LMFDB - Embedded newform 882.4.g.bh.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:	$\Q(\sqrt{-3}, \sqrt{58})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 58x^{2} + 3364 $ x^4 + 58*x^2 + 3364
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-3.80789 - 6.59545i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.bh.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.61577 - 13.1909i) q^{5} -8.00000 q^{8} +(15.2315 - 26.3818i) q^{10} +(1.00000 - 1.73205i) q^{11} +30.4631 q^{13} +(-8.00000 - 13.8564i) q^{16} +(22.8473 - 39.5727i) q^{17} +(76.1577 + 131.909i) q^{19} +60.9262 q^{20} +4.00000 q^{22} +(15.0000 + 25.9808i) q^{23} +(-53.5000 + 92.6647i) q^{25} +(30.4631 + 52.7636i) q^{26} -212.000 q^{29} +(106.621 - 184.673i) q^{31} +(16.0000 - 27.7128i) q^{32} +91.3893 q^{34} +(-123.000 - 213.042i) q^{37} +(-152.315 + 263.818i) q^{38} +(60.9262 + 105.527i) q^{40} -319.862 q^{41} -284.000 q^{43} +(4.00000 + 6.92820i) q^{44} +(-30.0000 + 51.9615i) q^{46} +(-30.4631 - 52.7636i) q^{47} -214.000 q^{50} +(-60.9262 + 105.527i) q^{52} +(274.000 - 474.582i) q^{53} -30.4631 q^{55} +(-212.000 - 367.195i) q^{58} +(335.094 - 580.400i) q^{59} +(-258.936 - 448.491i) q^{61} +426.483 q^{62} +64.0000 q^{64} +(-232.000 - 401.836i) q^{65} +(-326.000 + 564.649i) q^{67} +(91.3893 + 158.291i) q^{68} -770.000 q^{71} +(-487.409 + 844.218i) q^{73} +(246.000 - 426.084i) q^{74} -609.262 q^{76} +(-236.000 - 408.764i) q^{79} +(-121.852 + 211.054i) q^{80} +(-319.862 - 554.018i) q^{82} +182.779 q^{83} -696.000 q^{85} +(-284.000 - 491.902i) q^{86} +(-8.00000 + 13.8564i) q^{88} +(-357.941 - 619.973i) q^{89} -120.000 q^{92} +(60.9262 - 105.527i) q^{94} +(1160.00 - 2009.18i) q^{95} -304.631 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} + 4 q^{11} - 32 q^{16} + 16 q^{22} + 60 q^{23} - 214 q^{25} - 848 q^{29} + 64 q^{32} - 492 q^{37} - 1136 q^{43} + 16 q^{44} - 120 q^{46} - 856 q^{50} + 1096 q^{53} - 848 q^{58}+ \cdots + 4640 q^{95}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 + 4 * q^11 - 32 * q^16 + 16 * q^22 + 60 * q^23 - 214 * q^25 - 848 * q^29 + 64 * q^32 - 492 * q^37 - 1136 * q^43 + 16 * q^44 - 120 * q^46 - 856 * q^50 + 1096 * q^53 - 848 * q^58 + 256 * q^64 - 928 * q^65 - 1304 * q^67 - 3080 * q^71 + 984 * q^74 - 944 * q^79 - 2784 * q^85 - 1136 * q^86 - 32 * q^88 - 480 * q^92 + 4640 * q^95

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
$5$	−7.61577	−	13.1909i	−0.681175	−	1.17983i	−0.974622	−	0.223855i	$-0.928136\pi$
$5$	−7.61577	−	13.1909i	−0.681175	−	1.17983i	0.293447	−	0.955975i	$-0.405198\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$		0			0
$10$	15.2315	−	26.3818i	0.481664	−	0.834266i
$11$	1.00000	−	1.73205i	0.0274101	−	0.0474757i	−0.851995	−	0.523550i	$-0.824607\pi$
$11$	1.00000	−	1.73205i	0.0274101	−	0.0474757i	0.879405	+	0.476074i	$0.157941\pi$
$12$		0			0
$13$	30.4631			0.649919			0.324959	−	0.945728i	$-0.394649\pi$
$13$	30.4631			0.649919			0.324959	+	0.945728i	$0.394649\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	22.8473	−	39.5727i	0.325958	−	0.564576i	−0.655748	−	0.754980i	$-0.727646\pi$
$17$	22.8473	−	39.5727i	0.325958	−	0.564576i	0.981706	+	0.190404i	$0.0609798\pi$
$18$		0			0
$19$	76.1577	+	131.909i	0.919567	+	1.59274i	0.800073	+	0.599903i	$0.204794\pi$
$19$	76.1577	+	131.909i	0.919567	+	1.59274i	0.119494	+	0.992835i	$0.461873\pi$
$20$	60.9262			0.681175
$21$		0			0
$22$	4.00000			0.0387638
$23$	15.0000	+	25.9808i	0.135988	+	0.235538i	0.925974	−	0.377586i	$-0.123246\pi$
$23$	15.0000	+	25.9808i	0.135988	+	0.235538i	−0.789987	+	0.613124i	$0.789913\pi$
$24$		0			0
$25$	−53.5000	+	92.6647i	−0.428000	+	0.741318i
$26$	30.4631	+	52.7636i	0.229781	+	0.397992i
$27$		0			0
$28$		0			0
$29$	−212.000			−1.35750			−0.678748	−	0.734371i	$-0.737477\pi$
$29$	−212.000			−1.35750			−0.678748	+	0.734371i	$0.737477\pi$
$30$		0			0
$31$	106.621	−	184.673i	0.617731	−	1.06994i	−0.372168	−	0.928166i	$-0.621385\pi$
$31$	106.621	−	184.673i	0.617731	−	1.06994i	0.989899	−	0.141776i	$-0.0452813\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	91.3893			0.460974
$35$		0			0
$36$		0			0
$37$	−123.000	−	213.042i	−0.546516	−	0.946593i	−0.998510	−	0.0545719i	$-0.982621\pi$
$37$	−123.000	−	213.042i	−0.546516	−	0.946593i	0.451994	−	0.892021i	$-0.350713\pi$
$38$	−152.315	+	263.818i	−0.650232	+	1.12624i
$39$		0			0
$40$	60.9262	+	105.527i	0.240832	+	0.417133i
$41$	−319.862			−1.21839			−0.609197	−	0.793019i	$-0.708508\pi$
$41$	−319.862			−1.21839			−0.609197	+	0.793019i	$0.708508\pi$
$42$		0			0
$43$	−284.000			−1.00720			−0.503600	−	0.863937i	$-0.667991\pi$
$43$	−284.000			−1.00720			−0.503600	+	0.863937i	$0.667991\pi$
$44$	4.00000	+	6.92820i	0.0137051	+	0.0237379i
$45$		0			0
$46$	−30.0000	+	51.9615i	−0.0961578	+	0.166550i
$47$	−30.4631	−	52.7636i	−0.0945425	−	0.163752i	0.814875	−	0.579637i	$-0.196805\pi$
$47$	−30.4631	−	52.7636i	−0.0945425	−	0.163752i	−0.909418	+	0.415884i	$0.863472\pi$
$48$		0			0
$49$		0			0
$50$	−214.000			−0.605283
$51$		0			0
$52$	−60.9262	+	105.527i	−0.162480	+	0.281423i
$53$	274.000	−	474.582i	0.710128	−	1.22998i	−0.254680	−	0.967025i	$-0.581970\pi$
$53$	274.000	−	474.582i	0.710128	−	1.22998i	0.964809	−	0.262953i	$-0.0846964\pi$
$54$		0			0
$55$	−30.4631			−0.0746844
$56$		0			0
$57$		0			0
$58$	−212.000	−	367.195i	−0.479948	−	0.831294i
$59$	335.094	−	580.400i	0.739416	−	1.28071i	−0.213343	−	0.976977i	$-0.568435\pi$
$59$	335.094	−	580.400i	0.739416	−	1.28071i	0.952759	−	0.303728i	$-0.0982315\pi$
$60$		0			0
$61$	−258.936	−	448.491i	−0.543498	−	0.941367i	−0.998700	−	0.0509782i	$-0.983766\pi$
$61$	−258.936	−	448.491i	−0.543498	−	0.941367i	0.455202	−	0.890388i	$-0.349567\pi$
$62$	426.483			0.873604
$63$		0			0
$64$	64.0000			0.125000
$65$	−232.000	−	401.836i	−0.442709	−	0.766794i
$66$		0			0
$67$	−326.000	+	564.649i	−0.594436	+	1.02959i	0.399190	+	0.916868i	$0.369291\pi$
$67$	−326.000	+	564.649i	−0.594436	+	1.02959i	−0.993626	+	0.112726i	$0.964042\pi$
$68$	91.3893	+	158.291i	0.162979	+	0.282288i
$69$		0			0
$70$		0			0
$71$	−770.000			−1.28707			−0.643537	−	0.765415i	$-0.722534\pi$
$71$	−770.000			−1.28707			−0.643537	+	0.765415i	$0.722534\pi$
$72$		0			0
$73$	−487.409	+	844.218i	−0.781465	+	1.35354i	0.149623	+	0.988743i	$0.452194\pi$
$73$	−487.409	+	844.218i	−0.781465	+	1.35354i	−0.931088	+	0.364794i	$0.881139\pi$
$74$	246.000	−	426.084i	0.386445	−	0.669342i
$75$		0			0
$76$	−609.262			−0.919567
$77$		0			0
$78$		0			0
$79$	−236.000	−	408.764i	−0.336102	−	0.582146i	0.647594	−	0.761986i	$-0.275775\pi$
$79$	−236.000	−	408.764i	−0.336102	−	0.582146i	−0.983696	+	0.179840i	$0.942442\pi$
$80$	−121.852	+	211.054i	−0.170294	+	0.294958i
$81$		0			0
$82$	−319.862	−	554.018i	−0.430767	−	0.746110i
$83$	182.779			0.241718			0.120859	−	0.992670i	$-0.461435\pi$
$83$	182.779			0.241718			0.120859	+	0.992670i	$0.461435\pi$
$84$		0			0
$85$	−696.000			−0.888139
$86$	−284.000	−	491.902i	−0.356099	−	0.616781i
$87$		0			0
$88$	−8.00000	+	13.8564i	−0.00969094	+	0.0167852i
$89$	−357.941	−	619.973i	−0.426311	−	0.738393i	0.570231	−	0.821485i	$-0.306854\pi$
$89$	−357.941	−	619.973i	−0.426311	−	0.738393i	−0.996542	+	0.0830918i	$0.973521\pi$
$90$		0			0
$91$		0			0
$92$	−120.000			−0.135988
$93$		0			0
$94$	60.9262	−	105.527i	0.0668517	−	0.115790i
$95$	1160.00	−	2009.18i	1.25277	−	2.16987i
$96$		0			0
$97$	−304.631			−0.318872			−0.159436	−	0.987208i	$-0.550968\pi$
$97$	−304.631			−0.318872			−0.159436	+	0.987208i	$0.550968\pi$
$98$		0			0
$99$		0			0
$100$	−214.000	−	370.659i	−0.214000	−	0.370659i
$101$	−510.257	+	883.791i	−0.502698	+	0.870698i	0.497298	+	0.867580i	$0.334326\pi$
$101$	−510.257	+	883.791i	−0.502698	+	0.870698i	−0.999995	+	0.00311763i	$0.999008\pi$
$102$		0			0
$103$	−289.399	−	501.254i	−0.276848	−	0.479515i	0.693752	−	0.720214i	$-0.255957\pi$
$103$	−289.399	−	501.254i	−0.276848	−	0.479515i	−0.970600	+	0.240699i	$0.922623\pi$
$104$	−243.705			−0.229781
$105$		0			0
$106$	1096.00			1.00427
$107$	−823.000	−	1425.48i	−0.743574	−	1.28791i	−0.950858	−	0.309627i	$-0.899796\pi$
$107$	−823.000	−	1425.48i	−0.743574	−	1.28791i	0.207284	−	0.978281i	$-0.433538\pi$
$108$		0			0
$109$	−491.000	+	850.437i	−0.431461	+	0.747313i	−0.996999	−	0.0774094i	$-0.975335\pi$
$109$	−491.000	+	850.437i	−0.431461	+	0.747313i	0.565538	+	0.824722i	$0.308668\pi$
$110$	−30.4631	−	52.7636i	−0.0264049	−	0.0457347i
$111$		0			0
$112$		0			0
$113$	−1288.00			−1.07226			−0.536128	−	0.844137i	$-0.680113\pi$
$113$	−1288.00			−1.07226			−0.536128	+	0.844137i	$0.680113\pi$
$114$		0			0
$115$	228.473	−	395.727i	0.185263	−	0.320885i
$116$	424.000	−	734.390i	0.339374	−	0.587813i
$117$		0			0
$118$	1340.38			1.04569
$119$		0			0
$120$		0			0
$121$	663.500	+	1149.22i	0.498497	+	0.863423i
$122$	517.873	−	896.982i	0.384311	−	0.665647i
$123$		0			0
$124$	426.483	+	738.691i	0.308866	+	0.534971i
$125$	−274.168			−0.196179
$126$		0			0
$127$	−1072.00			−0.749013			−0.374506	−	0.927224i	$-0.622188\pi$
$127$	−1072.00			−0.749013			−0.374506	+	0.927224i	$0.622188\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	464.000	−	803.672i	0.313042	−	0.542205i
$131$	1370.84	+	2374.36i	0.914281	+	1.58358i	0.807951	+	0.589250i	$0.200577\pi$
$131$	1370.84	+	2374.36i	0.914281	+	1.58358i	0.106330	+	0.994331i	$0.466090\pi$
$132$		0			0
$133$		0			0
$134$	−1304.00			−0.840660
$135$		0			0
$136$	−182.779	+	316.582i	−0.115244	+	0.199608i
$137$	1468.00	−	2542.65i	0.915472	−	1.58564i	0.109264	−	0.994013i	$-0.465151\pi$
$137$	1468.00	−	2542.65i	0.915472	−	1.58564i	0.806208	−	0.591632i	$-0.201516\pi$
$138$		0			0
$139$	−182.779			−0.111533			−0.0557665	−	0.998444i	$-0.517760\pi$
$139$	−182.779			−0.111533			−0.0557665	+	0.998444i	$0.517760\pi$
$140$		0			0
$141$		0			0
$142$	−770.000	−	1333.68i	−0.455049	−	0.788168i
$143$	30.4631	−	52.7636i	0.0178143	−	0.0308554i
$144$		0			0
$145$	1614.54	+	2796.47i	0.924694	+	1.60162i
$146$	−1949.64			−1.10516
$147$		0			0
$148$	984.000			0.546516
$149$	−482.000	−	834.848i	−0.265013	−	0.459016i	0.702554	−	0.711631i	$-0.252043\pi$
$149$	−482.000	−	834.848i	−0.265013	−	0.459016i	−0.967567	+	0.252614i	$0.918710\pi$
$150$		0			0
$151$	844.000	−	1461.85i	0.454859	−	0.787839i	−0.543821	−	0.839201i	$-0.683023\pi$
$151$	844.000	−	1461.85i	0.454859	−	0.787839i	0.998680	+	0.0513620i	$0.0163562\pi$
$152$	−609.262	−	1055.27i	−0.325116	−	0.563118i
$153$		0			0
$154$		0			0
$155$	−3248.00			−1.68313
$156$		0			0
$157$	1721.16	−	2981.14i	0.874929	−	1.51542i	0.0180912	−	0.999836i	$-0.494241\pi$
$157$	1721.16	−	2981.14i	0.874929	−	1.51542i	0.856838	−	0.515586i	$-0.172426\pi$
$158$	472.000	−	817.528i	0.237660	−	0.411639i
$159$		0			0
$160$	−487.409			−0.240832
$161$		0			0
$162$		0			0
$163$	1662.00	+	2878.67i	0.798637	+	1.38328i	0.920504	+	0.390734i	$0.127779\pi$
$163$	1662.00	+	2878.67i	0.798637	+	1.38328i	−0.121866	+	0.992547i	$0.538888\pi$
$164$	639.725	−	1108.04i	0.304598	−	0.527580i
$165$		0			0
$166$	182.779	+	316.582i	0.0854600	+	0.148021i
$167$	3046.31			1.41156			0.705780	−	0.708431i	$-0.250597\pi$
$167$	3046.31			1.41156			0.705780	+	0.708431i	$0.250597\pi$
$168$		0			0
$169$	−1269.00			−0.577606
$170$	−696.000	−	1205.51i	−0.314004	−	0.543872i
$171$		0			0
$172$	568.000	−	983.805i	0.251800	−	0.436130i
$173$	−1637.39	−	2836.04i	−0.719587	−	1.24636i	−0.961164	−	0.275979i	$-0.910998\pi$
$173$	−1637.39	−	2836.04i	−0.719587	−	1.24636i	0.241577	−	0.970382i	$-0.422336\pi$
$174$		0			0
$175$		0			0
$176$	−32.0000			−0.0137051
$177$		0			0
$178$	715.883	−	1239.95i	0.301448	−	0.522123i
$179$	627.000	−	1086.00i	0.261811	−	0.453470i	−0.704912	−	0.709295i	$-0.749014\pi$
$179$	627.000	−	1086.00i	0.261811	−	0.453470i	0.966723	+	0.255825i	$0.0823469\pi$
$180$		0			0
$181$	3076.77			1.26351			0.631753	−	0.775170i	$-0.282336\pi$
$181$	3076.77			1.26351			0.631753	+	0.775170i	$0.282336\pi$
$182$		0			0
$183$		0			0
$184$	−120.000	−	207.846i	−0.0480789	−	0.0832751i
$185$	−1873.48	+	3244.96i	−0.744546	+	1.28959i
$186$		0			0
$187$	−45.6946	−	79.1454i	−0.0178691	−	0.0309502i
$188$	243.705			0.0945425
$189$		0			0
$190$	4640.00			1.77169
$191$	453.000	+	784.619i	0.171612	+	0.297241i	0.938984	−	0.343962i	$-0.111769\pi$
$191$	453.000	+	784.619i	0.171612	+	0.297241i	−0.767371	+	0.641203i	$0.778436\pi$
$192$		0			0
$193$	−91.0000	+	157.617i	−0.0339395	+	0.0587849i	−0.882496	−	0.470319i	$-0.844139\pi$
$193$	−91.0000	+	157.617i	−0.0339395	+	0.0587849i	0.848557	+	0.529104i	$0.177472\pi$
$194$	−304.631	−	527.636i	−0.112738	−	0.195268i
$195$		0			0
$196$		0			0
$197$	−3468.00			−1.25424			−0.627119	−	0.778924i	$-0.715766\pi$
$197$	−3468.00			−1.25424			−0.627119	+	0.778924i	$0.715766\pi$
$198$		0			0
$199$	−1949.64	+	3376.87i	−0.694503	+	1.20292i	0.275844	+	0.961202i	$0.411043\pi$
$199$	−1949.64	+	3376.87i	−0.694503	+	1.20292i	−0.970348	+	0.241713i	$0.922291\pi$
$200$	428.000	−	741.318i	0.151321	−	0.262095i
$201$		0			0
$202$	−2041.03			−0.710922
$203$		0			0
$204$		0			0
$205$	2436.00	+	4219.28i	0.829940	+	1.43750i
$206$	578.799	−	1002.51i	0.195761	−	0.339068i
$207$		0			0
$208$	−243.705	−	422.109i	−0.0812398	−	0.140712i
$209$	304.631			0.100822
$210$		0			0
$211$	−2620.00			−0.854826			−0.427413	−	0.904057i	$-0.640575\pi$
$211$	−2620.00			−0.854826			−0.427413	+	0.904057i	$0.640575\pi$
$212$	1096.00	+	1898.33i	0.355064	+	0.614989i
$213$		0			0
$214$	1646.00	−	2850.96i	0.525786	−	0.910688i
$215$	2162.88	+	3746.22i	0.686080	+	1.18833i
$216$		0			0
$217$		0			0
$218$	−1964.00			−0.610178
$219$		0			0
$220$	60.9262	−	105.527i	0.0186711	−	0.0323393i
$221$	696.000	−	1205.51i	0.211846	−	0.366929i
$222$		0			0
$223$	−1401.30			−0.420799			−0.210399	−	0.977616i	$-0.567476\pi$
$223$	−1401.30			−0.420799			−0.210399	+	0.977616i	$0.567476\pi$
$224$		0			0
$225$		0			0
$226$	−1288.00	−	2230.88i	−0.379099	−	0.656620i
$227$	1949.64	−	3376.87i	0.570053	−	0.987361i	−0.426507	−	0.904484i	$-0.640256\pi$
$227$	1949.64	−	3376.87i	0.570053	−	0.987361i	0.996560	−	0.0828763i	$-0.0264106\pi$
$228$		0			0
$229$	−2756.91	−	4775.11i	−0.795553	−	1.37794i	−0.922487	−	0.386028i	$-0.873847\pi$
$229$	−2756.91	−	4775.11i	−0.795553	−	1.37794i	0.126934	−	0.991911i	$-0.459486\pi$
$230$	913.893			0.262001
$231$		0			0
$232$	1696.00			0.479948
$233$	−356.000	−	616.610i	−0.100096	−	0.173371i	0.811628	−	0.584174i	$-0.198582\pi$
$233$	−356.000	−	616.610i	−0.100096	−	0.173371i	−0.911724	+	0.410803i	$0.865248\pi$
$234$		0			0
$235$	−464.000	+	803.672i	−0.128800	+	0.223088i
$236$	1340.38	+	2321.60i	0.369708	+	0.640353i
$237$		0			0
$238$		0			0
$239$	2586.00			0.699893			0.349947	−	0.936770i	$-0.386200\pi$
$239$	2586.00			0.699893			0.349947	+	0.936770i	$0.386200\pi$
$240$		0			0
$241$	−1127.13	+	1952.25i	−0.301266	+	0.521808i	−0.976423	−	0.215866i	$-0.930743\pi$
$241$	−1127.13	+	1952.25i	−0.301266	+	0.521808i	0.675157	+	0.737674i	$0.264076\pi$
$242$	−1327.00	+	2298.43i	−0.352491	+	0.610532i
$243$		0			0
$244$	2071.49			0.543498
$245$		0			0
$246$		0			0
$247$	2320.00	+	4018.36i	0.597644	+	1.03515i
$248$	−852.967	+	1477.38i	−0.218401	+	0.378282i
$249$		0			0
$250$	−274.168	−	474.873i	−0.0693596	−	0.120134i
$251$	−4508.54			−1.13377			−0.566885	−	0.823797i	$-0.691852\pi$
$251$	−4508.54			−1.13377			−0.566885	+	0.823797i	$0.691852\pi$
$252$		0			0
$253$	60.0000			0.0149098
$254$	−1072.00	−	1856.76i	−0.264816	−	0.458675i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2277.12	−	3944.08i	−0.552695	−	0.957296i	−0.998079	−	0.0619561i	$-0.980266\pi$
$257$	−2277.12	−	3944.08i	−0.552695	−	0.957296i	0.445384	−	0.895340i	$-0.353067\pi$
$258$		0			0
$259$		0			0
$260$	1856.00			0.442709
$261$		0			0
$262$	−2741.68	+	4748.73i	−0.646494	+	1.11976i
$263$	−1289.00	+	2232.61i	−0.302217	+	0.523456i	−0.976638	−	0.214892i	$-0.931060\pi$
$263$	−1289.00	+	2232.61i	−0.302217	+	0.523456i	0.674421	+	0.738347i	$0.264393\pi$
$264$		0			0
$265$	−8346.89			−1.93489
$266$		0			0
$267$		0			0
$268$	−1304.00	−	2258.59i	−0.297218	−	0.514797i
$269$	−464.562	+	804.645i	−0.105297	+	0.182380i	−0.913859	−	0.406031i	$-0.866913\pi$
$269$	−464.562	+	804.645i	−0.105297	+	0.182380i	0.808563	+	0.588410i	$0.200246\pi$
$270$		0			0
$271$	−563.567	−	976.127i	−0.126326	−	0.218803i	0.795925	−	0.605396i	$-0.206985\pi$
$271$	−563.567	−	976.127i	−0.126326	−	0.218803i	−0.922250	+	0.386593i	$0.873652\pi$
$272$	−731.114			−0.162979
$273$		0			0
$274$	5872.00			1.29467
$275$	107.000	+	185.329i	0.0234631	+	0.0406392i
$276$		0			0
$277$	−755.000	+	1307.70i	−0.163767	+	0.283653i	−0.936217	−	0.351423i	$-0.885698\pi$
$277$	−755.000	+	1307.70i	−0.163767	+	0.283653i	0.772450	+	0.635076i	$0.219031\pi$
$278$	−182.779	−	316.582i	−0.0394328	−	0.0682997i
$279$		0			0
$280$		0			0
$281$	4008.00			0.850880			0.425440	−	0.904987i	$-0.360119\pi$
$281$	4008.00			0.850880			0.425440	+	0.904987i	$0.360119\pi$
$282$		0			0
$283$	1203.29	−	2084.16i	0.252750	−	0.437776i	−0.711532	−	0.702654i	$-0.751998\pi$
$283$	1203.29	−	2084.16i	0.252750	−	0.437776i	0.964282	+	0.264878i	$0.0853316\pi$
$284$	1540.00	−	2667.36i	0.321768	−	0.557319i
$285$		0			0
$286$	121.852			0.0251933
$287$		0			0
$288$		0			0
$289$	1412.50	+	2446.52i	0.287503	+	0.497969i
$290$	−3229.09	+	5592.94i	−0.653857	+	1.13251i
$291$		0			0
$292$	−1949.64	−	3376.87i	−0.390733	−	0.676769i
$293$	−5254.88			−1.04776			−0.523880	−	0.851792i	$-0.675516\pi$
$293$	−5254.88			−1.04776			−0.523880	+	0.851792i	$0.675516\pi$
$294$		0			0
$295$	−10208.0			−2.01469
$296$	984.000	+	1704.34i	0.193222	+	0.334671i
$297$		0			0
$298$	964.000	−	1669.70i	0.187393	−	0.324574i
$299$	456.946	+	791.454i	0.0883809	+	0.153080i
$300$		0			0
$301$		0			0
$302$	3376.00			0.643268
$303$		0			0
$304$	1218.52	−	2110.54i	0.229892	−	0.398184i
$305$	−3944.00	+	6831.21i	−0.740435	+	1.28247i
$306$		0			0
$307$	6366.79			1.18362			0.591811	−	0.806077i	$-0.298413\pi$
$307$	6366.79			1.18362			0.591811	+	0.806077i	$0.298413\pi$
$308$		0			0
$309$		0			0
$310$	−3248.00	−	5625.70i	−0.595077	−	1.03070i
$311$	3686.03	−	6384.40i	0.672077	−	1.16407i	−0.305238	−	0.952276i	$-0.598736\pi$
$311$	3686.03	−	6384.40i	0.672077	−	1.16407i	0.977314	−	0.211795i	$-0.0679308\pi$
$312$		0			0
$313$	274.168	+	474.873i	0.0495108	+	0.0857552i	0.889719	−	0.456509i	$-0.150900\pi$
$313$	274.168	+	474.873i	0.0495108	+	0.0857552i	−0.840208	+	0.542264i	$0.817567\pi$
$314$	6884.66			1.23734
$315$		0			0
$316$	1888.00			0.336102
$317$	1890.00	+	3273.58i	0.334867	+	0.580007i	0.983459	−	0.181129i	$-0.0579751\pi$
$317$	1890.00	+	3273.58i	0.334867	+	0.580007i	−0.648592	+	0.761136i	$0.724642\pi$
$318$		0			0
$319$	−212.000	+	367.195i	−0.0372092	+	0.0644482i
$320$	−487.409	−	844.218i	−0.0851469	−	0.147479i
$321$		0			0
$322$		0			0
$323$	6960.00			1.19896
$324$		0			0
$325$	−1629.78	+	2822.85i	−0.278165	+	0.481796i
$326$	−3324.00	+	5757.34i	−0.564722	+	0.978127i
$327$		0			0
$328$	2558.90			0.430767
$329$		0			0
$330$		0			0
$331$	−3130.00	−	5421.32i	−0.519759	−	0.900250i	−0.999736	−	0.0229685i	$-0.992688\pi$
$331$	−3130.00	−	5421.32i	−0.519759	−	0.900250i	0.479977	−	0.877281i	$-0.340645\pi$
$332$	−365.557	+	633.163i	−0.0604294	+	0.104667i
$333$		0			0
$334$	3046.31	+	5276.36i	0.499062	+	0.864400i
$335$	9930.97			1.61966
$336$		0			0
$337$	−3166.00			−0.511760			−0.255880	−	0.966709i	$-0.582365\pi$
$337$	−3166.00			−0.511760			−0.255880	+	0.966709i	$0.582365\pi$
$338$	−1269.00	−	2197.97i	−0.204214	−	0.353710i
$339$		0			0
$340$	1392.00	−	2411.01i	0.222035	−	0.384575i
$341$	−213.242	−	369.345i	−0.0338642	−	0.0586545i
$342$		0			0
$343$		0			0
$344$	2272.00			0.356099
$345$		0			0
$346$	3274.78	−	5672.09i	0.508825	−	0.881310i
$347$	−1809.00	+	3133.28i	−0.279862	+	0.484736i	−0.971350	−	0.237652i	$-0.923622\pi$
$347$	−1809.00	+	3133.28i	−0.279862	+	0.484736i	0.691488	+	0.722388i	$0.256955\pi$
$348$		0			0
$349$	4478.07			0.686836			0.343418	−	0.939183i	$-0.388415\pi$
$349$	4478.07			0.686836			0.343418	+	0.939183i	$0.388415\pi$
$350$		0			0
$351$		0			0
$352$	−32.0000	−	55.4256i	−0.00484547	−	0.00839260i
$353$	1850.63	−	3205.39i	0.279035	−	0.483302i	−0.692110	−	0.721792i	$-0.743319\pi$
$353$	1850.63	−	3205.39i	0.279035	−	0.483302i	0.971145	+	0.238489i	$0.0766522\pi$
$354$		0			0
$355$	5864.15	+	10157.0i	0.876723	+	1.51853i
$356$	2863.53			0.426311
$357$		0			0
$358$	2508.00			0.370257
$359$	65.0000	+	112.583i	0.00955590	+	0.0165513i	0.870764	−	0.491702i	$-0.163625\pi$
$359$	65.0000	+	112.583i	0.00955590	+	0.0165513i	−0.861208	+	0.508253i	$0.830292\pi$
$360$		0			0
$361$	−8170.50	+	14151.7i	−1.19121	+	2.06323i
$362$	3076.77	+	5329.13i	0.446717	+	0.773737i
$363$		0			0
$364$		0			0
$365$	14848.0			2.12926
$366$		0			0
$367$	3899.28	−	6753.74i	0.554606	−	0.960606i	−0.443328	−	0.896360i	$-0.646202\pi$
$367$	3899.28	−	6753.74i	0.554606	−	0.960606i	0.997934	−	0.0642468i	$-0.0204645\pi$
$368$	240.000	−	415.692i	0.0339969	−	0.0588844i
$369$		0			0
$370$	−7493.92			−1.05295
$371$		0			0
$372$		0			0
$373$	25.0000	+	43.3013i	0.00347038	+	0.00601087i	0.867755	−	0.496992i	$-0.165562\pi$
$373$	25.0000	+	43.3013i	0.00347038	+	0.00601087i	−0.864285	+	0.503002i	$0.832229\pi$
$374$	91.3893	−	158.291i	0.0126354	−	0.0218851i
$375$		0			0
$376$	243.705	+	422.109i	0.0334258	+	0.0578952i
$377$	−6458.18			−0.882263
$378$		0			0
$379$	−4956.00			−0.671696			−0.335848	−	0.941916i	$-0.609023\pi$
$379$	−4956.00			−0.671696			−0.335848	+	0.941916i	$0.609023\pi$
$380$	4640.00	+	8036.72i	0.626387	+	1.08493i
$381$		0			0
$382$	−906.000	+	1569.24i	−0.121348	+	0.210181i
$383$	−3381.40	−	5856.76i	−0.451127	−	0.781375i	0.547329	−	0.836917i	$-0.315645\pi$
$383$	−3381.40	−	5856.76i	−0.451127	−	0.781375i	−0.998456	+	0.0555425i	$0.982311\pi$
$384$		0			0
$385$		0			0
$386$	−364.000			−0.0479977
$387$		0			0
$388$	609.262	−	1055.27i	0.0797180	−	0.138076i
$389$	−6570.00	+	11379.6i	−0.856330	+	1.48321i	0.0190764	+	0.999818i	$0.493927\pi$
$389$	−6570.00	+	11379.6i	−0.856330	+	1.48321i	−0.875406	+	0.483388i	$0.839406\pi$
$390$		0			0
$391$	1370.84			0.177305
$392$		0			0
$393$		0			0
$394$	−3468.00	−	6006.75i	−0.443440	−	0.768060i
$395$	−3594.64	+	6226.11i	−0.457889	+	0.793087i
$396$		0			0
$397$	1903.94	+	3297.73i	0.240696	+	0.416897i	0.960913	−	0.276852i	$-0.0892911\pi$
$397$	1903.94	+	3297.73i	0.240696	+	0.416897i	−0.720217	+	0.693749i	$0.755958\pi$
$398$	−7798.55			−0.982176
$399$		0			0
$400$	1712.00			0.214000
$401$	2412.00	+	4177.71i	0.300373	+	0.520261i	0.976220	−	0.216780i	$-0.0695555\pi$
$401$	2412.00	+	4177.71i	0.300373	+	0.520261i	−0.675848	+	0.737041i	$0.736222\pi$
$402$		0			0
$403$	3248.00	−	5625.70i	0.401475	−	0.695375i
$404$	−2041.03	−	3535.16i	−0.251349	−	0.435349i
$405$		0			0
$406$		0			0
$407$	−492.000			−0.0599202
$408$		0			0
$409$	2650.29	−	4590.44i	0.320412	−	0.554969i	−0.660161	−	0.751124i	$-0.729512\pi$
$409$	2650.29	−	4590.44i	0.320412	−	0.554969i	0.980573	+	0.196155i	$0.0628454\pi$
$410$	−4872.00	+	8438.55i	−0.586856	+	1.01646i
$411$		0			0
$412$	2315.20			0.276848
$413$		0			0
$414$		0			0
$415$	−1392.00	−	2411.01i	−0.164652	−	0.285186i
$416$	487.409	−	844.218i	0.0574452	−	0.0994981i
$417$		0			0
$418$	304.631	+	527.636i	0.0356459	+	0.0617405i
$419$	−10540.2			−1.22894			−0.614468	−	0.788942i	$-0.710629\pi$
$419$	−10540.2			−1.22894			−0.614468	+	0.788942i	$0.710629\pi$
$420$		0			0
$421$	−4458.00			−0.516080			−0.258040	−	0.966134i	$-0.583077\pi$
$421$	−4458.00			−0.516080			−0.258040	+	0.966134i	$0.583077\pi$
$422$	−2620.00	−	4537.97i	−0.302227	−	0.523472i
$423$		0			0
$424$	−2192.00	+	3796.66i	−0.251068	+	0.434863i
$425$	2444.66	+	4234.28i	0.279020	+	0.483277i
$426$		0			0
$427$		0			0
$428$	6584.00			0.743574
$429$		0			0
$430$	−4325.76	+	7492.43i	−0.485132	+	0.840273i
$431$	−8107.00	+	14041.7i	−0.906034	+	1.56930i	−0.0865097	+	0.996251i	$0.527571\pi$
$431$	−8107.00	+	14041.7i	−0.906034	+	1.56930i	−0.819524	+	0.573045i	$0.805762\pi$
$432$		0			0
$433$	3594.64			0.398955			0.199478	−	0.979902i	$-0.436075\pi$
$433$	3594.64			0.398955			0.199478	+	0.979902i	$0.436075\pi$
$434$		0			0
$435$		0			0
$436$	−1964.00	−	3401.75i	−0.215731	−	0.373656i
$437$	−2284.73	+	3957.27i	−0.250100	+	0.433185i
$438$		0			0
$439$	−4295.30	−	7439.67i	−0.466978	−	0.808829i	0.532310	−	0.846549i	$-0.321324\pi$
$439$	−4295.30	−	7439.67i	−0.466978	−	0.808829i	−0.999288	+	0.0377198i	$0.987991\pi$
$440$	243.705			0.0264049
$441$		0			0
$442$	2784.00			0.299596
$443$	7503.00	+	12995.6i	0.804691	+	1.39377i	0.916499	+	0.400037i	$0.131003\pi$
$443$	7503.00	+	12995.6i	0.804691	+	1.39377i	−0.111808	+	0.993730i	$0.535664\pi$
$444$		0			0
$445$	−5452.00	+	9443.14i	−0.580786	+	1.00595i
$446$	−1401.30	−	2427.13i	−0.148775	−	0.257686i
$447$		0			0
$448$		0			0
$449$	−1824.00			−0.191715			−0.0958573	−	0.995395i	$-0.530559\pi$
$449$	−1824.00			−0.191715			−0.0958573	+	0.995395i	$0.530559\pi$
$450$		0			0
$451$	−319.862	+	554.018i	−0.0333963	+	0.0578441i
$452$	2576.00	−	4461.76i	0.268064	−	0.464300i
$453$		0			0
$454$	7798.55			0.806177
$455$		0			0
$456$		0			0
$457$	293.000	+	507.491i	0.0299912	+	0.0519462i	0.880631	−	0.473802i	$-0.157119\pi$
$457$	293.000	+	507.491i	0.0299912	+	0.0519462i	−0.850640	+	0.525748i	$0.823785\pi$
$458$	5513.82	−	9550.22i	0.562541	−	0.974350i
$459$		0			0
$460$	913.893	+	1582.91i	0.0926315	+	0.160442i
$461$	15399.1			1.55576			0.777882	−	0.628410i	$-0.216294\pi$
$461$	15399.1			1.55576			0.777882	+	0.628410i	$0.216294\pi$
$462$		0			0
$463$	−88.0000			−0.00883306			−0.00441653	−	0.999990i	$-0.501406\pi$
$463$	−88.0000			−0.00883306			−0.00441653	+	0.999990i	$0.501406\pi$
$464$	1696.00	+	2937.56i	0.169687	+	0.293907i
$465$		0			0
$466$	712.000	−	1233.22i	0.0707785	−	0.122592i
$467$	4874.09	+	8442.18i	0.482968	+	0.836526i	0.999809	−	0.0195561i	$-0.00622529\pi$
$467$	4874.09	+	8442.18i	0.482968	+	0.836526i	−0.516840	+	0.856082i	$0.672892\pi$
$468$		0			0
$469$		0			0
$470$	−1856.00			−0.182151
$471$		0			0
$472$	−2680.75	+	4643.20i	−0.261423	+	0.452798i
$473$	−284.000	+	491.902i	−0.0276075	+	0.0478175i
$474$		0			0
$475$	−16297.8			−1.57430
$476$		0			0
$477$		0			0
$478$	2586.00	+	4479.08i	0.247450	+	0.428595i
$479$	−2467.51	+	4273.85i	−0.235373	+	0.407677i	−0.959381	−	0.282114i	$-0.908964\pi$
$479$	−2467.51	+	4273.85i	−0.235373	+	0.407677i	0.724008	+	0.689791i	$0.242298\pi$
$480$		0			0
$481$	−3746.96	−	6489.93i	−0.355191	−	0.615208i
$482$	−4508.54			−0.426054
$483$		0			0
$484$	−5308.00			−0.498497
$485$	2320.00	+	4018.36i	0.217208	+	0.376215i
$486$		0			0
$487$	412.000	−	713.605i	0.0383357	−	0.0663994i	−0.846221	−	0.532832i	$-0.821128\pi$
$487$	412.000	−	713.605i	0.0383357	−	0.0663994i	0.884557	+	0.466433i	$0.154461\pi$
$488$	2071.49	+	3587.93i	0.192156	+	0.332823i
$489$		0			0
$490$		0			0
$491$	15426.0			1.41785			0.708926	−	0.705283i	$-0.249180\pi$
$491$	15426.0			1.41785			0.708926	+	0.705283i	$0.249180\pi$
$492$		0			0
$493$	−4843.63	+	8389.42i	−0.442487	+	0.766410i
$494$	−4640.00	+	8036.72i	−0.422598	+	0.731961i
$495$		0			0
$496$	−3411.87			−0.308866
$497$		0			0
$498$		0			0
$499$	−2922.00	−	5061.05i	−0.262138	−	0.454036i	0.704672	−	0.709533i	$-0.251094\pi$
$499$	−2922.00	−	5061.05i	−0.262138	−	0.454036i	−0.966810	+	0.255497i	$0.917761\pi$
$500$	548.336	−	949.745i	0.0490446	−	0.0849478i
$501$		0			0
$502$	−4508.54	−	7809.02i	−0.400848	−	0.694290i
$503$	10174.7			0.901921			0.450960	−	0.892544i	$-0.351082\pi$
$503$	10174.7			0.901921			0.450960	+	0.892544i	$0.351082\pi$
$504$		0			0
$505$	15544.0			1.36970
$506$	60.0000	+	103.923i	0.00527139	+	0.00913032i
$507$		0			0
$508$	2144.00	−	3713.52i	0.187253	−	0.324332i
$509$	5902.22	+	10223.0i	0.513971	+	0.890225i	0.999869	+	0.0162087i	$0.00515962\pi$
$509$	5902.22	+	10223.0i	0.513971	+	0.890225i	−0.485897	+	0.874016i	$0.661507\pi$
$510$		0			0
$511$		0			0
$512$	−512.000			−0.0441942
$513$		0			0
$514$	4554.23	−	7888.16i	0.390814	−	0.676910i
$515$	−4408.00	+	7634.88i	−0.377164	+	0.653268i
$516$		0			0
$517$	−121.852			−0.0103657
$518$		0			0
$519$		0			0
$520$	1856.00	+	3214.69i	0.156521	+	0.271103i
$521$	784.425	−	1358.66i	0.0659621	−	0.114250i	−0.831158	−	0.556036i	$-0.812322\pi$
$521$	784.425	−	1358.66i	0.0659621	−	0.114250i	0.897120	+	0.441786i	$0.145655\pi$
$522$		0			0
$523$	−9565.41	−	16567.8i	−0.799744	−	1.38520i	−0.919783	−	0.392428i	$-0.871635\pi$
$523$	−9565.41	−	16567.8i	−0.799744	−	1.38520i	0.120038	−	0.992769i	$-0.461698\pi$
$524$	−10966.7			−0.914281
$525$		0			0
$526$	−5156.00			−0.427400
$527$	−4872.00	−	8438.55i	−0.402709	−	0.697512i
$528$		0			0
$529$	5633.50	−	9757.51i	0.463015	−	0.801965i
$530$	−8346.89	−	14457.2i	−0.684086	−	1.18487i
$531$		0			0
$532$		0			0
$533$	−9744.00			−0.791856
$534$		0			0
$535$	−12535.6	+	21712.2i	−1.01301	+	1.75458i
$536$	2608.00	−	4517.19i	0.210165	−	0.364016i
$537$		0			0
$538$	−1858.25			−0.148912
$539$		0			0
$540$		0			0
$541$	3313.00	+	5738.28i	0.263285	+	0.456022i	0.967113	−	0.254348i	$-0.0818608\pi$
$541$	3313.00	+	5738.28i	0.263285	+	0.456022i	−0.703828	+	0.710370i	$0.748527\pi$
$542$	1127.13	−	1952.25i	0.0893258	−	0.154717i
$543$		0			0
$544$	−731.114	−	1266.33i	−0.0576218	−	0.0998039i
$545$	14957.4			1.17560
$546$		0			0
$547$	−19964.0			−1.56051			−0.780255	−	0.625462i	$-0.784911\pi$
$547$	−19964.0			−1.56051			−0.780255	+	0.625462i	$0.784911\pi$
$548$	5872.00	+	10170.6i	0.457736	+	0.792822i
$549$		0			0
$550$	−214.000	+	370.659i	−0.0165909	+	0.0287363i
$551$	−16145.4	−	27964.7i	−1.24831	−	2.16214i
$552$		0			0
$553$		0			0
$554$	−3020.00			−0.231602
$555$		0			0
$556$	365.557	−	633.163i	0.0278832	−	0.0482952i
$557$	3390.00	−	5871.65i	0.257880	−	0.446660i	−0.707794	−	0.706419i	$-0.750310\pi$
$557$	3390.00	−	5871.65i	0.257880	−	0.446660i	0.965674	+	0.259758i	$0.0836429\pi$
$558$		0			0
$559$	−8651.52			−0.654598
$560$		0			0
$561$		0			0
$562$	4008.00	+	6942.06i	0.300831	+	0.521055i
$563$	−9474.02	+	16409.5i	−0.709205	+	1.22838i	0.255947	+	0.966691i	$0.417613\pi$
$563$	−9474.02	+	16409.5i	−0.709205	+	1.22838i	−0.965152	+	0.261688i	$0.915721\pi$
$564$		0			0
$565$	9809.12	+	16989.9i	0.730394	+	1.26508i
$566$	4813.17			0.357443
$567$		0			0
$568$	6160.00			0.455049
$569$	−96.0000	−	166.277i	−0.00707299	−	0.0122508i	0.862467	−	0.506113i	$-0.168918\pi$
$569$	−96.0000	−	166.277i	−0.00707299	−	0.0122508i	−0.869540	+	0.493862i	$0.835585\pi$
$570$		0			0
$571$	11514.0	−	19942.8i	0.843863	−	1.46161i	−0.0427415	−	0.999086i	$-0.513609\pi$
$571$	11514.0	−	19942.8i	0.843863	−	1.46161i	0.886605	−	0.462528i	$-0.153057\pi$
$572$	121.852	+	211.054i	0.00890717	+	0.0154277i
$573$		0			0
$574$		0			0
$575$	−3210.00			−0.232811
$576$		0			0
$577$	5361.50	−	9286.40i	0.386832	−	0.670014i	−0.605189	−	0.796082i	$-0.706902\pi$
$577$	5361.50	−	9286.40i	0.386832	−	0.670014i	0.992022	+	0.126068i	$0.0402358\pi$
$578$	−2825.00	+	4893.04i	−0.203295	+	0.352117i
$579$		0			0
$580$	−12916.4			−0.924694
$581$		0			0
$582$		0			0
$583$	−548.000	−	949.164i	−0.0389294	−	0.0674277i
$584$	3899.28	−	6753.74i	0.276290	−	0.478548i
$585$		0			0
$586$	−5254.88	−	9101.73i	−0.370439	−	0.641619i
$587$	−19496.4			−1.37087			−0.685436	−	0.728133i	$-0.740388\pi$
$587$	−19496.4			−1.37087			−0.685436	+	0.728133i	$0.740388\pi$
$588$		0			0
$589$	32480.0			2.27218
$590$	−10208.0	−	17680.8i	−0.712300	−	1.23374i
$591$		0			0
$592$	−1968.00	+	3408.68i	−0.136629	+	0.236648i
$593$	6694.26	+	11594.8i	0.463576	+	0.802937i	0.999136	−	0.0415601i	$-0.0132328\pi$
$593$	6694.26	+	11594.8i	0.463576	+	0.802937i	−0.535560	+	0.844497i	$0.679899\pi$
$594$		0			0
$595$		0			0
$596$	3856.00			0.265013
$597$		0			0
$598$	−913.893	+	1582.91i	−0.0624947	+	0.108244i
$599$	9033.00	−	15645.6i	0.616158	−	1.06722i	−0.374023	−	0.927420i	$-0.622022\pi$
$599$	9033.00	−	15645.6i	0.616158	−	1.06722i	0.990180	−	0.139797i	$-0.0446449\pi$
$600$		0			0
$601$	19861.9			1.34806			0.674031	−	0.738703i	$-0.264561\pi$
$601$	19861.9			1.34806			0.674031	+	0.738703i	$0.264561\pi$
$602$		0			0
$603$		0			0
$604$	3376.00	+	5847.40i	0.227430	+	0.393920i
$605$	10106.1	−	17504.3i	0.679128	−	1.17628i
$606$		0			0
$607$	2650.29	+	4590.44i	0.177219	+	0.306952i	0.940927	−	0.338610i	$-0.109957\pi$
$607$	2650.29	+	4590.44i	0.177219	+	0.306952i	−0.763708	+	0.645562i	$0.776623\pi$
$608$	4874.09			0.325116
$609$		0			0
$610$	−15776.0			−1.04713
$611$	−928.000	−	1607.34i	−0.0614449	−	0.106426i
$612$		0			0
$613$	−7969.00	+	13802.7i	−0.525065	+	0.909439i	0.474509	+	0.880251i	$0.342626\pi$
$613$	−7969.00	+	13802.7i	−0.525065	+	0.909439i	−0.999574	+	0.0291886i	$0.990708\pi$
$614$	6366.79	+	11027.6i	0.418473	+	0.724817i
$615$		0			0
$616$		0			0
$617$	11696.0			0.763149			0.381575	−	0.924338i	$-0.375382\pi$
$617$	11696.0			0.763149			0.381575	+	0.924338i	$0.375382\pi$
$618$		0			0
$619$	6732.34	−	11660.8i	0.437150	−	0.757166i	−0.560319	−	0.828277i	$-0.689321\pi$
$619$	6732.34	−	11660.8i	0.437150	−	0.757166i	0.997468	+	0.0711115i	$0.0226546\pi$
$620$	6496.00	−	11251.4i	0.420783	−	0.728818i
$621$		0			0
$622$	14744.1			0.950460
$623$		0			0
$624$		0			0
$625$	8775.50	+	15199.6i	0.561632	+	0.972775i
$626$	−548.336	+	949.745i	−0.0350094	+	0.0606381i
$627$		0			0
$628$	6884.66	+	11924.6i	0.437465	+	0.757711i
$629$	−11240.9			−0.712565
$630$		0			0
$631$	11856.0			0.747987			0.373994	−	0.927431i	$-0.377988\pi$
$631$	11856.0			0.747987			0.373994	+	0.927431i	$0.377988\pi$
$632$	1888.00	+	3270.11i	0.118830	+	0.205820i
$633$		0			0
$634$	−3780.00	+	6547.15i	−0.236787	+	0.410127i
$635$	8164.11	+	14140.7i	0.510209	+	0.883708i
$636$		0			0
$637$		0			0
$638$	−848.000			−0.0526217
$639$		0			0
$640$	974.819	−	1688.44i	0.0602080	−	0.104283i
$641$	2804.00	−	4856.67i	0.172779	−	0.299262i	−0.766611	−	0.642111i	$-0.778059\pi$
$641$	2804.00	−	4856.67i	0.172779	−	0.299262i	0.939390	+	0.342849i	$0.111392\pi$
$642$		0			0
$643$	25314.8			1.55260			0.776298	−	0.630366i	$-0.217095\pi$
$643$	25314.8			1.55260			0.776298	+	0.630366i	$0.217095\pi$
$644$		0			0
$645$		0			0
$646$	6960.00	+	12055.1i	0.423897	+	0.734211i
$647$	−2924.46	+	5065.31i	−0.177701	+	0.307786i	−0.941093	−	0.338149i	$-0.890199\pi$
$647$	−2924.46	+	5065.31i	−0.177701	+	0.307786i	0.763392	+	0.645936i	$0.223533\pi$
$648$		0			0
$649$	−670.188	−	1160.80i	−0.0405349	−	0.0702086i
$650$	−6519.10			−0.393385
$651$		0			0
$652$	−13296.0			−0.798637
$653$	−14318.0	−	24799.5i	−0.858050	−	1.48619i	−0.873786	−	0.486310i	$-0.838343\pi$
$653$	−14318.0	−	24799.5i	−0.858050	−	1.48619i	0.0157364	−	0.999876i	$-0.494991\pi$
$654$		0			0
$655$	20880.0	−	36165.2i	1.24557	−	2.15739i
$656$	2558.90	+	4432.14i	0.152299	+	0.263790i
$657$		0			0
$658$		0			0
$659$	−31786.0			−1.87892			−0.939459	−	0.342662i	$-0.888672\pi$
$659$	−31786.0			−1.87892			−0.939459	+	0.342662i	$0.888672\pi$
$660$		0			0
$661$	4737.01	−	8204.74i	0.278742	−	0.482795i	−0.692330	−	0.721581i	$-0.743416\pi$
$661$	4737.01	−	8204.74i	0.278742	−	0.482795i	0.971072	+	0.238786i	$0.0767493\pi$
$662$	6260.00	−	10842.6i	0.367525	−	0.636573i
$663$		0			0
$664$	−1462.23			−0.0854600
$665$		0			0
$666$		0			0
$667$	−3180.00	−	5507.92i	−0.184603	−	0.319741i
$668$	−6092.62	+	10552.7i	−0.352890	+	0.611223i
$669$		0			0
$670$	9930.97	+	17200.9i	0.572637	+	0.991836i
$671$	−1035.75			−0.0595894
$672$		0			0
$673$	24986.0			1.43111			0.715557	−	0.698555i	$-0.246173\pi$
$673$	24986.0			1.43111			0.715557	+	0.698555i	$0.246173\pi$
$674$	−3166.00	−	5483.67i	−0.180934	−	0.313388i
$675$		0			0
$676$	2538.00	−	4395.94i	0.144401	−	0.250111i
$677$	−22.8473	−	39.5727i	−0.00129704	−	0.00224653i	0.865376	−	0.501123i	$-0.167080\pi$
$677$	−22.8473	−	39.5727i	−0.00129704	−	0.00224653i	−0.866673	+	0.498876i	$0.833746\pi$
$678$		0			0
$679$		0			0
$680$	5568.00			0.314004
$681$		0			0
$682$	426.483	−	738.691i	0.0239456	−	0.0414750i
$683$	15047.0	−	26062.2i	0.842983	−	1.46009i	−0.0443782	−	0.999015i	$-0.514131\pi$
$683$	15047.0	−	26062.2i	0.842983	−	1.46009i	0.887361	−	0.461075i	$-0.152536\pi$
$684$		0			0
$685$	−44719.8			−2.49439
$686$		0			0
$687$		0			0
$688$	2272.00	+	3935.22i	0.125900	+	0.218065i
$689$	8346.89	−	14457.2i	0.461526	−	0.799386i
$690$		0			0
$691$	8468.74	+	14668.3i	0.466232	+	0.807537i	0.999256	−	0.0385629i	$-0.0122780\pi$
$691$	8468.74	+	14668.3i	0.466232	+	0.807537i	−0.533025	+	0.846100i	$0.678945\pi$
$692$	13099.1			0.719587
$693$		0			0
$694$	−7236.00			−0.395785
$695$	1392.00	+	2411.01i	0.0759735	+	0.131590i
$696$		0			0
$697$	−7308.00	+	12657.8i	−0.397145	+	0.687876i
$698$	4478.07	+	7756.25i	0.242833	+	0.420600i
$699$		0			0
$700$		0			0
$701$	−7660.00			−0.412716			−0.206358	−	0.978477i	$-0.566161\pi$
$701$	−7660.00			−0.412716			−0.206358	+	0.978477i	$0.566161\pi$
$702$		0			0
$703$	18734.8	−	32449.6i	1.00512	−	1.74091i
$704$	64.0000	−	110.851i	0.00342627	−	0.00593447i
$705$		0			0
$706$	7402.53			0.394615
$707$		0			0
$708$		0			0
$709$	−5327.00	−	9226.63i	−0.282172	−	0.488736i	0.689748	−	0.724050i	$-0.257721\pi$
$709$	−5327.00	−	9226.63i	−0.282172	−	0.488736i	−0.971919	+	0.235314i	$0.924388\pi$
$710$	−11728.3	+	20314.0i	−0.619936	+	1.07376i
$711$		0			0
$712$	2863.53	+	4959.78i	0.150724	+	0.261061i
$713$	6397.25			0.336015
$714$		0			0
$715$	−928.000			−0.0485388
$716$	2508.00	+	4343.98i	0.130906	+	0.226735i
$717$		0			0
$718$	−130.000	+	225.167i	−0.00675704	+	0.0117035i
$719$	−18552.0	−	32133.0i	−0.962272	−	1.66670i	−0.716772	−	0.697308i	$-0.754381\pi$
$719$	−18552.0	−	32133.0i	−0.962272	−	1.66670i	−0.245500	−	0.969396i	$-0.578952\pi$
$720$		0			0
$721$		0			0
$722$	−32682.0			−1.68462
$723$		0			0
$724$	−6153.54	+	10658.3i	−0.315877	+	0.547114i
$725$	11342.0	−	19644.9i	0.581009	−	1.00634i
$726$		0			0
$727$	17760.0			0.906027			0.453013	−	0.891504i	$-0.350349\pi$
$727$	17760.0			0.906027			0.453013	+	0.891504i	$0.350349\pi$
$728$		0			0
$729$		0			0
$730$	14848.0	+	25717.5i	0.752807	+	1.30390i
$731$	−6488.64	+	11238.7i	−0.328305	+	0.568641i
$732$		0			0
$733$	−1264.22	−	2189.69i	−0.0637039	−	0.110338i	0.832414	−	0.554154i	$-0.186958\pi$
$733$	−1264.22	−	2189.69i	−0.0637039	−	0.110338i	−0.896118	+	0.443815i	$0.853625\pi$
$734$	15597.1			0.784332
$735$		0			0
$736$	960.000			0.0480789
$737$	652.000	+	1129.30i	0.0325871	+	0.0564426i
$738$		0			0
$739$	4078.00	−	7063.30i	0.202993	−	0.351594i	−0.746499	−	0.665387i	$-0.768267\pi$
$739$	4078.00	−	7063.30i	0.202993	−	0.351594i	0.949491	+	0.313793i	$0.101600\pi$
$740$	−7493.92	−	12979.9i	−0.372273	−	0.644796i
$741$		0			0
$742$		0			0
$743$	2910.00			0.143684			0.0718422	−	0.997416i	$-0.477112\pi$
$743$	2910.00			0.143684			0.0718422	+	0.997416i	$0.477112\pi$
$744$		0			0
$745$	−7341.61	+	12716.0i	−0.361041	+	0.625341i
$746$	−50.0000	+	86.6025i	−0.00245393	+	0.00425033i
$747$		0			0
$748$	365.557			0.0178691
$749$		0			0
$750$		0			0
$751$	−6792.00	−	11764.1i	−0.330018	−	0.571608i	0.652497	−	0.757791i	$-0.273722\pi$
$751$	−6792.00	−	11764.1i	−0.330018	−	0.571608i	−0.982515	+	0.186183i	$0.940388\pi$
$752$	−487.409	+	844.218i	−0.0236356	+	0.0409381i
$753$		0			0
$754$	−6458.18	−	11185.9i	−0.311927	−	0.540273i
$755$	−25710.9			−1.23936
$756$		0			0
$757$	19054.0			0.914834			0.457417	−	0.889252i	$-0.348775\pi$
$757$	19054.0			0.914834			0.457417	+	0.889252i	$0.348775\pi$
$758$	−4956.00	−	8584.04i	−0.237480	−	0.411328i
$759$		0			0
$760$	−9280.00	+	16073.4i	−0.442922	+	0.767164i
$761$	2505.59	+	4339.81i	0.119353	+	0.206725i	0.919511	−	0.393063i	$-0.128585\pi$
$761$	2505.59	+	4339.81i	0.119353	+	0.206725i	−0.800159	+	0.599789i	$0.795251\pi$
$762$		0			0
$763$		0			0
$764$	−3624.00			−0.171612
$765$		0			0
$766$	6762.81	−	11713.5i	0.318995	−	0.552515i
$767$	10208.0	−	17680.8i	0.480560	−	0.832354i
$768$		0			0
$769$	21506.9			1.00853			0.504265	−	0.863549i	$-0.331763\pi$
$769$	21506.9			1.00853			0.504265	+	0.863549i	$0.331763\pi$
$770$		0			0
$771$		0			0
$772$	−364.000	−	630.466i	−0.0169697	−	0.0293925i
$773$	11857.8	−	20538.2i	0.551739	−	0.955639i	−0.446411	−	0.894828i	$-0.647298\pi$
$773$	11857.8	−	20538.2i	0.551739	−	0.955639i	0.998149	−	0.0608111i	$-0.0193687\pi$
$774$		0			0
$775$	11408.4	+	19760.0i	0.528778	+	0.915870i
$776$	2437.05			0.112738
$777$		0			0
$778$	−26280.0			−1.21103
$779$	−24360.0	−	42192.8i	−1.12039	−	1.94058i
$780$		0			0
$781$	−770.000	+	1333.68i	−0.0352788	+	0.0611047i
$782$	1370.84	+	2374.36i	0.0626868	+	0.108577i
$783$		0			0
$784$		0			0
$785$	−52432.0			−2.38392
$786$		0			0
$787$	−18491.1	+	32027.5i	−0.837530	+	1.45065i	0.0544230	+	0.998518i	$0.482668\pi$
$787$	−18491.1	+	32027.5i	−0.837530	+	1.45065i	−0.891953	+	0.452127i	$0.850665\pi$
$788$	6936.00	−	12013.5i	0.313559	−	0.543101i
$789$		0			0
$790$	−14378.6			−0.647553
$791$		0			0
$792$		0			0
$793$	−7888.00	−	13662.4i	−0.353230	−	0.611812i
$794$	−3807.89	+	6595.45i	−0.170198	+	0.294791i
$795$		0			0
$796$	−7798.55	−	13507.5i	−0.347252	−	0.601458i
$797$	5346.27			0.237609			0.118805	−	0.992918i	$-0.462094\pi$
$797$	5346.27			0.237609			0.118805	+	0.992918i	$0.462094\pi$
$798$		0			0
$799$	−2784.00			−0.123268
$800$	1712.00	+	2965.27i	0.0756604	+	0.131048i
$801$		0			0
$802$	−4824.00	+	8355.41i	−0.212396	+	0.367880i
$803$	974.819	+	1688.44i	0.0428401	+	0.0742013i
$804$		0			0
$805$		0			0
$806$	12992.0			0.567771
$807$		0			0
$808$	4082.05	−	7070.33i	0.177730	−	0.307838i
$809$	9888.00	−	17126.5i	0.429720	−	0.744297i	−0.567128	−	0.823630i	$-0.691946\pi$
$809$	9888.00	−	17126.5i	0.429720	−	0.744297i	0.996848	+	0.0793325i	$0.0252789\pi$
$810$		0			0
$811$	−15962.7			−0.691153			−0.345576	−	0.938391i	$-0.612317\pi$
$811$	−15962.7			−0.691153			−0.345576	+	0.938391i	$0.612317\pi$
$812$		0			0
$813$		0			0
$814$	−492.000	−	852.169i	−0.0211850	−	0.0366935i
$815$	25314.8	−	43846.6i	1.08802	−	1.88451i
$816$		0			0
$817$	−21628.8	−	37462.2i	−0.926188	−	1.60421i
$818$	10601.2			0.453130
$819$		0			0
$820$	−19488.0			−0.829940
$821$	14986.0	+	25956.5i	0.637046	+	1.10340i	0.986078	+	0.166286i	$0.0531773\pi$
$821$	14986.0	+	25956.5i	0.637046	+	1.10340i	−0.349031	+	0.937111i	$0.613489\pi$
$822$		0			0
$823$	19408.0	−	33615.6i	0.822017	−	1.42378i	−0.0821601	−	0.996619i	$-0.526182\pi$
$823$	19408.0	−	33615.6i	0.822017	−	1.42378i	0.904178	−	0.427157i	$-0.140485\pi$
$824$	2315.20	+	4010.04i	0.0978806	+	0.169534i
$825$		0			0
$826$		0			0
$827$	−34386.0			−1.44585			−0.722925	−	0.690926i	$-0.757203\pi$
$827$	−34386.0			−1.44585			−0.722925	+	0.690926i	$0.757203\pi$
$828$		0			0
$829$	−6564.80	+	11370.6i	−0.275036	+	0.476376i	−0.970144	−	0.242529i	$-0.922023\pi$
$829$	−6564.80	+	11370.6i	−0.275036	+	0.476376i	0.695108	+	0.718905i	$0.255356\pi$
$830$	2784.00	−	4822.03i	0.116427	−	0.201657i
$831$		0			0
$832$	1949.64			0.0812398
$833$		0			0
$834$		0			0
$835$	−23200.0	−	40183.6i	−0.961520	−	1.66540i
$836$	−609.262	+	1055.27i	−0.0252055	+	0.0436571i
$837$		0			0
$838$	−10540.2	−	18256.2i	−0.434494	−	0.752566i
$839$	27051.2			1.11313			0.556563	−	0.830806i	$-0.312120\pi$
$839$	27051.2			1.11313			0.556563	+	0.830806i	$0.312120\pi$
$840$		0			0
$841$	20555.0			0.842798
$842$	−4458.00	−	7721.48i	−0.182462	−	0.316033i
$843$		0			0
$844$	5240.00	−	9075.95i	0.213706	−	0.370150i
$845$	9664.42	+	16739.3i	0.393451	+	0.681477i
$846$		0			0
$847$		0			0
$848$	−8768.00			−0.355064
$849$		0			0
$850$	−4889.33	+	8468.56i	−0.197297	+	0.341729i
$851$	3690.00	−	6391.27i	0.148639	−	0.257450i
$852$		0			0
$853$	−14774.6			−0.593051			−0.296526	−	0.955025i	$-0.595828\pi$
$853$	−14774.6			−0.593051			−0.296526	+	0.955025i	$0.595828\pi$
$854$		0			0
$855$		0			0
$856$	6584.00	+	11403.8i	0.262893	+	0.455344i
$857$	−9801.50	+	16976.7i	−0.390680	+	0.676678i	−0.992539	−	0.121924i	$-0.961093\pi$
$857$	−9801.50	+	16976.7i	−0.390680	+	0.676678i	0.601859	+	0.798602i	$0.294427\pi$
$858$		0			0
$859$	−6260.17	−	10842.9i	−0.248654	−	0.430682i	0.714498	−	0.699637i	$-0.246655\pi$
$859$	−6260.17	−	10842.9i	−0.248654	−	0.430682i	−0.963153	+	0.268955i	$0.913322\pi$
$860$	−17303.0			−0.686080
$861$		0			0
$862$	−32428.0			−1.28132
$863$	15387.0	+	26651.1i	0.606929	+	1.05123i	0.991743	+	0.128238i	$0.0409320\pi$
$863$	15387.0	+	26651.1i	0.606929	+	1.05123i	−0.384815	+	0.922994i	$0.625735\pi$
$864$		0			0
$865$	−24940.0	+	43197.3i	−0.980330	+	1.69798i
$866$	3594.64	+	6226.11i	0.141052	+	0.244309i
$867$		0			0
$868$		0			0
$869$	−944.000			−0.0368504
$870$		0			0
$871$	−9930.97	+	17200.9i	−0.386335	+	0.669152i
$872$	3928.00	−	6803.50i	0.152545	−	0.264215i
$873$		0			0
$874$	−9138.93			−0.353694
$875$		0			0
$876$		0			0
$877$	8379.00	+	14512.9i	0.322621	+	0.558796i	0.981028	−	0.193866i	$-0.0621027\pi$
$877$	8379.00	+	14512.9i	0.322621	+	0.558796i	−0.658407	+	0.752662i	$0.728769\pi$
$878$	8590.59	−	14879.3i	0.330203	−	0.571929i
$879$		0			0
$880$	243.705	+	422.109i	0.00933555	+	0.0161696i
$881$	−25208.2			−0.964002			−0.482001	−	0.876171i	$-0.660090\pi$
$881$	−25208.2			−0.964002			−0.482001	+	0.876171i	$0.660090\pi$
$882$		0			0
$883$	−5468.00			−0.208395			−0.104198	−	0.994557i	$-0.533227\pi$
$883$	−5468.00			−0.208395			−0.104198	+	0.994557i	$0.533227\pi$
$884$	2784.00	+	4822.03i	0.105923	+	0.183464i
$885$		0			0
$886$	−15006.0	+	25991.2i	−0.569003	+	0.985542i
$887$	−13525.6	−	23427.0i	−0.512002	−	0.886813i	−0.999903	−	0.0139144i	$-0.995571\pi$
$887$	−13525.6	−	23427.0i	−0.512002	−	0.886813i	0.487901	−	0.872899i	$-0.337763\pi$
$888$		0			0
$889$		0			0
$890$	−21808.0			−0.821355
$891$		0			0
$892$	2802.60	−	4854.25i	0.105200	−	0.182211i
$893$	4640.00	−	8036.72i	0.173876	−	0.301163i
$894$		0			0
$895$	−19100.4			−0.713357
$896$		0			0
$897$		0			0
$898$	−1824.00	−	3159.26i	−0.0677814	−	0.117401i
$899$	−22603.6	+	39150.6i	−0.838568	+	1.45244i
$900$		0			0
$901$	−12520.3	−	21685.8i	−0.462944	−	0.801843i
$902$	−1279.45			−0.0472295
$903$		0			0
$904$	10304.0			0.379099
$905$	−23432.0	−	40585.4i	−0.860670	−	1.49072i
$906$		0			0
$907$	2938.00	−	5088.77i	0.107558	−	0.186295i	−0.807223	−	0.590247i	$-0.799030\pi$
$907$	2938.00	−	5088.77i	0.107558	−	0.186295i	0.914780	+	0.403952i	$0.132364\pi$
$908$	7798.55	+	13507.5i	0.285026	+	0.493680i
$909$		0			0
$910$		0			0
$911$	−17962.0			−0.653247			−0.326623	−	0.945155i	$-0.605911\pi$
$911$	−17962.0			−0.653247			−0.326623	+	0.945155i	$0.605911\pi$
$912$		0			0
$913$	182.779	−	316.582i	0.00662551	−	0.0114757i
$914$	−586.000	+	1014.98i	−0.0212070	+	0.0367315i
$915$		0			0
$916$	22055.3			0.795553
$917$		0			0
$918$		0			0
$919$	−26712.0	−	46266.5i	−0.958811	−	1.66071i	−0.725395	−	0.688333i	$-0.758343\pi$
$919$	−26712.0	−	46266.5i	−0.958811	−	1.66071i	−0.233416	−	0.972377i	$-0.574991\pi$
$920$	−1827.79	+	3165.82i	−0.0655003	+	0.113450i
$921$		0			0
$922$	15399.1	+	26672.0i	0.550046	+	0.952707i
$923$	−23456.6			−0.836493
$924$		0			0
$925$	26322.0			0.935635
$926$	−88.0000	−	152.420i	−0.00312296	−	0.00540912i
$927$		0			0
$928$	−3392.00	+	5875.12i	−0.119987	+	0.207823i
$929$	2993.00	+	5184.03i	0.105702	+	0.183081i	0.914025	−	0.405658i	$-0.132958\pi$
$929$	2993.00	+	5184.03i	0.105702	+	0.183081i	−0.808323	+	0.588739i	$0.799624\pi$
$930$		0			0
$931$		0			0
$932$	2848.00			0.100096
$933$		0			0
$934$	−9748.19	+	16884.4i	−0.341510	+	0.591513i
$935$	−696.000	+	1205.51i	−0.0243440	+	0.0421650i
$936$		0			0
$937$	−3655.57			−0.127452			−0.0637259	−	0.997967i	$-0.520298\pi$
$937$	−3655.57			−0.127452			−0.0637259	+	0.997967i	$0.520298\pi$
$938$		0			0
$939$		0			0
$940$	−1856.00	−	3214.69i	−0.0644000	−	0.111544i
$941$	−26571.4	+	46023.1i	−0.920514	+	1.59438i	−0.121893	+	0.992543i	$0.538897\pi$
$941$	−26571.4	+	46023.1i	−0.920514	+	1.59438i	−0.798621	+	0.601834i	$0.794437\pi$
$942$		0			0
$943$	−4797.94	−	8310.27i	−0.165686	−	0.286977i
$944$	−10723.0			−0.369708
$945$		0			0
$946$	−1136.00			−0.0390429
$947$	5101.00	+	8835.19i	0.175037	+	0.303173i	0.940174	−	0.340694i	$-0.110662\pi$
$947$	5101.00	+	8835.19i	0.175037	+	0.303173i	−0.765137	+	0.643868i	$0.777329\pi$
$948$		0			0
$949$	−14848.0	+	25717.5i	−0.507889	+	0.879689i
$950$	−16297.8	−	28228.5i	−0.556599	−	0.964058i
$951$		0			0
$952$		0			0
$953$	8856.00			0.301022			0.150511	−	0.988608i	$-0.451908\pi$
$953$	8856.00			0.301022			0.150511	+	0.988608i	$0.451908\pi$
$954$		0			0
$955$	6899.89	−	11951.0i	0.233796	−	0.404947i
$956$	−5172.00	+	8958.17i	−0.174973	+	0.303063i
$957$		0			0
$958$	−9870.04			−0.332867
$959$		0			0
$960$		0			0
$961$	−7840.50	−	13580.1i	−0.263184	−	0.455847i
$962$	7493.92	−	12979.9i	0.251158	−	0.435018i
$963$		0			0
$964$	−4508.54	−	7809.02i	−0.150633	−	0.260904i
$965$	2772.14			0.0924750
$966$		0			0
$967$	−40760.0			−1.35548			−0.677742	−	0.735300i	$-0.737041\pi$
$967$	−40760.0			−1.35548			−0.677742	+	0.735300i	$0.737041\pi$
$968$	−5308.00	−	9193.73i	−0.176245	−	0.305266i
$969$		0			0
$970$	−4640.00	+	8036.72i	−0.153589	+	0.266024i
$971$	23091.0	+	39994.8i	0.763158	+	1.32183i	0.941215	+	0.337808i	$0.109685\pi$
$971$	23091.0	+	39994.8i	0.763158	+	1.32183i	−0.178057	+	0.984020i	$0.556981\pi$
$972$		0			0
$973$		0			0
$974$	1648.00			0.0542149
$975$		0			0
$976$	−4142.98	+	7175.85i	−0.135875	+	0.235342i
$977$	11680.0	−	20230.4i	0.382473	−	0.662463i	−0.608942	−	0.793215i	$-0.708406\pi$
$977$	11680.0	−	20230.4i	0.382473	−	0.662463i	0.991415	+	0.130752i	$0.0417391\pi$
$978$		0			0
$979$	−1431.77			−0.0467410
$980$		0			0
$981$		0			0
$982$	15426.0	+	26718.6i	0.501287	+	0.868254i
$983$	6275.40	−	10869.3i	0.203616	−	0.352672i	−0.746075	−	0.665862i	$-0.768064\pi$
$983$	6275.40	−	10869.3i	0.203616	−	0.352672i	0.949691	+	0.313189i	$0.101397\pi$
$984$		0			0
$985$	26411.5	+	45746.1i	0.854356	+	1.47979i
$986$	−19374.5			−0.625771
$987$		0			0
$988$	−18560.0			−0.597644
$989$	−4260.00	−	7378.54i	−0.136967	−	0.237233i
$990$		0			0
$991$	9740.00	−	16870.2i	0.312211	−	0.540766i	−0.666630	−	0.745389i	$-0.732264\pi$
$991$	9740.00	−	16870.2i	0.312211	−	0.540766i	0.978841	+	0.204624i	$0.0655970\pi$
$992$	−3411.87	−	5909.53i	−0.109200	−	0.189141i
$993$		0			0
$994$		0			0
$995$	59392.0			1.89231
$996$		0			0
$997$	18262.6	−	31631.8i	0.580123	−	1.00480i	−0.415341	−	0.909666i	$-0.636338\pi$
$997$	18262.6	−	31631.8i	0.580123	−	1.00480i	0.995464	−	0.0951374i	$-0.0303290\pi$
$998$	5844.00	−	10122.1i	0.185359	−	0.321052i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.bh.361.1		4
3.2	odd	2		882.4.g.bb.361.2		4
7.2	even	3	inner	882.4.g.bh.667.1		4
7.3	odd	6		882.4.a.x.1.1	✓	2
7.4	even	3		882.4.a.x.1.2	yes	2
7.5	odd	6	inner	882.4.g.bh.667.2		4
7.6	odd	2	inner	882.4.g.bh.361.2		4
21.2	odd	6		882.4.g.bb.667.2		4
21.5	even	6		882.4.g.bb.667.1		4
21.11	odd	6		882.4.a.bf.1.1	yes	2
21.17	even	6		882.4.a.bf.1.2	yes	2
21.20	even	2		882.4.g.bb.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.4.a.x.1.1	✓	2	7.3	odd	6
882.4.a.x.1.2	yes	2	7.4	even	3
882.4.a.bf.1.1	yes	2	21.11	odd	6
882.4.a.bf.1.2	yes	2	21.17	even	6
882.4.g.bb.361.1		4	21.20	even	2
882.4.g.bb.361.2		4	3.2	odd	2
882.4.g.bb.667.1		4	21.5	even	6
882.4.g.bb.667.2		4	21.2	odd	6
882.4.g.bh.361.1		4	1.1	even	1	trivial
882.4.g.bh.361.2		4	7.6	odd	2	inner
882.4.g.bh.667.1		4	7.2	even	3	inner
882.4.g.bh.667.2		4	7.5	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.61577 - 13.1909i) q^{5} -8.00000 q^{8} +(15.2315 - 26.3818i) q^{10} +(1.00000 - 1.73205i) q^{11} +30.4631 q^{13} +(-8.00000 - 13.8564i) q^{16} +(22.8473 - 39.5727i) q^{17} +(76.1577 + 131.909i) q^{19} +60.9262 q^{20} +4.00000 q^{22} +(15.0000 + 25.9808i) q^{23} +(-53.5000 + 92.6647i) q^{25} +(30.4631 + 52.7636i) q^{26} -212.000 q^{29} +(106.621 - 184.673i) q^{31} +(16.0000 - 27.7128i) q^{32} +91.3893 q^{34} +(-123.000 - 213.042i) q^{37} +(-152.315 + 263.818i) q^{38} +(60.9262 + 105.527i) q^{40} -319.862 q^{41} -284.000 q^{43} +(4.00000 + 6.92820i) q^{44} +(-30.0000 + 51.9615i) q^{46} +(-30.4631 - 52.7636i) q^{47} -214.000 q^{50} +(-60.9262 + 105.527i) q^{52} +(274.000 - 474.582i) q^{53} -30.4631 q^{55} +(-212.000 - 367.195i) q^{58} +(335.094 - 580.400i) q^{59} +(-258.936 - 448.491i) q^{61} +426.483 q^{62} +64.0000 q^{64} +(-232.000 - 401.836i) q^{65} +(-326.000 + 564.649i) q^{67} +(91.3893 + 158.291i) q^{68} -770.000 q^{71} +(-487.409 + 844.218i) q^{73} +(246.000 - 426.084i) q^{74} -609.262 q^{76} +(-236.000 - 408.764i) q^{79} +(-121.852 + 211.054i) q^{80} +(-319.862 - 554.018i) q^{82} +182.779 q^{83} -696.000 q^{85} +(-284.000 - 491.902i) q^{86} +(-8.00000 + 13.8564i) q^{88} +(-357.941 - 619.973i) q^{89} -120.000 q^{92} +(60.9262 - 105.527i) q^{94} +(1160.00 - 2009.18i) q^{95} -304.631 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} - 32 q^{8} + 4 q^{11} - 32 q^{16} + 16 q^{22} + 60 q^{23} - 214 q^{25} - 848 q^{29} + 64 q^{32} - 492 q^{37} - 1136 q^{43} + 16 q^{44} - 120 q^{46} - 856 q^{50} + 1096 q^{53} - 848 q^{58}+ \cdots + 4640 q^{95}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 - 32 * q^8 + 4 * q^11 - 32 * q^16 + 16 * q^22 + 60 * q^23 - 214 * q^25 - 848 * q^29 + 64 * q^32 - 492 * q^37 - 1136 * q^43 + 16 * q^44 - 120 * q^46 - 856 * q^50 + 1096 * q^53 - 848 * q^58 + 256 * q^64 - 928 * q^65 - 1304 * q^67 - 3080 * q^71 + 984 * q^74 - 944 * q^79 - 2784 * q^85 - 1136 * q^86 - 32 * q^88 - 480 * q^92 + 4640 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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