LMFDB - Embedded newform 405.4.e.o.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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			136.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	405.136
Dual form			405.4.e.o.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 2.36603i) q^{2} +(0.267949 + 0.464102i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-3.46410 + 6.00000i) q^{7} -23.3205 q^{8} +O(q^{10})$	\(q+(-1.36603 + 2.36603i) q^{2} +(0.267949 + 0.464102i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-3.46410 + 6.00000i) q^{7} -23.3205 q^{8} +13.6603 q^{10} +(29.7487 - 51.5263i) q^{11} +(12.5359 + 21.7128i) q^{13} +(-9.46410 - 16.3923i) q^{14} +(29.7128 - 51.4641i) q^{16} +112.995 q^{17} -122.779 q^{19} +(1.33975 - 2.32051i) q^{20} +(81.2750 + 140.772i) q^{22} +(48.7128 + 84.3731i) q^{23} +(-12.5000 + 21.6506i) q^{25} -68.4974 q^{26} -3.71281 q^{28} +(63.2846 - 109.612i) q^{29} +(54.1077 + 93.7173i) q^{31} +(-12.1051 - 20.9667i) q^{32} +(-154.354 + 267.349i) q^{34} +34.6410 q^{35} +294.344 q^{37} +(167.720 - 290.499i) q^{38} +(58.3013 + 100.981i) q^{40} +(102.931 + 178.281i) q^{41} +(40.1000 - 69.4552i) q^{43} +31.8846 q^{44} -266.172 q^{46} +(134.856 - 233.578i) q^{47} +(147.500 + 255.477i) q^{49} +(-34.1506 - 59.1506i) q^{50} +(-6.71797 + 11.6359i) q^{52} -98.7949 q^{53} -297.487 q^{55} +(80.7846 - 139.923i) q^{56} +(172.897 + 299.466i) q^{58} +(152.251 + 263.707i) q^{59} +(-333.277 + 577.252i) q^{61} -295.650 q^{62} +541.549 q^{64} +(62.6795 - 108.564i) q^{65} +(317.967 + 550.734i) q^{67} +(30.2769 + 52.4411i) q^{68} +(-47.3205 + 81.9615i) q^{70} -826.482 q^{71} +751.349 q^{73} +(-402.081 + 696.424i) q^{74} +(-32.8987 - 56.9821i) q^{76} +(206.105 + 356.985i) q^{77} +(-11.9334 + 20.6692i) q^{79} -297.128 q^{80} -562.424 q^{82} +(-408.615 + 707.742i) q^{83} +(-282.487 - 489.282i) q^{85} +(109.555 + 189.755i) q^{86} +(-693.755 + 1201.62i) q^{88} -513.000 q^{89} -173.703 q^{91} +(-26.1051 + 45.2154i) q^{92} +(368.435 + 638.147i) q^{94} +(306.949 + 531.651i) q^{95} +(-214.051 + 370.748i) q^{97} -805.955 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 8 * q^4 - 10 * q^5 - 24 * q^8	$ 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8} + 20 q^{10} + 22 q^{11} + 64 q^{13} - 24 q^{14} + 8 q^{16} + 64 q^{17} - 20 q^{19} + 40 q^{20} + 190 q^{22} + 84 q^{23} - 50 q^{25} - 80 q^{26} + 96 q^{28} + 170 q^{29} + 258 q^{31} + 104 q^{32} - 368 q^{34} + 152 q^{37} + 418 q^{38} + 60 q^{40} + 578 q^{41} - 380 q^{43} - 496 q^{44} - 552 q^{46} + 484 q^{47} + 590 q^{49} - 50 q^{50} - 304 q^{52} - 1088 q^{53} - 220 q^{55} + 240 q^{56} + 314 q^{58} + 706 q^{59} - 668 q^{61} - 372 q^{62} + 448 q^{64} + 320 q^{65} + 1452 q^{67} - 544 q^{68} - 120 q^{70} - 1948 q^{71} + 2368 q^{73} - 964 q^{74} + 776 q^{76} + 672 q^{77} - 408 q^{79} - 80 q^{80} - 580 q^{82} + 444 q^{83} - 160 q^{85} + 556 q^{86} - 1812 q^{88} - 2052 q^{89} + 192 q^{91} + 48 q^{92} + 580 q^{94} + 50 q^{95} + 668 q^{97} - 1180 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 8 * q^4 - 10 * q^5 - 24 * q^8 + 20 * q^10 + 22 * q^11 + 64 * q^13 - 24 * q^14 + 8 * q^16 + 64 * q^17 - 20 * q^19 + 40 * q^20 + 190 * q^22 + 84 * q^23 - 50 * q^25 - 80 * q^26 + 96 * q^28 + 170 * q^29 + 258 * q^31 + 104 * q^32 - 368 * q^34 + 152 * q^37 + 418 * q^38 + 60 * q^40 + 578 * q^41 - 380 * q^43 - 496 * q^44 - 552 * q^46 + 484 * q^47 + 590 * q^49 - 50 * q^50 - 304 * q^52 - 1088 * q^53 - 220 * q^55 + 240 * q^56 + 314 * q^58 + 706 * q^59 - 668 * q^61 - 372 * q^62 + 448 * q^64 + 320 * q^65 + 1452 * q^67 - 544 * q^68 - 120 * q^70 - 1948 * q^71 + 2368 * q^73 - 964 * q^74 + 776 * q^76 + 672 * q^77 - 408 * q^79 - 80 * q^80 - 580 * q^82 + 444 * q^83 - 160 * q^85 + 556 * q^86 - 1812 * q^88 - 2052 * q^89 + 192 * q^91 + 48 * q^92 + 580 * q^94 + 50 * q^95 + 668 * q^97 - 1180 * 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 $

$2$	−1.36603	+	2.36603i	−0.482963	+	0.836516i	−0.999809	−	0.0195623i	$-0.993773\pi$
$2$	−1.36603	+	2.36603i	−0.482963	+	0.836516i	0.516846	+	0.856079i	$0.327106\pi$
$3$		0			0
$3$		0			0
$4$	0.267949	+	0.464102i	0.0334936	+	0.0580127i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$		0			0
$7$	−3.46410	+	6.00000i	−0.187044	+	0.323970i	−0.944263	−	0.329191i	$-0.893224\pi$
$7$	−3.46410	+	6.00000i	−0.187044	+	0.323970i	0.757219	+	0.653161i	$0.226557\pi$
$8$	−23.3205			−1.03063
$9$		0			0
$10$	13.6603			0.431975
$11$	29.7487	−	51.5263i	0.815416	−	1.41234i	−0.0936131	−	0.995609i	$-0.529842\pi$
$11$	29.7487	−	51.5263i	0.815416	−	1.41234i	0.909029	−	0.416733i	$-0.136825\pi$
$12$		0			0
$13$	12.5359	+	21.7128i	0.267449	+	0.463235i	0.968202	−	0.250169i	$-0.0804861\pi$
$13$	12.5359	+	21.7128i	0.267449	+	0.463235i	−0.700754	+	0.713403i	$0.747153\pi$
$14$	−9.46410	−	16.3923i	−0.180671	−	0.312931i
$15$		0			0
$16$	29.7128	−	51.4641i	0.464263	−	0.804127i
$17$	112.995			1.61208			0.806038	−	0.591864i	$-0.201608\pi$
$17$	112.995			1.61208			0.806038	+	0.591864i	$0.201608\pi$
$18$		0			0
$19$	−122.779			−1.48250			−0.741251	−	0.671228i	$-0.765767\pi$
$19$	−122.779			−1.48250			−0.741251	+	0.671228i	$0.765767\pi$
$20$	1.33975	−	2.32051i	0.0149788	−	0.0259441i
$21$		0			0
$22$	81.2750	+	140.772i	0.787631	+	1.36422i
$23$	48.7128	+	84.3731i	0.441623	+	0.764913i	0.997810	−	0.0661439i	$-0.0210696\pi$
$23$	48.7128	+	84.3731i	0.441623	+	0.764913i	−0.556187	+	0.831057i	$0.687736\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−68.4974			−0.516671
$27$		0			0
$28$	−3.71281			−0.0250591
$29$	63.2846	−	109.612i	0.405230	−	0.701878i	−0.589119	−	0.808047i	$-0.700525\pi$
$29$	63.2846	−	109.612i	0.405230	−	0.701878i	0.994348	+	0.106168i	$0.0338583\pi$
$30$		0			0
$31$	54.1077	+	93.7173i	0.313485	+	0.542972i	0.979114	−	0.203311i	$-0.0651702\pi$
$31$	54.1077	+	93.7173i	0.313485	+	0.542972i	−0.665629	+	0.746282i	$0.731837\pi$
$32$	−12.1051	−	20.9667i	−0.0668720	−	0.115826i
$33$		0			0
$34$	−154.354	+	267.349i	−0.778572	+	1.34853i
$35$	34.6410			0.167297
$36$		0			0
$37$	294.344			1.30783			0.653916	−	0.756567i	$-0.273125\pi$
$37$	294.344			1.30783			0.653916	+	0.756567i	$0.273125\pi$
$38$	167.720	−	290.499i	0.715994	−	1.24014i
$39$		0			0
$40$	58.3013	+	100.981i	0.230456	+	0.399162i
$41$	102.931	+	178.281i	0.392075	+	0.679094i	0.992723	−	0.120419i	$-0.0384239\pi$
$41$	102.931	+	178.281i	0.392075	+	0.679094i	−0.600648	+	0.799514i	$0.705091\pi$
$42$		0			0
$43$	40.1000	−	69.4552i	0.142214	−	0.246321i	−0.786116	−	0.618079i	$-0.787911\pi$
$43$	40.1000	−	69.4552i	0.142214	−	0.246321i	0.928330	+	0.371757i	$0.121245\pi$
$44$	31.8846			0.109245
$45$		0			0
$46$	−266.172			−0.853150
$47$	134.856	−	233.578i	0.418528	−	0.724912i	−0.577263	−	0.816558i	$-0.695879\pi$
$47$	134.856	−	233.578i	0.418528	−	0.724912i	0.995792	+	0.0916458i	$0.0292127\pi$
$48$		0			0
$49$	147.500	+	255.477i	0.430029	+	0.744832i
$50$	−34.1506	−	59.1506i	−0.0965926	−	0.167303i
$51$		0			0
$52$	−6.71797	+	11.6359i	−0.0179157	+	0.0310308i
$53$	−98.7949			−0.256048			−0.128024	−	0.991771i	$-0.540863\pi$
$53$	−98.7949			−0.256048			−0.128024	+	0.991771i	$0.540863\pi$
$54$		0			0
$55$	−297.487			−0.729330
$56$	80.7846	−	139.923i	0.192773	−	0.333893i
$57$		0			0
$58$	172.897	+	299.466i	0.391422	+	0.677962i
$59$	152.251	+	263.707i	0.335956	+	0.581894i	0.983668	−	0.179992i	$-0.0576072\pi$
$59$	152.251	+	263.707i	0.335956	+	0.581894i	−0.647712	+	0.761886i	$0.724274\pi$
$60$		0			0
$61$	−333.277	+	577.252i	−0.699537	+	1.21163i	0.269091	+	0.963115i	$0.413277\pi$
$61$	−333.277	+	577.252i	−0.699537	+	1.21163i	−0.968627	+	0.248518i	$0.920056\pi$
$62$	−295.650			−0.605606
$63$		0			0
$64$	541.549			1.05771
$65$	62.6795	−	108.564i	0.119607	−	0.207165i
$66$		0			0
$67$	317.967	+	550.734i	0.579788	+	1.00422i	0.995503	+	0.0947278i	$0.0301981\pi$
$67$	317.967	+	550.734i	0.579788	+	1.00422i	−0.415715	+	0.909495i	$0.636469\pi$
$68$	30.2769	+	52.4411i	0.0539943	+	0.0935208i
$69$		0			0
$70$	−47.3205	+	81.9615i	−0.0807983	+	0.139947i
$71$	−826.482			−1.38148			−0.690742	−	0.723101i	$-0.742716\pi$
$71$	−826.482			−1.38148			−0.690742	+	0.723101i	$0.742716\pi$
$72$		0			0
$73$	751.349			1.20464			0.602320	−	0.798255i	$-0.294243\pi$
$73$	751.349			1.20464			0.602320	+	0.798255i	$0.294243\pi$
$74$	−402.081	+	696.424i	−0.631634	+	1.09402i
$75$		0			0
$76$	−32.8987	−	56.9821i	−0.0496544	−	0.0860039i
$77$	206.105	+	356.985i	0.305037	+	0.528340i
$78$		0			0
$79$	−11.9334	+	20.6692i	−0.0169950	+	0.0294363i	−0.874398	−	0.485210i	$-0.838743\pi$
$79$	−11.9334	+	20.6692i	−0.0169950	+	0.0294363i	0.857403	+	0.514646i	$0.172077\pi$
$80$	−297.128			−0.415249
$81$		0			0
$82$	−562.424			−0.757431
$83$	−408.615	+	707.742i	−0.540378	+	0.935962i	0.458504	+	0.888692i	$0.348385\pi$
$83$	−408.615	+	707.742i	−0.540378	+	0.935962i	−0.998882	+	0.0472695i	$0.984948\pi$
$84$		0			0
$85$	−282.487	−	489.282i	−0.360471	−	0.624354i
$86$	109.555	+	189.755i	0.137368	+	0.237928i
$87$		0			0
$88$	−693.755	+	1201.62i	−0.840392	+	1.45560i
$89$	−513.000			−0.610988			−0.305494	−	0.952194i	$-0.598822\pi$
$89$	−513.000			−0.610988			−0.305494	+	0.952194i	$0.598822\pi$
$90$		0			0
$91$	−173.703			−0.200099
$92$	−26.1051	+	45.2154i	−0.0295831	+	0.0512395i
$93$		0			0
$94$	368.435	+	638.147i	0.404267	+	0.700211i
$95$	306.949	+	531.651i	0.331498	+	0.574171i
$96$		0			0
$97$	−214.051	+	370.748i	−0.224058	+	0.388079i	−0.956036	−	0.293248i	$-0.905264\pi$
$97$	−214.051	+	370.748i	−0.224058	+	0.388079i	0.731979	+	0.681328i	$0.238597\pi$
$98$	−805.955			−0.830753
$99$		0			0
$100$	−13.3975			−0.0133975
$101$	456.043	−	789.890i	0.449287	−	0.778188i	−0.549052	−	0.835788i	$-0.685011\pi$
$101$	456.043	−	789.890i	0.449287	−	0.778188i	0.998340	+	0.0575994i	$0.0183446\pi$
$102$		0			0
$103$	−139.249	−	241.186i	−0.133210	−	0.230726i	0.791703	−	0.610907i	$-0.209195\pi$
$103$	−139.249	−	241.186i	−0.133210	−	0.230726i	−0.924912	+	0.380181i	$0.875862\pi$
$104$	−292.344	−	506.354i	−0.275641	−	0.477424i
$105$		0			0
$106$	134.956	−	233.751i	0.123662	−	0.214188i
$107$	1512.33			1.36638			0.683191	−	0.730240i	$-0.260592\pi$
$107$	1512.33			1.36638			0.683191	+	0.730240i	$0.260592\pi$
$108$		0			0
$109$	1991.53			1.75004			0.875020	−	0.484087i	$-0.160848\pi$
$109$	1991.53			1.75004			0.875020	+	0.484087i	$0.160848\pi$
$110$	406.375	−	703.862i	0.352239	−	0.610096i
$111$		0			0
$112$	205.856	+	356.554i	0.173675	+	0.300814i
$113$	−253.951	−	439.856i	−0.211413	−	0.366179i	0.740744	−	0.671788i	$-0.234473\pi$
$113$	−253.951	−	439.856i	−0.211413	−	0.366179i	−0.952157	+	0.305609i	$0.901140\pi$
$114$		0			0
$115$	243.564	−	421.865i	0.197500	−	0.342080i
$116$	67.8282			0.0542905
$117$		0			0
$118$	−831.917			−0.649018
$119$	−391.426	+	677.969i	−0.301529	+	0.522263i
$120$		0			0
$121$	−1104.47	−	1913.00i	−0.829806	−	1.43727i
$122$	−910.529	−	1577.08i	−0.675700	−	1.17035i
$123$		0			0
$124$	−28.9962	+	50.2229i	−0.0209995	+	0.0363722i
$125$	125.000			0.0894427
$126$		0			0
$127$	1845.91			1.28975			0.644873	−	0.764290i	$-0.276910\pi$
$127$	1845.91			1.28975			0.644873	+	0.764290i	$0.276910\pi$
$128$	−642.928	+	1113.58i	−0.443964	+	0.768968i
$129$		0			0
$130$	171.244	+	296.603i	0.115531	+	0.200106i
$131$	1282.35	+	2221.10i	0.855265	+	1.48136i	0.876399	+	0.481586i	$0.159939\pi$
$131$	1282.35	+	2221.10i	0.855265	+	1.48136i	−0.0211333	+	0.999777i	$0.506727\pi$
$132$		0			0
$133$	425.321	−	736.677i	0.277293	−	0.480286i
$134$	−1737.40			−1.12006
$135$		0			0
$136$	−2635.10			−1.66145
$137$	253.390	−	438.884i	0.158019	−	0.273696i	−0.776135	−	0.630566i	$-0.782823\pi$
$137$	253.390	−	438.884i	0.158019	−	0.273696i	0.934154	+	0.356870i	$0.116156\pi$
$138$		0			0
$139$	−1111.32	−	1924.87i	−0.678138	−	1.17457i	−0.975541	−	0.219818i	$-0.929454\pi$
$139$	−1111.32	−	1924.87i	−0.678138	−	1.17457i	0.297403	−	0.954752i	$-0.403880\pi$
$140$	9.28203	+	16.0770i	0.00560339	+	0.00970536i
$141$		0			0
$142$	1129.00	−	1955.48i	0.667206	−	1.15563i
$143$	1491.71			0.872327
$144$		0			0
$145$	−632.846			−0.362448
$146$	−1026.36	+	1777.71i	−0.581796	+	1.00770i
$147$		0			0
$148$	78.8691	+	136.605i	0.0438041	+	0.0758709i
$149$	255.046	+	441.753i	0.140229	+	0.242884i	0.927583	−	0.373617i	$-0.121883\pi$
$149$	255.046	+	441.753i	0.140229	+	0.242884i	−0.787354	+	0.616502i	$0.788549\pi$
$150$		0			0
$151$	−337.631	+	584.793i	−0.181960	+	0.315164i	−0.942548	−	0.334071i	$-0.891578\pi$
$151$	−337.631	+	584.793i	−0.181960	+	0.315164i	0.760588	+	0.649235i	$0.224911\pi$
$152$	2863.28			1.52791
$153$		0			0
$154$	−1126.18			−0.589286
$155$	270.538	−	468.586i	0.140195	−	0.242824i
$156$		0			0
$157$	1813.99	+	3141.92i	0.922115	+	1.59715i	0.796136	+	0.605118i	$0.206874\pi$
$157$	1813.99	+	3141.92i	0.922115	+	1.59715i	0.125979	+	0.992033i	$0.459793\pi$
$158$	−32.6025	−	56.4693i	−0.0164159	−	0.0284332i
$159$		0			0
$160$	−60.5256	+	104.833i	−0.0299060	+	0.0517988i
$161$	−674.985			−0.330411
$162$		0			0
$163$	−119.559			−0.0574514			−0.0287257	−	0.999587i	$-0.509145\pi$
$163$	−119.559			−0.0574514			−0.0287257	+	0.999587i	$0.509145\pi$
$164$	−55.1604	+	95.5407i	−0.0262641	+	0.0454907i
$165$		0			0
$166$	−1116.36	−	1933.59i	−0.521965	−	0.904070i
$167$	−1534.49	−	2657.82i	−0.711035	−	1.23155i	−0.964469	−	0.264195i	$-0.914894\pi$
$167$	−1534.49	−	2657.82i	−0.711035	−	1.23155i	0.253435	−	0.967353i	$-0.418440\pi$
$168$		0			0
$169$	784.203	−	1358.28i	0.356942	−	0.618242i
$170$	1543.54			0.696376
$171$		0			0
$172$	42.9790			0.0190530
$173$	1056.30	−	1829.57i	0.464216	−	0.804046i	−0.534950	−	0.844884i	$-0.679669\pi$
$173$	1056.30	−	1829.57i	0.464216	−	0.804046i	0.999166	+	0.0408382i	$0.0130028\pi$
$174$		0			0
$175$	−86.6025	−	150.000i	−0.0374088	−	0.0647939i
$176$	−1767.84	−	3061.98i	−0.757134	−	1.31140i
$177$		0			0
$178$	700.771	−	1213.77i	0.295084	−	0.511101i
$179$	1624.79			0.678449			0.339225	−	0.940705i	$-0.389835\pi$
$179$	1624.79			0.678449			0.339225	+	0.940705i	$0.389835\pi$
$180$		0			0
$181$	−2545.41			−1.04530			−0.522649	−	0.852548i	$-0.675056\pi$
$181$	−2545.41			−1.04530			−0.522649	+	0.852548i	$0.675056\pi$
$182$	237.282	−	410.985i	0.0966402	−	0.167386i
$183$		0			0
$184$	−1136.01	−	1967.62i	−0.455150	−	0.788343i
$185$	−735.859	−	1274.54i	−0.292440	−	0.506521i
$186$		0			0
$187$	3361.45	−	5822.20i	1.31451	−	2.27680i
$188$	144.539			0.0560722
$189$		0			0
$190$	−1677.20			−0.640404
$191$	2402.83	−	4161.82i	0.910274	−	1.57664i	0.0965970	−	0.995324i	$-0.469204\pi$
$191$	2402.83	−	4161.82i	0.910274	−	1.57664i	0.813677	−	0.581317i	$-0.197462\pi$
$192$		0			0
$193$	−1788.92	−	3098.50i	−0.667198	−	1.15562i	−0.978684	−	0.205371i	$-0.934160\pi$
$193$	−1788.92	−	3098.50i	−0.667198	−	1.15562i	0.311486	−	0.950251i	$-0.399173\pi$
$194$	−584.799	−	1012.90i	−0.216423	−	0.374856i
$195$		0			0
$196$	−79.0450	+	136.910i	−0.0288065	+	0.0498943i
$197$	3788.88			1.37029			0.685144	−	0.728408i	$-0.259739\pi$
$197$	3788.88			1.37029			0.685144	+	0.728408i	$0.259739\pi$
$198$		0			0
$199$	2048.31			0.729652			0.364826	−	0.931076i	$-0.381129\pi$
$199$	2048.31			0.729652			0.364826	+	0.931076i	$0.381129\pi$
$200$	291.506	−	504.904i	0.103063	−	0.178510i
$201$		0			0
$202$	1245.93	+	2158.02i	0.433978	+	0.751672i
$203$	438.449	+	759.415i	0.151591	+	0.262564i
$204$		0			0
$205$	514.654	−	891.407i	0.175341	−	0.303700i
$206$	760.869			0.257341
$207$		0			0
$208$	1489.91			0.496666
$209$	−3652.53	+	6326.37i	−1.20886	+	2.09380i
$210$		0			0
$211$	−1190.90	−	2062.69i	−0.388553	−	0.672994i	0.603702	−	0.797210i	$-0.293692\pi$
$211$	−1190.90	−	2062.69i	−0.388553	−	0.672994i	−0.992255	+	0.124216i	$0.960358\pi$
$212$	−26.4720	−	45.8509i	−0.00857597	−	0.0148540i
$213$		0			0
$214$	−2065.89	+	3578.22i	−0.659911	+	1.14300i
$215$	−401.000			−0.127200
$216$		0			0
$217$	−749.738			−0.234542
$218$	−2720.48	+	4712.02i	−0.845204	+	1.46394i
$219$		0			0
$220$	−79.7114	−	138.064i	−0.0244279	−	0.0423104i
$221$	1416.49	+	2453.44i	0.431147	+	0.746769i
$222$		0			0
$223$	278.577	−	482.510i	0.0836543	−	0.144893i	−0.821163	−	0.570694i	$-0.806674\pi$
$223$	278.577	−	482.510i	0.0836543	−	0.144893i	0.904817	+	0.425801i	$0.140008\pi$
$224$	167.733			0.0500320
$225$		0			0
$226$	1387.62			0.408419
$227$	2589.04	−	4484.36i	0.757008	−	1.31118i	−0.187362	−	0.982291i	$-0.559994\pi$
$227$	2589.04	−	4484.36i	0.757008	−	1.31118i	0.944370	−	0.328886i	$-0.106673\pi$
$228$		0			0
$229$	459.138	+	795.250i	0.132492	+	0.229483i	0.924637	−	0.380850i	$-0.124369\pi$
$229$	459.138	+	795.250i	0.132492	+	0.229483i	−0.792145	+	0.610334i	$0.791035\pi$
$230$	665.429	+	1152.56i	0.190770	+	0.330423i
$231$		0			0
$232$	−1475.83	+	2556.21i	−0.417642	+	0.723377i
$233$	−5896.92			−1.65803			−0.829013	−	0.559230i	$-0.811097\pi$
$233$	−5896.92			−1.65803			−0.829013	+	0.559230i	$0.811097\pi$
$234$		0			0
$235$	−1348.56			−0.374343
$236$	−81.5912	+	141.320i	−0.0225048	+	0.0389795i
$237$		0			0
$238$	−1069.39	−	1852.25i	−0.291254	−	0.504468i
$239$	−263.420	−	456.257i	−0.0712938	−	0.123485i	0.828175	−	0.560470i	$-0.189379\pi$
$239$	−263.420	−	456.257i	−0.0712938	−	0.123485i	−0.899469	+	0.436985i	$0.856046\pi$
$240$		0			0
$241$	2911.60	−	5043.03i	0.778226	−	1.34793i	−0.154738	−	0.987956i	$-0.549453\pi$
$241$	2911.60	−	5043.03i	0.778226	−	1.34793i	0.932963	−	0.359971i	$-0.117213\pi$
$242$	6034.95			1.60306
$243$		0			0
$244$	−357.205			−0.0937201
$245$	737.500	−	1277.39i	0.192315	−	0.333099i
$246$		0			0
$247$	−1539.15	−	2665.89i	−0.396493	−	0.686746i
$248$	−1261.82	−	2185.53i	−0.323087	−	0.559603i
$249$		0			0
$250$	−170.753	+	295.753i	−0.0431975	+	0.0748203i
$251$	−3244.98			−0.816022			−0.408011	−	0.912977i	$-0.633778\pi$
$251$	−3244.98			−0.816022			−0.408011	+	0.912977i	$0.633778\pi$
$252$		0			0
$253$	5796.57			1.44042
$254$	−2521.56	+	4367.46i	−0.622900	+	1.07889i
$255$		0			0
$256$	409.682	+	709.590i	0.100020	+	0.173240i
$257$	630.700	+	1092.40i	0.153082	+	0.265145i	0.932359	−	0.361534i	$-0.117747\pi$
$257$	630.700	+	1092.40i	0.153082	+	0.265145i	−0.779277	+	0.626679i	$0.784414\pi$
$258$		0			0
$259$	−1019.64	+	1766.06i	−0.244622	+	0.423698i
$260$	67.1797			0.0160243
$261$		0			0
$262$	−7006.91			−1.65225
$263$	−962.141	+	1666.48i	−0.225582	+	0.390720i	−0.956494	−	0.291752i	$-0.905762\pi$
$263$	−962.141	+	1666.48i	−0.225582	+	0.390720i	0.730912	+	0.682472i	$0.239095\pi$
$264$		0			0
$265$	246.987	+	427.795i	0.0572540	+	0.0991668i
$266$	1162.00	+	2012.64i	0.267844	+	0.463920i
$267$		0			0
$268$	−170.398	+	295.138i	−0.0388384	+	0.0672702i
$269$	−4762.53			−1.07947			−0.539733	−	0.841836i	$-0.681475\pi$
$269$	−4762.53			−1.07947			−0.539733	+	0.841836i	$0.681475\pi$
$270$		0			0
$271$	1595.10			0.357547			0.178774	−	0.983890i	$-0.442787\pi$
$271$	1595.10			0.357547			0.178774	+	0.983890i	$0.442787\pi$
$272$	3357.39	−	5815.18i	0.748426	−	1.29631i
$273$		0			0
$274$	692.274	+	1199.05i	0.152634	+	0.264370i
$275$	743.718	+	1288.16i	0.163083	+	0.282468i
$276$		0			0
$277$	−524.792	+	908.966i	−0.113833	+	0.197164i	−0.917313	−	0.398168i	$-0.869646\pi$
$277$	−524.792	+	908.966i	−0.113833	+	0.197164i	0.803480	+	0.595332i	$0.202979\pi$
$278$	6072.38			1.31006
$279$		0			0
$280$	−807.846			−0.172422
$281$	−3788.02	+	6561.04i	−0.804179	+	1.39288i	0.112665	+	0.993633i	$0.464061\pi$
$281$	−3788.02	+	6561.04i	−0.804179	+	1.39288i	−0.916844	+	0.399246i	$0.869272\pi$
$282$		0			0
$283$	2926.47	+	5068.79i	0.614701	+	1.06469i	0.990437	+	0.137966i	$0.0440566\pi$
$283$	2926.47	+	5068.79i	0.614701	+	1.06469i	−0.375736	+	0.926727i	$0.622610\pi$
$284$	−221.455	−	383.572i	−0.0462709	−	0.0801436i
$285$		0			0
$286$	−2037.71	+	3529.42i	−0.421302	+	0.729716i
$287$	−1426.25			−0.293341
$288$		0			0
$289$	7854.84			1.59879
$290$	864.484	−	1497.33i	0.175049	−	0.303194i
$291$		0			0
$292$	201.323	+	348.702i	0.0403478	+	0.0698844i
$293$	1769.80	+	3065.38i	0.352876	+	0.611199i	0.986752	−	0.162235i	$-0.0518704\pi$
$293$	1769.80	+	3065.38i	0.352876	+	0.611199i	−0.633876	+	0.773435i	$0.718537\pi$
$294$		0			0
$295$	761.256	−	1318.53i	0.150244	−	0.260231i
$296$	−6864.24			−1.34789
$297$		0			0
$298$	−1393.60			−0.270902
$299$	−1221.32	+	2115.38i	−0.236223	+	0.409150i
$300$		0			0
$301$	277.821	+	481.200i	0.0532004	+	0.0921458i
$302$	−922.424	−	1597.68i	−0.175760	−	0.304425i
$303$		0			0
$304$	−3648.12	+	6318.73i	−0.688270	+	1.19212i
$305$	3332.77			0.625685
$306$		0			0
$307$	−293.303			−0.0545267			−0.0272634	−	0.999628i	$-0.508679\pi$
$307$	−293.303			−0.0545267			−0.0272634	+	0.999628i	$0.508679\pi$
$308$	−110.451	+	191.307i	−0.0204336	+	0.0353921i
$309$		0			0
$310$	739.125	+	1280.20i	0.135418	+	0.234550i
$311$	−2295.95	−	3976.70i	−0.418621	−	0.725074i	0.577180	−	0.816617i	$-0.304153\pi$
$311$	−2295.95	−	3976.70i	−0.418621	−	0.725074i	−0.995801	+	0.0915436i	$0.970820\pi$
$312$		0			0
$313$	−3870.53	+	6703.95i	−0.698962	+	1.21064i	0.269864	+	0.962898i	$0.413021\pi$
$313$	−3870.53	+	6703.95i	−0.698962	+	1.21064i	−0.968827	+	0.247740i	$0.920312\pi$
$314$	−9911.82			−1.78139
$315$		0			0
$316$	−12.7901			−0.00227690
$317$	958.662	−	1660.45i	0.169854	−	0.294196i	−0.768514	−	0.639833i	$-0.779004\pi$
$317$	958.662	−	1660.45i	0.169854	−	0.294196i	0.938369	+	0.345636i	$0.112337\pi$
$318$		0			0
$319$	−3765.27	−	6521.64i	−0.660861	−	1.14465i
$320$	−1353.87	−	2344.97i	−0.236512	−	0.409650i
$321$		0			0
$322$	922.046	−	1597.03i	0.159576	−	0.276395i
$323$	−13873.4			−2.38990
$324$		0			0
$325$	−626.795			−0.106979
$326$	163.321	−	282.879i	0.0277469	−	0.0480590i
$327$		0			0
$328$	−2400.40	−	4157.61i	−0.404085	−	0.699895i
$329$	934.313	+	1618.28i	0.156566	+	0.271181i
$330$		0			0
$331$	−4128.27	+	7150.37i	−0.685529	+	1.18737i	0.287742	+	0.957708i	$0.407096\pi$
$331$	−4128.27	+	7150.37i	−0.685529	+	1.18737i	−0.973270	+	0.229663i	$0.926238\pi$
$332$	−437.952			−0.0723969
$333$		0			0
$334$	8384.63			1.37361
$335$	1589.83	−	2753.67i	0.259289	−	0.449102i
$336$		0			0
$337$	4259.34	+	7377.40i	0.688490	+	1.19250i	0.972326	+	0.233627i	$0.0750594\pi$
$337$	4259.34	+	7377.40i	0.688490	+	1.19250i	−0.283836	+	0.958873i	$0.591607\pi$
$338$	2142.48	+	3710.89i	0.344780	+	0.597176i
$339$		0			0
$340$	151.384	−	262.205i	0.0241470	−	0.0418238i
$341$	6438.54			1.02248
$342$		0			0
$343$	−4420.19			−0.695825
$344$	−935.152	+	1619.73i	−0.146570	+	0.253866i
$345$		0			0
$346$	2885.88	+	4998.49i	0.448398	+	0.776648i
$347$	4813.82	+	8337.77i	0.744724	+	1.28990i	0.950324	+	0.311263i	$0.100752\pi$
$347$	4813.82	+	8337.77i	0.744724	+	1.28990i	−0.205600	+	0.978636i	$0.565915\pi$
$348$		0			0
$349$	3795.89	−	6574.68i	0.582205	−	1.00841i	−0.413013	−	0.910725i	$-0.635523\pi$
$349$	3795.89	−	6574.68i	0.582205	−	1.00841i	0.995218	−	0.0976832i	$-0.0311432\pi$
$350$	473.205			0.0722682
$351$		0			0
$352$	−1440.45			−0.218114
$353$	693.613	−	1201.37i	0.104582	−	0.181141i	−0.808986	−	0.587828i	$-0.799983\pi$
$353$	693.613	−	1201.37i	0.104582	−	0.181141i	0.913567	+	0.406688i	$0.133316\pi$
$354$		0			0
$355$	2066.20	+	3578.77i	0.308909	+	0.535046i
$356$	−137.458	−	238.084i	−0.0204642	−	0.0354450i
$357$		0			0
$358$	−2219.50	+	3844.29i	−0.327666	+	0.567534i
$359$	−6335.93			−0.931469			−0.465735	−	0.884924i	$-0.654210\pi$
$359$	−6335.93			−0.931469			−0.465735	+	0.884924i	$0.654210\pi$
$360$		0			0
$361$	8215.79			1.19781
$362$	3477.09	−	6022.50i	0.504840	−	0.874408i
$363$		0			0
$364$	−46.5434	−	80.6156i	−0.00670203	−	0.0116083i
$365$	−1878.37	−	3253.44i	−0.269366	−	0.466555i
$366$		0			0
$367$	4595.14	−	7959.01i	0.653581	−	1.13204i	−0.328667	−	0.944446i	$-0.606599\pi$
$367$	4595.14	−	7959.01i	0.653581	−	1.13204i	0.982248	−	0.187589i	$-0.0600674\pi$
$368$	5789.58			0.820116
$369$		0			0
$370$	4020.81			0.564951
$371$	342.236	−	592.770i	0.0478922	−	0.0829516i
$372$		0			0
$373$	6342.70	+	10985.9i	0.880462	+	1.52501i	0.850828	+	0.525444i	$0.176101\pi$
$373$	6342.70	+	10985.9i	0.880462	+	1.52501i	0.0296342	+	0.999561i	$0.490566\pi$
$374$	9183.66	+	15906.6i	1.26972	+	2.19922i
$375$		0			0
$376$	−3144.92	+	5447.16i	−0.431348	+	0.747117i
$377$	3173.32			0.433512
$378$		0			0
$379$	−13119.0			−1.77804			−0.889022	−	0.457865i	$-0.848614\pi$
$379$	−13119.0			−1.77804			−0.889022	+	0.457865i	$0.848614\pi$
$380$	−164.493	+	284.911i	−0.0222061	+	0.0384621i
$381$		0			0
$382$	6564.64	+	11370.3i	0.879257	+	1.52292i
$383$	−867.126	−	1501.91i	−0.115687	−	0.200376i	0.802367	−	0.596831i	$-0.203574\pi$
$383$	−867.126	−	1501.91i	−0.115687	−	0.200376i	−0.918054	+	0.396455i	$0.870240\pi$
$384$		0			0
$385$	1030.53	−	1784.92i	0.136417	−	0.236281i
$386$	9774.84			1.28893
$387$		0			0
$388$	−229.419			−0.0300181
$389$	4681.99	−	8109.45i	0.610248	−	1.05698i	−0.380950	−	0.924596i	$-0.624403\pi$
$389$	4681.99	−	8109.45i	0.610248	−	1.05698i	0.991198	−	0.132385i	$-0.0422636\pi$
$390$		0			0
$391$	5504.30	+	9533.72i	0.711929	+	1.23310i
$392$	−3439.77	−	5957.86i	−0.443201	−	0.767647i
$393$		0			0
$394$	−5175.71	+	8964.59i	−0.661798	+	1.14627i
$395$	119.334			0.0152008
$396$		0			0
$397$	−7661.94			−0.968619			−0.484309	−	0.874897i	$-0.660929\pi$
$397$	−7661.94			−0.968619			−0.484309	+	0.874897i	$0.660929\pi$
$398$	−2798.04	+	4846.35i	−0.352395	+	0.610366i
$399$		0			0
$400$	742.820	+	1286.60i	0.0928525	+	0.160825i
$401$	−72.8247	−	126.136i	−0.00906906	−	0.0157081i	0.861455	−	0.507833i	$-0.169553\pi$
$401$	−72.8247	−	126.136i	−0.00906906	−	0.0157081i	−0.870524	+	0.492125i	$0.836220\pi$
$402$		0			0
$403$	−1356.58	+	2349.66i	−0.167682	+	0.290434i
$404$	488.786			0.0601931
$405$		0			0
$406$	−2395.73			−0.292852
$407$	8756.34	−	15166.4i	1.06643	−	1.84711i
$408$		0			0
$409$	−4445.36	−	7699.59i	−0.537430	−	0.930856i	−0.999041	−	0.0437736i	$-0.986062\pi$
$409$	−4445.36	−	7699.59i	−0.537430	−	0.930856i	0.461612	−	0.887082i	$-0.347271\pi$
$410$	1406.06	+	2435.37i	0.169367	+	0.293352i
$411$		0			0
$412$	74.6232	−	129.251i	0.00892335	−	0.0154557i
$413$	−2109.66			−0.251354
$414$		0			0
$415$	4086.15			0.483329
$416$	303.497	−	525.672i	0.0357696	−	0.0619548i
$417$		0			0
$418$	−9978.90	−	17284.0i	−1.16766	−	2.02245i
$419$	−1584.20	−	2743.91i	−0.184709	−	0.319926i	0.758769	−	0.651360i	$-0.225801\pi$
$419$	−1584.20	−	2743.91i	−0.184709	−	0.319926i	−0.943479	+	0.331434i	$0.892468\pi$
$420$		0			0
$421$	4247.51	−	7356.91i	0.491713	−	0.851672i	−0.508241	−	0.861215i	$-0.669704\pi$
$421$	4247.51	−	7356.91i	0.491713	−	0.851672i	0.999954	+	0.00954269i	$0.00303758\pi$
$422$	6507.18			0.750627
$423$		0			0
$424$	2303.95			0.263891
$425$	−1412.44	+	2446.41i	−0.161208	+	0.279220i
$426$		0			0
$427$	−2309.01	−	3999.32i	−0.261688	−	0.453257i
$428$	405.228	+	701.876i	0.0457651	+	0.0792675i
$429$		0			0
$430$	547.776	−	948.775i	0.0614328	−	0.106405i
$431$	−2072.30			−0.231599			−0.115799	−	0.993273i	$-0.536943\pi$
$431$	−2072.30			−0.231599			−0.115799	+	0.993273i	$0.536943\pi$
$432$		0			0
$433$	2906.44			0.322574			0.161287	−	0.986908i	$-0.448435\pi$
$433$	2906.44			0.322574			0.161287	+	0.986908i	$0.448435\pi$
$434$	1024.16	−	1773.90i	0.113275	−	0.196198i
$435$		0			0
$436$	533.630	+	924.274i	0.0586152	+	0.101525i
$437$	−5980.93	−	10359.3i	−0.654707	−	1.13399i
$438$		0			0
$439$	−965.538	+	1672.36i	−0.104972	+	0.181817i	−0.913727	−	0.406329i	$-0.866809\pi$
$439$	−965.538	+	1672.36i	−0.104972	+	0.181817i	0.808755	+	0.588146i	$0.200142\pi$
$440$	6937.55			0.751670
$441$		0			0
$442$	−7739.86			−0.832913
$443$	−122.312	+	211.851i	−0.0131179	+	0.0227209i	−0.872510	−	0.488597i	$-0.837509\pi$
$443$	−122.312	+	211.851i	−0.0131179	+	0.0227209i	0.859392	+	0.511317i	$0.170842\pi$
$444$		0			0
$445$	1282.50	+	2221.36i	0.136621	+	0.236634i
$446$	761.087	+	1318.24i	0.0808038	+	0.139956i
$447$		0			0
$448$	−1875.98	+	3249.29i	−0.197839	+	0.342667i
$449$	−13276.7			−1.39547			−0.697734	−	0.716357i	$-0.745808\pi$
$449$	−13276.7			−1.39547			−0.697734	+	0.716357i	$0.745808\pi$
$450$		0			0
$451$	12248.2			1.27882
$452$	136.092	−	235.718i	0.0141620	−	0.0245293i
$453$		0			0
$454$	7073.40	+	12251.5i	0.731214	+	1.26650i
$455$	434.256	+	752.154i	0.0447434	+	0.0774978i
$456$		0			0
$457$	−6257.10	+	10837.6i	−0.640470	+	1.10933i	0.344859	+	0.938655i	$0.387927\pi$
$457$	−6257.10	+	10837.6i	−0.640470	+	1.10933i	−0.985328	+	0.170671i	$0.945406\pi$
$458$	−2508.78			−0.255955
$459$		0			0
$460$	261.051			0.0264599
$461$	2245.44	−	3889.22i	0.226856	−	0.392926i	−0.730019	−	0.683427i	$-0.760489\pi$
$461$	2245.44	−	3889.22i	0.226856	−	0.392926i	0.956875	+	0.290501i	$0.0938219\pi$
$462$		0			0
$463$	3046.44	+	5276.60i	0.305789	+	0.529642i	0.977437	−	0.211229i	$-0.0677465\pi$
$463$	3046.44	+	5276.60i	0.305789	+	0.529642i	−0.671648	+	0.740871i	$0.734413\pi$
$464$	−3760.73	−	6513.77i	−0.376266	−	0.651712i
$465$		0			0
$466$	8055.34	−	13952.3i	0.800765	−	1.38697i
$467$	5193.68			0.514635			0.257318	−	0.966327i	$-0.417161\pi$
$467$	5193.68			0.514635			0.257318	+	0.966327i	$0.417161\pi$
$468$		0			0
$469$	−4405.88			−0.433783
$470$	1842.17	−	3190.74i	0.180794	−	0.313144i
$471$		0			0
$472$	−3550.58	−	6149.78i	−0.346247	−	0.599717i
$473$	−2385.84	−	4132.40i	−0.231927	−	0.401709i
$474$		0			0
$475$	1534.74	−	2658.25i	0.148250	−	0.256777i
$476$	−419.529			−0.0403972
$477$		0			0
$478$	1439.35			0.137729
$479$	−9441.27	+	16352.8i	−0.900590	+	1.55987i	−0.0738604	+	0.997269i	$0.523532\pi$
$479$	−9441.27	+	16352.8i	−0.900590	+	1.55987i	−0.826730	+	0.562599i	$0.809801\pi$
$480$		0			0
$481$	3689.86	+	6391.03i	0.349778	+	0.605833i
$482$	7954.63	+	13777.8i	0.751708	+	1.30200i
$483$		0			0
$484$	591.885	−	1025.17i	0.0555865	−	0.0962786i
$485$	2140.51			0.200403
$486$		0			0
$487$	−17619.1			−1.63942			−0.819708	−	0.572781i	$-0.805864\pi$
$487$	−17619.1			−1.63942			−0.819708	+	0.572781i	$0.805864\pi$
$488$	7772.19	−	13461.8i	0.720964	−	1.24875i
$489$		0			0
$490$	2014.89	+	3489.89i	0.185762	+	0.321749i
$491$	−458.133	−	793.510i	−0.0421085	−	0.0729341i	0.844203	−	0.536024i	$-0.180074\pi$
$491$	−458.133	−	793.510i	−0.0421085	−	0.0729341i	−0.886312	+	0.463089i	$0.846741\pi$
$492$		0			0
$493$	7150.83	−	12385.6i	0.653260	−	1.13148i
$494$	8410.08			0.765966
$495$		0			0
$496$	6430.77			0.582157
$497$	2863.02	−	4958.89i	0.258398	−	0.447559i
$498$		0			0
$499$	−6231.71	−	10793.6i	−0.559058	−	0.968316i	−0.997575	−	0.0695938i	$-0.977830\pi$
$499$	−6231.71	−	10793.6i	−0.559058	−	0.968316i	0.438518	−	0.898723i	$-0.355504\pi$
$500$	33.4936	+	58.0127i	0.00299576	+	0.00518881i
$501$		0			0
$502$	4432.73	−	7677.71i	0.394108	−	0.682616i
$503$	−49.4842			−0.00438646			−0.00219323	−	0.999998i	$-0.500698\pi$
$503$	−49.4842			−0.00438646			−0.00219323	+	0.999998i	$0.500698\pi$
$504$		0			0
$505$	−4560.43			−0.401855
$506$	−7918.27	+	13714.8i	−0.695672	+	1.20494i
$507$		0			0
$508$	494.609	+	856.689i	0.0431983	+	0.0748217i
$509$	−3077.51	−	5330.40i	−0.267992	−	0.464176i	0.700351	−	0.713799i	$-0.253027\pi$
$509$	−3077.51	−	5330.40i	−0.267992	−	0.464176i	−0.968343	+	0.249622i	$0.919694\pi$
$510$		0			0
$511$	−2602.75	+	4508.09i	−0.225321	+	0.390267i
$512$	−12525.4			−1.08115
$513$		0			0
$514$	−3446.21			−0.295731
$515$	−696.244	+	1205.93i	−0.0595731	+	0.103184i
$516$		0			0
$517$	−8023.61	−	13897.3i	−0.682549	−	1.18221i
$518$	−2785.70	−	4824.97i	−0.236287	−	0.409261i
$519$		0			0
$520$	−1461.72	+	2531.77i	−0.123270	+	0.213510i
$521$	14718.1			1.23764			0.618821	−	0.785532i	$-0.287610\pi$
$521$	14718.1			1.23764			0.618821	+	0.785532i	$0.287610\pi$
$522$		0			0
$523$	−8318.46			−0.695489			−0.347744	−	0.937589i	$-0.613052\pi$
$523$	−8318.46			−0.695489			−0.347744	+	0.937589i	$0.613052\pi$
$524$	−687.211	+	1190.28i	−0.0572919	+	0.0992325i
$525$		0			0
$526$	−2628.62	−	4552.90i	−0.217896	−	0.377407i
$527$	6113.89	+	10589.6i	0.505361	+	0.875311i
$528$		0			0
$529$	1337.62	−	2316.83i	0.109939	−	0.190419i
$530$	−1349.56			−0.110606
$531$		0			0
$532$	455.857			0.0371502
$533$	−2580.66	+	4469.83i	−0.209720	+	0.363246i
$534$		0			0
$535$	−3780.83	−	6548.59i	−0.305532	−	0.529197i
$536$	−7415.14	−	12843.4i	−0.597548	−	1.03498i
$537$		0			0
$538$	6505.74	−	11268.3i	0.521342	−	0.902991i
$539$	17551.7			1.40261
$540$		0			0
$541$	19372.0			1.53949			0.769746	−	0.638350i	$-0.220383\pi$
$541$	19372.0			1.53949			0.769746	+	0.638350i	$0.220383\pi$
$542$	−2178.94	+	3774.04i	−0.172682	+	0.299094i
$543$		0			0
$544$	−1367.82	−	2369.13i	−0.107803	−	0.186720i
$545$	−4978.83	−	8623.59i	−0.391321	−	0.677787i
$546$		0			0
$547$	494.864	−	857.129i	0.0386816	−	0.0669985i	−0.846036	−	0.533125i	$-0.821018\pi$
$547$	494.864	−	857.129i	0.0386816	−	0.0669985i	0.884718	+	0.466127i	$0.154351\pi$
$548$	271.582			0.0211705
$549$		0			0
$550$	−4063.75			−0.315052
$551$	−7770.05	+	13458.1i	−0.600754	+	1.04054i
$552$		0			0
$553$	−82.6767	−	143.200i	−0.00635764	−	0.0110117i
$554$	−1433.76	−	2483.34i	−0.109954	−	0.190446i
$555$		0			0
$556$	595.556	−	1031.53i	0.0454266	−	0.0786812i
$557$	−4616.60			−0.351188			−0.175594	−	0.984463i	$-0.556185\pi$
$557$	−4616.60			−0.351188			−0.175594	+	0.984463i	$0.556185\pi$
$558$		0			0
$559$	2010.76			0.152139
$560$	1029.28	−	1782.77i	0.0776698	−	0.134528i
$561$		0			0
$562$	−10349.1	−	17925.1i	−0.776777	−	1.34542i
$563$	6754.79	+	11699.6i	0.505649	+	0.875809i	0.999979	+	0.00653505i	$0.00208019\pi$
$563$	6754.79	+	11699.6i	0.505649	+	0.875809i	−0.494330	+	0.869274i	$0.664586\pi$
$564$		0			0
$565$	−1269.76	+	2199.28i	−0.0945470	+	0.163760i
$566$	−15990.5			−1.18751
$567$		0			0
$568$	19274.0			1.42380
$569$	−5694.04	+	9862.37i	−0.419520	+	0.726629i	−0.995891	−	0.0905585i	$-0.971135\pi$
$569$	−5694.04	+	9862.37i	−0.419520	+	0.726629i	0.576372	+	0.817188i	$0.304468\pi$
$570$		0			0
$571$	−4708.69	−	8155.70i	−0.345101	−	0.597732i	0.640271	−	0.768149i	$-0.278822\pi$
$571$	−4708.69	−	8155.70i	−0.345101	−	0.597732i	−0.985372	+	0.170417i	$0.945489\pi$
$572$	399.702	+	692.304i	0.0292174	+	0.0506061i
$573$		0			0
$574$	1948.29	−	3374.55i	0.141673	−	0.245385i
$575$	−2435.64			−0.176649
$576$		0			0
$577$	−3751.39			−0.270663			−0.135332	−	0.990800i	$-0.543210\pi$
$577$	−3751.39			−0.270663			−0.135332	+	0.990800i	$0.543210\pi$
$578$	−10729.9	+	18584.7i	−0.772154	+	1.33741i
$579$		0			0
$580$	−169.571	−	293.705i	−0.0121397	−	0.0210266i
$581$	−2830.97	−	4903.38i	−0.202149	−	0.350132i
$582$		0			0
$583$	−2939.02	+	5090.53i	−0.208785	+	0.361627i
$584$	−17521.8			−1.24154
$585$		0			0
$586$	−9670.35			−0.681704
$587$	−4646.77	+	8048.45i	−0.326734	+	0.565920i	−0.981862	−	0.189598i	$-0.939281\pi$
$587$	−4646.77	+	8048.45i	−0.326734	+	0.565920i	0.655128	+	0.755518i	$0.272615\pi$
$588$		0			0
$589$	−6643.31	−	11506.6i	−0.464742	−	0.804957i
$590$	2079.79	+	3602.30i	0.145125	+	0.251364i
$591$		0			0
$592$	8745.77	−	15148.1i	0.607178	−	1.05166i
$593$	−1527.88			−0.105805			−0.0529027	−	0.998600i	$-0.516847\pi$
$593$	−1527.88			−0.105805			−0.0529027	+	0.998600i	$0.516847\pi$
$594$		0			0
$595$	3914.26			0.269696
$596$	−136.679	+	236.735i	−0.00939359	+	0.0162702i
$597$		0			0
$598$	−3336.70	−	5779.34i	−0.228174	−	0.395209i
$599$	835.199	+	1446.61i	0.0569704	+	0.0986757i	0.893104	−	0.449850i	$-0.148523\pi$
$599$	835.199	+	1446.61i	0.0569704	+	0.0986757i	−0.836134	+	0.548526i	$0.815189\pi$
$600$		0			0
$601$	−8696.95	+	15063.6i	−0.590276	+	1.02239i	0.403919	+	0.914795i	$0.367648\pi$
$601$	−8696.95	+	15063.6i	−0.590276	+	1.02239i	−0.994195	+	0.107593i	$0.965686\pi$
$602$	−1518.04			−0.102775
$603$		0			0
$604$	−361.871			−0.0243780
$605$	−5522.36	+	9565.01i	−0.371100	+	0.642765i
$606$		0			0
$607$	−2040.68	−	3534.56i	−0.136456	−	0.236348i	0.789697	−	0.613497i	$-0.210238\pi$
$607$	−2040.68	−	3534.56i	−0.136456	−	0.236348i	−0.926153	+	0.377149i	$0.876904\pi$
$608$	1486.26	+	2574.28i	0.0991378	+	0.171712i
$609$		0			0
$610$	−4552.65	+	7885.42i	−0.302182	+	0.523395i
$611$	6762.18			0.447739
$612$		0			0
$613$	2300.45			0.151573			0.0757866	−	0.997124i	$-0.475853\pi$
$613$	2300.45			0.151573			0.0757866	+	0.997124i	$0.475853\pi$
$614$	400.660	−	693.963i	0.0263344	−	0.0456125i
$615$		0			0
$616$	−4806.48	−	8325.06i	−0.314381	−	0.544523i
$617$	−1452.92	−	2516.53i	−0.0948012	−	0.164201i	0.814724	−	0.579848i	$-0.196888\pi$
$617$	−1452.92	−	2516.53i	−0.0948012	−	0.164201i	−0.909526	+	0.415648i	$0.863555\pi$
$618$		0			0
$619$	−8927.74	+	15463.3i	−0.579703	+	1.00408i	0.415810	+	0.909452i	$0.363498\pi$
$619$	−8927.74	+	15463.3i	−0.579703	+	1.00408i	−0.995513	+	0.0946238i	$0.969835\pi$
$620$	289.962			0.0187825
$621$		0			0
$622$	12545.3			0.808714
$623$	1777.08	−	3078.00i	0.114281	−	0.197941i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−10574.5	−	18315.5i	−0.675146	−	1.16939i
$627$		0			0
$628$	−972.114	+	1683.75i	−0.0617700	+	0.106989i
$629$	33259.3			2.10832
$630$		0			0
$631$	−24250.9			−1.52998			−0.764988	−	0.644045i	$-0.777255\pi$
$631$	−24250.9			−1.52998			−0.764988	+	0.644045i	$0.777255\pi$
$632$	278.292	−	482.016i	0.0175156	−	0.0303379i
$633$		0			0
$634$	2619.11	+	4536.44i	0.164067	+	0.284172i
$635$	−4614.77	−	7993.01i	−0.288396	−	0.499517i
$636$		0			0
$637$	−3698.09	+	6405.28i	−0.230021	+	0.398409i
$638$	20573.8			1.27669
$639$		0			0
$640$	6429.28			0.397093
$641$	749.919	−	1298.90i	0.0462091	−	0.0800364i	−0.841996	−	0.539484i	$-0.818619\pi$
$641$	749.919	−	1298.90i	0.0462091	−	0.0800364i	0.888205	+	0.459448i	$0.151953\pi$
$642$		0			0
$643$	−11560.1	−	20022.6i	−0.708996	−	1.22802i	−0.965230	−	0.261402i	$-0.915815\pi$
$643$	−11560.1	−	20022.6i	−0.708996	−	1.22802i	0.256234	−	0.966615i	$-0.417518\pi$
$644$	−180.862	−	313.261i	−0.0110667	−	0.0191681i
$645$		0			0
$646$	18951.5	−	32824.9i	1.15424	−	1.99919i
$647$	−10703.6			−0.650391			−0.325195	−	0.945647i	$-0.605430\pi$
$647$	−10703.6			−0.650391			−0.325195	+	0.945647i	$0.605430\pi$
$648$		0			0
$649$	18117.1			1.09578
$650$	856.218	−	1483.01i	0.0516671	−	0.0894901i
$651$		0			0
$652$	−32.0357	−	55.4875i	−0.00192426	−	0.00333291i
$653$	−9054.57	−	15683.0i	−0.542623	−	0.939850i	−0.998752	−	0.0499370i	$-0.984098\pi$
$653$	−9054.57	−	15683.0i	−0.542623	−	0.939850i	0.456129	−	0.889913i	$-0.349235\pi$
$654$		0			0
$655$	6411.77	−	11105.5i	0.382486	−	0.662486i
$656$	12233.5			0.728104
$657$		0			0
$658$	−5105.18			−0.302463
$659$	12556.7	−	21748.8i	0.742244	−	1.28560i	−0.209227	−	0.977867i	$-0.567095\pi$
$659$	12556.7	−	21748.8i	0.742244	−	1.28560i	0.951471	−	0.307737i	$-0.0995718\pi$
$660$		0			0
$661$	9296.80	+	16102.5i	0.547055	+	0.947528i	0.998474	+	0.0552157i	$0.0175847\pi$
$661$	9296.80	+	16102.5i	0.547055	+	0.947528i	−0.451419	+	0.892312i	$0.649082\pi$
$662$	−11278.6	−	19535.2i	−0.662170	−	1.14691i
$663$		0			0
$664$	9529.12	−	16504.9i	0.556930	−	0.964631i
$665$	−4253.21			−0.248018
$666$		0			0
$667$	12331.1			0.715834
$668$	822.333	−	1424.32i	0.0476303	−	0.0824981i
$669$		0			0
$670$	4343.51	+	7523.17i	0.250454	+	0.433799i
$671$	19829.1	+	34345.0i	1.14083	+	1.97597i
$672$		0			0
$673$	−2145.19	+	3715.58i	−0.122869	+	0.212816i	−0.920898	−	0.389803i	$-0.872543\pi$
$673$	−2145.19	+	3715.58i	−0.122869	+	0.212816i	0.798029	+	0.602619i	$0.205876\pi$
$674$	−23273.5			−1.33006
$675$		0			0
$676$	840.506			0.0478212
$677$	−13475.3	+	23339.8i	−0.764988	+	1.32500i	0.175266	+	0.984521i	$0.443922\pi$
$677$	−13475.3	+	23339.8i	−0.764988	+	1.32500i	−0.940253	+	0.340476i	$0.889412\pi$
$678$		0			0
$679$	−1482.99	−	2568.61i	−0.0838173	−	0.145176i
$680$	6587.74	+	11410.3i	0.371512	+	0.643478i
$681$		0			0
$682$	−8795.20	+	15233.7i	−0.493821	+	0.855323i
$683$	−18870.9			−1.05721			−0.528607	−	0.848867i	$-0.677285\pi$
$683$	−18870.9			−1.05721			−0.528607	+	0.848867i	$0.677285\pi$
$684$		0			0
$685$	−2533.90			−0.141336
$686$	6038.10	−	10458.3i	0.336058	−	0.582069i
$687$		0			0
$688$	−2382.97	−	4127.42i	−0.132049	−	0.228716i
$689$	−1238.48	−	2145.12i	−0.0684796	−	0.118610i
$690$		0			0
$691$	−1848.03	+	3200.88i	−0.101740	+	0.176219i	−0.912402	−	0.409296i	$-0.865774\pi$
$691$	−1848.03	+	3200.88i	−0.101740	+	0.176219i	0.810662	+	0.585515i	$0.199108\pi$
$692$	1132.14			0.0621931
$693$		0			0
$694$	−26303.2			−1.43870
$695$	−5556.62	+	9624.34i	−0.303273	+	0.525284i
$696$		0			0
$697$	11630.6	+	20144.9i	0.632055	+	1.09475i
$698$	10370.6	+	17962.4i	0.562367	+	0.974048i
$699$		0			0
$700$	46.4102	−	80.3848i	0.00250591	−	0.00434037i
$701$	1123.53			0.0605349			0.0302674	−	0.999542i	$-0.490364\pi$
$701$	1123.53			0.0605349			0.0302674	+	0.999542i	$0.490364\pi$
$702$		0			0
$703$	−36139.3			−1.93886
$704$	16110.4	−	27904.0i	0.862475	−	1.49385i
$705$		0			0
$706$	1894.99	+	3282.21i	0.101018	+	0.174968i
$707$	3159.56	+	5472.52i	0.168073	+	0.291111i
$708$		0			0
$709$	13233.8	−	22921.7i	0.700998	−	1.21416i	−0.267118	−	0.963664i	$-0.586071\pi$
$709$	13233.8	−	22921.7i	0.700998	−	1.21416i	0.968116	−	0.250501i	$-0.0805952\pi$
$710$	−11290.0			−0.596767
$711$		0			0
$712$	11963.4			0.629702
$713$	−5271.48	+	9130.46i	−0.276884	+	0.479577i
$714$		0			0
$715$	−3729.27	−	6459.28i	−0.195058	−	0.337851i
$716$	435.361	+	754.067i	0.0227237	+	0.0393587i
$717$		0			0
$718$	8655.04	−	14991.0i	0.449865	−	0.779189i
$719$	7882.34			0.408848			0.204424	−	0.978882i	$-0.434468\pi$
$719$	7882.34			0.408848			0.204424	+	0.978882i	$0.434468\pi$
$720$		0			0
$721$	1929.49			0.0996641
$722$	−11223.0	+	19438.8i	−0.578499	+	1.00199i
$723$		0			0
$724$	−682.040	−	1181.33i	−0.0350108	−	0.0606405i
$725$	1582.12	+	2740.30i	0.0810459	+	0.140376i
$726$		0			0
$727$	−10004.5	+	17328.2i	−0.510379	+	0.884002i	0.489549	+	0.871976i	$0.337161\pi$
$727$	−10004.5	+	17328.2i	−0.510379	+	0.884002i	−0.999928	+	0.0120259i	$0.996172\pi$
$728$	4050.83			0.206228
$729$		0			0
$730$	10263.6			0.520375
$731$	4531.09	−	7848.08i	0.229259	−	0.397088i
$732$		0			0
$733$	18146.7	+	31431.1i	0.914414	+	1.58381i	0.807757	+	0.589515i	$0.200681\pi$
$733$	18146.7	+	31431.1i	0.914414	+	1.58381i	0.106657	+	0.994296i	$0.465985\pi$
$734$	12554.1	+	21744.4i	0.631311	+	1.09346i
$735$		0			0
$736$	1179.35	−	2042.69i	0.0590644	−	0.102302i
$737$	37836.4			1.89107
$738$		0			0
$739$	−27475.5			−1.36766			−0.683832	−	0.729639i	$-0.739688\pi$
$739$	−27475.5			−1.36766			−0.683832	+	0.729639i	$0.739688\pi$
$740$	394.346	−	683.027i	0.0195898	−	0.0339305i
$741$		0			0
$742$	935.005	+	1619.48i	0.0462603	+	0.0801251i
$743$	−19074.4	−	33037.9i	−0.941822	−	1.63128i	−0.761993	−	0.647585i	$-0.775779\pi$
$743$	−19074.4	−	33037.9i	−0.941822	−	1.63128i	−0.179829	−	0.983698i	$-0.557554\pi$
$744$		0			0
$745$	1275.23	−	2208.76i	0.0627125	−	0.108621i
$746$	−34657.1			−1.70092
$747$		0			0
$748$	3602.79			0.176111
$749$	−5238.88	+	9074.00i	−0.255573	+	0.442666i
$750$		0			0
$751$	−14111.5	−	24441.9i	−0.685669	−	1.18761i	−0.973226	−	0.229850i	$-0.926177\pi$
$751$	−14111.5	−	24441.9i	−0.685669	−	1.18761i	0.287557	−	0.957763i	$-0.407157\pi$
$752$	−8013.93	−	13880.5i	−0.388614	−	0.673099i
$753$		0			0
$754$	−4334.83	+	7508.15i	−0.209370	+	0.362640i
$755$	3376.31			0.162750
$756$		0			0
$757$	34786.4			1.67019			0.835095	−	0.550106i	$-0.185413\pi$
$757$	34786.4			1.67019			0.835095	+	0.550106i	$0.185413\pi$
$758$	17920.9	−	31039.9i	0.858729	−	1.48736i
$759$		0			0
$760$	−7158.20	−	12398.4i	−0.341651	−	0.591758i
$761$	−582.982	−	1009.76i	−0.0277702	−	0.0480993i	0.851806	−	0.523857i	$-0.175507\pi$
$761$	−582.982	−	1009.76i	−0.0277702	−	0.0480993i	−0.879576	+	0.475758i	$0.842174\pi$
$762$		0			0
$763$	−6898.87	+	11949.2i	−0.327334	+	0.566959i
$764$	2575.34			0.121954
$765$		0			0
$766$	4738.07			0.223490
$767$	−3817.21	+	6611.61i	−0.179702	+	0.311253i
$768$		0			0
$769$	13172.7	+	22815.7i	0.617710	+	1.06990i	0.989903	+	0.141749i	$0.0452727\pi$
$769$	13172.7	+	22815.7i	0.617710	+	1.06990i	−0.372193	+	0.928155i	$0.621394\pi$
$770$	2815.45	+	4876.50i	0.131768	+	0.228230i
$771$		0			0
$772$	958.679	−	1660.48i	0.0446938	−	0.0774120i
$773$	25867.0			1.20358			0.601792	−	0.798653i	$-0.294454\pi$
$773$	25867.0			1.20358			0.601792	+	0.798653i	$0.294454\pi$
$774$		0			0
$775$	−2705.38			−0.125394
$776$	4991.78	−	8646.02i	0.230921	−	0.399967i
$777$		0			0
$778$	12791.4	+	22155.4i	0.589454	+	1.02096i
$779$	−12637.8	−	21889.3i	−0.581252	−	1.00676i
$780$		0			0
$781$	−24586.8	+	42585.5i	−1.12648	+	1.95113i
$782$	−30076.0			−1.37534
$783$		0			0
$784$	17530.6			0.798586
$785$	9069.95	−	15709.6i	0.412383	−	0.714267i
$786$		0			0
$787$	4035.49	+	6989.67i	0.182782	+	0.316588i	0.942827	−	0.333283i	$-0.108156\pi$
$787$	4035.49	+	6989.67i	0.182782	+	0.316588i	−0.760045	+	0.649871i	$0.774823\pi$
$788$	1015.23	+	1758.43i	0.0458959	+	0.0794941i
$789$		0			0
$790$	−163.013	+	282.346i	−0.00734143	+	0.0127157i
$791$	3518.85			0.158174
$792$		0			0
$793$	−16711.7			−0.748361
$794$	10466.4	−	18128.3i	0.467807	−	0.810265i
$795$		0			0
$796$	548.842	+	950.623i	0.0244387	+	0.0423291i
$797$	6450.54	+	11172.7i	0.286688	+	0.496557i	0.973017	−	0.230733i	$-0.0741125\pi$
$797$	6450.54	+	11172.7i	0.286688	+	0.496557i	−0.686329	+	0.727291i	$0.740779\pi$
$798$		0			0
$799$	15238.1	−	26393.1i	0.674699	−	1.16861i
$800$	605.256			0.0267488
$801$		0			0
$802$	397.922			0.0175201
$803$	22351.7	−	38714.2i	0.982282	−	1.70136i
$804$		0			0
$805$	1687.46	+	2922.77i	0.0738822	+	0.127968i
$806$	−3706.24	−	6419.39i	−0.161969	−	0.280538i
$807$		0			0
$808$	−10635.2	+	18420.6i	−0.463049	+	0.802025i
$809$	26916.2			1.16974			0.584872	−	0.811126i	$-0.301145\pi$
$809$	26916.2			1.16974			0.584872	+	0.811126i	$0.301145\pi$
$810$		0			0
$811$	−28082.5			−1.21592			−0.607959	−	0.793969i	$-0.708011\pi$
$811$	−28082.5			−1.21592			−0.607959	+	0.793969i	$0.708011\pi$
$812$	−234.964	+	406.969i	−0.0101547	+	0.0175885i
$813$		0			0
$814$	23922.8	+	41435.4i	1.03009	+	1.78417i
$815$	298.897	+	517.705i	0.0128465	+	0.0222508i
$816$		0			0
$817$	−4923.45	+	8527.67i	−0.210832	+	0.365172i
$818$	24289.9			1.03823
$819$		0			0
$820$	551.604			0.0234913
$821$	23186.8	−	40160.8i	0.985659	−	1.70721i	0.346688	−	0.937981i	$-0.387306\pi$
$821$	23186.8	−	40160.8i	0.985659	−	1.70721i	0.638971	−	0.769231i	$-0.279360\pi$
$822$		0			0
$823$	3902.27	+	6758.94i	0.165279	+	0.286272i	0.936754	−	0.349988i	$-0.113814\pi$
$823$	3902.27	+	6758.94i	0.165279	+	0.286272i	−0.771475	+	0.636259i	$0.780481\pi$
$824$	3247.35	+	5624.58i	0.137290	+	0.237793i
$825$		0			0
$826$	2881.84	−	4991.50i	0.121395	−	0.210262i
$827$	−23964.1			−1.00764			−0.503818	−	0.863810i	$-0.668072\pi$
$827$	−23964.1			−1.00764			−0.503818	+	0.863810i	$0.668072\pi$
$828$		0			0
$829$	−4583.86			−0.192044			−0.0960218	−	0.995379i	$-0.530612\pi$
$829$	−4583.86			−0.192044			−0.0960218	+	0.995379i	$0.530612\pi$
$830$	−5581.79	+	9667.94i	−0.233430	+	0.404312i
$831$		0			0
$832$	6788.80	+	11758.5i	0.282884	+	0.489969i
$833$	16666.7	+	28867.6i	0.693239	+	1.20073i
$834$		0			0
$835$	−7672.47	+	13289.1i	−0.317984	+	0.550765i
$836$	−3914.77			−0.161956
$837$		0			0
$838$	8656.23			0.356831
$839$	13464.2	−	23320.6i	0.554034	−	0.959614i	−0.443944	−	0.896054i	$-0.646421\pi$
$839$	13464.2	−	23320.6i	0.554034	−	0.959614i	0.997978	−	0.0635601i	$-0.0202455\pi$
$840$		0			0
$841$	4184.62	+	7247.97i	0.171578	+	0.297182i
$842$	11604.4	+	20099.5i	0.474958	+	0.822652i
$843$		0			0
$844$	638.200	−	1105.39i	0.0260281	−	0.0450821i
$845$	−7842.03			−0.319259
$846$		0			0
$847$	15304.0			0.620841
$848$	−2935.47	+	5084.39i	−0.118873	+	0.205895i
$849$		0			0
$850$	−3858.85	−	6683.72i	−0.155714	−	0.269705i
$851$	14338.3	+	24834.7i	0.577568	+	1.00038i
$852$		0			0
$853$	3506.70	−	6073.78i	0.140759	−	0.243801i	−0.787024	−	0.616922i	$-0.788379\pi$
$853$	3506.70	−	6073.78i	0.140759	−	0.243801i	0.927782	+	0.373122i	$0.121713\pi$
$854$	12616.7			0.505543
$855$		0			0
$856$	−35268.4			−1.40823
$857$	−10332.5	+	17896.4i	−0.411846	+	0.713338i	−0.995092	−	0.0989575i	$-0.968449\pi$
$857$	−10332.5	+	17896.4i	−0.411846	+	0.713338i	0.583246	+	0.812296i	$0.301783\pi$
$858$		0			0
$859$	10127.9	+	17542.1i	0.402283	+	0.696774i	0.994001	−	0.109371i	$-0.0348836\pi$
$859$	10127.9	+	17542.1i	0.402283	+	0.696774i	−0.591718	+	0.806145i	$0.701550\pi$
$860$	−107.448	−	186.105i	−0.00426038	−	0.00737920i
$861$		0			0
$862$	2830.81	−	4903.11i	0.111854	−	0.193736i
$863$	−16293.0			−0.642666			−0.321333	−	0.946966i	$-0.604131\pi$
$863$	−16293.0			−0.642666			−0.321333	+	0.946966i	$0.604131\pi$
$864$		0			0
$865$	−10563.0			−0.415207
$866$	−3970.27	+	6876.71i	−0.155791	+	0.269839i
$867$		0			0
$868$	−200.892	−	347.955i	−0.00785566	−	0.0136064i
$869$	710.004	+	1229.76i	0.0277160	+	0.0480056i
$870$		0			0
$871$	−7972.00	+	13807.9i	−0.310127	+	0.537156i
$872$	−46443.6			−1.80364
$873$		0			0
$874$	32680.4			1.26480
$875$	−433.013	+	750.000i	−0.0167297	+	0.0289767i
$876$		0			0
$877$	−14132.1	−	24477.4i	−0.544134	−	0.942468i	−0.998661	−	0.0517347i	$-0.983525\pi$
$877$	−14132.1	−	24477.4i	−0.544134	−	0.942468i	0.454527	−	0.890733i	$-0.349808\pi$
$878$	−2637.90	−	4568.98i	−0.101395	−	0.175621i
$879$		0			0
$880$	−8839.18	+	15309.9i	−0.338601	+	0.586474i
$881$	24644.6			0.942447			0.471224	−	0.882014i	$-0.343812\pi$
$881$	24644.6			0.942447			0.471224	+	0.882014i	$0.343812\pi$
$882$		0			0
$883$	36026.4			1.37303			0.686515	−	0.727116i	$-0.259140\pi$
$883$	36026.4			1.37303			0.686515	+	0.727116i	$0.259140\pi$
$884$	−759.096	+	1314.79i	−0.0288814	+	0.0500240i
$885$		0			0
$886$	−334.163	−	578.788i	−0.0126709	−	0.0219467i
$887$	7087.35	+	12275.6i	0.268286	+	0.464685i	0.968419	−	0.249327i	$-0.0802094\pi$
$887$	7087.35	+	12275.6i	0.268286	+	0.464685i	−0.700133	+	0.714012i	$0.746876\pi$
$888$		0			0
$889$	−6394.41	+	11075.4i	−0.241239	+	0.417839i
$890$	−7007.71			−0.263931
$891$		0			0
$892$	298.578			0.0112075
$893$	−16557.6	+	28678.6i	−0.620469	+	1.07468i
$894$		0			0
$895$	−4061.97	−	7035.54i	−0.151706	−	0.262762i
$896$	−4454.34	−	7715.14i	−0.166081	−	0.287661i
$897$		0			0
$898$	18136.3	−	31412.9i	0.673959	−	1.16733i
$899$	13696.7			0.508133
$900$		0			0
$901$	−11163.3			−0.412768
$902$	−16731.4	+	28979.6i	−0.617621	+	1.06975i
$903$		0			0
$904$	5922.27	+	10257.7i	0.217889	+	0.377395i
$905$	6363.52	+	11021.9i	0.233736	+	0.404842i
$906$		0			0
$907$	−18002.6	+	31181.4i	−0.659058	+	1.14152i	0.321802	+	0.946807i	$0.395711\pi$
$907$	−18002.6	+	31181.4i	−0.659058	+	1.14152i	−0.980860	+	0.194714i	$0.937622\pi$
$908$	2774.93			0.101420
$909$		0			0
$910$	−2372.82			−0.0864376
$911$	−601.245	+	1041.39i	−0.0218662	+	0.0378734i	−0.876751	−	0.480944i	$-0.840294\pi$
$911$	−601.245	+	1041.39i	−0.0218662	+	0.0378734i	0.854885	+	0.518817i	$0.173627\pi$
$912$		0			0
$913$	24311.6	+	42108.8i	0.881265	+	1.52640i
$914$	−17094.7	−	29608.9i	−0.618646	−	1.07153i
$915$		0			0
$916$	−246.051	+	426.173i	−0.00887529	+	0.0153725i
$917$	−17768.8			−0.639889
$918$		0			0
$919$	1151.63			0.0413370			0.0206685	−	0.999786i	$-0.493421\pi$
$919$	1151.63			0.0413370			0.0206685	+	0.999786i	$0.493421\pi$
$920$	−5680.04	+	9838.11i	−0.203549	+	0.352558i
$921$		0			0
$922$	6134.66	+	10625.6i	0.219126	+	0.379538i
$923$	−10360.7	−	17945.2i	−0.369476	−	0.639951i
$924$		0			0
$925$	−3679.29	+	6372.72i	−0.130783	+	0.226523i
$926$	−16646.1			−0.590739
$927$		0			0
$928$	−3064.27			−0.108394
$929$	−2698.53	+	4673.99i	−0.0953023	+	0.165068i	−0.909735	−	0.415190i	$-0.863715\pi$
$929$	−2698.53	+	4673.99i	−0.0953023	+	0.165068i	0.814432	+	0.580258i	$0.197048\pi$
$930$		0			0
$931$	−18110.0	−	31367.4i	−0.637519	−	1.10422i
$932$	−1580.07	−	2736.77i	−0.0555333	−	0.0961865i
$933$		0			0
$934$	−7094.70	+	12288.4i	−0.248550	+	0.430501i
$935$	−33614.5			−1.17573
$936$		0			0
$937$	45594.6			1.58966			0.794830	−	0.606832i	$-0.207560\pi$
$937$	45594.6			1.58966			0.794830	+	0.606832i	$0.207560\pi$
$938$	6018.54	−	10424.4i	0.209501	−	0.362867i
$939$		0			0
$940$	−361.347	−	625.871i	−0.0125381	−	0.0217167i
$941$	18622.8	+	32255.6i	0.645149	+	1.11743i	0.984267	+	0.176687i	$0.0565379\pi$
$941$	18622.8	+	32255.6i	0.645149	+	1.11743i	−0.339119	+	0.940744i	$0.610129\pi$
$942$		0			0
$943$	−10028.1	+	17369.2i	−0.346299	+	0.599807i
$944$	18095.3			0.623888
$945$		0			0
$946$	13036.5			0.448048
$947$	−2388.77	+	4137.47i	−0.0819689	+	0.141974i	−0.904096	−	0.427330i	$-0.859454\pi$
$947$	−2388.77	+	4137.47i	−0.0819689	+	0.141974i	0.822127	+	0.569305i	$0.192787\pi$
$948$		0			0
$949$	9418.83	+	16313.9i	0.322179	+	0.558031i
$950$	4193.00	+	7262.48i	0.143199	+	0.248027i
$951$		0			0
$952$	9128.24	−	15810.6i	0.310765	−	0.538260i
$953$	−56883.2			−1.93350			−0.966752	−	0.255717i	$-0.917689\pi$
$953$	−56883.2			−1.93350			−0.966752	+	0.255717i	$0.917689\pi$
$954$		0			0
$955$	−24028.3			−0.814174
$956$	141.166	−	244.507i	0.00477578	−	0.00827190i
$957$		0			0
$958$	−25794.0	−	44676.6i	−0.869903	−	1.50672i
$959$	1755.54	+	3040.68i	0.0591129	+	0.102386i
$960$		0			0
$961$	9040.21	−	15658.1i	0.303455	−	0.525599i
$962$	−20161.8			−0.675719
$963$		0			0
$964$	3120.64			0.104262
$965$	−8944.60	+	15492.5i	−0.298380	+	0.516810i
$966$		0			0
$967$	−7024.99	−	12167.6i	−0.233618	−	0.404638i	0.725252	−	0.688483i	$-0.241723\pi$
$967$	−7024.99	−	12167.6i	−0.233618	−	0.404638i	−0.958870	+	0.283845i	$0.908390\pi$
$968$	25756.8	+	44612.2i	0.855223	+	1.48129i
$969$		0			0
$970$	−2923.99	+	5064.51i	−0.0967874	+	0.167641i
$971$	779.492			0.0257622			0.0128811	−	0.999917i	$-0.495900\pi$
$971$	779.492			0.0257622			0.0128811	+	0.999917i	$0.495900\pi$
$972$		0			0
$973$	15398.9			0.507366
$974$	24068.1	−	41687.1i	0.791777	−	1.37140i
$975$		0			0
$976$	19805.2	+	34303.6i	0.649537	+	1.12503i
$977$	−23377.4	−	40490.9i	−0.765517	−	1.32592i	−0.939973	−	0.341250i	$-0.889150\pi$
$977$	−23377.4	−	40490.9i	−0.765517	−	1.32592i	0.174455	−	0.984665i	$-0.444184\pi$
$978$		0			0
$979$	−15261.1	+	26433.0i	−0.498209	+	0.862923i
$980$	790.450			0.0257653
$981$		0			0
$982$	2503.29			0.0813474
$983$	1798.05	−	3114.31i	0.0583406	−	0.101049i	−0.835380	−	0.549673i	$-0.814752\pi$
$983$	1798.05	−	3114.31i	0.0583406	−	0.101049i	0.893721	+	0.448624i	$0.148086\pi$
$984$		0			0
$985$	−9472.21	−	16406.3i	−0.306406	−	0.530710i
$986$	19536.4	+	33838.1i	0.631001	+	1.09293i
$987$		0			0
$988$	824.828	−	1428.64i	0.0265600	−	0.0460033i
$989$	7813.53			0.251219
$990$		0			0
$991$	−15143.8			−0.485427			−0.242713	−	0.970098i	$-0.578037\pi$
$991$	−15143.8			−0.485427			−0.242713	+	0.970098i	$0.578037\pi$
$992$	1309.96	−	2268.92i	0.0419267	−	0.0726192i
$993$		0			0
$994$	7821.91	+	13547.9i	0.249593	+	0.432309i
$995$	−5120.77	−	8869.43i	−0.163155	−	0.282593i
$996$		0			0
$997$	−11004.4	+	19060.3i	−0.349563	+	0.605461i	−0.986172	−	0.165726i	$-0.947003\pi$
$997$	−11004.4	+	19060.3i	−0.349563	+	0.605461i	0.636609	+	0.771187i	$0.280337\pi$
$998$	34050.7			1.08002
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.o.136.1		4
3.2	odd	2		405.4.e.p.136.2		4
9.2	odd	6		405.4.a.c.1.1	✓	2
9.4	even	3	inner	405.4.e.o.271.1		4
9.5	odd	6		405.4.e.p.271.2		4
9.7	even	3		405.4.a.f.1.2	yes	2
45.29	odd	6		2025.4.a.m.1.2		2
45.34	even	6		2025.4.a.i.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.4.a.c.1.1	✓	2	9.2	odd	6
405.4.a.f.1.2	yes	2	9.7	even	3
405.4.e.o.136.1		4	1.1	even	1	trivial
405.4.e.o.271.1		4	9.4	even	3	inner
405.4.e.p.136.2		4	3.2	odd	2
405.4.e.p.271.2		4	9.5	odd	6
2025.4.a.i.1.1		2	45.34	even	6
2025.4.a.m.1.2		2	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 2.36603i) q^{2} +(0.267949 + 0.464102i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-3.46410 + 6.00000i) q^{7} -23.3205 q^{8} +O(q^{10})\)	\(q+(-1.36603 + 2.36603i) q^{2} +(0.267949 + 0.464102i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-3.46410 + 6.00000i) q^{7} -23.3205 q^{8} +13.6603 q^{10} +(29.7487 - 51.5263i) q^{11} +(12.5359 + 21.7128i) q^{13} +(-9.46410 - 16.3923i) q^{14} +(29.7128 - 51.4641i) q^{16} +112.995 q^{17} -122.779 q^{19} +(1.33975 - 2.32051i) q^{20} +(81.2750 + 140.772i) q^{22} +(48.7128 + 84.3731i) q^{23} +(-12.5000 + 21.6506i) q^{25} -68.4974 q^{26} -3.71281 q^{28} +(63.2846 - 109.612i) q^{29} +(54.1077 + 93.7173i) q^{31} +(-12.1051 - 20.9667i) q^{32} +(-154.354 + 267.349i) q^{34} +34.6410 q^{35} +294.344 q^{37} +(167.720 - 290.499i) q^{38} +(58.3013 + 100.981i) q^{40} +(102.931 + 178.281i) q^{41} +(40.1000 - 69.4552i) q^{43} +31.8846 q^{44} -266.172 q^{46} +(134.856 - 233.578i) q^{47} +(147.500 + 255.477i) q^{49} +(-34.1506 - 59.1506i) q^{50} +(-6.71797 + 11.6359i) q^{52} -98.7949 q^{53} -297.487 q^{55} +(80.7846 - 139.923i) q^{56} +(172.897 + 299.466i) q^{58} +(152.251 + 263.707i) q^{59} +(-333.277 + 577.252i) q^{61} -295.650 q^{62} +541.549 q^{64} +(62.6795 - 108.564i) q^{65} +(317.967 + 550.734i) q^{67} +(30.2769 + 52.4411i) q^{68} +(-47.3205 + 81.9615i) q^{70} -826.482 q^{71} +751.349 q^{73} +(-402.081 + 696.424i) q^{74} +(-32.8987 - 56.9821i) q^{76} +(206.105 + 356.985i) q^{77} +(-11.9334 + 20.6692i) q^{79} -297.128 q^{80} -562.424 q^{82} +(-408.615 + 707.742i) q^{83} +(-282.487 - 489.282i) q^{85} +(109.555 + 189.755i) q^{86} +(-693.755 + 1201.62i) q^{88} -513.000 q^{89} -173.703 q^{91} +(-26.1051 + 45.2154i) q^{92} +(368.435 + 638.147i) q^{94} +(306.949 + 531.651i) q^{95} +(-214.051 + 370.748i) q^{97} -805.955 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 8 * q^4 - 10 * q^5 - 24 * q^8	\( 4 q - 2 q^{2} + 8 q^{4} - 10 q^{5} - 24 q^{8} + 20 q^{10} + 22 q^{11} + 64 q^{13} - 24 q^{14} + 8 q^{16} + 64 q^{17} - 20 q^{19} + 40 q^{20} + 190 q^{22} + 84 q^{23} - 50 q^{25} - 80 q^{26} + 96 q^{28} + 170 q^{29} + 258 q^{31} + 104 q^{32} - 368 q^{34} + 152 q^{37} + 418 q^{38} + 60 q^{40} + 578 q^{41} - 380 q^{43} - 496 q^{44} - 552 q^{46} + 484 q^{47} + 590 q^{49} - 50 q^{50} - 304 q^{52} - 1088 q^{53} - 220 q^{55} + 240 q^{56} + 314 q^{58} + 706 q^{59} - 668 q^{61} - 372 q^{62} + 448 q^{64} + 320 q^{65} + 1452 q^{67} - 544 q^{68} - 120 q^{70} - 1948 q^{71} + 2368 q^{73} - 964 q^{74} + 776 q^{76} + 672 q^{77} - 408 q^{79} - 80 q^{80} - 580 q^{82} + 444 q^{83} - 160 q^{85} + 556 q^{86} - 1812 q^{88} - 2052 q^{89} + 192 q^{91} + 48 q^{92} + 580 q^{94} + 50 q^{95} + 668 q^{97} - 1180 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 8 * q^4 - 10 * q^5 - 24 * q^8 + 20 * q^10 + 22 * q^11 + 64 * q^13 - 24 * q^14 + 8 * q^16 + 64 * q^17 - 20 * q^19 + 40 * q^20 + 190 * q^22 + 84 * q^23 - 50 * q^25 - 80 * q^26 + 96 * q^28 + 170 * q^29 + 258 * q^31 + 104 * q^32 - 368 * q^34 + 152 * q^37 + 418 * q^38 + 60 * q^40 + 578 * q^41 - 380 * q^43 - 496 * q^44 - 552 * q^46 + 484 * q^47 + 590 * q^49 - 50 * q^50 - 304 * q^52 - 1088 * q^53 - 220 * q^55 + 240 * q^56 + 314 * q^58 + 706 * q^59 - 668 * q^61 - 372 * q^62 + 448 * q^64 + 320 * q^65 + 1452 * q^67 - 544 * q^68 - 120 * q^70 - 1948 * q^71 + 2368 * q^73 - 964 * q^74 + 776 * q^76 + 672 * q^77 - 408 * q^79 - 80 * q^80 - 580 * q^82 + 444 * q^83 - 160 * q^85 + 556 * q^86 - 1812 * q^88 - 2052 * q^89 + 192 * q^91 + 48 * q^92 + 580 * q^94 + 50 * q^95 + 668 * q^97 - 1180 * q^98

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