LMFDB - Embedded newform 666.2.x.c.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(127,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("666.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.x (of order $9$, degree $6$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			127.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	666.127
Dual form			666.2.x.c.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.0209445 - 0.118782i) q^{5} +(0.233956 - 1.32683i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.0209445 - 0.118782i) q^{5} +(0.233956 - 1.32683i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0603074 + 0.104455i) q^{10} +(2.26604 + 3.92490i) q^{11} +(-0.592396 - 0.497079i) q^{13} +(-0.673648 + 1.16679i) q^{14} +(0.173648 + 0.984808i) q^{16} +(2.29813 - 1.92836i) q^{17} +(1.91875 - 0.698367i) q^{19} +(0.0923963 - 0.0775297i) q^{20} +(-0.786989 - 4.46324i) q^{22} +(0.0282185 - 0.0488759i) q^{23} +(4.68479 + 1.70513i) q^{25} +(0.386659 + 0.669713i) q^{26} +(1.03209 - 0.866025i) q^{28} +(-2.89053 - 5.00654i) q^{29} -3.34730 q^{31} +(0.173648 - 0.984808i) q^{32} +(-2.81908 + 1.02606i) q^{34} +(-0.152704 - 0.0555796i) q^{35} +(5.60607 + 2.36051i) q^{37} -2.04189 q^{38} +(-0.113341 + 0.0412527i) q^{40} +(5.47565 + 4.59462i) q^{41} +9.31315 q^{43} +(-0.786989 + 4.46324i) q^{44} +(-0.0432332 + 0.0362770i) q^{46} +(4.25877 - 7.37641i) q^{47} +(4.87211 + 1.77330i) q^{49} +(-3.81908 - 3.20459i) q^{50} +(-0.134285 - 0.761570i) q^{52} +(-0.482926 - 2.73881i) q^{53} +(0.513671 - 0.186961i) q^{55} +(-1.26604 + 0.460802i) q^{56} +(1.00387 + 5.69323i) q^{58} +(2.25624 + 12.7958i) q^{59} +(-8.82295 - 7.40333i) q^{61} +(3.14543 + 1.14484i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.0714517 + 0.0599551i) q^{65} +(0.889185 - 5.04282i) q^{67} +3.00000 q^{68} +(0.124485 + 0.104455i) q^{70} +(12.6236 - 4.59462i) q^{71} -8.71688 q^{73} +(-4.46064 - 4.13554i) q^{74} +(1.91875 + 0.698367i) q^{76} +(5.73783 - 2.08840i) q^{77} +(0.720285 - 4.08494i) q^{79} +0.120615 q^{80} +(-3.57398 - 6.19031i) q^{82} +(4.53596 - 3.80612i) q^{83} +(-0.180922 - 0.313366i) q^{85} +(-8.75150 - 3.18528i) q^{86} +(2.26604 - 3.92490i) q^{88} +(-1.32295 - 7.50281i) q^{89} +(-0.798133 + 0.669713i) q^{91} +(0.0530334 - 0.0193026i) q^{92} +(-6.52481 + 5.47497i) q^{94} +(-0.0427664 - 0.242540i) q^{95} +(5.12061 - 8.86916i) q^{97} +(-3.97178 - 3.33272i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} + 6 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 + 6 * q^7 - 3 * q^8	$ 6 q - 3 q^{5} + 6 q^{7} - 3 q^{8} - 6 q^{10} + 9 q^{11} - 3 q^{14} + 9 q^{19} - 3 q^{20} + 3 q^{22} + 15 q^{23} + 21 q^{25} + 9 q^{26} - 3 q^{28} - 18 q^{31} - 3 q^{35} + 9 q^{37} - 6 q^{38} + 6 q^{40} - 6 q^{41} + 12 q^{43} + 3 q^{44} + 15 q^{46} + 3 q^{47} - 6 q^{50} + 9 q^{52} + 18 q^{53} - 18 q^{55} - 3 q^{56} - 18 q^{58} + 6 q^{59} - 12 q^{61} + 3 q^{62} - 3 q^{64} - 3 q^{67} + 18 q^{68} - 12 q^{70} + 6 q^{71} - 36 q^{73} - 18 q^{74} + 9 q^{76} + 15 q^{77} + 30 q^{79} + 12 q^{80} - 6 q^{82} - 6 q^{83} - 18 q^{85} - 12 q^{86} + 9 q^{88} + 33 q^{89} + 9 q^{91} - 12 q^{92} - 12 q^{94} - 51 q^{95} + 42 q^{97} - 9 q^{98}+O(q^{100}) $ 6 * q - 3 * q^5 + 6 * q^7 - 3 * q^8 - 6 * q^10 + 9 * q^11 - 3 * q^14 + 9 * q^19 - 3 * q^20 + 3 * q^22 + 15 * q^23 + 21 * q^25 + 9 * q^26 - 3 * q^28 - 18 * q^31 - 3 * q^35 + 9 * q^37 - 6 * q^38 + 6 * q^40 - 6 * q^41 + 12 * q^43 + 3 * q^44 + 15 * q^46 + 3 * q^47 - 6 * q^50 + 9 * q^52 + 18 * q^53 - 18 * q^55 - 3 * q^56 - 18 * q^58 + 6 * q^59 - 12 * q^61 + 3 * q^62 - 3 * q^64 - 3 * q^67 + 18 * q^68 - 12 * q^70 + 6 * q^71 - 36 * q^73 - 18 * q^74 + 9 * q^76 + 15 * q^77 + 30 * q^79 + 12 * q^80 - 6 * q^82 - 6 * q^83 - 18 * q^85 - 12 * q^86 + 9 * q^88 + 33 * q^89 + 9 * q^91 - 12 * q^92 - 12 * q^94 - 51 * q^95 + 42 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.0209445	−	0.118782i	0.00936668	−	0.0531211i	−0.979766	−	0.200146i	$-0.935858\pi$
$5$	0.0209445	−	0.118782i	0.00936668	−	0.0531211i	0.989133	+	0.147024i	$0.0469696\pi$
$6$		0			0
$7$	0.233956	−	1.32683i	0.0884269	−	0.501494i	−0.908137	−	0.418672i	$-0.862496\pi$
$7$	0.233956	−	1.32683i	0.0884269	−	0.501494i	0.996564	−	0.0828217i	$-0.0263932\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	−0.0603074	+	0.104455i	−0.0190709	+	0.0330317i
$11$	2.26604	+	3.92490i	0.683238	+	1.18340i	0.973987	+	0.226604i	$0.0727622\pi$
$11$	2.26604	+	3.92490i	0.683238	+	1.18340i	−0.290749	+	0.956799i	$0.593904\pi$
$12$		0			0
$13$	−0.592396	−	0.497079i	−0.164301	−	0.137865i	0.556930	−	0.830559i	$-0.311979\pi$
$13$	−0.592396	−	0.497079i	−0.164301	−	0.137865i	−0.721231	+	0.692694i	$0.756424\pi$
$14$	−0.673648	+	1.16679i	−0.180040	+	0.311839i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	2.29813	−	1.92836i	0.557379	−	0.467697i	−0.320051	−	0.947400i	$-0.603700\pi$
$17$	2.29813	−	1.92836i	0.557379	−	0.467697i	0.877431	+	0.479703i	$0.159256\pi$
$18$		0			0
$19$	1.91875	−	0.698367i	0.440191	−	0.160216i	−0.112411	−	0.993662i	$-0.535857\pi$
$19$	1.91875	−	0.698367i	0.440191	−	0.160216i	0.552602	+	0.833445i	$0.313635\pi$
$20$	0.0923963	−	0.0775297i	0.0206604	−	0.0173362i
$21$		0			0
$22$	−0.786989	−	4.46324i	−0.167787	−	0.951565i
$23$	0.0282185	−	0.0488759i	0.00588396	−	0.0101913i	−0.863068	−	0.505087i	$-0.831460\pi$
$23$	0.0282185	−	0.0488759i	0.00588396	−	0.0101913i	0.868952	+	0.494896i	$0.164794\pi$
$24$		0			0
$25$	4.68479	+	1.70513i	0.936959	+	0.341025i
$26$	0.386659	+	0.669713i	0.0758301	+	0.131342i
$27$		0			0
$28$	1.03209	−	0.866025i	0.195046	−	0.163663i
$29$	−2.89053	−	5.00654i	−0.536758	−	0.929692i	−0.999076	−	0.0429778i	$-0.986316\pi$
$29$	−2.89053	−	5.00654i	−0.536758	−	0.929692i	0.462318	−	0.886714i	$-0.347018\pi$
$30$		0			0
$31$	−3.34730			−0.601192			−0.300596	−	0.953752i	$-0.597186\pi$
$31$	−3.34730			−0.601192			−0.300596	+	0.953752i	$0.597186\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$		0			0
$34$	−2.81908	+	1.02606i	−0.483468	+	0.175968i
$35$	−0.152704	−	0.0555796i	−0.0258116	−	0.00939466i
$36$		0			0
$37$	5.60607	+	2.36051i	0.921632	+	0.388066i
$37$	5.60607	+	2.36051i	0.921632	+	0.388066i
$38$	−2.04189			−0.331238
$39$		0			0
$40$	−0.113341	+	0.0412527i	−0.0179208	+	0.00652262i
$41$	5.47565	+	4.59462i	0.855153	+	0.717559i	0.960918	−	0.276832i	$-0.0892847\pi$
$41$	5.47565	+	4.59462i	0.855153	+	0.717559i	−0.105765	+	0.994391i	$0.533729\pi$
$42$		0			0
$43$	9.31315			1.42024			0.710121	−	0.704080i	$-0.248640\pi$
$43$	9.31315			1.42024			0.710121	+	0.704080i	$0.248640\pi$
$44$	−0.786989	+	4.46324i	−0.118643	+	0.672858i
$45$		0			0
$46$	−0.0432332	+	0.0362770i	−0.00637439	+	0.00534875i
$47$	4.25877	−	7.37641i	0.621206	−	1.07596i	−0.368056	−	0.929804i	$-0.619977\pi$
$47$	4.25877	−	7.37641i	0.621206	−	1.07596i	0.989262	−	0.146156i	$-0.0466901\pi$
$48$		0			0
$49$	4.87211	+	1.77330i	0.696016	+	0.253329i
$50$	−3.81908	−	3.20459i	−0.540099	−	0.453197i
$51$		0			0
$52$	−0.134285	−	0.761570i	−0.0186220	−	0.105611i
$53$	−0.482926	−	2.73881i	−0.0663350	−	0.376204i	−0.999844	−	0.0176510i	$-0.994381\pi$
$53$	−0.482926	−	2.73881i	−0.0663350	−	0.376204i	0.933509	−	0.358553i	$-0.116730\pi$
$54$		0			0
$55$	0.513671	−	0.186961i	0.0692633	−	0.0252098i
$56$	−1.26604	+	0.460802i	−0.169182	+	0.0615773i
$57$		0			0
$58$	1.00387	+	5.69323i	0.131815	+	0.747558i
$59$	2.25624	+	12.7958i	0.293738	+	1.66587i	0.672288	+	0.740290i	$0.265312\pi$
$59$	2.25624	+	12.7958i	0.293738	+	1.66587i	−0.378550	+	0.925581i	$0.623577\pi$
$60$		0			0
$61$	−8.82295	−	7.40333i	−1.12966	−	0.947900i	−0.130611	−	0.991434i	$-0.541694\pi$
$61$	−8.82295	−	7.40333i	−1.12966	−	0.947900i	−0.999052	+	0.0435341i	$0.986138\pi$
$62$	3.14543	+	1.14484i	0.399470	+	0.145395i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.0714517	+	0.0599551i	−0.00886250	+	0.00743652i
$66$		0			0
$67$	0.889185	−	5.04282i	0.108631	−	0.616079i	−0.881076	−	0.472974i	$-0.843180\pi$
$67$	0.889185	−	5.04282i	0.108631	−	0.616079i	0.989708	−	0.143104i	$-0.0457085\pi$
$68$	3.00000			0.363803
$69$		0			0
$70$	0.124485	+	0.104455i	0.0148788	+	0.0124848i
$71$	12.6236	−	4.59462i	1.49815	−	0.545281i	0.542567	−	0.840013i	$-0.317453\pi$
$71$	12.6236	−	4.59462i	1.49815	−	0.545281i	0.955580	+	0.294732i	$0.0952304\pi$
$72$		0			0
$73$	−8.71688			−1.02023			−0.510117	−	0.860105i	$-0.670398\pi$
$73$	−8.71688			−1.02023			−0.510117	+	0.860105i	$0.670398\pi$
$74$	−4.46064	−	4.13554i	−0.518539	−	0.480747i
$75$		0			0
$76$	1.91875	+	0.698367i	0.220096	+	0.0801082i
$77$	5.73783	−	2.08840i	0.653886	−	0.237995i
$78$		0			0
$79$	0.720285	−	4.08494i	0.0810384	−	0.459592i	−0.917103	−	0.398650i	$-0.869479\pi$
$79$	0.720285	−	4.08494i	0.0810384	−	0.459592i	0.998141	−	0.0609412i	$-0.0194102\pi$
$80$	0.120615			0.0134851
$81$		0			0
$82$	−3.57398	−	6.19031i	−0.394680	−	0.683606i
$83$	4.53596	−	3.80612i	0.497886	−	0.417776i	−0.358956	−	0.933354i	$-0.616867\pi$
$83$	4.53596	−	3.80612i	0.497886	−	0.417776i	0.856843	+	0.515578i	$0.172423\pi$
$84$		0			0
$85$	−0.180922	−	0.313366i	−0.0196238	−	0.0339894i
$86$	−8.75150	−	3.18528i	−0.943698	−	0.343478i
$87$		0			0
$88$	2.26604	−	3.92490i	0.241561	−	0.418396i
$89$	−1.32295	−	7.50281i	−0.140232	−	0.795297i	−0.971072	−	0.238785i	$-0.923251\pi$
$89$	−1.32295	−	7.50281i	−0.140232	−	0.795297i	0.830840	−	0.556511i	$-0.187860\pi$
$90$		0			0
$91$	−0.798133	+	0.669713i	−0.0836671	+	0.0702050i
$92$	0.0530334	−	0.0193026i	0.00552912	−	0.00201243i
$93$		0			0
$94$	−6.52481	+	5.47497i	−0.672983	+	0.564700i
$95$	−0.0427664	−	0.242540i	−0.00438774	−	0.0248841i
$96$		0			0
$97$	5.12061	−	8.86916i	0.519920	−	0.900527i	−0.479812	−	0.877371i	$-0.659295\pi$
$97$	5.12061	−	8.86916i	0.519920	−	0.900527i	0.999732	−	0.0231560i	$-0.00737146\pi$
$98$	−3.97178	−	3.33272i	−0.401211	−	0.336656i
$99$		0			0
$100$	2.49273	+	4.31753i	0.249273	+	0.431753i
$101$	−8.05690	+	13.9550i	−0.801692	+	1.38857i	0.116810	+	0.993154i	$0.462733\pi$
$101$	−8.05690	+	13.9550i	−0.801692	+	1.38857i	−0.918502	+	0.395417i	$0.870600\pi$
$102$		0			0
$103$	9.81567	+	17.0012i	0.967167	+	1.67518i	0.703676	+	0.710521i	$0.251541\pi$
$103$	9.81567	+	17.0012i	0.967167	+	1.67518i	0.263491	+	0.964662i	$0.415126\pi$
$104$	−0.134285	+	0.761570i	−0.0131678	+	0.0746781i
$105$		0			0
$106$	−0.482926	+	2.73881i	−0.0469059	+	0.266017i
$107$	0.488856	+	0.410199i	0.0472595	+	0.0396554i	0.666111	−	0.745852i	$-0.267957\pi$
$107$	0.488856	+	0.410199i	0.0472595	+	0.0396554i	−0.618852	+	0.785508i	$0.712402\pi$
$108$		0			0
$109$	−6.81908	−	2.48194i	−0.653149	−	0.237727i	−0.00587340	−	0.999983i	$-0.501870\pi$
$109$	−6.81908	−	2.48194i	−0.653149	−	0.237727i	−0.647276	+	0.762256i	$0.724092\pi$
$110$	−0.546637			−0.0521198
$111$		0			0
$112$	1.34730			0.127308
$113$	−12.9893	−	4.72773i	−1.22193	−	0.444747i	−0.351105	−	0.936336i	$-0.614194\pi$
$113$	−12.9893	−	4.72773i	−1.22193	−	0.444747i	−0.870827	+	0.491589i	$0.836416\pi$
$114$		0			0
$115$	−0.00521457	−	0.00437554i	−0.000486261	−	0.000408021i
$116$	1.00387	−	5.69323i	0.0932070	−	0.528603i
$117$		0			0
$118$	2.25624	−	12.7958i	0.207704	−	1.17795i
$119$	−2.02094	−	3.50038i	−0.185260	−	0.320879i
$120$		0			0
$121$	−4.76991	+	8.26173i	−0.433629	+	0.751067i
$122$	5.75877	+	9.97448i	0.521375	+	0.903047i
$123$		0			0
$124$	−2.56418	−	2.15160i	−0.230270	−	0.193219i
$125$	0.602196	−	1.04303i	0.0538621	−	0.0932919i
$126$		0			0
$127$	2.10354	+	11.9298i	0.186659	+	1.05860i	0.923805	+	0.382863i	$0.125062\pi$
$127$	2.10354	+	11.9298i	0.186659	+	1.05860i	−0.737146	+	0.675733i	$0.763827\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$		0			0
$130$	0.0876485	−	0.0319015i	0.00768728	−	0.00279794i
$131$	−16.5817	+	13.9137i	−1.44875	+	1.21565i	−0.515267	+	0.857030i	$0.672307\pi$
$131$	−16.5817	+	13.9137i	−1.44875	+	1.21565i	−0.933485	+	0.358617i	$0.883248\pi$
$132$		0			0
$133$	−0.477711	−	2.70924i	−0.0414228	−	0.234921i
$134$	−2.56031	+	4.43458i	−0.221177	+	0.383090i
$135$		0			0
$136$	−2.81908	−	1.02606i	−0.241734	−	0.0879840i
$137$	4.31908	+	7.48086i	0.369004	+	0.639133i	0.989410	−	0.145147i	$-0.0463656\pi$
$137$	4.31908	+	7.48086i	0.369004	+	0.639133i	−0.620406	+	0.784281i	$0.713032\pi$
$138$		0			0
$139$	−10.2686	+	8.61635i	−0.870969	+	0.730830i	−0.964302	−	0.264805i	$-0.914692\pi$
$139$	−10.2686	+	8.61635i	−0.870969	+	0.730830i	0.0933331	+	0.995635i	$0.470248\pi$
$140$	−0.0812519	−	0.140732i	−0.00686704	−	0.0118941i
$141$		0			0
$142$	−13.4338			−1.12734
$143$	0.608593	−	3.45150i	0.0508931	−	0.288629i
$144$		0			0
$145$	−0.655230	+	0.238484i	−0.0544139	+	0.0198050i
$146$	8.19119	+	2.98135i	0.677908	+	0.246738i
$147$		0			0
$148$	2.77719	+	5.41177i	0.228284	+	0.444845i
$149$	−4.39693			−0.360210			−0.180105	−	0.983647i	$-0.557644\pi$
$149$	−4.39693			−0.360210			−0.180105	+	0.983647i	$0.557644\pi$
$150$		0			0
$151$	−13.8550	+	5.04282i	−1.12751	+	0.410379i	−0.837387	−	0.546611i	$-0.815918\pi$
$151$	−13.8550	+	5.04282i	−1.12751	+	0.410379i	−0.290120	+	0.956990i	$0.593695\pi$
$152$	−1.56418	−	1.31250i	−0.126872	−	0.106458i
$153$		0			0
$154$	−6.10607			−0.492041
$155$	−0.0701076	+	0.397600i	−0.00563117	+	0.0319360i
$156$		0			0
$157$	−11.9907	+	10.0614i	−0.956959	+	0.802984i	−0.980456	−	0.196740i	$-0.936965\pi$
$157$	−11.9907	+	10.0614i	−0.956959	+	0.802984i	0.0234964	+	0.999724i	$0.492520\pi$
$158$	−2.07398	+	3.59224i	−0.164997	+	0.285783i
$159$		0			0
$160$	−0.113341	−	0.0412527i	−0.00896038	−	0.00326131i
$161$	−0.0582480	−	0.0488759i	−0.00459058	−	0.00385196i
$162$		0			0
$163$	−0.830222	−	4.70842i	−0.0650280	−	0.368792i	−0.999905	−	0.0138191i	$-0.995601\pi$
$163$	−0.830222	−	4.70842i	−0.0650280	−	0.368792i	0.934876	−	0.354973i	$-0.115510\pi$
$164$	1.24123	+	7.03936i	0.0969237	+	0.549682i
$165$		0			0
$166$	−5.56418	+	2.02520i	−0.431864	+	0.157186i
$167$	1.88413	−	0.685768i	0.145799	−	0.0530663i	−0.268090	−	0.963394i	$-0.586392\pi$
$167$	1.88413	−	0.685768i	0.145799	−	0.0530663i	0.413889	+	0.910327i	$0.364170\pi$
$168$		0			0
$169$	−2.15358	−	12.2136i	−0.165660	−	0.939505i
$170$	0.0628336	+	0.356347i	0.00481912	+	0.0273306i
$171$		0			0
$172$	7.13429	+	5.98638i	0.543984	+	0.456457i
$173$	−12.9500	−	4.71340i	−0.984567	−	0.358353i	−0.200953	−	0.979601i	$-0.564404\pi$
$173$	−12.9500	−	4.71340i	−0.984567	−	0.358353i	−0.783614	+	0.621248i	$0.786626\pi$
$174$		0			0
$175$	3.35844	−	5.81699i	0.253874	−	0.439723i
$176$	−3.47178	+	2.91317i	−0.261695	+	0.219588i
$177$		0			0
$178$	−1.32295	+	7.50281i	−0.0991592	+	0.562360i
$179$	14.7246			1.10057			0.550285	−	0.834977i	$-0.314519\pi$
$179$	14.7246			1.10057			0.550285	+	0.834977i	$0.314519\pi$
$180$		0			0
$181$	−8.34911	−	7.00573i	−0.620584	−	0.520732i	0.277403	−	0.960754i	$-0.410526\pi$
$181$	−8.34911	−	7.00573i	−0.620584	−	0.520732i	−0.897987	+	0.440022i	$0.854971\pi$
$182$	0.979055	−	0.356347i	0.0725724	−	0.0264142i
$183$		0			0
$184$	−0.0564370			−0.00416059
$185$	0.397804	−	0.616462i	0.0292471	−	0.0453232i
$186$		0			0
$187$	12.7763	+	4.65020i	0.934296	+	0.340056i
$188$	8.00387	−	2.91317i	0.583742	−	0.212465i
$189$		0			0
$190$	−0.0427664	+	0.242540i	−0.00310260	+	0.0175957i
$191$	−9.05737			−0.655368			−0.327684	−	0.944787i	$-0.606268\pi$
$191$	−9.05737			−0.655368			−0.327684	+	0.944787i	$0.606268\pi$
$192$		0			0
$193$	−6.29473	−	10.9028i	−0.453105	−	0.784800i	0.545472	−	0.838129i	$-0.316350\pi$
$193$	−6.29473	−	10.9028i	−0.453105	−	0.784800i	−0.998577	+	0.0533286i	$0.983017\pi$
$194$	−7.84524	+	6.58294i	−0.563255	+	0.472627i
$195$		0			0
$196$	2.59240	+	4.49016i	0.185171	+	0.320726i
$197$	−11.2169	−	4.08261i	−0.799170	−	0.290874i	−0.0900273	−	0.995939i	$-0.528695\pi$
$197$	−11.2169	−	4.08261i	−0.799170	−	0.290874i	−0.709142	+	0.705065i	$0.750918\pi$
$198$		0			0
$199$	−1.14543	+	1.98394i	−0.0811974	+	0.140638i	−0.903765	−	0.428030i	$-0.859208\pi$
$199$	−1.14543	+	1.98394i	−0.0811974	+	0.140638i	0.822567	+	0.568668i	$0.192541\pi$
$200$	−0.865715	−	4.90971i	−0.0612153	−	0.347169i
$201$		0			0
$202$	12.3439	−	10.3578i	0.868513	−	0.728769i
$203$	−7.31908	+	2.66393i	−0.513699	+	0.186971i
$204$		0			0
$205$	0.660444	−	0.554179i	0.0461274	−	0.0387055i
$206$	−3.40895	−	19.3331i	−0.237513	−	1.34700i
$207$		0			0
$208$	0.386659	−	0.669713i	0.0268100	−	0.0464363i
$209$	7.08899	+	5.94837i	0.490356	+	0.411457i
$210$		0			0
$211$	−0.477711	−	0.827420i	−0.0328870	−	0.0569620i	0.849113	−	0.528211i	$-0.177137\pi$
$211$	−0.477711	−	0.827420i	−0.0328870	−	0.0569620i	−0.882000	+	0.471249i	$0.843803\pi$
$212$	1.39053	−	2.40847i	0.0955020	−	0.165414i
$213$		0			0
$214$	−0.319078	−	0.552659i	−0.0218117	−	0.0377790i
$215$	0.195060	−	1.10624i	0.0133030	−	0.0754448i
$216$		0			0
$217$	−0.783119	+	4.44129i	−0.0531616	+	0.301494i
$218$	5.55896	+	4.66452i	0.376500	+	0.315921i
$219$		0			0
$220$	0.513671	+	0.186961i	0.0346317	+	0.0126049i
$221$	−2.31996			−0.156057
$222$		0			0
$223$	−17.8648			−1.19632			−0.598159	−	0.801377i	$-0.704101\pi$
$223$	−17.8648			−1.19632			−0.598159	+	0.801377i	$0.704101\pi$
$224$	−1.26604	−	0.460802i	−0.0845912	−	0.0307887i
$225$		0			0
$226$	10.5890	+	8.88522i	0.704369	+	0.591036i
$227$	−1.53684	+	8.71583i	−0.102003	+	0.578490i	0.890372	+	0.455235i	$0.150445\pi$
$227$	−1.53684	+	8.71583i	−0.102003	+	0.578490i	−0.992375	+	0.123256i	$0.960667\pi$
$228$		0			0
$229$	−3.02347	+	17.1470i	−0.199797	+	1.13310i	0.705624	+	0.708587i	$0.250667\pi$
$229$	−3.02347	+	17.1470i	−0.199797	+	1.13310i	−0.905420	+	0.424516i	$0.860444\pi$
$230$	0.00340357	+	0.00589515i	0.000224425	+	0.000388715i
$231$		0			0
$232$	−2.89053	+	5.00654i	−0.189773	+	0.328696i
$233$	−2.09627	−	3.63084i	−0.137331	−	0.237864i	0.789155	−	0.614195i	$-0.210519\pi$
$233$	−2.09627	−	3.63084i	−0.137331	−	0.237864i	−0.926485	+	0.376330i	$0.877186\pi$
$234$		0			0
$235$	−0.786989	−	0.660362i	−0.0513375	−	0.0430773i
$236$	−6.49660	+	11.2524i	−0.422892	+	0.732471i
$237$		0			0
$238$	0.701867	+	3.98048i	0.0454953	+	0.258016i
$239$	−6.57011	+	5.51297i	−0.424985	+	0.356605i	−0.830056	−	0.557681i	$-0.811691\pi$
$239$	−6.57011	+	5.51297i	−0.424985	+	0.356605i	0.405071	+	0.914285i	$0.367247\pi$
$240$		0			0
$241$	19.6532	−	7.15317i	1.26597	−	0.460776i	0.380203	−	0.924903i	$-0.375854\pi$
$241$	19.6532	−	7.15317i	1.26597	−	0.460776i	0.885769	+	0.464127i	$0.153632\pi$
$242$	7.30793	−	6.13208i	0.469772	−	0.394185i
$243$		0			0
$244$	−2.00000	−	11.3426i	−0.128037	−	0.726133i
$245$	0.312681	−	0.541580i	0.0199765	−	0.0346003i
$246$		0			0
$247$	−1.48380	−	0.540060i	−0.0944121	−	0.0343632i
$248$	1.67365	+	2.89884i	0.106277	+	0.184077i
$249$		0			0
$250$	−0.922618	+	0.774169i	−0.0583515	+	0.0489627i
$251$	3.39780	+	5.88517i	0.214467	+	0.371469i	0.953108	−	0.302631i	$-0.0978651\pi$
$251$	3.39780	+	5.88517i	0.214467	+	0.371469i	−0.738640	+	0.674100i	$0.764532\pi$
$252$		0			0
$253$	0.255777			0.0160806
$254$	2.10354	−	11.9298i	0.131988	−	0.748540i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−9.28611	−	3.37987i	−0.579252	−	0.210830i	0.0357438	−	0.999361i	$-0.488620\pi$
$257$	−9.28611	−	3.37987i	−0.579252	−	0.210830i	−0.614996	+	0.788531i	$0.710842\pi$
$258$		0			0
$259$	4.44356	−	6.88603i	0.276110	−	0.427877i
$260$	−0.0932736			−0.00578458
$261$		0			0
$262$	20.3405	−	7.40333i	1.25664	−	0.457379i
$263$	15.8195	+	13.2742i	0.975475	+	0.818521i	0.983401	−	0.181448i	$-0.0580784\pi$
$263$	15.8195	+	13.2742i	0.975475	+	0.818521i	−0.00792564	+	0.999969i	$0.502523\pi$
$264$		0			0
$265$	−0.335437			−0.0206057
$266$	−0.477711	+	2.70924i	−0.0292904	+	0.166114i
$267$		0			0
$268$	3.92262	−	3.29147i	0.239612	−	0.201058i
$269$	13.8131	−	23.9251i	0.842203	−	1.45874i	−0.0458262	−	0.998949i	$-0.514592\pi$
$269$	13.8131	−	23.9251i	0.842203	−	1.45874i	0.888029	−	0.459788i	$-0.152075\pi$
$270$		0			0
$271$	−6.42989	−	2.34029i	−0.390588	−	0.142162i	0.139258	−	0.990256i	$-0.455528\pi$
$271$	−6.42989	−	2.34029i	−0.390588	−	0.142162i	−0.529846	+	0.848094i	$0.677750\pi$
$272$	2.29813	+	1.92836i	0.139345	+	0.116924i
$273$		0			0
$274$	−1.50000	−	8.50692i	−0.0906183	−	0.513922i
$275$	3.92350	+	22.2513i	0.236596	+	1.34180i
$276$		0			0
$277$	22.3957	−	8.15138i	1.34563	−	0.489769i	0.434049	−	0.900889i	$-0.357085\pi$
$277$	22.3957	−	8.15138i	1.34563	−	0.489769i	0.911581	+	0.411120i	$0.134862\pi$
$278$	12.5963	−	4.58467i	0.755474	−	0.274970i
$279$		0			0
$280$	0.0282185	+	0.160035i	0.00168638	+	0.00956392i
$281$	−5.51367	−	31.2696i	−0.328918	−	1.86539i	−0.480575	−	0.876954i	$-0.659572\pi$
$281$	−5.51367	−	31.2696i	−0.328918	−	1.86539i	0.151657	−	0.988433i	$-0.451539\pi$
$282$		0			0
$283$	−4.52687	−	3.79850i	−0.269095	−	0.225797i	0.498248	−	0.867035i	$-0.333977\pi$
$283$	−4.52687	−	3.79850i	−0.269095	−	0.225797i	−0.767343	+	0.641237i	$0.778421\pi$
$284$	12.6236	+	4.59462i	0.749073	+	0.272640i
$285$		0			0
$286$	−1.75237	+	3.03520i	−0.103620	+	0.179475i
$287$	7.37733	−	6.19031i	0.435470	−	0.365403i
$288$		0			0
$289$	−1.38919	+	7.87846i	−0.0817168	+	0.463439i
$290$	0.697281			0.0409458
$291$		0			0
$292$	−6.67752	−	5.60310i	−0.390772	−	0.327897i
$293$	−1.59240	+	0.579585i	−0.0930288	+	0.0338597i	−0.388115	−	0.921611i	$-0.626874\pi$
$293$	−1.59240	+	0.579585i	−0.0930288	+	0.0338597i	0.295086	+	0.955471i	$0.404652\pi$
$294$		0			0
$295$	1.56717			0.0912442
$296$	−0.758770	−	6.03525i	−0.0441026	−	0.350792i
$297$		0			0
$298$	4.13176	+	1.50384i	0.239346	+	0.0871150i
$299$	−0.0410117	+	0.0149270i	−0.00237177	+	0.000863253i
$300$		0			0
$301$	2.17886	−	12.3569i	0.125588	−	0.712242i
$302$	14.7442			0.848435
$303$		0			0
$304$	1.02094	+	1.76833i	0.0585552	+	0.101421i
$305$	−1.06418	+	0.892951i	−0.0609346	+	0.0511302i
$306$		0			0
$307$	6.11334	+	10.5886i	0.348907	+	0.604324i	0.986056	−	0.166417i	$-0.0532196\pi$
$307$	6.11334	+	10.5886i	0.348907	+	0.604324i	−0.637149	+	0.770741i	$0.719886\pi$
$308$	5.73783	+	2.08840i	0.326943	+	0.118998i
$309$		0			0
$310$	0.201867	−	0.349643i	0.0114653	−	0.0198584i
$311$	0.212134	+	1.20307i	0.0120290	+	0.0682198i	0.990231	−	0.139434i	$-0.0445283\pi$
$311$	0.212134	+	1.20307i	0.0120290	+	0.0682198i	−0.978202	+	0.207654i	$0.933417\pi$
$312$		0			0
$313$	−13.3380	+	11.1919i	−0.753906	+	0.632602i	−0.936533	−	0.350580i	$-0.885985\pi$
$313$	−13.3380	+	11.1919i	−0.753906	+	0.632602i	0.182627	+	0.983182i	$0.441540\pi$
$314$	14.7087	−	5.35354i	0.830062	−	0.302118i
$315$		0			0
$316$	3.17752	−	2.66625i	0.178749	−	0.149989i
$317$	1.51027	+	8.56515i	0.0848250	+	0.481067i	0.997394	+	0.0721443i	$0.0229842\pi$
$317$	1.51027	+	8.56515i	0.0848250	+	0.481067i	−0.912569	+	0.408922i	$0.865905\pi$
$318$		0			0
$319$	13.1001	−	22.6901i	0.733467	−	1.27040i
$320$	0.0923963	+	0.0775297i	0.00516511	+	0.00433404i
$321$		0			0
$322$	0.0380187	+	0.0658503i	0.00211870	+	0.00366969i
$323$	3.06283	−	5.30498i	0.170421	−	0.295177i
$324$		0			0
$325$	−1.92767	−	3.33882i	−0.106928	−	0.185205i
$326$	−0.830222	+	4.70842i	−0.0459818	+	0.260775i
$327$		0			0
$328$	1.24123	−	7.03936i	0.0685354	−	0.388684i
$329$	−8.79086	−	7.37641i	−0.484656	−	0.406674i
$330$		0			0
$331$	7.74510	+	2.81899i	0.425709	+	0.154945i	0.545985	−	0.837795i	$-0.316156\pi$
$331$	7.74510	+	2.81899i	0.425709	+	0.154945i	−0.120276	+	0.992741i	$0.538378\pi$
$332$	5.92127			0.324972
$333$		0			0
$334$	−2.00505			−0.109712
$335$	−0.580375	−	0.211239i	−0.0317092	−	0.0115412i
$336$		0			0
$337$	10.7456	+	9.01660i	0.585348	+	0.491166i	0.886699	−	0.462348i	$-0.152993\pi$
$337$	10.7456	+	9.01660i	0.585348	+	0.491166i	−0.301350	+	0.953514i	$0.597437\pi$
$338$	−2.15358	+	12.2136i	−0.117139	+	0.664330i
$339$		0			0
$340$	0.0628336	−	0.356347i	0.00340763	−	0.0193256i
$341$	−7.58512	−	13.1378i	−0.410757	−	0.711453i
$342$		0			0
$343$	8.20826	−	14.2171i	0.443205	−	0.767653i
$344$	−4.65657	−	8.06542i	−0.251066	−	0.434858i
$345$		0			0
$346$	10.5569	+	8.85829i	0.567543	+	0.476225i
$347$	9.92262	−	17.1865i	0.532674	−	0.922619i	−0.466598	−	0.884470i	$-0.654521\pi$
$347$	9.92262	−	17.1865i	0.532674	−	0.922619i	0.999272	−	0.0381490i	$-0.0121462\pi$
$348$		0			0
$349$	2.98633	+	16.9363i	0.159855	+	0.906580i	0.954212	+	0.299130i	$0.0966964\pi$
$349$	2.98633	+	16.9363i	0.159855	+	0.906580i	−0.794358	+	0.607450i	$0.792192\pi$
$350$	−5.14543	+	4.31753i	−0.275035	+	0.230782i
$351$		0			0
$352$	4.25877	−	1.55007i	0.226993	−	0.0826188i
$353$	−12.9272	+	10.8472i	−0.688046	+	0.577339i	−0.918345	−	0.395781i	$-0.870474\pi$
$353$	−12.9272	+	10.8472i	−0.688046	+	0.577339i	0.230299	+	0.973120i	$0.426029\pi$
$354$		0			0
$355$	−0.281364	−	1.59569i	−0.0149332	−	0.0846906i
$356$	3.80928	−	6.59786i	0.201891	−	0.349686i
$357$		0			0
$358$	−13.8366	−	5.03612i	−0.731288	−	0.266167i
$359$	−8.05690	−	13.9550i	−0.425227	−	0.736515i	0.571214	−	0.820801i	$-0.306472\pi$
$359$	−8.05690	−	13.9550i	−0.425227	−	0.736515i	−0.996442	+	0.0842859i	$0.973139\pi$
$360$		0			0
$361$	−11.3610	+	9.53298i	−0.597946	+	0.501736i
$362$	5.44949	+	9.43880i	0.286419	+	0.496092i
$363$		0			0
$364$	−1.04189			−0.0546098
$365$	−0.182571	+	1.03541i	−0.00955620	+	0.0541959i
$366$		0			0
$367$	32.9666	−	11.9989i	1.72084	−	0.626336i	0.722931	−	0.690920i	$-0.242794\pi$
$367$	32.9666	−	11.9989i	1.72084	−	0.626336i	0.997912	+	0.0645839i	$0.0205720\pi$
$368$	0.0530334	+	0.0193026i	0.00276456	+	0.00100622i
$369$		0			0
$370$	−0.584655	+	0.443228i	−0.0303948	+	0.0230423i
$371$	−3.74691			−0.194530
$372$		0			0
$373$	27.9047	−	10.1565i	1.44485	−	0.525882i	0.503701	−	0.863878i	$-0.331971\pi$
$373$	27.9047	−	10.1565i	1.44485	−	0.525882i	0.941148	+	0.337996i	$0.109749\pi$
$374$	−10.4153	−	8.73951i	−0.538565	−	0.451909i
$375$		0			0
$376$	−8.51754			−0.439259
$377$	−0.776311	+	4.40268i	−0.0399821	+	0.226750i
$378$		0			0
$379$	0.321137	−	0.269466i	0.0164957	−	0.0138415i	−0.634502	−	0.772921i	$-0.718795\pi$
$379$	0.321137	−	0.269466i	0.0164957	−	0.0138415i	0.650998	+	0.759079i	$0.274351\pi$
$380$	0.123141	−	0.213286i	0.00631700	−	0.0109414i
$381$		0			0
$382$	8.51114	+	3.09780i	0.435468	+	0.158497i
$383$	4.92443	+	4.13209i	0.251627	+	0.211140i	0.759872	−	0.650072i	$-0.225261\pi$
$383$	4.92443	+	4.13209i	0.251627	+	0.211140i	−0.508246	+	0.861212i	$0.669706\pi$
$384$		0			0
$385$	−0.127889	−	0.725293i	−0.00651781	−	0.0369644i
$386$	2.18614	+	12.3982i	0.111271	+	0.631052i
$387$		0			0
$388$	9.62361	−	3.50271i	0.488565	−	0.177823i
$389$	−2.92602	+	1.06498i	−0.148355	+	0.0539969i	−0.415130	−	0.909762i	$-0.636264\pi$
$389$	−2.92602	+	1.06498i	−0.148355	+	0.0539969i	0.266775	+	0.963759i	$0.414042\pi$
$390$		0			0
$391$	−0.0294005	−	0.166739i	−0.00148685	−	0.00843234i
$392$	−0.900330	−	5.10602i	−0.0454735	−	0.257893i
$393$		0			0
$394$	9.14409	+	7.67280i	0.460672	+	0.386550i
$395$	−0.470133	−	0.171114i	−0.0236549	−	0.00860969i
$396$		0			0
$397$	−9.85369	+	17.0671i	−0.494543	+	0.856573i	−0.999980	−	0.00629016i	$-0.997998\pi$
$397$	−9.85369	+	17.0671i	−0.494543	+	0.856573i	0.505438	+	0.862863i	$0.331331\pi$
$398$	1.75490	−	1.47254i	0.0879652	−	0.0738116i
$399$		0			0
$400$	−0.865715	+	4.90971i	−0.0432857	+	0.245486i
$401$	−18.9162			−0.944631			−0.472316	−	0.881430i	$-0.656582\pi$
$401$	−18.9162			−0.944631			−0.472316	+	0.881430i	$0.656582\pi$
$402$		0			0
$403$	1.98293	+	1.66387i	0.0987766	+	0.0828834i
$404$	−15.1420	+	5.51125i	−0.753344	+	0.274195i
$405$		0			0
$406$	7.78880			0.386552
$407$	3.43882	+	27.3523i	0.170456	+	1.35580i
$408$		0			0
$409$	−5.99020	−	2.18025i	−0.296196	−	0.107807i	0.189648	−	0.981852i	$-0.439265\pi$
$409$	−5.99020	−	2.18025i	−0.296196	−	0.107807i	−0.485844	+	0.874046i	$0.661488\pi$
$410$	−0.810155	+	0.294872i	−0.0400107	+	0.0145627i
$411$		0			0
$412$	−3.40895	+	19.3331i	−0.167947	+	0.952474i
$413$	17.5057			0.861398
$414$		0			0
$415$	−0.357097	−	0.618509i	−0.0175292	−	0.0303614i
$416$	−0.592396	+	0.497079i	−0.0290446	+	0.0243713i
$417$		0			0
$418$	−4.62701	−	8.01422i	−0.226315	−	0.391988i
$419$	19.6258	+	7.14322i	0.958785	+	0.348969i	0.773557	−	0.633727i	$-0.218476\pi$
$419$	19.6258	+	7.14322i	0.958785	+	0.348969i	0.185227	+	0.982696i	$0.440698\pi$
$420$		0			0
$421$	2.90420	−	5.03022i	0.141542	−	0.245158i	−0.786535	−	0.617545i	$-0.788127\pi$
$421$	2.90420	−	5.03022i	0.141542	−	0.245158i	0.928077	+	0.372387i	$0.121461\pi$
$422$	0.165907	+	0.940908i	0.00807625	+	0.0458027i
$423$		0			0
$424$	−2.13041	+	1.78763i	−0.103462	+	0.0868150i
$425$	14.0544	−	5.11538i	0.681737	−	0.248132i
$426$		0			0
$427$	−11.8871	+	9.97448i	−0.575258	+	0.482699i
$428$	0.110815	+	0.628461i	0.00535642	+	0.0303778i
$429$		0			0
$430$	−0.561652	+	0.972809i	−0.0270852	+	0.0469130i
$431$	−8.70233	−	7.30212i	−0.419177	−	0.351731i	0.408673	−	0.912681i	$-0.365992\pi$
$431$	−8.70233	−	7.30212i	−0.419177	−	0.351731i	−0.827850	+	0.560950i	$0.810436\pi$
$432$		0			0
$433$	−17.8025	−	30.8348i	−0.855532	−	1.48183i	−0.876150	−	0.482038i	$-0.839897\pi$
$433$	−17.8025	−	30.8348i	−0.855532	−	1.48183i	0.0206183	−	0.999787i	$-0.493437\pi$
$434$	2.25490	−	3.90560i	0.108239	−	0.187475i
$435$		0			0
$436$	−3.62836	−	6.28450i	−0.173767	−	0.300973i
$437$	0.0200109	−	0.113487i	0.000957250	−	0.00542884i
$438$		0			0
$439$	3.90777	−	22.1620i	0.186507	−	1.05774i	−0.737496	−	0.675352i	$-0.763992\pi$
$439$	3.90777	−	22.1620i	0.186507	−	1.05774i	0.924003	−	0.382385i	$-0.124897\pi$
$440$	−0.418748	−	0.351371i	−0.0199630	−	0.0167510i
$441$		0			0
$442$	2.18004	+	0.793471i	0.103694	+	0.0377416i
$443$	26.0942			1.23977			0.619887	−	0.784691i	$-0.287179\pi$
$443$	26.0942			1.23977			0.619887	+	0.784691i	$0.287179\pi$
$444$		0			0
$445$	−0.918910			−0.0435605
$446$	16.7875	+	6.11013i	0.794909	+	0.289323i
$447$		0			0
$448$	1.03209	+	0.866025i	0.0487616	+	0.0409159i
$449$	1.13310	−	6.42615i	0.0534745	−	0.303269i	−0.946327	−	0.323212i	$-0.895237\pi$
$449$	1.13310	−	6.42615i	0.0534745	−	0.303269i	0.999801	+	0.0199431i	$0.00634850\pi$
$450$		0			0
$451$	−5.62536	+	31.9030i	−0.264888	+	1.50225i
$452$	−6.91147	−	11.9710i	−0.325088	−	0.563070i
$453$		0			0
$454$	4.42514	−	7.66458i	0.207682	−	0.359716i
$455$	0.0628336	+	0.108831i	0.00294568	+	0.00510208i
$456$		0			0
$457$	−25.0835	−	21.0476i	−1.17336	−	0.984564i	−0.173358	−	0.984859i	$-0.555462\pi$
$457$	−25.0835	−	21.0476i	−1.17336	−	0.984564i	−1.00000		0.000294571i	$0.999906\pi$
$458$	8.70574	−	15.0788i	0.406792	−	0.704585i
$459$		0			0
$460$	−0.00118205	−	0.00670372i	−5.51132e−5	−	0.000312562i
$461$	−14.9722	+	12.5632i	−0.697327	+	0.585127i	−0.921012	−	0.389535i	$-0.872636\pi$
$461$	−14.9722	+	12.5632i	−0.697327	+	0.585127i	0.223685	+	0.974662i	$0.428191\pi$
$462$		0			0
$463$	−40.2943	+	14.6659i	−1.87264	+	0.681584i	−0.907358	+	0.420359i	$0.861904\pi$
$463$	−40.2943	+	14.6659i	−1.87264	+	0.681584i	−0.965278	+	0.261224i	$0.915874\pi$
$464$	4.42855	−	3.71599i	0.205590	−	0.172511i
$465$		0			0
$466$	0.728026	+	4.12884i	0.0337251	+	0.191265i
$467$	10.5444	−	18.2635i	0.487937	−	0.845132i	−0.511966	−	0.859005i	$-0.671083\pi$
$467$	10.5444	−	18.2635i	0.487937	−	0.845132i	0.999904	+	0.0138732i	$0.00441611\pi$
$468$		0			0
$469$	−6.48293	−	2.35959i	−0.299354	−	0.108956i
$470$	0.513671	+	0.889704i	0.0236939	+	0.0410390i
$471$		0			0
$472$	9.95336	−	8.35186i	0.458141	−	0.384426i
$473$	21.1040	+	36.5532i	0.970363	+	1.68072i
$474$		0			0
$475$	10.1797			0.467079
$476$	0.701867	−	3.98048i	0.0321700	−	0.182445i
$477$		0			0
$478$	8.05943	−	2.93339i	0.368630	−	0.134170i
$479$	−22.7430	−	8.27779i	−1.03916	−	0.378222i	−0.234596	−	0.972093i	$-0.575377\pi$
$479$	−22.7430	−	8.27779i	−1.03916	−	0.378222i	−0.804560	+	0.593871i	$0.797599\pi$
$480$		0			0
$481$	−2.14765	−	4.18502i	−0.0979245	−	0.190820i
$482$	−20.9145			−0.952628
$483$		0			0
$484$	−8.96451	+	3.26281i	−0.407478	+	0.148310i
$485$	−0.946251	−	0.793999i	−0.0429671	−	0.0360536i
$486$		0			0
$487$	28.9682			1.31268			0.656338	−	0.754467i	$-0.272105\pi$
$487$	28.9682			1.31268			0.656338	+	0.754467i	$0.272105\pi$
$488$	−2.00000	+	11.3426i	−0.0905357	+	0.513454i
$489$		0			0
$490$	−0.479055	+	0.401975i	−0.0216415	+	0.0181594i
$491$	−14.0758	+	24.3800i	−0.635231	+	1.10025i	0.351235	+	0.936287i	$0.385762\pi$
$491$	−14.0758	+	24.3800i	−0.635231	+	1.10025i	−0.986466	+	0.163966i	$0.947571\pi$
$492$		0			0
$493$	−16.2973	−	5.93172i	−0.733991	−	0.267151i
$494$	1.20961	+	1.01498i	0.0544228	+	0.0456662i
$495$		0			0
$496$	−0.581252	−	3.29644i	−0.0260990	−	0.148015i
$497$	−3.14290	−	17.8243i	−0.140978	−	0.799529i
$498$		0			0
$499$	4.40255	−	1.60240i	0.197085	−	0.0717332i	−0.241592	−	0.970378i	$-0.577669\pi$
$499$	4.40255	−	1.60240i	0.197085	−	0.0717332i	0.438677	+	0.898645i	$0.355447\pi$
$500$	1.13176	−	0.411927i	0.0506138	−	0.0184219i
$501$		0			0
$502$	−1.18004	−	6.69237i	−0.0526680	−	0.298695i
$503$	−4.39037	−	24.8990i	−0.195757	−	1.11019i	−0.911337	−	0.411661i	$-0.864949\pi$
$503$	−4.39037	−	24.8990i	−0.195757	−	1.11019i	0.715580	−	0.698531i	$-0.246162\pi$
$504$		0			0
$505$	1.48886	+	1.24930i	0.0662532	+	0.0555930i
$506$	−0.240352	−	0.0874810i	−0.0106850	−	0.00388901i
$507$		0			0
$508$	−6.05690	+	10.4909i	−0.268732	+	0.465457i
$509$	−16.3739	+	13.7394i	−0.725761	+	0.608986i	−0.928972	−	0.370149i	$-0.879307\pi$
$509$	−16.3739	+	13.7394i	−0.725761	+	0.608986i	0.203211	+	0.979135i	$0.434862\pi$
$510$		0			0
$511$	−2.03936	+	11.5658i	−0.0902161	+	0.511641i
$512$	1.00000			0.0441942
$513$		0			0
$514$	7.57011	+	6.35207i	0.333903	+	0.280178i
$515$	2.22503	−	0.809846i	0.0980467	−	0.0356861i
$516$		0			0
$517$	38.6023			1.69773
$518$	−6.53074	+	4.95096i	−0.286944	+	0.217533i
$519$		0			0
$520$	0.0876485	+	0.0319015i	0.00384364	+	0.00139897i
$521$	−18.6853	+	6.80088i	−0.818616	+	0.297952i	−0.717178	−	0.696890i	$-0.754567\pi$
$521$	−18.6853	+	6.80088i	−0.818616	+	0.297952i	−0.101438	+	0.994842i	$0.532344\pi$
$522$		0			0
$523$	−2.94919	+	16.7257i	−0.128959	+	0.731363i	0.849918	+	0.526914i	$0.176651\pi$
$523$	−2.94919	+	16.7257i	−0.128959	+	0.731363i	−0.978877	+	0.204448i	$0.934460\pi$
$524$	−21.6459			−0.945605
$525$		0			0
$526$	−10.3255	−	17.8842i	−0.450212	−	0.779790i
$527$	−7.69253	+	6.45480i	−0.335092	+	0.281176i
$528$		0			0
$529$	11.4984	+	19.9158i	0.499931	+	0.865905i
$530$	0.315207	+	0.114726i	0.0136917	+	0.00498338i
$531$		0			0
$532$	1.37551	−	2.38246i	0.0596361	−	0.103293i
$533$	−0.959866	−	5.44367i	−0.0415764	−	0.235791i
$534$		0			0
$535$	0.0589632	−	0.0494760i	0.00254920	−	0.00213903i
$536$	−4.81180	+	1.75135i	−0.207838	+	0.0756469i
$537$		0			0
$538$	−21.1630	+	17.7578i	−0.912400	+	0.765595i
$539$	4.08037	+	23.1410i	0.175754	+	0.996751i
$540$		0			0
$541$	−14.6348	+	25.3481i	−0.629197	+	1.08980i	0.358516	+	0.933524i	$0.383283\pi$
$541$	−14.6348	+	25.3481i	−0.629197	+	1.08980i	−0.987713	+	0.156278i	$0.950050\pi$
$542$	5.24170	+	4.39831i	0.225150	+	0.188923i
$543$		0			0
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	−0.437633	+	0.758003i	−0.0187461	+	0.0324693i
$546$		0			0
$547$	0.666841	+	1.15500i	0.0285121	+	0.0493843i	0.879929	−	0.475105i	$-0.157590\pi$
$547$	0.666841	+	1.15500i	0.0285121	+	0.0493843i	−0.851417	+	0.524489i	$0.824256\pi$
$548$	−1.50000	+	8.50692i	−0.0640768	+	0.363398i
$549$		0			0
$550$	3.92350	−	22.2513i	0.167298	−	0.948797i
$551$	−9.04260	−	7.58765i	−0.385228	−	0.323245i
$552$		0			0
$553$	−5.25150	−	1.91139i	−0.223316	−	0.0812805i
$554$	−23.8331			−1.01257
$555$		0			0
$556$	−13.4047			−0.568485
$557$	30.3790	+	11.0570i	1.28720	+	0.468502i	0.892807	−	0.450440i	$-0.148733\pi$
$557$	30.3790	+	11.0570i	1.28720	+	0.468502i	0.394392	+	0.918942i	$0.370955\pi$
$558$		0			0
$559$	−5.51707	−	4.62937i	−0.233347	−	0.195802i
$560$	0.0282185	−	0.160035i	0.00119245	−	0.00676271i
$561$		0			0
$562$	−5.51367	+	31.2696i	−0.232580	+	1.31903i
$563$	−8.34389	−	14.4520i	−0.351653	−	0.609081i	0.634886	−	0.772606i	$-0.281047\pi$
$563$	−8.34389	−	14.4520i	−0.351653	−	0.609081i	−0.986539	+	0.163525i	$0.947714\pi$
$564$		0			0
$565$	−0.833626	+	1.44388i	−0.0350709	+	0.0607446i
$566$	2.95471	+	5.11770i	0.124196	+	0.215113i
$567$		0			0
$568$	−10.2909	−	8.63506i	−0.431795	−	0.362319i
$569$	−0.213011	+	0.368946i	−0.00892989	+	0.0154670i	−0.870456	−	0.492247i	$-0.836176\pi$
$569$	−0.213011	+	0.368946i	−0.00892989	+	0.0154670i	0.861526	+	0.507714i	$0.169509\pi$
$570$		0			0
$571$	2.42262	+	13.7394i	0.101383	+	0.574974i	0.992603	+	0.121403i	$0.0387392\pi$
$571$	2.42262	+	13.7394i	0.101383	+	0.574974i	−0.891220	+	0.453571i	$0.850150\pi$
$572$	2.68479	−	2.25281i	0.112257	−	0.0941947i
$573$		0			0
$574$	−9.04963	+	3.29380i	−0.377724	+	0.137480i
$575$	0.215537	−	0.180857i	0.00898852	−	0.00754227i
$576$		0			0
$577$	−1.90373	−	10.7966i	−0.0792535	−	0.449469i	−0.998449	−	0.0556680i	$-0.982271\pi$
$577$	−1.90373	−	10.7966i	−0.0792535	−	0.449469i	0.919196	−	0.393801i	$-0.128840\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	−0.655230	−	0.238484i	−0.0272069	−	0.00990252i
$581$	−3.98886	−	6.90890i	−0.165486	−	0.286629i
$582$		0			0
$583$	9.65523	−	8.10170i	0.399879	−	0.335538i
$584$	4.35844	+	7.54904i	0.180354	+	0.312382i
$585$		0			0
$586$	1.69459			0.0700030
$587$	2.21167	−	12.5430i	0.0912853	−	0.517704i	−0.904537	−	0.426395i	$-0.859784\pi$
$587$	2.21167	−	12.5430i	0.0912853	−	0.517704i	0.995823	−	0.0913099i	$-0.0291054\pi$
$588$		0			0
$589$	−6.42262	+	2.33764i	−0.264639	+	0.0963209i
$590$	−1.47266	−	0.536004i	−0.0606284	−	0.0220669i
$591$		0			0
$592$	−1.35117	+	5.93080i	−0.0555326	+	0.243754i
$593$	−33.6786			−1.38301			−0.691507	−	0.722369i	$-0.743053\pi$
$593$	−33.6786			−1.38301			−0.691507	+	0.722369i	$0.743053\pi$
$594$		0			0
$595$	−0.458111	+	0.166739i	−0.0187807	+	0.00683562i
$596$	−3.36824	−	2.82629i	−0.137969	−	0.115769i
$597$		0			0
$598$	0.0436438			0.00178473
$599$	2.36484	−	13.4117i	0.0966246	−	0.547986i	−0.897613	−	0.440785i	$-0.854700\pi$
$599$	2.36484	−	13.4117i	0.0966246	−	0.547986i	0.994237	−	0.107201i	$-0.0341887\pi$
$600$		0			0
$601$	12.3962	−	10.4017i	0.505652	−	0.424292i	−0.353944	−	0.935267i	$-0.615160\pi$
$601$	12.3962	−	10.4017i	0.505652	−	0.424292i	0.859596	+	0.510974i	$0.170715\pi$
$602$	−6.27379	+	10.8665i	−0.255700	+	0.442886i
$603$		0			0
$604$	−13.8550	−	5.04282i	−0.563753	−	0.205189i
$605$	0.881445	+	0.739620i	0.0358358	+	0.0300698i
$606$		0			0
$607$	−7.17247	−	40.6771i	−0.291121	−	1.65103i	−0.682562	−	0.730828i	$-0.739134\pi$
$607$	−7.17247	−	40.6771i	−0.291121	−	1.65103i	0.391440	−	0.920204i	$-0.371977\pi$
$608$	−0.354570	−	2.01087i	−0.0143797	−	0.0815515i
$609$		0			0
$610$	1.30541	−	0.475129i	0.0528544	−	0.0192374i
$611$	−6.18954	+	2.25281i	−0.250402	+	0.0911389i
$612$		0			0
$613$	−5.40255	−	30.6394i	−0.218207	−	1.23751i	−0.875254	−	0.483664i	$-0.839306\pi$
$613$	−5.40255	−	30.6394i	−0.218207	−	1.23751i	0.657047	−	0.753850i	$-0.271805\pi$
$614$	−2.12314	−	12.0409i	−0.0856830	−	0.485932i
$615$		0			0
$616$	−4.67752	−	3.92490i	−0.188463	−	0.158139i
$617$	17.9547	+	6.53498i	0.722829	+	0.263088i	0.677126	−	0.735867i	$-0.263225\pi$
$617$	17.9547	+	6.53498i	0.722829	+	0.263088i	0.0457029	+	0.998955i	$0.485447\pi$
$618$		0			0
$619$	−19.4636	+	33.7120i	−0.782309	+	1.35500i	0.148284	+	0.988945i	$0.452625\pi$
$619$	−19.4636	+	33.7120i	−0.782309	+	1.35500i	−0.930593	+	0.366055i	$0.880708\pi$
$620$	−0.309278	+	0.259515i	−0.0124209	+	0.0104224i
$621$		0			0
$622$	0.212134	−	1.20307i	0.00850579	−	0.0482387i
$623$	−10.2645			−0.411237
$624$		0			0
$625$	18.9841	+	15.9296i	0.759364	+	0.637182i
$626$	16.3614	−	5.95507i	0.653934	−	0.238013i
$627$		0			0
$628$	−15.6527			−0.624611
$629$	17.4354	−	5.38576i	0.695195	−	0.214744i
$630$		0			0
$631$	0.635163	+	0.231180i	0.0252854	+	0.00920314i	0.354632	−	0.935006i	$-0.384606\pi$
$631$	0.635163	+	0.231180i	0.0252854	+	0.00920314i	−0.329346	+	0.944209i	$0.606828\pi$
$632$	−3.89780	+	1.41868i	−0.155046	+	0.0564322i
$633$		0			0
$634$	1.51027	−	8.56515i	0.0599804	−	0.340166i
$635$	1.46110			0.0579821
$636$		0			0
$637$	−2.00475	−	3.47232i	−0.0794310	−	0.137579i
$638$	−20.0706	+	16.8412i	−0.794602	+	0.666750i
$639$		0			0
$640$	−0.0603074	−	0.104455i	−0.00238386	−	0.00412896i
$641$	17.6853	+	6.43691i	0.698526	+	0.254243i	0.666781	−	0.745253i	$-0.267672\pi$
$641$	17.6853	+	6.43691i	0.698526	+	0.254243i	0.0317444	+	0.999496i	$0.489894\pi$
$642$		0			0
$643$	−22.6582	+	39.2452i	−0.893553	+	1.54768i	−0.0579679	+	0.998318i	$0.518462\pi$
$643$	−22.6582	+	39.2452i	−0.893553	+	1.54768i	−0.835585	+	0.549361i	$0.814871\pi$
$644$	−0.0132037	−	0.0748822i	−0.000520300	−	0.00295077i
$645$		0			0
$646$	−4.69253	+	3.93750i	−0.184625	+	0.154919i
$647$	18.9859	−	6.91031i	0.746413	−	0.271672i	0.0593177	−	0.998239i	$-0.481107\pi$
$647$	18.9859	−	6.91031i	0.746413	−	0.271672i	0.687096	+	0.726567i	$0.258885\pi$
$648$		0			0
$649$	−45.1095	+	37.8514i	−1.77070	+	1.48580i
$650$	0.669473	+	3.79677i	0.0262589	+	0.148922i
$651$		0			0
$652$	2.39053	−	4.14052i	0.0936204	−	0.162155i
$653$	13.4586	+	11.2931i	0.526675	+	0.441933i	0.866951	−	0.498393i	$-0.166076\pi$
$653$	13.4586	+	11.2931i	0.526675	+	0.441933i	−0.340277	+	0.940325i	$0.610521\pi$
$654$		0			0
$655$	1.30541	+	2.26103i	0.0510065	+	0.0883458i
$656$	−3.57398	+	6.19031i	−0.139540	+	0.241691i
$657$		0			0
$658$	5.73783	+	9.93821i	0.223684	+	0.387432i
$659$	−5.65389	+	32.0648i	−0.220244	+	1.24907i	0.651327	+	0.758797i	$0.274213\pi$
$659$	−5.65389	+	32.0648i	−0.220244	+	1.24907i	−0.871571	+	0.490269i	$0.836898\pi$
$660$		0			0
$661$	4.07650	−	23.1190i	0.158558	−	0.899225i	−0.796903	−	0.604107i	$-0.793530\pi$
$661$	4.07650	−	23.1190i	0.158558	−	0.899225i	0.955461	−	0.295118i	$-0.0953590\pi$
$662$	−6.31386	−	5.29796i	−0.245395	−	0.205911i
$663$		0			0
$664$	−5.56418	−	2.02520i	−0.215932	−	0.0785928i
$665$	−0.331815			−0.0128672
$666$		0			0
$667$	−0.326266			−0.0126331
$668$	1.88413	+	0.685768i	0.0728993	+	0.0265332i
$669$		0			0
$670$	0.473126	+	0.397000i	0.0182784	+	0.0153374i
$671$	9.06418	−	51.4055i	0.349919	−	1.98449i
$672$		0			0
$673$	2.29989	−	13.0433i	0.0886542	−	0.502783i	−0.907854	−	0.419287i	$-0.862280\pi$
$673$	2.29989	−	13.0433i	0.0886542	−	0.502783i	0.996508	−	0.0834962i	$-0.0266086\pi$
$674$	−7.01367	−	12.1480i	−0.270156	−	0.467925i
$675$		0			0
$676$	6.20099	−	10.7404i	0.238500	−	0.413093i
$677$	2.69253	+	4.66360i	0.103482	+	0.179237i	0.913117	−	0.407697i	$-0.133668\pi$
$677$	2.69253	+	4.66360i	0.103482	+	0.179237i	−0.809635	+	0.586934i	$0.800335\pi$
$678$		0			0
$679$	−10.5699	−	8.86916i	−0.405634	−	0.340367i
$680$	−0.180922	+	0.313366i	−0.00693805	+	0.0120171i
$681$		0			0
$682$	2.63429	+	14.9398i	0.100872	+	0.572074i
$683$	−19.2547	+	16.1566i	−0.736759	+	0.618214i	−0.931965	−	0.362548i	$-0.881907\pi$
$683$	−19.2547	+	16.1566i	−0.736759	+	0.618214i	0.195206	+	0.980762i	$0.437462\pi$
$684$		0			0
$685$	0.979055	−	0.356347i	0.0374078	−	0.0136153i
$686$	−12.5758	+	10.5523i	−0.480146	+	0.402890i
$687$		0			0
$688$	1.61721	+	9.17166i	0.0616556	+	0.349666i
$689$	−1.07532	+	1.86251i	−0.0409665	+	0.0709561i
$690$		0			0
$691$	−38.6467	−	14.0662i	−1.47019	−	0.535105i	−0.522037	−	0.852923i	$-0.674828\pi$
$691$	−38.6467	−	14.0662i	−1.47019	−	0.535105i	−0.948152	+	0.317818i	$0.897050\pi$
$692$	−6.89053	−	11.9347i	−0.261939	−	0.453691i
$693$		0			0
$694$	−15.2023	+	12.7563i	−0.577073	+	0.484221i
$695$	0.808400	+	1.40019i	0.0306644	+	0.0531123i
$696$		0			0
$697$	21.4439			0.812244
$698$	2.98633	−	16.9363i	0.113034	−	0.641049i
$699$		0			0
$700$	6.31180	−	2.29731i	0.238564	−	0.0868301i
$701$	29.1523	+	10.6106i	1.10107	+	0.400756i	0.827709	−	0.561157i	$-0.189644\pi$
$701$	29.1523	+	10.6106i	1.10107	+	0.400756i	0.273357	+	0.961913i	$0.411866\pi$
$702$		0			0
$703$	12.4051	+	0.614134i	0.467868	+	0.0231625i
$704$	−4.53209			−0.170810
$705$		0			0
$706$	15.8576	−	5.77168i	0.596807	−	0.217220i
$707$	16.6309	+	13.9550i	0.625469	+	0.524831i
$708$		0			0
$709$	−19.3773			−0.727731			−0.363865	−	0.931452i	$-0.618543\pi$
$709$	−19.3773			−0.727731			−0.363865	+	0.931452i	$0.618543\pi$
$710$	−0.281364	+	1.59569i	−0.0105594	+	0.0598853i
$711$		0			0
$712$	−5.83615	+	4.89711i	−0.218719	+	0.183527i
$713$	−0.0944557	+	0.163602i	−0.00353739	+	0.00612694i
$714$		0			0
$715$	−0.397231	−	0.144580i	−0.0148556	−	0.00540699i
$716$	11.2797	+	9.46480i	0.421543	+	0.353716i
$717$		0			0
$718$	2.79813	+	15.8690i	0.104425	+	0.592226i
$719$	5.30675	+	30.0961i	0.197908	+	1.12239i	0.908216	+	0.418503i	$0.137445\pi$
$719$	5.30675	+	30.0961i	0.197908	+	1.12239i	−0.710307	+	0.703892i	$0.751444\pi$
$720$		0			0
$721$	24.8542	−	9.04617i	0.925617	−	0.336897i
$722$	13.9363	−	5.07239i	0.518655	−	0.188775i
$723$		0			0
$724$	−1.89259	−	10.7334i	−0.0703375	−	0.398904i
$725$	−5.00475	−	28.3833i	−0.185872	−	1.05413i
$726$		0			0
$727$	39.9843	+	33.5508i	1.48294	+	1.24433i	0.902979	+	0.429685i	$0.141375\pi$
$727$	39.9843	+	33.5508i	1.48294	+	1.24433i	0.579958	+	0.814647i	$0.303069\pi$
$728$	0.979055	+	0.356347i	0.0362862	+	0.0132071i
$729$		0			0
$730$	0.525692	−	0.910526i	0.0194567	−	0.0337001i
$731$	21.4029	−	17.9591i	0.791613	−	0.664242i
$732$		0			0
$733$	0.211829	−	1.20134i	0.00782408	−	0.0443726i	−0.980646	−	0.195790i	$-0.937273\pi$
$733$	0.211829	−	1.20134i	0.00782408	−	0.0443726i	0.988470	+	0.151418i	$0.0483839\pi$
$734$	−35.0823			−1.29491
$735$		0			0
$736$	−0.0432332	−	0.0362770i	−0.00159360	−	0.00133719i
$737$	21.8075	−	7.93729i	0.803290	−	0.292374i
$738$		0			0
$739$	−2.61318			−0.0961273			−0.0480637	−	0.998844i	$-0.515305\pi$
$739$	−2.61318			−0.0961273			−0.0480637	+	0.998844i	$0.515305\pi$
$740$	0.700989	−	0.216534i	0.0257689	−	0.00795995i
$741$		0			0
$742$	3.52094	+	1.28152i	0.129258	+	0.0470460i
$743$	−21.1989	+	7.71578i	−0.777713	+	0.283064i	−0.700219	−	0.713928i	$-0.746914\pi$
$743$	−21.1989	+	7.71578i	−0.777713	+	0.283064i	−0.0774945	+	0.996993i	$0.524692\pi$
$744$		0			0
$745$	−0.0920916	+	0.522277i	−0.00337397	+	0.0191348i
$746$	−29.6955			−1.08723
$747$		0			0
$748$	6.79813	+	11.7747i	0.248564	+	0.430526i
$749$	0.658633	−	0.552659i	0.0240659	−	0.0201937i
$750$		0			0
$751$	−21.3346	−	36.9525i	−0.778509	−	1.34842i	−0.932801	−	0.360392i	$-0.882643\pi$
$751$	−21.3346	−	36.9525i	−0.778509	−	1.34842i	0.154292	−	0.988025i	$-0.450690\pi$
$752$	8.00387	+	2.91317i	0.291871	+	0.106232i
$753$		0			0
$754$	2.23530	−	3.87165i	0.0814048	−	0.140997i
$755$	0.308811	+	1.75135i	0.0112388	+	0.0637383i
$756$		0			0
$757$	−17.8610	+	14.9871i	−0.649168	+	0.544717i	−0.906818	−	0.421522i	$-0.861496\pi$
$757$	−17.8610	+	14.9871i	−0.649168	+	0.544717i	0.257650	+	0.966238i	$0.417052\pi$
$758$	−0.393933	+	0.143380i	−0.0143083	+	0.00520779i
$759$		0			0
$760$	−0.188663	+	0.158307i	−0.00684352	+	0.00574240i
$761$	0.714822	+	4.05396i	0.0259123	+	0.146956i	0.995019	−	0.0996862i	$-0.0317839\pi$
$761$	0.714822	+	4.05396i	0.0259123	+	0.146956i	−0.969107	+	0.246642i	$0.920673\pi$
$762$		0			0
$763$	−4.88847	+	8.46708i	−0.176975	+	0.306529i
$764$	−6.93835	−	5.82197i	−0.251021	−	0.210631i
$765$		0			0
$766$	−3.21419	−	5.56715i	−0.116134	−	0.201149i
$767$	5.02394	−	8.70172i	0.181404	−	0.314201i
$768$		0			0
$769$	−3.09017	−	5.35234i	−0.111435	−	0.193010i	0.804914	−	0.593391i	$-0.202211\pi$
$769$	−3.09017	−	5.35234i	−0.111435	−	0.193010i	−0.916349	+	0.400381i	$0.868878\pi$
$770$	−0.127889	+	0.725293i	−0.00460879	+	0.0261377i
$771$		0			0
$772$	2.18614	−	12.3982i	0.0786808	−	0.446221i
$773$	−13.8773	−	11.6445i	−0.499133	−	0.418822i	0.358153	−	0.933663i	$-0.383407\pi$
$773$	−13.8773	−	11.6445i	−0.499133	−	0.418822i	−0.857286	+	0.514841i	$0.827851\pi$
$774$		0			0
$775$	−15.6814	−	5.70756i	−0.563292	−	0.205022i
$776$	−10.2412			−0.367639
$777$		0			0
$778$	3.11381			0.111635
$779$	13.7151	+	4.99190i	0.491395	+	0.178853i
$780$		0			0
$781$	46.6391	+	39.1348i	1.66888	+	1.40035i
$782$	−0.0294005	+	0.166739i	−0.00105136	+	0.00596257i
$783$		0			0
$784$	−0.900330	+	5.10602i	−0.0321546	+	0.182358i
$785$	0.943974	+	1.63501i	0.0336919	+	0.0583560i
$786$		0			0
$787$	13.9602	−	24.1798i	0.497628	−	0.861918i	−0.502368	−	0.864654i	$-0.667538\pi$
$787$	13.9602	−	24.1798i	0.497628	−	0.861918i	0.999996	+	0.00273640i	$0.000871024\pi$
$788$	−5.96838	−	10.3375i	−0.212615	−	0.368259i
$789$		0			0
$790$	0.383256	+	0.321590i	0.0136356	+	0.0114416i
$791$	−9.31180	+	16.1285i	−0.331090	+	0.573464i
$792$		0			0
$793$	1.54664	+	8.77141i	0.0549227	+	0.311482i
$794$	15.0967	−	12.6677i	0.535763	−	0.449559i
$795$		0			0
$796$	−2.15270	+	0.783520i	−0.0763006	+	0.0277711i
$797$	1.51114	−	1.26800i	0.0535275	−	0.0449149i	−0.615631	−	0.788034i	$-0.711099\pi$
$797$	1.51114	−	1.26800i	0.0535275	−	0.0449149i	0.669159	+	0.743119i	$0.266655\pi$
$798$		0			0
$799$	−4.43717	−	25.1644i	−0.156976	−	0.890253i
$800$	2.49273	−	4.31753i	0.0881312	−	0.152648i
$801$		0			0
$802$	17.7754	+	6.46973i	0.627672	+	0.228454i
$803$	−19.7528	−	34.2129i	−0.697063	−	1.20735i
$804$		0			0
$805$	−0.00702557	+	0.00589515i	−0.000247619	+	0.000207777i
$806$	−1.29426	−	2.24173i	−0.0455885	−	0.0789615i
$807$		0			0
$808$	16.1138			0.566882
$809$	−2.72699	+	15.4655i	−0.0958757	+	0.543738i	0.898600	+	0.438769i	$0.144585\pi$
$809$	−2.72699	+	15.4655i	−0.0958757	+	0.543738i	−0.994475	+	0.104969i	$0.966526\pi$
$810$		0			0
$811$	38.0984	−	13.8667i	1.33782	−	0.486925i	0.428691	−	0.903451i	$-0.358975\pi$
$811$	38.0984	−	13.8667i	1.33782	−	0.486925i	0.909124	+	0.416526i	$0.136753\pi$
$812$	−7.31908	−	2.66393i	−0.256849	−	0.0934855i
$813$		0			0
$814$	6.12361	−	26.8789i	0.214632	−	0.942105i
$815$	−0.576666			−0.0201997
$816$		0			0
$817$	17.8696	−	6.50400i	0.625178	−	0.227546i
$818$	4.88326	+	4.09754i	0.170739	+	0.143267i
$819$		0			0
$820$	0.862149			0.0301075
$821$	1.73190	−	9.82207i	0.0604436	−	0.342793i	−0.939556	−	0.342394i	$-0.888762\pi$
$821$	1.73190	−	9.82207i	0.0604436	−	0.342793i	1.00000		0.000398276i	$-0.000126775\pi$
$822$		0			0
$823$	−8.12180	+	6.81500i	−0.283108	+	0.237556i	−0.773272	−	0.634074i	$-0.781381\pi$
$823$	−8.12180	+	6.81500i	−0.283108	+	0.237556i	0.490164	+	0.871630i	$0.336937\pi$
$824$	9.81567	−	17.0012i	0.341945	−	0.592266i
$825$		0			0
$826$	−16.4500	−	5.98730i	−0.572367	−	0.208325i
$827$	−19.3195	−	16.2110i	−0.671806	−	0.563712i	0.241793	−	0.970328i	$-0.422264\pi$
$827$	−19.3195	−	16.2110i	−0.671806	−	0.563712i	−0.913599	+	0.406615i	$0.866709\pi$
$828$		0			0
$829$	0.950532	+	5.39074i	0.0330134	+	0.187228i	0.996855	−	0.0792478i	$-0.0252519\pi$
$829$	0.950532	+	5.39074i	0.0330134	+	0.187228i	−0.963842	+	0.266476i	$0.914141\pi$
$830$	0.124018	+	0.703343i	0.00430474	+	0.0244134i
$831$		0			0
$832$	0.726682	−	0.264490i	0.0251932	−	0.00916956i
$833$	14.6163	−	5.31991i	0.506426	−	0.184324i
$834$		0			0
$835$	−0.0419949	−	0.238165i	−0.00145329	−	0.00824203i
$836$	1.60694	+	9.11343i	0.0555773	+	0.315195i
$837$		0			0
$838$	−15.9991	−	13.4249i	−0.552681	−	0.463754i
$839$	12.7046	+	4.62408i	0.438610	+	0.159641i	0.551880	−	0.833923i	$-0.313910\pi$
$839$	12.7046	+	4.62408i	0.438610	+	0.159641i	−0.113271	+	0.993564i	$0.536133\pi$
$840$		0			0
$841$	−2.21032	+	3.82839i	−0.0762180	+	0.132013i
$842$	−4.44949	+	3.73357i	−0.153340	+	0.128667i
$843$		0			0
$844$	0.165907	−	0.940908i	0.00571077	−	0.0323874i
$845$	−1.49586			−0.0514592
$846$		0			0
$847$	9.84595	+	8.26173i	0.338311	+	0.283877i
$848$	2.61334	−	0.951178i	0.0897425	−	0.0326636i
$849$		0			0
$850$	−14.9564			−0.512999
$851$	0.273567	−	0.207391i	0.00937775	−	0.00710928i
$852$		0			0
$853$	21.2570	+	7.73692i	0.727826	+	0.264907i	0.679244	−	0.733912i	$-0.262308\pi$
$853$	21.2570	+	7.73692i	0.727826	+	0.264907i	0.0485819	+	0.998819i	$0.484530\pi$
$854$	14.5817	−	5.30731i	0.498976	−	0.181612i
$855$		0			0
$856$	0.110815	−	0.628461i	0.00378756	−	0.0214803i
$857$	28.4148			0.970630			0.485315	−	0.874339i	$-0.338705\pi$
$857$	28.4148			0.970630			0.485315	+	0.874339i	$0.338705\pi$
$858$		0			0
$859$	−11.2618	−	19.5059i	−0.384246	−	0.665534i	0.607418	−	0.794382i	$-0.292205\pi$
$859$	−11.2618	−	19.5059i	−0.384246	−	0.665534i	−0.991664	+	0.128848i	$0.958872\pi$
$860$	0.860500	−	0.722045i	0.0293428	−	0.0246215i
$861$		0			0
$862$	5.68004	+	9.83813i	0.193463	+	0.335088i
$863$	−9.35282	−	3.40415i	−0.318374	−	0.115878i	0.177890	−	0.984050i	$-0.443073\pi$
$863$	−9.35282	−	3.40415i	−0.318374	−	0.115878i	−0.496264	+	0.868172i	$0.665295\pi$
$864$		0			0
$865$	−0.831100	+	1.43951i	−0.0282582	+	0.0489447i
$866$	6.18273	+	35.0640i	0.210098	+	1.19152i
$867$		0			0
$868$	−3.45471	+	2.89884i	−0.117260	+	0.0983932i
$869$	17.6652	−	6.42960i	0.599251	−	0.218109i
$870$		0			0
$871$	−3.03343	+	2.54535i	−0.102784	+	0.0862460i
$872$	1.26011	+	7.14647i	0.0426729	+	0.242010i
$873$		0			0
$874$	−0.0576190	+	0.0997991i	−0.00194899	+	0.00337575i
$875$	−1.24304	−	1.04303i	−0.0420224	−	0.0352610i
$876$		0			0
$877$	−22.0021	−	38.1088i	−0.742959	−	1.28684i	−0.951142	−	0.308752i	$-0.900089\pi$
$877$	−22.0021	−	38.1088i	−0.742959	−	1.28684i	0.208184	−	0.978090i	$-0.433245\pi$
$878$	−11.2520	+	19.4890i	−0.379735	+	0.657721i
$879$		0			0
$880$	0.273318	+	0.473401i	0.00921356	+	0.0159584i
$881$	2.13862	−	12.1287i	0.0720520	−	0.408627i	−0.927355	−	0.374184i	$-0.877923\pi$
$881$	2.13862	−	12.1287i	0.0720520	−	0.408627i	0.999407	−	0.0344437i	$-0.0109659\pi$
$882$		0			0
$883$	3.77244	−	21.3946i	0.126953	−	0.719985i	−0.853176	−	0.521623i	$-0.825327\pi$
$883$	3.77244	−	21.3946i	0.126953	−	0.719985i	0.980129	−	0.198362i	$-0.0635621\pi$
$884$	−1.77719	−	1.49124i	−0.0597733	−	0.0501558i
$885$		0			0
$886$	−24.5205	−	8.92474i	−0.823783	−	0.299833i
$887$	−10.7145			−0.359758			−0.179879	−	0.983689i	$-0.557571\pi$
$887$	−10.7145			−0.359758			−0.179879	+	0.983689i	$0.557571\pi$
$888$		0			0
$889$	16.3209			0.547385
$890$	0.863493	+	0.314286i	0.0289444	+	0.0105349i
$891$		0			0
$892$	−13.6853	−	11.4833i	−0.458216	−	0.384489i
$893$	3.02007	−	17.1277i	0.101063	−	0.573155i
$894$		0			0
$895$	0.308400	−	1.74903i	0.0103087	−	0.0584635i
$896$	−0.673648	−	1.16679i	−0.0225050	−	0.0389798i
$897$		0			0
$898$	−3.26264	+	5.65106i	−0.108876	+	0.188578i
$899$	9.67546	+	16.7584i	0.322695	+	0.558923i
$900$		0			0
$901$	−6.39124	−	5.36289i	−0.212923	−	0.178664i
$902$	16.1976	−	28.0550i	0.539321	−	0.934131i
$903$		0			0
$904$	2.40033	+	13.6129i	0.0798338	+	0.452760i
$905$	−1.00703	+	0.844995i	−0.0334747	+	0.0280886i
$906$		0			0
$907$	−17.1122	+	6.22832i	−0.568200	+	0.206808i	−0.610114	−	0.792313i	$-0.708877\pi$
$907$	−17.1122	+	6.22832i	−0.568200	+	0.206808i	0.0419145	+	0.999121i	$0.486654\pi$
$908$	−6.77972	+	5.68886i	−0.224993	+	0.188791i
$909$		0			0
$910$	−0.0218219	−	0.123758i	−0.000723388	−	0.00410254i
$911$	10.3072	−	17.8526i	0.341493	−	0.591484i	−0.643217	−	0.765684i	$-0.722401\pi$
$911$	10.3072	−	17.8526i	0.341493	−	0.591484i	0.984710	+	0.174200i	$0.0557340\pi$
$912$		0			0
$913$	25.2173	+	9.17836i	0.834572	+	0.303760i
$914$	16.3721	+	28.3573i	0.541541	+	0.937977i
$915$		0			0
$916$	−13.3380	+	11.1919i	−0.440699	+	0.369790i
$917$	14.5817	+	25.2563i	0.481531	+	0.834036i
$918$		0			0
$919$	−25.1462			−0.829497			−0.414748	−	0.909936i	$-0.636130\pi$
$919$	−25.1462			−0.829497			−0.414748	+	0.909936i	$0.636130\pi$
$920$	−0.00118205	+	0.00670372i	−3.89709e−5	+	0.000221015i
$921$		0			0
$922$	18.3662	−	6.68474i	0.604858	−	0.220150i
$923$	−9.76207	−	3.55310i	−0.321322	−	0.116952i
$924$		0			0
$925$	22.2383	+	20.6176i	0.731191	+	0.677901i
$926$	42.8803			1.40913
$927$		0			0
$928$	−5.43242	+	1.97724i	−0.178328	+	0.0649060i
$929$	23.1912	+	19.4597i	0.760878	+	0.638453i	0.938355	−	0.345672i	$-0.112349\pi$
$929$	23.1912	+	19.4597i	0.760878	+	0.638453i	−0.177477	+	0.984125i	$0.556794\pi$
$930$		0			0
$931$	10.5868			0.346967
$932$	0.728026	−	4.12884i	0.0238473	−	0.135245i
$933$		0			0
$934$	−16.1550	+	13.5556i	−0.528607	+	0.443554i
$935$	0.819955	−	1.42020i	0.0268154	−	0.0464456i
$936$		0			0
$937$	15.1686	+	5.52092i	0.495536	+	0.180361i	0.577685	−	0.816260i	$-0.303956\pi$
$937$	15.1686	+	5.52092i	0.495536	+	0.180361i	−0.0821489	+	0.996620i	$0.526178\pi$
$938$	5.28493	+	4.43458i	0.172559	+	0.144794i
$939$		0			0
$940$	−0.178396	−	1.01173i	−0.00581863	−	0.0329991i
$941$	−1.70733	−	9.68275i	−0.0556574	−	0.315649i	0.944250	−	0.329228i	$-0.106788\pi$
$941$	−1.70733	−	9.68275i	−0.0556574	−	0.315649i	−0.999908	+	0.0135795i	$0.995677\pi$
$942$		0			0
$943$	0.379081	−	0.137974i	0.0123446	−	0.00449305i
$944$	−12.2096	+	4.44393i	−0.397389	+	0.144638i
$945$		0			0
$946$	−7.32934	−	41.5668i	−0.238298	−	1.35145i
$947$	9.23695	+	52.3853i	0.300160	+	1.70229i	0.645453	+	0.763800i	$0.276669\pi$
$947$	9.23695	+	52.3853i	0.300160	+	1.70229i	−0.345293	+	0.938495i	$0.612220\pi$
$948$		0			0
$949$	5.16385	+	4.33298i	0.167626	+	0.140655i
$950$	−9.56583	−	3.48168i	−0.310356	−	0.112960i
$951$		0			0
$952$	−2.02094	+	3.50038i	−0.0654992	+	0.113448i
$953$	−37.4181	+	31.3975i	−1.21209	+	1.01706i	−0.212891	+	0.977076i	$0.568288\pi$
$953$	−37.4181	+	31.3975i	−1.21209	+	1.01706i	−0.999200	+	0.0399889i	$0.987268\pi$
$954$		0			0
$955$	−0.189702	+	1.07586i	−0.00613863	+	0.0348139i
$956$	−8.57667			−0.277389
$957$		0			0
$958$	18.5403	+	15.5572i	0.599010	+	0.502629i
$959$	10.9363	−	3.98048i	0.353151	−	0.128537i
$960$		0			0
$961$	−19.7956			−0.638568
$962$	0.586771	+	4.66717i	0.0189183	+	0.150476i
$963$		0			0
$964$	19.6532	+	7.15317i	0.632986	+	0.230388i
$965$	−1.42690	+	0.519349i	−0.0459335	+	0.0167184i
$966$		0			0
$967$	1.45646	−	8.26001i	0.0468367	−	0.265624i	−0.952393	−	0.304874i	$-0.901386\pi$
$967$	1.45646	−	8.26001i	0.0468367	−	0.265624i	0.999229	+	0.0392499i	$0.0124968\pi$
$968$	9.53983			0.306622
$969$		0			0
$970$	0.617622	+	1.06975i	0.0198306	+	0.0343477i
$971$	−31.6771	+	26.5802i	−1.01657	+	0.853001i	−0.989192	−	0.146624i	$-0.953159\pi$
$971$	−31.6771	+	26.5802i	−1.01657	+	0.853001i	−0.0273745	+	0.999625i	$0.508715\pi$
$972$		0			0
$973$	9.03003	+	15.6405i	0.289489	+	0.501410i
$974$	−27.2212	−	9.90771i	−0.872224	−	0.317464i
$975$		0			0
$976$	5.75877	−	9.97448i	0.184334	−	0.319275i
$977$	−8.39662	−	47.6196i	−0.268632	−	1.52349i	−0.758490	−	0.651684i	$-0.774063\pi$
$977$	−8.39662	−	47.6196i	−0.268632	−	1.52349i	0.489859	−	0.871802i	$-0.337048\pi$
$978$		0			0
$979$	26.4500	−	22.1942i	0.845344	−	0.709328i
$980$	0.587649	−	0.213887i	0.0187717	−	0.00683236i
$981$		0			0
$982$	21.5654	−	18.0955i	0.688178	−	0.577450i
$983$	−9.44150	−	53.5454i	−0.301137	−	1.70783i	−0.641152	−	0.767414i	$-0.721543\pi$
$983$	−9.44150	−	53.5454i	−0.301137	−	1.70783i	0.340015	−	0.940420i	$-0.389568\pi$
$984$		0			0
$985$	−0.719874	+	1.24686i	−0.0229371	+	0.0397282i
$986$	13.2856	+	11.1480i	0.423101	+	0.355024i
$987$		0			0
$988$	−0.789515	−	1.36748i	−0.0251178	−	0.0435053i
$989$	0.262803	−	0.455188i	0.00835665	−	0.0144741i
$990$		0			0
$991$	15.9436	+	27.6151i	0.506464	+	0.877221i	0.999972	+	0.00748010i	$0.00238101\pi$
$991$	15.9436	+	27.6151i	0.506464	+	0.877221i	−0.493508	+	0.869741i	$0.664286\pi$
$992$	−0.581252	+	3.29644i	−0.0184548	+	0.104662i
$993$		0			0
$994$	−3.14290	+	17.8243i	−0.0996868	+	0.565352i
$995$	0.211667	+	0.177610i	0.00671029	+	0.00563060i
$996$		0			0
$997$	0.490505	+	0.178529i	0.0155344	+	0.00565407i	0.349776	−	0.936833i	$-0.386258\pi$
$997$	0.490505	+	0.178529i	0.0155344	+	0.00565407i	−0.334241	+	0.942488i	$0.608480\pi$
$998$	−4.68510			−0.148304
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.x.c.127.1		6
3.2	odd	2		74.2.f.a.53.1	yes	6
12.11	even	2		592.2.bc.b.497.1		6
37.7	even	9	inner	666.2.x.c.451.1		6
111.44	odd	18		74.2.f.a.7.1	✓	6
111.65	odd	18		2738.2.a.p.1.2		3
111.83	odd	18		2738.2.a.m.1.2		3
444.155	even	18		592.2.bc.b.81.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.f.a.7.1	✓	6	111.44	odd	18
74.2.f.a.53.1	yes	6	3.2	odd	2
592.2.bc.b.81.1		6	444.155	even	18
592.2.bc.b.497.1		6	12.11	even	2
666.2.x.c.127.1		6	1.1	even	1	trivial
666.2.x.c.451.1		6	37.7	even	9	inner
2738.2.a.m.1.2		3	111.83	odd	18
2738.2.a.p.1.2		3	111.65	odd	18

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.x (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.0209445 - 0.118782i) q^{5} +(0.233956 - 1.32683i) q^{7} +(-0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.0209445 - 0.118782i) q^{5} +(0.233956 - 1.32683i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.0603074 + 0.104455i) q^{10} +(2.26604 + 3.92490i) q^{11} +(-0.592396 - 0.497079i) q^{13} +(-0.673648 + 1.16679i) q^{14} +(0.173648 + 0.984808i) q^{16} +(2.29813 - 1.92836i) q^{17} +(1.91875 - 0.698367i) q^{19} +(0.0923963 - 0.0775297i) q^{20} +(-0.786989 - 4.46324i) q^{22} +(0.0282185 - 0.0488759i) q^{23} +(4.68479 + 1.70513i) q^{25} +(0.386659 + 0.669713i) q^{26} +(1.03209 - 0.866025i) q^{28} +(-2.89053 - 5.00654i) q^{29} -3.34730 q^{31} +(0.173648 - 0.984808i) q^{32} +(-2.81908 + 1.02606i) q^{34} +(-0.152704 - 0.0555796i) q^{35} +(5.60607 + 2.36051i) q^{37} -2.04189 q^{38} +(-0.113341 + 0.0412527i) q^{40} +(5.47565 + 4.59462i) q^{41} +9.31315 q^{43} +(-0.786989 + 4.46324i) q^{44} +(-0.0432332 + 0.0362770i) q^{46} +(4.25877 - 7.37641i) q^{47} +(4.87211 + 1.77330i) q^{49} +(-3.81908 - 3.20459i) q^{50} +(-0.134285 - 0.761570i) q^{52} +(-0.482926 - 2.73881i) q^{53} +(0.513671 - 0.186961i) q^{55} +(-1.26604 + 0.460802i) q^{56} +(1.00387 + 5.69323i) q^{58} +(2.25624 + 12.7958i) q^{59} +(-8.82295 - 7.40333i) q^{61} +(3.14543 + 1.14484i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.0714517 + 0.0599551i) q^{65} +(0.889185 - 5.04282i) q^{67} +3.00000 q^{68} +(0.124485 + 0.104455i) q^{70} +(12.6236 - 4.59462i) q^{71} -8.71688 q^{73} +(-4.46064 - 4.13554i) q^{74} +(1.91875 + 0.698367i) q^{76} +(5.73783 - 2.08840i) q^{77} +(0.720285 - 4.08494i) q^{79} +0.120615 q^{80} +(-3.57398 - 6.19031i) q^{82} +(4.53596 - 3.80612i) q^{83} +(-0.180922 - 0.313366i) q^{85} +(-8.75150 - 3.18528i) q^{86} +(2.26604 - 3.92490i) q^{88} +(-1.32295 - 7.50281i) q^{89} +(-0.798133 + 0.669713i) q^{91} +(0.0530334 - 0.0193026i) q^{92} +(-6.52481 + 5.47497i) q^{94} +(-0.0427664 - 0.242540i) q^{95} +(5.12061 - 8.86916i) q^{97} +(-3.97178 - 3.33272i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} + 6 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 + 6 * q^7 - 3 * q^8	\( 6 q - 3 q^{5} + 6 q^{7} - 3 q^{8} - 6 q^{10} + 9 q^{11} - 3 q^{14} + 9 q^{19} - 3 q^{20} + 3 q^{22} + 15 q^{23} + 21 q^{25} + 9 q^{26} - 3 q^{28} - 18 q^{31} - 3 q^{35} + 9 q^{37} - 6 q^{38} + 6 q^{40} - 6 q^{41} + 12 q^{43} + 3 q^{44} + 15 q^{46} + 3 q^{47} - 6 q^{50} + 9 q^{52} + 18 q^{53} - 18 q^{55} - 3 q^{56} - 18 q^{58} + 6 q^{59} - 12 q^{61} + 3 q^{62} - 3 q^{64} - 3 q^{67} + 18 q^{68} - 12 q^{70} + 6 q^{71} - 36 q^{73} - 18 q^{74} + 9 q^{76} + 15 q^{77} + 30 q^{79} + 12 q^{80} - 6 q^{82} - 6 q^{83} - 18 q^{85} - 12 q^{86} + 9 q^{88} + 33 q^{89} + 9 q^{91} - 12 q^{92} - 12 q^{94} - 51 q^{95} + 42 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q - 3 * q^5 + 6 * q^7 - 3 * q^8 - 6 * q^10 + 9 * q^11 - 3 * q^14 + 9 * q^19 - 3 * q^20 + 3 * q^22 + 15 * q^23 + 21 * q^25 + 9 * q^26 - 3 * q^28 - 18 * q^31 - 3 * q^35 + 9 * q^37 - 6 * q^38 + 6 * q^40 - 6 * q^41 + 12 * q^43 + 3 * q^44 + 15 * q^46 + 3 * q^47 - 6 * q^50 + 9 * q^52 + 18 * q^53 - 18 * q^55 - 3 * q^56 - 18 * q^58 + 6 * q^59 - 12 * q^61 + 3 * q^62 - 3 * q^64 - 3 * q^67 + 18 * q^68 - 12 * q^70 + 6 * q^71 - 36 * q^73 - 18 * q^74 + 9 * q^76 + 15 * q^77 + 30 * q^79 + 12 * q^80 - 6 * q^82 - 6 * q^83 - 18 * q^85 - 12 * q^86 + 9 * q^88 + 33 * q^89 + 9 * q^91 - 12 * q^92 - 12 * q^94 - 51 * q^95 + 42 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more