LMFDB - Embedded newform 414.2.i.f.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.1
Root			$-0.841254 - 0.540641i$ of defining polynomial
Character	$\chi$	$=$	414.361
Dual form			414.2.i.f.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(-0.985691 - 2.15836i) q^{5} +(0.381761 - 0.112095i) q^{7} +(-0.841254 - 0.540641i) q^{8} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(-0.985691 - 2.15836i) q^{5} +(0.381761 - 0.112095i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-2.27667 - 0.668491i) q^{10} +(-2.10260 - 2.42653i) q^{11} +(-0.149167 - 0.0437995i) q^{13} +(0.165284 - 0.361922i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.467137 - 3.24901i) q^{17} +(-0.404992 - 2.81678i) q^{19} +(-1.99611 + 1.28282i) q^{20} -3.21076 q^{22} +(-1.27778 + 4.62248i) q^{23} +(-0.412635 + 0.476206i) q^{25} +(-0.130785 + 0.0840506i) q^{26} +(-0.165284 - 0.361922i) q^{28} +(0.0538974 - 0.374864i) q^{29} +(2.31086 + 1.48510i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-2.14953 - 2.48069i) q^{34} +(-0.618239 - 0.713486i) q^{35} +(2.66750 - 5.84100i) q^{37} +(-2.39399 - 1.53853i) q^{38} +(-0.337683 + 2.34863i) q^{40} +(1.66324 + 3.64198i) q^{41} +(6.25061 - 4.01702i) q^{43} +(-2.10260 + 2.42653i) q^{44} +(2.65667 + 3.99276i) q^{46} -2.97017 q^{47} +(-5.75560 + 3.69890i) q^{49} +(0.0896742 + 0.623698i) q^{50} +(-0.0221250 + 0.153882i) q^{52} +(12.5046 - 3.67168i) q^{53} +(-3.16481 + 6.92998i) q^{55} +(-0.381761 - 0.112095i) q^{56} +(-0.248008 - 0.286217i) q^{58} +(8.29589 + 2.43589i) q^{59} +(9.37463 + 6.02471i) q^{61} +(2.63565 - 0.773896i) q^{62} +(0.415415 + 0.909632i) q^{64} +(0.0524978 + 0.365130i) q^{65} +(-5.50581 + 6.35404i) q^{67} -3.28242 q^{68} -0.944078 q^{70} +(0.233571 - 0.269556i) q^{71} +(-0.802078 - 5.57857i) q^{73} +(-2.66750 - 5.84100i) q^{74} +(-2.73047 + 0.801739i) q^{76} +(-1.07469 - 0.690662i) q^{77} +(7.23307 + 2.12382i) q^{79} +(1.55384 + 1.79323i) q^{80} +(3.84161 + 1.12800i) q^{82} +(-5.56234 + 12.1798i) q^{83} +(-7.47299 + 2.19427i) q^{85} +(1.05742 - 7.35448i) q^{86} +(0.456938 + 3.17808i) q^{88} +(-1.81771 + 1.16817i) q^{89} -0.0618559 q^{91} +(4.75727 + 0.606924i) q^{92} +(-1.94505 + 2.24471i) q^{94} +(-5.68043 + 3.65059i) q^{95} +(-1.09254 - 2.39234i) q^{97} +(-0.973675 + 6.77206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) $ 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8	$ 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} + 12 q^{11} - 14 q^{13} - 3 q^{14} - q^{16} - 15 q^{17} + 2 q^{19} - 5 q^{20} + 10 q^{22} + q^{23} + 13 q^{25} + 3 q^{26} + 3 q^{28} + 8 q^{29} - 21 q^{31} + q^{32} - 7 q^{34} - 7 q^{35} + 28 q^{37} + 9 q^{38} - 6 q^{40} + 31 q^{41} + 11 q^{43} + 12 q^{44} - 12 q^{46} - 18 q^{47} - 24 q^{49} - 2 q^{50} + 8 q^{52} + 21 q^{53} + 5 q^{55} - 3 q^{56} - 8 q^{58} + 5 q^{59} + 37 q^{61} - q^{62} - q^{64} - 37 q^{65} - 13 q^{67} - 26 q^{68} + 18 q^{70} - 49 q^{71} - 8 q^{73} - 28 q^{74} - 20 q^{76} + 8 q^{77} + 8 q^{79} - 5 q^{80} + 2 q^{82} + 7 q^{83} - 42 q^{85} - 22 q^{86} - q^{88} + 13 q^{89} - 24 q^{91} + 23 q^{92} - 37 q^{94} + 10 q^{95} - 32 q^{97} + 24 q^{98}+O(q^{100}) $ 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8 - 6 * q^10 + 12 * q^11 - 14 * q^13 - 3 * q^14 - q^16 - 15 * q^17 + 2 * q^19 - 5 * q^20 + 10 * q^22 + q^23 + 13 * q^25 + 3 * q^26 + 3 * q^28 + 8 * q^29 - 21 * q^31 + q^32 - 7 * q^34 - 7 * q^35 + 28 * q^37 + 9 * q^38 - 6 * q^40 + 31 * q^41 + 11 * q^43 + 12 * q^44 - 12 * q^46 - 18 * q^47 - 24 * q^49 - 2 * q^50 + 8 * q^52 + 21 * q^53 + 5 * q^55 - 3 * q^56 - 8 * q^58 + 5 * q^59 + 37 * q^61 - q^62 - q^64 - 37 * q^65 - 13 * q^67 - 26 * q^68 + 18 * q^70 - 49 * q^71 - 8 * q^73 - 28 * q^74 - 20 * q^76 + 8 * q^77 + 8 * q^79 - 5 * q^80 + 2 * q^82 + 7 * q^83 - 42 * q^85 - 22 * q^86 - q^88 + 13 * q^89 - 24 * q^91 + 23 * q^92 - 37 * q^94 + 10 * q^95 - 32 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$		0			0
$3$		0			0
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	−0.985691	−	2.15836i	−0.440814	−	0.965249i	−0.991448	−	0.130502i	$-0.958341\pi$
$5$	−0.985691	−	2.15836i	−0.440814	−	0.965249i	0.550634	−	0.834747i	$-0.314386\pi$
$6$		0			0
$7$	0.381761	−	0.112095i	0.144292	−	0.0423679i	−0.208789	−	0.977961i	$-0.566952\pi$
$7$	0.381761	−	0.112095i	0.144292	−	0.0423679i	0.353081	+	0.935593i	$0.385134\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$		0			0
$10$	−2.27667	−	0.668491i	−0.719947	−	0.211395i
$11$	−2.10260	−	2.42653i	−0.633957	−	0.731626i	0.344337	−	0.938846i	$-0.388104\pi$
$11$	−2.10260	−	2.42653i	−0.633957	−	0.731626i	−0.978294	+	0.207220i	$0.933558\pi$
$12$		0			0
$13$	−0.149167	−	0.0437995i	−0.0413716	−	0.0121478i	0.260981	−	0.965344i	$-0.415954\pi$
$13$	−0.149167	−	0.0437995i	−0.0413716	−	0.0121478i	−0.302353	+	0.953196i	$0.597772\pi$
$14$	0.165284	−	0.361922i	0.0441741	−	0.0967277i
$15$		0			0
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.467137	−	3.24901i	0.113297	−	0.788000i	−0.851377	−	0.524554i	$-0.824232\pi$
$17$	0.467137	−	3.24901i	0.113297	−	0.788000i	0.964674	−	0.263446i	$-0.0848590\pi$
$18$		0			0
$19$	−0.404992	−	2.81678i	−0.0929114	−	0.646213i	−0.982056	−	0.188588i	$-0.939609\pi$
$19$	−0.404992	−	2.81678i	−0.0929114	−	0.646213i	0.889145	−	0.457626i	$-0.151300\pi$
$20$	−1.99611	+	1.28282i	−0.446345	+	0.286848i
$21$		0			0
$22$	−3.21076			−0.684536
$23$	−1.27778	+	4.62248i	−0.266435	+	0.963853i
$23$	−1.27778	+	4.62248i	−0.266435	+	0.963853i
$24$		0			0
$25$	−0.412635	+	0.476206i	−0.0825271	+	0.0952413i
$26$	−0.130785	+	0.0840506i	−0.0256491	+	0.0164837i
$27$		0			0
$28$	−0.165284	−	0.361922i	−0.0312358	−	0.0683968i
$29$	0.0538974	−	0.374864i	0.0100085	−	0.0696106i	−0.984205	−	0.177032i	$-0.943350\pi$
$29$	0.0538974	−	0.374864i	0.0100085	−	0.0696106i	0.994214	+	0.107422i	$0.0342594\pi$
$30$		0			0
$31$	2.31086	+	1.48510i	0.415042	+	0.266731i	0.731454	−	0.681891i	$-0.238842\pi$
$31$	2.31086	+	1.48510i	0.415042	+	0.266731i	−0.316412	+	0.948622i	$0.602478\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$		0			0
$34$	−2.14953	−	2.48069i	−0.368641	−	0.425434i
$35$	−0.618239	−	0.713486i	−0.104502	−	0.120601i
$36$		0			0
$37$	2.66750	−	5.84100i	0.438534	−	0.960255i	−0.553331	−	0.832961i	$-0.686644\pi$
$37$	2.66750	−	5.84100i	0.438534	−	0.960255i	0.991865	−	0.127294i	$-0.0406290\pi$
$38$	−2.39399	−	1.53853i	−0.388357	−	0.249582i
$39$		0			0
$40$	−0.337683	+	2.34863i	−0.0533923	+	0.371352i
$41$	1.66324	+	3.64198i	0.259754	+	0.568782i	0.993909	−	0.110200i	$-0.0351490\pi$
$41$	1.66324	+	3.64198i	0.259754	+	0.568782i	−0.734156	+	0.678981i	$0.762422\pi$
$42$		0			0
$43$	6.25061	−	4.01702i	0.953209	−	0.612590i	0.0310980	−	0.999516i	$-0.490100\pi$
$43$	6.25061	−	4.01702i	0.953209	−	0.612590i	0.922111	+	0.386926i	$0.126463\pi$
$44$	−2.10260	+	2.42653i	−0.316979	+	0.365813i
$45$		0			0
$46$	2.65667	+	3.99276i	0.391704	+	0.588700i
$47$	−2.97017			−0.433244			−0.216622	−	0.976256i	$-0.569504\pi$
$47$	−2.97017			−0.433244			−0.216622	+	0.976256i	$0.569504\pi$
$48$		0			0
$49$	−5.75560	+	3.69890i	−0.822228	+	0.528414i
$50$	0.0896742	+	0.623698i	0.0126818	+	0.0882042i
$51$		0			0
$52$	−0.0221250	+	0.153882i	−0.00306818	+	0.0213397i
$53$	12.5046	−	3.67168i	1.71764	−	0.504344i	0.733191	−	0.680023i	$-0.238030\pi$
$53$	12.5046	−	3.67168i	1.71764	−	0.504344i	0.984447	+	0.175679i	$0.0562122\pi$
$54$		0			0
$55$	−3.16481	+	6.92998i	−0.426743	+	0.934438i
$56$	−0.381761	−	0.112095i	−0.0510149	−	0.0149793i
$57$		0			0
$58$	−0.248008	−	0.286217i	−0.0325651	−	0.0375821i
$59$	8.29589	+	2.43589i	1.08003	+	0.317126i	0.772892	−	0.634538i	$-0.218810\pi$
$59$	8.29589	+	2.43589i	1.08003	+	0.317126i	0.307141	+	0.951664i	$0.400628\pi$
$60$		0			0
$61$	9.37463	+	6.02471i	1.20030	+	0.771385i	0.979008	−	0.203823i	$-0.0653367\pi$
$61$	9.37463	+	6.02471i	1.20030	+	0.771385i	0.221291	+	0.975208i	$0.428973\pi$
$62$	2.63565	−	0.773896i	0.334728	−	0.0982850i
$63$		0			0
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.0524978	+	0.365130i	0.00651155	+	0.0452888i
$66$		0			0
$67$	−5.50581	+	6.35404i	−0.672642	+	0.776270i	−0.984787	−	0.173764i	$-0.944407\pi$
$67$	−5.50581	+	6.35404i	−0.672642	+	0.776270i	0.312145	+	0.950034i	$0.398952\pi$
$68$	−3.28242			−0.398052
$69$		0			0
$70$	−0.944078			−0.112839
$71$	0.233571	−	0.269556i	0.0277198	−	0.0319904i	−0.741720	−	0.670709i	$-0.765990\pi$
$71$	0.233571	−	0.269556i	0.0277198	−	0.0319904i	0.769440	+	0.638719i	$0.220535\pi$
$72$		0			0
$73$	−0.802078	−	5.57857i	−0.0938761	−	0.652923i	−0.981373	−	0.192110i	$-0.938467\pi$
$73$	−0.802078	−	5.57857i	−0.0938761	−	0.652923i	0.887497	−	0.460813i	$-0.152442\pi$
$74$	−2.66750	−	5.84100i	−0.310090	−	0.679003i
$75$		0			0
$76$	−2.73047	+	0.801739i	−0.313206	+	0.0919657i
$77$	−1.07469	−	0.690662i	−0.122472	−	0.0787082i
$78$		0			0
$79$	7.23307	+	2.12382i	0.813784	+	0.238949i	0.662037	−	0.749471i	$-0.269692\pi$
$79$	7.23307	+	2.12382i	0.813784	+	0.238949i	0.151747	+	0.988419i	$0.451510\pi$
$80$	1.55384	+	1.79323i	0.173725	+	0.200489i
$81$		0			0
$82$	3.84161	+	1.12800i	0.424235	+	0.124567i
$83$	−5.56234	+	12.1798i	−0.610547	+	1.33691i	0.311653	+	0.950196i	$0.399117\pi$
$83$	−5.56234	+	12.1798i	−0.610547	+	1.33691i	−0.922199	+	0.386715i	$0.873610\pi$
$84$		0			0
$85$	−7.47299	+	2.19427i	−0.810559	+	0.238002i
$86$	1.05742	−	7.35448i	0.114024	−	0.793054i
$87$		0			0
$88$	0.456938	+	3.17808i	0.0487098	+	0.338784i
$89$	−1.81771	+	1.16817i	−0.192677	+	0.123826i	−0.633422	−	0.773806i	$-0.718350\pi$
$89$	−1.81771	+	1.16817i	−0.192677	+	0.123826i	0.440746	+	0.897632i	$0.354714\pi$
$90$		0			0
$91$	−0.0618559			−0.00648426
$92$	4.75727	+	0.606924i	0.495980	+	0.0632762i
$93$		0			0
$94$	−1.94505	+	2.24471i	−0.200617	+	0.231524i
$95$	−5.68043	+	3.65059i	−0.582800	+	0.374543i
$96$		0			0
$97$	−1.09254	−	2.39234i	−0.110931	−	0.242905i	0.846022	−	0.533148i	$-0.178991\pi$
$97$	−1.09254	−	2.39234i	−0.110931	−	0.242905i	−0.956953	+	0.290243i	$0.906264\pi$
$98$	−0.973675	+	6.77206i	−0.0983560	+	0.684081i
$99$		0			0
$100$	0.530084	+	0.340664i	0.0530084	+	0.0340664i
$101$	3.62945	−	7.94740i	0.361144	−	0.790795i	−0.638629	−	0.769514i	$-0.720498\pi$
$101$	3.62945	−	7.94740i	0.361144	−	0.790795i	0.999774	−	0.0212810i	$-0.00677445\pi$
$102$		0			0
$103$	−2.80497	−	3.23711i	−0.276382	−	0.318962i	0.600540	−	0.799595i	$-0.294952\pi$
$103$	−2.80497	−	3.23711i	−0.276382	−	0.318962i	−0.876922	+	0.480633i	$0.840407\pi$
$104$	0.101808	+	0.117492i	0.00998308	+	0.0115211i
$105$		0			0
$106$	5.41390	−	11.8548i	0.525844	−	1.15144i
$107$	15.1529	+	9.73821i	1.46489	+	0.941428i	0.998379	+	0.0569126i	$0.0181256\pi$
$107$	15.1529	+	9.73821i	1.46489	+	0.941428i	0.466511	+	0.884515i	$0.345511\pi$
$108$		0			0
$109$	1.35720	−	9.43952i	0.129996	−	0.904142i	−0.815558	−	0.578676i	$-0.803570\pi$
$109$	1.35720	−	9.43952i	0.129996	−	0.904142i	0.945554	−	0.325466i	$-0.105521\pi$
$110$	3.16481	+	6.92998i	0.301753	+	0.660747i
$111$		0			0
$112$	−0.334716	+	0.215109i	−0.0316277	+	0.0203259i
$113$	−4.11470	+	4.74861i	−0.387078	+	0.446712i	−0.915529	−	0.402252i	$-0.868228\pi$
$113$	−4.11470	+	4.74861i	−0.387078	+	0.446712i	0.528451	+	0.848964i	$0.322773\pi$
$114$		0			0
$115$	11.2365	−	1.79843i	1.04781	−	0.167704i
$116$	−0.378719			−0.0351632
$117$		0			0
$118$	7.27358	−	4.67444i	0.669587	−	0.430317i
$119$	−0.185863	−	1.29271i	−0.0170380	−	0.118502i
$120$		0			0
$121$	0.0983447	−	0.684003i	0.00894043	−	0.0621821i
$122$	10.6922	−	3.13953i	0.968031	−	0.284239i
$123$		0			0
$124$	1.14111	−	2.49869i	0.102475	−	0.224389i
$125$	−9.94880	−	2.92123i	−0.889848	−	0.261283i
$126$		0			0
$127$	5.80796	+	6.70274i	0.515373	+	0.594772i	0.952466	−	0.304644i	$-0.0985375\pi$
$127$	5.80796	+	6.70274i	0.515373	+	0.594772i	−0.437093	+	0.899416i	$0.643992\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$		0			0
$130$	0.310326	+	0.199434i	0.0272174	+	0.0174915i
$131$	4.99107	−	1.46551i	0.436072	−	0.128042i	−0.0563262	−	0.998412i	$-0.517939\pi$
$131$	4.99107	−	1.46551i	0.436072	−	0.128042i	0.492398	+	0.870370i	$0.336120\pi$
$132$		0			0
$133$	−0.470357	−	1.02994i	−0.0407851	−	0.0893069i
$134$	1.19653	+	8.32203i	0.103364	+	0.718914i
$135$		0			0
$136$	−2.14953	+	2.48069i	−0.184320	+	0.212717i
$137$	0.501086			0.0428107			0.0214053	−	0.999771i	$-0.493186\pi$
$137$	0.501086			0.0428107			0.0214053	+	0.999771i	$0.493186\pi$
$138$		0			0
$139$	−15.7509			−1.33598			−0.667989	−	0.744171i	$-0.732845\pi$
$139$	−15.7509			−1.33598			−0.667989	+	0.744171i	$0.732845\pi$
$140$	−0.618239	+	0.713486i	−0.0522508	+	0.0603006i
$141$		0			0
$142$	−0.0507599	−	0.353043i	−0.00425968	−	0.0296267i
$143$	0.207359	+	0.454052i	0.0173402	+	0.0379697i
$144$		0			0
$145$	−0.862219	+	0.253170i	−0.0716034	+	0.0210247i
$146$	−4.74125	−	3.04702i	−0.392389	−	0.252173i
$147$		0			0
$148$	−6.16117	−	1.80908i	−0.506445	−	0.148706i
$149$	−2.53429	−	2.92473i	−0.207617	−	0.239603i	0.642385	−	0.766382i	$-0.277945\pi$
$149$	−2.53429	−	2.92473i	−0.207617	−	0.239603i	−0.850002	+	0.526779i	$0.823400\pi$
$150$		0			0
$151$	15.2097	+	4.46596i	1.23774	+	0.363435i	0.834167	−	0.551511i	$-0.185949\pi$
$151$	15.2097	+	4.46596i	1.23774	+	0.363435i	0.403577	+	0.914946i	$0.367767\pi$
$152$	−1.18216	+	2.58858i	−0.0958862	+	0.209961i
$153$		0			0
$154$	−1.22574	+	0.359910i	−0.0987730	+	0.0290024i
$155$	0.927587	−	6.45151i	0.0745056	−	0.518198i
$156$		0			0
$157$	−2.97025	−	20.6585i	−0.237051	−	1.64873i	−0.666403	−	0.745592i	$-0.732167\pi$
$157$	−2.97025	−	20.6585i	−0.237051	−	1.64873i	0.429352	−	0.903137i	$-0.358742\pi$
$158$	6.34173	−	4.07558i	0.504521	−	0.324236i
$159$		0			0
$160$	2.37279			0.187585
$161$	0.0303516	+	1.90791i	0.00239204	+	0.150364i
$162$		0			0
$163$	−15.5752	+	17.9747i	−1.21994	+	1.40789i	−0.334976	+	0.942227i	$0.608728\pi$
$163$	−15.5752	+	17.9747i	−1.21994	+	1.40789i	−0.884964	+	0.465659i	$0.845817\pi$
$164$	3.36821	−	2.16461i	0.263013	−	0.169028i
$165$		0			0
$166$	5.56234	+	12.1798i	0.431722	+	0.945339i
$167$	0.795161	−	5.53047i	0.0615314	−	0.427960i	−0.935650	−	0.352930i	$-0.885185\pi$
$167$	0.795161	−	5.53047i	0.0615314	−	0.427960i	0.997181	−	0.0750306i	$-0.0239054\pi$
$168$		0			0
$169$	−10.9160	−	7.01526i	−0.839689	−	0.539636i
$170$	−3.23545	+	7.08464i	−0.248148	+	0.543367i
$171$		0			0
$172$	−4.86569	−	5.61530i	−0.371005	−	0.428163i
$173$	−14.9062	−	17.2026i	−1.13329	−	1.30789i	−0.945478	−	0.325687i	$-0.894404\pi$
$173$	−14.9062	−	17.2026i	−1.13329	−	1.30789i	−0.187817	−	0.982204i	$-0.560141\pi$
$174$		0			0
$175$	−0.104147	+	0.228051i	−0.00787281	+	0.0172391i
$176$	2.70106	+	1.73587i	0.203600	+	0.130846i
$177$		0			0
$178$	−0.307502	+	2.13872i	−0.0230482	+	0.160304i
$179$	−1.03536	−	2.26712i	−0.0773864	−	0.169453i	0.866984	−	0.498335i	$-0.166055\pi$
$179$	−1.03536	−	2.26712i	−0.0773864	−	0.169453i	−0.944371	+	0.328883i	$0.893328\pi$
$180$		0			0
$181$	8.49697	−	5.46067i	0.631575	−	0.405888i	−0.185318	−	0.982679i	$-0.559331\pi$
$181$	8.49697	−	5.46067i	0.631575	−	0.405888i	0.816892	+	0.576790i	$0.195695\pi$
$182$	−0.0405070	+	0.0467476i	−0.00300258	+	0.00346516i
$183$		0			0
$184$	3.57403	−	3.19786i	0.263481	−	0.235749i
$185$	−15.2363			−1.12020
$186$		0			0
$187$	−8.86601	+	5.69784i	−0.648347	+	0.416667i
$188$	0.422700	+	2.93994i	0.0308285	+	0.214417i
$189$		0			0
$190$	−0.960958	+	6.68361i	−0.0697152	+	0.484880i
$191$	2.46643	−	0.724209i	0.178465	−	0.0524019i	−0.191279	−	0.981536i	$-0.561264\pi$
$191$	2.46643	−	0.724209i	0.178465	−	0.0524019i	0.369744	+	0.929134i	$0.379445\pi$
$192$		0			0
$193$	−9.38297	+	20.5458i	−0.675401	+	1.47892i	0.192043	+	0.981387i	$0.438489\pi$
$193$	−9.38297	+	20.5458i	−0.675401	+	1.47892i	−0.867444	+	0.497535i	$0.834239\pi$
$194$	−2.52347	−	0.740958i	−0.181175	−	0.0531977i
$195$		0			0
$196$	4.48036	+	5.17061i	0.320025	+	0.369329i
$197$	0.491527	+	0.144325i	0.0350198	+	0.0102828i	0.299196	−	0.954192i	$-0.403282\pi$
$197$	0.491527	+	0.144325i	0.0350198	+	0.0102828i	−0.264176	+	0.964475i	$0.585100\pi$
$198$		0			0
$199$	−1.10660	−	0.711170i	−0.0784449	−	0.0504135i	0.500830	−	0.865545i	$-0.333028\pi$
$199$	−1.10660	−	0.711170i	−0.0784449	−	0.0504135i	−0.579275	+	0.815132i	$0.696664\pi$
$200$	0.604588	−	0.177523i	0.0427508	−	0.0125528i
$201$		0			0
$202$	−3.62945	−	7.94740i	−0.255368	−	0.559177i
$203$	−0.0214445	−	0.149150i	−0.00150511	−	0.0104683i
$204$		0			0
$205$	6.22127	−	7.17973i	0.434513	−	0.501454i
$206$	−4.28331			−0.298433
$207$		0			0
$208$	0.155465			0.0107795
$209$	−5.98346	+	6.90528i	−0.413884	+	0.477648i
$210$		0			0
$211$	0.998177	+	6.94248i	0.0687174	+	0.477940i	0.994900	+	0.100865i	$0.0321610\pi$
$211$	0.998177	+	6.94248i	0.0687174	+	0.477940i	−0.926183	+	0.377075i	$0.876930\pi$
$212$	−5.41390	−	11.8548i	−0.371828	−	0.814190i
$213$		0			0
$214$	17.2827	−	5.07466i	1.18142	−	0.346897i
$215$	−14.8314	−	9.53153i	−1.01149	−	0.650045i
$216$		0			0
$217$	1.04867	+	0.307916i	0.0711880	+	0.0209027i
$218$	−6.24514	−	7.20727i	−0.422974	−	0.488138i
$219$		0			0
$220$	7.30984	+	2.14636i	0.492829	+	0.144708i
$221$	−0.211986	+	0.464186i	−0.0142598	+	0.0312245i
$222$		0			0
$223$	−12.3773	+	3.63430i	−0.828846	+	0.243371i	−0.668521	−	0.743693i	$-0.733072\pi$
$223$	−12.3773	+	3.63430i	−0.828846	+	0.243371i	−0.160325	+	0.987064i	$0.551254\pi$
$224$	−0.0566239	+	0.393828i	−0.00378334	+	0.0263137i
$225$		0			0
$226$	0.894209	+	6.21936i	0.0594819	+	0.413706i
$227$	0.648126	−	0.416525i	0.0430176	−	0.0276457i	−0.518955	−	0.854801i	$-0.673679\pi$
$227$	0.648126	−	0.416525i	0.0430176	−	0.0276457i	0.561973	+	0.827156i	$0.310043\pi$
$228$		0			0
$229$	−19.2701			−1.27341			−0.636703	−	0.771109i	$-0.719702\pi$
$229$	−19.2701			−1.27341			−0.636703	+	0.771109i	$0.719702\pi$
$230$	5.99916	−	9.66968i	0.395573	−	0.637600i
$231$		0			0
$232$	−0.248008	+	0.286217i	−0.0162825	+	0.0187911i
$233$	−7.12327	+	4.57785i	−0.466661	+	0.299905i	−0.752760	−	0.658295i	$-0.771278\pi$
$233$	−7.12327	+	4.57785i	−0.466661	+	0.299905i	0.286099	+	0.958200i	$0.407641\pi$
$234$		0			0
$235$	2.92767	+	6.41071i	0.190980	+	0.418189i
$236$	1.23047	−	8.55811i	0.0800968	−	0.557086i
$237$		0			0
$238$	−1.09868	−	0.706077i	−0.0712166	−	0.0457682i
$239$	−3.30114	+	7.22848i	−0.213533	+	0.467572i	−0.985842	−	0.167675i	$-0.946374\pi$
$239$	−3.30114	+	7.22848i	−0.213533	+	0.467572i	0.772310	+	0.635246i	$0.219101\pi$
$240$		0			0
$241$	−8.80435	−	10.1608i	−0.567138	−	0.654512i	0.397651	−	0.917537i	$-0.369825\pi$
$241$	−8.80435	−	10.1608i	−0.567138	−	0.654512i	−0.964789	+	0.263025i	$0.915280\pi$
$242$	−0.452533	−	0.522250i	−0.0290899	−	0.0335715i
$243$		0			0
$244$	4.62924	−	10.1366i	0.296357	−	0.648930i
$245$	13.6568	+	8.77669i	0.872501	+	0.560722i
$246$		0			0
$247$	−0.0629619	+	0.437910i	−0.00400617	+	0.0278635i
$248$	−1.14111	−	2.49869i	−0.0724606	−	0.158667i
$249$		0			0
$250$	−8.72280	+	5.60580i	−0.551678	+	0.354542i
$251$	9.85898	−	11.3779i	0.622293	−	0.718165i	−0.353848	−	0.935303i	$-0.615127\pi$
$251$	9.85898	−	11.3779i	0.622293	−	0.718165i	0.976141	+	0.217138i	$0.0696723\pi$
$252$		0			0
$253$	13.9032	−	6.61865i	0.874088	−	0.416111i
$254$	8.86900			0.556490
$255$		0			0
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−0.669316	−	4.65520i	−0.0417508	−	0.290383i	−0.999990	−	0.00441617i	$-0.998594\pi$
$257$	−0.669316	−	4.65520i	−0.0417508	−	0.290383i	0.958239	−	0.285967i	$-0.0923148\pi$
$258$		0			0
$259$	0.363598	−	2.52888i	0.0225929	−	0.157137i
$260$	0.353942	−	0.103927i	0.0219506	−	0.00644527i
$261$		0			0
$262$	2.16090	−	4.73170i	0.133501	−	0.292326i
$263$	−19.8270	−	5.82172i	−1.22258	−	0.358983i	−0.394137	−	0.919052i	$-0.628956\pi$
$263$	−19.8270	−	5.82172i	−1.22258	−	0.358983i	−0.828446	+	0.560069i	$0.810775\pi$
$264$		0			0
$265$	−20.2505	−	23.3703i	−1.24398	−	1.43563i
$266$	−1.08639	−	0.318994i	−0.0666110	−	0.0195588i
$267$		0			0
$268$	7.07293	+	4.54549i	0.432048	+	0.277660i
$269$	16.0994	−	4.72721i	0.981598	−	0.288223i	0.248714	−	0.968577i	$-0.419992\pi$
$269$	16.0994	−	4.72721i	0.981598	−	0.288223i	0.732884	+	0.680354i	$0.238174\pi$
$270$		0			0
$271$	4.26445	+	9.33785i	0.259047	+	0.567234i	0.993810	−	0.111090i	$-0.0354340\pi$
$271$	4.26445	+	9.33785i	0.259047	+	0.567234i	−0.734763	+	0.678324i	$0.762707\pi$
$272$	0.467137	+	3.24901i	0.0283243	+	0.197000i
$273$		0			0
$274$	0.328142	−	0.378696i	0.0198238	−	0.0228778i
$275$	2.02314			0.122000
$276$		0			0
$277$	25.2836			1.51914			0.759572	−	0.650423i	$-0.225408\pi$
$277$	25.2836			1.51914			0.759572	+	0.650423i	$0.225408\pi$
$278$	−10.3147	+	11.9038i	−0.618633	+	0.713941i
$279$		0			0
$280$	0.134356	+	0.934468i	0.00802932	+	0.0558452i
$281$	5.58559	+	12.2307i	0.333208	+	0.729624i	0.999876	−	0.0157304i	$-0.00500734\pi$
$281$	5.58559	+	12.2307i	0.333208	+	0.729624i	−0.666668	+	0.745355i	$0.732280\pi$
$282$		0			0
$283$	4.21075	−	1.23639i	0.250303	−	0.0734957i	−0.154174	−	0.988044i	$-0.549272\pi$
$283$	4.21075	−	1.23639i	0.250303	−	0.0734957i	0.404477	+	0.914548i	$0.367453\pi$
$284$	−0.300053	−	0.192832i	−0.0178049	−	0.0114425i
$285$		0			0
$286$	0.478940	+	0.140630i	0.0283203	+	0.00831560i
$287$	1.04321	+	1.20392i	0.0615785	+	0.0710654i
$288$		0			0
$289$	5.97355	+	1.75399i	0.351385	+	0.103176i
$290$	−0.373300	+	0.817413i	−0.0219209	+	0.0480002i
$291$		0			0
$292$	−5.40764	+	1.58783i	−0.316458	+	0.0929206i
$293$	−0.783862	+	5.45188i	−0.0457937	+	0.318502i	0.954030	+	0.299712i	$0.0968905\pi$
$293$	−0.783862	+	5.45188i	−0.0457937	+	0.318502i	−0.999823	+	0.0187902i	$0.994019\pi$
$294$		0			0
$295$	−2.91964	−	20.3066i	−0.169988	−	1.18229i
$296$	−5.40192	+	3.47161i	−0.313980	+	0.201783i
$297$		0			0
$298$	−3.86997			−0.224181
$299$	0.393065	−	0.633557i	0.0227315	−	0.0366395i
$300$		0			0
$301$	1.93595	−	2.23420i	0.111586	−	0.128777i
$302$	13.3354	−	8.57011i	0.767363	−	0.493154i
$303$		0			0
$304$	1.18216	+	2.58858i	0.0678018	+	0.148465i
$305$	3.76301	−	26.1723i	0.215470	−	1.49862i
$306$		0			0
$307$	−21.4631	−	13.7935i	−1.22497	−	0.787238i	−0.241867	−	0.970309i	$-0.577760\pi$
$307$	−21.4631	−	13.7935i	−1.22497	−	0.787238i	−0.983100	+	0.183071i	$0.941396\pi$
$308$	−0.530688	+	1.16204i	−0.0302387	+	0.0662136i
$309$		0			0
$310$	−4.26828	−	4.92586i	−0.242422	−	0.279770i
$311$	6.58523	+	7.59976i	0.373414	+	0.430943i	0.911089	−	0.412209i	$-0.135243\pi$
$311$	6.58523	+	7.59976i	0.373414	+	0.430943i	−0.537675	+	0.843152i	$0.680697\pi$
$312$		0			0
$313$	−1.46099	+	3.19913i	−0.0825803	+	0.180826i	−0.946418	−	0.322945i	$-0.895327\pi$
$313$	−1.46099	+	3.19913i	−0.0825803	+	0.180826i	0.863837	+	0.503771i	$0.168054\pi$
$314$	−17.5578	−	11.2837i	−0.990842	−	0.636775i
$315$		0			0
$316$	1.07283	−	7.46170i	0.0603514	−	0.419753i
$317$	14.5188	+	31.7918i	0.815459	+	1.78561i	0.581893	+	0.813265i	$0.302312\pi$
$317$	14.5188	+	31.7918i	0.815459	+	1.78561i	0.233566	+	0.972341i	$0.424961\pi$
$318$		0			0
$319$	−1.02294	+	0.657406i	−0.0572739	+	0.0368077i
$320$	1.55384	−	1.79323i	0.0868625	−	0.100245i
$321$		0			0
$322$	1.46178	+	1.22648i	0.0814618	+	0.0683490i
$323$	−9.34092			−0.519743
$324$		0			0
$325$	0.0824093	−	0.0529613i	0.00457125	−	0.00293776i
$326$	3.38480	+	23.5418i	0.187467	+	1.30386i
$327$		0			0
$328$	0.569799	−	3.96304i	0.0314619	−	0.218822i
$329$	−1.13390	+	0.332942i	−0.0625137	+	0.0183557i
$330$		0			0
$331$	0.978864	−	2.14341i	0.0538033	−	0.117813i	−0.880821	−	0.473449i	$-0.843009\pi$
$331$	0.978864	−	2.14341i	0.0538033	−	0.117813i	0.934624	+	0.355637i	$0.115736\pi$
$332$	12.8475	+	3.77236i	0.705096	+	0.207035i
$333$		0			0
$334$	−3.65893	−	4.22263i	−0.200208	−	0.231052i
$335$	19.1414	+	5.62041i	1.04580	+	0.307076i
$336$		0			0
$337$	14.9883	+	9.63237i	0.816462	+	0.524708i	0.880950	−	0.473210i	$-0.156905\pi$
$337$	14.9883	+	9.63237i	0.816462	+	0.524708i	−0.0644874	+	0.997919i	$0.520541\pi$
$338$	−12.4502	+	3.65571i	−0.677203	+	0.198845i
$339$		0			0
$340$	3.23545	+	7.08464i	0.175467	+	0.384219i
$341$	−1.25517	−	8.72992i	−0.0679714	−	0.472752i
$342$		0			0
$343$	−3.60651	+	4.16214i	−0.194733	+	0.224734i
$344$	−7.43011			−0.400605
$345$		0			0
$346$	−22.7623			−1.22371
$347$	−15.1382	+	17.4704i	−0.812660	+	0.937859i	−0.999004	−	0.0446251i	$-0.985791\pi$
$347$	−15.1382	+	17.4704i	−0.812660	+	0.937859i	0.186344	+	0.982485i	$0.440336\pi$
$348$		0			0
$349$	−1.41310	−	9.82834i	−0.0756416	−	0.526099i	−0.992049	−	0.125852i	$-0.959833\pi$
$349$	−1.41310	−	9.82834i	−0.0756416	−	0.526099i	0.916407	−	0.400247i	$-0.131076\pi$
$350$	0.104147	+	0.228051i	0.00556692	+	0.0121899i
$351$		0			0
$352$	3.08070	−	0.904575i	0.164202	−	0.0482140i
$353$	8.23891	+	5.29483i	0.438513	+	0.281815i	0.741212	−	0.671271i	$-0.234251\pi$
$353$	8.23891	+	5.29483i	0.438513	+	0.281815i	−0.302699	+	0.953086i	$0.597888\pi$
$354$		0			0
$355$	−0.812028	−	0.238433i	−0.0430980	−	0.0126547i
$356$	1.41497	+	1.63296i	0.0749931	+	0.0865466i
$357$		0			0
$358$	−2.39139	−	0.702176i	−0.126389	−	0.0371112i
$359$	11.1748	−	24.4694i	0.589783	−	1.29144i	−0.345790	−	0.938312i	$-0.612389\pi$
$359$	11.1748	−	24.4694i	0.589783	−	1.29144i	0.935573	−	0.353133i	$-0.114884\pi$
$360$		0			0
$361$	10.4601	−	3.07138i	0.550534	−	0.161651i
$362$	1.43743	−	9.99756i	0.0755498	−	0.525460i
$363$		0			0
$364$	0.00880302	+	0.0612263i	0.000461404	+	0.00320913i
$365$	−11.2500	+	7.22992i	−0.588851	+	0.378431i
$366$		0			0
$367$	20.9617			1.09419			0.547097	−	0.837069i	$-0.315733\pi$
$367$	20.9617			1.09419			0.547097	+	0.837069i	$0.315733\pi$
$368$	−0.0762839	−	4.79522i	−0.00397657	−	0.249968i
$369$		0			0
$370$	−9.97767	+	11.5148i	−0.518714	+	0.598628i
$371$	4.36218	−	2.80341i	0.226473	−	0.145546i
$372$		0			0
$373$	11.3868	+	24.9337i	0.589588	+	1.29102i	0.935691	+	0.352820i	$0.114777\pi$
$373$	11.3868	+	24.9337i	0.589588	+	1.29102i	−0.346103	+	0.938196i	$0.612495\pi$
$374$	−1.49986	+	10.4318i	−0.0775561	+	0.539414i
$375$		0			0
$376$	2.49867	+	1.60580i	0.128859	+	0.0828127i
$377$	−0.0244586	+	0.0535569i	−0.00125968	+	0.00275832i
$378$		0			0
$379$	2.66138	+	3.07140i	0.136706	+	0.157767i	0.819975	−	0.572400i	$-0.193988\pi$
$379$	2.66138	+	3.07140i	0.136706	+	0.157767i	−0.683268	+	0.730167i	$0.739442\pi$
$380$	4.42184	+	5.10308i	0.226836	+	0.261782i
$381$		0			0
$382$	1.06785	−	2.33826i	0.0546358	−	0.119636i
$383$	14.6836	+	9.43657i	0.750297	+	0.482186i	0.859056	−	0.511882i	$-0.171051\pi$
$383$	14.6836	+	9.43657i	0.750297	+	0.482186i	−0.108759	+	0.994068i	$0.534688\pi$
$384$		0			0
$385$	−0.431385	+	3.00035i	−0.0219854	+	0.152912i
$386$	9.38297	+	20.5458i	0.477581	+	1.04576i
$387$		0			0
$388$	−2.21250	+	1.42189i	−0.112323	+	0.0721854i
$389$	7.20827	−	8.31878i	0.365474	−	0.421779i	−0.542992	−	0.839738i	$-0.682709\pi$
$389$	7.20827	−	8.31878i	0.365474	−	0.421779i	0.908466	+	0.417959i	$0.137254\pi$
$390$		0			0
$391$	14.4216	+	6.31084i	0.729330	+	0.319153i
$392$	6.84169			0.345558
$393$		0			0
$394$	0.430955	−	0.276958i	0.0217112	−	0.0139530i
$395$	−2.54560	−	17.7050i	−0.128083	−	0.890836i
$396$		0			0
$397$	−3.19923	+	22.2511i	−0.160565	+	1.11675i	0.737007	+	0.675885i	$0.236238\pi$
$397$	−3.19923	+	22.2511i	−0.160565	+	1.11675i	−0.897572	+	0.440868i	$0.854671\pi$
$398$	−1.26214	+	0.370597i	−0.0632652	+	0.0185763i
$399$		0			0
$400$	0.261758	−	0.573170i	0.0130879	−	0.0286585i
$401$	−0.621311	−	0.182433i	−0.0310268	−	0.00911029i	0.266182	−	0.963923i	$-0.414238\pi$
$401$	−0.621311	−	0.182433i	−0.0310268	−	0.00911029i	−0.297209	+	0.954812i	$0.596056\pi$
$402$		0			0
$403$	−0.279658	−	0.322742i	−0.0139307	−	0.0160769i
$404$	−8.38303	−	2.46148i	−0.417071	−	0.122463i
$405$		0			0
$406$	−0.126763	−	0.0814658i	−0.00629116	−	0.00404308i
$407$	−19.7820	+	5.80853i	−0.980559	+	0.287918i
$408$		0			0
$409$	9.93727	+	21.7596i	0.491367	+	1.07594i	0.979180	+	0.202995i	$0.0650674\pi$
$409$	9.93727	+	21.7596i	0.491367	+	1.07594i	−0.487813	+	0.872948i	$0.662205\pi$
$410$	−1.35201	−	9.40345i	−0.0667711	−	0.464403i
$411$		0			0
$412$	−2.80497	+	3.23711i	−0.138191	+	0.159481i
$413$	3.44009			0.169276
$414$		0			0
$415$	31.7712			1.55959
$416$	0.101808	−	0.117492i	0.00499154	−	0.00576054i
$417$		0			0
$418$	1.30033	+	9.04399i	0.0636012	+	0.442356i
$419$	13.5866	+	29.7505i	0.663748	+	1.45340i	0.878988	+	0.476844i	$0.158219\pi$
$419$	13.5866	+	29.7505i	0.663748	+	1.45340i	−0.215240	+	0.976561i	$0.569053\pi$
$420$		0			0
$421$	26.8578	−	7.88616i	1.30897	−	0.384348i	0.448468	−	0.893799i	$-0.351970\pi$
$421$	26.8578	−	7.88616i	1.30897	−	0.384348i	0.860500	+	0.509451i	$0.170151\pi$
$422$	5.90044	+	3.79198i	0.287229	+	0.184591i
$423$		0			0
$424$	−12.5046	−	3.67168i	−0.607277	−	0.178313i
$425$	1.35444	+	1.56311i	0.0657001	+	0.0758219i
$426$		0			0
$427$	4.25420	+	1.24915i	0.205875	+	0.0604505i
$428$	7.48260	−	16.3846i	0.361685	−	0.791980i
$429$		0			0
$430$	−16.9159	+	4.96696i	−0.815758	+	0.239528i
$431$	0.854386	−	5.94238i	0.0411543	−	0.286235i	−0.958843	−	0.283937i	$-0.908359\pi$
$431$	0.854386	−	5.94238i	0.0411543	−	0.286235i	0.999997	−	0.00229793i	$-0.000731455\pi$
$432$		0			0
$433$	−1.51859	−	10.5621i	−0.0729790	−	0.507580i	−0.993222	−	0.116233i	$-0.962918\pi$
$433$	−1.51859	−	10.5621i	−0.0729790	−	0.507580i	0.920243	−	0.391347i	$-0.127991\pi$
$434$	0.919437	−	0.590886i	0.0441344	−	0.0283635i
$435$		0			0
$436$	−9.53659			−0.456720
$437$	13.5380	+	1.72715i	0.647609	+	0.0826208i
$438$		0			0
$439$	−21.5079	+	24.8215i	−1.02652	+	1.18466i	−0.0438973	+	0.999036i	$0.513977\pi$
$439$	−21.5079	+	24.8215i	−1.02652	+	1.18466i	−0.982620	+	0.185628i	$0.940568\pi$
$440$	6.40904	−	4.11884i	0.305539	−	0.196358i
$441$		0			0
$442$	0.211986	+	0.464186i	0.0100832	+	0.0220791i
$443$	−0.0587614	+	0.408695i	−0.00279184	+	0.0194177i	−0.991170	−	0.132599i	$-0.957668\pi$
$443$	−0.0587614	+	0.408695i	−0.00279184	+	0.0194177i	0.988378	+	0.152017i	$0.0485768\pi$
$444$		0			0
$445$	4.31303	+	2.77182i	0.204457	+	0.131397i
$446$	−5.35879	+	11.7341i	−0.253746	+	0.555626i
$447$		0			0
$448$	0.260554	+	0.300696i	0.0123100	+	0.0142065i
$449$	−6.17485	−	7.12616i	−0.291409	−	0.336304i	0.591101	−	0.806598i	$-0.298694\pi$
$449$	−6.17485	−	7.12616i	−0.291409	−	0.336304i	−0.882510	+	0.470293i	$0.844148\pi$
$450$		0			0
$451$	5.34025	−	11.6935i	0.251462	−	0.550626i
$452$	5.28586	+	3.39702i	0.248626	+	0.159782i
$453$		0			0
$454$	0.109643	−	0.762586i	0.00514582	−	0.0357900i
$455$	0.0609708	+	0.133507i	0.00285836	+	0.00625893i
$456$		0			0
$457$	−26.1069	+	16.7779i	−1.22123	+	0.784837i	−0.982502	−	0.186250i	$-0.940367\pi$
$457$	−26.1069	+	16.7779i	−1.22123	+	0.784837i	−0.238728	+	0.971087i	$0.576730\pi$
$458$	−12.6193	+	14.5634i	−0.589659	+	0.680503i
$459$		0			0
$460$	−3.37924	−	10.8662i	−0.157558	−	0.506637i
$461$	33.0117			1.53751			0.768753	−	0.639546i	$-0.220878\pi$
$461$	33.0117			1.53751			0.768753	+	0.639546i	$0.220878\pi$
$462$		0			0
$463$	−14.8651	+	9.55319i	−0.690838	+	0.443975i	−0.838384	−	0.545081i	$-0.816499\pi$
$463$	−14.8651	+	9.55319i	−0.690838	+	0.443975i	0.147546	+	0.989055i	$0.452863\pi$
$464$	0.0538974	+	0.374864i	0.00250212	+	0.0174026i
$465$		0			0
$466$	−1.20504	+	8.38126i	−0.0558225	+	0.388254i
$467$	−10.6555	+	3.12873i	−0.493076	+	0.144780i	−0.518812	−	0.854889i	$-0.673625\pi$
$467$	−10.6555	+	3.12873i	−0.493076	+	0.144780i	0.0257355	+	0.999669i	$0.491807\pi$
$468$		0			0
$469$	−1.38964	+	3.04290i	−0.0641678	+	0.140508i
$470$	6.76211	+	1.98553i	0.311913	+	0.0915859i
$471$		0			0
$472$	−5.66200	−	6.53430i	−0.260615	−	0.300766i
$473$	−22.8899	−	6.72109i	−1.05248	−	0.309036i
$474$		0			0
$475$	1.50848	+	0.969442i	0.0692139	+	0.0444811i
$476$	−1.25310	+	0.367943i	−0.0574356	+	0.0168646i
$477$		0			0
$478$	3.30114	+	7.22848i	0.150991	+	0.330623i
$479$	−1.46637	−	10.1988i	−0.0670002	−	0.465997i	−0.995508	−	0.0946826i	$-0.969816\pi$
$479$	−1.46637	−	10.1988i	−0.0670002	−	0.465997i	0.928507	−	0.371314i	$-0.121093\pi$
$480$		0			0
$481$	−0.653736	+	0.754452i	−0.0298078	+	0.0344001i
$482$	−13.4446			−0.612385
$483$		0			0
$484$	−0.691036			−0.0314107
$485$	−4.08662	+	4.71621i	−0.185564	+	0.214152i
$486$		0			0
$487$	1.60654	+	11.1737i	0.0727994	+	0.506331i	0.993298	+	0.115584i	$0.0368740\pi$
$487$	1.60654	+	11.1737i	0.0727994	+	0.506331i	−0.920498	+	0.390747i	$0.872217\pi$
$488$	−4.62924	−	10.1366i	−0.209556	−	0.458863i
$489$		0			0
$490$	15.5763	−	4.57361i	0.703665	−	0.206615i
$491$	7.70415	+	4.95115i	0.347683	+	0.223442i	0.702813	−	0.711375i	$-0.251927\pi$
$491$	7.70415	+	4.95115i	0.347683	+	0.223442i	−0.355130	+	0.934817i	$0.615563\pi$
$492$		0			0
$493$	−1.19276	−	0.350226i	−0.0537192	−	0.0157734i
$494$	0.289719	+	0.334353i	0.0130351	+	0.0150433i
$495$		0			0
$496$	−2.63565	−	0.773896i	−0.118344	−	0.0347490i
$497$	0.0589525	−	0.129088i	0.00264438	−	0.00579039i
$498$		0			0
$499$	29.9602	−	8.79710i	1.34120	−	0.393812i	0.469103	−	0.883143i	$-0.344577\pi$
$499$	29.9602	−	8.79710i	1.34120	−	0.393812i	0.872098	+	0.489331i	$0.162759\pi$
$500$	−1.47564	+	10.2633i	−0.0659924	+	0.458987i
$501$		0			0
$502$	−2.14256	−	14.9018i	−0.0956272	−	0.665102i
$503$	−14.3084	+	9.19543i	−0.637979	+	0.410004i	−0.819256	−	0.573428i	$-0.805613\pi$
$503$	−14.3084	+	9.19543i	−0.637979	+	0.410004i	0.181277	+	0.983432i	$0.441977\pi$
$504$		0			0
$505$	−20.7309			−0.922512
$506$	4.10263	−	14.8416i	0.182384	−	0.659792i
$507$		0			0
$508$	5.80796	−	6.70274i	0.257686	−	0.297386i
$509$	−15.4467	+	9.92700i	−0.684663	+	0.440007i	−0.836185	−	0.548447i	$-0.815219\pi$
$509$	−15.4467	+	9.92700i	−0.684663	+	0.440007i	0.151522	+	0.988454i	$0.451583\pi$
$510$		0			0
$511$	−0.931532	−	2.03977i	−0.0412085	−	0.0902341i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$		0			0
$514$	−3.95647	−	2.54267i	−0.174513	−	0.112152i
$515$	−4.22202	+	9.24494i	−0.186045	+	0.407381i
$516$		0			0
$517$	6.24508	+	7.20721i	0.274658	+	0.316973i
$518$	−1.67309	−	1.93085i	−0.0735114	−	0.0848367i
$519$		0			0
$520$	0.153240	−	0.335549i	0.00672003	−	0.0147148i
$521$	22.1100	+	14.2092i	0.968655	+	0.622517i	0.926380	−	0.376589i	$-0.122903\pi$
$521$	22.1100	+	14.2092i	0.968655	+	0.622517i	0.0422744	+	0.999106i	$0.486540\pi$
$522$		0			0
$523$	4.87720	−	33.9217i	0.213265	−	1.48329i	−0.548888	−	0.835896i	$-0.684949\pi$
$523$	4.87720	−	33.9217i	0.213265	−	1.48329i	0.762153	−	0.647397i	$-0.224142\pi$
$524$	−2.16090	−	4.73170i	−0.0943992	−	0.206705i
$525$		0			0
$526$	−17.3837	+	11.1718i	−0.757964	+	0.487114i
$527$	5.90457	−	6.81424i	0.257207	−	0.296833i
$528$		0			0
$529$	−19.7346	−	11.8130i	−0.858025	−	0.513608i
$530$	−30.9233			−1.34322
$531$		0			0
$532$	−0.952515	+	0.612144i	−0.0412968	+	0.0265398i
$533$	−0.0885838	−	0.616114i	−0.00383699	−	0.0266868i
$534$		0			0
$535$	6.08245	−	42.3044i	0.262967	−	1.82898i
$536$	8.06704	−	2.36870i	0.348443	−	0.102312i
$537$		0			0
$538$	6.97028	−	15.2628i	0.300510	−	0.658025i
$539$	21.0772	+	6.18882i	0.907859	+	0.266572i
$540$		0			0
$541$	−5.25176	−	6.06086i	−0.225791	−	0.260577i	0.631539	−	0.775344i	$-0.282424\pi$
$541$	−5.25176	−	6.06086i	−0.225791	−	0.260577i	−0.857330	+	0.514768i	$0.827878\pi$
$542$	9.84970	+	2.89213i	0.423081	+	0.124228i
$543$		0			0
$544$	2.76135	+	1.77461i	0.118392	+	0.0760857i
$545$	−21.7117	+	6.37512i	−0.930026	+	0.273080i
$546$		0			0
$547$	5.85916	+	12.8298i	0.250520	+	0.548562i	0.992555	−	0.121799i	$-0.0388665\pi$
$547$	5.85916	+	12.8298i	0.250520	+	0.548562i	−0.742035	+	0.670361i	$0.766139\pi$
$548$	−0.0713120	−	0.495986i	−0.00304630	−	0.0211875i
$549$		0			0
$550$	1.32487	−	1.52898i	0.0564927	−	0.0651961i
$551$	−1.07774			−0.0459132
$552$		0			0
$553$	2.99937			0.127546
$554$	16.5572	−	19.1081i	0.703450	−	0.811824i
$555$		0			0
$556$	2.24159	+	15.5906i	0.0950647	+	0.661190i
$557$	2.71856	+	5.95281i	0.115189	+	0.252229i	0.958442	−	0.285289i	$-0.0920895\pi$
$557$	2.71856	+	5.95281i	0.115189	+	0.252229i	−0.843253	+	0.537517i	$0.819362\pi$
$558$		0			0
$559$	−1.10833	+	0.325435i	−0.0468774	+	0.0137644i
$560$	0.794209	+	0.510407i	0.0335614	+	0.0215686i
$561$		0			0
$562$	12.9012	+	3.78812i	0.544202	+	0.159792i
$563$	−11.8897	−	13.7215i	−0.501093	−	0.578292i	0.447703	−	0.894183i	$-0.352242\pi$
$563$	−11.8897	−	13.7215i	−0.501093	−	0.578292i	−0.948796	+	0.315890i	$0.897697\pi$
$564$		0			0
$565$	14.3050	+	4.20034i	0.601818	+	0.176710i
$566$	1.82306	−	3.99194i	0.0766288	−	0.167794i
$567$		0			0
$568$	−0.342226	+	0.100487i	−0.0143595	+	0.00421632i
$569$	−0.552105	+	3.83998i	−0.0231455	+	0.160980i	−0.998116	−	0.0613534i	$-0.980458\pi$
$569$	−0.552105	+	3.83998i	−0.0231455	+	0.160980i	0.974971	+	0.222334i	$0.0713674\pi$
$570$		0			0
$571$	−4.70574	−	32.7291i	−0.196929	−	1.36967i	−0.813130	−	0.582083i	$-0.802238\pi$
$571$	−4.70574	−	32.7291i	−0.196929	−	1.36967i	0.616200	−	0.787589i	$-0.288671\pi$
$572$	0.419920	−	0.269866i	0.0175577	−	0.0112837i
$573$		0			0
$574$	1.59302			0.0664913
$575$	−1.67400	−	2.51588i	−0.0698105	−	0.104920i
$576$		0			0
$577$	−13.0284	+	15.0356i	−0.542380	+	0.625940i	−0.959091	−	0.283099i	$-0.908637\pi$
$577$	−13.0284	+	15.0356i	−0.542380	+	0.625940i	0.416711	+	0.909039i	$0.363183\pi$
$578$	5.23742	−	3.36589i	0.217848	−	0.140002i
$579$		0			0
$580$	0.373300	+	0.817413i	0.0155004	+	0.0339412i
$581$	−0.758185	+	5.27329i	−0.0314548	+	0.218773i
$582$		0			0
$583$	−35.2016	−	22.6227i	−1.45790	−	0.936936i
$584$	−2.34125	+	5.12663i	−0.0968818	+	0.212141i
$585$		0			0
$586$	3.60693	+	4.16262i	0.149001	+	0.171956i
$587$	−1.81135	−	2.09041i	−0.0747623	−	0.0862803i	0.717136	−	0.696933i	$-0.245453\pi$
$587$	−1.81135	−	2.09041i	−0.0747623	−	0.0862803i	−0.791898	+	0.610653i	$0.790907\pi$
$588$		0			0
$589$	3.24731	−	7.11062i	0.133803	−	0.292988i
$590$	−17.2586	−	11.0915i	−0.710527	−	0.456628i
$591$		0			0
$592$	−0.913843	+	6.35592i	−0.0375587	+	0.261227i
$593$	−17.7134	−	38.7869i	−0.727401	−	1.59279i	−0.803232	−	0.595666i	$-0.796888\pi$
$593$	−17.7134	−	38.7869i	−0.727401	−	1.59279i	0.0758313	−	0.997121i	$-0.475839\pi$
$594$		0			0
$595$	−2.60692	+	1.67537i	−0.106873	+	0.0686834i
$596$	−2.53429	+	2.92473i	−0.103809	+	0.119802i
$597$		0			0
$598$	−0.221408	−	0.711950i	−0.00905403	−	0.0291138i
$599$	20.1889			0.824895			0.412448	−	0.910981i	$-0.364674\pi$
$599$	20.1889			0.824895			0.412448	+	0.910981i	$0.364674\pi$
$600$		0			0
$601$	−12.5371	+	8.05708i	−0.511397	+	0.328655i	−0.770761	−	0.637125i	$-0.780124\pi$
$601$	−12.5371	+	8.05708i	−0.511397	+	0.328655i	0.259363	+	0.965780i	$0.416487\pi$
$602$	−0.420722	−	2.92618i	−0.0171473	−	0.119262i
$603$		0			0
$604$	2.25594	−	15.6904i	0.0917930	−	0.638434i
$605$	−1.57326	+	0.461952i	−0.0639622	+	0.0187810i
$606$		0			0
$607$	12.7592	−	27.9387i	0.517879	−	1.13400i	−0.452357	−	0.891837i	$-0.649417\pi$
$607$	12.7592	−	27.9387i	0.517879	−	1.13400i	0.970236	−	0.242161i	$-0.0778561\pi$
$608$	2.73047	+	0.801739i	0.110735	+	0.0325148i
$609$		0			0
$610$	−17.3155	−	19.9831i	−0.701083	−	0.809093i
$611$	0.443053	+	0.130092i	0.0179240	+	0.00526296i
$612$		0			0
$613$	15.9162	+	10.2287i	0.642850	+	0.413135i	0.821047	−	0.570860i	$-0.193390\pi$
$613$	15.9162	+	10.2287i	0.642850	+	0.413135i	−0.178197	+	0.983995i	$0.557026\pi$
$614$	−24.4798	+	7.18793i	−0.987925	+	0.290081i
$615$		0			0
$616$	0.530688	+	1.16204i	0.0213820	+	0.0468201i
$617$	−3.03989	−	21.1429i	−0.122381	−	0.851181i	−0.954846	−	0.297103i	$-0.903980\pi$
$617$	−3.03989	−	21.1429i	−0.122381	−	0.851181i	0.832464	−	0.554079i	$-0.186929\pi$
$618$		0			0
$619$	−5.27356	+	6.08601i	−0.211962	+	0.244618i	−0.851768	−	0.523919i	$-0.824469\pi$
$619$	−5.27356	+	6.08601i	−0.211962	+	0.244618i	0.639806	+	0.768537i	$0.279015\pi$
$620$	−6.51785			−0.261763
$621$		0			0
$622$	10.0559			0.403206
$623$	−0.562983	+	0.649717i	−0.0225554	+	0.0260304i
$624$		0			0
$625$	3.94974	+	27.4710i	0.157989	+	1.09884i
$626$	1.46099	+	3.19913i	0.0583931	+	0.127863i
$627$		0			0
$628$	−20.0255	+	5.88003i	−0.799106	+	0.234639i
$629$	−17.7314	−	11.3953i	−0.706996	−	0.454359i
$630$		0			0
$631$	−25.9629	−	7.62339i	−1.03357	−	0.303483i	−0.279406	−	0.960173i	$-0.590138\pi$
$631$	−25.9629	−	7.62339i	−1.03357	−	0.303483i	−0.754160	+	0.656690i	$0.771956\pi$
$632$	−4.93662	−	5.69716i	−0.196368	−	0.226621i
$633$		0			0
$634$	33.5345	+	9.84661i	1.33182	+	0.391059i
$635$	8.74209	−	19.1425i	0.346919	−	0.759647i
$636$		0			0
$637$	1.02056	−	0.299663i	0.0404360	−	0.0118731i
$638$	−0.173051	+	1.20360i	−0.00685117	+	0.0476509i
$639$		0			0
$640$	−0.337683	−	2.34863i	−0.0133481	−	0.0928379i
$641$	33.4278	−	21.4827i	1.32032	−	0.848517i	0.325051	−	0.945697i	$-0.394619\pi$
$641$	33.4278	−	21.4827i	1.32032	−	0.848517i	0.995267	+	0.0971801i	$0.0309823\pi$
$642$		0			0
$643$	−1.75237			−0.0691066			−0.0345533	−	0.999403i	$-0.511001\pi$
$643$	−1.75237			−0.0691066			−0.0345533	+	0.999403i	$0.511001\pi$
$644$	1.88417	−	0.301567i	0.0742468	−	0.0118834i
$645$		0			0
$646$	−6.11700	+	7.05940i	−0.240670	+	0.277748i
$647$	−7.48969	+	4.81333i	−0.294450	+	0.189232i	−0.679522	−	0.733655i	$-0.737813\pi$
$647$	−7.48969	+	4.81333i	−0.294450	+	0.189232i	0.385072	+	0.922886i	$0.374177\pi$
$648$		0			0
$649$	−11.5322	−	25.2519i	−0.452677	−	0.991224i
$650$	0.0139412	−	0.0969631i	0.000546818	−	0.00380320i
$651$		0			0
$652$	20.0083	+	12.8586i	0.783586	+	0.503580i
$653$	9.55387	−	20.9200i	0.373872	−	0.818665i	−0.625393	−	0.780310i	$-0.715061\pi$
$653$	9.55387	−	20.9200i	0.373872	−	0.818665i	0.999264	−	0.0383544i	$-0.0122116\pi$
$654$		0			0
$655$	−8.08275	−	9.32799i	−0.315819	−	0.364475i
$656$	−2.62193	−	3.02587i	−0.102369	−	0.118140i
$657$		0			0
$658$	−0.490923	+	1.07497i	−0.0191382	+	0.0419067i
$659$	−27.8796	−	17.9171i	−1.08604	−	0.697953i	−0.130092	−	0.991502i	$-0.541527\pi$
$659$	−27.8796	−	17.9171i	−1.08604	−	0.697953i	−0.955944	+	0.293549i	$0.905163\pi$
$660$		0			0
$661$	3.05748	−	21.2652i	0.118922	−	0.827121i	−0.839824	−	0.542858i	$-0.817342\pi$
$661$	3.05748	−	21.2652i	0.118922	−	0.827121i	0.958746	−	0.284263i	$-0.0917489\pi$
$662$	−0.978864	−	2.14341i	−0.0380446	−	0.0833062i
$663$		0			0
$664$	11.2643	−	7.23910i	0.437138	−	0.280932i
$665$	−1.75935	+	2.03040i	−0.0682247	+	0.0787355i
$666$		0			0
$667$	1.66393	+	0.728133i	0.0644278	+	0.0281934i
$668$	−5.58734			−0.216181
$669$		0			0
$670$	16.7825	−	10.7855i	0.648366	−	0.416680i
$671$	−5.09196	−	35.4154i	−0.196573	−	1.36719i
$672$		0			0
$673$	−3.63513	+	25.2829i	−0.140124	+	0.974583i	0.791503	+	0.611166i	$0.209299\pi$
$673$	−3.63513	+	25.2829i	−0.140124	+	0.974583i	−0.931627	+	0.363417i	$0.881610\pi$
$674$	17.0949	−	5.01951i	0.658470	−	0.193344i
$675$		0			0
$676$	−5.39035	+	11.8032i	−0.207321	+	0.453970i
$677$	−46.2052	−	13.5671i	−1.77581	−	0.521425i	−0.781123	−	0.624377i	$-0.785353\pi$
$677$	−46.2052	−	13.5671i	−1.77581	−	0.521425i	−0.994686	+	0.102952i	$0.967171\pi$
$678$		0			0
$679$	−0.685259	−	0.790831i	−0.0262978	−	0.0303493i
$680$	7.47299	+	2.19427i	0.286576	+	0.0841463i
$681$		0			0
$682$	−7.41960	−	4.76828i	−0.284111	−	0.182587i
$683$	−4.51551	+	1.32587i	−0.172781	+	0.0507331i	−0.366979	−	0.930229i	$-0.619608\pi$
$683$	−4.51551	+	1.32587i	−0.172781	+	0.0507331i	0.194198	+	0.980962i	$0.437790\pi$
$684$		0			0
$685$	−0.493916	−	1.08153i	−0.0188716	−	0.0413230i
$686$	0.783770	+	5.45124i	0.0299245	+	0.208129i
$687$		0			0
$688$	−4.86569	+	5.61530i	−0.185503	+	0.214081i
$689$	−2.02610			−0.0771881
$690$		0			0
$691$	−7.93027			−0.301682			−0.150841	−	0.988558i	$-0.548198\pi$
$691$	−7.93027			−0.301682			−0.150841	+	0.988558i	$0.548198\pi$
$692$	−14.9062	+	17.2026i	−0.566647	+	0.653946i
$693$		0			0
$694$	3.28984	+	22.8813i	0.124881	+	0.868564i
$695$	15.5256	+	33.9962i	0.588918	+	1.28955i
$696$		0			0
$697$	12.6098	−	3.70256i	0.477629	−	0.140245i
$698$	−8.35315	−	5.36824i	−0.316171	−	0.203191i
$699$		0			0
$700$	0.240552	+	0.0706324i	0.00909200	+	0.00266965i
$701$	21.4018	+	24.6990i	0.808335	+	0.932868i	0.998807	−	0.0488247i	$-0.0155476\pi$
$701$	21.4018	+	24.6990i	0.808335	+	0.932868i	−0.190473	+	0.981692i	$0.561002\pi$
$702$		0			0
$703$	−17.5331	−	5.14819i	−0.661274	−	0.194168i
$704$	1.33380	−	2.92061i	0.0502694	−	0.110075i
$705$		0			0
$706$	9.39691	−	2.75918i	0.353657	−	0.103843i
$707$	0.494719	−	3.44085i	0.0186058	−	0.129406i
$708$		0			0
$709$	7.03916	+	48.9584i	0.264361	+	1.83867i	0.499016	+	0.866593i	$0.333695\pi$
$709$	7.03916	+	48.9584i	0.264361	+	1.83867i	−0.234655	+	0.972079i	$0.575396\pi$
$710$	−0.711961	+	0.457550i	−0.0267194	+	0.0171715i
$711$		0			0
$712$	2.16071			0.0809762
$713$	−9.81758	+	8.78425i	−0.367671	+	0.328973i
$714$		0			0
$715$	0.775617	−	0.895109i	0.0290064	−	0.0334752i
$716$	−2.09670	+	1.34747i	−0.0783573	+	0.0503572i
$717$		0			0
$718$	−11.1748	−	24.4694i	−0.417040	−	0.913189i
$719$	−4.00200	+	27.8345i	−0.149249	+	1.03805i	0.768203	+	0.640207i	$0.221151\pi$
$719$	−4.00200	+	27.8345i	−0.149249	+	1.03805i	−0.917452	+	0.397846i	$0.869758\pi$
$720$		0			0
$721$	−1.43369	−	0.921379i	−0.0533935	−	0.0343139i
$722$	4.52875	−	9.91658i	0.168543	−	0.369057i
$723$		0			0
$724$	−6.61433	−	7.63335i	−0.245820	−	0.283691i
$725$	0.156273	+	0.180349i	0.00580383	+	0.00669798i
$726$		0			0
$727$	6.50239	−	14.2382i	0.241160	−	0.528067i	−0.749889	−	0.661564i	$-0.769893\pi$
$727$	6.50239	−	14.2382i	0.241160	−	0.528067i	0.991049	+	0.133496i	$0.0426204\pi$
$728$	0.0520365	+	0.0334418i	0.00192860	+	0.00123944i
$729$		0			0
$730$	−1.90316	+	13.2368i	−0.0704391	+	0.489914i
$731$	−10.1314	−	22.1848i	−0.374725	−	0.820533i
$732$		0			0
$733$	−8.51386	+	5.47152i	−0.314466	+	0.202095i	−0.688347	−	0.725382i	$-0.741663\pi$
$733$	−8.51386	+	5.47152i	−0.314466	+	0.202095i	0.373881	+	0.927477i	$0.378027\pi$
$734$	13.7270	−	15.8418i	0.506674	−	0.584733i
$735$		0			0
$736$	−3.67394	−	3.08255i	−0.135423	−	0.113624i
$737$	26.9948			0.994366
$738$		0			0
$739$	10.7530	−	6.91052i	0.395554	−	0.254207i	−0.327710	−	0.944778i	$-0.606277\pi$
$739$	10.7530	−	6.91052i	0.395554	−	0.254207i	0.723265	+	0.690571i	$0.242641\pi$
$740$	2.16835	+	15.0812i	0.0797103	+	0.554397i
$741$		0			0
$742$	0.737950	−	5.13256i	0.0270910	−	0.188422i
$743$	−34.6951	+	10.1874i	−1.27284	+	0.373739i	−0.847258	−	0.531181i	$-0.821748\pi$
$743$	−34.6951	+	10.1874i	−1.27284	+	0.373739i	−0.425581	+	0.904921i	$0.639930\pi$
$744$		0			0
$745$	−3.81459	+	8.35280i	−0.139756	+	0.306023i
$746$	26.3004	+	7.72250i	0.962926	+	0.282741i
$747$		0			0
$748$	6.90161	+	7.96488i	0.252348	+	0.291225i
$749$	6.87640	+	2.01909i	0.251258	+	0.0737761i
$750$		0			0
$751$	14.8497	+	9.54330i	0.541872	+	0.348240i	0.782771	−	0.622310i	$-0.213806\pi$
$751$	14.8497	+	9.54330i	0.541872	+	0.348240i	−0.240899	+	0.970550i	$0.577442\pi$
$752$	2.84986	−	0.836795i	0.103924	−	0.0305148i
$753$		0			0
$754$	0.0244586	+	0.0535569i	0.000890730	+	0.00195043i
$755$	−5.35287	−	37.2300i	−0.194811	−	1.35494i
$756$		0			0
$757$	−32.4005	+	37.3921i	−1.17762	+	1.35904i	−0.258036	+	0.966135i	$0.583075\pi$
$757$	−32.4005	+	37.3921i	−1.17762	+	1.35904i	−0.919579	+	0.392905i	$0.871470\pi$
$758$	4.06405			0.147613
$759$		0			0
$760$	6.75234			0.244933
$761$	−15.2253	+	17.5710i	−0.551918	+	0.636947i	−0.961329	−	0.275403i	$-0.911189\pi$
$761$	−15.2253	+	17.5710i	−0.551918	+	0.636947i	0.409411	+	0.912350i	$0.365734\pi$
$762$		0			0
$763$	−0.539999	−	3.75577i	−0.0195493	−	0.135968i
$764$	−1.06785	−	2.33826i	−0.0386334	−	0.0845953i
$765$		0			0
$766$	16.7474	−	4.91748i	0.605108	−	0.177676i
$767$	−1.13079	−	0.726712i	−0.0408303	−	0.0262400i
$768$		0			0
$769$	−40.5167	−	11.8968i	−1.46107	−	0.429009i	−0.547886	−	0.836553i	$-0.684567\pi$
$769$	−40.5167	−	11.8968i	−1.46107	−	0.429009i	−0.913186	+	0.407544i	$0.866385\pi$
$770$	1.98502	+	2.29083i	0.0715350	+	0.0825558i
$771$		0			0
$772$	21.6720	+	6.36349i	0.779994	+	0.229027i
$773$	−5.46707	+	11.9712i	−0.196637	+	0.430574i	−0.982107	−	0.188325i	$-0.939694\pi$
$773$	−5.46707	+	11.9712i	−0.196637	+	0.430574i	0.785470	+	0.618900i	$0.212421\pi$
$774$		0			0
$775$	−1.66075	+	0.487641i	−0.0596560	+	0.0175166i
$776$	−0.374289	+	2.60324i	−0.0134362	+	0.0934507i
$777$		0			0
$778$	−1.56651	−	10.8953i	−0.0561620	−	0.390615i
$779$	9.58505	−	6.15994i	0.343420	−	0.220703i
$780$		0			0
$781$	−1.14519			−0.0409782
$782$	14.2135	−	6.76637i	0.508275	−	0.241965i
$783$		0			0
$784$	4.48036	−	5.17061i	0.160013	−	0.184665i
$785$	−41.6608	+	26.7738i	−1.48694	+	0.955597i
$786$		0			0
$787$	15.6368	+	34.2398i	0.557391	+	1.22052i	0.953244	+	0.302202i	$0.0977217\pi$
$787$	15.6368	+	34.2398i	0.557391	+	1.22052i	−0.395853	+	0.918314i	$0.629551\pi$
$788$	0.0729047	−	0.507064i	0.00259712	−	0.0180634i
$789$		0			0
$790$	−15.0476	−	9.67048i	−0.535368	−	0.344060i
$791$	−1.03853	+	2.27407i	−0.0369260	+	0.0808566i
$792$		0			0
$793$	−1.13451	−	1.30929i	−0.0402876	−	0.0464944i
$794$	14.7212	+	16.9892i	0.522437	+	0.602924i
$795$		0			0
$796$	−0.546445	+	1.19655i	−0.0193682	+	0.0424105i
$797$	−5.36489	−	3.44780i	−0.190034	−	0.122127i	0.442164	−	0.896934i	$-0.354211\pi$
$797$	−5.36489	−	3.44780i	−0.190034	−	0.122127i	−0.632198	+	0.774807i	$0.717847\pi$
$798$		0			0
$799$	−1.38748	+	9.65012i	−0.0490854	+	0.341397i
$800$	−0.261758	−	0.573170i	−0.00925453	−	0.0202646i
$801$		0			0
$802$	−0.544746	+	0.350087i	−0.0192357	+	0.0123620i
$803$	−11.8501	+	13.6758i	−0.418182	+	0.482607i
$804$		0			0
$805$	4.08805	−	1.94612i	0.144085	−	0.0685917i
$806$	−0.427049			−0.0150422
$807$		0			0
$808$	−7.34998	+	4.72354i	−0.258571	+	0.166174i
$809$	3.74186	+	26.0252i	0.131557	+	0.914998i	0.943526	+	0.331298i	$0.107486\pi$
$809$	3.74186	+	26.0252i	0.131557	+	0.914998i	−0.811969	+	0.583700i	$0.801604\pi$
$810$		0			0
$811$	1.80260	−	12.5374i	0.0632978	−	0.440246i	−0.933386	−	0.358874i	$-0.883161\pi$
$811$	1.80260	−	12.5374i	0.0632978	−	0.440246i	0.996684	−	0.0813719i	$-0.0259301\pi$
$812$	−0.144580	+	0.0424525i	−0.00507377	+	0.00148979i
$813$		0			0
$814$	−8.56468	+	18.7540i	−0.300192	+	0.657329i
$815$	54.1482	+	15.8993i	1.89673	+	0.556929i
$816$		0			0
$817$	−13.8465	−	15.9797i	−0.484428	−	0.559059i
$818$	22.9523	+	6.73941i	0.802510	+	0.235638i
$819$		0			0
$820$	−7.99203	−	5.13617i	−0.279094	−	0.179363i
$821$	47.5748	−	13.9692i	1.66037	−	0.487529i	0.688933	−	0.724825i	$-0.258079\pi$
$821$	47.5748	−	13.9692i	1.66037	−	0.487529i	0.971437	+	0.237296i	$0.0762610\pi$
$822$		0			0
$823$	−12.4380	−	27.2354i	−0.433561	−	0.949365i	−0.992736	−	0.120316i	$-0.961609\pi$
$823$	−12.4380	−	27.2354i	−0.433561	−	0.949365i	0.559175	−	0.829050i	$-0.311118\pi$
$824$	0.609579	+	4.23972i	0.0212357	+	0.147698i
$825$		0			0
$826$	2.25278	−	2.59985i	0.0783843	−	0.0904603i
$827$	−19.8427			−0.689998			−0.344999	−	0.938603i	$-0.612121\pi$
$827$	−19.8427			−0.689998			−0.344999	+	0.938603i	$0.612121\pi$
$828$		0			0
$829$	38.9517			1.35285			0.676425	−	0.736512i	$-0.263528\pi$
$829$	38.9517			1.35285			0.676425	+	0.736512i	$0.263528\pi$
$830$	20.8057	−	24.0111i	0.722178	−	0.833438i
$831$		0			0
$832$	−0.0221250	−	0.153882i	−0.000767045	−	0.00533491i
$833$	9.32910	+	20.4279i	0.323234	+	0.707784i
$834$		0			0
$835$	−12.7205	+	3.73508i	−0.440212	+	0.129258i
$836$	7.68653	+	4.93983i	0.265844	+	0.170848i
$837$		0			0
$838$	31.3812	+	9.21435i	1.08405	+	0.318305i
$839$	−30.6040	−	35.3190i	−1.05657	−	1.21935i	−0.974890	−	0.222687i	$-0.928517\pi$
$839$	−30.6040	−	35.3190i	−1.05657	−	1.21935i	−0.0816792	−	0.996659i	$-0.526028\pi$
$840$		0			0
$841$	27.6877	+	8.12984i	0.954748	+	0.280339i
$842$	11.6281	−	25.4621i	0.400732	−	0.877482i
$843$		0			0
$844$	6.72976	−	1.97603i	0.231648	−	0.0680179i
$845$	−4.38171	+	30.4755i	−0.150735	+	1.04839i
$846$		0			0
$847$	−0.0391291	−	0.272149i	−0.00134449	−	0.00935116i
$848$	−10.9636	+	7.04590i	−0.376493	+	0.241957i
$849$		0			0
$850$	2.06829			0.0709417
$851$	23.5914	+	19.7939i	0.808704	+	0.678527i
$852$		0			0
$853$	−11.6361	+	13.4288i	−0.398414	+	0.459794i	−0.919141	−	0.393929i	$-0.871115\pi$
$853$	−11.6361	+	13.4288i	−0.398414	+	0.459794i	0.520727	+	0.853723i	$0.325661\pi$
$854$	3.72995	−	2.39710i	0.127636	−	0.0820269i
$855$		0			0
$856$	−7.48260	−	16.3846i	−0.255750	−	0.560014i
$857$	−3.35722	+	23.3500i	−0.114680	+	0.797620i	0.848583	+	0.529062i	$0.177456\pi$
$857$	−3.35722	+	23.3500i	−0.114680	+	0.797620i	−0.963264	+	0.268558i	$0.913453\pi$
$858$		0			0
$859$	19.5067	+	12.5362i	0.665561	+	0.427730i	0.829323	−	0.558770i	$-0.188726\pi$
$859$	19.5067	+	12.5362i	0.665561	+	0.427730i	−0.163762	+	0.986500i	$0.552363\pi$
$860$	−7.32379	+	16.0369i	−0.249739	+	0.546853i
$861$		0			0
$862$	−3.93145	−	4.53714i	−0.133906	−	0.154535i
$863$	23.0756	+	26.6307i	0.785502	+	0.906518i	0.997494	−	0.0707535i	$-0.0225404\pi$
$863$	23.0756	+	26.6307i	0.785502	+	0.906518i	−0.211992	+	0.977272i	$0.567995\pi$
$864$		0			0
$865$	−22.4366	+	49.1294i	−0.762868	+	1.67045i
$866$	−8.97674	−	5.76900i	−0.305042	−	0.196039i
$867$		0			0
$868$	0.155541	−	1.08181i	0.00527941	−	0.0367191i
$869$	−10.0547	−	22.0168i	−0.341083	−	0.746869i
$870$		0			0
$871$	1.09959	−	0.706665i	0.0372582	−	0.0239444i
$872$	−6.24514	+	7.20727i	−0.211487	+	0.244069i
$873$		0			0
$874$	10.1708	−	9.10028i	0.344032	−	0.307821i
$875$	−4.12551			−0.139468
$876$		0			0
$877$	27.9357	−	17.9532i	0.943323	−	0.606237i	0.0239879	−	0.999712i	$-0.492364\pi$
$877$	27.9357	−	17.9532i	0.943323	−	0.606237i	0.919335	+	0.393475i	$0.128727\pi$
$878$	4.67412	+	32.5092i	0.157744	+	1.09713i
$879$		0			0
$880$	1.08422	−	7.54089i	0.0365489	−	0.254203i
$881$	11.9769	−	3.51674i	0.403512	−	0.118482i	−0.0736776	−	0.997282i	$-0.523474\pi$
$881$	11.9769	−	3.51674i	0.403512	−	0.118482i	0.477190	+	0.878800i	$0.341655\pi$
$882$		0			0
$883$	−8.57642	+	18.7797i	−0.288620	+	0.631989i	−0.997292	−	0.0735494i	$-0.976567\pi$
$883$	−8.57642	+	18.7797i	−0.288620	+	0.631989i	0.708672	+	0.705538i	$0.249295\pi$
$884$	0.489630	+	0.143768i	0.0164680	+	0.00483545i
$885$		0			0
$886$	0.270390	+	0.312047i	0.00908394	+	0.0104834i
$887$	22.0294	+	6.46840i	0.739674	+	0.217188i	0.629799	−	0.776758i	$-0.283137\pi$
$887$	22.0294	+	6.46840i	0.739674	+	0.217188i	0.109874	+	0.993946i	$0.464955\pi$
$888$		0			0
$889$	2.96859	+	1.90780i	0.0995634	+	0.0639855i
$890$	4.91923	−	1.44442i	0.164893	−	0.0484170i
$891$		0			0
$892$	5.35879	+	11.7341i	0.179425	+	0.392887i
$893$	1.20289	+	8.36632i	0.0402533	+	0.279968i
$894$		0			0
$895$	−3.87272	+	4.46936i	−0.129451	+	0.149394i
$896$	0.397877			0.0132922
$897$		0			0
$898$	−9.42926			−0.314659
$899$	0.681259	−	0.786215i	0.0227213	−	0.0262217i
$900$		0			0
$901$	−6.08796	−	42.3427i	−0.202819	−	1.41064i
$902$	−5.34025	−	11.6935i	−0.177811	−	0.389351i
$903$		0			0
$904$	6.02880	−	1.77021i	0.200515	−	0.0588765i
$905$	−20.1615	−	12.9570i	−0.670191	−	0.430705i
$906$		0			0
$907$	−24.1820	−	7.10046i	−0.802949	−	0.235767i	−0.145590	−	0.989345i	$-0.546508\pi$
$907$	−24.1820	−	7.10046i	−0.802949	−	0.235767i	−0.657359	+	0.753578i	$0.728326\pi$
$908$	−0.504523	−	0.582251i	−0.0167432	−	0.0193227i
$909$		0			0
$910$	0.140826	+	0.0413501i	0.00466832	+	0.00137074i
$911$	−12.0923	+	26.4784i	−0.400636	+	0.877270i	0.596570	+	0.802561i	$0.296530\pi$
$911$	−12.0923	+	26.4784i	−0.400636	+	0.877270i	−0.997205	+	0.0747088i	$0.976197\pi$
$912$		0			0
$913$	41.2501	−	12.1121i	1.36518	−	0.400853i
$914$	−4.41651	+	30.7175i	−0.146085	+	1.01604i
$915$		0			0
$916$	2.74243	+	19.0740i	0.0906123	+	0.630222i
$917$	1.74112	−	1.11895i	0.0574967	−	0.0369509i
$918$		0			0
$919$	22.9832			0.758147			0.379074	−	0.925367i	$-0.376243\pi$
$919$	22.9832			0.758147			0.379074	+	0.925367i	$0.376243\pi$
$920$	−10.4250	−	4.56196i	−0.343703	−	0.150403i
$921$		0			0
$922$	21.6180	−	24.9485i	0.711952	−	0.821637i
$923$	−0.0466477	+	0.0299786i	−0.00153543	+	0.000986759i
$924$		0			0
$925$	1.68082	+	3.68048i	0.0552650	+	0.121014i
$926$	−2.51472	+	17.4903i	−0.0826389	+	0.574766i
$927$		0			0
$928$	0.318599	+	0.204751i	0.0104585	+	0.00672128i
$929$	7.30034	−	15.9855i	0.239516	−	0.524467i	−0.751255	−	0.660012i	$-0.770551\pi$
$929$	7.30034	−	15.9855i	0.239516	−	0.524467i	0.990771	+	0.135545i	$0.0432784\pi$
$930$		0			0
$931$	12.7499	+	14.7142i	0.417863	+	0.482239i
$932$	5.54500	+	6.39927i	0.181632	+	0.209615i
$933$		0			0
$934$	−4.61331	+	10.1017i	−0.150952	+	0.330539i
$935$	21.0371	+	13.5198i	0.687988	+	0.442143i
$936$		0			0
$937$	−2.69350	+	18.7337i	−0.0879930	+	0.612004i	0.897337	+	0.441346i	$0.145499\pi$
$937$	−2.69350	+	18.7337i	−0.0879930	+	0.612004i	−0.985330	+	0.170659i	$0.945410\pi$
$938$	1.38964	+	3.04290i	0.0453735	+	0.0993541i
$939$		0			0
$940$	5.92881	−	3.81021i	0.193376	−	0.124275i
$941$	−26.6714	+	30.7804i	−0.869463	+	1.00341i	0.130465	+	0.991453i	$0.458353\pi$
$941$	−26.6714	+	30.7804i	−0.869463	+	1.00341i	−0.999928	+	0.0119609i	$0.996193\pi$
$942$		0			0
$943$	−18.9602	+	3.03463i	−0.617429	+	0.0988212i
$944$	−8.64612			−0.281407
$945$		0			0
$946$	−20.0692	+	12.8977i	−0.652505	+	0.419340i
$947$	−2.24956	−	15.6460i	−0.0731009	−	0.508428i	−0.993170	−	0.116673i	$-0.962777\pi$
$947$	−2.24956	−	15.6460i	−0.0731009	−	0.508428i	0.920069	−	0.391755i	$-0.128132\pi$
$948$		0			0
$949$	−0.124695	+	0.867272i	−0.00404777	+	0.0281528i
$950$	1.72050	−	0.505185i	0.0558204	−	0.0163904i
$951$		0			0
$952$	−0.542532	+	1.18798i	−0.0175836	+	0.0385026i
$953$	−15.5810	−	4.57498i	−0.504717	−	0.148198i	0.0194551	−	0.999811i	$-0.493807\pi$
$953$	−15.5810	−	4.57498i	−0.504717	−	0.148198i	−0.524172	+	0.851613i	$0.675625\pi$
$954$		0			0
$955$	−3.99424	−	4.60960i	−0.129251	−	0.149163i
$956$	7.62471	+	2.23882i	0.246601	+	0.0724085i
$957$		0			0
$958$	−8.66804	−	5.57061i	−0.280052	−	0.179978i
$959$	0.191295	−	0.0561693i	0.00617724	−	0.00181380i
$960$		0			0
$961$	−9.74333	−	21.3349i	−0.314301	−	0.688223i
$962$	0.142071	+	0.988122i	0.00458054	+	0.0318583i
$963$		0			0
$964$	−8.80435	+	10.1608i	−0.283569	+	0.327256i
$965$	53.5941			1.72525
$966$		0			0
$967$	−22.9012			−0.736453			−0.368226	−	0.929736i	$-0.620035\pi$
$967$	−22.9012			−0.736453			−0.368226	+	0.929736i	$0.620035\pi$
$968$	−0.452533	+	0.522250i	−0.0145449	+	0.0167858i
$969$		0			0
$970$	0.888107	+	6.17692i	0.0285154	+	0.198329i
$971$	−11.1988	−	24.5220i	−0.359388	−	0.786949i	−0.999821	−	0.0189350i	$-0.993972\pi$
$971$	−11.1988	−	24.5220i	−0.359388	−	0.786949i	0.640433	−	0.768014i	$-0.278755\pi$
$972$		0			0
$973$	−6.01309	+	1.76560i	−0.192771	+	0.0566026i
$974$	9.49662	+	6.10311i	0.304291	+	0.195556i
$975$		0			0
$976$	−10.6922	−	3.13953i	−0.342251	−	0.100494i
$977$	18.1607	+	20.9585i	0.581012	+	0.670523i	0.967822	−	0.251636i	$-0.0809686\pi$
$977$	18.1607	+	20.9585i	0.581012	+	0.670523i	−0.386810	+	0.922159i	$0.626423\pi$
$978$		0			0
$979$	6.65651	+	1.95453i	0.212743	+	0.0624670i
$980$	6.74379	−	14.7668i	0.215423	−	0.471710i
$981$		0			0
$982$	8.78698	−	2.58009i	0.280404	−	0.0823339i
$983$	6.36764	−	44.2879i	0.203096	−	1.41256i	−0.591930	−	0.805989i	$-0.701634\pi$
$983$	6.36764	−	44.2879i	0.203096	−	1.41256i	0.795026	−	0.606575i	$-0.207457\pi$
$984$		0			0
$985$	−0.172987	−	1.20315i	−0.00551183	−	0.0383356i
$986$	−1.04577	+	0.672079i	−0.0333043	+	0.0214033i
$987$		0			0
$988$	0.442413			0.0140750
$989$	10.5817	+	34.0261i	0.336479	+	1.08197i
$990$		0			0
$991$	−1.42071	+	1.63959i	−0.0451305	+	0.0520833i	−0.777866	−	0.628430i	$-0.783698\pi$
$991$	−1.42071	+	1.63959i	−0.0451305	+	0.0520833i	0.732736	+	0.680514i	$0.238243\pi$
$992$	−2.31086	+	1.48510i	−0.0733697	+	0.0471519i
$993$		0			0
$994$	−0.0589525	−	0.129088i	−0.00186986	−	0.00409442i
$995$	−0.444195	+	3.08944i	−0.0140819	+	0.0979419i
$996$		0			0
$997$	9.17431	+	5.89597i	0.290553	+	0.186727i	0.677795	−	0.735251i	$-0.262936\pi$
$997$	9.17431	+	5.89597i	0.290553	+	0.186727i	−0.387242	+	0.921978i	$0.626572\pi$
$998$	12.9713	−	28.4033i	0.410600	−	0.899090i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.f.361.1		10
3.2	odd	2		46.2.c.a.39.1	yes	10
12.11	even	2		368.2.m.b.177.1		10
23.6	even	11		9522.2.a.bp.1.3		5
23.13	even	11	inner	414.2.i.f.289.1		10
23.17	odd	22		9522.2.a.bu.1.3		5
69.17	even	22		1058.2.a.l.1.1		5
69.29	odd	22		1058.2.a.m.1.1		5
69.59	odd	22		46.2.c.a.13.1	✓	10
276.59	even	22		368.2.m.b.289.1		10
276.155	odd	22		8464.2.a.bw.1.5		5
276.167	even	22		8464.2.a.bx.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.13.1	✓	10	69.59	odd	22
46.2.c.a.39.1	yes	10	3.2	odd	2
368.2.m.b.177.1		10	12.11	even	2
368.2.m.b.289.1		10	276.59	even	22
414.2.i.f.289.1		10	23.13	even	11	inner
414.2.i.f.361.1		10	1.1	even	1	trivial
1058.2.a.l.1.1		5	69.17	even	22
1058.2.a.m.1.1		5	69.29	odd	22
8464.2.a.bw.1.5		5	276.155	odd	22
8464.2.a.bx.1.5		5	276.167	even	22
9522.2.a.bp.1.3		5	23.6	even	11
9522.2.a.bu.1.3		5	23.17	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(-0.985691 - 2.15836i) q^{5} +(0.381761 - 0.112095i) q^{7} +(-0.841254 - 0.540641i) q^{8} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.142315 - 0.989821i) q^{4} +(-0.985691 - 2.15836i) q^{5} +(0.381761 - 0.112095i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-2.27667 - 0.668491i) q^{10} +(-2.10260 - 2.42653i) q^{11} +(-0.149167 - 0.0437995i) q^{13} +(0.165284 - 0.361922i) q^{14} +(-0.959493 + 0.281733i) q^{16} +(0.467137 - 3.24901i) q^{17} +(-0.404992 - 2.81678i) q^{19} +(-1.99611 + 1.28282i) q^{20} -3.21076 q^{22} +(-1.27778 + 4.62248i) q^{23} +(-0.412635 + 0.476206i) q^{25} +(-0.130785 + 0.0840506i) q^{26} +(-0.165284 - 0.361922i) q^{28} +(0.0538974 - 0.374864i) q^{29} +(2.31086 + 1.48510i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-2.14953 - 2.48069i) q^{34} +(-0.618239 - 0.713486i) q^{35} +(2.66750 - 5.84100i) q^{37} +(-2.39399 - 1.53853i) q^{38} +(-0.337683 + 2.34863i) q^{40} +(1.66324 + 3.64198i) q^{41} +(6.25061 - 4.01702i) q^{43} +(-2.10260 + 2.42653i) q^{44} +(2.65667 + 3.99276i) q^{46} -2.97017 q^{47} +(-5.75560 + 3.69890i) q^{49} +(0.0896742 + 0.623698i) q^{50} +(-0.0221250 + 0.153882i) q^{52} +(12.5046 - 3.67168i) q^{53} +(-3.16481 + 6.92998i) q^{55} +(-0.381761 - 0.112095i) q^{56} +(-0.248008 - 0.286217i) q^{58} +(8.29589 + 2.43589i) q^{59} +(9.37463 + 6.02471i) q^{61} +(2.63565 - 0.773896i) q^{62} +(0.415415 + 0.909632i) q^{64} +(0.0524978 + 0.365130i) q^{65} +(-5.50581 + 6.35404i) q^{67} -3.28242 q^{68} -0.944078 q^{70} +(0.233571 - 0.269556i) q^{71} +(-0.802078 - 5.57857i) q^{73} +(-2.66750 - 5.84100i) q^{74} +(-2.73047 + 0.801739i) q^{76} +(-1.07469 - 0.690662i) q^{77} +(7.23307 + 2.12382i) q^{79} +(1.55384 + 1.79323i) q^{80} +(3.84161 + 1.12800i) q^{82} +(-5.56234 + 12.1798i) q^{83} +(-7.47299 + 2.19427i) q^{85} +(1.05742 - 7.35448i) q^{86} +(0.456938 + 3.17808i) q^{88} +(-1.81771 + 1.16817i) q^{89} -0.0618559 q^{91} +(4.75727 + 0.606924i) q^{92} +(-1.94505 + 2.24471i) q^{94} +(-5.68043 + 3.65059i) q^{95} +(-1.09254 - 2.39234i) q^{97} +(-0.973675 + 6.77206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8	\( 10 q + q^{2} - q^{4} + 6 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} + 12 q^{11} - 14 q^{13} - 3 q^{14} - q^{16} - 15 q^{17} + 2 q^{19} - 5 q^{20} + 10 q^{22} + q^{23} + 13 q^{25} + 3 q^{26} + 3 q^{28} + 8 q^{29} - 21 q^{31} + q^{32} - 7 q^{34} - 7 q^{35} + 28 q^{37} + 9 q^{38} - 6 q^{40} + 31 q^{41} + 11 q^{43} + 12 q^{44} - 12 q^{46} - 18 q^{47} - 24 q^{49} - 2 q^{50} + 8 q^{52} + 21 q^{53} + 5 q^{55} - 3 q^{56} - 8 q^{58} + 5 q^{59} + 37 q^{61} - q^{62} - q^{64} - 37 q^{65} - 13 q^{67} - 26 q^{68} + 18 q^{70} - 49 q^{71} - 8 q^{73} - 28 q^{74} - 20 q^{76} + 8 q^{77} + 8 q^{79} - 5 q^{80} + 2 q^{82} + 7 q^{83} - 42 q^{85} - 22 q^{86} - q^{88} + 13 q^{89} - 24 q^{91} + 23 q^{92} - 37 q^{94} + 10 q^{95} - 32 q^{97} + 24 q^{98}+O(q^{100}) \) 10 * q + q^2 - q^4 + 6 * q^5 + 3 * q^7 + q^8 - 6 * q^10 + 12 * q^11 - 14 * q^13 - 3 * q^14 - q^16 - 15 * q^17 + 2 * q^19 - 5 * q^20 + 10 * q^22 + q^23 + 13 * q^25 + 3 * q^26 + 3 * q^28 + 8 * q^29 - 21 * q^31 + q^32 - 7 * q^34 - 7 * q^35 + 28 * q^37 + 9 * q^38 - 6 * q^40 + 31 * q^41 + 11 * q^43 + 12 * q^44 - 12 * q^46 - 18 * q^47 - 24 * q^49 - 2 * q^50 + 8 * q^52 + 21 * q^53 + 5 * q^55 - 3 * q^56 - 8 * q^58 + 5 * q^59 + 37 * q^61 - q^62 - q^64 - 37 * q^65 - 13 * q^67 - 26 * q^68 + 18 * q^70 - 49 * q^71 - 8 * q^73 - 28 * q^74 - 20 * q^76 + 8 * q^77 + 8 * q^79 - 5 * q^80 + 2 * q^82 + 7 * q^83 - 42 * q^85 - 22 * q^86 - q^88 + 13 * q^89 - 24 * q^91 + 23 * q^92 - 37 * q^94 + 10 * q^95 - 32 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more