LMFDB - Embedded newform 360.6.k.b.181.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,6,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("360.181");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	360.k (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$57.7381751327$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{42}\cdot 3^{8}\cdot 5^{12} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.16
Root			$0.593959 - 3.95566i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.6.k.b.181.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.36170 + 4.54962i) q^{2} +(-9.39799 + 30.5888i) q^{4} +25.0000i q^{5} +47.1406 q^{7} +(-170.761 + 60.0732i) q^{8} +O(q^{10})$	\(q+(3.36170 + 4.54962i) q^{2} +(-9.39799 + 30.5888i) q^{4} +25.0000i q^{5} +47.1406 q^{7} +(-170.761 + 60.0732i) q^{8} +(-113.740 + 84.0424i) q^{10} +253.791i q^{11} -1032.09i q^{13} +(158.472 + 214.472i) q^{14} +(-847.355 - 574.948i) q^{16} -756.546 q^{17} +344.235i q^{19} +(-764.721 - 234.950i) q^{20} +(-1154.65 + 853.167i) q^{22} -4976.22 q^{23} -625.000 q^{25} +(4695.61 - 3469.57i) q^{26} +(-443.027 + 1441.98i) q^{28} -372.003i q^{29} -134.803 q^{31} +(-232.761 - 5787.94i) q^{32} +(-2543.28 - 3442.00i) q^{34} +1178.52i q^{35} -6653.34i q^{37} +(-1566.14 + 1157.21i) q^{38} +(-1501.83 - 4269.02i) q^{40} +15933.8 q^{41} +4771.42i q^{43} +(-7763.17 - 2385.12i) q^{44} +(-16728.5 - 22639.9i) q^{46} -14043.7 q^{47} -14584.8 q^{49} +(-2101.06 - 2843.51i) q^{50} +(31570.4 + 9699.58i) q^{52} +5893.80i q^{53} -6344.77 q^{55} +(-8049.77 + 2831.89i) q^{56} +(1692.47 - 1250.56i) q^{58} -30117.5i q^{59} -23143.8i q^{61} +(-453.166 - 613.301i) q^{62} +(25550.4 - 20516.3i) q^{64} +25802.3 q^{65} -22646.3i q^{67} +(7110.02 - 23141.9i) q^{68} +(-5361.79 + 3961.81i) q^{70} +53900.1 q^{71} -51287.1 q^{73} +(30270.2 - 22366.5i) q^{74} +(-10529.8 - 3235.12i) q^{76} +11963.9i q^{77} +40838.6 q^{79} +(14373.7 - 21183.9i) q^{80} +(53564.7 + 72492.8i) q^{82} -108060. i q^{83} -18913.7i q^{85} +(-21708.1 + 16040.1i) q^{86} +(-15246.0 - 43337.5i) q^{88} -81947.9 q^{89} -48653.4i q^{91} +(46766.5 - 152217. i) q^{92} +(-47210.7 - 63893.5i) q^{94} -8605.88 q^{95} +52534.7 q^{97} +(-49029.5 - 66355.0i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8}+O(q^{10}) $ 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8	$ 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32} + 21132 q^{34} + 19580 q^{38} + 6200 q^{40} - 11608 q^{41} - 72296 q^{44} - 28516 q^{46} - 44180 q^{47} + 18756 q^{49} + 1250 q^{50} - 39680 q^{52} - 24200 q^{55} + 53624 q^{56} + 59496 q^{58} - 59824 q^{62} - 11264 q^{64} - 11576 q^{68} + 29800 q^{70} + 200312 q^{71} - 105136 q^{73} - 78876 q^{74} - 153872 q^{76} + 282080 q^{79} - 16000 q^{80} - 223032 q^{82} - 27452 q^{86} + 86896 q^{88} + 3160 q^{89} - 107916 q^{92} + 148820 q^{94} - 144400 q^{95} + 147376 q^{97} - 216942 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	3.36170	+	4.54962i	0.594270	+	0.804266i
$2$	3.36170	+	4.54962i	0.594270	+	0.804266i
$3$		0			0
$3$		0			0
$4$	−9.39799	+	30.5888i	−0.293687	+	0.955902i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$		0			0
$7$	47.1406			0.363622			0.181811	−	0.983333i	$-0.441804\pi$
$7$	47.1406			0.363622			0.181811	+	0.983333i	$0.441804\pi$
$8$	−170.761	+	60.0732i	−0.943328	+	0.331861i
$9$		0			0
$10$	−113.740	+	84.0424i	−0.359679	+	0.265765i
$11$			253.791i			0.632403i	0.948692	+	0.316202i	$0.102408\pi$
$11$			253.791i			0.632403i	−0.948692	+	0.316202i	$0.897592\pi$
$12$		0			0
$13$		−	1032.09i		−	1.69379i	−0.531761	−	0.846894i	$-0.678470\pi$
$13$		−	1032.09i		−	1.69379i	0.531761	−	0.846894i	$-0.321530\pi$
$14$	158.472	+	214.472i	0.216090	+	0.292449i
$15$		0			0
$16$	−847.355	−	574.948i	−0.827496	−	0.561472i
$17$	−756.546			−0.634912			−0.317456	−	0.948273i	$-0.602829\pi$
$17$	−756.546			−0.634912			−0.317456	+	0.948273i	$0.602829\pi$
$18$		0			0
$19$			344.235i			0.218762i	0.994000	+	0.109381i	$0.0348868\pi$
$19$			344.235i			0.218762i	−0.994000	+	0.109381i	$0.965113\pi$
$20$	−764.721	−	234.950i	−0.427492	−	0.131341i
$21$		0			0
$22$	−1154.65	+	853.167i	−0.508620	+	0.375818i
$23$	−4976.22			−1.96146			−0.980731	−	0.195363i	$-0.937411\pi$
$23$	−4976.22			−1.96146			−0.980731	+	0.195363i	$0.937411\pi$
$24$		0			0
$25$	−625.000			−0.200000
$26$	4695.61	−	3469.57i	1.36226	−	1.00657i
$27$		0			0
$28$	−443.027	+	1441.98i	−0.106791	+	0.347587i
$29$		−	372.003i		−	0.0821395i	−0.999156	−	0.0410697i	$-0.986923\pi$
$29$		−	372.003i		−	0.0821395i	0.999156	−	0.0410697i	$-0.0130766\pi$
$30$		0			0
$31$	−134.803			−0.0251939			−0.0125969	−	0.999921i	$-0.504010\pi$
$31$	−134.803			−0.0251939			−0.0125969	+	0.999921i	$0.504010\pi$
$32$	−232.761	−	5787.94i	−0.0401824	−	0.999192i
$33$		0			0
$34$	−2543.28	−	3442.00i	−0.377309	−	0.510638i
$35$			1178.52i			0.162617i
$36$		0			0
$37$		−	6653.34i		−	0.798980i	−0.916738	−	0.399490i	$-0.869187\pi$
$37$		−	6653.34i		−	0.798980i	0.916738	−	0.399490i	$-0.130813\pi$
$38$	−1566.14	+	1157.21i	−0.175943	+	0.130003i
$39$		0			0
$40$	−1501.83	−	4269.02i	−0.148413	−	0.421869i
$41$	15933.8			1.48034			0.740168	−	0.672421i	$-0.234746\pi$
$41$	15933.8			1.48034			0.740168	+	0.672421i	$0.234746\pi$
$42$		0			0
$43$			4771.42i			0.393529i	0.980451	+	0.196764i	$0.0630434\pi$
$43$			4771.42i			0.393529i	−0.980451	+	0.196764i	$0.936957\pi$
$44$	−7763.17	−	2385.12i	−0.604515	−	0.185729i
$45$		0			0
$46$	−16728.5	−	22639.9i	−1.16564	−	1.57754i
$47$	−14043.7			−0.927337			−0.463668	−	0.886009i	$-0.653467\pi$
$47$	−14043.7			−0.927337			−0.463668	+	0.886009i	$0.653467\pi$
$48$		0			0
$49$	−14584.8			−0.867779
$50$	−2101.06	−	2843.51i	−0.118854	−	0.160853i
$51$		0			0
$52$	31570.4	+	9699.58i	1.61910	+	0.497444i
$53$			5893.80i			0.288208i	0.989563	+	0.144104i	$0.0460300\pi$
$53$			5893.80i			0.288208i	−0.989563	+	0.144104i	$0.953970\pi$
$54$		0			0
$55$	−6344.77			−0.282819
$56$	−8049.77	+	2831.89i	−0.343015	+	0.120672i
$57$		0			0
$58$	1692.47	−	1250.56i	0.0660620	−	0.0488130i
$59$		−	30117.5i		−	1.12639i	−0.826324	−	0.563195i	$-0.809572\pi$
$59$		−	30117.5i		−	1.12639i	0.826324	−	0.563195i	$-0.190428\pi$
$60$		0			0
$61$		−	23143.8i		−	0.796362i	−0.917307	−	0.398181i	$-0.869642\pi$
$61$		−	23143.8i		−	0.796362i	0.917307	−	0.398181i	$-0.130358\pi$
$62$	−453.166	−	613.301i	−0.0149719	−	0.0202626i
$63$		0			0
$64$	25550.4	−	20516.3i	0.779737	−	0.626107i
$65$	25802.3			0.757485
$66$		0			0
$67$		−	22646.3i		−	0.616326i	−0.951334	−	0.308163i	$-0.900286\pi$
$67$		−	22646.3i		−	0.616326i	0.951334	−	0.308163i	$-0.0997142\pi$
$68$	7110.02	−	23141.9i	0.186466	−	0.606913i
$69$		0			0
$70$	−5361.79	+	3961.81i	−0.130787	+	0.0966382i
$71$	53900.1			1.26895			0.634473	−	0.772945i	$-0.281217\pi$
$71$	53900.1			1.26895			0.634473	+	0.772945i	$0.281217\pi$
$72$		0			0
$73$	−51287.1			−1.12642			−0.563211	−	0.826313i	$-0.690434\pi$
$73$	−51287.1			−1.12642			−0.563211	+	0.826313i	$0.690434\pi$
$74$	30270.2	−	22366.5i	0.642592	−	0.474809i
$75$		0			0
$76$	−10529.8	−	3235.12i	−0.209115	−	0.0642475i
$77$			11963.9i			0.229956i
$78$		0			0
$79$	40838.6			0.736212			0.368106	−	0.929784i	$-0.380006\pi$
$79$	40838.6			0.736212			0.368106	+	0.929784i	$0.380006\pi$
$80$	14373.7	−	21183.9i	0.251098	−	0.370067i
$81$		0			0
$82$	53564.7	+	72492.8i	0.879719	+	1.19058i
$83$		−	108060.i		−	1.72175i	−0.508814	−	0.860877i	$-0.669916\pi$
$83$		−	108060.i		−	1.72175i	0.508814	−	0.860877i	$-0.330084\pi$
$84$		0			0
$85$		−	18913.7i		−	0.283941i
$86$	−21708.1	+	16040.1i	−0.316502	+	0.233862i
$87$		0			0
$88$	−15246.0	−	43337.5i	−0.209870	−	0.596564i
$89$	−81947.9			−1.09664			−0.548318	−	0.836270i	$-0.684732\pi$
$89$	−81947.9			−1.09664			−0.548318	+	0.836270i	$0.684732\pi$
$90$		0			0
$91$		−	48653.4i		−	0.615899i
$92$	46766.5	−	152217.i	0.576056	−	1.87496i
$93$		0			0
$94$	−47210.7	−	63893.5i	−0.551088	−	0.745825i
$95$	−8605.88			−0.0978332
$96$		0			0
$97$	52534.7			0.566914			0.283457	−	0.958985i	$-0.408519\pi$
$97$	52534.7			0.566914			0.283457	+	0.958985i	$0.408519\pi$
$98$	−49029.5	−	66355.0i	−0.515695	−	0.697925i
$99$		0			0
$100$	5873.75	−	19118.0i	0.0587375	−	0.191180i
$101$		−	66010.1i		−	0.643883i	−0.946760	−	0.321942i	$-0.895665\pi$
$101$		−	66010.1i		−	0.643883i	0.946760	−	0.321942i	$-0.104335\pi$
$102$		0			0
$103$	−4624.62			−0.0429520			−0.0214760	−	0.999769i	$-0.506837\pi$
$103$	−4624.62			−0.0429520			−0.0214760	+	0.999769i	$0.506837\pi$
$104$	62000.9	+	176240.i	0.562102	+	1.59780i
$105$		0			0
$106$	−26814.5	+	19813.2i	−0.231796	+	0.171273i
$107$			177733.i			1.50075i	0.661013	+	0.750375i	$0.270127\pi$
$107$			177733.i			1.50075i	−0.661013	+	0.750375i	$0.729873\pi$
$108$		0			0
$109$			157581.i			1.27039i	0.772352	+	0.635194i	$0.219080\pi$
$109$			157581.i			1.27039i	−0.772352	+	0.635194i	$0.780920\pi$
$110$	−21329.2	−	28866.3i	−0.168071	−	0.227462i
$111$		0			0
$112$	−39944.9	−	27103.4i	−0.300896	−	0.204164i
$113$	−203402.			−1.49851			−0.749255	−	0.662282i	$-0.769588\pi$
$113$	−203402.			−1.49851			−0.749255	+	0.662282i	$0.769588\pi$
$114$		0			0
$115$		−	124405.i		−	0.877192i
$116$	11379.2	+	3496.09i	0.0785173	+	0.0241233i
$117$		0			0
$118$	137023.	−	101246.i	0.905917	−	0.669379i
$119$	−35664.1			−0.230868
$120$		0			0
$121$	96641.3			0.600066
$122$	105296.	−	77802.5i	0.640487	−	0.473254i
$123$		0			0
$124$	1266.88	−	4123.46i	0.00739912	−	0.0240829i
$125$		−	15625.0i		−	0.0894427i
$126$		0			0
$127$	−275318.			−1.51469			−0.757347	−	0.653012i	$-0.773505\pi$
$127$	−275318.			−1.51469			−0.757347	+	0.653012i	$0.773505\pi$
$128$	179234.	+	47275.1i	0.966931	+	0.255040i
$129$		0			0
$130$	86739.3	+	117390.i	0.450150	+	0.609220i
$131$		−	172997.i		−	0.880765i	−0.897810	−	0.440383i	$-0.854843\pi$
$131$		−	172997.i		−	0.880765i	0.897810	−	0.440383i	$-0.145157\pi$
$132$		0			0
$133$			16227.5i			0.0795466i
$134$	103032.	−	76130.0i	0.495690	−	0.366264i
$135$		0			0
$136$	129188.	−	45448.1i	0.598930	−	0.210702i
$137$	177934.			0.809947			0.404973	−	0.914328i	$-0.367281\pi$
$137$	177934.			0.809947			0.404973	+	0.914328i	$0.367281\pi$
$138$		0			0
$139$			133948.i			0.588028i	0.955801	+	0.294014i	$0.0949912\pi$
$139$			133948.i			0.588028i	−0.955801	+	0.294014i	$0.905009\pi$
$140$	−36049.4	−	11075.7i	−0.155446	−	0.0477585i
$141$		0			0
$142$	181196.	+	245225.i	0.754097	+	1.02057i
$143$	261935.			1.07116
$144$		0			0
$145$	9300.09			0.0367339
$146$	−172412.	−	233337.i	−0.669399	−	0.905943i
$147$		0			0
$148$	203518.	+	62528.1i	0.763746	+	0.234650i
$149$		−	494438.i		−	1.82451i	−0.409623	−	0.912255i	$-0.634340\pi$
$149$		−	494438.i		−	1.82451i	0.409623	−	0.912255i	$-0.365660\pi$
$150$		0			0
$151$	−162378.			−0.579543			−0.289772	−	0.957096i	$-0.593579\pi$
$151$	−162378.			−0.579543			−0.289772	+	0.957096i	$0.593579\pi$
$152$	−20679.3	−	58781.8i	−0.0725983	−	0.206364i
$153$		0			0
$154$	−54430.9	+	40218.9i	−0.184946	+	0.136656i
$155$		−	3370.07i		−	0.0112670i
$156$		0			0
$157$		−	152314.i		−	0.493163i	−0.969122	−	0.246581i	$-0.920693\pi$
$157$		−	152314.i		−	0.493163i	0.969122	−	0.246581i	$-0.0793073\pi$
$158$	137287.	+	185800.i	0.437509	+	0.592111i
$159$		0			0
$160$	144699.	−	5819.03i	0.446852	−	0.0179701i
$161$	−234582.			−0.713231
$162$		0			0
$163$			620995.i			1.83071i	0.402652	+	0.915353i	$0.368089\pi$
$163$			620995.i			1.83071i	−0.402652	+	0.915353i	$0.631911\pi$
$164$	−149746.	+	487398.i	−0.434756	+	1.41506i
$165$		0			0
$166$	491633.	−	363266.i	1.38475	−	1.02319i
$167$	252049.			0.699348			0.349674	−	0.936871i	$-0.386292\pi$
$167$	252049.			0.699348			0.349674	+	0.936871i	$0.386292\pi$
$168$		0			0
$169$	−693917.			−1.86892
$170$	86049.9	−	63582.0i	0.228364	−	0.168738i
$171$		0			0
$172$	−145952.	−	44841.8i	−0.376175	−	0.115574i
$173$			258619.i			0.656971i	0.944509	+	0.328485i	$0.106538\pi$
$173$			258619.i			0.656971i	−0.944509	+	0.328485i	$0.893462\pi$
$174$		0			0
$175$	−29462.9			−0.0727244
$176$	145916.	−	215051.i	0.355077	−	0.523311i
$177$		0			0
$178$	−275484.	−	372831.i	−0.651698	−	0.881988i
$179$			574713.i			1.34066i	0.742063	+	0.670330i	$0.233847\pi$
$179$			574713.i			1.34066i	−0.742063	+	0.670330i	$0.766153\pi$
$180$		0			0
$181$		−	428043.i		−	0.971160i	−0.874192	−	0.485580i	$-0.838609\pi$
$181$		−	428043.i		−	0.971160i	0.874192	−	0.485580i	$-0.161391\pi$
$182$	221354.	−	163558.i	0.495347	−	0.366010i
$183$		0			0
$184$	849743.	−	298937.i	1.85030	−	0.650932i
$185$	166334.			0.357315
$186$		0			0
$187$		−	192004.i		−	0.401520i
$188$	131983.	−	429581.i	0.272347	−	0.886443i
$189$		0			0
$190$	−28930.3	−	39153.4i	−0.0581393	−	0.0786839i
$191$	−590225.			−1.17067			−0.585335	−	0.810792i	$-0.699037\pi$
$191$	−590225.			−1.17067			−0.585335	+	0.810792i	$0.699037\pi$
$192$		0			0
$193$	−186892.			−0.361158			−0.180579	−	0.983560i	$-0.557797\pi$
$193$	−186892.			−0.361158			−0.180579	+	0.983560i	$0.557797\pi$
$194$	176606.	+	239013.i	0.336900	+	0.455949i
$195$		0			0
$196$	137067.	−	446131.i	0.254856	−	0.829511i
$197$			292002.i			0.536069i	0.963409	+	0.268034i	$0.0863741\pi$
$197$			292002.i			0.536069i	−0.963409	+	0.268034i	$0.913626\pi$
$198$		0			0
$199$	666267.			1.19266			0.596329	−	0.802740i	$-0.296625\pi$
$199$	666267.			1.19266			0.596329	+	0.802740i	$0.296625\pi$
$200$	106725.	−	37545.7i	0.188666	−	0.0663721i
$201$		0			0
$202$	300321.	−	221906.i	0.517853	−	0.382640i
$203$		−	17536.5i		−	0.0298677i
$204$		0			0
$205$			398346.i			0.662027i
$206$	−15546.6	−	21040.3i	−0.0255251	−	0.0345448i
$207$		0			0
$208$	−593398.	+	874547.i	−0.951015	+	1.40160i
$209$	−87363.7			−0.138346
$210$		0			0
$211$			881071.i			1.36240i	0.732097	+	0.681200i	$0.238542\pi$
$211$			881071.i			1.36240i	−0.732097	+	0.681200i	$0.761458\pi$
$212$	−180285.	−	55389.9i	−0.275498	−	0.0846430i
$213$		0			0
$214$	−808616.	+	597484.i	−1.20700	+	0.891850i
$215$	−119285.			−0.175991
$216$		0			0
$217$	−6354.69			−0.00916105
$218$	−716931.	+	529738.i	−1.02173	+	0.754953i
$219$		0			0
$220$	59628.1	−	194079.i	0.0830604	−	0.270347i
$221$			780824.i			1.07541i
$222$		0			0
$223$	−1.01162e6			−1.36225			−0.681124	−	0.732168i	$-0.738509\pi$
$223$	−1.01162e6			−1.36225			−0.681124	+	0.732168i	$0.738509\pi$
$224$	−10972.5	−	272847.i	−0.0146112	−	0.363328i
$225$		0			0
$226$	−683776.	−	925401.i	−0.890518	−	1.20520i
$227$		−	1.03227e6i		−	1.32962i	−0.747012	−	0.664811i	$-0.768512\pi$
$227$		−	1.03227e6i		−	1.32962i	0.747012	−	0.664811i	$-0.231488\pi$
$228$		0			0
$229$			269099.i			0.339097i	0.985522	+	0.169549i	$0.0542309\pi$
$229$			269099.i			0.339097i	−0.985522	+	0.169549i	$0.945769\pi$
$230$	565997.	−	418213.i	0.705496	−	0.521289i
$231$		0			0
$232$	22347.4	+	63523.6i	0.0272589	+	0.0774845i
$233$	−1.25412e6			−1.51339			−0.756693	−	0.653770i	$-0.773186\pi$
$233$	−1.25412e6			−1.51339			−0.756693	+	0.653770i	$0.773186\pi$
$234$		0			0
$235$		−	351093.i		−	0.414718i
$236$	921259.	+	283044.i	1.07672	+	0.330806i
$237$		0			0
$238$	−119892.	−	162258.i	−0.137198	−	0.185679i
$239$	−995406.			−1.12721			−0.563606	−	0.826044i	$-0.690586\pi$
$239$	−995406.			−1.12721			−0.563606	+	0.826044i	$0.690586\pi$
$240$		0			0
$241$	−1.38569e6			−1.53682			−0.768409	−	0.639959i	$-0.778951\pi$
$241$	−1.38569e6			−1.53682			−0.768409	+	0.639959i	$0.778951\pi$
$242$	324879.	+	439681.i	0.356601	+	0.482613i
$243$		0			0
$244$	707943.	+	217506.i	0.761244	+	0.233881i
$245$		−	364619.i		−	0.388083i
$246$		0			0
$247$	355282.			0.370536
$248$	23019.0	−	8098.03i	0.0237661	−	0.00836085i
$249$		0			0
$250$	71087.7	−	52526.5i	0.0719357	−	0.0531531i
$251$			856001.i			0.857610i	0.903397	+	0.428805i	$0.141065\pi$
$251$			856001.i			0.857610i	−0.903397	+	0.428805i	$0.858935\pi$
$252$		0			0
$253$		−	1.26292e6i		−	1.24043i
$254$	−925535.	−	1.25259e6i	−0.900137	−	1.21822i
$255$		0			0
$256$	387446.	+	974370.i	0.369498	+	0.929232i
$257$	−1.14881e6			−1.08497			−0.542484	−	0.840066i	$-0.682516\pi$
$257$	−1.14881e6			−1.08497			−0.542484	+	0.840066i	$0.682516\pi$
$258$		0			0
$259$		−	313643.i		−	0.290527i
$260$	−242489.	+	789261.i	−0.222464	+	0.724081i
$261$		0			0
$262$	787069.	−	581563.i	0.708369	−	0.523412i
$263$	133562.			0.119067			0.0595337	−	0.998226i	$-0.481039\pi$
$263$	133562.			0.119067			0.0595337	+	0.998226i	$0.481039\pi$
$264$		0			0
$265$	−147345.			−0.128891
$266$	−73828.7	+	54551.8i	−0.0639766	+	0.0472721i
$267$		0			0
$268$	692724.	+	212830.i	0.589147	+	0.181007i
$269$		−	476429.i		−	0.401437i	−0.979649	−	0.200718i	$-0.935672\pi$
$269$		−	476429.i		−	0.401437i	0.979649	−	0.200718i	$-0.0643276\pi$
$270$		0			0
$271$	−2.28597e6			−1.89081			−0.945404	−	0.325902i	$-0.894332\pi$
$271$	−2.28597e6			−1.89081			−0.945404	+	0.325902i	$0.894332\pi$
$272$	641064.	+	434975.i	0.525387	+	0.356485i
$273$		0			0
$274$	598159.	+	809529.i	0.481327	+	0.651413i
$275$		−	158619.i		−	0.126481i
$276$		0			0
$277$			1.02985e6i			0.806448i	0.915101	+	0.403224i	$0.132110\pi$
$277$			1.02985e6i			0.806448i	−0.915101	+	0.403224i	$0.867890\pi$
$278$	−609410.	+	450291.i	−0.472931	+	0.349447i
$279$		0			0
$280$	−70797.2	−	201244.i	−0.0539661	−	0.153401i
$281$	−494955.			−0.373938			−0.186969	−	0.982366i	$-0.559866\pi$
$281$	−494955.			−0.373938			−0.186969	+	0.982366i	$0.559866\pi$
$282$		0			0
$283$		−	299542.i		−	0.222327i	−0.993802	−	0.111163i	$-0.964542\pi$
$283$		−	299542.i		−	0.222327i	0.993802	−	0.111163i	$-0.0354577\pi$
$284$	−506553.	+	1.64874e6i	−0.372674	+	1.21299i
$285$		0			0
$286$	880546.	+	1.19170e6i	0.636556	+	0.861495i
$287$	751131.			0.538283
$288$		0			0
$289$	−847494.			−0.596887
$290$	31264.1	+	42311.8i	0.0218298	+	0.0295438i
$291$		0			0
$292$	481996.	−	1.56881e6i	0.330816	−	1.07675i
$293$			525785.i			0.357799i	0.983867	+	0.178900i	$0.0572537\pi$
$293$			525785.i			0.357799i	−0.983867	+	0.178900i	$0.942746\pi$
$294$		0			0
$295$	752937.			0.503737
$296$	399687.	+	1.13613e6i	0.265150	+	0.753700i
$297$		0			0
$298$	2.24950e6	−	1.66215e6i	1.46739	−	1.08425i
$299$			5.13591e6i			3.32230i
$300$		0			0
$301$			224928.i			0.143096i
$302$	−545867.	−	738759.i	−0.344405	−	0.466107i
$303$		0			0
$304$	197917.	−	291689.i	0.122829	−	0.181024i
$305$	578596.			0.356144
$306$		0			0
$307$			1.90796e6i			1.15538i	0.816257	+	0.577689i	$0.196045\pi$
$307$			1.90796e6i			1.15538i	−0.816257	+	0.577689i	$0.803955\pi$
$308$	−365961.	−	112436.i	−0.219815	−	0.0675351i
$309$		0			0
$310$	15332.5	−	11329.2i	0.00906170	−	0.00669566i
$311$	2.53102e6			1.48387			0.741933	−	0.670474i	$-0.233909\pi$
$311$	2.53102e6			1.48387			0.741933	+	0.670474i	$0.233909\pi$
$312$		0			0
$313$	−1.14121e6			−0.658423			−0.329212	−	0.944256i	$-0.606783\pi$
$313$	−1.14121e6			−0.658423			−0.329212	+	0.944256i	$0.606783\pi$
$314$	692970.	−	512033.i	0.396634	−	0.293072i
$315$		0			0
$316$	−383801.	+	1.24921e6i	−0.216216	+	0.703747i
$317$		−	2.71214e6i		−	1.51588i	−0.652326	−	0.757938i	$-0.726207\pi$
$317$		−	2.71214e6i		−	1.51588i	0.652326	−	0.757938i	$-0.273793\pi$
$318$		0			0
$319$	94411.0			0.0519453
$320$	512907.	+	638761.i	0.280004	+	0.348709i
$321$		0			0
$322$	−788594.	−	1.06726e6i	−0.423851	−	0.573627i
$323$		−	260430.i		−	0.138894i
$324$		0			0
$325$			645056.i			0.338758i
$326$	−2.82529e6	+	2.08760e6i	−1.47237	+	1.08793i
$327$		0			0
$328$	−2.72087e6	+	957196.i	−1.39644	+	0.491265i
$329$	−662030.			−0.337200
$330$		0			0
$331$			238802.i			0.119803i	0.998204	+	0.0599015i	$0.0190787\pi$
$331$			238802.i			0.119803i	−0.998204	+	0.0599015i	$0.980921\pi$
$332$	3.30544e6	+	1.01555e6i	1.64583	+	0.505657i
$333$		0			0
$334$	847312.	+	1.14672e6i	0.415601	+	0.562462i
$335$	566158.			0.275629
$336$		0			0
$337$	−21973.1			−0.0105394			−0.00526971	−	0.999986i	$-0.501677\pi$
$337$	−21973.1			−0.0105394			−0.00526971	+	0.999986i	$0.501677\pi$
$338$	−2.33274e6	−	3.15705e6i	−1.11064	−	1.50311i
$339$		0			0
$340$	578547.	+	177750.i	0.271420	+	0.0833899i
$341$		−	34211.7i		−	0.0159327i
$342$		0			0
$343$	−1.47983e6			−0.679166
$344$	−286634.	−	814771.i	−0.130597	−	0.371227i
$345$		0			0
$346$	−1.17662e6	+	869400.i	−0.528379	+	0.390418i
$347$			1.79508e6i			0.800312i	0.916447	+	0.400156i	$0.131044\pi$
$347$			1.79508e6i			0.800312i	−0.916447	+	0.400156i	$0.868956\pi$
$348$		0			0
$349$			2.42117e6i			1.06405i	0.846729	+	0.532025i	$0.178569\pi$
$349$			2.42117e6i			1.06405i	−0.846729	+	0.532025i	$0.821431\pi$
$350$	−99045.3	−	134045.i	−0.0432179	−	0.0584898i
$351$		0			0
$352$	1.46893e6	−	59072.6i	0.631892	−	0.0254115i
$353$	−2.66389e6			−1.13784			−0.568918	−	0.822395i	$-0.692638\pi$
$353$	−2.66389e6			−1.13784			−0.568918	+	0.822395i	$0.692638\pi$
$354$		0			0
$355$			1.34750e6i			0.567490i
$356$	770146.	−	2.50669e6i	0.322068	−	1.04828i
$357$		0			0
$358$	−2.61472e6	+	1.93201e6i	−1.07825	+	0.796713i
$359$	1.36013e6			0.556986			0.278493	−	0.960438i	$-0.410165\pi$
$359$	1.36013e6			0.556986			0.278493	+	0.960438i	$0.410165\pi$
$360$		0			0
$361$	2.35760e6			0.952143
$362$	1.94743e6	−	1.43895e6i	0.781071	−	0.577131i
$363$		0			0
$364$	1.48825e6	+	457244.i	0.588739	+	0.180882i
$365$		−	1.28218e6i		−	0.503751i
$366$		0			0
$367$	2.21077e6			0.856796			0.428398	−	0.903590i	$-0.359078\pi$
$367$	2.21077e6			0.856796			0.428398	+	0.903590i	$0.359078\pi$
$368$	4.21663e6	+	2.86107e6i	1.62310	+	1.10131i
$369$		0			0
$370$	559163.	+	756754.i	0.212341	+	0.287376i
$371$			277838.i			0.104799i
$372$		0			0
$373$		−	573375.i		−	0.213386i	−0.994292	−	0.106693i	$-0.965974\pi$
$373$		−	573375.i		−	0.213386i	0.994292	−	0.106693i	$-0.0340263\pi$
$374$	873547.	−	645461.i	0.322929	−	0.238611i
$375$		0			0
$376$	2.39811e6	−	843651.i	0.874783	−	0.307746i
$377$	−383941.			−0.139127
$378$		0			0
$379$		−	3.23007e6i		−	1.15509i	−0.816360	−	0.577543i	$-0.804012\pi$
$379$		−	3.23007e6i		−	1.15509i	0.816360	−	0.577543i	$-0.195988\pi$
$380$	80878.0	−	263244.i	0.0287324	−	0.0935189i
$381$		0			0
$382$	−1.98416e6	−	2.68530e6i	−0.695693	−	0.941530i
$383$	−452284.			−0.157549			−0.0787743	−	0.996892i	$-0.525101\pi$
$383$	−452284.			−0.157549			−0.0787743	+	0.996892i	$0.525101\pi$
$384$		0			0
$385$	−299096.			−0.102839
$386$	−628274.	−	850286.i	−0.214625	−	0.290467i
$387$		0			0
$388$	−493721.	+	1.60698e6i	−0.166495	+	0.541914i
$389$			2.60438e6i			0.872632i	0.899794	+	0.436316i	$0.143717\pi$
$389$			2.60438e6i			0.872632i	−0.899794	+	0.436316i	$0.856283\pi$
$390$		0			0
$391$	3.76474e6			1.24536
$392$	2.49050e6	−	876153.i	0.818601	−	0.287982i
$393$		0			0
$394$	−1.32850e6	+	981623.i	−0.431142	+	0.318569i
$395$			1.02097e6i			0.329244i
$396$		0			0
$397$		−	5.23930e6i		−	1.66839i	−0.551472	−	0.834193i	$-0.685934\pi$
$397$		−	5.23930e6i		−	1.66839i	0.551472	−	0.834193i	$-0.314066\pi$
$398$	2.23979e6	+	3.03126e6i	0.708760	+	0.959214i
$399$		0			0
$400$	529597.	+	359342.i	0.165499	+	0.112294i
$401$	−2.42996e6			−0.754639			−0.377319	−	0.926083i	$-0.623154\pi$
$401$	−2.42996e6			−0.754639			−0.377319	+	0.926083i	$0.623154\pi$
$402$		0			0
$403$			139129.i			0.0426731i
$404$	2.01917e6	+	620363.i	0.615489	+	0.189100i
$405$		0			0
$406$	79784.2	−	58952.3i	0.0240216	−	0.0177495i
$407$	1.68856e6			0.505277
$408$		0			0
$409$	2.21703e6			0.655336			0.327668	−	0.944793i	$-0.393737\pi$
$409$	2.21703e6			0.655336			0.327668	+	0.944793i	$0.393737\pi$
$410$	−1.81232e6	+	1.33912e6i	−0.532446	+	0.393422i
$411$		0			0
$412$	43462.2	−	141462.i	0.0126145	−	0.0410579i
$413$		−	1.41976e6i		−	0.409580i
$414$		0			0
$415$	2.70151e6			0.769991
$416$	−5.97368e6	+	240230.i	−1.69242	+	0.0680604i
$417$		0			0
$418$	−293690.	−	397471.i	−0.0822146	−	0.111267i
$419$		−	5.47841e6i		−	1.52447i	−0.647299	−	0.762236i	$-0.724101\pi$
$419$		−	5.47841e6i		−	1.52447i	0.647299	−	0.762236i	$-0.275899\pi$
$420$		0			0
$421$			1.25486e6i			0.345055i	0.985005	+	0.172528i	$0.0551934\pi$
$421$			1.25486e6i			0.345055i	−0.985005	+	0.172528i	$0.944807\pi$
$422$	−4.00853e6	+	2.96189e6i	−1.09573	+	0.809633i
$423$		0			0
$424$	−354059.	−	1.00643e6i	−0.0956448	−	0.271875i
$425$	472842.			0.126982
$426$		0			0
$427$		−	1.09101e6i		−	0.289575i
$428$	−5.43664e6	−	1.67033e6i	−1.43457	−	0.440751i
$429$		0			0
$430$	−401001.	−	542703.i	−0.104586	−	0.141544i
$431$	1.51168e6			0.391984			0.195992	−	0.980606i	$-0.437207\pi$
$431$	1.51168e6			0.391984			0.195992	+	0.980606i	$0.437207\pi$
$432$		0			0
$433$	−4.14633e6			−1.06278			−0.531390	−	0.847127i	$-0.678330\pi$
$433$	−4.14633e6			−1.06278			−0.531390	+	0.847127i	$0.678330\pi$
$434$	−21362.5	−	28911.4i	−0.00544413	−	0.00736792i
$435$		0			0
$436$	−4.82021e6	−	1.48094e6i	−1.21437	−	0.373097i
$437$		−	1.71299e6i		−	0.429093i
$438$		0			0
$439$	4.17351e6			1.03357			0.516786	−	0.856115i	$-0.327128\pi$
$439$	4.17351e6			1.03357			0.516786	+	0.856115i	$0.327128\pi$
$440$	1.08344e6	−	381150.i	0.266792	−	0.0938566i
$441$		0			0
$442$	−3.55245e6	+	2.62489e6i	−0.864913	+	0.639081i
$443$		−	1.12969e6i		−	0.273496i	−0.990606	−	0.136748i	$-0.956335\pi$
$443$		−	1.12969e6i		−	0.273496i	0.990606	−	0.136748i	$-0.0436651\pi$
$444$		0			0
$445$		−	2.04870e6i		−	0.490431i
$446$	−3.40077e6	−	4.60249e6i	−0.809543	−	1.09561i
$447$		0			0
$448$	1.20446e6	−	967150.i	0.283530	−	0.227666i
$449$	584617.			0.136853			0.0684266	−	0.997656i	$-0.478202\pi$
$449$	584617.			0.136853			0.0684266	+	0.997656i	$0.478202\pi$
$450$		0			0
$451$			4.04386e6i			0.936170i
$452$	1.91157e6	−	6.22184e6i	0.440093	−	1.43243i
$453$		0			0
$454$	4.69643e6	−	3.47017e6i	1.06937	−	0.790154i
$455$	1.21633e6			0.275438
$456$		0			0
$457$	−5.96781e6			−1.33667			−0.668335	−	0.743860i	$-0.732993\pi$
$457$	−5.96781e6			−1.33667			−0.668335	+	0.743860i	$0.732993\pi$
$458$	−1.22430e6	+	904630.i	−0.272724	+	0.201515i
$459$		0			0
$460$	3.80542e6	+	1.16916e6i	0.838510	+	0.257620i
$461$		−	5.60132e6i		−	1.22755i	−0.789482	−	0.613774i	$-0.789651\pi$
$461$		−	5.60132e6i		−	1.22755i	0.789482	−	0.613774i	$-0.210349\pi$
$462$		0			0
$463$	2.41865e6			0.524348			0.262174	−	0.965021i	$-0.415561\pi$
$463$	2.41865e6			0.524348			0.262174	+	0.965021i	$0.415561\pi$
$464$	−213883.	+	315219.i	−0.0461190	+	0.0679701i
$465$		0			0
$466$	−4.21598e6	−	5.70577e6i	−0.899360	−	1.21717i
$467$			598924.i			0.127081i	0.997979	+	0.0635403i	$0.0202392\pi$
$467$			598924.i			0.127081i	−0.997979	+	0.0635403i	$0.979761\pi$
$468$		0			0
$469$		−	1.06756e6i		−	0.224110i
$470$	1.59734e6	−	1.18027e6i	0.333543	−	0.246454i
$471$		0			0
$472$	1.80925e6	+	5.14288e6i	0.373804	+	1.06256i
$473$	−1.21094e6			−0.248869
$474$		0			0
$475$		−	215147.i		−	0.0437523i
$476$	335171.	−	1.09092e6i	0.0678030	−	0.220687i
$477$		0			0
$478$	−3.34625e6	−	4.52871e6i	−0.669868	−	0.906578i
$479$	6.30180e6			1.25495			0.627474	−	0.778637i	$-0.284089\pi$
$479$	6.30180e6			1.25495			0.627474	+	0.778637i	$0.284089\pi$
$480$		0			0
$481$	−6.86685e6			−1.35330
$482$	−4.65826e6	−	6.30434e6i	−0.913284	−	1.23601i
$483$		0			0
$484$	−908234.	+	2.95614e6i	−0.176232	+	0.573604i
$485$			1.31337e6i			0.253532i
$486$		0			0
$487$	4.59697e6			0.878314			0.439157	−	0.898410i	$-0.355277\pi$
$487$	4.59697e6			0.878314			0.439157	+	0.898410i	$0.355277\pi$
$488$	1.39032e6	+	3.95206e6i	0.264281	+	0.751231i
$489$		0			0
$490$	1.65888e6	−	1.22574e6i	0.312122	−	0.230626i
$491$			2.80880e6i			0.525795i	0.964824	+	0.262898i	$0.0846782\pi$
$491$			2.80880e6i			0.525795i	−0.964824	+	0.262898i	$0.915322\pi$
$492$		0			0
$493$			281438.i			0.0521513i
$494$	1.19435e6	+	1.61639e6i	0.220198	+	0.298009i
$495$		0			0
$496$	114226.	+	77504.6i	0.0208478	+	0.0141457i
$497$	2.54088e6			0.461417
$498$		0			0
$499$			8.10859e6i			1.45779i	0.684628	+	0.728893i	$0.259965\pi$
$499$			8.10859e6i			1.45779i	−0.684628	+	0.728893i	$0.740035\pi$
$500$	477951.	+	146844.i	0.0854984	+	0.0262682i
$501$		0			0
$502$	−3.89448e6	+	2.87762e6i	−0.689747	+	0.509652i
$503$	2.07254e6			0.365244			0.182622	−	0.983183i	$-0.441542\pi$
$503$	2.07254e6			0.365244			0.182622	+	0.983183i	$0.441542\pi$
$504$		0			0
$505$	1.65025e6			0.287953
$506$	5.74579e6	−	4.24555e6i	0.997639	−	0.737153i
$507$		0			0
$508$	2.58744e6	−	8.42166e6i	0.444847	−	1.44790i
$509$		−	5.79862e6i		−	0.992043i	−0.868310	−	0.496021i	$-0.834794\pi$
$509$		−	5.79862e6i		−	0.992043i	0.868310	−	0.496021i	$-0.165206\pi$
$510$		0			0
$511$	−2.41771e6			−0.409592
$512$	−3.13053e6	+	5.03827e6i	−0.527768	+	0.849388i
$513$		0			0
$514$	−3.86196e6	−	5.22666e6i	−0.644763	−	0.872603i
$515$		−	115616.i		−	0.0192087i
$516$		0			0
$517$		−	3.56417e6i		−	0.586451i
$518$	1.42695e6	−	1.05437e6i	0.233661	−	0.172651i
$519$		0			0
$520$	−4.40601e6	+	1.55002e6i	−0.714557	+	0.251379i
$521$	3.54910e6			0.572828			0.286414	−	0.958106i	$-0.407537\pi$
$521$	3.54910e6			0.572828			0.286414	+	0.958106i	$0.407537\pi$
$522$		0			0
$523$		−	1.24052e7i		−	1.98312i	−0.129651	−	0.991560i	$-0.541386\pi$
$523$		−	1.24052e7i		−	1.98312i	0.129651	−	0.991560i	$-0.458614\pi$
$524$	5.29178e6	+	1.62582e6i	0.841925	+	0.258670i
$525$		0			0
$526$	448995.	+	607655.i	0.0707582	+	0.0957619i
$527$	101985.			0.0159959
$528$		0			0
$529$	1.83264e7			2.84733
$530$	−495329.	−	670363.i	−0.0765957	−	0.103662i
$531$		0			0
$532$	−496379.	−	152506.i	−0.0760387	−	0.0233618i
$533$		−	1.64451e7i		−	2.50738i
$534$		0			0
$535$	−4.44332e6			−0.671155
$536$	1.36044e6	+	3.86710e6i	0.204534	+	0.581398i
$537$		0			0
$538$	2.16757e6	−	1.60161e6i	0.322862	−	0.238562i
$539$		−	3.70148e6i		−	0.548786i
$540$		0			0
$541$		−	9.81000e6i		−	1.44104i	−0.693434	−	0.720520i	$-0.743903\pi$
$541$		−	9.81000e6i		−	1.44104i	0.693434	−	0.720520i	$-0.256097\pi$
$542$	−7.68474e6	−	1.04003e7i	−1.12365	−	1.52071i
$543$		0			0
$544$	176095.	+	4.37885e6i	0.0255123	+	0.634399i
$545$	−3.93952e6			−0.568135
$546$		0			0
$547$		−	493400.i		−	0.0705067i	−0.999378	−	0.0352534i	$-0.988776\pi$
$547$		−	493400.i		−	0.0705067i	0.999378	−	0.0352534i	$-0.0112238\pi$
$548$	−1.67222e6	+	5.44278e6i	−0.237871	+	0.774229i
$549$		0			0
$550$	721656.	−	533230.i	0.101724	−	0.0751636i
$551$	128057.			0.0179690
$552$		0			0
$553$	1.92516e6			0.267703
$554$	−4.68544e6	+	3.46206e6i	−0.648599	+	0.479248i
$555$		0			0
$556$	−4.09730e6	−	1.25884e6i	−0.562096	−	0.172696i
$557$			8.46020e6i			1.15543i	0.816239	+	0.577714i	$0.196055\pi$
$557$			8.46020e6i			1.15543i	−0.816239	+	0.577714i	$0.803945\pi$
$558$		0			0
$559$	4.92453e6			0.666554
$560$	677585.	−	998622.i	0.0913048	−	0.134565i
$561$		0			0
$562$	−1.66389e6	−	2.25185e6i	−0.222220	−	0.300746i
$563$		−	2.63523e6i		−	0.350387i	−0.984534	−	0.175194i	$-0.943945\pi$
$563$		−	2.63523e6i		−	0.350387i	0.984534	−	0.175194i	$-0.0560551\pi$
$564$		0			0
$565$		−	5.08505e6i		−	0.670154i
$566$	1.36280e6	−	1.00697e6i	0.178810	−	0.132122i
$567$		0			0
$568$	−9.20401e6	+	3.23795e6i	−1.19703	+	0.421113i
$569$	−3.68731e6			−0.477451			−0.238725	−	0.971087i	$-0.576730\pi$
$569$	−3.68731e6			−0.477451			−0.238725	+	0.971087i	$0.576730\pi$
$570$		0			0
$571$		−	7.92295e6i		−	1.01694i	−0.861079	−	0.508471i	$-0.830211\pi$
$571$		−	7.92295e6i		−	1.01694i	0.861079	−	0.508471i	$-0.169789\pi$
$572$	−2.46166e6	+	8.01229e6i	−0.314585	+	1.02392i
$573$		0			0
$574$	2.52507e6	+	3.41736e6i	0.319885	+	0.432923i
$575$	3.11014e6			0.392292
$576$		0			0
$577$	7.78576e6			0.973558			0.486779	−	0.873525i	$-0.338172\pi$
$577$	7.78576e6			0.973558			0.486779	+	0.873525i	$0.338172\pi$
$578$	−2.84902e6	−	3.85577e6i	−0.354712	−	0.480056i
$579$		0			0
$580$	−87402.2	+	284479.i	−0.0107883	+	0.0351140i
$581$		−	5.09403e6i		−	0.626068i
$582$		0			0
$583$	−1.49579e6			−0.182264
$584$	8.75783e6	−	3.08098e6i	1.06259	−	0.373815i
$585$		0			0
$586$	−2.39212e6	+	1.76753e6i	−0.287766	+	0.212629i
$587$			8.90940e6i			1.06722i	0.845731	+	0.533609i	$0.179165\pi$
$587$			8.90940e6i			1.06722i	−0.845731	+	0.533609i	$0.820835\pi$
$588$		0			0
$589$		−	46403.9i		−	0.00551145i
$590$	2.53115e6	+	3.42557e6i	0.299356	+	0.405138i
$591$		0			0
$592$	−3.82532e6	+	5.63775e6i	−0.448605	+	0.661152i
$593$	−2.33553e6			−0.272740			−0.136370	−	0.990658i	$-0.543544\pi$
$593$	−2.33553e6			−0.272740			−0.136370	+	0.990658i	$0.543544\pi$
$594$		0			0
$595$		−	891602.i		−	0.103247i
$596$	1.51243e7	+	4.64673e6i	1.74405	+	0.535835i
$597$		0			0
$598$	−2.33664e7	+	1.72654e7i	−2.67201	+	1.97434i
$599$	1.19930e7			1.36572			0.682859	−	0.730550i	$-0.260736\pi$
$599$	1.19930e7			1.36572			0.682859	+	0.730550i	$0.260736\pi$
$600$		0			0
$601$	2.37038e6			0.267689			0.133845	−	0.991002i	$-0.457268\pi$
$601$	2.37038e6			0.267689			0.133845	+	0.991002i	$0.457268\pi$
$602$	−1.02333e6	+	756138.i	−0.115087	+	0.0850374i
$603$		0			0
$604$	1.52603e6	−	4.96697e6i	0.170205	−	0.553986i
$605$			2.41603e6i			0.268358i
$606$		0			0
$607$	3.22254e6			0.354998			0.177499	−	0.984121i	$-0.443199\pi$
$607$	3.22254e6			0.354998			0.177499	+	0.984121i	$0.443199\pi$
$608$	1.99241e6	−	80124.6i	0.218585	−	0.00879036i
$609$		0			0
$610$	1.94506e6	+	2.63239e6i	0.211646	+	0.286434i
$611$			1.44944e7i			1.57071i
$612$		0			0
$613$			1.82202e6i			0.195840i	0.995194	+	0.0979199i	$0.0312189\pi$
$613$			1.82202e6i			0.195840i	−0.995194	+	0.0979199i	$0.968781\pi$
$614$	−8.68050e6	+	6.41399e6i	−0.929231	+	0.686606i
$615$		0			0
$616$	−718707.	−	2.04296e6i	−0.0763132	−	0.216924i
$617$	−8.01310e6			−0.847399			−0.423699	−	0.905803i	$-0.639269\pi$
$617$	−8.01310e6			−0.847399			−0.423699	+	0.905803i	$0.639269\pi$
$618$		0			0
$619$			1.75655e7i			1.84261i	0.388839	+	0.921306i	$0.372876\pi$
$619$			1.75655e7i			1.84261i	−0.388839	+	0.921306i	$0.627124\pi$
$620$	103087.	+	31671.9i	0.0107702	+	0.00330899i
$621$		0			0
$622$	8.50853e6	+	1.15152e7i	0.881817	+	1.19342i
$623$	−3.86308e6			−0.398761
$624$		0			0
$625$	390625.			0.0400000
$626$	−3.83640e6	−	5.19207e6i	−0.391281	−	0.529547i
$627$		0			0
$628$	4.65911e6	+	1.43145e6i	0.471415	+	0.144836i
$629$			5.03356e6i			0.507281i
$630$		0			0
$631$	1.66158e6			0.166130			0.0830650	−	0.996544i	$-0.473529\pi$
$631$	1.66158e6			0.166130			0.0830650	+	0.996544i	$0.473529\pi$
$632$	−6.97363e6	+	2.45330e6i	−0.694490	+	0.244320i
$633$		0			0
$634$	1.23392e7	−	9.11739e6i	1.21917	−	0.900840i
$635$		−	6.88295e6i		−	0.677392i
$636$		0			0
$637$			1.50528e7i			1.46983i
$638$	317381.	+	429534.i	0.0308695	+	0.0417778i
$639$		0			0
$640$	−1.18188e6	+	4.48085e6i	−0.114057	+	0.432424i
$641$	−4.45104e6			−0.427875			−0.213937	−	0.976847i	$-0.568629\pi$
$641$	−4.45104e6			−0.427875			−0.213937	+	0.976847i	$0.568629\pi$
$642$		0			0
$643$		−	508859.i		−	0.0485367i	−0.999705	−	0.0242684i	$-0.992274\pi$
$643$		−	508859.i		−	0.0485367i	0.999705	−	0.0242684i	$-0.00772561\pi$
$644$	2.20460e6	−	7.17560e6i	0.209467	−	0.681779i
$645$		0			0
$646$	1.18486e6	−	875486.i	0.111708	−	0.0825407i
$647$	5.45061e6			0.511899			0.255949	−	0.966690i	$-0.417612\pi$
$647$	5.45061e6			0.511899			0.255949	+	0.966690i	$0.417612\pi$
$648$		0			0
$649$	7.64354e6			0.712333
$650$	−2.93476e6	+	2.16848e6i	−0.272451	+	0.201313i
$651$		0			0
$652$	−1.89955e7	−	5.83610e6i	−1.74998	−	0.537655i
$653$		−	5.95121e6i		−	0.546163i	−0.961991	−	0.273082i	$-0.911957\pi$
$653$		−	5.95121e6i		−	0.546163i	0.961991	−	0.273082i	$-0.0880429\pi$
$654$		0			0
$655$	4.32492e6			0.393890
$656$	−1.35016e7	−	9.16112e6i	−1.22497	−	0.831168i
$657$		0			0
$658$	−2.22554e6	−	3.01198e6i	−0.200388	−	0.271199i
$659$			3.61561e6i			0.324316i	0.986765	+	0.162158i	$0.0518454\pi$
$659$			3.61561e6i			0.324316i	−0.986765	+	0.162158i	$0.948155\pi$
$660$		0			0
$661$			8.17394e6i			0.727659i	0.931466	+	0.363829i	$0.118531\pi$
$661$			8.17394e6i			0.727659i	−0.931466	+	0.363829i	$0.881469\pi$
$662$	−1.08646e6	+	802779.i	−0.0963534	+	0.0711953i
$663$		0			0
$664$	6.49152e6	+	1.84525e7i	0.571382	+	1.62418i
$665$	−405686.			−0.0355743
$666$		0			0
$667$			1.85117e6i			0.161113i
$668$	−2.36875e6	+	7.70988e6i	−0.205390	+	0.668508i
$669$		0			0
$670$	1.90325e6	+	2.57580e6i	0.163798	+	0.221679i
$671$	5.87369e6			0.503622
$672$		0			0
$673$	−1.07614e7			−0.915867			−0.457933	−	0.888987i	$-0.651410\pi$
$673$	−1.07614e7			−0.915867			−0.457933	+	0.888987i	$0.651410\pi$
$674$	−73867.0	−	99969.2i	−0.00626326	−	0.00847650i
$675$		0			0
$676$	6.52143e6	−	2.12261e7i	0.548878	−	1.78650i
$677$			1.44154e7i			1.20880i	0.796680	+	0.604401i	$0.206588\pi$
$677$			1.44154e7i			1.20880i	−0.796680	+	0.604401i	$0.793412\pi$
$678$		0			0
$679$	2.47652e6			0.206142
$680$	1.13620e6	+	3.22971e6i	0.0942288	+	0.267850i
$681$		0			0
$682$	155650.	−	115009.i	0.0128141	−	0.00946831i
$683$			9.22051e6i			0.756316i	0.925741	+	0.378158i	$0.123442\pi$
$683$			9.22051e6i			0.756316i	−0.925741	+	0.378158i	$0.876558\pi$
$684$		0			0
$685$			4.44834e6i			0.362219i
$686$	−4.97473e6	−	6.73265e6i	−0.403608	−	0.546230i
$687$		0			0
$688$	2.74332e6	−	4.04309e6i	0.220955	−	0.325643i
$689$	6.08294e6			0.488163
$690$		0			0
$691$			7.56905e6i			0.603040i	0.953460	+	0.301520i	$0.0974940\pi$
$691$			7.56905e6i			0.603040i	−0.953460	+	0.301520i	$0.902506\pi$
$692$	−7.91087e6	−	2.43050e6i	−0.627999	−	0.192944i
$693$		0			0
$694$	−8.16691e6	+	6.03451e6i	−0.643664	+	0.475601i
$695$	−3.34869e6			−0.262974
$696$		0			0
$697$	−1.20547e7			−0.939883
$698$	−1.10154e7	+	8.13924e6i	−0.855779	+	0.632332i
$699$		0			0
$700$	276892.	−	901236.i	0.0213582	−	0.0695174i
$701$			1.80188e7i			1.38494i	0.721448	+	0.692469i	$0.243477\pi$
$701$			1.80188e7i			1.38494i	−0.721448	+	0.692469i	$0.756523\pi$
$702$		0			0
$703$	2.29031e6			0.174786
$704$	5.20684e6	+	6.48446e6i	0.395952	+	0.493108i
$705$		0			0
$706$	−8.95519e6	−	1.21197e7i	−0.676181	−	0.915122i
$707$		−	3.11176e6i		−	0.234130i
$708$		0			0
$709$		−	1.63602e7i		−	1.22229i	−0.791520	−	0.611143i	$-0.790710\pi$
$709$		−	1.63602e7i		−	1.22229i	0.791520	−	0.611143i	$-0.209290\pi$
$710$	−6.13061e6	+	4.52989e6i	−0.456413	+	0.337242i
$711$		0			0
$712$	1.39935e7	−	4.92287e6i	1.03449	−	0.363930i
$713$	670808.			0.0494168
$714$		0			0
$715$			6.54837e6i			0.479036i
$716$	−1.75798e7	−	5.40115e6i	−1.28154	−	0.393735i
$717$		0			0
$718$	4.57234e6	+	6.18807e6i	0.331000	+	0.447965i
$719$	1.78536e7			1.28796			0.643981	−	0.765042i	$-0.277282\pi$
$719$	1.78536e7			1.28796			0.643981	+	0.765042i	$0.277282\pi$
$720$		0			0
$721$	−218008.			−0.0156183
$722$	7.92554e6	+	1.07262e7i	0.565830	+	0.765776i
$723$		0			0
$724$	1.30933e7	+	4.02274e6i	0.928333	+	0.285217i
$725$			232502.i			0.0164279i
$726$		0			0
$727$	−1.64661e7			−1.15546			−0.577731	−	0.816227i	$-0.696062\pi$
$727$	−1.64661e7			−1.15546			−0.577731	+	0.816227i	$0.696062\pi$
$728$	2.92276e6	+	8.30808e6i	0.204393	+	0.580995i
$729$		0			0
$730$	5.83342e6	−	4.31029e6i	0.405150	−	0.299364i
$731$		−	3.60980e6i		−	0.249856i
$732$		0			0
$733$		−	1.89907e7i		−	1.30551i	−0.757568	−	0.652756i	$-0.773613\pi$
$733$		−	1.89907e7i		−	1.30551i	0.757568	−	0.652756i	$-0.226387\pi$
$734$	7.43192e6	+	1.00581e7i	0.509168	+	0.689092i
$735$		0			0
$736$	1.15827e6	+	2.88021e7i	0.0788162	+	1.95988i
$737$	5.74742e6			0.389766
$738$		0			0
$739$		−	1.31894e7i		−	0.888414i	−0.895924	−	0.444207i	$-0.853486\pi$
$739$		−	1.31894e7i		−	0.888414i	0.895924	−	0.444207i	$-0.146514\pi$
$740$	−1.56320e6	+	5.08795e6i	−0.104939	+	0.341557i
$741$		0			0
$742$	−1.26405e6	+	934006.i	−0.0842861	+	0.0622787i
$743$	−1.07718e7			−0.715839			−0.357919	−	0.933752i	$-0.616514\pi$
$743$	−1.07718e7			−0.715839			−0.357919	+	0.933752i	$0.616514\pi$
$744$		0			0
$745$	1.23610e7			0.815946
$746$	2.60863e6	−	1.92751e6i	0.171619	−	0.126809i
$747$		0			0
$748$	5.87320e6	+	1.80446e6i	0.383814	+	0.117921i
$749$			8.37844e6i			0.545706i
$750$		0			0
$751$	9.68507e6			0.626618			0.313309	−	0.949651i	$-0.398562\pi$
$751$	9.68507e6			0.626618			0.313309	+	0.949651i	$0.398562\pi$
$752$	1.19000e7	+	8.07440e6i	0.767367	+	0.520674i
$753$		0			0
$754$	−1.29069e6	−	1.74678e6i	−0.0826789	−	0.111895i
$755$		−	4.05946e6i		−	0.259180i
$756$		0			0
$757$			1.71192e7i			1.08578i	0.839803	+	0.542891i	$0.182670\pi$
$757$			1.71192e7i			1.08578i	−0.839803	+	0.542891i	$0.817330\pi$
$758$	1.46956e7	−	1.08585e7i	0.928996	−	0.686432i
$759$		0			0
$760$	1.46955e6	−	516982.i	0.0922888	−	0.0324670i
$761$	6.88918e6			0.431227			0.215614	−	0.976479i	$-0.430825\pi$
$761$	6.88918e6			0.431227			0.215614	+	0.976479i	$0.430825\pi$
$762$		0			0
$763$			7.42845e6i			0.461941i
$764$	5.54693e6	−	1.80543e7i	0.343811	−	1.11904i
$765$		0			0
$766$	−1.52044e6	−	2.05772e6i	−0.0936264	−	0.126711i
$767$	−3.10840e7			−1.90787
$768$		0			0
$769$	−2.01582e7			−1.22924			−0.614618	−	0.788825i	$-0.710690\pi$
$769$	−2.01582e7			−1.22924			−0.614618	+	0.788825i	$0.710690\pi$
$770$	−1.00547e6	−	1.36077e6i	−0.0611143	−	0.0827102i
$771$		0			0
$772$	1.75641e6	−	5.71681e6i	0.106067	−	0.345231i
$773$		−	9.58833e6i		−	0.577158i	−0.957456	−	0.288579i	$-0.906817\pi$
$773$		−	9.58833e6i		−	0.577158i	0.957456	−	0.288579i	$-0.0931827\pi$
$774$		0			0
$775$	84251.8			0.00503877
$776$	−8.97086e6	+	3.15593e6i	−0.534786	+	0.188136i
$777$		0			0
$778$	−1.18489e7	+	8.75515e6i	−0.701828	+	0.518579i
$779$			5.48498e6i			0.323841i
$780$		0			0
$781$			1.36793e7i			0.802486i
$782$	1.26559e7	+	1.71281e7i	0.740077	+	1.00160i
$783$		0			0
$784$	1.23585e7	+	8.38547e6i	0.718083	+	0.487234i
$785$	3.80785e6			0.220549
$786$		0			0
$787$		−	3.07200e6i		−	0.176801i	−0.996085	−	0.0884003i	$-0.971825\pi$
$787$		−	3.07200e6i		−	0.176801i	0.996085	−	0.0884003i	$-0.0281755\pi$
$788$	−8.93201e6	−	2.74423e6i	−0.512429	−	0.157437i
$789$		0			0
$790$	−4.64500e6	+	3.43217e6i	−0.264800	+	0.195660i
$791$	−9.58851e6			−0.544891
$792$		0			0
$793$	−2.38865e7			−1.34887
$794$	2.38368e7	−	1.76129e7i	1.34183	−	0.991471i
$795$		0			0
$796$	−6.26158e6	+	2.03803e7i	−0.350268	+	1.14006i
$797$		−	2.69531e6i		−	0.150301i	−0.997172	−	0.0751506i	$-0.976056\pi$
$797$		−	2.69531e6i		−	0.150301i	0.997172	−	0.0751506i	$-0.0239438\pi$
$798$		0			0
$799$	1.06247e7			0.588777
$800$	145476.	+	3.61746e6i	0.00803647	+	0.199838i
$801$		0			0
$802$	−8.16880e6	−	1.10554e7i	−0.448459	−	0.606930i
$803$		−	1.30162e7i		−	0.712353i
$804$		0			0
$805$		−	5.86455e6i		−	0.318967i
$806$	−632982.	+	467708.i	−0.0343205	+	0.0253593i
$807$		0			0
$808$	3.96544e6	+	1.12719e7i	0.213679	+	0.607393i
$809$	−1.37752e7			−0.739991			−0.369996	−	0.929034i	$-0.620641\pi$
$809$	−1.37752e7			−0.739991			−0.369996	+	0.929034i	$0.620641\pi$
$810$		0			0
$811$			1.00830e7i			0.538316i	0.963096	+	0.269158i	$0.0867454\pi$
$811$			1.00830e7i			0.538316i	−0.963096	+	0.269158i	$0.913255\pi$
$812$	536421.	+	164808.i	0.0285506	+	0.00877178i
$813$		0			0
$814$	5.67642e6	+	7.68228e6i	0.300271	+	0.406377i
$815$	−1.55249e7			−0.818717
$816$		0			0
$817$	−1.64249e6			−0.0860890
$818$	7.45299e6	+	1.00867e7i	0.389446	+	0.527064i
$819$		0			0
$820$	−1.21849e7	−	3.74365e6i	−0.632832	−	0.194429i
$821$			1.21926e7i			0.631303i	0.948875	+	0.315651i	$0.102223\pi$
$821$			1.21926e7i			0.631303i	−0.948875	+	0.315651i	$0.897777\pi$
$822$		0			0
$823$	−383000.			−0.0197105			−0.00985527	−	0.999951i	$-0.503137\pi$
$823$	−383000.			−0.0197105			−0.00985527	+	0.999951i	$0.503137\pi$
$824$	789704.	−	277816.i	0.0405178	−	0.0142541i
$825$		0			0
$826$	6.45935e6	−	4.77279e6i	0.329411	−	0.243401i
$827$		−	9.81451e6i		−	0.499005i	−0.968374	−	0.249502i	$-0.919733\pi$
$827$		−	9.81451e6i		−	0.499005i	0.968374	−	0.249502i	$-0.0802671\pi$
$828$		0			0
$829$		−	1.94664e6i		−	0.0983782i	−0.998789	−	0.0491891i	$-0.984336\pi$
$829$		−	1.94664e6i		−	0.0983782i	0.998789	−	0.0491891i	$-0.0156637\pi$
$830$	9.08165e6	+	1.22908e7i	0.457583	+	0.619278i
$831$		0			0
$832$	−2.11746e7	−	2.63703e7i	−1.06049	−	1.32071i
$833$	1.10340e7			0.550963
$834$		0			0
$835$			6.30122e6i			0.312758i
$836$	821043.	−	2.67235e6i	0.0406303	−	0.132245i
$837$		0			0
$838$	2.49247e7	−	1.84168e7i	1.22608	−	0.905948i
$839$	−1.04571e7			−0.512868			−0.256434	−	0.966562i	$-0.582548\pi$
$839$	−1.04571e7			−0.512868			−0.256434	+	0.966562i	$0.582548\pi$
$840$		0			0
$841$	2.03728e7			0.993253
$842$	−5.70911e6	+	4.21845e6i	−0.277516	+	0.205056i
$843$		0			0
$844$	−2.69510e7	−	8.28030e6i	−1.30232	−	0.400120i
$845$		−	1.73479e7i		−	0.835806i
$846$		0			0
$847$	4.55573e6			0.218197
$848$	3.38863e6	−	4.99415e6i	0.161821	−	0.238491i
$849$		0			0
$850$	1.58955e6	+	2.15125e6i	0.0754617	+	0.102128i
$851$			3.31085e7i			1.56717i
$852$		0			0
$853$		−	762753.i		−	0.0358931i	−0.999839	−	0.0179466i	$-0.994287\pi$
$853$		−	762753.i		−	0.0358931i	0.999839	−	0.0179466i	$-0.00571288\pi$
$854$	4.96370e6	−	3.66766e6i	0.232895	−	0.172086i
$855$		0			0
$856$	−1.06770e7	−	3.03498e7i	−0.498039	−	1.41570i
$857$	−1.88500e7			−0.876717			−0.438358	−	0.898800i	$-0.644440\pi$
$857$	−1.88500e7			−0.876717			−0.438358	+	0.898800i	$0.644440\pi$
$858$		0			0
$859$		−	2.00534e7i		−	0.927269i	−0.886027	−	0.463634i	$-0.846545\pi$
$859$		−	2.00534e7i		−	0.927269i	0.886027	−	0.463634i	$-0.153455\pi$
$860$	1.12104e6	−	3.64880e6i	0.0516864	−	0.168230i
$861$		0			0
$862$	5.08182e6	+	6.87758e6i	0.232944	+	0.315259i
$863$	3.43348e6			0.156931			0.0784653	−	0.996917i	$-0.474998\pi$
$863$	3.43348e6			0.156931			0.0784653	+	0.996917i	$0.474998\pi$
$864$		0			0
$865$	−6.46549e6			−0.293806
$866$	−1.39387e7	−	1.88642e7i	−0.631578	−	0.854758i
$867$		0			0
$868$	59721.3	−	194383.i	0.00269048	−	0.00875706i
$869$			1.03645e7i			0.465583i
$870$		0			0
$871$	−2.33730e7			−1.04393
$872$	−9.46637e6	−	2.69086e7i	−0.421592	−	1.19839i
$873$		0			0
$874$	7.79344e6	−	5.75855e6i	0.345105	−	0.254997i
$875$		−	736572.i		−	0.0325234i
$876$		0			0
$877$			522042.i			0.0229196i	0.999934	+	0.0114598i	$0.00364784\pi$
$877$			522042.i			0.0229196i	−0.999934	+	0.0114598i	$0.996352\pi$
$878$	1.40301e7	+	1.89879e7i	0.614220	+	0.831266i
$879$		0			0
$880$	5.37627e6	+	3.64791e6i	0.234032	+	0.158795i
$881$	7.98479e6			0.346596			0.173298	−	0.984869i	$-0.444558\pi$
$881$	7.98479e6			0.346596			0.173298	+	0.984869i	$0.444558\pi$
$882$		0			0
$883$		−	3.50061e7i		−	1.51092i	−0.655195	−	0.755460i	$-0.727413\pi$
$883$		−	3.50061e7i		−	1.51092i	0.655195	−	0.755460i	$-0.272587\pi$
$884$	−2.38845e7	−	7.33818e6i	−1.02798	−	0.315833i
$885$		0			0
$886$	5.13967e6	−	3.79768e6i	0.219964	−	0.162530i
$887$	1.12935e7			0.481967			0.240984	−	0.970529i	$-0.422530\pi$
$887$	1.12935e7			0.481967			0.240984	+	0.970529i	$0.422530\pi$
$888$		0			0
$889$	−1.29787e7			−0.550776
$890$	9.32079e6	−	6.88710e6i	0.394437	−	0.291448i
$891$		0			0
$892$	9.50722e6	−	3.09444e7i	0.400075	−	1.30218i
$893$		−	4.83434e6i		−	0.202866i
$894$		0			0
$895$	−1.43678e7			−0.599561
$896$	8.44920e6	+	2.22858e6i	0.351597	+	0.0927381i
$897$		0			0
$898$	1.96530e6	+	2.65978e6i	0.0813277	+	0.110066i
$899$			50147.1i			0.00206941i
$900$		0			0
$901$		−	4.45894e6i		−	0.182987i
$902$	−1.83980e7	+	1.35942e7i	−0.752929	+	0.556337i
$903$		0			0
$904$	3.47331e7	−	1.22190e7i	1.41359	−	0.497296i
$905$	1.07011e7			0.434316
$906$		0			0
$907$			2.01754e7i			0.814338i	0.913353	+	0.407169i	$0.133484\pi$
$907$			2.01754e7i			0.814338i	−0.913353	+	0.407169i	$0.866516\pi$
$908$	3.15759e7	+	9.70126e6i	1.27099	+	0.390493i
$909$		0			0
$910$	4.08895e6	+	5.53385e6i	0.163685	+	0.221526i
$911$	−1.61032e7			−0.642859			−0.321430	−	0.946933i	$-0.604163\pi$
$911$	−1.61032e7			−0.642859			−0.321430	+	0.946933i	$0.604163\pi$
$912$		0			0
$913$	2.74247e7			1.08884
$914$	−2.00620e7	−	2.71512e7i	−0.794343	−	1.07504i
$915$		0			0
$916$	−8.23144e6	−	2.52899e6i	−0.324143	−	0.0995885i
$917$		−	8.15518e6i		−	0.320266i
$918$		0			0
$919$	−7.96458e6			−0.311082			−0.155541	−	0.987829i	$-0.549712\pi$
$919$	−7.96458e6			−0.311082			−0.155541	+	0.987829i	$0.549712\pi$
$920$	7.47343e6	+	2.12436e7i	0.291106	+	0.827481i
$921$		0			0
$922$	2.54839e7	−	1.88299e7i	0.987274	−	0.729494i
$923$		−	5.56297e7i		−	2.14933i
$924$		0			0
$925$			4.15834e6i			0.159796i
$926$	8.13075e6	+	1.10039e7i	0.311604	+	0.421715i
$927$		0			0
$928$	−2.15313e6	+	86588.0i	−0.0820731	+	0.00330056i
$929$	1.21673e7			0.462547			0.231273	−	0.972889i	$-0.425711\pi$
$929$	1.21673e7			0.462547			0.231273	+	0.972889i	$0.425711\pi$
$930$		0			0
$931$		−	5.02059e6i		−	0.189837i
$932$	1.17862e7	−	3.83622e7i	0.444463	−	1.44665i
$933$		0			0
$934$	−2.72487e6	+	2.01340e6i	−0.102207	+	0.0755202i
$935$	4.80011e6			0.179565
$936$		0			0
$937$	−9.87499e6			−0.367441			−0.183720	−	0.982979i	$-0.558814\pi$
$937$	−9.87499e6			−0.367441			−0.183720	+	0.982979i	$0.558814\pi$
$938$	4.85699e6	−	3.58882e6i	0.180244	−	0.133182i
$939$		0			0
$940$	1.07395e7	+	3.29957e6i	0.396429	+	0.121797i
$941$			1.60023e7i			0.589126i	0.955632	+	0.294563i	$0.0951741\pi$
$941$			1.60023e7i			0.589126i	−0.955632	+	0.294563i	$0.904826\pi$
$942$		0			0
$943$	−7.92902e7			−2.90362
$944$	−1.73160e7	+	2.55202e7i	−0.632437	+	0.932083i
$945$		0			0
$946$	−4.07082e6	−	5.50932e6i	−0.147895	−	0.200157i
$947$		−	1.12341e6i		−	0.0407066i	−0.999793	−	0.0203533i	$-0.993521\pi$
$947$		−	1.12341e6i		−	0.0407066i	0.999793	−	0.0203533i	$-0.00647910\pi$
$948$		0			0
$949$			5.29329e7i			1.90792i
$950$	978836.	−	723259.i	0.0351885	−	0.0260007i
$951$		0			0
$952$	6.09002e6	−	2.14245e6i	0.217784	−	0.0766160i
$953$	−4.80409e7			−1.71348			−0.856740	−	0.515748i	$-0.827514\pi$
$953$	−4.80409e7			−1.71348			−0.856740	+	0.515748i	$0.827514\pi$
$954$		0			0
$955$		−	1.47556e7i		−	0.523539i
$956$	9.35482e6	−	3.04483e7i	0.331048	−	1.07750i
$957$		0			0
$958$	2.11847e7	+	2.86708e7i	0.745778	+	1.00931i
$959$	8.38790e6			0.294515
$960$		0			0
$961$	−2.86110e7			−0.999365
$962$	−2.30843e7	−	3.12415e7i	−0.804226	−	1.08842i
$963$		0			0
$964$	1.30227e7	−	4.23865e7i	0.451344	−	1.46905i
$965$		−	4.67230e6i		−	0.161515i
$966$		0			0
$967$	6.17173e6			0.212247			0.106123	−	0.994353i	$-0.466156\pi$
$967$	6.17173e6			0.212247			0.106123	+	0.994353i	$0.466156\pi$
$968$	−1.65025e7	+	5.80555e6i	−0.566060	+	0.199138i
$969$		0			0
$970$	−5.97532e6	+	4.41514e6i	−0.203907	+	0.150666i
$971$		−	4.28206e7i		−	1.45749i	−0.684788	−	0.728743i	$-0.740105\pi$
$971$		−	4.28206e7i		−	1.45749i	0.684788	−	0.728743i	$-0.259895\pi$
$972$		0			0
$973$			6.31437e6i			0.213820i
$974$	1.54536e7	+	2.09145e7i	0.521955	+	0.706398i
$975$		0			0
$976$	−1.33065e7	+	1.96110e7i	−0.447135	+	0.658986i
$977$	3.34844e7			1.12229			0.561147	−	0.827716i	$-0.310360\pi$
$977$	3.34844e7			1.12229			0.561147	+	0.827716i	$0.310360\pi$
$978$		0			0
$979$		−	2.07976e7i		−	0.693517i
$980$	1.11533e7	+	3.42669e6i	0.370969	+	0.113975i
$981$		0			0
$982$	−1.27790e7	+	9.44233e6i	−0.422879	+	0.312464i
$983$	−1.31219e7			−0.433124			−0.216562	−	0.976269i	$-0.569484\pi$
$983$	−1.31219e7			−0.433124			−0.216562	+	0.976269i	$0.569484\pi$
$984$		0			0
$985$	−7.30005e6			−0.239737
$986$	−1.28043e6	+	946109.i	−0.0419435	+	0.0309919i
$987$		0			0
$988$	−3.33893e6	+	1.08677e7i	−0.108822	+	0.354196i
$989$		−	2.37436e7i		−	0.771891i
$990$		0			0
$991$	−3.19619e7			−1.03383			−0.516914	−	0.856037i	$-0.672919\pi$
$991$	−3.19619e7			−1.03383			−0.516914	+	0.856037i	$0.672919\pi$
$992$	31376.9	+	780231.i	0.00101235	+	0.0251735i
$993$		0			0
$994$	8.54168e6	+	1.15600e7i	0.274206	+	0.371102i
$995$			1.66567e7i			0.533373i
$996$		0			0
$997$			1.01694e6i			0.0324009i	0.999869	+	0.0162005i	$0.00515699\pi$
$997$			1.01694e6i			0.0324009i	−0.999869	+	0.0162005i	$0.994843\pi$
$998$	−3.68909e7	+	2.72586e7i	−1.17245	+	0.866318i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.6.k.b.181.16		20
3.2	odd	2		40.6.d.a.21.5	✓	20
8.5	even	2	inner	360.6.k.b.181.15		20
12.11	even	2		160.6.d.a.81.9		20
15.2	even	4		200.6.f.c.149.15		20
15.8	even	4		200.6.f.b.149.6		20
15.14	odd	2		200.6.d.b.101.16		20
24.5	odd	2		40.6.d.a.21.6	yes	20
24.11	even	2		160.6.d.a.81.12		20
60.23	odd	4		800.6.f.c.49.12		20
60.47	odd	4		800.6.f.b.49.9		20
60.59	even	2		800.6.d.c.401.12		20
120.29	odd	2		200.6.d.b.101.15		20
120.53	even	4		200.6.f.c.149.16		20
120.59	even	2		800.6.d.c.401.9		20
120.77	even	4		200.6.f.b.149.5		20
120.83	odd	4		800.6.f.b.49.10		20
120.107	odd	4		800.6.f.c.49.11		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.5	✓	20	3.2	odd	2
40.6.d.a.21.6	yes	20	24.5	odd	2
160.6.d.a.81.9		20	12.11	even	2
160.6.d.a.81.12		20	24.11	even	2
200.6.d.b.101.15		20	120.29	odd	2
200.6.d.b.101.16		20	15.14	odd	2
200.6.f.b.149.5		20	120.77	even	4
200.6.f.b.149.6		20	15.8	even	4
200.6.f.c.149.15		20	15.2	even	4
200.6.f.c.149.16		20	120.53	even	4
360.6.k.b.181.15		20	8.5	even	2	inner
360.6.k.b.181.16		20	1.1	even	1	trivial
800.6.d.c.401.9		20	120.59	even	2
800.6.d.c.401.12		20	60.59	even	2
800.6.f.b.49.9		20	60.47	odd	4
800.6.f.b.49.10		20	120.83	odd	4
800.6.f.c.49.11		20	120.107	odd	4
800.6.f.c.49.12		20	60.23	odd	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.36170 + 4.54962i) q^{2} +(-9.39799 + 30.5888i) q^{4} +25.0000i q^{5} +47.1406 q^{7} +(-170.761 + 60.0732i) q^{8} +O(q^{10})\)	\(q+(3.36170 + 4.54962i) q^{2} +(-9.39799 + 30.5888i) q^{4} +25.0000i q^{5} +47.1406 q^{7} +(-170.761 + 60.0732i) q^{8} +(-113.740 + 84.0424i) q^{10} +253.791i q^{11} -1032.09i q^{13} +(158.472 + 214.472i) q^{14} +(-847.355 - 574.948i) q^{16} -756.546 q^{17} +344.235i q^{19} +(-764.721 - 234.950i) q^{20} +(-1154.65 + 853.167i) q^{22} -4976.22 q^{23} -625.000 q^{25} +(4695.61 - 3469.57i) q^{26} +(-443.027 + 1441.98i) q^{28} -372.003i q^{29} -134.803 q^{31} +(-232.761 - 5787.94i) q^{32} +(-2543.28 - 3442.00i) q^{34} +1178.52i q^{35} -6653.34i q^{37} +(-1566.14 + 1157.21i) q^{38} +(-1501.83 - 4269.02i) q^{40} +15933.8 q^{41} +4771.42i q^{43} +(-7763.17 - 2385.12i) q^{44} +(-16728.5 - 22639.9i) q^{46} -14043.7 q^{47} -14584.8 q^{49} +(-2101.06 - 2843.51i) q^{50} +(31570.4 + 9699.58i) q^{52} +5893.80i q^{53} -6344.77 q^{55} +(-8049.77 + 2831.89i) q^{56} +(1692.47 - 1250.56i) q^{58} -30117.5i q^{59} -23143.8i q^{61} +(-453.166 - 613.301i) q^{62} +(25550.4 - 20516.3i) q^{64} +25802.3 q^{65} -22646.3i q^{67} +(7110.02 - 23141.9i) q^{68} +(-5361.79 + 3961.81i) q^{70} +53900.1 q^{71} -51287.1 q^{73} +(30270.2 - 22366.5i) q^{74} +(-10529.8 - 3235.12i) q^{76} +11963.9i q^{77} +40838.6 q^{79} +(14373.7 - 21183.9i) q^{80} +(53564.7 + 72492.8i) q^{82} -108060. i q^{83} -18913.7i q^{85} +(-21708.1 + 16040.1i) q^{86} +(-15246.0 - 43337.5i) q^{88} -81947.9 q^{89} -48653.4i q^{91} +(46766.5 - 152217. i) q^{92} +(-47210.7 - 63893.5i) q^{94} -8605.88 q^{95} +52534.7 q^{97} +(-49029.5 - 66355.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8	\( 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32} + 21132 q^{34} + 19580 q^{38} + 6200 q^{40} - 11608 q^{41} - 72296 q^{44} - 28516 q^{46} - 44180 q^{47} + 18756 q^{49} + 1250 q^{50} - 39680 q^{52} - 24200 q^{55} + 53624 q^{56} + 59496 q^{58} - 59824 q^{62} - 11264 q^{64} - 11576 q^{68} + 29800 q^{70} + 200312 q^{71} - 105136 q^{73} - 78876 q^{74} - 153872 q^{76} + 282080 q^{79} - 16000 q^{80} - 223032 q^{82} - 27452 q^{86} + 86896 q^{88} + 3160 q^{89} - 107916 q^{92} + 148820 q^{94} - 144400 q^{95} + 147376 q^{97} - 216942 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more