LMFDB - Embedded newform 810.4.e.n.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,4,Mod(271,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("810.271");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	810.e (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:	$47.7915471046$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	810.271
Dual form			810.4.e.n.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} -10.0000 q^{10} +(-1.50000 - 2.59808i) q^{11} +(-23.5000 + 40.7032i) q^{13} +(14.0000 - 24.2487i) q^{14} +(-8.00000 - 13.8564i) q^{16} -39.0000 q^{17} +32.0000 q^{19} +(-10.0000 - 17.3205i) q^{20} +(3.00000 - 5.19615i) q^{22} +(49.5000 - 85.7365i) q^{23} +(-12.5000 - 21.6506i) q^{25} -94.0000 q^{26} +56.0000 q^{28} +(-25.5000 - 44.1673i) q^{29} +(-41.5000 + 71.8801i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-39.0000 - 67.5500i) q^{34} +70.0000 q^{35} +314.000 q^{37} +(32.0000 + 55.4256i) q^{38} +(20.0000 - 34.6410i) q^{40} +(54.0000 - 93.5307i) q^{41} +(-149.500 - 258.942i) q^{43} +12.0000 q^{44} +198.000 q^{46} +(-265.500 - 459.859i) q^{47} +(73.5000 - 127.306i) q^{49} +(25.0000 - 43.3013i) q^{50} +(-94.0000 - 162.813i) q^{52} +564.000 q^{53} +15.0000 q^{55} +(56.0000 + 96.9948i) q^{56} +(51.0000 - 88.3346i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-115.000 - 199.186i) q^{61} -166.000 q^{62} +64.0000 q^{64} +(-117.500 - 203.516i) q^{65} +(134.000 - 232.095i) q^{67} +(78.0000 - 135.100i) q^{68} +(70.0000 + 121.244i) q^{70} +120.000 q^{71} +1106.00 q^{73} +(314.000 + 543.864i) q^{74} +(-64.0000 + 110.851i) q^{76} +(-21.0000 + 36.3731i) q^{77} +(369.500 + 639.993i) q^{79} +80.0000 q^{80} +216.000 q^{82} +(-543.000 - 940.504i) q^{83} +(97.5000 - 168.875i) q^{85} +(299.000 - 517.883i) q^{86} +(12.0000 + 20.7846i) q^{88} -120.000 q^{89} +658.000 q^{91} +(198.000 + 342.946i) q^{92} +(531.000 - 919.719i) q^{94} +(-80.0000 + 138.564i) q^{95} +(821.000 + 1422.01i) q^{97} +294.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} - 14 q^{7} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 - 5 * q^5 - 14 * q^7 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} - 14 q^{7} - 16 q^{8} - 20 q^{10} - 3 q^{11} - 47 q^{13} + 28 q^{14} - 16 q^{16} - 78 q^{17} + 64 q^{19} - 20 q^{20} + 6 q^{22} + 99 q^{23} - 25 q^{25} - 188 q^{26} + 112 q^{28} - 51 q^{29} - 83 q^{31} + 32 q^{32} - 78 q^{34} + 140 q^{35} + 628 q^{37} + 64 q^{38} + 40 q^{40} + 108 q^{41} - 299 q^{43} + 24 q^{44} + 396 q^{46} - 531 q^{47} + 147 q^{49} + 50 q^{50} - 188 q^{52} + 1128 q^{53} + 30 q^{55} + 112 q^{56} + 102 q^{58} - 12 q^{59} - 230 q^{61} - 332 q^{62} + 128 q^{64} - 235 q^{65} + 268 q^{67} + 156 q^{68} + 140 q^{70} + 240 q^{71} + 2212 q^{73} + 628 q^{74} - 128 q^{76} - 42 q^{77} + 739 q^{79} + 160 q^{80} + 432 q^{82} - 1086 q^{83} + 195 q^{85} + 598 q^{86} + 24 q^{88} - 240 q^{89} + 1316 q^{91} + 396 q^{92} + 1062 q^{94} - 160 q^{95} + 1642 q^{97} + 588 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 - 5 * q^5 - 14 * q^7 - 16 * q^8 - 20 * q^10 - 3 * q^11 - 47 * q^13 + 28 * q^14 - 16 * q^16 - 78 * q^17 + 64 * q^19 - 20 * q^20 + 6 * q^22 + 99 * q^23 - 25 * q^25 - 188 * q^26 + 112 * q^28 - 51 * q^29 - 83 * q^31 + 32 * q^32 - 78 * q^34 + 140 * q^35 + 628 * q^37 + 64 * q^38 + 40 * q^40 + 108 * q^41 - 299 * q^43 + 24 * q^44 + 396 * q^46 - 531 * q^47 + 147 * q^49 + 50 * q^50 - 188 * q^52 + 1128 * q^53 + 30 * q^55 + 112 * q^56 + 102 * q^58 - 12 * q^59 - 230 * q^61 - 332 * q^62 + 128 * q^64 - 235 * q^65 + 268 * q^67 + 156 * q^68 + 140 * q^70 + 240 * q^71 + 2212 * q^73 + 628 * q^74 - 128 * q^76 - 42 * q^77 + 739 * q^79 + 160 * q^80 + 432 * q^82 - 1086 * q^83 + 195 * q^85 + 598 * q^86 + 24 * q^88 - 240 * q^89 + 1316 * q^91 + 396 * q^92 + 1062 * q^94 - 160 * q^95 + 1642 * q^97 + 588 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−7.00000	−	12.1244i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−7.00000	−	12.1244i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−10.0000			−0.316228
$11$	−1.50000	−	2.59808i	−0.0411152	−	0.0712136i	0.844736	−	0.535184i	$-0.179758\pi$
$11$	−1.50000	−	2.59808i	−0.0411152	−	0.0712136i	−0.885851	+	0.463970i	$0.846424\pi$
$12$		0			0
$13$	−23.5000	+	40.7032i	−0.501364	+	0.868387i	0.498635	+	0.866812i	$0.333835\pi$
$13$	−23.5000	+	40.7032i	−0.501364	+	0.868387i	−0.999999	+	0.00157531i	$0.999499\pi$
$14$	14.0000	−	24.2487i	0.267261	−	0.462910i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−39.0000			−0.556405			−0.278203	−	0.960522i	$-0.589739\pi$
$17$	−39.0000			−0.556405			−0.278203	+	0.960522i	$0.589739\pi$
$18$		0			0
$19$	32.0000			0.386384			0.193192	−	0.981161i	$-0.438116\pi$
$19$	32.0000			0.386384			0.193192	+	0.981161i	$0.438116\pi$
$20$	−10.0000	−	17.3205i	−0.111803	−	0.193649i
$21$		0			0
$22$	3.00000	−	5.19615i	0.0290728	−	0.0503556i
$23$	49.5000	−	85.7365i	0.448759	−	0.777274i	−0.549546	−	0.835463i	$-0.685199\pi$
$23$	49.5000	−	85.7365i	0.448759	−	0.777274i	0.998306	+	0.0581894i	$0.0185327\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−94.0000			−0.709035
$27$		0			0
$28$	56.0000			0.377964
$29$	−25.5000	−	44.1673i	−0.163284	−	0.282816i	0.772761	−	0.634698i	$-0.218875\pi$
$29$	−25.5000	−	44.1673i	−0.163284	−	0.282816i	−0.936045	+	0.351882i	$0.885542\pi$
$30$		0			0
$31$	−41.5000	+	71.8801i	−0.240439	+	0.416453i	−0.960840	−	0.277105i	$-0.910625\pi$
$31$	−41.5000	+	71.8801i	−0.240439	+	0.416453i	0.720400	+	0.693559i	$0.243958\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	−39.0000	−	67.5500i	−0.196719	−	0.340727i
$35$	70.0000			0.338062
$36$		0			0
$37$	314.000			1.39517			0.697585	−	0.716502i	$-0.254258\pi$
$37$	314.000			1.39517			0.697585	+	0.716502i	$0.254258\pi$
$38$	32.0000	+	55.4256i	0.136608	+	0.236611i
$39$		0			0
$40$	20.0000	−	34.6410i	0.0790569	−	0.136931i
$41$	54.0000	−	93.5307i	0.205692	−	0.356269i	−0.744661	−	0.667443i	$-0.767389\pi$
$41$	54.0000	−	93.5307i	0.205692	−	0.356269i	0.950353	+	0.311174i	$0.100722\pi$
$42$		0			0
$43$	−149.500	−	258.942i	−0.530199	−	0.918331i	−0.999379	−	0.0352286i	$-0.988784\pi$
$43$	−149.500	−	258.942i	−0.530199	−	0.918331i	0.469181	−	0.883102i	$-0.344549\pi$
$44$	12.0000			0.0411152
$45$		0			0
$46$	198.000			0.634641
$47$	−265.500	−	459.859i	−0.823982	−	1.42718i	−0.902695	−	0.430281i	$-0.858414\pi$
$47$	−265.500	−	459.859i	−0.823982	−	1.42718i	0.0787128	−	0.996897i	$-0.474919\pi$
$48$		0			0
$49$	73.5000	−	127.306i	0.214286	−	0.371154i
$50$	25.0000	−	43.3013i	0.0707107	−	0.122474i
$51$		0			0
$52$	−94.0000	−	162.813i	−0.250682	−	0.434194i
$53$	564.000			1.46172			0.730862	−	0.682525i	$-0.239118\pi$
$53$	564.000			1.46172			0.730862	+	0.682525i	$0.239118\pi$
$54$		0			0
$55$	15.0000			0.0367745
$56$	56.0000	+	96.9948i	0.133631	+	0.231455i
$57$		0			0
$58$	51.0000	−	88.3346i	0.115459	−	0.199981i
$59$	−6.00000	+	10.3923i	−0.0132396	+	0.0229316i	−0.872569	−	0.488490i	$-0.837548\pi$
$59$	−6.00000	+	10.3923i	−0.0132396	+	0.0229316i	0.859330	+	0.511422i	$0.170881\pi$
$60$		0			0
$61$	−115.000	−	199.186i	−0.241381	−	0.418084i	0.719727	−	0.694257i	$-0.244267\pi$
$61$	−115.000	−	199.186i	−0.241381	−	0.418084i	−0.961108	+	0.276173i	$0.910934\pi$
$62$	−166.000			−0.340033
$63$		0			0
$64$	64.0000			0.125000
$65$	−117.500	−	203.516i	−0.224217	−	0.388355i
$66$		0			0
$67$	134.000	−	232.095i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	134.000	−	232.095i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	78.0000	−	135.100i	0.139101	−	0.240931i
$69$		0			0
$70$	70.0000	+	121.244i	0.119523	+	0.207020i
$71$	120.000			0.200583			0.100291	−	0.994958i	$-0.468022\pi$
$71$	120.000			0.200583			0.100291	+	0.994958i	$0.468022\pi$
$72$		0			0
$73$	1106.00			1.77325			0.886627	−	0.462486i	$-0.153042\pi$
$73$	1106.00			1.77325			0.886627	+	0.462486i	$0.153042\pi$
$74$	314.000	+	543.864i	0.493267	+	0.854364i
$75$		0			0
$76$	−64.0000	+	110.851i	−0.0965961	+	0.167309i
$77$	−21.0000	+	36.3731i	−0.0310802	+	0.0538324i
$78$		0			0
$79$	369.500	+	639.993i	0.526228	+	0.911453i	0.999533	+	0.0305548i	$0.00972742\pi$
$79$	369.500	+	639.993i	0.526228	+	0.911453i	−0.473305	+	0.880898i	$0.656939\pi$
$80$	80.0000			0.111803
$81$		0			0
$82$	216.000			0.290893
$83$	−543.000	−	940.504i	−0.718096	−	1.24378i	−0.961753	−	0.273918i	$-0.911680\pi$
$83$	−543.000	−	940.504i	−0.718096	−	1.24378i	0.243657	−	0.969862i	$-0.421653\pi$
$84$		0			0
$85$	97.5000	−	168.875i	0.124416	−	0.215495i
$86$	299.000	−	517.883i	0.374907	−	0.649358i
$87$		0			0
$88$	12.0000	+	20.7846i	0.0145364	+	0.0251778i
$89$	−120.000			−0.142921			−0.0714605	−	0.997443i	$-0.522766\pi$
$89$	−120.000			−0.142921			−0.0714605	+	0.997443i	$0.522766\pi$
$90$		0			0
$91$	658.000			0.757991
$92$	198.000	+	342.946i	0.224380	+	0.388637i
$93$		0			0
$94$	531.000	−	919.719i	0.582643	−	1.00917i
$95$	−80.0000	+	138.564i	−0.0863982	+	0.149646i
$96$		0			0
$97$	821.000	+	1422.01i	0.859381	+	1.48849i	0.872521	+	0.488577i	$0.162484\pi$
$97$	821.000	+	1422.01i	0.859381	+	1.48849i	−0.0131400	+	0.999914i	$0.504183\pi$
$98$	294.000			0.303046
$99$		0			0
$100$	100.000			0.100000
$101$	−16.5000	−	28.5788i	−0.0162556	−	0.0281555i	0.857783	−	0.514012i	$-0.171841\pi$
$101$	−16.5000	−	28.5788i	−0.0162556	−	0.0281555i	−0.874039	+	0.485856i	$0.838508\pi$
$102$		0			0
$103$	599.000	−	1037.50i	0.573022	−	0.992503i	−0.423232	−	0.906021i	$-0.639104\pi$
$103$	599.000	−	1037.50i	0.573022	−	0.992503i	0.996253	−	0.0864811i	$-0.0275622\pi$
$104$	188.000	−	325.626i	0.177259	−	0.307021i
$105$		0			0
$106$	564.000	+	976.877i	0.516797	+	0.895119i
$107$	−1542.00			−1.39318			−0.696592	−	0.717467i	$-0.745301\pi$
$107$	−1542.00			−1.39318			−0.696592	+	0.717467i	$0.745301\pi$
$108$		0			0
$109$	−556.000			−0.488579			−0.244290	−	0.969702i	$-0.578555\pi$
$109$	−556.000			−0.488579			−0.244290	+	0.969702i	$0.578555\pi$
$110$	15.0000	+	25.9808i	0.0130018	+	0.0225197i
$111$		0			0
$112$	−112.000	+	193.990i	−0.0944911	+	0.163663i
$113$	−802.500	+	1389.97i	−0.668078	+	1.15715i	0.310363	+	0.950618i	$0.399550\pi$
$113$	−802.500	+	1389.97i	−0.668078	+	1.15715i	−0.978441	+	0.206527i	$0.933784\pi$
$114$		0			0
$115$	247.500	+	428.683i	0.200691	+	0.347607i
$116$	204.000			0.163284
$117$		0			0
$118$	−24.0000			−0.0187236
$119$	273.000	+	472.850i	0.210301	+	0.364253i
$120$		0			0
$121$	661.000	−	1144.89i	0.496619	−	0.860169i
$122$	230.000	−	398.372i	0.170682	−	0.295630i
$123$		0			0
$124$	−166.000	−	287.520i	−0.120220	−	0.208227i
$125$	125.000			0.0894427
$126$		0			0
$127$	1334.00			0.932074			0.466037	−	0.884765i	$-0.345681\pi$
$127$	1334.00			0.932074			0.466037	+	0.884765i	$0.345681\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	235.000	−	407.032i	0.158545	−	0.274608i
$131$	1441.50	−	2496.75i	0.961408	−	1.66521i	0.242437	−	0.970167i	$-0.422053\pi$
$131$	1441.50	−	2496.75i	0.961408	−	1.66521i	0.718971	−	0.695040i	$-0.244613\pi$
$132$		0			0
$133$	−224.000	−	387.979i	−0.146040	−	0.252948i
$134$	536.000			0.345547
$135$		0			0
$136$	312.000			0.196719
$137$	−141.000	−	244.219i	−0.0879302	−	0.152300i	0.818706	−	0.574213i	$-0.194692\pi$
$137$	−141.000	−	244.219i	−0.0879302	−	0.152300i	−0.906636	+	0.421913i	$0.861359\pi$
$138$		0			0
$139$	1247.00	−	2159.87i	0.760929	−	1.31797i	−0.181443	−	0.983401i	$-0.558077\pi$
$139$	1247.00	−	2159.87i	0.760929	−	1.31797i	0.942372	−	0.334567i	$-0.108590\pi$
$140$	−140.000	+	242.487i	−0.0845154	+	0.146385i
$141$		0			0
$142$	120.000	+	207.846i	0.0709167	+	0.122831i
$143$	141.000			0.0824546
$144$		0			0
$145$	255.000			0.146045
$146$	1106.00	+	1915.65i	0.626940	+	1.08589i
$147$		0			0
$148$	−628.000	+	1087.73i	−0.348792	+	0.604126i
$149$	−1297.50	+	2247.34i	−0.713392	+	1.23563i	0.250185	+	0.968198i	$0.419509\pi$
$149$	−1297.50	+	2247.34i	−0.713392	+	1.23563i	−0.963577	+	0.267432i	$0.913825\pi$
$150$		0			0
$151$	−614.500	−	1064.35i	−0.331174	−	0.573611i	0.651568	−	0.758590i	$-0.274111\pi$
$151$	−614.500	−	1064.35i	−0.331174	−	0.573611i	−0.982742	+	0.184980i	$0.940778\pi$
$152$	−256.000			−0.136608
$153$		0			0
$154$	−84.0000			−0.0439540
$155$	−207.500	−	359.401i	−0.107528	−	0.186244i
$156$		0			0
$157$	795.500	−	1377.85i	0.404381	−	0.700408i	−0.589868	−	0.807500i	$-0.700820\pi$
$157$	795.500	−	1377.85i	0.404381	−	0.700408i	0.994249	+	0.107091i	$0.0341537\pi$
$158$	−739.000	+	1279.99i	−0.372099	+	0.644495i
$159$		0			0
$160$	80.0000	+	138.564i	0.0395285	+	0.0684653i
$161$	−1386.00			−0.678460
$162$		0			0
$163$	−457.000			−0.219601			−0.109801	−	0.993954i	$-0.535021\pi$
$163$	−457.000			−0.219601			−0.109801	+	0.993954i	$0.535021\pi$
$164$	216.000	+	374.123i	0.102846	+	0.178135i
$165$		0			0
$166$	1086.00	−	1881.01i	0.507771	−	0.879485i
$167$	582.000	−	1008.05i	0.269680	−	0.467099i	−0.699099	−	0.715025i	$-0.746416\pi$
$167$	582.000	−	1008.05i	0.269680	−	0.467099i	0.968779	+	0.247926i	$0.0797488\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.00273100	−	0.00473023i
$170$	390.000			0.175951
$171$		0			0
$172$	1196.00			0.530199
$173$	−1971.00	−	3413.87i	−0.866199	−	1.50030i	−0.865852	−	0.500300i	$-0.833223\pi$
$173$	−1971.00	−	3413.87i	−0.866199	−	1.50030i	−0.000346465	−	1.00000i	$-0.500110\pi$
$174$		0			0
$175$	−175.000	+	303.109i	−0.0755929	+	0.130931i
$176$	−24.0000	+	41.5692i	−0.0102788	+	0.0178034i
$177$		0			0
$178$	−120.000	−	207.846i	−0.0505302	−	0.0875209i
$179$	−1212.00			−0.506085			−0.253042	−	0.967455i	$-0.581431\pi$
$179$	−1212.00			−0.506085			−0.253042	+	0.967455i	$0.581431\pi$
$180$		0			0
$181$	2288.00			0.939590			0.469795	−	0.882776i	$-0.344328\pi$
$181$	2288.00			0.939590			0.469795	+	0.882776i	$0.344328\pi$
$182$	658.000	+	1139.69i	0.267990	+	0.464173i
$183$		0			0
$184$	−396.000	+	685.892i	−0.158660	+	0.274808i
$185$	−785.000	+	1359.66i	−0.311969	+	0.540347i
$186$		0			0
$187$	58.5000	+	101.325i	0.0228767	+	0.0396236i
$188$	2124.00			0.823982
$189$		0			0
$190$	−320.000			−0.122185
$191$	969.000	+	1678.36i	0.367091	+	0.635820i	0.989109	−	0.147182i	$-0.0470204\pi$
$191$	969.000	+	1678.36i	0.367091	+	0.635820i	−0.622018	+	0.783003i	$0.713687\pi$
$192$		0			0
$193$	749.000	−	1297.31i	0.279348	−	0.483845i	−0.691875	−	0.722018i	$-0.743215\pi$
$193$	749.000	−	1297.31i	0.279348	−	0.483845i	0.971223	+	0.238172i	$0.0765483\pi$
$194$	−1642.00	+	2844.03i	−0.607674	+	1.05252i
$195$		0			0
$196$	294.000	+	509.223i	0.107143	+	0.185577i
$197$	−2124.00			−0.768166			−0.384083	−	0.923299i	$-0.625482\pi$
$197$	−2124.00			−0.768166			−0.384083	+	0.923299i	$0.625482\pi$
$198$		0			0
$199$	−385.000			−0.137145			−0.0685727	−	0.997646i	$-0.521845\pi$
$199$	−385.000			−0.137145			−0.0685727	+	0.997646i	$0.521845\pi$
$200$	100.000	+	173.205i	0.0353553	+	0.0612372i
$201$		0			0
$202$	33.0000	−	57.1577i	0.0114944	−	0.0199089i
$203$	−357.000	+	618.342i	−0.123431	+	0.213789i
$204$		0			0
$205$	270.000	+	467.654i	0.0919884	+	0.159329i
$206$	2396.00			0.810375
$207$		0			0
$208$	752.000			0.250682
$209$	−48.0000	−	83.1384i	−0.0158863	−	0.0275158i
$210$		0			0
$211$	−1585.00	+	2745.30i	−0.517137	+	0.895708i	0.482665	+	0.875805i	$0.339669\pi$
$211$	−1585.00	+	2745.30i	−0.517137	+	0.895708i	−0.999802	+	0.0199024i	$0.993664\pi$
$212$	−1128.00	+	1953.75i	−0.365431	+	0.632945i
$213$		0			0
$214$	−1542.00	−	2670.82i	−0.492565	−	0.853148i
$215$	1495.00			0.474224
$216$		0			0
$217$	1162.00			0.363510
$218$	−556.000	−	963.020i	−0.172739	−	0.299192i
$219$		0			0
$220$	−30.0000	+	51.9615i	−0.00919363	+	0.0159238i
$221$	916.500	−	1587.42i	0.278961	−	0.483175i
$222$		0			0
$223$	−694.000	−	1202.04i	−0.208402	−	0.360963i	0.742809	−	0.669503i	$-0.233493\pi$
$223$	−694.000	−	1202.04i	−0.208402	−	0.360963i	−0.951211	+	0.308540i	$0.900160\pi$
$224$	−448.000			−0.133631
$225$		0			0
$226$	−3210.00			−0.944805
$227$	2322.00	+	4021.82i	0.678928	+	1.17594i	0.975304	+	0.220866i	$0.0708883\pi$
$227$	2322.00	+	4021.82i	0.678928	+	1.17594i	−0.296377	+	0.955071i	$0.595778\pi$
$228$		0			0
$229$	−2368.00	+	4101.50i	−0.683327	+	1.18356i	0.290633	+	0.956835i	$0.406134\pi$
$229$	−2368.00	+	4101.50i	−0.683327	+	1.18356i	−0.973959	+	0.226722i	$0.927199\pi$
$230$	−495.000	+	857.365i	−0.141910	+	0.245796i
$231$		0			0
$232$	204.000	+	353.338i	0.0577296	+	0.0999905i
$233$	2814.00			0.791207			0.395604	−	0.918421i	$-0.370535\pi$
$233$	2814.00			0.791207			0.395604	+	0.918421i	$0.370535\pi$
$234$		0			0
$235$	2655.00			0.736992
$236$	−24.0000	−	41.5692i	−0.00661978	−	0.0114658i
$237$		0			0
$238$	−546.000	+	945.700i	−0.148706	+	0.257566i
$239$	1101.00	−	1906.99i	0.297982	−	0.516120i	−0.677692	−	0.735346i	$-0.737020\pi$
$239$	1101.00	−	1906.99i	0.297982	−	0.516120i	0.975674	+	0.219225i	$0.0703530\pi$
$240$		0			0
$241$	−1742.50	−	3018.10i	−0.465744	−	0.806692i	0.533491	−	0.845806i	$-0.320880\pi$
$241$	−1742.50	−	3018.10i	−0.465744	−	0.806692i	−0.999235	+	0.0391137i	$0.987547\pi$
$242$	2644.00			0.702325
$243$		0			0
$244$	920.000			0.241381
$245$	367.500	+	636.529i	0.0958315	+	0.165985i
$246$		0			0
$247$	−752.000	+	1302.50i	−0.193719	+	0.335531i
$248$	332.000	−	575.041i	0.0850081	−	0.147238i
$249$		0			0
$250$	125.000	+	216.506i	0.0316228	+	0.0547723i
$251$	−6345.00			−1.59559			−0.797795	−	0.602929i	$-0.794000\pi$
$251$	−6345.00			−1.59559			−0.797795	+	0.602929i	$0.794000\pi$
$252$		0			0
$253$	−297.000			−0.0738033
$254$	1334.00	+	2310.56i	0.329538	+	0.570776i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−262.500	+	454.663i	−0.0637132	+	0.110355i	−0.896122	−	0.443807i	$-0.853628\pi$
$257$	−262.500	+	454.663i	−0.0637132	+	0.110355i	0.832409	+	0.554161i	$0.186961\pi$
$258$		0			0
$259$	−2198.00	−	3807.05i	−0.527325	−	0.913353i
$260$	940.000			0.224217
$261$		0			0
$262$	5766.00			1.35964
$263$	−2598.00	−	4499.87i	−0.609124	−	1.05503i	−0.991385	−	0.130979i	$-0.958188\pi$
$263$	−2598.00	−	4499.87i	−0.609124	−	1.05503i	0.382261	−	0.924054i	$-0.375145\pi$
$264$		0			0
$265$	−1410.00	+	2442.19i	−0.326851	+	0.566123i
$266$	448.000	−	775.959i	0.103266	−	0.178861i
$267$		0			0
$268$	536.000	+	928.379i	0.122169	+	0.211604i
$269$	−7479.00			−1.69518			−0.847589	−	0.530654i	$-0.821946\pi$
$269$	−7479.00			−1.69518			−0.847589	+	0.530654i	$0.821946\pi$
$270$		0			0
$271$	−856.000			−0.191876			−0.0959378	−	0.995387i	$-0.530585\pi$
$271$	−856.000			−0.191876			−0.0959378	+	0.995387i	$0.530585\pi$
$272$	312.000	+	540.400i	0.0695507	+	0.120465i
$273$		0			0
$274$	282.000	−	488.438i	0.0621761	−	0.107692i
$275$	−37.5000	+	64.9519i	−0.00822304	+	0.0142427i
$276$		0			0
$277$	3527.00	+	6108.94i	0.765043	+	1.32509i	0.940224	+	0.340557i	$0.110616\pi$
$277$	3527.00	+	6108.94i	0.765043	+	1.32509i	−0.175181	+	0.984536i	$0.556051\pi$
$278$	4988.00			1.07612
$279$		0			0
$280$	−560.000			−0.119523
$281$	−507.000	−	878.150i	−0.107634	−	0.186427i	0.807177	−	0.590309i	$-0.200994\pi$
$281$	−507.000	−	878.150i	−0.107634	−	0.186427i	−0.914811	+	0.403882i	$0.867661\pi$
$282$		0			0
$283$	−496.000	+	859.097i	−0.104184	+	0.180452i	−0.913405	−	0.407053i	$-0.866556\pi$
$283$	−496.000	+	859.097i	−0.104184	+	0.180452i	0.809220	+	0.587505i	$0.199890\pi$
$284$	−240.000	+	415.692i	−0.0501457	+	0.0868549i
$285$		0			0
$286$	141.000	+	244.219i	0.0291521	+	0.0504929i
$287$	−1512.00			−0.310977
$288$		0			0
$289$	−3392.00			−0.690413
$290$	255.000	+	441.673i	0.0516349	+	0.0894342i
$291$		0			0
$292$	−2212.00	+	3831.30i	−0.443313	+	0.767841i
$293$	2475.00	−	4286.83i	0.493485	−	0.854741i	−0.506487	−	0.862248i	$-0.669056\pi$
$293$	2475.00	−	4286.83i	0.493485	−	0.854741i	0.999972	+	0.00750685i	$0.00238953\pi$
$294$		0			0
$295$	−30.0000	−	51.9615i	−0.00592091	−	0.0102553i
$296$	−2512.00			−0.493267
$297$		0			0
$298$	−5190.00			−1.00889
$299$	2326.50	+	4029.62i	0.449983	+	0.779394i
$300$		0			0
$301$	−2093.00	+	3625.18i	−0.400792	+	0.694193i
$302$	1229.00	−	2128.69i	0.234176	−	0.405604i
$303$		0			0
$304$	−256.000	−	443.405i	−0.0482980	−	0.0836547i
$305$	1150.00			0.215898
$306$		0			0
$307$	−4777.00			−0.888071			−0.444035	−	0.896009i	$-0.646454\pi$
$307$	−4777.00			−0.888071			−0.444035	+	0.896009i	$0.646454\pi$
$308$	−84.0000	−	145.492i	−0.0155401	−	0.0269162i
$309$		0			0
$310$	415.000	−	718.801i	0.0760336	−	0.131694i
$311$	3846.00	−	6661.47i	0.701243	−	1.21459i	−0.266787	−	0.963756i	$-0.585962\pi$
$311$	3846.00	−	6661.47i	0.701243	−	1.21459i	0.968030	−	0.250833i	$-0.0807046\pi$
$312$		0			0
$313$	1466.00	+	2539.19i	0.264739	+	0.458541i	0.967495	−	0.252890i	$-0.0813810\pi$
$313$	1466.00	+	2539.19i	0.264739	+	0.458541i	−0.702756	+	0.711431i	$0.748048\pi$
$314$	3182.00			0.571881
$315$		0			0
$316$	−2956.00			−0.526228
$317$	−4176.00	−	7233.04i	−0.739898	−	1.28154i	−0.952541	−	0.304410i	$-0.901541\pi$
$317$	−4176.00	−	7233.04i	−0.739898	−	1.28154i	0.212643	−	0.977130i	$-0.431793\pi$
$318$		0			0
$319$	−76.5000	+	132.502i	−0.0134269	+	0.0232561i
$320$	−160.000	+	277.128i	−0.0279508	+	0.0484123i
$321$		0			0
$322$	−1386.00	−	2400.62i	−0.239872	−	0.415470i
$323$	−1248.00			−0.214986
$324$		0			0
$325$	1175.00			0.200545
$326$	−457.000	−	791.547i	−0.0776408	−	0.134478i
$327$		0			0
$328$	−432.000	+	748.246i	−0.0727232	+	0.125960i
$329$	−3717.00	+	6438.03i	−0.622872	+	1.07885i
$330$		0			0
$331$	1535.00	+	2658.70i	0.254898	+	0.441496i	0.964868	−	0.262736i	$-0.0846248\pi$
$331$	1535.00	+	2658.70i	0.254898	+	0.441496i	−0.709970	+	0.704232i	$0.751291\pi$
$332$	4344.00			0.718096
$333$		0			0
$334$	2328.00			0.381385
$335$	670.000	+	1160.47i	0.109272	+	0.189264i
$336$		0			0
$337$	836.000	−	1447.99i	0.135133	−	0.234057i	−0.790515	−	0.612442i	$-0.790187\pi$
$337$	836.000	−	1447.99i	0.135133	−	0.234057i	0.925648	+	0.378385i	$0.123520\pi$
$338$	12.0000	−	20.7846i	0.00193111	−	0.00334477i
$339$		0			0
$340$	390.000	+	675.500i	0.0622080	+	0.107747i
$341$	249.000			0.0395428
$342$		0			0
$343$	−6860.00			−1.07990
$344$	1196.00	+	2071.53i	0.187453	+	0.324679i
$345$		0			0
$346$	3942.00	−	6827.74i	0.612495	−	1.06087i
$347$	2538.00	−	4395.94i	0.392643	−	0.680077i	−0.600155	−	0.799884i	$-0.704894\pi$
$347$	2538.00	−	4395.94i	0.392643	−	0.680077i	0.992797	+	0.119807i	$0.0382276\pi$
$348$		0			0
$349$	−4297.00	−	7442.62i	−0.659063	−	1.14153i	−0.980858	−	0.194722i	$-0.937620\pi$
$349$	−4297.00	−	7442.62i	−0.659063	−	1.14153i	0.321795	−	0.946809i	$-0.395714\pi$
$350$	−700.000			−0.106904
$351$		0			0
$352$	−96.0000			−0.0145364
$353$	−6355.50	−	11008.0i	−0.958269	−	1.65977i	−0.726702	−	0.686953i	$-0.758948\pi$
$353$	−6355.50	−	11008.0i	−0.958269	−	1.65977i	−0.231567	−	0.972819i	$-0.574385\pi$
$354$		0			0
$355$	−300.000	+	519.615i	−0.0448517	+	0.0776854i
$356$	240.000	−	415.692i	0.0357303	−	0.0618866i
$357$		0			0
$358$	−1212.00	−	2099.25i	−0.178928	−	0.309912i
$359$	−1464.00			−0.215228			−0.107614	−	0.994193i	$-0.534321\pi$
$359$	−1464.00			−0.215228			−0.107614	+	0.994193i	$0.534321\pi$
$360$		0			0
$361$	−5835.00			−0.850707
$362$	2288.00	+	3962.93i	0.332195	+	0.575379i
$363$		0			0
$364$	−1316.00	+	2279.38i	−0.189498	+	0.328220i
$365$	−2765.00	+	4789.12i	−0.396512	+	0.686778i
$366$		0			0
$367$	3815.00	+	6607.77i	0.542620	+	0.939845i	0.998753	+	0.0499330i	$0.0159008\pi$
$367$	3815.00	+	6607.77i	0.542620	+	0.939845i	−0.456133	+	0.889912i	$0.650766\pi$
$368$	−1584.00			−0.224380
$369$		0			0
$370$	−3140.00			−0.441191
$371$	−3948.00	−	6838.14i	−0.552480	−	0.956923i
$372$		0			0
$373$	1941.50	−	3362.78i	0.269510	−	0.466804i	−0.699226	−	0.714901i	$-0.746472\pi$
$373$	1941.50	−	3362.78i	0.269510	−	0.466804i	0.968735	+	0.248097i	$0.0798051\pi$
$374$	−117.000	+	202.650i	−0.0161763	+	0.0280181i
$375$		0			0
$376$	2124.00	+	3678.88i	0.291322	+	0.504584i
$377$	2397.00			0.327458
$378$		0			0
$379$	−13768.0			−1.86600			−0.933001	−	0.359874i	$-0.882820\pi$
$379$	−13768.0			−1.86600			−0.933001	+	0.359874i	$0.882820\pi$
$380$	−320.000	−	554.256i	−0.0431991	−	0.0748230i
$381$		0			0
$382$	−1938.00	+	3356.71i	−0.259573	+	0.449593i
$383$	7069.50	−	12244.7i	0.943171	−	1.63362i	0.183799	−	0.982964i	$-0.441160\pi$
$383$	7069.50	−	12244.7i	0.943171	−	1.63362i	0.759372	−	0.650657i	$-0.225506\pi$
$384$		0			0
$385$	−105.000	−	181.865i	−0.0138995	−	0.0240746i
$386$	2996.00			0.395058
$387$		0			0
$388$	−6568.00			−0.859381
$389$	−283.500	−	491.036i	−0.0369512	−	0.0640014i	0.846958	−	0.531659i	$-0.178431\pi$
$389$	−283.500	−	491.036i	−0.0369512	−	0.0640014i	−0.883910	+	0.467658i	$0.845098\pi$
$390$		0			0
$391$	−1930.50	+	3343.72i	−0.249692	+	0.432479i
$392$	−588.000	+	1018.45i	−0.0757614	+	0.131223i
$393$		0			0
$394$	−2124.00	−	3678.88i	−0.271588	−	0.470404i
$395$	−3695.00			−0.470672
$396$		0			0
$397$	−6685.00			−0.845115			−0.422557	−	0.906336i	$-0.638867\pi$
$397$	−6685.00			−0.845115			−0.422557	+	0.906336i	$0.638867\pi$
$398$	−385.000	−	666.840i	−0.0484882	−	0.0839840i
$399$		0			0
$400$	−200.000	+	346.410i	−0.0250000	+	0.0433013i
$401$	−2286.00	+	3959.47i	−0.284682	+	0.493083i	−0.972532	−	0.232769i	$-0.925221\pi$
$401$	−2286.00	+	3959.47i	−0.284682	+	0.493083i	0.687850	+	0.725853i	$0.258555\pi$
$402$		0			0
$403$	−1950.50	−	3378.37i	−0.241095	−	0.417589i
$404$	132.000			0.0162556
$405$		0			0
$406$	−1428.00			−0.174558
$407$	−471.000	−	815.796i	−0.0573627	−	0.0993550i
$408$		0			0
$409$	12.5000	−	21.6506i	0.00151121	−	0.00261749i	−0.865269	−	0.501308i	$-0.832852\pi$
$409$	12.5000	−	21.6506i	0.00151121	−	0.00261749i	0.866780	+	0.498691i	$0.166186\pi$
$410$	−540.000	+	935.307i	−0.0650456	+	0.112662i
$411$		0			0
$412$	2396.00	+	4149.99i	0.286511	+	0.496251i
$413$	168.000			0.0200163
$414$		0			0
$415$	5430.00			0.642285
$416$	752.000	+	1302.50i	0.0886294	+	0.153511i
$417$		0			0
$418$	96.0000	−	166.277i	0.0112333	−	0.0194566i
$419$	−6226.50	+	10784.6i	−0.725977	+	1.25743i	0.232593	+	0.972574i	$0.425279\pi$
$419$	−6226.50	+	10784.6i	−0.725977	+	1.25743i	−0.958571	+	0.284855i	$0.908054\pi$
$420$		0			0
$421$	−2524.00	−	4371.70i	−0.292191	−	0.506089i	0.682137	−	0.731225i	$-0.261051\pi$
$421$	−2524.00	−	4371.70i	−0.292191	−	0.506089i	−0.974327	+	0.225136i	$0.927717\pi$
$422$	−6340.00			−0.731342
$423$		0			0
$424$	−4512.00			−0.516797
$425$	487.500	+	844.375i	0.0556405	+	0.0963722i
$426$		0			0
$427$	−1610.00	+	2788.60i	−0.182467	+	0.316042i
$428$	3084.00	−	5341.64i	0.348296	−	0.603267i
$429$		0			0
$430$	1495.00	+	2589.42i	0.167663	+	0.290402i
$431$	5400.00			0.603501			0.301750	−	0.953387i	$-0.402429\pi$
$431$	5400.00			0.603501			0.301750	+	0.953387i	$0.402429\pi$
$432$		0			0
$433$	−6298.00			−0.698990			−0.349495	−	0.936938i	$-0.613647\pi$
$433$	−6298.00			−0.698990			−0.349495	+	0.936938i	$0.613647\pi$
$434$	1162.00	+	2012.64i	0.128520	+	0.222604i
$435$		0			0
$436$	1112.00	−	1926.04i	0.122145	−	0.211561i
$437$	1584.00	−	2743.57i	0.173394	−	0.300326i
$438$		0			0
$439$	3104.00	+	5376.29i	0.337462	+	0.584501i	0.983955	−	0.178419i	$-0.0570982\pi$
$439$	3104.00	+	5376.29i	0.337462	+	0.584501i	−0.646493	+	0.762920i	$0.723765\pi$
$440$	−120.000			−0.0130018
$441$		0			0
$442$	3666.00			0.394511
$443$	1680.00	+	2909.85i	0.180179	+	0.312079i	0.941941	−	0.335778i	$-0.108999\pi$
$443$	1680.00	+	2909.85i	0.180179	+	0.312079i	−0.761763	+	0.647856i	$0.775666\pi$
$444$		0			0
$445$	300.000	−	519.615i	0.0319581	−	0.0553531i
$446$	1388.00	−	2404.09i	0.147363	−	0.255239i
$447$		0			0
$448$	−448.000	−	775.959i	−0.0472456	−	0.0818317i
$449$	14394.0			1.51291			0.756453	−	0.654048i	$-0.226931\pi$
$449$	14394.0			1.51291			0.756453	+	0.654048i	$0.226931\pi$
$450$		0			0
$451$	−324.000			−0.0338283
$452$	−3210.00	−	5559.88i	−0.334039	−	0.578573i
$453$		0			0
$454$	−4644.00	+	8043.64i	−0.480074	+	0.831513i
$455$	−1645.00	+	2849.22i	−0.169492	+	0.293568i
$456$		0			0
$457$	458.000	+	793.279i	0.0468804	+	0.0811992i	0.888513	−	0.458851i	$-0.151739\pi$
$457$	458.000	+	793.279i	0.0468804	+	0.0811992i	−0.841633	+	0.540050i	$0.818405\pi$
$458$	−9472.00			−0.966370
$459$		0			0
$460$	−1980.00			−0.200691
$461$	−4275.00	−	7404.52i	−0.431902	−	0.748075i	0.565136	−	0.824998i	$-0.308824\pi$
$461$	−4275.00	−	7404.52i	−0.431902	−	0.748075i	−0.997037	+	0.0769227i	$0.975491\pi$
$462$		0			0
$463$	−1867.00	+	3233.74i	−0.187401	+	0.324589i	−0.944383	−	0.328847i	$-0.893340\pi$
$463$	−1867.00	+	3233.74i	−0.187401	+	0.324589i	0.756982	+	0.653436i	$0.226673\pi$
$464$	−408.000	+	706.677i	−0.0408210	+	0.0707040i
$465$		0			0
$466$	2814.00	+	4873.99i	0.279734	+	0.484513i
$467$	9840.00			0.975034			0.487517	−	0.873113i	$-0.337903\pi$
$467$	9840.00			0.975034			0.487517	+	0.873113i	$0.337903\pi$
$468$		0			0
$469$	−3752.00			−0.369406
$470$	2655.00	+	4598.59i	0.260566	+	0.451314i
$471$		0			0
$472$	48.0000	−	83.1384i	0.00468089	−	0.00810754i
$473$	−448.500	+	776.825i	−0.0435984	+	0.0755147i
$474$		0			0
$475$	−400.000	−	692.820i	−0.0386384	−	0.0669237i
$476$	−2184.00			−0.210301
$477$		0			0
$478$	4404.00			0.421411
$479$	8640.00	+	14964.9i	0.824158	+	1.42748i	0.902561	+	0.430562i	$0.141685\pi$
$479$	8640.00	+	14964.9i	0.824158	+	1.42748i	−0.0784031	+	0.996922i	$0.524982\pi$
$480$		0			0
$481$	−7379.00	+	12780.8i	−0.699487	+	1.21155i
$482$	3485.00	−	6036.20i	0.329331	−	0.570418i
$483$		0			0
$484$	2644.00	+	4579.54i	0.248310	+	0.430085i
$485$	−8210.00			−0.768653
$486$		0			0
$487$	−4588.00			−0.426904			−0.213452	−	0.976954i	$-0.568471\pi$
$487$	−4588.00			−0.426904			−0.213452	+	0.976954i	$0.568471\pi$
$488$	920.000	+	1593.49i	0.0853411	+	0.147815i
$489$		0			0
$490$	−735.000	+	1273.06i	−0.0677631	+	0.117369i
$491$	−318.000	+	550.792i	−0.0292284	+	0.0506251i	−0.880270	−	0.474474i	$-0.842638\pi$
$491$	−318.000	+	550.792i	−0.0292284	+	0.0506251i	0.851041	+	0.525099i	$0.175972\pi$
$492$		0			0
$493$	994.500	+	1722.52i	0.0908520	+	0.157360i
$494$	−3008.00			−0.273960
$495$		0			0
$496$	1328.00			0.120220
$497$	−840.000	−	1454.92i	−0.0758132	−	0.131312i
$498$		0			0
$499$	5858.00	−	10146.4i	0.525531	−	0.910247i	−0.474027	−	0.880511i	$-0.657200\pi$
$499$	5858.00	−	10146.4i	0.525531	−	0.910247i	0.999558	−	0.0297363i	$-0.00946674\pi$
$500$	−250.000	+	433.013i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	−6345.00	−	10989.9i	−0.564126	−	0.977095i
$503$	4653.00			0.412459			0.206230	−	0.978504i	$-0.433881\pi$
$503$	4653.00			0.412459			0.206230	+	0.978504i	$0.433881\pi$
$504$		0			0
$505$	165.000			0.0145394
$506$	−297.000	−	514.419i	−0.0260934	−	0.0451951i
$507$		0			0
$508$	−2668.00	+	4621.11i	−0.233018	+	0.403600i
$509$	−8239.50	+	14271.2i	−0.717504	+	1.24275i	0.244482	+	0.969654i	$0.421382\pi$
$509$	−8239.50	+	14271.2i	−0.717504	+	1.24275i	−0.961986	+	0.273099i	$0.911951\pi$
$510$		0			0
$511$	−7742.00	−	13409.5i	−0.670227	−	1.16087i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−1050.00			−0.0901041
$515$	2995.00	+	5187.49i	0.256263	+	0.443861i
$516$		0			0
$517$	−796.500	+	1379.58i	−0.0677563	+	0.117357i
$518$	4396.00	−	7614.10i	0.372875	−	0.645838i
$519$		0			0
$520$	940.000	+	1628.13i	0.0792726	+	0.137304i
$521$	3120.00			0.262360			0.131180	−	0.991359i	$-0.458123\pi$
$521$	3120.00			0.262360			0.131180	+	0.991359i	$0.458123\pi$
$522$		0			0
$523$	17645.0			1.47526			0.737631	−	0.675204i	$-0.235944\pi$
$523$	17645.0			1.47526			0.737631	+	0.675204i	$0.235944\pi$
$524$	5766.00	+	9987.00i	0.480704	+	0.832604i
$525$		0			0
$526$	5196.00	−	8999.74i	0.430716	−	0.746021i
$527$	1618.50	−	2803.32i	0.133782	−	0.231717i
$528$		0			0
$529$	1183.00	+	2049.02i	0.0972302	+	0.168408i
$530$	−5640.00			−0.462238
$531$		0			0
$532$	1792.00			0.146040
$533$	2538.00	+	4395.94i	0.206253	+	0.357241i
$534$		0			0
$535$	3855.00	−	6677.06i	0.311526	−	0.539578i
$536$	−1072.00	+	1856.76i	−0.0863868	+	0.149626i
$537$		0			0
$538$	−7479.00	−	12954.0i	−0.599336	−	1.03808i
$539$	−441.000			−0.0352416
$540$		0			0
$541$	−2182.00			−0.173404			−0.0867019	−	0.996234i	$-0.527633\pi$
$541$	−2182.00			−0.173404			−0.0867019	+	0.996234i	$0.527633\pi$
$542$	−856.000	−	1482.64i	−0.0678383	−	0.117499i
$543$		0			0
$544$	−624.000	+	1080.80i	−0.0491797	+	0.0851818i
$545$	1390.00	−	2407.55i	0.109250	−	0.189226i
$546$		0			0
$547$	2016.50	+	3492.68i	0.157622	+	0.273010i	0.934011	−	0.357245i	$-0.116284\pi$
$547$	2016.50	+	3492.68i	0.157622	+	0.273010i	−0.776389	+	0.630255i	$0.782951\pi$
$548$	1128.00			0.0879302
$549$		0			0
$550$	−150.000			−0.0116291
$551$	−816.000	−	1413.35i	−0.0630903	−	0.109276i
$552$		0			0
$553$	5173.00	−	8959.90i	0.397791	−	0.688994i
$554$	−7054.00	+	12217.9i	−0.540967	+	0.936982i
$555$		0			0
$556$	4988.00	+	8639.47i	0.380465	+	0.658984i
$557$	−960.000			−0.0730278			−0.0365139	−	0.999333i	$-0.511625\pi$
$557$	−960.000			−0.0730278			−0.0365139	+	0.999333i	$0.511625\pi$
$558$		0			0
$559$	14053.0			1.06329
$560$	−560.000	−	969.948i	−0.0422577	−	0.0731925i
$561$		0			0
$562$	1014.00	−	1756.30i	0.0761086	−	0.131824i
$563$	11877.0	−	20571.6i	0.889087	−	1.53994i	0.0481301	−	0.998841i	$-0.484674\pi$
$563$	11877.0	−	20571.6i	0.889087	−	1.53994i	0.840957	−	0.541102i	$-0.181993\pi$
$564$		0			0
$565$	−4012.50	−	6949.85i	−0.298774	−	0.517491i
$566$	−1984.00			−0.147339
$567$		0			0
$568$	−960.000			−0.0709167
$569$	11268.0	+	19516.7i	0.830192	+	1.43793i	0.897886	+	0.440228i	$0.145102\pi$
$569$	11268.0	+	19516.7i	0.830192	+	1.43793i	−0.0676941	+	0.997706i	$0.521564\pi$
$570$		0			0
$571$	−8863.00	+	15351.2i	−0.649571	+	1.12509i	0.333655	+	0.942695i	$0.391718\pi$
$571$	−8863.00	+	15351.2i	−0.649571	+	1.12509i	−0.983225	+	0.182394i	$0.941615\pi$
$572$	−282.000	+	488.438i	−0.0206137	+	0.0357039i
$573$		0			0
$574$	−1512.00	−	2618.86i	−0.109947	−	0.190434i
$575$	−2475.00			−0.179504
$576$		0			0
$577$	17168.0			1.23867			0.619336	−	0.785126i	$-0.287402\pi$
$577$	17168.0			1.23867			0.619336	+	0.785126i	$0.287402\pi$
$578$	−3392.00	−	5875.12i	−0.244098	−	0.422790i
$579$		0			0
$580$	−510.000	+	883.346i	−0.0365114	+	0.0632396i
$581$	−7602.00	+	13167.1i	−0.542830	+	0.940209i
$582$		0			0
$583$	−846.000	−	1465.31i	−0.0600990	−	0.104095i
$584$	−8848.00			−0.626940
$585$		0			0
$586$	9900.00			0.697893
$587$	−3771.00	−	6531.56i	−0.265155	−	0.459261i	0.702449	−	0.711734i	$-0.252090\pi$
$587$	−3771.00	−	6531.56i	−0.265155	−	0.459261i	−0.967604	+	0.252472i	$0.918756\pi$
$588$		0			0
$589$	−1328.00	+	2300.16i	−0.0929020	+	0.160911i
$590$	60.0000	−	103.923i	0.00418671	−	0.00725160i
$591$		0			0
$592$	−2512.00	−	4350.91i	−0.174396	−	0.302063i
$593$	−15543.0			−1.07635			−0.538174	−	0.842834i	$-0.680886\pi$
$593$	−15543.0			−1.07635			−0.538174	+	0.842834i	$0.680886\pi$
$594$		0			0
$595$	−2730.00			−0.188099
$596$	−5190.00	−	8989.34i	−0.356696	−	0.617815i
$597$		0			0
$598$	−4653.00	+	8059.23i	−0.318186	+	0.551115i
$599$	−8013.00	+	13878.9i	−0.546581	+	0.946707i	0.451924	+	0.892056i	$0.350738\pi$
$599$	−8013.00	+	13878.9i	−0.546581	+	0.946707i	−0.998506	+	0.0546505i	$0.982596\pi$
$600$		0			0
$601$	−5234.50	−	9066.42i	−0.355274	−	0.615353i	0.631891	−	0.775057i	$-0.282279\pi$
$601$	−5234.50	−	9066.42i	−0.355274	−	0.615353i	−0.987165	+	0.159705i	$0.948946\pi$
$602$	−8372.00			−0.566806
$603$		0			0
$604$	4916.00			0.331174
$605$	3305.00	+	5724.43i	0.222095	+	0.384679i
$606$		0			0
$607$	4037.00	−	6992.29i	0.269945	−	0.467559i	−0.698902	−	0.715217i	$-0.746328\pi$
$607$	4037.00	−	6992.29i	0.269945	−	0.467559i	0.968847	+	0.247658i	$0.0796611\pi$
$608$	512.000	−	886.810i	0.0341519	−	0.0591528i
$609$		0			0
$610$	1150.00	+	1991.86i	0.0763314	+	0.132210i
$611$	24957.0			1.65246
$612$		0			0
$613$	26855.0			1.76943			0.884717	−	0.466128i	$-0.154351\pi$
$613$	26855.0			1.76943			0.884717	+	0.466128i	$0.154351\pi$
$614$	−4777.00	−	8274.01i	−0.313981	−	0.543830i
$615$		0			0
$616$	168.000	−	290.985i	0.0109885	−	0.0190326i
$617$	−12223.5	+	21171.7i	−0.797568	+	1.38143i	0.123627	+	0.992329i	$0.460547\pi$
$617$	−12223.5	+	21171.7i	−0.797568	+	1.38143i	−0.921196	+	0.389100i	$0.872786\pi$
$618$		0			0
$619$	−925.000	−	1602.15i	−0.0600628	−	0.104032i	0.834430	−	0.551113i	$-0.185797\pi$
$619$	−925.000	−	1602.15i	−0.0600628	−	0.104032i	−0.894493	+	0.447081i	$0.852463\pi$
$620$	1660.00			0.107528
$621$		0			0
$622$	15384.0			0.991708
$623$	840.000	+	1454.92i	0.0540191	+	0.0935638i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−2932.00	+	5078.37i	−0.187199	+	0.324237i
$627$		0			0
$628$	3182.00	+	5511.39i	0.202190	+	0.350204i
$629$	−12246.0			−0.776280
$630$		0			0
$631$	21728.0			1.37081			0.685403	−	0.728164i	$-0.259626\pi$
$631$	21728.0			1.37081			0.685403	+	0.728164i	$0.259626\pi$
$632$	−2956.00	−	5119.94i	−0.186050	−	0.322247i
$633$		0			0
$634$	8352.00	−	14466.1i	0.523187	−	0.906186i
$635$	−3335.00	+	5776.39i	−0.208418	+	0.360991i
$636$		0			0
$637$	3454.50	+	5983.37i	0.214870	+	0.372166i
$638$	−306.000			−0.0189885
$639$		0			0
$640$	−640.000			−0.0395285
$641$	−11931.0	−	20665.1i	−0.735173	−	1.27336i	−0.954647	−	0.297739i	$-0.903767\pi$
$641$	−11931.0	−	20665.1i	−0.735173	−	1.27336i	0.219474	−	0.975618i	$-0.429566\pi$
$642$		0			0
$643$	−5261.50	+	9113.19i	−0.322696	+	0.558925i	−0.981043	−	0.193789i	$-0.937922\pi$
$643$	−5261.50	+	9113.19i	−0.322696	+	0.558925i	0.658348	+	0.752714i	$0.271256\pi$
$644$	2772.00	−	4801.24i	0.169615	−	0.293782i
$645$		0			0
$646$	−1248.00	−	2161.60i	−0.0760091	−	0.131652i
$647$	5484.00			0.333228			0.166614	−	0.986022i	$-0.446717\pi$
$647$	5484.00			0.333228			0.166614	+	0.986022i	$0.446717\pi$
$648$		0			0
$649$	36.0000			0.00217739
$650$	1175.00	+	2035.16i	0.0709035	+	0.122809i
$651$		0			0
$652$	914.000	−	1583.09i	0.0549003	−	0.0950901i
$653$	13392.0	−	23195.6i	0.802557	−	1.39007i	−0.115372	−	0.993322i	$-0.536806\pi$
$653$	13392.0	−	23195.6i	0.802557	−	1.39007i	0.917928	−	0.396746i	$-0.129861\pi$
$654$		0			0
$655$	7207.50	+	12483.8i	0.429955	+	0.744703i
$656$	−1728.00			−0.102846
$657$		0			0
$658$	−14868.0			−0.880874
$659$	6060.00	+	10496.2i	0.358216	+	0.620448i	0.987663	−	0.156596i	$-0.0500519\pi$
$659$	6060.00	+	10496.2i	0.358216	+	0.620448i	−0.629447	+	0.777043i	$0.716719\pi$
$660$		0			0
$661$	9113.00	−	15784.2i	0.536240	−	0.928795i	−0.462862	−	0.886430i	$-0.653178\pi$
$661$	9113.00	−	15784.2i	0.536240	−	0.928795i	0.999102	−	0.0423646i	$-0.0134891\pi$
$662$	−3070.00	+	5317.40i	−0.180240	+	0.312185i
$663$		0			0
$664$	4344.00	+	7524.03i	0.253885	+	0.439742i
$665$	2240.00			0.130622
$666$		0			0
$667$	−5049.00			−0.293101
$668$	2328.00	+	4032.21i	0.134840	+	0.233549i
$669$		0			0
$670$	−1340.00	+	2320.95i	−0.0772667	+	0.133830i
$671$	−345.000	+	597.558i	−0.0198488	+	0.0343792i
$672$		0			0
$673$	5531.00	+	9579.97i	0.316797	+	0.548709i	0.979818	−	0.199892i	$-0.0640593\pi$
$673$	5531.00	+	9579.97i	0.316797	+	0.548709i	−0.663021	+	0.748601i	$0.730726\pi$
$674$	3344.00			0.191107
$675$		0			0
$676$	48.0000			0.00273100
$677$	4674.00	+	8095.61i	0.265342	+	0.459586i	0.967653	−	0.252284i	$-0.0811819\pi$
$677$	4674.00	+	8095.61i	0.265342	+	0.459586i	−0.702311	+	0.711870i	$0.747849\pi$
$678$		0			0
$679$	11494.0	−	19908.2i	0.649631	−	1.12519i
$680$	−780.000	+	1351.00i	−0.0439877	+	0.0761889i
$681$		0			0
$682$	249.000	+	431.281i	0.0139805	+	0.0242149i
$683$	19248.0			1.07834			0.539169	−	0.842198i	$-0.318739\pi$
$683$	19248.0			1.07834			0.539169	+	0.842198i	$0.318739\pi$
$684$		0			0
$685$	1410.00			0.0786472
$686$	−6860.00	−	11881.9i	−0.381802	−	0.661300i
$687$		0			0
$688$	−2392.00	+	4143.07i	−0.132550	+	0.229583i
$689$	−13254.0	+	22956.6i	−0.732855	+	1.26934i
$690$		0			0
$691$	8855.00	+	15337.3i	0.487496	+	0.844369i	0.999897	−	0.0143781i	$-0.00457686\pi$
$691$	8855.00	+	15337.3i	0.487496	+	0.844369i	−0.512400	+	0.858747i	$0.671244\pi$
$692$	15768.0			0.866199
$693$		0			0
$694$	10152.0			0.555280
$695$	6235.00	+	10799.3i	0.340298	+	0.589413i
$696$		0			0
$697$	−2106.00	+	3647.70i	−0.114448	+	0.198230i
$698$	8594.00	−	14885.2i	0.466028	−	0.807185i
$699$		0			0
$700$	−700.000	−	1212.44i	−0.0377964	−	0.0654654i
$701$	−19437.0			−1.04725			−0.523627	−	0.851947i	$-0.675422\pi$
$701$	−19437.0			−1.04725			−0.523627	+	0.851947i	$0.675422\pi$
$702$		0			0
$703$	10048.0			0.539072
$704$	−96.0000	−	166.277i	−0.00513940	−	0.00890170i
$705$		0			0
$706$	12711.0	−	22016.1i	0.677599	−	1.17364i
$707$	−231.000	+	400.104i	−0.0122880	+	0.0212835i
$708$		0			0
$709$	9758.00	+	16901.4i	0.516882	+	0.895266i	0.999808	+	0.0196047i	$0.00624077\pi$
$709$	9758.00	+	16901.4i	0.516882	+	0.895266i	−0.482926	+	0.875661i	$0.660426\pi$
$710$	−1200.00			−0.0634299
$711$		0			0
$712$	960.000			0.0505302
$713$	4108.50	+	7116.13i	0.215799	+	0.373774i
$714$		0			0
$715$	−352.500	+	610.548i	−0.0184374	+	0.0319345i
$716$	2424.00	−	4198.49i	0.126521	−	0.219141i
$717$		0			0
$718$	−1464.00	−	2535.72i	−0.0760947	−	0.131800i
$719$	17358.0			0.900340			0.450170	−	0.892943i	$-0.351363\pi$
$719$	17358.0			0.900340			0.450170	+	0.892943i	$0.351363\pi$
$720$		0			0
$721$	−16772.0			−0.866327
$722$	−5835.00	−	10106.5i	−0.300770	−	0.520950i
$723$		0			0
$724$	−4576.00	+	7925.86i	−0.234897	+	0.406854i
$725$	−637.500	+	1104.18i	−0.0326568	+	0.0565632i
$726$		0			0
$727$	−12214.0	−	21155.3i	−0.623098	−	1.07924i	−0.988905	−	0.148547i	$-0.952540\pi$
$727$	−12214.0	−	21155.3i	−0.623098	−	1.07924i	0.365807	−	0.930691i	$-0.380793\pi$
$728$	−5264.00			−0.267990
$729$		0			0
$730$	−11060.0			−0.560752
$731$	5830.50	+	10098.7i	0.295005	+	0.510964i
$732$		0			0
$733$	10709.0	−	18548.5i	0.539626	−	0.934660i	−0.459298	−	0.888282i	$-0.651899\pi$
$733$	10709.0	−	18548.5i	0.539626	−	0.934660i	0.998924	−	0.0463775i	$-0.0147677\pi$
$734$	−7630.00	+	13215.5i	−0.383690	+	0.664571i
$735$		0			0
$736$	−1584.00	−	2743.57i	−0.0793302	−	0.137404i
$737$	−804.000			−0.0401842
$738$		0			0
$739$	−664.000			−0.0330523			−0.0165261	−	0.999863i	$-0.505261\pi$
$739$	−664.000			−0.0330523			−0.0165261	+	0.999863i	$0.505261\pi$
$740$	−3140.00	−	5438.64i	−0.155985	−	0.270173i
$741$		0			0
$742$	7896.00	−	13676.3i	0.390662	−	0.676647i
$743$	17104.5	−	29625.9i	0.844553	−	1.46281i	−0.0414549	−	0.999140i	$-0.513199\pi$
$743$	17104.5	−	29625.9i	0.844553	−	1.46281i	0.886008	−	0.463669i	$-0.153467\pi$
$744$		0			0
$745$	−6487.50	−	11236.7i	−0.319038	−	0.552591i
$746$	7766.00			0.381144
$747$		0			0
$748$	−468.000			−0.0228767
$749$	10794.0	+	18695.8i	0.526574	+	0.912054i
$750$		0			0
$751$	−3428.50	+	5938.34i	−0.166588	+	0.288539i	−0.937218	−	0.348744i	$-0.886608\pi$
$751$	−3428.50	+	5938.34i	−0.166588	+	0.288539i	0.770630	+	0.637283i	$0.219942\pi$
$752$	−4248.00	+	7357.75i	−0.205996	+	0.356795i
$753$		0			0
$754$	2397.00	+	4151.73i	0.115774	+	0.200526i
$755$	6145.00			0.296211
$756$		0			0
$757$	−23719.0			−1.13881			−0.569407	−	0.822056i	$-0.692827\pi$
$757$	−23719.0			−1.13881			−0.569407	+	0.822056i	$0.692827\pi$
$758$	−13768.0	−	23846.9i	−0.659731	−	1.14269i
$759$		0			0
$760$	640.000	−	1108.51i	0.0305464	−	0.0529079i
$761$	7209.00	−	12486.4i	0.343398	−	0.594783i	−0.641663	−	0.766987i	$-0.721755\pi$
$761$	7209.00	−	12486.4i	0.343398	−	0.594783i	0.985061	+	0.172203i	$0.0550886\pi$
$762$		0			0
$763$	3892.00	+	6741.14i	0.184666	+	0.319850i
$764$	−7752.00			−0.367091
$765$		0			0
$766$	28278.0			1.33385
$767$	−282.000	−	488.438i	−0.0132757	−	0.0229941i
$768$		0			0
$769$	2424.50	−	4199.36i	0.113693	−	0.196922i	−0.803564	−	0.595219i	$-0.797065\pi$
$769$	2424.50	−	4199.36i	0.113693	−	0.196922i	0.917256	+	0.398297i	$0.130399\pi$
$770$	210.000	−	363.731i	0.00982841	−	0.0170233i
$771$		0			0
$772$	2996.00	+	5189.22i	0.139674	+	0.241923i
$773$	−36258.0			−1.68708			−0.843538	−	0.537070i	$-0.819531\pi$
$773$	−36258.0			−1.68708			−0.843538	+	0.537070i	$0.819531\pi$
$774$		0			0
$775$	2075.00			0.0961757
$776$	−6568.00	−	11376.1i	−0.303837	−	0.526261i
$777$		0			0
$778$	567.000	−	982.073i	0.0261285	−	0.0452558i
$779$	1728.00	−	2992.98i	0.0794763	−	0.137657i
$780$		0			0
$781$	−180.000	−	311.769i	−0.00824700	−	0.0142842i
$782$	−7722.00			−0.353118
$783$		0			0
$784$	−2352.00			−0.107143
$785$	3977.50	+	6889.23i	0.180845	+	0.313232i
$786$		0			0
$787$	9438.50	−	16348.0i	0.427505	−	0.740460i	−0.569146	−	0.822236i	$-0.692726\pi$
$787$	9438.50	−	16348.0i	0.427505	−	0.740460i	0.996651	+	0.0817766i	$0.0260594\pi$
$788$	4248.00	−	7357.75i	0.192042	−	0.332626i
$789$		0			0
$790$	−3695.00	−	6399.93i	−0.166408	−	0.288227i
$791$	22470.0			1.01004
$792$		0			0
$793$	10810.0			0.484079
$794$	−6685.00	−	11578.8i	−0.298793	−	0.517525i
$795$		0			0
$796$	770.000	−	1333.68i	0.0342863	−	0.0593857i
$797$	8100.00	−	14029.6i	0.359996	−	0.623531i	−0.627964	−	0.778243i	$-0.716111\pi$
$797$	8100.00	−	14029.6i	0.359996	−	0.623531i	0.987960	+	0.154711i	$0.0494448\pi$
$798$		0			0
$799$	10354.5	+	17934.5i	0.458468	+	0.794090i
$800$	−800.000			−0.0353553
$801$		0			0
$802$	−9144.00			−0.402601
$803$	−1659.00	−	2873.47i	−0.0729076	−	0.126280i
$804$		0			0
$805$	3465.00	−	6001.56i	0.151708	−	0.262767i
$806$	3901.00	−	6756.73i	0.170480	−	0.295280i
$807$		0			0
$808$	132.000	+	228.631i	0.00574721	+	0.00995446i
$809$	−26760.0			−1.16296			−0.581478	−	0.813562i	$-0.697525\pi$
$809$	−26760.0			−1.16296			−0.581478	+	0.813562i	$0.697525\pi$
$810$		0			0
$811$	−10510.0			−0.455063			−0.227531	−	0.973771i	$-0.573065\pi$
$811$	−10510.0			−0.455063			−0.227531	+	0.973771i	$0.573065\pi$
$812$	−1428.00	−	2473.37i	−0.0617155	−	0.106894i
$813$		0			0
$814$	942.000	−	1631.59i	0.0405615	−	0.0702546i
$815$	1142.50	−	1978.87i	0.0491043	−	0.0850512i
$816$		0			0
$817$	−4784.00	−	8286.13i	−0.204860	−	0.354829i
$818$	50.0000			0.00213717
$819$		0			0
$820$	−2160.00			−0.0919884
$821$	14115.0	+	24447.9i	0.600021	+	1.03927i	0.992817	+	0.119641i	$0.0381743\pi$
$821$	14115.0	+	24447.9i	0.600021	+	1.03927i	−0.392797	+	0.919625i	$0.628492\pi$
$822$		0			0
$823$	19934.0	−	34526.7i	0.844296	−	1.46236i	−0.0419353	−	0.999120i	$-0.513352\pi$
$823$	19934.0	−	34526.7i	0.844296	−	1.46236i	0.886231	−	0.463243i	$-0.153314\pi$
$824$	−4792.00	+	8299.99i	−0.202594	+	0.350903i
$825$		0			0
$826$	168.000	+	290.985i	0.00707684	+	0.0122574i
$827$	32394.0			1.36209			0.681046	−	0.732241i	$-0.261525\pi$
$827$	32394.0			1.36209			0.681046	+	0.732241i	$0.261525\pi$
$828$		0			0
$829$	34820.0			1.45880			0.729402	−	0.684085i	$-0.239798\pi$
$829$	34820.0			1.45880			0.729402	+	0.684085i	$0.239798\pi$
$830$	5430.00	+	9405.04i	0.227082	+	0.393318i
$831$		0			0
$832$	−1504.00	+	2605.00i	−0.0626705	+	0.108548i
$833$	−2866.50	+	4964.92i	−0.119230	+	0.206512i
$834$		0			0
$835$	2910.00	+	5040.27i	0.120604	+	0.208893i
$836$	384.000			0.0158863
$837$		0			0
$838$	−24906.0			−1.02669
$839$	573.000	+	992.465i	0.0235783	+	0.0408387i	0.877574	−	0.479442i	$-0.159161\pi$
$839$	573.000	+	992.465i	0.0235783	+	0.0408387i	−0.853996	+	0.520280i	$0.825827\pi$
$840$		0			0
$841$	10894.0	−	18869.0i	0.446677	−	0.773667i
$842$	5048.00	−	8743.39i	0.206610	−	0.357859i
$843$		0			0
$844$	−6340.00	−	10981.2i	−0.258568	−	0.447854i
$845$	60.0000			0.00244268
$846$		0			0
$847$	−18508.0			−0.750817
$848$	−4512.00	−	7815.01i	−0.182715	−	0.316472i
$849$		0			0
$850$	−975.000	+	1688.75i	−0.0393438	+	0.0681454i
$851$	15543.0	−	26921.3i	0.626095	−	1.08443i
$852$		0			0
$853$	9696.50	+	16794.8i	0.389217	+	0.674143i	0.992344	−	0.123502i	$-0.0394124\pi$
$853$	9696.50	+	16794.8i	0.389217	+	0.674143i	−0.603128	+	0.797645i	$0.706079\pi$
$854$	−6440.00			−0.258047
$855$		0			0
$856$	12336.0			0.492565
$857$	4215.00	+	7300.59i	0.168007	+	0.290996i	0.937719	−	0.347395i	$-0.112934\pi$
$857$	4215.00	+	7300.59i	0.168007	+	0.290996i	−0.769712	+	0.638391i	$0.779600\pi$
$858$		0			0
$859$	−7735.00	+	13397.4i	−0.307235	+	0.532146i	−0.977756	−	0.209744i	$-0.932737\pi$
$859$	−7735.00	+	13397.4i	−0.307235	+	0.532146i	0.670522	+	0.741890i	$0.266070\pi$
$860$	−2990.00	+	5178.83i	−0.118556	+	0.205345i
$861$		0			0
$862$	5400.00	+	9353.07i	0.213370	+	0.369567i
$863$	5871.00			0.231577			0.115789	−	0.993274i	$-0.463060\pi$
$863$	5871.00			0.231577			0.115789	+	0.993274i	$0.463060\pi$
$864$		0			0
$865$	19710.0			0.774752
$866$	−6298.00	−	10908.5i	−0.247130	−	0.428042i
$867$		0			0
$868$	−2324.00	+	4025.29i	−0.0908775	+	0.157405i
$869$	1108.50	−	1919.98i	0.0432719	−	0.0749491i
$870$		0			0
$871$	6298.00	+	10908.5i	0.245005	+	0.424362i
$872$	4448.00			0.172739
$873$		0			0
$874$	6336.00			0.245216
$875$	−875.000	−	1515.54i	−0.0338062	−	0.0585540i
$876$		0			0
$877$	5649.50	−	9785.22i	0.217526	−	0.376766i	−0.736525	−	0.676410i	$-0.763535\pi$
$877$	5649.50	−	9785.22i	0.217526	−	0.376766i	0.954051	+	0.299644i	$0.0968681\pi$
$878$	−6208.00	+	10752.6i	−0.238622	+	0.413305i
$879$		0			0
$880$	−120.000	−	207.846i	−0.00459682	−	0.00796192i
$881$	29682.0			1.13509			0.567544	−	0.823343i	$-0.307894\pi$
$881$	29682.0			1.13509			0.567544	+	0.823343i	$0.307894\pi$
$882$		0			0
$883$	40316.0			1.53651			0.768257	−	0.640142i	$-0.221124\pi$
$883$	40316.0			1.53651			0.768257	+	0.640142i	$0.221124\pi$
$884$	3666.00	+	6349.70i	0.139481	+	0.241588i
$885$		0			0
$886$	−3360.00	+	5819.69i	−0.127406	+	0.220673i
$887$	10972.5	−	19004.9i	0.415356	−	0.719417i	−0.580110	−	0.814538i	$-0.696990\pi$
$887$	10972.5	−	19004.9i	0.415356	−	0.719417i	0.995466	+	0.0951210i	$0.0303238\pi$
$888$		0			0
$889$	−9338.00	−	16173.9i	−0.352291	−	0.610185i
$890$	1200.00			0.0451956
$891$		0			0
$892$	5552.00			0.208402
$893$	−8496.00	−	14715.5i	−0.318374	−	0.551440i
$894$		0			0
$895$	3030.00	−	5248.11i	0.113164	−	0.196006i
$896$	896.000	−	1551.92i	0.0334077	−	0.0578638i
$897$		0			0
$898$	14394.0	+	24931.1i	0.534893	+	0.926462i
$899$	4233.00			0.157039
$900$		0			0
$901$	−21996.0			−0.813311
$902$	−324.000	−	561.184i	−0.0119601	−	0.0207155i
$903$		0			0
$904$	6420.00	−	11119.8i	0.236201	−	0.409113i
$905$	−5720.00	+	9907.33i	−0.210099	+	0.363901i
$906$		0			0
$907$	−12455.5	−	21573.6i	−0.455985	−	0.789789i	0.542760	−	0.839888i	$-0.317379\pi$
$907$	−12455.5	−	21573.6i	−0.455985	−	0.789789i	−0.998744	+	0.0500995i	$0.984046\pi$
$908$	−18576.0			−0.678928
$909$		0			0
$910$	−6580.00			−0.239698
$911$	−16632.0	−	28807.5i	−0.604877	−	1.04768i	−0.992071	−	0.125679i	$-0.959889\pi$
$911$	−16632.0	−	28807.5i	−0.604877	−	1.04768i	0.387194	−	0.921998i	$-0.373444\pi$
$912$		0			0
$913$	−1629.00	+	2821.51i	−0.0590493	+	0.102276i
$914$	−916.000	+	1586.56i	−0.0331494	+	0.0574165i
$915$		0			0
$916$	−9472.00	−	16406.0i	−0.341663	−	0.591778i
$917$	−40362.0			−1.45351
$918$		0			0
$919$	−23191.0			−0.832427			−0.416214	−	0.909267i	$-0.636643\pi$
$919$	−23191.0			−0.832427			−0.416214	+	0.909267i	$0.636643\pi$
$920$	−1980.00	−	3429.46i	−0.0709551	−	0.122898i
$921$		0			0
$922$	8550.00	−	14809.0i	0.305400	−	0.528969i
$923$	−2820.00	+	4884.38i	−0.100565	+	0.174184i
$924$		0			0
$925$	−3925.00	−	6798.30i	−0.139517	−	0.241650i
$926$	−7468.00			−0.265026
$927$		0			0
$928$	−1632.00			−0.0577296
$929$	−1080.00	−	1870.61i	−0.0381417	−	0.0660634i	0.846324	−	0.532668i	$-0.178810\pi$
$929$	−1080.00	−	1870.61i	−0.0381417	−	0.0660634i	−0.884466	+	0.466604i	$0.845477\pi$
$930$		0			0
$931$	2352.00	−	4073.78i	0.0827967	−	0.143408i
$932$	−5628.00	+	9747.98i	−0.197802	+	0.342603i
$933$		0			0
$934$	9840.00	+	17043.4i	0.344727	+	0.597084i
$935$	−585.000			−0.0204615
$936$		0			0
$937$	2066.00			0.0720312			0.0360156	−	0.999351i	$-0.488533\pi$
$937$	2066.00			0.0720312			0.0360156	+	0.999351i	$0.488533\pi$
$938$	−3752.00	−	6498.65i	−0.130605	−	0.226214i
$939$		0			0
$940$	−5310.00	+	9197.19i	−0.184248	+	0.319127i
$941$	11116.5	−	19254.3i	0.385109	−	0.667028i	−0.606675	−	0.794950i	$-0.707497\pi$
$941$	11116.5	−	19254.3i	0.385109	−	0.667028i	0.991784	+	0.127921i	$0.0408305\pi$
$942$		0			0
$943$	−5346.00	−	9259.54i	−0.184613	−	0.319758i
$944$	192.000			0.00661978
$945$		0			0
$946$	−1794.00			−0.0616575
$947$	8877.00	+	15375.4i	0.304608	+	0.527596i	0.977174	−	0.212441i	$-0.0681412\pi$
$947$	8877.00	+	15375.4i	0.304608	+	0.527596i	−0.672566	+	0.740037i	$0.734808\pi$
$948$		0			0
$949$	−25991.0	+	45017.7i	−0.889045	+	1.53987i
$950$	800.000	−	1385.64i	0.0273215	−	0.0473222i
$951$		0			0
$952$	−2184.00	−	3782.80i	−0.0743528	−	0.128783i
$953$	33891.0			1.15198			0.575990	−	0.817457i	$-0.304617\pi$
$953$	33891.0			1.15198			0.575990	+	0.817457i	$0.304617\pi$
$954$		0			0
$955$	−9690.00			−0.328336
$956$	4404.00	+	7627.95i	0.148991	+	0.258060i
$957$		0			0
$958$	−17280.0	+	29929.8i	−0.582768	+	1.00938i
$959$	−1974.00	+	3419.07i	−0.0664690	+	0.115128i
$960$		0			0
$961$	11451.0	+	19833.7i	0.384378	+	0.665762i
$962$	−29516.0			−0.989225
$963$		0			0
$964$	13940.0			0.465744
$965$	3745.00	+	6486.53i	0.124928	+	0.216382i
$966$		0			0
$967$	−25537.0	+	44231.4i	−0.849239	+	1.47093i	0.0326485	+	0.999467i	$0.489606\pi$
$967$	−25537.0	+	44231.4i	−0.849239	+	1.47093i	−0.881888	+	0.471459i	$0.843728\pi$
$968$	−5288.00	+	9159.08i	−0.175581	+	0.304116i
$969$		0			0
$970$	−8210.00	−	14220.1i	−0.271760	−	0.470702i
$971$	20967.0			0.692959			0.346479	−	0.938058i	$-0.387377\pi$
$971$	20967.0			0.692959			0.346479	+	0.938058i	$0.387377\pi$
$972$		0			0
$973$	−34916.0			−1.15042
$974$	−4588.00	−	7946.65i	−0.150933	−	0.261424i
$975$		0			0
$976$	−1840.00	+	3186.97i	−0.0603453	+	0.104521i
$977$	−15874.5	+	27495.4i	−0.519826	+	0.900365i	0.479908	+	0.877319i	$0.340670\pi$
$977$	−15874.5	+	27495.4i	−0.519826	+	0.900365i	−0.999734	+	0.0230467i	$0.992663\pi$
$978$		0			0
$979$	180.000	+	311.769i	0.00587623	+	0.0101779i
$980$	−2940.00			−0.0958315
$981$		0			0
$982$	−1272.00			−0.0413352
$983$	−23662.5	−	40984.7i	−0.767769	−	1.32981i	−0.938770	−	0.344544i	$-0.888034\pi$
$983$	−23662.5	−	40984.7i	−0.767769	−	1.32981i	0.171002	−	0.985271i	$-0.445300\pi$
$984$		0			0
$985$	5310.00	−	9197.19i	0.171767	−	0.297509i
$986$	−1989.00	+	3445.05i	−0.0642421	+	0.111270i
$987$		0			0
$988$	−3008.00	−	5210.01i	−0.0968595	−	0.167766i
$989$	−29601.0			−0.951726
$990$		0			0
$991$	2363.00			0.0757449			0.0378724	−	0.999283i	$-0.487942\pi$
$991$	2363.00			0.0757449			0.0378724	+	0.999283i	$0.487942\pi$
$992$	1328.00	+	2300.16i	0.0425041	+	0.0736192i
$993$		0			0
$994$	1680.00	−	2909.85i	0.0536080	−	0.0928518i
$995$	962.500	−	1667.10i	0.0306666	−	0.0531162i
$996$		0			0
$997$	−22784.5	−	39463.9i	−0.723764	−	1.25360i	−0.959481	−	0.281774i	$-0.909077\pi$
$997$	−22784.5	−	39463.9i	−0.723764	−	1.25360i	0.235717	−	0.971822i	$-0.424256\pi$
$998$	23432.0			0.743213
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.4.e.n.271.1		2
3.2	odd	2		810.4.e.f.271.1		2
9.2	odd	6		810.4.e.f.541.1		2
9.4	even	3		270.4.a.f.1.1	✓	1
9.5	odd	6		270.4.a.j.1.1	yes	1
9.7	even	3	inner	810.4.e.n.541.1		2
36.23	even	6		2160.4.a.b.1.1		1
36.31	odd	6		2160.4.a.l.1.1		1
45.4	even	6		1350.4.a.r.1.1		1
45.13	odd	12		1350.4.c.k.649.2		2
45.14	odd	6		1350.4.a.e.1.1		1
45.22	odd	12		1350.4.c.k.649.1		2
45.23	even	12		1350.4.c.j.649.1		2
45.32	even	12		1350.4.c.j.649.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.4.a.f.1.1	✓	1	9.4	even	3
270.4.a.j.1.1	yes	1	9.5	odd	6
810.4.e.f.271.1		2	3.2	odd	2
810.4.e.f.541.1		2	9.2	odd	6
810.4.e.n.271.1		2	1.1	even	1	trivial
810.4.e.n.541.1		2	9.7	even	3	inner
1350.4.a.e.1.1		1	45.14	odd	6
1350.4.a.r.1.1		1	45.4	even	6
1350.4.c.j.649.1		2	45.23	even	12
1350.4.c.j.649.2		2	45.32	even	12
1350.4.c.k.649.1		2	45.22	odd	12
1350.4.c.k.649.2		2	45.13	odd	12
2160.4.a.b.1.1		1	36.23	even	6
2160.4.a.l.1.1		1	36.31	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	810.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} -10.0000 q^{10} +(-1.50000 - 2.59808i) q^{11} +(-23.5000 + 40.7032i) q^{13} +(14.0000 - 24.2487i) q^{14} +(-8.00000 - 13.8564i) q^{16} -39.0000 q^{17} +32.0000 q^{19} +(-10.0000 - 17.3205i) q^{20} +(3.00000 - 5.19615i) q^{22} +(49.5000 - 85.7365i) q^{23} +(-12.5000 - 21.6506i) q^{25} -94.0000 q^{26} +56.0000 q^{28} +(-25.5000 - 44.1673i) q^{29} +(-41.5000 + 71.8801i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-39.0000 - 67.5500i) q^{34} +70.0000 q^{35} +314.000 q^{37} +(32.0000 + 55.4256i) q^{38} +(20.0000 - 34.6410i) q^{40} +(54.0000 - 93.5307i) q^{41} +(-149.500 - 258.942i) q^{43} +12.0000 q^{44} +198.000 q^{46} +(-265.500 - 459.859i) q^{47} +(73.5000 - 127.306i) q^{49} +(25.0000 - 43.3013i) q^{50} +(-94.0000 - 162.813i) q^{52} +564.000 q^{53} +15.0000 q^{55} +(56.0000 + 96.9948i) q^{56} +(51.0000 - 88.3346i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-115.000 - 199.186i) q^{61} -166.000 q^{62} +64.0000 q^{64} +(-117.500 - 203.516i) q^{65} +(134.000 - 232.095i) q^{67} +(78.0000 - 135.100i) q^{68} +(70.0000 + 121.244i) q^{70} +120.000 q^{71} +1106.00 q^{73} +(314.000 + 543.864i) q^{74} +(-64.0000 + 110.851i) q^{76} +(-21.0000 + 36.3731i) q^{77} +(369.500 + 639.993i) q^{79} +80.0000 q^{80} +216.000 q^{82} +(-543.000 - 940.504i) q^{83} +(97.5000 - 168.875i) q^{85} +(299.000 - 517.883i) q^{86} +(12.0000 + 20.7846i) q^{88} -120.000 q^{89} +658.000 q^{91} +(198.000 + 342.946i) q^{92} +(531.000 - 919.719i) q^{94} +(-80.0000 + 138.564i) q^{95} +(821.000 + 1422.01i) q^{97} +294.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} - 14 q^{7} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 - 5 * q^5 - 14 * q^7 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} - 5 q^{5} - 14 q^{7} - 16 q^{8} - 20 q^{10} - 3 q^{11} - 47 q^{13} + 28 q^{14} - 16 q^{16} - 78 q^{17} + 64 q^{19} - 20 q^{20} + 6 q^{22} + 99 q^{23} - 25 q^{25} - 188 q^{26} + 112 q^{28} - 51 q^{29} - 83 q^{31} + 32 q^{32} - 78 q^{34} + 140 q^{35} + 628 q^{37} + 64 q^{38} + 40 q^{40} + 108 q^{41} - 299 q^{43} + 24 q^{44} + 396 q^{46} - 531 q^{47} + 147 q^{49} + 50 q^{50} - 188 q^{52} + 1128 q^{53} + 30 q^{55} + 112 q^{56} + 102 q^{58} - 12 q^{59} - 230 q^{61} - 332 q^{62} + 128 q^{64} - 235 q^{65} + 268 q^{67} + 156 q^{68} + 140 q^{70} + 240 q^{71} + 2212 q^{73} + 628 q^{74} - 128 q^{76} - 42 q^{77} + 739 q^{79} + 160 q^{80} + 432 q^{82} - 1086 q^{83} + 195 q^{85} + 598 q^{86} + 24 q^{88} - 240 q^{89} + 1316 q^{91} + 396 q^{92} + 1062 q^{94} - 160 q^{95} + 1642 q^{97} + 588 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 - 5 * q^5 - 14 * q^7 - 16 * q^8 - 20 * q^10 - 3 * q^11 - 47 * q^13 + 28 * q^14 - 16 * q^16 - 78 * q^17 + 64 * q^19 - 20 * q^20 + 6 * q^22 + 99 * q^23 - 25 * q^25 - 188 * q^26 + 112 * q^28 - 51 * q^29 - 83 * q^31 + 32 * q^32 - 78 * q^34 + 140 * q^35 + 628 * q^37 + 64 * q^38 + 40 * q^40 + 108 * q^41 - 299 * q^43 + 24 * q^44 + 396 * q^46 - 531 * q^47 + 147 * q^49 + 50 * q^50 - 188 * q^52 + 1128 * q^53 + 30 * q^55 + 112 * q^56 + 102 * q^58 - 12 * q^59 - 230 * q^61 - 332 * q^62 + 128 * q^64 - 235 * q^65 + 268 * q^67 + 156 * q^68 + 140 * q^70 + 240 * q^71 + 2212 * q^73 + 628 * q^74 - 128 * q^76 - 42 * q^77 + 739 * q^79 + 160 * q^80 + 432 * q^82 - 1086 * q^83 + 195 * q^85 + 598 * q^86 + 24 * q^88 - 240 * q^89 + 1316 * q^91 + 396 * q^92 + 1062 * q^94 - 160 * q^95 + 1642 * q^97 + 588 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more