LMFDB - Embedded newform 675.2.bd.a.8.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(8,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("675.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.bd (of order $60$, degree $16$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 225)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	675.8
Dual form			675.2.bd.a.422.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42019 - 2.18691i) q^{2} +(-1.95214 + 4.38458i) q^{4} +(-0.865670 - 2.06170i) q^{5} +(0.0498024 + 0.185865i) q^{7} +(7.21013 - 1.14197i) q^{8} +O(q^{10})$	\(q+(-1.42019 - 2.18691i) q^{2} +(-1.95214 + 4.38458i) q^{4} +(-0.865670 - 2.06170i) q^{5} +(0.0498024 + 0.185865i) q^{7} +(7.21013 - 1.14197i) q^{8} +(-3.27933 + 4.82116i) q^{10} +(-0.215500 + 1.01385i) q^{11} +(4.92281 + 3.19691i) q^{13} +(0.335741 - 0.372878i) q^{14} +(-6.31416 - 7.01258i) q^{16} +(0.716344 + 4.52282i) q^{17} +(0.702199 - 0.966494i) q^{19} +(10.7296 + 0.229135i) q^{20} +(2.52324 - 0.968581i) q^{22} +(0.279886 + 5.34054i) q^{23} +(-3.50123 + 3.56951i) q^{25} -15.3060i q^{26} +(-0.912162 - 0.144472i) q^{28} +(0.582814 + 5.54510i) q^{29} +(0.860356 - 8.18574i) q^{31} +(-2.58978 + 9.66520i) q^{32} +(8.87363 - 7.98986i) q^{34} +(0.340086 - 0.263576i) q^{35} +(1.13229 + 2.22225i) q^{37} +(-3.11089 - 0.163035i) q^{38} +(-8.59599 - 13.8766i) q^{40} +(-1.28346 - 6.03819i) q^{41} +(8.00751 - 2.14560i) q^{43} +(-4.02460 - 2.92405i) q^{44} +(11.2818 - 8.19669i) q^{46} +(5.76953 - 7.12478i) q^{47} +(6.03011 - 3.48149i) q^{49} +(12.7786 + 2.58748i) q^{50} +(-23.6271 + 15.3436i) q^{52} +(0.643842 - 4.06506i) q^{53} +(2.27680 - 0.433360i) q^{55} +(0.571334 + 1.28324i) q^{56} +(11.2989 - 9.14969i) q^{58} +(2.09415 - 0.445125i) q^{59} +(-11.1134 - 2.36223i) q^{61} +(-19.1233 + 9.74383i) q^{62} +(6.86587 - 2.23086i) q^{64} +(2.32955 - 12.9168i) q^{65} +(4.51315 + 5.57327i) q^{67} +(-21.2291 - 5.68831i) q^{68} +(-1.05940 - 0.369409i) q^{70} +(8.94457 + 12.3111i) q^{71} +(-4.07989 + 8.00724i) q^{73} +(3.25178 - 5.63224i) q^{74} +(2.86688 + 4.96558i) q^{76} +(-0.199171 + 0.0104381i) q^{77} +(-4.08814 + 0.429681i) q^{79} +(-8.99188 + 19.0885i) q^{80} +(-11.3822 + 11.3822i) q^{82} +(0.0425784 - 0.110921i) q^{83} +(8.70458 - 5.39215i) q^{85} +(-16.0645 - 14.4645i) q^{86} +(-0.395996 + 7.55605i) q^{88} +(0.144332 + 0.444208i) q^{89} +(-0.349026 + 1.07419i) q^{91} +(-23.9624 - 9.19830i) q^{92} +(-23.7751 - 2.49886i) q^{94} +(-2.60050 - 0.611061i) q^{95} +(-5.55734 - 4.50025i) q^{97} +(-16.1776 - 8.24291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q + 24 q^{2} - 10 q^{4} + 24 q^{5} - 8 q^{7}+O(q^{10}) $ 448 * q + 24 * q^2 - 10 * q^4 + 24 * q^5 - 8 * q^7	$ 448 q + 24 q^{2} - 10 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 18 q^{11} - 8 q^{13} + 30 q^{14} - 50 q^{16} - 40 q^{19} + 48 q^{20} + 48 q^{23} + 16 q^{25} - 24 q^{28} + 30 q^{29} - 6 q^{31} + 60 q^{32} - 10 q^{34} - 44 q^{37} - 16 q^{40} + 18 q^{41} - 8 q^{43} - 24 q^{46} + 18 q^{47} - 24 q^{50} + 24 q^{52} - 24 q^{55} + 18 q^{56} - 4 q^{58} - 6 q^{61} - 40 q^{64} + 96 q^{65} - 14 q^{67} - 288 q^{68} - 28 q^{70} - 32 q^{73} - 32 q^{76} - 216 q^{77} - 10 q^{79} - 72 q^{82} - 36 q^{83} - 32 q^{85} + 18 q^{86} - 28 q^{88} - 24 q^{91} - 30 q^{92} - 130 q^{94} - 6 q^{95} - 38 q^{97}+O(q^{100}) $ 448 * q + 24 * q^2 - 10 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 18 * q^11 - 8 * q^13 + 30 * q^14 - 50 * q^16 - 40 * q^19 + 48 * q^20 + 48 * q^23 + 16 * q^25 - 24 * q^28 + 30 * q^29 - 6 * q^31 + 60 * q^32 - 10 * q^34 - 44 * q^37 - 16 * q^40 + 18 * q^41 - 8 * q^43 - 24 * q^46 + 18 * q^47 - 24 * q^50 + 24 * q^52 - 24 * q^55 + 18 * q^56 - 4 * q^58 - 6 * q^61 - 40 * q^64 + 96 * q^65 - 14 * q^67 - 288 * q^68 - 28 * q^70 - 32 * q^73 - 32 * q^76 - 216 * q^77 - 10 * q^79 - 72 * q^82 - 36 * q^83 - 32 * q^85 + 18 * q^86 - 28 * q^88 - 24 * q^91 - 30 * q^92 - 130 * q^94 - 6 * q^95 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

Coefficient data

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

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

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

$2$	−1.42019	−	2.18691i	−1.00423	−	1.54638i	−0.826995	−	0.562209i	$-0.809952\pi$
$2$	−1.42019	−	2.18691i	−1.00423	−	1.54638i	−0.177234	−	0.984169i	$-0.556715\pi$
$3$		0			0
$3$		0			0
$4$	−1.95214	+	4.38458i	−0.976071	+	2.19229i
$5$	−0.865670	−	2.06170i	−0.387139	−	0.922021i
$5$	−0.865670	−	2.06170i	−0.387139	−	0.922021i
$6$		0			0
$7$	0.0498024	+	0.185865i	0.0188235	+	0.0702504i	0.974699	−	0.223523i	$-0.0717557\pi$
$7$	0.0498024	+	0.185865i	0.0188235	+	0.0702504i	−0.955875	+	0.293773i	$0.905089\pi$
$8$	7.21013	−	1.14197i	2.54916	−	0.403748i
$9$		0			0
$10$	−3.27933	+	4.82116i	−1.03702	+	1.52458i
$11$	−0.215500	+	1.01385i	−0.0649756	+	0.305686i	−0.998620	−	0.0525147i	$-0.983276\pi$
$11$	−0.215500	+	1.01385i	−0.0649756	+	0.305686i	0.933645	+	0.358201i	$0.116610\pi$
$12$		0			0
$13$	4.92281	+	3.19691i	1.36534	+	0.886663i	0.999039	−	0.0438328i	$-0.0139569\pi$
$13$	4.92281	+	3.19691i	1.36534	+	0.886663i	0.366302	+	0.930496i	$0.380624\pi$
$14$	0.335741	−	0.372878i	0.0897305	−	0.0996559i
$15$		0			0
$16$	−6.31416	−	7.01258i	−1.57854	−	1.75315i
$17$	0.716344	+	4.52282i	0.173739	+	1.09694i	0.908275	+	0.418374i	$0.137400\pi$
$17$	0.716344	+	4.52282i	0.173739	+	1.09694i	−0.734536	+	0.678570i	$0.762600\pi$
$18$		0			0
$19$	0.702199	−	0.966494i	0.161096	−	0.221729i	−0.720837	−	0.693105i	$-0.756242\pi$
$19$	0.702199	−	0.966494i	0.161096	−	0.221729i	0.881933	+	0.471376i	$0.156242\pi$
$20$	10.7296	+	0.229135i	2.39921	+	0.0512361i
$21$		0			0
$22$	2.52324	−	0.968581i	0.537956	−	0.206502i
$23$	0.279886	+	5.34054i	0.0583602	+	1.11358i	0.858183	+	0.513343i	$0.171593\pi$
$23$	0.279886	+	5.34054i	0.0583602	+	1.11358i	−0.799823	+	0.600236i	$0.795073\pi$
$24$		0			0
$25$	−3.50123	+	3.56951i	−0.700246	+	0.713901i
$26$		−	15.3060i		−	3.00175i
$27$		0			0
$28$	−0.912162	−	0.144472i	−0.172382	−	0.0273027i
$29$	0.582814	+	5.54510i	0.108226	+	1.02970i	0.904997	+	0.425418i	$0.139873\pi$
$29$	0.582814	+	5.54510i	0.108226	+	1.02970i	−0.796771	+	0.604281i	$0.793460\pi$
$30$		0			0
$31$	0.860356	−	8.18574i	0.154525	−	1.47020i	−0.592588	−	0.805505i	$-0.701894\pi$
$31$	0.860356	−	8.18574i	0.154525	−	1.47020i	0.747113	−	0.664697i	$-0.231439\pi$
$32$	−2.58978	+	9.66520i	−0.457813	+	1.70858i
$33$		0			0
$34$	8.87363	−	7.98986i	1.52182	−	1.37025i
$35$	0.340086	−	0.263576i	0.0574851	−	0.0445524i
$36$		0			0
$37$	1.13229	+	2.22225i	0.186148	+	0.365335i	0.965155	−	0.261680i	$-0.0842765\pi$
$37$	1.13229	+	2.22225i	0.186148	+	0.365335i	−0.779007	+	0.627015i	$0.784276\pi$
$38$	−3.11089	−	0.163035i	−0.504654	−	0.0264478i
$39$		0			0
$40$	−8.59599	−	13.8766i	−1.35915	−	2.19408i
$41$	−1.28346	−	6.03819i	−0.200442	−	0.943006i	−0.957226	−	0.289341i	$-0.906564\pi$
$41$	−1.28346	−	6.03819i	−0.200442	−	0.943006i	0.756784	−	0.653665i	$-0.226770\pi$
$42$		0			0
$43$	8.00751	−	2.14560i	1.22113	−	0.327202i	0.410012	−	0.912080i	$-0.365524\pi$
$43$	8.00751	−	2.14560i	1.22113	−	0.327202i	0.811121	+	0.584878i	$0.198858\pi$
$44$	−4.02460	−	2.92405i	−0.606732	−	0.440816i
$45$		0			0
$46$	11.2818	−	8.19669i	1.66341	−	1.20854i
$47$	5.76953	−	7.12478i	0.841573	−	1.03926i	−0.157091	−	0.987584i	$-0.550212\pi$
$47$	5.76953	−	7.12478i	0.841573	−	1.03926i	0.998664	−	0.0516717i	$-0.0164549\pi$
$48$		0			0
$49$	6.03011	−	3.48149i	0.861445	−	0.497355i
$50$	12.7786	+	2.58748i	1.80717	+	0.365925i
$51$		0			0
$52$	−23.6271	+	15.3436i	−3.27649	+	2.12778i
$53$	0.643842	−	4.06506i	0.0884384	−	0.558378i	−0.903189	−	0.429244i	$-0.858780\pi$
$53$	0.643842	−	4.06506i	0.0884384	−	0.558378i	0.991627	−	0.129135i	$-0.0412199\pi$
$54$		0			0
$55$	2.27680	−	0.433360i	0.307004	−	0.0584342i
$56$	0.571334	+	1.28324i	0.0763478	+	0.171480i
$57$		0			0
$58$	11.2989	−	9.14969i	1.48362	−	1.20141i
$59$	2.09415	−	0.445125i	0.272635	−	0.0579504i	−0.0695652	−	0.997577i	$-0.522161\pi$
$59$	2.09415	−	0.445125i	0.272635	−	0.0579504i	0.342200	+	0.939627i	$0.388828\pi$
$60$		0			0
$61$	−11.1134	−	2.36223i	−1.42292	−	0.302452i	−0.568781	−	0.822489i	$-0.692585\pi$
$61$	−11.1134	−	2.36223i	−1.42292	−	0.302452i	−0.854144	+	0.520037i	$0.825918\pi$
$62$	−19.1233	+	9.74383i	−2.42867	+	1.23747i
$63$		0			0
$64$	6.86587	−	2.23086i	0.858234	−	0.278857i
$65$	2.32955	−	12.9168i	0.288945	−	1.60214i
$66$		0			0
$67$	4.51315	+	5.57327i	0.551368	+	0.680883i	0.974294	−	0.225281i	$-0.0723301\pi$
$67$	4.51315	+	5.57327i	0.551368	+	0.680883i	−0.422925	+	0.906165i	$0.638997\pi$
$68$	−21.2291	−	5.68831i	−2.57440	−	0.689809i
$69$		0			0
$70$	−1.05940	−	0.369409i	−0.126623	−	0.0441528i
$71$	8.94457	+	12.3111i	1.06153	+	1.46106i	0.878370	+	0.477981i	$0.158631\pi$
$71$	8.94457	+	12.3111i	1.06153	+	1.46106i	0.183155	+	0.983084i	$0.441369\pi$
$72$		0			0
$73$	−4.07989	+	8.00724i	−0.477515	+	0.937176i	0.519080	+	0.854726i	$0.326275\pi$
$73$	−4.07989	+	8.00724i	−0.477515	+	0.937176i	−0.996595	+	0.0824507i	$0.973725\pi$
$74$	3.25178	−	5.63224i	0.378011	−	0.654735i
$75$		0			0
$76$	2.86688	+	4.96558i	0.328854	+	0.569591i
$77$	−0.199171	+	0.0104381i	−0.0226976	+	0.00118953i
$78$		0			0
$79$	−4.08814	+	0.429681i	−0.459952	+	0.0483429i	−0.331671	−	0.943395i	$-0.607612\pi$
$79$	−4.08814	+	0.429681i	−0.459952	+	0.0483429i	−0.128280	+	0.991738i	$0.540946\pi$
$80$	−8.99188	+	19.0885i	−1.00532	+	2.13416i
$81$		0			0
$82$	−11.3822	+	11.3822i	−1.25695	+	1.25695i
$83$	0.0425784	−	0.110921i	0.00467359	−	0.0121751i	−0.931224	−	0.364448i	$-0.881258\pi$
$83$	0.0425784	−	0.110921i	0.00467359	−	0.0121751i	0.935897	+	0.352273i	$0.114591\pi$
$84$		0			0
$85$	8.70458	−	5.39215i	0.944144	−	0.584861i
$86$	−16.0645	−	14.4645i	−1.73228	−	1.55975i
$87$		0			0
$88$	−0.395996	+	7.55605i	−0.0422133	+	0.805478i
$89$	0.144332	+	0.444208i	0.0152992	+	0.0470859i	0.958415	−	0.285379i	$-0.0921196\pi$
$89$	0.144332	+	0.444208i	0.0152992	+	0.0470859i	−0.943115	+	0.332465i	$0.892120\pi$
$90$		0			0
$91$	−0.349026	+	1.07419i	−0.0365879	+	0.112606i
$92$	−23.9624	−	9.19830i	−2.49825	−	0.958989i
$93$		0			0
$94$	−23.7751	−	2.49886i	−2.45221	−	0.257738i
$95$	−2.60050	−	0.611061i	−0.266805	−	0.0626935i
$96$		0			0
$97$	−5.55734	−	4.50025i	−0.564262	−	0.456931i	0.304254	−	0.952591i	$-0.401593\pi$
$97$	−5.55734	−	4.50025i	−0.564262	−	0.456931i	−0.868517	+	0.495660i	$0.834926\pi$
$98$	−16.1776	−	8.24291i	−1.63419	−	0.832660i
$99$		0			0
$100$	−8.81589	−	22.3196i	−0.881589	−	2.23196i
$101$	4.22381	+	2.43862i	0.420285	+	0.242652i	0.695199	−	0.718817i	$-0.255316\pi$
$101$	4.22381	+	2.43862i	0.420285	+	0.242652i	−0.274914	+	0.961469i	$0.588650\pi$
$102$		0			0
$103$	3.53127	+	9.19928i	0.347947	+	0.906432i	0.990164	+	0.139910i	$0.0446812\pi$
$103$	3.53127	+	9.19928i	0.347947	+	0.906432i	−0.642218	+	0.766522i	$0.721985\pi$
$104$	39.1448	+	17.4284i	3.83847	+	1.70900i
$105$		0			0
$106$	−9.80429	+	4.36515i	−0.952276	+	0.423981i
$107$	6.46784	+	6.46784i	0.625270	+	0.625270i	0.946874	−	0.321605i	$-0.104222\pi$
$107$	6.46784	+	6.46784i	0.625270	+	0.625270i	−0.321605	+	0.946874i	$0.604222\pi$
$108$		0			0
$109$	−8.25780	−	2.68312i	−0.790953	−	0.256996i	−0.114443	−	0.993430i	$-0.536508\pi$
$109$	−8.25780	−	2.68312i	−0.790953	−	0.256996i	−0.676510	+	0.736433i	$0.736508\pi$
$110$	−4.18122	−	4.36370i	−0.398663	−	0.416062i
$111$		0			0
$112$	0.988934	−	1.52283i	0.0934455	−	0.143893i
$113$	1.15227	−	1.77433i	0.108396	−	0.166915i	−0.780310	−	0.625393i	$-0.784939\pi$
$113$	1.15227	−	1.77433i	0.108396	−	0.166915i	0.888706	+	0.458478i	$0.151605\pi$
$114$		0			0
$115$	10.7683	−	5.20018i	1.00415	−	0.484920i
$116$	−25.4507	−	8.26943i	−2.36304	−	0.767797i
$117$		0			0
$118$	−3.94755	−	3.94755i	−0.363401	−	0.363401i
$119$	−0.804958	+	0.358390i	−0.0737904	+	0.0328536i
$120$		0			0
$121$	9.06756	+	4.03714i	0.824323	+	0.367012i
$122$	10.6172	+	27.6588i	0.961238	+	2.50411i
$123$		0			0
$124$	34.2115	+	19.7520i	3.07228	+	1.77378i
$125$	10.3902	+	4.12848i	0.929325	+	0.369263i
$126$		0			0
$127$	9.22643	+	4.70110i	0.818713	+	0.417155i	0.812597	−	0.582826i	$-0.198053\pi$
$127$	9.22643	+	4.70110i	0.818713	+	0.417155i	0.00611627	+	0.999981i	$0.498053\pi$
$128$	0.922920	+	0.747366i	0.0815754	+	0.0660585i
$129$		0			0
$130$	−31.5563	+	13.2499i	−2.76767	+	1.16209i
$131$	3.79330	+	0.398692i	0.331422	+	0.0348339i	0.268778	−	0.963202i	$-0.413380\pi$
$131$	3.79330	+	0.398692i	0.331422	+	0.0348339i	0.0626438	+	0.998036i	$0.480047\pi$
$132$		0			0
$133$	0.214609	+	0.0823806i	0.0186089	+	0.00714331i
$134$	5.77869	−	17.7850i	0.499202	−	1.53639i
$135$		0			0
$136$	10.3299	+	31.7920i	0.885778	+	2.72614i
$137$	0.287732	−	5.49025i	0.0245826	−	0.469064i	−0.958407	−	0.285404i	$-0.907872\pi$
$137$	0.287732	−	5.49025i	0.0245826	−	0.469064i	0.982990	−	0.183660i	$-0.0587945\pi$
$138$		0			0
$139$	0.902142	+	0.812292i	0.0765187	+	0.0688977i	0.706503	−	0.707710i	$-0.250272\pi$
$139$	0.902142	+	0.812292i	0.0765187	+	0.0688977i	−0.629984	+	0.776608i	$0.716939\pi$
$140$	0.491772	+	2.00567i	0.0415624	+	0.169510i
$141$		0			0
$142$	14.2203	−	37.0452i	1.19334	−	3.10876i
$143$	−4.30204	+	4.30204i	−0.359754	+	0.359754i
$144$		0			0
$145$	10.9278	−	6.00182i	0.907507	−	0.498424i
$146$	23.3053	−	2.44949i	1.92876	−	0.202721i
$147$		0			0
$148$	−11.9540	+	0.626483i	−0.982614	+	0.0514966i
$149$	−1.46365	−	2.53511i	−0.119907	−	0.207684i	0.799824	−	0.600235i	$-0.204926\pi$
$149$	−1.46365	−	2.53511i	−0.119907	−	0.207684i	−0.919730	+	0.392550i	$0.871593\pi$
$150$		0			0
$151$	6.39515	−	11.0767i	0.520430	−	0.901411i	−0.479288	−	0.877658i	$-0.659105\pi$
$151$	6.39515	−	11.0767i	0.520430	−	0.901411i	0.999718	−	0.0237532i	$-0.00756158\pi$
$152$	3.95924	−	7.77044i	0.321136	−	0.630266i
$153$		0			0
$154$	0.305689	+	0.420745i	0.0246331	+	0.0339046i
$155$	−17.6213	+	5.31235i	−1.41538	+	0.426698i
$156$		0			0
$157$	5.70463	+	1.52855i	0.455279	+	0.121992i	0.479168	−	0.877723i	$-0.340938\pi$
$157$	5.70463	+	1.52855i	0.455279	+	0.121992i	−0.0238894	+	0.999715i	$0.507605\pi$
$158$	6.74563	+	8.33016i	0.536653	+	0.662712i
$159$		0			0
$160$	22.1687	−	3.02751i	1.75259	−	0.239346i
$161$	−0.978681	+	0.317993i	−0.0771309	+	0.0250613i
$162$		0			0
$163$	6.03072	−	3.07281i	0.472363	−	0.240681i	−0.201569	−	0.979474i	$-0.564604\pi$
$163$	6.03072	−	3.07281i	0.472363	−	0.240681i	0.673932	+	0.738793i	$0.264604\pi$
$164$	28.9804	+	6.15998i	2.26299	+	0.481013i
$165$		0			0
$166$	−0.303043	+	0.0644137i	−0.0235207	+	0.00499947i
$167$	7.35549	−	5.95636i	0.569185	−	0.460917i	−0.301013	−	0.953620i	$-0.597325\pi$
$167$	7.35549	−	5.95636i	0.569185	−	0.460917i	0.870197	+	0.492703i	$0.163991\pi$
$168$		0			0
$169$	8.72624	+	19.5994i	0.671249	+	1.50765i
$170$	−24.1543	−	11.3782i	−1.85255	−	0.872669i
$171$		0			0
$172$	−6.22420	+	39.2981i	−0.474591	+	2.99645i
$173$	−19.0443	+	12.3675i	−1.44791	+	0.940283i	−0.449003	+	0.893530i	$0.648221\pi$
$173$	−19.0443	+	12.3675i	−1.44791	+	0.940283i	−0.998906	+	0.0467532i	$0.985113\pi$
$174$		0			0
$175$	−0.837817	−	0.472987i	−0.0633330	−	0.0357545i
$176$	8.47038	−	4.89037i	0.638479	−	0.368626i
$177$		0			0
$178$	0.766463	−	0.946503i	0.0574488	−	0.0709434i
$179$	−0.852570	+	0.619428i	−0.0637241	+	0.0462982i	−0.619191	−	0.785240i	$-0.712539\pi$
$179$	−0.852570	+	0.619428i	−0.0637241	+	0.0462982i	0.555467	+	0.831538i	$0.312539\pi$
$180$		0			0
$181$	−13.1372	−	9.54476i	−0.976484	−	0.709457i	−0.0195635	−	0.999809i	$-0.506228\pi$
$181$	−13.1372	−	9.54476i	−0.976484	−	0.709457i	−0.956920	+	0.290352i	$0.906228\pi$
$182$	2.84485	−	0.762274i	0.210874	−	0.0565035i
$183$		0			0
$184$	8.11675	+	38.1863i	0.598375	+	2.81513i
$185$	3.60142	−	4.25818i	0.264782	−	0.313068i
$186$		0			0
$187$	−4.73981	−	0.248403i	−0.346609	−	0.0181650i
$188$	19.9762	+	39.2055i	1.45692	+	2.85936i
$189$		0			0
$190$	2.35688	+	6.55487i	0.170986	+	0.475540i
$191$	6.37956	−	5.74418i	0.461608	−	0.415634i	−0.405237	−	0.914212i	$-0.632811\pi$
$191$	6.37956	−	5.74418i	0.461608	−	0.415634i	0.866845	+	0.498578i	$0.166144\pi$
$192$		0			0
$193$	0.125892	−	0.469835i	0.00906189	−	0.0338194i	−0.961247	−	0.275689i	$-0.911094\pi$
$193$	0.125892	−	0.469835i	0.00906189	−	0.0338194i	0.970309	+	0.241870i	$0.0777606\pi$
$194$	−1.94912	+	18.5446i	−0.139939	+	1.33143i
$195$		0			0
$196$	3.49323	+	33.2359i	0.249516	+	2.37399i
$197$	10.8596	+	1.72000i	0.773718	+	0.122545i	0.530794	−	0.847501i	$-0.321894\pi$
$197$	10.8596	+	1.72000i	0.773718	+	0.122545i	0.242923	+	0.970045i	$0.421894\pi$
$198$		0			0
$199$			26.7050i			1.89307i	0.322602	+	0.946535i	$0.395442\pi$
$199$			26.7050i			1.89307i	−0.322602	+	0.946535i	$0.604558\pi$
$200$	−21.1680	+	29.7349i	−1.49681	+	2.10257i
$201$		0			0
$202$	−0.665600	−	12.7004i	−0.0468314	−	0.893597i
$203$	−1.00162	+	0.384484i	−0.0702997	+	0.0269855i
$204$		0			0
$205$	−11.3379	+	7.87318i	−0.791873	+	0.549887i
$206$	15.1029	−	20.7873i	1.05227	−	1.44832i
$207$		0			0
$208$	−8.66480	−	54.7074i	−0.600796	−	3.79327i
$209$	0.828553	+	0.920201i	0.0573122	+	0.0636516i
$210$		0			0
$211$	−2.77994	+	3.08743i	−0.191379	+	0.212547i	−0.831196	−	0.555979i	$-0.812343\pi$
$211$	−2.77994	+	3.08743i	−0.191379	+	0.212547i	0.639817	+	0.768527i	$0.279010\pi$
$212$	16.5667	+	10.7585i	1.13781	+	0.738899i
$213$		0			0
$214$	4.95898	−	23.3302i	0.338989	−	1.59482i
$215$	−11.3555	−	14.6517i	−0.774435	−	0.999238i
$216$		0			0
$217$	1.56429	−	0.247760i	0.106191	−	0.0168190i
$218$	5.85994	+	21.8696i	0.396885	+	1.48120i
$219$		0			0
$220$	−2.54453	+	10.8288i	−0.171552	+	0.730077i
$221$	−10.9326	+	24.5550i	−0.735407	+	1.65175i
$222$		0			0
$223$	−1.95069	−	3.00380i	−0.130628	−	0.201149i	0.767304	−	0.641283i	$-0.221598\pi$
$223$	−1.95069	−	3.00380i	−0.130628	−	0.201149i	−0.897932	+	0.440134i	$0.854931\pi$
$224$	−1.92540			−0.128646
$225$		0			0
$226$	−5.51675			−0.366969
$227$	9.26068	+	14.2602i	0.614653	+	0.946483i	0.999722	+	0.0235948i	$0.00751116\pi$
$227$	9.26068	+	14.2602i	0.614653	+	0.946483i	−0.385068	+	0.922888i	$0.625822\pi$
$228$		0			0
$229$	−0.399806	+	0.897980i	−0.0264199	+	0.0593402i	−0.926273	−	0.376852i	$-0.877007\pi$
$229$	−0.399806	+	0.897980i	−0.0264199	+	0.0593402i	0.899854	+	0.436192i	$0.143673\pi$
$230$	−26.6654	−	16.1640i	−1.75827	−	1.06582i
$231$		0			0
$232$	10.5345	+	39.3153i	0.691625	+	2.58118i
$233$	−10.6475	+	1.68639i	−0.697538	+	0.110479i	−0.495126	−	0.868821i	$-0.664878\pi$
$233$	−10.6475	+	1.68639i	−0.697538	+	0.110479i	−0.202412	+	0.979300i	$0.564878\pi$
$234$		0			0
$235$	−19.6837	−	5.72735i	−1.28402	−	0.373611i
$236$	−2.13639	+	10.0509i	−0.139067	+	0.654259i
$237$		0			0
$238$	1.92696	+	1.25139i	0.124907	+	0.0811153i
$239$	−7.84214	+	8.70958i	−0.507266	+	0.563376i	−0.941322	−	0.337510i	$-0.890415\pi$
$239$	−7.84214	+	8.70958i	−0.507266	+	0.563376i	0.434056	+	0.900886i	$0.357082\pi$
$240$		0			0
$241$	−10.5827	−	11.7533i	−0.681693	−	0.757097i	0.298657	−	0.954360i	$-0.403461\pi$
$241$	−10.5827	−	11.7533i	−0.681693	−	0.757097i	−0.980351	+	0.197263i	$0.936795\pi$
$242$	−4.04885	−	25.5634i	−0.260270	−	1.64328i
$243$		0			0
$244$	32.0523	−	44.1162i	2.05194	−	2.82425i
$245$	−12.3979	−	9.41848i	−0.792071	−	0.601724i
$246$		0			0
$247$	6.54659	−	2.51300i	0.416549	−	0.159898i
$248$	−3.14461	−	60.0027i	−0.199683	−	3.81018i
$249$		0			0
$250$	−5.72745	−	28.5856i	−0.362236	−	1.80791i
$251$		−	15.9608i		−	1.00744i	−0.863867	−	0.503720i	$-0.831964\pi$
$251$		−	15.9608i		−	1.00744i	0.863867	−	0.503720i	$-0.168036\pi$
$252$		0			0
$253$	−5.47480	−	0.867123i	−0.344198	−	0.0545155i
$254$	−2.82245	−	26.8538i	−0.177096	−	1.68496i
$255$		0			0
$256$	1.83292	−	17.4391i	0.114557	−	1.08994i
$257$	4.63647	−	17.3035i	0.289215	−	1.07937i	−0.656489	−	0.754336i	$-0.727959\pi$
$257$	4.63647	−	17.3035i	0.289215	−	1.07937i	0.945704	−	0.325030i	$-0.105374\pi$
$258$		0			0
$259$	−0.356647	+	0.321127i	−0.0221610	+	0.0199538i
$260$	52.0873	+	35.4296i	3.23032	+	2.19725i
$261$		0			0
$262$	−4.51532	−	8.86182i	−0.278957	−	0.547485i
$263$	−4.80976	−	0.252069i	−0.296583	−	0.0155432i	−0.0965355	−	0.995330i	$-0.530776\pi$
$263$	−4.80976	−	0.252069i	−0.296583	−	0.0155432i	−0.200047	+	0.979786i	$0.564109\pi$
$264$		0			0
$265$	−8.93829	+	2.19159i	−0.549075	+	0.134628i
$266$	−0.124628	−	0.586326i	−0.00764140	−	0.0359500i
$267$		0			0
$268$	−33.2468	+	8.90844i	−2.03087	+	0.544170i
$269$	−14.6607	−	10.6516i	−0.893877	−	0.649440i	0.0430091	−	0.999075i	$-0.486306\pi$
$269$	−14.6607	−	10.6516i	−0.893877	−	0.649440i	−0.936886	+	0.349635i	$0.886306\pi$
$270$		0			0
$271$	7.21965	−	5.24538i	0.438562	−	0.318634i	−0.346501	−	0.938050i	$-0.612630\pi$
$271$	7.21965	−	5.24538i	0.438562	−	0.318634i	0.785063	+	0.619415i	$0.212630\pi$
$272$	27.1935	−	33.5812i	1.64885	−	2.03616i
$273$		0			0
$274$	−12.4153	+	7.16798i	−0.750036	+	0.433034i
$275$	−2.86442	−	4.31894i	−0.172731	−	0.260442i
$276$		0			0
$277$	16.4837	−	10.7046i	0.990410	−	0.643180i	0.0556466	−	0.998451i	$-0.482278\pi$
$277$	16.4837	−	10.7046i	0.990410	−	0.643180i	0.934763	+	0.355271i	$0.115611\pi$
$278$	0.495191	−	3.12651i	0.0296996	−	0.187516i
$279$		0			0
$280$	2.15107	−	2.28878i	0.128551	−	0.136781i
$281$	8.98776	+	20.1868i	0.536165	+	1.20425i	0.955115	+	0.296237i	$0.0957318\pi$
$281$	8.98776	+	20.1868i	0.536165	+	1.20425i	−0.418950	+	0.908010i	$0.637602\pi$
$282$		0			0
$283$	−3.47249	+	2.81197i	−0.206418	+	0.167154i	−0.726955	−	0.686685i	$-0.759065\pi$
$283$	−3.47249	+	2.81197i	−0.206418	+	0.167154i	0.520537	+	0.853839i	$0.325732\pi$
$284$	−71.4403	+	15.1851i	−4.23920	+	0.901070i
$285$		0			0
$286$	15.5179	+	3.29843i	0.917592	+	0.195040i
$287$	1.05837	−	0.539266i	0.0624736	−	0.0318319i
$288$		0			0
$289$	−3.77475	+	1.22649i	−0.222044	+	0.0721465i
$290$	−28.6451	−	15.3744i	−1.68210	−	0.902816i
$291$		0			0
$292$	−27.1439	−	33.5199i	−1.58847	−	1.96160i
$293$	−7.40079	−	1.98304i	−0.432359	−	0.115850i	0.0360745	−	0.999349i	$-0.488515\pi$
$293$	−7.40079	−	1.98304i	−0.432359	−	0.115850i	−0.468433	+	0.883499i	$0.655181\pi$
$294$		0			0
$295$	−2.73056	−	3.93218i	−0.158979	−	0.228940i
$296$	10.7017	+	14.7296i	0.622024	+	0.856143i
$297$		0			0
$298$	−3.46539	+	6.80121i	−0.200745	+	0.393983i
$299$	−15.6954	+	27.1852i	−0.907688	+	1.57216i
$300$		0			0
$301$	0.797586	+	1.38146i	0.0459721	+	0.0796260i
$302$	−33.3061	+	1.74550i	−1.91655	+	0.100442i
$303$		0			0
$304$	−11.2114	+	1.17837i	−0.643019	+	0.0675840i
$305$	4.75033	+	24.9574i	0.272003	+	1.42906i
$306$		0			0
$307$	12.8886	−	12.8886i	0.735591	−	0.735591i	−0.236130	−	0.971721i	$-0.575879\pi$
$307$	12.8886	−	12.8886i	0.735591	−	0.735591i	0.971721	+	0.236130i	$0.0758792\pi$
$308$	0.343043	−	0.893658i	0.0195467	−	0.0509209i
$309$		0			0
$310$	36.6434	+	30.9917i	2.08120	+	1.76021i
$311$	5.20241	+	4.68427i	0.295002	+	0.265621i	0.803319	−	0.595549i	$-0.203066\pi$
$311$	5.20241	+	4.68427i	0.295002	+	0.265621i	−0.508317	+	0.861170i	$0.669732\pi$
$312$		0			0
$313$	−0.373756	+	7.13169i	−0.0211259	+	0.403107i	0.967515	+	0.252812i	$0.0813556\pi$
$313$	−0.373756	+	7.13169i	−0.0211259	+	0.403107i	−0.988641	+	0.150295i	$0.951978\pi$
$314$	−4.75888	−	14.6463i	−0.268559	−	0.826541i
$315$		0			0
$316$	6.09666	−	18.7636i	0.342964	−	1.05553i
$317$	5.62363	+	2.15871i	0.315854	+	0.121245i	0.511130	−	0.859503i	$-0.329227\pi$
$317$	5.62363	+	2.15871i	0.315854	+	0.121245i	−0.195276	+	0.980748i	$0.562560\pi$
$318$		0			0
$319$	−5.74748	−	0.604084i	−0.321797	−	0.0338222i
$320$	−10.5429	−	12.2242i	−0.589368	−	0.683353i
$321$		0			0
$322$	2.08534	+	1.68867i	0.116211	+	0.0941061i
$323$	4.87429	+	2.48358i	0.271213	+	0.138190i
$324$		0			0
$325$	−28.6473	+	6.37888i	−1.58907	+	0.353836i
$326$	−15.2848	−	8.82466i	−0.846544	−	0.488752i
$327$		0			0
$328$	−16.1493	−	42.0704i	−0.891697	−	2.32295i
$329$	1.61158	+	0.717524i	0.0888495	+	0.0395584i
$330$		0			0
$331$	−5.87433	+	2.61542i	−0.322882	+	0.143757i	−0.561776	−	0.827289i	$-0.689882\pi$
$331$	−5.87433	+	2.61542i	−0.322882	+	0.143757i	0.238894	+	0.971046i	$0.423215\pi$
$332$	0.403221	+	0.403221i	0.0221296	+	0.0221296i
$333$		0			0
$334$	−23.4722	−	7.62659i	−1.28434	−	0.417308i
$335$	7.58353	−	14.1294i	0.414333	−	0.771970i
$336$		0			0
$337$	−10.4445	+	16.0831i	−0.568946	+	0.876100i	−0.999652	−	0.0263927i	$-0.991598\pi$
$337$	−10.4445	+	16.0831i	−0.568946	+	0.876100i	0.430706	+	0.902492i	$0.358265\pi$
$338$	30.4692	−	46.9185i	1.65731	−	2.55203i
$339$		0			0
$340$	6.64975	+	48.6922i	0.360633	+	2.64070i
$341$	8.11367	+	2.63629i	0.439380	+	0.142763i
$342$		0			0
$343$	1.89984	+	1.89984i	0.102582	+	0.102582i
$344$	55.2849	−	24.6144i	2.98076	−	1.32712i
$345$		0			0
$346$	54.0932	+	24.0838i	2.90807	+	1.29475i
$347$	−3.31095	−	8.62531i	−0.177741	−	0.463031i	0.815548	−	0.578689i	$-0.196436\pi$
$347$	−3.31095	−	8.62531i	−0.177741	−	0.463031i	−0.993289	+	0.115658i	$0.963102\pi$
$348$		0			0
$349$	−26.1129	−	15.0763i	−1.39779	−	0.807014i	−0.403628	−	0.914923i	$-0.632251\pi$
$349$	−26.1129	−	15.0763i	−1.39779	−	0.807014i	−0.994161	+	0.107909i	$0.965584\pi$
$350$	0.155484	+	2.50396i	0.00831096	+	0.133842i
$351$		0			0
$352$	−9.24092	−	4.70849i	−0.492543	−	0.250963i
$353$	−10.5138	−	8.51387i	−0.559590	−	0.453147i	0.307324	−	0.951605i	$-0.400567\pi$
$353$	−10.5138	−	8.51387i	−0.559590	−	0.453147i	−0.866914	+	0.498458i	$0.833900\pi$
$354$		0			0
$355$	17.6389	−	29.0984i	0.936174	−	1.54438i
$356$	−2.22942	−	0.234322i	−0.118159	−	0.0124190i
$357$		0			0
$358$	2.56545	+	0.984783i	0.135588	+	0.0520474i
$359$	2.74332	−	8.44306i	0.144787	−	0.445608i	−0.852197	−	0.523221i	$-0.824730\pi$
$359$	2.74332	−	8.44306i	0.144787	−	0.445608i	0.996984	+	0.0776138i	$0.0247301\pi$
$360$		0			0
$361$	5.43030	+	16.7127i	0.285805	+	0.879617i
$362$	−2.21608	+	42.2854i	−0.116475	+	2.22247i
$363$		0			0
$364$	−4.02853	−	3.62731i	−0.211153	−	0.190123i
$365$	20.0404	+	1.47990i	1.04896	+	0.0774614i
$366$		0			0
$367$	6.20619	−	16.1677i	0.323960	−	0.843946i	−0.670793	−	0.741645i	$-0.734046\pi$
$367$	6.20619	−	16.1677i	0.323960	−	0.843946i	0.994753	−	0.102301i	$-0.0326205\pi$
$368$	35.6837	−	35.6837i	1.86014	−	1.86014i
$369$		0			0
$370$	−14.4270	−	1.82853i	−0.750022	−	0.0950609i
$371$	0.787617	−	0.0827819i	0.0408910	−	0.00429782i
$372$		0			0
$373$	−16.3708	+	0.857957i	−0.847647	+	0.0444233i	−0.471213	−	0.882020i	$-0.656184\pi$
$373$	−16.3708	+	0.857957i	−0.847647	+	0.0444233i	−0.376435	+	0.926443i	$0.622850\pi$
$374$	6.18822	+	10.7183i	0.319985	+	0.554231i
$375$		0			0
$376$	33.4628	−	57.9592i	1.72571	−	2.98902i
$377$	−14.8581	+	29.1607i	−0.765232	+	1.50185i
$378$		0			0
$379$	−8.68816	−	11.9582i	−0.446281	−	0.614253i	0.525313	−	0.850909i	$-0.323948\pi$
$379$	−8.68816	−	11.9582i	−0.446281	−	0.614253i	−0.971593	+	0.236657i	$0.923948\pi$
$380$	7.75578	−	10.2092i	0.397863	−	0.523721i
$381$		0			0
$382$	−21.6222	−	5.79365i	−1.10629	−	0.296429i
$383$	13.3542	+	16.4911i	0.682368	+	0.842654i	0.994207	−	0.107481i	$-0.0342783\pi$
$383$	13.3542	+	16.4911i	0.682368	+	0.842654i	−0.311839	+	0.950135i	$0.600945\pi$
$384$		0			0
$385$	0.193937	+	0.401595i	0.00988393	+	0.0204672i
$386$	−1.20628	+	0.391943i	−0.0613978	+	0.0199494i
$387$		0			0
$388$	30.5804	−	15.5815i	1.55248	−	0.791031i
$389$	−31.2191	−	6.63582i	−1.58287	−	0.336449i	−0.669256	−	0.743032i	$-0.733387\pi$
$389$	−31.2191	−	6.63582i	−1.58287	−	0.336449i	−0.913614	+	0.406583i	$0.866720\pi$
$390$		0			0
$391$	−23.9538	+	5.09153i	−1.21139	+	0.257490i
$392$	39.5021	−	31.9882i	1.99516	−	1.61565i
$393$		0			0
$394$	−11.6613	−	26.1918i	−0.587490	−	1.31952i
$395$	4.42485	+	8.05656i	0.222638	+	0.405370i
$396$		0			0
$397$	−1.86584	+	11.7804i	−0.0936438	+	0.591244i	0.895588	+	0.444885i	$0.146755\pi$
$397$	−1.86584	+	11.7804i	−0.0936438	+	0.591244i	−0.989232	+	0.146359i	$0.953245\pi$
$398$	58.4015	−	37.9263i	2.92740	−	1.90108i
$399$		0			0
$400$	47.1388	+	2.01425i	2.35694	+	0.100713i
$401$	−13.7250	+	7.92411i	−0.685392	+	0.395711i	−0.801883	−	0.597481i	$-0.796168\pi$
$401$	−13.7250	+	7.92411i	−0.685392	+	0.395711i	0.116492	+	0.993192i	$0.462835\pi$
$402$		0			0
$403$	30.4044	−	37.5464i	1.51455	−	1.87032i
$404$	−18.9378	+	13.7591i	−0.942190	+	0.684541i
$405$		0			0
$406$	2.26332	+	1.64440i	0.112327	+	0.0816102i
$407$	−2.49702	+	0.669076i	−0.123773	+	0.0331648i
$408$		0			0
$409$	5.64934	+	26.5780i	0.279342	+	1.31420i	0.864234	+	0.503089i	$0.167803\pi$
$409$	5.64934	+	26.5780i	0.279342	+	1.31420i	−0.584893	+	0.811111i	$0.698863\pi$
$410$	33.3199	+	13.6135i	1.64555	+	0.672322i
$411$		0			0
$412$	−47.2285	−	2.47514i	−2.32678	−	0.121942i
$413$	0.187027	+	0.367061i	0.00920300	+	0.0180619i
$414$		0			0
$415$	−0.265544	+	0.00823656i	−0.0130350	+	0.000404317i
$416$	−43.6478	+	39.3006i	−2.14001	+	1.92687i
$417$		0			0
$418$	0.835689	−	3.11883i	0.0408749	−	0.152547i
$419$	2.08906	−	19.8761i	0.102057	−	0.971012i	−0.816933	−	0.576732i	$-0.804328\pi$
$419$	2.08906	−	19.8761i	0.102057	−	0.971012i	0.918991	−	0.394279i	$-0.129006\pi$
$420$		0			0
$421$	−2.00233	−	19.0509i	−0.0975874	−	0.928482i	−0.928313	−	0.371800i	$-0.878741\pi$
$421$	−2.00233	−	19.0509i	−0.0975874	−	0.928482i	0.830726	−	0.556682i	$-0.187926\pi$
$422$	10.7000	+	1.69471i	0.520867	+	0.0824972i
$423$		0			0
$424$		−	30.0448i		−	1.45911i
$425$	−18.6523	−	13.2784i	−0.904770	−	0.644099i
$426$		0			0
$427$	−0.114419	−	2.18324i	−0.00553711	−	0.105654i
$428$	−40.9849	+	15.7326i	−1.98108	+	0.760465i
$429$		0			0
$430$	−15.9150	+	45.6416i	−0.767489	+	2.20103i
$431$	0.761042	−	1.04748i	0.0366581	−	0.0504556i	−0.790295	−	0.612727i	$-0.790072\pi$
$431$	0.761042	−	1.04748i	0.0366581	−	0.0504556i	0.826953	+	0.562272i	$0.190072\pi$
$432$		0			0
$433$	5.70393	+	36.0132i	0.274113	+	1.73068i	0.613200	+	0.789927i	$0.289882\pi$
$433$	5.70393	+	36.0132i	0.274113	+	1.73068i	−0.339087	+	0.940755i	$0.610118\pi$
$434$	−2.76343	−	3.06910i	−0.132649	−	0.147321i
$435$		0			0
$436$	27.8847	−	30.9691i	1.33544	−	1.48315i
$437$	5.35813	+	3.47961i	0.256314	+	0.166452i
$438$		0			0
$439$	−5.86360	+	27.5861i	−0.279854	+	1.31661i	0.583541	+	0.812083i	$0.301667\pi$
$439$	−5.86360	+	27.5861i	−0.279854	+	1.31661i	−0.863396	+	0.504527i	$0.831667\pi$
$440$	15.9211	−	5.72462i	0.759010	−	0.272911i
$441$		0			0
$442$	69.2260	−	10.9643i	3.29275	−	0.521520i
$443$	7.36632	+	27.4915i	0.349984	+	1.30616i	0.886680	+	0.462383i	$0.153006\pi$
$443$	7.36632	+	27.4915i	0.349984	+	1.30616i	−0.536696	+	0.843776i	$0.680328\pi$
$444$		0			0
$445$	0.790881	−	0.682107i	0.0374913	−	0.0323350i
$446$	−3.79867	+	8.53196i	−0.179872	+	0.404000i
$447$		0			0
$448$	0.756576	+	1.16502i	0.0357448	+	0.0550422i
$449$	12.9427			0.610804			0.305402	−	0.952224i	$-0.401209\pi$
$449$	12.9427			0.610804			0.305402	+	0.952224i	$0.401209\pi$
$450$		0			0
$451$	6.39838			0.301288
$452$	5.53032	+	8.51595i	0.260125	+	0.400557i
$453$		0			0
$454$	18.0338	−	40.5045i	0.846367	−	1.90097i
$455$	2.51681	−	0.210308i	0.117990	−	0.00985937i
$456$		0			0
$457$	5.60338	+	20.9121i	0.262115	+	0.978226i	0.963993	+	0.265929i	$0.0856785\pi$
$457$	5.60338	+	20.9121i	0.262115	+	0.978226i	−0.701878	+	0.712297i	$0.747655\pi$
$458$	2.53160	−	0.400966i	0.118294	−	0.0187359i
$459$		0			0
$460$	1.77936	+	57.3660i	0.0829632	+	2.67470i
$461$	7.76668	−	36.5394i	0.361730	−	1.70181i	−0.301561	−	0.953447i	$-0.597508\pi$
$461$	7.76668	−	36.5394i	0.361730	−	1.70181i	0.663291	−	0.748361i	$-0.269159\pi$
$462$		0			0
$463$	−32.5427	−	21.1335i	−1.51239	−	0.982157i	−0.991723	−	0.128396i	$-0.959017\pi$
$463$	−32.5427	−	21.1335i	−1.51239	−	0.982157i	−0.520666	−	0.853761i	$-0.674316\pi$
$464$	35.2055	−	39.0997i	1.63437	−	1.81516i
$465$		0			0
$466$	18.8094	+	20.8900i	0.871330	+	0.967710i
$467$	1.54404	+	9.74869i	0.0714497	+	0.451115i	0.997313	+	0.0732571i	$0.0233394\pi$
$467$	1.54404	+	9.74869i	0.0714497	+	0.451115i	−0.925863	+	0.377858i	$0.876661\pi$
$468$		0			0
$469$	−0.811111	+	1.11640i	−0.0374536	+	0.0515505i
$470$	15.4295	+	51.1804i	0.711708	+	2.36077i
$471$		0			0
$472$	14.5908	−	5.60087i	0.671594	−	0.257801i
$473$	0.449698	+	8.58075i	0.0206771	+	0.394543i
$474$		0			0
$475$	0.991346	+	5.89043i	0.0454861	+	0.270271i
$476$		−	4.22903i		−	0.193837i
$477$		0			0
$478$	30.1844	+	4.78074i	1.38060	+	0.218666i
$479$	−0.846574	−	8.05462i	−0.0386810	−	0.368025i	−0.996691	−	0.0812888i	$-0.974096\pi$
$479$	−0.846574	−	8.05462i	−0.0386810	−	0.368025i	0.958010	−	0.286736i	$-0.0925703\pi$
$480$		0			0
$481$	−1.53027	+	14.5595i	−0.0697742	+	0.663857i
$482$	−10.6739	+	39.8354i	−0.486182	+	1.81445i
$483$		0			0
$484$	−35.4023	+	31.8764i	−1.60920	+	1.44893i
$485$	−4.46734	+	15.3533i	−0.202852	+	0.697158i
$486$		0			0
$487$	−13.5819	−	26.6560i	−0.615454	−	1.20790i	−0.962814	−	0.270165i	$-0.912922\pi$
$487$	−13.5819	−	26.6560i	−0.615454	−	1.20790i	0.347360	−	0.937732i	$-0.387078\pi$
$488$	−82.8266	−	4.34076i	−3.74938	−	0.196497i
$489$		0			0
$490$	−2.98995	+	40.4891i	−0.135072	+	1.82911i
$491$	−4.84568	−	22.7971i	−0.218683	−	1.02882i	−0.941300	−	0.337572i	$-0.890394\pi$
$491$	−4.84568	−	22.7971i	−0.218683	−	1.02882i	0.722617	−	0.691249i	$-0.242939\pi$
$492$		0			0
$493$	−24.6620	+	6.60816i	−1.11072	+	0.297616i
$494$	−14.7931	−	10.7478i	−0.665574	−	0.483568i
$495$		0			0
$496$	−62.8356	+	45.6527i	−2.82140	+	2.04987i
$497$	−1.84275	+	2.27561i	−0.0826587	+	0.102075i
$498$		0			0
$499$	−0.864468	+	0.499101i	−0.0386989	+	0.0223428i	−0.519225	−	0.854638i	$-0.673779\pi$
$499$	−0.864468	+	0.499101i	−0.0386989	+	0.0223428i	0.480526	+	0.876981i	$0.340446\pi$
$500$	−38.3847	+	37.4972i	−1.71662	+	1.67692i
$501$		0			0
$502$	−34.9049	+	22.6675i	−1.55788	+	1.01170i
$503$	3.87979	−	24.4960i	0.172991	−	1.09222i	−0.736481	−	0.676459i	$-0.763514\pi$
$503$	3.87979	−	24.4960i	0.172991	−	1.09222i	0.909472	−	0.415765i	$-0.136486\pi$
$504$		0			0
$505$	1.37128	−	10.8193i	0.0610211	−	0.481451i
$506$	5.87896	+	13.2044i	0.261352	+	0.587006i
$507$		0			0
$508$	−38.6236	+	31.2768i	−1.71365	+	1.38768i
$509$	11.3133	−	2.40473i	0.501455	−	0.106588i	0.0497623	−	0.998761i	$-0.484154\pi$
$509$	11.3133	−	2.40473i	0.501455	−	0.106588i	0.451693	+	0.892173i	$0.350820\pi$
$510$		0			0
$511$	−1.69146	−	0.359530i	−0.0748256	−	0.0159047i
$512$	−38.6245	+	19.6801i	−1.70698	+	0.869748i
$513$		0			0
$514$	−44.4260	+	14.4349i	−1.95955	+	0.636695i
$515$	15.9093	−	15.2440i	0.701046	−	0.671730i
$516$		0			0
$517$	5.98010	+	7.38480i	0.263004	+	0.324783i
$518$	1.20878	+	0.323893i	0.0531109	+	0.0142310i
$519$		0			0
$520$	2.04568	−	95.7923i	0.0897089	−	4.20077i
$521$	−20.6888	−	28.4757i	−0.906392	−	1.24754i	−0.968384	−	0.249465i	$-0.919745\pi$
$521$	−20.6888	−	28.4757i	−0.906392	−	1.24754i	0.0619913	−	0.998077i	$-0.480255\pi$
$522$		0			0
$523$	−3.11506	+	6.11364i	−0.136212	+	0.267331i	−0.949029	−	0.315188i	$-0.897933\pi$
$523$	−3.11506	+	6.11364i	−0.136212	+	0.267331i	0.812818	+	0.582518i	$0.197933\pi$
$524$	−9.15315	+	15.8537i	−0.399857	+	0.692573i
$525$		0			0
$526$	6.27954	+	10.8765i	0.273801	+	0.474238i
$527$	37.6389	−	1.97257i	1.63958	−	0.0859266i
$528$		0			0
$529$	−5.56900	+	0.585325i	−0.242130	+	0.0254489i
$530$	17.4869	+	16.4347i	0.759583	+	0.713879i
$531$		0			0
$532$	−0.780151	+	0.780151i	−0.0338238	+	0.0338238i
$533$	12.9853	−	33.8279i	0.562457	−	1.46525i
$534$		0			0
$535$	7.73574	−	18.9338i	0.334445	−	0.818578i
$536$	38.9049	+	35.0301i	1.68043	+	1.51307i
$537$		0			0
$538$	−2.47307	+	47.1889i	−0.106621	+	2.03446i
$539$	2.23020	+	6.86386i	0.0960617	+	0.295648i
$540$		0			0
$541$	2.01612	−	6.20499i	0.0866799	−	0.266773i	−0.898316	−	0.439349i	$-0.855209\pi$
$541$	2.01612	−	6.20499i	0.0866799	−	0.266773i	0.984996	+	0.172576i	$0.0552090\pi$
$542$	−21.7245	−	8.33925i	−0.933146	−	0.358201i
$543$		0			0
$544$	−45.5691	−	4.78950i	−1.95376	−	0.205348i
$545$	1.61673	+	19.3478i	0.0692531	+	0.828769i
$546$		0			0
$547$	7.56348	+	6.12478i	0.323391	+	0.261877i	0.777243	−	0.629200i	$-0.216617\pi$
$547$	7.56348	+	6.12478i	0.323391	+	0.261877i	−0.453853	+	0.891077i	$0.649951\pi$
$548$	23.5108	+	11.9793i	1.00433	+	0.511732i
$549$		0			0
$550$	−5.37709	+	12.3979i	−0.229280	+	0.528650i
$551$	5.76856	+	3.33048i	0.245749	+	0.141883i
$552$		0			0
$553$	−0.283462	−	0.738444i	−0.0120540	−	0.0314018i
$554$	−46.8202	−	20.8457i	−1.98920	−	0.885648i
$555$		0			0
$556$	−5.32267	+	2.36980i	−0.225731	+	0.100502i
$557$	11.4927	+	11.4927i	0.486962	+	0.486962i	0.907346	−	0.420384i	$-0.138105\pi$
$557$	11.4927	+	11.4927i	0.486962	+	0.486962i	−0.420384	+	0.907346i	$0.638105\pi$
$558$		0			0
$559$	46.2787	+	15.0369i	1.95738	+	0.635992i
$560$	−3.99570	−	0.720624i	−0.168849	−	0.0304519i
$561$		0			0
$562$	31.3824	−	48.3247i	1.32379	−	2.03845i
$563$	9.35256	−	14.4017i	0.394163	−	0.606959i	−0.584755	−	0.811210i	$-0.698809\pi$
$563$	9.35256	−	14.4017i	0.394163	−	0.606959i	0.978918	+	0.204251i	$0.0654760\pi$
$564$		0			0
$565$	−4.65563	−	0.839642i	−0.195864	−	0.0353240i
$566$	11.0811	+	3.60048i	0.465775	+	0.151339i
$567$		0			0
$568$	78.5505	+	78.5505i	3.29590	+	3.29590i
$569$	−14.5275	+	6.46808i	−0.609026	+	0.271156i	−0.687989	−	0.725722i	$-0.741506\pi$
$569$	−14.5275	+	6.46808i	−0.609026	+	0.271156i	0.0789621	+	0.996878i	$0.474839\pi$
$570$		0			0
$571$	−21.1093	−	9.39847i	−0.883398	−	0.393314i	−0.0856640	−	0.996324i	$-0.527301\pi$
$571$	−21.1093	−	9.39847i	−0.883398	−	0.393314i	−0.797734	+	0.603010i	$0.793968\pi$
$572$	−10.4644	−	27.2608i	−0.437540	−	1.13983i
$573$		0			0
$574$	−2.68242	−	1.54869i	−0.111962	−	0.0646412i
$575$	−20.0430	−	17.6994i	−0.835852	−	0.738116i
$576$		0			0
$577$	−4.48458	−	2.28501i	−0.186695	−	0.0951260i	0.358144	−	0.933666i	$-0.383410\pi$
$577$	−4.48458	−	2.28501i	−0.186695	−	0.0951260i	−0.544840	+	0.838540i	$0.683410\pi$
$578$	8.04310	+	6.51317i	0.334549	+	0.270912i
$579$		0			0
$580$	4.98279	+	59.6303i	0.206899	+	2.47601i
$581$	0.0227368	+	0.00238973i	0.000943280	+	9.91427e-5i
$582$		0			0
$583$	3.98259	+	1.52877i	0.164942	+	0.0633154i
$584$	−20.2725	+	62.3923i	−0.838882	+	2.58181i
$585$		0			0
$586$	6.17385	+	19.0011i	0.255039	+	0.784930i
$587$	−0.613837	+	11.7127i	−0.0253358	+	0.483435i	0.956266	+	0.292497i	$0.0944863\pi$
$587$	−0.613837	+	11.7127i	−0.0253358	+	0.483435i	−0.981602	+	0.190938i	$0.938847\pi$
$588$		0			0
$589$	−7.30733	−	6.57955i	−0.301093	−	0.271106i
$590$	−4.72140	+	11.5559i	−0.194377	+	0.475751i
$591$		0			0
$592$	8.43422	−	21.9719i	0.346644	−	0.903040i
$593$	−12.0477	+	12.0477i	−0.494741	+	0.494741i	−0.909796	−	0.415055i	$-0.863762\pi$
$593$	−12.0477	+	12.0477i	−0.494741	+	0.494741i	0.415055	+	0.909796i	$0.363762\pi$
$594$		0			0
$595$	1.43572	+	1.34934i	0.0588589	+	0.0553174i
$596$	13.9726	−	1.46858i	0.572341	−	0.0601555i
$597$		0			0
$598$	81.7421	−	4.28392i	3.34268	−	0.175183i
$599$	−7.53225	−	13.0462i	−0.307759	−	0.533055i	0.670112	−	0.742260i	$-0.266246\pi$
$599$	−7.53225	−	13.0462i	−0.307759	−	0.533055i	−0.977872	+	0.209205i	$0.932913\pi$
$600$		0			0
$601$	6.33031	−	10.9644i	0.258219	−	0.447248i	−0.707546	−	0.706667i	$-0.750198\pi$
$601$	6.33031	−	10.9644i	0.258219	−	0.447248i	0.965765	+	0.259419i	$0.0835311\pi$
$602$	1.88840	−	3.70619i	0.0769654	−	0.151053i
$603$		0			0
$604$	36.0825	+	49.6634i	1.46818	+	2.02077i
$605$	0.473863	−	22.1894i	0.0192653	−	0.902129i
$606$		0			0
$607$	6.08783	+	1.63123i	0.247097	+	0.0662095i	0.380242	−	0.924887i	$-0.375841\pi$
$607$	6.08783	+	1.63123i	0.247097	+	0.0662095i	−0.133145	+	0.991097i	$0.542507\pi$
$608$	7.52282	+	9.28990i	0.305091	+	0.376755i
$609$		0			0
$610$	47.8332	−	45.8329i	1.93671	−	1.85572i
$611$	51.1796	−	16.6292i	2.07050	−	0.672747i
$612$		0			0
$613$	22.0736	−	11.2471i	0.891545	−	0.454265i	0.0526845	−	0.998611i	$-0.483222\pi$
$613$	22.0736	−	11.2471i	0.891545	−	0.454265i	0.838861	+	0.544346i	$0.183222\pi$
$614$	−46.4905	−	9.88186i	−1.87620	−	0.398800i
$615$		0			0
$616$	−1.42413	+	0.302708i	−0.0573798	+	0.0121964i
$617$	12.0032	−	9.72000i	0.483231	−	0.391313i	−0.356517	−	0.934289i	$-0.616036\pi$
$617$	12.0032	−	9.72000i	0.483231	−	0.391313i	0.839748	+	0.542976i	$0.182703\pi$
$618$		0			0
$619$	0.586541	+	1.31739i	0.0235751	+	0.0529505i	0.924949	−	0.380091i	$-0.124107\pi$
$619$	0.586541	+	1.31739i	0.0235751	+	0.0529505i	−0.901374	+	0.433041i	$0.857441\pi$
$620$	11.1069	−	87.6327i	0.446065	−	3.51941i
$621$		0			0
$622$	2.85564	−	18.0298i	0.114501	−	0.722928i
$623$	−0.0753747	+	0.0489489i	−0.00301982	+	0.00196110i
$624$		0			0
$625$	−0.482752	−	24.9953i	−0.0193101	−	0.999814i
$626$	16.1272	−	9.31102i	0.644571	−	0.372143i
$627$		0			0
$628$	−17.8383	+	22.0285i	−0.711825	+	0.879031i
$629$	−9.23970	+	6.71304i	−0.368411	+	0.267666i
$630$		0			0
$631$	−27.9118	−	20.2791i	−1.11115	−	0.807297i	−0.128305	−	0.991735i	$-0.540954\pi$
$631$	−27.9118	−	20.2791i	−1.11115	−	0.807297i	−0.982844	+	0.184437i	$0.940954\pi$
$632$	−28.9853	+	7.76659i	−1.15297	+	0.308938i
$633$		0			0
$634$	−3.26575	−	15.3641i	−0.129700	−	0.610188i
$635$	1.70523	−	23.0917i	0.0676699	−	0.916368i
$636$		0			0
$637$	40.8151	+	2.13903i	1.61715	+	0.0847514i
$638$	6.84146	+	13.4271i	0.270856	+	0.531585i
$639$		0			0
$640$	0.741902	−	2.54976i	0.0293263	−	0.100788i
$641$	−33.6337	+	30.2839i	−1.32845	+	1.19614i	−0.364150	+	0.931340i	$0.618640\pi$
$641$	−33.6337	+	30.2839i	−1.32845	+	1.19614i	−0.964302	+	0.264804i	$0.914693\pi$
$642$		0			0
$643$	9.38741	−	35.0343i	0.370203	−	1.38162i	−0.490025	−	0.871708i	$-0.663012\pi$
$643$	9.38741	−	35.0343i	0.370203	−	1.38162i	0.860228	−	0.509909i	$-0.170321\pi$
$644$	0.516259	−	4.91187i	0.0203434	−	0.193555i
$645$		0			0
$646$	−1.49109	−	14.1868i	−0.0586662	−	0.558172i
$647$	3.83742	+	0.607788i	0.150865	+	0.0238946i	0.231410	−	0.972856i	$-0.425666\pi$
$647$	3.83742	+	0.607788i	0.150865	+	0.0238946i	−0.0805453	+	0.996751i	$0.525666\pi$
$648$		0			0
$649$			2.21907i			0.0871061i
$650$	54.6347	+	53.5897i	2.14295	+	2.10196i
$651$		0			0
$652$	1.70015	+	32.4408i	0.0665829	+	1.27048i
$653$	−14.8932	+	5.71695i	−0.582814	+	0.223722i	−0.631870	−	0.775075i	$-0.717712\pi$
$653$	−14.8932	+	5.71695i	−0.582814	+	0.223722i	0.0490553	+	0.998796i	$0.484379\pi$
$654$		0			0
$655$	−2.46176	−	8.16579i	−0.0961889	−	0.319064i
$656$	−34.2393	+	47.1264i	−1.33682	+	1.83998i
$657$		0			0
$658$	−0.719606	−	4.54341i	−0.0280532	−	0.177121i
$659$	27.4767	+	30.5160i	1.07034	+	1.18873i	0.981256	+	0.192710i	$0.0617277\pi$
$659$	27.4767	+	30.5160i	1.07034	+	1.18873i	0.0890853	+	0.996024i	$0.471606\pi$
$660$		0			0
$661$	5.68147	−	6.30991i	0.220984	−	0.245427i	−0.622451	−	0.782659i	$-0.713863\pi$
$661$	5.68147	−	6.30991i	0.220984	−	0.245427i	0.843435	+	0.537231i	$0.180530\pi$
$662$	14.0624	+	9.13222i	0.546550	+	0.354934i
$663$		0			0
$664$	0.180327	−	0.848374i	0.00699806	−	0.0329233i
$665$	−0.0159361	−	0.513774i	−0.000617975	−	0.0199233i
$666$		0			0
$667$	−29.4507	+	4.66453i	−1.14034	+	0.180611i
$668$	11.7572	+	43.8784i	0.454899	+	1.69771i
$669$		0			0
$670$	−41.6697	+	3.48198i	−1.60984	+	0.134521i
$671$	4.78987	−	10.7582i	0.184911	−	0.415316i
$672$		0			0
$673$	21.8208	+	33.6010i	0.841128	+	1.29522i	0.953450	+	0.301552i	$0.0975047\pi$
$673$	21.8208	+	33.6010i	0.841128	+	1.29522i	−0.112321	+	0.993672i	$0.535829\pi$
$674$	50.0053			1.92613
$675$		0			0
$676$	−102.970			−3.96039
$677$	−25.9409	−	39.9454i	−0.996989	−	1.53523i	−0.836336	−	0.548217i	$-0.815307\pi$
$677$	−25.9409	−	39.9454i	−0.996989	−	1.53523i	−0.160653	−	0.987011i	$-0.551360\pi$
$678$		0			0
$679$	0.559670	−	1.25704i	0.0214782	−	0.0482407i
$680$	56.6034	−	48.8185i	2.17064	−	1.87210i
$681$		0			0
$682$	−5.75767	−	21.4879i	−0.220473	−	0.822815i
$683$	−21.4897	+	3.40364i	−0.822281	+	0.130237i	−0.553378	−	0.832930i	$-0.686661\pi$
$683$	−21.4897	+	3.40364i	−0.822281	+	0.130237i	−0.268904	+	0.963167i	$0.586661\pi$
$684$		0			0
$685$	−11.5683	+	4.15953i	−0.442004	+	0.158927i
$686$	1.45663	−	6.85292i	0.0556145	−	0.261646i
$687$		0			0
$688$	−65.6069	−	42.6056i	−2.50124	−	1.62432i
$689$	16.1651	−	17.9532i	0.615842	−	0.683962i
$690$		0			0
$691$	13.9366	+	15.4782i	0.530174	+	0.588818i	0.947427	−	0.319973i	$-0.103674\pi$
$691$	13.9366	+	15.4782i	0.530174	+	0.588818i	−0.417253	+	0.908790i	$0.637007\pi$
$692$	−17.0492	−	107.644i	−0.648112	−	4.09202i
$693$		0			0
$694$	−14.1606	+	19.4904i	−0.537528	+	0.739844i
$695$	0.893748	−	2.56312i	0.0339018	−	0.0972249i
$696$		0			0
$697$	26.3902	−	10.1303i	0.999600	−	0.383711i
$698$	4.11494	+	78.5177i	0.155753	+	2.97194i
$699$		0			0
$700$	3.70939	−	2.75014i	0.140202	−	0.103945i
$701$			17.9503i			0.677975i	0.940791	+	0.338988i	$0.110084\pi$
$701$			17.9503i			0.677975i	−0.940791	+	0.338988i	$0.889916\pi$
$702$		0			0
$703$	2.94288	+	0.466107i	0.110993	+	0.0175796i
$704$	0.782153	+	7.44169i	0.0294785	+	0.280469i
$705$		0			0
$706$	−3.68747	+	35.0840i	−0.138780	+	1.32040i
$707$	−0.242898	+	0.906508i	−0.00913512	+	0.0340927i
$708$		0			0
$709$	−9.47258	+	8.52915i	−0.355750	+	0.320319i	−0.827556	−	0.561384i	$-0.810269\pi$
$709$	−9.47258	+	8.52915i	−0.355750	+	0.320319i	0.471805	+	0.881703i	$0.343603\pi$
$710$	−88.6862	+	2.75084i	−3.32834	+	0.103237i
$711$		0			0
$712$	1.54792	+	3.03797i	0.0580109	+	0.113853i
$713$	43.9571	+	2.30369i	1.64620	+	0.0862739i
$714$		0			0
$715$	12.5937	+	5.14538i	0.470976	+	0.192426i
$716$	−1.05160	−	4.94737i	−0.0393000	−	0.184892i
$717$		0			0
$718$	−22.3602	+	5.99141i	−0.834477	+	0.223597i
$719$	15.0229	+	10.9147i	0.560258	+	0.407051i	0.831553	−	0.555445i	$-0.187452\pi$
$719$	15.0229	+	10.9147i	0.560258	+	0.407051i	−0.271295	+	0.962496i	$0.587452\pi$
$720$		0			0
$721$	−1.53396	+	1.11449i	−0.0571277	+	0.0415057i
$722$	28.8371	−	35.6109i	1.07321	−	1.32530i
$723$		0			0
$724$	67.4955	−	38.9686i	2.50845	−	1.44826i
$725$	−21.8338	−	17.3343i	−0.810889	−	0.643781i
$726$		0			0
$727$	−23.4755	+	15.2452i	−0.870660	+	0.565413i	−0.900850	−	0.434131i	$-0.857055\pi$
$727$	−23.4755	+	15.2452i	−0.870660	+	0.565413i	0.0301901	+	0.999544i	$0.490389\pi$
$728$	−1.28983	+	8.14364i	−0.0478041	+	0.301823i
$729$		0			0
$730$	−25.2248	−	45.9282i	−0.933613	−	1.69988i
$731$	15.4403	+	34.6795i	0.571080	+	1.28267i
$732$		0			0
$733$	−10.9445	+	8.86267i	−0.404244	+	0.327350i	−0.809785	−	0.586727i	$-0.800416\pi$
$733$	−10.9445	+	8.86267i	−0.404244	+	0.327350i	0.405541	+	0.914077i	$0.367083\pi$
$734$	−44.1712	+	9.38888i	−1.63039	+	0.346550i
$735$		0			0
$736$	−52.3422	−	11.1257i	−1.92936	−	0.410098i
$737$	−6.62302	+	3.37460i	−0.243962	+	0.124305i
$738$		0			0
$739$	0.635495	−	0.206485i	0.0233771	−	0.00759567i	−0.297305	−	0.954783i	$-0.596088\pi$
$739$	0.635495	−	0.206485i	0.0233771	−	0.00759567i	0.320682	+	0.947187i	$0.396088\pi$
$740$	11.6398	+	24.1033i	0.427889	+	0.886054i
$741$		0			0
$742$	−1.29961	−	1.60488i	−0.0477100	−	0.0589170i
$743$	−41.7676	−	11.1916i	−1.53230	−	0.410580i	−0.608535	−	0.793527i	$-0.708242\pi$
$743$	−41.7676	−	11.1916i	−1.53230	−	0.410580i	−0.923770	+	0.382947i	$0.874909\pi$
$744$		0			0
$745$	−3.95961	+	5.21217i	−0.145069	+	0.190959i
$746$	25.1260	+	34.5830i	0.919928	+	1.26617i
$747$		0			0
$748$	10.3419	−	20.2972i	0.378138	−	0.742138i
$749$	−0.880032	+	1.52426i	−0.0321557	+	0.0556952i
$750$		0			0
$751$	25.8256	+	44.7313i	0.942391	+	1.63227i	0.760893	+	0.648878i	$0.224761\pi$
$751$	25.8256	+	44.7313i	0.942391	+	1.63227i	0.181498	+	0.983391i	$0.441905\pi$
$752$	−86.3928	+	4.52766i	−3.15042	+	0.165107i
$753$		0			0
$754$	84.8731	−	8.92053i	3.09090	−	0.324866i
$755$	−28.3730	−	3.59611i	−1.03260	−	0.130876i
$756$		0			0
$757$	35.5304	−	35.5304i	1.29137	−	1.29137i	0.357436	−	0.933938i	$-0.383651\pi$
$757$	35.5304	−	35.5304i	1.29137	−	1.29137i	0.933938	−	0.357436i	$-0.116349\pi$
$758$	−13.8127	+	35.9832i	−0.501698	+	1.30697i
$759$		0			0
$760$	−19.4477	−	1.43613i	−0.705443	−	0.0520940i
$761$	−18.2697	−	16.4501i	−0.662276	−	0.596316i	0.267893	−	0.963449i	$-0.413673\pi$
$761$	−18.2697	−	16.4501i	−0.662276	−	0.596316i	−0.930169	+	0.367133i	$0.880339\pi$
$762$		0			0
$763$	0.0874404	−	1.66846i	0.00316556	−	0.0604024i
$764$	12.7320	+	39.1851i	0.460628	+	1.41767i
$765$		0			0
$766$	17.0989	−	52.6250i	0.617808	−	1.90142i
$767$	11.7321	+	4.50354i	0.423622	+	0.162613i
$768$		0			0
$769$	23.0073	+	2.41816i	0.829665	+	0.0872013i	0.509833	−	0.860273i	$-0.329707\pi$
$769$	23.0073	+	2.41816i	0.829665	+	0.0872013i	0.319831	+	0.947475i	$0.396374\pi$
$770$	0.602825	−	0.994465i	0.0217243	−	0.0358380i
$771$		0			0
$772$	1.81427	+	1.46917i	0.0652970	+	0.0528764i
$773$	−27.5078	−	14.0159i	−0.989386	−	0.504117i	−0.117104	−	0.993120i	$-0.537361\pi$
$773$	−27.5078	−	14.0159i	−0.989386	−	0.504117i	−0.872283	+	0.489002i	$0.837361\pi$
$774$		0			0
$775$	26.2068	+	31.7312i	0.941374	+	1.13982i
$776$	−45.2083	−	26.1010i	−1.62288	−	0.936972i
$777$		0			0
$778$	29.8252	+	77.6974i	1.06929	+	2.78559i
$779$	−6.73712	−	2.99956i	−0.241382	−	0.107470i
$780$		0			0
$781$	−14.4092	+	6.41537i	−0.515600	+	0.229560i
$782$	45.1537	+	45.1537i	1.61469	+	1.61469i
$783$		0			0
$784$	−62.4893	−	20.3040i	−2.23176	−	0.725143i
$785$	−1.78691	−	13.0845i	−0.0637775	−	0.467005i
$786$		0			0
$787$	−17.9745	+	27.6783i	−0.640721	+	0.986624i	0.357881	+	0.933767i	$0.383499\pi$
$787$	−17.9745	+	27.6783i	−0.640721	+	0.986624i	−0.998602	+	0.0528567i	$0.983167\pi$
$788$	−28.7410	+	44.2573i	−1.02386	+	1.57660i
$789$		0			0
$790$	11.3348	−	21.1186i	0.403275	−	0.751367i
$791$	0.387172	+	0.125800i	0.0137663	+	0.00447293i
$792$		0			0
$793$	−47.1573	−	47.1573i	−1.67461	−	1.67461i
$794$	28.4126	−	12.6501i	1.00833	−	0.448936i
$795$		0			0
$796$	−117.090	−	52.1320i	−4.15016	−	1.84777i
$797$	−16.1009	−	41.9444i	−0.570325	−	1.48575i	−0.850593	−	0.525825i	$-0.823757\pi$
$797$	−16.1009	−	41.9444i	−0.570325	−	1.48575i	0.280268	−	0.959922i	$-0.409577\pi$
$798$		0			0
$799$	36.3570	+	20.9907i	1.28622	+	0.742599i
$800$	−25.4326	−	43.0843i	−0.899177	−	1.52326i
$801$		0			0
$802$	36.8214	+	18.7614i	1.30021	+	0.662490i
$803$	−7.23889	−	5.86194i	−0.255455	−	0.206863i
$804$		0			0
$805$	1.50282	+	1.74247i	0.0529675	+	0.0614141i
$806$	−125.291	−	13.1686i	−4.41318	−	0.463843i
$807$		0			0
$808$	33.2390	+	12.7593i	1.16935	+	0.448870i
$809$	15.6697	−	48.2265i	0.550919	−	1.69555i	−0.155565	−	0.987826i	$-0.549720\pi$
$809$	15.6697	−	48.2265i	0.550919	−	1.69555i	0.706484	−	0.707729i	$-0.250280\pi$
$810$		0			0
$811$	0.0963463	+	0.296523i	0.00338318	+	0.0104123i	0.952734	−	0.303806i	$-0.0982575\pi$
$811$	0.0963463	+	0.296523i	0.00338318	+	0.0104123i	−0.949351	+	0.314219i	$0.898258\pi$
$812$	0.269493	−	5.14223i	0.00945735	−	0.180457i
$813$		0			0
$814$	5.00947	+	4.51055i	0.175582	+	0.158095i
$815$	−11.5558	−	9.77352i	−0.404783	−	0.342352i
$816$		0			0
$817$	3.54915	−	9.24585i	0.124169	−	0.323471i
$818$	50.1006	−	50.1006i	1.75173	−	1.75173i
$819$		0			0
$820$	−12.3874	−	65.0815i	−0.432588	−	2.27274i
$821$	−4.46807	+	0.469613i	−0.155937	+	0.0163896i	−0.182175	−	0.983266i	$-0.558314\pi$
$821$	−4.46807	+	0.469613i	−0.155937	+	0.0163896i	0.0262383	+	0.999656i	$0.491647\pi$
$822$		0			0
$823$	−35.0415	+	1.83645i	−1.22147	+	0.0640145i	−0.652142	−	0.758096i	$-0.726130\pi$
$823$	−35.0415	+	1.83645i	−1.22147	+	0.0640145i	−0.569327	+	0.822111i	$0.692796\pi$
$824$	35.9662	+	62.2954i	1.25294	+	2.17016i
$825$		0			0
$826$	0.537114	−	0.930309i	0.0186886	−	0.0323696i
$827$	4.99423	−	9.80173i	0.173666	−	0.340840i	−0.787724	−	0.616029i	$-0.788740\pi$
$827$	4.99423	−	9.80173i	0.173666	−	0.340840i	0.961390	+	0.275189i	$0.0887405\pi$
$828$		0			0
$829$	−6.32378	−	8.70393i	−0.219634	−	0.302300i	0.684955	−	0.728586i	$-0.259822\pi$
$829$	−6.32378	−	8.70393i	−0.219634	−	0.302300i	−0.904589	+	0.426285i	$0.859822\pi$
$830$	0.395137	+	0.569023i	0.0137154	+	0.0197511i
$831$		0			0
$832$	40.9312	+	10.9675i	1.41903	+	0.380229i
$833$	20.0658	+	24.7791i	0.695237	+	0.858546i
$834$		0			0
$835$	−18.6477	−	10.0086i	−0.645329	−	0.346361i
$836$	−5.65215	+	1.83649i	−0.195484	+	0.0635165i
$837$		0			0
$838$	−46.4341	+	23.6594i	−1.60404	+	0.817299i
$839$	37.1582	+	7.89823i	1.28285	+	0.272677i	0.798391	−	0.602140i	$-0.205685\pi$
$839$	37.1582	+	7.89823i	1.28285	+	0.272677i	0.484454	+	0.874817i	$0.339018\pi$
$840$		0			0
$841$	−2.04221	+	0.434085i	−0.0704211	+	0.0149685i
$842$	−38.8188	+	31.4348i	−1.33778	+	1.08332i
$843$		0			0
$844$	−8.11026	−	18.2160i	−0.279167	−	0.627019i
$845$	32.8542	−	34.9576i	1.13022	−	1.20258i
$846$		0			0
$847$	−0.298777	+	1.88640i	−0.0102661	+	0.0648175i
$848$	−32.5719	+	21.1524i	−1.11852	+	0.726377i
$849$		0			0
$850$	−2.54881	+	59.6488i	−0.0874234	+	2.04594i
$851$	−11.5511	+	6.66902i	−0.395966	+	0.228611i
$852$		0			0
$853$	−29.2774	+	36.1546i	−1.00244	+	1.23791i	−0.0312727	+	0.999511i	$0.509956\pi$
$853$	−29.2774	+	36.1546i	−1.00244	+	1.23791i	−0.971167	+	0.238399i	$0.923377\pi$
$854$	−4.61205	+	3.35085i	−0.157821	+	0.114664i
$855$		0			0
$856$	54.0200	+	39.2478i	1.84637	+	1.34146i
$857$	−17.2446	+	4.62067i	−0.589063	+	0.157839i	−0.541025	−	0.841006i	$-0.681964\pi$
$857$	−17.2446	+	4.62067i	−0.589063	+	0.157839i	−0.0480382	+	0.998846i	$0.515297\pi$
$858$		0			0
$859$	−8.76993	−	41.2593i	−0.299226	−	1.40775i	−0.828829	−	0.559502i	$-0.810992\pi$
$859$	−8.76993	−	41.2593i	−0.299226	−	1.40775i	0.529603	−	0.848246i	$-0.322341\pi$
$860$	86.4090	−	21.1867i	2.94652	−	0.722461i
$861$		0			0
$862$	−3.37158	−	0.176697i	−0.114837	−	0.00601833i
$863$	−17.1339	−	33.6272i	−0.583245	−	1.14468i	−0.974497	−	0.224400i	$-0.927958\pi$
$863$	−17.1339	−	33.6272i	−0.583245	−	1.14468i	0.391252	−	0.920284i	$-0.372042\pi$
$864$		0			0
$865$	41.9842	+	28.5575i	1.42750	+	0.970983i
$866$	70.6568	−	63.6197i	2.40102	−	2.16188i
$867$		0			0
$868$	−1.96740	+	7.34243i	−0.0667778	+	0.249218i
$869$	0.445362	−	4.23734i	0.0151079	−	0.143742i
$870$		0			0
$871$	4.40011	+	41.8643i	0.149092	+	1.41852i
$872$	−62.6038	−	9.91547i	−2.12003	−	0.335780i
$873$		0			0
$874$		−	16.6595i		−	0.563515i
$875$	−0.249886	+	2.13678i	−0.00844768	+	0.0722363i
$876$		0			0
$877$	−0.0984162	−	1.87789i	−0.00332328	−	0.0634120i	0.996464	−	0.0840156i	$-0.0267745\pi$
$877$	−0.0984162	−	1.87789i	−0.00332328	−	0.0634120i	−0.999788	+	0.0206036i	$0.993441\pi$
$878$	68.6556	−	26.3544i	2.31702	−	0.889419i
$879$		0			0
$880$	−17.4150	−	13.2299i	−0.587061	−	0.445981i
$881$	−19.6130	+	26.9950i	−0.660778	+	0.909483i	−0.999507	−	0.0314009i	$-0.990003\pi$
$881$	−19.6130	+	26.9950i	−0.660778	+	0.909483i	0.338729	+	0.940884i	$0.390003\pi$
$882$		0			0
$883$	−3.51986	−	22.2235i	−0.118453	−	0.747881i	−0.973391	−	0.229151i	$-0.926405\pi$
$883$	−3.51986	−	22.2235i	−0.118453	−	0.747881i	0.854938	−	0.518730i	$-0.173595\pi$
$884$	−86.3215	−	95.8698i	−2.90331	−	3.22445i
$885$		0			0
$886$	49.6597	−	55.1527i	1.66835	−	1.85289i
$887$	−34.7052	−	22.5378i	−1.16529	−	0.756747i	−0.190898	−	0.981610i	$-0.561140\pi$
$887$	−34.7052	−	22.5378i	−1.16529	−	0.756747i	−0.974390	+	0.224863i	$0.927807\pi$
$888$		0			0
$889$	−0.414272	+	1.94900i	−0.0138942	+	0.0653673i
$890$	−2.61491	−	0.760859i	−0.0876520	−	0.0255041i
$891$		0			0
$892$	16.9784	−	2.68912i	0.568479	−	0.0900383i
$893$	−2.83470	−	10.5792i	−0.0948595	−	0.354021i
$894$		0			0
$895$	2.01512	+	1.22152i	0.0673580	+	0.0408311i
$896$	−0.0929457	+	0.208759i	−0.00310510	+	0.00697416i
$897$		0			0
$898$	−18.3812	−	28.3045i	−0.613387	−	0.944533i
$899$	45.8922			1.53059
$900$		0			0
$901$	18.8467			0.627875
$902$	−9.08694	−	13.9927i	−0.302562	−	0.465905i
$903$		0			0
$904$	6.28174	−	14.1090i	0.208928	−	0.469259i
$905$	−8.30595	+	35.3477i	−0.276099	+	1.17500i
$906$		0			0
$907$	−1.92316	−	7.17733i	−0.0638574	−	0.238319i	0.926619	−	0.376002i	$-0.122701\pi$
$907$	−1.92316	−	7.17733i	−0.0638574	−	0.238319i	−0.990476	+	0.137682i	$0.956035\pi$
$908$	−80.6032	+	12.7663i	−2.67491	+	0.423664i
$909$		0			0
$910$	−4.03428	−	5.20535i	−0.133735	−	0.172556i
$911$	−3.36360	+	15.8245i	−0.111441	+	0.524288i	0.886645	+	0.462450i	$0.153030\pi$
$911$	−3.36360	+	15.8245i	−0.111441	+	0.524288i	−0.998086	+	0.0618380i	$0.980304\pi$
$912$		0			0
$913$	0.103281	+	0.0670713i	0.00341809	+	0.00221973i
$914$	37.7749	−	41.9533i	1.24948	−	1.38769i
$915$		0			0
$916$	−3.15679	−	3.50597i	−0.104303	−	0.115840i
$917$	0.114813	+	0.724898i	0.00379144	+	0.0239382i
$918$		0			0
$919$	7.19202	−	9.89897i	0.237243	−	0.326537i	−0.673750	−	0.738960i	$-0.735317\pi$
$919$	7.19202	−	9.89897i	0.237243	−	0.326537i	0.910993	+	0.412423i	$0.135317\pi$
$920$	71.7024	−	49.7911i	2.36396	−	1.64156i
$921$		0			0
$922$	−90.9385	+	34.9080i	−2.99490	+	1.14963i
$923$	4.67480	+	89.2004i	0.153873	+	2.93607i
$924$		0			0
$925$	−11.8967	−	3.73888i	−0.391162	−	0.122934i
$926$			101.182i			3.32503i
$927$		0			0
$928$	−55.1039	−	8.72760i	−1.80887	−	0.286497i
$929$	3.76572	+	35.8284i	0.123549	+	1.17549i	0.864039	+	0.503424i	$0.167927\pi$
$929$	3.76572	+	35.8284i	0.123549	+	1.17549i	−0.740490	+	0.672067i	$0.765407\pi$
$930$		0			0
$931$	0.869503	−	8.27277i	0.0284968	−	0.271129i
$932$	13.3912	−	49.9767i	0.438644	−	1.63704i
$933$		0			0
$934$	19.1266	−	17.2217i	0.625843	−	0.563512i
$935$	3.59098	+	9.98711i	0.117438	+	0.326613i
$936$		0			0
$937$	6.63981	+	13.0314i	0.216913	+	0.425716i	0.973664	−	0.227987i	$-0.0732145\pi$
$937$	6.63981	+	13.0314i	0.216913	+	0.425716i	−0.756751	+	0.653703i	$0.773214\pi$
$938$	3.59340	+	0.188322i	0.117329	+	0.00614893i
$939$		0			0
$940$	63.5374	−	75.1241i	2.07236	−	2.45028i
$941$	5.83274	+	27.4409i	0.190142	+	0.894547i	0.964967	+	0.262371i	$0.0845045\pi$
$941$	5.83274	+	27.4409i	0.190142	+	0.894547i	−0.774825	+	0.632176i	$0.782162\pi$
$942$		0			0
$943$	31.8879	−	8.54435i	1.03841	−	0.278242i
$944$	−16.3443	−	11.8748i	−0.531961	−	0.386492i
$945$		0			0
$946$	18.1267	−	13.1698i	0.589349	−	0.428187i
$947$	−29.2717	+	36.1476i	−0.951203	+	1.17464i	0.0333313	+	0.999444i	$0.489388\pi$
$947$	−29.2717	+	36.1476i	−0.951203	+	1.17464i	−0.984534	+	0.175193i	$0.943945\pi$
$948$		0			0
$949$	−45.6829	+	26.3751i	−1.48293	+	0.856171i
$950$	11.4739	−	10.5335i	0.372263	−	0.341753i
$951$		0			0
$952$	−5.39458	+	3.50328i	−0.174839	+	0.113542i
$953$	−6.60365	+	41.6938i	−0.213913	+	1.35060i	0.613808	+	0.789456i	$0.289637\pi$
$953$	−6.60365	+	41.6938i	−0.213913	+	1.35060i	−0.827721	+	0.561140i	$0.810363\pi$
$954$		0			0
$955$	−17.3654	−	8.18018i	−0.561930	−	0.264705i
$956$	−22.8789	−	51.3868i	−0.739956	−	1.66197i
$957$		0			0
$958$	−16.4124	+	13.2905i	−0.530261	+	0.429397i
$959$	1.03478	−	0.219949i	0.0334147	−	0.00710251i
$960$		0			0
$961$	−35.9436	−	7.64004i	−1.15947	−	0.246453i
$962$	34.0136	−	17.3308i	1.09664	−	0.558768i
$963$		0			0
$964$	72.1923	−	23.4567i	2.32516	−	0.755489i
$965$	−1.07764	+	0.147170i	−0.0346904	+	0.00473758i
$966$		0			0
$967$	8.79898	+	10.8658i	0.282956	+	0.349422i	0.898731	−	0.438500i	$-0.144490\pi$
$967$	8.79898	+	10.8658i	0.282956	+	0.349422i	−0.615775	+	0.787922i	$0.711157\pi$
$968$	69.9885	+	18.7534i	2.24952	+	0.602756i
$969$		0			0
$970$	39.9208	−	12.0350i	1.28178	−	0.386421i
$971$	−30.5890	−	42.1022i	−0.981649	−	1.35112i	−0.935936	−	0.352169i	$-0.885444\pi$
$971$	−30.5890	−	42.1022i	−0.981649	−	1.35112i	−0.0457128	−	0.998955i	$-0.514556\pi$
$972$		0			0
$973$	−0.106048	+	0.208131i	−0.00339974	+	0.00667237i
$974$	−39.0052	+	67.5590i	−1.24981	+	2.16473i
$975$		0			0
$976$	53.6064	+	92.8491i	1.71590	+	2.97203i
$977$	−5.34531	+	0.280136i	−0.171011	+	0.00896233i	−0.137650	−	0.990481i	$-0.543955\pi$
$977$	−5.34531	+	0.280136i	−0.171011	+	0.00896233i	−0.0333620	+	0.999443i	$0.510621\pi$
$978$		0			0
$979$	−0.481462	+	0.0506037i	−0.0153876	+	0.00161730i
$980$	65.4985	−	35.9733i	2.09227	−	1.14912i
$981$		0			0
$982$	−42.9735	+	42.9735i	−1.37134	+	1.37134i
$983$	20.3280	−	52.9562i	0.648361	−	1.68904i	−0.0737625	−	0.997276i	$-0.523501\pi$
$983$	20.3280	−	52.9562i	0.648361	−	1.68904i	0.722124	−	0.691764i	$-0.243166\pi$
$984$		0			0
$985$	−5.85474	−	23.8783i	−0.186548	−	0.760826i
$986$	49.4762	+	44.5486i	1.57564	+	1.41872i
$987$		0			0
$988$	−1.76141	+	33.6098i	−0.0560380	+	1.06927i
$989$	13.6999	+	42.1639i	0.435630	+	1.34073i
$990$		0			0
$991$	−4.77479	+	14.6953i	−0.151676	+	0.466811i	−0.997809	−	0.0661610i	$-0.978925\pi$
$991$	−4.77479	+	14.6953i	−0.151676	+	0.466811i	0.846133	+	0.532972i	$0.178925\pi$
$992$	76.8887	+	29.5148i	2.44122	+	0.937096i
$993$		0			0
$994$	7.59362	+	0.798121i	0.240855	+	0.0253149i
$995$	55.0578	−	23.1177i	1.74545	−	0.732882i
$996$		0			0
$997$	46.8194	+	37.9136i	1.48278	+	1.20074i	0.930079	+	0.367359i	$0.119738\pi$
$997$	46.8194	+	37.9136i	1.48278	+	1.20074i	0.552706	+	0.833377i	$0.313595\pi$
$998$	2.31920	+	1.18169i	0.0734130	+	0.0374058i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.bd.a.8.1		448
3.2	odd	2		225.2.w.a.83.28	yes	448
9.4	even	3		225.2.w.a.158.28	yes	448
9.5	odd	6	inner	675.2.bd.a.233.1		448
25.22	odd	20	inner	675.2.bd.a.197.1		448
75.47	even	20		225.2.w.a.47.28	✓	448
225.22	odd	60		225.2.w.a.122.28	yes	448
225.122	even	60	inner	675.2.bd.a.422.1		448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.47.28	✓	448	75.47	even	20
225.2.w.a.83.28	yes	448	3.2	odd	2
225.2.w.a.122.28	yes	448	225.22	odd	60
225.2.w.a.158.28	yes	448	9.4	even	3
675.2.bd.a.8.1		448	1.1	even	1	trivial
675.2.bd.a.197.1		448	25.22	odd	20	inner
675.2.bd.a.233.1		448	9.5	odd	6	inner
675.2.bd.a.422.1		448	225.122	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.bd (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.42019 - 2.18691i) q^{2} +(-1.95214 + 4.38458i) q^{4} +(-0.865670 - 2.06170i) q^{5} +(0.0498024 + 0.185865i) q^{7} +(7.21013 - 1.14197i) q^{8} +O(q^{10})\)	\(q+(-1.42019 - 2.18691i) q^{2} +(-1.95214 + 4.38458i) q^{4} +(-0.865670 - 2.06170i) q^{5} +(0.0498024 + 0.185865i) q^{7} +(7.21013 - 1.14197i) q^{8} +(-3.27933 + 4.82116i) q^{10} +(-0.215500 + 1.01385i) q^{11} +(4.92281 + 3.19691i) q^{13} +(0.335741 - 0.372878i) q^{14} +(-6.31416 - 7.01258i) q^{16} +(0.716344 + 4.52282i) q^{17} +(0.702199 - 0.966494i) q^{19} +(10.7296 + 0.229135i) q^{20} +(2.52324 - 0.968581i) q^{22} +(0.279886 + 5.34054i) q^{23} +(-3.50123 + 3.56951i) q^{25} -15.3060i q^{26} +(-0.912162 - 0.144472i) q^{28} +(0.582814 + 5.54510i) q^{29} +(0.860356 - 8.18574i) q^{31} +(-2.58978 + 9.66520i) q^{32} +(8.87363 - 7.98986i) q^{34} +(0.340086 - 0.263576i) q^{35} +(1.13229 + 2.22225i) q^{37} +(-3.11089 - 0.163035i) q^{38} +(-8.59599 - 13.8766i) q^{40} +(-1.28346 - 6.03819i) q^{41} +(8.00751 - 2.14560i) q^{43} +(-4.02460 - 2.92405i) q^{44} +(11.2818 - 8.19669i) q^{46} +(5.76953 - 7.12478i) q^{47} +(6.03011 - 3.48149i) q^{49} +(12.7786 + 2.58748i) q^{50} +(-23.6271 + 15.3436i) q^{52} +(0.643842 - 4.06506i) q^{53} +(2.27680 - 0.433360i) q^{55} +(0.571334 + 1.28324i) q^{56} +(11.2989 - 9.14969i) q^{58} +(2.09415 - 0.445125i) q^{59} +(-11.1134 - 2.36223i) q^{61} +(-19.1233 + 9.74383i) q^{62} +(6.86587 - 2.23086i) q^{64} +(2.32955 - 12.9168i) q^{65} +(4.51315 + 5.57327i) q^{67} +(-21.2291 - 5.68831i) q^{68} +(-1.05940 - 0.369409i) q^{70} +(8.94457 + 12.3111i) q^{71} +(-4.07989 + 8.00724i) q^{73} +(3.25178 - 5.63224i) q^{74} +(2.86688 + 4.96558i) q^{76} +(-0.199171 + 0.0104381i) q^{77} +(-4.08814 + 0.429681i) q^{79} +(-8.99188 + 19.0885i) q^{80} +(-11.3822 + 11.3822i) q^{82} +(0.0425784 - 0.110921i) q^{83} +(8.70458 - 5.39215i) q^{85} +(-16.0645 - 14.4645i) q^{86} +(-0.395996 + 7.55605i) q^{88} +(0.144332 + 0.444208i) q^{89} +(-0.349026 + 1.07419i) q^{91} +(-23.9624 - 9.19830i) q^{92} +(-23.7751 - 2.49886i) q^{94} +(-2.60050 - 0.611061i) q^{95} +(-5.55734 - 4.50025i) q^{97} +(-16.1776 - 8.24291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q + 24 q^{2} - 10 q^{4} + 24 q^{5} - 8 q^{7}+O(q^{10}) \) 448 * q + 24 * q^2 - 10 * q^4 + 24 * q^5 - 8 * q^7	\( 448 q + 24 q^{2} - 10 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 18 q^{11} - 8 q^{13} + 30 q^{14} - 50 q^{16} - 40 q^{19} + 48 q^{20} + 48 q^{23} + 16 q^{25} - 24 q^{28} + 30 q^{29} - 6 q^{31} + 60 q^{32} - 10 q^{34} - 44 q^{37} - 16 q^{40} + 18 q^{41} - 8 q^{43} - 24 q^{46} + 18 q^{47} - 24 q^{50} + 24 q^{52} - 24 q^{55} + 18 q^{56} - 4 q^{58} - 6 q^{61} - 40 q^{64} + 96 q^{65} - 14 q^{67} - 288 q^{68} - 28 q^{70} - 32 q^{73} - 32 q^{76} - 216 q^{77} - 10 q^{79} - 72 q^{82} - 36 q^{83} - 32 q^{85} + 18 q^{86} - 28 q^{88} - 24 q^{91} - 30 q^{92} - 130 q^{94} - 6 q^{95} - 38 q^{97}+O(q^{100}) \) 448 * q + 24 * q^2 - 10 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 18 * q^11 - 8 * q^13 + 30 * q^14 - 50 * q^16 - 40 * q^19 + 48 * q^20 + 48 * q^23 + 16 * q^25 - 24 * q^28 + 30 * q^29 - 6 * q^31 + 60 * q^32 - 10 * q^34 - 44 * q^37 - 16 * q^40 + 18 * q^41 - 8 * q^43 - 24 * q^46 + 18 * q^47 - 24 * q^50 + 24 * q^52 - 24 * q^55 + 18 * q^56 - 4 * q^58 - 6 * q^61 - 40 * q^64 + 96 * q^65 - 14 * q^67 - 288 * q^68 - 28 * q^70 - 32 * q^73 - 32 * q^76 - 216 * q^77 - 10 * q^79 - 72 * q^82 - 36 * q^83 - 32 * q^85 + 18 * q^86 - 28 * q^88 - 24 * q^91 - 30 * q^92 - 130 * q^94 - 6 * q^95 - 38 * q^97

Introduction

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