LMFDB - Embedded newform 900.3.u.d.149.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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, 5, 3]))

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

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

chi := DirichletCharacter("900.149");

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.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.6
Character	$\chi$	$=$	900.149
Dual form			900.3.u.d.749.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28947 - 2.70874i) q^{3} +(-9.36178 + 5.40503i) q^{7} +(-5.67451 + 6.98569i) q^{9} +O(q^{10})$	\(q+(-1.28947 - 2.70874i) q^{3} +(-9.36178 + 5.40503i) q^{7} +(-5.67451 + 6.98569i) q^{9} +(7.78876 - 4.49684i) q^{11} +(-3.96157 - 2.28721i) q^{13} -7.55187 q^{17} -8.73166 q^{19} +(26.7126 + 18.3890i) q^{21} +(-4.02351 + 6.96892i) q^{23} +(26.2395 + 6.36289i) q^{27} +(38.2046 - 22.0575i) q^{29} +(4.53586 - 7.85634i) q^{31} +(-22.2242 - 15.2991i) q^{33} +56.1237i q^{37} +(-1.08712 + 13.6801i) q^{39} +(53.9651 + 31.1568i) q^{41} +(34.7294 - 20.0510i) q^{43} +(-9.10452 - 15.7695i) q^{47} +(33.9287 - 58.7662i) q^{49} +(9.73794 + 20.4560i) q^{51} +23.7994 q^{53} +(11.2592 + 23.6518i) q^{57} +(59.3003 + 34.2370i) q^{59} +(16.3946 + 28.3963i) q^{61} +(15.3657 - 96.0695i) q^{63} +(7.20078 + 4.15737i) q^{67} +(24.0652 + 1.91238i) q^{69} -115.480i q^{71} -125.300i q^{73} +(-48.6111 + 84.1969i) q^{77} +(-15.5289 - 26.8968i) q^{79} +(-16.5998 - 79.2808i) q^{81} +(-77.0272 - 133.415i) q^{83} +(-109.012 - 75.0438i) q^{87} +131.044i q^{89} +49.4498 q^{91} +(-27.1296 - 2.15590i) q^{93} +(143.990 - 83.1329i) q^{97} +(-12.7839 + 79.9272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{9}+O(q^{10}) $ 32 * q - 28 * q^9	$ 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) $ 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * 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
$3$	−1.28947	−	2.70874i	−0.429825	−	0.902912i
$3$	−1.28947	−	2.70874i	−0.429825	−	0.902912i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−9.36178	+	5.40503i	−1.33740	+	0.772147i	−0.986421	−	0.164237i	$-0.947484\pi$
$7$	−9.36178	+	5.40503i	−1.33740	+	0.772147i	−0.350977	+	0.936384i	$0.614150\pi$
$8$		0			0
$9$	−5.67451	+	6.98569i	−0.630501	+	0.776188i
$10$		0			0
$11$	7.78876	−	4.49684i	0.708069	−	0.408804i	−0.102277	−	0.994756i	$-0.532613\pi$
$11$	7.78876	−	4.49684i	0.708069	−	0.408804i	0.810346	+	0.585952i	$0.199279\pi$
$12$		0			0
$13$	−3.96157	−	2.28721i	−0.304736	−	0.175939i	0.339833	−	0.940486i	$-0.389630\pi$
$13$	−3.96157	−	2.28721i	−0.304736	−	0.175939i	−0.644568	+	0.764547i	$0.722963\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−7.55187			−0.444227			−0.222114	−	0.975021i	$-0.571296\pi$
$17$	−7.55187			−0.444227			−0.222114	+	0.975021i	$0.571296\pi$
$18$		0			0
$19$	−8.73166			−0.459561			−0.229780	−	0.973242i	$-0.573801\pi$
$19$	−8.73166			−0.459561			−0.229780	+	0.973242i	$0.573801\pi$
$20$		0			0
$21$	26.7126	+	18.3890i	1.27203	+	0.875665i
$22$		0			0
$23$	−4.02351	+	6.96892i	−0.174935	+	0.302997i	−0.940139	−	0.340792i	$-0.889305\pi$
$23$	−4.02351	+	6.96892i	−0.174935	+	0.302997i	0.765204	+	0.643788i	$0.222638\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	26.2395	+	6.36289i	0.971835	+	0.235663i
$28$		0			0
$29$	38.2046	−	22.0575i	1.31740	−	0.760602i	0.334092	−	0.942541i	$-0.391571\pi$
$29$	38.2046	−	22.0575i	1.31740	−	0.760602i	0.983310	+	0.181939i	$0.0582372\pi$
$30$		0			0
$31$	4.53586	−	7.85634i	0.146318	−	0.253430i	−0.783546	−	0.621334i	$-0.786591\pi$
$31$	4.53586	−	7.85634i	0.146318	−	0.253430i	0.929864	+	0.367904i	$0.119924\pi$
$32$		0			0
$33$	−22.2242	−	15.2991i	−0.673459	−	0.463610i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			56.1237i			1.51686i	0.651756	+	0.758428i	$0.274032\pi$
$37$			56.1237i			1.51686i	−0.651756	+	0.758428i	$0.725968\pi$
$38$		0			0
$39$	−1.08712	+	13.6801i	−0.0278748	+	0.350773i
$40$		0			0
$41$	53.9651	+	31.1568i	1.31622	+	0.759921i	0.983119	−	0.182969i	$-0.0585709\pi$
$41$	53.9651	+	31.1568i	1.31622	+	0.759921i	0.333103	+	0.942890i	$0.391904\pi$
$42$		0			0
$43$	34.7294	−	20.0510i	0.807660	−	0.466303i	−0.0384827	−	0.999259i	$-0.512252\pi$
$43$	34.7294	−	20.0510i	0.807660	−	0.466303i	0.846143	+	0.532957i	$0.178919\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−9.10452	−	15.7695i	−0.193713	−	0.335521i	0.752765	−	0.658290i	$-0.228720\pi$
$47$	−9.10452	−	15.7695i	−0.193713	−	0.335521i	−0.946478	+	0.322769i	$0.895386\pi$
$48$		0			0
$49$	33.9287	−	58.7662i	0.692422	−	1.19931i
$50$		0			0
$51$	9.73794	+	20.4560i	0.190940	+	0.401098i
$52$		0			0
$53$	23.7994			0.449045			0.224522	−	0.974469i	$-0.427918\pi$
$53$	23.7994			0.449045			0.224522	+	0.974469i	$0.427918\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	11.2592	+	23.6518i	0.197531	+	0.414943i
$58$		0			0
$59$	59.3003	+	34.2370i	1.00509	+	0.580289i	0.909750	−	0.415156i	$-0.136273\pi$
$59$	59.3003	+	34.2370i	1.00509	+	0.580289i	0.0953396	+	0.995445i	$0.469606\pi$
$60$		0			0
$61$	16.3946	+	28.3963i	0.268765	+	0.465514i	0.968543	−	0.248846i	$-0.0800513\pi$
$61$	16.3946	+	28.3963i	0.268765	+	0.465514i	−0.699779	+	0.714360i	$0.746718\pi$
$62$		0			0
$63$	15.3657	−	96.0695i	0.243900	−	1.52491i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	7.20078	+	4.15737i	0.107474	+	0.0620503i	0.552774	−	0.833331i	$-0.313569\pi$
$67$	7.20078	+	4.15737i	0.107474	+	0.0620503i	−0.445299	+	0.895382i	$0.646903\pi$
$68$		0			0
$69$	24.0652	+	1.91238i	0.348771	+	0.0277157i
$70$		0			0
$71$		−	115.480i		−	1.62648i	−0.581930	−	0.813239i	$-0.697702\pi$
$71$		−	115.480i		−	1.62648i	0.581930	−	0.813239i	$-0.302298\pi$
$72$		0			0
$73$		−	125.300i		−	1.71643i	−0.513287	−	0.858217i	$-0.671572\pi$
$73$		−	125.300i		−	1.71643i	0.513287	−	0.858217i	$-0.328428\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−48.6111	+	84.1969i	−0.631313	+	1.09347i
$78$		0			0
$79$	−15.5289	−	26.8968i	−0.196568	−	0.340466i	0.750845	−	0.660478i	$-0.229646\pi$
$79$	−15.5289	−	26.8968i	−0.196568	−	0.340466i	−0.947413	+	0.320012i	$0.896313\pi$
$80$		0			0
$81$	−16.5998	−	79.2808i	−0.204936	−	0.978775i
$82$		0			0
$83$	−77.0272	−	133.415i	−0.928038	−	1.60741i	−0.786601	−	0.617462i	$-0.788161\pi$
$83$	−77.0272	−	133.415i	−0.928038	−	1.60741i	−0.141438	−	0.989947i	$-0.545173\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−109.012	−	75.0438i	−1.25301	−	0.862572i
$88$		0			0
$89$			131.044i			1.47241i	0.676760	+	0.736204i	$0.263384\pi$
$89$			131.044i			1.47241i	−0.676760	+	0.736204i	$0.736616\pi$
$90$		0			0
$91$	49.4498			0.543404
$92$		0			0
$93$	−27.1296	−	2.15590i	−0.291716	−	0.0231818i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	143.990	−	83.1329i	1.48444	−	0.857040i	0.484594	−	0.874739i	$-0.338967\pi$
$97$	143.990	−	83.1329i	1.48444	−	0.857040i	0.999843	+	0.0176993i	$0.00563416\pi$
$98$		0			0
$99$	−12.7839	+	79.9272i	−0.129130	+	0.807346i
$100$		0			0
$101$	−140.647	+	81.2027i	−1.39255	+	0.803987i	−0.993597	−	0.112985i	$-0.963959\pi$
$101$	−140.647	+	81.2027i	−1.39255	+	0.803987i	−0.398950	+	0.916973i	$0.630625\pi$
$102$		0			0
$103$	56.8073	+	32.7977i	0.551527	+	0.318424i	0.749738	−	0.661735i	$-0.230180\pi$
$103$	56.8073	+	32.7977i	0.551527	+	0.318424i	−0.198211	+	0.980159i	$0.563513\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.4315			0.106837			0.0534184	−	0.998572i	$-0.482988\pi$
$107$	11.4315			0.106837			0.0534184	+	0.998572i	$0.482988\pi$
$108$		0			0
$109$	157.169			1.44191			0.720957	−	0.692980i	$-0.243703\pi$
$109$	157.169			1.44191			0.720957	+	0.692980i	$0.243703\pi$
$110$		0			0
$111$	152.024	−	72.3701i	1.36959	−	0.651983i
$112$		0			0
$113$	−11.4504	+	19.8326i	−0.101331	+	0.175510i	−0.912233	−	0.409672i	$-0.865643\pi$
$113$	−11.4504	+	19.8326i	−0.101331	+	0.175510i	0.810903	+	0.585181i	$0.198977\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	38.4577	−	14.6955i	0.328698	−	0.125602i
$118$		0			0
$119$	70.6990	−	40.8181i	0.594109	−	0.343009i
$120$		0			0
$121$	−20.0568	+	34.7395i	−0.165759	+	0.287103i
$122$		0			0
$123$	14.8089	−	186.353i	0.120397	−	1.51507i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	99.3417i		−	0.782218i	−0.920344	−	0.391109i	$-0.872092\pi$
$127$		−	99.3417i		−	0.782218i	0.920344	−	0.391109i	$-0.127908\pi$
$128$		0			0
$129$	−99.0956	−	68.2175i	−0.768183	−	0.528818i
$130$		0			0
$131$	6.22017	+	3.59122i	0.0474822	+	0.0274139i	0.523553	−	0.851993i	$-0.324606\pi$
$131$	6.22017	+	3.59122i	0.0474822	+	0.0274139i	−0.476071	+	0.879407i	$0.657939\pi$
$132$		0			0
$133$	81.7439	−	47.1949i	0.614616	−	0.354849i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	125.761	+	217.824i	0.917962	+	1.58996i	0.802506	+	0.596644i	$0.203499\pi$
$137$	125.761	+	217.824i	0.917962	+	1.58996i	0.115455	+	0.993313i	$0.463167\pi$
$138$		0			0
$139$	82.6116	−	143.087i	0.594328	−	1.02941i	−0.399313	−	0.916815i	$-0.630751\pi$
$139$	82.6116	−	143.087i	0.594328	−	1.02941i	0.993641	−	0.112592i	$-0.0359152\pi$
$140$		0			0
$141$	−30.9753	+	44.9961i	−0.219683	+	0.319121i
$142$		0			0
$143$	−41.1409			−0.287699
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−202.932	−	16.1264i	−1.38049	−	0.109703i
$148$		0			0
$149$	197.430	+	113.986i	1.32503	+	0.765008i	0.984527	−	0.175234i	$-0.0560683\pi$
$149$	197.430	+	113.986i	1.32503	+	0.765008i	0.340506	+	0.940242i	$0.389402\pi$
$150$		0			0
$151$	86.0019	+	148.960i	0.569549	+	0.986488i	0.996610	+	0.0822653i	$0.0262155\pi$
$151$	86.0019	+	148.960i	0.569549	+	0.986488i	−0.427061	+	0.904223i	$0.640451\pi$
$152$		0			0
$153$	42.8532	−	52.7550i	0.280086	−	0.344804i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	211.376	+	122.038i	1.34634	+	0.777313i	0.987730	−	0.156173i	$-0.0499157\pi$
$157$	211.376	+	122.038i	1.34634	+	0.777313i	0.358615	+	0.933485i	$0.383249\pi$
$158$		0			0
$159$	−30.6887	−	64.4662i	−0.193010	−	0.405448i
$160$		0			0
$161$		−	86.9887i		−	0.540303i
$162$		0			0
$163$			192.188i			1.17907i	0.807744	+	0.589534i	$0.200689\pi$
$163$			192.188i			1.17907i	−0.807744	+	0.589534i	$0.799311\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−105.498	+	182.728i	−0.631726	+	1.09418i	0.355472	+	0.934687i	$0.384320\pi$
$167$	−105.498	+	182.728i	−0.631726	+	1.09418i	−0.987199	+	0.159495i	$0.949013\pi$
$168$		0			0
$169$	−74.0373	−	128.236i	−0.438091	−	0.758795i
$170$		0			0
$171$	49.5479	−	60.9967i	0.289754	−	0.356706i
$172$		0			0
$173$	74.8995	+	129.730i	0.432945	+	0.749882i	0.997125	−	0.0757690i	$-0.0241411\pi$
$173$	74.8995	+	129.730i	0.432945	+	0.749882i	−0.564181	+	0.825651i	$0.690808\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	16.2729	−	204.777i	0.0919376	−	1.15693i
$178$		0			0
$179$		−	58.2813i		−	0.325594i	−0.986660	−	0.162797i	$-0.947948\pi$
$179$		−	58.2813i		−	0.325594i	0.986660	−	0.162797i	$-0.0520516\pi$
$180$		0			0
$181$	−26.7702			−0.147902			−0.0739508	−	0.997262i	$-0.523561\pi$
$181$	−26.7702			−0.147902			−0.0739508	+	0.997262i	$0.523561\pi$
$182$		0			0
$183$	55.7778	−	81.0251i	0.304797	−	0.442760i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−58.8197	+	33.9595i	−0.314544	+	0.181602i
$188$		0			0
$189$	−280.041	+	82.2574i	−1.48170	+	0.435225i
$190$		0			0
$191$	−72.3294	+	41.7594i	−0.378688	+	0.218636i	−0.677247	−	0.735755i	$-0.736827\pi$
$191$	−72.3294	+	41.7594i	−0.378688	+	0.218636i	0.298559	+	0.954391i	$0.403494\pi$
$192$		0			0
$193$	72.0695	+	41.6094i	0.373417	+	0.215593i	0.674950	−	0.737863i	$-0.264165\pi$
$193$	72.0695	+	41.6094i	0.373417	+	0.215593i	−0.301533	+	0.953456i	$0.597498\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−171.229			−0.869183			−0.434592	−	0.900628i	$-0.643107\pi$
$197$	−171.229			−0.869183			−0.434592	+	0.900628i	$0.643107\pi$
$198$		0			0
$199$	−151.309			−0.760348			−0.380174	−	0.924915i	$-0.624136\pi$
$199$	−151.309			−0.760348			−0.380174	+	0.924915i	$0.624136\pi$
$200$		0			0
$201$	1.97601	−	24.8658i	0.00983089	−	0.123711i
$202$		0			0
$203$	−238.442	+	412.994i	−1.17459	+	2.03445i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−25.8513	−	67.6522i	−0.124886	−	0.326822i
$208$		0			0
$209$	−68.0088	+	39.2649i	−0.325401	+	0.187870i
$210$		0			0
$211$	−44.8904	+	77.7525i	−0.212751	+	0.368495i	−0.952574	−	0.304306i	$-0.901576\pi$
$211$	−44.8904	+	77.7525i	−0.212751	+	0.368495i	0.739824	+	0.672801i	$0.234909\pi$
$212$		0			0
$213$	−312.805	+	148.908i	−1.46857	+	0.699100i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			98.0658i			0.451916i
$218$		0			0
$219$	−339.404	+	161.571i	−1.54979	+	0.737766i
$220$		0			0
$221$	29.9172	+	17.2727i	0.135372	+	0.0781571i
$222$		0			0
$223$	80.4290	−	46.4357i	0.360668	−	0.208232i	−0.308706	−	0.951158i	$-0.599896\pi$
$223$	80.4290	−	46.4357i	0.360668	−	0.208232i	0.669374	+	0.742926i	$0.266562\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−111.320	−	192.811i	−0.490395	−	0.849389i	0.509544	−	0.860445i	$-0.329814\pi$
$227$	−111.320	−	192.811i	−0.490395	−	0.849389i	−0.999939	+	0.0110555i	$0.996481\pi$
$228$		0			0
$229$	92.0380	−	159.414i	0.401913	−	0.696133i	−0.592044	−	0.805906i	$-0.701679\pi$
$229$	92.0380	−	159.414i	0.401913	−	0.696133i	0.993957	+	0.109772i	$0.0350122\pi$
$230$		0			0
$231$	290.750	+	23.1050i	1.25866	+	0.100022i
$232$		0			0
$233$	−56.6725			−0.243230			−0.121615	−	0.992577i	$-0.538807\pi$
$233$	−56.6725			−0.243230			−0.121615	+	0.992577i	$0.538807\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−52.8323	+	76.7464i	−0.222921	+	0.323824i
$238$		0			0
$239$	358.499	+	206.980i	1.50000	+	0.866024i	1.00000		2.96133e-6i	$-9.42621e-7\pi$
$239$	358.499	+	206.980i	1.50000	+	0.866024i	0.499997	+	0.866027i	$0.333334\pi$
$240$		0			0
$241$	−58.6707	−	101.621i	−0.243447	−	0.421663i	0.718247	−	0.695788i	$-0.244945\pi$
$241$	−58.6707	−	101.621i	−0.243447	−	0.421663i	−0.961694	+	0.274126i	$0.911612\pi$
$242$		0			0
$243$	−193.346	+	147.195i	−0.795662	+	0.605741i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	34.5910	+	19.9711i	0.140045	+	0.0808548i
$248$		0			0
$249$	−262.062	+	380.682i	−1.05246	+	1.52884i
$250$		0			0
$251$		−	122.169i		−	0.486729i	−0.969935	−	0.243364i	$-0.921749\pi$
$251$		−	122.169i		−	0.486729i	0.969935	−	0.243364i	$-0.0782511\pi$
$252$		0			0
$253$			72.3723i			0.286057i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	144.758	−	250.728i	0.563260	−	0.975596i	−0.433949	−	0.900938i	$-0.642880\pi$
$257$	144.758	−	250.728i	0.563260	−	0.975596i	0.997209	−	0.0746580i	$-0.0237865\pi$
$258$		0			0
$259$	−303.350	−	525.418i	−1.17124	−	2.02864i
$260$		0			0
$261$	−62.7061	+	392.051i	−0.240253	+	1.50211i
$262$		0			0
$263$	98.2473	+	170.169i	0.373564	+	0.647032i	0.990111	−	0.140286i	$-0.0448023\pi$
$263$	98.2473	+	170.169i	0.373564	+	0.647032i	−0.616547	+	0.787318i	$0.711469\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	354.964	−	168.978i	1.32946	−	0.632877i
$268$		0			0
$269$			254.946i			0.947756i	0.880591	+	0.473878i	$0.157146\pi$
$269$			254.946i			0.947756i	−0.880591	+	0.473878i	$0.842854\pi$
$270$		0			0
$271$	−139.138			−0.513425			−0.256713	−	0.966488i	$-0.582639\pi$
$271$	−139.138			−0.513425			−0.256713	+	0.966488i	$0.582639\pi$
$272$		0			0
$273$	−63.7642	−	133.946i	−0.233568	−	0.490646i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	75.5437	−	43.6152i	0.272721	−	0.157456i	−0.357403	−	0.933950i	$-0.616338\pi$
$277$	75.5437	−	43.6152i	0.272721	−	0.157456i	0.630124	+	0.776495i	$0.283004\pi$
$278$		0			0
$279$	29.1432	+	76.2670i	0.104456	+	0.273358i
$280$		0			0
$281$	32.2605	−	18.6256i	0.114806	−	0.0662833i	−0.441497	−	0.897263i	$-0.645553\pi$
$281$	32.2605	−	18.6256i	0.114806	−	0.0662833i	0.556303	+	0.830979i	$0.312219\pi$
$282$		0			0
$283$	396.990	+	229.202i	1.40279	+	0.809902i	0.994678	−	0.103029i	$-0.0328535\pi$
$283$	396.990	+	229.202i	1.40279	+	0.809902i	0.408113	+	0.912931i	$0.366187\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−673.613			−2.34708
$288$		0			0
$289$	−231.969			−0.802662
$290$		0			0
$291$	−410.857	−	282.834i	−1.41188	−	0.971939i
$292$		0			0
$293$	−193.893	+	335.832i	−0.661750	+	1.14618i	0.318406	+	0.947954i	$0.396853\pi$
$293$	−193.893	+	335.832i	−0.661750	+	1.14618i	−0.980156	+	0.198230i	$0.936481\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	232.986	−	68.4360i	0.784466	−	0.230424i
$298$		0			0
$299$	31.8788	−	18.4052i	0.106618	−	0.0615560i
$300$		0			0
$301$	−216.753	+	375.427i	−0.720108	+	1.24726i
$302$		0			0
$303$	401.318	+	276.268i	1.32448	+	0.911774i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	34.0128i		−	0.110791i	−0.998464	−	0.0553955i	$-0.982358\pi$
$307$		−	34.0128i		−	0.110791i	0.998464	−	0.0553955i	$-0.0176420\pi$
$308$		0			0
$309$	15.5888	−	196.168i	0.0504492	−	0.634847i
$310$		0			0
$311$	−465.755	−	268.904i	−1.49760	−	0.864642i	−0.497607	−	0.867402i	$-0.665788\pi$
$311$	−465.755	−	268.904i	−1.49760	−	0.864642i	−0.999996	+	0.00276044i	$0.999121\pi$
$312$		0			0
$313$	141.592	−	81.7480i	0.452370	−	0.261176i	−0.256461	−	0.966555i	$-0.582556\pi$
$313$	141.592	−	81.7480i	0.452370	−	0.261176i	0.708830	+	0.705379i	$0.249223\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	270.355	+	468.269i	0.852856	+	1.47719i	0.878620	+	0.477522i	$0.158465\pi$
$317$	270.355	+	468.269i	0.852856	+	1.47719i	−0.0257634	+	0.999668i	$0.508202\pi$
$318$		0			0
$319$	198.378	−	343.600i	0.621874	−	1.07712i
$320$		0			0
$321$	−14.7407	−	30.9650i	−0.0459211	−	0.0964642i
$322$		0			0
$323$	65.9403			0.204150
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−202.665	−	425.728i	−0.619770	−	1.30192i
$328$		0			0
$329$	170.469	+	98.4203i	0.518143	+	0.299150i
$330$		0			0
$331$	−121.090	−	209.734i	−0.365831	−	0.633638i	0.623078	−	0.782160i	$-0.285882\pi$
$331$	−121.090	−	209.734i	−0.365831	−	0.633638i	−0.988909	+	0.148522i	$0.952549\pi$
$332$		0			0
$333$	−392.063	−	318.475i	−1.17737	−	0.956380i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	286.441	+	165.377i	0.849973	+	0.490732i	0.860642	−	0.509211i	$-0.170063\pi$
$337$	286.441	+	165.377i	0.849973	+	0.490732i	−0.0106686	+	0.999943i	$0.503396\pi$
$338$		0			0
$339$	68.4862	+	5.44238i	0.202024	+	0.0160542i
$340$		0			0
$341$		−	81.5882i		−	0.239261i
$342$		0			0
$343$			203.849i			0.594312i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	249.485	−	432.122i	0.718978	−	1.24531i	−0.242427	−	0.970170i	$-0.577943\pi$
$347$	249.485	−	432.122i	0.718978	−	1.24531i	0.961405	−	0.275137i	$-0.0887233\pi$
$348$		0			0
$349$	−144.309	−	249.950i	−0.413492	−	0.716190i	0.581777	−	0.813349i	$-0.302358\pi$
$349$	−144.309	−	249.950i	−0.413492	−	0.716190i	−0.995269	+	0.0971589i	$0.969024\pi$
$350$		0			0
$351$	−89.3964	−	85.2224i	−0.254691	−	0.242799i
$352$		0			0
$353$	173.782	+	300.999i	0.492299	+	0.852687i	0.999961	−	0.00886928i	$-0.00282322\pi$
$353$	173.782	+	300.999i	0.492299	+	0.852687i	−0.507661	+	0.861557i	$0.669490\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−201.730	−	138.871i	−0.565070	−	0.388994i
$358$		0			0
$359$		−	408.046i		−	1.13662i	−0.822815	−	0.568310i	$-0.807597\pi$
$359$		−	408.046i		−	1.13662i	0.822815	−	0.568310i	$-0.192403\pi$
$360$		0			0
$361$	−284.758			−0.788804
$362$		0			0
$363$	119.963	+	9.53306i	0.330476	+	0.0262619i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	239.351	−	138.189i	0.652183	−	0.376538i	−0.137109	−	0.990556i	$-0.543781\pi$
$367$	239.351	−	138.189i	0.652183	−	0.376538i	0.789292	+	0.614018i	$0.210448\pi$
$368$		0			0
$369$	−523.877	+	200.184i	−1.41972	+	0.542504i
$370$		0			0
$371$	−222.804	+	128.636i	−0.600551	+	0.346728i
$372$		0			0
$373$	129.870	+	74.9808i	0.348178	+	0.201021i	0.663883	−	0.747837i	$-0.268907\pi$
$373$	129.870	+	74.9808i	0.348178	+	0.201021i	−0.315704	+	0.948858i	$0.602241\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−201.800			−0.535279
$378$		0			0
$379$	385.068			1.01601			0.508005	−	0.861354i	$-0.330383\pi$
$379$	385.068			1.01601			0.508005	+	0.861354i	$0.330383\pi$
$380$		0			0
$381$	−269.091	+	128.099i	−0.706274	+	0.336217i
$382$		0			0
$383$	66.9947	−	116.038i	0.174921	−	0.302972i	−0.765213	−	0.643777i	$-0.777366\pi$
$383$	66.9947	−	116.038i	0.174921	−	0.302972i	0.940134	+	0.340805i	$0.110700\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−57.0021	+	356.388i	−0.147292	+	0.920901i
$388$		0			0
$389$	−360.786	+	208.300i	−0.927470	+	0.535475i	−0.886011	−	0.463665i	$-0.846534\pi$
$389$	−360.786	+	208.300i	−0.927470	+	0.535475i	−0.0414597	+	0.999140i	$0.513201\pi$
$390$		0			0
$391$	30.3850	−	52.6284i	0.0777110	−	0.134599i
$392$		0			0
$393$	1.70691	−	21.4796i	0.00434329	−	0.0546554i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	414.289i		−	1.04355i	−0.853083	−	0.521775i	$-0.825270\pi$
$397$		−	414.289i		−	1.04355i	0.853083	−	0.521775i	$-0.174730\pi$
$398$		0			0
$399$	−233.245	−	160.566i	−0.584574	−	0.402421i
$400$		0			0
$401$	−210.716	−	121.657i	−0.525476	−	0.303384i	0.213696	−	0.976900i	$-0.431450\pi$
$401$	−210.716	−	121.657i	−0.525476	−	0.303384i	−0.739172	+	0.673516i	$0.764783\pi$
$402$		0			0
$403$	−35.9382	+	20.7489i	−0.0891767	+	0.0514862i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	252.379	+	437.134i	0.620097	+	1.07404i
$408$		0			0
$409$	−308.993	+	535.191i	−0.755483	+	1.30854i	0.189650	+	0.981852i	$0.439265\pi$
$409$	−308.993	+	535.191i	−0.755483	+	1.30854i	−0.945134	+	0.326684i	$0.894069\pi$
$410$		0			0
$411$	427.863	−	621.531i	1.04103	−	1.51224i
$412$		0			0
$413$	−740.209			−1.79227
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−494.112	−	39.2655i	−1.18492	−	0.0941618i
$418$		0			0
$419$	601.137	+	347.066i	1.43469	+	0.828321i	0.997474	−	0.0710339i	$-0.0226299\pi$
$419$	601.137	+	347.066i	1.43469	+	0.828321i	0.437220	+	0.899355i	$0.355963\pi$
$420$		0			0
$421$	56.2394	+	97.4094i	0.133585	+	0.231376i	0.925056	−	0.379831i	$-0.124018\pi$
$421$	56.2394	+	97.4094i	0.133585	+	0.231376i	−0.791471	+	0.611207i	$0.790684\pi$
$422$		0			0
$423$	161.824	+	25.8828i	0.382564	+	0.0611886i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−306.966	−	177.227i	−0.718890	−	0.415051i
$428$		0			0
$429$	53.0501	+	111.440i	0.123660	+	0.259767i
$430$		0			0
$431$			419.462i			0.973229i	0.873617	+	0.486615i	$0.161768\pi$
$431$			419.462i			0.973229i	−0.873617	+	0.486615i	$0.838232\pi$
$432$		0			0
$433$			21.7422i			0.0502129i	0.999685	+	0.0251065i	$0.00799248\pi$
$433$			21.7422i			0.0502129i	−0.999685	+	0.0251065i	$0.992008\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	35.1319	−	60.8502i	0.0803934	−	0.139245i
$438$		0			0
$439$	348.778	+	604.101i	0.794483	+	1.37608i	0.923167	+	0.384399i	$0.125591\pi$
$439$	348.778	+	604.101i	0.794483	+	1.37608i	−0.128684	+	0.991686i	$0.541075\pi$
$440$		0			0
$441$	217.994	+	570.485i	0.494317	+	1.29362i
$442$		0			0
$443$	−111.780	−	193.609i	−0.252325	−	0.437040i	0.711840	−	0.702341i	$-0.247862\pi$
$443$	−111.780	−	193.609i	−0.252325	−	0.437040i	−0.964166	+	0.265301i	$0.914529\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	54.1779	−	681.768i	0.121203	−	1.52521i
$448$		0			0
$449$			104.042i			0.231719i	0.993266	+	0.115860i	$0.0369623\pi$
$449$			104.042i			0.231719i	−0.993266	+	0.115860i	$0.963038\pi$
$450$		0			0
$451$	560.428			1.24263
$452$		0			0
$453$	292.595	−	425.036i	0.645906	−	0.938270i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	579.342	−	334.483i	1.26771	−	0.731910i	0.293153	−	0.956066i	$-0.405296\pi$
$457$	579.342	−	334.483i	1.26771	−	0.731910i	0.974553	+	0.224155i	$0.0719623\pi$
$458$		0			0
$459$	−198.158	−	48.0517i	−0.431716	−	0.104688i
$460$		0			0
$461$	0.222592	−	0.128513i	0.000482846	−	0.000278771i	−0.499759	−	0.866165i	$-0.666578\pi$
$461$	0.222592	−	0.128513i	0.000482846	−	0.000278771i	0.500241	+	0.865886i	$0.333245\pi$
$462$		0			0
$463$	−481.854	−	278.199i	−1.04072	−	0.600861i	−0.120684	−	0.992691i	$-0.538509\pi$
$463$	−481.854	−	278.199i	−1.04072	−	0.600861i	−0.920038	+	0.391830i	$0.871842\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−357.378			−0.765262			−0.382631	−	0.923901i	$-0.624982\pi$
$467$	−357.378			−0.765262			−0.382631	+	0.923901i	$0.624982\pi$
$468$		0			0
$469$	−89.8828			−0.191648
$470$		0			0
$471$	58.0050	−	729.927i	0.123153	−	1.54974i
$472$		0			0
$473$	180.332	−	312.345i	0.381253	−	0.660349i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−135.050	+	166.255i	−0.283123	+	0.348543i
$478$		0			0
$479$	−350.791	+	202.529i	−0.732341	+	0.422817i	−0.819278	−	0.573397i	$-0.805625\pi$
$479$	−350.791	+	202.529i	−0.732341	+	0.422817i	0.0869370	+	0.996214i	$0.472292\pi$
$480$		0			0
$481$	128.367	−	222.338i	0.266875	−	0.462241i
$482$		0			0
$483$	−235.630	+	112.170i	−0.487846	+	0.232235i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			586.853i			1.20504i	0.798105	+	0.602518i	$0.205836\pi$
$487$			586.853i			1.20504i	−0.798105	+	0.602518i	$0.794164\pi$
$488$		0			0
$489$	520.587	−	247.822i	1.06459	−	0.506792i
$490$		0			0
$491$	304.133	+	175.591i	0.619415	+	0.357619i	0.776641	−	0.629943i	$-0.216922\pi$
$491$	304.133	+	175.591i	0.619415	+	0.357619i	−0.157226	+	0.987563i	$0.550255\pi$
$492$		0			0
$493$	−288.516	+	166.575i	−0.585226	+	0.337880i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	624.172	+	1081.10i	1.25588	+	2.17525i
$498$		0			0
$499$	481.765	−	834.442i	0.965461	−	1.67223i	0.257091	−	0.966387i	$-0.417236\pi$
$499$	481.765	−	834.442i	0.965461	−	1.67223i	0.708370	−	0.705841i	$-0.249431\pi$
$500$		0			0
$501$	631.001	+	50.1436i	1.25948	+	0.100087i
$502$		0			0
$503$	858.481			1.70672			0.853361	−	0.521321i	$-0.174561\pi$
$503$	858.481			1.70672			0.853361	+	0.521321i	$0.174561\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−251.890	+	365.905i	−0.496824	+	0.721707i
$508$		0			0
$509$	−437.729	−	252.723i	−0.859978	−	0.496508i	0.00402718	−	0.999992i	$-0.498718\pi$
$509$	−437.729	−	252.723i	−0.859978	−	0.496508i	−0.864005	+	0.503484i	$0.832051\pi$
$510$		0			0
$511$	677.249	+	1173.03i	1.32534	+	2.29556i
$512$		0			0
$513$	−229.115	−	55.5586i	−0.446617	−	0.108301i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−141.826	−	81.8831i	−0.274324	−	0.158381i
$518$		0			0
$519$	254.823	−	370.166i	0.490988	−	0.713229i
$520$		0			0
$521$		−	640.397i		−	1.22917i	−0.788851	−	0.614585i	$-0.789324\pi$
$521$		−	640.397i		−	1.22917i	0.788851	−	0.614585i	$-0.210676\pi$
$522$		0			0
$523$		−	91.8967i		−	0.175711i	−0.996133	−	0.0878553i	$-0.971999\pi$
$523$		−	91.8967i		−	0.175711i	0.996133	−	0.0878553i	$-0.0280013\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−34.2542	+	59.3300i	−0.0649985	+	0.112581i
$528$		0			0
$529$	232.123	+	402.048i	0.438795	+	0.760016i
$530$		0			0
$531$	−575.670	+	219.975i	−1.08412	+	0.414266i
$532$		0			0
$533$	−142.524	−	246.859i	−0.267400	−	0.463150i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−157.869	+	75.1523i	−0.293983	+	0.139948i
$538$		0			0
$539$		−	610.287i		−	1.13226i
$540$		0			0
$541$	−391.152			−0.723017			−0.361509	−	0.932369i	$-0.617738\pi$
$541$	−391.152			−0.723017			−0.361509	+	0.932369i	$0.617738\pi$
$542$		0			0
$543$	34.5195	+	72.5134i	0.0635718	+	0.133542i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−712.576	+	411.406i	−1.30270	+	0.752113i	−0.980866	−	0.194683i	$-0.937632\pi$
$547$	−712.576	+	411.406i	−1.30270	+	0.752113i	−0.321832	+	0.946797i	$0.604299\pi$
$548$		0			0
$549$	−291.400	−	46.6075i	−0.530783	−	0.0848953i
$550$		0			0
$551$	−333.590	+	192.598i	−0.605426	+	0.349543i
$552$		0			0
$553$	290.756	+	167.868i	0.525779	+	0.303559i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−111.213			−0.199665			−0.0998323	−	0.995004i	$-0.531831\pi$
$557$	−111.213			−0.199665			−0.0998323	+	0.995004i	$0.531831\pi$
$558$		0			0
$559$	−183.444			−0.328164
$560$		0			0
$561$	167.834	+	115.537i	0.299169	+	0.205948i
$562$		0			0
$563$	−108.786	+	188.423i	−0.193226	+	0.334677i	−0.946317	−	0.323239i	$-0.895228\pi$
$563$	−108.786	+	188.423i	−0.193226	+	0.334677i	0.753092	+	0.657916i	$0.228562\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	583.919	+	652.487i	1.02984	+	1.15077i
$568$		0			0
$569$	141.705	−	81.8136i	0.249043	−	0.143785i	−0.370283	−	0.928919i	$-0.620739\pi$
$569$	141.705	−	81.8136i	0.249043	−	0.143785i	0.619326	+	0.785134i	$0.287406\pi$
$570$		0			0
$571$	380.199	−	658.524i	0.665848	−	1.15328i	−0.313207	−	0.949685i	$-0.601403\pi$
$571$	380.199	−	658.524i	0.665848	−	1.15328i	0.979055	−	0.203598i	$-0.0652635\pi$
$572$		0			0
$573$	206.382	+	142.074i	0.360178	+	0.247947i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	26.9318i		−	0.0466756i	−0.999728	−	0.0233378i	$-0.992571\pi$
$577$		−	26.9318i		−	0.0466756i	0.999728	−	0.0233378i	$-0.00742932\pi$
$578$		0			0
$579$	19.7770	−	248.872i	0.0341572	−	0.429830i
$580$		0			0
$581$	1442.22	+	832.668i	2.48231	+	1.43316i
$582$		0			0
$583$	185.367	−	107.022i	0.317954	−	0.183571i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−247.572	−	428.807i	−0.421758	−	0.730506i	0.574354	−	0.818607i	$-0.305253\pi$
$587$	−247.572	−	428.807i	−0.421758	−	0.730506i	−0.996112	+	0.0881015i	$0.971920\pi$
$588$		0			0
$589$	−39.6056	+	68.5989i	−0.0672420	+	0.116467i
$590$		0			0
$591$	220.796	+	463.815i	0.373597	+	0.784796i
$592$		0			0
$593$	102.991			0.173678			0.0868392	−	0.996222i	$-0.472323\pi$
$593$	102.991			0.173678			0.0868392	+	0.996222i	$0.472323\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	195.109	+	409.857i	0.326817	+	0.686528i
$598$		0			0
$599$	492.666	+	284.441i	0.822481	+	0.474860i	0.851271	−	0.524726i	$-0.175832\pi$
$599$	492.666	+	284.441i	0.822481	+	0.474860i	−0.0287900	+	0.999585i	$0.509165\pi$
$600$		0			0
$601$	−445.951	−	772.410i	−0.742016	−	1.28521i	−0.951576	−	0.307413i	$-0.900537\pi$
$601$	−445.951	−	772.410i	−0.742016	−	1.28521i	0.209561	−	0.977796i	$-0.432797\pi$
$602$		0			0
$603$	−69.9030	+	26.7114i	−0.115925	+	0.0442975i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	356.909	+	206.061i	0.587988	+	0.339475i	0.764301	−	0.644859i	$-0.223084\pi$
$607$	356.909	+	206.061i	0.587988	+	0.339475i	−0.176314	+	0.984334i	$0.556417\pi$
$608$		0			0
$609$	1426.16	+	113.332i	2.34180	+	0.186096i
$610$		0			0
$611$			83.2958i			0.136327i
$612$		0			0
$613$		−	994.307i		−	1.62203i	−0.585023	−	0.811017i	$-0.698914\pi$
$613$		−	994.307i		−	1.62203i	0.585023	−	0.811017i	$-0.301086\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	340.183	−	589.215i	0.551351	−	0.954967i	−0.446827	−	0.894620i	$-0.647446\pi$
$617$	340.183	−	589.215i	0.551351	−	0.954967i	0.998177	−	0.0603468i	$-0.0192207\pi$
$618$		0			0
$619$	−371.748	−	643.887i	−0.600563	−	1.04021i	−0.992736	−	0.120314i	$-0.961610\pi$
$619$	−371.748	−	643.887i	−0.600563	−	1.04021i	0.392173	−	0.919891i	$-0.371723\pi$
$620$		0			0
$621$	−149.918	+	157.260i	−0.241413	+	0.253237i
$622$		0			0
$623$	−708.298	−	1226.81i	−1.13692	−	1.96919i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	194.054	+	133.587i	0.309496	+	0.213057i
$628$		0			0
$629$		−	423.839i		−	0.673829i
$630$		0			0
$631$	894.208			1.41713			0.708564	−	0.705646i	$-0.249343\pi$
$631$	894.208			1.41713			0.708564	+	0.705646i	$0.249343\pi$
$632$		0			0
$633$	268.496	+	21.3365i	0.424165	+	0.0337070i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−268.821	+	155.204i	−0.422011	+	0.243648i
$638$		0			0
$639$	806.707	+	655.292i	1.26245	+	1.02550i
$640$		0			0
$641$	446.198	−	257.613i	0.696097	−	0.401892i	−0.109795	−	0.993954i	$-0.535019\pi$
$641$	446.198	−	257.613i	0.696097	−	0.401892i	0.805892	+	0.592062i	$0.201686\pi$
$642$		0			0
$643$	−591.217	−	341.339i	−0.919466	−	0.530854i	−0.0360013	−	0.999352i	$-0.511462\pi$
$643$	−591.217	−	341.339i	−0.919466	−	0.530854i	−0.883465	+	0.468498i	$0.844795\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−740.660			−1.14476			−0.572380	−	0.819988i	$-0.693980\pi$
$647$	−740.660			−1.14476			−0.572380	+	0.819988i	$0.693980\pi$
$648$		0			0
$649$	615.834			0.948897
$650$		0			0
$651$	265.634	−	126.453i	0.408041	−	0.194245i
$652$		0			0
$653$	155.252	−	268.904i	0.237751	−	0.411797i	−0.722317	−	0.691562i	$-0.756923\pi$
$653$	155.252	−	268.904i	0.237751	−	0.411797i	0.960069	+	0.279764i	$0.0902564\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	875.305	+	711.015i	1.33228	+	1.08221i
$658$		0			0
$659$	−218.218	+	125.988i	−0.331135	+	0.191181i	−0.656345	−	0.754461i	$-0.727898\pi$
$659$	−218.218	+	125.988i	−0.331135	+	0.191181i	0.325210	+	0.945642i	$0.394565\pi$
$660$		0			0
$661$	−154.032	+	266.791i	−0.233029	+	0.403618i	−0.958698	−	0.284426i	$-0.908197\pi$
$661$	−154.032	+	266.791i	−0.233029	+	0.403618i	0.725669	+	0.688044i	$0.241530\pi$
$662$		0			0
$663$	8.20976	−	103.311i	0.0123827	−	0.155823i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			354.994i			0.532224i
$668$		0			0
$669$	−229.493	−	157.983i	−0.343039	−	0.236148i
$670$		0			0
$671$	255.388	+	147.448i	0.380608	+	0.219744i
$672$		0			0
$673$	610.473	−	352.456i	0.907091	−	0.523709i	0.0275972	−	0.999619i	$-0.491214\pi$
$673$	610.473	−	352.456i	0.907091	−	0.523709i	0.879494	+	0.475910i	$0.157881\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−123.043	−	213.117i	−0.181748	−	0.314797i	0.760728	−	0.649071i	$-0.224842\pi$
$677$	−123.043	−	213.117i	−0.181748	−	0.314797i	−0.942476	+	0.334274i	$0.891509\pi$
$678$		0			0
$679$	−898.671	+	1556.54i	−1.32352	+	2.29241i
$680$		0			0
$681$	−378.731	+	550.161i	−0.556140	+	0.807872i
$682$		0			0
$683$	430.637			0.630507			0.315254	−	0.949007i	$-0.397910\pi$
$683$	430.637			0.630507			0.315254	+	0.949007i	$0.397910\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−550.493	−	43.7459i	−0.801299	−	0.0636767i
$688$		0			0
$689$	−94.2827	−	54.4342i	−0.136840	−	0.0790046i
$690$		0			0
$691$	−244.885	−	424.153i	−0.354392	−	0.613825i	0.632622	−	0.774461i	$-0.281979\pi$
$691$	−244.885	−	424.153i	−0.354392	−	0.613825i	−0.987014	+	0.160636i	$0.948645\pi$
$692$		0			0
$693$	−312.329	−	817.359i	−0.450692	−	1.17945i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−407.537	−	235.292i	−0.584702	−	0.337578i
$698$		0			0
$699$	73.0777	+	153.511i	0.104546	+	0.219615i
$700$		0			0
$701$		−	1398.45i		−	1.99494i	−0.0711109	−	0.997468i	$-0.522654\pi$
$701$		−	1398.45i		−	1.99494i	0.0711109	−	0.997468i	$-0.477346\pi$
$702$		0			0
$703$		−	490.053i		−	0.697088i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	877.806	−	1520.40i	1.24159	−	2.15050i
$708$		0			0
$709$	615.327	+	1065.78i	0.867880	+	1.50321i	0.864158	+	0.503220i	$0.167851\pi$
$709$	615.327	+	1065.78i	0.867880	+	1.50321i	0.00372210	+	0.999993i	$0.498815\pi$
$710$		0			0
$711$	276.012	+	44.1463i	0.388202	+	0.0620904i
$712$		0			0
$713$	36.5001	+	63.2201i	0.0511924	+	0.0886678i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	98.3779	−	1237.98i	0.137208	−	1.72660i
$718$		0			0
$719$		−	205.324i		−	0.285569i	−0.989754	−	0.142785i	$-0.954394\pi$
$719$		−	205.324i		−	0.285569i	0.989754	−	0.142785i	$-0.0456056\pi$
$720$		0			0
$721$	−709.090			−0.983481
$722$		0			0
$723$	−199.609	+	289.961i	−0.276085	+	0.401052i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−801.453	+	462.719i	−1.10241	+	0.636477i	−0.936853	−	0.349723i	$-0.886276\pi$
$727$	−801.453	+	462.719i	−1.10241	+	0.636477i	−0.165558	+	0.986200i	$0.552942\pi$
$728$		0			0
$729$	648.027	+	333.919i	0.888926	+	0.458050i
$730$		0			0
$731$	−262.272	+	151.423i	−0.358785	+	0.207144i
$732$		0			0
$733$	−541.875	−	312.852i	−0.739257	−	0.426810i	0.0825420	−	0.996588i	$-0.473696\pi$
$733$	−541.875	−	312.852i	−0.739257	−	0.426810i	−0.821799	+	0.569777i	$0.807029\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	74.7801			0.101466
$738$		0			0
$739$	−487.290			−0.659392			−0.329696	−	0.944087i	$-0.606946\pi$
$739$	−487.290			−0.659392			−0.329696	+	0.944087i	$0.606946\pi$
$740$		0			0
$741$	9.49233	−	119.450i	0.0128102	−	0.161201i
$742$		0			0
$743$	303.238	−	525.224i	0.408127	−	0.706897i	−0.586553	−	0.809911i	$-0.699515\pi$
$743$	303.238	−	525.224i	0.408127	−	0.706897i	0.994680	+	0.103014i	$0.0328488\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1369.09	+	218.977i	1.83278	+	0.293142i
$748$		0			0
$749$	−107.020	+	61.7877i	−0.142883	+	0.0824937i
$750$		0			0
$751$	−174.790	+	302.746i	−0.232744	+	0.403124i	−0.958615	−	0.284707i	$-0.908104\pi$
$751$	−174.790	+	302.746i	−0.232744	+	0.403124i	0.725871	+	0.687831i	$0.241437\pi$
$752$		0			0
$753$	−330.923	+	157.534i	−0.439473	+	0.209208i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			242.544i			0.320402i	0.987084	+	0.160201i	$0.0512142\pi$
$757$			242.544i			0.320402i	−0.987084	+	0.160201i	$0.948786\pi$
$758$		0			0
$759$	196.038	−	93.3223i	0.258284	−	0.122954i
$760$		0			0
$761$	1023.42	+	590.870i	1.34483	+	0.776439i	0.987512	−	0.157543i	$-0.0503574\pi$
$761$	1023.42	+	590.870i	1.34483	+	0.776439i	0.357319	+	0.933982i	$0.383691\pi$
$762$		0			0
$763$	−1471.38	+	849.500i	−1.92841	+	1.11337i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−156.615	−	271.265i	−0.204191	−	0.353670i
$768$		0			0
$769$	219.654	−	380.451i	0.285635	−	0.494735i	−0.687128	−	0.726537i	$-0.741129\pi$
$769$	219.654	−	380.451i	0.285635	−	0.494735i	0.972763	+	0.231802i	$0.0744620\pi$
$770$		0			0
$771$	−865.818	−	68.8038i	−1.12298	−	0.0892397i
$772$		0			0
$773$	1157.27			1.49711			0.748556	−	0.663072i	$-0.230748\pi$
$773$	1157.27			1.49711			0.748556	+	0.663072i	$0.230748\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1032.06	+	1499.21i	−1.32826	+	1.92948i
$778$		0			0
$779$	−471.205	−	272.050i	−0.604884	−	0.349230i
$780$		0			0
$781$	−519.295	−	899.445i	−0.664910	−	1.15166i
$782$		0			0
$783$	1142.82	−	335.686i	1.45954	−	0.428717i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1018.63	−	588.108i	−1.29432	−	0.747279i	−0.314907	−	0.949122i	$-0.601973\pi$
$787$	−1018.63	−	588.108i	−1.29432	−	0.747279i	−0.979418	+	0.201844i	$0.935307\pi$
$788$		0			0
$789$	334.257	−	485.555i	0.423646	−	0.615406i
$790$		0			0
$791$		−	247.558i		−	0.312968i
$792$		0			0
$793$		−	149.992i		−	0.189145i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.9607	−	18.9845i	0.0137525	−	0.0238200i	−0.859067	−	0.511863i	$-0.828956\pi$
$797$	10.9607	−	18.9845i	0.0137525	−	0.0238200i	0.872820	+	0.488043i	$0.162289\pi$
$798$		0			0
$799$	68.7561	+	119.089i	0.0860527	+	0.149048i
$800$		0			0
$801$	−915.435	−	743.612i	−1.14287	−	0.928355i
$802$		0			0
$803$	−563.453	−	975.929i	−0.701685	−	1.21535i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	690.583	−	328.747i	0.855741	−	0.407369i
$808$		0			0
$809$		−	1548.54i		−	1.91414i	−0.289857	−	0.957070i	$-0.593608\pi$
$809$		−	1548.54i		−	1.91414i	0.289857	−	0.957070i	$-0.406392\pi$
$810$		0			0
$811$	235.109			0.289900			0.144950	−	0.989439i	$-0.453698\pi$
$811$	235.109			0.289900			0.144950	+	0.989439i	$0.453698\pi$
$812$		0			0
$813$	179.415	+	376.889i	0.220683	+	0.463578i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−303.245	+	175.079i	−0.371169	+	0.214294i
$818$		0			0
$819$	−280.603	+	345.441i	−0.342617	+	0.421784i
$820$		0			0
$821$	−814.987	+	470.533i	−0.992676	+	0.573122i	−0.906073	−	0.423121i	$-0.860935\pi$
$821$	−814.987	+	470.533i	−0.992676	+	0.573122i	−0.0866031	+	0.996243i	$0.527601\pi$
$822$		0			0
$823$	250.019	+	144.349i	0.303790	+	0.175393i	0.644144	−	0.764904i	$-0.277214\pi$
$823$	250.019	+	144.349i	0.303790	+	0.175393i	−0.340354	+	0.940297i	$0.610547\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	853.621			1.03219			0.516095	−	0.856531i	$-0.327385\pi$
$827$	853.621			1.03219			0.516095	+	0.856531i	$0.327385\pi$
$828$		0			0
$829$	13.6812			0.0165033			0.00825164	−	0.999966i	$-0.497373\pi$
$829$	13.6812			0.0165033			0.00825164	+	0.999966i	$0.497373\pi$
$830$		0			0
$831$	−215.554	−	148.387i	−0.259391	−	0.178565i
$832$		0			0
$833$	−256.225	+	443.794i	−0.307593	+	0.532766i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	169.008	−	177.286i	0.201921	−	0.211811i
$838$		0			0
$839$	−102.968	+	59.4488i	−0.122727	+	0.0708567i	−0.560107	−	0.828420i	$-0.689240\pi$
$839$	−102.968	+	59.4488i	−0.122727	+	0.0708567i	0.437380	+	0.899277i	$0.355907\pi$
$840$		0			0
$841$	552.563	−	957.067i	0.657031	−	1.13801i
$842$		0			0
$843$	−92.0509	−	63.3679i	−0.109194	−	0.0751696i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	433.631i		−	0.511961i
$848$		0			0
$849$	108.940	−	1370.89i	0.128316	−	1.61471i
$850$		0			0
$851$	−391.122	−	225.814i	−0.459603	−	0.265352i
$852$		0			0
$853$	577.231	−	333.265i	0.676707	−	0.390697i	−0.121906	−	0.992542i	$-0.538901\pi$
$853$	577.231	−	333.265i	0.676707	−	0.390697i	0.798613	+	0.601845i	$0.205567\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	306.171	+	530.304i	0.357259	+	0.618791i	0.987502	−	0.157607i	$-0.0503780\pi$
$857$	306.171	+	530.304i	0.357259	+	0.618791i	−0.630243	+	0.776398i	$0.717045\pi$
$858$		0			0
$859$	−665.233	+	1152.22i	−0.774427	+	1.34135i	0.160689	+	0.987005i	$0.448628\pi$
$859$	−665.233	+	1152.22i	−0.774427	+	1.34135i	−0.935116	+	0.354342i	$0.884705\pi$
$860$		0			0
$861$	868.606	+	1824.64i	1.00883	+	2.11921i
$862$		0			0
$863$	1042.02			1.20744			0.603719	−	0.797197i	$-0.293685\pi$
$863$	1042.02			1.20744			0.603719	+	0.797197i	$0.293685\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	299.118	+	628.344i	0.345004	+	0.724733i
$868$		0			0
$869$	−241.901	−	139.662i	−0.278367	−	0.160716i
$870$		0			0
$871$	−19.0176	−	32.9394i	−0.0218342	−	0.0378179i
$872$		0			0
$873$	−236.334	+	1477.61i	−0.270715	+	1.69257i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	193.736	+	111.854i	0.220908	+	0.127541i	0.606371	−	0.795182i	$-0.292625\pi$
$877$	193.736	+	111.854i	0.220908	+	0.127541i	−0.385463	+	0.922723i	$0.625958\pi$
$878$		0			0
$879$	1159.70	+	92.1576i	1.31934	+	0.104844i
$880$		0			0
$881$			447.183i			0.507586i	0.967259	+	0.253793i	$0.0816782\pi$
$881$			447.183i			0.507586i	−0.967259	+	0.253793i	$0.918322\pi$
$882$		0			0
$883$			1028.50i			1.16478i	0.812910	+	0.582389i	$0.197882\pi$
$883$			1028.50i			1.16478i	−0.812910	+	0.582389i	$0.802118\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	228.301	−	395.428i	0.257385	−	0.445804i	−0.708155	−	0.706057i	$-0.750472\pi$
$887$	228.301	−	395.428i	0.257385	−	0.445804i	0.965541	+	0.260252i	$0.0838057\pi$
$888$		0			0
$889$	536.945	+	930.016i	0.603987	+	1.04614i
$890$		0			0
$891$	−485.805	−	542.852i	−0.545236	−	0.609262i
$892$		0			0
$893$	79.4975	+	137.694i	0.0890230	+	0.154192i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−90.9618	−	62.6182i	−0.101407	−	0.0698085i
$898$		0			0
$899$		−	400.198i		−	0.445159i
$900$		0			0
$901$	−179.730			−0.199478
$902$		0			0
$903$	1296.43	+	103.023i	1.43569	+	0.114090i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	331.435	−	191.354i	0.365419	−	0.210975i	−0.306036	−	0.952020i	$-0.599003\pi$
$907$	331.435	−	191.354i	0.365419	−	0.210975i	0.671455	+	0.741045i	$0.265670\pi$
$908$		0			0
$909$	230.847	−	1443.30i	0.253957	−	1.58779i
$910$		0			0
$911$	−1556.93	+	898.893i	−1.70903	+	0.986710i	−0.773272	+	0.634075i	$0.781381\pi$
$911$	−1556.93	+	898.893i	−1.70903	+	0.986710i	−0.935761	+	0.352636i	$0.885286\pi$
$912$		0			0
$913$	−1199.89	−	692.758i	−1.31423	−	0.758771i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−77.6425			−0.0846702
$918$		0			0
$919$	888.894			0.967240			0.483620	−	0.875278i	$-0.339322\pi$
$919$	888.894			0.967240			0.483620	+	0.875278i	$0.339322\pi$
$920$		0			0
$921$	−92.1318	+	43.8587i	−0.100035	+	0.0476207i
$922$		0			0
$923$	−264.127	+	457.481i	−0.286161	+	0.495646i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−551.468	+	210.727i	−0.594895	+	0.227322i
$928$		0			0
$929$	−1525.09	+	880.512i	−1.64165	+	0.947807i	−0.661402	+	0.750032i	$0.730038\pi$
$929$	−1525.09	+	880.512i	−1.64165	+	0.947807i	−0.980247	+	0.197775i	$0.936628\pi$
$930$		0			0
$931$	−296.254	+	513.126i	−0.318210	+	0.551156i
$932$		0			0
$933$	−127.811	+	1608.35i	−0.136989	+	1.72385i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	1536.39i		−	1.63969i	−0.572588	−	0.819843i	$-0.694060\pi$
$937$		−	1536.39i		−	1.63969i	0.572588	−	0.819843i	$-0.305940\pi$
$938$		0			0
$939$	−404.013	−	278.123i	−0.430258	−	0.296190i
$940$		0			0
$941$	1324.15	+	764.496i	1.40717	+	0.812429i	0.995114	−	0.0987296i	$-0.0314779\pi$
$941$	1324.15	+	764.496i	1.40717	+	0.812429i	0.412055	+	0.911159i	$0.364811\pi$
$942$		0			0
$943$	−434.258	+	250.719i	−0.460507	+	0.265874i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	498.186	+	862.884i	0.526068	+	0.911176i	0.999539	+	0.0303669i	$0.00966757\pi$
$947$	498.186	+	862.884i	0.526068	+	0.911176i	−0.473471	+	0.880809i	$0.656999\pi$
$948$		0			0
$949$	−286.587	+	496.383i	−0.301988	+	0.523059i
$950$		0			0
$951$	919.802	−	1336.14i	0.967195	−	1.40499i
$952$		0			0
$953$	1005.97			1.05559			0.527794	−	0.849373i	$-0.323019\pi$
$953$	1005.97			1.05559			0.527794	+	0.849373i	$0.323019\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1186.53	−	94.2894i	−1.23984	−	0.0985260i
$958$		0			0
$959$	−2354.69	−	1359.48i	−2.45536	−	1.41760i
$960$		0			0
$961$	439.352	+	760.980i	0.457182	+	0.791863i
$962$		0			0
$963$	−64.8684	+	79.8572i	−0.0673607	+	0.0829254i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	558.267	+	322.316i	0.577319	+	0.333315i	0.760067	−	0.649844i	$-0.225166\pi$
$967$	558.267	+	322.316i	0.577319	+	0.333315i	−0.182748	+	0.983160i	$0.558499\pi$
$968$		0			0
$969$	−85.0283	−	178.615i	−0.0877485	−	0.184329i
$970$		0			0
$971$		−	215.087i		−	0.221511i	−0.993848	−	0.110756i	$-0.964673\pi$
$971$		−	215.087i		−	0.221511i	0.993848	−	0.110756i	$-0.0353271\pi$
$972$		0			0
$973$			1786.07i			1.83563i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.6583	−	53.1017i	0.0313800	−	0.0543518i	−0.849909	−	0.526930i	$-0.823343\pi$
$977$	30.6583	−	53.1017i	0.0313800	−	0.0543518i	0.881289	+	0.472578i	$0.156676\pi$
$978$		0			0
$979$	589.285	+	1020.67i	0.601926	+	1.04257i
$980$		0			0
$981$	−891.855	+	1097.93i	−0.909128	+	1.11920i
$982$		0			0
$983$	−580.428	−	1005.33i	−0.590466	−	1.02272i	−0.994170	−	0.107827i	$-0.965611\pi$
$983$	−580.428	−	1005.33i	−0.590466	−	1.02272i	0.403704	−	0.914890i	$-0.367723\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	46.7794	−	588.666i	0.0473956	−	0.596420i
$988$		0			0
$989$			322.702i			0.326291i
$990$		0			0
$991$	763.478			0.770412			0.385206	−	0.922831i	$-0.374130\pi$
$991$	763.478			0.770412			0.385206	+	0.922831i	$0.374130\pi$
$992$		0			0
$993$	−411.972	+	598.448i	−0.414876	+	0.602667i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	89.2750	−	51.5429i	0.0895436	−	0.0516980i	−0.454560	−	0.890716i	$-0.650203\pi$
$997$	89.2750	−	51.5429i	0.0895436	−	0.0516980i	0.544103	+	0.839018i	$0.316870\pi$
$998$		0			0
$999$	−357.109	+	1472.66i	−0.357467	+	1.47413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.d.149.6		32
3.2	odd	2		2700.3.u.d.449.1		32
5.2	odd	4		900.3.p.e.401.2	yes	16
5.3	odd	4		900.3.p.d.401.7	yes	16
5.4	even	2	inner	900.3.u.d.149.11		32
9.2	odd	6	inner	900.3.u.d.749.11		32
9.7	even	3		2700.3.u.d.2249.16		32
15.2	even	4		2700.3.p.d.2501.1		16
15.8	even	4		2700.3.p.e.2501.8		16
15.14	odd	2		2700.3.u.d.449.16		32
45.2	even	12		900.3.p.e.101.2	yes	16
45.7	odd	12		2700.3.p.d.1601.1		16
45.29	odd	6	inner	900.3.u.d.749.6		32
45.34	even	6		2700.3.u.d.2249.1		32
45.38	even	12		900.3.p.d.101.7	✓	16
45.43	odd	12		2700.3.p.e.1601.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.7	✓	16	45.38	even	12
900.3.p.d.401.7	yes	16	5.3	odd	4
900.3.p.e.101.2	yes	16	45.2	even	12
900.3.p.e.401.2	yes	16	5.2	odd	4
900.3.u.d.149.6		32	1.1	even	1	trivial
900.3.u.d.149.11		32	5.4	even	2	inner
900.3.u.d.749.6		32	45.29	odd	6	inner
900.3.u.d.749.11		32	9.2	odd	6	inner
2700.3.p.d.1601.1		16	45.7	odd	12
2700.3.p.d.2501.1		16	15.2	even	4
2700.3.p.e.1601.8		16	45.43	odd	12
2700.3.p.e.2501.8		16	15.8	even	4
2700.3.u.d.449.1		32	3.2	odd	2
2700.3.u.d.449.16		32	15.14	odd	2
2700.3.u.d.2249.1		32	45.34	even	6
2700.3.u.d.2249.16		32	9.7	even	3

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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.28947 - 2.70874i) q^{3} +(-9.36178 + 5.40503i) q^{7} +(-5.67451 + 6.98569i) q^{9} +O(q^{10})\)	\(q+(-1.28947 - 2.70874i) q^{3} +(-9.36178 + 5.40503i) q^{7} +(-5.67451 + 6.98569i) q^{9} +(7.78876 - 4.49684i) q^{11} +(-3.96157 - 2.28721i) q^{13} -7.55187 q^{17} -8.73166 q^{19} +(26.7126 + 18.3890i) q^{21} +(-4.02351 + 6.96892i) q^{23} +(26.2395 + 6.36289i) q^{27} +(38.2046 - 22.0575i) q^{29} +(4.53586 - 7.85634i) q^{31} +(-22.2242 - 15.2991i) q^{33} +56.1237i q^{37} +(-1.08712 + 13.6801i) q^{39} +(53.9651 + 31.1568i) q^{41} +(34.7294 - 20.0510i) q^{43} +(-9.10452 - 15.7695i) q^{47} +(33.9287 - 58.7662i) q^{49} +(9.73794 + 20.4560i) q^{51} +23.7994 q^{53} +(11.2592 + 23.6518i) q^{57} +(59.3003 + 34.2370i) q^{59} +(16.3946 + 28.3963i) q^{61} +(15.3657 - 96.0695i) q^{63} +(7.20078 + 4.15737i) q^{67} +(24.0652 + 1.91238i) q^{69} -115.480i q^{71} -125.300i q^{73} +(-48.6111 + 84.1969i) q^{77} +(-15.5289 - 26.8968i) q^{79} +(-16.5998 - 79.2808i) q^{81} +(-77.0272 - 133.415i) q^{83} +(-109.012 - 75.0438i) q^{87} +131.044i q^{89} +49.4498 q^{91} +(-27.1296 - 2.15590i) q^{93} +(143.990 - 83.1329i) q^{97} +(-12.7839 + 79.9272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{9}+O(q^{10}) \) 32 * q - 28 * q^9	\( 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) \) 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more