LMFDB - Embedded newform 900.3.c.t.451.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(451,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("900.451");

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.c (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.4069419264.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 $ x^8 - 7x^6 + 50x^4 - 84x^3 + 55x^2 - 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			451.3
Root			$0.845613 + 0.488215i$ of defining polynomial
Character	$\chi$	$=$	900.451
Dual form			900.3.c.t.451.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.177680 - 1.99209i) q^{2} +(-3.93686 + 0.707911i) q^{4} +1.19501i q^{7} +(2.10973 + 7.71680i) q^{8} +O(q^{10})$	\(q+(-0.177680 - 1.99209i) q^{2} +(-3.93686 + 0.707911i) q^{4} +1.19501i q^{7} +(2.10973 + 7.71680i) q^{8} +8.22072i q^{11} -11.1863 q^{13} +(2.38058 - 0.212331i) q^{14} +(14.9977 - 5.57389i) q^{16} +20.9256 q^{17} -27.9657i q^{19} +(16.3764 - 1.46066i) q^{22} +9.48564i q^{23} +(1.98759 + 22.2842i) q^{26} +(-0.845964 - 4.70460i) q^{28} -40.4205 q^{29} -55.3130i q^{31} +(-13.7685 - 28.8865i) q^{32} +(-3.71807 - 41.6858i) q^{34} -50.1890 q^{37} +(-55.7102 + 4.96895i) q^{38} +73.6361 q^{41} -19.0843i q^{43} +(-5.81954 - 32.3638i) q^{44} +(18.8963 - 1.68541i) q^{46} -18.0598i q^{47} +47.5719 q^{49} +(44.0391 - 7.91894i) q^{52} -57.2212 q^{53} +(-9.22169 + 2.52115i) q^{56} +(7.18193 + 80.5213i) q^{58} -60.6645i q^{59} -21.3518 q^{61} +(-110.189 + 9.82804i) q^{62} +(-55.0981 + 32.5607i) q^{64} +9.68679i q^{67} +(-82.3812 + 14.8135i) q^{68} -68.6944i q^{71} -84.7825 q^{73} +(8.91760 + 99.9811i) q^{74} +(19.7972 + 110.097i) q^{76} -9.82388 q^{77} -23.2903i q^{79} +(-13.0837 - 146.690i) q^{82} -93.2595i q^{83} +(-38.0177 + 3.39091i) q^{86} +(-63.4377 + 17.3435i) q^{88} -62.9898 q^{89} -13.3678i q^{91} +(-6.71499 - 37.3436i) q^{92} +(-35.9767 + 3.20887i) q^{94} -91.3962 q^{97} +(-8.45260 - 94.7677i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 8 q^{4} + 20 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 8 * q^4 + 20 * q^8	$ 8 q + 2 q^{2} - 8 q^{4} + 20 q^{8} - 8 q^{13} - 22 q^{14} + 40 q^{16} - 4 q^{22} + 66 q^{26} - 104 q^{28} + 32 q^{29} + 112 q^{32} + 124 q^{34} + 176 q^{37} - 170 q^{38} + 16 q^{41} - 40 q^{44} - 76 q^{46} + 16 q^{49} - 56 q^{52} - 304 q^{53} + 172 q^{56} + 12 q^{58} + 136 q^{61} - 238 q^{62} + 16 q^{64} + 88 q^{68} - 240 q^{73} + 108 q^{74} + 120 q^{76} - 384 q^{77} - 320 q^{82} - 214 q^{86} + 200 q^{88} - 128 q^{89} + 312 q^{92} + 12 q^{94} - 216 q^{97} + 60 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 8 * q^4 + 20 * q^8 - 8 * q^13 - 22 * q^14 + 40 * q^16 - 4 * q^22 + 66 * q^26 - 104 * q^28 + 32 * q^29 + 112 * q^32 + 124 * q^34 + 176 * q^37 - 170 * q^38 + 16 * q^41 - 40 * q^44 - 76 * q^46 + 16 * q^49 - 56 * q^52 - 304 * q^53 + 172 * q^56 + 12 * q^58 + 136 * q^61 - 238 * q^62 + 16 * q^64 + 88 * q^68 - 240 * q^73 + 108 * q^74 + 120 * q^76 - 384 * q^77 - 320 * q^82 - 214 * q^86 + 200 * q^88 - 128 * q^89 + 312 * q^92 + 12 * q^94 - 216 * q^97 + 60 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.177680	−	1.99209i	−0.0888402	−	0.996046i
$2$	−0.177680	−	1.99209i	−0.0888402	−	0.996046i
$3$		0			0
$3$		0			0
$4$	−3.93686	+	0.707911i	−0.984215	+	0.176978i
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.19501i			0.170716i	0.996350	+	0.0853582i	$0.0272035\pi$
$7$			1.19501i			0.170716i	−0.996350	+	0.0853582i	$0.972797\pi$
$8$	2.10973	+	7.71680i	0.263716	+	0.964600i
$9$		0			0
$10$		0			0
$11$			8.22072i			0.747338i	0.927562	+	0.373669i	$0.121900\pi$
$11$			8.22072i			0.747338i	−0.927562	+	0.373669i	$0.878100\pi$
$12$		0			0
$13$	−11.1863			−0.860488			−0.430244	−	0.902713i	$-0.641572\pi$
$13$	−11.1863			−0.860488			−0.430244	+	0.902713i	$0.641572\pi$
$14$	2.38058	−	0.212331i	0.170041	−	0.0151665i
$15$		0			0
$16$	14.9977	−	5.57389i	0.937358	−	0.348368i
$17$	20.9256			1.23092			0.615459	−	0.788169i	$-0.288970\pi$
$17$	20.9256			1.23092			0.615459	+	0.788169i	$0.288970\pi$
$18$		0			0
$19$		−	27.9657i		−	1.47188i	−0.677048	−	0.735939i	$-0.736741\pi$
$19$		−	27.9657i		−	1.47188i	0.677048	−	0.735939i	$-0.263259\pi$
$20$		0			0
$21$		0			0
$22$	16.3764	−	1.46066i	0.744383	−	0.0663937i
$23$			9.48564i			0.412419i	0.978508	+	0.206209i	$0.0661128\pi$
$23$			9.48564i			0.412419i	−0.978508	+	0.206209i	$0.933887\pi$
$24$		0			0
$25$		0			0
$26$	1.98759	+	22.2842i	0.0764459	+	0.857085i
$27$		0			0
$28$	−0.845964	−	4.70460i	−0.0302130	−	0.168022i
$29$	−40.4205			−1.39381			−0.696905	−	0.717163i	$-0.745440\pi$
$29$	−40.4205			−1.39381			−0.696905	+	0.717163i	$0.745440\pi$
$30$		0			0
$31$		−	55.3130i		−	1.78429i	−0.451748	−	0.892145i	$-0.649200\pi$
$31$		−	55.3130i		−	1.78429i	0.451748	−	0.892145i	$-0.350800\pi$
$32$	−13.7685	−	28.8865i	−0.430266	−	0.902702i
$33$		0			0
$34$	−3.71807	−	41.6858i	−0.109355	−	1.22605i
$35$		0			0
$36$		0			0
$37$	−50.1890			−1.35646			−0.678230	−	0.734850i	$-0.737253\pi$
$37$	−50.1890			−1.35646			−0.678230	+	0.734850i	$0.737253\pi$
$38$	−55.7102	+	4.96895i	−1.46606	+	0.130762i
$39$		0			0
$40$		0			0
$41$	73.6361			1.79600			0.898001	−	0.439994i	$-0.145019\pi$
$41$	73.6361			1.79600			0.898001	+	0.439994i	$0.145019\pi$
$42$		0			0
$43$		−	19.0843i		−	0.443822i	−0.975067	−	0.221911i	$-0.928771\pi$
$43$		−	19.0843i		−	0.443822i	0.975067	−	0.221911i	$-0.0712294\pi$
$44$	−5.81954	−	32.3638i	−0.132262	−	0.735541i
$45$		0			0
$46$	18.8963	−	1.68541i	0.410788	−	0.0366394i
$47$		−	18.0598i		−	0.384251i	−0.981370	−	0.192125i	$-0.938462\pi$
$47$		−	18.0598i		−	0.384251i	0.981370	−	0.192125i	$-0.0615380\pi$
$48$		0			0
$49$	47.5719			0.970856
$50$		0			0
$51$		0			0
$52$	44.0391	−	7.91894i	0.846905	−	0.152287i
$53$	−57.2212			−1.07965			−0.539823	−	0.841779i	$-0.681509\pi$
$53$	−57.2212			−1.07965			−0.539823	+	0.841779i	$0.681509\pi$
$54$		0			0
$55$		0			0
$56$	−9.22169	+	2.52115i	−0.164673	+	0.0450206i
$57$		0			0
$58$	7.18193	+	80.5213i	0.123826	+	1.38830i
$59$		−	60.6645i		−	1.02821i	−0.857727	−	0.514106i	$-0.828124\pi$
$59$		−	60.6645i		−	1.02821i	0.857727	−	0.514106i	$-0.171876\pi$
$60$		0			0
$61$	−21.3518			−0.350030			−0.175015	−	0.984566i	$-0.555997\pi$
$61$	−21.3518			−0.350030			−0.175015	+	0.984566i	$0.555997\pi$
$62$	−110.189	+	9.82804i	−1.77724	+	0.158517i
$63$		0			0
$64$	−55.0981	+	32.5607i	−0.860908	+	0.508761i
$65$		0			0
$66$		0			0
$67$			9.68679i			0.144579i	0.997384	+	0.0722895i	$0.0230305\pi$
$67$			9.68679i			0.144579i	−0.997384	+	0.0722895i	$0.976969\pi$
$68$	−82.3812	+	14.8135i	−1.21149	+	0.217845i
$69$		0			0
$70$		0			0
$71$		−	68.6944i		−	0.967527i	−0.875199	−	0.483763i	$-0.839270\pi$
$71$		−	68.6944i		−	0.967527i	0.875199	−	0.483763i	$-0.160730\pi$
$72$		0			0
$73$	−84.7825			−1.16140			−0.580702	−	0.814116i	$-0.697222\pi$
$73$	−84.7825			−1.16140			−0.580702	+	0.814116i	$0.697222\pi$
$74$	8.91760	+	99.9811i	0.120508	+	1.35110i
$75$		0			0
$76$	19.7972	+	110.097i	0.260490	+	1.44864i
$77$	−9.82388			−0.127583
$78$		0			0
$79$		−	23.2903i		−	0.294814i	−0.989076	−	0.147407i	$-0.952907\pi$
$79$		−	23.2903i		−	0.294814i	0.989076	−	0.147407i	$-0.0470928\pi$
$80$		0			0
$81$		0			0
$82$	−13.0837	−	146.690i	−0.159557	−	1.78890i
$83$		−	93.2595i		−	1.12361i	−0.827270	−	0.561804i	$-0.810107\pi$
$83$		−	93.2595i		−	1.12361i	0.827270	−	0.561804i	$-0.189893\pi$
$84$		0			0
$85$		0			0
$86$	−38.0177	+	3.39091i	−0.442067	+	0.0394292i
$87$		0			0
$88$	−63.4377	+	17.3435i	−0.720883	+	0.197085i
$89$	−62.9898			−0.707750			−0.353875	−	0.935293i	$-0.615136\pi$
$89$	−62.9898			−0.707750			−0.353875	+	0.935293i	$0.615136\pi$
$90$		0			0
$91$		−	13.3678i		−	0.146899i
$92$	−6.71499	−	37.3436i	−0.0729890	−	0.405909i
$93$		0			0
$94$	−35.9767	+	3.20887i	−0.382731	+	0.0341369i
$95$		0			0
$96$		0			0
$97$	−91.3962			−0.942229			−0.471115	−	0.882072i	$-0.656148\pi$
$97$	−91.3962			−0.942229			−0.471115	+	0.882072i	$0.656148\pi$
$98$	−8.45260	−	94.7677i	−0.0862510	−	0.967017i
$99$		0			0
$100$		0			0
$101$	29.9780			0.296811			0.148406	−	0.988927i	$-0.452586\pi$
$101$	29.9780			0.296811			0.148406	+	0.988927i	$0.452586\pi$
$102$		0			0
$103$		−	88.7485i		−	0.861636i	−0.902439	−	0.430818i	$-0.858225\pi$
$103$		−	88.7485i		−	0.861636i	0.902439	−	0.430818i	$-0.141775\pi$
$104$	−23.6001	−	86.3228i	−0.226924	−	0.830027i
$105$		0			0
$106$	10.1671	+	113.990i	0.0959159	+	1.07538i
$107$			162.922i			1.52263i	0.648381	+	0.761316i	$0.275447\pi$
$107$			162.922i			1.52263i	−0.648381	+	0.761316i	$0.724553\pi$
$108$		0			0
$109$	−103.352			−0.948182			−0.474091	−	0.880476i	$-0.657223\pi$
$109$	−103.352			−0.948182			−0.474091	+	0.880476i	$0.657223\pi$
$110$		0			0
$111$		0			0
$112$	6.66088	+	17.9225i	0.0594722	+	0.160022i
$113$	−31.2691			−0.276717			−0.138359	−	0.990382i	$-0.544183\pi$
$113$	−31.2691			−0.276717			−0.138359	+	0.990382i	$0.544183\pi$
$114$		0			0
$115$		0			0
$116$	159.130	−	28.6141i	1.37181	−	0.246673i
$117$		0			0
$118$	−120.849	+	10.7789i	−1.02415	+	0.0913465i
$119$			25.0064i			0.210138i
$120$		0			0
$121$	53.4198			0.441486
$122$	3.79380	+	42.5348i	0.0310967	+	0.348646i
$123$		0			0
$124$	39.1567	+	217.760i	0.315780	+	1.75613i
$125$		0			0
$126$		0			0
$127$			178.474i			1.40531i	0.711531	+	0.702655i	$0.248002\pi$
$127$			178.474i			1.40531i	−0.711531	+	0.702655i	$0.751998\pi$
$128$	74.6537	+	103.975i	0.583232	+	0.812305i
$129$		0			0
$130$		0			0
$131$		−	153.743i		−	1.17361i	−0.809727	−	0.586806i	$-0.800385\pi$
$131$		−	153.743i		−	1.17361i	0.809727	−	0.586806i	$-0.199615\pi$
$132$		0			0
$133$	33.4194			0.251274
$134$	19.2970	−	1.72115i	0.144007	−	0.0128444i
$135$		0			0
$136$	44.1473	+	161.479i	0.324613	+	1.18734i
$137$	−52.9928			−0.386809			−0.193405	−	0.981119i	$-0.561953\pi$
$137$	−52.9928			−0.386809			−0.193405	+	0.981119i	$0.561953\pi$
$138$		0			0
$139$			21.8420i			0.157137i	0.996909	+	0.0785684i	$0.0250349\pi$
$139$			21.8420i			0.157137i	−0.996909	+	0.0785684i	$0.974965\pi$
$140$		0			0
$141$		0			0
$142$	−136.846	+	12.2056i	−0.963701	+	0.0859552i
$143$		−	91.9598i		−	0.643076i
$144$		0			0
$145$		0			0
$146$	15.0642	+	168.895i	0.103179	+	1.15681i
$147$		0			0
$148$	197.587	−	35.5294i	1.33505	−	0.240063i
$149$	3.12940			0.0210027			0.0105013	−	0.999945i	$-0.496657\pi$
$149$	3.12940			0.0210027			0.0105013	+	0.999945i	$0.496657\pi$
$150$		0			0
$151$		−	296.461i		−	1.96332i	−0.190646	−	0.981659i	$-0.561058\pi$
$151$		−	296.461i		−	1.96332i	0.190646	−	0.981659i	$-0.438942\pi$
$152$	215.806	−	58.9999i	1.41977	−	0.388157i
$153$		0			0
$154$	1.74551	+	19.5701i	0.0113345	+	0.127078i
$155$		0			0
$156$		0			0
$157$	265.686			1.69227			0.846133	−	0.532972i	$-0.178925\pi$
$157$	265.686			1.69227			0.846133	+	0.532972i	$0.178925\pi$
$158$	−46.3965	+	4.13824i	−0.293649	+	0.0261914i
$159$		0			0
$160$		0			0
$161$	−11.3355			−0.0704067
$162$		0			0
$163$		−	205.531i		−	1.26093i	−0.776218	−	0.630465i	$-0.782864\pi$
$163$		−	205.531i		−	1.26093i	0.776218	−	0.630465i	$-0.217136\pi$
$164$	−289.895	+	52.1278i	−1.76765	+	0.317852i
$165$		0			0
$166$	−185.781	+	16.5704i	−1.11917	+	0.0998215i
$167$		−	11.6359i		−	0.0696763i	−0.999393	−	0.0348381i	$-0.988908\pi$
$167$		−	11.6359i		−	0.0696763i	0.999393	−	0.0348381i	$-0.0110916\pi$
$168$		0			0
$169$	−43.8657			−0.259560
$170$		0			0
$171$		0			0
$172$	13.5100	+	75.1323i	0.0785466	+	0.436816i
$173$	−106.062			−0.613077			−0.306538	−	0.951858i	$-0.599171\pi$
$173$	−106.062			−0.613077			−0.306538	+	0.951858i	$0.599171\pi$
$174$		0			0
$175$		0			0
$176$	45.8214	+	123.292i	0.260349	+	0.700523i
$177$		0			0
$178$	11.1920	+	125.481i	0.0628766	+	0.704951i
$179$			43.3304i			0.242069i	0.992648	+	0.121035i	$0.0386212\pi$
$179$			43.3304i			0.242069i	−0.992648	+	0.121035i	$0.961379\pi$
$180$		0			0
$181$	203.614			1.12494			0.562469	−	0.826819i	$-0.309852\pi$
$181$	203.614			1.12494			0.562469	+	0.826819i	$0.309852\pi$
$182$	−26.6300	+	2.37520i	−0.146319	+	0.0130506i
$183$		0			0
$184$	−73.1988	+	20.0121i	−0.397819	+	0.108761i
$185$		0			0
$186$		0			0
$187$			172.024i			0.919913i
$188$	12.7847	+	71.0988i	0.0680038	+	0.378185i
$189$		0			0
$190$		0			0
$191$			251.536i			1.31694i	0.752606	+	0.658471i	$0.228796\pi$
$191$			251.536i			1.31694i	−0.752606	+	0.658471i	$0.771204\pi$
$192$		0			0
$193$	281.811			1.46016			0.730081	−	0.683360i	$-0.239482\pi$
$193$	281.811			1.46016			0.730081	+	0.683360i	$0.239482\pi$
$194$	16.2393	+	182.070i	0.0837078	+	0.938503i
$195$		0			0
$196$	−187.284	+	33.6767i	−0.955531	+	0.171820i
$197$	−243.485			−1.23596			−0.617982	−	0.786193i	$-0.712049\pi$
$197$	−243.485			−1.23596			−0.617982	+	0.786193i	$0.712049\pi$
$198$		0			0
$199$		−	121.958i		−	0.612853i	−0.951894	−	0.306427i	$-0.900867\pi$
$199$		−	121.958i		−	0.612853i	0.951894	−	0.306427i	$-0.0991335\pi$
$200$		0			0
$201$		0			0
$202$	−5.32649	−	59.7188i	−0.0263688	−	0.295638i
$203$		−	48.3031i		−	0.237946i
$204$		0			0
$205$		0			0
$206$	−176.795	+	15.7689i	−0.858229	+	0.0765479i
$207$		0			0
$208$	−167.770	+	62.3515i	−0.806585	+	0.299767i
$209$	229.898			1.09999
$210$		0			0
$211$		−	132.543i		−	0.628168i	−0.949395	−	0.314084i	$-0.898303\pi$
$211$		−	132.543i		−	0.628168i	0.949395	−	0.314084i	$-0.101697\pi$
$212$	225.272	−	40.5076i	1.06260	−	0.191073i
$213$		0			0
$214$	324.555	−	28.9480i	1.51661	−	0.135271i
$215$		0			0
$216$		0			0
$217$	66.0998			0.304608
$218$	18.3636	+	205.886i	0.0842366	+	0.944433i
$219$		0			0
$220$		0			0
$221$	−234.081			−1.05919
$222$		0			0
$223$		−	225.442i		−	1.01095i	−0.862841	−	0.505475i	$-0.831317\pi$
$223$		−	225.442i		−	1.01095i	0.862841	−	0.505475i	$-0.168683\pi$
$224$	34.5198	−	16.4536i	0.154106	−	0.0734534i
$225$		0			0
$226$	5.55590	+	62.2908i	0.0245836	+	0.275623i
$227$		−	108.080i		−	0.476124i	−0.971250	−	0.238062i	$-0.923488\pi$
$227$		−	108.080i		−	0.476124i	0.971250	−	0.238062i	$-0.0765122\pi$
$228$		0			0
$229$	−57.3495			−0.250435			−0.125217	−	0.992129i	$-0.539963\pi$
$229$	−57.3495			−0.250435			−0.125217	+	0.992129i	$0.539963\pi$
$230$		0			0
$231$		0			0
$232$	−85.2762	−	311.917i	−0.367570	−	1.34447i
$233$	285.320			1.22455			0.612274	−	0.790646i	$-0.290255\pi$
$233$	285.320			1.22455			0.612274	+	0.790646i	$0.290255\pi$
$234$		0			0
$235$		0			0
$236$	42.9451	+	238.828i	0.181971	+	1.01198i
$237$		0			0
$238$	49.8151	−	4.44315i	0.209307	−	0.0186687i
$239$		−	77.2471i		−	0.323210i	−0.986856	−	0.161605i	$-0.948333\pi$
$239$		−	77.2471i		−	0.323210i	0.986856	−	0.161605i	$-0.0516670\pi$
$240$		0			0
$241$	−130.557			−0.541732			−0.270866	−	0.962617i	$-0.587310\pi$
$241$	−130.557			−0.541732			−0.270866	+	0.962617i	$0.587310\pi$
$242$	−9.49164	−	106.417i	−0.0392217	−	0.439740i
$243$		0			0
$244$	84.0591	−	15.1152i	0.344504	−	0.0619475i
$245$		0			0
$246$		0			0
$247$			312.834i			1.26653i
$248$	426.840	−	116.695i	1.72113	−	0.470546i
$249$		0			0
$250$		0			0
$251$		−	437.197i		−	1.74182i	−0.491441	−	0.870911i	$-0.663530\pi$
$251$		−	437.197i		−	1.74182i	0.491441	−	0.870911i	$-0.336470\pi$
$252$		0			0
$253$	−77.9788			−0.308216
$254$	355.537	−	31.7114i	1.39975	−	0.124848i
$255$		0			0
$256$	193.863	−	167.191i	0.757279	−	0.653091i
$257$	74.3682			0.289370			0.144685	−	0.989478i	$-0.453783\pi$
$257$	74.3682			0.289370			0.144685	+	0.989478i	$0.453783\pi$
$258$		0			0
$259$		−	59.9766i		−	0.231570i
$260$		0			0
$261$		0			0
$262$	−306.271	+	27.3172i	−1.16897	+	0.104264i
$263$			458.790i			1.74445i	0.489105	+	0.872225i	$0.337324\pi$
$263$			458.790i			1.74445i	−0.489105	+	0.872225i	$0.662676\pi$
$264$		0			0
$265$		0			0
$266$	−5.93797	−	66.5745i	−0.0223232	−	0.250280i
$267$		0			0
$268$	−6.85739	−	38.1355i	−0.0255873	−	0.142297i
$269$	320.405			1.19110			0.595549	−	0.803319i	$-0.296935\pi$
$269$	320.405			1.19110			0.595549	+	0.803319i	$0.296935\pi$
$270$		0			0
$271$		−	359.059i		−	1.32494i	−0.749088	−	0.662470i	$-0.769508\pi$
$271$		−	359.059i		−	1.32494i	0.749088	−	0.662470i	$-0.230492\pi$
$272$	313.837	−	116.637i	1.15381	−	0.428813i
$273$		0			0
$274$	9.41579	+	105.567i	0.0343642	+	0.385280i
$275$		0			0
$276$		0			0
$277$	−138.027			−0.498293			−0.249147	−	0.968466i	$-0.580150\pi$
$277$	−138.027			−0.498293			−0.249147	+	0.968466i	$0.580150\pi$
$278$	43.5113	−	3.88090i	0.156516	−	0.0139601i
$279$		0			0
$280$		0			0
$281$	−462.504			−1.64592			−0.822960	−	0.568099i	$-0.807679\pi$
$281$	−462.504			−1.64592			−0.822960	+	0.568099i	$0.807679\pi$
$282$		0			0
$283$			323.973i			1.14478i	0.819981	+	0.572391i	$0.193984\pi$
$283$			323.973i			1.14478i	−0.819981	+	0.572391i	$0.806016\pi$
$284$	48.6295	+	270.440i	0.171231	+	0.952254i
$285$		0			0
$286$	−183.192	+	16.3394i	−0.640533	+	0.0571309i
$287$			87.9962i			0.306607i
$288$		0			0
$289$	148.882			0.515161
$290$		0			0
$291$		0			0
$292$	333.777	−	60.0185i	1.14307	−	0.205543i
$293$	150.416			0.513365			0.256683	−	0.966496i	$-0.417371\pi$
$293$	150.416			0.513365			0.256683	+	0.966496i	$0.417371\pi$
$294$		0			0
$295$		0			0
$296$	−105.885	−	387.299i	−0.357720	−	1.30844i
$297$		0			0
$298$	−0.556033	−	6.23406i	−0.00186588	−	0.0209196i
$299$		−	106.110i		−	0.354882i
$300$		0			0
$301$	22.8060			0.0757676
$302$	−590.577	+	52.6753i	−1.95555	+	0.174421i
$303$		0			0
$304$	−155.878	−	419.421i	−0.512755	−	1.37968i
$305$		0			0
$306$		0			0
$307$		−	563.915i		−	1.83686i	−0.395587	−	0.918428i	$-0.629459\pi$
$307$		−	563.915i		−	1.83686i	0.395587	−	0.918428i	$-0.370541\pi$
$308$	38.6752	−	6.95443i	0.125569	−	0.0225793i
$309$		0			0
$310$		0			0
$311$		−	40.0214i		−	0.128686i	−0.997928	−	0.0643431i	$-0.979505\pi$
$311$		−	40.0214i		−	0.128686i	0.997928	−	0.0643431i	$-0.0204952\pi$
$312$		0			0
$313$	−1.82657			−0.00583568			−0.00291784	−	0.999996i	$-0.500929\pi$
$313$	−1.82657			−0.00583568			−0.00291784	+	0.999996i	$0.500929\pi$
$314$	−47.2071	−	529.270i	−0.150341	−	1.68557i
$315$		0			0
$316$	16.4875	+	91.6908i	0.0521756	+	0.290161i
$317$	246.416			0.777338			0.388669	−	0.921378i	$-0.372935\pi$
$317$	246.416			0.777338			0.388669	+	0.921378i	$0.372935\pi$
$318$		0			0
$319$		−	332.286i		−	1.04165i
$320$		0			0
$321$		0			0
$322$	2.01409	+	22.5813i	0.00625494	+	0.0701283i
$323$		−	585.199i		−	1.81176i
$324$		0			0
$325$		0			0
$326$	−409.438	+	36.5189i	−1.25594	+	0.112021i
$327$		0			0
$328$	155.352	+	568.235i	0.473634	+	1.73242i
$329$	21.5817			0.0655978
$330$		0			0
$331$			417.672i			1.26185i	0.775844	+	0.630925i	$0.217325\pi$
$331$			417.672i			1.26185i	−0.775844	+	0.630925i	$0.782675\pi$
$332$	66.0194	+	367.149i	0.198854	+	1.10587i
$333$		0			0
$334$	−23.1798	+	2.06748i	−0.0694007	+	0.00619005i
$335$		0			0
$336$		0			0
$337$	317.379			0.941779			0.470889	−	0.882192i	$-0.343933\pi$
$337$	317.379			0.941779			0.470889	+	0.882192i	$0.343933\pi$
$338$	7.79408	+	87.3845i	0.0230594	+	0.258534i
$339$		0			0
$340$		0			0
$341$	454.713			1.33347
$342$		0			0
$343$			115.405i			0.336457i
$344$	147.270	−	40.2627i	0.428110	−	0.117043i
$345$		0			0
$346$	18.8452	+	211.286i	0.0544659	+	0.610653i
$347$			222.581i			0.641443i	0.947174	+	0.320721i	$0.103925\pi$
$347$			222.581i			0.641443i	−0.947174	+	0.320721i	$0.896075\pi$
$348$		0			0
$349$	560.812			1.60691			0.803455	−	0.595366i	$-0.202993\pi$
$349$	560.812			1.60691			0.803455	+	0.595366i	$0.202993\pi$
$350$		0			0
$351$		0			0
$352$	237.468	−	113.187i	0.674624	−	0.321554i
$353$	304.856			0.863616			0.431808	−	0.901966i	$-0.357876\pi$
$353$	304.856			0.863616			0.431808	+	0.901966i	$0.357876\pi$
$354$		0			0
$355$		0			0
$356$	247.982	−	44.5911i	0.696578	−	0.125256i
$357$		0			0
$358$	86.3181	−	7.69896i	0.241112	−	0.0215055i
$359$			105.860i			0.294874i	0.989071	+	0.147437i	$0.0471023\pi$
$359$			105.860i			0.294874i	−0.989071	+	0.147437i	$0.952898\pi$
$360$		0			0
$361$	−421.079			−1.16642
$362$	−36.1782	−	405.617i	−0.0999396	−	1.12049i
$363$		0			0
$364$	9.46324	+	52.6273i	0.0259979	+	0.144581i
$365$		0			0
$366$		0			0
$367$		−	360.200i		−	0.981470i	−0.871309	−	0.490735i	$-0.836728\pi$
$367$		−	360.200i		−	0.981470i	0.871309	−	0.490735i	$-0.163272\pi$
$368$	52.8719	+	142.263i	0.143674	+	0.386584i
$369$		0			0
$370$		0			0
$371$		−	68.3802i		−	0.184313i
$372$		0			0
$373$	135.489			0.363242			0.181621	−	0.983369i	$-0.441866\pi$
$373$	135.489			0.363242			0.181621	+	0.983369i	$0.441866\pi$
$374$	342.687	−	30.5652i	0.916275	−	0.0817252i
$375$		0			0
$376$	139.364	−	38.1012i	0.370648	−	0.101333i
$377$	452.158			1.19936
$378$		0			0
$379$			310.686i			0.819753i	0.912141	+	0.409876i	$0.134428\pi$
$379$			310.686i			0.819753i	−0.912141	+	0.409876i	$0.865572\pi$
$380$		0			0
$381$		0			0
$382$	501.083	−	44.6930i	1.31173	−	0.116997i
$383$			121.981i			0.318487i	0.987239	+	0.159244i	$0.0509056\pi$
$383$			121.981i			0.318487i	−0.987239	+	0.159244i	$0.949094\pi$
$384$		0			0
$385$		0			0
$386$	−50.0723	−	561.394i	−0.129721	−	1.45439i
$387$		0			0
$388$	359.814	−	64.7004i	0.927356	−	0.166754i
$389$	−544.266			−1.39914			−0.699570	−	0.714564i	$-0.746625\pi$
$389$	−544.266			−1.39914			−0.699570	+	0.714564i	$0.746625\pi$
$390$		0			0
$391$			198.493i			0.507654i
$392$	100.364	+	367.103i	0.256030	+	0.936488i
$393$		0			0
$394$	43.2625	+	485.044i	0.109803	+	1.23108i
$395$		0			0
$396$		0			0
$397$	−504.528			−1.27085			−0.635425	−	0.772162i	$-0.719175\pi$
$397$	−504.528			−1.27085			−0.635425	+	0.772162i	$0.719175\pi$
$398$	−242.951	+	21.6695i	−0.610430	+	0.0544460i
$399$		0			0
$400$		0			0
$401$	278.018			0.693312			0.346656	−	0.937992i	$-0.387317\pi$
$401$	278.018			0.693312			0.346656	+	0.937992i	$0.387317\pi$
$402$		0			0
$403$			618.750i			1.53536i
$404$	−118.019	+	21.2217i	−0.292126	+	0.0525290i
$405$		0			0
$406$	−96.2242	+	8.58251i	−0.237005	+	0.0211392i
$407$		−	412.590i		−	1.01373i
$408$		0			0
$409$	−296.549			−0.725059			−0.362530	−	0.931972i	$-0.618087\pi$
$409$	−296.549			−0.725059			−0.362530	+	0.931972i	$0.618087\pi$
$410$		0			0
$411$		0			0
$412$	62.8261	+	349.390i	0.152490	+	0.848035i
$413$	72.4950			0.175533
$414$		0			0
$415$		0			0
$416$	154.019	+	323.134i	0.370239	+	0.776764i
$417$		0			0
$418$	−40.8483	−	457.978i	−0.0977233	−	1.09564i
$419$		−	315.615i		−	0.753258i	−0.926364	−	0.376629i	$-0.877083\pi$
$419$		−	315.615i		−	0.753258i	0.926364	−	0.376629i	$-0.122917\pi$
$420$		0			0
$421$	−360.355			−0.855951			−0.427975	−	0.903790i	$-0.640773\pi$
$421$	−360.355			−0.855951			−0.427975	+	0.903790i	$0.640773\pi$
$422$	−264.039	+	23.5504i	−0.625684	+	0.0558066i
$423$		0			0
$424$	−120.721	−	441.565i	−0.284720	−	1.04143i
$425$		0			0
$426$		0			0
$427$		−	25.5157i		−	0.0597558i
$428$	−115.334	−	641.400i	−0.269472	−	1.49860i
$429$		0			0
$430$		0			0
$431$			523.617i			1.21489i	0.794362	+	0.607445i	$0.207805\pi$
$431$			523.617i			1.21489i	−0.794362	+	0.607445i	$0.792195\pi$
$432$		0			0
$433$	21.5381			0.0497415			0.0248707	−	0.999691i	$-0.492083\pi$
$433$	21.5381			0.0497415			0.0248707	+	0.999691i	$0.492083\pi$
$434$	−11.7446	−	131.677i	−0.0270614	−	0.303403i
$435$		0			0
$436$	406.882	−	73.1639i	0.933215	−	0.167807i
$437$	265.272			0.607030
$438$		0			0
$439$			247.777i			0.564412i	0.959354	+	0.282206i	$0.0910662\pi$
$439$			247.777i			0.564412i	−0.959354	+	0.282206i	$0.908934\pi$
$440$		0			0
$441$		0			0
$442$	41.5916	+	466.311i	0.0940987	+	1.05500i
$443$			584.775i			1.32003i	0.751251	+	0.660017i	$0.229451\pi$
$443$			584.775i			1.32003i	−0.751251	+	0.660017i	$0.770549\pi$
$444$		0			0
$445$		0			0
$446$	−449.101	+	40.0566i	−1.00695	+	0.0898130i
$447$		0			0
$448$	−38.9105	−	65.8430i	−0.0868538	−	0.146971i
$449$	−152.093			−0.338738			−0.169369	−	0.985553i	$-0.554173\pi$
$449$	−152.093			−0.338738			−0.169369	+	0.985553i	$0.554173\pi$
$450$		0			0
$451$			605.342i			1.34222i
$452$	123.102	−	22.1357i	0.272349	−	0.0489728i
$453$		0			0
$454$	−215.306	+	19.2037i	−0.474242	+	0.0422990i
$455$		0			0
$456$		0			0
$457$	−602.441			−1.31825			−0.659126	−	0.752033i	$-0.729074\pi$
$457$	−602.441			−1.31825			−0.659126	+	0.752033i	$0.729074\pi$
$458$	10.1899	+	114.246i	0.0222487	+	0.249444i
$459$		0			0
$460$		0			0
$461$	504.912			1.09525			0.547626	−	0.836723i	$-0.315532\pi$
$461$	504.912			1.09525			0.547626	+	0.836723i	$0.315532\pi$
$462$		0			0
$463$		−	504.560i		−	1.08976i	−0.838513	−	0.544881i	$-0.816575\pi$
$463$		−	504.560i		−	1.08976i	0.838513	−	0.544881i	$-0.183425\pi$
$464$	−606.215	+	225.300i	−1.30650	+	0.485559i
$465$		0			0
$466$	−50.6957	−	568.383i	−0.108789	−	1.21971i
$467$			751.418i			1.60903i	0.593931	+	0.804516i	$0.297575\pi$
$467$			751.418i			1.60903i	−0.593931	+	0.804516i	$0.702425\pi$
$468$		0			0
$469$	−11.5759			−0.0246820
$470$		0			0
$471$		0			0
$472$	468.136	−	127.986i	0.991814	−	0.271156i
$473$	156.887			0.331685
$474$		0			0
$475$		0			0
$476$	−17.7023	−	98.4468i	−0.0371898	−	0.206821i
$477$		0			0
$478$	−153.883	+	13.7253i	−0.321932	+	0.0287140i
$479$			581.401i			1.21378i	0.794786	+	0.606890i	$0.207583\pi$
$479$			581.401i			1.21378i	−0.794786	+	0.606890i	$0.792417\pi$
$480$		0			0
$481$	561.431			1.16722
$482$	23.1975	+	260.082i	0.0481276	+	0.539590i
$483$		0			0
$484$	−210.306	+	37.8164i	−0.434517	+	0.0781331i
$485$		0			0
$486$		0			0
$487$			557.489i			1.14474i	0.819995	+	0.572371i	$0.193976\pi$
$487$			557.489i			1.14474i	−0.819995	+	0.572371i	$0.806024\pi$
$488$	−45.0465	−	164.768i	−0.0923084	−	0.337639i
$489$		0			0
$490$		0			0
$491$		−	26.2032i		−	0.0533670i	−0.999644	−	0.0266835i	$-0.991505\pi$
$491$		−	26.2032i		−	0.0533670i	0.999644	−	0.0266835i	$-0.00849463\pi$
$492$		0			0
$493$	−845.824			−1.71567
$494$	623.193	−	55.5844i	1.26152	−	0.112519i
$495$		0			0
$496$	−308.309	−	829.569i	−0.621590	−	1.67252i
$497$	82.0908			0.165173
$498$		0			0
$499$			444.615i			0.891011i	0.895279	+	0.445506i	$0.146976\pi$
$499$			444.615i			0.891011i	−0.895279	+	0.445506i	$0.853024\pi$
$500$		0			0
$501$		0			0
$502$	−870.937	+	77.6814i	−1.73493	+	0.154744i
$503$		−	216.819i		−	0.431052i	−0.976498	−	0.215526i	$-0.930853\pi$
$503$		−	216.819i		−	0.431052i	0.976498	−	0.215526i	$-0.0691466\pi$
$504$		0			0
$505$		0			0
$506$	13.8553	+	155.341i	0.0273820	+	0.306998i
$507$		0			0
$508$	−126.344	−	702.628i	−0.248708	−	1.38313i
$509$	−202.830			−0.398488			−0.199244	−	0.979950i	$-0.563849\pi$
$509$	−202.830			−0.398488			−0.199244	+	0.979950i	$0.563849\pi$
$510$		0			0
$511$		−	101.316i		−	0.198271i
$512$	−367.506	−	356.487i	−0.717786	−	0.696264i
$513$		0			0
$514$	−13.2138	−	148.148i	−0.0257077	−	0.288226i
$515$		0			0
$516$		0			0
$517$	148.464			0.287165
$518$	−119.479	+	10.6567i	−0.230654	+	0.0205727i
$519$		0			0
$520$		0			0
$521$	−769.410			−1.47679			−0.738397	−	0.674366i	$-0.764417\pi$
$521$	−769.410			−1.47679			−0.738397	+	0.674366i	$0.764417\pi$
$522$		0			0
$523$			38.9898i			0.0745502i	0.999305	+	0.0372751i	$0.0118678\pi$
$523$			38.9898i			0.0745502i	−0.999305	+	0.0372751i	$0.988132\pi$
$524$	108.837	+	605.266i	0.207703	+	1.15509i
$525$		0			0
$526$	913.953	−	81.5180i	1.73755	−	0.154977i
$527$		−	1157.46i		−	2.19632i
$528$		0			0
$529$	439.023			0.829911
$530$		0			0
$531$		0			0
$532$	−131.567	+	23.6579i	−0.247307	+	0.0444698i
$533$	−823.718			−1.54544
$534$		0			0
$535$		0			0
$536$	−74.7510	+	20.4365i	−0.139461	+	0.0381277i
$537$		0			0
$538$	−56.9297	−	638.277i	−0.105817	−	1.18639i
$539$			391.076i			0.725558i
$540$		0			0
$541$	−32.0904			−0.0593168			−0.0296584	−	0.999560i	$-0.509442\pi$
$541$	−32.0904			−0.0593168			−0.0296584	+	0.999560i	$0.509442\pi$
$542$	−715.278	+	63.7977i	−1.31970	+	0.117708i
$543$		0			0
$544$	−288.115	−	604.467i	−0.529622	−	1.11115i
$545$		0			0
$546$		0			0
$547$		−	254.839i		−	0.465885i	−0.972491	−	0.232942i	$-0.925165\pi$
$547$		−	254.839i		−	0.465885i	0.972491	−	0.232942i	$-0.0748354\pi$
$548$	208.625	−	37.5142i	0.380703	−	0.0684566i
$549$		0			0
$550$		0			0
$551$			1130.39i			2.05152i
$552$		0			0
$553$	27.8323			0.0503296
$554$	24.5247	+	274.963i	0.0442685	+	0.496323i
$555$		0			0
$556$	−15.4622	−	85.9890i	−0.0278097	−	0.154656i
$557$	−577.439			−1.03670			−0.518348	−	0.855170i	$-0.673453\pi$
$557$	−577.439			−1.03670			−0.518348	+	0.855170i	$0.673453\pi$
$558$		0			0
$559$			213.484i			0.381903i
$560$		0			0
$561$		0			0
$562$	82.1778	+	921.350i	0.146224	+	1.63941i
$563$			367.058i			0.651967i	0.945375	+	0.325984i	$0.105695\pi$
$563$			367.058i			0.651967i	−0.945375	+	0.325984i	$0.894305\pi$
$564$		0			0
$565$		0			0
$566$	645.384	−	57.5636i	1.14025	−	0.101703i
$567$		0			0
$568$	530.101	−	144.926i	0.933277	−	0.255152i
$569$	522.006			0.917410			0.458705	−	0.888589i	$-0.348313\pi$
$569$	522.006			0.917410			0.458705	+	0.888589i	$0.348313\pi$
$570$		0			0
$571$			832.421i			1.45783i	0.684604	+	0.728915i	$0.259975\pi$
$571$			832.421i			1.45783i	−0.684604	+	0.728915i	$0.740025\pi$
$572$	65.0994	+	362.033i	0.113810	+	0.632925i
$573$		0			0
$574$	175.296	−	15.6352i	0.305394	−	0.0272390i
$575$		0			0
$576$		0			0
$577$	427.659			0.741177			0.370588	−	0.928797i	$-0.379156\pi$
$577$	427.659			0.741177			0.370588	+	0.928797i	$0.379156\pi$
$578$	−26.4533	−	296.586i	−0.0457670	−	0.513124i
$579$		0			0
$580$		0			0
$581$	111.446			0.191818
$582$		0			0
$583$		−	470.400i		−	0.806861i
$584$	−178.868	−	654.250i	−0.306281	−	1.12029i
$585$		0			0
$586$	−26.7260	−	299.642i	−0.0456074	−	0.511335i
$587$		−	586.262i		−	0.998743i	−0.866388	−	0.499372i	$-0.833564\pi$
$587$		−	586.262i		−	0.998743i	0.866388	−	0.499372i	$-0.166436\pi$
$588$		0			0
$589$	−1546.87			−2.62626
$590$		0			0
$591$		0			0
$592$	−752.721	+	279.748i	−1.27149	+	0.472548i
$593$	−518.375			−0.874156			−0.437078	−	0.899424i	$-0.643987\pi$
$593$	−518.375			−0.874156			−0.437078	+	0.899424i	$0.643987\pi$
$594$		0			0
$595$		0			0
$596$	−12.3200	+	2.21534i	−0.0206712	+	0.00371701i
$597$		0			0
$598$	−211.380	+	18.8536i	−0.353478	+	0.0315277i
$599$		−	405.480i		−	0.676928i	−0.940979	−	0.338464i	$-0.890093\pi$
$599$		−	405.480i		−	0.676928i	0.940979	−	0.338464i	$-0.109907\pi$
$600$		0			0
$601$	−350.551			−0.583279			−0.291640	−	0.956528i	$-0.594201\pi$
$601$	−350.551			−0.583279			−0.291640	+	0.956528i	$0.594201\pi$
$602$	−4.05219	−	45.4317i	−0.00673121	−	0.0754680i
$603$		0			0
$604$	209.868	+	1167.13i	0.347464	+	1.93233i
$605$		0			0
$606$		0			0
$607$		−	737.786i		−	1.21546i	−0.794143	−	0.607731i	$-0.792080\pi$
$607$		−	737.786i		−	1.21546i	0.794143	−	0.607731i	$-0.207920\pi$
$608$	−807.829	+	385.046i	−1.32867	+	0.633299i
$609$		0			0
$610$		0			0
$611$			202.023i			0.330643i
$612$		0			0
$613$	345.495			0.563614			0.281807	−	0.959471i	$-0.409066\pi$
$613$	345.495			0.563614			0.281807	+	0.959471i	$0.409066\pi$
$614$	−1123.37	+	100.197i	−1.82959	+	0.163187i
$615$		0			0
$616$	−20.7257	−	75.8090i	−0.0336456	−	0.123066i
$617$	−862.171			−1.39736			−0.698680	−	0.715434i	$-0.746229\pi$
$617$	−862.171			−1.39736			−0.698680	+	0.715434i	$0.746229\pi$
$618$		0			0
$619$			469.363i			0.758260i	0.925343	+	0.379130i	$0.123777\pi$
$619$			469.363i			0.758260i	−0.925343	+	0.379130i	$0.876223\pi$
$620$		0			0
$621$		0			0
$622$	−79.7264	+	7.11102i	−0.128177	+	0.0114325i
$623$		−	75.2737i		−	0.120824i
$624$		0			0
$625$		0			0
$626$	0.324545	+	3.63869i	0.000518443	+	0.00581260i
$627$		0			0
$628$	−1045.97	+	188.082i	−1.66555	+	0.299494i
$629$	−1050.24			−1.66969
$630$		0			0
$631$			323.243i			0.512271i	0.966641	+	0.256136i	$0.0824494\pi$
$631$			323.243i			0.512271i	−0.966641	+	0.256136i	$0.917551\pi$
$632$	179.727	−	49.1362i	0.284378	−	0.0777472i
$633$		0			0
$634$	−43.7833	−	490.883i	−0.0690588	−	0.774264i
$635$		0			0
$636$		0			0
$637$	−532.156			−0.835410
$638$	−661.943	+	59.0406i	−1.03753	+	0.0925402i
$639$		0			0
$640$		0			0
$641$	44.1100			0.0688144			0.0344072	−	0.999408i	$-0.489046\pi$
$641$	44.1100			0.0688144			0.0344072	+	0.999408i	$0.489046\pi$
$642$		0			0
$643$			934.204i			1.45288i	0.687228	+	0.726442i	$0.258827\pi$
$643$			934.204i			1.45288i	−0.687228	+	0.726442i	$0.741173\pi$
$644$	44.6262	−	8.02451i	0.0692953	−	0.0124604i
$645$		0			0
$646$	−1165.77	+	103.978i	−1.80460	+	0.160957i
$647$			481.023i			0.743467i	0.928339	+	0.371734i	$0.121237\pi$
$647$			481.023i			0.743467i	−0.928339	+	0.371734i	$0.878763\pi$
$648$		0			0
$649$	498.706			0.768422
$650$		0			0
$651$		0			0
$652$	145.498	+	809.148i	0.223156	+	1.24103i
$653$	−1131.38			−1.73259			−0.866293	−	0.499536i	$-0.833504\pi$
$653$	−1131.38			−1.73259			−0.866293	+	0.499536i	$0.833504\pi$
$654$		0			0
$655$		0			0
$656$	1104.37	−	410.440i	1.68350	−	0.625670i
$657$		0			0
$658$	−3.83464	−	42.9927i	−0.00582772	−	0.0653385i
$659$			154.348i			0.234215i	0.993119	+	0.117107i	$0.0373622\pi$
$659$			154.348i			0.234215i	−0.993119	+	0.117107i	$0.962638\pi$
$660$		0			0
$661$	795.115			1.20290			0.601448	−	0.798912i	$-0.294591\pi$
$661$	795.115			1.20290			0.601448	+	0.798912i	$0.294591\pi$
$662$	832.042	−	74.2122i	1.25686	−	0.112103i
$663$		0			0
$664$	719.665	−	196.752i	1.08383	−	0.296313i
$665$		0			0
$666$		0			0
$667$		−	383.414i		−	0.574834i
$668$	8.23721	+	45.8090i	0.0123311	+	0.0685764i
$669$		0			0
$670$		0			0
$671$		−	175.527i		−	0.261591i
$672$		0			0
$673$	197.215			0.293039			0.146520	−	0.989208i	$-0.453193\pi$
$673$	197.215			0.293039			0.146520	+	0.989208i	$0.453193\pi$
$674$	−56.3921	−	632.249i	−0.0836678	−	0.938055i
$675$		0			0
$676$	172.693	−	31.0530i	0.255463	−	0.0459364i
$677$	−530.367			−0.783408			−0.391704	−	0.920091i	$-0.628114\pi$
$677$	−530.367			−0.783408			−0.391704	+	0.920091i	$0.628114\pi$
$678$		0			0
$679$		−	109.220i		−	0.160854i
$680$		0			0
$681$		0			0
$682$	−80.7935	−	905.830i	−0.118466	−	1.32820i
$683$		−	797.231i		−	1.16725i	−0.812024	−	0.583625i	$-0.801634\pi$
$683$		−	797.231i		−	1.16725i	0.812024	−	0.583625i	$-0.198366\pi$
$684$		0			0
$685$		0			0
$686$	229.897	−	20.5052i	0.335127	−	0.0298909i
$687$		0			0
$688$	−106.374	−	286.221i	−0.154613	−	0.416020i
$689$	640.096			0.929022
$690$		0			0
$691$			498.569i			0.721518i	0.932659	+	0.360759i	$0.117482\pi$
$691$			498.569i			0.721518i	−0.932659	+	0.360759i	$0.882518\pi$
$692$	417.552	−	75.0827i	0.603399	−	0.108501i
$693$		0			0
$694$	443.401	−	39.5482i	0.638906	−	0.0569859i
$695$		0			0
$696$		0			0
$697$	1540.88			2.21073
$698$	−99.6452	−	1117.19i	−0.142758	−	1.60056i
$699$		0			0
$700$		0			0
$701$	455.939			0.650412			0.325206	−	0.945643i	$-0.394566\pi$
$701$	455.939			0.650412			0.325206	+	0.945643i	$0.394566\pi$
$702$		0			0
$703$			1403.57i			1.99654i
$704$	−267.672	−	452.946i	−0.380216	−	0.643389i
$705$		0			0
$706$	−54.1670	−	607.302i	−0.0767238	−	0.860201i
$707$			35.8241i			0.0506706i
$708$		0			0
$709$	−44.4190			−0.0626502			−0.0313251	−	0.999509i	$-0.509973\pi$
$709$	−44.4190			−0.0626502			−0.0313251	+	0.999509i	$0.509973\pi$
$710$		0			0
$711$		0			0
$712$	−132.891	−	486.080i	−0.186645	−	0.682696i
$713$	524.679			0.735875
$714$		0			0
$715$		0			0
$716$	−30.6741	−	170.586i	−0.0428409	−	0.238248i
$717$		0			0
$718$	210.882	−	18.8092i	0.293708	−	0.0261966i
$719$			1349.94i			1.87752i	0.344566	+	0.938762i	$0.388026\pi$
$719$			1349.94i			1.87752i	−0.344566	+	0.938762i	$0.611974\pi$
$720$		0			0
$721$	106.056			0.147095
$722$	74.8174	+	838.827i	0.103625	+	1.16181i
$723$		0			0
$724$	−801.599	+	144.140i	−1.10718	+	0.199089i
$725$		0			0
$726$		0			0
$727$		−	191.470i		−	0.263370i	−0.991292	−	0.131685i	$-0.957961\pi$
$727$		−	191.470i		−	0.263370i	0.991292	−	0.131685i	$-0.0420387\pi$
$728$	103.157	−	28.2025i	0.141699	−	0.0387397i
$729$		0			0
$730$		0			0
$731$		−	399.351i		−	0.546308i
$732$		0			0
$733$	−358.832			−0.489539			−0.244769	−	0.969581i	$-0.578712\pi$
$733$	−358.832			−0.489539			−0.244769	+	0.969581i	$0.578712\pi$
$734$	−717.551	+	64.0004i	−0.977589	+	0.0871940i
$735$		0			0
$736$	274.007	−	130.603i	0.372291	−	0.177450i
$737$	−79.6324			−0.108049
$738$		0			0
$739$		−	756.311i		−	1.02342i	−0.859157	−	0.511712i	$-0.829011\pi$
$739$		−	756.311i		−	1.02342i	0.859157	−	0.511712i	$-0.170989\pi$
$740$		0			0
$741$		0			0
$742$	−136.220	+	12.1498i	−0.183584	+	0.0163744i
$743$			1148.65i			1.54596i	0.634432	+	0.772979i	$0.281234\pi$
$743$			1148.65i			1.54596i	−0.634432	+	0.772979i	$0.718766\pi$
$744$		0			0
$745$		0			0
$746$	−24.0738	−	269.907i	−0.0322705	−	0.361805i
$747$		0			0
$748$	−121.777	−	677.233i	−0.162804	−	0.905392i
$749$	−194.694			−0.259938
$750$		0			0
$751$			431.186i			0.574149i	0.957908	+	0.287074i	$0.0926827\pi$
$751$			431.186i			0.574149i	−0.957908	+	0.287074i	$0.907317\pi$
$752$	−100.663	−	270.856i	−0.133861	−	0.360180i
$753$		0			0
$754$	−80.3395	−	900.739i	−0.106551	−	1.19461i
$755$		0			0
$756$		0			0
$757$	645.657			0.852916			0.426458	−	0.904507i	$-0.359761\pi$
$757$	645.657			0.852916			0.426458	+	0.904507i	$0.359761\pi$
$758$	618.916	−	55.2029i	0.816511	−	0.0728270i
$759$		0			0
$760$		0			0
$761$	291.287			0.382768			0.191384	−	0.981515i	$-0.438702\pi$
$761$	291.287			0.382768			0.191384	+	0.981515i	$0.438702\pi$
$762$		0			0
$763$		−	123.507i		−	0.161870i
$764$	−178.065	−	990.261i	−0.233069	−	1.29615i
$765$		0			0
$766$	242.997	−	21.6736i	0.317228	−	0.0282945i
$767$			678.614i			0.884764i
$768$		0			0
$769$	−724.076			−0.941582			−0.470791	−	0.882245i	$-0.656031\pi$
$769$	−724.076			−0.941582			−0.470791	+	0.882245i	$0.656031\pi$
$770$		0			0
$771$		0			0
$772$	−1109.45	+	199.497i	−1.43711	+	0.258416i
$773$	−399.686			−0.517058			−0.258529	−	0.966003i	$-0.583238\pi$
$773$	−399.686			−0.517058			−0.258529	+	0.966003i	$0.583238\pi$
$774$		0			0
$775$		0			0
$776$	−192.821	−	705.287i	−0.248481	−	0.908875i
$777$		0			0
$778$	96.7053	+	1084.23i	0.124300	+	1.39361i
$779$		−	2059.28i		−	2.64349i
$780$		0			0
$781$	564.717			0.723070
$782$	395.416	−	35.2683i	0.505647	−	0.0451001i
$783$		0			0
$784$	713.471	−	265.161i	0.910039	−	0.338215i
$785$		0			0
$786$		0			0
$787$		−	381.830i		−	0.485172i	−0.970130	−	0.242586i	$-0.922004\pi$
$787$		−	381.830i		−	0.485172i	0.970130	−	0.242586i	$-0.0779957\pi$
$788$	958.565	−	172.366i	1.21645	−	0.218738i
$789$		0			0
$790$		0			0
$791$		−	37.3670i		−	0.0472402i
$792$		0			0
$793$	238.849			0.301196
$794$	89.6446	+	1005.07i	0.112903	+	1.26583i
$795$		0			0
$796$	86.3353	+	480.131i	0.108461	+	0.603180i
$797$	−18.3955			−0.0230810			−0.0115405	−	0.999933i	$-0.503674\pi$
$797$	−18.3955			−0.0230810			−0.0115405	+	0.999933i	$0.503674\pi$
$798$		0			0
$799$		−	377.912i		−	0.472981i
$800$		0			0
$801$		0			0
$802$	−49.3983	−	553.837i	−0.0615939	−	0.690570i
$803$		−	696.974i		−	0.867962i
$804$		0			0
$805$		0			0
$806$	1232.61	−	109.940i	1.52929	−	0.136402i
$807$		0			0
$808$	63.2453	+	231.334i	0.0782739	+	0.286304i
$809$	992.161			1.22640			0.613202	−	0.789926i	$-0.289881\pi$
$809$	992.161			1.22640			0.613202	+	0.789926i	$0.289881\pi$
$810$		0			0
$811$			482.957i			0.595509i	0.954643	+	0.297754i	$0.0962376\pi$
$811$			482.957i			0.595509i	−0.954643	+	0.297754i	$0.903762\pi$
$812$	34.1943	+	190.162i	0.0421112	+	0.234190i
$813$		0			0
$814$	−821.917	+	73.3091i	−1.00973	+	0.0900603i
$815$		0			0
$816$		0			0
$817$	−533.706			−0.653251
$818$	52.6910	+	590.753i	0.0644144	+	0.722192i
$819$		0			0
$820$		0			0
$821$	−614.955			−0.749031			−0.374516	−	0.927221i	$-0.622191\pi$
$821$	−614.955			−0.749031			−0.374516	+	0.927221i	$0.622191\pi$
$822$		0			0
$823$			11.2878i			0.0137154i	0.999976	+	0.00685772i	$0.00218290\pi$
$823$			11.2878i			0.0137154i	−0.999976	+	0.00685772i	$0.997817\pi$
$824$	684.855	−	187.235i	0.831135	−	0.227227i
$825$		0			0
$826$	−12.8809	−	144.417i	−0.0155943	−	0.174839i
$827$		−	449.125i		−	0.543078i	−0.962427	−	0.271539i	$-0.912467\pi$
$827$		−	449.125i		−	0.543078i	0.962427	−	0.271539i	$-0.0875325\pi$
$828$		0			0
$829$	135.766			0.163771			0.0818855	−	0.996642i	$-0.473906\pi$
$829$	135.766			0.163771			0.0818855	+	0.996642i	$0.473906\pi$
$830$		0			0
$831$		0			0
$832$	616.346	−	364.235i	0.740801	−	0.437782i
$833$	995.472			1.19504
$834$		0			0
$835$		0			0
$836$	−905.076	+	162.747i	−1.08263	+	0.194674i
$837$		0			0
$838$	−628.734	+	56.0786i	−0.750280	+	0.0669196i
$839$		−	1509.47i		−	1.79913i	−0.436789	−	0.899564i	$-0.643884\pi$
$839$		−	1509.47i		−	1.79913i	0.436789	−	0.899564i	$-0.356116\pi$
$840$		0			0
$841$	792.817			0.942707
$842$	64.0280	+	717.861i	0.0760428	+	0.852566i
$843$		0			0
$844$	93.8290	+	521.805i	0.111172	+	0.618252i
$845$		0			0
$846$		0			0
$847$			63.8374i			0.0753688i
$848$	−858.188	+	318.945i	−1.01201	+	0.376114i
$849$		0			0
$850$		0			0
$851$		−	476.075i		−	0.559430i
$852$		0			0
$853$	−909.826			−1.06662			−0.533310	−	0.845920i	$-0.679052\pi$
$853$	−909.826			−1.06662			−0.533310	+	0.845920i	$0.679052\pi$
$854$	−50.8297	+	4.53364i	−0.0595195	+	0.00530872i
$855$		0			0
$856$	−1257.23	+	343.720i	−1.46873	+	0.401542i
$857$	505.304			0.589620			0.294810	−	0.955556i	$-0.404744\pi$
$857$	505.304			0.589620			0.294810	+	0.955556i	$0.404744\pi$
$858$		0			0
$859$		−	45.9728i		−	0.0535189i	−0.999642	−	0.0267595i	$-0.991481\pi$
$859$		−	45.9728i		−	0.0535189i	0.999642	−	0.0267595i	$-0.00851882\pi$
$860$		0			0
$861$		0			0
$862$	1043.09	−	93.0365i	1.21009	−	0.107931i
$863$			142.006i			0.164549i	0.996610	+	0.0822746i	$0.0262185\pi$
$863$			142.006i			0.164549i	−0.996610	+	0.0822746i	$0.973782\pi$
$864$		0			0
$865$		0			0
$866$	−3.82689	−	42.9058i	−0.00441904	−	0.0495448i
$867$		0			0
$868$	−260.226	+	46.7928i	−0.299799	+	0.0539088i
$869$	191.463			0.220326
$870$		0			0
$871$		−	108.360i		−	0.124408i
$872$	−218.044	−	797.546i	−0.250051	−	0.914617i
$873$		0			0
$874$	−47.1336	−	528.446i	−0.0539287	−	0.604630i
$875$		0			0
$876$		0			0
$877$	549.975			0.627109			0.313555	−	0.949570i	$-0.398480\pi$
$877$	549.975			0.627109			0.313555	+	0.949570i	$0.398480\pi$
$878$	493.594	−	44.0251i	0.562180	−	0.0501425i
$879$		0			0
$880$		0			0
$881$	−636.072			−0.721989			−0.360995	−	0.932568i	$-0.617563\pi$
$881$	−636.072			−0.721989			−0.360995	+	0.932568i	$0.617563\pi$
$882$		0			0
$883$		−	689.661i		−	0.781043i	−0.920594	−	0.390521i	$-0.872295\pi$
$883$		−	689.661i		−	0.781043i	0.920594	−	0.390521i	$-0.127705\pi$
$884$	921.545	−	165.709i	1.04247	−	0.187453i
$885$		0			0
$886$	1164.93	−	103.903i	1.31481	−	0.117272i
$887$		−	1053.94i		−	1.18821i	−0.804389	−	0.594103i	$-0.797507\pi$
$887$		−	1053.94i		−	1.18821i	0.804389	−	0.594103i	$-0.202493\pi$
$888$		0			0
$889$	−213.279			−0.239909
$890$		0			0
$891$		0			0
$892$	159.593	+	887.533i	0.178916	+	0.994992i
$893$	−505.054			−0.565570
$894$		0			0
$895$		0			0
$896$	−124.252	+	89.2123i	−0.138674	+	0.0995673i
$897$		0			0
$898$	27.0240	+	302.984i	0.0300936	+	0.337399i
$899$			2235.78i			2.48696i
$900$		0			0
$901$	−1197.39			−1.32896
$902$	1205.90	−	107.557i	1.33691	−	0.119243i
$903$		0			0
$904$	−65.9691	−	241.297i	−0.0729747	−	0.266922i
$905$		0			0
$906$		0			0
$907$		−	496.037i		−	0.546899i	−0.961886	−	0.273449i	$-0.911835\pi$
$907$		−	496.037i		−	0.546899i	0.961886	−	0.273449i	$-0.0881646\pi$
$908$	76.5112	+	425.497i	0.0842635	+	0.468609i
$909$		0			0
$910$		0			0
$911$		−	336.684i		−	0.369577i	−0.982778	−	0.184788i	$-0.940840\pi$
$911$		−	336.684i		−	0.369577i	0.982778	−	0.184788i	$-0.0591599\pi$
$912$		0			0
$913$	766.660			0.839715
$914$	107.042	+	1200.12i	0.117114	+	1.31304i
$915$		0			0
$916$	225.777	−	40.5984i	0.246481	−	0.0443214i
$917$	183.725			0.200355
$918$		0			0
$919$			937.464i			1.02009i	0.860147	+	0.510046i	$0.170371\pi$
$919$			937.464i			1.02009i	−0.860147	+	0.510046i	$0.829629\pi$
$920$		0			0
$921$		0			0
$922$	−89.7129	−	1005.83i	−0.0973025	−	1.09092i
$923$			768.439i			0.832545i
$924$		0			0
$925$		0			0
$926$	−1005.13	+	89.6504i	−1.08545	+	0.0968147i
$927$		0			0
$928$	556.530	+	1167.61i	0.599709	+	1.25820i
$929$	−858.647			−0.924270			−0.462135	−	0.886810i	$-0.652916\pi$
$929$	−858.647			−0.924270			−0.462135	+	0.886810i	$0.652916\pi$
$930$		0			0
$931$		−	1330.38i		−	1.42898i
$932$	−1123.26	+	201.981i	−1.20522	+	0.216718i
$933$		0			0
$934$	1496.89	−	133.512i	1.60267	−	0.142947i
$935$		0			0
$936$		0			0
$937$	−1276.09			−1.36189			−0.680943	−	0.732336i	$-0.738430\pi$
$937$	−1276.09			−1.36189			−0.680943	+	0.732336i	$0.738430\pi$
$938$	2.05680	+	23.0602i	0.00219275	+	0.0245844i
$939$		0			0
$940$		0			0
$941$	−536.218			−0.569838			−0.284919	−	0.958552i	$-0.591967\pi$
$941$	−536.218			−0.569838			−0.284919	+	0.958552i	$0.591967\pi$
$942$		0			0
$943$			698.485i			0.740705i
$944$	−338.138	−	909.830i	−0.358197	−	0.963803i
$945$		0			0
$946$	−27.8757	−	312.533i	−0.0294669	−	0.330373i
$947$		−	48.1723i		−	0.0508683i	−0.999677	−	0.0254341i	$-0.991903\pi$
$947$		−	48.1723i		−	0.0508683i	0.999677	−	0.0254341i	$-0.00809681\pi$
$948$		0			0
$949$	948.407			0.999375
$950$		0			0
$951$		0			0
$952$	−192.970	+	52.7567i	−0.202699	+	0.0554167i
$953$	1449.85			1.52136			0.760679	−	0.649129i	$-0.224866\pi$
$953$	1449.85			1.52136			0.760679	+	0.649129i	$0.224866\pi$
$954$		0			0
$955$		0			0
$956$	54.6841	+	304.111i	0.0572009	+	0.318108i
$957$		0			0
$958$	1158.20	−	103.303i	1.20898	−	0.107832i
$959$		−	63.3272i		−	0.0660346i
$960$		0			0
$961$	−2098.53			−2.18369
$962$	−99.7553	−	1118.42i	−0.103696	−	1.16260i
$963$		0			0
$964$	513.986	−	92.4231i	0.533181	−	0.0958746i
$965$		0			0
$966$		0			0
$967$			1320.06i			1.36510i	0.730837	+	0.682552i	$0.239130\pi$
$967$			1320.06i			1.36510i	−0.730837	+	0.682552i	$0.760870\pi$
$968$	112.701	+	412.230i	0.116427	+	0.425857i
$969$		0			0
$970$		0			0
$971$			1269.58i			1.30749i	0.756713	+	0.653747i	$0.226804\pi$
$971$			1269.58i			1.30749i	−0.756713	+	0.653747i	$0.773196\pi$
$972$		0			0
$973$	−26.1015			−0.0268258
$974$	1110.57	−	99.0548i	1.14021	−	0.101699i
$975$		0			0
$976$	−320.229	+	119.013i	−0.328103	+	0.121939i
$977$	1262.18			1.29190			0.645948	−	0.763382i	$-0.276462\pi$
$977$	1262.18			1.29190			0.645948	+	0.763382i	$0.276462\pi$
$978$		0			0
$979$		−	517.821i		−	0.528929i
$980$		0			0
$981$		0			0
$982$	−52.1992	+	4.65580i	−0.0531560	+	0.00474114i
$983$		−	235.722i		−	0.239798i	−0.992786	−	0.119899i	$-0.961743\pi$
$983$		−	235.722i		−	0.239798i	0.992786	−	0.119899i	$-0.0382571\pi$
$984$		0			0
$985$		0			0
$986$	150.286	+	1684.96i	0.152420	+	1.70888i
$987$		0			0
$988$	−221.458	−	1231.58i	−0.224148	−	1.24654i
$989$	181.027			0.183040
$990$		0			0
$991$		−	1601.53i		−	1.61607i	−0.589135	−	0.808035i	$-0.700531\pi$
$991$		−	1601.53i		−	1.61607i	0.589135	−	0.808035i	$-0.299469\pi$
$992$	−1597.80	+	761.578i	−1.61068	+	0.767719i
$993$		0			0
$994$	−14.5859	−	163.532i	−0.0146740	−	0.164520i
$995$		0			0
$996$		0			0
$997$	−984.298			−0.987260			−0.493630	−	0.869672i	$-0.664330\pi$
$997$	−984.298			−0.987260			−0.493630	+	0.869672i	$0.664330\pi$
$998$	885.713	−	78.9993i	0.887488	−	0.0791576i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.c.t.451.3		8
3.2	odd	2		300.3.c.e.151.6	yes	8
4.3	odd	2	inner	900.3.c.t.451.4		8
5.2	odd	4		900.3.f.h.199.15		16
5.3	odd	4		900.3.f.h.199.2		16
5.4	even	2		900.3.c.n.451.6		8
12.11	even	2		300.3.c.e.151.5	✓	8
15.2	even	4		300.3.f.c.199.2		16
15.8	even	4		300.3.f.c.199.15		16
15.14	odd	2		300.3.c.g.151.3	yes	8
20.3	even	4		900.3.f.h.199.16		16
20.7	even	4		900.3.f.h.199.1		16
20.19	odd	2		900.3.c.n.451.5		8
60.23	odd	4		300.3.f.c.199.1		16
60.47	odd	4		300.3.f.c.199.16		16
60.59	even	2		300.3.c.g.151.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.3.c.e.151.5	✓	8	12.11	even	2
300.3.c.e.151.6	yes	8	3.2	odd	2
300.3.c.g.151.3	yes	8	15.14	odd	2
300.3.c.g.151.4	yes	8	60.59	even	2
300.3.f.c.199.1		16	60.23	odd	4
300.3.f.c.199.2		16	15.2	even	4
300.3.f.c.199.15		16	15.8	even	4
300.3.f.c.199.16		16	60.47	odd	4
900.3.c.n.451.5		8	20.19	odd	2
900.3.c.n.451.6		8	5.4	even	2
900.3.c.t.451.3		8	1.1	even	1	trivial
900.3.c.t.451.4		8	4.3	odd	2	inner
900.3.f.h.199.1		16	20.7	even	4
900.3.f.h.199.2		16	5.3	odd	4
900.3.f.h.199.15		16	5.2	odd	4
900.3.f.h.199.16		16	20.3	even	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.177680 - 1.99209i) q^{2} +(-3.93686 + 0.707911i) q^{4} +1.19501i q^{7} +(2.10973 + 7.71680i) q^{8} +O(q^{10})\)	\(q+(-0.177680 - 1.99209i) q^{2} +(-3.93686 + 0.707911i) q^{4} +1.19501i q^{7} +(2.10973 + 7.71680i) q^{8} +8.22072i q^{11} -11.1863 q^{13} +(2.38058 - 0.212331i) q^{14} +(14.9977 - 5.57389i) q^{16} +20.9256 q^{17} -27.9657i q^{19} +(16.3764 - 1.46066i) q^{22} +9.48564i q^{23} +(1.98759 + 22.2842i) q^{26} +(-0.845964 - 4.70460i) q^{28} -40.4205 q^{29} -55.3130i q^{31} +(-13.7685 - 28.8865i) q^{32} +(-3.71807 - 41.6858i) q^{34} -50.1890 q^{37} +(-55.7102 + 4.96895i) q^{38} +73.6361 q^{41} -19.0843i q^{43} +(-5.81954 - 32.3638i) q^{44} +(18.8963 - 1.68541i) q^{46} -18.0598i q^{47} +47.5719 q^{49} +(44.0391 - 7.91894i) q^{52} -57.2212 q^{53} +(-9.22169 + 2.52115i) q^{56} +(7.18193 + 80.5213i) q^{58} -60.6645i q^{59} -21.3518 q^{61} +(-110.189 + 9.82804i) q^{62} +(-55.0981 + 32.5607i) q^{64} +9.68679i q^{67} +(-82.3812 + 14.8135i) q^{68} -68.6944i q^{71} -84.7825 q^{73} +(8.91760 + 99.9811i) q^{74} +(19.7972 + 110.097i) q^{76} -9.82388 q^{77} -23.2903i q^{79} +(-13.0837 - 146.690i) q^{82} -93.2595i q^{83} +(-38.0177 + 3.39091i) q^{86} +(-63.4377 + 17.3435i) q^{88} -62.9898 q^{89} -13.3678i q^{91} +(-6.71499 - 37.3436i) q^{92} +(-35.9767 + 3.20887i) q^{94} -91.3962 q^{97} +(-8.45260 - 94.7677i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 8 q^{4} + 20 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 8 * q^4 + 20 * q^8	\( 8 q + 2 q^{2} - 8 q^{4} + 20 q^{8} - 8 q^{13} - 22 q^{14} + 40 q^{16} - 4 q^{22} + 66 q^{26} - 104 q^{28} + 32 q^{29} + 112 q^{32} + 124 q^{34} + 176 q^{37} - 170 q^{38} + 16 q^{41} - 40 q^{44} - 76 q^{46} + 16 q^{49} - 56 q^{52} - 304 q^{53} + 172 q^{56} + 12 q^{58} + 136 q^{61} - 238 q^{62} + 16 q^{64} + 88 q^{68} - 240 q^{73} + 108 q^{74} + 120 q^{76} - 384 q^{77} - 320 q^{82} - 214 q^{86} + 200 q^{88} - 128 q^{89} + 312 q^{92} + 12 q^{94} - 216 q^{97} + 60 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 8 * q^4 + 20 * q^8 - 8 * q^13 - 22 * q^14 + 40 * q^16 - 4 * q^22 + 66 * q^26 - 104 * q^28 + 32 * q^29 + 112 * q^32 + 124 * q^34 + 176 * q^37 - 170 * q^38 + 16 * q^41 - 40 * q^44 - 76 * q^46 + 16 * q^49 - 56 * q^52 - 304 * q^53 + 172 * q^56 + 12 * q^58 + 136 * q^61 - 238 * q^62 + 16 * q^64 + 88 * q^68 - 240 * q^73 + 108 * q^74 + 120 * q^76 - 384 * q^77 - 320 * q^82 - 214 * q^86 + 200 * q^88 - 128 * q^89 + 312 * q^92 + 12 * q^94 - 216 * q^97 + 60 * q^98

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