LMFDB - Embedded newform 405.4.e.r.136.1

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			136.1
Root			$0.500000 + 0.0280269i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.4.e.r.271.1

$q$-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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.60034	+	4.50391i	−0.919357	+	1.59237i	−0.118964	+	0.992899i	$0.537957\pi$
$2$	−2.60034	+	4.50391i	−0.919357	+	1.59237i	−0.800393	+	0.599475i	$0.795376\pi$
$3$		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	0.322159	+	0.946686i	$0.395591\pi$
$7$	−12.2007	+	21.1322i	−0.658774	+	1.14103i	−0.980933	+	0.194345i	$0.937742\pi$
$8$	57.4517			2.53903
$9$		0			0
$10$	−26.0034			−0.822298
$11$	14.4919	−	25.1008i	0.397226	−	0.688015i	−0.596157	−	0.802868i	$-0.703306\pi$
$11$	14.4919	−	25.1008i	0.397226	−	0.688015i	0.993383	+	0.114853i	$0.0366397\pi$
$12$		0			0
$13$	32.6960	+	56.6311i	0.697556	+	1.20820i	0.969311	+	0.245836i	$0.0790625\pi$
$13$	32.6960	+	56.6311i	0.697556	+	1.20820i	−0.271756	+	0.962366i	$0.587604\pi$
$14$	−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	0.967860	+	0.251490i	$0.0809205\pi$
$23$	77.4033	+	134.067i	0.701727	+	1.21543i	−0.266133	+	0.963936i	$0.585746\pi$
$24$		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	−0.322576	−	0.946544i	$-0.604549\pi$
$29$	102.829	−	178.105i	0.658443	−	1.14046i	0.981019	−	0.193913i	$-0.0621179\pi$
$30$		0			0
$31$	9.12485	+	15.8047i	0.0528668	+	0.0915680i	0.891248	−	0.453517i	$-0.149831\pi$
$31$	9.12485	+	15.8047i	0.0528668	+	0.0915680i	−0.838381	+	0.545085i	$0.816497\pi$
$32$	−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	0.990061	−	0.140638i	$-0.0449154\pi$
$41$	97.9845	+	169.714i	0.373234	+	0.646461i	−0.616827	+	0.787099i	$0.711582\pi$
$42$		0			0
$43$	−167.441	+	290.016i	−0.593826	+	1.02854i	0.399886	+	0.916565i	$0.369050\pi$
$43$	−167.441	+	290.016i	−0.593826	+	1.02854i	−0.993711	+	0.111971i	$0.964284\pi$
$44$	−552.055			−1.89149
$45$		0			0
$46$	−805.098			−2.58055
$47$	2.50199	−	4.33358i	0.00776496	−	0.0134493i	−0.862117	−	0.506710i	$-0.830862\pi$
$47$	2.50199	−	4.33358i	0.00776496	−	0.0134493i	0.869882	+	0.493260i	$0.164195\pi$
$48$		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	0.524502	−	0.851409i	$-0.324251\pi$
$59$	−215.305	−	372.920i	−0.475091	−	0.822882i	−0.999593	+	0.0285276i	$0.990918\pi$
$60$		0			0
$61$	−297.291	+	514.922i	−0.624002	+	1.08080i	0.364730	+	0.931113i	$0.381161\pi$
$61$	−297.291	+	514.922i	−0.624002	+	1.08080i	−0.988733	+	0.149691i	$0.952172\pi$
$62$	−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	0.762812	−	0.646620i	$-0.223818\pi$
$67$	−97.9382	−	169.634i	−0.178583	−	0.309315i	−0.941395	+	0.337305i	$0.890485\pi$
$68$	−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	−0.874592	−	0.484859i	$-0.838871\pi$
$79$	−12.2148	+	21.1567i	−0.0173959	+	0.0301305i	0.857196	+	0.514990i	$0.172204\pi$
$80$	−732.057			−1.02308
$81$		0			0
$82$	−1019.17			−1.37254
$83$	272.929	−	472.727i	0.360938	−	0.625164i	−0.627177	−	0.778877i	$-0.715790\pi$
$83$	272.929	−	472.727i	0.360938	−	0.625164i	0.988116	+	0.153713i	$0.0491231\pi$
$84$		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	−0.997143	−	0.0755403i	$-0.975932\pi$
$97$	−413.807	+	716.734i	−0.433152	+	0.750241i	0.563991	+	0.825781i	$0.309265\pi$
$98$	1312.78			1.35317
$99$		0			0
$100$	476.174			0.476174
$101$	−411.788	+	713.238i	−0.405688	+	0.702671i	−0.994401	−	0.105670i	$-0.966301\pi$
$101$	−411.788	+	713.238i	−0.405688	+	0.702671i	0.588714	+	0.808342i	$0.299635\pi$
$102$		0			0
$103$	−585.595	−	1014.28i	−0.560198	−	0.970291i	−0.997479	−	0.0709659i	$-0.977392\pi$
$103$	−585.595	−	1014.28i	−0.560198	−	0.970291i	0.437281	−	0.899325i	$-0.355941\pi$
$104$	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	0.547950	−	0.836511i	$-0.315409\pi$
$113$	−541.102	−	937.216i	−0.450465	−	0.780229i	−0.998415	+	0.0562825i	$0.982075\pi$
$114$		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	0.994304	−	0.106580i	$-0.0339901\pi$
$131$	607.019	+	1051.39i	0.404851	+	0.701222i	−0.589453	+	0.807802i	$0.700657\pi$
$132$		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	0.244895	+	0.969550i	$0.421247\pi$
$137$	−1150.07	+	1991.99i	−0.717207	+	1.24224i	−0.962102	+	0.272690i	$0.912087\pi$
$138$		0			0
$139$	677.963	+	1174.27i	0.413698	+	0.716546i	0.995291	−	0.0969339i	$-0.0309035\pi$
$139$	677.963	+	1174.27i	0.413698	+	0.716546i	−0.581593	+	0.813480i	$0.697570\pi$
$140$	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	0.828096	−	0.560586i	$-0.189424\pi$
$149$	−129.923	−	225.032i	−0.0714340	−	0.123727i	−0.899530	+	0.436859i	$0.856091\pi$
$150$		0			0
$151$	254.152	−	440.204i	0.136971	−	0.237240i	−0.789378	−	0.613908i	$-0.789597\pi$
$151$	254.152	−	440.204i	0.136971	−	0.237240i	0.926349	+	0.376667i	$0.122930\pi$
$152$	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	0.868972	−	0.494861i	$-0.164781\pi$
$157$	11.6526	+	20.1829i	0.00592342	+	0.0102597i	−0.863049	+	0.505121i	$0.831448\pi$
$158$	−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	0.933303	−	0.359090i	$-0.116913\pi$
$167$	335.955	+	581.892i	0.155671	+	0.269630i	−0.777632	+	0.628719i	$0.783579\pi$
$168$		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	−0.987785	−	0.155825i	$-0.950197\pi$
$173$	−816.764	+	1414.68i	−0.358944	+	0.621710i	0.628840	+	0.777534i	$0.283530\pi$
$174$		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	−0.788986	−	0.614411i	$-0.789394\pi$
$191$	363.226	−	629.125i	0.137603	−	0.238335i	0.926589	+	0.376076i	$0.122727\pi$
$192$		0			0
$193$	−2123.63	−	3678.24i	−0.792032	−	1.37184i	−0.924707	−	0.380681i	$-0.875690\pi$
$193$	−2123.63	−	3678.24i	−0.792032	−	1.37184i	0.132674	−	0.991160i	$-0.457644\pi$
$194$	−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	0.927483	+	0.373866i	$0.121968\pi$
$211$	2413.71	+	4180.66i	0.787519	+	1.36402i	−0.139964	+	0.990157i	$0.544699\pi$
$212$	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	−0.995593	−	0.0937845i	$-0.970104\pi$
$223$	−1387.24	+	2402.77i	−0.416576	+	0.721532i	0.579016	+	0.815316i	$0.303437\pi$
$224$	7364.91			2.19683
$225$		0			0
$226$	5628.19			1.65655
$227$	2550.67	−	4417.89i	0.745788	−	1.29174i	−0.204038	−	0.978963i	$-0.565407\pi$
$227$	2550.67	−	4417.89i	0.745788	−	1.29174i	0.949826	−	0.312779i	$-0.101260\pi$
$228$		0			0
$229$	2048.91	+	3548.82i	0.591249	+	1.02407i	0.994065	+	0.108792i	$0.0346983\pi$
$229$	2048.91	+	3548.82i	0.591249	+	1.02407i	−0.402816	+	0.915281i	$0.631968\pi$
$230$	−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	0.888840	−	0.458219i	$-0.151512\pi$
$239$	175.841	+	304.566i	0.0475909	+	0.0824298i	−0.841249	+	0.540648i	$0.818179\pi$
$240$		0			0
$241$	3082.76	−	5339.51i	0.823976	−	1.42717i	−0.0787225	−	0.996897i	$-0.525084\pi$
$241$	3082.76	−	5339.51i	0.823976	−	1.42717i	0.902699	−	0.430273i	$-0.141583\pi$
$242$	−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	0.565878	−	0.824489i	$-0.308537\pi$
$257$	−1776.10	−	3076.29i	−0.431089	−	0.746668i	−0.996967	+	0.0778206i	$0.975204\pi$
$258$		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	0.482033	+	0.876153i	$0.339898\pi$
$263$	−2208.29	+	3824.88i	−0.517754	+	0.896776i	−0.999787	+	0.0206232i	$0.993435\pi$
$264$		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	−0.899477	−	0.436969i	$-0.856052\pi$
$277$	−328.764	+	569.437i	−0.0713124	+	0.123517i	0.828164	+	0.560485i	$0.189385\pi$
$278$	−7051.72			−1.52135
$279$		0			0
$280$	−7009.49			−1.49606
$281$	−756.957	+	1311.09i	−0.160698	+	0.278338i	−0.935119	−	0.354333i	$-0.884708\pi$
$281$	−756.957	+	1311.09i	−0.160698	+	0.278338i	0.774421	+	0.632671i	$0.218041\pi$
$282$		0			0
$283$	−1953.19	−	3383.03i	−0.410266	−	0.710601i	0.584653	−	0.811284i	$-0.301231\pi$
$283$	−1953.19	−	3383.03i	−0.410266	−	0.710601i	−0.994919	+	0.100682i	$0.967897\pi$
$284$	−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	0.918024	+	0.396525i	$0.129784\pi$
$293$	4024.38	+	6970.43i	0.802413	+	1.38982i	−0.115611	+	0.993295i	$0.536883\pi$
$294$		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	0.968268	+	0.249916i	$0.0804030\pi$
$311$	3842.29	+	6655.05i	0.700567	+	1.21342i	−0.267700	+	0.963502i	$0.586264\pi$
$312$		0			0
$313$	672.575	−	1164.93i	0.121457	−	0.210370i	−0.798885	−	0.601484i	$-0.794577\pi$
$313$	672.575	−	1164.93i	0.121457	−	0.210370i	0.920343	+	0.391113i	$0.127910\pi$
$314$	−121.202			−0.0217830
$315$		0			0
$316$	465.310			0.0828346
$317$	−3811.17	+	6601.13i	−0.675257	+	1.16958i	0.301137	+	0.953581i	$0.402634\pi$
$317$	−3811.17	+	6601.13i	−0.675257	+	1.16958i	−0.976394	+	0.215998i	$0.930699\pi$
$318$		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	−0.451744	−	0.892148i	$-0.649198\pi$
$331$	3292.54	−	5702.85i	0.546751	−	0.947000i	0.998494	−	0.0548525i	$-0.0174689\pi$
$332$	−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	0.960191	−	0.279345i	$-0.0901174\pi$
$337$	1473.47	+	2552.13i	0.238175	+	0.412532i	−0.722015	+	0.691877i	$0.756784\pi$
$338$	−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	−0.981390	−	0.192025i	$-0.938494\pi$
$347$	−4246.74	−	7355.57i	−0.656994	−	1.13795i	0.324396	−	0.945921i	$-0.394839\pi$
$348$		0			0
$349$	−2823.27	+	4890.05i	−0.433027	+	0.750024i	−0.997132	−	0.0756785i	$-0.975888\pi$
$349$	−2823.27	+	4890.05i	−0.433027	+	0.750024i	0.564106	+	0.825703i	$0.309221\pi$
$350$	3172.58			0.484519
$351$		0			0
$352$	−8748.03			−1.32464
$353$	610.966	−	1058.22i	0.0921202	−	0.159557i	−0.816283	−	0.577652i	$-0.803969\pi$
$353$	610.966	−	1058.22i	0.0921202	−	0.159557i	0.908403	+	0.418096i	$0.137302\pi$
$354$		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	−0.499430	−	0.866354i	$-0.666457\pi$
$367$	3519.36	−	6095.70i	0.500569	−	0.867011i	1.00000		0.000657484i	$-0.000209284\pi$
$368$	−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	0.999977	−	0.00674002i	$-0.00214543\pi$
$373$	3559.78	+	6165.72i	0.494152	+	0.855896i	−0.505826	+	0.862636i	$0.668812\pi$
$374$	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	0.703250	−	0.710942i	$-0.251731\pi$
$383$	−1979.32	−	3428.28i	−0.264069	−	0.457381i	−0.967319	+	0.253562i	$0.918398\pi$
$384$		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	0.358574	+	0.933501i	$0.383263\pi$
$389$	−4827.00	+	8360.61i	−0.629148	+	1.08972i	−0.987723	+	0.156216i	$0.950070\pi$
$390$		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	0.710337	−	0.703862i	$-0.248542\pi$
$401$	−2042.78	−	3538.21i	−0.254393	−	0.440622i	−0.964731	+	0.263239i	$0.915209\pi$
$402$		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	−0.990571	−	0.136998i	$-0.956255\pi$
$409$	−5078.13	−	8795.57i	−0.613930	−	1.06336i	0.376642	−	0.926359i	$-0.377079\pi$
$410$	−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	−0.790443	−	0.612536i	$-0.790149\pi$
$419$	−7939.41	−	13751.5i	−0.925693	−	1.60335i	−0.135250	−	0.990811i	$-0.543184\pi$
$420$		0			0
$421$	1139.92	−	1974.40i	0.131963	−	0.228567i	−0.792470	−	0.609911i	$-0.791205\pi$
$421$	1139.92	−	1974.40i	0.131963	−	0.228567i	0.924433	+	0.381344i	$0.124539\pi$
$422$	−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	−0.00881399	−	0.999961i	$-0.502806\pi$
$439$	7924.92	−	13726.4i	0.861585	−	1.49231i	0.870399	−	0.492347i	$-0.163861\pi$
$440$	8325.86			0.902090
$441$		0			0
$442$	−23184.0			−2.49491
$443$	8727.78	−	15117.0i	0.936048	−	1.62128i	0.163294	−	0.986577i	$-0.447788\pi$
$443$	8727.78	−	15117.0i	0.936048	−	1.62128i	0.772754	−	0.634706i	$-0.218879\pi$
$444$		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	0.382858	+	0.923807i	$0.374940\pi$
$457$	−5945.86	+	10298.5i	−0.608612	+	1.05415i	−0.991469	+	0.130339i	$0.958393\pi$
$458$	−21311.4			−2.17428
$459$		0			0
$460$	14743.0			1.49434
$461$	1401.11	−	2426.80i	0.141554	−	0.245179i	−0.786528	−	0.617555i	$-0.788123\pi$
$461$	1401.11	−	2426.80i	0.141554	−	0.245179i	0.928082	+	0.372376i	$0.121457\pi$
$462$		0			0
$463$	6466.66	+	11200.6i	0.649096	+	1.12427i	0.983339	+	0.181780i	$0.0581859\pi$
$463$	6466.66	+	11200.6i	0.649096	+	1.12427i	−0.334244	+	0.942487i	$0.608481\pi$
$464$	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	−0.464161	−	0.885751i	$-0.653644\pi$
$479$	5608.66	−	9714.48i	0.535002	−	0.926651i	0.999163	−	0.0409004i	$-0.0130226\pi$
$480$		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	0.976399	−	0.215976i	$-0.0692934\pi$
$491$	3276.55	+	5675.15i	0.301158	+	0.521621i	−0.675240	+	0.737598i	$0.735960\pi$
$492$		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	0.950701	−	0.310108i	$-0.100365\pi$
$499$	2305.04	+	3992.45i	0.206789	+	0.358170i	−0.743912	+	0.668278i	$0.767032\pi$
$500$	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	−0.970639	−	0.240542i	$-0.922675\pi$
$509$	−7965.40	−	13796.5i	−0.693635	−	1.20141i	0.277004	−	0.960869i	$-0.410659\pi$
$510$		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	−0.791347	−	0.611367i	$-0.790620\pi$
$547$	1711.56	−	2964.50i	0.133786	−	0.231724i	0.925133	+	0.379643i	$0.123953\pi$
$548$	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	0.990517	−	0.137389i	$-0.0438711\pi$
$563$	5026.54	+	8706.22i	0.376276	+	0.651729i	−0.614241	+	0.789118i	$0.710538\pi$
$564$		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	−0.716607	−	0.697477i	$-0.754306\pi$
$569$	3335.23	−	5776.78i	0.245729	−	0.425616i	0.962336	+	0.271861i	$0.0876392\pi$
$570$		0			0
$571$	−2316.78	−	4012.77i	−0.169797	−	0.294097i	0.768551	−	0.639788i	$-0.220978\pi$
$571$	−2316.78	−	4012.77i	−0.169797	−	0.294097i	−0.938348	+	0.345691i	$0.887645\pi$
$572$	−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	−0.690410	−	0.723419i	$-0.742570\pi$
$587$	4000.53	−	6929.12i	0.281294	−	0.487216i	0.971704	+	0.236203i	$0.0759030\pi$
$588$		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	−0.954771	−	0.297341i	$-0.903900\pi$
$599$	−10773.6	−	18660.5i	−0.734890	−	1.27287i	0.219881	−	0.975527i	$-0.429433\pi$
$600$		0			0
$601$	6077.53	−	10526.6i	0.412492	−	0.714456i	−0.582670	−	0.812709i	$-0.697992\pi$
$601$	6077.53	−	10526.6i	0.412492	−	0.714456i	0.995162	+	0.0982525i	$0.0313253\pi$
$602$	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	−0.998504	−	0.0546827i	$-0.982585\pi$
$607$	−8174.47	−	14158.6i	−0.546608	−	0.946754i	0.451895	−	0.892071i	$-0.350748\pi$
$608$	−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	0.828643	−	0.559778i	$-0.189113\pi$
$617$	−1079.87	−	1870.39i	−0.0704603	−	0.122041i	−0.899103	+	0.437737i	$0.855780\pi$
$618$		0			0
$619$	−11050.4	+	19139.9i	−0.717535	+	1.24281i	0.244439	+	0.969665i	$0.421396\pi$
$619$	−11050.4	+	19139.9i	−0.717535	+	1.24281i	−0.961974	+	0.273142i	$0.911937\pi$
$620$	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	−0.334381	−	0.942438i	$-0.608527\pi$
$641$	10532.3	−	18242.4i	0.648985	−	1.12407i	0.983366	−	0.181636i	$-0.0581393\pi$
$642$		0			0
$643$	5269.57	+	9127.16i	0.323190	+	0.559782i	0.981144	−	0.193276i	$-0.0619112\pi$
$643$	5269.57	+	9127.16i	0.323190	+	0.559782i	−0.657954	+	0.753058i	$0.728578\pi$
$644$	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	−0.975610	−	0.219512i	$-0.929554\pi$
$653$	−11312.0	−	19593.0i	−0.677908	−	1.17417i	0.297702	−	0.954659i	$-0.403780\pi$
$654$		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	−0.944739	−	0.327824i	$-0.893685\pi$
$659$	−3188.30	+	5522.29i	−0.188465	+	0.326431i	0.756274	+	0.654255i	$0.227018\pi$
$660$		0			0
$661$	11048.8	+	19137.0i	0.650146	+	1.12609i	0.983087	+	0.183139i	$0.0586258\pi$
$661$	11048.8	+	19137.0i	0.650146	+	1.12609i	−0.332941	+	0.942948i	$0.608041\pi$
$662$	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	0.284136	+	0.958784i	$0.408293\pi$
$673$	−12016.5	+	20813.2i	−0.688264	+	1.19211i	−0.972399	+	0.233323i	$0.925040\pi$
$674$	−15326.1			−0.875873
$675$		0			0
$676$	39600.6			2.25311
$677$	−89.8191	+	155.571i	−0.00509901	+	0.00883175i	−0.868564	−	0.495578i	$-0.834956\pi$
$677$	−89.8191	+	155.571i	−0.00509901	+	0.00883175i	0.863465	+	0.504409i	$0.168290\pi$
$678$		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	−0.968748	−	0.248045i	$-0.920212\pi$
$691$	−4896.36	+	8480.75i	−0.269561	+	0.466893i	0.699188	+	0.714938i	$0.253545\pi$
$692$	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	−0.794463	−	0.607312i	$-0.792248\pi$
$709$	2429.98	−	4208.84i	0.128716	−	0.222943i	0.923179	+	0.384369i	$0.125581\pi$
$710$	−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	−0.895382	−	0.445299i	$-0.853098\pi$
$727$	−1216.33	+	2106.75i	−0.0620512	+	0.107476i	0.833331	+	0.552774i	$0.186431\pi$
$728$	−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	0.998552	−	0.0537895i	$-0.0171300\pi$
$733$	8983.79	+	15560.4i	0.452693	+	0.784087i	−0.545859	+	0.837877i	$0.683797\pi$
$734$	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	0.899205	+	0.437527i	$0.144146\pi$
$743$	16779.6	+	29063.2i	0.828512	+	1.43503i	−0.0706932	+	0.997498i	$0.522521\pi$
$744$		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	0.944943	−	0.327234i	$-0.106116\pi$
$751$	3891.38	+	6740.06i	0.189079	+	0.327495i	−0.755864	+	0.654728i	$0.772783\pi$
$752$	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	0.526347	−	0.850270i	$-0.323561\pi$
$761$	−9933.56	−	17205.4i	−0.473182	−	0.819575i	−0.999529	+	0.0306951i	$0.990228\pi$
$762$		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	0.989310	−	0.145827i	$-0.0465843\pi$
$769$	7855.40	+	13605.9i	0.368365	+	0.638027i	−0.620945	+	0.783854i	$0.713251\pi$
$770$	−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	0.980023	+	0.198887i	$0.0637326\pi$
$787$	14621.3	+	25324.8i	0.662252	+	1.14705i	−0.317770	+	0.948168i	$0.602934\pi$
$788$	−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	−0.959445	−	0.281898i	$-0.909036\pi$
$797$	−16286.9	−	28209.7i	−0.723853	−	1.25375i	0.235592	−	0.971852i	$-0.424297\pi$
$798$		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	−0.392647	+	0.919689i	$0.628441\pi$
$821$	−23354.8	+	40451.6i	−0.992798	+	1.71958i	−0.600150	+	0.799887i	$0.704893\pi$
$822$		0			0
$823$	1734.05	+	3003.46i	0.0734450	+	0.127210i	0.900409	−	0.435044i	$-0.143267\pi$
$823$	1734.05	+	3003.46i	0.0734450	+	0.127210i	−0.826964	+	0.562255i	$0.809934\pi$
$824$	−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	−0.297423	−	0.954746i	$-0.596127\pi$
$839$	16479.8	−	28543.8i	0.678123	−	1.17454i	0.975546	−	0.219797i	$-0.0705396\pi$
$840$		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	0.152518	+	0.988301i	$0.451262\pi$
$853$	−19422.9	+	33641.5i	−0.779634	+	1.35037i	−0.932153	+	0.362066i	$0.882072\pi$
$854$	75454.3			3.02341
$855$		0			0
$856$	58785.0			2.34723
$857$	14652.6	−	25379.1i	0.584043	−	1.01159i	−0.410951	−	0.911657i	$-0.634803\pi$
$857$	14652.6	−	25379.1i	0.584043	−	1.01159i	0.994994	−	0.0999343i	$-0.0318632\pi$
$858$		0			0
$859$	454.830	+	787.788i	0.0180659	+	0.0312910i	0.874917	−	0.484273i	$-0.160916\pi$
$859$	454.830	+	787.788i	0.0180659	+	0.0312910i	−0.856851	+	0.515564i	$0.827582\pi$
$860$	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	0.832959	−	0.553335i	$-0.186645\pi$
$877$	−1629.01	−	2821.52i	−0.0627225	−	0.108639i	−0.895681	+	0.444696i	$0.853312\pi$
$878$	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	0.918857	−	0.394590i	$-0.129113\pi$
$887$	3109.40	+	5385.64i	0.117704	+	0.203869i	−0.801153	+	0.598459i	$0.795780\pi$
$888$		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	−0.577034	−	0.816720i	$-0.695790\pi$
$907$	11439.3	−	19813.5i	0.418783	−	0.725354i	0.995817	+	0.0913663i	$0.0291234\pi$
$908$	−97165.0			−3.55125
$909$		0			0
$910$	41492.3			1.51149
$911$	15072.4	−	26106.2i	0.548157	−	0.949435i	−0.450244	−	0.892905i	$-0.648663\pi$
$911$	15072.4	−	26106.2i	0.548157	−	0.949435i	0.998401	−	0.0565298i	$-0.0180036\pi$
$912$		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	−0.867136	−	0.498072i	$-0.834041\pi$
$929$	−62.9925	+	109.106i	−0.00222467	+	0.00385324i	0.864911	+	0.501925i	$0.167375\pi$
$930$		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	0.879282	+	0.476301i	$0.158023\pi$
$941$	24597.5	+	42604.0i	0.852130	+	1.47593i	−0.0271524	+	0.999631i	$0.508644\pi$
$942$		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	−0.714433	−	0.699704i	$-0.753315\pi$
$947$	7249.02	−	12555.7i	0.248745	−	0.430839i	0.963178	+	0.268865i	$0.0866485\pi$
$948$		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	−0.720559	−	0.693394i	$-0.756115\pi$
$967$	−28891.0	−	50040.6i	−0.960776	−	1.66411i	−0.240217	−	0.970719i	$-0.577219\pi$
$968$	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	0.998266	+	0.0588563i	$0.0187454\pi$
$977$	16799.1	+	29097.0i	0.550104	+	0.952809i	−0.448162	+	0.893952i	$0.647921\pi$
$978$		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	−0.344729	−	0.938702i	$-0.612029\pi$
$983$	19742.4	−	34194.9i	0.640575	−	1.10951i	0.985305	−	0.170807i	$-0.0546374\pi$
$984$		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	−0.586917	−	0.809647i	$-0.699659\pi$
$997$	12835.1	−	22231.1i	0.407716	−	0.706185i	0.994633	+	0.103462i	$0.0329920\pi$
$998$	−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.136.1		6
3.2	odd	2		405.4.e.t.136.3		6
9.2	odd	6		135.4.a.f.1.1	✓	3
9.4	even	3	inner	405.4.e.r.271.1		6
9.5	odd	6		405.4.e.t.271.3		6
9.7	even	3		135.4.a.g.1.3	yes	3
36.7	odd	6		2160.4.a.be.1.1		3
36.11	even	6		2160.4.a.bm.1.1		3
45.2	even	12		675.4.b.l.649.1		6
45.7	odd	12		675.4.b.k.649.6		6
45.29	odd	6		675.4.a.r.1.3		3
45.34	even	6		675.4.a.q.1.1		3
45.38	even	12		675.4.b.l.649.6		6
45.43	odd	12		675.4.b.k.649.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.a.f.1.1	✓	3	9.2	odd	6
135.4.a.g.1.3	yes	3	9.7	even	3
405.4.e.r.136.1		6	1.1	even	1	trivial
405.4.e.r.271.1		6	9.4	even	3	inner
405.4.e.t.136.3		6	3.2	odd	2
405.4.e.t.271.3		6	9.5	odd	6
675.4.a.q.1.1		3	45.34	even	6
675.4.a.r.1.3		3	45.29	odd	6
675.4.b.k.649.1		6	45.43	odd	12
675.4.b.k.649.6		6	45.7	odd	12
675.4.b.l.649.1		6	45.2	even	12
675.4.b.l.649.6		6	45.38	even	12
2160.4.a.be.1.1		3	36.7	odd	6
2160.4.a.bm.1.1		3	36.11	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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