LMFDB - Embedded newform 400.2.u.e.321.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(81,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(10))

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("400.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			321.2
Root			$1.66637 + 0.917186i$ of defining polynomial
Character	$\chi$	$=$	400.321
Dual form			400.2.u.e.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 + 0.951057i) q^{3} +(1.52988 - 1.63079i) q^{5} +2.77447 q^{7} +(-0.118034 - 0.363271i) q^{9} +O(q^{10})$	\(q+(1.30902 + 0.951057i) q^{3} +(1.52988 - 1.63079i) q^{5} +2.77447 q^{7} +(-0.118034 - 0.363271i) q^{9} +(-0.481536 + 1.48201i) q^{11} +(-1.19625 - 3.68168i) q^{13} +(3.55361 - 0.679734i) q^{15} +(-1.46545 + 1.06471i) q^{17} +(-1.83889 + 1.33603i) q^{19} +(3.63182 + 2.63868i) q^{21} +(-1.13650 + 3.49778i) q^{23} +(-0.318958 - 4.98982i) q^{25} +(1.69098 - 5.20431i) q^{27} +(4.41097 + 3.20475i) q^{29} +(-2.41097 + 1.75167i) q^{31} +(-2.03982 + 1.48201i) q^{33} +(4.24459 - 4.52458i) q^{35} +(3.31808 + 10.2120i) q^{37} +(1.93557 - 5.95708i) q^{39} +(2.81428 + 8.66148i) q^{41} -12.1055 q^{43} +(-0.772997 - 0.363271i) q^{45} +(5.93232 + 4.31008i) q^{47} +0.697669 q^{49} -2.93090 q^{51} +(-5.84416 - 4.24603i) q^{53} +(1.68017 + 3.05258i) q^{55} -3.67779 q^{57} +(-3.54454 - 10.9090i) q^{59} +(4.28441 - 13.1861i) q^{61} +(-0.327481 - 1.00788i) q^{63} +(-7.83417 - 3.68168i) q^{65} +(-7.93232 + 5.76317i) q^{67} +(-4.81428 + 3.49778i) q^{69} +(9.36175 + 6.80171i) q^{71} +(0.897175 - 2.76122i) q^{73} +(4.32808 - 6.83510i) q^{75} +(-1.33600 + 4.11180i) q^{77} +(-6.32281 - 4.59379i) q^{79} +(6.23607 - 4.53077i) q^{81} +(-3.17490 + 2.30670i) q^{83} +(-0.505635 + 4.01872i) q^{85} +(2.72613 + 8.39016i) q^{87} +(-0.447862 + 1.37838i) q^{89} +(-3.31896 - 10.2147i) q^{91} -4.82193 q^{93} +(-0.634486 + 5.04282i) q^{95} +(-5.88636 - 4.27669i) q^{97} +0.595211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9	$ 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9} + 2 q^{11} + 8 q^{13} + 5 q^{15} + 10 q^{17} - 3 q^{19} - 3 q^{21} - 6 q^{23} - 5 q^{25} + 18 q^{27} + 6 q^{29} + 10 q^{31} - 16 q^{33} + 15 q^{35} - 2 q^{37} + q^{39} - 4 q^{41} + 12 q^{43} + 12 q^{47} - 4 q^{49} + 20 q^{51} - 13 q^{53} - 20 q^{55} - 6 q^{57} - 29 q^{59} + 15 q^{61} - 4 q^{63} - 50 q^{65} - 28 q^{67} - 12 q^{69} + 16 q^{71} + q^{73} - 15 q^{75} - 11 q^{77} - 23 q^{79} + 32 q^{81} - 14 q^{83} - 15 q^{85} - 3 q^{87} - 7 q^{89} - 29 q^{91} + 20 q^{93} - 45 q^{95} - 3 q^{97} + 22 q^{99}+O(q^{100}) $ 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9 + 2 * q^11 + 8 * q^13 + 5 * q^15 + 10 * q^17 - 3 * q^19 - 3 * q^21 - 6 * q^23 - 5 * q^25 + 18 * q^27 + 6 * q^29 + 10 * q^31 - 16 * q^33 + 15 * q^35 - 2 * q^37 + q^39 - 4 * q^41 + 12 * q^43 + 12 * q^47 - 4 * q^49 + 20 * q^51 - 13 * q^53 - 20 * q^55 - 6 * q^57 - 29 * q^59 + 15 * q^61 - 4 * q^63 - 50 * q^65 - 28 * q^67 - 12 * q^69 + 16 * q^71 + q^73 - 15 * q^75 - 11 * q^77 - 23 * q^79 + 32 * q^81 - 14 * q^83 - 15 * q^85 - 3 * q^87 - 7 * q^89 - 29 * q^91 + 20 * q^93 - 45 * q^95 - 3 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.30902	+	0.951057i	0.755761	+	0.549093i	0.897607	−	0.440796i	$-0.145304\pi$
$3$	1.30902	+	0.951057i	0.755761	+	0.549093i	−0.141846	+	0.989889i	$0.545304\pi$
$4$		0			0
$5$	1.52988	−	1.63079i	0.684181	−	0.729312i
$5$	1.52988	−	1.63079i	0.684181	−	0.729312i
$6$		0			0
$7$	2.77447			1.04865			0.524325	−	0.851518i	$-0.324318\pi$
$7$	2.77447			1.04865			0.524325	+	0.851518i	$0.324318\pi$
$8$		0			0
$9$	−0.118034	−	0.363271i	−0.0393447	−	0.121090i
$10$		0			0
$11$	−0.481536	+	1.48201i	−0.145188	+	0.446844i	−0.997035	−	0.0769471i	$-0.975483\pi$
$11$	−0.481536	+	1.48201i	−0.145188	+	0.446844i	0.851847	+	0.523791i	$0.175483\pi$
$12$		0			0
$13$	−1.19625	−	3.68168i	−0.331780	−	1.02111i	−0.968286	−	0.249843i	$-0.919621\pi$
$13$	−1.19625	−	3.68168i	−0.331780	−	1.02111i	0.636506	−	0.771272i	$-0.280379\pi$
$14$		0			0
$15$	3.55361	−	0.679734i	0.917538	−	0.175507i
$16$		0			0
$17$	−1.46545	+	1.06471i	−0.355424	+	0.258231i	−0.751141	−	0.660142i	$-0.770496\pi$
$17$	−1.46545	+	1.06471i	−0.355424	+	0.258231i	0.395717	+	0.918373i	$0.370496\pi$
$18$		0			0
$19$	−1.83889	+	1.33603i	−0.421871	+	0.306507i	−0.778390	−	0.627781i	$-0.783963\pi$
$19$	−1.83889	+	1.33603i	−0.421871	+	0.306507i	0.356519	+	0.934288i	$0.383963\pi$
$20$		0			0
$21$	3.63182	+	2.63868i	0.792529	+	0.575806i
$22$		0			0
$23$	−1.13650	+	3.49778i	−0.236976	+	0.729338i	0.759877	+	0.650067i	$0.225259\pi$
$23$	−1.13650	+	3.49778i	−0.236976	+	0.729338i	−0.996853	+	0.0792710i	$0.974741\pi$
$24$		0			0
$25$	−0.318958	−	4.98982i	−0.0637916	−	0.997963i
$26$		0			0
$27$	1.69098	−	5.20431i	0.325430	−	1.00157i
$28$		0			0
$29$	4.41097	+	3.20475i	0.819096	+	0.595108i	0.916453	−	0.400142i	$-0.131039\pi$
$29$	4.41097	+	3.20475i	0.819096	+	0.595108i	−0.0973576	+	0.995249i	$0.531039\pi$
$30$		0			0
$31$	−2.41097	+	1.75167i	−0.433022	+	0.314609i	−0.782856	−	0.622203i	$-0.786238\pi$
$31$	−2.41097	+	1.75167i	−0.433022	+	0.314609i	0.349834	+	0.936812i	$0.386238\pi$
$32$		0			0
$33$	−2.03982	+	1.48201i	−0.355087	+	0.257986i
$34$		0			0
$35$	4.24459	−	4.52458i	0.717467	−	0.764793i
$36$		0			0
$37$	3.31808	+	10.2120i	0.545489	+	1.67884i	0.719824	+	0.694157i	$0.244223\pi$
$37$	3.31808	+	10.2120i	0.545489	+	1.67884i	−0.174334	+	0.984687i	$0.555777\pi$
$38$		0			0
$39$	1.93557	−	5.95708i	0.309940	−	0.953897i
$40$		0			0
$41$	2.81428	+	8.66148i	0.439517	+	1.35270i	0.888386	+	0.459098i	$0.151827\pi$
$41$	2.81428	+	8.66148i	0.439517	+	1.35270i	−0.448868	+	0.893598i	$0.648173\pi$
$42$		0			0
$43$	−12.1055			−1.84607			−0.923033	−	0.384721i	$-0.874298\pi$
$43$	−12.1055			−1.84607			−0.923033	+	0.384721i	$0.874298\pi$
$44$		0			0
$45$	−0.772997	−	0.363271i	−0.115232	−	0.0541533i
$46$		0			0
$47$	5.93232	+	4.31008i	0.865318	+	0.628690i	0.929326	−	0.369259i	$-0.120389\pi$
$47$	5.93232	+	4.31008i	0.865318	+	0.628690i	−0.0640088	+	0.997949i	$0.520389\pi$
$48$		0			0
$49$	0.697669			0.0996670
$50$		0			0
$51$	−2.93090			−0.410408
$52$		0			0
$53$	−5.84416	−	4.24603i	−0.802757	−	0.583237i	0.108964	−	0.994046i	$-0.465247\pi$
$53$	−5.84416	−	4.24603i	−0.802757	−	0.583237i	−0.911722	+	0.410808i	$0.865247\pi$
$54$		0			0
$55$	1.68017	+	3.05258i	0.226553	+	0.411610i
$56$		0			0
$57$	−3.67779			−0.487135
$58$		0			0
$59$	−3.54454	−	10.9090i	−0.461460	−	1.42023i	−0.863380	−	0.504554i	$-0.831657\pi$
$59$	−3.54454	−	10.9090i	−0.461460	−	1.42023i	0.401920	−	0.915675i	$-0.368343\pi$
$60$		0			0
$61$	4.28441	−	13.1861i	0.548562	−	1.68830i	−0.163804	−	0.986493i	$-0.552376\pi$
$61$	4.28441	−	13.1861i	0.548562	−	1.68830i	0.712366	−	0.701808i	$-0.247624\pi$
$62$		0			0
$63$	−0.327481	−	1.00788i	−0.0412588	−	0.126981i
$64$		0			0
$65$	−7.83417	−	3.68168i	−0.971709	−	0.456656i
$66$		0			0
$67$	−7.93232	+	5.76317i	−0.969087	+	0.704083i	−0.955243	−	0.295821i	$-0.904407\pi$
$67$	−7.93232	+	5.76317i	−0.969087	+	0.704083i	−0.0138437	+	0.999904i	$0.504407\pi$
$68$		0			0
$69$	−4.81428	+	3.49778i	−0.579572	+	0.421084i
$70$		0			0
$71$	9.36175	+	6.80171i	1.11104	+	0.807214i	0.982826	−	0.184533i	$-0.0590772\pi$
$71$	9.36175	+	6.80171i	1.11104	+	0.807214i	0.128209	+	0.991747i	$0.459077\pi$
$72$		0			0
$73$	0.897175	−	2.76122i	0.105006	−	0.323176i	−0.884726	−	0.466112i	$-0.845654\pi$
$73$	0.897175	−	2.76122i	0.105006	−	0.323176i	0.989732	+	0.142936i	$0.0456543\pi$
$74$		0			0
$75$	4.32808	−	6.83510i	0.499763	−	0.789250i
$76$		0			0
$77$	−1.33600	+	4.11180i	−0.152252	+	0.468583i
$78$		0			0
$79$	−6.32281	−	4.59379i	−0.711371	−	0.516842i	0.172244	−	0.985054i	$-0.444898\pi$
$79$	−6.32281	−	4.59379i	−0.711371	−	0.516842i	−0.883616	+	0.468213i	$0.844898\pi$
$80$		0			0
$81$	6.23607	−	4.53077i	0.692896	−	0.503419i
$82$		0			0
$83$	−3.17490	+	2.30670i	−0.348490	+	0.253193i	−0.748235	−	0.663433i	$-0.769099\pi$
$83$	−3.17490	+	2.30670i	−0.348490	+	0.253193i	0.399745	+	0.916626i	$0.369099\pi$
$84$		0			0
$85$	−0.505635	+	4.01872i	−0.0548438	+	0.435891i
$86$		0			0
$87$	2.72613	+	8.39016i	0.292271	+	0.899519i
$88$		0			0
$89$	−0.447862	+	1.37838i	−0.0474733	+	0.146108i	−0.971983	−	0.235050i	$-0.924475\pi$
$89$	−0.447862	+	1.37838i	−0.0474733	+	0.146108i	0.924510	+	0.381158i	$0.124475\pi$
$90$		0			0
$91$	−3.31896	−	10.2147i	−0.347921	−	1.07079i
$92$		0			0
$93$	−4.82193			−0.500011
$94$		0			0
$95$	−0.634486	+	5.04282i	−0.0650969	+	0.517382i
$96$		0			0
$97$	−5.88636	−	4.27669i	−0.597669	−	0.434232i	0.247382	−	0.968918i	$-0.420430\pi$
$97$	−5.88636	−	4.27669i	−0.597669	−	0.434232i	−0.845051	+	0.534686i	$0.820430\pi$
$98$		0			0
$99$	0.595211			0.0598209
$100$		0			0
$101$	−10.7574			−1.07040			−0.535202	−	0.844724i	$-0.679764\pi$
$101$	−10.7574			−1.07040			−0.535202	+	0.844724i	$0.679764\pi$
$102$		0			0
$103$	−0.229382	−	0.166656i	−0.0226017	−	0.0164211i	0.576427	−	0.817149i	$-0.304446\pi$
$103$	−0.229382	−	0.166656i	−0.0226017	−	0.0164211i	−0.599029	+	0.800728i	$0.704446\pi$
$104$		0			0
$105$	9.85937	−	1.88590i	0.962176	−	0.184045i
$106$		0			0
$107$	−10.9110			−1.05481			−0.527404	−	0.849615i	$-0.676835\pi$
$107$	−10.9110			−1.05481			−0.527404	+	0.849615i	$0.676835\pi$
$108$		0			0
$109$	−4.90445	−	15.0944i	−0.469762	−	1.44578i	−0.852894	−	0.522084i	$-0.825155\pi$
$109$	−4.90445	−	15.0944i	−0.469762	−	1.44578i	0.383133	−	0.923693i	$-0.374845\pi$
$110$		0			0
$111$	−5.36877	+	16.5234i	−0.509581	+	1.56833i
$112$		0			0
$113$	2.92325	+	8.99685i	0.274997	+	0.846352i	0.989220	+	0.146435i	$0.0467799\pi$
$113$	2.92325	+	8.99685i	0.274997	+	0.846352i	−0.714224	+	0.699917i	$0.753220\pi$
$114$		0			0
$115$	3.96545	+	7.20457i	0.369780	+	0.671829i
$116$		0			0
$117$	−1.19625	+	0.869127i	−0.110593	+	0.0803508i
$118$		0			0
$119$	−4.06584	+	2.95401i	−0.372715	+	0.270794i
$120$		0			0
$121$	6.93470	+	5.03835i	0.630427	+	0.458032i
$122$		0			0
$123$	−4.55361	+	14.0146i	−0.410585	+	1.26365i
$124$		0			0
$125$	−8.62531	−	7.11365i	−0.771472	−	0.636264i
$126$		0			0
$127$	1.35118	−	4.15851i	0.119898	−	0.369008i	−0.873039	−	0.487650i	$-0.837854\pi$
$127$	1.35118	−	4.15851i	0.119898	−	0.369008i	0.992937	+	0.118642i	$0.0378542\pi$
$128$		0			0
$129$	−15.8463	−	11.5130i	−1.39519	−	1.01366i
$130$		0			0
$131$	12.2926	−	8.93113i	1.07401	−	0.780317i	0.0973843	−	0.995247i	$-0.468952\pi$
$131$	12.2926	−	8.93113i	1.07401	−	0.780317i	0.976629	+	0.214930i	$0.0689524\pi$
$132$		0			0
$133$	−5.10195	+	3.70678i	−0.442395	+	0.321419i
$134$		0			0
$135$	−5.90015	−	10.7196i	−0.507804	−	0.922595i
$136$		0			0
$137$	3.06791	+	9.44205i	0.262109	+	0.806689i	0.992345	+	0.123494i	$0.0394100\pi$
$137$	3.06791	+	9.44205i	0.262109	+	0.806689i	−0.730236	+	0.683195i	$0.760590\pi$
$138$		0			0
$139$	−3.02195	+	9.30060i	−0.256318	+	0.788866i	0.737249	+	0.675621i	$0.236125\pi$
$139$	−3.02195	+	9.30060i	−0.256318	+	0.788866i	−0.993567	+	0.113245i	$0.963875\pi$
$140$		0			0
$141$	3.66637	+	11.2839i	0.308764	+	0.950279i
$142$		0			0
$143$	6.03234			0.504450
$144$		0			0
$145$	11.9745	−	2.29049i	0.994429	−	0.190215i
$146$		0			0
$147$	0.913260	+	0.663522i	0.0753244	+	0.0547264i
$148$		0			0
$149$	8.57760			0.702704			0.351352	−	0.936243i	$-0.385722\pi$
$149$	8.57760			0.702704			0.351352	+	0.936243i	$0.385722\pi$
$150$		0			0
$151$	19.4505			1.58286			0.791430	−	0.611260i	$-0.209337\pi$
$151$	19.4505			1.58286			0.791430	+	0.611260i	$0.209337\pi$
$152$		0			0
$153$	0.559752	+	0.406684i	0.0452533	+	0.0328784i
$154$		0			0
$155$	−0.831873	+	6.61162i	−0.0668176	+	0.531058i
$156$		0			0
$157$	−10.5103			−0.838809			−0.419405	−	0.907799i	$-0.637761\pi$
$157$	−10.5103			−0.838809			−0.419405	+	0.907799i	$0.637761\pi$
$158$		0			0
$159$	−3.61189	−	11.1163i	−0.286442	−	0.881576i
$160$		0			0
$161$	−3.15318	+	9.70448i	−0.248505	+	0.764820i
$162$		0			0
$163$	−5.26886	−	16.2159i	−0.412689	−	1.27013i	−0.914301	−	0.405035i	$-0.867259\pi$
$163$	−5.26886	−	16.2159i	−0.412689	−	1.27013i	0.501612	−	0.865093i	$-0.332741\pi$
$164$		0			0
$165$	−0.703813	+	5.59381i	−0.0547917	+	0.435478i
$166$		0			0
$167$	−8.61336	+	6.25797i	−0.666522	+	0.484256i	−0.868859	−	0.495059i	$-0.835146\pi$
$167$	−8.61336	+	6.25797i	−0.666522	+	0.484256i	0.202337	+	0.979316i	$0.435146\pi$
$168$		0			0
$169$	−1.60654	+	1.16722i	−0.123580	+	0.0897860i
$170$		0			0
$171$	0.702395	+	0.510320i	0.0537135	+	0.0390251i
$172$		0			0
$173$	−0.219389	+	0.675209i	−0.0166798	+	0.0513352i	−0.959050	−	0.283237i	$-0.908592\pi$
$173$	−0.219389	+	0.675209i	−0.0166798	+	0.0513352i	0.942370	+	0.334572i	$0.108592\pi$
$174$		0			0
$175$	−0.884939	−	13.8441i	−0.0668951	−	1.04651i
$176$		0			0
$177$	5.73519	−	17.6511i	0.431083	−	1.32674i
$178$		0			0
$179$	10.4045	+	7.55928i	0.777665	+	0.565007i	0.904277	−	0.426945i	$-0.140410\pi$
$179$	10.4045	+	7.55928i	0.777665	+	0.565007i	−0.126612	+	0.991952i	$0.540410\pi$
$180$		0			0
$181$	11.2367	−	8.16391i	0.835215	−	0.606819i	−0.0858153	−	0.996311i	$-0.527349\pi$
$181$	11.2367	−	8.16391i	0.835215	−	0.606819i	0.921030	+	0.389492i	$0.127349\pi$
$182$		0			0
$183$	18.1490	−	13.1861i	1.34162	−	0.974741i
$184$		0			0
$185$	21.7299	+	10.2120i	1.59761	+	0.750802i
$186$		0			0
$187$	−0.872252	−	2.68451i	−0.0637854	−	0.196311i
$188$		0			0
$189$	4.69158	−	14.4392i	0.341262	−	1.05030i
$190$		0			0
$191$	−5.33564	−	16.4214i	−0.386073	−	1.18821i	−0.935699	−	0.352800i	$-0.885230\pi$
$191$	−5.33564	−	16.4214i	−0.386073	−	1.18821i	0.549626	−	0.835411i	$-0.314770\pi$
$192$		0			0
$193$	10.5706			0.760886			0.380443	−	0.924804i	$-0.375771\pi$
$193$	10.5706			0.760886			0.380443	+	0.924804i	$0.375771\pi$
$194$		0			0
$195$	−6.75357	−	12.2701i	−0.483633	−	0.878681i
$196$		0			0
$197$	17.9192	+	13.0191i	1.27669	+	0.927570i	0.999448	−	0.0332299i	$-0.0105793\pi$
$197$	17.9192	+	13.0191i	1.27669	+	0.927570i	0.277243	+	0.960800i	$0.410579\pi$
$198$		0			0
$199$	5.63032			0.399123			0.199561	−	0.979885i	$-0.436048\pi$
$199$	5.63032			0.399123			0.199561	+	0.979885i	$0.436048\pi$
$200$		0			0
$201$	−15.8646			−1.11901
$202$		0			0
$203$	12.2381	+	8.89149i	0.858945	+	0.624060i
$204$		0			0
$205$	18.4306	+	8.66148i	1.28725	+	0.604944i
$206$		0			0
$207$	1.40479			0.0976396
$208$		0			0
$209$	−1.09453	−	3.36861i	−0.0757101	−	0.233012i
$210$		0			0
$211$	0.864430	−	2.66044i	0.0595098	−	0.183152i	−0.916882	−	0.399157i	$-0.869303\pi$
$211$	0.864430	−	2.66044i	0.0595098	−	0.183152i	0.976392	+	0.216005i	$0.0693027\pi$
$212$		0			0
$213$	5.78588	+	17.8071i	0.396442	+	1.22012i
$214$		0			0
$215$	−18.5199	+	19.7415i	−1.26304	+	1.34636i
$216$		0			0
$217$	−6.68915	+	4.85995i	−0.454089	+	0.329915i
$218$		0			0
$219$	3.80049	−	2.76122i	0.256814	−	0.186586i
$220$		0			0
$221$	5.67298	+	4.12166i	0.381606	+	0.277253i
$222$		0			0
$223$	3.49389	−	10.7531i	0.233968	−	0.720080i	−0.763289	−	0.646058i	$-0.776417\pi$
$223$	3.49389	−	10.7531i	0.233968	−	0.720080i	0.997257	−	0.0740219i	$-0.0235835\pi$
$224$		0			0
$225$	−1.77501	+	0.704836i	−0.118334	+	0.0469891i
$226$		0			0
$227$	−0.710009	+	2.18518i	−0.0471250	+	0.145036i	−0.971850	−	0.235600i	$-0.924295\pi$
$227$	−0.710009	+	2.18518i	−0.0471250	+	0.145036i	0.924725	+	0.380635i	$0.124295\pi$
$228$		0			0
$229$	6.36877	+	4.62718i	0.420860	+	0.305773i	0.777984	−	0.628284i	$-0.216243\pi$
$229$	6.36877	+	4.62718i	0.420860	+	0.305773i	−0.357124	+	0.934057i	$0.616243\pi$
$230$		0			0
$231$	−5.65941	+	4.11180i	−0.372362	+	0.270537i
$232$		0			0
$233$	−13.5589	+	9.85110i	−0.888271	+	0.645367i	−0.935427	−	0.353521i	$-0.884984\pi$
$233$	−13.5589	+	9.85110i	−0.888271	+	0.645367i	0.0471553	+	0.998888i	$0.484984\pi$
$234$		0			0
$235$	16.1046	−	3.08048i	1.05055	−	0.200948i
$236$		0			0
$237$	−3.90771	−	12.0267i	−0.253833	−	0.781218i
$238$		0			0
$239$	0.246711	−	0.759299i	0.0159584	−	0.0491149i	−0.942760	−	0.333471i	$-0.891780\pi$
$239$	0.246711	−	0.759299i	0.0159584	−	0.0491149i	0.958719	+	0.284356i	$0.0917799\pi$
$240$		0			0
$241$	−4.85323	−	14.9367i	−0.312624	−	0.962157i	−0.976722	−	0.214511i	$-0.931184\pi$
$241$	−4.85323	−	14.9367i	−0.312624	−	0.962157i	0.664098	−	0.747646i	$-0.268816\pi$
$242$		0			0
$243$	−3.94427			−0.253025
$244$		0			0
$245$	1.06735	−	1.13775i	0.0681903	−	0.0726883i
$246$		0			0
$247$	7.11863	+	5.17199i	0.452947	+	0.329086i
$248$		0			0
$249$	−6.34980			−0.402402
$250$		0			0
$251$	24.3655			1.53794			0.768970	−	0.639285i	$-0.220770\pi$
$251$	24.3655			1.53794			0.768970	+	0.639285i	$0.220770\pi$
$252$		0			0
$253$	−4.63650	−	3.36861i	−0.291494	−	0.211783i
$254$		0			0
$255$	−4.48391	+	4.77969i	−0.280794	+	0.299316i
$256$		0			0
$257$	14.1073			0.879991			0.439995	−	0.898000i	$-0.354980\pi$
$257$	14.1073			0.879991			0.439995	+	0.898000i	$0.354980\pi$
$258$		0			0
$259$	9.20591	+	28.3329i	0.572027	+	1.76052i
$260$		0			0
$261$	0.643551	−	1.98065i	0.0398348	−	0.122599i
$262$		0			0
$263$	−1.99003	−	6.12467i	−0.122710	−	0.377663i	0.870767	−	0.491696i	$-0.163623\pi$
$263$	−1.99003	−	6.12467i	−0.122710	−	0.377663i	−0.993477	+	0.114033i	$0.963623\pi$
$264$		0			0
$265$	−15.8652	+	3.03470i	−0.974593	+	0.186420i
$266$		0			0
$267$	−1.89717	+	1.37838i	−0.116105	+	0.0843554i
$268$		0			0
$269$	0.802788	−	0.583260i	0.0489469	−	0.0355620i	−0.563043	−	0.826428i	$-0.690369\pi$
$269$	0.802788	−	0.583260i	0.0489469	−	0.0355620i	0.611990	+	0.790866i	$0.290369\pi$
$270$		0			0
$271$	1.06443	+	0.773351i	0.0646593	+	0.0469777i	0.619645	−	0.784882i	$-0.287276\pi$
$271$	1.06443	+	0.773351i	0.0646593	+	0.0469777i	−0.554986	+	0.831860i	$0.687276\pi$
$272$		0			0
$273$	5.37019	−	16.5277i	0.325019	−	1.00030i
$274$		0			0
$275$	7.54857	+	1.93007i	0.455196	+	0.116388i
$276$		0			0
$277$	8.72488	−	26.8524i	0.524227	−	1.61341i	−0.241611	−	0.970373i	$-0.577676\pi$
$277$	8.72488	−	26.8524i	0.524227	−	1.61341i	0.765839	−	0.643033i	$-0.222324\pi$
$278$		0			0
$279$	0.920907	+	0.669078i	0.0551333	+	0.0400567i
$280$		0			0
$281$	−3.64420	+	2.64766i	−0.217395	+	0.157946i	−0.691153	−	0.722708i	$-0.742897\pi$
$281$	−3.64420	+	2.64766i	−0.217395	+	0.157946i	0.473758	+	0.880655i	$0.342897\pi$
$282$		0			0
$283$	−11.4024	+	8.28436i	−0.677805	+	0.492454i	−0.872629	−	0.488384i	$-0.837586\pi$
$283$	−11.4024	+	8.28436i	−0.677805	+	0.492454i	0.194824	+	0.980838i	$0.437586\pi$
$284$		0			0
$285$	−5.62656	+	5.99770i	−0.333288	+	0.355273i
$286$		0			0
$287$	7.80814	+	24.0310i	0.460900	+	1.41850i
$288$		0			0
$289$	−4.23936	+	13.0474i	−0.249374	+	0.767494i
$290$		0			0
$291$	−3.63797	−	11.1965i	−0.213262	−	0.656351i
$292$		0			0
$293$	11.4465			0.668710			0.334355	−	0.942447i	$-0.391482\pi$
$293$	11.4465			0.668710			0.334355	+	0.942447i	$0.391482\pi$
$294$		0			0
$295$	−23.2130	−	10.9090i	−1.35151	−	0.635146i
$296$		0			0
$297$	6.89859	+	5.01212i	0.400297	+	0.290833i
$298$		0			0
$299$	14.2373			0.823362
$300$		0			0
$301$	−33.5862			−1.93588
$302$		0			0
$303$	−14.0816	−	10.2309i	−0.808969	−	0.587751i
$304$		0			0
$305$	−14.9491	−	27.1600i	−0.855982	−	1.55518i
$306$		0			0
$307$	−16.5706			−0.945732			−0.472866	−	0.881134i	$-0.656781\pi$
$307$	−16.5706			−0.945732			−0.472866	+	0.881134i	$0.656781\pi$
$308$		0			0
$309$	−0.141766	−	0.436311i	−0.00806479	−	0.0248209i
$310$		0			0
$311$	−9.62010	+	29.6076i	−0.545506	+	1.67889i	0.174279	+	0.984696i	$0.444241\pi$
$311$	−9.62010	+	29.6076i	−0.545506	+	1.67889i	−0.719784	+	0.694198i	$0.755759\pi$
$312$		0			0
$313$	2.05593	+	6.32752i	0.116208	+	0.357652i	0.992197	−	0.124679i	$-0.0397901\pi$
$313$	2.05593	+	6.32752i	0.116208	+	0.357652i	−0.875989	+	0.482331i	$0.839790\pi$
$314$		0			0
$315$	−2.14465	−	1.00788i	−0.120838	−	0.0567878i
$316$		0			0
$317$	5.93475	−	4.31185i	0.333329	−	0.242178i	−0.408513	−	0.912753i	$-0.633953\pi$
$317$	5.93475	−	4.31185i	0.333329	−	0.242178i	0.741842	+	0.670575i	$0.233953\pi$
$318$		0			0
$319$	−6.87353	+	4.99391i	−0.384844	+	0.279605i
$320$		0			0
$321$	−14.2827	−	10.3770i	−0.797183	−	0.579187i
$322$		0			0
$323$	1.27231	−	3.91578i	0.0707935	−	0.217880i
$324$		0			0
$325$	−17.9894	+	7.14337i	−0.997870	+	0.396243i
$326$		0			0
$327$	7.93557	−	24.4232i	0.438838	−	1.35061i
$328$		0			0
$329$	16.4590	+	11.9582i	0.907415	+	0.659276i
$330$		0			0
$331$	−2.58578	+	1.87868i	−0.142127	+	0.103261i	−0.656577	−	0.754259i	$-0.727996\pi$
$331$	−2.58578	+	1.87868i	−0.142127	+	0.103261i	0.514450	+	0.857521i	$0.327996\pi$
$332$		0			0
$333$	3.31808	−	2.41073i	0.181830	−	0.132107i
$334$		0			0
$335$	−2.73694	+	21.7529i	−0.149535	+	1.18849i
$336$		0			0
$337$	0.0307849	+	0.0947461i	0.00167696	+	0.00516115i	0.951891	−	0.306435i	$-0.0991363\pi$
$337$	0.0307849	+	0.0947461i	0.00167696	+	0.00516115i	−0.950215	+	0.311596i	$0.899136\pi$
$338$		0			0
$339$	−4.72992	+	14.5572i	−0.256894	+	0.790639i
$340$		0			0
$341$	−1.43503	−	4.41658i	−0.0777114	−	0.239171i
$342$		0			0
$343$	−17.4856			−0.944134
$344$		0			0
$345$	−1.66111	+	13.2023i	−0.0894310	+	0.710786i
$346$		0			0
$347$	−14.7803	−	10.7385i	−0.793450	−	0.576475i	0.115536	−	0.993303i	$-0.463142\pi$
$347$	−14.7803	−	10.7385i	−0.793450	−	0.576475i	−0.908985	+	0.416828i	$0.863142\pi$
$348$		0			0
$349$	0.00101856			5.45223e−5			2.72611e−5	−	1.00000i	$-0.499991\pi$
$349$	0.00101856			5.45223e−5			2.72611e−5		1.00000i	$0.499991\pi$
$350$		0			0
$351$	−21.1835			−1.13069
$352$		0			0
$353$	−17.8547	−	12.9722i	−0.950310	−	0.690440i	0.000570491	−	1.00000i	$-0.499818\pi$
$353$	−17.8547	−	12.9722i	−0.950310	−	0.690440i	−0.950880	+	0.309560i	$0.899818\pi$
$354$		0			0
$355$	25.4145	−	4.86128i	1.34886	−	0.258010i
$356$		0			0
$357$	−8.13169			−0.430375
$358$		0			0
$359$	−5.54512	−	17.0661i	−0.292660	−	0.900715i	−0.983997	−	0.178183i	$-0.942978\pi$
$359$	−5.54512	−	17.0661i	−0.292660	−	0.900715i	0.691337	−	0.722532i	$-0.257022\pi$
$360$		0			0
$361$	−4.27478	+	13.1564i	−0.224989	+	0.692443i
$362$		0			0
$363$	4.28588	+	13.1906i	0.224950	+	0.692326i
$364$		0			0
$365$	−3.13041	−	5.68743i	−0.163853	−	0.297694i
$366$		0			0
$367$	22.5544	−	16.3867i	1.17733	−	0.855380i	0.185461	−	0.982652i	$-0.440622\pi$
$367$	22.5544	−	16.3867i	1.17733	−	0.855380i	0.991868	+	0.127272i	$0.0406221\pi$
$368$		0			0
$369$	2.81428	−	2.04470i	0.146506	−	0.106443i
$370$		0			0
$371$	−16.2144	−	11.7805i	−0.841811	−	0.611612i
$372$		0			0
$373$	−3.59702	+	11.0705i	−0.186246	+	0.573208i	−0.999968	−	0.00804784i	$-0.997438\pi$
$373$	−3.59702	+	11.0705i	−0.186246	+	0.573208i	0.813721	+	0.581255i	$0.197438\pi$
$374$		0			0
$375$	−4.52520	−	17.5150i	−0.233680	−	0.904473i
$376$		0			0
$377$	6.52226	−	20.0735i	0.335914	−	1.03384i
$378$		0			0
$379$	19.9810	+	14.5170i	1.02635	+	0.745689i	0.967576	−	0.252582i	$-0.0812796\pi$
$379$	19.9810	+	14.5170i	1.02635	+	0.745689i	0.0587779	+	0.998271i	$0.481280\pi$
$380$		0			0
$381$	5.72370	−	4.15851i	0.293234	−	0.213047i
$382$		0			0
$383$	23.7302	−	17.2410i	1.21256	−	0.880973i	0.217095	−	0.976150i	$-0.430342\pi$
$383$	23.7302	−	17.2410i	1.21256	−	0.880973i	0.995460	+	0.0951771i	$0.0303417\pi$
$384$		0			0
$385$	4.66156	+	8.46929i	0.237575	+	0.431635i
$386$		0			0
$387$	1.42886	+	4.39757i	0.0726328	+	0.223541i
$388$		0			0
$389$	−8.99881	+	27.6955i	−0.456258	+	1.40422i	0.413395	+	0.910552i	$0.364343\pi$
$389$	−8.99881	+	27.6955i	−0.456258	+	1.40422i	−0.869652	+	0.493665i	$0.835657\pi$
$390$		0			0
$391$	−2.05865	−	6.33587i	−0.104110	−	0.320419i
$392$		0			0
$393$	24.5853			1.24016
$394$		0			0
$395$	−17.1646	+	3.28325i	−0.863646	+	0.165198i
$396$		0			0
$397$	−3.35891	−	2.44039i	−0.168579	−	0.122480i	0.500297	−	0.865854i	$-0.333224\pi$
$397$	−3.35891	−	2.44039i	−0.168579	−	0.122480i	−0.668876	+	0.743374i	$0.733224\pi$
$398$		0			0
$399$	−10.2039			−0.510834
$400$		0			0
$401$	−7.88050			−0.393533			−0.196767	−	0.980450i	$-0.563044\pi$
$401$	−7.88050			−0.393533			−0.196767	+	0.980450i	$0.563044\pi$
$402$		0			0
$403$	9.33321	+	6.78097i	0.464920	+	0.337784i
$404$		0			0
$405$	2.15167	−	17.1012i	0.106918	−	0.849767i
$406$		0			0
$407$	−16.7321			−0.829380
$408$		0			0
$409$	6.80963	+	20.9579i	0.336715	+	1.03630i	0.965871	+	0.259022i	$0.0834004\pi$
$409$	6.80963	+	20.9579i	0.336715	+	1.03630i	−0.629157	+	0.777278i	$0.716600\pi$
$410$		0			0
$411$	−4.96398	+	15.2776i	−0.244855	+	0.753586i
$412$		0			0
$413$	−9.83422	−	30.2666i	−0.483910	−	1.48932i
$414$		0			0
$415$	−1.09546	+	8.70656i	−0.0537739	+	0.427388i
$416$		0			0
$417$	−12.8012	+	9.30060i	−0.626876	+	0.455452i
$418$		0			0
$419$	−8.79211	+	6.38784i	−0.429523	+	0.312066i	−0.781458	−	0.623958i	$-0.785524\pi$
$419$	−8.79211	+	6.38784i	−0.429523	+	0.312066i	0.351935	+	0.936024i	$0.385524\pi$
$420$		0			0
$421$	18.0533	+	13.1165i	0.879865	+	0.639260i	0.933216	−	0.359316i	$-0.116990\pi$
$421$	18.0533	+	13.1165i	0.879865	+	0.639260i	−0.0533506	+	0.998576i	$0.516990\pi$
$422$		0			0
$423$	0.865514	−	2.66378i	0.0420827	−	0.129517i
$424$		0			0
$425$	5.78013	+	6.97273i	0.280378	+	0.338227i
$426$		0			0
$427$	11.8870	−	36.5843i	0.575250	−	1.77044i
$428$		0			0
$429$	7.89644	+	5.73710i	0.381244	+	0.276990i
$430$		0			0
$431$	−12.8148	+	9.31052i	−0.617268	+	0.448472i	−0.851966	−	0.523597i	$-0.824590\pi$
$431$	−12.8148	+	9.31052i	−0.617268	+	0.448472i	0.234698	+	0.972068i	$0.424590\pi$
$432$		0			0
$433$	−2.53982	+	1.84529i	−0.122056	+	0.0886788i	−0.647138	−	0.762373i	$-0.724034\pi$
$433$	−2.53982	+	1.84529i	−0.122056	+	0.0886788i	0.525083	+	0.851051i	$0.324034\pi$
$434$		0			0
$435$	17.8532	+	8.39016i	0.855997	+	0.402277i
$436$		0			0
$437$	−2.58326	−	7.95045i	−0.123574	−	0.380322i
$438$		0			0
$439$	7.20094	−	22.1622i	0.343682	−	1.05775i	−0.618603	−	0.785704i	$-0.712301\pi$
$439$	7.20094	−	22.1622i	0.343682	−	1.05775i	0.962285	−	0.272042i	$-0.0876989\pi$
$440$		0			0
$441$	−0.0823486	−	0.253443i	−0.00392136	−	0.0120687i
$442$		0			0
$443$	16.2390			0.771539			0.385769	−	0.922595i	$-0.373936\pi$
$443$	16.2390			0.771539			0.385769	+	0.922595i	$0.373936\pi$
$444$		0			0
$445$	1.56267	+	2.83912i	0.0740778	+	0.134587i
$446$		0			0
$447$	11.2282	+	8.15778i	0.531077	+	0.385850i
$448$		0			0
$449$	7.63333			0.360239			0.180120	−	0.983645i	$-0.442352\pi$
$449$	7.63333			0.360239			0.180120	+	0.983645i	$0.442352\pi$
$450$		0			0
$451$	−14.1916			−0.668257
$452$		0			0
$453$	25.4610	+	18.4985i	1.19626	+	0.869137i
$454$		0			0
$455$	−21.7356	−	10.2147i	−1.01898	−	0.478873i
$456$		0			0
$457$	−38.0943			−1.78198			−0.890988	−	0.454027i	$-0.849987\pi$
$457$	−38.0943			−1.78198			−0.890988	+	0.454027i	$0.849987\pi$
$458$		0			0
$459$	3.06304	+	9.42707i	0.142970	+	0.440018i
$460$		0			0
$461$	−4.86031	+	14.9585i	−0.226367	+	0.696687i	0.771783	+	0.635886i	$0.219365\pi$
$461$	−4.86031	+	14.9585i	−0.226367	+	0.696687i	−0.998150	+	0.0608004i	$0.980635\pi$
$462$		0			0
$463$	2.88287	+	8.87258i	0.133979	+	0.412344i	0.995430	−	0.0954968i	$-0.0304440\pi$
$463$	2.88287	+	8.87258i	0.133979	+	0.412344i	−0.861451	+	0.507840i	$0.830444\pi$
$464$		0			0
$465$	−7.37696	+	7.86356i	−0.342098	+	0.364664i
$466$		0			0
$467$	13.1656	−	9.56533i	0.609229	−	0.442631i	−0.239914	−	0.970794i	$-0.577119\pi$
$467$	13.1656	−	9.56533i	0.609229	−	0.442631i	0.849143	+	0.528163i	$0.177119\pi$
$468$		0			0
$469$	−22.0080	+	15.9897i	−1.01623	+	0.738337i
$470$		0			0
$471$	−13.7581	−	9.99584i	−0.633940	−	0.460584i
$472$		0			0
$473$	5.82921	−	17.9405i	0.268027	−	0.824904i
$474$		0			0
$475$	7.25309	+	8.74960i	0.332795	+	0.401459i
$476$		0			0
$477$	−0.852652	+	2.62419i	−0.0390402	+	0.120153i
$478$		0			0
$479$	−29.3198	−	21.3021i	−1.33966	−	0.973317i	−0.999457	−	0.0329642i	$-0.989505\pi$
$479$	−29.3198	−	21.3021i	−1.33966	−	0.973317i	−0.340200	−	0.940353i	$-0.610495\pi$
$480$		0			0
$481$	33.6281	−	24.4322i	1.53331	−	1.11401i
$482$		0			0
$483$	−13.3571	+	9.70448i	−0.607768	+	0.441569i
$484$		0			0
$485$	−15.9798	+	3.05661i	−0.725605	+	0.138794i
$486$		0			0
$487$	−7.48335	−	23.0314i	−0.339103	−	1.04365i	−0.964665	−	0.263478i	$-0.915130\pi$
$487$	−7.48335	−	23.0314i	−0.339103	−	1.04365i	0.625562	−	0.780174i	$-0.284870\pi$
$488$		0			0
$489$	8.52520	−	26.2379i	0.385523	−	1.18652i
$490$		0			0
$491$	−12.3336	−	37.9588i	−0.556606	−	1.71306i	−0.691663	−	0.722220i	$-0.743122\pi$
$491$	−12.3336	−	37.9588i	−0.556606	−	1.71306i	0.135057	−	0.990838i	$-0.456878\pi$
$492$		0			0
$493$	−9.87619			−0.444801
$494$		0			0
$495$	0.910599	−	0.970664i	0.0409284	−	0.0436281i
$496$		0			0
$497$	25.9739	+	18.8711i	1.16509	+	0.846485i
$498$		0			0
$499$	−13.0305			−0.583326			−0.291663	−	0.956521i	$-0.594209\pi$
$499$	−13.0305			−0.583326			−0.291663	+	0.956521i	$0.594209\pi$
$500$		0			0
$501$	−17.2267			−0.769633
$502$		0			0
$503$	23.1682	+	16.8327i	1.03302	+	0.750534i	0.968911	−	0.247409i	$-0.0795792\pi$
$503$	23.1682	+	16.8327i	1.03302	+	0.750534i	0.0641098	+	0.997943i	$0.479579\pi$
$504$		0			0
$505$	−16.4575	+	17.5431i	−0.732350	+	0.780658i
$506$		0			0
$507$	−3.21308			−0.142698
$508$		0			0
$509$	4.98099	+	15.3299i	0.220779	+	0.679487i	0.998693	+	0.0511162i	$0.0162779\pi$
$509$	4.98099	+	15.3299i	0.220779	+	0.679487i	−0.777914	+	0.628371i	$0.783722\pi$
$510$		0			0
$511$	2.48918	−	7.66092i	0.110115	−	0.338899i
$512$		0			0
$513$	3.84360	+	11.8294i	0.169699	+	0.522280i
$514$		0			0
$515$	−0.622708	+	0.119112i	−0.0274398	+	0.00524868i
$516$		0			0
$517$	−9.24422	+	6.71632i	−0.406561	+	0.295384i
$518$		0			0
$519$	−0.929345	+	0.675209i	−0.0407937	+	0.0296384i
$520$		0			0
$521$	−0.228454	−	0.165981i	−0.0100087	−	0.00727177i	0.582770	−	0.812637i	$-0.301969\pi$
$521$	−0.228454	−	0.165981i	−0.0100087	−	0.00727177i	−0.592778	+	0.805366i	$0.701969\pi$
$522$		0			0
$523$	−6.77886	+	20.8632i	−0.296419	+	0.912283i	0.686322	+	0.727297i	$0.259224\pi$
$523$	−6.77886	+	20.8632i	−0.296419	+	0.912283i	−0.982741	+	0.184986i	$0.940776\pi$
$524$		0			0
$525$	12.0081	−	18.9638i	0.524077	−	0.827647i
$526$		0			0
$527$	1.66813	−	5.13397i	0.0726648	−	0.223639i
$528$		0			0
$529$	7.66454	+	5.56861i	0.333241	+	0.242114i
$530$		0			0
$531$	−3.54454	+	2.57526i	−0.153820	+	0.111757i
$532$		0			0
$533$	28.5222	−	20.7226i	1.23543	−	0.897595i
$534$		0			0
$535$	−16.6925	+	17.7936i	−0.721680	+	0.769284i
$536$		0			0
$537$	6.43031	+	19.7904i	0.277488	+	0.854021i
$538$		0			0
$539$	−0.335952	+	1.03395i	−0.0144705	+	0.0445356i
$540$		0			0
$541$	−3.32041	−	10.2192i	−0.142756	−	0.439356i	0.853960	−	0.520339i	$-0.174194\pi$
$541$	−3.32041	−	10.2192i	−0.142756	−	0.439356i	−0.996716	+	0.0809823i	$0.974194\pi$
$542$		0			0
$543$	22.4733			0.964423
$544$		0			0
$545$	−32.1190	−	15.0944i	−1.37582	−	0.646571i
$546$		0			0
$547$	10.5175	+	7.64141i	0.449696	+	0.326723i	0.789476	−	0.613782i	$-0.210353\pi$
$547$	10.5175	+	7.64141i	0.449696	+	0.326723i	−0.339780	+	0.940505i	$0.610353\pi$
$548$		0			0
$549$	−5.29582			−0.226020
$550$		0			0
$551$	−12.3930			−0.527958
$552$		0			0
$553$	−17.5424	−	12.7453i	−0.745980	−	0.541986i
$554$		0			0
$555$	18.7326	+	34.0341i	0.795155	+	1.44467i
$556$		0			0
$557$	−29.1903			−1.23683			−0.618417	−	0.785850i	$-0.712226\pi$
$557$	−29.1903			−1.23683			−0.618417	+	0.785850i	$0.712226\pi$
$558$		0			0
$559$	14.4812	+	44.5685i	0.612488	+	1.88504i
$560$		0			0
$561$	1.41133	−	4.34364i	0.0595865	−	0.183388i
$562$		0			0
$563$	1.01291	+	3.11743i	0.0426893	+	0.131384i	0.970130	−	0.242587i	$-0.0779960\pi$
$563$	1.01291	+	3.11743i	0.0426893	+	0.131384i	−0.927440	+	0.373971i	$0.877996\pi$
$564$		0			0
$565$	19.1442	+	8.99685i	0.805402	+	0.378500i
$566$		0			0
$567$	17.3018	−	12.5705i	0.726606	−	0.527910i
$568$		0			0
$569$	32.6938	−	23.7534i	1.37059	−	0.995795i	0.372903	−	0.927870i	$-0.378362\pi$
$569$	32.6938	−	23.7534i	1.37059	−	0.995795i	0.997690	−	0.0679246i	$-0.0216377\pi$
$570$		0			0
$571$	11.4959	+	8.35224i	0.481087	+	0.349530i	0.801746	−	0.597664i	$-0.203904\pi$
$571$	11.4959	+	8.35224i	0.481087	+	0.349530i	−0.320659	+	0.947195i	$0.603904\pi$
$572$		0			0
$573$	8.63324	−	26.5704i	0.360659	−	1.10999i
$574$		0			0
$575$	17.8158	+	4.55527i	0.742970	+	0.189968i
$576$		0			0
$577$	6.10251	−	18.7816i	0.254051	−	0.781888i	−0.739964	−	0.672646i	$-0.765158\pi$
$577$	6.10251	−	18.7816i	0.254051	−	0.781888i	0.994015	−	0.109242i	$-0.0348423\pi$
$578$		0			0
$579$	13.8371	+	10.0532i	0.575048	+	0.417797i
$580$		0			0
$581$	−8.80865	+	6.39986i	−0.365444	+	0.265511i
$582$		0			0
$583$	9.10685	−	6.61651i	0.377167	−	0.274028i
$584$		0			0
$585$	−0.412751	+	3.28049i	−0.0170651	+	0.135632i
$586$		0			0
$587$	−0.392868	−	1.20912i	−0.0162154	−	0.0499059i	0.942621	−	0.333864i	$-0.108352\pi$
$587$	−0.392868	−	1.20912i	−0.0162154	−	0.0499059i	−0.958837	+	0.283958i	$0.908352\pi$
$588$		0			0
$589$	2.09322	−	6.44226i	0.0862496	−	0.265449i
$590$		0			0
$591$	11.0747	+	34.0844i	0.455551	+	1.40204i
$592$		0			0
$593$	0.0773634			0.00317693			0.00158847	−	0.999999i	$-0.499494\pi$
$593$	0.0773634			0.00317693			0.00158847	+	0.999999i	$0.499494\pi$
$594$		0			0
$595$	−1.40287	+	11.1498i	−0.0575119	+	0.457098i
$596$		0			0
$597$	7.37019	+	5.35475i	0.301642	+	0.219156i
$598$		0			0
$599$	11.7236			0.479013			0.239507	−	0.970895i	$-0.423014\pi$
$599$	11.7236			0.479013			0.239507	+	0.970895i	$0.423014\pi$
$600$		0			0
$601$	46.2601			1.88699			0.943494	−	0.331390i	$-0.107517\pi$
$601$	46.2601			1.88699			0.943494	+	0.331390i	$0.107517\pi$
$602$		0			0
$603$	3.02988	+	2.20133i	0.123386	+	0.0896452i
$604$		0			0
$605$	18.8257	−	3.60099i	0.765375	−	0.146401i
$606$		0			0
$607$	0.690913			0.0280433			0.0140217	−	0.999902i	$-0.495537\pi$
$607$	0.690913			0.0280433			0.0140217	+	0.999902i	$0.495537\pi$
$608$		0			0
$609$	7.56355	+	23.2782i	0.306490	+	0.943281i
$610$		0			0
$611$	8.77181	−	26.9968i	0.354869	−	1.09218i
$612$		0			0
$613$	1.36121	+	4.18936i	0.0549786	+	0.169207i	0.974775	−	0.223188i	$-0.0716465\pi$
$613$	1.36121	+	4.18936i	0.0549786	+	0.169207i	−0.919797	+	0.392395i	$0.871647\pi$
$614$		0			0
$615$	15.8884	+	28.8665i	0.640681	+	1.16401i
$616$		0			0
$617$	12.9238	−	9.38969i	0.520292	−	0.378015i	−0.296422	−	0.955057i	$-0.595793\pi$
$617$	12.9238	−	9.38969i	0.520292	−	0.378015i	0.816714	+	0.577043i	$0.195793\pi$
$618$		0			0
$619$	37.4238	−	27.1900i	1.50419	−	1.09286i	0.535513	−	0.844527i	$-0.320118\pi$
$619$	37.4238	−	27.1900i	1.50419	−	1.09286i	0.968676	−	0.248330i	$-0.0798817\pi$
$620$		0			0
$621$	16.2817	+	11.8294i	0.653364	+	0.474697i
$622$		0			0
$623$	−1.24258	+	3.82427i	−0.0497829	+	0.153216i
$624$		0			0
$625$	−24.7965	+	3.18309i	−0.991861	+	0.127323i
$626$		0			0
$627$	1.77098	−	5.45053i	0.0707263	−	0.217673i
$628$		0			0
$629$	−15.7353	−	11.4324i	−0.627409	−	0.455839i
$630$		0			0
$631$	18.3333	−	13.3200i	0.729839	−	0.530259i	−0.159674	−	0.987170i	$-0.551044\pi$
$631$	18.3333	−	13.3200i	0.729839	−	0.530259i	0.889512	+	0.456911i	$0.151044\pi$
$632$		0			0
$633$	3.66179	−	2.66044i	0.145543	−	0.105743i
$634$		0			0
$635$	−4.71452	−	8.56550i	−0.187090	−	0.339911i
$636$		0			0
$637$	−0.834587	−	2.56859i	−0.0330675	−	0.101771i
$638$		0			0
$639$	1.36586	−	4.20369i	0.0540326	−	0.166295i
$640$		0			0
$641$	−10.9656	−	33.7488i	−0.433117	−	1.33300i	−0.895004	−	0.446058i	$-0.852827\pi$
$641$	−10.9656	−	33.7488i	−0.433117	−	1.33300i	0.461887	−	0.886939i	$-0.347173\pi$
$642$		0			0
$643$	−3.09301			−0.121976			−0.0609881	−	0.998138i	$-0.519425\pi$
$643$	−3.09301			−0.121976			−0.0609881	+	0.998138i	$0.519425\pi$
$644$		0			0
$645$	−43.0181	+	8.22850i	−1.69384	+	0.323997i
$646$		0			0
$647$	19.3382	+	14.0500i	0.760263	+	0.552363i	0.898991	−	0.437967i	$-0.144301\pi$
$647$	19.3382	+	14.0500i	0.760263	+	0.552363i	−0.138728	+	0.990330i	$0.544301\pi$
$648$		0			0
$649$	17.8741			0.701619
$650$		0			0
$651$	−13.3783			−0.524337
$652$		0			0
$653$	13.4642	+	9.78232i	0.526895	+	0.382812i	0.819195	−	0.573515i	$-0.194421\pi$
$653$	13.4642	+	9.78232i	0.526895	+	0.382812i	−0.292300	+	0.956327i	$0.594421\pi$
$654$		0			0
$655$	4.24142	−	33.7103i	0.165726	−	1.31717i
$656$		0			0
$657$	−1.10897			−0.0432650
$658$		0			0
$659$	−14.9625	−	46.0497i	−0.582854	−	1.79384i	−0.607721	−	0.794151i	$-0.707916\pi$
$659$	−14.9625	−	46.0497i	−0.582854	−	1.79384i	0.0248663	−	0.999691i	$-0.492084\pi$
$660$		0			0
$661$	13.9981	−	43.0818i	0.544465	−	1.67569i	−0.177795	−	0.984068i	$-0.556896\pi$
$661$	13.9981	−	43.0818i	0.544465	−	1.67569i	0.722260	−	0.691622i	$-0.243104\pi$
$662$		0			0
$663$	3.50609	+	10.7906i	0.136165	+	0.419074i
$664$		0			0
$665$	−1.76036	+	13.9911i	−0.0682639	+	0.542553i
$666$		0			0
$667$	−16.2226	+	11.7864i	−0.628141	+	0.456371i
$668$		0			0
$669$	14.8003	−	10.7531i	0.572215	−	0.415738i
$670$		0			0
$671$	17.4788	+	12.6991i	0.674762	+	0.490244i
$672$		0			0
$673$	−6.27155	+	19.3018i	−0.241750	+	0.744031i	0.754404	+	0.656411i	$0.227926\pi$
$673$	−6.27155	+	19.3018i	−0.241750	+	0.744031i	−0.996154	+	0.0876202i	$0.972074\pi$
$674$		0			0
$675$	−26.5079	−	6.77774i	−1.02029	−	0.260875i
$676$		0			0
$677$	−0.618241	+	1.90275i	−0.0237609	+	0.0731286i	−0.962234	−	0.272224i	$-0.912241\pi$
$677$	−0.618241	+	1.90275i	−0.0237609	+	0.0731286i	0.938473	+	0.345353i	$0.112241\pi$
$678$		0			0
$679$	−16.3315	−	11.8655i	−0.626746	−	0.455357i
$680$		0			0
$681$	−3.00765	+	2.18518i	−0.115253	+	0.0837364i
$682$		0			0
$683$	−22.5515	+	16.3847i	−0.862911	+	0.626941i	−0.928675	−	0.370894i	$-0.879051\pi$
$683$	−22.5515	+	16.3847i	−0.862911	+	0.626941i	0.0657646	+	0.997835i	$0.479051\pi$
$684$		0			0
$685$	20.0915	+	9.44205i	0.767658	+	0.360762i
$686$		0			0
$687$	3.93612	+	12.1141i	0.150172	+	0.462182i
$688$		0			0
$689$	−8.64145	+	26.5957i	−0.329213	+	1.01321i
$690$		0			0
$691$	−1.05593	−	3.24983i	−0.0401697	−	0.123630i	0.928961	−	0.370178i	$-0.120703\pi$
$691$	−1.05593	−	3.24983i	−0.0401697	−	0.123630i	−0.969130	+	0.246549i	$0.920703\pi$
$692$		0			0
$693$	1.65139			0.0627312
$694$		0			0
$695$	10.5441	+	19.1569i	0.399961	+	0.726664i
$696$		0			0
$697$	−13.3462	−	9.69656i	−0.505522	−	0.367283i
$698$		0			0
$699$	−27.1178			−1.02569
$700$		0			0
$701$	−11.3651			−0.429253			−0.214627	−	0.976696i	$-0.568854\pi$
$701$	−11.3651			−0.429253			−0.214627	+	0.976696i	$0.568854\pi$
$702$		0			0
$703$	−19.7452	−	14.3457i	−0.744704	−	0.541059i
$704$		0			0
$705$	24.0108	+	11.2839i	0.904301	+	0.424978i
$706$		0			0
$707$	−29.8461			−1.12248
$708$		0			0
$709$	4.94898	+	15.2314i	0.185863	+	0.572027i	0.999962	−	0.00869878i	$-0.00276894\pi$
$709$	4.94898	+	15.2314i	0.185863	+	0.572027i	−0.814099	+	0.580726i	$0.802769\pi$
$710$		0			0
$711$	−0.922485	+	2.83912i	−0.0345959	+	0.106475i
$712$		0			0
$713$	−3.38690	−	10.4238i	−0.126840	−	0.390374i
$714$		0			0
$715$	9.22873	−	9.83749i	0.345135	−	0.367901i
$716$		0			0
$717$	1.04508	−	0.759299i	0.0390294	−	0.0283565i
$718$		0			0
$719$	20.9330	−	15.2087i	0.780669	−	0.567189i	−0.124511	−	0.992218i	$-0.539736\pi$
$719$	20.9330	−	15.2087i	0.780669	−	0.567189i	0.905180	+	0.425029i	$0.139736\pi$
$720$		0			0
$721$	−0.636414	−	0.462382i	−0.0237013	−	0.0172200i
$722$		0			0
$723$	7.85268	−	24.1681i	0.292044	−	0.898820i
$724$		0			0
$725$	14.5842	−	23.0321i	0.541644	−	0.855390i
$726$		0			0
$727$	−7.11693	+	21.9037i	−0.263952	+	0.812362i	0.727981	+	0.685598i	$0.240459\pi$
$727$	−7.11693	+	21.9037i	−0.263952	+	0.812362i	−0.991933	+	0.126764i	$0.959541\pi$
$728$		0			0
$729$	−23.8713	−	17.3435i	−0.884123	−	0.642353i
$730$		0			0
$731$	17.7400	−	12.8888i	0.656136	−	0.476711i
$732$		0			0
$733$	11.7258	−	8.51932i	0.433104	−	0.314668i	−0.349785	−	0.936830i	$-0.613745\pi$
$733$	11.7258	−	8.51932i	0.433104	−	0.314668i	0.782889	+	0.622162i	$0.213745\pi$
$734$		0			0
$735$	2.47924	−	0.474229i	0.0914482	−	0.0174922i
$736$		0			0
$737$	−4.72140	−	14.5310i	−0.173915	−	0.535255i
$738$		0			0
$739$	−5.77126	+	17.7621i	−0.212299	+	0.653390i	0.787035	+	0.616908i	$0.211615\pi$
$739$	−5.77126	+	17.7621i	−0.212299	+	0.653390i	−0.999334	+	0.0364819i	$0.988385\pi$
$740$		0			0
$741$	4.39955	+	13.5404i	0.161622	+	0.497420i
$742$		0			0
$743$	8.17880			0.300051			0.150026	−	0.988682i	$-0.452064\pi$
$743$	8.17880			0.300051			0.150026	+	0.988682i	$0.452064\pi$
$744$		0			0
$745$	13.1227	−	13.9883i	0.480777	−	0.512491i
$746$		0			0
$747$	1.21270	+	0.881080i	0.0443705	+	0.0322370i
$748$		0			0
$749$	−30.2723			−1.10612
$750$		0			0
$751$	−34.4410			−1.25677			−0.628386	−	0.777902i	$-0.716284\pi$
$751$	−34.4410			−1.25677			−0.628386	+	0.777902i	$0.716284\pi$
$752$		0			0
$753$	31.8949	+	23.1730i	1.16232	+	0.844471i
$754$		0			0
$755$	29.7569	−	31.7197i	1.08296	−	1.15440i
$756$		0			0
$757$	17.7950			0.646769			0.323385	−	0.946268i	$-0.395179\pi$
$757$	17.7950			0.646769			0.323385	+	0.946268i	$0.395179\pi$
$758$		0			0
$759$	−2.86551	−	8.81914i	−0.104012	−	0.320115i
$760$		0			0
$761$	−7.70908	+	23.7261i	−0.279454	+	0.860071i	0.708552	+	0.705658i	$0.249349\pi$
$761$	−7.70908	+	23.7261i	−0.279454	+	0.860071i	−0.988006	+	0.154413i	$0.950651\pi$
$762$		0			0
$763$	−13.6072	−	41.8788i	−0.492615	−	1.51611i
$764$		0			0
$765$	1.51957	−	0.290663i	0.0549401	−	0.0105089i
$766$		0			0
$767$	−35.9232	+	26.0998i	−1.29711	+	0.942408i
$768$		0			0
$769$	−13.2338	+	9.61494i	−0.477224	+	0.346724i	−0.800250	−	0.599667i	$-0.795300\pi$
$769$	−13.2338	+	9.61494i	−0.477224	+	0.346724i	0.323026	+	0.946390i	$0.395300\pi$
$770$		0			0
$771$	18.4667	+	13.4169i	0.665063	+	0.483196i
$772$		0			0
$773$	−12.7809	+	39.3355i	−0.459696	+	1.41480i	0.405836	+	0.913946i	$0.366980\pi$
$773$	−12.7809	+	39.3355i	−0.459696	+	1.41480i	−0.865532	+	0.500853i	$0.833020\pi$
$774$		0			0
$775$	9.50950	+	11.4716i	0.341591	+	0.412071i
$776$		0			0
$777$	−14.8955	+	45.8436i	−0.534372	+	1.64463i
$778$		0			0
$779$	−16.7472	−	12.1676i	−0.600031	−	0.435948i
$780$		0			0
$781$	−14.5882	+	10.5990i	−0.522008	+	0.379261i
$782$		0			0
$783$	24.1374	−	17.5369i	0.862600	−	0.626716i
$784$		0			0
$785$	−16.0794	+	17.1400i	−0.573898	+	0.611754i
$786$		0			0
$787$	−10.1542	−	31.2516i	−0.361960	−	1.11400i	−0.951863	−	0.306524i	$-0.900834\pi$
$787$	−10.1542	−	31.2516i	−0.361960	−	1.11400i	0.589903	−	0.807474i	$-0.299166\pi$
$788$		0			0
$789$	3.21993	−	9.90993i	0.114633	−	0.352803i
$790$		0			0
$791$	8.11047	+	24.9615i	0.288375	+	0.887528i
$792$		0			0
$793$	−53.6721			−1.90595
$794$		0			0
$795$	−23.6540	−	11.1163i	−0.838922	−	0.394253i
$796$		0			0
$797$	0.748982	+	0.544168i	0.0265303	+	0.0192754i	0.600971	−	0.799271i	$-0.294781\pi$
$797$	0.748982	+	0.544168i	0.0265303	+	0.0192754i	−0.574441	+	0.818546i	$0.694781\pi$
$798$		0			0
$799$	−13.2825			−0.469902
$800$		0			0
$801$	0.553588			0.0195601
$802$		0			0
$803$	3.66015	+	2.65925i	0.129164	+	0.0938429i
$804$		0			0
$805$	11.0020	+	19.9888i	0.387770	+	0.704514i
$806$		0			0
$807$	1.60558			0.0565190
$808$		0			0
$809$	−11.3223	−	34.8464i	−0.398070	−	1.22513i	−0.926545	−	0.376184i	$-0.877236\pi$
$809$	−11.3223	−	34.8464i	−0.398070	−	1.22513i	0.528475	−	0.848949i	$-0.322764\pi$
$810$		0			0
$811$	−1.82559	+	5.61858i	−0.0641051	+	0.197295i	−0.977979	−	0.208703i	$-0.933076\pi$
$811$	−1.82559	+	5.61858i	−0.0641051	+	0.197295i	0.913874	+	0.405998i	$0.133076\pi$
$812$		0			0
$813$	0.657851	+	2.02466i	0.0230719	+	0.0710079i
$814$		0			0
$815$	−34.5055	−	16.2159i	−1.20867	−	0.568018i
$816$		0			0
$817$	22.2607	−	16.1733i	0.778802	−	0.565833i
$818$		0			0
$819$	−3.31896	+	2.41136i	−0.115974	+	0.0842599i
$820$		0			0
$821$	−8.71298	−	6.33035i	−0.304085	−	0.220931i	0.425269	−	0.905067i	$-0.360179\pi$
$821$	−8.71298	−	6.33035i	−0.304085	−	0.220931i	−0.729354	+	0.684136i	$0.760179\pi$
$822$		0			0
$823$	−9.59092	+	29.5178i	−0.334319	+	1.02893i	0.632738	+	0.774366i	$0.281931\pi$
$823$	−9.59092	+	29.5178i	−0.334319	+	1.02893i	−0.967057	+	0.254561i	$0.918069\pi$
$824$		0			0
$825$	8.04559	+	9.70561i	0.280112	+	0.337906i
$826$		0			0
$827$	0.0247830	−	0.0762742i	0.000861789	−	0.00265231i	−0.950625	−	0.310343i	$-0.899556\pi$
$827$	0.0247830	−	0.0762742i	0.000861789	−	0.00265231i	0.951486	+	0.307691i	$0.0995561\pi$
$828$		0			0
$829$	−9.29064	−	6.75004i	−0.322677	−	0.234439i	0.414640	−	0.909986i	$-0.363908\pi$
$829$	−9.29064	−	6.75004i	−0.322677	−	0.234439i	−0.737317	+	0.675547i	$0.763908\pi$
$830$		0			0
$831$	36.9592	−	26.8524i	1.28210	−	0.931500i
$832$		0			0
$833$	−1.02240	+	0.742816i	−0.0354240	+	0.0257371i
$834$		0			0
$835$	−2.97193	+	23.6205i	−0.102848	+	0.817422i
$836$		0			0
$837$	5.03933	+	15.5095i	0.174185	+	0.536085i
$838$		0			0
$839$	1.57930	−	4.86059i	0.0545235	−	0.167806i	−0.920087	−	0.391715i	$-0.871882\pi$
$839$	1.57930	−	4.86059i	0.0545235	−	0.167806i	0.974610	+	0.223909i	$0.0718819\pi$
$840$		0			0
$841$	0.224676	+	0.691483i	0.00774746	+	0.0238442i
$842$		0			0
$843$	−7.28840			−0.251026
$844$		0			0
$845$	−0.554315	+	4.40563i	−0.0190690	+	0.151558i
$846$		0			0
$847$	19.2401	+	13.9787i	0.661097	+	0.480315i
$848$		0			0
$849$	−22.8049			−0.782662
$850$		0			0
$851$	−39.4904			−1.35371
$852$		0			0
$853$	13.6853	+	9.94295i	0.468576	+	0.340440i	0.796886	−	0.604130i	$-0.206479\pi$
$853$	13.6853	+	9.94295i	0.468576	+	0.340440i	−0.328310	+	0.944570i	$0.606479\pi$
$854$		0			0
$855$	1.90680	−	0.364733i	0.0652112	−	0.0124736i
$856$		0			0
$857$	−29.7007			−1.01456			−0.507278	−	0.861783i	$-0.669348\pi$
$857$	−29.7007			−1.01456			−0.507278	+	0.861783i	$0.669348\pi$
$858$		0			0
$859$	15.0089	+	46.1926i	0.512097	+	1.57607i	0.788503	+	0.615031i	$0.210856\pi$
$859$	15.0089	+	46.1926i	0.512097	+	1.57607i	−0.276406	+	0.961041i	$0.589144\pi$
$860$		0			0
$861$	−12.6338	+	38.8830i	−0.430560	+	1.32513i
$862$		0			0
$863$	3.01486	+	9.27879i	0.102627	+	0.315854i	0.989166	−	0.146800i	$-0.0468974\pi$
$863$	3.01486	+	9.27879i	0.102627	+	0.315854i	−0.886539	+	0.462654i	$0.846897\pi$
$864$		0			0
$865$	0.765487	+	1.39076i	0.0260273	+	0.0472874i
$866$		0			0
$867$	−17.9582	+	13.0474i	−0.609892	+	0.443113i
$868$		0			0
$869$	9.85272	−	7.15842i	0.334231	−	0.242833i
$870$		0			0
$871$	30.7072	+	22.3101i	1.04047	+	0.755948i
$872$		0			0
$873$	−0.858808	+	2.64314i	−0.0290662	+	0.0894567i
$874$		0			0
$875$	−23.9307	−	19.7366i	−0.809004	−	0.667218i
$876$		0			0
$877$	4.51904	−	13.9082i	0.152597	−	0.469646i	−0.845312	−	0.534272i	$-0.820586\pi$
$877$	4.51904	−	13.9082i	0.152597	−	0.469646i	0.997910	+	0.0646268i	$0.0205857\pi$
$878$		0			0
$879$	14.9836	+	10.8862i	0.505385	+	0.367184i
$880$		0			0
$881$	−25.6919	+	18.6663i	−0.865583	+	0.628883i	−0.929398	−	0.369079i	$-0.879673\pi$
$881$	−25.6919	+	18.6663i	−0.865583	+	0.628883i	0.0638152	+	0.997962i	$0.479673\pi$
$882$		0			0
$883$	−43.2649	+	31.4338i	−1.45598	+	1.05783i	−0.471593	+	0.881817i	$0.656321\pi$
$883$	−43.2649	+	31.4338i	−1.45598	+	1.05783i	−0.984388	+	0.176015i	$0.943679\pi$
$884$		0			0
$885$	−20.0111	−	36.3569i	−0.672667	−	1.22212i
$886$		0			0
$887$	−4.60930	−	14.1860i	−0.154765	−	0.476319i	0.843372	−	0.537331i	$-0.180567\pi$
$887$	−4.60930	−	14.1860i	−0.154765	−	0.476319i	−0.998137	+	0.0610120i	$0.980567\pi$
$888$		0			0
$889$	3.74881	−	11.5376i	0.125731	−	0.386960i
$890$		0			0
$891$	3.71177	+	11.4237i	0.124349	+	0.382707i
$892$		0			0
$893$	−16.6673			−0.557750
$894$		0			0
$895$	28.2451	−	5.40273i	0.944131	−	0.180593i
$896$		0			0
$897$	18.6368	+	13.5404i	0.622265	+	0.452102i
$898$		0			0
$899$	−16.2484			−0.541913
$900$		0			0
$901$	13.0851			0.435929
$902$		0			0
$903$	−43.9649	−	31.9424i	−1.46306	−	1.06298i
$904$		0			0
$905$	3.87707	−	30.8144i	0.128878	−	1.02431i
$906$		0			0
$907$	−41.9245			−1.39208			−0.696040	−	0.718003i	$-0.745056\pi$
$907$	−41.9245			−1.39208			−0.696040	+	0.718003i	$0.745056\pi$
$908$		0			0
$909$	1.26974	+	3.90786i	0.0421147	+	0.129616i
$910$		0			0
$911$	8.01167	−	24.6574i	0.265438	−	0.816936i	−0.726154	−	0.687533i	$-0.758694\pi$
$911$	8.01167	−	24.6574i	0.265438	−	0.816936i	0.991592	−	0.129403i	$-0.0413061\pi$
$912$		0			0
$913$	−1.88973	−	5.81600i	−0.0625410	−	0.192482i
$914$		0			0
$915$	6.26209	−	49.7703i	0.207018	−	1.64536i
$916$		0			0
$917$	34.1056	−	24.7791i	1.12626	−	0.818279i
$918$		0			0
$919$	−29.8996	+	21.7233i	−0.986296	+	0.716586i	−0.959107	−	0.283044i	$-0.908656\pi$
$919$	−29.8996	+	21.7233i	−0.986296	+	0.716586i	−0.0271894	+	0.999630i	$0.508656\pi$
$920$		0			0
$921$	−21.6912	−	15.7595i	−0.714748	−	0.519295i
$922$		0			0
$923$	13.8427	−	42.6035i	0.455639	−	1.40231i
$924$		0			0
$925$	49.8977	−	19.8138i	1.64063	−	0.651474i
$926$		0			0
$927$	−0.0334664	+	0.102999i	−0.00109918	+	0.00338293i
$928$		0			0
$929$	−4.08473	−	2.96773i	−0.134016	−	0.0973680i	0.518758	−	0.854921i	$-0.326395\pi$
$929$	−4.08473	−	2.96773i	−0.134016	−	0.0973680i	−0.652773	+	0.757553i	$0.726395\pi$
$930$		0			0
$931$	−1.28294	+	0.932109i	−0.0420466	+	0.0305486i
$932$		0			0
$933$	−40.7514	+	29.6076i	−1.33414	+	0.969310i
$934$		0			0
$935$	−5.71232	−	2.68451i	−0.186813	−	0.0877930i
$936$		0			0
$937$	−4.63967	−	14.2794i	−0.151571	−	0.466488i	0.846226	−	0.532824i	$-0.178869\pi$
$937$	−4.63967	−	14.2794i	−0.151571	−	0.466488i	−0.997797	+	0.0663355i	$0.978869\pi$
$938$		0			0
$939$	−3.32657	+	10.2381i	−0.108559	+	0.334109i
$940$		0			0
$941$	6.20803	+	19.1063i	0.202376	+	0.622849i	0.999811	+	0.0194443i	$0.00618970\pi$
$941$	6.20803	+	19.1063i	0.202376	+	0.622849i	−0.797435	+	0.603405i	$0.793810\pi$
$942$		0			0
$943$	−33.4944			−1.09073
$944$		0			0
$945$	−16.3698	−	29.7412i	−0.532509	−	0.967480i
$946$		0			0
$947$	40.3873	+	29.3431i	1.31241	+	0.953521i	0.999994	+	0.00357610i	$0.00113831\pi$
$947$	40.3873	+	29.3431i	1.31241	+	0.953521i	0.312416	+	0.949945i	$0.398862\pi$
$948$		0			0
$949$	−11.2392			−0.364839
$950$		0			0
$951$	11.8695			0.384895
$952$		0			0
$953$	−32.6679	−	23.7346i	−1.05822	−	0.768839i	−0.0844582	−	0.996427i	$-0.526916\pi$
$953$	−32.6679	−	23.7346i	−1.05822	−	0.768839i	−0.973757	+	0.227588i	$0.926916\pi$
$954$		0			0
$955$	−34.9427	−	16.4214i	−1.13072	−	0.531384i
$956$		0			0
$957$	−13.7471			−0.444379
$958$		0			0
$959$	8.51181	+	26.1967i	0.274861	+	0.845934i
$960$		0			0
$961$	−6.83512	+	21.0363i	−0.220488	+	0.678591i
$962$		0			0
$963$	1.28787	+	3.96366i	0.0415011	+	0.127727i
$964$		0			0
$965$	16.1717	−	17.2384i	0.520584	−	0.554923i
$966$		0			0
$967$	6.86880	−	4.99048i	0.220886	−	0.160483i	−0.471840	−	0.881684i	$-0.656410\pi$
$967$	6.86880	−	4.99048i	0.220886	−	0.160483i	0.692725	+	0.721202i	$0.256410\pi$
$968$		0			0
$969$	5.38961	−	3.91578i	0.173139	−	0.125793i
$970$		0			0
$971$	26.0720	+	18.9424i	0.836689	+	0.607890i	0.921444	−	0.388512i	$-0.127011\pi$
$971$	26.0720	+	18.9424i	0.836689	+	0.607890i	−0.0847547	+	0.996402i	$0.527011\pi$
$972$		0			0
$973$	−8.38429	+	25.8042i	−0.268788	+	0.827245i
$974$		0			0
$975$	−30.3421	−	7.75810i	−0.971726	−	0.248458i
$976$		0			0
$977$	−7.45045	+	22.9301i	−0.238361	+	0.733600i	0.758297	+	0.651909i	$0.226032\pi$
$977$	−7.45045	+	22.9301i	−0.238361	+	0.733600i	−0.996658	+	0.0816901i	$0.973968\pi$
$978$		0			0
$979$	−1.82711	−	1.32748i	−0.0583948	−	0.0424263i
$980$		0			0
$981$	−4.90445	+	3.56329i	−0.156587	+	0.113767i
$982$		0			0
$983$	13.3694	−	9.71347i	0.426419	−	0.309812i	−0.353796	−	0.935322i	$-0.615109\pi$
$983$	13.3694	−	9.71347i	0.426419	−	0.309812i	0.780215	+	0.625511i	$0.215109\pi$
$984$		0			0
$985$	48.6455	−	9.30492i	1.54998	−	0.296479i
$986$		0			0
$987$	10.1722	+	31.3069i	0.323786	+	0.996510i
$988$		0			0
$989$	13.7578	−	42.3423i	0.437474	−	1.34641i
$990$		0			0
$991$	−1.76806	−	5.44154i	−0.0561644	−	0.172856i	0.919039	−	0.394166i	$-0.128967\pi$
$991$	−1.76806	−	5.44154i	−0.0561644	−	0.172856i	−0.975203	+	0.221310i	$0.928967\pi$
$992$		0			0
$993$	−5.17156			−0.164114
$994$		0			0
$995$	8.61370	−	9.18188i	0.273072	−	0.291085i
$996$		0			0
$997$	−16.5087	−	11.9943i	−0.522837	−	0.379863i	0.294835	−	0.955548i	$-0.404735\pi$
$997$	−16.5087	−	11.9943i	−0.522837	−	0.379863i	−0.817671	+	0.575685i	$0.804735\pi$
$998$		0			0
$999$	58.7573			1.85900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.u.e.321.2		8
4.3	odd	2		200.2.m.b.121.2	yes	8
20.3	even	4		1000.2.q.b.649.4		16
20.7	even	4		1000.2.q.b.649.1		16
20.19	odd	2		1000.2.m.b.601.2		8
25.6	even	5	inner	400.2.u.e.81.2		8
25.9	even	10		10000.2.a.z.1.3		4
25.16	even	5		10000.2.a.q.1.2		4
100.19	odd	10		1000.2.m.b.401.2		8
100.31	odd	10		200.2.m.b.81.2	✓	8
100.59	odd	10		5000.2.a.f.1.2		4
100.67	even	20		1000.2.q.b.849.3		16
100.83	even	20		1000.2.q.b.849.2		16
100.91	odd	10		5000.2.a.i.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.b.81.2	✓	8	100.31	odd	10
200.2.m.b.121.2	yes	8	4.3	odd	2
400.2.u.e.81.2		8	25.6	even	5	inner
400.2.u.e.321.2		8	1.1	even	1	trivial
1000.2.m.b.401.2		8	100.19	odd	10
1000.2.m.b.601.2		8	20.19	odd	2
1000.2.q.b.649.1		16	20.7	even	4
1000.2.q.b.649.4		16	20.3	even	4
1000.2.q.b.849.2		16	100.83	even	20
1000.2.q.b.849.3		16	100.67	even	20
5000.2.a.f.1.2		4	100.59	odd	10
5000.2.a.i.1.3		4	100.91	odd	10
10000.2.a.q.1.2		4	25.16	even	5
10000.2.a.z.1.3		4	25.9	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 + 0.951057i) q^{3} +(1.52988 - 1.63079i) q^{5} +2.77447 q^{7} +(-0.118034 - 0.363271i) q^{9} +O(q^{10})\)	\(q+(1.30902 + 0.951057i) q^{3} +(1.52988 - 1.63079i) q^{5} +2.77447 q^{7} +(-0.118034 - 0.363271i) q^{9} +(-0.481536 + 1.48201i) q^{11} +(-1.19625 - 3.68168i) q^{13} +(3.55361 - 0.679734i) q^{15} +(-1.46545 + 1.06471i) q^{17} +(-1.83889 + 1.33603i) q^{19} +(3.63182 + 2.63868i) q^{21} +(-1.13650 + 3.49778i) q^{23} +(-0.318958 - 4.98982i) q^{25} +(1.69098 - 5.20431i) q^{27} +(4.41097 + 3.20475i) q^{29} +(-2.41097 + 1.75167i) q^{31} +(-2.03982 + 1.48201i) q^{33} +(4.24459 - 4.52458i) q^{35} +(3.31808 + 10.2120i) q^{37} +(1.93557 - 5.95708i) q^{39} +(2.81428 + 8.66148i) q^{41} -12.1055 q^{43} +(-0.772997 - 0.363271i) q^{45} +(5.93232 + 4.31008i) q^{47} +0.697669 q^{49} -2.93090 q^{51} +(-5.84416 - 4.24603i) q^{53} +(1.68017 + 3.05258i) q^{55} -3.67779 q^{57} +(-3.54454 - 10.9090i) q^{59} +(4.28441 - 13.1861i) q^{61} +(-0.327481 - 1.00788i) q^{63} +(-7.83417 - 3.68168i) q^{65} +(-7.93232 + 5.76317i) q^{67} +(-4.81428 + 3.49778i) q^{69} +(9.36175 + 6.80171i) q^{71} +(0.897175 - 2.76122i) q^{73} +(4.32808 - 6.83510i) q^{75} +(-1.33600 + 4.11180i) q^{77} +(-6.32281 - 4.59379i) q^{79} +(6.23607 - 4.53077i) q^{81} +(-3.17490 + 2.30670i) q^{83} +(-0.505635 + 4.01872i) q^{85} +(2.72613 + 8.39016i) q^{87} +(-0.447862 + 1.37838i) q^{89} +(-3.31896 - 10.2147i) q^{91} -4.82193 q^{93} +(-0.634486 + 5.04282i) q^{95} +(-5.88636 - 4.27669i) q^{97} +0.595211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9	\( 8 q + 6 q^{3} + 5 q^{5} - 4 q^{7} + 8 q^{9} + 2 q^{11} + 8 q^{13} + 5 q^{15} + 10 q^{17} - 3 q^{19} - 3 q^{21} - 6 q^{23} - 5 q^{25} + 18 q^{27} + 6 q^{29} + 10 q^{31} - 16 q^{33} + 15 q^{35} - 2 q^{37} + q^{39} - 4 q^{41} + 12 q^{43} + 12 q^{47} - 4 q^{49} + 20 q^{51} - 13 q^{53} - 20 q^{55} - 6 q^{57} - 29 q^{59} + 15 q^{61} - 4 q^{63} - 50 q^{65} - 28 q^{67} - 12 q^{69} + 16 q^{71} + q^{73} - 15 q^{75} - 11 q^{77} - 23 q^{79} + 32 q^{81} - 14 q^{83} - 15 q^{85} - 3 q^{87} - 7 q^{89} - 29 q^{91} + 20 q^{93} - 45 q^{95} - 3 q^{97} + 22 q^{99}+O(q^{100}) \) 8 * q + 6 * q^3 + 5 * q^5 - 4 * q^7 + 8 * q^9 + 2 * q^11 + 8 * q^13 + 5 * q^15 + 10 * q^17 - 3 * q^19 - 3 * q^21 - 6 * q^23 - 5 * q^25 + 18 * q^27 + 6 * q^29 + 10 * q^31 - 16 * q^33 + 15 * q^35 - 2 * q^37 + q^39 - 4 * q^41 + 12 * q^43 + 12 * q^47 - 4 * q^49 + 20 * q^51 - 13 * q^53 - 20 * q^55 - 6 * q^57 - 29 * q^59 + 15 * q^61 - 4 * q^63 - 50 * q^65 - 28 * q^67 - 12 * q^69 + 16 * q^71 + q^73 - 15 * q^75 - 11 * q^77 - 23 * q^79 + 32 * q^81 - 14 * q^83 - 15 * q^85 - 3 * q^87 - 7 * q^89 - 29 * q^91 + 20 * q^93 - 45 * q^95 - 3 * q^97 + 22 * q^99

Introduction

L-functions

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