LMFDB - Embedded newform 882.4.g.bk.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 294)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.bk.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.29289 + 3.97141i) q^{5} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.29289 + 3.97141i) q^{5} -8.00000 q^{8} +(-4.58579 + 7.94282i) q^{10} +(-3.24264 + 5.61642i) q^{11} +45.2132 q^{13} +(-8.00000 - 13.8564i) q^{16} +(40.7782 - 70.6299i) q^{17} +(2.52691 + 4.37674i) q^{19} -18.3431 q^{20} -12.9706 q^{22} +(53.1249 + 92.0150i) q^{23} +(51.9853 - 90.0411i) q^{25} +(45.2132 + 78.3116i) q^{26} +268.132 q^{29} +(-146.184 + 253.198i) q^{31} +(16.0000 - 27.7128i) q^{32} +163.113 q^{34} +(-57.2792 - 99.2105i) q^{37} +(-5.05382 + 8.75348i) q^{38} +(-18.3431 - 31.7713i) q^{40} +161.605 q^{41} -471.294 q^{43} +(-12.9706 - 22.4657i) q^{44} +(-106.250 + 184.030i) q^{46} +(173.002 + 299.648i) q^{47} +207.941 q^{50} +(-90.4264 + 156.623i) q^{52} +(202.765 - 351.198i) q^{53} -29.7401 q^{55} +(268.132 + 464.418i) q^{58} +(-126.718 + 219.482i) q^{59} +(375.609 + 650.573i) q^{61} -584.735 q^{62} +64.0000 q^{64} +(103.669 + 179.560i) q^{65} +(-5.82338 + 10.0864i) q^{67} +(163.113 + 282.519i) q^{68} +681.661 q^{71} +(-342.729 + 593.623i) q^{73} +(114.558 - 198.421i) q^{74} -20.2153 q^{76} +(-0.132034 - 0.228690i) q^{79} +(36.6863 - 63.5425i) q^{80} +(161.605 + 279.908i) q^{82} +437.137 q^{83} +374.000 q^{85} +(-471.294 - 816.304i) q^{86} +(25.9411 - 44.9313i) q^{88} +(-29.2563 - 50.6734i) q^{89} -424.999 q^{92} +(-346.004 + 599.297i) q^{94} +(-11.5879 + 20.0708i) q^{95} -1280.09 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 12 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 32 q^{8} - 24 q^{10} + 4 q^{11} + 96 q^{13} - 32 q^{16} + 132 q^{17} - 120 q^{19} - 96 q^{20} + 16 q^{22} - 76 q^{23} + 174 q^{25} + 96 q^{26} + 224 q^{29} - 432 q^{31} + 64 q^{32} + 528 q^{34} + 280 q^{37} + 240 q^{38} - 96 q^{40} - 72 q^{41} - 256 q^{43} + 16 q^{44} + 152 q^{46} - 264 q^{47} + 696 q^{50} - 192 q^{52} + 268 q^{53} + 96 q^{55} + 224 q^{58} + 336 q^{59} + 504 q^{61} - 1728 q^{62} + 256 q^{64} + 228 q^{65} + 384 q^{67} + 528 q^{68} + 792 q^{71} + 312 q^{73} - 560 q^{74} + 960 q^{76} + 848 q^{79} + 192 q^{80} - 72 q^{82} + 1296 q^{83} + 1496 q^{85} - 256 q^{86} - 32 q^{88} - 612 q^{89} + 608 q^{92} + 528 q^{94} + 904 q^{95} - 4368 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 12 * q^5 - 32 * q^8 - 24 * q^10 + 4 * q^11 + 96 * q^13 - 32 * q^16 + 132 * q^17 - 120 * q^19 - 96 * q^20 + 16 * q^22 - 76 * q^23 + 174 * q^25 + 96 * q^26 + 224 * q^29 - 432 * q^31 + 64 * q^32 + 528 * q^34 + 280 * q^37 + 240 * q^38 - 96 * q^40 - 72 * q^41 - 256 * q^43 + 16 * q^44 + 152 * q^46 - 264 * q^47 + 696 * q^50 - 192 * q^52 + 268 * q^53 + 96 * q^55 + 224 * q^58 + 336 * q^59 + 504 * q^61 - 1728 * q^62 + 256 * q^64 + 228 * q^65 + 384 * q^67 + 528 * q^68 + 792 * q^71 + 312 * q^73 - 560 * q^74 + 960 * q^76 + 848 * q^79 + 192 * q^80 - 72 * q^82 + 1296 * q^83 + 1496 * q^85 - 256 * q^86 - 32 * q^88 - 612 * q^89 + 608 * q^92 + 528 * q^94 + 904 * q^95 - 4368 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.29289	+	3.97141i	0.205083	+	0.355213i	0.950159	−	0.311766i	$-0.100920\pi$
$5$	2.29289	+	3.97141i	0.205083	+	0.355213i	−0.745076	+	0.666979i	$0.767587\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−4.58579	+	7.94282i	−0.145015	+	0.251174i
$11$	−3.24264	+	5.61642i	−0.0888812	+	0.153947i	−0.907038	−	0.421048i	$-0.861662\pi$
$11$	−3.24264	+	5.61642i	−0.0888812	+	0.153947i	0.818157	+	0.574994i	$0.194996\pi$
$12$		0			0
$13$	45.2132			0.964607			0.482303	−	0.876004i	$-0.339800\pi$
$13$	45.2132			0.964607			0.482303	+	0.876004i	$0.339800\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	40.7782	−	70.6299i	0.581774	−	1.00766i	−0.413495	−	0.910506i	$-0.635692\pi$
$17$	40.7782	−	70.6299i	0.581774	−	1.00766i	0.995269	−	0.0971560i	$-0.0309746\pi$
$18$		0			0
$19$	2.52691	+	4.37674i	0.0305112	+	0.0528470i	0.880878	−	0.473344i	$-0.156953\pi$
$19$	2.52691	+	4.37674i	0.0305112	+	0.0528470i	−0.850367	+	0.526191i	$0.823620\pi$
$20$	−18.3431			−0.205083
$21$		0			0
$22$	−12.9706			−0.125697
$23$	53.1249	+	92.0150i	0.481622	+	0.834194i	0.999778	−	0.0210927i	$-0.00671450\pi$
$23$	53.1249	+	92.0150i	0.481622	+	0.834194i	−0.518156	+	0.855286i	$0.673381\pi$
$24$		0			0
$25$	51.9853	−	90.0411i	0.415882	−	0.720329i
$26$	45.2132	+	78.3116i	0.341040	+	0.590699i
$27$		0			0
$28$		0			0
$29$	268.132			1.71693			0.858463	−	0.512875i	$-0.171420\pi$
$29$	268.132			1.71693			0.858463	+	0.512875i	$0.171420\pi$
$30$		0			0
$31$	−146.184	+	253.198i	−0.846948	+	1.46696i	0.0369712	+	0.999316i	$0.488229\pi$
$31$	−146.184	+	253.198i	−0.846948	+	1.46696i	−0.883919	+	0.467640i	$0.845104\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	163.113			0.822753
$35$		0			0
$36$		0			0
$37$	−57.2792	−	99.2105i	−0.254504	−	0.440814i	0.710257	−	0.703943i	$-0.248579\pi$
$37$	−57.2792	−	99.2105i	−0.254504	−	0.440814i	−0.964761	+	0.263129i	$0.915246\pi$
$38$	−5.05382	+	8.75348i	−0.0215747	+	0.0373685i
$39$		0			0
$40$	−18.3431	−	31.7713i	−0.0725077	−	0.125587i
$41$	161.605			0.615573			0.307786	−	0.951456i	$-0.400412\pi$
$41$	161.605			0.615573			0.307786	+	0.951456i	$0.400412\pi$
$42$		0			0
$43$	−471.294			−1.67143			−0.835716	−	0.549162i	$-0.814947\pi$
$43$	−471.294			−1.67143			−0.835716	+	0.549162i	$0.814947\pi$
$44$	−12.9706	−	22.4657i	−0.0444406	−	0.0769734i
$45$		0			0
$46$	−106.250	+	184.030i	−0.340558	+	0.589864i
$47$	173.002	+	299.648i	0.536914	+	0.929962i	0.999068	+	0.0431624i	$0.0137433\pi$
$47$	173.002	+	299.648i	0.536914	+	0.929962i	−0.462154	+	0.886800i	$0.652923\pi$
$48$		0			0
$49$		0			0
$50$	207.941			0.588146
$51$		0			0
$52$	−90.4264	+	156.623i	−0.241152	+	0.417687i
$53$	202.765	−	351.198i	0.525507	−	0.910204i	−0.474052	−	0.880497i	$-0.657209\pi$
$53$	202.765	−	351.198i	0.525507	−	0.910204i	0.999559	−	0.0297072i	$-0.00945750\pi$
$54$		0			0
$55$	−29.7401			−0.0729119
$56$		0			0
$57$		0			0
$58$	268.132	+	464.418i	0.607025	+	1.05140i
$59$	−126.718	+	219.482i	−0.279614	+	0.484307i	−0.971289	−	0.237903i	$-0.923540\pi$
$59$	−126.718	+	219.482i	−0.279614	+	0.484307i	0.691674	+	0.722209i	$0.256873\pi$
$60$		0			0
$61$	375.609	+	650.573i	0.788390	+	1.36553i	0.926953	+	0.375177i	$0.122418\pi$
$61$	375.609	+	650.573i	0.788390	+	1.36553i	−0.138563	+	0.990354i	$0.544248\pi$
$62$	−584.735			−1.19776
$63$		0			0
$64$	64.0000			0.125000
$65$	103.669	+	179.560i	0.197824	+	0.342641i
$66$		0			0
$67$	−5.82338	+	10.0864i	−0.0106185	+	0.0183918i	−0.871286	−	0.490776i	$-0.836713\pi$
$67$	−5.82338	+	10.0864i	−0.0106185	+	0.0183918i	0.860667	+	0.509168i	$0.170047\pi$
$68$	163.113	+	282.519i	0.290887	+	0.503831i
$69$		0			0
$70$		0			0
$71$	681.661			1.13941			0.569706	−	0.821848i	$-0.307057\pi$
$71$	681.661			1.13941			0.569706	+	0.821848i	$0.307057\pi$
$72$		0			0
$73$	−342.729	+	593.623i	−0.549498	+	0.951758i	0.448811	+	0.893627i	$0.351848\pi$
$73$	−342.729	+	593.623i	−0.549498	+	0.951758i	−0.998309	+	0.0581315i	$0.981486\pi$
$74$	114.558	−	198.421i	0.179961	−	0.311702i
$75$		0			0
$76$	−20.2153			−0.0305112
$77$		0			0
$78$		0			0
$79$	−0.132034	−	0.228690i	−0.000188038	−	0.000325692i	0.865931	−	0.500163i	$-0.166727\pi$
$79$	−0.132034	−	0.228690i	−0.000188038	−	0.000325692i	−0.866119	+	0.499837i	$0.833393\pi$
$80$	36.6863	−	63.5425i	0.0512707	−	0.0888034i
$81$		0			0
$82$	161.605	+	279.908i	0.217638	+	0.376960i
$83$	437.137			0.578097			0.289048	−	0.957314i	$-0.406661\pi$
$83$	437.137			0.578097			0.289048	+	0.957314i	$0.406661\pi$
$84$		0			0
$85$	374.000			0.477247
$86$	−471.294	−	816.304i	−0.590941	−	1.02354i
$87$		0			0
$88$	25.9411	−	44.9313i	0.0314242	−	0.0544284i
$89$	−29.2563	−	50.6734i	−0.0348445	−	0.0603525i	0.848077	−	0.529873i	$-0.177760\pi$
$89$	−29.2563	−	50.6734i	−0.0348445	−	0.0603525i	−0.882922	+	0.469520i	$0.844427\pi$
$90$		0			0
$91$		0			0
$92$	−424.999			−0.481622
$93$		0			0
$94$	−346.004	+	599.297i	−0.379655	+	0.657582i
$95$	−11.5879	+	20.0708i	−0.0125146	+	0.0216760i
$96$		0			0
$97$	−1280.09			−1.33993			−0.669966	−	0.742391i	$-0.733692\pi$
$97$	−1280.09			−1.33993			−0.669966	+	0.742391i	$0.733692\pi$
$98$		0			0
$99$		0			0
$100$	207.941	+	360.165i	0.207941	+	0.360165i
$101$	−653.194	+	1131.37i	−0.643518	+	1.11461i	0.341124	+	0.940018i	$0.389192\pi$
$101$	−653.194	+	1131.37i	−0.643518	+	1.11461i	−0.984642	+	0.174587i	$0.944141\pi$
$102$		0			0
$103$	379.487	+	657.291i	0.363029	+	0.628785i	0.988458	−	0.151496i	$-0.0484092\pi$
$103$	379.487	+	657.291i	0.363029	+	0.628785i	−0.625429	+	0.780281i	$0.715076\pi$
$104$	−361.706			−0.341040
$105$		0			0
$106$	811.058			0.743178
$107$	631.257	+	1093.37i	0.570336	+	0.987850i	0.996531	+	0.0832192i	$0.0265202\pi$
$107$	631.257	+	1093.37i	0.570336	+	0.987850i	−0.426196	+	0.904631i	$0.640146\pi$
$108$		0			0
$109$	1052.76	−	1823.44i	0.925105	−	1.60233i	0.133713	−	0.991020i	$-0.457310\pi$
$109$	1052.76	−	1823.44i	0.925105	−	1.60233i	0.791392	−	0.611309i	$-0.209357\pi$
$110$	−29.7401	−	51.5114i	−0.0257783	−	0.0446493i
$111$		0			0
$112$		0			0
$113$	−1535.76			−1.27852			−0.639258	−	0.768992i	$-0.720759\pi$
$113$	−1535.76			−1.27852			−0.639258	+	0.768992i	$0.720759\pi$
$114$		0			0
$115$	−243.619	+	421.961i	−0.197545	+	0.342157i
$116$	−536.264	+	928.837i	−0.429232	+	0.743451i
$117$		0			0
$118$	−506.871			−0.395435
$119$		0			0
$120$		0			0
$121$	644.471	+	1116.26i	0.484200	+	0.838659i
$122$	−751.217	+	1301.15i	−0.557476	+	0.965576i
$123$		0			0
$124$	−584.735	−	1012.79i	−0.423474	−	0.733478i
$125$	1050.01			0.751326
$126$		0			0
$127$	24.1749			0.0168911			0.00844557	−	0.999964i	$-0.497312\pi$
$127$	24.1749			0.0168911			0.00844557	+	0.999964i	$0.497312\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−207.338	+	359.120i	−0.139883	+	0.242284i
$131$	790.764	+	1369.64i	0.527400	+	0.913483i	0.999490	+	0.0319327i	$0.0101662\pi$
$131$	790.764	+	1369.64i	0.527400	+	0.913483i	−0.472090	+	0.881550i	$0.656500\pi$
$132$		0			0
$133$		0			0
$134$	−23.2935			−0.0150168
$135$		0			0
$136$	−326.225	+	565.039i	−0.205688	+	0.356262i
$137$	−372.594	+	645.352i	−0.232357	+	0.402454i	−0.958501	−	0.285089i	$-0.907977\pi$
$137$	−372.594	+	645.352i	−0.232357	+	0.402454i	0.726144	+	0.687542i	$0.241310\pi$
$138$		0			0
$139$	−1373.60			−0.838179			−0.419090	−	0.907945i	$-0.637651\pi$
$139$	−1373.60			−0.838179			−0.419090	+	0.907945i	$0.637651\pi$
$140$		0			0
$141$		0			0
$142$	681.661	+	1180.67i	0.402843	+	0.697745i
$143$	−146.610	+	253.936i	−0.0857354	+	0.148498i
$144$		0			0
$145$	614.798	+	1064.86i	0.352112	+	0.609875i
$146$	−1370.91			−0.777107
$147$		0			0
$148$	458.234			0.254504
$149$	310.265	+	537.395i	0.170590	+	0.295470i	0.938626	−	0.344936i	$-0.112099\pi$
$149$	310.265	+	537.395i	0.170590	+	0.295470i	−0.768036	+	0.640406i	$0.778766\pi$
$150$		0			0
$151$	969.632	−	1679.45i	0.522567	−	0.905112i	−0.477089	−	0.878855i	$-0.658308\pi$
$151$	969.632	−	1679.45i	0.522567	−	0.905112i	0.999655	−	0.0262568i	$-0.00835877\pi$
$152$	−20.2153	−	35.0139i	−0.0107873	−	0.0186842i
$153$		0			0
$154$		0			0
$155$	−1340.74			−0.694777
$156$		0			0
$157$	206.422	−	357.533i	0.104931	−	0.181747i	−0.808779	−	0.588113i	$-0.799871\pi$
$157$	206.422	−	357.533i	0.104931	−	0.181747i	0.913710	+	0.406366i	$0.133204\pi$
$158$	0.264069	−	0.457380i	0.000132963	−	0.000230299i
$159$		0			0
$160$	146.745			0.0725077
$161$		0			0
$162$		0			0
$163$	1953.72	+	3383.94i	0.938817	+	1.62608i	0.767682	+	0.640831i	$0.221410\pi$
$163$	1953.72	+	3383.94i	0.938817	+	1.62608i	0.171135	+	0.985248i	$0.445257\pi$
$164$	−323.210	+	559.817i	−0.153893	+	0.266551i
$165$		0			0
$166$	437.137	+	757.144i	0.204388	+	0.354011i
$167$	1286.41			0.596082			0.298041	−	0.954553i	$-0.403667\pi$
$167$	1286.41			0.596082			0.298041	+	0.954553i	$0.403667\pi$
$168$		0			0
$169$	−152.766			−0.0695340
$170$	374.000	+	647.787i	0.168732	+	0.292253i
$171$		0			0
$172$	942.587	−	1632.61i	0.417858	−	0.723751i
$173$	−625.628	−	1083.62i	−0.274946	−	0.476220i	0.695176	−	0.718840i	$-0.255327\pi$
$173$	−625.628	−	1083.62i	−0.274946	−	0.476220i	−0.970121	+	0.242620i	$0.921993\pi$
$174$		0			0
$175$		0			0
$176$	103.765			0.0444406
$177$		0			0
$178$	58.5126	−	101.347i	0.0246388	−	0.0426757i
$179$	1811.76	−	3138.05i	0.756520	−	1.31033i	−0.188095	−	0.982151i	$-0.560231\pi$
$179$	1811.76	−	3138.05i	0.756520	−	1.31033i	0.944615	−	0.328180i	$-0.106435\pi$
$180$		0			0
$181$	181.727			0.0746280			0.0373140	−	0.999304i	$-0.488120\pi$
$181$	181.727			0.0746280			0.0373140	+	0.999304i	$0.488120\pi$
$182$		0			0
$183$		0			0
$184$	−424.999	−	736.120i	−0.170279	−	0.294932i
$185$	262.670	−	454.958i	0.104389	−	0.180806i
$186$		0			0
$187$	264.458	+	458.055i	0.103418	+	0.179124i
$188$	−1384.02			−0.536914
$189$		0			0
$190$	−46.3515			−0.0176984
$191$	740.640	+	1282.83i	0.280580	+	0.485979i	0.971528	−	0.236926i	$-0.0761398\pi$
$191$	740.640	+	1282.83i	0.280580	+	0.485979i	−0.690948	+	0.722905i	$0.742806\pi$
$192$		0			0
$193$	178.354	−	308.918i	0.0665192	−	0.115215i	−0.830848	−	0.556500i	$-0.812144\pi$
$193$	178.354	−	308.918i	0.0665192	−	0.115215i	0.897367	+	0.441285i	$0.145477\pi$
$194$	−1280.09	−	2217.18i	−0.473738	−	0.820538i
$195$		0			0
$196$		0			0
$197$	−4890.53			−1.76871			−0.884355	−	0.466816i	$-0.845401\pi$
$197$	−4890.53			−1.76871			−0.884355	+	0.466816i	$0.845401\pi$
$198$		0			0
$199$	−1771.43	+	3068.20i	−0.631020	+	1.09296i	0.356323	+	0.934363i	$0.384030\pi$
$199$	−1771.43	+	3068.20i	−0.631020	+	1.09296i	−0.987344	+	0.158596i	$0.949303\pi$
$200$	−415.882	+	720.329i	−0.147037	+	0.254675i
$201$		0			0
$202$	−2612.78			−0.910071
$203$		0			0
$204$		0			0
$205$	370.543	+	641.800i	0.126243	+	0.218660i
$206$	−758.975	+	1314.58i	−0.256700	+	0.444618i
$207$		0			0
$208$	−361.706	−	626.493i	−0.120576	−	0.208843i
$209$	−32.7755			−0.0108475
$210$		0			0
$211$	−4289.50			−1.39953			−0.699765	−	0.714373i	$-0.746712\pi$
$211$	−4289.50			−1.39953			−0.699765	+	0.714373i	$0.746712\pi$
$212$	811.058	+	1404.79i	0.262753	+	0.455102i
$213$		0			0
$214$	−1262.51	+	2186.74i	−0.403288	+	0.698516i
$215$	−1080.63	−	1871.70i	−0.342782	−	0.593715i
$216$		0			0
$217$		0			0
$218$	4211.05			1.30830
$219$		0			0
$220$	59.4802	−	103.023i	0.0182280	−	0.0315718i
$221$	1843.71	−	3193.40i	0.561183	−	0.971998i
$222$		0			0
$223$	5795.73			1.74041			0.870204	−	0.492692i	$-0.163987\pi$
$223$	5795.73			1.74041			0.870204	+	0.492692i	$0.163987\pi$
$224$		0			0
$225$		0			0
$226$	−1535.76	−	2660.02i	−0.452024	−	0.782929i
$227$	2052.02	−	3554.21i	0.599989	−	1.03921i	−0.392833	−	0.919610i	$-0.628505\pi$
$227$	2052.02	−	3554.21i	0.599989	−	1.03921i	0.992822	−	0.119601i	$-0.0381616\pi$
$228$		0			0
$229$	648.416	+	1123.09i	0.187111	+	0.324086i	0.944286	−	0.329126i	$-0.106754\pi$
$229$	648.416	+	1123.09i	0.187111	+	0.324086i	−0.757175	+	0.653213i	$0.773421\pi$
$230$	−974.478			−0.279370
$231$		0			0
$232$	−2145.06			−0.607025
$233$	−739.167	−	1280.27i	−0.207830	−	0.359972i	0.743201	−	0.669069i	$-0.233307\pi$
$233$	−739.167	−	1280.27i	−0.207830	−	0.359972i	−0.951031	+	0.309096i	$0.899973\pi$
$234$		0			0
$235$	−793.351	+	1374.12i	−0.220223	+	0.381438i
$236$	−506.871	−	877.927i	−0.139807	−	0.242153i
$237$		0			0
$238$		0			0
$239$	3776.92			1.02221			0.511106	−	0.859518i	$-0.329236\pi$
$239$	3776.92			1.02221			0.511106	+	0.859518i	$0.329236\pi$
$240$		0			0
$241$	1998.19	−	3460.97i	0.534086	−	0.925065i	−0.465121	−	0.885247i	$-0.653989\pi$
$241$	1998.19	−	3460.97i	0.534086	−	0.925065i	0.999207	−	0.0398173i	$-0.0126776\pi$
$242$	−1288.94	+	2232.51i	−0.342381	+	0.593022i
$243$		0			0
$244$	−3004.87			−0.788390
$245$		0			0
$246$		0			0
$247$	114.250	+	197.886i	0.0294313	+	0.0509766i
$248$	1169.47	−	2025.58i	0.299441	−	0.518647i
$249$		0			0
$250$	1050.01	+	1818.67i	0.265634	+	0.460091i
$251$	−5423.58			−1.36388			−0.681939	−	0.731409i	$-0.738863\pi$
$251$	−5423.58			−1.36388			−0.681939	+	0.731409i	$0.738863\pi$
$252$		0			0
$253$	−689.060			−0.171229
$254$	24.1749	+	41.8721i	0.00597192	+	0.0103437i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2982.11	+	5165.17i	0.723809	+	1.25367i	0.959462	+	0.281837i	$0.0909438\pi$
$257$	2982.11	+	5165.17i	0.723809	+	1.25367i	−0.235653	+	0.971837i	$0.575723\pi$
$258$		0			0
$259$		0			0
$260$	−829.352			−0.197824
$261$		0			0
$262$	−1581.53	+	2739.29i	−0.372928	+	0.645930i
$263$	2583.00	−	4473.89i	0.605608	−	1.04894i	−0.386347	−	0.922353i	$-0.626263\pi$
$263$	2583.00	−	4473.89i	0.605608	−	1.04894i	0.991955	−	0.126590i	$-0.0404033\pi$
$264$		0			0
$265$	1859.67			0.431089
$266$		0			0
$267$		0			0
$268$	−23.2935	−	40.3455i	−0.00530924	−	0.00919588i
$269$	1941.65	−	3363.03i	0.440090	−	0.762259i	−0.557605	−	0.830106i	$-0.688280\pi$
$269$	1941.65	−	3363.03i	0.440090	−	0.762259i	0.997696	+	0.0678474i	$0.0216131\pi$
$270$		0			0
$271$	−2763.83	−	4787.09i	−0.619522	−	1.07304i	−0.989573	−	0.144032i	$-0.953993\pi$
$271$	−2763.83	−	4787.09i	−0.619522	−	1.07304i	0.370051	−	0.929011i	$-0.379340\pi$
$272$	−1304.90			−0.290887
$273$		0			0
$274$	−1490.38			−0.328602
$275$	337.139	+	583.942i	0.0739282	+	0.128047i
$276$		0			0
$277$	−1134.06	+	1964.25i	−0.245989	+	0.426066i	−0.962409	−	0.271603i	$-0.912446\pi$
$277$	−1134.06	+	1964.25i	−0.245989	+	0.426066i	0.716420	+	0.697669i	$0.245779\pi$
$278$	−1373.60	−	2379.14i	−0.296341	−	0.513278i
$279$		0			0
$280$		0			0
$281$	−725.656			−0.154053			−0.0770267	−	0.997029i	$-0.524543\pi$
$281$	−725.656			−0.154053			−0.0770267	+	0.997029i	$0.524543\pi$
$282$		0			0
$283$	−2118.50	+	3669.35i	−0.444988	+	0.770742i	−0.998051	−	0.0623972i	$-0.980125\pi$
$283$	−2118.50	+	3669.35i	−0.444988	+	0.770742i	0.553063	+	0.833139i	$0.313459\pi$
$284$	−1363.32	+	2361.34i	−0.284853	+	0.493380i
$285$		0			0
$286$	−586.441			−0.121248
$287$		0			0
$288$		0			0
$289$	−869.219	−	1505.53i	−0.176922	−	0.306438i
$290$	−1229.60	+	2129.72i	−0.248981	+	0.431247i
$291$		0			0
$292$	−1370.91	−	2374.49i	−0.274749	−	0.475879i
$293$	4373.78			0.872079			0.436039	−	0.899928i	$-0.356381\pi$
$293$	4373.78			0.872079			0.436039	+	0.899928i	$0.356381\pi$
$294$		0			0
$295$	−1162.20			−0.229376
$296$	458.234	+	793.684i	0.0899807	+	0.155851i
$297$		0			0
$298$	−620.530	+	1074.79i	−0.120625	+	0.208929i
$299$	2401.95	+	4160.29i	0.464576	+	0.804669i
$300$		0			0
$301$		0			0
$302$	3878.53			0.739021
$303$		0			0
$304$	40.4306	−	70.0278i	0.00762781	−	0.0132117i
$305$	−1722.46	+	2983.39i	−0.323370	+	0.560093i
$306$		0			0
$307$	4133.47			0.768435			0.384217	−	0.923243i	$-0.374471\pi$
$307$	4133.47			0.768435			0.384217	+	0.923243i	$0.374471\pi$
$308$		0			0
$309$		0			0
$310$	−1340.74	−	2322.22i	−0.245641	−	0.425462i
$311$	2531.62	−	4384.89i	0.461591	−	0.799499i	−0.537450	−	0.843296i	$-0.680612\pi$
$311$	2531.62	−	4384.89i	0.461591	−	0.799499i	0.999040	+	0.0437972i	$0.0139455\pi$
$312$		0			0
$313$	−3705.78	−	6418.60i	−0.669211	−	1.15911i	−0.978125	−	0.208017i	$-0.933299\pi$
$313$	−3705.78	−	6418.60i	−0.669211	−	1.15911i	0.308914	−	0.951090i	$-0.400034\pi$
$314$	825.686			0.148395
$315$		0			0
$316$	1.05627			0.000188038
$317$	−3368.53	−	5834.46i	−0.596831	−	1.03374i	−0.993286	−	0.115687i	$-0.963093\pi$
$317$	−3368.53	−	5834.46i	−0.596831	−	1.03374i	0.396455	−	0.918054i	$-0.370240\pi$
$318$		0			0
$319$	−869.456	+	1505.94i	−0.152602	+	0.264315i
$320$	146.745	+	254.170i	0.0256353	+	0.0444017i
$321$		0			0
$322$		0			0
$323$	412.171			0.0710026
$324$		0			0
$325$	2350.42	−	4071.05i	0.401163	−	0.694834i
$326$	−3907.44	+	6767.88i	−0.663844	+	1.14981i
$327$		0			0
$328$	−1292.84			−0.217638
$329$		0			0
$330$		0			0
$331$	−5587.97	−	9678.65i	−0.927923	−	1.60721i	−0.786791	−	0.617219i	$-0.788259\pi$
$331$	−5587.97	−	9678.65i	−0.927923	−	1.60721i	−0.141132	−	0.989991i	$-0.545074\pi$
$332$	−874.274	+	1514.29i	−0.144524	+	0.250323i
$333$		0			0
$334$	1286.41	+	2228.14i	0.210747	+	0.365024i
$335$	−53.4095			−0.00871067
$336$		0			0
$337$	9379.78			1.51617			0.758085	−	0.652156i	$-0.226135\pi$
$337$	9379.78			1.51617			0.758085	+	0.652156i	$0.226135\pi$
$338$	−152.766	−	264.599i	−0.0245840	−	0.0425807i
$339$		0			0
$340$	−748.000	+	1295.57i	−0.119312	+	0.206654i
$341$	−948.043	−	1642.06i	−0.150555	−	0.260770i
$342$		0			0
$343$		0			0
$344$	3770.35			0.590941
$345$		0			0
$346$	1251.26	−	2167.24i	0.194416	−	0.336738i
$347$	2840.73	−	4920.29i	0.439476	−	0.761195i	−0.558173	−	0.829725i	$-0.688497\pi$
$347$	2840.73	−	4920.29i	0.439476	−	0.761195i	0.997649	+	0.0685293i	$0.0218307\pi$
$348$		0			0
$349$	−704.250			−0.108016			−0.0540080	−	0.998541i	$-0.517200\pi$
$349$	−704.250			−0.108016			−0.0540080	+	0.998541i	$0.517200\pi$
$350$		0			0
$351$		0			0
$352$	103.765	+	179.725i	0.0157121	+	0.0272142i
$353$	−2142.48	+	3710.89i	−0.323039	+	0.559520i	−0.981114	−	0.193433i	$-0.938038\pi$
$353$	−2142.48	+	3710.89i	−0.323039	+	0.559520i	0.658074	+	0.752953i	$0.271371\pi$
$354$		0			0
$355$	1562.98	+	2707.15i	0.233674	+	0.404735i
$356$	234.051			0.0348445
$357$		0			0
$358$	7247.03			1.06988
$359$	2330.64	+	4036.78i	0.342636	+	0.593463i	0.984921	−	0.173003i	$-0.0553470\pi$
$359$	2330.64	+	4036.78i	0.342636	+	0.593463i	−0.642285	+	0.766465i	$0.722014\pi$
$360$		0			0
$361$	3416.73	−	5917.95i	0.498138	−	0.862801i
$362$	181.727	+	314.760i	0.0263850	+	0.0457001i
$363$		0			0
$364$		0			0
$365$	−3143.36			−0.450770
$366$		0			0
$367$	3467.65	−	6006.15i	0.493215	−	0.854274i	−0.506754	−	0.862091i	$-0.669155\pi$
$367$	3467.65	−	6006.15i	0.493215	−	0.854274i	0.999969	+	0.00781688i	$0.00248822\pi$
$368$	849.998	−	1472.24i	0.120405	−	0.208548i
$369$		0			0
$370$	1050.68			0.147628
$371$		0			0
$372$		0			0
$373$	1540.55	+	2668.31i	0.213852	+	0.370402i	0.952917	−	0.303232i	$-0.0980657\pi$
$373$	1540.55	+	2668.31i	0.213852	+	0.370402i	−0.739065	+	0.673634i	$0.764732\pi$
$374$	−528.916	+	916.109i	−0.0731272	+	0.126660i
$375$		0			0
$376$	−1384.02	−	2397.19i	−0.189828	−	0.328791i
$377$	12123.1			1.65616
$378$		0			0
$379$	941.827			0.127647			0.0638237	−	0.997961i	$-0.479670\pi$
$379$	941.827			0.127647			0.0638237	+	0.997961i	$0.479670\pi$
$380$	−46.3515	−	80.2832i	−0.00625732	−	0.0108380i
$381$		0			0
$382$	−1481.28	+	2565.65i	−0.198400	+	0.343639i
$383$	−338.763	−	586.755i	−0.0451958	−	0.0782814i	0.842543	−	0.538630i	$-0.181058\pi$
$383$	−338.763	−	586.755i	−0.0451958	−	0.0782814i	−0.887738	+	0.460348i	$0.847724\pi$
$384$		0			0
$385$		0			0
$386$	713.416			0.0940724
$387$		0			0
$388$	2560.18	−	4434.36i	0.334983	−	0.580208i
$389$	−5932.71	+	10275.8i	−0.773266	+	1.33934i	0.162498	+	0.986709i	$0.448045\pi$
$389$	−5932.71	+	10275.8i	−0.773266	+	1.33934i	−0.935764	+	0.352627i	$0.885289\pi$
$390$		0			0
$391$	8665.34			1.12078
$392$		0			0
$393$		0			0
$394$	−4890.53	−	8470.64i	−0.625333	−	1.08311i
$395$	0.605481	−	1.04872i	7.71268e−5	−	0.000133587i
$396$		0			0
$397$	2570.38	+	4452.03i	0.324947	+	0.562824i	0.981502	−	0.191454i	$-0.0613203\pi$
$397$	2570.38	+	4452.03i	0.324947	+	0.562824i	−0.656555	+	0.754278i	$0.727987\pi$
$398$	−7085.70			−0.892397
$399$		0			0
$400$	−1663.53			−0.207941
$401$	−6190.99	−	10723.1i	−0.770981	−	1.33538i	−0.937026	−	0.349260i	$-0.886433\pi$
$401$	−6190.99	−	10723.1i	−0.770981	−	1.33538i	0.166045	−	0.986118i	$-0.446900\pi$
$402$		0			0
$403$	−6609.44	+	11447.9i	−0.816971	+	1.41504i
$404$	−2612.78	−	4525.46i	−0.321759	−	0.557303i
$405$		0			0
$406$		0			0
$407$	742.944			0.0904824
$408$		0			0
$409$	7937.82	−	13748.7i	0.959657	−	1.66217i	0.236326	−	0.971674i	$-0.424057\pi$
$409$	7937.82	−	13748.7i	0.959657	−	1.66217i	0.723331	−	0.690501i	$-0.242610\pi$
$410$	−741.087	+	1283.60i	−0.0892675	+	0.154616i
$411$		0			0
$412$	−3035.90			−0.363029
$413$		0			0
$414$		0			0
$415$	1002.31	+	1736.05i	0.118558	+	0.205348i
$416$	723.411	−	1252.99i	0.0852600	−	0.147675i
$417$		0			0
$418$	−32.7755	−	56.7688i	−0.00383517	−	0.00664271i
$419$	16111.9			1.87857			0.939283	−	0.343145i	$-0.111492\pi$
$419$	16111.9			1.87857			0.939283	+	0.343145i	$0.111492\pi$
$420$		0			0
$421$	8691.58			1.00618			0.503090	−	0.864234i	$-0.332197\pi$
$421$	8691.58			1.00618			0.503090	+	0.864234i	$0.332197\pi$
$422$	−4289.50	−	7429.62i	−0.494809	−	0.857034i
$423$		0			0
$424$	−1622.12	+	2809.59i	−0.185795	+	0.321806i
$425$	−4239.73	−	7343.43i	−0.483899	−	0.838138i
$426$		0			0
$427$		0			0
$428$	−5050.06			−0.570336
$429$		0			0
$430$	2161.25	−	3743.40i	0.242383	−	0.419820i
$431$	−2097.55	+	3633.07i	−0.234421	+	0.406029i	−0.959104	−	0.283053i	$-0.908653\pi$
$431$	−2097.55	+	3633.07i	−0.234421	+	0.406029i	0.724683	+	0.689082i	$0.241986\pi$
$432$		0			0
$433$	−5426.54			−0.602270			−0.301135	−	0.953582i	$-0.597365\pi$
$433$	−5426.54			−0.602270			−0.301135	+	0.953582i	$0.597365\pi$
$434$		0			0
$435$		0			0
$436$	4211.05	+	7293.76i	0.462553	+	0.801165i
$437$	−268.484	+	465.028i	−0.0293898	+	0.0509046i
$438$		0			0
$439$	1885.62	+	3265.99i	0.205002	+	0.355073i	0.950133	−	0.311844i	$-0.100947\pi$
$439$	1885.62	+	3265.99i	0.205002	+	0.355073i	−0.745132	+	0.666917i	$0.767613\pi$
$440$	237.921			0.0257783
$441$		0			0
$442$	7374.85			0.793633
$443$	−2965.15	−	5135.79i	−0.318010	−	0.550810i	0.662063	−	0.749449i	$-0.269681\pi$
$443$	−2965.15	−	5135.79i	−0.318010	−	0.550810i	−0.980073	+	0.198639i	$0.936348\pi$
$444$		0			0
$445$	134.163	−	232.377i	0.0142920	−	0.0247545i
$446$	5795.73	+	10038.5i	0.615327	+	1.06578i
$447$		0			0
$448$		0			0
$449$	529.065			0.0556083			0.0278041	−	0.999613i	$-0.491149\pi$
$449$	529.065			0.0556083			0.0278041	+	0.999613i	$0.491149\pi$
$450$		0			0
$451$	−524.027	+	907.642i	−0.0547128	+	0.0947654i
$452$	3071.53	−	5320.04i	0.319629	−	0.553614i
$453$		0			0
$454$	8208.09			0.848512
$455$		0			0
$456$		0			0
$457$	−5028.59	−	8709.77i	−0.514721	−	0.891523i	−0.999854	−	0.0170824i	$-0.994562\pi$
$457$	−5028.59	−	8709.77i	−0.514721	−	0.891523i	0.485133	−	0.874440i	$-0.338771\pi$
$458$	−1296.83	+	2246.18i	−0.132308	+	0.229164i
$459$		0			0
$460$	−974.478	−	1687.84i	−0.0987723	−	0.171079i
$461$	5010.31			0.506190			0.253095	−	0.967441i	$-0.418552\pi$
$461$	5010.31			0.506190			0.253095	+	0.967441i	$0.418552\pi$
$462$		0			0
$463$	−7124.38			−0.715114			−0.357557	−	0.933891i	$-0.616390\pi$
$463$	−7124.38			−0.715114			−0.357557	+	0.933891i	$0.616390\pi$
$464$	−2145.06	−	3715.35i	−0.214616	−	0.371725i
$465$		0			0
$466$	1478.33	−	2560.55i	0.146958	−	0.254539i
$467$	3750.72	+	6496.44i	0.371654	+	0.643724i	0.989820	−	0.142323i	$-0.0454573\pi$
$467$	3750.72	+	6496.44i	0.371654	+	0.643724i	−0.618166	+	0.786048i	$0.712124\pi$
$468$		0			0
$469$		0			0
$470$	−3173.40			−0.311443
$471$		0			0
$472$	1013.74	−	1755.85i	0.0988587	−	0.171228i
$473$	1528.24	−	2646.98i	0.148559	−	0.257312i
$474$		0			0
$475$	525.449			0.0507563
$476$		0			0
$477$		0			0
$478$	3776.92	+	6541.82i	0.361406	+	0.625974i
$479$	−4086.90	+	7078.72i	−0.389844	+	0.675230i	−0.992428	−	0.122826i	$-0.960804\pi$
$479$	−4086.90	+	7078.72i	−0.389844	+	0.675230i	0.602584	+	0.798055i	$0.294138\pi$
$480$		0			0
$481$	−2589.78	−	4485.63i	−0.245496	−	0.425212i
$482$	7992.76			0.755312
$483$		0			0
$484$	−5155.76			−0.484200
$485$	−2935.11	−	5083.76i	−0.274797	−	0.475962i
$486$		0			0
$487$	5984.39	−	10365.3i	0.556835	−	0.964467i	−0.440923	−	0.897545i	$-0.645349\pi$
$487$	5984.39	−	10365.3i	0.556835	−	0.964467i	0.997758	−	0.0669221i	$-0.0213179\pi$
$488$	−3004.87	−	5204.59i	−0.278738	−	0.482788i
$489$		0			0
$490$		0			0
$491$	−2079.96			−0.191176			−0.0955878	−	0.995421i	$-0.530473\pi$
$491$	−2079.96			−0.191176			−0.0955878	+	0.995421i	$0.530473\pi$
$492$		0			0
$493$	10933.9	−	18938.1i	0.998863	−	1.73008i
$494$	−228.500	+	395.773i	−0.0208111	+	0.0360459i
$495$		0			0
$496$	4677.88			0.423474
$497$		0			0
$498$		0			0
$499$	−6417.21	−	11114.9i	−0.575699	−	0.997140i	−0.995965	−	0.0897390i	$-0.971397\pi$
$499$	−6417.21	−	11114.9i	−0.575699	−	0.997140i	0.420266	−	0.907401i	$-0.361937\pi$
$500$	−2100.02	+	3637.34i	−0.187832	+	0.325334i
$501$		0			0
$502$	−5423.58	−	9393.92i	−0.482204	−	0.835202i
$503$	−16808.8			−1.48999			−0.744997	−	0.667068i	$-0.767549\pi$
$503$	−16808.8			−1.48999			−0.744997	+	0.667068i	$0.767549\pi$
$504$		0			0
$505$	−5990.82			−0.527897
$506$	−689.060	−	1193.49i	−0.0605384	−	0.104856i
$507$		0			0
$508$	−48.3498	+	83.7443i	−0.00422278	+	0.00731408i
$509$	−2135.13	−	3698.16i	−0.185929	−	0.322039i	0.757960	−	0.652301i	$-0.226196\pi$
$509$	−2135.13	−	3698.16i	−0.185929	−	0.322039i	−0.943889	+	0.330262i	$0.892863\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−5964.22	+	10330.3i	−0.511811	+	0.886482i
$515$	−1740.25	+	3014.20i	−0.148902	+	0.257906i
$516$		0			0
$517$	−2243.93			−0.190886
$518$		0			0
$519$		0			0
$520$	−829.352	−	1436.48i	−0.0699414	−	0.121142i
$521$	7641.64	−	13235.7i	0.642584	−	1.11299i	−0.342270	−	0.939602i	$-0.611196\pi$
$521$	7641.64	−	13235.7i	0.642584	−	1.11299i	0.984854	−	0.173386i	$-0.0554709\pi$
$522$		0			0
$523$	2249.66	+	3896.53i	0.188090	+	0.325781i	0.944613	−	0.328185i	$-0.106437\pi$
$523$	2249.66	+	3896.53i	0.188090	+	0.325781i	−0.756524	+	0.653966i	$0.773104\pi$
$524$	−6326.11			−0.527400
$525$		0			0
$526$	10332.0			0.856459
$527$	11922.2	+	20649.9i	0.985465	+	1.70687i
$528$		0			0
$529$	438.992	−	760.356i	0.0360805	−	0.0624933i
$530$	1859.67	+	3221.04i	0.152413	+	0.263987i
$531$		0			0
$532$		0			0
$533$	7306.69			0.593785
$534$		0			0
$535$	−2894.81	+	5013.96i	−0.233932	+	0.405182i
$536$	46.5870	−	80.6911i	0.00375420	−	0.00650247i
$537$		0			0
$538$	7766.59			0.622382
$539$		0			0
$540$		0			0
$541$	−1985.41	−	3438.83i	−0.157781	−	0.273284i	0.776287	−	0.630379i	$-0.217101\pi$
$541$	−1985.41	−	3438.83i	−0.157781	−	0.273284i	−0.934068	+	0.357095i	$0.883767\pi$
$542$	5527.65	−	9574.18i	0.438068	−	0.758757i
$543$		0			0
$544$	−1304.90	−	2260.16i	−0.102844	−	0.178131i
$545$	9655.50			0.758892
$546$		0			0
$547$	−2703.90			−0.211353			−0.105677	−	0.994401i	$-0.533701\pi$
$547$	−2703.90			−0.211353			−0.105677	+	0.994401i	$0.533701\pi$
$548$	−1490.38	−	2581.41i	−0.116178	−	0.201227i
$549$		0			0
$550$	−674.278	+	1167.88i	−0.0522751	+	0.0905432i
$551$	677.546	+	1173.54i	0.0523855	+	0.0907344i
$552$		0			0
$553$		0			0
$554$	−4536.24			−0.347881
$555$		0			0
$556$	2747.19	−	4758.28i	0.209545	−	0.362942i
$557$	395.412	−	684.874i	0.0300793	−	0.0520988i	−0.850594	−	0.525823i	$-0.823757\pi$
$557$	395.412	−	684.874i	0.0300793	−	0.0520988i	0.880673	+	0.473724i	$0.157091\pi$
$558$		0			0
$559$	−21308.7			−1.61227
$560$		0			0
$561$		0			0
$562$	−725.656	−	1256.87i	−0.0544661	−	0.0943380i
$563$	3758.58	−	6510.05i	0.281359	−	0.487328i	−0.690361	−	0.723465i	$-0.742548\pi$
$563$	3758.58	−	6510.05i	0.281359	−	0.487328i	0.971720	+	0.236137i	$0.0758815\pi$
$564$		0			0
$565$	−3521.34	−	6099.14i	−0.262202	−	0.454146i
$566$	−8473.99			−0.629308
$567$		0			0
$568$	−5453.29			−0.402843
$569$	6972.72	+	12077.1i	0.513728	+	0.889804i	0.999873	+	0.0159254i	$0.00506942\pi$
$569$	6972.72	+	12077.1i	0.513728	+	0.889804i	−0.486145	+	0.873878i	$0.661597\pi$
$570$		0			0
$571$	1059.25	−	1834.67i	0.0776323	−	0.134463i	−0.824596	−	0.565723i	$-0.808597\pi$
$571$	1059.25	−	1834.67i	0.0776323	−	0.134463i	0.902228	+	0.431259i	$0.141931\pi$
$572$	−586.441	−	1015.75i	−0.0428677	−	0.0742490i
$573$		0			0
$574$		0			0
$575$	11046.8			0.801192
$576$		0			0
$577$	−11428.9	+	19795.4i	−0.824592	+	1.42823i	0.0776391	+	0.996982i	$0.475262\pi$
$577$	−11428.9	+	19795.4i	−0.824592	+	1.42823i	−0.902231	+	0.431253i	$0.858072\pi$
$578$	1738.44	−	3011.06i	0.125103	−	0.216685i
$579$		0			0
$580$	−4918.38			−0.352112
$581$		0			0
$582$		0			0
$583$	1314.98	+	2277.62i	0.0934153	+	0.161800i
$584$	2741.83	−	4748.99i	0.194277	−	0.336497i
$585$		0			0
$586$	4373.78	+	7575.61i	0.308326	+	0.534037i
$587$	−23955.3			−1.68440			−0.842199	−	0.539167i	$-0.818739\pi$
$587$	−23955.3			−1.68440			−0.842199	+	0.539167i	$0.818739\pi$
$588$		0			0
$589$	−1477.57			−0.103366
$590$	−1162.20	−	2012.99i	−0.0810968	−	0.140464i
$591$		0			0
$592$	−916.468	+	1587.37i	−0.0636260	+	0.110203i
$593$	−5388.99	−	9334.01i	−0.373186	−	0.646378i	0.616867	−	0.787067i	$-0.288401\pi$
$593$	−5388.99	−	9334.01i	−0.373186	−	0.646378i	−0.990054	+	0.140689i	$0.955068\pi$
$594$		0			0
$595$		0			0
$596$	−2482.12			−0.170590
$597$		0			0
$598$	−4803.89	+	8320.59i	−0.328505	+	0.568987i
$599$	3798.79	−	6579.69i	0.259122	−	0.448813i	−0.706885	−	0.707329i	$-0.749900\pi$
$599$	3798.79	−	6579.69i	0.259122	−	0.448813i	0.966007	+	0.258516i	$0.0832334\pi$
$600$		0			0
$601$	19956.1			1.35445			0.677225	−	0.735776i	$-0.263182\pi$
$601$	19956.1			1.35445			0.677225	+	0.735776i	$0.263182\pi$
$602$		0			0
$603$		0			0
$604$	3878.53	+	6717.81i	0.261283	+	0.452556i
$605$	−2955.40	+	5118.91i	−0.198602	+	0.343989i
$606$		0			0
$607$	118.155	+	204.651i	0.00790079	+	0.0136846i	0.869949	−	0.493142i	$-0.164152\pi$
$607$	118.155	+	204.651i	0.00790079	+	0.0136846i	−0.862048	+	0.506827i	$0.830818\pi$
$608$	161.722			0.0107873
$609$		0			0
$610$	−6889.85			−0.457314
$611$	7821.98	+	13548.1i	0.517911	+	0.897048i
$612$		0			0
$613$	−13207.5	+	22876.0i	−0.870219	+	1.50726i	−0.00844986	+	0.999964i	$0.502690\pi$
$613$	−13207.5	+	22876.0i	−0.870219	+	1.50726i	−0.861770	+	0.507300i	$0.830644\pi$
$614$	4133.47	+	7159.38i	0.271683	+	0.470568i
$615$		0			0
$616$		0			0
$617$	−18473.6			−1.20538			−0.602689	−	0.797976i	$-0.705904\pi$
$617$	−18473.6			−1.20538			−0.602689	+	0.797976i	$0.705904\pi$
$618$		0			0
$619$	−8023.96	+	13897.9i	−0.521018	+	0.902430i	0.478683	+	0.877988i	$0.341114\pi$
$619$	−8023.96	+	13897.9i	−0.521018	+	0.902430i	−0.999701	+	0.0244421i	$0.992219\pi$
$620$	2681.47	−	4644.44i	0.173694	−	0.300847i
$621$		0			0
$622$	10126.5			0.652788
$623$		0			0
$624$		0			0
$625$	−4090.60	−	7085.13i	−0.261798	−	0.453448i
$626$	7411.56	−	12837.2i	0.473204	−	0.819613i
$627$		0			0
$628$	825.686	+	1430.13i	0.0524657	+	0.0908733i
$629$	−9342.97			−0.592255
$630$		0			0
$631$	−15065.7			−0.950487			−0.475243	−	0.879854i	$-0.657640\pi$
$631$	−15065.7			−0.950487			−0.475243	+	0.879854i	$0.657640\pi$
$632$	1.05627	+	1.82952i	6.64816e−5	+	0.000115149i
$633$		0			0
$634$	6737.05	−	11668.9i	0.422023	−	0.730965i
$635$	55.4304	+	96.0083i	0.00346408	+	0.00599996i
$636$		0			0
$637$		0			0
$638$	−3477.82			−0.215812
$639$		0			0
$640$	−293.490	+	508.340i	−0.0181269	+	0.0313967i
$641$	−15599.2	+	27018.6i	−0.961203	+	1.66485i	−0.241715	+	0.970347i	$0.577710\pi$
$641$	−15599.2	+	27018.6i	−0.961203	+	1.66485i	−0.719488	+	0.694505i	$0.755623\pi$
$642$		0			0
$643$	−12497.9			−0.766517			−0.383259	−	0.923641i	$-0.625198\pi$
$643$	−12497.9			−0.766517			−0.383259	+	0.923641i	$0.625198\pi$
$644$		0			0
$645$		0			0
$646$	412.171	+	713.902i	0.0251032	+	0.0434800i
$647$	−4964.86	+	8599.39i	−0.301683	+	0.522530i	−0.976517	−	0.215439i	$-0.930882\pi$
$647$	−4964.86	+	8599.39i	−0.301683	+	0.522530i	0.674834	+	0.737969i	$0.264215\pi$
$648$		0			0
$649$	−821.801	−	1423.40i	−0.0497049	−	0.0860915i
$650$	9401.68			0.567330
$651$		0			0
$652$	−15629.8			−0.938817
$653$	−4072.79	−	7054.28i	−0.244075	−	0.422750i	0.717796	−	0.696253i	$-0.245151\pi$
$653$	−4072.79	−	7054.28i	−0.244075	−	0.422750i	−0.961871	+	0.273503i	$0.911817\pi$
$654$		0			0
$655$	−3626.27	+	6280.89i	−0.216321	+	0.374679i
$656$	−1292.84	−	2239.27i	−0.0769466	−	0.133275i
$657$		0			0
$658$		0			0
$659$	16975.8			1.00347			0.501733	−	0.865022i	$-0.332696\pi$
$659$	16975.8			1.00347			0.501733	+	0.865022i	$0.332696\pi$
$660$		0			0
$661$	−10318.9	+	17872.8i	−0.607199	+	1.05170i	0.384501	+	0.923124i	$0.374373\pi$
$661$	−10318.9	+	17872.8i	−0.607199	+	1.05170i	−0.991700	+	0.128574i	$0.958960\pi$
$662$	11175.9	−	19357.3i	0.656141	−	1.13647i
$663$		0			0
$664$	−3497.10			−0.204388
$665$		0			0
$666$		0			0
$667$	14244.5	+	24672.2i	0.826910	+	1.43225i
$668$	−2572.83	+	4456.27i	−0.149021	+	0.258111i
$669$		0			0
$670$	−53.4095	−	92.5080i	−0.00307969	−	0.00533417i
$671$	−4871.86			−0.280292
$672$		0			0
$673$	−2150.29			−0.123161			−0.0615807	−	0.998102i	$-0.519614\pi$
$673$	−2150.29			−0.123161			−0.0615807	+	0.998102i	$0.519614\pi$
$674$	9379.78	+	16246.3i	0.536047	+	0.928461i
$675$		0			0
$676$	305.532	−	529.198i	0.0173835	−	0.0301091i
$677$	−13891.7	−	24061.1i	−0.788628	−	1.36594i	−0.926808	−	0.375536i	$-0.877459\pi$
$677$	−13891.7	−	24061.1i	−0.788628	−	1.36594i	0.138180	−	0.990407i	$-0.455875\pi$
$678$		0			0
$679$		0			0
$680$	−2992.00			−0.168732
$681$		0			0
$682$	1896.09	−	3284.12i	0.106459	−	0.184392i
$683$	9090.89	−	15745.9i	0.509302	−	0.882137i	−0.490640	−	0.871362i	$-0.663237\pi$
$683$	9090.89	−	15745.9i	0.509302	−	0.882137i	0.999942	−	0.0107743i	$-0.00342962\pi$
$684$		0			0
$685$	−3417.27			−0.190609
$686$		0			0
$687$		0			0
$688$	3770.35	+	6530.43i	0.208929	+	0.361876i
$689$	9167.63	−	15878.8i	0.506907	−	0.877989i
$690$		0			0
$691$	−11967.6	−	20728.4i	−0.658853	−	1.14117i	−0.980913	−	0.194447i	$-0.937709\pi$
$691$	−11967.6	−	20728.4i	−0.658853	−	1.14117i	0.322060	−	0.946719i	$-0.395625\pi$
$692$	5005.02			0.274946
$693$		0			0
$694$	11362.9			0.621513
$695$	−3149.51	−	5455.11i	−0.171896	−	0.297733i
$696$		0			0
$697$	6589.96	−	11414.1i	0.358124	−	0.620289i
$698$	−704.250	−	1219.80i	−0.0381895	−	0.0661461i
$699$		0			0
$700$		0			0
$701$	20627.2			1.11138			0.555691	−	0.831389i	$-0.312454\pi$
$701$	20627.2			1.11138			0.555691	+	0.831389i	$0.312454\pi$
$702$		0			0
$703$	289.479	−	501.392i	0.0155305	−	0.0268995i
$704$	−207.529	+	359.451i	−0.0111101	+	0.0192433i
$705$		0			0
$706$	−8569.93			−0.456846
$707$		0			0
$708$		0			0
$709$	3292.32	+	5702.46i	0.174394	+	0.302060i	0.939952	−	0.341308i	$-0.110870\pi$
$709$	3292.32	+	5702.46i	0.174394	+	0.302060i	−0.765557	+	0.643368i	$0.777537\pi$
$710$	−3125.95	+	5414.31i	−0.165232	+	0.286191i
$711$		0			0
$712$	234.051	+	405.387i	0.0123194	+	0.0213378i
$713$	−31064.0			−1.63163
$714$		0			0
$715$	−1344.65			−0.0703313
$716$	7247.03	+	12552.2i	0.378260	+	0.655165i
$717$		0			0
$718$	−4661.27	+	8073.56i	−0.242280	+	0.419642i
$719$	85.4430	+	147.992i	0.00443183	+	0.00767616i	0.868233	−	0.496157i	$-0.165256\pi$
$719$	85.4430	+	147.992i	0.00443183	+	0.00767616i	−0.863801	+	0.503833i	$0.831923\pi$
$720$		0			0
$721$		0			0
$722$	13666.9			0.704474
$723$		0			0
$724$	−363.454	+	629.521i	−0.0186570	+	0.0323149i
$725$	13938.9	−	24142.9i	0.714039	−	1.23675i
$726$		0			0
$727$	−11127.5			−0.567671			−0.283836	−	0.958873i	$-0.591607\pi$
$727$	−11127.5			−0.567671			−0.283836	+	0.958873i	$0.591607\pi$
$728$		0			0
$729$		0			0
$730$	−3143.36	−	5444.46i	−0.159371	−	0.276039i
$731$	−19218.5	+	33287.4i	−0.972396	+	1.68424i
$732$		0			0
$733$	11288.0	+	19551.3i	0.568800	+	0.985191i	0.996685	+	0.0813578i	$0.0259256\pi$
$733$	11288.0	+	19551.3i	0.568800	+	0.985191i	−0.427885	+	0.903833i	$0.640741\pi$
$734$	13870.6			0.697511
$735$		0			0
$736$	3399.99			0.170279
$737$	−37.7662	−	65.4130i	−0.00188757	−	0.00326936i
$738$		0			0
$739$	11468.2	−	19863.5i	0.570860	−	0.988758i	−0.425618	−	0.904903i	$-0.639943\pi$
$739$	11468.2	−	19863.5i	0.570860	−	0.988758i	0.996478	−	0.0838550i	$-0.0267233\pi$
$740$	1050.68	+	1819.83i	0.0521943	+	0.0904032i
$741$		0			0
$742$		0			0
$743$	−16973.4			−0.838081			−0.419041	−	0.907967i	$-0.637634\pi$
$743$	−16973.4			−0.838081			−0.419041	+	0.907967i	$0.637634\pi$
$744$		0			0
$745$	−1422.81	+	2464.38i	−0.0699700	+	0.121192i
$746$	−3081.10	+	5336.63i	−0.151216	+	0.261914i
$747$		0			0
$748$	−2115.66			−0.103418
$749$		0			0
$750$		0			0
$751$	10598.9	+	18357.9i	0.514994	+	0.891995i	0.999849	+	0.0174007i	$0.00553909\pi$
$751$	10598.9	+	18357.9i	0.514994	+	0.891995i	−0.484855	+	0.874595i	$0.661128\pi$
$752$	2768.03	−	4794.37i	0.134228	−	0.232490i
$753$		0			0
$754$	12123.1	+	20997.8i	0.585541	+	1.01419i
$755$	8893.05			0.428677
$756$		0			0
$757$	−7962.24			−0.382289			−0.191144	−	0.981562i	$-0.561220\pi$
$757$	−7962.24			−0.382289			−0.191144	+	0.981562i	$0.561220\pi$
$758$	941.827	+	1631.29i	0.0451302	+	0.0781678i
$759$		0			0
$760$	92.7030	−	160.566i	0.00442460	−	0.00766362i
$761$	13428.1	+	23258.1i	0.639642	+	1.10789i	0.985511	+	0.169610i	$0.0542508\pi$
$761$	13428.1	+	23258.1i	0.639642	+	1.10789i	−0.345869	+	0.938283i	$0.612416\pi$
$762$		0			0
$763$		0			0
$764$	−5925.12			−0.280580
$765$		0			0
$766$	677.526	−	1173.51i	0.0319582	−	0.0553533i
$767$	−5729.32	+	9923.47i	−0.269718	+	0.467165i
$768$		0			0
$769$	−12183.6			−0.571331			−0.285666	−	0.958329i	$-0.592215\pi$
$769$	−12183.6			−0.571331			−0.285666	+	0.958329i	$0.592215\pi$
$770$		0			0
$771$		0			0
$772$	713.416	+	1235.67i	0.0332596	+	0.0576073i
$773$	−8727.61	+	15116.7i	−0.406093	+	0.703374i	−0.994448	−	0.105229i	$-0.966443\pi$
$773$	−8727.61	+	15116.7i	−0.406093	+	0.703374i	0.588355	+	0.808603i	$0.299776\pi$
$774$		0			0
$775$	15198.8	+	26325.1i	0.704461	+	1.22016i
$776$	10240.7			0.473738
$777$		0			0
$778$	−23730.8			−1.09356
$779$	408.362	+	707.304i	0.0187819	+	0.0325312i
$780$		0			0
$781$	−2210.38	+	3828.49i	−0.101272	+	0.175409i
$782$	8665.34	+	15008.8i	0.396256	+	0.686335i
$783$		0			0
$784$		0			0
$785$	1893.21			0.0860785
$786$		0			0
$787$	−15490.5	+	26830.3i	−0.701622	+	1.21524i	0.266275	+	0.963897i	$0.414207\pi$
$787$	−15490.5	+	26830.3i	−0.701622	+	1.21524i	−0.967897	+	0.251348i	$0.919126\pi$
$788$	9781.06	−	16941.3i	0.442177	−	0.765874i
$789$		0			0
$790$	2.42193			0.000109074
$791$		0			0
$792$		0			0
$793$	16982.5	+	29414.5i	0.760486	+	1.31720i
$794$	−5140.76	+	8904.07i	−0.229772	+	0.397977i
$795$		0			0
$796$	−7085.70	−	12272.8i	−0.315510	−	0.546480i
$797$	10517.6			0.467446			0.233723	−	0.972303i	$-0.424909\pi$
$797$	10517.6			0.467446			0.233723	+	0.972303i	$0.424909\pi$
$798$		0			0
$799$	28218.8			1.24945
$800$	−1663.53	−	2881.32i	−0.0735183	−	0.127337i
$801$		0			0
$802$	12382.0	−	21446.2i	0.545166	−	0.944255i
$803$	−2222.69	−	3849.81i	−0.0976800	−	0.169187i
$804$		0			0
$805$		0			0
$806$	−26437.7			−1.15537
$807$		0			0
$808$	5225.56	−	9050.93i	0.227518	−	0.394072i
$809$	−20889.2	+	36181.2i	−0.907819	+	1.57239i	−0.0907320	+	0.995875i	$0.528921\pi$
$809$	−20889.2	+	36181.2i	−0.907819	+	1.57239i	−0.817087	+	0.576514i	$0.804413\pi$
$810$		0			0
$811$	−12935.4			−0.560079			−0.280039	−	0.959988i	$-0.590348\pi$
$811$	−12935.4			−0.560079			−0.280039	+	0.959988i	$0.590348\pi$
$812$		0			0
$813$		0			0
$814$	742.944	+	1286.82i	0.0319904	+	0.0554090i
$815$	−8959.34	+	15518.0i	−0.385070	+	0.666961i
$816$		0			0
$817$	−1190.92	−	2062.73i	−0.0509975	−	0.0883302i
$818$	31751.3			1.35716
$819$		0			0
$820$	−2964.35			−0.126243
$821$	−7249.61	−	12556.7i	−0.308177	−	0.533778i	0.669787	−	0.742554i	$-0.266386\pi$
$821$	−7249.61	−	12556.7i	−0.308177	−	0.533778i	−0.977964	+	0.208776i	$0.933052\pi$
$822$		0			0
$823$	5988.57	−	10372.5i	0.253643	−	0.439323i	−0.710883	−	0.703310i	$-0.751704\pi$
$823$	5988.57	−	10372.5i	0.253643	−	0.439323i	0.964526	+	0.263987i	$0.0850377\pi$
$824$	−3035.90	−	5258.33i	−0.128350	−	0.222309i
$825$		0			0
$826$		0			0
$827$	−27613.5			−1.16108			−0.580541	−	0.814231i	$-0.697159\pi$
$827$	−27613.5			−1.16108			−0.580541	+	0.814231i	$0.697159\pi$
$828$		0			0
$829$	338.918	−	587.023i	0.0141992	−	0.0245937i	−0.858839	−	0.512246i	$-0.828813\pi$
$829$	338.918	−	587.023i	0.0141992	−	0.0245937i	0.873038	+	0.487653i	$0.162147\pi$
$830$	−2004.62	+	3472.10i	−0.0838329	+	0.145203i
$831$		0			0
$832$	2893.65			0.120576
$833$		0			0
$834$		0			0
$835$	2949.61	+	5108.88i	0.122246	+	0.211736i
$836$	65.5509	−	113.538i	0.00271187	−	0.00469710i
$837$		0			0
$838$	16111.9	+	27906.7i	0.664173	+	1.15038i
$839$	−42209.6			−1.73687			−0.868436	−	0.495801i	$-0.834874\pi$
$839$	−42209.6			−1.73687			−0.868436	+	0.495801i	$0.834874\pi$
$840$		0			0
$841$	47505.8			1.94784
$842$	8691.58	+	15054.3i	0.355738	+	0.616157i
$843$		0			0
$844$	8578.99	−	14859.2i	0.349883	−	0.606015i
$845$	−350.277	−	606.697i	−0.0142602	−	0.0246994i
$846$		0			0
$847$		0			0
$848$	−6488.46			−0.262753
$849$		0			0
$850$	8479.46	−	14686.9i	0.342168	−	0.592653i
$851$	6085.90	−	10541.1i	0.245149	−	0.424611i
$852$		0			0
$853$	−2796.45			−0.112249			−0.0561247	−	0.998424i	$-0.517874\pi$
$853$	−2796.45			−0.112249			−0.0561247	+	0.998424i	$0.517874\pi$
$854$		0			0
$855$		0			0
$856$	−5050.06	−	8746.95i	−0.201644	−	0.349258i
$857$	11590.5	−	20075.4i	0.461989	−	0.800189i	−0.537071	−	0.843537i	$-0.680469\pi$
$857$	11590.5	−	20075.4i	0.461989	−	0.800189i	0.999060	+	0.0433483i	$0.0138025\pi$
$858$		0			0
$859$	5948.75	+	10303.5i	0.236285	+	0.409257i	0.959645	−	0.281213i	$-0.0907369\pi$
$859$	5948.75	+	10303.5i	0.236285	+	0.409257i	−0.723361	+	0.690471i	$0.757404\pi$
$860$	8645.01			0.342782
$861$		0			0
$862$	−8390.21			−0.331521
$863$	−14907.9	−	25821.3i	−0.588033	−	1.01850i	−0.994490	−	0.104833i	$-0.966569\pi$
$863$	−14907.9	−	25821.3i	−0.588033	−	1.01850i	0.406457	−	0.913670i	$-0.366764\pi$
$864$		0			0
$865$	2869.00	−	4969.25i	0.112773	−	0.195329i
$866$	−5426.54	−	9399.04i	−0.212934	−	0.368813i
$867$		0			0
$868$		0			0
$869$	1.71256			6.68523e−5
$870$		0			0
$871$	−263.294	+	456.038i	−0.0102427	+	0.0177408i
$872$	−8422.11	+	14587.5i	−0.327074	+	0.566509i
$873$		0			0
$874$	−1073.94			−0.0415634
$875$		0			0
$876$		0			0
$877$	5169.42	+	8953.70i	0.199041	+	0.344749i	0.948218	−	0.317621i	$-0.102884\pi$
$877$	5169.42	+	8953.70i	0.199041	+	0.344749i	−0.749177	+	0.662370i	$0.769551\pi$
$878$	−3771.24	+	6531.98i	−0.144958	+	0.251075i
$879$		0			0
$880$	237.921	+	412.091i	0.00911399	+	0.0157859i
$881$	−24140.2			−0.923160			−0.461580	−	0.887099i	$-0.652717\pi$
$881$	−24140.2			−0.923160			−0.461580	+	0.887099i	$0.652717\pi$
$882$		0			0
$883$	12997.6			0.495361			0.247681	−	0.968842i	$-0.420332\pi$
$883$	12997.6			0.495361			0.247681	+	0.968842i	$0.420332\pi$
$884$	7374.85	+	12773.6i	0.280592	+	0.485999i
$885$		0			0
$886$	5930.30	−	10271.6i	0.224867	−	0.389481i
$887$	22633.3	+	39202.0i	0.856766	+	1.48396i	0.874997	+	0.484129i	$0.160863\pi$
$887$	22633.3	+	39202.0i	0.856766	+	1.48396i	−0.0182306	+	0.999834i	$0.505803\pi$
$888$		0			0
$889$		0			0
$890$	536.653			0.0202120
$891$		0			0
$892$	−11591.5	+	20077.0i	−0.435102	+	0.753619i
$893$	−874.322	+	1514.37i	−0.0327638	+	0.0567486i
$894$		0			0
$895$	16616.7			0.620596
$896$		0			0
$897$		0			0
$898$	529.065	+	916.367i	0.0196605	+	0.0340530i
$899$	−39196.6	+	67890.4i	−1.45415	+	2.51866i
$900$		0			0
$901$	−16536.7	−	28642.5i	−0.611452	−	1.05907i
$902$	−2096.11			−0.0773756
$903$		0			0
$904$	12286.1			0.452024
$905$	416.681	+	721.712i	0.0153049	+	0.0265089i
$906$		0			0
$907$	13883.2	−	24046.5i	0.508253	−	0.880319i	−0.491702	−	0.870764i	$-0.663625\pi$
$907$	13883.2	−	24046.5i	0.508253	−	0.880319i	0.999954	−	0.00955575i	$-0.00304174\pi$
$908$	8208.09	+	14216.8i	0.299994	+	0.519605i
$909$		0			0
$910$		0			0
$911$	−18531.2			−0.673948			−0.336974	−	0.941514i	$-0.609403\pi$
$911$	−18531.2			−0.673948			−0.336974	+	0.941514i	$0.609403\pi$
$912$		0			0
$913$	−1417.48	+	2455.14i	−0.0513819	+	0.0889961i
$914$	10057.2	−	17419.5i	0.363963	−	0.630402i
$915$		0			0
$916$	−5187.33			−0.187111
$917$		0			0
$918$		0			0
$919$	9046.70	+	15669.3i	0.324726	+	0.562442i	0.981457	−	0.191683i	$-0.0613947\pi$
$919$	9046.70	+	15669.3i	0.324726	+	0.562442i	−0.656731	+	0.754125i	$0.728061\pi$
$920$	1948.96	−	3375.69i	0.0698426	−	0.120971i
$921$		0			0
$922$	5010.31	+	8678.11i	0.178965	+	0.309977i
$923$	30820.1			1.09908
$924$		0			0
$925$	−11910.7			−0.423375
$926$	−7124.38	−	12339.8i	−0.252831	−	0.437916i
$927$		0			0
$928$	4290.11	−	7430.69i	0.151756	−	0.262850i
$929$	5311.26	+	9199.37i	0.187574	+	0.324888i	0.944441	−	0.328681i	$-0.106604\pi$
$929$	5311.26	+	9199.37i	0.187574	+	0.324888i	−0.756867	+	0.653569i	$0.773271\pi$
$930$		0			0
$931$		0			0
$932$	5913.34			0.207830
$933$		0			0
$934$	−7501.44	+	12992.9i	−0.262799	+	0.455182i
$935$	−1212.75	+	2100.54i	−0.0424183	+	0.0734706i
$936$		0			0
$937$	16057.6			0.559851			0.279925	−	0.960022i	$-0.409690\pi$
$937$	16057.6			0.559851			0.279925	+	0.960022i	$0.409690\pi$
$938$		0			0
$939$		0			0
$940$	−3173.40	−	5496.49i	−0.110112	−	0.190719i
$941$	27576.6	−	47764.1i	0.955338	−	1.65469i	0.221745	−	0.975105i	$-0.428825\pi$
$941$	27576.6	−	47764.1i	0.955338	−	1.65469i	0.733593	−	0.679589i	$-0.237842\pi$
$942$		0			0
$943$	8585.25	+	14870.1i	0.296473	+	0.513507i
$944$	4054.97			0.139807
$945$		0			0
$946$	6112.94			0.210094
$947$	9392.86	+	16268.9i	0.322309	+	0.558256i	0.980964	−	0.194189i	$-0.0622075\pi$
$947$	9392.86	+	16268.9i	0.322309	+	0.558256i	−0.658655	+	0.752445i	$0.728874\pi$
$948$		0			0
$949$	−15495.9	+	26839.6i	−0.530049	+	0.918072i
$950$	525.449	+	910.104i	0.0179451	+	0.0310818i
$951$		0			0
$952$		0			0
$953$	36499.4			1.24064			0.620321	−	0.784348i	$-0.287002\pi$
$953$	36499.4			1.24064			0.620321	+	0.784348i	$0.287002\pi$
$954$		0			0
$955$	−3396.42	+	5882.76i	−0.115084	+	0.199332i
$956$	−7553.84	+	13083.6i	−0.255553	+	0.442631i
$957$		0			0
$958$	−16347.6			−0.551323
$959$		0			0
$960$		0			0
$961$	−27843.9	−	48227.0i	−0.934641	−	1.61885i
$962$	5179.55	−	8971.25i	0.173592	−	0.300670i
$963$		0			0
$964$	7992.76	+	13843.9i	0.267043	+	0.462532i
$965$	1635.79			0.0545677
$966$		0			0
$967$	26059.9			0.866627			0.433314	−	0.901243i	$-0.357344\pi$
$967$	26059.9			0.866627			0.433314	+	0.901243i	$0.357344\pi$
$968$	−5155.76	−	8930.05i	−0.171191	−	0.296511i
$969$		0			0
$970$	5870.22	−	10167.5i	0.194311	−	0.336556i
$971$	10844.5	+	18783.2i	0.358410	+	0.620785i	0.987695	−	0.156390i	$-0.0499856\pi$
$971$	10844.5	+	18783.2i	0.358410	+	0.620785i	−0.629285	+	0.777174i	$0.716652\pi$
$972$		0			0
$973$		0			0
$974$	23937.6			0.787484
$975$		0			0
$976$	6009.74	−	10409.2i	0.197097	−	0.341383i
$977$	1059.59	−	1835.27i	0.0346975	−	0.0600978i	−0.848155	−	0.529748i	$-0.822287\pi$
$977$	1059.59	−	1835.27i	0.0346975	−	0.0600978i	0.882853	+	0.469650i	$0.155620\pi$
$978$		0			0
$979$	379.471			0.0123881
$980$		0			0
$981$		0			0
$982$	−2079.96	−	3602.59i	−0.0675908	−	0.117071i
$983$	−24252.1	+	42005.8i	−0.786898	+	1.36295i	0.140960	+	0.990015i	$0.454981\pi$
$983$	−24252.1	+	42005.8i	−0.786898	+	1.36295i	−0.927859	+	0.372932i	$0.878352\pi$
$984$		0			0
$985$	−11213.5	−	19422.3i	−0.362731	−	0.628269i
$986$	43735.7			1.41261
$987$		0			0
$988$	−913.998			−0.0294313
$989$	−25037.4	−	43366.1i	−0.804999	−	1.39430i
$990$		0			0
$991$	−1021.92	+	1770.02i	−0.0327572	+	0.0567372i	−0.881939	−	0.471363i	$-0.843762\pi$
$991$	−1021.92	+	1770.02i	−0.0327572	+	0.0567372i	0.849182	+	0.528100i	$0.177095\pi$
$992$	4677.88	+	8102.33i	0.149721	+	0.259324i
$993$		0			0
$994$		0			0
$995$	−16246.8			−0.517645
$996$		0			0
$997$	13369.5	−	23156.6i	0.424689	−	0.735583i	−0.571702	−	0.820461i	$-0.693717\pi$
$997$	13369.5	−	23156.6i	0.424689	−	0.735583i	0.996391	+	0.0848782i	$0.0270501\pi$
$998$	12834.4	−	22229.9i	0.407081	−	0.705084i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.bk.361.1		4
3.2	odd	2		294.4.e.k.67.2		4
7.2	even	3	inner	882.4.g.bk.667.1		4
7.3	odd	6		882.4.a.bb.1.1		2
7.4	even	3		882.4.a.t.1.2		2
7.5	odd	6		882.4.g.be.667.2		4
7.6	odd	2		882.4.g.be.361.2		4
21.2	odd	6		294.4.e.k.79.2		4
21.5	even	6		294.4.e.m.79.1		4
21.11	odd	6		294.4.a.o.1.1	yes	2
21.17	even	6		294.4.a.l.1.2	✓	2
21.20	even	2		294.4.e.m.67.1		4
84.11	even	6		2352.4.a.bu.1.1		2
84.59	odd	6		2352.4.a.bw.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.l.1.2	✓	2	21.17	even	6
294.4.a.o.1.1	yes	2	21.11	odd	6
294.4.e.k.67.2		4	3.2	odd	2
294.4.e.k.79.2		4	21.2	odd	6
294.4.e.m.67.1		4	21.20	even	2
294.4.e.m.79.1		4	21.5	even	6
882.4.a.t.1.2		2	7.4	even	3
882.4.a.bb.1.1		2	7.3	odd	6
882.4.g.be.361.2		4	7.6	odd	2
882.4.g.be.667.2		4	7.5	odd	6
882.4.g.bk.361.1		4	1.1	even	1	trivial
882.4.g.bk.667.1		4	7.2	even	3	inner
2352.4.a.bu.1.1		2	84.11	even	6
2352.4.a.bw.1.2		2	84.59	odd	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.29289 + 3.97141i) q^{5} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.29289 + 3.97141i) q^{5} -8.00000 q^{8} +(-4.58579 + 7.94282i) q^{10} +(-3.24264 + 5.61642i) q^{11} +45.2132 q^{13} +(-8.00000 - 13.8564i) q^{16} +(40.7782 - 70.6299i) q^{17} +(2.52691 + 4.37674i) q^{19} -18.3431 q^{20} -12.9706 q^{22} +(53.1249 + 92.0150i) q^{23} +(51.9853 - 90.0411i) q^{25} +(45.2132 + 78.3116i) q^{26} +268.132 q^{29} +(-146.184 + 253.198i) q^{31} +(16.0000 - 27.7128i) q^{32} +163.113 q^{34} +(-57.2792 - 99.2105i) q^{37} +(-5.05382 + 8.75348i) q^{38} +(-18.3431 - 31.7713i) q^{40} +161.605 q^{41} -471.294 q^{43} +(-12.9706 - 22.4657i) q^{44} +(-106.250 + 184.030i) q^{46} +(173.002 + 299.648i) q^{47} +207.941 q^{50} +(-90.4264 + 156.623i) q^{52} +(202.765 - 351.198i) q^{53} -29.7401 q^{55} +(268.132 + 464.418i) q^{58} +(-126.718 + 219.482i) q^{59} +(375.609 + 650.573i) q^{61} -584.735 q^{62} +64.0000 q^{64} +(103.669 + 179.560i) q^{65} +(-5.82338 + 10.0864i) q^{67} +(163.113 + 282.519i) q^{68} +681.661 q^{71} +(-342.729 + 593.623i) q^{73} +(114.558 - 198.421i) q^{74} -20.2153 q^{76} +(-0.132034 - 0.228690i) q^{79} +(36.6863 - 63.5425i) q^{80} +(161.605 + 279.908i) q^{82} +437.137 q^{83} +374.000 q^{85} +(-471.294 - 816.304i) q^{86} +(25.9411 - 44.9313i) q^{88} +(-29.2563 - 50.6734i) q^{89} -424.999 q^{92} +(-346.004 + 599.297i) q^{94} +(-11.5879 + 20.0708i) q^{95} -1280.09 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 12 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 12 q^{5} - 32 q^{8} - 24 q^{10} + 4 q^{11} + 96 q^{13} - 32 q^{16} + 132 q^{17} - 120 q^{19} - 96 q^{20} + 16 q^{22} - 76 q^{23} + 174 q^{25} + 96 q^{26} + 224 q^{29} - 432 q^{31} + 64 q^{32} + 528 q^{34} + 280 q^{37} + 240 q^{38} - 96 q^{40} - 72 q^{41} - 256 q^{43} + 16 q^{44} + 152 q^{46} - 264 q^{47} + 696 q^{50} - 192 q^{52} + 268 q^{53} + 96 q^{55} + 224 q^{58} + 336 q^{59} + 504 q^{61} - 1728 q^{62} + 256 q^{64} + 228 q^{65} + 384 q^{67} + 528 q^{68} + 792 q^{71} + 312 q^{73} - 560 q^{74} + 960 q^{76} + 848 q^{79} + 192 q^{80} - 72 q^{82} + 1296 q^{83} + 1496 q^{85} - 256 q^{86} - 32 q^{88} - 612 q^{89} + 608 q^{92} + 528 q^{94} + 904 q^{95} - 4368 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 12 * q^5 - 32 * q^8 - 24 * q^10 + 4 * q^11 + 96 * q^13 - 32 * q^16 + 132 * q^17 - 120 * q^19 - 96 * q^20 + 16 * q^22 - 76 * q^23 + 174 * q^25 + 96 * q^26 + 224 * q^29 - 432 * q^31 + 64 * q^32 + 528 * q^34 + 280 * q^37 + 240 * q^38 - 96 * q^40 - 72 * q^41 - 256 * q^43 + 16 * q^44 + 152 * q^46 - 264 * q^47 + 696 * q^50 - 192 * q^52 + 268 * q^53 + 96 * q^55 + 224 * q^58 + 336 * q^59 + 504 * q^61 - 1728 * q^62 + 256 * q^64 + 228 * q^65 + 384 * q^67 + 528 * q^68 + 792 * q^71 + 312 * q^73 - 560 * q^74 + 960 * q^76 + 848 * q^79 + 192 * q^80 - 72 * q^82 + 1296 * q^83 + 1496 * q^85 - 256 * q^86 - 32 * q^88 - 612 * q^89 + 608 * q^92 + 528 * q^94 + 904 * q^95 - 4368 * q^97

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