LMFDB - Embedded newform 400.2.u.e.81.2

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			81.2
Root			$1.66637 - 0.917186i$ of defining polynomial
Character	$\chi$	$=$	400.81
Dual form			400.2.u.e.321.2

$q$-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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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	−0.141846	−	0.989889i	$-0.545304\pi$
$3$	1.30902	−	0.951057i	0.755761	−	0.549093i	0.897607	+	0.440796i	$0.145304\pi$
$4$		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	0.851847	−	0.523791i	$-0.175483\pi$
$11$	−0.481536	−	1.48201i	−0.145188	−	0.446844i	−0.997035	+	0.0769471i	$0.975483\pi$
$12$		0			0
$13$	−1.19625	+	3.68168i	−0.331780	+	1.02111i	0.636506	+	0.771272i	$0.280379\pi$
$13$	−1.19625	+	3.68168i	−0.331780	+	1.02111i	−0.968286	+	0.249843i	$0.919621\pi$
$14$		0			0
$15$	3.55361	+	0.679734i	0.917538	+	0.175507i
$16$		0			0
$17$	−1.46545	−	1.06471i	−0.355424	−	0.258231i	0.395717	−	0.918373i	$-0.370496\pi$
$17$	−1.46545	−	1.06471i	−0.355424	−	0.258231i	−0.751141	+	0.660142i	$0.770496\pi$
$18$		0			0
$19$	−1.83889	−	1.33603i	−0.421871	−	0.306507i	0.356519	−	0.934288i	$-0.383963\pi$
$19$	−1.83889	−	1.33603i	−0.421871	−	0.306507i	−0.778390	+	0.627781i	$0.783963\pi$
$20$		0			0
$21$	3.63182	−	2.63868i	0.792529	−	0.575806i
$22$		0			0
$23$	−1.13650	−	3.49778i	−0.236976	−	0.729338i	−0.996853	−	0.0792710i	$-0.974741\pi$
$23$	−1.13650	−	3.49778i	−0.236976	−	0.729338i	0.759877	−	0.650067i	$-0.225259\pi$
$24$		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	−0.0973576	−	0.995249i	$-0.531039\pi$
$29$	4.41097	−	3.20475i	0.819096	−	0.595108i	0.916453	+	0.400142i	$0.131039\pi$
$30$		0			0
$31$	−2.41097	−	1.75167i	−0.433022	−	0.314609i	0.349834	−	0.936812i	$-0.386238\pi$
$31$	−2.41097	−	1.75167i	−0.433022	−	0.314609i	−0.782856	+	0.622203i	$0.786238\pi$
$32$		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	−0.174334	−	0.984687i	$-0.555777\pi$
$37$	3.31808	−	10.2120i	0.545489	−	1.67884i	0.719824	−	0.694157i	$-0.244223\pi$
$38$		0			0
$39$	1.93557	+	5.95708i	0.309940	+	0.953897i
$40$		0			0
$41$	2.81428	−	8.66148i	0.439517	−	1.35270i	−0.448868	−	0.893598i	$-0.648173\pi$
$41$	2.81428	−	8.66148i	0.439517	−	1.35270i	0.888386	−	0.459098i	$-0.151827\pi$
$42$		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	−0.0640088	−	0.997949i	$-0.520389\pi$
$47$	5.93232	−	4.31008i	0.865318	−	0.628690i	0.929326	+	0.369259i	$0.120389\pi$
$48$		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	−0.911722	−	0.410808i	$-0.865247\pi$
$53$	−5.84416	+	4.24603i	−0.802757	+	0.583237i	0.108964	+	0.994046i	$0.465247\pi$
$54$		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	0.401920	+	0.915675i	$0.368343\pi$
$59$	−3.54454	+	10.9090i	−0.461460	+	1.42023i	−0.863380	+	0.504554i	$0.831657\pi$
$60$		0			0
$61$	4.28441	+	13.1861i	0.548562	+	1.68830i	0.712366	+	0.701808i	$0.247624\pi$
$61$	4.28441	+	13.1861i	0.548562	+	1.68830i	−0.163804	+	0.986493i	$0.552376\pi$
$62$		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	−0.0138437	−	0.999904i	$-0.504407\pi$
$67$	−7.93232	−	5.76317i	−0.969087	−	0.704083i	−0.955243	+	0.295821i	$0.904407\pi$
$68$		0			0
$69$	−4.81428	−	3.49778i	−0.579572	−	0.421084i
$70$		0			0
$71$	9.36175	−	6.80171i	1.11104	−	0.807214i	0.128209	−	0.991747i	$-0.459077\pi$
$71$	9.36175	−	6.80171i	1.11104	−	0.807214i	0.982826	+	0.184533i	$0.0590772\pi$
$72$		0			0
$73$	0.897175	+	2.76122i	0.105006	+	0.323176i	0.989732	−	0.142936i	$-0.0456543\pi$
$73$	0.897175	+	2.76122i	0.105006	+	0.323176i	−0.884726	+	0.466112i	$0.845654\pi$
$74$		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	−0.883616	−	0.468213i	$-0.844898\pi$
$79$	−6.32281	+	4.59379i	−0.711371	+	0.516842i	0.172244	+	0.985054i	$0.444898\pi$
$80$		0			0
$81$	6.23607	+	4.53077i	0.692896	+	0.503419i
$82$		0			0
$83$	−3.17490	−	2.30670i	−0.348490	−	0.253193i	0.399745	−	0.916626i	$-0.369099\pi$
$83$	−3.17490	−	2.30670i	−0.348490	−	0.253193i	−0.748235	+	0.663433i	$0.769099\pi$
$84$		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	0.924510	−	0.381158i	$-0.124475\pi$
$89$	−0.447862	−	1.37838i	−0.0474733	−	0.146108i	−0.971983	+	0.235050i	$0.924475\pi$
$90$		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	−0.845051	−	0.534686i	$-0.820430\pi$
$97$	−5.88636	+	4.27669i	−0.597669	+	0.434232i	0.247382	+	0.968918i	$0.420430\pi$
$98$		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	−0.599029	−	0.800728i	$-0.704446\pi$
$103$	−0.229382	+	0.166656i	−0.0226017	+	0.0164211i	0.576427	+	0.817149i	$0.304446\pi$
$104$		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	0.383133	+	0.923693i	$0.374845\pi$
$109$	−4.90445	+	15.0944i	−0.469762	+	1.44578i	−0.852894	+	0.522084i	$0.825155\pi$
$110$		0			0
$111$	−5.36877	−	16.5234i	−0.509581	−	1.56833i
$112$		0			0
$113$	2.92325	−	8.99685i	0.274997	−	0.846352i	−0.714224	−	0.699917i	$-0.753220\pi$
$113$	2.92325	−	8.99685i	0.274997	−	0.846352i	0.989220	−	0.146435i	$-0.0467799\pi$
$114$		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	0.992937	−	0.118642i	$-0.0378542\pi$
$127$	1.35118	+	4.15851i	0.119898	+	0.369008i	−0.873039	+	0.487650i	$0.837854\pi$
$128$		0			0
$129$	−15.8463	+	11.5130i	−1.39519	+	1.01366i
$130$		0			0
$131$	12.2926	+	8.93113i	1.07401	+	0.780317i	0.976629	−	0.214930i	$-0.0689524\pi$
$131$	12.2926	+	8.93113i	1.07401	+	0.780317i	0.0973843	+	0.995247i	$0.468952\pi$
$132$		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	−0.730236	−	0.683195i	$-0.760590\pi$
$137$	3.06791	−	9.44205i	0.262109	−	0.806689i	0.992345	−	0.123494i	$-0.0394100\pi$
$138$		0			0
$139$	−3.02195	−	9.30060i	−0.256318	−	0.788866i	−0.993567	−	0.113245i	$-0.963875\pi$
$139$	−3.02195	−	9.30060i	−0.256318	−	0.788866i	0.737249	−	0.675621i	$-0.236125\pi$
$140$		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	0.501612	+	0.865093i	$0.332741\pi$
$163$	−5.26886	+	16.2159i	−0.412689	+	1.27013i	−0.914301	+	0.405035i	$0.867259\pi$
$164$		0			0
$165$	−0.703813	−	5.59381i	−0.0547917	−	0.435478i
$166$		0			0
$167$	−8.61336	−	6.25797i	−0.666522	−	0.484256i	0.202337	−	0.979316i	$-0.435146\pi$
$167$	−8.61336	−	6.25797i	−0.666522	−	0.484256i	−0.868859	+	0.495059i	$0.835146\pi$
$168$		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	0.942370	−	0.334572i	$-0.108592\pi$
$173$	−0.219389	−	0.675209i	−0.0166798	−	0.0513352i	−0.959050	+	0.283237i	$0.908592\pi$
$174$		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	−0.126612	−	0.991952i	$-0.540410\pi$
$179$	10.4045	−	7.55928i	0.777665	−	0.565007i	0.904277	+	0.426945i	$0.140410\pi$
$180$		0			0
$181$	11.2367	+	8.16391i	0.835215	+	0.606819i	0.921030	−	0.389492i	$-0.127349\pi$
$181$	11.2367	+	8.16391i	0.835215	+	0.606819i	−0.0858153	+	0.996311i	$0.527349\pi$
$182$		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	0.549626	+	0.835411i	$0.314770\pi$
$191$	−5.33564	+	16.4214i	−0.386073	+	1.18821i	−0.935699	+	0.352800i	$0.885230\pi$
$192$		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	0.277243	−	0.960800i	$-0.410579\pi$
$197$	17.9192	−	13.0191i	1.27669	−	0.927570i	0.999448	+	0.0332299i	$0.0105793\pi$
$198$		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	0.976392	−	0.216005i	$-0.0693027\pi$
$211$	0.864430	+	2.66044i	0.0595098	+	0.183152i	−0.916882	+	0.399157i	$0.869303\pi$
$212$		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	0.997257	+	0.0740219i	$0.0235835\pi$
$223$	3.49389	+	10.7531i	0.233968	+	0.720080i	−0.763289	+	0.646058i	$0.776417\pi$
$224$		0			0
$225$	−1.77501	−	0.704836i	−0.118334	−	0.0469891i
$226$		0			0
$227$	−0.710009	−	2.18518i	−0.0471250	−	0.145036i	0.924725	−	0.380635i	$-0.124295\pi$
$227$	−0.710009	−	2.18518i	−0.0471250	−	0.145036i	−0.971850	+	0.235600i	$0.924295\pi$
$228$		0			0
$229$	6.36877	−	4.62718i	0.420860	−	0.305773i	−0.357124	−	0.934057i	$-0.616243\pi$
$229$	6.36877	−	4.62718i	0.420860	−	0.305773i	0.777984	+	0.628284i	$0.216243\pi$
$230$		0			0
$231$	−5.65941	−	4.11180i	−0.372362	−	0.270537i
$232$		0			0
$233$	−13.5589	−	9.85110i	−0.888271	−	0.645367i	0.0471553	−	0.998888i	$-0.484984\pi$
$233$	−13.5589	−	9.85110i	−0.888271	−	0.645367i	−0.935427	+	0.353521i	$0.884984\pi$
$234$		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	0.958719	−	0.284356i	$-0.0917799\pi$
$239$	0.246711	+	0.759299i	0.0159584	+	0.0491149i	−0.942760	+	0.333471i	$0.891780\pi$
$240$		0			0
$241$	−4.85323	+	14.9367i	−0.312624	+	0.962157i	0.664098	+	0.747646i	$0.268816\pi$
$241$	−4.85323	+	14.9367i	−0.312624	+	0.962157i	−0.976722	+	0.214511i	$0.931184\pi$
$242$		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	−0.993477	−	0.114033i	$-0.963623\pi$
$263$	−1.99003	+	6.12467i	−0.122710	+	0.377663i	0.870767	+	0.491696i	$0.163623\pi$
$264$		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	0.611990	−	0.790866i	$-0.290369\pi$
$269$	0.802788	+	0.583260i	0.0489469	+	0.0355620i	−0.563043	+	0.826428i	$0.690369\pi$
$270$		0			0
$271$	1.06443	−	0.773351i	0.0646593	−	0.0469777i	−0.554986	−	0.831860i	$-0.687276\pi$
$271$	1.06443	−	0.773351i	0.0646593	−	0.0469777i	0.619645	+	0.784882i	$0.287276\pi$
$272$		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	0.765839	+	0.643033i	$0.222324\pi$
$277$	8.72488	+	26.8524i	0.524227	+	1.61341i	−0.241611	+	0.970373i	$0.577676\pi$
$278$		0			0
$279$	0.920907	−	0.669078i	0.0551333	−	0.0400567i
$280$		0			0
$281$	−3.64420	−	2.64766i	−0.217395	−	0.157946i	0.473758	−	0.880655i	$-0.342897\pi$
$281$	−3.64420	−	2.64766i	−0.217395	−	0.157946i	−0.691153	+	0.722708i	$0.742897\pi$
$282$		0			0
$283$	−11.4024	−	8.28436i	−0.677805	−	0.492454i	0.194824	−	0.980838i	$-0.437586\pi$
$283$	−11.4024	−	8.28436i	−0.677805	−	0.492454i	−0.872629	+	0.488384i	$0.837586\pi$
$284$		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	−0.719784	−	0.694198i	$-0.755759\pi$
$311$	−9.62010	−	29.6076i	−0.545506	−	1.67889i	0.174279	−	0.984696i	$-0.444241\pi$
$312$		0			0
$313$	2.05593	−	6.32752i	0.116208	−	0.357652i	−0.875989	−	0.482331i	$-0.839790\pi$
$313$	2.05593	−	6.32752i	0.116208	−	0.357652i	0.992197	+	0.124679i	$0.0397901\pi$
$314$		0			0
$315$	−2.14465	+	1.00788i	−0.120838	+	0.0567878i
$316$		0			0
$317$	5.93475	+	4.31185i	0.333329	+	0.242178i	0.741842	−	0.670575i	$-0.233953\pi$
$317$	5.93475	+	4.31185i	0.333329	+	0.242178i	−0.408513	+	0.912753i	$0.633953\pi$
$318$		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	0.514450	−	0.857521i	$-0.327996\pi$
$331$	−2.58578	−	1.87868i	−0.142127	−	0.103261i	−0.656577	+	0.754259i	$0.727996\pi$
$332$		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	−0.950215	−	0.311596i	$-0.899136\pi$
$337$	0.0307849	−	0.0947461i	0.00167696	−	0.00516115i	0.951891	+	0.306435i	$0.0991363\pi$
$338$		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	−0.908985	−	0.416828i	$-0.863142\pi$
$347$	−14.7803	+	10.7385i	−0.793450	+	0.576475i	0.115536	+	0.993303i	$0.463142\pi$
$348$		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	−0.950880	−	0.309560i	$-0.899818\pi$
$353$	−17.8547	+	12.9722i	−0.950310	+	0.690440i	0.000570491		1.00000i	$0.499818\pi$
$354$		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	0.691337	+	0.722532i	$0.257022\pi$
$359$	−5.54512	+	17.0661i	−0.292660	+	0.900715i	−0.983997	+	0.178183i	$0.942978\pi$
$360$		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	0.991868	−	0.127272i	$-0.0406221\pi$
$367$	22.5544	+	16.3867i	1.17733	+	0.855380i	0.185461	+	0.982652i	$0.440622\pi$
$368$		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	0.813721	−	0.581255i	$-0.197438\pi$
$373$	−3.59702	−	11.0705i	−0.186246	−	0.573208i	−0.999968	+	0.00804784i	$0.997438\pi$
$374$		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	0.0587779	−	0.998271i	$-0.481280\pi$
$379$	19.9810	−	14.5170i	1.02635	−	0.745689i	0.967576	+	0.252582i	$0.0812796\pi$
$380$		0			0
$381$	5.72370	+	4.15851i	0.293234	+	0.213047i
$382$		0			0
$383$	23.7302	+	17.2410i	1.21256	+	0.880973i	0.995460	−	0.0951771i	$-0.0303417\pi$
$383$	23.7302	+	17.2410i	1.21256	+	0.880973i	0.217095	+	0.976150i	$0.430342\pi$
$384$		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	−0.869652	−	0.493665i	$-0.835657\pi$
$389$	−8.99881	−	27.6955i	−0.456258	−	1.40422i	0.413395	−	0.910552i	$-0.364343\pi$
$390$		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	−0.668876	−	0.743374i	$-0.733224\pi$
$397$	−3.35891	+	2.44039i	−0.168579	+	0.122480i	0.500297	+	0.865854i	$0.333224\pi$
$398$		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	−0.629157	−	0.777278i	$-0.716600\pi$
$409$	6.80963	−	20.9579i	0.336715	−	1.03630i	0.965871	−	0.259022i	$-0.0834004\pi$
$410$		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	0.351935	−	0.936024i	$-0.385524\pi$
$419$	−8.79211	−	6.38784i	−0.429523	−	0.312066i	−0.781458	+	0.623958i	$0.785524\pi$
$420$		0			0
$421$	18.0533	−	13.1165i	0.879865	−	0.639260i	−0.0533506	−	0.998576i	$-0.516990\pi$
$421$	18.0533	−	13.1165i	0.879865	−	0.639260i	0.933216	+	0.359316i	$0.116990\pi$
$422$		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	0.234698	−	0.972068i	$-0.424590\pi$
$431$	−12.8148	−	9.31052i	−0.617268	−	0.448472i	−0.851966	+	0.523597i	$0.824590\pi$
$432$		0			0
$433$	−2.53982	−	1.84529i	−0.122056	−	0.0886788i	0.525083	−	0.851051i	$-0.324034\pi$
$433$	−2.53982	−	1.84529i	−0.122056	−	0.0886788i	−0.647138	+	0.762373i	$0.724034\pi$
$434$		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	0.962285	+	0.272042i	$0.0876989\pi$
$439$	7.20094	+	22.1622i	0.343682	+	1.05775i	−0.618603	+	0.785704i	$0.712301\pi$
$440$		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	−0.998150	−	0.0608004i	$-0.980635\pi$
$461$	−4.86031	−	14.9585i	−0.226367	−	0.696687i	0.771783	−	0.635886i	$-0.219365\pi$
$462$		0			0
$463$	2.88287	−	8.87258i	0.133979	−	0.412344i	−0.861451	−	0.507840i	$-0.830444\pi$
$463$	2.88287	−	8.87258i	0.133979	−	0.412344i	0.995430	+	0.0954968i	$0.0304440\pi$
$464$		0			0
$465$	−7.37696	−	7.86356i	−0.342098	−	0.364664i
$466$		0			0
$467$	13.1656	+	9.56533i	0.609229	+	0.442631i	0.849143	−	0.528163i	$-0.177119\pi$
$467$	13.1656	+	9.56533i	0.609229	+	0.442631i	−0.239914	+	0.970794i	$0.577119\pi$
$468$		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	−0.340200	+	0.940353i	$0.610495\pi$
$479$	−29.3198	+	21.3021i	−1.33966	+	0.973317i	−0.999457	+	0.0329642i	$0.989505\pi$
$480$		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	0.625562	+	0.780174i	$0.284870\pi$
$487$	−7.48335	+	23.0314i	−0.339103	+	1.04365i	−0.964665	+	0.263478i	$0.915130\pi$
$488$		0			0
$489$	8.52520	+	26.2379i	0.385523	+	1.18652i
$490$		0			0
$491$	−12.3336	+	37.9588i	−0.556606	+	1.71306i	0.135057	+	0.990838i	$0.456878\pi$
$491$	−12.3336	+	37.9588i	−0.556606	+	1.71306i	−0.691663	+	0.722220i	$0.743122\pi$
$492$		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	0.0641098	−	0.997943i	$-0.479579\pi$
$503$	23.1682	−	16.8327i	1.03302	−	0.750534i	0.968911	+	0.247409i	$0.0795792\pi$
$504$		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	−0.777914	−	0.628371i	$-0.783722\pi$
$509$	4.98099	−	15.3299i	0.220779	−	0.679487i	0.998693	−	0.0511162i	$-0.0162779\pi$
$510$		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	−0.592778	−	0.805366i	$-0.701969\pi$
$521$	−0.228454	+	0.165981i	−0.0100087	+	0.00727177i	0.582770	+	0.812637i	$0.301969\pi$
$522$		0			0
$523$	−6.77886	−	20.8632i	−0.296419	−	0.912283i	−0.982741	−	0.184986i	$-0.940776\pi$
$523$	−6.77886	−	20.8632i	−0.296419	−	0.912283i	0.686322	−	0.727297i	$-0.259224\pi$
$524$		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	−0.996716	−	0.0809823i	$-0.974194\pi$
$541$	−3.32041	+	10.2192i	−0.142756	+	0.439356i	0.853960	+	0.520339i	$0.174194\pi$
$542$		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	−0.339780	−	0.940505i	$-0.610353\pi$
$547$	10.5175	−	7.64141i	0.449696	−	0.326723i	0.789476	+	0.613782i	$0.210353\pi$
$548$		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	−0.927440	−	0.373971i	$-0.877996\pi$
$563$	1.01291	−	3.11743i	0.0426893	−	0.131384i	0.970130	+	0.242587i	$0.0779960\pi$
$564$		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	0.997690	+	0.0679246i	$0.0216377\pi$
$569$	32.6938	+	23.7534i	1.37059	+	0.995795i	0.372903	+	0.927870i	$0.378362\pi$
$570$		0			0
$571$	11.4959	−	8.35224i	0.481087	−	0.349530i	−0.320659	−	0.947195i	$-0.603904\pi$
$571$	11.4959	−	8.35224i	0.481087	−	0.349530i	0.801746	+	0.597664i	$0.203904\pi$
$572$		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	0.994015	+	0.109242i	$0.0348423\pi$
$577$	6.10251	+	18.7816i	0.254051	+	0.781888i	−0.739964	+	0.672646i	$0.765158\pi$
$578$		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	−0.958837	−	0.283958i	$-0.908352\pi$
$587$	−0.392868	+	1.20912i	−0.0162154	+	0.0499059i	0.942621	+	0.333864i	$0.108352\pi$
$588$		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	−0.919797	−	0.392395i	$-0.871647\pi$
$613$	1.36121	−	4.18936i	0.0549786	−	0.169207i	0.974775	+	0.223188i	$0.0716465\pi$
$614$		0			0
$615$	15.8884	−	28.8665i	0.640681	−	1.16401i
$616$		0			0
$617$	12.9238	+	9.38969i	0.520292	+	0.378015i	0.816714	−	0.577043i	$-0.195793\pi$
$617$	12.9238	+	9.38969i	0.520292	+	0.378015i	−0.296422	+	0.955057i	$0.595793\pi$
$618$		0			0
$619$	37.4238	+	27.1900i	1.50419	+	1.09286i	0.968676	+	0.248330i	$0.0798817\pi$
$619$	37.4238	+	27.1900i	1.50419	+	1.09286i	0.535513	+	0.844527i	$0.320118\pi$
$620$		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	0.889512	−	0.456911i	$-0.151044\pi$
$631$	18.3333	+	13.3200i	0.729839	+	0.530259i	−0.159674	+	0.987170i	$0.551044\pi$
$632$		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	0.461887	+	0.886939i	$0.347173\pi$
$641$	−10.9656	+	33.7488i	−0.433117	+	1.33300i	−0.895004	+	0.446058i	$0.852827\pi$
$642$		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	−0.138728	−	0.990330i	$-0.544301\pi$
$647$	19.3382	−	14.0500i	0.760263	−	0.552363i	0.898991	+	0.437967i	$0.144301\pi$
$648$		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	−0.292300	−	0.956327i	$-0.594421\pi$
$653$	13.4642	−	9.78232i	0.526895	−	0.382812i	0.819195	+	0.573515i	$0.194421\pi$
$654$		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	0.0248663	+	0.999691i	$0.492084\pi$
$659$	−14.9625	+	46.0497i	−0.582854	+	1.79384i	−0.607721	+	0.794151i	$0.707916\pi$
$660$		0			0
$661$	13.9981	+	43.0818i	0.544465	+	1.67569i	0.722260	+	0.691622i	$0.243104\pi$
$661$	13.9981	+	43.0818i	0.544465	+	1.67569i	−0.177795	+	0.984068i	$0.556896\pi$
$662$		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	−0.996154	−	0.0876202i	$-0.972074\pi$
$673$	−6.27155	−	19.3018i	−0.241750	−	0.744031i	0.754404	−	0.656411i	$-0.227926\pi$
$674$		0			0
$675$	−26.5079	+	6.77774i	−1.02029	+	0.260875i
$676$		0			0
$677$	−0.618241	−	1.90275i	−0.0237609	−	0.0731286i	0.938473	−	0.345353i	$-0.112241\pi$
$677$	−0.618241	−	1.90275i	−0.0237609	−	0.0731286i	−0.962234	+	0.272224i	$0.912241\pi$
$678$		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	0.0657646	−	0.997835i	$-0.479051\pi$
$683$	−22.5515	−	16.3847i	−0.862911	−	0.626941i	−0.928675	+	0.370894i	$0.879051\pi$
$684$		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	−0.969130	−	0.246549i	$-0.920703\pi$
$691$	−1.05593	+	3.24983i	−0.0401697	+	0.123630i	0.928961	+	0.370178i	$0.120703\pi$
$692$		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	−0.814099	−	0.580726i	$-0.802769\pi$
$709$	4.94898	−	15.2314i	0.185863	−	0.572027i	0.999962	+	0.00869878i	$0.00276894\pi$
$710$		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	0.905180	−	0.425029i	$-0.139736\pi$
$719$	20.9330	+	15.2087i	0.780669	+	0.567189i	−0.124511	+	0.992218i	$0.539736\pi$
$720$		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	−0.991933	−	0.126764i	$-0.959541\pi$
$727$	−7.11693	−	21.9037i	−0.263952	−	0.812362i	0.727981	−	0.685598i	$-0.240459\pi$
$728$		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	0.782889	−	0.622162i	$-0.213745\pi$
$733$	11.7258	+	8.51932i	0.433104	+	0.314668i	−0.349785	+	0.936830i	$0.613745\pi$
$734$		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	−0.999334	−	0.0364819i	$-0.988385\pi$
$739$	−5.77126	−	17.7621i	−0.212299	−	0.653390i	0.787035	−	0.616908i	$-0.211615\pi$
$740$		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	−0.988006	−	0.154413i	$-0.950651\pi$
$761$	−7.70908	−	23.7261i	−0.279454	−	0.860071i	0.708552	−	0.705658i	$-0.249349\pi$
$762$		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	0.323026	−	0.946390i	$-0.395300\pi$
$769$	−13.2338	−	9.61494i	−0.477224	−	0.346724i	−0.800250	+	0.599667i	$0.795300\pi$
$770$		0			0
$771$	18.4667	−	13.4169i	0.665063	−	0.483196i
$772$		0			0
$773$	−12.7809	−	39.3355i	−0.459696	−	1.41480i	−0.865532	−	0.500853i	$-0.833020\pi$
$773$	−12.7809	−	39.3355i	−0.459696	−	1.41480i	0.405836	−	0.913946i	$-0.366980\pi$
$774$		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	0.589903	+	0.807474i	$0.299166\pi$
$787$	−10.1542	+	31.2516i	−0.361960	+	1.11400i	−0.951863	+	0.306524i	$0.900834\pi$
$788$		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	−0.574441	−	0.818546i	$-0.694781\pi$
$797$	0.748982	−	0.544168i	0.0265303	−	0.0192754i	0.600971	+	0.799271i	$0.294781\pi$
$798$		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	0.528475	+	0.848949i	$0.322764\pi$
$809$	−11.3223	+	34.8464i	−0.398070	+	1.22513i	−0.926545	+	0.376184i	$0.877236\pi$
$810$		0			0
$811$	−1.82559	−	5.61858i	−0.0641051	−	0.197295i	0.913874	−	0.405998i	$-0.133076\pi$
$811$	−1.82559	−	5.61858i	−0.0641051	−	0.197295i	−0.977979	+	0.208703i	$0.933076\pi$
$812$		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	−0.729354	−	0.684136i	$-0.760179\pi$
$821$	−8.71298	+	6.33035i	−0.304085	+	0.220931i	0.425269	+	0.905067i	$0.360179\pi$
$822$		0			0
$823$	−9.59092	−	29.5178i	−0.334319	−	1.02893i	−0.967057	−	0.254561i	$-0.918069\pi$
$823$	−9.59092	−	29.5178i	−0.334319	−	1.02893i	0.632738	−	0.774366i	$-0.281931\pi$
$824$		0			0
$825$	8.04559	−	9.70561i	0.280112	−	0.337906i
$826$		0			0
$827$	0.0247830	+	0.0762742i	0.000861789	+	0.00265231i	0.951486	−	0.307691i	$-0.0995561\pi$
$827$	0.0247830	+	0.0762742i	0.000861789	+	0.00265231i	−0.950625	+	0.310343i	$0.899556\pi$
$828$		0			0
$829$	−9.29064	+	6.75004i	−0.322677	+	0.234439i	−0.737317	−	0.675547i	$-0.763908\pi$
$829$	−9.29064	+	6.75004i	−0.322677	+	0.234439i	0.414640	+	0.909986i	$0.363908\pi$
$830$		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	0.974610	−	0.223909i	$-0.0718819\pi$
$839$	1.57930	+	4.86059i	0.0545235	+	0.167806i	−0.920087	+	0.391715i	$0.871882\pi$
$840$		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	−0.328310	−	0.944570i	$-0.606479\pi$
$853$	13.6853	−	9.94295i	0.468576	−	0.340440i	0.796886	+	0.604130i	$0.206479\pi$
$854$		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	−0.276406	−	0.961041i	$-0.589144\pi$
$859$	15.0089	−	46.1926i	0.512097	−	1.57607i	0.788503	−	0.615031i	$-0.210856\pi$
$860$		0			0
$861$	−12.6338	−	38.8830i	−0.430560	−	1.32513i
$862$		0			0
$863$	3.01486	−	9.27879i	0.102627	−	0.315854i	−0.886539	−	0.462654i	$-0.846897\pi$
$863$	3.01486	−	9.27879i	0.102627	−	0.315854i	0.989166	+	0.146800i	$0.0468974\pi$
$864$		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	0.997910	−	0.0646268i	$-0.0205857\pi$
$877$	4.51904	+	13.9082i	0.152597	+	0.469646i	−0.845312	+	0.534272i	$0.820586\pi$
$878$		0			0
$879$	14.9836	−	10.8862i	0.505385	−	0.367184i
$880$		0			0
$881$	−25.6919	−	18.6663i	−0.865583	−	0.628883i	0.0638152	−	0.997962i	$-0.479673\pi$
$881$	−25.6919	−	18.6663i	−0.865583	−	0.628883i	−0.929398	+	0.369079i	$0.879673\pi$
$882$		0			0
$883$	−43.2649	−	31.4338i	−1.45598	−	1.05783i	−0.984388	−	0.176015i	$-0.943679\pi$
$883$	−43.2649	−	31.4338i	−1.45598	−	1.05783i	−0.471593	−	0.881817i	$-0.656321\pi$
$884$		0			0
$885$	−20.0111	+	36.3569i	−0.672667	+	1.22212i
$886$		0			0
$887$	−4.60930	+	14.1860i	−0.154765	+	0.476319i	−0.998137	−	0.0610120i	$-0.980567\pi$
$887$	−4.60930	+	14.1860i	−0.154765	+	0.476319i	0.843372	+	0.537331i	$0.180567\pi$
$888$		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	0.991592	+	0.129403i	$0.0413061\pi$
$911$	8.01167	+	24.6574i	0.265438	+	0.816936i	−0.726154	+	0.687533i	$0.758694\pi$
$912$		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	−0.0271894	−	0.999630i	$-0.508656\pi$
$919$	−29.8996	−	21.7233i	−0.986296	−	0.716586i	−0.959107	+	0.283044i	$0.908656\pi$
$920$		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	−0.652773	−	0.757553i	$-0.726395\pi$
$929$	−4.08473	+	2.96773i	−0.134016	+	0.0973680i	0.518758	+	0.854921i	$0.326395\pi$
$930$		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	−0.997797	−	0.0663355i	$-0.978869\pi$
$937$	−4.63967	+	14.2794i	−0.151571	+	0.466488i	0.846226	+	0.532824i	$0.178869\pi$
$938$		0			0
$939$	−3.32657	−	10.2381i	−0.108559	−	0.334109i
$940$		0			0
$941$	6.20803	−	19.1063i	0.202376	−	0.622849i	−0.797435	−	0.603405i	$-0.793810\pi$
$941$	6.20803	−	19.1063i	0.202376	−	0.622849i	0.999811	−	0.0194443i	$-0.00618970\pi$
$942$		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	0.312416	−	0.949945i	$-0.398862\pi$
$947$	40.3873	−	29.3431i	1.31241	−	0.953521i	0.999994	−	0.00357610i	$-0.00113831\pi$
$948$		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	−0.973757	−	0.227588i	$-0.926916\pi$
$953$	−32.6679	+	23.7346i	−1.05822	+	0.768839i	−0.0844582	+	0.996427i	$0.526916\pi$
$954$		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	0.692725	−	0.721202i	$-0.256410\pi$
$967$	6.86880	+	4.99048i	0.220886	+	0.160483i	−0.471840	+	0.881684i	$0.656410\pi$
$968$		0			0
$969$	5.38961	+	3.91578i	0.173139	+	0.125793i
$970$		0			0
$971$	26.0720	−	18.9424i	0.836689	−	0.607890i	−0.0847547	−	0.996402i	$-0.527011\pi$
$971$	26.0720	−	18.9424i	0.836689	−	0.607890i	0.921444	+	0.388512i	$0.127011\pi$
$972$		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	−0.996658	−	0.0816901i	$-0.973968\pi$
$977$	−7.45045	−	22.9301i	−0.238361	−	0.733600i	0.758297	−	0.651909i	$-0.226032\pi$
$978$		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	0.780215	−	0.625511i	$-0.215109\pi$
$983$	13.3694	+	9.71347i	0.426419	+	0.309812i	−0.353796	+	0.935322i	$0.615109\pi$
$984$		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	−0.975203	−	0.221310i	$-0.928967\pi$
$991$	−1.76806	+	5.44154i	−0.0561644	+	0.172856i	0.919039	+	0.394166i	$0.128967\pi$
$992$		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	−0.817671	−	0.575685i	$-0.804735\pi$
$997$	−16.5087	+	11.9943i	−0.522837	+	0.379863i	0.294835	+	0.955548i	$0.404735\pi$
$998$		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.81.2		8
4.3	odd	2		200.2.m.b.81.2	✓	8
20.3	even	4		1000.2.q.b.849.2		16
20.7	even	4		1000.2.q.b.849.3		16
20.19	odd	2		1000.2.m.b.401.2		8
25.11	even	5		10000.2.a.q.1.2		4
25.14	even	10		10000.2.a.z.1.3		4
25.21	even	5	inner	400.2.u.e.321.2		8
100.3	even	20		1000.2.q.b.649.4		16
100.11	odd	10		5000.2.a.i.1.3		4
100.39	odd	10		5000.2.a.f.1.2		4
100.47	even	20		1000.2.q.b.649.1		16
100.71	odd	10		200.2.m.b.121.2	yes	8
100.79	odd	10		1000.2.m.b.601.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.m.b.81.2	✓	8	4.3	odd	2
200.2.m.b.121.2	yes	8	100.71	odd	10
400.2.u.e.81.2		8	1.1	even	1	trivial
400.2.u.e.321.2		8	25.21	even	5	inner
1000.2.m.b.401.2		8	20.19	odd	2
1000.2.m.b.601.2		8	100.79	odd	10
1000.2.q.b.649.1		16	100.47	even	20
1000.2.q.b.649.4		16	100.3	even	20
1000.2.q.b.849.2		16	20.3	even	4
1000.2.q.b.849.3		16	20.7	even	4
5000.2.a.f.1.2		4	100.39	odd	10
5000.2.a.i.1.3		4	100.11	odd	10
10000.2.a.q.1.2		4	25.11	even	5
10000.2.a.z.1.3		4	25.14	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

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