LMFDB - Embedded newform 441.2.u.d.253.2

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:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			253.2
Character	$\chi$	$=$	441.253
Dual form			441.2.u.d.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34250 - 1.68344i) q^{2} +(-0.586625 + 2.57017i) q^{4} +(2.99194 - 1.44084i) q^{5} +(2.53827 + 0.746462i) q^{7} +(1.23434 - 0.594424i) q^{8} +O(q^{10})$	\(q+(-1.34250 - 1.68344i) q^{2} +(-0.586625 + 2.57017i) q^{4} +(2.99194 - 1.44084i) q^{5} +(2.53827 + 0.746462i) q^{7} +(1.23434 - 0.594424i) q^{8} +(-6.44225 - 3.10242i) q^{10} +(0.574309 + 0.720161i) q^{11} +(1.96720 + 2.46678i) q^{13} +(-2.15099 - 5.27514i) q^{14} +(2.09262 + 1.00775i) q^{16} +(1.19298 + 5.22678i) q^{17} +5.32624 q^{19} +(1.94807 + 8.53504i) q^{20} +(0.441338 - 1.93363i) q^{22} +(-0.320566 + 1.40449i) q^{23} +(3.75825 - 4.71269i) q^{25} +(1.51173 - 6.62331i) q^{26} +(-3.40754 + 6.08588i) q^{28} +(-0.472424 - 2.06982i) q^{29} -9.98825 q^{31} +(-1.72256 - 7.54702i) q^{32} +(7.19740 - 9.02525i) q^{34} +(8.66989 - 1.42387i) q^{35} +(-1.87052 - 8.19530i) q^{37} +(-7.15046 - 8.96640i) q^{38} +(2.83659 - 3.55697i) q^{40} +(-6.36553 + 3.06548i) q^{41} +(-3.89625 - 1.87633i) q^{43} +(-2.18784 + 1.05361i) q^{44} +(2.79473 - 1.34587i) q^{46} +(2.59183 + 3.25005i) q^{47} +(5.88559 + 3.78944i) q^{49} -12.9790 q^{50} +(-7.49406 + 3.60895i) q^{52} +(2.21870 - 9.72074i) q^{53} +(2.75594 + 1.32719i) q^{55} +(3.57679 - 0.587423i) q^{56} +(-2.85019 + 3.57403i) q^{58} +(-6.17762 - 2.97499i) q^{59} +(-1.19007 - 5.21403i) q^{61} +(13.4092 + 16.8146i) q^{62} +(-7.49614 + 9.39987i) q^{64} +(9.43999 + 4.54606i) q^{65} -8.94751 q^{67} -14.1335 q^{68} +(-14.0363 - 12.6837i) q^{70} +(-1.42029 + 6.22270i) q^{71} +(8.70165 - 10.9115i) q^{73} +(-11.2851 + 14.1511i) q^{74} +(-3.12450 + 13.6893i) q^{76} +(0.920177 + 2.25666i) q^{77} -13.1382 q^{79} +7.71301 q^{80} +(13.7062 + 6.60058i) q^{82} +(9.25512 - 11.6055i) q^{83} +(11.1003 + 13.9193i) q^{85} +(2.07201 + 9.07807i) q^{86} +(1.13697 + 0.547537i) q^{88} +(-0.756573 + 0.948713i) q^{89} +(3.15190 + 7.72979i) q^{91} +(-3.42173 - 1.64782i) q^{92} +(1.99173 - 8.72636i) q^{94} +(15.9358 - 7.67428i) q^{95} +1.28690 q^{97} +(-1.52210 - 14.9953i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	$ 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) $ 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

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 $

$2$	−1.34250	−	1.68344i	−0.949289	−	1.19037i	−0.981611	−	0.190894i	$-0.938861\pi$
$2$	−1.34250	−	1.68344i	−0.949289	−	1.19037i	0.0323215	−	0.999478i	$-0.489710\pi$
$3$		0			0
$3$		0			0
$4$	−0.586625	+	2.57017i	−0.293312	+	1.28508i
$5$	2.99194	−	1.44084i	1.33804	−	0.644365i	0.378410	−	0.925638i	$-0.376471\pi$
$5$	2.99194	−	1.44084i	1.33804	−	0.644365i	0.959628	+	0.281273i	$0.0907566\pi$
$6$		0			0
$7$	2.53827	+	0.746462i	0.959374	+	0.282136i
$7$	2.53827	+	0.746462i	0.959374	+	0.282136i
$8$	1.23434	−	0.594424i	0.436403	−	0.210161i
$9$		0			0
$10$	−6.44225	−	3.10242i	−2.03722	−	0.981073i
$11$	0.574309	+	0.720161i	0.173161	+	0.217137i	0.860837	−	0.508881i	$-0.169941\pi$
$11$	0.574309	+	0.720161i	0.173161	+	0.217137i	−0.687676	+	0.726017i	$0.741369\pi$
$12$		0			0
$13$	1.96720	+	2.46678i	0.545602	+	0.684163i	0.975823	−	0.218560i	$-0.0701360\pi$
$13$	1.96720	+	2.46678i	0.545602	+	0.684163i	−0.430222	+	0.902723i	$0.641565\pi$
$14$	−2.15099	−	5.27514i	−0.574877	−	1.40984i
$15$		0			0
$16$	2.09262	+	1.00775i	0.523155	+	0.251938i
$17$	1.19298	+	5.22678i	0.289340	+	1.26768i	0.885434	+	0.464766i	$0.153862\pi$
$17$	1.19298	+	5.22678i	0.289340	+	1.26768i	−0.596094	+	0.802915i	$0.703281\pi$
$18$		0			0
$19$	5.32624			1.22192			0.610961	−	0.791660i	$-0.290783\pi$
$19$	5.32624			1.22192			0.610961	+	0.791660i	$0.290783\pi$
$20$	1.94807	+	8.53504i	0.435601	+	1.90849i
$21$		0			0
$22$	0.441338	−	1.93363i	0.0940936	−	0.412251i
$23$	−0.320566	+	1.40449i	−0.0668426	+	0.292856i	−0.997290	−	0.0735686i	$-0.976561\pi$
$23$	−0.320566	+	1.40449i	−0.0668426	+	0.292856i	0.930448	+	0.366425i	$0.119418\pi$
$24$		0			0
$25$	3.75825	−	4.71269i	0.751650	−	0.942539i
$26$	1.51173	−	6.62331i	0.296474	−	1.29894i
$27$		0			0
$28$	−3.40754	+	6.08588i	−0.643965	+	1.15012i
$29$	−0.472424	−	2.06982i	−0.0877268	−	0.384356i	0.911936	−	0.410333i	$-0.134588\pi$
$29$	−0.472424	−	2.06982i	−0.0877268	−	0.384356i	−0.999663	+	0.0259767i	$0.991730\pi$
$30$		0			0
$31$	−9.98825			−1.79394			−0.896972	−	0.442088i	$-0.854238\pi$
$31$	−9.98825			−1.79394			−0.896972	+	0.442088i	$0.854238\pi$
$32$	−1.72256	−	7.54702i	−0.304508	−	1.33414i
$33$		0			0
$34$	7.19740	−	9.02525i	1.23434	−	1.54782i
$35$	8.66989	−	1.42387i	1.46548	−	0.240679i
$36$		0			0
$37$	−1.87052	−	8.19530i	−0.307512	−	1.34730i	−0.858512	−	0.512793i	$-0.828611\pi$
$37$	−1.87052	−	8.19530i	−0.307512	−	1.34730i	0.551000	−	0.834505i	$-0.314246\pi$
$38$	−7.15046	−	8.96640i	−1.15996	−	1.45454i
$39$		0			0
$40$	2.83659	−	3.55697i	0.448504	−	0.562406i
$41$	−6.36553	+	3.06548i	−0.994128	+	0.478747i	−0.858942	−	0.512073i	$-0.828878\pi$
$41$	−6.36553	+	3.06548i	−0.994128	+	0.478747i	−0.135186	+	0.990820i	$0.543163\pi$
$42$		0			0
$43$	−3.89625	−	1.87633i	−0.594172	−	0.286138i	0.112531	−	0.993648i	$-0.464104\pi$
$43$	−3.89625	−	1.87633i	−0.594172	−	0.286138i	−0.706703	+	0.707510i	$0.749818\pi$
$44$	−2.18784	+	1.05361i	−0.329829	+	0.158837i
$45$		0			0
$46$	2.79473	−	1.34587i	0.412061	−	0.198438i
$47$	2.59183	+	3.25005i	0.378057	+	0.474068i	0.934062	−	0.357111i	$-0.116238\pi$
$47$	2.59183	+	3.25005i	0.378057	+	0.474068i	−0.556006	+	0.831179i	$0.687667\pi$
$48$		0			0
$49$	5.88559	+	3.78944i	0.840798	+	0.541348i
$50$	−12.9790			−1.83550
$51$		0			0
$52$	−7.49406	+	3.60895i	−1.03924	+	0.500471i
$53$	2.21870	−	9.72074i	0.304761	−	1.33525i	−0.558086	−	0.829783i	$-0.688464\pi$
$53$	2.21870	−	9.72074i	0.304761	−	1.33525i	0.862848	−	0.505464i	$-0.168679\pi$
$54$		0			0
$55$	2.75594	+	1.32719i	0.371611	+	0.178958i
$56$	3.57679	−	0.587423i	0.477968	−	0.0784977i
$57$		0			0
$58$	−2.85019	+	3.57403i	−0.374249	+	0.469293i
$59$	−6.17762	−	2.97499i	−0.804258	−	0.387310i	−0.0138598	−	0.999904i	$-0.504412\pi$
$59$	−6.17762	−	2.97499i	−0.804258	−	0.387310i	−0.790398	+	0.612594i	$0.790126\pi$
$60$		0			0
$61$	−1.19007	−	5.21403i	−0.152373	−	0.667589i	−0.992192	−	0.124722i	$-0.960196\pi$
$61$	−1.19007	−	5.21403i	−0.152373	−	0.667589i	0.839819	−	0.542867i	$-0.182661\pi$
$62$	13.4092	+	16.8146i	1.70297	+	2.13546i
$63$		0			0
$64$	−7.49614	+	9.39987i	−0.937018	+	1.17498i
$65$	9.43999	+	4.54606i	1.17089	+	0.563869i
$66$		0			0
$67$	−8.94751			−1.09311			−0.546556	−	0.837423i	$-0.684061\pi$
$67$	−8.94751			−1.09311			−0.546556	+	0.837423i	$0.684061\pi$
$68$	−14.1335			−1.71394
$69$		0			0
$70$	−14.0363	−	12.6837i	−1.67766	−	1.51599i
$71$	−1.42029	+	6.22270i	−0.168557	+	0.738498i	0.818018	+	0.575193i	$0.195073\pi$
$71$	−1.42029	+	6.22270i	−0.168557	+	0.738498i	−0.986575	+	0.163306i	$0.947784\pi$
$72$		0			0
$73$	8.70165	−	10.9115i	1.01845	−	1.27710i	0.0580981	−	0.998311i	$-0.481496\pi$
$73$	8.70165	−	10.9115i	1.01845	−	1.27710i	0.960353	−	0.278787i	$-0.0899322\pi$
$74$	−11.2851	+	14.1511i	−1.31187	+	1.64503i
$75$		0			0
$76$	−3.12450	+	13.6893i	−0.358405	+	1.57027i
$77$	0.920177	+	2.25666i	0.104864	+	0.257170i
$78$		0			0
$79$	−13.1382			−1.47817			−0.739083	−	0.673614i	$-0.764741\pi$
$79$	−13.1382			−1.47817			−0.739083	+	0.673614i	$0.764741\pi$
$80$	7.71301			0.862341
$81$		0			0
$82$	13.7062	+	6.60058i	1.51360	+	0.728912i
$83$	9.25512	−	11.6055i	1.01588	−	1.27387i	0.0545407	−	0.998512i	$-0.482631\pi$
$83$	9.25512	−	11.6055i	1.01588	−	1.27387i	0.961340	−	0.275363i	$-0.0887980\pi$
$84$		0			0
$85$	11.1003	+	13.9193i	1.20400	+	1.50976i
$86$	2.07201	+	9.07807i	0.223431	+	0.978913i
$87$		0			0
$88$	1.13697	+	0.547537i	0.121202	+	0.0583676i
$89$	−0.756573	+	0.948713i	−0.0801966	+	0.100563i	−0.820311	−	0.571917i	$-0.806200\pi$
$89$	−0.756573	+	0.948713i	−0.0801966	+	0.100563i	0.740115	+	0.672481i	$0.234771\pi$
$90$		0			0
$91$	3.15190	+	7.72979i	0.330409	+	0.810302i
$92$	−3.42173	−	1.64782i	−0.356740	−	0.171797i
$93$		0			0
$94$	1.99173	−	8.72636i	0.205432	−	0.900055i
$95$	15.9358	−	7.67428i	1.63498	−	0.787365i
$96$		0			0
$97$	1.28690			0.130664			0.0653322	−	0.997864i	$-0.479189\pi$
$97$	1.28690			0.130664			0.0653322	+	0.997864i	$0.479189\pi$
$98$	−1.52210	−	14.9953i	−0.153755	−	1.51476i
$99$		0			0
$100$	9.90774	+	12.4239i	0.990774	+	1.24239i
$101$	−6.74572	+	3.24857i	−0.671225	+	0.323245i	−0.738270	−	0.674505i	$-0.764357\pi$
$101$	−6.74572	+	3.24857i	−0.671225	+	0.323245i	0.0670456	+	0.997750i	$0.478643\pi$
$102$		0			0
$103$	0.634036	−	0.305336i	0.0624734	−	0.0300856i	−0.402386	−	0.915470i	$-0.631819\pi$
$103$	0.634036	−	0.305336i	0.0624734	−	0.0300856i	0.464860	+	0.885384i	$0.346105\pi$
$104$	3.89450	+	1.87549i	0.381887	+	0.183907i
$105$		0			0
$106$	−19.3429	+	9.31504i	−1.87875	+	0.904756i
$107$	−4.28839	+	5.37747i	−0.414574	+	0.519860i	−0.944645	−	0.328093i	$-0.893594\pi$
$107$	−4.28839	+	5.37747i	−0.414574	+	0.519860i	0.530071	+	0.847953i	$0.322165\pi$
$108$		0			0
$109$	8.98921	+	11.2721i	0.861010	+	1.07967i	0.996047	+	0.0888323i	$0.0283135\pi$
$109$	8.98921	+	11.2721i	0.861010	+	1.07967i	−0.135036	+	0.990841i	$0.543115\pi$
$110$	−1.46560	−	6.42121i	−0.139739	−	0.612238i
$111$		0			0
$112$	4.55937	+	4.12000i	0.430820	+	0.389304i
$113$	−2.22779	+	2.79356i	−0.209573	+	0.262796i	−0.875497	−	0.483223i	$-0.839466\pi$
$113$	−2.22779	+	2.79356i	−0.209573	+	0.262796i	0.665924	+	0.746019i	$0.268037\pi$
$114$		0			0
$115$	1.06454	+	4.66404i	0.0992686	+	0.434924i
$116$	5.59693			0.519662
$117$		0			0
$118$	3.28524	+	14.3936i	0.302430	+	1.32503i
$119$	−0.873497	+	14.1575i	−0.0800734	+	1.29781i
$120$		0			0
$121$	2.25893	−	9.89702i	0.205357	−	0.899729i
$122$	−7.17984	+	9.00324i	−0.650032	+	0.815115i
$123$		0			0
$124$	5.85935	−	25.6715i	0.526185	−	2.30537i
$125$	0.759464	−	3.32743i	0.0679285	−	0.297614i
$126$		0			0
$127$	2.83004	+	12.3992i	0.251125	+	1.10025i	0.930451	+	0.366415i	$0.119415\pi$
$127$	2.83004	+	12.3992i	0.251125	+	1.10025i	−0.679326	+	0.733836i	$0.737728\pi$
$128$	10.4054			0.919720
$129$		0			0
$130$	−5.02015	−	21.9947i	−0.440296	−	1.92907i
$131$	−5.65400	−	2.72282i	−0.493993	−	0.237894i	0.170265	−	0.985398i	$-0.445538\pi$
$131$	−5.65400	−	2.72282i	−0.493993	−	0.237894i	−0.664257	+	0.747504i	$0.731252\pi$
$132$		0			0
$133$	13.5194	+	3.97584i	1.17228	+	0.344749i
$134$	12.0120	+	15.0626i	1.03768	+	1.30121i
$135$		0			0
$136$	4.57946	+	5.74247i	0.392686	+	0.492412i
$137$	13.5913	+	6.54524i	1.16119	+	0.559197i	0.912375	−	0.409355i	$-0.134246\pi$
$137$	13.5913	+	6.54524i	1.16119	+	0.559197i	0.248810	+	0.968552i	$0.419960\pi$
$138$		0			0
$139$	−9.90157	+	4.76835i	−0.839840	+	0.404446i	−0.803796	−	0.594904i	$-0.797190\pi$
$139$	−9.90157	+	4.76835i	−0.839840	+	0.404446i	−0.0360439	+	0.999350i	$0.511476\pi$
$140$	−1.42637	+	23.1184i	−0.120550	+	1.95386i
$141$		0			0
$142$	12.3823	−	5.96299i	1.03910	−	0.500403i
$143$	−0.646704	+	2.83340i	−0.0540801	+	0.236940i
$144$		0			0
$145$	−4.39576	−	5.51211i	−0.365048	−	0.457755i
$146$	−30.0508			−2.48702
$147$		0			0
$148$	22.1606			1.82159
$149$	−5.53857	−	6.94515i	−0.453737	−	0.568968i	0.501368	−	0.865234i	$-0.332830\pi$
$149$	−5.53857	−	6.94515i	−0.453737	−	0.568968i	−0.955106	+	0.296265i	$0.904259\pi$
$150$		0			0
$151$	−1.70722	+	7.47982i	−0.138932	+	0.608699i	0.856739	+	0.515750i	$0.172487\pi$
$151$	−1.70722	+	7.47982i	−0.138932	+	0.608699i	−0.995671	+	0.0929493i	$0.970371\pi$
$152$	6.57436	−	3.16605i	0.533251	−	0.256800i
$153$		0			0
$154$	2.56362	−	4.57862i	0.206582	−	0.368956i
$155$	−29.8843	+	14.3915i	−2.40036	+	1.15595i
$156$		0			0
$157$	−0.631830	−	0.304273i	−0.0504256	−	0.0242837i	0.408501	−	0.912758i	$-0.366052\pi$
$157$	−0.631830	−	0.304273i	−0.0504256	−	0.0242837i	−0.458927	+	0.888474i	$0.651766\pi$
$158$	17.6380	+	22.1174i	1.40321	+	1.75957i
$159$		0			0
$160$	−16.0279	−	20.0983i	−1.26712	−	1.58891i
$161$	−1.86208	+	3.32568i	−0.146752	+	0.262100i
$162$		0			0
$163$	−10.2257	−	4.92443i	−0.800937	−	0.385711i	−0.0118018	−	0.999930i	$-0.503757\pi$
$163$	−10.2257	−	4.92443i	−0.800937	−	0.385711i	−0.789135	+	0.614219i	$0.789471\pi$
$164$	−4.14462	−	18.1588i	−0.323640	−	1.41796i
$165$		0			0
$166$	−31.9622			−2.48075
$167$	−3.06121	−	13.4120i	−0.236884	−	1.03785i	−0.943789	−	0.330547i	$-0.892767\pi$
$167$	−3.06121	−	13.4120i	−0.236884	−	1.03785i	0.706906	−	0.707308i	$-0.250090\pi$
$168$		0			0
$169$	0.677602	−	2.96877i	0.0521232	−	0.228367i
$170$	8.53023	−	37.3734i	0.654239	−	2.86641i
$171$		0			0
$172$	7.10813	−	8.91331i	0.541990	−	0.679634i
$173$	3.79837	−	16.6417i	0.288785	−	1.26525i	−0.597410	−	0.801936i	$-0.703804\pi$
$173$	3.79837	−	16.6417i	0.288785	−	1.26525i	0.886195	−	0.463312i	$-0.153339\pi$
$174$		0			0
$175$	13.0573	−	9.15668i	0.987038	−	0.692180i
$176$	0.476067	+	2.08578i	0.0358849	+	0.157222i
$177$		0			0
$178$	2.61280			0.195838
$179$	2.69362	+	11.8015i	0.201331	+	0.882088i	0.970128	+	0.242595i	$0.0779985\pi$
$179$	2.69362	+	11.8015i	0.201331	+	0.882088i	−0.768797	+	0.639493i	$0.779144\pi$
$180$		0			0
$181$	0.975797	−	1.22361i	0.0725304	−	0.0909503i	−0.744243	−	0.667909i	$-0.767189\pi$
$181$	0.975797	−	1.22361i	0.0725304	−	0.0909503i	0.816773	+	0.576959i	$0.195761\pi$
$182$	8.78121	−	15.6833i	0.650907	−	1.16252i
$183$		0			0
$184$	0.439178	+	1.92416i	0.0323766	+	0.141851i
$185$	−17.4046	−	21.8247i	−1.27962	−	1.60459i
$186$		0			0
$187$	−3.07899	+	3.86093i	−0.225158	+	0.282339i
$188$	−9.87360	+	4.75487i	−0.720106	+	0.346785i
$189$		0			0
$190$	−34.3130	−	16.5243i	−2.48932	−	1.19880i
$191$	−13.6245	+	6.56122i	−0.985835	+	0.474753i	−0.856108	−	0.516797i	$-0.827124\pi$
$191$	−13.6245	+	6.56122i	−0.985835	+	0.474753i	−0.129727	+	0.991550i	$0.541410\pi$
$192$		0			0
$193$	−6.05426	+	2.91558i	−0.435795	+	0.209868i	−0.638901	−	0.769289i	$-0.720611\pi$
$193$	−6.05426	+	2.91558i	−0.435795	+	0.209868i	0.203106	+	0.979157i	$0.434896\pi$
$194$	−1.72765	−	2.16641i	−0.124038	−	0.155539i
$195$		0			0
$196$	−13.1921	+	12.9040i	−0.942295	+	0.921713i
$197$	11.5444			0.822501			0.411251	−	0.911522i	$-0.365092\pi$
$197$	11.5444			0.822501			0.411251	+	0.911522i	$0.365092\pi$
$198$		0			0
$199$	4.56362	−	2.19772i	0.323507	−	0.155793i	−0.265081	−	0.964226i	$-0.585399\pi$
$199$	4.56362	−	2.19772i	0.323507	−	0.155793i	0.588587	+	0.808434i	$0.299684\pi$
$200$	1.83760	−	8.05104i	0.129938	−	0.569294i
$201$		0			0
$202$	14.5249	+	6.99482i	1.02197	+	0.492154i
$203$	0.345908	−	5.60641i	0.0242780	−	0.393493i
$204$		0			0
$205$	−14.6284	+	18.3435i	−1.02169	+	1.28116i
$206$	−1.36521	−	0.657448i	−0.0951184	−	0.0458066i
$207$		0			0
$208$	1.63068	+	7.14449i	0.113067	+	0.495381i
$209$	3.05891	+	3.83575i	0.211589	+	0.265324i
$210$		0			0
$211$	5.73065	−	7.18601i	0.394514	−	0.494705i	−0.544415	−	0.838816i	$-0.683248\pi$
$211$	5.73065	−	7.18601i	0.394514	−	0.494705i	0.938929	+	0.344111i	$0.111820\pi$
$212$	23.6824	+	11.4049i	1.62652	+	0.783289i
$213$		0			0
$214$	14.8098			1.01238
$215$	−14.3609			−0.979402
$216$		0			0
$217$	−25.3528	−	7.45585i	−1.72106	−	0.506136i
$218$	6.90792	−	30.2656i	0.467863	−	2.04984i
$219$		0			0
$220$	−5.02781	+	6.30468i	−0.338975	+	0.425061i
$221$	−10.5465	+	13.2249i	−0.709436	+	0.889605i
$222$		0			0
$223$	−3.16703	+	13.8756i	−0.212080	+	0.929182i	0.751071	+	0.660221i	$0.229537\pi$
$223$	−3.16703	+	13.8756i	−0.212080	+	0.929182i	−0.963151	+	0.268961i	$0.913320\pi$
$224$	1.26125	−	20.4422i	0.0842711	−	1.36585i
$225$		0			0
$226$	7.69359			0.511770
$227$	28.2914			1.87777			0.938884	−	0.344234i	$-0.111861\pi$
$227$	28.2914			1.87777			0.938884	+	0.344234i	$0.111861\pi$
$228$		0			0
$229$	−15.0372	−	7.24154i	−0.993688	−	0.478535i	−0.134896	−	0.990860i	$-0.543070\pi$
$229$	−15.0372	−	7.24154i	−0.993688	−	0.478535i	−0.858792	+	0.512325i	$0.828784\pi$
$230$	6.42249	−	8.05355i	0.423486	−	0.531035i
$231$		0			0
$232$	−1.81348	−	2.27403i	−0.119061	−	0.149298i
$233$	−3.98797	−	17.4724i	−0.261261	−	1.14466i	−0.919886	−	0.392186i	$-0.871719\pi$
$233$	−3.98797	−	17.4724i	−0.261261	−	1.14466i	0.658625	−	0.752471i	$-0.271138\pi$
$234$		0			0
$235$	12.4374	+	5.98954i	0.811327	+	0.390714i
$236$	11.2702	−	14.1323i	0.733625	−	0.919937i
$237$		0			0
$238$	25.0059	−	17.5359i	1.62089	−	1.13668i
$239$	16.0719	+	7.73982i	1.03961	+	0.500648i	0.874194	−	0.485577i	$-0.161390\pi$
$239$	16.0719	+	7.73982i	1.03961	+	0.500648i	0.165412	+	0.986225i	$0.447105\pi$
$240$		0			0
$241$	1.74108	−	7.62817i	0.112153	−	0.491374i	−0.887387	−	0.461026i	$-0.847481\pi$
$241$	1.74108	−	7.62817i	0.112153	−	0.491374i	0.999539	−	0.0303475i	$-0.00966139\pi$
$242$	−19.6936	+	9.48395i	−1.26595	+	0.609652i
$243$		0			0
$244$	14.0991			0.902601
$245$	23.0693	+	2.85757i	1.47385	+	0.182564i
$246$		0			0
$247$	10.4778	+	13.1387i	0.666683	+	0.835995i
$248$	−12.3289	+	5.93726i	−0.782883	+	0.377016i
$249$		0			0
$250$	−6.62110	+	3.18856i	−0.418755	+	0.201662i
$251$	1.96537	+	0.946472i	0.124053	+	0.0597408i	0.494881	−	0.868961i	$-0.335212\pi$
$251$	1.96537	+	0.946472i	0.124053	+	0.0597408i	−0.370828	+	0.928702i	$0.620926\pi$
$252$		0			0
$253$	−1.19556	+	0.575753i	−0.0751644	+	0.0361973i
$254$	17.0740	−	21.4101i	1.07132	−	1.34339i
$255$		0			0
$256$	1.02300	+	1.28281i	0.0639377	+	0.0801754i
$257$	1.00572	+	4.40635i	0.0627351	+	0.274860i	0.996560	−	0.0828687i	$-0.0264082\pi$
$257$	1.00572	+	4.40635i	0.0627351	+	0.274860i	−0.933825	+	0.357729i	$0.883551\pi$
$258$		0			0
$259$	1.36959	−	22.1981i	0.0851024	−	1.37932i
$260$	−17.2219	+	21.5956i	−1.06806	+	1.33930i
$261$		0			0
$262$	3.00678	+	13.1736i	0.185759	+	0.813865i
$263$	−7.14902			−0.440828			−0.220414	−	0.975406i	$-0.570741\pi$
$263$	−7.14902			−0.440828			−0.220414	+	0.975406i	$0.570741\pi$
$264$		0			0
$265$	−7.36786	−	32.2807i	−0.452604	−	1.98299i
$266$	−11.4567	−	28.0967i	−0.702455	−	1.72272i
$267$		0			0
$268$	5.24883	−	22.9966i	0.320623	−	1.40474i
$269$	4.76259	−	5.97210i	0.290380	−	0.364126i	−0.615148	−	0.788412i	$-0.710904\pi$
$269$	4.76259	−	5.97210i	0.290380	−	0.364126i	0.905528	+	0.424286i	$0.139475\pi$
$270$		0			0
$271$	−1.81991	+	7.97355i	−0.110552	+	0.484359i	0.889094	+	0.457725i	$0.151336\pi$
$271$	−1.81991	+	7.97355i	−0.110552	+	0.484359i	−0.999645	+	0.0266331i	$0.991521\pi$
$272$	−2.77085	+	12.1399i	−0.168007	+	0.736089i
$273$		0			0
$274$	−7.22782	−	31.6671i	−0.436648	−	1.91308i
$275$	5.55230			0.334816
$276$		0			0
$277$	1.40794	+	6.16858i	0.0845948	+	0.370634i	0.999450	−	0.0331470i	$-0.0105529\pi$
$277$	1.40794	+	6.16858i	0.0845948	+	0.370634i	−0.914856	+	0.403781i	$0.867696\pi$
$278$	21.3201	+	10.2672i	1.27869	+	0.615786i
$279$		0			0
$280$	9.85516	−	6.91113i	0.588958	−	0.413019i
$281$	−5.25138	−	6.58502i	−0.313271	−	0.392829i	0.600122	−	0.799909i	$-0.295119\pi$
$281$	−5.25138	−	6.58502i	−0.313271	−	0.392829i	−0.913393	+	0.407079i	$0.866547\pi$
$282$		0			0
$283$	−5.42203	−	6.79901i	−0.322306	−	0.404159i	0.594111	−	0.804383i	$-0.297504\pi$
$283$	−5.42203	−	6.79901i	−0.322306	−	0.404159i	−0.916418	+	0.400223i	$0.868932\pi$
$284$	−15.1602	−	7.30078i	−0.899593	−	0.433221i
$285$		0			0
$286$	5.63805	−	2.71514i	0.333385	−	0.160550i
$287$	−18.4457	+	3.02937i	−1.08881	+	0.178818i
$288$		0			0
$289$	−10.5796	+	5.09486i	−0.622328	+	0.299698i
$290$	−3.37800	+	14.8000i	−0.198363	+	0.869085i
$291$		0			0
$292$	22.9399	+	28.7657i	1.34245	+	1.68338i
$293$	25.8107			1.50787			0.753937	−	0.656946i	$-0.228152\pi$
$293$	25.8107			1.50787			0.753937	+	0.656946i	$0.228152\pi$
$294$		0			0
$295$	−22.7696			−1.32570
$296$	−7.18034	−	9.00386i	−0.417349	−	0.523339i
$297$		0			0
$298$	−4.25621	+	18.6477i	−0.246556	+	1.08023i
$299$	−4.09519	+	1.97214i	−0.236831	+	0.114052i
$300$		0			0
$301$	−8.48910	−	7.67103i	−0.489303	−	0.442151i
$302$	14.8838	−	7.16764i	0.856464	−	0.412451i
$303$		0			0
$304$	11.1458	+	5.36753i	0.639255	+	0.307849i
$305$	−11.0732	−	13.8854i	−0.634051	−	0.795075i
$306$		0			0
$307$	−7.16969	−	8.99051i	−0.409196	−	0.513115i	0.533940	−	0.845522i	$-0.320711\pi$
$307$	−7.16969	−	8.99051i	−0.409196	−	0.513115i	−0.943136	+	0.332407i	$0.892139\pi$
$308$	−6.33980	+	1.04120i	−0.361244	+	0.0593278i
$309$		0			0
$310$	64.3468	+	30.9878i	3.65465	+	1.75999i
$311$	0.321650	+	1.40924i	0.0182391	+	0.0799108i	0.983228	−	0.182379i	$-0.0583796\pi$
$311$	0.321650	+	1.40924i	0.0182391	+	0.0799108i	−0.964989	+	0.262289i	$0.915523\pi$
$312$		0			0
$313$	−29.3677			−1.65996			−0.829980	−	0.557794i	$-0.811648\pi$
$313$	−29.3677			−1.65996			−0.829980	+	0.557794i	$0.811648\pi$
$314$	0.336005	+	1.47213i	0.0189619	+	0.0830773i
$315$		0			0
$316$	7.70721	−	33.7675i	0.433564	−	1.89957i
$317$	−5.98084	+	26.2038i	−0.335918	+	1.47175i	0.471550	+	0.881839i	$0.343695\pi$
$317$	−5.98084	+	26.2038i	−0.335918	+	1.47175i	−0.807468	+	0.589912i	$0.799163\pi$
$318$		0			0
$319$	1.21929	−	1.52894i	0.0682671	−	0.0856042i
$320$	−8.88430	+	38.9246i	−0.496647	+	2.17595i
$321$		0			0
$322$	8.09841	−	1.33002i	0.451307	−	0.0741191i
$323$	6.35409	+	27.8391i	0.353551	+	1.54901i
$324$		0			0
$325$	19.0184			1.05495
$326$	5.43798	+	23.8253i	0.301182	+	1.31956i
$327$		0			0
$328$	−6.03500	+	7.56765i	−0.333227	+	0.417854i
$329$	4.15271	+	10.1842i	0.228946	+	0.561472i
$330$		0			0
$331$	−1.86198	−	8.15788i	−0.102344	−	0.448398i	−0.999971	−	0.00764179i	$-0.997568\pi$
$331$	−1.86198	−	8.15788i	−0.102344	−	0.448398i	0.897627	−	0.440756i	$-0.145290\pi$
$332$	24.3990	+	30.5953i	1.33907	+	1.67914i
$333$		0			0
$334$	−18.4687	+	23.1590i	−1.01056	+	1.26720i
$335$	−26.7704	+	12.8920i	−1.46263	+	0.704363i
$336$		0			0
$337$	22.6456	+	10.9055i	1.23358	+	0.594063i	0.933063	−	0.359712i	$-0.117125\pi$
$337$	22.6456	+	10.9055i	1.23358	+	0.594063i	0.300521	+	0.953775i	$0.402839\pi$
$338$	−5.90742	+	2.84486i	−0.321321	+	0.154740i
$339$		0			0
$340$	−42.2868	+	20.3642i	−2.29332	+	1.10441i
$341$	−5.73635	−	7.19315i	−0.310641	−	0.389531i
$342$		0			0
$343$	12.1105	+	14.0120i	0.653906	+	0.756575i
$344$	−5.92461			−0.319434
$345$		0			0
$346$	−33.1147	+	15.9472i	−1.78025	+	0.857325i
$347$	5.08322	−	22.2710i	0.272882	−	1.19557i	−0.633712	−	0.773569i	$-0.718470\pi$
$347$	5.08322	−	22.2710i	0.272882	−	1.19557i	0.906594	−	0.422004i	$-0.138673\pi$
$348$		0			0
$349$	13.6906	+	6.59305i	0.732842	+	0.352918i	0.762801	−	0.646633i	$-0.223824\pi$
$349$	13.6906	+	6.59305i	0.732842	+	0.352918i	−0.0299595	+	0.999551i	$0.509538\pi$
$350$	−32.9441	−	9.68831i	−1.76094	−	0.517862i
$351$		0			0
$352$	4.44579	−	5.57484i	0.236961	−	0.297140i
$353$	−10.7509	−	5.17738i	−0.572215	−	0.275564i	0.125319	−	0.992117i	$-0.460005\pi$
$353$	−10.7509	−	5.17738i	−0.572215	−	0.275564i	−0.697533	+	0.716553i	$0.745719\pi$
$354$		0			0
$355$	4.71651	+	20.6644i	0.250326	+	1.09675i
$356$	−1.99453	−	2.50106i	−0.105710	−	0.132556i
$357$		0			0
$358$	16.2510	−	20.3781i	0.858890	−	1.07701i
$359$	−6.89807	−	3.32193i	−0.364066	−	0.175325i	0.242903	−	0.970051i	$-0.421900\pi$
$359$	−6.89807	−	3.32193i	−0.364066	−	0.175325i	−0.606969	+	0.794726i	$0.707615\pi$
$360$		0			0
$361$	9.36882			0.493096
$362$	−3.36988			−0.177117
$363$		0			0
$364$	−21.7159	+	3.56644i	−1.13822	+	0.186932i
$365$	10.3130	−	45.1844i	0.539809	−	2.36506i
$366$		0			0
$367$	6.57252	−	8.24168i	0.343083	−	0.430212i	−0.580117	−	0.814533i	$-0.696993\pi$
$367$	6.57252	−	8.24168i	0.343083	−	0.430212i	0.923199	+	0.384321i	$0.125565\pi$
$368$	−2.08620	+	2.61601i	−0.108751	+	0.136369i
$369$		0			0
$370$	−13.3749	+	58.5993i	−0.695329	+	3.04643i
$371$	12.8878	−	23.0177i	0.669102	−	1.19502i
$372$		0			0
$373$	−21.8056			−1.12905			−0.564526	−	0.825415i	$-0.690941\pi$
$373$	−21.8056			−1.12905			−0.564526	+	0.825415i	$0.690941\pi$
$374$	10.6332			0.549828
$375$		0			0
$376$	5.13109	+	2.47100i	0.264616	+	0.127432i
$377$	4.17646	−	5.23711i	0.215099	−	0.269725i
$378$		0			0
$379$	6.50542	+	8.15754i	0.334161	+	0.419025i	0.920317	−	0.391173i	$-0.127931\pi$
$379$	6.50542	+	8.15754i	0.334161	+	0.419025i	−0.586156	+	0.810198i	$0.699359\pi$
$380$	10.3759	+	45.4597i	0.532271	+	2.33203i
$381$		0			0
$382$	29.3363	+	14.1276i	1.50097	+	0.722831i
$383$	−4.99571	+	6.26443i	−0.255269	+	0.320097i	−0.892909	−	0.450237i	$-0.851339\pi$
$383$	−4.99571	+	6.26443i	−0.255269	+	0.320097i	0.637640	+	0.770335i	$0.279911\pi$
$384$		0			0
$385$	6.00461	+	5.42597i	0.306024	+	0.276533i
$386$	13.0360	+	6.27782i	0.663516	+	0.319532i
$387$		0			0
$388$	−0.754925	+	3.30754i	−0.0383255	+	0.167915i
$389$	−25.6925	+	12.3728i	−1.30266	+	0.627328i	−0.951113	−	0.308843i	$-0.900058\pi$
$389$	−25.6925	+	12.3728i	−1.30266	+	0.627328i	−0.351546	+	0.936171i	$0.614344\pi$
$390$		0			0
$391$	−7.72339			−0.390589
$392$	9.51732	+	1.17890i	0.480697	+	0.0595434i
$393$		0			0
$394$	−15.4983	−	19.4342i	−0.780791	−	0.979081i
$395$	−39.3089	+	18.9302i	−1.97784	+	0.952479i
$396$		0			0
$397$	28.5465	−	13.7473i	1.43271	−	0.689956i	0.453210	−	0.891404i	$-0.350279\pi$
$397$	28.5465	−	13.7473i	1.43271	−	0.689956i	0.979499	+	0.201448i	$0.0645646\pi$
$398$	−9.82639	−	4.73214i	−0.492552	−	0.237201i
$399$		0			0
$400$	12.6138	−	6.07449i	0.630690	−	0.303725i
$401$	6.95614	−	8.72273i	0.347373	−	0.435592i	−0.577196	−	0.816605i	$-0.695853\pi$
$401$	6.95614	−	8.72273i	0.347373	−	0.435592i	0.924570	+	0.381013i	$0.124425\pi$
$402$		0			0
$403$	−19.6488	−	24.6389i	−0.978779	−	1.22735i
$404$	−4.39217	−	19.2433i	−0.218519	−	0.957392i
$405$		0			0
$406$	−9.90242	+	6.94427i	−0.491449	+	0.344639i
$407$	4.82768	−	6.05371i	0.239299	−	0.300071i
$408$		0			0
$409$	3.98121	+	17.4428i	0.196858	+	0.862492i	0.972792	+	0.231678i	$0.0744217\pi$
$409$	3.98121	+	17.4428i	0.196858	+	0.862492i	−0.775934	+	0.630814i	$0.782721\pi$
$410$	50.5187			2.49494
$411$		0			0
$412$	0.412823	+	1.80870i	0.0203383	+	0.0891081i
$413$	−13.4597	−	12.1627i	−0.662310	−	0.598486i
$414$		0			0
$415$	10.9690	−	48.0583i	0.538447	−	2.35909i
$416$	15.2283	−	19.0956i	0.746627	−	0.936241i
$417$		0			0
$418$	2.35067	−	10.2990i	0.114975	−	0.503739i
$419$	−0.662086	+	2.90079i	−0.0323450	+	0.141713i	−0.988522	−	0.151076i	$-0.951726\pi$
$419$	−0.662086	+	2.90079i	−0.0323450	+	0.141713i	0.956177	+	0.292789i	$0.0945833\pi$
$420$		0			0
$421$	−2.05976	−	9.02441i	−0.100387	−	0.439823i	−0.999995	−	0.00312527i	$-0.999005\pi$
$421$	−2.05976	−	9.02441i	−0.100387	−	0.439823i	0.899608	−	0.436697i	$-0.143852\pi$
$422$	−19.7906			−0.963391
$423$		0			0
$424$	−3.03963	−	13.3175i	−0.147618	−	0.646755i
$425$	29.1157	+	14.0214i	1.41232	+	0.680138i
$426$		0			0
$427$	0.871367	−	14.1229i	0.0421684	−	0.683457i
$428$	−11.3053	−	14.1765i	−0.546464	−	0.685245i
$429$		0			0
$430$	19.2794	+	24.1756i	0.929736	+	1.16585i
$431$	5.39568	+	2.59842i	0.259901	+	0.125162i	0.559297	−	0.828967i	$-0.311071\pi$
$431$	5.39568	+	2.59842i	0.259901	+	0.125162i	−0.299396	+	0.954129i	$0.596785\pi$
$432$		0			0
$433$	−5.86935	+	2.82653i	−0.282063	+	0.135834i	−0.569567	−	0.821945i	$-0.692889\pi$
$433$	−5.86935	+	2.82653i	−0.282063	+	0.135834i	0.287504	+	0.957780i	$0.407175\pi$
$434$	21.4847	+	52.6894i	1.03130	+	2.52917i
$435$		0			0
$436$	−34.2445	+	16.4913i	−1.64002	+	0.789790i
$437$	−1.70741	+	7.48065i	−0.0816764	+	0.357848i
$438$		0			0
$439$	−4.28694	−	5.37565i	−0.204604	−	0.256566i	0.668933	−	0.743322i	$-0.266751\pi$
$439$	−4.28694	−	5.37565i	−0.204604	−	0.256566i	−0.873537	+	0.486757i	$0.838180\pi$
$440$	4.19067			0.199782
$441$		0			0
$442$	36.4220			1.73242
$443$	19.9860	+	25.0617i	0.949565	+	1.19072i	0.981546	+	0.191228i	$0.0612471\pi$
$443$	19.9860	+	25.0617i	0.949565	+	1.19072i	−0.0319805	+	0.999488i	$0.510181\pi$
$444$		0			0
$445$	−0.896678	+	3.92860i	−0.0425066	+	0.186234i
$446$	27.6105	−	13.2965i	1.30740	−	0.629609i
$447$		0			0
$448$	−26.0438	+	18.2638i	−1.23046	+	0.862882i
$449$	21.0634	−	10.1436i	0.994044	−	0.478707i	0.135131	−	0.990828i	$-0.456854\pi$
$449$	21.0634	−	10.1436i	0.994044	−	0.478707i	0.858913	+	0.512121i	$0.171140\pi$
$450$		0			0
$451$	−5.86342	−	2.82367i	−0.276098	−	0.132962i
$452$	−5.87305	−	7.36457i	−0.276245	−	0.346400i
$453$		0			0
$454$	−37.9812	−	47.6269i	−1.78254	−	2.23524i
$455$	20.5677	+	18.5857i	0.964231	+	0.871311i
$456$		0			0
$457$	25.1097	+	12.0922i	1.17458	+	0.565649i	0.916328	−	0.400429i	$-0.131139\pi$
$457$	25.1097	+	12.0922i	1.17458	+	0.565649i	0.258253	+	0.966077i	$0.416853\pi$
$458$	7.99674	+	35.0360i	0.373663	+	1.63712i
$459$		0			0
$460$	−12.6119			−0.588031
$461$	0.461346	+	2.02129i	0.0214870	+	0.0941408i	0.984534	−	0.175191i	$-0.0560543\pi$
$461$	0.461346	+	2.02129i	0.0214870	+	0.0941408i	−0.963047	+	0.269332i	$0.913197\pi$
$462$		0			0
$463$	−8.04686	+	35.2556i	−0.373970	+	1.63847i	0.341542	+	0.939867i	$0.389051\pi$
$463$	−8.04686	+	35.2556i	−0.373970	+	1.63847i	−0.715512	+	0.698601i	$0.753806\pi$
$464$	1.09727	−	4.80744i	0.0509393	−	0.223180i
$465$		0			0
$466$	−24.0599	+	30.1702i	−1.11455	+	1.39761i
$467$	−0.540164	+	2.36662i	−0.0249958	+	0.109514i	−0.985887	−	0.167413i	$-0.946459\pi$
$467$	−0.540164	+	2.36662i	−0.0249958	+	0.109514i	0.960891	+	0.276927i	$0.0893159\pi$
$468$		0			0
$469$	−22.7112	−	6.67897i	−1.04870	−	0.308406i
$470$	−6.61417	−	28.9786i	−0.305089	−	1.33668i
$471$		0			0
$472$	−9.39366			−0.432378
$473$	−0.886388	−	3.88352i	−0.0407562	−	0.178564i
$474$		0			0
$475$	20.0173	−	25.1009i	0.918458	−	1.15171i
$476$	−35.8747	−	10.5502i	−1.64431	−	0.483566i
$477$		0			0
$478$	−8.54698	−	37.4468i	−0.390930	−	1.71278i
$479$	−10.4347	−	13.0847i	−0.476773	−	0.597854i	0.484042	−	0.875045i	$-0.339168\pi$
$479$	−10.4347	−	13.0847i	−0.476773	−	0.597854i	−0.960815	+	0.277190i	$0.910597\pi$
$480$		0			0
$481$	16.5364	−	20.7359i	0.753993	−	0.945477i
$482$	−15.1790	+	7.30980i	−0.691382	+	0.332952i
$483$		0			0
$484$	24.1119	+	11.6117i	1.09599	+	0.527803i
$485$	3.85032	−	1.85422i	0.174834	−	0.0841956i
$486$		0			0
$487$	3.36541	−	1.62070i	0.152501	−	0.0734408i	−0.356076	−	0.934457i	$-0.615886\pi$
$487$	3.36541	−	1.62070i	0.152501	−	0.0734408i	0.508578	+	0.861016i	$0.330171\pi$
$488$	−4.56829	−	5.72846i	−0.206797	−	0.259315i
$489$		0			0
$490$	−26.1600	−	42.6721i	−1.18179	−	1.92773i
$491$	−28.1067			−1.26844			−0.634220	−	0.773153i	$-0.718679\pi$
$491$	−28.1067			−1.26844			−0.634220	+	0.773153i	$0.718679\pi$
$492$		0			0
$493$	10.2549	−	4.93851i	0.461858	−	0.222419i
$494$	8.05182	−	35.2773i	0.362268	−	1.58720i
$495$		0			0
$496$	−20.9016	−	10.0657i	−0.938510	−	0.451962i
$497$	−8.25008	+	14.7347i	−0.370067	+	0.660940i
$498$		0			0
$499$	−21.0506	+	26.3966i	−0.942355	+	1.18168i	0.0408491	+	0.999165i	$0.486994\pi$
$499$	−21.0506	+	26.3966i	−0.942355	+	1.18168i	−0.983204	+	0.182510i	$0.941578\pi$
$500$	8.10654	+	3.90390i	0.362535	+	0.174588i
$501$		0			0
$502$	−1.04518	−	4.57922i	−0.0466485	−	0.204380i
$503$	−17.0451	−	21.3739i	−0.760005	−	0.953016i	0.239837	−	0.970813i	$-0.422906\pi$
$503$	−17.0451	−	21.3739i	−0.760005	−	0.953016i	−0.999842	+	0.0177974i	$0.994335\pi$
$504$		0			0
$505$	−15.5021	+	19.4391i	−0.689836	+	0.865027i
$506$	2.57428	+	1.23971i	0.114441	+	0.0551118i
$507$		0			0
$508$	−33.5282			−1.48757
$509$	−22.9249			−1.01613			−0.508063	−	0.861320i	$-0.669638\pi$
$509$	−22.9249			−1.01613			−0.508063	+	0.861320i	$0.669638\pi$
$510$		0			0
$511$	30.2321	−	21.2009i	1.33739	−	0.937873i
$512$	5.41700	−	23.7334i	0.239400	−	1.04888i
$513$		0			0
$514$	6.06764	−	7.60858i	0.267632	−	0.335600i
$515$	1.45706	−	1.82709i	0.0642057	−	0.0805114i
$516$		0			0
$517$	−0.852047	+	3.73306i	−0.0374730	+	0.164180i
$518$	−39.2079	+	27.4953i	−1.72269	+	1.20807i
$519$		0			0
$520$	14.3544			0.629482
$521$	−13.1750			−0.577206			−0.288603	−	0.957449i	$-0.593191\pi$
$521$	−13.1750			−0.577206			−0.288603	+	0.957449i	$0.593191\pi$
$522$		0			0
$523$	32.8389	+	15.8144i	1.43595	+	0.691515i	0.980093	−	0.198539i	$-0.0636197\pi$
$523$	32.8389	+	15.8144i	1.43595	+	0.691515i	0.455854	+	0.890055i	$0.349334\pi$
$524$	10.3149	−	12.9345i	0.450608	−	0.565045i
$525$		0			0
$526$	9.59754	+	12.0349i	0.418473	+	0.524748i
$527$	−11.9158	−	52.2064i	−0.519059	−	2.27415i
$528$		0			0
$529$	18.8525	+	9.07886i	0.819672	+	0.394733i
$530$	−44.4513	+	55.7401i	−1.93084	+	2.42120i
$531$		0			0
$532$	−18.1494	+	32.4149i	−0.786876	+	1.40536i
$533$	−20.0841	−	9.67199i	−0.869939	−	0.418941i
$534$		0			0
$535$	−5.08253	+	22.2680i	−0.219737	+	0.962730i
$536$	−11.0442	+	5.31862i	−0.477038	+	0.229729i
$537$		0			0
$538$	−16.4474			−0.709100
$539$	0.651142	+	6.41488i	0.0280467	+	0.276309i
$540$		0			0
$541$	17.5098	+	21.9566i	0.752805	+	0.943988i	0.999686	−	0.0250579i	$-0.00797703\pi$
$541$	17.5098	+	21.9566i	0.752805	+	0.943988i	−0.246881	+	0.969046i	$0.579406\pi$
$542$	15.8662	−	7.64076i	0.681512	−	0.328199i
$543$		0			0
$544$	37.3917	−	18.0069i	1.60315	−	0.772038i
$545$	43.1366	+	20.7735i	1.84777	+	0.889838i
$546$		0			0
$547$	19.0593	−	9.17849i	0.814918	−	0.392444i	0.0204808	−	0.999790i	$-0.493480\pi$
$547$	19.0593	−	9.17849i	0.814918	−	0.392444i	0.794437	+	0.607347i	$0.207766\pi$
$548$	−24.7954	+	31.0924i	−1.05921	+	1.32820i
$549$		0			0
$550$	−7.45395	−	9.34695i	−0.317837	−	0.398555i
$551$	−2.51624	−	11.0244i	−0.107195	−	0.469654i
$552$		0			0
$553$	−33.3483	−	9.80719i	−1.41812	−	0.417044i
$554$	8.49427	−	10.6515i	0.360887	−	0.452538i
$555$		0			0
$556$	−6.44695	−	28.2460i	−0.273412	−	1.19790i
$557$	−6.69060			−0.283490			−0.141745	−	0.989903i	$-0.545271\pi$
$557$	−6.69060			−0.283490			−0.141745	+	0.989903i	$0.545271\pi$
$558$		0			0
$559$	−3.03617	−	13.3023i	−0.128416	−	0.562628i
$560$	19.5777	+	5.75747i	0.827308	+	0.243298i
$561$		0			0
$562$	−4.03552	+	17.6808i	−0.170228	+	0.745817i
$563$	12.0111	−	15.0614i	0.506206	−	0.634762i	−0.461411	−	0.887187i	$-0.652656\pi$
$563$	12.0111	−	15.0614i	0.506206	−	0.634762i	0.967617	+	0.252424i	$0.0812279\pi$
$564$		0			0
$565$	−2.64034	+	11.5681i	−0.111080	+	0.486672i
$566$	−4.16666	+	18.2553i	−0.175138	+	0.767328i
$567$		0			0
$568$	1.94581	+	8.52515i	0.0816444	+	0.357707i
$569$	−9.98311			−0.418514			−0.209257	−	0.977861i	$-0.567104\pi$
$569$	−9.98311			−0.418514			−0.209257	+	0.977861i	$0.567104\pi$
$570$		0			0
$571$	2.62785	+	11.5133i	0.109972	+	0.481818i	0.999680	+	0.0252889i	$0.00805056\pi$
$571$	2.62785	+	11.5133i	0.109972	+	0.481818i	−0.889708	+	0.456529i	$0.849092\pi$
$572$	−6.90294	−	3.32428i	−0.288626	−	0.138995i
$573$		0			0
$574$	29.8630	+	26.9852i	1.24646	+	1.12634i
$575$	5.41417	+	6.78915i	0.225786	+	0.283127i
$576$		0			0
$577$	−18.3272	−	22.9816i	−0.762972	−	0.956736i	0.236919	−	0.971529i	$-0.423862\pi$
$577$	−18.3272	−	22.9816i	−0.762972	−	0.956736i	−0.999891	+	0.0147931i	$0.995291\pi$
$578$	22.7799	+	10.9702i	0.947521	+	0.456302i
$579$		0			0
$580$	16.7457	−	8.06431i	0.695328	−	0.334852i
$581$	32.1551	−	22.5494i	1.33402	−	0.935506i
$582$		0			0
$583$	8.27472	−	3.98490i	0.342704	−	0.165038i
$584$	4.25468	−	18.6410i	0.176060	−	0.771368i
$585$		0			0
$586$	−34.6507	−	43.4507i	−1.43141	−	1.79493i
$587$	−11.6357			−0.480256			−0.240128	−	0.970741i	$-0.577189\pi$
$587$	−11.6357			−0.480256			−0.240128	+	0.970741i	$0.577189\pi$
$588$		0			0
$589$	−53.1998			−2.19206
$590$	30.5681	+	38.3312i	1.25847	+	1.57807i
$591$		0			0
$592$	4.34454	−	19.0347i	0.178559	−	0.782320i
$593$	−26.1606	+	12.5983i	−1.07429	+	0.517349i	−0.885486	−	0.464666i	$-0.846174\pi$
$593$	−26.1606	+	12.5983i	−1.07429	+	0.517349i	−0.188801	+	0.982015i	$0.560460\pi$
$594$		0			0
$595$	17.7853	+	43.6170i	0.729125	+	1.78812i
$596$	21.0993	−	10.1609i	0.864259	−	0.416205i
$597$		0			0
$598$	8.81776	+	4.24641i	0.360585	+	0.173649i
$599$	−28.2111	−	35.3755i	−1.15267	−	1.44541i	−0.874600	−	0.484845i	$-0.838876\pi$
$599$	−28.2111	−	35.3755i	−1.15267	−	1.44541i	−0.278073	−	0.960560i	$-0.589696\pi$
$600$		0			0
$601$	1.54377	+	1.93582i	0.0629716	+	0.0789639i	0.812320	−	0.583212i	$-0.198204\pi$
$601$	1.54377	+	1.93582i	0.0629716	+	0.0789639i	−0.749348	+	0.662176i	$0.769633\pi$
$602$	−1.51712	+	24.5892i	−0.0618333	+	1.00218i
$603$		0			0
$604$	−18.2229	−	8.77569i	−0.741480	−	0.357078i
$605$	−7.50147	−	32.8661i	−0.304978	−	1.33620i
$606$		0			0
$607$	−3.92071			−0.159137			−0.0795684	−	0.996829i	$-0.525354\pi$
$607$	−3.92071			−0.159137			−0.0795684	+	0.996829i	$0.525354\pi$
$608$	−9.17476	−	40.1972i	−0.372085	−	1.63021i
$609$		0			0
$610$	−8.50942	+	37.2822i	−0.344536	+	1.50951i
$611$	−2.91854	+	12.7870i	−0.118071	+	0.517305i
$612$		0			0
$613$	14.8045	−	18.5642i	0.597948	−	0.749803i	−0.387109	−	0.922034i	$-0.626526\pi$
$613$	14.8045	−	18.5642i	0.597948	−	0.749803i	0.985057	+	0.172231i	$0.0550977\pi$
$614$	−5.50968	+	24.1395i	−0.222352	+	0.974190i
$615$		0			0
$616$	2.47722	+	2.23850i	0.0998101	+	0.0901917i
$617$	11.0374	+	48.3579i	0.444348	+	1.94681i	0.276603	+	0.960984i	$0.410791\pi$
$617$	11.0374	+	48.3579i	0.444348	+	1.94681i	0.167745	+	0.985830i	$0.446351\pi$
$618$		0			0
$619$	20.3020			0.816006			0.408003	−	0.912980i	$-0.366225\pi$
$619$	20.3020			0.816006			0.408003	+	0.912980i	$0.366225\pi$
$620$	−19.4578	−	85.2501i	−0.781443	−	3.42373i
$621$		0			0
$622$	1.94056	−	2.43338i	0.0778093	−	0.0975698i
$623$	−2.62856	+	1.84333i	−0.105311	+	0.0738516i
$624$		0			0
$625$	4.18448	+	18.3334i	0.167379	+	0.733337i
$626$	39.4260	+	49.4387i	1.57578	+	1.97597i
$627$		0			0
$628$	1.15268	−	1.44542i	0.0459970	−	0.0576784i
$629$	40.6035	−	19.5536i	1.61897	−	0.779654i
$630$		0			0
$631$	−15.6606	−	7.54174i	−0.623438	−	0.300232i	0.0953684	−	0.995442i	$-0.469597\pi$
$631$	−15.6606	−	7.54174i	−0.623438	−	0.300232i	−0.718807	+	0.695210i	$0.755311\pi$
$632$	−16.2170	+	7.80969i	−0.645077	+	0.310653i
$633$		0			0
$634$	52.1417	−	25.1101i	2.07081	−	0.997251i
$635$	26.3326	+	33.0201i	1.04498	+	1.31036i
$636$		0			0
$637$	2.23037	+	21.9730i	0.0883705	+	0.870604i
$638$	−4.21077			−0.166706
$639$		0			0
$640$	31.1325	−	14.9926i	1.23062	−	0.592635i
$641$	−1.49307	+	6.54156i	−0.0589726	+	0.258376i	−0.995817	−	0.0913706i	$-0.970875\pi$
$641$	−1.49307	+	6.54156i	−0.0589726	+	0.258376i	0.936844	+	0.349747i	$0.113732\pi$
$642$		0			0
$643$	−2.75531	−	1.32689i	−0.108659	−	0.0523273i	0.378765	−	0.925493i	$-0.376349\pi$
$643$	−2.75531	−	1.32689i	−0.108659	−	0.0523273i	−0.487424	+	0.873166i	$0.662063\pi$
$644$	−7.45522	−	6.73678i	−0.293777	−	0.265466i
$645$		0			0
$646$	38.3351	−	48.0706i	1.50827	−	1.89131i
$647$	30.0943	+	14.4926i	1.18313	+	0.569765i	0.918821	−	0.394674i	$-0.129142\pi$
$647$	30.0943	+	14.4926i	1.18313	+	0.569765i	0.264307	+	0.964439i	$0.414857\pi$
$648$		0			0
$649$	−1.40540	−	6.15744i	−0.0551666	−	0.241701i
$650$	−25.5322	−	32.0163i	−1.00145	−	1.25578i
$651$		0			0
$652$	18.6553	−	23.3929i	0.730596	−	0.916138i
$653$	−14.0919	−	6.78628i	−0.551457	−	0.265568i	0.137338	−	0.990524i	$-0.456145\pi$
$653$	−14.0919	−	6.78628i	−0.551457	−	0.265568i	−0.688794	+	0.724957i	$0.741860\pi$
$654$		0			0
$655$	−20.8396			−0.814272
$656$	−16.4099			−0.640697
$657$		0			0
$658$	11.5694	−	20.6631i	0.451024	−	0.805530i
$659$	−10.1648	+	44.5348i	−0.395963	+	1.73483i	0.247077	+	0.968996i	$0.420530\pi$
$659$	−10.1648	+	44.5348i	−0.395963	+	1.73483i	−0.643041	+	0.765832i	$0.722327\pi$
$660$		0			0
$661$	3.63911	−	4.56330i	0.141545	−	0.177492i	−0.706006	−	0.708206i	$-0.749505\pi$
$661$	3.63911	−	4.56330i	0.141545	−	0.177492i	0.847551	+	0.530714i	$0.178076\pi$
$662$	−11.2336	+	14.0865i	−0.436606	+	0.547486i
$663$		0			0
$664$	4.52529	−	19.8266i	0.175615	−	0.769422i
$665$	46.1779	−	7.58389i	1.79070	−	0.294091i
$666$		0			0
$667$	3.05849			0.118425
$668$	36.2670			1.40321
$669$		0			0
$670$	57.6421	+	27.7590i	2.22691	+	1.07242i
$671$	3.07148	−	3.85151i	0.118573	−	0.148686i
$672$		0			0
$673$	5.22731	+	6.55484i	0.201498	+	0.252670i	0.872306	−	0.488961i	$-0.162624\pi$
$673$	5.22731	+	6.55484i	0.201498	+	0.252670i	−0.670808	+	0.741631i	$0.734052\pi$
$674$	−12.0428	−	52.7632i	−0.463873	−	2.03236i
$675$		0			0
$676$	7.23274	+	3.48310i	0.278182	+	0.133966i
$677$	22.0590	−	27.6611i	0.847797	−	1.06310i	−0.149436	−	0.988771i	$-0.547746\pi$
$677$	22.0590	−	27.6611i	0.847797	−	1.06310i	0.997234	−	0.0743327i	$-0.0236827\pi$
$678$		0			0
$679$	3.26648	+	0.960619i	0.125356	+	0.0368652i
$680$	21.9755	+	10.5828i	0.842722	+	0.405833i
$681$		0			0
$682$	−4.40820	+	19.3136i	−0.168799	+	0.739555i
$683$	6.46119	−	3.11154i	0.247230	−	0.119060i	−0.306165	−	0.951978i	$-0.599046\pi$
$683$	6.46119	−	3.11154i	0.247230	−	0.119060i	0.553396	+	0.832918i	$0.313332\pi$
$684$		0			0
$685$	50.0952			1.91404
$686$	7.32996	−	39.1984i	0.279859	−	1.49660i
$687$		0			0
$688$	−6.26248	−	7.85290i	−0.238755	−	0.299389i
$689$	28.3436	−	13.6496i	1.07980	−	0.520007i
$690$		0			0
$691$	−7.51859	+	3.62076i	−0.286021	+	0.137740i	−0.571393	−	0.820676i	$-0.693597\pi$
$691$	−7.51859	+	3.62076i	−0.286021	+	0.137740i	0.285373	+	0.958417i	$0.407883\pi$
$692$	40.5439	+	19.5249i	1.54125	+	0.742225i
$693$		0			0
$694$	−44.3162	+	21.3415i	−1.68222	+	0.810114i
$695$	−22.7545	+	28.5333i	−0.863128	+	1.08233i
$696$		0			0
$697$	−23.6165	−	29.6142i	−0.894539	−	1.12172i
$698$	−7.28062	−	31.8985i	−0.275575	−	1.20737i
$699$		0			0
$700$	15.8745	+	38.9310i	0.600000	+	1.47145i
$701$	−6.78044	+	8.50240i	−0.256094	+	0.321131i	−0.893213	−	0.449634i	$-0.851554\pi$
$701$	−6.78044	+	8.50240i	−0.256094	+	0.321131i	0.637119	+	0.770765i	$0.280126\pi$
$702$		0			0
$703$	−9.96285	−	43.6501i	−0.375756	−	1.64630i
$704$	−11.0745			−0.417387
$705$		0			0
$706$	5.71731	+	25.0492i	0.215174	+	0.942738i
$707$	−19.5474	+	3.21031i	−0.735155	+	0.120736i
$708$		0			0
$709$	−8.09889	+	35.4836i	−0.304160	+	1.33261i	0.559622	+	0.828748i	$0.310946\pi$
$709$	−8.09889	+	35.4836i	−0.304160	+	1.33261i	−0.863782	+	0.503865i	$0.831911\pi$
$710$	28.4553	−	35.6818i	1.06791	−	1.33912i
$711$		0			0
$712$	−0.369927	+	1.62076i	−0.0138636	+	0.0607404i
$713$	3.20189	−	14.0284i	0.119912	−	0.525368i
$714$		0			0
$715$	2.14758	+	9.40916i	0.0803149	+	0.351883i
$716$	−31.9121			−1.19261
$717$		0			0
$718$	3.66837	+	16.0722i	0.136902	+	0.599808i
$719$	4.31400	+	2.07751i	0.160885	+	0.0774782i	0.512593	−	0.858631i	$-0.328685\pi$
$719$	4.31400	+	2.07751i	0.160885	+	0.0774782i	−0.351708	+	0.936110i	$0.614399\pi$
$720$		0			0
$721$	1.83727	−	0.301739i	0.0684236	−	0.0112374i
$722$	−12.5776	−	15.7718i	−0.468091	−	0.586967i
$723$		0			0
$724$	2.57246	+	3.22577i	0.0956048	+	0.119885i
$725$	−11.5299	−	5.55252i	−0.428211	−	0.206215i
$726$		0			0
$727$	−21.3492	+	10.2812i	−0.791796	+	0.381309i	−0.785649	−	0.618672i	$-0.787671\pi$
$727$	−21.3492	+	10.2812i	−0.791796	+	0.381309i	−0.00614695	+	0.999981i	$0.501957\pi$
$728$	8.48528	+	7.66759i	0.314486	+	0.284180i
$729$		0			0
$730$	−89.9104	+	43.2986i	−3.32773	+	1.60255i
$731$	5.15905	−	22.6033i	0.190814	−	0.836012i
$732$		0			0
$733$	−12.9409	−	16.2274i	−0.477985	−	0.599374i	0.483121	−	0.875553i	$-0.339503\pi$
$733$	−12.9409	−	16.2274i	−0.477985	−	0.599374i	−0.961106	+	0.276180i	$0.910932\pi$
$734$	−22.6980			−0.837797
$735$		0			0
$736$	11.1519			0.411065
$737$	−5.13864	−	6.44365i	−0.189284	−	0.237355i
$738$		0			0
$739$	−1.07699	+	4.71859i	−0.0396176	+	0.173576i	−0.990866	−	0.134849i	$-0.956945\pi$
$739$	−1.07699	+	4.71859i	−0.0396176	+	0.173576i	0.951248	+	0.308426i	$0.0998021\pi$
$740$	66.3033	−	31.9300i	2.43736	−	1.17377i
$741$		0			0
$742$	−56.0507	+	9.20532i	−2.05769	+	0.337938i
$743$	−8.38006	+	4.03562i	−0.307435	+	0.148053i	−0.581239	−	0.813733i	$-0.697432\pi$
$743$	−8.38006	+	4.03562i	−0.307435	+	0.148053i	0.273805	+	0.961785i	$0.411718\pi$
$744$		0			0
$745$	−26.5780	−	12.7993i	−0.973741	−	0.468929i
$746$	29.2740	+	36.7085i	1.07180	+	1.34399i
$747$		0			0
$748$	−8.11703	−	10.1784i	−0.296788	−	0.372160i
$749$	−14.8992	+	10.4483i	−0.544403	+	0.381774i
$750$		0			0
$751$	2.51655	+	1.21191i	0.0918301	+	0.0442230i	0.479235	−	0.877687i	$-0.340914\pi$
$751$	2.51655	+	1.21191i	0.0918301	+	0.0442230i	−0.387405	+	0.921910i	$0.626628\pi$
$752$	2.14846	+	9.41303i	0.0783463	+	0.343258i
$753$		0			0
$754$	−14.4232			−0.525264
$755$	5.66935	+	24.8390i	0.206329	+	0.903985i
$756$		0			0
$757$	9.20803	−	40.3430i	0.334672	−	1.46629i	−0.475301	−	0.879823i	$-0.657661\pi$
$757$	9.20803	−	40.3430i	0.334672	−	1.46629i	0.809972	−	0.586468i	$-0.199482\pi$
$758$	4.99921	−	21.9030i	0.181579	−	0.795552i
$759$		0			0
$760$	15.1083	−	18.9453i	0.548037	−	0.687217i
$761$	3.11153	−	13.6325i	0.112793	−	0.494178i	−0.886700	−	0.462345i	$-0.847008\pi$
$761$	3.11153	−	13.6325i	0.112793	−	0.494178i	0.999493	−	0.0318335i	$-0.0101346\pi$
$762$		0			0
$763$	14.4028	+	35.3217i	0.521417	+	1.27873i
$764$	−8.87097	−	38.8663i	−0.320940	−	1.40613i
$765$		0			0
$766$	17.2525			0.623359
$767$	−4.81394	−	21.0912i	−0.173821	−	0.761560i
$768$		0			0
$769$	16.6263	−	20.8488i	0.599561	−	0.751826i	−0.385749	−	0.922604i	$-0.626057\pi$
$769$	16.6263	−	20.8488i	0.599561	−	0.751826i	0.985309	+	0.170778i	$0.0546282\pi$
$770$	1.07311	−	17.3928i	0.0386722	−	0.626791i
$771$		0			0
$772$	−3.94195	−	17.2708i	−0.141874	−	0.621590i
$773$	21.6955	+	27.2053i	0.780333	+	0.978507i	0.999996	+	0.00293090i	$0.000932936\pi$
$773$	21.6955	+	27.2053i	0.780333	+	0.978507i	−0.219663	+	0.975576i	$0.570496\pi$
$774$		0			0
$775$	−37.5383	+	47.0716i	−1.34842	+	1.69086i
$776$	1.58846	−	0.764962i	0.0570224	−	0.0274605i
$777$		0			0
$778$	55.3210	+	26.6412i	1.98335	+	0.955133i
$779$	−33.9043	+	16.3275i	−1.21475	+	0.584992i
$780$		0			0
$781$	−5.29703	+	2.55092i	−0.189543	+	0.0912790i
$782$	10.3686	+	13.0019i	0.370782	+	0.464945i
$783$		0			0
$784$	8.49748	+	13.8611i	0.303481	+	0.495038i
$785$	−2.32881			−0.0831189
$786$		0			0
$787$	−18.3569	+	8.84022i	−0.654353	+	0.315120i	−0.731441	−	0.681904i	$-0.761152\pi$
$787$	−18.3569	+	8.84022i	−0.654353	+	0.315120i	0.0770881	+	0.997024i	$0.475438\pi$
$788$	−6.77220	+	29.6709i	−0.241250	+	1.05698i
$789$		0			0
$790$	84.6398	+	40.7604i	3.01135	+	1.45019i
$791$	−7.74001	+	5.42784i	−0.275203	+	0.192992i
$792$		0			0
$793$	10.5208	−	13.1927i	0.373605	−	0.468485i
$794$	−61.4663	−	29.6006i	−2.18136	−	1.05049i
$795$		0			0
$796$	2.97139	+	13.0185i	0.105318	+	0.461429i
$797$	10.6801	+	13.3925i	0.378309	+	0.474385i	0.934138	−	0.356912i	$-0.116170\pi$
$797$	10.6801	+	13.3925i	0.378309	+	0.474385i	−0.555829	+	0.831297i	$0.687599\pi$
$798$		0			0
$799$	−13.8953	+	17.4241i	−0.491580	+	0.616422i
$800$	−42.0406	−	20.2457i	−1.48636	−	0.715793i
$801$		0			0
$802$	−24.0228			−0.848274
$803$	12.8555			0.453661
$804$		0			0
$805$	−0.779452	+	12.6332i	−0.0274721	+	0.445262i
$806$	−15.0995	+	66.1553i	−0.531857	+	2.33022i
$807$		0			0
$808$	−6.39545	+	8.01965i	−0.224991	+	0.282130i
$809$	15.3061	−	19.1933i	0.538134	−	0.674799i	−0.436214	−	0.899843i	$-0.643681\pi$
$809$	15.3061	−	19.1933i	0.538134	−	0.674799i	0.974349	+	0.225044i	$0.0722525\pi$
$810$		0			0
$811$	9.47009	−	41.4912i	0.332540	−	1.45695i	−0.481655	−	0.876361i	$-0.659964\pi$
$811$	9.47009	−	41.4912i	0.332540	−	1.45695i	0.814195	−	0.580591i	$-0.197179\pi$
$812$	14.2065	+	4.17790i	0.498550	+	0.146615i
$813$		0			0
$814$	−16.6722			−0.584360
$815$	−37.6900			−1.32022
$816$		0			0
$817$	−20.7523	−	9.99380i	−0.726032	−	0.349639i
$818$	24.0192	−	30.1191i	0.839810	−	1.05309i
$819$		0			0
$820$	−38.5644	−	48.3583i	−1.34673	−	1.68874i
$821$	0.308068	+	1.34973i	0.0107516	+	0.0471060i	0.980019	−	0.198903i	$-0.0637379\pi$
$821$	0.308068	+	1.34973i	0.0107516	+	0.0471060i	−0.969268	+	0.246009i	$0.920881\pi$
$822$		0			0
$823$	−7.69757	−	3.70695i	−0.268320	−	0.129216i	0.294886	−	0.955532i	$-0.404718\pi$
$823$	−7.69757	−	3.70695i	−0.268320	−	0.129216i	−0.563207	+	0.826316i	$0.690433\pi$
$824$	0.601114	−	0.753773i	0.0209408	−	0.0262589i
$825$		0			0
$826$	−2.40544	+	38.9870i	−0.0836961	+	1.35653i
$827$	32.2279	+	15.5201i	1.12067	+	0.539687i	0.900100	−	0.435683i	$-0.143493\pi$
$827$	32.2279	+	15.5201i	1.12067	+	0.539687i	0.220572	+	0.975371i	$0.429207\pi$
$828$		0			0
$829$	−9.04357	+	39.6225i	−0.314096	+	1.37614i	0.533633	+	0.845716i	$0.320826\pi$
$829$	−9.04357	+	39.6225i	−0.314096	+	1.37614i	−0.847729	+	0.530429i	$0.822031\pi$
$830$	−95.6291	+	46.0526i	−3.31934	+	1.59851i
$831$		0			0
$832$	−37.9338			−1.31512
$833$	−12.7852	+	35.2834i	−0.442981	+	1.22250i
$834$		0			0
$835$	−28.4836	−	35.7173i	−0.985717	−	1.23605i
$836$	−11.6530	+	5.61177i	−0.403026	+	0.194087i
$837$		0			0
$838$	5.77215	−	2.77972i	0.199396	−	0.0960238i
$839$	−35.7591	−	17.2207i	−1.23454	−	0.594525i	−0.301217	−	0.953556i	$-0.597393\pi$
$839$	−35.7591	−	17.2207i	−1.23454	−	0.594525i	−0.933326	+	0.359031i	$0.883107\pi$
$840$		0			0
$841$	22.0671	−	10.6270i	0.760935	−	0.366447i
$842$	−12.4268	+	15.5827i	−0.428256	+	0.537016i
$843$		0			0
$844$	15.1075	+	18.9442i	0.520023	+	0.652088i
$845$	−2.25018	−	9.85870i	−0.0774087	−	0.339150i
$846$		0			0
$847$	13.1215	−	23.4351i	0.450860	−	0.805238i
$848$	14.4390	−	18.1059i	0.495837	−	0.621760i
$849$		0			0
$850$	−15.4836	−	67.8383i	−0.531085	−	2.32683i
$851$	12.1098			0.415120
$852$		0			0
$853$	−0.434522	−	1.90377i	−0.0148778	−	0.0651837i	0.966944	−	0.254988i	$-0.0820717\pi$
$853$	−0.434522	−	1.90377i	−0.0148778	−	0.0651837i	−0.981822	+	0.189805i	$0.939215\pi$
$854$	−24.9449	+	17.4931i	−0.853598	+	0.598603i
$855$		0			0
$856$	−2.09681	+	9.18673i	−0.0716675	+	0.313996i
$857$	−11.2988	+	14.1683i	−0.385961	+	0.483980i	−0.936419	−	0.350883i	$-0.885882\pi$
$857$	−11.2988	+	14.1683i	−0.385961	+	0.483980i	0.550458	+	0.834863i	$0.314453\pi$
$858$		0			0
$859$	−5.97788	+	26.1908i	−0.203963	+	0.893619i	0.764532	+	0.644585i	$0.222970\pi$
$859$	−5.97788	+	26.1908i	−0.203963	+	0.893619i	−0.968495	+	0.249033i	$0.919887\pi$
$860$	8.42443	−	36.9098i	0.287271	−	1.25862i
$861$		0			0
$862$	−2.86940	−	12.5717i	−0.0977323	−	0.428193i
$863$	−17.4957			−0.595560			−0.297780	−	0.954634i	$-0.596246\pi$
$863$	−17.4957			−0.595560			−0.297780	+	0.954634i	$0.596246\pi$
$864$		0			0
$865$	−12.6136	−	55.2640i	−0.428877	−	1.87903i
$866$	12.6379	+	6.08608i	0.429453	+	0.206814i
$867$		0			0
$868$	34.0354	−	60.7873i	1.15524	−	2.06326i
$869$	−7.54541	−	9.46165i	−0.255961	−	0.320964i
$870$		0			0
$871$	−17.6015	−	22.0716i	−0.596404	−	0.747867i
$872$	17.7961	+	8.57016i	0.602653	+	0.290222i
$873$		0			0
$874$	14.8854	−	7.16843i	0.503506	−	0.242476i
$875$	4.41152	−	7.87899i	0.149137	−	0.266359i
$876$		0			0
$877$	−36.2923	+	17.4775i	−1.22550	+	0.590172i	−0.930839	−	0.365429i	$-0.880922\pi$
$877$	−36.2923	+	17.4775i	−1.22550	+	0.590172i	−0.294665	+	0.955601i	$0.595208\pi$
$878$	−3.29437	+	14.4336i	−0.111180	+	0.487110i
$879$		0			0
$880$	4.42966	+	5.55461i	0.149324	+	0.187246i
$881$	−4.82087			−0.162419			−0.0812095	−	0.996697i	$-0.525878\pi$
$881$	−4.82087			−0.162419			−0.0812095	+	0.996697i	$0.525878\pi$
$882$		0			0
$883$	15.5894			0.524624			0.262312	−	0.964983i	$-0.415515\pi$
$883$	15.5894			0.524624			0.262312	+	0.964983i	$0.415515\pi$
$884$	−27.8035	−	34.8644i	−0.935131	−	1.17262i
$885$		0			0
$886$	15.3586	−	67.2905i	0.515983	−	2.26067i
$887$	40.6637	−	19.5826i	1.36535	−	0.657519i	0.399529	−	0.916721i	$-0.369174\pi$
$887$	40.6637	−	19.5826i	1.36535	−	0.657519i	0.965823	+	0.259202i	$0.0834594\pi$
$888$		0			0
$889$	−2.07215	+	33.5850i	−0.0694976	+	1.12640i
$890$	7.81735	−	3.76464i	0.262038	−	0.126191i
$891$		0			0
$892$	−33.8049	−	16.2796i	−1.13187	−	0.545081i
$893$	13.8047	+	17.3105i	0.461956	+	0.579275i
$894$		0			0
$895$	25.0633	+	31.4284i	0.837775	+	1.05054i
$896$	26.4118	+	7.76727i	0.882356	+	0.259486i
$897$		0			0
$898$	−45.3537	−	21.8412i	−1.51347	−	0.728851i
$899$	4.71869	+	20.6739i	0.157377	+	0.689514i
$900$		0			0
$901$	53.4551			1.78085
$902$	3.11814	+	13.6615i	0.103823	+	0.454878i
$903$		0			0
$904$	−1.08928	+	4.77244i	−0.0362289	+	0.158729i
$905$	1.15650	−	5.06695i	0.0384433	−	0.168431i
$906$		0			0
$907$	6.56490	−	8.23213i	0.217984	−	0.273343i	−0.660801	−	0.750561i	$-0.729783\pi$
$907$	6.56490	−	8.23213i	0.217984	−	0.273343i	0.878785	+	0.477218i	$0.158355\pi$
$908$	−16.5964	+	72.7138i	−0.550772	+	2.41309i
$909$		0			0
$910$	3.67575	−	59.5758i	0.121850	−	1.97492i
$911$	1.37547	+	6.02633i	0.0455714	+	0.199661i	0.992589	−	0.121521i	$-0.0387770\pi$
$911$	1.37547	+	6.02633i	0.0455714	+	0.199661i	−0.947018	+	0.321182i	$0.895920\pi$
$912$		0			0
$913$	13.6732			0.452516
$914$	−13.3532	−	58.5043i	−0.441686	−	1.93515i
$915$		0			0
$916$	27.4332	−	34.4001i	0.906418	−	1.13661i
$917$	−12.3189	−	11.1318i	−0.406805	−	0.367603i
$918$		0			0
$919$	−4.99743	−	21.8952i	−0.164850	−	0.722256i	−0.988003	−	0.154436i	$-0.950644\pi$
$919$	−4.99743	−	21.8952i	−0.164850	−	0.722256i	0.823153	−	0.567820i	$-0.192213\pi$
$920$	4.08641	+	5.12420i	0.134725	+	0.168940i
$921$		0			0
$922$	2.78336	−	3.49022i	0.0916651	−	0.114944i
$923$	−18.1440	+	8.73771i	−0.597219	+	0.287605i
$924$		0			0
$925$	−45.6518	−	21.9848i	−1.50102	−	0.722854i
$926$	70.1536	−	33.7842i	2.30539	−	1.11022i
$927$		0			0
$928$	−14.8072	+	7.13078i	−0.486071	+	0.234079i
$929$	−0.258223	−	0.323801i	−0.00847201	−	0.0106236i	0.777577	−	0.628787i	$-0.216448\pi$
$929$	−0.258223	−	0.323801i	−0.00847201	−	0.0106236i	−0.786049	+	0.618164i	$0.787877\pi$
$930$		0			0
$931$	31.3481	+	20.1835i	1.02739	+	0.661486i
$932$	47.2466			1.54761
$933$		0			0
$934$	4.70922	−	2.26784i	0.154090	−	0.0742060i
$935$	−3.64916	+	15.9880i	−0.119340	+	0.522864i
$936$		0			0
$937$	1.59554	+	0.768374i	0.0521242	+	0.0251017i	0.459764	−	0.888041i	$-0.347934\pi$
$937$	1.59554	+	0.768374i	0.0521242	+	0.0251017i	−0.407640	+	0.913143i	$0.633648\pi$
$938$	19.2460	+	47.1993i	0.628405	+	1.54111i
$939$		0			0
$940$	−22.6902	+	28.4526i	−0.740073	+	0.928023i
$941$	−3.83275	−	1.84575i	−0.124944	−	0.0601699i	0.370367	−	0.928885i	$-0.379232\pi$
$941$	−3.83275	−	1.84575i	−0.124944	−	0.0601699i	−0.495311	+	0.868715i	$0.664946\pi$
$942$		0			0
$943$	−2.26486	−	9.92300i	−0.0737540	−	0.323137i
$944$	−9.92936	−	12.4510i	−0.323173	−	0.405246i
$945$		0			0
$946$	−5.34770	+	6.70580i	−0.173869	+	0.218024i
$947$	24.5484	+	11.8219i	0.797716	+	0.384160i	0.787909	−	0.615792i	$-0.211164\pi$
$947$	24.5484	+	11.8219i	0.797716	+	0.384160i	0.00980751	+	0.999952i	$0.496878\pi$
$948$		0			0
$949$	44.0342			1.42941
$950$	−69.1291			−2.24284
$951$		0			0
$952$	7.33736	+	17.9943i	0.237805	+	0.583199i
$953$	−5.39771	+	23.6489i	−0.174849	+	0.766064i	0.809108	+	0.587660i	$0.199951\pi$
$953$	−5.39771	+	23.6489i	−0.174849	+	0.766064i	−0.983957	+	0.178404i	$0.942907\pi$
$954$		0			0
$955$	−31.3101	+	39.2616i	−1.01317	+	1.27047i
$956$	−29.3208	+	36.7672i	−0.948304	+	1.18914i
$957$		0			0
$958$	−8.01872	+	35.1323i	−0.259073	+	1.13507i
$959$	29.6126	+	26.7590i	0.956242	+	0.864092i
$960$		0			0
$961$	68.7652			2.21823
$962$	−57.1077			−1.84123
$963$		0			0
$964$	18.5843	+	8.94974i	0.598561	+	0.288252i
$965$	−13.9131	+	17.4465i	−0.447879	+	0.561622i
$966$		0			0
$967$	−24.8321	−	31.1384i	−0.798546	−	1.00134i	−0.999762	−	0.0217980i	$-0.993061\pi$
$967$	−24.8321	−	31.1384i	−0.798546	−	1.00134i	0.201217	−	0.979547i	$-0.435511\pi$
$968$	−3.09475	−	13.5590i	−0.0994691	−	0.435803i
$969$		0			0
$970$	−8.29051	−	3.99250i	−0.266192	−	0.128191i
$971$	21.7914	−	27.3256i	0.699320	−	0.876920i	−0.297652	−	0.954674i	$-0.596204\pi$
$971$	21.7914	−	27.3256i	0.699320	−	0.876920i	0.996973	+	0.0777546i	$0.0247751\pi$
$972$		0			0
$973$	−28.6922	+	4.71218i	−0.919830	+	0.151066i
$974$	−7.24640	−	3.48968i	−0.232190	−	0.111817i
$975$		0			0
$976$	2.76409	−	12.1103i	0.0884764	−	0.387641i
$977$	−10.1991	+	4.91164i	−0.326299	+	0.157137i	−0.589860	−	0.807505i	$-0.700817\pi$
$977$	−10.1991	+	4.91164i	−0.326299	+	0.157137i	0.263561	+	0.964643i	$0.415103\pi$
$978$		0			0
$979$	−1.11773			−0.0357229
$980$	−20.8775	+	57.6158i	−0.666907	+	1.84047i
$981$		0			0
$982$	37.7332	+	47.3160i	1.20412	+	1.50991i
$983$	3.05237	−	1.46994i	0.0973555	−	0.0468839i	−0.384572	−	0.923095i	$-0.625651\pi$
$983$	3.05237	−	1.46994i	0.0973555	−	0.0468839i	0.481928	+	0.876211i	$0.339937\pi$
$984$		0			0
$985$	34.5401	−	16.6336i	1.10054	−	0.529991i
$986$	−22.0809	−	10.6336i	−0.703199	−	0.338643i
$987$		0			0
$988$	−39.9152	+	19.2221i	−1.26987	+	0.611537i
$989$	3.88429	−	4.87075i	0.123513	−	0.154881i
$990$		0			0
$991$	11.5252	+	14.4521i	0.366109	+	0.459086i	0.930430	−	0.366469i	$-0.119433\pi$
$991$	11.5252	+	14.4521i	0.366109	+	0.459086i	−0.564321	+	0.825555i	$0.690862\pi$
$992$	17.2053	+	75.3815i	0.546270	+	2.39337i
$993$		0			0
$994$	35.8806	−	5.89275i	1.13806	−	0.186907i
$995$	10.4875	−	13.1509i	0.332477	−	0.416913i
$996$		0			0
$997$	12.6269	+	55.3221i	0.399898	+	1.75207i	0.627791	+	0.778382i	$0.283959\pi$
$997$	12.6269	+	55.3221i	0.399898	+	1.75207i	−0.227893	+	0.973686i	$0.573184\pi$
$998$	72.6975			2.30120
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.u.d.253.2		36
3.2	odd	2		147.2.i.b.106.5	yes	36
49.43	even	7	inner	441.2.u.d.190.2		36
147.71	odd	14		7203.2.a.h.1.15		18
147.92	odd	14		147.2.i.b.43.5	✓	36
147.125	even	14		7203.2.a.g.1.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.i.b.43.5	✓	36	147.92	odd	14
147.2.i.b.106.5	yes	36	3.2	odd	2
441.2.u.d.190.2		36	49.43	even	7	inner
441.2.u.d.253.2		36	1.1	even	1	trivial
7203.2.a.g.1.15		18	147.125	even	14
7203.2.a.h.1.15		18	147.71	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)

\(f(q)\)	\(=\)	\(q+(-1.34250 - 1.68344i) q^{2} +(-0.586625 + 2.57017i) q^{4} +(2.99194 - 1.44084i) q^{5} +(2.53827 + 0.746462i) q^{7} +(1.23434 - 0.594424i) q^{8} +O(q^{10})\)	\(q+(-1.34250 - 1.68344i) q^{2} +(-0.586625 + 2.57017i) q^{4} +(2.99194 - 1.44084i) q^{5} +(2.53827 + 0.746462i) q^{7} +(1.23434 - 0.594424i) q^{8} +(-6.44225 - 3.10242i) q^{10} +(0.574309 + 0.720161i) q^{11} +(1.96720 + 2.46678i) q^{13} +(-2.15099 - 5.27514i) q^{14} +(2.09262 + 1.00775i) q^{16} +(1.19298 + 5.22678i) q^{17} +5.32624 q^{19} +(1.94807 + 8.53504i) q^{20} +(0.441338 - 1.93363i) q^{22} +(-0.320566 + 1.40449i) q^{23} +(3.75825 - 4.71269i) q^{25} +(1.51173 - 6.62331i) q^{26} +(-3.40754 + 6.08588i) q^{28} +(-0.472424 - 2.06982i) q^{29} -9.98825 q^{31} +(-1.72256 - 7.54702i) q^{32} +(7.19740 - 9.02525i) q^{34} +(8.66989 - 1.42387i) q^{35} +(-1.87052 - 8.19530i) q^{37} +(-7.15046 - 8.96640i) q^{38} +(2.83659 - 3.55697i) q^{40} +(-6.36553 + 3.06548i) q^{41} +(-3.89625 - 1.87633i) q^{43} +(-2.18784 + 1.05361i) q^{44} +(2.79473 - 1.34587i) q^{46} +(2.59183 + 3.25005i) q^{47} +(5.88559 + 3.78944i) q^{49} -12.9790 q^{50} +(-7.49406 + 3.60895i) q^{52} +(2.21870 - 9.72074i) q^{53} +(2.75594 + 1.32719i) q^{55} +(3.57679 - 0.587423i) q^{56} +(-2.85019 + 3.57403i) q^{58} +(-6.17762 - 2.97499i) q^{59} +(-1.19007 - 5.21403i) q^{61} +(13.4092 + 16.8146i) q^{62} +(-7.49614 + 9.39987i) q^{64} +(9.43999 + 4.54606i) q^{65} -8.94751 q^{67} -14.1335 q^{68} +(-14.0363 - 12.6837i) q^{70} +(-1.42029 + 6.22270i) q^{71} +(8.70165 - 10.9115i) q^{73} +(-11.2851 + 14.1511i) q^{74} +(-3.12450 + 13.6893i) q^{76} +(0.920177 + 2.25666i) q^{77} -13.1382 q^{79} +7.71301 q^{80} +(13.7062 + 6.60058i) q^{82} +(9.25512 - 11.6055i) q^{83} +(11.1003 + 13.9193i) q^{85} +(2.07201 + 9.07807i) q^{86} +(1.13697 + 0.547537i) q^{88} +(-0.756573 + 0.948713i) q^{89} +(3.15190 + 7.72979i) q^{91} +(-3.42173 - 1.64782i) q^{92} +(1.99173 - 8.72636i) q^{94} +(15.9358 - 7.67428i) q^{95} +1.28690 q^{97} +(-1.52210 - 14.9953i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8	\( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) 36 * q + q^2 - 9 * q^4 + 4 * q^5 - 6 * q^7 + 15 * q^8 + 10 * q^10 + 7 * q^11 - 12 * q^13 + q^14 - 3 * q^16 + 3 * q^17 + 6 * q^19 - 25 * q^20 - 21 * q^22 + 20 * q^23 - 2 * q^25 - 6 * q^26 - q^28 + 22 * q^29 + 16 * q^31 - 26 * q^32 + 6 * q^34 + 9 * q^35 + 32 * q^37 - 17 * q^38 - 21 * q^40 + 5 * q^41 - 34 * q^43 - 2 * q^44 - 32 * q^46 + 7 * q^47 + 20 * q^49 - 236 * q^50 + 20 * q^52 + 32 * q^53 - 17 * q^55 + 39 * q^56 - 53 * q^58 + q^59 + 14 * q^61 + 60 * q^62 - 21 * q^64 + 39 * q^65 - 22 * q^67 + 110 * q^68 - 40 * q^70 - 36 * q^71 - 11 * q^73 + 46 * q^74 - 101 * q^76 + 17 * q^77 - 14 * q^79 + 112 * q^80 + 2 * q^82 - 12 * q^83 - 44 * q^85 - 184 * q^86 + 204 * q^88 - 12 * q^89 - 16 * q^91 + 105 * q^92 - 5 * q^94 - 18 * q^95 + 172 * q^97 - q^98

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