LMFDB - Embedded newform 261.3.s.a.73.3

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			73.3
Character	$\chi$	$=$	261.73
Dual form			261.3.s.a.118.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68783 - 0.190173i) q^{2} +(-1.08711 + 0.248126i) q^{4} +(-0.141728 - 0.113024i) q^{5} +(-1.55116 + 6.79606i) q^{7} +(-8.20045 + 2.86946i) q^{8} +O(q^{10})$	\(q+(1.68783 - 0.190173i) q^{2} +(-1.08711 + 0.248126i) q^{4} +(-0.141728 - 0.113024i) q^{5} +(-1.55116 + 6.79606i) q^{7} +(-8.20045 + 2.86946i) q^{8} +(-0.260707 - 0.163813i) q^{10} +(12.2566 + 4.28875i) q^{11} +(9.66173 + 20.0628i) q^{13} +(-1.32566 + 11.7656i) q^{14} +(-9.27670 + 4.46742i) q^{16} +(5.90660 + 5.90660i) q^{17} +(-10.7431 + 17.0975i) q^{19} +(0.182118 + 0.0877036i) q^{20} +(21.5026 + 4.90782i) q^{22} +(-15.0384 - 18.8575i) q^{23} +(-5.55571 - 24.3412i) q^{25} +(20.1228 + 32.0252i) q^{26} -7.77294i q^{28} +(-28.5764 + 4.93832i) q^{29} +(35.5909 - 4.01014i) q^{31} +(14.6174 - 9.18473i) q^{32} +(11.0926 + 8.84605i) q^{34} +(0.987964 - 0.787875i) q^{35} +(-23.0925 + 8.08043i) q^{37} +(-14.8810 + 30.9007i) q^{38} +(1.48655 + 0.520168i) q^{40} +(14.1288 - 14.1288i) q^{41} +(-4.31425 + 38.2901i) q^{43} +(-14.3884 - 1.62118i) q^{44} +(-28.9684 - 28.9684i) q^{46} +(-1.53295 + 4.38091i) q^{47} +(0.367152 + 0.176811i) q^{49} +(-14.0061 - 40.0272i) q^{50} +(-15.4815 - 19.4131i) q^{52} +(51.0246 - 63.9828i) q^{53} +(-1.25237 - 1.99313i) q^{55} +(-6.78085 - 60.1817i) q^{56} +(-47.2930 + 13.7695i) q^{58} -28.0326 q^{59} +(-3.26475 + 2.05138i) q^{61} +(59.3088 - 13.5368i) q^{62} +(55.1251 - 43.9608i) q^{64} +(0.898247 - 3.93548i) q^{65} +(-2.88318 + 5.98698i) q^{67} +(-7.88670 - 4.95554i) q^{68} +(1.51768 - 1.51768i) q^{70} +(15.5711 + 32.3337i) q^{71} +(103.524 + 11.6644i) q^{73} +(-37.4396 + 18.0300i) q^{74} +(7.43657 - 21.2525i) q^{76} +(-48.1585 + 76.6437i) q^{77} +(-28.1618 - 80.4819i) q^{79} +(1.81970 + 0.415334i) q^{80} +(21.1601 - 26.5339i) q^{82} +(6.13681 + 26.8871i) q^{83} +(-0.169541 - 1.50472i) q^{85} +65.4475i q^{86} -112.816 q^{88} +(-26.8243 + 3.02237i) q^{89} +(-151.335 + 34.5412i) q^{91} +(21.0274 + 16.7688i) q^{92} +(-1.75422 + 7.68575i) q^{94} +(3.45503 - 1.20897i) q^{95} +(-6.09419 - 3.82923i) q^{97} +(0.653314 + 0.228604i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{27}{28}\right)$	$1$

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 $

$2$	1.68783	−	0.190173i	0.843915	−	0.0950863i	0.320588	−	0.947219i	$-0.396119\pi$
$2$	1.68783	−	0.190173i	0.843915	−	0.0950863i	0.523326	+	0.852132i	$0.324691\pi$
$3$		0			0
$3$		0			0
$4$	−1.08711	+	0.248126i	−0.271777	+	0.0620314i
$5$	−0.141728	−	0.113024i	−0.0283456	−	0.0226049i	0.609215	−	0.793005i	$-0.291485\pi$
$5$	−0.141728	−	0.113024i	−0.0283456	−	0.0226049i	−0.637560	+	0.770401i	$0.720056\pi$
$6$		0			0
$7$	−1.55116	+	6.79606i	−0.221594	+	0.970865i	0.734685	+	0.678408i	$0.237330\pi$
$7$	−1.55116	+	6.79606i	−0.221594	+	0.970865i	−0.956279	+	0.292457i	$0.905527\pi$
$8$	−8.20045	+	2.86946i	−1.02506	+	0.358683i
$9$		0			0
$10$	−0.260707	−	0.163813i	−0.0260707	−	0.0163813i
$11$	12.2566	+	4.28875i	1.11423	+	0.389887i	0.823727	−	0.566987i	$-0.191891\pi$
$11$	12.2566	+	4.28875i	1.11423	+	0.389887i	0.290505	+	0.956873i	$0.406177\pi$
$12$		0			0
$13$	9.66173	+	20.0628i	0.743210	+	1.54329i	0.836694	+	0.547671i	$0.184486\pi$
$13$	9.66173	+	20.0628i	0.743210	+	1.54329i	−0.0934833	+	0.995621i	$0.529800\pi$
$14$	−1.32566	+	11.7656i	−0.0946901	+	0.840398i
$15$		0			0
$16$	−9.27670	+	4.46742i	−0.579794	+	0.279214i
$17$	5.90660	+	5.90660i	0.347447	+	0.347447i	0.859158	−	0.511711i	$-0.170988\pi$
$17$	5.90660	+	5.90660i	0.347447	+	0.347447i	−0.511711	+	0.859158i	$0.670988\pi$
$18$		0			0
$19$	−10.7431	+	17.0975i	−0.565425	+	0.899868i	−1.00000		0.000767373i	$-0.999756\pi$
$19$	−10.7431	+	17.0975i	−0.565425	+	0.899868i	0.434575	+	0.900636i	$0.356899\pi$
$20$	0.182118	+	0.0877036i	0.00910592	+	0.00438518i
$21$		0			0
$22$	21.5026	+	4.90782i	0.977390	+	0.223083i
$23$	−15.0384	−	18.8575i	−0.653843	−	0.819893i	0.338814	−	0.940853i	$-0.389974\pi$
$23$	−15.0384	−	18.8575i	−0.653843	−	0.819893i	−0.992657	+	0.120960i	$0.961403\pi$
$24$		0			0
$25$	−5.55571	−	24.3412i	−0.222228	−	0.973646i
$26$	20.1228	+	32.0252i	0.773952	+	1.23174i
$27$		0			0
$28$		−	7.77294i		−	0.277605i
$29$	−28.5764	+	4.93832i	−0.985395	+	0.170287i
$29$	−28.5764	+	4.93832i	−0.985395	+	0.170287i
$30$		0			0
$31$	35.5909	−	4.01014i	1.14809	−	0.129359i	0.482655	−	0.875811i	$-0.339673\pi$
$31$	35.5909	−	4.01014i	1.14809	−	0.129359i	0.665440	+	0.746451i	$0.268244\pi$
$32$	14.6174	−	9.18473i	0.456794	−	0.287023i
$33$		0			0
$34$	11.0926	+	8.84605i	0.326253	+	0.260178i
$35$	0.987964	−	0.787875i	0.0282275	−	0.0225107i
$36$		0			0
$37$	−23.0925	+	8.08043i	−0.624123	+	0.218390i	−0.623767	−	0.781610i	$-0.714399\pi$
$37$	−23.0925	+	8.08043i	−0.624123	+	0.218390i	−0.000355153		1.00000i	$0.500113\pi$
$38$	−14.8810	+	30.9007i	−0.391605	+	0.813176i
$39$		0			0
$40$	1.48655	+	0.520168i	0.0371639	+	0.0130042i
$41$	14.1288	−	14.1288i	0.344605	−	0.344605i	−0.513490	−	0.858095i	$-0.671648\pi$
$41$	14.1288	−	14.1288i	0.344605	−	0.344605i	0.858095	+	0.513490i	$0.171648\pi$
$42$		0			0
$43$	−4.31425	+	38.2901i	−0.100331	+	0.890466i	0.838221	+	0.545330i	$0.183596\pi$
$43$	−4.31425	+	38.2901i	−0.100331	+	0.890466i	−0.938553	+	0.345136i	$0.887833\pi$
$44$	−14.3884	−	1.62118i	−0.327008	−	0.0368450i
$45$		0			0
$46$	−28.9684	−	28.9684i	−0.629748	−	0.629748i
$47$	−1.53295	+	4.38091i	−0.0326159	+	0.0932108i	−0.959040	−	0.283271i	$-0.908580\pi$
$47$	−1.53295	+	4.38091i	−0.0326159	+	0.0932108i	0.926424	+	0.376482i	$0.122866\pi$
$48$		0			0
$49$	0.367152	+	0.176811i	0.00749289	+	0.00360839i
$50$	−14.0061	−	40.0272i	−0.280122	−	0.800544i
$51$		0			0
$52$	−15.4815	−	19.4131i	−0.297720	−	0.373330i
$53$	51.0246	−	63.9828i	0.962728	−	1.20722i	−0.0155405	−	0.999879i	$-0.504947\pi$
$53$	51.0246	−	63.9828i	0.962728	−	1.20722i	0.978268	−	0.207343i	$-0.0664817\pi$
$54$		0			0
$55$	−1.25237	−	1.99313i	−0.0227703	−	0.0362387i
$56$	−6.78085	−	60.1817i	−0.121087	−	1.07467i
$57$		0			0
$58$	−47.2930	+	13.7695i	−0.815397	+	0.237405i
$59$	−28.0326			−0.475129			−0.237564	−	0.971372i	$-0.576349\pi$
$59$	−28.0326			−0.475129			−0.237564	+	0.971372i	$0.576349\pi$
$60$		0			0
$61$	−3.26475	+	2.05138i	−0.0535205	+	0.0336292i	−0.558527	−	0.829487i	$-0.688633\pi$
$61$	−3.26475	+	2.05138i	−0.0535205	+	0.0336292i	0.505006	+	0.863116i	$0.331490\pi$
$62$	59.3088	−	13.5368i	0.956594	−	0.218336i
$63$		0			0
$64$	55.1251	−	43.9608i	0.861329	−	0.686887i
$65$	0.898247	−	3.93548i	0.0138192	−	0.0605458i
$66$		0			0
$67$	−2.88318	+	5.98698i	−0.0430325	+	0.0893579i	−0.921377	−	0.388671i	$-0.872934\pi$
$67$	−2.88318	+	5.98698i	−0.0430325	+	0.0893579i	0.878344	+	0.478029i	$0.158649\pi$
$68$	−7.88670	−	4.95554i	−0.115981	−	0.0728756i
$69$		0			0
$70$	1.51768	−	1.51768i	0.0216812	−	0.0216812i
$71$	15.5711	+	32.3337i	0.219311	+	0.455404i	0.981376	−	0.192096i	$-0.0615286\pi$
$71$	15.5711	+	32.3337i	0.219311	+	0.455404i	−0.762065	+	0.647501i	$0.775814\pi$
$72$		0			0
$73$	103.524	+	11.6644i	1.41814	+	0.159786i	0.787511	−	0.616301i	$-0.211370\pi$
$73$	103.524	+	11.6644i	1.41814	+	0.159786i	0.630626	+	0.776087i	$0.282798\pi$
$74$	−37.4396	+	18.0300i	−0.505940	+	0.243648i
$75$		0			0
$76$	7.43657	−	21.2525i	0.0978496	−	0.279638i
$77$	−48.1585	+	76.6437i	−0.625434	+	0.995373i
$78$		0			0
$79$	−28.1618	−	80.4819i	−0.356479	−	1.01876i	−0.972877	−	0.231323i	$-0.925694\pi$
$79$	−28.1618	−	80.4819i	−0.356479	−	1.01876i	0.616398	−	0.787435i	$-0.288591\pi$
$80$	1.81970	+	0.415334i	0.0227462	+	0.00519168i
$81$		0			0
$82$	21.1601	−	26.5339i	0.258050	−	0.323584i
$83$	6.13681	+	26.8871i	0.0739375	+	0.323941i	0.998348	−	0.0574578i	$-0.0182995\pi$
$83$	6.13681	+	26.8871i	0.0739375	+	0.323941i	−0.924410	+	0.381399i	$0.875442\pi$
$84$		0			0
$85$	−0.169541	−	1.50472i	−0.00199461	−	0.0177026i
$86$			65.4475i			0.761018i
$87$		0			0
$88$	−112.816			−1.28200
$89$	−26.8243	+	3.02237i	−0.301397	+	0.0339592i	−0.261368	−	0.965239i	$-0.584174\pi$
$89$	−26.8243	+	3.02237i	−0.301397	+	0.0339592i	−0.0400288	+	0.999199i	$0.512745\pi$
$90$		0			0
$91$	−151.335	+	34.5412i	−1.66302	+	0.379573i
$92$	21.0274	+	16.7688i	0.228559	+	0.182270i
$93$		0			0
$94$	−1.75422	+	7.68575i	−0.0186619	+	0.0817633i
$95$	3.45503	−	1.20897i	0.0363688	−	0.0127260i
$96$		0			0
$97$	−6.09419	−	3.82923i	−0.0628267	−	0.0394766i	0.500252	−	0.865880i	$-0.333241\pi$
$97$	−6.09419	−	3.82923i	−0.0628267	−	0.0394766i	−0.563079	+	0.826403i	$0.690383\pi$
$98$	0.653314	+	0.228604i	0.00666647	+	0.00233270i
$99$		0			0
$100$	12.0793	+	25.0830i	0.120793	+	0.250830i
$101$	12.4952	−	110.898i	0.123715	−	1.09800i	−0.766433	−	0.642324i	$-0.777970\pi$
$101$	12.4952	−	110.898i	0.123715	−	1.09800i	0.890148	−	0.455672i	$-0.150601\pi$
$102$		0			0
$103$	108.481	−	52.2416i	1.05321	−	0.507200i	0.174552	−	0.984648i	$-0.444152\pi$
$103$	108.481	−	52.2416i	1.05321	−	0.507200i	0.878660	+	0.477448i	$0.158438\pi$
$104$	−136.800	−	136.800i	−1.31538	−	1.31538i
$105$		0			0
$106$	73.9530	−	117.696i	0.697670	−	1.11033i
$107$	127.998	+	61.6404i	1.19624	+	0.576079i	0.922602	−	0.385754i	$-0.126059\pi$
$107$	127.998	+	61.6404i	1.19624	+	0.576079i	0.273638	+	0.961833i	$0.411773\pi$
$108$		0			0
$109$	30.7554	+	7.01972i	0.282160	+	0.0644011i	0.361259	−	0.932466i	$-0.382347\pi$
$109$	30.7554	+	7.01972i	0.282160	+	0.0644011i	−0.0790990	+	0.996867i	$0.525204\pi$
$110$	−2.49282	−	3.12590i	−0.0226620	−	0.0284172i
$111$		0			0
$112$	−15.9713	−	69.9747i	−0.142601	−	0.624774i
$113$	51.3355	+	81.7000i	0.454297	+	0.723009i	0.992822	−	0.119600i	$-0.0381613\pi$
$113$	51.3355	+	81.7000i	0.454297	+	0.723009i	−0.538526	+	0.842609i	$0.681018\pi$
$114$		0			0
$115$			4.37235i			0.0380205i
$116$	29.8404	−	12.4590i	0.257245	−	0.107406i
$117$		0			0
$118$	−47.3143	+	5.33104i	−0.400968	+	0.0451783i
$119$	−49.3036	+	30.9795i	−0.414316	+	0.260332i
$120$		0			0
$121$	37.2281	+	29.6884i	0.307671	+	0.245359i
$122$	−5.12023	+	4.08324i	−0.0419691	+	0.0334692i
$123$		0			0
$124$	−37.6962	+	13.1905i	−0.304002	+	0.106375i
$125$	−3.93008	+	8.16089i	−0.0314406	+	0.0652871i
$126$		0			0
$127$	95.5607	+	33.4381i	0.752446	+	0.263292i	0.679132	−	0.734017i	$-0.262357\pi$
$127$	95.5607	+	33.4381i	0.752446	+	0.263292i	0.0733147	+	0.997309i	$0.476642\pi$
$128$	35.8531	−	35.8531i	0.280102	−	0.280102i
$129$		0			0
$130$	0.767667	−	6.81324i	0.00590513	−	0.0524095i
$131$	−95.6113	−	10.7728i	−0.729857	−	0.0822352i	−0.260787	−	0.965396i	$-0.583982\pi$
$131$	−95.6113	−	10.7728i	−0.729857	−	0.0822352i	−0.469070	+	0.883161i	$0.655411\pi$
$132$		0			0
$133$	−99.5314	−	99.5314i	−0.748356	−	0.748356i
$134$	−3.72775	+	10.6533i	−0.0278190	+	0.0795022i
$135$		0			0
$136$	−65.3855	−	31.4880i	−0.480776	−	0.231529i
$137$	−60.7818	−	173.704i	−0.443662	−	1.26791i	−0.921127	−	0.389263i	$-0.872730\pi$
$137$	−60.7818	−	173.704i	−0.443662	−	1.26791i	0.477464	−	0.878651i	$-0.341556\pi$
$138$		0			0
$139$	116.483	+	146.065i	0.838009	+	1.05083i	0.997969	+	0.0637063i	$0.0202921\pi$
$139$	116.483	+	146.065i	0.838009	+	1.05083i	−0.159960	+	0.987124i	$0.551136\pi$
$140$	−0.878533	+	1.10165i	−0.00627524	+	0.00786890i
$141$		0			0
$142$	32.4303	+	51.6126i	0.228383	+	0.363469i
$143$	32.3752	+	287.338i	0.226400	+	2.00935i
$144$		0			0
$145$	4.60824	+	2.52994i	0.0317810	+	0.0174479i
$146$	176.949			1.21198
$147$		0			0
$148$	23.0992	−	14.5142i	0.156075	−	0.0980687i
$149$	−112.412	+	25.6572i	−0.754440	+	0.172196i	−0.582410	−	0.812896i	$-0.697890\pi$
$149$	−112.412	+	25.6572i	−0.754440	+	0.172196i	−0.172031	+	0.985092i	$0.555033\pi$
$150$		0			0
$151$	−7.95750	+	6.34590i	−0.0526987	+	0.0420258i	−0.649485	−	0.760374i	$-0.725015\pi$
$151$	−7.95750	+	6.34590i	−0.0526987	+	0.0420258i	0.596786	+	0.802400i	$0.296444\pi$
$152$	39.0374	−	171.034i	0.256825	−	1.12522i
$153$		0			0
$154$	−66.7077	+	138.520i	−0.433167	+	0.899480i
$155$	−5.49748	−	3.45430i	−0.0354676	−	0.0222858i
$156$		0			0
$157$	−54.2399	+	54.2399i	−0.345477	+	0.345477i	−0.858422	−	0.512945i	$-0.828555\pi$
$157$	−54.2399	+	54.2399i	−0.345477	+	0.345477i	0.512945	+	0.858422i	$0.328555\pi$
$158$	−62.8378	−	130.484i	−0.397708	−	0.825849i
$159$		0			0
$160$	−3.10980	−	0.350390i	−0.0194363	−	0.00218994i
$161$	151.484	−	72.9508i	0.940894	−	0.453111i
$162$		0			0
$163$	−9.39776	+	26.8573i	−0.0576550	+	0.164768i	−0.969109	−	0.246634i	$-0.920675\pi$
$163$	−9.39776	+	26.8573i	−0.0576550	+	0.164768i	0.911454	+	0.411403i	$0.134961\pi$
$164$	−11.8538	+	18.8653i	−0.0722795	+	0.115032i
$165$		0			0
$166$	15.4711	+	44.2138i	0.0931994	+	0.266348i
$167$	41.1889	+	9.40109i	0.246640	+	0.0562939i	0.344053	−	0.938950i	$-0.388200\pi$
$167$	41.1889	+	9.40109i	0.246640	+	0.0562939i	−0.0974137	+	0.995244i	$0.531057\pi$
$168$		0			0
$169$	−203.797	+	255.553i	−1.20590	+	1.51215i
$170$	−0.572314	−	2.50747i	−0.00336655	−	0.0147498i
$171$		0			0
$172$	−4.81068	−	42.6960i	−0.0279691	−	0.248232i
$173$		−	127.036i		−	0.734309i	−0.930160	−	0.367155i	$-0.880332\pi$
$173$		−	127.036i		−	0.734309i	0.930160	−	0.367155i	$-0.119668\pi$
$174$		0			0
$175$	174.042			0.994524
$176$	−132.860	+	14.9697i	−0.754887	+	0.0850553i
$177$		0			0
$178$	−44.7001	+	10.2025i	−0.251124	+	0.0573174i
$179$	114.042	+	90.9455i	0.637106	+	0.508075i	0.887943	−	0.459954i	$-0.152134\pi$
$179$	114.042	+	90.9455i	0.637106	+	0.508075i	−0.250836	+	0.968030i	$0.580706\pi$
$180$		0			0
$181$	48.4132	−	212.112i	0.267476	−	1.17189i	−0.645462	−	0.763792i	$-0.723335\pi$
$181$	48.4132	−	212.112i	0.267476	−	1.17189i	0.912938	−	0.408098i	$-0.133808\pi$
$182$	−248.859	+	87.0794i	−1.36735	+	0.478458i
$183$		0			0
$184$	177.433	+	111.488i	0.964307	+	0.605914i
$185$	4.18615	+	1.46480i	0.0226278	+	0.00791782i
$186$		0			0
$187$	47.0626	+	97.7265i	0.251672	+	0.522602i
$188$	0.579465	−	5.14289i	0.00308226	−	0.0273558i
$189$		0			0
$190$	5.60159	−	2.69758i	0.0294821	−	0.0141978i
$191$	140.809	+	140.809i	0.737221	+	0.737221i	0.972039	−	0.234818i	$-0.0754495\pi$
$191$	140.809	+	140.809i	0.737221	+	0.737221i	−0.234818	+	0.972039i	$0.575450\pi$
$192$		0			0
$193$	−170.596	+	271.502i	−0.883916	+	1.40674i	0.0294336	+	0.999567i	$0.490630\pi$
$193$	−170.596	+	271.502i	−0.883916	+	1.40674i	−0.913349	+	0.407177i	$0.866513\pi$
$194$	−11.0142	−	5.30414i	−0.0567740	−	0.0273409i
$195$		0			0
$196$	−0.443006	−	0.101113i	−0.00226023	−	0.000515883i
$197$	35.3554	+	44.3343i	0.179469	+	0.225047i	0.863426	−	0.504475i	$-0.168314\pi$
$197$	35.3554	+	44.3343i	0.179469	+	0.225047i	−0.683957	+	0.729522i	$0.739742\pi$
$198$		0			0
$199$	−6.42619	−	28.1550i	−0.0322924	−	0.141482i	0.956212	−	0.292676i	$-0.0945456\pi$
$199$	−6.42619	−	28.1550i	−0.0322924	−	0.141482i	−0.988504	+	0.151193i	$0.951688\pi$
$200$	115.405	+	183.666i	0.577027	+	0.918332i
$201$		0			0
$202$		−	189.553i		−	0.938379i
$203$	10.7654	−	201.867i	0.0530317	−	0.994420i
$204$		0			0
$205$	−3.59935	+	0.405549i	−0.0175578	+	0.00197829i
$206$	173.162	−	108.805i	0.840593	−	0.528179i
$207$		0			0
$208$	−179.258	−	142.953i	−0.861817	−	0.687276i
$209$	−205.000	+	163.482i	−0.980861	+	0.782211i
$210$		0			0
$211$	281.518	−	98.5074i	1.33421	−	0.466860i	0.433449	−	0.901178i	$-0.357296\pi$
$211$	281.518	−	98.5074i	1.33421	−	0.466860i	0.900759	+	0.434318i	$0.143011\pi$
$212$	−39.5935	+	82.2168i	−0.186762	+	0.387815i
$213$		0			0
$214$	227.761	+	79.6969i	1.06430	+	0.372415i
$215$	4.93917	−	4.93917i	0.0229729	−	0.0229729i
$216$		0			0
$217$	−27.9540	+	248.098i	−0.128820	+	1.14331i
$218$	53.2448	+	5.99925i	0.244242	+	0.0275195i
$219$		0			0
$220$	1.85601	+	1.85601i	0.00843639	+	0.00843639i
$221$	−61.4349	+	175.571i	−0.277986	+	0.794438i
$222$		0			0
$223$	−61.9105	−	29.8145i	−0.277625	−	0.133697i	0.289890	−	0.957060i	$-0.406381\pi$
$223$	−61.9105	−	29.8145i	−0.277625	−	0.133697i	−0.567516	+	0.823363i	$0.692095\pi$
$224$	39.7461	+	113.588i	0.177438	+	0.507088i
$225$		0			0
$226$	102.183	+	128.133i	0.452136	+	0.566960i
$227$	−275.667	+	345.675i	−1.21439	+	1.52280i	−0.429625	+	0.903007i	$0.641354\pi$
$227$	−275.667	+	345.675i	−1.21439	+	1.52280i	−0.784766	+	0.619792i	$0.787217\pi$
$228$		0			0
$229$	−48.7472	−	77.5808i	−0.212870	−	0.338781i	0.723173	−	0.690667i	$-0.242683\pi$
$229$	−48.7472	−	77.5808i	−0.212870	−	0.338781i	−0.936043	+	0.351887i	$0.885540\pi$
$230$	0.831502	+	7.37979i	0.00361523	+	0.0320860i
$231$		0			0
$232$	220.169	−	122.495i	0.949006	−	0.527997i
$233$	115.705			0.496587			0.248294	−	0.968685i	$-0.420130\pi$
$233$	115.705			0.496587			0.248294	+	0.968685i	$0.420130\pi$
$234$		0			0
$235$	0.712412	−	0.447638i	0.00303154	−	0.00190484i
$236$	30.4745	−	6.95561i	0.129129	−	0.0294729i
$237$		0			0
$238$	−77.3247	+	61.6644i	−0.324893	+	0.259094i
$239$	39.0003	−	170.872i	0.163181	−	0.714944i	−0.825436	−	0.564495i	$-0.809071\pi$
$239$	39.0003	−	170.872i	0.163181	−	0.714944i	0.988618	−	0.150449i	$-0.0480719\pi$
$240$		0			0
$241$	1.62503	−	3.37442i	0.00674288	−	0.0140017i	−0.897570	−	0.440872i	$-0.854669\pi$
$241$	1.62503	−	3.37442i	0.00674288	−	0.0140017i	0.904313	+	0.426870i	$0.140384\pi$
$242$	68.4807	+	43.0293i	0.282978	+	0.177807i
$243$		0			0
$244$	3.04014	−	3.04014i	0.0124596	−	0.0124596i
$245$	−0.0320518	−	0.0665563i	−0.000130824	−	0.000271658i
$246$		0			0
$247$	−446.820	−	50.3446i	−1.80899	−	0.203824i
$248$	−280.355	+	135.012i	−1.13046	+	0.544402i
$249$		0			0
$250$	−5.08132	+	14.5216i	−0.0203253	+	0.0580863i
$251$	101.330	−	161.266i	0.403705	−	0.642493i	−0.581565	−	0.813500i	$-0.697559\pi$
$251$	101.330	−	161.266i	0.403705	−	0.642493i	0.985270	+	0.171007i	$0.0547022\pi$
$252$		0			0
$253$	−103.444	−	295.625i	−0.408868	−	1.16848i
$254$	167.649	+	38.2648i	0.660036	+	0.150649i
$255$		0			0
$256$	−122.148	+	153.168i	−0.477139	+	0.598313i
$257$	−31.9955	−	140.182i	−0.124496	−	0.545454i	−0.998253	−	0.0590900i	$-0.981180\pi$
$257$	−31.9955	−	140.182i	−0.124496	−	0.545454i	0.873756	−	0.486364i	$-0.161677\pi$
$258$		0			0
$259$	−19.0949	−	169.472i	−0.0737256	−	0.654333i
$260$			4.50117i			0.0173122i
$261$		0			0
$262$	−163.424			−0.623757
$263$	14.2134	−	1.60147i	0.0540434	−	0.00608923i	−0.0849014	−	0.996389i	$-0.527058\pi$
$263$	14.2134	−	1.60147i	0.0540434	−	0.00608923i	0.138945	+	0.990300i	$0.455629\pi$
$264$		0			0
$265$	−14.4632	+	3.30114i	−0.0545783	+	0.0124571i
$266$	−186.920	−	149.064i	−0.702707	−	0.560390i
$267$		0			0
$268$	1.64881	−	7.22389i	0.00615226	−	0.0269548i
$269$	−115.482	+	40.4089i	−0.429301	+	0.150219i	−0.536276	−	0.844043i	$-0.680169\pi$
$269$	−115.482	+	40.4089i	−0.429301	+	0.150219i	0.106975	+	0.994262i	$0.465884\pi$
$270$		0			0
$271$	364.109	+	228.785i	1.34358	+	0.844225i	0.995639	−	0.0932924i	$-0.0297391\pi$
$271$	364.109	+	228.785i	1.34358	+	0.844225i	0.347938	+	0.937518i	$0.386882\pi$
$272$	−81.1810	−	28.4065i	−0.298460	−	0.104435i
$273$		0			0
$274$	−135.623	−	281.624i	−0.494975	−	1.02783i
$275$	36.2994	−	322.166i	0.131998	−	1.17151i
$276$		0			0
$277$	363.232	−	174.923i	1.31131	−	0.631492i	0.358064	−	0.933697i	$-0.383437\pi$
$277$	363.232	−	174.923i	1.31131	−	0.631492i	0.953243	+	0.302205i	$0.0977227\pi$
$278$	224.381	+	224.381i	0.807127	+	0.807127i
$279$		0			0
$280$	−5.84097	+	9.29585i	−0.0208606	+	0.0331995i
$281$	−55.4249	−	26.6912i	−0.197242	−	0.0949865i	0.332656	−	0.943048i	$-0.392055\pi$
$281$	−55.4249	−	26.6912i	−0.197242	−	0.0949865i	−0.529897	+	0.848062i	$0.677770\pi$
$282$		0			0
$283$	172.772	+	39.4340i	0.610501	+	0.139343i	0.516583	−	0.856237i	$-0.327204\pi$
$283$	172.772	+	39.4340i	0.610501	+	0.139343i	0.0939179	+	0.995580i	$0.470061\pi$
$284$	−24.9503	−	31.2867i	−0.0878532	−	0.110164i
$285$		0			0
$286$	109.288	+	478.820i	0.382124	+	1.67420i
$287$	74.1042	+	117.936i	0.258203	+	0.410927i
$288$		0			0
$289$		−	219.224i		−	0.758561i
$290$	8.25905	+	3.39374i	0.0284795	+	0.0117026i
$291$		0			0
$292$	−115.436	+	13.0065i	−0.395329	+	0.0445429i
$293$	42.8502	−	26.9246i	0.146246	−	0.0918927i	−0.456921	−	0.889507i	$-0.651048\pi$
$293$	42.8502	−	26.9246i	0.146246	−	0.0918927i	0.603168	+	0.797614i	$0.293905\pi$
$294$		0			0
$295$	3.97301	+	3.16837i	0.0134678	+	0.0107402i
$296$	166.183	−	132.526i	0.561428	−	0.447724i
$297$		0			0
$298$	−184.852	+	64.6826i	−0.620310	+	0.217056i
$299$	233.038	−	483.909i	0.779392	−	1.61842i
$300$		0			0
$301$	−253.529	−	88.7138i	−0.842290	−	0.294730i
$302$	−12.2241	+	12.2241i	−0.0404771	+	0.0404771i
$303$		0			0
$304$	23.2785	−	206.602i	0.0765739	−	0.679612i
$305$	0.694563	+	0.0782585i	0.00227726	+	0.000256585i
$306$		0			0
$307$	91.5953	+	91.5953i	0.298356	+	0.298356i	0.840370	−	0.542014i	$-0.182338\pi$
$307$	91.5953	+	91.5953i	0.298356	+	0.298356i	−0.542014	+	0.840370i	$0.682338\pi$
$308$	33.3362	−	95.2695i	0.108235	−	0.309317i
$309$		0			0
$310$	−9.93573	−	4.78479i	−0.0320507	−	0.0154348i
$311$	−161.202	−	460.688i	−0.518333	−	1.48131i	−0.844269	−	0.535919i	$-0.819965\pi$
$311$	−161.202	−	460.688i	−0.518333	−	1.48131i	0.325936	−	0.945392i	$-0.394320\pi$
$312$		0			0
$313$	−331.292	−	415.427i	−1.05844	−	1.32724i	−0.942581	−	0.333979i	$-0.891609\pi$
$313$	−331.292	−	415.427i	−1.05844	−	1.32724i	−0.115861	−	0.993265i	$-0.536963\pi$
$314$	−81.2328	+	101.863i	−0.258703	+	0.324403i
$315$		0			0
$316$	50.5846	+	80.5050i	0.160078	+	0.254763i
$317$	−49.7527	−	441.567i	−0.156948	−	1.39296i	−0.787264	−	0.616617i	$-0.788503\pi$
$317$	−49.7527	−	441.567i	−0.156948	−	1.39296i	0.630315	−	0.776339i	$-0.282926\pi$
$318$		0			0
$319$	−371.428	−	62.0306i	−1.16435	−	0.194453i
$320$	−12.7814			−0.0399420
$321$		0			0
$322$	241.806	−	151.937i	0.750949	−	0.471853i
$323$	−164.443	+	37.5330i	−0.509112	+	0.116201i
$324$		0			0
$325$	434.674	−	346.641i	1.33746	−	1.06659i
$326$	−10.7543	+	47.1177i	−0.0329886	+	0.144533i
$327$		0			0
$328$	−75.3204	+	156.404i	−0.229635	+	0.476843i
$329$	−27.3951	−	17.2135i	−0.0832677	−	0.0523205i
$330$		0			0
$331$	−206.567	+	206.567i	−0.624068	+	0.624068i	−0.946569	−	0.322501i	$-0.895477\pi$
$331$	−206.567	+	206.567i	−0.624068	+	0.624068i	0.322501	+	0.946569i	$0.395477\pi$
$332$	−13.3428	−	27.7066i	−0.0401891	−	0.0834535i
$333$		0			0
$334$	71.3076	+	8.03443i	0.213496	+	0.0240552i
$335$	1.08530	−	0.522654i	0.00323971	−	0.00156016i
$336$		0			0
$337$	156.253	−	446.546i	0.463659	−	1.32506i	−0.440457	−	0.897774i	$-0.645184\pi$
$337$	156.253	−	446.546i	0.463659	−	1.32506i	0.904116	−	0.427287i	$-0.140531\pi$
$338$	−295.375	+	470.087i	−0.873891	+	1.39079i
$339$		0			0
$340$	0.557670	+	1.59373i	0.00164021	+	0.00468744i
$341$	453.421	+	103.490i	1.32968	+	0.303491i
$342$		0			0
$343$	−214.737	+	269.272i	−0.626055	+	0.785049i
$344$	−74.4930	−	326.375i	−0.216549	−	0.948765i
$345$		0			0
$346$	−24.1587	−	214.414i	−0.0698228	−	0.619694i
$347$			511.474i			1.47399i	0.675899	+	0.736994i	$0.263755\pi$
$347$			511.474i			1.47399i	−0.675899	+	0.736994i	$0.736245\pi$
$348$		0			0
$349$	−482.022			−1.38115			−0.690576	−	0.723260i	$-0.742643\pi$
$349$	−482.022			−1.38115			−0.690576	+	0.723260i	$0.742643\pi$
$350$	293.753	−	33.0980i	0.839293	−	0.0945657i
$351$		0			0
$352$	218.550	−	49.8827i	0.620881	−	0.141712i
$353$	−190.763	−	152.128i	−0.540404	−	0.430958i	0.314869	−	0.949135i	$-0.398039\pi$
$353$	−190.763	−	152.128i	−0.540404	−	0.430958i	−0.855273	+	0.518177i	$0.826611\pi$
$354$		0			0
$355$	1.44764	−	6.34252i	0.00407785	−	0.0178662i
$356$	28.4110	−	9.94145i	0.0798063	−	0.0279254i
$357$		0			0
$358$	209.779	+	131.813i	0.585975	+	0.368192i
$359$	−569.212	−	199.176i	−1.58555	−	0.554808i	−0.613522	−	0.789677i	$-0.710248\pi$
$359$	−569.212	−	199.176i	−1.58555	−	0.554808i	−0.972027	+	0.234870i	$0.924534\pi$
$360$		0			0
$361$	−20.2788	−	42.1094i	−0.0561741	−	0.116647i
$362$	41.3753	−	367.216i	0.114296	−	1.01441i
$363$		0			0
$364$	155.947	−	75.1001i	0.428426	−	0.206319i
$365$	−13.3539	−	13.3539i	−0.0365861	−	0.0365861i
$366$		0			0
$367$	137.681	−	219.118i	0.375153	−	0.597052i	−0.604777	−	0.796395i	$-0.706738\pi$
$367$	137.681	−	219.118i	0.375153	−	0.597052i	0.979930	+	0.199343i	$0.0638807\pi$
$368$	223.751	+	107.753i	0.608020	+	0.292807i
$369$		0			0
$370$	7.34407	+	1.67624i	0.0198488	+	0.00453037i
$371$	355.684	+	446.013i	0.958716	+	1.20219i
$372$		0			0
$373$	−135.641	−	594.282i	−0.363649	−	1.59325i	−0.743850	−	0.668347i	$-0.767002\pi$
$373$	−135.641	−	594.282i	−0.363649	−	1.59325i	0.380201	−	0.924904i	$-0.375855\pi$
$374$	98.0185	+	155.996i	0.262082	+	0.417101i
$375$		0			0
$376$		−	40.3241i		−	0.107245i
$377$	−375.174	−	525.611i	−0.995158	−	1.39419i
$378$		0			0
$379$	−160.764	+	18.1138i	−0.424180	+	0.0477936i	−0.321475	−	0.946918i	$-0.604179\pi$
$379$	−160.764	+	18.1138i	−0.424180	+	0.0477936i	−0.102706	+	0.994712i	$0.532750\pi$
$380$	−3.45602	+	2.17156i	−0.00909480	+	0.00571464i
$381$		0			0
$382$	264.440	+	210.884i	0.692251	+	0.552052i
$383$	272.105	−	216.997i	0.710458	−	0.566571i	−0.200189	−	0.979757i	$-0.564155\pi$
$383$	272.105	−	216.997i	0.710458	−	0.566571i	0.910647	+	0.413186i	$0.135584\pi$
$384$		0			0
$385$	15.4880	−	5.41950i	0.0402287	−	0.0140766i
$386$	−236.304	+	490.691i	−0.612187	+	1.27122i
$387$		0			0
$388$	7.57518	+	2.65067i	0.0195237	+	0.00683163i
$389$	−254.246	+	254.246i	−0.653588	+	0.653588i	−0.953855	−	0.300267i	$-0.902924\pi$
$389$	−254.246	+	254.246i	−0.653588	+	0.653588i	0.300267	+	0.953855i	$0.402924\pi$
$390$		0			0
$391$	22.5582	−	200.210i	0.0576936	−	0.512045i
$392$	−3.51816	−	0.396401i	−0.00897490	−	0.00101123i
$393$		0			0
$394$	68.1051	+	68.1051i	0.172856	+	0.172856i
$395$	−5.10510	+	14.5895i	−0.0129243	+	0.0369355i
$396$		0			0
$397$	110.601	+	53.2627i	0.278592	+	0.134163i	0.567963	−	0.823054i	$-0.307732\pi$
$397$	110.601	+	53.2627i	0.278592	+	0.134163i	−0.289371	+	0.957217i	$0.593446\pi$
$398$	−16.2006	−	46.2987i	−0.0407051	−	0.116328i
$399$		0			0
$400$	160.281	+	200.986i	0.400702	+	0.502465i
$401$	−158.554	+	198.821i	−0.395398	+	0.495813i	−0.939186	−	0.343410i	$-0.888418\pi$
$401$	−158.554	+	198.821i	−0.395398	+	0.495813i	0.543788	+	0.839223i	$0.316990\pi$
$402$		0			0
$403$	424.325	+	675.309i	1.05292	+	1.67570i
$404$	13.9329	+	123.658i	0.0344875	+	0.306085i
$405$		0			0
$406$	−20.2194	−	342.765i	−0.0498015	−	0.844248i
$407$	−317.690			−0.780565
$408$		0			0
$409$	−55.7403	+	35.0239i	−0.136284	+	0.0856331i	−0.598449	−	0.801161i	$-0.704216\pi$
$409$	−55.7403	+	35.0239i	−0.136284	+	0.0856331i	0.462164	+	0.886794i	$0.347073\pi$
$410$	−5.99796	+	1.36900i	−0.0146292	+	0.00333901i
$411$		0			0
$412$	−104.968	+	83.7092i	−0.254777	+	0.203178i
$413$	43.4830	−	190.511i	0.105286	−	0.461286i
$414$		0			0
$415$	2.16915	−	4.50428i	0.00522686	−	0.0108537i
$416$	325.501	+	204.526i	0.782454	+	0.491649i
$417$		0			0
$418$	−314.915	+	314.915i	−0.753386	+	0.753386i
$419$	226.933	+	471.231i	0.541606	+	1.12466i	0.974743	+	0.223329i	$0.0716923\pi$
$419$	226.933	+	471.231i	0.541606	+	1.12466i	−0.433137	+	0.901328i	$0.642593\pi$
$420$		0			0
$421$	−192.380	−	21.6760i	−0.456960	−	0.0514871i	−0.119515	−	0.992832i	$-0.538134\pi$
$421$	−192.380	−	21.6760i	−0.456960	−	0.0514871i	−0.337445	+	0.941345i	$0.609563\pi$
$422$	456.421	−	219.801i	1.08157	−	0.520855i
$423$		0			0
$424$	−234.828	+	671.100i	−0.553840	+	1.58278i
$425$	110.958	−	176.589i	0.261078	−	0.415503i
$426$		0			0
$427$	−8.87715	−	25.3694i	−0.0207896	−	0.0594132i
$428$	−154.442	−	35.2504i	−0.360846	−	0.0823608i
$429$		0			0
$430$	7.39717	−	9.27576i	0.0172027	−	0.0215715i
$431$	58.0221	+	254.212i	0.134622	+	0.589818i	0.996565	+	0.0828129i	$0.0263904\pi$
$431$	58.0221	+	254.212i	0.134622	+	0.589818i	−0.861943	+	0.507005i	$0.830752\pi$
$432$		0			0
$433$	6.90278	+	61.2639i	0.0159418	+	0.141487i	0.999162	−	0.0409369i	$-0.0130343\pi$
$433$	6.90278	+	61.2639i	0.0159418	+	0.141487i	−0.983220	+	0.182424i	$0.941606\pi$
$434$			424.064i			0.977106i
$435$		0			0
$436$	−35.1763			−0.0806795
$437$	483.975	−	54.5309i	1.10750	−	0.124785i
$438$		0			0
$439$	−173.225	+	39.5375i	−0.394590	+	0.0900626i	−0.415212	−	0.909725i	$-0.636293\pi$
$439$	−173.225	+	39.5375i	−0.394590	+	0.0900626i	0.0206218	+	0.999787i	$0.493435\pi$
$440$	15.9892	+	12.7509i	0.0363390	+	0.0289794i
$441$		0			0
$442$	−70.3028	+	308.017i	−0.159056	+	0.696871i
$443$	−632.160	+	221.202i	−1.42700	+	0.499328i	−0.929721	−	0.368265i	$-0.879952\pi$
$443$	−632.160	+	221.202i	−1.42700	+	0.499328i	−0.497276	+	0.867592i	$0.665666\pi$
$444$		0			0
$445$	4.14336	+	2.60345i	0.00931093	+	0.00585044i
$446$	−110.164	−	38.5481i	−0.247005	−	0.0864308i
$447$		0			0
$448$	213.252	+	442.823i	0.476010	+	0.988445i
$449$	−28.7774	+	255.406i	−0.0640921	+	0.568834i	0.920094	+	0.391697i	$0.128112\pi$
$449$	−28.7774	+	255.406i	−0.0640921	+	0.568834i	−0.984186	+	0.177136i	$0.943317\pi$
$450$		0			0
$451$	233.765	−	112.575i	0.518327	−	0.249613i
$452$	−76.0792	−	76.0792i	−0.168317	−	0.168317i
$453$		0			0
$454$	−399.541	+	635.865i	−0.880045	+	1.40058i
$455$	25.3524	+	12.2091i	0.0557196	+	0.0268331i
$456$		0			0
$457$	508.462	+	116.053i	1.11261	+	0.253946i	0.739043	−	0.673658i	$-0.235278\pi$
$457$	508.462	+	116.053i	1.11261	+	0.253946i	0.373566	+	0.927604i	$0.378135\pi$
$458$	−97.0308	−	121.673i	−0.211858	−	0.265661i
$459$		0			0
$460$	−1.08489	−	4.75323i	−0.00235846	−	0.0103331i
$461$	305.337	+	485.941i	0.662336	+	1.05410i	0.993859	+	0.110655i	$0.0352948\pi$
$461$	305.337	+	485.941i	0.662336	+	1.05410i	−0.331523	+	0.943447i	$0.607562\pi$
$462$		0			0
$463$			548.047i			1.18369i	0.806053	+	0.591843i	$0.201600\pi$
$463$			548.047i			1.18369i	−0.806053	+	0.591843i	$0.798400\pi$
$464$	243.033	−	173.474i	0.523779	−	0.373867i
$465$		0			0
$466$	195.290	−	22.0039i	0.419077	−	0.0472187i
$467$	696.323	−	437.528i	1.49105	−	0.936892i	0.493304	−	0.869857i	$-0.335789\pi$
$467$	696.323	−	437.528i	1.49105	−	0.936892i	0.997751	−	0.0670350i	$-0.0213539\pi$
$468$		0			0
$469$	−36.2156	−	28.8810i	−0.0772187	−	0.0615799i
$470$	1.11730	−	0.891017i	0.00237724	−	0.00189578i
$471$		0			0
$472$	229.880	−	80.4385i	0.487034	−	0.170420i
$473$	−217.095	+	450.801i	−0.458974	+	0.953069i
$474$		0			0
$475$	475.858	+	166.510i	1.00181	+	0.350547i
$476$	45.9116	−	45.9116i	0.0964530	−	0.0964530i
$477$		0			0
$478$	33.3308	−	295.819i	0.0697297	−	0.618868i
$479$	−272.204	−	30.6701i	−0.568277	−	0.0640294i	−0.176848	−	0.984238i	$-0.556590\pi$
$479$	−272.204	−	30.6701i	−0.568277	−	0.0640294i	−0.391428	+	0.920209i	$0.628019\pi$
$480$		0			0
$481$	−385.230	−	385.230i	−0.800894	−	0.800894i
$482$	2.10106	−	6.00448i	0.00435904	−	0.0124574i
$483$		0			0
$484$	−47.8375	−	23.0373i	−0.0988379	−	0.0475978i
$485$	0.430922	+	1.23150i	0.000888498	+	0.00253918i
$486$		0			0
$487$	77.1649	+	96.7617i	0.158449	+	0.198689i	0.854719	−	0.519091i	$-0.173730\pi$
$487$	77.1649	+	96.7617i	0.158449	+	0.198689i	−0.696269	+	0.717781i	$0.745158\pi$
$488$	20.8861	−	26.1903i	0.0427993	−	0.0536686i
$489$		0			0
$490$	−0.0667551	−	0.106240i	−0.000136235	−	0.000216817i
$491$	−11.6732	−	103.602i	−0.0237743	−	0.211002i	0.976209	−	0.216833i	$-0.0695727\pi$
$491$	−11.6732	−	103.602i	−0.0237743	−	0.211002i	−0.999983	+	0.00583045i	$0.998144\pi$
$492$		0			0
$493$	−197.958	−	139.621i	−0.401538	−	0.283207i
$494$	−763.731			−1.54601
$495$		0			0
$496$	−312.251	+	196.201i	−0.629539	+	0.395566i
$497$	−243.895	+	55.6675i	−0.490734	+	0.112007i
$498$		0			0
$499$	−276.912	+	220.830i	−0.554935	+	0.442546i	−0.860372	−	0.509666i	$-0.829769\pi$
$499$	−276.912	+	220.830i	−0.554935	+	0.442546i	0.305437	+	0.952212i	$0.401197\pi$
$500$	2.24750	−	9.84694i	0.00449500	−	0.0196939i
$501$		0			0
$502$	140.359	−	291.459i	0.279600	−	0.580596i
$503$	437.771	+	275.070i	0.870320	+	0.546858i	0.891553	−	0.452916i	$-0.149616\pi$
$503$	437.771	+	275.070i	0.870320	+	0.546858i	−0.0212333	+	0.999775i	$0.506759\pi$
$504$		0			0
$505$	−14.3051	+	14.3051i	−0.0283269	+	0.0283269i
$506$	−230.815	−	479.292i	−0.456155	−	0.947217i
$507$		0			0
$508$	−112.182	−	12.6399i	−0.220830	−	0.0248816i
$509$	−282.331	+	135.964i	−0.554679	+	0.267119i	−0.690155	−	0.723661i	$-0.742458\pi$
$509$	−282.331	+	135.964i	−0.554679	+	0.267119i	0.135477	+	0.990781i	$0.456743\pi$
$510$		0			0
$511$	−239.853	+	685.462i	−0.469381	+	1.34141i
$512$	−284.940	+	453.480i	−0.556524	+	0.885703i
$513$		0			0
$514$	−80.6617	−	230.518i	−0.156929	−	0.448479i
$515$	−21.2794	−	4.85688i	−0.0413192	−	0.00943083i
$516$		0			0
$517$	−37.5773	+	47.1204i	−0.0726833	+	0.0911420i
$518$	−64.4580	−	282.409i	−0.124436	−	0.545191i
$519$		0			0
$520$	3.92667	+	34.8502i	0.00755129	+	0.0670195i
$521$		−	903.060i		−	1.73332i	−0.498898	−	0.866661i	$-0.666262\pi$
$521$		−	903.060i		−	1.73332i	0.498898	−	0.866661i	$-0.333738\pi$
$522$		0			0
$523$	643.715			1.23081			0.615407	−	0.788210i	$-0.288992\pi$
$523$	643.715			1.23081			0.615407	+	0.788210i	$0.288992\pi$
$524$	106.613	−	12.0124i	0.203460	−	0.0229244i
$525$		0			0
$526$	23.6853	−	5.40601i	0.0450290	−	0.0102776i
$527$	233.908	+	186.535i	0.443847	+	0.353957i
$528$		0			0
$529$	−11.7403	+	51.4375i	−0.0221934	+	0.0972354i
$530$	−23.7837	+	8.32228i	−0.0448749	+	0.0157024i
$531$		0			0
$532$	132.898	+	83.5053i	0.249808	+	0.156965i
$533$	419.972	+	146.955i	0.787940	+	0.275712i
$534$		0			0
$535$	−11.1740	−	23.2031i	−0.0208860	−	0.0433702i
$536$	6.46394	−	57.3690i	0.0120596	−	0.107032i
$537$		0			0
$538$	−187.229	+	90.1649i	−0.348010	+	0.167593i
$539$	3.74172	+	3.74172i	0.00694196	+	0.00694196i
$540$		0			0
$541$	63.1537	−	100.509i	0.116735	−	0.185783i	−0.783246	−	0.621712i	$-0.786437\pi$
$541$	63.1537	−	100.509i	0.116735	−	0.185783i	0.899981	+	0.435929i	$0.143580\pi$
$542$	658.063	+	316.906i	1.21414	+	0.584698i
$543$		0			0
$544$	140.590	+	32.0887i	0.258437	+	0.0589865i
$545$	−3.56551	−	4.47101i	−0.00654222	−	0.00820368i
$546$		0			0
$547$	−141.842	−	621.450i	−0.259309	−	1.13611i	−0.921993	−	0.387206i	$-0.873440\pi$
$547$	−141.842	−	621.450i	−0.259309	−	1.13611i	0.662684	−	0.748899i	$-0.269417\pi$
$548$	109.177	+	173.754i	0.199228	+	0.317070i
$549$		0			0
$550$		−	550.664i		−	1.00121i
$551$	222.566	−	541.638i	0.403931	−	0.983010i
$552$		0			0
$553$	590.643	−	66.5495i	1.06807	−	0.120343i
$554$	579.808	−	364.317i	1.04658	−	0.657613i
$555$		0			0
$556$	−162.873	−	129.887i	−0.292936	−	0.233609i
$557$	−593.908	+	473.626i	−1.06626	+	0.850316i	−0.989180	−	0.146709i	$-0.953132\pi$
$557$	−593.908	+	473.626i	−1.06626	+	0.850316i	−0.0770829	+	0.997025i	$0.524561\pi$
$558$		0			0
$559$	−809.889	+	283.392i	−1.44882	+	0.506963i
$560$	−5.64527	+	11.7225i	−0.0100808	+	0.0209331i
$561$		0			0
$562$	−98.6237	−	34.5099i	−0.175487	−	0.0614055i
$563$	443.544	−	443.544i	0.787822	−	0.787822i	−0.193315	−	0.981137i	$-0.561924\pi$
$563$	443.544	−	443.544i	0.787822	−	0.787822i	0.981137	+	0.193315i	$0.0619240\pi$
$564$		0			0
$565$	1.95841	−	17.3814i	0.00346621	−	0.0307635i
$566$	299.109	+	33.7014i	0.528460	+	0.0595432i
$567$		0			0
$568$	−220.470	−	220.470i	−0.388152	−	0.388152i
$569$	−92.2750	+	263.707i	−0.162170	+	0.463456i	−0.996081	−	0.0884427i	$-0.971811\pi$
$569$	−92.2750	+	263.707i	−0.162170	+	0.463456i	0.833911	+	0.551899i	$0.186097\pi$
$570$		0			0
$571$	438.799	+	211.315i	0.768475	+	0.370078i	0.776686	−	0.629888i	$-0.216899\pi$
$571$	438.799	+	211.315i	0.768475	+	0.370078i	−0.00821061	+	0.999966i	$0.502614\pi$
$572$	−106.491	−	304.334i	−0.186173	−	0.532053i
$573$		0			0
$574$	147.503	+	184.963i	0.256975	+	0.322236i
$575$	−375.466	+	470.819i	−0.652984	+	0.818816i
$576$		0			0
$577$	150.219	+	239.072i	0.260345	+	0.414336i	0.951161	−	0.308694i	$-0.0998918\pi$
$577$	150.219	+	239.072i	0.260345	+	0.414336i	−0.690817	+	0.723030i	$0.742749\pi$
$578$	−41.6905	−	370.013i	−0.0721288	−	0.640161i
$579$		0			0
$580$	−5.63741	−	1.60690i	−0.00971966	−	0.00277052i
$581$	−192.246			−0.330888
$582$		0			0
$583$	899.792	−	565.377i	1.54338	−	0.969771i
$584$	−882.413	+	201.405i	−1.51098	+	0.344872i
$585$		0			0
$586$	67.2035	−	53.5930i	0.114682	−	0.0914556i
$587$	−36.9042	+	161.688i	−0.0628691	+	0.275448i	−0.996586	−	0.0825656i	$-0.973689\pi$
$587$	−36.9042	+	161.688i	−0.0628691	+	0.275448i	0.933717	+	0.358013i	$0.116546\pi$
$588$		0			0
$589$	−313.793	+	651.597i	−0.532755	+	1.10628i
$590$	7.30830	+	4.59211i	0.0123870	+	0.00778324i
$591$		0			0
$592$	178.124	−	178.124i	0.300885	−	0.300885i
$593$	−464.417	−	964.372i	−0.783165	−	1.62626i	−0.779610	−	0.626266i	$-0.784582\pi$
$593$	−464.417	−	964.372i	−0.783165	−	1.62626i	−0.00355571	−	0.999994i	$-0.501132\pi$
$594$		0			0
$595$	10.4892	+	1.18184i	0.0176288	+	0.00198629i
$596$	115.838	−	55.7844i	0.194358	−	0.0935980i
$597$		0			0
$598$	301.302	−	861.073i	0.503850	−	1.43992i
$599$	−19.6237	+	31.2310i	−0.0327608	+	0.0521385i	−0.862703	−	0.505711i	$-0.831230\pi$
$599$	−19.6237	+	31.2310i	−0.0327608	+	0.0521385i	0.829942	+	0.557849i	$0.188373\pi$
$600$		0			0
$601$	−165.010	−	471.571i	−0.274559	−	0.784645i	−0.995766	−	0.0919249i	$-0.970698\pi$
$601$	−165.010	−	471.571i	−0.274559	−	0.784645i	0.721207	−	0.692720i	$-0.243588\pi$
$602$	−444.785	−	101.519i	−0.738846	−	0.168637i
$603$		0			0
$604$	7.07610	−	8.87315i	0.0117154	−	0.0146906i
$605$	−1.92076	−	8.41538i	−0.00317480	−	0.0139097i
$606$		0			0
$607$	−18.5846	−	164.942i	−0.0306171	−	0.271734i	−0.999689	−	0.0249540i	$-0.992056\pi$
$607$	−18.5846	−	164.942i	−0.0306171	−	0.271734i	0.969072	−	0.246780i	$-0.0793725\pi$
$608$			348.593i			0.573344i
$609$		0			0
$610$	1.18719			0.00194621
$611$	−102.704	+	11.5720i	−0.168092	+	0.0189394i
$612$		0			0
$613$	−793.283	+	181.062i	−1.29410	+	0.295370i	−0.813497	−	0.581569i	$-0.802439\pi$
$613$	−793.283	+	181.062i	−1.29410	+	0.295370i	−0.480602	+	0.876939i	$0.659582\pi$
$614$	172.016	+	137.178i	0.280157	+	0.223418i
$615$		0			0
$616$	174.995	−	766.702i	0.284082	−	1.24465i
$617$	889.197	−	311.143i	1.44116	−	0.504284i	0.507254	−	0.861797i	$-0.330661\pi$
$617$	889.197	−	311.143i	1.44116	−	0.504284i	0.933908	+	0.357512i	$0.116375\pi$
$618$		0			0
$619$	−690.219	−	433.693i	−1.11505	−	0.700635i	−0.157108	−	0.987581i	$-0.550217\pi$
$619$	−690.219	−	433.693i	−1.11505	−	0.700635i	−0.957947	+	0.286946i	$0.907360\pi$
$620$	6.83347	+	2.39113i	0.0110217	+	0.00385667i
$621$		0			0
$622$	−359.691	−	746.906i	−0.578281	−	1.20081i
$623$	21.0685	−	186.988i	0.0338177	−	0.300141i
$624$		0			0
$625$	−560.886	+	270.108i	−0.897418	+	0.432174i
$626$	−638.168	−	638.168i	−1.01944	−	1.01944i
$627$		0			0
$628$	45.5064	−	72.4231i	0.0724625	−	0.115323i
$629$	−184.126	−	88.6705i	−0.292728	−	0.140971i
$630$		0			0
$631$	430.841	+	98.3366i	0.682791	+	0.155842i	0.549827	−	0.835278i	$-0.314694\pi$
$631$	430.841	+	98.3366i	0.682791	+	0.155842i	0.132963	+	0.991121i	$0.457551\pi$
$632$	461.879	+	579.178i	0.730822	+	0.916421i
$633$		0			0
$634$	−167.948	−	735.828i	−0.264902	−	1.16061i
$635$	−9.76432	−	15.5398i	−0.0153769	−	0.0244722i
$636$		0			0
$637$			9.07439i			0.0142455i
$638$	−638.704	−	34.0616i	−1.00110	−	0.0533881i
$639$		0			0
$640$	−9.13367	+	1.02912i	−0.0142714	+	0.00160800i
$641$	−439.716	+	276.292i	−0.685984	+	0.431032i	−0.829419	−	0.558628i	$-0.811328\pi$
$641$	−439.716	+	276.292i	−0.685984	+	0.431032i	0.143435	+	0.989660i	$0.454185\pi$
$642$		0			0
$643$	886.679	+	707.103i	1.37897	+	1.09969i	0.983439	+	0.181241i	$0.0580115\pi$
$643$	886.679	+	707.103i	1.37897	+	1.09969i	0.395533	+	0.918452i	$0.370560\pi$
$644$	−146.579	+	116.893i	−0.227607	+	0.181510i
$645$		0			0
$646$	−270.414	+	94.6219i	−0.418597	+	0.146474i
$647$	64.3196	−	133.561i	0.0994120	−	0.206431i	−0.845331	−	0.534243i	$-0.820597\pi$
$647$	64.3196	−	133.561i	0.0994120	−	0.206431i	0.944743	+	0.327812i	$0.106311\pi$
$648$		0			0
$649$	−343.583	−	120.225i	−0.529404	−	0.185246i
$650$	667.734	−	667.734i	1.02728	−	1.02728i
$651$		0			0
$652$	3.55242	−	31.5286i	0.00544850	−	0.0483568i
$653$	828.414	+	93.3398i	1.26863	+	0.142940i	0.720500	−	0.693455i	$-0.243912\pi$
$653$	828.414	+	93.3398i	1.26863	+	0.142940i	0.548128	+	0.836395i	$0.315341\pi$
$654$		0			0
$655$	12.3332	+	12.3332i	0.0188294	+	0.0188294i
$656$	−67.9493	+	194.188i	−0.103581	+	0.296018i
$657$		0			0
$658$	−49.5117	−	23.8436i	−0.0752458	−	0.0362365i
$659$	−30.0943	−	86.0046i	−0.0456666	−	0.130508i	0.918792	−	0.394743i	$-0.129166\pi$
$659$	−30.0943	−	86.0046i	−0.0456666	−	0.130508i	−0.964458	+	0.264235i	$0.914881\pi$
$660$		0			0
$661$	−17.7926	−	22.3113i	−0.0269177	−	0.0337538i	0.768190	−	0.640221i	$-0.221157\pi$
$661$	−17.7926	−	22.3113i	−0.0269177	−	0.0337538i	−0.795108	+	0.606468i	$0.792586\pi$
$662$	−309.366	+	387.933i	−0.467320	+	0.586001i
$663$		0			0
$664$	−127.476	−	202.877i	−0.191982	−	0.305538i
$665$	2.85692	+	25.3559i	0.00429613	+	0.0381292i
$666$		0			0
$667$	522.868	+	464.617i	0.783910	+	0.696578i
$668$	−47.1095			−0.0705231
$669$		0			0
$670$	1.73241	−	1.08855i	0.00258569	−	0.00162470i
$671$	−48.8125	+	11.1411i	−0.0727458	+	0.0166038i
$672$		0			0
$673$	−459.480	+	366.423i	−0.682734	+	0.544463i	−0.902286	−	0.431138i	$-0.858112\pi$
$673$	−459.480	+	366.423i	−0.682734	+	0.544463i	0.219551	+	0.975601i	$0.429541\pi$
$674$	178.808	−	783.408i	0.265293	−	1.16233i
$675$		0			0
$676$	158.140	−	328.382i	0.233935	−	0.485772i
$677$	104.008	+	65.3523i	0.153630	+	0.0965322i	0.606653	−	0.794967i	$-0.292512\pi$
$677$	104.008	+	65.3523i	0.153630	+	0.0965322i	−0.453023	+	0.891499i	$0.649654\pi$
$678$		0			0
$679$	35.4767	−	35.4767i	0.0522485	−	0.0522485i
$680$	5.70806	+	11.8529i	0.00839420	+	0.0174307i
$681$		0			0
$682$	784.978	+	88.4458i	1.15099	+	0.129686i
$683$	−909.152	+	437.825i	−1.33112	+	0.641032i	−0.958004	−	0.286755i	$-0.907423\pi$
$683$	−909.152	+	437.825i	−1.33112	+	0.641032i	−0.373112	+	0.927786i	$0.621709\pi$
$684$		0			0
$685$	−11.0183	+	31.4886i	−0.0160852	+	0.0459688i
$686$	−311.231	+	495.322i	−0.453690	+	0.722043i
$687$		0			0
$688$	−131.036	−	374.479i	−0.190459	−	0.544301i
$689$	1776.66	+	405.511i	2.57861	+	0.588550i
$690$		0			0
$691$	−82.1865	+	103.059i	−0.118938	+	0.149144i	−0.837736	−	0.546075i	$-0.816121\pi$
$691$	−82.1865	+	103.059i	−0.118938	+	0.149144i	0.718798	+	0.695219i	$0.244693\pi$
$692$	31.5208	+	138.102i	0.0455503	+	0.199569i
$693$		0			0
$694$	97.2684	+	863.280i	0.140156	+	1.24392i
$695$		−	33.8670i		−	0.0487296i
$696$		0			0
$697$	166.906			0.239464
$698$	−813.571	+	91.6674i	−1.16557	+	0.131329i
$699$		0			0
$700$	−189.202	+	43.1842i	−0.270289	+	0.0616918i
$701$	−205.200	−	163.642i	−0.292725	−	0.233441i	0.466104	−	0.884730i	$-0.345657\pi$
$701$	−205.200	−	163.642i	−0.292725	−	0.233441i	−0.758830	+	0.651289i	$0.774229\pi$
$702$		0			0
$703$	109.930	−	481.633i	0.156372	−	0.685111i
$704$	864.181	−	302.390i	1.22753	−	0.429531i
$705$		0			0
$706$	−350.905	−	220.488i	−0.497033	−	0.312307i
$707$	734.285	+	256.937i	1.03859	+	0.363419i
$708$		0			0
$709$	242.106	+	502.738i	0.341475	+	0.709081i	0.999017	−	0.0443379i	$-0.0141178\pi$
$709$	242.106	+	502.738i	0.341475	+	0.709081i	−0.657541	+	0.753418i	$0.728404\pi$
$710$	1.23719	−	10.9804i	0.00174252	−	0.0154653i
$711$		0			0
$712$	211.299	−	101.756i	0.296768	−	0.142916i
$713$	−610.852	−	610.852i	−0.856735	−	0.856735i
$714$		0			0
$715$	27.8877	−	44.3830i	0.0390038	−	0.0620742i
$716$	−146.542	−	70.5710i	−0.204668	−	0.0985628i
$717$		0			0
$718$	−998.611	−	227.926i	−1.39082	−	0.317446i
$719$	−173.291	−	217.300i	−0.241017	−	0.302225i	0.646581	−	0.762846i	$-0.276198\pi$
$719$	−173.291	−	217.300i	−0.241017	−	0.302225i	−0.887597	+	0.460620i	$0.847627\pi$
$720$		0			0
$721$	186.766	+	818.277i	0.259038	+	1.13492i
$722$	−42.2353	−	67.2171i	−0.0584976	−	0.0930984i
$723$		0			0
$724$			242.602i			0.335085i
$725$	278.967	+	668.148i	0.384782	+	0.921583i
$726$		0			0
$727$	−868.909	+	97.9026i	−1.19520	+	0.134667i	−0.687055	−	0.726606i	$-0.741097\pi$
$727$	−868.909	+	97.9026i	−1.19520	+	0.134667i	−0.508144	+	0.861272i	$0.669668\pi$
$728$	1141.90	−	717.502i	1.56854	−	0.985580i
$729$		0			0
$730$	−25.0787	−	19.9996i	−0.0343543	−	0.0273967i
$731$	−251.647	+	200.681i	−0.344250	+	0.274530i
$732$		0			0
$733$	121.421	−	42.4869i	0.165649	−	0.0579631i	−0.246181	−	0.969224i	$-0.579176\pi$
$733$	121.421	−	42.4869i	0.165649	−	0.0579631i	0.411830	+	0.911261i	$0.364890\pi$
$734$	190.712	−	396.017i	0.259825	−	0.539533i
$735$		0			0
$736$	−393.024	−	137.525i	−0.534000	−	0.186855i
$737$	−61.0145	+	61.0145i	−0.0827876	+	0.0827876i
$738$		0			0
$739$	61.1890	−	543.068i	0.0827998	−	0.734868i	−0.881886	−	0.471463i	$-0.843726\pi$
$739$	61.1890	−	543.068i	0.0827998	−	0.734868i	0.964685	−	0.263405i	$-0.0848455\pi$
$740$	−4.91426	−	0.553704i	−0.00664089	−	0.000748249i
$741$		0			0
$742$	685.153	+	685.153i	0.923387	+	0.923387i
$743$	−73.3592	+	209.649i	−0.0987338	+	0.282165i	−0.982647	−	0.185486i	$-0.940614\pi$
$743$	−73.3592	+	209.649i	−0.0987338	+	0.282165i	0.883913	+	0.467651i	$0.154900\pi$
$744$		0			0
$745$	18.8318	+	9.06891i	0.0252776	+	0.0121730i
$746$	−341.955	−	977.252i	−0.458385	−	1.30999i
$747$		0			0
$748$	−75.4107	−	94.5620i	−0.100816	−	0.126420i
$749$	−617.456	+	774.266i	−0.824374	+	1.03373i
$750$		0			0
$751$	−4.56022	−	7.25755i	−0.00607220	−	0.00966385i	0.843674	−	0.536855i	$-0.180388\pi$
$751$	−4.56022	−	7.25755i	−0.00607220	−	0.00966385i	−0.849747	+	0.527191i	$0.823245\pi$
$752$	−5.35069	−	47.4887i	−0.00711528	−	0.0631498i
$753$		0			0
$754$	−733.187	−	815.793i	−0.972397	−	1.08195i
$755$	1.84504			0.00244377
$756$		0			0
$757$	642.972	−	404.006i	0.849368	−	0.533693i	−0.0355886	−	0.999367i	$-0.511331\pi$
$757$	642.972	−	404.006i	0.849368	−	0.533693i	0.884957	+	0.465673i	$0.154188\pi$
$758$	−267.898	+	61.1460i	−0.353427	+	0.0806675i
$759$		0			0
$760$	−24.8637	+	19.8282i	−0.0327154	+	0.0260897i
$761$	61.0011	−	267.263i	0.0801592	−	0.351200i	−0.918904	−	0.394482i	$-0.870924\pi$
$761$	61.0011	−	267.263i	0.0801592	−	0.351200i	0.999063	+	0.0432815i	$0.0137812\pi$
$762$		0			0
$763$	−95.4128	+	198.127i	−0.125050	+	0.259668i
$764$	−188.013	−	118.137i	−0.246091	−	0.154629i
$765$		0			0
$766$	418.001	−	418.001i	0.545693	−	0.545693i
$767$	−270.844	−	562.413i	−0.353121	−	0.733263i
$768$		0			0
$769$	1376.20	+	155.060i	1.78959	+	0.201639i	0.943494	−	0.331390i	$-0.107518\pi$
$769$	1376.20	+	155.060i	1.78959	+	0.201639i	0.846097	+	0.533028i	$0.178946\pi$
$770$	25.1105	−	12.0926i	0.0326111	−	0.0157047i
$771$		0			0
$772$	118.090	−	337.481i	0.152966	−	0.437152i
$773$	−566.278	+	901.226i	−0.732572	+	1.16588i	0.247817	+	0.968807i	$0.420287\pi$
$773$	−566.278	+	901.226i	−0.732572	+	1.16588i	−0.980389	+	0.197075i	$0.936856\pi$
$774$		0			0
$775$	−295.344	−	844.046i	−0.381089	−	1.08909i
$776$	60.9629	+	13.9144i	0.0785604	+	0.0179309i
$777$		0			0
$778$	−380.773	+	477.474i	−0.489425	+	0.613720i
$779$	89.7804	+	393.354i	0.115251	+	0.504947i
$780$		0			0
$781$	52.1767	+	463.081i	0.0668075	+	0.592933i
$782$		−	342.210i		−	0.437608i
$783$		0			0
$784$	−4.19585			−0.00535184
$785$	13.8178	−	1.55689i	0.0176023	−	0.00198330i
$786$		0			0
$787$	−526.723	+	120.221i	−0.669280	+	0.152759i	−0.543642	−	0.839317i	$-0.682955\pi$
$787$	−526.723	+	120.221i	−0.669280	+	0.152759i	−0.125638	+	0.992076i	$0.540098\pi$
$788$	−49.4357	−	39.4237i	−0.0627357	−	0.0500300i
$789$		0			0
$790$	−5.84200	+	25.5955i	−0.00739494	+	0.0323994i
$791$	−634.867	+	222.150i	−0.802614	+	0.280847i
$792$		0			0
$793$	−72.6996	−	45.6802i	−0.0916766	−	0.0576042i
$794$	196.805	+	68.8650i	0.247865	+	0.0867318i
$795$		0			0
$796$	13.9720	+	29.0131i	0.0175527	+	0.0364486i
$797$	98.7882	−	876.770i	0.123950	−	1.10009i	−0.765621	−	0.643292i	$-0.777568\pi$
$797$	98.7882	−	876.770i	0.123950	−	1.10009i	0.889571	−	0.456796i	$-0.151003\pi$
$798$		0			0
$799$	−34.9307	+	16.8218i	−0.0437181	+	0.0210535i
$800$	−304.777	−	304.777i	−0.380971	−	0.380971i
$801$		0			0
$802$	−229.803	+	365.729i	−0.286537	+	0.456021i
$803$	1218.82	+	586.954i	1.51784	+	0.730951i
$804$		0			0
$805$	−29.7148	−	6.78220i	−0.0369128	−	0.00842510i
$806$	844.613	+	1059.11i	1.04791	+	1.31403i
$807$		0			0
$808$	215.751	+	945.265i	0.267018	+	1.16988i
$809$	466.005	+	741.642i	0.576026	+	0.916740i	0.999939	+	0.0110369i	$0.00351322\pi$
$809$	466.005	+	741.642i	0.576026	+	0.916740i	−0.423913	+	0.905703i	$0.639344\pi$
$810$		0			0
$811$			1115.45i			1.37540i	0.725996	+	0.687699i	$0.241379\pi$
$811$			1115.45i			1.37540i	−0.725996	+	0.687699i	$0.758621\pi$
$812$	38.3852	+	222.123i	0.0472725	+	0.273551i
$813$		0			0
$814$	−536.206	+	60.4159i	−0.658730	+	0.0742211i
$815$	4.36746	−	2.74425i	0.00535884	−	0.00336718i
$816$		0			0
$817$	−608.316	−	485.116i	−0.744573	−	0.593777i
$818$	−87.4194	+	69.7147i	−0.106870	+	0.0852258i
$819$		0			0
$820$	3.81226	−	1.33397i	0.00464910	−	0.00162679i
$821$	−608.619	+	1263.81i	−0.741314	+	1.53936i	0.0976818	+	0.995218i	$0.468857\pi$
$821$	−608.619	+	1263.81i	−0.741314	+	1.53936i	−0.838996	+	0.544137i	$0.816857\pi$
$822$		0			0
$823$	115.112	+	40.2794i	0.139869	+	0.0489421i	0.399306	−	0.916818i	$-0.369251\pi$
$823$	115.112	+	40.2794i	0.139869	+	0.0489421i	−0.259437	+	0.965760i	$0.583537\pi$
$824$	−739.686	+	739.686i	−0.897677	+	0.897677i
$825$		0			0
$826$	37.1618	−	329.820i	0.0449900	−	0.399297i
$827$	−74.2024	−	8.36060i	−0.0897248	−	0.0101096i	0.0669879	−	0.997754i	$-0.478661\pi$
$827$	−74.2024	−	8.36060i	−0.0897248	−	0.0101096i	−0.156713	+	0.987644i	$0.550090\pi$
$828$		0			0
$829$	−67.2027	−	67.2027i	−0.0810648	−	0.0810648i	0.665412	−	0.746477i	$-0.268256\pi$
$829$	−67.2027	−	67.2027i	−0.0810648	−	0.0810648i	−0.746477	+	0.665412i	$0.768256\pi$
$830$	2.80456	−	8.01496i	0.00337898	−	0.00965658i
$831$		0			0
$832$	1414.58	+	681.226i	1.70022	+	0.818781i
$833$	1.12427	+	3.21297i	0.00134966	+	0.00385711i
$834$		0			0
$835$	−4.77507	−	5.98775i	−0.00571865	−	0.00717096i
$836$	182.293	−	228.589i	0.218054	−	0.273431i
$837$		0			0
$838$	472.639	+	752.201i	0.564009	+	0.897615i
$839$	−130.828	−	1161.13i	−0.155933	−	1.38394i	−0.791156	−	0.611614i	$-0.790520\pi$
$839$	−130.828	−	1161.13i	−0.155933	−	1.38394i	0.635223	−	0.772329i	$-0.280908\pi$
$840$		0			0
$841$	792.226	−	282.239i	0.942005	−	0.335599i
$842$	−328.827			−0.390531
$843$		0			0
$844$	−281.599	+	176.940i	−0.333648	+	0.209645i
$845$	57.7676	−	13.1851i	0.0683640	−	0.0156036i
$846$		0			0
$847$	−259.511	+	206.953i	−0.306388	+	0.244337i
$848$	−187.501	+	821.497i	−0.221110	+	0.968747i
$849$		0			0
$850$	153.696	−	319.153i	0.180819	−	0.375474i
$851$	499.652	+	313.952i	0.587135	+	0.368921i
$852$		0			0
$853$	898.967	−	898.967i	1.05389	−	1.05389i	0.0554262	−	0.998463i	$-0.482348\pi$
$853$	898.967	−	898.967i	1.05389	−	1.05389i	0.998463	−	0.0554262i	$-0.0176517\pi$
$854$	−19.8077	−	41.1311i	−0.0231940	−	0.0481629i
$855$		0			0
$856$	−1226.51	−	138.195i	−1.43284	−	0.161443i
$857$	1206.82	−	581.175i	1.40819	−	0.678151i	0.433389	−	0.901207i	$-0.357318\pi$
$857$	1206.82	−	581.175i	1.40819	−	0.678151i	0.974806	+	0.223056i	$0.0716033\pi$
$858$		0			0
$859$	50.0032	−	142.901i	0.0582109	−	0.166357i	−0.911106	−	0.412173i	$-0.864770\pi$
$859$	50.0032	−	142.901i	0.0582109	−	0.166357i	0.969317	+	0.245816i	$0.0790557\pi$
$860$	−4.14388	+	6.59495i	−0.00481847	+	0.00766855i
$861$		0			0
$862$	146.276	+	418.032i	0.169693	+	0.484955i
$863$	21.6830	+	4.94901i	0.0251252	+	0.00573466i	0.235065	−	0.971980i	$-0.424470\pi$
$863$	21.6830	+	4.94901i	0.0251252	+	0.00573466i	−0.209940	+	0.977714i	$0.567327\pi$
$864$		0			0
$865$	−14.3581	+	18.0045i	−0.0165990	+	0.0208145i
$866$	23.3014	+	102.090i	0.0269070	+	0.117887i
$867$		0			0
$868$	−31.1706	−	276.646i	−0.0359108	−	0.318717i
$869$		−	1107.21i		−	1.27412i
$870$		0			0
$871$	−147.972			−0.169887
$872$	−272.351	+	30.6866i	−0.312329	+	0.0351910i
$873$		0			0
$874$	806.497	−	184.078i	0.922766	−	0.210615i
$875$	−49.3657	−	39.3678i	−0.0564180	−	0.0449918i
$876$		0			0
$877$	217.881	−	954.597i	0.248439	−	1.08848i	−0.684661	−	0.728862i	$-0.740050\pi$
$877$	217.881	−	954.597i	0.248439	−	1.08848i	0.933099	−	0.359619i	$-0.117093\pi$
$878$	−284.855	+	99.6752i	−0.324437	+	0.113525i
$879$		0			0
$880$	20.5220	+	12.8948i	0.0233204	+	0.0146532i
$881$	−1438.74	−	503.438i	−1.63308	−	0.571439i	−0.650864	−	0.759194i	$-0.725593\pi$
$881$	−1438.74	−	503.438i	−1.63308	−	0.571439i	−0.982216	+	0.187755i	$0.939879\pi$
$882$		0			0
$883$	82.4632	+	171.237i	0.0933898	+	0.193926i	0.942431	−	0.334401i	$-0.108534\pi$
$883$	82.4632	+	171.237i	0.0933898	+	0.193926i	−0.849041	+	0.528327i	$0.822820\pi$
$884$	23.2228	−	206.108i	0.0262702	−	0.233154i
$885$		0			0
$886$	−1024.91	+	493.571i	−1.15678	+	0.557078i
$887$	341.806	+	341.806i	0.385350	+	0.385350i	0.873025	−	0.487675i	$-0.162155\pi$
$887$	341.806	+	341.806i	0.385350	+	0.385350i	−0.487675	+	0.873025i	$0.662155\pi$
$888$		0			0
$889$	−375.477	+	597.568i	−0.422359	+	0.672180i
$890$	7.48839	+	3.60622i	0.00841393	+	0.00405193i
$891$		0			0
$892$	74.7012	+	17.0501i	0.0837458	+	0.0191144i
$893$	−58.4340	−	73.2739i	−0.0654356	−	0.0820537i
$894$		0			0
$895$	−5.88391	−	25.7791i	−0.00657420	−	0.0288035i
$896$	188.046	+	299.273i	0.209873	+	0.334010i
$897$		0			0
$898$			436.555i			0.486141i
$899$	−997.259	+	290.355i	−1.10930	+	0.322975i
$900$		0			0
$901$	679.302	−	76.5390i	0.753942	−	0.0849489i
$902$	373.147	−	234.464i	0.413689	−	0.259938i
$903$		0			0
$904$	−655.409	−	522.671i	−0.725010	−	0.578176i
$905$	−30.8354	+	24.5904i	−0.0340723	+	0.0271717i
$906$		0			0
$907$	114.416	−	40.0359i	0.126148	−	0.0441410i	−0.266467	−	0.963844i	$-0.585856\pi$
$907$	114.416	−	40.0359i	0.126148	−	0.0441410i	0.392615	+	0.919703i	$0.371571\pi$
$908$	213.909	−	444.187i	0.235583	−	0.489193i
$909$		0			0
$910$	45.1124	+	15.7855i	0.0495740	+	0.0173467i
$911$	743.327	−	743.327i	0.815946	−	0.815946i	−0.169572	−	0.985518i	$-0.554238\pi$
$911$	743.327	−	743.327i	0.815946	−	0.815946i	0.985518	+	0.169572i	$0.0542384\pi$
$912$		0			0
$913$	−40.0961	+	355.863i	−0.0439169	+	0.389773i
$914$	880.268	+	99.1824i	0.963094	+	0.108515i
$915$		0			0
$916$	72.2434	+	72.2434i	0.0788683	+	0.0788683i
$917$	221.521	−	633.070i	0.241571	−	0.690371i
$918$		0			0
$919$	−547.562	−	263.692i	−0.595824	−	0.286934i	0.111566	−	0.993757i	$-0.464413\pi$
$919$	−547.562	−	263.692i	−0.595824	−	0.286934i	−0.707390	+	0.706823i	$0.750128\pi$
$920$	−12.5463	−	35.8553i	−0.0136373	−	0.0389731i
$921$		0			0
$922$	607.770	+	762.119i	0.659186	+	0.826593i
$923$	−498.261	+	624.800i	−0.539828	+	0.676923i
$924$		0			0
$925$	324.982	+	517.207i	0.351332	+	0.559142i
$926$	104.224	+	925.009i	0.112552	+	0.998930i
$927$		0			0
$928$	−372.357	+	334.652i	−0.401246	+	0.360617i
$929$	−1245.42			−1.34060			−0.670301	−	0.742090i	$-0.733835\pi$
$929$	−1245.42			−1.34060			−0.670301	+	0.742090i	$0.733835\pi$
$930$		0			0
$931$	−6.96736	+	4.37788i	−0.00748374	+	0.00470235i
$932$	−125.784	+	28.7093i	−0.134961	+	0.0308040i
$933$		0			0
$934$	1092.07	−	870.895i	1.16924	−	0.932436i
$935$	4.37539	−	19.1698i	0.00467956	−	0.0205025i
$936$		0			0
$937$	−174.644	+	362.653i	−0.186387	+	0.387036i	−0.973134	−	0.230239i	$-0.926049\pi$
$937$	−174.644	+	362.653i	−0.186387	+	0.387036i	0.786747	+	0.617275i	$0.211763\pi$
$938$	−66.6181	−	41.8589i	−0.0710214	−	0.0446257i
$939$		0			0
$940$	−0.663399	+	0.663399i	−0.000705744	+	0.000705744i
$941$	−238.487	−	495.224i	−0.253440	−	0.526274i	0.734966	−	0.678103i	$-0.237198\pi$
$941$	−238.487	−	495.224i	−0.253440	−	0.526274i	−0.988407	+	0.151829i	$0.951484\pi$
$942$		0			0
$943$	−478.909	−	53.9601i	−0.507857	−	0.0572217i
$944$	260.050	−	125.234i	0.275477	−	0.132663i
$945$		0			0
$946$	−280.688	+	802.161i	−0.296711	+	0.847951i
$947$	592.004	−	942.169i	0.625136	−	0.994898i	−0.372623	−	0.927983i	$-0.621541\pi$
$947$	592.004	−	942.169i	0.625136	−	0.994898i	0.997759	−	0.0669152i	$-0.0213157\pi$
$948$		0			0
$949$	766.202	+	2189.68i	0.807378	+	2.30735i
$950$	834.833	+	190.545i	0.878772	+	0.200574i
$951$		0			0
$952$	315.417	−	395.521i	0.331321	−	0.415463i
$953$	58.4095	+	255.909i	0.0612902	+	0.268530i	0.996283	−	0.0861357i	$-0.0274519\pi$
$953$	58.4095	+	255.909i	0.0612902	+	0.268530i	−0.934993	+	0.354666i	$0.884595\pi$
$954$		0			0
$955$	−4.04175	−	35.8715i	−0.00423220	−	0.0375618i
$956$			195.433i			0.204428i
$957$		0			0
$958$	−465.267			−0.485665
$959$	1274.79	−	143.634i	1.32929	−	0.149775i
$960$		0			0
$961$	313.728	−	71.6064i	0.326460	−	0.0745124i
$962$	−723.463	−	576.942i	−0.752040	−	0.599732i
$963$		0			0
$964$	−0.929311	+	4.07158i	−0.000964015	+	0.00422363i
$965$	54.8646	−	19.1979i	0.0568545	−	0.0198942i
$966$		0			0
$967$	302.551	+	190.106i	0.312876	+	0.196593i	0.679311	−	0.733851i	$-0.262279\pi$
$967$	302.551	+	190.106i	0.312876	+	0.196593i	−0.366435	+	0.930444i	$0.619422\pi$
$968$	−390.477	−	136.634i	−0.403385	−	0.141151i
$969$		0			0
$970$	0.961520	+	1.99662i	0.000991258	+	0.00205837i
$971$	−36.4644	+	323.630i	−0.0375534	+	0.333296i	0.960862	+	0.277027i	$0.0893490\pi$
$971$	−36.4644	+	323.630i	−0.0375534	+	0.333296i	−0.998416	+	0.0562690i	$0.982080\pi$
$972$		0			0
$973$	−1173.35	+	565.057i	−1.20591	+	0.580737i
$974$	148.643	+	148.643i	0.152610	+	0.152610i
$975$		0			0
$976$	21.1217	−	33.6150i	0.0216411	−	0.0344416i
$977$	1535.16	+	739.292i	1.57130	+	0.756696i	0.998034	−	0.0626765i	$-0.0199636\pi$
$977$	1535.16	+	739.292i	1.57130	+	0.756696i	0.573262	+	0.819372i	$0.305678\pi$
$978$		0			0
$979$	−341.736	−	77.9990i	−0.349066	−	0.0796721i
$980$	0.0513581	+	0.0644011i	5.24063e−5	+	6.57154e-5i
$981$		0			0
$982$	−39.4046	−	172.643i	−0.0401269	−	0.175807i
$983$	−252.311	−	401.550i	−0.256674	−	0.408494i	0.693384	−	0.720569i	$-0.256119\pi$
$983$	−252.311	−	401.550i	−0.256674	−	0.408494i	−0.950058	+	0.312074i	$0.898976\pi$
$984$		0			0
$985$		−	10.2795i		−	0.0104360i
$986$	−360.672	−	198.010i	−0.365793	−	0.200821i
$987$		0			0
$988$	498.235	−	56.1376i	0.504286	−	0.0568194i
$989$	786.936	−	494.465i	0.795689	−	0.499964i
$990$		0			0
$991$	−831.950	−	663.458i	−0.839505	−	0.669483i	0.106258	−	0.994339i	$-0.466113\pi$
$991$	−831.950	−	663.458i	−0.839505	−	0.669483i	−0.945764	+	0.324855i	$0.894684\pi$
$992$	483.416	−	385.511i	0.487314	−	0.388620i
$993$		0			0
$994$	−401.067	+	140.339i	−0.403488	+	0.141186i
$995$	−2.27143	+	4.71668i	−0.00228285	+	0.00474038i
$996$		0			0
$997$	−1385.13	−	484.679i	−1.38930	−	0.486138i	−0.471040	−	0.882112i	$-0.656121\pi$
$997$	−1385.13	−	484.679i	−1.38930	−	0.486138i	−0.918262	+	0.395974i	$0.870407\pi$
$998$	−425.385	+	425.385i	−0.426238	+	0.426238i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.3.s.a.73.3		48
3.2	odd	2		29.3.f.a.15.2	yes	48
29.2	odd	28	inner	261.3.s.a.118.3		48
87.2	even	28		29.3.f.a.2.2	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.3.f.a.2.2	✓	48	87.2	even	28
29.3.f.a.15.2	yes	48	3.2	odd	2
261.3.s.a.73.3		48	1.1	even	1	trivial
261.3.s.a.118.3		48	29.2	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)

\(f(q)\)	\(=\)	\(q+(1.68783 - 0.190173i) q^{2} +(-1.08711 + 0.248126i) q^{4} +(-0.141728 - 0.113024i) q^{5} +(-1.55116 + 6.79606i) q^{7} +(-8.20045 + 2.86946i) q^{8} +O(q^{10})\)	\(q+(1.68783 - 0.190173i) q^{2} +(-1.08711 + 0.248126i) q^{4} +(-0.141728 - 0.113024i) q^{5} +(-1.55116 + 6.79606i) q^{7} +(-8.20045 + 2.86946i) q^{8} +(-0.260707 - 0.163813i) q^{10} +(12.2566 + 4.28875i) q^{11} +(9.66173 + 20.0628i) q^{13} +(-1.32566 + 11.7656i) q^{14} +(-9.27670 + 4.46742i) q^{16} +(5.90660 + 5.90660i) q^{17} +(-10.7431 + 17.0975i) q^{19} +(0.182118 + 0.0877036i) q^{20} +(21.5026 + 4.90782i) q^{22} +(-15.0384 - 18.8575i) q^{23} +(-5.55571 - 24.3412i) q^{25} +(20.1228 + 32.0252i) q^{26} -7.77294i q^{28} +(-28.5764 + 4.93832i) q^{29} +(35.5909 - 4.01014i) q^{31} +(14.6174 - 9.18473i) q^{32} +(11.0926 + 8.84605i) q^{34} +(0.987964 - 0.787875i) q^{35} +(-23.0925 + 8.08043i) q^{37} +(-14.8810 + 30.9007i) q^{38} +(1.48655 + 0.520168i) q^{40} +(14.1288 - 14.1288i) q^{41} +(-4.31425 + 38.2901i) q^{43} +(-14.3884 - 1.62118i) q^{44} +(-28.9684 - 28.9684i) q^{46} +(-1.53295 + 4.38091i) q^{47} +(0.367152 + 0.176811i) q^{49} +(-14.0061 - 40.0272i) q^{50} +(-15.4815 - 19.4131i) q^{52} +(51.0246 - 63.9828i) q^{53} +(-1.25237 - 1.99313i) q^{55} +(-6.78085 - 60.1817i) q^{56} +(-47.2930 + 13.7695i) q^{58} -28.0326 q^{59} +(-3.26475 + 2.05138i) q^{61} +(59.3088 - 13.5368i) q^{62} +(55.1251 - 43.9608i) q^{64} +(0.898247 - 3.93548i) q^{65} +(-2.88318 + 5.98698i) q^{67} +(-7.88670 - 4.95554i) q^{68} +(1.51768 - 1.51768i) q^{70} +(15.5711 + 32.3337i) q^{71} +(103.524 + 11.6644i) q^{73} +(-37.4396 + 18.0300i) q^{74} +(7.43657 - 21.2525i) q^{76} +(-48.1585 + 76.6437i) q^{77} +(-28.1618 - 80.4819i) q^{79} +(1.81970 + 0.415334i) q^{80} +(21.1601 - 26.5339i) q^{82} +(6.13681 + 26.8871i) q^{83} +(-0.169541 - 1.50472i) q^{85} +65.4475i q^{86} -112.816 q^{88} +(-26.8243 + 3.02237i) q^{89} +(-151.335 + 34.5412i) q^{91} +(21.0274 + 16.7688i) q^{92} +(-1.75422 + 7.68575i) q^{94} +(3.45503 - 1.20897i) q^{95} +(-6.09419 - 3.82923i) q^{97} +(0.653314 + 0.228604i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{2} - 14 q^{4} + 14 q^{5} - 10 q^{7} - 28 q^{8}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more