LMFDB - Embedded newform 405.4.e.r.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,4,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	405.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:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.95327307.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 85x^2 - 68*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 - 0.0280269i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.r.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.60034 - 4.50391i) q^{2} +(-9.52349 + 16.4952i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-12.2007 - 21.1322i) q^{7} +57.4517 q^{8} +O(q^{10})$	\(q+(-2.60034 - 4.50391i) q^{2} +(-9.52349 + 16.4952i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-12.2007 - 21.1322i) q^{7} +57.4517 q^{8} -26.0034 q^{10} +(14.4919 + 25.1008i) q^{11} +(32.6960 - 56.6311i) q^{13} +(-63.4517 + 109.902i) q^{14} +(-73.2057 - 126.796i) q^{16} +68.1718 q^{17} +104.424 q^{19} +(47.6174 + 82.4758i) q^{20} +(75.3678 - 130.541i) q^{22} +(77.4033 - 134.067i) q^{23} +(-12.5000 - 21.6506i) q^{25} -340.082 q^{26} +464.772 q^{28} +(102.829 + 178.105i) q^{29} +(9.12485 - 15.8047i) q^{31} +(-150.912 + 261.387i) q^{32} +(-177.269 - 307.040i) q^{34} -122.007 q^{35} -337.613 q^{37} +(-271.538 - 470.317i) q^{38} +(143.629 - 248.773i) q^{40} +(97.9845 - 169.714i) q^{41} +(-167.441 - 290.016i) q^{43} -552.055 q^{44} -805.098 q^{46} +(2.50199 + 4.33358i) q^{47} +(-126.213 + 218.607i) q^{49} +(-65.0084 + 112.598i) q^{50} +(622.759 + 1078.65i) q^{52} -319.965 q^{53} +144.919 q^{55} +(-700.949 - 1214.08i) q^{56} +(534.779 - 926.265i) q^{58} +(-215.305 + 372.920i) q^{59} +(-297.291 - 514.922i) q^{61} -94.9106 q^{62} +398.396 q^{64} +(-163.480 - 283.155i) q^{65} +(-97.9382 + 169.634i) q^{67} +(-649.233 + 1124.50i) q^{68} +(317.258 + 549.508i) q^{70} +425.955 q^{71} +929.193 q^{73} +(877.908 + 1520.58i) q^{74} +(-994.482 + 1722.49i) q^{76} +(353.623 - 612.492i) q^{77} +(-12.2148 - 21.1567i) q^{79} -732.057 q^{80} -1019.17 q^{82} +(272.929 + 472.727i) q^{83} +(170.429 - 295.192i) q^{85} +(-870.805 + 1508.28i) q^{86} +(832.586 + 1442.08i) q^{88} -84.1332 q^{89} -1595.65 q^{91} +(1474.30 + 2553.56i) q^{92} +(13.0120 - 22.5375i) q^{94} +(261.060 - 452.170i) q^{95} +(-413.807 - 716.734i) q^{97} +1312.78 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8}+O(q^{10}) $ 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8	$ 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} - 10 q^{10} + 38 q^{11} - 28 q^{13} - 108 q^{14} - 191 q^{16} + 38 q^{17} + 374 q^{19} + 115 q^{20} - 122 q^{22} - 81 q^{23} - 75 q^{25} - 832 q^{26} + 820 q^{28} + 160 q^{29} - 227 q^{31} - 569 q^{32} - 17 q^{34} - 440 q^{35} + 156 q^{37} - 757 q^{38} + 180 q^{40} - 338 q^{41} - 22 q^{43} - 3272 q^{44} - 2850 q^{46} - 472 q^{47} + 197 q^{49} - 25 q^{50} + 1566 q^{52} - 1042 q^{53} + 380 q^{55} - 1254 q^{56} + 2096 q^{58} + 140 q^{59} - 595 q^{61} - 2814 q^{62} - 1836 q^{64} + 140 q^{65} - 878 q^{67} - 3053 q^{68} + 540 q^{70} + 1204 q^{71} + 2588 q^{73} + 2878 q^{74} - 525 q^{76} + 288 q^{77} - 629 q^{79} - 1910 q^{80} - 3364 q^{82} - 1287 q^{83} + 95 q^{85} - 3730 q^{86} + 858 q^{88} - 4308 q^{89} - 880 q^{91} + 1959 q^{92} + 1108 q^{94} + 935 q^{95} - 1392 q^{97} + 5386 q^{98}+O(q^{100}) $ 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8 - 10 * q^10 + 38 * q^11 - 28 * q^13 - 108 * q^14 - 191 * q^16 + 38 * q^17 + 374 * q^19 + 115 * q^20 - 122 * q^22 - 81 * q^23 - 75 * q^25 - 832 * q^26 + 820 * q^28 + 160 * q^29 - 227 * q^31 - 569 * q^32 - 17 * q^34 - 440 * q^35 + 156 * q^37 - 757 * q^38 + 180 * q^40 - 338 * q^41 - 22 * q^43 - 3272 * q^44 - 2850 * q^46 - 472 * q^47 + 197 * q^49 - 25 * q^50 + 1566 * q^52 - 1042 * q^53 + 380 * q^55 - 1254 * q^56 + 2096 * q^58 + 140 * q^59 - 595 * q^61 - 2814 * q^62 - 1836 * q^64 + 140 * q^65 - 878 * q^67 - 3053 * q^68 + 540 * q^70 + 1204 * q^71 + 2588 * q^73 + 2878 * q^74 - 525 * q^76 + 288 * q^77 - 629 * q^79 - 1910 * q^80 - 3364 * q^82 - 1287 * q^83 + 95 * q^85 - 3730 * q^86 + 858 * q^88 - 4308 * q^89 - 880 * q^91 + 1959 * q^92 + 1108 * q^94 + 935 * q^95 - 1392 * q^97 + 5386 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.60034	−	4.50391i	−0.919357	−	1.59237i	−0.800393	−	0.599475i	$-0.795376\pi$
$2$	−2.60034	−	4.50391i	−0.919357	−	1.59237i	−0.118964	−	0.992899i	$-0.537957\pi$
$3$		0			0
$3$		0			0
$4$	−9.52349	+	16.4952i	−1.19044	+	2.06190i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	−12.2007	−	21.1322i	−0.658774	−	1.14103i	−0.980933	−	0.194345i	$-0.937742\pi$
$7$	−12.2007	−	21.1322i	−0.658774	−	1.14103i	0.322159	−	0.946686i	$-0.395591\pi$
$8$	57.4517			2.53903
$9$		0			0
$10$	−26.0034			−0.822298
$11$	14.4919	+	25.1008i	0.397226	+	0.688015i	0.993383	−	0.114853i	$-0.0366397\pi$
$11$	14.4919	+	25.1008i	0.397226	+	0.688015i	−0.596157	+	0.802868i	$0.703306\pi$
$12$		0			0
$13$	32.6960	−	56.6311i	0.697556	−	1.20820i	−0.271756	−	0.962366i	$-0.587604\pi$
$13$	32.6960	−	56.6311i	0.697556	−	1.20820i	0.969311	−	0.245836i	$-0.0790625\pi$
$14$	−63.4517	+	109.902i	−1.21130	+	2.09803i
$15$		0			0
$16$	−73.2057	−	126.796i	−1.14384	−	1.98119i
$17$	68.1718			0.972593			0.486296	−	0.873794i	$-0.338347\pi$
$17$	68.1718			0.972593			0.486296	+	0.873794i	$0.338347\pi$
$18$		0			0
$19$	104.424			1.26087			0.630435	−	0.776242i	$-0.282876\pi$
$19$	104.424			1.26087			0.630435	+	0.776242i	$0.282876\pi$
$20$	47.6174	+	82.4758i	0.532379	+	0.922108i
$21$		0			0
$22$	75.3678	−	130.541i	0.730385	−	1.26506i
$23$	77.4033	−	134.067i	0.701727	−	1.21543i	−0.266133	−	0.963936i	$-0.585746\pi$
$23$	77.4033	−	134.067i	0.701727	−	1.21543i	0.967860	−	0.251490i	$-0.0809205\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−340.082			−2.56521
$27$		0			0
$28$	464.772			3.13691
$29$	102.829	+	178.105i	0.658443	+	1.14046i	0.981019	+	0.193913i	$0.0621179\pi$
$29$	102.829	+	178.105i	0.658443	+	1.14046i	−0.322576	+	0.946544i	$0.604549\pi$
$30$		0			0
$31$	9.12485	−	15.8047i	0.0528668	−	0.0915680i	−0.838381	−	0.545085i	$-0.816497\pi$
$31$	9.12485	−	15.8047i	0.0528668	−	0.0915680i	0.891248	+	0.453517i	$0.149831\pi$
$32$	−150.912	+	261.387i	−0.833679	+	1.44397i
$33$		0			0
$34$	−177.269	−	307.040i	−0.894160	−	1.54873i
$35$	−122.007			−0.589226
$36$		0			0
$37$	−337.613			−1.50009			−0.750044	−	0.661387i	$-0.769968\pi$
$37$	−337.613			−1.50009			−0.750044	+	0.661387i	$0.769968\pi$
$38$	−271.538	−	470.317i	−1.15919	−	2.00778i
$39$		0			0
$40$	143.629	−	248.773i	0.567744	−	0.983362i
$41$	97.9845	−	169.714i	0.373234	−	0.646461i	−0.616827	−	0.787099i	$-0.711582\pi$
$41$	97.9845	−	169.714i	0.373234	−	0.646461i	0.990061	+	0.140638i	$0.0449154\pi$
$42$		0			0
$43$	−167.441	−	290.016i	−0.593826	−	1.02854i	−0.993711	−	0.111971i	$-0.964284\pi$
$43$	−167.441	−	290.016i	−0.593826	−	1.02854i	0.399886	−	0.916565i	$-0.369050\pi$
$44$	−552.055			−1.89149
$45$		0			0
$46$	−805.098			−2.58055
$47$	2.50199	+	4.33358i	0.00776496	+	0.0134493i	0.869882	−	0.493260i	$-0.164195\pi$
$47$	2.50199	+	4.33358i	0.00776496	+	0.0134493i	−0.862117	+	0.506710i	$0.830862\pi$
$48$		0			0
$49$	−126.213	+	218.607i	−0.367967	+	0.637338i
$50$	−65.0084	+	112.598i	−0.183871	+	0.318475i
$51$		0			0
$52$	622.759	+	1078.65i	1.66079	+	2.87657i
$53$	−319.965			−0.829256			−0.414628	−	0.909991i	$-0.636088\pi$
$53$	−319.965			−0.829256			−0.414628	+	0.909991i	$0.636088\pi$
$54$		0			0
$55$	144.919			0.355289
$56$	−700.949	−	1214.08i	−1.67265	−	2.89711i
$57$		0			0
$58$	534.779	−	926.265i	1.21069	−	2.09697i
$59$	−215.305	+	372.920i	−0.475091	+	0.822882i	−0.999593	−	0.0285276i	$-0.990918\pi$
$59$	−215.305	+	372.920i	−0.475091	+	0.822882i	0.524502	+	0.851409i	$0.324251\pi$
$60$		0			0
$61$	−297.291	−	514.922i	−0.624002	−	1.08080i	−0.988733	−	0.149691i	$-0.952172\pi$
$61$	−297.291	−	514.922i	−0.624002	−	1.08080i	0.364730	−	0.931113i	$-0.381161\pi$
$62$	−94.9106			−0.194414
$63$		0			0
$64$	398.396			0.778118
$65$	−163.480	−	283.155i	−0.311956	−	0.540324i
$66$		0			0
$67$	−97.9382	+	169.634i	−0.178583	+	0.309315i	−0.941395	−	0.337305i	$-0.890485\pi$
$67$	−97.9382	+	169.634i	−0.178583	+	0.309315i	0.762812	+	0.646620i	$0.223818\pi$
$68$	−649.233	+	1124.50i	−1.15781	+	2.00538i
$69$		0			0
$70$	317.258	+	549.508i	0.541709	+	0.938267i
$71$	425.955			0.711994			0.355997	−	0.934487i	$-0.384141\pi$
$71$	425.955			0.711994			0.355997	+	0.934487i	$0.384141\pi$
$72$		0			0
$73$	929.193			1.48978			0.744889	−	0.667188i	$-0.232502\pi$
$73$	929.193			1.48978			0.744889	+	0.667188i	$0.232502\pi$
$74$	877.908	+	1520.58i	1.37912	+	2.38870i
$75$		0			0
$76$	−994.482	+	1722.49i	−1.50099	+	2.59978i
$77$	353.623	−	612.492i	0.523364	−	0.906493i
$78$		0			0
$79$	−12.2148	−	21.1567i	−0.0173959	−	0.0301305i	0.857196	−	0.514990i	$-0.172204\pi$
$79$	−12.2148	−	21.1567i	−0.0173959	−	0.0301305i	−0.874592	+	0.484859i	$0.838871\pi$
$80$	−732.057			−1.02308
$81$		0			0
$82$	−1019.17			−1.37254
$83$	272.929	+	472.727i	0.360938	+	0.625164i	0.988116	−	0.153713i	$-0.0491231\pi$
$83$	272.929	+	472.727i	0.360938	+	0.625164i	−0.627177	+	0.778877i	$0.715790\pi$
$84$		0			0
$85$	170.429	−	295.192i	0.217478	−	0.376684i
$86$	−870.805	+	1508.28i	−1.09188	+	1.89118i
$87$		0			0
$88$	832.586	+	1442.08i	1.00857	+	1.74689i
$89$	−84.1332			−0.100203			−0.0501017	−	0.998744i	$-0.515955\pi$
$89$	−84.1332			−0.100203			−0.0501017	+	0.998744i	$0.515955\pi$
$90$		0			0
$91$	−1595.65			−1.83813
$92$	1474.30	+	2553.56i	1.67072	+	2.89377i
$93$		0			0
$94$	13.0120	−	22.5375i	0.0142775	−	0.0247294i
$95$	261.060	−	452.170i	0.281939	−	0.488333i
$96$		0			0
$97$	−413.807	−	716.734i	−0.433152	−	0.750241i	0.563991	−	0.825781i	$-0.309265\pi$
$97$	−413.807	−	716.734i	−0.433152	−	0.750241i	−0.997143	+	0.0755403i	$0.975932\pi$
$98$	1312.78			1.35317
$99$		0			0
$100$	476.174			0.476174
$101$	−411.788	−	713.238i	−0.405688	−	0.702671i	0.588714	−	0.808342i	$-0.299635\pi$
$101$	−411.788	−	713.238i	−0.405688	−	0.702671i	−0.994401	+	0.105670i	$0.966301\pi$
$102$		0			0
$103$	−585.595	+	1014.28i	−0.560198	+	0.970291i	0.437281	+	0.899325i	$0.355941\pi$
$103$	−585.595	+	1014.28i	−0.560198	+	0.970291i	−0.997479	+	0.0709659i	$0.977392\pi$
$104$	1878.44	−	3253.55i	1.77111	−	3.06766i
$105$		0			0
$106$	832.016	+	1441.09i	0.762383	+	1.32049i
$107$	1023.21			0.924460			0.462230	−	0.886760i	$-0.347049\pi$
$107$	1023.21			0.924460			0.462230	+	0.886760i	$0.347049\pi$
$108$		0			0
$109$	−403.647			−0.354700			−0.177350	−	0.984148i	$-0.556753\pi$
$109$	−403.647			−0.354700			−0.177350	+	0.984148i	$0.556753\pi$
$110$	−376.839	−	652.704i	−0.326638	−	0.565754i
$111$		0			0
$112$	−1786.32	+	3093.99i	−1.50706	+	2.61031i
$113$	−541.102	+	937.216i	−0.450465	+	0.780229i	−0.998415	−	0.0562825i	$-0.982075\pi$
$113$	−541.102	+	937.216i	−0.450465	+	0.780229i	0.547950	+	0.836511i	$0.315409\pi$
$114$		0			0
$115$	−387.017	−	670.333i	−0.313822	−	0.543555i
$116$	−3917.16			−3.13534
$117$		0			0
$118$	2239.46			1.74711
$119$	−831.741	−	1440.62i	−0.640719	−	1.10976i
$120$		0			0
$121$	245.468	−	425.162i	0.184423	−	0.319431i
$122$	−1546.11	+	2677.94i	−1.14736	+	1.98729i
$123$		0			0
$124$	173.801	+	301.032i	0.125869	+	0.218012i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−774.132			−0.540890			−0.270445	−	0.962735i	$-0.587171\pi$
$127$	−774.132			−0.540890			−0.270445	+	0.962735i	$0.587171\pi$
$128$	171.332	+	296.756i	0.118311	+	0.204920i
$129$		0			0
$130$	−850.204	+	1472.60i	−0.573599	+	0.993503i
$131$	607.019	−	1051.39i	0.404851	−	0.701222i	−0.589453	−	0.807802i	$-0.700657\pi$
$131$	607.019	−	1051.39i	0.404851	−	0.701222i	0.994304	+	0.106580i	$0.0339901\pi$
$132$		0			0
$133$	−1274.04	−	2206.71i	−0.830629	−	1.43869i
$134$	1018.69			0.656726
$135$		0			0
$136$	3916.58			2.46944
$137$	−1150.07	−	1991.99i	−0.717207	−	1.24224i	−0.962102	−	0.272690i	$-0.912087\pi$
$137$	−1150.07	−	1991.99i	−0.717207	−	1.24224i	0.244895	−	0.969550i	$-0.421247\pi$
$138$		0			0
$139$	677.963	−	1174.27i	0.413698	−	0.716546i	−0.581593	−	0.813480i	$-0.697570\pi$
$139$	677.963	−	1174.27i	0.413698	−	0.716546i	0.995291	+	0.0969339i	$0.0309035\pi$
$140$	1161.93	−	2012.52i	0.701435	−	1.21492i
$141$		0			0
$142$	−1107.63	−	1918.47i	−0.654577	−	1.13376i
$143$	1895.31			1.10835
$144$		0			0
$145$	1028.29			0.588929
$146$	−2416.21	−	4185.00i	−1.36964	−	2.37228i
$147$		0			0
$148$	3215.26	−	5568.99i	1.78576	−	3.09303i
$149$	−129.923	+	225.032i	−0.0714340	+	0.123727i	−0.899530	−	0.436859i	$-0.856091\pi$
$149$	−129.923	+	225.032i	−0.0714340	+	0.123727i	0.828096	+	0.560586i	$0.189424\pi$
$150$		0			0
$151$	254.152	+	440.204i	0.136971	+	0.237240i	0.926349	−	0.376667i	$-0.122930\pi$
$151$	254.152	+	440.204i	0.136971	+	0.237240i	−0.789378	+	0.613908i	$0.789597\pi$
$152$	5999.34			3.20139
$153$		0			0
$154$	−3678.15			−1.92463
$155$	−45.6242	−	79.0235i	−0.0236428	−	0.0409504i
$156$		0			0
$157$	11.6526	−	20.1829i	0.00592342	−	0.0102597i	−0.863049	−	0.505121i	$-0.831448\pi$
$157$	11.6526	−	20.1829i	0.00592342	−	0.0102597i	0.868972	+	0.494861i	$0.164781\pi$
$158$	−63.5252	+	110.029i	−0.0319860	+	0.0554014i
$159$		0			0
$160$	754.560	+	1306.94i	0.372833	+	0.645765i
$161$	−3777.49			−1.84912
$162$		0			0
$163$	−4032.10			−1.93754			−0.968769	−	0.247964i	$-0.920238\pi$
$163$	−4032.10			−1.93754			−0.968769	+	0.247964i	$0.920238\pi$
$164$	1866.31	+	3232.54i	0.888623	+	1.53914i
$165$		0			0
$166$	1419.42	−	2458.50i	0.663663	−	1.14950i
$167$	335.955	−	581.892i	0.155671	−	0.269630i	−0.777632	−	0.628719i	$-0.783579\pi$
$167$	335.955	−	581.892i	0.155671	−	0.269630i	0.933303	+	0.359090i	$0.116913\pi$
$168$		0			0
$169$	−1039.55	−	1800.56i	−0.473169	−	0.819552i
$170$	−1772.69			−0.799761
$171$		0			0
$172$	6378.49			2.82765
$173$	−816.764	−	1414.68i	−0.358944	−	0.621710i	0.628840	−	0.777534i	$-0.283530\pi$
$173$	−816.764	−	1414.68i	−0.358944	−	0.621710i	−0.987785	+	0.155825i	$0.950197\pi$
$174$		0			0
$175$	−305.017	+	528.305i	−0.131755	+	0.228206i
$176$	2121.78	−	3675.04i	0.908725	−	1.57396i
$177$		0			0
$178$	218.775	+	378.929i	0.0921227	+	0.159561i
$179$	341.260			0.142497			0.0712485	−	0.997459i	$-0.477302\pi$
$179$	341.260			0.142497			0.0712485	+	0.997459i	$0.477302\pi$
$180$		0			0
$181$	−1695.92			−0.696447			−0.348223	−	0.937412i	$-0.613215\pi$
$181$	−1695.92			−0.696447			−0.348223	+	0.937412i	$0.613215\pi$
$182$	4149.23	+	7186.67i	1.68990	+	2.92699i
$183$		0			0
$184$	4446.95	−	7702.34i	1.78170	−	3.08600i
$185$	−844.033	+	1461.91i	−0.335430	+	0.580982i
$186$		0			0
$187$	987.941	+	1711.16i	0.386339	+	0.669159i
$188$	−95.3107			−0.0369747
$189$		0			0
$190$	−2715.38			−1.03681
$191$	363.226	+	629.125i	0.137603	+	0.238335i	0.926589	−	0.376076i	$-0.122727\pi$
$191$	363.226	+	629.125i	0.137603	+	0.238335i	−0.788986	+	0.614411i	$0.789394\pi$
$192$		0			0
$193$	−2123.63	+	3678.24i	−0.792032	+	1.37184i	0.132674	+	0.991160i	$0.457644\pi$
$193$	−2123.63	+	3678.24i	−0.792032	+	1.37184i	−0.924707	+	0.380681i	$0.875690\pi$
$194$	−2152.07	+	3727.50i	−0.796442	+	1.37948i
$195$		0			0
$196$	−2403.97	−	4163.80i	−0.876082	−	1.51742i
$197$	2678.52			0.968713			0.484357	−	0.874871i	$-0.339054\pi$
$197$	2678.52			0.968713			0.484357	+	0.874871i	$0.339054\pi$
$198$		0			0
$199$	1486.48			0.529517			0.264759	−	0.964315i	$-0.414708\pi$
$199$	1486.48			0.529517			0.264759	+	0.964315i	$0.414708\pi$
$200$	−718.146	−	1243.87i	−0.253903	−	0.439773i
$201$		0			0
$202$	−2141.57	+	3709.31i	−0.745944	+	1.29201i
$203$	2509.16	−	4346.00i	0.867530	−	1.50261i
$204$		0			0
$205$	−489.923	−	848.571i	−0.166915	−	0.289106i
$206$	6090.97			2.06009
$207$		0			0
$208$	−9574.12			−3.19157
$209$	1513.31	+	2621.13i	0.500850	+	0.867498i
$210$		0			0
$211$	2413.71	−	4180.66i	0.787519	−	1.36402i	−0.139964	−	0.990157i	$-0.544699\pi$
$211$	2413.71	−	4180.66i	0.787519	−	1.36402i	0.927483	−	0.373866i	$-0.121968\pi$
$212$	3047.18	−	5277.87i	0.987176	−	1.70984i
$213$		0			0
$214$	−2660.68	−	4608.44i	−0.849909	−	1.47209i
$215$	−1674.41			−0.531134
$216$		0			0
$217$	−445.317			−0.139309
$218$	1049.62	+	1817.99i	0.326096	+	0.564815i
$219$		0			0
$220$	−1380.14	+	2390.47i	−0.422949	+	0.732570i
$221$	2228.94	−	3860.64i	0.678438	−	1.17509i
$222$		0			0
$223$	−1387.24	−	2402.77i	−0.416576	−	0.721532i	0.579016	−	0.815316i	$-0.303437\pi$
$223$	−1387.24	−	2402.77i	−0.416576	−	0.721532i	−0.995593	+	0.0937845i	$0.970104\pi$
$224$	7364.91			2.19683
$225$		0			0
$226$	5628.19			1.65655
$227$	2550.67	+	4417.89i	0.745788	+	1.29174i	0.949826	+	0.312779i	$0.101260\pi$
$227$	2550.67	+	4417.89i	0.745788	+	1.29174i	−0.204038	+	0.978963i	$0.565407\pi$
$228$		0			0
$229$	2048.91	−	3548.82i	0.591249	−	1.02407i	−0.402816	−	0.915281i	$-0.631968\pi$
$229$	2048.91	−	3548.82i	0.591249	−	1.02407i	0.994065	−	0.108792i	$-0.0346983\pi$
$230$	−2012.75	+	3486.18i	−0.577028	+	0.999443i
$231$		0			0
$232$	5907.69	+	10232.4i	1.67181	+	2.89565i
$233$	357.613			0.100549			0.0502747	−	0.998735i	$-0.483990\pi$
$233$	357.613			0.100549			0.0502747	+	0.998735i	$0.483990\pi$
$234$		0			0
$235$	25.0199			0.00694519
$236$	−4100.91	−	7102.99i	−1.13113	−	1.95918i
$237$		0			0
$238$	−4325.61	+	7492.18i	−1.17810	+	2.04053i
$239$	175.841	−	304.566i	0.0475909	−	0.0824298i	−0.841249	−	0.540648i	$-0.818179\pi$
$239$	175.841	−	304.566i	0.0475909	−	0.0824298i	0.888840	+	0.458219i	$0.151512\pi$
$240$		0			0
$241$	3082.76	+	5339.51i	0.823976	+	1.42717i	0.902699	+	0.430273i	$0.141583\pi$
$241$	3082.76	+	5339.51i	0.823976	+	1.42717i	−0.0787225	+	0.996897i	$0.525084\pi$
$242$	−2553.19			−0.678204
$243$		0			0
$244$	11325.0			2.97134
$245$	631.064	+	1093.03i	0.164560	+	0.285026i
$246$		0			0
$247$	3414.25	−	5913.65i	0.879528	−	1.52339i
$248$	524.238	−	908.006i	0.134230	−	0.232494i
$249$		0			0
$250$	325.042	+	562.989i	0.0822298	+	0.142426i
$251$	3245.53			0.816160			0.408080	−	0.912946i	$-0.366198\pi$
$251$	3245.53			0.816160			0.408080	+	0.912946i	$0.366198\pi$
$252$		0			0
$253$	4486.90			1.11498
$254$	2013.00	+	3486.62i	0.497271	+	0.861299i
$255$		0			0
$256$	2484.63	−	4303.50i	0.606598	−	1.05066i
$257$	−1776.10	+	3076.29i	−0.431089	+	0.746668i	−0.996967	−	0.0778206i	$-0.975204\pi$
$257$	−1776.10	+	3076.29i	−0.431089	+	0.746668i	0.565878	+	0.824489i	$0.308537\pi$
$258$		0			0
$259$	4119.11	+	7134.51i	0.988220	+	1.71165i
$260$	6227.59			1.48546
$261$		0			0
$262$	−6313.81			−1.48881
$263$	−2208.29	−	3824.88i	−0.517754	−	0.896776i	−0.999787	−	0.0206232i	$-0.993435\pi$
$263$	−2208.29	−	3824.88i	−0.517754	−	0.896776i	0.482033	−	0.876153i	$-0.339898\pi$
$264$		0			0
$265$	−799.913	+	1385.49i	−0.185427	+	0.321170i
$266$	−6625.89	+	11476.4i	−1.52729	+	2.64534i
$267$		0			0
$268$	−1865.43	−	3231.01i	−0.425183	−	0.736439i
$269$	−3419.93			−0.775155			−0.387578	−	0.921837i	$-0.626688\pi$
$269$	−3419.93			−0.775155			−0.387578	+	0.921837i	$0.626688\pi$
$270$		0			0
$271$	716.407			0.160585			0.0802927	−	0.996771i	$-0.474415\pi$
$271$	716.407			0.160585			0.0802927	+	0.996771i	$0.474415\pi$
$272$	−4990.56	−	8643.91i	−1.11249	−	1.92689i
$273$		0			0
$274$	−5981.15	+	10359.7i	−1.31874	+	2.28412i
$275$	362.298	−	627.519i	0.0794451	−	0.137603i
$276$		0			0
$277$	−328.764	−	569.437i	−0.0713124	−	0.123517i	0.828164	−	0.560485i	$-0.189385\pi$
$277$	−328.764	−	569.437i	−0.0713124	−	0.123517i	−0.899477	+	0.436969i	$0.856052\pi$
$278$	−7051.72			−1.52135
$279$		0			0
$280$	−7009.49			−1.49606
$281$	−756.957	−	1311.09i	−0.160698	−	0.278338i	0.774421	−	0.632671i	$-0.218041\pi$
$281$	−756.957	−	1311.09i	−0.160698	−	0.278338i	−0.935119	+	0.354333i	$0.884708\pi$
$282$		0			0
$283$	−1953.19	+	3383.03i	−0.410266	+	0.710601i	−0.994919	−	0.100682i	$-0.967897\pi$
$283$	−1953.19	+	3383.03i	−0.410266	+	0.710601i	0.584653	+	0.811284i	$0.301231\pi$
$284$	−4056.58	+	7026.20i	−0.847584	+	1.46806i
$285$		0			0
$286$	−4928.44	−	8536.31i	−1.01897	−	1.76491i
$287$	−4781.91			−0.983509
$288$		0			0
$289$	−265.611			−0.0540629
$290$	−2673.90	−	4631.32i	−0.541436	−	0.937795i
$291$		0			0
$292$	−8849.16	+	15327.2i	−1.77349	+	3.07177i
$293$	4024.38	−	6970.43i	0.802413	−	1.38982i	−0.115611	−	0.993295i	$-0.536883\pi$
$293$	4024.38	−	6970.43i	0.802413	−	1.38982i	0.918024	−	0.396525i	$-0.129784\pi$
$294$		0			0
$295$	1076.53	+	1864.60i	0.212467	+	0.368004i
$296$	−19396.4			−3.80877
$297$		0			0
$298$	1351.37			0.262693
$299$	−5061.55	−	8766.87i	−0.978987	−	1.69566i
$300$		0			0
$301$	−4085.78	+	7076.78i	−0.782394	+	1.35515i
$302$	1321.76	−	2289.35i	0.251850	−	0.436217i
$303$		0			0
$304$	−7644.44	−	13240.6i	−1.44223	−	2.49802i
$305$	−2972.91			−0.558125
$306$		0			0
$307$	101.564			0.0188814			0.00944068	−	0.999955i	$-0.496995\pi$
$307$	101.564			0.0188814			0.00944068	+	0.999955i	$0.496995\pi$
$308$	6735.44	+	11666.1i	1.24606	+	2.15824i
$309$		0			0
$310$	−237.277	+	410.975i	−0.0434723	+	0.0752962i
$311$	3842.29	−	6655.05i	0.700567	−	1.21342i	−0.267700	−	0.963502i	$-0.586264\pi$
$311$	3842.29	−	6655.05i	0.700567	−	1.21342i	0.968268	−	0.249916i	$-0.0804030\pi$
$312$		0			0
$313$	672.575	+	1164.93i	0.121457	+	0.210370i	0.920343	−	0.391113i	$-0.127910\pi$
$313$	672.575	+	1164.93i	0.121457	+	0.210370i	−0.798885	+	0.601484i	$0.794577\pi$
$314$	−121.202			−0.0217830
$315$		0			0
$316$	465.310			0.0828346
$317$	−3811.17	−	6601.13i	−0.675257	−	1.16958i	−0.976394	−	0.215998i	$-0.930699\pi$
$317$	−3811.17	−	6601.13i	−0.675257	−	1.16958i	0.301137	−	0.953581i	$-0.402634\pi$
$318$		0			0
$319$	−2980.38	+	5162.17i	−0.523101	+	0.906037i
$320$	995.991	−	1725.11i	0.173993	−	0.301364i
$321$		0			0
$322$	9822.74	+	17013.5i	1.70000	+	2.94449i
$323$	7118.78			1.22631
$324$		0			0
$325$	−1634.80			−0.279022
$326$	10484.8	+	18160.2i	1.78129	+	3.08528i
$327$		0			0
$328$	5629.37	−	9750.36i	0.947653	−	1.64138i
$329$	61.0519	−	105.745i	0.0102307	−	0.0177201i
$330$		0			0
$331$	3292.54	+	5702.85i	0.546751	+	0.947000i	0.998494	+	0.0548525i	$0.0174689\pi$
$331$	3292.54	+	5702.85i	0.546751	+	0.947000i	−0.451744	+	0.892148i	$0.649198\pi$
$332$	−10397.0			−1.71870
$333$		0			0
$334$	−3494.39			−0.572468
$335$	489.691	+	848.170i	0.0798647	+	0.138330i
$336$		0			0
$337$	1473.47	−	2552.13i	0.238175	−	0.412532i	−0.722015	−	0.691877i	$-0.756784\pi$
$337$	1473.47	−	2552.13i	0.238175	−	0.412532i	0.960191	+	0.279345i	$0.0901174\pi$
$338$	−5406.36	+	9364.10i	−0.870022	+	1.50692i
$339$		0			0
$340$	3246.16	+	5622.52i	0.517788	+	0.896835i
$341$	528.947			0.0840002
$342$		0			0
$343$	−2210.14			−0.347919
$344$	−9619.76	−	16661.9i	−1.50774	−	2.61148i
$345$		0			0
$346$	−4247.72	+	7357.26i	−0.659996	+	1.14315i
$347$	−4246.74	+	7355.57i	−0.656994	+	1.13795i	0.324396	+	0.945921i	$0.394839\pi$
$347$	−4246.74	+	7355.57i	−0.656994	+	1.13795i	−0.981390	+	0.192025i	$0.938494\pi$
$348$		0			0
$349$	−2823.27	−	4890.05i	−0.433027	−	0.750024i	0.564106	−	0.825703i	$-0.309221\pi$
$349$	−2823.27	−	4890.05i	−0.433027	−	0.750024i	−0.997132	+	0.0756785i	$0.975888\pi$
$350$	3172.58			0.484519
$351$		0			0
$352$	−8748.03			−1.32464
$353$	610.966	+	1058.22i	0.0921202	+	0.159557i	0.908403	−	0.418096i	$-0.137302\pi$
$353$	610.966	+	1058.22i	0.0921202	+	0.159557i	−0.816283	+	0.577652i	$0.803969\pi$
$354$		0			0
$355$	1064.89	−	1844.44i	0.159207	−	0.275754i
$356$	801.242	−	1387.79i	0.119286	−	0.206609i
$357$		0			0
$358$	−887.390	−	1537.00i	−0.131006	−	0.226908i
$359$	−4151.44			−0.610319			−0.305160	−	0.952301i	$-0.598710\pi$
$359$	−4151.44			−0.610319			−0.305160	+	0.952301i	$0.598710\pi$
$360$		0			0
$361$	4045.41			0.589796
$362$	4409.96	+	7638.28i	0.640283	+	1.10900i
$363$		0			0
$364$	15196.2	−	26320.5i	2.18817	−	3.79003i
$365$	2322.98	−	4023.52i	0.333125	−	0.576989i
$366$		0			0
$367$	3519.36	+	6095.70i	0.500569	+	0.867011i	1.00000		0.000657484i	$0.000209284\pi$
$367$	3519.36	+	6095.70i	0.500569	+	0.867011i	−0.499430	+	0.866354i	$0.666457\pi$
$368$	−22665.5			−3.21065
$369$		0			0
$370$	8779.08			1.23352
$371$	3903.79	+	6761.56i	0.546293	+	0.946207i
$372$		0			0
$373$	3559.78	−	6165.72i	0.494152	−	0.855896i	−0.505826	−	0.862636i	$-0.668812\pi$
$373$	3559.78	−	6165.72i	0.494152	−	0.855896i	0.999977	+	0.00674002i	$0.00214543\pi$
$374$	5137.95	−	8899.20i	0.710367	−	1.23039i
$375$		0			0
$376$	143.744	+	248.971i	0.0197154	+	0.0341482i
$377$	13448.4			1.83720
$378$		0			0
$379$	3372.29			0.457053			0.228526	−	0.973538i	$-0.426609\pi$
$379$	3372.29			0.457053			0.228526	+	0.973538i	$0.426609\pi$
$380$	4972.41	+	8612.47i	0.671261	+	1.16266i
$381$		0			0
$382$	1889.02	−	3271.87i	0.253012	−	0.438229i
$383$	−1979.32	+	3428.28i	−0.264069	+	0.457381i	−0.967319	−	0.253562i	$-0.918398\pi$
$383$	−1979.32	+	3428.28i	−0.264069	+	0.457381i	0.703250	+	0.710942i	$0.251731\pi$
$384$		0			0
$385$	−1768.11	−	3062.46i	−0.234056	−	0.405396i
$386$	22088.6			2.91264
$387$		0			0
$388$	15763.5			2.06256
$389$	−4827.00	−	8360.61i	−0.629148	−	1.08972i	−0.987723	−	0.156216i	$-0.950070\pi$
$389$	−4827.00	−	8360.61i	−0.629148	−	1.08972i	0.358574	−	0.933501i	$-0.383263\pi$
$390$		0			0
$391$	5276.72	−	9139.55i	0.682494	−	1.18211i
$392$	−7251.13	+	12559.3i	−0.934279	+	1.61822i
$393$		0			0
$394$	−6965.04	−	12063.8i	−0.890594	−	1.54255i
$395$	−122.148			−0.0155593
$396$		0			0
$397$	10928.3			1.38155			0.690776	−	0.723068i	$-0.257269\pi$
$397$	10928.3			1.38155			0.690776	+	0.723068i	$0.257269\pi$
$398$	−3865.35	−	6694.99i	−0.486816	−	0.843189i
$399$		0			0
$400$	−1830.14	+	3169.90i	−0.228768	+	0.396237i
$401$	−2042.78	+	3538.21i	−0.254393	+	0.440622i	−0.964731	−	0.263239i	$-0.915209\pi$
$401$	−2042.78	+	3538.21i	−0.254393	+	0.440622i	0.710337	+	0.703862i	$0.248542\pi$
$402$		0			0
$403$	−596.691	−	1033.50i	−0.0737551	−	0.127748i
$404$	15686.6			1.93178
$405$		0			0
$406$	−26098.7			−3.19028
$407$	−4892.67	−	8474.35i	−0.595874	−	1.03208i
$408$		0			0
$409$	−5078.13	+	8795.57i	−0.613930	+	1.06336i	0.376642	+	0.926359i	$0.377079\pi$
$409$	−5078.13	+	8795.57i	−0.613930	+	1.06336i	−0.990571	+	0.136998i	$0.956255\pi$
$410$	−2547.93	+	4413.14i	−0.306910	+	0.531584i
$411$		0			0
$412$	−11153.8	−	19319.0i	−1.33376	−	2.31014i
$413$	10507.5			1.25191
$414$		0			0
$415$	2729.29			0.322833
$416$	9868.43	+	17092.6i	1.16308	+	2.01451i
$417$		0			0
$418$	7870.22	−	13631.6i	0.920921	−	1.59508i
$419$	−7939.41	+	13751.5i	−0.925693	+	1.60335i	−0.135250	+	0.990811i	$0.543184\pi$
$419$	−7939.41	+	13751.5i	−0.925693	+	1.60335i	−0.790443	+	0.612536i	$0.790149\pi$
$420$		0			0
$421$	1139.92	+	1974.40i	0.131963	+	0.228567i	0.924433	−	0.381344i	$-0.124539\pi$
$421$	1139.92	+	1974.40i	0.131963	+	0.228567i	−0.792470	+	0.609911i	$0.791205\pi$
$422$	−25105.8			−2.89604
$423$		0			0
$424$	−18382.5			−2.10551
$425$	−852.147	−	1475.96i	−0.0972593	−	0.168458i
$426$		0			0
$427$	−7254.29	+	12564.8i	−0.822154	+	1.42401i
$428$	−9744.51	+	16878.0i	−1.10051	+	1.90614i
$429$		0			0
$430$	4354.03	+	7541.39i	0.488302	+	0.845763i
$431$	−1947.38			−0.217638			−0.108819	−	0.994062i	$-0.534707\pi$
$431$	−1947.38			−0.217638			−0.108819	+	0.994062i	$0.534707\pi$
$432$		0			0
$433$	12636.2			1.40244			0.701219	−	0.712946i	$-0.252639\pi$
$433$	12636.2			1.40244			0.701219	+	0.712946i	$0.252639\pi$
$434$	1157.97	+	2005.67i	0.128075	+	0.221832i
$435$		0			0
$436$	3844.12	−	6658.22i	0.422248	−	0.731355i
$437$	8082.78	−	13999.8i	0.884787	−	1.53250i
$438$		0			0
$439$	7924.92	+	13726.4i	0.861585	+	1.49231i	0.870399	+	0.492347i	$0.163861\pi$
$439$	7924.92	+	13726.4i	0.861585	+	1.49231i	−0.00881399	+	0.999961i	$0.502806\pi$
$440$	8325.86			0.902090
$441$		0			0
$442$	−23184.0			−2.49491
$443$	8727.78	+	15117.0i	0.936048	+	1.62128i	0.772754	+	0.634706i	$0.218879\pi$
$443$	8727.78	+	15117.0i	0.936048	+	1.62128i	0.163294	+	0.986577i	$0.447788\pi$
$444$		0			0
$445$	−210.333	+	364.308i	−0.0224062	+	0.0388086i
$446$	−7214.59	+	12496.0i	−0.765965	+	1.32669i
$447$		0			0
$448$	−4860.70	−	8418.99i	−0.512604	−	0.887857i
$449$	−16068.1			−1.68887			−0.844435	−	0.535658i	$-0.820064\pi$
$449$	−16068.1			−1.68887			−0.844435	+	0.535658i	$0.820064\pi$
$450$		0			0
$451$	5679.94			0.593033
$452$	−10306.4	−	17851.1i	−1.07250	−	1.85762i
$453$		0			0
$454$	13265.2	−	22976.0i	1.37129	−	2.37515i
$455$	−3989.13	+	6909.37i	−0.411018	+	0.711904i
$456$		0			0
$457$	−5945.86	−	10298.5i	−0.608612	−	1.05415i	−0.991469	−	0.130339i	$-0.958393\pi$
$457$	−5945.86	−	10298.5i	−0.608612	−	1.05415i	0.382858	−	0.923807i	$-0.374940\pi$
$458$	−21311.4			−2.17428
$459$		0			0
$460$	14743.0			1.49434
$461$	1401.11	+	2426.80i	0.141554	+	0.245179i	0.928082	−	0.372376i	$-0.121457\pi$
$461$	1401.11	+	2426.80i	0.141554	+	0.245179i	−0.786528	+	0.617555i	$0.788123\pi$
$462$		0			0
$463$	6466.66	−	11200.6i	0.649096	−	1.12427i	−0.334244	−	0.942487i	$-0.608481\pi$
$463$	6466.66	−	11200.6i	0.649096	−	1.12427i	0.983339	−	0.181780i	$-0.0581859\pi$
$464$	15055.3	−	26076.6i	1.50631	−	2.60900i
$465$		0			0
$466$	−929.915	−	1610.66i	−0.0924409	−	0.160112i
$467$	5748.11			0.569573			0.284787	−	0.958591i	$-0.408077\pi$
$467$	5748.11			0.569573			0.284787	+	0.958591i	$0.408077\pi$
$468$		0			0
$469$	4779.65			0.470583
$470$	−65.0602	−	112.688i	−0.00638511	−	0.0110593i
$471$		0			0
$472$	−12369.6	+	21424.9i	−1.20627	+	2.08932i
$473$	4853.09	−	8405.79i	0.471766	−	0.817122i
$474$		0			0
$475$	−1305.30	−	2260.85i	−0.126087	−	0.218389i
$476$	31684.3			3.05094
$477$		0			0
$478$	−1828.98			−0.175012
$479$	5608.66	+	9714.48i	0.535002	+	0.926651i	0.999163	+	0.0409004i	$0.0130226\pi$
$479$	5608.66	+	9714.48i	0.535002	+	0.926651i	−0.464161	+	0.885751i	$0.653644\pi$
$480$		0			0
$481$	−11038.6	+	19119.4i	−1.04640	+	1.81241i
$482$	16032.4	−	27769.0i	1.51506	−	2.62416i
$483$		0			0
$484$	4675.42	+	8098.06i	0.439089	+	0.760524i
$485$	−4138.07			−0.387423
$486$		0			0
$487$	−8905.12			−0.828603			−0.414301	−	0.910140i	$-0.635974\pi$
$487$	−8905.12			−0.828603			−0.414301	+	0.910140i	$0.635974\pi$
$488$	−17079.8	−	29583.1i	−1.58436	−	2.74419i
$489$		0			0
$490$	3281.95	−	5684.51i	0.302579	−	0.524082i
$491$	3276.55	−	5675.15i	0.301158	−	0.521621i	−0.675240	−	0.737598i	$-0.735960\pi$
$491$	3276.55	−	5675.15i	0.301158	−	0.521621i	0.976399	+	0.215976i	$0.0692934\pi$
$492$		0			0
$493$	7010.03	+	12141.7i	0.640397	+	1.10920i
$494$	−35512.8			−3.23440
$495$		0			0
$496$	−2671.96			−0.241884
$497$	−5196.94	−	9001.37i	−0.469044	−	0.812407i
$498$		0			0
$499$	2305.04	−	3992.45i	0.206789	−	0.358170i	−0.743912	−	0.668278i	$-0.767032\pi$
$499$	2305.04	−	3992.45i	0.206789	−	0.358170i	0.950701	+	0.310108i	$0.100365\pi$
$500$	1190.44	−	2061.90i	0.106476	−	0.184422i
$501$		0			0
$502$	−8439.47	−	14617.6i	−0.750343	−	1.29963i
$503$	13069.1			1.15850			0.579249	−	0.815151i	$-0.303346\pi$
$503$	13069.1			1.15850			0.579249	+	0.815151i	$0.303346\pi$
$504$		0			0
$505$	−4117.88			−0.362858
$506$	−11667.4	−	20208.6i	−1.02506	−	1.77546i
$507$		0			0
$508$	7372.43	−	12769.4i	0.643895	−	1.11526i
$509$	−7965.40	+	13796.5i	−0.693635	+	1.20141i	0.277004	+	0.960869i	$0.410659\pi$
$509$	−7965.40	+	13796.5i	−0.693635	+	1.20141i	−0.970639	+	0.240542i	$0.922675\pi$
$510$		0			0
$511$	−11336.8	−	19635.9i	−0.981428	−	1.69988i
$512$	−23102.1			−1.99410
$513$		0			0
$514$	18473.8			1.58530
$515$	2927.97	+	5071.40i	0.250528	+	0.433927i
$516$		0			0
$517$	−72.5174	+	125.604i	−0.00616888	+	0.0106848i
$518$	21422.1	−	37104.2i	1.81705	−	3.14723i
$519$		0			0
$520$	−9392.19	−	16267.7i	−0.792067	−	1.37190i
$521$	3654.38			0.307296			0.153648	−	0.988126i	$-0.450898\pi$
$521$	3654.38			0.307296			0.153648	+	0.988126i	$0.450898\pi$
$522$		0			0
$523$	−5138.66			−0.429633			−0.214816	−	0.976654i	$-0.568915\pi$
$523$	−5138.66			−0.429633			−0.214816	+	0.976654i	$0.568915\pi$
$524$	11561.9	+	20025.7i	0.963898	+	1.66952i
$525$		0			0
$526$	−11484.6	+	19891.9i	−0.952002	+	1.64892i
$527$	622.057	−	1077.43i	0.0514179	−	0.0890584i
$528$		0			0
$529$	−5899.05	−	10217.5i	−0.484840	−	0.839768i
$530$	8320.16			0.681896
$531$		0			0
$532$	48533.4			3.95524
$533$	−6407.39	−	11097.9i	−0.520704	−	0.901885i
$534$		0			0
$535$	2558.02	−	4430.62i	0.206716	−	0.358042i
$536$	−5626.71	+	9745.75i	−0.453427	+	0.785359i
$537$		0			0
$538$	8892.96	+	15403.1i	0.712645	+	1.23434i
$539$	−7316.27			−0.584664
$540$		0			0
$541$	6932.06			0.550892			0.275446	−	0.961317i	$-0.411175\pi$
$541$	6932.06			0.550892			0.275446	+	0.961317i	$0.411175\pi$
$542$	−1862.90	−	3226.64i	−0.147635	−	0.255712i
$543$		0			0
$544$	−10287.9	+	17819.2i	−0.810831	+	1.40440i
$545$	−1009.12	+	1747.84i	−0.0793134	+	0.137375i
$546$		0			0
$547$	1711.56	+	2964.50i	0.133786	+	0.231724i	0.925133	−	0.379643i	$-0.123953\pi$
$547$	1711.56	+	2964.50i	0.133786	+	0.231724i	−0.791347	+	0.611367i	$0.790620\pi$
$548$	43810.8			3.41516
$549$		0			0
$550$	−3768.39			−0.292154
$551$	10737.8	+	18598.4i	0.830211	+	1.43797i
$552$		0			0
$553$	−298.058	+	516.251i	−0.0229199	+	0.0396984i
$554$	−1709.79	+	2961.45i	−0.131123	+	0.227112i
$555$		0			0
$556$	12913.1	+	22366.2i	0.984962	+	1.70600i
$557$	−24489.2			−1.86291			−0.931455	−	0.363856i	$-0.881460\pi$
$557$	−24489.2			−1.86291			−0.931455	+	0.363856i	$0.881460\pi$
$558$		0			0
$559$	−21898.6			−1.65691
$560$	8931.59	+	15470.0i	0.673979	+	1.16737i
$561$		0			0
$562$	−3936.68	+	6818.54i	−0.295479	+	0.511784i
$563$	5026.54	−	8706.22i	0.376276	−	0.651729i	−0.614241	−	0.789118i	$-0.710538\pi$
$563$	5026.54	−	8706.22i	0.376276	−	0.651729i	0.990517	+	0.137389i	$0.0438711\pi$
$564$		0			0
$565$	2705.51	+	4686.08i	0.201454	+	0.348929i
$566$	20315.8			1.50872
$567$		0			0
$568$	24471.8			1.80777
$569$	3335.23	+	5776.78i	0.245729	+	0.425616i	0.962336	−	0.271861i	$-0.0876392\pi$
$569$	3335.23	+	5776.78i	0.245729	+	0.425616i	−0.716607	+	0.697477i	$0.754306\pi$
$570$		0			0
$571$	−2316.78	+	4012.77i	−0.169797	+	0.294097i	−0.938348	−	0.345691i	$-0.887645\pi$
$571$	−2316.78	+	4012.77i	−0.169797	+	0.294097i	0.768551	+	0.639788i	$0.220978\pi$
$572$	−18050.0	+	31263.5i	−1.31942	+	2.28530i
$573$		0			0
$574$	12434.6	+	21537.3i	0.904196	+	1.56611i
$575$	−3870.17			−0.280691
$576$		0			0
$577$	7045.15			0.508307			0.254154	−	0.967164i	$-0.418203\pi$
$577$	7045.15			0.508307			0.254154	+	0.967164i	$0.418203\pi$
$578$	690.677	+	1196.29i	0.0497031	+	0.0860883i
$579$		0			0
$580$	−9792.89	+	16961.8i	−0.701082	+	1.21431i
$581$	6659.84	−	11535.2i	0.475554	−	0.823683i
$582$		0			0
$583$	−4636.91	−	8031.37i	−0.329402	−	0.570541i
$584$	53383.7			3.78259
$585$		0			0
$586$	−41859.0			−2.95082
$587$	4000.53	+	6929.12i	0.281294	+	0.487216i	0.971704	−	0.236203i	$-0.0759030\pi$
$587$	4000.53	+	6929.12i	0.281294	+	0.487216i	−0.690410	+	0.723419i	$0.742570\pi$
$588$		0			0
$589$	952.855	−	1650.39i	0.0666582	−	0.115455i
$590$	5598.66	−	9697.16i	0.390666	−	0.676654i
$591$		0			0
$592$	24715.2	+	42808.0i	1.71586	+	2.97196i
$593$	6747.53			0.467265			0.233632	−	0.972325i	$-0.424939\pi$
$593$	6747.53			0.467265			0.233632	+	0.972325i	$0.424939\pi$
$594$		0			0
$595$	−8317.41			−0.573077
$596$	−2474.63	−	4286.19i	−0.170075	−	0.294579i
$597$		0			0
$598$	−26323.5	+	45593.6i	−1.80008	+	3.11783i
$599$	−10773.6	+	18660.5i	−0.734890	+	1.27287i	0.219881	+	0.975527i	$0.429433\pi$
$599$	−10773.6	+	18660.5i	−0.734890	+	1.27287i	−0.954771	+	0.297341i	$0.903900\pi$
$600$		0			0
$601$	6077.53	+	10526.6i	0.412492	+	0.714456i	0.995162	−	0.0982525i	$-0.0313253\pi$
$601$	6077.53	+	10526.6i	0.412492	+	0.714456i	−0.582670	+	0.812709i	$0.697992\pi$
$602$	42497.6			2.87720
$603$		0			0
$604$	−9681.64			−0.652219
$605$	−1227.34	−	2125.81i	−0.0824767	−	0.142854i
$606$		0			0
$607$	−8174.47	+	14158.6i	−0.546608	+	0.946754i	0.451895	+	0.892071i	$0.350748\pi$
$607$	−8174.47	+	14158.6i	−0.546608	+	0.946754i	−0.998504	+	0.0546827i	$0.982585\pi$
$608$	−15758.9	+	27295.2i	−1.05116	+	1.82067i
$609$		0			0
$610$	7730.55	+	13389.7i	0.513116	+	0.888743i
$611$	327.220			0.0216660
$612$		0			0
$613$	−29955.5			−1.97372			−0.986859	−	0.161581i	$-0.948341\pi$
$613$	−29955.5			−1.97372			−0.986859	+	0.161581i	$0.948341\pi$
$614$	−264.101	−	457.437i	−0.0173587	−	0.0300662i
$615$		0			0
$616$	20316.2	−	35188.7i	1.32884	−	2.30161i
$617$	−1079.87	+	1870.39i	−0.0704603	+	0.122041i	−0.899103	−	0.437737i	$-0.855780\pi$
$617$	−1079.87	+	1870.39i	−0.0704603	+	0.122041i	0.828643	+	0.559778i	$0.189113\pi$
$618$		0			0
$619$	−11050.4	−	19139.9i	−0.717535	−	1.24281i	−0.961974	−	0.273142i	$-0.911937\pi$
$619$	−11050.4	−	19139.9i	−0.717535	−	1.24281i	0.244439	−	0.969665i	$-0.421396\pi$
$620$	1738.01			0.112581
$621$		0			0
$622$	−39965.0			−2.57629
$623$	1026.48	+	1777.92i	0.0660114	+	0.114335i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	3497.84	−	6058.44i	0.223326	−	0.386811i
$627$		0			0
$628$	221.946	+	384.422i	0.0141029	+	0.0244269i
$629$	−23015.7			−1.45898
$630$		0			0
$631$	18360.1			1.15833			0.579164	−	0.815211i	$-0.303379\pi$
$631$	18360.1			1.15833			0.579164	+	0.815211i	$0.303379\pi$
$632$	−701.761	−	1215.49i	−0.0441686	−	0.0765023i
$633$		0			0
$634$	−19820.6	+	34330.3i	−1.24160	+	2.15052i
$635$	−1935.33	+	3352.09i	−0.120947	+	0.209486i
$636$		0			0
$637$	8253.29	+	14295.1i	0.513355	+	0.889157i
$638$	30999.9			1.92367
$639$		0			0
$640$	1713.32			0.105820
$641$	10532.3	+	18242.4i	0.648985	+	1.12407i	0.983366	+	0.181636i	$0.0581393\pi$
$641$	10532.3	+	18242.4i	0.648985	+	1.12407i	−0.334381	+	0.942438i	$0.608527\pi$
$642$		0			0
$643$	5269.57	−	9127.16i	0.323190	−	0.559782i	−0.657954	−	0.753058i	$-0.728578\pi$
$643$	5269.57	−	9127.16i	0.323190	−	0.559782i	0.981144	+	0.193276i	$0.0619112\pi$
$644$	35974.9	−	62310.3i	2.20126	−	3.81269i
$645$		0			0
$646$	−18511.2	−	32062.4i	−1.12742	−	1.95275i
$647$	22553.4			1.37043			0.685213	−	0.728343i	$-0.259709\pi$
$647$	22553.4			1.37043			0.685213	+	0.728343i	$0.259709\pi$
$648$		0			0
$649$	−12480.8			−0.754873
$650$	4251.02	+	7362.99i	0.256521	+	0.444308i
$651$		0			0
$652$	38399.7	−	66510.2i	2.30652	−	3.99500i
$653$	−11312.0	+	19593.0i	−0.677908	+	1.17417i	0.297702	+	0.954659i	$0.403780\pi$
$653$	−11312.0	+	19593.0i	−0.677908	+	1.17417i	−0.975610	+	0.219512i	$0.929554\pi$
$654$		0			0
$655$	−3035.09	−	5256.94i	−0.181055	−	0.313596i
$656$	−28692.1			−1.70768
$657$		0			0
$658$	−635.022			−0.0376227
$659$	−3188.30	−	5522.29i	−0.188465	−	0.326431i	0.756274	−	0.654255i	$-0.227018\pi$
$659$	−3188.30	−	5522.29i	−0.188465	−	0.326431i	−0.944739	+	0.327824i	$0.893685\pi$
$660$		0			0
$661$	11048.8	−	19137.0i	0.650146	−	1.12609i	−0.332941	−	0.942948i	$-0.608041\pi$
$661$	11048.8	−	19137.0i	0.650146	−	1.12609i	0.983087	−	0.183139i	$-0.0586258\pi$
$662$	17123.4	−	29658.7i	1.00532	−	1.74126i
$663$		0			0
$664$	15680.2	+	27159.0i	0.916433	+	1.58731i
$665$	−12740.4			−0.742938
$666$		0			0
$667$	31837.2			1.84819
$668$	6398.93	+	11083.3i	0.370632	+	0.641953i
$669$		0			0
$670$	2546.72	−	4411.05i	0.146848	−	0.254349i
$671$	8616.63	−	14924.4i	0.495740	−	0.858646i
$672$		0			0
$673$	−12016.5	−	20813.2i	−0.688264	−	1.19211i	−0.972399	−	0.233323i	$-0.925040\pi$
$673$	−12016.5	−	20813.2i	−0.688264	−	1.19211i	0.284136	−	0.958784i	$-0.408293\pi$
$674$	−15326.1			−0.875873
$675$		0			0
$676$	39600.6			2.25311
$677$	−89.8191	−	155.571i	−0.00509901	−	0.00883175i	0.863465	−	0.504409i	$-0.168290\pi$
$677$	−89.8191	−	155.571i	−0.00509901	−	0.00883175i	−0.868564	+	0.495578i	$0.834956\pi$
$678$		0			0
$679$	−10097.4	+	17489.3i	−0.570698	+	0.988478i
$680$	9791.45	−	16959.3i	0.552184	−	0.956411i
$681$		0			0
$682$	−1375.44	−	2382.33i	−0.0772262	−	0.133760i
$683$	−30434.2			−1.70502			−0.852511	−	0.522709i	$-0.824921\pi$
$683$	−30434.2			−1.70502			−0.852511	+	0.522709i	$0.824921\pi$
$684$		0			0
$685$	−11500.7			−0.641490
$686$	5747.11	+	9954.28i	0.319862	+	0.554018i
$687$		0			0
$688$	−24515.3	+	42461.7i	−1.35848	+	2.35296i
$689$	−10461.6	+	18120.0i	−0.578453	+	1.00191i
$690$		0			0
$691$	−4896.36	−	8480.75i	−0.269561	−	0.466893i	0.699188	−	0.714938i	$-0.253545\pi$
$691$	−4896.36	−	8480.75i	−0.269561	−	0.466893i	−0.968748	+	0.248045i	$0.920212\pi$
$692$	31113.7			1.70920
$693$		0			0
$694$	44171.8			2.41605
$695$	−3389.81	−	5871.33i	−0.185011	−	0.320449i
$696$		0			0
$697$	6679.78	−	11569.7i	0.363005	−	0.628743i
$698$	−14682.9	+	25431.5i	−0.796212	+	1.37908i
$699$		0			0
$700$	−5809.65	−	10062.6i	−0.313691	−	0.543329i
$701$	8130.47			0.438065			0.219032	−	0.975718i	$-0.429710\pi$
$701$	8130.47			0.438065			0.219032	+	0.975718i	$0.429710\pi$
$702$		0			0
$703$	−35255.0			−1.89142
$704$	5773.54	+	10000.1i	0.309089	+	0.535357i
$705$		0			0
$706$	3177.43	−	5503.47i	0.169383	−	0.293379i
$707$	−10048.2	+	17404.0i	−0.534513	+	0.925804i
$708$		0			0
$709$	2429.98	+	4208.84i	0.128716	+	0.222943i	0.923179	−	0.384369i	$-0.125581\pi$
$709$	2429.98	+	4208.84i	0.128716	+	0.222943i	−0.794463	+	0.607312i	$0.792248\pi$
$710$	−11076.3			−0.585472
$711$		0			0
$712$	−4833.59			−0.254419
$713$	−1412.59	−	2446.67i	−0.0741961	−	0.128511i
$714$		0			0
$715$	4738.28	−	8206.94i	0.247834	−	0.429262i
$716$	−3249.98	+	5629.13i	−0.169633	+	0.293814i
$717$		0			0
$718$	10795.1	+	18697.7i	0.561101	+	0.971856i
$719$	19463.0			1.00952			0.504762	−	0.863259i	$-0.331580\pi$
$719$	19463.0			1.00952			0.504762	+	0.863259i	$0.331580\pi$
$720$		0			0
$721$	28578.6			1.47618
$722$	−10519.4	−	18220.2i	−0.542233	−	0.939175i
$723$		0			0
$724$	16151.1	−	27974.5i	0.829075	−	1.43600i
$725$	2570.72	−	4452.62i	0.131689	−	0.228091i
$726$		0			0
$727$	−1216.33	−	2106.75i	−0.0620512	−	0.107476i	0.833331	−	0.552774i	$-0.186431\pi$
$727$	−1216.33	−	2106.75i	−0.0620512	−	0.107476i	−0.895382	+	0.445299i	$0.853098\pi$
$728$	−91672.8			−4.66706
$729$		0			0
$730$	−24162.1			−1.22504
$731$	−11414.7	−	19770.9i	−0.577551	−	1.00035i
$732$		0			0
$733$	8983.79	−	15560.4i	0.452693	−	0.784087i	−0.545859	−	0.837877i	$-0.683797\pi$
$733$	8983.79	−	15560.4i	0.452693	−	0.784087i	0.998552	+	0.0537895i	$0.0171300\pi$
$734$	18303.0	−	31701.8i	0.920404	−	1.59419i
$735$		0			0
$736$	23362.2	+	40464.5i	1.17003	+	2.02655i
$737$	−5677.26			−0.283751
$738$		0			0
$739$	23473.0			1.16843			0.584214	−	0.811599i	$-0.301403\pi$
$739$	23473.0			1.16843			0.584214	+	0.811599i	$0.301403\pi$
$740$	−16076.3	−	27844.9i	−0.798616	−	1.38324i
$741$		0			0
$742$	20302.3	−	35164.6i	1.00448	−	1.73980i
$743$	16779.6	−	29063.2i	0.828512	−	1.43503i	−0.0706932	−	0.997498i	$-0.522521\pi$
$743$	16779.6	−	29063.2i	0.828512	−	1.43503i	0.899205	−	0.437527i	$-0.144146\pi$
$744$		0			0
$745$	649.613	+	1125.16i	0.0319463	+	0.0553325i
$746$	−37026.5			−1.81721
$747$		0			0
$748$	−37634.6			−1.83965
$749$	−12483.8	−	21622.6i	−0.609011	−	1.05484i
$750$		0			0
$751$	3891.38	−	6740.06i	0.189079	−	0.327495i	−0.755864	−	0.654728i	$-0.772783\pi$
$751$	3891.38	−	6740.06i	0.189079	−	0.327495i	0.944943	+	0.327234i	$0.106116\pi$
$752$	366.320	−	634.485i	0.0177637	−	0.0307677i
$753$		0			0
$754$	−34970.2	−	60570.2i	−1.68905	−	2.92551i
$755$	2541.52			0.122510
$756$		0			0
$757$	−38154.3			−1.83189			−0.915946	−	0.401300i	$-0.868558\pi$
$757$	−38154.3			−1.83189			−0.915946	+	0.401300i	$0.868558\pi$
$758$	−8769.09	−	15188.5i	−0.420195	−	0.727799i
$759$		0			0
$760$	14998.4	−	25977.9i	0.715852	−	1.23989i
$761$	−9933.56	+	17205.4i	−0.473182	+	0.819575i	−0.999529	−	0.0306951i	$-0.990228\pi$
$761$	−9933.56	+	17205.4i	−0.473182	+	0.819575i	0.526347	+	0.850270i	$0.323561\pi$
$762$		0			0
$763$	4924.76	+	8529.93i	0.233667	+	0.404724i
$764$	−13836.7			−0.655228
$765$		0			0
$766$	20587.5			0.971094
$767$	14079.2	+	24385.9i	0.662805	+	1.14801i
$768$		0			0
$769$	7855.40	−	13605.9i	0.368365	−	0.638027i	−0.620945	−	0.783854i	$-0.713251\pi$
$769$	7855.40	−	13605.9i	0.368365	−	0.638027i	0.989310	+	0.145827i	$0.0465843\pi$
$770$	−9195.37	+	15926.9i	−0.430361	+	0.745408i
$771$		0			0
$772$	−40448.7	−	70059.3i	−1.88573	−	3.26618i
$773$	25811.9			1.20102			0.600510	−	0.799617i	$-0.294964\pi$
$773$	25811.9			1.20102			0.600510	+	0.799617i	$0.294964\pi$
$774$		0			0
$775$	−456.242			−0.0211467
$776$	−23773.9	−	41177.6i	−1.09978	−	1.90488i
$777$		0			0
$778$	−25103.6	+	43480.8i	−1.15682	+	2.00368i
$779$	10232.0	−	17722.3i	0.470600	−	0.815104i
$780$		0			0
$781$	6172.92	+	10691.8i	0.282822	+	0.489863i
$782$	−54885.0			−2.50982
$783$		0			0
$784$	36958.0			1.68358
$785$	−58.2629	−	100.914i	−0.00264903	−	0.00458826i
$786$		0			0
$787$	14621.3	−	25324.8i	0.662252	−	1.14705i	−0.317770	−	0.948168i	$-0.602934\pi$
$787$	14621.3	−	25324.8i	0.662252	−	1.14705i	0.980023	−	0.198887i	$-0.0637326\pi$
$788$	−25508.8	+	44182.6i	−1.15319	+	1.99739i
$789$		0			0
$790$	317.626	+	550.144i	0.0143046	+	0.0247763i
$791$	26407.2			1.18702
$792$		0			0
$793$	−38880.8			−1.74111
$794$	−28417.3	−	49220.2i	−1.27014	−	2.19995i
$795$		0			0
$796$	−14156.5	+	24519.8i	−0.630356	+	1.09181i
$797$	−16286.9	+	28209.7i	−0.723853	+	1.25375i	0.235592	+	0.971852i	$0.424297\pi$
$797$	−16286.9	+	28209.7i	−0.723853	+	1.25375i	−0.959445	+	0.281898i	$0.909036\pi$
$798$		0			0
$799$	170.565	+	295.428i	0.00755214	+	0.0130807i
$800$	7545.60			0.333472
$801$		0			0
$802$	21247.7			0.935514
$803$	13465.8	+	23323.5i	0.591778	+	1.02499i
$804$		0			0
$805$	−9443.73	+	16357.0i	−0.413475	+	0.716160i
$806$	−3103.19	+	5374.89i	−0.135615	+	0.234891i
$807$		0			0
$808$	−23657.9	−	40976.7i	−1.03005	−	1.78410i
$809$	−34644.9			−1.50562			−0.752812	−	0.658236i	$-0.771303\pi$
$809$	−34644.9			−1.50562			−0.752812	+	0.658236i	$0.771303\pi$
$810$		0			0
$811$	−29057.9			−1.25815			−0.629077	−	0.777343i	$-0.716567\pi$
$811$	−29057.9			−1.25815			−0.629077	+	0.777343i	$0.716567\pi$
$812$	47791.9	+	82778.1i	2.06548	+	3.57751i
$813$		0			0
$814$	−25445.2	+	44072.3i	−1.09564	+	1.89771i
$815$	−10080.3	+	17459.5i	−0.433247	+	0.750405i
$816$		0			0
$817$	−17484.9	−	30284.7i	−0.748738	−	1.29685i
$818$	52819.3			2.25768
$819$		0			0
$820$	18663.1			0.794809
$821$	−23354.8	−	40451.6i	−0.992798	−	1.71958i	−0.600150	−	0.799887i	$-0.704893\pi$
$821$	−23354.8	−	40451.6i	−0.992798	−	1.71958i	−0.392647	−	0.919689i	$-0.628441\pi$
$822$		0			0
$823$	1734.05	−	3003.46i	0.0734450	−	0.127210i	−0.826964	−	0.562255i	$-0.809934\pi$
$823$	1734.05	−	3003.46i	0.0734450	−	0.127210i	0.900409	+	0.435044i	$0.143267\pi$
$824$	−33643.4	+	58272.1i	−1.42236	+	2.46360i
$825$		0			0
$826$	−27323.0	−	47324.8i	−1.15095	−	1.99351i
$827$	42454.9			1.78513			0.892564	−	0.450920i	$-0.148904\pi$
$827$	42454.9			1.78513			0.892564	+	0.450920i	$0.148904\pi$
$828$		0			0
$829$	−3933.47			−0.164795			−0.0823975	−	0.996600i	$-0.526258\pi$
$829$	−3933.47			−0.164795			−0.0823975	+	0.996600i	$0.526258\pi$
$830$	−7097.08	−	12292.5i	−0.296799	−	0.514071i
$831$		0			0
$832$	13026.0	−	22561.6i	0.542781	−	0.940124i
$833$	−8604.14	+	14902.8i	−0.357882	+	0.619870i
$834$		0			0
$835$	−1679.78	−	2909.46i	−0.0696181	−	0.120582i
$836$	−57647.9			−2.38492
$837$		0			0
$838$	82580.5			3.40417
$839$	16479.8	+	28543.8i	0.678123	+	1.17454i	0.975546	+	0.219797i	$0.0705396\pi$
$839$	16479.8	+	28543.8i	0.678123	+	1.17454i	−0.297423	+	0.954746i	$0.596127\pi$
$840$		0			0
$841$	−8953.05	+	15507.1i	−0.367094	+	0.635825i
$842$	5928.36	−	10268.2i	0.242642	−	0.420269i
$843$		0			0
$844$	45973.8	+	79629.0i	1.87498	+	3.24756i
$845$	−10395.5			−0.423215
$846$		0			0
$847$	−11979.5			−0.485974
$848$	23423.3	+	40570.3i	0.948536	+	1.64291i
$849$		0			0
$850$	−4431.74	+	7675.99i	−0.178832	+	0.309746i
$851$	−26132.4	+	45262.6i	−1.05265	+	1.82325i
$852$		0			0
$853$	−19422.9	−	33641.5i	−0.779634	−	1.35037i	−0.932153	−	0.362066i	$-0.882072\pi$
$853$	−19422.9	−	33641.5i	−0.779634	−	1.35037i	0.152518	−	0.988301i	$-0.451262\pi$
$854$	75454.3			3.02341
$855$		0			0
$856$	58785.0			2.34723
$857$	14652.6	+	25379.1i	0.584043	+	1.01159i	0.994994	+	0.0999343i	$0.0318632\pi$
$857$	14652.6	+	25379.1i	0.584043	+	1.01159i	−0.410951	+	0.911657i	$0.634803\pi$
$858$		0			0
$859$	454.830	−	787.788i	0.0180659	−	0.0312910i	−0.856851	−	0.515564i	$-0.827582\pi$
$859$	454.830	−	787.788i	0.0180659	−	0.0312910i	0.874917	+	0.484273i	$0.160916\pi$
$860$	15946.2	−	27619.7i	0.632281	−	1.09514i
$861$		0			0
$862$	5063.83	+	8770.81i	0.200087	+	0.346560i
$863$	47998.0			1.89324			0.946622	−	0.322346i	$-0.104471\pi$
$863$	47998.0			1.89324			0.946622	+	0.322346i	$0.104471\pi$
$864$		0			0
$865$	−8167.64			−0.321050
$866$	−32858.3	−	56912.2i	−1.28934	−	2.23321i
$867$		0			0
$868$	4240.97	−	7345.58i	0.165839	−	0.287241i
$869$	354.032	−	613.202i	0.0138202	−	0.0239372i
$870$		0			0
$871$	6404.37	+	11092.7i	0.249143	+	0.431529i
$872$	−23190.2			−0.900594
$873$		0			0
$874$	−84071.7			−3.25374
$875$	1525.08	+	2641.52i	0.0589226	+	0.102057i
$876$		0			0
$877$	−1629.01	+	2821.52i	−0.0627225	+	0.108639i	−0.895681	−	0.444696i	$-0.853312\pi$
$877$	−1629.01	+	2821.52i	−0.0627225	+	0.108639i	0.832959	+	0.553335i	$0.186645\pi$
$878$	41214.9	−	71386.3i	1.58421	−	2.74393i
$879$		0			0
$880$	−10608.9	−	18375.2i	−0.406394	−	0.703895i
$881$	−33380.2			−1.27651			−0.638256	−	0.769824i	$-0.720344\pi$
$881$	−33380.2			−1.27651			−0.638256	+	0.769824i	$0.720344\pi$
$882$		0			0
$883$	33714.6			1.28492			0.642460	−	0.766319i	$-0.277914\pi$
$883$	33714.6			1.28492			0.642460	+	0.766319i	$0.277914\pi$
$884$	42454.6	+	73533.5i	1.61527	+	2.79774i
$885$		0			0
$886$	45390.3	−	78618.3i	1.72113	−	2.98108i
$887$	3109.40	−	5385.64i	0.117704	−	0.203869i	−0.801153	−	0.598459i	$-0.795780\pi$
$887$	3109.40	−	5385.64i	0.117704	−	0.203869i	0.918857	+	0.394590i	$0.129113\pi$
$888$		0			0
$889$	9444.92	+	16359.1i	0.356325	+	0.617172i
$890$	2187.75			0.0823971
$891$		0			0
$892$	52845.5			1.98363
$893$	261.268	+	452.530i	0.00979061	+	0.0169578i
$894$		0			0
$895$	853.149	−	1477.70i	0.0318633	−	0.0551888i
$896$	4180.73	−	7241.24i	0.155880	−	0.269992i
$897$		0			0
$898$	41782.6	+	72369.5i	1.55268	+	2.68931i
$899$	3753.19			0.139239
$900$		0			0
$901$	−21812.6			−0.806529
$902$	−14769.7	−	25582.0i	−0.545209	−	0.944330i
$903$		0			0
$904$	−31087.2	+	53844.6i	−1.14374	+	1.98102i
$905$	−4239.80	+	7343.56i	−0.155730	+	0.269733i
$906$		0			0
$907$	11439.3	+	19813.5i	0.418783	+	0.725354i	0.995817	−	0.0913663i	$-0.0291234\pi$
$907$	11439.3	+	19813.5i	0.418783	+	0.725354i	−0.577034	+	0.816720i	$0.695790\pi$
$908$	−97165.0			−3.55125
$909$		0			0
$910$	41492.3			1.51149
$911$	15072.4	+	26106.2i	0.548157	+	0.949435i	0.998401	+	0.0565298i	$0.0180036\pi$
$911$	15072.4	+	26106.2i	0.548157	+	0.949435i	−0.450244	+	0.892905i	$0.648663\pi$
$912$		0			0
$913$	−7910.55	+	13701.5i	−0.286748	+	0.496662i
$914$	−30922.4	+	53559.2i	−1.11906	+	1.93827i
$915$		0			0
$916$	39025.6	+	67594.3i	1.40769	+	2.43819i
$917$	−29624.1			−1.06682
$918$		0			0
$919$	3803.52			0.136525			0.0682625	−	0.997667i	$-0.478254\pi$
$919$	3803.52			0.136525			0.0682625	+	0.997667i	$0.478254\pi$
$920$	−22234.8	−	38511.7i	−0.796802	−	1.38010i
$921$		0			0
$922$	7286.74	−	12621.0i	0.260277	−	0.450814i
$923$	13927.0	−	24122.3i	0.496656	−	0.860233i
$924$		0			0
$925$	4220.17	+	7309.54i	0.150009	+	0.259823i
$926$	−67262.0			−2.38700
$927$		0			0
$928$	−62072.5			−2.19572
$929$	−62.9925	−	109.106i	−0.00222467	−	0.00385324i	0.864911	−	0.501925i	$-0.167375\pi$
$929$	−62.9925	−	109.106i	−0.00222467	−	0.00385324i	−0.867136	+	0.498072i	$0.834041\pi$
$930$		0			0
$931$	−13179.7	+	22827.8i	−0.463959	+	0.803601i
$932$	−3405.73	+	5898.89i	−0.119698	+	0.207322i
$933$		0			0
$934$	−14947.0	−	25889.0i	−0.523642	−	0.906974i
$935$	9879.41			0.345552
$936$		0			0
$937$	28107.9			0.979984			0.489992	−	0.871727i	$-0.337000\pi$
$937$	28107.9			0.979984			0.489992	+	0.871727i	$0.337000\pi$
$938$	−12428.7	−	21527.1i	−0.432634	−	0.749344i
$939$		0			0
$940$	−238.277	+	412.708i	−0.00826780	+	0.0143203i
$941$	24597.5	−	42604.0i	0.852130	−	1.47593i	−0.0271524	−	0.999631i	$-0.508644\pi$
$941$	24597.5	−	42604.0i	0.852130	−	1.47593i	0.879282	−	0.476301i	$-0.158023\pi$
$942$		0			0
$943$	−15168.7	−	26272.9i	−0.523817	−	0.907277i
$944$	63046.3			2.17371
$945$		0			0
$946$	−50478.6			−1.73488
$947$	7249.02	+	12555.7i	0.248745	+	0.430839i	0.963178	−	0.268865i	$-0.0866485\pi$
$947$	7249.02	+	12555.7i	0.248745	+	0.430839i	−0.714433	+	0.699704i	$0.753315\pi$
$948$		0			0
$949$	30380.9	−	52621.2i	1.03920	−	1.79995i
$950$	−6788.45	+	11757.9i	−0.231838	+	0.401556i
$951$		0			0
$952$	−47784.9	−	82765.9i	−1.62680	−	2.81771i
$953$	3201.79			0.108831			0.0544155	−	0.998518i	$-0.482670\pi$
$953$	3201.79			0.108831			0.0544155	+	0.998518i	$0.482670\pi$
$954$		0			0
$955$	3632.26			0.123075
$956$	3349.24	+	5801.06i	0.113308	+	0.196255i
$957$		0			0
$958$	29168.8	−	50521.8i	0.983717	−	1.70385i
$959$	−28063.3	+	48607.1i	−0.944956	+	1.63671i
$960$		0			0
$961$	14729.0	+	25511.3i	0.494410	+	0.856344i
$962$	114816.			3.84805
$963$		0			0
$964$	−117435.			−3.92356
$965$	10618.2	+	18391.2i	0.354208	+	0.613506i
$966$		0			0
$967$	−28891.0	+	50040.6i	−0.960776	+	1.66411i	−0.240217	+	0.970719i	$0.577219\pi$
$967$	−28891.0	+	50040.6i	−0.960776	+	1.66411i	−0.720559	+	0.693394i	$0.756115\pi$
$968$	14102.5	−	24426.3i	0.468257	−	0.811044i
$969$		0			0
$970$	10760.4	+	18637.5i	0.356180	+	0.616921i
$971$	2611.60			0.0863133			0.0431566	−	0.999068i	$-0.486259\pi$
$971$	2611.60			0.0863133			0.0431566	+	0.999068i	$0.486259\pi$
$972$		0			0
$973$	−33086.4			−1.09013
$974$	23156.3	+	40107.9i	0.761782	+	1.31945i
$975$		0			0
$976$	−43526.7	+	75390.5i	−1.42752	+	2.47253i
$977$	16799.1	−	29097.0i	0.550104	−	0.952809i	−0.448162	−	0.893952i	$-0.647921\pi$
$977$	16799.1	−	29097.0i	0.550104	−	0.952809i	0.998266	−	0.0588563i	$-0.0187454\pi$
$978$		0			0
$979$	−1219.25	−	2111.81i	−0.0398034	−	0.0689415i
$980$	−24039.7			−0.783592
$981$		0			0
$982$	−34080.5			−1.10749
$983$	19742.4	+	34194.9i	0.640575	+	1.10951i	0.985305	+	0.170807i	$0.0546374\pi$
$983$	19742.4	+	34194.9i	0.640575	+	1.10951i	−0.344729	+	0.938702i	$0.612029\pi$
$984$		0			0
$985$	6696.30	−	11598.3i	0.216611	−	0.375181i
$986$	36456.8	−	63145.1i	1.17751	−	2.03950i
$987$		0			0
$988$	65031.1	+	112637.i	2.09404	+	3.62699i
$989$	−51841.9			−1.66681
$990$		0			0
$991$	39918.6			1.27957			0.639786	−	0.768553i	$-0.279023\pi$
$991$	39918.6			1.27957			0.639786	+	0.768553i	$0.279023\pi$
$992$	2754.10	+	4770.24i	0.0881479	+	0.152677i
$993$		0			0
$994$	−27027.6	+	46813.1i	−0.862437	+	1.49379i
$995$	3716.21	−	6436.66i	0.118404	−	0.205081i
$996$		0			0
$997$	12835.1	+	22231.1i	0.407716	+	0.706185i	0.994633	−	0.103462i	$-0.0329920\pi$
$997$	12835.1	+	22231.1i	0.407716	+	0.706185i	−0.586917	+	0.809647i	$0.699659\pi$
$998$	−23975.6			−0.760454
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.r.271.1		6
3.2	odd	2		405.4.e.t.271.3		6
9.2	odd	6		405.4.e.t.136.3		6
9.4	even	3		135.4.a.g.1.3	yes	3
9.5	odd	6		135.4.a.f.1.1	✓	3
9.7	even	3	inner	405.4.e.r.136.1		6
36.23	even	6		2160.4.a.bm.1.1		3
36.31	odd	6		2160.4.a.be.1.1		3
45.4	even	6		675.4.a.q.1.1		3
45.13	odd	12		675.4.b.k.649.1		6
45.14	odd	6		675.4.a.r.1.3		3
45.22	odd	12		675.4.b.k.649.6		6
45.23	even	12		675.4.b.l.649.6		6
45.32	even	12		675.4.b.l.649.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.a.f.1.1	✓	3	9.5	odd	6
135.4.a.g.1.3	yes	3	9.4	even	3
405.4.e.r.136.1		6	9.7	even	3	inner
405.4.e.r.271.1		6	1.1	even	1	trivial
405.4.e.t.136.3		6	9.2	odd	6
405.4.e.t.271.3		6	3.2	odd	2
675.4.a.q.1.1		3	45.4	even	6
675.4.a.r.1.3		3	45.14	odd	6
675.4.b.k.649.1		6	45.13	odd	12
675.4.b.k.649.6		6	45.22	odd	12
675.4.b.l.649.1		6	45.32	even	12
675.4.b.l.649.6		6	45.23	even	12
2160.4.a.be.1.1		3	36.31	odd	6
2160.4.a.bm.1.1		3	36.23	even	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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.60034 - 4.50391i) q^{2} +(-9.52349 + 16.4952i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-12.2007 - 21.1322i) q^{7} +57.4517 q^{8} +O(q^{10})\)	\(q+(-2.60034 - 4.50391i) q^{2} +(-9.52349 + 16.4952i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-12.2007 - 21.1322i) q^{7} +57.4517 q^{8} -26.0034 q^{10} +(14.4919 + 25.1008i) q^{11} +(32.6960 - 56.6311i) q^{13} +(-63.4517 + 109.902i) q^{14} +(-73.2057 - 126.796i) q^{16} +68.1718 q^{17} +104.424 q^{19} +(47.6174 + 82.4758i) q^{20} +(75.3678 - 130.541i) q^{22} +(77.4033 - 134.067i) q^{23} +(-12.5000 - 21.6506i) q^{25} -340.082 q^{26} +464.772 q^{28} +(102.829 + 178.105i) q^{29} +(9.12485 - 15.8047i) q^{31} +(-150.912 + 261.387i) q^{32} +(-177.269 - 307.040i) q^{34} -122.007 q^{35} -337.613 q^{37} +(-271.538 - 470.317i) q^{38} +(143.629 - 248.773i) q^{40} +(97.9845 - 169.714i) q^{41} +(-167.441 - 290.016i) q^{43} -552.055 q^{44} -805.098 q^{46} +(2.50199 + 4.33358i) q^{47} +(-126.213 + 218.607i) q^{49} +(-65.0084 + 112.598i) q^{50} +(622.759 + 1078.65i) q^{52} -319.965 q^{53} +144.919 q^{55} +(-700.949 - 1214.08i) q^{56} +(534.779 - 926.265i) q^{58} +(-215.305 + 372.920i) q^{59} +(-297.291 - 514.922i) q^{61} -94.9106 q^{62} +398.396 q^{64} +(-163.480 - 283.155i) q^{65} +(-97.9382 + 169.634i) q^{67} +(-649.233 + 1124.50i) q^{68} +(317.258 + 549.508i) q^{70} +425.955 q^{71} +929.193 q^{73} +(877.908 + 1520.58i) q^{74} +(-994.482 + 1722.49i) q^{76} +(353.623 - 612.492i) q^{77} +(-12.2148 - 21.1567i) q^{79} -732.057 q^{80} -1019.17 q^{82} +(272.929 + 472.727i) q^{83} +(170.429 - 295.192i) q^{85} +(-870.805 + 1508.28i) q^{86} +(832.586 + 1442.08i) q^{88} -84.1332 q^{89} -1595.65 q^{91} +(1474.30 + 2553.56i) q^{92} +(13.0120 - 22.5375i) q^{94} +(261.060 - 452.170i) q^{95} +(-413.807 - 716.734i) q^{97} +1312.78 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8}+O(q^{10}) \) 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8	\( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} - 10 q^{10} + 38 q^{11} - 28 q^{13} - 108 q^{14} - 191 q^{16} + 38 q^{17} + 374 q^{19} + 115 q^{20} - 122 q^{22} - 81 q^{23} - 75 q^{25} - 832 q^{26} + 820 q^{28} + 160 q^{29} - 227 q^{31} - 569 q^{32} - 17 q^{34} - 440 q^{35} + 156 q^{37} - 757 q^{38} + 180 q^{40} - 338 q^{41} - 22 q^{43} - 3272 q^{44} - 2850 q^{46} - 472 q^{47} + 197 q^{49} - 25 q^{50} + 1566 q^{52} - 1042 q^{53} + 380 q^{55} - 1254 q^{56} + 2096 q^{58} + 140 q^{59} - 595 q^{61} - 2814 q^{62} - 1836 q^{64} + 140 q^{65} - 878 q^{67} - 3053 q^{68} + 540 q^{70} + 1204 q^{71} + 2588 q^{73} + 2878 q^{74} - 525 q^{76} + 288 q^{77} - 629 q^{79} - 1910 q^{80} - 3364 q^{82} - 1287 q^{83} + 95 q^{85} - 3730 q^{86} + 858 q^{88} - 4308 q^{89} - 880 q^{91} + 1959 q^{92} + 1108 q^{94} + 935 q^{95} - 1392 q^{97} + 5386 q^{98}+O(q^{100}) \) 6 * q - q^2 - 23 * q^4 + 15 * q^5 - 44 * q^7 + 72 * q^8 - 10 * q^10 + 38 * q^11 - 28 * q^13 - 108 * q^14 - 191 * q^16 + 38 * q^17 + 374 * q^19 + 115 * q^20 - 122 * q^22 - 81 * q^23 - 75 * q^25 - 832 * q^26 + 820 * q^28 + 160 * q^29 - 227 * q^31 - 569 * q^32 - 17 * q^34 - 440 * q^35 + 156 * q^37 - 757 * q^38 + 180 * q^40 - 338 * q^41 - 22 * q^43 - 3272 * q^44 - 2850 * q^46 - 472 * q^47 + 197 * q^49 - 25 * q^50 + 1566 * q^52 - 1042 * q^53 + 380 * q^55 - 1254 * q^56 + 2096 * q^58 + 140 * q^59 - 595 * q^61 - 2814 * q^62 - 1836 * q^64 + 140 * q^65 - 878 * q^67 - 3053 * q^68 + 540 * q^70 + 1204 * q^71 + 2588 * q^73 + 2878 * q^74 - 525 * q^76 + 288 * q^77 - 629 * q^79 - 1910 * q^80 - 3364 * q^82 - 1287 * q^83 + 95 * q^85 - 3730 * q^86 + 858 * q^88 - 4308 * q^89 - 880 * q^91 + 1959 * q^92 + 1108 * q^94 + 935 * q^95 - 1392 * q^97 + 5386 * q^98

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