LMFDB - Embedded newform 900.3.p.e.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} + \cdots + 43046721 $ x^16 - 2x^15 + 10x^14 - 12x^13 + 6x^12 - 27x^11 - 585x^10 + 3618x^9 - 12150x^8 + 32562x^7 - 47385x^6 - 19683x^5 + 39366x^4 - 708588x^3 + 5314410x^2 - 9565938*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{41}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.2
Root			$2.47109 - 1.70110i$ of defining polynomial
Character	$\chi$	$=$	900.101
Dual form			900.3.p.e.401.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.70874 - 1.28947i) q^{3} +(-5.40503 + 9.36178i) q^{7} +(5.67451 + 6.98569i) q^{9} +O(q^{10})$	\(q+(-2.70874 - 1.28947i) q^{3} +(-5.40503 + 9.36178i) q^{7} +(5.67451 + 6.98569i) q^{9} +(7.78876 + 4.49684i) q^{11} +(-2.28721 - 3.96157i) q^{13} +7.55187i q^{17} +8.73166 q^{19} +(26.7126 - 18.3890i) q^{21} +(6.96892 - 4.02351i) q^{23} +(-6.36289 - 26.2395i) q^{27} +(-38.2046 - 22.0575i) q^{29} +(4.53586 + 7.85634i) q^{31} +(-15.2991 - 22.2242i) q^{33} -56.1237 q^{37} +(1.08712 + 13.6801i) q^{39} +(53.9651 - 31.1568i) q^{41} +(-20.0510 + 34.7294i) q^{43} +(15.7695 + 9.10452i) q^{47} +(-33.9287 - 58.7662i) q^{49} +(9.73794 - 20.4560i) q^{51} +23.7994i q^{53} +(-23.6518 - 11.2592i) q^{57} +(-59.3003 + 34.2370i) q^{59} +(16.3946 - 28.3963i) q^{61} +(-96.0695 + 15.3657i) q^{63} +(-4.15737 - 7.20078i) q^{67} +(-24.0652 + 1.91238i) q^{69} +115.480i q^{71} -125.300 q^{73} +(-84.1969 + 48.6111i) q^{77} +(15.5289 - 26.8968i) q^{79} +(-16.5998 + 79.2808i) q^{81} +(-133.415 - 77.0272i) q^{83} +(75.0438 + 109.012i) q^{87} +131.044i q^{89} +49.4498 q^{91} +(-2.15590 - 27.1296i) q^{93} +(83.1329 - 143.990i) q^{97} +(12.7839 + 79.9272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - q^{7} + 14 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 - q^7 + 14 * q^9	$ 16 q + 2 q^{3} - q^{7} + 14 q^{9} - 10 q^{13} + 2 q^{19} + q^{21} + 27 q^{23} - 16 q^{27} + 9 q^{29} + 8 q^{31} + 36 q^{33} - 22 q^{37} + 19 q^{39} + 54 q^{41} + 44 q^{43} - 108 q^{47} - 45 q^{49} + 90 q^{51} - 68 q^{57} + 9 q^{59} - 55 q^{61} - 107 q^{63} - 28 q^{67} - 147 q^{69} + 86 q^{73} + 342 q^{77} + 11 q^{79} - 130 q^{81} - 306 q^{83} + 375 q^{87} - 134 q^{91} - 83 q^{93} + 41 q^{97} + 252 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - q^7 + 14 * q^9 - 10 * q^13 + 2 * q^19 + q^21 + 27 * q^23 - 16 * q^27 + 9 * q^29 + 8 * q^31 + 36 * q^33 - 22 * q^37 + 19 * q^39 + 54 * q^41 + 44 * q^43 - 108 * q^47 - 45 * q^49 + 90 * q^51 - 68 * q^57 + 9 * q^59 - 55 * q^61 - 107 * q^63 - 28 * q^67 - 147 * q^69 + 86 * q^73 + 342 * q^77 + 11 * q^79 - 130 * q^81 - 306 * q^83 + 375 * q^87 - 134 * q^91 - 83 * q^93 + 41 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.70874	−	1.28947i	−0.902912	−	0.429825i
$3$	−2.70874	−	1.28947i	−0.902912	−	0.429825i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−5.40503	+	9.36178i	−0.772147	+	1.33740i	0.164237	+	0.986421i	$0.447484\pi$
$7$	−5.40503	+	9.36178i	−0.772147	+	1.33740i	−0.936384	+	0.350977i	$0.885850\pi$
$8$		0			0
$9$	5.67451	+	6.98569i	0.630501	+	0.776188i
$10$		0			0
$11$	7.78876	+	4.49684i	0.708069	+	0.408804i	0.810346	−	0.585952i	$-0.199279\pi$
$11$	7.78876	+	4.49684i	0.708069	+	0.408804i	−0.102277	+	0.994756i	$0.532613\pi$
$12$		0			0
$13$	−2.28721	−	3.96157i	−0.175939	−	0.304736i	0.764547	−	0.644568i	$-0.222963\pi$
$13$	−2.28721	−	3.96157i	−0.175939	−	0.304736i	−0.940486	+	0.339833i	$0.889630\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			7.55187i			0.444227i	0.975021	+	0.222114i	$0.0712956\pi$
$17$			7.55187i			0.444227i	−0.975021	+	0.222114i	$0.928704\pi$
$18$		0			0
$19$	8.73166			0.459561			0.229780	−	0.973242i	$-0.426199\pi$
$19$	8.73166			0.459561			0.229780	+	0.973242i	$0.426199\pi$
$20$		0			0
$21$	26.7126	−	18.3890i	1.27203	−	0.875665i
$22$		0			0
$23$	6.96892	−	4.02351i	0.302997	−	0.174935i	−0.340792	−	0.940139i	$-0.610695\pi$
$23$	6.96892	−	4.02351i	0.302997	−	0.174935i	0.643788	+	0.765204i	$0.277362\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−6.36289	−	26.2395i	−0.235663	−	0.971835i
$28$		0			0
$29$	−38.2046	−	22.0575i	−1.31740	−	0.760602i	−0.334092	−	0.942541i	$-0.608429\pi$
$29$	−38.2046	−	22.0575i	−1.31740	−	0.760602i	−0.983310	+	0.181939i	$0.941763\pi$
$30$		0			0
$31$	4.53586	+	7.85634i	0.146318	+	0.253430i	0.929864	−	0.367904i	$-0.119924\pi$
$31$	4.53586	+	7.85634i	0.146318	+	0.253430i	−0.783546	+	0.621334i	$0.786591\pi$
$32$		0			0
$33$	−15.2991	−	22.2242i	−0.463610	−	0.673459i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−56.1237			−1.51686			−0.758428	−	0.651756i	$-0.774032\pi$
$37$	−56.1237			−1.51686			−0.758428	+	0.651756i	$0.774032\pi$
$38$		0			0
$39$	1.08712	+	13.6801i	0.0278748	+	0.350773i
$40$		0			0
$41$	53.9651	−	31.1568i	1.31622	−	0.759921i	0.333103	−	0.942890i	$-0.391904\pi$
$41$	53.9651	−	31.1568i	1.31622	−	0.759921i	0.983119	+	0.182969i	$0.0585709\pi$
$42$		0			0
$43$	−20.0510	+	34.7294i	−0.466303	+	0.807660i	−0.999259	−	0.0384827i	$-0.987748\pi$
$43$	−20.0510	+	34.7294i	−0.466303	+	0.807660i	0.532957	+	0.846143i	$0.321081\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	15.7695	+	9.10452i	0.335521	+	0.193713i	0.658290	−	0.752765i	$-0.271280\pi$
$47$	15.7695	+	9.10452i	0.335521	+	0.193713i	−0.322769	+	0.946478i	$0.604614\pi$
$48$		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
$53$			23.7994i			0.449045i	0.974469	+	0.224522i	$0.0720822\pi$
$53$			23.7994i			0.449045i	−0.974469	+	0.224522i	$0.927918\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−23.6518	−	11.2592i	−0.414943	−	0.197531i
$58$		0			0
$59$	−59.3003	+	34.2370i	−1.00509	+	0.580289i	−0.909750	−	0.415156i	$-0.863727\pi$
$59$	−59.3003	+	34.2370i	−1.00509	+	0.580289i	−0.0953396	+	0.995445i	$0.530394\pi$
$60$		0			0
$61$	16.3946	−	28.3963i	0.268765	−	0.465514i	−0.699779	−	0.714360i	$-0.746718\pi$
$61$	16.3946	−	28.3963i	0.268765	−	0.465514i	0.968543	+	0.248846i	$0.0800513\pi$
$62$		0			0
$63$	−96.0695	+	15.3657i	−1.52491	+	0.243900i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.15737	−	7.20078i	−0.0620503	−	0.107474i	0.833331	−	0.552774i	$-0.186431\pi$
$67$	−4.15737	−	7.20078i	−0.0620503	−	0.107474i	−0.895382	+	0.445299i	$0.853097\pi$
$68$		0			0
$69$	−24.0652	+	1.91238i	−0.348771	+	0.0277157i
$70$		0			0
$71$			115.480i			1.62648i	0.581930	+	0.813239i	$0.302298\pi$
$71$			115.480i			1.62648i	−0.581930	+	0.813239i	$0.697702\pi$
$72$		0			0
$73$	−125.300			−1.71643			−0.858217	−	0.513287i	$-0.828428\pi$
$73$	−125.300			−1.71643			−0.858217	+	0.513287i	$0.828428\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−84.1969	+	48.6111i	−1.09347	+	0.631313i
$78$		0			0
$79$	15.5289	−	26.8968i	0.196568	−	0.340466i	−0.750845	−	0.660478i	$-0.770354\pi$
$79$	15.5289	−	26.8968i	0.196568	−	0.340466i	0.947413	+	0.320012i	$0.103687\pi$
$80$		0			0
$81$	−16.5998	+	79.2808i	−0.204936	+	0.978775i
$82$		0			0
$83$	−133.415	−	77.0272i	−1.60741	−	0.928038i	−0.989947	−	0.141438i	$-0.954827\pi$
$83$	−133.415	−	77.0272i	−1.60741	−	0.928038i	−0.617462	−	0.786601i	$-0.711839\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	75.0438	+	109.012i	0.862572	+	1.25301i
$88$		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
$93$	−2.15590	−	27.1296i	−0.0231818	−	0.291716i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	83.1329	−	143.990i	0.857040	−	1.48444i	−0.0176993	−	0.999843i	$-0.505634\pi$
$97$	83.1329	−	143.990i	0.857040	−	1.48444i	0.874739	−	0.484594i	$-0.161033\pi$
$98$		0			0
$99$	12.7839	+	79.9272i	0.129130	+	0.807346i
$100$		0			0
$101$	−140.647	−	81.2027i	−1.39255	−	0.803987i	−0.398950	−	0.916973i	$-0.630625\pi$
$101$	−140.647	−	81.2027i	−1.39255	−	0.803987i	−0.993597	+	0.112985i	$0.963959\pi$
$102$		0			0
$103$	32.7977	+	56.8073i	0.318424	+	0.551527i	0.980159	−	0.198211i	$-0.0635131\pi$
$103$	32.7977	+	56.8073i	0.318424	+	0.551527i	−0.661735	+	0.749738i	$0.730180\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	11.4315i		−	0.106837i	−0.998572	−	0.0534184i	$-0.982988\pi$
$107$		−	11.4315i		−	0.106837i	0.998572	−	0.0534184i	$-0.0170117\pi$
$108$		0			0
$109$	−157.169			−1.44191			−0.720957	−	0.692980i	$-0.756297\pi$
$109$	−157.169			−1.44191			−0.720957	+	0.692980i	$0.756297\pi$
$110$		0			0
$111$	152.024	+	72.3701i	1.36959	+	0.651983i
$112$		0			0
$113$	19.8326	−	11.4504i	0.175510	−	0.101331i	−0.409672	−	0.912233i	$-0.634357\pi$
$113$	19.8326	−	11.4504i	0.175510	−	0.101331i	0.585181	+	0.810903i	$0.301023\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	14.6955	−	38.4577i	0.125602	−	0.328698i
$118$		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
$123$	−186.353	+	14.8089i	−1.51507	+	0.120397i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	99.3417			0.782218			0.391109	−	0.920344i	$-0.372092\pi$
$127$	99.3417			0.782218			0.391109	+	0.920344i	$0.372092\pi$
$128$		0			0
$129$	99.0956	−	68.2175i	0.768183	−	0.528818i
$130$		0			0
$131$	6.22017	−	3.59122i	0.0474822	−	0.0274139i	−0.476071	−	0.879407i	$-0.657939\pi$
$131$	6.22017	−	3.59122i	0.0474822	−	0.0274139i	0.523553	+	0.851993i	$0.324606\pi$
$132$		0			0
$133$	−47.1949	+	81.7439i	−0.354849	+	0.614616i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−217.824	−	125.761i	−1.58996	−	0.917962i	−0.993313	−	0.115455i	$-0.963167\pi$
$137$	−217.824	−	125.761i	−1.58996	−	0.917962i	−0.596644	−	0.802506i	$-0.703499\pi$
$138$		0			0
$139$	−82.6116	−	143.087i	−0.594328	−	1.02941i	−0.993641	−	0.112592i	$-0.964085\pi$
$139$	−82.6116	−	143.087i	−0.594328	−	1.02941i	0.399313	−	0.916815i	$-0.369249\pi$
$140$		0			0
$141$	−30.9753	−	44.9961i	−0.219683	−	0.319121i
$142$		0			0
$143$		−	41.1409i		−	0.287699i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	16.1264	+	202.932i	0.109703	+	1.38049i
$148$		0			0
$149$	−197.430	+	113.986i	−1.32503	+	0.765008i	−0.984527	−	0.175234i	$-0.943932\pi$
$149$	−197.430	+	113.986i	−1.32503	+	0.765008i	−0.340506	+	0.940242i	$0.610598\pi$
$150$		0			0
$151$	86.0019	−	148.960i	0.569549	−	0.986488i	−0.427061	−	0.904223i	$-0.640451\pi$
$151$	86.0019	−	148.960i	0.569549	−	0.986488i	0.996610	−	0.0822653i	$-0.0262155\pi$
$152$		0			0
$153$	−52.7550	+	42.8532i	−0.344804	+	0.280086i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−122.038	−	211.376i	−0.777313	−	1.34634i	−0.933485	−	0.358615i	$-0.883249\pi$
$157$	−122.038	−	211.376i	−0.777313	−	1.34634i	0.156173	−	0.987730i	$-0.450084\pi$
$158$		0			0
$159$	30.6887	−	64.4662i	0.193010	−	0.405448i
$160$		0			0
$161$			86.9887i			0.540303i
$162$		0			0
$163$	192.188			1.17907			0.589534	−	0.807744i	$-0.299311\pi$
$163$	192.188			1.17907			0.589534	+	0.807744i	$0.299311\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−182.728	+	105.498i	−1.09418	+	0.631726i	−0.934687	−	0.355472i	$-0.884320\pi$
$167$	−182.728	+	105.498i	−1.09418	+	0.631726i	−0.159495	+	0.987199i	$0.550987\pi$
$168$		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
$173$	129.730	+	74.8995i	0.749882	+	0.432945i	0.825651	−	0.564181i	$-0.190808\pi$
$173$	129.730	+	74.8995i	0.749882	+	0.432945i	−0.0757690	+	0.997125i	$0.524141\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	204.777	−	16.2729i	1.15693	−	0.0919376i
$178$		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
$183$	−81.0251	+	55.7778i	−0.442760	+	0.304797i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−33.9595	+	58.8197i	−0.181602	+	0.314544i
$188$		0			0
$189$	280.041	+	82.2574i	1.48170	+	0.435225i
$190$		0			0
$191$	−72.3294	−	41.7594i	−0.378688	−	0.218636i	0.298559	−	0.954391i	$-0.403494\pi$
$191$	−72.3294	−	41.7594i	−0.378688	−	0.218636i	−0.677247	+	0.735755i	$0.736827\pi$
$192$		0			0
$193$	41.6094	+	72.0695i	0.215593	+	0.373417i	0.953456	−	0.301533i	$-0.0974984\pi$
$193$	41.6094	+	72.0695i	0.215593	+	0.373417i	−0.737863	+	0.674950i	$0.764165\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			171.229i			0.869183i	0.900628	+	0.434592i	$0.143107\pi$
$197$			171.229i			0.869183i	−0.900628	+	0.434592i	$0.856893\pi$
$198$		0			0
$199$	151.309			0.760348			0.380174	−	0.924915i	$-0.375864\pi$
$199$	151.309			0.760348			0.380174	+	0.924915i	$0.375864\pi$
$200$		0			0
$201$	1.97601	+	24.8658i	0.00983089	+	0.123711i
$202$		0			0
$203$	412.994	−	238.442i	2.03445	−	1.17459i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	67.6522	+	25.8513i	0.326822	+	0.124886i
$208$		0			0
$209$	68.0088	+	39.2649i	0.325401	+	0.187870i
$210$		0			0
$211$	−44.8904	−	77.7525i	−0.212751	−	0.368495i	0.739824	−	0.672801i	$-0.234909\pi$
$211$	−44.8904	−	77.7525i	−0.212751	−	0.368495i	−0.952574	+	0.304306i	$0.901576\pi$
$212$		0			0
$213$	148.908	−	312.805i	0.699100	−	1.46857i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−98.0658			−0.451916
$218$		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
$223$	−46.4357	+	80.4290i	−0.208232	+	0.360668i	−0.951158	−	0.308706i	$-0.900104\pi$
$223$	−46.4357	+	80.4290i	−0.208232	+	0.360668i	0.742926	+	0.669374i	$0.233438\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	192.811	+	111.320i	0.849389	+	0.490395i	0.860445	−	0.509544i	$-0.170186\pi$
$227$	192.811	+	111.320i	0.849389	+	0.490395i	−0.0110555	+	0.999939i	$0.503519\pi$
$228$		0			0
$229$	−92.0380	−	159.414i	−0.401913	−	0.696133i	0.592044	−	0.805906i	$-0.298321\pi$
$229$	−92.0380	−	159.414i	−0.401913	−	0.696133i	−0.993957	+	0.109772i	$0.964988\pi$
$230$		0			0
$231$	290.750	−	23.1050i	1.25866	−	0.100022i
$232$		0			0
$233$		−	56.6725i		−	0.243230i	−0.992577	−	0.121615i	$-0.961193\pi$
$233$		−	56.6725i		−	0.243230i	0.992577	−	0.121615i	$-0.0388073\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−76.7464	+	52.8323i	−0.323824	+	0.222921i
$238$		0			0
$239$	−358.499	+	206.980i	−1.50000	+	0.866024i	−1.00000		2.96133e-6i	$-0.999999\pi$
$239$	−358.499	+	206.980i	−1.50000	+	0.866024i	−0.499997	+	0.866027i	$0.666666\pi$
$240$		0			0
$241$	−58.6707	+	101.621i	−0.243447	+	0.421663i	−0.961694	−	0.274126i	$-0.911612\pi$
$241$	−58.6707	+	101.621i	−0.243447	+	0.421663i	0.718247	+	0.695788i	$0.244945\pi$
$242$		0			0
$243$	147.195	−	193.346i	0.605741	−	0.795662i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−19.9711	−	34.5910i	−0.0808548	−	0.140045i
$248$		0			0
$249$	262.062	+	380.682i	1.05246	+	1.52884i
$250$		0			0
$251$			122.169i			0.486729i	0.969935	+	0.243364i	$0.0782511\pi$
$251$			122.169i			0.486729i	−0.969935	+	0.243364i	$0.921749\pi$
$252$		0			0
$253$	72.3723			0.286057
$254$		0			0
$255$		0			0
$256$		0			0
$257$	250.728	−	144.758i	0.975596	−	0.563260i	0.0746580	−	0.997209i	$-0.476213\pi$
$257$	250.728	−	144.758i	0.975596	−	0.563260i	0.900938	+	0.433949i	$0.142880\pi$
$258$		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
$263$	170.169	+	98.2473i	0.647032	+	0.373564i	0.787318	−	0.616547i	$-0.211469\pi$
$263$	170.169	+	98.2473i	0.647032	+	0.373564i	−0.140286	+	0.990111i	$0.544802\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	168.978	−	354.964i	0.632877	−	1.32946i
$268$		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
$273$	−133.946	−	63.7642i	−0.490646	−	0.233568i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	43.6152	−	75.5437i	0.157456	−	0.272721i	−0.776495	−	0.630124i	$-0.783004\pi$
$277$	43.6152	−	75.5437i	0.157456	−	0.272721i	0.933950	+	0.357403i	$0.116338\pi$
$278$		0			0
$279$	−29.1432	+	76.2670i	−0.104456	+	0.273358i
$280$		0			0
$281$	32.2605	+	18.6256i	0.114806	+	0.0662833i	0.556303	−	0.830979i	$-0.312219\pi$
$281$	32.2605	+	18.6256i	0.114806	+	0.0662833i	−0.441497	+	0.897263i	$0.645553\pi$
$282$		0			0
$283$	229.202	+	396.990i	0.809902	+	1.40279i	0.912931	+	0.408113i	$0.133813\pi$
$283$	229.202	+	396.990i	0.809902	+	1.40279i	−0.103029	+	0.994678i	$0.532854\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			673.613i			2.34708i
$288$		0			0
$289$	231.969			0.802662
$290$		0			0
$291$	−410.857	+	282.834i	−1.41188	+	0.971939i
$292$		0			0
$293$	335.832	−	193.893i	1.14618	−	0.661750i	0.198230	−	0.980156i	$-0.436481\pi$
$293$	335.832	−	193.893i	1.14618	−	0.661750i	0.947954	+	0.318406i	$0.103147\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	68.4360	−	232.986i	0.230424	−	0.784466i
$298$		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
$303$	276.268	+	401.318i	0.911774	+	1.32448i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	34.0128			0.110791			0.0553955	−	0.998464i	$-0.482358\pi$
$307$	34.0128			0.110791			0.0553955	+	0.998464i	$0.482358\pi$
$308$		0			0
$309$	−15.5888	−	196.168i	−0.0504492	−	0.634847i
$310$		0			0
$311$	−465.755	+	268.904i	−1.49760	+	0.864642i	−0.999996	−	0.00276044i	$-0.999121\pi$
$311$	−465.755	+	268.904i	−1.49760	+	0.864642i	−0.497607	+	0.867402i	$0.665788\pi$
$312$		0			0
$313$	−81.7480	+	141.592i	−0.261176	+	0.452370i	−0.966555	−	0.256461i	$-0.917444\pi$
$313$	−81.7480	+	141.592i	−0.261176	+	0.452370i	0.705379	+	0.708830i	$0.250777\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−468.269	−	270.355i	−1.47719	−	0.852856i	−0.477522	−	0.878620i	$-0.658465\pi$
$317$	−468.269	−	270.355i	−1.47719	−	0.852856i	−0.999668	+	0.0257634i	$0.991798\pi$
$318$		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
$323$			65.9403i			0.204150i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	425.728	+	202.665i	1.30192	+	0.619770i
$328$		0			0
$329$	−170.469	+	98.4203i	−0.518143	+	0.299150i
$330$		0			0
$331$	−121.090	+	209.734i	−0.365831	+	0.633638i	−0.988909	−	0.148522i	$-0.952549\pi$
$331$	−121.090	+	209.734i	−0.365831	+	0.633638i	0.623078	+	0.782160i	$0.285882\pi$
$332$		0			0
$333$	−318.475	−	392.063i	−0.956380	−	1.17737i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−165.377	−	286.441i	−0.490732	−	0.849973i	0.509211	−	0.860642i	$-0.329937\pi$
$337$	−165.377	−	286.441i	−0.490732	−	0.849973i	−0.999943	+	0.0106686i	$0.996604\pi$
$338$		0			0
$339$	−68.4862	+	5.44238i	−0.202024	+	0.0160542i
$340$		0			0
$341$			81.5882i			0.239261i
$342$		0			0
$343$	203.849			0.594312
$344$		0			0
$345$		0			0
$346$		0			0
$347$	432.122	−	249.485i	1.24531	−	0.718978i	0.275137	−	0.961405i	$-0.411277\pi$
$347$	432.122	−	249.485i	1.24531	−	0.718978i	0.970170	+	0.242427i	$0.0779433\pi$
$348$		0			0
$349$	144.309	−	249.950i	0.413492	−	0.716190i	−0.581777	−	0.813349i	$-0.697642\pi$
$349$	144.309	−	249.950i	0.413492	−	0.716190i	0.995269	+	0.0971589i	$0.0309755\pi$
$350$		0			0
$351$	−89.3964	+	85.2224i	−0.254691	+	0.242799i
$352$		0			0
$353$	300.999	+	173.782i	0.852687	+	0.492299i	0.861557	−	0.507661i	$-0.169490\pi$
$353$	300.999	+	173.782i	0.852687	+	0.492299i	−0.00886928	+	0.999961i	$0.502823\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	138.871	+	201.730i	0.388994	+	0.565070i
$358$		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
$363$	9.53306	+	119.963i	0.0262619	+	0.330476i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	138.189	−	239.351i	0.376538	−	0.652183i	−0.614018	−	0.789292i	$-0.710448\pi$
$367$	138.189	−	239.351i	0.376538	−	0.652183i	0.990556	+	0.137109i	$0.0437812\pi$
$368$		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
$373$	74.9808	+	129.870i	0.201021	+	0.348178i	0.948858	−	0.315704i	$-0.102241\pi$
$373$	74.9808	+	129.870i	0.201021	+	0.348178i	−0.747837	+	0.663883i	$0.768907\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			201.800i			0.535279i
$378$		0			0
$379$	−385.068			−1.01601			−0.508005	−	0.861354i	$-0.669617\pi$
$379$	−385.068			−1.01601			−0.508005	+	0.861354i	$0.669617\pi$
$380$		0			0
$381$	−269.091	−	128.099i	−0.706274	−	0.336217i
$382$		0			0
$383$	−116.038	+	66.9947i	−0.302972	+	0.174921i	−0.643777	−	0.765213i	$-0.722634\pi$
$383$	−116.038	+	66.9947i	−0.302972	+	0.174921i	0.340805	+	0.940134i	$0.389300\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−356.388	+	57.0021i	−0.920901	+	0.147292i
$388$		0			0
$389$	360.786	+	208.300i	0.927470	+	0.535475i	0.886011	−	0.463665i	$-0.153466\pi$
$389$	360.786	+	208.300i	0.927470	+	0.535475i	0.0414597	+	0.999140i	$0.486799\pi$
$390$		0			0
$391$	30.3850	+	52.6284i	0.0777110	+	0.134599i
$392$		0			0
$393$	−21.4796	+	1.70691i	−0.0546554	+	0.00434329i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	414.289			1.04355			0.521775	−	0.853083i	$-0.325270\pi$
$397$	414.289			1.04355			0.521775	+	0.853083i	$0.325270\pi$
$398$		0			0
$399$	233.245	−	160.566i	0.584574	−	0.402421i
$400$		0			0
$401$	−210.716	+	121.657i	−0.525476	+	0.303384i	−0.739172	−	0.673516i	$-0.764783\pi$
$401$	−210.716	+	121.657i	−0.525476	+	0.303384i	0.213696	+	0.976900i	$0.431450\pi$
$402$		0			0
$403$	20.7489	−	35.9382i	0.0514862	−	0.0891767i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−437.134	−	252.379i	−1.07404	−	0.620097i
$408$		0			0
$409$	308.993	+	535.191i	0.755483	+	1.30854i	0.945134	+	0.326684i	$0.105931\pi$
$409$	308.993	+	535.191i	0.755483	+	1.30854i	−0.189650	+	0.981852i	$0.560735\pi$
$410$		0			0
$411$	427.863	+	621.531i	1.04103	+	1.51224i
$412$		0			0
$413$		−	740.209i		−	1.79227i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	39.2655	+	494.112i	0.0941618	+	1.18492i
$418$		0			0
$419$	−601.137	+	347.066i	−1.43469	+	0.828321i	−0.997474	−	0.0710339i	$-0.977370\pi$
$419$	−601.137	+	347.066i	−1.43469	+	0.828321i	−0.437220	+	0.899355i	$0.644037\pi$
$420$		0			0
$421$	56.2394	−	97.4094i	0.133585	−	0.231376i	−0.791471	−	0.611207i	$-0.790684\pi$
$421$	56.2394	−	97.4094i	0.133585	−	0.231376i	0.925056	+	0.379831i	$0.124018\pi$
$422$		0			0
$423$	25.8828	+	161.824i	0.0611886	+	0.382564i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	177.227	+	306.966i	0.415051	+	0.718890i
$428$		0			0
$429$	−53.0501	+	111.440i	−0.123660	+	0.259767i
$430$		0			0
$431$		−	419.462i		−	0.973229i	−0.873617	−	0.486615i	$-0.838232\pi$
$431$		−	419.462i		−	0.973229i	0.873617	−	0.486615i	$-0.161768\pi$
$432$		0			0
$433$	21.7422			0.0502129			0.0251065	−	0.999685i	$-0.492008\pi$
$433$	21.7422			0.0502129			0.0251065	+	0.999685i	$0.492008\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	60.8502	−	35.1319i	0.139245	−	0.0803934i
$438$		0			0
$439$	−348.778	+	604.101i	−0.794483	+	1.37608i	0.128684	+	0.991686i	$0.458925\pi$
$439$	−348.778	+	604.101i	−0.794483	+	1.37608i	−0.923167	+	0.384399i	$0.874409\pi$
$440$		0			0
$441$	217.994	−	570.485i	0.494317	−	1.29362i
$442$		0			0
$443$	−193.609	−	111.780i	−0.437040	−	0.252325i	0.265301	−	0.964166i	$-0.414529\pi$
$443$	−193.609	−	111.780i	−0.437040	−	0.252325i	−0.702341	+	0.711840i	$0.747862\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	681.768	−	54.1779i	1.52521	−	0.121203i
$448$		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
$453$	−425.036	+	292.595i	−0.938270	+	0.645906i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	334.483	−	579.342i	0.731910	−	1.26771i	−0.224155	−	0.974553i	$-0.571962\pi$
$457$	334.483	−	579.342i	0.731910	−	1.26771i	0.956066	−	0.293153i	$-0.0947044\pi$
$458$		0			0
$459$	198.158	−	48.0517i	0.431716	−	0.104688i
$460$		0			0
$461$	0.222592	+	0.128513i	0.000482846	+	0.000278771i	0.500241	−	0.865886i	$-0.333245\pi$
$461$	0.222592	+	0.128513i	0.000482846	+	0.000278771i	−0.499759	+	0.866165i	$0.666578\pi$
$462$		0			0
$463$	−278.199	−	481.854i	−0.600861	−	1.04072i	−0.992691	−	0.120684i	$-0.961491\pi$
$463$	−278.199	−	481.854i	−0.600861	−	1.04072i	0.391830	−	0.920038i	$-0.371842\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			357.378i			0.765262i	0.923901	+	0.382631i	$0.124982\pi$
$467$			357.378i			0.765262i	−0.923901	+	0.382631i	$0.875018\pi$
$468$		0			0
$469$	89.8828			0.191648
$470$		0			0
$471$	58.0050	+	729.927i	0.123153	+	1.54974i
$472$		0			0
$473$	−312.345	+	180.332i	−0.660349	+	0.381253i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−166.255	+	135.050i	−0.348543	+	0.283123i
$478$		0			0
$479$	350.791	+	202.529i	0.732341	+	0.422817i	0.819278	−	0.573397i	$-0.194375\pi$
$479$	350.791	+	202.529i	0.732341	+	0.422817i	−0.0869370	+	0.996214i	$0.527708\pi$
$480$		0			0
$481$	128.367	+	222.338i	0.266875	+	0.462241i
$482$		0			0
$483$	112.170	−	235.630i	0.232235	−	0.487846i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−586.853			−1.20504			−0.602518	−	0.798105i	$-0.705836\pi$
$487$	−586.853			−1.20504			−0.602518	+	0.798105i	$0.705836\pi$
$488$		0			0
$489$	−520.587	−	247.822i	−1.06459	−	0.506792i
$490$		0			0
$491$	304.133	−	175.591i	0.619415	−	0.357619i	−0.157226	−	0.987563i	$-0.550255\pi$
$491$	304.133	−	175.591i	0.619415	−	0.357619i	0.776641	+	0.629943i	$0.216922\pi$
$492$		0			0
$493$	166.575	−	288.516i	0.337880	−	0.585226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1081.10	−	624.172i	−2.17525	−	1.25588i
$498$		0			0
$499$	−481.765	−	834.442i	−0.965461	−	1.67223i	−0.708370	−	0.705841i	$-0.750569\pi$
$499$	−481.765	−	834.442i	−0.965461	−	1.67223i	−0.257091	−	0.966387i	$-0.582764\pi$
$500$		0			0
$501$	631.001	−	50.1436i	1.25948	−	0.100087i
$502$		0			0
$503$			858.481i			1.70672i	0.521321	+	0.853361i	$0.325439\pi$
$503$			858.481i			1.70672i	−0.521321	+	0.853361i	$0.674561\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−365.905	+	251.890i	−0.721707	+	0.496824i
$508$		0			0
$509$	437.729	−	252.723i	0.859978	−	0.496508i	−0.00402718	−	0.999992i	$-0.501282\pi$
$509$	437.729	−	252.723i	0.859978	−	0.496508i	0.864005	+	0.503484i	$0.167949\pi$
$510$		0			0
$511$	677.249	−	1173.03i	1.32534	−	2.29556i
$512$		0			0
$513$	−55.5586	−	229.115i	−0.108301	−	0.446617i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	81.8831	+	141.826i	0.158381	+	0.274324i
$518$		0			0
$519$	−254.823	−	370.166i	−0.490988	−	0.713229i
$520$		0			0
$521$			640.397i			1.22917i	0.788851	+	0.614585i	$0.210676\pi$
$521$			640.397i			1.22917i	−0.788851	+	0.614585i	$0.789324\pi$
$522$		0			0
$523$	−91.8967			−0.175711			−0.0878553	−	0.996133i	$-0.528001\pi$
$523$	−91.8967			−0.175711			−0.0878553	+	0.996133i	$0.528001\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−59.3300	+	34.2542i	−0.112581	+	0.0649985i
$528$		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
$533$	−246.859	−	142.524i	−0.463150	−	0.267400i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−75.1523	+	157.869i	−0.139948	+	0.293983i
$538$		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
$543$	72.5134	+	34.5195i	0.133542	+	0.0635718i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−411.406	+	712.576i	−0.752113	+	1.30270i	0.194683	+	0.980866i	$0.437632\pi$
$547$	−411.406	+	712.576i	−0.752113	+	1.30270i	−0.946797	+	0.321832i	$0.895701\pi$
$548$		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
$553$	167.868	+	290.756i	0.303559	+	0.525779i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			111.213i			0.199665i	0.995004	+	0.0998323i	$0.0318306\pi$
$557$			111.213i			0.199665i	−0.995004	+	0.0998323i	$0.968169\pi$
$558$		0			0
$559$	183.444			0.328164
$560$		0			0
$561$	167.834	−	115.537i	0.299169	−	0.205948i
$562$		0			0
$563$	188.423	−	108.786i	0.334677	−	0.193226i	−0.323239	−	0.946317i	$-0.604772\pi$
$563$	188.423	−	108.786i	0.334677	−	0.193226i	0.657916	+	0.753092i	$0.271438\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−652.487	−	583.919i	−1.15077	−	1.02984i
$568$		0			0
$569$	−141.705	−	81.8136i	−0.249043	−	0.143785i	0.370283	−	0.928919i	$-0.379261\pi$
$569$	−141.705	−	81.8136i	−0.249043	−	0.143785i	−0.619326	+	0.785134i	$0.712594\pi$
$570$		0			0
$571$	380.199	+	658.524i	0.665848	+	1.15328i	0.979055	+	0.203598i	$0.0652635\pi$
$571$	380.199	+	658.524i	0.665848	+	1.15328i	−0.313207	+	0.949685i	$0.601403\pi$
$572$		0			0
$573$	142.074	+	206.382i	0.247947	+	0.360178i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	26.9318			0.0466756			0.0233378	−	0.999728i	$-0.492571\pi$
$577$	26.9318			0.0466756			0.0233378	+	0.999728i	$0.492571\pi$
$578$		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
$583$	−107.022	+	185.367i	−0.183571	+	0.317954i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	428.807	+	247.572i	0.730506	+	0.421758i	0.818607	−	0.574354i	$-0.194747\pi$
$587$	428.807	+	247.572i	0.730506	+	0.421758i	−0.0881015	+	0.996112i	$0.528080\pi$
$588$		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
$593$			102.991i			0.173678i	0.996222	+	0.0868392i	$0.0276766\pi$
$593$			102.991i			0.173678i	−0.996222	+	0.0868392i	$0.972323\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−409.857	−	195.109i	−0.686528	−	0.326817i
$598$		0			0
$599$	−492.666	+	284.441i	−0.822481	+	0.474860i	−0.851271	−	0.524726i	$-0.824168\pi$
$599$	−492.666	+	284.441i	−0.822481	+	0.474860i	0.0287900	+	0.999585i	$0.490835\pi$
$600$		0			0
$601$	−445.951	+	772.410i	−0.742016	+	1.28521i	0.209561	+	0.977796i	$0.432797\pi$
$601$	−445.951	+	772.410i	−0.742016	+	1.28521i	−0.951576	+	0.307413i	$0.900537\pi$
$602$		0			0
$603$	26.7114	−	69.9030i	0.0442975	−	0.115925i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−206.061	−	356.909i	−0.339475	−	0.587988i	0.644859	−	0.764301i	$-0.276916\pi$
$607$	−206.061	−	356.909i	−0.339475	−	0.587988i	−0.984334	+	0.176314i	$0.943583\pi$
$608$		0			0
$609$	−1426.16	+	113.332i	−2.34180	+	0.186096i
$610$		0			0
$611$		−	83.2958i		−	0.136327i
$612$		0			0
$613$	−994.307			−1.62203			−0.811017	−	0.585023i	$-0.801086\pi$
$613$	−994.307			−1.62203			−0.811017	+	0.585023i	$0.801086\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	589.215	−	340.183i	0.954967	−	0.551351i	0.0603468	−	0.998177i	$-0.480779\pi$
$617$	589.215	−	340.183i	0.954967	−	0.551351i	0.894620	+	0.446827i	$0.147446\pi$
$618$		0			0
$619$	371.748	−	643.887i	0.600563	−	1.04021i	−0.392173	−	0.919891i	$-0.628277\pi$
$619$	371.748	−	643.887i	0.600563	−	1.04021i	0.992736	−	0.120314i	$-0.0383901\pi$
$620$		0			0
$621$	−149.918	−	157.260i	−0.241413	−	0.253237i
$622$		0			0
$623$	−1226.81	−	708.298i	−1.96919	−	1.13692i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−133.587	−	194.054i	−0.213057	−	0.309496i
$628$		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
$633$	21.3365	+	268.496i	0.0337070	+	0.424165i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−155.204	+	268.821i	−0.243648	+	0.422011i
$638$		0			0
$639$	−806.707	+	655.292i	−1.26245	+	1.02550i
$640$		0			0
$641$	446.198	+	257.613i	0.696097	+	0.401892i	0.805892	−	0.592062i	$-0.201686\pi$
$641$	446.198	+	257.613i	0.696097	+	0.401892i	−0.109795	+	0.993954i	$0.535019\pi$
$642$		0			0
$643$	−341.339	−	591.217i	−0.530854	−	0.919466i	−0.999352	−	0.0360013i	$-0.988538\pi$
$643$	−341.339	−	591.217i	−0.530854	−	0.919466i	0.468498	−	0.883465i	$-0.344795\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			740.660i			1.14476i	0.819988	+	0.572380i	$0.193980\pi$
$647$			740.660i			1.14476i	−0.819988	+	0.572380i	$0.806020\pi$
$648$		0			0
$649$	−615.834			−0.948897
$650$		0			0
$651$	265.634	+	126.453i	0.408041	+	0.194245i
$652$		0			0
$653$	−268.904	+	155.252i	−0.411797	+	0.237751i	−0.691562	−	0.722317i	$-0.743077\pi$
$653$	−268.904	+	155.252i	−0.411797	+	0.237751i	0.279764	+	0.960069i	$0.409744\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−711.015	−	875.305i	−1.08221	−	1.33228i
$658$		0			0
$659$	218.218	+	125.988i	0.331135	+	0.191181i	0.656345	−	0.754461i	$-0.272102\pi$
$659$	218.218	+	125.988i	0.331135	+	0.191181i	−0.325210	+	0.945642i	$0.605435\pi$
$660$		0			0
$661$	−154.032	−	266.791i	−0.233029	−	0.403618i	0.725669	−	0.688044i	$-0.241530\pi$
$661$	−154.032	−	266.791i	−0.233029	−	0.403618i	−0.958698	+	0.284426i	$0.908197\pi$
$662$		0			0
$663$	−103.311	+	8.20976i	−0.155823	+	0.0123827i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−354.994			−0.532224
$668$		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
$673$	−352.456	+	610.473i	−0.523709	+	0.907091i	0.475910	+	0.879494i	$0.342119\pi$
$673$	−352.456	+	610.473i	−0.523709	+	0.907091i	−0.999619	+	0.0275972i	$0.991214\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	213.117	+	123.043i	0.314797	+	0.181748i	0.649071	−	0.760728i	$-0.275158\pi$
$677$	213.117	+	123.043i	0.314797	+	0.181748i	−0.334274	+	0.942476i	$0.608491\pi$
$678$		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
$683$			430.637i			0.630507i	0.949007	+	0.315254i	$0.102090\pi$
$683$			430.637i			0.630507i	−0.949007	+	0.315254i	$0.897910\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	43.7459	+	550.493i	0.0636767	+	0.801299i
$688$		0			0
$689$	94.2827	−	54.4342i	0.136840	−	0.0790046i
$690$		0			0
$691$	−244.885	+	424.153i	−0.354392	+	0.613825i	−0.987014	−	0.160636i	$-0.948645\pi$
$691$	−244.885	+	424.153i	−0.354392	+	0.613825i	0.632622	+	0.774461i	$0.281979\pi$
$692$		0			0
$693$	−817.359	−	312.329i	−1.17945	−	0.450692i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	235.292	+	407.537i	0.337578	+	0.584702i
$698$		0			0
$699$	−73.0777	+	153.511i	−0.104546	+	0.219615i
$700$		0			0
$701$			1398.45i			1.99494i	0.0711109	+	0.997468i	$0.477346\pi$
$701$			1398.45i			1.99494i	−0.0711109	+	0.997468i	$0.522654\pi$
$702$		0			0
$703$	−490.053			−0.697088
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1520.40	−	877.806i	2.15050	−	1.24159i
$708$		0			0
$709$	−615.327	+	1065.78i	−0.867880	+	1.50321i	−0.00372210	+	0.999993i	$0.501185\pi$
$709$	−615.327	+	1065.78i	−0.867880	+	1.50321i	−0.864158	+	0.503220i	$0.832149\pi$
$710$		0			0
$711$	276.012	−	44.1463i	0.388202	−	0.0620904i
$712$		0			0
$713$	63.2201	+	36.5001i	0.0886678	+	0.0511924i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1237.98	−	98.3779i	1.72660	−	0.137208i
$718$		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
$723$	289.961	−	199.609i	0.401052	−	0.276085i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−462.719	+	801.453i	−0.636477	+	1.10241i	0.349723	+	0.936853i	$0.386276\pi$
$727$	−462.719	+	801.453i	−0.636477	+	1.10241i	−0.986200	+	0.165558i	$0.947058\pi$
$728$		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
$733$	−312.852	−	541.875i	−0.426810	−	0.739257i	0.569777	−	0.821799i	$-0.307029\pi$
$733$	−312.852	−	541.875i	−0.426810	−	0.739257i	−0.996588	+	0.0825420i	$0.973696\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	74.7801i		−	0.101466i
$738$		0			0
$739$	487.290			0.659392			0.329696	−	0.944087i	$-0.393054\pi$
$739$	487.290			0.659392			0.329696	+	0.944087i	$0.393054\pi$
$740$		0			0
$741$	9.49233	+	119.450i	0.0128102	+	0.161201i
$742$		0			0
$743$	−525.224	+	303.238i	−0.706897	+	0.408127i	−0.809911	−	0.586553i	$-0.800485\pi$
$743$	−525.224	+	303.238i	−0.706897	+	0.408127i	0.103014	+	0.994680i	$0.467151\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−218.977	−	1369.09i	−0.293142	−	1.83278i
$748$		0			0
$749$	107.020	+	61.7877i	0.142883	+	0.0824937i
$750$		0			0
$751$	−174.790	−	302.746i	−0.232744	−	0.403124i	0.725871	−	0.687831i	$-0.241437\pi$
$751$	−174.790	−	302.746i	−0.232744	−	0.403124i	−0.958615	+	0.284707i	$0.908104\pi$
$752$		0			0
$753$	157.534	−	330.923i	0.209208	−	0.439473i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−242.544			−0.320402			−0.160201	−	0.987084i	$-0.551214\pi$
$757$	−242.544			−0.320402			−0.160201	+	0.987084i	$0.551214\pi$
$758$		0			0
$759$	−196.038	−	93.3223i	−0.258284	−	0.122954i
$760$		0			0
$761$	1023.42	−	590.870i	1.34483	−	0.776439i	0.357319	−	0.933982i	$-0.383691\pi$
$761$	1023.42	−	590.870i	1.34483	−	0.776439i	0.987512	+	0.157543i	$0.0503574\pi$
$762$		0			0
$763$	849.500	−	1471.38i	1.11337	−	1.92841i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	271.265	+	156.615i	0.353670	+	0.204191i
$768$		0			0
$769$	−219.654	−	380.451i	−0.285635	−	0.494735i	0.687128	−	0.726537i	$-0.258871\pi$
$769$	−219.654	−	380.451i	−0.285635	−	0.494735i	−0.972763	+	0.231802i	$0.925538\pi$
$770$		0			0
$771$	−865.818	+	68.8038i	−1.12298	+	0.0892397i
$772$		0			0
$773$			1157.27i			1.49711i	0.663072	+	0.748556i	$0.269252\pi$
$773$			1157.27i			1.49711i	−0.663072	+	0.748556i	$0.730748\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1499.21	+	1032.06i	−1.92948	+	1.32826i
$778$		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
$783$	−335.686	+	1142.82i	−0.428717	+	1.45954i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	588.108	+	1018.63i	0.747279	+	1.29432i	0.949122	+	0.314907i	$0.101973\pi$
$787$	588.108	+	1018.63i	0.747279	+	1.29432i	−0.201844	+	0.979418i	$0.564693\pi$
$788$		0			0
$789$	−334.257	−	485.555i	−0.423646	−	0.615406i
$790$		0			0
$791$			247.558i			0.312968i
$792$		0			0
$793$	−149.992			−0.189145
$794$		0			0
$795$		0			0
$796$		0			0
$797$	18.9845	−	10.9607i	0.0238200	−	0.0137525i	−0.488043	−	0.872820i	$-0.662289\pi$
$797$	18.9845	−	10.9607i	0.0238200	−	0.0137525i	0.511863	+	0.859067i	$0.328956\pi$
$798$		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
$803$	−975.929	−	563.453i	−1.21535	−	0.701685i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	328.747	−	690.583i	0.407369	−	0.855741i
$808$		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
$813$	376.889	+	179.415i	0.463578	+	0.220683i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−175.079	+	303.245i	−0.214294	+	0.371169i
$818$		0			0
$819$	280.603	+	345.441i	0.342617	+	0.421784i
$820$		0			0
$821$	−814.987	−	470.533i	−0.992676	−	0.573122i	−0.0866031	−	0.996243i	$-0.527601\pi$
$821$	−814.987	−	470.533i	−0.992676	−	0.573122i	−0.906073	+	0.423121i	$0.860935\pi$
$822$		0			0
$823$	144.349	+	250.019i	0.175393	+	0.303790i	0.940297	−	0.340354i	$-0.110547\pi$
$823$	144.349	+	250.019i	0.175393	+	0.303790i	−0.764904	+	0.644144i	$0.777214\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	853.621i		−	1.03219i	−0.856531	−	0.516095i	$-0.827385\pi$
$827$		−	853.621i		−	1.03219i	0.856531	−	0.516095i	$-0.172615\pi$
$828$		0			0
$829$	−13.6812			−0.0165033			−0.00825164	−	0.999966i	$-0.502627\pi$
$829$	−13.6812			−0.0165033			−0.00825164	+	0.999966i	$0.502627\pi$
$830$		0			0
$831$	−215.554	+	148.387i	−0.259391	+	0.178565i
$832$		0			0
$833$	443.794	−	256.225i	0.532766	−	0.307593i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	177.286	−	169.008i	0.211811	−	0.201921i
$838$		0			0
$839$	102.968	+	59.4488i	0.122727	+	0.0708567i	0.560107	−	0.828420i	$-0.310760\pi$
$839$	102.968	+	59.4488i	0.122727	+	0.0708567i	−0.437380	+	0.899277i	$0.644093\pi$
$840$		0			0
$841$	552.563	+	957.067i	0.657031	+	1.13801i
$842$		0			0
$843$	−63.3679	−	92.0509i	−0.0751696	−	0.109194i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	433.631			0.511961
$848$		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
$853$	−333.265	+	577.231i	−0.390697	+	0.676707i	−0.992542	−	0.121906i	$-0.961099\pi$
$853$	−333.265	+	577.231i	−0.390697	+	0.676707i	0.601845	+	0.798613i	$0.294433\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−530.304	−	306.171i	−0.618791	−	0.357259i	0.157607	−	0.987502i	$-0.449622\pi$
$857$	−530.304	−	306.171i	−0.618791	−	0.357259i	−0.776398	+	0.630243i	$0.782955\pi$
$858$		0			0
$859$	665.233	+	1152.22i	0.774427	+	1.34135i	0.935116	+	0.354342i	$0.115295\pi$
$859$	665.233	+	1152.22i	0.774427	+	1.34135i	−0.160689	+	0.987005i	$0.551372\pi$
$860$		0			0
$861$	868.606	−	1824.64i	1.00883	−	2.11921i
$862$		0			0
$863$			1042.02i			1.20744i	0.797197	+	0.603719i	$0.206315\pi$
$863$			1042.02i			1.20744i	−0.797197	+	0.603719i	$0.793685\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−628.344	−	299.118i	−0.724733	−	0.345004i
$868$		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
$873$	1477.61	−	236.334i	1.69257	−	0.270715i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−111.854	−	193.736i	−0.127541	−	0.220908i	0.795182	−	0.606371i	$-0.207375\pi$
$877$	−111.854	−	193.736i	−0.127541	−	0.220908i	−0.922723	+	0.385463i	$0.874042\pi$
$878$		0			0
$879$	−1159.70	+	92.1576i	−1.31934	+	0.104844i
$880$		0			0
$881$		−	447.183i		−	0.507586i	−0.967259	−	0.253793i	$-0.918322\pi$
$881$		−	447.183i		−	0.507586i	0.967259	−	0.253793i	$-0.0816782\pi$
$882$		0			0
$883$	1028.50			1.16478			0.582389	−	0.812910i	$-0.302118\pi$
$883$	1028.50			1.16478			0.582389	+	0.812910i	$0.302118\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	395.428	−	228.301i	0.445804	−	0.257385i	−0.260252	−	0.965541i	$-0.583806\pi$
$887$	395.428	−	228.301i	0.445804	−	0.257385i	0.706057	+	0.708155i	$0.250472\pi$
$888$		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
$893$	137.694	+	79.4975i	0.154192	+	0.0890230i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	62.6182	+	90.9618i	0.0698085	+	0.101407i
$898$		0			0
$899$		−	400.198i		−	0.445159i
$900$		0			0
$901$	−179.730			−0.199478
$902$		0			0
$903$	103.023	+	1296.43i	0.114090	+	1.43569i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	191.354	−	331.435i	0.210975	−	0.365419i	−0.741045	−	0.671455i	$-0.765670\pi$
$907$	191.354	−	331.435i	0.210975	−	0.365419i	0.952020	+	0.306036i	$0.0990030\pi$
$908$		0			0
$909$	−230.847	−	1443.30i	−0.253957	−	1.58779i
$910$		0			0
$911$	−1556.93	−	898.893i	−1.70903	−	0.986710i	−0.935761	−	0.352636i	$-0.885286\pi$
$911$	−1556.93	−	898.893i	−1.70903	−	0.986710i	−0.773272	−	0.634075i	$-0.781381\pi$
$912$		0			0
$913$	−692.758	−	1199.89i	−0.758771	−	1.31423i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			77.6425i			0.0846702i
$918$		0			0
$919$	−888.894			−0.967240			−0.483620	−	0.875278i	$-0.660678\pi$
$919$	−888.894			−0.967240			−0.483620	+	0.875278i	$0.660678\pi$
$920$		0			0
$921$	−92.1318	−	43.8587i	−0.100035	−	0.0476207i
$922$		0			0
$923$	457.481	−	264.127i	0.495646	−	0.286161i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−210.727	+	551.468i	−0.227322	+	0.594895i
$928$		0			0
$929$	1525.09	+	880.512i	1.64165	+	0.947807i	0.980247	+	0.197775i	$0.0633715\pi$
$929$	1525.09	+	880.512i	1.64165	+	0.947807i	0.661402	+	0.750032i	$0.269962\pi$
$930$		0			0
$931$	−296.254	−	513.126i	−0.318210	−	0.551156i
$932$		0			0
$933$	1608.35	−	127.811i	1.72385	−	0.136989i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1536.39			1.63969			0.819843	−	0.572588i	$-0.194060\pi$
$937$	1536.39			1.63969			0.819843	+	0.572588i	$0.194060\pi$
$938$		0			0
$939$	404.013	−	278.123i	0.430258	−	0.296190i
$940$		0			0
$941$	1324.15	−	764.496i	1.40717	−	0.812429i	0.412055	−	0.911159i	$-0.364811\pi$
$941$	1324.15	−	764.496i	1.40717	−	0.812429i	0.995114	+	0.0987296i	$0.0314779\pi$
$942$		0			0
$943$	250.719	−	434.258i	0.265874	−	0.460507i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−862.884	−	498.186i	−0.911176	−	0.526068i	−0.0303669	−	0.999539i	$-0.509668\pi$
$947$	−862.884	−	498.186i	−0.911176	−	0.526068i	−0.880809	+	0.473471i	$0.843001\pi$
$948$		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
$953$			1005.97i			1.05559i	0.849373	+	0.527794i	$0.176981\pi$
$953$			1005.97i			1.05559i	−0.849373	+	0.527794i	$0.823019\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	94.2894	+	1186.53i	0.0985260	+	1.23984i
$958$		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
$963$	79.8572	−	64.8684i	0.0829254	−	0.0673607i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−322.316	−	558.267i	−0.333315	−	0.577319i	0.649844	−	0.760067i	$-0.274834\pi$
$967$	−322.316	−	558.267i	−0.333315	−	0.577319i	−0.983160	+	0.182748i	$0.941501\pi$
$968$		0			0
$969$	85.0283	−	178.615i	0.0877485	−	0.184329i
$970$		0			0
$971$			215.087i			0.221511i	0.993848	+	0.110756i	$0.0353271\pi$
$971$			215.087i			0.221511i	−0.993848	+	0.110756i	$0.964673\pi$
$972$		0			0
$973$	1786.07			1.83563
$974$		0			0
$975$		0			0
$976$		0			0
$977$	53.1017	−	30.6583i	0.0543518	−	0.0313800i	−0.472578	−	0.881289i	$-0.656676\pi$
$977$	53.1017	−	30.6583i	0.0543518	−	0.0313800i	0.526930	+	0.849909i	$0.323343\pi$
$978$		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
$983$	−1005.33	−	580.428i	−1.02272	−	0.590466i	−0.107827	−	0.994170i	$-0.534389\pi$
$983$	−1005.33	−	580.428i	−1.02272	−	0.590466i	−0.914890	+	0.403704i	$0.867723\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	588.666	−	46.7794i	0.596420	−	0.0473956i
$988$		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
$993$	598.448	−	411.972i	0.602667	−	0.414876i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	51.5429	−	89.2750i	0.0516980	−	0.0895436i	−0.839018	−	0.544103i	$-0.816870\pi$
$997$	51.5429	−	89.2750i	0.0516980	−	0.0895436i	0.890716	+	0.454560i	$0.150203\pi$
$998$		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.p.e.101.2	yes	16
3.2	odd	2		2700.3.p.d.1601.1		16
5.2	odd	4		900.3.u.d.749.6		32
5.3	odd	4		900.3.u.d.749.11		32
5.4	even	2		900.3.p.d.101.7	✓	16
9.4	even	3		2700.3.p.d.2501.1		16
9.5	odd	6	inner	900.3.p.e.401.2	yes	16
15.2	even	4		2700.3.u.d.2249.1		32
15.8	even	4		2700.3.u.d.2249.16		32
15.14	odd	2		2700.3.p.e.1601.8		16
45.4	even	6		2700.3.p.e.2501.8		16
45.13	odd	12		2700.3.u.d.449.1		32
45.14	odd	6		900.3.p.d.401.7	yes	16
45.22	odd	12		2700.3.u.d.449.16		32
45.23	even	12		900.3.u.d.149.6		32
45.32	even	12		900.3.u.d.149.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.7	✓	16	5.4	even	2
900.3.p.d.401.7	yes	16	45.14	odd	6
900.3.p.e.101.2	yes	16	1.1	even	1	trivial
900.3.p.e.401.2	yes	16	9.5	odd	6	inner
900.3.u.d.149.6		32	45.23	even	12
900.3.u.d.149.11		32	45.32	even	12
900.3.u.d.749.6		32	5.2	odd	4
900.3.u.d.749.11		32	5.3	odd	4
2700.3.p.d.1601.1		16	3.2	odd	2
2700.3.p.d.2501.1		16	9.4	even	3
2700.3.p.e.1601.8		16	15.14	odd	2
2700.3.p.e.2501.8		16	45.4	even	6
2700.3.u.d.449.1		32	45.13	odd	12
2700.3.u.d.449.16		32	45.22	odd	12
2700.3.u.d.2249.1		32	15.2	even	4
2700.3.u.d.2249.16		32	15.8	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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.70874 - 1.28947i) q^{3} +(-5.40503 + 9.36178i) q^{7} +(5.67451 + 6.98569i) q^{9} +O(q^{10})\)	\(q+(-2.70874 - 1.28947i) q^{3} +(-5.40503 + 9.36178i) q^{7} +(5.67451 + 6.98569i) q^{9} +(7.78876 + 4.49684i) q^{11} +(-2.28721 - 3.96157i) q^{13} +7.55187i q^{17} +8.73166 q^{19} +(26.7126 - 18.3890i) q^{21} +(6.96892 - 4.02351i) q^{23} +(-6.36289 - 26.2395i) q^{27} +(-38.2046 - 22.0575i) q^{29} +(4.53586 + 7.85634i) q^{31} +(-15.2991 - 22.2242i) q^{33} -56.1237 q^{37} +(1.08712 + 13.6801i) q^{39} +(53.9651 - 31.1568i) q^{41} +(-20.0510 + 34.7294i) q^{43} +(15.7695 + 9.10452i) q^{47} +(-33.9287 - 58.7662i) q^{49} +(9.73794 - 20.4560i) q^{51} +23.7994i q^{53} +(-23.6518 - 11.2592i) q^{57} +(-59.3003 + 34.2370i) q^{59} +(16.3946 - 28.3963i) q^{61} +(-96.0695 + 15.3657i) q^{63} +(-4.15737 - 7.20078i) q^{67} +(-24.0652 + 1.91238i) q^{69} +115.480i q^{71} -125.300 q^{73} +(-84.1969 + 48.6111i) q^{77} +(15.5289 - 26.8968i) q^{79} +(-16.5998 + 79.2808i) q^{81} +(-133.415 - 77.0272i) q^{83} +(75.0438 + 109.012i) q^{87} +131.044i q^{89} +49.4498 q^{91} +(-2.15590 - 27.1296i) q^{93} +(83.1329 - 143.990i) q^{97} +(12.7839 + 79.9272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - q^{7} + 14 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 - q^7 + 14 * q^9	\( 16 q + 2 q^{3} - q^{7} + 14 q^{9} - 10 q^{13} + 2 q^{19} + q^{21} + 27 q^{23} - 16 q^{27} + 9 q^{29} + 8 q^{31} + 36 q^{33} - 22 q^{37} + 19 q^{39} + 54 q^{41} + 44 q^{43} - 108 q^{47} - 45 q^{49} + 90 q^{51} - 68 q^{57} + 9 q^{59} - 55 q^{61} - 107 q^{63} - 28 q^{67} - 147 q^{69} + 86 q^{73} + 342 q^{77} + 11 q^{79} - 130 q^{81} - 306 q^{83} + 375 q^{87} - 134 q^{91} - 83 q^{93} + 41 q^{97} + 252 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - q^7 + 14 * q^9 - 10 * q^13 + 2 * q^19 + q^21 + 27 * q^23 - 16 * q^27 + 9 * q^29 + 8 * q^31 + 36 * q^33 - 22 * q^37 + 19 * q^39 + 54 * q^41 + 44 * q^43 - 108 * q^47 - 45 * q^49 + 90 * q^51 - 68 * q^57 + 9 * q^59 - 55 * q^61 - 107 * q^63 - 28 * q^67 - 147 * q^69 + 86 * q^73 + 342 * q^77 + 11 * q^79 - 130 * q^81 - 306 * q^83 + 375 * q^87 - 134 * q^91 - 83 * q^93 + 41 * q^97 + 252 * q^99

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