LMFDB - Embedded newform 900.3.p.c.401.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (of order $6$, degree $2$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 11 x^{10} + 60 x^{9} - 120 x^{8} - 342 x^{7} + 2709 x^{6} - 3078 x^{5} + \cdots + 531441 $ x^12 - 2x^11 - 11x^10 + 60x^9 - 120x^8 - 342x^7 + 2709x^6 - 3078x^5 - 9720x^4 + 43740x^3 - 72171x^2 - 118098*x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			401.6
Root			$-2.99781 + 0.114662i$ of defining polynomial
Character	$\chi$	$=$	900.401
Dual form			900.3.p.c.101.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.99781 - 0.114662i) q^{3} +(0.801399 + 1.38806i) q^{7} +(8.97371 - 0.687471i) q^{9} +O(q^{10})$	\(q+(2.99781 - 0.114662i) q^{3} +(0.801399 + 1.38806i) q^{7} +(8.97371 - 0.687471i) q^{9} +(-6.10409 + 3.52420i) q^{11} +(10.9287 - 18.9291i) q^{13} -33.1463i q^{17} -6.82330 q^{19} +(2.56160 + 4.06926i) q^{21} +(-12.2854 - 7.09299i) q^{23} +(26.8226 - 3.08985i) q^{27} +(31.4868 - 18.1789i) q^{29} +(-17.2065 + 29.8025i) q^{31} +(-17.8948 + 11.2648i) q^{33} +43.1114 q^{37} +(30.5917 - 57.9989i) q^{39} +(18.2263 + 10.5230i) q^{41} +(30.6752 + 53.1311i) q^{43} +(-14.6270 + 8.44488i) q^{47} +(23.2155 - 40.2105i) q^{49} +(-3.80063 - 99.3663i) q^{51} -12.1221i q^{53} +(-20.4549 + 0.782375i) q^{57} +(54.3639 + 31.3870i) q^{59} +(3.38717 + 5.86675i) q^{61} +(8.14577 + 11.9051i) q^{63} +(53.4565 - 92.5894i) q^{67} +(-37.6426 - 19.8547i) q^{69} -23.4326i q^{71} -69.5613 q^{73} +(-9.78362 - 5.64858i) q^{77} +(-27.8659 - 48.2651i) q^{79} +(80.0548 - 12.3383i) q^{81} +(-71.6843 + 41.3869i) q^{83} +(92.3071 - 58.1073i) q^{87} -13.5312i q^{89} +35.0331 q^{91} +(-48.1645 + 91.3151i) q^{93} +(64.6979 + 112.060i) q^{97} +(-52.3535 + 35.8215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{7} + 26 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 + 6 * q^7 + 26 * q^9	$ 12 q - 2 q^{3} + 6 q^{7} + 26 q^{9} + 48 q^{11} + 30 q^{13} + 72 q^{19} - 128 q^{21} + 78 q^{23} + 106 q^{27} + 150 q^{29} - 12 q^{31} - 96 q^{33} + 12 q^{37} + 40 q^{39} + 90 q^{41} - 114 q^{43} - 12 q^{47} + 48 q^{49} - 144 q^{51} + 158 q^{57} + 48 q^{59} - 78 q^{61} + 212 q^{63} + 168 q^{67} - 150 q^{69} + 24 q^{73} + 258 q^{77} + 120 q^{79} + 434 q^{81} - 114 q^{83} + 330 q^{87} + 120 q^{91} - 82 q^{93} - 96 q^{97} - 120 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^7 + 26 * q^9 + 48 * q^11 + 30 * q^13 + 72 * q^19 - 128 * q^21 + 78 * q^23 + 106 * q^27 + 150 * q^29 - 12 * q^31 - 96 * q^33 + 12 * q^37 + 40 * q^39 + 90 * q^41 - 114 * q^43 - 12 * q^47 + 48 * q^49 - 144 * q^51 + 158 * q^57 + 48 * q^59 - 78 * q^61 + 212 * q^63 + 168 * q^67 - 150 * q^69 + 24 * q^73 + 258 * q^77 + 120 * q^79 + 434 * q^81 - 114 * q^83 + 330 * q^87 + 120 * q^91 - 82 * q^93 - 96 * q^97 - 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.99781	−	0.114662i	0.999269	−	0.0382208i
$3$	2.99781	−	0.114662i	0.999269	−	0.0382208i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.801399	+	1.38806i	0.114486	+	0.198295i	0.917574	−	0.397565i	$-0.130145\pi$
$7$	0.801399	+	1.38806i	0.114486	+	0.198295i	−0.803088	+	0.595860i	$0.796811\pi$
$8$		0			0
$9$	8.97371	−	0.687471i	0.997078	−	0.0763857i
$10$		0			0
$11$	−6.10409	+	3.52420i	−0.554917	+	0.320382i	−0.751103	−	0.660185i	$-0.770478\pi$
$11$	−6.10409	+	3.52420i	−0.554917	+	0.320382i	0.196186	+	0.980567i	$0.437144\pi$
$12$		0			0
$13$	10.9287	−	18.9291i	0.840671	−	1.45608i	−0.0486581	−	0.998815i	$-0.515494\pi$
$13$	10.9287	−	18.9291i	0.840671	−	1.45608i	0.889329	−	0.457269i	$-0.151172\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	33.1463i		−	1.94978i	−0.222679	−	0.974892i	$-0.571480\pi$
$17$		−	33.1463i		−	1.94978i	0.222679	−	0.974892i	$-0.428520\pi$
$18$		0			0
$19$	−6.82330			−0.359121			−0.179561	−	0.983747i	$-0.557468\pi$
$19$	−6.82330			−0.359121			−0.179561	+	0.983747i	$0.557468\pi$
$20$		0			0
$21$	2.56160	+	4.06926i	0.121981	+	0.193774i
$22$		0			0
$23$	−12.2854	−	7.09299i	−0.534149	−	0.308391i	0.208556	−	0.978011i	$-0.433124\pi$
$23$	−12.2854	−	7.09299i	−0.534149	−	0.308391i	−0.742704	+	0.669620i	$0.766457\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	26.8226	−	3.08985i	0.993430	−	0.114439i
$28$		0			0
$29$	31.4868	−	18.1789i	1.08575	−	0.626860i	0.153311	−	0.988178i	$-0.451006\pi$
$29$	31.4868	−	18.1789i	1.08575	−	0.626860i	0.932443	+	0.361318i	$0.117673\pi$
$30$		0			0
$31$	−17.2065	+	29.8025i	−0.555048	+	0.961370i	0.442852	+	0.896595i	$0.353967\pi$
$31$	−17.2065	+	29.8025i	−0.555048	+	0.961370i	−0.997900	+	0.0647759i	$0.979367\pi$
$32$		0			0
$33$	−17.8948	+	11.2648i	−0.542266	+	0.341357i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	43.1114			1.16517			0.582587	−	0.812768i	$-0.302041\pi$
$37$	43.1114			1.16517			0.582587	+	0.812768i	$0.302041\pi$
$38$		0			0
$39$	30.5917	−	57.9989i	0.784404	−	1.48715i
$40$		0			0
$41$	18.2263	+	10.5230i	0.444544	+	0.256658i	0.705523	−	0.708687i	$-0.250712\pi$
$41$	18.2263	+	10.5230i	0.444544	+	0.256658i	−0.260979	+	0.965344i	$0.584045\pi$
$42$		0			0
$43$	30.6752	+	53.1311i	0.713378	+	1.23561i	0.963582	+	0.267414i	$0.0861690\pi$
$43$	30.6752	+	53.1311i	0.713378	+	1.23561i	−0.250204	+	0.968193i	$0.580498\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−14.6270	+	8.44488i	−0.311212	+	0.179678i	−0.647469	−	0.762092i	$-0.724172\pi$
$47$	−14.6270	+	8.44488i	−0.311212	+	0.179678i	0.336257	+	0.941770i	$0.390839\pi$
$48$		0			0
$49$	23.2155	−	40.2105i	0.473786	−	0.820622i
$50$		0			0
$51$	−3.80063	−	99.3663i	−0.0745222	−	1.94836i
$52$		0			0
$53$		−	12.1221i		−	0.228718i	−0.993439	−	0.114359i	$-0.963519\pi$
$53$		−	12.1221i		−	0.228718i	0.993439	−	0.114359i	$-0.0364814\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−20.4549	+	0.782375i	−0.358859	+	0.0137259i
$58$		0			0
$59$	54.3639	+	31.3870i	0.921422	+	0.531983i	0.884089	−	0.467319i	$-0.154780\pi$
$59$	54.3639	+	31.3870i	0.921422	+	0.531983i	0.0373338	+	0.999303i	$0.488114\pi$
$60$		0			0
$61$	3.38717	+	5.86675i	0.0555274	+	0.0961763i	0.892453	−	0.451140i	$-0.148983\pi$
$61$	3.38717	+	5.86675i	0.0555274	+	0.0961763i	−0.836926	+	0.547317i	$0.815649\pi$
$62$		0			0
$63$	8.14577	+	11.9051i	0.129298	+	0.188970i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	53.4565	−	92.5894i	0.797858	−	1.38193i	−0.123150	−	0.992388i	$-0.539300\pi$
$67$	53.4565	−	92.5894i	0.797858	−	1.38193i	0.921008	−	0.389543i	$-0.127367\pi$
$68$		0			0
$69$	−37.6426	−	19.8547i	−0.545545	−	0.287750i
$70$		0			0
$71$		−	23.4326i		−	0.330036i	−0.986291	−	0.165018i	$-0.947232\pi$
$71$		−	23.4326i		−	0.330036i	0.986291	−	0.165018i	$-0.0527683\pi$
$72$		0			0
$73$	−69.5613			−0.952895			−0.476447	−	0.879203i	$-0.658076\pi$
$73$	−69.5613			−0.952895			−0.476447	+	0.879203i	$0.658076\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.78362	−	5.64858i	−0.127060	−	0.0733581i
$78$		0			0
$79$	−27.8659	−	48.2651i	−0.352733	−	0.610951i	0.633994	−	0.773338i	$-0.281414\pi$
$79$	−27.8659	−	48.2651i	−0.352733	−	0.610951i	−0.986727	+	0.162386i	$0.948081\pi$
$80$		0			0
$81$	80.0548	−	12.3383i	0.988330	−	0.152325i
$82$		0			0
$83$	−71.6843	+	41.3869i	−0.863666	+	0.498638i	−0.865238	−	0.501361i	$-0.832833\pi$
$83$	−71.6843	+	41.3869i	−0.863666	+	0.498638i	0.00157207	+	0.999999i	$0.499500\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	92.3071	−	58.1073i	1.06100	−	0.667900i
$88$		0			0
$89$		−	13.5312i		−	0.152036i	−0.997106	−	0.0760180i	$-0.975779\pi$
$89$		−	13.5312i		−	0.152036i	0.997106	−	0.0760180i	$-0.0242206\pi$
$90$		0			0
$91$	35.0331			0.384979
$92$		0			0
$93$	−48.1645	+	91.3151i	−0.517898	+	0.981882i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	64.6979	+	112.060i	0.666988	+	1.15526i	0.978742	+	0.205095i	$0.0657502\pi$
$97$	64.6979	+	112.060i	0.666988	+	1.15526i	−0.311754	+	0.950163i	$0.600916\pi$
$98$		0			0
$99$	−52.3535	+	35.8215i	−0.528823	+	0.361833i
$100$		0			0
$101$	−89.9838	+	51.9522i	−0.890929	+	0.514378i	−0.874246	−	0.485483i	$-0.838644\pi$
$101$	−89.9838	+	51.9522i	−0.890929	+	0.514378i	−0.0166826	+	0.999861i	$0.505310\pi$
$102$		0			0
$103$	3.99074	−	6.91217i	0.0387451	−	0.0671085i	−0.846003	−	0.533179i	$-0.820997\pi$
$103$	3.99074	−	6.91217i	0.0387451	−	0.0671085i	0.884748	+	0.466070i	$0.154331\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	113.941i		−	1.06487i	−0.846472	−	0.532433i	$-0.821278\pi$
$107$		−	113.941i		−	1.06487i	0.846472	−	0.532433i	$-0.178722\pi$
$108$		0			0
$109$	76.8649			0.705182			0.352591	−	0.935777i	$-0.385301\pi$
$109$	76.8649			0.705182			0.352591	+	0.935777i	$0.385301\pi$
$110$		0			0
$111$	129.240	−	4.94326i	1.16432	−	0.0445338i
$112$		0			0
$113$	−43.2859	−	24.9911i	−0.383061	−	0.221160i	0.296088	−	0.955161i	$-0.404318\pi$
$113$	−43.2859	−	24.9911i	−0.383061	−	0.221160i	−0.679149	+	0.734000i	$0.737651\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	85.0579	−	177.377i	0.726990	−	1.51605i
$118$		0			0
$119$	46.0092	−	26.5634i	0.386632	−	0.223222i
$120$		0			0
$121$	−35.6601	+	61.7651i	−0.294711	+	0.510455i
$122$		0			0
$123$	55.8456	+	29.4560i	0.454029	+	0.239479i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−53.8806			−0.424257			−0.212128	−	0.977242i	$-0.568040\pi$
$127$	−53.8806			−0.424257			−0.212128	+	0.977242i	$0.568040\pi$
$128$		0			0
$129$	98.0506	+	155.760i	0.760082	+	1.20744i
$130$		0			0
$131$	−221.724	−	128.012i	−1.69255	−	0.977193i	−0.952450	−	0.304694i	$-0.901446\pi$
$131$	−221.724	−	128.012i	−1.69255	−	0.977193i	−0.740098	−	0.672499i	$-0.765221\pi$
$132$		0			0
$133$	−5.46819	−	9.47118i	−0.0411142	−	0.0712119i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.3239	−	6.53788i	0.0826565	−	0.0477217i	−0.458102	−	0.888900i	$-0.651471\pi$
$137$	11.3239	−	6.53788i	0.0826565	−	0.0477217i	0.540759	+	0.841178i	$0.318137\pi$
$138$		0			0
$139$	−61.9474	+	107.296i	−0.445664	+	0.771913i	−0.998098	−	0.0616433i	$-0.980366\pi$
$139$	−61.9474	+	107.296i	−0.445664	+	0.771913i	0.552434	+	0.833557i	$0.313699\pi$
$140$		0			0
$141$	−42.8805	+	26.9933i	−0.304117	+	0.191442i
$142$		0			0
$143$			154.060i			1.07734i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	64.9850	−	123.205i	0.442075	−	0.838130i
$148$		0			0
$149$	−54.2591	−	31.3265i	−0.364155	−	0.210245i	0.306747	−	0.951791i	$-0.400759\pi$
$149$	−54.2591	−	31.3265i	−0.364155	−	0.210245i	−0.670902	+	0.741546i	$0.734093\pi$
$150$		0			0
$151$	122.920	+	212.903i	0.814038	+	1.40996i	0.910016	+	0.414572i	$0.136069\pi$
$151$	122.920	+	212.903i	0.814038	+	1.40996i	−0.0959781	+	0.995383i	$0.530598\pi$
$152$		0			0
$153$	−22.7871	−	297.445i	−0.148936	−	1.94409i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−107.824	+	186.757i	−0.686777	+	1.18953i	0.286098	+	0.958200i	$0.407642\pi$
$157$	−107.824	+	186.757i	−0.686777	+	1.18953i	−0.972875	+	0.231332i	$0.925692\pi$
$158$		0			0
$159$	−1.38994	−	36.3396i	−0.00874178	−	0.228551i
$160$		0			0
$161$		−	22.7373i		−	0.141225i
$162$		0			0
$163$	−43.7518			−0.268416			−0.134208	−	0.990953i	$-0.542849\pi$
$163$	−43.7518			−0.268416			−0.134208	+	0.990953i	$0.542849\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−193.025	−	111.443i	−1.15584	−	0.667325i	−0.205537	−	0.978649i	$-0.565894\pi$
$167$	−193.025	−	111.443i	−1.15584	−	0.667325i	−0.950304	+	0.311324i	$0.899227\pi$
$168$		0			0
$169$	−154.374	−	267.383i	−0.913454	−	1.58215i
$170$		0			0
$171$	−61.2303	+	4.69082i	−0.358072	+	0.0274317i
$172$		0			0
$173$	258.742	−	149.385i	1.49562	−	0.863494i	0.495629	−	0.868534i	$-0.334938\pi$
$173$	258.742	−	149.385i	1.49562	−	0.863494i	0.999987	+	0.00503988i	$0.00160425\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	166.571	+	87.8588i	0.941082	+	0.496377i
$178$		0			0
$179$		−	105.801i		−	0.591067i	−0.955332	−	0.295533i	$-0.904503\pi$
$179$		−	105.801i		−	0.591067i	0.955332	−	0.295533i	$-0.0954973\pi$
$180$		0			0
$181$	278.743			1.54002			0.770009	−	0.638033i	$-0.220252\pi$
$181$	278.743			1.54002			0.770009	+	0.638033i	$0.220252\pi$
$182$		0			0
$183$	10.8268	+	17.1990i	0.0591627	+	0.0939837i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	116.814	+	202.328i	0.624675	+	1.08197i
$188$		0			0
$189$	25.7845	+	34.7553i	0.136426	+	0.183891i
$190$		0			0
$191$	121.948	−	70.4065i	0.638470	−	0.368621i	−0.145555	−	0.989350i	$-0.546497\pi$
$191$	121.948	−	70.4065i	0.638470	−	0.368621i	0.784025	+	0.620729i	$0.213163\pi$
$192$		0			0
$193$	−77.7522	+	134.671i	−0.402861	+	0.697776i	−0.994070	−	0.108743i	$-0.965318\pi$
$193$	−77.7522	+	134.671i	−0.402861	+	0.697776i	0.591209	+	0.806518i	$0.298651\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			229.378i			1.16436i	0.813062	+	0.582178i	$0.197799\pi$
$197$			229.378i			1.16436i	−0.813062	+	0.582178i	$0.802201\pi$
$198$		0			0
$199$	362.645			1.82234			0.911168	−	0.412036i	$-0.135182\pi$
$199$	362.645			1.82234			0.911168	+	0.412036i	$0.135182\pi$
$200$		0			0
$201$	149.636	−	283.695i	0.744457	−	1.41142i
$202$		0			0
$203$	50.4671	+	29.1372i	0.248606	+	0.143533i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−115.122	−	55.2045i	−0.556145	−	0.266689i
$208$		0			0
$209$	41.6500	−	24.0467i	0.199282	−	0.115056i
$210$		0			0
$211$	−171.458	+	296.974i	−0.812598	+	1.40746i	0.0984416	+	0.995143i	$0.468614\pi$
$211$	−171.458	+	296.974i	−0.812598	+	1.40746i	−0.911040	+	0.412318i	$0.864719\pi$
$212$		0			0
$213$	−2.68683	−	70.2464i	−0.0126142	−	0.329795i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−55.1570			−0.254180
$218$		0			0
$219$	−208.532	+	7.97606i	−0.952199	+	0.0364204i
$220$		0			0
$221$	−627.430	−	362.247i	−2.83905	−	1.63913i
$222$		0			0
$223$	47.1836	+	81.7243i	0.211586	+	0.366477i	0.952211	−	0.305441i	$-0.0988040\pi$
$223$	47.1836	+	81.7243i	0.211586	+	0.366477i	−0.740625	+	0.671918i	$0.765471\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−290.757	+	167.869i	−1.28087	+	0.739510i	−0.977007	−	0.213206i	$-0.931610\pi$
$227$	−290.757	+	167.869i	−1.28087	+	0.739510i	−0.303862	+	0.952716i	$0.598276\pi$
$228$		0			0
$229$	108.283	−	187.552i	0.472854	−	0.819006i	−0.526664	−	0.850074i	$-0.676557\pi$
$229$	108.283	−	187.552i	0.472854	−	0.819006i	0.999517	+	0.0310674i	$0.00989064\pi$
$230$		0			0
$231$	−29.9771	−	15.8115i	−0.129771	−	0.0684482i
$232$		0			0
$233$		−	35.0415i		−	0.150393i	−0.997169	−	0.0751963i	$-0.976042\pi$
$233$		−	35.0415i		−	0.150393i	0.997169	−	0.0751963i	$-0.0239583\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−89.0708	−	141.494i	−0.375826	−	0.597023i
$238$		0			0
$239$	212.383	+	122.619i	0.888631	+	0.513051i	0.873494	−	0.486834i	$-0.161848\pi$
$239$	212.383	+	122.619i	0.888631	+	0.513051i	0.0151363	+	0.999885i	$0.495182\pi$
$240$		0			0
$241$	0.672639	+	1.16504i	0.00279103	+	0.00483421i	0.867418	−	0.497581i	$-0.165778\pi$
$241$	0.672639	+	1.16504i	0.00279103	+	0.00483421i	−0.864627	+	0.502415i	$0.832445\pi$
$242$		0			0
$243$	238.574	−	46.1672i	0.981786	−	0.189988i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−74.5699	+	129.159i	−0.301902	+	0.522910i
$248$		0			0
$249$	−210.150	+	132.290i	−0.843977	+	0.531284i
$250$		0			0
$251$			397.075i			1.58197i	0.611834	+	0.790986i	$0.290432\pi$
$251$			397.075i			1.58197i	−0.611834	+	0.790986i	$0.709568\pi$
$252$		0			0
$253$	99.9884			0.395211
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−18.3001	−	10.5655i	−0.0712064	−	0.0411111i	0.463974	−	0.885849i	$-0.346423\pi$
$257$	−18.3001	−	10.5655i	−0.0712064	−	0.0411111i	−0.535181	+	0.844738i	$0.679756\pi$
$258$		0			0
$259$	34.5495	+	59.8414i	0.133396	+	0.231048i
$260$		0			0
$261$	270.056	−	184.779i	1.03470	−	0.707965i
$262$		0			0
$263$	−110.367	+	63.7204i	−0.419646	+	0.242283i	−0.694926	−	0.719081i	$-0.744563\pi$
$263$	−110.367	+	63.7204i	−0.419646	+	0.242283i	0.275280	+	0.961364i	$0.411230\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.55152	−	40.5639i	−0.00581093	−	0.151925i
$268$		0			0
$269$			234.170i			0.870520i	0.900305	+	0.435260i	$0.143343\pi$
$269$			234.170i			0.870520i	−0.900305	+	0.435260i	$0.856657\pi$
$270$		0			0
$271$	108.333			0.399753			0.199876	−	0.979821i	$-0.435946\pi$
$271$	108.333			0.399753			0.199876	+	0.979821i	$0.435946\pi$
$272$		0			0
$273$	105.022	−	4.01697i	0.384697	−	0.0147142i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	127.060	+	220.075i	0.458701	+	0.794494i	0.998893	−	0.0470483i	$-0.0149815\pi$
$277$	127.060	+	220.075i	0.458701	+	0.794494i	−0.540191	+	0.841542i	$0.681648\pi$
$278$		0			0
$279$	−133.917	+	279.268i	−0.479991	+	1.00096i
$280$		0			0
$281$	−342.882	+	197.963i	−1.22022	+	0.704494i	−0.964965	−	0.262379i	$-0.915493\pi$
$281$	−342.882	+	197.963i	−1.22022	+	0.704494i	−0.255255	+	0.966874i	$0.582160\pi$
$282$		0			0
$283$	189.868	−	328.861i	0.670912	−	1.16205i	−0.306734	−	0.951795i	$-0.599236\pi$
$283$	189.868	−	328.861i	0.670912	−	1.16205i	0.977646	−	0.210259i	$-0.0674306\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			33.7324i			0.117534i
$288$		0			0
$289$	−809.679			−2.80166
$290$		0			0
$291$	206.801	+	328.516i	0.710656	+	1.12892i
$292$		0			0
$293$	−424.309	−	244.975i	−1.44815	−	0.836092i	−0.449782	−	0.893138i	$-0.648498\pi$
$293$	−424.309	−	244.975i	−1.44815	−	0.836092i	−0.998372	+	0.0570460i	$0.981832\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−152.838	+	113.389i	−0.514607	+	0.381781i
$298$		0			0
$299$	−268.528	+	155.035i	−0.898086	+	0.518510i
$300$		0			0
$301$	−49.1662	+	85.1584i	−0.163343	+	0.282918i
$302$		0			0
$303$	−263.797	+	166.060i	−0.870618	+	0.548054i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−110.535			−0.360048			−0.180024	−	0.983662i	$-0.557618\pi$
$307$	−110.535			−0.360048			−0.180024	+	0.983662i	$0.557618\pi$
$308$		0			0
$309$	11.1709	−	21.1790i	0.0361518	−	0.0685403i
$310$		0			0
$311$	155.652	+	89.8659i	0.500490	+	0.288958i	0.728916	−	0.684603i	$-0.240025\pi$
$311$	155.652	+	89.8659i	0.500490	+	0.288958i	−0.228426	+	0.973561i	$0.573358\pi$
$312$		0			0
$313$	−101.417	−	175.659i	−0.324016	−	0.561212i	0.657297	−	0.753632i	$-0.271700\pi$
$313$	−101.417	−	175.659i	−0.324016	−	0.561212i	−0.981313	+	0.192420i	$0.938366\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−456.210	+	263.393i	−1.43915	+	0.830893i	−0.997791	−	0.0664385i	$-0.978836\pi$
$317$	−456.210	+	263.393i	−1.43915	+	0.830893i	−0.441358	+	0.897331i	$0.645503\pi$
$318$		0			0
$319$	−128.132	+	221.932i	−0.401669	+	0.695711i
$320$		0			0
$321$	−13.0647	−	341.572i	−0.0407000	−	1.06409i
$322$		0			0
$323$			226.167i			0.700208i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	230.426	−	8.81350i	0.704667	−	0.0269526i
$328$		0			0
$329$	−23.4441	−	13.5354i	−0.0712586	−	0.0411411i
$330$		0			0
$331$	163.057	+	282.424i	0.492621	+	0.853244i	0.999964	−	0.00849989i	$-0.00270563\pi$
$331$	163.057	+	282.424i	0.492621	+	0.853244i	−0.507343	+	0.861744i	$0.669372\pi$
$332$		0			0
$333$	386.869	−	29.6379i	1.16177	−	0.0890026i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−168.104	+	291.165i	−0.498825	+	0.863991i	−0.999999	−	0.00135593i	$-0.999568\pi$
$337$	−168.104	+	291.165i	−0.498825	+	0.863991i	0.501174	+	0.865347i	$0.332902\pi$
$338$		0			0
$339$	−132.628	−	69.9553i	−0.391234	−	0.206358i
$340$		0			0
$341$		−	242.556i		−	0.711308i
$342$		0			0
$343$	152.957			0.445938
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−424.342	−	244.994i	−1.22289	−	0.706034i	−0.257355	−	0.966317i	$-0.582851\pi$
$347$	−424.342	−	244.994i	−1.22289	−	0.706034i	−0.965532	+	0.260283i	$0.916184\pi$
$348$		0			0
$349$	231.672	+	401.268i	0.663817	+	1.14976i	0.979605	+	0.200934i	$0.0643978\pi$
$349$	231.672	+	401.268i	0.663817	+	1.14976i	−0.315788	+	0.948830i	$0.602269\pi$
$350$		0			0
$351$	234.649	−	541.496i	0.668515	−	1.54272i
$352$		0			0
$353$	394.752	−	227.910i	1.11828	−	0.645639i	0.177318	−	0.984154i	$-0.443258\pi$
$353$	394.752	−	227.910i	1.11828	−	0.645639i	0.940961	+	0.338515i	$0.109925\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	134.881	−	84.9076i	0.377818	−	0.237836i
$358$		0			0
$359$			479.550i			1.33579i	0.744254	+	0.667896i	$0.232805\pi$
$359$			479.550i			1.33579i	−0.744254	+	0.667896i	$0.767195\pi$
$360$		0			0
$361$	−314.443			−0.871032
$362$		0			0
$363$	−99.8199	+	189.249i	−0.274986	+	0.521346i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	127.663	+	221.120i	0.347857	+	0.602506i	0.985869	−	0.167521i	$-0.0535762\pi$
$367$	127.663	+	221.120i	0.347857	+	0.602506i	−0.638012	+	0.770027i	$0.720243\pi$
$368$		0			0
$369$	170.792	+	81.9000i	0.462850	+	0.221951i
$370$		0			0
$371$	16.8262	−	9.71461i	0.0453536	−	0.0261849i
$372$		0			0
$373$	−16.7470	+	29.0066i	−0.0448981	+	0.0777657i	−0.887601	−	0.460613i	$-0.847630\pi$
$373$	−16.7470	+	29.0066i	−0.0448981	+	0.0777657i	0.842703	+	0.538379i	$0.180963\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	794.690i		−	2.10793i
$378$		0			0
$379$	−376.776			−0.994131			−0.497065	−	0.867713i	$-0.665589\pi$
$379$	−376.776			−0.994131			−0.497065	+	0.867713i	$0.665589\pi$
$380$		0			0
$381$	−161.524	+	6.17808i	−0.423947	+	0.0162154i
$382$		0			0
$383$	−205.748	−	118.789i	−0.537201	−	0.310153i	0.206743	−	0.978395i	$-0.433714\pi$
$383$	−205.748	−	118.789i	−0.537201	−	0.310153i	−0.743944	+	0.668242i	$0.767047\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	311.797	+	455.694i	0.805676	+	1.17750i
$388$		0			0
$389$	355.753	−	205.394i	0.914533	−	0.528006i	0.0326463	−	0.999467i	$-0.489607\pi$
$389$	355.753	−	205.394i	0.914533	−	0.528006i	0.881887	+	0.471461i	$0.156273\pi$
$390$		0			0
$391$	−235.107	+	407.216i	−0.601295	+	1.04147i
$392$		0			0
$393$	−679.364	−	358.333i	−1.72866	−	0.911789i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	208.481			0.525142			0.262571	−	0.964913i	$-0.415430\pi$
$397$	208.481			0.525142			0.262571	+	0.964913i	$0.415430\pi$
$398$		0			0
$399$	−17.4786	−	27.7658i	−0.0438059	−	0.0695884i
$400$		0			0
$401$	22.8279	+	13.1797i	0.0569274	+	0.0328671i	0.528194	−	0.849124i	$-0.322870\pi$
$401$	22.8279	+	13.1797i	0.0569274	+	0.0328671i	−0.471266	+	0.881991i	$0.656203\pi$
$402$		0			0
$403$	376.089	+	651.406i	0.933224	+	1.61639i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−263.156	+	151.933i	−0.646575	+	0.373300i
$408$		0			0
$409$	−87.1760	+	150.993i	−0.213144	+	0.369177i	−0.952697	−	0.303922i	$-0.901704\pi$
$409$	−87.1760	+	150.993i	−0.213144	+	0.369177i	0.739553	+	0.673099i	$0.235037\pi$
$410$		0			0
$411$	33.1973	−	20.8977i	0.0807721	−	0.0508461i
$412$		0			0
$413$			100.614i			0.243618i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−173.403	+	328.756i	−0.415836	+	0.788383i
$418$		0			0
$419$	−227.887	−	131.571i	−0.543883	−	0.314011i	0.202768	−	0.979227i	$-0.435006\pi$
$419$	−227.887	−	131.571i	−0.543883	−	0.314011i	−0.746651	+	0.665216i	$0.768340\pi$
$420$		0			0
$421$	188.486	+	326.467i	0.447710	+	0.775456i	0.998237	−	0.0593612i	$-0.0189064\pi$
$421$	188.486	+	326.467i	0.447710	+	0.775456i	−0.550527	+	0.834818i	$0.685573\pi$
$422$		0			0
$423$	−125.452	+	85.8375i	−0.296578	+	0.202925i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.42895	+	9.40322i	−0.0127142	+	0.0220216i
$428$		0			0
$429$	17.6648	+	461.842i	0.0411768	+	1.07655i
$430$		0			0
$431$			24.6406i			0.0571707i	0.999591	+	0.0285854i	$0.00910024\pi$
$431$			24.6406i			0.0571707i	−0.999591	+	0.0285854i	$0.990900\pi$
$432$		0			0
$433$	−149.886			−0.346157			−0.173079	−	0.984908i	$-0.555371\pi$
$433$	−149.886			−0.346157			−0.173079	+	0.984908i	$0.555371\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	83.8271	+	48.3976i	0.191824	+	0.110750i
$438$		0			0
$439$	−210.058	−	363.831i	−0.478492	−	0.828773i	0.521204	−	0.853432i	$-0.325483\pi$
$439$	−210.058	−	363.831i	−0.478492	−	0.828773i	−0.999696	+	0.0246596i	$0.992150\pi$
$440$		0			0
$441$	180.686	−	376.797i	0.409718	−	0.854414i
$442$		0			0
$443$	167.409	−	96.6537i	0.377899	−	0.218180i	−0.299005	−	0.954252i	$-0.596655\pi$
$443$	167.409	−	96.6537i	0.377899	−	0.218180i	0.676904	+	0.736072i	$0.263321\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−166.250	−	87.6893i	−0.371924	−	0.196173i
$448$		0			0
$449$		−	267.368i		−	0.595475i	−0.954648	−	0.297738i	$-0.903768\pi$
$449$		−	267.368i		−	0.595475i	0.954648	−	0.297738i	$-0.0962320\pi$
$450$		0			0
$451$	−148.340			−0.328914
$452$		0			0
$453$	392.902	+	624.149i	0.867333	+	1.37781i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−58.6341	−	101.557i	−0.128302	−	0.222226i	0.794717	−	0.606981i	$-0.207619\pi$
$457$	−58.6341	−	101.557i	−0.128302	−	0.222226i	−0.923019	+	0.384755i	$0.874286\pi$
$458$		0			0
$459$	−102.417	−	889.071i	−0.223131	−	1.93697i
$460$		0			0
$461$	576.193	−	332.665i	1.24988	−	0.721616i	0.278792	−	0.960352i	$-0.410066\pi$
$461$	576.193	−	332.665i	1.24988	−	0.721616i	0.971085	+	0.238735i	$0.0767328\pi$
$462$		0			0
$463$	−196.498	+	340.345i	−0.424403	+	0.735087i	−0.996364	−	0.0851934i	$-0.972849\pi$
$463$	−196.498	+	340.345i	−0.424403	+	0.735087i	0.571962	+	0.820280i	$0.306183\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			323.816i			0.693397i	0.937977	+	0.346698i	$0.112697\pi$
$467$			323.816i			0.693397i	−0.937977	+	0.346698i	$0.887303\pi$
$468$		0			0
$469$	171.360			0.365373
$470$		0			0
$471$	−301.822	+	572.224i	−0.640810	+	1.21491i
$472$		0			0
$473$	−374.489	−	216.211i	−0.791731	−	0.457106i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−8.33356	−	108.780i	−0.0174708	−	0.228050i
$478$		0			0
$479$	193.983	−	111.996i	0.404976	−	0.233813i	−0.283653	−	0.958927i	$-0.591546\pi$
$479$	193.983	−	111.996i	0.404976	−	0.233813i	0.688629	+	0.725114i	$0.258213\pi$
$480$		0			0
$481$	471.153	−	816.061i	0.979528	−	1.69659i
$482$		0			0
$483$	−2.60711	−	68.1619i	−0.00539774	−	0.141122i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	666.654			1.36890			0.684450	−	0.729060i	$-0.260043\pi$
$487$	666.654			1.36890			0.684450	+	0.729060i	$0.260043\pi$
$488$		0			0
$489$	−131.160	+	5.01668i	−0.268220	+	0.0102591i
$490$		0			0
$491$	−490.592	−	283.244i	−0.999170	−	0.576871i	−0.0911673	−	0.995836i	$-0.529060\pi$
$491$	−490.592	−	283.244i	−0.999170	−	0.576871i	−0.908003	+	0.418965i	$0.862393\pi$
$492$		0			0
$493$	−602.565	−	1043.67i	−1.22224	−	2.11698i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	32.5259	−	18.7789i	0.0654445	−	0.0377844i
$498$		0			0
$499$	449.283	−	778.182i	0.900367	−	1.55948i	0.0733495	−	0.997306i	$-0.476631\pi$
$499$	449.283	−	778.182i	0.900367	−	1.55948i	0.827018	−	0.562176i	$-0.190036\pi$
$500$		0			0
$501$	−591.432	−	311.953i	−1.18050	−	0.622660i
$502$		0			0
$503$			744.710i			1.48054i	0.672312	+	0.740268i	$0.265301\pi$
$503$			744.710i			1.48054i	−0.672312	+	0.740268i	$0.734699\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−493.442	−	783.862i	−0.973257	−	1.54608i
$508$		0			0
$509$	461.074	+	266.201i	0.905842	+	0.522988i	0.879091	−	0.476654i	$-0.158150\pi$
$509$	461.074	+	266.201i	0.905842	+	0.522988i	0.0267513	+	0.999642i	$0.491484\pi$
$510$		0			0
$511$	−55.7464	−	96.5556i	−0.109093	−	0.188954i
$512$		0			0
$513$	−183.019	+	21.0830i	−0.356762	+	0.0410974i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	59.5228	−	103.097i	0.115131	−	0.199413i
$518$		0			0
$519$	758.529	−	477.494i	1.46152	−	0.920027i
$520$		0			0
$521$			527.079i			1.01167i	0.862631	+	0.505834i	$0.168815\pi$
$521$			527.079i			1.01167i	−0.862631	+	0.505834i	$0.831185\pi$
$522$		0			0
$523$	615.733			1.17731			0.588655	−	0.808385i	$-0.299658\pi$
$523$	615.733			1.17731			0.588655	+	0.808385i	$0.299658\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	987.843	+	570.331i	1.87446	+	1.08222i
$528$		0			0
$529$	−163.879	−	283.847i	−0.309790	−	0.536572i
$530$		0			0
$531$	509.423	+	244.284i	0.959366	+	0.460046i
$532$		0			0
$533$	398.381	−	230.005i	0.747431	−	0.431529i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−12.1314	−	317.171i	−0.0225910	−	0.590635i
$538$		0			0
$539$			327.264i			0.607169i
$540$		0			0
$541$	−400.878			−0.740994			−0.370497	−	0.928834i	$-0.620813\pi$
$541$	−400.878			−0.740994			−0.370497	+	0.928834i	$0.620813\pi$
$542$		0			0
$543$	835.619	−	31.9613i	1.53889	−	0.0588607i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−474.342	−	821.585i	−0.867171	−	1.50198i	−0.864876	−	0.501986i	$-0.832603\pi$
$547$	−474.342	−	821.585i	−0.867171	−	1.50198i	−0.00229498	−	0.999997i	$-0.500731\pi$
$548$		0			0
$549$	34.4287	+	50.3179i	0.0627116	+	0.0916538i
$550$		0			0
$551$	−214.844	+	124.040i	−0.389917	+	0.225119i
$552$		0			0
$553$	44.6634	−	77.3593i	0.0807657	−	0.139890i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	303.811i		−	0.545441i	−0.962093	−	0.272720i	$-0.912077\pi$
$557$		−	303.811i		−	0.545441i	0.962093	−	0.272720i	$-0.0879234\pi$
$558$		0			0
$559$	1340.96			2.39886
$560$		0			0
$561$	373.386	+	593.147i	0.665572	+	1.05730i
$562$		0			0
$563$	−289.548	−	167.171i	−0.514295	−	0.296928i	0.220302	−	0.975432i	$-0.429296\pi$
$563$	−289.548	−	167.171i	−0.514295	−	0.296928i	−0.734597	+	0.678503i	$0.762629\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	81.2822	+	101.233i	0.143355	+	0.178542i
$568$		0			0
$569$	429.145	−	247.767i	0.754210	−	0.435443i	−0.0730032	−	0.997332i	$-0.523258\pi$
$569$	429.145	−	247.767i	0.754210	−	0.435443i	0.827213	+	0.561889i	$0.189925\pi$
$570$		0			0
$571$	242.752	−	420.458i	0.425134	−	0.736354i	−0.571299	−	0.820742i	$-0.693560\pi$
$571$	242.752	−	420.458i	0.425134	−	0.736354i	0.996433	+	0.0843881i	$0.0268936\pi$
$572$		0			0
$573$	357.503	−	225.048i	0.623914	−	0.392754i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	294.155			0.509800			0.254900	−	0.966967i	$-0.417957\pi$
$577$	294.155			0.509800			0.254900	+	0.966967i	$0.417957\pi$
$578$		0			0
$579$	−217.644	+	412.632i	−0.375897	+	0.712663i
$580$		0			0
$581$	−114.895	−	66.3349i	−0.197755	−	0.114174i
$582$		0			0
$583$	42.7205	+	73.9941i	0.0732770	+	0.126920i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	857.331	−	494.980i	1.46053	−	0.843237i	0.461494	−	0.887143i	$-0.347314\pi$
$587$	857.331	−	494.980i	1.46053	−	0.843237i	0.999036	+	0.0439064i	$0.0139803\pi$
$588$		0			0
$589$	117.405	−	203.351i	0.199329	−	0.345248i
$590$		0			0
$591$	26.3010	+	687.631i	0.0445025	+	1.16350i
$592$		0			0
$593$		−	291.067i		−	0.490838i	−0.969417	−	0.245419i	$-0.921074\pi$
$593$		−	291.067i		−	0.490838i	0.969417	−	0.245419i	$-0.0789256\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1087.14	−	41.5817i	1.82100	−	0.0696510i
$598$		0			0
$599$	−703.617	−	406.233i	−1.17465	−	0.678186i	−0.219881	−	0.975527i	$-0.570567\pi$
$599$	−703.617	−	406.233i	−1.17465	−	0.678186i	−0.954771	+	0.297341i	$0.903900\pi$
$600$		0			0
$601$	155.483	+	269.304i	0.258707	+	0.448094i	0.965896	−	0.258931i	$-0.0833703\pi$
$601$	155.483	+	269.304i	0.258707	+	0.448094i	−0.707189	+	0.707025i	$0.750037\pi$
$602$		0			0
$603$	416.050	−	867.620i	0.689967	−	1.43884i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	12.2573	−	21.2303i	0.0201933	−	0.0349758i	−0.855752	−	0.517386i	$-0.826905\pi$
$607$	12.2573	−	21.2303i	0.0201933	−	0.0349758i	0.875945	+	0.482410i	$0.160239\pi$
$608$		0			0
$609$	154.631	+	81.5610i	0.253911	+	0.133926i
$610$		0			0
$611$			369.167i			0.604201i
$612$		0			0
$613$	−448.122			−0.731031			−0.365516	−	0.930805i	$-0.619107\pi$
$613$	−448.122			−0.731031			−0.365516	+	0.930805i	$0.619107\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	429.814	+	248.153i	0.696619	+	0.402193i	0.806087	−	0.591797i	$-0.201581\pi$
$617$	429.814	+	248.153i	0.696619	+	0.402193i	−0.109468	+	0.993990i	$0.534915\pi$
$618$		0			0
$619$	473.442	+	820.025i	0.764849	+	1.32476i	0.940326	+	0.340275i	$0.110520\pi$
$619$	473.442	+	820.025i	0.764849	+	1.32476i	−0.175477	+	0.984484i	$0.556147\pi$
$620$		0			0
$621$	−351.443	−	152.292i	−0.565931	−	0.245237i
$622$		0			0
$623$	18.7822	−	10.8439i	0.0301479	−	0.0174059i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	122.102	−	76.8629i	0.194739	−	0.122588i
$628$		0			0
$629$		−	1428.99i		−	2.27184i
$630$		0			0
$631$	158.441			0.251096			0.125548	−	0.992088i	$-0.459931\pi$
$631$	158.441			0.251096			0.125548	+	0.992088i	$0.459931\pi$
$632$		0			0
$633$	−479.947	+	909.932i	−0.758210	+	1.43749i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−507.432	−	878.897i	−0.796596	−	1.37974i
$638$		0			0
$639$	−16.1092	−	210.277i	−0.0252101	−	0.329072i
$640$		0			0
$641$	594.168	−	343.043i	0.926940	−	0.535169i	0.0410973	−	0.999155i	$-0.486915\pi$
$641$	594.168	−	343.043i	0.926940	−	0.535169i	0.885842	+	0.463986i	$0.153581\pi$
$642$		0			0
$643$	−439.898	+	761.925i	−0.684133	+	1.18495i	0.289575	+	0.957155i	$0.406486\pi$
$643$	−439.898	+	761.925i	−0.684133	+	1.18495i	−0.973708	+	0.227798i	$0.926847\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	594.407i		−	0.918712i	−0.888252	−	0.459356i	$-0.848080\pi$
$647$		−	594.407i		−	0.918712i	0.888252	−	0.459356i	$-0.151920\pi$
$648$		0			0
$649$	−442.456			−0.681751
$650$		0			0
$651$	−165.350	+	6.32443i	−0.253994	+	0.00971494i
$652$		0			0
$653$	566.753	+	327.215i	0.867921	+	0.501095i	0.866657	−	0.498905i	$-0.166264\pi$
$653$	566.753	+	327.215i	0.867921	+	0.501095i	0.00126434	+	0.999999i	$0.499598\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−624.223	+	47.8214i	−0.950111	+	0.0727875i
$658$		0			0
$659$	−630.422	+	363.974i	−0.956634	+	0.552313i	−0.895136	−	0.445794i	$-0.852921\pi$
$659$	−630.422	+	363.974i	−0.956634	+	0.552313i	−0.0614989	+	0.998107i	$0.519588\pi$
$660$		0			0
$661$	125.226	−	216.898i	0.189450	−	0.328137i	−0.755617	−	0.655014i	$-0.772663\pi$
$661$	125.226	−	216.898i	0.189450	−	0.328137i	0.945067	+	0.326877i	$0.105996\pi$
$662$		0			0
$663$	−1922.45	−	1014.00i	−2.89962	−	1.52942i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−515.772			−0.773272
$668$		0			0
$669$	150.818	+	239.584i	0.225438	+	0.358122i
$670$		0			0
$671$	−41.3512	−	23.8741i	−0.0616262	−	0.0355799i
$672$		0			0
$673$	−15.9032	−	27.5452i	−0.0236304	−	0.0409290i	0.853968	−	0.520325i	$-0.174189\pi$
$673$	−15.9032	−	27.5452i	−0.0236304	−	0.0409290i	−0.877599	+	0.479396i	$0.840856\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.6805	+	9.63052i	−0.0246389	+	0.0142253i	−0.512269	−	0.858825i	$-0.671195\pi$
$677$	−16.6805	+	9.63052i	−0.0246389	+	0.0142253i	0.487630	+	0.873050i	$0.337862\pi$
$678$		0			0
$679$	−103.698	+	179.610i	−0.152721	+	0.264521i
$680$		0			0
$681$	−852.387	+	536.577i	−1.25167	+	0.787926i
$682$		0			0
$683$			1241.35i			1.81750i	0.417337	+	0.908752i	$0.362963\pi$
$683$			1241.35i			1.81750i	−0.417337	+	0.908752i	$0.637037\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	303.108	−	574.662i	0.441205	−	0.836481i
$688$		0			0
$689$	−229.460	−	132.479i	−0.333033	−	0.192277i
$690$		0			0
$691$	−622.274	−	1077.81i	−0.900542	−	1.55978i	−0.826793	−	0.562507i	$-0.809837\pi$
$691$	−622.274	−	1077.81i	−0.900542	−	1.55978i	−0.0737491	−	0.997277i	$-0.523496\pi$
$692$		0			0
$693$	−91.6786	−	43.9627i	−0.132292	−	0.0634382i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	348.798	−	604.135i	0.500427	−	0.866765i
$698$		0			0
$699$	−4.01794	−	105.048i	−0.00574812	−	0.150283i
$700$		0			0
$701$			603.491i			0.860900i	0.902614	+	0.430450i	$0.141645\pi$
$701$			603.491i			0.860900i	−0.902614	+	0.430450i	$0.858355\pi$
$702$		0			0
$703$	−294.162			−0.418439
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−144.226	−	83.2689i	−0.203997	−	0.117778i
$708$		0			0
$709$	29.6788	+	51.4053i	0.0418601	+	0.0725039i	0.886196	−	0.463310i	$-0.153338\pi$
$709$	29.6788	+	51.4053i	0.0418601	+	0.0725039i	−0.844336	+	0.535814i	$0.820005\pi$
$710$		0			0
$711$	−283.241	−	413.960i	−0.398370	−	0.582223i
$712$		0			0
$713$	422.777	−	244.091i	0.592956	−	0.342343i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	650.742	+	343.237i	0.907591	+	0.478712i
$718$		0			0
$719$			194.207i			0.270108i	0.990838	+	0.135054i	$0.0431207\pi$
$719$			194.207i			0.270108i	−0.990838	+	0.135054i	$0.956879\pi$
$720$		0			0
$721$	12.7927			0.0177430
$722$		0			0
$723$	2.15003	+	3.41545i	0.00297376	+	0.00472400i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	279.179	+	483.552i	0.384015	+	0.665134i	0.991632	−	0.129096i	$-0.0412077\pi$
$727$	279.179	+	483.552i	0.384015	+	0.665134i	−0.607617	+	0.794230i	$0.707874\pi$
$728$		0			0
$729$	709.906	−	165.756i	0.973807	−	0.227374i
$730$		0			0
$731$	1761.10	−	1016.77i	2.40917	−	1.39093i
$732$		0			0
$733$	−232.077	+	401.969i	−0.316613	+	0.548389i	−0.979779	−	0.200083i	$-0.935879\pi$
$733$	−232.077	+	401.969i	−0.316613	+	0.548389i	0.663166	+	0.748472i	$0.269212\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			753.565i			1.02248i
$738$		0			0
$739$	−117.307			−0.158738			−0.0793688	−	0.996845i	$-0.525290\pi$
$739$	−117.307			−0.158738			−0.0793688	+	0.996845i	$0.525290\pi$
$740$		0			0
$741$	−208.737	+	395.744i	−0.281696	+	0.534067i
$742$		0			0
$743$	−454.133	−	262.194i	−0.611216	−	0.352885i	0.162225	−	0.986754i	$-0.448133\pi$
$743$	−454.133	−	262.194i	−0.611216	−	0.352885i	−0.773441	+	0.633868i	$0.781466\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−614.821	+	420.675i	−0.823054	+	0.563153i
$748$		0			0
$749$	158.157	−	91.3120i	0.211158	−	0.121912i
$750$		0			0
$751$	218.646	−	378.706i	0.291140	−	0.504269i	−0.682940	−	0.730475i	$-0.739299\pi$
$751$	218.646	−	378.706i	0.291140	−	0.504269i	0.974080	+	0.226206i	$0.0726322\pi$
$752$		0			0
$753$	45.5295	+	1190.36i	0.0604642	+	1.58082i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−695.704			−0.919028			−0.459514	−	0.888171i	$-0.651976\pi$
$757$	−695.704			−0.919028			−0.459514	+	0.888171i	$0.651976\pi$
$758$		0			0
$759$	299.746	−	11.4649i	0.394922	−	0.0151053i
$760$		0			0
$761$	102.405	+	59.1234i	0.134566	+	0.0776917i	0.565772	−	0.824562i	$-0.308578\pi$
$761$	102.405	+	59.1234i	0.134566	+	0.0776917i	−0.431206	+	0.902254i	$0.641912\pi$
$762$		0			0
$763$	61.5994	+	106.693i	0.0807332	+	0.139834i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1188.26	−	686.040i	1.54923	−	0.894446i
$768$		0			0
$769$	−9.47193	+	16.4059i	−0.0123172	+	0.0213340i	−0.872118	−	0.489295i	$-0.837254\pi$
$769$	−9.47193	+	16.4059i	−0.0123172	+	0.0213340i	0.859801	+	0.510629i	$0.170587\pi$
$770$		0			0
$771$	−56.0715	−	29.5751i	−0.0727257	−	0.0383594i
$772$		0			0
$773$			1332.30i			1.72355i	0.507292	+	0.861774i	$0.330646\pi$
$773$			1332.30i			1.72355i	−0.507292	+	0.861774i	$0.669354\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	110.434	+	175.432i	0.142129	+	0.225781i
$778$		0			0
$779$	−124.364	−	71.8014i	−0.159645	−	0.0921712i
$780$		0			0
$781$	82.5811	+	143.035i	0.105738	+	0.183143i
$782$		0			0
$783$	788.389	−	584.896i	1.00688	−	0.746994i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	112.829	−	195.426i	0.143366	−	0.248318i	−0.785396	−	0.618994i	$-0.787541\pi$
$787$	112.829	−	195.426i	0.143366	−	0.248318i	0.928762	+	0.370676i	$0.120874\pi$
$788$		0			0
$789$	−323.553	+	203.677i	−0.410080	+	0.258145i
$790$		0			0
$791$		−	80.1115i		−	0.101279i
$792$		0			0
$793$	148.070			0.186721
$794$		0			0
$795$		0			0
$796$		0			0
$797$	618.519	+	357.102i	0.776059	+	0.448058i	0.835032	−	0.550202i	$-0.185449\pi$
$797$	618.519	+	357.102i	0.776059	+	0.448058i	−0.0589729	+	0.998260i	$0.518783\pi$
$798$		0			0
$799$	279.917	+	484.830i	0.350334	+	0.606796i
$800$		0			0
$801$	−9.30231	−	121.425i	−0.0116134	−	0.151592i
$802$		0			0
$803$	424.609	−	245.148i	0.528778	−	0.305290i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	26.8504	+	701.996i	0.0332719	+	0.869884i
$808$		0			0
$809$		−	32.6602i		−	0.0403710i	−0.999796	−	0.0201855i	$-0.993574\pi$
$809$		−	32.6602i		−	0.0403710i	0.999796	−	0.0201855i	$-0.00642568\pi$
$810$		0			0
$811$	418.250			0.515721			0.257860	−	0.966182i	$-0.416983\pi$
$811$	418.250			0.515721			0.257860	+	0.966182i	$0.416983\pi$
$812$		0			0
$813$	324.761	−	12.4217i	0.399461	−	0.0152788i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−209.306	−	362.529i	−0.256189	−	0.443732i
$818$		0			0
$819$	314.376	−	24.0842i	0.383854	−	0.0294068i
$820$		0			0
$821$	601.495	−	347.273i	0.732637	−	0.422988i	−0.0867493	−	0.996230i	$-0.527648\pi$
$821$	601.495	−	347.273i	0.732637	−	0.422988i	0.819386	+	0.573242i	$0.194315\pi$
$822$		0			0
$823$	500.472	−	866.843i	0.608107	−	1.05327i	−0.383445	−	0.923564i	$-0.625262\pi$
$823$	500.472	−	866.843i	0.608107	−	1.05327i	0.991552	−	0.129709i	$-0.0414042\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			115.896i			0.140140i	0.997542	+	0.0700700i	$0.0223223\pi$
$827$			115.896i			0.140140i	−0.997542	+	0.0700700i	$0.977678\pi$
$828$		0			0
$829$	−1108.02			−1.33657			−0.668286	−	0.743904i	$-0.732972\pi$
$829$	−1108.02			−1.33657			−0.668286	+	0.743904i	$0.732972\pi$
$830$		0			0
$831$	406.137	+	645.173i	0.488732	+	0.776381i
$832$		0			0
$833$	−1332.83	−	769.509i	−1.60003	−	0.923780i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−369.437	+	852.546i	−0.441383	+	1.01857i
$838$		0			0
$839$	−432.796	+	249.875i	−0.515848	+	0.297825i	−0.735234	−	0.677813i	$-0.762928\pi$
$839$	−432.796	+	249.875i	−0.515848	+	0.297825i	0.219386	+	0.975638i	$0.429594\pi$
$840$		0			0
$841$	240.448	−	416.468i	0.285907	−	0.495205i
$842$		0			0
$843$	−1005.20	+	632.770i	−1.19240	+	0.750617i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−114.312			−0.134961
$848$		0			0
$849$	531.480	−	1007.63i	0.626007	−	1.18685i
$850$		0			0
$851$	−529.642	−	305.789i	−0.622376	−	0.359329i
$852$		0			0
$853$	108.529	+	187.977i	0.127232	+	0.220372i	0.922603	−	0.385751i	$-0.126058\pi$
$853$	108.529	+	187.977i	0.127232	+	0.220372i	−0.795371	+	0.606122i	$0.792724\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−168.514	+	97.2915i	−0.196632	+	0.113526i	−0.595084	−	0.803664i	$-0.702881\pi$
$857$	−168.514	+	97.2915i	−0.196632	+	0.113526i	0.398451	+	0.917189i	$0.369548\pi$
$858$		0			0
$859$	178.061	−	308.411i	0.207289	−	0.359035i	−0.743571	−	0.668657i	$-0.766869\pi$
$859$	178.061	−	308.411i	0.207289	−	0.359035i	0.950860	+	0.309623i	$0.100203\pi$
$860$		0			0
$861$	3.86783	+	101.123i	0.00449226	+	0.117449i
$862$		0			0
$863$		−	477.201i		−	0.552955i	−0.961020	−	0.276478i	$-0.910833\pi$
$863$		−	477.201i		−	0.552955i	0.961020	−	0.276478i	$-0.0891672\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−2427.26	+	92.8396i	−2.79961	+	0.107081i
$868$		0			0
$869$	340.192	+	196.410i	0.391475	+	0.226018i
$870$		0			0
$871$	−1168.42	−	2023.77i	−1.34147	−	2.32350i
$872$		0			0
$873$	657.618	+	961.115i	0.753285	+	1.10093i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	110.006	−	190.536i	0.125434	−	0.217259i	−0.796468	−	0.604680i	$-0.793301\pi$
$877$	110.006	−	190.536i	0.125434	−	0.217259i	0.921903	+	0.387422i	$0.126634\pi$
$878$		0			0
$879$	−1300.09	−	685.736i	−1.47905	−	0.780132i
$880$		0			0
$881$			1644.86i			1.86704i	0.358530	+	0.933518i	$0.383278\pi$
$881$			1644.86i			1.86704i	−0.358530	+	0.933518i	$0.616722\pi$
$882$		0			0
$883$	−146.724			−0.166165			−0.0830827	−	0.996543i	$-0.526477\pi$
$883$	−146.724			−0.166165			−0.0830827	+	0.996543i	$0.526477\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	431.426	+	249.084i	0.486388	+	0.280816i	0.723075	−	0.690770i	$-0.242728\pi$
$887$	431.426	+	249.084i	0.486388	+	0.280816i	−0.236687	+	0.971586i	$0.576062\pi$
$888$		0			0
$889$	−43.1799	−	74.7898i	−0.0485713	−	0.0841280i
$890$		0			0
$891$	−445.179	+	357.443i	−0.499639	+	0.401171i
$892$		0			0
$893$	99.8041	−	57.6219i	0.111763	−	0.0645262i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−787.218	+	495.554i	−0.877612	+	0.552457i
$898$		0			0
$899$			1251.18i			1.39175i
$900$		0			0
$901$	−401.802			−0.445951
$902$		0			0
$903$	−137.626	+	260.926i	−0.152410	+	0.288955i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−20.5381	−	35.5731i	−0.0226440	−	0.0392206i	0.854481	−	0.519482i	$-0.173875\pi$
$907$	−20.5381	−	35.5731i	−0.0226440	−	0.0392206i	−0.877125	+	0.480261i	$0.840542\pi$
$908$		0			0
$909$	−771.773	+	528.065i	−0.849035	+	0.580929i
$910$		0			0
$911$	753.467	−	435.014i	0.827077	−	0.477513i	−0.0257741	−	0.999668i	$-0.508205\pi$
$911$	753.467	−	435.014i	0.827077	−	0.477513i	0.852851	+	0.522155i	$0.174872\pi$
$912$		0			0
$913$	291.712	−	505.259i	0.319509	−	0.553405i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	410.356i		−	0.447498i
$918$		0			0
$919$	1217.72			1.32505			0.662524	−	0.749041i	$-0.269485\pi$
$919$	1217.72			1.32505			0.662524	+	0.749041i	$0.269485\pi$
$920$		0			0
$921$	−331.362	+	12.6742i	−0.359785	+	0.0137613i
$922$		0			0
$923$	−443.558	−	256.088i	−0.480561	−	0.277452i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	31.0598	−	64.7713i	0.0335058	−	0.0698720i
$928$		0			0
$929$	−994.384	+	574.108i	−1.07038	+	0.617985i	−0.928285	−	0.371868i	$-0.878717\pi$
$929$	−994.384	+	574.108i	−1.07038	+	0.617985i	−0.142095	+	0.989853i	$0.545384\pi$
$930$		0			0
$931$	−158.406	+	274.368i	−0.170147	+	0.294702i
$932$		0			0
$933$	476.920	+	251.553i	0.511168	+	0.269618i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1064.28			1.13584			0.567920	−	0.823084i	$-0.307748\pi$
$937$	1064.28			1.13584			0.567920	+	0.823084i	$0.307748\pi$
$938$		0			0
$939$	−324.170	−	514.964i	−0.345229	−	0.548417i
$940$		0			0
$941$	1271.42	+	734.053i	1.35113	+	0.780078i	0.988408	−	0.151818i	$-0.0485128\pi$
$941$	1271.42	+	734.053i	1.35113	+	0.780078i	0.362726	+	0.931896i	$0.381846\pi$
$942$		0			0
$943$	−149.279	−	258.558i	−0.158302	−	0.274187i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1520.87	+	878.076i	−1.60599	+	0.927218i	−0.615734	+	0.787954i	$0.711140\pi$
$947$	−1520.87	+	878.076i	−1.60599	+	0.927218i	−0.990255	+	0.139264i	$0.955526\pi$
$948$		0			0
$949$	−760.216	+	1316.73i	−0.801071	+	1.38750i
$950$		0			0
$951$	−1337.43	+	841.912i	−1.40634	+	0.885291i
$952$		0			0
$953$		−	860.237i		−	0.902662i	−0.892357	−	0.451331i	$-0.850949\pi$
$953$		−	860.237i		−	0.902662i	0.892357	−	0.451331i	$-0.149051\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−358.669	+	680.001i	−0.374785	+	0.710554i
$958$		0			0
$959$	18.1500	+	10.4789i	0.0189260	+	0.0109269i
$960$		0			0
$961$	−111.625	−	193.341i	−0.116155	−	0.201187i
$962$		0			0
$963$	−78.3309	−	1022.47i	−0.0813405	−	1.06176i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	914.632	−	1584.19i	0.945845	−	1.63825i	0.191795	−	0.981435i	$-0.438569\pi$
$967$	914.632	−	1584.19i	0.945845	−	1.63825i	0.754050	−	0.656817i	$-0.228097\pi$
$968$		0			0
$969$	25.9329	+	678.006i	0.0267625	+	0.699697i
$970$		0			0
$971$			992.165i			1.02180i	0.859641	+	0.510898i	$0.170687\pi$
$971$			992.165i			1.02180i	−0.859641	+	0.510898i	$0.829313\pi$
$972$		0			0
$973$	−198.578			−0.204089
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1100.96	+	635.640i	1.12688	+	0.650604i	0.943148	−	0.332372i	$-0.107849\pi$
$977$	1100.96	+	635.640i	1.12688	+	0.650604i	0.183731	+	0.982977i	$0.441182\pi$
$978$		0			0
$979$	47.6866	+	82.5956i	0.0487095	+	0.0843674i
$980$		0			0
$981$	689.763	−	52.8424i	0.703122	−	0.0538658i
$982$		0			0
$983$	859.940	−	496.487i	0.874812	−	0.505073i	0.00586774	−	0.999983i	$-0.498132\pi$
$983$	859.940	−	496.487i	0.874812	−	0.505073i	0.868944	+	0.494910i	$0.164799\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−71.8328	−	37.8885i	−0.0727789	−	0.0383875i
$988$		0			0
$989$		−	870.317i		−	0.879997i
$990$		0			0
$991$	−884.132			−0.892161			−0.446081	−	0.894993i	$-0.647181\pi$
$991$	−884.132			−0.892161			−0.446081	+	0.894993i	$0.647181\pi$
$992$		0			0
$993$	521.198	+	827.956i	0.524873	+	0.833792i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−423.930	−	734.268i	−0.425205	−	0.736477i	0.571234	−	0.820787i	$-0.306465\pi$
$997$	−423.930	−	734.268i	−0.425205	−	0.736477i	−0.996440	+	0.0843097i	$0.973132\pi$
$998$		0			0
$999$	1156.36	−	133.208i	1.15752	−	0.133341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.c.401.6		12
3.2	odd	2		2700.3.p.c.2501.4		12
5.2	odd	4		900.3.u.c.149.6		24
5.3	odd	4		900.3.u.c.149.7		24
5.4	even	2		180.3.o.b.41.1	✓	12
9.2	odd	6	inner	900.3.p.c.101.6		12
9.7	even	3		2700.3.p.c.1601.4		12
15.2	even	4		2700.3.u.c.449.5		24
15.8	even	4		2700.3.u.c.449.8		24
15.14	odd	2		540.3.o.b.341.2		12
20.19	odd	2		720.3.bs.b.401.6		12
45.2	even	12		900.3.u.c.749.7		24
45.4	even	6		1620.3.g.b.161.4		12
45.7	odd	12		2700.3.u.c.2249.8		24
45.14	odd	6		1620.3.g.b.161.10		12
45.29	odd	6		180.3.o.b.101.1	yes	12
45.34	even	6		540.3.o.b.521.2		12
45.38	even	12		900.3.u.c.749.6		24
45.43	odd	12		2700.3.u.c.2249.5		24
60.59	even	2		2160.3.bs.b.881.2		12
180.79	odd	6		2160.3.bs.b.1601.2		12
180.119	even	6		720.3.bs.b.641.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.b.41.1	✓	12	5.4	even	2
180.3.o.b.101.1	yes	12	45.29	odd	6
540.3.o.b.341.2		12	15.14	odd	2
540.3.o.b.521.2		12	45.34	even	6
720.3.bs.b.401.6		12	20.19	odd	2
720.3.bs.b.641.6		12	180.119	even	6
900.3.p.c.101.6		12	9.2	odd	6	inner
900.3.p.c.401.6		12	1.1	even	1	trivial
900.3.u.c.149.6		24	5.2	odd	4
900.3.u.c.149.7		24	5.3	odd	4
900.3.u.c.749.6		24	45.38	even	12
900.3.u.c.749.7		24	45.2	even	12
1620.3.g.b.161.4		12	45.4	even	6
1620.3.g.b.161.10		12	45.14	odd	6
2160.3.bs.b.881.2		12	60.59	even	2
2160.3.bs.b.1601.2		12	180.79	odd	6
2700.3.p.c.1601.4		12	9.7	even	3
2700.3.p.c.2501.4		12	3.2	odd	2
2700.3.u.c.449.5		24	15.2	even	4
2700.3.u.c.449.8		24	15.8	even	4
2700.3.u.c.2249.5		24	45.43	odd	12
2700.3.u.c.2249.8		24	45.7	odd	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.99781 - 0.114662i) q^{3} +(0.801399 + 1.38806i) q^{7} +(8.97371 - 0.687471i) q^{9} +O(q^{10})\)	\(q+(2.99781 - 0.114662i) q^{3} +(0.801399 + 1.38806i) q^{7} +(8.97371 - 0.687471i) q^{9} +(-6.10409 + 3.52420i) q^{11} +(10.9287 - 18.9291i) q^{13} -33.1463i q^{17} -6.82330 q^{19} +(2.56160 + 4.06926i) q^{21} +(-12.2854 - 7.09299i) q^{23} +(26.8226 - 3.08985i) q^{27} +(31.4868 - 18.1789i) q^{29} +(-17.2065 + 29.8025i) q^{31} +(-17.8948 + 11.2648i) q^{33} +43.1114 q^{37} +(30.5917 - 57.9989i) q^{39} +(18.2263 + 10.5230i) q^{41} +(30.6752 + 53.1311i) q^{43} +(-14.6270 + 8.44488i) q^{47} +(23.2155 - 40.2105i) q^{49} +(-3.80063 - 99.3663i) q^{51} -12.1221i q^{53} +(-20.4549 + 0.782375i) q^{57} +(54.3639 + 31.3870i) q^{59} +(3.38717 + 5.86675i) q^{61} +(8.14577 + 11.9051i) q^{63} +(53.4565 - 92.5894i) q^{67} +(-37.6426 - 19.8547i) q^{69} -23.4326i q^{71} -69.5613 q^{73} +(-9.78362 - 5.64858i) q^{77} +(-27.8659 - 48.2651i) q^{79} +(80.0548 - 12.3383i) q^{81} +(-71.6843 + 41.3869i) q^{83} +(92.3071 - 58.1073i) q^{87} -13.5312i q^{89} +35.0331 q^{91} +(-48.1645 + 91.3151i) q^{93} +(64.6979 + 112.060i) q^{97} +(-52.3535 + 35.8215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{7} + 26 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 + 6 * q^7 + 26 * q^9	\( 12 q - 2 q^{3} + 6 q^{7} + 26 q^{9} + 48 q^{11} + 30 q^{13} + 72 q^{19} - 128 q^{21} + 78 q^{23} + 106 q^{27} + 150 q^{29} - 12 q^{31} - 96 q^{33} + 12 q^{37} + 40 q^{39} + 90 q^{41} - 114 q^{43} - 12 q^{47} + 48 q^{49} - 144 q^{51} + 158 q^{57} + 48 q^{59} - 78 q^{61} + 212 q^{63} + 168 q^{67} - 150 q^{69} + 24 q^{73} + 258 q^{77} + 120 q^{79} + 434 q^{81} - 114 q^{83} + 330 q^{87} + 120 q^{91} - 82 q^{93} - 96 q^{97} - 120 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^7 + 26 * q^9 + 48 * q^11 + 30 * q^13 + 72 * q^19 - 128 * q^21 + 78 * q^23 + 106 * q^27 + 150 * q^29 - 12 * q^31 - 96 * q^33 + 12 * q^37 + 40 * q^39 + 90 * q^41 - 114 * q^43 - 12 * q^47 + 48 * q^49 - 144 * q^51 + 158 * q^57 + 48 * q^59 - 78 * q^61 + 212 * q^63 + 168 * q^67 - 150 * q^69 + 24 * q^73 + 258 * q^77 + 120 * q^79 + 434 * q^81 - 114 * q^83 + 330 * q^87 + 120 * q^91 - 82 * q^93 - 96 * q^97 - 120 * q^99

Introduction

L-functions

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