LMFDB - Embedded newform 819.2.fm.e.748.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			748.3
Character	$\chi$	$=$	819.748
Dual form			819.2.fm.e.496.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34112 + 0.359352i) q^{2} +(-0.0625832 + 0.0361324i) q^{4} +(-2.52867 + 2.52867i) q^{5} +(-0.324044 - 2.62583i) q^{7} +(2.03448 - 2.03448i) q^{8} +O(q^{10})$	\(q+(-1.34112 + 0.359352i) q^{2} +(-0.0625832 + 0.0361324i) q^{4} +(-2.52867 + 2.52867i) q^{5} +(-0.324044 - 2.62583i) q^{7} +(2.03448 - 2.03448i) q^{8} +(2.48257 - 4.29993i) q^{10} +(-0.0529715 - 0.197692i) q^{11} +(-2.07540 + 2.94834i) q^{13} +(1.37818 + 3.40511i) q^{14} +(-1.92512 + 3.33441i) q^{16} +(-1.13739 - 1.97002i) q^{17} +(-1.50152 - 0.402330i) q^{19} +(0.0668853 - 0.249619i) q^{20} +(0.142082 + 0.246094i) q^{22} +(-2.59661 - 1.49915i) q^{23} -7.78835i q^{25} +(1.72386 - 4.69988i) q^{26} +(0.115157 + 0.152625i) q^{28} +(4.75430 - 8.23469i) q^{29} +(2.75209 - 2.75209i) q^{31} +(-0.105751 + 0.394667i) q^{32} +(2.23331 + 2.23331i) q^{34} +(7.45927 + 5.82046i) q^{35} +(1.17697 + 4.39250i) q^{37} +2.15829 q^{38} +10.2891i q^{40} +(1.36054 + 5.07760i) q^{41} +(1.76513 - 1.01910i) q^{43} +(0.0104582 + 0.0104582i) q^{44} +(4.02109 + 1.07745i) q^{46} +(9.42358 + 9.42358i) q^{47} +(-6.78999 + 1.70177i) q^{49} +(2.79876 + 10.4451i) q^{50} +(0.0233541 - 0.259506i) q^{52} +12.6997 q^{53} +(0.633846 + 0.365951i) q^{55} +(-6.00147 - 4.68295i) q^{56} +(-3.41693 + 12.7522i) q^{58} +(0.510631 - 1.90570i) q^{59} +(-0.850570 + 0.491077i) q^{61} +(-2.70191 + 4.67985i) q^{62} -8.26779i q^{64} +(-2.20740 - 12.7034i) q^{65} +(15.1633 - 4.06300i) q^{67} +(0.142363 + 0.0821934i) q^{68} +(-12.0954 - 5.12543i) q^{70} +(-0.00355777 + 0.0132778i) q^{71} +(2.24560 + 2.24560i) q^{73} +(-3.15691 - 5.46792i) q^{74} +(0.108507 - 0.0290743i) q^{76} +(-0.501942 + 0.203155i) q^{77} +12.7231 q^{79} +(-3.56363 - 13.2996i) q^{80} +(-3.64929 - 6.32076i) q^{82} +(-3.37812 + 3.37812i) q^{83} +(7.85762 + 2.10544i) q^{85} +(-2.00104 + 2.00104i) q^{86} +(-0.509971 - 0.294432i) q^{88} +(-11.8364 + 3.17155i) q^{89} +(8.41438 + 4.49425i) q^{91} +0.216672 q^{92} +(-16.0245 - 9.25177i) q^{94} +(4.81420 - 2.77948i) q^{95} +(-7.85674 - 2.10521i) q^{97} +(8.49465 - 4.72228i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	−1.34112	+	0.359352i	−0.948315	+	0.254100i	−0.699647	−	0.714489i	$-0.746659\pi$
$2$	−1.34112	+	0.359352i	−0.948315	+	0.254100i	−0.248668	+	0.968589i	$0.579993\pi$
$3$		0			0
$3$		0			0
$4$	−0.0625832	+	0.0361324i	−0.0312916	+	0.0180662i
$5$	−2.52867	+	2.52867i	−1.13086	+	1.13086i	−0.140821	+	0.990035i	$0.544974\pi$
$5$	−2.52867	+	2.52867i	−1.13086	+	1.13086i	−0.990035	+	0.140821i	$0.955026\pi$
$6$		0			0
$7$	−0.324044	−	2.62583i	−0.122477	−	0.992471i
$7$	−0.324044	−	2.62583i	−0.122477	−	0.992471i
$8$	2.03448	−	2.03448i	0.719298	−	0.719298i
$9$		0			0
$10$	2.48257	−	4.29993i	0.785056	−	1.35976i
$11$	−0.0529715	−	0.197692i	−0.0159715	−	0.0596065i	0.957480	−	0.288499i	$-0.0931562\pi$
$11$	−0.0529715	−	0.197692i	−0.0159715	−	0.0596065i	−0.973452	+	0.228893i	$0.926490\pi$
$12$		0			0
$13$	−2.07540	+	2.94834i	−0.575611	+	0.817724i
$13$	−2.07540	+	2.94834i	−0.575611	+	0.817724i
$14$	1.37818	+	3.40511i	0.368334	+	0.910054i
$15$		0			0
$16$	−1.92512	+	3.33441i	−0.481281	+	0.833603i
$17$	−1.13739	−	1.97002i	−0.275858	−	0.477800i	0.694493	−	0.719499i	$-0.255629\pi$
$17$	−1.13739	−	1.97002i	−0.275858	−	0.477800i	−0.970351	+	0.241699i	$0.922295\pi$
$18$		0			0
$19$	−1.50152	−	0.402330i	−0.344472	−	0.0923009i	0.0824354	−	0.996596i	$-0.473730\pi$
$19$	−1.50152	−	0.402330i	−0.344472	−	0.0923009i	−0.426907	+	0.904296i	$0.640397\pi$
$20$	0.0668853	−	0.249619i	0.0149560	−	0.0558166i
$21$		0			0
$22$	0.142082	+	0.246094i	0.0302920	+	0.0524673i
$23$	−2.59661	−	1.49915i	−0.541430	−	0.312595i	0.204228	−	0.978923i	$-0.434532\pi$
$23$	−2.59661	−	1.49915i	−0.541430	−	0.312595i	−0.745658	+	0.666328i	$0.767865\pi$
$24$		0			0
$25$		−	7.78835i		−	1.55767i
$26$	1.72386	−	4.69988i	0.338077	−	0.921722i
$27$		0			0
$28$	0.115157	+	0.152625i	0.0217627	+	0.0288433i
$29$	4.75430	−	8.23469i	0.882852	−	1.52914i	0.0346955	−	0.999398i	$-0.488954\pi$
$29$	4.75430	−	8.23469i	0.882852	−	1.52914i	0.848156	−	0.529746i	$-0.177713\pi$
$30$		0			0
$31$	2.75209	−	2.75209i	0.494290	−	0.494290i	−0.415365	−	0.909655i	$-0.636346\pi$
$31$	2.75209	−	2.75209i	0.494290	−	0.494290i	0.909655	+	0.415365i	$0.136346\pi$
$32$	−0.105751	+	0.394667i	−0.0186943	+	0.0697679i
$33$		0			0
$34$	2.23331	+	2.23331i	0.383009	+	0.383009i
$35$	7.45927	+	5.82046i	1.26085	+	0.983838i
$36$		0			0
$37$	1.17697	+	4.39250i	0.193492	+	0.722122i	0.992652	+	0.121004i	$0.0386114\pi$
$37$	1.17697	+	4.39250i	0.193492	+	0.722122i	−0.799160	+	0.601119i	$0.794722\pi$
$38$	2.15829			0.350121
$39$		0			0
$40$			10.2891i			1.62684i
$41$	1.36054	+	5.07760i	0.212480	+	0.792988i	0.987038	+	0.160485i	$0.0513058\pi$
$41$	1.36054	+	5.07760i	0.212480	+	0.792988i	−0.774558	+	0.632503i	$0.782028\pi$
$42$		0			0
$43$	1.76513	−	1.01910i	0.269180	−	0.155411i	−0.359335	−	0.933209i	$-0.616996\pi$
$43$	1.76513	−	1.01910i	0.269180	−	0.155411i	0.628515	+	0.777798i	$0.283663\pi$
$44$	0.0104582	+	0.0104582i	0.00157664	+	0.00157664i
$45$		0			0
$46$	4.02109	+	1.07745i	0.592877	+	0.158861i
$47$	9.42358	+	9.42358i	1.37457	+	1.37457i	0.853535	+	0.521036i	$0.174454\pi$
$47$	9.42358	+	9.42358i	1.37457	+	1.37457i	0.521036	+	0.853535i	$0.325546\pi$
$48$		0			0
$49$	−6.78999	+	1.70177i	−0.969999	+	0.243110i
$50$	2.79876	+	10.4451i	0.395804	+	1.47716i
$51$		0			0
$52$	0.0233541	−	0.259506i	0.00323863	−	0.0359870i
$53$	12.6997			1.74444			0.872218	−	0.489117i	$-0.162681\pi$
$53$	12.6997			1.74444			0.872218	+	0.489117i	$0.162681\pi$
$54$		0			0
$55$	0.633846	+	0.365951i	0.0854678	+	0.0493449i
$56$	−6.00147	−	4.68295i	−0.801980	−	0.625785i
$57$		0			0
$58$	−3.41693	+	12.7522i	−0.448666	+	1.67444i
$59$	0.510631	−	1.90570i	0.0664785	−	0.248101i	−0.924688	−	0.380726i	$-0.875674\pi$
$59$	0.510631	−	1.90570i	0.0664785	−	0.248101i	0.991166	+	0.132625i	$0.0423407\pi$
$60$		0			0
$61$	−0.850570	+	0.491077i	−0.108904	+	0.0628760i	−0.553463	−	0.832874i	$-0.686694\pi$
$61$	−0.850570	+	0.491077i	−0.108904	+	0.0628760i	0.444558	+	0.895750i	$0.353361\pi$
$62$	−2.70191	+	4.67985i	−0.343143	+	0.594342i
$63$		0			0
$64$		−	8.26779i		−	1.03347i
$65$	−2.20740	−	12.7034i	−0.273794	−	1.57566i
$66$		0			0
$67$	15.1633	−	4.06300i	1.85249	−	0.496374i	0.852828	−	0.522192i	$-0.174885\pi$
$67$	15.1633	−	4.06300i	1.85249	−	0.496374i	0.999667	+	0.0258173i	$0.00821883\pi$
$68$	0.142363	+	0.0821934i	0.0172641	+	0.00996742i
$69$		0			0
$70$	−12.0954	−	5.12543i	−1.44567	−	0.612607i
$71$	−0.00355777	+	0.0132778i	−0.000422230	+	0.00157578i	−0.966137	−	0.258031i	$-0.916926\pi$
$71$	−0.00355777	+	0.0132778i	−0.000422230	+	0.00157578i	0.965714	+	0.259607i	$0.0835930\pi$
$72$		0			0
$73$	2.24560	+	2.24560i	0.262827	+	0.262827i	0.826202	−	0.563374i	$-0.190497\pi$
$73$	2.24560	+	2.24560i	0.262827	+	0.262827i	−0.563374	+	0.826202i	$0.690497\pi$
$74$	−3.15691	−	5.46792i	−0.366983	−	0.635633i
$75$		0			0
$76$	0.108507	−	0.0290743i	0.0124466	−	0.00333506i
$77$	−0.501942	+	0.203155i	−0.0572016	+	0.0231517i
$78$		0			0
$79$	12.7231			1.43146			0.715732	−	0.698375i	$-0.246093\pi$
$79$	12.7231			1.43146			0.715732	+	0.698375i	$0.246093\pi$
$80$	−3.56363	−	13.2996i	−0.398425	−	1.48694i
$81$		0			0
$82$	−3.64929	−	6.32076i	−0.402997	−	0.698011i
$83$	−3.37812	+	3.37812i	−0.370797	+	0.370797i	−0.867767	−	0.496971i	$-0.834446\pi$
$83$	−3.37812	+	3.37812i	−0.370797	+	0.370797i	0.496971	+	0.867767i	$0.334446\pi$
$84$		0			0
$85$	7.85762	+	2.10544i	0.852278	+	0.228367i
$86$	−2.00104	+	2.00104i	−0.215777	+	0.215777i
$87$		0			0
$88$	−0.509971	−	0.294432i	−0.0543631	−	0.0313866i
$89$	−11.8364	+	3.17155i	−1.25466	+	0.336184i	−0.824133	−	0.566396i	$-0.808337\pi$
$89$	−11.8364	+	3.17155i	−1.25466	+	0.336184i	−0.430523	+	0.902580i	$0.641671\pi$
$90$		0			0
$91$	8.41438	+	4.49425i	0.882066	+	0.471125i
$92$	0.216672			0.0225896
$93$		0			0
$94$	−16.0245	−	9.25177i	−1.65280	−	0.954247i
$95$	4.81420	−	2.77948i	0.493927	−	0.285169i
$96$		0			0
$97$	−7.85674	−	2.10521i	−0.797731	−	0.213751i	−0.163143	−	0.986602i	$-0.552163\pi$
$97$	−7.85674	−	2.10521i	−0.797731	−	0.213751i	−0.634587	+	0.772851i	$0.718830\pi$
$98$	8.49465	−	4.72228i	0.858090	−	0.477022i
$99$		0			0
$100$	0.281412	+	0.487420i	0.0281412	+	0.0487420i
$101$	5.41672	−	9.38204i	0.538984	−	0.933548i	−0.459975	−	0.887932i	$-0.652142\pi$
$101$	5.41672	−	9.38204i	0.538984	−	0.933548i	0.998959	−	0.0456161i	$-0.0145251\pi$
$102$		0			0
$103$	2.40912			0.237378			0.118689	−	0.992931i	$-0.462131\pi$
$103$	2.40912			0.237378			0.118689	+	0.992931i	$0.462131\pi$
$104$	1.77600	+	10.2207i	0.174151	+	1.00222i
$105$		0			0
$106$	−17.0318	+	4.56366i	−1.65428	+	0.443262i
$107$	2.22804	−	3.85907i	0.215392	−	0.373071i	−0.738001	−	0.674799i	$-0.764230\pi$
$107$	2.22804	−	3.85907i	0.215392	−	0.373071i	0.953394	+	0.301728i	$0.0975636\pi$
$108$		0			0
$109$	−11.9987	−	11.9987i	−1.14927	−	1.14927i	−0.986697	−	0.162570i	$-0.948022\pi$
$109$	−11.9987	−	11.9987i	−1.14927	−	1.14927i	−0.162570	−	0.986697i	$-0.551978\pi$
$110$	−0.981569	−	0.263010i	−0.0935889	−	0.0250771i
$111$		0			0
$112$	9.37943	+	3.97455i	0.886273	+	0.375560i
$113$	−0.238333	−	0.412805i	−0.0224205	−	0.0388334i	0.854597	−	0.519291i	$-0.173804\pi$
$113$	−0.238333	−	0.412805i	−0.0224205	−	0.0388334i	−0.877018	+	0.480458i	$0.840471\pi$
$114$		0			0
$115$	10.3568	−	2.77510i	0.965780	−	0.258780i
$116$			0.687138i			0.0637992i
$117$		0			0
$118$			2.73927i			0.252170i
$119$	−4.80438	+	3.62497i	−0.440416	+	0.332301i
$120$		0			0
$121$	9.49000	−	5.47906i	0.862728	−	0.498096i
$122$	0.964247	−	0.964247i	0.0872988	−	0.0872988i
$123$		0			0
$124$	−0.0727950	+	0.271675i	−0.00653718	+	0.0243971i
$125$	7.05081	+	7.05081i	0.630643	+	0.630643i
$126$		0			0
$127$	−1.88759	−	1.08980i	−0.167496	−	0.0967041i	0.413908	−	0.910319i	$-0.364163\pi$
$127$	−1.88759	−	1.08980i	−0.167496	−	0.0967041i	−0.581405	+	0.813614i	$0.697497\pi$
$128$	2.75955	+	10.2988i	0.243912	+	0.910291i
$129$		0			0
$130$	7.52537	+	16.2435i	0.660019	+	1.42465i
$131$			7.17276i			0.626687i	0.949640	+	0.313344i	$0.101449\pi$
$131$			7.17276i			0.626687i	−0.949640	+	0.313344i	$0.898551\pi$
$132$		0			0
$133$	−0.569893	+	4.07310i	−0.0494160	+	0.353183i
$134$	−18.8758	+	10.8979i	−1.63062	+	0.941438i
$135$		0			0
$136$	−6.32197	−	1.69397i	−0.542105	−	0.145257i
$137$	−12.1825	−	3.26430i	−1.04082	−	0.278888i	−0.302369	−	0.953191i	$-0.597778\pi$
$137$	−12.1825	−	3.26430i	−1.04082	−	0.278888i	−0.738455	+	0.674303i	$0.764444\pi$
$138$		0			0
$139$	17.5612	−	10.1390i	1.48952	−	0.859975i	0.489592	−	0.871952i	$-0.337146\pi$
$139$	17.5612	−	10.1390i	1.48952	−	0.859975i	0.999928	+	0.0119768i	$0.00381244\pi$
$140$	−0.677132	−	0.0947418i	−0.0572281	−	0.00800715i
$141$		0			0
$142$		−	0.0190856i		−	0.00160163i
$143$	0.692802	+	0.254112i	0.0579350	+	0.0212499i
$144$		0			0
$145$	8.80076	+	32.8449i	0.730863	+	2.72762i
$146$	−3.81857	−	2.20465i	−0.316027	−	0.182459i
$147$		0			0
$148$	−0.232370	−	0.232370i	−0.0191007	−	0.0191007i
$149$	2.91147	−	10.8658i	0.238517	−	0.890157i	−0.738015	−	0.674784i	$-0.764237\pi$
$149$	2.91147	−	10.8658i	0.238517	−	0.890157i	0.976532	−	0.215373i	$-0.0690967\pi$
$150$		0			0
$151$	−9.18076	+	9.18076i	−0.747120	+	0.747120i	−0.973937	−	0.226818i	$-0.927168\pi$
$151$	−9.18076	+	9.18076i	−0.747120	+	0.747120i	0.226818	+	0.973937i	$0.427168\pi$
$152$	−3.87334	+	2.23628i	−0.314170	+	0.181386i
$153$		0			0
$154$	0.600160	−	0.452829i	0.0483622	−	0.0364900i
$155$			13.9183i			1.11794i
$156$		0			0
$157$		−	20.3277i		−	1.62232i	−0.584821	−	0.811162i	$-0.698835\pi$
$157$		−	20.3277i		−	1.62232i	0.584821	−	0.811162i	$-0.301165\pi$
$158$	−17.0632	+	4.57208i	−1.35748	+	0.363735i
$159$		0			0
$160$	−0.730574	−	1.26539i	−0.0577569	−	0.100038i
$161$	−3.09511	+	7.30405i	−0.243929	+	0.575640i
$162$		0			0
$163$	0.193660	+	0.0518911i	0.0151686	+	0.00406442i	0.266395	−	0.963864i	$-0.414167\pi$
$163$	0.193660	+	0.0518911i	0.0151686	+	0.00406442i	−0.251227	+	0.967928i	$0.580834\pi$
$164$	−0.268613	−	0.268613i	−0.0209752	−	0.0209752i
$165$		0			0
$166$	3.31653	−	5.74439i	0.257412	−	0.445852i
$167$	13.5813	−	3.63909i	1.05095	−	0.281602i	0.308306	−	0.951287i	$-0.400238\pi$
$167$	13.5813	−	3.63909i	1.05095	−	0.281602i	0.742645	+	0.669686i	$0.233571\pi$
$168$		0			0
$169$	−4.38547	−	12.2380i	−0.337344	−	0.941382i
$170$	−11.2946			−0.866256
$171$		0			0
$172$	−0.0736451	+	0.127557i	−0.00561538	+	0.00972613i
$173$	−6.32817	−	10.9607i	−0.481122	−	0.833328i	0.518643	−	0.854991i	$-0.326437\pi$
$173$	−6.32817	−	10.9607i	−0.481122	−	0.833328i	−0.999765	+	0.0216628i	$0.993104\pi$
$174$		0			0
$175$	−20.4509	+	2.52377i	−1.54594	+	0.190779i
$176$	0.761164	+	0.203953i	0.0573749	+	0.0153736i
$177$		0			0
$178$	14.7343	−	8.50687i	1.10438	−	0.637617i
$179$	8.90908	+	5.14366i	0.665896	+	0.384455i	0.794520	−	0.607238i	$-0.207723\pi$
$179$	8.90908	+	5.14366i	0.665896	+	0.384455i	−0.128624	+	0.991693i	$0.541056\pi$
$180$		0			0
$181$	8.60644			0.639711			0.319856	−	0.947466i	$-0.396366\pi$
$181$	8.60644			0.639711			0.319856	+	0.947466i	$0.396366\pi$
$182$	−12.8997	−	3.00360i	−0.956189	−	0.222642i
$183$		0			0
$184$	−8.33276	+	2.23276i	−0.614299	+	0.164601i
$185$	−14.0833	−	8.13102i	−1.03543	−	0.597805i
$186$		0			0
$187$	−0.329208	+	0.329208i	−0.0240741	+	0.0240741i
$188$	−0.930255	−	0.249261i	−0.0678458	−	0.0181792i
$189$		0			0
$190$	−5.45761	+	5.45761i	−0.395936	+	0.395936i
$191$	−8.10759	−	14.0428i	−0.586645	−	1.01610i	−0.994668	−	0.103127i	$-0.967115\pi$
$191$	−8.10759	−	14.0428i	−0.586645	−	1.01610i	0.408023	−	0.912971i	$-0.366218\pi$
$192$		0			0
$193$	5.21705	+	19.4703i	0.375531	+	1.40150i	0.852567	+	0.522618i	$0.175045\pi$
$193$	5.21705	+	19.4703i	0.375531	+	1.40150i	−0.477035	+	0.878884i	$0.658289\pi$
$194$	11.2933			0.810814
$195$		0			0
$196$	0.363450	−	0.351841i	0.0259607	−	0.0251315i
$197$	−2.43284	+	0.651878i	−0.173333	+	0.0464444i	−0.344442	−	0.938808i	$-0.611932\pi$
$197$	−2.43284	+	0.651878i	−0.173333	+	0.0464444i	0.171109	+	0.985252i	$0.445265\pi$
$198$		0			0
$199$	−8.23179	−	14.2579i	−0.583536	−	1.01071i	−0.995056	−	0.0993137i	$-0.968335\pi$
$199$	−8.23179	−	14.2579i	−0.583536	−	1.01071i	0.411520	−	0.911401i	$-0.364998\pi$
$200$	−15.8453	−	15.8453i	−1.12043	−	1.12043i
$201$		0			0
$202$	−3.89302	+	14.5289i	−0.273912	+	1.02225i
$203$	−23.1635	−	9.81559i	−1.62576	−	0.688920i
$204$		0			0
$205$	−16.2799	−	9.39922i	−1.13704	−	0.656470i
$206$	−3.23092	+	0.865723i	−0.225109	+	0.0603178i
$207$		0			0
$208$	−5.83560	−	12.5962i	−0.404626	−	0.873386i
$209$			0.318150i			0.0220069i
$210$		0			0
$211$	−3.66647	+	6.35051i	−0.252410	+	0.437187i	−0.964189	−	0.265217i	$-0.914557\pi$
$211$	−3.66647	+	6.35051i	−0.252410	+	0.437187i	0.711779	+	0.702404i	$0.247890\pi$
$212$	−0.794788	+	0.458871i	−0.0545862	+	0.0315154i
$213$		0			0
$214$	−1.60130	+	5.97613i	−0.109463	+	0.408520i
$215$	−1.88647	+	7.04040i	−0.128656	+	0.480151i
$216$		0			0
$217$	−8.11833	−	6.33473i	−0.551108	−	0.430029i
$218$	20.4034	+	11.7799i	1.38190	+	0.797838i
$219$		0			0
$220$	−0.0528908			−0.00356590
$221$	8.16883	+	0.735149i	0.549495	+	0.0494515i
$222$		0			0
$223$	−0.683979	−	2.55265i	−0.0458026	−	0.170938i	0.939236	−	0.343273i	$-0.111536\pi$
$223$	−0.683979	−	2.55265i	−0.0458026	−	0.170938i	−0.985038	+	0.172335i	$0.944869\pi$
$224$	1.07060	+	0.149794i	0.0715323	+	0.0100085i
$225$		0			0
$226$	0.467975	+	0.467975i	0.0311293	+	0.0311293i
$227$	17.7461	+	4.75506i	1.17785	+	0.315604i	0.794074	−	0.607821i	$-0.207956\pi$
$227$	17.7461	+	4.75506i	1.17785	+	0.315604i	0.383777	+	0.923426i	$0.374623\pi$
$228$		0			0
$229$	5.79771	+	5.79771i	0.383124	+	0.383124i	0.872226	−	0.489103i	$-0.162676\pi$
$229$	5.79771	+	5.79771i	0.383124	+	0.383124i	−0.489103	+	0.872226i	$0.662676\pi$
$230$	−12.8925	+	7.44349i	−0.850107	+	0.490809i
$231$		0			0
$232$	−7.08079	−	26.4259i	−0.464877	−	1.73494i
$233$			21.0210i			1.37713i	0.725173	+	0.688567i	$0.241760\pi$
$233$			21.0210i			1.37713i	−0.725173	+	0.688567i	$0.758240\pi$
$234$		0			0
$235$	−47.6583			−3.10888
$236$	0.0369007	+	0.137715i	0.00240203	+	0.00896450i
$237$		0			0
$238$	5.14060	−	6.58798i	0.333216	−	0.427035i
$239$	−10.3794	−	10.3794i	−0.671386	−	0.671386i	0.286650	−	0.958036i	$-0.407458\pi$
$239$	−10.3794	−	10.3794i	−0.671386	−	0.671386i	−0.958036	+	0.286650i	$0.907458\pi$
$240$		0			0
$241$	−0.355487	+	1.32670i	−0.0228989	+	0.0854600i	−0.976430	−	0.215836i	$-0.930752\pi$
$241$	−0.355487	+	1.32670i	−0.0228989	+	0.0854600i	0.953531	+	0.301296i	$0.0974191\pi$
$242$	−10.7583	+	10.7583i	−0.691571	+	0.691571i
$243$		0			0
$244$	0.0354876	−	0.0614664i	0.00227186	−	0.00393498i
$245$	12.8664	−	21.4729i	0.822006	−	1.37185i
$246$		0			0
$247$	4.30245	−	3.59199i	0.273758	−	0.228553i
$248$		−	11.1982i		−	0.711084i
$249$		0			0
$250$	−11.9897	−	6.92225i	−0.758295	−	0.437802i
$251$	−1.76834	−	3.06285i	−0.111616	−	0.193325i	0.804806	−	0.593538i	$-0.202269\pi$
$251$	−1.76834	−	3.06285i	−0.111616	−	0.193325i	−0.916422	+	0.400213i	$0.868936\pi$
$252$		0			0
$253$	−0.158825	+	0.592742i	−0.00998523	+	0.0372654i
$254$	2.92310	+	0.783243i	0.183412	+	0.0491451i
$255$		0			0
$256$	0.866033	+	1.50001i	0.0541271	+	0.0937508i
$257$	10.0381	−	17.3866i	0.626163	−	1.08455i	−0.362152	−	0.932119i	$-0.617958\pi$
$257$	10.0381	−	17.3866i	0.626163	−	1.08455i	0.988315	−	0.152426i	$-0.0487087\pi$
$258$		0			0
$259$	11.1526	−	4.51388i	0.692987	−	0.280479i
$260$	0.597150	+	0.715260i	0.0370337	+	0.0443585i
$261$		0			0
$262$	−2.57755	−	9.61953i	−0.159241	−	0.594297i
$263$	−10.5381	+	18.2526i	−0.649809	+	1.12550i	0.333360	+	0.942800i	$0.391818\pi$
$263$	−10.5381	+	18.2526i	−0.649809	+	1.12550i	−0.983168	+	0.182702i	$0.941516\pi$
$264$		0			0
$265$	−32.1133	+	32.1133i	−1.97271	+	1.97271i
$266$	−0.699382	−	5.66731i	−0.0428819	−	0.347485i
$267$		0			0
$268$	−0.802164	+	0.802164i	−0.0489999	+	0.0489999i
$269$	21.4982	−	12.4120i	1.31077	−	0.756773i	0.328546	−	0.944488i	$-0.393441\pi$
$269$	21.4982	−	12.4120i	1.31077	−	0.756773i	0.982224	+	0.187715i	$0.0601081\pi$
$270$		0			0
$271$	−12.1049	+	3.24351i	−0.735323	+	0.197029i	−0.606999	−	0.794703i	$-0.707627\pi$
$271$	−12.1049	+	3.24351i	−0.735323	+	0.197029i	−0.128325	+	0.991732i	$0.540960\pi$
$272$	8.75848			0.531061
$273$		0			0
$274$	17.5113			1.05789
$275$	−1.53970	+	0.412560i	−0.0928472	+	0.0248783i
$276$		0			0
$277$	14.3673	−	8.29496i	0.863247	−	0.498396i	−0.00185106	−	0.999998i	$-0.500589\pi$
$277$	14.3673	−	8.29496i	0.863247	−	0.498396i	0.865098	+	0.501602i	$0.167256\pi$
$278$	−19.9082	+	19.9082i	−1.19401	+	1.19401i
$279$		0			0
$280$	27.0174	−	3.33412i	1.61460	−	0.199252i
$281$	5.40004	−	5.40004i	0.322140	−	0.322140i	−0.527448	−	0.849587i	$-0.676851\pi$
$281$	5.40004	−	5.40004i	0.322140	−	0.322140i	0.849587	+	0.527448i	$0.176851\pi$
$282$		0			0
$283$	−12.4721	+	21.6023i	−0.741390	+	1.28412i	0.210473	+	0.977600i	$0.432500\pi$
$283$	−12.4721	+	21.6023i	−0.741390	+	1.28412i	−0.951863	+	0.306525i	$0.900834\pi$
$284$	−0.000257102	0	0.000959517i	−1.52562e−5	0	5.69369e-5i
$285$		0			0
$286$	−1.02045	−	0.0918343i	−0.0603402	−	0.00543028i
$287$	12.8921	−	5.21792i	0.760994	−	0.308004i
$288$		0			0
$289$	5.91268	−	10.2411i	0.347805	−	0.602416i
$290$	−23.6057	−	40.8863i	−1.38618	−	2.40093i
$291$		0			0
$292$	−0.221676	−	0.0593978i	−0.0129726	−	0.00347599i
$293$	3.65015	−	13.6225i	0.213244	−	0.795838i	−0.773533	−	0.633756i	$-0.781512\pi$
$293$	3.65015	−	13.6225i	0.213244	−	0.795838i	0.986777	−	0.162082i	$-0.0518209\pi$
$294$		0			0
$295$	3.52767	+	6.11011i	0.205389	+	0.355744i
$296$	11.3310	+	6.54195i	0.658600	+	0.380243i
$297$		0			0
$298$			15.6185i			0.904756i
$299$	9.80901	−	4.54436i	0.567270	−	0.262807i
$300$		0			0
$301$	−3.24796	−	4.30471i	−0.187210	−	0.248119i
$302$	9.01337	−	15.6116i	0.518661	−	0.898348i
$303$		0			0
$304$	4.23214	−	4.23214i	0.242730	−	0.242730i
$305$	0.909040	−	3.39258i	0.0520515	−	0.194259i
$306$		0			0
$307$	−6.57661	−	6.57661i	−0.375347	−	0.375347i	0.494073	−	0.869420i	$-0.335507\pi$
$307$	−6.57661	−	6.57661i	−0.375347	−	0.375347i	−0.869420	+	0.494073i	$0.835507\pi$
$308$	0.0240726	−	0.0308505i	0.00137167	−	0.00175787i
$309$		0			0
$310$	−5.00155	−	18.6660i	−0.284069	−	1.06016i
$311$	−6.01960			−0.341340			−0.170670	−	0.985328i	$-0.554593\pi$
$311$	−6.01960			−0.341340			−0.170670	+	0.985328i	$0.554593\pi$
$312$		0			0
$313$			4.19182i			0.236935i	0.992958	+	0.118468i	$0.0377982\pi$
$313$			4.19182i			0.236935i	−0.992958	+	0.118468i	$0.962202\pi$
$314$	7.30479	+	27.2618i	0.412233	+	1.53847i
$315$		0			0
$316$	−0.796254	+	0.459718i	−0.0447928	+	0.0258611i
$317$	10.1411	+	10.1411i	0.569578	+	0.569578i	0.932010	−	0.362432i	$-0.118054\pi$
$317$	10.1411	+	10.1411i	0.569578	+	0.569578i	−0.362432	+	0.932010i	$0.618054\pi$
$318$		0			0
$319$	−1.87978	−	0.503685i	−0.105247	−	0.0282009i
$320$	20.9065	+	20.9065i	1.16871	+	1.16871i
$321$		0			0
$322$	1.52618	−	10.9078i	0.0850509	−	0.607870i
$323$	0.915214	+	3.41562i	0.0509239	+	0.190050i
$324$		0			0
$325$	22.9627	+	16.1639i	1.27374	+	0.896612i
$326$	−0.278368			−0.0154174
$327$		0			0
$328$	13.0983	+	7.56230i	0.723232	+	0.417558i
$329$	21.6911	−	27.7984i	1.19587	−	1.53258i
$330$		0			0
$331$	3.99969	−	14.9270i	0.219843	−	0.820465i	−0.764563	−	0.644550i	$-0.777045\pi$
$331$	3.99969	−	14.9270i	0.219843	−	0.820465i	0.984405	−	0.175915i	$-0.0562884\pi$
$332$	0.0893539	−	0.333473i	0.00490393	−	0.0183017i
$333$		0			0
$334$	−16.9064	+	9.76092i	−0.925077	+	0.534094i
$335$	−28.0691	+	48.6170i	−1.53358	+	2.65623i
$336$		0			0
$337$			32.5729i			1.77436i	0.461427	+	0.887178i	$0.347338\pi$
$337$			32.5729i			1.77436i	−0.461427	+	0.887178i	$0.652662\pi$
$338$	10.2792	+	14.8366i	0.559113	+	0.807007i
$339$		0			0
$340$	−0.567830	+	0.152150i	−0.0307949	+	0.00825147i
$341$	−0.689850	−	0.398285i	−0.0373574	−	0.0215683i
$342$		0			0
$343$	6.66883	+	17.2779i	0.360083	+	0.932920i
$344$	1.51779	−	5.66447i	0.0818337	−	0.305408i
$345$		0			0
$346$	12.4256	+	12.4256i	0.668004	+	0.668004i
$347$	11.6943	+	20.2551i	0.627783	+	1.08735i	0.987996	+	0.154481i	$0.0493706\pi$
$347$	11.6943	+	20.2551i	0.627783	+	1.08735i	−0.360213	+	0.932870i	$0.617296\pi$
$348$		0			0
$349$	21.3942	−	5.73255i	1.14520	−	0.306856i	0.364162	−	0.931336i	$-0.381356\pi$
$349$	21.3942	−	5.73255i	1.14520	−	0.306856i	0.781041	+	0.624479i	$0.214689\pi$
$350$	26.5202	−	10.7337i	1.41756	−	0.573743i
$351$		0			0
$352$	0.0836244			0.00445720
$353$	3.15762	+	11.7844i	0.168063	+	0.627220i	0.997630	+	0.0688124i	$0.0219210\pi$
$353$	3.15762	+	11.7844i	0.168063	+	0.627220i	−0.829566	+	0.558408i	$0.811412\pi$
$354$		0			0
$355$	−0.0245787	−	0.0425715i	−0.00130450	−	0.00225946i
$356$	0.626164	−	0.626164i	0.0331866	−	0.0331866i
$357$		0			0
$358$	−13.7965	−	3.69677i	−0.729169	−	0.195380i
$359$	−7.63230	+	7.63230i	−0.402818	+	0.402818i	−0.879225	−	0.476407i	$-0.841939\pi$
$359$	−7.63230	+	7.63230i	−0.402818	+	0.402818i	0.476407	+	0.879225i	$0.341939\pi$
$360$		0			0
$361$	−14.3618	−	8.29179i	−0.755884	−	0.436410i
$362$	−11.5423	+	3.09274i	−0.606648	+	0.162551i
$363$		0			0
$364$	−0.688987	+	0.0227676i	−0.0361127	+	0.00119335i
$365$	−11.3568			−0.594440
$366$		0			0
$367$	−29.9667	−	17.3013i	−1.56425	−	0.903118i	−0.996819	−	0.0796947i	$-0.974605\pi$
$367$	−29.9667	−	17.3013i	−1.56425	−	0.903118i	−0.567427	−	0.823423i	$-0.692061\pi$
$368$	9.99759	−	5.77211i	0.521160	−	0.300892i
$369$		0			0
$370$	21.8093	+	5.84380i	1.13381	+	0.303804i
$371$	−4.11526	−	33.3473i	−0.213654	−	1.73130i
$372$		0			0
$373$	7.12384	+	12.3388i	0.368858	+	0.638881i	0.989387	−	0.145302i	$-0.0464154\pi$
$373$	7.12384	+	12.3388i	0.368858	+	0.638881i	−0.620529	+	0.784183i	$0.713082\pi$
$374$	0.323206	−	0.559809i	0.0167126	−	0.0289471i
$375$		0			0
$376$	38.3442			1.97745
$377$	14.4117	+	31.1076i	0.742238	+	1.60212i
$378$		0			0
$379$	21.6859	−	5.81071i	1.11393	−	0.298476i	0.345504	−	0.938417i	$-0.387708\pi$
$379$	21.6859	−	5.81071i	1.11393	−	0.298476i	0.768424	+	0.639941i	$0.221041\pi$
$380$	−0.200859	+	0.347898i	−0.0103038	+	0.0178468i
$381$		0			0
$382$	15.9195	+	15.9195i	0.814515	+	0.814515i
$383$	13.1230	+	3.51630i	0.670554	+	0.179674i	0.578004	−	0.816034i	$-0.303832\pi$
$383$	13.1230	+	3.51630i	0.670554	+	0.179674i	0.0925494	+	0.995708i	$0.470498\pi$
$384$		0			0
$385$	0.755532	−	1.78296i	0.0385055	−	0.0908680i
$386$	−13.9934	−	24.2372i	−0.712244	−	1.23364i
$387$		0			0
$388$	0.567766	−	0.152132i	0.0288240	−	0.00772336i
$389$		−	20.6138i		−	1.04516i	−0.852590	−	0.522581i	$-0.824969\pi$
$389$		−	20.6138i		−	1.04516i	0.852590	−	0.522581i	$-0.175031\pi$
$390$		0			0
$391$			6.82049i			0.344927i
$392$	−10.3519	+	17.2763i	−0.522849	+	0.872587i
$393$		0			0
$394$	3.02848	−	1.74849i	0.152572	−	0.0880877i
$395$	−32.1726	+	32.1726i	−1.61878	+	1.61878i
$396$		0			0
$397$	4.36581	−	16.2934i	0.219114	−	0.817743i	−0.765564	−	0.643360i	$-0.777540\pi$
$397$	4.36581	−	16.2934i	0.219114	−	0.817743i	0.984678	−	0.174384i	$-0.0557933\pi$
$398$	16.1634	+	16.1634i	0.810199	+	0.810199i
$399$		0			0
$400$	25.9696	+	14.9935i	1.29848	+	0.749677i
$401$	−3.52338	−	13.1494i	−0.175949	−	0.656652i	−0.996388	−	0.0849175i	$-0.972937\pi$
$401$	−3.52338	−	13.1494i	−0.175949	−	0.656652i	0.820439	−	0.571735i	$-0.193729\pi$
$402$		0			0
$403$	2.40243	+	13.8258i	0.119674	+	0.688712i
$404$			0.782878i			0.0389496i
$405$		0			0
$406$	34.5923	+	4.84003i	1.71679	+	0.240206i
$407$	0.806018	−	0.465355i	0.0399528	−	0.0230668i
$408$		0			0
$409$	30.8141	+	8.25662i	1.52366	+	0.408263i	0.920945	−	0.389693i	$-0.127419\pi$
$409$	30.8141	+	8.25662i	1.52366	+	0.408263i	0.602715	+	0.797956i	$0.294086\pi$
$410$	25.2110	+	6.75526i	1.24508	+	0.333618i
$411$		0			0
$412$	−0.150771	+	0.0870475i	−0.00742794	+	0.00428852i
$413$	−5.16952	−	0.723300i	−0.254375	−	0.0355913i
$414$		0			0
$415$		−	17.0843i		−	0.838635i
$416$	−0.944140	−	1.13088i	−0.0462903	−	0.0554459i
$417$		0			0
$418$	−0.114328	−	0.426678i	−0.00559196	−	0.0208695i
$419$	−25.3302	−	14.6244i	−1.23746	−	0.714449i	−0.268888	−	0.963172i	$-0.586656\pi$
$419$	−25.3302	−	14.6244i	−1.23746	−	0.714449i	−0.968575	+	0.248722i	$0.919989\pi$
$420$		0			0
$421$	19.1090	+	19.1090i	0.931318	+	0.931318i	0.997788	−	0.0664703i	$-0.0211738\pi$
$421$	19.1090	+	19.1090i	0.931318	+	0.931318i	−0.0664703	+	0.997788i	$0.521174\pi$
$422$	2.63510	−	9.83434i	0.128275	−	0.478728i
$423$		0			0
$424$	25.8373	−	25.8373i	1.25477	−	1.25477i
$425$	−15.3432	+	8.85840i	−0.744254	+	0.429695i
$426$		0			0
$427$	1.56511	+	2.07432i	0.0757409	+	0.100384i
$428$			0.322018i			0.0155653i
$429$		0			0
$430$		−	10.1199i		−	0.488026i
$431$	26.6643	−	7.14467i	1.28437	−	0.344147i	0.448852	−	0.893606i	$-0.351833\pi$
$431$	26.6643	−	7.14467i	1.28437	−	0.344147i	0.835520	+	0.549460i	$0.185166\pi$
$432$		0			0
$433$	−11.9677	−	20.7287i	−0.575132	−	0.996157i	−0.996027	−	0.0890483i	$-0.971617\pi$
$433$	−11.9677	−	20.7287i	−0.575132	−	0.996157i	0.420896	−	0.907109i	$-0.361716\pi$
$434$	13.1640	+	5.57829i	0.631894	+	0.267767i
$435$		0			0
$436$	1.18446	+	0.317375i	0.0567253	+	0.0151995i
$437$	3.29570	+	3.29570i	0.157655	+	0.157655i
$438$		0			0
$439$	5.23894	−	9.07411i	0.250041	−	0.433083i	−0.713496	−	0.700659i	$-0.752889\pi$
$439$	5.23894	−	9.07411i	0.250041	−	0.433083i	0.963537	+	0.267576i	$0.0862226\pi$
$440$	2.03407	−	0.545027i	0.0969705	−	0.0259832i
$441$		0			0
$442$	−11.2196	+	1.94956i	−0.533660	+	0.0927312i
$443$	19.7645			0.939041			0.469521	−	0.882922i	$-0.344427\pi$
$443$	19.7645			0.939041			0.469521	+	0.882922i	$0.344427\pi$
$444$		0			0
$445$	21.9105	−	37.9502i	1.03866	−	1.79901i
$446$	1.83460	+	3.17761i	0.0868706	+	0.150464i
$447$		0			0
$448$	−21.7098	+	2.67913i	−1.02569	+	0.126577i
$449$	−27.2909	−	7.31258i	−1.28794	−	0.345102i	−0.451061	−	0.892493i	$-0.648954\pi$
$449$	−27.2909	−	7.31258i	−1.28794	−	0.345102i	−0.836877	+	0.547391i	$0.815621\pi$
$450$		0			0
$451$	0.931733	−	0.537936i	0.0438736	−	0.0253304i
$452$	0.0298313	+	0.0172231i	0.00140315	+	0.000810107i
$453$		0			0
$454$	−25.5084			−1.19717
$455$	−32.6417	+	9.91272i	−1.53026	+	0.464715i
$456$		0			0
$457$	−18.9311	+	5.07256i	−0.885558	+	0.237285i	−0.672804	−	0.739821i	$-0.734910\pi$
$457$	−18.9311	+	5.07256i	−0.885558	+	0.237285i	−0.212754	+	0.977106i	$0.568243\pi$
$458$	−9.85884	−	5.69201i	−0.460673	−	0.265970i
$459$		0			0
$460$	−0.547893	+	0.547893i	−0.0255456	+	0.0255456i
$461$	−14.1139	−	3.78182i	−0.657351	−	0.176137i	−0.0853010	−	0.996355i	$-0.527185\pi$
$461$	−14.1139	−	3.78182i	−0.657351	−	0.176137i	−0.572050	+	0.820218i	$0.693852\pi$
$462$		0			0
$463$	0.639781	−	0.639781i	0.0297332	−	0.0297332i	−0.692084	−	0.721817i	$-0.743307\pi$
$463$	0.639781	−	0.639781i	0.0297332	−	0.0297332i	0.721817	+	0.692084i	$0.243307\pi$
$464$	18.3052	+	31.7056i	0.849800	+	1.47190i
$465$		0			0
$466$	−7.55395	−	28.1917i	−0.349930	−	1.30596i
$467$	−18.2232			−0.843268			−0.421634	−	0.906766i	$-0.638543\pi$
$467$	−18.2232			−0.843268			−0.421634	+	0.906766i	$0.638543\pi$
$468$		0			0
$469$	−15.5823	−	38.4998i	−0.719526	−	1.77775i
$470$	63.9154	−	17.1261i	2.94820	−	0.789967i
$471$		0			0
$472$	−2.83825	−	4.91599i	−0.130641	−	0.226277i
$473$	−0.294970	−	0.294970i	−0.0135627	−	0.0135627i
$474$		0			0
$475$	−3.13349	+	11.6943i	−0.143774	+	0.536573i
$476$	0.169694	−	0.400456i	0.00777792	−	0.0183549i
$477$		0			0
$478$	17.6498	+	10.1901i	0.807284	+	0.466086i
$479$	37.9467	−	10.1678i	1.73383	−	0.464578i	0.752770	−	0.658284i	$-0.228717\pi$
$479$	37.9467	−	10.1678i	1.73383	−	0.464578i	0.981060	+	0.193706i	$0.0620507\pi$
$480$		0			0
$481$	−15.3933	−	5.64607i	−0.701873	−	0.257439i
$482$		−	1.90700i		−	0.0868616i
$483$		0			0
$484$	−0.395943	+	0.685794i	−0.0179974	+	0.0311725i
$485$	25.1905	−	14.5437i	1.14384	−	0.660396i
$486$		0			0
$487$	5.80987	−	21.6827i	0.263270	−	0.982538i	−0.700030	−	0.714113i	$-0.746830\pi$
$487$	5.80987	−	21.6827i	0.263270	−	0.982538i	0.963301	−	0.268425i	$-0.0865031\pi$
$488$	−0.731383	+	2.72956i	−0.0331081	+	0.123561i
$489$		0			0
$490$	−9.53910	+	33.4213i	−0.430932	+	1.50982i
$491$	−5.46145	−	3.15317i	−0.246472	−	0.142301i	0.371676	−	0.928363i	$-0.378783\pi$
$491$	−5.46145	−	3.15317i	−0.246472	−	0.142301i	−0.618148	+	0.786062i	$0.712117\pi$
$492$		0			0
$493$	−21.6300			−0.974166
$494$	−4.47931	+	6.36339i	−0.201534	+	0.286302i
$495$		0			0
$496$	3.87849	+	14.4747i	0.174149	+	0.649934i
$497$	0.0360181	+	0.00503952i	0.00161563	+	0.000226053i
$498$		0			0
$499$	−0.186545	−	0.186545i	−0.00835090	−	0.00835090i	0.702919	−	0.711270i	$-0.251880\pi$
$499$	−0.186545	−	0.186545i	−0.00835090	−	0.00835090i	−0.711270	+	0.702919i	$0.751880\pi$
$500$	−0.696025	−	0.186499i	−0.0311272	−	0.00834050i
$501$		0			0
$502$	3.47219	+	3.47219i	0.154971	+	0.154971i
$503$	−14.8498	+	8.57353i	−0.662119	+	0.382275i	−0.793084	−	0.609112i	$-0.791526\pi$
$503$	−14.8498	+	8.57353i	−0.662119	+	0.382275i	0.130965	+	0.991387i	$0.458193\pi$
$504$		0			0
$505$	10.0270	+	37.4212i	0.446195	+	1.66522i
$506$		−	0.852012i		−	0.0378765i
$507$		0			0
$508$	0.157509			0.00698831
$509$	−4.12567	−	15.3972i	−0.182867	−	0.682470i	−0.995077	−	0.0991045i	$-0.968402\pi$
$509$	−4.12567	−	15.3972i	−0.182867	−	0.682470i	0.812210	−	0.583366i	$-0.198264\pi$
$510$		0			0
$511$	5.16889	−	6.62424i	0.228658	−	0.293039i
$512$	−16.7789	−	16.7789i	−0.741531	−	0.741531i
$513$		0			0
$514$	−7.21446	+	26.9247i	−0.318216	+	1.18760i
$515$	−6.09188	+	6.09188i	−0.268440	+	0.268440i
$516$		0			0
$517$	1.36379	−	2.36215i	0.0599793	−	0.103887i
$518$	−13.3349	+	10.0614i	−0.585900	+	0.442071i
$519$		0			0
$520$	−30.3357	−	21.3539i	−1.33031	−	0.936430i
$521$			5.95318i			0.260814i	0.991461	+	0.130407i	$0.0416283\pi$
$521$			5.95318i			0.260814i	−0.991461	+	0.130407i	$0.958372\pi$
$522$		0			0
$523$	−7.98659	−	4.61106i	−0.349229	−	0.201628i	0.315116	−	0.949053i	$-0.397956\pi$
$523$	−7.98659	−	4.61106i	−0.349229	−	0.201628i	−0.664346	+	0.747425i	$0.731290\pi$
$524$	−0.259170	−	0.448895i	−0.0113219	−	0.0196101i
$525$		0			0
$526$	7.57379	−	28.2658i	0.330233	−	1.23245i
$527$	−8.55188	−	2.29147i	−0.372526	−	0.0998179i
$528$		0			0
$529$	−7.00508	−	12.1332i	−0.304569	−	0.527528i
$530$	31.5278	−	54.6078i	1.36948	−	2.37201i
$531$		0			0
$532$	−0.111505	−	0.275500i	−0.00483437	−	0.0119444i
$533$	−17.7942	−	6.52669i	−0.770751	−	0.282702i
$534$		0			0
$535$	4.12435	+	15.3923i	0.178311	+	0.665467i
$536$	22.5834	−	39.1156i	0.975455	−	1.68954i
$537$		0			0
$538$	−24.3714	+	24.3714i	−1.05073	+	1.05073i
$539$	0.696103	+	1.25218i	0.0299833	+	0.0539354i
$540$		0			0
$541$	−18.1277	+	18.1277i	−0.779369	+	0.779369i	−0.979723	−	0.200354i	$-0.935791\pi$
$541$	−18.1277	+	18.1277i	−0.779369	+	0.779369i	0.200354	+	0.979723i	$0.435791\pi$
$542$	15.0686	−	8.69987i	0.647253	−	0.373691i
$543$		0			0
$544$	0.897782	−	0.240560i	0.0384921	−	0.0103139i
$545$	60.6815			2.59931
$546$		0			0
$547$	−9.47939			−0.405309			−0.202655	−	0.979250i	$-0.564957\pi$
$547$	−9.47939			−0.405309			−0.202655	+	0.979250i	$0.564957\pi$
$548$	0.880370	−	0.235894i	0.0376075	−	0.0100769i
$549$		0			0
$550$	1.91666	−	1.10659i	0.0817267	−	0.0471850i
$551$	−10.4517	+	10.4517i	−0.445259	+	0.445259i
$552$		0			0
$553$	−4.12286	−	33.4088i	−0.175322	−	1.42069i
$554$	−16.2875	+	16.2875i	−0.691988	+	0.691988i
$555$		0			0
$556$	−0.732690	+	1.26906i	−0.0310730	+	0.0538200i
$557$	4.20935	+	15.7095i	0.178356	+	0.665633i	0.995956	+	0.0898459i	$0.0286375\pi$
$557$	4.20935	+	15.7095i	0.178356	+	0.665633i	−0.817600	+	0.575787i	$0.804696\pi$
$558$		0			0
$559$	−0.658691	+	7.31925i	−0.0278597	+	0.309571i
$560$	−33.7678	+	13.6672i	−1.42695	+	0.577543i
$561$		0			0
$562$	−5.30159	+	9.18262i	−0.223634	+	0.387345i
$563$	8.25217	+	14.2932i	0.347788	+	0.602386i	0.985856	−	0.167594i	$-0.0535997\pi$
$563$	8.25217	+	14.2932i	0.347788	+	0.602386i	−0.638068	+	0.769980i	$0.720266\pi$
$564$		0			0
$565$	1.64651	+	0.441182i	0.0692693	+	0.0185607i
$566$	8.96375	−	33.4532i	0.376774	−	1.40614i
$567$		0			0
$568$	0.0197752	+	0.0342516i	0.000829748	+	0.00143717i
$569$	17.3607	+	10.0232i	0.727797	+	0.420194i	0.817616	−	0.575764i	$-0.195295\pi$
$569$	17.3607	+	10.0232i	0.727797	+	0.420194i	−0.0898186	+	0.995958i	$0.528629\pi$
$570$		0			0
$571$			37.7943i			1.58164i	0.612046	+	0.790822i	$0.290347\pi$
$571$			37.7943i			1.58164i	−0.612046	+	0.790822i	$0.709653\pi$
$572$	−0.0525394	+	0.00912950i	−0.00219678	+	0.000381724i
$573$		0			0
$574$	−15.4147	+	11.6306i	−0.643398	+	0.485453i
$575$	−11.6759	+	20.2233i	−0.486920	+	0.843370i
$576$		0			0
$577$	−7.30060	+	7.30060i	−0.303928	+	0.303928i	−0.842548	−	0.538621i	$-0.818946\pi$
$577$	−7.30060	+	7.30060i	−0.303928	+	0.303928i	0.538621	+	0.842548i	$0.318946\pi$
$578$	−4.24947	+	15.8592i	−0.176755	+	0.659657i
$579$		0			0
$580$	−1.73755	−	1.73755i	−0.0721477	−	0.0721477i
$581$	9.96504	+	7.77571i	0.413419	+	0.322591i
$582$		0			0
$583$	−0.672722	−	2.51063i	−0.0278613	−	0.103980i
$584$	9.13726			0.378102
$585$		0			0
$586$			19.5812i			0.808890i
$587$	−5.01367	−	18.7113i	−0.206936	−	0.772296i	−0.988851	−	0.148911i	$-0.952423\pi$
$587$	−5.01367	−	18.7113i	−0.206936	−	0.772296i	0.781915	−	0.623386i	$-0.214243\pi$
$588$		0			0
$589$	−5.23956	+	3.02506i	−0.215892	+	0.124645i
$590$	−6.92671	−	6.92671i	−0.285168	−	0.285168i
$591$		0			0
$592$	−16.9122	−	4.53161i	−0.695088	−	0.186248i
$593$	11.9510	+	11.9510i	0.490769	+	0.490769i	0.908548	−	0.417780i	$-0.137192\pi$
$593$	11.9510	+	11.9510i	0.490769	+	0.490769i	−0.417780	+	0.908548i	$0.637192\pi$
$594$		0			0
$595$	2.98232	−	21.3150i	0.122263	−	0.873831i
$596$	0.210397	+	0.785213i	0.00861820	+	0.0321636i
$597$		0			0
$598$	−11.5220	+	9.61942i	−0.471171	+	0.393367i
$599$	−14.2777			−0.583372			−0.291686	−	0.956514i	$-0.594216\pi$
$599$	−14.2777			−0.583372			−0.291686	+	0.956514i	$0.594216\pi$
$600$		0			0
$601$	20.5084	+	11.8405i	0.836556	+	0.482986i	0.856092	−	0.516824i	$-0.172886\pi$
$601$	20.5084	+	11.8405i	0.836556	+	0.482986i	−0.0195364	+	0.999809i	$0.506219\pi$
$602$	5.90281	+	4.60596i	0.240581	+	0.187725i
$603$		0			0
$604$	0.242838	−	0.906285i	0.00988095	−	0.0368762i
$605$	−10.1424	+	37.8518i	−0.412346	+	1.53890i
$606$		0			0
$607$	12.8523	−	7.42026i	0.521657	−	0.301179i	−0.215955	−	0.976403i	$-0.569287\pi$
$607$	12.8523	−	7.42026i	0.521657	−	0.301179i	0.737612	+	0.675224i	$0.235953\pi$
$608$	0.317573	−	0.550052i	0.0128793	−	0.0223076i
$609$		0			0
$610$			4.87652i			0.197445i
$611$	−47.3416	+	8.22630i	−1.91524	+	0.332801i
$612$		0			0
$613$	15.9485	−	4.27337i	0.644152	−	0.172600i	0.0780686	−	0.996948i	$-0.475125\pi$
$613$	15.9485	−	4.27337i	0.644152	−	0.172600i	0.566083	+	0.824348i	$0.308458\pi$
$614$	11.1833	+	6.45671i	0.451323	+	0.260571i
$615$		0			0
$616$	−0.607876	+	1.43451i	−0.0244920	+	0.0577980i
$617$	−1.60910	+	6.00524i	−0.0647799	+	0.241762i	−0.990722	−	0.135903i	$-0.956606\pi$
$617$	−1.60910	+	6.00524i	−0.0647799	+	0.241762i	0.925942	+	0.377665i	$0.123273\pi$
$618$		0			0
$619$	19.0180	+	19.0180i	0.764399	+	0.764399i	0.977114	−	0.212715i	$-0.0682306\pi$
$619$	19.0180	+	19.0180i	0.764399	+	0.764399i	−0.212715	+	0.977114i	$0.568231\pi$
$620$	−0.502901	−	0.871050i	−0.0201970	−	0.0349822i
$621$		0			0
$622$	8.07300	−	2.16316i	0.323698	−	0.0867346i
$623$	12.1635	+	30.0527i	0.487320	+	1.20404i
$624$		0			0
$625$	3.28341			0.131336
$626$	−1.50634	−	5.62173i	−0.0602053	−	0.224689i
$627$		0			0
$628$	0.734488	+	1.27217i	0.0293093	+	0.0507652i
$629$	7.31464	−	7.31464i	0.291654	−	0.291654i
$630$		0			0
$631$	−31.4581	−	8.42917i	−1.25233	−	0.335560i	−0.429092	−	0.903261i	$-0.641166\pi$
$631$	−31.4581	−	8.42917i	−1.25233	−	0.335560i	−0.823235	+	0.567701i	$0.807833\pi$
$632$	25.8850	−	25.8850i	1.02965	−	1.02965i
$633$		0			0
$634$	−17.2446	−	9.95615i	−0.684869	−	0.395409i
$635$	7.52884	−	2.01735i	0.298773	−	0.0800559i
$636$		0			0
$637$	9.07450	−	23.5511i	0.359545	−	0.933128i
$638$	2.70201			0.106973
$639$		0			0
$640$	−33.0202	−	19.0642i	−1.30524	−	0.753579i
$641$	−10.6137	+	6.12780i	−0.419214	+	0.242034i	−0.694741	−	0.719260i	$-0.744481\pi$
$641$	−10.6137	+	6.12780i	−0.419214	+	0.242034i	0.275527	+	0.961293i	$0.411148\pi$
$642$		0			0
$643$	−10.2233	−	2.73933i	−0.403169	−	0.108029i	0.0515356	−	0.998671i	$-0.483588\pi$
$643$	−10.2233	−	2.73933i	−0.403169	−	0.108029i	−0.454704	+	0.890642i	$0.650255\pi$
$644$	−0.0702114	−	0.568945i	−0.00276672	−	0.0224196i
$645$		0			0
$646$	−2.45482	−	4.25188i	−0.0965837	−	0.167288i
$647$	12.5880	−	21.8030i	0.494884	−	0.857164i	−0.505099	−	0.863061i	$-0.668544\pi$
$647$	12.5880	−	21.8030i	0.494884	−	0.857164i	0.999983	+	0.00589775i	$0.00187732\pi$
$648$		0			0
$649$	−0.403791			−0.0158502
$650$	−36.6043	−	13.4260i	−1.43574	−	0.526612i
$651$		0			0
$652$	−0.0139948	+	0.00374990i	−0.000548080	+	0.000146857i
$653$	−5.72589	+	9.91753i	−0.224071	+	0.388103i	−0.956040	−	0.293235i	$-0.905268\pi$
$653$	−5.72589	+	9.91753i	−0.224071	+	0.388103i	0.731969	+	0.681338i	$0.238602\pi$
$654$		0			0
$655$	−18.1376	−	18.1376i	−0.708693	−	0.708693i
$656$	−19.5500	−	5.23841i	−0.763300	−	0.204526i
$657$		0			0
$658$	−19.1009	+	45.0757i	−0.744632	+	1.75723i
$659$	−10.2755	−	17.7977i	−0.400276	−	0.693298i	0.593483	−	0.804846i	$-0.297752\pi$
$659$	−10.2755	−	17.7977i	−0.400276	−	0.693298i	−0.993759	+	0.111548i	$0.964419\pi$
$660$		0			0
$661$	−0.197372	+	0.0528857i	−0.00767689	+	0.00205702i	−0.262655	−	0.964890i	$-0.584598\pi$
$661$	−0.197372	+	0.0528857i	−0.00767689	+	0.00205702i	0.254979	+	0.966947i	$0.417932\pi$
$662$			21.4562i			0.833921i
$663$		0			0
$664$			13.7454i			0.533427i
$665$	−8.85846	−	11.7406i	−0.343517	−	0.455281i
$666$		0			0
$667$	−24.6901	+	14.2549i	−0.956006	+	0.551950i
$668$	−0.718471	+	0.718471i	−0.0277985	+	0.0277985i
$669$		0			0
$670$	20.1733	−	75.2879i	0.779364	−	2.90863i
$671$	0.142138	+	0.142138i	0.00548718	+	0.00548718i
$672$		0			0
$673$	22.6738	+	13.0907i	0.874010	+	0.504610i	0.868679	−	0.495376i	$-0.164970\pi$
$673$	22.6738	+	13.0907i	0.874010	+	0.504610i	0.00533138	+	0.999986i	$0.498303\pi$
$674$	−11.7051	−	43.6841i	−0.450864	−	1.68265i
$675$		0			0
$676$	0.716644	+	0.607434i	0.0275632	+	0.0233628i
$677$		−	17.3226i		−	0.665762i	−0.942969	−	0.332881i	$-0.891979\pi$
$677$		−	17.3226i		−	0.665762i	0.942969	−	0.332881i	$-0.108021\pi$
$678$		0			0
$679$	−2.98199	+	21.3127i	−0.114438	+	0.817905i
$680$	20.2697	−	11.7027i	0.777306	−	0.448778i
$681$		0			0
$682$	1.06830	+	0.286249i	0.0409071	+	0.0109610i
$683$	33.8713	+	9.07578i	1.29605	+	0.347275i	0.839954	−	0.542657i	$-0.182582\pi$
$683$	33.8713	+	9.07578i	1.29605	+	0.347275i	0.456094	+	0.889932i	$0.349248\pi$
$684$		0			0
$685$	39.0600	−	22.5513i	1.49240	−	0.861640i
$686$	−15.1526	−	20.7753i	−0.578527	−	0.793205i
$687$		0			0
$688$			7.84757i			0.299186i
$689$	−26.3569	+	37.4431i	−1.00412	+	1.42647i
$690$		0			0
$691$	4.51121	+	16.8361i	0.171614	+	0.640474i	0.997104	+	0.0760557i	$0.0242327\pi$
$691$	4.51121	+	16.8361i	0.171614	+	0.640474i	−0.825489	+	0.564418i	$0.809101\pi$
$692$	0.792075	+	0.457305i	0.0301102	+	0.0173841i
$693$		0			0
$694$	−22.9622	−	22.9622i	−0.871631	−	0.871631i
$695$	−18.7684	+	70.0445i	−0.711925	+	2.65694i
$696$		0			0
$697$	8.45551	−	8.45551i	0.320275	−	0.320275i
$698$	−26.6321	+	15.3761i	−1.00804	+	0.581993i
$699$		0			0
$700$	1.18869	−	0.896886i	0.0449284	−	0.0338991i
$701$		−	18.7752i		−	0.709130i	−0.935031	−	0.354565i	$-0.884629\pi$
$701$		−	18.7752i		−	0.709130i	0.935031	−	0.354565i	$-0.115371\pi$
$702$		0			0
$703$		−	7.06894i		−	0.266610i
$704$	−1.63448	+	0.437957i	−0.0616018	+	0.0165061i
$705$		0			0
$706$	−8.46949	−	14.6696i	−0.318754	−	0.552097i
$707$	−26.3909	−	11.1832i	−0.992533	−	0.420588i
$708$		0			0
$709$	−0.672100	−	0.180089i	−0.0252412	−	0.00676337i	0.246176	−	0.969225i	$-0.420826\pi$
$709$	−0.672100	−	0.180089i	−0.0252412	−	0.00676337i	−0.271418	+	0.962462i	$0.587492\pi$
$710$	0.0482611	+	0.0482611i	0.00181121	+	0.00181121i
$711$		0			0
$712$	−17.6285	+	30.5334i	−0.660655	+	1.14429i
$713$	−11.2719	+	3.02030i	−0.422136	+	0.113111i
$714$		0			0
$715$	−2.39443	+	1.10930i	−0.0895467	+	0.0414856i
$716$	−0.743412			−0.0277826
$717$		0			0
$718$	7.49315	−	12.9785i	0.279642	−	0.484354i
$719$	−15.1031	−	26.1593i	−0.563249	−	0.975576i	−0.997210	−	0.0746442i	$-0.976218\pi$
$719$	−15.1031	−	26.1593i	−0.563249	−	0.975576i	0.433961	−	0.900931i	$-0.357115\pi$
$720$		0			0
$721$	−0.780663	−	6.32595i	−0.0290734	−	0.235591i
$722$	22.2406	+	5.95934i	0.827708	+	0.221784i
$723$		0			0
$724$	−0.538619	+	0.310972i	−0.0200176	+	0.0115572i
$725$	−64.1346	−	37.0281i	−2.38190	−	1.37519i
$726$		0			0
$727$	−8.42295			−0.312390			−0.156195	−	0.987726i	$-0.549923\pi$
$727$	−8.42295			−0.312390			−0.156195	+	0.987726i	$0.549923\pi$
$728$	26.2624	−	7.97544i	0.973348	−	0.295589i
$729$		0			0
$730$	15.2308	−	4.08107i	0.563716	−	0.151047i
$731$	−4.01529	−	2.31823i	−0.148511	−	0.0857428i
$732$		0			0
$733$	22.1020	−	22.1020i	0.816357	−	0.816357i	−0.169221	−	0.985578i	$-0.554125\pi$
$733$	22.1020	−	22.1020i	0.816357	−	0.816357i	0.985578	+	0.169221i	$0.0541253\pi$
$734$	46.4061	+	12.4345i	1.71288	+	0.458965i
$735$		0			0
$736$	0.866260	−	0.866260i	0.0319308	−	0.0319308i
$737$	−1.60645	−	2.78245i	−0.0591743	−	0.102493i
$738$		0			0
$739$	13.4932	+	50.3573i	0.496356	+	1.85242i	0.522301	+	0.852761i	$0.325074\pi$
$739$	13.4932	+	50.3573i	0.496356	+	1.85242i	−0.0259454	+	0.999663i	$0.508260\pi$
$740$	1.17517			0.0432003
$741$		0			0
$742$	17.5025	+	43.2438i	0.642536	+	1.58753i
$743$	−39.2722	+	10.5230i	−1.44076	+	0.386050i	−0.892799	−	0.450456i	$-0.851261\pi$
$743$	−39.2722	+	10.5230i	−1.44076	+	0.386050i	−0.547958	+	0.836506i	$0.684595\pi$
$744$		0			0
$745$	20.1138	+	34.8381i	0.736911	+	1.27637i
$746$	−13.9879	−	13.9879i	−0.512134	−	0.512134i
$747$		0			0
$748$	0.00870782	−	0.0324980i	0.000318389	−	0.00118825i
$749$	−10.8553	−	4.59994i	−0.396643	−	0.168078i
$750$		0			0
$751$	34.2507	+	19.7747i	1.24983	+	0.721588i	0.971075	−	0.238775i	$-0.0767459\pi$
$751$	34.2507	+	19.7747i	1.24983	+	0.721588i	0.278752	+	0.960363i	$0.410079\pi$
$752$	−49.5637	+	13.2805i	−1.80740	+	0.484292i
$753$		0			0
$754$	−30.5063	−	36.5401i	−1.11097	−	1.33071i
$755$		−	46.4302i		−	1.68977i
$756$		0			0
$757$	10.7369	−	18.5969i	0.390241	−	0.675917i	−0.602240	−	0.798315i	$-0.705725\pi$
$757$	10.7369	−	18.5969i	0.390241	−	0.675917i	0.992481	+	0.122398i	$0.0390584\pi$
$758$	−26.9953	+	15.5857i	−0.980512	+	0.566099i
$759$		0			0
$760$	4.13960	−	15.4492i	0.150159	−	0.560402i
$761$	5.26977	−	19.6670i	0.191029	−	0.712930i	−0.802230	−	0.597015i	$-0.796353\pi$
$761$	5.26977	−	19.6670i	0.191029	−	0.712930i	0.993259	−	0.115915i	$-0.0369800\pi$
$762$		0			0
$763$	−27.6185	+	35.3947i	−0.999856	+	1.28137i
$764$	1.01480	+	0.585894i	0.0367141	+	0.0211969i
$765$		0			0
$766$	−18.8631			−0.681551
$767$	4.55890	+	5.46060i	0.164612	+	0.197171i
$768$		0			0
$769$	−11.7253	−	43.7592i	−0.422823	−	1.57800i	−0.768631	−	0.639693i	$-0.779062\pi$
$769$	−11.7253	−	43.7592i	−0.422823	−	1.57800i	0.345807	−	0.938306i	$-0.387605\pi$
$770$	−0.372550	+	2.66266i	−0.0134258	+	0.0959557i
$771$		0			0
$772$	−1.03001	−	1.03001i	−0.0370708	−	0.0370708i
$773$	19.0521	+	5.10499i	0.685256	+	0.183614i	0.584617	−	0.811309i	$-0.301245\pi$
$773$	19.0521	+	5.10499i	0.685256	+	0.183614i	0.100638	+	0.994923i	$0.467911\pi$
$774$		0			0
$775$	−21.4342	−	21.4342i	−0.769940	−	0.769940i
$776$	−20.2674	+	11.7014i	−0.727557	+	0.420055i
$777$		0			0
$778$	7.40762	+	27.6456i	0.265576	+	0.991143i
$779$		−	8.17149i		−	0.292774i
$780$		0			0
$781$	0.00281338			0.000100670
$782$	−2.45096	−	9.14710i	−0.0876461	−	0.327100i
$783$		0			0
$784$	7.39716	−	25.9168i	0.264184	−	0.925598i
$785$	51.4020	+	51.4020i	1.83461	+	1.83461i
$786$		0			0
$787$	−6.36046	+	23.7376i	−0.226726	+	0.846153i	0.754980	+	0.655748i	$0.227647\pi$
$787$	−6.36046	+	23.7376i	−0.226726	+	0.846153i	−0.981706	+	0.190405i	$0.939020\pi$
$788$	0.128701	−	0.128701i	0.00458479	−	0.00458479i
$789$		0			0
$790$	31.5860	−	54.7086i	1.12378	−	1.94644i
$791$	−1.00673	+	0.759590i	−0.0357951	+	0.0270079i
$792$		0			0
$793$	0.317406	−	3.52695i	0.0112714	−	0.125246i
$794$			23.4203i			0.831155i
$795$		0			0
$796$	1.03034	+	0.594870i	0.0365196	+	0.0210846i
$797$	10.4117	+	18.0336i	0.368802	+	0.638783i	0.989378	−	0.145362i	$-0.0464348\pi$
$797$	10.4117	+	18.0336i	0.368802	+	0.638783i	−0.620577	+	0.784146i	$0.713102\pi$
$798$		0			0
$799$	7.84634	−	29.2829i	0.277584	−	1.03596i
$800$	3.07380	+	0.823623i	0.108675	+	0.0291195i
$801$		0			0
$802$	9.45056	+	16.3688i	0.333711	+	0.578004i
$803$	0.324985	−	0.562890i	0.0114685	−	0.0198640i
$804$		0			0
$805$	−10.6430	−	26.2960i	−0.375118	−	0.926814i
$806$	−8.19027	−	17.6787i	−0.288490	−	0.622706i
$807$		0			0
$808$	−8.06737	−	30.1078i	−0.283809	−	1.05919i
$809$	8.68330	−	15.0399i	0.305289	−	0.528776i	−0.672037	−	0.740518i	$-0.734580\pi$
$809$	8.68330	−	15.0399i	0.305289	−	0.528776i	0.977326	+	0.211742i	$0.0679137\pi$
$810$		0			0
$811$	9.89362	−	9.89362i	0.347412	−	0.347412i	−0.511733	−	0.859145i	$-0.670996\pi$
$811$	9.89362	−	9.89362i	0.347412	−	0.347412i	0.859145	+	0.511733i	$0.170996\pi$
$812$	1.80431	−	0.222663i	0.0633189	−	0.00781395i
$813$		0			0
$814$	−0.913740	+	0.913740i	−0.0320266	+	0.0320266i
$815$	−0.620918	+	0.358487i	−0.0217498	+	0.0125573i
$816$		0			0
$817$	−3.06039	+	0.820029i	−0.107069	+	0.0286892i
$818$	−44.2924			−1.54865
$819$		0			0
$820$	1.35847			0.0474397
$821$	−1.09064	+	0.292235i	−0.0380635	+	0.0101991i	−0.277801	−	0.960639i	$-0.589605\pi$
$821$	−1.09064	+	0.292235i	−0.0380635	+	0.0101991i	0.239737	+	0.970838i	$0.422939\pi$
$822$		0			0
$823$	−18.7452	+	10.8226i	−0.653417	+	0.377250i	−0.789764	−	0.613411i	$-0.789797\pi$
$823$	−18.7452	+	10.8226i	−0.653417	+	0.377250i	0.136347	+	0.990661i	$0.456464\pi$
$824$	4.90132	−	4.90132i	0.170746	−	0.170746i
$825$		0			0
$826$	7.19286	−	0.887645i	0.250272	−	0.0308851i
$827$	22.8457	−	22.8457i	0.794421	−	0.794421i	−0.187788	−	0.982210i	$-0.560132\pi$
$827$	22.8457	−	22.8457i	0.794421	−	0.794421i	0.982210	+	0.187788i	$0.0601318\pi$
$828$		0			0
$829$	−23.5978	+	40.8725i	−0.819585	+	1.41956i	0.0864042	+	0.996260i	$0.472462\pi$
$829$	−23.5978	+	40.8725i	−0.819585	+	1.41956i	−0.905989	+	0.423302i	$0.860871\pi$
$830$	6.13927	+	22.9121i	0.213097	+	0.795290i
$831$		0			0
$832$	24.3763	+	17.1589i	0.845096	+	0.594879i
$833$	11.0754	+	11.4408i	0.383740	+	0.396401i
$834$		0			0
$835$	−25.1405	+	43.5446i	−0.870023	+	1.50692i
$836$	−0.0114956	−	0.0199109i	−0.000397582	−	0.000688632i
$837$		0			0
$838$	39.2262	+	10.5106i	1.35505	+	0.363083i
$839$	−6.00349	+	22.4053i	−0.207263	+	0.773518i	0.781484	+	0.623925i	$0.214463\pi$
$839$	−6.00349	+	22.4053i	−0.207263	+	0.773518i	−0.988748	+	0.149593i	$0.952204\pi$
$840$		0			0
$841$	−30.7068	−	53.1857i	−1.05885	−	1.83399i
$842$	−32.4944	−	18.7606i	−1.11983	−	0.646535i
$843$		0			0
$844$		−	0.529914i		−	0.0182404i
$845$	42.0352	+	19.8564i	1.44605	+	0.683080i
$846$		0			0
$847$	−17.4623	−	23.1437i	−0.600011	−	0.795227i
$848$	−24.4485	+	42.3460i	−0.839564	+	1.45417i
$849$		0			0
$850$	17.3938	−	17.3938i	0.596601	−	0.596601i
$851$	3.52891	−	13.1701i	0.120969	−	0.451464i
$852$		0			0
$853$	−11.1326	−	11.1326i	−0.381173	−	0.381173i	0.490352	−	0.871525i	$-0.336868\pi$
$853$	−11.1326	−	11.1326i	−0.381173	−	0.381173i	−0.871525	+	0.490352i	$0.836868\pi$
$854$	−2.84441	−	2.21949i	−0.0973337	−	0.0759495i
$855$		0			0
$856$	−3.31831	−	12.3841i	−0.113418	−	0.423281i
$857$	−13.9305			−0.475858			−0.237929	−	0.971283i	$-0.576469\pi$
$857$	−13.9305			−0.475858			−0.237929	+	0.971283i	$0.576469\pi$
$858$		0			0
$859$			39.1906i			1.33717i	0.743638	+	0.668583i	$0.233099\pi$
$859$			39.1906i			1.33717i	−0.743638	+	0.668583i	$0.766901\pi$
$860$	−0.136326	−	0.508774i	−0.00464866	−	0.0173490i
$861$		0			0
$862$	−33.1925	+	19.1637i	−1.13054	+	0.652718i
$863$	−13.9862	−	13.9862i	−0.476097	−	0.476097i	0.427784	−	0.903881i	$-0.359294\pi$
$863$	−13.9862	−	13.9862i	−0.476097	−	0.476097i	−0.903881	+	0.427784i	$0.859294\pi$
$864$		0			0
$865$	43.7179	+	11.7142i	1.48645	+	0.398294i
$866$	23.4990	+	23.4990i	0.798530	+	0.798530i
$867$		0			0
$868$	0.736960	+	0.103113i	0.0250141	+	0.00349987i
$869$	−0.673963	−	2.51526i	−0.0228626	−	0.0853245i
$870$		0			0
$871$	−19.4908	+	53.1390i	−0.660420	+	1.80055i
$872$	−48.8223			−1.65333
$873$		0			0
$874$	−5.60424	−	3.23561i	−0.189566	−	0.109446i
$875$	16.2295	−	20.7990i	0.548656	−	0.703135i
$876$		0			0
$877$	−3.66574	+	13.6807i	−0.123783	+	0.461965i	−0.999793	−	0.0203276i	$-0.993529\pi$
$877$	−3.66574	+	13.6807i	−0.123783	+	0.461965i	0.876010	+	0.482292i	$0.160196\pi$
$878$	−3.76524	+	14.0521i	−0.127071	+	0.474235i
$879$		0			0
$880$	−2.44046	+	1.40900i	−0.0822680	+	0.0474975i
$881$	12.7604	−	22.1016i	0.429908	−	0.744623i	−0.566957	−	0.823748i	$-0.691879\pi$
$881$	12.7604	−	22.1016i	0.429908	−	0.744623i	0.996865	+	0.0791249i	$0.0252126\pi$
$882$		0			0
$883$		−	24.3281i		−	0.818705i	−0.912376	−	0.409352i	$-0.865755\pi$
$883$		−	24.3281i		−	0.818705i	0.912376	−	0.409352i	$-0.134245\pi$
$884$	−0.537795	+	0.249152i	−0.0180880	+	0.00837988i
$885$		0			0
$886$	−26.5066	+	7.10242i	−0.890506	+	0.238610i
$887$	11.5771	+	6.68405i	0.388722	+	0.224429i	0.681606	−	0.731719i	$-0.261282\pi$
$887$	11.5771	+	6.68405i	0.388722	+	0.224429i	−0.292884	+	0.956148i	$0.594615\pi$
$888$		0			0
$889$	−2.24997	+	5.30964i	−0.0754616	+	0.178079i
$890$	−15.7472	+	58.7693i	−0.527847	+	1.96995i
$891$		0			0
$892$	0.135039	+	0.135039i	0.00452144	+	0.00452144i
$893$	−10.3583	−	17.9411i	−0.346626	−	0.600375i
$894$		0			0
$895$	−35.5347	+	9.52150i	−1.18780	+	0.318269i
$896$	26.1486	−	10.5834i	0.873564	−	0.353565i
$897$		0			0
$898$	39.2282			1.30906
$899$	−9.57835	−	35.7469i	−0.319456	−	1.19223i
$900$		0			0
$901$	−14.4445	−	25.0186i	−0.481217	−	0.833492i
$902$	−1.05626	+	1.05626i	−0.0351695	+	0.0351695i
$903$		0			0
$904$	−1.32473	−	0.354960i	−0.0440598	−	0.0118058i
$905$	−21.7628	+	21.7628i	−0.723421	+	0.723421i
$906$		0			0
$907$	31.5715	+	18.2278i	1.04831	+	0.605244i	0.922177	−	0.386769i	$-0.126409\pi$
$907$	31.5715	+	18.2278i	1.04831	+	0.605244i	0.126137	+	0.992013i	$0.459742\pi$
$908$	−1.28242	+	0.343624i	−0.0425586	+	0.0114036i
$909$		0			0
$910$	40.2142	−	25.0240i	1.33309	−	0.829537i
$911$	23.9100			0.792174			0.396087	−	0.918213i	$-0.370368\pi$
$911$	23.9100			0.792174			0.396087	+	0.918213i	$0.370368\pi$
$912$		0			0
$913$	0.846772	+	0.488884i	0.0280241	+	0.0161797i
$914$	23.5660	−	13.6058i	0.779494	−	0.450041i
$915$		0			0
$916$	−0.572325	−	0.153354i	−0.0189102	−	0.00506696i
$917$	18.8345	−	2.32429i	0.621969	−	0.0767550i
$918$		0			0
$919$	−5.06332	−	8.76993i	−0.167024	−	0.289293i	0.770348	−	0.637623i	$-0.220082\pi$
$919$	−5.06332	−	8.76993i	−0.167024	−	0.289293i	−0.937372	+	0.348330i	$0.886749\pi$
$920$	15.4249	−	26.7167i	0.508544	−	0.880823i
$921$		0			0
$922$	20.2875			0.668132
$923$	−0.0317637	−	0.0380462i	−0.00104551	−	0.00125231i
$924$		0			0
$925$	34.2103	−	9.16662i	1.12483	−	0.301397i
$926$	−0.628116	+	1.08793i	−0.0206412	+	0.0357516i
$927$		0			0
$928$	2.74719	+	2.74719i	0.0901810	+	0.0901810i
$929$	−38.8295	−	10.4043i	−1.27396	−	0.341355i	−0.442411	−	0.896813i	$-0.645877\pi$
$929$	−38.8295	−	10.4043i	−1.27396	−	0.341355i	−0.831545	+	0.555457i	$0.812543\pi$
$930$		0			0
$931$	10.8800	+	0.176578i	0.356576	+	0.00578711i
$932$	−0.759542	−	1.31556i	−0.0248796	−	0.0430928i
$933$		0			0
$934$	24.4394	−	6.54853i	0.799683	−	0.214274i
$935$		−	1.66492i		−	0.0544487i
$936$		0			0
$937$		−	0.991729i		−	0.0323984i	−0.999869	−	0.0161992i	$-0.994843\pi$
$937$		−	0.991729i		−	0.0323984i	0.999869	−	0.0161992i	$-0.00515658\pi$
$938$	34.7327	+	46.0332i	1.13406	+	1.50304i
$939$		0			0
$940$	2.98261	−	1.72201i	0.0972819	−	0.0561658i
$941$	−10.1768	+	10.1768i	−0.331753	+	0.331753i	−0.853252	−	0.521499i	$-0.825373\pi$
$941$	−10.1768	+	10.1768i	−0.331753	+	0.331753i	0.521499	+	0.853252i	$0.325373\pi$
$942$		0			0
$943$	4.07931	−	15.2242i	0.132841	−	0.495768i
$944$	5.37137	+	5.37137i	0.174823	+	0.174823i
$945$		0			0
$946$	0.501587	+	0.289592i	0.0163080	+	0.00941544i
$947$	−2.29842	−	8.57781i	−0.0746885	−	0.278741i	0.918474	−	0.395481i	$-0.129422\pi$
$947$	−2.29842	−	8.57781i	−0.0746885	−	0.278741i	−0.993163	+	0.116740i	$0.962756\pi$
$948$		0			0
$949$	−11.2813	+	1.96029i	−0.366206	+	0.0636337i
$950$		−	16.8095i		−	0.545373i
$951$		0			0
$952$	−2.39947	+	17.1494i	−0.0777674	+	0.555814i
$953$	−13.1520	+	7.59333i	−0.426036	+	0.245972i	−0.697657	−	0.716432i	$-0.745774\pi$
$953$	−13.1520	+	7.59333i	−0.426036	+	0.245972i	0.271620	+	0.962404i	$0.412440\pi$
$954$		0			0
$955$	56.0109	+	15.0081i	1.81247	+	0.485650i
$956$	1.02461	+	0.274543i	0.0331382	+	0.00887934i
$957$		0			0
$958$	−47.2373	+	27.2724i	−1.52617	+	0.881133i
$959$	−4.62382	+	33.0471i	−0.149311	+	1.06715i
$960$		0			0
$961$			15.8520i			0.511355i
$962$	22.6731	+	2.04046i	0.731011	+	0.0657869i
$963$		0			0
$964$	−0.0256892	−	0.0958735i	−0.000827394	−	0.00308788i
$965$	−62.4262	−	36.0418i	−2.00957	−	1.16023i
$966$		0			0
$967$	−31.1019	−	31.1019i	−1.00017	−	1.00017i	−1.00000		0.000170581i	$-0.999946\pi$
$967$	−31.1019	−	31.1019i	−1.00017	−	1.00017i	−0.000170581	−	1.00000i	$-0.500054\pi$
$968$	8.16020	−	30.4543i	0.262279	−	0.978838i
$969$		0			0
$970$	−28.5571	+	28.5571i	−0.916914	+	0.916914i
$971$	5.28808	−	3.05308i	0.169703	−	0.0979778i	−0.412743	−	0.910848i	$-0.635429\pi$
$971$	5.28808	−	3.05308i	0.169703	−	0.0979778i	0.582446	+	0.812870i	$0.302096\pi$
$972$		0			0
$973$	−32.3138	−	42.8273i	−1.03593	−	1.37298i
$974$			31.1669i			0.998652i
$975$		0			0
$976$		−	3.78154i		−	0.121044i
$977$	−45.5205	+	12.1972i	−1.45633	+	0.390222i	−0.898221	−	0.439545i	$-0.855140\pi$
$977$	−45.5205	+	12.1972i	−1.45633	+	0.390222i	−0.558109	+	0.829767i	$0.688473\pi$
$978$		0			0
$979$	1.25398	+	2.17196i	0.0400775	+	0.0694163i
$980$	−0.0293552	+	1.80874i	−0.000937716	+	0.0577780i
$981$		0			0
$982$	8.45756	+	2.26620i	0.269891	+	0.0723172i
$983$	11.6944	+	11.6944i	0.372994	+	0.372994i	0.868567	−	0.495572i	$-0.165042\pi$
$983$	11.6944	+	11.6944i	0.372994	+	0.372994i	−0.495572	+	0.868567i	$0.665042\pi$
$984$		0			0
$985$	4.50347	−	7.80024i	0.143492	−	0.248536i
$986$	29.0084	−	7.77278i	0.923816	−	0.247536i
$987$		0			0
$988$	−0.139474	+	0.380257i	−0.00443725	+	0.0120976i
$989$	−6.11114			−0.194323
$990$		0			0
$991$	−10.3485	+	17.9242i	−0.328732	+	0.569381i	−0.982261	−	0.187521i	$-0.939955\pi$
$991$	−10.3485	+	17.9242i	−0.328732	+	0.569381i	0.653529	+	0.756902i	$0.273288\pi$
$992$	0.795124	+	1.37720i	0.0252452	+	0.0437260i
$993$		0			0
$994$	−0.0501155	+	0.00618458i	−0.00158957	+	0.000196163i
$995$	56.8690	+	15.2380i	1.80287	+	0.483077i
$996$		0			0
$997$	−1.20776	+	0.697298i	−0.0382500	+	0.0220836i	−0.519003	−	0.854772i	$-0.673697\pi$
$997$	−1.20776	+	0.697298i	−0.0382500	+	0.0220836i	0.480753	+	0.876856i	$0.340363\pi$
$998$	0.317214	+	0.183144i	0.0100412	+	0.00579731i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.e.748.3		32
3.2	odd	2		273.2.by.d.202.6	yes	32
7.6	odd	2		819.2.fm.f.748.3		32
13.2	odd	12		819.2.fm.f.496.3		32
21.20	even	2		273.2.by.c.202.6	✓	32
39.2	even	12		273.2.by.c.223.6	yes	32
91.41	even	12	inner	819.2.fm.e.496.3		32
273.41	odd	12		273.2.by.d.223.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.6	✓	32	21.20	even	2
273.2.by.c.223.6	yes	32	39.2	even	12
273.2.by.d.202.6	yes	32	3.2	odd	2
273.2.by.d.223.6	yes	32	273.41	odd	12
819.2.fm.e.496.3		32	91.41	even	12	inner
819.2.fm.e.748.3		32	1.1	even	1	trivial
819.2.fm.f.496.3		32	13.2	odd	12
819.2.fm.f.748.3		32	7.6	odd	2

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34112 + 0.359352i) q^{2} +(-0.0625832 + 0.0361324i) q^{4} +(-2.52867 + 2.52867i) q^{5} +(-0.324044 - 2.62583i) q^{7} +(2.03448 - 2.03448i) q^{8} +O(q^{10})\)	\(q+(-1.34112 + 0.359352i) q^{2} +(-0.0625832 + 0.0361324i) q^{4} +(-2.52867 + 2.52867i) q^{5} +(-0.324044 - 2.62583i) q^{7} +(2.03448 - 2.03448i) q^{8} +(2.48257 - 4.29993i) q^{10} +(-0.0529715 - 0.197692i) q^{11} +(-2.07540 + 2.94834i) q^{13} +(1.37818 + 3.40511i) q^{14} +(-1.92512 + 3.33441i) q^{16} +(-1.13739 - 1.97002i) q^{17} +(-1.50152 - 0.402330i) q^{19} +(0.0668853 - 0.249619i) q^{20} +(0.142082 + 0.246094i) q^{22} +(-2.59661 - 1.49915i) q^{23} -7.78835i q^{25} +(1.72386 - 4.69988i) q^{26} +(0.115157 + 0.152625i) q^{28} +(4.75430 - 8.23469i) q^{29} +(2.75209 - 2.75209i) q^{31} +(-0.105751 + 0.394667i) q^{32} +(2.23331 + 2.23331i) q^{34} +(7.45927 + 5.82046i) q^{35} +(1.17697 + 4.39250i) q^{37} +2.15829 q^{38} +10.2891i q^{40} +(1.36054 + 5.07760i) q^{41} +(1.76513 - 1.01910i) q^{43} +(0.0104582 + 0.0104582i) q^{44} +(4.02109 + 1.07745i) q^{46} +(9.42358 + 9.42358i) q^{47} +(-6.78999 + 1.70177i) q^{49} +(2.79876 + 10.4451i) q^{50} +(0.0233541 - 0.259506i) q^{52} +12.6997 q^{53} +(0.633846 + 0.365951i) q^{55} +(-6.00147 - 4.68295i) q^{56} +(-3.41693 + 12.7522i) q^{58} +(0.510631 - 1.90570i) q^{59} +(-0.850570 + 0.491077i) q^{61} +(-2.70191 + 4.67985i) q^{62} -8.26779i q^{64} +(-2.20740 - 12.7034i) q^{65} +(15.1633 - 4.06300i) q^{67} +(0.142363 + 0.0821934i) q^{68} +(-12.0954 - 5.12543i) q^{70} +(-0.00355777 + 0.0132778i) q^{71} +(2.24560 + 2.24560i) q^{73} +(-3.15691 - 5.46792i) q^{74} +(0.108507 - 0.0290743i) q^{76} +(-0.501942 + 0.203155i) q^{77} +12.7231 q^{79} +(-3.56363 - 13.2996i) q^{80} +(-3.64929 - 6.32076i) q^{82} +(-3.37812 + 3.37812i) q^{83} +(7.85762 + 2.10544i) q^{85} +(-2.00104 + 2.00104i) q^{86} +(-0.509971 - 0.294432i) q^{88} +(-11.8364 + 3.17155i) q^{89} +(8.41438 + 4.49425i) q^{91} +0.216672 q^{92} +(-16.0245 - 9.25177i) q^{94} +(4.81420 - 2.77948i) q^{95} +(-7.85674 - 2.10521i) q^{97} +(8.49465 - 4.72228i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 2 q^{10} + 4 q^{11} + 6 q^{13} - 34 q^{14} + 14 q^{16} + 8 q^{17} + 2 q^{19} - 44 q^{20} - 4 q^{22} + 18 q^{23} + 28 q^{26} - 32 q^{28} + 18 q^{29} - 14 q^{31} + 8 q^{32} - 66 q^{34} - 22 q^{35} - 24 q^{37} - 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} + 28 q^{47} + 8 q^{49} - 70 q^{50} + 28 q^{52} + 80 q^{53} + 60 q^{55} + 54 q^{56} - 4 q^{58} + 42 q^{59} + 36 q^{61} - 52 q^{62} - 14 q^{65} + 26 q^{67} + 72 q^{68} - 116 q^{70} + 4 q^{71} + 12 q^{73} + 18 q^{74} - 48 q^{76} - 28 q^{77} - 4 q^{79} + 98 q^{80} + 20 q^{82} + 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} + 54 q^{89} + 148 q^{91} + 4 q^{92} - 60 q^{95} - 40 q^{97} - 36 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 2 * q^10 + 4 * q^11 + 6 * q^13 - 34 * q^14 + 14 * q^16 + 8 * q^17 + 2 * q^19 - 44 * q^20 - 4 * q^22 + 18 * q^23 + 28 * q^26 - 32 * q^28 + 18 * q^29 - 14 * q^31 + 8 * q^32 - 66 * q^34 - 22 * q^35 - 24 * q^37 - 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 + 28 * q^47 + 8 * q^49 - 70 * q^50 + 28 * q^52 + 80 * q^53 + 60 * q^55 + 54 * q^56 - 4 * q^58 + 42 * q^59 + 36 * q^61 - 52 * q^62 - 14 * q^65 + 26 * q^67 + 72 * q^68 - 116 * q^70 + 4 * q^71 + 12 * q^73 + 18 * q^74 - 48 * q^76 - 28 * q^77 - 4 * q^79 + 98 * q^80 + 20 * q^82 + 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 + 54 * q^89 + 148 * q^91 + 4 * q^92 - 60 * q^95 - 40 * q^97 - 36 * q^98

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