LMFDB - Embedded newform 276.3.f.b.139.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,3,Mod(139,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("276.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	276.f (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:	$7.52045529634$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.6
Character	$\chi$	$=$	276.139
Dual form			276.3.f.b.139.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87686 + 0.690935i) q^{2} -1.73205i q^{3} +(3.04522 - 2.59358i) q^{4} -1.28200 q^{5} +(1.19673 + 3.25082i) q^{6} -2.36368i q^{7} +(-3.92345 + 6.97184i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-1.87686 + 0.690935i) q^{2} -1.73205i q^{3} +(3.04522 - 2.59358i) q^{4} -1.28200 q^{5} +(1.19673 + 3.25082i) q^{6} -2.36368i q^{7} +(-3.92345 + 6.97184i) q^{8} -3.00000 q^{9} +(2.40614 - 0.885782i) q^{10} -11.7095i q^{11} +(-4.49221 - 5.27447i) q^{12} +14.2932 q^{13} +(1.63315 + 4.43629i) q^{14} +2.22050i q^{15} +(2.54669 - 15.7960i) q^{16} -25.0814 q^{17} +(5.63058 - 2.07281i) q^{18} +8.65991i q^{19} +(-3.90398 + 3.32498i) q^{20} -4.09401 q^{21} +(8.09052 + 21.9771i) q^{22} +4.79583i q^{23} +(12.0756 + 6.79562i) q^{24} -23.3565 q^{25} +(-26.8263 + 9.87567i) q^{26} +5.19615i q^{27} +(-6.13038 - 7.19791i) q^{28} -19.9990 q^{29} +(-1.53422 - 4.16756i) q^{30} -57.1500i q^{31} +(6.13424 + 31.4065i) q^{32} -20.2815 q^{33} +(47.0743 - 17.3296i) q^{34} +3.03024i q^{35} +(-9.13565 + 7.78074i) q^{36} -40.2347 q^{37} +(-5.98344 - 16.2535i) q^{38} -24.7565i q^{39} +(5.02989 - 8.93792i) q^{40} -58.4149 q^{41} +(7.68388 - 2.82869i) q^{42} -54.5207i q^{43} +(-30.3696 - 35.6580i) q^{44} +3.84601 q^{45} +(-3.31361 - 9.00111i) q^{46} -20.9305i q^{47} +(-27.3595 - 4.41100i) q^{48} +43.4130 q^{49} +(43.8368 - 16.1378i) q^{50} +43.4423i q^{51} +(43.5259 - 37.0705i) q^{52} +19.7518 q^{53} +(-3.59020 - 9.75246i) q^{54} +15.0117i q^{55} +(16.4792 + 9.27378i) q^{56} +14.9994 q^{57} +(37.5353 - 13.8180i) q^{58} +3.65506i q^{59} +(5.75903 + 6.76189i) q^{60} -98.1380 q^{61} +(39.4870 + 107.263i) q^{62} +7.09103i q^{63} +(-33.2130 - 54.7074i) q^{64} -18.3239 q^{65} +(38.0655 - 14.0132i) q^{66} +39.0165i q^{67} +(-76.3784 + 65.0506i) q^{68} +8.30662 q^{69} +(-2.09370 - 5.68735i) q^{70} -65.6873i q^{71} +(11.7704 - 20.9155i) q^{72} +27.5706 q^{73} +(75.5150 - 27.7996i) q^{74} +40.4546i q^{75} +(22.4602 + 26.3713i) q^{76} -27.6775 q^{77} +(17.1052 + 46.4646i) q^{78} +95.2812i q^{79} +(-3.26487 + 20.2506i) q^{80} +9.00000 q^{81} +(109.637 - 40.3609i) q^{82} +6.19926i q^{83} +(-12.4671 + 10.6181i) q^{84} +32.1545 q^{85} +(37.6703 + 102.328i) q^{86} +34.6392i q^{87} +(81.6369 + 45.9418i) q^{88} +47.1874 q^{89} +(-7.21843 + 2.65735i) q^{90} -33.7845i q^{91} +(12.4384 + 14.6043i) q^{92} -98.9867 q^{93} +(14.4617 + 39.2837i) q^{94} -11.1020i q^{95} +(54.3977 - 10.6248i) q^{96} +185.894 q^{97} +(-81.4802 + 29.9956i) q^{98} +35.1286i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.87686	+	0.690935i	−0.938431	+	0.345468i
$2$	−1.87686	+	0.690935i	−0.938431	+	0.345468i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	3.04522	−	2.59358i	0.761304	−	0.648395i
$5$	−1.28200			−0.256401			−0.128200	−	0.991748i	$-0.540920\pi$
$5$	−1.28200			−0.256401			−0.128200	+	0.991748i	$0.540920\pi$
$6$	1.19673	+	3.25082i	0.199456	+	0.541803i
$7$		−	2.36368i		−	0.337668i	−0.985644	−	0.168834i	$-0.946000\pi$
$7$		−	2.36368i		−	0.337668i	0.985644	−	0.168834i	$-0.0540002\pi$
$8$	−3.92345	+	6.97184i	−0.490432	+	0.871480i
$9$	−3.00000			−0.333333
$10$	2.40614	−	0.885782i	0.240614	−	0.0885782i
$11$		−	11.7095i		−	1.06450i	−0.846587	−	0.532251i	$-0.821346\pi$
$11$		−	11.7095i		−	1.06450i	0.846587	−	0.532251i	$-0.178654\pi$
$12$	−4.49221	−	5.27447i	−0.374351	−	0.439539i
$13$	14.2932			1.09948			0.549738	−	0.835337i	$-0.314727\pi$
$13$	14.2932			1.09948			0.549738	+	0.835337i	$0.314727\pi$
$14$	1.63315	+	4.43629i	0.116653	+	0.316878i
$15$			2.22050i			0.148033i
$16$	2.54669	−	15.7960i	0.159168	−	0.987251i
$17$	−25.0814			−1.47538			−0.737689	−	0.675141i	$-0.764083\pi$
$17$	−25.0814			−1.47538			−0.737689	+	0.675141i	$0.764083\pi$
$18$	5.63058	−	2.07281i	0.312810	−	0.115156i
$19$			8.65991i			0.455785i	0.973686	+	0.227892i	$0.0731834\pi$
$19$			8.65991i			0.455785i	−0.973686	+	0.227892i	$0.926817\pi$
$20$	−3.90398	+	3.32498i	−0.195199	+	0.166249i
$21$	−4.09401			−0.194953
$22$	8.09052	+	21.9771i	0.367751	+	0.998961i
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	12.0756	+	6.79562i	0.503149	+	0.283151i
$25$	−23.3565			−0.934259
$26$	−26.8263	+	9.87567i	−1.03178	+	0.379834i
$27$			5.19615i			0.192450i
$28$	−6.13038	−	7.19791i	−0.218942	−	0.257068i
$29$	−19.9990			−0.689620			−0.344810	−	0.938673i	$-0.612057\pi$
$29$	−19.9990			−0.689620			−0.344810	+	0.938673i	$0.612057\pi$
$30$	−1.53422	−	4.16756i	−0.0511406	−	0.138919i
$31$		−	57.1500i		−	1.84355i	−0.387727	−	0.921774i	$-0.626740\pi$
$31$		−	57.1500i		−	1.84355i	0.387727	−	0.921774i	$-0.373260\pi$
$32$	6.13424	+	31.4065i	0.191695	+	0.981455i
$33$	−20.2815			−0.614591
$34$	47.0743	−	17.3296i	1.38454	−	0.509695i
$35$			3.03024i			0.0865784i
$36$	−9.13565	+	7.78074i	−0.253768	+	0.216132i
$37$	−40.2347			−1.08743			−0.543713	−	0.839271i	$-0.682982\pi$
$37$	−40.2347			−1.08743			−0.543713	+	0.839271i	$0.682982\pi$
$38$	−5.98344	−	16.2535i	−0.157459	−	0.427722i
$39$		−	24.7565i		−	0.634783i
$40$	5.02989	−	8.93792i	0.125747	−	0.223448i
$41$	−58.4149			−1.42475			−0.712377	−	0.701797i	$-0.752381\pi$
$41$	−58.4149			−1.42475			−0.712377	+	0.701797i	$0.752381\pi$
$42$	7.68388	−	2.82869i	0.182950	−	0.0673499i
$43$		−	54.5207i		−	1.26792i	−0.773364	−	0.633962i	$-0.781428\pi$
$43$		−	54.5207i		−	1.26792i	0.773364	−	0.633962i	$-0.218572\pi$
$44$	−30.3696	−	35.6580i	−0.690218	−	0.810410i
$45$	3.84601			0.0854670
$46$	−3.31361	−	9.00111i	−0.0720350	−	0.195676i
$47$		−	20.9305i		−	0.445331i	−0.974895	−	0.222665i	$-0.928524\pi$
$47$		−	20.9305i		−	0.445331i	0.974895	−	0.222665i	$-0.0714757\pi$
$48$	−27.3595	−	4.41100i	−0.569990	−	0.0918959i
$49$	43.4130			0.885980
$50$	43.8368	−	16.1378i	0.876737	−	0.322756i
$51$			43.4423i			0.851810i
$52$	43.5259	−	37.0705i	0.837036	−	0.712895i
$53$	19.7518			0.372676			0.186338	−	0.982486i	$-0.440338\pi$
$53$	19.7518			0.372676			0.186338	+	0.982486i	$0.440338\pi$
$54$	−3.59020	−	9.75246i	−0.0664853	−	0.180601i
$55$			15.0117i			0.272939i
$56$	16.4792	+	9.27378i	0.294271	+	0.165603i
$57$	14.9994			0.263147
$58$	37.5353	−	13.8180i	0.647160	−	0.238241i
$59$			3.65506i			0.0619501i	0.999520	+	0.0309750i	$0.00986124\pi$
$59$			3.65506i			0.0619501i	−0.999520	+	0.0309750i	$0.990139\pi$
$60$	5.75903	+	6.76189i	0.0959839	+	0.112698i
$61$	−98.1380			−1.60882			−0.804410	−	0.594074i	$-0.797518\pi$
$61$	−98.1380			−1.60882			−0.804410	+	0.594074i	$0.797518\pi$
$62$	39.4870	+	107.263i	0.636886	+	1.73004i
$63$			7.09103i			0.112556i
$64$	−33.2130	−	54.7074i	−0.518953	−	0.854803i
$65$	−18.3239			−0.281907
$66$	38.0655	−	14.0132i	0.576751	−	0.212321i
$67$			39.0165i			0.582336i	0.956672	+	0.291168i	$0.0940438\pi$
$67$			39.0165i			0.582336i	−0.956672	+	0.291168i	$0.905956\pi$
$68$	−76.3784	+	65.0506i	−1.12321	+	0.956627i
$69$	8.30662			0.120386
$70$	−2.09370	−	5.68735i	−0.0299100	−	0.0812478i
$71$		−	65.6873i		−	0.925174i	−0.886574	−	0.462587i	$-0.846921\pi$
$71$		−	65.6873i		−	0.925174i	0.886574	−	0.462587i	$-0.153079\pi$
$72$	11.7704	−	20.9155i	0.163477	−	0.290493i
$73$	27.5706			0.377679			0.188840	−	0.982008i	$-0.439527\pi$
$73$	27.5706			0.377679			0.188840	+	0.982008i	$0.439527\pi$
$74$	75.5150	−	27.7996i	1.02047	−	0.375670i
$75$			40.4546i			0.539394i
$76$	22.4602	+	26.3713i	0.295529	+	0.346991i
$77$	−27.6775			−0.359448
$78$	17.1052	+	46.4646i	0.219297	+	0.595700i
$79$			95.2812i			1.20609i	0.797707	+	0.603045i	$0.206046\pi$
$79$			95.2812i			1.20609i	−0.797707	+	0.603045i	$0.793954\pi$
$80$	−3.26487	+	20.2506i	−0.0408109	+	0.253132i
$81$	9.00000			0.111111
$82$	109.637	−	40.3609i	1.33703	−	0.492206i
$83$			6.19926i			0.0746899i	0.999302	+	0.0373450i	$0.0118900\pi$
$83$			6.19926i			0.0746899i	−0.999302	+	0.0373450i	$0.988110\pi$
$84$	−12.4671	+	10.6181i	−0.148418	+	0.126406i
$85$	32.1545			0.378288
$86$	37.6703	+	102.328i	0.438027	+	1.18986i
$87$			34.6392i			0.398152i
$88$	81.6369	+	45.9418i	0.927692	+	0.522066i
$89$	47.1874			0.530196			0.265098	−	0.964221i	$-0.414596\pi$
$89$	47.1874			0.530196			0.265098	+	0.964221i	$0.414596\pi$
$90$	−7.21843	+	2.65735i	−0.0802048	+	0.0295261i
$91$		−	33.7845i		−	0.371258i
$92$	12.4384	+	14.6043i	0.135200	+	0.158743i
$93$	−98.9867			−1.06437
$94$	14.4617	+	39.2837i	0.153847	+	0.417912i
$95$		−	11.1020i		−	0.116864i
$96$	54.3977	−	10.6248i	0.566643	−	0.110675i
$97$	185.894			1.91643			0.958217	−	0.286043i	$-0.0923400\pi$
$97$	185.894			1.91643			0.958217	+	0.286043i	$0.0923400\pi$
$98$	−81.4802	+	29.9956i	−0.831431	+	0.306077i
$99$			35.1286i			0.354834i
$100$	−71.1255	+	60.5768i	−0.711255	+	0.605768i
$101$	48.2129			0.477356			0.238678	−	0.971099i	$-0.423286\pi$
$101$	48.2129			0.477356			0.238678	+	0.971099i	$0.423286\pi$
$102$	−30.0158	−	81.5352i	−0.294273	−	0.799364i
$103$			87.4427i			0.848959i	0.905438	+	0.424479i	$0.139543\pi$
$103$			87.4427i			0.848959i	−0.905438	+	0.424479i	$0.860457\pi$
$104$	−56.0787	+	99.6498i	−0.539218	+	0.958171i
$105$	5.24854			0.0499861
$106$	−37.0714	+	13.6472i	−0.349730	+	0.128747i
$107$			9.60780i			0.0897925i	0.998992	+	0.0448962i	$0.0142957\pi$
$107$			9.60780i			0.0897925i	−0.998992	+	0.0448962i	$0.985704\pi$
$108$	13.4766	+	15.8234i	0.124784	+	0.146513i
$109$	−4.16843			−0.0382425			−0.0191212	−	0.999817i	$-0.506087\pi$
$109$	−4.16843			−0.0382425			−0.0191212	+	0.999817i	$0.506087\pi$
$110$	−10.3721	−	28.1748i	−0.0942917	−	0.256135i
$111$			69.6886i			0.627825i
$112$	−37.3367	−	6.01956i	−0.333363	−	0.0537461i
$113$	129.805			1.14871			0.574357	−	0.818605i	$-0.305252\pi$
$113$	129.805			1.14871			0.574357	+	0.818605i	$0.305252\pi$
$114$	−28.1518	+	10.3636i	−0.246946	+	0.0909089i
$115$		−	6.14828i		−	0.0534633i
$116$	−60.9012	+	51.8689i	−0.525011	+	0.447146i
$117$	−42.8796			−0.366492
$118$	−2.52541	−	6.86003i	−0.0214018	−	0.0581359i
$119$			59.2844i			0.498188i
$120$	−15.4809	−	8.71202i	−0.129008	−	0.0726002i
$121$	−16.1129			−0.133165
$122$	184.191	−	67.8070i	1.50977	−	0.555795i
$123$			101.178i			0.822582i
$124$	−148.223	−	174.034i	−1.19535	−	1.40350i
$125$	61.9932			0.495946
$126$	−4.89944	−	13.3089i	−0.0388845	−	0.105626i
$127$		−	86.5140i		−	0.681213i	−0.940206	−	0.340606i	$-0.889368\pi$
$127$		−	86.5140i		−	0.681213i	0.940206	−	0.340606i	$-0.110632\pi$
$128$	100.135	+	79.7301i	0.782308	+	0.622892i
$129$	−94.4327			−0.732036
$130$	34.3915	−	12.6607i	0.264550	−	0.0973897i
$131$		−	183.578i		−	1.40136i	−0.713476	−	0.700679i	$-0.752880\pi$
$131$		−	183.578i		−	1.40136i	0.713476	−	0.700679i	$-0.247120\pi$
$132$	−61.7615	+	52.6016i	−0.467890	+	0.398497i
$133$	20.4692			0.153904
$134$	−26.9579	−	73.2285i	−0.201178	−	0.546482i
$135$		−	6.66149i		−	0.0493444i
$136$	98.4058	−	174.864i	0.723572	−	1.28576i
$137$	114.699			0.837217			0.418609	−	0.908167i	$-0.362518\pi$
$137$	114.699			0.837217			0.418609	+	0.908167i	$0.362518\pi$
$138$	−15.5904	+	5.73934i	−0.112974	+	0.0415894i
$139$		−	113.411i		−	0.815905i	−0.913003	−	0.407953i	$-0.866243\pi$
$139$		−	113.411i		−	0.815905i	0.913003	−	0.407953i	$-0.133757\pi$
$140$	7.85918	+	9.22775i	0.0561370	+	0.0659125i
$141$	−36.2528			−0.257112
$142$	45.3857	+	123.286i	0.319618	+	0.868211i
$143$		−	167.366i		−	1.17039i
$144$	−7.64008	+	47.3881i	−0.0530561	+	0.329084i
$145$	25.6388			0.176819
$146$	−51.7461	+	19.0495i	−0.354426	+	0.130476i
$147$		−	75.1936i		−	0.511521i
$148$	−122.524	+	104.352i	−0.827862	+	0.705081i
$149$	−157.567			−1.05750			−0.528749	−	0.848778i	$-0.677339\pi$
$149$	−157.567			−1.05750			−0.528749	+	0.848778i	$0.677339\pi$
$150$	−27.9515	−	75.9276i	−0.186343	−	0.506184i
$151$		−	147.399i		−	0.976153i	−0.872801	−	0.488076i	$-0.837699\pi$
$151$		−	147.399i		−	0.976153i	0.872801	−	0.488076i	$-0.162301\pi$
$152$	−60.3755	−	33.9768i	−0.397207	−	0.223531i
$153$	75.2442			0.491792
$154$	51.9469	−	19.1234i	0.337317	−	0.124178i
$155$			73.2666i			0.472688i
$156$	−64.2080	−	75.3890i	−0.411590	−	0.483263i
$157$	−190.128			−1.21101			−0.605504	−	0.795842i	$-0.707028\pi$
$157$	−190.128			−1.21101			−0.605504	+	0.795842i	$0.707028\pi$
$158$	−65.8331	−	178.830i	−0.416665	−	1.13183i
$159$		−	34.2112i		−	0.215165i
$160$	−7.86412	−	40.2633i	−0.0491508	−	0.251646i
$161$	11.3358			0.0704087
$162$	−16.8918	+	6.21842i	−0.104270	+	0.0383853i
$163$			253.811i			1.55712i	0.627569	+	0.778561i	$0.284050\pi$
$163$			253.811i			1.55712i	−0.627569	+	0.778561i	$0.715950\pi$
$164$	−177.886	+	151.504i	−1.08467	+	0.923803i
$165$	26.0010			0.157582
$166$	−4.28329	−	11.6352i	−0.0258029	−	0.0700913i
$167$		−	12.8347i		−	0.0768546i	−0.999261	−	0.0384273i	$-0.987765\pi$
$167$		−	12.8347i		−	0.0768546i	0.999261	−	0.0384273i	$-0.0122348\pi$
$168$	16.0627	−	28.5428i	0.0956110	−	0.169897i
$169$	35.2954			0.208849
$170$	−60.3495	+	22.2167i	−0.354997	+	0.130686i
$171$		−	25.9797i		−	0.151928i
$172$	−141.404	−	166.027i	−0.822115	−	0.965276i
$173$	197.944			1.14418			0.572091	−	0.820190i	$-0.306132\pi$
$173$	197.944			1.14418			0.572091	+	0.820190i	$0.306132\pi$
$174$	−23.9335	−	65.0131i	−0.137549	−	0.373638i
$175$			55.2071i			0.315469i
$176$	−184.964	−	29.8206i	−1.05093	−	0.169435i
$177$	6.33074			0.0357669
$178$	−88.5643	+	32.6035i	−0.497552	+	0.183166i
$179$		−	195.746i		−	1.09355i	−0.837279	−	0.546776i	$-0.815855\pi$
$179$		−	195.746i		−	1.09355i	0.837279	−	0.546776i	$-0.184145\pi$
$180$	11.7119	−	9.97494i	0.0650664	−	0.0554163i
$181$	170.547			0.942248			0.471124	−	0.882067i	$-0.343848\pi$
$181$	170.547			0.942248			0.471124	+	0.882067i	$0.343848\pi$
$182$	23.3429	+	63.4088i	0.128258	+	0.348400i
$183$			169.980i			0.928853i
$184$	−33.4358	−	18.8162i	−0.181716	−	0.102262i
$185$	51.5811			0.278817
$186$	185.784	−	68.3934i	0.998841	−	0.367707i
$187$			293.691i			1.57054i
$188$	−54.2850	−	63.7381i	−0.288750	−	0.339032i
$189$	12.2820			0.0649842
$190$	7.67079	+	20.8370i	0.0403726	+	0.109668i
$191$		−	319.162i		−	1.67101i	−0.549486	−	0.835503i	$-0.685176\pi$
$191$		−	319.162i		−	1.67101i	0.549486	−	0.835503i	$-0.314824\pi$
$192$	−94.7559	+	57.5266i	−0.493521	+	0.299618i
$193$	−187.248			−0.970194			−0.485097	−	0.874460i	$-0.661216\pi$
$193$	−187.248			−0.970194			−0.485097	+	0.874460i	$0.661216\pi$
$194$	−348.897	+	128.441i	−1.79844	+	0.662066i
$195$			31.7380i			0.162759i
$196$	132.202	−	112.595i	0.674501	−	0.574465i
$197$	298.949			1.51751			0.758754	−	0.651377i	$-0.225808\pi$
$197$	298.949			1.51751			0.758754	+	0.651377i	$0.225808\pi$
$198$	−24.2716	−	65.9314i	−0.122584	−	0.332987i
$199$			65.2300i			0.327789i	0.986478	+	0.163894i	$0.0524056\pi$
$199$			65.2300i			0.327789i	−0.986478	+	0.163894i	$0.947594\pi$
$200$	91.6380	−	162.837i	0.458190	−	0.814187i
$201$	67.5785			0.336212
$202$	−90.4890	+	33.3120i	−0.447965	+	0.164911i
$203$			47.2711i			0.232863i
$204$	112.671	+	132.291i	0.552309	+	0.648486i
$205$	74.8881			0.365308
$206$	−60.4173	−	164.118i	−0.293288	−	0.796689i
$207$		−	14.3875i		−	0.0695048i
$208$	36.4004	−	225.776i	0.175002	−	1.08546i
$209$	101.403			0.485184
$210$	−9.85077	+	3.62640i	−0.0469084	+	0.0172686i
$211$			119.738i			0.567480i	0.958901	+	0.283740i	$0.0915753\pi$
$211$			119.738i			0.567480i	−0.958901	+	0.283740i	$0.908425\pi$
$212$	60.1486	−	51.2279i	0.283720	−	0.241641i
$213$	−113.774			−0.534149
$214$	−6.63836	−	18.0325i	−0.0310204	−	0.0842640i
$215$			69.8958i			0.325097i
$216$	−36.2267	−	20.3869i	−0.167716	−	0.0943837i
$217$	−135.084			−0.622508
$218$	7.82357	−	2.88012i	0.0358879	−	0.0132115i
$219$		−	47.7536i		−	0.218053i
$220$	38.9339	+	45.7138i	0.176972	+	0.207790i
$221$	−358.494			−1.62214
$222$	−48.1503	−	130.796i	−0.216893	−	0.589171i
$223$		−	41.6101i		−	0.186592i	−0.995638	−	0.0932962i	$-0.970260\pi$
$223$		−	41.6101i		−	0.186592i	0.995638	−	0.0932962i	$-0.0297403\pi$
$224$	74.2349	−	14.4994i	0.331406	−	0.0647293i
$225$	70.0694			0.311420
$226$	−243.625	+	89.6866i	−1.07799	+	0.396843i
$227$		−	88.0086i		−	0.387703i	−0.981031	−	0.193852i	$-0.937902\pi$
$227$		−	88.0086i		−	0.387703i	0.981031	−	0.193852i	$-0.0620980\pi$
$228$	45.6764	−	38.9021i	0.200335	−	0.170623i
$229$	−425.862			−1.85966			−0.929830	−	0.367988i	$-0.880047\pi$
$229$	−425.862			−1.85966			−0.929830	+	0.367988i	$0.880047\pi$
$230$	4.24806	+	11.5395i	0.0184698	+	0.0501716i
$231$			47.9389i			0.207528i
$232$	78.4651	−	139.430i	0.338212	−	0.600990i
$233$	−118.803			−0.509886			−0.254943	−	0.966956i	$-0.582057\pi$
$233$	−118.803			−0.509886			−0.254943	+	0.966956i	$0.582057\pi$
$234$	80.4790	−	29.6270i	0.343927	−	0.126611i
$235$			26.8331i			0.114183i
$236$	9.47968	+	11.1304i	0.0401681	+	0.0471629i
$237$	165.032			0.696337
$238$	−40.9616	−	111.269i	−0.172108	−	0.467515i
$239$			315.154i			1.31864i	0.751864	+	0.659318i	$0.229155\pi$
$239$			315.154i			1.31864i	−0.751864	+	0.659318i	$0.770845\pi$
$240$	35.0750	+	5.65492i	0.146146	+	0.0235622i
$241$	222.239			0.922151			0.461076	−	0.887361i	$-0.347464\pi$
$241$	222.239			0.922151			0.461076	+	0.887361i	$0.347464\pi$
$242$	30.2417	−	11.1330i	0.124966	−	0.0460040i
$243$		−	15.5885i		−	0.0641500i
$244$	−298.852	+	254.529i	−1.22480	+	1.04315i
$245$	−55.6557			−0.227166
$246$	−69.9071	−	189.896i	−0.284175	−	0.771936i
$247$			123.778i			0.501125i
$248$	398.441	+	224.225i	1.60662	+	0.904135i
$249$	10.7374			0.0431222
$250$	−116.353	+	42.8333i	−0.465411	+	0.171333i
$251$			37.1877i			0.148158i	0.997252	+	0.0740790i	$0.0236017\pi$
$251$			37.1877i			0.148158i	−0.997252	+	0.0740790i	$0.976398\pi$
$252$	18.3911	+	21.5937i	0.0729807	+	0.0856894i
$253$	56.1569			0.221964
$254$	59.7756	+	162.375i	0.235337	+	0.639271i
$255$		−	55.6932i		−	0.218405i
$256$	−243.029	−	80.4553i	−0.949331	−	0.314278i
$257$	478.795			1.86302			0.931508	−	0.363722i	$-0.118494\pi$
$257$	478.795			1.86302			0.931508	+	0.363722i	$0.118494\pi$
$258$	177.237	−	65.2469i	0.686965	−	0.252895i
$259$			95.1019i			0.367189i
$260$	−55.8004	+	47.5246i	−0.214617	+	0.182787i
$261$	59.9969			0.229873
$262$	126.840	+	344.550i	0.484124	+	1.31508i
$263$		−	413.401i		−	1.57187i	−0.618311	−	0.785933i	$-0.712183\pi$
$263$		−	413.401i		−	1.57187i	0.618311	−	0.785933i	$-0.287817\pi$
$264$	79.5735	−	141.399i	0.301415	−	0.535603i
$265$	−25.3219			−0.0955544
$266$	−38.4179	+	14.1429i	−0.144428	+	0.0531688i
$267$		−	81.7310i		−	0.306109i
$268$	101.192	+	118.814i	0.377583	+	0.443335i
$269$	65.3829			0.243059			0.121530	−	0.992588i	$-0.461220\pi$
$269$	65.3829			0.243059			0.121530	+	0.992588i	$0.461220\pi$
$270$	4.60266	+	12.5027i	0.0170469	+	0.0463063i
$271$		−	106.656i		−	0.393563i	−0.980447	−	0.196782i	$-0.936951\pi$
$271$		−	106.656i		−	0.393563i	0.980447	−	0.196782i	$-0.0630490\pi$
$272$	−63.8747	+	396.187i	−0.234833	+	1.45657i
$273$	−58.5164			−0.214346
$274$	−215.274	+	79.2494i	−0.785670	+	0.289231i
$275$			273.493i			0.994520i
$276$	25.2955	−	21.5439i	0.0916503	−	0.0780576i
$277$	55.5191			0.200430			0.100215	−	0.994966i	$-0.468047\pi$
$277$	55.5191			0.200430			0.100215	+	0.994966i	$0.468047\pi$
$278$	78.3595	+	212.856i	0.281869	+	0.765671i
$279$			171.450i			0.614516i
$280$	−21.1264	−	11.8890i	−0.0754513	−	0.0424608i
$281$	−181.953			−0.647520			−0.323760	−	0.946139i	$-0.604947\pi$
$281$	−181.953			−0.647520			−0.323760	+	0.946139i	$0.604947\pi$
$282$	68.0414	−	25.0483i	0.241282	−	0.0888238i
$283$			111.106i			0.392601i	0.980544	+	0.196301i	$0.0628928\pi$
$283$			111.106i			0.392601i	−0.980544	+	0.196301i	$0.937107\pi$
$284$	−170.365	−	200.032i	−0.599878	−	0.704339i
$285$	−19.2293			−0.0674712
$286$	115.639	+	314.124i	0.404334	+	1.09833i
$287$			138.074i			0.481094i
$288$	−18.4027	−	94.2196i	−0.0638983	−	0.327152i
$289$	340.077			1.17674
$290$	−48.1204	+	17.7147i	−0.165933	+	0.0610853i
$291$		−	321.978i		−	1.10645i
$292$	83.9584	−	71.5065i	0.287529	−	0.244885i
$293$	−358.035			−1.22196			−0.610981	−	0.791646i	$-0.709225\pi$
$293$	−358.035			−1.22196			−0.610981	+	0.791646i	$0.709225\pi$
$294$	51.9539	+	141.128i	0.176714	+	0.480027i
$295$		−	4.68580i		−	0.0158841i
$296$	157.859	−	280.510i	0.533308	−	0.947669i
$297$	60.8445			0.204864
$298$	295.732	−	108.869i	0.992389	−	0.365332i
$299$			68.5478i			0.229257i
$300$	104.922	+	123.193i	0.349741	+	0.410643i
$301$	−128.869			−0.428138
$302$	101.843	+	276.648i	0.337229	+	0.916052i
$303$		−	83.5073i		−	0.275602i
$304$	136.792	+	22.0541i	0.449974	+	0.0725465i
$305$	125.813			0.412503
$306$	−141.223	+	51.9889i	−0.461513	+	0.169898i
$307$			393.696i			1.28240i	0.767375	+	0.641199i	$0.221563\pi$
$307$			393.696i			1.28240i	−0.767375	+	0.641199i	$0.778437\pi$
$308$	−84.2841	+	71.7838i	−0.273650	+	0.233064i
$309$	151.455			0.490147
$310$	−50.6225	−	137.511i	−0.163298	−	0.443584i
$311$		−	317.227i		−	1.02002i	−0.860167	−	0.510012i	$-0.829641\pi$
$311$		−	317.227i		−	1.02002i	0.860167	−	0.510012i	$-0.170359\pi$
$312$	172.599	+	97.1312i	0.553200	+	0.311318i
$313$	−92.9551			−0.296981			−0.148491	−	0.988914i	$-0.547441\pi$
$313$	−92.9551			−0.296981			−0.148491	+	0.988914i	$0.547441\pi$
$314$	356.844	−	131.366i	1.13645	−	0.418364i
$315$		−	9.09073i		−	0.0288595i
$316$	247.119	+	290.152i	0.782023	+	0.918202i
$317$	267.483			0.843796			0.421898	−	0.906643i	$-0.361364\pi$
$317$	267.483			0.843796			0.421898	+	0.906643i	$0.361364\pi$
$318$	23.6377	+	64.2096i	0.0743324	+	0.201917i
$319$			234.178i			0.734102i
$320$	42.5792	+	70.1351i	0.133060	+	0.219172i
$321$	16.6412			0.0518417
$322$	−21.2757	+	7.83230i	−0.0660736	+	0.0243239i
$323$		−	217.203i		−	0.672455i
$324$	27.4070	−	23.3422i	0.0845894	−	0.0720439i
$325$	−333.838			−1.02720
$326$	−175.367	−	476.368i	−0.537935	−	1.46125i
$327$			7.21993i			0.0220793i
$328$	229.188	−	407.259i	0.698744	−	1.24164i
$329$	−49.4730			−0.150374
$330$	−48.8002	+	17.9650i	−0.147879	+	0.0544393i
$331$		−	623.718i		−	1.88434i	−0.335130	−	0.942172i	$-0.608780\pi$
$331$		−	623.718i		−	1.88434i	0.335130	−	0.942172i	$-0.391220\pi$
$332$	16.0783	+	18.8781i	0.0484286	+	0.0568618i
$333$	120.704			0.362475
$334$	8.86796	+	24.0890i	0.0265508	+	0.0721227i
$335$		−	50.0193i		−	0.149311i
$336$	−10.4262	+	64.6690i	−0.0310303	+	0.192467i
$337$	133.188			0.395217			0.197609	−	0.980281i	$-0.436682\pi$
$337$	133.188			0.395217			0.197609	+	0.980281i	$0.436682\pi$
$338$	−66.2446	+	24.3868i	−0.195990	+	0.0721504i
$339$		−	224.828i		−	0.663210i
$340$	97.9174	−	83.3952i	0.287992	−	0.245280i
$341$	−669.199			−1.96246
$342$	17.9503	+	48.7604i	0.0524863	+	0.142574i
$343$		−	218.435i		−	0.636835i
$344$	380.110	+	213.910i	1.10497	+	0.621830i
$345$	−10.6491			−0.0308670
$346$	−371.513	+	136.766i	−1.07374	+	0.395278i
$347$			532.152i			1.53358i	0.641899	+	0.766789i	$0.278147\pi$
$347$			532.152i			1.53358i	−0.641899	+	0.766789i	$0.721853\pi$
$348$	89.8396	+	105.484i	0.258160	+	0.303115i
$349$	−17.1654			−0.0491845			−0.0245922	−	0.999698i	$-0.507829\pi$
$349$	−17.1654			−0.0491845			−0.0245922	+	0.999698i	$0.507829\pi$
$350$	−38.1445	−	103.616i	−0.108984	−	0.296046i
$351$			74.2696i			0.211594i
$352$	367.756	−	71.8290i	1.04476	−	0.204060i
$353$	−215.059			−0.609232			−0.304616	−	0.952475i	$-0.598528\pi$
$353$	−215.059			−0.609232			−0.304616	+	0.952475i	$0.598528\pi$
$354$	−11.8819	+	4.37413i	−0.0335648	+	0.0123563i
$355$			84.2114i			0.237215i
$356$	143.696	−	122.384i	0.403640	−	0.343776i
$357$	102.684			0.287629
$358$	135.248	+	367.388i	0.377787	+	1.02622i
$359$		−	31.4688i		−	0.0876568i	−0.999039	−	0.0438284i	$-0.986045\pi$
$359$		−	31.4688i		−	0.0876568i	0.999039	−	0.0438284i	$-0.0139555\pi$
$360$	−15.0897	+	26.8138i	−0.0419157	+	0.0744827i
$361$	286.006			0.792260
$362$	−320.093	+	117.837i	−0.884235	+	0.325516i
$363$			27.9084i			0.0768826i
$364$	−87.6227	−	102.881i	−0.240722	−	0.282640i
$365$	−35.3456			−0.0968372
$366$	−117.445	−	319.029i	−0.320889	−	0.871664i
$367$		−	202.972i		−	0.553058i	−0.961006	−	0.276529i	$-0.910816\pi$
$367$		−	202.972i		−	0.553058i	0.961006	−	0.276529i	$-0.0891843\pi$
$368$	75.7551	+	12.2135i	0.205856	+	0.0331889i
$369$	175.245			0.474918
$370$	−96.8106	+	35.6392i	−0.261650	+	0.0963222i
$371$		−	46.6869i		−	0.125841i
$372$	−301.436	+	256.730i	−0.810312	+	0.690134i
$373$	−117.460			−0.314905			−0.157453	−	0.987527i	$-0.550328\pi$
$373$	−117.460			−0.314905			−0.157453	+	0.987527i	$0.550328\pi$
$374$	−202.922	−	551.218i	−0.542571	−	1.47385i
$375$		−	107.375i		−	0.286334i
$376$	145.924	+	82.1201i	0.388097	+	0.218404i
$377$	−285.849			−0.758221
$378$	−23.0517	+	8.48608i	−0.0609832	+	0.0224500i
$379$			86.2006i			0.227442i	0.993513	+	0.113721i	$0.0362770\pi$
$379$			86.2006i			0.227442i	−0.993513	+	0.113721i	$0.963723\pi$
$380$	−28.7940	−	33.8081i	−0.0757738	−	0.0889688i
$381$	−149.847			−0.393298
$382$	220.520	+	599.023i	0.577279	+	1.56812i
$383$			170.918i			0.446260i	0.974789	+	0.223130i	$0.0716274\pi$
$383$			170.918i			0.446260i	−0.974789	+	0.223130i	$0.928373\pi$
$384$	138.097	−	173.440i	0.359627	−	0.451666i
$385$	35.4827			0.0921629
$386$	351.438	−	129.376i	0.910460	−	0.335171i
$387$			163.562i			0.422641i
$388$	566.088	−	482.131i	1.45899	−	1.24261i
$389$	−332.186			−0.853949			−0.426974	−	0.904264i	$-0.640421\pi$
$389$	−332.186			−0.853949			−0.426974	+	0.904264i	$0.640421\pi$
$390$	−21.9289	−	59.5678i	−0.0562279	−	0.152738i
$391$		−	120.286i		−	0.307637i
$392$	−170.329	+	302.669i	−0.434513	+	0.772114i
$393$	−317.966			−0.809075
$394$	−561.086	+	206.555i	−1.42408	+	0.524250i
$395$		−	122.151i		−	0.309243i
$396$	91.1087	+	106.974i	0.230073	+	0.270137i
$397$	−430.099			−1.08337			−0.541687	−	0.840580i	$-0.682214\pi$
$397$	−430.099			−1.08337			−0.541687	+	0.840580i	$0.682214\pi$
$398$	−45.0697	−	122.428i	−0.113240	−	0.307607i
$399$		−	35.4537i		−	0.0888565i
$400$	−59.4818	+	368.939i	−0.148704	+	0.922348i
$401$	346.383			0.863797			0.431899	−	0.901922i	$-0.357844\pi$
$401$	346.383			0.863797			0.431899	+	0.901922i	$0.357844\pi$
$402$	−126.836	+	46.6924i	−0.315511	+	0.116150i
$403$		−	816.856i		−	2.02694i
$404$	146.819	−	125.044i	0.363413	−	0.309515i
$405$	−11.5380			−0.0284890
$406$	−32.6613	−	88.7213i	−0.0804465	−	0.218525i
$407$			471.130i			1.15757i
$408$	−302.873	−	170.444i	−0.742335	−	0.417755i
$409$	63.1125			0.154309			0.0771546	−	0.997019i	$-0.475416\pi$
$409$	63.1125			0.154309			0.0771546	+	0.997019i	$0.475416\pi$
$410$	−140.555	+	51.7429i	−0.342816	+	0.126202i
$411$		−	198.664i		−	0.483368i
$412$	226.790	+	266.282i	0.550460	+	0.646316i
$413$	8.63937			0.0209186
$414$	9.94083	+	27.0033i	0.0240117	+	0.0652254i
$415$		−	7.94748i		−	0.0191506i
$416$	87.6779	+	448.900i	0.210764	+	1.07909i
$417$	−196.433			−0.471063
$418$	−190.320	+	70.0632i	−0.455311	+	0.167615i
$419$		−	641.415i		−	1.53082i	−0.643541	−	0.765411i	$-0.722536\pi$
$419$		−	641.415i		−	1.53082i	0.643541	−	0.765411i	$-0.277464\pi$
$420$	15.9829	−	13.6125i	0.0380546	−	0.0324107i
$421$	−227.237			−0.539754			−0.269877	−	0.962895i	$-0.586983\pi$
$421$	−227.237			−0.539754			−0.269877	+	0.962895i	$0.586983\pi$
$422$	−82.7314	−	224.732i	−0.196046	−	0.532541i
$423$			62.7916i			0.148444i
$424$	−77.4954	+	137.706i	−0.182772	+	0.324779i
$425$	585.813			1.37838
$426$	213.538	−	78.6103i	0.501262	−	0.184531i
$427$			231.967i			0.543247i
$428$	24.9186	+	29.2578i	0.0582210	+	0.0683594i
$429$	−289.887			−0.675728
$430$	−48.2935	−	131.185i	−0.112310	−	0.305081i
$431$			500.152i			1.16044i	0.814458	+	0.580222i	$0.197034\pi$
$431$			500.152i			1.16044i	−0.814458	+	0.580222i	$0.802966\pi$
$432$	82.0785	+	13.2330i	0.189997	+	0.0306320i
$433$	−616.073			−1.42280			−0.711401	−	0.702786i	$-0.751939\pi$
$433$	−616.073			−1.42280			−0.711401	+	0.702786i	$0.751939\pi$
$434$	253.534	−	93.3344i	0.584180	−	0.215056i
$435$		−	44.4077i		−	0.102087i
$436$	−12.6938	+	10.8112i	−0.0291142	+	0.0247962i
$437$	−41.5315			−0.0950377
$438$	32.9947	+	89.6269i	0.0753303	+	0.204628i
$439$		−	584.689i		−	1.33187i	−0.746012	−	0.665933i	$-0.768034\pi$
$439$		−	584.689i		−	1.33187i	0.746012	−	0.665933i	$-0.231966\pi$
$440$	−104.659	−	58.8976i	−0.237861	−	0.133858i
$441$	−130.239			−0.295327
$442$	672.843	−	247.696i	1.52227	−	0.560398i
$443$			363.066i			0.819563i	0.912184	+	0.409781i	$0.134395\pi$
$443$			363.066i			0.819563i	−0.912184	+	0.409781i	$0.865605\pi$
$444$	180.743	+	212.217i	0.407079	+	0.477966i
$445$	−60.4945			−0.135943
$446$	28.7499	+	78.0964i	0.0644616	+	0.175104i
$447$			272.915i			0.610547i
$448$	−129.311	+	78.5048i	−0.288640	+	0.175234i
$449$	539.692			1.20199			0.600994	−	0.799254i	$-0.294772\pi$
$449$	539.692			1.20199			0.600994	+	0.799254i	$0.294772\pi$
$450$	−131.511	+	48.4134i	−0.292246	+	0.107585i
$451$			684.010i			1.51665i
$452$	395.283	−	336.658i	0.874520	−	0.744820i
$453$	−255.303			−0.563582
$454$	60.8082	+	165.180i	0.133939	+	0.363832i
$455$			43.3119i			0.0951909i
$456$	−58.8495	+	104.573i	−0.129056	+	0.229328i
$457$	616.941			1.34998			0.674990	−	0.737826i	$-0.264148\pi$
$457$	616.941			1.34998			0.674990	+	0.737826i	$0.264148\pi$
$458$	799.285	−	294.243i	1.74516	−	0.642453i
$459$		−	130.327i		−	0.283937i
$460$	−15.9460	−	18.7228i	−0.0346653	−	0.0407018i
$461$	−94.5149			−0.205022			−0.102511	−	0.994732i	$-0.532688\pi$
$461$	−94.5149			−0.205022			−0.102511	+	0.994732i	$0.532688\pi$
$462$	−33.1227	−	89.9746i	−0.0716941	−	0.194750i
$463$			575.504i			1.24299i	0.783419	+	0.621494i	$0.213474\pi$
$463$			575.504i			1.24299i	−0.783419	+	0.621494i	$0.786526\pi$
$464$	−50.9313	+	315.904i	−0.109766	+	0.680828i
$465$	126.901			0.272906
$466$	222.977	−	82.0854i	0.478492	−	0.176149i
$467$		−	747.861i		−	1.60142i	−0.599055	−	0.800708i	$-0.704457\pi$
$467$		−	747.861i		−	1.60142i	0.599055	−	0.800708i	$-0.295543\pi$
$468$	−130.578	+	111.212i	−0.279012	+	0.237632i
$469$	92.2223			0.196636
$470$	−18.5399	−	50.3619i	−0.0394466	−	0.107153i
$471$			329.312i			0.699176i
$472$	−25.4824	−	14.3404i	−0.0539882	−	0.0303823i
$473$	−638.412			−1.34971
$474$	−309.742	+	114.026i	−0.653464	+	0.240562i
$475$		−	202.265i		−	0.425821i
$476$	153.759	+	180.534i	0.323022	+	0.379273i
$477$	−59.2555			−0.124225
$478$	−217.751	−	591.500i	−0.455546	−	1.23745i
$479$			759.395i			1.58538i	0.609628	+	0.792688i	$0.291319\pi$
$479$			759.395i			1.58538i	−0.609628	+	0.792688i	$0.708681\pi$
$480$	−69.7381	+	13.6211i	−0.145288	+	0.0283772i
$481$	−575.083			−1.19560
$482$	−417.111	+	153.552i	−0.865375	+	0.318573i
$483$		−	19.6342i		−	0.0406505i
$484$	−49.0673	+	41.7901i	−0.101379	+	0.0863432i
$485$	−238.317			−0.491375
$486$	10.7706	+	29.2574i	0.0221618	+	0.0602004i
$487$		−	177.759i		−	0.365009i	−0.983205	−	0.182504i	$-0.941580\pi$
$487$		−	177.759i		−	0.365009i	0.983205	−	0.182504i	$-0.0584204\pi$
$488$	385.040	−	684.202i	0.789017	−	1.40205i
$489$	439.613			0.899005
$490$	104.458	−	38.4545i	0.213180	−	0.0784785i
$491$		−	34.4717i		−	0.0702072i	−0.999384	−	0.0351036i	$-0.988824\pi$
$491$		−	34.4717i		−	0.0702072i	0.999384	−	0.0351036i	$-0.0111761\pi$
$492$	262.412	+	308.108i	0.533358	+	0.626235i
$493$	501.603			1.01745
$494$	−85.5224	−	232.314i	−0.173122	−	0.470271i
$495$		−	45.0350i		−	0.0909798i
$496$	−902.743	−	145.544i	−1.82005	−	0.293435i
$497$	−155.264			−0.312402
$498$	−20.1527	+	7.41888i	−0.0404672	+	0.0148973i
$499$		−	466.319i		−	0.934508i	−0.884123	−	0.467254i	$-0.845243\pi$
$499$		−	466.319i		−	0.934508i	0.884123	−	0.467254i	$-0.154757\pi$
$500$	188.783	−	160.784i	0.377565	−	0.321569i
$501$	−22.2304			−0.0443720
$502$	−25.6943	−	69.7961i	−0.0511838	−	0.139036i
$503$		−	82.5847i		−	0.164184i	−0.996625	−	0.0820921i	$-0.973840\pi$
$503$		−	82.5847i		−	0.164184i	0.996625	−	0.0820921i	$-0.0261602\pi$
$504$	−49.4375	−	27.8213i	−0.0980903	−	0.0552011i
$505$	−61.8092			−0.122394
$506$	−105.399	+	38.8008i	−0.208298	+	0.0766814i
$507$		−	61.1334i		−	0.120579i
$508$	−224.381	−	263.454i	−0.441695	−	0.518610i
$509$	−570.982			−1.12177			−0.560886	−	0.827893i	$-0.689539\pi$
$509$	−570.982			−1.12177			−0.560886	+	0.827893i	$0.689539\pi$
$510$	38.4804	+	104.528i	0.0754518	+	0.204958i
$511$		−	65.1679i		−	0.127530i
$512$	511.721	−	16.9137i	0.999454	−	0.0330346i
$513$	−44.9982			−0.0877158
$514$	−898.632	+	330.816i	−1.74831	+	0.643611i
$515$		−	112.102i		−	0.217674i
$516$	−287.568	+	244.919i	−0.557302	+	0.474649i
$517$	−245.087			−0.474056
$518$	−65.7093	−	178.493i	−0.126852	−	0.344581i
$519$		−	342.848i		−	0.660594i
$520$	71.8931	−	127.751i	0.138256	−	0.245676i
$521$	546.978			1.04986			0.524931	−	0.851145i	$-0.324091\pi$
$521$	546.978			1.04986			0.524931	+	0.851145i	$0.324091\pi$
$522$	−112.606	+	41.4540i	−0.215720	+	0.0794138i
$523$			288.630i			0.551874i	0.961176	+	0.275937i	$0.0889881\pi$
$523$			288.630i			0.551874i	−0.961176	+	0.275937i	$0.911012\pi$
$524$	−476.124	−	559.035i	−0.908634	−	1.06686i
$525$	95.6215			0.182136
$526$	285.633	+	775.896i	0.543029	+	1.47509i
$527$			1433.40i			2.71993i
$528$	−51.6507	+	320.367i	−0.0978234	+	0.606755i
$529$	−23.0000			−0.0434783
$530$	47.5257	−	17.4958i	0.0896712	−	0.0330110i
$531$		−	10.9652i		−	0.0206500i
$532$	62.3332	−	53.0886i	0.117168	−	0.0997905i
$533$	−834.935			−1.56648
$534$	56.4709	+	153.398i	0.105751	+	0.287262i
$535$		−	12.3172i		−	0.0230229i
$536$	−272.017	−	153.079i	−0.507494	−	0.285596i
$537$	−339.042			−0.631363
$538$	−122.715	+	45.1753i	−0.228094	+	0.0839690i
$539$		−	508.346i		−	0.943128i
$540$	−17.2771	−	20.2857i	−0.0319946	−	0.0375661i
$541$	829.452			1.53318			0.766592	−	0.642135i	$-0.221951\pi$
$541$	829.452			1.53318			0.766592	+	0.642135i	$0.221951\pi$
$542$	73.6922	+	200.178i	0.135963	+	0.369332i
$543$		−	295.396i		−	0.544007i
$544$	−153.855	−	787.721i	−0.282822	−	1.44802i
$545$	5.34395			0.00980541
$546$	109.827	−	40.4311i	0.201149	−	0.0740496i
$547$		−	829.361i		−	1.51620i	−0.652139	−	0.758099i	$-0.726128\pi$
$547$		−	829.361i		−	1.51620i	0.652139	−	0.758099i	$-0.273872\pi$
$548$	349.283	−	297.480i	0.637377	−	0.542847i
$549$	294.414			0.536273
$550$	−188.966	−	513.309i	−0.343575	−	0.933288i
$551$		−	173.189i		−	0.314318i
$552$	−32.5907	+	57.9124i	−0.0590411	+	0.104914i
$553$	225.214			0.407258
$554$	−104.202	+	38.3601i	−0.188090	+	0.0692421i
$555$		−	89.3411i		−	0.160975i
$556$	−294.140	−	345.361i	−0.529029	−	0.621152i
$557$	412.753			0.741028			0.370514	−	0.928827i	$-0.379182\pi$
$557$	412.753			0.741028			0.370514	+	0.928827i	$0.379182\pi$
$558$	−118.461	−	321.788i	−0.212295	−	0.576681i
$559$		−	779.276i		−	1.39405i
$560$	47.8658	+	7.71710i	0.0854746	+	0.0137805i
$561$	508.688			0.906753
$562$	341.501	−	125.718i	0.607653	−	0.223697i
$563$			962.077i			1.70884i	0.519583	+	0.854420i	$0.326087\pi$
$563$			962.077i			1.70884i	−0.519583	+	0.854420i	$0.673913\pi$
$564$	−110.398	+	94.0244i	−0.195740	+	0.166710i
$565$	−166.410			−0.294531
$566$	−76.7671	−	208.531i	−0.135631	−	0.368429i
$567$		−	21.2731i		−	0.0375187i
$568$	457.961	+	257.721i	0.806270	+	0.453735i
$569$	−128.259			−0.225411			−0.112706	−	0.993628i	$-0.535952\pi$
$569$	−128.259			−0.225411			−0.112706	+	0.993628i	$0.535952\pi$
$570$	36.0907	−	13.2862i	0.0633171	−	0.0233091i
$571$			74.0046i			0.129605i	0.997898	+	0.0648026i	$0.0206418\pi$
$571$			74.0046i			0.129605i	−0.997898	+	0.0648026i	$0.979358\pi$
$572$	−434.078	−	509.667i	−0.758878	−	0.891027i
$573$	−552.805			−0.964756
$574$	−95.4001	−	259.146i	−0.166202	−	0.451473i
$575$		−	112.014i		−	0.194806i
$576$	99.6390	+	164.122i	0.172984	+	0.284934i
$577$	48.8940			0.0847384			0.0423692	−	0.999102i	$-0.486509\pi$
$577$	48.8940			0.0847384			0.0423692	+	0.999102i	$0.486509\pi$
$578$	−638.278	+	234.971i	−1.10429	+	0.406525i
$579$			324.322i			0.560142i
$580$	78.0756	−	66.4962i	0.134613	−	0.114649i
$581$	14.6531			0.0252204
$582$	222.466	+	604.308i	0.382244	+	1.03833i
$583$		−	231.284i		−	0.396714i
$584$	−108.172	+	192.218i	−0.185226	+	0.329140i
$585$	54.9718			0.0939689
$586$	671.981	−	247.379i	1.14673	−	0.422148i
$587$		−	55.3242i		−	0.0942491i	−0.998889	−	0.0471246i	$-0.984994\pi$
$587$		−	55.3242i		−	0.0942491i	0.998889	−	0.0471246i	$-0.0150058\pi$
$588$	−195.021	−	228.981i	−0.331668	−	0.389423i
$589$	494.914			0.840262
$590$	3.23758	+	8.79459i	0.00548743	+	0.0149061i
$591$		−	517.795i		−	0.876134i
$592$	−102.466	+	635.549i	−0.173084	+	1.07356i
$593$	685.851			1.15658			0.578289	−	0.815832i	$-0.303721\pi$
$593$	685.851			1.15658			0.578289	+	0.815832i	$0.303721\pi$
$594$	−114.197	+	42.0396i	−0.192250	+	0.0707737i
$595$		−	76.0028i		−	0.127736i
$596$	−479.827	+	408.663i	−0.805078	+	0.685677i
$597$	112.982			0.189249
$598$	−47.3621	−	128.655i	−0.0792008	−	0.215142i
$599$		−	442.222i		−	0.738266i	−0.929376	−	0.369133i	$-0.879655\pi$
$599$		−	442.222i		−	0.738266i	0.929376	−	0.369133i	$-0.120345\pi$
$600$	−282.043	−	158.722i	−0.470071	−	0.264536i
$601$	73.9199			0.122995			0.0614974	−	0.998107i	$-0.480412\pi$
$601$	73.9199			0.122995			0.0614974	+	0.998107i	$0.480412\pi$
$602$	241.870	−	89.0404i	0.401777	−	0.147908i
$603$		−	117.049i		−	0.194112i
$604$	−382.291	−	448.862i	−0.632932	−	0.743149i
$605$	20.6568			0.0341435
$606$	57.6981	+	156.732i	0.0952114	+	0.258633i
$607$		−	1117.65i		−	1.84127i	−0.390421	−	0.920636i	$-0.627671\pi$
$607$		−	1117.65i		−	1.84127i	0.390421	−	0.920636i	$-0.372329\pi$
$608$	−271.978	+	53.1220i	−0.447332	+	0.0873716i
$609$	81.8760			0.134443
$610$	−236.134	+	86.9289i	−0.387105	+	0.142506i
$611$		−	299.164i		−	0.489631i
$612$	229.135	−	195.152i	0.374404	−	0.318876i
$613$	−398.940			−0.650799			−0.325400	−	0.945577i	$-0.605499\pi$
$613$	−398.940			−0.650799			−0.325400	+	0.945577i	$0.605499\pi$
$614$	−272.019	−	738.913i	−0.443027	−	1.20344i
$615$		−	129.710i		−	0.210911i
$616$	108.592	−	192.963i	0.176285	−	0.313252i
$617$	−242.774			−0.393474			−0.196737	−	0.980456i	$-0.563035\pi$
$617$	−242.774			−0.393474			−0.196737	+	0.980456i	$0.563035\pi$
$618$	−284.261	+	104.646i	−0.459969	+	0.169330i
$619$			1138.94i			1.83997i	0.391954	+	0.919985i	$0.371799\pi$
$619$			1138.94i			1.83997i	−0.391954	+	0.919985i	$0.628201\pi$
$620$	190.023	+	223.113i	0.306488	+	0.359859i
$621$	−24.9199			−0.0401286
$622$	219.184	+	595.392i	0.352385	+	0.957222i
$623$		−	111.536i		−	0.179030i
$624$	−391.055	−	63.0473i	−0.626690	−	0.101037i
$625$	504.436			0.807098
$626$	174.464	−	64.2260i	0.278696	−	0.102597i
$627$		−	175.636i		−	0.280121i
$628$	−578.982	+	493.113i	−0.921945	+	0.785211i
$629$	1009.14			1.60436
$630$	6.28111	+	17.0620i	0.00997001	+	0.0270826i
$631$		−	80.0531i		−	0.126867i	−0.997986	−	0.0634335i	$-0.979795\pi$
$631$		−	80.0531i		−	0.126867i	0.997986	−	0.0634335i	$-0.0202051\pi$
$632$	−664.285	−	373.831i	−1.05108	−	0.591505i
$633$	207.393			0.327635
$634$	−502.029	+	184.814i	−0.791844	+	0.291504i
$635$			110.911i			0.174664i
$636$	−88.7294	−	104.180i	−0.139512	−	0.163806i
$637$	620.511			0.974114
$638$	−161.802	−	439.521i	−0.253608	−	0.688904i
$639$			197.062i			0.308391i
$640$	−128.374	−	102.214i	−0.200585	−	0.159710i
$641$	−283.432			−0.442172			−0.221086	−	0.975254i	$-0.570960\pi$
$641$	−283.432			−0.442172			−0.221086	+	0.975254i	$0.570960\pi$
$642$	−31.2332	+	11.4980i	−0.0486499	+	0.0179096i
$643$			881.312i			1.37063i	0.728249	+	0.685313i	$0.240334\pi$
$643$			881.312i			1.37063i	−0.728249	+	0.685313i	$0.759666\pi$
$644$	34.5200	−	29.4003i	0.0536024	−	0.0456526i
$645$	121.063			0.187695
$646$	150.073	+	407.660i	0.232311	+	0.631052i
$647$			1259.13i			1.94611i	0.230569	+	0.973056i	$0.425941\pi$
$647$			1259.13i			1.94611i	−0.230569	+	0.973056i	$0.574059\pi$
$648$	−35.3111	+	62.7465i	−0.0544924	+	0.0968311i
$649$	42.7990			0.0659460
$650$	626.569	−	230.661i	0.963952	−	0.354863i
$651$			233.973i			0.359405i
$652$	658.279	+	772.909i	1.00963	+	1.18544i
$653$	239.275			0.366425			0.183212	−	0.983073i	$-0.441350\pi$
$653$	239.275			0.366425			0.183212	+	0.983073i	$0.441350\pi$
$654$	−4.98851	−	13.5508i	−0.00762769	−	0.0207199i
$655$			235.348i			0.359310i
$656$	−148.765	+	922.723i	−0.226776	+	1.40659i
$657$	−82.7117			−0.125893
$658$	92.8540	−	34.1827i	0.141116	−	0.0519493i
$659$			1262.55i			1.91586i	0.287006	+	0.957929i	$0.407340\pi$
$659$			1262.55i			1.91586i	−0.287006	+	0.957929i	$0.592660\pi$
$660$	79.1786	−	67.4355i	0.119968	−	0.102175i
$661$	−335.780			−0.507988			−0.253994	−	0.967206i	$-0.581744\pi$
$661$	−335.780			−0.507988			−0.253994	+	0.967206i	$0.581744\pi$
$662$	430.949	+	1170.63i	0.650980	+	1.76833i
$663$			620.929i			0.936545i
$664$	−43.2203	−	24.3225i	−0.0650907	−	0.0366303i
$665$	−26.2416			−0.0394611
$666$	−226.545	+	83.3988i	−0.340158	+	0.125223i
$667$		−	95.9117i		−	0.143796i
$668$	−33.2879	−	39.0845i	−0.0498321	−	0.0585097i
$669$	−72.0708			−0.107729
$670$	34.5601	+	93.8793i	0.0515822	+	0.140118i
$671$			1149.15i			1.71259i
$672$	−25.1136	−	128.579i	−0.0373715	−	0.191337i
$673$	1083.30			1.60966			0.804828	−	0.593509i	$-0.202258\pi$
$673$	1083.30			1.60966			0.804828	+	0.593509i	$0.202258\pi$
$674$	−249.976	+	92.0245i	−0.370884	+	0.136535i
$675$		−	121.364i		−	0.179798i
$676$	107.482	−	91.5414i	0.158997	−	0.135416i
$677$	−1104.85			−1.63198			−0.815992	−	0.578064i	$-0.803809\pi$
$677$	−1104.85			−1.63198			−0.815992	+	0.578064i	$0.803809\pi$
$678$	155.342	+	421.971i	0.229117	+	0.622376i
$679$		−	439.393i		−	0.647118i
$680$	−126.157	+	224.176i	−0.185525	+	0.329670i
$681$	−152.435			−0.223840
$682$	1255.99	−	462.373i	1.84163	−	0.677967i
$683$		−	1084.68i		−	1.58812i	−0.607841	−	0.794059i	$-0.707964\pi$
$683$		−	1084.68i		−	1.58812i	0.607841	−	0.794059i	$-0.292036\pi$
$684$	−67.3805	−	79.1139i	−0.0985095	−	0.115664i
$685$	−147.044			−0.214663
$686$	150.924	+	409.971i	0.220006	+	0.597626i
$687$			737.615i			1.07368i
$688$	−861.211	−	138.848i	−1.25176	−	0.201813i
$689$	282.317			0.409748
$690$	19.9869	−	7.35786i	0.0289666	−	0.0106636i
$691$		−	733.855i		−	1.06202i	−0.847366	−	0.531009i	$-0.821813\pi$
$691$		−	733.855i		−	1.06202i	0.847366	−	0.531009i	$-0.178187\pi$
$692$	602.781	−	513.382i	0.871071	−	0.741882i
$693$	83.0326			0.119816
$694$	−367.682	−	998.775i	−0.529802	−	1.43916i
$695$			145.393i			0.209199i
$696$	−241.499	−	135.906i	−0.346982	−	0.195267i
$697$	1465.13			2.10205
$698$	32.2171	−	11.8602i	0.0461562	−	0.0169916i
$699$			205.773i			0.294383i
$700$	143.184	+	168.118i	0.204549	+	0.240168i
$701$	−396.483			−0.565597			−0.282798	−	0.959179i	$-0.591263\pi$
$701$	−396.483			−0.565597			−0.282798	+	0.959179i	$0.591263\pi$
$702$	−51.3155	−	139.394i	−0.0730990	−	0.198567i
$703$		−	348.429i		−	0.495632i
$704$	−640.597	+	388.908i	−0.909939	+	0.552427i
$705$	46.4762			0.0659237
$706$	403.636	−	148.592i	0.571722	−	0.210470i
$707$		−	113.960i		−	0.161188i
$708$	19.2785	−	16.4193i	0.0272295	−	0.0231911i
$709$	429.980			0.606459			0.303230	−	0.952918i	$-0.401935\pi$
$709$	429.980			0.606459			0.303230	+	0.952918i	$0.401935\pi$
$710$	−58.1847	−	158.053i	−0.0819502	−	0.222610i
$711$		−	285.844i		−	0.402030i
$712$	−185.138	+	328.983i	−0.260025	+	0.462055i
$713$	274.082			0.384407
$714$	−192.723	+	70.9477i	−0.269920	+	0.0993665i
$715$			214.565i			0.300090i
$716$	−507.682	−	596.088i	−0.709053	−	0.832526i
$717$	545.863			0.761315
$718$	21.7429	+	59.0626i	0.0302826	+	0.0822598i
$719$		−	1062.95i		−	1.47837i	−0.673501	−	0.739187i	$-0.735210\pi$
$719$		−	1062.95i		−	1.47837i	0.673501	−	0.739187i	$-0.264790\pi$
$720$	9.79462	−	60.7517i	0.0136036	−	0.0843774i
$721$	206.686			0.286666
$722$	−536.793	+	197.612i	−0.743481	+	0.273700i
$723$		−	384.928i		−	0.532404i
$724$	519.353	−	442.327i	0.717338	−	0.610949i
$725$	467.105			0.644283
$726$	−19.2829	−	52.3802i	−0.0265604	−	0.0721490i
$727$		−	559.356i		−	0.769403i	−0.923041	−	0.384701i	$-0.874304\pi$
$727$		−	559.356i		−	0.769403i	0.923041	−	0.384701i	$-0.125696\pi$
$728$	235.540	+	132.552i	0.323544	+	0.182077i
$729$	−27.0000			−0.0370370
$730$	66.3388	−	24.4215i	0.0908750	−	0.0334541i
$731$			1367.46i			1.87067i
$732$	440.857	+	517.626i	0.602263	+	0.707140i
$733$	−507.215			−0.691972			−0.345986	−	0.938240i	$-0.612455\pi$
$733$	−507.215			−0.691972			−0.345986	+	0.938240i	$0.612455\pi$
$734$	140.241	+	380.951i	0.191064	+	0.519007i
$735$			96.3985i			0.131154i
$736$	−150.621	+	29.4188i	−0.204647	+	0.0399712i
$737$	456.864			0.619897
$738$	−328.910	+	121.083i	−0.445677	+	0.164069i
$739$			571.547i			0.773406i	0.922204	+	0.386703i	$0.126386\pi$
$739$			571.547i			0.773406i	−0.922204	+	0.386703i	$0.873614\pi$
$740$	157.076	−	133.780i	0.212264	−	0.180783i
$741$	214.389			0.289324
$742$	32.2576	+	87.6249i	0.0434739	+	0.118093i
$743$			361.444i			0.486465i	0.969968	+	0.243233i	$0.0782079\pi$
$743$			361.444i			0.486465i	−0.969968	+	0.243233i	$0.921792\pi$
$744$	388.370	−	690.119i	0.522003	−	0.927580i
$745$	202.002			0.271144
$746$	220.455	−	81.1570i	0.295517	−	0.108789i
$747$		−	18.5978i		−	0.0248966i
$748$	761.712	+	894.354i	1.01833	+	1.19566i
$749$	22.7097			0.0303201
$750$	74.1894	+	201.529i	0.0989192	+	0.268705i
$751$			234.548i			0.312314i	0.987732	+	0.156157i	$0.0499105\pi$
$751$			234.548i			0.312314i	−0.987732	+	0.156157i	$0.950089\pi$
$752$	−330.619	−	53.3037i	−0.439654	−	0.0708826i
$753$	64.4110			0.0855391
$754$	536.499	−	197.503i	0.711538	−	0.261941i
$755$			188.966i			0.250286i
$756$	37.4014	−	31.8544i	0.0494728	−	0.0421355i
$757$	1491.00			1.96961			0.984807	−	0.173650i	$-0.0555563\pi$
$757$	1491.00			1.96961			0.984807	+	0.173650i	$0.0555563\pi$
$758$	−59.5591	−	161.787i	−0.0785739	−	0.213439i
$759$		−	97.2666i		−	0.128151i
$760$	77.4016	+	43.5584i	0.101844	+	0.0573136i
$761$	−326.608			−0.429183			−0.214591	−	0.976704i	$-0.568842\pi$
$761$	−326.608			−0.429183			−0.214591	+	0.976704i	$0.568842\pi$
$762$	281.241	−	103.534i	0.369083	−	0.135872i
$763$			9.85282i			0.0129133i
$764$	−827.773	−	971.918i	−1.08347	−	1.27214i
$765$	−96.4635			−0.126096
$766$	−118.093	−	320.788i	−0.154168	−	0.418784i
$767$			52.2424i			0.0681127i
$768$	−139.353	+	420.938i	−0.181449	+	0.548096i
$769$	377.015			0.490267			0.245133	−	0.969489i	$-0.421168\pi$
$769$	377.015			0.490267			0.245133	+	0.969489i	$0.421168\pi$
$770$	−66.5961	+	24.5163i	−0.0864885	+	0.0318393i
$771$		−	829.297i		−	1.07561i
$772$	−570.209	+	485.641i	−0.738613	+	0.629069i
$773$	646.899			0.836868			0.418434	−	0.908247i	$-0.362579\pi$
$773$	646.899			0.836868			0.418434	+	0.908247i	$0.362579\pi$
$774$	−113.011	−	306.984i	−0.146009	−	0.396620i
$775$			1334.82i			1.72235i
$776$	−729.347	+	1296.02i	−0.939880	+	1.67013i
$777$	164.721			0.211997
$778$	623.467	−	229.519i	0.801372	−	0.295012i
$779$		−	505.868i		−	0.649381i
$780$	82.3150	+	96.6491i	0.105532	+	0.123909i
$781$	−769.167			−0.984849
$782$	83.1100	+	225.761i	0.106279	+	0.288696i
$783$		−	103.918i		−	0.132717i
$784$	110.560	−	685.753i	0.141020	−	0.874685i
$785$	243.745			0.310503
$786$	596.779	−	219.694i	0.759261	−	0.279509i
$787$			398.112i			0.505860i	0.967485	+	0.252930i	$0.0813943\pi$
$787$			398.112i			0.505860i	−0.967485	+	0.252930i	$0.918606\pi$
$788$	910.365	−	775.348i	1.15529	−	0.983945i
$789$	−716.031			−0.907517
$790$	84.3983	+	229.260i	0.106833	+	0.290203i
$791$		−	306.816i		−	0.387884i
$792$	−244.911	−	137.825i	−0.309231	−	0.174022i
$793$	−1402.71			−1.76886
$794$	807.237	−	297.171i	1.01667	−	0.374270i
$795$			43.8589i			0.0551684i
$796$	169.179	+	198.639i	0.212537	+	0.249547i
$797$	203.750			0.255646			0.127823	−	0.991797i	$-0.459201\pi$
$797$	203.750			0.255646			0.127823	+	0.991797i	$0.459201\pi$
$798$	24.4962	+	66.5418i	0.0306970	+	0.0833857i
$799$			524.968i			0.657031i
$800$	−143.274	−	733.546i	−0.179093	−	0.916932i
$801$	−141.562			−0.176732
$802$	−650.112	+	239.328i	−0.810614	+	0.298414i
$803$		−	322.838i		−	0.402040i
$804$	205.791	−	175.270i	0.255959	−	0.217998i
$805$	−14.5325			−0.0180528
$806$	564.395	+	1533.13i	0.700242	+	1.90214i
$807$		−	113.246i		−	0.140330i
$808$	−189.161	+	336.133i	−0.234111	+	0.416006i
$809$	−550.790			−0.680828			−0.340414	−	0.940276i	$-0.610567\pi$
$809$	−550.790			−0.680828			−0.340414	+	0.940276i	$0.610567\pi$
$810$	21.6553	−	7.97204i	0.0267349	−	0.00984202i
$811$			920.854i			1.13546i	0.823216	+	0.567728i	$0.192177\pi$
$811$			920.854i			1.13546i	−0.823216	+	0.567728i	$0.807823\pi$
$812$	122.601	+	143.951i	0.150987	+	0.177279i
$813$	−184.733			−0.227224
$814$	−325.520	−	884.245i	−0.399902	−	1.08630i
$815$		−	325.387i		−	0.399248i
$816$	686.215	+	110.634i	0.840950	+	0.135581i
$817$	472.145			0.577901
$818$	−118.453	+	43.6067i	−0.144809	+	0.0533089i
$819$			101.353i			0.123753i
$820$	228.051	−	194.228i	0.278111	−	0.236864i
$821$	−128.455			−0.156462			−0.0782309	−	0.996935i	$-0.524927\pi$
$821$	−128.455			−0.156462			−0.0782309	+	0.996935i	$0.524927\pi$
$822$	137.264	+	372.865i	0.166988	+	0.453607i
$823$		−	1418.76i		−	1.72389i	−0.507001	−	0.861945i	$-0.669246\pi$
$823$		−	1418.76i		−	1.72389i	0.507001	−	0.861945i	$-0.330754\pi$
$824$	−609.637	−	343.078i	−0.739850	−	0.416356i
$825$	473.704			0.574186
$826$	−16.2149	+	5.96924i	−0.0196306	+	0.00722669i
$827$			1211.37i			1.46478i	0.680886	+	0.732390i	$0.261595\pi$
$827$			1211.37i			1.46478i	−0.680886	+	0.732390i	$0.738405\pi$
$828$	−37.3151	−	43.8130i	−0.0450666	−	0.0529143i
$829$	−1393.35			−1.68076			−0.840380	−	0.541998i	$-0.817668\pi$
$829$	−1393.35			−1.68076			−0.840380	+	0.541998i	$0.817668\pi$
$830$	5.49120	+	14.9163i	0.00661590	+	0.0179715i
$831$		−	96.1620i		−	0.115718i
$832$	−474.720	−	781.943i	−0.570577	−	0.939835i
$833$	−1088.86			−1.30716
$834$	368.678	−	135.723i	0.442060	−	0.162737i
$835$			16.4542i			0.0197056i
$836$	308.795	−	262.998i	0.369373	−	0.314591i
$837$	296.960			0.354791
$838$	443.176	+	1203.85i	0.528850	+	1.43657i
$839$			569.978i			0.679354i	0.940542	+	0.339677i	$0.110318\pi$
$839$			569.978i			0.679354i	−0.940542	+	0.339677i	$0.889682\pi$
$840$	−20.5924	+	36.5919i	−0.0245148	+	0.0435618i
$841$	−441.041			−0.524424
$842$	426.491	−	157.006i	0.506522	−	0.186468i
$843$			315.152i			0.373846i
$844$	310.551	+	364.629i	0.367951	+	0.432025i
$845$	−45.2489			−0.0535490
$846$	−43.3850	−	117.851i	−0.0512825	−	0.139304i
$847$			38.0857i			0.0449654i
$848$	50.3018	−	312.000i	0.0593182	−	0.367925i
$849$	192.441			0.226668
$850$	−1099.49	+	404.759i	−1.29352	+	0.476187i
$851$		−	192.959i		−	0.226744i
$852$	−346.466	+	295.081i	−0.406650	+	0.346340i
$853$	−1472.40			−1.72615			−0.863074	−	0.505077i	$-0.831464\pi$
$853$	−1472.40			−1.72615			−0.863074	+	0.505077i	$0.831464\pi$
$854$	−160.274	−	435.369i	−0.187674	−	0.509800i
$855$			33.3061i			0.0389545i
$856$	−66.9840	−	37.6958i	−0.0782523	−	0.0440371i
$857$	−1553.44			−1.81265			−0.906324	−	0.422583i	$-0.861123\pi$
$857$	−1553.44			−1.81265			−0.906324	+	0.422583i	$0.861123\pi$
$858$	544.078	−	200.293i	0.634124	−	0.233442i
$859$		−	173.746i		−	0.202266i	−0.994873	−	0.101133i	$-0.967753\pi$
$859$		−	173.746i		−	0.202266i	0.994873	−	0.101133i	$-0.0322467\pi$
$860$	181.280	+	212.848i	0.210791	+	0.247498i
$861$	239.151			0.277760
$862$	−345.572	−	938.716i	−0.400896	−	1.08900i
$863$		−	1377.36i		−	1.59601i	−0.602650	−	0.798006i	$-0.705888\pi$
$863$		−	1377.36i		−	1.59601i	0.602650	−	0.798006i	$-0.294112\pi$
$864$	−163.193	+	31.8744i	−0.188881	+	0.0368917i
$865$	−253.765			−0.293369
$866$	1156.28	−	425.667i	1.33520	−	0.491532i
$867$		−	589.031i		−	0.679390i
$868$	−411.361	+	350.351i	−0.473918	+	0.403631i
$869$	1115.70			1.28389
$870$	30.6828	+	83.3470i	0.0352676	+	0.0958012i
$871$			557.670i			0.640264i
$872$	16.3547	−	29.0616i	0.0187553	−	0.0333275i
$873$	−557.682			−0.638811
$874$	77.9488	−	28.6956i	0.0891863	−	0.0328324i
$875$		−	146.532i		−	0.167465i
$876$	−123.853	−	145.420i	−0.141385	−	0.166005i
$877$	739.573			0.843299			0.421649	−	0.906759i	$-0.361451\pi$
$877$	739.573			0.843299			0.421649	+	0.906759i	$0.361451\pi$
$878$	403.982	+	1097.38i	0.460116	+	1.24986i
$879$			620.134i			0.705500i
$880$	237.125	+	38.2301i	0.269460	+	0.0434433i
$881$	156.256			0.177362			0.0886809	−	0.996060i	$-0.471735\pi$
$881$	156.256			0.177362			0.0886809	+	0.996060i	$0.471735\pi$
$882$	244.441	−	89.9868i	0.277144	−	0.102026i
$883$			261.539i			0.296194i	0.988973	+	0.148097i	$0.0473147\pi$
$883$			261.539i			0.296194i	−0.988973	+	0.148097i	$0.952685\pi$
$884$	−1091.69	+	929.781i	−1.23494	+	1.05179i
$885$	−8.11604			−0.00917067
$886$	−250.855	−	681.425i	−0.283132	−	0.769103i
$887$			312.592i			0.352415i	0.984353	+	0.176208i	$0.0563830\pi$
$887$			312.592i			0.352415i	−0.984353	+	0.176208i	$0.943617\pi$
$888$	−485.858	−	273.420i	−0.547137	−	0.307906i
$889$	−204.491			−0.230024
$890$	113.540	−	41.7978i	0.127573	−	0.0469638i
$891$		−	105.386i		−	0.118278i
$892$	−107.919	−	126.712i	−0.120986	−	0.142054i
$893$	181.257			0.202975
$894$	−188.566	−	512.223i	−0.210924	−	0.572956i
$895$			250.947i			0.280388i
$896$	188.456	−	236.688i	0.210331	−	0.264161i
$897$	118.728			0.132361
$898$	−1012.93	+	372.893i	−1.12798	+	0.415248i
$899$			1142.94i			1.27135i
$900$	213.377	−	181.731i	0.237085	−	0.201923i
$901$	−495.404			−0.549838
$902$	−472.607	−	1283.79i	−0.523954	−	1.42327i
$903$			223.208i			0.247185i
$904$	−509.282	+	904.976i	−0.563365	+	1.00108i
$905$	−218.642			−0.241593
$906$	479.168	−	176.398i	0.528883	−	0.194699i
$907$		−	1788.29i		−	1.97165i	−0.167771	−	0.985826i	$-0.553657\pi$
$907$		−	1788.29i		−	1.97165i	0.167771	−	0.985826i	$-0.446343\pi$
$908$	−228.257	−	268.005i	−0.251385	−	0.295160i
$909$	−144.639			−0.159119
$910$	−29.9257	−	81.2904i	−0.0328854	−	0.0893301i
$911$		−	1438.81i		−	1.57938i	−0.613509	−	0.789688i	$-0.710243\pi$
$911$		−	1438.81i		−	1.57938i	0.613509	−	0.789688i	$-0.289757\pi$
$912$	38.1989	−	236.931i	0.0418847	−	0.259793i
$913$	72.5904			0.0795076
$914$	−1157.91	+	426.266i	−1.26686	+	0.466375i
$915$		−	217.915i		−	0.238159i
$916$	−1296.84	+	1104.51i	−1.41577	+	1.20579i
$917$	−433.919			−0.473194
$918$	90.0474	+	244.605i	0.0980909	+	0.266455i
$919$			10.7612i			0.0117097i	0.999983	+	0.00585485i	$0.00186367\pi$
$919$			10.7612i			0.0117097i	−0.999983	+	0.00585485i	$0.998136\pi$
$920$	42.8648	+	24.1225i	0.0465922	+	0.0262201i
$921$	681.902			0.740393
$922$	177.391	−	65.3037i	0.192398	−	0.0708283i
$923$		−	938.882i		−	1.01721i
$924$	124.333	+	145.984i	0.134560	+	0.157992i
$925$	939.741			1.01594
$926$	−397.636	−	1080.14i	−0.429412	−	1.16646i
$927$		−	262.328i		−	0.282986i
$928$	−122.678	−	628.099i	−0.132197	−	0.676831i
$929$	680.534			0.732545			0.366273	−	0.930508i	$-0.380634\pi$
$929$	680.534			0.732545			0.366273	+	0.930508i	$0.380634\pi$
$930$	−238.176	+	87.6807i	−0.256104	+	0.0942803i
$931$			375.953i			0.403816i
$932$	−361.782	+	308.126i	−0.388178	+	0.330607i
$933$	−549.454			−0.588911
$934$	516.724	+	1403.63i	0.553237	+	1.50282i
$935$		−	376.514i		−	0.402688i
$936$	168.236	−	298.949i	0.179739	−	0.319390i
$937$	−1525.66			−1.62824			−0.814118	−	0.580700i	$-0.802779\pi$
$937$	−1525.66			−1.62824			−0.814118	+	0.580700i	$0.802779\pi$
$938$	−173.089	+	63.7197i	−0.184529	+	0.0679314i
$939$			161.003i			0.171462i
$940$	69.5937	+	81.7125i	0.0740358	+	0.0869282i
$941$	−819.066			−0.870420			−0.435210	−	0.900329i	$-0.643326\pi$
$941$	−819.066			−0.870420			−0.435210	+	0.900329i	$0.643326\pi$
$942$	−227.533	−	618.073i	−0.241543	−	0.656128i
$943$		−	280.148i		−	0.297082i
$944$	57.7353	+	9.30831i	0.0611603	+	0.00986049i
$945$	−15.7456			−0.0166620
$946$	1198.21	−	441.101i	1.26661	−	0.466280i
$947$		−	1197.03i		−	1.26403i	−0.774957	−	0.632014i	$-0.782229\pi$
$947$		−	1197.03i		−	1.26403i	0.774957	−	0.632014i	$-0.217771\pi$
$948$	502.558	−	428.023i	0.530124	−	0.451501i
$949$	394.072			0.415249
$950$	139.752	+	379.623i	0.147107	+	0.399603i
$951$		−	463.295i		−	0.487166i
$952$	−413.321	−	232.599i	−0.434161	−	0.244327i
$953$	620.935			0.651558			0.325779	−	0.945446i	$-0.394374\pi$
$953$	620.935			0.651558			0.325779	+	0.945446i	$0.394374\pi$
$954$	111.214	−	40.9417i	0.116577	−	0.0429158i
$955$			409.167i			0.428448i
$956$	817.377	+	959.712i	0.854997	+	1.00388i
$957$	405.609			0.423834
$958$	−524.693	−	1425.28i	−0.547696	−	1.48776i
$959$		−	271.111i		−	0.282702i
$960$	121.478	−	73.7494i	0.126539	−	0.0768223i
$961$	−2305.12			−2.39867
$962$	1079.35	−	397.345i	1.12199	−	0.413041i
$963$		−	28.8234i		−	0.0299308i
$964$	676.764	−	576.393i	0.702038	−	0.597918i
$965$	240.052			0.248759
$966$	13.5659	+	36.8506i	0.0140434	+	0.0381476i
$967$		−	749.500i		−	0.775077i	−0.921853	−	0.387539i	$-0.873325\pi$
$967$		−	749.500i		−	0.775077i	0.921853	−	0.387539i	$-0.126675\pi$
$968$	63.2183	−	112.337i	0.0653081	−	0.116050i
$969$	−376.206			−0.388242
$970$	447.288	−	164.662i	0.461122	−	0.169754i
$971$		−	1148.05i		−	1.18233i	−0.806549	−	0.591167i	$-0.798668\pi$
$971$		−	1148.05i		−	1.18233i	0.806549	−	0.591167i	$-0.201332\pi$
$972$	−40.4299	−	47.4702i	−0.0415945	−	0.0488377i
$973$	−268.067			−0.275505
$974$	122.820	+	333.629i	0.126099	+	0.342535i
$975$			578.225i			0.593052i
$976$	−249.927	+	1550.19i	−0.256073	+	1.58831i
$977$	−1776.23			−1.81805			−0.909025	−	0.416742i	$-0.863172\pi$
$977$	−1776.23			−1.81805			−0.909025	+	0.416742i	$0.863172\pi$
$978$	−825.093	+	303.744i	−0.843654	+	0.310577i
$979$		−	552.542i		−	0.564395i
$980$	−169.484	+	144.347i	−0.172943	+	0.147293i
$981$	12.5053			0.0127475
$982$	23.8177	+	64.6987i	0.0242543	+	0.0658846i
$983$		−	1787.05i		−	1.81796i	−0.416840	−	0.908980i	$-0.636862\pi$
$983$		−	1787.05i		−	1.81796i	0.416840	−	0.908980i	$-0.363138\pi$
$984$	−705.393	−	396.966i	−0.716863	−	0.403420i
$985$	−383.254			−0.389091
$986$	−941.439	+	346.575i	−0.954806	+	0.351496i
$987$			85.6898i			0.0868185i
$988$	321.028	+	376.930i	0.324927	+	0.381508i
$989$	261.472			0.264380
$990$	31.1163	+	84.5244i	0.0314306	+	0.0853782i
$991$			113.963i			0.114998i	0.998346	+	0.0574990i	$0.0183126\pi$
$991$			113.963i			0.114998i	−0.998346	+	0.0574990i	$0.981687\pi$
$992$	1794.88	−	350.572i	1.80936	−	0.353399i
$993$	−1080.31			−1.08793
$994$	291.408	−	107.277i	0.293167	−	0.107925i
$995$		−	83.6251i		−	0.0840453i
$996$	32.6978	−	27.8484i	0.0328291	−	0.0279602i
$997$	−282.778			−0.283629			−0.141815	−	0.989893i	$-0.545294\pi$
$997$	−282.778			−0.283629			−0.141815	+	0.989893i	$0.545294\pi$
$998$	322.196	+	875.217i	0.322842	+	0.876971i
$999$		−	209.066i		−	0.209275i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.3.f.b.139.6	yes	40
4.3	odd	2	inner	276.3.f.b.139.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.3.f.b.139.5	✓	40	4.3	odd	2	inner
276.3.f.b.139.6	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	276.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87686 + 0.690935i) q^{2} -1.73205i q^{3} +(3.04522 - 2.59358i) q^{4} -1.28200 q^{5} +(1.19673 + 3.25082i) q^{6} -2.36368i q^{7} +(-3.92345 + 6.97184i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-1.87686 + 0.690935i) q^{2} -1.73205i q^{3} +(3.04522 - 2.59358i) q^{4} -1.28200 q^{5} +(1.19673 + 3.25082i) q^{6} -2.36368i q^{7} +(-3.92345 + 6.97184i) q^{8} -3.00000 q^{9} +(2.40614 - 0.885782i) q^{10} -11.7095i q^{11} +(-4.49221 - 5.27447i) q^{12} +14.2932 q^{13} +(1.63315 + 4.43629i) q^{14} +2.22050i q^{15} +(2.54669 - 15.7960i) q^{16} -25.0814 q^{17} +(5.63058 - 2.07281i) q^{18} +8.65991i q^{19} +(-3.90398 + 3.32498i) q^{20} -4.09401 q^{21} +(8.09052 + 21.9771i) q^{22} +4.79583i q^{23} +(12.0756 + 6.79562i) q^{24} -23.3565 q^{25} +(-26.8263 + 9.87567i) q^{26} +5.19615i q^{27} +(-6.13038 - 7.19791i) q^{28} -19.9990 q^{29} +(-1.53422 - 4.16756i) q^{30} -57.1500i q^{31} +(6.13424 + 31.4065i) q^{32} -20.2815 q^{33} +(47.0743 - 17.3296i) q^{34} +3.03024i q^{35} +(-9.13565 + 7.78074i) q^{36} -40.2347 q^{37} +(-5.98344 - 16.2535i) q^{38} -24.7565i q^{39} +(5.02989 - 8.93792i) q^{40} -58.4149 q^{41} +(7.68388 - 2.82869i) q^{42} -54.5207i q^{43} +(-30.3696 - 35.6580i) q^{44} +3.84601 q^{45} +(-3.31361 - 9.00111i) q^{46} -20.9305i q^{47} +(-27.3595 - 4.41100i) q^{48} +43.4130 q^{49} +(43.8368 - 16.1378i) q^{50} +43.4423i q^{51} +(43.5259 - 37.0705i) q^{52} +19.7518 q^{53} +(-3.59020 - 9.75246i) q^{54} +15.0117i q^{55} +(16.4792 + 9.27378i) q^{56} +14.9994 q^{57} +(37.5353 - 13.8180i) q^{58} +3.65506i q^{59} +(5.75903 + 6.76189i) q^{60} -98.1380 q^{61} +(39.4870 + 107.263i) q^{62} +7.09103i q^{63} +(-33.2130 - 54.7074i) q^{64} -18.3239 q^{65} +(38.0655 - 14.0132i) q^{66} +39.0165i q^{67} +(-76.3784 + 65.0506i) q^{68} +8.30662 q^{69} +(-2.09370 - 5.68735i) q^{70} -65.6873i q^{71} +(11.7704 - 20.9155i) q^{72} +27.5706 q^{73} +(75.5150 - 27.7996i) q^{74} +40.4546i q^{75} +(22.4602 + 26.3713i) q^{76} -27.6775 q^{77} +(17.1052 + 46.4646i) q^{78} +95.2812i q^{79} +(-3.26487 + 20.2506i) q^{80} +9.00000 q^{81} +(109.637 - 40.3609i) q^{82} +6.19926i q^{83} +(-12.4671 + 10.6181i) q^{84} +32.1545 q^{85} +(37.6703 + 102.328i) q^{86} +34.6392i q^{87} +(81.6369 + 45.9418i) q^{88} +47.1874 q^{89} +(-7.21843 + 2.65735i) q^{90} -33.7845i q^{91} +(12.4384 + 14.6043i) q^{92} -98.9867 q^{93} +(14.4617 + 39.2837i) q^{94} -11.1020i q^{95} +(54.3977 - 10.6248i) q^{96} +185.894 q^{97} +(-81.4802 + 29.9956i) q^{98} +35.1286i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more