LMFDB - Embedded newform 900.3.p.d.401.7

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			401.7
Root			$2.47109 + 1.70110i$ of defining polynomial
Character	$\chi$	$=$	900.401
Dual form			900.3.p.d.101.7

$q$-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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.70874	−	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	0.936384	+	0.350977i	$0.114150\pi$
$7$	5.40503	+	9.36178i	0.772147	+	1.33740i	−0.164237	+	0.986421i	$0.552516\pi$
$8$		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
$13$	2.28721	−	3.96157i	0.175939	−	0.304736i	−0.764547	−	0.644568i	$-0.777037\pi$
$13$	2.28721	−	3.96157i	0.175939	−	0.304736i	0.940486	+	0.339833i	$0.110370\pi$
$14$		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	$-0.389305\pi$
$23$	−6.96892	−	4.02351i	−0.302997	−	0.174935i	−0.643788	+	0.765204i	$0.722638\pi$
$24$		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	−0.983310	−	0.181939i	$-0.941763\pi$
$29$	−38.2046	+	22.0575i	−1.31740	+	0.760602i	−0.334092	+	0.942541i	$0.608429\pi$
$30$		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
$33$	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	$-0.225968\pi$
$37$	56.1237			1.51686			0.758428	+	0.651756i	$0.225968\pi$
$38$		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
$43$	20.0510	+	34.7294i	0.466303	+	0.807660i	0.999259	−	0.0384827i	$-0.0122524\pi$
$43$	20.0510	+	34.7294i	0.466303	+	0.807660i	−0.532957	+	0.846143i	$0.678919\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−15.7695	+	9.10452i	−0.335521	+	0.193713i	−0.658290	−	0.752765i	$-0.728720\pi$
$47$	−15.7695	+	9.10452i	−0.335521	+	0.193713i	0.322769	+	0.946478i	$0.395386\pi$
$48$		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	−0.0953396	−	0.995445i	$-0.530394\pi$
$59$	−59.3003	−	34.2370i	−1.00509	−	0.580289i	−0.909750	+	0.415156i	$0.863727\pi$
$60$		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
$63$	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	$-0.813569\pi$
$67$	4.15737	−	7.20078i	0.0620503	−	0.107474i	0.895382	+	0.445299i	$0.146903\pi$
$68$		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
$73$	125.300			1.71643			0.858217	−	0.513287i	$-0.171572\pi$
$73$	125.300			1.71643			0.858217	+	0.513287i	$0.171572\pi$
$74$		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	0.947413	−	0.320012i	$-0.103687\pi$
$79$	15.5289	+	26.8968i	0.196568	+	0.340466i	−0.750845	+	0.660478i	$0.770354\pi$
$80$		0			0
$81$	−16.5998	−	79.2808i	−0.204936	−	0.978775i
$82$		0			0
$83$	133.415	−	77.0272i	1.60741	−	0.928038i	0.617462	−	0.786601i	$-0.288161\pi$
$83$	133.415	−	77.0272i	1.60741	−	0.928038i	0.989947	−	0.141438i	$-0.0451725\pi$
$84$		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	$-0.736616\pi$
$89$		−	131.044i		−	1.47241i	0.676760	−	0.736204i	$-0.263384\pi$
$90$		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	−0.874739	−	0.484594i	$-0.838967\pi$
$97$	−83.1329	−	143.990i	−0.857040	−	1.48444i	0.0176993	−	0.999843i	$-0.494366\pi$
$98$		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
$103$	−32.7977	+	56.8073i	−0.318424	+	0.551527i	−0.980159	−	0.198211i	$-0.936487\pi$
$103$	−32.7977	+	56.8073i	−0.318424	+	0.551527i	0.661735	+	0.749738i	$0.269820\pi$
$104$		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	$-0.365643\pi$
$113$	−19.8326	−	11.4504i	−0.175510	−	0.101331i	−0.585181	+	0.810903i	$0.698977\pi$
$114$		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	$-0.627908\pi$
$127$	−99.3417			−0.782218			−0.391109	+	0.920344i	$0.627908\pi$
$128$		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
$133$	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	0.596644	−	0.802506i	$-0.296501\pi$
$137$	217.824	−	125.761i	1.58996	−	0.917962i	0.993313	−	0.115455i	$-0.0368327\pi$
$138$		0			0
$139$	−82.6116	+	143.087i	−0.594328	+	1.02941i	0.399313	+	0.916815i	$0.369249\pi$
$139$	−82.6116	+	143.087i	−0.594328	+	1.02941i	−0.993641	+	0.112592i	$0.964085\pi$
$140$		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	−0.340506	−	0.940242i	$-0.610598\pi$
$149$	−197.430	−	113.986i	−1.32503	−	0.765008i	−0.984527	+	0.175234i	$0.943932\pi$
$150$		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
$153$	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	−0.156173	−	0.987730i	$-0.549916\pi$
$157$	122.038	−	211.376i	0.777313	−	1.34634i	0.933485	−	0.358615i	$-0.116751\pi$
$158$		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	$-0.700689\pi$
$163$	−192.188			−1.17907			−0.589534	+	0.807744i	$0.700689\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	182.728	+	105.498i	1.09418	+	0.631726i	0.934687	−	0.355472i	$-0.115680\pi$
$167$	182.728	+	105.498i	1.09418	+	0.631726i	0.159495	+	0.987199i	$0.449013\pi$
$168$		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	$-0.809192\pi$
$173$	−129.730	+	74.8995i	−0.749882	+	0.432945i	0.0757690	+	0.997125i	$0.475859\pi$
$174$		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	$0.0520516\pi$
$179$			58.2813i			0.325594i	−0.986660	+	0.162797i	$0.947948\pi$
$180$		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	−0.677247	−	0.735755i	$-0.736827\pi$
$191$	−72.3294	+	41.7594i	−0.378688	+	0.218636i	0.298559	+	0.954391i	$0.403494\pi$
$192$		0			0
$193$	−41.6094	+	72.0695i	−0.215593	+	0.373417i	−0.953456	−	0.301533i	$-0.902502\pi$
$193$	−41.6094	+	72.0695i	−0.215593	+	0.373417i	0.737863	+	0.674950i	$0.235835\pi$
$194$		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	−0.952574	−	0.304306i	$-0.901576\pi$
$211$	−44.8904	+	77.7525i	−0.212751	+	0.368495i	0.739824	+	0.672801i	$0.234909\pi$
$212$		0			0
$213$	−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	$-0.0998958\pi$
$223$	46.4357	+	80.4290i	0.208232	+	0.360668i	−0.742926	+	0.669374i	$0.766562\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−192.811	+	111.320i	−0.849389	+	0.490395i	−0.860445	−	0.509544i	$-0.829814\pi$
$227$	−192.811	+	111.320i	−0.849389	+	0.490395i	0.0110555	+	0.999939i	$0.496481\pi$
$228$		0			0
$229$	−92.0380	+	159.414i	−0.401913	+	0.696133i	−0.993957	−	0.109772i	$-0.964988\pi$
$229$	−92.0380	+	159.414i	−0.401913	+	0.696133i	0.592044	+	0.805906i	$0.298321\pi$
$230$		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	−0.499997	−	0.866027i	$-0.666666\pi$
$239$	−358.499	−	206.980i	−1.50000	−	0.866024i	−1.00000		2.96133e-6i	$0.999999\pi$
$240$		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
$243$	−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	$-0.921749\pi$
$251$		−	122.169i		−	0.486729i	0.969935	−	0.243364i	$-0.0782511\pi$
$252$		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	$-0.523787\pi$
$257$	−250.728	−	144.758i	−0.975596	−	0.563260i	−0.900938	+	0.433949i	$0.857120\pi$
$258$		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	$-0.788531\pi$
$263$	−170.169	+	98.2473i	−0.647032	+	0.373564i	0.140286	+	0.990111i	$0.455198\pi$
$264$		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	$-0.842854\pi$
$269$		−	254.946i		−	0.947756i	0.880591	−	0.473878i	$-0.157146\pi$
$270$		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	$-0.216996\pi$
$277$	−43.6152	−	75.5437i	−0.157456	−	0.272721i	−0.933950	+	0.357403i	$0.883662\pi$
$278$		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
$283$	−229.202	+	396.990i	−0.809902	+	1.40279i	0.103029	+	0.994678i	$0.467146\pi$
$283$	−229.202	+	396.990i	−0.809902	+	1.40279i	−0.912931	+	0.408113i	$0.866187\pi$
$284$		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	$-0.563519\pi$
$293$	−335.832	−	193.893i	−1.14618	−	0.661750i	−0.947954	+	0.318406i	$0.896853\pi$
$294$		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	$-0.517642\pi$
$307$	−34.0128			−0.110791			−0.0553955	+	0.998464i	$0.517642\pi$
$308$		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
$313$	81.7480	+	141.592i	0.261176	+	0.452370i	0.966555	−	0.256461i	$-0.0825565\pi$
$313$	81.7480	+	141.592i	0.261176	+	0.452370i	−0.705379	+	0.708830i	$0.749223\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	468.269	−	270.355i	1.47719	−	0.852856i	0.477522	−	0.878620i	$-0.341535\pi$
$317$	468.269	−	270.355i	1.47719	−	0.852856i	0.999668	+	0.0257634i	$0.00820165\pi$
$318$		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	0.623078	−	0.782160i	$-0.285882\pi$
$331$	−121.090	−	209.734i	−0.365831	−	0.633638i	−0.988909	+	0.148522i	$0.952549\pi$
$332$		0			0
$333$	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	$-0.670063\pi$
$337$	165.377	−	286.441i	0.490732	−	0.849973i	0.999943	+	0.0106686i	$0.00339599\pi$
$338$		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	$-0.588723\pi$
$347$	−432.122	−	249.485i	−1.24531	−	0.718978i	−0.970170	+	0.242427i	$0.922057\pi$
$348$		0			0
$349$	144.309	+	249.950i	0.413492	+	0.716190i	0.995269	−	0.0971589i	$-0.0309755\pi$
$349$	144.309	+	249.950i	0.413492	+	0.716190i	−0.581777	+	0.813349i	$0.697642\pi$
$350$		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	$-0.830510\pi$
$353$	−300.999	+	173.782i	−0.852687	+	0.492299i	0.00886928	+	0.999961i	$0.497177\pi$
$354$		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	$0.192403\pi$
$359$			408.046i			1.13662i	−0.822815	+	0.568310i	$0.807597\pi$
$360$		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	$-0.289552\pi$
$367$	−138.189	−	239.351i	−0.376538	−	0.652183i	−0.990556	+	0.137109i	$0.956219\pi$
$368$		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	$-0.897759\pi$
$373$	−74.9808	+	129.870i	−0.201021	+	0.348178i	0.747837	+	0.663883i	$0.231093\pi$
$374$		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	$-0.277366\pi$
$383$	116.038	+	66.9947i	0.302972	+	0.174921i	−0.340805	+	0.940134i	$0.610700\pi$
$384$		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	0.0414597	−	0.999140i	$-0.486799\pi$
$389$	360.786	−	208.300i	0.927470	−	0.535475i	0.886011	+	0.463665i	$0.153466\pi$
$390$		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	$-0.674730\pi$
$397$	−414.289			−1.04355			−0.521775	+	0.853083i	$0.674730\pi$
$398$		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
$403$	−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	−0.189650	−	0.981852i	$-0.560735\pi$
$409$	308.993	−	535.191i	0.755483	−	1.30854i	0.945134	−	0.326684i	$-0.105931\pi$
$410$		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	−0.437220	−	0.899355i	$-0.644037\pi$
$419$	−601.137	−	347.066i	−1.43469	−	0.828321i	−0.997474	+	0.0710339i	$0.977370\pi$
$420$		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
$423$	−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	$0.161768\pi$
$431$			419.462i			0.973229i	−0.873617	+	0.486615i	$0.838232\pi$
$432$		0			0
$433$	−21.7422			−0.0502129			−0.0251065	−	0.999685i	$-0.507992\pi$
$433$	−21.7422			−0.0502129			−0.0251065	+	0.999685i	$0.507992\pi$
$434$		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	−0.923167	−	0.384399i	$-0.874409\pi$
$439$	−348.778	−	604.101i	−0.794483	−	1.37608i	0.128684	−	0.991686i	$-0.458925\pi$
$440$		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	$-0.585471\pi$
$443$	193.609	−	111.780i	0.437040	−	0.252325i	0.702341	+	0.711840i	$0.252138\pi$
$444$		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	$-0.963038\pi$
$449$		−	104.042i		−	0.231719i	0.993266	−	0.115860i	$-0.0369623\pi$
$450$		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	−0.956066	−	0.293153i	$-0.905296\pi$
$457$	−334.483	−	579.342i	−0.731910	−	1.26771i	0.224155	−	0.974553i	$-0.428038\pi$
$458$		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
$463$	278.199	−	481.854i	0.600861	−	1.04072i	−0.391830	−	0.920038i	$-0.628158\pi$
$463$	278.199	−	481.854i	0.600861	−	1.04072i	0.992691	−	0.120684i	$-0.0385088\pi$
$464$		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	−0.0869370	−	0.996214i	$-0.527708\pi$
$479$	350.791	−	202.529i	0.732341	−	0.422817i	0.819278	+	0.573397i	$0.194375\pi$
$480$		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	$-0.294164\pi$
$487$	586.853			1.20504			0.602518	+	0.798105i	$0.294164\pi$
$488$		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
$493$	−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	−0.257091	+	0.966387i	$0.582764\pi$
$499$	−481.765	+	834.442i	−0.965461	+	1.67223i	−0.708370	+	0.705841i	$0.750569\pi$
$500$		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	0.864005	−	0.503484i	$-0.167949\pi$
$509$	437.729	+	252.723i	0.859978	+	0.496508i	−0.00402718	+	0.999992i	$0.501282\pi$
$510$		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	$-0.789324\pi$
$521$		−	640.397i		−	1.22917i	0.788851	−	0.614585i	$-0.210676\pi$
$522$		0			0
$523$	91.8967			0.175711			0.0878553	−	0.996133i	$-0.471999\pi$
$523$	91.8967			0.175711			0.0878553	+	0.996133i	$0.471999\pi$
$524$		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	0.946797	+	0.321832i	$0.104299\pi$
$547$	411.406	+	712.576i	0.752113	+	1.30270i	−0.194683	+	0.980866i	$0.562368\pi$
$548$		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	$-0.395228\pi$
$563$	−188.423	−	108.786i	−0.334677	−	0.193226i	−0.657916	+	0.753092i	$0.728562\pi$
$564$		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	−0.619326	−	0.785134i	$-0.712594\pi$
$569$	−141.705	+	81.8136i	−0.249043	+	0.143785i	0.370283	+	0.928919i	$0.379261\pi$
$570$		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
$573$	−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	$-0.507429\pi$
$577$	−26.9318			−0.0466756			−0.0233378	+	0.999728i	$0.507429\pi$
$578$		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	$-0.805253\pi$
$587$	−428.807	+	247.572i	−0.730506	+	0.421758i	0.0881015	+	0.996112i	$0.471920\pi$
$588$		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	0.0287900	−	0.999585i	$-0.490835\pi$
$599$	−492.666	−	284.441i	−0.822481	−	0.474860i	−0.851271	+	0.524726i	$0.824168\pi$
$600$		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
$603$	−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	$-0.723084\pi$
$607$	206.061	−	356.909i	0.339475	−	0.587988i	0.984334	+	0.176314i	$0.0564173\pi$
$608$		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	$-0.198914\pi$
$613$	994.307			1.62203			0.811017	+	0.585023i	$0.198914\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−589.215	−	340.183i	−0.954967	−	0.551351i	−0.0603468	−	0.998177i	$-0.519221\pi$
$617$	−589.215	−	340.183i	−0.954967	−	0.551351i	−0.894620	+	0.446827i	$0.852554\pi$
$618$		0			0
$619$	371.748	+	643.887i	0.600563	+	1.04021i	0.992736	+	0.120314i	$0.0383901\pi$
$619$	371.748	+	643.887i	0.600563	+	1.04021i	−0.392173	+	0.919891i	$0.628277\pi$
$620$		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	−0.109795	−	0.993954i	$-0.535019\pi$
$641$	446.198	−	257.613i	0.696097	−	0.401892i	0.805892	+	0.592062i	$0.201686\pi$
$642$		0			0
$643$	341.339	−	591.217i	0.530854	−	0.919466i	−0.468498	−	0.883465i	$-0.655205\pi$
$643$	341.339	−	591.217i	0.530854	−	0.919466i	0.999352	−	0.0360013i	$-0.0114620\pi$
$644$		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	$-0.256923\pi$
$653$	268.904	+	155.252i	0.411797	+	0.237751i	−0.279764	+	0.960069i	$0.590256\pi$
$654$		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	−0.325210	−	0.945642i	$-0.605435\pi$
$659$	218.218	−	125.988i	0.331135	−	0.191181i	0.656345	+	0.754461i	$0.272102\pi$
$660$		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
$663$	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	0.999619	+	0.0275972i	$0.00878559\pi$
$673$	352.456	+	610.473i	0.523709	+	0.907091i	−0.475910	+	0.879494i	$0.657881\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−213.117	+	123.043i	−0.314797	+	0.181748i	−0.649071	−	0.760728i	$-0.724842\pi$
$677$	−213.117	+	123.043i	−0.314797	+	0.181748i	0.334274	+	0.942476i	$0.391509\pi$
$678$		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	0.632622	−	0.774461i	$-0.281979\pi$
$691$	−244.885	−	424.153i	−0.354392	−	0.613825i	−0.987014	+	0.160636i	$0.948645\pi$
$692$		0			0
$693$	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	$-0.522654\pi$
$701$		−	1398.45i		−	1.99494i	0.0711109	−	0.997468i	$-0.477346\pi$
$702$		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	−0.864158	−	0.503220i	$-0.832149\pi$
$709$	−615.327	−	1065.78i	−0.867880	−	1.50321i	−0.00372210	−	0.999993i	$-0.501185\pi$
$710$		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	$0.0456056\pi$
$719$			205.324i			0.285569i	−0.989754	+	0.142785i	$0.954394\pi$
$720$		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	0.986200	+	0.165558i	$0.0529424\pi$
$727$	462.719	+	801.453i	0.636477	+	1.10241i	−0.349723	+	0.936853i	$0.613724\pi$
$728$		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	$-0.692971\pi$
$733$	312.852	−	541.875i	0.426810	−	0.739257i	0.996588	+	0.0825420i	$0.0263039\pi$
$734$		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	$-0.199515\pi$
$743$	525.224	+	303.238i	0.706897	+	0.408127i	−0.103014	+	0.994680i	$0.532849\pi$
$744$		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	−0.958615	−	0.284707i	$-0.908104\pi$
$751$	−174.790	+	302.746i	−0.232744	+	0.403124i	0.725871	+	0.687831i	$0.241437\pi$
$752$		0			0
$753$	−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	$-0.448786\pi$
$757$	242.544			0.320402			0.160201	+	0.987084i	$0.448786\pi$
$758$		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
$763$	−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	−0.972763	−	0.231802i	$-0.925538\pi$
$769$	−219.654	+	380.451i	−0.285635	+	0.494735i	0.687128	+	0.726537i	$0.258871\pi$
$770$		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	0.201844	+	0.979418i	$0.435307\pi$
$787$	−588.108	+	1018.63i	−0.747279	+	1.29432i	−0.949122	+	0.314907i	$0.898027\pi$
$788$		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	$-0.337711\pi$
$797$	−18.9845	−	10.9607i	−0.0238200	−	0.0137525i	−0.511863	+	0.859067i	$0.671044\pi$
$798$		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	$0.406392\pi$
$809$			1548.54i			1.91414i	−0.289857	+	0.957070i	$0.593608\pi$
$810$		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	−0.906073	−	0.423121i	$-0.860935\pi$
$821$	−814.987	+	470.533i	−0.992676	+	0.573122i	−0.0866031	+	0.996243i	$0.527601\pi$
$822$		0			0
$823$	−144.349	+	250.019i	−0.175393	+	0.303790i	−0.940297	−	0.340354i	$-0.889453\pi$
$823$	−144.349	+	250.019i	−0.175393	+	0.303790i	0.764904	+	0.644144i	$0.222786\pi$
$824$		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	−0.437380	−	0.899277i	$-0.644093\pi$
$839$	102.968	−	59.4488i	0.122727	−	0.0708567i	0.560107	+	0.828420i	$0.310760\pi$
$840$		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	$-0.0389007\pi$
$853$	333.265	+	577.231i	0.390697	+	0.676707i	−0.601845	+	0.798613i	$0.705567\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	530.304	−	306.171i	0.618791	−	0.357259i	−0.157607	−	0.987502i	$-0.550378\pi$
$857$	530.304	−	306.171i	0.618791	−	0.357259i	0.776398	+	0.630243i	$0.217045\pi$
$858$		0			0
$859$	665.233	−	1152.22i	0.774427	−	1.34135i	−0.160689	−	0.987005i	$-0.551372\pi$
$859$	665.233	−	1152.22i	0.774427	−	1.34135i	0.935116	−	0.354342i	$-0.115295\pi$
$860$		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	$-0.792625\pi$
$877$	111.854	−	193.736i	0.127541	−	0.220908i	0.922723	+	0.385463i	$0.125958\pi$
$878$		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
$883$	−1028.50			−1.16478			−0.582389	−	0.812910i	$-0.697882\pi$
$883$	−1028.50			−1.16478			−0.582389	+	0.812910i	$0.697882\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−395.428	−	228.301i	−0.445804	−	0.257385i	0.260252	−	0.965541i	$-0.416194\pi$
$887$	−395.428	−	228.301i	−0.445804	−	0.257385i	−0.706057	+	0.708155i	$0.749528\pi$
$888$		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	$-0.234330\pi$
$907$	−191.354	−	331.435i	−0.210975	−	0.365419i	−0.952020	+	0.306036i	$0.900997\pi$
$908$		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
$913$	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	0.661402	−	0.750032i	$-0.269962\pi$
$929$	1525.09	−	880.512i	1.64165	−	0.947807i	0.980247	−	0.197775i	$-0.0633715\pi$
$930$		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	$-0.805940\pi$
$937$	−1536.39			−1.63969			−0.819843	+	0.572588i	$0.805940\pi$
$938$		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
$943$	−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	$-0.490332\pi$
$947$	862.884	−	498.186i	0.911176	−	0.526068i	0.880809	+	0.473471i	$0.156999\pi$
$948$		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	$-0.725166\pi$
$967$	322.316	−	558.267i	0.333315	−	0.577319i	0.983160	+	0.182748i	$0.0584993\pi$
$968$		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
$973$	−1786.07			−1.83563
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−53.1017	−	30.6583i	−0.0543518	−	0.0313800i	0.472578	−	0.881289i	$-0.343324\pi$
$977$	−53.1017	−	30.6583i	−0.0543518	−	0.0313800i	−0.526930	+	0.849909i	$0.676657\pi$
$978$		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	$-0.465611\pi$
$983$	1005.33	−	580.428i	1.02272	−	0.590466i	0.914890	+	0.403704i	$0.132277\pi$
$984$		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	$-0.183130\pi$
$997$	−51.5429	−	89.2750i	−0.0516980	−	0.0895436i	−0.890716	+	0.454560i	$0.849797\pi$
$998$		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.d.401.7	yes	16
3.2	odd	2		2700.3.p.e.2501.8		16
5.2	odd	4		900.3.u.d.149.6		32
5.3	odd	4		900.3.u.d.149.11		32
5.4	even	2		900.3.p.e.401.2	yes	16
9.2	odd	6	inner	900.3.p.d.101.7	✓	16
9.7	even	3		2700.3.p.e.1601.8		16
15.2	even	4		2700.3.u.d.449.1		32
15.8	even	4		2700.3.u.d.449.16		32
15.14	odd	2		2700.3.p.d.2501.1		16
45.2	even	12		900.3.u.d.749.11		32
45.7	odd	12		2700.3.u.d.2249.16		32
45.29	odd	6		900.3.p.e.101.2	yes	16
45.34	even	6		2700.3.p.d.1601.1		16
45.38	even	12		900.3.u.d.749.6		32
45.43	odd	12		2700.3.u.d.2249.1		32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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