LMFDB - Embedded newform 912.2.ci.c.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(79,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))

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

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

chi := DirichletCharacter("912.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.ci (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.101559956668416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{6} + 64 $ x^12 - 8*x^6 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			79.1
Root			$-0.483690 + 1.32893i$ of defining polynomial
Character	$\chi$	$=$	912.79
Dual form			912.2.ci.c.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{3} +(-0.749734 + 4.25195i) q^{5} +(-3.63109 + 2.09641i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{3} +(-0.749734 + 4.25195i) q^{5} +(-3.63109 + 2.09641i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-3.21257 - 1.85478i) q^{11} +(1.64866 - 4.52965i) q^{13} +(0.749734 + 4.25195i) q^{15} +(0.869318 + 0.729445i) q^{17} +(-4.06484 + 1.57386i) q^{19} +(-2.69509 + 3.21188i) q^{21} +(0.795263 - 0.140226i) q^{23} +(-12.8185 - 4.66557i) q^{25} +(0.500000 - 0.866025i) q^{27} +(2.83436 + 3.37786i) q^{29} +(-2.66547 - 4.61673i) q^{31} +(-3.65320 - 0.644157i) q^{33} +(-6.19148 - 17.0110i) q^{35} +4.90852i q^{37} -4.82036i q^{39} +(-1.34603 - 3.69820i) q^{41} +(-4.88064 - 0.860588i) q^{43} +(2.15877 + 3.73910i) q^{45} +(0.921622 + 1.09835i) q^{47} +(5.28986 - 9.16231i) q^{49} +(1.06638 + 0.388129i) q^{51} +(-9.28362 + 1.63695i) q^{53} +(10.2950 - 12.2691i) q^{55} +(-3.28141 + 2.86920i) q^{57} +(1.86774 + 1.56722i) q^{59} +(2.46479 + 13.9785i) q^{61} +(-1.43403 + 3.93996i) q^{63} +(18.0238 + 10.4061i) q^{65} +(-0.583051 + 0.489238i) q^{67} +(0.699342 - 0.403766i) q^{69} +(-2.17112 + 12.3130i) q^{71} +(-7.65469 + 2.78608i) q^{73} -13.6412 q^{75} +15.5535 q^{77} +(-5.89366 + 2.14512i) q^{79} +(0.173648 - 0.984808i) q^{81} +(5.90341 - 3.40833i) q^{83} +(-3.75332 + 3.14941i) q^{85} +(3.81872 + 2.20474i) q^{87} +(-0.639674 + 1.75749i) q^{89} +(3.50958 + 19.9038i) q^{91} +(-4.08373 - 3.42666i) q^{93} +(-3.64443 - 18.4635i) q^{95} +(-10.5194 + 12.5365i) q^{97} +(-3.65320 + 0.644157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 18 q^{7}+O(q^{10}) $ 12 * q + 6 * q^5 - 18 * q^7	$ 12 q + 6 q^{5} - 18 q^{7} + 18 q^{13} - 6 q^{15} + 6 q^{17} - 12 q^{19} - 6 q^{21} + 18 q^{23} - 30 q^{25} + 6 q^{27} - 6 q^{29} - 18 q^{31} + 6 q^{33} - 36 q^{35} + 6 q^{41} + 6 q^{43} - 6 q^{47} + 12 q^{49} - 6 q^{51} - 36 q^{53} + 42 q^{55} + 6 q^{59} - 6 q^{61} - 6 q^{63} + 72 q^{65} - 6 q^{67} - 54 q^{71} - 12 q^{73} - 12 q^{75} - 36 q^{77} + 6 q^{79} - 18 q^{83} - 36 q^{85} + 36 q^{87} + 24 q^{89} - 12 q^{91} - 18 q^{93} - 24 q^{95} + 24 q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 6 * q^5 - 18 * q^7 + 18 * q^13 - 6 * q^15 + 6 * q^17 - 12 * q^19 - 6 * q^21 + 18 * q^23 - 30 * q^25 + 6 * q^27 - 6 * q^29 - 18 * q^31 + 6 * q^33 - 36 * q^35 + 6 * q^41 + 6 * q^43 - 6 * q^47 + 12 * q^49 - 6 * q^51 - 36 * q^53 + 42 * q^55 + 6 * q^59 - 6 * q^61 - 6 * q^63 + 72 * q^65 - 6 * q^67 - 54 * q^71 - 12 * q^73 - 12 * q^75 - 36 * q^77 + 6 * q^79 - 18 * q^83 - 36 * q^85 + 36 * q^87 + 24 * q^89 - 12 * q^91 - 18 * q^93 - 24 * q^95 + 24 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$1$	$-1$

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
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$4$		0			0
$5$	−0.749734	+	4.25195i	−0.335291	+	1.90153i	0.0890473	+	0.996027i	$0.471618\pi$
$5$	−0.749734	+	4.25195i	−0.335291	+	1.90153i	−0.424339	+	0.905504i	$0.639493\pi$
$6$		0			0
$7$	−3.63109	+	2.09641i	−1.37242	+	0.792368i	−0.991233	−	0.132129i	$-0.957819\pi$
$7$	−3.63109	+	2.09641i	−1.37242	+	0.792368i	−0.381189	+	0.924497i	$0.624485\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	−3.21257	−	1.85478i	−0.968625	−	0.559236i	−0.0698085	−	0.997560i	$-0.522239\pi$
$11$	−3.21257	−	1.85478i	−0.968625	−	0.559236i	−0.898817	+	0.438324i	$0.855572\pi$
$12$		0			0
$13$	1.64866	−	4.52965i	0.457256	−	1.25630i	−0.470264	−	0.882526i	$-0.655841\pi$
$13$	1.64866	−	4.52965i	0.457256	−	1.25630i	0.927520	−	0.373774i	$-0.121936\pi$
$14$		0			0
$15$	0.749734	+	4.25195i	0.193580	+	1.09785i
$16$		0			0
$17$	0.869318	+	0.729445i	0.210841	+	0.176916i	0.742092	−	0.670298i	$-0.233834\pi$
$17$	0.869318	+	0.729445i	0.210841	+	0.176916i	−0.531252	+	0.847214i	$0.678278\pi$
$18$		0			0
$19$	−4.06484	+	1.57386i	−0.932539	+	0.361068i
$19$	−4.06484	+	1.57386i	−0.932539	+	0.361068i
$20$		0			0
$21$	−2.69509	+	3.21188i	−0.588117	+	0.700891i
$22$		0			0
$23$	0.795263	−	0.140226i	0.165824	−	0.0292392i	−0.0901198	−	0.995931i	$-0.528725\pi$
$23$	0.795263	−	0.140226i	0.165824	−	0.0292392i	0.255944	+	0.966692i	$0.417614\pi$
$24$		0			0
$25$	−12.8185	−	4.66557i	−2.56371	−	0.933113i
$26$		0			0
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$		0			0
$29$	2.83436	+	3.37786i	0.526327	+	0.627252i	0.962065	−	0.272822i	$-0.0879569\pi$
$29$	2.83436	+	3.37786i	0.526327	+	0.627252i	−0.435738	+	0.900074i	$0.643512\pi$
$30$		0			0
$31$	−2.66547	−	4.61673i	−0.478732	−	0.829188i	0.520970	−	0.853575i	$-0.325570\pi$
$31$	−2.66547	−	4.61673i	−0.478732	−	0.829188i	−0.999703	+	0.0243863i	$0.992237\pi$
$32$		0			0
$33$	−3.65320	−	0.644157i	−0.635940	−	0.112133i
$34$		0			0
$35$	−6.19148	−	17.0110i	−1.04655	−	2.87538i
$36$		0			0
$37$			4.90852i			0.806955i	0.914990	+	0.403478i	$0.132199\pi$
$37$			4.90852i			0.806955i	−0.914990	+	0.403478i	$0.867801\pi$
$38$		0			0
$39$		−	4.82036i		−	0.771875i
$40$		0			0
$41$	−1.34603	−	3.69820i	−0.210215	−	0.577562i	0.789112	−	0.614250i	$-0.210541\pi$
$41$	−1.34603	−	3.69820i	−0.210215	−	0.577562i	−0.999327	+	0.0366883i	$0.988319\pi$
$42$		0			0
$43$	−4.88064	−	0.860588i	−0.744290	−	0.131238i	−0.211373	−	0.977406i	$-0.567793\pi$
$43$	−4.88064	−	0.860588i	−0.744290	−	0.131238i	−0.532918	+	0.846167i	$0.678904\pi$
$44$		0			0
$45$	2.15877	+	3.73910i	0.321811	+	0.557393i
$46$		0			0
$47$	0.921622	+	1.09835i	0.134432	+	0.160210i	0.829061	−	0.559158i	$-0.188876\pi$
$47$	0.921622	+	1.09835i	0.134432	+	0.160210i	−0.694628	+	0.719369i	$0.744431\pi$
$48$		0			0
$49$	5.28986	−	9.16231i	0.755694	−	1.30890i
$50$		0			0
$51$	1.06638	+	0.388129i	0.149323	+	0.0543490i
$52$		0			0
$53$	−9.28362	+	1.63695i	−1.27520	+	0.224853i	−0.769942	−	0.638114i	$-0.779715\pi$
$53$	−9.28362	+	1.63695i	−1.27520	+	0.224853i	−0.505261	+	0.862967i	$0.668604\pi$
$54$		0			0
$55$	10.2950	−	12.2691i	1.38818	−	1.65436i
$56$		0			0
$57$	−3.28141	+	2.86920i	−0.434634	+	0.380035i
$58$		0			0
$59$	1.86774	+	1.56722i	0.243159	+	0.204035i	0.756220	−	0.654318i	$-0.227044\pi$
$59$	1.86774	+	1.56722i	0.243159	+	0.204035i	−0.513061	+	0.858352i	$0.671488\pi$
$60$		0			0
$61$	2.46479	+	13.9785i	0.315584	+	1.78977i	0.568924	+	0.822390i	$0.307360\pi$
$61$	2.46479	+	13.9785i	0.315584	+	1.78977i	−0.253340	+	0.967377i	$0.581529\pi$
$62$		0			0
$63$	−1.43403	+	3.93996i	−0.180671	+	0.496388i
$64$		0			0
$65$	18.0238	+	10.4061i	2.23558	+	1.29071i
$66$		0			0
$67$	−0.583051	+	0.489238i	−0.0712310	+	0.0597699i	−0.677708	−	0.735331i	$-0.737027\pi$
$67$	−0.583051	+	0.489238i	−0.0712310	+	0.0597699i	0.606477	+	0.795101i	$0.292582\pi$
$68$		0			0
$69$	0.699342	−	0.403766i	0.0841909	−	0.0486077i
$70$		0			0
$71$	−2.17112	+	12.3130i	−0.257665	+	1.46129i	0.531474	+	0.847075i	$0.321638\pi$
$71$	−2.17112	+	12.3130i	−0.257665	+	1.46129i	−0.789139	+	0.614215i	$0.789473\pi$
$72$		0			0
$73$	−7.65469	+	2.78608i	−0.895914	+	0.326086i	−0.748614	−	0.663006i	$-0.769280\pi$
$73$	−7.65469	+	2.78608i	−0.895914	+	0.326086i	−0.147300	+	0.989092i	$0.547058\pi$
$74$		0			0
$75$	−13.6412			−1.57515
$76$		0			0
$77$	15.5535			1.77248
$78$		0			0
$79$	−5.89366	+	2.14512i	−0.663088	+	0.241344i	−0.651569	−	0.758589i	$-0.725889\pi$
$79$	−5.89366	+	2.14512i	−0.663088	+	0.241344i	−0.0115191	+	0.999934i	$0.503667\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	5.90341	−	3.40833i	0.647983	−	0.374113i	−0.139700	−	0.990194i	$-0.544614\pi$
$83$	5.90341	−	3.40833i	0.647983	−	0.374113i	0.787683	+	0.616081i	$0.211280\pi$
$84$		0			0
$85$	−3.75332	+	3.14941i	−0.407105	+	0.341602i
$86$		0			0
$87$	3.81872	+	2.20474i	0.409410	+	0.236373i
$88$		0			0
$89$	−0.639674	+	1.75749i	−0.0678053	+	0.186294i	−0.968967	−	0.247189i	$-0.920493\pi$
$89$	−0.639674	+	1.75749i	−0.0678053	+	0.186294i	0.901162	+	0.433482i	$0.142715\pi$
$90$		0			0
$91$	3.50958	+	19.9038i	0.367904	+	2.08649i
$92$		0			0
$93$	−4.08373	−	3.42666i	−0.423463	−	0.355328i
$94$		0			0
$95$	−3.64443	−	18.4635i	−0.373911	−	1.89432i
$96$		0			0
$97$	−10.5194	+	12.5365i	−1.06808	+	1.27289i	−0.107709	+	0.994183i	$0.534351\pi$
$97$	−10.5194	+	12.5365i	−1.06808	+	1.27289i	−0.960375	+	0.278710i	$0.910093\pi$
$98$		0			0
$99$	−3.65320	+	0.644157i	−0.367160	+	0.0647402i
$100$		0			0
$101$	9.92309	+	3.61171i	0.987384	+	0.359378i	0.784707	−	0.619867i	$-0.212813\pi$
$101$	9.92309	+	3.61171i	0.987384	+	0.359378i	0.202677	+	0.979246i	$0.435036\pi$
$102$		0			0
$103$	−0.974576	+	1.68801i	−0.0960278	+	0.166325i	−0.910037	−	0.414527i	$-0.863947\pi$
$103$	−0.974576	+	1.68801i	−0.0960278	+	0.166325i	0.814009	+	0.580852i	$0.197280\pi$
$104$		0			0
$105$	−11.6362	−	13.8675i	−1.13557	−	1.35333i
$106$		0			0
$107$	9.77610	+	16.9327i	0.945092	+	1.63695i	0.755568	+	0.655070i	$0.227361\pi$
$107$	9.77610	+	16.9327i	0.945092	+	1.63695i	0.189524	+	0.981876i	$0.439306\pi$
$108$		0			0
$109$	5.87746	+	1.03635i	0.562958	+	0.0992647i	0.447883	−	0.894092i	$-0.352178\pi$
$109$	5.87746	+	1.03635i	0.562958	+	0.0992647i	0.115075	+	0.993357i	$0.463289\pi$
$110$		0			0
$111$	1.67881	+	4.61250i	0.159346	+	0.437799i
$112$		0			0
$113$		−	17.1022i		−	1.60884i	−0.594060	−	0.804420i	$-0.702476\pi$
$113$		−	17.1022i		−	1.60884i	0.594060	−	0.804420i	$-0.297524\pi$
$114$		0			0
$115$			3.48655i			0.325123i
$116$		0			0
$117$	−1.64866	−	4.52965i	−0.152419	−	0.418767i
$118$		0			0
$119$	−4.68578	−	0.826230i	−0.429545	−	0.0757404i
$120$		0			0
$121$	1.38039	+	2.39091i	0.125490	+	0.217355i
$122$		0			0
$123$	−2.52972	−	3.01480i	−0.228097	−	0.271835i
$124$		0			0
$125$	18.6544	−	32.3104i	1.66850	−	2.88993i
$126$		0			0
$127$	−3.38192	−	1.23092i	−0.300097	−	0.109226i	0.187583	−	0.982249i	$-0.439935\pi$
$127$	−3.38192	−	1.23092i	−0.300097	−	0.109226i	−0.487680	+	0.873022i	$0.662157\pi$
$128$		0			0
$129$	−4.88064	+	0.860588i	−0.429716	+	0.0757706i
$130$		0			0
$131$	9.97885	−	11.8923i	0.871856	−	1.03904i	−0.127032	−	0.991899i	$-0.540545\pi$
$131$	9.97885	−	11.8923i	0.871856	−	1.03904i	0.998888	−	0.0471389i	$-0.0150103\pi$
$132$		0			0
$133$	11.4603	−	14.2364i	0.993738	−	1.23445i
$134$		0			0
$135$	3.30743	+	2.77526i	0.284658	+	0.238857i
$136$		0			0
$137$	2.69794	+	15.3008i	0.230501	+	1.30723i	0.851885	+	0.523728i	$0.175459\pi$
$137$	2.69794	+	15.3008i	0.230501	+	1.30723i	−0.621385	+	0.783506i	$0.713430\pi$
$138$		0			0
$139$	−0.849484	+	2.33394i	−0.0720523	+	0.197962i	−0.970491	−	0.241137i	$-0.922480\pi$
$139$	−0.849484	+	2.33394i	−0.0720523	+	0.197962i	0.898439	+	0.439098i	$0.144702\pi$
$140$		0			0
$141$	1.24170	+	0.716894i	0.104570	+	0.0603734i
$142$		0			0
$143$	−13.6979	+	11.4939i	−1.14548	+	0.961170i
$144$		0			0
$145$	−16.4875	+	9.51906i	−1.36921	+	0.790515i
$146$		0			0
$147$	1.83715	−	10.4190i	0.151525	−	0.859344i
$148$		0			0
$149$	−12.0534	+	4.38709i	−0.987456	+	0.359405i	−0.784735	−	0.619832i	$-0.787201\pi$
$149$	−12.0534	+	4.38709i	−0.987456	+	0.359405i	−0.202721	+	0.979236i	$0.564979\pi$
$150$		0			0
$151$	−10.7482			−0.874675			−0.437338	−	0.899297i	$-0.644079\pi$
$151$	−10.7482			−0.874675			−0.437338	+	0.899297i	$0.644079\pi$
$152$		0			0
$153$	1.13481			0.0917443
$154$		0			0
$155$	21.6285	−	7.87213i	1.73724	−	0.632304i
$156$		0			0
$157$	−0.594723	+	3.37284i	−0.0474640	+	0.269182i	−0.999299	−	0.0374279i	$-0.988084\pi$
$157$	−0.594723	+	3.37284i	−0.0474640	+	0.269182i	0.951835	+	0.306610i	$0.0991947\pi$
$158$		0			0
$159$	−8.16387	+	4.71342i	−0.647437	+	0.373798i
$160$		0			0
$161$	−2.59370	+	2.17637i	−0.204412	+	0.171522i
$162$		0			0
$163$	9.02620	+	5.21128i	0.706986	+	0.408179i	0.809944	−	0.586507i	$-0.199497\pi$
$163$	9.02620	+	5.21128i	0.706986	+	0.408179i	−0.102958	+	0.994686i	$0.532831\pi$
$164$		0			0
$165$	5.47785	−	15.0503i	0.426450	−	1.17166i
$166$		0			0
$167$	−0.0524382	−	0.297392i	−0.00405779	−	0.0230129i	0.982712	−	0.185143i	$-0.0592748\pi$
$167$	−0.0524382	−	0.297392i	−0.00405779	−	0.0230129i	−0.986769	+	0.162130i	$0.948164\pi$
$168$		0			0
$169$	−7.84111	−	6.57947i	−0.603162	−	0.506113i
$170$		0			0
$171$	−2.10219	+	3.81848i	−0.160759	+	0.292006i
$172$		0			0
$173$	0.388698	−	0.463232i	0.0295522	−	0.0352189i	−0.751066	−	0.660227i	$-0.770460\pi$
$173$	0.388698	−	0.463232i	0.0295522	−	0.0352189i	0.780618	+	0.625008i	$0.214904\pi$
$174$		0			0
$175$	56.3261	−	9.93182i	4.25786	−	0.750775i
$176$		0			0
$177$	2.29112	+	0.833900i	0.172211	+	0.0626798i
$178$		0			0
$179$	−1.91154	+	3.31088i	−0.142875	+	0.247467i	−0.928578	−	0.371137i	$-0.878968\pi$
$179$	−1.91154	+	3.31088i	−0.142875	+	0.247467i	0.785703	+	0.618604i	$0.212301\pi$
$180$		0			0
$181$	−13.1606	−	15.6842i	−0.978220	−	1.16580i	−0.986155	−	0.165828i	$-0.946970\pi$
$181$	−13.1606	−	15.6842i	−0.978220	−	1.16580i	0.00793506	−	0.999969i	$-0.497474\pi$
$182$		0			0
$183$	7.09708	+	12.2925i	0.524632	+	0.908689i
$184$		0			0
$185$	−20.8708	−	3.68008i	−1.53445	−	0.270565i
$186$		0			0
$187$	−1.43979	−	3.95578i	−0.105288	−	0.289275i
$188$		0			0
$189$			4.19282i			0.304983i
$190$		0			0
$191$		−	13.9484i		−	1.00927i	−0.863333	−	0.504634i	$-0.831627\pi$
$191$		−	13.9484i		−	1.00927i	0.863333	−	0.504634i	$-0.168373\pi$
$192$		0			0
$193$	−0.622427	−	1.71010i	−0.0448033	−	0.123096i	0.915273	−	0.402834i	$-0.131975\pi$
$193$	−0.622427	−	1.71010i	−0.0448033	−	0.123096i	−0.960076	+	0.279738i	$0.909752\pi$
$194$		0			0
$195$	20.4959	+	3.61399i	1.46774	+	0.258803i
$196$		0			0
$197$	1.23602	+	2.14086i	0.0880631	+	0.152530i	0.906692	−	0.421793i	$-0.138599\pi$
$197$	1.23602	+	2.14086i	0.0880631	+	0.152530i	−0.818629	+	0.574322i	$0.805266\pi$
$198$		0			0
$199$	−6.57641	−	7.83746i	−0.466189	−	0.555583i	0.480807	−	0.876826i	$-0.340344\pi$
$199$	−6.57641	−	7.83746i	−0.466189	−	0.555583i	−0.946997	+	0.321243i	$0.895899\pi$
$200$		0			0
$201$	−0.380559	+	0.659148i	−0.0268426	+	0.0464927i
$202$		0			0
$203$	−17.3732	−	6.32332i	−1.21936	−	0.443810i
$204$		0			0
$205$	16.7337	−	2.95061i	1.16873	−	0.206079i
$206$		0			0
$207$	0.519071	−	0.618605i	0.0360779	−	0.0429960i
$208$		0			0
$209$	15.9777	+	2.48324i	1.10520	+	0.171770i
$210$		0			0
$211$	17.4578	+	14.6489i	1.20185	+	1.00847i	0.999575	+	0.0291403i	$0.00927697\pi$
$211$	17.4578	+	14.6489i	1.20185	+	1.00847i	0.202272	+	0.979329i	$0.435167\pi$
$212$		0			0
$213$	2.17112	+	12.3130i	0.148763	+	0.843676i
$214$		0			0
$215$	7.31836	−	20.1070i	0.499108	−	1.37129i
$216$		0			0
$217$	19.3571	+	11.1758i	1.31404	+	0.758664i
$218$		0			0
$219$	−6.24016	+	5.23612i	−0.421671	+	0.353824i
$220$		0			0
$221$	4.73734	−	2.73510i	0.318668	−	0.183983i
$222$		0			0
$223$	−4.76854	+	27.0437i	−0.319325	+	1.81098i	0.227549	+	0.973767i	$0.426929\pi$
$223$	−4.76854	+	27.0437i	−0.319325	+	1.81098i	−0.546874	+	0.837215i	$0.684182\pi$
$224$		0			0
$225$	−12.8185	+	4.66557i	−0.854569	+	0.311038i
$226$		0			0
$227$	7.24527			0.480886			0.240443	−	0.970663i	$-0.422707\pi$
$227$	7.24527			0.480886			0.240443	+	0.970663i	$0.422707\pi$
$228$		0			0
$229$	−9.25578			−0.611639			−0.305820	−	0.952089i	$-0.598930\pi$
$229$	−9.25578			−0.611639			−0.305820	+	0.952089i	$0.598930\pi$
$230$		0			0
$231$	14.6155	−	5.31960i	0.961629	−	0.350004i
$232$		0			0
$233$	4.23949	−	24.0434i	0.277738	−	1.57513i	−0.452389	−	0.891821i	$-0.649428\pi$
$233$	4.23949	−	24.0434i	0.277738	−	1.57513i	0.730127	−	0.683311i	$-0.239461\pi$
$234$		0			0
$235$	−5.36109	+	3.09522i	−0.349719	+	0.201910i
$236$		0			0
$237$	−4.80455	+	4.03150i	−0.312089	+	0.261874i
$238$		0			0
$239$	−4.98726	−	2.87939i	−0.322599	−	0.186253i	0.329951	−	0.943998i	$-0.392968\pi$
$239$	−4.98726	−	2.87939i	−0.322599	−	0.186253i	−0.652550	+	0.757745i	$0.726301\pi$
$240$		0			0
$241$	6.56430	−	18.0353i	0.422844	−	1.16175i	−0.527229	−	0.849724i	$-0.676769\pi$
$241$	6.56430	−	18.0353i	0.422844	−	1.16175i	0.950072	−	0.312030i	$-0.101009\pi$
$242$		0			0
$243$	−0.173648	−	0.984808i	−0.0111395	−	0.0631754i
$244$		0			0
$245$	34.9917	+	29.3615i	2.23554	+	1.87584i
$246$		0			0
$247$	0.427501	+	21.0071i	0.0272013	+	1.33665i
$248$		0			0
$249$	4.38167	−	5.22187i	0.277677	−	0.330923i
$250$		0			0
$251$	−19.7092	+	3.47526i	−1.24403	+	0.219357i	−0.756643	−	0.653828i	$-0.773162\pi$
$251$	−19.7092	+	3.47526i	−1.24403	+	0.219357i	−0.487390	+	0.873185i	$0.662051\pi$
$252$		0			0
$253$	−2.81492	−	1.02455i	−0.176973	−	0.0644128i
$254$		0			0
$255$	−2.44981	+	4.24319i	−0.153413	+	0.265719i
$256$		0			0
$257$	12.9352	+	15.4156i	0.806878	+	0.961599i	0.999808	−	0.0196131i	$-0.00624346\pi$
$257$	12.9352	+	15.4156i	0.806878	+	0.961599i	−0.192930	+	0.981213i	$0.561799\pi$
$258$		0			0
$259$	−10.2903	−	17.8232i	−0.639405	−	1.10748i
$260$		0			0
$261$	4.34249	+	0.765698i	0.268793	+	0.0473955i
$262$		0			0
$263$	5.52715	+	15.1857i	0.340819	+	0.936391i	0.985158	+	0.171651i	$0.0549103\pi$
$263$	5.52715	+	15.1857i	0.340819	+	0.936391i	−0.644339	+	0.764740i	$0.722868\pi$
$264$		0			0
$265$		−	40.7008i		−	2.50023i
$266$		0			0
$267$			1.87028i			0.114459i
$268$		0			0
$269$	1.10689	+	3.04116i	0.0674885	+	0.185423i	0.968852	−	0.247640i	$-0.0796550\pi$
$269$	1.10689	+	3.04116i	0.0674885	+	0.185423i	−0.901364	+	0.433063i	$0.857433\pi$
$270$		0			0
$271$	−11.0706	−	1.95205i	−0.672492	−	0.118579i	−0.173033	−	0.984916i	$-0.555357\pi$
$271$	−11.0706	−	1.95205i	−0.672492	−	0.118579i	−0.499459	+	0.866337i	$0.666468\pi$
$272$		0			0
$273$	10.1054	+	17.5031i	0.611609	+	1.05934i
$274$		0			0
$275$	32.5268	+	38.7640i	1.96144	+	2.33755i
$276$		0			0
$277$	4.06328	−	7.03781i	0.244139	−	0.422861i	−0.717750	−	0.696301i	$-0.754828\pi$
$277$	4.06328	−	7.03781i	0.244139	−	0.422861i	0.961889	+	0.273440i	$0.0881614\pi$
$278$		0			0
$279$	−5.00944	−	1.82329i	−0.299907	−	0.109157i
$280$		0			0
$281$	−18.1113	+	3.19351i	−1.08043	+	0.190509i	−0.685406	−	0.728161i	$-0.740375\pi$
$281$	−18.1113	+	3.19351i	−1.08043	+	0.190509i	−0.395025	+	0.918670i	$0.629264\pi$
$282$		0			0
$283$	4.44596	−	5.29849i	0.264285	−	0.314962i	−0.617540	−	0.786539i	$-0.711871\pi$
$283$	4.44596	−	5.29849i	0.264285	−	0.314962i	0.881825	+	0.471577i	$0.156315\pi$
$284$		0			0
$285$	−9.73953	−	16.1035i	−0.576920	−	0.953892i
$286$		0			0
$287$	12.6405	+	10.6066i	0.746145	+	0.626090i
$288$		0			0
$289$	−2.72839	−	15.4735i	−0.160494	−	0.910205i
$290$		0			0
$291$	−5.59726	+	15.3783i	−0.328117	+	0.901494i
$292$		0			0
$293$	25.5509	+	14.7518i	1.49270	+	0.861812i	0.999965	−	0.00836600i	$-0.00266301\pi$
$293$	25.5509	+	14.7518i	1.49270	+	0.861812i	0.492737	+	0.870178i	$0.335996\pi$
$294$		0			0
$295$	−8.06405	+	6.76654i	−0.469507	+	0.393963i
$296$		0			0
$297$	−3.21257	+	1.85478i	−0.186412	+	0.107625i
$298$		0			0
$299$	0.675941	−	3.83345i	0.0390907	−	0.221694i
$300$		0			0
$301$	19.5262	−	7.10694i	1.12547	−	0.409637i
$302$		0			0
$303$	10.5599			0.606652
$304$		0			0
$305$	−61.2840			−3.50911
$306$		0			0
$307$	−25.6585	+	9.33891i	−1.46441	+	0.533000i	−0.946575	−	0.322483i	$-0.895482\pi$
$307$	−25.6585	+	9.33891i	−1.46441	+	0.533000i	−0.517830	+	0.855483i	$0.673260\pi$
$308$		0			0
$309$	−0.338467	+	1.91954i	−0.0192547	+	0.109199i
$310$		0			0
$311$	−14.0874	+	8.13337i	−0.798824	+	0.461201i	−0.843060	−	0.537820i	$-0.819248\pi$
$311$	−14.0874	+	8.13337i	−0.798824	+	0.461201i	0.0442357	+	0.999021i	$0.485915\pi$
$312$		0			0
$313$	10.1759	−	8.53858i	0.575175	−	0.482629i	−0.308184	−	0.951327i	$-0.599721\pi$
$313$	10.1759	−	8.53858i	0.575175	−	0.482629i	0.883359	+	0.468698i	$0.155277\pi$
$314$		0			0
$315$	−15.6774	−	9.05134i	−0.883320	−	0.509985i
$316$		0			0
$317$	−0.768295	+	2.11087i	−0.0431517	+	0.118558i	−0.959397	−	0.282060i	$-0.908982\pi$
$317$	−0.768295	+	2.11087i	−0.0431517	+	0.118558i	0.916245	+	0.400618i	$0.131205\pi$
$318$		0			0
$319$	−2.84040	−	16.1087i	−0.159032	−	0.901913i
$320$		0			0
$321$	14.9779	+	12.5679i	0.835983	+	0.701473i
$322$		0			0
$323$	−4.68169	−	1.59689i	−0.260496	−	0.0888535i
$324$		0			0
$325$	−42.2668	+	50.3716i	−2.34454	+	2.79411i
$326$		0			0
$327$	5.87746	−	1.03635i	0.325024	−	0.0573105i
$328$		0			0
$329$	−5.64907	−	2.05609i	−0.311443	−	0.113356i
$330$		0			0
$331$	12.0934	−	20.9464i	0.664714	−	1.15132i	−0.314649	−	0.949208i	$-0.601887\pi$
$331$	12.0934	−	20.9464i	0.664714	−	1.15132i	0.979363	−	0.202110i	$-0.0647800\pi$
$332$		0			0
$333$	3.15513	+	3.76014i	0.172900	+	0.206054i
$334$		0			0
$335$	−1.64308	−	2.84590i	−0.0897712	−	0.155488i
$336$		0			0
$337$	−0.976535	−	0.172190i	−0.0531953	−	0.00937976i	0.146987	−	0.989138i	$-0.453042\pi$
$337$	−0.976535	−	0.172190i	−0.0531953	−	0.00937976i	−0.200182	+	0.979759i	$0.564153\pi$
$338$		0			0
$339$	−5.84930	−	16.0708i	−0.317690	−	0.872847i
$340$		0			0
$341$			19.7754i			1.07090i
$342$		0			0
$343$			15.0091i			0.810416i
$344$		0			0
$345$	1.19247	+	3.27629i	0.0642005	+	0.176389i
$346$		0			0
$347$	35.7703	+	6.30727i	1.92025	+	0.338592i	0.998759	−	0.0498044i	$-0.0158598\pi$
$347$	35.7703	+	6.30727i	1.92025	+	0.338592i	0.921492	+	0.388397i	$0.126971\pi$
$348$		0			0
$349$	−0.455395	−	0.788767i	−0.0243767	−	0.0422217i	0.853580	−	0.520962i	$-0.174427\pi$
$349$	−0.455395	−	0.788767i	−0.0243767	−	0.0422217i	−0.877956	+	0.478741i	$0.841093\pi$
$350$		0			0
$351$	−3.09847	−	3.69261i	−0.165384	−	0.197097i
$352$		0			0
$353$	8.92006	−	15.4500i	0.474767	−	0.822320i	−0.524816	−	0.851216i	$-0.675866\pi$
$353$	8.92006	−	15.4500i	0.474767	−	0.822320i	0.999582	+	0.0288957i	$0.00919908\pi$
$354$		0			0
$355$	−50.7267	−	18.4630i	−2.69229	−	0.979915i
$356$		0			0
$357$	−4.68578	+	0.826230i	−0.247998	+	0.0437287i
$358$		0			0
$359$	1.66439	−	1.98354i	0.0878429	−	0.104687i	−0.720333	−	0.693629i	$-0.756011\pi$
$359$	1.66439	−	1.98354i	0.0878429	−	0.104687i	0.808175	+	0.588942i	$0.200455\pi$
$360$		0			0
$361$	14.0459	−	12.7950i	0.739259	−	0.673421i
$362$		0			0
$363$	2.11488	+	1.77460i	0.111002	+	0.0931422i
$364$		0			0
$365$	−6.10730	−	34.6362i	−0.319671	−	1.81294i
$366$		0			0
$367$	9.23390	−	25.3699i	0.482006	−	1.32430i	−0.425765	−	0.904834i	$-0.639995\pi$
$367$	9.23390	−	25.3699i	0.482006	−	1.32430i	0.907771	−	0.419466i	$-0.137783\pi$
$368$		0			0
$369$	−3.40828	−	1.96777i	−0.177428	−	0.102438i
$370$		0			0
$371$	30.2779	−	25.4062i	1.57195	−	1.31902i
$372$		0			0
$373$	19.3287	−	11.1594i	1.00080	−	0.577814i	0.0923177	−	0.995730i	$-0.470572\pi$
$373$	19.3287	−	11.1594i	1.00080	−	0.577814i	0.908486	+	0.417915i	$0.137239\pi$
$374$		0			0
$375$	6.47860	−	36.7420i	0.334554	−	1.89735i
$376$		0			0
$377$	19.9734	−	7.26973i	1.02868	−	0.374410i
$378$		0			0
$379$	31.5077			1.61844			0.809221	−	0.587504i	$-0.199889\pi$
$379$	31.5077			1.61844			0.809221	+	0.587504i	$0.199889\pi$
$380$		0			0
$381$	−3.59896			−0.184380
$382$		0			0
$383$	−16.0369	+	5.83697i	−0.819450	+	0.298255i	−0.717521	−	0.696536i	$-0.754723\pi$
$383$	−16.0369	+	5.83697i	−0.819450	+	0.298255i	−0.101928	+	0.994792i	$0.532501\pi$
$384$		0			0
$385$	−11.6610	+	66.1327i	−0.594298	+	3.37043i
$386$		0			0
$387$	−4.29196	+	2.47797i	−0.218173	+	0.125962i
$388$		0			0
$389$	−21.0142	+	17.6330i	−1.06546	+	0.894031i	−0.994634	−	0.103458i	$-0.967009\pi$
$389$	−21.0142	+	17.6330i	−1.06546	+	0.894031i	−0.0708306	+	0.997488i	$0.522565\pi$
$390$		0			0
$391$	0.793624	+	0.458199i	0.0401353	+	0.0231721i
$392$		0			0
$393$	5.30963	−	14.5881i	0.267836	−	0.735872i
$394$		0			0
$395$	−4.70226	−	26.6678i	−0.236596	−	1.34180i
$396$		0			0
$397$	−18.4198	−	15.4560i	−0.924462	−	0.775715i	0.0503531	−	0.998731i	$-0.483965\pi$
$397$	−18.4198	−	15.4560i	−0.924462	−	0.775715i	−0.974815	+	0.223016i	$0.928410\pi$
$398$		0			0
$399$	5.90007	−	17.2975i	0.295373	−	0.865959i
$400$		0			0
$401$	1.06015	−	1.26344i	0.0529414	−	0.0630931i	−0.738924	−	0.673789i	$-0.764666\pi$
$401$	1.06015	−	1.26344i	0.0529414	−	0.0630931i	0.791865	+	0.610696i	$0.209110\pi$
$402$		0			0
$403$	−25.3066	+	4.46224i	−1.26061	+	0.222280i
$404$		0			0
$405$	4.05717	+	1.47669i	0.201602	+	0.0733772i
$406$		0			0
$407$	9.10420	−	15.7689i	0.451278	−	0.781637i
$408$		0			0
$409$	8.33660	+	9.93517i	0.412218	+	0.491263i	0.931705	−	0.363216i	$-0.118321\pi$
$409$	8.33660	+	9.93517i	0.412218	+	0.491263i	−0.519487	+	0.854479i	$0.673877\pi$
$410$		0			0
$411$	7.76841	+	13.4553i	0.383187	+	0.663700i
$412$		0			0
$413$	−10.0675	−	1.77516i	−0.495387	−	0.0873501i
$414$		0			0
$415$	10.0661	+	27.6563i	0.494125	+	1.35760i
$416$		0			0
$417$			2.48372i			0.121628i
$418$		0			0
$419$			13.6567i			0.667172i	0.942720	+	0.333586i	$0.108259\pi$
$419$			13.6567i			0.667172i	−0.942720	+	0.333586i	$0.891741\pi$
$420$		0			0
$421$	7.81747	+	21.4783i	0.381000	+	1.04679i	0.970936	+	0.239339i	$0.0769309\pi$
$421$	7.81747	+	21.4783i	0.381000	+	1.04679i	−0.589936	+	0.807450i	$0.700847\pi$
$422$		0			0
$423$	1.41201	+	0.248975i	0.0686541	+	0.0121056i
$424$		0			0
$425$	−7.74012	−	13.4063i	−0.375451	−	0.650300i
$426$		0			0
$427$	−38.2546	−	45.5900i	−1.85127	−	2.20626i
$428$		0			0
$429$	−8.94068	+	15.4857i	−0.431660	+	0.747658i
$430$		0			0
$431$	−16.8311	−	6.12602i	−0.810725	−	0.295080i	−0.0968019	−	0.995304i	$-0.530861\pi$
$431$	−16.8311	−	6.12602i	−0.810725	−	0.295080i	−0.713923	+	0.700224i	$0.753084\pi$
$432$		0			0
$433$	−11.9115	+	2.10031i	−0.572429	+	0.100935i	−0.452367	−	0.891832i	$-0.649420\pi$
$433$	−11.9115	+	2.10031i	−0.572429	+	0.100935i	−0.120062	+	0.992766i	$0.538309\pi$
$434$		0			0
$435$	−12.2375	+	14.5840i	−0.586742	+	0.699252i
$436$		0			0
$437$	−3.01192	+	1.82163i	−0.144080	+	0.0871404i
$438$		0			0
$439$	−8.66073	−	7.26722i	−0.413354	−	0.346845i	0.412274	−	0.911060i	$-0.364735\pi$
$439$	−8.66073	−	7.26722i	−0.413354	−	0.346845i	−0.825628	+	0.564215i	$0.809179\pi$
$440$		0			0
$441$	−1.83715	−	10.4190i	−0.0874833	−	0.496142i
$442$		0			0
$443$	−8.60550	+	23.6434i	−0.408860	+	1.12333i	0.548931	+	0.835868i	$0.315035\pi$
$443$	−8.60550	+	23.6434i	−0.408860	+	1.12333i	−0.957791	+	0.287466i	$0.907187\pi$
$444$		0			0
$445$	−6.99318	−	4.03751i	−0.331508	−	0.191397i
$446$		0			0
$447$	−9.82605	+	8.24504i	−0.464756	+	0.389977i
$448$		0			0
$449$	−4.57682	+	2.64243i	−0.215993	+	0.124704i	−0.604094	−	0.796913i	$-0.706465\pi$
$449$	−4.57682	+	2.64243i	−0.215993	+	0.124704i	0.388100	+	0.921617i	$0.373131\pi$
$450$		0			0
$451$	−2.53511	+	14.3773i	−0.119374	+	0.677001i
$452$		0			0
$453$	−10.1000	+	3.67610i	−0.474539	+	0.172718i
$454$		0			0
$455$	−87.2614			−4.09088
$456$		0			0
$457$	3.71344			0.173708			0.0868538	−	0.996221i	$-0.472319\pi$
$457$	3.71344			0.173708			0.0868538	+	0.996221i	$0.472319\pi$
$458$		0			0
$459$	1.06638	−	0.388129i	0.0497742	−	0.0181163i
$460$		0			0
$461$	−3.92265	+	22.2464i	−0.182696	+	1.03612i	0.746184	+	0.665740i	$0.231884\pi$
$461$	−3.92265	+	22.2464i	−0.182696	+	1.03612i	−0.928880	+	0.370380i	$0.879227\pi$
$462$		0			0
$463$	28.4251	−	16.4112i	1.32103	−	0.762695i	0.337134	−	0.941457i	$-0.390542\pi$
$463$	28.4251	−	16.4112i	1.32103	−	0.762695i	0.983892	+	0.178761i	$0.0572090\pi$
$464$		0			0
$465$	17.6317	−	14.7948i	0.817651	−	0.686091i
$466$		0			0
$467$	−7.70417	−	4.44800i	−0.356506	−	0.205829i	0.311041	−	0.950397i	$-0.399322\pi$
$467$	−7.70417	−	4.44800i	−0.356506	−	0.205829i	−0.667547	+	0.744568i	$0.732656\pi$
$468$		0			0
$469$	1.09147	−	2.99878i	0.0503992	−	0.138471i
$470$		0			0
$471$	0.594723	+	3.37284i	0.0274034	+	0.155412i
$472$		0			0
$473$	14.0832	+	11.8172i	0.647545	+	0.543355i
$474$		0			0
$475$	59.4483	−	1.20979i	2.72768	−	0.0555091i
$476$		0			0
$477$	−6.05945	+	7.22137i	−0.277443	+	0.330644i
$478$		0			0
$479$	−31.7678	+	5.60151i	−1.45151	+	0.255940i	−0.843130	−	0.537709i	$-0.819290\pi$
$479$	−31.7678	+	5.60151i	−1.45151	+	0.255940i	−0.608376	+	0.793649i	$0.708179\pi$
$480$		0			0
$481$	22.2339	+	8.09247i	1.01378	+	0.368985i
$482$		0			0
$483$	−1.69292	+	2.93222i	−0.0770303	+	0.133420i
$484$		0			0
$485$	−45.4180	−	54.1271i	−2.06233	−	2.45778i
$486$		0			0
$487$	−1.19935	−	2.07734i	−0.0543478	−	0.0941331i	0.837572	−	0.546328i	$-0.183975\pi$
$487$	−1.19935	−	2.07734i	−0.0543478	−	0.0941331i	−0.891919	+	0.452194i	$0.850641\pi$
$488$		0			0
$489$	10.2642	+	1.80986i	0.464164	+	0.0818446i
$490$		0			0
$491$	9.38486	+	25.7847i	0.423533	+	1.16365i	0.949671	+	0.313248i	$0.101417\pi$
$491$	9.38486	+	25.7847i	0.423533	+	1.16365i	−0.526139	+	0.850399i	$0.676361\pi$
$492$		0			0
$493$			5.00394i			0.225366i
$494$		0			0
$495$		−	16.0162i		−	0.719873i
$496$		0			0
$497$	−17.9296	−	49.2613i	−0.804254	−	2.20967i
$498$		0			0
$499$	−13.3230	−	2.34920i	−0.596417	−	0.105164i	−0.132713	−	0.991154i	$-0.542369\pi$
$499$	−13.3230	−	2.34920i	−0.596417	−	0.105164i	−0.463704	+	0.885990i	$0.653480\pi$
$500$		0			0
$501$	−0.150990	−	0.261522i	−0.00674573	−	0.0116839i
$502$		0			0
$503$	20.2361	+	24.1164i	0.902282	+	1.07530i	0.996813	+	0.0797754i	$0.0254203\pi$
$503$	20.2361	+	24.1164i	0.902282	+	1.07530i	−0.0945313	+	0.995522i	$0.530135\pi$
$504$		0			0
$505$	−22.7965	+	39.4847i	−1.01443	+	1.75705i
$506$		0			0
$507$	−9.61854	−	3.50086i	−0.427174	−	0.155479i
$508$		0			0
$509$	−32.3045	+	5.69616i	−1.43187	+	0.252478i	−0.835173	−	0.549987i	$-0.814633\pi$
$509$	−32.3045	+	5.69616i	−1.43187	+	0.252478i	−0.596700	+	0.802465i	$0.703522\pi$
$510$		0			0
$511$	21.9541	−	26.1639i	0.971192	−	1.15742i
$512$		0			0
$513$	−0.669419	+	4.30719i	−0.0295556	+	0.190167i
$514$		0			0
$515$	−6.44669	−	5.40941i	−0.284075	−	0.238367i
$516$		0			0
$517$	−0.923585	−	5.23791i	−0.0406192	−	0.230363i
$518$		0			0
$519$	0.206822	−	0.568239i	0.00907848	−	0.0249429i
$520$		0			0
$521$	−15.4724	−	8.93299i	−0.677858	−	0.391362i	0.121189	−	0.992629i	$-0.461329\pi$
$521$	−15.4724	−	8.93299i	−0.677858	−	0.391362i	−0.799048	+	0.601268i	$0.794662\pi$
$522$		0			0
$523$	14.2504	−	11.9575i	0.623125	−	0.522864i	−0.275659	−	0.961255i	$-0.588896\pi$
$523$	14.2504	−	11.9575i	0.623125	−	0.522864i	0.898784	+	0.438391i	$0.144452\pi$
$524$		0			0
$525$	49.5324	−	28.5975i	2.16177	−	1.24810i
$526$		0			0
$527$	1.05051	−	5.95772i	0.0457608	−	0.259522i
$528$		0			0
$529$	−21.0002	+	7.64343i	−0.913050	+	0.332323i
$530$		0			0
$531$	2.43816			0.105807
$532$		0			0
$533$	−18.9707			−0.821713
$534$		0			0
$535$	−79.3265	+	28.8725i	−3.42959	+	1.24827i
$536$		0			0
$537$	−0.663870	+	3.76499i	−0.0286481	+	0.162471i
$538$		0			0
$539$	−33.9881	+	19.6230i	−1.46397	+	0.845223i
$540$		0			0
$541$	−6.79790	+	5.70411i	−0.292264	+	0.245239i	−0.777116	−	0.629358i	$-0.783318\pi$
$541$	−6.79790	+	5.70411i	−0.292264	+	0.245239i	0.484851	+	0.874597i	$0.338874\pi$
$542$		0			0
$543$	−17.7312	−	10.2371i	−0.760920	−	0.439317i
$544$		0			0
$545$	−8.81306	+	24.2137i	−0.377510	+	1.03720i
$546$		0			0
$547$	0.965009	+	5.47284i	0.0412608	+	0.234002i	0.998463	−	0.0554175i	$-0.0176490\pi$
$547$	0.965009	+	5.47284i	0.0412608	+	0.234002i	−0.957202	+	0.289419i	$0.906538\pi$
$548$		0			0
$549$	10.8734	+	9.12384i	0.464064	+	0.389396i
$550$		0			0
$551$	−16.8375	−	9.26958i	−0.717302	−	0.394897i
$552$		0			0
$553$	16.9033	−	20.1446i	0.718803	−	0.856636i
$554$		0			0
$555$	−20.8708	+	3.68008i	−0.885915	+	0.156211i
$556$		0			0
$557$	23.7636	+	8.64923i	1.00689	+	0.366480i	0.792240	−	0.610210i	$-0.208915\pi$
$557$	23.7636	+	8.64923i	1.00689	+	0.366480i	0.214655	+	0.976690i	$0.431137\pi$
$558$		0			0
$559$	−11.9447	+	20.6888i	−0.505206	+	0.875042i
$560$		0			0
$561$	−2.70591	−	3.22478i	−0.114244	−	0.136150i
$562$		0			0
$563$	−1.73177	−	2.99951i	−0.0729853	−	0.126414i	0.827223	−	0.561874i	$-0.189919\pi$
$563$	−1.73177	−	2.99951i	−0.0729853	−	0.126414i	−0.900208	+	0.435459i	$0.856586\pi$
$564$		0			0
$565$	72.7178	+	12.8221i	3.05926	+	0.539430i
$566$		0			0
$567$	1.43403	+	3.93996i	0.0602235	+	0.165463i
$568$		0			0
$569$			8.31206i			0.348460i	0.984705	+	0.174230i	$0.0557436\pi$
$569$			8.31206i			0.348460i	−0.984705	+	0.174230i	$0.944256\pi$
$570$		0			0
$571$			25.8477i			1.08169i	0.841122	+	0.540846i	$0.181896\pi$
$571$			25.8477i			1.08169i	−0.841122	+	0.540846i	$0.818104\pi$
$572$		0			0
$573$	−4.77062	−	13.1072i	−0.199296	−	0.547560i
$574$		0			0
$575$	−10.8483	−	1.91286i	−0.452407	−	0.0797716i
$576$		0			0
$577$	−6.74803	−	11.6879i	−0.280924	−	0.486575i	0.690689	−	0.723152i	$-0.257308\pi$
$577$	−6.74803	−	11.6879i	−0.280924	−	0.486575i	−0.971613	+	0.236578i	$0.923974\pi$
$578$		0			0
$579$	−1.16978	−	1.39409i	−0.0486144	−	0.0579364i
$580$		0			0
$581$	−14.2905	+	24.7519i	−0.592871	+	1.02688i
$582$		0			0
$583$	32.8604	+	11.9602i	1.36094	+	0.495341i
$584$		0			0
$585$	20.4959	−	3.61399i	0.847402	−	0.149420i
$586$		0			0
$587$	−13.4945	+	16.0821i	−0.556978	+	0.663780i	−0.968904	−	0.247437i	$-0.920412\pi$
$587$	−13.4945	+	16.0821i	−0.556978	+	0.663780i	0.411926	+	0.911217i	$0.364856\pi$
$588$		0			0
$589$	18.1008	+	14.5712i	0.745830	+	0.600396i
$590$		0			0
$591$	1.89370	+	1.58900i	0.0778964	+	0.0653628i
$592$		0			0
$593$	2.92347	+	16.5798i	0.120052	+	0.680851i	0.984124	+	0.177482i	$0.0567951\pi$
$593$	2.92347	+	16.5798i	0.120052	+	0.680851i	−0.864072	+	0.503369i	$0.832094\pi$
$594$		0			0
$595$	7.02618	−	19.3043i	0.288045	−	0.791398i
$596$		0			0
$597$	−8.86037	−	5.11554i	−0.362631	−	0.209365i
$598$		0			0
$599$	17.6018	−	14.7697i	0.719192	−	0.603473i	−0.207970	−	0.978135i	$-0.566686\pi$
$599$	17.6018	−	14.7697i	0.719192	−	0.603473i	0.927162	+	0.374662i	$0.122241\pi$
$600$		0			0
$601$	0.932019	−	0.538101i	0.0380178	−	0.0219496i	−0.480871	−	0.876792i	$-0.659679\pi$
$601$	0.932019	−	0.538101i	0.0380178	−	0.0219496i	0.518888	+	0.854842i	$0.326346\pi$
$602$		0			0
$603$	−0.132167	+	0.749556i	−0.00538225	+	0.0305243i
$604$		0			0
$605$	−11.2010	+	4.07681i	−0.455383	+	0.165746i
$606$		0			0
$607$	27.6911			1.12395			0.561974	−	0.827155i	$-0.310042\pi$
$607$	27.6911			1.12395			0.561974	+	0.827155i	$0.310042\pi$
$608$		0			0
$609$	−18.4881			−0.749177
$610$		0			0
$611$	6.49457	−	2.36383i	0.262742	−	0.0956303i
$612$		0			0
$613$	−3.47674	+	19.7176i	−0.140424	+	0.796386i	0.830504	+	0.557013i	$0.188053\pi$
$613$	−3.47674	+	19.7176i	−0.140424	+	0.796386i	−0.970928	+	0.239372i	$0.923058\pi$
$614$		0			0
$615$	14.7154	−	8.49594i	0.593382	−	0.342589i
$616$		0			0
$617$	5.54646	−	4.65404i	0.223292	−	0.187364i	−0.524278	−	0.851547i	$-0.675665\pi$
$617$	5.54646	−	4.65404i	0.223292	−	0.187364i	0.747570	+	0.664183i	$0.231220\pi$
$618$		0			0
$619$	−33.4399	−	19.3065i	−1.34406	−	0.775995i	−0.356662	−	0.934234i	$-0.616085\pi$
$619$	−33.4399	−	19.3065i	−1.34406	−	0.775995i	−0.987401	+	0.158239i	$0.949418\pi$
$620$		0			0
$621$	0.276192	−	0.758831i	0.0110832	−	0.0304508i
$622$		0			0
$623$	−1.36171	−	7.72262i	−0.0545556	−	0.309400i
$624$		0			0
$625$	71.1474	+	59.6998i	2.84590	+	2.38799i
$626$		0			0
$627$	15.8635	−	3.13122i	0.633527	−	0.125049i
$628$		0			0
$629$	−3.58049	+	4.26706i	−0.142763	+	0.170139i
$630$		0			0
$631$	33.4021	−	5.88968i	1.32972	−	0.234465i	0.536755	−	0.843738i	$-0.319650\pi$
$631$	33.4021	−	5.88968i	1.32972	−	0.234465i	0.792960	+	0.609274i	$0.208539\pi$
$632$		0			0
$633$	21.4152	+	7.79450i	0.851178	+	0.309804i
$634$		0			0
$635$	7.76934	−	13.4569i	0.308317	−	0.534020i
$636$		0			0
$637$	−32.7809	−	39.0667i	−1.29883	−	1.54788i
$638$		0			0
$639$	6.25150	+	10.8279i	0.247305	+	0.428345i
$640$		0			0
$641$	1.70272	+	0.300236i	0.0672536	+	0.0118586i	0.207174	−	0.978304i	$-0.433573\pi$
$641$	1.70272	+	0.300236i	0.0672536	+	0.0118586i	−0.139920	+	0.990163i	$0.544685\pi$
$642$		0			0
$643$	0.387667	+	1.06511i	0.0152881	+	0.0420037i	0.947102	−	0.320933i	$-0.103996\pi$
$643$	0.387667	+	1.06511i	0.0152881	+	0.0420037i	−0.931814	+	0.362937i	$0.881774\pi$
$644$		0			0
$645$		−	21.3975i		−	0.842524i
$646$		0			0
$647$			29.5430i			1.16146i	0.814098	+	0.580728i	$0.197232\pi$
$647$			29.5430i			1.16146i	−0.814098	+	0.580728i	$0.802768\pi$
$648$		0			0
$649$	−3.09340	−	8.49904i	−0.121426	−	0.333616i
$650$		0			0
$651$	22.0121	+	3.88132i	0.862721	+	0.152121i
$652$		0			0
$653$	−14.7645	−	25.5729i	−0.577780	−	1.00074i	−0.995734	−	0.0922755i	$-0.970586\pi$
$653$	−14.7645	−	25.5729i	−0.577780	−	1.00074i	0.417954	−	0.908468i	$-0.362747\pi$
$654$		0			0
$655$	43.0841	+	51.3457i	1.68344	+	2.00624i
$656$		0			0
$657$	−4.07298	+	7.05460i	−0.158902	+	0.275226i
$658$		0			0
$659$	11.5480	+	4.20312i	0.449846	+	0.163730i	0.557001	−	0.830512i	$-0.311952\pi$
$659$	11.5480	+	4.20312i	0.449846	+	0.163730i	−0.107155	+	0.994242i	$0.534174\pi$
$660$		0			0
$661$	14.8328	−	2.61543i	0.576931	−	0.101728i	0.122434	−	0.992477i	$-0.460930\pi$
$661$	14.8328	−	2.61543i	0.576931	−	0.101728i	0.454497	+	0.890748i	$0.349819\pi$
$662$		0			0
$663$	3.51618	−	4.19042i	0.136557	−	0.162743i
$664$		0			0
$665$	51.9403	+	59.4024i	2.01416	+	2.30352i
$666$		0			0
$667$	2.72772	+	2.28883i	0.105618	+	0.0886239i
$668$		0			0
$669$	4.76854	+	27.0437i	0.184362	+	1.04557i
$670$		0			0
$671$	18.0087	−	49.4786i	0.695220	−	1.91010i
$672$		0			0
$673$	−17.9300	−	10.3519i	−0.691149	−	0.399035i	0.112893	−	0.993607i	$-0.463988\pi$
$673$	−17.9300	−	10.3519i	−0.691149	−	0.399035i	−0.804042	+	0.594572i	$0.797322\pi$
$674$		0			0
$675$	−10.4498	+	8.76840i	−0.402212	+	0.337496i
$676$		0			0
$677$	13.3028	−	7.68040i	0.511270	−	0.295182i	−0.222086	−	0.975027i	$-0.571286\pi$
$677$	13.3028	−	7.68040i	0.511270	−	0.295182i	0.733355	+	0.679845i	$0.237953\pi$
$678$		0			0
$679$	11.9152	−	67.5742i	0.457262	−	2.59326i
$680$		0			0
$681$	6.80833	−	2.47803i	0.260896	−	0.0949583i
$682$		0			0
$683$	49.7492			1.90360			0.951801	−	0.306716i	$-0.0992303\pi$
$683$	49.7492			1.90360			0.951801	+	0.306716i	$0.0992303\pi$
$684$		0			0
$685$	−67.0809			−2.56303
$686$		0			0
$687$	−8.69759	+	3.16566i	−0.331834	+	0.120778i
$688$		0			0
$689$	−7.89069	+	44.7503i	−0.300611	+	1.70485i
$690$		0			0
$691$	7.95481	−	4.59271i	0.302615	−	0.174715i	−0.341002	−	0.940063i	$-0.610766\pi$
$691$	7.95481	−	4.59271i	0.302615	−	0.174715i	0.643617	+	0.765348i	$0.277433\pi$
$692$		0			0
$693$	11.9147	−	9.99758i	0.452600	−	0.379777i
$694$		0			0
$695$	−9.28690	−	5.36180i	−0.352272	−	0.203385i
$696$		0			0
$697$	1.52750	−	4.19677i	0.0578581	−	0.158964i
$698$		0			0
$699$	−4.23949	−	24.0434i	−0.160352	−	0.909403i
$700$		0			0
$701$	−6.63362	−	5.56627i	−0.250548	−	0.210235i	0.508860	−	0.860849i	$-0.330067\pi$
$701$	−6.63362	−	5.56627i	−0.250548	−	0.210235i	−0.759408	+	0.650614i	$0.774512\pi$
$702$		0			0
$703$	−7.72532	−	19.9524i	−0.291366	−	0.752517i
$704$		0			0
$705$	−3.97914	+	4.74216i	−0.149863	+	0.178600i
$706$		0			0
$707$	−43.6032	+	7.68842i	−1.63987	+	0.289153i
$708$		0			0
$709$	1.04667	+	0.380956i	0.0393085	+	0.0143071i	0.361600	−	0.932333i	$-0.382231\pi$
$709$	1.04667	+	0.380956i	0.0393085	+	0.0143071i	−0.322291	+	0.946641i	$0.604453\pi$
$710$		0			0
$711$	−3.13595	+	5.43162i	−0.117607	+	0.203702i
$712$		0			0
$713$	−2.76713	−	3.29774i	−0.103630	−	0.123501i
$714$		0			0
$715$	−38.6018	−	66.8603i	−1.44363	−	2.50043i
$716$		0			0
$717$	−5.67130	−	1.00000i	−0.211799	−	0.0373458i
$718$		0			0
$719$	2.48250	+	6.82060i	0.0925815	+	0.254366i	0.977337	−	0.211690i	$-0.0678968\pi$
$719$	2.48250	+	6.82060i	0.0925815	+	0.254366i	−0.884755	+	0.466056i	$0.845675\pi$
$720$		0			0
$721$		−	8.17244i		−	0.304357i
$722$		0			0
$723$		−	19.1927i		−	0.713785i
$724$		0			0
$725$	−20.5727	−	56.5231i	−0.764051	−	2.09921i
$726$		0			0
$727$	−17.5834	−	3.10042i	−0.652131	−	0.114988i	−0.162212	−	0.986756i	$-0.551863\pi$
$727$	−17.5834	−	3.10042i	−0.652131	−	0.114988i	−0.489919	+	0.871768i	$0.662974\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	−3.61508	−	4.30828i	−0.133708	−	0.159348i
$732$		0			0
$733$	16.3128	−	28.2545i	0.602525	−	1.04360i	−0.389912	−	0.920852i	$-0.627495\pi$
$733$	16.3128	−	28.2545i	0.602525	−	1.04360i	0.992437	−	0.122752i	$-0.0391721\pi$
$734$		0			0
$735$	42.9237	+	15.6229i	1.58326	+	0.576261i
$736$		0			0
$737$	2.78052	−	0.490280i	0.102422	−	0.0180597i
$738$		0			0
$739$	14.2373	−	16.9673i	0.523726	−	0.624153i	−0.437731	−	0.899106i	$-0.644218\pi$
$739$	14.2373	−	16.9673i	0.523726	−	0.624153i	0.961458	+	0.274953i	$0.0886623\pi$
$740$		0			0
$741$	7.58657	+	19.5940i	0.278700	+	0.719804i
$742$		0			0
$743$	38.5958	+	32.3857i	1.41594	+	1.18812i	0.953471	+	0.301484i	$0.0974819\pi$
$743$	38.5958	+	32.3857i	1.41594	+	1.18812i	0.462472	+	0.886634i	$0.346963\pi$
$744$		0			0
$745$	−9.61684	−	54.5398i	−0.352334	−	1.99818i
$746$		0			0
$747$	2.33144	−	6.40557i	0.0853028	−	0.234368i
$748$		0			0
$749$	−70.9957	−	40.9894i	−2.59413	−	1.49772i
$750$		0			0
$751$	−31.0701	+	26.0709i	−1.13376	+	0.951341i	−0.999217	−	0.0395656i	$-0.987403\pi$
$751$	−31.0701	+	26.0709i	−1.13376	+	0.951341i	−0.134548	+	0.990907i	$0.542958\pi$
$752$		0			0
$753$	−17.3320	+	10.0066i	−0.631612	+	0.364661i
$754$		0			0
$755$	8.05828	−	45.7008i	0.293271	−	1.66322i
$756$		0			0
$757$	5.03897	−	1.83404i	0.183145	−	0.0666592i	−0.248820	−	0.968550i	$-0.580043\pi$
$757$	5.03897	−	1.83404i	0.183145	−	0.0666592i	0.431965	+	0.901891i	$0.357821\pi$
$758$		0			0
$759$	−2.99558			−0.108733
$760$		0			0
$761$	−22.5976			−0.819162			−0.409581	−	0.912274i	$-0.634325\pi$
$761$	−22.5976			−0.819162			−0.409581	+	0.912274i	$0.634325\pi$
$762$		0			0
$763$	−23.5142	+	8.55846i	−0.851270	+	0.309837i
$764$		0			0
$765$	−0.850809	+	4.82518i	−0.0307611	+	0.174455i
$766$		0			0
$767$	10.1782	−	5.87640i	0.367514	−	0.212185i
$768$		0			0
$769$	−12.5701	+	10.5476i	−0.453290	+	0.380355i	−0.840655	−	0.541571i	$-0.817830\pi$
$769$	−12.5701	+	10.5476i	−0.453290	+	0.380355i	0.387365	+	0.921926i	$0.373385\pi$
$770$		0			0
$771$	17.4276	+	10.0618i	0.627639	+	0.362368i
$772$		0			0
$773$	−7.43658	+	20.4318i	−0.267475	+	0.734882i	0.731138	+	0.682230i	$0.238990\pi$
$773$	−7.43658	+	20.4318i	−0.267475	+	0.734882i	−0.998613	+	0.0526522i	$0.983233\pi$
$774$		0			0
$775$	12.6278	+	71.6156i	0.453603	+	2.57251i
$776$		0			0
$777$	−15.7656	−	13.2289i	−0.565587	−	0.474584i
$778$		0			0
$779$	11.2919	+	12.9141i	0.404573	+	0.462697i
$780$		0			0
$781$	29.8128	−	35.5295i	1.06679	−	1.27135i
$782$		0			0
$783$	4.34249	−	0.765698i	0.155188	−	0.0273638i
$784$		0			0
$785$	−13.8953	−	5.05746i	−0.495943	−	0.180509i
$786$		0			0
$787$	−20.6960	+	35.8466i	−0.737734	+	1.27779i	0.215780	+	0.976442i	$0.430771\pi$
$787$	−20.6960	+	35.8466i	−0.737734	+	1.27779i	−0.953513	+	0.301350i	$0.902563\pi$
$788$		0			0
$789$	10.3876	+	12.3795i	0.369810	+	0.440722i
$790$		0			0
$791$	35.8532	+	62.0996i	1.27479	+	2.20801i
$792$		0			0
$793$	67.3815	+	11.8812i	2.39279	+	0.421913i
$794$		0			0
$795$	−13.9205	−	38.2462i	−0.493709	−	1.35645i
$796$		0			0
$797$		−	35.2685i		−	1.24927i	−0.780915	−	0.624637i	$-0.785247\pi$
$797$		−	35.2685i		−	1.24927i	0.780915	−	0.624637i	$-0.214753\pi$
$798$		0			0
$799$			1.62708i			0.0575621i
$800$		0			0
$801$	0.639674	+	1.75749i	0.0226018	+	0.0620979i
$802$		0			0
$803$	29.7588	+	5.24728i	1.05016	+	0.185172i
$804$		0			0
$805$	−7.30924	−	12.6600i	−0.257617	−	0.446205i
$806$		0			0
$807$	2.08028	+	2.47918i	0.0732293	+	0.0872713i
$808$		0			0
$809$	8.25714	−	14.3018i	0.290306	−	0.502824i	−0.683576	−	0.729879i	$-0.739576\pi$
$809$	8.25714	−	14.3018i	0.290306	−	0.502824i	0.973882	+	0.227055i	$0.0729097\pi$
$810$		0			0
$811$	12.8339	+	4.67117i	0.450660	+	0.164027i	0.557372	−	0.830263i	$-0.311810\pi$
$811$	12.8339	+	4.67117i	0.450660	+	0.164027i	−0.106711	+	0.994290i	$0.534032\pi$
$812$		0			0
$813$	−11.0706	+	1.95205i	−0.388264	+	0.0684614i
$814$		0			0
$815$	−28.9253	+	34.4719i	−1.01321	+	1.20750i
$816$		0			0
$817$	21.1935	−	4.18329i	0.741466	−	0.146355i
$818$		0			0
$819$	15.4824	+	12.9913i	0.541000	+	0.453953i
$820$		0			0
$821$	−5.20418	−	29.5143i	−0.181627	−	1.03006i	−0.930213	−	0.367020i	$-0.880378\pi$
$821$	−5.20418	−	29.5143i	−0.181627	−	1.03006i	0.748586	−	0.663038i	$-0.230733\pi$
$822$		0			0
$823$	3.29002	−	9.03926i	0.114683	−	0.315089i	−0.869050	−	0.494724i	$-0.835269\pi$
$823$	3.29002	−	9.03926i	0.114683	−	0.315089i	0.983733	+	0.179635i	$0.0574915\pi$
$824$		0			0
$825$	43.8233	+	25.3014i	1.52573	+	0.880881i
$826$		0			0
$827$	12.6364	−	10.6032i	0.439412	−	0.368710i	−0.396077	−	0.918217i	$-0.629629\pi$
$827$	12.6364	−	10.6032i	0.439412	−	0.368710i	0.835489	+	0.549507i	$0.185184\pi$
$828$		0			0
$829$	−20.4341	+	11.7976i	−0.709705	+	0.409748i	−0.810952	−	0.585113i	$-0.801050\pi$
$829$	−20.4341	+	11.7976i	−0.709705	+	0.409748i	0.101247	+	0.994861i	$0.467717\pi$
$830$		0			0
$831$	1.41116	−	8.00310i	0.0489527	−	0.277625i
$832$		0			0
$833$	11.2820	−	4.10630i	0.390897	−	0.142275i
$834$		0			0
$835$	1.30381			0.0451203
$836$		0			0
$837$	−5.33094			−0.184264
$838$		0			0
$839$	34.8763	−	12.6939i	1.20406	−	0.438244i	0.339424	−	0.940634i	$-0.389768\pi$
$839$	34.8763	−	12.6939i	1.20406	−	0.438244i	0.864641	+	0.502390i	$0.167546\pi$
$840$		0			0
$841$	1.65947	−	9.41132i	0.0572231	−	0.324528i
$842$		0			0
$843$	−15.9268	+	9.19535i	−0.548549	+	0.316705i
$844$		0			0
$845$	33.8543	−	28.4072i	1.16462	−	0.977236i
$846$		0			0
$847$	−10.0246	−	5.78773i	−0.344451	−	0.198869i
$848$		0			0
$849$	2.36565	−	6.49956i	0.0811888	−	0.223064i
$850$		0			0
$851$	0.688303	+	3.90356i	0.0235947	+	0.133812i
$852$		0			0
$853$	−12.4368	−	10.4357i	−0.425829	−	0.357313i	0.404546	−	0.914518i	$-0.367430\pi$
$853$	−12.4368	−	10.4357i	−0.425829	−	0.357313i	−0.830375	+	0.557204i	$0.811874\pi$
$854$		0			0
$855$	−14.6599	−	11.8013i	−0.501358	−	0.403595i
$856$		0			0
$857$	−14.2174	+	16.9436i	−0.485657	+	0.578784i	−0.952107	−	0.305764i	$-0.901088\pi$
$857$	−14.2174	+	16.9436i	−0.485657	+	0.578784i	0.466450	+	0.884547i	$0.345533\pi$
$858$		0			0
$859$	−9.27308	+	1.63509i	−0.316393	+	0.0557887i	−0.329590	−	0.944124i	$-0.606910\pi$
$859$	−9.27308	+	1.63509i	−0.316393	+	0.0557887i	0.0131964	+	0.999913i	$0.495799\pi$
$860$		0			0
$861$	15.5059	+	5.64368i	0.528439	+	0.192336i
$862$		0			0
$863$	−10.4749	+	18.1431i	−0.356571	+	0.617599i	−0.987386	−	0.158335i	$-0.949388\pi$
$863$	−10.4749	+	18.1431i	−0.356571	+	0.617599i	0.630815	+	0.775934i	$0.282721\pi$
$864$		0			0
$865$	1.67822	+	2.00003i	0.0570613	+	0.0680030i
$866$		0			0
$867$	−7.85610	−	13.6072i	−0.266807	−	0.462123i
$868$		0			0
$869$	22.9125	+	4.04009i	0.777252	+	0.137051i
$870$		0			0
$871$	1.25483	+	3.44760i	0.0425181	+	0.116818i
$872$		0			0
$873$			16.3653i			0.553881i
$874$		0			0
$875$			156.429i			5.28826i
$876$		0			0
$877$	−3.12329	−	8.58116i	−0.105466	−	0.289765i	0.875723	−	0.482813i	$-0.160385\pi$
$877$	−3.12329	−	8.58116i	−0.105466	−	0.289765i	−0.981189	+	0.193048i	$0.938163\pi$
$878$		0			0
$879$	29.0555	+	5.12326i	0.980017	+	0.172803i
$880$		0			0
$881$	12.0111	+	20.8038i	0.404663	+	0.700897i	0.994282	−	0.106784i	$-0.0340554\pi$
$881$	12.0111	+	20.8038i	0.404663	+	0.700897i	−0.589619	+	0.807682i	$0.700722\pi$
$882$		0			0
$883$	−0.0886722	−	0.105675i	−0.00298406	−	0.00355626i	0.764550	−	0.644564i	$-0.222961\pi$
$883$	−0.0886722	−	0.105675i	−0.00298406	−	0.00355626i	−0.767534	+	0.641008i	$0.778517\pi$
$884$		0			0
$885$	−5.26344	+	9.11654i	−0.176928	+	0.306449i
$886$		0			0
$887$	4.59420	+	1.67215i	0.154258	+	0.0561454i	0.417995	−	0.908449i	$-0.362733\pi$
$887$	4.59420	+	1.67215i	0.154258	+	0.0561454i	−0.263737	+	0.964595i	$0.584955\pi$
$888$		0			0
$889$	14.8605	−	2.62031i	0.498406	−	0.0878825i
$890$		0			0
$891$	−2.38445	+	2.84168i	−0.0798822	+	0.0951999i
$892$		0			0
$893$	−5.47489	−	3.01410i	−0.183210	−	0.100863i
$894$		0			0
$895$	−12.6446	−	10.6100i	−0.422661	−	0.354655i
$896$		0			0
$897$	−0.675941	−	3.83345i	−0.0225690	−	0.127995i
$898$		0			0
$899$	8.03975	−	22.0890i	0.268141	−	0.736710i
$900$		0			0
$901$	−9.26448	−	5.34885i	−0.308645	−	0.178196i
$902$		0			0
$903$	15.9179	−	13.3567i	0.529714	−	0.444483i
$904$		0			0
$905$	76.5554	−	44.1993i	2.54479	−	1.46923i
$906$		0			0
$907$	−2.59473	+	14.7154i	−0.0861565	+	0.488618i	0.910945	+	0.412529i	$0.135354\pi$
$907$	−2.59473	+	14.7154i	−0.0861565	+	0.488618i	−0.997101	+	0.0760889i	$0.975757\pi$
$908$		0			0
$909$	9.92309	−	3.61171i	0.329128	−	0.119793i
$910$		0			0
$911$	−38.8136			−1.28595			−0.642976	−	0.765886i	$-0.722300\pi$
$911$	−38.8136			−1.28595			−0.642976	+	0.765886i	$0.722300\pi$
$912$		0			0
$913$	−25.2868			−0.836870
$914$		0			0
$915$	−57.5881	+	20.9604i	−1.90380	+	0.692928i
$916$		0			0
$917$	−11.3029	+	64.1018i	−0.373254	+	2.11683i
$918$		0			0
$919$	11.2847	−	6.51523i	0.372248	−	0.214918i	−0.302192	−	0.953247i	$-0.597718\pi$
$919$	11.2847	−	6.51523i	0.372248	−	0.214918i	0.674440	+	0.738329i	$0.264385\pi$
$920$		0			0
$921$	−20.9170	+	17.5514i	−0.689237	+	0.578339i
$922$		0			0
$923$	52.1944	+	30.1344i	1.71800	+	0.991887i
$924$		0			0
$925$	22.9010	−	62.9200i	0.752980	−	2.06880i
$926$		0			0
$927$	0.338467	+	1.91954i	0.0111167	+	0.0630459i
$928$		0			0
$929$	14.5684	+	12.2243i	0.477973	+	0.401067i	0.849693	−	0.527278i	$-0.176787\pi$
$929$	14.5684	+	12.2243i	0.477973	+	0.401067i	−0.371720	+	0.928345i	$0.621232\pi$
$930$		0			0
$931$	−7.08226	+	45.5689i	−0.232112	+	1.49346i
$932$		0			0
$933$	−10.4561	+	12.4611i	−0.342316	+	0.407957i
$934$		0			0
$935$	17.8992	−	3.15612i	0.585368	−	0.103216i
$936$		0			0
$937$	−12.0679	−	4.39236i	−0.394242	−	0.143492i	0.137290	−	0.990531i	$-0.456161\pi$
$937$	−12.0679	−	4.39236i	−0.394242	−	0.143492i	−0.531531	+	0.847039i	$0.678383\pi$
$938$		0			0
$939$	6.64184	−	11.5040i	0.216748	−	0.375419i
$940$		0			0
$941$	31.7753	+	37.8683i	1.03584	+	1.23447i	0.971623	+	0.236535i	$0.0760117\pi$
$941$	31.7753	+	37.8683i	1.03584	+	1.23447i	0.0642206	+	0.997936i	$0.479544\pi$
$942$		0			0
$943$	−1.58904	−	2.75229i	−0.0517461	−	0.0896269i
$944$		0			0
$945$	−17.8277	−	3.14350i	−0.579934	−	0.102258i
$946$		0			0
$947$	−2.12342	−	5.83404i	−0.0690018	−	0.189581i	0.900399	−	0.435066i	$-0.143275\pi$
$947$	−2.12342	−	5.83404i	−0.0690018	−	0.189581i	−0.969400	+	0.245485i	$0.921053\pi$
$948$		0			0
$949$			39.2664i			1.27464i
$950$		0			0
$951$			2.24634i			0.0728427i
$952$		0			0
$953$	−7.41157	−	20.3631i	−0.240084	−	0.659626i	−0.999954	−	0.00955133i	$-0.996960\pi$
$953$	−7.41157	−	20.3631i	−0.240084	−	0.659626i	0.759870	−	0.650075i	$-0.225263\pi$
$954$		0			0
$955$	59.3078	+	10.4576i	1.91916	+	0.338399i
$956$		0			0
$957$	−8.17860	−	14.1657i	−0.264376	−	0.457913i
$958$		0			0
$959$	−41.8731	−	49.9025i	−1.35215	−	1.61144i
$960$		0			0
$961$	1.29056	−	2.23532i	0.0416310	−	0.0721070i
$962$		0			0
$963$	18.3731	+	6.68725i	0.592064	+	0.215494i
$964$		0			0
$965$	7.73794	−	1.36441i	0.249093	−	0.0439218i
$966$		0			0
$967$	10.3992	−	12.3932i	0.334414	−	0.398540i	−0.572465	−	0.819929i	$-0.694013\pi$
$967$	10.3992	−	12.3932i	0.334414	−	0.398540i	0.906880	+	0.421389i	$0.138457\pi$
$968$		0			0
$969$	−4.94552	+	0.100643i	−0.158873	+	0.00323312i
$970$		0			0
$971$	−11.0802	−	9.29740i	−0.355581	−	0.298368i	0.447446	−	0.894311i	$-0.352334\pi$
$971$	−11.0802	−	9.29740i	−0.355581	−	0.298368i	−0.803026	+	0.595943i	$0.796778\pi$
$972$		0			0
$973$	−1.80834	−	10.2556i	−0.0579726	−	0.328779i
$974$		0			0
$975$	−22.4897	+	61.7899i	−0.720247	+	1.97886i
$976$		0			0
$977$	3.88920	+	2.24543i	0.124427	+	0.0718378i	0.560921	−	0.827869i	$-0.310447\pi$
$977$	3.88920	+	2.24543i	0.124427	+	0.0718378i	−0.436495	+	0.899707i	$0.643780\pi$
$978$		0			0
$979$	5.31475	−	4.45960i	0.169860	−	0.142530i
$980$		0			0
$981$	5.16855	−	2.98406i	0.165019	−	0.0952738i
$982$		0			0
$983$	−3.09328	+	17.5429i	−0.0986602	+	0.559530i	0.894904	+	0.446259i	$0.147244\pi$
$983$	−3.09328	+	17.5429i	−0.0986602	+	0.559530i	−0.993564	+	0.113271i	$0.963867\pi$
$984$		0			0
$985$	−10.0295	+	3.65044i	−0.319567	+	0.116313i
$986$		0			0
$987$	−6.01161			−0.191352
$988$		0			0
$989$	−4.00207			−0.127258
$990$		0			0
$991$	21.7017	−	7.89877i	0.689377	−	0.250913i	0.0265087	−	0.999649i	$-0.491561\pi$
$991$	21.7017	−	7.89877i	0.689377	−	0.250913i	0.662869	+	0.748736i	$0.269339\pi$
$992$		0			0
$993$	4.20000	−	23.8194i	0.133283	−	0.755885i
$994$		0			0
$995$	38.2551	−	22.0866i	1.21277	−	0.700191i
$996$		0			0
$997$	14.4864	−	12.1555i	0.458787	−	0.384968i	−0.383897	−	0.923376i	$-0.625418\pi$
$997$	14.4864	−	12.1555i	0.458787	−	0.384968i	0.842685	+	0.538408i	$0.180974\pi$
$998$		0			0
$999$	4.25090	+	2.45426i	0.134493	+	0.0776493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.c.79.1	✓	12
4.3	odd	2		912.2.ci.d.79.1	yes	12
19.13	odd	18		912.2.ci.d.127.1	yes	12
76.51	even	18	inner	912.2.ci.c.127.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.c.79.1	✓	12	1.1	even	1	trivial
912.2.ci.c.127.1	yes	12	76.51	even	18	inner
912.2.ci.d.79.1	yes	12	4.3	odd	2
912.2.ci.d.127.1	yes	12	19.13	odd	18

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{3} +(-0.749734 + 4.25195i) q^{5} +(-3.63109 + 2.09641i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{3} +(-0.749734 + 4.25195i) q^{5} +(-3.63109 + 2.09641i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-3.21257 - 1.85478i) q^{11} +(1.64866 - 4.52965i) q^{13} +(0.749734 + 4.25195i) q^{15} +(0.869318 + 0.729445i) q^{17} +(-4.06484 + 1.57386i) q^{19} +(-2.69509 + 3.21188i) q^{21} +(0.795263 - 0.140226i) q^{23} +(-12.8185 - 4.66557i) q^{25} +(0.500000 - 0.866025i) q^{27} +(2.83436 + 3.37786i) q^{29} +(-2.66547 - 4.61673i) q^{31} +(-3.65320 - 0.644157i) q^{33} +(-6.19148 - 17.0110i) q^{35} +4.90852i q^{37} -4.82036i q^{39} +(-1.34603 - 3.69820i) q^{41} +(-4.88064 - 0.860588i) q^{43} +(2.15877 + 3.73910i) q^{45} +(0.921622 + 1.09835i) q^{47} +(5.28986 - 9.16231i) q^{49} +(1.06638 + 0.388129i) q^{51} +(-9.28362 + 1.63695i) q^{53} +(10.2950 - 12.2691i) q^{55} +(-3.28141 + 2.86920i) q^{57} +(1.86774 + 1.56722i) q^{59} +(2.46479 + 13.9785i) q^{61} +(-1.43403 + 3.93996i) q^{63} +(18.0238 + 10.4061i) q^{65} +(-0.583051 + 0.489238i) q^{67} +(0.699342 - 0.403766i) q^{69} +(-2.17112 + 12.3130i) q^{71} +(-7.65469 + 2.78608i) q^{73} -13.6412 q^{75} +15.5535 q^{77} +(-5.89366 + 2.14512i) q^{79} +(0.173648 - 0.984808i) q^{81} +(5.90341 - 3.40833i) q^{83} +(-3.75332 + 3.14941i) q^{85} +(3.81872 + 2.20474i) q^{87} +(-0.639674 + 1.75749i) q^{89} +(3.50958 + 19.9038i) q^{91} +(-4.08373 - 3.42666i) q^{93} +(-3.64443 - 18.4635i) q^{95} +(-10.5194 + 12.5365i) q^{97} +(-3.65320 + 0.644157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 18 q^{7}+O(q^{10}) \) 12 * q + 6 * q^5 - 18 * q^7	\( 12 q + 6 q^{5} - 18 q^{7} + 18 q^{13} - 6 q^{15} + 6 q^{17} - 12 q^{19} - 6 q^{21} + 18 q^{23} - 30 q^{25} + 6 q^{27} - 6 q^{29} - 18 q^{31} + 6 q^{33} - 36 q^{35} + 6 q^{41} + 6 q^{43} - 6 q^{47} + 12 q^{49} - 6 q^{51} - 36 q^{53} + 42 q^{55} + 6 q^{59} - 6 q^{61} - 6 q^{63} + 72 q^{65} - 6 q^{67} - 54 q^{71} - 12 q^{73} - 12 q^{75} - 36 q^{77} + 6 q^{79} - 18 q^{83} - 36 q^{85} + 36 q^{87} + 24 q^{89} - 12 q^{91} - 18 q^{93} - 24 q^{95} + 24 q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 6 * q^5 - 18 * q^7 + 18 * q^13 - 6 * q^15 + 6 * q^17 - 12 * q^19 - 6 * q^21 + 18 * q^23 - 30 * q^25 + 6 * q^27 - 6 * q^29 - 18 * q^31 + 6 * q^33 - 36 * q^35 + 6 * q^41 + 6 * q^43 - 6 * q^47 + 12 * q^49 - 6 * q^51 - 36 * q^53 + 42 * q^55 + 6 * q^59 - 6 * q^61 - 6 * q^63 + 72 * q^65 - 6 * q^67 - 54 * q^71 - 12 * q^73 - 12 * q^75 - 36 * q^77 + 6 * q^79 - 18 * q^83 - 36 * q^85 + 36 * q^87 + 24 * q^89 - 12 * q^91 - 18 * q^93 - 24 * q^95 + 24 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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