LMFDB - Embedded newform 261.3.s.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,3,Mod(10,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("261.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, 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:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	261.37
Dual form			261.3.s.a.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0310749 + 0.0108736i) q^{2} +(-3.12648 - 2.49328i) q^{4} +(-3.79007 - 7.87017i) q^{5} +(3.62612 + 4.54701i) q^{7} +(-0.140107 - 0.222980i) q^{8} +O(q^{10})$	\(q+(0.0310749 + 0.0108736i) q^{2} +(-3.12648 - 2.49328i) q^{4} +(-3.79007 - 7.87017i) q^{5} +(3.62612 + 4.54701i) q^{7} +(-0.140107 - 0.222980i) q^{8} +(-0.0321993 - 0.285777i) q^{10} +(-3.95365 + 6.29219i) q^{11} +(-10.7515 + 2.45395i) q^{13} +(0.0632391 + 0.180727i) q^{14} +(3.55744 + 15.5862i) q^{16} +(4.26171 + 4.26171i) q^{17} +(-13.0613 + 1.47165i) q^{19} +(-7.77298 + 34.0556i) q^{20} +(-0.191278 + 0.152539i) q^{22} +(6.32686 + 3.04685i) q^{23} +(-31.9876 + 40.1112i) q^{25} +(-0.360785 - 0.0406507i) q^{26} -23.2571i q^{28} +(-29.0000 - 0.0339620i) q^{29} +(2.37249 + 0.830170i) q^{31} +(-0.176871 + 1.56977i) q^{32} +(0.0860924 + 0.178773i) q^{34} +(22.0425 - 45.7716i) q^{35} +(-17.7197 - 28.2007i) q^{37} +(-0.421880 - 0.0962915i) q^{38} +(-1.22387 + 1.94778i) q^{40} +(2.70371 - 2.70371i) q^{41} +(-11.9973 - 34.2863i) q^{43} +(28.0492 - 9.81484i) q^{44} +(0.163476 + 0.163476i) q^{46} +(-7.75262 - 4.87130i) q^{47} +(3.37698 - 14.7955i) q^{49} +(-1.43017 + 0.898634i) q^{50} +(39.7327 + 19.1342i) q^{52} +(-39.1941 + 18.8749i) q^{53} +(64.5052 + 7.26799i) q^{55} +(0.505844 - 1.44562i) q^{56} +(-0.900803 - 0.316389i) q^{58} -70.7916 q^{59} +(-11.5282 + 102.316i) q^{61} +(0.0646980 + 0.0515949i) q^{62} +(27.7234 - 57.5683i) q^{64} +(60.0619 + 75.3153i) q^{65} +(26.2176 + 5.98401i) q^{67} +(-2.69850 - 23.9498i) q^{68} +(1.18267 - 1.18267i) q^{70} +(93.3221 - 21.3002i) q^{71} +(-83.5084 + 29.2208i) q^{73} +(-0.243995 - 1.06901i) q^{74} +(44.5050 + 27.9644i) q^{76} +(-42.9470 + 4.83897i) q^{77} +(51.8104 - 32.5546i) q^{79} +(109.183 - 87.0704i) q^{80} +(0.113416 - 0.0546185i) q^{82} +(-18.9679 + 23.7849i) q^{83} +(17.3882 - 49.6926i) q^{85} -1.19590i q^{86} +1.95696 q^{88} +(-97.6073 - 34.1543i) q^{89} +(-50.1443 - 39.9887i) q^{91} +(-12.1841 - 25.3006i) q^{92} +(-0.187944 - 0.235674i) q^{94} +(61.0853 + 97.2168i) q^{95} +(-12.7840 - 113.461i) q^{97} +(0.265820 - 0.423050i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	$ 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) $ 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{3}{28}\right)$	$1$

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 $

$2$	0.0310749	+	0.0108736i	0.0155375	+	0.00543680i	0.338037	−	0.941133i	$-0.390237\pi$
$2$	0.0310749	+	0.0108736i	0.0155375	+	0.00543680i	−0.322499	+	0.946570i	$0.604523\pi$
$3$		0			0
$3$		0			0
$4$	−3.12648	−	2.49328i	−0.781620	−	0.623321i
$5$	−3.79007	−	7.87017i	−0.758015	−	1.57403i	−0.817584	−	0.575809i	$-0.804687\pi$
$5$	−3.79007	−	7.87017i	−0.758015	−	1.57403i	0.0595693	−	0.998224i	$-0.481027\pi$
$6$		0			0
$7$	3.62612	+	4.54701i	0.518017	+	0.649572i	0.970187	−	0.242360i	$-0.0779214\pi$
$7$	3.62612	+	4.54701i	0.518017	+	0.649572i	−0.452170	+	0.891932i	$0.649350\pi$
$8$	−0.140107	−	0.222980i	−0.0175134	−	0.0278724i
$9$		0			0
$10$	−0.0321993	−	0.285777i	−0.00321993	−	0.0285777i
$11$	−3.95365	+	6.29219i	−0.359422	+	0.572017i	−0.976668	−	0.214753i	$-0.931105\pi$
$11$	−3.95365	+	6.29219i	−0.359422	+	0.572017i	0.617246	+	0.786770i	$0.288248\pi$
$12$		0			0
$13$	−10.7515	+	2.45395i	−0.827037	+	0.188766i	−0.615031	−	0.788503i	$-0.710857\pi$
$13$	−10.7515	+	2.45395i	−0.827037	+	0.188766i	−0.212006	+	0.977268i	$0.567999\pi$
$14$	0.0632391	+	0.180727i	0.00451708	+	0.0129091i
$15$		0			0
$16$	3.55744	+	15.5862i	0.222340	+	0.974135i
$17$	4.26171	+	4.26171i	0.250689	+	0.250689i	0.821253	−	0.570564i	$-0.193275\pi$
$17$	4.26171	+	4.26171i	0.250689	+	0.250689i	−0.570564	+	0.821253i	$0.693275\pi$
$18$		0			0
$19$	−13.0613	+	1.47165i	−0.687436	+	0.0774554i	−0.448771	−	0.893647i	$-0.648138\pi$
$19$	−13.0613	+	1.47165i	−0.687436	+	0.0774554i	−0.238664	+	0.971102i	$0.576710\pi$
$20$	−7.77298	+	34.0556i	−0.388649	+	1.70278i
$21$		0			0
$22$	−0.191278	+	0.152539i	−0.00869445	+	0.00693360i
$23$	6.32686	+	3.04685i	0.275081	+	0.132472i	0.566339	−	0.824173i	$-0.308359\pi$
$23$	6.32686	+	3.04685i	0.275081	+	0.132472i	−0.291258	+	0.956645i	$0.594074\pi$
$24$		0			0
$25$	−31.9876	+	40.1112i	−1.27951	+	1.60445i
$26$	−0.360785	−	0.0406507i	−0.0138763	−	0.00156349i
$27$		0			0
$28$		−	23.2571i		−	0.830609i
$29$	−29.0000	−	0.0339620i	−0.999999	−	0.00117110i
$29$	−29.0000	−	0.0339620i	−0.999999	−	0.00117110i
$30$		0			0
$31$	2.37249	+	0.830170i	0.0765319	+	0.0267797i	0.368273	−	0.929718i	$-0.379949\pi$
$31$	2.37249	+	0.830170i	0.0765319	+	0.0267797i	−0.291742	+	0.956497i	$0.594235\pi$
$32$	−0.176871	+	1.56977i	−0.00552722	+	0.0490554i
$33$		0			0
$34$	0.0860924	+	0.178773i	0.00253213	+	0.00525802i
$35$	22.0425	−	45.7716i	0.629784	−	1.30776i
$36$		0			0
$37$	−17.7197	−	28.2007i	−0.478910	−	0.762182i	0.516661	−	0.856190i	$-0.327175\pi$
$37$	−17.7197	−	28.2007i	−0.478910	−	0.762182i	−0.995571	+	0.0940085i	$0.970032\pi$
$38$	−0.421880	−	0.0962915i	−0.0111021	−	0.00253399i
$39$		0			0
$40$	−1.22387	+	1.94778i	−0.0305967	+	0.0486944i
$41$	2.70371	−	2.70371i	0.0659440	−	0.0659440i	−0.673366	−	0.739310i	$-0.735152\pi$
$41$	2.70371	−	2.70371i	0.0659440	−	0.0659440i	0.739310	+	0.673366i	$0.235152\pi$
$42$		0			0
$43$	−11.9973	−	34.2863i	−0.279007	−	0.797356i	−0.995057	−	0.0993068i	$-0.968337\pi$
$43$	−11.9973	−	34.2863i	−0.279007	−	0.797356i	0.716050	−	0.698049i	$-0.245948\pi$
$44$	28.0492	−	9.81484i	0.637482	−	0.223065i
$45$		0			0
$46$	0.163476	+	0.163476i	0.00355384	+	0.00355384i
$47$	−7.75262	−	4.87130i	−0.164949	−	0.103645i	0.447027	−	0.894520i	$-0.352483\pi$
$47$	−7.75262	−	4.87130i	−0.164949	−	0.103645i	−0.611977	+	0.790876i	$0.709625\pi$
$48$		0			0
$49$	3.37698	−	14.7955i	0.0689180	−	0.301949i
$50$	−1.43017	+	0.898634i	−0.0286033	+	0.0179727i
$51$		0			0
$52$	39.7327	+	19.1342i	0.764090	+	0.367966i
$53$	−39.1941	+	18.8749i	−0.739511	+	0.356130i	−0.765417	−	0.643535i	$-0.777467\pi$
$53$	−39.1941	+	18.8749i	−0.739511	+	0.356130i	0.0259061	+	0.999664i	$0.491753\pi$
$54$		0			0
$55$	64.5052	+	7.26799i	1.17282	+	0.132145i
$56$	0.505844	−	1.44562i	0.00903293	−	0.0258146i
$57$		0			0
$58$	−0.900803	−	0.316389i	−0.0155311	−	0.00545499i
$59$	−70.7916			−1.19986			−0.599929	−	0.800054i	$-0.704804\pi$
$59$	−70.7916			−1.19986			−0.599929	+	0.800054i	$0.704804\pi$
$60$		0			0
$61$	−11.5282	+	102.316i	−0.188988	+	1.67731i	0.438537	+	0.898713i	$0.355497\pi$
$61$	−11.5282	+	102.316i	−0.188988	+	1.67731i	−0.627524	+	0.778597i	$0.715932\pi$
$62$	0.0646980	+	0.0515949i	0.00104352	+	0.000832176i
$63$		0			0
$64$	27.7234	−	57.5683i	0.433178	−	0.899504i
$65$	60.0619	+	75.3153i	0.924030	+	1.15870i
$66$		0			0
$67$	26.2176	+	5.98401i	0.391308	+	0.0893135i	0.413648	−	0.910437i	$-0.364254\pi$
$67$	26.2176	+	5.98401i	0.391308	+	0.0893135i	−0.0223398	+	0.999750i	$0.507112\pi$
$68$	−2.69850	−	23.9498i	−0.0396838	−	0.352203i
$69$		0			0
$70$	1.18267	−	1.18267i	0.0168953	−	0.0168953i
$71$	93.3221	−	21.3002i	1.31440	−	0.300002i	0.492835	−	0.870123i	$-0.335961\pi$
$71$	93.3221	−	21.3002i	1.31440	−	0.300002i	0.821561	+	0.570121i	$0.193104\pi$
$72$		0			0
$73$	−83.5084	+	29.2208i	−1.14395	+	0.400286i	−0.834705	−	0.550697i	$-0.814362\pi$
$73$	−83.5084	+	29.2208i	−1.14395	+	0.400286i	−0.309245	+	0.950982i	$0.600076\pi$
$74$	−0.243995	−	1.06901i	−0.00329723	−	0.0144461i
$75$		0			0
$76$	44.5050	+	27.9644i	0.585593	+	0.367952i
$77$	−42.9470	+	4.83897i	−0.557753	+	0.0628437i
$78$		0			0
$79$	51.8104	−	32.5546i	0.655828	−	0.412084i	−0.162601	−	0.986692i	$-0.551988\pi$
$79$	51.8104	−	32.5546i	0.655828	−	0.412084i	0.818429	+	0.574608i	$0.194846\pi$
$80$	109.183	−	87.0704i	1.36478	−	1.08838i
$81$		0			0
$82$	0.113416	−	0.0546185i	0.00138313	−	0.000666079i
$83$	−18.9679	+	23.7849i	−0.228528	+	0.286566i	−0.882854	−	0.469647i	$-0.844381\pi$
$83$	−18.9679	+	23.7849i	−0.228528	+	0.286566i	0.654326	+	0.756213i	$0.272953\pi$
$84$		0			0
$85$	17.3882	−	49.6926i	0.204567	−	0.584619i
$86$		−	1.19590i		−	0.0139058i
$87$		0			0
$88$	1.95696			0.0222382
$89$	−97.6073	−	34.1543i	−1.09671	−	0.383756i	−0.279530	−	0.960137i	$-0.590179\pi$
$89$	−97.6073	−	34.1543i	−1.09671	−	0.383756i	−0.817181	+	0.576381i	$0.804464\pi$
$90$		0			0
$91$	−50.1443	−	39.9887i	−0.551036	−	0.439436i
$92$	−12.1841	−	25.3006i	−0.132436	−	0.275006i
$93$		0			0
$94$	−0.187944	−	0.235674i	−0.00199940	−	0.00250717i
$95$	61.0853	+	97.2168i	0.643004	+	1.02333i
$96$		0			0
$97$	−12.7840	−	113.461i	−0.131794	−	1.16970i	−0.869273	−	0.494333i	$-0.835413\pi$
$97$	−12.7840	−	113.461i	−0.131794	−	1.16970i	0.737479	−	0.675370i	$-0.236016\pi$
$98$	0.265820	−	0.423050i	0.00271245	−	0.00431684i
$99$		0			0
$100$	200.017	−	45.6527i	2.00017	−	0.456527i
$101$	−42.0839	−	120.269i	−0.416672	−	1.19078i	−0.940747	−	0.339109i	$-0.889875\pi$
$101$	−42.0839	−	120.269i	−0.416672	−	1.19078i	0.524075	−	0.851672i	$-0.324411\pi$
$102$		0			0
$103$	−36.2231	−	158.704i	−0.351681	−	1.54081i	−0.773299	−	0.634041i	$-0.781395\pi$
$103$	−36.2231	−	158.704i	−0.351681	−	1.54081i	0.421618	−	0.906773i	$-0.361462\pi$
$104$	2.05354	+	2.05354i	0.0197456	+	0.0197456i
$105$		0			0
$106$	−1.42319	+	0.160355i	−0.0134263	+	0.00151278i
$107$	15.1003	−	66.1586i	0.141124	−	0.618304i	−0.854051	−	0.520189i	$-0.825861\pi$
$107$	15.1003	−	66.1586i	0.141124	−	0.618304i	0.995175	−	0.0981152i	$-0.0312814\pi$
$108$		0			0
$109$	−8.50965	+	6.78622i	−0.0780702	+	0.0622589i	−0.661747	−	0.749727i	$-0.730185\pi$
$109$	−8.50965	+	6.78622i	−0.0780702	+	0.0622589i	0.583677	+	0.811986i	$0.301613\pi$
$110$	1.92547	+	0.927256i	0.0175042	+	0.00842960i
$111$		0			0
$112$	−57.9707	+	72.6930i	−0.517596	+	0.649044i
$113$	56.1593	+	6.32764i	0.496985	+	0.0559968i	0.356900	−	0.934143i	$-0.383834\pi$
$113$	56.1593	+	6.32764i	0.496985	+	0.0559968i	0.140085	+	0.990139i	$0.455262\pi$
$114$		0			0
$115$		−	61.3412i		−	0.533402i
$116$	90.5831	+	72.4114i	0.780889	+	0.624236i
$117$		0			0
$118$	−2.19984	−	0.769759i	−0.0186427	−	0.00652338i
$119$	−3.92457	+	34.8315i	−0.0329796	+	0.292702i
$120$		0			0
$121$	28.5396	+	59.2630i	0.235864	+	0.489777i
$122$	−1.47078	+	3.05411i	−0.0120556	+	0.0250337i
$123$		0			0
$124$	−5.34769	−	8.51079i	−0.0431265	−	0.0686354i
$125$	224.012	+	51.1293i	1.79210	+	0.409035i
$126$		0			0
$127$	−121.534	+	193.421i	−0.956962	+	1.52300i	−0.108262	+	0.994122i	$0.534529\pi$
$127$	−121.534	+	193.421i	−0.956962	+	1.52300i	−0.848700	+	0.528875i	$0.822614\pi$
$128$	5.95556	−	5.95556i	0.0465278	−	0.0465278i
$129$		0			0
$130$	1.04747	+	2.99351i	0.00805749	+	0.0230270i
$131$	−196.490	+	68.7549i	−1.49993	+	0.524847i	−0.950508	−	0.310701i	$-0.899436\pi$
$131$	−196.490	+	68.7549i	−1.49993	+	0.524847i	−0.549418	+	0.835547i	$0.685151\pi$
$132$		0			0
$133$	−54.0533	−	54.0533i	−0.406416	−	0.406416i
$134$	0.749644	+	0.471033i	0.00559436	+	0.00351517i
$135$		0			0
$136$	0.353178	−	1.54737i	0.00259689	−	0.0113777i
$137$	−58.6681	+	36.8636i	−0.428235	+	0.269078i	−0.728857	−	0.684665i	$-0.759948\pi$
$137$	−58.6681	+	36.8636i	−0.428235	+	0.269078i	0.300623	+	0.953743i	$0.402805\pi$
$138$		0			0
$139$	97.5136	+	46.9601i	0.701537	+	0.337842i	0.750419	−	0.660962i	$-0.229852\pi$
$139$	97.5136	+	46.9601i	0.701537	+	0.337842i	−0.0488824	+	0.998805i	$0.515566\pi$
$140$	−183.037	+	88.1459i	−1.30741	+	0.629614i
$141$		0			0
$142$	3.13159	+	0.352845i	0.0220534	+	0.00248482i
$143$	27.0668	−	77.3524i	0.189278	−	0.540926i
$144$		0			0
$145$	109.645	+	228.363i	0.756171	+	1.57492i
$146$	−2.91275			−0.0199504
$147$		0			0
$148$	−14.9122	+	132.349i	−0.100758	+	0.894251i
$149$	−42.7218	−	34.0695i	−0.286724	−	0.228654i	0.469556	−	0.882902i	$-0.344414\pi$
$149$	−42.7218	−	34.0695i	−0.286724	−	0.228654i	−0.756280	+	0.654248i	$0.772985\pi$
$150$		0			0
$151$	83.0312	−	172.416i	0.549875	−	1.14183i	−0.422058	−	0.906569i	$-0.638692\pi$
$151$	83.0312	−	172.416i	0.549875	−	1.14183i	0.971933	−	0.235259i	$-0.0755937\pi$
$152$	2.15813	+	2.70621i	0.0141982	+	0.0178040i
$153$		0			0
$154$	−1.38719	−	0.316618i	−0.00900774	−	0.00205596i
$155$	−2.45833	−	21.8183i	−0.0158602	−	0.140763i
$156$		0			0
$157$	−45.4322	+	45.4322i	−0.289377	+	0.289377i	−0.836834	−	0.547457i	$-0.815596\pi$
$157$	−45.4322	+	45.4322i	−0.289377	+	0.289377i	0.547457	+	0.836834i	$0.315596\pi$
$158$	1.96399	−	0.448268i	0.0124303	−	0.00283714i
$159$		0			0
$160$	13.0247	−	4.55755i	0.0814046	−	0.0284847i
$161$	9.08786	+	39.8165i	0.0564463	+	0.247307i
$162$		0			0
$163$	−249.812	−	156.967i	−1.53259	−	0.962990i	−0.992615	−	0.121309i	$-0.961291\pi$
$163$	−249.812	−	156.967i	−1.53259	−	0.962990i	−0.539975	−	0.841681i	$-0.681566\pi$
$164$	−15.1942	+	1.71197i	−0.0926474	+	0.0104389i
$165$		0			0
$166$	−0.848053	+	0.532867i	−0.00510875	+	0.00321004i
$167$	−44.5238	+	35.5065i	−0.266610	+	0.212614i	−0.747665	−	0.664076i	$-0.768825\pi$
$167$	−44.5238	+	35.5065i	−0.266610	+	0.212614i	0.481055	+	0.876690i	$0.340254\pi$
$168$		0			0
$169$	−42.6913	+	20.5591i	−0.252611	+	0.121651i
$170$	1.08067	−	1.35512i	0.00635691	−	0.00797131i
$171$		0			0
$172$	−47.9762	+	137.108i	−0.278931	+	0.797140i
$173$		−	335.481i		−	1.93920i	−0.244702	−	0.969598i	$-0.578690\pi$
$173$		−	335.481i		−	1.93920i	0.244702	−	0.969598i	$-0.421310\pi$
$174$		0			0
$175$	−298.377			−1.70501
$176$	−112.136	−	39.2381i	−0.637136	−	0.222944i
$177$		0			0
$178$	−2.66176	−	2.12268i	−0.0149537	−	0.0119252i
$179$	−69.3056	−	143.915i	−0.387182	−	0.803992i	−0.999906	−	0.0136949i	$-0.995641\pi$
$179$	−69.3056	−	143.915i	−0.387182	−	0.803992i	0.612724	−	0.790297i	$-0.290074\pi$
$180$		0			0
$181$	152.161	+	190.804i	0.840671	+	1.05417i	0.997781	+	0.0665866i	$0.0212109\pi$
$181$	152.161	+	190.804i	0.840671	+	1.05417i	−0.157110	+	0.987581i	$0.550218\pi$
$182$	−1.12341	−	1.78790i	−0.00617258	−	0.00982360i
$183$		0			0
$184$	−0.207053	−	1.83765i	−0.00112529	−	0.00998721i
$185$	−154.785	+	246.340i	−0.836678	+	1.33157i
$186$		0			0
$187$	−43.6648	+	9.96621i	−0.233502	+	0.0532952i
$188$	12.0929	+	34.5595i	0.0643239	+	0.183827i
$189$		0			0
$190$	0.841128	+	3.68522i	0.00442699	+	0.0193959i
$191$	166.578	+	166.578i	0.872137	+	0.872137i	0.992705	−	0.120568i	$-0.0384716\pi$
$191$	166.578	+	166.578i	0.872137	+	0.872137i	−0.120568	+	0.992705i	$0.538472\pi$
$192$		0			0
$193$	188.693	−	21.2606i	0.977683	−	0.110158i	0.391362	−	0.920237i	$-0.372004\pi$
$193$	188.693	−	21.2606i	0.977683	−	0.110158i	0.586321	+	0.810078i	$0.300576\pi$
$194$	0.836468	−	3.66481i	0.00431169	−	0.0188908i
$195$		0			0
$196$	−47.4475	+	37.8381i	−0.242079	+	0.193052i
$197$	208.010	+	100.172i	1.05589	+	0.508488i	0.879532	−	0.475839i	$-0.157856\pi$
$197$	208.010	+	100.172i	1.05589	+	0.508488i	0.176353	+	0.984327i	$0.443570\pi$
$198$		0			0
$199$	−93.3547	+	117.063i	−0.469119	+	0.588257i	−0.958955	−	0.283558i	$-0.908485\pi$
$199$	−93.3547	+	117.063i	−0.469119	+	0.588257i	0.489836	+	0.871815i	$0.337057\pi$
$200$	13.4257	+	1.51271i	0.0671285	+	0.00756356i
$201$		0			0
$202$		−	4.19495i		−	0.0207671i
$203$	−105.003	−	131.986i	−0.517256	−	0.650179i
$204$		0			0
$205$	−31.5259	−	11.0314i	−0.153785	−	0.0538116i
$206$	0.600050	−	5.32559i	0.00291286	−	0.0258524i
$207$		0			0
$208$	−76.4955	−	158.845i	−0.367767	−	0.763676i
$209$	42.3797	−	88.0024i	0.202774	−	0.421064i
$210$		0			0
$211$	−66.0800	−	105.166i	−0.313175	−	0.498416i	0.652632	−	0.757675i	$-0.273665\pi$
$211$	−66.0800	−	105.166i	−0.313175	−	0.498416i	−0.965808	+	0.259259i	$0.916522\pi$
$212$	169.600	+	38.7101i	0.799999	+	0.182595i
$213$		0			0
$214$	1.18862	−	1.89168i	0.00555430	−	0.00883962i
$215$	−224.368	+	224.368i	−1.04357	+	1.04357i
$216$		0			0
$217$	4.82813	+	13.7980i	0.0222495	+	0.0635853i
$218$	−0.338227	+	0.118351i	−0.00155150	+	0.000542894i
$219$		0			0
$220$	−183.553	−	183.553i	−0.834332	−	0.834332i
$221$	−56.2778	−	35.3617i	−0.254651	−	0.160008i
$222$		0			0
$223$	−26.1358	+	114.508i	−0.117201	+	0.513491i	0.881913	+	0.471412i	$0.156255\pi$
$223$	−26.1358	+	114.508i	−0.117201	+	0.513491i	−0.999114	+	0.0420792i	$0.986602\pi$
$224$	−7.77912	+	4.88795i	−0.0347282	+	0.0218212i
$225$		0			0
$226$	1.67634	+	0.807285i	0.00741745	+	0.00357206i
$227$	−223.061	+	107.420i	−0.982646	+	0.473217i	−0.855014	−	0.518604i	$-0.826452\pi$
$227$	−223.061	+	107.420i	−0.982646	+	0.473217i	−0.127632	+	0.991822i	$0.540738\pi$
$228$		0			0
$229$	131.941	+	14.8662i	0.576162	+	0.0649179i	0.395237	−	0.918579i	$-0.370662\pi$
$229$	131.941	+	14.8662i	0.576162	+	0.0649179i	0.180925	+	0.983497i	$0.442091\pi$
$230$	0.666999	−	1.90617i	0.00290000	−	0.00828772i
$231$		0			0
$232$	4.05554	+	6.47116i	0.0174808	+	0.0278929i
$233$	300.048			1.28776			0.643879	−	0.765128i	$-0.277324\pi$
$233$	300.048			1.28776			0.643879	+	0.765128i	$0.277324\pi$
$234$		0			0
$235$	−8.95491	+	79.4770i	−0.0381060	+	0.338200i
$236$	221.328	+	176.503i	0.937832	+	0.747896i
$237$		0			0
$238$	−0.500699	+	1.03971i	−0.00210378	+	0.00436854i
$239$	137.342	+	172.222i	0.574654	+	0.720594i	0.981191	−	0.193041i	$-0.0618350\pi$
$239$	137.342	+	172.222i	0.574654	+	0.720594i	−0.406536	+	0.913635i	$0.633264\pi$
$240$		0			0
$241$	−32.7575	−	7.47668i	−0.135923	−	0.0310236i	0.154018	−	0.988068i	$-0.450779\pi$
$241$	−32.7575	−	7.47668i	−0.135923	−	0.0310236i	−0.289941	+	0.957044i	$0.593636\pi$
$242$	0.242464	+	2.15192i	0.00100192	+	0.00889224i
$243$		0			0
$244$	291.145	−	291.145i	1.19322	−	1.19322i
$245$	−129.242	+	29.4987i	−0.527519	+	0.120403i
$246$		0			0
$247$	136.817	−	47.8742i	0.553914	−	0.193823i
$248$	−0.147292	−	0.645329i	−0.000593920	−	0.00260213i
$249$		0			0
$250$	6.40521	+	4.02466i	0.0256208	+	0.0160986i
$251$	51.8762	−	5.84504i	0.206678	−	0.0232870i	−0.00801842	−	0.999968i	$-0.502552\pi$
$251$	51.8762	−	5.84504i	0.206678	−	0.0232870i	0.214696	+	0.976681i	$0.431124\pi$
$252$		0			0
$253$	−44.1855	+	27.7636i	−0.174646	+	0.109738i
$254$	−5.87984	+	4.68902i	−0.0231490	+	0.0184607i
$255$		0			0
$256$	−230.023	+	110.773i	−0.898528	+	0.432709i
$257$	21.9630	−	27.5408i	0.0854593	−	0.107163i	−0.737264	−	0.675605i	$-0.763882\pi$
$257$	21.9630	−	27.5408i	0.0854593	−	0.107163i	0.822723	+	0.568443i	$0.192454\pi$
$258$		0			0
$259$	63.9752	−	182.831i	0.247008	−	0.705910i
$260$		−	385.223i		−	1.48163i
$261$		0			0
$262$	−6.85354			−0.0261585
$263$	−72.7181	−	25.4452i	−0.276495	−	0.0967497i	0.188470	−	0.982079i	$-0.439647\pi$
$263$	−72.7181	−	25.4452i	−0.276495	−	0.0967497i	−0.464965	+	0.885329i	$0.653933\pi$
$264$		0			0
$265$	297.097	+	236.927i	1.12112	+	0.894063i
$266$	−1.09195	−	2.26746i	−0.00410507	−	0.00852428i
$267$		0			0
$268$	−67.0491	−	84.0769i	−0.250183	−	0.313720i
$269$	40.6748	+	64.7335i	0.151207	+	0.240645i	0.913735	−	0.406310i	$-0.133185\pi$
$269$	40.6748	+	64.7335i	0.151207	+	0.240645i	−0.762528	+	0.646955i	$0.776042\pi$
$270$		0			0
$271$	−38.5675	−	342.296i	−0.142316	−	1.26309i	−0.838372	−	0.545098i	$-0.816492\pi$
$271$	−38.5675	−	342.296i	−0.142316	−	1.26309i	0.696057	−	0.717987i	$-0.254936\pi$
$272$	−51.2630	+	81.5846i	−0.188467	+	0.299943i
$273$		0			0
$274$	−2.22395	+	0.507602i	−0.00811660	+	0.00185256i
$275$	−125.920	−	359.858i	−0.457890	−	1.30857i
$276$		0			0
$277$	57.6112	+	252.411i	0.207983	+	0.911232i	0.965907	+	0.258889i	$0.0833565\pi$
$277$	57.6112	+	252.411i	0.207983	+	0.911232i	−0.757924	+	0.652343i	$0.773786\pi$
$278$	2.51960	+	2.51960i	0.00906333	+	0.00906333i
$279$		0			0
$280$	−13.2944	+	1.49792i	−0.0474802	+	0.00534973i
$281$	90.9123	−	398.313i	0.323531	−	1.41748i	−0.507689	−	0.861540i	$-0.669500\pi$
$281$	90.9123	−	398.313i	0.323531	−	1.41748i	0.831220	−	0.555943i	$-0.187643\pi$
$282$		0			0
$283$	−122.197	+	97.4487i	−0.431791	+	0.344342i	−0.815142	−	0.579261i	$-0.803341\pi$
$283$	−122.197	+	97.4487i	−0.431791	+	0.344342i	0.383351	+	0.923603i	$0.374770\pi$
$284$	−344.877	−	166.084i	−1.21435	−	0.584802i
$285$		0			0
$286$	1.68220	−	2.10941i	0.00588181	−	0.00737555i
$287$	22.0977	+	2.48981i	0.0769955	+	0.00867531i
$288$		0			0
$289$		−	252.676i		−	0.874310i
$290$	0.924073	+	8.28861i	0.00318646	+	0.0285814i
$291$		0			0
$292$	333.943	+	116.852i	1.14364	+	0.400177i
$293$	−15.8049	+	140.273i	−0.0539417	+	0.478746i	0.937480	+	0.348040i	$0.113153\pi$
$293$	−15.8049	+	140.273i	−0.0539417	+	0.478746i	−0.991421	+	0.130706i	$0.958276\pi$
$294$		0			0
$295$	268.305	+	557.142i	0.909509	+	1.88862i
$296$	−3.80553	+	7.90226i	−0.0128565	+	0.0266968i
$297$		0			0
$298$	−0.957120	−	1.52325i	−0.00321181	−	0.00511157i
$299$	−75.4999	−	17.2324i	−0.252508	−	0.0576333i
$300$		0			0
$301$	112.396	−	178.878i	0.373410	−	0.594279i
$302$	4.45497	−	4.45497i	0.0147516	−	0.0147516i
$303$		0			0
$304$	−69.4021	−	198.340i	−0.228297	−	0.652434i
$305$	848.937	−	297.056i	2.78340	−	0.973953i
$306$		0			0
$307$	211.914	+	211.914i	0.690275	+	0.690275i	0.962292	−	0.272017i	$-0.0876908\pi$
$307$	211.914	+	211.914i	0.690275	+	0.690275i	−0.272017	+	0.962292i	$0.587691\pi$
$308$	146.338	+	91.9501i	0.475123	+	0.298539i
$309$		0			0
$310$	0.160851	−	0.704733i	0.000518873	−	0.00227333i
$311$	−0.482806	+	0.303367i	−0.00155243	+	0.000975456i	−0.532808	−	0.846236i	$-0.678863\pi$
$311$	−0.482806	+	0.303367i	−0.00155243	+	0.000975456i	0.531256	+	0.847212i	$0.321720\pi$
$312$		0			0
$313$	−11.9391	−	5.74959i	−0.0381442	−	0.0183693i	0.414714	−	0.909952i	$-0.363881\pi$
$313$	−11.9391	−	5.74959i	−0.0381442	−	0.0183693i	−0.452859	+	0.891582i	$0.649596\pi$
$314$	−1.90581	+	0.917792i	−0.00606947	+	0.00292290i
$315$		0			0
$316$	−243.152	−	27.3966i	−0.769468	−	0.0866982i
$317$	−168.368	+	481.169i	−0.531131	+	1.51788i	0.295614	+	0.955307i	$0.404476\pi$
$317$	−168.368	+	481.169i	−0.531131	+	1.51788i	−0.826745	+	0.562577i	$0.809810\pi$
$318$		0			0
$319$	114.869	−	182.339i	0.360092	−	0.571596i
$320$	−558.146			−1.74421
$321$		0			0
$322$	−0.150544	+	1.33611i	−0.000467527	+	0.00414942i
$323$	−61.9352	−	49.3917i	−0.191750	−	0.152915i
$324$		0			0
$325$	245.483	−	509.751i	0.755333	−	1.56847i
$326$	−6.05610	−	7.59411i	−0.0185770	−	0.0232948i
$327$		0			0
$328$	−0.981680	−	0.224062i	−0.00299293	−	0.000683116i
$329$	−5.96210	−	52.9151i	−0.0181219	−	0.160836i
$330$		0			0
$331$	−88.5260	+	88.5260i	−0.267450	+	0.267450i	−0.828072	−	0.560622i	$-0.810562\pi$
$331$	−88.5260	+	88.5260i	−0.267450	+	0.267450i	0.560622	+	0.828072i	$0.310562\pi$
$332$	118.605	−	27.0709i	0.357245	−	0.0815388i
$333$		0			0
$334$	−1.76966	+	0.619230i	−0.00529838	+	0.00185398i
$335$	−52.2717	−	229.017i	−0.156035	−	0.683633i
$336$		0			0
$337$	175.703	+	110.401i	0.521373	+	0.327601i	0.766876	−	0.641795i	$-0.221810\pi$
$337$	175.703	+	110.401i	0.521373	+	0.327601i	−0.245503	+	0.969396i	$0.578953\pi$
$338$	−1.55018	+	0.174664i	−0.00458634	+	0.000516756i
$339$		0			0
$340$	−178.262	+	112.009i	−0.524299	+	0.329439i
$341$	−14.6036	+	11.6460i	−0.0428257	+	0.0341524i
$342$		0			0
$343$	336.275	−	161.942i	0.980394	−	0.472133i
$344$	−5.96424	+	7.47891i	−0.0173379	+	0.0217410i
$345$		0			0
$346$	3.64788	−	10.4251i	0.0105430	−	0.0301302i
$347$			98.9513i			0.285162i	0.989783	+	0.142581i	$0.0455402\pi$
$347$			98.9513i			0.285162i	−0.989783	+	0.142581i	$0.954460\pi$
$348$		0			0
$349$	293.432			0.840780			0.420390	−	0.907343i	$-0.361893\pi$
$349$	293.432			0.840780			0.420390	+	0.907343i	$0.361893\pi$
$350$	−9.27205	−	3.24443i	−0.0264916	−	0.00926980i
$351$		0			0
$352$	−9.17803	−	7.31923i	−0.0260739	−	0.0207933i
$353$	139.632	+	289.949i	0.395558	+	0.821385i	0.999700	+	0.0245079i	$0.00780188\pi$
$353$	139.632	+	289.949i	0.395558	+	0.821385i	−0.604142	+	0.796877i	$0.706484\pi$
$354$		0			0
$355$	−521.333	−	653.731i	−1.46854	−	1.84150i
$356$	220.011	+	350.145i	0.618008	+	0.983554i
$357$		0			0
$358$	−0.588799	−	5.22573i	−0.00164469	−	0.0145970i
$359$	246.904	−	392.946i	0.687756	−	1.09456i	−0.302209	−	0.953242i	$-0.597724\pi$
$359$	246.904	−	392.946i	0.687756	−	1.09456i	0.989965	−	0.141315i	$-0.0451332\pi$
$360$		0			0
$361$	−183.518	+	41.8867i	−0.508360	+	0.116030i
$362$	2.65368	+	7.58377i	0.00733060	+	0.0209497i
$363$		0			0
$364$	57.0718	+	250.048i	0.156791	+	0.686944i
$365$	546.476	+	546.476i	1.49719	+	1.49719i
$366$		0			0
$367$	97.2298	−	10.9552i	0.264931	−	0.0298506i	0.0215005	−	0.999769i	$-0.493156\pi$
$367$	97.2298	−	10.9552i	0.264931	−	0.0298506i	0.243431	+	0.969918i	$0.421727\pi$
$368$	−24.9814	+	109.450i	−0.0678841	+	0.297420i
$369$		0			0
$370$	−7.48855	+	5.97192i	−0.0202393	+	0.0161403i
$371$	−227.946	−	109.773i	−0.614411	−	0.295885i
$372$		0			0
$373$	205.926	−	258.222i	0.552079	−	0.692285i	−0.424992	−	0.905197i	$-0.639723\pi$
$373$	205.926	−	258.222i	0.552079	−	0.692285i	0.977071	+	0.212912i	$0.0682946\pi$
$374$	−1.46525	−	0.165094i	−0.00391778	−	0.000441428i
$375$		0			0
$376$			2.41118i			0.00641272i
$377$	311.876	−	70.7995i	0.827257	−	0.187797i
$378$		0			0
$379$	−219.932	−	76.9574i	−0.580295	−	0.203054i	0.0241400	−	0.999709i	$-0.492315\pi$
$379$	−219.932	−	76.9574i	−0.580295	−	0.203054i	−0.604435	+	0.796655i	$0.706601\pi$
$380$	51.4069	−	456.249i	0.135281	−	1.20066i
$381$		0			0
$382$	3.36510	+	6.98771i	0.00880917	+	0.0182924i
$383$	101.754	−	211.295i	0.265677	−	0.551685i	−0.724865	−	0.688891i	$-0.758098\pi$
$383$	101.754	−	211.295i	0.265677	−	0.551685i	0.990543	+	0.137206i	$0.0438123\pi$
$384$		0			0
$385$	200.856	+	319.660i	0.521703	+	0.830286i
$386$	6.09480	+	1.39110i	0.0157896	+	0.00360388i
$387$		0			0
$388$	−242.922	+	386.608i	−0.626087	+	0.996412i
$389$	−297.193	+	297.193i	−0.763992	+	0.763992i	−0.977041	−	0.213049i	$-0.931661\pi$
$389$	−297.193	+	297.193i	−0.763992	+	0.763992i	0.213049	+	0.977041i	$0.431661\pi$
$390$		0			0
$391$	13.9784	+	39.9481i	0.0357505	+	0.102169i
$392$	−3.77224	+	1.31996i	−0.00962306	+	0.00336725i
$393$		0			0
$394$	5.37465	+	5.37465i	0.0136412	+	0.0136412i
$395$	−452.575	−	284.372i	−1.14576	−	0.719929i
$396$		0			0
$397$	61.8313	−	270.901i	0.155746	−	0.682370i	−0.835405	−	0.549635i	$-0.814767\pi$
$397$	61.8313	−	270.901i	0.155746	−	0.682370i	0.991152	−	0.132735i	$-0.0423759\pi$
$398$	−4.17389	+	2.62263i	−0.0104872	+	0.00658952i
$399$		0			0
$400$	−738.975	−	355.871i	−1.84744	−	0.889679i
$401$	−198.105	+	95.4022i	−0.494027	+	0.237911i	−0.664272	−	0.747491i	$-0.731258\pi$
$401$	−198.105	+	95.4022i	−0.494027	+	0.237911i	0.170245	+	0.985402i	$0.445544\pi$
$402$		0			0
$403$	−27.5450	−	3.10357i	−0.0683498	−	0.00770117i
$404$	−168.290	+	480.945i	−0.416559	+	1.19046i
$405$		0			0
$406$	−1.82779	−	5.24322i	−0.00450195	−	0.0129143i
$407$	247.502			0.608112
$408$		0			0
$409$	43.0110	−	381.733i	0.105161	−	0.933333i	−0.824737	−	0.565516i	$-0.808677\pi$
$409$	43.0110	−	381.733i	0.105161	−	0.933333i	0.929898	−	0.367816i	$-0.119895\pi$
$410$	−0.859713	−	0.685599i	−0.00209686	−	0.00167219i
$411$		0			0
$412$	−282.443	+	586.499i	−0.685541	+	1.42354i
$413$	−256.698	−	321.890i	−0.621546	−	0.779394i
$414$		0			0
$415$	259.081	+	59.1336i	0.624292	+	0.142491i
$416$	−1.95053	−	17.3114i	−0.00468877	−	0.0416140i
$417$		0			0
$418$	2.27385	−	2.27385i	0.00543983	−	0.00543983i
$419$	258.143	−	58.9194i	0.616092	−	0.140619i	0.0969251	−	0.995292i	$-0.469099\pi$
$419$	258.143	−	58.9194i	0.616092	−	0.140619i	0.519167	+	0.854673i	$0.326242\pi$
$420$		0			0
$421$	210.923	−	73.8051i	0.501005	−	0.175309i	−0.0679329	−	0.997690i	$-0.521640\pi$
$421$	210.923	−	73.8051i	0.501005	−	0.175309i	0.568937	+	0.822381i	$0.307355\pi$
$422$	−0.909903	−	3.98655i	−0.00215617	−	0.00944679i
$423$		0			0
$424$	9.70009	+	6.09497i	0.0228776	+	0.0143749i
$425$	−307.265	+	34.6204i	−0.722976	+	0.0814598i
$426$		0			0
$427$	−507.034	+	318.591i	−1.18743	+	0.746114i
$428$	−212.163	+	169.194i	−0.495707	+	0.395313i
$429$		0			0
$430$	−9.41192	+	4.53254i	−0.0218882	+	0.0105408i
$431$	131.485	−	164.877i	0.305069	−	0.382545i	−0.605539	−	0.795816i	$-0.707042\pi$
$431$	131.485	−	164.877i	0.305069	−	0.382545i	0.910608	+	0.413271i	$0.135614\pi$
$432$		0			0
$433$	−53.6896	+	153.436i	−0.123995	+	0.354356i	−0.989102	−	0.147230i	$-0.952964\pi$
$433$	−53.6896	+	153.436i	−0.123995	+	0.354356i	0.865108	+	0.501586i	$0.167250\pi$
$434$			0.481271i			0.00110892i
$435$		0			0
$436$	43.5252			0.0998284
$437$	−87.1207	−	30.4849i	−0.199361	−	0.0697594i
$438$		0			0
$439$	−404.677	−	322.719i	−0.921816	−	0.735124i	0.0427165	−	0.999087i	$-0.486399\pi$
$439$	−404.677	−	322.719i	−0.921816	−	0.735124i	−0.964533	+	0.263963i	$0.914970\pi$
$440$	−7.41704	−	15.4016i	−0.0168569	−	0.0350037i
$441$		0			0
$442$	−1.36432	−	1.71080i	−0.00308670	−	0.00387060i
$443$	205.271	+	326.686i	0.463365	+	0.737440i	0.993907	−	0.110218i	$-0.0351548\pi$
$443$	205.271	+	326.686i	0.463365	+	0.737440i	−0.530543	+	0.847658i	$0.678012\pi$
$444$		0			0
$445$	101.139	+	897.633i	0.227278	+	2.01715i
$446$	−2.05729	+	3.27415i	−0.00461275	+	0.00734115i
$447$		0			0
$448$	362.292	−	82.6907i	0.808687	−	0.184577i
$449$	−51.5162	−	147.225i	−0.114735	−	0.327895i	0.872168	−	0.489206i	$-0.162713\pi$
$449$	−51.5162	−	147.225i	−0.114735	−	0.327895i	−0.986904	+	0.161311i	$0.948428\pi$
$450$		0			0
$451$	6.32274	+	27.7017i	0.0140194	+	0.0614229i
$452$	−159.804	−	159.804i	−0.353549	−	0.353549i
$453$		0			0
$454$	−8.09964	+	0.912610i	−0.0178406	+	0.00201016i
$455$	−124.667	+	546.204i	−0.273994	+	1.20045i
$456$		0			0
$457$	−551.243	+	439.602i	−1.20622	+	0.961930i	−0.999863	−	0.0165465i	$-0.994733\pi$
$457$	−551.243	+	439.602i	−1.20622	+	0.961930i	−0.206359	+	0.978476i	$0.566161\pi$
$458$	3.93841	+	1.89664i	0.00859916	+	0.00414114i
$459$		0			0
$460$	−152.941	+	191.782i	−0.332481	+	0.416917i
$461$	−472.975	−	53.2915i	−1.02598	−	0.115600i	−0.417097	−	0.908862i	$-0.636952\pi$
$461$	−472.975	−	53.2915i	−1.02598	−	0.115600i	−0.608880	+	0.793262i	$0.708381\pi$
$462$		0			0
$463$			436.814i			0.943442i	0.881748	+	0.471721i	$0.156367\pi$
$463$			436.814i			0.943442i	−0.881748	+	0.471721i	$0.843633\pi$
$464$	−102.636	−	452.119i	−0.221199	−	0.974395i
$465$		0			0
$466$	9.32396	+	3.26259i	0.0200085	+	0.00700127i
$467$	−22.5274	+	199.936i	−0.0482385	+	0.428128i	0.946262	+	0.323400i	$0.104826\pi$
$467$	−22.5274	+	199.936i	−0.0482385	+	0.428128i	−0.994501	+	0.104728i	$0.966603\pi$
$468$		0			0
$469$	67.8589	+	140.911i	0.144689	+	0.300449i
$470$	−1.14247	+	2.37237i	−0.00243080	+	0.00504760i
$471$		0			0
$472$	9.91842	+	15.7851i	0.0210136	+	0.0334430i
$473$	263.169	+	60.0666i	0.556383	+	0.126991i
$474$		0			0
$475$	358.770	−	570.979i	0.755305	−	1.20206i
$476$	99.1149	−	99.1149i	0.208225	−	0.208225i
$477$		0			0
$478$	2.39524	+	6.84519i	0.00501095	+	0.0143205i
$479$	625.859	−	218.997i	1.30659	−	0.457197i	0.414913	−	0.909861i	$-0.363812\pi$
$479$	625.859	−	218.997i	1.30659	−	0.457197i	0.891681	+	0.452664i	$0.149526\pi$
$480$		0			0
$481$	259.716	+	259.716i	0.539950	+	0.539950i
$482$	−0.936638	−	0.588529i	−0.00194323	−	0.00122101i
$483$		0			0
$484$	58.5312	−	256.442i	0.120932	−	0.529839i
$485$	−844.506	+	530.638i	−1.74125	+	1.09410i
$486$		0			0
$487$	−98.2132	−	47.2970i	−0.201670	−	0.0971191i	0.330323	−	0.943868i	$-0.392842\pi$
$487$	−98.2132	−	47.2970i	−0.201670	−	0.0971191i	−0.531993	+	0.846749i	$0.678557\pi$
$488$	24.4296	−	11.7647i	0.0500606	−	0.0241079i
$489$		0			0
$490$	−4.33695	−	0.488657i	−0.00885092	−	0.000997259i
$491$	152.864	−	436.860i	0.311332	−	0.889735i	−0.676805	−	0.736162i	$-0.736636\pi$
$491$	152.864	−	436.860i	0.311332	−	0.889735i	0.988137	−	0.153573i	$-0.0490781\pi$
$492$		0			0
$493$	−123.445	−	123.734i	−0.250395	−	0.250982i
$494$	4.77213			0.00966019
$495$		0			0
$496$	−4.49917	+	39.9313i	−0.00907092	+	0.0805066i
$497$	435.249	+	347.099i	0.875752	+	0.698389i
$498$		0			0
$499$	−119.381	+	247.898i	−0.239241	+	0.496789i	−0.985672	−	0.168674i	$-0.946052\pi$
$499$	−119.381	+	247.898i	−0.239241	+	0.496789i	0.746431	+	0.665463i	$0.231766\pi$
$500$	−572.890	−	718.381i	−1.14578	−	1.43676i
$501$		0			0
$502$	1.67561	+	0.382446i	0.00333786	+	0.000761845i
$503$	59.4343	+	527.494i	0.118160	+	1.04870i	0.903191	+	0.429239i	$0.141218\pi$
$503$	59.4343	+	527.494i	0.118160	+	1.04870i	−0.785031	+	0.619456i	$0.787353\pi$
$504$		0			0
$505$	−787.035	+	787.035i	−1.55849	+	1.55849i
$506$	−1.67495	+	0.382297i	−0.00331018	+	0.000755528i
$507$		0			0
$508$	862.227	−	301.706i	1.69730	−	0.593910i
$509$	−19.4786	−	85.3413i	−0.0382683	−	0.167665i	0.952183	−	0.305529i	$-0.0988333\pi$
$509$	−19.4786	−	85.3413i	−0.0382683	−	0.167665i	−0.990451	+	0.137864i	$0.955976\pi$
$510$		0			0
$511$	−435.679	−	273.755i	−0.852600	−	0.535724i
$512$	−41.8304	+	4.71315i	−0.0816999	+	0.00920537i
$513$		0			0
$514$	0.981968	−	0.617011i	0.00191044	−	0.00120041i
$515$	−1111.74	+	886.582i	−2.15871	+	1.72152i
$516$		0			0
$517$	61.3023	−	29.5216i	0.118573	−	0.0571018i
$518$	3.97605	−	4.98581i	0.00767577	−	0.00962512i
$519$		0			0
$520$	8.37865	−	23.9448i	0.0161128	−	0.0460477i
$521$		−	416.078i		−	0.798613i	−0.916817	−	0.399307i	$-0.869251\pi$
$521$		−	416.078i		−	0.798613i	0.916817	−	0.399307i	$-0.130749\pi$
$522$		0			0
$523$	−244.076			−0.466684			−0.233342	−	0.972395i	$-0.574966\pi$
$523$	−244.076			−0.466684			−0.233342	+	0.972395i	$0.574966\pi$
$524$	785.748	+	274.945i	1.49952	+	0.524705i
$525$		0			0
$526$	−1.98303	−	1.58141i	−0.00377002	−	0.00300649i
$527$	6.57292	+	13.6488i	0.0124723	+	0.0258991i
$528$		0			0
$529$	−299.080	−	375.035i	−0.565369	−	0.708951i
$530$	6.65602	+	10.5930i	0.0125585	+	0.0199868i
$531$		0			0
$532$	34.2263	+	303.767i	0.0643351	+	0.570990i
$533$	−22.4341	+	35.7036i	−0.0420902	+	0.0669861i
$534$		0			0
$535$	−577.910	+	131.904i	−1.08021	+	0.246550i
$536$	−2.33897	−	6.68440i	−0.00436376	−	0.0124709i
$537$		0			0
$538$	0.560080	+	2.45387i	0.00104104	+	0.00456110i
$539$	79.7449	+	79.7449i	0.147950	+	0.147950i
$540$		0			0
$541$	741.239	−	83.5176i	1.37013	−	0.154376i	0.603959	−	0.797015i	$-0.293589\pi$
$541$	741.239	−	83.5176i	1.37013	−	0.154376i	0.766169	+	0.642639i	$0.222160\pi$
$542$	2.52350	−	11.0562i	0.00465591	−	0.0203989i
$543$		0			0
$544$	−7.44370	+	5.93615i	−0.0136833	+	0.0109120i
$545$	85.6609	+	41.2521i	0.157176	+	0.0756919i
$546$		0			0
$547$	206.292	−	258.682i	0.377133	−	0.472910i	−0.556651	−	0.830746i	$-0.687914\pi$
$547$	206.292	−	258.682i	0.377133	−	0.472910i	0.933784	+	0.357836i	$0.116485\pi$
$548$	275.336	+	31.0229i	0.502438	+	0.0566112i
$549$		0			0
$550$		−	12.5518i		−	0.0228214i
$551$	378.827	−	42.2343i	0.687526	−	0.0766503i
$552$		0			0
$553$	335.897	+	117.535i	0.607408	+	0.212541i
$554$	−0.954352	+	8.47011i	−0.00172266	+	0.0152890i
$555$		0			0
$556$	−187.789	−	389.949i	−0.337751	−	0.701347i
$557$	−8.12730	+	16.8765i	−0.0145912	+	0.0302989i	−0.908137	−	0.418673i	$-0.862495\pi$
$557$	−8.12730	+	16.8765i	−0.0145912	+	0.0302989i	0.893546	+	0.448972i	$0.148210\pi$
$558$		0			0
$559$	213.126	+	339.188i	0.381262	+	0.606776i
$560$	791.819	+	180.728i	1.41396	+	0.322728i
$561$		0			0
$562$	7.15619	−	11.3890i	0.0127334	−	0.0202651i
$563$	682.747	−	682.747i	1.21269	−	1.21269i	0.242557	−	0.970137i	$-0.422014\pi$
$563$	682.747	−	682.747i	1.21269	−	1.21269i	0.970137	−	0.242557i	$-0.0779860\pi$
$564$		0			0
$565$	−163.048	−	465.966i	−0.288581	−	0.824718i
$566$	−4.85688	+	1.69949i	−0.00858105	+	0.00300264i
$567$		0			0
$568$	−17.8246	−	17.8246i	−0.0313814	−	0.0313814i
$569$	−814.946	−	512.065i	−1.43224	−	0.899938i	−0.432245	−	0.901756i	$-0.642278\pi$
$569$	−814.946	−	512.065i	−1.43224	−	0.899938i	−0.999998	+	0.00181851i	$0.999421\pi$
$570$		0			0
$571$	−32.2889	+	141.467i	−0.0565480	+	0.247753i	−0.995300	−	0.0968408i	$-0.969126\pi$
$571$	−32.2889	+	141.467i	−0.0565480	+	0.247753i	0.938752	+	0.344594i	$0.111983\pi$
$572$	−277.485	+	174.356i	−0.485114	+	0.304817i
$573$		0			0
$574$	0.659612	+	0.317652i	0.00114915	+	0.000553401i
$575$	−324.594	+	156.316i	−0.564512	+	0.271855i
$576$		0			0
$577$	263.320	+	29.6690i	0.456360	+	0.0514194i	0.337153	−	0.941450i	$-0.390536\pi$
$577$	263.320	+	29.6690i	0.456360	+	0.0514194i	0.119207	+	0.992869i	$0.461965\pi$
$578$	2.74749	−	7.85188i	0.00475344	−	0.0135846i
$579$		0			0
$580$	226.573	−	987.349i	0.390643	−	1.70233i
$581$	−176.930			−0.304527
$582$		0			0
$583$	36.1952	−	321.241i	0.0620844	−	0.551014i
$584$	18.2158	+	14.5266i	0.0311914	+	0.0248743i
$585$		0			0
$586$	−2.01640	+	4.18711i	−0.00344096	+	0.00714523i
$587$	−606.443	−	760.455i	−1.03312	−	1.29549i	−0.954379	−	0.298599i	$-0.903481\pi$
$587$	−606.443	−	760.455i	−1.03312	−	1.29549i	−0.0787436	−	0.996895i	$-0.525091\pi$
$588$		0			0
$589$	−32.2094	−	7.35160i	−0.0546850	−	0.0124815i
$590$	2.27944	+	20.2306i	0.00386346	+	0.0342891i
$591$		0			0
$592$	376.504	−	376.504i	0.635987	−	0.635987i
$593$	−829.756	+	189.386i	−1.39925	+	0.319370i	−0.854597	−	0.519291i	$-0.826196\pi$
$593$	−829.756	+	189.386i	−1.39925	+	0.319370i	−0.544654	+	0.838661i	$0.683339\pi$
$594$		0			0
$595$	289.004	−	101.127i	0.485721	−	0.169961i
$596$	48.6239	+	213.035i	0.0815837	+	0.357442i
$597$		0			0
$598$	−2.15878	−	1.35645i	−0.00361000	−	0.00226831i
$599$	970.894	−	109.393i	1.62086	−	0.182627i	0.745638	−	0.666351i	$-0.232145\pi$
$599$	970.894	−	109.393i	1.62086	−	0.182627i	0.875220	+	0.483724i	$0.160716\pi$
$600$		0			0
$601$	−265.894	+	167.072i	−0.442419	+	0.277990i	−0.734764	−	0.678323i	$-0.762707\pi$
$601$	−265.894	+	167.072i	−0.442419	+	0.277990i	0.292345	+	0.956313i	$0.405564\pi$
$602$	5.43776	−	4.33647i	0.00903282	−	0.00720343i
$603$		0			0
$604$	−689.477	+	332.035i	−1.14152	+	0.549726i
$605$	358.243	−	449.223i	0.592137	−	0.742517i
$606$		0			0
$607$	−250.177	+	714.965i	−0.412154	+	1.17787i	0.531536	+	0.847036i	$0.321615\pi$
$607$	−250.177	+	714.965i	−0.412154	+	1.17787i	−0.943690	+	0.330832i	$0.892671\pi$
$608$		−	20.7635i		−	0.0341505i
$609$		0			0
$610$	29.6107			0.0485422
$611$	95.3061	+	33.3491i	0.155984	+	0.0545811i
$612$		0			0
$613$	−84.7718	−	67.6033i	−0.138290	−	0.110283i	0.551902	−	0.833909i	$-0.313902\pi$
$613$	−84.7718	−	67.6033i	−0.138290	−	0.110283i	−0.690192	+	0.723627i	$0.742474\pi$
$614$	4.28096	+	8.88950i	0.00697224	+	0.0144780i
$615$		0			0
$616$	7.09618	+	8.89833i	0.0115198	+	0.0144453i
$617$	477.375	+	759.739i	0.773704	+	1.23134i	0.968136	+	0.250427i	$0.0805709\pi$
$617$	477.375	+	759.739i	0.773704	+	1.23134i	−0.194432	+	0.980916i	$0.562286\pi$
$618$		0			0
$619$	−34.8184	−	309.021i	−0.0562494	−	0.499227i	−0.989976	−	0.141239i	$-0.954891\pi$
$619$	−34.8184	−	309.021i	−0.0562494	−	0.499227i	0.933726	−	0.357988i	$-0.116537\pi$
$620$	−46.7133	+	74.3437i	−0.0753440	+	0.119909i
$621$		0			0
$622$	−0.0183018	+	0.00417728i	−2.94242e−5	+	6.71588e-6i
$623$	−198.636	−	567.668i	−0.318837	−	0.911185i
$624$		0			0
$625$	−161.220	−	706.351i	−0.257952	−	1.13016i
$626$	−0.308489	−	0.308489i	−0.000492794	−	0.000492794i
$627$		0			0
$628$	255.318	−	28.7674i	0.406558	−	0.0458080i
$629$	44.6672	−	195.700i	0.0710130	−	0.311128i
$630$		0			0
$631$	−60.2526	+	48.0499i	−0.0954875	+	0.0761487i	−0.670070	−	0.742298i	$-0.733736\pi$
$631$	−60.2526	+	48.0499i	−0.0954875	+	0.0761487i	0.574582	+	0.818447i	$0.305164\pi$
$632$	−14.5180	−	6.99151i	−0.0229716	−	0.0110625i
$633$		0			0
$634$	−10.4641	+	13.1215i	−0.0165049	+	0.0206964i
$635$	1982.88	+	223.416i	3.12264	+	0.351837i
$636$		0			0
$637$			167.361i			0.262733i
$638$	5.55224	−	4.41714i	0.00870257	−	0.00692341i
$639$		0			0
$640$	−69.4433	−	24.2993i	−0.108505	−	0.0379676i
$641$	−36.9672	+	328.093i	−0.0576712	+	0.511846i	0.931356	+	0.364110i	$0.118627\pi$
$641$	−36.9672	+	328.093i	−0.0576712	+	0.511846i	−0.989027	+	0.147735i	$0.952802\pi$
$642$		0			0
$643$	−351.977	−	730.888i	−0.547399	−	1.13668i	−0.972793	−	0.231677i	$-0.925579\pi$
$643$	−351.977	−	730.888i	−0.547399	−	1.13668i	0.425394	−	0.905008i	$-0.360135\pi$
$644$	70.8608	−	147.144i	0.110032	−	0.228485i
$645$		0			0
$646$	−1.38757	−	2.20830i	−0.00214794	−	0.00341842i
$647$	−643.781	−	146.939i	−0.995024	−	0.227108i	−0.306146	−	0.951985i	$-0.599039\pi$
$647$	−643.781	−	146.939i	−0.995024	−	0.227108i	−0.688878	+	0.724877i	$0.741897\pi$
$648$		0			0
$649$	279.885	−	445.434i	0.431255	−	0.686339i
$650$	13.1712	−	13.1712i	0.0202634	−	0.0202634i
$651$		0			0
$652$	389.668	+	1113.61i	0.597650	+	1.70799i
$653$	−510.481	+	178.625i	−0.781747	+	0.273545i	−0.691502	−	0.722375i	$-0.743051\pi$
$653$	−510.481	+	178.625i	−0.781747	+	0.273545i	−0.0902449	+	0.995920i	$0.528765\pi$
$654$		0			0
$655$	1285.83	+	1285.83i	1.96309	+	1.96309i
$656$	51.7587	+	32.5221i	0.0789004	+	0.0495764i
$657$		0			0
$658$	0.390105	−	1.70916i	0.000592865	−	0.00259751i
$659$	−67.5559	+	42.4482i	−0.102513	+	0.0644131i	−0.582313	−	0.812965i	$-0.697852\pi$
$659$	−67.5559	+	42.4482i	−0.102513	+	0.0644131i	0.479800	+	0.877378i	$0.340709\pi$
$660$		0			0
$661$	−174.005	−	83.7962i	−0.263245	−	0.126772i	0.297606	−	0.954689i	$-0.403812\pi$
$661$	−174.005	−	83.7962i	−0.263245	−	0.126772i	−0.560851	+	0.827917i	$0.689526\pi$
$662$	−3.71354	+	1.78834i	−0.00560957	+	0.00270143i
$663$		0			0
$664$	7.96109	+	0.897000i	0.0119896	+	0.00135090i
$665$	−220.543	+	630.275i	−0.331643	+	0.947782i
$666$		0			0
$667$	−183.375	−	88.5736i	−0.274925	−	0.132794i
$668$	227.731			0.340914
$669$		0			0
$670$	0.865900	−	7.68507i	0.00129239	−	0.0114703i
$671$	−598.213	−	477.059i	−0.891524	−	0.710967i
$672$		0			0
$673$	217.268	−	451.162i	0.322835	−	0.670374i	−0.674880	−	0.737927i	$-0.735805\pi$
$673$	217.268	−	451.162i	0.322835	−	0.670374i	0.997716	+	0.0675528i	$0.0215191\pi$
$674$	4.25949	+	5.34124i	0.00631973	+	0.00792469i
$675$		0			0
$676$	184.733	+	42.1641i	0.273274	+	0.0623730i
$677$	−32.4892	−	288.350i	−0.0479900	−	0.425923i	−0.994619	−	0.103598i	$-0.966964\pi$
$677$	−32.4892	−	288.350i	−0.0479900	−	0.425923i	0.946629	−	0.322325i	$-0.104464\pi$
$678$		0			0
$679$	469.552	−	469.552i	0.691535	−	0.691535i
$680$	−13.5166	+	3.08509i	−0.0198774	+	0.00453689i
$681$		0			0
$682$	−0.580438	+	0.203104i	−0.000851082	+	0.000297807i
$683$	135.936	+	595.576i	0.199028	+	0.871999i	0.971517	+	0.236971i	$0.0761546\pi$
$683$	135.936	+	595.576i	0.199028	+	0.871999i	−0.772489	+	0.635029i	$0.780988\pi$
$684$		0			0
$685$	512.480	+	322.012i	0.748145	+	0.470091i
$686$	12.2106	−	1.37581i	0.0177997	−	0.00200555i
$687$		0			0
$688$	491.712	−	308.963i	0.714698	−	0.449075i
$689$	375.076	−	299.113i	0.544378	−	0.434127i
$690$		0			0
$691$	525.520	−	253.077i	0.760521	−	0.366248i	−0.0130852	−	0.999914i	$-0.504165\pi$
$691$	525.520	−	253.077i	0.760521	−	0.366248i	0.773606	+	0.633667i	$0.218451\pi$
$692$	−836.449	+	1048.87i	−1.20874	+	1.51571i
$693$		0			0
$694$	−1.07596	+	3.07490i	−0.00155037	+	0.00443070i
$695$		−	945.431i		−	1.36033i
$696$		0			0
$697$	23.0448			0.0330629
$698$	9.11839	+	3.19066i	0.0130636	+	0.00457115i
$699$		0			0
$700$	932.869	+	743.938i	1.33267	+	1.06277i
$701$	400.779	+	832.225i	0.571724	+	1.18720i	0.963642	+	0.267197i	$0.0860975\pi$
$701$	400.779	+	832.225i	0.571724	+	1.18720i	−0.391918	+	0.920000i	$0.628188\pi$
$702$		0			0
$703$	272.943	+	342.260i	0.388255	+	0.486857i
$704$	252.622	+	402.046i	0.358838	+	0.571088i
$705$		0			0
$706$	1.18627	+	10.5284i	0.00168027	+	0.0149128i
$707$	394.262	−	627.465i	0.557655	−	0.887503i
$708$		0			0
$709$	−776.868	+	177.315i	−1.09572	+	0.250092i	−0.731924	−	0.681386i	$-0.761378\pi$
$709$	−776.868	+	177.315i	−1.09572	+	0.250092i	−0.363799	+	0.931478i	$0.618520\pi$
$710$	−9.09199	−	25.9834i	−0.0128056	−	0.0365964i
$711$		0			0
$712$	6.05979	+	26.5497i	0.00851094	+	0.0372889i
$713$	12.4810	+	12.4810i	0.0175049	+	0.0175049i
$714$		0			0
$715$	−711.362	+	80.1512i	−0.994911	+	0.112100i
$716$	−142.137	+	622.744i	−0.198516	+	0.869754i
$717$		0			0
$718$	11.9453	−	9.52604i	0.0166369	−	0.0132675i
$719$	−1063.27	−	512.044i	−1.47882	−	0.712162i	−0.491495	−	0.870880i	$-0.663550\pi$
$719$	−1063.27	−	512.044i	−1.47882	−	0.712162i	−0.987324	+	0.158718i	$0.949264\pi$
$720$		0			0
$721$	590.278	−	740.186i	0.818694	−	1.02661i
$722$	−6.15826	−	0.693870i	−0.00852945	−	0.000961038i
$723$		0			0
$724$		−	975.927i		−	1.34797i
$725$	929.003	−	1162.14i	1.28138	−	1.60295i
$726$		0			0
$727$	−870.912	−	304.745i	−1.19795	−	0.419182i	−0.343721	−	0.939072i	$-0.611687\pi$
$727$	−870.912	−	304.745i	−1.19795	−	0.419182i	−0.854233	+	0.519890i	$0.825973\pi$
$728$	−1.89109	+	16.7839i	−0.00259765	+	0.0230548i
$729$		0			0
$730$	11.0395	+	22.9239i	0.0151227	+	0.0314025i
$731$	94.9894	−	197.247i	0.129944	−	0.269832i
$732$		0			0
$733$	503.422	+	801.192i	0.686797	+	1.09303i	0.990131	+	0.140147i	$0.0447574\pi$
$733$	503.422	+	801.192i	0.686797	+	1.09303i	−0.303334	+	0.952884i	$0.598100\pi$
$734$	3.14053	+	0.716806i	0.00427866	+	0.000976575i
$735$		0			0
$736$	−5.90191	+	9.39283i	−0.00801890	+	0.0127620i
$737$	−141.308	+	141.308i	−0.191734	+	0.191734i
$738$		0			0
$739$	−400.530	−	1144.65i	−0.541990	−	1.54892i	−0.810559	−	0.585657i	$-0.800836\pi$
$739$	−400.530	−	1144.65i	−0.541990	−	1.54892i	0.268569	−	0.963260i	$-0.413449\pi$
$740$	1098.13	−	384.252i	1.48396	−	0.519259i
$741$		0			0
$742$	−5.88979	−	5.88979i	−0.00793772	−	0.00793772i
$743$	−670.026	−	421.005i	−0.901785	−	0.566629i	−0.000569123	−	1.00000i	$-0.500181\pi$
$743$	−670.026	−	421.005i	−0.901785	−	0.566629i	−0.901216	+	0.433371i	$0.857324\pi$
$744$		0			0
$745$	−106.214	+	465.354i	−0.142569	+	0.624636i
$746$	9.20693	−	5.78510i	0.0123417	−	0.00775482i
$747$		0			0
$748$	161.366	+	77.7096i	0.215730	+	0.103890i
$749$	355.579	−	171.238i	0.474738	−	0.228622i
$750$		0			0
$751$	−73.9585	−	8.33312i	−0.0984800	−	0.0110960i	0.0625869	−	0.998040i	$-0.480065\pi$
$751$	−73.9585	−	8.33312i	−0.0984800	−	0.0110960i	−0.161067	+	0.986943i	$0.551494\pi$
$752$	48.3453	−	138.163i	0.0642890	−	0.183727i
$753$		0			0
$754$	10.4614	+	1.19112i	0.0138745	+	0.00157974i
$755$	−1671.64			−2.21409
$756$		0			0
$757$	−21.2663	+	188.743i	−0.0280928	+	0.249331i	0.971815	+	0.235745i	$0.0757531\pi$
$757$	−21.2663	+	188.743i	−0.0280928	+	0.249331i	−0.999908	+	0.0135854i	$0.995675\pi$
$758$	−5.99756	−	4.78289i	−0.00791235	−	0.00630989i
$759$		0			0
$760$	13.1188	−	27.2416i	0.0172616	−	0.0358442i
$761$	−363.348	−	455.624i	−0.477461	−	0.598717i	0.483520	−	0.875334i	$-0.339358\pi$
$761$	−363.348	−	455.624i	−0.477461	−	0.598717i	−0.960980	+	0.276617i	$0.910787\pi$
$762$		0			0
$763$	−61.7139	−	14.0858i	−0.0808833	−	0.0184611i
$764$	−105.476	−	936.130i	−0.138058	−	1.22530i
$765$		0			0
$766$	5.45955	−	5.45955i	0.00712735	−	0.00712735i
$767$	761.114	−	173.719i	0.992326	−	0.226492i
$768$		0			0
$769$	−652.165	+	228.202i	−0.848069	+	0.296752i	−0.719109	−	0.694898i	$-0.755450\pi$
$769$	−652.165	+	228.202i	−0.848069	+	0.296752i	−0.128960	+	0.991650i	$0.541164\pi$
$770$	2.76573	+	12.1174i	0.00359185	+	0.0157369i
$771$		0			0
$772$	−642.953	−	403.994i	−0.832840	−	0.523308i
$773$	42.4335	−	4.78110i	0.0548945	−	0.00618513i	−0.0844745	−	0.996426i	$-0.526921\pi$
$773$	42.4335	−	4.78110i	0.0548945	−	0.00618513i	0.139369	+	0.990241i	$0.455493\pi$
$774$		0			0
$775$	−109.189	+	68.6083i	−0.140890	+	0.0885268i
$776$	−23.5084	+	18.7473i	−0.0302943	+	0.0241589i
$777$		0			0
$778$	−12.4668	+	6.00370i	−0.0160242	+	0.00771684i
$779$	−31.3349	+	39.2928i	−0.0402246	+	0.0504400i
$780$		0			0
$781$	−234.938	+	671.414i	−0.300817	+	0.859684i
$782$			1.39338i			0.00178182i
$783$		0			0
$784$	242.619			0.309463
$785$	529.750	+	185.368i	0.674841	+	0.236137i
$786$		0			0
$787$	−294.003	−	234.460i	−0.373575	−	0.297916i	0.418647	−	0.908149i	$-0.362504\pi$
$787$	−294.003	−	234.460i	−0.373575	−	0.297916i	−0.792222	+	0.610233i	$0.791076\pi$
$788$	−400.580	−	831.813i	−0.508350	−	1.05560i
$789$		0			0
$790$	−10.9716	−	13.7580i	−0.0138881	−	0.0174151i
$791$	174.868	+	278.302i	0.221073	+	0.351835i
$792$		0			0
$793$	−127.133	−	1128.34i	−0.160319	−	1.42287i
$794$	4.86707	−	7.74589i	0.00612981	−	0.00975554i
$795$		0			0
$796$	583.743	−	133.236i	0.733346	−	0.167381i
$797$	340.277	+	972.455i	0.426947	+	1.22014i	0.933701	+	0.358054i	$0.116560\pi$
$797$	340.277	+	972.455i	0.426947	+	1.22014i	−0.506754	+	0.862091i	$0.669155\pi$
$798$		0			0
$799$	−12.2794	−	53.7995i	−0.0153685	−	0.0673336i
$800$	−57.3079	−	57.3079i	−0.0716348	−	0.0716348i
$801$		0			0
$802$	−7.19346	+	0.810508i	−0.00896940	+	0.00101061i
$803$	146.299	−	640.980i	0.182191	−	0.798231i
$804$		0			0
$805$	278.919	−	222.430i	0.346483	−	0.276311i
$806$	−0.822211	−	0.395956i	−0.00102011	−	0.000491260i
$807$		0			0
$808$	−20.9212	+	26.2344i	−0.0258926	+	0.0324683i
$809$	413.981	+	46.6445i	0.511720	+	0.0576570i	0.364049	−	0.931380i	$-0.381394\pi$
$809$	413.981	+	46.6445i	0.511720	+	0.0576570i	0.147670	+	0.989037i	$0.452822\pi$
$810$		0			0
$811$		−	572.435i		−	0.705838i	−0.935654	−	0.352919i	$-0.885189\pi$
$811$		−	572.435i		−	0.705838i	0.935654	−	0.352919i	$-0.114811\pi$
$812$	−0.789856	+	674.454i	−0.000972730	+	0.830608i
$813$		0			0
$814$	7.69110	+	2.69123i	0.00944852	+	0.00330618i
$815$	−288.553	+	2560.98i	−0.354053	+	3.14231i
$816$		0			0
$817$	207.158	+	430.167i	0.253559	+	0.526520i
$818$	5.48737	−	11.3946i	0.00670828	−	0.0139299i
$819$		0			0
$820$	71.0606	+	113.092i	0.0866592	+	0.137917i
$821$	−839.464	−	191.602i	−1.02249	−	0.233376i	−0.321773	−	0.946817i	$-0.604279\pi$
$821$	−839.464	−	191.602i	−1.02249	−	0.233376i	−0.700716	+	0.713440i	$0.747136\pi$
$822$		0			0
$823$	−428.435	+	681.850i	−0.520577	+	0.828493i	−0.998761	−	0.0497666i	$-0.984152\pi$
$823$	−428.435	+	681.850i	−0.520577	+	0.828493i	0.478184	+	0.878260i	$0.341295\pi$
$824$	−30.3126	+	30.3126i	−0.0367871	+	0.0367871i
$825$		0			0
$826$	−4.47679	−	12.7939i	−0.00541985	−	0.0154890i
$827$	88.3126	−	30.9019i	0.106787	−	0.0373663i	−0.276357	−	0.961055i	$-0.589127\pi$
$827$	88.3126	−	30.9019i	0.106787	−	0.0373663i	0.383144	+	0.923689i	$0.374841\pi$
$828$		0			0
$829$	−587.801	−	587.801i	−0.709048	−	0.709048i	0.257287	−	0.966335i	$-0.417171\pi$
$829$	−587.801	−	587.801i	−0.709048	−	0.709048i	−0.966335	+	0.257287i	$0.917171\pi$
$830$	7.40793	+	4.65471i	0.00892522	+	0.00560809i
$831$		0			0
$832$	−156.798	+	686.976i	−0.188459	+	0.825693i
$833$	77.4460	−	48.6625i	0.0929724	−	0.0584184i
$834$		0			0
$835$	448.191	+	215.837i	0.536755	+	0.258488i
$836$	−351.914	+	169.473i	−0.420950	+	0.202719i
$837$		0			0
$838$	8.66244	+	0.976022i	0.0103370	+	0.00116470i
$839$	−273.856	+	782.636i	−0.326408	+	0.932820i	0.657392	+	0.753549i	$0.271660\pi$
$839$	−273.856	+	782.636i	−0.326408	+	0.932820i	−0.983800	+	0.179271i	$0.942626\pi$
$840$		0			0
$841$	840.998	+	1.96980i	0.999997	+	0.00234221i
$842$	7.35694			0.00873746
$843$		0			0
$844$	−55.6103	+	493.555i	−0.0658889	+	0.584780i
$845$	323.607	+	258.068i	0.382966	+	0.305405i
$846$		0			0
$847$	−165.982	+	344.664i	−0.195964	+	0.406924i
$848$	−433.617	−	543.739i	−0.511341	−	0.641202i
$849$		0			0
$850$	−9.92468	−	2.26524i	−0.0116761	−	0.00266499i
$851$	−26.1865	−	232.411i	−0.0307714	−	0.273104i
$852$		0			0
$853$	−862.103	+	862.103i	−1.01067	+	1.01067i	−0.0107293	+	0.999942i	$0.503415\pi$
$853$	−862.103	+	862.103i	−1.01067	+	1.01067i	−0.999942	+	0.0107293i	$0.996585\pi$
$854$	−19.2203	+	4.38690i	−0.0225062	+	0.00513689i
$855$		0			0
$856$	−16.8677	+	5.90225i	−0.0197052	+	0.00689515i
$857$	−172.103	−	754.033i	−0.200821	−	0.879852i	−0.970439	−	0.241348i	$-0.922411\pi$
$857$	−172.103	−	754.033i	−0.200821	−	0.879852i	0.769618	−	0.638504i	$-0.220447\pi$
$858$		0			0
$859$	−415.831	−	261.284i	−0.484087	−	0.304172i	0.267788	−	0.963478i	$-0.413707\pi$
$859$	−415.831	−	261.284i	−0.484087	−	0.304172i	−0.751875	+	0.659306i	$0.770850\pi$
$860$	1260.90	−	142.069i	1.46616	−	0.165196i
$861$		0			0
$862$	5.87869	−	3.69382i	0.00681982	−	0.00428518i
$863$	−1303.93	+	1039.85i	−1.51093	+	1.20493i	−0.594911	+	0.803792i	$0.702813\pi$
$863$	−1303.93	+	1039.85i	−1.51093	+	1.20493i	−0.916019	+	0.401135i	$0.868616\pi$
$864$		0			0
$865$	−2640.29	+	1271.50i	−3.05236	+	1.46994i
$866$	−3.33680	+	4.18422i	−0.00385312	+	0.00483166i
$867$		0			0
$868$	19.3073	−	55.1771i	0.0222434	−	0.0635681i
$869$			454.710i			0.523257i
$870$		0			0
$871$	−296.563			−0.340486
$872$	2.70545	+	0.946679i	0.00310258	+	0.00108564i
$873$		0			0
$874$	−2.37579	−	1.89463i	−0.00271830	−	0.00216777i
$875$	579.809	+	1203.99i	0.662639	+	1.37598i
$876$		0			0
$877$	−120.936	−	151.649i	−0.137898	−	0.172918i	0.708087	−	0.706125i	$-0.249558\pi$
$877$	−120.936	−	151.649i	−0.137898	−	0.172918i	−0.845985	+	0.533207i	$0.820987\pi$
$878$	−9.06620	−	14.4288i	−0.0103260	−	0.0164337i
$879$		0			0
$880$	116.193	+	1031.24i	0.132038	+	1.17187i
$881$	−606.620	+	965.430i	−0.688558	+	1.09583i	0.301266	+	0.953540i	$0.402591\pi$
$881$	−606.620	+	965.430i	−0.688558	+	1.09583i	−0.989824	+	0.142294i	$0.954552\pi$
$882$		0			0
$883$	621.243	−	141.795i	0.703559	−	0.160583i	0.144249	−	0.989541i	$-0.453923\pi$
$883$	621.243	−	141.795i	0.703559	−	0.160583i	0.559310	+	0.828959i	$0.311066\pi$
$884$	87.7846	+	250.874i	0.0993038	+	0.283794i
$885$		0			0
$886$	2.82652	+	12.3838i	0.00319020	+	0.0139772i
$887$	874.721	+	874.721i	0.986157	+	0.986157i	0.999905	−	0.0137484i	$-0.00437639\pi$
$887$	874.721	+	874.721i	0.986157	+	0.986157i	−0.0137484	+	0.999905i	$0.504376\pi$
$888$		0			0
$889$	−1320.18	+	148.749i	−1.48502	+	0.167321i
$890$	−6.61760	+	28.9936i	−0.00743551	+	0.0325771i
$891$		0			0
$892$	367.215	−	292.844i	0.411676	−	0.328301i
$893$	108.428	+	52.2162i	0.121420	+	0.0584728i
$894$		0			0
$895$	−869.958	+	1090.89i	−0.972020	+	1.21887i
$896$	48.6755	+	5.48441i	0.0543254	+	0.00612100i
$897$		0			0
$898$		−	5.13517i		−	0.00571845i
$899$	−68.7739	−	24.1555i	−0.0765005	−	0.0268693i
$900$		0			0
$901$	−247.473	−	86.5946i	−0.274665	−	0.0961094i
$902$	−0.104739	+	0.929580i	−0.000116118	+	0.00103058i
$903$		0			0
$904$	−6.45740	−	13.4089i	−0.00714314	−	0.0148329i
$905$	924.960	−	1920.70i	1.02205	−	2.12232i
$906$		0			0
$907$	595.833	+	948.263i	0.656927	+	1.04549i	0.994555	+	0.104214i	$0.0332328\pi$
$907$	595.833	+	948.263i	0.656927	+	1.04549i	−0.337627	+	0.941280i	$0.609624\pi$
$908$	965.224	+	220.306i	1.06302	+	0.242628i
$909$		0			0
$910$	−9.81323	+	15.6177i	−0.0107838	+	0.0171623i
$911$	−616.759	+	616.759i	−0.677013	+	0.677013i	−0.959323	−	0.282310i	$-0.908899\pi$
$911$	−616.759	+	616.759i	−0.677013	+	0.677013i	0.282310	+	0.959323i	$0.408899\pi$
$912$		0			0
$913$	−74.6672	−	213.387i	−0.0817823	−	0.233720i
$914$	−21.9099	+	7.66661i	−0.0239715	+	0.00838797i
$915$		0			0
$916$	−375.446	−	375.446i	−0.409875	−	0.409875i
$917$	−1025.13	−	644.129i	−1.11791	−	0.702431i
$918$		0			0
$919$	11.3108	−	49.5559i	0.0123077	−	0.0539238i	−0.968401	−	0.249398i	$-0.919767\pi$
$919$	11.3108	−	49.5559i	0.0123077	−	0.0539238i	0.980709	+	0.195474i	$0.0626245\pi$
$920$	−13.6778	+	8.59436i	−0.0148672	+	0.00934169i
$921$		0			0
$922$	−14.1182	−	6.79897i	−0.0153126	−	0.00737415i
$923$	−951.081	+	458.016i	−1.03042	+	0.496226i
$924$		0			0
$925$	1697.98	+	191.316i	1.83565	+	0.206828i
$926$	−4.74974	+	13.5740i	−0.00512930	+	0.0146587i
$927$		0			0
$928$	5.18257	−	45.5174i	0.00558466	−	0.0490489i
$929$	235.953			0.253986			0.126993	−	0.991904i	$-0.459467\pi$
$929$	235.953			0.253986			0.126993	+	0.991904i	$0.459467\pi$
$930$		0			0
$931$	−22.3338	+	198.218i	−0.0239891	+	0.212909i
$932$	−938.092	−	748.103i	−1.00654	−	0.802686i
$933$		0			0
$934$	−2.87406	+	5.96804i	−0.00307715	+	0.00638977i
$935$	243.929	+	305.877i	0.260886	+	0.327141i
$936$		0			0
$937$	616.083	+	140.617i	0.657506	+	0.150072i	0.538241	−	0.842791i	$-0.319089\pi$
$937$	616.083	+	140.617i	0.657506	+	0.150072i	0.119265	+	0.992862i	$0.461946\pi$
$938$	0.576509	+	5.11666i	0.000614615	+	0.00545486i
$939$		0			0
$940$	226.156	−	226.156i	0.240592	−	0.240592i
$941$	1147.00	−	261.796i	1.21892	−	0.278210i	0.435778	−	0.900054i	$-0.356473\pi$
$941$	1147.00	−	261.796i	1.21892	−	0.278210i	0.783141	+	0.621844i	$0.213616\pi$
$942$		0			0
$943$	25.3438	−	8.86816i	0.0268757	−	0.00940420i
$944$	−251.837	−	1103.37i	−0.266776	−	1.16882i
$945$		0			0
$946$	7.52482	+	4.72816i	0.00795436	+	0.00499805i
$947$	−1021.26	+	115.069i	−1.07842	+	0.121509i	−0.633258	−	0.773941i	$-0.718283\pi$
$947$	−1021.26	+	115.069i	−1.07842	+	0.121509i	−0.445163	+	0.895450i	$0.646854\pi$
$948$		0			0
$949$	826.132	−	519.093i	0.870529	−	0.546990i
$950$	17.3573	−	13.8420i	0.0182709	−	0.0145705i
$951$		0			0
$952$	8.31658	−	4.00505i	0.00873590	−	0.00420699i
$953$	−19.5708	+	24.5410i	−0.0205360	+	0.0257514i	−0.791993	−	0.610530i	$-0.790957\pi$
$953$	−19.5708	+	24.5410i	−0.0205360	+	0.0257514i	0.771457	+	0.636281i	$0.219528\pi$
$954$		0			0
$955$	679.655	−	1942.34i	0.711680	−	2.03387i
$956$		−	880.882i		−	0.921424i
$957$		0			0
$958$	21.8298			0.0227869
$959$	−380.357	−	133.093i	−0.396618	−	0.138783i
$960$		0			0
$961$	−746.401	−	595.235i	−0.776692	−	0.619391i
$962$	5.24662	+	10.8947i	0.00545386	+	0.0113251i
$963$		0			0
$964$	83.7740	+	105.049i	0.0869025	+	0.108972i
$965$	−882.484	−	1404.47i	−0.914491	−	1.45540i
$966$		0			0
$967$	14.3688	+	127.526i	0.0148591	+	0.131878i	0.998952	−	0.0457785i	$-0.0145768\pi$
$967$	14.3688	+	127.526i	0.0148591	+	0.131878i	−0.984092	+	0.177657i	$0.943148\pi$
$968$	9.21584	−	14.6669i	0.00952050	−	0.0151518i
$969$		0			0
$970$	−32.0129	+	7.30674i	−0.0330030	+	0.00753272i
$971$	−536.186	−	1532.33i	−0.552200	−	1.57810i	−0.794094	−	0.607794i	$-0.792055\pi$
$971$	−536.186	−	1532.33i	−0.552200	−	1.57810i	0.241895	−	0.970303i	$-0.422231\pi$
$972$		0			0
$973$	140.068	+	613.678i	0.143955	+	0.630707i
$974$	−2.53768	−	2.53768i	−0.00260542	−	0.00260542i
$975$		0			0
$976$	−1635.72	+	184.302i	−1.67595	+	0.188834i
$977$	−314.486	+	1377.85i	−0.321889	+	1.41029i	0.512298	+	0.858808i	$0.328794\pi$
$977$	−314.486	+	1377.85i	−0.321889	+	1.41029i	−0.834187	+	0.551481i	$0.814063\pi$
$978$		0			0
$979$	600.810	−	479.130i	0.613697	−	0.489407i
$980$	477.622	+	230.010i	0.487369	+	0.234705i
$981$		0			0
$982$	9.50048	−	11.9132i	0.00967462	−	0.0121316i
$983$	−1072.31	−	120.821i	−1.09086	−	0.122910i	−0.451838	−	0.892100i	$-0.649231\pi$
$983$	−1072.31	−	120.821i	−1.09086	−	0.122910i	−0.639020	+	0.769190i	$0.720660\pi$
$984$		0			0
$985$		−	2016.73i		−	2.04744i
$986$	−2.49061	−	5.18733i	−0.00252597	−	0.00526098i
$987$		0			0
$988$	−547.118	−	191.445i	−0.553764	−	0.193770i
$989$	28.5602	−	253.479i	0.0288778	−	0.256298i
$990$		0			0
$991$	248.463	+	515.939i	0.250719	+	0.520624i	0.987904	−	0.155067i	$-0.0495594\pi$
$991$	248.463	+	515.939i	0.250719	+	0.520624i	−0.737184	+	0.675692i	$0.763845\pi$
$992$	−1.72280	+	3.57744i	−0.00173670	+	0.00360629i
$993$		0			0
$994$	9.75111	+	15.5188i	0.00980997	+	0.0156125i
$995$	1275.13	+	291.040i	1.28154	+	0.292502i
$996$		0			0
$997$	256.454	−	408.145i	0.257226	−	0.409373i	−0.692998	−	0.720939i	$-0.743711\pi$
$997$	256.454	−	408.145i	0.257226	−	0.409373i	0.950224	+	0.311566i	$0.100854\pi$
$998$	−6.40531	+	6.40531i	−0.00641815	+	0.00641815i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.37.2		48
3.2	odd	2		29.3.f.a.8.3	✓	48
29.11	odd	28	inner	261.3.s.a.127.2		48
87.11	even	28		29.3.f.a.11.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.8.3	✓	48	3.2	odd	2
29.3.f.a.11.3	yes	48	87.11	even	28
261.3.s.a.37.2		48	1.1	even	1	trivial
261.3.s.a.127.2		48	29.11	odd	28	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0310749 + 0.0108736i) q^{2} +(-3.12648 - 2.49328i) q^{4} +(-3.79007 - 7.87017i) q^{5} +(3.62612 + 4.54701i) q^{7} +(-0.140107 - 0.222980i) q^{8} +O(q^{10})\)	\(q+(0.0310749 + 0.0108736i) q^{2} +(-3.12648 - 2.49328i) q^{4} +(-3.79007 - 7.87017i) q^{5} +(3.62612 + 4.54701i) q^{7} +(-0.140107 - 0.222980i) q^{8} +(-0.0321993 - 0.285777i) q^{10} +(-3.95365 + 6.29219i) q^{11} +(-10.7515 + 2.45395i) q^{13} +(0.0632391 + 0.180727i) q^{14} +(3.55744 + 15.5862i) q^{16} +(4.26171 + 4.26171i) q^{17} +(-13.0613 + 1.47165i) q^{19} +(-7.77298 + 34.0556i) q^{20} +(-0.191278 + 0.152539i) q^{22} +(6.32686 + 3.04685i) q^{23} +(-31.9876 + 40.1112i) q^{25} +(-0.360785 - 0.0406507i) q^{26} -23.2571i q^{28} +(-29.0000 - 0.0339620i) q^{29} +(2.37249 + 0.830170i) q^{31} +(-0.176871 + 1.56977i) q^{32} +(0.0860924 + 0.178773i) q^{34} +(22.0425 - 45.7716i) q^{35} +(-17.7197 - 28.2007i) q^{37} +(-0.421880 - 0.0962915i) q^{38} +(-1.22387 + 1.94778i) q^{40} +(2.70371 - 2.70371i) q^{41} +(-11.9973 - 34.2863i) q^{43} +(28.0492 - 9.81484i) q^{44} +(0.163476 + 0.163476i) q^{46} +(-7.75262 - 4.87130i) q^{47} +(3.37698 - 14.7955i) q^{49} +(-1.43017 + 0.898634i) q^{50} +(39.7327 + 19.1342i) q^{52} +(-39.1941 + 18.8749i) q^{53} +(64.5052 + 7.26799i) q^{55} +(0.505844 - 1.44562i) q^{56} +(-0.900803 - 0.316389i) q^{58} -70.7916 q^{59} +(-11.5282 + 102.316i) q^{61} +(0.0646980 + 0.0515949i) q^{62} +(27.7234 - 57.5683i) q^{64} +(60.0619 + 75.3153i) q^{65} +(26.2176 + 5.98401i) q^{67} +(-2.69850 - 23.9498i) q^{68} +(1.18267 - 1.18267i) q^{70} +(93.3221 - 21.3002i) q^{71} +(-83.5084 + 29.2208i) q^{73} +(-0.243995 - 1.06901i) q^{74} +(44.5050 + 27.9644i) q^{76} +(-42.9470 + 4.83897i) q^{77} +(51.8104 - 32.5546i) q^{79} +(109.183 - 87.0704i) q^{80} +(0.113416 - 0.0546185i) q^{82} +(-18.9679 + 23.7849i) q^{83} +(17.3882 - 49.6926i) q^{85} -1.19590i q^{86} +1.95696 q^{88} +(-97.6073 - 34.1543i) q^{89} +(-50.1443 - 39.9887i) q^{91} +(-12.1841 - 25.3006i) q^{92} +(-0.187944 - 0.235674i) q^{94} +(61.0853 + 97.2168i) q^{95} +(-12.7840 - 113.461i) q^{97} +(0.265820 - 0.423050i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8} - 20 q^{10} + 8 q^{11} - 14 q^{13} - 26 q^{14} + 18 q^{16} + 26 q^{17} + 2 q^{19} - 46 q^{20} + 154 q^{22} - 56 q^{23} - 34 q^{25} - 110 q^{26} + 170 q^{29} - 88 q^{31} + 132 q^{32} - 224 q^{34} + 210 q^{35} - 56 q^{37} + 294 q^{38} - 492 q^{40} + 34 q^{41} + 176 q^{43} - 126 q^{44} + 744 q^{46} - 208 q^{47} + 506 q^{49} - 732 q^{50} + 690 q^{52} + 14 q^{53} + 284 q^{55} - 332 q^{56} - 508 q^{58} + 44 q^{59} - 30 q^{61} + 504 q^{62} - 896 q^{64} + 554 q^{65} - 574 q^{67} + 796 q^{68} - 1066 q^{70} - 224 q^{71} - 22 q^{73} - 820 q^{74} + 514 q^{76} - 436 q^{77} + 564 q^{79} - 1162 q^{80} - 18 q^{82} + 126 q^{83} + 38 q^{85} - 384 q^{88} + 160 q^{89} - 434 q^{91} + 1022 q^{92} - 2 q^{94} + 642 q^{95} + 604 q^{97} + 102 q^{98}+O(q^{100}) \) 48 * q + 16 * q^2 - 14 * q^4 + 14 * q^5 - 10 * q^7 - 28 * q^8 - 20 * q^10 + 8 * q^11 - 14 * q^13 - 26 * q^14 + 18 * q^16 + 26 * q^17 + 2 * q^19 - 46 * q^20 + 154 * q^22 - 56 * q^23 - 34 * q^25 - 110 * q^26 + 170 * q^29 - 88 * q^31 + 132 * q^32 - 224 * q^34 + 210 * q^35 - 56 * q^37 + 294 * q^38 - 492 * q^40 + 34 * q^41 + 176 * q^43 - 126 * q^44 + 744 * q^46 - 208 * q^47 + 506 * q^49 - 732 * q^50 + 690 * q^52 + 14 * q^53 + 284 * q^55 - 332 * q^56 - 508 * q^58 + 44 * q^59 - 30 * q^61 + 504 * q^62 - 896 * q^64 + 554 * q^65 - 574 * q^67 + 796 * q^68 - 1066 * q^70 - 224 * q^71 - 22 * q^73 - 820 * q^74 + 514 * q^76 - 436 * q^77 + 564 * q^79 - 1162 * q^80 - 18 * q^82 + 126 * q^83 + 38 * q^85 - 384 * q^88 + 160 * q^89 - 434 * q^91 + 1022 * q^92 - 2 * q^94 + 642 * q^95 + 604 * q^97 + 102 * q^98

Introduction

L-functions

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