LMFDB - Embedded newform 28.3.c.a.15.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [28,3,Mod(15,28)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(28, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("28.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	28.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.762944740209$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1539727.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{3} - 8x + 8 $ x^6 - 2x^5 + 3x^3 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			15.2
Root			$0.841985 + 1.13625i$ of defining polynomial
Character	$\chi$	$=$	28.15
Dual form			28.3.c.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.92411 + 0.545716i) q^{2} -4.54500i q^{3} +(3.40439 - 2.10003i) q^{4} +1.36794 q^{5} +(2.48028 + 8.74507i) q^{6} -2.64575i q^{7} +(-5.40439 + 5.89853i) q^{8} -11.6570 q^{9} +O(q^{10})$	\(q+(-1.92411 + 0.545716i) q^{2} -4.54500i q^{3} +(3.40439 - 2.10003i) q^{4} +1.36794 q^{5} +(2.48028 + 8.74507i) q^{6} -2.64575i q^{7} +(-5.40439 + 5.89853i) q^{8} -11.6570 q^{9} +(-2.63206 + 0.746506i) q^{10} +15.3073i q^{11} +(-9.54465 - 15.4729i) q^{12} +19.9460 q^{13} +(1.44383 + 5.09071i) q^{14} -6.21727i q^{15} +(7.17971 - 14.2987i) q^{16} -4.73588 q^{17} +(22.4293 - 6.36141i) q^{18} +13.2765i q^{19} +(4.65699 - 2.87272i) q^{20} -12.0249 q^{21} +(-8.35343 - 29.4528i) q^{22} -14.9487i q^{23} +(26.8088 + 24.5629i) q^{24} -23.1287 q^{25} +(-38.3784 + 10.8849i) q^{26} +12.0760i q^{27} +(-5.55617 - 9.00716i) q^{28} +6.20763 q^{29} +(3.39287 + 11.9627i) q^{30} +18.5385i q^{31} +(-6.01152 + 31.4303i) q^{32} +69.5715 q^{33} +(9.11234 - 2.58445i) q^{34} -3.61922i q^{35} +(-39.6849 + 24.4801i) q^{36} -27.5216 q^{37} +(-7.24518 - 25.5453i) q^{38} -90.6547i q^{39} +(-7.39287 + 8.06882i) q^{40} -11.1064 q^{41} +(23.1373 - 6.56220i) q^{42} +27.0248i q^{43} +(32.1458 + 52.1119i) q^{44} -15.9460 q^{45} +(8.15777 + 28.7630i) q^{46} -30.9731i q^{47} +(-64.9874 - 32.6317i) q^{48} -7.00000 q^{49} +(44.5022 - 12.6217i) q^{50} +21.5245i q^{51} +(67.9041 - 41.8874i) q^{52} -12.7857 q^{53} +(-6.59008 - 23.2356i) q^{54} +20.9394i q^{55} +(15.6060 + 14.2987i) q^{56} +60.3415 q^{57} +(-11.9442 + 3.38760i) q^{58} -28.8289i q^{59} +(-13.0565 - 21.1660i) q^{60} +6.52415 q^{61} +(-10.1168 - 35.6701i) q^{62} +30.8415i q^{63} +(-5.58519 - 63.7558i) q^{64} +27.2850 q^{65} +(-133.863 + 37.9663i) q^{66} +102.863i q^{67} +(-16.1228 + 9.94551i) q^{68} -67.9420 q^{69} +(1.97507 + 6.96378i) q^{70} +45.8085i q^{71} +(62.9989 - 68.7591i) q^{72} -70.0997 q^{73} +(52.9546 - 15.0190i) q^{74} +105.120i q^{75} +(27.8810 + 45.1982i) q^{76} +40.4992 q^{77} +(49.4718 + 174.429i) q^{78} -33.3739i q^{79} +(9.82140 - 19.5597i) q^{80} -50.0275 q^{81} +(21.3698 - 6.06092i) q^{82} -159.301i q^{83} +(-40.9375 + 25.2528i) q^{84} -6.47839 q^{85} +(-14.7478 - 51.9986i) q^{86} -28.2137i q^{87} +(-90.2903 - 82.7264i) q^{88} -50.0417 q^{89} +(30.6819 - 8.70202i) q^{90} -52.7723i q^{91} +(-31.3929 - 50.8913i) q^{92} +84.2575 q^{93} +(16.9025 + 59.5955i) q^{94} +18.1614i q^{95} +(142.850 + 27.3223i) q^{96} +89.7343 q^{97} +(13.4688 - 3.82001i) q^{98} -178.437i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9}+O(q^{10}) $ 6 * q - q^2 + q^4 - 4 * q^5 + 6 * q^6 - 13 * q^8 - 10 * q^9	$ 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9} - 28 q^{10} + 6 q^{12} + 12 q^{13} + 7 q^{14} + 17 q^{16} - 4 q^{17} + 43 q^{18} - 32 q^{20} + 52 q^{22} + 122 q^{24} - 30 q^{25} - 56 q^{26} - 35 q^{28} - 36 q^{29} - 64 q^{30} - 101 q^{32} + 80 q^{33} + 58 q^{34} - 131 q^{36} + 28 q^{37} - 190 q^{38} + 40 q^{40} - 20 q^{41} + 70 q^{42} + 164 q^{44} + 12 q^{45} + 120 q^{46} - 98 q^{48} - 42 q^{49} + 161 q^{50} + 292 q^{52} + 92 q^{53} - 44 q^{54} - 49 q^{56} + 160 q^{57} - 166 q^{58} - 176 q^{60} - 164 q^{61} + 148 q^{62} - 215 q^{64} - 136 q^{65} - 408 q^{66} + 62 q^{68} - 48 q^{69} + 84 q^{70} + 151 q^{72} - 132 q^{73} + 250 q^{74} - 78 q^{76} + 112 q^{77} + 248 q^{78} + 312 q^{80} - 218 q^{81} - 86 q^{82} - 98 q^{84} - 232 q^{85} - 164 q^{86} - 100 q^{88} + 348 q^{89} + 52 q^{90} - 104 q^{92} + 288 q^{93} - 276 q^{94} + 170 q^{96} + 252 q^{97} + 7 q^{98}+O(q^{100}) $ 6 * q - q^2 + q^4 - 4 * q^5 + 6 * q^6 - 13 * q^8 - 10 * q^9 - 28 * q^10 + 6 * q^12 + 12 * q^13 + 7 * q^14 + 17 * q^16 - 4 * q^17 + 43 * q^18 - 32 * q^20 + 52 * q^22 + 122 * q^24 - 30 * q^25 - 56 * q^26 - 35 * q^28 - 36 * q^29 - 64 * q^30 - 101 * q^32 + 80 * q^33 + 58 * q^34 - 131 * q^36 + 28 * q^37 - 190 * q^38 + 40 * q^40 - 20 * q^41 + 70 * q^42 + 164 * q^44 + 12 * q^45 + 120 * q^46 - 98 * q^48 - 42 * q^49 + 161 * q^50 + 292 * q^52 + 92 * q^53 - 44 * q^54 - 49 * q^56 + 160 * q^57 - 166 * q^58 - 176 * q^60 - 164 * q^61 + 148 * q^62 - 215 * q^64 - 136 * q^65 - 408 * q^66 + 62 * q^68 - 48 * q^69 + 84 * q^70 + 151 * q^72 - 132 * q^73 + 250 * q^74 - 78 * q^76 + 112 * q^77 + 248 * q^78 + 312 * q^80 - 218 * q^81 - 86 * q^82 - 98 * q^84 - 232 * q^85 - 164 * q^86 - 100 * q^88 + 348 * q^89 + 52 * q^90 - 104 * q^92 + 288 * q^93 - 276 * q^94 + 170 * q^96 + 252 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.92411	+	0.545716i	−0.962054	+	0.272858i
$2$	−1.92411	+	0.545716i	−0.962054	+	0.272858i
$3$		−	4.54500i		−	1.51500i	−0.652836	−	0.757499i	$-0.726421\pi$
$3$		−	4.54500i		−	1.51500i	0.652836	−	0.757499i	$-0.273579\pi$
$4$	3.40439	−	2.10003i	0.851097	−	0.525009i
$5$	1.36794			0.273588			0.136794	−	0.990600i	$-0.456320\pi$
$5$	1.36794			0.273588			0.136794	+	0.990600i	$0.456320\pi$
$6$	2.48028	+	8.74507i	0.413380	+	1.45751i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−5.40439	+	5.89853i	−0.675548	+	0.737316i
$9$	−11.6570			−1.29522
$10$	−2.63206	+	0.746506i	−0.263206	+	0.0746506i
$11$			15.3073i			1.39157i	0.718250	+	0.695785i	$0.244943\pi$
$11$			15.3073i			1.39157i	−0.718250	+	0.695785i	$0.755057\pi$
$12$	−9.54465	−	15.4729i	−0.795388	−	1.28941i
$13$	19.9460			1.53431			0.767156	−	0.641461i	$-0.221671\pi$
$13$	19.9460			1.53431			0.767156	+	0.641461i	$0.221671\pi$
$14$	1.44383	+	5.09071i	0.103131	+	0.363622i
$15$		−	6.21727i		−	0.414485i
$16$	7.17971	−	14.2987i	0.448732	−	0.893667i
$17$	−4.73588			−0.278581			−0.139290	−	0.990252i	$-0.544482\pi$
$17$	−4.73588			−0.278581			−0.139290	+	0.990252i	$0.544482\pi$
$18$	22.4293	−	6.36141i	1.24607	−	0.353412i
$19$			13.2765i			0.698761i	0.936981	+	0.349380i	$0.113608\pi$
$19$			13.2765i			0.698761i	−0.936981	+	0.349380i	$0.886392\pi$
$20$	4.65699	−	2.87272i	0.232850	−	0.143636i
$21$	−12.0249			−0.572616
$22$	−8.35343	−	29.4528i	−0.379701	−	1.33877i
$23$		−	14.9487i		−	0.649945i	−0.945723	−	0.324973i	$-0.894645\pi$
$23$		−	14.9487i		−	0.649945i	0.945723	−	0.324973i	$-0.105355\pi$
$24$	26.8088	+	24.5629i	1.11703	+	1.02346i
$25$	−23.1287			−0.925150
$26$	−38.3784	+	10.8849i	−1.47609	+	0.418649i
$27$			12.0760i			0.447260i
$28$	−5.55617	−	9.00716i	−0.198435	−	0.321684i
$29$	6.20763			0.214056			0.107028	−	0.994256i	$-0.465867\pi$
$29$	6.20763			0.214056			0.107028	+	0.994256i	$0.465867\pi$
$30$	3.39287	+	11.9627i	0.113096	+	0.398757i
$31$			18.5385i			0.598017i	0.954251	+	0.299008i	$0.0966558\pi$
$31$			18.5385i			0.598017i	−0.954251	+	0.299008i	$0.903344\pi$
$32$	−6.01152	+	31.4303i	−0.187860	+	0.982196i
$33$	69.5715			2.10823
$34$	9.11234	−	2.58445i	0.268010	−	0.0760131i
$35$		−	3.61922i		−	0.103406i
$36$	−39.6849	+	24.4801i	−1.10236	+	0.680003i
$37$	−27.5216			−0.743827			−0.371914	−	0.928267i	$-0.621298\pi$
$37$	−27.5216			−0.743827			−0.371914	+	0.928267i	$0.621298\pi$
$38$	−7.24518	−	25.5453i	−0.190663	−	0.672246i
$39$		−	90.6547i		−	2.32448i
$40$	−7.39287	+	8.06882i	−0.184822	+	0.201720i
$41$	−11.1064			−0.270887			−0.135443	−	0.990785i	$-0.543246\pi$
$41$	−11.1064			−0.270887			−0.135443	+	0.990785i	$0.543246\pi$
$42$	23.1373	−	6.56220i	0.550887	−	0.156243i
$43$			27.0248i			0.628483i	0.949343	+	0.314241i	$0.101750\pi$
$43$			27.0248i			0.628483i	−0.949343	+	0.314241i	$0.898250\pi$
$44$	32.1458	+	52.1119i	0.730586	+	1.18436i
$45$	−15.9460			−0.354357
$46$	8.15777	+	28.7630i	0.177343	+	0.625282i
$47$		−	30.9731i		−	0.659001i	−0.944155	−	0.329501i	$-0.893120\pi$
$47$		−	30.9731i		−	0.659001i	0.944155	−	0.329501i	$-0.106880\pi$
$48$	−64.9874	−	32.6317i	−1.35390	−	0.679828i
$49$	−7.00000			−0.142857
$50$	44.5022	−	12.6217i	0.890044	−	0.252435i
$51$			21.5245i			0.422050i
$52$	67.9041	−	41.8874i	1.30585	−	0.805527i
$53$	−12.7857			−0.241240			−0.120620	−	0.992699i	$-0.538488\pi$
$53$	−12.7857			−0.241240			−0.120620	+	0.992699i	$0.538488\pi$
$54$	−6.59008	−	23.2356i	−0.122039	−	0.430288i
$55$			20.9394i			0.380716i
$56$	15.6060	+	14.2987i	0.278679	+	0.255333i
$57$	60.3415			1.05862
$58$	−11.9442	+	3.38760i	−0.205934	+	0.0584070i
$59$		−	28.8289i		−	0.488626i	−0.969696	−	0.244313i	$-0.921438\pi$
$59$		−	28.8289i		−	0.488626i	0.969696	−	0.244313i	$-0.0785625\pi$
$60$	−13.0565	−	21.1660i	−0.217608	−	0.352767i
$61$	6.52415			0.106953			0.0534767	−	0.998569i	$-0.482970\pi$
$61$	6.52415			0.106953			0.0534767	+	0.998569i	$0.482970\pi$
$62$	−10.1168	−	35.6701i	−0.163174	−	0.575324i
$63$			30.8415i			0.489548i
$64$	−5.58519	−	63.7558i	−0.0872687	−	0.996185i
$65$	27.2850			0.419769
$66$	−133.863	+	37.9663i	−2.02823	+	0.575247i
$67$			102.863i			1.53526i	0.640891	+	0.767632i	$0.278565\pi$
$67$			102.863i			1.53526i	−0.640891	+	0.767632i	$0.721435\pi$
$68$	−16.1228	+	9.94551i	−0.237099	+	0.146257i
$69$	−67.9420			−0.984666
$70$	1.97507	+	6.96378i	0.0282153	+	0.0994826i
$71$			45.8085i			0.645190i	0.946537	+	0.322595i	$0.104555\pi$
$71$			45.8085i			0.645190i	−0.946537	+	0.322595i	$0.895445\pi$
$72$	62.9989	−	68.7591i	0.874985	−	0.954987i
$73$	−70.0997			−0.960270			−0.480135	−	0.877195i	$-0.659412\pi$
$73$	−70.0997			−0.960270			−0.480135	+	0.877195i	$0.659412\pi$
$74$	52.9546	−	15.0190i	0.715602	−	0.202959i
$75$			105.120i			1.40160i
$76$	27.8810	+	45.1982i	0.366856	+	0.594713i
$77$	40.4992			0.525964
$78$	49.4718	+	174.429i	0.634253	+	2.23628i
$79$		−	33.3739i		−	0.422455i	−0.977437	−	0.211228i	$-0.932254\pi$
$79$		−	33.3739i		−	0.422455i	0.977437	−	0.211228i	$-0.0677461\pi$
$80$	9.82140	−	19.5597i	0.122767	−	0.244496i
$81$	−50.0275			−0.617623
$82$	21.3698	−	6.06092i	0.260608	−	0.0739136i
$83$		−	159.301i		−	1.91930i	−0.281206	−	0.959648i	$-0.590734\pi$
$83$		−	159.301i		−	1.91930i	0.281206	−	0.959648i	$-0.409266\pi$
$84$	−40.9375	+	25.2528i	−0.487351	+	0.300628i
$85$	−6.47839			−0.0762163
$86$	−14.7478	−	51.9986i	−0.171487	−	0.604634i
$87$		−	28.2137i		−	0.324295i
$88$	−90.2903	−	82.7264i	−1.02603	−	0.940073i
$89$	−50.0417			−0.562266			−0.281133	−	0.959669i	$-0.590710\pi$
$89$	−50.0417			−0.562266			−0.281133	+	0.959669i	$0.590710\pi$
$90$	30.6819	−	8.70202i	0.340910	−	0.0966891i
$91$		−	52.7723i		−	0.579915i
$92$	−31.3929	−	50.8913i	−0.341227	−	0.553166i
$93$	84.2575			0.905995
$94$	16.9025	+	59.5955i	0.179814	+	0.633995i
$95$			18.1614i			0.191172i
$96$	142.850	+	27.3223i	1.48803	+	0.284608i
$97$	89.7343			0.925096			0.462548	−	0.886594i	$-0.346935\pi$
$97$	89.7343			0.925096			0.462548	+	0.886594i	$0.346935\pi$
$98$	13.4688	−	3.82001i	0.137436	−	0.0389797i
$99$		−	178.437i		−	1.80239i
$100$	−78.7392	+	48.5712i	−0.787392	+	0.485712i
$101$	162.881			1.61269			0.806343	−	0.591448i	$-0.201443\pi$
$101$	162.881			1.61269			0.806343	+	0.591448i	$0.201443\pi$
$102$	−11.7463	−	41.4156i	−0.115160	−	0.406035i
$103$		−	86.1212i		−	0.836129i	−0.908417	−	0.418064i	$-0.862709\pi$
$103$		−	86.1212i		−	0.836129i	0.908417	−	0.418064i	$-0.137291\pi$
$104$	−107.796	+	117.652i	−1.03650	+	1.13127i
$105$	−16.4494			−0.156661
$106$	24.6011	−	6.97739i	0.232086	−	0.0658244i
$107$			102.146i			0.954632i	0.878732	+	0.477316i	$0.158390\pi$
$107$			102.146i			0.954632i	−0.878732	+	0.477316i	$0.841610\pi$
$108$	25.3601	+	41.1114i	0.234815	+	0.380662i
$109$	152.037			1.39483			0.697416	−	0.716667i	$-0.254333\pi$
$109$	152.037			1.39483			0.697416	+	0.716667i	$0.254333\pi$
$110$	−11.4270	−	40.2897i	−0.103882	−	0.366270i
$111$			125.086i			1.12690i
$112$	−37.8307	−	18.9957i	−0.337774	−	0.169605i
$113$	−168.112			−1.48772			−0.743860	−	0.668335i	$-0.767007\pi$
$113$	−168.112			−1.48772			−0.743860	+	0.668335i	$0.767007\pi$
$114$	−116.104	+	32.9293i	−1.01845	+	0.288854i
$115$		−	20.4489i		−	0.177817i
$116$	21.1332	−	13.0362i	0.182183	−	0.112381i
$117$	−232.511			−1.98727
$118$	15.7324	+	55.4700i	0.133326	+	0.470085i
$119$			12.5300i			0.105294i
$120$	36.6727	+	33.6006i	0.305606	+	0.280005i
$121$	−113.312			−0.936466
$122$	−12.5532	+	3.56034i	−0.102895	+	0.0291831i
$123$			50.4783i			0.410393i
$124$	38.9315	+	63.1123i	0.313964	+	0.508970i
$125$	−65.8372			−0.526697
$126$	−16.8307	−	59.3424i	−0.133577	−	0.470971i
$127$			87.8953i			0.692089i	0.938218	+	0.346044i	$0.112475\pi$
$127$			87.8953i			0.692089i	−0.938218	+	0.346044i	$0.887525\pi$
$128$	45.5391	+	119.625i	0.355774	+	0.934572i
$129$	122.827			0.952150
$130$	−52.4992	+	14.8898i	−0.403840	+	0.114537i
$131$		−	140.141i		−	1.06978i	−0.844923	−	0.534888i	$-0.820354\pi$
$131$		−	140.141i		−	1.06978i	0.844923	−	0.534888i	$-0.179646\pi$
$132$	236.848	−	146.103i	1.79430	−	1.10684i
$133$	35.1262			0.264107
$134$	−56.1338	−	197.919i	−0.418909	−	1.47701i
$135$			16.5192i			0.122365i
$136$	25.5945	−	27.9347i	0.188195	−	0.205402i
$137$	118.725			0.866603			0.433301	−	0.901249i	$-0.357349\pi$
$137$	118.725			0.866603			0.433301	+	0.901249i	$0.357349\pi$
$138$	130.728	−	37.0770i	0.947302	−	0.268674i
$139$			72.1046i			0.518738i	0.965778	+	0.259369i	$0.0835147\pi$
$139$			72.1046i			0.518738i	−0.965778	+	0.259369i	$0.916485\pi$
$140$	−7.60050	−	12.3212i	−0.0542893	−	0.0880089i
$141$	−140.772			−0.998386
$142$	−24.9984	−	88.1405i	−0.176045	−	0.620708i
$143$			305.319i			2.13510i
$144$	−83.6938	+	166.679i	−0.581207	+	1.15750i
$145$	8.49165			0.0585631
$146$	134.879	−	38.2546i	0.923832	−	0.262018i
$147$			31.8150i			0.216428i
$148$	−93.6942	+	57.7963i	−0.633069	+	0.390516i
$149$	218.299			1.46510			0.732548	−	0.680716i	$-0.238331\pi$
$149$	218.299			1.46510			0.732548	+	0.680716i	$0.238331\pi$
$150$	−57.3657	−	202.262i	−0.382438	−	1.34842i
$151$		−	180.946i		−	1.19832i	−0.800629	−	0.599160i	$-0.795501\pi$
$151$		−	180.946i		−	1.19832i	0.800629	−	0.599160i	$-0.204499\pi$
$152$	−78.3115	−	71.7511i	−0.515207	−	0.472047i
$153$	55.2061			0.360824
$154$	−77.9249	+	22.1011i	−0.506006	+	0.143514i
$155$			25.3595i			0.163610i
$156$	−190.378	−	308.624i	−1.22037	−	1.97836i
$157$	−191.081			−1.21708			−0.608538	−	0.793525i	$-0.708244\pi$
$157$	−191.081			−1.21708			−0.608538	+	0.793525i	$0.708244\pi$
$158$	18.2127	+	64.2151i	0.115270	+	0.406425i
$159$			58.1111i			0.365479i
$160$	−8.22339	+	42.9947i	−0.0513962	+	0.268717i
$161$	−39.5506			−0.245656
$162$	96.2583	−	27.3008i	0.594187	−	0.168524i
$163$		−	287.743i		−	1.76530i	−0.470035	−	0.882648i	$-0.655759\pi$
$163$		−	287.743i		−	1.76530i	0.470035	−	0.882648i	$-0.344241\pi$
$164$	−37.8103	+	23.3237i	−0.230551	+	0.142218i
$165$	95.1695			0.576785
$166$	86.9334	+	306.513i	0.523695	+	1.84647i
$167$			124.859i			0.747659i	0.927497	+	0.373829i	$0.121955\pi$
$167$			124.859i			0.747659i	−0.927497	+	0.373829i	$0.878045\pi$
$168$	64.9874	−	70.9294i	0.386830	−	0.422199i
$169$	228.845			1.35411
$170$	12.4651	−	3.53536i	0.0733242	−	0.0207962i
$171$		−	154.764i		−	0.905050i
$172$	56.7529	+	92.0027i	0.329959	+	0.534900i
$173$	−275.207			−1.59079			−0.795396	−	0.606090i	$-0.792737\pi$
$173$	−275.207			−1.59079			−0.795396	+	0.606090i	$0.792737\pi$
$174$	15.3967	+	54.2861i	0.0884865	+	0.311989i
$175$			61.1929i			0.349674i
$176$	218.873	+	109.902i	1.24360	+	0.624441i
$177$	−131.027			−0.740268
$178$	96.2856	−	27.3086i	0.540930	−	0.153419i
$179$			7.42479i			0.0414792i	0.999785	+	0.0207396i	$0.00660210\pi$
$179$			7.42479i			0.0414792i	−0.999785	+	0.0207396i	$0.993398\pi$
$180$	−54.2865	+	33.4873i	−0.301592	+	0.186040i
$181$	99.5623			0.550068			0.275034	−	0.961435i	$-0.411311\pi$
$181$	99.5623			0.550068			0.275034	+	0.961435i	$0.411311\pi$
$182$	28.7987	+	101.540i	0.158235	+	0.557910i
$183$		−	29.6522i		−	0.162034i
$184$	88.1755	+	80.7888i	0.479215	+	0.439069i
$185$	−37.6479			−0.203502
$186$	−162.121	+	45.9807i	−0.871616	+	0.247208i
$187$		−	72.4933i		−	0.387665i
$188$	−65.0445	−	105.444i	−0.345981	−	0.560874i
$189$	31.9501			0.169048
$190$	−9.91096	−	34.9445i	−0.0521629	−	0.183918i
$191$			58.2058i			0.304743i	0.988323	+	0.152371i	$0.0486909\pi$
$191$			58.2058i			0.304743i	−0.988323	+	0.152371i	$0.951309\pi$
$192$	−289.770	+	25.3847i	−1.50922	+	0.132212i
$193$	−103.881			−0.538246			−0.269123	−	0.963106i	$-0.586734\pi$
$193$	−103.881			−0.538246			−0.269123	+	0.963106i	$0.586734\pi$
$194$	−172.659	+	48.9695i	−0.889993	+	0.252420i
$195$		−	124.010i		−	0.635949i
$196$	−23.8307	+	14.7002i	−0.121585	+	0.0750012i
$197$	−181.201			−0.919802			−0.459901	−	0.887970i	$-0.652115\pi$
$197$	−181.201			−0.919802			−0.459901	+	0.887970i	$0.652115\pi$
$198$	97.3758	+	343.332i	0.491797	+	1.73400i
$199$		−	217.919i		−	1.09507i	−0.836783	−	0.547535i	$-0.815566\pi$
$199$		−	217.919i		−	1.09507i	0.836783	−	0.547535i	$-0.184434\pi$
$200$	124.997	−	136.425i	0.624983	−	0.682127i
$201$	467.510			2.32592
$202$	−313.401	+	88.8870i	−1.55149	+	0.440035i
$203$		−	16.4238i		−	0.0809056i
$204$	45.2023	+	73.2779i	0.221580	+	0.359205i
$205$	−15.1928			−0.0741113
$206$	46.9978	+	165.707i	0.228145	+	0.804401i
$207$			174.257i			0.841823i
$208$	143.207	−	285.202i	0.688494	−	1.37116i
$209$	−203.226			−0.972375
$210$	31.6504	−	8.97669i	0.150716	−	0.0427461i
$211$			107.401i			0.509007i	0.967072	+	0.254504i	$0.0819121\pi$
$211$			107.401i			0.509007i	−0.967072	+	0.254504i	$0.918088\pi$
$212$	−43.5276	+	26.8505i	−0.205319	+	0.126653i
$213$	208.199			0.977462
$214$	−55.7425	−	196.539i	−0.260479	−	0.918407i
$215$			36.9682i			0.171945i
$216$	−71.2307	−	65.2635i	−0.329772	−	0.302146i
$217$	49.0483			0.226029
$218$	−292.535	+	82.9689i	−1.34190	+	0.380591i
$219$			318.603i			1.45481i
$220$	43.9735	+	71.2858i	0.199879	+	0.324026i
$221$	−94.4620			−0.427430
$222$	−68.2613	−	240.678i	−0.307483	−	1.08414i
$223$		−	349.685i		−	1.56809i	−0.620702	−	0.784047i	$-0.713152\pi$
$223$		−	349.685i		−	1.56809i	0.620702	−	0.784047i	$-0.286848\pi$
$224$	83.1567	+	15.9050i	0.371235	+	0.0710044i
$225$	269.612			1.19827
$226$	323.466	−	91.7417i	1.43127	−	0.405937i
$227$			18.3421i			0.0808020i	0.999184	+	0.0404010i	$0.0128635\pi$
$227$			18.3421i			0.0808020i	−0.999184	+	0.0404010i	$0.987136\pi$
$228$	205.426	−	126.719i	0.900990	−	0.555786i
$229$	68.5444			0.299320			0.149660	−	0.988737i	$-0.452182\pi$
$229$	68.5444			0.299320			0.149660	+	0.988737i	$0.452182\pi$
$230$	11.1593	+	39.3460i	0.0485188	+	0.171070i
$231$		−	184.069i		−	0.796835i
$232$	−33.5484	+	36.6159i	−0.144605	+	0.157827i
$233$	61.4788			0.263858			0.131929	−	0.991259i	$-0.457883\pi$
$233$	61.4788			0.263858			0.131929	+	0.991259i	$0.457883\pi$
$234$	447.376	−	126.885i	1.91186	−	0.542244i
$235$		−	42.3692i		−	0.180295i
$236$	−60.5418	−	98.1449i	−0.256533	−	0.415868i
$237$	−151.684			−0.640019
$238$	−6.83780	−	24.1090i	−0.0287302	−	0.101298i
$239$		−	204.645i		−	0.856256i	−0.903718	−	0.428128i	$-0.859173\pi$
$239$		−	204.645i		−	0.856256i	0.903718	−	0.428128i	$-0.140827\pi$
$240$	−88.8987	−	44.6382i	−0.370411	−	0.185993i
$241$	−389.266			−1.61521			−0.807606	−	0.589723i	$-0.799237\pi$
$241$	−389.266			−1.61521			−0.807606	+	0.589723i	$0.799237\pi$
$242$	218.025	−	61.8364i	0.900931	−	0.255522i
$243$			336.059i			1.38296i
$244$	22.2107	−	13.7009i	0.0910276	−	0.0561514i
$245$	−9.57557			−0.0390840
$246$	−27.5469	−	97.1258i	−0.111979	−	0.394820i
$247$			264.813i			1.07212i
$248$	−109.350	−	100.189i	−0.440927	−	0.403989i
$249$	−724.025			−2.90773
$250$	126.678	−	35.9284i	0.506711	−	0.143714i
$251$			115.082i			0.458494i	0.973368	+	0.229247i	$0.0736264\pi$
$251$			115.082i			0.458494i	−0.973368	+	0.229247i	$0.926374\pi$
$252$	64.7682	+	104.996i	0.257017	+	0.416652i
$253$	228.824			0.904444
$254$	−47.9659	−	169.120i	−0.188842	−	0.665827i
$255$			29.4442i			0.115468i
$256$	−152.904	−	205.320i	−0.597280	−	0.802033i
$257$	337.233			1.31219			0.656094	−	0.754679i	$-0.272207\pi$
$257$	337.233			1.31219			0.656094	+	0.754679i	$0.272207\pi$
$258$	−236.333	+	67.0289i	−0.916020	+	0.259802i
$259$			72.8153i			0.281140i
$260$	92.8886	−	57.2994i	0.357264	−	0.220382i
$261$	−72.3623			−0.277250
$262$	76.4770	+	269.646i	0.291897	+	1.02918i
$263$			163.729i			0.622543i	0.950321	+	0.311271i	$0.100755\pi$
$263$			163.729i			0.622543i	−0.950321	+	0.311271i	$0.899245\pi$
$264$	−375.991	+	410.369i	−1.42421	+	1.55443i
$265$	−17.4901			−0.0660004
$266$	−67.5866	+	19.1689i	−0.254085	+	0.0720637i
$267$			227.439i			0.851832i
$268$	216.015	+	350.184i	0.806027	+	1.30666i
$269$	290.784			1.08098			0.540490	−	0.841350i	$-0.318239\pi$
$269$	290.784			1.08098			0.540490	+	0.841350i	$0.318239\pi$
$270$	−9.01482	−	31.7848i	−0.0333882	−	0.117722i
$271$			368.628i			1.36025i	0.733096	+	0.680126i	$0.238075\pi$
$271$			368.628i			1.36025i	−0.733096	+	0.680126i	$0.761925\pi$
$272$	−34.0022	+	67.7167i	−0.125008	+	0.248958i
$273$	−239.850			−0.878571
$274$	−228.439	+	64.7899i	−0.833719	+	0.236460i
$275$		−	354.038i		−	1.28741i
$276$	−231.301	+	142.680i	−0.838046	+	0.516958i
$277$	254.425			0.918503			0.459252	−	0.888306i	$-0.348118\pi$
$277$	254.425			0.918503			0.459252	+	0.888306i	$0.348118\pi$
$278$	−39.3487	−	138.737i	−0.141542	−	0.499055i
$279$		−	216.103i		−	0.774564i
$280$	21.3481	+	19.5597i	0.0762432	+	0.0698560i
$281$	146.631			0.521819			0.260909	−	0.965363i	$-0.415978\pi$
$281$	146.631			0.521819			0.260909	+	0.965363i	$0.415978\pi$
$282$	270.862	−	76.8218i	0.960502	−	0.272418i
$283$			191.554i			0.676868i	0.940990	+	0.338434i	$0.109897\pi$
$283$			191.554i			0.676868i	−0.940990	+	0.338434i	$0.890103\pi$
$284$	96.1994	+	155.950i	0.338730	+	0.549119i
$285$	82.5434			0.289626
$286$	−166.618	−	587.468i	−0.582580	−	2.05408i
$287$			29.3847i			0.102386i
$288$	70.0762	−	366.382i	0.243320	−	1.27216i
$289$	−266.571			−0.922393
$290$	−16.3389	+	4.63403i	−0.0563409	+	0.0159794i
$291$		−	407.842i		−	1.40152i
$292$	−238.647	+	147.212i	−0.817283	+	0.504150i
$293$	315.496			1.07678			0.538389	−	0.842696i	$-0.319033\pi$
$293$	315.496			1.07678			0.538389	+	0.842696i	$0.319033\pi$
$294$	−17.3620	−	61.2155i	−0.0590543	−	0.208216i
$295$		−	39.4362i		−	0.133682i
$296$	148.737	−	162.337i	0.502491	−	0.548436i
$297$	−184.851			−0.622393
$298$	−420.031	+	119.129i	−1.40950	+	0.399763i
$299$		−	298.168i		−	0.997218i
$300$	220.756	+	357.869i	0.735853	+	1.19290i
$301$	71.5008			0.237544
$302$	98.7454	+	348.161i	0.326972	+	1.15285i
$303$		−	740.295i		−	2.44322i
$304$	189.836	+	95.3211i	0.624459	+	0.313556i
$305$	8.92464			0.0292611
$306$	−106.222	+	30.1269i	−0.347132	+	0.0984538i
$307$			452.508i			1.47397i	0.675911	+	0.736983i	$0.263750\pi$
$307$			452.508i			1.47397i	−0.675911	+	0.736983i	$0.736250\pi$
$308$	137.875	−	85.0498i	0.447646	−	0.276136i
$309$	−391.421			−1.26673
$310$	−13.8391	−	48.7945i	−0.0446423	−	0.157402i
$311$		−	477.817i		−	1.53639i	−0.640217	−	0.768194i	$-0.721155\pi$
$311$		−	477.817i		−	1.53639i	0.640217	−	0.768194i	$-0.278845\pi$
$312$	534.729	+	489.933i	1.71388	+	1.57030i
$313$	209.435			0.669122			0.334561	−	0.942374i	$-0.391412\pi$
$313$	209.435			0.669122			0.334561	+	0.942374i	$0.391412\pi$
$314$	367.660	−	104.276i	1.17089	−	0.332089i
$315$			42.1893i			0.133934i
$316$	−70.0865	−	113.618i	−0.221793	−	0.359550i
$317$	1.74873			0.00551651			0.00275825	−	0.999996i	$-0.499122\pi$
$317$	1.74873			0.00551651			0.00275825	+	0.999996i	$0.499122\pi$
$318$	−31.7122	−	111.812i	−0.0997239	−	0.351610i
$319$			95.0218i			0.297874i
$320$	−7.64020	−	87.2140i	−0.0238756	−	0.272544i
$321$	464.251			1.44627
$322$	76.0997	−	21.5834i	0.236335	−	0.0670293i
$323$		−	62.8757i		−	0.194662i
$324$	−170.313	+	105.059i	−0.525657	+	0.324258i
$325$	−461.327			−1.41947
$326$	157.026	+	553.649i	0.481675	+	1.69831i
$327$		−	691.006i		−	2.11317i
$328$	60.0230	−	65.5111i	0.182997	−	0.199729i
$329$	−81.9470			−0.249079
$330$	−183.116	+	51.9355i	−0.554898	+	0.157380i
$331$			375.049i			1.13308i	0.824035	+	0.566539i	$0.191718\pi$
$331$			375.049i			1.13308i	−0.824035	+	0.566539i	$0.808282\pi$
$332$	−334.539	−	542.324i	−1.00765	−	1.63351i
$333$	320.819			0.963421
$334$	−68.1376	−	240.242i	−0.204005	−	0.719288i
$335$			140.710i			0.420029i
$336$	−86.3355	+	171.940i	−0.256951	+	0.511728i
$337$	254.740			0.755906			0.377953	−	0.925825i	$-0.376628\pi$
$337$	254.740			0.755906			0.377953	+	0.925825i	$0.376628\pi$
$338$	−440.322	+	124.884i	−1.30273	+	0.369480i
$339$			764.070i			2.25389i
$340$	−22.0549	+	13.6048i	−0.0648675	+	0.0400142i
$341$	−283.774			−0.832182
$342$	84.4570	+	297.782i	0.246950	+	0.870707i
$343$			18.5203i			0.0539949i
$344$	−159.406	−	146.052i	−0.463390	−	0.424570i
$345$	−92.9404			−0.269392
$346$	529.528	−	150.185i	1.53043	−	0.434061i
$347$		−	511.422i		−	1.47384i	−0.675981	−	0.736919i	$-0.736280\pi$
$347$		−	511.422i		−	1.47384i	0.675981	−	0.736919i	$-0.263720\pi$
$348$	−59.2497	−	96.0502i	−0.170258	−	0.276006i
$349$	−383.129			−1.09779			−0.548895	−	0.835891i	$-0.684951\pi$
$349$	−383.129			−1.09779			−0.548895	+	0.835891i	$0.684951\pi$
$350$	−33.3940	−	117.742i	−0.0954113	−	0.336405i
$351$			240.869i			0.686236i
$352$	−481.111	−	92.0199i	−1.36679	−	0.261420i
$353$	217.384			0.615819			0.307909	−	0.951416i	$-0.400371\pi$
$353$	217.384			0.615819			0.307909	+	0.951416i	$0.400371\pi$
$354$	252.111	−	71.5038i	0.712178	−	0.201988i
$355$			62.6632i			0.176516i
$356$	−170.361	+	105.089i	−0.478543	+	0.295195i
$357$	56.9486			0.159520
$358$	−4.05183	−	14.2861i	−0.0113180	−	0.0399053i
$359$			483.099i			1.34568i	0.739788	+	0.672840i	$0.234926\pi$
$359$			483.099i			1.34568i	−0.739788	+	0.672840i	$0.765074\pi$
$360$	86.1786	−	94.0581i	0.239385	−	0.261273i
$361$	184.736			0.511733
$362$	−191.569	+	54.3328i	−0.529195	+	0.150091i
$363$			515.005i			1.41875i
$364$	−110.824	−	179.657i	−0.304461	−	0.493564i
$365$	−95.8921			−0.262718
$366$	16.1817	+	57.0541i	0.0442123	+	0.155886i
$367$		−	470.944i		−	1.28323i	−0.767028	−	0.641614i	$-0.778265\pi$
$367$		−	470.944i		−	1.28323i	0.767028	−	0.641614i	$-0.221735\pi$
$368$	−213.747	−	107.328i	−0.580834	−	0.291651i
$369$	129.467			0.350858
$370$	72.4386	−	20.5451i	0.195780	−	0.0555272i
$371$			33.8279i			0.0911803i
$372$	286.845	−	176.944i	0.771089	−	0.475655i
$373$	−179.535			−0.481326			−0.240663	−	0.970609i	$-0.577365\pi$
$373$	−179.535			−0.481326			−0.240663	+	0.970609i	$0.577365\pi$
$374$	39.5608	+	139.485i	0.105778	+	0.372955i
$375$			299.230i			0.797946i
$376$	182.695	+	167.390i	0.485892	+	0.445187i
$377$	123.818			0.328429
$378$	−61.4755	+	17.4357i	−0.162634	+	0.0461262i
$379$			87.8468i			0.231786i	0.993262	+	0.115893i	$0.0369729\pi$
$379$			87.8468i			0.231786i	−0.993262	+	0.115893i	$0.963027\pi$
$380$	38.1395	+	61.8284i	0.100367	+	0.162706i
$381$	399.484			1.04851
$382$	−31.7639	−	111.994i	−0.0831515	−	0.293179i
$383$			653.584i			1.70649i	0.521513	+	0.853243i	$0.325368\pi$
$383$			653.584i			1.70649i	−0.521513	+	0.853243i	$0.674632\pi$
$384$	543.696	−	206.975i	1.41588	−	0.538998i
$385$	55.4004			0.143897
$386$	199.879	−	56.6898i	0.517822	−	0.146865i
$387$		−	315.027i		−	0.814024i
$388$	305.490	−	188.445i	0.787346	−	0.485684i
$389$	−168.861			−0.434090			−0.217045	−	0.976162i	$-0.569642\pi$
$389$	−168.861			−0.434090			−0.217045	+	0.976162i	$0.569642\pi$
$390$	67.6743	+	238.609i	0.173524	+	0.611817i
$391$			70.7954i			0.181062i
$392$	37.8307	−	41.2897i	0.0965069	−	0.105331i
$393$	−636.939			−1.62071
$394$	348.650	−	98.8843i	0.884899	−	0.250975i
$395$		−	45.6535i		−	0.115578i
$396$	−374.723	−	607.468i	−0.946271	−	1.53401i
$397$	−691.521			−1.74187			−0.870934	−	0.491401i	$-0.836485\pi$
$397$	−691.521			−1.74187			−0.870934	+	0.491401i	$0.836485\pi$
$398$	118.922	+	419.300i	0.298799	+	1.05352i
$399$		−	159.648i		−	0.400121i
$400$	−166.058	+	330.710i	−0.415144	+	0.826775i
$401$	−399.834			−0.997091			−0.498546	−	0.866864i	$-0.666132\pi$
$401$	−399.834			−0.997091			−0.498546	+	0.866864i	$0.666132\pi$
$402$	−899.541	+	255.128i	−2.23766	+	0.634647i
$403$			369.770i			0.917544i
$404$	554.511	−	342.057i	1.37255	−	0.846675i
$405$	−68.4345			−0.168974
$406$	8.96276	+	31.6013i	0.0220758	+	0.0778356i
$407$		−	421.281i		−	1.03509i
$408$	−126.963	−	116.327i	−0.311184	−	0.285115i
$409$	111.079			0.271586			0.135793	−	0.990737i	$-0.456642\pi$
$409$	111.079			0.271586			0.135793	+	0.990737i	$0.456642\pi$
$410$	29.2326	−	8.29096i	0.0712990	−	0.0202219i
$411$		−	539.603i		−	1.31290i
$412$	−180.858	−	293.190i	−0.438975	−	0.711626i
$413$	−76.2742			−0.184683
$414$	−95.0951	−	335.290i	−0.229698	−	0.809879i
$415$		−	217.915i		−	0.525095i
$416$	−119.906	+	626.910i	−0.288236	+	1.50699i
$417$	327.715			0.785888
$418$	391.029	−	110.904i	0.935477	−	0.265320i
$419$		−	641.986i		−	1.53219i	−0.642729	−	0.766094i	$-0.722198\pi$
$419$		−	641.986i		−	1.53219i	0.642729	−	0.766094i	$-0.277802\pi$
$420$	−56.0000	+	34.5442i	−0.133333	+	0.0822482i
$421$	151.970			0.360975			0.180487	−	0.983577i	$-0.442233\pi$
$421$	151.970			0.360975			0.180487	+	0.983577i	$0.442233\pi$
$422$	−58.6102	−	206.650i	−0.138887	−	0.489693i
$423$			361.053i			0.853553i
$424$	69.0991	−	75.4170i	0.162970	−	0.177870i
$425$	109.535			0.257729
$426$	−400.598	+	113.618i	−0.940372	+	0.266709i
$427$		−	17.2613i		−	0.0404246i
$428$	214.509	+	347.743i	0.501190	+	0.812484i
$429$	1387.68			3.23468
$430$	−20.1741	−	71.1308i	−0.0469166	−	0.165421i
$431$			459.854i			1.06695i	0.845817	+	0.533473i	$0.179113\pi$
$431$			459.854i			1.06695i	−0.845817	+	0.533473i	$0.820887\pi$
$432$	172.671	+	86.7023i	0.399701	+	0.200700i
$433$	534.370			1.23411			0.617056	−	0.786919i	$-0.288325\pi$
$433$	534.370			1.23411			0.617056	+	0.786919i	$0.288325\pi$
$434$	−94.3743	+	26.7665i	−0.217452	+	0.0616739i
$435$		−	38.5945i		−	0.0887231i
$436$	517.591	−	319.282i	1.18714	−	0.732299i
$437$	198.466			0.454156
$438$	−173.867	−	613.027i	−0.396956	−	1.39960i
$439$			201.259i			0.458449i	0.973374	+	0.229224i	$0.0736189\pi$
$439$			201.259i			0.458449i	−0.973374	+	0.229224i	$0.926381\pi$
$440$	−123.512	−	113.165i	−0.280708	−	0.257192i
$441$	81.5989			0.185032
$442$	181.755	−	51.5495i	0.411211	−	0.116628i
$443$			73.4928i			0.165898i	0.996554	+	0.0829490i	$0.0264339\pi$
$443$			73.4928i			0.165898i	−0.996554	+	0.0829490i	$0.973566\pi$
$444$	262.684	+	425.840i	0.591631	+	0.959099i
$445$	−68.4539			−0.153829
$446$	190.829	+	672.832i	0.427867	+	1.50859i
$447$		−	992.169i		−	2.21962i
$448$	−168.682	+	14.7770i	−0.376522	+	0.0329845i
$449$	−41.4382			−0.0922899			−0.0461450	−	0.998935i	$-0.514694\pi$
$449$	−41.4382			−0.0922899			−0.0461450	+	0.998935i	$0.514694\pi$
$450$	−518.762	+	147.131i	−1.15280	+	0.326959i
$451$		−	170.008i		−	0.376958i
$452$	−572.320	+	353.042i	−1.26619	+	0.781066i
$453$	−822.401			−1.81545
$454$	−10.0096	−	35.2921i	−0.0220475	−	0.0777359i
$455$		−	72.1892i		−	0.158658i
$456$	−326.109	+	355.926i	−0.715150	+	0.780539i
$457$	270.205			0.591258			0.295629	−	0.955303i	$-0.404471\pi$
$457$	270.205			0.591258			0.295629	+	0.955303i	$0.404471\pi$
$458$	−131.887	+	37.4058i	−0.287962	+	0.0816720i
$459$		−	57.1905i		−	0.124598i
$460$	−42.9435	−	69.6161i	−0.0933554	−	0.151339i
$461$	−735.133			−1.59465			−0.797324	−	0.603552i	$-0.793752\pi$
$461$	−735.133			−1.59465			−0.797324	+	0.603552i	$0.793752\pi$
$462$	100.449	+	354.168i	0.217423	+	0.766598i
$463$		−	742.356i		−	1.60336i	−0.597753	−	0.801681i	$-0.703940\pi$
$463$		−	742.356i		−	1.60336i	0.597753	−	0.801681i	$-0.296060\pi$
$464$	44.5690	−	88.7608i	0.0960538	−	0.191295i
$465$	115.259			0.247869
$466$	−118.292	+	33.5500i	−0.253845	+	0.0719957i
$467$			402.152i			0.861140i	0.902557	+	0.430570i	$0.141687\pi$
$467$			402.152i			0.861140i	−0.902557	+	0.430570i	$0.858313\pi$
$468$	−791.557	+	488.281i	−1.69136	+	1.04334i
$469$	272.149			0.580275
$470$	23.1216	+	81.5230i	0.0491949	+	0.173453i
$471$			868.462i			1.84387i
$472$	170.048	+	155.803i	0.360272	+	0.330091i
$473$	−413.675			−0.874577
$474$	291.857	−	82.7767i	0.615733	−	0.174634i
$475$		−	307.068i		−	0.646459i
$476$	26.3133	+	42.6568i	0.0552801	+	0.0896151i
$477$	149.043			0.312460
$478$	111.678	+	393.760i	0.233636	+	0.823765i
$479$			356.741i			0.744763i	0.928080	+	0.372381i	$0.121459\pi$
$479$			356.741i			0.744763i	−0.928080	+	0.372381i	$0.878541\pi$
$480$	195.411	+	37.3753i	0.407105	+	0.0778651i
$481$	−548.947			−1.14126
$482$	748.990	−	212.429i	1.55392	−	0.440724i
$483$			179.758i			0.372169i
$484$	−385.759	+	237.960i	−0.797024	+	0.491653i
$485$	122.751			0.253095
$486$	−183.393	−	646.614i	−0.377351	−	1.33048i
$487$			121.123i			0.248713i	0.992238	+	0.124356i	$0.0396866\pi$
$487$			121.123i			0.248713i	−0.992238	+	0.124356i	$0.960313\pi$
$488$	−35.2590	+	38.4829i	−0.0722521	+	0.0788584i
$489$	−1307.79			−2.67442
$490$	18.4244	−	5.22554i	0.0376009	−	0.0106644i
$491$			18.4535i			0.0375835i	0.999823	+	0.0187917i	$0.00598195\pi$
$491$			18.4535i			0.0375835i	−0.999823	+	0.0187917i	$0.994018\pi$
$492$	106.006	+	171.848i	0.215460	+	0.349284i
$493$	−29.3986			−0.0596320
$494$	−144.513	−	509.529i	−0.292536	−	1.03143i
$495$		−	244.090i		−	0.493112i
$496$	265.076	+	133.101i	0.534427	+	0.268349i
$497$	121.198			0.243859
$498$	1393.10	−	395.112i	2.79739	−	0.793398i
$499$		−	149.571i		−	0.299742i	−0.988706	−	0.149871i	$-0.952114\pi$
$499$		−	149.571i		−	0.299742i	0.988706	−	0.149871i	$-0.0478859\pi$
$500$	−224.135	+	138.260i	−0.448270	+	0.276521i
$501$	567.484			1.13270
$502$	−62.8022	−	221.430i	−0.125104	−	0.441097i
$503$			651.239i			1.29471i	0.762189	+	0.647354i	$0.224125\pi$
$503$			651.239i			1.29471i	−0.762189	+	0.647354i	$0.775875\pi$
$504$	−181.919	−	166.679i	−0.360951	−	0.330713i
$505$	222.812			0.441211
$506$	−440.283	+	124.873i	−0.870124	+	0.246785i
$507$		−	1040.10i		−	2.05148i
$508$	184.583	+	299.230i	0.363353	+	0.589035i
$509$	817.972			1.60702			0.803509	−	0.595293i	$-0.202964\pi$
$509$	817.972			1.60702			0.803509	+	0.595293i	$0.202964\pi$
$510$	−16.0682	−	56.6539i	−0.0315063	−	0.111086i
$511$			185.466i			0.362948i
$512$	406.250	+	311.617i	0.793457	+	0.608627i
$513$	−160.327			−0.312528
$514$	−648.872	+	184.033i	−1.26240	+	0.358041i
$515$		−	117.809i		−	0.228754i
$516$	418.152	−	257.942i	0.810372	−	0.499887i
$517$	474.113			0.917046
$518$	−39.7365	−	140.105i	−0.0767114	−	0.270472i
$519$			1250.82i			2.41005i
$520$	−147.458	+	160.941i	−0.283574	+	0.309502i
$521$	−173.603			−0.333211			−0.166606	−	0.986024i	$-0.553281\pi$
$521$	−173.603			−0.333211			−0.166606	+	0.986024i	$0.553281\pi$
$522$	139.233	−	39.4893i	0.266730	−	0.0756500i
$523$		−	680.630i		−	1.30139i	−0.759337	−	0.650697i	$-0.774477\pi$
$523$		−	680.630i		−	1.30139i	0.759337	−	0.650697i	$-0.225523\pi$
$524$	−294.300	−	477.093i	−0.561642	−	0.910483i
$525$	278.122			0.529755
$526$	−89.3494	−	315.032i	−0.169866	−	0.598920i
$527$		−	87.7961i		−	0.166596i
$528$	499.503	−	994.779i	0.946028	−	1.88405i
$529$	305.535			0.577571
$530$	33.6528	−	9.54463i	0.0634959	−	0.0180087i
$531$			336.059i			0.632879i
$532$	119.583	−	73.7663i	0.224780	−	0.138658i
$533$	−221.528			−0.415624
$534$	−124.117	−	437.618i	−0.232429	−	0.819509i
$535$			139.729i			0.261175i
$536$	−606.738	−	555.910i	−1.13197	−	1.03714i
$537$	33.7456			0.0628410
$538$	−559.499	+	158.685i	−1.03996	+	0.294954i
$539$		−	107.151i		−	0.198796i
$540$	34.6910	+	56.2379i	0.0642426	+	0.104144i
$541$	−313.190			−0.578909			−0.289454	−	0.957192i	$-0.593474\pi$
$541$	−313.190			−0.578909			−0.289454	+	0.957192i	$0.593474\pi$
$542$	−201.166	−	709.280i	−0.371156	−	1.30864i
$543$		−	452.510i		−	0.833352i
$544$	28.4698	−	148.850i	0.0523342	−	0.273621i
$545$	207.977			0.381609
$546$	461.497	−	130.890i	0.845233	−	0.239725i
$547$			352.784i			0.644944i	0.946579	+	0.322472i	$0.104514\pi$
$547$			352.784i			0.644944i	−0.946579	+	0.322472i	$0.895486\pi$
$548$	404.184	−	249.326i	0.737563	−	0.454974i
$549$	−76.0520			−0.138528
$550$	193.204	+	681.207i	0.351280	+	1.23856i
$551$			82.4153i			0.149574i
$552$	367.185	−	400.757i	0.665190	−	0.726010i
$553$	−88.2992			−0.159673
$554$	−489.542	+	138.844i	−0.883650	+	0.250621i
$555$			171.109i			0.308305i
$556$	151.422	+	245.472i	0.272342	+	0.441497i
$557$	−135.925			−0.244030			−0.122015	−	0.992528i	$-0.538936\pi$
$557$	−135.925			−0.244030			−0.122015	+	0.992528i	$0.538936\pi$
$558$	117.931	+	415.806i	0.211346	+	0.745173i
$559$			539.037i			0.964288i
$560$	−51.7501	−	25.9850i	−0.0924109	−	0.0464017i
$561$	−329.482			−0.587312
$562$	−282.134	+	80.0190i	−0.502018	+	0.142383i
$563$			160.363i			0.284836i	0.989807	+	0.142418i	$0.0454878\pi$
$563$			160.363i			0.284836i	−0.989807	+	0.142418i	$0.954512\pi$
$564$	−479.244	+	295.627i	−0.849723	+	0.524162i
$565$	−229.967			−0.407022
$566$	−104.534	−	368.570i	−0.184689	−	0.651184i
$567$			132.360i			0.233440i
$568$	−270.203	−	247.567i	−0.475709	−	0.435857i
$569$	611.297			1.07434			0.537168	−	0.843475i	$-0.319494\pi$
$569$	611.297			1.07434			0.537168	+	0.843475i	$0.319494\pi$
$570$	−158.822	+	45.0453i	−0.278636	+	0.0790268i
$571$		−	286.952i		−	0.502542i	−0.967917	−	0.251271i	$-0.919151\pi$
$571$		−	286.952i		−	0.502542i	0.967917	−	0.251271i	$-0.0808486\pi$
$572$	641.182	+	1039.43i	1.12095	+	1.81718i
$573$	264.545			0.461685
$574$	−16.0357	−	56.5393i	−0.0279367	−	0.0985004i
$575$			345.746i			0.601297i
$576$	65.1066	+	743.201i	0.113032	+	1.29028i
$577$	−530.428			−0.919286			−0.459643	−	0.888104i	$-0.652023\pi$
$577$	−530.428			−0.919286			−0.459643	+	0.888104i	$0.652023\pi$
$578$	512.912	−	145.472i	0.887392	−	0.251682i
$579$			472.141i			0.815442i
$580$	28.9089	−	17.8328i	0.0498429	−	0.0307462i
$581$	−421.472			−0.725425
$582$	222.566	+	784.733i	0.382416	+	1.34834i
$583$		−	195.715i		−	0.335703i
$584$	378.846	−	413.485i	0.648709	−	0.708022i
$585$	−318.061			−0.543693
$586$	−607.049	+	172.171i	−1.03592	+	0.293808i
$587$		−	10.9359i		−	0.0186301i	−0.999957	−	0.00931506i	$-0.997035\pi$
$587$		−	10.9359i		−	0.0186301i	0.999957	−	0.00931506i	$-0.00296512\pi$
$588$	66.8126	+	108.310i	0.113627	+	0.184202i
$589$	−246.126			−0.417871
$590$	21.5210	+	75.8796i	0.0364763	+	0.128609i
$591$			823.558i			1.39350i
$592$	−197.597	+	393.522i	−0.333779	+	0.664734i
$593$	119.459			0.201449			0.100725	−	0.994914i	$-0.467884\pi$
$593$	119.459			0.201449			0.100725	+	0.994914i	$0.467884\pi$
$594$	355.673	−	100.876i	0.598776	−	0.169825i
$595$			17.1402i			0.0288071i
$596$	743.175	−	458.436i	1.24694	−	0.769188i
$597$	−990.441			−1.65903
$598$	162.715	+	573.708i	0.272099	+	0.959378i
$599$		−	1020.35i		−	1.70342i	−0.524014	−	0.851710i	$-0.675566\pi$
$599$		−	1020.35i		−	1.70342i	0.524014	−	0.851710i	$-0.324434\pi$
$600$	−620.053	−	568.110i	−1.03342	−	0.946849i
$601$	−109.785			−0.182671			−0.0913356	−	0.995820i	$-0.529114\pi$
$601$	−109.785			−0.182671			−0.0913356	+	0.995820i	$0.529114\pi$
$602$	−137.575	+	39.0191i	−0.228530	+	0.0648159i
$603$		−	1199.07i		−	1.98851i
$604$	−379.994	−	616.012i	−0.629129	−	1.01989i
$605$	−155.004			−0.256206
$606$	403.991	+	1424.41i	0.666652	+	2.35051i
$607$		−	649.557i		−	1.07011i	−0.844817	−	0.535055i	$-0.820291\pi$
$607$		−	649.557i		−	1.07011i	0.844817	−	0.535055i	$-0.179709\pi$
$608$	−417.283	−	79.8117i	−0.686320	−	0.131269i
$609$	−74.6463			−0.122572
$610$	−17.1720	+	4.87032i	−0.0281508	+	0.00798413i
$611$		−	617.790i		−	1.01111i
$612$	187.943	−	115.935i	0.307096	−	0.189436i
$613$	802.148			1.30856			0.654281	−	0.756252i	$-0.272971\pi$
$613$	802.148			1.30856			0.654281	+	0.756252i	$0.272971\pi$
$614$	−246.941	−	870.674i	−0.402184	−	1.41804i
$615$			69.0513i			0.112278i
$616$	−218.873	+	238.886i	−0.355314	+	0.387801i
$617$	1151.11			1.86565			0.932825	−	0.360329i	$-0.117336\pi$
$617$	1151.11			1.86565			0.932825	+	0.360329i	$0.117336\pi$
$618$	753.136	−	213.605i	1.21867	−	0.345639i
$619$			223.829i			0.361598i	0.983520	+	0.180799i	$0.0578683\pi$
$619$			223.829i			0.361598i	−0.983520	+	0.180799i	$0.942132\pi$
$620$	53.2559	+	86.3337i	0.0858967	+	0.139248i
$621$	180.521			0.290694
$622$	260.752	+	919.371i	0.419216	+	1.47809i
$623$			132.398i			0.212517i
$624$	−1296.24	−	650.874i	−2.07731	−	1.04307i
$625$	488.157			0.781052
$626$	−402.976	+	114.292i	−0.643732	+	0.182575i
$627$			923.663i			1.47315i
$628$	−650.513	+	401.276i	−1.03585	+	0.638975i
$629$	130.339			0.207216
$630$	−23.0234	−	81.1767i	−0.0365450	−	0.128852i
$631$		−	385.557i		−	0.611026i	−0.952188	−	0.305513i	$-0.901172\pi$
$631$		−	385.557i		−	0.611026i	0.952188	−	0.305513i	$-0.0988279\pi$
$632$	196.857	+	180.366i	0.311483	+	0.285389i
$633$	488.135			0.771146
$634$	−3.36475	+	0.954312i	−0.00530718	+	0.00150522i
$635$			120.235i			0.189347i
$636$	122.035	+	197.833i	0.191880	+	0.311058i
$637$	−139.622			−0.219187
$638$	−51.8550	−	182.832i	−0.0812774	−	0.286571i
$639$		−	533.989i		−	0.835664i
$640$	62.2947	+	163.640i	0.0973355	+	0.255687i
$641$	−289.861			−0.452201			−0.226100	−	0.974104i	$-0.572598\pi$
$641$	−289.861			−0.452201			−0.226100	+	0.974104i	$0.572598\pi$
$642$	−893.270	+	253.350i	−1.39139	+	0.394625i
$643$		−	525.629i		−	0.817463i	−0.912655	−	0.408731i	$-0.865971\pi$
$643$		−	525.629i		−	0.817463i	0.912655	−	0.408731i	$-0.134029\pi$
$644$	−134.646	+	83.0577i	−0.209077	+	0.128972i
$645$	168.020			0.260497
$646$	34.3123	+	120.980i	0.0531150	+	0.187275i
$647$		−	95.6042i		−	0.147765i	−0.997267	−	0.0738827i	$-0.976461\pi$
$647$		−	95.6042i		−	0.147765i	0.997267	−	0.0738827i	$-0.0235390\pi$
$648$	270.368	−	295.088i	0.417234	−	0.455383i
$649$	441.292			0.679958
$650$	887.643	−	251.754i	1.36560	−	0.387313i
$651$		−	222.924i		−	0.342434i
$652$	−604.271	−	979.589i	−0.926796	−	1.50244i
$653$	−627.508			−0.960962			−0.480481	−	0.877005i	$-0.659538\pi$
$653$	−627.508			−0.960962			−0.480481	+	0.877005i	$0.659538\pi$
$654$	377.093	+	1329.57i	0.576595	+	2.03298i
$655$		−	191.704i		−	0.292677i
$656$	−79.7404	+	158.806i	−0.121555	+	0.242082i
$657$	817.152			1.24376
$658$	157.675	−	44.7198i	0.239628	−	0.0679633i
$659$			220.070i			0.333945i	0.985962	+	0.166972i	$0.0533991\pi$
$659$			220.070i			0.333945i	−0.985962	+	0.166972i	$0.946601\pi$
$660$	323.994	−	199.859i	0.490900	−	0.302817i
$661$	743.710			1.12513			0.562564	−	0.826754i	$-0.309815\pi$
$661$	743.710			1.12513			0.562564	+	0.826754i	$0.309815\pi$
$662$	−204.670	−	721.635i	−0.309170	−	1.09008i
$663$			429.329i			0.647556i
$664$	939.644	+	860.927i	1.41513	+	1.29658i
$665$	48.0505			0.0722564
$666$	−617.291	+	175.076i	−0.926863	+	0.262877i
$667$		−	92.7962i		−	0.139125i
$668$	262.208	+	425.068i	0.392527	+	0.636330i
$669$	−1589.32			−2.37566
$670$	−76.7876	−	270.741i	−0.114608	−	0.404091i
$671$			99.8669i			0.148833i
$672$	72.2881	−	377.947i	0.107572	−	0.562421i
$673$	−1017.05			−1.51122			−0.755610	−	0.655022i	$-0.772659\pi$
$673$	−1017.05			−1.51122			−0.755610	+	0.655022i	$0.772659\pi$
$674$	−490.148	+	139.016i	−0.727223	+	0.206255i
$675$		−	279.303i		−	0.413782i
$676$	779.076	−	480.582i	1.15248	−	0.710920i
$677$	861.905			1.27312			0.636562	−	0.771225i	$-0.280356\pi$
$677$	861.905			1.27312			0.636562	+	0.771225i	$0.280356\pi$
$678$	−416.966	−	1470.15i	−0.614993	−	2.16837i
$679$		−	237.415i		−	0.349653i
$680$	35.0117	−	38.2129i	0.0514878	−	0.0561955i
$681$	83.3646			0.122415
$682$	546.012	−	154.860i	0.800604	−	0.227068i
$683$			635.790i			0.930879i	0.885080	+	0.465440i	$0.154104\pi$
$683$			635.790i			0.930879i	−0.885080	+	0.465440i	$0.845896\pi$
$684$	−325.009	−	526.875i	−0.475159	−	0.770285i
$685$	162.408			0.237092
$686$	−10.1068	−	35.6350i	−0.0147330	−	0.0519460i
$687$		−	311.534i		−	0.453470i
$688$	386.418	+	194.030i	0.561654	+	0.282020i
$689$	−255.025			−0.370138
$690$	178.827	−	50.7191i	0.259170	−	0.0735059i
$691$			214.780i			0.310825i	0.987850	+	0.155412i	$0.0496706\pi$
$691$			214.780i			0.310825i	−0.987850	+	0.155412i	$0.950329\pi$
$692$	−936.911	+	577.944i	−1.35392	+	0.835180i
$693$	−472.099			−0.681240
$694$	279.091	+	984.031i	0.402149	+	1.41791i
$695$			98.6347i			0.141920i
$696$	166.419	+	152.478i	0.239108	+	0.219077i
$697$	52.5983			0.0754639
$698$	737.181	−	209.080i	1.05613	−	0.299541i
$699$		−	279.421i		−	0.399744i
$700$	128.507	+	208.324i	0.183582	+	0.297606i
$701$	−271.746			−0.387655			−0.193828	−	0.981036i	$-0.562090\pi$
$701$	−271.746			−0.387655			−0.193828	+	0.981036i	$0.562090\pi$
$702$	−131.446	−	463.458i	−0.187245	−	0.660196i
$703$		−	365.390i		−	0.519758i
$704$	975.927	−	85.4941i	1.38626	−	0.121440i
$705$	−192.568			−0.273146
$706$	−418.271	+	118.630i	−0.592451	+	0.168031i
$707$		−	430.944i		−	0.609538i
$708$	−446.068	+	275.162i	−0.630040	+	0.388647i
$709$	−616.894			−0.870090			−0.435045	−	0.900409i	$-0.643267\pi$
$709$	−616.894			−0.870090			−0.435045	+	0.900409i	$0.643267\pi$
$710$	−34.1963	−	120.571i	−0.0481638	−	0.169818i
$711$			389.040i			0.547173i
$712$	270.445	−	295.172i	0.379838	−	0.414567i
$713$	277.127			0.388678
$714$	−109.575	+	31.0778i	−0.153467	+	0.0435263i
$715$			417.658i			0.584137i
$716$	15.5923	+	25.2768i	0.0217770	+	0.0353029i
$717$	−930.112			−1.29723
$718$	−263.635	−	929.536i	−0.367180	−	1.29462i
$719$		−	55.3428i		−	0.0769719i	−0.999259	−	0.0384859i	$-0.987747\pi$
$719$		−	55.3428i		−	0.0769719i	0.999259	−	0.0384859i	$-0.0122535\pi$
$720$	−114.488	+	228.007i	−0.159011	+	0.316677i
$721$	−227.855			−0.316027
$722$	−355.451	+	100.813i	−0.492315	+	0.139631i
$723$			1769.21i			2.44704i
$724$	338.949	−	209.084i	0.468161	−	0.288790i
$725$	−143.575			−0.198034
$726$	−281.046	−	990.925i	−0.387116	−	1.36491i
$727$			1046.07i			1.43888i	0.694554	+	0.719440i	$0.255602\pi$
$727$			1046.07i			1.43888i	−0.694554	+	0.719440i	$0.744398\pi$
$728$	311.279	+	285.202i	0.427580	+	0.391761i
$729$	1077.14			1.47756
$730$	184.507	−	52.3299i	0.252749	−	0.0716848i
$731$		−	127.986i		−	0.175083i
$732$	−62.2708	−	100.948i	−0.0850693	−	0.137907i
$733$	851.328			1.16143			0.580715	−	0.814107i	$-0.302773\pi$
$733$	851.328			1.16143			0.580715	+	0.814107i	$0.302773\pi$
$734$	257.002	+	906.148i	0.350139	+	1.23453i
$735$			43.5209i			0.0592121i
$736$	469.843	+	89.8646i	0.638373	+	0.122099i
$737$	−1574.55			−2.13643
$738$	−249.108	+	70.6521i	−0.337545	+	0.0957345i
$739$			789.585i			1.06845i	0.845342	+	0.534226i	$0.179397\pi$
$739$			789.585i			1.06845i	−0.845342	+	0.534226i	$0.820603\pi$
$740$	−128.168	+	79.0618i	−0.173200	+	0.106840i
$741$	1203.57			1.62426
$742$	−18.4604	−	65.0885i	−0.0248793	−	0.0877204i
$743$			892.788i			1.20160i	0.799400	+	0.600799i	$0.205151\pi$
$743$			892.788i			1.20160i	−0.799400	+	0.600799i	$0.794849\pi$
$744$	−455.360	+	496.995i	−0.612043	+	0.668004i
$745$	298.620			0.400832
$746$	345.444	−	97.9751i	0.463062	−	0.131334i
$747$			1856.98i			2.48591i
$748$	−152.239	−	246.795i	−0.203527	−	0.329940i
$749$	270.252			0.360817
$750$	−163.294	−	575.750i	−0.217726	−	0.767667i
$751$		−	406.211i		−	0.540894i	−0.962735	−	0.270447i	$-0.912829\pi$
$751$		−	406.211i		−	0.540894i	0.962735	−	0.270447i	$-0.0871715\pi$
$752$	−442.873	−	222.378i	−0.588928	−	0.295715i
$753$	523.048			0.694619
$754$	−238.239	+	67.5693i	−0.315966	+	0.0896145i
$755$		−	247.524i		−	0.327846i
$756$	108.771	−	67.0964i	0.143877	−	0.0887519i
$757$	89.9062			0.118766			0.0593832	−	0.998235i	$-0.481087\pi$
$757$	89.9062			0.118766			0.0593832	+	0.998235i	$0.481087\pi$
$758$	−47.9394	−	169.027i	−0.0632446	−	0.222990i
$759$		−	1040.01i		−	1.37023i
$760$	−107.125	−	98.1511i	−0.140954	−	0.129146i
$761$	−261.751			−0.343956			−0.171978	−	0.985101i	$-0.555016\pi$
$761$	−261.751			−0.343956			−0.171978	+	0.985101i	$0.555016\pi$
$762$	−768.650	+	218.005i	−1.00873	+	0.286096i
$763$		−	402.251i		−	0.527197i
$764$	122.234	+	198.155i	0.159992	+	0.259365i
$765$	75.5185			0.0987170
$766$	−356.672	−	1257.57i	−0.465629	−	1.64173i
$767$		−	575.024i		−	0.749705i
$768$	−933.181	+	694.946i	−1.21508	+	0.904878i
$769$	−753.905			−0.980370			−0.490185	−	0.871618i	$-0.663071\pi$
$769$	−753.905			−0.980370			−0.490185	+	0.871618i	$0.663071\pi$
$770$	−106.596	+	30.2329i	−0.138437	+	0.0392635i
$771$		−	1532.72i		−	1.98796i
$772$	−353.653	+	218.155i	−0.458099	+	0.282584i
$773$	−463.530			−0.599650			−0.299825	−	0.953994i	$-0.596928\pi$
$773$	−463.530			−0.599650			−0.299825	+	0.953994i	$0.596928\pi$
$774$	171.916	+	606.147i	0.222113	+	0.783135i
$775$		−	428.773i		−	0.553255i
$776$	−484.959	+	529.300i	−0.624947	+	0.682088i
$777$	330.945			0.425927
$778$	324.907	−	92.1501i	0.417618	−	0.118445i
$779$		−	147.453i		−	0.189285i
$780$	−260.425	−	422.178i	−0.333879	−	0.541254i
$781$	−701.203			−0.897827
$782$	−38.6342	−	136.218i	−0.0494043	−	0.174192i
$783$			74.9634i			0.0957388i
$784$	−50.2579	+	100.091i	−0.0641045	+	0.127667i
$785$	−261.387			−0.332977
$786$	1225.54	−	347.588i	1.55921	−	0.442224i
$787$			618.821i			0.786304i	0.919473	+	0.393152i	$0.128615\pi$
$787$			618.821i			0.786304i	−0.919473	+	0.393152i	$0.871385\pi$
$788$	−616.878	+	380.528i	−0.782841	+	0.482904i
$789$	744.146			0.943151
$790$	24.9139	+	87.8423i	0.0315365	+	0.111193i
$791$			444.784i			0.562305i
$792$	1052.51	+	964.341i	1.32893	+	1.21760i
$793$	130.131			0.164100
$794$	1330.56	−	377.375i	1.67577	−	0.475283i
$795$			79.4924i			0.0999905i
$796$	−457.638	−	741.881i	−0.574922	−	0.932011i
$797$	−441.998			−0.554577			−0.277289	−	0.960787i	$-0.589436\pi$
$797$	−441.998			−0.554577			−0.277289	+	0.960787i	$0.589436\pi$
$798$	87.1228	+	307.181i	0.109176	+	0.384939i
$799$			146.685i			0.183585i
$800$	139.039	−	726.943i	0.173799	−	0.908678i
$801$	583.335			0.728259
$802$	769.323	−	218.196i	0.959256	−	0.272064i
$803$		−	1073.04i		−	1.33628i
$804$	1591.59	−	981.788i	1.97958	−	1.22113i
$805$	−54.1028			−0.0672085
$806$	−201.790	−	711.478i	−0.250359	−	0.882727i
$807$		−	1321.61i		−	1.63768i
$808$	−880.274	+	960.760i	−1.08945	+	1.18906i
$809$	311.447			0.384978			0.192489	−	0.981299i	$-0.438344\pi$
$809$	311.447			0.384978			0.192489	+	0.981299i	$0.438344\pi$
$810$	131.675	−	37.3458i	0.162562	−	0.0461060i
$811$		−	965.110i		−	1.19002i	−0.803717	−	0.595012i	$-0.797147\pi$
$811$		−	965.110i		−	1.19002i	0.803717	−	0.595012i	$-0.202853\pi$
$812$	−34.4906	−	55.9131i	−0.0424762	−	0.0688585i
$813$	1675.41			2.06078
$814$	229.900	+	810.590i	0.282432	+	0.995811i
$815$		−	393.615i		−	0.482963i
$816$	307.772	+	154.540i	0.377172	+	0.189387i
$817$	−358.793			−0.439159
$818$	−213.728	+	60.6175i	−0.261281	+	0.0741045i
$819$			615.166i			0.751118i
$820$	−51.7222	+	31.9054i	−0.0630759	+	0.0389091i
$821$	1464.81			1.78417			0.892087	−	0.451864i	$-0.149241\pi$
$821$	1464.81			1.78417			0.892087	+	0.451864i	$0.149241\pi$
$822$	294.470	+	1038.25i	0.358236	+	1.26308i
$823$		−	967.159i		−	1.17516i	−0.809165	−	0.587581i	$-0.800080\pi$
$823$		−	967.159i		−	1.17516i	0.809165	−	0.587581i	$-0.199920\pi$
$824$	507.988	+	465.433i	0.616491	+	0.564845i
$825$	−1609.10			−1.95043
$826$	146.760	−	41.6241i	0.177675	−	0.0503924i
$827$			1298.46i			1.57009i	0.619441	+	0.785043i	$0.287359\pi$
$827$			1298.46i			1.57009i	−0.619441	+	0.785043i	$0.712641\pi$
$828$	365.946	+	593.239i	0.441964	+	0.716473i
$829$	−771.397			−0.930515			−0.465258	−	0.885175i	$-0.654038\pi$
$829$	−771.397			−0.930515			−0.465258	+	0.885175i	$0.654038\pi$
$830$	118.920	+	419.291i	0.143277	+	0.505170i
$831$		−	1156.36i		−	1.39153i
$832$	−111.403	−	1271.68i	−0.133897	−	1.52846i
$833$	33.1511			0.0397973
$834$	−630.560	+	178.840i	−0.756067	+	0.214436i
$835$			170.799i			0.204550i
$836$	−691.861	+	426.782i	−0.827585	+	0.510505i
$837$	−223.871			−0.267469
$838$	350.343	+	1235.25i	0.418070	+	1.47405i
$839$		−	1088.04i		−	1.29683i	−0.761287	−	0.648415i	$-0.775432\pi$
$839$		−	1088.04i		−	1.29683i	0.761287	−	0.648415i	$-0.224568\pi$
$840$	88.8987	−	97.0270i	0.105832	−	0.115508i
$841$	−802.465			−0.954180
$842$	−292.407	+	82.9327i	−0.347277	+	0.0984949i
$843$		−	666.438i		−	0.790555i
$844$	225.545	+	365.633i	0.267233	+	0.433215i
$845$	313.045			0.370468
$846$	−197.032	−	694.705i	−0.232899	−	0.821164i
$847$			299.797i			0.353951i
$848$	−91.7978	+	182.819i	−0.108252	+	0.215588i
$849$	870.611			1.02545
$850$	−210.757	+	59.7750i	−0.247949	+	0.0703235i
$851$			411.413i			0.483447i
$852$	708.792	−	437.226i	0.831915	−	0.513176i
$853$	126.051			0.147774			0.0738870	−	0.997267i	$-0.476460\pi$
$853$	126.051			0.147774			0.0738870	+	0.997267i	$0.476460\pi$
$854$	9.41976	+	33.2126i	0.0110302	+	0.0388906i
$855$		−	211.707i		−	0.247611i
$856$	−602.508	−	552.034i	−0.703865	−	0.644900i
$857$	−1135.93			−1.32547			−0.662736	−	0.748853i	$-0.730605\pi$
$857$	−1135.93			−1.32547			−0.662736	+	0.748853i	$0.730605\pi$
$858$	−2670.04	+	757.277i	−3.11193	+	0.882608i
$859$			590.556i			0.687492i	0.939063	+	0.343746i	$0.111696\pi$
$859$			590.556i			0.687492i	−0.939063	+	0.343746i	$0.888304\pi$
$860$	77.6345	+	125.854i	0.0902727	+	0.146342i
$861$	133.553			0.155114
$862$	−250.950	−	884.809i	−0.291125	−	1.02646i
$863$			292.067i			0.338432i	0.985579	+	0.169216i	$0.0541235\pi$
$863$			292.067i			0.338432i	−0.985579	+	0.169216i	$0.945876\pi$
$864$	−379.552	−	72.5952i	−0.439297	−	0.0840222i
$865$	−376.466			−0.435221
$866$	−1028.19	+	291.615i	−1.18728	+	0.336737i
$867$			1211.57i			1.39742i
$868$	166.979	−	103.003i	0.192373	−	0.118667i
$869$	510.864			0.587876
$870$	21.0617	+	74.2601i	0.0242088	+	0.0853564i
$871$			2051.70i			2.35557i
$872$	−821.665	+	896.792i	−0.942276	+	1.02843i
$873$	−1046.03			−1.19820
$874$	−381.871	+	108.306i	−0.436923	+	0.123920i
$875$			174.189i			0.199073i
$876$	669.077	+	1084.65i	0.763787	+	1.23818i
$877$	1087.23			1.23971			0.619856	−	0.784715i	$-0.287191\pi$
$877$	1087.23			1.23971			0.619856	+	0.784715i	$0.287191\pi$
$878$	−109.830	−	387.244i	−0.125091	−	0.441053i
$879$		−	1433.93i		−	1.63132i
$880$	299.405	+	150.339i	0.340233	+	0.170839i
$881$	1217.53			1.38198			0.690991	−	0.722863i	$-0.257174\pi$
$881$	1217.53			1.38198			0.690991	+	0.722863i	$0.257174\pi$
$882$	−157.005	+	44.5299i	−0.178010	+	0.0504874i
$883$			1141.10i			1.29230i	0.763212	+	0.646148i	$0.223621\pi$
$883$			1141.10i			1.29230i	−0.763212	+	0.646148i	$0.776379\pi$
$884$	−321.585	+	198.374i	−0.363784	+	0.224404i
$885$	−179.237			−0.202528
$886$	−40.1062	−	141.408i	−0.0452666	−	0.159603i
$887$			368.518i			0.415466i	0.978186	+	0.207733i	$0.0666085\pi$
$887$			368.518i			0.415466i	−0.978186	+	0.207733i	$0.933391\pi$
$888$	−737.821	−	676.011i	−0.830879	−	0.761274i
$889$	232.549			0.261585
$890$	131.713	−	37.3564i	0.147992	−	0.0419735i
$891$		−	765.784i		−	0.859466i
$892$	−734.350	−	1190.46i	−0.823263	−	1.33460i
$893$	411.213			0.460484
$894$	541.443	+	1909.04i	0.605641	+	2.13539i
$895$			10.1566i			0.0113482i
$896$	316.499	−	120.485i	0.353235	−	0.134470i
$897$	−1355.17			−1.51078
$898$	79.7315	−	22.6135i	0.0887879	−	0.0251821i
$899$			115.080i			0.128009i
$900$	917.862	−	566.194i	1.01985	−	0.629104i
$901$	60.5517			0.0672050
$902$	92.7761	+	327.114i	0.102856	+	0.362654i
$903$		−	324.971i		−	0.359879i
$904$	908.544	−	991.615i	1.00503	−	1.09692i
$905$	136.195			0.150492
$906$	1582.39	−	448.798i	1.74657	−	0.495362i
$907$		−	341.525i		−	0.376544i	−0.982117	−	0.188272i	$-0.939711\pi$
$907$		−	341.525i		−	0.376544i	0.982117	−	0.188272i	$-0.0602886\pi$
$908$	38.5190	+	62.4435i	0.0424218	+	0.0687703i
$909$	−1898.71			−2.08879
$910$	39.3948	+	138.900i	0.0432910	+	0.152637i
$911$		−	536.979i		−	0.589439i	−0.955584	−	0.294719i	$-0.904774\pi$
$911$		−	536.979i		−	0.589439i	0.955584	−	0.294719i	$-0.0952262\pi$
$912$	433.234	−	862.802i	0.475037	−	0.946055i
$913$	2438.47			2.67083
$914$	−519.904	+	147.455i	−0.568823	+	0.161330i
$915$		−	40.5624i		−	0.0443305i
$916$	233.352	−	143.946i	0.254751	−	0.157146i
$917$	−370.777			−0.404337
$918$	31.2098	+	110.041i	0.0339976	+	0.119870i
$919$			987.383i			1.07441i	0.843452	+	0.537205i	$0.180520\pi$
$919$			987.383i			1.07441i	−0.843452	+	0.537205i	$0.819480\pi$
$920$	120.619	+	110.514i	0.131107	+	0.120124i
$921$	2056.65			2.23306
$922$	1414.47	−	401.174i	1.53414	−	0.435113i
$923$			913.698i			0.989922i
$924$	−386.551	−	626.642i	−0.418345	−	0.678183i
$925$	636.540			0.688152
$926$	405.116	+	1428.37i	0.437490	+	1.54252i
$927$			1003.91i			1.08297i
$928$	−37.3173	+	195.107i	−0.0402126	+	0.210245i
$929$	−1285.67			−1.38393			−0.691965	−	0.721932i	$-0.743255\pi$
$929$	−1285.67			−1.38393			−0.691965	+	0.721932i	$0.743255\pi$
$930$	−221.771	+	62.8987i	−0.238463	+	0.0676331i
$931$		−	92.9352i		−	0.0998230i
$932$	209.298	−	129.108i	0.224568	−	0.138527i
$933$	−2171.68			−2.32763
$934$	−219.461	−	773.785i	−0.234969	−	0.828463i
$935$		−	99.1664i		−	0.106060i
$936$	1256.58	−	1371.47i	1.34250	−	1.46525i
$937$	−887.657			−0.947339			−0.473670	−	0.880703i	$-0.657071\pi$
$937$	−887.657			−0.947339			−0.473670	+	0.880703i	$0.657071\pi$
$938$	−523.644	+	148.516i	−0.558256	+	0.158333i
$939$		−	951.882i		−	1.01372i
$940$	−88.9769	−	144.241i	−0.0946563	−	0.153448i
$941$	380.526			0.404385			0.202192	−	0.979346i	$-0.435193\pi$
$941$	380.526			0.404385			0.202192	+	0.979346i	$0.435193\pi$
$942$	−473.934	−	1671.01i	−0.503114	−	1.77390i
$943$			166.026i			0.176061i
$944$	−412.215	−	206.983i	−0.436669	−	0.219262i
$945$	43.7058			0.0462495
$946$	795.956	−	225.749i	0.841391	−	0.238636i
$947$			363.169i			0.383494i	0.981444	+	0.191747i	$0.0614153\pi$
$947$			363.169i			0.383494i	−0.981444	+	0.191747i	$0.938585\pi$
$948$	−516.393	+	318.543i	−0.544718	+	0.336015i
$949$	−1398.21			−1.47335
$950$	167.572	+	590.832i	0.176391	+	0.621928i
$951$		−	7.94799i		−	0.00835750i
$952$	−73.9082	−	67.7167i	−0.0776347	−	0.0711310i
$953$	−679.479			−0.712990			−0.356495	−	0.934297i	$-0.616028\pi$
$953$	−679.479			−0.712990			−0.356495	+	0.934297i	$0.616028\pi$
$954$	−286.775	+	81.3353i	−0.300603	+	0.0852572i
$955$			79.6220i			0.0833738i
$956$	−429.762	−	696.692i	−0.449542	−	0.728757i
$957$	431.874			0.451279
$958$	−194.680	−	686.409i	−0.203215	−	0.716502i
$959$		−	314.116i		−	0.327545i
$960$	−396.387	+	34.7247i	−0.412904	+	0.0361716i
$961$	617.323			0.642376
$962$	1056.23	−	299.570i	1.09796	−	0.311403i
$963$		−	1190.71i		−	1.23646i
$964$	−1325.21	+	817.472i	−1.37470	+	0.848000i
$965$	−142.103			−0.147257
$966$	−98.0966	−	345.873i	−0.101549	−	0.358047i
$967$		−	209.525i		−	0.216675i	−0.994114	−	0.108337i	$-0.965447\pi$
$967$		−	209.525i		−	0.216675i	0.994114	−	0.108337i	$-0.0345527\pi$
$968$	612.384	−	668.376i	0.632628	−	0.690471i
$969$	−285.770			−0.294912
$970$	−236.186	+	66.9872i	−0.243491	+	0.0690590i
$971$		−	538.867i		−	0.554961i	−0.960731	−	0.277481i	$-0.910501\pi$
$971$		−	538.867i		−	0.554961i	0.960731	−	0.277481i	$-0.0894994\pi$
$972$	705.735	+	1144.07i	0.726065	+	1.17703i
$973$	190.771			0.196065
$974$	−66.0989	−	233.054i	−0.0678633	−	0.239275i
$975$			2096.73i			2.15049i
$976$	46.8415	−	93.2867i	0.0479933	−	0.0955806i
$977$	1028.30			1.05250			0.526252	−	0.850329i	$-0.323597\pi$
$977$	1028.30			1.05250			0.526252	+	0.850329i	$0.323597\pi$
$978$	2516.33	−	713.683i	2.57294	−	0.729738i
$979$		−	766.001i		−	0.782432i
$980$	−32.5989	+	20.1090i	−0.0332642	+	0.0205194i
$981$	−1772.29			−1.80661
$982$	−10.0704	−	35.5065i	−0.0102550	−	0.0361574i
$983$		−	520.479i		−	0.529480i	−0.964320	−	0.264740i	$-0.914714\pi$
$983$		−	520.479i		−	0.529480i	0.964320	−	0.264740i	$-0.0852862\pi$
$984$	−297.748	−	272.804i	−0.302589	−	0.277240i
$985$	−247.872			−0.251646
$986$	56.5660	−	16.0433i	0.0573692	−	0.0162711i
$987$			372.449i			0.377355i
$988$	556.116	+	901.525i	0.562871	+	0.912475i
$989$	403.986			0.408479
$990$	133.204	+	469.656i	0.134550	+	0.474400i
$991$			1849.00i			1.86579i	0.360148	+	0.932895i	$0.382726\pi$
$991$			1849.00i			1.86579i	−0.360148	+	0.932895i	$0.617274\pi$
$992$	−582.671	−	111.445i	−0.587369	−	0.112343i
$993$	1704.60			1.71661
$994$	−233.198	+	66.1397i	−0.234606	+	0.0665389i
$995$		−	298.100i		−	0.299598i
$996$	−2464.86	+	1520.48i	−2.47476	+	1.52658i
$997$	1010.23			1.01327			0.506635	−	0.862161i	$-0.330889\pi$
$997$	1010.23			1.01327			0.506635	+	0.862161i	$0.330889\pi$
$998$	81.6236	+	287.792i	0.0817872	+	0.288368i
$999$		−	332.351i		−	0.332684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.3.c.a.15.2	yes	6
3.2	odd	2		252.3.g.a.127.5		6
4.3	odd	2	inner	28.3.c.a.15.1	✓	6
7.2	even	3		196.3.g.k.67.5		12
7.3	odd	6		196.3.g.j.79.4		12
7.4	even	3		196.3.g.k.79.4		12
7.5	odd	6		196.3.g.j.67.5		12
7.6	odd	2		196.3.c.g.99.2		6
8.3	odd	2		448.3.d.d.127.1		6
8.5	even	2		448.3.d.d.127.6		6
12.11	even	2		252.3.g.a.127.6		6
16.3	odd	4		1792.3.g.g.127.1		12
16.5	even	4		1792.3.g.g.127.2		12
16.11	odd	4		1792.3.g.g.127.12		12
16.13	even	4		1792.3.g.g.127.11		12
28.3	even	6		196.3.g.j.79.5		12
28.11	odd	6		196.3.g.k.79.5		12
28.19	even	6		196.3.g.j.67.4		12
28.23	odd	6		196.3.g.k.67.4		12
28.27	even	2		196.3.c.g.99.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.c.a.15.1	✓	6	4.3	odd	2	inner
28.3.c.a.15.2	yes	6	1.1	even	1	trivial
196.3.c.g.99.1		6	28.27	even	2
196.3.c.g.99.2		6	7.6	odd	2
196.3.g.j.67.4		12	28.19	even	6
196.3.g.j.67.5		12	7.5	odd	6
196.3.g.j.79.4		12	7.3	odd	6
196.3.g.j.79.5		12	28.3	even	6
196.3.g.k.67.4		12	28.23	odd	6
196.3.g.k.67.5		12	7.2	even	3
196.3.g.k.79.4		12	7.4	even	3
196.3.g.k.79.5		12	28.11	odd	6
252.3.g.a.127.5		6	3.2	odd	2
252.3.g.a.127.6		6	12.11	even	2
448.3.d.d.127.1		6	8.3	odd	2
448.3.d.d.127.6		6	8.5	even	2
1792.3.g.g.127.1		12	16.3	odd	4
1792.3.g.g.127.2		12	16.5	even	4
1792.3.g.g.127.11		12	16.13	even	4
1792.3.g.g.127.12		12	16.11	odd	4

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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	28.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92411 + 0.545716i) q^{2} -4.54500i q^{3} +(3.40439 - 2.10003i) q^{4} +1.36794 q^{5} +(2.48028 + 8.74507i) q^{6} -2.64575i q^{7} +(-5.40439 + 5.89853i) q^{8} -11.6570 q^{9} +O(q^{10})\)	\(q+(-1.92411 + 0.545716i) q^{2} -4.54500i q^{3} +(3.40439 - 2.10003i) q^{4} +1.36794 q^{5} +(2.48028 + 8.74507i) q^{6} -2.64575i q^{7} +(-5.40439 + 5.89853i) q^{8} -11.6570 q^{9} +(-2.63206 + 0.746506i) q^{10} +15.3073i q^{11} +(-9.54465 - 15.4729i) q^{12} +19.9460 q^{13} +(1.44383 + 5.09071i) q^{14} -6.21727i q^{15} +(7.17971 - 14.2987i) q^{16} -4.73588 q^{17} +(22.4293 - 6.36141i) q^{18} +13.2765i q^{19} +(4.65699 - 2.87272i) q^{20} -12.0249 q^{21} +(-8.35343 - 29.4528i) q^{22} -14.9487i q^{23} +(26.8088 + 24.5629i) q^{24} -23.1287 q^{25} +(-38.3784 + 10.8849i) q^{26} +12.0760i q^{27} +(-5.55617 - 9.00716i) q^{28} +6.20763 q^{29} +(3.39287 + 11.9627i) q^{30} +18.5385i q^{31} +(-6.01152 + 31.4303i) q^{32} +69.5715 q^{33} +(9.11234 - 2.58445i) q^{34} -3.61922i q^{35} +(-39.6849 + 24.4801i) q^{36} -27.5216 q^{37} +(-7.24518 - 25.5453i) q^{38} -90.6547i q^{39} +(-7.39287 + 8.06882i) q^{40} -11.1064 q^{41} +(23.1373 - 6.56220i) q^{42} +27.0248i q^{43} +(32.1458 + 52.1119i) q^{44} -15.9460 q^{45} +(8.15777 + 28.7630i) q^{46} -30.9731i q^{47} +(-64.9874 - 32.6317i) q^{48} -7.00000 q^{49} +(44.5022 - 12.6217i) q^{50} +21.5245i q^{51} +(67.9041 - 41.8874i) q^{52} -12.7857 q^{53} +(-6.59008 - 23.2356i) q^{54} +20.9394i q^{55} +(15.6060 + 14.2987i) q^{56} +60.3415 q^{57} +(-11.9442 + 3.38760i) q^{58} -28.8289i q^{59} +(-13.0565 - 21.1660i) q^{60} +6.52415 q^{61} +(-10.1168 - 35.6701i) q^{62} +30.8415i q^{63} +(-5.58519 - 63.7558i) q^{64} +27.2850 q^{65} +(-133.863 + 37.9663i) q^{66} +102.863i q^{67} +(-16.1228 + 9.94551i) q^{68} -67.9420 q^{69} +(1.97507 + 6.96378i) q^{70} +45.8085i q^{71} +(62.9989 - 68.7591i) q^{72} -70.0997 q^{73} +(52.9546 - 15.0190i) q^{74} +105.120i q^{75} +(27.8810 + 45.1982i) q^{76} +40.4992 q^{77} +(49.4718 + 174.429i) q^{78} -33.3739i q^{79} +(9.82140 - 19.5597i) q^{80} -50.0275 q^{81} +(21.3698 - 6.06092i) q^{82} -159.301i q^{83} +(-40.9375 + 25.2528i) q^{84} -6.47839 q^{85} +(-14.7478 - 51.9986i) q^{86} -28.2137i q^{87} +(-90.2903 - 82.7264i) q^{88} -50.0417 q^{89} +(30.6819 - 8.70202i) q^{90} -52.7723i q^{91} +(-31.3929 - 50.8913i) q^{92} +84.2575 q^{93} +(16.9025 + 59.5955i) q^{94} +18.1614i q^{95} +(142.850 + 27.3223i) q^{96} +89.7343 q^{97} +(13.4688 - 3.82001i) q^{98} -178.437i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9}+O(q^{10}) \) 6 * q - q^2 + q^4 - 4 * q^5 + 6 * q^6 - 13 * q^8 - 10 * q^9	\( 6 q - q^{2} + q^{4} - 4 q^{5} + 6 q^{6} - 13 q^{8} - 10 q^{9} - 28 q^{10} + 6 q^{12} + 12 q^{13} + 7 q^{14} + 17 q^{16} - 4 q^{17} + 43 q^{18} - 32 q^{20} + 52 q^{22} + 122 q^{24} - 30 q^{25} - 56 q^{26} - 35 q^{28} - 36 q^{29} - 64 q^{30} - 101 q^{32} + 80 q^{33} + 58 q^{34} - 131 q^{36} + 28 q^{37} - 190 q^{38} + 40 q^{40} - 20 q^{41} + 70 q^{42} + 164 q^{44} + 12 q^{45} + 120 q^{46} - 98 q^{48} - 42 q^{49} + 161 q^{50} + 292 q^{52} + 92 q^{53} - 44 q^{54} - 49 q^{56} + 160 q^{57} - 166 q^{58} - 176 q^{60} - 164 q^{61} + 148 q^{62} - 215 q^{64} - 136 q^{65} - 408 q^{66} + 62 q^{68} - 48 q^{69} + 84 q^{70} + 151 q^{72} - 132 q^{73} + 250 q^{74} - 78 q^{76} + 112 q^{77} + 248 q^{78} + 312 q^{80} - 218 q^{81} - 86 q^{82} - 98 q^{84} - 232 q^{85} - 164 q^{86} - 100 q^{88} + 348 q^{89} + 52 q^{90} - 104 q^{92} + 288 q^{93} - 276 q^{94} + 170 q^{96} + 252 q^{97} + 7 q^{98}+O(q^{100}) \) 6 * q - q^2 + q^4 - 4 * q^5 + 6 * q^6 - 13 * q^8 - 10 * q^9 - 28 * q^10 + 6 * q^12 + 12 * q^13 + 7 * q^14 + 17 * q^16 - 4 * q^17 + 43 * q^18 - 32 * q^20 + 52 * q^22 + 122 * q^24 - 30 * q^25 - 56 * q^26 - 35 * q^28 - 36 * q^29 - 64 * q^30 - 101 * q^32 + 80 * q^33 + 58 * q^34 - 131 * q^36 + 28 * q^37 - 190 * q^38 + 40 * q^40 - 20 * q^41 + 70 * q^42 + 164 * q^44 + 12 * q^45 + 120 * q^46 - 98 * q^48 - 42 * q^49 + 161 * q^50 + 292 * q^52 + 92 * q^53 - 44 * q^54 - 49 * q^56 + 160 * q^57 - 166 * q^58 - 176 * q^60 - 164 * q^61 + 148 * q^62 - 215 * q^64 - 136 * q^65 - 408 * q^66 + 62 * q^68 - 48 * q^69 + 84 * q^70 + 151 * q^72 - 132 * q^73 + 250 * q^74 - 78 * q^76 + 112 * q^77 + 248 * q^78 + 312 * q^80 - 218 * q^81 - 86 * q^82 - 98 * q^84 - 232 * q^85 - 164 * q^86 - 100 * q^88 + 348 * q^89 + 52 * q^90 - 104 * q^92 + 288 * q^93 - 276 * q^94 + 170 * q^96 + 252 * q^97 + 7 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more