LMFDB - Embedded newform 124.5.b.a.63.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(63,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("124.63");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			63.17
Character	$\chi$	$=$	124.63
Dual form			124.5.b.a.63.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06596 - 3.42518i) q^{2} +0.636071i q^{3} +(-7.46365 + 14.1525i) q^{4} -5.80492 q^{5} +(2.17865 - 1.31409i) q^{6} -53.1144i q^{7} +(63.8944 - 3.67417i) q^{8} +80.5954 q^{9} +O(q^{10})$	\(q+(-2.06596 - 3.42518i) q^{2} +0.636071i q^{3} +(-7.46365 + 14.1525i) q^{4} -5.80492 q^{5} +(2.17865 - 1.31409i) q^{6} -53.1144i q^{7} +(63.8944 - 3.67417i) q^{8} +80.5954 q^{9} +(11.9927 + 19.8829i) q^{10} -1.53657i q^{11} +(-9.00201 - 4.74741i) q^{12} -160.847 q^{13} +(-181.926 + 109.732i) q^{14} -3.69234i q^{15} +(-144.588 - 211.259i) q^{16} -332.484 q^{17} +(-166.507 - 276.053i) q^{18} +6.64805i q^{19} +(43.3259 - 82.1543i) q^{20} +33.7845 q^{21} +(-5.26304 + 3.17450i) q^{22} +5.19763i q^{23} +(2.33703 + 40.6414i) q^{24} -591.303 q^{25} +(332.304 + 550.930i) q^{26} +102.786i q^{27} +(751.702 + 396.427i) q^{28} -1205.23 q^{29} +(-12.6469 + 7.62822i) q^{30} +172.601i q^{31} +(-424.887 + 931.690i) q^{32} +0.977371 q^{33} +(686.898 + 1138.82i) q^{34} +308.325i q^{35} +(-601.536 + 1140.63i) q^{36} -1020.73 q^{37} +(22.7707 - 13.7346i) q^{38} -102.310i q^{39} +(-370.902 + 21.3283i) q^{40} +198.276 q^{41} +(-69.7973 - 115.718i) q^{42} +904.464i q^{43} +(21.7464 + 11.4685i) q^{44} -467.850 q^{45} +(17.8028 - 10.7381i) q^{46} -3541.83i q^{47} +(134.376 - 91.9681i) q^{48} -420.137 q^{49} +(1221.61 + 2025.32i) q^{50} -211.484i q^{51} +(1200.51 - 2276.40i) q^{52} -2381.78 q^{53} +(352.061 - 212.352i) q^{54} +8.91970i q^{55} +(-195.151 - 3393.71i) q^{56} -4.22863 q^{57} +(2489.95 + 4128.13i) q^{58} +2014.51i q^{59} +(52.2560 + 27.5584i) q^{60} -1512.16 q^{61} +(591.188 - 356.585i) q^{62} -4280.78i q^{63} +(4069.00 - 469.518i) q^{64} +933.707 q^{65} +(-2.01920 - 3.34767i) q^{66} -1525.81i q^{67} +(2481.55 - 4705.49i) q^{68} -3.30606 q^{69} +(1056.07 - 636.986i) q^{70} -8888.39i q^{71} +(5149.60 - 296.121i) q^{72} -3186.76 q^{73} +(2108.78 + 3496.17i) q^{74} -376.111i q^{75} +(-94.0867 - 49.6187i) q^{76} -81.6142 q^{77} +(-350.431 + 211.369i) q^{78} +5421.26i q^{79} +(839.321 + 1226.34i) q^{80} +6462.85 q^{81} +(-409.630 - 679.131i) q^{82} -9432.85i q^{83} +(-252.156 + 478.136i) q^{84} +1930.05 q^{85} +(3097.95 - 1868.58i) q^{86} -766.612i q^{87} +(-5.64564 - 98.1786i) q^{88} +9486.28 q^{89} +(966.558 + 1602.47i) q^{90} +8543.31i q^{91} +(-73.5596 - 38.7933i) q^{92} -109.786 q^{93} +(-12131.4 + 7317.25i) q^{94} -38.5914i q^{95} +(-592.621 - 270.258i) q^{96} -8168.28 q^{97} +(867.985 + 1439.04i) q^{98} -123.841i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) $ 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9	$ 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) $ 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9 + 53 * q^10 + 130 * q^12 + 120 * q^13 - 231 * q^14 - 590 * q^16 - 648 * q^17 + 230 * q^18 + 1113 * q^20 + 608 * q^21 + 1080 * q^22 - 1028 * q^24 + 8340 * q^25 - 1554 * q^26 - 165 * q^28 - 168 * q^29 - 2238 * q^30 - 1674 * q^32 - 1120 * q^33 + 1844 * q^34 + 1966 * q^36 - 2248 * q^37 - 5055 * q^38 - 1716 * q^40 + 6072 * q^41 + 5794 * q^42 - 120 * q^44 - 4040 * q^45 + 8850 * q^46 + 2276 * q^48 - 17604 * q^49 - 4539 * q^50 + 5896 * q^52 + 3480 * q^53 + 5148 * q^54 - 396 * q^56 - 10912 * q^57 - 7484 * q^58 + 22812 * q^60 + 2200 * q^61 - 19299 * q^64 - 9168 * q^65 - 468 * q^66 - 21930 * q^68 + 6496 * q^69 - 9615 * q^70 - 10079 * q^72 + 13752 * q^73 - 2106 * q^74 + 20099 * q^76 + 16608 * q^77 + 39460 * q^78 - 5787 * q^80 + 20732 * q^81 - 30525 * q^82 - 21760 * q^84 - 21200 * q^85 - 13398 * q^86 + 34690 * q^88 + 22296 * q^89 - 25419 * q^90 - 18852 * q^92 + 3196 * q^94 + 20790 * q^96 + 12120 * q^97 + 21921 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$1$

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 $

$2$	−2.06596	−	3.42518i	−0.516489	−	0.856294i
$2$	−2.06596	−	3.42518i	−0.516489	−	0.856294i
$3$			0.636071i			0.0706745i	0.999375	+	0.0353373i	$0.0112505\pi$
$3$			0.636071i			0.0706745i	−0.999375	+	0.0353373i	$0.988749\pi$
$4$	−7.46365	+	14.1525i	−0.466478	+	0.884533i
$5$	−5.80492			−0.232197			−0.116098	−	0.993238i	$-0.537039\pi$
$5$	−5.80492			−0.232197			−0.116098	+	0.993238i	$0.537039\pi$
$6$	2.17865	−	1.31409i	0.0605182	−	0.0365026i
$7$		−	53.1144i		−	1.08397i	−0.840389	−	0.541983i	$-0.817674\pi$
$7$		−	53.1144i		−	1.08397i	0.840389	−	0.541983i	$-0.182326\pi$
$8$	63.8944	−	3.67417i	0.998351	−	0.0574090i
$9$	80.5954			0.995005
$10$	11.9927	+	19.8829i	0.119927	+	0.198829i
$11$		−	1.53657i		−	0.0126990i	−0.999980	−	0.00634948i	$-0.997979\pi$
$11$		−	1.53657i		−	0.0126990i	0.999980	−	0.00634948i	$-0.00202112\pi$
$12$	−9.00201	−	4.74741i	−0.0625139	−	0.0329681i
$13$	−160.847			−0.951760			−0.475880	−	0.879510i	$-0.657870\pi$
$13$	−160.847			−0.951760			−0.475880	+	0.879510i	$0.657870\pi$
$14$	−181.926	+	109.732i	−0.928194	+	0.559857i
$15$		−	3.69234i		−	0.0164104i
$16$	−144.588	−	211.259i	−0.564796	−	0.825230i
$17$	−332.484			−1.15046			−0.575232	−	0.817990i	$-0.695088\pi$
$17$	−332.484			−1.15046			−0.575232	+	0.817990i	$0.695088\pi$
$18$	−166.507	−	276.053i	−0.513909	−	0.852017i
$19$			6.64805i			0.0184156i	0.999958	+	0.00920782i	$0.00293098\pi$
$19$			6.64805i			0.0184156i	−0.999958	+	0.00920782i	$0.997069\pi$
$20$	43.3259	−	82.1543i	0.108315	−	0.205386i
$21$	33.7845			0.0766089
$22$	−5.26304	+	3.17450i	−0.0108740	+	0.00655888i
$23$			5.19763i			0.00982539i	0.999988	+	0.00491269i	$0.00156377\pi$
$23$			5.19763i			0.00982539i	−0.999988	+	0.00491269i	$0.998436\pi$
$24$	2.33703	+	40.6414i	0.00405735	+	0.0705580i
$25$	−591.303			−0.946085
$26$	332.304	+	550.930i	0.491573	+	0.814986i
$27$			102.786i			0.140996i
$28$	751.702	+	396.427i	0.958804	+	0.505647i
$29$	−1205.23			−1.43309			−0.716546	−	0.697540i	$-0.754278\pi$
$29$	−1205.23			−1.43309			−0.716546	+	0.697540i	$0.754278\pi$
$30$	−12.6469	+	7.62822i	−0.0140521	+	0.00847580i
$31$			172.601i			0.179605i
$31$			172.601i			0.179605i
$32$	−424.887	+	931.690i	−0.414929	+	0.909854i
$33$	0.977371			0.000897494
$34$	686.898	+	1138.82i	0.594202	+	0.985136i
$35$			308.325i			0.251694i
$36$	−601.536	+	1140.63i	−0.464148	+	0.880115i
$37$	−1020.73			−0.745600			−0.372800	−	0.927912i	$-0.621602\pi$
$37$	−1020.73			−0.745600			−0.372800	+	0.927912i	$0.621602\pi$
$38$	22.7707	−	13.7346i	0.0157692	−	0.00951148i
$39$		−	102.310i		−	0.0672652i
$40$	−370.902	+	21.3283i	−0.231814	+	0.0133302i
$41$	198.276			0.117951			0.0589757	−	0.998259i	$-0.481217\pi$
$41$	198.276			0.117951			0.0589757	+	0.998259i	$0.481217\pi$
$42$	−69.7973	−	115.718i	−0.0395676	−	0.0655997i
$43$			904.464i			0.489164i	0.969629	+	0.244582i	$0.0786507\pi$
$43$			904.464i			0.489164i	−0.969629	+	0.244582i	$0.921349\pi$
$44$	21.7464	+	11.4685i	0.0112327	+	0.00592379i
$45$	−467.850			−0.231037
$46$	17.8028	−	10.7381i	0.00841342	−	0.00507470i
$47$		−	3541.83i		−	1.60336i	−0.597753	−	0.801681i	$-0.703939\pi$
$47$		−	3541.83i		−	1.60336i	0.597753	−	0.801681i	$-0.296061\pi$
$48$	134.376	−	91.9681i	0.0583228	−	0.0399167i
$49$	−420.137			−0.174984
$50$	1221.61	+	2025.32i	0.488642	+	0.810126i
$51$		−	211.484i		−	0.0813086i
$52$	1200.51	−	2276.40i	0.443975	−	0.841862i
$53$	−2381.78			−0.847911			−0.423956	−	0.905683i	$-0.639359\pi$
$53$	−2381.78			−0.847911			−0.423956	+	0.905683i	$0.639359\pi$
$54$	352.061	−	212.352i	0.120734	−	0.0728229i
$55$			8.91970i			0.00294866i
$56$	−195.151	−	3393.71i	−0.0622294	−	1.08218i
$57$	−4.22863			−0.00130152
$58$	2489.95	+	4128.13i	0.740177	+	1.22715i
$59$			2014.51i			0.578717i	0.957221	+	0.289359i	$0.0934420\pi$
$59$			2014.51i			0.578717i	−0.957221	+	0.289359i	$0.906558\pi$
$60$	52.2560	+	27.5584i	0.0145155	+	0.00765510i
$61$	−1512.16			−0.406385			−0.203193	−	0.979139i	$-0.565132\pi$
$61$	−1512.16			−0.406385			−0.203193	+	0.979139i	$0.565132\pi$
$62$	591.188	−	356.585i	0.153795	−	0.0927642i
$63$		−	4280.78i		−	1.07855i
$64$	4069.00	−	469.518i	0.993408	−	0.114629i
$65$	933.707			0.220996
$66$	−2.01920	−	3.34767i	−0.000463546	−	0.000768518i
$67$		−	1525.81i		−	0.339900i	−0.985453	−	0.169950i	$-0.945639\pi$
$67$		−	1525.81i		−	0.339900i	0.985453	−	0.169950i	$-0.0543606\pi$
$68$	2481.55	−	4705.49i	0.536667	−	1.01762i
$69$	−3.30606			−0.000694405
$70$	1056.07	−	636.986i	0.215524	−	0.129997i
$71$		−	8888.39i		−	1.76322i	−0.471979	−	0.881610i	$-0.656460\pi$
$71$		−	8888.39i		−	1.76322i	0.471979	−	0.881610i	$-0.343540\pi$
$72$	5149.60	−	296.121i	0.993364	−	0.0571222i
$73$	−3186.76			−0.598004			−0.299002	−	0.954253i	$-0.596654\pi$
$73$	−3186.76			−0.598004			−0.299002	+	0.954253i	$0.596654\pi$
$74$	2108.78	+	3496.17i	0.385094	+	0.638453i
$75$		−	376.111i		−	0.0668641i
$76$	−94.0867	−	49.6187i	−0.0162892	−	0.00859050i
$77$	−81.6142			−0.0137653
$78$	−350.431	+	211.369i	−0.0575988	+	0.0347417i
$79$			5421.26i			0.868652i	0.900756	+	0.434326i	$0.143013\pi$
$79$			5421.26i			0.868652i	−0.900756	+	0.434326i	$0.856987\pi$
$80$	839.321	+	1226.34i	0.131144	+	0.191616i
$81$	6462.85			0.985040
$82$	−409.630	−	679.131i	−0.0609206	−	0.101001i
$83$		−	9432.85i		−	1.36926i	−0.728890	−	0.684631i	$-0.759963\pi$
$83$		−	9432.85i		−	1.36926i	0.728890	−	0.684631i	$-0.240037\pi$
$84$	−252.156	+	478.136i	−0.0357364	+	0.0677630i
$85$	1930.05			0.267134
$86$	3097.95	−	1868.58i	0.418868	−	0.252648i
$87$		−	766.612i		−	0.101283i
$88$	−5.64564	−	98.1786i	−0.000729034	−	0.0126780i
$89$	9486.28			1.19761			0.598805	−	0.800894i	$-0.295642\pi$
$89$	9486.28			1.19761			0.598805	+	0.800894i	$0.295642\pi$
$90$	966.558	+	1602.47i	0.119328	+	0.197836i
$91$			8543.31i			1.03168i
$92$	−73.5596	−	38.7933i	−0.00869088	−	0.00458333i
$93$	−109.786			−0.0126935
$94$	−12131.4	+	7317.25i	−1.37295	+	0.828118i
$95$		−	38.5914i		−	0.00427606i
$96$	−592.621	−	270.258i	−0.0643035	−	0.0293249i
$97$	−8168.28			−0.868135			−0.434068	−	0.900880i	$-0.642922\pi$
$97$	−8168.28			−0.868135			−0.434068	+	0.900880i	$0.642922\pi$
$98$	867.985	+	1439.04i	0.0903774	+	0.149838i
$99$		−	123.841i		−	0.0126355i
$100$	4413.28	−	8368.43i	0.441328	−	0.836843i
$101$	−7971.18			−0.781411			−0.390706	−	0.920516i	$-0.627769\pi$
$101$	−7971.18			−0.781411			−0.390706	+	0.920516i	$0.627769\pi$
$102$	−724.368	+	436.916i	−0.0696240	+	0.0419950i
$103$			13095.9i			1.23442i	0.786800	+	0.617208i	$0.211736\pi$
$103$			13095.9i			1.23442i	−0.786800	+	0.617208i	$0.788264\pi$
$104$	−10277.3	+	590.981i	−0.950190	+	0.0546395i
$105$	−196.116			−0.0177883
$106$	4920.66	+	8158.02i	0.437937	+	0.726061i
$107$		−	3122.08i		−	0.272695i	−0.990661	−	0.136347i	$-0.956464\pi$
$107$		−	3122.08i		−	0.272695i	0.990661	−	0.136347i	$-0.0435363\pi$
$108$	−1454.68	−	767.160i	−0.124716	−	0.0657716i
$109$	10920.2			0.919128			0.459564	−	0.888145i	$-0.348006\pi$
$109$	10920.2			0.919128			0.459564	+	0.888145i	$0.348006\pi$
$110$	30.5515	−	18.4277i	0.00252492	−	0.00152295i
$111$		−	649.254i		−	0.0526949i
$112$	−11220.9	+	7679.69i	−0.894523	+	0.612220i
$113$	−12000.1			−0.939782			−0.469891	−	0.882724i	$-0.655707\pi$
$113$	−12000.1			−0.939782			−0.469891	+	0.882724i	$0.655707\pi$
$114$	8.73616	+	14.4838i	0.000672219	+	0.00111448i
$115$		−	30.1718i		−	0.00228142i
$116$	8995.42	−	17057.1i	0.668507	−	1.26762i
$117$	−12963.6			−0.947006
$118$	6900.06	−	4161.90i	0.495552	−	0.298901i
$119$			17659.7i			1.24707i
$120$	−13.5663	−	235.920i	−0.000942105	−	0.0163833i
$121$	14638.6			0.999839
$122$	3124.05	+	5179.41i	0.209893	+	0.347985i
$123$			126.118i			0.00833616i
$124$	−2442.74	−	1288.23i	−0.158867	−	0.0837820i
$125$	7060.54			0.451875
$126$	−14662.4	+	8843.89i	−0.923558	+	0.557061i
$127$			9620.22i			0.596455i	0.954495	+	0.298227i	$0.0963954\pi$
$127$			9620.22i			0.596455i	−0.954495	+	0.298227i	$0.903605\pi$
$128$	−10014.6	−	12967.0i	−0.611240	−	0.791445i
$129$	−575.303			−0.0345714
$130$	−1929.00	−	3198.11i	−0.114142	−	0.189237i
$131$		−	7587.58i		−	0.442141i	−0.975258	−	0.221070i	$-0.929045\pi$
$131$		−	7587.58i		−	0.442141i	0.975258	−	0.221070i	$-0.0709551\pi$
$132$	−7.29475	+	13.8323i	−0.000418661	+	0.000793862i
$133$	353.107			0.0199620
$134$	−5226.17	+	3152.26i	−0.291054	+	0.175555i
$135$		−	596.666i		−	0.0327389i
$136$	−21243.9	+	1221.60i	−1.14857	+	0.0660470i
$137$	6273.69			0.334258			0.167129	−	0.985935i	$-0.446550\pi$
$137$	6273.69			0.334258			0.167129	+	0.985935i	$0.446550\pi$
$138$	6.83018	+	11.3238i	0.000358652	+	0.000594615i
$139$			36350.5i			1.88140i	0.339243	+	0.940699i	$0.389829\pi$
$139$			36350.5i			1.88140i	−0.339243	+	0.940699i	$0.610171\pi$
$140$	−4363.57	−	2301.23i	−0.222631	−	0.117410i
$141$	2252.85			0.113317
$142$	−30444.3	+	18363.0i	−1.50983	+	0.910684i
$143$			247.154i			0.0120864i
$144$	−11653.1	−	17026.5i	−0.561975	−	0.821109i
$145$	6996.27			0.332760
$146$	6583.71	+	10915.2i	0.308862	+	0.512067i
$147$		−	267.237i		−	0.0123669i
$148$	7618.35	−	14445.9i	0.347806	−	0.659508i
$149$	41934.6			1.88886			0.944431	−	0.328710i	$-0.106614\pi$
$149$	41934.6			1.88886			0.944431	+	0.328710i	$0.106614\pi$
$150$	−1288.24	+	777.028i	−0.0572553	+	0.0345346i
$151$		−	32613.9i		−	1.43037i	−0.698935	−	0.715185i	$-0.746342\pi$
$151$		−	32613.9i		−	1.43037i	0.698935	−	0.715185i	$-0.253658\pi$
$152$	24.4261	+	424.773i	0.00105722	+	0.0183853i
$153$	−26796.7			−1.14472
$154$	168.611	+	279.543i	0.00710960	+	0.0117871i
$155$		−	1001.93i		−	0.0417038i
$156$	1447.95	+	763.609i	0.0594983	+	0.0313777i
$157$	−6574.45			−0.266723			−0.133361	−	0.991067i	$-0.542577\pi$
$157$	−6574.45			−0.266723			−0.133361	+	0.991067i	$0.542577\pi$
$158$	18568.8	−	11200.1i	0.743822	−	0.448649i
$159$		−	1514.98i		−	0.0599257i
$160$	2466.44	−	5408.39i	0.0963452	−	0.211265i
$161$	276.069			0.0106504
$162$	−13352.0	−	22136.4i	−0.508762	−	0.843484i
$163$		−	9055.38i		−	0.340825i	−0.985373	−	0.170412i	$-0.945490\pi$
$163$		−	9055.38i		−	0.340825i	0.985373	−	0.170412i	$-0.0545100\pi$
$164$	−1479.87	+	2806.11i	−0.0550218	+	0.104332i
$165$	−5.67356			−0.000208395
$166$	−32309.2	+	19487.8i	−1.17249	+	0.707209i
$167$		−	38486.4i		−	1.37998i	−0.723817	−	0.689992i	$-0.757614\pi$
$167$		−	38486.4i		−	1.37998i	0.723817	−	0.689992i	$-0.242386\pi$
$168$	2158.64	−	124.130i	0.0764825	−	0.00439803i
$169$	−2689.12			−0.0941536
$170$	−3987.39	−	6610.74i	−0.137972	−	0.228745i
$171$			535.802i			0.0183237i
$172$	−12800.4	−	6750.60i	−0.432681	−	0.228184i
$173$	18422.6			0.615544			0.307772	−	0.951460i	$-0.400417\pi$
$173$	18422.6			0.615544			0.307772	+	0.951460i	$0.400417\pi$
$174$	−2625.78	+	1583.79i	−0.0867282	+	0.0523116i
$175$			31406.7i			1.02552i
$176$	−324.615	+	222.170i	−0.0104796	+	0.00717233i
$177$	−1281.37			−0.0409006
$178$	−19598.2	−	32492.2i	−0.618553	−	1.02551i
$179$			36685.6i			1.14496i	0.819919	+	0.572479i	$0.194018\pi$
$179$			36685.6i			1.14496i	−0.819919	+	0.572479i	$0.805982\pi$
$180$	3491.87	−	6621.26i	0.107774	−	0.204360i
$181$	−6275.49			−0.191554			−0.0957769	−	0.995403i	$-0.530534\pi$
$181$	−6275.49			−0.191554			−0.0957769	+	0.995403i	$0.530534\pi$
$182$	29262.3	−	17650.1i	0.883418	−	0.532849i
$183$		−	961.841i		−	0.0287211i
$184$	19.0970	+	332.100i	0.000564065	+	0.00980918i
$185$	5925.24			0.173126
$186$	226.814	+	376.037i	0.00655607	+	0.0108694i
$187$			510.887i			0.0146097i
$188$	50125.8	+	26434.9i	1.41823	+	0.747933i
$189$	5459.42			0.152835
$190$	−132.182	+	79.7282i	−0.00366156	+	0.00220854i
$191$			24646.7i			0.675602i	0.941217	+	0.337801i	$0.109683\pi$
$191$			24646.7i			0.675602i	−0.941217	+	0.337801i	$0.890317\pi$
$192$	298.647	+	2588.17i	0.00810132	+	0.0702087i
$193$	38577.0			1.03565			0.517826	−	0.855486i	$-0.326742\pi$
$193$	38577.0			1.03565			0.517826	+	0.855486i	$0.326742\pi$
$194$	16875.3	+	27977.8i	0.448382	+	0.743379i
$195$			593.904i			0.0156188i
$196$	3135.76	−	5946.00i	0.0816263	−	0.154779i
$197$	−5764.78			−0.148542			−0.0742712	−	0.997238i	$-0.523663\pi$
$197$	−5764.78			−0.148542			−0.0742712	+	0.997238i	$0.523663\pi$
$198$	−424.177	+	255.850i	−0.0108197	+	0.00652612i
$199$		−	31698.8i		−	0.800456i	−0.916416	−	0.400228i	$-0.868931\pi$
$199$		−	31698.8i		−	0.800456i	0.916416	−	0.400228i	$-0.131069\pi$
$200$	−37781.0	+	2172.55i	−0.944524	+	0.0543137i
$201$	970.524			0.0240223
$202$	16468.1	+	27302.7i	0.403590	+	0.669118i
$203$			64015.1i			1.55342i
$204$	2993.03	+	1578.44i	0.0719201	+	0.0379287i
$205$	−1150.98			−0.0273880
$206$	44855.8	−	27055.6i	1.05702	−	0.637562i
$207$			418.905i			0.00977631i
$208$	23256.6	+	33980.5i	0.537550	+	0.785421i
$209$	10.2152			0.000233860
$210$	405.168	+	671.733i	0.00918748	+	0.0152320i
$211$			5552.62i			0.124719i	0.998054	+	0.0623596i	$0.0198626\pi$
$211$			5552.62i			0.124719i	−0.998054	+	0.0623596i	$0.980137\pi$
$212$	17776.8	−	33708.2i	0.395532	−	0.750005i
$213$	5653.65			0.124615
$214$	−10693.7	+	6450.08i	−0.233507	+	0.140844i
$215$		−	5250.34i		−	0.113582i
$216$	377.654	+	6567.46i	0.00809444	+	0.140764i
$217$	9167.58			0.194686
$218$	−22560.6	−	37403.5i	−0.474719	−	0.787043i
$219$		−	2027.01i		−	0.0422636i
$220$	−126.236	−	66.5735i	−0.00260819	−	0.00137549i
$221$	53479.2			1.09497
$222$	−2223.81	+	1341.33i	−0.0451224	+	0.0272164i
$223$		−	46531.3i		−	0.935697i	−0.883809	−	0.467848i	$-0.845029\pi$
$223$		−	46531.3i		−	0.935697i	0.883809	−	0.467848i	$-0.154971\pi$
$224$	49486.2	+	22567.6i	0.986251	+	0.449769i
$225$	−47656.3			−0.941359
$226$	24791.6	+	41102.4i	0.485387	+	0.804730i
$227$		−	55225.6i		−	1.07174i	−0.844301	−	0.535869i	$-0.819984\pi$
$227$		−	55225.6i		−	1.07174i	0.844301	−	0.535869i	$-0.180016\pi$
$228$	31.5610	−	59.8458i	0.000607130	−	0.00115123i
$229$	−7371.68			−0.140571			−0.0702855	−	0.997527i	$-0.522391\pi$
$229$	−7371.68			−0.140571			−0.0702855	+	0.997527i	$0.522391\pi$
$230$	−103.344	+	62.3337i	−0.00195357	+	0.00117833i
$231$		−	51.9124i		−	0.000972853i
$232$	−77007.6	+	4428.23i	−1.43073	+	0.0822723i
$233$	67789.7			1.24868			0.624341	−	0.781152i	$-0.285367\pi$
$233$	67789.7			1.24868			0.624341	+	0.781152i	$0.285367\pi$
$234$	26782.1	+	44402.5i	0.489118	+	0.810915i
$235$			20560.0i			0.372296i
$236$	−28510.5	−	15035.6i	−0.511894	−	0.269959i
$237$	−3448.31			−0.0613916
$238$	60487.6	−	36484.2i	1.06785	−	0.644096i
$239$		−	80303.3i		−	1.40584i	−0.711267	−	0.702922i	$-0.751878\pi$
$239$		−	80303.3i		−	1.40584i	0.711267	−	0.702922i	$-0.248122\pi$
$240$	−780.041	+	533.868i	−0.0135424	+	0.00926854i
$241$	−89579.2			−1.54232			−0.771158	−	0.636644i	$-0.780322\pi$
$241$	−89579.2			−1.54232			−0.771158	+	0.636644i	$0.780322\pi$
$242$	−30242.8	−	50139.9i	−0.516406	−	0.856156i
$243$			12436.5i			0.210613i
$244$	11286.2	−	21400.9i	0.189570	−	0.359461i
$245$	2438.86			0.0406308
$246$	431.976	−	260.554i	0.00713821	−	0.00430554i
$247$		−	1069.32i		−	0.0175273i
$248$	634.165	+	11028.2i	0.0103110	+	0.179309i
$249$	5999.96			0.0967720
$250$	−14586.8	−	24183.6i	−0.233388	−	0.386938i
$251$		−	92459.7i		−	1.46759i	−0.679371	−	0.733795i	$-0.737747\pi$
$251$		−	92459.7i		−	1.46759i	0.679371	−	0.733795i	$-0.262253\pi$
$252$	60583.8	+	31950.2i	0.954015	+	0.503121i
$253$	7.98655			0.000124772
$254$	32950.9	−	19875.0i	0.510741	−	0.308062i
$255$			1227.65i			0.0188796i
$256$	−23724.7	+	61091.0i	−0.362011	+	0.932174i
$257$	−41810.0			−0.633014			−0.316507	−	0.948590i	$-0.602510\pi$
$257$	−41810.0			−0.633014			−0.316507	+	0.948590i	$0.602510\pi$
$258$	1188.55	+	1970.51i	0.0178558	+	0.0296033i
$259$			54215.2i			0.808206i
$260$	−6968.86	+	13214.3i	−0.103090	+	0.195478i
$261$	−97136.1			−1.42593
$262$	−25988.8	+	15675.6i	−0.378603	+	0.228361i
$263$		−	44370.0i		−	0.641472i	−0.947169	−	0.320736i	$-0.896070\pi$
$263$		−	44370.0i		−	0.641472i	0.947169	−	0.320736i	$-0.103930\pi$
$264$	62.4486	−	3.59103i	0.000896013	−	5.15242e-5i
$265$	13826.1			0.196882
$266$	−729.503	−	1209.45i	−0.0103101	−	0.0170933i
$267$			6033.94i			0.0846406i
$268$	21594.1	+	11388.1i	0.300653	+	0.158556i
$269$	−60959.7			−0.842439			−0.421219	−	0.906959i	$-0.638398\pi$
$269$	−60959.7			−0.842439			−0.421219	+	0.906959i	$0.638398\pi$
$270$	−2043.68	+	1232.68i	−0.0280341	+	0.0169093i
$271$		−	36264.2i		−	0.493787i	−0.969043	−	0.246894i	$-0.920590\pi$
$271$		−	36264.2i		−	0.493787i	0.969043	−	0.246894i	$-0.0794099\pi$
$272$	48073.2	+	70240.3i	0.649778	+	0.949399i
$273$	−5434.15			−0.0729132
$274$	−12961.2	−	21488.5i	−0.172641	−	0.286223i
$275$			908.581i			0.0120143i
$276$	24.6753	−	46.7891i	0.000323925	−	0.000614224i
$277$	−89408.9			−1.16526			−0.582628	−	0.812739i	$-0.697975\pi$
$277$	−89408.9			−1.16526			−0.582628	+	0.812739i	$0.697975\pi$
$278$	124507.	−	75098.5i	1.61103	−	0.971721i
$279$			13910.8i			0.178708i
$280$	1132.84	+	19700.2i	0.0144495	+	0.251279i
$281$	−53095.3			−0.672424			−0.336212	−	0.941786i	$-0.609146\pi$
$281$	−53095.3			−0.672424			−0.336212	+	0.941786i	$0.609146\pi$
$282$	−4654.29	−	7716.41i	−0.0585269	−	0.0970325i
$283$		−	2252.42i		−	0.0281240i	−0.999901	−	0.0140620i	$-0.995524\pi$
$283$		−	2252.42i		−	0.0281240i	0.999901	−	0.0140620i	$-0.00447622\pi$
$284$	125793.	+	66339.9i	1.55963	+	0.822504i
$285$	24.5469			0.000302208
$286$	846.546	−	510.609i	0.0103495	−	0.00624247i
$287$		−	10531.3i		−	0.127855i
$288$	−34244.0	+	75090.0i	−0.412856	+	0.905309i
$289$	27024.8			0.323569
$290$	−14454.0	−	23963.5i	−0.171867	−	0.284940i
$291$		−	5195.61i		−	0.0613551i
$292$	23784.9	−	45100.7i	0.278956	−	0.528954i
$293$	−139964.			−1.63035			−0.815175	−	0.579215i	$-0.803359\pi$
$293$	−139964.			−1.63035			−0.815175	+	0.579215i	$0.803359\pi$
$294$	−915.334	+	552.100i	−0.0105897	+	0.00638738i
$295$		−	11694.1i		−	0.134376i
$296$	−65218.7	+	3750.33i	−0.744370	+	0.0428041i
$297$	157.939			0.00179050
$298$	−86635.1	−	143633.i	−0.975576	−	1.61742i
$299$		−	836.025i		−	0.00935141i
$300$	5322.91	+	2807.16i	0.0591435	+	0.0311906i
$301$	48040.0			0.530237
$302$	−111708.	+	67378.8i	−1.22482	+	0.738771i
$303$		−	5070.23i		−	0.0552259i
$304$	1404.46	−	961.227i	0.0151972	−	0.0104011i
$305$	8777.97			0.0943614
$306$	55360.8	+	91783.4i	0.591234	+	0.980215i
$307$			154675.i			1.64113i	0.571554	+	0.820564i	$0.306341\pi$
$307$			154675.i			1.64113i	−0.571554	+	0.820564i	$0.693659\pi$
$308$	609.140	−	1155.05i	0.00642119	−	0.0121758i
$309$	−8329.93			−0.0872418
$310$	−3431.80	+	2069.95i	−0.0357107	+	0.0215396i
$311$			19235.1i			0.198872i	0.995044	+	0.0994359i	$0.0317038\pi$
$311$			19235.1i			0.198872i	−0.995044	+	0.0994359i	$0.968296\pi$
$312$	−375.906	−	6537.06i	−0.00386162	−	0.0671542i
$313$	85227.0			0.869938			0.434969	−	0.900445i	$-0.356759\pi$
$313$	85227.0			0.869938			0.434969	+	0.900445i	$0.356759\pi$
$314$	13582.5	+	22518.6i	0.137759	+	0.228393i
$315$			24849.6i			0.250437i
$316$	−76724.5	−	40462.4i	−0.768351	−	0.405207i
$317$	69536.6			0.691983			0.345991	−	0.938238i	$-0.387543\pi$
$317$	69536.6			0.691983			0.345991	+	0.938238i	$0.387543\pi$
$318$	−5189.08	+	3129.89i	−0.0513140	+	0.0309510i
$319$			1851.93i			0.0181988i
$320$	−23620.2	+	2725.52i	−0.230666	+	0.0266164i
$321$	1985.86			0.0192726
$322$	−570.346	−	945.584i	−0.00550081	−	0.00911987i
$323$		−	2210.37i		−	0.0211866i
$324$	−48236.5	+	91465.6i	−0.459500	+	0.871300i
$325$	95109.5			0.900445
$326$	−31016.3	+	18708.0i	−0.291846	+	0.176032i
$327$			6945.99i			0.0649589i
$328$	12668.8	−	728.502i	0.117757	−	0.00677147i
$329$	−188122.			−1.73799
$330$	11.7213	+	19.4329i	0.000107634	+	0.000178448i
$331$			97410.4i			0.889097i	0.895755	+	0.444549i	$0.146636\pi$
$331$			97410.4i			0.889097i	−0.895755	+	0.444549i	$0.853364\pi$
$332$	133499.	+	70403.5i	1.21116	+	0.638731i
$333$	−82265.9			−0.741876
$334$	−131823.	+	79511.2i	−1.18167	+	0.712747i
$335$			8857.22i			0.0789237i
$336$	−4884.83	−	7137.28i	−0.0432684	−	0.0632200i
$337$	10018.8			0.0882178			0.0441089	−	0.999027i	$-0.485955\pi$
$337$	10018.8			0.0882178			0.0441089	+	0.999027i	$0.485955\pi$
$338$	5555.60	+	9210.71i	0.0486293	+	0.0806231i
$339$		−	7632.90i		−	0.0664187i
$340$	−14405.2	+	27315.0i	−0.124612	+	0.236289i
$341$	265.214			0.00228080
$342$	1835.22	−	1106.94i	0.0156904	−	0.00946397i
$343$		−	105212.i		−	0.894290i
$344$	3323.16	+	57790.2i	0.0280824	+	0.488357i
$345$	19.1914			0.000161239
$346$	−38060.3	−	63100.7i	−0.317922	−	0.527087i
$347$		−	134616.i		−	1.11799i	−0.829171	−	0.558996i	$-0.811187\pi$
$347$		−	134616.i		−	1.11799i	0.829171	−	0.558996i	$-0.188813\pi$
$348$	10849.5	+	5721.73i	0.0895883	+	0.0472464i
$349$	−152495.			−1.25200			−0.625999	−	0.779824i	$-0.715309\pi$
$349$	−152495.			−1.25200			−0.625999	+	0.779824i	$0.715309\pi$
$350$	107573.	−	64884.8i	0.878150	−	0.529672i
$351$		−	16532.9i		−	0.134194i
$352$	1431.61	+	652.871i	0.0115542	+	0.00526917i
$353$	−9667.19			−0.0775802			−0.0387901	−	0.999247i	$-0.512350\pi$
$353$	−9667.19			−0.0775802			−0.0387901	+	0.999247i	$0.512350\pi$
$354$	2647.26	+	4388.93i	0.0211247	+	0.0350229i
$355$			51596.4i			0.409414i
$356$	−70802.3	+	134255.i	−0.558659	+	1.05933i
$357$	−11232.8			−0.0881358
$358$	125655.	−	75790.8i	0.980420	−	0.591358i
$359$			69641.2i			0.540353i	0.962811	+	0.270177i	$0.0870821\pi$
$359$			69641.2i			0.540353i	−0.962811	+	0.270177i	$0.912918\pi$
$360$	−29893.0	+	1718.96i	−0.230656	+	0.0132636i
$361$	130277.			0.999661
$362$	12964.9	+	21494.7i	0.0989354	+	0.164026i
$363$			9311.21i			0.0706632i
$364$	−120909.	−	63764.3i	−0.912551	−	0.481254i
$365$	18498.9			0.138855
$366$	−3294.47	+	1987.12i	−0.0245937	+	0.0148341i
$367$		−	129975.i		−	0.965003i	−0.875895	−	0.482501i	$-0.839728\pi$
$367$		−	129975.i		−	0.965003i	0.875895	−	0.482501i	$-0.160272\pi$
$368$	1098.05	−	751.514i	0.00810821	−	0.00554934i
$369$	15980.2			0.117362
$370$	−12241.3	−	20295.0i	−0.0894177	−	0.148247i
$371$			126507.i			0.919107i
$372$	819.407	−	1553.75i	0.00592125	−	0.0112278i
$373$	54138.0			0.389121			0.194560	−	0.980891i	$-0.437672\pi$
$373$	54138.0			0.389121			0.194560	+	0.980891i	$0.437672\pi$
$374$	1749.88	−	1055.47i	0.0125102	−	0.00754576i
$375$			4491.01i			0.0319360i
$376$	−13013.3	−	226303.i	−0.0920473	−	1.60072i
$377$	193858.			1.36396
$378$	−11278.9	−	18699.5i	−0.0789376	−	0.130872i
$379$			140812.i			0.980302i	0.871637	+	0.490151i	$0.163058\pi$
$379$			140812.i			0.980302i	−0.871637	+	0.490151i	$0.836942\pi$
$380$	546.166	+	288.033i	0.00378231	+	0.00199469i
$381$	−6119.14			−0.0421542
$382$	84419.1	−	50918.9i	0.578514	−	0.348941i
$383$		−	95064.3i		−	0.648067i	−0.946046	−	0.324033i	$-0.894961\pi$
$383$		−	95064.3i		−	0.648067i	0.946046	−	0.324033i	$-0.105039\pi$
$384$	8247.96	−	6369.97i	0.0559350	−	0.0431991i
$385$	473.764			0.00319625
$386$	−79698.3	−	132133.i	−0.534902	−	0.886822i
$387$			72895.6i			0.486720i
$388$	60965.2	−	115602.i	0.404966	−	0.767894i
$389$	187867.			1.24151			0.620756	−	0.784003i	$-0.286826\pi$
$389$	187867.			1.24151			0.620756	+	0.784003i	$0.286826\pi$
$390$	2034.22	−	1226.98i	0.0133743	−	0.00806692i
$391$		−	1728.13i		−	0.0113038i
$392$	−26844.4	+	1543.66i	−0.174696	+	0.0100457i
$393$	4826.24			0.0312481
$394$	11909.8	+	19745.4i	0.0767205	+	0.127196i
$395$		−	31470.0i		−	0.201698i
$396$	1752.66	+	924.305i	0.0111765	+	0.00589420i
$397$	244833.			1.55342			0.776709	−	0.629859i	$-0.216887\pi$
$397$	244833.			1.55342			0.776709	+	0.629859i	$0.216887\pi$
$398$	−108574.	+	65488.4i	−0.685425	+	0.413427i
$399$			224.601i			0.00141080i
$400$	85495.2	+	124918.i	0.534345	+	0.780738i
$401$	44516.6			0.276843			0.138421	−	0.990373i	$-0.455797\pi$
$401$	44516.6			0.276843			0.138421	+	0.990373i	$0.455797\pi$
$402$	−2005.06	−	3324.22i	−0.0124072	−	0.0205701i
$403$		−	27762.4i		−	0.170941i
$404$	59494.1	−	112812.i	0.364511	−	0.691184i
$405$	−37516.3			−0.228723
$406$	219263.	−	132252.i	1.33019	−	0.802327i
$407$			1568.42i			0.00946835i
$408$	−777.027	−	13512.6i	−0.00466784	−	0.0811745i
$409$	−93398.1			−0.558331			−0.279165	−	0.960243i	$-0.590058\pi$
$409$	−93398.1			−0.558331			−0.279165	+	0.960243i	$0.590058\pi$
$410$	2377.87	+	3942.30i	0.0141456	+	0.0234521i
$411$			3990.51i			0.0236235i
$412$	−185340.	−	97743.3i	−1.09188	−	0.575828i
$413$	107000.			0.627310
$414$	1434.82	−	865.440i	0.00837139	−	0.00504936i
$415$			54756.9i			0.317938i
$416$	68342.0	−	149860.i	0.394912	−	0.865962i
$417$	−23121.5			−0.132967
$418$	−21.1042	−	34.9889i	−0.000120786	−	0.000200253i
$419$			287385.i			1.63695i	0.574540	+	0.818477i	$0.305181\pi$
$419$			287385.i			1.63695i	−0.574540	+	0.818477i	$0.694819\pi$
$420$	1463.75	−	2775.54i	0.00829787	−	0.0157344i
$421$	156527.			0.883130			0.441565	−	0.897229i	$-0.354423\pi$
$421$	156527.			0.883130			0.441565	+	0.897229i	$0.354423\pi$
$422$	19018.7	−	11471.5i	0.106796	−	0.0644160i
$423$		−	285455.i		−	1.59535i
$424$	−152183.	+	8751.08i	−0.846513	+	0.0486777i
$425$	196599.			1.08844
$426$	−11680.2	−	19364.7i	−0.0643622	−	0.106707i
$427$			80317.4i			0.440508i
$428$	44185.3	+	23302.1i	0.241207	+	0.127206i
$429$	−157.208			−0.000854198
$430$	−17983.3	+	10847.0i	−0.0972598	+	0.0586640i
$431$		−	14253.0i		−	0.0767274i	−0.999264	−	0.0383637i	$-0.987785\pi$
$431$		−	14253.0i		−	0.0767274i	0.999264	−	0.0383637i	$-0.0122145\pi$
$432$	21714.5	−	14861.6i	0.116354	−	0.0796340i
$433$	288396.			1.53820			0.769102	−	0.639126i	$-0.220704\pi$
$433$	288396.			1.53820			0.769102	+	0.639126i	$0.220704\pi$
$434$	−18939.8	−	31400.6i	−0.100553	−	0.166709i
$435$			4450.13i			0.0235176i
$436$	−81504.2	+	154548.i	−0.428753	+	0.812999i
$437$	−34.5541			−0.000180941
$438$	−6942.85	+	4187.71i	−0.0361901	+	0.0218287i
$439$		−	259997.i		−	1.34909i	−0.738236	−	0.674543i	$-0.764341\pi$
$439$		−	259997.i		−	1.34909i	0.738236	−	0.674543i	$-0.235659\pi$
$440$	32.7725	+	569.919i	0.000169280	+	0.00294380i
$441$	−33861.1			−0.174110
$442$	−110486.	−	183176.i	−0.565538	−	0.937613i
$443$		−	135084.i		−	0.688329i	−0.938909	−	0.344164i	$-0.888162\pi$
$443$		−	135084.i		−	0.688329i	0.938909	−	0.344164i	$-0.111838\pi$
$444$	9188.59	+	4845.81i	0.0466104	+	0.0245810i
$445$	−55067.1			−0.278082
$446$	−159378.	+	96131.6i	−0.801231	+	0.483277i
$447$			26673.4i			0.133494i
$448$	−24938.2	−	216122.i	−0.124254	−	1.07682i
$449$	−154156.			−0.764658			−0.382329	−	0.924026i	$-0.624878\pi$
$449$	−154156.			−0.764658			−0.382329	+	0.924026i	$0.624878\pi$
$450$	98455.8	+	163231.i	0.486202	+	0.806080i
$451$		−	304.666i		−	0.00149786i
$452$	89564.4	−	169831.i	0.438388	−	0.831268i
$453$	20744.7			0.101091
$454$	−189157.	+	114094.i	−0.917723	+	0.553541i
$455$		−	49593.2i		−	0.239552i
$456$	−270.186	+	15.5367i	−0.00129937	+	7.47188e-5i
$457$	−208699.			−0.999283			−0.499642	−	0.866232i	$-0.666535\pi$
$457$	−208699.			−0.999283			−0.499642	+	0.866232i	$0.666535\pi$
$458$	15229.6	+	25249.3i	0.0726033	+	0.120370i
$459$		−	34174.8i		−	0.162211i
$460$	427.008	+	225.192i	0.00201799	+	0.00106423i
$461$	193081.			0.908526			0.454263	−	0.890868i	$-0.349903\pi$
$461$	193081.			0.908526			0.454263	+	0.890868i	$0.349903\pi$
$462$	−177.809	+	107.249i	−0.000833048	+	0.000502468i
$463$		−	105034.i		−	0.489970i	−0.969527	−	0.244985i	$-0.921217\pi$
$463$		−	105034.i		−	0.489970i	0.969527	−	0.244985i	$-0.0787830\pi$
$464$	174262.	+	254616.i	0.809405	+	1.18263i
$465$	637.301			0.00294740
$466$	−140051.	−	232192.i	−0.644931	−	1.06924i
$467$			185770.i			0.851808i	0.904768	+	0.425904i	$0.140044\pi$
$467$			185770.i			0.851808i	−0.904768	+	0.425904i	$0.859956\pi$
$468$	96755.5	−	183467.i	0.441758	−	0.837657i
$469$	−81042.5			−0.368440
$470$	70421.7	−	42476.1i	0.318794	−	0.192287i
$471$		−	4181.82i		−	0.0188505i
$472$	7401.67	+	128716.i	0.0332235	+	0.577763i
$473$	1389.78			0.00621187
$474$	7124.05	+	11811.1i	0.0317081	+	0.0525693i
$475$		−	3931.01i		−	0.0174228i
$476$	−249929.	−	131806.i	−1.10307	−	0.581729i
$477$	−191961.			−0.843676
$478$	−275053.	+	165903.i	−1.20382	+	0.726103i
$479$		−	73504.2i		−	0.320362i	−0.987088	−	0.160181i	$-0.948792\pi$
$479$		−	73504.2i		−	0.320362i	0.987088	−	0.160181i	$-0.0512078\pi$
$480$	3440.12	+	1568.83i	0.0149311	+	0.00680915i
$481$	164181.			0.709632
$482$	185067.	+	306825.i	0.796589	+	1.32068i
$483$			175.599i			0.000752712i
$484$	−109258.	+	207174.i	−0.466403	+	0.884390i
$485$	47416.3			0.201578
$486$	42597.2	−	25693.3i	0.180347	−	0.108779i
$487$			408751.i			1.72346i	0.507368	+	0.861729i	$0.330618\pi$
$487$			408751.i			1.72346i	−0.507368	+	0.861729i	$0.669382\pi$
$488$	−96618.6	+	5555.93i	−0.405715	+	0.0233301i
$489$	5759.86			0.0240877
$490$	−5038.58	−	8353.53i	−0.0209854	−	0.0347919i
$491$			145311.i			0.602750i	0.953506	+	0.301375i	$0.0974455\pi$
$491$			145311.i			0.602750i	−0.953506	+	0.301375i	$0.902554\pi$
$492$	−1784.89	−	941.299i	−0.00737361	−	0.00388864i
$493$	400720.			1.64872
$494$	−3662.61	+	2209.17i	−0.0150085	+	0.00905264i
$495$			718.887i			0.00293393i
$496$	36463.5	−	24956.0i	0.148216	−	0.101440i
$497$	−472101.			−1.91127
$498$	−12395.7	−	20550.9i	−0.0499817	−	0.0828653i
$499$			477015.i			1.91572i	0.287243	+	0.957858i	$0.407261\pi$
$499$			477015.i			1.91572i	−0.287243	+	0.957858i	$0.592739\pi$
$500$	−52697.4	+	99924.5i	−0.210790	+	0.399698i
$501$	24480.1			0.0975297
$502$	−316691.	+	191018.i	−1.25669	+	0.757994i
$503$		−	72213.7i		−	0.285419i	−0.989765	−	0.142710i	$-0.954418\pi$
$503$		−	72213.7i		−	0.285419i	0.989765	−	0.142710i	$-0.0455815\pi$
$504$	−15728.3	−	273518.i	−0.0619186	−	1.07677i
$505$	46272.1			0.181441
$506$	−16.4999	−	27.3553i	−6.44435e−5	−	0.000106842i
$507$		−	1710.47i		−	0.00665426i
$508$	−136150.	−	71802.0i	−0.527584	−	0.278233i
$509$	−22857.7			−0.0882261			−0.0441130	−	0.999027i	$-0.514046\pi$
$509$	−22857.7			−0.0882261			−0.0441130	+	0.999027i	$0.514046\pi$
$510$	4204.90	−	2536.26i	0.0161665	−	0.00975111i
$511$			169263.i			0.648216i
$512$	258261.	−	44949.8i	0.985189	−	0.171470i
$513$	−683.327			−0.00259653
$514$	86377.5	+	143206.i	0.326945	+	0.542046i
$515$		−	76020.8i		−	0.286627i
$516$	4293.86	−	8141.99i	0.0161268	−	0.0305796i
$517$	−5442.28			−0.0203610
$518$	185697.	−	112006.i	0.692062	−	0.417429i
$519$			11718.1i			0.0435033i
$520$	59658.7	−	3430.60i	0.220631	−	0.0126871i
$521$	−500171.			−1.84265			−0.921325	−	0.388794i	$-0.872892\pi$
$521$	−500171.			−1.84265			−0.921325	+	0.388794i	$0.872892\pi$
$522$	200679.	+	332708.i	0.736479	+	1.22102i
$523$			225160.i			0.823168i	0.911372	+	0.411584i	$0.135024\pi$
$523$			225160.i			0.823168i	−0.911372	+	0.411584i	$0.864976\pi$
$524$	107383.	+	56631.1i	0.391088	+	0.206249i
$525$	−19976.9			−0.0724785
$526$	−151975.	+	91666.4i	−0.549288	+	0.331313i
$527$		−	57387.0i		−	0.206630i
$528$	−141.316	−	206.478i	−0.000506901	−	0.000740639i
$529$	279814.			0.999903
$530$	−28564.0	−	47356.7i	−0.101688	−	0.168589i
$531$			162361.i			0.575826i
$532$	−2635.47	+	4997.35i	−0.00931182	+	0.0176570i
$533$	−31892.2			−0.112261
$534$	20667.3	−	12465.9i	0.0724772	−	0.0437159i
$535$			18123.4i			0.0633188i
$536$	−5606.09	−	97490.9i	−0.0195133	−	0.339339i
$537$	−23334.6			−0.0809194
$538$	125940.	+	208798.i	0.435110	+	0.721375i
$539$			645.572i			0.00222212i
$540$	8444.32	+	4453.30i	0.0289586	+	0.0152720i
$541$	−426337.			−1.45666			−0.728331	−	0.685226i	$-0.759704\pi$
$541$	−426337.			−1.45666			−0.728331	+	0.685226i	$0.759704\pi$
$542$	−124211.	+	74920.3i	−0.422827	+	0.255036i
$543$		−	3991.66i		−	0.0135380i
$544$	141268.	−	309772.i	0.477361	−	1.04675i
$545$	−63390.7			−0.213419
$546$	11226.7	+	18612.9i	0.0376589	+	0.0624351i
$547$		−	359756.i		−	1.20236i	−0.799115	−	0.601178i	$-0.794698\pi$
$547$		−	359756.i		−	1.20236i	0.799115	−	0.601178i	$-0.205302\pi$
$548$	−46824.7	+	88788.6i	−0.155924	+	0.295662i
$549$	−121873.			−0.404355
$550$	3112.05	−	1877.09i	0.0102878	−	0.00620525i
$551$		−	8012.43i		−	0.0263913i
$552$	−211.239	+	12.1470i	−0.000693260	+	3.98651e-5i
$553$	287947.			0.941590
$554$	184715.	+	306241.i	0.601841	+	0.997801i
$555$			3768.87i			0.0122356i
$556$	−514451.	−	271307.i	−1.66416	−	0.877631i
$557$	−402974.			−1.29887			−0.649436	−	0.760416i	$-0.724995\pi$
$557$	−402974.			−1.29887			−0.649436	+	0.760416i	$0.724995\pi$
$558$	47647.0	−	28739.2i	0.153027	−	0.0923008i
$559$		−	145481.i		−	0.465566i
$560$	65136.4	−	44580.0i	0.207705	−	0.142156i
$561$	−324.960			−0.00103253
$562$	109693.	+	181861.i	0.347300	+	0.575793i
$563$		−	326194.i		−	1.02910i	−0.857459	−	0.514552i	$-0.827958\pi$
$563$		−	326194.i		−	1.02910i	0.857459	−	0.514552i	$-0.172042\pi$
$564$	−16814.5	+	31883.5i	−0.0528598	+	0.100232i
$565$	69659.5			0.218215
$566$	−7714.95	+	4653.41i	−0.0240824	+	0.0145257i
$567$		−	343270.i		−	1.06775i
$568$	−32657.5	−	567919.i	−0.101225	−	1.76031i
$569$	−457864.			−1.41420			−0.707102	−	0.707112i	$-0.749998\pi$
$569$	−457864.			−1.41420			−0.707102	+	0.707112i	$0.749998\pi$
$570$	−50.7128	−	84.0773i	−0.000156087	−	0.000258779i
$571$		−	169889.i		−	0.521068i	−0.965465	−	0.260534i	$-0.916101\pi$
$571$		−	169889.i		−	0.521068i	0.965465	−	0.260534i	$-0.0838986\pi$
$572$	−3497.85	−	1844.67i	−0.0106908	−	0.00563803i
$573$	−15677.0			−0.0477479
$574$	−36071.6	+	21757.3i	−0.109482	+	0.0660359i
$575$		−	3073.37i		−	0.00929565i
$576$	327943.	−	37841.0i	0.988446	−	0.114056i
$577$	14490.7			0.0435249			0.0217624	−	0.999763i	$-0.493072\pi$
$577$	14490.7			0.0435249			0.0217624	+	0.999763i	$0.493072\pi$
$578$	−55832.1	−	92564.7i	−0.167120	−	0.277070i
$579$			24537.7i			0.0731942i
$580$	−52217.7	+	99014.9i	−0.155225	+	0.294337i
$581$	−501020.			−1.48423
$582$	−17795.9	+	10733.9i	−0.0525380	+	0.0316892i
$583$			3659.79i			0.0107676i
$584$	−203616.	+	11708.7i	−0.597018	+	0.0343308i
$585$	75252.5			0.219892
$586$	289159.	+	479401.i	0.842058	+	1.39606i
$587$		−	3759.62i		−	0.0109111i	−0.999985	−	0.00545554i	$-0.998263\pi$
$587$		−	3759.62i		−	0.0109111i	0.999985	−	0.00545554i	$-0.00173656\pi$
$588$	3782.08	+	1994.56i	0.0109390	+	0.00576890i
$589$	−1147.46			−0.00330755
$590$	−40054.3	+	24159.5i	−0.115066	+	0.0694039i
$591$		−	3666.81i		−	0.0104982i
$592$	147585.	+	215638.i	0.421112	+	0.615292i
$593$	−382173.			−1.08680			−0.543401	−	0.839473i	$-0.682864\pi$
$593$	−382173.			−1.08680			−0.543401	+	0.839473i	$0.682864\pi$
$594$	−326.294	−	540.967i	−0.000924776	−	0.00153320i
$595$		−	102513.i		−	0.289565i
$596$	−312985.	+	593481.i	−0.881113	+	1.67076i
$597$	20162.7			0.0565719
$598$	−2863.53	+	1727.19i	−0.00800755	+	0.00482990i
$599$		−	643342.i		−	1.79303i	−0.443010	−	0.896517i	$-0.646089\pi$
$599$		−	643342.i		−	1.79303i	0.443010	−	0.896517i	$-0.353911\pi$
$600$	−1381.90	−	24031.4i	−0.00383860	−	0.0667538i
$601$	−240035.			−0.664547			−0.332273	−	0.943183i	$-0.607816\pi$
$601$	−240035.			−0.664547			−0.332273	+	0.943183i	$0.607816\pi$
$602$	−99248.6	−	164546.i	−0.273862	−	0.454039i
$603$		−	122973.i		−	0.338202i
$604$	461569.	+	243419.i	1.26521	+	0.667237i
$605$	−84976.2			−0.232159
$606$	−17366.4	+	10474.9i	−0.0472896	+	0.0285236i
$607$		−	480843.i		−	1.30505i	−0.757768	−	0.652524i	$-0.773710\pi$
$607$		−	480843.i		−	1.30505i	0.757768	−	0.652524i	$-0.226290\pi$
$608$	−6193.92	−	2824.67i	−0.0167555	−	0.00764118i
$609$	−40718.1			−0.109788
$610$	−18134.9	−	30066.1i	−0.0487366	−	0.0808011i
$611$			569693.i			1.52601i
$612$	200001.	−	379241.i	0.533986	−	1.01254i
$613$	517109.			1.37613			0.688067	−	0.725647i	$-0.258459\pi$
$613$	517109.			1.37613			0.688067	+	0.725647i	$0.258459\pi$
$614$	529788.	−	319551.i	1.40529	−	0.847625i
$615$		−	732.104i		−	0.00193563i
$616$	−5214.70	+	299.865i	−0.0137426	+	0.000790249i
$617$	202878.			0.532924			0.266462	−	0.963845i	$-0.414145\pi$
$617$	202878.			0.532924			0.266462	+	0.963845i	$0.414145\pi$
$618$	17209.3	+	28531.5i	0.0450594	+	0.0747046i
$619$			643253.i			1.67881i	0.543510	+	0.839403i	$0.317095\pi$
$619$			643253.i			1.67881i	−0.543510	+	0.839403i	$0.682905\pi$
$620$	14179.9	+	7478.08i	0.0368884	+	0.0194539i
$621$	−534.244			−0.00138534
$622$	65883.5	−	39738.8i	0.170293	−	0.102715i
$623$		−	503858.i		−	1.29817i
$624$	−21614.0	+	14792.8i	−0.0555093	+	0.0379911i
$625$	328578.			0.841161
$626$	−176075.	−	291917.i	−0.449313	−	0.744923i
$627$			6.49761i			1.65279e-5i
$628$	49069.4	−	93045.0i	0.124420	−	0.235925i
$629$	339375.			0.857786
$630$	85114.1	−	51338.1i	0.214447	−	0.129348i
$631$			122797.i			0.308412i	0.988039	+	0.154206i	$0.0492819\pi$
$631$			122797.i			0.308412i	−0.988039	+	0.154206i	$0.950718\pi$
$632$	19918.6	+	346388.i	0.0498684	+	0.867220i
$633$	−3531.86			−0.00881447
$634$	−143660.	−	238175.i	−0.357401	−	0.592540i
$635$		−	55844.6i		−	0.138495i
$636$	21440.8	+	11307.3i	0.0530063	+	0.0279540i
$637$	67578.0			0.166543
$638$	6343.18	−	3826.00i	0.0155835	−	0.00939948i
$639$		−	716364.i		−	1.75441i
$640$	58133.7	+	75272.6i	0.141928	+	0.183771i
$641$	198793.			0.483821			0.241910	−	0.970299i	$-0.422226\pi$
$641$	198793.			0.483821			0.241910	+	0.970299i	$0.422226\pi$
$642$	−4102.71	−	6801.93i	−0.00995407	−	0.0165030i
$643$		−	58173.1i		−	0.140702i	−0.997522	−	0.0703510i	$-0.977588\pi$
$643$		−	58173.1i		−	0.140702i	0.997522	−	0.0703510i	$-0.0224119\pi$
$644$	−2060.48	+	3907.07i	−0.00496818	+	0.00942062i
$645$	3339.59			0.00802738
$646$	−7570.91	+	4566.53i	−0.0181419	+	0.0109426i
$647$			518018.i			1.23747i	0.785598	+	0.618737i	$0.212355\pi$
$647$			518018.i			1.23747i	−0.785598	+	0.618737i	$0.787645\pi$
$648$	412940.	−	23745.6i	0.983416	−	0.0565501i
$649$	3095.45			0.00734911
$650$	−196492.	−	325767.i	−0.465070	−	0.771046i
$651$			5831.23i			0.0137594i
$652$	128156.	+	67586.2i	0.301471	+	0.158987i
$653$	80622.4			0.189073			0.0945365	−	0.995521i	$-0.469863\pi$
$653$	80622.4			0.189073			0.0945365	+	0.995521i	$0.469863\pi$
$654$	23791.2	−	14350.1i	0.0556239	−	0.0335506i
$655$			44045.3i			0.102664i
$656$	−28668.3	−	41887.7i	−0.0666185	−	0.0973371i
$657$	−256838.			−0.595017
$658$	388651.	+	644350.i	0.897653	+	1.48823i
$659$			270521.i			0.622917i	0.950260	+	0.311459i	$0.100818\pi$
$659$			270521.i			0.622917i	−0.950260	+	0.311459i	$0.899182\pi$
$660$	42.3455	−	80.2952i	9.72119e−5	−	0.000184332i
$661$	−147037.			−0.336531			−0.168265	−	0.985742i	$-0.553817\pi$
$661$	−147037.			−0.336531			−0.168265	+	0.985742i	$0.553817\pi$
$662$	333648.	−	201246.i	0.761328	−	0.459209i
$663$			34016.6i			0.0773862i
$664$	−34657.9	−	602707.i	−0.0786079	−	1.36700i
$665$	−2049.76			−0.00463510
$666$	169958.	+	281775.i	0.383171	+	0.635264i
$667$		−	6264.34i		−	0.0140807i
$668$	544679.	+	287249.i	1.22064	+	0.643732i
$669$	29597.2			0.0661300
$670$	30337.5	−	18298.6i	0.0675819	−	0.0407632i
$671$			2323.55i			0.00516067i
$672$	−14354.6	+	31476.7i	−0.0317872	+	0.0697029i
$673$	439396.			0.970122			0.485061	−	0.874480i	$-0.338797\pi$
$673$	439396.			0.970122			0.485061	+	0.874480i	$0.338797\pi$
$674$	−20698.4	−	34316.2i	−0.0455635	−	0.0755403i
$675$		−	60777.7i		−	0.133394i
$676$	20070.7	−	38057.8i	0.0439206	−	0.0832819i
$677$	−821336.			−1.79202			−0.896011	−	0.444031i	$-0.853548\pi$
$677$	−821336.			−1.79202			−0.896011	+	0.444031i	$0.853548\pi$
$678$	−26144.0	+	15769.2i	−0.0568739	+	0.0343045i
$679$			433853.i			0.941030i
$680$	123319.	−	7091.32i	0.266694	−	0.0153359i
$681$	35127.4			0.0757446
$682$	−547.920	−	908.404i	−0.00117801	−	0.00195304i
$683$		−	64432.2i		−	0.138122i	−0.997612	−	0.0690608i	$-0.978000\pi$
$683$		−	64432.2i		−	0.138122i	0.997612	−	0.0690608i	$-0.0220002\pi$
$684$	−7582.95	−	3999.04i	−0.0162079	−	0.00854759i
$685$	−36418.3			−0.0776137
$686$	−360371.	+	217364.i	−0.765775	+	0.461891i
$687$		−	4688.91i		−	0.00993479i
$688$	191076.	−	130774.i	0.403673	−	0.276278i
$689$	383103.			0.807007
$690$	−39.6486	−	65.7340i	−8.32780e−5	−	0.000138068i
$691$		−	29184.6i		−	0.0611219i	−0.999533	−	0.0305610i	$-0.990271\pi$
$691$		−	29184.6i		−	0.0611219i	0.999533	−	0.0305610i	$-0.00972937\pi$
$692$	−137500.	+	260727.i	−0.287138	+	0.544469i
$693$	−6577.73			−0.0136965
$694$	−461084.	+	278111.i	−0.957329	+	0.577430i
$695$		−	211012.i		−	0.436855i
$696$	−2816.67	−	48982.3i	−0.00581456	−	0.101116i
$697$	−65923.8			−0.135699
$698$	315047.	+	522321.i	0.646643	+	1.07208i
$699$			43119.1i			0.0882501i
$700$	−444484.	−	234409.i	−0.907110	−	0.478385i
$701$	−642156.			−1.30679			−0.653393	−	0.757019i	$-0.726655\pi$
$701$	−642156.			−1.30679			−0.653393	+	0.757019i	$0.726655\pi$
$702$	−56628.0	+	34156.2i	−0.114910	+	0.0693099i
$703$		−	6785.84i		−	0.0137307i
$704$	−721.450	−	6252.32i	−0.00145566	−	0.0126153i
$705$	−13077.6			−0.0263118
$706$	19972.0	+	33111.8i	0.0400693	+	0.0664314i
$707$			423384.i			0.847024i
$708$	9563.73	−	18134.7i	0.0190792	−	0.0361779i
$709$	73252.6			0.145724			0.0728619	−	0.997342i	$-0.476787\pi$
$709$	73252.6			0.145724			0.0728619	+	0.997342i	$0.476787\pi$
$710$	176727.	−	106596.i	0.350579	−	0.211458i
$711$			436929.i			0.864314i
$712$	606120.	−	34854.2i	1.19564	−	0.0687536i
$713$	−897.115			−0.00176469
$714$	23206.5	+	38474.4i	0.0455212	+	0.0754701i
$715$		−	1434.71i		−	0.00280642i
$716$	−519194.	−	273808.i	−1.01275	−	0.534098i
$717$	51078.6			0.0993575
$718$	238533.	−	143876.i	0.462701	−	0.279086i
$719$		−	932868.i		−	1.80452i	−0.431189	−	0.902262i	$-0.641906\pi$
$719$		−	932868.i		−	1.80452i	0.431189	−	0.902262i	$-0.358094\pi$
$720$	67645.4	+	98837.6i	0.130489	+	0.190659i
$721$	695581.			1.33807
$722$	−269146.	−	446221.i	−0.516314	−	0.856003i
$723$		−	56978.8i		−	0.109002i
$724$	46838.1	−	88814.1i	0.0893557	−	0.169436i
$725$	712656.			1.35583
$726$	31892.5	−	19236.6i	0.0605084	−	0.0364967i
$727$			545096.i			1.03134i	0.856786	+	0.515672i	$0.172458\pi$
$727$			545096.i			1.03134i	−0.856786	+	0.515672i	$0.827542\pi$
$728$	31389.6	+	545870.i	0.0592274	+	1.02997i
$729$	515580.			0.970155
$730$	−38217.9	−	63362.0i	−0.0717169	−	0.118900i
$731$		−	300720.i		−	0.562766i
$732$	13612.5	+	7178.84i	0.0254047	+	0.0133978i
$733$	−73392.7			−0.136598			−0.0682991	−	0.997665i	$-0.521757\pi$
$733$	−73392.7			−0.136598			−0.0682991	+	0.997665i	$0.521757\pi$
$734$	−445188.	+	268523.i	−0.826326	+	0.498413i
$735$			1551.29i			0.00287156i
$736$	−4842.58	−	2208.41i	−0.00893967	−	0.00407684i
$737$	−2344.52			−0.00431638
$738$	−33014.3	−	54734.9i	−0.0606163	−	0.100497i
$739$		−	798795.i		−	1.46267i	−0.682018	−	0.731335i	$-0.738897\pi$
$739$		−	798795.i		−	1.46267i	0.682018	−	0.731335i	$-0.261103\pi$
$740$	−44223.9	+	83857.1i	−0.0807595	+	0.153136i
$741$	680.164			0.00123873
$742$	433308.	−	261358.i	0.787026	−	0.474709i
$743$			798806.i			1.44698i	0.690333	+	0.723492i	$0.257464\pi$
$743$			798806.i			1.44698i	−0.690333	+	0.723492i	$0.742536\pi$
$744$	−7014.73	+	403.374i	−0.0126726	+	0.000728722i
$745$	−243427.			−0.438588
$746$	−111847.	−	185432.i	−0.200977	−	0.333202i
$747$		−	760244.i		−	1.36242i
$748$	−7230.34	−	3813.08i	−0.0129228	−	0.00681511i
$749$	−165827.			−0.295592
$750$	15382.5	−	9278.22i	0.0273466	−	0.0164946i
$751$			846377.i			1.50067i	0.661060	+	0.750333i	$0.270107\pi$
$751$			846377.i			1.50067i	−0.661060	+	0.750333i	$0.729893\pi$
$752$	−748242.	+	512105.i	−1.32314	+	0.905572i
$753$	58810.9			0.103721
$754$	−400503.	−	663998.i	−0.704470	−	1.16795i
$755$			189321.i			0.332128i
$756$	−40747.2	+	77264.6i	−0.0712942	+	0.135188i
$757$	72169.3			0.125939			0.0629696	−	0.998015i	$-0.479943\pi$
$757$	72169.3			0.125939			0.0629696	+	0.998015i	$0.479943\pi$
$758$	482305.	−	290911.i	0.839427	−	0.506315i
$759$			5.08001i			8.81822e-6i
$760$	−141.792	−	2465.78i	−0.000245484	−	0.00426900i
$761$	−192148.			−0.331793			−0.165896	−	0.986143i	$-0.553052\pi$
$761$	−192148.			−0.331793			−0.165896	+	0.986143i	$0.553052\pi$
$762$	12641.9	+	20959.1i	0.0217722	+	0.0360964i
$763$		−	580017.i		−	0.996304i
$764$	−348812.	−	183954.i	−0.597592	−	0.315154i
$765$	155553.			0.265800
$766$	−325612.	+	196399.i	−0.554936	+	0.334719i
$767$		−	324029.i		−	0.550800i
$768$	−38858.2	−	15090.6i	−0.0658810	−	0.0255849i
$769$	−750686.			−1.26942			−0.634711	−	0.772750i	$-0.718881\pi$
$769$	−750686.			−1.26942			−0.634711	+	0.772750i	$0.718881\pi$
$770$	−978.776	−	1622.73i	−0.00165083	−	0.00273693i
$771$		−	26594.1i		−	0.0447380i
$772$	−287925.	+	545961.i	−0.483109	+	0.916067i
$773$	47062.1			0.0787612			0.0393806	−	0.999224i	$-0.487462\pi$
$773$	47062.1			0.0787612			0.0393806	+	0.999224i	$0.487462\pi$
$774$	249680.	−	150599.i	0.416776	−	0.251386i
$775$		−	102059.i		−	0.169922i
$776$	−521908.	+	30011.7i	−0.866703	+	0.0498387i
$777$	−34484.7			−0.0571196
$778$	−388125.	−	643477.i	−0.641228	−	1.06310i
$779$			1318.15i			0.00217215i
$780$	−8405.23	−	4432.69i	−0.0138153	−	0.00728582i
$781$	−13657.7			−0.0223911
$782$	−5919.15	+	3570.24i	−0.00967934	+	0.00583827i
$783$		−	123881.i		−	0.202060i
$784$	60746.7	+	88757.7i	0.0988304	+	0.144402i
$785$	38164.2			0.0619322
$786$	−9970.80	−	16530.7i	−0.0161393	−	0.0267576i
$787$		−	506587.i		−	0.817908i	−0.912555	−	0.408954i	$-0.865894\pi$
$787$		−	506587.i		−	0.817908i	0.912555	−	0.408954i	$-0.134106\pi$
$788$	43026.3	−	81586.2i	0.0692918	−	0.131391i
$789$	28222.4			0.0453357
$790$	−107790.	+	65015.6i	−0.172713	+	0.104175i
$791$			637377.i			1.01869i
$792$	−455.013	−	7912.75i	−0.000725393	−	0.0126147i
$793$	243227.			0.386781
$794$	−505814.	−	838595.i	−0.802324	−	1.33018i
$795$			8794.36i			0.0139146i
$796$	448619.	+	236589.i	0.708029	+	0.373395i
$797$	431404.			0.679152			0.339576	−	0.940579i	$-0.389716\pi$
$797$	431404.			0.679152			0.339576	+	0.940579i	$0.389716\pi$
$798$	769.298	−	464.016i	0.00120806	−	0.000728664i
$799$			1.17760e6i			1.84461i
$800$	251237.	−	550911.i	0.392558	−	0.860799i
$801$	764550.			1.19163
$802$	−91969.3	−	152477.i	−0.142986	−	0.237059i
$803$			4896.70i			0.00759403i
$804$	−7243.65	+	13735.4i	−0.0112059	+	0.0212485i
$805$	−1602.56			−0.00247299
$806$	−95091.0	+	57355.8i	−0.146376	+	0.0882892i
$807$		−	38774.7i		−	0.0595390i
$808$	−509314.	+	29287.5i	−0.780123	+	0.0448600i
$809$	−556946.			−0.850973			−0.425486	−	0.904965i	$-0.639897\pi$
$809$	−556946.			−0.850973			−0.425486	+	0.904965i	$0.639897\pi$
$810$	77507.1	+	128500.i	0.118133	+	0.195854i
$811$			430193.i			0.654066i	0.945013	+	0.327033i	$0.106049\pi$
$811$			430193.i			0.654066i	−0.945013	+	0.327033i	$0.893951\pi$
$812$	−905975.	−	477786.i	−1.37406	−	0.724639i
$813$	23066.6			0.0348982
$814$	5372.12	−	3240.29i	0.00810769	−	0.00489030i
$815$			52565.8i			0.0791385i
$816$	−44677.8	+	30577.9i	−0.0670983	+	0.0459228i
$817$	−6012.92			−0.00900827
$818$	192956.	+	319905.i	0.288372	+	0.478095i
$819$			688551.i			1.02652i
$820$	8590.51	−	16289.3i	0.0127759	−	0.0242255i
$821$	977714.			1.45053			0.725263	−	0.688472i	$-0.241718\pi$
$821$	977714.			1.45053			0.725263	+	0.688472i	$0.241718\pi$
$822$	13668.2	−	8244.23i	0.0202287	−	0.0122013i
$823$			714901.i			1.05547i	0.849409	+	0.527736i	$0.176959\pi$
$823$			714901.i			1.05547i	−0.849409	+	0.527736i	$0.823041\pi$
$824$	48116.7	+	836756.i	0.0708665	+	1.23238i
$825$	−577.922			−0.000849105
$826$	−221057.	−	366493.i	−0.323999	−	0.537162i
$827$			647852.i			0.947250i	0.880727	+	0.473625i	$0.157055\pi$
$827$			647852.i			0.947250i	−0.880727	+	0.473625i	$0.842945\pi$
$828$	−5928.56	−	3126.56i	−0.00864747	−	0.00456044i
$829$	−316717.			−0.460854			−0.230427	−	0.973090i	$-0.574012\pi$
$829$	−316717.			−0.460854			−0.230427	+	0.973090i	$0.574012\pi$
$830$	187552.	−	113125.i	0.272249	−	0.164212i
$831$		−	56870.4i		−	0.0823539i
$832$	−654488.	+	75520.8i	−0.945486	+	0.109099i
$833$	139689.			0.201313
$834$	47768.0	+	79195.1i	0.0686759	+	0.113859i
$835$			223410.i			0.320428i
$836$	−76.2429	+	144.571i	−0.000109090	+	0.000206857i
$837$	−17741.0			−0.0253236
$838$	984345.	−	593725.i	1.40171	−	0.845469i
$839$		−	141774.i		−	0.201407i	−0.994916	−	0.100703i	$-0.967891\pi$
$839$		−	141774.i		−	0.201407i	0.994916	−	0.100703i	$-0.0321093\pi$
$840$	−12530.8	+	720.566i	−0.0177590	+	0.00102121i
$841$	745300.			1.05375
$842$	−323378.	−	536132.i	−0.456127	−	0.756219i
$843$		−	33772.4i		−	0.0475233i
$844$	−78583.6	−	41442.8i	−0.110318	−	0.0581788i
$845$	15610.1			0.0218622
$846$	−977733.	+	589737.i	−1.36609	+	0.823982i
$847$		−	777522.i		−	1.08379i
$848$	344377.	+	503173.i	0.478897	+	0.699722i
$849$	1432.70			0.00198765
$850$	−406165.	−	673386.i	−0.562166	−	0.932022i
$851$		−	5305.36i		−	0.00732581i
$852$	−42196.9	+	80013.4i	−0.0581301	+	0.110226i
$853$	−408081.			−0.560852			−0.280426	−	0.959876i	$-0.590476\pi$
$853$	−408081.			−0.560852			−0.280426	+	0.959876i	$0.590476\pi$
$854$	275101.	−	165932.i	0.377204	−	0.227518i
$855$		−	3110.29i		−	0.00425470i
$856$	−11471.1	−	199484.i	−0.0156551	−	0.272245i
$857$	−387932.			−0.528194			−0.264097	−	0.964496i	$-0.585074\pi$
$857$	−387932.			−0.528194			−0.264097	+	0.964496i	$0.585074\pi$
$858$	324.784	+	538.463i	0.000441184	+	0.000731445i
$859$		−	377490.i		−	0.511586i	−0.966732	−	0.255793i	$-0.917663\pi$
$859$		−	377490.i		−	0.511586i	0.966732	−	0.255793i	$-0.0823365\pi$
$860$	74305.6	+	39186.7i	0.100467	+	0.0529837i
$861$	6698.67			0.00903613
$862$	−48818.9	+	29446.0i	−0.0657012	+	0.0396289i
$863$			463746.i			0.622671i	0.950300	+	0.311336i	$0.100776\pi$
$863$			463746.i			0.622671i	−0.950300	+	0.311336i	$0.899224\pi$
$864$	−95764.9	−	43672.5i	−0.128286	−	0.0585033i
$865$	−106942.			−0.142927
$866$	−595814.	−	987808.i	−0.794465	−	1.31715i
$867$			17189.7i			0.0228681i
$868$	−68423.6	+	129744.i	−0.0908169	+	0.172206i
$869$	8330.17			0.0110310
$870$	15242.5	−	9193.76i	0.0201380	−	0.0121466i
$871$			245423.i			0.323503i
$872$	697737.	−	40122.5i	0.917612	−	0.0527662i
$873$	−658326.			−0.863799
$874$	71.3872	+	118.354i	9.34540e−5	+	0.000154939i
$875$		−	375016.i		−	0.489817i
$876$	28687.3	+	15128.9i	0.0373836	+	0.0197151i
$877$	−437724.			−0.569117			−0.284558	−	0.958659i	$-0.591847\pi$
$877$	−437724.			−0.569117			−0.284558	+	0.958659i	$0.591847\pi$
$878$	−890535.	+	537142.i	−1.15521	+	0.696788i
$879$		−	89027.0i		−	0.115224i
$880$	1884.37	−	1289.68i	0.00243332	−	0.00166539i
$881$	−1.01104e6			−1.30261			−0.651307	−	0.758814i	$-0.725779\pi$
$881$	−1.01104e6			−1.30261			−0.651307	+	0.758814i	$0.725779\pi$
$882$	69955.6	+	115980.i	0.0899260	+	0.149089i
$883$			1.00270e6i			1.28602i	0.765858	+	0.643010i	$0.222315\pi$
$883$			1.00270e6i			1.28602i	−0.765858	+	0.643010i	$0.777685\pi$
$884$	−399150.	+	756866.i	−0.510778	+	0.968533i
$885$	7438.28			0.00949698
$886$	−462686.	+	279077.i	−0.589412	+	0.355514i
$887$			32797.5i			0.0416863i	0.999783	+	0.0208432i	$0.00663506\pi$
$887$			32797.5i			0.0416863i	−0.999783	+	0.0208432i	$0.993365\pi$
$888$	−2385.47	−	41483.7i	−0.00302516	−	0.0526080i
$889$	510972.			0.646537
$890$	113766.	+	188614.i	0.143626	+	0.238120i
$891$		−	9930.65i		−	0.0125090i
$892$	658535.	+	347293.i	0.827654	+	0.436482i
$893$	23546.2			0.0295269
$894$	91361.0	−	55106.0i	0.114310	−	0.0689484i
$895$		−	212957.i		−	0.265856i
$896$	−688736.	+	531917.i	−0.857900	+	0.662564i
$897$	531.771			0.000660906
$898$	318479.	+	528011.i	0.394937	+	0.654772i
$899$		−	208024.i		−	0.257391i
$900$	355690.	−	674457.i	0.439123	−	0.832663i
$901$	791905.			0.975492
$902$	−1043.54	+	629.427i	−0.00128261	+	0.000773629i
$903$			30556.9i			0.0374743i
$904$	−766738.	+	44090.4i	−0.938232	+	0.0539519i
$905$	36428.8			0.0444782
$906$	−42857.7	−	71054.4i	−0.0522123	−	0.0865634i
$907$		−	929947.i		−	1.13043i	−0.824943	−	0.565215i	$-0.808793\pi$
$907$		−	929947.i		−	1.13043i	0.824943	−	0.565215i	$-0.191207\pi$
$908$	781581.	+	412185.i	0.947987	+	0.499942i
$909$	−642440.			−0.777508
$910$	−169866.	+	102457.i	−0.205127	+	0.123726i
$911$		−	696215.i		−	0.838893i	−0.907780	−	0.419446i	$-0.862224\pi$
$911$		−	696215.i		−	0.838893i	0.907780	−	0.419446i	$-0.137776\pi$
$912$	611.408	+	893.336i	0.000735092	+	0.00107405i
$913$	−14494.3			−0.0173882
$914$	431164.	+	714832.i	0.516119	+	0.855680i
$915$			5583.41i			0.00666895i
$916$	55019.6	−	104328.i	0.0655733	−	0.124340i
$917$	−403010.			−0.479266
$918$	−117055.	+	70603.6i	−0.138900	+	0.0837802i
$919$		−	1.27715e6i		−	1.51220i	−0.654456	−	0.756100i	$-0.727102\pi$
$919$		−	1.27715e6i		−	1.51220i	0.654456	−	0.756100i	$-0.272898\pi$
$920$	−110.857	−	1927.81i	−0.000130974	−	0.00227766i
$921$	−98384.1			−0.115986
$922$	−398896.	−	661336.i	−0.469244	−	0.777965i
$923$			1.42967e6i			1.67816i
$924$	734.692	+	387.456i	0.000860521	+	0.000453815i
$925$	603558.			0.705401
$926$	−359761.	+	216996.i	−0.419558	+	0.253064i
$927$			1.05547e6i			1.22825i
$928$	512087.	−	1.12290e6i	0.594631	−	1.30390i
$929$	753707.			0.873315			0.436658	−	0.899628i	$-0.356162\pi$
$929$	753707.			0.873315			0.436658	+	0.899628i	$0.356162\pi$
$930$	−1316.64	−	2182.87i	−0.00152230	−	0.00252384i
$931$		−	2793.09i		−	0.00322245i
$932$	−505959.	+	959396.i	−0.582483	+	1.10450i
$933$	−12234.9			−0.0140552
$934$	636295.	−	383793.i	0.729398	−	0.439950i
$935$		−	2965.66i		−	0.00339233i
$936$	−828300.	+	47630.4i	−0.945444	+	0.0543666i
$937$	−150366.			−0.171265			−0.0856327	−	0.996327i	$-0.527291\pi$
$937$	−150366.			−0.171265			−0.0856327	+	0.996327i	$0.527291\pi$
$938$	167430.	+	277585.i	0.190295	+	0.315493i
$939$			54210.4i			0.0614825i
$940$	−290976.	−	153453.i	−0.329308	−	0.173668i
$941$	1.36602e6			1.54269			0.771345	−	0.636417i	$-0.219584\pi$
$941$	1.36602e6			1.54269			0.771345	+	0.636417i	$0.219584\pi$
$942$	−14323.5	+	8639.45i	−0.0161416	+	0.00973608i
$943$			1030.57i			0.00115892i
$944$	425584.	−	291274.i	0.477575	−	0.326857i
$945$	−31691.5			−0.0354878
$946$	−2871.22	−	4760.23i	−0.00320836	−	0.00531919i
$947$			1.72155e6i			1.91964i	0.280615	+	0.959820i	$0.409462\pi$
$947$			1.72155e6i			1.91964i	−0.280615	+	0.959820i	$0.590538\pi$
$948$	25737.0	−	48802.2i	0.0286379	−	0.0543029i
$949$	512582.			0.569156
$950$	−13464.4	+	8121.29i	−0.0149190	+	0.00899866i
$951$			44230.2i			0.0489056i
$952$	64884.8	+	1.12836e6i	0.0715927	+	1.24501i
$953$	512976.			0.564822			0.282411	−	0.959294i	$-0.408866\pi$
$953$	512976.			0.564822			0.282411	+	0.959294i	$0.408866\pi$
$954$	396582.	+	657499.i	0.435749	+	0.722434i
$955$		−	143072.i		−	0.156873i
$956$	1.13649e6	+	599356.i	1.24352	+	0.655796i
$957$	−1177.96			−0.00128619
$958$	−251765.	+	151856.i	−0.274324	+	0.165463i
$959$		−	333223.i		−	0.362325i
$960$	−1733.62	−	15024.1i	−0.00188110	−	0.0163022i
$961$	−29791.0			−0.0322581
$962$	−339191.	−	562349.i	−0.366517	−	0.607653i
$963$		−	251625.i		−	0.271332i
$964$	668588.	−	1.26777e6i	0.719457	−	1.36423i
$965$	−223936.			−0.240475
$966$	601.459	−	362.781i	0.000644542	−	0.000388767i
$967$		−	1.45952e6i		−	1.56083i	−0.625260	−	0.780416i	$-0.715007\pi$
$967$		−	1.45952e6i		−	1.56083i	0.625260	−	0.780416i	$-0.284993\pi$
$968$	935328.	−	53784.9i	0.998190	−	0.0573997i
$969$	1405.95			0.00149735
$970$	−97959.9	−	162409.i	−0.104113	−	0.172610i
$971$		−	1.35779e6i		−	1.44010i	−0.693920	−	0.720052i	$-0.744118\pi$
$971$		−	1.35779e6i		−	1.44010i	0.693920	−	0.720052i	$-0.255882\pi$
$972$	−176008.	−	92821.8i	−0.186294	−	0.0982466i
$973$	1.93073e6			2.03937
$974$	1.40004e6	−	844461.i	1.47579	−	0.890147i
$975$			60496.4i			0.0636386i
$976$	218640.	+	319457.i	0.229525	+	0.335361i
$977$	227574.			0.238414			0.119207	−	0.992869i	$-0.461965\pi$
$977$	227574.			0.238414			0.119207	+	0.992869i	$0.461965\pi$
$978$	−11899.6	−	19728.5i	−0.0124410	−	0.0206261i
$979$		−	14576.4i		−	0.0152084i
$980$	−18202.8	+	34516.1i	−0.0189534	+	0.0359393i
$981$	880115.			0.914537
$982$	497717.	−	300207.i	0.516131	−	0.311314i
$983$			507499.i			0.525204i	0.964904	+	0.262602i	$0.0845806\pi$
$983$			507499.i			0.525204i	−0.964904	+	0.262602i	$0.915419\pi$
$984$	463.379	+	8058.23i	0.000478570	+	0.00832241i
$985$	33464.1			0.0344911
$986$	−827871.	−	1.37254e6i	−0.851547	−	1.41179i
$987$		−	119659.i		−	0.122832i
$988$	15133.6	+	7981.04i	0.0155034	+	0.00817609i
$989$	−4701.07			−0.00480622
$990$	2462.31	−	1485.19i	0.00251231	−	0.00151534i
$991$			1.12591e6i			1.14645i	0.819398	+	0.573226i	$0.194308\pi$
$991$			1.12591e6i			1.14645i	−0.819398	+	0.573226i	$0.805692\pi$
$992$	−160810.	−	73335.8i	−0.163415	−	0.0745234i
$993$	−61959.9			−0.0628365
$994$	975341.	+	1.61703e6i	0.987151	+	1.63661i
$995$			184009.i			0.185863i
$996$	−44781.6	+	84914.6i	−0.0451420	+	0.0855980i
$997$	−1.96406e6			−1.97589			−0.987947	−	0.154792i	$-0.950529\pi$
$997$	−1.96406e6			−1.97589			−0.987947	+	0.154792i	$0.950529\pi$
$998$	1.63386e6	−	985492.i	1.64042	−	0.989446i
$999$		−	104917.i		−	0.105127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.b.a.63.17	✓	60
4.3	odd	2	inner	124.5.b.a.63.18	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.b.a.63.17	✓	60	1.1	even	1	trivial
124.5.b.a.63.18	yes	60	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06596 - 3.42518i) q^{2} +0.636071i q^{3} +(-7.46365 + 14.1525i) q^{4} -5.80492 q^{5} +(2.17865 - 1.31409i) q^{6} -53.1144i q^{7} +(63.8944 - 3.67417i) q^{8} +80.5954 q^{9} +O(q^{10})\)	\(q+(-2.06596 - 3.42518i) q^{2} +0.636071i q^{3} +(-7.46365 + 14.1525i) q^{4} -5.80492 q^{5} +(2.17865 - 1.31409i) q^{6} -53.1144i q^{7} +(63.8944 - 3.67417i) q^{8} +80.5954 q^{9} +(11.9927 + 19.8829i) q^{10} -1.53657i q^{11} +(-9.00201 - 4.74741i) q^{12} -160.847 q^{13} +(-181.926 + 109.732i) q^{14} -3.69234i q^{15} +(-144.588 - 211.259i) q^{16} -332.484 q^{17} +(-166.507 - 276.053i) q^{18} +6.64805i q^{19} +(43.3259 - 82.1543i) q^{20} +33.7845 q^{21} +(-5.26304 + 3.17450i) q^{22} +5.19763i q^{23} +(2.33703 + 40.6414i) q^{24} -591.303 q^{25} +(332.304 + 550.930i) q^{26} +102.786i q^{27} +(751.702 + 396.427i) q^{28} -1205.23 q^{29} +(-12.6469 + 7.62822i) q^{30} +172.601i q^{31} +(-424.887 + 931.690i) q^{32} +0.977371 q^{33} +(686.898 + 1138.82i) q^{34} +308.325i q^{35} +(-601.536 + 1140.63i) q^{36} -1020.73 q^{37} +(22.7707 - 13.7346i) q^{38} -102.310i q^{39} +(-370.902 + 21.3283i) q^{40} +198.276 q^{41} +(-69.7973 - 115.718i) q^{42} +904.464i q^{43} +(21.7464 + 11.4685i) q^{44} -467.850 q^{45} +(17.8028 - 10.7381i) q^{46} -3541.83i q^{47} +(134.376 - 91.9681i) q^{48} -420.137 q^{49} +(1221.61 + 2025.32i) q^{50} -211.484i q^{51} +(1200.51 - 2276.40i) q^{52} -2381.78 q^{53} +(352.061 - 212.352i) q^{54} +8.91970i q^{55} +(-195.151 - 3393.71i) q^{56} -4.22863 q^{57} +(2489.95 + 4128.13i) q^{58} +2014.51i q^{59} +(52.2560 + 27.5584i) q^{60} -1512.16 q^{61} +(591.188 - 356.585i) q^{62} -4280.78i q^{63} +(4069.00 - 469.518i) q^{64} +933.707 q^{65} +(-2.01920 - 3.34767i) q^{66} -1525.81i q^{67} +(2481.55 - 4705.49i) q^{68} -3.30606 q^{69} +(1056.07 - 636.986i) q^{70} -8888.39i q^{71} +(5149.60 - 296.121i) q^{72} -3186.76 q^{73} +(2108.78 + 3496.17i) q^{74} -376.111i q^{75} +(-94.0867 - 49.6187i) q^{76} -81.6142 q^{77} +(-350.431 + 211.369i) q^{78} +5421.26i q^{79} +(839.321 + 1226.34i) q^{80} +6462.85 q^{81} +(-409.630 - 679.131i) q^{82} -9432.85i q^{83} +(-252.156 + 478.136i) q^{84} +1930.05 q^{85} +(3097.95 - 1868.58i) q^{86} -766.612i q^{87} +(-5.64564 - 98.1786i) q^{88} +9486.28 q^{89} +(966.558 + 1602.47i) q^{90} +8543.31i q^{91} +(-73.5596 - 38.7933i) q^{92} -109.786 q^{93} +(-12131.4 + 7317.25i) q^{94} -38.5914i q^{95} +(-592.621 - 270.258i) q^{96} -8168.28 q^{97} +(867.985 + 1439.04i) q^{98} -123.841i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9}+O(q^{10}) \) 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9	\( 60 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 45 q^{8} - 1732 q^{9} + 53 q^{10} + 130 q^{12} + 120 q^{13} - 231 q^{14} - 590 q^{16} - 648 q^{17} + 230 q^{18} + 1113 q^{20} + 608 q^{21} + 1080 q^{22} - 1028 q^{24} + 8340 q^{25} - 1554 q^{26} - 165 q^{28} - 168 q^{29} - 2238 q^{30} - 1674 q^{32} - 1120 q^{33} + 1844 q^{34} + 1966 q^{36} - 2248 q^{37} - 5055 q^{38} - 1716 q^{40} + 6072 q^{41} + 5794 q^{42} - 120 q^{44} - 4040 q^{45} + 8850 q^{46} + 2276 q^{48} - 17604 q^{49} - 4539 q^{50} + 5896 q^{52} + 3480 q^{53} + 5148 q^{54} - 396 q^{56} - 10912 q^{57} - 7484 q^{58} + 22812 q^{60} + 2200 q^{61} - 19299 q^{64} - 9168 q^{65} - 468 q^{66} - 21930 q^{68} + 6496 q^{69} - 9615 q^{70} - 10079 q^{72} + 13752 q^{73} - 2106 q^{74} + 20099 q^{76} + 16608 q^{77} + 39460 q^{78} - 5787 q^{80} + 20732 q^{81} - 30525 q^{82} - 21760 q^{84} - 21200 q^{85} - 13398 q^{86} + 34690 q^{88} + 22296 q^{89} - 25419 q^{90} - 18852 q^{92} + 3196 q^{94} + 20790 q^{96} + 12120 q^{97} + 21921 q^{98}+O(q^{100}) \) 60 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 45 * q^8 - 1732 * q^9 + 53 * q^10 + 130 * q^12 + 120 * q^13 - 231 * q^14 - 590 * q^16 - 648 * q^17 + 230 * q^18 + 1113 * q^20 + 608 * q^21 + 1080 * q^22 - 1028 * q^24 + 8340 * q^25 - 1554 * q^26 - 165 * q^28 - 168 * q^29 - 2238 * q^30 - 1674 * q^32 - 1120 * q^33 + 1844 * q^34 + 1966 * q^36 - 2248 * q^37 - 5055 * q^38 - 1716 * q^40 + 6072 * q^41 + 5794 * q^42 - 120 * q^44 - 4040 * q^45 + 8850 * q^46 + 2276 * q^48 - 17604 * q^49 - 4539 * q^50 + 5896 * q^52 + 3480 * q^53 + 5148 * q^54 - 396 * q^56 - 10912 * q^57 - 7484 * q^58 + 22812 * q^60 + 2200 * q^61 - 19299 * q^64 - 9168 * q^65 - 468 * q^66 - 21930 * q^68 + 6496 * q^69 - 9615 * q^70 - 10079 * q^72 + 13752 * q^73 - 2106 * q^74 + 20099 * q^76 + 16608 * q^77 + 39460 * q^78 - 5787 * q^80 + 20732 * q^81 - 30525 * q^82 - 21760 * q^84 - 21200 * q^85 - 13398 * q^86 + 34690 * q^88 + 22296 * q^89 - 25419 * q^90 - 18852 * q^92 + 3196 * q^94 + 20790 * q^96 + 12120 * q^97 + 21921 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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