LMFDB - Embedded newform 810.4.e.bf.541.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [810,4,Mod(271,810)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,4,0,-8,10,0,26,-32,0,40,-36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$47.7915471046$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	810.541
Dual form			810.4.e.bf.271.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(7.36603 - 12.7583i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(-18.5263 + 32.0885i) q^{11} +(3.26795 + 5.66025i) q^{13} +(-14.7321 - 25.5167i) q^{14} +(-8.00000 + 13.8564i) q^{16} -46.7987 q^{17} +8.71281 q^{19} +(10.0000 - 17.3205i) q^{20} +(37.0526 + 64.1769i) q^{22} +(-49.0526 - 84.9615i) q^{23} +(-12.5000 + 21.6506i) q^{25} +13.0718 q^{26} -58.9282 q^{28} +(-107.847 + 186.796i) q^{29} +(-9.55256 - 16.5455i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-46.7987 + 81.0577i) q^{34} +73.6603 q^{35} -369.181 q^{37} +(8.71281 - 15.0910i) q^{38} +(-20.0000 - 34.6410i) q^{40} +(-91.5788 - 158.619i) q^{41} +(33.6199 - 58.2314i) q^{43} +148.210 q^{44} -196.210 q^{46} +(-58.3224 + 101.017i) q^{47} +(62.9833 + 109.090i) q^{49} +(25.0000 + 43.3013i) q^{50} +(13.0718 - 22.6410i) q^{52} -51.5551 q^{53} -185.263 q^{55} +(-58.9282 + 102.067i) q^{56} +(215.694 + 373.592i) q^{58} +(292.903 + 507.323i) q^{59} +(164.746 - 285.349i) q^{61} -38.2102 q^{62} +64.0000 q^{64} +(-16.3397 + 28.3013i) q^{65} +(-191.004 - 330.828i) q^{67} +(93.5974 + 162.115i) q^{68} +(73.6603 - 127.583i) q^{70} -332.065 q^{71} -817.458 q^{73} +(-369.181 + 639.440i) q^{74} +(-17.4256 - 30.1821i) q^{76} +(272.930 + 472.729i) q^{77} +(-311.865 + 540.167i) q^{79} -80.0000 q^{80} -366.315 q^{82} +(-505.804 + 876.079i) q^{83} +(-116.997 - 202.644i) q^{85} +(-67.2398 - 116.463i) q^{86} +(148.210 - 256.708i) q^{88} +670.765 q^{89} +96.2872 q^{91} +(-196.210 + 339.846i) q^{92} +(116.645 + 202.035i) q^{94} +(21.7820 + 37.7276i) q^{95} +(259.357 - 449.220i) q^{97} +251.933 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 10 q^{5} + 26 q^{7} - 32 q^{8} + 40 q^{10} - 36 q^{11} + 20 q^{13} - 52 q^{14} - 32 q^{16} + 180 q^{17} - 76 q^{19} + 40 q^{20} + 72 q^{22} - 120 q^{23} - 50 q^{25} + 80 q^{26}+ \cdots + 1368 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 10 * q^5 + 26 * q^7 - 32 * q^8 + 40 * q^10 - 36 * q^11 + 20 * q^13 - 52 * q^14 - 32 * q^16 + 180 * q^17 - 76 * q^19 + 40 * q^20 + 72 * q^22 - 120 * q^23 - 50 * q^25 + 80 * q^26 - 208 * q^28 - 324 * q^29 + 38 * q^31 + 64 * q^32 + 180 * q^34 + 260 * q^35 - 292 * q^37 - 76 * q^38 - 80 * q^40 - 252 * q^41 + 422 * q^43 + 288 * q^44 - 480 * q^46 + 366 * q^47 + 342 * q^49 + 100 * q^50 + 80 * q^52 - 324 * q^53 - 360 * q^55 - 208 * q^56 + 648 * q^58 - 72 * q^59 + 368 * q^61 + 152 * q^62 + 256 * q^64 - 100 * q^65 + 296 * q^67 - 360 * q^68 + 260 * q^70 + 480 * q^71 - 1420 * q^73 - 292 * q^74 + 152 * q^76 + 534 * q^77 - 520 * q^79 - 320 * q^80 - 1008 * q^82 - 66 * q^83 + 450 * q^85 - 844 * q^86 + 288 * q^88 + 2496 * q^89 + 496 * q^91 - 480 * q^92 - 732 * q^94 - 190 * q^95 + 1706 * q^97 + 1368 * q^98

Character values

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

$n$	$487$	$731$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$7$	7.36603	−	12.7583i	0.397728	−	0.688885i	−0.595717	−	0.803194i	$-0.703132\pi$
$7$	7.36603	−	12.7583i	0.397728	−	0.688885i	0.993445	+	0.114309i	$0.0364654\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	10.0000			0.316228
$11$	−18.5263	+	32.0885i	−0.507808	+	0.879549i	0.492152	+	0.870510i	$0.336211\pi$
$11$	−18.5263	+	32.0885i	−0.507808	+	0.879549i	−0.999959	+	0.00903901i	$0.997123\pi$
$12$		0			0
$13$	3.26795	+	5.66025i	0.0697205	+	0.120759i	0.898778	−	0.438404i	$-0.144456\pi$
$13$	3.26795	+	5.66025i	0.0697205	+	0.120759i	−0.829058	+	0.559163i	$0.811123\pi$
$14$	−14.7321	−	25.5167i	−0.281236	−	0.487115i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−46.7987			−0.667668			−0.333834	−	0.942632i	$-0.608342\pi$
$17$	−46.7987			−0.667668			−0.333834	+	0.942632i	$0.608342\pi$
$18$		0			0
$19$	8.71281			0.105203			0.0526015	−	0.998616i	$-0.483249\pi$
$19$	8.71281			0.105203			0.0526015	+	0.998616i	$0.483249\pi$
$20$	10.0000	−	17.3205i	0.111803	−	0.193649i
$21$		0			0
$22$	37.0526	+	64.1769i	0.359074	+	0.621935i
$23$	−49.0526	−	84.9615i	−0.444703	−	0.770248i	0.553329	−	0.832963i	$-0.313357\pi$
$23$	−49.0526	−	84.9615i	−0.444703	−	0.770248i	−0.998031	+	0.0627151i	$0.980024\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	13.0718			0.0985996
$27$		0			0
$28$	−58.9282			−0.397728
$29$	−107.847	+	186.796i	−0.690574	+	1.19611i	0.281076	+	0.959685i	$0.409309\pi$
$29$	−107.847	+	186.796i	−0.690574	+	1.19611i	−0.971650	+	0.236424i	$0.924025\pi$
$30$		0			0
$31$	−9.55256	−	16.5455i	−0.0553448	−	0.0958601i	0.837026	−	0.547164i	$-0.184292\pi$
$31$	−9.55256	−	16.5455i	−0.0553448	−	0.0958601i	−0.892370	+	0.451304i	$0.850959\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	−46.7987	+	81.0577i	−0.236056	+	0.408861i
$35$	73.6603			0.355739
$36$		0			0
$37$	−369.181			−1.64035			−0.820175	−	0.572113i	$-0.806124\pi$
$37$	−369.181			−1.64035			−0.820175	+	0.572113i	$0.806124\pi$
$38$	8.71281	−	15.0910i	0.0371949	−	0.0644234i
$39$		0			0
$40$	−20.0000	−	34.6410i	−0.0790569	−	0.136931i
$41$	−91.5788	−	158.619i	−0.348834	−	0.604199i	0.637208	−	0.770692i	$-0.280089\pi$
$41$	−91.5788	−	158.619i	−0.348834	−	0.604199i	−0.986043	+	0.166493i	$0.946756\pi$
$42$		0			0
$43$	33.6199	−	58.2314i	0.119232	−	0.206516i	−0.800231	−	0.599691i	$-0.795290\pi$
$43$	33.6199	−	58.2314i	0.119232	−	0.206516i	0.919464	+	0.393175i	$0.128623\pi$
$44$	148.210			0.507808
$45$		0			0
$46$	−196.210			−0.628905
$47$	−58.3224	+	101.017i	−0.181004	+	0.313508i	−0.942223	−	0.334987i	$-0.891268\pi$
$47$	−58.3224	+	101.017i	−0.181004	+	0.313508i	0.761219	+	0.648495i	$0.224601\pi$
$48$		0			0
$49$	62.9833	+	109.090i	0.183625	+	0.318048i
$50$	25.0000	+	43.3013i	0.0707107	+	0.122474i
$51$		0			0
$52$	13.0718	−	22.6410i	0.0348602	−	0.0603797i
$53$	−51.5551			−0.133616			−0.0668079	−	0.997766i	$-0.521281\pi$
$53$	−51.5551			−0.133616			−0.0668079	+	0.997766i	$0.521281\pi$
$54$		0			0
$55$	−185.263			−0.454197
$56$	−58.9282	+	102.067i	−0.140618	+	0.243558i
$57$		0			0
$58$	215.694	+	373.592i	0.488310	+	0.845777i
$59$	292.903	+	507.323i	0.646318	+	1.11945i	0.983996	+	0.178193i	$0.0570252\pi$
$59$	292.903	+	507.323i	0.646318	+	1.11945i	−0.337678	+	0.941262i	$0.609641\pi$
$60$		0			0
$61$	164.746	−	285.349i	0.345796	−	0.598937i	−0.639702	−	0.768623i	$-0.720942\pi$
$61$	164.746	−	285.349i	0.345796	−	0.598937i	0.985498	+	0.169686i	$0.0542754\pi$
$62$	−38.2102			−0.0782694
$63$		0			0
$64$	64.0000			0.125000
$65$	−16.3397	+	28.3013i	−0.0311799	+	0.0540052i
$66$		0			0
$67$	−191.004	−	330.828i	−0.348281	−	0.603240i	0.637663	−	0.770315i	$-0.279901\pi$
$67$	−191.004	−	330.828i	−0.348281	−	0.603240i	−0.985944	+	0.167075i	$0.946568\pi$
$68$	93.5974	+	162.115i	0.166917	+	0.289109i
$69$		0			0
$70$	73.6603	−	127.583i	0.125773	−	0.217845i
$71$	−332.065			−0.555055			−0.277527	−	0.960718i	$-0.589515\pi$
$71$	−332.065			−0.555055			−0.277527	+	0.960718i	$0.589515\pi$
$72$		0			0
$73$	−817.458			−1.31063			−0.655316	−	0.755355i	$-0.727465\pi$
$73$	−817.458			−1.31063			−0.655316	+	0.755355i	$0.727465\pi$
$74$	−369.181	+	639.440i	−0.579951	+	1.00450i
$75$		0			0
$76$	−17.4256	−	30.1821i	−0.0263007	−	0.0455542i
$77$	272.930	+	472.729i	0.403939	+	0.699642i
$78$		0			0
$79$	−311.865	+	540.167i	−0.444147	+	0.769285i	−0.997992	−	0.0633347i	$-0.979826\pi$
$79$	−311.865	+	540.167i	−0.444147	+	0.769285i	0.553846	+	0.832619i	$0.313160\pi$
$80$	−80.0000			−0.111803
$81$		0			0
$82$	−366.315			−0.493326
$83$	−505.804	+	876.079i	−0.668907	+	1.15858i	0.309304	+	0.950963i	$0.399904\pi$
$83$	−505.804	+	876.079i	−0.668907	+	1.15858i	−0.978210	+	0.207617i	$0.933429\pi$
$84$		0			0
$85$	−116.997	−	202.644i	−0.149295	−	0.258587i
$86$	−67.2398	−	116.463i	−0.0843099	−	0.146029i
$87$		0			0
$88$	148.210	−	256.708i	0.179537	−	0.310967i
$89$	670.765			0.798887			0.399444	−	0.916758i	$-0.369203\pi$
$89$	670.765			0.798887			0.399444	+	0.916758i	$0.369203\pi$
$90$		0			0
$91$	96.2872			0.110919
$92$	−196.210	+	339.846i	−0.222351	+	0.385124i
$93$		0			0
$94$	116.645	+	202.035i	0.127989	+	0.221684i
$95$	21.7820	+	37.7276i	0.0235241	+	0.0407449i
$96$		0			0
$97$	259.357	−	449.220i	0.271482	−	0.470220i	−0.697760	−	0.716332i	$-0.745820\pi$
$97$	259.357	−	449.220i	0.271482	−	0.470220i	0.969241	+	0.246112i	$0.0791530\pi$
$98$	251.933			0.259685
$99$		0			0
$100$	100.000			0.100000
$101$	−746.418	+	1292.83i	−0.735360	+	1.27368i	0.219205	+	0.975679i	$0.429654\pi$
$101$	−746.418	+	1292.83i	−0.735360	+	1.27368i	−0.954565	+	0.298003i	$0.903680\pi$
$102$		0			0
$103$	149.904	+	259.641i	0.143403	+	0.248380i	0.928776	−	0.370642i	$-0.120862\pi$
$103$	149.904	+	259.641i	0.143403	+	0.248380i	−0.785373	+	0.619022i	$0.787529\pi$
$104$	−26.1436	−	45.2820i	−0.0246499	−	0.0426949i
$105$		0			0
$106$	−51.5551	+	89.2961i	−0.0472404	+	0.0818227i
$107$	−2130.22			−1.92463			−0.962317	−	0.271929i	$-0.912339\pi$
$107$	−2130.22			−1.92463			−0.962317	+	0.271929i	$0.912339\pi$
$108$		0			0
$109$	−1288.88			−1.13259			−0.566296	−	0.824202i	$-0.691624\pi$
$109$	−1288.88			−1.13259			−0.566296	+	0.824202i	$0.691624\pi$
$110$	−185.263	+	320.885i	−0.160583	+	0.278138i
$111$		0			0
$112$	117.856	+	204.133i	0.0994320	+	0.172221i
$113$	564.934	+	978.494i	0.470305	+	0.814593i	0.999423	−	0.0339555i	$-0.0108104\pi$
$113$	564.934	+	978.494i	0.470305	+	0.814593i	−0.529118	+	0.848548i	$0.677477\pi$
$114$		0			0
$115$	245.263	−	424.808i	0.198877	−	0.344465i
$116$	862.774			0.690574
$117$		0			0
$118$	1171.61			0.914031
$119$	−344.720	+	597.073i	−0.265550	+	0.459946i
$120$		0			0
$121$	−20.9461	−	36.2796i	−0.0157371	−	0.0272574i
$122$	−329.492	−	570.697i	−0.244515	−	0.423512i
$123$		0			0
$124$	−38.2102	+	66.1821i	−0.0276724	+	0.0479300i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−1147.80			−0.801977			−0.400989	−	0.916083i	$-0.631333\pi$
$127$	−1147.80			−0.801977			−0.400989	+	0.916083i	$0.631333\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	32.6795	+	56.6025i	0.0220475	+	0.0381875i
$131$	1221.48	+	2115.67i	0.814666	+	1.41104i	0.909568	+	0.415556i	$0.136413\pi$
$131$	1221.48	+	2115.67i	0.814666	+	1.41104i	−0.0949022	+	0.995487i	$0.530254\pi$
$132$		0			0
$133$	64.1788	−	111.161i	0.0418422	−	0.0724728i
$134$	−764.015			−0.492544
$135$		0			0
$136$	374.390			0.236056
$137$	281.958	−	488.365i	0.175834	−	0.304554i	−0.764615	−	0.644487i	$-0.777071\pi$
$137$	281.958	−	488.365i	0.175834	−	0.304554i	0.940450	+	0.339933i	$0.110404\pi$
$138$		0			0
$139$	515.208	+	892.366i	0.314384	+	0.544529i	0.979306	−	0.202384i	$-0.0648688\pi$
$139$	515.208	+	892.366i	0.314384	+	0.544529i	−0.664923	+	0.746912i	$0.731535\pi$
$140$	−147.321	−	255.167i	−0.0889347	−	0.154039i
$141$		0			0
$142$	−332.065	+	575.154i	−0.196242	+	0.339900i
$143$	−242.172			−0.141618
$144$		0			0
$145$	−1078.47			−0.617668
$146$	−817.458	+	1415.88i	−0.463379	+	0.802595i
$147$		0			0
$148$	738.361	+	1278.88i	0.410087	+	0.710292i
$149$	505.892	+	876.231i	0.278150	+	0.481769i	0.970925	−	0.239384i	$-0.0769456\pi$
$149$	505.892	+	876.231i	0.278150	+	0.481769i	−0.692775	+	0.721154i	$0.743612\pi$
$150$		0			0
$151$	1634.59	−	2831.20i	0.880935	−	1.52582i	0.0306324	−	0.999531i	$-0.490248\pi$
$151$	1634.59	−	2831.20i	0.880935	−	1.52582i	0.850303	−	0.526294i	$-0.176419\pi$
$152$	−69.7025			−0.0371949
$153$		0			0
$154$	1091.72			0.571255
$155$	47.7628	−	82.7276i	0.0247510	−	0.0428699i
$156$		0			0
$157$	1327.35	+	2299.04i	0.674740	+	1.16868i	0.976545	+	0.215314i	$0.0690774\pi$
$157$	1327.35	+	2299.04i	0.674740	+	1.16868i	−0.301805	+	0.953370i	$0.597589\pi$
$158$	623.731	+	1080.33i	0.314059	+	0.543966i
$159$		0			0
$160$	−80.0000	+	138.564i	−0.0395285	+	0.0684653i
$161$	−1445.29			−0.707483
$162$		0			0
$163$	2159.78			1.03783			0.518917	−	0.854825i	$-0.326335\pi$
$163$	2159.78			1.03783			0.518917	+	0.854825i	$0.326335\pi$
$164$	−366.315	+	634.477i	−0.174417	+	0.302099i
$165$		0			0
$166$	1011.61	+	1752.16i	0.472988	+	0.819240i
$167$	392.919	+	680.555i	0.182066	+	0.315347i	0.942584	−	0.333970i	$-0.108388\pi$
$167$	392.919	+	680.555i	0.182066	+	0.315347i	−0.760518	+	0.649317i	$0.775055\pi$
$168$		0			0
$169$	1077.14	−	1865.66i	0.490278	−	0.849187i
$170$	−467.987			−0.211135
$171$		0			0
$172$	−268.959			−0.119232
$173$	107.476	−	186.154i	0.0472326	−	0.0818092i	−0.841443	−	0.540347i	$-0.818293\pi$
$173$	107.476	−	186.154i	0.0472326	−	0.0818092i	0.888675	+	0.458537i	$0.151626\pi$
$174$		0			0
$175$	184.151	+	318.958i	0.0795456	+	0.137777i
$176$	−296.420	−	513.415i	−0.126952	−	0.219887i
$177$		0			0
$178$	670.765	−	1161.80i	0.282449	−	0.489217i
$179$	56.5853			0.0236279			0.0118139	−	0.999930i	$-0.496239\pi$
$179$	56.5853			0.0236279			0.0118139	+	0.999930i	$0.496239\pi$
$180$		0			0
$181$	−28.3570			−0.0116451			−0.00582253	−	0.999983i	$-0.501853\pi$
$181$	−28.3570			−0.0116451			−0.00582253	+	0.999983i	$0.501853\pi$
$182$	96.2872	−	166.774i	0.0392158	−	0.0679238i
$183$		0			0
$184$	392.420	+	679.692i	0.157226	+	0.272324i
$185$	−922.952	−	1598.60i	−0.366793	−	0.635305i
$186$		0			0
$187$	867.006	−	1501.70i	0.339047	−	0.587246i
$188$	466.579			0.181004
$189$		0			0
$190$	87.1281			0.0332681
$191$	634.172	−	1098.42i	0.240247	−	0.416119i	−0.720538	−	0.693416i	$-0.756105\pi$
$191$	634.172	−	1098.42i	0.240247	−	0.416119i	0.960784	+	0.277296i	$0.0894383\pi$
$192$		0			0
$193$	−1668.84	−	2890.52i	−0.622415	−	1.07805i	−0.989035	−	0.147683i	$-0.952818\pi$
$193$	−1668.84	−	2890.52i	−0.622415	−	1.07805i	0.366620	−	0.930371i	$-0.380515\pi$
$194$	−518.714	−	898.439i	−0.191967	−	0.332496i
$195$		0			0
$196$	251.933	−	436.361i	0.0918124	−	0.159024i
$197$	−1107.59			−0.400571			−0.200285	−	0.979738i	$-0.564187\pi$
$197$	−1107.59			−0.400571			−0.200285	+	0.979738i	$0.564187\pi$
$198$		0			0
$199$	−2702.45			−0.962672			−0.481336	−	0.876536i	$-0.659848\pi$
$199$	−2702.45			−0.962672			−0.481336	+	0.876536i	$0.659848\pi$
$200$	100.000	−	173.205i	0.0353553	−	0.0612372i
$201$		0			0
$202$	1492.84	+	2585.67i	0.519978	+	0.900629i
$203$	1588.80	+	2751.89i	0.549321	+	0.951452i
$204$		0			0
$205$	457.894	−	793.096i	0.156004	−	0.270206i
$206$	599.615			0.202802
$207$		0			0
$208$	−104.574			−0.0348602
$209$	−161.416	+	279.581i	−0.0534229	+	0.0925311i
$210$		0			0
$211$	−1453.90	−	2518.23i	−0.474363	−	0.821621i	0.525206	−	0.850975i	$-0.323988\pi$
$211$	−1453.90	−	2518.23i	−0.474363	−	0.821621i	−0.999569	+	0.0293539i	$0.990655\pi$
$212$	103.110	+	178.592i	0.0334040	+	0.0578574i
$213$		0			0
$214$	−2130.22	+	3689.65i	−0.680461	+	1.17859i
$215$	336.199			0.106645
$216$		0			0
$217$	−281.458			−0.0880488
$218$	−1288.88	+	2232.41i	−0.400432	+	0.693568i
$219$		0			0
$220$	370.526	+	641.769i	0.113549	+	0.196673i
$221$	−152.936	−	264.892i	−0.0465501	−	0.0806271i
$222$		0			0
$223$	25.3431	−	43.8956i	0.00761033	−	0.0131815i	−0.862195	−	0.506576i	$-0.830911\pi$
$223$	25.3431	−	43.8956i	0.00761033	−	0.0131815i	0.869805	+	0.493395i	$0.164244\pi$
$224$	471.426			0.140618
$225$		0			0
$226$	2259.74			0.665112
$227$	883.571	−	1530.39i	0.258347	−	0.447469i	−0.707453	−	0.706761i	$-0.750156\pi$
$227$	883.571	−	1530.39i	0.258347	−	0.447469i	0.965799	+	0.259291i	$0.0834890\pi$
$228$		0			0
$229$	−3362.95	−	5824.80i	−0.970436	−	1.68084i	−0.694240	−	0.719743i	$-0.744260\pi$
$229$	−3362.95	−	5824.80i	−0.970436	−	1.68084i	−0.276196	−	0.961101i	$-0.589074\pi$
$230$	−490.526	−	849.615i	−0.140627	−	0.243574i
$231$		0			0
$232$	862.774	−	1494.37i	0.244155	−	0.422888i
$233$	−5993.32			−1.68513			−0.842565	−	0.538594i	$-0.818956\pi$
$233$	−5993.32			−1.68513			−0.842565	+	0.538594i	$0.818956\pi$
$234$		0			0
$235$	−583.224			−0.161895
$236$	1171.61	−	2029.29i	0.323159	−	0.559727i
$237$		0			0
$238$	689.441	+	1194.15i	0.187772	+	0.325231i
$239$	1644.24	+	2847.92i	0.445010	+	0.770780i	0.998053	−	0.0623731i	$-0.0198669\pi$
$239$	1644.24	+	2847.92i	0.445010	+	0.770780i	−0.553043	+	0.833153i	$0.686534\pi$
$240$		0			0
$241$	167.885	−	290.786i	0.0448732	−	0.0777227i	−0.842716	−	0.538358i	$-0.819045\pi$
$241$	167.885	−	290.786i	0.0448732	−	0.0777227i	0.887590	+	0.460635i	$0.152378\pi$
$242$	−83.7842			−0.0222556
$243$		0			0
$244$	−1317.97			−0.345796
$245$	−314.917	+	545.452i	−0.0821196	+	0.142235i
$246$		0			0
$247$	28.4730	+	49.3167i	0.00733480	+	0.0127042i
$248$	76.4205	+	132.364i	0.0195674	+	0.0338917i
$249$		0			0
$250$	−125.000	+	216.506i	−0.0316228	+	0.0547723i
$251$	360.587			0.0906774			0.0453387	−	0.998972i	$-0.485563\pi$
$251$	360.587			0.0906774			0.0453387	+	0.998972i	$0.485563\pi$
$252$		0			0
$253$	3635.05			0.903294
$254$	−1147.80	+	1988.05i	−0.283542	+	0.491109i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2911.59	−	5043.02i	−0.706693	−	1.22403i	−0.966077	−	0.258254i	$-0.916853\pi$
$257$	−2911.59	−	5043.02i	−0.706693	−	1.22403i	0.259384	−	0.965774i	$-0.416480\pi$
$258$		0			0
$259$	−2719.39	+	4710.13i	−0.652413	+	1.13001i
$260$	130.718			0.0311799
$261$		0			0
$262$	4885.92			1.15211
$263$	2606.08	−	4513.87i	0.611019	−	1.05832i	−0.380050	−	0.924966i	$-0.624093\pi$
$263$	2606.08	−	4513.87i	0.611019	−	1.05832i	0.991069	−	0.133350i	$-0.0425734\pi$
$264$		0			0
$265$	−128.888	−	223.240i	−0.0298774	−	0.0517492i
$266$	−128.358	−	222.322i	−0.0295869	−	0.0512460i
$267$		0			0
$268$	−764.015	+	1323.31i	−0.174140	+	0.301620i
$269$	4047.57			0.917415			0.458707	−	0.888587i	$-0.348313\pi$
$269$	4047.57			0.917415			0.458707	+	0.888587i	$0.348313\pi$
$270$		0			0
$271$	3004.68			0.673510			0.336755	−	0.941592i	$-0.390671\pi$
$271$	3004.68			0.673510			0.336755	+	0.941592i	$0.390671\pi$
$272$	374.390	−	648.462i	0.0834585	−	0.144554i
$273$		0			0
$274$	−563.916	−	976.730i	−0.124334	−	0.215352i
$275$	−463.157	−	802.211i	−0.101562	−	0.175910i
$276$		0			0
$277$	575.161	−	996.208i	0.124758	−	0.216088i	−0.796880	−	0.604138i	$-0.793518\pi$
$277$	575.161	−	996.208i	0.124758	−	0.216088i	0.921638	+	0.388050i	$0.126851\pi$
$278$	2060.83			0.444606
$279$		0			0
$280$	−589.282			−0.125773
$281$	1240.98	−	2149.45i	0.263455	−	0.456317i	−0.703703	−	0.710495i	$-0.748471\pi$
$281$	1240.98	−	2149.45i	0.263455	−	0.456317i	0.967158	+	0.254177i	$0.0818046\pi$
$282$		0			0
$283$	−382.137	−	661.881i	−0.0802675	−	0.139027i	0.823097	−	0.567900i	$-0.192244\pi$
$283$	−382.137	−	661.881i	−0.0802675	−	0.139027i	−0.903365	+	0.428873i	$0.858911\pi$
$284$	664.131	+	1150.31i	0.138764	+	0.240346i
$285$		0			0
$286$	−242.172	+	419.454i	−0.0500696	+	0.0867232i
$287$	−2698.29			−0.554965
$288$		0			0
$289$	−2722.88			−0.554220
$290$	−1078.47	+	1867.96i	−0.218379	+	0.378243i
$291$		0			0
$292$	1634.92	+	2831.76i	0.327658	+	0.567521i
$293$	1584.80	+	2744.95i	0.315989	+	0.547310i	0.979647	−	0.200726i	$-0.0643303\pi$
$293$	1584.80	+	2744.95i	0.315989	+	0.547310i	−0.663658	+	0.748036i	$0.730997\pi$
$294$		0			0
$295$	−1464.52	+	2536.62i	−0.289042	+	0.500635i
$296$	2953.45			0.579951
$297$		0			0
$298$	2023.57			0.393363
$299$	320.603	−	555.300i	0.0620098	−	0.107404i
$300$		0			0
$301$	−495.290	−	857.867i	−0.0948440	−	0.164275i
$302$	−3269.18	−	5662.39i	−0.622915	−	1.07892i
$303$		0			0
$304$	−69.7025	+	120.728i	−0.0131504	+	0.0227771i
$305$	1647.46			0.309290
$306$		0			0
$307$	−7582.99			−1.40972			−0.704860	−	0.709347i	$-0.748990\pi$
$307$	−7582.99			−1.40972			−0.704860	+	0.709347i	$0.748990\pi$
$308$	1091.72	−	1890.92i	0.201969	−	0.349821i
$309$		0			0
$310$	−95.5256	−	165.455i	−0.0175016	−	0.0303136i
$311$	1059.58	+	1835.25i	0.193194	+	0.334621i	0.946307	−	0.323270i	$-0.104782\pi$
$311$	1059.58	+	1835.25i	0.193194	+	0.334621i	−0.753113	+	0.657891i	$0.771449\pi$
$312$		0			0
$313$	2017.20	−	3493.89i	0.364277	−	0.630946i	−0.624383	−	0.781118i	$-0.714649\pi$
$313$	2017.20	−	3493.89i	0.364277	−	0.630946i	0.988660	+	0.150172i	$0.0479828\pi$
$314$	5309.40			0.954226
$315$		0			0
$316$	2494.92			0.444147
$317$	−277.935	+	481.397i	−0.0492440	+	0.0852932i	−0.889597	−	0.456747i	$-0.849015\pi$
$317$	−277.935	+	481.397i	−0.0492440	+	0.0852932i	0.840353	+	0.542040i	$0.182348\pi$
$318$		0			0
$319$	−3996.00	−	6921.27i	−0.701357	−	1.21479i
$320$	160.000	+	277.128i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−1445.29	+	2503.31i	−0.250133	+	0.433243i
$323$	−407.748			−0.0702406
$324$		0			0
$325$	−163.397			−0.0278882
$326$	2159.78	−	3740.84i	0.366930	−	0.635541i
$327$		0			0
$328$	732.631	+	1268.95i	0.123332	+	0.213617i
$329$	859.208	+	1488.19i	0.143981	+	0.249382i
$330$		0			0
$331$	−3219.31	+	5576.00i	−0.534589	+	0.925936i	0.464594	+	0.885524i	$0.346200\pi$
$331$	−3219.31	+	5576.00i	−0.534589	+	0.925936i	−0.999183	+	0.0404121i	$0.987133\pi$
$332$	4046.43			0.668907
$333$		0			0
$334$	1571.68			0.257480
$335$	955.019	−	1654.14i	0.155756	−	0.269777i
$336$		0			0
$337$	−195.337	−	338.333i	−0.0315747	−	0.0546889i	0.849806	−	0.527095i	$-0.176719\pi$
$337$	−195.337	−	338.333i	−0.0315747	−	0.0546889i	−0.881381	+	0.472406i	$0.843386\pi$
$338$	−2154.28	−	3731.33i	−0.346679	−	0.600466i
$339$		0			0
$340$	−467.987	+	810.577i	−0.0746475	+	0.129293i
$341$	707.894			0.112418
$342$		0			0
$343$	6908.84			1.08759
$344$	−268.959	+	465.851i	−0.0421550	+	0.0730145i
$345$		0			0
$346$	−214.952	−	372.307i	−0.0333985	−	0.0578478i
$347$	−3970.25	−	6876.68i	−0.614220	−	1.06386i	−0.990521	−	0.137363i	$-0.956137\pi$
$347$	−3970.25	−	6876.68i	−0.614220	−	1.06386i	0.376300	−	0.926498i	$-0.377196\pi$
$348$		0			0
$349$	−5570.57	+	9648.51i	−0.854400	+	1.47986i	0.0227998	+	0.999740i	$0.492742\pi$
$349$	−5570.57	+	9648.51i	−0.854400	+	1.47986i	−0.877200	+	0.480125i	$0.840591\pi$
$350$	736.603			0.112494
$351$		0			0
$352$	−1185.68			−0.179537
$353$	5456.27	−	9450.54i	0.822686	−	1.42493i	−0.0809890	−	0.996715i	$-0.525808\pi$
$353$	5456.27	−	9450.54i	0.822686	−	1.42493i	0.903675	−	0.428219i	$-0.140859\pi$
$354$		0			0
$355$	−830.163	−	1437.88i	−0.124114	−	0.214972i
$356$	−1341.53	−	2323.60i	−0.199722	−	0.345928i
$357$		0			0
$358$	56.5853	−	98.0087i	0.00835371	−	0.0144690i
$359$	13534.9			1.98982			0.994908	−	0.100784i	$-0.0321351\pi$
$359$	13534.9			1.98982			0.994908	+	0.100784i	$0.0321351\pi$
$360$		0			0
$361$	−6783.09			−0.988932
$362$	−28.3570	+	49.1157i	−0.00411715	+	0.00713112i
$363$		0			0
$364$	−192.574	−	333.549i	−0.0277298	−	0.0480294i
$365$	−2043.64	−	3539.70i	−0.293066	−	0.507606i
$366$		0			0
$367$	−901.642	+	1561.69i	−0.128243	+	0.222124i	−0.922996	−	0.384809i	$-0.874267\pi$
$367$	−901.642	+	1561.69i	−0.128243	+	0.222124i	0.794753	+	0.606933i	$0.207601\pi$
$368$	1569.68			0.222351
$369$		0			0
$370$	−3691.81			−0.518724
$371$	−379.756	+	657.757i	−0.0531428	+	0.0920460i
$372$		0			0
$373$	−994.174	−	1721.96i	−0.138006	−	0.239034i	0.788736	−	0.614733i	$-0.210736\pi$
$373$	−994.174	−	1721.96i	−0.138006	−	0.239034i	−0.926742	+	0.375699i	$0.877403\pi$
$374$	−1734.01	−	3003.40i	−0.239742	−	0.415246i
$375$		0			0
$376$	466.579	−	808.139i	0.0639946	−	0.110842i
$377$	−1409.75			−0.192589
$378$		0			0
$379$	−10809.6			−1.46504			−0.732522	−	0.680743i	$-0.761657\pi$
$379$	−10809.6			−1.46504			−0.732522	+	0.680743i	$0.761657\pi$
$380$	87.1281	−	150.910i	0.0117620	−	0.0203725i
$381$		0			0
$382$	−1268.34	−	2196.84i	−0.169880	−	0.294241i
$383$	−2723.27	−	4716.85i	−0.363323	−	0.629294i	0.625182	−	0.780479i	$-0.285025\pi$
$383$	−2723.27	−	4716.85i	−0.363323	−	0.629294i	−0.988506	+	0.151184i	$0.951691\pi$
$384$		0			0
$385$	−1364.65	+	2363.64i	−0.180647	+	0.312889i
$386$	−6675.38			−0.880227
$387$		0			0
$388$	−2074.86			−0.271482
$389$	−2389.81	+	4139.27i	−0.311486	+	0.539509i	−0.978684	−	0.205371i	$-0.934160\pi$
$389$	−2389.81	+	4139.27i	−0.311486	+	0.539509i	0.667198	+	0.744880i	$0.267493\pi$
$390$		0			0
$391$	2295.60	+	3976.09i	0.296914	+	0.514270i
$392$	−503.867	−	872.723i	−0.0649212	−	0.112447i
$393$		0			0
$394$	−1107.59	+	1918.40i	−0.141623	+	0.245299i
$395$	−3118.65			−0.397257
$396$		0			0
$397$	11892.7			1.50347			0.751737	−	0.659463i	$-0.229216\pi$
$397$	11892.7			1.50347			0.751737	+	0.659463i	$0.229216\pi$
$398$	−2702.45	+	4680.78i	−0.340356	+	0.589514i
$399$		0			0
$400$	−200.000	−	346.410i	−0.0250000	−	0.0433013i
$401$	−1602.23	−	2775.14i	−0.199530	−	0.345596i	0.748846	−	0.662744i	$-0.230608\pi$
$401$	−1602.23	−	2775.14i	−0.199530	−	0.345596i	−0.948376	+	0.317148i	$0.897275\pi$
$402$		0			0
$403$	62.4346	−	108.140i	0.00771734	−	0.0133668i
$404$	5971.35			0.735360
$405$		0			0
$406$	6355.22			0.776857
$407$	6839.54	−	11846.4i	0.832982	−	1.44277i
$408$		0			0
$409$	−7652.31	−	13254.2i	−0.925140	−	1.60239i	−0.791336	−	0.611382i	$-0.790614\pi$
$409$	−7652.31	−	13254.2i	−0.925140	−	1.60239i	−0.133805	−	0.991008i	$-0.542719\pi$
$410$	−915.788	−	1586.19i	−0.110311	−	0.191064i
$411$		0			0
$412$	599.615	−	1038.56i	0.0717013	−	0.124190i
$413$	8630.13			1.02823
$414$		0			0
$415$	−5058.04			−0.598288
$416$	−104.574	+	181.128i	−0.0123250	+	0.0213474i
$417$		0			0
$418$	322.832	+	559.161i	0.0377757	+	0.0654294i
$419$	−6626.55	−	11477.5i	−0.772621	−	1.33822i	−0.936122	−	0.351676i	$-0.885612\pi$
$419$	−6626.55	−	11477.5i	−0.772621	−	1.33822i	0.163501	−	0.986543i	$-0.447721\pi$
$420$		0			0
$421$	4718.63	−	8172.91i	0.546252	−	0.946136i	−0.452275	−	0.891878i	$-0.649388\pi$
$421$	4718.63	−	8172.91i	0.546252	−	0.946136i	0.998527	−	0.0542573i	$-0.0172791\pi$
$422$	−5815.60			−0.670851
$423$		0			0
$424$	412.441			0.0472404
$425$	584.984	−	1013.22i	0.0667668	−	0.115643i
$426$		0			0
$427$	−2427.05	−	4203.77i	−0.275066	−	0.476428i
$428$	4260.44	+	7379.29i	0.481159	+	0.833391i
$429$		0			0
$430$	336.199	−	582.314i	0.0377045	−	0.0653062i
$431$	−8049.50			−0.899608			−0.449804	−	0.893127i	$-0.648506\pi$
$431$	−8049.50			−0.899608			−0.449804	+	0.893127i	$0.648506\pi$
$432$		0			0
$433$	16268.1			1.80554			0.902768	−	0.430129i	$-0.141532\pi$
$433$	16268.1			1.80554			0.902768	+	0.430129i	$0.141532\pi$
$434$	−281.458	+	487.499i	−0.0311299	+	0.0539186i
$435$		0			0
$436$	2577.76	+	4464.82i	0.283148	+	0.490427i
$437$	−427.386	−	740.254i	−0.0467841	−	0.0810324i
$438$		0			0
$439$	−6765.96	+	11719.0i	−0.735585	+	1.27407i	0.218882	+	0.975751i	$0.429759\pi$
$439$	−6765.96	+	11719.0i	−0.735585	+	1.27407i	−0.954466	+	0.298319i	$0.903574\pi$
$440$	1482.10			0.160583
$441$		0			0
$442$	−611.743			−0.0658318
$443$	6828.46	−	11827.2i	0.732347	−	1.26846i	−0.223530	−	0.974697i	$-0.571758\pi$
$443$	6828.46	−	11827.2i	0.732347	−	1.26846i	0.955877	−	0.293766i	$-0.0949086\pi$
$444$		0			0
$445$	1676.91	+	2904.50i	0.178637	+	0.309408i
$446$	−50.6863	−	87.7912i	−0.00538131	−	0.00932071i
$447$		0			0
$448$	471.426	−	816.533i	0.0497160	−	0.0861106i
$449$	754.853			0.0793402			0.0396701	−	0.999213i	$-0.487369\pi$
$449$	754.853			0.0793402			0.0396701	+	0.999213i	$0.487369\pi$
$450$		0			0
$451$	6786.46			0.708563
$452$	2259.74	−	3913.98i	0.235153	−	0.407296i
$453$		0			0
$454$	−1767.14	−	3060.78i	−0.182679	−	0.316409i
$455$	240.718	+	416.936i	0.0248023	+	0.0429588i
$456$		0			0
$457$	5936.95	−	10283.1i	0.607699	−	1.05257i	−0.383919	−	0.923367i	$-0.625426\pi$
$457$	5936.95	−	10283.1i	0.607699	−	1.05257i	0.991619	−	0.129200i	$-0.0412408\pi$
$458$	−13451.8			−1.37240
$459$		0			0
$460$	−1962.10			−0.198877
$461$	4098.55	−	7098.90i	0.414075	−	0.717199i	−0.581256	−	0.813721i	$-0.697438\pi$
$461$	4098.55	−	7098.90i	0.414075	−	0.717199i	0.995331	+	0.0965218i	$0.0307718\pi$
$462$		0			0
$463$	96.3572	+	166.896i	0.00967192	+	0.0167523i	0.870821	−	0.491600i	$-0.163588\pi$
$463$	96.3572	+	166.896i	0.00967192	+	0.0167523i	−0.861149	+	0.508353i	$0.830255\pi$
$464$	−1725.55	−	2988.74i	−0.172643	−	0.299027i
$465$		0			0
$466$	−5993.32	+	10380.7i	−0.595784	+	1.03193i
$467$	−5254.00			−0.520613			−0.260306	−	0.965526i	$-0.583824\pi$
$467$	−5254.00			−0.520613			−0.260306	+	0.965526i	$0.583824\pi$
$468$		0			0
$469$	−5627.75			−0.554084
$470$	−583.224	+	1010.17i	−0.0572385	+	0.0991401i
$471$		0			0
$472$	−2343.22	−	4058.58i	−0.228508	−	0.395787i
$473$	1245.70	+	2157.62i	0.121094	+	0.209741i
$474$		0			0
$475$	−108.910	+	188.638i	−0.0105203	+	0.0182217i
$476$	2757.76			0.265550
$477$		0			0
$478$	6576.98			0.629339
$479$	−7626.31	+	13209.2i	−0.727463	+	1.26000i	0.230489	+	0.973075i	$0.425968\pi$
$479$	−7626.31	+	13209.2i	−0.727463	+	1.26000i	−0.957952	+	0.286928i	$0.907366\pi$
$480$		0			0
$481$	−1206.46	−	2089.66i	−0.114366	−	0.198088i
$482$	−335.771	−	581.572i	−0.0317302	−	0.0549583i
$483$		0			0
$484$	−83.7842	+	145.119i	−0.00786854	+	0.0136287i
$485$	2593.57			0.242821
$486$		0			0
$487$	−11485.1			−1.06867			−0.534333	−	0.845274i	$-0.679437\pi$
$487$	−11485.1			−1.06867			−0.534333	+	0.845274i	$0.679437\pi$
$488$	−1317.97	+	2282.79i	−0.122257	+	0.211756i
$489$		0			0
$490$	629.833	+	1090.90i	0.0580673	+	0.100575i
$491$	6944.60	+	12028.4i	0.638301	+	1.10557i	0.985806	+	0.167891i	$0.0536956\pi$
$491$	6944.60	+	12028.4i	0.638301	+	1.10557i	−0.347505	+	0.937678i	$0.612971\pi$
$492$		0			0
$493$	5047.09	−	8741.81i	0.461074	−	0.798603i
$494$	113.892			0.0103730
$495$		0			0
$496$	305.682			0.0276724
$497$	−2446.00	+	4236.60i	−0.220761	+	0.382369i
$498$		0			0
$499$	9974.98	+	17277.2i	0.894873	+	1.54997i	0.833962	+	0.551822i	$0.186067\pi$
$499$	9974.98	+	17277.2i	0.894873	+	1.54997i	0.0609111	+	0.998143i	$0.480599\pi$
$500$	250.000	+	433.013i	0.0223607	+	0.0387298i
$501$		0			0
$502$	360.587	−	624.554i	0.0320593	−	0.0555283i
$503$	−978.744			−0.0867595			−0.0433797	−	0.999059i	$-0.513813\pi$
$503$	−978.744			−0.0867595			−0.0433797	+	0.999059i	$0.513813\pi$
$504$		0			0
$505$	−7464.18			−0.657726
$506$	3635.05	−	6296.08i	0.319363	−	0.553152i
$507$		0			0
$508$	2295.61	+	3976.11i	0.200494	+	0.347266i
$509$	−5567.91	−	9643.90i	−0.484859	−	0.839800i	0.514990	−	0.857196i	$-0.327796\pi$
$509$	−5567.91	−	9643.90i	−0.484859	−	0.839800i	−0.999849	+	0.0173960i	$0.994462\pi$
$510$		0			0
$511$	−6021.41	+	10429.4i	−0.521275	+	0.902875i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−11646.4			−0.999414
$515$	−749.519	+	1298.21i	−0.0641316	+	0.111079i
$516$		0			0
$517$	−2160.99	−	3742.95i	−0.183831	−	0.318404i
$518$	5438.79	+	9420.26i	0.461326	+	0.799039i
$519$		0			0
$520$	130.718	−	226.410i	0.0110238	−	0.0190937i
$521$	−1429.84			−0.120235			−0.0601174	−	0.998191i	$-0.519148\pi$
$521$	−1429.84			−0.120235			−0.0601174	+	0.998191i	$0.519148\pi$
$522$		0			0
$523$	11997.2			1.00306			0.501529	−	0.865141i	$-0.332771\pi$
$523$	11997.2			1.00306			0.501529	+	0.865141i	$0.332771\pi$
$524$	4885.92	−	8462.66i	0.407333	−	0.705521i
$525$		0			0
$526$	−5212.17	−	9027.74i	−0.432056	−	0.748342i
$527$	447.047	+	774.309i	0.0369520	+	0.0640027i
$528$		0			0
$529$	1271.19	−	2201.77i	0.104479	−	0.180963i
$530$	−515.551			−0.0422531
$531$		0			0
$532$	−513.430			−0.0418422
$533$	598.550	−	1036.72i	0.0486418	−	0.0842501i
$534$		0			0
$535$	−5325.54	−	9224.11i	−0.430361	−	0.745408i
$536$	1528.03	+	2646.63i	0.123136	+	0.213278i
$537$		0			0
$538$	4047.57	−	7010.59i	0.324355	−	0.561799i
$539$	−4667.39			−0.372984
$540$		0			0
$541$	13340.1			1.06014			0.530070	−	0.847954i	$-0.322166\pi$
$541$	13340.1			1.06014			0.530070	+	0.847954i	$0.322166\pi$
$542$	3004.68	−	5204.25i	0.238122	−	0.412439i
$543$		0			0
$544$	−748.779	−	1296.92i	−0.0590140	−	0.102215i
$545$	−3222.20	−	5581.02i	−0.253255	−	0.438651i
$546$		0			0
$547$	5363.18	−	9289.29i	0.419219	−	0.726109i	−0.576642	−	0.816997i	$-0.695637\pi$
$547$	5363.18	−	9289.29i	0.419219	−	0.726109i	0.995861	+	0.0908881i	$0.0289706\pi$
$548$	−2255.66			−0.175834
$549$		0			0
$550$	−1852.63			−0.143630
$551$	−939.649	+	1627.52i	−0.0726504	+	0.125834i
$552$		0			0
$553$	4594.42	+	7957.76i	0.353299	+	0.611932i
$554$	−1150.32	−	1992.42i	−0.0882175	−	0.152797i
$555$		0			0
$556$	2060.83	−	3569.46i	0.157192	−	0.272264i
$557$	16993.1			1.29268			0.646338	−	0.763052i	$-0.276300\pi$
$557$	16993.1			1.29268			0.646338	+	0.763052i	$0.276300\pi$
$558$		0			0
$559$	439.472			0.0332517
$560$	−589.282	+	1020.67i	−0.0444673	+	0.0770197i
$561$		0			0
$562$	−2481.97	−	4298.89i	−0.186291	−	0.322665i
$563$	12960.2	+	22447.7i	0.970171	+	1.68039i	0.695028	+	0.718982i	$0.255392\pi$
$563$	12960.2	+	22447.7i	0.970171	+	1.68039i	0.275143	+	0.961403i	$0.411275\pi$
$564$		0			0
$565$	−2824.67	+	4892.47i	−0.210327	+	0.364297i
$566$	−1528.55			−0.113515
$567$		0			0
$568$	2656.52			0.196242
$569$	−5183.52	+	8978.12i	−0.381906	+	0.661481i	−0.991335	−	0.131360i	$-0.958066\pi$
$569$	−5183.52	+	8978.12i	−0.381906	+	0.661481i	0.609429	+	0.792841i	$0.291399\pi$
$570$		0			0
$571$	8391.71	+	14534.9i	0.615030	+	1.06526i	0.990379	+	0.138380i	$0.0441895\pi$
$571$	8391.71	+	14534.9i	0.615030	+	1.06526i	−0.375349	+	0.926884i	$0.622477\pi$
$572$	484.344	+	838.908i	0.0354046	+	0.0613225i
$573$		0			0
$574$	−2698.29	+	4673.57i	−0.196210	+	0.339845i
$575$	2452.63			0.177881
$576$		0			0
$577$	3580.35			0.258323			0.129161	−	0.991624i	$-0.458772\pi$
$577$	3580.35			0.258323			0.129161	+	0.991624i	$0.458772\pi$
$578$	−2722.88	+	4716.17i	−0.195946	+	0.339389i
$579$		0			0
$580$	2156.94	+	3735.92i	0.154417	+	0.267458i
$581$	7451.54	+	12906.4i	0.532086	+	0.921599i
$582$		0			0
$583$	955.125	−	1654.32i	0.0678512	−	0.117522i
$584$	6539.66			0.463379
$585$		0			0
$586$	6339.19			0.446877
$587$	−6503.27	+	11264.0i	−0.457272	+	0.792018i	−0.998816	−	0.0486543i	$-0.984507\pi$
$587$	−6503.27	+	11264.0i	−0.457272	+	0.792018i	0.541544	+	0.840673i	$0.317840\pi$
$588$		0			0
$589$	−83.2297	−	144.158i	−0.00582244	−	0.0100848i
$590$	2929.03	+	5073.23i	0.204384	+	0.354003i
$591$		0			0
$592$	2953.45	−	5115.52i	0.205044	−	0.355146i
$593$	2996.59			0.207513			0.103757	−	0.994603i	$-0.466914\pi$
$593$	2996.59			0.207513			0.103757	+	0.994603i	$0.466914\pi$
$594$		0			0
$595$	−3447.20			−0.237515
$596$	2023.57	−	3504.92i	0.139075	−	0.240885i
$597$		0			0
$598$	−641.205	−	1110.60i	−0.0438475	−	0.0759462i
$599$	−5808.70	−	10061.0i	−0.396222	−	0.686277i	0.597034	−	0.802216i	$-0.296346\pi$
$599$	−5808.70	−	10061.0i	−0.396222	−	0.686277i	−0.993256	+	0.115939i	$0.963012\pi$
$600$		0			0
$601$	13223.2	−	22903.3i	0.897483	−	1.55449i	0.0667820	−	0.997768i	$-0.478727\pi$
$601$	13223.2	−	22903.3i	0.897483	−	1.55449i	0.830701	−	0.556719i	$-0.187940\pi$
$602$	−1981.16			−0.134130
$603$		0			0
$604$	−13076.7			−0.880935
$605$	104.730	−	181.398i	0.00703784	−	0.0121899i
$606$		0			0
$607$	10007.7	+	17333.8i	0.669193	+	1.15908i	0.978130	+	0.207993i	$0.0666932\pi$
$607$	10007.7	+	17333.8i	0.669193	+	1.15908i	−0.308938	+	0.951082i	$0.599973\pi$
$608$	139.405	+	241.457i	0.00929872	+	0.0161058i
$609$		0			0
$610$	1647.46	−	2853.49i	0.109350	−	0.189400i
$611$	−762.378			−0.0504788
$612$		0			0
$613$	25246.4			1.66344			0.831722	−	0.555193i	$-0.187356\pi$
$613$	25246.4			1.66344			0.831722	+	0.555193i	$0.187356\pi$
$614$	−7582.99	+	13134.1i	−0.498411	+	0.863274i
$615$		0			0
$616$	−2183.44	−	3781.83i	−0.142814	−	0.247361i
$617$	10100.3	+	17494.1i	0.659029	+	1.14147i	0.980867	+	0.194677i	$0.0623658\pi$
$617$	10100.3	+	17494.1i	0.659029	+	1.14147i	−0.321839	+	0.946795i	$0.604301\pi$
$618$		0			0
$619$	−5815.74	+	10073.2i	−0.377632	+	0.654079i	−0.990717	−	0.135938i	$-0.956595\pi$
$619$	−5815.74	+	10073.2i	−0.377632	+	0.654079i	0.613085	+	0.790017i	$0.289928\pi$
$620$	−382.102			−0.0247510
$621$		0			0
$622$	4238.32			0.273217
$623$	4940.87	−	8557.85i	0.317740	−	0.550342i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−4034.39	−	6987.77i	−0.257583	−	0.446146i
$627$		0			0
$628$	5309.40	−	9196.15i	0.337370	−	0.584342i
$629$	17277.2			1.09521
$630$		0			0
$631$	3857.24			0.243351			0.121675	−	0.992570i	$-0.461173\pi$
$631$	3857.24			0.243351			0.121675	+	0.992570i	$0.461173\pi$
$632$	2494.92	−	4321.33i	0.157030	−	0.271983i
$633$		0			0
$634$	555.869	+	962.794i	0.0348208	+	0.0603114i
$635$	−2869.51	−	4970.14i	−0.179328	−	0.310604i
$636$		0			0
$637$	−411.653	+	713.003i	−0.0256048	+	0.0443489i
$638$	−15984.0			−0.991869
$639$		0			0
$640$	640.000			0.0395285
$641$	−9263.70	+	16045.2i	−0.570818	+	0.988685i	0.425665	+	0.904881i	$0.360040\pi$
$641$	−9263.70	+	16045.2i	−0.570818	+	0.988685i	−0.996482	+	0.0838040i	$0.973293\pi$
$642$		0			0
$643$	10774.9	+	18662.7i	0.660842	+	1.14461i	0.980395	+	0.197044i	$0.0631341\pi$
$643$	10774.9	+	18662.7i	0.660842	+	1.14461i	−0.319552	+	0.947569i	$0.603533\pi$
$644$	2890.58	+	5006.63i	0.176871	+	0.306349i
$645$		0			0
$646$	−407.748	+	706.241i	−0.0248338	+	0.0430134i
$647$	−28952.4			−1.75925			−0.879627	−	0.475664i	$-0.842208\pi$
$647$	−28952.4			−1.75925			−0.879627	+	0.475664i	$0.842208\pi$
$648$		0			0
$649$	−21705.6			−1.31282
$650$	−163.397	+	283.013i	−0.00985996	+	0.0170780i
$651$		0			0
$652$	−4319.56	−	7481.69i	−0.259458	−	0.449395i
$653$	−6232.62	−	10795.2i	−0.373509	−	0.646936i	0.616594	−	0.787282i	$-0.288512\pi$
$653$	−6232.62	−	10795.2i	−0.373509	−	0.646936i	−0.990103	+	0.140345i	$0.955179\pi$
$654$		0			0
$655$	−6107.40	+	10578.3i	−0.364330	+	0.631037i
$656$	2930.52			0.174417
$657$		0			0
$658$	3436.83			0.203620
$659$	−8102.37	+	14033.7i	−0.478943	+	0.829554i	−0.999708	−	0.0241459i	$-0.992313\pi$
$659$	−8102.37	+	14033.7i	−0.478943	+	0.829554i	0.520765	+	0.853700i	$0.325647\pi$
$660$		0			0
$661$	14262.1	+	24702.7i	0.839231	+	1.45359i	0.890538	+	0.454908i	$0.150328\pi$
$661$	14262.1	+	24702.7i	0.839231	+	1.45359i	−0.0513071	+	0.998683i	$0.516339\pi$
$662$	6438.61	+	11152.0i	0.378012	+	0.654736i
$663$		0			0
$664$	4046.43	−	7008.63i	0.236494	−	0.409620i
$665$	641.788			0.0374248
$666$		0			0
$667$	21160.6			1.22840
$668$	1571.68	−	2722.22i	0.0910328	−	0.157673i
$669$		0			0
$670$	−1910.04	−	3308.28i	−0.110136	−	0.190761i
$671$	6104.27	+	10572.9i	0.351196	+	0.608289i
$672$		0			0
$673$	3314.19	−	5740.35i	0.189826	−	0.328788i	−0.755366	−	0.655303i	$-0.772541\pi$
$673$	3314.19	−	5740.35i	0.189826	−	0.328788i	0.945192	+	0.326515i	$0.105874\pi$
$674$	−781.346			−0.0446533
$675$		0			0
$676$	−8617.13			−0.490278
$677$	−11813.3	+	20461.2i	−0.670637	+	1.16158i	0.307086	+	0.951682i	$0.400646\pi$
$677$	−11813.3	+	20461.2i	−0.670637	+	1.16158i	−0.977724	+	0.209896i	$0.932687\pi$
$678$		0			0
$679$	−3820.86	−	6617.93i	−0.215952	−	0.374039i
$680$	935.974	+	1621.15i	0.0527838	+	0.0914242i
$681$		0			0
$682$	707.894	−	1226.11i	0.0397458	−	0.0688418i
$683$	−22943.8			−1.28539			−0.642693	−	0.766124i	$-0.722183\pi$
$683$	−22943.8			−1.28539			−0.642693	+	0.766124i	$0.722183\pi$
$684$		0			0
$685$	2819.58			0.157271
$686$	6908.84	−	11966.5i	0.384520	−	0.666008i
$687$		0			0
$688$	537.918	+	931.702i	0.0298081	+	0.0516291i
$689$	−168.480	−	291.815i	−0.00931576	−	0.0161354i
$690$		0			0
$691$	8859.93	−	15345.8i	0.487768	−	0.844839i	−0.512133	−	0.858906i	$-0.671145\pi$
$691$	8859.93	−	15345.8i	0.487768	−	0.844839i	0.999901	+	0.0140673i	$0.00447790\pi$
$692$	−859.806			−0.0472326
$693$		0			0
$694$	−15881.0			−0.868639
$695$	−2576.04	+	4461.83i	−0.140597	+	0.243521i
$696$		0			0
$697$	4285.77	+	7423.17i	0.232905	+	0.403404i
$698$	11141.1	+	19297.0i	0.604152	+	1.04642i
$699$		0			0
$700$	736.603	−	1275.83i	0.0397728	−	0.0688885i
$701$	−27863.4			−1.50126			−0.750632	−	0.660721i	$-0.770251\pi$
$701$	−27863.4			−1.50126			−0.750632	+	0.660721i	$0.770251\pi$
$702$		0			0
$703$	−3216.60			−0.172570
$704$	−1185.68	+	2053.66i	−0.0634759	+	0.109944i
$705$		0			0
$706$	−10912.5	−	18901.1i	−0.581727	−	1.00758i
$707$	10996.3	+	19046.1i	0.584947	+	1.01316i
$708$		0			0
$709$	−2481.96	+	4298.88i	−0.131470	+	0.227712i	−0.924243	−	0.381804i	$-0.875303\pi$
$709$	−2481.96	+	4298.88i	−0.131470	+	0.227712i	0.792774	+	0.609516i	$0.208636\pi$
$710$	−3320.65			−0.175524
$711$		0			0
$712$	−5366.12			−0.282449
$713$	−937.155	+	1623.20i	−0.0492240	+	0.0852585i
$714$		0			0
$715$	−605.429	−	1048.63i	−0.0316668	−	0.0548485i
$716$	−113.171	−	196.017i	−0.00590696	−	0.0102312i
$717$		0			0
$718$	13534.9	−	23443.1i	0.703506	−	1.21851i
$719$	−2419.94			−0.125519			−0.0627597	−	0.998029i	$-0.519990\pi$
$719$	−2419.94			−0.125519			−0.0627597	+	0.998029i	$0.519990\pi$
$720$		0			0
$721$	4416.78			0.228141
$722$	−6783.09	+	11748.7i	−0.349640	+	0.605595i
$723$		0			0
$724$	56.7139	+	98.2314i	0.00291127	+	0.00504246i
$725$	−2696.17	−	4669.90i	−0.138115	−	0.239222i
$726$		0			0
$727$	−8556.38	+	14820.1i	−0.436504	+	0.756047i	−0.997417	−	0.0718275i	$-0.977117\pi$
$727$	−8556.38	+	14820.1i	−0.436504	+	0.756047i	0.560913	+	0.827875i	$0.310450\pi$
$728$	−770.297			−0.0392158
$729$		0			0
$730$	−8174.58			−0.414458
$731$	−1573.37	+	2725.15i	−0.0796075	+	0.137884i
$732$		0			0
$733$	−7131.45	−	12352.0i	−0.359353	−	0.622418i	0.628500	−	0.777810i	$-0.283669\pi$
$733$	−7131.45	−	12352.0i	−0.359353	−	0.622418i	−0.987853	+	0.155392i	$0.950336\pi$
$734$	1803.28	+	3123.38i	0.0906818	+	0.157065i
$735$		0			0
$736$	1569.68	−	2718.77i	0.0786131	−	0.136162i
$737$	14154.4			0.707439
$738$		0			0
$739$	−37374.6			−1.86041			−0.930207	−	0.367036i	$-0.880373\pi$
$739$	−37374.6			−1.86041			−0.930207	+	0.367036i	$0.880373\pi$
$740$	−3691.81	+	6394.40i	−0.183397	+	0.317652i
$741$		0			0
$742$	759.513	+	1315.51i	0.0375776	+	0.0650863i
$743$	−12971.9	−	22468.0i	−0.640502	−	1.10938i	−0.985321	−	0.170712i	$-0.945393\pi$
$743$	−12971.9	−	22468.0i	−0.640502	−	1.10938i	0.344819	−	0.938669i	$-0.387940\pi$
$744$		0			0
$745$	−2529.46	+	4381.15i	−0.124392	+	0.215454i
$746$	−3976.70			−0.195170
$747$		0			0
$748$	−6936.05			−0.339047
$749$	−15691.2	+	27178.0i	−0.765481	+	1.32585i
$750$		0			0
$751$	12218.1	+	21162.4i	0.593669	+	1.02827i	0.993733	+	0.111778i	$0.0356546\pi$
$751$	12218.1	+	21162.4i	0.593669	+	1.02827i	−0.400064	+	0.916487i	$0.631012\pi$
$752$	−933.158	−	1616.28i	−0.0452510	−	0.0783771i
$753$		0			0
$754$	−1409.75	+	2441.76i	−0.0680903	+	0.117936i
$755$	16345.9			0.787932
$756$		0			0
$757$	−11000.0			−0.528141			−0.264070	−	0.964503i	$-0.585065\pi$
$757$	−11000.0			−0.528141			−0.264070	+	0.964503i	$0.585065\pi$
$758$	−10809.6	+	18722.8i	−0.517971	+	0.897153i
$759$		0			0
$760$	−174.256	−	301.821i	−0.00831702	−	0.0144055i
$761$	−9872.38	−	17099.5i	−0.470268	−	0.814527i	0.529154	−	0.848526i	$-0.322509\pi$
$761$	−9872.38	−	17099.5i	−0.470268	−	0.814527i	−0.999422	+	0.0339984i	$0.989176\pi$
$762$		0			0
$763$	−9493.94	+	16444.0i	−0.450463	+	0.780225i
$764$	−5073.38			−0.240247
$765$		0			0
$766$	−10893.1			−0.513817
$767$	−1914.39	+	3315.81i	−0.0901231	+	0.156098i
$768$		0			0
$769$	−4080.51	−	7067.64i	−0.191348	−	0.331425i	0.754349	−	0.656474i	$-0.227953\pi$
$769$	−4080.51	−	7067.64i	−0.191348	−	0.331425i	−0.945697	+	0.325049i	$0.894619\pi$
$770$	2729.30	+	4727.29i	0.127737	+	0.221246i
$771$		0			0
$772$	−6675.38	+	11562.1i	−0.311207	+	0.539027i
$773$	−5138.20			−0.239079			−0.119540	−	0.992829i	$-0.538142\pi$
$773$	−5138.20			−0.239079			−0.119540	+	0.992829i	$0.538142\pi$
$774$		0			0
$775$	477.628			0.0221379
$776$	−2074.86	+	3593.76i	−0.0959833	+	0.166248i
$777$		0			0
$778$	4779.61	+	8278.53i	0.220254	+	0.381491i
$779$	−797.909	−	1382.02i	−0.0366984	−	0.0635635i
$780$		0			0
$781$	6151.93	−	10655.5i	0.281861	−	0.488198i
$782$	9182.38			0.419899
$783$		0			0
$784$	−2015.47			−0.0918124
$785$	−6636.75	+	11495.2i	−0.301753	+	0.522651i
$786$		0			0
$787$	5966.05	+	10333.5i	0.270225	+	0.468043i	0.968919	−	0.247377i	$-0.0795687\pi$
$787$	5966.05	+	10333.5i	0.270225	+	0.468043i	−0.698695	+	0.715420i	$0.746235\pi$
$788$	2215.18	+	3836.80i	0.100143	+	0.173452i
$789$		0			0
$790$	−3118.65	+	5401.67i	−0.140452	+	0.243269i
$791$	16645.3			0.748214
$792$		0			0
$793$	2153.53			0.0964363
$794$	11892.7	−	20598.8i	0.531558	−	0.920686i
$795$		0			0
$796$	5404.90	+	9361.56i	0.240668	+	0.416849i
$797$	−642.187	−	1112.30i	−0.0285413	−	0.0494350i	0.851402	−	0.524514i	$-0.175753\pi$
$797$	−642.187	−	1112.30i	−0.0285413	−	0.0494350i	−0.879943	+	0.475079i	$0.842420\pi$
$798$		0			0
$799$	2729.41	−	4727.48i	0.120851	−	0.209319i
$800$	−800.000			−0.0353553
$801$		0			0
$802$	−6408.92			−0.282178
$803$	15144.4	−	26231.0i	0.665549	−	1.15276i
$804$		0			0
$805$	−3613.22	−	6258.29i	−0.158198	−	0.274007i
$806$	−124.869	−	216.280i	−0.00545698	−	0.00945177i
$807$		0			0
$808$	5971.35	−	10342.7i	0.259989	−	0.450314i
$809$	7030.60			0.305541			0.152771	−	0.988262i	$-0.451180\pi$
$809$	7030.60			0.305541			0.152771	+	0.988262i	$0.451180\pi$
$810$		0			0
$811$	−17584.1			−0.761359			−0.380680	−	0.924707i	$-0.624310\pi$
$811$	−17584.1			−0.761359			−0.380680	+	0.924707i	$0.624310\pi$
$812$	6355.22	−	11007.6i	0.274661	−	0.475726i
$813$		0			0
$814$	−13679.1	−	23692.9i	−0.589007	−	1.02019i
$815$	5399.44	+	9352.11i	0.232067	+	0.401951i
$816$		0			0
$817$	292.924	−	507.359i	0.0125436	−	0.0217261i
$818$	−30609.2			−1.30835
$819$		0			0
$820$	−3663.15			−0.156004
$821$	−21564.1	+	37350.1i	−0.916678	+	1.58773i	−0.112251	+	0.993680i	$0.535806\pi$
$821$	−21564.1	+	37350.1i	−0.916678	+	1.58773i	−0.804426	+	0.594052i	$0.797527\pi$
$822$		0			0
$823$	18962.0	+	32843.1i	0.803126	+	1.39105i	0.917549	+	0.397623i	$0.130165\pi$
$823$	18962.0	+	32843.1i	0.803126	+	1.39105i	−0.114423	+	0.993432i	$0.536502\pi$
$824$	−1199.23	−	2077.13i	−0.0507005	−	0.0878158i
$825$		0			0
$826$	8630.13	−	14947.8i	0.363536	−	0.629662i
$827$	8327.50			0.350152			0.175076	−	0.984555i	$-0.443983\pi$
$827$	8327.50			0.350152			0.175076	+	0.984555i	$0.443983\pi$
$828$		0			0
$829$	−23689.2			−0.992471			−0.496236	−	0.868188i	$-0.665285\pi$
$829$	−23689.2			−0.992471			−0.496236	+	0.868188i	$0.665285\pi$
$830$	−5058.04	+	8760.79i	−0.211527	+	0.366375i
$831$		0			0
$832$	209.149	+	362.256i	0.00871506	+	0.0150949i
$833$	−2947.54	−	5105.29i	−0.122600	−	0.212350i
$834$		0			0
$835$	−1964.59	+	3402.78i	−0.0814222	+	0.141027i
$836$	1291.33			0.0534229
$837$		0			0
$838$	−26506.2			−1.09265
$839$	8559.13	−	14824.8i	0.352198	−	0.610024i	−0.634436	−	0.772975i	$-0.718768\pi$
$839$	8559.13	−	14824.8i	0.352198	−	0.610024i	0.986634	+	0.162951i	$0.0521011\pi$
$840$		0			0
$841$	−11067.4	−	19169.2i	−0.453785	−	0.785978i
$842$	−9437.26	−	16345.8i	−0.386258	−	0.669019i
$843$		0			0
$844$	−5815.60	+	10072.9i	−0.237182	+	0.410811i
$845$	10771.4			0.438518
$846$		0			0
$847$	−617.157			−0.0250363
$848$	412.441	−	714.369i	0.0167020	−	0.0289287i
$849$		0			0
$850$	−1169.97	−	2026.44i	−0.0472112	−	0.0817723i
$851$	18109.3	+	31366.2i	0.729468	+	1.26348i
$852$		0			0
$853$	21333.6	−	36950.8i	0.856327	−	1.48320i	−0.0190812	−	0.999818i	$-0.506074\pi$
$853$	21333.6	−	36950.8i	0.856327	−	1.48320i	0.875408	−	0.483384i	$-0.160593\pi$
$854$	−9708.19			−0.389002
$855$		0			0
$856$	17041.7			0.680461
$857$	−5954.46	+	10313.4i	−0.237340	+	0.411085i	−0.959950	−	0.280171i	$-0.909609\pi$
$857$	−5954.46	+	10313.4i	−0.237340	+	0.411085i	0.722610	+	0.691256i	$0.242942\pi$
$858$		0			0
$859$	13436.1	+	23272.1i	0.533685	+	0.924369i	0.999226	+	0.0393426i	$0.0125264\pi$
$859$	13436.1	+	23272.1i	0.533685	+	0.924369i	−0.465541	+	0.885026i	$0.654140\pi$
$860$	−672.398	−	1164.63i	−0.0266611	−	0.0461784i
$861$		0			0
$862$	−8049.50	+	13942.1i	−0.318059	+	0.550895i
$863$	−10968.0			−0.432624			−0.216312	−	0.976324i	$-0.569403\pi$
$863$	−10968.0			−0.432624			−0.216312	+	0.976324i	$0.569403\pi$
$864$		0			0
$865$	1074.76			0.0422461
$866$	16268.1	−	28177.2i	0.638353	−	1.10566i
$867$		0			0
$868$	562.915	+	974.998i	0.0220122	+	0.0381262i
$869$	−11555.4	−	20014.6i	−0.451082	−	0.781297i
$870$		0			0
$871$	1248.38	−	2162.26i	0.0485646	−	0.0841164i
$872$	10311.1			0.400432
$873$		0			0
$874$	−1709.54			−0.0661627
$875$	−920.753	+	1594.79i	−0.0355739	+	0.0616158i
$876$		0			0
$877$	7403.23	+	12822.8i	0.285050	+	0.493722i	0.972621	−	0.232395i	$-0.0746563\pi$
$877$	7403.23	+	12822.8i	0.285050	+	0.493722i	−0.687571	+	0.726117i	$0.741323\pi$
$878$	13531.9	+	23438.0i	0.520137	+	0.900904i
$879$		0			0
$880$	1482.10	−	2567.08i	0.0567746	−	0.0983365i
$881$	9635.92			0.368493			0.184246	−	0.982880i	$-0.441016\pi$
$881$	9635.92			0.368493			0.184246	+	0.982880i	$0.441016\pi$
$882$		0			0
$883$	29048.0			1.10707			0.553535	−	0.832826i	$-0.313278\pi$
$883$	29048.0			1.10707			0.553535	+	0.832826i	$0.313278\pi$
$884$	−611.743	+	1059.57i	−0.0232750	+	0.0403136i
$885$		0			0
$886$	−13656.9	−	23654.5i	−0.517848	−	0.896939i
$887$	2867.88	+	4967.32i	0.108562	+	0.188034i	0.915188	−	0.403028i	$-0.132042\pi$
$887$	2867.88	+	4967.32i	0.108562	+	0.188034i	−0.806626	+	0.591062i	$0.798709\pi$
$888$		0			0
$889$	−8454.75	+	14644.1i	−0.318969	+	0.552470i
$890$	6707.65			0.252630
$891$		0			0
$892$	−202.745			−0.00761033
$893$	−508.152	+	880.145i	−0.0190422	+	0.0329820i
$894$		0			0
$895$	141.463	+	245.022i	0.00528335	+	0.00915103i
$896$	−942.851	−	1633.07i	−0.0351545	−	0.0608894i
$897$		0			0
$898$	754.853	−	1307.44i	0.0280510	−	0.0485857i
$899$	4120.85			0.152879
$900$		0			0
$901$	2412.71			0.0892110
$902$	6786.46	−	11754.5i	0.250515	−	0.433904i
$903$		0			0
$904$	−4519.47	−	7827.95i	−0.166278	−	0.288002i
$905$	−70.8924	−	122.789i	−0.00260392	−	0.00451011i
$906$		0			0
$907$	−1557.64	+	2697.92i	−0.0570240	+	0.0987684i	−0.893128	−	0.449802i	$-0.851494\pi$
$907$	−1557.64	+	2697.92i	−0.0570240	+	0.0987684i	0.836104	+	0.548571i	$0.184828\pi$
$908$	−7068.57			−0.258347
$909$		0			0
$910$	962.872			0.0350757
$911$	−5745.33	+	9951.20i	−0.208948	+	0.361908i	−0.951383	−	0.308010i	$-0.900337\pi$
$911$	−5745.33	+	9951.20i	−0.208948	+	0.361908i	0.742436	+	0.669917i	$0.233670\pi$
$912$		0			0
$913$	−18741.3	−	32461.0i	−0.679352	−	1.17667i
$914$	−11873.9	−	20566.2i	−0.429708	−	0.744277i
$915$		0			0
$916$	−13451.8	+	23299.2i	−0.485218	+	0.840422i
$917$	35989.8			1.29606
$918$		0			0
$919$	−42808.1			−1.53657			−0.768286	−	0.640107i	$-0.778890\pi$
$919$	−42808.1			−1.53657			−0.768286	+	0.640107i	$0.778890\pi$
$920$	−1962.10	+	3398.46i	−0.0703137	+	0.121787i
$921$		0			0
$922$	−8197.10	−	14197.8i	−0.292795	−	0.507136i
$923$	−1085.17	−	1879.57i	−0.0386987	−	0.0670281i
$924$		0			0
$925$	4614.76	−	7993.00i	0.164035	−	0.284117i
$926$	385.429			0.0136782
$927$		0			0
$928$	−6902.19			−0.244155
$929$	−12801.3	+	22172.5i	−0.452096	+	0.783053i	−0.998516	−	0.0544579i	$-0.982657\pi$
$929$	−12801.3	+	22172.5i	−0.452096	+	0.783053i	0.546420	+	0.837511i	$0.315990\pi$
$930$		0			0
$931$	548.762	+	950.484i	0.0193179	+	0.0334596i
$932$	11986.6	+	20761.5i	0.421283	+	0.729683i
$933$		0			0
$934$	−5254.00	+	9100.20i	−0.184064	+	0.318809i
$935$	8670.06			0.303253
$936$		0			0
$937$	38597.2			1.34570			0.672848	−	0.739781i	$-0.265071\pi$
$937$	38597.2			1.34570			0.672848	+	0.739781i	$0.265071\pi$
$938$	−5627.75	+	9747.56i	−0.195898	+	0.339306i
$939$		0			0
$940$	1166.45	+	2020.35i	0.0404738	+	0.0701026i
$941$	−15461.4	−	26779.8i	−0.535628	−	0.927734i	−0.999133	−	0.0416401i	$-0.986742\pi$
$941$	−15461.4	−	26779.8i	−0.535628	−	0.927734i	0.463505	−	0.886094i	$-0.346592\pi$
$942$		0			0
$943$	−8984.35	+	15561.4i	−0.310255	+	0.537378i
$944$	−9372.90			−0.323159
$945$		0			0
$946$	4982.81			0.171253
$947$	−4213.49	+	7297.97i	−0.144583	+	0.250425i	−0.929217	−	0.369534i	$-0.879517\pi$
$947$	−4213.49	+	7297.97i	−0.144583	+	0.250425i	0.784634	+	0.619959i	$0.212851\pi$
$948$		0			0
$949$	−2671.41	−	4627.02i	−0.0913779	−	0.158271i
$950$	217.820	+	377.276i	0.00743897	+	0.0128847i
$951$		0			0
$952$	2757.76	−	4776.59i	0.0938861	−	0.162616i
$953$	8456.53			0.287444			0.143722	−	0.989618i	$-0.454093\pi$
$953$	8456.53			0.287444			0.143722	+	0.989618i	$0.454093\pi$
$954$		0			0
$955$	6341.72			0.214883
$956$	6576.98	−	11391.7i	0.222505	−	0.385390i
$957$		0			0
$958$	15252.6	+	26418.3i	0.514394	+	0.890957i
$959$	−4153.82	−	7194.62i	−0.139868	−	0.242259i
$960$		0			0
$961$	14713.0	−	25483.7i	0.493874	−	0.855415i
$962$	−4825.85			−0.161738
$963$		0			0
$964$	−1343.08			−0.0448732
$965$	8344.22	−	14452.6i	0.278352	−	0.482120i
$966$		0			0
$967$	3723.37	+	6449.06i	0.123822	+	0.214465i	0.921272	−	0.388920i	$-0.127152\pi$
$967$	3723.37	+	6449.06i	0.123822	+	0.214465i	−0.797450	+	0.603385i	$0.793818\pi$
$968$	167.568	+	290.237i	0.00556390	+	0.00963696i
$969$		0			0
$970$	2593.57	−	4492.20i	0.0858500	−	0.148697i
$971$	−17139.7			−0.566467			−0.283234	−	0.959051i	$-0.591407\pi$
$971$	−17139.7			−0.566467			−0.283234	+	0.959051i	$0.591407\pi$
$972$		0			0
$973$	15180.1			0.500157
$974$	−11485.1	+	19892.8i	−0.377831	+	0.654422i
$975$		0			0
$976$	2635.94	+	4565.58i	0.0864491	+	0.149734i
$977$	12417.2	+	21507.2i	0.406613	+	0.704275i	0.994508	−	0.104663i	$-0.0333763\pi$
$977$	12417.2	+	21507.2i	0.406613	+	0.704275i	−0.587894	+	0.808938i	$0.700043\pi$
$978$		0			0
$979$	−12426.8	+	21523.8i	−0.405681	+	0.702660i
$980$	2519.33			0.0821196
$981$		0			0
$982$	27778.4			0.902693
$983$	10635.7	−	18421.6i	0.345093	−	0.597719i	−0.640278	−	0.768144i	$-0.721181\pi$
$983$	10635.7	−	18421.6i	0.345093	−	0.597719i	0.985371	+	0.170425i	$0.0545140\pi$
$984$		0			0
$985$	−2768.97	−	4796.00i	−0.0895704	−	0.155140i
$986$	−10094.2	−	17483.6i	−0.326028	−	0.564698i
$987$		0			0
$988$	113.892	−	197.267i	0.00366740	−	0.00635212i
$989$	−6596.57			−0.212092
$990$		0			0
$991$	−1931.89			−0.0619259			−0.0309630	−	0.999521i	$-0.509857\pi$
$991$	−1931.89			−0.0619259			−0.0309630	+	0.999521i	$0.509857\pi$
$992$	305.682	−	529.457i	0.00978368	−	0.0169458i
$993$		0			0
$994$	4892.00	+	8473.20i	0.156101	+	0.270376i
$995$	−6756.13	−	11702.0i	−0.215260	−	0.372841i
$996$		0			0
$997$	−13076.3	+	22648.9i	−0.415378	+	0.719455i	−0.995468	−	0.0950970i	$-0.969684\pi$
$997$	−13076.3	+	22648.9i	−0.415378	+	0.719455i	0.580090	+	0.814552i	$0.303017\pi$
$998$	39899.9			1.26554
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.4.e.bf.541.2		4
3.2	odd	2		810.4.e.bb.541.2		4
9.2	odd	6		810.4.a.m.1.1	yes	2
9.4	even	3	inner	810.4.e.bf.271.2		4
9.5	odd	6		810.4.e.bb.271.2		4
9.7	even	3		810.4.a.g.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.4.a.g.1.1	✓	2	9.7	even	3
810.4.a.m.1.1	yes	2	9.2	odd	6
810.4.e.bb.271.2		4	9.5	odd	6
810.4.e.bb.541.2		4	3.2	odd	2
810.4.e.bf.271.2		4	9.4	even	3	inner
810.4.e.bf.541.2		4	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	810.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(7.36603 - 12.7583i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(-18.5263 + 32.0885i) q^{11} +(3.26795 + 5.66025i) q^{13} +(-14.7321 - 25.5167i) q^{14} +(-8.00000 + 13.8564i) q^{16} -46.7987 q^{17} +8.71281 q^{19} +(10.0000 - 17.3205i) q^{20} +(37.0526 + 64.1769i) q^{22} +(-49.0526 - 84.9615i) q^{23} +(-12.5000 + 21.6506i) q^{25} +13.0718 q^{26} -58.9282 q^{28} +(-107.847 + 186.796i) q^{29} +(-9.55256 - 16.5455i) q^{31} +(16.0000 + 27.7128i) q^{32} +(-46.7987 + 81.0577i) q^{34} +73.6603 q^{35} -369.181 q^{37} +(8.71281 - 15.0910i) q^{38} +(-20.0000 - 34.6410i) q^{40} +(-91.5788 - 158.619i) q^{41} +(33.6199 - 58.2314i) q^{43} +148.210 q^{44} -196.210 q^{46} +(-58.3224 + 101.017i) q^{47} +(62.9833 + 109.090i) q^{49} +(25.0000 + 43.3013i) q^{50} +(13.0718 - 22.6410i) q^{52} -51.5551 q^{53} -185.263 q^{55} +(-58.9282 + 102.067i) q^{56} +(215.694 + 373.592i) q^{58} +(292.903 + 507.323i) q^{59} +(164.746 - 285.349i) q^{61} -38.2102 q^{62} +64.0000 q^{64} +(-16.3397 + 28.3013i) q^{65} +(-191.004 - 330.828i) q^{67} +(93.5974 + 162.115i) q^{68} +(73.6603 - 127.583i) q^{70} -332.065 q^{71} -817.458 q^{73} +(-369.181 + 639.440i) q^{74} +(-17.4256 - 30.1821i) q^{76} +(272.930 + 472.729i) q^{77} +(-311.865 + 540.167i) q^{79} -80.0000 q^{80} -366.315 q^{82} +(-505.804 + 876.079i) q^{83} +(-116.997 - 202.644i) q^{85} +(-67.2398 - 116.463i) q^{86} +(148.210 - 256.708i) q^{88} +670.765 q^{89} +96.2872 q^{91} +(-196.210 + 339.846i) q^{92} +(116.645 + 202.035i) q^{94} +(21.7820 + 37.7276i) q^{95} +(259.357 - 449.220i) q^{97} +251.933 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 10 q^{5} + 26 q^{7} - 32 q^{8} + 40 q^{10} - 36 q^{11} + 20 q^{13} - 52 q^{14} - 32 q^{16} + 180 q^{17} - 76 q^{19} + 40 q^{20} + 72 q^{22} - 120 q^{23} - 50 q^{25} + 80 q^{26}+ \cdots + 1368 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 10 * q^5 + 26 * q^7 - 32 * q^8 + 40 * q^10 - 36 * q^11 + 20 * q^13 - 52 * q^14 - 32 * q^16 + 180 * q^17 - 76 * q^19 + 40 * q^20 + 72 * q^22 - 120 * q^23 - 50 * q^25 + 80 * q^26 - 208 * q^28 - 324 * q^29 + 38 * q^31 + 64 * q^32 + 180 * q^34 + 260 * q^35 - 292 * q^37 - 76 * q^38 - 80 * q^40 - 252 * q^41 + 422 * q^43 + 288 * q^44 - 480 * q^46 + 366 * q^47 + 342 * q^49 + 100 * q^50 + 80 * q^52 - 324 * q^53 - 360 * q^55 - 208 * q^56 + 648 * q^58 - 72 * q^59 + 368 * q^61 + 152 * q^62 + 256 * q^64 - 100 * q^65 + 296 * q^67 - 360 * q^68 + 260 * q^70 + 480 * q^71 - 1420 * q^73 - 292 * q^74 + 152 * q^76 + 534 * q^77 - 520 * q^79 - 320 * q^80 - 1008 * q^82 - 66 * q^83 + 450 * q^85 - 844 * q^86 + 288 * q^88 + 2496 * q^89 + 496 * q^91 - 480 * q^92 - 732 * q^94 - 190 * q^95 + 1706 * q^97 + 1368 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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