LMFDB - Embedded newform 880.2.bo.g.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(81,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("880.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.bo (of order $5$, degree $4$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.682515625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} + 2x^{5} + 19x^{4} + 28x^{3} + 100x^{2} + 88x + 121 $ x^8 - 3x^7 + 5x^6 + 2x^5 + 19x^4 + 28x^3 + 100x^2 + 88*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			401.1
Root			$0.581882 + 1.79085i$ of defining polynomial
Character	$\chi$	$=$	880.401
Dual form			880.2.bo.g.801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.214371 - 0.155750i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-3.48828 + 2.53438i) q^{7} +(-0.905354 - 2.78639i) q^{9} +O(q^{10})$	\(q+(-0.214371 - 0.155750i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-3.48828 + 2.53438i) q^{7} +(-0.905354 - 2.78639i) q^{9} +(1.42705 - 2.99391i) q^{11} +(0.374078 + 1.15129i) q^{13} +(-0.214371 + 0.155750i) q^{15} +(-2.21437 + 6.81513i) q^{17} +(2.19992 + 1.59833i) q^{19} +1.14252 q^{21} -7.01787 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.485545 + 1.49436i) q^{27} +(-8.54782 + 6.21036i) q^{29} +(-1.11908 - 3.44417i) q^{31} +(-0.772220 + 0.419546i) q^{33} +(1.33240 + 4.10072i) q^{35} +(-1.71437 + 1.24556i) q^{37} +(0.0991220 - 0.305066i) q^{39} +(-2.22713 - 1.61811i) q^{41} -6.59251 q^{43} -2.92979 q^{45} +(4.64416 + 3.37418i) q^{47} +(3.58188 - 11.0239i) q^{49} +(1.53615 - 1.11608i) q^{51} +(-1.81558 - 5.58779i) q^{53} +(-2.40640 - 2.28238i) q^{55} +(-0.222659 - 0.685272i) q^{57} +(-4.77117 + 3.46646i) q^{59} +(-1.89879 + 5.84387i) q^{61} +(10.2199 + 7.42521i) q^{63} +1.21054 q^{65} +1.63381 q^{67} +(1.50443 + 1.09303i) q^{69} +(-2.29862 + 7.07443i) q^{71} +(5.98039 - 4.34501i) q^{73} +(0.0818824 + 0.252008i) q^{75} +(2.60978 + 14.0603i) q^{77} +(-2.16376 - 6.65938i) q^{79} +(-6.77391 + 4.92153i) q^{81} +(0.492758 - 1.51655i) q^{83} +(5.79730 + 4.21198i) q^{85} +2.79967 q^{87} +1.24711 q^{89} +(-4.22271 - 3.06798i) q^{91} +(-0.296530 + 0.912627i) q^{93} +(2.19992 - 1.59833i) q^{95} +(-2.13632 - 6.57491i) q^{97} +(-9.63421 - 1.26577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 2 q^{5} + q^{7} - 6 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 2 * q^5 + q^7 - 6 * q^9	$ 8 q + 4 q^{3} - 2 q^{5} + q^{7} - 6 q^{9} - 2 q^{11} + q^{13} + 4 q^{15} - 12 q^{17} + 7 q^{19} + 32 q^{21} - 26 q^{23} - 2 q^{25} + q^{27} - 22 q^{29} + 26 q^{31} + 19 q^{33} - 4 q^{35} - 8 q^{37} + 48 q^{39} - 15 q^{41} - 38 q^{43} + 14 q^{45} - 6 q^{47} + 27 q^{49} + 5 q^{51} - 4 q^{53} + 8 q^{55} + 47 q^{57} - 39 q^{59} - 20 q^{61} + 57 q^{63} - 14 q^{65} + 26 q^{67} - 10 q^{69} - 2 q^{71} + 8 q^{73} - q^{75} + 16 q^{77} - 14 q^{79} - 31 q^{81} + 21 q^{83} + 13 q^{85} - 20 q^{87} + 32 q^{89} - 53 q^{91} - 38 q^{93} + 7 q^{95} - 31 q^{97} - 36 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 2 * q^5 + q^7 - 6 * q^9 - 2 * q^11 + q^13 + 4 * q^15 - 12 * q^17 + 7 * q^19 + 32 * q^21 - 26 * q^23 - 2 * q^25 + q^27 - 22 * q^29 + 26 * q^31 + 19 * q^33 - 4 * q^35 - 8 * q^37 + 48 * q^39 - 15 * q^41 - 38 * q^43 + 14 * q^45 - 6 * q^47 + 27 * q^49 + 5 * q^51 - 4 * q^53 + 8 * q^55 + 47 * q^57 - 39 * q^59 - 20 * q^61 + 57 * q^63 - 14 * q^65 + 26 * q^67 - 10 * q^69 - 2 * q^71 + 8 * q^73 - q^75 + 16 * q^77 - 14 * q^79 - 31 * q^81 + 21 * q^83 + 13 * q^85 - 20 * q^87 + 32 * q^89 - 53 * q^91 - 38 * q^93 + 7 * q^95 - 31 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.214371	−	0.155750i	−0.123767	−	0.0899221i	0.524180	−	0.851608i	$-0.324372\pi$
$3$	−0.214371	−	0.155750i	−0.123767	−	0.0899221i	−0.647947	+	0.761686i	$0.724372\pi$
$4$		0			0
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$5$	0.309017	−	0.951057i	0.138197	−	0.425325i
$6$		0			0
$7$	−3.48828	+	2.53438i	−1.31845	+	0.957907i	−0.318496	+	0.947924i	$0.603178\pi$
$7$	−3.48828	+	2.53438i	−1.31845	+	0.957907i	−0.999950	+	0.00998336i	$0.996822\pi$
$8$		0			0
$9$	−0.905354	−	2.78639i	−0.301785	−	0.928798i
$10$		0			0
$11$	1.42705	−	2.99391i	0.430272	−	0.902699i
$11$	1.42705	−	2.99391i	0.430272	−	0.902699i
$12$		0			0
$13$	0.374078	+	1.15129i	0.103750	+	0.319311i	0.989435	−	0.144976i	$-0.0463105\pi$
$13$	0.374078	+	1.15129i	0.103750	+	0.319311i	−0.885685	+	0.464287i	$0.846311\pi$
$14$		0			0
$15$	−0.214371	+	0.155750i	−0.0553504	+	0.0402144i
$16$		0			0
$17$	−2.21437	+	6.81513i	−0.537064	+	1.65291i	0.202083	+	0.979368i	$0.435229\pi$
$17$	−2.21437	+	6.81513i	−0.537064	+	1.65291i	−0.739147	+	0.673544i	$0.764771\pi$
$18$		0			0
$19$	2.19992	+	1.59833i	0.504695	+	0.366683i	0.810808	−	0.585313i	$-0.199028\pi$
$19$	2.19992	+	1.59833i	0.504695	+	0.366683i	−0.306112	+	0.951995i	$0.599028\pi$
$20$		0			0
$21$	1.14252			0.249317
$22$		0			0
$23$	−7.01787			−1.46333			−0.731663	−	0.681666i	$-0.761256\pi$
$23$	−7.01787			−1.46333			−0.731663	+	0.681666i	$0.761256\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$	−0.485545	+	1.49436i	−0.0934433	+	0.287589i
$28$		0			0
$29$	−8.54782	+	6.21036i	−1.58729	+	1.15323i	−0.679609	+	0.733575i	$0.737850\pi$
$29$	−8.54782	+	6.21036i	−1.58729	+	1.15323i	−0.907682	+	0.419659i	$0.862150\pi$
$30$		0			0
$31$	−1.11908	−	3.44417i	−0.200993	−	0.618591i	−0.999854	−	0.0170766i	$-0.994564\pi$
$31$	−1.11908	−	3.44417i	−0.200993	−	0.618591i	0.798862	−	0.601515i	$-0.205436\pi$
$32$		0			0
$33$	−0.772220	+	0.419546i	−0.134426	+	0.0730336i
$34$		0			0
$35$	1.33240	+	4.10072i	0.225218	+	0.693148i
$36$		0			0
$37$	−1.71437	+	1.24556i	−0.281841	+	0.204769i	−0.719720	−	0.694265i	$-0.755730\pi$
$37$	−1.71437	+	1.24556i	−0.281841	+	0.204769i	0.437879	+	0.899034i	$0.355730\pi$
$38$		0			0
$39$	0.0991220	−	0.305066i	0.0158722	−	0.0488497i
$40$		0			0
$41$	−2.22713	−	1.61811i	−0.347820	−	0.252706i	0.400134	−	0.916457i	$-0.368964\pi$
$41$	−2.22713	−	1.61811i	−0.347820	−	0.252706i	−0.747954	+	0.663751i	$0.768964\pi$
$42$		0			0
$43$	−6.59251			−1.00535			−0.502674	−	0.864476i	$-0.667650\pi$
$43$	−6.59251			−1.00535			−0.502674	+	0.864476i	$0.667650\pi$
$44$		0			0
$45$	−2.92979			−0.436747
$46$		0			0
$47$	4.64416	+	3.37418i	0.677420	+	0.492175i	0.872501	−	0.488613i	$-0.162497\pi$
$47$	4.64416	+	3.37418i	0.677420	+	0.492175i	−0.195081	+	0.980787i	$0.562497\pi$
$48$		0			0
$49$	3.58188	−	11.0239i	0.511697	−	1.57484i
$50$		0			0
$51$	1.53615	−	1.11608i	0.215104	−	0.156282i
$52$		0			0
$53$	−1.81558	−	5.58779i	−0.249390	−	0.767542i	−0.994883	−	0.101030i	$-0.967786\pi$
$53$	−1.81558	−	5.58779i	−0.249390	−	0.767542i	0.745494	−	0.666512i	$-0.232214\pi$
$54$		0			0
$55$	−2.40640	−	2.28238i	−0.324479	−	0.307756i
$56$		0			0
$57$	−0.222659	−	0.685272i	−0.0294918	−	0.0907666i
$58$		0			0
$59$	−4.77117	+	3.46646i	−0.621154	+	0.451295i	−0.853324	−	0.521380i	$-0.825417\pi$
$59$	−4.77117	+	3.46646i	−0.621154	+	0.451295i	0.232170	+	0.972675i	$0.425417\pi$
$60$		0			0
$61$	−1.89879	+	5.84387i	−0.243115	+	0.748231i	0.752826	+	0.658220i	$0.228690\pi$
$61$	−1.89879	+	5.84387i	−0.243115	+	0.748231i	−0.995941	+	0.0900109i	$0.971310\pi$
$62$		0			0
$63$	10.2199	+	7.42521i	1.28759	+	0.935488i
$64$		0			0
$65$	1.21054			0.150149
$66$		0			0
$67$	1.63381			0.199602			0.0998009	−	0.995007i	$-0.468179\pi$
$67$	1.63381			0.199602			0.0998009	+	0.995007i	$0.468179\pi$
$68$		0			0
$69$	1.50443	+	1.09303i	0.181112	+	0.131585i
$70$		0			0
$71$	−2.29862	+	7.07443i	−0.272796	+	0.839580i	0.716998	+	0.697075i	$0.245516\pi$
$71$	−2.29862	+	7.07443i	−0.272796	+	0.839580i	−0.989794	+	0.142505i	$0.954484\pi$
$72$		0			0
$73$	5.98039	−	4.34501i	0.699952	−	0.508545i	−0.179965	−	0.983673i	$-0.557598\pi$
$73$	5.98039	−	4.34501i	0.699952	−	0.508545i	0.879917	+	0.475128i	$0.157598\pi$
$74$		0			0
$75$	0.0818824	+	0.252008i	0.00945497	+	0.0290994i
$76$		0			0
$77$	2.60978	+	14.0603i	0.297412	+	1.60232i
$78$		0			0
$79$	−2.16376	−	6.65938i	−0.243443	−	0.749239i	−0.995889	−	0.0905854i	$-0.971126\pi$
$79$	−2.16376	−	6.65938i	−0.243443	−	0.749239i	0.752446	−	0.658654i	$-0.228874\pi$
$80$		0			0
$81$	−6.77391	+	4.92153i	−0.752657	+	0.546837i
$82$		0			0
$83$	0.492758	−	1.51655i	0.0540872	−	0.166463i	−0.920364	−	0.391063i	$-0.872107\pi$
$83$	0.492758	−	1.51655i	0.0540872	−	0.166463i	0.974451	+	0.224600i	$0.0721075\pi$
$84$		0			0
$85$	5.79730	+	4.21198i	0.628805	+	0.456854i
$86$		0			0
$87$	2.79967			0.300156
$88$		0			0
$89$	1.24711			0.132193			0.0660967	−	0.997813i	$-0.478945\pi$
$89$	1.24711			0.132193			0.0660967	+	0.997813i	$0.478945\pi$
$90$		0			0
$91$	−4.22271	−	3.06798i	−0.442660	−	0.321611i
$92$		0			0
$93$	−0.296530	+	0.912627i	−0.0307488	+	0.0946350i
$94$		0			0
$95$	2.19992	−	1.59833i	0.225707	−	0.163985i
$96$		0			0
$97$	−2.13632	−	6.57491i	−0.216910	−	0.667581i	−0.999012	−	0.0444310i	$-0.985853\pi$
$97$	−2.13632	−	6.57491i	−0.216910	−	0.667581i	0.782102	−	0.623150i	$-0.214147\pi$
$98$		0			0
$99$	−9.63421	−	1.26577i	−0.968275	−	0.127215i
$100$		0			0
$101$	1.00000	+	3.07768i	0.0995037	+	0.306241i	0.988401	−	0.151865i	$-0.0485280\pi$
$101$	1.00000	+	3.07768i	0.0995037	+	0.306241i	−0.888897	+	0.458106i	$0.848528\pi$
$102$		0			0
$103$	4.67307	−	3.39518i	0.460451	−	0.334537i	−0.333257	−	0.942836i	$-0.608148\pi$
$103$	4.67307	−	3.39518i	0.460451	−	0.334537i	0.793708	+	0.608299i	$0.208148\pi$
$104$		0			0
$105$	0.353057	−	1.08660i	0.0344548	−	0.106041i
$106$		0			0
$107$	0.138686	+	0.100761i	0.0134073	+	0.00974095i	0.594469	−	0.804119i	$-0.297362\pi$
$107$	0.138686	+	0.100761i	0.0134073	+	0.00974095i	−0.581061	+	0.813860i	$0.697362\pi$
$108$		0			0
$109$	−2.32753			−0.222937			−0.111468	−	0.993768i	$-0.535555\pi$
$109$	−2.32753			−0.222937			−0.111468	+	0.993768i	$0.535555\pi$
$110$		0			0
$111$	0.561508			0.0532959
$112$		0			0
$113$	−3.48555	−	2.53240i	−0.327893	−	0.238228i	0.411643	−	0.911345i	$-0.364955\pi$
$113$	−3.48555	−	2.53240i	−0.327893	−	0.238228i	−0.739536	+	0.673117i	$0.764955\pi$
$114$		0			0
$115$	−2.16864	+	6.67439i	−0.202227	+	0.622390i
$116$		0			0
$117$	2.86928	−	2.08466i	0.265265	−	0.192726i
$118$		0			0
$119$	−9.54782	−	29.3852i	−0.875247	−	2.69373i
$120$		0			0
$121$	−6.92705	−	8.54494i	−0.629732	−	0.776813i
$122$		0			0
$123$	0.225413	+	0.693751i	0.0203248	+	0.0625534i
$124$		0			0
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$		0			0
$127$	−3.34855	+	10.3058i	−0.297136	+	0.914490i	0.685360	+	0.728205i	$0.259645\pi$
$127$	−3.34855	+	10.3058i	−0.297136	+	0.914490i	−0.982496	+	0.186285i	$0.940355\pi$
$128$		0			0
$129$	1.41324	+	1.02678i	0.124429	+	0.0904030i
$130$		0			0
$131$	−5.78518			−0.505454			−0.252727	−	0.967538i	$-0.581327\pi$
$131$	−5.78518			−0.505454			−0.252727	+	0.967538i	$0.581327\pi$
$132$		0			0
$133$	−11.7247			−1.01666
$134$		0			0
$135$	1.27117	+	0.923562i	0.109405	+	0.0794876i
$136$		0			0
$137$	2.67310	−	8.22695i	0.228378	−	0.702876i	−0.769553	−	0.638583i	$-0.779521\pi$
$137$	2.67310	−	8.22695i	0.228378	−	0.702876i	0.997931	−	0.0642926i	$-0.0204791\pi$
$138$		0			0
$139$	10.3135	−	7.49318i	0.874777	−	0.635563i	−0.0570872	−	0.998369i	$-0.518181\pi$
$139$	10.3135	−	7.49318i	0.874777	−	0.635563i	0.931865	+	0.362806i	$0.118181\pi$
$140$		0			0
$141$	−0.470046	−	1.44665i	−0.0395850	−	0.121830i
$142$		0			0
$143$	3.98070	+	0.522997i	0.332883	+	0.0437352i
$144$		0			0
$145$	3.26498	+	10.0486i	0.271142	+	0.834488i
$146$		0			0
$147$	−2.48482	+	1.80533i	−0.204945	+	0.148901i
$148$		0			0
$149$	2.04339	−	6.28892i	0.167401	−	0.515208i	−0.831804	−	0.555070i	$-0.812692\pi$
$149$	2.04339	−	6.28892i	0.167401	−	0.515208i	0.999205	+	0.0398613i	$0.0126916\pi$
$150$		0			0
$151$	16.9064	+	12.2832i	1.37582	+	0.999591i	0.997257	+	0.0740153i	$0.0235814\pi$
$151$	16.9064	+	12.2832i	1.37582	+	0.999591i	0.378562	+	0.925576i	$0.376419\pi$
$152$		0			0
$153$	20.9944			1.69730
$154$		0			0
$155$	−3.62142			−0.290879
$156$		0			0
$157$	16.3657	+	11.8904i	1.30613	+	0.948957i	0.999995	−	0.00303254i	$-0.000965289\pi$
$157$	16.3657	+	11.8904i	1.30613	+	0.948957i	0.306131	+	0.951989i	$0.400965\pi$
$158$		0			0
$159$	−0.481088	+	1.48064i	−0.0381528	+	0.117422i
$160$		0			0
$161$	24.4803	−	17.7860i	1.92932	−	1.40173i
$162$		0			0
$163$	2.49721	+	7.68564i	0.195597	+	0.601986i	0.999969	+	0.00785979i	$0.00250187\pi$
$163$	2.49721	+	7.68564i	0.195597	+	0.601986i	−0.804372	+	0.594126i	$0.797498\pi$
$164$		0			0
$165$	0.160383	+	0.864071i	0.0124858	+	0.0672679i
$166$		0			0
$167$	−5.33751	−	16.4272i	−0.413029	−	1.27117i	−0.914002	−	0.405709i	$-0.867025\pi$
$167$	−5.33751	−	16.4272i	−0.413029	−	1.27117i	0.500973	−	0.865463i	$-0.332975\pi$
$168$		0			0
$169$	9.33168	−	6.77986i	0.717822	−	0.521528i
$170$		0			0
$171$	2.46188	−	7.57689i	0.188265	−	0.579419i
$172$		0			0
$173$	−11.6286	−	8.44868i	−0.884107	−	0.642341i	0.0502280	−	0.998738i	$-0.484005\pi$
$173$	−11.6286	−	8.44868i	−0.884107	−	0.642341i	−0.934335	+	0.356397i	$0.884005\pi$
$174$		0			0
$175$	4.31175			0.325938
$176$		0			0
$177$	1.56270			0.117460
$178$		0			0
$179$	15.2533	+	11.0822i	1.14008	+	0.828320i	0.987131	−	0.159914i	$-0.0511216\pi$
$179$	15.2533	+	11.0822i	1.14008	+	0.828320i	0.152953	+	0.988233i	$0.451122\pi$
$180$		0			0
$181$	−4.04887	+	12.4611i	−0.300950	+	0.926228i	0.680208	+	0.733019i	$0.261890\pi$
$181$	−4.04887	+	12.4611i	−0.300950	+	0.926228i	−0.981158	+	0.193209i	$0.938110\pi$
$182$		0			0
$183$	1.31723	−	0.957020i	0.0973721	−	0.0707450i
$184$		0			0
$185$	0.654831	+	2.01536i	0.0481442	+	0.148173i
$186$		0			0
$187$	17.2439	+	16.3552i	1.26100	+	1.19601i
$188$		0			0
$189$	−2.09355	−	6.44329i	−0.152283	−	0.468680i
$190$		0			0
$191$	−9.11908	+	6.62540i	−0.659833	+	0.479397i	−0.866607	−	0.498992i	$-0.833704\pi$
$191$	−9.11908	+	6.62540i	−0.659833	+	0.479397i	0.206773	+	0.978389i	$0.433704\pi$
$192$		0			0
$193$	2.14590	−	6.60440i	0.154465	−	0.475395i	−0.843641	−	0.536907i	$-0.819592\pi$
$193$	2.14590	−	6.60440i	0.154465	−	0.475395i	0.998106	+	0.0615126i	$0.0195924\pi$
$194$		0			0
$195$	−0.259505	−	0.188541i	−0.0185835	−	0.0135017i
$196$		0			0
$197$	−13.4389			−0.957485			−0.478743	−	0.877955i	$-0.658907\pi$
$197$	−13.4389			−0.957485			−0.478743	+	0.877955i	$0.658907\pi$
$198$		0			0
$199$	19.4427			1.37825			0.689127	−	0.724640i	$-0.257994\pi$
$199$	19.4427			1.37825			0.689127	+	0.724640i	$0.257994\pi$
$200$		0			0
$201$	−0.350242	−	0.254465i	−0.0247041	−	0.0179486i
$202$		0			0
$203$	14.0778	−	43.3269i	0.988066	−	3.04095i
$204$		0			0
$205$	−2.22713	+	1.61811i	−0.155550	+	0.113014i
$206$		0			0
$207$	6.35365	+	19.5545i	0.441609	+	1.35913i
$208$		0			0
$209$	7.92467	−	4.30546i	0.548161	−	0.297815i
$210$		0			0
$211$	0.728826	+	2.24309i	0.0501744	+	0.154421i	0.973004	−	0.230786i	$-0.0741299\pi$
$211$	0.728826	+	2.24309i	0.0501744	+	0.154421i	−0.922830	+	0.385207i	$0.874130\pi$
$212$		0			0
$213$	1.59460	−	1.15854i	0.109260	−	0.0793820i
$214$		0			0
$215$	−2.03720	+	6.26985i	−0.138936	+	0.427600i
$216$		0			0
$217$	12.6325	+	9.17806i	0.857551	+	0.623047i
$218$		0			0
$219$	−1.95876			−0.132361
$220$		0			0
$221$	−8.67456			−0.583514
$222$		0			0
$223$	−11.8090	−	8.57978i	−0.790792	−	0.574544i	0.117406	−	0.993084i	$-0.462542\pi$
$223$	−11.8090	−	8.57978i	−0.790792	−	0.574544i	−0.908198	+	0.418540i	$0.862542\pi$
$224$		0			0
$225$	−0.905354	+	2.78639i	−0.0603569	+	0.185760i
$226$		0			0
$227$	2.41871	−	1.75730i	0.160536	−	0.116636i	−0.504617	−	0.863343i	$-0.668366\pi$
$227$	2.41871	−	1.75730i	0.160536	−	0.116636i	0.665153	+	0.746707i	$0.268366\pi$
$228$		0			0
$229$	0.487913	+	1.50164i	0.0322422	+	0.0992312i	0.965883	−	0.258981i	$-0.0833866\pi$
$229$	0.487913	+	1.50164i	0.0322422	+	0.0992312i	−0.933640	+	0.358212i	$0.883387\pi$
$230$		0			0
$231$	1.63043	−	3.42060i	0.107274	−	0.225059i
$232$		0			0
$233$	0.156276	+	0.480967i	0.0102380	+	0.0315092i	0.956045	−	0.293220i	$-0.0947268\pi$
$233$	0.156276	+	0.480967i	0.0102380	+	0.0315092i	−0.945807	+	0.324729i	$0.894727\pi$
$234$		0			0
$235$	4.64416	−	3.37418i	0.302951	−	0.220107i
$236$		0			0
$237$	−0.573348	+	1.76458i	−0.0372430	+	0.114622i
$238$		0			0
$239$	−13.5444	−	9.84061i	−0.876117	−	0.636536i	0.0561044	−	0.998425i	$-0.482132\pi$
$239$	−13.5444	−	9.84061i	−0.876117	−	0.636536i	−0.932221	+	0.361889i	$0.882132\pi$
$240$		0			0
$241$	−15.2947			−0.985217			−0.492609	−	0.870251i	$-0.663957\pi$
$241$	−15.2947			−0.985217			−0.492609	+	0.870251i	$0.663957\pi$
$242$		0			0
$243$	6.93243			0.444716
$244$		0			0
$245$	−9.37749	−	6.81315i	−0.599106	−	0.435276i
$246$		0			0
$247$	−1.01721	+	3.13065i	−0.0647235	+	0.199198i
$248$		0			0
$249$	−0.341835	+	0.248358i	−0.0216629	+	0.0157390i
$250$		0			0
$251$	0.132071	+	0.406472i	0.00833623	+	0.0256563i	0.955138	−	0.296161i	$-0.0957064\pi$
$251$	0.132071	+	0.406472i	0.00833623	+	0.0256563i	−0.946802	+	0.321817i	$0.895706\pi$
$252$		0			0
$253$	−10.0149	+	21.0109i	−0.629628	+	1.32094i
$254$		0			0
$255$	−0.586758	−	1.80585i	−0.0367442	−	0.113087i
$256$		0			0
$257$	−14.4614	+	10.5068i	−0.902076	+	0.655397i	−0.938998	−	0.343921i	$-0.888245\pi$
$257$	−14.4614	+	10.5068i	−0.902076	+	0.655397i	0.0369221	+	0.999318i	$0.488245\pi$
$258$		0			0
$259$	2.82347	−	8.68975i	0.175442	−	0.539955i
$260$		0			0
$261$	25.0433	+	18.1950i	1.55014	+	1.12624i
$262$		0			0
$263$	−14.4977			−0.893964			−0.446982	−	0.894543i	$-0.647501\pi$
$263$	−14.4977			−0.893964			−0.446982	+	0.894543i	$0.647501\pi$
$264$		0			0
$265$	−5.87535			−0.360920
$266$		0			0
$267$	−0.267344	−	0.194237i	−0.0163612	−	0.0118871i
$268$		0			0
$269$	8.63326	−	26.5704i	0.526379	−	1.62003i	−0.235194	−	0.971948i	$-0.575573\pi$
$269$	8.63326	−	26.5704i	0.526379	−	1.62003i	0.761573	−	0.648079i	$-0.224427\pi$
$270$		0			0
$271$	8.40531	−	6.10681i	0.510586	−	0.370962i	−0.302460	−	0.953162i	$-0.597808\pi$
$271$	8.40531	−	6.10681i	0.510586	−	0.370962i	0.813046	+	0.582200i	$0.197808\pi$
$272$		0			0
$273$	0.427390	+	1.31537i	0.0258668	+	0.0796098i
$274$		0			0
$275$	−2.91429	+	1.58333i	−0.175738	+	0.0954783i
$276$		0			0
$277$	−0.194167	−	0.597585i	−0.0116664	−	0.0359054i	0.945054	−	0.326915i	$-0.106009\pi$
$277$	−0.194167	−	0.597585i	−0.0116664	−	0.0359054i	−0.956720	+	0.291009i	$0.906009\pi$
$278$		0			0
$279$	−8.58365	+	6.23639i	−0.513890	+	0.373363i
$280$		0			0
$281$	9.30347	−	28.6331i	0.554998	−	1.70811i	−0.140950	−	0.990017i	$-0.545016\pi$
$281$	9.30347	−	28.6331i	0.554998	−	1.70811i	0.695948	−	0.718092i	$-0.254984\pi$
$282$		0			0
$283$	−13.0288	−	9.46599i	−0.774482	−	0.562694i	0.128836	−	0.991666i	$-0.458876\pi$
$283$	−13.0288	−	9.46599i	−0.774482	−	0.562694i	−0.903318	+	0.428972i	$0.858876\pi$
$284$		0			0
$285$	−0.720538			−0.0426810
$286$		0			0
$287$	11.8698			0.700651
$288$		0			0
$289$	−27.7893	−	20.1901i	−1.63467	−	1.18765i
$290$		0			0
$291$	−0.566076	+	1.74220i	−0.0331839	+	0.102130i
$292$		0			0
$293$	3.21992	−	2.33941i	0.188110	−	0.136670i	−0.489745	−	0.871866i	$-0.662910\pi$
$293$	3.21992	−	2.33941i	0.188110	−	0.136670i	0.677854	+	0.735196i	$0.262910\pi$
$294$		0			0
$295$	1.82243	+	5.60885i	0.106106	+	0.326560i
$296$		0			0
$297$	3.78107	+	3.58620i	0.219400	+	0.208093i
$298$		0			0
$299$	−2.62523	−	8.07962i	−0.151821	−	0.467256i
$300$		0			0
$301$	22.9965	−	16.7079i	1.32550	−	0.963030i
$302$		0			0
$303$	0.264977	−	0.815516i	0.0152225	−	0.0468502i
$304$		0			0
$305$	4.97109	+	3.61171i	0.284644	+	0.206806i
$306$		0			0
$307$	−17.6055			−1.00480			−0.502401	−	0.864635i	$-0.667550\pi$
$307$	−17.6055			−1.00480			−0.502401	+	0.864635i	$0.667550\pi$
$308$		0			0
$309$	−1.53057			−0.0870710
$310$		0			0
$311$	−18.3117	−	13.3042i	−1.03836	−	0.754412i	−0.0683942	−	0.997658i	$-0.521788\pi$
$311$	−18.3117	−	13.3042i	−1.03836	−	0.754412i	−0.969964	+	0.243247i	$0.921788\pi$
$312$		0			0
$313$	−3.89659	+	11.9925i	−0.220248	+	0.677855i	0.778491	+	0.627656i	$0.215986\pi$
$313$	−3.89659	+	11.9925i	−0.220248	+	0.677855i	−0.998739	+	0.0501989i	$0.984014\pi$
$314$		0			0
$315$	10.2199	−	7.42521i	0.575827	−	0.418363i
$316$		0			0
$317$	8.11722	+	24.9822i	0.455908	+	1.40314i	0.870065	+	0.492936i	$0.164076\pi$
$317$	8.11722	+	24.9822i	0.455908	+	1.40314i	−0.414157	+	0.910205i	$0.635924\pi$
$318$		0			0
$319$	6.39510	+	34.4539i	0.358057	+	1.92905i
$320$		0			0
$321$	−0.0140367	−	0.0432005i	−0.000783453	−	0.00241122i
$322$		0			0
$323$	−15.7643	+	11.4534i	−0.877148	+	0.637285i
$324$		0			0
$325$	0.374078	−	1.15129i	0.0207501	−	0.0638622i
$326$		0			0
$327$	0.498955	+	0.362512i	0.0275923	+	0.0200470i
$328$		0			0
$329$	−24.7516			−1.36460
$330$		0			0
$331$	−12.7406			−0.700284			−0.350142	−	0.936697i	$-0.613867\pi$
$331$	−12.7406			−0.700284			−0.350142	+	0.936697i	$0.613867\pi$
$332$		0			0
$333$	5.02274	+	3.64924i	0.275245	+	0.199977i
$334$		0			0
$335$	0.504875	−	1.55385i	0.0275843	−	0.0848957i
$336$		0			0
$337$	15.4174	−	11.2014i	0.839841	−	0.610180i	−0.0824856	−	0.996592i	$-0.526286\pi$
$337$	15.4174	−	11.2014i	0.839841	−	0.610180i	0.922326	+	0.386412i	$0.126286\pi$
$338$		0			0
$339$	0.352780	+	1.08574i	0.0191604	+	0.0589696i
$340$		0			0
$341$	−11.9085	−	1.56458i	−0.644884	−	0.0847268i
$342$		0			0
$343$	6.11736	+	18.8273i	0.330306	+	1.01658i
$344$		0			0
$345$	1.50443	−	1.09303i	0.0809956	−	0.0588468i
$346$		0			0
$347$	−5.81663	+	17.9017i	−0.312253	+	0.961016i	0.664617	+	0.747184i	$0.268595\pi$
$347$	−5.81663	+	17.9017i	−0.312253	+	0.961016i	−0.976870	+	0.213832i	$0.931405\pi$
$348$		0			0
$349$	22.0200	+	15.9984i	1.17870	+	0.856377i	0.992025	−	0.126045i	$-0.0402283\pi$
$349$	22.0200	+	15.9984i	1.17870	+	0.856377i	0.186677	+	0.982421i	$0.440228\pi$
$350$		0			0
$351$	−1.90207			−0.101525
$352$		0			0
$353$	25.6380			1.36457			0.682286	−	0.731085i	$-0.260986\pi$
$353$	25.6380			1.36457			0.682286	+	0.731085i	$0.260986\pi$
$354$		0			0
$355$	6.01787	+	4.37224i	0.319395	+	0.232054i
$356$		0			0
$357$	−2.52995	+	7.78640i	−0.133899	+	0.412100i
$358$		0			0
$359$	7.82857	−	5.68779i	0.413176	−	0.300190i	−0.361710	−	0.932291i	$-0.617807\pi$
$359$	7.82857	−	5.68779i	0.413176	−	0.300190i	0.774886	+	0.632100i	$0.217807\pi$
$360$		0			0
$361$	−3.58636	−	11.0377i	−0.188756	−	0.580930i
$362$		0			0
$363$	0.154088	+	2.91067i	0.00808751	+	0.152771i
$364$		0			0
$365$	−2.28431	−	7.03037i	−0.119566	−	0.367987i
$366$		0			0
$367$	−16.7495	+	12.1692i	−0.874317	+	0.635229i	−0.931742	−	0.363121i	$-0.881711\pi$
$367$	−16.7495	+	12.1692i	−0.874317	+	0.635229i	0.0574247	+	0.998350i	$0.481711\pi$
$368$		0			0
$369$	−2.49234	+	7.67063i	−0.129746	+	0.399317i
$370$		0			0
$371$	20.4949	+	14.8904i	1.06404	+	0.773071i
$372$		0			0
$373$	−16.1463			−0.836021			−0.418011	−	0.908442i	$-0.637273\pi$
$373$	−16.1463			−0.836021			−0.418011	+	0.908442i	$0.637273\pi$
$374$		0			0
$375$	0.264977			0.0136834
$376$		0			0
$377$	−10.3475	−	7.51789i	−0.532923	−	0.387191i
$378$		0			0
$379$	0.0709811	−	0.218457i	0.00364605	−	0.0112214i	−0.949217	−	0.314622i	$-0.898122\pi$
$379$	0.0709811	−	0.218457i	0.00364605	−	0.0112214i	0.952863	+	0.303401i	$0.0981221\pi$
$380$		0			0
$381$	2.32295	−	1.68772i	0.119009	−	0.0864648i
$382$		0			0
$383$	−4.02403	−	12.3847i	−0.205619	−	0.632829i	−0.999687	−	0.0250010i	$-0.992041\pi$
$383$	−4.02403	−	12.3847i	−0.205619	−	0.632829i	0.794069	−	0.607828i	$-0.207959\pi$
$384$		0			0
$385$	14.1786	+	1.86283i	0.722609	+	0.0949387i
$386$		0			0
$387$	5.96855	+	18.3693i	0.303399	+	0.933765i
$388$		0			0
$389$	−23.9676	+	17.4135i	−1.21521	+	0.882899i	−0.995693	−	0.0927106i	$-0.970447\pi$
$389$	−23.9676	+	17.4135i	−1.21521	+	0.882899i	−0.219513	+	0.975610i	$0.570447\pi$
$390$		0			0
$391$	15.5402	−	47.8277i	0.785900	−	2.41875i
$392$		0			0
$393$	1.24018	+	0.901040i	0.0625586	+	0.0454515i
$394$		0			0
$395$	−7.00209			−0.352313
$396$		0			0
$397$	2.18665			0.109745			0.0548724	−	0.998493i	$-0.482525\pi$
$397$	2.18665			0.109745			0.0548724	+	0.998493i	$0.482525\pi$
$398$		0			0
$399$	2.51344	+	1.82612i	0.125829	+	0.0914204i
$400$		0			0
$401$	−4.04638	+	12.4535i	−0.202066	+	0.621896i	0.797755	+	0.602982i	$0.206021\pi$
$401$	−4.04638	+	12.4535i	−0.202066	+	0.621896i	−0.999821	+	0.0189143i	$0.993979\pi$
$402$		0			0
$403$	3.54663	−	2.57678i	0.176670	−	0.128358i
$404$		0			0
$405$	2.58740	+	7.96321i	0.128569	+	0.395695i
$406$		0			0
$407$	1.28262	+	6.91016i	0.0635769	+	0.342524i
$408$		0			0
$409$	9.40299	+	28.9394i	0.464948	+	1.43096i	0.859048	+	0.511895i	$0.171056\pi$
$409$	9.40299	+	28.9394i	0.464948	+	1.43096i	−0.394100	+	0.919067i	$0.628944\pi$
$410$		0			0
$411$	−1.85438	+	1.34729i	−0.0914698	+	0.0664567i
$412$		0			0
$413$	7.85785	−	24.1840i	0.386660	−	1.19002i
$414$		0			0
$415$	−1.29006	−	0.937281i	−0.0633264	−	0.0460093i
$416$		0			0
$417$	−3.37797			−0.165420
$418$		0			0
$419$	−26.7473			−1.30669			−0.653346	−	0.757059i	$-0.726635\pi$
$419$	−26.7473			−1.30669			−0.653346	+	0.757059i	$0.726635\pi$
$420$		0			0
$421$	24.5477	+	17.8350i	1.19638	+	0.869223i	0.993924	−	0.110068i	$-0.0351068\pi$
$421$	24.5477	+	17.8350i	1.19638	+	0.869223i	0.202459	+	0.979291i	$0.435107\pi$
$422$		0			0
$423$	5.19718	−	15.9953i	0.252696	−	0.777717i
$424$		0			0
$425$	5.79730	−	4.21198i	0.281210	−	0.204311i
$426$		0			0
$427$	−8.18710	−	25.1973i	−0.396202	−	1.21938i
$428$		0			0
$429$	−0.771890	−	0.732108i	−0.0372672	−	0.0353465i
$430$		0			0
$431$	3.65506	+	11.2491i	0.176058	+	0.541851i	0.999680	−	0.0252880i	$-0.00805028\pi$
$431$	3.65506	+	11.2491i	0.176058	+	0.541851i	−0.823622	+	0.567139i	$0.808050\pi$
$432$		0			0
$433$	−26.3685	+	19.1578i	−1.26719	+	0.920665i	−0.999087	−	0.0427255i	$-0.986396\pi$
$433$	−26.3685	+	19.1578i	−1.26719	+	0.920665i	−0.268100	+	0.963391i	$0.586396\pi$
$434$		0			0
$435$	0.865144	−	2.66264i	0.0414805	−	0.127664i
$436$		0			0
$437$	−15.4387	−	11.2169i	−0.738534	−	0.536576i
$438$		0			0
$439$	−5.09564			−0.243202			−0.121601	−	0.992579i	$-0.538803\pi$
$439$	−5.09564			−0.243202			−0.121601	+	0.992579i	$0.538803\pi$
$440$		0			0
$441$	−33.9598			−1.61713
$442$		0			0
$443$	19.9660	+	14.5061i	0.948612	+	0.689207i	0.950478	−	0.310791i	$-0.100594\pi$
$443$	19.9660	+	14.5061i	0.948612	+	0.689207i	−0.00186632	+	0.999998i	$0.500594\pi$
$444$		0			0
$445$	0.385378	−	1.18607i	0.0182687	−	0.0562252i
$446$		0			0
$447$	−1.41754	+	1.02990i	−0.0670474	+	0.0487128i
$448$		0			0
$449$	−5.86154	−	18.0400i	−0.276623	−	0.851359i	−0.988785	−	0.149344i	$-0.952284\pi$
$449$	−5.86154	−	18.0400i	−0.276623	−	0.851359i	0.712162	−	0.702015i	$-0.247716\pi$
$450$		0			0
$451$	−8.02271	+	4.35873i	−0.377775	+	0.205245i
$452$		0			0
$453$	−1.71113	−	5.26632i	−0.0803959	−	0.247433i
$454$		0			0
$455$	−4.22271	+	3.06798i	−0.197964	+	0.143829i
$456$		0			0
$457$	−8.81134	+	27.1185i	−0.412177	+	1.26855i	0.502575	+	0.864534i	$0.332386\pi$
$457$	−8.81134	+	27.1185i	−0.412177	+	1.26855i	−0.914752	+	0.404016i	$0.867614\pi$
$458$		0			0
$459$	−9.10905	−	6.61811i	−0.425174	−	0.308907i
$460$		0			0
$461$	−35.3117			−1.64463			−0.822315	−	0.569032i	$-0.807318\pi$
$461$	−35.3117			−1.64463			−0.822315	+	0.569032i	$0.807318\pi$
$462$		0			0
$463$	−3.89605			−0.181065			−0.0905323	−	0.995894i	$-0.528857\pi$
$463$	−3.89605			−0.181065			−0.0905323	+	0.995894i	$0.528857\pi$
$464$		0			0
$465$	0.776327	+	0.564034i	0.0360013	+	0.0261565i
$466$		0			0
$467$	3.66272	−	11.2727i	0.169490	−	0.521638i	−0.829849	−	0.557989i	$-0.811573\pi$
$467$	3.66272	−	11.2727i	0.169490	−	0.521638i	0.999339	+	0.0363506i	$0.0115733\pi$
$468$		0			0
$469$	−5.69919	+	4.14070i	−0.263164	+	0.191200i
$470$		0			0
$471$	−1.65641	−	5.09791i	−0.0763234	−	0.234899i
$472$		0			0
$473$	−9.40784	+	19.7374i	−0.432573	+	0.907527i
$474$		0			0
$475$	−0.840293	−	2.58616i	−0.0385553	−	0.118661i
$476$		0			0
$477$	−13.9260	+	10.1179i	−0.637629	+	0.463265i
$478$		0			0
$479$	−3.22158	+	9.91501i	−0.147198	+	0.453029i	−0.997287	−	0.0736102i	$-0.976548\pi$
$479$	−3.22158	+	9.91501i	−0.147198	+	0.453029i	0.850089	+	0.526639i	$0.176548\pi$
$480$		0			0
$481$	−2.07532	−	1.50781i	−0.0946263	−	0.0687500i
$482$		0			0
$483$	−8.01803			−0.364833
$484$		0			0
$485$	−6.91327			−0.313916
$486$		0			0
$487$	−19.9030	−	14.4604i	−0.901890	−	0.655261i	0.0370611	−	0.999313i	$-0.488200\pi$
$487$	−19.9030	−	14.4604i	−0.901890	−	0.655261i	−0.938951	+	0.344052i	$0.888200\pi$
$488$		0			0
$489$	0.661705	−	2.03652i	0.0299233	−	0.0920945i
$490$		0			0
$491$	−18.7305	+	13.6085i	−0.845296	+	0.614143i	−0.923845	−	0.382767i	$-0.874971\pi$
$491$	−18.7305	+	13.6085i	−0.845296	+	0.614143i	0.0785493	+	0.996910i	$0.474971\pi$
$492$		0			0
$493$	−23.3964	−	72.0066i	−1.05372	−	3.24301i
$494$		0			0
$495$	−4.18096	+	8.77153i	−0.187920	+	0.394251i
$496$		0			0
$497$	−9.91108	−	30.5032i	−0.444573	−	1.36825i
$498$		0			0
$499$	18.3406	−	13.3253i	0.821040	−	0.596520i	−0.0959702	−	0.995384i	$-0.530595\pi$
$499$	18.3406	−	13.3253i	0.821040	−	0.596520i	0.917010	+	0.398864i	$0.130595\pi$
$500$		0			0
$501$	−1.41432	+	4.35282i	−0.0631871	+	0.194470i
$502$		0			0
$503$	17.5238	+	12.7318i	0.781347	+	0.567682i	0.905383	−	0.424596i	$-0.139584\pi$
$503$	17.5238	+	12.7318i	0.781347	+	0.567682i	−0.124036	+	0.992278i	$0.539584\pi$
$504$		0			0
$505$	3.23607			0.144003
$506$		0			0
$507$	−3.05640			−0.135740
$508$		0			0
$509$	12.4590	+	9.05200i	0.552236	+	0.401223i	0.828609	−	0.559828i	$-0.189133\pi$
$509$	12.4590	+	9.05200i	0.552236	+	0.401223i	−0.276373	+	0.961050i	$0.589133\pi$
$510$		0			0
$511$	−9.84937	+	30.3132i	−0.435710	+	1.34098i
$512$		0			0
$513$	−3.45664	+	2.51139i	−0.152614	+	0.110881i
$514$		0			0
$515$	−1.78495	−	5.49352i	−0.0786544	−	0.242073i
$516$		0			0
$517$	16.7295	−	9.08909i	0.735760	−	0.399738i
$518$		0			0
$519$	1.17696	+	3.62230i	0.0516627	+	0.159001i
$520$		0			0
$521$	−23.3132	+	16.9380i	−1.02137	+	0.742069i	−0.966563	−	0.256428i	$-0.917454\pi$
$521$	−23.3132	+	16.9380i	−1.02137	+	0.742069i	−0.0548065	+	0.998497i	$0.517454\pi$
$522$		0			0
$523$	−11.0884	+	34.1267i	−0.484863	+	1.49226i	0.347316	+	0.937748i	$0.387093\pi$
$523$	−11.0884	+	34.1267i	−0.484863	+	1.49226i	−0.832179	+	0.554507i	$0.812907\pi$
$524$		0			0
$525$	−0.924315	−	0.671554i	−0.0403404	−	0.0293090i
$526$		0			0
$527$	25.9505			1.13042
$528$		0			0
$529$	26.2505			1.14132
$530$		0			0
$531$	13.9785	+	10.1560i	0.606616	+	0.440733i
$532$		0			0
$533$	1.02979	−	3.16938i	0.0446054	−	0.137281i
$534$		0			0
$535$	0.138686	−	0.100761i	0.00599591	−	0.00435629i
$536$		0			0
$537$	−1.54382	−	4.75139i	−0.0666207	−	0.205038i
$538$		0			0
$539$	−27.8931	−	26.4555i	−1.20144	−	1.13952i
$540$		0			0
$541$	2.17819	+	6.70378i	0.0936477	+	0.288218i	0.986899	−	0.161340i	$-0.0515816\pi$
$541$	2.17819	+	6.70378i	0.0936477	+	0.288218i	−0.893251	+	0.449558i	$0.851582\pi$
$542$		0			0
$543$	2.80878	−	2.04070i	0.120536	−	0.0875746i
$544$		0			0
$545$	−0.719246	+	2.21361i	−0.0308091	+	0.0948207i
$546$		0			0
$547$	12.2661	+	8.91181i	0.524459	+	0.381041i	0.818281	−	0.574819i	$-0.194927\pi$
$547$	12.2661	+	8.91181i	0.524459	+	0.381041i	−0.293822	+	0.955860i	$0.594927\pi$
$548$		0			0
$549$	18.0024			0.768323
$550$		0			0
$551$	−28.7307			−1.22397
$552$		0			0
$553$	24.4253	+	17.7460i	1.03867	+	0.754636i
$554$		0			0
$555$	0.173515	−	0.534025i	0.00736532	−	0.0226681i
$556$		0			0
$557$	9.32902	−	6.77793i	0.395283	−	0.287190i	−0.372334	−	0.928099i	$-0.621442\pi$
$557$	9.32902	−	6.77793i	0.395283	−	0.287190i	0.767617	+	0.640909i	$0.221442\pi$
$558$		0			0
$559$	−2.46611	−	7.58991i	−0.104305	−	0.321019i
$560$		0			0
$561$	−1.14928	−	6.19181i	−0.0485226	−	0.261418i
$562$		0			0
$563$	10.5443	+	32.4519i	0.444388	+	1.36769i	0.883154	+	0.469084i	$0.155416\pi$
$563$	10.5443	+	32.4519i	0.444388	+	1.36769i	−0.438766	+	0.898601i	$0.644584\pi$
$564$		0			0
$565$	−3.48555	+	2.53240i	−0.146638	+	0.106539i
$566$		0			0
$567$	11.1562	−	34.3354i	0.468518	−	1.44195i
$568$		0			0
$569$	6.45701	+	4.69129i	0.270692	+	0.196669i	0.714847	−	0.699281i	$-0.246496\pi$
$569$	6.45701	+	4.69129i	0.270692	+	0.196669i	−0.444155	+	0.895950i	$0.646496\pi$
$570$		0			0
$571$	3.62605			0.151746			0.0758728	−	0.997118i	$-0.475826\pi$
$571$	3.62605			0.151746			0.0758728	+	0.997118i	$0.475826\pi$
$572$		0			0
$573$	2.98677			0.124774
$574$		0			0
$575$	5.67757	+	4.12500i	0.236771	+	0.172024i
$576$		0			0
$577$	−1.13103	+	3.48094i	−0.0470852	+	0.144913i	−0.971835	−	0.235662i	$-0.924274\pi$
$577$	−1.13103	+	3.48094i	−0.0470852	+	0.144913i	0.924750	+	0.380576i	$0.124274\pi$
$578$		0			0
$579$	−1.48865	+	1.08157i	−0.0618662	+	0.0449484i
$580$		0			0
$581$	2.12465	+	6.53900i	0.0881453	+	0.271283i
$582$		0			0
$583$	−19.3203	−	2.53836i	−0.800165	−	0.105128i
$584$		0			0
$585$	−1.09597	−	3.37304i	−0.0453127	−	0.139458i
$586$		0			0
$587$	−14.4242	+	10.4798i	−0.595350	+	0.432547i	−0.844225	−	0.535988i	$-0.819939\pi$
$587$	−14.4242	+	10.4798i	−0.595350	+	0.432547i	0.248875	+	0.968536i	$0.419939\pi$
$588$		0			0
$589$	3.04305	−	9.36555i	0.125387	−	0.385901i
$590$		0			0
$591$	2.88092	+	2.09311i	0.118505	+	0.0860991i
$592$		0			0
$593$	23.0006			0.944523			0.472262	−	0.881458i	$-0.343438\pi$
$593$	23.0006			0.944523			0.472262	+	0.881458i	$0.343438\pi$
$594$		0			0
$595$	−30.8974			−1.26667
$596$		0			0
$597$	−4.16795	−	3.02819i	−0.170583	−	0.123936i
$598$		0			0
$599$	−1.03235	+	3.17725i	−0.0421807	+	0.129819i	−0.969929	−	0.243387i	$-0.921742\pi$
$599$	−1.03235	+	3.17725i	−0.0421807	+	0.129819i	0.927749	+	0.373206i	$0.121742\pi$
$600$		0			0
$601$	−28.2605	+	20.5324i	−1.15277	+	0.837535i	−0.988846	−	0.148939i	$-0.952414\pi$
$601$	−28.2605	+	20.5324i	−1.15277	+	0.837535i	−0.163921	+	0.986473i	$0.552414\pi$
$602$		0			0
$603$	−1.47918	−	4.55244i	−0.0602367	−	0.185390i
$604$		0			0
$605$	−10.2673	+	3.94749i	−0.417425	+	0.160488i
$606$		0			0
$607$	−3.89620	−	11.9913i	−0.158142	−	0.486711i	0.840324	−	0.542085i	$-0.182365\pi$
$607$	−3.89620	−	11.9913i	−0.158142	−	0.486711i	−0.998466	+	0.0553739i	$0.982365\pi$
$608$		0			0
$609$	−9.76602	+	7.09543i	−0.395739	+	0.287521i
$610$		0			0
$611$	−2.14739	+	6.60899i	−0.0868742	+	0.267371i
$612$		0			0
$613$	−6.92760	−	5.03320i	−0.279803	−	0.203289i	0.439028	−	0.898473i	$-0.355323\pi$
$613$	−6.92760	−	5.03320i	−0.279803	−	0.203289i	−0.718832	+	0.695184i	$0.755323\pi$
$614$		0			0
$615$	0.729453			0.0294144
$616$		0			0
$617$	1.77165			0.0713241			0.0356620	−	0.999364i	$-0.488646\pi$
$617$	1.77165			0.0713241			0.0356620	+	0.999364i	$0.488646\pi$
$618$		0			0
$619$	−15.6706	−	11.3854i	−0.629855	−	0.457616i	0.226495	−	0.974012i	$-0.427273\pi$
$619$	−15.6706	−	11.3854i	−0.629855	−	0.457616i	−0.856350	+	0.516396i	$0.827273\pi$
$620$		0			0
$621$	3.40749	−	10.4872i	0.136738	−	0.420836i
$622$		0			0
$623$	−4.35027	+	3.16066i	−0.174290	+	0.126629i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	−2.36939	−	0.311298i	−0.0946244	−	0.0124320i
$628$		0			0
$629$	−4.69243	−	14.4418i	−0.187099	−	0.575833i
$630$		0			0
$631$	22.1727	−	16.1094i	0.882680	−	0.641305i	−0.0512788	−	0.998684i	$-0.516330\pi$
$631$	22.1727	−	16.1094i	0.882680	−	0.641305i	0.933959	+	0.357379i	$0.116330\pi$
$632$		0			0
$633$	0.193122	−	0.594369i	0.00767591	−	0.0236240i
$634$		0			0
$635$	8.76662	+	6.36932i	0.347893	+	0.252759i
$636$		0			0
$637$	14.0316			0.555954
$638$		0			0
$639$	21.7932			0.862126
$640$		0			0
$641$	19.3094	+	14.0291i	0.762676	+	0.554117i	0.899730	−	0.436447i	$-0.143763\pi$
$641$	19.3094	+	14.0291i	0.762676	+	0.554117i	−0.137054	+	0.990564i	$0.543763\pi$
$642$		0			0
$643$	−3.85766	+	11.8726i	−0.152131	+	0.468211i	−0.997859	−	0.0654032i	$-0.979167\pi$
$643$	−3.85766	+	11.8726i	−0.152131	+	0.468211i	0.845728	+	0.533614i	$0.179167\pi$
$644$		0			0
$645$	1.41324	−	1.02678i	0.0556464	−	0.0404294i
$646$		0			0
$647$	−2.18034	−	6.71040i	−0.0857180	−	0.263813i	0.899006	−	0.437937i	$-0.144291\pi$
$647$	−2.18034	−	6.71040i	−0.0857180	−	0.263813i	−0.984724	+	0.174124i	$0.944291\pi$
$648$		0			0
$649$	3.56958	+	19.2313i	0.140118	+	0.754895i
$650$		0			0
$651$	−1.27857	−	3.93502i	−0.0501109	−	0.154226i
$652$		0			0
$653$	−2.16526	+	1.57315i	−0.0847331	+	0.0615622i	−0.629345	−	0.777126i	$-0.716677\pi$
$653$	−2.16526	+	1.57315i	−0.0847331	+	0.0615622i	0.544612	+	0.838688i	$0.316677\pi$
$654$		0			0
$655$	−1.78772	+	5.50203i	−0.0698520	+	0.214982i
$656$		0			0
$657$	−17.5213	−	12.7300i	−0.683570	−	0.496643i
$658$		0			0
$659$	36.5069			1.42211			0.711053	−	0.703138i	$-0.248219\pi$
$659$	36.5069			1.42211			0.711053	+	0.703138i	$0.248219\pi$
$660$		0			0
$661$	40.3521			1.56952			0.784758	−	0.619802i	$-0.212787\pi$
$661$	40.3521			1.56952			0.784758	+	0.619802i	$0.212787\pi$
$662$		0			0
$663$	1.85957	+	1.35106i	0.0722199	+	0.0524708i
$664$		0			0
$665$	−3.62314	+	11.1509i	−0.140499	+	0.432412i
$666$		0			0
$667$	59.9875	−	43.5834i	2.32272	−	1.68756i
$668$		0			0
$669$	1.19522	+	3.67851i	0.0462099	+	0.142219i
$670$		0			0
$671$	14.7864	+	14.0243i	0.570822	+	0.541402i
$672$		0			0
$673$	3.94257	+	12.1340i	0.151975	+	0.467731i	0.997842	−	0.0656634i	$-0.0209163\pi$
$673$	3.94257	+	12.1340i	0.151975	+	0.467731i	−0.845867	+	0.533394i	$0.820916\pi$
$674$		0			0
$675$	1.27117	−	0.923562i	0.0489275	−	0.0355479i
$676$		0			0
$677$	−3.85703	+	11.8707i	−0.148238	+	0.456228i	−0.997413	−	0.0718823i	$-0.977099\pi$
$677$	−3.85703	+	11.8707i	−0.148238	+	0.456228i	0.849175	+	0.528111i	$0.177099\pi$
$678$		0			0
$679$	24.1154	+	17.5209i	0.925466	+	0.672390i
$680$		0			0
$681$	−0.792201			−0.0303572
$682$		0			0
$683$	−5.10260			−0.195246			−0.0976228	−	0.995223i	$-0.531124\pi$
$683$	−5.10260			−0.195246			−0.0976228	+	0.995223i	$0.531124\pi$
$684$		0			0
$685$	−6.99826	−	5.08453i	−0.267390	−	0.194270i
$686$		0			0
$687$	0.129286	−	0.397900i	0.00493256	−	0.0151808i
$688$		0			0
$689$	5.75401	−	4.18054i	0.219210	−	0.159266i
$690$		0			0
$691$	−3.68372	−	11.3373i	−0.140135	−	0.431292i	0.856218	−	0.516615i	$-0.172808\pi$
$691$	−3.68372	−	11.3373i	−0.140135	−	0.431292i	−0.996353	+	0.0853223i	$0.972808\pi$
$692$		0			0
$693$	36.8148	−	20.0014i	1.39848	−	0.759791i
$694$		0			0
$695$	−3.93940	−	12.1242i	−0.149430	−	0.459898i
$696$		0			0
$697$	15.9593	−	11.5951i	0.604502	−	0.439197i
$698$		0			0
$699$	0.0414095	−	0.127445i	0.00156625	−	0.00482043i
$700$		0			0
$701$	9.19138	+	6.67793i	0.347154	+	0.252222i	0.747674	−	0.664066i	$-0.231171\pi$
$701$	9.19138	+	6.67793i	0.347154	+	0.252222i	−0.400520	+	0.916288i	$0.631171\pi$
$702$		0			0
$703$	−5.76230			−0.217329
$704$		0			0
$705$	−1.52110			−0.0572879
$706$		0			0
$707$	−11.2883	−	8.20144i	−0.424541	−	0.308447i
$708$		0			0
$709$	3.75791	−	11.5656i	0.141131	−	0.434357i	−0.855362	−	0.518031i	$-0.826665\pi$
$709$	3.75791	−	11.5656i	0.141131	−	0.434357i	0.996493	+	0.0836737i	$0.0266653\pi$
$710$		0			0
$711$	−16.5967	+	12.0582i	−0.622424	+	0.452218i
$712$		0			0
$713$	7.85355	+	24.1707i	0.294118	+	0.905201i
$714$		0			0
$715$	1.72750	−	3.62426i	0.0646050	−	0.135539i
$716$		0			0
$717$	1.37086	+	4.21908i	0.0511958	+	0.157565i
$718$		0			0
$719$	−27.9662	+	20.3186i	−1.04296	+	0.757756i	−0.970862	−	0.239641i	$-0.922970\pi$
$719$	−27.9662	+	20.3186i	−1.04296	+	0.757756i	−0.0721003	+	0.997397i	$0.522970\pi$
$720$		0			0
$721$	−7.69628	+	23.6867i	−0.286624	+	0.882139i
$722$		0			0
$723$	3.27874	+	2.38214i	0.121938	+	0.0885928i
$724$		0			0
$725$	10.5657			0.392400
$726$		0			0
$727$	−46.4273			−1.72189			−0.860947	−	0.508695i	$-0.830128\pi$
$727$	−46.4273			−1.72189			−0.860947	+	0.508695i	$0.830128\pi$
$728$		0			0
$729$	18.8356	+	13.6849i	0.697616	+	0.506847i
$730$		0			0
$731$	14.5983	−	44.9288i	0.539936	−	1.66175i
$732$		0			0
$733$	−11.8252	+	8.59151i	−0.436773	+	0.317334i	−0.784352	−	0.620317i	$-0.787004\pi$
$733$	−11.8252	+	8.59151i	−0.436773	+	0.317334i	0.347578	+	0.937651i	$0.387004\pi$
$734$		0			0
$735$	0.949117	+	2.92108i	0.0350087	+	0.107746i
$736$		0			0
$737$	2.33153	−	4.89149i	0.0858830	−	0.180180i
$738$		0			0
$739$	12.8330	+	39.4959i	0.472070	+	1.45288i	0.849869	+	0.526994i	$0.176681\pi$
$739$	12.8330	+	39.4959i	0.472070	+	1.45288i	−0.377800	+	0.925887i	$0.623319\pi$
$740$		0			0
$741$	0.705658	−	0.512690i	0.0259230	−	0.0188341i
$742$		0			0
$743$	12.3655	−	38.0571i	0.453646	−	1.39618i	−0.419071	−	0.907953i	$-0.637644\pi$
$743$	12.3655	−	38.0571i	0.453646	−	1.39618i	0.872717	−	0.488226i	$-0.162356\pi$
$744$		0			0
$745$	−5.34967	−	3.88677i	−0.195997	−	0.142400i
$746$		0			0
$747$	−4.67183			−0.170933
$748$		0			0
$749$	−0.739143			−0.0270077
$750$		0			0
$751$	11.5210	+	8.37050i	0.420407	+	0.305444i	0.777802	−	0.628510i	$-0.216335\pi$
$751$	11.5210	+	8.37050i	0.420407	+	0.305444i	−0.357394	+	0.933954i	$0.616335\pi$
$752$		0			0
$753$	0.0349957	−	0.107706i	0.00127531	−	0.00392502i
$754$		0			0
$755$	16.9064	−	12.2832i	0.615285	−	0.447031i
$756$		0			0
$757$	−9.20948	−	28.3439i	−0.334724	−	1.03017i	−0.966858	−	0.255316i	$-0.917821\pi$
$757$	−9.20948	−	28.3439i	−0.334724	−	1.03017i	0.632134	−	0.774859i	$-0.282179\pi$
$758$		0			0
$759$	5.41933	−	2.94432i	0.196709	−	0.106872i
$760$		0			0
$761$	−4.10031	−	12.6195i	−0.148636	−	0.457455i	0.848825	−	0.528675i	$-0.177311\pi$
$761$	−4.10031	−	12.6195i	−0.148636	−	0.457455i	−0.997461	+	0.0712199i	$0.977311\pi$
$762$		0			0
$763$	8.11908	−	5.89886i	0.293930	−	0.213553i
$764$		0			0
$765$	6.48764	−	19.9669i	0.234561	−	0.721904i
$766$		0			0
$767$	−5.77570	−	4.19629i	−0.208548	−	0.151519i
$768$		0			0
$769$	−46.3160			−1.67020			−0.835099	−	0.550099i	$-0.814590\pi$
$769$	−46.3160			−1.67020			−0.835099	+	0.550099i	$0.814590\pi$
$770$		0			0
$771$	4.73653			0.170582
$772$		0			0
$773$	−41.3802	−	30.0645i	−1.48834	−	1.08134i	−0.974747	−	0.223312i	$-0.928313\pi$
$773$	−41.3802	−	30.0645i	−1.48834	−	1.08134i	−0.513596	−	0.858032i	$-0.671687\pi$
$774$		0			0
$775$	−1.11908	+	3.44417i	−0.0401985	+	0.123718i
$776$		0			0
$777$	−1.95870	+	1.42308i	−0.0702678	+	0.0510526i
$778$		0			0
$779$	−2.31323	−	7.11940i	−0.0828802	−	0.255079i
$780$		0			0
$781$	17.9000	+	16.9774i	0.640512	+	0.607501i
$782$		0			0
$783$	−5.13012	−	15.7889i	−0.183336	−	0.564249i
$784$		0			0
$785$	16.3657	−	11.8904i	0.584118	−	0.424386i
$786$		0			0
$787$	−10.7231	+	33.0022i	−0.382236	+	1.17640i	0.556229	+	0.831029i	$0.312248\pi$
$787$	−10.7231	+	33.0022i	−0.382236	+	1.17640i	−0.938465	+	0.345374i	$0.887752\pi$
$788$		0			0
$789$	3.10788	+	2.25801i	0.110643	+	0.0803871i
$790$		0			0
$791$	18.5766			0.660509
$792$		0			0
$793$	−7.43830			−0.264142
$794$		0			0
$795$	1.25950	+	0.915084i	0.0446700	+	0.0324547i
$796$		0			0
$797$	13.8054	−	42.4885i	0.489011	−	1.50502i	−0.337075	−	0.941478i	$-0.609438\pi$
$797$	13.8054	−	42.4885i	0.489011	−	1.50502i	0.826086	−	0.563544i	$-0.190562\pi$
$798$		0			0
$799$	−33.2794	+	24.1789i	−1.17734	+	0.855387i
$800$		0			0
$801$	−1.12908	−	3.47494i	−0.0398939	−	0.122781i
$802$		0			0
$803$	−4.47426	−	24.1053i	−0.157893	−	0.850659i
$804$		0			0
$805$	−9.35064	−	28.7783i	−0.329567	−	1.01430i
$806$		0			0
$807$	−5.98906	+	4.35130i	−0.210825	+	0.153173i
$808$		0			0
$809$	−4.04819	+	12.4590i	−0.142327	+	0.438037i	−0.996658	−	0.0816929i	$-0.973967\pi$
$809$	−4.04819	+	12.4590i	−0.142327	+	0.438037i	0.854331	+	0.519730i	$0.173967\pi$
$810$		0			0
$811$	−6.33646	−	4.60371i	−0.222503	−	0.161658i	0.470949	−	0.882160i	$-0.343911\pi$
$811$	−6.33646	−	4.60371i	−0.222503	−	0.161658i	−0.693453	+	0.720502i	$0.743911\pi$
$812$		0			0
$813$	−2.75299			−0.0965515
$814$		0			0
$815$	8.08116			0.283071
$816$		0			0
$817$	−14.5030	−	10.5370i	−0.507394	−	0.368644i
$818$		0			0
$819$	−4.72554	+	14.5437i	−0.165124	+	0.508199i
$820$		0			0
$821$	19.4432	−	14.1263i	0.678573	−	0.493012i	−0.194311	−	0.980940i	$-0.562247\pi$
$821$	19.4432	−	14.1263i	0.678573	−	0.493012i	0.872884	+	0.487928i	$0.162247\pi$
$822$		0			0
$823$	−3.73052	−	11.4813i	−0.130038	−	0.400215i	0.864748	−	0.502207i	$-0.167478\pi$
$823$	−3.73052	−	11.4813i	−0.130038	−	0.400215i	−0.994785	+	0.101992i	$0.967478\pi$
$824$		0			0
$825$	0.871342	+	0.114480i	0.0303362	+	0.00398567i
$826$		0			0
$827$	−10.8899	−	33.5158i	−0.378680	−	1.16546i	−0.940962	−	0.338512i	$-0.890076\pi$
$827$	−10.8899	−	33.5158i	−0.378680	−	1.16546i	0.562282	−	0.826946i	$-0.309924\pi$
$828$		0			0
$829$	−19.6457	+	14.2734i	−0.682322	+	0.495736i	−0.874127	−	0.485697i	$-0.838566\pi$
$829$	−19.6457	+	14.2734i	−0.682322	+	0.495736i	0.191805	+	0.981433i	$0.438566\pi$
$830$		0			0
$831$	−0.0514499	+	0.158346i	−0.00178478	+	0.00549298i
$832$		0			0
$833$	67.1977	+	48.8220i	2.32826	+	1.69158i
$834$		0			0
$835$	−17.2725			−0.597741
$836$		0			0
$837$	5.69018			0.196681
$838$		0			0
$839$	12.3220	+	8.95243i	0.425401	+	0.309072i	0.779807	−	0.626019i	$-0.215317\pi$
$839$	12.3220	+	8.95243i	0.425401	+	0.309072i	−0.354406	+	0.935092i	$0.615317\pi$
$840$		0			0
$841$	25.5352	−	78.5894i	0.880525	−	2.70998i
$842$		0			0
$843$	−6.45399	+	4.68910i	−0.222287	+	0.161501i
$844$		0			0
$845$	−3.56438	−	10.9700i	−0.122619	−	0.377381i
$846$		0			0
$847$	45.8197	+	12.2513i	1.57438	+	0.420961i
$848$		0			0
$849$	1.31868	+	4.05847i	0.0452568	+	0.139286i
$850$		0			0
$851$	12.0312	−	8.74120i	0.412425	−	0.299644i
$852$		0			0
$853$	−2.13420	+	6.56839i	−0.0730736	+	0.224897i	−0.980922	−	0.194401i	$-0.937724\pi$
$853$	−2.13420	+	6.56839i	−0.0730736	+	0.224897i	0.907849	+	0.419298i	$0.137724\pi$
$854$		0			0
$855$	−6.44529	−	4.68277i	−0.220424	−	0.160148i
$856$		0			0
$857$	−1.68576			−0.0575845			−0.0287922	−	0.999585i	$-0.509166\pi$
$857$	−1.68576			−0.0575845			−0.0287922	+	0.999585i	$0.509166\pi$
$858$		0			0
$859$	52.7330			1.79923			0.899613	−	0.436688i	$-0.143849\pi$
$859$	52.7330			1.79923			0.899613	+	0.436688i	$0.143849\pi$
$860$		0			0
$861$	−2.54454	−	1.84871i	−0.0867176	−	0.0630040i
$862$		0			0
$863$	−9.11412	+	28.0504i	−0.310248	+	0.954846i	0.667418	+	0.744683i	$0.267399\pi$
$863$	−9.11412	+	28.0504i	−0.310248	+	0.954846i	−0.977666	+	0.210163i	$0.932601\pi$
$864$		0			0
$865$	−11.6286	+	8.44868i	−0.395385	+	0.287264i
$866$		0			0
$867$	2.81262	+	8.65635i	0.0955216	+	0.293985i
$868$		0			0
$869$	−23.0254	−	3.02515i	−0.781084	−	0.102621i
$870$		0			0
$871$	0.611172	+	1.88099i	0.0207088	+	0.0637351i
$872$		0			0
$873$	−16.3862	+	11.9052i	−0.554588	+	0.402932i
$874$		0			0
$875$	1.33240	−	4.10072i	0.0450435	−	0.138630i
$876$		0			0
$877$	22.6710	+	16.4715i	0.765547	+	0.556202i	0.900607	−	0.434635i	$-0.143123\pi$
$877$	22.6710	+	16.4715i	0.765547	+	0.556202i	−0.135060	+	0.990837i	$0.543123\pi$
$878$		0			0
$879$	−1.05462			−0.0355715
$880$		0			0
$881$	−28.1345			−0.947875			−0.473937	−	0.880559i	$-0.657168\pi$
$881$	−28.1345			−0.947875			−0.473937	+	0.880559i	$0.657168\pi$
$882$		0			0
$883$	32.7842	+	23.8191i	1.10328	+	0.801578i	0.981592	−	0.190991i	$-0.0611700\pi$
$883$	32.7842	+	23.8191i	1.10328	+	0.801578i	0.121686	+	0.992569i	$0.461170\pi$
$884$		0			0
$885$	0.482901	−	1.48622i	0.0162326	−	0.0499587i
$886$		0			0
$887$	11.5317	−	8.37825i	0.387196	−	0.281314i	−0.377110	−	0.926169i	$-0.623082\pi$
$887$	11.5317	−	8.37825i	0.387196	−	0.281314i	0.764305	+	0.644854i	$0.223082\pi$
$888$		0			0
$889$	−14.4381	−	44.4360i	−0.484239	−	1.49033i
$890$		0			0
$891$	5.06794	+	27.3038i	0.169782	+	0.914711i
$892$		0			0
$893$	4.82370	+	14.8458i	0.161419	+	0.496796i
$894$		0			0
$895$	15.2533	−	11.0822i	0.509861	−	0.370436i
$896$		0			0
$897$	−0.695625	+	2.14091i	−0.0232263	+	0.0714831i
$898$		0			0
$899$	30.9552	+	22.4903i	1.03241	+	0.750093i
$900$		0			0
$901$	42.1019			1.40262
$902$		0			0
$903$	−7.53204			−0.250651
$904$		0			0
$905$	10.6001	+	7.70140i	0.352358	+	0.256003i
$906$		0			0
$907$	13.3997	−	41.2401i	0.444931	−	1.36936i	−0.437629	−	0.899156i	$-0.644182\pi$
$907$	13.3997	−	41.2401i	0.444931	−	1.36936i	0.882560	−	0.470200i	$-0.155818\pi$
$908$		0			0
$909$	7.67028	−	5.57279i	0.254407	−	0.184838i
$910$		0			0
$911$	−7.33435	−	22.5728i	−0.242998	−	0.747871i	−0.995959	−	0.0898061i	$-0.971375\pi$
$911$	−7.33435	−	22.5728i	−0.242998	−	0.747871i	0.752961	−	0.658065i	$-0.228625\pi$
$912$		0			0
$913$	−3.83724	−	3.63947i	−0.126994	−	0.120449i
$914$		0			0
$915$	−0.503135	−	1.54849i	−0.0166331	−	0.0511915i
$916$		0			0
$917$	20.1803	−	14.6619i	0.666414	−	0.484178i
$918$		0			0
$919$	4.34410	−	13.3698i	0.143299	−	0.441028i	−0.853490	−	0.521110i	$-0.825518\pi$
$919$	4.34410	−	13.3698i	0.143299	−	0.441028i	0.996788	+	0.0800817i	$0.0255181\pi$
$920$		0			0
$921$	3.77412	+	2.74206i	0.124361	+	0.0903538i
$922$		0			0
$923$	−9.00460			−0.296390
$924$		0			0
$925$	2.11908			0.0696749
$926$		0			0
$927$	−13.6911	−	9.94716i	−0.449674	−	0.326708i
$928$		0			0
$929$	−17.2507	+	53.0922i	−0.565977	+	1.74190i	0.0990531	+	0.995082i	$0.468419\pi$
$929$	−17.2507	+	53.0922i	−0.565977	+	1.74190i	−0.665030	+	0.746816i	$0.731581\pi$
$930$		0			0
$931$	25.4997	−	18.5266i	0.835719	−	0.607185i
$932$		0			0
$933$	1.85336	+	5.70407i	0.0606764	+	0.186743i
$934$		0			0
$935$	20.8834	−	11.3459i	0.682959	−	0.371051i
$936$		0			0
$937$	−3.84000	−	11.8183i	−0.125447	−	0.386088i	0.868535	−	0.495628i	$-0.165062\pi$
$937$	−3.84000	−	11.8183i	−0.125447	−	0.386088i	−0.993982	+	0.109540i	$0.965062\pi$
$938$		0			0
$939$	2.70314	−	1.96395i	0.0882136	−	0.0640910i
$940$		0			0
$941$	−4.50996	+	13.8802i	−0.147020	+	0.452483i	−0.997265	−	0.0739049i	$-0.976454\pi$
$941$	−4.50996	+	13.8802i	−0.147020	+	0.452483i	0.850245	+	0.526387i	$0.176454\pi$
$942$		0			0
$943$	15.6297	+	11.3557i	0.508974	+	0.369791i
$944$		0			0
$945$	−6.77488			−0.220387
$946$		0			0
$947$	−38.1184			−1.23868			−0.619340	−	0.785123i	$-0.712600\pi$
$947$	−38.1184			−1.23868			−0.619340	+	0.785123i	$0.712600\pi$
$948$		0			0
$949$	7.23951	+	5.25981i	0.235004	+	0.170741i
$950$		0			0
$951$	2.15088	−	6.61972i	0.0697470	−	0.214659i
$952$		0			0
$953$	−0.381518	+	0.277189i	−0.0123586	+	0.00897903i	−0.593947	−	0.804504i	$-0.702431\pi$
$953$	−0.381518	+	0.277189i	−0.0123586	+	0.00897903i	0.581589	+	0.813483i	$0.302431\pi$
$954$		0			0
$955$	3.48318	+	10.7201i	0.112713	+	0.346895i
$956$		0			0
$957$	3.99527	−	8.38196i	0.129149	−	0.270950i
$958$		0			0
$959$	11.5257	+	35.4726i	0.372185	+	1.14547i
$960$		0			0
$961$	14.4695	−	10.5127i	0.466760	−	0.339121i
$962$		0			0
$963$	0.155200	−	0.477658i	0.00500126	−	0.0153923i
$964$		0			0
$965$	−5.61803	−	4.08174i	−0.180851	−	0.131396i
$966$		0			0
$967$	29.1678			0.937975			0.468987	−	0.883205i	$-0.344619\pi$
$967$	29.1678			0.937975			0.468987	+	0.883205i	$0.344619\pi$
$968$		0			0
$969$	5.16327			0.165868
$970$		0			0
$971$	−12.8033	−	9.30216i	−0.410878	−	0.298520i	0.363079	−	0.931758i	$-0.381725\pi$
$971$	−12.8033	−	9.30216i	−0.410878	−	0.298520i	−0.773957	+	0.633238i	$0.781725\pi$
$972$		0			0
$973$	−16.9857	+	52.2766i	−0.544537	+	1.67591i
$974$		0			0
$975$	−0.259505	+	0.188541i	−0.00831081	+	0.00603815i
$976$		0			0
$977$	12.9305	+	39.7961i	0.413684	+	1.27319i	0.913423	+	0.407013i	$0.133429\pi$
$977$	12.9305	+	39.7961i	0.413684	+	1.27319i	−0.499738	+	0.866176i	$0.666571\pi$
$978$		0			0
$979$	1.77969	−	3.73374i	0.0568791	−	0.119331i
$980$		0			0
$981$	2.10724	+	6.48541i	0.0672789	+	0.207063i
$982$		0			0
$983$	4.12492	−	2.99693i	0.131565	−	0.0955872i	−0.520057	−	0.854132i	$-0.674089\pi$
$983$	4.12492	−	2.99693i	0.131565	−	0.0955872i	0.651621	+	0.758545i	$0.274089\pi$
$984$		0			0
$985$	−4.15286	+	12.7812i	−0.132321	+	0.407243i
$986$		0			0
$987$	5.30602	+	3.85505i	0.168893	+	0.122708i
$988$		0			0
$989$	46.2653			1.47115
$990$		0			0
$991$	14.8133			0.470560			0.235280	−	0.971928i	$-0.424399\pi$
$991$	14.8133			0.470560			0.235280	+	0.971928i	$0.424399\pi$
$992$		0			0
$993$	2.73121	+	1.98434i	0.0866722	+	0.0629710i
$994$		0			0
$995$	6.00812	−	18.4911i	0.190470	−	0.586207i
$996$		0			0
$997$	46.9861	−	34.1374i	1.48807	−	1.08114i	0.513221	−	0.858257i	$-0.328452\pi$
$997$	46.9861	−	34.1374i	1.48807	−	1.08114i	0.974844	−	0.222886i	$-0.0715478\pi$
$998$		0			0
$999$	−1.02891	−	3.16666i	−0.0325532	−	0.100189i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.bo.g.401.1		8
4.3	odd	2		110.2.g.c.71.2	yes	8
11.3	even	5		9680.2.a.cj.1.3		4
11.8	odd	10		9680.2.a.ci.1.3		4
11.9	even	5	inner	880.2.bo.g.801.1		8
12.11	even	2		990.2.n.j.181.2		8
20.3	even	4		550.2.ba.f.49.1		16
20.7	even	4		550.2.ba.f.49.4		16
20.19	odd	2		550.2.h.l.401.1		8
44.3	odd	10		1210.2.a.u.1.2		4
44.19	even	10		1210.2.a.v.1.2		4
44.31	odd	10		110.2.g.c.31.2	✓	8
132.119	even	10		990.2.n.j.361.2		8
220.19	even	10		6050.2.a.cy.1.3		4
220.119	odd	10		550.2.h.l.251.1		8
220.163	even	20		550.2.ba.f.449.4		16
220.179	odd	10		6050.2.a.dh.1.3		4
220.207	even	20		550.2.ba.f.449.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.g.c.31.2	✓	8	44.31	odd	10
110.2.g.c.71.2	yes	8	4.3	odd	2
550.2.h.l.251.1		8	220.119	odd	10
550.2.h.l.401.1		8	20.19	odd	2
550.2.ba.f.49.1		16	20.3	even	4
550.2.ba.f.49.4		16	20.7	even	4
550.2.ba.f.449.1		16	220.207	even	20
550.2.ba.f.449.4		16	220.163	even	20
880.2.bo.g.401.1		8	1.1	even	1	trivial
880.2.bo.g.801.1		8	11.9	even	5	inner
990.2.n.j.181.2		8	12.11	even	2
990.2.n.j.361.2		8	132.119	even	10
1210.2.a.u.1.2		4	44.3	odd	10
1210.2.a.v.1.2		4	44.19	even	10
6050.2.a.cy.1.3		4	220.19	even	10
6050.2.a.dh.1.3		4	220.179	odd	10
9680.2.a.ci.1.3		4	11.8	odd	10
9680.2.a.cj.1.3		4	11.3	even	5

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.bo (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.214371 - 0.155750i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-3.48828 + 2.53438i) q^{7} +(-0.905354 - 2.78639i) q^{9} +O(q^{10})\)	\(q+(-0.214371 - 0.155750i) q^{3} +(0.309017 - 0.951057i) q^{5} +(-3.48828 + 2.53438i) q^{7} +(-0.905354 - 2.78639i) q^{9} +(1.42705 - 2.99391i) q^{11} +(0.374078 + 1.15129i) q^{13} +(-0.214371 + 0.155750i) q^{15} +(-2.21437 + 6.81513i) q^{17} +(2.19992 + 1.59833i) q^{19} +1.14252 q^{21} -7.01787 q^{23} +(-0.809017 - 0.587785i) q^{25} +(-0.485545 + 1.49436i) q^{27} +(-8.54782 + 6.21036i) q^{29} +(-1.11908 - 3.44417i) q^{31} +(-0.772220 + 0.419546i) q^{33} +(1.33240 + 4.10072i) q^{35} +(-1.71437 + 1.24556i) q^{37} +(0.0991220 - 0.305066i) q^{39} +(-2.22713 - 1.61811i) q^{41} -6.59251 q^{43} -2.92979 q^{45} +(4.64416 + 3.37418i) q^{47} +(3.58188 - 11.0239i) q^{49} +(1.53615 - 1.11608i) q^{51} +(-1.81558 - 5.58779i) q^{53} +(-2.40640 - 2.28238i) q^{55} +(-0.222659 - 0.685272i) q^{57} +(-4.77117 + 3.46646i) q^{59} +(-1.89879 + 5.84387i) q^{61} +(10.2199 + 7.42521i) q^{63} +1.21054 q^{65} +1.63381 q^{67} +(1.50443 + 1.09303i) q^{69} +(-2.29862 + 7.07443i) q^{71} +(5.98039 - 4.34501i) q^{73} +(0.0818824 + 0.252008i) q^{75} +(2.60978 + 14.0603i) q^{77} +(-2.16376 - 6.65938i) q^{79} +(-6.77391 + 4.92153i) q^{81} +(0.492758 - 1.51655i) q^{83} +(5.79730 + 4.21198i) q^{85} +2.79967 q^{87} +1.24711 q^{89} +(-4.22271 - 3.06798i) q^{91} +(-0.296530 + 0.912627i) q^{93} +(2.19992 - 1.59833i) q^{95} +(-2.13632 - 6.57491i) q^{97} +(-9.63421 - 1.26577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 2 q^{5} + q^{7} - 6 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 2 * q^5 + q^7 - 6 * q^9	\( 8 q + 4 q^{3} - 2 q^{5} + q^{7} - 6 q^{9} - 2 q^{11} + q^{13} + 4 q^{15} - 12 q^{17} + 7 q^{19} + 32 q^{21} - 26 q^{23} - 2 q^{25} + q^{27} - 22 q^{29} + 26 q^{31} + 19 q^{33} - 4 q^{35} - 8 q^{37} + 48 q^{39} - 15 q^{41} - 38 q^{43} + 14 q^{45} - 6 q^{47} + 27 q^{49} + 5 q^{51} - 4 q^{53} + 8 q^{55} + 47 q^{57} - 39 q^{59} - 20 q^{61} + 57 q^{63} - 14 q^{65} + 26 q^{67} - 10 q^{69} - 2 q^{71} + 8 q^{73} - q^{75} + 16 q^{77} - 14 q^{79} - 31 q^{81} + 21 q^{83} + 13 q^{85} - 20 q^{87} + 32 q^{89} - 53 q^{91} - 38 q^{93} + 7 q^{95} - 31 q^{97} - 36 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 2 * q^5 + q^7 - 6 * q^9 - 2 * q^11 + q^13 + 4 * q^15 - 12 * q^17 + 7 * q^19 + 32 * q^21 - 26 * q^23 - 2 * q^25 + q^27 - 22 * q^29 + 26 * q^31 + 19 * q^33 - 4 * q^35 - 8 * q^37 + 48 * q^39 - 15 * q^41 - 38 * q^43 + 14 * q^45 - 6 * q^47 + 27 * q^49 + 5 * q^51 - 4 * q^53 + 8 * q^55 + 47 * q^57 - 39 * q^59 - 20 * q^61 + 57 * q^63 - 14 * q^65 + 26 * q^67 - 10 * q^69 - 2 * q^71 + 8 * q^73 - q^75 + 16 * q^77 - 14 * q^79 - 31 * q^81 + 21 * q^83 + 13 * q^85 - 20 * q^87 + 32 * q^89 - 53 * q^91 - 38 * q^93 + 7 * q^95 - 31 * q^97 - 36 * q^99

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