LMFDB - Embedded newform 684.2.bo.e.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(73,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("684.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.bo (of order $9$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 27 x^{10} + 309 x^{8} + 42 x^{7} + 2059 x^{6} + 1245 x^{5} + 8226 x^{4} + \cdots + 16129 $ x^12 - 3x^11 + 27x^10 + 309x^8 + 42x^7 + 2059x^6 + 1245x^5 + 8226x^4 + 2250x^3 + 14496x^2 + 6096x + 16129
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			541.2
Root			$0.731383 - 1.26679i$ of defining polynomial
Character	$\chi$	$=$	684.541
Dual form			684.2.bo.e.397.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.14060 + 1.14308i) q^{5} +(0.794193 - 1.37558i) q^{7} +O(q^{10})$	$q+(3.14060 + 1.14308i) q^{5} +(0.794193 - 1.37558i) q^{7} +(2.93229 + 5.07887i) q^{11} +(-0.411545 - 0.345327i) q^{13} +(-0.110839 - 0.628599i) q^{17} +(-3.41216 - 2.71240i) q^{19} +(-0.444394 + 0.161746i) q^{23} +(4.72648 + 3.96599i) q^{25} +(0.266355 - 1.51057i) q^{29} +(-1.63641 + 2.83435i) q^{31} +(4.06664 - 3.41232i) q^{35} +8.60894 q^{37} +(6.43798 - 5.40211i) q^{41} +(-10.5495 - 3.83970i) q^{43} +(-1.98663 + 11.2667i) q^{47} +(2.23852 + 3.87722i) q^{49} +(-3.40684 + 1.23999i) q^{53} +(3.40356 + 19.3025i) q^{55} +(-1.13313 - 6.42629i) q^{59} +(11.2912 - 4.10968i) q^{61} +(-0.897758 - 1.55496i) q^{65} +(0.920357 - 5.21960i) q^{67} +(-6.30259 - 2.29395i) q^{71} +(-6.37537 + 5.34957i) q^{73} +9.31520 q^{77} +(11.0329 - 9.25768i) q^{79} +(-0.0384940 + 0.0666736i) q^{83} +(0.370441 - 2.10087i) q^{85} +(12.8415 + 10.7753i) q^{89} +(-0.801871 + 0.291857i) q^{91} +(-7.61573 - 12.4190i) q^{95} +(-2.00723 - 11.3836i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{5} - 9 q^{7}+O(q^{10}) $ 12 * q + 6 * q^5 - 9 * q^7	$ 12 q + 6 q^{5} - 9 q^{7} + 9 q^{11} - 3 q^{13} - 12 q^{17} + 9 q^{19} - 15 q^{23} + 12 q^{25} + 24 q^{29} - 6 q^{31} + 42 q^{35} + 12 q^{37} - 6 q^{41} - 39 q^{43} + 3 q^{47} - 21 q^{49} - 18 q^{53} + 45 q^{55} + 33 q^{61} + 33 q^{65} - 27 q^{67} - 6 q^{71} - 24 q^{73} + 18 q^{79} - 3 q^{83} + 39 q^{85} + 15 q^{89} + 18 q^{91} + 30 q^{95} - 15 q^{97}+O(q^{100}) $ 12 * q + 6 * q^5 - 9 * q^7 + 9 * q^11 - 3 * q^13 - 12 * q^17 + 9 * q^19 - 15 * q^23 + 12 * q^25 + 24 * q^29 - 6 * q^31 + 42 * q^35 + 12 * q^37 - 6 * q^41 - 39 * q^43 + 3 * q^47 - 21 * q^49 - 18 * q^53 + 45 * q^55 + 33 * q^61 + 33 * q^65 - 27 * q^67 - 6 * q^71 - 24 * q^73 + 18 * q^79 - 3 * q^83 + 39 * q^85 + 15 * q^89 + 18 * q^91 + 30 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$1$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	3.14060	+	1.14308i	1.40452	+	0.511202i	0.929516	−	0.368783i	$-0.120225\pi$
$5$	3.14060	+	1.14308i	1.40452	+	0.511202i	0.475001	+	0.879985i	$0.342448\pi$
$6$		0			0
$7$	0.794193	−	1.37558i	0.300177	−	0.519921i	−0.675999	−	0.736902i	$-0.736288\pi$
$7$	0.794193	−	1.37558i	0.300177	−	0.519921i	0.976176	+	0.216981i	$0.0696211\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.93229	+	5.07887i	0.884118	+	1.53134i	0.846722	+	0.532036i	$0.178573\pi$
$11$	2.93229	+	5.07887i	0.884118	+	1.53134i	0.0373959	+	0.999301i	$0.488094\pi$
$12$		0			0
$13$	−0.411545	−	0.345327i	−0.114142	−	0.0957764i	0.583930	−	0.811804i	$-0.301514\pi$
$13$	−0.411545	−	0.345327i	−0.114142	−	0.0957764i	−0.698072	+	0.716027i	$0.745959\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.110839	−	0.628599i	−0.0268824	−	0.152458i	0.968412	−	0.249356i	$-0.0802189\pi$
$17$	−0.110839	−	0.628599i	−0.0268824	−	0.152458i	−0.995294	+	0.0968983i	$0.969108\pi$
$18$		0			0
$19$	−3.41216	−	2.71240i	−0.782804	−	0.622268i
$19$	−3.41216	−	2.71240i	−0.782804	−	0.622268i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.444394	+	0.161746i	−0.0926626	+	0.0337264i	−0.387935	−	0.921687i	$-0.626812\pi$
$23$	−0.444394	+	0.161746i	−0.0926626	+	0.0337264i	0.295273	+	0.955413i	$0.404589\pi$
$24$		0			0
$25$	4.72648	+	3.96599i	0.945296	+	0.793197i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.266355	−	1.51057i	0.0494608	−	0.280506i	−0.950039	−	0.312131i	$-0.898957\pi$
$29$	0.266355	−	1.51057i	0.0494608	−	0.280506i	0.999500	+	0.0316250i	$0.0100682\pi$
$30$		0			0
$31$	−1.63641	+	2.83435i	−0.293909	+	0.509065i	−0.974730	−	0.223384i	$-0.928290\pi$
$31$	−1.63641	+	2.83435i	−0.293909	+	0.509065i	0.680822	+	0.732449i	$0.261623\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.06664	−	3.41232i	0.687388	−	0.576787i
$36$		0			0
$37$	8.60894			1.41530			0.707650	−	0.706563i	$-0.249755\pi$
$37$	8.60894			1.41530			0.707650	+	0.706563i	$0.249755\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.43798	−	5.40211i	1.00544	−	0.843667i	0.0177143	−	0.999843i	$-0.494361\pi$
$41$	6.43798	−	5.40211i	1.00544	−	0.843667i	0.987729	+	0.156176i	$0.0499166\pi$
$42$		0			0
$43$	−10.5495	−	3.83970i	−1.60878	−	0.585549i	−0.627584	−	0.778549i	$-0.715956\pi$
$43$	−10.5495	−	3.83970i	−1.60878	−	0.585549i	−0.981199	+	0.192999i	$0.938178\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.98663	+	11.2667i	−0.289780	+	1.64342i	0.397914	+	0.917423i	$0.369734\pi$
$47$	−1.98663	+	11.2667i	−0.289780	+	1.64342i	−0.687694	+	0.726001i	$0.741377\pi$
$48$		0			0
$49$	2.23852	+	3.87722i	0.319788	+	0.553889i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.40684	+	1.23999i	−0.467966	+	0.170326i	−0.565231	−	0.824933i	$-0.691213\pi$
$53$	−3.40684	+	1.23999i	−0.467966	+	0.170326i	0.0972648	+	0.995259i	$0.468991\pi$
$54$		0			0
$55$	3.40356	+	19.3025i	0.458935	+	2.60275i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.13313	−	6.42629i	−0.147521	−	0.836631i	−0.965309	−	0.261112i	$-0.915911\pi$
$59$	−1.13313	−	6.42629i	−0.147521	−	0.836631i	0.817788	−	0.575520i	$-0.195200\pi$
$60$		0			0
$61$	11.2912	−	4.10968i	1.44570	−	0.526190i	0.504310	−	0.863523i	$-0.331747\pi$
$61$	11.2912	−	4.10968i	1.44570	−	0.526190i	0.941385	+	0.337333i	$0.109525\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.897758	−	1.55496i	−0.111353	−	0.192869i
$66$		0			0
$67$	0.920357	−	5.21960i	0.112439	−	0.637676i	−0.875547	−	0.483133i	$-0.839499\pi$
$67$	0.920357	−	5.21960i	0.112439	−	0.637676i	0.987986	−	0.154542i	$-0.0493903\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.30259	−	2.29395i	−0.747979	−	0.272242i	−0.0602241	−	0.998185i	$-0.519182\pi$
$71$	−6.30259	−	2.29395i	−0.747979	−	0.272242i	−0.687755	+	0.725943i	$0.741404\pi$
$72$		0			0
$73$	−6.37537	+	5.34957i	−0.746181	+	0.626120i	−0.934490	−	0.355990i	$-0.884144\pi$
$73$	−6.37537	+	5.34957i	−0.746181	+	0.626120i	0.188309	+	0.982110i	$0.439699\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.31520			1.06157
$78$		0			0
$79$	11.0329	−	9.25768i	1.24130	−	1.04157i	0.243874	−	0.969807i	$-0.421582\pi$
$79$	11.0329	−	9.25768i	1.24130	−	1.04157i	0.997422	−	0.0717640i	$-0.0228628\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.0384940	+	0.0666736i	−0.00422526	+	0.00731837i	−0.868130	−	0.496336i	$-0.834678\pi$
$83$	−0.0384940	+	0.0666736i	−0.00422526	+	0.00731837i	0.863905	+	0.503655i	$0.168012\pi$
$84$		0			0
$85$	0.370441	−	2.10087i	0.0401800	−	0.227872i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	12.8415	+	10.7753i	1.36119	+	1.14218i	0.975611	+	0.219505i	$0.0704442\pi$
$89$	12.8415	+	10.7753i	1.36119	+	1.14218i	0.385583	+	0.922673i	$0.374000\pi$
$90$		0			0
$91$	−0.801871	+	0.291857i	−0.0840589	+	0.0305949i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.61573	−	12.4190i	−0.781357	−	1.27416i
$96$		0			0
$97$	−2.00723	−	11.3836i	−0.203803	−	1.15582i	−0.899312	−	0.437307i	$-0.855932\pi$
$97$	−2.00723	−	11.3836i	−0.203803	−	1.15582i	0.695509	−	0.718517i	$-0.255179\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.65500	−	1.38871i	−0.164679	−	0.138182i	0.556724	−	0.830697i	$-0.312058\pi$
$101$	−1.65500	−	1.38871i	−0.164679	−	0.138182i	−0.721403	+	0.692515i	$0.756502\pi$
$102$		0			0
$103$	−5.16704	−	8.94958i	−0.509124	−	0.881828i	−0.999944	−	0.0105673i	$-0.996636\pi$
$103$	−5.16704	−	8.94958i	−0.509124	−	0.881828i	0.490821	−	0.871261i	$-0.336697\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.11533	+	10.5921i	−0.591191	+	1.02397i	0.402881	+	0.915252i	$0.368009\pi$
$107$	−6.11533	+	10.5921i	−0.591191	+	1.02397i	−0.994072	+	0.108721i	$0.965325\pi$
$108$		0			0
$109$	−17.3640	−	6.31998i	−1.66317	−	0.605344i	−0.672313	−	0.740267i	$-0.734699\pi$
$109$	−17.3640	−	6.31998i	−1.66317	−	0.605344i	−0.990856	+	0.134924i	$0.956921\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−15.3154			−1.44075			−0.720376	−	0.693583i	$-0.756031\pi$
$113$	−15.3154			−1.44075			−0.720376	+	0.693583i	$0.756031\pi$
$114$		0			0
$115$	−1.58055			−0.147387
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.952717	−	0.346761i	−0.0873355	−	0.0317875i
$120$		0			0
$121$	−11.6966	+	20.2591i	−1.06333	+	1.84174i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.95513	+	3.38638i	0.174872	+	0.302887i
$126$		0			0
$127$	−8.57402	−	7.19445i	−0.760821	−	0.638404i	0.177520	−	0.984117i	$-0.443193\pi$
$127$	−8.57402	−	7.19445i	−0.760821	−	0.638404i	−0.938340	+	0.345713i	$0.887637\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.76476	−	10.0084i	−0.154188	−	0.874442i	−0.959525	−	0.281625i	$-0.909127\pi$
$131$	−1.76476	−	10.0084i	−0.154188	−	0.874442i	0.805337	−	0.592817i	$-0.201984\pi$
$132$		0			0
$133$	−6.44105	+	2.53954i	−0.558510	+	0.220206i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.38041	+	1.59434i	−0.374244	+	0.136214i	−0.522292	−	0.852767i	$-0.674923\pi$
$137$	−4.38041	+	1.59434i	−0.374244	+	0.136214i	0.148049	+	0.988980i	$0.452701\pi$
$138$		0			0
$139$	1.41839	+	1.19017i	0.120306	+	0.100949i	0.700956	−	0.713205i	$-0.252757\pi$
$139$	1.41839	+	1.19017i	0.120306	+	0.100949i	−0.580650	+	0.814153i	$0.697201\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.547103	−	3.10278i	0.0457511	−	0.259467i
$144$		0			0
$145$	2.56322	−	4.43963i	0.212864	−	0.368691i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.2575	+	8.60709i	−0.840330	+	0.705121i	−0.957638	−	0.287975i	$-0.907018\pi$
$149$	−10.2575	+	8.60709i	−0.840330	+	0.705121i	0.117308	+	0.993096i	$0.462574\pi$
$150$		0			0
$151$	0.201035			0.0163600			0.00818000	−	0.999967i	$-0.497396\pi$
$151$	0.201035			0.0163600			0.00818000	+	0.999967i	$0.497396\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.37922	+	7.03100i	−0.673035	+	0.564744i
$156$		0			0
$157$	−3.39105	−	1.23424i	−0.270635	−	0.0985032i	0.203138	−	0.979150i	$-0.434886\pi$
$157$	−3.39105	−	1.23424i	−0.270635	−	0.0985032i	−0.473773	+	0.880647i	$0.657108\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.130439	+	0.739759i	−0.0102801	+	0.0583011i
$162$		0			0
$163$	−3.73885	−	6.47588i	−0.292849	−	0.507230i	0.681633	−	0.731694i	$-0.261270\pi$
$163$	−3.73885	−	6.47588i	−0.292849	−	0.507230i	−0.974482	+	0.224464i	$0.927937\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−15.5991	+	5.67762i	−1.20710	+	0.439347i	−0.865696	−	0.500571i	$-0.833124\pi$
$167$	−15.5991	+	5.67762i	−1.20710	+	0.439347i	−0.341401	+	0.939918i	$0.610901\pi$
$168$		0			0
$169$	−2.20731	−	12.5183i	−0.169793	−	0.962944i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.07599	−	23.1161i	−0.309892	−	1.75748i	−0.599534	−	0.800349i	$-0.704647\pi$
$173$	−4.07599	−	23.1161i	−0.309892	−	1.75748i	0.289642	−	0.957135i	$-0.406464\pi$
$174$		0			0
$175$	9.20927	−	3.35190i	0.696156	−	0.253380i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.42820	−	4.20577i	−0.181493	−	0.314354i	0.760896	−	0.648873i	$-0.224759\pi$
$179$	−2.42820	−	4.20577i	−0.181493	−	0.314354i	−0.942389	+	0.334519i	$0.891426\pi$
$180$		0			0
$181$	−2.99830	+	17.0042i	−0.222862	+	1.26391i	0.643869	+	0.765135i	$0.277328\pi$
$181$	−2.99830	+	17.0042i	−0.222862	+	1.26391i	−0.866731	+	0.498776i	$0.833783\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	27.0372	+	9.84073i	1.98781	+	0.723505i
$186$		0			0
$187$	2.86756	−	2.40617i	0.209697	−	0.175957i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.44491			0.538695			0.269347	−	0.963043i	$-0.413192\pi$
$191$	7.44491			0.538695			0.269347	+	0.963043i	$0.413192\pi$
$192$		0			0
$193$	15.6395	−	13.1231i	1.12575	−	0.944619i	0.126872	−	0.991919i	$-0.459506\pi$
$193$	15.6395	−	13.1231i	1.12575	−	0.944619i	0.998881	+	0.0473006i	$0.0150619\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.67376	−	4.63108i	0.190497	−	0.329951i	−0.754918	−	0.655819i	$-0.772323\pi$
$197$	2.67376	−	4.63108i	0.190497	−	0.329951i	0.945415	+	0.325868i	$0.105657\pi$
$198$		0			0
$199$	−4.10286	+	23.2685i	−0.290844	+	1.64946i	0.392785	+	0.919630i	$0.371512\pi$
$199$	−4.10286	+	23.2685i	−0.290844	+	1.64946i	−0.683629	+	0.729829i	$0.739600\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.86638	−	1.56608i	−0.130994	−	0.109917i
$204$		0			0
$205$	26.3942	−	9.60669i	1.84345	−	0.670960i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.77050	−	25.2835i	0.260811	−	1.74889i
$210$		0			0
$211$	1.85776	+	10.5359i	0.127893	+	0.725319i	0.979547	+	0.201215i	$0.0644888\pi$
$211$	1.85776	+	10.5359i	0.127893	+	0.725319i	−0.851654	+	0.524105i	$0.824400\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−28.7426	−	24.1179i	−1.96023	−	1.64483i
$216$		0			0
$217$	2.59926	+	4.50205i	0.176449	+	0.305619i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.171457	+	0.296972i	−0.0115335	+	0.0199765i
$222$		0			0
$223$	14.3289	+	5.21528i	0.959533	+	0.349241i	0.773850	−	0.633369i	$-0.218328\pi$
$223$	14.3289	+	5.21528i	0.959533	+	0.349241i	0.185682	+	0.982610i	$0.440550\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.57171			−0.568924			−0.284462	−	0.958687i	$-0.591815\pi$
$227$	−8.57171			−0.568924			−0.284462	+	0.958687i	$0.591815\pi$
$228$		0			0
$229$	−2.84667			−0.188113			−0.0940565	−	0.995567i	$-0.529983\pi$
$229$	−2.84667			−0.188113			−0.0940565	+	0.995567i	$0.529983\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.77030	−	1.00831i	−0.181488	−	0.0660563i	0.249678	−	0.968329i	$-0.419675\pi$
$233$	−2.77030	−	1.00831i	−0.181488	−	0.0660563i	−0.431166	+	0.902273i	$0.641898\pi$
$234$		0			0
$235$	−19.1180	+	33.1134i	−1.24712	+	2.16008i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.01605	+	1.75985i	0.0657227	+	0.113835i	0.897014	−	0.442001i	$-0.145731\pi$
$239$	1.01605	+	1.75985i	0.0657227	+	0.113835i	−0.831292	+	0.555837i	$0.812398\pi$
$240$		0			0
$241$	−3.09070	−	2.59341i	−0.199090	−	0.167056i	0.537793	−	0.843077i	$-0.319258\pi$
$241$	−3.09070	−	2.59341i	−0.199090	−	0.167056i	−0.736882	+	0.676021i	$0.763703\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.59828	+	14.7356i	0.165998	+	0.941423i
$246$		0			0
$247$	0.467592	+	2.29459i	0.0297522	+	0.146001i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	20.5061	−	7.46363i	1.29434	−	0.471100i	0.399188	−	0.916869i	$-0.369292\pi$
$251$	20.5061	−	7.46363i	1.29434	−	0.471100i	0.895148	+	0.445769i	$0.147070\pi$
$252$		0			0
$253$	−2.12458	−	1.78273i	−0.133571	−	0.112080i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.35395	+	7.67861i	−0.0844568	+	0.478978i	0.913016	+	0.407924i	$0.133747\pi$
$257$	−1.35395	+	7.67861i	−0.0844568	+	0.478978i	−0.997472	+	0.0710539i	$0.977364\pi$
$258$		0			0
$259$	6.83715	−	11.8423i	0.424840	−	0.735844i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.72819	−	3.96743i	0.291553	−	0.244642i	−0.485265	−	0.874367i	$-0.661277\pi$
$263$	4.72819	−	3.96743i	0.291553	−	0.244642i	0.776818	+	0.629725i	$0.216832\pi$
$264$		0			0
$265$	−12.1169			−0.744337
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−15.5692	+	13.0641i	−0.949273	+	0.796535i	−0.979175	−	0.203018i	$-0.934925\pi$
$269$	−15.5692	+	13.0641i	−0.949273	+	0.796535i	0.0299018	+	0.999553i	$0.490481\pi$
$270$		0			0
$271$	−14.2800	−	5.19748i	−0.867445	−	0.315724i	−0.130313	−	0.991473i	$-0.541598\pi$
$271$	−14.2800	−	5.19748i	−0.867445	−	0.315724i	−0.737132	+	0.675749i	$0.763821\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.28334	+	35.6346i	−0.378899	+	2.14885i
$276$		0			0
$277$	−5.57590	−	9.65775i	−0.335024	−	0.580278i	0.648466	−	0.761244i	$-0.275411\pi$
$277$	−5.57590	−	9.65775i	−0.335024	−	0.580278i	−0.983489	+	0.180966i	$0.942078\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.3274	−	7.39858i	1.21263	−	0.441362i	0.345016	−	0.938597i	$-0.387873\pi$
$281$	20.3274	−	7.39858i	1.21263	−	0.441362i	0.867616	+	0.497235i	$0.165651\pi$
$282$		0			0
$283$	1.57180	+	8.91413i	0.0934340	+	0.529890i	0.995216	+	0.0976992i	$0.0311483\pi$
$283$	1.57180	+	8.91413i	0.0934340	+	0.529890i	−0.901782	+	0.432191i	$0.857741\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.31804	−	13.1463i	−0.136830	−	0.776000i
$288$		0			0
$289$	15.5919	−	5.67500i	0.917172	−	0.333823i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.19065	+	12.4546i	0.420082	+	0.727604i	0.995947	−	0.0899410i	$-0.0286678\pi$
$293$	7.19065	+	12.4546i	0.420082	+	0.727604i	−0.575865	+	0.817545i	$0.695335\pi$
$294$		0			0
$295$	3.78709	−	21.4776i	0.220493	−	1.25048i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.238743	+	0.0868955i	0.0138069	+	0.00502530i
$300$		0			0
$301$	−13.6602	+	11.4622i	−0.787358	+	0.660672i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	40.1589			2.29949
$306$		0			0
$307$	−7.01456	+	5.88591i	−0.400342	+	0.335927i	−0.820626	−	0.571466i	$-0.806375\pi$
$307$	−7.01456	+	5.88591i	−0.400342	+	0.335927i	0.420284	+	0.907393i	$0.361930\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.58942	+	16.6094i	−0.543766	+	0.941831i	0.454917	+	0.890534i	$0.349669\pi$
$311$	−9.58942	+	16.6094i	−0.543766	+	0.941831i	−0.998683	+	0.0512971i	$0.983664\pi$
$312$		0			0
$313$	3.56368	−	20.2106i	0.201431	−	1.14237i	−0.701527	−	0.712643i	$-0.747498\pi$
$313$	3.56368	−	20.2106i	0.201431	−	1.14237i	0.902958	−	0.429729i	$-0.141391\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.61869	+	3.03644i	0.203246	+	0.170543i	0.738729	−	0.674002i	$-0.235426\pi$
$317$	3.61869	+	3.03644i	0.203246	+	0.170543i	−0.535484	+	0.844546i	$0.679871\pi$
$318$		0			0
$319$	8.45303	−	3.07665i	0.473279	−	0.172259i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.32681	+	2.44552i	−0.0738259	+	0.136073i
$324$		0			0
$325$	−0.575595	−	3.26436i	−0.0319283	−	0.181074i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	13.9206	+	11.6807i	0.767465	+	0.643980i
$330$		0			0
$331$	−5.55149	−	9.61546i	−0.305137	−	0.528513i	0.672155	−	0.740411i	$-0.265369\pi$
$331$	−5.55149	−	9.61546i	−0.305137	−	0.528513i	−0.977292	+	0.211898i	$0.932036\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.85691	−	15.3406i	0.483905	−	0.838147i
$336$		0			0
$337$	15.5000	+	5.64155i	0.844340	+	0.307315i	0.727731	−	0.685863i	$-0.240575\pi$
$337$	15.5000	+	5.64155i	0.844340	+	0.307315i	0.116610	+	0.993178i	$0.462797\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−19.1937			−1.03940
$342$		0			0
$343$	18.2299			0.984325
$344$		0			0
$345$		0			0
$346$		0			0
$347$	30.9107	+	11.2506i	1.65937	+	0.603963i	0.990264	−	0.139201i	$-0.0444535\pi$
$347$	30.9107	+	11.2506i	1.65937	+	0.603963i	0.669110	+	0.743164i	$0.266676\pi$
$348$		0			0
$349$	−3.48915	+	6.04339i	−0.186770	+	0.323495i	−0.944172	−	0.329454i	$-0.893135\pi$
$349$	−3.48915	+	6.04339i	−0.186770	+	0.323495i	0.757401	+	0.652949i	$0.226469\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.301479	−	0.522178i	−0.0160461	−	0.0277927i	0.857891	−	0.513832i	$-0.171775\pi$
$353$	−0.301479	−	0.522178i	−0.0160461	−	0.0277927i	−0.873937	+	0.486039i	$0.838441\pi$
$354$		0			0
$355$	−17.1717	−	14.4088i	−0.911379	−	0.764738i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.22536	+	12.6207i	0.117450	+	0.666093i	0.985508	+	0.169629i	$0.0542571\pi$
$359$	2.22536	+	12.6207i	0.117450	+	0.666093i	−0.868058	+	0.496463i	$0.834632\pi$
$360$		0			0
$361$	4.28574	+	18.5103i	0.225565	+	0.974228i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−26.1375	+	9.51326i	−1.36810	+	0.497947i
$366$		0			0
$367$	1.52052	+	1.27587i	0.0793705	+	0.0665997i	0.681610	−	0.731716i	$-0.261280\pi$
$367$	1.52052	+	1.27587i	0.0793705	+	0.0665997i	−0.602239	+	0.798316i	$0.705725\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.999982	+	5.67118i	−0.0519165	+	0.294433i
$372$		0			0
$373$	−8.36606	+	14.4904i	−0.433178	+	0.750287i	−0.997145	−	0.0755108i	$-0.975941\pi$
$373$	−8.36606	+	14.4904i	−0.433178	+	0.750287i	0.563967	+	0.825797i	$0.309275\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.631258	+	0.529688i	−0.0325114	+	0.0272803i
$378$		0			0
$379$	−5.98558			−0.307459			−0.153729	−	0.988113i	$-0.549128\pi$
$379$	−5.98558			−0.307459			−0.153729	+	0.988113i	$0.549128\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	20.7651	−	17.4240i	1.06104	−	0.890322i	0.0668336	−	0.997764i	$-0.478710\pi$
$383$	20.7651	−	17.4240i	1.06104	−	0.890322i	0.994211	+	0.107442i	$0.0342659\pi$
$384$		0			0
$385$	29.2553	+	10.6480i	1.49099	+	0.542675i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.212392	−	1.20454i	0.0107687	−	0.0610724i	−0.978950	−	0.204101i	$-0.934573\pi$
$389$	0.212392	−	1.20454i	0.0107687	−	0.0610724i	0.989719	+	0.143028i	$0.0456841\pi$
$390$		0			0
$391$	0.150930	+	0.261418i	0.00763285	+	0.0132205i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	45.2321	−	16.4631i	2.27587	−	0.828351i
$396$		0			0
$397$	−3.15392	−	17.8868i	−0.158291	−	0.897712i	−0.955715	−	0.294293i	$-0.904916\pi$
$397$	−3.15392	−	17.8868i	−0.158291	−	0.897712i	0.797424	−	0.603419i	$-0.206195\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.98618	−	11.2642i	−0.0991850	−	0.562506i	−0.993384	−	0.114837i	$-0.963365\pi$
$401$	−1.98618	−	11.2642i	−0.0991850	−	0.562506i	0.894199	−	0.447669i	$-0.147746\pi$
$402$		0			0
$403$	1.65224	−	0.601365i	0.0823037	−	0.0299561i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	25.2439	+	43.7237i	1.25129	+	2.16730i
$408$		0			0
$409$	2.63019	−	14.9165i	0.130054	−	0.737575i	−0.848122	−	0.529800i	$-0.822267\pi$
$409$	2.63019	−	14.9165i	0.130054	−	0.737575i	0.978177	−	0.207775i	$-0.0666220\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−9.73980	−	3.54500i	−0.479264	−	0.174438i
$414$		0			0
$415$	−0.197107	+	0.165393i	−0.00967563	+	0.00811881i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.3675			0.848456			0.424228	−	0.905555i	$-0.360545\pi$
$419$	17.3675			0.848456			0.424228	+	0.905555i	$0.360545\pi$
$420$		0			0
$421$	−8.51898	+	7.14827i	−0.415190	+	0.348385i	−0.826330	−	0.563187i	$-0.809575\pi$
$421$	−8.51898	+	7.14827i	−0.415190	+	0.348385i	0.411140	+	0.911572i	$0.365131\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.96914	−	3.41065i	0.0955172	−	0.165441i
$426$		0			0
$427$	3.31422	−	18.7959i	0.160387	−	0.909597i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.81068	−	2.35844i	−0.135386	−	0.113602i	0.572580	−	0.819849i	$-0.305943\pi$
$431$	−2.81068	−	2.35844i	−0.135386	−	0.113602i	−0.707966	+	0.706247i	$0.750387\pi$
$432$		0			0
$433$	−18.5745	+	6.76055i	−0.892632	+	0.324891i	−0.747296	−	0.664491i	$-0.768648\pi$
$433$	−18.5745	+	6.76055i	−0.892632	+	0.324891i	−0.145336	+	0.989382i	$0.546426\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.95507	+	0.653472i	0.0935236	+	0.0312598i
$438$		0			0
$439$	0.671899	+	3.81053i	0.0320680	+	0.181867i	0.996635	−	0.0819730i	$-0.0261221\pi$
$439$	0.671899	+	3.81053i	0.0320680	+	0.181867i	−0.964567	+	0.263840i	$0.915011\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−20.4596	−	17.1677i	−0.972066	−	0.815660i	0.0108074	−	0.999942i	$-0.496560\pi$
$443$	−20.4596	−	17.1677i	−0.972066	−	0.815660i	−0.982874	+	0.184281i	$0.941004\pi$
$444$		0			0
$445$	28.0129	+	48.5197i	1.32794	+	2.30005i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.7836	+	35.9982i	−0.980838	+	1.69886i	−0.321694	+	0.946844i	$0.604252\pi$
$449$	−20.7836	+	35.9982i	−0.980838	+	1.69886i	−0.659144	+	0.752017i	$0.729081\pi$
$450$		0			0
$451$	46.3146	+	16.8571i	2.18087	+	0.793771i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.85197			−0.133702
$456$		0			0
$457$	35.4121			1.65651			0.828254	−	0.560354i	$-0.189335\pi$
$457$	35.4121			1.65651			0.828254	+	0.560354i	$0.189335\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−8.56919	−	3.11893i	−0.399107	−	0.145263i	0.134666	−	0.990891i	$-0.457004\pi$
$461$	−8.56919	−	3.11893i	−0.399107	−	0.145263i	−0.533773	+	0.845628i	$0.679226\pi$
$462$		0			0
$463$	18.7382	−	32.4555i	0.870837	−	1.50833i	0.00970528	−	0.999953i	$-0.496911\pi$
$463$	18.7382	−	32.4555i	0.870837	−	1.50833i	0.861132	−	0.508381i	$-0.169756\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.01439	+	10.4172i	0.278313	+	0.482052i	0.970966	−	0.239219i	$-0.0768915\pi$
$467$	6.01439	+	10.4172i	0.278313	+	0.482052i	−0.692653	+	0.721271i	$0.743558\pi$
$468$		0			0
$469$	−6.44905	−	5.41139i	−0.297789	−	0.249875i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.4328	−	64.8386i	−0.525681	−	2.98128i
$474$		0			0
$475$	−5.37017	−	26.3527i	−0.246400	−	1.20915i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.56749	+	1.66243i	−0.208694	+	0.0759584i	−0.444252	−	0.895902i	$-0.646530\pi$
$479$	−4.56749	+	1.66243i	−0.208694	+	0.0759584i	0.235558	+	0.971860i	$0.424308\pi$
$480$		0			0
$481$	−3.54296	−	2.97290i	−0.161545	−	0.135552i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.70846	−	38.0456i	0.304616	−	1.72756i
$486$		0			0
$487$	−21.2332	+	36.7769i	−0.962167	+	1.66652i	−0.245124	+	0.969492i	$0.578829\pi$
$487$	−21.2332	+	36.7769i	−0.962167	+	1.66652i	−0.717042	+	0.697030i	$0.754505\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.05851	−	2.56639i	0.138029	−	0.115820i	−0.571159	−	0.820839i	$-0.693506\pi$
$491$	3.05851	−	2.56639i	0.138029	−	0.115820i	0.709188	+	0.705019i	$0.249062\pi$
$492$		0			0
$493$	−0.979067			−0.0440950
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.16099	+	6.84788i	−0.366070	+	0.307169i
$498$		0			0
$499$	−2.49486	−	0.908053i	−0.111685	−	0.0406501i	0.285573	−	0.958357i	$-0.407816\pi$
$499$	−2.49486	−	0.908053i	−0.111685	−	0.0406501i	−0.397258	+	0.917707i	$0.630038\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.48408	+	25.4305i	−0.199935	+	1.13389i	0.705278	+	0.708931i	$0.250822\pi$
$503$	−4.48408	+	25.4305i	−0.199935	+	1.13389i	−0.905213	+	0.424958i	$0.860289\pi$
$504$		0			0
$505$	−3.61028	−	6.25319i	−0.160655	−	0.278263i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−27.2542	+	9.91972i	−1.20802	+	0.439684i	−0.866017	−	0.500014i	$-0.833328\pi$
$509$	−27.2542	+	9.91972i	−1.20802	+	0.439684i	−0.342004	+	0.939698i	$0.611106\pi$
$510$		0			0
$511$	2.29550	+	13.0184i	0.101547	+	0.575902i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.99747	−	34.0134i	−0.264280	−	1.49881i
$516$		0			0
$517$	−63.0477	+	22.9475i	−2.77283	+	1.00923i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.5496	+	32.1289i	0.812673	+	1.40759i	0.910987	+	0.412436i	$0.135322\pi$
$521$	18.5496	+	32.1289i	0.812673	+	1.40759i	−0.0983136	+	0.995155i	$0.531345\pi$
$522$		0			0
$523$	1.06124	−	6.01860i	0.0464049	−	0.263175i	−0.952775	−	0.303679i	$-0.901785\pi$
$523$	1.06124	−	6.01860i	0.0464049	−	0.263175i	0.999179	+	0.0405035i	$0.0128962\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.96305	+	0.714492i	0.0855119	+	0.0311238i
$528$		0			0
$529$	−17.4477	+	14.6404i	−0.758596	+	0.636537i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.51501			−0.195567
$534$		0			0
$535$	−31.3134	+	26.2751i	−1.35380	+	1.13597i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−13.1279	+	22.7383i	−0.565461	+	0.979406i
$540$		0			0
$541$	−2.77826	+	15.7563i	−0.119447	+	0.677416i	0.865005	+	0.501762i	$0.167315\pi$
$541$	−2.77826	+	15.7563i	−0.119447	+	0.677416i	−0.984452	+	0.175653i	$0.943796\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−47.3090	−	39.6970i	−2.02650	−	1.70043i
$546$		0			0
$547$	20.1150	−	7.32126i	0.860055	−	0.313034i	0.125922	−	0.992040i	$-0.459811\pi$
$547$	20.1150	−	7.32126i	0.860055	−	0.313034i	0.734133	+	0.679006i	$0.237589\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.00613	+	4.43186i	−0.213268	+	0.188804i
$552$		0			0
$553$	−3.97247	−	22.5290i	−0.168927	−	0.958031i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−28.6486	−	24.0390i	−1.21388	−	1.01857i	−0.999122	−	0.0418976i	$-0.986660\pi$
$557$	−28.6486	−	24.0390i	−1.21388	−	1.01857i	−0.214757	−	0.976668i	$-0.568896\pi$
$558$		0			0
$559$	3.01564	+	5.22323i	0.127548	+	0.220919i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.76859	−	13.4556i	0.327407	−	0.567086i	−0.654589	−	0.755985i	$-0.727158\pi$
$563$	7.76859	−	13.4556i	0.327407	−	0.567086i	0.981997	+	0.188899i	$0.0604918\pi$
$564$		0			0
$565$	−48.0995	−	17.5068i	−2.02356	−	0.736516i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.3328			0.768550			0.384275	−	0.923219i	$-0.374451\pi$
$569$	18.3328			0.768550			0.384275	+	0.923219i	$0.374451\pi$
$570$		0			0
$571$	13.4713			0.563758			0.281879	−	0.959450i	$-0.409042\pi$
$571$	13.4713			0.563758			0.281879	+	0.959450i	$0.409042\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.74190	−	0.997972i	−0.114345	−	0.0416183i
$576$		0			0
$577$	13.1313	−	22.7441i	0.546664	−	0.946851i	−0.451836	−	0.892101i	$-0.649231\pi$
$577$	13.1313	−	22.7441i	0.546664	−	0.946851i	0.998500	−	0.0547494i	$-0.0174360\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.0611433	+	0.105903i	0.00253665	+	0.00439361i
$582$		0			0
$583$	−16.2876	−	13.6669i	−0.674563	−	0.566025i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.01199	+	28.4244i	0.206867	+	1.17320i	0.894475	+	0.447118i	$0.147550\pi$
$587$	5.01199	+	28.4244i	0.206867	+	1.17320i	−0.687608	+	0.726082i	$0.741339\pi$
$588$		0			0
$589$	13.2716	−	5.23266i	0.546848	−	0.215608i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	12.6622	−	4.60865i	0.519973	−	0.189255i	−0.0686827	−	0.997639i	$-0.521880\pi$
$593$	12.6622	−	4.60865i	0.519973	−	0.189255i	0.588656	+	0.808384i	$0.299657\pi$
$594$		0			0
$595$	−2.59572	−	2.17807i	−0.106414	−	0.0892922i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.37172	−	30.4645i	0.219482	−	1.24475i	−0.653474	−	0.756949i	$-0.726689\pi$
$599$	5.37172	−	30.4645i	0.219482	−	1.24475i	0.872957	−	0.487798i	$-0.162200\pi$
$600$		0			0
$601$	−1.22723	+	2.12563i	−0.0500598	+	0.0867061i	−0.889969	−	0.456020i	$-0.849275\pi$
$601$	−1.22723	+	2.12563i	−0.0500598	+	0.0867061i	0.839910	+	0.542726i	$0.182608\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−59.8922	+	50.2555i	−2.43496	+	2.04318i
$606$		0			0
$607$	−1.40984			−0.0572236			−0.0286118	−	0.999591i	$-0.509109\pi$
$607$	−1.40984			−0.0572236			−0.0286118	+	0.999591i	$0.509109\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.70830	−	3.95073i	0.190477	−	0.159829i
$612$		0			0
$613$	−10.9067	−	3.96971i	−0.440517	−	0.160335i	0.112234	−	0.993682i	$-0.464199\pi$
$613$	−10.9067	−	3.96971i	−0.440517	−	0.160335i	−0.552750	+	0.833347i	$0.686422\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.45197	−	30.9197i	0.219488	−	1.24478i	−0.653459	−	0.756962i	$-0.726683\pi$
$617$	5.45197	−	30.9197i	0.219488	−	1.24478i	0.872947	−	0.487816i	$-0.162206\pi$
$618$		0			0
$619$	17.7183	+	30.6890i	0.712159	+	1.23350i	0.964045	+	0.265739i	$0.0856159\pi$
$619$	17.7183	+	30.6890i	0.712159	+	1.23350i	−0.251886	+	0.967757i	$0.581051\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	25.0209	−	9.10686i	1.00244	−	0.364859i
$624$		0			0
$625$	−3.08768	−	17.5111i	−0.123507	−	0.700444i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−0.954206	−	5.41157i	−0.0380467	−	0.215774i
$630$		0			0
$631$	−10.8903	+	3.96375i	−0.433536	+	0.157794i	−0.549564	−	0.835452i	$-0.685206\pi$
$631$	−10.8903	+	3.96375i	−0.433536	+	0.157794i	0.116028	+	0.993246i	$0.462984\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−18.7037	−	32.3957i	−0.742232	−	1.28558i
$636$		0			0
$637$	0.417661	−	2.36867i	0.0165483	−	0.0938501i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	7.00425	+	2.54934i	0.276651	+	0.100693i	0.476620	−	0.879109i	$-0.341862\pi$
$641$	7.00425	+	2.54934i	0.276651	+	0.100693i	−0.199969	+	0.979802i	$0.564084\pi$
$642$		0			0
$643$	11.5420	−	9.68486i	0.455171	−	0.381933i	−0.386180	−	0.922424i	$-0.626206\pi$
$643$	11.5420	−	9.68486i	0.455171	−	0.381933i	0.841350	+	0.540490i	$0.181761\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.3426			0.839064			0.419532	−	0.907741i	$-0.362194\pi$
$647$	21.3426			0.839064			0.419532	+	0.907741i	$0.362194\pi$
$648$		0			0
$649$	29.3156	−	24.5987i	1.15074	−	0.965584i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.9605	+	20.7161i	−0.468049	+	0.810685i	−0.999333	−	0.0365084i	$-0.988376\pi$
$653$	−11.9605	+	20.7161i	−0.468049	+	0.810685i	0.531284	+	0.847194i	$0.321710\pi$
$654$		0			0
$655$	5.89809	−	33.4497i	0.230458	−	1.30699i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−15.0973	−	12.6681i	−0.588108	−	0.493481i	0.299491	−	0.954099i	$-0.403183\pi$
$659$	−15.0973	−	12.6681i	−0.588108	−	0.493481i	−0.887598	+	0.460618i	$0.847628\pi$
$660$		0			0
$661$	27.7105	−	10.0858i	1.07781	−	0.392291i	0.258719	−	0.965953i	$-0.416700\pi$
$661$	27.7105	−	10.0858i	1.07781	−	0.392291i	0.819093	+	0.573661i	$0.194477\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−23.1316	+	0.613017i	−0.897006	+	0.0237718i
$666$		0			0
$667$	0.125963	+	0.714372i	0.00487731	+	0.0276606i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	53.9816	+	45.2960i	2.08394	+	1.74863i
$672$		0			0
$673$	12.3068	+	21.3161i	0.474394	+	0.821674i	0.999570	−	0.0293194i	$-0.00933399\pi$
$673$	12.3068	+	21.3161i	0.474394	+	0.821674i	−0.525176	+	0.850993i	$0.676001\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.0655	+	20.8981i	−0.463716	+	0.803179i	−0.999143	−	0.0414026i	$-0.986817\pi$
$677$	−12.0655	+	20.8981i	−0.463716	+	0.803179i	0.535427	+	0.844582i	$0.320151\pi$
$678$		0			0
$679$	−17.2531	−	6.27963i	−0.662115	−	0.240990i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−43.2768			−1.65594			−0.827970	−	0.560772i	$-0.810504\pi$
$683$	−43.2768			−1.65594			−0.827970	+	0.560772i	$0.810504\pi$
$684$		0			0
$685$	−15.5796			−0.595264
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.83027	+	0.666164i	0.0697277	+	0.0253788i
$690$		0			0
$691$	10.0200	−	17.3552i	0.381179	−	0.660222i	−0.610052	−	0.792362i	$-0.708851\pi$
$691$	10.0200	−	17.3552i	0.381179	−	0.660222i	0.991231	+	0.132140i	$0.0421847\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.09412	+	5.35917i	0.117367	+	0.203285i
$696$		0			0
$697$	−4.10934	−	3.44815i	−0.155652	−	0.130608i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	6.84393	+	38.8139i	0.258492	+	1.46598i	0.786948	+	0.617019i	$0.211660\pi$
$701$	6.84393	+	38.8139i	0.258492	+	1.46598i	−0.528456	+	0.848961i	$0.677229\pi$
$702$		0			0
$703$	−29.3751	−	23.3509i	−1.10790	−	0.880696i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.22468	+	1.17369i	−0.121277	+	0.0441410i
$708$		0			0
$709$	−20.3272	−	17.0565i	−0.763404	−	0.640572i	0.175606	−	0.984460i	$-0.443811\pi$
$709$	−20.3272	−	17.0565i	−0.763404	−	0.640572i	−0.939011	+	0.343888i	$0.888256\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.268767	−	1.52426i	0.0100654	−	0.0570838i
$714$		0			0
$715$	5.26496	−	9.11919i	0.196899	−	0.341038i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	10.1219	−	8.49326i	0.377482	−	0.316745i	−0.434231	−	0.900802i	$-0.642980\pi$
$719$	10.1219	−	8.49326i	0.377482	−	0.316745i	0.811713	+	0.584056i	$0.198535\pi$
$720$		0			0
$721$	−16.4145			−0.611308
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.24983	−	6.08333i	0.269252	−	0.225929i
$726$		0			0
$727$	27.8866	+	10.1499i	1.03426	+	0.376439i	0.802701	−	0.596382i	$-0.203396\pi$
$727$	27.8866	+	10.1499i	1.03426	+	0.376439i	0.231557	+	0.972821i	$0.425618\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.24434	+	7.05700i	−0.0460235	+	0.261012i
$732$		0			0
$733$	5.51190	+	9.54689i	0.203587	+	0.352622i	0.949681	−	0.313217i	$-0.101407\pi$
$733$	5.51190	+	9.54689i	0.203587	+	0.352622i	−0.746095	+	0.665840i	$0.768073\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	29.2084	−	10.6310i	1.07591	−	0.391598i
$738$		0			0
$739$	0.305185	+	1.73079i	0.0112264	+	0.0636681i	0.989906	−	0.141723i	$-0.0452644\pi$
$739$	0.305185	+	1.73079i	0.0112264	+	0.0636681i	−0.978680	+	0.205391i	$0.934153\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.963500	+	5.46428i	0.0353474	+	0.200465i	0.997367	−	0.0725140i	$-0.0231022\pi$
$743$	0.963500	+	5.46428i	0.0353474	+	0.200465i	−0.962020	+	0.272979i	$0.911991\pi$
$744$		0			0
$745$	−42.0534	+	15.3062i	−1.54072	+	0.560775i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.71350	+	16.8243i	0.354923	+	0.614746i
$750$		0			0
$751$	0.299887	−	1.70074i	0.0109430	−	0.0620610i	−0.978847	−	0.204592i	$-0.934413\pi$
$751$	0.299887	−	1.70074i	0.0109430	−	0.0620610i	0.989790	+	0.142531i	$0.0455242\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.631370	+	0.229800i	0.0229779	+	0.00836328i
$756$		0			0
$757$	12.3711	−	10.3806i	0.449636	−	0.377290i	−0.389665	−	0.920957i	$-0.627409\pi$
$757$	12.3711	−	10.3806i	0.449636	−	0.377290i	0.839301	+	0.543667i	$0.182965\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	37.8068			1.37049			0.685247	−	0.728310i	$-0.259694\pi$
$761$	37.8068			1.37049			0.685247	+	0.728310i	$0.259694\pi$
$762$		0			0
$763$	−22.4840	+	18.8663i	−0.813975	+	0.683006i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.75284	+	3.03600i	−0.0632913	+	0.109624i
$768$		0			0
$769$	−9.22012	+	52.2899i	−0.332486	+	1.88562i	0.118281	+	0.992980i	$0.462262\pi$
$769$	−9.22012	+	52.2899i	−0.332486	+	1.88562i	−0.450767	+	0.892642i	$0.648849\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−30.2885	−	25.4150i	−1.08940	−	0.914116i	−0.0927335	−	0.995691i	$-0.529560\pi$
$773$	−30.2885	−	25.4150i	−1.08940	−	0.914116i	−0.996667	+	0.0815753i	$0.974005\pi$
$774$		0			0
$775$	−18.9755	+	6.90651i	−0.681620	+	0.248089i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−36.6201	+	0.970479i	−1.31205	+	0.0347710i
$780$		0			0
$781$	−6.83030	−	38.7365i	−0.244407	−	1.38610i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.23908	−	7.75251i	−0.329757	−	0.276699i
$786$		0			0
$787$	11.6739	+	20.2198i	0.416129	+	0.720757i	0.995546	−	0.0942740i	$-0.0300530\pi$
$787$	11.6739	+	20.2198i	0.416129	+	0.720757i	−0.579417	+	0.815031i	$0.696720\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.1634	+	21.0676i	−0.432480	+	0.749078i
$792$		0			0
$793$	−6.06603	−	2.20785i	−0.215411	−	0.0784032i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.0433			−0.922502			−0.461251	−	0.887270i	$-0.652599\pi$
$797$	−26.0433			−0.922502			−0.461251	+	0.887270i	$0.652599\pi$
$798$		0			0
$799$	7.30247			0.258343
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−45.8642	−	16.6932i	−1.61851	−	0.589090i
$804$		0			0
$805$	−1.25526	+	2.17418i	−0.0442422	+	0.0766298i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−12.3342	−	21.3635i	−0.433648	−	0.751101i	0.563536	−	0.826092i	$-0.309441\pi$
$809$	−12.3342	−	21.3635i	−0.433648	−	0.751101i	−0.997184	+	0.0749905i	$0.976107\pi$
$810$		0			0
$811$	23.1994	+	19.4666i	0.814643	+	0.683566i	0.951711	−	0.306995i	$-0.0993236\pi$
$811$	23.1994	+	19.4666i	0.814643	+	0.683566i	−0.137068	+	0.990562i	$0.543768\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.33975	−	24.6119i	−0.152015	−	0.862119i
$816$		0			0
$817$	25.5818	+	41.7162i	0.894994	+	1.45946i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.02184	+	3.28368i	−0.314864	+	0.114601i	−0.494618	−	0.869110i	$-0.664692\pi$
$821$	−9.02184	+	3.28368i	−0.314864	+	0.114601i	0.179754	+	0.983712i	$0.442470\pi$
$822$		0			0
$823$	−19.8920	−	16.6914i	−0.693391	−	0.581824i	0.226494	−	0.974013i	$-0.427274\pi$
$823$	−19.8920	−	16.6914i	−0.693391	−	0.581824i	−0.919885	+	0.392189i	$0.871718\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.65006	−	26.3718i	0.161698	−	0.917038i	−0.790705	−	0.612197i	$-0.790286\pi$
$827$	4.65006	−	26.3718i	0.161698	−	0.917038i	0.952403	−	0.304840i	$-0.0986031\pi$
$828$		0			0
$829$	6.19747	−	10.7343i	0.215247	−	0.372819i	−0.738102	−	0.674689i	$-0.764278\pi$
$829$	6.19747	−	10.7343i	0.215247	−	0.372819i	0.953349	+	0.301870i	$0.0976110\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.18911	−	1.83688i	0.0758480	−	0.0636440i
$834$		0			0
$835$	−55.4805			−1.91998
$836$		0			0
$837$		0			0
$838$		0			0
$839$	26.6649	−	22.3745i	0.920574	−	0.772453i	−0.0535269	−	0.998566i	$-0.517046\pi$
$839$	26.6649	−	22.3745i	0.920574	−	0.772453i	0.974101	+	0.226113i	$0.0726019\pi$
$840$		0			0
$841$	25.0402	+	9.11389i	0.863455	+	0.314272i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.37716	−	41.8379i	0.253782	−	1.43927i
$846$		0			0
$847$	18.5787	+	32.1793i	0.638372	+	1.10569i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.82576	+	1.39246i	−0.131145	+	0.0477330i
$852$		0			0
$853$	−2.26421	−	12.8410i	−0.0775250	−	0.439666i	−0.998721	−	0.0505667i	$-0.983897\pi$
$853$	−2.26421	−	12.8410i	−0.0775250	−	0.439666i	0.921196	−	0.389100i	$-0.127214\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.32717	+	30.2119i	0.181973	+	1.03202i	0.929784	+	0.368106i	$0.119994\pi$
$857$	5.32717	+	30.2119i	0.181973	+	1.03202i	−0.747811	+	0.663911i	$0.768895\pi$
$858$		0			0
$859$	38.1033	−	13.8685i	1.30007	−	0.473186i	0.403049	−	0.915179i	$-0.367951\pi$
$859$	38.1033	−	13.8685i	1.30007	−	0.473186i	0.897019	+	0.441993i	$0.145728\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−9.81186	−	16.9946i	−0.334000	−	0.578504i	0.649292	−	0.760539i	$-0.275065\pi$
$863$	−9.81186	−	16.9946i	−0.334000	−	0.578504i	−0.983292	+	0.182034i	$0.941732\pi$
$864$		0			0
$865$	13.6226	−	77.2575i	0.463182	−	2.62683i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	79.3701	+	28.8884i	2.69245	+	0.979971i
$870$		0			0
$871$	−2.18124	+	1.83027i	−0.0739084	+	0.0620165i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.21098			0.209970
$876$		0			0
$877$	−14.2218	+	11.9335i	−0.480237	+	0.402967i	−0.850512	−	0.525955i	$-0.823708\pi$
$877$	−14.2218	+	11.9335i	−0.480237	+	0.402967i	0.370275	+	0.928922i	$0.379263\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−5.73165	+	9.92751i	−0.193104	+	0.334466i	−0.946277	−	0.323356i	$-0.895189\pi$
$881$	−5.73165	+	9.92751i	−0.193104	+	0.334466i	0.753173	+	0.657822i	$0.228522\pi$
$882$		0			0
$883$	−7.16504	+	40.6350i	−0.241123	+	1.36747i	0.588205	+	0.808712i	$0.299835\pi$
$883$	−7.16504	+	40.6350i	−0.241123	+	1.36747i	−0.829327	+	0.558763i	$0.811276\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.7364	−	11.5262i	−0.461222	−	0.387011i	0.382358	−	0.924014i	$-0.375112\pi$
$887$	−13.7364	−	11.5262i	−0.461222	−	0.387011i	−0.843580	+	0.537003i	$0.819556\pi$
$888$		0			0
$889$	−16.7060	+	6.08048i	−0.560301	+	0.203933i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	37.3387	−	33.0554i	1.24949	−	1.10616i
$894$		0			0
$895$	−2.81846	−	15.9843i	−0.0942107	−	0.534295i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.84563	+	3.22687i	0.128259	+	0.107622i
$900$		0			0
$901$	1.15707	+	2.00410i	0.0385475	+	0.0667663i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−28.8536	+	49.9760i	−0.959127	+	1.66126i
$906$		0			0
$907$	37.9244	+	13.8034i	1.25926	+	0.458333i	0.883521	−	0.468392i	$-0.155167\pi$
$907$	37.9244	+	13.8034i	1.25926	+	0.458333i	0.375739	+	0.926725i	$0.377389\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.9120			0.394663			0.197331	−	0.980337i	$-0.436772\pi$
$911$	11.9120			0.394663			0.197331	+	0.980337i	$0.436772\pi$
$912$		0			0
$913$	−0.451502			−0.0149425
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.1690	−	5.52106i	−0.500924	−	0.182322i
$918$		0			0
$919$	2.45602	−	4.25395i	0.0810166	−	0.140325i	−0.822670	−	0.568519i	$-0.807517\pi$
$919$	2.45602	−	4.25395i	0.0810166	−	0.140325i	0.903687	+	0.428194i	$0.140850\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.80163	+	3.12052i	0.0593014	+	0.102713i
$924$		0			0
$925$	40.6900	+	34.1429i	1.33788	+	1.12261i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	4.33485	+	24.5842i	0.142222	+	0.806581i	0.969556	+	0.244870i	$0.0787454\pi$
$929$	4.33485	+	24.5842i	0.142222	+	0.806581i	−0.827334	+	0.561710i	$0.810144\pi$
$930$		0			0
$931$	2.87841	−	19.3015i	0.0943361	−	0.632581i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	11.7563	−	4.27895i	0.384472	−	0.139936i
$936$		0			0
$937$	−34.4563	−	28.9123i	−1.12564	−	0.944523i	−0.126763	−	0.991933i	$-0.540459\pi$
$937$	−34.4563	−	28.9123i	−1.12564	−	0.944523i	−0.998875	+	0.0474104i	$0.984903\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.10898	−	6.28935i	0.0361518	−	0.205027i	−0.961382	−	0.275218i	$-0.911250\pi$
$941$	1.10898	−	6.28935i	0.0361518	−	0.205027i	0.997534	+	0.0701913i	$0.0223610\pi$
$942$		0			0
$943$	−1.98723	+	3.44199i	−0.0647132	+	0.112086i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.53940	−	2.13081i	0.0825194	−	0.0692420i	−0.600595	−	0.799554i	$-0.705070\pi$
$947$	2.53940	−	2.13081i	0.0825194	−	0.0692420i	0.683114	+	0.730311i	$0.260625\pi$
$948$		0			0
$949$	4.47110			0.145138
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.89561	+	5.78610i	−0.223371	+	0.187430i	−0.747605	−	0.664144i	$-0.768796\pi$
$953$	−6.89561	+	5.78610i	−0.223371	+	0.187430i	0.524234	+	0.851574i	$0.324352\pi$
$954$		0			0
$955$	23.3815	+	8.51015i	0.756606	+	0.275382i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.28575	+	7.29183i	−0.0415189	+	0.235465i
$960$		0			0
$961$	10.1443	+	17.5704i	0.327235	+	0.566788i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	64.1180	−	23.3370i	2.06403	−	0.751245i
$966$		0			0
$967$	−3.61729	−	20.5147i	−0.116324	−	0.659708i	−0.986086	−	0.166236i	$-0.946839\pi$
$967$	−3.61729	−	20.5147i	−0.116324	−	0.659708i	0.869762	−	0.493472i	$-0.164272\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.75920	+	9.97690i	0.0564553	+	0.320174i	0.999937	−	0.0112515i	$-0.00358154\pi$
$971$	1.75920	+	9.97690i	0.0564553	+	0.320174i	−0.943481	+	0.331426i	$0.892470\pi$
$972$		0			0
$973$	2.76365	−	1.00589i	0.0885985	−	0.0322472i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.49751	+	9.52197i	0.175881	+	0.304635i	0.940466	−	0.339888i	$-0.110389\pi$
$977$	5.49751	+	9.52197i	0.175881	+	0.304635i	−0.764585	+	0.644523i	$0.777056\pi$
$978$		0			0
$979$	−17.0714	+	96.8164i	−0.545603	+	3.09427i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−35.2630	−	12.8347i	−1.12472	−	0.409363i	−0.288345	−	0.957527i	$-0.593105\pi$
$983$	−35.2630	−	12.8347i	−1.12472	−	0.409363i	−0.836371	+	0.548163i	$0.815327\pi$
$984$		0			0
$985$	13.6909	−	11.4880i	0.436228	−	0.366039i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.30920			0.168823
$990$		0			0
$991$	15.9058	−	13.3466i	0.505266	−	0.423968i	−0.354194	−	0.935172i	$-0.615245\pi$
$991$	15.9058	−	13.3466i	0.505266	−	0.423968i	0.859460	+	0.511204i	$0.170800\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−39.4833	+	68.3870i	−1.25170	+	2.16801i
$996$		0			0
$997$	−4.16713	+	23.6329i	−0.131974	+	0.748463i	0.844945	+	0.534853i	$0.179633\pi$
$997$	−4.16713	+	23.6329i	−0.131974	+	0.748463i	−0.976919	+	0.213610i	$0.931478\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bo.e.541.2		12
3.2	odd	2		228.2.q.b.85.1	✓	12
12.11	even	2		912.2.bo.g.769.1		12
19.17	even	9	inner	684.2.bo.e.397.2		12
57.17	odd	18		228.2.q.b.169.1	yes	12
57.32	even	18		4332.2.a.u.1.6		6
57.44	odd	18		4332.2.a.t.1.6		6
228.131	even	18		912.2.bo.g.625.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.q.b.85.1	✓	12	3.2	odd	2
228.2.q.b.169.1	yes	12	57.17	odd	18
684.2.bo.e.397.2		12	19.17	even	9	inner
684.2.bo.e.541.2		12	1.1	even	1	trivial
912.2.bo.g.625.1		12	228.131	even	18
912.2.bo.g.769.1		12	12.11	even	2
4332.2.a.t.1.6		6	57.44	odd	18
4332.2.a.u.1.6		6	57.32	even	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(3.14060 + 1.14308i) q^{5} +(0.794193 - 1.37558i) q^{7} +O(q^{10})\)	\(q+(3.14060 + 1.14308i) q^{5} +(0.794193 - 1.37558i) q^{7} +(2.93229 + 5.07887i) q^{11} +(-0.411545 - 0.345327i) q^{13} +(-0.110839 - 0.628599i) q^{17} +(-3.41216 - 2.71240i) q^{19} +(-0.444394 + 0.161746i) q^{23} +(4.72648 + 3.96599i) q^{25} +(0.266355 - 1.51057i) q^{29} +(-1.63641 + 2.83435i) q^{31} +(4.06664 - 3.41232i) q^{35} +8.60894 q^{37} +(6.43798 - 5.40211i) q^{41} +(-10.5495 - 3.83970i) q^{43} +(-1.98663 + 11.2667i) q^{47} +(2.23852 + 3.87722i) q^{49} +(-3.40684 + 1.23999i) q^{53} +(3.40356 + 19.3025i) q^{55} +(-1.13313 - 6.42629i) q^{59} +(11.2912 - 4.10968i) q^{61} +(-0.897758 - 1.55496i) q^{65} +(0.920357 - 5.21960i) q^{67} +(-6.30259 - 2.29395i) q^{71} +(-6.37537 + 5.34957i) q^{73} +9.31520 q^{77} +(11.0329 - 9.25768i) q^{79} +(-0.0384940 + 0.0666736i) q^{83} +(0.370441 - 2.10087i) q^{85} +(12.8415 + 10.7753i) q^{89} +(-0.801871 + 0.291857i) q^{91} +(-7.61573 - 12.4190i) q^{95} +(-2.00723 - 11.3836i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{5} - 9 q^{7}+O(q^{10}) \) 12 * q + 6 * q^5 - 9 * q^7	\( 12 q + 6 q^{5} - 9 q^{7} + 9 q^{11} - 3 q^{13} - 12 q^{17} + 9 q^{19} - 15 q^{23} + 12 q^{25} + 24 q^{29} - 6 q^{31} + 42 q^{35} + 12 q^{37} - 6 q^{41} - 39 q^{43} + 3 q^{47} - 21 q^{49} - 18 q^{53} + 45 q^{55} + 33 q^{61} + 33 q^{65} - 27 q^{67} - 6 q^{71} - 24 q^{73} + 18 q^{79} - 3 q^{83} + 39 q^{85} + 15 q^{89} + 18 q^{91} + 30 q^{95} - 15 q^{97}+O(q^{100}) \) 12 * q + 6 * q^5 - 9 * q^7 + 9 * q^11 - 3 * q^13 - 12 * q^17 + 9 * q^19 - 15 * q^23 + 12 * q^25 + 24 * q^29 - 6 * q^31 + 42 * q^35 + 12 * q^37 - 6 * q^41 - 39 * q^43 + 3 * q^47 - 21 * q^49 - 18 * q^53 + 45 * q^55 + 33 * q^61 + 33 * q^65 - 27 * q^67 - 6 * q^71 - 24 * q^73 + 18 * q^79 - 3 * q^83 + 39 * q^85 + 15 * q^89 + 18 * q^91 + 30 * q^95 - 15 * q^97

Introduction

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