LMFDB - Embedded newform 912.2.ci.f.79.2

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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 3 x^{16} + 100 x^{15} - 171 x^{14} - 471 x^{13} + 1537 x^{12} + 321 x^{11} + \cdots + 1367631 $ x^18 - 6x^17 - 3x^16 + 100x^15 - 171x^14 - 471x^13 + 1537x^12 + 321x^11 - 3936x^10 - 1317x^9 + 4941x^8 + 21078x^7 - 14829x^6 - 68589x^5 - 45711x^4 + 421452x^3 - 61938x^2 - 1219779*x + 1367631
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			79.2
Root			$-0.489413 - 1.79677i$ of defining polynomial
Character	$\chi$	$=$	912.79
Dual form			912.2.ci.f.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{3} +(-0.0537040 + 0.304570i) q^{5} +(-4.22544 + 2.43956i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.0537040 + 0.304570i) q^{5} +(-4.22544 + 2.43956i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-1.67322 - 0.966032i) q^{11} +(1.49685 - 4.11257i) q^{13} +(-0.0537040 - 0.304570i) q^{15} +(-3.57294 - 2.99805i) q^{17} +(3.42972 - 2.69017i) q^{19} +(3.13624 - 3.73762i) q^{21} +(7.72421 - 1.36199i) q^{23} +(4.60858 + 1.67739i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(5.51775 + 6.57580i) q^{29} +(1.67069 + 2.89373i) q^{31} +(1.90271 + 0.335499i) q^{33} +(-0.516095 - 1.41796i) q^{35} +1.17512i q^{37} +4.37651i q^{39} +(-3.68090 - 10.1132i) q^{41} +(-2.64198 - 0.465852i) q^{43} +(0.154634 + 0.267835i) q^{45} +(-5.72472 - 6.82246i) q^{47} +(8.40289 - 14.5542i) q^{49} +(4.38286 + 1.59523i) q^{51} +(11.3935 - 2.00898i) q^{53} +(0.384083 - 0.457733i) q^{55} +(-2.30279 + 3.70097i) q^{57} +(2.80526 + 2.35389i) q^{59} +(-0.0154881 - 0.0878376i) q^{61} +(-1.66876 + 4.58487i) q^{63} +(1.17218 + 0.676759i) q^{65} +(-3.50277 + 2.93917i) q^{67} +(-6.79255 + 3.92168i) q^{69} +(2.43826 - 13.8280i) q^{71} +(-11.0620 + 4.02625i) q^{73} -4.90435 q^{75} +9.42677 q^{77} +(-4.56918 + 1.66304i) q^{79} +(0.173648 - 0.984808i) q^{81} +(9.83589 - 5.67875i) q^{83} +(1.10500 - 0.927204i) q^{85} +(-7.43404 - 4.29205i) q^{87} +(4.29457 - 11.7992i) q^{89} +(3.70800 + 21.0291i) q^{91} +(-2.55965 - 2.14780i) q^{93} +(0.635157 + 1.18906i) q^{95} +(-10.0001 + 11.9176i) q^{97} +(-1.90271 + 0.335499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q+O(q^{10}) $ 18 * q	$ 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) $ 18 * q + 3 * q^13 + 12 * q^17 + 3 * q^19 + 15 * q^21 + 6 * q^23 + 24 * q^25 - 9 * q^27 + 12 * q^29 + 12 * q^31 + 6 * q^33 - 36 * q^35 + 12 * q^41 + 21 * q^43 - 6 * q^45 - 24 * q^47 - 3 * q^49 - 6 * q^51 + 6 * q^53 + 12 * q^55 + 54 * q^59 - 24 * q^61 + 12 * q^63 + 36 * q^65 - 21 * q^67 + 15 * q^73 + 18 * q^75 - 60 * q^79 + 54 * q^85 + 18 * q^87 + 36 * q^89 + 24 * q^91 + 24 * q^93 - 6 * q^95 - 6 * 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
$5$	−0.0537040	+	0.304570i	−0.0240172	+	0.136208i	−0.994459	−	0.105128i	$-0.966475\pi$
$5$	−0.0537040	+	0.304570i	−0.0240172	+	0.136208i	0.970441	+	0.241336i	$0.0775857\pi$
$6$		0			0
$7$	−4.22544	+	2.43956i	−1.59707	+	0.922067i	−0.605017	+	0.796212i	$0.706834\pi$
$7$	−4.22544	+	2.43956i	−1.59707	+	0.922067i	−0.992049	+	0.125854i	$0.959833\pi$
$8$		0			0
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$		0			0
$11$	−1.67322	−	0.966032i	−0.504494	−	0.291270i	0.226074	−	0.974110i	$-0.427411\pi$
$11$	−1.67322	−	0.966032i	−0.504494	−	0.291270i	−0.730567	+	0.682841i	$0.760744\pi$
$12$		0			0
$13$	1.49685	−	4.11257i	0.415153	−	1.14062i	−0.539262	−	0.842138i	$-0.681297\pi$
$13$	1.49685	−	4.11257i	0.415153	−	1.14062i	0.954414	−	0.298485i	$-0.0964811\pi$
$14$		0			0
$15$	−0.0537040	−	0.304570i	−0.0138663	−	0.0786398i
$16$		0			0
$17$	−3.57294	−	2.99805i	−0.866564	−	0.727134i	0.0968075	−	0.995303i	$-0.469137\pi$
$17$	−3.57294	−	2.99805i	−0.866564	−	0.727134i	−0.963372	+	0.268169i	$0.913581\pi$
$18$		0			0
$19$	3.42972	−	2.69017i	0.786832	−	0.617167i
$19$	3.42972	−	2.69017i	0.786832	−	0.617167i
$20$		0			0
$21$	3.13624	−	3.73762i	0.684383	−	0.815616i
$22$		0			0
$23$	7.72421	−	1.36199i	1.61061	−	0.283994i	0.705352	−	0.708858i	$-0.250789\pi$
$23$	7.72421	−	1.36199i	1.61061	−	0.283994i	0.905257	+	0.424864i	$0.139678\pi$
$24$		0			0
$25$	4.60858	+	1.67739i	0.921717	+	0.335477i
$26$		0			0
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$		0			0
$29$	5.51775	+	6.57580i	1.02462	+	1.22109i	0.974972	+	0.222328i	$0.0713655\pi$
$29$	5.51775	+	6.57580i	1.02462	+	1.22109i	0.0496481	+	0.998767i	$0.484190\pi$
$30$		0			0
$31$	1.67069	+	2.89373i	0.300066	+	0.519729i	0.976151	−	0.217095i	$-0.0696581\pi$
$31$	1.67069	+	2.89373i	0.300066	+	0.519729i	−0.676085	+	0.736824i	$0.736325\pi$
$32$		0			0
$33$	1.90271	+	0.335499i	0.331220	+	0.0584030i
$34$		0			0
$35$	−0.516095	−	1.41796i	−0.0872359	−	0.239679i
$36$		0			0
$37$			1.17512i			0.193189i	0.995324	+	0.0965943i	$0.0307949\pi$
$37$			1.17512i			0.193189i	−0.995324	+	0.0965943i	$0.969205\pi$
$38$		0			0
$39$			4.37651i			0.700802i
$40$		0			0
$41$	−3.68090	−	10.1132i	−0.574860	−	1.57942i	−0.796727	−	0.604339i	$-0.793437\pi$
$41$	−3.68090	−	10.1132i	−0.574860	−	1.57942i	0.221867	−	0.975077i	$-0.428785\pi$
$42$		0			0
$43$	−2.64198	−	0.465852i	−0.402898	−	0.0710418i	−0.0314728	−	0.999505i	$-0.510020\pi$
$43$	−2.64198	−	0.465852i	−0.402898	−	0.0710418i	−0.371425	+	0.928463i	$0.621131\pi$
$44$		0			0
$45$	0.154634	+	0.267835i	0.0230515	+	0.0399265i
$46$		0			0
$47$	−5.72472	−	6.82246i	−0.835036	−	0.995157i	−0.999961	−	0.00885122i	$-0.997183\pi$
$47$	−5.72472	−	6.82246i	−0.835036	−	0.995157i	0.164925	−	0.986306i	$-0.447262\pi$
$48$		0			0
$49$	8.40289	−	14.5542i	1.20041	−	2.07918i
$50$		0			0
$51$	4.38286	+	1.59523i	0.613722	+	0.223377i
$52$		0			0
$53$	11.3935	−	2.00898i	1.56501	−	0.275954i	0.677074	−	0.735915i	$-0.263248\pi$
$53$	11.3935	−	2.00898i	1.56501	−	0.275954i	0.887939	+	0.459961i	$0.152137\pi$
$54$		0			0
$55$	0.384083	−	0.457733i	0.0517898	−	0.0617207i
$56$		0			0
$57$	−2.30279	+	3.70097i	−0.305012	+	0.490205i
$58$		0			0
$59$	2.80526	+	2.35389i	0.365213	+	0.306450i	0.806865	−	0.590737i	$-0.201163\pi$
$59$	2.80526	+	2.35389i	0.365213	+	0.306450i	−0.441651	+	0.897187i	$0.645607\pi$
$60$		0			0
$61$	−0.0154881	−	0.0878376i	−0.00198305	−	0.0112465i	0.983800	−	0.179269i	$-0.0573731\pi$
$61$	−0.0154881	−	0.0878376i	−0.00198305	−	0.0112465i	−0.985783	+	0.168022i	$0.946262\pi$
$62$		0			0
$63$	−1.66876	+	4.58487i	−0.210244	+	0.577639i
$64$		0			0
$65$	1.17218	+	0.676759i	0.145391	+	0.0839417i
$66$		0			0
$67$	−3.50277	+	2.93917i	−0.427931	+	0.359077i	−0.831171	−	0.556018i	$-0.812329\pi$
$67$	−3.50277	+	2.93917i	−0.427931	+	0.359077i	0.403239	+	0.915095i	$0.367884\pi$
$68$		0			0
$69$	−6.79255	+	3.92168i	−0.817728	+	0.472115i
$70$		0			0
$71$	2.43826	−	13.8280i	0.289368	−	1.64109i	−0.399885	−	0.916566i	$-0.630950\pi$
$71$	2.43826	−	13.8280i	0.289368	−	1.64109i	0.689252	−	0.724521i	$-0.257939\pi$
$72$		0			0
$73$	−11.0620	+	4.02625i	−1.29471	+	0.471237i	−0.895272	−	0.445521i	$-0.853019\pi$
$73$	−11.0620	+	4.02625i	−1.29471	+	0.471237i	−0.399443	+	0.916758i	$0.630796\pi$
$74$		0			0
$75$	−4.90435			−0.566306
$76$		0			0
$77$	9.42677			1.07428
$78$		0			0
$79$	−4.56918	+	1.66304i	−0.514073	+	0.187107i	−0.586013	−	0.810302i	$-0.699303\pi$
$79$	−4.56918	+	1.66304i	−0.514073	+	0.187107i	0.0719402	+	0.997409i	$0.477081\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	9.83589	−	5.67875i	1.07963	−	0.623324i	0.148833	−	0.988862i	$-0.452448\pi$
$83$	9.83589	−	5.67875i	1.07963	−	0.623324i	0.930796	+	0.365538i	$0.119115\pi$
$84$		0			0
$85$	1.10500	−	0.927204i	0.119854	−	0.100569i
$86$		0			0
$87$	−7.43404	−	4.29205i	−0.797013	−	0.460156i
$88$		0			0
$89$	4.29457	−	11.7992i	0.455224	−	1.25072i	−0.473779	−	0.880644i	$-0.657110\pi$
$89$	4.29457	−	11.7992i	0.455224	−	1.25072i	0.929003	−	0.370073i	$-0.120667\pi$
$90$		0			0
$91$	3.70800	+	21.0291i	0.388704	+	2.20445i
$92$		0			0
$93$	−2.55965	−	2.14780i	−0.265424	−	0.222717i
$94$		0			0
$95$	0.635157	+	1.18906i	0.0651657	+	0.121995i
$96$		0			0
$97$	−10.0001	+	11.9176i	−1.01535	+	1.21005i	−0.0378147	+	0.999285i	$0.512040\pi$
$97$	−10.0001	+	11.9176i	−1.01535	+	1.21005i	−0.977537	+	0.210764i	$0.932405\pi$
$98$		0			0
$99$	−1.90271	+	0.335499i	−0.191230	+	0.0337190i
$100$		0			0
$101$	−1.72450	−	0.627668i	−0.171595	−	0.0624553i	0.254794	−	0.966995i	$-0.417992\pi$
$101$	−1.72450	−	0.627668i	−0.171595	−	0.0624553i	−0.426389	+	0.904540i	$0.640214\pi$
$102$		0			0
$103$	4.82401	−	8.35543i	0.475324	−	0.823285i	−0.524277	−	0.851548i	$-0.675664\pi$
$103$	4.82401	−	8.35543i	0.475324	−	0.823285i	0.999601	+	0.0282629i	$0.00899757\pi$
$104$		0			0
$105$	0.969941	+	1.15593i	0.0946565	+	0.112807i
$106$		0			0
$107$	−5.55236	−	9.61698i	−0.536767	−	0.929708i	−0.999076	−	0.0429890i	$-0.986312\pi$
$107$	−5.55236	−	9.61698i	−0.536767	−	0.929708i	0.462308	−	0.886719i	$-0.347021\pi$
$108$		0			0
$109$	10.1146	+	1.78347i	0.968802	+	0.170826i	0.635590	−	0.772026i	$-0.280757\pi$
$109$	10.1146	+	1.78347i	0.968802	+	0.170826i	0.333211	+	0.942852i	$0.391868\pi$
$110$		0			0
$111$	−0.401915	−	1.10425i	−0.0381481	−	0.104811i
$112$		0			0
$113$			5.00185i			0.470535i	0.971931	+	0.235267i	$0.0755966\pi$
$113$			5.00185i			0.470535i	−0.971931	+	0.235267i	$0.924403\pi$
$114$		0			0
$115$			2.42571i			0.226199i
$116$		0			0
$117$	−1.49685	−	4.11257i	−0.138384	−	0.380208i
$118$		0			0
$119$	22.4111	+	3.95169i	2.05443	+	0.362251i
$120$		0			0
$121$	−3.63356	−	6.29352i	−0.330324	−	0.572138i
$122$		0			0
$123$	6.91783	+	8.24435i	0.623760	+	0.743368i
$124$		0			0
$125$	−1.53155	+	2.65273i	−0.136986	+	0.237267i
$126$		0			0
$127$	−5.78923	−	2.10711i	−0.513711	−	0.186976i	0.0721394	−	0.997395i	$-0.477017\pi$
$127$	−5.78923	−	2.10711i	−0.513711	−	0.186976i	−0.585851	+	0.810419i	$0.699240\pi$
$128$		0			0
$129$	2.64198	−	0.465852i	0.232613	−	0.0410160i
$130$		0			0
$131$	6.89310	−	8.21488i	0.602253	−	0.717737i	−0.375658	−	0.926758i	$-0.622583\pi$
$131$	6.89310	−	8.21488i	0.602253	−	0.717737i	0.977911	+	0.209021i	$0.0670278\pi$
$132$		0			0
$133$	−7.92925	+	19.7342i	−0.687553	+	1.71117i
$134$		0			0
$135$	−0.236914	−	0.198794i	−0.0203903	−	0.0171095i
$136$		0			0
$137$	−1.36935	−	7.76599i	−0.116992	−	0.663494i	−0.985745	−	0.168248i	$-0.946189\pi$
$137$	−1.36935	−	7.76599i	−0.116992	−	0.663494i	0.868753	−	0.495246i	$-0.164922\pi$
$138$		0			0
$139$	2.10120	−	5.77301i	0.178222	−	0.489660i	−0.818127	−	0.575038i	$-0.804987\pi$
$139$	2.10120	−	5.77301i	0.178222	−	0.489660i	0.996349	+	0.0853774i	$0.0272096\pi$
$140$		0			0
$141$	7.71289	+	4.45304i	0.649543	+	0.375014i
$142$		0			0
$143$	−6.47744	+	5.43522i	−0.541671	+	0.454516i
$144$		0			0
$145$	−2.29912	+	1.32740i	−0.190931	+	0.110234i
$146$		0			0
$147$	−2.91829	+	16.5505i	−0.240697	+	1.36506i
$148$		0			0
$149$	−10.3028	+	3.74990i	−0.844036	+	0.307204i	−0.727606	−	0.685995i	$-0.759367\pi$
$149$	−10.3028	+	3.74990i	−0.844036	+	0.307204i	−0.116430	+	0.993199i	$0.537145\pi$
$150$		0			0
$151$	−1.66027			−0.135110			−0.0675552	−	0.997716i	$-0.521520\pi$
$151$	−1.66027			−0.135110			−0.0675552	+	0.997716i	$0.521520\pi$
$152$		0			0
$153$	−4.66414			−0.377073
$154$		0			0
$155$	−0.971067	+	0.353439i	−0.0779980	+	0.0283889i
$156$		0			0
$157$	2.28210	−	12.9424i	0.182132	−	1.03292i	−0.747454	−	0.664313i	$-0.768724\pi$
$157$	2.28210	−	12.9424i	0.182132	−	1.03292i	0.929586	−	0.368606i	$-0.120165\pi$
$158$		0			0
$159$	−10.0192	+	5.78462i	−0.794578	+	0.458750i
$160$		0			0
$161$	−29.3155	+	24.5987i	−2.31039	+	1.93865i
$162$		0			0
$163$	−7.53822	−	4.35219i	−0.590439	−	0.340890i	0.174832	−	0.984598i	$-0.444062\pi$
$163$	−7.53822	−	4.35219i	−0.590439	−	0.340890i	−0.765271	+	0.643708i	$0.777395\pi$
$164$		0			0
$165$	−0.204366	+	0.561492i	−0.0159099	+	0.0437121i
$166$		0			0
$167$	−2.27477	−	12.9009i	−0.176027	−	0.998300i	−0.936951	−	0.349459i	$-0.886365\pi$
$167$	−2.27477	−	12.9009i	−0.176027	−	0.998300i	0.760924	−	0.648841i	$-0.224746\pi$
$168$		0			0
$169$	−4.71411	−	3.95561i	−0.362624	−	0.304278i
$170$		0			0
$171$	0.898110	−	4.26537i	0.0686802	−	0.326181i
$172$		0			0
$173$	−4.41217	+	5.25822i	−0.335451	+	0.399775i	−0.907232	−	0.420632i	$-0.861808\pi$
$173$	−4.41217	+	5.25822i	−0.335451	+	0.399775i	0.571780	+	0.820407i	$0.306253\pi$
$174$		0			0
$175$	−23.5654	+	4.15521i	−1.78138	+	0.314105i
$176$		0			0
$177$	−3.44116	−	1.25248i	−0.258653	−	0.0941420i
$178$		0			0
$179$	−0.0507409	+	0.0878858i	−0.00379255	+	0.00656889i	−0.867915	−	0.496712i	$-0.834541\pi$
$179$	−0.0507409	+	0.0878858i	−0.00379255	+	0.00656889i	0.864123	+	0.503281i	$0.167874\pi$
$180$		0			0
$181$	11.7409	+	13.9923i	0.872695	+	1.04004i	0.998846	+	0.0480268i	$0.0152933\pi$
$181$	11.7409	+	13.9923i	0.872695	+	1.04004i	−0.126151	+	0.992011i	$0.540262\pi$
$182$		0			0
$183$	0.0445963	+	0.0772431i	0.00329665	+	0.00570997i
$184$		0			0
$185$	−0.357907	−	0.0631087i	−0.0263138	−	0.00463984i
$186$		0			0
$187$	3.08208	+	8.46796i	0.225384	+	0.619238i
$188$		0			0
$189$		−	4.87912i		−	0.354904i
$190$		0			0
$191$		−	4.24962i		−	0.307492i	−0.988110	−	0.153746i	$-0.950866\pi$
$191$		−	4.24962i		−	0.307492i	0.988110	−	0.153746i	$-0.0491337\pi$
$192$		0			0
$193$	−0.483847	−	1.32936i	−0.0348281	−	0.0956894i	0.921060	−	0.389421i	$-0.127325\pi$
$193$	−0.483847	−	1.32936i	−0.0348281	−	0.0956894i	−0.955888	+	0.293732i	$0.905103\pi$
$194$		0			0
$195$	−1.33296	−	0.235036i	−0.0954549	−	0.0168313i
$196$		0			0
$197$	8.55243	+	14.8132i	0.609335	+	1.05540i	0.991350	+	0.131243i	$0.0418970\pi$
$197$	8.55243	+	14.8132i	0.609335	+	1.05540i	−0.382015	+	0.924156i	$0.624770\pi$
$198$		0			0
$199$	15.4265	+	18.3846i	1.09356	+	1.30325i	0.949530	+	0.313677i	$0.101561\pi$
$199$	15.4265	+	18.3846i	1.09356	+	1.30325i	0.144027	+	0.989574i	$0.453995\pi$
$200$		0			0
$201$	2.28627	−	3.95994i	0.161261	−	0.279312i
$202$		0			0
$203$	−39.3570	−	14.3248i	−2.76232	−	1.00540i
$204$		0			0
$205$	3.27786	−	0.577975i	0.228936	−	0.0403675i
$206$		0			0
$207$	5.04162	−	6.00837i	0.350417	−	0.417610i
$208$		0			0
$209$	−8.33746	+	1.18802i	−0.576714	+	0.0821769i
$210$		0			0
$211$	4.76878	+	4.00148i	0.328296	+	0.275473i	0.792005	−	0.610514i	$-0.209037\pi$
$211$	4.76878	+	4.00148i	0.328296	+	0.275473i	−0.463709	+	0.885988i	$0.653482\pi$
$212$		0			0
$213$	2.43826	+	13.8280i	0.167067	+	0.947482i
$214$		0			0
$215$	0.283770	−	0.779651i	0.0193529	−	0.0531718i
$216$		0			0
$217$	−14.1188	−	8.15151i	−0.958449	−	0.553361i
$218$		0			0
$219$	9.01786	−	7.56688i	0.609371	−	0.511323i
$220$		0			0
$221$	−17.6779	+	10.2063i	−1.18914	+	0.686551i
$222$		0			0
$223$	−1.85361	+	10.5124i	−0.124127	+	0.703960i	0.857695	+	0.514158i	$0.171896\pi$
$223$	−1.85361	+	10.5124i	−0.124127	+	0.703960i	−0.981822	+	0.189801i	$0.939216\pi$
$224$		0			0
$225$	4.60858	−	1.67739i	0.307239	−	0.111826i
$226$		0			0
$227$	−6.02146			−0.399658			−0.199829	−	0.979831i	$-0.564039\pi$
$227$	−6.02146			−0.399658			−0.199829	+	0.979831i	$0.564039\pi$
$228$		0			0
$229$	1.01550			0.0671064			0.0335532	−	0.999437i	$-0.489318\pi$
$229$	1.01550			0.0671064			0.0335532	+	0.999437i	$0.489318\pi$
$230$		0			0
$231$	−8.85827	+	3.22414i	−0.582831	+	0.212133i
$232$		0			0
$233$	0.117889	−	0.668580i	0.00772315	−	0.0438002i	−0.980703	−	0.195505i	$-0.937365\pi$
$233$	0.117889	−	0.668580i	0.00772315	−	0.0438002i	0.988426	+	0.151705i	$0.0484764\pi$
$234$		0			0
$235$	2.38536	−	1.37719i	0.155604	−	0.0898378i
$236$		0			0
$237$	3.72483	−	3.12550i	0.241954	−	0.203023i
$238$		0			0
$239$	20.1517	+	11.6346i	1.30350	+	0.752578i	0.981003	−	0.193992i	$-0.0621435\pi$
$239$	20.1517	+	11.6346i	1.30350	+	0.752578i	0.322500	+	0.946570i	$0.395477\pi$
$240$		0			0
$241$	−3.09156	+	8.49400i	−0.199145	+	0.547147i	−0.998561	−	0.0536317i	$-0.982920\pi$
$241$	−3.09156	+	8.49400i	−0.199145	+	0.547147i	0.799416	+	0.600778i	$0.205143\pi$
$242$		0			0
$243$	0.173648	+	0.984808i	0.0111395	+	0.0631754i
$244$		0			0
$245$	3.98152	+	3.34089i	0.254370	+	0.213442i
$246$		0			0
$247$	−5.92973	−	18.1318i	−0.377300	−	1.15370i
$248$		0			0
$249$	−7.30047	+	8.70036i	−0.462648	+	0.551363i
$250$		0			0
$251$	23.1936	−	4.08966i	1.46397	−	0.258137i	0.615816	−	0.787890i	$-0.288827\pi$
$251$	23.1936	−	4.08966i	1.46397	−	0.258137i	0.848152	+	0.529753i	$0.177715\pi$
$252$		0			0
$253$	−14.2400	−	5.18294i	−0.895261	−	0.325848i
$254$		0			0
$255$	−0.721236	+	1.24922i	−0.0451656	+	0.0782291i
$256$		0			0
$257$	−7.52214	−	8.96454i	−0.469219	−	0.559193i	0.478588	−	0.878040i	$-0.341149\pi$
$257$	−7.52214	−	8.96454i	−0.469219	−	0.559193i	−0.947806	+	0.318847i	$0.896704\pi$
$258$		0			0
$259$	−2.86678	−	4.96540i	−0.178133	−	0.308535i
$260$		0			0
$261$	8.45368	+	1.49061i	0.523270	+	0.0922666i
$262$		0			0
$263$	2.36698	+	6.50322i	0.145954	+	0.401006i	0.991030	−	0.133641i	$-0.0426669\pi$
$263$	2.36698	+	6.50322i	0.145954	+	0.401006i	−0.845076	+	0.534647i	$0.820445\pi$
$264$		0			0
$265$			3.57800i			0.219795i
$266$		0			0
$267$			12.5565i			0.768445i
$268$		0			0
$269$	−0.0460123	−	0.126418i	−0.00280542	−	0.00770783i	0.938282	−	0.345871i	$-0.112417\pi$
$269$	−0.0460123	−	0.126418i	−0.00280542	−	0.00770783i	−0.941087	+	0.338163i	$0.890194\pi$
$270$		0			0
$271$	11.0397	+	1.94659i	0.670611	+	0.118247i	0.498579	−	0.866844i	$-0.333855\pi$
$271$	11.0397	+	1.94659i	0.670611	+	0.118247i	0.172033	+	0.985091i	$0.444967\pi$
$272$		0			0
$273$	−10.6768	−	18.4927i	−0.646186	−	1.11923i
$274$		0			0
$275$	−6.09075	−	7.25867i	−0.367286	−	0.437714i
$276$		0			0
$277$	−13.6972	+	23.7242i	−0.822982	+	1.42545i	0.0804693	+	0.996757i	$0.474358\pi$
$277$	−13.6972	+	23.7242i	−0.822982	+	1.42545i	−0.903452	+	0.428690i	$0.858975\pi$
$278$		0			0
$279$	3.13988	+	1.14282i	0.187980	+	0.0684190i
$280$		0			0
$281$	−3.81377	+	0.672470i	−0.227510	+	0.0401162i	−0.286241	−	0.958158i	$-0.592406\pi$
$281$	−3.81377	+	0.672470i	−0.227510	+	0.0401162i	0.0587307	+	0.998274i	$0.481295\pi$
$282$		0			0
$283$	14.7694	−	17.6015i	0.877949	−	1.04630i	−0.120613	−	0.992700i	$-0.538486\pi$
$283$	14.7694	−	17.6015i	0.877949	−	1.04630i	0.998563	−	0.0535994i	$-0.0170694\pi$
$284$		0			0
$285$	−1.00354	−	0.900119i	−0.0594443	−	0.0533184i
$286$		0			0
$287$	40.2252	+	33.7529i	2.37442	+	1.99237i
$288$		0			0
$289$	0.825554	+	4.68195i	0.0485620	+	0.275409i
$290$		0			0
$291$	5.32092	−	14.6191i	0.311918	−	0.856987i
$292$		0			0
$293$	−7.37553	−	4.25827i	−0.430883	−	0.248770i	0.268840	−	0.963185i	$-0.413360\pi$
$293$	−7.37553	−	4.25827i	−0.430883	−	0.248770i	−0.699723	+	0.714414i	$0.746693\pi$
$294$		0			0
$295$	−0.867579	+	0.727985i	−0.0505124	+	0.0423849i
$296$		0			0
$297$	1.67322	−	0.966032i	0.0970899	−	0.0560549i
$298$		0			0
$299$	5.96075	−	33.8051i	0.344719	−	1.95500i
$300$		0			0
$301$	12.3000	−	4.47684i	0.708960	−	0.258040i
$302$		0			0
$303$	1.83518			0.105428
$304$		0			0
$305$	0.0275845			0.00157948
$306$		0			0
$307$	−8.73075	+	3.17773i	−0.498290	+	0.181363i	−0.578925	−	0.815381i	$-0.696527\pi$
$307$	−8.73075	+	3.17773i	−0.498290	+	0.181363i	0.0806347	+	0.996744i	$0.474305\pi$
$308$		0			0
$309$	−1.67536	+	9.50144i	−0.0953080	+	0.540518i
$310$		0			0
$311$	11.9799	−	6.91660i	0.679318	−	0.392204i	−0.120280	−	0.992740i	$-0.538379\pi$
$311$	11.9799	−	6.91660i	0.679318	−	0.392204i	0.799598	+	0.600536i	$0.205046\pi$
$312$		0			0
$313$	11.5289	−	9.67394i	0.651655	−	0.546803i	−0.255918	−	0.966699i	$-0.582378\pi$
$313$	11.5289	−	9.67394i	0.651655	−	0.546803i	0.907573	+	0.419895i	$0.137933\pi$
$314$		0			0
$315$	−1.30680	−	0.754480i	−0.0736297	−	0.0425101i
$316$		0			0
$317$	6.66678	−	18.3168i	0.374443	−	1.02878i	−0.599180	−	0.800614i	$-0.704507\pi$
$317$	6.66678	−	18.3168i	0.374443	−	1.02878i	0.973623	−	0.228161i	$-0.0732712\pi$
$318$		0			0
$319$	−2.87996	−	16.3331i	−0.161247	−	0.914476i
$320$		0			0
$321$	8.50672	+	7.13798i	0.474799	+	0.398403i
$322$		0			0
$323$	−20.3194	−	0.670666i	−1.13060	−	0.0373168i
$324$		0			0
$325$	13.7968	−	16.4423i	0.765306	−	0.912057i
$326$		0			0
$327$	−10.1146	+	1.78347i	−0.559338	+	0.0986264i
$328$		0			0
$329$	40.8332	+	14.8621i	2.25121	+	0.819373i
$330$		0			0
$331$	5.61585	−	9.72694i	0.308675	−	0.534641i	−0.669398	−	0.742904i	$-0.733448\pi$
$331$	5.61585	−	9.72694i	0.308675	−	0.534641i	0.978073	+	0.208263i	$0.0667811\pi$
$332$		0			0
$333$	0.755353	+	0.900194i	0.0413931	+	0.0493304i
$334$		0			0
$335$	−0.707072	−	1.22469i	−0.0386315	−	0.0669117i
$336$		0			0
$337$	−12.3862	−	2.18402i	−0.674720	−	0.118971i	−0.174219	−	0.984707i	$-0.555740\pi$
$337$	−12.3862	−	2.18402i	−0.674720	−	0.118971i	−0.500502	+	0.865736i	$0.666851\pi$
$338$		0			0
$339$	−1.71073	−	4.70021i	−0.0929144	−	0.255280i
$340$		0			0
$341$		−	6.45578i		−	0.349600i
$342$		0			0
$343$			47.8436i			2.58331i
$344$		0			0
$345$	−0.829642	−	2.27942i	−0.0446664	−	0.122720i
$346$		0			0
$347$	2.60502	+	0.459335i	0.139845	+	0.0246584i	0.243132	−	0.969993i	$-0.421825\pi$
$347$	2.60502	+	0.459335i	0.139845	+	0.0246584i	−0.103288	+	0.994652i	$0.532936\pi$
$348$		0			0
$349$	2.38187	+	4.12552i	0.127499	+	0.220834i	0.922707	−	0.385502i	$-0.125972\pi$
$349$	2.38187	+	4.12552i	0.127499	+	0.220834i	−0.795208	+	0.606336i	$0.792639\pi$
$350$		0			0
$351$	2.81317	+	3.35260i	0.150156	+	0.178949i
$352$		0			0
$353$	−0.924355	+	1.60103i	−0.0491984	+	0.0852142i	−0.889576	−	0.456787i	$-0.849000\pi$
$353$	−0.924355	+	1.60103i	−0.0491984	+	0.0852142i	0.840377	+	0.542002i	$0.182333\pi$
$354$		0			0
$355$	4.08067	+	1.48524i	0.216579	+	0.0788285i
$356$		0			0
$357$	−22.4111	+	3.95169i	−1.18612	+	0.209146i
$358$		0			0
$359$	−7.12135	+	8.48690i	−0.375851	+	0.447921i	−0.920500	−	0.390743i	$-0.872218\pi$
$359$	−7.12135	+	8.48690i	−0.375851	+	0.447921i	0.544649	+	0.838664i	$0.316663\pi$
$360$		0			0
$361$	4.52597	−	18.4531i	0.238209	−	0.971214i
$362$		0			0
$363$	5.56694	+	4.67122i	0.292189	+	0.245175i
$364$		0			0
$365$	−0.632202	−	3.58540i	−0.0330910	−	0.187668i
$366$		0			0
$367$	9.71428	−	26.6898i	0.507081	−	1.39319i	−0.377153	−	0.926151i	$-0.623097\pi$
$367$	9.71428	−	26.6898i	0.507081	−	1.39319i	0.884234	−	0.467043i	$-0.154681\pi$
$368$		0			0
$369$	−9.32037	−	5.38112i	−0.485199	−	0.280130i
$370$		0			0
$371$	−43.2414	+	36.2838i	−2.24498	+	1.88376i
$372$		0			0
$373$	−17.1406	+	9.89614i	−0.887508	+	0.512403i	−0.873127	−	0.487494i	$-0.837911\pi$
$373$	−17.1406	+	9.89614i	−0.887508	+	0.512403i	−0.0143814	+	0.999897i	$0.504578\pi$
$374$		0			0
$375$	0.531903	−	3.01657i	0.0274674	−	0.155775i
$376$		0			0
$377$	35.3027	−	12.8491i	1.81818	−	0.661764i
$378$		0			0
$379$	−18.4749			−0.948991			−0.474496	−	0.880258i	$-0.657370\pi$
$379$	−18.4749			−0.948991			−0.474496	+	0.880258i	$0.657370\pi$
$380$		0			0
$381$	6.16077			0.315626
$382$		0			0
$383$	−8.81762	+	3.20935i	−0.450559	+	0.163990i	−0.557326	−	0.830294i	$-0.688173\pi$
$383$	−8.81762	+	3.20935i	−0.450559	+	0.163990i	0.106766	+	0.994284i	$0.465950\pi$
$384$		0			0
$385$	−0.506255	+	2.87112i	−0.0258011	+	0.146326i
$386$		0			0
$387$	−2.32332	+	1.34137i	−0.118101	+	0.0681856i
$388$		0			0
$389$	21.7806	−	18.2761i	1.10432	−	0.926634i	0.106611	−	0.994301i	$-0.466000\pi$
$389$	21.7806	−	18.2761i	1.10432	−	0.926634i	0.997708	+	0.0676671i	$0.0215556\pi$
$390$		0			0
$391$	−31.6814	−	18.2913i	−1.60220	−	0.925029i
$392$		0			0
$393$	−3.66774	+	10.0770i	−0.185013	+	0.508319i
$394$		0			0
$395$	−0.261131	−	1.48095i	−0.0131389	−	0.0745146i
$396$		0			0
$397$	28.2230	+	23.6819i	1.41647	+	1.18856i	0.953198	+	0.302346i	$0.0977698\pi$
$397$	28.2230	+	23.6819i	1.41647	+	1.18856i	0.463274	+	0.886215i	$0.346675\pi$
$398$		0			0
$399$	0.701578	−	21.2560i	0.0351228	−	1.06413i
$400$		0			0
$401$	−4.62124	+	5.50738i	−0.230774	+	0.275025i	−0.868988	−	0.494834i	$-0.835229\pi$
$401$	−4.62124	+	5.50738i	−0.230774	+	0.275025i	0.638214	+	0.769859i	$0.279673\pi$
$402$		0			0
$403$	14.4015	−	2.53937i	0.717388	−	0.126495i
$404$		0			0
$405$	0.290618	+	0.105776i	0.0144409	+	0.00525606i
$406$		0			0
$407$	1.13520	−	1.96623i	0.0562700	−	0.0974625i
$408$		0			0
$409$	1.20702	+	1.43847i	0.0596834	+	0.0711279i	0.795060	−	0.606531i	$-0.207439\pi$
$409$	1.20702	+	1.43847i	0.0596834	+	0.0711279i	−0.735377	+	0.677658i	$0.762995\pi$
$410$		0			0
$411$	3.94290	+	6.82930i	0.194489	+	0.336864i
$412$		0			0
$413$	−17.5959	−	3.10263i	−0.865837	−	0.152670i
$414$		0			0
$415$	1.20135	+	3.30069i	0.0589722	+	0.162025i
$416$		0			0
$417$			6.14351i			0.300849i
$418$		0			0
$419$			39.3106i			1.92045i	0.279226	+	0.960225i	$0.409922\pi$
$419$			39.3106i			1.92045i	−0.279226	+	0.960225i	$0.590078\pi$
$420$		0			0
$421$	−4.70770	−	12.9343i	−0.229439	−	0.630379i	0.770536	−	0.637396i	$-0.219989\pi$
$421$	−4.70770	−	12.9343i	−0.229439	−	0.630379i	−0.999975	+	0.00701724i	$0.997766\pi$
$422$		0			0
$423$	−8.77078	−	1.54653i	−0.426450	−	0.0751946i
$424$		0			0
$425$	−11.4373	−	19.8100i	−0.554790	−	0.960924i
$426$		0			0
$427$	0.279729	+	0.333368i	0.0135370	+	0.0161328i
$428$		0			0
$429$	4.22785	−	7.32285i	0.204122	−	0.353550i
$430$		0			0
$431$	−17.7538	−	6.46186i	−0.855171	−	0.311257i	−0.123024	−	0.992404i	$-0.539259\pi$
$431$	−17.7538	−	6.46186i	−0.855171	−	0.311257i	−0.732147	+	0.681147i	$0.761482\pi$
$432$		0			0
$433$	−28.8391	+	5.08511i	−1.38592	+	0.244375i	−0.816345	−	0.577565i	$-0.804003\pi$
$433$	−28.8391	+	5.08511i	−1.38592	+	0.244375i	−0.569574	+	0.821940i	$0.692892\pi$
$434$		0			0
$435$	1.70647	−	2.03369i	0.0818189	−	0.0975080i
$436$		0			0
$437$	22.8279	−	25.4507i	1.09201	−	1.21747i
$438$		0			0
$439$	−8.42847	−	7.07233i	−0.402269	−	0.337544i	0.419101	−	0.907940i	$-0.362345\pi$
$439$	−8.42847	−	7.07233i	−0.402269	−	0.337544i	−0.821370	+	0.570396i	$0.806790\pi$
$440$		0			0
$441$	−2.91829	−	16.5505i	−0.138966	−	0.788118i
$442$		0			0
$443$	−1.70401	+	4.68173i	−0.0809600	+	0.222436i	−0.973568	−	0.228398i	$-0.926651\pi$
$443$	−1.70401	+	4.68173i	−0.0809600	+	0.222436i	0.892608	+	0.450834i	$0.148873\pi$
$444$		0			0
$445$	3.36306	+	1.94167i	0.159425	+	0.0920438i
$446$		0			0
$447$	8.39890	−	7.04751i	0.397254	−	0.333336i
$448$		0			0
$449$	24.3367	−	14.0508i	1.14852	−	0.663099i	0.199995	−	0.979797i	$-0.435907\pi$
$449$	24.3367	−	14.0508i	1.14852	−	0.663099i	0.948527	+	0.316697i	$0.102574\pi$
$450$		0			0
$451$	−3.61072	+	20.4774i	−0.170022	+	0.964245i
$452$		0			0
$453$	1.56014	−	0.567844i	0.0733017	−	0.0266797i
$454$		0			0
$455$	−6.60398			−0.309599
$456$		0			0
$457$	19.8941			0.930607			0.465304	−	0.885151i	$-0.345945\pi$
$457$	19.8941			0.930607			0.465304	+	0.885151i	$0.345945\pi$
$458$		0			0
$459$	4.38286	−	1.59523i	0.204574	−	0.0744589i
$460$		0			0
$461$	1.56088	−	8.85219i	0.0726974	−	0.412287i	−0.926642	−	0.375945i	$-0.877318\pi$
$461$	1.56088	−	8.85219i	0.0726974	−	0.412287i	0.999339	−	0.0363424i	$-0.0115707\pi$
$462$		0			0
$463$	−5.60293	+	3.23485i	−0.260390	+	0.150336i	−0.624513	−	0.781015i	$-0.714702\pi$
$463$	−5.60293	+	3.23485i	−0.260390	+	0.150336i	0.364122	+	0.931351i	$0.381369\pi$
$464$		0			0
$465$	0.791621	−	0.664249i	0.0367105	−	0.0308038i
$466$		0			0
$467$	−2.56688	−	1.48199i	−0.118781	−	0.0685781i	0.439432	−	0.898276i	$-0.355180\pi$
$467$	−2.56688	−	1.48199i	−0.118781	−	0.0685781i	−0.558213	+	0.829697i	$0.688513\pi$
$468$		0			0
$469$	7.63046	−	20.9645i	0.352342	−	0.968051i
$470$		0			0
$471$	2.28210	+	12.9424i	0.105154	+	0.596356i
$472$		0			0
$473$	3.97058	+	3.33171i	0.182567	+	0.153192i
$474$		0			0
$475$	20.3186	−	6.64491i	0.932282	−	0.304889i
$476$		0			0
$477$	7.43656	−	8.86255i	0.340497	−	0.405788i
$478$		0			0
$479$	−23.4427	+	4.13358i	−1.07112	+	0.188868i	−0.681288	−	0.732016i	$-0.738580\pi$
$479$	−23.4427	+	4.13358i	−1.07112	+	0.188868i	−0.389837	+	0.920884i	$0.627469\pi$
$480$		0			0
$481$	4.83277	+	1.75898i	0.220355	+	0.0802028i
$482$		0			0
$483$	19.1344	−	33.1417i	0.870643	−	1.50800i
$484$		0			0
$485$	−3.09271	−	3.68574i	−0.140433	−	0.167361i
$486$		0			0
$487$	1.96250	+	3.39914i	0.0889292	+	0.154030i	0.907059	−	0.421004i	$-0.138322\pi$
$487$	1.96250	+	3.39914i	0.0889292	+	0.154030i	−0.818130	+	0.575034i	$0.804989\pi$
$488$		0			0
$489$	8.57215	+	1.51150i	0.387646	+	0.0683525i
$490$		0			0
$491$	12.0457	+	33.0952i	0.543613	+	1.49356i	0.842191	+	0.539179i	$0.181265\pi$
$491$	12.0457	+	33.0952i	0.543613	+	1.49356i	−0.298578	+	0.954385i	$0.596512\pi$
$492$		0			0
$493$		−	40.0374i		−	1.80319i
$494$		0			0
$495$		−	0.597528i		−	0.0268569i
$496$		0			0
$497$	23.4316	+	64.3778i	1.05105	+	2.88774i
$498$		0			0
$499$	42.8558	+	7.55664i	1.91849	+	0.338281i	0.998553	−	0.0537847i	$-0.0171285\pi$
$499$	42.8558	+	7.55664i	1.91849	+	0.338281i	0.919937	+	0.392066i	$0.128240\pi$
$500$		0			0
$501$	6.54995	+	11.3448i	0.292630	+	0.506850i
$502$		0			0
$503$	−17.5162	−	20.8750i	−0.781008	−	0.930769i	0.217970	−	0.975955i	$-0.430056\pi$
$503$	−17.5162	−	20.8750i	−0.781008	−	0.930769i	−0.998979	+	0.0451861i	$0.985612\pi$
$504$		0			0
$505$	0.283782	−	0.491525i	0.0126281	−	0.0218726i
$506$		0			0
$507$	5.78271	+	2.10474i	0.256819	+	0.0934746i
$508$		0			0
$509$	29.8085	−	5.25604i	1.32124	−	0.232970i	0.531836	−	0.846847i	$-0.321502\pi$
$509$	29.8085	−	5.25604i	1.32124	−	0.232970i	0.789401	+	0.613877i	$0.210391\pi$
$510$		0			0
$511$	36.9197	−	43.9992i	1.63323	−	1.94641i
$512$		0			0
$513$	0.614895	+	4.31531i	0.0271483	+	0.190526i
$514$		0			0
$515$	2.28575	+	1.91797i	0.100722	+	0.0845159i
$516$		0			0
$517$	2.98799	+	16.9457i	0.131411	+	0.745272i
$518$		0			0
$519$	2.34767	−	6.45016i	0.103051	−	0.283131i
$520$		0			0
$521$	−32.1911	−	18.5856i	−1.41032	−	0.814248i	−0.414901	−	0.909867i	$-0.636184\pi$
$521$	−32.1911	−	18.5856i	−1.41032	−	0.814248i	−0.995418	+	0.0956187i	$0.969517\pi$
$522$		0			0
$523$	−2.31904	+	1.94591i	−0.101405	+	0.0850886i	−0.692080	−	0.721820i	$-0.743306\pi$
$523$	−2.31904	+	1.94591i	−0.101405	+	0.0850886i	0.590676	+	0.806909i	$0.298861\pi$
$524$		0			0
$525$	20.7230	−	11.9645i	0.904428	−	0.522172i
$526$		0			0
$527$	2.70625	−	15.3479i	0.117886	−	0.668566i
$528$		0			0
$529$	36.1955	−	13.1741i	1.57372	−	0.572786i
$530$		0			0
$531$	3.66200			0.158917
$532$		0			0
$533$	−47.1010			−2.04017
$534$		0			0
$535$	3.22723	−	1.17462i	0.139525	−	0.0507831i
$536$		0			0
$537$	0.0176221	−	0.0999401i	0.000760451	−	0.00431273i
$538$		0			0
$539$	−28.1197	+	16.2349i	−1.21120	+	0.699288i
$540$		0			0
$541$	7.33536	−	6.15510i	0.315372	−	0.264628i	−0.471336	−	0.881954i	$-0.656228\pi$
$541$	7.33536	−	6.15510i	0.315372	−	0.264628i	0.786708	+	0.617325i	$0.211784\pi$
$542$		0			0
$543$	−15.8185	−	9.13281i	−0.678837	−	0.391926i
$544$		0			0
$545$	−1.08639	+	2.98482i	−0.0465357	+	0.127856i
$546$		0			0
$547$	0.835008	+	4.73557i	0.0357024	+	0.202478i	0.997441	−	0.0714891i	$-0.0227751\pi$
$547$	0.835008	+	4.73557i	0.0357024	+	0.202478i	−0.961739	+	0.273967i	$0.911664\pi$
$548$		0			0
$549$	−0.0683255	−	0.0573319i	−0.00291606	−	0.00244687i
$550$		0			0
$551$	36.6143	+	7.70946i	1.55982	+	0.328434i
$552$		0			0
$553$	15.2497	−	18.1739i	0.648483	−	0.772831i
$554$		0			0
$555$	0.357907	−	0.0631087i	0.0151923	−	0.00267881i
$556$		0			0
$557$	−14.1305	−	5.14308i	−0.598728	−	0.217919i	0.0248360	−	0.999692i	$-0.492094\pi$
$557$	−14.1305	−	5.14308i	−0.598728	−	0.217919i	−0.623564	+	0.781772i	$0.714316\pi$
$558$		0			0
$559$	−5.87051	+	10.1680i	−0.248296	+	0.430062i
$560$		0			0
$561$	−5.79242	−	6.90314i	−0.244556	−	0.291451i
$562$		0			0
$563$	−0.563769	−	0.976476i	−0.0237600	−	0.0411536i	0.853901	−	0.520436i	$-0.174230\pi$
$563$	−0.563769	−	0.976476i	−0.0237600	−	0.0411536i	−0.877661	+	0.479282i	$0.840897\pi$
$564$		0			0
$565$	−1.52342	−	0.268620i	−0.0640906	−	0.0113009i
$566$		0			0
$567$	1.66876	+	4.58487i	0.0700812	+	0.192546i
$568$		0			0
$569$		−	8.03677i		−	0.336919i	−0.985709	−	0.168460i	$-0.946121\pi$
$569$		−	8.03677i		−	0.336919i	0.985709	−	0.168460i	$-0.0538792\pi$
$570$		0			0
$571$		−	8.88393i		−	0.371781i	−0.982570	−	0.185890i	$-0.940483\pi$
$571$		−	8.88393i		−	0.371781i	0.982570	−	0.185890i	$-0.0595169\pi$
$572$		0			0
$573$	1.45346	+	3.99334i	0.0607190	+	0.166824i
$574$		0			0
$575$	37.8822	+	6.67966i	1.57980	+	0.278561i
$576$		0			0
$577$	−10.0755	−	17.4513i	−0.419450	−	0.726508i	0.576434	−	0.817143i	$-0.304444\pi$
$577$	−10.0755	−	17.4513i	−0.419450	−	0.726508i	−0.995884	+	0.0906351i	$0.971110\pi$
$578$		0			0
$579$	0.909335	+	1.08370i	0.0377907	+	0.0450372i
$580$		0			0
$581$	−27.7073	+	47.9905i	−1.14949	+	1.99098i
$582$		0			0
$583$	−21.0045	−	7.64501i	−0.869917	−	0.316624i
$584$		0			0
$585$	1.33296	−	0.235036i	0.0551109	−	0.00971754i
$586$		0			0
$587$	14.9114	−	17.7707i	0.615458	−	0.733474i	−0.364825	−	0.931076i	$-0.618871\pi$
$587$	14.9114	−	17.7707i	0.615458	−	0.733474i	0.980282	+	0.197602i	$0.0633155\pi$
$588$		0			0
$589$	13.5146	+	5.43023i	0.556861	+	0.223749i
$590$		0			0
$591$	−13.1031	−	10.9948i	−0.538989	−	0.452265i
$592$		0			0
$593$	2.99379	+	16.9786i	0.122940	+	0.697229i	0.982510	+	0.186211i	$0.0596207\pi$
$593$	2.99379	+	16.9786i	0.122940	+	0.697229i	−0.859570	+	0.511019i	$0.829268\pi$
$594$		0			0
$595$	−2.40714	+	6.61355i	−0.0986829	+	0.271129i
$596$		0			0
$597$	−20.7841	−	11.9997i	−0.850636	−	0.491115i
$598$		0			0
$599$	−23.4281	+	19.6585i	−0.957246	+	0.803225i	−0.980503	−	0.196504i	$-0.937041\pi$
$599$	−23.4281	+	19.6585i	−0.957246	+	0.803225i	0.0232565	+	0.999730i	$0.492597\pi$
$600$		0			0
$601$	26.6795	−	15.4034i	1.08828	−	0.628318i	0.155161	−	0.987889i	$-0.450410\pi$
$601$	26.6795	−	15.4034i	1.08828	−	0.628318i	0.933118	+	0.359571i	$0.117077\pi$
$602$		0			0
$603$	−0.794013	+	4.50307i	−0.0323347	+	0.183379i
$604$		0			0
$605$	2.11196	−	0.768689i	0.0858632	−	0.0312517i
$606$		0			0
$607$	−26.8497			−1.08979			−0.544897	−	0.838503i	$-0.683431\pi$
$607$	−26.8497			−1.08979			−0.544897	+	0.838503i	$0.683431\pi$
$608$		0			0
$609$	41.8828			1.69718
$610$		0			0
$611$	−36.6269	+	13.3311i	−1.48177	+	0.539319i
$612$		0			0
$613$	−4.87921	+	27.6714i	−0.197069	+	1.11764i	0.712372	+	0.701802i	$0.247621\pi$
$613$	−4.87921	+	27.6714i	−0.197069	+	1.11764i	−0.909441	+	0.415833i	$0.863490\pi$
$614$		0			0
$615$	−2.88250	+	1.66421i	−0.116234	+	0.0671075i
$616$		0			0
$617$	−4.01928	+	3.37258i	−0.161810	+	0.135775i	−0.720098	−	0.693873i	$-0.755903\pi$
$617$	−4.01928	+	3.37258i	−0.161810	+	0.135775i	0.558287	+	0.829648i	$0.311459\pi$
$618$		0			0
$619$	−24.7817	−	14.3077i	−0.996062	−	0.575077i	−0.0889816	−	0.996033i	$-0.528361\pi$
$619$	−24.7817	−	14.3077i	−0.996062	−	0.575077i	−0.907081	+	0.420956i	$0.861695\pi$
$620$		0			0
$621$	−2.68259	+	7.37035i	−0.107649	+	0.295762i
$622$		0			0
$623$	10.6385	+	60.3338i	0.426222	+	2.41722i
$624$		0			0
$625$	18.0591	+	15.1534i	0.722363	+	0.606134i
$626$		0			0
$627$	7.42832	−	3.96795i	0.296659	−	0.158465i
$628$		0			0
$629$	3.52307	−	4.19863i	0.140474	−	0.167410i
$630$		0			0
$631$	−2.25046	+	0.396817i	−0.0895893	+	0.0157970i	−0.218263	−	0.975890i	$-0.570039\pi$
$631$	−2.25046	+	0.396817i	−0.0895893	+	0.0157970i	0.128674	+	0.991687i	$0.458928\pi$
$632$		0			0
$633$	−5.84977	−	2.12914i	−0.232508	−	0.0846258i
$634$		0			0
$635$	0.952668	−	1.65007i	0.0378055	−	0.0654810i
$636$		0			0
$637$	−47.2775	−	56.3431i	−1.87320	−	2.23239i
$638$		0			0
$639$	−7.02068	−	12.1602i	−0.277734	−	0.481049i
$640$		0			0
$641$	−19.3186	−	3.40639i	−0.763039	−	0.134544i	−0.221432	−	0.975176i	$-0.571073\pi$
$641$	−19.3186	−	3.40639i	−0.763039	−	0.134544i	−0.541607	+	0.840632i	$0.682184\pi$
$642$		0			0
$643$	−12.4853	−	34.3032i	−0.492374	−	1.35279i	−0.898502	−	0.438970i	$-0.855344\pi$
$643$	−12.4853	−	34.3032i	−0.492374	−	1.35279i	0.406128	−	0.913816i	$-0.366879\pi$
$644$		0			0
$645$			0.829687i			0.0326689i
$646$		0			0
$647$			33.1703i			1.30406i	0.758193	+	0.652030i	$0.226082\pi$
$647$			33.1703i			1.30406i	−0.758193	+	0.652030i	$0.773918\pi$
$648$		0			0
$649$	−2.41987	−	6.64853i	−0.0949882	−	0.260978i
$650$		0			0
$651$	16.0554	+	2.83099i	0.629259	+	0.110955i
$652$		0			0
$653$	−11.3118	−	19.5927i	−0.442666	−	0.766720i	0.555220	−	0.831703i	$-0.312634\pi$
$653$	−11.3118	−	19.5927i	−0.442666	−	0.766720i	−0.997886	+	0.0649835i	$0.979301\pi$
$654$		0			0
$655$	2.13182	+	2.54061i	0.0832972	+	0.0992697i
$656$		0			0
$657$	−5.88599	+	10.1948i	−0.229634	+	0.397738i
$658$		0			0
$659$	−39.1922	−	14.2648i	−1.52671	−	0.555678i	−0.563899	−	0.825844i	$-0.690699\pi$
$659$	−39.1922	−	14.2648i	−1.52671	−	0.555678i	−0.962814	+	0.270166i	$0.912922\pi$
$660$		0			0
$661$	−23.4769	+	4.13960i	−0.913144	+	0.161012i	−0.610431	−	0.792070i	$-0.709004\pi$
$661$	−23.4769	+	4.13960i	−0.913144	+	0.161012i	−0.302713	+	0.953082i	$0.597892\pi$
$662$		0			0
$663$	13.1210	−	15.6370i	0.509577	−	0.607290i
$664$		0			0
$665$	−5.58461	−	3.47482i	−0.216562	−	0.134748i
$666$		0			0
$667$	51.5764	+	43.2777i	1.99705	+	1.67572i
$668$		0			0
$669$	−1.85361	−	10.5124i	−0.0716648	−	0.406431i
$670$		0			0
$671$	−0.0589389	+	0.161933i	−0.00227531	+	0.00625137i
$672$		0			0
$673$	31.3177	+	18.0813i	1.20721	+	0.696982i	0.962148	−	0.272527i	$-0.0878593\pi$
$673$	31.3177	+	18.0813i	1.20721	+	0.696982i	0.245059	+	0.969508i	$0.421193\pi$
$674$		0			0
$675$	−3.75695	+	3.15246i	−0.144605	+	0.121338i
$676$		0			0
$677$	−13.1741	+	7.60605i	−0.506320	+	0.292324i	−0.731320	−	0.682035i	$-0.761095\pi$
$677$	−13.1741	+	7.60605i	−0.506320	+	0.292324i	0.225000	+	0.974359i	$0.427762\pi$
$678$		0			0
$679$	13.1809	−	74.7528i	0.505838	−	2.86875i
$680$		0			0
$681$	5.65832	−	2.05946i	0.216827	−	0.0789186i
$682$		0			0
$683$	−0.959626			−0.0367191			−0.0183595	−	0.999831i	$-0.505844\pi$
$683$	−0.959626			−0.0367191			−0.0183595	+	0.999831i	$0.505844\pi$
$684$		0			0
$685$	2.43883			0.0931830
$686$		0			0
$687$	−0.954261	+	0.347323i	−0.0364073	+	0.0132512i
$688$		0			0
$689$	8.79230	−	49.8636i	0.334960	−	1.89965i
$690$		0			0
$691$	0.625152	−	0.360932i	0.0237819	−	0.0137305i	−0.488062	−	0.872809i	$-0.662296\pi$
$691$	0.625152	−	0.360932i	0.0237819	−	0.0137305i	0.511844	+	0.859079i	$0.328963\pi$
$692$		0			0
$693$	7.22132	−	6.05941i	0.274315	−	0.230178i
$694$		0			0
$695$	1.64545	+	0.949998i	0.0624153	+	0.0360355i
$696$		0			0
$697$	−17.1682	+	47.1693i	−0.650293	+	1.78667i
$698$		0			0
$699$	0.117889	+	0.668580i	0.00445896	+	0.0252880i
$700$		0			0
$701$	6.66025	+	5.58862i	0.251554	+	0.211079i	0.759841	−	0.650109i	$-0.225277\pi$
$701$	6.66025	+	5.58862i	0.251554	+	0.211079i	−0.508287	+	0.861188i	$0.669721\pi$
$702$		0			0
$703$	3.16127	+	4.03033i	0.119230	+	0.152007i
$704$		0			0
$705$	−1.77048	+	2.10997i	−0.0666801	+	0.0794662i
$706$		0			0
$707$	8.81802	−	1.55485i	0.331636	−	0.0584763i
$708$		0			0
$709$	−21.7859	−	7.92940i	−0.818185	−	0.297795i	−0.101185	−	0.994868i	$-0.532263\pi$
$709$	−21.7859	−	7.92940i	−0.818185	−	0.297795i	−0.717001	+	0.697073i	$0.754486\pi$
$710$		0			0
$711$	−2.43121	+	4.21098i	−0.0911774	+	0.157924i
$712$		0			0
$713$	16.8460	+	20.0763i	0.630888	+	0.751863i
$714$		0			0
$715$	−1.30754	−	2.26473i	−0.0488993	−	0.0846961i
$716$		0			0
$717$	−22.9156	−	4.04064i	−0.855800	−	0.150901i
$718$		0			0
$719$	−0.209863	−	0.576593i	−0.00782656	−	0.0215033i	0.935718	−	0.352749i	$-0.114753\pi$
$719$	−0.209863	−	0.576593i	−0.00782656	−	0.0215033i	−0.943544	+	0.331246i	$0.892531\pi$
$720$		0			0
$721$			47.0738i			1.75312i
$722$		0			0
$723$		−	9.03912i		−	0.336169i
$724$		0			0
$725$	14.3988	+	39.5605i	0.534760	+	1.46924i
$726$		0			0
$727$	11.7510	+	2.07202i	0.435821	+	0.0768470i	0.387254	−	0.921973i	$-0.373424\pi$
$727$	11.7510	+	2.07202i	0.435821	+	0.0768470i	0.0485666	+	0.998820i	$0.484535\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$		0			0
$731$	8.04298	+	9.58525i	0.297480	+	0.354523i
$732$		0			0
$733$	−7.25030	+	12.5579i	−0.267796	+	0.463836i	−0.968292	−	0.249820i	$-0.919629\pi$
$733$	−7.25030	+	12.5579i	−0.267796	+	0.463836i	0.700496	+	0.713656i	$0.252962\pi$
$734$		0			0
$735$	−4.88406	−	1.77765i	−0.180151	−	0.0655697i
$736$		0			0
$737$	8.70023	−	1.53408i	0.320477	−	0.0565087i
$738$		0			0
$739$	13.4373	−	16.0140i	0.494300	−	0.589084i	−0.460005	−	0.887916i	$-0.652153\pi$
$739$	13.4373	−	16.0140i	0.494300	−	0.589084i	0.954306	+	0.298832i	$0.0965970\pi$
$740$		0			0
$741$	11.7736	+	15.0102i	0.432512	+	0.551414i
$742$		0			0
$743$	21.1026	+	17.7072i	0.774179	+	0.649613i	0.941775	−	0.336242i	$-0.109156\pi$
$743$	21.1026	+	17.7072i	0.774179	+	0.649613i	−0.167597	+	0.985856i	$0.553601\pi$
$744$		0			0
$745$	−0.588810	−	3.33931i	−0.0215723	−	0.122343i
$746$		0			0
$747$	3.88450	−	10.6726i	0.142126	−	0.390489i
$748$		0			0
$749$	46.9224	+	27.0906i	1.71451	+	0.989870i
$750$		0			0
$751$	8.44207	−	7.08374i	0.308055	−	0.258489i	−0.475632	−	0.879644i	$-0.657781\pi$
$751$	8.44207	−	7.08374i	0.308055	−	0.258489i	0.783688	+	0.621155i	$0.213336\pi$
$752$		0			0
$753$	−20.3961	+	11.7757i	−0.743276	+	0.429130i
$754$		0			0
$755$	0.0891629	−	0.505668i	0.00324497	−	0.0184031i
$756$		0			0
$757$	4.41383	−	1.60650i	0.160423	−	0.0583893i	−0.260560	−	0.965458i	$-0.583907\pi$
$757$	4.41383	−	1.60650i	0.160423	−	0.0583893i	0.420983	+	0.907068i	$0.361685\pi$
$758$		0			0
$759$	15.1539			0.550051
$760$		0			0
$761$	−17.2111			−0.623903			−0.311951	−	0.950098i	$-0.600983\pi$
$761$	−17.2111			−0.623903			−0.311951	+	0.950098i	$0.600983\pi$
$762$		0			0
$763$	−47.0895	+	17.1392i	−1.70475	+	0.620479i
$764$		0			0
$765$	0.250483	−	1.42056i	0.00905622	−	0.0513604i
$766$		0			0
$767$	13.8796	−	8.01339i	0.501163	−	0.289347i
$768$		0			0
$769$	−33.4711	+	28.0856i	−1.20700	+	1.01279i	−0.207596	+	0.978215i	$0.566564\pi$
$769$	−33.4711	+	28.0856i	−1.20700	+	1.01279i	−0.999402	+	0.0345770i	$0.988992\pi$
$770$		0			0
$771$	10.1346	+	5.85119i	0.364987	+	0.210725i
$772$		0			0
$773$	3.71914	−	10.2183i	0.133768	−	0.367525i	−0.854665	−	0.519179i	$-0.826238\pi$
$773$	3.71914	−	10.2183i	0.133768	−	0.367525i	0.988434	+	0.151654i	$0.0484599\pi$
$774$		0			0
$775$	2.84563	+	16.1384i	0.102218	+	0.579708i
$776$		0			0
$777$	4.39215	+	3.68546i	0.157568	+	0.132215i
$778$		0			0
$779$	−39.8307	−	24.7832i	−1.42708	−	0.887950i
$780$		0			0
$781$	−17.4381	+	20.7819i	−0.623983	+	0.743634i
$782$		0			0
$783$	−8.45368	+	1.49061i	−0.302110	+	0.0532701i
$784$		0			0
$785$	3.81933	+	1.39012i	0.136318	+	0.0496156i
$786$		0			0
$787$	16.3719	−	28.3569i	0.583594	−	1.01082i	−0.411455	−	0.911430i	$-0.634979\pi$
$787$	16.3719	−	28.3569i	0.583594	−	1.01082i	0.995049	−	0.0993850i	$-0.0316875\pi$
$788$		0			0
$789$	−4.44846	−	5.30147i	−0.158369	−	0.188737i
$790$		0			0
$791$	−12.2023	−	21.1350i	−0.433864	−	0.751475i
$792$		0			0
$793$	−0.384422	−	0.0677840i	−0.0136512	−	0.00240708i
$794$		0			0
$795$	−1.22375	−	3.36222i	−0.0434019	−	0.119246i
$796$		0			0
$797$		−	29.9518i		−	1.06095i	−0.847701	−	0.530474i	$-0.822014\pi$
$797$		−	29.9518i		−	1.06095i	0.847701	−	0.530474i	$-0.177986\pi$
$798$		0			0
$799$			41.5392i			1.46955i
$800$		0			0
$801$	−4.29457	−	11.7992i	−0.151741	−	0.416906i
$802$		0			0
$803$	22.3987	+	3.94949i	0.790433	+	0.139375i
$804$		0			0
$805$	−5.91766	−	10.2497i	−0.208570	−	0.361254i
$806$		0			0
$807$	0.0864749	+	0.103057i	0.00304406	+	0.00362777i
$808$		0			0
$809$	6.12900	−	10.6157i	0.215484	−	0.373230i	−0.737938	−	0.674868i	$-0.764200\pi$
$809$	6.12900	−	10.6157i	0.215484	−	0.373230i	0.953422	+	0.301639i	$0.0975337\pi$
$810$		0			0
$811$	17.4324	+	6.34486i	0.612133	+	0.222798i	0.629436	−	0.777052i	$-0.283286\pi$
$811$	17.4324	+	6.34486i	0.612133	+	0.222798i	−0.0173033	+	0.999850i	$0.505508\pi$
$812$		0			0
$813$	−11.0397	+	1.94659i	−0.387178	+	0.0682699i
$814$		0			0
$815$	1.73038	−	2.06219i	0.0606127	−	0.0722353i
$816$		0			0
$817$	−10.3145	+	5.50963i	−0.360858	+	0.192758i
$818$		0			0
$819$	16.3577	+	13.7258i	0.571585	+	0.479617i
$820$		0			0
$821$	−5.28063	−	29.9479i	−0.184295	−	1.04519i	−0.926857	−	0.375413i	$-0.877501\pi$
$821$	−5.28063	−	29.9479i	−0.184295	−	1.04519i	0.742562	−	0.669777i	$-0.233610\pi$
$822$		0			0
$823$	−1.26735	+	3.48202i	−0.0441770	+	0.121375i	−0.959819	−	0.280618i	$-0.909460\pi$
$823$	−1.26735	+	3.48202i	−0.0441770	+	0.121375i	0.915642	+	0.401994i	$0.131683\pi$
$824$		0			0
$825$	8.20605	+	4.73776i	0.285698	+	0.164948i
$826$		0			0
$827$	10.7645	−	9.03246i	0.374317	−	0.314089i	−0.436149	−	0.899874i	$-0.643658\pi$
$827$	10.7645	−	9.03246i	0.374317	−	0.314089i	0.810467	+	0.585785i	$0.199214\pi$
$828$		0			0
$829$	12.3753	−	7.14490i	0.429813	−	0.248153i	−0.269454	−	0.963013i	$-0.586843\pi$
$829$	12.3753	−	7.14490i	0.429813	−	0.248153i	0.699267	+	0.714861i	$0.253510\pi$
$830$		0			0
$831$	4.75697	−	26.9781i	0.165018	−	0.935861i
$832$		0			0
$833$	−73.6573	+	26.8091i	−2.55208	+	0.928879i
$834$		0			0
$835$	4.05139			0.140204
$836$		0			0
$837$	−3.34139			−0.115495
$838$		0			0
$839$	−32.4254	+	11.8019i	−1.11945	+	0.407447i	−0.834452	−	0.551081i	$-0.814215\pi$
$839$	−32.4254	+	11.8019i	−1.11945	+	0.407447i	−0.284999	+	0.958528i	$0.591993\pi$
$840$		0			0
$841$	−7.75975	+	44.0077i	−0.267578	+	1.51751i
$842$		0			0
$843$	3.35377	−	1.93630i	0.115510	−	0.0666897i
$844$		0			0
$845$	1.45793	−	1.22335i	0.0501543	−	0.0420844i
$846$		0			0
$847$	30.7068	+	17.7286i	1.05510	+	0.609161i
$848$		0			0
$849$	−7.85863	+	21.5914i	−0.269707	+	0.741015i
$850$		0			0
$851$	1.60050	+	9.07687i	0.0548644	+	0.311151i
$852$		0			0
$853$	−20.3538	−	17.0789i	−0.696902	−	0.584770i	0.223988	−	0.974592i	$-0.428092\pi$
$853$	−20.3538	−	17.0789i	−0.696902	−	0.584770i	−0.920890	+	0.389821i	$0.872537\pi$
$854$		0			0
$855$	1.25087	+	0.502605i	0.0427790	+	0.0171887i
$856$		0			0
$857$	11.2820	−	13.4453i	0.385384	−	0.459283i	−0.538122	−	0.842867i	$-0.680866\pi$
$857$	11.2820	−	13.4453i	0.385384	−	0.459283i	0.923506	+	0.383584i	$0.125310\pi$
$858$		0			0
$859$	−8.34593	+	1.47161i	−0.284759	+	0.0502107i	−0.314203	−	0.949356i	$-0.601737\pi$
$859$	−8.34593	+	1.47161i	−0.284759	+	0.0502107i	0.0294441	+	0.999566i	$0.490626\pi$
$860$		0			0
$861$	−49.3435	−	17.9596i	−1.68162	−	0.612060i
$862$		0			0
$863$	−3.29230	+	5.70244i	−0.112071	+	0.194113i	−0.916605	−	0.399793i	$-0.869082\pi$
$863$	−3.29230	+	5.70244i	−0.112071	+	0.194113i	0.804534	+	0.593907i	$0.202415\pi$
$864$		0			0
$865$	−1.36455	−	1.62620i	−0.0463960	−	0.0552926i
$866$		0			0
$867$	−2.37709	−	4.11723i	−0.0807301	−	0.139829i
$868$		0			0
$869$	9.25178	+	1.63134i	0.313845	+	0.0553394i
$870$		0			0
$871$	6.84443	+	18.8049i	0.231915	+	0.637180i
$872$		0			0
$873$			15.5573i			0.526536i
$874$		0			0
$875$		−	14.9453i		−	0.505242i
$876$		0			0
$877$	−14.1004	−	38.7406i	−0.476138	−	1.30818i	−0.912747	−	0.408526i	$-0.866043\pi$
$877$	−14.1004	−	38.7406i	−0.476138	−	1.30818i	0.436609	−	0.899651i	$-0.356179\pi$
$878$		0			0
$879$	8.38714	+	1.47888i	0.282891	+	0.0498814i
$880$		0			0
$881$	19.8429	+	34.3689i	0.668525	+	1.15792i	0.978317	+	0.207114i	$0.0664072\pi$
$881$	19.8429	+	34.3689i	0.668525	+	1.15792i	−0.309792	+	0.950804i	$0.600259\pi$
$882$		0			0
$883$	1.92126	+	2.28967i	0.0646557	+	0.0770536i	0.797403	−	0.603447i	$-0.206207\pi$
$883$	1.92126	+	2.28967i	0.0646557	+	0.0770536i	−0.732747	+	0.680501i	$0.761762\pi$
$884$		0			0
$885$	0.566272	−	0.980811i	0.0190350	−	0.0329696i
$886$		0			0
$887$	15.6929	+	5.71174i	0.526915	+	0.191781i	0.591760	−	0.806114i	$-0.298433\pi$
$887$	15.6929	+	5.71174i	0.526915	+	0.191781i	−0.0648453	+	0.997895i	$0.520655\pi$
$888$		0			0
$889$	29.6025	−	5.21971i	0.992835	−	0.175064i
$890$		0			0
$891$	−1.24191	+	1.48005i	−0.0416055	+	0.0495834i
$892$		0			0
$893$	−37.9878	−	7.99865i	−1.27121	−	0.267664i
$894$		0			0
$895$	−0.0240424	−	0.0201740i	−0.000803650	−	0.000674342i
$896$		0			0
$897$	5.96075	+	33.8051i	0.199024	+	1.12872i
$898$		0			0
$899$	−9.81009	+	26.9530i	−0.327185	+	0.898933i
$900$		0			0
$901$	−46.7311	−	26.9802i	−1.55684	−	0.898842i
$902$		0			0
$903$	−10.0271	+	8.41370i	−0.333679	+	0.279990i
$904$		0			0
$905$	−4.89217	+	2.82450i	−0.162621	+	0.0938894i
$906$		0			0
$907$	−6.35444	+	36.0378i	−0.210996	+	1.19662i	0.676726	+	0.736235i	$0.263398\pi$
$907$	−6.35444	+	36.0378i	−0.210996	+	1.19662i	−0.887722	+	0.460380i	$0.847713\pi$
$908$		0			0
$909$	−1.72450	+	0.627668i	−0.0571982	+	0.0208184i
$910$		0			0
$911$	−39.5093			−1.30900			−0.654500	−	0.756062i	$-0.727121\pi$
$911$	−39.5093			−1.30900			−0.654500	+	0.756062i	$0.727121\pi$
$912$		0			0
$913$	−21.9434			−0.726222
$914$		0			0
$915$	−0.0259210	+	0.00943446i	−0.000856921	+	0.000311894i
$916$		0			0
$917$	−9.08570	+	51.5276i	−0.300036	+	1.70159i
$918$		0			0
$919$	−10.6452	+	6.14598i	−0.351151	+	0.202737i	−0.665192	−	0.746672i	$-0.731650\pi$
$919$	−10.6452	+	6.14598i	−0.351151	+	0.202737i	0.314041	+	0.949409i	$0.398317\pi$
$920$		0			0
$921$	7.11737	−	5.97218i	0.234525	−	0.196790i
$922$		0			0
$923$	−53.2191	−	30.7261i	−1.75173	−	1.01136i
$924$		0			0
$925$	−1.97113	+	5.41564i	−0.0648104	+	0.178065i
$926$		0			0
$927$	−1.67536	−	9.50144i	−0.0550261	−	0.312068i
$928$		0			0
$929$	−14.0512	−	11.7903i	−0.461003	−	0.386828i	0.382497	−	0.923957i	$-0.375064\pi$
$929$	−14.0512	−	11.7903i	−0.461003	−	0.386828i	−0.843500	+	0.537129i	$0.819509\pi$
$930$		0			0
$931$	−10.3338	−	72.5222i	−0.338677	−	2.37682i
$932$		0			0
$933$	−8.89181	+	10.5968i	−0.291105	+	0.346925i
$934$		0			0
$935$	−2.74461	+	0.483949i	−0.0897584	+	0.0158268i
$936$		0			0
$937$	22.4279	+	8.16308i	0.732686	+	0.266676i	0.681302	−	0.732003i	$-0.261414\pi$
$937$	22.4279	+	8.16308i	0.732686	+	0.266676i	0.0513849	+	0.998679i	$0.483636\pi$
$938$		0			0
$939$	−7.52499	+	13.0337i	−0.245569	+	0.425337i
$940$		0			0
$941$	−8.40953	−	10.0221i	−0.274143	−	0.326711i	0.611353	−	0.791358i	$-0.290626\pi$
$941$	−8.40953	−	10.0221i	−0.274143	−	0.326711i	−0.885496	+	0.464647i	$0.846181\pi$
$942$		0			0
$943$	−42.2061	−	73.1031i	−1.37442	−	2.38056i
$944$		0			0
$945$	1.48604	+	0.262028i	0.0483407	+	0.00852377i
$946$		0			0
$947$	1.00032	+	2.74836i	0.0325061	+	0.0893098i	0.954884	−	0.296979i	$-0.0959791\pi$
$947$	1.00032	+	2.74836i	0.0325061	+	0.0893098i	−0.922378	+	0.386289i	$0.873757\pi$
$948$		0			0
$949$			51.5202i			1.67242i
$950$		0			0
$951$			19.4924i			0.632083i
$952$		0			0
$953$	12.8554	+	35.3200i	0.416429	+	1.14413i	0.953711	+	0.300726i	$0.0972289\pi$
$953$	12.8554	+	35.3200i	0.416429	+	1.14413i	−0.537282	+	0.843403i	$0.680549\pi$
$954$		0			0
$955$	1.29431	+	0.228222i	0.0418829	+	0.00738508i
$956$		0			0
$957$	8.29251	+	14.3630i	0.268059	+	0.464291i
$958$		0			0
$959$	24.7317	+	29.4741i	0.798629	+	0.951769i
$960$		0			0
$961$	9.91756	−	17.1777i	0.319921	−	0.554120i
$962$		0			0
$963$	−10.4350	−	3.79804i	−0.336264	−	0.122390i
$964$		0			0
$965$	0.430868	−	0.0759737i	0.0138701	−	0.00244568i
$966$		0			0
$967$	−28.7153	+	34.2216i	−0.923423	+	1.10049i	0.0712544	+	0.997458i	$0.477300\pi$
$967$	−28.7153	+	34.2216i	−0.923423	+	1.10049i	−0.994678	+	0.103035i	$0.967145\pi$
$968$		0			0
$969$	19.3234	−	6.31944i	0.620757	−	0.203010i
$970$		0			0
$971$	3.13072	+	2.62699i	0.100470	+	0.0843040i	0.691639	−	0.722244i	$-0.256889\pi$
$971$	3.13072	+	2.62699i	0.100470	+	0.0843040i	−0.591169	+	0.806548i	$0.701333\pi$
$972$		0			0
$973$	5.20509	+	29.5195i	0.166867	+	0.946352i
$974$		0			0
$975$	−7.34110	+	20.1695i	−0.235103	+	0.645941i
$976$		0			0
$977$	39.2562	+	22.6646i	1.25592	+	0.725104i	0.972278	−	0.233827i	$-0.0751251\pi$
$977$	39.2562	+	22.6646i	1.25592	+	0.725104i	0.283639	+	0.958931i	$0.408458\pi$
$978$		0			0
$979$	−18.5842	+	15.5940i	−0.593953	+	0.498386i
$980$		0			0
$981$	8.89462	−	5.13531i	0.283983	−	0.163958i
$982$		0			0
$983$	−7.11745	+	40.3651i	−0.227011	+	1.28745i	0.631791	+	0.775139i	$0.282320\pi$
$983$	−7.11745	+	40.3651i	−0.227011	+	1.28745i	−0.858802	+	0.512307i	$0.828791\pi$
$984$		0			0
$985$	−4.97097	+	1.80929i	−0.158388	+	0.0576487i
$986$		0			0
$987$	−43.4538			−1.38315
$988$		0			0
$989$	−21.0417			−0.669087
$990$		0			0
$991$	−43.1089	+	15.6904i	−1.36940	+	0.498421i	−0.918948	−	0.394380i	$-0.870959\pi$
$991$	−43.1089	+	15.6904i	−1.36940	+	0.498421i	−0.450452	+	0.892801i	$0.648737\pi$
$992$		0			0
$993$	−1.95036	+	11.0611i	−0.0618929	+	0.351012i
$994$		0			0
$995$	−6.42788	+	3.71114i	−0.203777	+	0.117651i
$996$		0			0
$997$	−7.05855	+	5.92283i	−0.223547	+	0.187578i	−0.747682	−	0.664057i	$-0.768833\pi$
$997$	−7.05855	+	5.92283i	−0.223547	+	0.187578i	0.524135	+	0.851635i	$0.324389\pi$
$998$		0			0
$999$	−1.01768	−	0.587560i	−0.0321981	−	0.0185896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.ci.f.79.2	yes	18
4.3	odd	2		912.2.ci.e.79.2	✓	18
19.13	odd	18		912.2.ci.e.127.2	yes	18
76.51	even	18	inner	912.2.ci.f.127.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.ci.e.79.2	✓	18	4.3	odd	2
912.2.ci.e.127.2	yes	18	19.13	odd	18
912.2.ci.f.79.2	yes	18	1.1	even	1	trivial
912.2.ci.f.127.2	yes	18	76.51	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.0537040 + 0.304570i) q^{5} +(-4.22544 + 2.43956i) q^{7} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{3} +(-0.0537040 + 0.304570i) q^{5} +(-4.22544 + 2.43956i) q^{7} +(0.766044 - 0.642788i) q^{9} +(-1.67322 - 0.966032i) q^{11} +(1.49685 - 4.11257i) q^{13} +(-0.0537040 - 0.304570i) q^{15} +(-3.57294 - 2.99805i) q^{17} +(3.42972 - 2.69017i) q^{19} +(3.13624 - 3.73762i) q^{21} +(7.72421 - 1.36199i) q^{23} +(4.60858 + 1.67739i) q^{25} +(-0.500000 + 0.866025i) q^{27} +(5.51775 + 6.57580i) q^{29} +(1.67069 + 2.89373i) q^{31} +(1.90271 + 0.335499i) q^{33} +(-0.516095 - 1.41796i) q^{35} +1.17512i q^{37} +4.37651i q^{39} +(-3.68090 - 10.1132i) q^{41} +(-2.64198 - 0.465852i) q^{43} +(0.154634 + 0.267835i) q^{45} +(-5.72472 - 6.82246i) q^{47} +(8.40289 - 14.5542i) q^{49} +(4.38286 + 1.59523i) q^{51} +(11.3935 - 2.00898i) q^{53} +(0.384083 - 0.457733i) q^{55} +(-2.30279 + 3.70097i) q^{57} +(2.80526 + 2.35389i) q^{59} +(-0.0154881 - 0.0878376i) q^{61} +(-1.66876 + 4.58487i) q^{63} +(1.17218 + 0.676759i) q^{65} +(-3.50277 + 2.93917i) q^{67} +(-6.79255 + 3.92168i) q^{69} +(2.43826 - 13.8280i) q^{71} +(-11.0620 + 4.02625i) q^{73} -4.90435 q^{75} +9.42677 q^{77} +(-4.56918 + 1.66304i) q^{79} +(0.173648 - 0.984808i) q^{81} +(9.83589 - 5.67875i) q^{83} +(1.10500 - 0.927204i) q^{85} +(-7.43404 - 4.29205i) q^{87} +(4.29457 - 11.7992i) q^{89} +(3.70800 + 21.0291i) q^{91} +(-2.55965 - 2.14780i) q^{93} +(0.635157 + 1.18906i) q^{95} +(-10.0001 + 11.9176i) q^{97} +(-1.90271 + 0.335499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q+O(q^{10}) \) 18 * q	\( 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) \) 18 * q + 3 * q^13 + 12 * q^17 + 3 * q^19 + 15 * q^21 + 6 * q^23 + 24 * q^25 - 9 * q^27 + 12 * q^29 + 12 * q^31 + 6 * q^33 - 36 * q^35 + 12 * q^41 + 21 * q^43 - 6 * q^45 - 24 * q^47 - 3 * q^49 - 6 * q^51 + 6 * q^53 + 12 * q^55 + 54 * q^59 - 24 * q^61 + 12 * q^63 + 36 * q^65 - 21 * q^67 + 15 * q^73 + 18 * q^75 - 60 * q^79 + 54 * q^85 + 18 * q^87 + 36 * q^89 + 24 * q^91 + 24 * q^93 - 6 * q^95 - 6 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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