LMFDB - Embedded newform 441.2.u.a.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(64,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

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("441.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.u (of order $7$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ 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 49)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			379.1
Root			$0.222521 - 0.974928i$ of defining polynomial
Character	$\chi$	$=$	441.379
Dual form			441.2.u.a.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 2.19064i) q^{2} +(-2.74698 + 1.32288i) q^{4} +(-0.153989 - 0.193096i) q^{5} +(2.06853 + 1.64960i) q^{7} +(-1.46950 - 1.84270i) q^{8} +O(q^{10})$	\(q+(0.500000 + 2.19064i) q^{2} +(-2.74698 + 1.32288i) q^{4} +(-0.153989 - 0.193096i) q^{5} +(2.06853 + 1.64960i) q^{7} +(-1.46950 - 1.84270i) q^{8} +(0.346011 - 0.433884i) q^{10} +(0.233406 + 1.02262i) q^{11} +(1.18933 + 5.21081i) q^{13} +(-2.57942 + 5.35621i) q^{14} +(-0.500000 + 0.626980i) q^{16} +(-4.44989 - 2.14295i) q^{17} -5.85086 q^{19} +(0.678448 + 0.326723i) q^{20} +(-2.12349 + 1.02262i) q^{22} +(5.44989 - 2.62453i) q^{23} +(1.09903 - 4.81517i) q^{25} +(-10.8204 + 5.21081i) q^{26} +(-7.86443 - 1.79500i) q^{28} +(2.04407 + 0.984374i) q^{29} -0.198062 q^{31} +(-5.87047 - 2.82707i) q^{32} +(2.46950 - 10.8196i) q^{34} -0.653447i q^{35} +(5.29590 + 2.55037i) q^{37} +(-2.92543 - 12.8171i) q^{38} +(-0.129531 + 0.567511i) q^{40} +(3.04892 + 3.82322i) q^{41} +(2.67845 - 3.35867i) q^{43} +(-1.99396 - 2.50035i) q^{44} +(8.47434 + 10.6265i) q^{46} +(1.82155 + 7.98074i) q^{47} +(1.55765 + 6.82450i) q^{49} +11.0978 q^{50} +(-10.1603 - 12.7406i) q^{52} +(3.08815 - 1.48717i) q^{53} +(0.161522 - 0.202542i) q^{55} -6.23576i q^{56} +(-1.13437 + 4.97002i) q^{58} +(2.96346 - 3.71606i) q^{59} +(-2.96950 - 1.43004i) q^{61} +(-0.0990311 - 0.433884i) q^{62} +(2.90097 - 12.7100i) q^{64} +(0.823044 - 1.03206i) q^{65} -3.35690 q^{67} +15.0586 q^{68} +(1.43147 - 0.326723i) q^{70} +(-3.65883 + 1.76200i) q^{71} +(3.09299 - 13.5513i) q^{73} +(-2.93900 + 12.8766i) q^{74} +(16.0722 - 7.73995i) q^{76} +(-1.20410 + 2.50035i) q^{77} +8.64310 q^{79} +0.198062 q^{80} +(-6.85086 + 8.59070i) q^{82} +(2.62080 - 11.4825i) q^{83} +(0.271438 + 1.18925i) q^{85} +(8.69687 + 4.18819i) q^{86} +(1.54138 - 1.93284i) q^{88} +(3.70775 - 16.2447i) q^{89} +(-6.13557 + 12.7406i) q^{91} +(-11.4988 + 14.4190i) q^{92} +(-16.5722 + 7.98074i) q^{94} +(0.900969 + 1.12978i) q^{95} -1.69202 q^{97} +(-14.1712 + 6.82450i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 7 q^{4} - 6 q^{5} + 7 q^{7} + q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 7 * q^4 - 6 * q^5 + 7 * q^7 + q^8	$ 6 q + 3 q^{2} - 7 q^{4} - 6 q^{5} + 7 q^{7} + q^{8} - 3 q^{10} - 2 q^{11} - 7 q^{14} - 3 q^{16} - 4 q^{17} - 8 q^{19} - 8 q^{22} + 10 q^{23} + 11 q^{25} - 28 q^{26} - 14 q^{28} + 16 q^{29} - 10 q^{31} - 21 q^{32} + 5 q^{34} + 4 q^{37} - 4 q^{38} - 15 q^{40} + 12 q^{43} + 7 q^{44} + 19 q^{46} + 15 q^{47} + 7 q^{49} + 30 q^{50} + 26 q^{53} - 19 q^{55} + q^{58} - 11 q^{59} - 8 q^{61} - 5 q^{62} + 13 q^{64} - 35 q^{65} - 12 q^{67} + 28 q^{68} + 14 q^{70} - 5 q^{71} + 4 q^{73} + 2 q^{74} + 28 q^{76} - 35 q^{77} + 60 q^{79} + 10 q^{80} - 14 q^{82} + 14 q^{83} - 17 q^{85} + 20 q^{86} + 16 q^{88} - 13 q^{89} - 70 q^{91} - 28 q^{92} - 31 q^{94} + q^{95} - 21 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 7 * q^4 - 6 * q^5 + 7 * q^7 + q^8 - 3 * q^10 - 2 * q^11 - 7 * q^14 - 3 * q^16 - 4 * q^17 - 8 * q^19 - 8 * q^22 + 10 * q^23 + 11 * q^25 - 28 * q^26 - 14 * q^28 + 16 * q^29 - 10 * q^31 - 21 * q^32 + 5 * q^34 + 4 * q^37 - 4 * q^38 - 15 * q^40 + 12 * q^43 + 7 * q^44 + 19 * q^46 + 15 * q^47 + 7 * q^49 + 30 * q^50 + 26 * q^53 - 19 * q^55 + q^58 - 11 * q^59 - 8 * q^61 - 5 * q^62 + 13 * q^64 - 35 * q^65 - 12 * q^67 + 28 * q^68 + 14 * q^70 - 5 * q^71 + 4 * q^73 + 2 * q^74 + 28 * q^76 - 35 * q^77 + 60 * q^79 + 10 * q^80 - 14 * q^82 + 14 * q^83 - 17 * q^85 + 20 * q^86 + 16 * q^88 - 13 * q^89 - 70 * q^91 - 28 * q^92 - 31 * q^94 + q^95 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	2.19064i	0.353553	+	1.54902i	0.768908	+	0.639359i	$0.220800\pi$
$2$	0.500000	+	2.19064i	0.353553	+	1.54902i	−0.415355	+	0.909659i	$0.636343\pi$
$3$		0			0
$3$		0			0
$4$	−2.74698	+	1.32288i	−1.37349	+	0.661438i
$5$	−0.153989	−	0.193096i	−0.0688661	−	0.0863553i	0.746205	−	0.665716i	$-0.231874\pi$
$5$	−0.153989	−	0.193096i	−0.0688661	−	0.0863553i	−0.815071	+	0.579361i	$0.803302\pi$
$6$		0			0
$7$	2.06853	+	1.64960i	0.781831	+	0.623490i
$7$	2.06853	+	1.64960i	0.781831	+	0.623490i
$8$	−1.46950	−	1.84270i	−0.519547	−	0.651491i
$9$		0			0
$10$	0.346011	−	0.433884i	0.109418	−	0.137206i
$11$	0.233406	+	1.02262i	0.0703746	+	0.308331i	0.997849	−	0.0655557i	$-0.0208820\pi$
$11$	0.233406	+	1.02262i	0.0703746	+	0.308331i	−0.927474	+	0.373887i	$0.878025\pi$
$12$		0			0
$13$	1.18933	+	5.21081i	0.329862	+	1.44522i	0.819393	+	0.573232i	$0.194311\pi$
$13$	1.18933	+	5.21081i	0.329862	+	1.44522i	−0.489531	+	0.871986i	$0.662832\pi$
$14$	−2.57942	+	5.35621i	−0.689378	+	1.43151i
$15$		0			0
$16$	−0.500000	+	0.626980i	−0.125000	+	0.156745i
$17$	−4.44989	−	2.14295i	−1.07926	−	0.519742i	−0.192177	−	0.981360i	$-0.561555\pi$
$17$	−4.44989	−	2.14295i	−1.07926	−	0.519742i	−0.887079	+	0.461618i	$0.847269\pi$
$18$		0			0
$19$	−5.85086			−1.34228			−0.671139	−	0.741331i	$-0.734195\pi$
$19$	−5.85086			−1.34228			−0.671139	+	0.741331i	$0.734195\pi$
$20$	0.678448	+	0.326723i	0.151706	+	0.0730576i
$21$		0			0
$22$	−2.12349	+	1.02262i	−0.452730	+	0.218023i
$23$	5.44989	−	2.62453i	1.13638	−	0.547252i	0.231465	−	0.972843i	$-0.425648\pi$
$23$	5.44989	−	2.62453i	1.13638	−	0.547252i	0.904915	+	0.425592i	$0.139934\pi$
$24$		0			0
$25$	1.09903	−	4.81517i	0.219806	−	0.963034i
$26$	−10.8204	+	5.21081i	−2.12205	+	1.02192i
$27$		0			0
$28$	−7.86443	−	1.79500i	−1.48624	−	0.339224i
$29$	2.04407	+	0.984374i	0.379575	+	0.182794i	0.613936	−	0.789356i	$-0.289585\pi$
$29$	2.04407	+	0.984374i	0.379575	+	0.182794i	−0.234361	+	0.972150i	$0.575300\pi$
$30$		0			0
$31$	−0.198062			−0.0355730			−0.0177865	−	0.999842i	$-0.505662\pi$
$31$	−0.198062			−0.0355730			−0.0177865	+	0.999842i	$0.505662\pi$
$32$	−5.87047	−	2.82707i	−1.03776	−	0.499760i
$33$		0			0
$34$	2.46950	−	10.8196i	0.423516	−	1.85554i
$35$		−	0.653447i		−	0.110453i
$36$		0			0
$37$	5.29590	+	2.55037i	0.870640	+	0.419278i	0.815197	−	0.579184i	$-0.196629\pi$
$37$	5.29590	+	2.55037i	0.870640	+	0.419278i	0.0554430	+	0.998462i	$0.482343\pi$
$38$	−2.92543	−	12.8171i	−0.474567	−	2.07921i
$39$		0			0
$40$	−0.129531	+	0.567511i	−0.0204806	+	0.0897313i
$41$	3.04892	+	3.82322i	0.476161	+	0.597087i	0.960668	−	0.277701i	$-0.0895723\pi$
$41$	3.04892	+	3.82322i	0.476161	+	0.597087i	−0.484507	+	0.874788i	$0.661001\pi$
$42$		0			0
$43$	2.67845	−	3.35867i	0.408459	−	0.512192i	−0.534469	−	0.845188i	$-0.679488\pi$
$43$	2.67845	−	3.35867i	0.408459	−	0.512192i	0.942928	+	0.332996i	$0.108060\pi$
$44$	−1.99396	−	2.50035i	−0.300601	−	0.376941i
$45$		0			0
$46$	8.47434	+	10.6265i	1.24947	+	1.56679i
$47$	1.82155	+	7.98074i	0.265701	+	1.16411i	0.914960	+	0.403544i	$0.132222\pi$
$47$	1.82155	+	7.98074i	0.265701	+	1.16411i	−0.649260	+	0.760567i	$0.724921\pi$
$48$		0			0
$49$	1.55765	+	6.82450i	0.222521	+	0.974928i
$50$	11.0978			1.56947
$51$		0			0
$52$	−10.1603	−	12.7406i	−1.40898	−	1.76681i
$53$	3.08815	−	1.48717i	0.424189	−	0.204279i	−0.209595	−	0.977788i	$-0.567215\pi$
$53$	3.08815	−	1.48717i	0.424189	−	0.204279i	0.633785	+	0.773509i	$0.281500\pi$
$54$		0			0
$55$	0.161522	−	0.202542i	0.0217796	−	0.0273108i
$56$		−	6.23576i		−	0.833289i
$57$		0			0
$58$	−1.13437	+	4.97002i	−0.148951	+	0.652596i
$59$	2.96346	−	3.71606i	0.385810	−	0.483790i	−0.550565	−	0.834792i	$-0.685588\pi$
$59$	2.96346	−	3.71606i	0.385810	−	0.483790i	0.936375	+	0.351002i	$0.114159\pi$
$60$		0			0
$61$	−2.96950	−	1.43004i	−0.380206	−	0.183097i	0.234013	−	0.972234i	$-0.424814\pi$
$61$	−2.96950	−	1.43004i	−0.380206	−	0.183097i	−0.614218	+	0.789136i	$0.710529\pi$
$62$	−0.0990311	−	0.433884i	−0.0125770	−	0.0551033i
$63$		0			0
$64$	2.90097	−	12.7100i	0.362621	−	1.58875i
$65$	0.823044	−	1.03206i	0.102086	−	0.128012i
$66$		0			0
$67$	−3.35690			−0.410110			−0.205055	−	0.978750i	$-0.565737\pi$
$67$	−3.35690			−0.410110			−0.205055	+	0.978750i	$0.565737\pi$
$68$	15.0586			1.82612
$69$		0			0
$70$	1.43147	−	0.326723i	0.171093	−	0.0390509i
$71$	−3.65883	+	1.76200i	−0.434224	+	0.209111i	−0.638209	−	0.769863i	$-0.720325\pi$
$71$	−3.65883	+	1.76200i	−0.434224	+	0.209111i	0.203986	+	0.978974i	$0.434610\pi$
$72$		0			0
$73$	3.09299	−	13.5513i	0.362007	−	1.58606i	−0.386086	−	0.922463i	$-0.626173\pi$
$73$	3.09299	−	13.5513i	0.362007	−	1.58606i	0.748093	−	0.663594i	$-0.230970\pi$
$74$	−2.93900	+	12.8766i	−0.341652	+	1.49687i
$75$		0			0
$76$	16.0722	−	7.73995i	1.84361	−	0.887834i
$77$	−1.20410	+	2.50035i	−0.137220	+	0.284941i
$78$		0			0
$79$	8.64310			0.972425			0.486213	−	0.873841i	$-0.338378\pi$
$79$	8.64310			0.972425			0.486213	+	0.873841i	$0.338378\pi$
$80$	0.198062			0.0221440
$81$		0			0
$82$	−6.85086	+	8.59070i	−0.756550	+	0.948684i
$83$	2.62080	−	11.4825i	0.287670	−	1.26037i	−0.600042	−	0.799968i	$-0.704850\pi$
$83$	2.62080	−	11.4825i	0.287670	−	1.26037i	0.887713	−	0.460398i	$-0.152293\pi$
$84$		0			0
$85$	0.271438	+	1.18925i	0.0294416	+	0.128992i
$86$	8.69687	+	4.18819i	0.937807	+	0.451624i
$87$		0			0
$88$	1.54138	−	1.93284i	0.164312	−	0.206041i
$89$	3.70775	−	16.2447i	0.393021	−	1.72194i	−0.260893	−	0.965368i	$-0.584017\pi$
$89$	3.70775	−	16.2447i	0.393021	−	1.72194i	0.653914	−	0.756569i	$-0.273126\pi$
$90$		0			0
$91$	−6.13557	+	12.7406i	−0.643183	+	1.33558i
$92$	−11.4988	+	14.4190i	−1.19883	+	1.50329i
$93$		0			0
$94$	−16.5722	+	7.98074i	−1.70929	+	0.823151i
$95$	0.900969	+	1.12978i	0.0924375	+	0.115913i
$96$		0			0
$97$	−1.69202			−0.171799			−0.0858994	−	0.996304i	$-0.527376\pi$
$97$	−1.69202			−0.171799			−0.0858994	+	0.996304i	$0.527376\pi$
$98$	−14.1712	+	6.82450i	−1.43151	+	0.689378i
$99$		0			0
$100$	3.35086	+	14.6811i	0.335086	+	1.46811i
$101$	6.03534	+	7.56808i	0.600539	+	0.753052i	0.985462	−	0.169897i	$-0.0543433\pi$
$101$	6.03534	+	7.56808i	0.600539	+	0.753052i	−0.384923	+	0.922949i	$0.625772\pi$
$102$		0			0
$103$	1.96197	+	2.46023i	0.193318	+	0.242414i	0.869038	−	0.494745i	$-0.164739\pi$
$103$	1.96197	+	2.46023i	0.193318	+	0.242414i	−0.675720	+	0.737159i	$0.736167\pi$
$104$	7.85421	−	9.84886i	0.770168	−	0.965761i
$105$		0			0
$106$	4.80194	+	6.02144i	0.466405	+	0.584854i
$107$	−1.17725	+	5.15788i	−0.113809	+	0.498631i	0.885606	+	0.464437i	$0.153743\pi$
$107$	−1.17725	+	5.15788i	−0.113809	+	0.498631i	−0.999415	+	0.0341934i	$0.989114\pi$
$108$		0			0
$109$	1.29925	+	5.69238i	0.124446	+	0.545231i	0.998260	+	0.0589714i	$0.0187821\pi$
$109$	1.29925	+	5.69238i	0.124446	+	0.545231i	−0.873814	+	0.486260i	$0.838361\pi$
$110$	0.524459	+	0.252566i	0.0500052	+	0.0240812i
$111$		0			0
$112$	−2.06853	+	0.472129i	−0.195458	+	0.0446120i
$113$	0.292249	−	1.28043i	0.0274925	−	0.120452i	−0.959320	−	0.282322i	$-0.908895\pi$
$113$	0.292249	−	1.28043i	0.0274925	−	0.120452i	0.986812	+	0.161870i	$0.0517524\pi$
$114$		0			0
$115$	−1.34601	−	0.648205i	−0.125516	−	0.0604454i
$116$	−6.91723			−0.642249
$117$		0			0
$118$	9.62229	+	4.63385i	0.885804	+	0.426581i
$119$	−5.66972	−	11.7733i	−0.519742	−	1.07926i
$120$		0			0
$121$	8.91939	−	4.29535i	0.810853	−	0.390486i
$122$	1.64795	−	7.22013i	0.149198	−	0.653680i
$123$		0			0
$124$	0.544073	−	0.262012i	0.0488592	−	0.0235293i
$125$	−2.21164	+	1.06507i	−0.197815	+	0.0952625i
$126$		0			0
$127$	10.1066	+	4.86706i	0.896813	+	0.431882i	0.824737	−	0.565517i	$-0.191323\pi$
$127$	10.1066	+	4.86706i	0.896813	+	0.431882i	0.0720759	+	0.997399i	$0.477038\pi$
$128$	16.2620			1.43738
$129$		0			0
$130$	2.67241	+	1.28696i	0.234386	+	0.112874i
$131$	−12.1453	+	15.2297i	−1.06114	+	1.33062i	−0.119933	+	0.992782i	$0.538268\pi$
$131$	−12.1453	+	15.2297i	−1.06114	+	1.33062i	−0.941203	+	0.337841i	$0.890303\pi$
$132$		0			0
$133$	−12.1027	−	9.65156i	−1.04944	−	0.836897i
$134$	−1.67845	−	7.35376i	−0.144996	−	0.635268i
$135$		0			0
$136$	2.59030	+	11.3489i	0.222117	+	0.973156i
$137$	5.72737	−	7.18189i	0.489322	−	0.613590i	−0.474462	−	0.880276i	$-0.657357\pi$
$137$	5.72737	−	7.18189i	0.489322	−	0.613590i	0.963783	+	0.266686i	$0.0859287\pi$
$138$		0			0
$139$	−9.23155	−	11.5760i	−0.783009	−	0.981863i	−0.999984	−	0.00568553i	$-0.998190\pi$
$139$	−9.23155	−	11.5760i	−0.783009	−	0.981863i	0.216974	−	0.976177i	$-0.430381\pi$
$140$	0.864429	+	1.79500i	0.0730576	+	0.151706i
$141$		0			0
$142$	−5.68933	−	7.13420i	−0.477438	−	0.598689i
$143$	−5.05107	+	2.43247i	−0.422392	+	0.203413i
$144$		0			0
$145$	−0.124686	−	0.546286i	−0.0103546	−	0.0453666i
$146$	31.2325			2.58482
$147$		0			0
$148$	−17.9215			−1.47314
$149$	0.0304995	+	0.133627i	0.00249861	+	0.0109471i	0.976162	−	0.217044i	$-0.0696415\pi$
$149$	0.0304995	+	0.133627i	0.00249861	+	0.0109471i	−0.973663	+	0.227991i	$0.926784\pi$
$150$		0			0
$151$	8.89493	−	4.28357i	0.723859	−	0.348592i	−0.0354066	−	0.999373i	$-0.511273\pi$
$151$	8.89493	−	4.28357i	0.723859	−	0.348592i	0.759266	+	0.650781i	$0.225558\pi$
$152$	8.59783	+	10.7813i	0.697376	+	0.874482i
$153$		0			0
$154$	−6.07942	−	1.38759i	−0.489893	−	0.111815i
$155$	0.0304995	+	0.0382451i	0.00244978	+	0.00307192i
$156$		0			0
$157$	4.52446	−	5.67349i	0.361091	−	0.452794i	−0.567789	−	0.823174i	$-0.692201\pi$
$157$	4.52446	−	5.67349i	0.361091	−	0.452794i	0.928880	+	0.370380i	$0.120773\pi$
$158$	4.32155	+	18.9340i	0.343804	+	1.50630i
$159$		0			0
$160$	0.358092	+	1.56890i	0.0283097	+	0.124033i
$161$	15.6027	+	3.56121i	1.22966	+	0.280663i
$162$		0			0
$163$	−7.93631	+	9.95182i	−0.621620	+	0.779487i	−0.988571	−	0.150753i	$-0.951830\pi$
$163$	−7.93631	+	9.95182i	−0.621620	+	0.779487i	0.366951	+	0.930240i	$0.380402\pi$
$164$	−13.4330	−	6.46897i	−1.04894	−	0.505142i
$165$		0			0
$166$	26.4644			2.05404
$167$	−7.21260	−	3.47340i	−0.558127	−	0.268780i	0.133483	−	0.991051i	$-0.457384\pi$
$167$	−7.21260	−	3.47340i	−0.558127	−	0.268780i	−0.691610	+	0.722271i	$0.743098\pi$
$168$		0			0
$169$	−14.0254	+	6.75429i	−1.07888	+	0.519560i
$170$	−2.46950	+	1.18925i	−0.189402	+	0.0912112i
$171$		0			0
$172$	−2.91454	+	12.7694i	−0.222232	+	0.973661i
$173$	11.0281	−	5.31086i	0.838451	−	0.403777i	0.0351734	−	0.999381i	$-0.488802\pi$
$173$	11.0281	−	5.31086i	0.838451	−	0.403777i	0.803278	+	0.595604i	$0.203087\pi$
$174$		0			0
$175$	10.2165	−	8.14737i	0.772293	−	0.615883i
$176$	−0.757865	−	0.364968i	−0.0571262	−	0.0275105i
$177$		0			0
$178$	37.4403			2.80627
$179$	−0.411854	−	0.198338i	−0.0307834	−	0.0148245i	0.418429	−	0.908250i	$-0.362581\pi$
$179$	−0.411854	−	0.198338i	−0.0307834	−	0.0148245i	−0.449212	+	0.893425i	$0.648295\pi$
$180$		0			0
$181$	2.08695	−	9.14352i	0.155122	−	0.679633i	−0.836228	−	0.548383i	$-0.815244\pi$
$181$	2.08695	−	9.14352i	0.155122	−	0.679633i	0.991349	−	0.131250i	$-0.0418991\pi$
$182$	−30.9780	−	7.07052i	−2.29624	−	0.524102i
$183$		0			0
$184$	−12.8448	−	6.18574i	−0.946932	−	0.456019i
$185$	−0.323044	−	1.41535i	−0.0237507	−	0.104058i
$186$		0			0
$187$	1.15279	−	5.05072i	0.0843006	−	0.369345i
$188$	−15.5613	−	19.5132i	−1.13492	−	1.42315i
$189$		0			0
$190$	−2.02446	+	2.53859i	−0.146870	+	0.184169i
$191$	3.36294	+	4.21699i	0.243334	+	0.305131i	0.888468	−	0.458938i	$-0.151770\pi$
$191$	3.36294	+	4.21699i	0.243334	+	0.305131i	−0.645135	+	0.764069i	$0.723199\pi$
$192$		0			0
$193$	−14.0097	−	17.5676i	−1.00844	−	1.26454i	−0.964104	−	0.265526i	$-0.914454\pi$
$193$	−14.0097	−	17.5676i	−1.00844	−	1.26454i	−0.0443359	−	0.999017i	$-0.514117\pi$
$194$	−0.846011	−	3.70662i	−0.0607400	−	0.266119i
$195$		0			0
$196$	−13.3068	−	16.6862i	−0.950484	−	1.19187i
$197$	−2.81940			−0.200874			−0.100437	−	0.994943i	$-0.532024\pi$
$197$	−2.81940			−0.200874			−0.100437	+	0.994943i	$0.532024\pi$
$198$		0			0
$199$	1.66152	+	2.08348i	0.117782	+	0.147694i	0.837227	−	0.546855i	$-0.184175\pi$
$199$	1.66152	+	2.08348i	0.117782	+	0.147694i	−0.719445	+	0.694549i	$0.755604\pi$
$200$	−10.4879	+	5.05072i	−0.741608	+	0.357140i
$201$		0			0
$202$	−13.5613	+	17.0053i	−0.954169	+	1.19649i
$203$	2.60441	+	5.40811i	0.182794	+	0.379575i
$204$		0			0
$205$	0.268750	−	1.17747i	0.0187703	−	0.0822381i
$206$	−4.40850	+	5.52809i	−0.307155	+	0.385160i
$207$		0			0
$208$	−3.86174	−	1.85972i	−0.267764	−	0.128948i
$209$	−1.36563	−	5.98319i	−0.0944623	−	0.413866i
$210$		0			0
$211$	−0.538032	+	2.35727i	−0.0370397	+	0.162281i	−0.990065	−	0.140608i	$-0.955094\pi$
$211$	−0.538032	+	2.35727i	−0.0370397	+	0.162281i	0.953026	+	0.302890i	$0.0979513\pi$
$212$	−6.51573	+	8.17047i	−0.447502	+	0.561150i
$213$		0			0
$214$	−11.8877			−0.812626
$215$	−1.06100			−0.0723595
$216$		0			0
$217$	−0.409698	−	0.326723i	−0.0278121	−	0.0221794i
$218$	−11.8204	+	5.69238i	−0.800576	+	0.385537i
$219$		0			0
$220$	−0.175760	+	0.770053i	−0.0118497	+	0.0519169i
$221$	5.87412	−	25.7362i	0.395136	−	1.73120i
$222$		0			0
$223$	−12.7397	+	6.13514i	−0.853116	+	0.410839i	−0.808733	−	0.588175i	$-0.799846\pi$
$223$	−12.7397	+	6.13514i	−0.853116	+	0.410839i	−0.0443829	+	0.999015i	$0.514132\pi$
$224$	−7.47972	−	15.5318i	−0.499760	−	1.03776i
$225$		0			0
$226$	2.95108			0.196303
$227$	11.1564			0.740479			0.370239	−	0.928936i	$-0.379276\pi$
$227$	11.1564			0.740479			0.370239	+	0.928936i	$0.379276\pi$
$228$		0			0
$229$	4.94653	−	6.20276i	0.326876	−	0.409890i	−0.591054	−	0.806632i	$-0.701288\pi$
$229$	4.94653	−	6.20276i	0.326876	−	0.409890i	0.917930	+	0.396742i	$0.129859\pi$
$230$	0.746980	−	3.27273i	0.0492544	−	0.215798i
$231$		0			0
$232$	−1.18987	−	5.21314i	−0.0781185	−	0.342260i
$233$	−15.9487	−	7.68048i	−1.04483	−	0.503165i	−0.168918	−	0.985630i	$-0.554027\pi$
$233$	−15.9487	−	7.68048i	−1.04483	−	0.503165i	−0.875915	+	0.482465i	$0.839742\pi$
$234$		0			0
$235$	1.26055	−	1.58068i	0.0822294	−	0.103112i
$236$	−3.22468	+	14.1282i	−0.209909	+	0.919670i
$237$		0			0
$238$	22.9562	−	18.3070i	1.48803	−	1.18667i
$239$	−10.3110	+	12.9295i	−0.666961	+	0.836342i	−0.994081	−	0.108640i	$-0.965350\pi$
$239$	−10.3110	+	12.9295i	−0.666961	+	0.836342i	0.327120	+	0.944983i	$0.393922\pi$
$240$		0			0
$241$	−9.85570	+	4.74625i	−0.634861	+	0.305733i	−0.723493	−	0.690331i	$-0.757465\pi$
$241$	−9.85570	+	4.74625i	−0.634861	+	0.305733i	0.0886320	+	0.996064i	$0.471750\pi$
$242$	13.8693	+	17.3915i	0.891551	+	1.11797i
$243$		0			0
$244$	10.0489			0.643316
$245$	1.07792	−	1.35168i	0.0688661	−	0.0863553i
$246$		0			0
$247$	−6.95862	−	30.4877i	−0.442766	−	1.93989i
$248$	0.291053	+	0.364968i	0.0184819	+	0.0231755i
$249$		0			0
$250$	−3.43900	−	4.31237i	−0.217502	−	0.272738i
$251$	−8.49127	+	10.6477i	−0.535964	+	0.672078i	−0.973913	−	0.226922i	$-0.927134\pi$
$251$	−8.49127	+	10.6477i	−0.535964	+	0.672078i	0.437949	+	0.899000i	$0.355705\pi$
$252$		0			0
$253$	3.95593	+	4.96058i	0.248707	+	0.311869i
$254$	−5.60872	+	24.5734i	−0.351922	+	1.54187i
$255$		0			0
$256$	2.32908	+	10.2044i	0.145568	+	0.637774i
$257$	−14.5075	−	6.98646i	−0.904955	−	0.435803i	−0.0772790	−	0.997010i	$-0.524623\pi$
$257$	−14.5075	−	6.98646i	−0.904955	−	0.435803i	−0.827676	+	0.561206i	$0.810337\pi$
$258$		0			0
$259$	6.74764	+	14.0116i	0.419278	+	0.870640i
$260$	−0.895592	+	3.92385i	−0.0555423	+	0.243347i
$261$		0			0
$262$	−39.4354	−	18.9911i	−2.43633	−	1.17327i
$263$	−31.5013			−1.94245			−0.971225	−	0.238163i	$-0.923455\pi$
$263$	−31.5013			−1.94245			−0.971225	+	0.238163i	$0.923455\pi$
$264$		0			0
$265$	−0.762709	−	0.367301i	−0.0468528	−	0.0225631i
$266$	15.0918	−	31.3384i	0.925337	−	1.92148i
$267$		0			0
$268$	9.22132	−	4.44076i	0.563282	−	0.271262i
$269$	−0.730718	+	3.20148i	−0.0445526	+	0.195198i	−0.992307	−	0.123804i	$-0.960491\pi$
$269$	−0.730718	+	3.20148i	−0.0445526	+	0.195198i	0.947754	+	0.319002i	$0.103348\pi$
$270$		0			0
$271$	−9.42543	+	4.53905i	−0.572554	+	0.275727i	−0.697675	−	0.716414i	$-0.745782\pi$
$271$	−9.42543	+	4.53905i	−0.572554	+	0.275727i	0.125121	+	0.992141i	$0.460068\pi$
$272$	3.56853	−	1.71851i	0.216374	−	0.104200i
$273$		0			0
$274$	18.5966	+	8.95567i	1.12346	+	0.541032i
$275$	5.18060			0.312402
$276$		0			0
$277$	−21.8925	−	10.5429i	−1.31539	−	0.633461i	−0.361156	−	0.932505i	$-0.617618\pi$
$277$	−21.8925	−	10.5429i	−1.31539	−	0.633461i	−0.954239	+	0.299045i	$0.903332\pi$
$278$	20.7431	−	26.0110i	1.24409	−	1.56004i
$279$		0			0
$280$	−1.20410	+	0.960240i	−0.0719589	+	0.0573853i
$281$	0.955927	+	4.18819i	0.0570258	+	0.249846i	0.995404	−	0.0957634i	$-0.0305292\pi$
$281$	0.955927	+	4.18819i	0.0570258	+	0.249846i	−0.938378	+	0.345610i	$0.887672\pi$
$282$		0			0
$283$	4.36347	+	19.1176i	0.259381	+	1.13642i	0.921915	+	0.387392i	$0.126624\pi$
$283$	4.36347	+	19.1176i	0.259381	+	1.13642i	−0.662534	+	0.749032i	$0.730519\pi$
$284$	7.71983	−	9.68036i	0.458088	−	0.574424i
$285$		0			0
$286$	−7.85421	−	9.84886i	−0.464429	−	0.582376i
$287$			12.9379i			0.763703i
$288$		0			0
$289$	4.60992	+	5.78065i	0.271172	+	0.340038i
$290$	1.13437	−	0.546286i	0.0666128	−	0.0320790i
$291$		0			0
$292$	9.43027	+	41.3167i	0.551865	+	2.41788i
$293$	−32.1280			−1.87694			−0.938468	−	0.345366i	$-0.887755\pi$
$293$	−32.1280			−1.87694			−0.938468	+	0.345366i	$0.887755\pi$
$294$		0			0
$295$	−1.17390			−0.0683470
$296$	−3.08277	−	13.5065i	−0.179182	−	0.785049i
$297$		0			0
$298$	−0.277479	+	0.133627i	−0.0160739	+	0.00774080i
$299$	20.1576	+	25.2769i	1.16575	+	1.46180i
$300$		0			0
$301$	11.0809	−	2.52915i	0.638693	−	0.145778i
$302$	13.8312	+	17.3438i	0.795898	+	0.998025i
$303$		0			0
$304$	2.92543	−	3.66837i	0.167785	−	0.210395i
$305$	0.181136	+	0.793610i	0.0103718	+	0.0454420i
$306$		0			0
$307$	5.39642	+	23.6433i	0.307990	+	1.34939i	0.857749	+	0.514069i	$0.171862\pi$
$307$	5.39642	+	23.6433i	0.307990	+	1.34939i	−0.549759	+	0.835323i	$0.685280\pi$
$308$		−	8.46128i		−	0.482126i
$309$		0			0
$310$	−0.0685317	+	0.0859360i	−0.00389234	+	0.00488084i
$311$	−9.81767	−	4.72794i	−0.556709	−	0.268097i	0.134303	−	0.990940i	$-0.457120\pi$
$311$	−9.81767	−	4.72794i	−0.556709	−	0.268097i	−0.691012	+	0.722843i	$0.742835\pi$
$312$		0			0
$313$	8.42519			0.476220			0.238110	−	0.971238i	$-0.423472\pi$
$313$	8.42519			0.476220			0.238110	+	0.971238i	$0.423472\pi$
$314$	14.6908	+	7.07473i	0.829051	+	0.399250i
$315$		0			0
$316$	−23.7424	+	11.4338i	−1.33562	+	0.643199i
$317$	30.8364	−	14.8500i	1.73194	−	0.834060i	0.746218	−	0.665702i	$-0.231868\pi$
$317$	30.8364	−	14.8500i	1.73194	−	0.834060i	0.985726	−	0.168358i	$-0.0538465\pi$
$318$		0			0
$319$	−0.529540	+	2.32007i	−0.0296485	+	0.129899i
$320$	−2.90097	+	1.39703i	−0.162169	+	0.0780965i
$321$		0			0
$322$			35.9605i			2.00400i
$323$	26.0356	+	12.5381i	1.44866	+	0.697639i
$324$		0			0
$325$	26.3980			1.46430
$326$	−25.7690	−	12.4097i	−1.42722	−	0.687311i
$327$		0			0
$328$	2.56465	−	11.2365i	0.141609	−	0.620429i
$329$	−9.39708	+	19.5132i	−0.518078	+	1.07580i
$330$		0			0
$331$	8.97823	+	4.32369i	0.493488	+	0.237651i	0.664040	−	0.747697i	$-0.268841\pi$
$331$	8.97823	+	4.32369i	0.493488	+	0.237651i	−0.170551	+	0.985349i	$0.554555\pi$
$332$	7.99061	+	35.0091i	0.438542	+	1.92138i
$333$		0			0
$334$	4.00269	−	17.5369i	0.219017	−	0.959578i
$335$	0.516926	+	0.648205i	0.0282427	+	0.0354152i
$336$		0			0
$337$	−13.7473	+	17.2385i	−0.748862	+	0.939043i	−0.999579	−	0.0290174i	$-0.990762\pi$
$337$	−13.7473	+	17.2385i	−0.748862	+	0.939043i	0.250717	+	0.968060i	$0.419334\pi$
$338$	−21.8089	−	27.3475i	−1.18625	−	1.48751i
$339$		0			0
$340$	−2.31886	−	2.90776i	−0.125758	−	0.157696i
$341$	−0.0462289	−	0.202542i	−0.00250344	−	0.0109683i
$342$		0			0
$343$	−8.03564	+	16.6862i	−0.433884	+	0.900969i
$344$	−10.1250			−0.545902
$345$		0			0
$346$	17.1482	+	21.5032i	0.921895	+	1.15602i
$347$	−22.4807	+	10.8261i	−1.20683	+	0.581177i	−0.925614	−	0.378469i	$-0.876451\pi$
$347$	−22.4807	+	10.8261i	−1.20683	+	0.581177i	−0.281212	+	0.959646i	$0.590736\pi$
$348$		0			0
$349$	−1.97554	+	2.47725i	−0.105748	+	0.132604i	−0.831889	−	0.554942i	$-0.812741\pi$
$349$	−1.97554	+	2.47725i	−0.105748	+	0.132604i	0.726141	+	0.687546i	$0.241312\pi$
$350$	22.9562	+	18.3070i	1.22706	+	0.978549i
$351$		0			0
$352$	1.52081	−	6.66311i	0.0810595	−	0.355145i
$353$	14.9547	−	18.7526i	0.795960	−	0.998102i	−0.203858	−	0.979001i	$-0.565348\pi$
$353$	14.9547	−	18.7526i	0.795960	−	0.998102i	0.999818	−	0.0191017i	$-0.00608063\pi$
$354$		0			0
$355$	0.903657	+	0.435178i	0.0479611	+	0.0230969i
$356$	11.3046	+	49.5288i	0.599144	+	2.62502i
$357$		0			0
$358$	0.228562	−	1.00139i	0.0120799	−	0.0529253i
$359$	19.4249	−	24.3580i	1.02521	−	1.28557i	0.0675317	−	0.997717i	$-0.478488\pi$
$359$	19.4249	−	24.3580i	1.02521	−	1.28557i	0.957675	−	0.287851i	$-0.0929409\pi$
$360$		0			0
$361$	15.2325			0.801711
$362$	21.0737			1.10761
$363$		0			0
$364$		−	43.1149i		−	2.25983i
$365$	−3.09299	+	1.48951i	−0.161895	+	0.0779643i
$366$		0			0
$367$	−2.13587	+	9.35784i	−0.111491	+	0.488475i	0.888093	+	0.459663i	$0.152030\pi$
$367$	−2.13587	+	9.35784i	−0.111491	+	0.488475i	−0.999585	+	0.0288126i	$0.990827\pi$
$368$	−1.07942	+	4.72923i	−0.0562685	+	0.246528i
$369$		0			0
$370$	2.93900	−	1.41535i	0.152791	−	0.0735805i
$371$	8.84117	+	2.01794i	0.459010	+	0.104766i
$372$		0			0
$373$	1.69633			0.0878328			0.0439164	−	0.999035i	$-0.486016\pi$
$373$	1.69633			0.0878328			0.0439164	+	0.999035i	$0.486016\pi$
$374$	11.6407			0.601927
$375$		0			0
$376$	12.0293	−	15.0843i	0.620364	−	0.777912i
$377$	−2.69830	+	11.8220i	−0.138969	+	0.608865i
$378$		0			0
$379$	−4.66487	−	20.4382i	−0.239619	−	1.04984i	−0.941360	−	0.337405i	$-0.890451\pi$
$379$	−4.66487	−	20.4382i	−0.239619	−	1.04984i	0.701741	−	0.712432i	$-0.252406\pi$
$380$	−3.96950	−	1.91161i	−0.203631	−	0.0980636i
$381$		0			0
$382$	−7.55645	+	9.47549i	−0.386622	+	0.484808i
$383$	0.714988	−	3.13257i	0.0365342	−	0.160067i	−0.953370	−	0.301803i	$-0.902411\pi$
$383$	0.714988	−	3.13257i	0.0365342	−	0.160067i	0.989904	+	0.141737i	$0.0452686\pi$
$384$		0			0
$385$	0.668227	−	0.152518i	0.0340560	−	0.00777306i
$386$	31.4795	−	39.4740i	1.60226	−	2.00917i
$387$		0			0
$388$	4.64795	−	2.23833i	0.235964	−	0.113634i
$389$	−8.08008	−	10.1321i	−0.409676	−	0.513718i	0.533595	−	0.845740i	$-0.320841\pi$
$389$	−8.08008	−	10.1321i	−0.409676	−	0.513718i	−0.943272	+	0.332022i	$0.892269\pi$
$390$		0			0
$391$	−29.8756			−1.51087
$392$	10.2865	−	12.8989i	0.519547	−	0.651491i
$393$		0			0
$394$	−1.40970	−	6.17629i	−0.0710196	−	0.311157i
$395$	−1.33095	−	1.66895i	−0.0669671	−	0.0839741i
$396$		0			0
$397$	1.85623	+	2.32764i	0.0931616	+	0.116821i	0.826227	−	0.563337i	$-0.190483\pi$
$397$	1.85623	+	2.32764i	0.0931616	+	0.116821i	−0.733066	+	0.680158i	$0.761911\pi$
$398$	−3.73341	+	4.68154i	−0.187139	+	0.234665i
$399$		0			0
$400$	2.46950	+	3.09666i	0.123475	+	0.154833i
$401$	1.94989	−	8.54301i	0.0973727	−	0.426618i	−0.902620	−	0.430438i	$-0.858359\pi$
$401$	1.94989	−	8.54301i	0.0973727	−	0.426618i	0.999993	+	0.00382070i	$0.00121617\pi$
$402$		0			0
$403$	−0.235562	−	1.03206i	−0.0117342	−	0.0514108i
$404$	−26.5906	−	12.8054i	−1.32293	−	0.637090i
$405$		0			0
$406$	−10.5450	+	8.40938i	−0.523341	+	0.417351i
$407$	−1.37196	+	6.01096i	−0.0680056	+	0.297952i
$408$		0			0
$409$	0.226406	+	0.109031i	0.0111950	+	0.00539125i	0.439473	−	0.898256i	$-0.355165\pi$
$409$	0.226406	+	0.109031i	0.0111950	+	0.00539125i	−0.428278	+	0.903647i	$0.640880\pi$
$410$	2.71379			0.134025
$411$		0			0
$412$	−8.64406	−	4.16276i	−0.425862	−	0.205085i
$413$	12.2600	−	2.79827i	0.603276	−	0.137694i
$414$		0			0
$415$	−2.62080	+	1.26211i	−0.128650	+	0.0619546i
$416$	7.74937	−	33.9522i	0.379944	−	1.66464i
$417$		0			0
$418$	12.4242	−	5.98319i	0.607689	−	0.292648i
$419$	−4.63318	+	2.23122i	−0.226346	+	0.109002i	−0.543620	−	0.839332i	$-0.682947\pi$
$419$	−4.63318	+	2.23122i	−0.226346	+	0.109002i	0.317274	+	0.948334i	$0.397232\pi$
$420$		0			0
$421$	28.9376	+	13.9356i	1.41033	+	0.679179i	0.975228	−	0.221201i	$-0.0709978\pi$
$421$	28.9376	+	13.9356i	1.41033	+	0.679179i	0.435103	+	0.900381i	$0.356712\pi$
$422$	−5.43296			−0.264472
$423$		0			0
$424$	−7.27844	−	3.50511i	−0.353472	−	0.170223i
$425$	−15.2092	+	19.0718i	−0.737757	+	0.925118i
$426$		0			0
$427$	−3.78352	−	7.85656i	−0.183097	−	0.380206i
$428$	−3.58934	−	15.7259i	−0.173497	−	0.760142i
$429$		0			0
$430$	−0.530499	−	2.32427i	−0.0255830	−	0.112086i
$431$	7.10723	−	8.91218i	0.342343	−	0.429285i	−0.580619	−	0.814175i	$-0.697189\pi$
$431$	7.10723	−	8.91218i	0.342343	−	0.429285i	0.922962	+	0.384891i	$0.125761\pi$
$432$		0			0
$433$	−5.26205	−	6.59840i	−0.252878	−	0.317099i	0.639148	−	0.769084i	$-0.279287\pi$
$433$	−5.26205	−	6.59840i	−0.252878	−	0.317099i	−0.892025	+	0.451985i	$0.850716\pi$
$434$	0.510885	−	1.06086i	0.0245233	−	0.0509231i
$435$		0			0
$436$	−11.0993	−	13.9181i	−0.531561	−	0.666557i
$437$	−31.8865	+	15.3557i	−1.52534	+	0.734564i
$438$		0			0
$439$	−3.88716	−	17.0308i	−0.185524	−	0.812834i	−0.978939	−	0.204153i	$-0.934556\pi$
$439$	−3.88716	−	17.0308i	−0.185524	−	0.812834i	0.793415	−	0.608681i	$-0.208301\pi$
$440$	−0.610580			−0.0291083
$441$		0			0
$442$	59.3159			2.82137
$443$	1.94331	+	8.51421i	0.0923296	+	0.404522i	0.999881	−	0.0154184i	$-0.00490801\pi$
$443$	1.94331	+	8.51421i	0.0923296	+	0.404522i	−0.907552	+	0.419941i	$0.862051\pi$
$444$		0			0
$445$	−3.70775	+	1.78556i	−0.175764	+	0.0846436i
$446$	−19.8098	−	24.8407i	−0.938020	−	1.17624i
$447$		0			0
$448$	26.9671	−	21.5056i	1.27408	−	1.01604i
$449$	5.73005	+	7.18526i	0.270418	+	0.339093i	0.898435	−	0.439106i	$-0.144705\pi$
$449$	5.73005	+	7.18526i	0.270418	+	0.339093i	−0.628017	+	0.778199i	$0.716133\pi$
$450$		0			0
$451$	−3.19806	+	4.01024i	−0.150591	+	0.188835i
$452$	0.891043	+	3.90392i	0.0419111	+	0.183625i
$453$		0			0
$454$	5.57822	+	24.4398i	0.261799	+	1.14702i
$455$	3.40499	−	0.777166i	0.159628	−	0.0364341i
$456$		0			0
$457$	20.4163	−	25.6013i	0.955036	−	1.19758i	−0.0251878	−	0.999683i	$-0.508018\pi$
$457$	20.4163	−	25.6013i	0.955036	−	1.19758i	0.980223	−	0.197894i	$-0.0634102\pi$
$458$	16.0613	+	7.73471i	0.750495	+	0.361419i
$459$		0			0
$460$	4.55496			0.212376
$461$	−12.5804	−	6.05839i	−0.585927	−	0.282167i	0.117342	−	0.993092i	$-0.462563\pi$
$461$	−12.5804	−	6.05839i	−0.585927	−	0.282167i	−0.703269	+	0.710924i	$0.748277\pi$
$462$		0			0
$463$	−15.4025	+	7.41743i	−0.715813	+	0.344717i	−0.756087	−	0.654471i	$-0.772891\pi$
$463$	−15.4025	+	7.41743i	−0.715813	+	0.344717i	0.0402738	+	0.999189i	$0.487177\pi$
$464$	−1.63922	+	0.789406i	−0.0760988	+	0.0366473i
$465$		0			0
$466$	8.85086	−	38.7781i	0.410008	−	1.79636i
$467$	−7.71648	+	3.71606i	−0.357076	+	0.171959i	−0.603818	−	0.797123i	$-0.706354\pi$
$467$	−7.71648	+	3.71606i	−0.357076	+	0.171959i	0.246741	+	0.969081i	$0.420640\pi$
$468$		0			0
$469$	−6.94385	−	5.53753i	−0.320637	−	0.255699i
$470$	4.09299	+	1.97108i	0.188796	+	0.0909192i
$471$		0			0
$472$	−11.2024			−0.515631
$473$	4.05980	+	1.95510i	0.186670	+	0.0898955i
$474$		0			0
$475$	−6.43027	+	28.1729i	−0.295041	+	1.29266i
$476$	31.1492	+	24.8407i	1.42772	+	1.13857i
$477$		0			0
$478$	−33.4795	−	16.1229i	−1.53132	−	0.737443i
$479$	0.202611	+	0.887697i	0.00925754	+	0.0405599i	0.979346	−	0.202193i	$-0.0648068\pi$
$479$	0.202611	+	0.887697i	0.00925754	+	0.0405599i	−0.970088	+	0.242753i	$0.921950\pi$
$480$		0			0
$481$	−6.99090	+	30.6291i	−0.318758	+	1.39657i
$482$	−15.3252	−	19.2172i	−0.698044	−	0.875319i
$483$		0			0
$484$	−18.8192	+	23.5985i	−0.855416	+	1.07266i
$485$	0.260553	+	0.326723i	0.0118311	+	0.0148357i
$486$		0			0
$487$	−10.6875	−	13.4017i	−0.484296	−	0.607287i	0.478311	−	0.878190i	$-0.341249\pi$
$487$	−10.6875	−	13.4017i	−0.484296	−	0.607287i	−0.962607	+	0.270903i	$0.912678\pi$
$488$	1.72856	+	7.57332i	0.0782483	+	0.342828i
$489$		0			0
$490$	3.50000	+	1.68551i	0.158114	+	0.0761436i
$491$	−24.2078			−1.09248			−0.546240	−	0.837629i	$-0.683941\pi$
$491$	−24.2078			−1.09248			−0.546240	+	0.837629i	$0.683941\pi$
$492$		0			0
$493$	−6.98643	−	8.76070i	−0.314653	−	0.394562i
$494$	63.3083	−	30.4877i	2.84838	−	1.37171i
$495$		0			0
$496$	0.0990311	−	0.124181i	0.00444663	−	0.00557590i
$497$	−10.4750	−	2.39085i	−0.469868	−	0.107244i
$498$		0			0
$499$	2.34159	−	10.2592i	0.104824	−	0.459264i	−0.895086	−	0.445893i	$-0.852886\pi$
$499$	2.34159	−	10.2592i	0.104824	−	0.459264i	0.999911	−	0.0133719i	$-0.00425653\pi$
$500$	4.66637	−	5.85144i	0.208686	−	0.261684i
$501$		0			0
$502$	−27.5710	−	13.2775i	−1.23055	−	0.592603i
$503$	6.45593	+	28.2853i	0.287856	+	1.26118i	0.887461	+	0.460882i	$0.152467\pi$
$503$	6.45593	+	28.2853i	0.287856	+	1.26118i	−0.599606	+	0.800295i	$0.704676\pi$
$504$		0			0
$505$	0.531991	−	2.33081i	0.0236733	−	0.103720i
$506$	−8.88889	+	11.1463i	−0.395159	+	0.495514i
$507$		0			0
$508$	−34.2010			−1.51743
$509$	22.7178			1.00695			0.503475	−	0.864010i	$-0.332054\pi$
$509$	22.7178			1.00695			0.503475	+	0.864010i	$0.332054\pi$
$510$		0			0
$511$	28.7521	−	22.9291i	1.27192	−	1.01432i
$512$	8.11356	−	3.90729i	0.358572	−	0.172679i
$513$		0			0
$514$	8.05107	−	35.2741i	0.355118	−	1.55587i
$515$	0.172940	−	0.757698i	0.00762063	−	0.0333882i
$516$		0			0
$517$	−7.73609	+	3.72551i	−0.340233	+	0.163848i
$518$	−27.3207	+	21.7875i	−1.20040	+	0.957287i
$519$		0			0
$520$	−3.11124			−0.136437
$521$	31.9573			1.40008			0.700038	−	0.714106i	$-0.253167\pi$
$521$	31.9573			1.40008			0.700038	+	0.714106i	$0.253167\pi$
$522$		0			0
$523$	−0.348699	+	0.437255i	−0.0152475	+	0.0191198i	−0.789397	−	0.613883i	$-0.789607\pi$
$523$	−0.348699	+	0.437255i	−0.0152475	+	0.0191198i	0.774149	+	0.633003i	$0.218178\pi$
$524$	13.2158	−	57.9023i	0.577336	−	2.52947i
$525$		0			0
$526$	−15.7506	−	69.0080i	−0.686760	−	3.00889i
$527$	0.881355	+	0.424438i	0.0383924	+	0.0184888i
$528$		0			0
$529$	8.47285	−	10.6246i	0.368385	−	0.461940i
$530$	0.423272	−	1.85447i	0.0183857	−	0.0805532i
$531$		0			0
$532$	46.0136	+	10.5023i	1.99494	+	0.455333i
$533$	−16.2959	+	20.4344i	−0.705854	+	0.885112i
$534$		0			0
$535$	1.17725	−	0.566934i	0.0508970	−	0.0245107i
$536$	4.93296	+	6.18574i	0.213071	+	0.267183i
$537$		0			0
$538$	−7.37867			−0.318117
$539$	−6.61529	+	3.18576i	−0.284941	+	0.137220i
$540$		0			0
$541$	10.2008	+	44.6924i	0.438565	+	1.92148i	0.385012	+	0.922912i	$0.374197\pi$
$541$	10.2008	+	44.6924i	0.438565	+	1.92148i	0.0535529	+	0.998565i	$0.482945\pi$
$542$	−14.6561	−	18.3782i	−0.629535	−	0.789412i
$543$		0			0
$544$	20.0646	+	25.1603i	0.860265	+	1.07874i
$545$	0.899108	−	1.12745i	0.0385136	−	0.0482945i
$546$		0			0
$547$	10.6047	+	13.2979i	0.453424	+	0.568576i	0.955026	−	0.296523i	$-0.0958270\pi$
$547$	10.6047	+	13.2979i	0.453424	+	0.568576i	−0.501601	+	0.865099i	$0.667256\pi$
$548$	−6.23221	+	27.3051i	−0.266227	+	1.16642i
$549$		0			0
$550$	2.59030	+	11.3489i	0.110451	+	0.483917i
$551$	−11.9596	−	5.75943i	−0.509495	−	0.245360i
$552$		0			0
$553$	17.8785	+	14.2577i	0.760273	+	0.606297i
$554$	12.1494	−	53.2302i	0.516180	−	2.26153i
$555$		0			0
$556$	40.6725	+	19.5868i	1.72490	+	0.830666i
$557$	30.7071			1.30110			0.650551	−	0.759463i	$-0.274538\pi$
$557$	30.7071			1.30110			0.650551	+	0.759463i	$0.274538\pi$
$558$		0			0
$559$	20.6869	+	9.96231i	0.874964	+	0.421361i
$560$	0.409698	+	0.326723i	0.0173129	+	0.0138066i
$561$		0			0
$562$	−8.69687	+	4.18819i	−0.366855	+	0.176668i
$563$	−9.61237	+	42.1145i	−0.405113	+	1.77492i	0.201056	+	0.979580i	$0.435563\pi$
$563$	−9.61237	+	42.1145i	−0.405113	+	1.77492i	−0.606169	+	0.795336i	$0.707294\pi$
$564$		0			0
$565$	−0.292249	+	0.140740i	−0.0122950	+	0.00592096i
$566$	−39.6981	+	19.1176i	−1.66864	+	0.803573i
$567$		0			0
$568$	8.62349	+	4.15285i	0.361834	+	0.174250i
$569$	10.3002			0.431807			0.215904	−	0.976415i	$-0.430730\pi$
$569$	10.3002			0.431807			0.215904	+	0.976415i	$0.430730\pi$
$570$		0			0
$571$	5.86443	+	2.82416i	0.245419	+	0.118187i	0.552550	−	0.833480i	$-0.313655\pi$
$571$	5.86443	+	2.82416i	0.245419	+	0.118187i	−0.307131	+	0.951667i	$0.599369\pi$
$572$	10.6573	−	13.3639i	0.445606	−	0.558772i
$573$		0			0
$574$	−28.3424	+	6.46897i	−1.18299	+	0.270010i
$575$	−6.64795	−	29.1266i	−0.277239	−	1.21466i
$576$		0			0
$577$	1.61811	+	7.08942i	0.0673629	+	0.295136i	0.997376	−	0.0723890i	$-0.0230623\pi$
$577$	1.61811	+	7.08942i	0.0673629	+	0.295136i	−0.930014	+	0.367525i	$0.880205\pi$
$578$	−10.3584	+	12.9890i	−0.430852	+	0.540271i
$579$		0			0
$580$	1.06518	+	1.33569i	0.0442292	+	0.0554616i
$581$	24.3627	−	19.4286i	1.01074	−	0.806034i
$582$		0			0
$583$	2.24160	+	2.81088i	0.0928377	+	0.116415i
$584$	−29.5160	+	14.2142i	−1.22138	+	0.588186i
$585$		0			0
$586$	−16.0640	−	70.3809i	−0.663597	−	2.90741i
$587$	23.8006			0.982356			0.491178	−	0.871059i	$-0.336566\pi$
$587$	23.8006			0.982356			0.491178	+	0.871059i	$0.336566\pi$
$588$		0			0
$589$	1.15883			0.0477489
$590$	−0.586950	−	2.57159i	−0.0241643	−	0.105871i
$591$		0			0
$592$	−4.24698	+	2.04524i	−0.174550	+	0.0840587i
$593$	−12.5274	−	15.7089i	−0.514440	−	0.645088i	0.454978	−	0.890503i	$-0.349647\pi$
$593$	−12.5274	−	15.7089i	−0.514440	−	0.645088i	−0.969418	+	0.245415i	$0.921076\pi$
$594$		0			0
$595$	−1.40030	+	2.90776i	−0.0574069	+	0.119207i
$596$	−0.260553	−	0.326723i	−0.0106727	−	0.0133831i
$597$		0			0
$598$	−45.2938	+	56.7966i	−1.85220	+	2.32259i
$599$	−3.33004	−	14.5899i	−0.136062	−	0.596126i	−0.996278	−	0.0861968i	$-0.972529\pi$
$599$	−3.33004	−	14.5899i	−0.136062	−	0.596126i	0.860216	−	0.509929i	$-0.170329\pi$
$600$		0			0
$601$	−4.50700	−	19.7465i	−0.183844	−	0.805475i	−0.979777	−	0.200090i	$-0.935876\pi$
$601$	−4.50700	−	19.7465i	−0.183844	−	0.805475i	0.795933	−	0.605385i	$-0.206981\pi$
$602$	11.0809	+	23.0097i	0.451624	+	0.937807i
$603$		0			0
$604$	−18.7676	+	23.5338i	−0.763641	+	0.957575i
$605$	−2.20291	−	1.06086i	−0.0895609	−	0.0431303i
$606$		0			0
$607$	−17.0411			−0.691679			−0.345839	−	0.938294i	$-0.612406\pi$
$607$	−17.0411			−0.691679			−0.345839	+	0.938294i	$0.612406\pi$
$608$	34.3473	+	16.5408i	1.39297	+	0.670817i
$609$		0			0
$610$	−1.64795	+	0.793610i	−0.0667235	+	0.0321323i
$611$	−39.4197	+	18.9835i	−1.59475	+	0.767991i
$612$		0			0
$613$	−3.16434	+	13.8639i	−0.127807	+	0.559957i	0.869958	+	0.493126i	$0.164146\pi$
$613$	−3.16434	+	13.8639i	−0.127807	+	0.559957i	−0.997764	+	0.0668309i	$0.978711\pi$
$614$	−49.0957	+	23.6433i	−1.98134	+	0.954164i
$615$		0			0
$616$	6.37681	−	1.45546i	0.256929	−	0.0586423i
$617$	1.27263	+	0.612869i	0.0512343	+	0.0246732i	0.459325	−	0.888268i	$-0.348091\pi$
$617$	1.27263	+	0.612869i	0.0512343	+	0.0246732i	−0.408091	+	0.912941i	$0.633805\pi$
$618$		0			0
$619$	9.00192			0.361818			0.180909	−	0.983500i	$-0.442096\pi$
$619$	9.00192			0.361818			0.180909	+	0.983500i	$0.442096\pi$
$620$	−0.134375	−	0.0647116i	−0.00539663	−	0.00259888i
$621$		0			0
$622$	5.44839	−	23.8710i	0.218461	−	0.957139i
$623$	34.4669	−	27.4864i	1.38089	−	1.10122i
$624$		0			0
$625$	−21.7032	−	10.4517i	−0.868128	−	0.418068i
$626$	4.21260	+	18.4566i	0.168369	+	0.737674i
$627$		0			0
$628$	−4.92327	+	21.5703i	−0.196460	+	0.860747i
$629$	−18.1008	−	22.6977i	−0.721727	−	0.905017i
$630$		0			0
$631$	−18.6833	+	23.4281i	−0.743770	+	0.932658i	−0.999418	−	0.0341117i	$-0.989140\pi$
$631$	−18.6833	+	23.4281i	−0.743770	+	0.932658i	0.255648	+	0.966770i	$0.417711\pi$
$632$	−12.7010	−	15.9266i	−0.505220	−	0.633526i
$633$		0			0
$634$	47.9493	+	60.1265i	1.90431	+	2.38793i
$635$	−0.616490	−	2.70102i	−0.0244646	−	0.107187i
$636$		0			0
$637$	−33.7086	+	16.2332i	−1.33558	+	0.643183i
$638$	−5.34721			−0.211698
$639$		0			0
$640$	−2.50418	−	3.14014i	−0.0989864	−	0.124125i
$641$	1.97046	−	0.948924i	0.0778285	−	0.0374802i	−0.394565	−	0.918868i	$-0.629105\pi$
$641$	1.97046	−	0.948924i	0.0778285	−	0.0374802i	0.472393	+	0.881388i	$0.343390\pi$
$642$		0			0
$643$	16.0538	−	20.1308i	0.633099	−	0.793880i	−0.357022	−	0.934096i	$-0.616208\pi$
$643$	16.0538	−	20.1308i	0.633099	−	0.793880i	0.990121	+	0.140215i	$0.0447795\pi$
$644$	−47.5713	+	10.8578i	−1.87457	+	0.427859i
$645$		0			0
$646$	−14.4487	+	63.3038i	−0.568476	+	2.49066i
$647$	−5.04809	+	6.33010i	−0.198461	+	0.248862i	−0.871097	−	0.491112i	$-0.836591\pi$
$647$	−5.04809	+	6.33010i	−0.198461	+	0.248862i	0.672636	+	0.739974i	$0.265162\pi$
$648$		0			0
$649$	4.49180	+	2.16314i	0.176319	+	0.0849106i
$650$	13.1990	+	57.8287i	0.517708	+	2.26823i
$651$		0			0
$652$	8.63587	−	37.8362i	0.338207	−	1.48178i
$653$	−21.5127	+	26.9760i	−0.841856	+	1.05565i	0.155838	+	0.987783i	$0.450192\pi$
$653$	−21.5127	+	26.9760i	−0.841856	+	1.05565i	−0.997694	+	0.0678713i	$0.978379\pi$
$654$		0			0
$655$	4.81104			0.187983
$656$	−3.92154			−0.153111
$657$		0			0
$658$	−47.4451	−	10.8290i	−1.84960	−	0.422160i
$659$	−17.3044	+	8.33335i	−0.674083	+	0.324621i	−0.739422	−	0.673242i	$-0.764901\pi$
$659$	−17.3044	+	8.33335i	−0.674083	+	0.324621i	0.0653392	+	0.997863i	$0.479187\pi$
$660$		0			0
$661$	2.72760	−	11.9504i	0.106091	−	0.464817i	−0.893776	−	0.448514i	$-0.851953\pi$
$661$	2.72760	−	11.9504i	0.106091	−	0.464817i	0.999867	−	0.0163027i	$-0.00518953\pi$
$662$	−4.98254	+	21.8299i	−0.193652	+	0.848445i
$663$		0			0
$664$	−25.0100	+	12.0442i	−0.970576	+	0.467405i
$665$			3.82322i			0.148258i
$666$		0			0
$667$	13.7235			0.531375
$668$	24.4077			0.944364
$669$		0			0
$670$	−1.16152	+	1.45650i	−0.0448735	+	0.0562696i
$671$	0.769282	−	3.37045i	0.0296978	−	0.130115i
$672$		0			0
$673$	1.09946	+	4.81704i	0.0423810	+	0.185683i	0.991688	−	0.128668i	$-0.0410702\pi$
$673$	1.09946	+	4.81704i	0.0423810	+	0.185683i	−0.949307	+	0.314351i	$0.898213\pi$
$674$	−44.6371	−	21.4961i	−1.71936	−	0.827999i
$675$		0			0
$676$	29.5925	−	37.1078i	1.13817	−	1.42722i
$677$	−4.14848	+	18.1757i	−0.159439	+	0.698548i	0.830496	+	0.557025i	$0.188057\pi$
$677$	−4.14848	+	18.1757i	−0.159439	+	0.698548i	−0.989935	+	0.141523i	$0.954800\pi$
$678$		0			0
$679$	−3.50000	−	2.79116i	−0.134318	−	0.107115i
$680$	1.79254	−	2.24778i	0.0687409	−	0.0861984i
$681$		0			0
$682$	0.420583	−	0.202542i	0.0161050	−	0.00775574i
$683$	−6.80798	−	8.53694i	−0.260500	−	0.326657i	0.634331	−	0.773061i	$-0.281276\pi$
$683$	−6.80798	−	8.53694i	−0.260500	−	0.326657i	−0.894831	+	0.446405i	$0.852704\pi$
$684$		0			0
$685$	−2.26875			−0.0866845
$686$	−40.5713	−	9.26013i	−1.54902	−	0.353553i
$687$		0			0
$688$	0.766594	+	3.35867i	0.0292261	+	0.128048i
$689$	11.4222	+	14.3230i	0.435151	+	0.545663i
$690$		0			0
$691$	1.62229	+	2.03429i	0.0617149	+	0.0773881i	0.811731	−	0.584032i	$-0.198526\pi$
$691$	1.62229	+	2.03429i	0.0617149	+	0.0773881i	−0.750016	+	0.661420i	$0.769954\pi$
$692$	−23.2684	+	29.1776i	−0.884531	+	1.10917i
$693$		0			0
$694$	−34.9565	−	43.8341i	−1.32693	−	1.66392i
$695$	−0.813724	+	3.56516i	−0.0308663	+	0.135234i
$696$		0			0
$697$	−5.37435	−	23.5466i	−0.203568	−	0.891890i
$698$	−6.41454	−	3.08908i	−0.242794	−	0.116923i
$699$		0			0
$700$	−17.2865	+	35.8958i	−0.653368	+	1.35673i
$701$	5.79643	−	25.3958i	0.218928	−	0.959187i	−0.739344	−	0.673328i	$-0.764864\pi$
$701$	5.79643	−	25.3958i	0.218928	−	0.959187i	0.958272	−	0.285859i	$-0.0922787\pi$
$702$		0			0
$703$	−30.9855	−	14.9218i	−1.16864	−	0.562788i
$704$	13.6746			0.515379
$705$		0			0
$706$	48.5577	+	23.3842i	1.82749	+	0.880074i
$707$			25.6107i			0.963190i
$708$		0			0
$709$	−4.83124	+	2.32660i	−0.181441	+	0.0873774i	−0.522399	−	0.852701i	$-0.674963\pi$
$709$	−4.83124	+	2.32660i	−0.181441	+	0.0873774i	0.340958	+	0.940079i	$0.389249\pi$
$710$	−0.501492	+	2.19718i	−0.0188207	+	0.0824587i
$711$		0			0
$712$	−35.3826	+	17.0394i	−1.32602	+	0.638577i
$713$	−1.07942	+	0.519820i	−0.0404245	+	0.0194674i
$714$		0			0
$715$	1.24751	+	0.600770i	0.0466543	+	0.0224675i
$716$	1.39373			0.0520862
$717$		0			0
$718$	63.0722	+	30.3740i	2.35384	+	1.13355i
$719$	28.8567	−	36.1851i	1.07617	−	1.34948i	0.143132	−	0.989704i	$-0.454283\pi$
$719$	28.8567	−	36.1851i	1.07617	−	1.34948i	0.933040	−	0.359773i	$-0.117146\pi$
$720$		0			0
$721$			8.32552i			0.310059i
$722$	7.61625	+	33.3690i	0.283448	+	1.24186i
$723$		0			0
$724$	6.36294	+	27.8778i	0.236477	+	1.03607i
$725$	6.98643	−	8.76070i	0.259469	−	0.325364i
$726$		0			0
$727$	−0.933329	−	1.17036i	−0.0346152	−	0.0434061i	0.764223	−	0.644953i	$-0.223123\pi$
$727$	−0.933329	−	1.17036i	−0.0346152	−	0.0434061i	−0.798838	+	0.601546i	$0.794551\pi$
$728$	32.4934	−	7.41640i	1.20428	−	0.274870i
$729$		0			0
$730$	−4.80947	−	6.03089i	−0.178006	−	0.223213i
$731$	−19.1163	+	9.20590i	−0.707040	+	0.340493i
$732$		0			0
$733$	−6.21624	−	27.2351i	−0.229602	−	1.00595i	−0.949965	−	0.312356i	$-0.898882\pi$
$733$	−6.21624	−	27.2351i	−0.229602	−	1.00595i	0.720363	−	0.693597i	$-0.243975\pi$
$734$	−21.5676			−0.796076
$735$		0			0
$736$	−39.4131			−1.45279
$737$	−0.783520	−	3.43282i	−0.0288613	−	0.126450i
$738$		0			0
$739$	17.0679	−	8.21945i	0.627852	−	0.302357i	−0.0927683	−	0.995688i	$-0.529572\pi$
$739$	17.0679	−	8.21945i	0.627852	−	0.302357i	0.720620	+	0.693330i	$0.243857\pi$
$740$	2.75973	+	3.46059i	0.101450	+	0.127214i
$741$		0			0
$742$			20.3768i			0.748056i
$743$	−19.9813	−	25.0558i	−0.733044	−	0.919209i	0.265953	−	0.963986i	$-0.414314\pi$
$743$	−19.9813	−	25.0558i	−0.733044	−	0.919209i	−0.998997	+	0.0447775i	$0.985742\pi$
$744$		0			0
$745$	0.0211063	−	0.0264664i	0.000773274	−	0.000969655i
$746$	0.848167	+	3.71606i	0.0310536	+	0.136055i
$747$		0			0
$748$	3.51477	+	15.3992i	0.128513	+	0.563051i
$749$	−10.9436	+	8.72724i	−0.399871	+	0.318886i
$750$		0			0
$751$	0.0752364	−	0.0943435i	0.00274542	−	0.00344264i	−0.780457	−	0.625210i	$-0.785013\pi$
$751$	0.0752364	−	0.0943435i	0.00274542	−	0.00344264i	0.783202	+	0.621767i	$0.213585\pi$
$752$	−5.91454	−	2.84829i	−0.215681	−	0.103867i
$753$		0			0
$754$	−27.2470			−0.992276
$755$	−2.19687	−	1.05795i	−0.0799521	−	0.0385029i
$756$		0			0
$757$	19.6114	−	9.44436i	0.712789	−	0.343261i	−0.0421004	−	0.999113i	$-0.513405\pi$
$757$	19.6114	−	9.44436i	0.712789	−	0.343261i	0.754889	+	0.655852i	$0.227691\pi$
$758$	42.4403	−	20.4382i	1.54150	−	0.742347i
$759$		0			0
$760$	0.757865	−	3.32042i	0.0274906	−	0.120444i
$761$	24.4943	−	11.7958i	0.887916	−	0.427598i	0.0664065	−	0.997793i	$-0.478847\pi$
$761$	24.4943	−	11.7958i	0.887916	−	0.427598i	0.821510	+	0.570195i	$0.193132\pi$
$762$		0			0
$763$	−6.70261	+	13.9181i	−0.242651	+	0.503870i
$764$	−14.8165	−	7.13524i	−0.536041	−	0.258144i
$765$		0			0
$766$	7.21983			0.260863
$767$	22.8882	+	11.0224i	0.826446	+	0.397995i
$768$		0			0
$769$	9.52691	−	41.7401i	0.343549	−	1.50519i	−0.447973	−	0.894047i	$-0.647854\pi$
$769$	9.52691	−	41.7401i	0.343549	−	1.50519i	0.791522	−	0.611140i	$-0.209289\pi$
$770$	0.668227	+	1.38759i	0.0240812	+	0.0500052i
$771$		0			0
$772$	61.7241	+	29.7247i	2.22150	+	1.06982i
$773$	6.44707	+	28.2464i	0.231885	+	1.01595i	0.948075	+	0.318048i	$0.103027\pi$
$773$	6.44707	+	28.2464i	0.231885	+	1.01595i	−0.716190	+	0.697906i	$0.754115\pi$
$774$		0			0
$775$	−0.217677	+	0.953703i	−0.00781917	+	0.0342580i
$776$	2.48643	+	3.11788i	0.0892575	+	0.111925i
$777$		0			0
$778$	18.1558	−	22.7666i	0.650916	−	0.816223i
$779$	−17.8388	−	22.3691i	−0.639140	−	0.801457i
$780$		0			0
$781$	−2.65585	−	3.33033i	−0.0950338	−	0.119169i
$782$	−14.9378	−	65.4468i	−0.534175	−	2.34037i
$783$		0			0
$784$	−5.05765	−	2.43563i	−0.180630	−	0.0869869i
$785$	−1.79225			−0.0639681
$786$		0			0
$787$	−16.3448	−	20.4957i	−0.582630	−	0.730595i	0.399929	−	0.916546i	$-0.369035\pi$
$787$	−16.3448	−	20.4957i	−0.582630	−	0.730595i	−0.982559	+	0.185951i	$0.940463\pi$
$788$	7.74482	−	3.72971i	0.275898	−	0.132865i
$789$		0			0
$790$	2.99061	−	3.75010i	0.106401	−	0.133423i
$791$	2.71672	−	2.16651i	0.0965953	−	0.0770322i
$792$		0			0
$793$	3.91992	−	17.1743i	0.139200	−	0.609877i
$794$	−4.17092	+	5.23016i	−0.148020	+	0.185612i
$795$		0			0
$796$	−7.32036	−	3.52530i	−0.259463	−	0.124951i
$797$	−12.2068	−	53.4814i	−0.432387	−	1.89441i	−0.447033	−	0.894517i	$-0.647519\pi$
$797$	−12.2068	−	53.4814i	−0.432387	−	1.89441i	0.0146465	−	0.999893i	$-0.495338\pi$
$798$		0			0
$799$	8.99665	−	39.4169i	0.318279	−	1.39447i
$800$	−20.0646	+	25.1603i	−0.709392	+	0.889550i
$801$		0			0
$802$	19.6896			0.695265
$803$	14.5797			0.514507
$804$		0			0
$805$	−1.71499	−	3.56121i	−0.0604454	−	0.125516i
$806$	2.14310	−	1.03206i	0.0754876	−	0.0363529i
$807$		0			0
$808$	5.07673	−	22.2426i	0.178599	−	0.782492i
$809$	−8.74376	+	38.3089i	−0.307414	+	1.34687i	0.551254	+	0.834338i	$0.314150\pi$
$809$	−8.74376	+	38.3089i	−0.307414	+	1.34687i	−0.858668	+	0.512532i	$0.828708\pi$
$810$		0			0
$811$	33.6754	−	16.2172i	1.18250	−	0.569463i	0.263863	−	0.964560i	$-0.415003\pi$
$811$	33.6754	−	16.2172i	1.18250	−	0.569463i	0.918640	+	0.395097i	$0.129289\pi$
$812$	−14.3085	−	11.4107i	−0.502130	−	0.400436i
$813$		0			0
$814$	−13.8538			−0.485577
$815$	3.14377			0.110121
$816$		0			0
$817$	−15.6712	+	19.6511i	−0.548266	+	0.687504i
$818$	−0.125646	+	0.550490i	−0.00439310	+	0.0192474i
$819$		0			0
$820$	0.819396	+	3.59001i	0.0286146	+	0.125369i
$821$	40.6432	+	19.5727i	1.41846	+	0.683092i	0.976812	−	0.214098i	$-0.0686812\pi$
$821$	40.6432	+	19.5727i	1.41846	+	0.683092i	0.441644	+	0.897190i	$0.354395\pi$
$822$		0			0
$823$	−24.8428	+	31.1519i	−0.865965	+	1.08589i	0.129577	+	0.991569i	$0.458638\pi$
$823$	−24.8428	+	31.1519i	−0.865965	+	1.08589i	−0.995542	+	0.0943167i	$0.969933\pi$
$824$	1.65034	−	7.23062i	0.0574924	−	0.251891i
$825$		0			0
$826$	12.2600	+	25.4582i	0.426581	+	0.885804i
$827$	17.2989	−	21.6921i	0.601541	−	0.754309i	−0.384076	−	0.923301i	$-0.625480\pi$
$827$	17.2989	−	21.6921i	0.601541	−	0.754309i	0.985617	+	0.168993i	$0.0540515\pi$
$828$		0			0
$829$	−20.2848	+	9.76863i	−0.704519	+	0.339279i	−0.751606	−	0.659612i	$-0.770721\pi$
$829$	−20.2848	+	9.76863i	−0.704519	+	0.339279i	0.0470868	+	0.998891i	$0.485006\pi$
$830$	−4.07524	−	5.11018i	−0.141454	−	0.177377i
$831$		0			0
$832$	69.6795			2.41570
$833$	7.69322	−	33.7062i	0.266554	−	1.16785i
$834$		0			0
$835$	0.439961	+	1.92759i	0.0152255	+	0.0667071i
$836$	11.6664	+	14.6292i	0.403490	+	0.505960i
$837$		0			0
$838$	−7.20440	−	9.03403i	−0.248872	−	0.312075i
$839$	19.6377	−	24.6248i	0.677967	−	0.850144i	−0.317198	−	0.948359i	$-0.602742\pi$
$839$	19.6377	−	24.6248i	0.677967	−	0.850144i	0.995165	+	0.0982154i	$0.0313134\pi$
$840$		0			0
$841$	−14.8720	−	18.6488i	−0.512826	−	0.643064i
$842$	−16.0591	+	70.3597i	−0.553434	+	2.42475i
$843$		0			0
$844$	−1.64042	−	7.18713i	−0.0564654	−	0.247391i
$845$	3.46399	+	1.66817i	0.119165	+	0.0573868i
$846$		0			0
$847$	25.5356	+	5.82834i	0.877415	+	0.200264i
$848$	−0.611645	+	2.67979i	−0.0210040	+	0.0920245i
$849$		0			0
$850$	−49.3841	−	23.7821i	−1.69386	−	0.815720i
$851$	35.5555			1.21883
$852$		0			0
$853$	−40.2657	−	19.3909i	−1.37867	−	0.663933i	−0.409955	−	0.912106i	$-0.634456\pi$
$853$	−40.2657	−	19.3909i	−1.37867	−	0.663933i	−0.968716	+	0.248173i	$0.920170\pi$
$854$	15.3192	−	12.2166i	0.524211	−	0.418044i
$855$		0			0
$856$	11.2344	−	5.41019i	0.383983	−	0.184916i
$857$	6.74698	−	29.5604i	0.230472	−	1.00977i	−0.718777	−	0.695241i	$-0.755298\pi$
$857$	6.74698	−	29.5604i	0.230472	−	1.00977i	0.949249	−	0.314525i	$-0.101845\pi$
$858$		0			0
$859$	17.2213	−	8.29335i	0.587584	−	0.282966i	−0.116376	−	0.993205i	$-0.537128\pi$
$859$	17.2213	−	8.29335i	0.587584	−	0.282966i	0.703960	+	0.710240i	$0.251413\pi$
$860$	2.91454	−	1.40357i	0.0993851	−	0.0478613i
$861$		0			0
$862$	23.0770	+	11.1133i	0.786007	+	0.378521i
$863$	−25.1987			−0.857772			−0.428886	−	0.903359i	$-0.641094\pi$
$863$	−25.1987			−0.857772			−0.428886	+	0.903359i	$0.641094\pi$
$864$		0			0
$865$	−2.72372	−	1.31167i	−0.0926092	−	0.0445982i
$866$	11.8237	−	14.8265i	0.401786	−	0.503824i
$867$		0			0
$868$	1.55765	+	0.355523i	0.0528700	+	0.0120672i
$869$	2.01735	+	8.83860i	0.0684340	+	0.299829i
$870$		0			0
$871$	−3.99247	−	17.4921i	−0.135280	−	0.592699i
$872$	8.58008	−	10.7591i	0.290558	−	0.364348i
$873$		0			0
$874$	−49.5822	−	62.1741i	−1.67714	−	2.10307i
$875$	−6.33177	−	1.44519i	−0.214053	−	0.0488562i
$876$		0			0
$877$	−6.04102	−	7.57519i	−0.203991	−	0.255796i	0.669304	−	0.742989i	$-0.266592\pi$
$877$	−6.04102	−	7.57519i	−0.203991	−	0.255796i	−0.873295	+	0.487193i	$0.838021\pi$
$878$	35.3647	−	17.0308i	1.19350	−	0.574760i
$879$		0			0
$880$	0.0462289	+	0.202542i	0.00155838	+	0.00682770i
$881$	18.1371			0.611053			0.305527	−	0.952184i	$-0.401168\pi$
$881$	18.1371			0.611053			0.305527	+	0.952184i	$0.401168\pi$
$882$		0			0
$883$	17.4397			0.586891			0.293446	−	0.955976i	$-0.405198\pi$
$883$	17.4397			0.586891			0.293446	+	0.955976i	$0.405198\pi$
$884$	17.9097	+	78.4675i	0.602368	+	2.63915i
$885$		0			0
$886$	−17.6799	+	8.51421i	−0.593969	+	0.286040i
$887$	33.6512	+	42.1973i	1.12990	+	1.41685i	0.895701	+	0.444658i	$0.146675\pi$
$887$	33.6512	+	42.1973i	1.12990	+	1.41685i	0.234197	+	0.972189i	$0.424754\pi$
$888$		0			0
$889$	12.8770	+	26.7395i	0.431882	+	0.896813i
$890$	−5.76540	−	7.22958i	−0.193257	−	0.242336i
$891$		0			0
$892$	26.8798	−	33.7062i	0.900002	−	1.12857i
$893$	−10.6576	−	46.6942i	−0.356644	−	1.56256i
$894$		0			0
$895$	0.0251227	+	0.110070i	0.000839758	+	0.00367922i
$896$	33.6386	+	26.8259i	1.12379	+	0.896189i
$897$		0			0
$898$	−12.8753	+	16.1451i	−0.429655	+	0.538770i
$899$	−0.404854	−	0.194967i	−0.0135026	−	0.00650252i
$900$		0			0
$901$	−16.9288			−0.563981
$902$	−10.3840	−	5.00069i	−0.345751	−	0.166505i
$903$		0			0
$904$	−2.78890	+	1.34306i	−0.0927573	+	0.0446696i
$905$	−2.08695	+	1.00502i	−0.0693726	+	0.0334081i
$906$		0			0
$907$	−7.45785	+	32.6750i	−0.247634	+	1.08495i	0.686247	+	0.727369i	$0.259257\pi$
$907$	−7.45785	+	32.6750i	−0.247634	+	1.08495i	−0.933880	+	0.357585i	$0.883600\pi$
$908$	−30.6465	+	14.7586i	−1.01704	+	0.489781i
$909$		0			0
$910$	3.40499	+	7.07052i	0.112874	+	0.234386i
$911$	−13.5402	−	6.52061i	−0.448606	−	0.216037i	0.195919	−	0.980620i	$-0.437231\pi$
$911$	−13.5402	−	6.52061i	−0.448606	−	0.216037i	−0.644526	+	0.764583i	$0.722945\pi$
$912$		0			0
$913$	12.3539			0.408855
$914$	66.2914	+	31.9243i	2.19272	+	1.05596i
$915$		0			0
$916$	−5.38255	+	23.5825i	−0.177844	+	0.779188i
$917$	−50.2457	+	11.4683i	−1.65926	+	0.378715i
$918$		0			0
$919$	19.0095	+	9.15447i	0.627064	+	0.301978i	0.720297	−	0.693666i	$-0.244006\pi$
$919$	19.0095	+	9.15447i	0.627064	+	0.301978i	−0.0932326	+	0.995644i	$0.529720\pi$
$920$	0.783520	+	3.43282i	0.0258319	+	0.113177i
$921$		0			0
$922$	6.98158	−	30.5883i	0.229926	−	1.00737i
$923$	−13.5330	−	16.9699i	−0.445445	−	0.558570i
$924$		0			0
$925$	18.1008	−	22.6977i	0.595151	−	0.746296i
$926$	−23.9502	−	30.0326i	−0.787052	−	0.986932i
$927$		0			0
$928$	−9.21678	−	11.5575i	−0.302555	−	0.379393i
$929$	−6.46807	−	28.3385i	−0.212210	−	0.929755i	−0.963061	−	0.269283i	$-0.913213\pi$
$929$	−6.46807	−	28.3385i	−0.212210	−	0.929755i	0.750851	−	0.660472i	$-0.229644\pi$
$930$		0			0
$931$	−9.11356	−	39.9291i	−0.298685	−	1.30862i
$932$	53.9711			1.76788
$933$		0			0
$934$	−11.9988	−	15.0460i	−0.392613	−	0.492321i
$935$	−1.15279	+	0.555156i	−0.0377004	+	0.0181555i
$936$		0			0
$937$	−33.3014	+	41.7586i	−1.08791	+	1.36420i	−0.161851	+	0.986815i	$0.551746\pi$
$937$	−33.3014	+	41.7586i	−1.08791	+	1.36420i	−0.926058	+	0.377380i	$0.876825\pi$
$938$	8.65883	−	17.9803i	0.282721	−	0.587076i
$939$		0			0
$940$	−1.37167	+	6.00966i	−0.0447388	+	0.196014i
$941$	−10.4925	+	13.1571i	−0.342045	+	0.428910i	−0.922866	−	0.385120i	$-0.874160\pi$
$941$	−10.4925	+	13.1571i	−0.342045	+	0.428910i	0.580822	+	0.814031i	$0.302731\pi$
$942$		0			0
$943$	26.6504	+	12.8342i	0.867856	+	0.417938i
$944$	0.848167	+	3.71606i	0.0276055	+	0.120947i
$945$		0			0
$946$	−2.25302	+	9.87113i	−0.0732520	+	0.320938i
$947$	25.2928	−	31.7162i	0.821907	−	1.03064i	−0.177015	−	0.984208i	$-0.556644\pi$
$947$	25.2928	−	31.7162i	0.821907	−	1.03064i	0.998922	−	0.0464304i	$-0.0147846\pi$
$948$		0			0
$949$	74.2917			2.41161
$950$	−64.9318			−2.10667
$951$		0			0
$952$	−13.3629	+	27.7484i	−0.433095	+	0.899332i
$953$	−17.8632	+	8.60248i	−0.578647	+	0.278662i	−0.700227	−	0.713920i	$-0.746918\pi$
$953$	−17.8632	+	8.60248i	−0.578647	+	0.278662i	0.121580	+	0.992582i	$0.461204\pi$
$954$		0			0
$955$	0.296429	−	1.29874i	0.00959223	−	0.0420263i
$956$	11.2198	−	49.1573i	0.362875	−	1.58986i
$957$		0			0
$958$	−1.84332	+	0.887697i	−0.0595550	+	0.0286802i
$959$	23.6945	−	5.40811i	0.765134	−	0.174637i
$960$		0			0
$961$	−30.9608			−0.998735
$962$	−70.5930			−2.27601
$963$		0			0
$964$	20.7947	−	26.0757i	0.669752	−	0.839843i
$965$	−1.23490	+	5.41044i	−0.0397528	+	0.174168i
$966$		0			0
$967$	−3.43416	−	15.0460i	−0.110435	−	0.483848i	−0.999652	−	0.0263626i	$-0.991608\pi$
$967$	−3.43416	−	15.0460i	−0.110435	−	0.483848i	0.889217	−	0.457485i	$-0.151250\pi$
$968$	−21.0221	−	10.1237i	−0.675675	−	0.325388i
$969$		0			0
$970$	−0.585458	+	0.734141i	−0.0187979	+	0.0235718i
$971$	−10.6974	+	46.8684i	−0.343296	+	1.50408i	0.448773	+	0.893646i	$0.351861\pi$
$971$	−10.6974	+	46.8684i	−0.343296	+	1.50408i	−0.792069	+	0.610432i	$0.790996\pi$
$972$		0			0
$973$		−	39.1737i		−	1.25585i
$974$	24.0145	−	30.1133i	0.769475	−	0.964891i
$975$		0			0
$976$	2.38135	−	1.14680i	0.0762253	−	0.0367082i
$977$	−2.78687	−	3.49463i	−0.0891599	−	0.111803i	0.735250	−	0.677796i	$-0.237065\pi$
$977$	−2.78687	−	3.49463i	−0.0891599	−	0.111803i	−0.824410	+	0.565992i	$0.808493\pi$
$978$		0			0
$979$	17.4776			0.558585
$980$	−1.17294	+	5.13898i	−0.0374682	+	0.164159i
$981$		0			0
$982$	−12.1039	−	53.0305i	−0.386250	−	1.69227i
$983$	−24.9943	−	31.3418i	−0.797193	−	0.999648i	−0.999792	−	0.0203866i	$-0.993510\pi$
$983$	−24.9943	−	31.3418i	−0.797193	−	0.999648i	0.202599	−	0.979262i	$-0.435061\pi$
$984$		0			0
$985$	0.434157	+	0.544415i	0.0138334	+	0.0173465i
$986$	15.6984	−	19.6851i	0.499938	−	0.626902i
$987$		0			0
$988$	59.4466	+	74.5437i	1.89125	+	2.37155i
$989$	5.78232	−	25.3340i	0.183867	−	0.805575i
$990$		0			0
$991$	−6.95718	−	30.4814i	−0.221002	−	0.968274i	−0.956726	−	0.290992i	$-0.906015\pi$
$991$	−6.95718	−	30.4814i	−0.221002	−	0.968274i	0.735723	−	0.677282i	$-0.236842\pi$
$992$	1.16272	+	0.559936i	0.0369163	+	0.0177780i
$993$		0			0
$994$		−	24.1424i		−	0.765751i
$995$	0.146457	−	0.641668i	0.00464298	−	0.0203422i
$996$		0			0
$997$	31.4804	+	15.1602i	0.996996	+	0.480128i	0.859918	−	0.510432i	$-0.170515\pi$
$997$	31.4804	+	15.1602i	0.996996	+	0.480128i	0.137078	+	0.990560i	$0.456229\pi$
$998$	23.6450			0.748470
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.a.379.1		6
3.2	odd	2		49.2.e.a.36.1	yes	6
12.11	even	2		784.2.u.a.673.1		6
21.2	odd	6		343.2.g.f.312.1		12
21.5	even	6		343.2.g.e.312.1		12
21.11	odd	6		343.2.g.f.128.1		12
21.17	even	6		343.2.g.e.128.1		12
21.20	even	2		343.2.e.a.246.1		6
49.15	even	7	inner	441.2.u.a.64.1		6
147.8	odd	14		2401.2.a.b.1.3		3
147.41	even	14		2401.2.a.a.1.3		3
147.74	odd	42		343.2.g.f.177.1		12
147.83	even	14		343.2.e.a.99.1		6
147.89	even	42		343.2.g.e.67.1		12
147.107	odd	42		343.2.g.f.67.1		12
147.113	odd	14		49.2.e.a.15.1	✓	6
147.122	even	42		343.2.g.e.177.1		12
588.407	even	14		784.2.u.a.113.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.2.e.a.15.1	✓	6	147.113	odd	14
49.2.e.a.36.1	yes	6	3.2	odd	2
343.2.e.a.99.1		6	147.83	even	14
343.2.e.a.246.1		6	21.20	even	2
343.2.g.e.67.1		12	147.89	even	42
343.2.g.e.128.1		12	21.17	even	6
343.2.g.e.177.1		12	147.122	even	42
343.2.g.e.312.1		12	21.5	even	6
343.2.g.f.67.1		12	147.107	odd	42
343.2.g.f.128.1		12	21.11	odd	6
343.2.g.f.177.1		12	147.74	odd	42
343.2.g.f.312.1		12	21.2	odd	6
441.2.u.a.64.1		6	49.15	even	7	inner
441.2.u.a.379.1		6	1.1	even	1	trivial
784.2.u.a.113.1		6	588.407	even	14
784.2.u.a.673.1		6	12.11	even	2
2401.2.a.a.1.3		3	147.41	even	14
2401.2.a.b.1.3		3	147.8	odd	14

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.u (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 2.19064i) q^{2} +(-2.74698 + 1.32288i) q^{4} +(-0.153989 - 0.193096i) q^{5} +(2.06853 + 1.64960i) q^{7} +(-1.46950 - 1.84270i) q^{8} +O(q^{10})\)	\(q+(0.500000 + 2.19064i) q^{2} +(-2.74698 + 1.32288i) q^{4} +(-0.153989 - 0.193096i) q^{5} +(2.06853 + 1.64960i) q^{7} +(-1.46950 - 1.84270i) q^{8} +(0.346011 - 0.433884i) q^{10} +(0.233406 + 1.02262i) q^{11} +(1.18933 + 5.21081i) q^{13} +(-2.57942 + 5.35621i) q^{14} +(-0.500000 + 0.626980i) q^{16} +(-4.44989 - 2.14295i) q^{17} -5.85086 q^{19} +(0.678448 + 0.326723i) q^{20} +(-2.12349 + 1.02262i) q^{22} +(5.44989 - 2.62453i) q^{23} +(1.09903 - 4.81517i) q^{25} +(-10.8204 + 5.21081i) q^{26} +(-7.86443 - 1.79500i) q^{28} +(2.04407 + 0.984374i) q^{29} -0.198062 q^{31} +(-5.87047 - 2.82707i) q^{32} +(2.46950 - 10.8196i) q^{34} -0.653447i q^{35} +(5.29590 + 2.55037i) q^{37} +(-2.92543 - 12.8171i) q^{38} +(-0.129531 + 0.567511i) q^{40} +(3.04892 + 3.82322i) q^{41} +(2.67845 - 3.35867i) q^{43} +(-1.99396 - 2.50035i) q^{44} +(8.47434 + 10.6265i) q^{46} +(1.82155 + 7.98074i) q^{47} +(1.55765 + 6.82450i) q^{49} +11.0978 q^{50} +(-10.1603 - 12.7406i) q^{52} +(3.08815 - 1.48717i) q^{53} +(0.161522 - 0.202542i) q^{55} -6.23576i q^{56} +(-1.13437 + 4.97002i) q^{58} +(2.96346 - 3.71606i) q^{59} +(-2.96950 - 1.43004i) q^{61} +(-0.0990311 - 0.433884i) q^{62} +(2.90097 - 12.7100i) q^{64} +(0.823044 - 1.03206i) q^{65} -3.35690 q^{67} +15.0586 q^{68} +(1.43147 - 0.326723i) q^{70} +(-3.65883 + 1.76200i) q^{71} +(3.09299 - 13.5513i) q^{73} +(-2.93900 + 12.8766i) q^{74} +(16.0722 - 7.73995i) q^{76} +(-1.20410 + 2.50035i) q^{77} +8.64310 q^{79} +0.198062 q^{80} +(-6.85086 + 8.59070i) q^{82} +(2.62080 - 11.4825i) q^{83} +(0.271438 + 1.18925i) q^{85} +(8.69687 + 4.18819i) q^{86} +(1.54138 - 1.93284i) q^{88} +(3.70775 - 16.2447i) q^{89} +(-6.13557 + 12.7406i) q^{91} +(-11.4988 + 14.4190i) q^{92} +(-16.5722 + 7.98074i) q^{94} +(0.900969 + 1.12978i) q^{95} -1.69202 q^{97} +(-14.1712 + 6.82450i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 7 q^{4} - 6 q^{5} + 7 q^{7} + q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 7 * q^4 - 6 * q^5 + 7 * q^7 + q^8	\( 6 q + 3 q^{2} - 7 q^{4} - 6 q^{5} + 7 q^{7} + q^{8} - 3 q^{10} - 2 q^{11} - 7 q^{14} - 3 q^{16} - 4 q^{17} - 8 q^{19} - 8 q^{22} + 10 q^{23} + 11 q^{25} - 28 q^{26} - 14 q^{28} + 16 q^{29} - 10 q^{31} - 21 q^{32} + 5 q^{34} + 4 q^{37} - 4 q^{38} - 15 q^{40} + 12 q^{43} + 7 q^{44} + 19 q^{46} + 15 q^{47} + 7 q^{49} + 30 q^{50} + 26 q^{53} - 19 q^{55} + q^{58} - 11 q^{59} - 8 q^{61} - 5 q^{62} + 13 q^{64} - 35 q^{65} - 12 q^{67} + 28 q^{68} + 14 q^{70} - 5 q^{71} + 4 q^{73} + 2 q^{74} + 28 q^{76} - 35 q^{77} + 60 q^{79} + 10 q^{80} - 14 q^{82} + 14 q^{83} - 17 q^{85} + 20 q^{86} + 16 q^{88} - 13 q^{89} - 70 q^{91} - 28 q^{92} - 31 q^{94} + q^{95} - 21 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 7 * q^4 - 6 * q^5 + 7 * q^7 + q^8 - 3 * q^10 - 2 * q^11 - 7 * q^14 - 3 * q^16 - 4 * q^17 - 8 * q^19 - 8 * q^22 + 10 * q^23 + 11 * q^25 - 28 * q^26 - 14 * q^28 + 16 * q^29 - 10 * q^31 - 21 * q^32 + 5 * q^34 + 4 * q^37 - 4 * q^38 - 15 * q^40 + 12 * q^43 + 7 * q^44 + 19 * q^46 + 15 * q^47 + 7 * q^49 + 30 * q^50 + 26 * q^53 - 19 * q^55 + q^58 - 11 * q^59 - 8 * q^61 - 5 * q^62 + 13 * q^64 - 35 * q^65 - 12 * q^67 + 28 * q^68 + 14 * q^70 - 5 * q^71 + 4 * q^73 + 2 * q^74 + 28 * q^76 - 35 * q^77 + 60 * q^79 + 10 * q^80 - 14 * q^82 + 14 * q^83 - 17 * q^85 + 20 * q^86 + 16 * q^88 - 13 * q^89 - 70 * q^91 - 28 * q^92 - 31 * q^94 + q^95 - 21 * q^98

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