LMFDB - Embedded newform 229.3.d.a.107.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [229,3,Mod(107,229)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(229, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3]))

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

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

chi := DirichletCharacter("229.107");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 229 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	229.d (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.23979805385$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.18
Character	$\chi$	$=$	229.107
Dual form			229.3.d.a.122.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.132366 + 0.132366i) q^{2} +3.73689 q^{3} +3.96496i q^{4} -8.10000i q^{5} +(-0.494638 + 0.494638i) q^{6} +(7.72510 + 7.72510i) q^{7} +(-1.05429 - 1.05429i) q^{8} +4.96435 q^{9} +O(q^{10})$	\(q+(-0.132366 + 0.132366i) q^{2} +3.73689 q^{3} +3.96496i q^{4} -8.10000i q^{5} +(-0.494638 + 0.494638i) q^{6} +(7.72510 + 7.72510i) q^{7} +(-1.05429 - 1.05429i) q^{8} +4.96435 q^{9} +(1.07217 + 1.07217i) q^{10} +3.03819i q^{11} +14.8166i q^{12} +(6.87724 - 6.87724i) q^{13} -2.04509 q^{14} -30.2688i q^{15} -15.5807 q^{16} +11.5509 q^{17} +(-0.657112 + 0.657112i) q^{18} +7.63169 q^{19} +32.1162 q^{20} +(28.8679 + 28.8679i) q^{21} +(-0.402154 - 0.402154i) q^{22} +(-0.196129 + 0.196129i) q^{23} +(-3.93977 - 3.93977i) q^{24} -40.6100 q^{25} +1.82063i q^{26} -15.0808 q^{27} +(-30.6297 + 30.6297i) q^{28} +(12.4769 - 12.4769i) q^{29} +(4.00657 + 4.00657i) q^{30} +(-27.0099 + 27.0099i) q^{31} +(6.27953 - 6.27953i) q^{32} +11.3534i q^{33} +(-1.52895 + 1.52895i) q^{34} +(62.5733 - 62.5733i) q^{35} +19.6834i q^{36} -7.35410 q^{37} +(-1.01018 + 1.01018i) q^{38} +(25.6995 - 25.6995i) q^{39} +(-8.53976 + 8.53976i) q^{40} +(18.3012 + 18.3012i) q^{41} -7.64226 q^{42} +46.3156 q^{43} -12.0463 q^{44} -40.2112i q^{45} -0.0519218i q^{46} +(-39.1211 - 39.1211i) q^{47} -58.2235 q^{48} +70.3544i q^{49} +(5.37540 - 5.37540i) q^{50} +43.1645 q^{51} +(27.2680 + 27.2680i) q^{52} -94.5091 q^{53} +(1.99619 - 1.99619i) q^{54} +24.6094 q^{55} -16.2890i q^{56} +28.5188 q^{57} +3.30305i q^{58} +(57.9071 - 57.9071i) q^{59} +120.015 q^{60} -42.2508 q^{61} -7.15040i q^{62} +(38.3501 + 38.3501i) q^{63} -60.6605i q^{64} +(-55.7056 - 55.7056i) q^{65} +(-1.50281 - 1.50281i) q^{66} +(-87.2153 - 87.2153i) q^{67} +45.7989i q^{68} +(-0.732914 + 0.732914i) q^{69} +16.5652i q^{70} +35.6734i q^{71} +(-5.23387 - 5.23387i) q^{72} +(-89.6694 + 89.6694i) q^{73} +(0.973435 - 0.973435i) q^{74} -151.755 q^{75} +30.2593i q^{76} +(-23.4703 + 23.4703i) q^{77} +6.80349i q^{78} +(-63.5426 - 63.5426i) q^{79} +126.204i q^{80} -101.034 q^{81} -4.84492 q^{82} +28.3259 q^{83} +(-114.460 + 114.460i) q^{84} -93.5625i q^{85} +(-6.13062 + 6.13062i) q^{86} +(46.6249 - 46.6249i) q^{87} +(3.20314 - 3.20314i) q^{88} +(-26.1493 + 26.1493i) q^{89} +(5.32261 + 5.32261i) q^{90} +106.255 q^{91} +(-0.777645 - 0.777645i) q^{92} +(-100.933 + 100.933i) q^{93} +10.3566 q^{94} -61.8167i q^{95} +(23.4659 - 23.4659i) q^{96} -8.85513i q^{97} +(-9.31255 - 9.31255i) q^{98} +15.0826i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 4 q^{3} - 6 q^{6} - 18 q^{7} - 6 q^{8} + 204 q^{9}+O(q^{10}) $ 76 * q - 4 * q^3 - 6 * q^6 - 18 * q^7 - 6 * q^8 + 204 * q^9	$ 76 q - 4 q^{3} - 6 q^{6} - 18 q^{7} - 6 q^{8} + 204 q^{9} + 2 q^{10} - 72 q^{13} - 20 q^{14} - 228 q^{16} - 40 q^{17} + 36 q^{18} - 40 q^{19} - 20 q^{20} - 98 q^{21} + 6 q^{22} - 8 q^{23} + 70 q^{24} - 268 q^{25} - 100 q^{27} - 88 q^{28} - 64 q^{29} + 144 q^{30} + 6 q^{31} + 16 q^{32} - 38 q^{34} + 50 q^{35} + 76 q^{37} + 192 q^{38} + 36 q^{39} - 82 q^{40} - 68 q^{41} + 292 q^{42} + 84 q^{43} + 108 q^{44} + 164 q^{47} - 284 q^{48} - 36 q^{50} - 152 q^{51} + 670 q^{52} - 404 q^{53} - 466 q^{54} + 16 q^{55} + 56 q^{57} + 8 q^{59} + 1148 q^{60} - 128 q^{61} - 156 q^{63} + 76 q^{65} + 384 q^{66} + 14 q^{67} - 418 q^{69} - 662 q^{72} + 186 q^{73} - 78 q^{74} + 124 q^{75} + 154 q^{77} - 142 q^{79} + 228 q^{81} - 72 q^{82} + 212 q^{83} - 1034 q^{84} - 26 q^{86} + 554 q^{87} + 160 q^{88} + 110 q^{89} - 226 q^{90} + 588 q^{91} - 262 q^{92} - 602 q^{93} + 568 q^{94} + 1380 q^{96} - 854 q^{98}+O(q^{100}) $ 76 * q - 4 * q^3 - 6 * q^6 - 18 * q^7 - 6 * q^8 + 204 * q^9 + 2 * q^10 - 72 * q^13 - 20 * q^14 - 228 * q^16 - 40 * q^17 + 36 * q^18 - 40 * q^19 - 20 * q^20 - 98 * q^21 + 6 * q^22 - 8 * q^23 + 70 * q^24 - 268 * q^25 - 100 * q^27 - 88 * q^28 - 64 * q^29 + 144 * q^30 + 6 * q^31 + 16 * q^32 - 38 * q^34 + 50 * q^35 + 76 * q^37 + 192 * q^38 + 36 * q^39 - 82 * q^40 - 68 * q^41 + 292 * q^42 + 84 * q^43 + 108 * q^44 + 164 * q^47 - 284 * q^48 - 36 * q^50 - 152 * q^51 + 670 * q^52 - 404 * q^53 - 466 * q^54 + 16 * q^55 + 56 * q^57 + 8 * q^59 + 1148 * q^60 - 128 * q^61 - 156 * q^63 + 76 * q^65 + 384 * q^66 + 14 * q^67 - 418 * q^69 - 662 * q^72 + 186 * q^73 - 78 * q^74 + 124 * q^75 + 154 * q^77 - 142 * q^79 + 228 * q^81 - 72 * q^82 + 212 * q^83 - 1034 * q^84 - 26 * q^86 + 554 * q^87 + 160 * q^88 + 110 * q^89 - 226 * q^90 + 588 * q^91 - 262 * q^92 - 602 * q^93 + 568 * q^94 + 1380 * q^96 - 854 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/229\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.132366	+	0.132366i	−0.0661831	+	0.0661831i	−0.739424	−	0.673240i	$-0.764902\pi$
$2$	−0.132366	+	0.132366i	−0.0661831	+	0.0661831i	0.673240	+	0.739424i	$0.264902\pi$
$3$	3.73689			1.24563			0.622815	−	0.782369i	$-0.285989\pi$
$3$	3.73689			1.24563			0.622815	+	0.782369i	$0.285989\pi$
$4$			3.96496i			0.991240i
$5$		−	8.10000i		−	1.62000i	−0.586430	−	0.810000i	$-0.699467\pi$
$5$		−	8.10000i		−	1.62000i	0.586430	−	0.810000i	$-0.300533\pi$
$6$	−0.494638	+	0.494638i	−0.0824397	+	0.0824397i
$7$	7.72510	+	7.72510i	1.10359	+	1.10359i	0.993975	+	0.109612i	$0.0349607\pi$
$7$	7.72510	+	7.72510i	1.10359	+	1.10359i	0.109612	+	0.993975i	$0.465039\pi$
$8$	−1.05429	−	1.05429i	−0.131786	−	0.131786i
$9$	4.96435			0.551594
$10$	1.07217	+	1.07217i	0.107217	+	0.107217i
$11$			3.03819i			0.276199i	0.990418	+	0.138100i	$0.0440994\pi$
$11$			3.03819i			0.276199i	−0.990418	+	0.138100i	$0.955901\pi$
$12$			14.8166i			1.23472i
$13$	6.87724	−	6.87724i	0.529018	−	0.529018i	−0.391261	−	0.920280i	$-0.627961\pi$
$13$	6.87724	−	6.87724i	0.529018	−	0.529018i	0.920280	+	0.391261i	$0.127961\pi$
$14$	−2.04509			−0.146078
$15$		−	30.2688i		−	2.01792i
$16$	−15.5807			−0.973796
$17$	11.5509			0.679466			0.339733	−	0.940522i	$-0.389663\pi$
$17$	11.5509			0.679466			0.339733	+	0.940522i	$0.389663\pi$
$18$	−0.657112	+	0.657112i	−0.0365062	+	0.0365062i
$19$	7.63169			0.401668			0.200834	−	0.979625i	$-0.435635\pi$
$19$	7.63169			0.401668			0.200834	+	0.979625i	$0.435635\pi$
$20$	32.1162			1.60581
$21$	28.8679	+	28.8679i	1.37466	+	1.37466i
$22$	−0.402154	−	0.402154i	−0.0182797	−	0.0182797i
$23$	−0.196129	+	0.196129i	−0.00852736	+	0.00852736i	−0.711358	−	0.702830i	$-0.751919\pi$
$23$	−0.196129	+	0.196129i	−0.00852736	+	0.00852736i	0.702830	+	0.711358i	$0.251919\pi$
$24$	−3.93977	−	3.93977i	−0.164157	−	0.164157i
$25$	−40.6100			−1.62440
$26$			1.82063i			0.0700241i
$27$	−15.0808			−0.558548
$28$	−30.6297	+	30.6297i	−1.09392	+	1.09392i
$29$	12.4769	−	12.4769i	0.430239	−	0.430239i	−0.458471	−	0.888710i	$-0.651603\pi$
$29$	12.4769	−	12.4769i	0.430239	−	0.430239i	0.888710	+	0.458471i	$0.151603\pi$
$30$	4.00657	+	4.00657i	0.133552	+	0.133552i
$31$	−27.0099	+	27.0099i	−0.871287	+	0.871287i	−0.992613	−	0.121326i	$-0.961285\pi$
$31$	−27.0099	+	27.0099i	−0.871287	+	0.871287i	0.121326	+	0.992613i	$0.461285\pi$
$32$	6.27953	−	6.27953i	0.196235	−	0.196235i
$33$			11.3534i			0.344042i
$34$	−1.52895	+	1.52895i	−0.0449692	+	0.0449692i
$35$	62.5733	−	62.5733i	1.78781	−	1.78781i
$36$			19.6834i			0.546762i
$37$	−7.35410			−0.198759			−0.0993797	−	0.995050i	$-0.531686\pi$
$37$	−7.35410			−0.198759			−0.0993797	+	0.995050i	$0.531686\pi$
$38$	−1.01018	+	1.01018i	−0.0265836	+	0.0265836i
$39$	25.6995	−	25.6995i	0.658961	−	0.658961i
$40$	−8.53976	+	8.53976i	−0.213494	+	0.213494i
$41$	18.3012	+	18.3012i	0.446370	+	0.446370i	0.894146	−	0.447776i	$-0.147784\pi$
$41$	18.3012	+	18.3012i	0.446370	+	0.446370i	−0.447776	+	0.894146i	$0.647784\pi$
$42$	−7.64226			−0.181959
$43$	46.3156			1.07711			0.538553	−	0.842591i	$-0.318971\pi$
$43$	46.3156			1.07711			0.538553	+	0.842591i	$0.318971\pi$
$44$	−12.0463			−0.273780
$45$		−	40.2112i		−	0.893582i
$46$		−	0.0519218i		−	0.00112873i
$47$	−39.1211	−	39.1211i	−0.832365	−	0.832365i	0.155475	−	0.987840i	$-0.450309\pi$
$47$	−39.1211	−	39.1211i	−0.832365	−	0.832365i	−0.987840	+	0.155475i	$0.950309\pi$
$48$	−58.2235			−1.21299
$49$			70.3544i			1.43580i
$50$	5.37540	−	5.37540i	0.107508	−	0.107508i
$51$	43.1645			0.846363
$52$	27.2680	+	27.2680i	0.524384	+	0.524384i
$53$	−94.5091			−1.78319			−0.891596	−	0.452832i	$-0.850414\pi$
$53$	−94.5091			−1.78319			−0.891596	+	0.452832i	$0.850414\pi$
$54$	1.99619	−	1.99619i	0.0369664	−	0.0369664i
$55$	24.6094			0.447443
$56$		−	16.2890i		−	0.290875i
$57$	28.5188			0.500329
$58$			3.30305i			0.0569491i
$59$	57.9071	−	57.9071i	0.981476	−	0.981476i	−0.0183559	−	0.999832i	$-0.505843\pi$
$59$	57.9071	−	57.9071i	0.981476	−	0.981476i	0.999832	+	0.0183559i	$0.00584320\pi$
$60$	120.015			2.00024
$61$	−42.2508			−0.692636			−0.346318	−	0.938117i	$-0.612568\pi$
$61$	−42.2508			−0.692636			−0.346318	+	0.938117i	$0.612568\pi$
$62$		−	7.15040i		−	0.115329i
$63$	38.3501	+	38.3501i	0.608731	+	0.608731i
$64$		−	60.6605i		−	0.947821i
$65$	−55.7056	−	55.7056i	−0.857010	−	0.857010i
$66$	−1.50281	−	1.50281i	−0.0227698	−	0.0227698i
$67$	−87.2153	−	87.2153i	−1.30172	−	1.30172i	−0.927231	−	0.374490i	$-0.877818\pi$
$67$	−87.2153	−	87.2153i	−1.30172	−	1.30172i	−0.374490	−	0.927231i	$-0.622182\pi$
$68$			45.7989i			0.673514i
$69$	−0.732914	+	0.732914i	−0.0106219	+	0.0106219i
$70$			16.5652i			0.236646i
$71$			35.6734i			0.502442i	0.967930	+	0.251221i	$0.0808322\pi$
$71$			35.6734i			0.502442i	−0.967930	+	0.251221i	$0.919168\pi$
$72$	−5.23387	−	5.23387i	−0.0726926	−	0.0726926i
$73$	−89.6694	+	89.6694i	−1.22835	+	1.22835i	−0.263759	+	0.964589i	$0.584962\pi$
$73$	−89.6694	+	89.6694i	−1.22835	+	1.22835i	−0.964589	+	0.263759i	$0.915038\pi$
$74$	0.973435	−	0.973435i	0.0131545	−	0.0131545i
$75$	−151.755			−2.02340
$76$			30.2593i			0.398149i
$77$	−23.4703	+	23.4703i	−0.304810	+	0.304810i
$78$			6.80349i			0.0872242i
$79$	−63.5426	−	63.5426i	−0.804337	−	0.804337i	0.179433	−	0.983770i	$-0.442574\pi$
$79$	−63.5426	−	63.5426i	−0.804337	−	0.804337i	−0.983770	+	0.179433i	$0.942574\pi$
$80$			126.204i			1.57755i
$81$	−101.034			−1.24734
$82$	−4.84492			−0.0590843
$83$	28.3259			0.341276			0.170638	−	0.985334i	$-0.445417\pi$
$83$	28.3259			0.341276			0.170638	+	0.985334i	$0.445417\pi$
$84$	−114.460	+	114.460i	−1.36262	+	1.36262i
$85$		−	93.5625i		−	1.10074i
$86$	−6.13062	+	6.13062i	−0.0712863	+	0.0712863i
$87$	46.6249	−	46.6249i	0.535919	−	0.535919i
$88$	3.20314	−	3.20314i	0.0363993	−	0.0363993i
$89$	−26.1493	+	26.1493i	−0.293812	+	0.293812i	−0.838584	−	0.544772i	$-0.816616\pi$
$89$	−26.1493	+	26.1493i	−0.293812	+	0.293812i	0.544772	+	0.838584i	$0.316616\pi$
$90$	5.32261	+	5.32261i	0.0591401	+	0.0591401i
$91$	106.255			1.16763
$92$	−0.777645	−	0.777645i	−0.00845266	−	0.00845266i
$93$	−100.933	+	100.933i	−1.08530	+	1.08530i
$94$	10.3566			0.110177
$95$		−	61.8167i		−	0.650702i
$96$	23.4659	−	23.4659i	0.244437	−	0.244437i
$97$		−	8.85513i		−	0.0912900i	−0.998958	−	0.0456450i	$-0.985466\pi$
$97$		−	8.85513i		−	0.0912900i	0.998958	−	0.0456450i	$-0.0145343\pi$
$98$	−9.31255	−	9.31255i	−0.0950260	−	0.0950260i
$99$			15.0826i			0.152350i
$100$		−	161.017i		−	1.61017i
$101$	−97.8251	+	97.8251i	−0.968566	+	0.968566i	−0.999521	−	0.0309551i	$-0.990145\pi$
$101$	−97.8251	+	97.8251i	−0.968566	+	0.968566i	0.0309551	+	0.999521i	$0.490145\pi$
$102$	−5.71353	+	5.71353i	−0.0560150	+	0.0560150i
$103$		−	59.7975i		−	0.580558i	−0.956942	−	0.290279i	$-0.906252\pi$
$103$		−	59.7975i		−	0.580558i	0.956942	−	0.290279i	$-0.0937482\pi$
$104$	−14.5012			−0.139435
$105$	233.830	−	233.830i	2.22695	−	2.22695i
$106$	12.5098	−	12.5098i	0.118017	−	0.118017i
$107$	−67.7344	−	67.7344i	−0.633032	−	0.633032i	0.315796	−	0.948827i	$-0.397729\pi$
$107$	−67.7344	−	67.7344i	−0.633032	−	0.633032i	−0.948827	+	0.315796i	$0.897729\pi$
$108$		−	59.7947i		−	0.553655i
$109$	39.8322	+	39.8322i	0.365433	+	0.365433i	0.865808	−	0.500376i	$-0.166805\pi$
$109$	39.8322	+	39.8322i	0.365433	+	0.365433i	−0.500376	+	0.865808i	$0.666805\pi$
$110$	−3.25745	+	3.25745i	−0.0296132	+	0.0296132i
$111$	−27.4815			−0.247581
$112$	−120.363	−	120.363i	−1.07467	−	1.07467i
$113$	95.3582	−	95.3582i	0.843878	−	0.843878i	−0.145483	−	0.989361i	$-0.546474\pi$
$113$	95.3582	−	95.3582i	0.843878	−	0.843878i	0.989361	+	0.145483i	$0.0464737\pi$
$114$	−3.77492	+	3.77492i	−0.0331134	+	0.0331134i
$115$	1.58865	+	1.58865i	0.0138143	+	0.0138143i
$116$	49.4705	+	49.4705i	0.426470	+	0.426470i
$117$	34.1410	−	34.1410i	0.291803	−	0.291803i
$118$			15.3299i			0.129914i
$119$	89.2321	+	89.2321i	0.749849	+	0.749849i
$120$	−31.9122	+	31.9122i	−0.265935	+	0.265935i
$121$	111.769			0.923714
$122$	5.59258	−	5.59258i	0.0458408	−	0.0458408i
$123$	68.3895	+	68.3895i	0.556012	+	0.556012i
$124$	−107.093	−	107.093i	−0.863654	−	0.863654i
$125$			126.441i			1.01153i
$126$	−10.1525			−0.0805755
$127$	100.103	+	100.103i	0.788210	+	0.788210i	0.981201	−	0.192991i	$-0.0618188\pi$
$127$	100.103	+	100.103i	0.788210	+	0.788210i	−0.192991	+	0.981201i	$0.561819\pi$
$128$	33.1475	+	33.1475i	0.258965	+	0.258965i
$129$	173.076			1.34168
$130$	14.7471			0.113439
$131$	144.802	−	144.802i	1.10536	−	1.10536i	0.111606	−	0.993753i	$-0.464401\pi$
$131$	144.802	−	144.802i	1.10536	−	1.10536i	0.993753	−	0.111606i	$-0.0355994\pi$
$132$	−45.0157			−0.341028
$133$	58.9556	+	58.9556i	0.443275	+	0.443275i
$134$	23.0887			0.172304
$135$			122.154i			0.904848i
$136$	−12.1780	−	12.1780i	−0.0895444	−	0.0895444i
$137$	−163.176	+	163.176i	−1.19107	+	1.19107i	−0.214299	+	0.976768i	$0.568747\pi$
$137$	−163.176	+	163.176i	−1.19107	+	1.19107i	−0.976768	+	0.214299i	$0.931253\pi$
$138$		−	0.194026i		−	0.00140599i
$139$	−151.244	+	151.244i	−1.08808	+	1.08808i	−0.0923579	+	0.995726i	$0.529440\pi$
$139$	−151.244	+	151.244i	−1.08808	+	1.08808i	−0.995726	+	0.0923579i	$0.970560\pi$
$140$	248.101	+	248.101i	1.77215	+	1.77215i
$141$	−146.191	−	146.191i	−1.03682	−	1.03682i
$142$	−4.72196	−	4.72196i	−0.0332532	−	0.0332532i
$143$	20.8944	+	20.8944i	0.146114	+	0.146114i
$144$	−77.3481			−0.537140
$145$	−101.063	−	101.063i	−0.696987	−	0.696987i
$146$		−	23.7384i		−	0.162592i
$147$			262.907i			1.78848i
$148$		−	29.1587i		−	0.197018i
$149$	189.632			1.27269			0.636347	−	0.771403i	$-0.280444\pi$
$149$	189.632			1.27269			0.636347	+	0.771403i	$0.280444\pi$
$150$	20.0873	−	20.0873i	0.133915	−	0.133915i
$151$	137.404			0.909958			0.454979	−	0.890502i	$-0.349647\pi$
$151$	137.404			0.909958			0.454979	+	0.890502i	$0.349647\pi$
$152$	−8.04602	−	8.04602i	−0.0529344	−	0.0529344i
$153$	57.3428			0.374789
$154$		−	6.21336i		−	0.0403465i
$155$	218.780	+	218.780i	1.41149	+	1.41149i
$156$	101.897	+	101.897i	0.653188	+	0.653188i
$157$	200.743	−	200.743i	1.27862	−	1.27862i	0.337177	−	0.941441i	$-0.390528\pi$
$157$	200.743	−	200.743i	1.27862	−	1.27862i	0.941441	−	0.337177i	$-0.109472\pi$
$158$	16.8218			0.106467
$159$	−353.170			−2.22120
$160$	−50.8642	−	50.8642i	−0.317901	−	0.317901i
$161$	−3.03024			−0.0188214
$162$	13.3735	−	13.3735i	0.0825527	−	0.0825527i
$163$	7.80262	−	7.80262i	0.0478689	−	0.0478689i	−0.682767	−	0.730636i	$-0.739224\pi$
$163$	7.80262	−	7.80262i	0.0478689	−	0.0478689i	0.730636	+	0.682767i	$0.239224\pi$
$164$	−72.5634	+	72.5634i	−0.442460	+	0.442460i
$165$	91.9625			0.557348
$166$	−3.74940	+	3.74940i	−0.0225867	+	0.0225867i
$167$	−263.062			−1.57522			−0.787610	−	0.616175i	$-0.788682\pi$
$167$	−263.062			−1.57522			−0.787610	+	0.616175i	$0.788682\pi$
$168$		−	60.8703i		−	0.362323i
$169$			74.4072i			0.440280i
$170$	12.3845	+	12.3845i	0.0728501	+	0.0728501i
$171$	37.8863			0.221558
$172$			183.639i			1.06767i
$173$	158.512			0.916255			0.458127	−	0.888887i	$-0.348520\pi$
$173$	158.512			0.916255			0.458127	+	0.888887i	$0.348520\pi$
$174$			12.3431i			0.0709375i
$175$	−313.717	−	313.717i	−1.79267	−	1.79267i
$176$		−	47.3372i		−	0.268962i
$177$	216.392	−	216.392i	1.22256	−	1.22256i
$178$		−	6.92257i		−	0.0388908i
$179$	173.866	+	173.866i	0.971320	+	0.971320i	0.999600	−	0.0282805i	$-0.00900317\pi$
$179$	173.866	+	173.866i	0.971320	+	0.971320i	−0.0282805	+	0.999600i	$0.509003\pi$
$180$	159.436			0.885754
$181$			178.367i			0.985453i	0.870184	+	0.492727i	$0.164000\pi$
$181$			178.367i			0.985453i	−0.870184	+	0.492727i	$0.836000\pi$
$182$	−14.0645	+	14.0645i	−0.0772777	+	0.0772777i
$183$	−157.887			−0.862769
$184$	0.413555			0.00224758
$185$			59.5682i			0.321990i
$186$		−	26.7202i		−	0.143657i
$187$			35.0939i			0.187668i
$188$	155.114	−	155.114i	0.825073	−	0.825073i
$189$	−116.501	−	116.501i	−0.616406	−	0.616406i
$190$	8.18244	+	8.18244i	0.0430655	+	0.0430655i
$191$	4.75047	+	4.75047i	0.0248716	+	0.0248716i	0.719433	−	0.694562i	$-0.244402\pi$
$191$	4.75047	+	4.75047i	0.0248716	+	0.0248716i	−0.694562	+	0.719433i	$0.744402\pi$
$192$		−	226.682i		−	1.18063i
$193$	365.439			1.89347			0.946734	−	0.322016i	$-0.104360\pi$
$193$	365.439			1.89347			0.946734	+	0.322016i	$0.104360\pi$
$194$	1.17212	+	1.17212i	0.00604185	+	0.00604185i
$195$	−208.166	−	208.166i	−1.06752	−	1.06752i
$196$	−278.952			−1.42323
$197$	−78.7652	−	78.7652i	−0.399823	−	0.399823i	0.478347	−	0.878171i	$-0.341236\pi$
$197$	−78.7652	−	78.7652i	−0.399823	−	0.399823i	−0.878171	+	0.478347i	$0.841236\pi$
$198$	−1.99643	−	1.99643i	−0.0100830	−	0.0100830i
$199$	193.060	−	193.060i	0.970149	−	0.970149i	−0.0294178	−	0.999567i	$-0.509365\pi$
$199$	193.060	−	193.060i	0.970149	−	0.970149i	0.999567	+	0.0294178i	$0.00936531\pi$
$200$	42.8148	+	42.8148i	0.214074	+	0.214074i
$201$	−325.914	−	325.914i	−1.62146	−	1.62146i
$202$		−	25.8975i		−	0.128205i
$203$	192.771			0.949611
$204$			171.146i			0.838949i
$205$	148.240	−	148.240i	0.723120	−	0.723120i
$206$	7.91517	+	7.91517i	0.0384232	+	0.0384232i
$207$	−0.973654	+	0.973654i	−0.00470364	+	0.00470364i
$208$	−107.152	+	107.152i	−0.515156	+	0.515156i
$209$			23.1865i			0.110940i
$210$			61.9023i			0.294773i
$211$	142.979	+	142.979i	0.677628	+	0.677628i	0.959463	−	0.281835i	$-0.0909431\pi$
$211$	142.979	+	142.979i	0.677628	+	0.677628i	−0.281835	+	0.959463i	$0.590943\pi$
$212$		−	374.725i		−	1.76757i
$213$			133.308i			0.625857i
$214$	17.9315			0.0837920
$215$		−	375.156i		−	1.74491i
$216$	15.8996	+	15.8996i	0.0736091	+	0.0736091i
$217$	−417.308			−1.92308
$218$	−10.5449			−0.0483710
$219$	−335.085	+	335.085i	−1.53007	+	1.53007i
$220$			97.5751i			0.443523i
$221$	79.4384	−	79.4384i	0.359450	−	0.359450i
$222$	3.63762	−	3.63762i	0.0163857	−	0.0163857i
$223$	13.4331	+	13.4331i	0.0602383	+	0.0602383i	0.736584	−	0.676346i	$-0.236438\pi$
$223$	13.4331	+	13.4331i	0.0602383	+	0.0602383i	−0.676346	+	0.736584i	$0.736438\pi$
$224$	97.0200			0.433125
$225$	−201.602			−0.896010
$226$			25.2444i			0.111701i
$227$	−9.14090	−	9.14090i	−0.0402683	−	0.0402683i	0.686686	−	0.726954i	$-0.259065\pi$
$227$	−9.14090	−	9.14090i	−0.0402683	−	0.0402683i	−0.726954	+	0.686686i	$0.759065\pi$
$228$			113.076i			0.495946i
$229$	43.8880	+	224.755i	0.191650	+	0.981463i
$229$	43.8880	+	224.755i	0.191650	+	0.981463i
$230$	−0.420567			−0.00182855
$231$	−87.7061	+	87.7061i	−0.379680	+	0.379680i
$232$	−26.3086			−0.113399
$233$			189.721i			0.814252i	0.913372	+	0.407126i	$0.133469\pi$
$233$			189.721i			0.814252i	−0.913372	+	0.407126i	$0.866531\pi$
$234$			9.03823i			0.0386249i
$235$	−316.881	+	316.881i	−1.34843	+	1.34843i
$236$	229.599	+	229.599i	0.972877	+	0.972877i
$237$	−237.452	−	237.452i	−1.00191	−	1.00191i
$238$	−23.6226			−0.0992547
$239$	−321.015	−	321.015i	−1.34316	−	1.34316i	−0.892897	−	0.450260i	$-0.851331\pi$
$239$	−321.015	−	321.015i	−1.34316	−	1.34316i	−0.450260	−	0.892897i	$-0.648669\pi$
$240$			471.610i			1.96504i
$241$		−	106.740i		−	0.442905i	−0.975171	−	0.221452i	$-0.928920\pi$
$241$		−	106.740i		−	0.442905i	0.975171	−	0.221452i	$-0.0710797\pi$
$242$	−14.7945	+	14.7945i	−0.0611343	+	0.0611343i
$243$	−241.827			−0.995174
$244$		−	167.523i		−	0.686569i
$245$	569.871			2.32600
$246$	−18.1049			−0.0735972
$247$	52.4849	−	52.4849i	0.212490	−	0.212490i
$248$	56.9526			0.229648
$249$	105.851			0.425104
$250$	−16.7366	−	16.7366i	−0.0669462	−	0.0669462i
$251$	228.672	+	228.672i	0.911042	+	0.911042i	0.996354	−	0.0853123i	$-0.0271888\pi$
$251$	228.672	+	228.672i	0.911042	+	0.911042i	−0.0853123	+	0.996354i	$0.527189\pi$
$252$	−152.056	+	152.056i	−0.603399	+	0.603399i
$253$	−0.595879	−	0.595879i	−0.00235525	−	0.00235525i
$254$	−26.5004			−0.104332
$255$		−	349.633i		−	1.37111i
$256$	233.867			0.913542
$257$	−167.698	+	167.698i	−0.652521	+	0.652521i	−0.953599	−	0.301078i	$-0.902654\pi$
$257$	−167.698	+	167.698i	−0.652521	+	0.652521i	0.301078	+	0.953599i	$0.402654\pi$
$258$	−22.9095	+	22.9095i	−0.0887963	+	0.0887963i
$259$	−56.8112	−	56.8112i	−0.219348	−	0.219348i
$260$	220.870	−	220.870i	0.849502	−	0.849502i
$261$	61.9398	−	61.9398i	0.237317	−	0.237317i
$262$			38.3338i			0.146312i
$263$	14.8317	−	14.8317i	0.0563945	−	0.0563945i	−0.678347	−	0.734742i	$-0.737303\pi$
$263$	14.8317	−	14.8317i	0.0563945	−	0.0563945i	0.734742	+	0.678347i	$0.237303\pi$
$264$	11.9698	−	11.9698i	0.0453401	−	0.0453401i
$265$			765.524i			2.88877i
$266$	−15.6075			−0.0586746
$267$	−97.7170	+	97.7170i	−0.365981	+	0.365981i
$268$	345.805	−	345.805i	1.29032	−	1.29032i
$269$	−172.912	+	172.912i	−0.642795	+	0.642795i	−0.951242	−	0.308447i	$-0.900191\pi$
$269$	−172.912	+	172.912i	−0.642795	+	0.642795i	0.308447	+	0.951242i	$0.400191\pi$
$270$	−16.1691	−	16.1691i	−0.0598857	−	0.0598857i
$271$	−243.637			−0.899029			−0.449515	−	0.893273i	$-0.648403\pi$
$271$	−243.637			−0.899029			−0.449515	+	0.893273i	$0.648403\pi$
$272$	−179.972			−0.661661
$273$	397.062			1.45444
$274$		−	43.1980i		−	0.157657i
$275$		−	123.381i		−	0.448658i
$276$	−2.90597	−	2.90597i	−0.0105289	−	0.0105289i
$277$	312.275			1.12735			0.563673	−	0.825998i	$-0.309388\pi$
$277$	312.275			1.12735			0.563673	+	0.825998i	$0.309388\pi$
$278$		−	40.0391i		−	0.144026i
$279$	−134.086	+	134.086i	−0.480597	+	0.480597i
$280$	−131.941			−0.471218
$281$	21.9024	+	21.9024i	0.0779444	+	0.0779444i	0.745004	−	0.667060i	$-0.232447\pi$
$281$	21.9024	+	21.9024i	0.0779444	+	0.0779444i	−0.667060	+	0.745004i	$0.732447\pi$
$282$	38.7016			0.137240
$283$	54.3566	−	54.3566i	0.192073	−	0.192073i	−0.604518	−	0.796591i	$-0.706634\pi$
$283$	54.3566	−	54.3566i	0.192073	−	0.192073i	0.796591	+	0.604518i	$0.206634\pi$
$284$	−141.444			−0.498041
$285$		−	231.002i		−	0.810534i
$286$	−5.53142			−0.0193406
$287$			282.757i			0.985216i
$288$	31.1738	−	31.1738i	0.108242	−	0.108242i
$289$	−155.576			−0.538326
$290$	26.7547			0.0922576
$291$		−	33.0906i		−	0.113714i
$292$	−355.535	−	355.535i	−1.21759	−	1.21759i
$293$		−	470.955i		−	1.60736i	−0.595064	−	0.803678i	$-0.702873\pi$
$293$		−	470.955i		−	1.60736i	0.595064	−	0.803678i	$-0.297127\pi$
$294$	−34.8000	−	34.8000i	−0.118367	−	0.118367i
$295$	−469.047	−	469.047i	−1.58999	−	1.58999i
$296$	7.75337	+	7.75337i	0.0261938	+	0.0261938i
$297$		−	45.8184i		−	0.154271i
$298$	−25.1008	+	25.1008i	−0.0842309	+	0.0842309i
$299$			2.69766i			0.00902226i
$300$		−	601.703i		−	2.00568i
$301$	357.793	+	357.793i	1.18868	+	1.18868i
$302$	−18.1876	+	18.1876i	−0.0602239	+	0.0602239i
$303$	−365.562	+	365.562i	−1.20647	+	1.20647i
$304$	−118.907			−0.391142
$305$			342.232i			1.12207i
$306$	−7.59025	+	7.59025i	−0.0248047	+	0.0248047i
$307$			279.361i			0.909970i	0.890499	+	0.454985i	$0.150355\pi$
$307$			279.361i			0.909970i	−0.890499	+	0.454985i	$0.849645\pi$
$308$	−93.0589	−	93.0589i	−0.302139	−	0.302139i
$309$		−	223.457i		−	0.723161i
$310$	−57.9182			−0.186833
$311$	395.491			1.27168			0.635838	−	0.771823i	$-0.280655\pi$
$311$	395.491			1.27168			0.635838	+	0.771823i	$0.280655\pi$
$312$	−54.1895			−0.173684
$313$	−246.805	+	246.805i	−0.788515	+	0.788515i	−0.981251	−	0.192736i	$-0.938264\pi$
$313$	−246.805	+	246.805i	−0.788515	+	0.788515i	0.192736	+	0.981251i	$0.438264\pi$
$314$			53.1432i			0.169246i
$315$	310.636	−	310.636i	0.986145	−	0.986145i
$316$	251.944	−	251.944i	0.797290	−	0.797290i
$317$	255.766	−	255.766i	0.806832	−	0.806832i	−0.177321	−	0.984153i	$-0.556743\pi$
$317$	255.766	−	255.766i	0.806832	−	0.806832i	0.984153	+	0.177321i	$0.0567432\pi$
$318$	46.7478	−	46.7478i	0.147006	−	0.147006i
$319$	37.9073	+	37.9073i	0.118832	+	0.118832i
$320$	−491.350			−1.53547
$321$	−253.116	−	253.116i	−0.788523	−	0.788523i
$322$	0.401101	−	0.401101i	0.00124566	−	0.00124566i
$323$	88.1530			0.272920
$324$		−	400.597i		−	1.23641i
$325$	−279.285	+	279.285i	−0.859338	+	0.859338i
$326$			2.06561i			0.00633622i
$327$	148.849	+	148.849i	0.455194	+	0.455194i
$328$		−	38.5895i		−	0.117651i
$329$		−	604.430i		−	1.83717i
$330$	−12.1727	+	12.1727i	−0.0368871	+	0.0368871i
$331$	−128.977	+	128.977i	−0.389659	+	0.389659i	−0.874566	−	0.484907i	$-0.838853\pi$
$331$	−128.977	+	128.977i	−0.389659	+	0.389659i	0.484907	+	0.874566i	$0.338853\pi$
$332$			112.311i			0.338286i
$333$	−36.5083			−0.109635
$334$	34.8205	−	34.8205i	0.104253	−	0.104253i
$335$	−706.444	+	706.444i	−2.10879	+	2.10879i
$336$	−449.782	−	449.782i	−1.33864	−	1.33864i
$337$			317.861i			0.943207i	0.881811	+	0.471603i	$0.156325\pi$
$337$			317.861i			0.943207i	−0.881811	+	0.471603i	$0.843675\pi$
$338$	−9.84901	−	9.84901i	−0.0291391	−	0.0291391i
$339$	356.343	−	356.343i	1.05116	−	1.05116i
$340$	370.971			1.09109
$341$	−82.0613	−	82.0613i	−0.240649	−	0.240649i
$342$	−5.01487	+	5.01487i	−0.0146634	+	0.0146634i
$343$	−164.965	+	164.965i	−0.480947	+	0.480947i
$344$	−48.8301	−	48.8301i	−0.141948	−	0.141948i
$345$	5.93660	+	5.93660i	0.0172075	+	0.0172075i
$346$	−20.9817	+	20.9817i	−0.0606406	+	0.0606406i
$347$		−	37.5017i		−	0.108074i	−0.998539	−	0.0540370i	$-0.982791\pi$
$347$		−	37.5017i		−	0.108074i	0.998539	−	0.0540370i	$-0.0172089\pi$
$348$	184.866	+	184.866i	0.531224	+	0.531224i
$349$	−187.081	+	187.081i	−0.536048	+	0.536048i	−0.922366	−	0.386318i	$-0.873747\pi$
$349$	−187.081	+	187.081i	−0.536048	+	0.536048i	0.386318	+	0.922366i	$0.373747\pi$
$350$	83.0510			0.237288
$351$	−103.714	+	103.714i	−0.295482	+	0.295482i
$352$	19.0784	+	19.0784i	0.0542000	+	0.0542000i
$353$	124.773	+	124.773i	0.353465	+	0.353465i	0.861397	−	0.507932i	$-0.169590\pi$
$353$	124.773	+	124.773i	0.353465	+	0.353465i	−0.507932	+	0.861397i	$0.669590\pi$
$354$			57.2861i			0.161825i
$355$	288.955			0.813957
$356$	−103.681	−	103.681i	−0.291238	−	0.291238i
$357$	333.450	+	333.450i	0.934035	+	0.934035i
$358$	−46.0280			−0.128570
$359$	180.867			0.503808			0.251904	−	0.967752i	$-0.418943\pi$
$359$	180.867			0.503808			0.251904	+	0.967752i	$0.418943\pi$
$360$	−42.3943	+	42.3943i	−0.117762	+	0.117762i
$361$	−302.757			−0.838663
$362$	−23.6098	−	23.6098i	−0.0652204	−	0.0652204i
$363$	417.670			1.15061
$364$			421.295i			1.15741i
$365$	726.322	+	726.322i	1.98992	+	1.98992i
$366$	20.8989	−	20.8989i	0.0571007	−	0.0571007i
$367$		−	341.770i		−	0.931253i	−0.884981	−	0.465627i	$-0.845829\pi$
$367$		−	341.770i		−	0.931253i	0.884981	−	0.465627i	$-0.154171\pi$
$368$	3.05584	−	3.05584i	0.00830391	−	0.00830391i
$369$	90.8534	+	90.8534i	0.246215	+	0.246215i
$370$	−7.88482	−	7.88482i	−0.0213103	−	0.0213103i
$371$	−730.093	−	730.093i	−1.96790	−	1.96790i
$372$	−400.195	−	400.195i	−1.07579	−	1.07579i
$373$	268.543			0.719955			0.359977	−	0.932961i	$-0.382784\pi$
$373$	268.543			0.719955			0.359977	+	0.932961i	$0.382784\pi$
$374$	−4.64525	−	4.64525i	−0.0124205	−	0.0124205i
$375$			472.497i			1.25999i
$376$			82.4902i			0.219389i
$377$		−	171.614i		−	0.455208i
$378$	30.8415			0.0815913
$379$	361.227	−	361.227i	0.953107	−	0.953107i	−0.0458421	−	0.998949i	$-0.514597\pi$
$379$	361.227	−	361.227i	0.953107	−	0.953107i	0.998949	+	0.0458421i	$0.0145971\pi$
$380$	245.101			0.645001
$381$	374.072	+	374.072i	0.981817	+	0.981817i
$382$	−1.25760			−0.00329216
$383$			392.623i			1.02513i	0.858650	+	0.512563i	$0.171304\pi$
$383$			392.623i			1.02513i	−0.858650	+	0.512563i	$0.828696\pi$
$384$	123.869	+	123.869i	0.322575	+	0.322575i
$385$	190.110	+	190.110i	0.493792	+	0.493792i
$386$	−48.3718	+	48.3718i	−0.125316	+	0.125316i
$387$	229.927			0.594126
$388$	35.1102			0.0904902
$389$	−14.5568	−	14.5568i	−0.0374212	−	0.0374212i	0.688149	−	0.725570i	$-0.258424\pi$
$389$	−14.5568	−	14.5568i	−0.0374212	−	0.0374212i	−0.725570	+	0.688149i	$0.758424\pi$
$390$	55.1082			0.141303
$391$	−2.26548	+	2.26548i	−0.00579405	+	0.00579405i
$392$	74.1741	−	74.1741i	0.189220	−	0.189220i
$393$	541.109	−	541.109i	1.37687	−	1.37687i
$394$	20.8517			0.0529231
$395$	−514.695	+	514.695i	−1.30303	+	1.30303i
$396$	−59.8020			−0.151015
$397$		−	146.271i		−	0.368441i	−0.982885	−	0.184221i	$-0.941024\pi$
$397$		−	146.271i		−	0.368441i	0.982885	−	0.184221i	$-0.0589761\pi$
$398$			51.1092i			0.128415i
$399$	220.310	+	220.310i	0.552156	+	0.552156i
$400$	632.734			1.58183
$401$		−	256.380i		−	0.639351i	−0.947527	−	0.319676i	$-0.896426\pi$
$401$		−	256.380i		−	0.639351i	0.947527	−	0.319676i	$-0.103574\pi$
$402$	86.2800			0.214627
$403$			371.507i			0.921853i
$404$	−387.873	−	387.873i	−0.960081	−	0.960081i
$405$			818.379i			2.02069i
$406$	−25.5164	+	25.5164i	−0.0628482	+	0.0628482i
$407$		−	22.3432i		−	0.0548972i
$408$	−45.5080	−	45.5080i	−0.111539	−	0.111539i
$409$	−91.6452			−0.224071			−0.112036	−	0.993704i	$-0.535737\pi$
$409$	−91.6452			−0.224071			−0.112036	+	0.993704i	$0.535737\pi$
$410$			39.2438i			0.0957166i
$411$	−609.771	+	609.771i	−1.48363	+	1.48363i
$412$	237.095			0.575473
$413$	894.676			2.16629
$414$		−	0.257758i		−	0.000622603i
$415$		−	229.440i		−	0.552867i
$416$		−	86.3716i		−	0.207624i
$417$	−565.181	+	565.181i	−1.35535	+	1.35535i
$418$	−3.06911	−	3.06911i	−0.00734238	−	0.00734238i
$419$	−289.172	−	289.172i	−0.690149	−	0.690149i	0.272116	−	0.962264i	$-0.412277\pi$
$419$	−289.172	−	289.172i	−0.690149	−	0.690149i	−0.962264	+	0.272116i	$0.912277\pi$
$420$	927.125	+	927.125i	2.20744	+	2.20744i
$421$		−	615.782i		−	1.46267i	−0.682021	−	0.731333i	$-0.738899\pi$
$421$		−	615.782i		−	1.46267i	0.682021	−	0.731333i	$-0.261101\pi$
$422$	−37.8513			−0.0896950
$423$	−194.211	−	194.211i	−0.459127	−	0.459127i
$424$	99.6402	+	99.6402i	0.235000	+	0.235000i
$425$	−469.083			−1.10373
$426$	−17.6454	−	17.6454i	−0.0414212	−	0.0414212i
$427$	−326.392	−	326.392i	−0.764384	−	0.764384i
$428$	268.564	−	268.564i	0.627486	−	0.627486i
$429$	78.0799	+	78.0799i	0.182005	+	0.182005i
$430$	49.6580	+	49.6580i	0.115484	+	0.115484i
$431$		−	537.378i		−	1.24682i	−0.781896	−	0.623409i	$-0.785747\pi$
$431$		−	537.378i		−	1.24682i	0.781896	−	0.623409i	$-0.214253\pi$
$432$	234.970			0.543912
$433$		−	47.5768i		−	0.109877i	−0.998490	−	0.0549385i	$-0.982504\pi$
$433$		−	47.5768i		−	0.109877i	0.998490	−	0.0549385i	$-0.0174963\pi$
$434$	55.2376	−	55.2376i	0.127275	−	0.127275i
$435$	−377.662	−	377.662i	−0.868188	−	0.868188i
$436$	−157.933	+	157.933i	−0.362232	+	0.362232i
$437$	−1.49680	+	1.49680i	−0.00342517	+	0.00342517i
$438$		−	88.7078i		−	0.202529i
$439$		−	402.607i		−	0.917100i	−0.888669	−	0.458550i	$-0.848369\pi$
$439$		−	402.607i		−	0.917100i	0.888669	−	0.458550i	$-0.151631\pi$
$440$	−25.9454	−	25.9454i	−0.0589669	−	0.0589669i
$441$			349.264i			0.791981i
$442$			21.0299i			0.0475790i
$443$	349.373			0.788652			0.394326	−	0.918971i	$-0.370978\pi$
$443$	349.373			0.788652			0.394326	+	0.918971i	$0.370978\pi$
$444$		−	108.963i		−	0.245412i
$445$	211.809	+	211.809i	0.475976	+	0.475976i
$446$	−3.55619			−0.00797352
$447$	708.632			1.58531
$448$	468.609	−	468.609i	1.04600	−	1.04600i
$449$		−	74.2240i		−	0.165310i	−0.996578	−	0.0826548i	$-0.973660\pi$
$449$		−	74.2240i		−	0.165310i	0.996578	−	0.0826548i	$-0.0263399\pi$
$450$	26.6853	−	26.6853i	0.0593007	−	0.0593007i
$451$	−55.6025	+	55.6025i	−0.123287	+	0.123287i
$452$	378.091	+	378.091i	0.836485	+	0.836485i
$453$	513.462			1.13347
$454$	2.41989			0.00533016
$455$		−	860.663i		−	1.89157i
$456$	−30.0671	−	30.0671i	−0.0659366	−	0.0659366i
$457$		−	94.2574i		−	0.206253i	−0.994668	−	0.103126i	$-0.967115\pi$
$457$		−	94.2574i		−	0.206253i	0.994668	−	0.103126i	$-0.0328846\pi$
$458$	−35.5593	−	23.9407i	−0.0776403	−	0.0522723i
$459$	−174.197			−0.379514
$460$	−6.29892	+	6.29892i	−0.0136933	+	0.0136933i
$461$	−616.239			−1.33674			−0.668372	−	0.743828i	$-0.733008\pi$
$461$	−616.239			−1.33674			−0.668372	+	0.743828i	$0.733008\pi$
$462$		−	23.2187i		−	0.0502568i
$463$			11.8111i			0.0255099i	0.999919	+	0.0127549i	$0.00406013\pi$
$463$			11.8111i			0.0255099i	−0.999919	+	0.0127549i	$0.995940\pi$
$464$	−194.400	+	194.400i	−0.418965	+	0.418965i
$465$	817.558	+	817.558i	1.75819	+	1.75819i
$466$	−25.1126	−	25.1126i	−0.0538898	−	0.0538898i
$467$	127.209			0.272396			0.136198	−	0.990682i	$-0.456512\pi$
$467$	127.209			0.272396			0.136198	+	0.990682i	$0.456512\pi$
$468$	135.368	+	135.368i	0.289247	+	0.289247i
$469$		−	1347.49i		−	2.87312i
$470$		−	83.8888i		−	0.178487i
$471$	750.155	−	750.155i	1.59269	−	1.59269i
$472$	−122.102			−0.258690
$473$			140.716i			0.297496i
$474$	62.8612			0.132619
$475$	−309.923			−0.652469
$476$	−353.801	+	353.801i	−0.743280	+	0.743280i
$477$	−469.176			−0.983598
$478$	84.9830			0.177789
$479$	227.270	+	227.270i	0.474468	+	0.474468i	0.903357	−	0.428889i	$-0.141095\pi$
$479$	227.270	+	227.270i	0.474468	+	0.474468i	−0.428889	+	0.903357i	$0.641095\pi$
$480$	−190.074	−	190.074i	−0.395987	−	0.395987i
$481$	−50.5759	+	50.5759i	−0.105147	+	0.105147i
$482$	14.1288	+	14.1288i	0.0293128	+	0.0293128i
$483$	−11.3237			−0.0234444
$484$			443.161i			0.915622i
$485$	−71.7265			−0.147890
$486$	32.0098	−	32.0098i	0.0658637	−	0.0658637i
$487$	26.8194	−	26.8194i	0.0550706	−	0.0550706i	−0.679035	−	0.734106i	$-0.737602\pi$
$487$	26.8194	−	26.8194i	0.0550706	−	0.0550706i	0.734106	+	0.679035i	$0.237602\pi$
$488$	44.5447	+	44.5447i	0.0912801	+	0.0912801i
$489$	29.1575	−	29.1575i	0.0596269	−	0.0596269i
$490$	−75.4317	+	75.4317i	−0.153942	+	0.153942i
$491$		−	300.731i		−	0.612486i	−0.951953	−	0.306243i	$-0.900928\pi$
$491$		−	300.731i		−	0.612486i	0.951953	−	0.306243i	$-0.0990721\pi$
$492$	−271.161	+	271.161i	−0.551141	+	0.551141i
$493$	144.120	−	144.120i	0.292333	−	0.292333i
$494$			13.8945i			0.0281264i
$495$	122.169			0.246807
$496$	420.834	−	420.834i	0.848455	−	0.848455i
$497$	−275.581	+	275.581i	−0.554489	+	0.554489i
$498$	−14.0111	+	14.0111i	−0.0281347	+	0.0281347i
$499$	−412.941	−	412.941i	−0.827537	−	0.827537i	0.159639	−	0.987175i	$-0.448967\pi$
$499$	−412.941	−	412.941i	−0.827537	−	0.827537i	−0.987175	+	0.159639i	$0.948967\pi$
$500$	−501.334			−1.00267
$501$	−983.032			−1.96214
$502$	−60.5368			−0.120591
$503$		−	269.516i		−	0.535818i	−0.963444	−	0.267909i	$-0.913667\pi$
$503$		−	269.516i		−	0.535818i	0.963444	−	0.267909i	$-0.0863326\pi$
$504$		−	80.8643i		−	0.160445i
$505$	792.384	+	792.384i	1.56908	+	1.56908i
$506$	0.157748			0.000311756
$507$			278.052i			0.548425i
$508$	−396.903	+	396.903i	−0.781305	+	0.781305i
$509$	95.5732			0.187767			0.0938833	−	0.995583i	$-0.470072\pi$
$509$	95.5732			0.187767			0.0938833	+	0.995583i	$0.470072\pi$
$510$	46.2796	+	46.2796i	0.0907443	+	0.0907443i
$511$	−1385.41			−2.71118
$512$	−163.546	+	163.546i	−0.319426	+	0.319426i
$513$	−115.092			−0.224351
$514$		−	44.3951i		−	0.0863718i
$515$	−484.360			−0.940505
$516$			686.240i			1.32992i
$517$	118.858	−	118.858i	0.229899	−	0.229899i
$518$	15.0398			0.0290343
$519$	592.342			1.14131
$520$			117.460i			0.225885i
$521$	206.235	+	206.235i	0.395845	+	0.395845i	0.876765	−	0.480919i	$-0.159697\pi$
$521$	206.235	+	206.235i	0.395845	+	0.395845i	−0.480919	+	0.876765i	$0.659697\pi$
$522$			16.3975i			0.0314128i
$523$	327.893	+	327.893i	0.626947	+	0.626947i	0.947299	−	0.320352i	$-0.103801\pi$
$523$	327.893	+	327.893i	0.626947	+	0.626947i	−0.320352	+	0.947299i	$0.603801\pi$
$524$	574.134	+	574.134i	1.09567	+	1.09567i
$525$	−1172.32	−	1172.32i	−2.23300	−	2.23300i
$526$			3.92644i			0.00746472i
$527$	−311.989	+	311.989i	−0.592010	+	0.592010i
$528$		−	176.894i		−	0.335027i
$529$			528.923i			0.999855i
$530$	−101.330	−	101.330i	−0.191188	−	0.191188i
$531$	287.471	−	287.471i	0.541376	−	0.541376i
$532$	−233.756	+	233.756i	−0.439392	+	0.439392i
$533$	251.723			0.472276
$534$		−	25.8689i		−	0.0484436i
$535$	−548.649	+	548.649i	−1.02551	+	1.02551i
$536$			183.901i			0.343098i
$537$	649.719	+	649.719i	1.20990	+	1.20990i
$538$		−	45.7754i		−	0.0850844i
$539$	−213.750			−0.396568
$540$	−484.337			−0.896921
$541$	−696.634			−1.28768			−0.643839	−	0.765161i	$-0.722659\pi$
$541$	−696.634			−1.28768			−0.643839	+	0.765161i	$0.722659\pi$
$542$	32.2493	−	32.2493i	0.0595006	−	0.0595006i
$543$			666.538i			1.22751i
$544$	72.5344	−	72.5344i	0.133335	−	0.133335i
$545$	322.641	−	322.641i	0.592002	−	0.592002i
$546$	−52.5576	+	52.5576i	−0.0962594	+	0.0962594i
$547$	156.632	−	156.632i	0.286348	−	0.286348i	−0.549286	−	0.835634i	$-0.685100\pi$
$547$	156.632	−	156.632i	0.286348	−	0.286348i	0.835634	+	0.549286i	$0.185100\pi$
$548$	−646.987	−	646.987i	−1.18063	−	1.18063i
$549$	−209.748			−0.382054
$550$	16.3315	+	16.3315i	0.0296936	+	0.0296936i
$551$	95.2200	−	95.2200i	0.172813	−	0.172813i
$552$	1.54541			0.00279965
$553$		−	981.746i		−	1.77531i
$554$	−41.3346	+	41.3346i	−0.0746113	+	0.0746113i
$555$			222.600i			0.401081i
$556$	−599.675	−	599.675i	−1.07855	−	1.07855i
$557$		−	109.574i		−	0.196723i	−0.995151	−	0.0983613i	$-0.968640\pi$
$557$		−	109.574i		−	0.196723i	0.995151	−	0.0983613i	$-0.0313601\pi$
$558$		−	35.4970i		−	0.0636148i
$559$	318.523	−	318.523i	0.569809	−	0.569809i
$560$	−974.938	+	974.938i	−1.74096	+	1.74096i
$561$			131.142i			0.233765i
$562$	−5.79827			−0.0103172
$563$	−468.300	+	468.300i	−0.831794	+	0.831794i	−0.987762	−	0.155968i	$-0.950150\pi$
$563$	−468.300	+	468.300i	−0.831794	+	0.831794i	0.155968	+	0.987762i	$0.450150\pi$
$564$	579.643	−	579.643i	1.02774	−	1.02774i
$565$	−772.401	−	772.401i	−1.36708	−	1.36708i
$566$			14.3900i			0.0254240i
$567$	−780.501	−	780.501i	−1.37654	−	1.37654i
$568$	37.6102	−	37.6102i	0.0662151	−	0.0662151i
$569$	−17.0254			−0.0299216			−0.0149608	−	0.999888i	$-0.504762\pi$
$569$	−17.0254			−0.0299216			−0.0149608	+	0.999888i	$0.504762\pi$
$570$	30.5769	+	30.5769i	0.0536437	+	0.0536437i
$571$	−568.835	+	568.835i	−0.996208	+	0.996208i	−0.999993	−	0.00378456i	$-0.998795\pi$
$571$	−568.835	+	568.835i	−0.996208	+	0.996208i	0.00378456	+	0.999993i	$0.498795\pi$
$572$	−82.8453	+	82.8453i	−0.144834	+	0.144834i
$573$	17.7520	+	17.7520i	0.0309808	+	0.0309808i
$574$	−37.4275	−	37.4275i	−0.0652046	−	0.0652046i
$575$	7.96482	−	7.96482i	0.0138519	−	0.0138519i
$576$		−	301.140i		−	0.522812i
$577$	298.074	+	298.074i	0.516593	+	0.516593i	0.916539	−	0.399946i	$-0.130971\pi$
$577$	298.074	+	298.074i	0.516593	+	0.516593i	−0.399946	+	0.916539i	$0.630971\pi$
$578$	20.5930	−	20.5930i	0.0356281	−	0.0356281i
$579$	1365.61			2.35856
$580$	400.711	−	400.711i	0.690881	−	0.690881i
$581$	218.821	+	218.821i	0.376628	+	0.376628i
$582$	4.38008	+	4.38008i	0.00752592	+	0.00752592i
$583$		−	287.137i		−	0.492516i
$584$	189.075			0.323759
$585$	−276.542	−	276.542i	−0.472721	−	0.472721i
$586$	62.3386	+	62.3386i	0.106380	+	0.106380i
$587$	402.035			0.684898			0.342449	−	0.939536i	$-0.388744\pi$
$587$	402.035			0.684898			0.342449	+	0.939536i	$0.388744\pi$
$588$	−1042.41			−1.77281
$589$	−206.131	+	206.131i	−0.349968	+	0.349968i
$590$	124.172			0.210461
$591$	−294.337	−	294.337i	−0.498032	−	0.498032i
$592$	114.582			0.193551
$593$			298.499i			0.503370i	0.967809	+	0.251685i	$0.0809848\pi$
$593$			298.499i			0.503370i	−0.967809	+	0.251685i	$0.919015\pi$
$594$	6.06480	+	6.06480i	0.0102101	+	0.0102101i
$595$	722.780	−	722.780i	1.21476	−	1.21476i
$596$			751.881i			1.26155i
$597$	721.443	−	721.443i	1.20845	−	1.20845i
$598$	−0.357079	−	0.357079i	−0.000597121	−	0.000597121i
$599$	−130.057	−	130.057i	−0.217124	−	0.217124i	0.590161	−	0.807285i	$-0.299064\pi$
$599$	−130.057	−	130.057i	−0.217124	−	0.217124i	−0.807285	+	0.590161i	$0.799064\pi$
$600$	159.994	+	159.994i	0.266657	+	0.266657i
$601$	−46.6388	−	46.6388i	−0.0776020	−	0.0776020i	0.667240	−	0.744842i	$-0.267475\pi$
$601$	−46.6388	−	46.6388i	−0.0776020	−	0.0776020i	−0.744842	+	0.667240i	$0.767475\pi$
$602$	−94.7194			−0.157341
$603$	−432.967	−	432.967i	−0.718021	−	0.718021i
$604$			544.800i			0.901986i
$605$		−	905.332i		−	1.49642i
$606$		−	96.7761i		−	0.159696i
$607$	875.209			1.44186			0.720930	−	0.693008i	$-0.243715\pi$
$607$	875.209			1.44186			0.720930	+	0.693008i	$0.243715\pi$
$608$	47.9234	−	47.9234i	0.0788214	−	0.0788214i
$609$	720.364			1.18286
$610$	−45.2999	−	45.2999i	−0.0742622	−	0.0742622i
$611$	−538.091			−0.880672
$612$			227.362i			0.371506i
$613$	585.225	+	585.225i	0.954690	+	0.954690i	0.999017	−	0.0443271i	$-0.0141144\pi$
$613$	585.225	+	585.225i	0.954690	+	0.954690i	−0.0443271	+	0.999017i	$0.514114\pi$
$614$	−36.9779	−	36.9779i	−0.0602246	−	0.0602246i
$615$	553.955	−	553.955i	0.900740	−	0.900740i
$616$	49.4892			0.0803396
$617$	972.992			1.57697			0.788486	−	0.615052i	$-0.210865\pi$
$617$	972.992			1.57697			0.788486	+	0.615052i	$0.210865\pi$
$618$	29.5781	+	29.5781i	0.0478611	+	0.0478611i
$619$	42.1218			0.0680481			0.0340240	−	0.999421i	$-0.489168\pi$
$619$	42.1218			0.0680481			0.0340240	+	0.999421i	$0.489168\pi$
$620$	−867.454	+	867.454i	−1.39912	+	1.39912i
$621$	2.95779	−	2.95779i	0.00476294	−	0.00476294i
$622$	−52.3497	+	52.3497i	−0.0841635	+	0.0841635i
$623$	−404.012			−0.648494
$624$	−400.417	+	400.417i	−0.641693	+	0.641693i
$625$	8.92355			0.0142777
$626$		−	65.3373i		−	0.104373i
$627$			86.6455i			0.138191i
$628$	795.938	+	795.938i	1.26742	+	1.26742i
$629$	−84.9466			−0.135050
$630$			82.2354i			0.130532i
$631$	240.154			0.380593			0.190297	−	0.981727i	$-0.439055\pi$
$631$	240.154			0.380593			0.190297	+	0.981727i	$0.439055\pi$
$632$			133.985i			0.212001i
$633$	534.298	+	534.298i	0.844073	+	0.844073i
$634$			67.7095i			0.106797i
$635$	810.831	−	810.831i	1.27690	−	1.27690i
$636$		−	1400.31i		−	2.20174i
$637$	483.844	+	483.844i	0.759567	+	0.759567i
$638$	−10.0353			−0.0157293
$639$			177.095i			0.277144i
$640$	268.495	−	268.495i	0.419523	−	0.419523i
$641$	−158.893			−0.247884			−0.123942	−	0.992289i	$-0.539554\pi$
$641$	−158.893			−0.247884			−0.123942	+	0.992289i	$0.539554\pi$
$642$	67.0080			0.104374
$643$			1100.26i			1.71113i	0.517695	+	0.855565i	$0.326790\pi$
$643$			1100.26i			1.71113i	−0.517695	+	0.855565i	$0.673210\pi$
$644$		−	12.0148i		−	0.0186565i
$645$		−	1401.92i		−	2.17352i
$646$	−11.6685	+	11.6685i	−0.0180627	+	0.0180627i
$647$	−803.669	−	803.669i	−1.24215	−	1.24215i	−0.959109	−	0.283038i	$-0.908658\pi$
$647$	−803.669	−	803.669i	−1.24215	−	1.24215i	−0.283038	−	0.959109i	$-0.591342\pi$
$648$	106.520	+	106.520i	0.164382	+	0.164382i
$649$	175.933	+	175.933i	0.271083	+	0.271083i
$650$		−	73.9357i		−	0.113747i
$651$	−1559.44			−2.39545
$652$	30.9371	+	30.9371i	0.0474495	+	0.0474495i
$653$	−652.433	−	652.433i	−0.999132	−	0.999132i	0.000867907	−	1.00000i	$-0.499724\pi$
$653$	−652.433	−	652.433i	−0.999132	−	0.999132i	−1.00000		0.000867907i	$0.999724\pi$
$654$	−39.4050			−0.0602524
$655$	−1172.90	−	1172.90i	−1.79068	−	1.79068i
$656$	−285.146	−	285.146i	−0.434673	−	0.434673i
$657$	−445.150	+	445.150i	−0.677549	+	0.677549i
$658$	80.0061	+	80.0061i	0.121590	+	0.121590i
$659$	244.566	+	244.566i	0.371117	+	0.371117i	0.867884	−	0.496767i	$-0.165480\pi$
$659$	244.566	+	244.566i	0.371117	+	0.371117i	−0.496767	+	0.867884i	$0.665480\pi$
$660$			364.627i			0.552466i
$661$	−79.3862			−0.120100			−0.0600501	−	0.998195i	$-0.519126\pi$
$661$	−79.3862			−0.120100			−0.0600501	+	0.998195i	$0.519126\pi$
$662$		−	34.1444i		−	0.0515777i
$663$	296.853	−	296.853i	0.447742	−	0.447742i
$664$	−29.8638	−	29.8638i	−0.0449756	−	0.0449756i
$665$	477.540	−	477.540i	0.718105	−	0.718105i
$666$	4.83247	−	4.83247i	0.00725595	−	0.00725595i
$667$			4.89418i			0.00733761i
$668$		−	1043.03i		−	1.56142i
$669$	50.1982	+	50.1982i	0.0750347	+	0.0750347i
$670$		−	187.019i		−	0.279132i
$671$		−	128.366i		−	0.191306i
$672$	362.553			0.539513
$673$			382.555i			0.568433i	0.958760	+	0.284216i	$0.0917334\pi$
$673$			382.555i			0.568433i	−0.958760	+	0.284216i	$0.908267\pi$
$674$	−42.0740	−	42.0740i	−0.0624244	−	0.0624244i
$675$	612.431			0.907306
$676$	−295.022			−0.436423
$677$	−827.550	+	827.550i	−1.22238	+	1.22238i	−0.255595	+	0.966784i	$0.582271\pi$
$677$	−827.550	+	827.550i	−1.22238	+	1.22238i	−0.966784	+	0.255595i	$0.917729\pi$
$678$			94.3356i			0.139138i
$679$	68.4068	−	68.4068i	0.100746	−	0.100746i
$680$	−98.6422	+	98.6422i	−0.145062	+	0.145062i
$681$	−34.1585	−	34.1585i	−0.0501594	−	0.0501594i
$682$	21.7243			0.0318538
$683$	−897.834			−1.31454			−0.657272	−	0.753653i	$-0.728290\pi$
$683$	−897.834			−1.31454			−0.657272	+	0.753653i	$0.728290\pi$
$684$			150.218i			0.219617i
$685$	1321.73	+	1321.73i	1.92953	+	1.92953i
$686$		−	43.6716i		−	0.0636612i
$687$	164.004	+	839.885i	0.238726	+	1.22254i
$688$	−721.631			−1.04888
$689$	−649.962	+	649.962i	−0.943341	+	0.943341i
$690$	−1.57161			−0.00227770
$691$			190.705i			0.275984i	0.990433	+	0.137992i	$0.0440649\pi$
$691$			190.705i			0.275984i	−0.990433	+	0.137992i	$0.955935\pi$
$692$			628.494i			0.908228i
$693$	−116.515	+	116.515i	−0.168131	+	0.168131i
$694$	4.96395	+	4.96395i	0.00715267	+	0.00715267i
$695$	1225.07	+	1225.07i	1.76270	+	1.76270i
$696$	−98.3125			−0.141254
$697$	211.395	+	211.395i	0.303293	+	0.303293i
$698$		−	49.5264i		−	0.0709547i
$699$			708.966i			1.01426i
$700$	1243.87	−	1243.87i	1.77696	−	1.77696i
$701$	815.503			1.16334			0.581671	−	0.813424i	$-0.302399\pi$
$701$	815.503			1.16334			0.581671	+	0.813424i	$0.302399\pi$
$702$		−	27.4565i		−	0.0391118i
$703$	−56.1242			−0.0798353
$704$	184.298			0.261787
$705$	−1184.15	+	1184.15i	−1.67965	+	1.67965i
$706$	−33.0315			−0.0467868
$707$	−1511.42			−2.13779
$708$	857.986	+	857.986i	1.21185	+	1.21185i
$709$	−534.952	−	534.952i	−0.754516	−	0.754516i	0.220802	−	0.975319i	$-0.429132\pi$
$709$	−534.952	−	534.952i	−0.754516	−	0.754516i	−0.975319	+	0.220802i	$0.929132\pi$
$710$	−38.2479	+	38.2479i	−0.0538702	+	0.0538702i
$711$	−315.447	−	315.447i	−0.443667	−	0.443667i
$712$	55.1380			0.0774410
$713$		−	10.5949i		−	0.0148596i
$714$	−88.2752			−0.123635
$715$	169.244	−	169.244i	0.236705	−	0.236705i
$716$	−689.372	+	689.372i	−0.962810	+	0.962810i
$717$	−1199.60	−	1199.60i	−1.67308	−	1.67308i
$718$	−23.9407	+	23.9407i	−0.0333436	+	0.0333436i
$719$	−312.667	+	312.667i	−0.434864	+	0.434864i	−0.890279	−	0.455415i	$-0.849491\pi$
$719$	−312.667	+	312.667i	−0.434864	+	0.434864i	0.455415	+	0.890279i	$0.349491\pi$
$720$			626.520i			0.870167i
$721$	461.942	−	461.942i	0.640696	−	0.640696i
$722$	40.0749	−	40.0749i	0.0555053	−	0.0555053i
$723$		−	398.876i		−	0.551696i
$724$	−707.218			−0.976820
$725$	−506.688	+	506.688i	−0.698881	+	0.698881i
$726$	−55.2854	+	55.2854i	−0.0761507	+	0.0761507i
$727$	−30.7260	+	30.7260i	−0.0422641	+	0.0422641i	−0.727923	−	0.685659i	$-0.759514\pi$
$727$	−30.7260	+	30.7260i	−0.0422641	+	0.0422641i	0.685659	+	0.727923i	$0.259514\pi$
$728$	−112.023	−	112.023i	−0.153878	−	0.153878i
$729$	5.62781			0.00771991
$730$	−192.281			−0.263399
$731$	534.988			0.731858
$732$		−	626.014i		−	0.855210i
$733$			930.702i			1.26972i	0.772629	+	0.634858i	$0.218941\pi$
$733$			930.702i			1.26972i	−0.772629	+	0.634858i	$0.781059\pi$
$734$	45.2388	+	45.2388i	0.0616332	+	0.0616332i
$735$	2129.54			2.89734
$736$			2.46320i			0.00334674i
$737$	264.977	−	264.977i	0.359534	−	0.359534i
$738$	−24.0518			−0.0325906
$739$	765.636	+	765.636i	1.03604	+	1.03604i	0.999326	+	0.0367180i	$0.0116903\pi$
$739$	765.636	+	765.636i	1.03604	+	1.03604i	0.0367180	+	0.999326i	$0.488310\pi$
$740$	−236.186			−0.319170
$741$	196.130	−	196.130i	0.264683	−	0.264683i
$742$	193.279			0.260484
$743$		−	569.604i		−	0.766627i	−0.923618	−	0.383313i	$-0.874783\pi$
$743$		−	569.604i		−	0.766627i	0.923618	−	0.383313i	$-0.125217\pi$
$744$	212.826			0.286056
$745$		−	1536.02i		−	2.06177i
$746$	−35.5460	+	35.5460i	−0.0476488	+	0.0476488i
$747$	140.620			0.188246
$748$	−139.146			−0.186024
$749$		−	1046.51i		−	1.39721i
$750$	−62.5426	−	62.5426i	−0.0833902	−	0.0833902i
$751$			1491.27i			1.98571i	0.119343	+	0.992853i	$0.461921\pi$
$751$			1491.27i			1.98571i	−0.119343	+	0.992853i	$0.538079\pi$
$752$	609.536	+	609.536i	0.810553	+	0.810553i
$753$	854.520	+	854.520i	1.13482	+	1.13482i
$754$	22.7158	+	22.7158i	0.0301271	+	0.0301271i
$755$		−	1112.97i		−	1.47413i
$756$	461.920	−	461.920i	0.611006	−	0.611006i
$757$		−	1075.05i		−	1.42015i	−0.704127	−	0.710074i	$-0.748661\pi$
$757$		−	1075.05i		−	1.42015i	0.704127	−	0.710074i	$-0.251339\pi$
$758$			95.6286i			0.126159i
$759$	−2.22673	−	2.22673i	−0.00293377	−	0.00293377i
$760$	−65.1728	+	65.1728i	−0.0857537	+	0.0857537i
$761$	494.605	−	494.605i	0.649940	−	0.649940i	−0.303038	−	0.952978i	$-0.598001\pi$
$761$	494.605	−	494.605i	0.649940	−	0.649940i	0.952978	+	0.303038i	$0.0980010\pi$
$762$	−99.0291			−0.129959
$763$			615.416i			0.806573i
$764$	−18.8354	+	18.8354i	−0.0246537	+	0.0246537i
$765$		−	464.477i		−	0.607159i
$766$	−51.9700	−	51.9700i	−0.0678460	−	0.0678460i
$767$		−	796.481i		−	1.03844i
$768$	873.935			1.13794
$769$	−937.756			−1.21945			−0.609724	−	0.792614i	$-0.708720\pi$
$769$	−937.756			−1.21945			−0.609724	+	0.792614i	$0.708720\pi$
$770$	−50.3282			−0.0653614
$771$	−626.669	+	626.669i	−0.812800	+	0.812800i
$772$			1448.95i			1.87688i
$773$	612.674	−	612.674i	0.792593	−	0.792593i	−0.189322	−	0.981915i	$-0.560629\pi$
$773$	612.674	−	612.674i	0.792593	−	0.792593i	0.981915	+	0.189322i	$0.0606290\pi$
$774$	−30.4345	+	30.4345i	−0.0393211	+	0.0393211i
$775$	1096.87	−	1096.87i	1.41532	−	1.41532i
$776$	−9.33589	+	9.33589i	−0.0120308	+	0.0120308i
$777$	−212.297	−	212.297i	−0.273227	−	0.273227i
$778$	3.85367			0.00495330
$779$	139.669	+	139.669i	0.179292	+	0.179292i
$780$	825.369	−	825.369i	1.05816	−	1.05816i
$781$	−108.383			−0.138774
$782$		−	0.599745i		−	0.000766937i
$783$	−188.162	+	188.162i	−0.240309	+	0.240309i
$784$		−	1096.17i		−	1.39818i
$785$	−1626.02	−	1626.02i	−2.07136	−	2.07136i
$786$			143.249i			0.182251i
$787$		−	1309.23i		−	1.66358i	−0.555093	−	0.831788i	$-0.687318\pi$
$787$		−	1309.23i		−	1.66358i	0.555093	−	0.831788i	$-0.312682\pi$
$788$	312.301	−	312.301i	0.396321	−	0.396321i
$789$	55.4246	−	55.4246i	0.0702466	−	0.0702466i
$790$		−	136.257i		−	0.172477i
$791$	1473.30			1.86258
$792$	15.9015	−	15.9015i	0.0200776	−	0.0200776i
$793$	−290.569	+	290.569i	−0.366417	+	0.366417i
$794$	19.3614	+	19.3614i	0.0243846	+	0.0243846i
$795$			2860.68i			3.59834i
$796$	765.474	+	765.474i	0.961651	+	0.961651i
$797$	−41.8222	+	41.8222i	−0.0524746	+	0.0524746i	−0.732857	−	0.680383i	$-0.761814\pi$
$797$	−41.8222	+	41.8222i	−0.0524746	+	0.0524746i	0.680383	+	0.732857i	$0.261814\pi$
$798$	−58.3233			−0.0730869
$799$	−451.885	−	451.885i	−0.565564	−	0.565564i
$800$	−255.012	+	255.012i	−0.318765	+	0.318765i
$801$	−129.814	+	129.814i	−0.162065	+	0.162065i
$802$	33.9360	+	33.9360i	0.0423143	+	0.0423143i
$803$	−272.433	−	272.433i	−0.339269	−	0.339269i
$804$	1292.24	−	1292.24i	1.60726	−	1.60726i
$805$			24.5449i			0.0304906i
$806$	−49.1750	−	49.1750i	−0.0610111	−	0.0610111i
$807$	−646.153	+	646.153i	−0.800685	+	0.800685i
$808$	206.272			0.255288
$809$	−323.348	+	323.348i	−0.399688	+	0.399688i	−0.878123	−	0.478435i	$-0.841204\pi$
$809$	−323.348	+	323.348i	−0.399688	+	0.399688i	0.478435	+	0.878123i	$0.341204\pi$
$810$	−108.326	−	108.326i	−0.133735	−	0.133735i
$811$	128.070	+	128.070i	0.157916	+	0.157916i	0.781642	−	0.623727i	$-0.214382\pi$
$811$	128.070	+	128.070i	0.157916	+	0.157916i	−0.623727	+	0.781642i	$0.714382\pi$
$812$			764.329i			0.941292i
$813$	−910.444			−1.11986
$814$	2.95748	+	2.95748i	0.00363327	+	0.00363327i
$815$	−63.2013	−	63.2013i	−0.0775476	−	0.0775476i
$816$	−672.535			−0.824185
$817$	353.466			0.432639
$818$	12.1307	−	12.1307i	0.0148297	−	0.0148297i
$819$	527.485			0.644060
$820$	587.764	+	587.764i	0.716785	+	0.716785i
$821$	−845.120			−1.02938			−0.514689	−	0.857377i	$-0.672093\pi$
$821$	−845.120			−1.02938			−0.514689	+	0.857377i	$0.672093\pi$
$822$		−	161.426i		−	0.196382i
$823$	1079.50	+	1079.50i	1.31166	+	1.31166i	0.920188	+	0.391477i	$0.128036\pi$
$823$	1079.50	+	1079.50i	1.31166	+	1.31166i	0.391477	+	0.920188i	$0.371964\pi$
$824$	−63.0440	+	63.0440i	−0.0765097	+	0.0765097i
$825$		−	461.061i		−	0.558862i
$826$	−118.425	+	118.425i	−0.143372	+	0.143372i
$827$	471.161	+	471.161i	0.569723	+	0.569723i	0.932051	−	0.362328i	$-0.118018\pi$
$827$	471.161	+	471.161i	0.569723	+	0.569723i	−0.362328	+	0.932051i	$0.618018\pi$
$828$	−3.86050	−	3.86050i	−0.00466244	−	0.00466244i
$829$	916.511	+	916.511i	1.10556	+	1.10556i	0.993727	+	0.111835i	$0.0356727\pi$
$829$	916.511	+	916.511i	1.10556	+	1.10556i	0.111835	+	0.993727i	$0.464327\pi$
$830$	30.3701	+	30.3701i	0.0365905	+	0.0365905i
$831$	1166.94			1.40426
$832$	−417.177	−	417.177i	−0.501414	−	0.501414i
$833$			812.658i			0.975580i
$834$		−	149.622i		−	0.179403i
$835$			2130.80i			2.55186i
$836$	−91.9336			−0.109968
$837$	407.331	−	407.331i	0.486656	−	0.486656i
$838$	76.5533			0.0913524
$839$	−247.035	−	247.035i	−0.294440	−	0.294440i	0.544391	−	0.838831i	$-0.316761\pi$
$839$	−247.035	−	247.035i	−0.294440	−	0.294440i	−0.838831	+	0.544391i	$0.816761\pi$
$840$	−493.049			−0.586963
$841$			529.652i			0.629789i
$842$	81.5088	+	81.5088i	0.0968038	+	0.0968038i
$843$	81.8467	+	81.8467i	0.0970899	+	0.0970899i
$844$	−566.907	+	566.907i	−0.671691	+	0.671691i
$845$	602.699			0.713253
$846$	51.4139			0.0607730
$847$	863.430	+	863.430i	1.01940	+	1.01940i
$848$	1472.52			1.73646
$849$	203.125	−	203.125i	0.239252	−	0.239252i
$850$	62.0908	−	62.0908i	0.0730480	−	0.0730480i
$851$	1.44235	−	1.44235i	0.00169489	−	0.00169489i
$852$	−528.559			−0.620375
$853$	−191.756	+	191.756i	−0.224802	+	0.224802i	−0.810517	−	0.585715i	$-0.800814\pi$
$853$	−191.756	+	191.756i	−0.224802	+	0.224802i	0.585715	+	0.810517i	$0.300814\pi$
$854$	86.4065			0.101179
$855$		−	306.879i		−	0.358923i
$856$			142.824i			0.166850i
$857$	−776.550	−	776.550i	−0.906126	−	0.906126i	0.0898308	−	0.995957i	$-0.471367\pi$
$857$	−776.550	−	776.550i	−0.906126	−	0.906126i	−0.995957	+	0.0898308i	$0.971367\pi$
$858$	−20.6703			−0.0240913
$859$			586.192i			0.682412i	0.939989	+	0.341206i	$0.110835\pi$
$859$			586.192i			0.682412i	−0.939989	+	0.341206i	$0.889165\pi$
$860$	1487.48			1.72963
$861$			1056.63i			1.22721i
$862$	71.1307	+	71.1307i	0.0825182	+	0.0825182i
$863$		−	40.0608i		−	0.0464204i	−0.999731	−	0.0232102i	$-0.992611\pi$
$863$		−	40.0608i		−	0.0464204i	0.999731	−	0.0232102i	$-0.00738869\pi$
$864$	−94.7003	+	94.7003i	−0.109607	+	0.109607i
$865$		−	1283.95i		−	1.48433i
$866$	6.29756	+	6.29756i	0.00727200	+	0.00727200i
$867$	−581.371			−0.670555
$868$		−	1654.61i		−	1.90623i
$869$	193.055	−	193.055i	0.222157	−	0.222157i
$870$	99.9794			0.114919
$871$	−1199.60			−1.37727
$872$		−	83.9895i		−	0.0963182i
$873$		−	43.9599i		−	0.0503550i
$874$		−	0.396251i		−	0.000453376i
$875$	−976.771	+	976.771i	−1.11631	+	1.11631i
$876$	−1328.60	−	1328.60i	−1.51666	−	1.51666i
$877$	−545.440	−	545.440i	−0.621938	−	0.621938i	0.324088	−	0.946027i	$-0.394942\pi$
$877$	−545.440	−	545.440i	−0.621938	−	0.621938i	−0.946027	+	0.324088i	$0.894942\pi$
$878$	53.2915	+	53.2915i	0.0606965	+	0.0606965i
$879$		−	1759.91i		−	2.00217i
$880$	−383.432			−0.435718
$881$	−784.228	−	784.228i	−0.890157	−	0.890157i	0.104381	−	0.994537i	$-0.466714\pi$
$881$	−784.228	−	784.228i	−0.890157	−	0.890157i	−0.994537	+	0.104381i	$0.966714\pi$
$882$	−46.2307	−	46.2307i	−0.0524158	−	0.0524158i
$883$	1624.14			1.83935			0.919674	−	0.392683i	$-0.128453\pi$
$883$	1624.14			1.83935			0.919674	+	0.392683i	$0.128453\pi$
$884$	314.970	+	314.970i	0.356301	+	0.356301i
$885$	−1752.78	−	1752.78i	−1.98054	−	1.98054i
$886$	−46.2452	+	46.2452i	−0.0521954	+	0.0521954i
$887$	1115.54	+	1115.54i	1.25766	+	1.25766i	0.952209	+	0.305446i	$0.0988056\pi$
$887$	1115.54	+	1115.54i	1.25766	+	1.25766i	0.305446	+	0.952209i	$0.401194\pi$
$888$	28.9735	+	28.9735i	0.0326278	+	0.0326278i
$889$			1546.61i			1.73971i
$890$	−56.0728			−0.0630031
$891$		−	306.962i		−	0.344514i
$892$	−53.2619	+	53.2619i	−0.0597106	+	0.0597106i
$893$	−298.560	−	298.560i	−0.334334	−	0.334334i
$894$	−93.7990	+	93.7990i	−0.104921	+	0.104921i
$895$	1408.32	−	1408.32i	1.57354	−	1.57354i
$896$			512.136i			0.571580i
$897$			10.0808i			0.0112384i
$898$	9.82476	+	9.82476i	0.0109407	+	0.0109407i
$899$			674.001i			0.749723i
$900$		−	799.344i		−	0.888160i
$901$	−1091.67			−1.21162
$902$		−	14.7198i		−	0.0163191i
$903$	1337.03	+	1337.03i	1.48066	+	1.48066i
$904$	−201.071			−0.222423
$905$	1444.77			1.59643
$906$	−67.9651	+	67.9651i	−0.0750166	+	0.0750166i
$907$		−	1002.83i		−	1.10565i	−0.833297	−	0.552825i	$-0.813550\pi$
$907$		−	1002.83i		−	1.10565i	0.833297	−	0.552825i	$-0.186450\pi$
$908$	36.2433	−	36.2433i	0.0399155	−	0.0399155i
$909$	−485.638	+	485.638i	−0.534255	+	0.534255i
$910$	113.923	+	113.923i	0.125190	+	0.125190i
$911$	−1588.46			−1.74365			−0.871823	−	0.489821i	$-0.837062\pi$
$911$	−1588.46			−1.74365			−0.871823	+	0.489821i	$0.837062\pi$
$912$	−444.343			−0.487218
$913$			86.0596i			0.0942602i
$914$	12.4765	+	12.4765i	0.0136504	+	0.0136504i
$915$			1278.88i			1.39769i
$916$	−891.145	+	174.014i	−0.972865	+	0.189972i
$917$	2237.22			2.43972
$918$	23.0578	−	23.0578i	0.0251174	−	0.0251174i
$919$	2.37871			0.00258836			0.00129418	−	0.999999i	$-0.499588\pi$
$919$	2.37871			0.00258836			0.00129418	+	0.999999i	$0.499588\pi$
$920$		−	3.34980i		−	0.00364108i
$921$			1043.94i			1.13349i
$922$	81.5692	−	81.5692i	0.0884698	−	0.0884698i
$923$	245.335	+	245.335i	0.265801	+	0.265801i
$924$	−347.751	−	347.751i	−0.376354	−	0.376354i
$925$	298.650			0.322865
$926$	−1.56339	−	1.56339i	−0.00168832	−	0.00168832i
$927$		−	296.856i		−	0.320233i
$928$		−	156.698i		−	0.168856i
$929$	86.7390	−	86.7390i	0.0933682	−	0.0933682i	−0.658880	−	0.752248i	$-0.728969\pi$
$929$	86.7390	−	86.7390i	0.0933682	−	0.0933682i	0.752248	+	0.658880i	$0.228969\pi$
$930$	−216.434			−0.232725
$931$			536.923i			0.576716i
$932$	−752.235			−0.807119
$933$	1477.91			1.58404
$934$	−16.8382	+	16.8382i	−0.0180280	+	0.0180280i
$935$	284.261			0.304022
$936$	−71.9891			−0.0769114
$937$	−292.028	−	292.028i	−0.311663	−	0.311663i	0.533891	−	0.845553i	$-0.320729\pi$
$937$	−292.028	−	292.028i	−0.311663	−	0.311663i	−0.845553	+	0.533891i	$0.820729\pi$
$938$	178.363	+	178.363i	0.190152	+	0.190152i
$939$	−922.284	+	922.284i	−0.982198	+	0.982198i
$940$	−1256.42	−	1256.42i	−1.33662	−	1.33662i
$941$	108.167			0.114949			0.0574745	−	0.998347i	$-0.481695\pi$
$941$	108.167			0.114949			0.0574745	+	0.998347i	$0.481695\pi$
$942$			198.590i			0.210818i
$943$	−7.17879			−0.00761272
$944$	−902.234	+	902.234i	−0.955757	+	0.955757i
$945$	−943.656	+	943.656i	−0.998577	+	0.998577i
$946$	−18.6260	−	18.6260i	−0.0196892	−	0.0196892i
$947$	933.060	−	933.060i	0.985279	−	0.985279i	−0.0146138	−	0.999893i	$-0.504652\pi$
$947$	933.060	−	933.060i	0.985279	−	0.985279i	0.999893	+	0.0146138i	$0.00465187\pi$
$948$	941.486	−	941.486i	0.993129	−	0.993129i
$949$			1233.36i			1.29964i
$950$	41.0233	−	41.0233i	0.0431825	−	0.0431825i
$951$	955.768	−	955.768i	1.00501	−	1.00501i
$952$		−	188.153i		−	0.197640i
$953$	117.155			0.122933			0.0614665	−	0.998109i	$-0.480422\pi$
$953$	117.155			0.122933			0.0614665	+	0.998109i	$0.480422\pi$
$954$	62.1031	−	62.1031i	0.0650976	−	0.0650976i
$955$	38.4788	−	38.4788i	0.0402920	−	0.0402920i
$956$	1272.81	−	1272.81i	1.33139	−	1.33139i
$957$	141.655	+	141.655i	0.148020	+	0.148020i
$958$	−60.1658			−0.0628035
$959$	−2521.11			−2.62889
$960$	−1836.12			−1.91263
$961$		−	498.069i		−	0.518282i
$962$		−	13.3891i		−	0.0139180i
$963$	−336.257	−	336.257i	−0.349176	−	0.349176i
$964$	423.220			0.439025
$965$		−	2960.06i		−	3.06742i
$966$	1.49887	−	1.49887i	0.00155163	−	0.00155163i
$967$	−613.146			−0.634070			−0.317035	−	0.948414i	$-0.602687\pi$
$967$	−613.146			−0.634070			−0.317035	+	0.948414i	$0.602687\pi$
$968$	−117.838	−	117.838i	−0.121733	−	0.121733i
$969$	329.418			0.339957
$970$	9.49417	−	9.49417i	0.00978781	−	0.00978781i
$971$	807.566			0.831685			0.415842	−	0.909437i	$-0.363487\pi$
$971$	807.566			0.831685			0.415842	+	0.909437i	$0.363487\pi$
$972$		−	958.835i		−	0.986456i
$973$	−2336.75			−2.40159
$974$			7.09996i			0.00728949i
$975$	−1043.66	+	1043.66i	−1.07042	+	1.07042i
$976$	658.298			0.674486
$977$	−1626.59			−1.66489			−0.832444	−	0.554110i	$-0.813059\pi$
$977$	−1626.59			−1.66489			−0.832444	+	0.554110i	$0.813059\pi$
$978$			7.71895i			0.00789259i
$979$	−79.4466	−	79.4466i	−0.0811507	−	0.0811507i
$980$			2259.51i			2.30563i
$981$	197.741	+	197.741i	0.201571	+	0.201571i
$982$	39.8066	+	39.8066i	0.0405363	+	0.0405363i
$983$	198.965	+	198.965i	0.202406	+	0.202406i	0.801030	−	0.598624i	$-0.204286\pi$
$983$	198.965	+	198.965i	0.202406	+	0.202406i	−0.598624	+	0.801030i	$0.704286\pi$
$984$		−	144.205i		−	0.146550i
$985$	−637.998	+	637.998i	−0.647714	+	0.647714i
$986$			38.1533i			0.0386950i
$987$		−	2258.69i		−	2.28844i
$988$	208.100	+	208.100i	0.210628	+	0.210628i
$989$	−9.08385	+	9.08385i	−0.00918488	+	0.00918488i
$990$	−16.1711	+	16.1711i	−0.0163344	+	0.0163344i
$991$	1066.18			1.07586			0.537932	−	0.842989i	$-0.319206\pi$
$991$	1066.18			1.07586			0.537932	+	0.842989i	$0.319206\pi$
$992$			339.219i			0.341955i
$993$	−481.973	+	481.973i	−0.485371	+	0.485371i
$994$		−	72.9552i		−	0.0733956i
$995$	−1563.78	−	1563.78i	−1.57164	−	1.57164i
$996$			419.694i			0.421380i
$997$	−286.479			−0.287341			−0.143670	−	0.989626i	$-0.545891\pi$
$997$	−286.479			−0.287341			−0.143670	+	0.989626i	$0.545891\pi$
$998$	109.319			0.109538
$999$	110.906			0.111017

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	229.3.d.a.107.18	✓	76
229.122	odd	4	inner	229.3.d.a.122.18	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
229.3.d.a.107.18	✓	76	1.1	even	1	trivial
229.3.d.a.122.18	yes	76	229.122	odd	4	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:	\( N \)	\(=\)	\( 229 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	229.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.132366 + 0.132366i) q^{2} +3.73689 q^{3} +3.96496i q^{4} -8.10000i q^{5} +(-0.494638 + 0.494638i) q^{6} +(7.72510 + 7.72510i) q^{7} +(-1.05429 - 1.05429i) q^{8} +4.96435 q^{9} +O(q^{10})\)	\(q+(-0.132366 + 0.132366i) q^{2} +3.73689 q^{3} +3.96496i q^{4} -8.10000i q^{5} +(-0.494638 + 0.494638i) q^{6} +(7.72510 + 7.72510i) q^{7} +(-1.05429 - 1.05429i) q^{8} +4.96435 q^{9} +(1.07217 + 1.07217i) q^{10} +3.03819i q^{11} +14.8166i q^{12} +(6.87724 - 6.87724i) q^{13} -2.04509 q^{14} -30.2688i q^{15} -15.5807 q^{16} +11.5509 q^{17} +(-0.657112 + 0.657112i) q^{18} +7.63169 q^{19} +32.1162 q^{20} +(28.8679 + 28.8679i) q^{21} +(-0.402154 - 0.402154i) q^{22} +(-0.196129 + 0.196129i) q^{23} +(-3.93977 - 3.93977i) q^{24} -40.6100 q^{25} +1.82063i q^{26} -15.0808 q^{27} +(-30.6297 + 30.6297i) q^{28} +(12.4769 - 12.4769i) q^{29} +(4.00657 + 4.00657i) q^{30} +(-27.0099 + 27.0099i) q^{31} +(6.27953 - 6.27953i) q^{32} +11.3534i q^{33} +(-1.52895 + 1.52895i) q^{34} +(62.5733 - 62.5733i) q^{35} +19.6834i q^{36} -7.35410 q^{37} +(-1.01018 + 1.01018i) q^{38} +(25.6995 - 25.6995i) q^{39} +(-8.53976 + 8.53976i) q^{40} +(18.3012 + 18.3012i) q^{41} -7.64226 q^{42} +46.3156 q^{43} -12.0463 q^{44} -40.2112i q^{45} -0.0519218i q^{46} +(-39.1211 - 39.1211i) q^{47} -58.2235 q^{48} +70.3544i q^{49} +(5.37540 - 5.37540i) q^{50} +43.1645 q^{51} +(27.2680 + 27.2680i) q^{52} -94.5091 q^{53} +(1.99619 - 1.99619i) q^{54} +24.6094 q^{55} -16.2890i q^{56} +28.5188 q^{57} +3.30305i q^{58} +(57.9071 - 57.9071i) q^{59} +120.015 q^{60} -42.2508 q^{61} -7.15040i q^{62} +(38.3501 + 38.3501i) q^{63} -60.6605i q^{64} +(-55.7056 - 55.7056i) q^{65} +(-1.50281 - 1.50281i) q^{66} +(-87.2153 - 87.2153i) q^{67} +45.7989i q^{68} +(-0.732914 + 0.732914i) q^{69} +16.5652i q^{70} +35.6734i q^{71} +(-5.23387 - 5.23387i) q^{72} +(-89.6694 + 89.6694i) q^{73} +(0.973435 - 0.973435i) q^{74} -151.755 q^{75} +30.2593i q^{76} +(-23.4703 + 23.4703i) q^{77} +6.80349i q^{78} +(-63.5426 - 63.5426i) q^{79} +126.204i q^{80} -101.034 q^{81} -4.84492 q^{82} +28.3259 q^{83} +(-114.460 + 114.460i) q^{84} -93.5625i q^{85} +(-6.13062 + 6.13062i) q^{86} +(46.6249 - 46.6249i) q^{87} +(3.20314 - 3.20314i) q^{88} +(-26.1493 + 26.1493i) q^{89} +(5.32261 + 5.32261i) q^{90} +106.255 q^{91} +(-0.777645 - 0.777645i) q^{92} +(-100.933 + 100.933i) q^{93} +10.3566 q^{94} -61.8167i q^{95} +(23.4659 - 23.4659i) q^{96} -8.85513i q^{97} +(-9.31255 - 9.31255i) q^{98} +15.0826i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 4 q^{3} - 6 q^{6} - 18 q^{7} - 6 q^{8} + 204 q^{9}+O(q^{10}) \) 76 * q - 4 * q^3 - 6 * q^6 - 18 * q^7 - 6 * q^8 + 204 * q^9	\( 76 q - 4 q^{3} - 6 q^{6} - 18 q^{7} - 6 q^{8} + 204 q^{9} + 2 q^{10} - 72 q^{13} - 20 q^{14} - 228 q^{16} - 40 q^{17} + 36 q^{18} - 40 q^{19} - 20 q^{20} - 98 q^{21} + 6 q^{22} - 8 q^{23} + 70 q^{24} - 268 q^{25} - 100 q^{27} - 88 q^{28} - 64 q^{29} + 144 q^{30} + 6 q^{31} + 16 q^{32} - 38 q^{34} + 50 q^{35} + 76 q^{37} + 192 q^{38} + 36 q^{39} - 82 q^{40} - 68 q^{41} + 292 q^{42} + 84 q^{43} + 108 q^{44} + 164 q^{47} - 284 q^{48} - 36 q^{50} - 152 q^{51} + 670 q^{52} - 404 q^{53} - 466 q^{54} + 16 q^{55} + 56 q^{57} + 8 q^{59} + 1148 q^{60} - 128 q^{61} - 156 q^{63} + 76 q^{65} + 384 q^{66} + 14 q^{67} - 418 q^{69} - 662 q^{72} + 186 q^{73} - 78 q^{74} + 124 q^{75} + 154 q^{77} - 142 q^{79} + 228 q^{81} - 72 q^{82} + 212 q^{83} - 1034 q^{84} - 26 q^{86} + 554 q^{87} + 160 q^{88} + 110 q^{89} - 226 q^{90} + 588 q^{91} - 262 q^{92} - 602 q^{93} + 568 q^{94} + 1380 q^{96} - 854 q^{98}+O(q^{100}) \) 76 * q - 4 * q^3 - 6 * q^6 - 18 * q^7 - 6 * q^8 + 204 * q^9 + 2 * q^10 - 72 * q^13 - 20 * q^14 - 228 * q^16 - 40 * q^17 + 36 * q^18 - 40 * q^19 - 20 * q^20 - 98 * q^21 + 6 * q^22 - 8 * q^23 + 70 * q^24 - 268 * q^25 - 100 * q^27 - 88 * q^28 - 64 * q^29 + 144 * q^30 + 6 * q^31 + 16 * q^32 - 38 * q^34 + 50 * q^35 + 76 * q^37 + 192 * q^38 + 36 * q^39 - 82 * q^40 - 68 * q^41 + 292 * q^42 + 84 * q^43 + 108 * q^44 + 164 * q^47 - 284 * q^48 - 36 * q^50 - 152 * q^51 + 670 * q^52 - 404 * q^53 - 466 * q^54 + 16 * q^55 + 56 * q^57 + 8 * q^59 + 1148 * q^60 - 128 * q^61 - 156 * q^63 + 76 * q^65 + 384 * q^66 + 14 * q^67 - 418 * q^69 - 662 * q^72 + 186 * q^73 - 78 * q^74 + 124 * q^75 + 154 * q^77 - 142 * q^79 + 228 * q^81 - 72 * q^82 + 212 * q^83 - 1034 * q^84 - 26 * q^86 + 554 * q^87 + 160 * q^88 + 110 * q^89 - 226 * q^90 + 588 * q^91 - 262 * q^92 - 602 * q^93 + 568 * q^94 + 1380 * q^96 - 854 * q^98

Introduction

L-functions

Modular forms

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