LMFDB - Embedded newform 88.2.i.b.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(9,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("88.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.i (of order $5$, 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:	$0.702683537787$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$2.51217 - 1.82520i$ of defining polynomial
Character	$\chi$	$=$	88.9
Dual form			88.2.i.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.55261 + 1.12804i) q^{3} +(1.05261 + 3.23960i) q^{5} +(-0.703158 - 0.510874i) q^{7} +(0.211078 - 0.649631i) q^{9} +O(q^{10})$	\(q+(-1.55261 + 1.12804i) q^{3} +(1.05261 + 3.23960i) q^{5} +(-0.703158 - 0.510874i) q^{7} +(0.211078 - 0.649631i) q^{9} +(3.16272 + 0.998590i) q^{11} +(0.866521 - 2.66688i) q^{13} +(-5.28868 - 3.84245i) q^{15} +(-2.25314 - 6.93444i) q^{17} +(-1.92705 + 1.40008i) q^{19} +1.66801 q^{21} +7.44651 q^{23} +(-5.34193 + 3.88114i) q^{25} +(-1.37405 - 4.22888i) q^{27} +(5.93923 + 4.31510i) q^{29} +(-0.816541 + 2.51306i) q^{31} +(-6.03692 + 2.01725i) q^{33} +(0.914876 - 2.81570i) q^{35} +(-0.834007 - 0.605942i) q^{37} +(1.66297 + 5.11809i) q^{39} +(-2.34089 + 1.70076i) q^{41} +2.18609 q^{43} +2.32673 q^{45} +(3.19034 - 2.31792i) q^{47} +(-1.92968 - 5.93895i) q^{49} +(11.3206 + 8.22486i) q^{51} +(-2.19851 + 6.76631i) q^{53} +(0.0940804 + 11.2971i) q^{55} +(1.41261 - 4.34757i) q^{57} +(-6.54508 - 4.75528i) q^{59} +(-0.832382 - 2.56181i) q^{61} +(-0.480301 + 0.348959i) q^{63} +9.55172 q^{65} -13.7720 q^{67} +(-11.5615 + 8.39993i) q^{69} +(-0.596314 - 1.83527i) q^{71} +(-4.03979 - 2.93508i) q^{73} +(3.91586 - 12.0518i) q^{75} +(-1.71374 - 2.31792i) q^{77} +(4.15783 - 12.7965i) q^{79} +(8.56151 + 6.22030i) q^{81} +(-0.0601338 - 0.185073i) q^{83} +(20.0931 - 14.5985i) q^{85} -14.0889 q^{87} +4.18609 q^{89} +(-1.97174 + 1.43255i) q^{91} +(-1.56705 - 4.82288i) q^{93} +(-6.56414 - 4.76913i) q^{95} +(1.54206 - 4.74597i) q^{97} +(1.31630 - 1.84382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 3 q^{5} + 7 q^{7} - 13 q^{9}+O(q^{10}) $ 8 * q - q^3 - 3 * q^5 + 7 * q^7 - 13 * q^9	$ 8 q - q^{3} - 3 q^{5} + 7 q^{7} - 13 q^{9} + 7 q^{11} + 7 q^{13} - 13 q^{15} + q^{17} - 2 q^{19} - 2 q^{21} - 4 q^{23} - 33 q^{25} - 22 q^{27} + 17 q^{29} - 13 q^{31} + 16 q^{33} + 11 q^{35} + q^{37} + 39 q^{39} + 9 q^{41} + 6 q^{43} + 44 q^{45} - q^{47} + 3 q^{49} + 38 q^{51} - 33 q^{53} + 13 q^{55} - 6 q^{57} - 30 q^{59} - 9 q^{61} - 10 q^{63} - 10 q^{65} - 10 q^{67} - 38 q^{69} - 25 q^{71} - 7 q^{73} - 6 q^{75} - 7 q^{77} - q^{79} + 14 q^{81} + 39 q^{85} - 6 q^{87} + 22 q^{89} + 7 q^{91} - 5 q^{93} + 7 q^{95} + 8 q^{97} - 27 q^{99}+O(q^{100}) $ 8 * q - q^3 - 3 * q^5 + 7 * q^7 - 13 * q^9 + 7 * q^11 + 7 * q^13 - 13 * q^15 + q^17 - 2 * q^19 - 2 * q^21 - 4 * q^23 - 33 * q^25 - 22 * q^27 + 17 * q^29 - 13 * q^31 + 16 * q^33 + 11 * q^35 + q^37 + 39 * q^39 + 9 * q^41 + 6 * q^43 + 44 * q^45 - q^47 + 3 * q^49 + 38 * q^51 - 33 * q^53 + 13 * q^55 - 6 * q^57 - 30 * q^59 - 9 * q^61 - 10 * q^63 - 10 * q^65 - 10 * q^67 - 38 * q^69 - 25 * q^71 - 7 * q^73 - 6 * q^75 - 7 * q^77 - q^79 + 14 * q^81 + 39 * q^85 - 6 * q^87 + 22 * q^89 + 7 * q^91 - 5 * q^93 + 7 * q^95 + 8 * q^97 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.55261	+	1.12804i	−0.896399	+	0.651272i	−0.937539	−	0.347881i	$-0.886901\pi$
$3$	−1.55261	+	1.12804i	−0.896399	+	0.651272i	0.0411392	+	0.999153i	$0.486901\pi$
$4$		0			0
$5$	1.05261	+	3.23960i	0.470741	+	1.44879i	0.851616	+	0.524166i	$0.175623\pi$
$5$	1.05261	+	3.23960i	0.470741	+	1.44879i	−0.380875	+	0.924627i	$0.624377\pi$
$6$		0			0
$7$	−0.703158	−	0.510874i	−0.265769	−	0.193092i	0.446918	−	0.894575i	$-0.352522\pi$
$7$	−0.703158	−	0.510874i	−0.265769	−	0.193092i	−0.712686	+	0.701483i	$0.752522\pi$
$8$		0			0
$9$	0.211078	−	0.649631i	0.0703593	−	0.216544i
$10$		0			0
$11$	3.16272	+	0.998590i	0.953597	+	0.301086i
$11$	3.16272	+	0.998590i	0.953597	+	0.301086i
$12$		0			0
$13$	0.866521	−	2.66688i	0.240330	−	0.739659i	−0.756040	−	0.654526i	$-0.772868\pi$
$13$	0.866521	−	2.66688i	0.240330	−	0.739659i	0.996370	−	0.0851334i	$-0.0271316\pi$
$14$		0			0
$15$	−5.28868	−	3.84245i	−1.36553	−	0.992116i
$16$		0			0
$17$	−2.25314	−	6.93444i	−0.546466	−	1.68185i	−0.717478	−	0.696581i	$-0.754704\pi$
$17$	−2.25314	−	6.93444i	−0.546466	−	1.68185i	0.171012	−	0.985269i	$-0.445296\pi$
$18$		0			0
$19$	−1.92705	+	1.40008i	−0.442096	+	0.321201i	−0.786467	−	0.617632i	$-0.788092\pi$
$19$	−1.92705	+	1.40008i	−0.442096	+	0.321201i	0.344371	+	0.938834i	$0.388092\pi$
$20$		0			0
$21$	1.66801			0.363990
$22$		0			0
$23$	7.44651			1.55270			0.776352	−	0.630300i	$-0.217068\pi$
$23$	7.44651			1.55270			0.776352	+	0.630300i	$0.217068\pi$
$24$		0			0
$25$	−5.34193	+	3.88114i	−1.06839	+	0.776227i
$26$		0			0
$27$	−1.37405	−	4.22888i	−0.264435	−	0.813848i
$28$		0			0
$29$	5.93923	+	4.31510i	1.10289	+	0.801294i	0.981529	−	0.191315i	$-0.0612752\pi$
$29$	5.93923	+	4.31510i	1.10289	+	0.801294i	0.121358	+	0.992609i	$0.461275\pi$
$30$		0			0
$31$	−0.816541	+	2.51306i	−0.146655	+	0.451358i	−0.997220	−	0.0745118i	$-0.976260\pi$
$31$	−0.816541	+	2.51306i	−0.146655	+	0.451358i	0.850565	+	0.525870i	$0.176260\pi$
$32$		0			0
$33$	−6.03692	+	2.01725i	−1.05089	+	0.351158i
$34$		0			0
$35$	0.914876	−	2.81570i	0.154642	−	0.475940i
$36$		0			0
$37$	−0.834007	−	0.605942i	−0.137110	−	0.0996162i	0.517116	−	0.855915i	$-0.327006\pi$
$37$	−0.834007	−	0.605942i	−0.137110	−	0.0996162i	−0.654226	+	0.756299i	$0.727006\pi$
$38$		0			0
$39$	1.66297	+	5.11809i	0.266288	+	0.819550i
$40$		0			0
$41$	−2.34089	+	1.70076i	−0.365586	+	0.265614i	−0.755378	−	0.655289i	$-0.772547\pi$
$41$	−2.34089	+	1.70076i	−0.365586	+	0.265614i	0.389792	+	0.920903i	$0.372547\pi$
$42$		0			0
$43$	2.18609			0.333375			0.166688	−	0.986010i	$-0.446693\pi$
$43$	2.18609			0.333375			0.166688	+	0.986010i	$0.446693\pi$
$44$		0			0
$45$	2.32673			0.346848
$46$		0			0
$47$	3.19034	−	2.31792i	0.465359	−	0.338103i	−0.330271	−	0.943886i	$-0.607140\pi$
$47$	3.19034	−	2.31792i	0.465359	−	0.338103i	0.795630	+	0.605783i	$0.207140\pi$
$48$		0			0
$49$	−1.92968	−	5.93895i	−0.275669	−	0.848421i
$50$		0			0
$51$	11.3206	+	8.22486i	1.58519	+	1.15171i
$52$		0			0
$53$	−2.19851	+	6.76631i	−0.301988	+	0.929424i	0.678796	+	0.734327i	$0.262502\pi$
$53$	−2.19851	+	6.76631i	−0.301988	+	0.929424i	−0.980784	+	0.195097i	$0.937498\pi$
$54$		0			0
$55$	0.0940804	+	11.2971i	0.0126858	+	1.52330i
$56$		0			0
$57$	1.41261	−	4.34757i	0.187105	−	0.575850i
$58$		0			0
$59$	−6.54508	−	4.75528i	−0.852097	−	0.619085i	0.0736261	−	0.997286i	$-0.476543\pi$
$59$	−6.54508	−	4.75528i	−0.852097	−	0.619085i	−0.925724	+	0.378201i	$0.876543\pi$
$60$		0			0
$61$	−0.832382	−	2.56181i	−0.106576	−	0.328006i	0.883521	−	0.468391i	$-0.155166\pi$
$61$	−0.832382	−	2.56181i	−0.106576	−	0.328006i	−0.990097	+	0.140385i	$0.955166\pi$
$62$		0			0
$63$	−0.480301	+	0.348959i	−0.0605122	+	0.0439647i
$64$		0			0
$65$	9.55172			1.18475
$66$		0			0
$67$	−13.7720			−1.68251			−0.841256	−	0.540637i	$-0.818183\pi$
$67$	−13.7720			−1.68251			−0.841256	+	0.540637i	$0.818183\pi$
$68$		0			0
$69$	−11.5615	+	8.39993i	−1.39184	+	1.01123i
$70$		0			0
$71$	−0.596314	−	1.83527i	−0.0707694	−	0.217806i	0.909416	−	0.415887i	$-0.136529\pi$
$71$	−0.596314	−	1.83527i	−0.0707694	−	0.217806i	−0.980186	+	0.198081i	$0.936529\pi$
$72$		0			0
$73$	−4.03979	−	2.93508i	−0.472822	−	0.343525i	0.325718	−	0.945467i	$-0.394394\pi$
$73$	−4.03979	−	2.93508i	−0.472822	−	0.343525i	−0.798540	+	0.601942i	$0.794394\pi$
$74$		0			0
$75$	3.91586	−	12.0518i	0.452165	−	1.39162i
$76$		0			0
$77$	−1.71374	−	2.31792i	−0.195299	−	0.264151i
$78$		0			0
$79$	4.15783	−	12.7965i	0.467792	−	1.43972i	−0.387644	−	0.921809i	$-0.626711\pi$
$79$	4.15783	−	12.7965i	0.467792	−	1.43972i	0.855437	−	0.517907i	$-0.173289\pi$
$80$		0			0
$81$	8.56151	+	6.22030i	0.951279	+	0.691145i
$82$		0			0
$83$	−0.0601338	−	0.185073i	−0.00660054	−	0.0203144i	0.947702	−	0.319157i	$-0.103400\pi$
$83$	−0.0601338	−	0.185073i	−0.00660054	−	0.0203144i	−0.954303	+	0.298842i	$0.903400\pi$
$84$		0			0
$85$	20.0931	−	14.5985i	2.17941	−	1.58343i
$86$		0			0
$87$	−14.0889			−1.51049
$88$		0			0
$89$	4.18609			0.443724			0.221862	−	0.975078i	$-0.428786\pi$
$89$	4.18609			0.443724			0.221862	+	0.975078i	$0.428786\pi$
$90$		0			0
$91$	−1.97174	+	1.43255i	−0.206695	+	0.150172i
$92$		0			0
$93$	−1.56705	−	4.82288i	−0.162495	−	0.500110i
$94$		0			0
$95$	−6.56414	−	4.76913i	−0.673467	−	0.489302i
$96$		0			0
$97$	1.54206	−	4.74597i	0.156572	−	0.481880i	−0.841744	−	0.539876i	$-0.818471\pi$
$97$	1.54206	−	4.74597i	0.156572	−	0.481880i	0.998317	+	0.0579959i	$0.0184710\pi$
$98$		0			0
$99$	1.31630	−	1.84382i	0.132293	−	0.185311i
$100$		0			0
$101$	−2.55563	+	7.86543i	−0.254295	+	0.782640i	0.739673	+	0.672967i	$0.234980\pi$
$101$	−2.55563	+	7.86543i	−0.254295	+	0.782640i	−0.993968	+	0.109673i	$0.965020\pi$
$102$		0			0
$103$	−0.663759	−	0.482249i	−0.0654022	−	0.0475175i	0.554604	−	0.832115i	$-0.312870\pi$
$103$	−0.663759	−	0.482249i	−0.0654022	−	0.0475175i	−0.620006	+	0.784597i	$0.712870\pi$
$104$		0			0
$105$	1.75577	+	5.40370i	0.171345	+	0.527347i
$106$		0			0
$107$	−10.0247	+	7.28340i	−0.969129	+	0.704113i	−0.955253	−	0.295791i	$-0.904417\pi$
$107$	−10.0247	+	7.28340i	−0.969129	+	0.704113i	−0.0138759	+	0.999904i	$0.504417\pi$
$108$		0			0
$109$	−7.20439			−0.690055			−0.345028	−	0.938593i	$-0.612130\pi$
$109$	−7.20439			−0.690055			−0.345028	+	0.938593i	$0.612130\pi$
$110$		0			0
$111$	1.97841			0.187782
$112$		0			0
$113$	−1.66535	+	1.20995i	−0.156663	+	0.113822i	−0.663355	−	0.748305i	$-0.730868\pi$
$113$	−1.66535	+	1.20995i	−0.156663	+	0.113822i	0.506692	+	0.862127i	$0.330868\pi$
$114$		0			0
$115$	7.83826	+	24.1237i	0.730922	+	2.24955i
$116$		0			0
$117$	−1.54958	−	1.12584i	−0.143259	−	0.104084i
$118$		0			0
$119$	−1.95832	+	6.02708i	−0.179519	+	0.552501i
$120$		0			0
$121$	9.00563	+	6.31653i	0.818694	+	0.574230i
$122$		0			0
$123$	1.71597	−	5.28122i	0.154724	−	0.476192i
$124$		0			0
$125$	−4.41745	−	3.20947i	−0.395109	−	0.287064i
$126$		0			0
$127$	2.58652	+	7.96050i	0.229517	+	0.706380i	0.997802	+	0.0662721i	$0.0211105\pi$
$127$	2.58652	+	7.96050i	0.229517	+	0.706380i	−0.768285	+	0.640108i	$0.778889\pi$
$128$		0			0
$129$	−3.39414	+	2.46599i	−0.298837	+	0.217118i
$130$		0			0
$131$	13.3511			1.16649			0.583244	−	0.812297i	$-0.301783\pi$
$131$	13.3511			1.16649			0.583244	+	0.812297i	$0.301783\pi$
$132$		0			0
$133$	2.07029			0.179517
$134$		0			0
$135$	12.2535	−	8.90271i	1.05462	−	0.766224i
$136$		0			0
$137$	0.305992	+	0.941746i	0.0261426	+	0.0804588i	0.963277	−	0.268511i	$-0.0865316\pi$
$137$	0.305992	+	0.941746i	0.0261426	+	0.0804588i	−0.937134	+	0.348970i	$0.886532\pi$
$138$		0			0
$139$	−4.84985	−	3.52362i	−0.411359	−	0.298870i	0.362793	−	0.931870i	$-0.381823\pi$
$139$	−4.84985	−	3.52362i	−0.411359	−	0.298870i	−0.774152	+	0.633000i	$0.781823\pi$
$140$		0			0
$141$	−2.33866	+	7.19765i	−0.196950	+	0.606151i
$142$		0			0
$143$	5.40369	−	7.56930i	0.451879	−	0.632977i
$144$		0			0
$145$	−7.72751	+	23.7828i	−0.641735	+	1.97506i
$146$		0			0
$147$	9.69539	+	7.04411i	0.799662	+	0.580989i
$148$		0			0
$149$	−5.34392	−	16.4469i	−0.437791	−	1.34738i	−0.890200	−	0.455571i	$-0.849435\pi$
$149$	−5.34392	−	16.4469i	−0.437791	−	1.34738i	0.452409	−	0.891811i	$-0.350565\pi$
$150$		0			0
$151$	0.639410	−	0.464559i	0.0520344	−	0.0378052i	−0.561464	−	0.827501i	$-0.689762\pi$
$151$	0.639410	−	0.464559i	0.0520344	−	0.0378052i	0.613498	+	0.789696i	$0.289762\pi$
$152$		0			0
$153$	−4.98042			−0.402643
$154$		0			0
$155$	−9.00079			−0.722961
$156$		0			0
$157$	10.3041	−	7.48635i	0.822354	−	0.597475i	−0.0950316	−	0.995474i	$-0.530295\pi$
$157$	10.3041	−	7.48635i	0.822354	−	0.597475i	0.917386	+	0.397999i	$0.130295\pi$
$158$		0			0
$159$	−4.21922	−	12.9854i	−0.334606	−	1.02981i
$160$		0			0
$161$	−5.23607	−	3.80423i	−0.412660	−	0.299815i
$162$		0			0
$163$	−0.0512092	+	0.157606i	−0.00401101	+	0.0123446i	−0.953042	−	0.302838i	$-0.902066\pi$
$163$	−0.0512092	+	0.157606i	−0.00401101	+	0.0123446i	0.949031	+	0.315183i	$0.102066\pi$
$164$		0			0
$165$	−12.8896	−	17.4338i	−1.00345	−	1.35722i
$166$		0			0
$167$	−6.70153	+	20.6252i	−0.518580	+	1.59603i	0.258092	+	0.966120i	$0.416906\pi$
$167$	−6.70153	+	20.6252i	−0.518580	+	1.59603i	−0.776672	+	0.629905i	$0.783094\pi$
$168$		0			0
$169$	4.15584	+	3.01939i	0.319680	+	0.232261i
$170$		0			0
$171$	0.502781	+	1.54740i	0.0384486	+	0.118333i
$172$		0			0
$173$	−10.5967	+	7.69892i	−0.805649	+	0.585338i	−0.912566	−	0.408930i	$-0.865902\pi$
$173$	−10.5967	+	7.69892i	−0.805649	+	0.585338i	0.106917	+	0.994268i	$0.465902\pi$
$174$		0			0
$175$	5.73899			0.433827
$176$		0			0
$177$	15.5261			1.16701
$178$		0			0
$179$	8.56943	−	6.22606i	0.640510	−	0.465357i	−0.219516	−	0.975609i	$-0.570448\pi$
$179$	8.56943	−	6.22606i	0.640510	−	0.465357i	0.860025	+	0.510252i	$0.170448\pi$
$180$		0			0
$181$	1.97828	+	6.08852i	0.147044	+	0.452556i	0.997268	−	0.0738652i	$-0.0235335\pi$
$181$	1.97828	+	6.08852i	0.147044	+	0.452556i	−0.850224	+	0.526421i	$0.823533\pi$
$182$		0			0
$183$	4.18218	+	3.03853i	0.309155	+	0.224615i
$184$		0			0
$185$	1.08512	−	3.33967i	0.0797799	−	0.245537i
$186$		0			0
$187$	−0.201381	−	24.1817i	−0.0147265	−	1.76834i
$188$		0			0
$189$	−1.19425	+	3.67553i	−0.0868691	+	0.267356i
$190$		0			0
$191$	−5.49144	−	3.98976i	−0.397347	−	0.288689i	0.371113	−	0.928588i	$-0.378976\pi$
$191$	−5.49144	−	3.98976i	−0.397347	−	0.288689i	−0.768459	+	0.639899i	$0.778976\pi$
$192$		0			0
$193$	−2.51465	−	7.73931i	−0.181009	−	0.557087i	0.818848	−	0.574010i	$-0.194613\pi$
$193$	−2.51465	−	7.73931i	−0.181009	−	0.557087i	−0.999857	+	0.0169228i	$0.994613\pi$
$194$		0			0
$195$	−14.8301	+	10.7747i	−1.06201	+	0.771592i
$196$		0			0
$197$	−16.4907			−1.17492			−0.587458	−	0.809255i	$-0.699871\pi$
$197$	−16.4907			−1.17492			−0.587458	+	0.809255i	$0.699871\pi$
$198$		0			0
$199$	3.39781			0.240864			0.120432	−	0.992722i	$-0.461572\pi$
$199$	3.39781			0.240864			0.120432	+	0.992722i	$0.461572\pi$
$200$		0			0
$201$	21.3825	−	15.5353i	1.50820	−	1.09577i
$202$		0			0
$203$	−1.97174	−	6.06839i	−0.138389	−	0.425918i
$204$		0			0
$205$	−7.97381	−	5.79331i	−0.556915	−	0.404623i
$206$		0			0
$207$	1.57179	−	4.83748i	0.109247	−	0.336228i
$208$		0			0
$209$	−7.49284	+	2.50375i	−0.518291	+	0.173188i
$210$		0			0
$211$	4.93907	−	15.2009i	0.340020	−	1.04647i	−0.624176	−	0.781284i	$-0.714565\pi$
$211$	4.93907	−	15.2009i	0.340020	−	1.04647i	0.964196	−	0.265190i	$-0.0854347\pi$
$212$		0			0
$213$	2.99609	+	2.17679i	0.205289	+	0.149151i
$214$		0			0
$215$	2.30110	+	7.08205i	0.156933	+	0.482992i
$216$		0			0
$217$	1.85801	−	1.34993i	0.126130	−	0.0916389i
$218$		0			0
$219$	9.58310			0.647566
$220$		0			0
$221$	−20.4457			−1.37533
$222$		0			0
$223$	−6.13382	+	4.45648i	−0.410751	+	0.298428i	−0.773906	−	0.633301i	$-0.781700\pi$
$223$	−6.13382	+	4.45648i	−0.410751	+	0.298428i	0.363155	+	0.931729i	$0.381700\pi$
$224$		0			0
$225$	1.39374	+	4.28951i	0.0929163	+	0.285967i
$226$		0			0
$227$	−12.1460	−	8.82458i	−0.806158	−	0.585708i	0.106556	−	0.994307i	$-0.466018\pi$
$227$	−12.1460	−	8.82458i	−0.806158	−	0.585708i	−0.912714	+	0.408599i	$0.866018\pi$
$228$		0			0
$229$	0.742212	−	2.28429i	0.0490467	−	0.150950i	−0.923534	−	0.383518i	$-0.874713\pi$
$229$	0.742212	−	2.28429i	0.0490467	−	0.150950i	0.972580	+	0.232567i	$0.0747126\pi$
$230$		0			0
$231$	5.27547	+	1.66566i	0.347100	+	0.109593i
$232$		0			0
$233$	1.92928	−	5.93773i	0.126392	−	0.388993i	−0.867760	−	0.496983i	$-0.834441\pi$
$233$	1.92928	−	5.93773i	0.126392	−	0.388993i	0.994152	+	0.107989i	$0.0344412\pi$
$234$		0			0
$235$	10.8673	+	7.89557i	0.708905	+	0.515050i
$236$		0			0
$237$	7.97942	+	24.5581i	0.518319	+	1.59522i
$238$		0			0
$239$	13.8018	−	10.0276i	0.892767	−	0.648633i	−0.0438313	−	0.999039i	$-0.513956\pi$
$239$	13.8018	−	10.0276i	0.892767	−	0.648633i	0.936598	+	0.350406i	$0.113956\pi$
$240$		0			0
$241$	0.0166322			0.00107138			0.000535688	−	1.00000i	$-0.499829\pi$
$241$	0.0166322			0.00107138			0.000535688		1.00000i	$0.499829\pi$
$242$		0			0
$243$	−6.96990			−0.447119
$244$		0			0
$245$	17.2086	−	12.5028i	1.09942	−	0.798773i
$246$		0			0
$247$	2.06402	+	6.35241i	0.131331	+	0.404194i
$248$		0			0
$249$	0.302133	+	0.219513i	0.0191469	+	0.0139110i
$250$		0			0
$251$	−7.47477	+	23.0050i	−0.471803	+	1.45206i	0.378418	+	0.925635i	$0.376468\pi$
$251$	−7.47477	+	23.0050i	−0.471803	+	1.45206i	−0.850221	+	0.526426i	$0.823532\pi$
$252$		0			0
$253$	23.5512	+	7.43601i	1.48065	+	0.467498i
$254$		0			0
$255$	−14.7291	+	45.3316i	−0.922374	+	2.83878i
$256$		0			0
$257$	23.4041	+	17.0041i	1.45991	+	1.06069i	0.983386	+	0.181526i	$0.0581037\pi$
$257$	23.4041	+	17.0041i	1.45991	+	1.06069i	0.476525	+	0.879161i	$0.341896\pi$
$258$		0			0
$259$	0.276879	+	0.852145i	0.0172044	+	0.0529497i
$260$		0			0
$261$	4.05686	−	2.94748i	0.251114	−	0.182445i
$262$		0			0
$263$	−17.2531			−1.06387			−0.531935	−	0.846785i	$-0.678535\pi$
$263$	−17.2531			−1.06387			−0.531935	+	0.846785i	$0.678535\pi$
$264$		0			0
$265$	−24.2343			−1.48870
$266$		0			0
$267$	−6.49936	+	4.72206i	−0.397754	+	0.288985i
$268$		0			0
$269$	0.866521	+	2.66688i	0.0528327	+	0.162602i	0.973991	−	0.226585i	$-0.0727560\pi$
$269$	0.866521	+	2.66688i	0.0528327	+	0.162602i	−0.921159	+	0.389187i	$0.872756\pi$
$270$		0			0
$271$	−18.4114	−	13.3766i	−1.11841	−	0.812573i	−0.134443	−	0.990921i	$-0.542925\pi$
$271$	−18.4114	−	13.3766i	−1.11841	−	0.812573i	−0.983967	+	0.178348i	$0.942925\pi$
$272$		0			0
$273$	1.44537	−	4.44839i	0.0874778	−	0.269229i
$274$		0			0
$275$	−20.7707	+	6.94057i	−1.25252	+	0.418532i
$276$		0			0
$277$	1.02826	−	3.16466i	0.0617821	−	0.190146i	−0.915401	−	0.402542i	$-0.868127\pi$
$277$	1.02826	−	3.16466i	0.0617821	−	0.190146i	0.977184	+	0.212396i	$0.0681267\pi$
$278$		0			0
$279$	1.46021	+	1.06090i	0.0874202	+	0.0635145i
$280$		0			0
$281$	2.69322	+	8.28887i	0.160664	+	0.494472i	0.998691	−	0.0511566i	$-0.0162908\pi$
$281$	2.69322	+	8.28887i	0.160664	+	0.494472i	−0.838027	+	0.545629i	$0.816291\pi$
$282$		0			0
$283$	23.5494	−	17.1097i	1.39987	−	1.01706i	0.405169	−	0.914242i	$-0.367213\pi$
$283$	23.5494	−	17.1097i	1.39987	−	1.01706i	0.994700	−	0.102822i	$-0.0327874\pi$
$284$		0			0
$285$	15.5713			0.922364
$286$		0			0
$287$	2.51489			0.148449
$288$		0			0
$289$	−29.2566	+	21.2562i	−1.72098	+	1.25036i
$290$		0			0
$291$	2.95941	+	9.10814i	0.173484	+	0.533929i
$292$		0			0
$293$	17.7624	+	12.9052i	1.03769	+	0.753928i	0.969834	−	0.243767i	$-0.0783832\pi$
$293$	17.7624	+	12.9052i	1.03769	+	0.753928i	0.0678589	+	0.997695i	$0.478383\pi$
$294$		0			0
$295$	8.51579	−	26.2089i	0.495808	−	1.52594i
$296$		0			0
$297$	−0.122810	−	14.7469i	−0.00712615	−	0.855701i
$298$		0			0
$299$	6.45256	−	19.8589i	0.373161	−	1.14847i
$300$		0			0
$301$	−1.53716	−	1.11682i	−0.0886007	−	0.0643722i
$302$		0			0
$303$	−4.90460	−	15.0948i	−0.281762	−	0.867173i
$304$		0			0
$305$	7.42306	−	5.39317i	0.425043	−	0.308812i
$306$		0			0
$307$	−24.1835			−1.38023			−0.690113	−	0.723701i	$-0.742439\pi$
$307$	−24.1835			−1.38023			−0.690113	+	0.723701i	$0.742439\pi$
$308$		0			0
$309$	1.57455			0.0895733
$310$		0			0
$311$	2.88925	−	2.09916i	0.163834	−	0.119032i	−0.502847	−	0.864375i	$-0.667714\pi$
$311$	2.88925	−	2.09916i	0.163834	−	0.119032i	0.666681	+	0.745343i	$0.267714\pi$
$312$		0			0
$313$	2.69113	+	8.28246i	0.152112	+	0.468152i	0.997857	−	0.0654351i	$-0.0208435\pi$
$313$	2.69113	+	8.28246i	0.152112	+	0.468152i	−0.845745	+	0.533587i	$0.820844\pi$
$314$		0			0
$315$	−1.63606	−	1.18866i	−0.0921813	−	0.0669737i
$316$		0			0
$317$	6.80474	−	20.9428i	0.382192	−	1.17627i	−0.556304	−	0.830979i	$-0.687781\pi$
$317$	6.80474	−	20.9428i	0.382192	−	1.17627i	0.938497	−	0.345289i	$-0.112219\pi$
$318$		0			0
$319$	14.4751	+	19.5783i	0.810451	+	1.09618i
$320$		0			0
$321$	7.34857	−	22.6166i	0.410157	−	1.26233i
$322$		0			0
$323$	14.0507	+	10.2084i	0.781803	+	0.568013i
$324$		0			0
$325$	5.72163	+	17.6094i	0.317379	+	0.976792i
$326$		0			0
$327$	11.1856	−	8.12681i	0.618565	−	0.449414i
$328$		0			0
$329$	−3.42748			−0.188963
$330$		0			0
$331$	−2.07719			−0.114173			−0.0570865	−	0.998369i	$-0.518181\pi$
$331$	−2.07719			−0.114173			−0.0570865	+	0.998369i	$0.518181\pi$
$332$		0			0
$333$	−0.569679	+	0.413896i	−0.0312182	+	0.0226814i
$334$		0			0
$335$	−14.4965	−	44.6156i	−0.792028	−	2.43761i
$336$		0			0
$337$	−20.4479	−	14.8563i	−1.11387	−	0.809272i	−0.130599	−	0.991435i	$-0.541690\pi$
$337$	−20.4479	−	14.8563i	−1.11387	−	0.809272i	−0.983268	+	0.182163i	$0.941690\pi$
$338$		0			0
$339$	1.22077	−	3.75716i	0.0663034	−	0.204061i
$340$		0			0
$341$	−5.09201	+	7.13271i	−0.275748	+	0.386258i
$342$		0			0
$343$	−3.55726	+	10.9481i	−0.192074	+	0.591143i
$344$		0			0
$345$	−39.3822	−	28.6128i	−2.12026	−	1.54046i
$346$		0			0
$347$	6.50377	+	20.0165i	0.349140	+	1.07454i	0.959330	+	0.282288i	$0.0910934\pi$
$347$	6.50377	+	20.0165i	0.349140	+	1.07454i	−0.610189	+	0.792256i	$0.708907\pi$
$348$		0			0
$349$	−18.8164	+	13.6709i	−1.00722	+	0.731787i	−0.963624	−	0.267262i	$-0.913881\pi$
$349$	−18.8164	+	13.6709i	−1.00722	+	0.731787i	−0.0435947	+	0.999049i	$0.513881\pi$
$350$		0			0
$351$	−12.4685			−0.665522
$352$		0			0
$353$	−18.6464			−0.992446			−0.496223	−	0.868195i	$-0.665280\pi$
$353$	−18.6464			−0.992446			−0.496223	+	0.868195i	$0.665280\pi$
$354$		0			0
$355$	5.31784	−	3.86364i	0.282242	−	0.205060i
$356$		0			0
$357$	−3.75827	−	11.5668i	−0.198908	−	0.612177i
$358$		0			0
$359$	30.4417	+	22.1172i	1.60665	+	1.16730i	0.872929	+	0.487847i	$0.162218\pi$
$359$	30.4417	+	22.1172i	1.60665	+	1.16730i	0.733720	+	0.679452i	$0.237782\pi$
$360$		0			0
$361$	−4.11803	+	12.6740i	−0.216739	+	0.667053i
$362$		0			0
$363$	−21.1075	+	0.351585i	−1.10786	+	0.0184534i
$364$		0			0
$365$	5.25616	−	16.1768i	0.275120	−	0.846733i
$366$		0			0
$367$	6.91280	+	5.02245i	0.360845	+	0.262170i	0.753405	−	0.657557i	$-0.228410\pi$
$367$	6.91280	+	5.02245i	0.360845	+	0.262170i	−0.392559	+	0.919727i	$0.628410\pi$
$368$		0			0
$369$	0.610754	+	1.87971i	0.0317946	+	0.0978537i
$370$		0			0
$371$	5.00263	−	3.63462i	0.259724	−	0.188700i
$372$		0			0
$373$	18.1461			0.939569			0.469785	−	0.882781i	$-0.344332\pi$
$373$	18.1461			0.939569			0.469785	+	0.882781i	$0.344332\pi$
$374$		0			0
$375$	10.4790			0.541132
$376$		0			0
$377$	16.6543	−	12.1001i	0.857741	−	0.623185i
$378$		0			0
$379$	8.68422	+	26.7273i	0.446078	+	1.37289i	0.881297	+	0.472563i	$0.156671\pi$
$379$	8.68422	+	26.7273i	0.446078	+	1.37289i	−0.435219	+	0.900325i	$0.643329\pi$
$380$		0			0
$381$	−12.9956	−	9.44186i	−0.665785	−	0.483721i
$382$		0			0
$383$	−5.47477	+	16.8496i	−0.279747	+	0.860974i	0.708177	+	0.706035i	$0.249518\pi$
$383$	−5.47477	+	16.8496i	−0.279747	+	0.860974i	−0.987924	+	0.154939i	$0.950482\pi$
$384$		0			0
$385$	5.70523	−	7.99169i	0.290765	−	0.407294i
$386$		0			0
$387$	0.461435	−	1.42015i	0.0234561	−	0.0721903i
$388$		0			0
$389$	1.06800	+	0.775949i	0.0541499	+	0.0393422i	0.614531	−	0.788893i	$-0.289345\pi$
$389$	1.06800	+	0.775949i	0.0541499	+	0.0393422i	−0.560381	+	0.828235i	$0.689345\pi$
$390$		0			0
$391$	−16.7780	−	51.6374i	−0.848500	−	2.61141i
$392$		0			0
$393$	−20.7290	+	15.0605i	−1.04564	+	0.759702i
$394$		0			0
$395$	45.8320			2.30606
$396$		0			0
$397$	13.7700			0.691096			0.345548	−	0.938401i	$-0.387693\pi$
$397$	13.7700			0.691096			0.345548	+	0.938401i	$0.387693\pi$
$398$		0			0
$399$	−3.21435	+	2.33536i	−0.160919	+	0.116914i
$400$		0			0
$401$	−5.30875	−	16.3387i	−0.265106	−	0.815914i	−0.991669	−	0.128813i	$-0.958883\pi$
$401$	−5.30875	−	16.3387i	−0.265106	−	0.815914i	0.726562	−	0.687100i	$-0.241117\pi$
$402$		0			0
$403$	5.99446	+	4.35523i	0.298606	+	0.216950i
$404$		0			0
$405$	−11.1394	+	34.2834i	−0.553519	+	1.70356i
$406$		0			0
$407$	−2.03265	−	2.74926i	−0.100755	−	0.136276i
$408$		0			0
$409$	2.60935	−	8.03077i	0.129024	−	0.397096i	−0.865589	−	0.500756i	$-0.833055\pi$
$409$	2.60935	−	8.03077i	0.129024	−	0.397096i	0.994613	+	0.103660i	$0.0330554\pi$
$410$		0			0
$411$	−1.53741	−	1.11699i	−0.0758348	−	0.0550972i
$412$		0			0
$413$	2.17288	+	6.68743i	0.106920	+	0.329067i
$414$		0			0
$415$	0.536264	−	0.389619i	0.0263242	−	0.0191256i
$416$		0			0
$417$	11.5047			0.563387
$418$		0			0
$419$	30.9791			1.51343			0.756715	−	0.653745i	$-0.226803\pi$
$419$	30.9791			1.51343			0.756715	+	0.653745i	$0.226803\pi$
$420$		0			0
$421$	−20.6770	+	15.0227i	−1.00774	+	0.732164i	−0.963733	−	0.266867i	$-0.914011\pi$
$421$	−20.6770	+	15.0227i	−1.00774	+	0.732164i	−0.0440039	+	0.999031i	$0.514011\pi$
$422$		0			0
$423$	−0.832382	−	2.56181i	−0.0404718	−	0.124559i
$424$		0			0
$425$	38.9496	+	28.2986i	1.88933	+	1.37268i
$426$		0			0
$427$	−0.723465	+	2.22660i	−0.0350109	+	0.107753i
$428$		0			0
$429$	0.148633	+	17.8477i	0.00717607	+	0.861696i
$430$		0			0
$431$	−5.57473	+	17.1572i	−0.268525	+	0.826435i	0.722335	+	0.691543i	$0.243069\pi$
$431$	−5.57473	+	17.1572i	−0.268525	+	0.826435i	−0.990860	+	0.134892i	$0.956931\pi$
$432$		0			0
$433$	−20.4722	−	14.8739i	−0.983833	−	0.714796i	−0.0252709	−	0.999681i	$-0.508045\pi$
$433$	−20.4722	−	14.8739i	−0.983833	−	0.714796i	−0.958562	+	0.284884i	$0.908045\pi$
$434$		0			0
$435$	−14.8301	−	45.6423i	−0.711049	−	2.18838i
$436$		0			0
$437$	−14.3498	+	10.4257i	−0.686444	+	0.498731i
$438$		0			0
$439$	−28.5630			−1.36324			−0.681620	−	0.731707i	$-0.738724\pi$
$439$	−28.5630			−1.36324			−0.681620	+	0.731707i	$0.738724\pi$
$440$		0			0
$441$	−4.26544			−0.203116
$442$		0			0
$443$	−30.0734	+	21.8496i	−1.42883	+	1.03811i	−0.438600	+	0.898682i	$0.644525\pi$
$443$	−30.0734	+	21.8496i	−1.42883	+	1.03811i	−0.990233	+	0.139425i	$0.955475\pi$
$444$		0			0
$445$	4.40632	+	13.5612i	0.208879	+	0.642865i
$446$		0			0
$447$	26.8497	+	19.5075i	1.26995	+	0.922671i
$448$		0			0
$449$	3.22505	−	9.92568i	0.152199	−	0.468422i	−0.845667	−	0.533711i	$-0.820797\pi$
$449$	3.22505	−	9.92568i	0.152199	−	0.468422i	0.997866	+	0.0652892i	$0.0207970\pi$
$450$		0			0
$451$	−9.10195	+	3.04143i	−0.428594	+	0.143215i
$452$		0			0
$453$	−0.468715	+	1.44256i	−0.0220221	+	0.0677772i
$454$		0			0
$455$	−6.71637	−	4.87973i	−0.314868	−	0.228765i
$456$		0			0
$457$	8.07597	+	24.8553i	0.377778	+	1.16268i	0.941585	+	0.336775i	$0.109336\pi$
$457$	8.07597	+	24.8553i	0.377778	+	1.16268i	−0.563807	+	0.825907i	$0.690664\pi$
$458$		0			0
$459$	−26.2290	+	19.0565i	−1.22427	+	0.889481i
$460$		0			0
$461$	11.1743			0.520439			0.260219	−	0.965550i	$-0.416205\pi$
$461$	11.1743			0.520439			0.260219	+	0.965550i	$0.416205\pi$
$462$		0			0
$463$	38.7695			1.80177			0.900885	−	0.434059i	$-0.142919\pi$
$463$	38.7695			1.80177			0.900885	+	0.434059i	$0.142919\pi$
$464$		0			0
$465$	13.9747	−	10.1532i	0.648062	−	0.470844i
$466$		0			0
$467$	−0.717071	−	2.20692i	−0.0331821	−	0.102124i	0.933094	−	0.359633i	$-0.117098\pi$
$467$	−0.717071	−	2.20692i	−0.0331821	−	0.102124i	−0.966276	+	0.257509i	$0.917098\pi$
$468$		0			0
$469$	9.68385	+	7.03573i	0.447159	+	0.324880i
$470$		0			0
$471$	−7.55332	+	23.2467i	−0.348039	+	1.07115i
$472$		0			0
$473$	6.91399	+	2.18301i	0.317906	+	0.100375i
$474$		0			0
$475$	4.86025	−	14.9583i	0.223003	−	0.686334i
$476$		0			0
$477$	3.93155	+	2.85644i	0.180013	+	0.130787i
$478$		0			0
$479$	7.66660	+	23.5954i	0.350296	+	1.07810i	0.958687	+	0.284463i	$0.0918152\pi$
$479$	7.66660	+	23.5954i	0.350296	+	1.07810i	−0.608391	+	0.793637i	$0.708185\pi$
$480$		0			0
$481$	−2.33866	+	1.69913i	−0.106634	+	0.0774738i
$482$		0			0
$483$	12.4209			0.565169
$484$		0			0
$485$	16.9982			0.771850
$486$		0			0
$487$	−14.8506	+	10.7896i	−0.672947	+	0.488924i	−0.871010	−	0.491265i	$-0.836535\pi$
$487$	−14.8506	+	10.7896i	−0.672947	+	0.488924i	0.198064	+	0.980189i	$0.436535\pi$
$488$		0			0
$489$	−0.0982771	−	0.302466i	−0.00444424	−	0.0136780i
$490$		0			0
$491$	−17.4798	−	12.6998i	−0.788851	−	0.573133i	0.118772	−	0.992922i	$-0.462104\pi$
$491$	−17.4798	−	12.6998i	−0.788851	−	0.573133i	−0.907622	+	0.419788i	$0.862104\pi$
$492$		0			0
$493$	16.5409	−	50.9077i	0.744966	−	2.29277i
$494$		0			0
$495$	7.35879	+	2.32345i	0.330753	+	0.104431i
$496$		0			0
$497$	−0.518287	+	1.59512i	−0.0232483	+	0.0715510i
$498$		0			0
$499$	−24.9657	−	18.1386i	−1.11762	−	0.811996i	−0.133770	−	0.991012i	$-0.542708\pi$
$499$	−24.9657	−	18.1386i	−1.11762	−	0.811996i	−0.983846	+	0.179016i	$0.942708\pi$
$500$		0			0
$501$	−12.8611	−	39.5824i	−0.574592	−	1.76841i
$502$		0			0
$503$	2.62755	−	1.90902i	0.117157	−	0.0851192i	−0.527664	−	0.849453i	$-0.676932\pi$
$503$	2.62755	−	1.90902i	0.117157	−	0.0851192i	0.644821	+	0.764334i	$0.276932\pi$
$504$		0			0
$505$	−28.1709			−1.25359
$506$		0			0
$507$	−9.85838			−0.437826
$508$		0			0
$509$	3.76819	−	2.73775i	0.167022	−	0.121349i	−0.501134	−	0.865369i	$-0.667084\pi$
$509$	3.76819	−	2.73775i	0.167022	−	0.121349i	0.668156	+	0.744021i	$0.267084\pi$
$510$		0			0
$511$	1.34116	+	4.12765i	0.0593292	+	0.182597i
$512$		0			0
$513$	8.56864	+	6.22548i	0.378315	+	0.274862i
$514$		0			0
$515$	0.863615	−	2.65793i	0.0380554	−	0.117123i
$516$		0			0
$517$	12.4048	−	4.14509i	0.545563	−	0.182301i
$518$		0			0
$519$	7.76780	−	23.9068i	0.340969	−	1.04939i
$520$		0			0
$521$	−34.2935	−	24.9157i	−1.50242	−	1.09158i	−0.969403	−	0.245474i	$-0.921057\pi$
$521$	−34.2935	−	24.9157i	−1.50242	−	1.09158i	−0.533021	−	0.846102i	$-0.678943\pi$
$522$		0			0
$523$	0.0934079	+	0.287480i	0.00408444	+	0.0125706i	0.953078	−	0.302725i	$-0.0978964\pi$
$523$	0.0934079	+	0.287480i	0.00408444	+	0.0125706i	−0.948994	+	0.315296i	$0.897896\pi$
$524$		0			0
$525$	−8.91041	+	6.47379i	−0.388882	+	0.282539i
$526$		0			0
$527$	19.2664			0.839259
$528$		0			0
$529$	32.4504			1.41089
$530$		0			0
$531$	−4.47070	+	3.24816i	−0.194012	+	0.140958i
$532$		0			0
$533$	2.50728	+	7.71661i	0.108602	+	0.334244i
$534$		0			0
$535$	−34.1474	−	24.8096i	−1.47632	−	1.07261i
$536$		0			0
$537$	−6.28176	+	19.3333i	−0.271078	+	0.834292i
$538$		0			0
$539$	−0.172471	−	20.7102i	−0.00742887	−	0.892051i
$540$		0			0
$541$	5.21912	−	16.0628i	0.224387	−	0.690593i	−0.773966	−	0.633227i	$-0.781730\pi$
$541$	5.21912	−	16.0628i	0.224387	−	0.690593i	0.998353	−	0.0573660i	$-0.0182702\pi$
$542$		0			0
$543$	−9.93957	−	7.22152i	−0.426548	−	0.309905i
$544$		0			0
$545$	−7.58341	−	23.3393i	−0.324837	−	0.999747i
$546$		0			0
$547$	14.0947	−	10.2404i	0.602647	−	0.437849i	−0.244170	−	0.969732i	$-0.578516\pi$
$547$	14.0947	−	10.2404i	0.602647	−	0.437849i	0.846818	+	0.531883i	$0.178516\pi$
$548$		0			0
$549$	−1.83993			−0.0785262
$550$		0			0
$551$	−17.4867			−0.744958
$552$		0			0
$553$	−9.46100	+	6.87382i	−0.402323	+	0.292304i
$554$		0			0
$555$	2.08249	+	6.40926i	0.0883970	+	0.272058i
$556$		0			0
$557$	−16.6848	−	12.1222i	−0.706956	−	0.513633i	0.175234	−	0.984527i	$-0.443932\pi$
$557$	−16.6848	−	12.1222i	−0.706956	−	0.513633i	−0.882190	+	0.470893i	$0.843932\pi$
$558$		0			0
$559$	1.89429	−	5.83003i	0.0801200	−	0.246584i
$560$		0			0
$561$	27.5905	+	37.3176i	1.16487	+	1.57555i
$562$		0			0
$563$	6.06369	−	18.6621i	0.255554	−	0.786514i	−0.738166	−	0.674619i	$-0.764308\pi$
$563$	6.06369	−	18.6621i	0.255554	−	0.786514i	0.993720	−	0.111895i	$-0.0356921\pi$
$564$		0			0
$565$	−5.67272	−	4.12147i	−0.238653	−	0.173392i
$566$		0			0
$567$	−2.84230	−	8.74771i	−0.119366	−	0.367369i
$568$		0			0
$569$	27.3007	−	19.8351i	1.14451	−	0.831532i	0.156765	−	0.987636i	$-0.449894\pi$
$569$	27.3007	−	19.8351i	1.14451	−	0.831532i	0.987741	+	0.156104i	$0.0498936\pi$
$570$		0			0
$571$	19.8373			0.830164			0.415082	−	0.909784i	$-0.363753\pi$
$571$	19.8373			0.830164			0.415082	+	0.909784i	$0.363753\pi$
$572$		0			0
$573$	13.0267			0.544197
$574$		0			0
$575$	−39.7787	+	28.9009i	−1.65889	+	1.20525i
$576$		0			0
$577$	9.80486	+	30.1763i	0.408182	+	1.25625i	0.918209	+	0.396096i	$0.129635\pi$
$577$	9.80486	+	30.1763i	0.408182	+	1.25625i	−0.510027	+	0.860158i	$0.670365\pi$
$578$		0			0
$579$	12.6345	+	9.17950i	0.525072	+	0.381487i
$580$		0			0
$581$	−0.0522653	+	0.160856i	−0.00216833	+	0.00667344i
$582$		0			0
$583$	−13.7100	+	19.2046i	−0.567812	+	0.795371i
$584$		0			0
$585$	2.01616	−	6.20510i	0.0833579	−	0.256549i
$586$		0			0
$587$	15.5596	+	11.3047i	0.642215	+	0.466597i	0.860611	−	0.509264i	$-0.170082\pi$
$587$	15.5596	+	11.3047i	0.642215	+	0.466597i	−0.218395	+	0.975860i	$0.570082\pi$
$588$		0			0
$589$	−1.94497	−	5.98601i	−0.0801413	−	0.246649i
$590$		0			0
$591$	25.6037	−	18.6022i	1.05319	−	0.765191i
$592$		0			0
$593$	−36.8924			−1.51499			−0.757495	−	0.652841i	$-0.773577\pi$
$593$	−36.8924			−1.51499			−0.757495	+	0.652841i	$0.773577\pi$
$594$		0			0
$595$	−21.5867			−0.884967
$596$		0			0
$597$	−5.27547	+	3.83285i	−0.215910	+	0.156868i
$598$		0			0
$599$	−1.26482	−	3.89271i	−0.0516790	−	0.159052i	0.921886	−	0.387461i	$-0.126648\pi$
$599$	−1.26482	−	3.89271i	−0.0516790	−	0.159052i	−0.973565	+	0.228409i	$0.926648\pi$
$600$		0			0
$601$	18.1681	+	13.1999i	0.741091	+	0.538434i	0.893053	−	0.449952i	$-0.148559\pi$
$601$	18.1681	+	13.1999i	0.741091	+	0.538434i	−0.151961	+	0.988386i	$0.548559\pi$
$602$		0			0
$603$	−2.90696	+	8.94669i	−0.118380	+	0.364337i
$604$		0			0
$605$	−10.9836	+	35.8235i	−0.446547	+	1.45643i
$606$		0			0
$607$	−4.39764	+	13.5345i	−0.178495	+	0.549350i	−0.999776	−	0.0211738i	$-0.993260\pi$
$607$	−4.39764	+	13.5345i	−0.178495	+	0.549350i	0.821281	+	0.570523i	$0.193260\pi$
$608$		0			0
$609$	9.90671	+	7.19765i	0.401440	+	0.291663i
$610$		0			0
$611$	−3.41711	−	10.5168i	−0.138241	−	0.425463i
$612$		0			0
$613$	12.4021	−	9.01062i	0.500915	−	0.363936i	−0.308452	−	0.951240i	$-0.599811\pi$
$613$	12.4021	−	9.01062i	0.500915	−	0.363936i	0.809366	+	0.587304i	$0.199811\pi$
$614$		0			0
$615$	18.9153			0.762738
$616$		0			0
$617$	12.4466			0.501080			0.250540	−	0.968106i	$-0.419392\pi$
$617$	12.4466			0.501080			0.250540	+	0.968106i	$0.419392\pi$
$618$		0			0
$619$	−26.2349	+	19.0608i	−1.05447	+	0.766117i	−0.973057	−	0.230564i	$-0.925943\pi$
$619$	−26.2349	+	19.0608i	−1.05447	+	0.766117i	−0.0814119	+	0.996681i	$0.525943\pi$
$620$		0			0
$621$	−10.2318	−	31.4904i	−0.410590	−	1.26366i
$622$		0			0
$623$	−2.94348	−	2.13856i	−0.117928	−	0.0856797i
$624$		0			0
$625$	−4.45464	+	13.7100i	−0.178186	+	0.548399i
$626$		0			0
$627$	8.80914	−	12.3395i	0.351803	−	0.492794i
$628$		0			0
$629$	−2.32274	+	7.14865i	−0.0926135	+	0.285035i
$630$		0			0
$631$	13.4849	+	9.79735i	0.536825	+	0.390026i	0.822905	−	0.568179i	$-0.192352\pi$
$631$	13.4849	+	9.79735i	0.536825	+	0.390026i	−0.286079	+	0.958206i	$0.592352\pi$
$632$		0			0
$633$	9.47873	+	29.1725i	0.376746	+	1.15950i
$634$		0			0
$635$	−23.0662	+	16.7586i	−0.915355	+	0.665045i
$636$		0			0
$637$	−17.5106			−0.693793
$638$		0			0
$639$	−1.31811			−0.0521438
$640$		0			0
$641$	14.8138	−	10.7629i	0.585111	−	0.425108i	−0.255452	−	0.966822i	$-0.582224\pi$
$641$	14.8138	−	10.7629i	0.585111	−	0.425108i	0.840563	+	0.541714i	$0.182224\pi$
$642$		0			0
$643$	1.58274	+	4.87117i	0.0624171	+	0.192100i	0.977402	−	0.211387i	$-0.0677980\pi$
$643$	1.58274	+	4.87117i	0.0624171	+	0.192100i	−0.914985	+	0.403487i	$0.867798\pi$
$644$		0			0
$645$	−11.5615	−	8.39993i	−0.455234	−	0.330747i
$646$		0			0
$647$	12.1774	−	37.4782i	0.478743	−	1.47342i	−0.362099	−	0.932140i	$-0.617940\pi$
$647$	12.1774	−	37.4782i	0.478743	−	1.47342i	0.840842	−	0.541281i	$-0.182060\pi$
$648$		0			0
$649$	−15.9517	−	21.5755i	−0.626159	−	0.846912i
$650$		0			0
$651$	−1.36200	+	4.19181i	−0.0533811	+	0.164290i
$652$		0			0
$653$	2.45332	+	1.78244i	0.0960059	+	0.0697524i	0.634753	−	0.772715i	$-0.281102\pi$
$653$	2.45332	+	1.78244i	0.0960059	+	0.0697524i	−0.538747	+	0.842468i	$0.681102\pi$
$654$		0			0
$655$	14.0535	+	43.2521i	0.549114	+	1.69000i
$656$		0			0
$657$	−2.75943	+	2.00485i	−0.107656	+	0.0782165i
$658$		0			0
$659$	−1.09096			−0.0424978			−0.0212489	−	0.999774i	$-0.506764\pi$
$659$	−1.09096			−0.0424978			−0.0212489	+	0.999774i	$0.506764\pi$
$660$		0			0
$661$	−46.1346			−1.79443			−0.897214	−	0.441596i	$-0.854412\pi$
$661$	−46.1346			−1.79443			−0.897214	+	0.441596i	$0.854412\pi$
$662$		0			0
$663$	31.7442	−	23.0635i	1.23284	−	0.895713i
$664$		0			0
$665$	2.17920	+	6.70690i	0.0845059	+	0.260082i
$666$		0			0
$667$	44.2265	+	32.1324i	1.71246	+	1.24417i
$668$		0			0
$669$	4.49635	−	13.8384i	0.173839	−	0.535022i
$670$		0			0
$671$	−0.0743968	−	8.93350i	−0.00287206	−	0.344874i
$672$		0			0
$673$	6.10596	−	18.7922i	0.235367	−	0.724386i	−0.761705	−	0.647924i	$-0.775637\pi$
$673$	6.10596	−	18.7922i	0.235367	−	0.724386i	0.997072	−	0.0764625i	$-0.0243625\pi$
$674$		0			0
$675$	23.7529	+	17.2575i	0.914250	+	0.664241i
$676$		0			0
$677$	7.84542	+	24.1457i	0.301524	+	0.927996i	0.980951	+	0.194253i	$0.0622282\pi$
$677$	7.84542	+	24.1457i	0.301524	+	0.927996i	−0.679427	+	0.733743i	$0.737772\pi$
$678$		0			0
$679$	−3.50890	+	2.54937i	−0.134659	+	0.0978358i
$680$		0			0
$681$	28.8124			1.10410
$682$		0			0
$683$	−3.69756			−0.141483			−0.0707416	−	0.997495i	$-0.522537\pi$
$683$	−3.69756			−0.141483			−0.0707416	+	0.997495i	$0.522537\pi$
$684$		0			0
$685$	−2.72879	+	1.98258i	−0.104262	+	0.0757505i
$686$		0			0
$687$	1.42440	+	4.38386i	0.0543443	+	0.167255i
$688$		0			0
$689$	16.1399	+	11.7263i	0.614880	+	0.446737i
$690$		0			0
$691$	0.790302	−	2.43230i	0.0300645	−	0.0925291i	−0.934898	−	0.354916i	$-0.884510\pi$
$691$	0.790302	−	2.43230i	0.0300645	−	0.0925291i	0.964963	+	0.262387i	$0.0845096\pi$
$692$		0			0
$693$	−1.86753	+	0.624037i	−0.0709414	+	0.0237052i
$694$		0			0
$695$	6.31012	−	19.4206i	0.239357	−	0.736664i
$696$		0			0
$697$	17.0682	+	12.4007i	0.646502	+	0.469711i
$698$		0			0
$699$	3.70255	+	11.3953i	0.140043	+	0.431009i
$700$		0			0
$701$	−29.9131	+	21.7331i	−1.12980	+	0.820850i	−0.985666	−	0.168708i	$-0.946040\pi$
$701$	−29.9131	+	21.7331i	−1.12980	+	0.820850i	−0.144136	+	0.989558i	$0.546040\pi$
$702$		0			0
$703$	2.45554			0.0926126
$704$		0			0
$705$	−25.7792			−0.970900
$706$		0			0
$707$	5.81526	−	4.22503i	0.218705	−	0.158899i
$708$		0			0
$709$	−10.3529	−	31.8630i	−0.388812	−	1.19664i	−0.933677	−	0.358116i	$-0.883419\pi$
$709$	−10.3529	−	31.8630i	−0.388812	−	1.19664i	0.544865	−	0.838524i	$-0.316581\pi$
$710$		0			0
$711$	−7.43537	−	5.40211i	−0.278848	−	0.202595i
$712$		0			0
$713$	−6.08038	+	18.7135i	−0.227712	+	0.700826i
$714$		0			0
$715$	30.2095	+	9.53826i	1.12977	+	0.356711i
$716$		0			0
$717$	−10.1173	+	31.1380i	−0.377839	+	1.16287i
$718$		0			0
$719$	−24.3134	−	17.6647i	−0.906736	−	0.658782i	0.0334515	−	0.999440i	$-0.489350\pi$
$719$	−24.3134	−	17.6647i	−0.906736	−	0.658782i	−0.940187	+	0.340658i	$0.889350\pi$
$720$		0			0
$721$	0.220359	+	0.678195i	0.00820659	+	0.0252573i
$722$		0			0
$723$	−0.0258233	+	0.0187618i	−0.000960380	+	0.000697757i
$724$		0			0
$725$	−48.4744			−1.80029
$726$		0			0
$727$	22.4183			0.831449			0.415725	−	0.909491i	$-0.363528\pi$
$727$	22.4183			0.831449			0.415725	+	0.909491i	$0.363528\pi$
$728$		0			0
$729$	−14.8630	+	10.7986i	−0.550482	+	0.399948i
$730$		0			0
$731$	−4.92556	−	15.1593i	−0.182178	−	0.560687i
$732$		0			0
$733$	−19.8494	−	14.4214i	−0.733153	−	0.532667i	0.157406	−	0.987534i	$-0.449687\pi$
$733$	−19.8494	−	14.4214i	−0.733153	−	0.532667i	−0.890559	+	0.454867i	$0.849687\pi$
$734$		0			0
$735$	−12.6146	+	38.8239i	−0.465298	+	1.43204i
$736$		0			0
$737$	−43.5569	−	13.7525i	−1.60444	−	0.506581i
$738$		0			0
$739$	1.04270	−	3.20910i	0.0383563	−	0.118049i	−0.930045	−	0.367446i	$-0.880232\pi$
$739$	1.04270	−	3.20910i	0.0383563	−	0.118049i	0.968401	+	0.249397i	$0.0802324\pi$
$740$		0			0
$741$	−10.3704	−	7.53452i	−0.380965	−	0.276788i
$742$		0			0
$743$	−1.88683	−	5.80706i	−0.0692210	−	0.213040i	0.910462	−	0.413593i	$-0.135726\pi$
$743$	−1.88683	−	5.80706i	−0.0692210	−	0.213040i	−0.979683	+	0.200552i	$0.935726\pi$
$744$		0			0
$745$	47.6562	−	34.6243i	1.74599	−	1.26854i
$746$		0			0
$747$	−0.132922			−0.00486336
$748$		0			0
$749$	10.7699			0.393523
$750$		0			0
$751$	40.5404	−	29.4544i	1.47934	−	1.07480i	0.501574	−	0.865115i	$-0.332755\pi$
$751$	40.5404	−	29.4544i	1.47934	−	1.07480i	0.977768	−	0.209690i	$-0.0672454\pi$
$752$		0			0
$753$	−14.3451	−	44.1495i	−0.522763	−	1.60890i
$754$		0			0
$755$	2.17803	+	1.58243i	0.0792667	+	0.0575906i
$756$		0			0
$757$	1.88482	−	5.80088i	0.0685050	−	0.210837i	−0.910944	−	0.412531i	$-0.864645\pi$
$757$	1.88482	−	5.80088i	0.0685050	−	0.210837i	0.979448	+	0.201695i	$0.0646448\pi$
$758$		0			0
$759$	−44.9540	+	15.0214i	−1.63173	+	0.545244i
$760$		0			0
$761$	−13.6183	+	41.9128i	−0.493662	+	1.51934i	0.325368	+	0.945587i	$0.394512\pi$
$761$	−13.6183	+	41.9128i	−0.493662	+	1.51934i	−0.819031	+	0.573749i	$0.805488\pi$
$762$		0			0
$763$	5.06582	+	3.68053i	0.183395	+	0.133244i
$764$		0			0
$765$	−5.24244	−	16.1346i	−0.189541	−	0.583346i
$766$		0			0
$767$	−18.3532	+	13.3344i	−0.662696	+	0.481477i
$768$		0			0
$769$	53.7688			1.93895			0.969476	−	0.245185i	$-0.0788488\pi$
$769$	53.7688			1.93895			0.969476	+	0.245185i	$0.0788488\pi$
$770$		0			0
$771$	−55.5188			−1.99946
$772$		0			0
$773$	25.5645	−	18.5737i	0.919491	−	0.668049i	−0.0239065	−	0.999714i	$-0.507610\pi$
$773$	25.5645	−	18.5737i	0.919491	−	0.668049i	0.943397	+	0.331665i	$0.107610\pi$
$774$		0			0
$775$	−5.39161	−	16.5937i	−0.193672	−	0.596062i
$776$		0			0
$777$	−1.39114	−	1.01072i	−0.0499067	−	0.0362593i
$778$		0			0
$779$	2.12981	−	6.55489i	0.0763085	−	0.234853i
$780$		0			0
$781$	−0.0532975	−	6.39991i	−0.00190713	−	0.229007i
$782$		0			0
$783$	10.0873	−	31.0454i	0.360489	−	1.10947i
$784$		0			0
$785$	35.0989	+	25.5009i	1.25273	+	0.910164i
$786$		0			0
$787$	−0.00679045	−	0.0208988i	−0.000242053	−	0.000744964i	0.950935	−	0.309389i	$-0.100125\pi$
$787$	−0.00679045	−	0.0208988i	−0.000242053	−	0.000744964i	−0.951177	+	0.308644i	$0.900125\pi$
$788$		0			0
$789$	26.7873	−	19.4621i	0.953653	−	0.692870i
$790$		0			0
$791$	1.78914			0.0636144
$792$		0			0
$793$	−7.55331			−0.268226
$794$		0			0
$795$	37.6264	−	27.3372i	1.33447	−	0.969550i
$796$		0			0
$797$	−2.33212	−	7.17752i	−0.0826078	−	0.254241i	0.901219	−	0.433365i	$-0.142674\pi$
$797$	−2.33212	−	7.17752i	−0.0826078	−	0.254241i	−0.983827	+	0.179124i	$0.942674\pi$
$798$		0			0
$799$	−23.2618	−	16.9007i	−0.822942	−	0.597902i
$800$		0			0
$801$	0.883591	−	2.71941i	0.0312202	−	0.0960858i
$802$		0			0
$803$	−9.84581	−	13.3170i	−0.347451	−	0.469945i
$804$		0			0
$805$	6.81263	−	20.9671i	0.240114	−	0.738994i
$806$		0			0
$807$	−4.35371	−	3.16315i	−0.153258	−	0.111348i
$808$		0			0
$809$	−14.0296	−	43.1787i	−0.493255	−	1.51808i	−0.819658	−	0.572853i	$-0.805837\pi$
$809$	−14.0296	−	43.1787i	−0.493255	−	1.51808i	0.326403	−	0.945231i	$-0.394163\pi$
$810$		0			0
$811$	11.4192	−	8.29653i	0.400982	−	0.291331i	−0.368959	−	0.929446i	$-0.620286\pi$
$811$	11.4192	−	8.29653i	0.400982	−	0.291331i	0.769941	+	0.638115i	$0.220286\pi$
$812$		0			0
$813$	43.6750			1.53175
$814$		0			0
$815$	−0.564482			−0.0197729
$816$		0			0
$817$	−4.21270	+	3.06071i	−0.147384	+	0.107081i
$818$		0			0
$819$	0.514440	+	1.58328i	0.0179760	+	0.0553244i
$820$		0			0
$821$	0.291583	+	0.211848i	0.0101763	+	0.00739354i	0.592862	−	0.805304i	$-0.297998\pi$
$821$	0.291583	+	0.211848i	0.0101763	+	0.00739354i	−0.582685	+	0.812698i	$0.697998\pi$
$822$		0			0
$823$	−3.52800	+	10.8581i	−0.122978	+	0.378488i	−0.993527	−	0.113594i	$-0.963764\pi$
$823$	−3.52800	+	10.8581i	−0.122978	+	0.378488i	0.870549	+	0.492082i	$0.163764\pi$
$824$		0			0
$825$	24.4196	−	34.2061i	0.850180	−	1.19090i
$826$		0			0
$827$	−12.1120	+	37.2769i	−0.421176	+	1.29625i	0.485433	+	0.874274i	$0.338662\pi$
$827$	−12.1120	+	37.2769i	−0.421176	+	1.29625i	−0.906609	+	0.421972i	$0.861338\pi$
$828$		0			0
$829$	23.9729	+	17.4173i	0.832612	+	0.604928i	0.920297	−	0.391220i	$-0.127947\pi$
$829$	23.9729	+	17.4173i	0.832612	+	0.604928i	−0.0876848	+	0.996148i	$0.527947\pi$
$830$		0			0
$831$	1.97337	+	6.07339i	0.0684553	+	0.210684i
$832$		0			0
$833$	−36.8355	+	26.7625i	−1.27627	+	0.927267i
$834$		0			0
$835$	−73.8715			−2.55643
$836$		0			0
$837$	11.7494			0.406118
$838$		0			0
$839$	22.6388	−	16.4481i	0.781579	−	0.567850i	−0.123874	−	0.992298i	$-0.539532\pi$
$839$	22.6388	−	16.4481i	0.781579	−	0.567850i	0.905452	+	0.424448i	$0.139532\pi$
$840$		0			0
$841$	7.69282	+	23.6761i	0.265270	+	0.816416i
$842$		0			0
$843$	−13.5317	−	9.83133i	−0.466055	−	0.338609i
$844$		0			0
$845$	−5.40715	+	16.6415i	−0.186012	+	0.572485i
$846$		0			0
$847$	−3.10543	−	9.04226i	−0.106704	−	0.310696i
$848$		0			0
$849$	−17.2627	+	53.1293i	−0.592456	+	1.82339i
$850$		0			0
$851$	−6.21044	−	4.51215i	−0.212891	−	0.154674i
$852$		0			0
$853$	12.6246	+	38.8547i	0.432259	+	1.33036i	0.895869	+	0.444318i	$0.146554\pi$
$853$	12.6246	+	38.8547i	0.432259	+	1.33036i	−0.463610	+	0.886040i	$0.653446\pi$
$854$		0			0
$855$	−4.48372	+	3.25761i	−0.153340	+	0.111408i
$856$		0			0
$857$	−28.8702			−0.986189			−0.493094	−	0.869976i	$-0.664134\pi$
$857$	−28.8702			−0.986189			−0.493094	+	0.869976i	$0.664134\pi$
$858$		0			0
$859$	−8.76432			−0.299035			−0.149517	−	0.988759i	$-0.547772\pi$
$859$	−8.76432			−0.299035			−0.149517	+	0.988759i	$0.547772\pi$
$860$		0			0
$861$	−3.90464	+	2.83689i	−0.133070	+	0.0966808i
$862$		0			0
$863$	11.4027	+	35.0939i	0.388153	+	1.19461i	0.934167	+	0.356835i	$0.116144\pi$
$863$	11.4027	+	35.0939i	0.388153	+	1.19461i	−0.546015	+	0.837776i	$0.683856\pi$
$864$		0			0
$865$	−36.0956	−	26.2250i	−1.22729	−	0.891675i
$866$		0			0
$867$	21.4463	−	66.0051i	0.728356	−	2.24165i
$868$		0			0
$869$	25.9285	−	36.3198i	0.879564	−	1.23206i
$870$		0			0
$871$	−11.9337	+	36.7281i	−0.404358	+	1.24448i
$872$		0			0
$873$	−2.75764	−	2.00354i	−0.0933319	−	0.0678096i
$874$		0			0
$875$	1.46653	+	4.51352i	0.0495779	+	0.152585i
$876$		0			0
$877$	−20.1655	+	14.6511i	−0.680941	+	0.494732i	−0.873670	−	0.486520i	$-0.838266\pi$
$877$	−20.1655	+	14.6511i	−0.680941	+	0.494732i	0.192729	+	0.981252i	$0.438266\pi$
$878$		0			0
$879$	−42.1356			−1.42120
$880$		0			0
$881$	25.1252			0.846491			0.423245	−	0.906015i	$-0.360891\pi$
$881$	25.1252			0.846491			0.423245	+	0.906015i	$0.360891\pi$
$882$		0			0
$883$	3.69532	−	2.68481i	0.124357	−	0.0903510i	−0.523868	−	0.851800i	$-0.675511\pi$
$883$	3.69532	−	2.68481i	0.124357	−	0.0903510i	0.648225	+	0.761449i	$0.275511\pi$
$884$		0			0
$885$	16.3429	+	50.2983i	0.549361	+	1.69076i
$886$		0			0
$887$	−2.45848	−	1.78619i	−0.0825476	−	0.0599743i	0.545746	−	0.837951i	$-0.316246\pi$
$887$	−2.45848	−	1.78619i	−0.0825476	−	0.0599743i	−0.628294	+	0.777976i	$0.716246\pi$
$888$		0			0
$889$	2.24808	−	6.91888i	0.0753982	−	0.232052i
$890$		0			0
$891$	20.8662	+	28.2225i	0.699043	+	0.945491i
$892$		0			0
$893$	−2.90267	+	8.93350i	−0.0971341	+	0.298948i
$894$		0			0
$895$	29.1902	+	21.2079i	0.975721	+	0.708903i
$896$		0			0
$897$	12.3833	+	38.1119i	0.413466	+	1.27252i
$898$		0			0
$899$	−15.6937	+	11.4021i	−0.523415	+	0.380283i
$900$		0			0
$901$	51.8741			1.72818
$902$		0			0
$903$	3.64643			0.121345
$904$		0			0
$905$	−17.6420	+	12.8177i	−0.586440	+	0.426074i
$906$		0			0
$907$	−4.33775	−	13.3502i	−0.144033	−	0.443286i	0.852853	−	0.522151i	$-0.174870\pi$
$907$	−4.33775	−	13.3502i	−0.144033	−	0.443286i	−0.996885	+	0.0788649i	$0.974870\pi$
$908$		0			0
$909$	4.57019	+	3.32044i	0.151584	+	0.110132i
$910$		0			0
$911$	−9.29223	+	28.5985i	−0.307865	+	0.947512i	0.670727	+	0.741704i	$0.265982\pi$
$911$	−9.29223	+	28.5985i	−0.307865	+	0.947512i	−0.978592	+	0.205808i	$0.934018\pi$
$912$		0			0
$913$	−0.00537465	−	0.645383i	−0.000177875	−	0.0213591i
$914$		0			0
$915$	−5.44142	+	16.7470i	−0.179888	+	0.553637i
$916$		0			0
$917$	−9.38791	−	6.82072i	−0.310016	−	0.225240i
$918$		0			0
$919$	11.9047	+	36.6389i	0.392700	+	1.20861i	0.930738	+	0.365686i	$0.119166\pi$
$919$	11.9047	+	36.6389i	0.392700	+	1.20861i	−0.538038	+	0.842920i	$0.680834\pi$
$920$		0			0
$921$	37.5476	−	27.2799i	1.23723	−	0.898903i
$922$		0			0
$923$	−5.41115			−0.178110
$924$		0			0
$925$	6.80695			0.223811
$926$		0			0
$927$	−0.453389	+	0.329407i	−0.0148913	+	0.0108191i
$928$		0			0
$929$	9.58354	+	29.4951i	0.314426	+	0.967703i	0.975990	+	0.217815i	$0.0698928\pi$
$929$	9.58354	+	29.4951i	0.314426	+	0.967703i	−0.661564	+	0.749888i	$0.730107\pi$
$930$		0			0
$931$	12.0336	+	8.74294i	0.394386	+	0.286538i
$932$		0			0
$933$	−2.11794	+	6.51835i	−0.0693383	+	0.213401i
$934$		0			0
$935$	78.1270	−	26.1063i	2.55503	−	0.853766i
$936$		0			0
$937$	10.7606	−	33.1178i	0.351534	−	1.08191i	−0.606457	−	0.795116i	$-0.707410\pi$
$937$	10.7606	−	33.1178i	0.351534	−	1.08191i	0.957992	−	0.286796i	$-0.0925901\pi$
$938$		0			0
$939$	−13.5212	−	9.82373i	−0.441248	−	0.320585i
$940$		0			0
$941$	−10.5435	−	32.4497i	−0.343709	−	1.05783i	−0.962271	−	0.272092i	$-0.912284\pi$
$941$	−10.5435	−	32.4497i	−0.343709	−	1.05783i	0.618562	−	0.785736i	$-0.287716\pi$
$942$		0			0
$943$	−17.4315	+	12.6647i	−0.567646	+	0.412419i
$944$		0			0
$945$	−13.1643			−0.428236
$946$		0			0
$947$	14.3465			0.466198			0.233099	−	0.972453i	$-0.425113\pi$
$947$	14.3465			0.466198			0.233099	+	0.972453i	$0.425113\pi$
$948$		0			0
$949$	−11.3281	+	8.23033i	−0.367725	+	0.267168i
$950$		0			0
$951$	13.0592	+	40.1921i	0.423473	+	1.30332i
$952$		0			0
$953$	−29.4915	−	21.4268i	−0.955322	−	0.694082i	−0.00326235	−	0.999995i	$-0.501038\pi$
$953$	−29.4915	−	21.4268i	−0.955322	−	0.694082i	−0.952060	+	0.305913i	$0.901038\pi$
$954$		0			0
$955$	7.14489	−	21.9897i	0.231203	−	0.711571i
$956$		0			0
$957$	−44.5593	−	14.0690i	−1.44040	−	0.454787i
$958$		0			0
$959$	0.265953	−	0.818519i	0.00858807	−	0.0264314i
$960$		0			0
$961$	19.4308	+	14.1173i	0.626801	+	0.455397i
$962$		0			0
$963$	2.61552	+	8.04975i	0.0842841	+	0.259400i
$964$		0			0
$965$	22.4253	−	16.2929i	0.721896	−	0.524488i
$966$		0			0
$967$	−48.0950			−1.54663			−0.773315	−	0.634022i	$-0.781403\pi$
$967$	−48.0950			−1.54663			−0.773315	+	0.634022i	$0.781403\pi$
$968$		0			0
$969$	−33.3308			−1.07074
$970$		0			0
$971$	19.2115	−	13.9580i	0.616527	−	0.447933i	−0.235180	−	0.971952i	$-0.575568\pi$
$971$	19.2115	−	13.9580i	0.616527	−	0.447933i	0.851707	+	0.524019i	$0.175568\pi$
$972$		0			0
$973$	1.61008	+	4.95532i	0.0516169	+	0.158860i
$974$		0			0
$975$	−28.7475	−	20.8863i	−0.920655	−	0.668895i
$976$		0			0
$977$	8.34018	−	25.6684i	0.266826	−	0.821206i	−0.724441	−	0.689337i	$-0.757902\pi$
$977$	8.34018	−	25.6684i	0.266826	−	0.821206i	0.991267	−	0.131869i	$-0.0420979\pi$
$978$		0			0
$979$	13.2394	+	4.18019i	0.423134	+	0.133599i
$980$		0			0
$981$	−1.52069	+	4.68020i	−0.0485518	+	0.149427i
$982$		0			0
$983$	−19.2858	−	14.0119i	−0.615121	−	0.446911i	0.236093	−	0.971730i	$-0.424133\pi$
$983$	−19.2858	−	14.0119i	−0.615121	−	0.446911i	−0.851214	+	0.524819i	$0.824133\pi$
$984$		0			0
$985$	−17.3583	−	53.4234i	−0.553082	−	1.70221i
$986$		0			0
$987$	5.32154	−	3.86632i	0.169386	−	0.123066i
$988$		0			0
$989$	16.2787			0.517633
$990$		0			0
$991$	−10.6048			−0.336871			−0.168436	−	0.985713i	$-0.553872\pi$
$991$	−10.6048			−0.336871			−0.168436	+	0.985713i	$0.553872\pi$
$992$		0			0
$993$	3.22507	−	2.34315i	0.102345	−	0.0743576i
$994$		0			0
$995$	3.57656	+	11.0075i	0.113385	+	0.348962i
$996$		0			0
$997$	−2.18311	−	1.58613i	−0.0691399	−	0.0502331i	0.552678	−	0.833395i	$-0.313606\pi$
$997$	−2.18311	−	1.58613i	−0.0691399	−	0.0502331i	−0.621818	+	0.783162i	$0.713606\pi$
$998$		0			0
$999$	−1.41649	+	4.35951i	−0.0448157	+	0.137929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.i.b.9.1	✓	8
3.2	odd	2		792.2.r.g.361.1		8
4.3	odd	2		176.2.m.d.97.2		8
8.3	odd	2		704.2.m.i.449.1		8
8.5	even	2		704.2.m.l.449.2		8
11.2	odd	10		968.2.i.t.729.2		8
11.3	even	5		968.2.i.s.81.2		8
11.4	even	5		968.2.a.n.1.3		4
11.5	even	5	inner	88.2.i.b.49.1	yes	8
11.6	odd	10		968.2.i.p.753.1		8
11.7	odd	10		968.2.a.m.1.3		4
11.8	odd	10		968.2.i.t.81.2		8
11.9	even	5		968.2.i.s.729.2		8
11.10	odd	2		968.2.i.p.9.1		8
33.5	odd	10		792.2.r.g.577.1		8
33.26	odd	10		8712.2.a.ce.1.1		4
33.29	even	10		8712.2.a.cd.1.1		4
44.7	even	10		1936.2.a.bc.1.2		4
44.15	odd	10		1936.2.a.bb.1.2		4
44.27	odd	10		176.2.m.d.49.2		8
88.5	even	10		704.2.m.l.577.2		8
88.27	odd	10		704.2.m.i.577.1		8
88.29	odd	10		7744.2.a.dh.1.2		4
88.37	even	10		7744.2.a.di.1.2		4
88.51	even	10		7744.2.a.ds.1.3		4
88.59	odd	10		7744.2.a.dr.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.i.b.9.1	✓	8	1.1	even	1	trivial
88.2.i.b.49.1	yes	8	11.5	even	5	inner
176.2.m.d.49.2		8	44.27	odd	10
176.2.m.d.97.2		8	4.3	odd	2
704.2.m.i.449.1		8	8.3	odd	2
704.2.m.i.577.1		8	88.27	odd	10
704.2.m.l.449.2		8	8.5	even	2
704.2.m.l.577.2		8	88.5	even	10
792.2.r.g.361.1		8	3.2	odd	2
792.2.r.g.577.1		8	33.5	odd	10
968.2.a.m.1.3		4	11.7	odd	10
968.2.a.n.1.3		4	11.4	even	5
968.2.i.p.9.1		8	11.10	odd	2
968.2.i.p.753.1		8	11.6	odd	10
968.2.i.s.81.2		8	11.3	even	5
968.2.i.s.729.2		8	11.9	even	5
968.2.i.t.81.2		8	11.8	odd	10
968.2.i.t.729.2		8	11.2	odd	10
1936.2.a.bb.1.2		4	44.15	odd	10
1936.2.a.bc.1.2		4	44.7	even	10
7744.2.a.dh.1.2		4	88.29	odd	10
7744.2.a.di.1.2		4	88.37	even	10
7744.2.a.dr.1.3		4	88.59	odd	10
7744.2.a.ds.1.3		4	88.51	even	10
8712.2.a.cd.1.1		4	33.29	even	10
8712.2.a.ce.1.1		4	33.26	odd	10

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.55261 + 1.12804i) q^{3} +(1.05261 + 3.23960i) q^{5} +(-0.703158 - 0.510874i) q^{7} +(0.211078 - 0.649631i) q^{9} +O(q^{10})\)	\(q+(-1.55261 + 1.12804i) q^{3} +(1.05261 + 3.23960i) q^{5} +(-0.703158 - 0.510874i) q^{7} +(0.211078 - 0.649631i) q^{9} +(3.16272 + 0.998590i) q^{11} +(0.866521 - 2.66688i) q^{13} +(-5.28868 - 3.84245i) q^{15} +(-2.25314 - 6.93444i) q^{17} +(-1.92705 + 1.40008i) q^{19} +1.66801 q^{21} +7.44651 q^{23} +(-5.34193 + 3.88114i) q^{25} +(-1.37405 - 4.22888i) q^{27} +(5.93923 + 4.31510i) q^{29} +(-0.816541 + 2.51306i) q^{31} +(-6.03692 + 2.01725i) q^{33} +(0.914876 - 2.81570i) q^{35} +(-0.834007 - 0.605942i) q^{37} +(1.66297 + 5.11809i) q^{39} +(-2.34089 + 1.70076i) q^{41} +2.18609 q^{43} +2.32673 q^{45} +(3.19034 - 2.31792i) q^{47} +(-1.92968 - 5.93895i) q^{49} +(11.3206 + 8.22486i) q^{51} +(-2.19851 + 6.76631i) q^{53} +(0.0940804 + 11.2971i) q^{55} +(1.41261 - 4.34757i) q^{57} +(-6.54508 - 4.75528i) q^{59} +(-0.832382 - 2.56181i) q^{61} +(-0.480301 + 0.348959i) q^{63} +9.55172 q^{65} -13.7720 q^{67} +(-11.5615 + 8.39993i) q^{69} +(-0.596314 - 1.83527i) q^{71} +(-4.03979 - 2.93508i) q^{73} +(3.91586 - 12.0518i) q^{75} +(-1.71374 - 2.31792i) q^{77} +(4.15783 - 12.7965i) q^{79} +(8.56151 + 6.22030i) q^{81} +(-0.0601338 - 0.185073i) q^{83} +(20.0931 - 14.5985i) q^{85} -14.0889 q^{87} +4.18609 q^{89} +(-1.97174 + 1.43255i) q^{91} +(-1.56705 - 4.82288i) q^{93} +(-6.56414 - 4.76913i) q^{95} +(1.54206 - 4.74597i) q^{97} +(1.31630 - 1.84382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 3 q^{5} + 7 q^{7} - 13 q^{9}+O(q^{10}) \) 8 * q - q^3 - 3 * q^5 + 7 * q^7 - 13 * q^9	\( 8 q - q^{3} - 3 q^{5} + 7 q^{7} - 13 q^{9} + 7 q^{11} + 7 q^{13} - 13 q^{15} + q^{17} - 2 q^{19} - 2 q^{21} - 4 q^{23} - 33 q^{25} - 22 q^{27} + 17 q^{29} - 13 q^{31} + 16 q^{33} + 11 q^{35} + q^{37} + 39 q^{39} + 9 q^{41} + 6 q^{43} + 44 q^{45} - q^{47} + 3 q^{49} + 38 q^{51} - 33 q^{53} + 13 q^{55} - 6 q^{57} - 30 q^{59} - 9 q^{61} - 10 q^{63} - 10 q^{65} - 10 q^{67} - 38 q^{69} - 25 q^{71} - 7 q^{73} - 6 q^{75} - 7 q^{77} - q^{79} + 14 q^{81} + 39 q^{85} - 6 q^{87} + 22 q^{89} + 7 q^{91} - 5 q^{93} + 7 q^{95} + 8 q^{97} - 27 q^{99}+O(q^{100}) \) 8 * q - q^3 - 3 * q^5 + 7 * q^7 - 13 * q^9 + 7 * q^11 + 7 * q^13 - 13 * q^15 + q^17 - 2 * q^19 - 2 * q^21 - 4 * q^23 - 33 * q^25 - 22 * q^27 + 17 * q^29 - 13 * q^31 + 16 * q^33 + 11 * q^35 + q^37 + 39 * q^39 + 9 * q^41 + 6 * q^43 + 44 * q^45 - q^47 + 3 * q^49 + 38 * q^51 - 33 * q^53 + 13 * q^55 - 6 * q^57 - 30 * q^59 - 9 * q^61 - 10 * q^63 - 10 * q^65 - 10 * q^67 - 38 * q^69 - 25 * q^71 - 7 * q^73 - 6 * q^75 - 7 * q^77 - q^79 + 14 * q^81 + 39 * q^85 - 6 * q^87 + 22 * q^89 + 7 * q^91 - 5 * q^93 + 7 * q^95 + 8 * q^97 - 27 * q^99

Introduction

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