227$	−201.143	+	116.130i	−0.886093	+	0.511586i	−0.0134307	+	0.999910i	$0.504275\pi$
$228$	−3.00000	−	5.19615i	−0.0131579	−	0.0227901i
$229$	72.4188	+	41.8110i	0.316239	+	0.182581i	0.649715	−	0.760178i	$-0.274888\pi$
$229$	72.4188	+	41.8110i	0.316239	+	0.182581i	−0.333476	+	0.942759i	$0.608222\pi$
$230$			10.1760i			0.0442434i
$231$		0			0
$232$	−57.9411			−0.249746
$233$	−109.537	+	189.723i	−0.470114	+	0.814261i	−0.999416	−	0.0341721i	$-0.989121\pi$
$233$	−109.537	+	189.723i	−0.470114	+	0.814261i	0.529302	+	0.848434i	$0.322454\pi$
$234$	57.0883	−	32.9600i	0.243967	−	0.140854i
$235$	75.6579	+	131.043i	0.321949	+	0.557631i
$236$	−145.066	−	83.7539i	−0.614687	−	0.354889i
$237$		−	318.689i		−	1.34468i
$238$		0			0
$239$	193.103			0.807961			0.403980	−	0.914768i	$-0.367626\pi$
$239$	193.103			0.807961			0.403980	+	0.914768i	$0.367626\pi$
$240$	26.4853	−	45.8739i	0.110355	−	0.191141i
$241$	−42.8970	+	24.7666i	−0.177996	+	0.102766i	−0.586351	−	0.810057i	$-0.699436\pi$
$241$	−42.8970	+	24.7666i	−0.177996	+	0.102766i	0.408355	+	0.912823i	$0.366103\pi$
$242$	38.4437	+	66.5864i	0.158858	+	0.275150i
$243$	292.368	+	168.798i	1.20316	+	0.694644i
$244$			132.519i			0.543109i
$245$		0			0
$246$	124.368			0.505559
$247$	−1.97056	+	3.41311i	−0.00797799	+	0.0138183i
$248$	60.3015	−	34.8151i	0.243151	−	0.140383i
$249$	−225.765	−	391.036i	−0.906685	−	1.57042i
$250$	155.033	+	89.5083i	0.620132	+	0.358033i
$251$		−	162.524i		−	0.647507i	−0.946141	−	0.323754i	$-0.895055\pi$
$251$		−	162.524i		−	0.647507i	0.946141	−	0.323754i	$-0.104945\pi$
$252$		0			0
$253$	30.0883			0.118926
$254$	−42.8944	+	74.2954i	−0.168876	+	0.292501i
$255$	−155.504	+	89.7800i	−0.609818	+	0.352079i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	85.8747	+	49.5798i	0.334143	+	0.192917i	0.657679	−	0.753298i	$-0.271538\pi$
$257$	85.8747	+	49.5798i	0.334143	+	0.192917i	−0.323536	+	0.946216i	$0.604872\pi$
$258$		−	38.3513i		−	0.148648i
$259$		0			0
$260$	−34.7939			−0.133823
$261$	86.9117	−	150.535i	0.332995	−	0.576764i
$262$	162.827	−	94.0082i	0.621477	−	0.358810i
$263$	−217.173	−	376.154i	−0.825751	−	1.43024i	−0.901344	−	0.433105i	$-0.857418\pi$
$263$	−217.173	−	376.154i	−0.825751	−	1.43024i	0.0755923	−	0.997139i	$-0.475915\pi$
$264$	−135.640	−	78.3116i	−0.513786	−	0.296635i
$265$			69.7657i			0.263267i
$266$		0			0
$267$	702.110			2.62962
$268$	−92.6396	+	160.457i	−0.345670	+	0.598718i
$269$	79.1619	−	45.7041i	0.294282	−	0.169904i	−0.345589	−	0.938386i	$-0.612321\pi$
$269$	79.1619	−	45.7041i	0.294282	−	0.169904i	0.639871	+	0.768482i	$0.278988\pi$
$270$	−4.81981	−	8.34815i	−0.0178511	−	0.0309191i
$271$	−14.8051	−	8.54772i	−0.0546313	−	0.0315414i	0.472436	−	0.881365i	$-0.343375\pi$
$271$	−14.8051	−	8.54772i	−0.0546313	−	0.0315414i	−0.527067	+	0.849824i	$0.676708\pi$
$272$			54.2369i			0.199400i
$273$		0			0
$274$	166.066			0.606080
$275$	99.1249	−	171.689i	0.360454	−	0.624325i
$276$	−16.4558	+	9.50079i	−0.0596226	+	0.0344231i
$277$	200.206	+	346.766i	0.722764	+	1.25186i	0.959888	+	0.280385i	$0.0904620\pi$
$277$	200.206	+	346.766i	0.722764	+	1.25186i	−0.237124	+	0.971479i	$0.576205\pi$
$278$	−84.0000	−	48.4974i	−0.302158	−	0.174451i
$279$			208.891i			0.748712i
$280$		0			0
$281$	−538.690			−1.91705			−0.958524	−	0.285012i	$-0.908002\pi$
$281$	−538.690			−1.91705			−0.958524	+	0.285012i	$0.908002\pi$
$282$	−141.276	+	244.697i	−0.500977	+	0.867718i
$283$	267.783	−	154.604i	0.946229	−	0.546306i	0.0543215	−	0.998523i	$-0.482700\pi$
$283$	267.783	−	154.604i	0.946229	−	0.546306i	0.891907	+	0.452218i	$0.149367\pi$
$284$	48.4264	+	83.8770i	0.170516	+	0.295342i
$285$	−8.22792	−	4.75039i	−0.0288699	−	0.0166680i
$286$			102.879i			0.359715i
$287$		0			0
$288$	48.0000			0.166667
$289$	−52.5736	+	91.0601i	−0.181916	+	0.315087i
$290$	−79.4558	+	45.8739i	−0.273986	+	0.158186i
$291$	−53.4853	−	92.6392i	−0.183798	−	0.318348i
$292$	226.882	+	130.991i	0.776994	+	0.448598i
$293$		−	327.391i		−	1.11738i	−0.829378	−	0.558688i	$-0.811305\pi$
$293$		−	327.391i		−	1.11738i	0.829378	−	0.558688i	$-0.188695\pi$
$294$		0			0
$295$	−265.243			−0.899128
$296$	91.8406	−	159.073i	0.310272	−	0.537408i
$297$	−24.6838	+	14.2512i	−0.0831103	+	0.0479838i
$298$	−18.6655	−	32.3296i	−0.0626358	−	0.108488i
$299$	10.8091	+	6.24063i	0.0361508	+	0.0208717i
$300$			125.200i			0.417333i
$301$		0			0
$302$	189.806			0.628497
$303$	−59.5919	+	103.216i	−0.196673	+	0.340647i
$304$	−2.48528	+	1.43488i	−0.00817527	+	0.00471999i
$305$	104.919	+	181.725i	0.343998	+	0.595821i
$306$	−140.912	−	81.3554i	−0.460496	−	0.265867i
$307$		−	256.140i		−	0.834331i	−0.908831	−	0.417165i	$-0.863024\pi$
$307$		−	256.140i		−	0.834331i	0.908831	−	0.417165i	$-0.136976\pi$
$308$		0			0
$309$	−236.220			−0.764467
$310$	55.1285	−	95.4853i	0.177834	−	0.308017i
$311$	−187.349	+	108.166i	−0.602409	+	0.347801i	−0.769989	−	0.638057i	$-0.779738\pi$
$311$	−187.349	+	108.166i	−0.602409	+	0.347801i	0.167580	+	0.985859i	$0.446405\pi$
$312$	−32.4853	−	56.2662i	−0.104119	−	0.180340i
$313$	−135.809	−	78.4092i	−0.433893	−	0.250509i	0.267110	−	0.963666i	$-0.413931\pi$
$313$	−135.809	−	78.4092i	−0.433893	−	0.250509i	−0.701004	+	0.713157i	$0.747264\pi$
$314$		−	320.595i		−	1.02100i
$315$		0			0
$316$	−152.426			−0.482362
$317$	224.015	−	388.005i	0.706671	−	1.22399i	−0.259414	−	0.965766i	$-0.583529\pi$
$317$	224.015	−	388.005i	0.706671	−	1.22399i	0.966085	−	0.258224i	$-0.0831372\pi$
$318$	−112.820	+	65.1365i	−0.354779	+	0.204832i
$319$	135.640	+	234.935i	0.425203	+	0.736472i
$320$	−21.9411	−	12.6677i	−0.0685660	−	0.0395866i
$321$			199.084i			0.620199i
$322$		0			0
$323$	9.72792			0.0301174
$324$	85.3675	−	147.861i	0.263480	−	0.456361i
$325$	71.2203	−	41.1191i	0.219140	−	0.126520i
$326$	−65.0381	−	112.649i	−0.199503	−	0.345550i
$327$	−272.717	−	157.453i	−0.833996	−	0.481508i
$328$		−	59.4841i		−	0.181354i
$329$		0			0
$330$	−248.007			−0.751537
$331$	27.5036	−	47.6376i	0.0830924	−	0.143920i	−0.821484	−	0.570231i	$-0.806854\pi$
$331$	27.5036	−	47.6376i	0.0830924	−	0.143920i	0.904577	+	0.426311i	$0.140187\pi$
$332$	−187.029	+	107.981i	−0.563342	+	0.325245i
$333$	275.522	+	477.218i	0.827393	+	1.43309i
$334$	−249.213	−	143.883i	−0.746147	−	0.430788i
$335$			293.383i			0.875770i
$336$		0			0
$337$	−111.632			−0.331254			−0.165627	−	0.986189i	$-0.552965\pi$
$337$	−111.632			−0.331254			−0.165627	+	0.986189i	$0.552965\pi$
$338$	98.1630	−	170.023i	0.290423	−	0.503027i
$339$	309.463	−	178.669i	0.912870	−	0.527046i
$340$	42.9411	+	74.3762i	0.126297	+	0.218754i
$341$	−282.331	−	163.004i	−0.827949	−	0.478016i
$342$		−	8.60927i		−	0.0251733i
$343$		0			0
$344$	−18.3431			−0.0533231
$345$	−15.0442	+	26.0572i	−0.0436062	+	0.0755282i
$346$	−86.7244	+	50.0703i	−0.250648	+	0.144712i
$347$	−188.628	−	326.714i	−0.543598	−	0.941539i	−0.998694	−	0.0510967i	$-0.983728\pi$
$347$	−188.628	−	326.714i	−0.543598	−	0.941539i	0.455096	−	0.890442i	$-0.349605\pi$
$348$	−148.368	−	85.6600i	−0.426343	−	0.246150i
$349$			204.034i			0.584624i	0.956323	+	0.292312i	$0.0944246\pi$
$349$			204.034i			0.584624i	−0.956323	+	0.292312i	$0.905575\pi$
$350$		0			0
$351$	−11.8234			−0.0336848
$352$	−37.4558	+	64.8754i	−0.106409	+	0.184305i
$353$	361.198	−	208.538i	1.02323	−	0.590759i	0.108189	−	0.994130i	$-0.465495\pi$
$353$	361.198	−	208.538i	1.02323	−	0.590759i	0.915036	+	0.403371i	$0.132162\pi$
$354$	−247.643	−	428.931i	−0.699557	−	1.21167i
$355$	132.816	+	76.6815i	0.374130	+	0.216004i
$356$		−	335.814i		−	0.943297i
$357$		0			0
$358$	−153.889			−0.429859
$359$	89.4153	−	154.872i	0.249068	−	0.431398i	−0.714200	−	0.699942i	$-0.753209\pi$
$359$	89.4153	−	154.872i	0.249068	−	0.431398i	0.963267	+	0.268544i	$0.0865425\pi$
$360$	65.8234	−	38.0031i	0.182843	−	0.105564i
$361$	−180.243	−	312.189i	−0.499287	−	0.864791i
$362$	122.059	+	70.4707i	0.337179	+	0.194671i
$363$			227.340i			0.626281i
$364$		0			0
$365$	414.838			1.13654
$366$	−195.915	+	339.335i	−0.535288	+	0.927145i
$367$	544.724	−	314.497i	1.48426	−	0.856939i	0.484422	−	0.874835i	$-0.339030\pi$
$367$	544.724	−	314.497i	1.48426	−	0.856939i	0.999840	+	0.0178960i	$0.00569679\pi$
$368$	4.54416	+	7.87071i	0.0123482	+	0.0213878i
$369$	154.544	+	89.2261i	0.418819	+	0.241805i
$370$		−	290.853i		−	0.786088i
$371$		0			0
$372$	205.882			0.553447
$373$	127.779	−	221.320i	0.342572	−	0.593351i	−0.642338	−	0.766422i	$-0.722035\pi$
$373$	127.779	−	221.320i	0.342572	−	0.593351i	0.984910	+	0.173070i	$0.0553687\pi$
$374$	219.915	−	126.968i	0.588009	−	0.339487i
$375$	264.658	+	458.401i	0.705754	+	1.22240i
$376$	117.037	+	67.5711i	0.311267	+	0.179710i
$377$			112.532i			0.298494i
$378$		0			0
$379$	219.750			0.579816			0.289908	−	0.957055i	$-0.406375\pi$
$379$	219.750			0.579816			0.289908	+	0.957055i	$0.406375\pi$
$380$	−2.27208	+	3.93535i	−0.00597915	+	0.0103562i
$381$	−219.676	+	126.830i	−0.576578	+	0.332887i
$382$	49.4300	+	85.6152i	0.129398	+	0.224124i
$383$	14.7534	+	8.51785i	0.0385205	+	0.0222398i	0.519137	−	0.854691i	$-0.326254\pi$
$383$	14.7534	+	8.51785i	0.0385205	+	0.0222398i	−0.480616	+	0.876931i	$0.659587\pi$
$384$		−	47.3087i		−	0.123200i
$385$		0			0
$386$	45.7330			0.118479
$387$	27.5147	−	47.6569i	0.0710975	−	0.123144i
$388$	−44.3087	+	25.5816i	−0.114198	+	0.0659320i
$389$	76.1102	+	131.827i	0.195656	+	0.338886i	0.947115	−	0.320893i	$-0.103983\pi$
$389$	76.1102	+	131.827i	0.195656	+	0.338886i	−0.751459	+	0.659779i	$0.770650\pi$
$390$	−89.0955	−	51.4393i	−0.228450	−	0.131896i
$391$		−	30.8076i		−	0.0787919i
$392$		0			0
$393$	555.926			1.41457
$394$	195.941	−	339.380i	0.497313	−	0.861371i
$395$	−209.025	+	120.681i	−0.529178	+	0.305521i
$396$	−112.368	−	194.626i	−0.283756	−	0.491480i
$397$	322.786	+	186.361i	0.813064	+	0.469423i	0.848019	−	0.529966i	$-0.177795\pi$
$397$	322.786	+	186.361i	0.813064	+	0.469423i	−0.0349549	+	0.999389i	$0.511129\pi$
$398$			236.802i			0.594980i
$399$		0			0
$400$	59.8823			0.149706
$401$	−325.786	+	564.279i	−0.812435	+	1.40718i	0.0987205	+	0.995115i	$0.468525\pi$
$401$	−325.786	+	564.279i	−0.812435	+	1.40718i	−0.911155	+	0.412063i	$0.864808\pi$
$402$	−474.437	+	273.916i	−1.18019	+	0.681384i
$403$	−67.6173	−	117.117i	−0.167785	−	0.290612i
$404$	49.3675	+	28.5024i	0.122197	+	0.0705504i
$405$		−	270.353i		−	0.667538i
$406$		0			0
$407$	−859.992			−2.11300
$408$	−80.1838	+	138.882i	−0.196529	+	0.340398i
$409$	−462.081	+	266.782i	−1.12978	+	0.652280i	−0.943880	−	0.330289i	$-0.892854\pi$
$409$	−462.081	+	266.782i	−1.12978	+	0.652280i	−0.185902	+	0.982568i	$0.559521\pi$
$410$	−47.0955	−	81.5717i	−0.114867	−	0.198955i
$411$	425.239	+	245.512i	1.03464	+	0.597352i
$412$			112.982i			0.274229i
$413$		0			0
$414$	−27.2649			−0.0658573
$415$	−170.985	+	296.154i	−0.412012	+	0.713625i
$416$	−26.9117	+	15.5375i	−0.0646916	+	0.0373497i
$417$	−143.397	−	248.371i	−0.343878	−	0.595614i
$418$	11.6360	+	6.71807i	0.0278374	+	0.0160719i
$419$		−	534.252i		−	1.27507i	−0.770423	−	0.637533i	$-0.779955\pi$
$419$		−	534.252i		−	1.27507i	0.770423	−	0.637533i	$-0.220045\pi$
$420$		0			0
$421$	157.220			0.373445			0.186723	−	0.982413i	$-0.440213\pi$
$421$	157.220			0.373445			0.186723	+	0.982413i	$0.440213\pi$
$422$	−90.5614	+	156.857i	−0.214600	+	0.371699i
$423$	−351.110	+	202.713i	−0.830047	+	0.479228i
$424$	31.1543	+	53.9609i	0.0734772	+	0.127266i
$425$	−175.794	−	101.495i	−0.413633	−	0.238811i
$426$			286.374i			0.672239i
$427$		0			0
$428$	95.2203			0.222477
$429$	−152.095	+	263.437i	−0.354535	+	0.614072i
$430$	−25.1543	+	14.5229i	−0.0584984	+	0.0337741i
$431$	114.268	+	197.918i	0.265123	+	0.459207i	0.967596	−	0.252504i	$-0.0812541\pi$
$431$	114.268	+	197.918i	0.265123	+	0.459207i	−0.702473	+	0.711711i	$0.747921\pi$
$432$	−7.45584	−	4.30463i	−0.0172589	−	0.00996443i
$433$			47.5549i			0.109827i	0.998491	+	0.0549133i	$0.0174882\pi$
$433$			47.5549i			0.109827i	−0.998491	+	0.0549133i	$0.982512\pi$
$434$		0			0
$435$	−271.279			−0.623630
$436$	−75.3087	+	130.438i	−0.172726	+	0.299171i
$437$	1.41169	−	0.815039i	0.00323041	−	0.00186508i
$438$	387.312	+	670.844i	0.884274	+	1.53161i
$439$	63.9594	+	36.9270i	0.145693	+	0.0841161i	0.571075	−	0.820898i	$-0.306527\pi$
$439$	63.9594	+	36.9270i	0.145693	+	0.0841161i	−0.425381	+	0.905014i	$0.639860\pi$
$440$			118.620i			0.269591i
$441$		0			0
$442$	105.338			0.238321
$443$	−117.320	+	203.204i	−0.264830	+	0.458699i	−0.967519	−	0.252798i	$-0.918649\pi$
$443$	−117.320	+	203.204i	−0.264830	+	0.458699i	0.702689	+	0.711497i	$0.251983\pi$
$444$	470.345	−	271.554i	1.05934	−	0.611608i
$445$	−265.875	−	460.508i	−0.597471	−	1.03485i
$446$	510.926	+	294.983i	1.14557	+	0.661397i
$447$		−	110.380i		−	0.246935i
$448$		0			0
$449$	−255.161			−0.568288			−0.284144	−	0.958782i	$-0.591709\pi$
$449$	−255.161			−0.568288			−0.284144	+	0.958782i	$0.591709\pi$
$450$	−89.8234	+	155.579i	−0.199608	+	0.345730i
$451$	−241.191	+	139.252i	−0.534791	+	0.308762i
$452$	−85.4558	−	148.014i	−0.189062	−	0.327464i
$453$	486.029	+	280.609i	1.07291	+	0.619446i
$454$			328.465i			0.723492i
$455$		0			0
$456$	−8.48528			−0.0186081
$457$	72.8675	−	126.210i	0.159448	−	0.276171i	−0.775222	−	0.631689i	$-0.782362\pi$
$457$	72.8675	−	126.210i	0.159448	−	0.276171i	0.934670	+	0.355518i	$0.115695\pi$
$458$	102.416	−	59.1297i	0.223615	−	0.129104i
$459$	14.5919	+	25.2739i	0.0317906	+	0.0550629i
$460$	12.4630	+	7.19551i	0.0270934	+	0.0156424i
$461$			888.329i			1.92696i	0.267777	+	0.963481i	$0.413711\pi$
$461$			888.329i			1.92696i	−0.267777	+	0.963481i	$0.586289\pi$
$462$		0			0
$463$	234.014			0.505430			0.252715	−	0.967541i	$-0.418676\pi$
$463$	234.014			0.505430			0.252715	+	0.967541i	$0.418676\pi$
$464$	−40.9706	+	70.9631i	−0.0882986	+	0.152938i
$465$	282.331	−	163.004i	0.607162	−	0.350545i
$466$	154.908	+	268.309i	0.332421	+	0.575770i
$467$	−681.231	−	393.309i	−1.45874	−	0.842204i	−0.459790	−	0.888028i	$-0.652075\pi$
$467$	−681.231	−	393.309i	−1.45874	−	0.842204i	−0.998950	+	0.0458237i	$0.985409\pi$
$468$		−	93.2248i		−	0.199198i
$469$		0			0
$470$	213.993			0.455304
$471$	473.967	−	820.934i	1.00630	−	1.74296i
$472$	−205.154	+	118.446i	−0.434649	+	0.250945i
$473$	42.9411	+	74.3762i	0.0907846	+	0.157244i
$474$	−390.312	−	225.347i	−0.823444	−	0.475415i
$475$		−	10.7405i		−	0.0226115i
$476$		0			0
$477$	−186.926			−0.391878
$478$	136.544	−	236.501i	0.285657	−	0.494773i
$479$	−638.202	+	368.466i	−1.33236	+	0.769240i	−0.985661	−	0.168735i	$-0.946032\pi$
$479$	−638.202	+	368.466i	−1.33236	+	0.769240i	−0.346702	+	0.937975i	$0.612698\pi$
$480$	−37.4558	−	64.8754i	−0.0780330	−	0.135157i
$481$	−308.948	−	178.371i	−0.642304	−	0.370834i
$482$			70.0505i			0.145333i
$483$		0			0
$484$	108.735			0.224659
$485$	−40.5076	+	70.1612i	−0.0835208	+	0.144662i
$486$	413.470	−	238.717i	0.850762	−	0.491187i
$487$	−135.349	−	234.432i	−0.277925	−	0.481379i	0.692944	−	0.720991i	$-0.256313\pi$
$487$	−135.349	−	234.432i	−0.277925	−	0.481379i	−0.970869	+	0.239612i	$0.922980\pi$
$488$	162.302	+	93.7048i	0.332585	+	0.192018i
$489$		−	384.609i		−	0.786520i
$490$		0			0
$491$	760.161			1.54819			0.774094	−	0.633070i	$-0.218206\pi$
$491$	760.161			1.54819			0.774094	+	0.633070i	$0.218206\pi$
$492$	87.9411	−	152.318i	0.178742	−	0.309590i
$493$	240.551	−	138.882i	0.487934	−	0.281709i
$494$	2.78680	+	4.82687i	0.00564129	+	0.00977100i
$495$	−308.184	−	177.930i	−0.622593	−	0.359455i
$496$		−	98.4720i		−	0.198532i
$497$		0			0
$498$	−638.558			−1.28225
$499$	−62.7462	+	108.680i	−0.125744	+	0.217795i	−0.922023	−	0.387134i	$-0.873465\pi$
$499$	−62.7462	+	108.680i	−0.125744	+	0.217795i	0.796280	+	0.604929i	$0.206798\pi$
$500$	219.250	−	126.584i	0.438500	−	0.253168i
$501$	−425.434	−	736.873i	−0.849169	−	1.47080i
$502$	−199.051	−	114.922i	−0.396516	−	0.228928i
$503$			117.083i			0.232770i	0.993204	+	0.116385i	$0.0371306\pi$
$503$			117.083i			0.232770i	−0.993204	+	0.116385i	$0.962869\pi$
$504$		0			0
$505$	90.2649			0.178742
$506$	21.2756	−	36.8505i	0.0420467	−	0.0728271i
$507$	502.724	−	290.248i	0.991566	−	0.572481i
$508$	60.6619	+	105.070i	0.119413	+	0.206830i
$509$	574.110	+	331.463i	1.12792	+	0.651204i	0.943410	−	0.331627i	$-0.107598\pi$
$509$	574.110	+	331.463i	1.12792	+	0.651204i	0.184507	+	0.982831i	$0.440931\pi$
$510$			253.936i			0.497914i
$511$		0			0
$512$	−22.6274			−0.0441942
$513$	−0.772078	+	1.33728i	−0.00150503	+	0.00260678i
$514$	121.445	−	70.1164i	0.236275	−	0.136413i
$515$	89.4518	+	154.935i	0.173693	+	0.300845i
$516$	−46.9706	−	27.1185i	−0.0910282	−	0.0525552i
$517$		−	632.733i		−	1.22386i
$518$		0			0
$519$	−296.095			−0.570511
$520$	−24.6030	+	42.6137i	−0.0473135	+	0.0819494i
$521$	40.8229	−	23.5691i	0.0783550	−	0.0452383i	−0.460311	−	0.887758i	$-0.652262\pi$
$521$	40.8229	−	23.5691i	0.0783550	−	0.0452383i	0.538666	+	0.842520i	$0.318929\pi$
$522$	−122.912	−	212.889i	−0.235463	−	0.407834i
$523$	−432.554	−	249.735i	−0.827064	−	0.477506i	0.0257824	−	0.999668i	$-0.491792\pi$
$523$	−432.554	−	249.735i	−0.827064	−	0.477506i	−0.852846	+	0.522162i	$0.825126\pi$
$524$		−	265.895i		−	0.507434i
$525$		0			0
$526$	−614.257			−1.16779
$527$	−166.901	+	289.080i	−0.316699	+	0.548539i
$528$	−191.823	+	110.749i	−0.363302	+	0.209752i
$529$	261.919	+	453.657i	0.495121	+	0.857574i
$530$	85.4451	+	49.3318i	0.161217	+	0.0930788i
$531$		−	710.675i		−	1.33837i
$532$		0			0
$533$	−115.529			−0.216752
$534$	496.467	−	859.905i	0.929713	−	1.61031i
$535$	130.578	−	75.3890i	0.244070	−	0.140914i
$536$	131.012	+	226.920i	0.244426	+	0.423358i
$537$	−394.058	−	227.510i	−0.733815	−	0.423668i
$538$		−	129.271i		−	0.240280i
$539$		0			0
$540$	−13.6325			−0.0252453
$541$	−249.405	+	431.981i	−0.461007	+	0.798487i	−0.999011	−	0.0444550i	$-0.985845\pi$
$541$	−249.405	+	431.981i	−0.461007	+	0.798487i	0.538005	+	0.842942i	$0.319178\pi$
$542$	−20.9376	+	12.0883i	−0.0386302	+	0.0223031i
$543$	208.368	+	360.903i	0.383734	+	0.664647i
$544$	66.4264	+	38.3513i	0.122107	+	0.0704987i
$545$			238.497i			0.437609i
$546$		0			0
$547$	−279.897			−0.511694			−0.255847	−	0.966717i	$-0.582354\pi$
$547$	−279.897			−0.511694			−0.255847	+	0.966717i	$0.582354\pi$
$548$	117.426	−	203.389i	0.214282	−	0.371147i
$549$	−486.905	+	281.114i	−0.886894	+	0.512048i
$550$	−140.184	−	242.805i	−0.254880	−	0.441464i
$551$	12.7279	+	7.34847i	0.0230997	+	0.0133366i
$552$			26.8723i			0.0486817i
$553$		0			0
$554$	566.267			1.02214
$555$	429.996	−	744.775i	0.774768	−	1.34194i
$556$	−118.794	+	68.5857i	−0.213658	+	0.123356i
$557$	130.890	+	226.708i	0.234991	+	0.407016i	0.959270	−	0.282491i	$-0.0911607\pi$
$557$	130.890	+	226.708i	0.234991	+	0.407016i	−0.724279	+	0.689507i	$0.757827\pi$
$558$	255.838	+	147.708i	0.458490	+	0.264710i
$559$			35.6258i			0.0637312i
$560$		0			0
$561$	750.838			1.33839
$562$	−380.912	+	659.758i	−0.677779	+	1.17395i
$563$	420.076	−	242.531i	0.746139	−	0.430784i	−0.0781581	−	0.996941i	$-0.524904\pi$
$563$	420.076	−	242.531i	0.746139	−	0.430784i	0.824297	+	0.566157i	$0.191571\pi$
$564$	199.794	+	346.053i	0.354245	+	0.613570i
$565$	−234.375	−	135.316i	−0.414822	−	0.239498i
$566$		−	437.287i		−	0.772593i
$567$		0			0
$568$	136.971			0.241145
$569$	227.000	−	393.175i	0.398945	−	0.690993i	−0.594651	−	0.803984i	$-0.702710\pi$
$569$	227.000	−	393.175i	0.398945	−	0.690993i	0.993596	+	0.112991i	$0.0360432\pi$
$570$	−11.6360	+	6.71807i	−0.0204141	+	0.0117861i
$571$	115.769	+	200.517i	0.202747	+	0.351168i	0.949413	−	0.314032i	$-0.101680\pi$
$571$	115.769	+	200.517i	0.202747	+	0.351168i	−0.746666	+	0.665200i	$0.768346\pi$
$572$	126.000	+	72.7461i	0.220280	+	0.127179i
$573$			292.309i			0.510137i
$574$		0			0
$575$	−34.0143			−0.0591553
$576$	33.9411	−	58.7878i	0.0589256	−	0.102062i
$577$	−564.014	+	325.634i	−0.977494	+	0.564356i	−0.901513	−	0.432753i	$-0.857542\pi$
$577$	−564.014	+	325.634i	−0.977494	+	0.564356i	−0.0759812	+	0.997109i	$0.524209\pi$
$578$	74.3503	+	128.778i	0.128634	+	0.222800i
$579$	117.107	+	67.6115i	0.202257	+	0.116773i
$580$			129.751i			0.223708i
$581$		0			0
$582$	−151.279			−0.259930
$583$	145.864	−	252.644i	0.250195	−	0.433351i
$584$	320.860	−	185.249i	0.549418	−	0.317206i
$585$	−73.8091	−	127.841i	−0.126169	−	0.218532i
$586$	−400.971	−	231.500i	−0.684250	−	0.395052i
$587$			823.029i			1.40209i	0.713116	+	0.701046i	$0.247283\pi$
$587$			823.029i			1.40209i	−0.713116	+	0.701046i	$0.752717\pi$
$588$		0			0
$589$	−17.6619			−0.0299863
$590$	−187.555	+	324.855i	−0.317890	+	0.550601i
$591$	1003.48	−	579.358i	1.69793	−	0.980301i
$592$	−129.882	−	224.963i	−0.219396	−	0.380004i
$593$	700.110	+	404.209i	1.18062	+	0.681634i	0.956159	−	0.292848i	$-0.0946031\pi$
$593$	700.110	+	404.209i	1.18062	+	0.681634i	0.224465	+	0.974482i	$0.427936\pi$
$594$			40.3084i			0.0678593i
$595$		0			0
$596$	−52.7939			−0.0885804
$597$	−350.088	+	606.370i	−0.586412	+	1.01570i
$598$	15.2864	−	8.82559i	0.0255625	−	0.0147585i
$599$	−265.422	−	459.725i	−0.443109	−	0.767488i	0.554809	−	0.831978i	$-0.312791\pi$
$599$	−265.422	−	459.725i	−0.443109	−	0.767488i	−0.997918	+	0.0644900i	$0.979458\pi$
$600$	153.338	+	88.5298i	0.255563	+	0.147550i
$601$		−	936.503i		−	1.55824i	−0.626874	−	0.779121i	$-0.715666\pi$
$601$		−	936.503i		−	1.55824i	0.626874	−	0.779121i	$-0.284334\pi$
$602$		0			0
$603$	−786.073			−1.30360
$604$	134.213	−	232.464i	0.222207	−	0.384874i
$605$	149.111	−	86.0890i	0.246464	−	0.142296i
$606$	84.2756	+	145.970i	0.139069	+	0.240874i
$607$	−521.452	−	301.060i	−0.859064	−	0.495981i	0.00463474	−	0.999989i	$-0.498525\pi$
$607$	−521.452	−	301.060i	−0.859064	−	0.495981i	−0.863699	+	0.504008i	$0.831858\pi$
$608$			4.05845i			0.00667508i
$609$		0			0
$610$	296.756			0.486486
$611$	131.235	−	227.307i	0.214788	−	0.372024i
$612$	−199.279	+	115.054i	−0.325620	+	0.187997i
$613$	−548.448	−	949.940i	−0.894695	−	1.54966i	−0.834181	−	0.551491i	$-0.814059\pi$
$613$	−548.448	−	949.940i	−0.894695	−	1.54966i	−0.0605142	−	0.998167i	$-0.519274\pi$
$614$	−313.706	−	181.118i	−0.510921	−	0.294981i
$615$		−	278.503i		−	0.452851i
$616$		0			0
$617$	−432.956			−0.701712			−0.350856	−	0.936429i	$-0.614109\pi$
$617$	−432.956			−0.701712			−0.350856	+	0.936429i	$0.614109\pi$
$618$	−167.033	+	289.310i	−0.270280	+	0.468139i
$619$	−194.951	+	112.555i	−0.314946	+	0.181834i	−0.649137	−	0.760671i	$-0.724870\pi$
$619$	−194.951	+	112.555i	−0.314946	+	0.181834i	0.334192	+	0.942505i	$0.391537\pi$
$620$	−77.9634	−	135.037i	−0.125747	−	0.217801i
$621$	4.23506	+	2.44512i	0.00681975	+	0.00393738i
$622$			305.940i			0.491865i
$623$		0			0
$624$	−91.8823			−0.147247
$625$	13.3091	−	23.0520i	0.0212945	−	0.0368832i
$626$	−192.062	+	110.887i	−0.306809	+	0.177136i
$627$	19.8640	+	34.4054i	0.0316810	+	0.0548730i
$628$	−392.647	−	226.695i	−0.625234	−	0.360979i
$629$			880.552i			1.39992i
$630$		0			0
$631$	750.514			1.18940			0.594702	−	0.803946i	$-0.297270\pi$
$631$	750.514			1.18940			0.594702	+	0.803946i	$0.297270\pi$
$632$	−107.782	+	186.683i	−0.170541	+	0.295385i
$633$	−463.794	+	267.772i	−0.732692	+	0.423020i
$634$	−316.805	−	548.722i	−0.499692	−	0.865492i
$635$	166.374	+	96.0560i	0.262006	+	0.151269i
$636$			184.234i			0.289676i
$637$		0			0
$638$	383.647			0.601327
$639$	−205.456	+	355.860i	−0.321527	+	0.556901i
$640$	−31.0294	+	17.9149i	−0.0484835	+	0.0279920i
$641$	580.926	+	1006.19i	0.906281	+	1.56973i	0.819188	+	0.573525i	$0.194425\pi$
$641$	580.926	+	1006.19i	0.906281	+	1.56973i	0.0870937	+	0.996200i	$0.472242\pi$
$642$	243.827	+	140.774i	0.379793	+	0.219273i
$643$			121.957i			0.189669i	0.995493	+	0.0948347i	$0.0302322\pi$
$643$			121.957i			0.189669i	−0.995493	+	0.0948347i	$0.969768\pi$
$644$		0			0
$645$	−85.8823			−0.133151
$646$	6.87868	−	11.9142i	0.0106481	−	0.0184431i
$647$	137.504	−	79.3877i	0.212525	−	0.122701i	−0.389959	−	0.920832i	$-0.627511\pi$
$647$	137.504	−	79.3877i	0.212525	−	0.122701i	0.602484	+	0.798131i	$0.294178\pi$
$648$	−120.728	−	209.107i	−0.186309	−	0.322696i
$649$	960.529	+	554.561i	1.48001	+	0.854486i
$650$		−	116.302i		−	0.178927i
$651$		0			0
$652$	−183.955			−0.282140
$653$	195.471	−	338.565i	0.299342	−	0.518476i	−0.676643	−	0.736311i	$-0.736566\pi$
$653$	195.471	−	338.565i	0.299342	−	0.518476i	0.975986	+	0.217835i	$0.0698994\pi$
$654$	−385.680	+	222.672i	−0.589724	+	0.340478i
$655$	−210.518	−	364.628i	−0.321401	−	0.556683i
$656$	−72.8528	−	42.0616i	−0.111056	−	0.0641183i
$657$			1111.49i			1.69177i
$658$		0			0
$659$	−331.955			−0.503726			−0.251863	−	0.967763i	$-0.581043\pi$
$659$	−331.955			−0.503726			−0.251863	+	0.967763i	$0.581043\pi$
$660$	−175.368	+	303.745i	−0.265708	+	0.460220i
$661$	−561.029	+	323.910i	−0.848758	+	0.490031i	−0.860232	−	0.509904i	$-0.829681\pi$
$661$	−561.029	+	323.910i	−0.848758	+	0.490031i	0.0114736	+	0.999934i	$0.496348\pi$
$662$	−38.8959	−	67.3697i	−0.0587552	−	0.101767i
$663$	269.735	+	155.732i	0.406840	+	0.234889i
$664$			305.418i			0.459967i
$665$		0			0
$666$	779.294			1.17011
$667$	23.2721	−	40.3084i	0.0348907	−	0.0604324i
$668$	−352.441	+	203.482i	−0.527606	+	0.304613i
$669$	872.205	+	1510.70i	1.30374	+	2.25815i
$670$	359.319	+	207.453i	0.536298	+	0.309632i
$671$		−	877.448i		−	1.30767i
$672$		0			0
$673$	100.956			0.150009			0.0750047	−	0.997183i	$-0.476103\pi$
$673$	100.956			0.150009			0.0750047	+	0.997183i	$0.476103\pi$
$674$	−78.9361	+	136.721i	−0.117116	+	0.202851i
$675$	27.9045	−	16.1107i	0.0413401	−	0.0238677i
$676$	−138.823	−	240.449i	−0.205360	−	0.355694i
$677$	−643.610	−	371.588i	−0.950679	−	0.548875i	−0.0573873	−	0.998352i	$-0.518277\pi$
$677$	−643.610	−	371.588i	−0.950679	−	0.548875i	−0.893292	+	0.449477i	$0.851610\pi$
$678$		−	505.351i		−	0.745355i
$679$		0			0
$680$	121.456			0.178612
$681$	−485.603	+	841.088i	−0.713073	+	1.23508i
$682$	−399.276	+	230.522i	−0.585448	+	0.338009i
$683$	−2.21721	−	3.84032i	−0.00324628	−	0.00562272i	0.864398	−	0.502809i	$-0.167700\pi$
$683$	−2.21721	−	3.84032i	−0.00324628	−	0.00562272i	−0.867644	+	0.497186i	$0.834367\pi$
$684$	−10.5442	−	6.08767i	−0.0154154	−	0.00890010i
$685$		−	371.881i		−	0.542892i
$686$		0			0
$687$	349.669			0.508980
$688$	−12.9706	+	22.4657i	−0.0188526	+	0.0326536i
$689$	104.802	−	60.5074i	0.152107	−	0.0878192i
$690$	21.2756	+	36.8505i	0.0308343	+	0.0534065i
$691$	846.253	+	488.584i	1.22468	+	0.707069i	0.965912	−	0.258871i	$-0.0833506\pi$
$691$	846.253	+	488.584i	1.22468	+	0.707069i	0.258767	+	0.965940i	$0.416684\pi$
$692$			141.620i			0.204654i
$693$		0			0
$694$	−533.522			−0.768763
$695$	−108.603	+	188.106i	−0.156263	+	0.270656i
$696$	−209.823	+	121.142i	−0.301470	+	0.174054i
$697$	142.581	+	246.957i	0.204563	+	0.354314i
$698$	249.889	+	144.274i	0.358008	+	0.206696i
$699$			916.063i			1.31053i
$700$		0			0
$701$	−840.177			−1.19854			−0.599270	−	0.800547i	$-0.704542\pi$
$701$	−840.177			−1.19854			−0.599270	+	0.800547i	$0.704542\pi$
$702$	−8.36039	+	14.4806i	−0.0119094	+	0.0206277i
$703$	−40.3492	+	23.2956i	−0.0573958	+	0.0331375i
$704$	52.9706	+	91.7477i	0.0752423	+	0.130323i
$705$	547.963	+	316.367i	0.777252	+	0.448747i
$706$		−	589.835i		−	0.835460i
$707$		0			0
$708$	−700.441			−0.989323
$709$	−341.279	+	591.112i	−0.481352	+	0.833727i	−0.999771	−	0.0214003i	$-0.993188\pi$
$709$	−341.279	+	591.112i	−0.481352	+	0.833727i	0.518419	+	0.855127i	$0.326521\pi$
$710$	187.831	−	108.444i	0.264550	−	0.152738i
$711$	−323.345	−	560.050i	−0.454775	−	0.787694i
$712$	−411.286	−	237.456i	−0.577649	−	0.333506i
$713$			55.9340i			0.0784488i
$714$		0			0
$715$	230.382			0.322212
$716$	−108.816	+	188.475i	−0.151978	+	0.263234i
$717$	699.286	−	403.733i	0.975295	−	0.563087i
$718$	−126.452	−	219.022i	−0.176117	−	0.305044i
$719$	−119.187	−	68.8126i	−0.165768	−	0.0957060i	0.414821	−	0.909903i	$-0.363844\pi$
$719$	−119.187	−	68.8126i	−0.165768	−	0.0957060i	−0.580589	+	0.814197i	$0.697178\pi$
$720$		−	107.489i		−	0.149290i
$721$		0			0
$722$	−509.803			−0.706099
$723$	−103.562	+	179.375i	−0.143240	+	0.248099i
$724$	172.617	−	99.6607i	0.238422	−	0.137653i
$725$	−153.338	−	265.589i	−0.211501	−	0.366330i
$726$	278.434	+	160.754i	0.383517	+	0.221424i
$727$			264.137i			0.363325i	0.983361	+	0.181662i	$0.0581478\pi$
$727$			264.137i			0.363325i	−0.983361	+	0.181662i	$0.941852\pi$
$728$		0			0
$729$	643.368			0.882534
$730$	293.335	−	508.070i	0.401828	−	0.695987i
$731$	76.1543	−	43.9677i	0.104178	−	0.0601474i
$732$	277.066	+	479.892i	0.378505	+	0.655591i
$733$	−501.705	−	289.660i	−0.684455	−	0.395170i	0.117077	−	0.993123i	$-0.462648\pi$
$733$	−501.705	−	289.660i	−0.684455	−	0.395170i	−0.801531	+	0.597953i	$0.795981\pi$
$734$		−	889.530i		−	1.21189i
$735$		0			0
$736$	12.8528			0.0174631
$737$	613.397	−	1062.43i	0.832288	−	1.44157i
$738$	218.558	−	126.185i	0.296150	−	0.170982i
$739$	99.0477	+	171.556i	0.134029	+	0.232146i	0.925226	−	0.379416i	$-0.123875\pi$
$739$	99.0477	+	171.556i	0.134029	+	0.232146i	−0.791197	+	0.611562i	$0.790542\pi$
$740$	−356.220	−	205.664i	−0.481379	−	0.277924i
$741$			16.4800i			0.0222402i
$742$		0			0
$743$	976.690			1.31452			0.657261	−	0.753663i	$-0.271715\pi$
$743$	976.690			1.31452			0.657261	+	0.753663i	$0.271715\pi$
$744$	145.581	−	252.153i	0.195673	−	0.338916i
$745$	−72.3974	+	41.7987i	−0.0971777	+	0.0561056i
$746$	−180.707	−	312.994i	−0.242235	−	0.419563i
$747$	−793.499	−	458.127i	−1.06225	−	0.613289i
$748$		−	359.120i		−	0.480107i
$749$		0			0
$750$	748.566			0.998087
$751$	417.665	−	723.417i	0.556145	−	0.963272i	−0.441668	−	0.897178i	$-0.645613\pi$
$751$	417.665	−	723.417i	0.556145	−	0.963272i	0.997813	−	0.0660933i	$-0.0210535\pi$
$752$	165.515	−	95.5600i	0.220099	−	0.127074i
$753$	−339.801	−	588.553i	−0.451263	−	0.781611i
$754$	137.823	+	79.5724i	0.182790	+	0.105534i
$755$		−	425.044i		−	0.562972i
$756$		0			0
$757$	104.221			0.137677			0.0688383	−	0.997628i	$-0.478071\pi$
$757$	104.221			0.137677			0.0688383	+	0.997628i	$0.478071\pi$
$758$	155.387	−	269.138i	0.204996	−	0.355063i
$759$	108.959	−	62.9077i	0.143557	−	0.0828824i
$760$	3.21320	+	5.56543i	0.00422790	+	0.00732294i
$761$	473.785	+	273.540i	0.622583	+	0.359448i	0.777874	−	0.628420i	$-0.216298\pi$
$761$	473.785	+	273.540i	0.622583	+	0.359448i	−0.155291	+	0.987869i	$0.549632\pi$
$762$			358.730i			0.470774i
$763$		0			0
$764$	139.809			0.182996
$765$	−182.184	+	315.552i	−0.238149	+	0.412486i
$766$	20.8644	−	12.0461i	0.0272381	−	0.0157259i
$767$	230.044	+	398.447i	0.299927	+	0.519488i
$768$	−57.9411	−	33.4523i	−0.0754442	−	0.0435577i
$769$		−	341.205i		−	0.443700i	−0.975081	−	0.221850i	$-0.928790\pi$
$769$		−	341.205i		−	0.443700i	0.975081	−	0.221850i	$-0.0712095\pi$
$770$		0			0
$771$	414.640			0.537795
$772$	32.3381	−	56.0112i	0.0418887	−	0.0725534i
$773$	425.213	−	245.497i	0.550081	−	0.317590i	−0.199074	−	0.979985i	$-0.563793\pi$
$773$	425.213	−	245.497i	0.550081	−	0.317590i	0.749155	+	0.662395i	$0.230460\pi$
$774$	−38.9117	−	67.3970i	−0.0502735	−	0.0870763i
$775$	319.169	+	184.273i	0.411832	+	0.237771i
$776$			72.3557i			0.0932419i
$777$		0			0
$778$	215.272			0.276699
$779$	−7.54416	+	13.0669i	−0.00968441	+	0.0167739i
$780$	−126.000	+	72.7461i	−0.161538	+	0.0932643i
$781$	−320.647	−	555.376i	−0.410559	−	0.711109i
$782$	−37.7315	−	21.7843i	−0.0482500	−	0.0278571i
$783$			44.0908i			0.0563101i
$784$		0			0
$785$	−717.926			−0.914555
$786$	393.099	−	680.867i	0.500126	−	0.866244i
$787$	−260.202	+	150.228i	−0.330625	+	0.190887i	−0.656119	−	0.754658i	$-0.727803\pi$
$787$	−260.202	+	150.228i	−0.330625	+	0.190887i	0.325493	+	0.945544i	$0.394470\pi$
$788$	−277.103	−	479.956i	−0.351653	−	0.609081i
$789$	−1572.90	−	908.116i	−1.99354	−	1.15097i
$790$			341.337i			0.432072i
$791$		0			0
$792$	−317.823			−0.401292
$793$	181.992	−	315.219i	0.229498	−	0.397502i
$794$	456.489	−	263.554i	0.574923	−	0.331932i
$795$	145.864	+	252.644i	0.183477	+	0.317791i
$796$	290.022	+	167.444i	0.364350	+	0.210357i
$797$		−	370.072i		−	0.464331i	−0.972676	−	0.232165i	$-0.925419\pi$
$797$		−	370.072i		−	0.464331i	0.972676	−	0.232165i	$-0.0745811\pi$
$798$		0			0
$799$	−647.860			−0.810838
$800$	42.3431	−	73.3405i	0.0529289	−	0.0916756i
$801$	1233.86	−	712.369i	1.54040	−	0.889349i
$802$	460.731	+	798.010i	0.574478	+	0.995025i
$803$	−1502.26	−	867.330i	−1.87081	−	1.08011i
$804$			774.753i			0.963623i
$805$		0			0
$806$	−191.251			−0.237284
$807$	191.114	−	331.019i	0.236820	−	0.410184i
$808$	69.8162	−	40.3084i	0.0864062	−	0.0498867i
$809$	−245.618	−	425.422i	−0.303607	−	0.525862i	0.673344	−	0.739330i	$-0.264858\pi$
$809$	−245.618	−	425.422i	−0.303607	−	0.525862i	−0.976950	+	0.213468i	$0.931524\pi$
$810$	−331.113	−	191.168i	−0.408782	−	0.236010i
$811$			156.802i			0.193344i	0.995316	+	0.0966722i	$0.0308199\pi$
$811$			156.802i			0.193344i	−0.995316	+	0.0966722i	$0.969180\pi$
$812$		0			0
$813$	−71.4853			−0.0879278
$814$	−608.106	+	1053.27i	−0.747059	+	1.29394i
$815$	−252.262	+	145.643i	−0.309524	+	0.178704i
$816$	113.397	+	196.409i	0.138967	+	0.240698i
$817$	4.02944	+	2.32640i	0.00493199	+	0.00284749i
$818$			754.575i			0.922463i
$819$		0			0
$820$	−133.206			−0.162446
$821$	215.316	−	372.939i	0.262261	−	0.454249i	−0.704581	−	0.709623i	$-0.748865\pi$
$821$	215.316	−	372.939i	0.262261	−	0.454249i	0.966842	+	0.255374i	$0.0821986\pi$
$822$	601.378	−	347.206i	0.731604	−	0.422392i
$823$	354.371	+	613.788i	0.430584	+	0.745793i	0.996924	−	0.0783785i	$-0.0249743\pi$
$823$	354.371	+	613.788i	0.430584	+	0.745793i	−0.566340	+	0.824172i	$0.691641\pi$
$824$	138.375	+	79.8907i	0.167930	+	0.0969547i
$825$		−	828.990i		−	1.00484i
$826$		0			0
$827$	−1460.10			−1.76554			−0.882770	−	0.469805i	$-0.844324\pi$
$827$	−1460.10			−1.76554			−0.882770	+	0.469805i	$0.844324\pi$
$828$	−19.2792	+	33.3926i	−0.0232841	+	0.0403292i
$829$	223.095	−	128.804i	0.269113	−	0.155373i	−0.359371	−	0.933195i	$-0.617009\pi$
$829$	223.095	−	128.804i	0.269113	−	0.155373i	0.628485	+	0.777822i	$0.283675\pi$
$830$	241.809	+	418.826i	0.291336	+	0.504609i
$831$	1450.02	+	837.168i	1.74491	+	1.00742i
$832$			43.9466i			0.0528204i
$833$		0			0
$834$	−405.588			−0.486316
$835$	−322.206	+	558.077i	−0.385876	+	0.668356i
$836$	16.4558	−	9.50079i	0.0196840	−	0.0113646i
$837$	−26.4929	−	45.8870i	−0.0316522	−	0.0548231i
$838$	−654.323	−	377.774i	−0.780815	−	0.450804i
$839$		−	213.621i		−	0.254613i	−0.991863	−	0.127307i	$-0.959367\pi$
$839$		−	213.621i		−	0.254613i	0.991863	−	0.127307i	$-0.0406332\pi$
$840$		0			0
$841$	−421.353			−0.501015
$842$	111.172	−	192.555i	0.132033	−	0.228687i
$843$	−1950.77	+	1126.28i	−2.31408	+	1.33604i
$844$	128.073	+	221.829i	0.151745	+	0.262831i
$845$	−380.743	−	219.822i	−0.450583	−	0.260144i
$846$			573.360i			0.677730i
$847$		0			0
$848$	88.1177			0.103912
$849$	646.485	−	1119.74i	0.761466	−	1.31890i
$850$	−248.610	+	143.535i	−0.292483	+	0.168865i
$851$	73.7756	+	127.783i	0.0866929	+	0.150156i
$852$	350.735	+	202.497i	0.411661	+	0.237673i
$853$		−	1127.37i		−	1.32165i	−0.750539	−	0.660826i	$-0.770206\pi$
$853$		−	1127.37i		−	1.32165i	0.750539	−	0.660826i	$-0.229794\pi$
$854$		0			0
$855$	−19.2792			−0.0225488
$856$	67.3310	−	116.621i	0.0786577	−	0.136239i
$857$	−1100.22	+	635.212i	−1.28380	+	0.741204i	−0.977541	−	0.210744i	$-0.932412\pi$
$857$	−1100.22	+	635.212i	−1.28380	+	0.741204i	−0.306261	+	0.951947i	$0.599078\pi$
$858$	215.095	+	372.556i	0.250694	+	0.434215i
$859$	221.488	+	127.876i	0.257844	+	0.148867i	0.623351	−	0.781942i	$-0.285771\pi$
$859$	221.488	+	127.876i	0.257844	+	0.148867i	−0.365506	+	0.930809i	$0.619104\pi$
$860$			41.0768i			0.0477638i
$861$		0			0
$862$	323.199			0.374941
$863$	−557.364	+	965.382i	−0.645844	+	1.11863i	0.338262	+	0.941052i	$0.390161\pi$
$863$	−557.364	+	965.382i	−0.645844	+	1.11863i	−0.984106	+	0.177583i	$0.943172\pi$
$864$	−10.5442	+	6.08767i	−0.0122039	+	0.00704592i
$865$	112.125	+	194.207i	0.129625	+	0.224516i
$866$	58.2426	+	33.6264i	0.0672548	+	0.0388296i
$867$			439.677i			0.507125i
$868$		0			0
$869$	1009.26			1.16141
$870$	−191.823	+	332.248i	−0.220487	+	0.381894i
$871$	440.720	−	254.450i	0.505993	−	0.292135i
$872$	106.503	+	184.468i	0.122136	+	0.211546i
$873$	−187.986	−	108.534i	−0.215333	−	0.124323i
$874$		−	2.30528i		−	0.00263762i
$875$		0			0
$876$	1095.48			1.25055
$877$	550.904	−	954.194i	0.628169	−	1.08802i	−0.359750	−	0.933049i	$-0.617138\pi$
$877$	550.904	−	954.194i	0.628169	−	1.08802i	0.987919	−	0.154972i	$-0.0495286\pi$
$878$	90.4523	−	52.2226i	0.103021	−	0.0594791i
$879$	−684.500	−	1185.59i	−0.778725	−	1.34879i
$880$	145.279	+	83.8770i	0.165090	+	0.0953148i
$881$			217.067i			0.246387i	0.992383	+	0.123194i	$0.0393136\pi$
$881$			217.067i			0.246387i	−0.992383	+	0.123194i	$0.960686\pi$
$882$		0			0
$883$	−516.544			−0.584988			−0.292494	−	0.956267i	$-0.594485\pi$
$883$	−516.544			−0.584988			−0.292494	+	0.956267i	$0.594485\pi$
$884$	74.4853	−	129.012i	0.0842594	−	0.145942i
$885$	−960.529	+	554.561i	−1.08534	+	0.626623i
$886$	165.915	+	287.374i	0.187263	+	0.324350i
$887$	978.445	+	564.905i	1.10309	+	0.636872i	0.937032	−	0.349243i	$-0.113561\pi$
$887$	978.445	+	564.905i	1.10309	+	0.636872i	0.166062	+	0.986115i	$0.446895\pi$
$888$		−	768.071i		−	0.864944i
$889$		0			0
$890$	−752.007			−0.844952
$891$	−565.246	+	979.034i	−0.634395	+	1.09880i
$892$	722.558	−	417.169i	0.810043	−	0.467679i
$893$	−17.1396	−	29.6867i	−0.0191933	−	0.0332438i
$894$	−135.187	−	78.0504i	−0.151216	−	0.0873047i
$895$			344.613i			0.385043i
$896$		0			0
$897$	52.1909			0.0581838
$898$	−180.426	+	312.508i	−0.200920	+	0.348004i
$899$	−436.742	+	252.153i	−0.485809	+	0.280482i
$900$	127.029	+	220.021i	0.141144	+	0.244468i
$901$	−258.684	−	149.351i	−0.287107	−	0.165762i
$902$			393.863i			0.436655i
$903$		0			0
$904$	−241.706			−0.267373
$905$	157.809	−	273.333i	0.174375	−	0.302026i
$906$	687.349	−	396.841i	0.758663	−	0.438014i
$907$	−30.0111	−	51.9808i	−0.0330884	−	0.0573107i	0.849007	−	0.528382i	$-0.177201\pi$
$907$	−30.0111	−	51.9808i	−0.0330884	−	0.0573107i	−0.882095	+	0.471071i	$0.843868\pi$
$908$	402.286	+	232.260i	0.443047	+	0.255793i
$909$			241.851i			0.266062i
$910$		0			0
$911$	1422.25			1.56120			0.780598	−	0.625033i	$-0.214915\pi$
$911$	1422.25			1.56120			0.780598	+	0.625033i	$0.214915\pi$
$912$	−6.00000	+	10.3923i	−0.00657895	+	0.0113951i
$913$	1238.38	−	714.980i	1.35639	−	0.783111i
$914$	−103.050	−	178.488i	−0.112746	−	0.195283i
$915$	759.893	+	438.724i	0.830484	+	0.479480i
$916$		−	167.244i		−	0.182581i
$917$		0			0
$918$	41.2721			0.0449587
$919$	−834.849	+	1446.00i	−0.908432	+	1.57345i	−0.0921886	+	0.995742i	$0.529386\pi$
$919$	−834.849	+	1446.00i	−0.908432	+	1.57345i	−0.816243	+	0.577708i	$0.803947\pi$
$920$	17.6253	−	10.1760i	0.0191580	−	0.0110609i
$921$	−535.529	−	927.563i	−0.581465	−	1.00713i
$922$	1087.98	+	628.144i	1.18002	+	0.681284i
$923$		−	266.022i		−	0.288215i
$924$		0			0
$925$	972.205			1.05103
$926$	165.473	−	286.608i	0.178697	−	0.309512i
$927$	−415.124	+	239.672i	−0.447814	+	0.258546i
$928$	57.9411	+	100.357i	0.0624366	+	0.108143i
$929$	−839.058	−	484.430i	−0.903184	−	0.521453i	−0.0249519	−	0.999689i	$-0.507943\pi$
$929$	−839.058	−	484.430i	−0.903184	−	0.521453i	−0.878232	+	0.478235i	$0.841277\pi$
$930$		−	461.044i		−	0.495746i
$931$		0			0
$932$	438.146			0.470114
$933$	−452.301	+	783.408i	−0.484781	+	0.839666i
$934$	−963.407	+	556.223i	−1.03148	+	0.595528i
$935$	−284.327	−	492.469i	−0.304093	−	0.526705i
$936$	−114.177	−	65.9199i	−0.121984	−	0.0704272i
$937$			1212.57i			1.29410i	0.762449	+	0.647049i	$0.223997\pi$
$937$			1212.57i			1.29410i	−0.762449	+	0.647049i	$0.776003\pi$
$938$		0			0
$939$	−655.742			−0.698341
$940$	151.316	−	262.087i	0.160974	−	0.278816i
$941$	1293.90	−	747.032i	1.37502	−	0.793870i	0.383468	−	0.923554i	$-0.374730\pi$
$941$	1293.90	−	747.032i	1.37502	−	0.793870i	0.991555	+	0.129684i	$0.0413963\pi$
$942$	−670.290	−	1160.98i	−0.711560	−	1.23246i
$943$	41.3818	+	23.8918i	0.0438832	+	0.0253360i
$944$			335.016i			0.354889i
$945$		0			0
$946$	121.456			0.128389
$947$	−387.731	+	671.570i	−0.409431	+	0.709155i	−0.994826	−	0.101593i	$-0.967606\pi$
$947$	−387.731	+	671.570i	−0.409431	+	0.709155i	0.585395	+	0.810748i	$0.300939\pi$
$948$	−551.985	+	318.689i	−0.582262	+	0.336169i
$949$	−359.787	−	623.169i	−0.379122	−	0.656659i
$950$	−13.1543	−	7.59466i	−0.0138467	−	0.00799437i
$951$		−	1873.45i		−	1.96998i
$952$		0			0
$953$	1055.40			1.10745			0.553723	−	0.832701i	$-0.313206\pi$
$953$	1055.40			1.10745			0.553723	+	0.832701i	$0.313206\pi$
$954$	−132.177	+	228.937i	−0.138550	+	0.239976i
$955$	191.723	−	110.691i	0.200757	−	0.115907i
$956$	−193.103	−	334.464i	−0.201990	−	0.349857i
$957$	982.389	+	567.183i	1.02653	+	0.592667i
$958$			1042.18i			1.08787i
$959$		0			0
$960$	−105.941			−0.110355
$961$	−177.477	+	307.400i	−0.184680	+	0.319875i
$962$	−436.919	+	252.255i	−0.454178	+	0.262220i
$963$	201.993	+	349.862i	0.209754	+	0.363304i
$964$	85.7939	+	49.5332i	0.0889979	+	0.0513829i
$965$		−	102.412i		−	0.106127i
$966$		0			0
$967$	1221.63			1.26332			0.631661	−	0.775245i	$-0.282373\pi$
$967$	1221.63			1.26332			0.631661	+	0.775245i	$0.282373\pi$
$968$	76.8873	−	133.173i	0.0794290	−	0.137575i
$969$	35.2279	−	20.3389i	0.0363549	−	0.0209895i
$970$	57.2864	+	99.2229i	0.0590581	+	0.102292i
$971$	455.753	+	263.129i	0.469365	+	0.270988i	0.715974	−	0.698127i	$-0.245983\pi$
$971$	455.753	+	263.129i	0.469365	+	0.270988i	−0.246609	+	0.969115i	$0.579316\pi$
$972$		−	675.194i		−	0.694644i
$973$		0			0
$974$	−382.825			−0.393045
$975$	171.941	−	297.811i	0.176350	−	0.305447i
$976$	229.529	−	132.519i	0.235173	−	0.135777i
$977$	500.051	+	866.114i	0.511823	+	0.886504i	0.999906	+	0.0137065i	$0.00436306\pi$
$977$	500.051	+	866.114i	0.511823	+	0.886504i	−0.488083	+	0.872797i	$0.662304\pi$
$978$	−471.047	−	271.959i	−0.481643	−	0.278077i
$979$			2223.53i			2.27123i
$980$		0			0
$981$	−639.015			−0.651392
$982$	537.515	−	931.003i	0.547367	−	0.948068i
$983$	−931.584	+	537.850i	−0.947695	+	0.547152i	−0.892364	−	0.451316i	$-0.850955\pi$
$983$	−931.584	+	537.850i	−0.947695	+	0.547152i	−0.0553306	+	0.998468i	$0.517621\pi$
$984$	−124.368	−	215.411i	−0.126390	−	0.218914i
$985$	−759.993	−	438.782i	−0.771566	−	0.445464i
$986$		−	392.819i		−	0.398396i
$987$		0			0
$988$	7.88225			0.00797799
$989$	7.36753	−	12.7609i	0.00744948	−	0.0129029i
$990$	−435.838	+	251.631i	−0.440240	+	0.254173i
$991$	938.017	+	1624.69i	0.946536	+	1.63945i	0.752646	+	0.658426i	$0.228777\pi$
$991$	938.017	+	1624.69i	0.946536	+	1.63945i	0.193891	+	0.981023i	$0.437889\pi$
$992$	−120.603	−	69.6302i	−0.121576	−	0.0701917i
$993$		−	230.015i		−	0.231636i
$994$		0			0
$995$	530.285			0.532949
$996$	−451.529	+	782.071i	−0.453342	+	0.785212i
$997$	−504.221	+	291.112i	−0.505738	+	0.291988i	−0.731080	−	0.682292i	$-0.760983\pi$
$997$	−504.221	+	291.112i	−0.505738	+	0.291988i	0.225342	+	0.974280i	$0.427650\pi$
$998$	88.7365	+	153.696i	0.0889144	+	0.154004i
$999$	−121.048	−	69.8869i	−0.121169	−	0.0699569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.3.d.a.19.2		4
3.2	odd	2		882.3.n.b.19.1		4
4.3	odd	2		784.3.s.c.705.1		4
7.2	even	3		98.3.b.b.97.2		4
7.3	odd	6	inner	98.3.d.a.31.2		4
7.4	even	3		14.3.d.a.3.2	✓	4
7.5	odd	6		98.3.b.b.97.1		4
7.6	odd	2		14.3.d.a.5.2	yes	4
21.2	odd	6		882.3.c.f.685.3		4
21.5	even	6		882.3.c.f.685.4		4
21.11	odd	6		126.3.n.c.73.1		4
21.17	even	6		882.3.n.b.325.1		4
21.20	even	2		126.3.n.c.19.1		4
28.3	even	6		784.3.s.c.129.1		4
28.11	odd	6		112.3.s.b.17.2		4
28.19	even	6		784.3.c.e.97.4		4
28.23	odd	6		784.3.c.e.97.1		4
28.27	even	2		112.3.s.b.33.2		4
35.4	even	6		350.3.k.a.101.1		4
35.13	even	4		350.3.i.a.299.1		8
35.18	odd	12		350.3.i.a.199.4		8
35.27	even	4		350.3.i.a.299.4		8
35.32	odd	12		350.3.i.a.199.1		8
35.34	odd	2		350.3.k.a.201.1		4
56.11	odd	6		448.3.s.c.129.1		4
56.13	odd	2		448.3.s.d.257.2		4
56.27	even	2		448.3.s.c.257.1		4
56.53	even	6		448.3.s.d.129.2		4
84.11	even	6		1008.3.cg.l.577.1		4
84.83	odd	2		1008.3.cg.l.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.2	✓	4	7.4	even	3
14.3.d.a.5.2	yes	4	7.6	odd	2
98.3.b.b.97.1		4	7.5	odd	6
98.3.b.b.97.2		4	7.2	even	3
98.3.d.a.19.2		4	1.1	even	1	trivial
98.3.d.a.31.2		4	7.3	odd	6	inner
112.3.s.b.17.2		4	28.11	odd	6
112.3.s.b.33.2		4	28.27	even	2
126.3.n.c.19.1		4	21.20	even	2
126.3.n.c.73.1		4	21.11	odd	6
350.3.i.a.199.1		8	35.32	odd	12
350.3.i.a.199.4		8	35.18	odd	12
350.3.i.a.299.1		8	35.13	even	4
350.3.i.a.299.4		8	35.27	even	4
350.3.k.a.101.1		4	35.4	even	6
350.3.k.a.201.1		4	35.34	odd	2
448.3.s.c.129.1		4	56.11	odd	6
448.3.s.c.257.1		4	56.27	even	2
448.3.s.d.129.2		4	56.53	even	6
448.3.s.d.257.2		4	56.13	odd	2
784.3.c.e.97.1		4	28.23	odd	6
784.3.c.e.97.4		4	28.19	even	6
784.3.s.c.129.1		4	28.3	even	6
784.3.s.c.705.1		4	4.3	odd	2
882.3.c.f.685.3		4	21.2	odd	6
882.3.c.f.685.4		4	21.5	even	6
882.3.n.b.19.1		4	3.2	odd	2
882.3.n.b.325.1		4	21.17	even	6
1008.3.cg.l.145.1		4	84.83	odd	2
1008.3.cg.l.577.1		4	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(3.62132 - 2.09077i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-2.74264 - 1.58346i) q^{5} -5.91359i q^{6} -2.82843 q^{8} +(4.24264 - 7.34847i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(3.62132 - 2.09077i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-2.74264 - 1.58346i) q^{5} -5.91359i q^{6} -2.82843 q^{8} +(4.24264 - 7.34847i) q^{9} +(-3.87868 + 2.23936i) q^{10} +(6.62132 + 11.4685i) q^{11} +(-7.24264 - 4.18154i) q^{12} +5.49333i q^{13} -13.2426 q^{15} +(-2.00000 + 3.46410i) q^{16} +(11.7426 - 6.77962i) q^{17} +(-6.00000 - 10.3923i) q^{18} +(0.621320 + 0.358719i) q^{19} +6.33386i q^{20} +18.7279 q^{22} +(1.13604 - 1.96768i) q^{23} +(-10.2426 + 5.91359i) q^{24} +(-7.48528 - 12.9649i) q^{25} +(6.72792 + 3.88437i) q^{26} +2.15232i q^{27} +20.4853 q^{29} +(-9.36396 + 16.2189i) q^{30} +(-21.3198 + 12.3090i) q^{31} +(2.82843 + 4.89898i) q^{32} +(47.9558 + 27.6873i) q^{33} -19.1757i q^{34} -16.9706 q^{36} +(-32.4706 + 56.2407i) q^{37} +(0.878680 - 0.507306i) q^{38} +(11.4853 + 19.8931i) q^{39} +(7.75736 + 4.47871i) q^{40} +21.0308i q^{41} +6.48528 q^{43} +(13.2426 - 22.9369i) q^{44} +(-23.2721 + 13.4361i) q^{45} +(-1.60660 - 2.78272i) q^{46} +(-41.3787 - 23.8900i) q^{47} +16.7262i q^{48} -21.1716 q^{50} +(28.3492 - 49.1023i) q^{51} +(9.51472 - 5.49333i) q^{52} +(-11.0147 - 19.0781i) q^{53} +(2.63604 + 1.52192i) q^{54} -41.9385i q^{55} +3.00000 q^{57} +(14.4853 - 25.0892i) q^{58} +(72.5330 - 41.8770i) q^{59} +(13.2426 + 22.9369i) q^{60} +(-57.3823 - 33.1297i) q^{61} +34.8151i q^{62} +8.00000 q^{64} +(8.69848 - 15.0662i) q^{65} +(67.8198 - 39.1558i) q^{66} +(-46.3198 - 80.2283i) q^{67} +(-23.4853 - 13.5592i) q^{68} -9.50079i q^{69} -48.4264 q^{71} +(-12.0000 + 20.7846i) q^{72} +(-113.441 + 65.4953i) q^{73} +(45.9203 + 79.5363i) q^{74} +(-54.2132 - 31.3000i) q^{75} -1.43488i q^{76} +32.4853 q^{78} +(38.1066 - 66.0026i) q^{79} +(10.9706 - 6.33386i) q^{80} +(42.6838 + 73.9305i) q^{81} +(25.7574 + 14.8710i) q^{82} -107.981i q^{83} -42.9411 q^{85} +(4.58579 - 7.94282i) q^{86} +(74.1838 - 42.8300i) q^{87} +(-18.7279 - 32.4377i) q^{88} +(145.412 + 83.9535i) q^{89} +38.0031i q^{90} -4.54416 q^{92} +(-51.4706 + 89.1496i) q^{93} +(-58.5183 + 33.7856i) q^{94} +(-1.13604 - 1.96768i) q^{95} +(20.4853 + 11.8272i) q^{96} -25.5816i q^{97} +112.368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 4 q^{4} + 6 q^{5}+O(q^{10}) \) 4 * q + 6 * q^3 - 4 * q^4 + 6 * q^5	\( 4 q + 6 q^{3} - 4 q^{4} + 6 q^{5} - 24 q^{10} + 18 q^{11} - 12 q^{12} - 36 q^{15} - 8 q^{16} + 30 q^{17} - 24 q^{18} - 6 q^{19} + 24 q^{22} + 30 q^{23} - 24 q^{24} + 4 q^{25} - 24 q^{26} + 48 q^{29} - 12 q^{30} + 42 q^{31} + 90 q^{33} - 62 q^{37} + 12 q^{38} + 12 q^{39} + 48 q^{40} - 8 q^{43} + 36 q^{44} - 144 q^{45} + 36 q^{46} - 174 q^{47} - 96 q^{50} + 54 q^{51} + 72 q^{52} - 78 q^{53} + 36 q^{54} + 12 q^{57} + 24 q^{58} + 78 q^{59} + 36 q^{60} + 42 q^{61} + 32 q^{64} - 84 q^{65} + 144 q^{66} - 58 q^{67} - 60 q^{68} - 24 q^{71} - 48 q^{72} - 318 q^{73} + 96 q^{74} - 132 q^{75} + 96 q^{78} + 110 q^{79} - 24 q^{80} + 18 q^{81} + 120 q^{82} - 36 q^{85} + 24 q^{86} + 144 q^{87} - 24 q^{88} + 378 q^{89} - 120 q^{92} - 138 q^{93} + 12 q^{94} - 30 q^{95} + 48 q^{96} + 144 q^{99}+O(q^{100}) \) 4 * q + 6 * q^3 - 4 * q^4 + 6 * q^5 - 24 * q^10 + 18 * q^11 - 12 * q^12 - 36 * q^15 - 8 * q^16 + 30 * q^17 - 24 * q^18 - 6 * q^19 + 24 * q^22 + 30 * q^23 - 24 * q^24 + 4 * q^25 - 24 * q^26 + 48 * q^29 - 12 * q^30 + 42 * q^31 + 90 * q^33 - 62 * q^37 + 12 * q^38 + 12 * q^39 + 48 * q^40 - 8 * q^43 + 36 * q^44 - 144 * q^45 + 36 * q^46 - 174 * q^47 - 96 * q^50 + 54 * q^51 + 72 * q^52 - 78 * q^53 + 36 * q^54 + 12 * q^57 + 24 * q^58 + 78 * q^59 + 36 * q^60 + 42 * q^61 + 32 * q^64 - 84 * q^65 + 144 * q^66 - 58 * q^67 - 60 * q^68 - 24 * q^71 - 48 * q^72 - 318 * q^73 + 96 * q^74 - 132 * q^75 + 96 * q^78 + 110 * q^79 - 24 * q^80 + 18 * q^81 + 120 * q^82 - 36 * q^85 + 24 * q^86 + 144 * q^87 - 24 * q^88 + 378 * q^89 - 120 * q^92 - 138 * q^93 + 12 * q^94 - 30 * q^95 + 48 * q^96 + 144 * q^99

Introduction

L-functions

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