LMFDB - Embedded newform 810.4.e.u.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("810.271");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$47.7915471046$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(-3.00000 - 5.19615i) q^{11} +(-34.0000 + 58.8897i) q^{13} +(14.0000 - 24.2487i) q^{14} +(-8.00000 - 13.8564i) q^{16} +78.0000 q^{17} +44.0000 q^{19} +(10.0000 + 17.3205i) q^{20} +(6.00000 - 10.3923i) q^{22} +(-60.0000 + 103.923i) q^{23} +(-12.5000 - 21.6506i) q^{25} -136.000 q^{26} +56.0000 q^{28} +(-63.0000 - 109.119i) q^{29} +(122.000 - 211.310i) q^{31} +(16.0000 - 27.7128i) q^{32} +(78.0000 + 135.100i) q^{34} -70.0000 q^{35} -304.000 q^{37} +(44.0000 + 76.2102i) q^{38} +(-20.0000 + 34.6410i) q^{40} +(240.000 - 415.692i) q^{41} +(-52.0000 - 90.0666i) q^{43} +24.0000 q^{44} -240.000 q^{46} +(-300.000 - 519.615i) q^{47} +(73.5000 - 127.306i) q^{49} +(25.0000 - 43.3013i) q^{50} +(-136.000 - 235.559i) q^{52} -258.000 q^{53} -30.0000 q^{55} +(56.0000 + 96.9948i) q^{56} +(126.000 - 218.238i) q^{58} +(-267.000 + 462.458i) q^{59} +(-181.000 - 313.501i) q^{61} +488.000 q^{62} +64.0000 q^{64} +(170.000 + 294.449i) q^{65} +(134.000 - 232.095i) q^{67} +(-156.000 + 270.200i) q^{68} +(-70.0000 - 121.244i) q^{70} -972.000 q^{71} +470.000 q^{73} +(-304.000 - 526.543i) q^{74} +(-88.0000 + 152.420i) q^{76} +(-42.0000 + 72.7461i) q^{77} +(-622.000 - 1077.34i) q^{79} -80.0000 q^{80} +960.000 q^{82} +(-198.000 - 342.946i) q^{83} +(195.000 - 337.750i) q^{85} +(104.000 - 180.133i) q^{86} +(24.0000 + 41.5692i) q^{88} -972.000 q^{89} +952.000 q^{91} +(-240.000 - 415.692i) q^{92} +(600.000 - 1039.23i) q^{94} +(110.000 - 190.526i) q^{95} +(23.0000 + 39.8372i) q^{97} +294.000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} - 14 q^{7} - 16 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^4 + 5 * q^5 - 14 * q^7 - 16 * q^8	$ 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} - 14 q^{7} - 16 q^{8} + 20 q^{10} - 6 q^{11} - 68 q^{13} + 28 q^{14} - 16 q^{16} + 156 q^{17} + 88 q^{19} + 20 q^{20} + 12 q^{22} - 120 q^{23} - 25 q^{25} - 272 q^{26} + 112 q^{28} - 126 q^{29} + 244 q^{31} + 32 q^{32} + 156 q^{34} - 140 q^{35} - 608 q^{37} + 88 q^{38} - 40 q^{40} + 480 q^{41} - 104 q^{43} + 48 q^{44} - 480 q^{46} - 600 q^{47} + 147 q^{49} + 50 q^{50} - 272 q^{52} - 516 q^{53} - 60 q^{55} + 112 q^{56} + 252 q^{58} - 534 q^{59} - 362 q^{61} + 976 q^{62} + 128 q^{64} + 340 q^{65} + 268 q^{67} - 312 q^{68} - 140 q^{70} - 1944 q^{71} + 940 q^{73} - 608 q^{74} - 176 q^{76} - 84 q^{77} - 1244 q^{79} - 160 q^{80} + 1920 q^{82} - 396 q^{83} + 390 q^{85} + 208 q^{86} + 48 q^{88} - 1944 q^{89} + 1904 q^{91} - 480 q^{92} + 1200 q^{94} + 220 q^{95} + 46 q^{97} + 588 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 + 5 * q^5 - 14 * q^7 - 16 * q^8 + 20 * q^10 - 6 * q^11 - 68 * q^13 + 28 * q^14 - 16 * q^16 + 156 * q^17 + 88 * q^19 + 20 * q^20 + 12 * q^22 - 120 * q^23 - 25 * q^25 - 272 * q^26 + 112 * q^28 - 126 * q^29 + 244 * q^31 + 32 * q^32 + 156 * q^34 - 140 * q^35 - 608 * q^37 + 88 * q^38 - 40 * q^40 + 480 * q^41 - 104 * q^43 + 48 * q^44 - 480 * q^46 - 600 * q^47 + 147 * q^49 + 50 * q^50 - 272 * q^52 - 516 * q^53 - 60 * q^55 + 112 * q^56 + 252 * q^58 - 534 * q^59 - 362 * q^61 + 976 * q^62 + 128 * q^64 + 340 * q^65 + 268 * q^67 - 312 * q^68 - 140 * q^70 - 1944 * q^71 + 940 * q^73 - 608 * q^74 - 176 * q^76 - 84 * q^77 - 1244 * q^79 - 160 * q^80 + 1920 * q^82 - 396 * q^83 + 390 * q^85 + 208 * q^86 + 48 * q^88 - 1944 * q^89 + 1904 * q^91 - 480 * q^92 + 1200 * q^94 + 220 * q^95 + 46 * q^97 + 588 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$		0			0
$7$	−7.00000	−	12.1244i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−7.00000	−	12.1244i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	10.0000			0.316228
$11$	−3.00000	−	5.19615i	−0.0822304	−	0.142427i	0.821977	−	0.569520i	$-0.192871\pi$
$11$	−3.00000	−	5.19615i	−0.0822304	−	0.142427i	−0.904208	+	0.427093i	$0.859538\pi$
$12$		0			0
$13$	−34.0000	+	58.8897i	−0.725377	+	1.25639i	0.233441	+	0.972371i	$0.425001\pi$
$13$	−34.0000	+	58.8897i	−0.725377	+	1.25639i	−0.958819	+	0.284019i	$0.908332\pi$
$14$	14.0000	−	24.2487i	0.267261	−	0.462910i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	78.0000			1.11281			0.556405	−	0.830911i	$-0.312180\pi$
$17$	78.0000			1.11281			0.556405	+	0.830911i	$0.312180\pi$
$18$		0			0
$19$	44.0000			0.531279			0.265639	−	0.964072i	$-0.414417\pi$
$19$	44.0000			0.531279			0.265639	+	0.964072i	$0.414417\pi$
$20$	10.0000	+	17.3205i	0.111803	+	0.193649i
$21$		0			0
$22$	6.00000	−	10.3923i	0.0581456	−	0.100711i
$23$	−60.0000	+	103.923i	−0.543951	+	0.942150i	0.454721	+	0.890634i	$0.349739\pi$
$23$	−60.0000	+	103.923i	−0.543951	+	0.942150i	−0.998672	+	0.0515165i	$0.983595\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−136.000			−1.02584
$27$		0			0
$28$	56.0000			0.377964
$29$	−63.0000	−	109.119i	−0.403407	−	0.698722i	0.590728	−	0.806871i	$-0.298841\pi$
$29$	−63.0000	−	109.119i	−0.403407	−	0.698722i	−0.994135	+	0.108149i	$0.965507\pi$
$30$		0			0
$31$	122.000	−	211.310i	0.706834	−	1.22427i	−0.259192	−	0.965826i	$-0.583456\pi$
$31$	122.000	−	211.310i	0.706834	−	1.22427i	0.966026	−	0.258446i	$-0.0832105\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$		0			0
$34$	78.0000	+	135.100i	0.393438	+	0.681454i
$35$	−70.0000			−0.338062
$36$		0			0
$37$	−304.000			−1.35074			−0.675369	−	0.737480i	$-0.736016\pi$
$37$	−304.000			−1.35074			−0.675369	+	0.737480i	$0.736016\pi$
$38$	44.0000	+	76.2102i	0.187835	+	0.325340i
$39$		0			0
$40$	−20.0000	+	34.6410i	−0.0790569	+	0.136931i
$41$	240.000	−	415.692i	0.914188	−	1.58342i	0.106102	−	0.994355i	$-0.466163\pi$
$41$	240.000	−	415.692i	0.914188	−	1.58342i	0.808086	−	0.589065i	$-0.200504\pi$
$42$		0			0
$43$	−52.0000	−	90.0666i	−0.184417	−	0.319419i	0.758963	−	0.651134i	$-0.225706\pi$
$43$	−52.0000	−	90.0666i	−0.184417	−	0.319419i	−0.943380	+	0.331714i	$0.892373\pi$
$44$	24.0000			0.0822304
$45$		0			0
$46$	−240.000			−0.769262
$47$	−300.000	−	519.615i	−0.931053	−	1.61263i	−0.781525	−	0.623874i	$-0.785558\pi$
$47$	−300.000	−	519.615i	−0.931053	−	1.61263i	−0.149528	−	0.988757i	$-0.547775\pi$
$48$		0			0
$49$	73.5000	−	127.306i	0.214286	−	0.371154i
$50$	25.0000	−	43.3013i	0.0707107	−	0.122474i
$51$		0			0
$52$	−136.000	−	235.559i	−0.362689	−	0.628195i
$53$	−258.000			−0.668661			−0.334330	−	0.942456i	$-0.608510\pi$
$53$	−258.000			−0.668661			−0.334330	+	0.942456i	$0.608510\pi$
$54$		0			0
$55$	−30.0000			−0.0735491
$56$	56.0000	+	96.9948i	0.133631	+	0.231455i
$57$		0			0
$58$	126.000	−	218.238i	0.285252	−	0.494071i
$59$	−267.000	+	462.458i	−0.589160	+	1.02046i	0.405183	+	0.914236i	$0.367208\pi$
$59$	−267.000	+	462.458i	−0.589160	+	1.02046i	−0.994343	+	0.106219i	$0.966125\pi$
$60$		0			0
$61$	−181.000	−	313.501i	−0.379913	−	0.658028i	0.611136	−	0.791525i	$-0.290713\pi$
$61$	−181.000	−	313.501i	−0.379913	−	0.658028i	−0.991049	+	0.133497i	$0.957379\pi$
$62$	488.000			0.999614
$63$		0			0
$64$	64.0000			0.125000
$65$	170.000	+	294.449i	0.324399	+	0.561875i
$66$		0			0
$67$	134.000	−	232.095i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	134.000	−	232.095i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−156.000	+	270.200i	−0.278203	+	0.481861i
$69$		0			0
$70$	−70.0000	−	121.244i	−0.119523	−	0.207020i
$71$	−972.000			−1.62472			−0.812360	−	0.583156i	$-0.801818\pi$
$71$	−972.000			−1.62472			−0.812360	+	0.583156i	$0.801818\pi$
$72$		0			0
$73$	470.000			0.753553			0.376776	−	0.926304i	$-0.377033\pi$
$73$	470.000			0.753553			0.376776	+	0.926304i	$0.377033\pi$
$74$	−304.000	−	526.543i	−0.477558	−	0.827154i
$75$		0			0
$76$	−88.0000	+	152.420i	−0.132820	+	0.230050i
$77$	−42.0000	+	72.7461i	−0.0621603	+	0.107665i
$78$		0			0
$79$	−622.000	−	1077.34i	−0.885829	−	1.53430i	−0.844761	−	0.535144i	$-0.820257\pi$
$79$	−622.000	−	1077.34i	−0.885829	−	1.53430i	−0.0410678	−	0.999156i	$-0.513076\pi$
$80$	−80.0000			−0.111803
$81$		0			0
$82$	960.000			1.29286
$83$	−198.000	−	342.946i	−0.261847	−	0.453533i	0.704886	−	0.709321i	$-0.250998\pi$
$83$	−198.000	−	342.946i	−0.261847	−	0.453533i	−0.966733	+	0.255788i	$0.917665\pi$
$84$		0			0
$85$	195.000	−	337.750i	0.248832	−	0.430990i
$86$	104.000	−	180.133i	0.130402	−	0.225864i
$87$		0			0
$88$	24.0000	+	41.5692i	0.0290728	+	0.0503556i
$89$	−972.000			−1.15766			−0.578830	−	0.815448i	$-0.696491\pi$
$89$	−972.000			−1.15766			−0.578830	+	0.815448i	$0.696491\pi$
$90$		0			0
$91$	952.000			1.09667
$92$	−240.000	−	415.692i	−0.271975	−	0.471075i
$93$		0			0
$94$	600.000	−	1039.23i	0.658354	−	1.14030i
$95$	110.000	−	190.526i	0.118797	−	0.205763i
$96$		0			0
$97$	23.0000	+	39.8372i	0.0240752	+	0.0416995i	0.877812	−	0.479005i	$-0.159003\pi$
$97$	23.0000	+	39.8372i	0.0240752	+	0.0416995i	−0.853737	+	0.520705i	$0.825669\pi$
$98$	294.000			0.303046
$99$		0			0
$100$	100.000			0.100000
$101$	753.000	+	1304.23i	0.741845	+	1.28491i	0.951655	+	0.307170i	$0.0993821\pi$
$101$	753.000	+	1304.23i	0.741845	+	1.28491i	−0.209810	+	0.977742i	$0.567285\pi$
$102$		0			0
$103$	737.000	−	1276.52i	0.705037	−	1.22116i	−0.261642	−	0.965165i	$-0.584264\pi$
$103$	737.000	−	1276.52i	0.705037	−	1.22116i	0.966678	−	0.255994i	$-0.0824028\pi$
$104$	272.000	−	471.118i	0.256460	−	0.444201i
$105$		0			0
$106$	−258.000	−	446.869i	−0.236407	−	0.409469i
$107$	924.000			0.834827			0.417413	−	0.908717i	$-0.362937\pi$
$107$	924.000			0.834827			0.417413	+	0.908717i	$0.362937\pi$
$108$		0			0
$109$	698.000			0.613360			0.306680	−	0.951813i	$-0.400782\pi$
$109$	698.000			0.613360			0.306680	+	0.951813i	$0.400782\pi$
$110$	−30.0000	−	51.9615i	−0.0260035	−	0.0450394i
$111$		0			0
$112$	−112.000	+	193.990i	−0.0944911	+	0.163663i
$113$	111.000	−	192.258i	0.0924071	−	0.160054i	−0.816116	−	0.577888i	$-0.803877\pi$
$113$	111.000	−	192.258i	0.0924071	−	0.160054i	0.908523	+	0.417834i	$0.137211\pi$
$114$		0			0
$115$	300.000	+	519.615i	0.243262	+	0.421342i
$116$	504.000			0.403407
$117$		0			0
$118$	−1068.00			−0.833198
$119$	−546.000	−	945.700i	−0.420603	−	0.728505i
$120$		0			0
$121$	647.500	−	1121.50i	0.486476	−	0.842602i
$122$	362.000	−	627.002i	0.268639	−	0.465296i
$123$		0			0
$124$	488.000	+	845.241i	0.353417	+	0.612136i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−1906.00			−1.33173			−0.665867	−	0.746071i	$-0.731938\pi$
$127$	−1906.00			−1.33173			−0.665867	+	0.746071i	$0.731938\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−340.000	+	588.897i	−0.229384	+	0.397305i
$131$	−1437.00	+	2488.96i	−0.958407	+	1.66001i	−0.232034	+	0.972708i	$0.574538\pi$
$131$	−1437.00	+	2488.96i	−0.958407	+	1.66001i	−0.726372	+	0.687301i	$0.758795\pi$
$132$		0			0
$133$	−308.000	−	533.472i	−0.200804	−	0.347803i
$134$	536.000			0.345547
$135$		0			0
$136$	−624.000			−0.393438
$137$	399.000	+	691.088i	0.248824	+	0.430976i	0.963200	−	0.268787i	$-0.0866226\pi$
$137$	399.000	+	691.088i	0.248824	+	0.430976i	−0.714376	+	0.699762i	$0.753289\pi$
$138$		0			0
$139$	350.000	−	606.218i	0.213573	−	0.369919i	−0.739257	−	0.673423i	$-0.764823\pi$
$139$	350.000	−	606.218i	0.213573	−	0.369919i	0.952830	+	0.303504i	$0.0981566\pi$
$140$	140.000	−	242.487i	0.0845154	−	0.146385i
$141$		0			0
$142$	−972.000	−	1683.55i	−0.574426	−	0.994934i
$143$	408.000			0.238592
$144$		0			0
$145$	−630.000			−0.360818
$146$	470.000	+	814.064i	0.266421	+	0.461455i
$147$		0			0
$148$	608.000	−	1053.09i	0.337684	−	0.584887i
$149$	−57.0000	+	98.7269i	−0.0313397	+	0.0542820i	−0.881270	−	0.472613i	$-0.843311\pi$
$149$	−57.0000	+	98.7269i	−0.0313397	+	0.0542820i	0.849930	+	0.526895i	$0.176644\pi$
$150$		0			0
$151$	−532.000	−	921.451i	−0.286712	−	0.496600i	0.686311	−	0.727308i	$-0.259229\pi$
$151$	−532.000	−	921.451i	−0.286712	−	0.496600i	−0.973023	+	0.230708i	$0.925896\pi$
$152$	−352.000			−0.187835
$153$		0			0
$154$	−168.000			−0.0879080
$155$	−610.000	−	1056.55i	−0.316106	−	0.547511i
$156$		0			0
$157$	974.000	−	1687.02i	0.495119	−	0.857571i	−0.504865	−	0.863198i	$-0.668458\pi$
$157$	974.000	−	1687.02i	0.495119	−	0.857571i	0.999984	+	0.00562710i	$0.00179117\pi$
$158$	1244.00	−	2154.67i	0.626375	−	1.08491i
$159$		0			0
$160$	−80.0000	−	138.564i	−0.0395285	−	0.0684653i
$161$	1680.00			0.822376
$162$		0			0
$163$	2060.00			0.989887			0.494944	−	0.868925i	$-0.335189\pi$
$163$	2060.00			0.989887			0.494944	+	0.868925i	$0.335189\pi$
$164$	960.000	+	1662.77i	0.457094	+	0.791710i
$165$		0			0
$166$	396.000	−	685.892i	0.185154	−	0.320696i
$167$	624.000	−	1080.80i	0.289141	−	0.500807i	−0.684464	−	0.729047i	$-0.739964\pi$
$167$	624.000	−	1080.80i	0.289141	−	0.500807i	0.973605	+	0.228240i	$0.0732970\pi$
$168$		0			0
$169$	−1213.50	−	2101.84i	−0.552344	−	0.956688i
$170$	780.000			0.351902
$171$		0			0
$172$	416.000			0.184417
$173$	573.000	+	992.465i	0.251817	+	0.436160i	0.964026	−	0.265807i	$-0.0856385\pi$
$173$	573.000	+	992.465i	0.251817	+	0.436160i	−0.712209	+	0.701968i	$0.752305\pi$
$174$		0			0
$175$	−175.000	+	303.109i	−0.0755929	+	0.130931i
$176$	−48.0000	+	83.1384i	−0.0205576	+	0.0356068i
$177$		0			0
$178$	−972.000	−	1683.55i	−0.409295	−	0.708919i
$179$	−1146.00			−0.478525			−0.239263	−	0.970955i	$-0.576906\pi$
$179$	−1146.00			−0.478525			−0.239263	+	0.970955i	$0.576906\pi$
$180$		0			0
$181$	−118.000			−0.0484579			−0.0242289	−	0.999706i	$-0.507713\pi$
$181$	−118.000			−0.0484579			−0.0242289	+	0.999706i	$0.507713\pi$
$182$	952.000	+	1648.91i	0.387730	+	0.671569i
$183$		0			0
$184$	480.000	−	831.384i	0.192316	−	0.333100i
$185$	−760.000	+	1316.36i	−0.302034	+	0.523138i
$186$		0			0
$187$	−234.000	−	405.300i	−0.0915068	−	0.158494i
$188$	2400.00			0.931053
$189$		0			0
$190$	440.000			0.168005
$191$	−846.000	−	1465.31i	−0.320494	−	0.555112i	0.660096	−	0.751181i	$-0.270516\pi$
$191$	−846.000	−	1465.31i	−0.320494	−	0.555112i	−0.980590	+	0.196069i	$0.937182\pi$
$192$		0			0
$193$	−1675.00	+	2901.19i	−0.624711	+	1.08203i	0.363886	+	0.931443i	$0.381450\pi$
$193$	−1675.00	+	2901.19i	−0.624711	+	1.08203i	−0.988597	+	0.150587i	$0.951884\pi$
$194$	−46.0000	+	79.6743i	−0.0170238	+	0.0294860i
$195$		0			0
$196$	294.000	+	509.223i	0.107143	+	0.185577i
$197$	−3606.00			−1.30415			−0.652073	−	0.758156i	$-0.726101\pi$
$197$	−3606.00			−1.30415			−0.652073	+	0.758156i	$0.726101\pi$
$198$		0			0
$199$	2696.00			0.960374			0.480187	−	0.877166i	$-0.340569\pi$
$199$	2696.00			0.960374			0.480187	+	0.877166i	$0.340569\pi$
$200$	100.000	+	173.205i	0.0353553	+	0.0612372i
$201$		0			0
$202$	−1506.00	+	2608.47i	−0.524563	+	0.908570i
$203$	−882.000	+	1527.67i	−0.304947	+	0.528184i
$204$		0			0
$205$	−1200.00	−	2078.46i	−0.408837	−	0.708127i
$206$	2948.00			0.997072
$207$		0			0
$208$	1088.00			0.362689
$209$	−132.000	−	228.631i	−0.0436872	−	0.0756685i
$210$		0			0
$211$	2.00000	−	3.46410i	0.000652539	−	0.00113023i	−0.865699	−	0.500565i	$-0.833126\pi$
$211$	2.00000	−	3.46410i	0.000652539	−	0.00113023i	0.866351	+	0.499435i	$0.166459\pi$
$212$	516.000	−	893.738i	0.167165	−	0.289539i
$213$		0			0
$214$	924.000	+	1600.41i	0.295156	+	0.511225i
$215$	−520.000			−0.164947
$216$		0			0
$217$	−3416.00			−1.06863
$218$	698.000	+	1208.97i	0.216856	+	0.375605i
$219$		0			0
$220$	60.0000	−	103.923i	0.0183873	−	0.0318477i
$221$	−2652.00	+	4593.40i	−0.807207	+	1.39812i
$222$		0			0
$223$	581.000	+	1006.32i	0.174469	+	0.302190i	0.939977	−	0.341237i	$-0.110846\pi$
$223$	581.000	+	1006.32i	0.174469	+	0.302190i	−0.765508	+	0.643426i	$0.777512\pi$
$224$	−448.000			−0.133631
$225$		0			0
$226$	444.000			0.130683
$227$	1200.00	+	2078.46i	0.350867	+	0.607719i	0.986402	−	0.164353i	$-0.0525536\pi$
$227$	1200.00	+	2078.46i	0.350867	+	0.607719i	−0.635535	+	0.772072i	$0.719220\pi$
$228$		0			0
$229$	1157.00	−	2003.98i	0.333872	−	0.578283i	−0.649395	−	0.760451i	$-0.724978\pi$
$229$	1157.00	−	2003.98i	0.333872	−	0.578283i	0.983268	+	0.182167i	$0.0583113\pi$
$230$	−600.000	+	1039.23i	−0.172012	+	0.297934i
$231$		0			0
$232$	504.000	+	872.954i	0.142626	+	0.247035i
$233$	−18.0000			−0.00506103			−0.00253051	−	0.999997i	$-0.500805\pi$
$233$	−18.0000			−0.00506103			−0.00253051	+	0.999997i	$0.500805\pi$
$234$		0			0
$235$	−3000.00			−0.832759
$236$	−1068.00	−	1849.83i	−0.294580	−	0.510228i
$237$		0			0
$238$	1092.00	−	1891.40i	0.297411	−	0.515131i
$239$	2934.00	−	5081.84i	0.794078	−	1.37538i	−0.129345	−	0.991600i	$-0.541287\pi$
$239$	2934.00	−	5081.84i	0.794078	−	1.37538i	0.923423	−	0.383784i	$-0.125379\pi$
$240$		0			0
$241$	2165.00	+	3749.89i	0.578672	+	1.00229i	0.995632	+	0.0933643i	$0.0297621\pi$
$241$	2165.00	+	3749.89i	0.578672	+	1.00229i	−0.416960	+	0.908925i	$0.636905\pi$
$242$	2590.00			0.687981
$243$		0			0
$244$	1448.00			0.379913
$245$	−367.500	−	636.529i	−0.0958315	−	0.165985i
$246$		0			0
$247$	−1496.00	+	2591.15i	−0.385377	+	0.667493i
$248$	−976.000	+	1690.48i	−0.249903	+	0.432846i
$249$		0			0
$250$	−125.000	−	216.506i	−0.0316228	−	0.0547723i
$251$	498.000			0.125233			0.0626165	−	0.998038i	$-0.480056\pi$
$251$	498.000			0.125233			0.0626165	+	0.998038i	$0.480056\pi$
$252$		0			0
$253$	720.000			0.178917
$254$	−1906.00	−	3301.29i	−0.470839	−	0.815517i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−321.000	+	555.988i	−0.0779122	+	0.134948i	−0.902349	−	0.431006i	$-0.858159\pi$
$257$	−321.000	+	555.988i	−0.0779122	+	0.134948i	0.824437	+	0.565954i	$0.191492\pi$
$258$		0			0
$259$	2128.00	+	3685.80i	0.510531	+	0.884265i
$260$	−1360.00			−0.324399
$261$		0			0
$262$	−5748.00			−1.35539
$263$	3984.00	+	6900.49i	0.934084	+	1.61788i	0.776260	+	0.630413i	$0.217114\pi$
$263$	3984.00	+	6900.49i	0.934084	+	1.61788i	0.157823	+	0.987467i	$0.449552\pi$
$264$		0			0
$265$	−645.000	+	1117.17i	−0.149517	+	0.258971i
$266$	616.000	−	1066.94i	0.141990	−	0.245934i
$267$		0			0
$268$	536.000	+	928.379i	0.122169	+	0.211604i
$269$	−4218.00			−0.956045			−0.478022	−	0.878348i	$-0.658646\pi$
$269$	−4218.00			−0.956045			−0.478022	+	0.878348i	$0.658646\pi$
$270$		0			0
$271$	848.000			0.190082			0.0950412	−	0.995473i	$-0.469702\pi$
$271$	848.000			0.190082			0.0950412	+	0.995473i	$0.469702\pi$
$272$	−624.000	−	1080.80i	−0.139101	−	0.240931i
$273$		0			0
$274$	−798.000	+	1382.18i	−0.175945	+	0.304746i
$275$	−75.0000	+	129.904i	−0.0164461	+	0.0284854i
$276$		0			0
$277$	752.000	+	1302.50i	0.163117	+	0.282526i	0.935985	−	0.352040i	$-0.114512\pi$
$277$	752.000	+	1302.50i	0.163117	+	0.282526i	−0.772868	+	0.634567i	$0.781179\pi$
$278$	1400.00			0.302037
$279$		0			0
$280$	560.000			0.119523
$281$	654.000	+	1132.76i	0.138841	+	0.240480i	0.927058	−	0.374917i	$-0.122329\pi$
$281$	654.000	+	1132.76i	0.138841	+	0.240480i	−0.788217	+	0.615397i	$0.788996\pi$
$282$		0			0
$283$	2966.00	−	5137.26i	0.623005	−	1.07908i	−0.365918	−	0.930647i	$-0.619245\pi$
$283$	2966.00	−	5137.26i	0.623005	−	1.07908i	0.988923	−	0.148429i	$-0.0474217\pi$
$284$	1944.00	−	3367.11i	0.406180	−	0.703525i
$285$		0			0
$286$	408.000	+	706.677i	0.0843551	+	0.146107i
$287$	−6720.00			−1.38212
$288$		0			0
$289$	1171.00			0.238347
$290$	−630.000	−	1091.19i	−0.127569	−	0.220955i
$291$		0			0
$292$	−940.000	+	1628.13i	−0.188388	+	0.326298i
$293$	−2613.00	+	4525.85i	−0.521000	+	0.902399i	0.478701	+	0.877978i	$0.341108\pi$
$293$	−2613.00	+	4525.85i	−0.521000	+	0.902399i	−0.999702	+	0.0244213i	$0.992226\pi$
$294$		0			0
$295$	1335.00	+	2312.29i	0.263480	+	0.456361i
$296$	2432.00			0.477558
$297$		0			0
$298$	−228.000			−0.0443211
$299$	−4080.00	−	7066.77i	−0.789139	−	1.36683i
$300$		0			0
$301$	−728.000	+	1260.93i	−0.139406	+	0.241458i
$302$	1064.00	−	1842.90i	0.202736	−	0.351149i
$303$		0			0
$304$	−352.000	−	609.682i	−0.0664098	−	0.115025i
$305$	−1810.00			−0.339804
$306$		0			0
$307$	4448.00			0.826908			0.413454	−	0.910525i	$-0.364322\pi$
$307$	4448.00			0.826908			0.413454	+	0.910525i	$0.364322\pi$
$308$	−168.000	−	290.985i	−0.0310802	−	0.0538324i
$309$		0			0
$310$	1220.00	−	2113.10i	0.223520	−	0.387149i
$311$	4566.00	−	7908.54i	0.832521	−	1.44197i	−0.0635115	−	0.997981i	$-0.520230\pi$
$311$	4566.00	−	7908.54i	0.832521	−	1.44197i	0.896033	−	0.443988i	$-0.146437\pi$
$312$		0			0
$313$	1085.00	+	1879.28i	0.195936	+	0.339370i	0.947207	−	0.320623i	$-0.103892\pi$
$313$	1085.00	+	1879.28i	0.195936	+	0.339370i	−0.751271	+	0.659994i	$0.770559\pi$
$314$	3896.00			0.700204
$315$		0			0
$316$	4976.00			0.885829
$317$	−3837.00	−	6645.88i	−0.679834	−	1.17751i	−0.975031	−	0.222071i	$-0.928718\pi$
$317$	−3837.00	−	6645.88i	−0.679834	−	1.17751i	0.295197	−	0.955437i	$-0.404615\pi$
$318$		0			0
$319$	−378.000	+	654.715i	−0.0663446	+	0.114912i
$320$	160.000	−	277.128i	0.0279508	−	0.0484123i
$321$		0			0
$322$	1680.00	+	2909.85i	0.290754	+	0.503600i
$323$	3432.00			0.591212
$324$		0			0
$325$	1700.00			0.290151
$326$	2060.00	+	3568.02i	0.349978	+	0.606180i
$327$		0			0
$328$	−1920.00	+	3325.54i	−0.323214	+	0.559823i
$329$	−4200.00	+	7274.61i	−0.703810	+	1.21903i
$330$		0			0
$331$	−4798.00	−	8310.38i	−0.796743	−	1.38000i	−0.921726	−	0.387841i	$-0.873221\pi$
$331$	−4798.00	−	8310.38i	−0.796743	−	1.38000i	0.124983	−	0.992159i	$-0.460112\pi$
$332$	1584.00			0.261847
$333$		0			0
$334$	2496.00			0.408907
$335$	−670.000	−	1160.47i	−0.109272	−	0.189264i
$336$		0			0
$337$	−6079.00	+	10529.1i	−0.982624	+	1.70195i	−0.330570	+	0.943781i	$0.607241\pi$
$337$	−6079.00	+	10529.1i	−0.982624	+	1.70195i	−0.652053	+	0.758173i	$0.726092\pi$
$338$	2427.00	−	4203.69i	0.390566	−	0.676481i
$339$		0			0
$340$	780.000	+	1351.00i	0.124416	+	0.215495i
$341$	−1464.00			−0.232493
$342$		0			0
$343$	−6860.00			−1.07990
$344$	416.000	+	720.533i	0.0652012	+	0.112932i
$345$		0			0
$346$	−1146.00	+	1984.93i	−0.178062	+	0.308412i
$347$	−5160.00	+	8937.38i	−0.798280	+	1.38266i	0.122455	+	0.992474i	$0.460923\pi$
$347$	−5160.00	+	8937.38i	−0.798280	+	1.38266i	−0.920735	+	0.390188i	$0.872410\pi$
$348$		0			0
$349$	1079.00	+	1868.88i	0.165494	+	0.286645i	0.936831	−	0.349783i	$-0.113745\pi$
$349$	1079.00	+	1868.88i	0.165494	+	0.286645i	−0.771336	+	0.636428i	$0.780411\pi$
$350$	−700.000			−0.106904
$351$		0			0
$352$	−192.000			−0.0290728
$353$	165.000	+	285.788i	0.0248784	+	0.0430906i	0.878197	−	0.478300i	$-0.158747\pi$
$353$	165.000	+	285.788i	0.0248784	+	0.0430906i	−0.853318	+	0.521391i	$0.825413\pi$
$354$		0			0
$355$	−2430.00	+	4208.88i	−0.363299	+	0.629252i
$356$	1944.00	−	3367.11i	0.289415	−	0.501282i
$357$		0			0
$358$	−1146.00	−	1984.93i	−0.169184	−	0.293036i
$359$	−8664.00			−1.27373			−0.636864	−	0.770976i	$-0.719769\pi$
$359$	−8664.00			−1.27373			−0.636864	+	0.770976i	$0.719769\pi$
$360$		0			0
$361$	−4923.00			−0.717743
$362$	−118.000	−	204.382i	−0.0171324	−	0.0296743i
$363$		0			0
$364$	−1904.00	+	3297.82i	−0.274167	+	0.474871i
$365$	1175.00	−	2035.16i	0.168499	−	0.291850i
$366$		0			0
$367$	−1891.00	−	3275.31i	−0.268963	−	0.465857i	0.699631	−	0.714504i	$-0.253348\pi$
$367$	−1891.00	−	3275.31i	−0.268963	−	0.465857i	−0.968594	+	0.248647i	$0.920014\pi$
$368$	1920.00			0.271975
$369$		0			0
$370$	−3040.00			−0.427141
$371$	1806.00	+	3128.08i	0.252730	+	0.437741i
$372$		0			0
$373$	−5638.00	+	9765.30i	−0.782640	+	1.35557i	0.147759	+	0.989023i	$0.452794\pi$
$373$	−5638.00	+	9765.30i	−0.782640	+	1.35557i	−0.930399	+	0.366548i	$0.880539\pi$
$374$	468.000	−	810.600i	0.0647051	−	0.112073i
$375$		0			0
$376$	2400.00	+	4156.92i	0.329177	+	0.570151i
$377$	8568.00			1.17049
$378$		0			0
$379$	980.000			0.132821			0.0664106	−	0.997792i	$-0.478845\pi$
$379$	980.000			0.132821			0.0664106	+	0.997792i	$0.478845\pi$
$380$	440.000	+	762.102i	0.0593987	+	0.102882i
$381$		0			0
$382$	1692.00	−	2930.63i	0.226624	−	0.392524i
$383$	2100.00	−	3637.31i	0.280170	−	0.485268i	−0.691257	−	0.722609i	$-0.742943\pi$
$383$	2100.00	−	3637.31i	0.280170	−	0.485268i	0.971426	+	0.237341i	$0.0762759\pi$
$384$		0			0
$385$	210.000	+	363.731i	0.0277989	+	0.0481492i
$386$	−6700.00			−0.883474
$387$		0			0
$388$	−184.000			−0.0240752
$389$	−6669.00	−	11551.0i	−0.869233	−	1.50556i	−0.862782	−	0.505577i	$-0.831280\pi$
$389$	−6669.00	−	11551.0i	−0.869233	−	1.50556i	−0.00645168	−	0.999979i	$-0.502054\pi$
$390$		0			0
$391$	−4680.00	+	8106.00i	−0.605314	+	1.04843i
$392$	−588.000	+	1018.45i	−0.0757614	+	0.131223i
$393$		0			0
$394$	−3606.00	−	6245.78i	−0.461085	−	0.798623i
$395$	−6220.00			−0.792309
$396$		0			0
$397$	−7192.00			−0.909209			−0.454605	−	0.890693i	$-0.650219\pi$
$397$	−7192.00			−0.909209			−0.454605	+	0.890693i	$0.650219\pi$
$398$	2696.00	+	4669.61i	0.339543	+	0.588106i
$399$		0			0
$400$	−200.000	+	346.410i	−0.0250000	+	0.0433013i
$401$	1158.00	−	2005.71i	0.144209	−	0.249777i	−0.784869	−	0.619662i	$-0.787270\pi$
$401$	1158.00	−	2005.71i	0.144209	−	0.249777i	0.929078	+	0.369885i	$0.120603\pi$
$402$		0			0
$403$	8296.00	+	14369.1i	1.02544	+	1.77612i
$404$	−6024.00			−0.741845
$405$		0			0
$406$	−3528.00			−0.431260
$407$	912.000	+	1579.63i	0.111072	+	0.192382i
$408$		0			0
$409$	6179.00	−	10702.3i	0.747022	−	1.29388i	−0.202222	−	0.979340i	$-0.564816\pi$
$409$	6179.00	−	10702.3i	0.747022	−	1.29388i	0.949244	−	0.314540i	$-0.101850\pi$
$410$	2400.00	−	4156.92i	0.289092	−	0.500721i
$411$		0			0
$412$	2948.00	+	5106.09i	0.352518	+	0.610580i
$413$	7476.00			0.890726
$414$		0			0
$415$	−1980.00			−0.234203
$416$	1088.00	+	1884.47i	0.128230	+	0.222100i
$417$		0			0
$418$	264.000	−	457.261i	0.0308915	−	0.0535057i
$419$	−1653.00	+	2863.08i	−0.192731	+	0.333820i	−0.946154	−	0.323716i	$-0.895068\pi$
$419$	−1653.00	+	2863.08i	−0.192731	+	0.333820i	0.753423	+	0.657536i	$0.228401\pi$
$420$		0			0
$421$	7253.00	+	12562.6i	0.839643	+	1.45430i	0.890194	+	0.455582i	$0.150569\pi$
$421$	7253.00	+	12562.6i	0.839643	+	1.45430i	−0.0505509	+	0.998721i	$0.516098\pi$
$422$	8.00000			0.000922829
$423$		0			0
$424$	2064.00			0.236407
$425$	−975.000	−	1688.75i	−0.111281	−	0.192744i
$426$		0			0
$427$	−2534.00	+	4389.02i	−0.287187	+	0.497422i
$428$	−1848.00	+	3200.83i	−0.208707	+	0.361491i
$429$		0			0
$430$	−520.000	−	900.666i	−0.0583177	−	0.101009i
$431$	−6480.00			−0.724201			−0.362100	−	0.932139i	$-0.617940\pi$
$431$	−6480.00			−0.724201			−0.362100	+	0.932139i	$0.617940\pi$
$432$		0			0
$433$	11894.0			1.32007			0.660034	−	0.751236i	$-0.270542\pi$
$433$	11894.0			1.32007			0.660034	+	0.751236i	$0.270542\pi$
$434$	−3416.00	−	5916.69i	−0.377819	−	0.654401i
$435$		0			0
$436$	−1396.00	+	2417.94i	−0.153340	+	0.265593i
$437$	−2640.00	+	4572.61i	−0.288989	+	0.500544i
$438$		0			0
$439$	6344.00	+	10988.1i	0.689710	+	1.19461i	0.971932	+	0.235263i	$0.0755952\pi$
$439$	6344.00	+	10988.1i	0.689710	+	1.19461i	−0.282222	+	0.959349i	$0.591071\pi$
$440$	240.000			0.0260035
$441$		0			0
$442$	−10608.0			−1.14156
$443$	−2484.00	−	4302.41i	−0.266407	−	0.461431i	0.701524	−	0.712646i	$-0.252503\pi$
$443$	−2484.00	−	4302.41i	−0.266407	−	0.461431i	−0.967931	+	0.251215i	$0.919170\pi$
$444$		0			0
$445$	−2430.00	+	4208.88i	−0.258861	+	0.448360i
$446$	−1162.00	+	2012.64i	−0.123368	+	0.213680i
$447$		0			0
$448$	−448.000	−	775.959i	−0.0472456	−	0.0818317i
$449$	−11508.0			−1.20957			−0.604784	−	0.796389i	$-0.706741\pi$
$449$	−11508.0			−1.20957			−0.604784	+	0.796389i	$0.706741\pi$
$450$		0			0
$451$	−2880.00			−0.300696
$452$	444.000	+	769.031i	0.0462035	+	0.0800269i
$453$		0			0
$454$	−2400.00	+	4156.92i	−0.248100	+	0.429722i
$455$	2380.00	−	4122.28i	0.245222	−	0.424737i
$456$		0			0
$457$	−541.000	−	937.039i	−0.0553762	−	0.0959144i	0.837008	−	0.547190i	$-0.184302\pi$
$457$	−541.000	−	937.039i	−0.0553762	−	0.0959144i	−0.892385	+	0.451276i	$0.850969\pi$
$458$	4628.00			0.472166
$459$		0			0
$460$	−2400.00			−0.243262
$461$	5619.00	+	9732.39i	0.567685	+	0.983260i	0.996794	+	0.0800071i	$0.0254943\pi$
$461$	5619.00	+	9732.39i	0.567685	+	0.983260i	−0.429109	+	0.903253i	$0.641172\pi$
$462$		0			0
$463$	1151.00	−	1993.59i	0.115532	−	0.200108i	−0.802460	−	0.596706i	$-0.796476\pi$
$463$	1151.00	−	1993.59i	0.115532	−	0.200108i	0.917992	+	0.396598i	$0.129809\pi$
$464$	−1008.00	+	1745.91i	−0.100852	+	0.174680i
$465$		0			0
$466$	−18.0000	−	31.1769i	−0.00178934	−	0.00309923i
$467$	15876.0			1.57313			0.786567	−	0.617505i	$-0.211856\pi$
$467$	15876.0			1.57313			0.786567	+	0.617505i	$0.211856\pi$
$468$		0			0
$469$	−3752.00			−0.369406
$470$	−3000.00	−	5196.15i	−0.294425	−	0.509959i
$471$		0			0
$472$	2136.00	−	3699.66i	0.208300	−	0.360785i
$473$	−312.000	+	540.400i	−0.0303293	+	0.0525319i
$474$		0			0
$475$	−550.000	−	952.628i	−0.0531279	−	0.0920201i
$476$	4368.00			0.420603
$477$		0			0
$478$	11736.0			1.12300
$479$	−2322.00	−	4021.82i	−0.221492	−	0.383636i	0.733769	−	0.679399i	$-0.237759\pi$
$479$	−2322.00	−	4021.82i	−0.221492	−	0.383636i	−0.955261	+	0.295763i	$0.904426\pi$
$480$		0			0
$481$	10336.0	−	17902.5i	0.979794	−	1.69705i
$482$	−4330.00	+	7499.78i	−0.409183	+	0.708725i
$483$		0			0
$484$	2590.00	+	4486.01i	0.243238	+	0.421301i
$485$	230.000			0.0215335
$486$		0			0
$487$	2426.00			0.225734			0.112867	−	0.993610i	$-0.463997\pi$
$487$	2426.00			0.225734			0.112867	+	0.993610i	$0.463997\pi$
$488$	1448.00	+	2508.01i	0.134319	+	0.232648i
$489$		0			0
$490$	735.000	−	1273.06i	0.0677631	−	0.117369i
$491$	−117.000	+	202.650i	−0.0107538	+	0.0186262i	−0.871352	−	0.490658i	$-0.836756\pi$
$491$	−117.000	+	202.650i	−0.0107538	+	0.0186262i	0.860598	+	0.509284i	$0.170090\pi$
$492$		0			0
$493$	−4914.00	−	8511.30i	−0.448916	−	0.777545i
$494$	−5984.00			−0.545006
$495$		0			0
$496$	−3904.00			−0.353417
$497$	6804.00	+	11784.9i	0.614087	+	1.06363i
$498$		0			0
$499$	−7102.00	+	12301.0i	−0.637133	+	1.10355i	0.348926	+	0.937150i	$0.386546\pi$
$499$	−7102.00	+	12301.0i	−0.637133	+	1.10355i	−0.986059	+	0.166396i	$0.946787\pi$
$500$	250.000	−	433.013i	0.0223607	−	0.0387298i
$501$		0			0
$502$	498.000	+	862.561i	0.0442765	+	0.0766892i
$503$	4920.00			0.436127			0.218064	−	0.975935i	$-0.430026\pi$
$503$	4920.00			0.436127			0.218064	+	0.975935i	$0.430026\pi$
$504$		0			0
$505$	7530.00			0.663526
$506$	720.000	+	1247.08i	0.0632567	+	0.109564i
$507$		0			0
$508$	3812.00	−	6602.58i	0.332933	−	0.576658i
$509$	2229.00	−	3860.74i	0.194104	−	0.336197i	−0.752503	−	0.658589i	$-0.771154\pi$
$509$	2229.00	−	3860.74i	0.194104	−	0.336197i	0.946606	+	0.322392i	$0.104487\pi$
$510$		0			0
$511$	−3290.00	−	5698.45i	−0.284816	−	0.493316i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−1284.00			−0.110184
$515$	−3685.00	−	6382.61i	−0.315302	−	0.546119i
$516$		0			0
$517$	−1800.00	+	3117.69i	−0.153122	+	0.265215i
$518$	−4256.00	+	7371.61i	−0.361000	+	0.625270i
$519$		0			0
$520$	−1360.00	−	2355.59i	−0.114692	−	0.198653i
$521$	4212.00			0.354186			0.177093	−	0.984194i	$-0.443331\pi$
$521$	4212.00			0.354186			0.177093	+	0.984194i	$0.443331\pi$
$522$		0			0
$523$	−11212.0			−0.937412			−0.468706	−	0.883354i	$-0.655280\pi$
$523$	−11212.0			−0.937412			−0.468706	+	0.883354i	$0.655280\pi$
$524$	−5748.00	−	9955.83i	−0.479203	−	0.830005i
$525$		0			0
$526$	−7968.00	+	13801.0i	−0.660497	+	1.14401i
$527$	9516.00	−	16482.2i	0.786572	−	1.36238i
$528$		0			0
$529$	−1116.50	−	1933.83i	−0.0917646	−	0.158941i
$530$	−2580.00			−0.211449
$531$		0			0
$532$	2464.00			0.200804
$533$	16320.0	+	28267.1i	1.32626	+	2.29715i
$534$		0			0
$535$	2310.00	−	4001.04i	0.186673	−	0.323327i
$536$	−1072.00	+	1856.76i	−0.0863868	+	0.149626i
$537$		0			0
$538$	−4218.00	−	7305.79i	−0.338013	−	0.585455i
$539$	−882.000			−0.0704832
$540$		0			0
$541$	14018.0			1.11401			0.557006	−	0.830508i	$-0.311950\pi$
$541$	14018.0			1.11401			0.557006	+	0.830508i	$0.311950\pi$
$542$	848.000	+	1468.78i	0.0672043	+	0.116401i
$543$		0			0
$544$	1248.00	−	2161.60i	0.0983595	−	0.170364i
$545$	1745.00	−	3022.43i	0.137152	−	0.237553i
$546$		0			0
$547$	−9100.00	−	15761.7i	−0.711312	−	1.23203i	−0.964365	−	0.264577i	$-0.914768\pi$
$547$	−9100.00	−	15761.7i	−0.711312	−	1.23203i	0.253052	−	0.967453i	$-0.418566\pi$
$548$	−3192.00			−0.248824
$549$		0			0
$550$	−300.000			−0.0232583
$551$	−2772.00	−	4801.24i	−0.214322	−	0.371216i
$552$		0			0
$553$	−8708.00	+	15082.7i	−0.669624	+	1.15982i
$554$	−1504.00	+	2605.00i	−0.115341	+	0.199776i
$555$		0			0
$556$	1400.00	+	2424.87i	0.106786	+	0.184959i
$557$	−11826.0			−0.899612			−0.449806	−	0.893126i	$-0.648507\pi$
$557$	−11826.0			−0.899612			−0.449806	+	0.893126i	$0.648507\pi$
$558$		0			0
$559$	7072.00			0.535087
$560$	560.000	+	969.948i	0.0422577	+	0.0731925i
$561$		0			0
$562$	−1308.00	+	2265.52i	−0.0981755	+	0.170045i
$563$	1476.00	−	2556.51i	0.110490	−	0.191375i	−0.805478	−	0.592626i	$-0.798091\pi$
$563$	1476.00	−	2556.51i	0.110490	−	0.191375i	0.915968	+	0.401251i	$0.131425\pi$
$564$		0			0
$565$	−555.000	−	961.288i	−0.0413257	−	0.0715782i
$566$	11864.0			0.881062
$567$		0			0
$568$	7776.00			0.574426
$569$	−1542.00	−	2670.82i	−0.113610	−	0.196778i	0.803613	−	0.595152i	$-0.202908\pi$
$569$	−1542.00	−	2670.82i	−0.113610	−	0.196778i	−0.917223	+	0.398374i	$0.869575\pi$
$570$		0			0
$571$	2378.00	−	4118.82i	0.174284	−	0.301869i	−0.765629	−	0.643282i	$-0.777572\pi$
$571$	2378.00	−	4118.82i	0.174284	−	0.301869i	0.939913	+	0.341413i	$0.110906\pi$
$572$	−816.000	+	1413.35i	−0.0596480	+	0.103313i
$573$		0			0
$574$	−6720.00	−	11639.4i	−0.488654	−	0.846374i
$575$	3000.00			0.217580
$576$		0			0
$577$	−11014.0			−0.794660			−0.397330	−	0.917676i	$-0.630063\pi$
$577$	−11014.0			−0.794660			−0.397330	+	0.917676i	$0.630063\pi$
$578$	1171.00	+	2028.23i	0.0842685	+	0.145957i
$579$		0			0
$580$	1260.00	−	2182.38i	0.0902046	−	0.156239i
$581$	−2772.00	+	4801.24i	−0.197938	+	0.342839i
$582$		0			0
$583$	774.000	+	1340.61i	0.0549842	+	0.0952355i
$584$	−3760.00			−0.266421
$585$		0			0
$586$	−10452.0			−0.736806
$587$	426.000	+	737.854i	0.0299538	+	0.0518816i	0.880614	−	0.473835i	$-0.157131\pi$
$587$	426.000	+	737.854i	0.0299538	+	0.0518816i	−0.850660	+	0.525716i	$0.823797\pi$
$588$		0			0
$589$	5368.00	−	9297.65i	0.375526	−	0.650429i
$590$	−2670.00	+	4624.58i	−0.186309	+	0.322696i
$591$		0			0
$592$	2432.00	+	4212.35i	0.168842	+	0.292443i
$593$	15546.0			1.07656			0.538278	−	0.842767i	$-0.319075\pi$
$593$	15546.0			1.07656			0.538278	+	0.842767i	$0.319075\pi$
$594$		0			0
$595$	−5460.00			−0.376199
$596$	−228.000	−	394.908i	−0.0156699	−	0.0271410i
$597$		0			0
$598$	8160.00	−	14133.5i	0.558005	−	0.966494i
$599$	4308.00	−	7461.67i	0.293857	−	0.508975i	−0.680862	−	0.732412i	$-0.738395\pi$
$599$	4308.00	−	7461.67i	0.293857	−	0.508975i	0.974718	+	0.223437i	$0.0717278\pi$
$600$		0			0
$601$	−8755.00	−	15164.1i	−0.594216	−	1.02921i	−0.993657	−	0.112454i	$-0.964129\pi$
$601$	−8755.00	−	15164.1i	−0.594216	−	1.02921i	0.399441	−	0.916759i	$-0.369204\pi$
$602$	−2912.00			−0.197150
$603$		0			0
$604$	4256.00			0.286712
$605$	−3237.50	−	5607.51i	−0.217559	−	0.376823i
$606$		0			0
$607$	6947.00	−	12032.6i	0.464531	−	0.804590i	−0.534650	−	0.845074i	$-0.679556\pi$
$607$	6947.00	−	12032.6i	0.464531	−	0.804590i	0.999180	+	0.0404833i	$0.0128898\pi$
$608$	704.000	−	1219.36i	0.0469588	−	0.0813351i
$609$		0			0
$610$	−1810.00	−	3135.01i	−0.120139	−	0.208087i
$611$	40800.0			2.70146
$612$		0			0
$613$	−6496.00			−0.428011			−0.214006	−	0.976832i	$-0.568651\pi$
$613$	−6496.00			−0.428011			−0.214006	+	0.976832i	$0.568651\pi$
$614$	4448.00	+	7704.16i	0.292356	+	0.506376i
$615$		0			0
$616$	336.000	−	581.969i	0.0219770	−	0.0380653i
$617$	285.000	−	493.634i	0.0185959	−	0.0322090i	−0.856578	−	0.516018i	$-0.827414\pi$
$617$	285.000	−	493.634i	0.0185959	−	0.0322090i	0.875174	+	0.483809i	$0.160747\pi$
$618$		0			0
$619$	1070.00	+	1853.29i	0.0694781	+	0.120340i	0.898672	−	0.438622i	$-0.144533\pi$
$619$	1070.00	+	1853.29i	0.0694781	+	0.120340i	−0.829194	+	0.558962i	$0.811200\pi$
$620$	4880.00			0.316106
$621$		0			0
$622$	18264.0			1.17736
$623$	6804.00	+	11784.9i	0.437555	+	0.757867i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−2170.00	+	3758.55i	−0.138547	+	0.239971i
$627$		0			0
$628$	3896.00	+	6748.07i	0.247559	+	0.428786i
$629$	−23712.0			−1.50312
$630$		0			0
$631$	14660.0			0.924890			0.462445	−	0.886648i	$-0.346972\pi$
$631$	14660.0			0.924890			0.462445	+	0.886648i	$0.346972\pi$
$632$	4976.00	+	8618.68i	0.313188	+	0.542457i
$633$		0			0
$634$	7674.00	−	13291.8i	0.480715	−	0.832623i
$635$	−4765.00	+	8253.22i	−0.297785	+	0.515778i
$636$		0			0
$637$	4998.00	+	8656.79i	0.310876	+	0.538453i
$638$	−1512.00			−0.0938255
$639$		0			0
$640$	640.000			0.0395285
$641$	228.000	+	394.908i	0.0140491	+	0.0243337i	0.872964	−	0.487784i	$-0.162195\pi$
$641$	228.000	+	394.908i	0.0140491	+	0.0243337i	−0.858915	+	0.512118i	$0.828861\pi$
$642$		0			0
$643$	11726.0	−	20310.0i	0.719173	−	1.24564i	−0.242155	−	0.970238i	$-0.577854\pi$
$643$	11726.0	−	20310.0i	0.719173	−	1.24564i	0.961328	−	0.275407i	$-0.0888125\pi$
$644$	−3360.00	+	5819.69i	−0.205594	+	0.356099i
$645$		0			0
$646$	3432.00	+	5944.40i	0.209025	+	0.362042i
$647$	7224.00			0.438956			0.219478	−	0.975617i	$-0.429565\pi$
$647$	7224.00			0.438956			0.219478	+	0.975617i	$0.429565\pi$
$648$		0			0
$649$	3204.00			0.193787
$650$	1700.00	+	2944.49i	0.102584	+	0.177680i
$651$		0			0
$652$	−4120.00	+	7136.05i	−0.247472	+	0.428634i
$653$	−9573.00	+	16580.9i	−0.573691	+	0.993663i	0.422491	+	0.906367i	$0.361156\pi$
$653$	−9573.00	+	16580.9i	−0.573691	+	0.993663i	−0.996182	+	0.0872955i	$0.972178\pi$
$654$		0			0
$655$	7185.00	+	12444.8i	0.428612	+	0.742379i
$656$	−7680.00			−0.457094
$657$		0			0
$658$	−16800.0			−0.995338
$659$	−13905.0	−	24084.2i	−0.821945	−	1.42365i	−0.904232	−	0.427042i	$-0.859556\pi$
$659$	−13905.0	−	24084.2i	−0.821945	−	1.42365i	0.0822865	−	0.996609i	$-0.473778\pi$
$660$		0			0
$661$	15299.0	−	26498.6i	0.900245	−	1.55927i	0.0730698	−	0.997327i	$-0.476720\pi$
$661$	15299.0	−	26498.6i	0.900245	−	1.55927i	0.827175	−	0.561944i	$-0.189946\pi$
$662$	9596.00	−	16620.8i	0.563382	−	0.975807i
$663$		0			0
$664$	1584.00	+	2743.57i	0.0925770	+	0.160348i
$665$	−3080.00			−0.179605
$666$		0			0
$667$	15120.0			0.877734
$668$	2496.00	+	4323.20i	0.144571	+	0.250404i
$669$		0			0
$670$	1340.00	−	2320.95i	0.0772667	−	0.133830i
$671$	−1086.00	+	1881.01i	−0.0624807	+	0.108220i
$672$		0			0
$673$	1889.00	+	3271.84i	0.108196	+	0.187400i	0.915039	−	0.403365i	$-0.132159\pi$
$673$	1889.00	+	3271.84i	0.108196	+	0.187400i	−0.806844	+	0.590765i	$0.798826\pi$
$674$	−24316.0			−1.38964
$675$		0			0
$676$	9708.00			0.552344
$677$	13599.0	+	23554.2i	0.772012	+	1.33716i	0.936459	+	0.350778i	$0.114083\pi$
$677$	13599.0	+	23554.2i	0.772012	+	1.33716i	−0.164447	+	0.986386i	$0.552584\pi$
$678$		0			0
$679$	322.000	−	557.720i	0.0181992	−	0.0315219i
$680$	−1560.00	+	2702.00i	−0.0879754	+	0.152378i
$681$		0			0
$682$	−1464.00	−	2535.72i	−0.0821986	−	0.142372i
$683$	32316.0			1.81045			0.905225	−	0.424933i	$-0.139702\pi$
$683$	32316.0			1.81045			0.905225	+	0.424933i	$0.139702\pi$
$684$		0			0
$685$	3990.00			0.222555
$686$	−6860.00	−	11881.9i	−0.381802	−	0.661300i
$687$		0			0
$688$	−832.000	+	1441.07i	−0.0461042	+	0.0798548i
$689$	8772.00	−	15193.5i	0.485031	−	0.840099i
$690$		0			0
$691$	−14662.0	−	25395.3i	−0.807191	−	1.39810i	−0.914802	−	0.403902i	$-0.867654\pi$
$691$	−14662.0	−	25395.3i	−0.807191	−	1.39810i	0.107611	−	0.994193i	$-0.465680\pi$
$692$	−4584.00			−0.251817
$693$		0			0
$694$	−20640.0			−1.12894
$695$	−1750.00	−	3031.09i	−0.0955126	−	0.165433i
$696$		0			0
$697$	18720.0	−	32424.0i	1.01732	−	1.76205i
$698$	−2158.00	+	3737.77i	−0.117022	+	0.202688i
$699$		0			0
$700$	−700.000	−	1212.44i	−0.0377964	−	0.0654654i
$701$	22782.0			1.22748			0.613741	−	0.789508i	$-0.289664\pi$
$701$	22782.0			1.22748			0.613741	+	0.789508i	$0.289664\pi$
$702$		0			0
$703$	−13376.0			−0.717618
$704$	−192.000	−	332.554i	−0.0102788	−	0.0178034i
$705$		0			0
$706$	−330.000	+	571.577i	−0.0175917	+	0.0304697i
$707$	10542.0	−	18259.3i	0.560782	−	0.971303i
$708$		0			0
$709$	−13027.0	−	22563.4i	−0.690041	−	1.19519i	−0.971824	−	0.235708i	$-0.924259\pi$
$709$	−13027.0	−	22563.4i	−0.690041	−	1.19519i	0.281783	−	0.959478i	$-0.409074\pi$
$710$	−9720.00			−0.513782
$711$		0			0
$712$	7776.00			0.409295
$713$	14640.0	+	25357.2i	0.768965	+	1.33189i
$714$		0			0
$715$	1020.00	−	1766.69i	0.0533508	−	0.0924063i
$716$	2292.00	−	3969.86i	0.119631	−	0.207208i
$717$		0			0
$718$	−8664.00	−	15006.5i	−0.450331	−	0.779996i
$719$	−5976.00			−0.309968			−0.154984	−	0.987917i	$-0.549533\pi$
$719$	−5976.00			−0.309968			−0.154984	+	0.987917i	$0.549533\pi$
$720$		0			0
$721$	−20636.0			−1.06592
$722$	−4923.00	−	8526.89i	−0.253761	−	0.439526i
$723$		0			0
$724$	236.000	−	408.764i	0.0121145	−	0.0209829i
$725$	−1575.00	+	2727.98i	−0.0806814	+	0.139744i
$726$		0			0
$727$	2555.00	+	4425.39i	0.130343	+	0.225762i	0.923809	−	0.382854i	$-0.125059\pi$
$727$	2555.00	+	4425.39i	0.130343	+	0.225762i	−0.793466	+	0.608615i	$0.791725\pi$
$728$	−7616.00			−0.387730
$729$		0			0
$730$	4700.00			0.238294
$731$	−4056.00	−	7025.20i	−0.205221	−	0.355453i
$732$		0			0
$733$	−8668.00	+	15013.4i	−0.436780	+	0.756525i	−0.997439	−	0.0715214i	$-0.977215\pi$
$733$	−8668.00	+	15013.4i	−0.436780	+	0.756525i	0.560659	+	0.828047i	$0.310548\pi$
$734$	3782.00	−	6550.62i	0.190186	−	0.329411i
$735$		0			0
$736$	1920.00	+	3325.54i	0.0961578	+	0.166550i
$737$	−1608.00			−0.0803683
$738$		0			0
$739$	−13660.0			−0.679961			−0.339981	−	0.940432i	$-0.610420\pi$
$739$	−13660.0			−0.679961			−0.339981	+	0.940432i	$0.610420\pi$
$740$	−3040.00	−	5265.43i	−0.151017	−	0.261569i
$741$		0			0
$742$	−3612.00	+	6256.17i	−0.178707	+	0.309530i
$743$	−660.000	+	1143.15i	−0.0325882	+	0.0564445i	−0.881860	−	0.471512i	$-0.843708\pi$
$743$	−660.000	+	1143.15i	−0.0325882	+	0.0564445i	0.849271	+	0.527957i	$0.177042\pi$
$744$		0			0
$745$	285.000	+	493.634i	0.0140156	+	0.0242757i
$746$	−22552.0			−1.10682
$747$		0			0
$748$	1872.00			0.0915068
$749$	−6468.00	−	11202.9i	−0.315535	−	0.546522i
$750$		0			0
$751$	−7930.00	+	13735.2i	−0.385313	+	0.667381i	−0.991813	−	0.127702i	$-0.959240\pi$
$751$	−7930.00	+	13735.2i	−0.385313	+	0.667381i	0.606500	+	0.795084i	$0.292573\pi$
$752$	−4800.00	+	8313.84i	−0.232763	+	0.403158i
$753$		0			0
$754$	8568.00	+	14840.2i	0.413830	+	0.716775i
$755$	−5320.00			−0.256443
$756$		0			0
$757$	22160.0			1.06396			0.531981	−	0.846756i	$-0.321448\pi$
$757$	22160.0			1.06396			0.531981	+	0.846756i	$0.321448\pi$
$758$	980.000	+	1697.41i	0.0469594	+	0.0813360i
$759$		0			0
$760$	−880.000	+	1524.20i	−0.0420013	+	0.0727483i
$761$	−6558.00	+	11358.8i	−0.312388	+	0.541072i	−0.978879	−	0.204441i	$-0.934462\pi$
$761$	−6558.00	+	11358.8i	−0.312388	+	0.541072i	0.666491	+	0.745513i	$0.267796\pi$
$762$		0			0
$763$	−4886.00	−	8462.80i	−0.231828	−	0.401539i
$764$	6768.00			0.320494
$765$		0			0
$766$	8400.00			0.396220
$767$	−18156.0	−	31447.1i	−0.854726	−	1.48043i
$768$		0			0
$769$	−16423.0	+	28445.5i	−0.770128	+	1.33390i	0.167364	+	0.985895i	$0.446474\pi$
$769$	−16423.0	+	28445.5i	−0.770128	+	1.33390i	−0.937492	+	0.348006i	$0.886859\pi$
$770$	−420.000	+	727.461i	−0.0196568	+	0.0340466i
$771$		0			0
$772$	−6700.00	−	11604.7i	−0.312355	−	0.541015i
$773$	−11982.0			−0.557520			−0.278760	−	0.960361i	$-0.589923\pi$
$773$	−11982.0			−0.557520			−0.278760	+	0.960361i	$0.589923\pi$
$774$		0			0
$775$	−6100.00			−0.282734
$776$	−184.000	−	318.697i	−0.00851188	−	0.0147430i
$777$		0			0
$778$	13338.0	−	23102.1i	0.614641	−	1.06459i
$779$	10560.0	−	18290.5i	0.485688	−	0.841237i
$780$		0			0
$781$	2916.00	+	5050.66i	0.133601	+	0.231404i
$782$	−18720.0			−0.856043
$783$		0			0
$784$	−2352.00			−0.107143
$785$	−4870.00	−	8435.09i	−0.221424	−	0.383517i
$786$		0			0
$787$	10538.0	−	18252.4i	0.477305	−	0.826717i	−0.522357	−	0.852727i	$-0.674947\pi$
$787$	10538.0	−	18252.4i	0.477305	−	0.826717i	0.999662	+	0.0260105i	$0.00828032\pi$
$788$	7212.00	−	12491.6i	0.326037	−	0.564712i
$789$		0			0
$790$	−6220.00	−	10773.4i	−0.280124	−	0.485188i
$791$	−3108.00			−0.139706
$792$		0			0
$793$	24616.0			1.10232
$794$	−7192.00	−	12456.9i	−0.321454	−	0.556775i
$795$		0			0
$796$	−5392.00	+	9339.22i	−0.240093	+	0.415854i
$797$	−11043.0	+	19127.0i	−0.490794	+	0.850081i	−0.999944	−	0.0105973i	$-0.996627\pi$
$797$	−11043.0	+	19127.0i	−0.490794	+	0.850081i	0.509149	+	0.860678i	$0.329960\pi$
$798$		0			0
$799$	−23400.0	−	40530.0i	−1.03609	−	1.79455i
$800$	−800.000			−0.0353553
$801$		0			0
$802$	4632.00			0.203942
$803$	−1410.00	−	2442.19i	−0.0619649	−	0.107326i
$804$		0			0
$805$	4200.00	−	7274.61i	0.183889	−	0.318505i
$806$	−16592.0	+	28738.2i	−0.725097	+	1.25591i
$807$		0			0
$808$	−6024.00	−	10433.9i	−0.262282	−	0.454285i
$809$	21384.0			0.929322			0.464661	−	0.885489i	$-0.346176\pi$
$809$	21384.0			0.929322			0.464661	+	0.885489i	$0.346176\pi$
$810$		0			0
$811$	5228.00			0.226362			0.113181	−	0.993574i	$-0.463896\pi$
$811$	5228.00			0.226362			0.113181	+	0.993574i	$0.463896\pi$
$812$	−3528.00	−	6110.68i	−0.152474	−	0.264092i
$813$		0			0
$814$	−1824.00	+	3159.26i	−0.0785395	+	0.136034i
$815$	5150.00	−	8920.06i	0.221346	−	0.383382i
$816$		0			0
$817$	−2288.00	−	3962.93i	−0.0979767	−	0.169701i
$818$	24716.0			1.05645
$819$		0			0
$820$	9600.00			0.408837
$821$	19005.0	+	32917.6i	0.807892	+	1.39931i	0.914321	+	0.404989i	$0.132725\pi$
$821$	19005.0	+	32917.6i	0.807892	+	1.39931i	−0.106430	+	0.994320i	$0.533942\pi$
$822$		0			0
$823$	−19321.0	+	33465.0i	−0.818333	+	1.41739i	0.0885774	+	0.996069i	$0.471768\pi$
$823$	−19321.0	+	33465.0i	−0.818333	+	1.41739i	−0.906910	+	0.421324i	$0.861565\pi$
$824$	−5896.00	+	10212.2i	−0.249268	+	0.431745i
$825$		0			0
$826$	7476.00	+	12948.8i	0.314919	+	0.545456i
$827$	−15432.0			−0.648879			−0.324440	−	0.945906i	$-0.605176\pi$
$827$	−15432.0			−0.648879			−0.324440	+	0.945906i	$0.605176\pi$
$828$		0			0
$829$	−3886.00			−0.162806			−0.0814031	−	0.996681i	$-0.525940\pi$
$829$	−3886.00			−0.162806			−0.0814031	+	0.996681i	$0.525940\pi$
$830$	−1980.00	−	3429.46i	−0.0828034	−	0.143420i
$831$		0			0
$832$	−2176.00	+	3768.94i	−0.0906721	+	0.157049i
$833$	5733.00	−	9929.85i	0.238459	−	0.413024i
$834$		0			0
$835$	−3120.00	−	5404.00i	−0.129308	−	0.223968i
$836$	1056.00			0.0436872
$837$		0			0
$838$	−6612.00			−0.272563
$839$	−13776.0	−	23860.7i	−0.566866	−	0.981840i	−0.996873	−	0.0790150i	$-0.974822\pi$
$839$	−13776.0	−	23860.7i	−0.566866	−	0.981840i	0.430008	−	0.902825i	$-0.358511\pi$
$840$		0			0
$841$	4256.50	−	7372.47i	0.174525	−	0.302287i
$842$	−14506.0	+	25125.1i	−0.593717	+	1.02835i
$843$		0			0
$844$	8.00000	+	13.8564i	0.000326269	+	0.000565115i
$845$	−12135.0			−0.494032
$846$		0			0
$847$	−18130.0			−0.735483
$848$	2064.00	+	3574.95i	0.0835826	+	0.144769i
$849$		0			0
$850$	1950.00	−	3377.50i	0.0786876	−	0.136291i
$851$	18240.0	−	31592.6i	0.734735	−	1.27260i
$852$		0			0
$853$	−7552.00	−	13080.4i	−0.303137	−	0.525048i	0.673708	−	0.738998i	$-0.264701\pi$
$853$	−7552.00	−	13080.4i	−0.303137	−	0.525048i	−0.976845	+	0.213950i	$0.931367\pi$
$854$	−10136.0			−0.406144
$855$		0			0
$856$	−7392.00			−0.295156
$857$	6153.00	+	10657.3i	0.245254	+	0.424792i	0.962203	−	0.272333i	$-0.0877954\pi$
$857$	6153.00	+	10657.3i	0.245254	+	0.424792i	−0.716949	+	0.697125i	$0.754462\pi$
$858$		0			0
$859$	23750.0	−	41136.2i	0.943352	−	1.63393i	0.184335	−	0.982863i	$-0.440987\pi$
$859$	23750.0	−	41136.2i	0.943352	−	1.63393i	0.759017	−	0.651070i	$-0.225680\pi$
$860$	1040.00	−	1801.33i	0.0412369	−	0.0714243i
$861$		0			0
$862$	−6480.00	−	11223.7i	−0.256044	−	0.443481i
$863$	4272.00			0.168506			0.0842529	−	0.996444i	$-0.473150\pi$
$863$	4272.00			0.168506			0.0842529	+	0.996444i	$0.473150\pi$
$864$		0			0
$865$	5730.00			0.225232
$866$	11894.0	+	20601.0i	0.466714	+	0.808373i
$867$		0			0
$868$	6832.00	−	11833.4i	0.267158	−	0.462731i
$869$	−3732.00	+	6464.01i	−0.145684	+	0.252332i
$870$		0			0
$871$	9112.00	+	15782.4i	0.354476	+	0.613970i
$872$	−5584.00			−0.216856
$873$		0			0
$874$	−10560.0			−0.408693
$875$	875.000	+	1515.54i	0.0338062	+	0.0585540i
$876$		0			0
$877$	13898.0	−	24072.0i	0.535122	−	0.926859i	−0.464035	−	0.885817i	$-0.653599\pi$
$877$	13898.0	−	24072.0i	0.535122	−	0.926859i	0.999157	−	0.0410420i	$-0.0130677\pi$
$878$	−12688.0	+	21976.3i	−0.487698	+	0.844719i
$879$		0			0
$880$	240.000	+	415.692i	0.00919363	+	0.0159238i
$881$	−39996.0			−1.52951			−0.764756	−	0.644320i	$-0.777140\pi$
$881$	−39996.0			−1.52951			−0.764756	+	0.644320i	$0.777140\pi$
$882$		0			0
$883$	−3772.00			−0.143758			−0.0718788	−	0.997413i	$-0.522899\pi$
$883$	−3772.00			−0.143758			−0.0718788	+	0.997413i	$0.522899\pi$
$884$	−10608.0	−	18373.6i	−0.403604	−	0.699062i
$885$		0			0
$886$	4968.00	−	8604.83i	0.188378	−	0.326281i
$887$	2892.00	−	5009.09i	0.109474	−	0.189615i	−0.806083	−	0.591802i	$-0.798417\pi$
$887$	2892.00	−	5009.09i	0.109474	−	0.189615i	0.915557	+	0.402187i	$0.131750\pi$
$888$		0			0
$889$	13342.0	+	23109.0i	0.503348	+	0.871824i
$890$	−9720.00			−0.366084
$891$		0			0
$892$	−4648.00			−0.174469
$893$	−13200.0	−	22863.1i	−0.494649	−	0.856756i
$894$		0			0
$895$	−2865.00	+	4962.33i	−0.107002	+	0.185332i
$896$	896.000	−	1551.92i	0.0334077	−	0.0578638i
$897$		0			0
$898$	−11508.0	−	19932.4i	−0.427647	−	0.740706i
$899$	−30744.0			−1.14057
$900$		0			0
$901$	−20124.0			−0.744093
$902$	−2880.00	−	4988.31i	−0.106312	−	0.184138i
$903$		0			0
$904$	−888.000	+	1538.06i	−0.0326708	+	0.0565876i
$905$	−295.000	+	510.955i	−0.0108355	+	0.0187676i
$906$		0			0
$907$	4220.00	+	7309.25i	0.154490	+	0.267585i	0.932873	−	0.360205i	$-0.117293\pi$
$907$	4220.00	+	7309.25i	0.154490	+	0.267585i	−0.778383	+	0.627790i	$0.783960\pi$
$908$	−9600.00			−0.350867
$909$		0			0
$910$	9520.00			0.346797
$911$	15960.0	+	27643.5i	0.580437	+	1.00535i	0.995427	+	0.0955210i	$0.0304517\pi$
$911$	15960.0	+	27643.5i	0.580437	+	1.00535i	−0.414990	+	0.909826i	$0.636215\pi$
$912$		0			0
$913$	−1188.00	+	2057.68i	−0.0430636	+	0.0745883i
$914$	1082.00	−	1874.08i	0.0391569	−	0.0678217i
$915$		0			0
$916$	4628.00	+	8015.93i	0.166936	+	0.289142i
$917$	40236.0			1.44897
$918$		0			0
$919$	34652.0			1.24381			0.621906	−	0.783092i	$-0.286358\pi$
$919$	34652.0			1.24381			0.621906	+	0.783092i	$0.286358\pi$
$920$	−2400.00	−	4156.92i	−0.0860061	−	0.148967i
$921$		0			0
$922$	−11238.0	+	19464.8i	−0.401414	+	0.695270i
$923$	33048.0	−	57240.8i	1.17854	−	2.04128i
$924$		0			0
$925$	3800.00	+	6581.79i	0.135074	+	0.233955i
$926$	4604.00			0.163388
$927$		0			0
$928$	−4032.00			−0.142626
$929$	−702.000	−	1215.90i	−0.0247921	−	0.0429412i	0.853363	−	0.521317i	$-0.174559\pi$
$929$	−702.000	−	1215.90i	−0.0247921	−	0.0429412i	−0.878155	+	0.478376i	$0.841226\pi$
$930$		0			0
$931$	3234.00	−	5601.45i	0.113845	−	0.197186i
$932$	36.0000	−	62.3538i	0.00126526	−	0.00219149i
$933$		0			0
$934$	15876.0	+	27498.0i	0.556187	+	0.963344i
$935$	−2340.00			−0.0818462
$936$		0			0
$937$	−7654.00			−0.266857			−0.133429	−	0.991058i	$-0.542599\pi$
$937$	−7654.00			−0.266857			−0.133429	+	0.991058i	$0.542599\pi$
$938$	−3752.00	−	6498.65i	−0.130605	−	0.226214i
$939$		0			0
$940$	6000.00	−	10392.3i	0.208190	−	0.360595i
$941$	−5649.00	+	9784.36i	−0.195698	+	0.338959i	−0.947129	−	0.320852i	$-0.896031\pi$
$941$	−5649.00	+	9784.36i	−0.195698	+	0.338959i	0.751431	+	0.659812i	$0.229364\pi$
$942$		0			0
$943$	28800.0	+	49883.1i	0.994546	+	1.72260i
$944$	8544.00			0.294580
$945$		0			0
$946$	−1248.00			−0.0428922
$947$	−14484.0	−	25087.0i	−0.497008	−	0.860843i	0.502986	−	0.864295i	$-0.332235\pi$
$947$	−14484.0	−	25087.0i	−0.497008	−	0.860843i	−0.999994	+	0.00345120i	$0.998901\pi$
$948$		0			0
$949$	−15980.0	+	27678.2i	−0.546610	+	0.946756i
$950$	1100.00	−	1905.26i	0.0375671	−	0.0650681i
$951$		0			0
$952$	4368.00	+	7565.60i	0.148706	+	0.257566i
$953$	46410.0			1.57751			0.788755	−	0.614707i	$-0.210726\pi$
$953$	46410.0			1.57751			0.788755	+	0.614707i	$0.210726\pi$
$954$		0			0
$955$	−8460.00			−0.286659
$956$	11736.0	+	20327.3i	0.397039	+	0.687692i
$957$		0			0
$958$	4644.00	−	8043.64i	0.156619	−	0.271272i
$959$	5586.00	−	9675.24i	0.188093	−	0.325787i
$960$		0			0
$961$	−14872.5	−	25759.9i	−0.499228	−	0.864688i
$962$	41344.0			1.38564
$963$		0			0
$964$	−17320.0			−0.578672
$965$	8375.00	+	14505.9i	0.279379	+	0.483899i
$966$		0			0
$967$	20753.0	−	35945.3i	0.690146	−	1.19537i	−0.281643	−	0.959519i	$-0.590879\pi$
$967$	20753.0	−	35945.3i	0.690146	−	1.19537i	0.971790	−	0.235849i	$-0.0757872\pi$
$968$	−5180.00	+	8972.02i	−0.171995	+	0.297905i
$969$		0			0
$970$	230.000	+	398.372i	0.00761325	+	0.0131865i
$971$	−18246.0			−0.603030			−0.301515	−	0.953461i	$-0.597492\pi$
$971$	−18246.0			−0.603030			−0.301515	+	0.953461i	$0.597492\pi$
$972$		0			0
$973$	−9800.00			−0.322892
$974$	2426.00	+	4201.96i	0.0798091	+	0.138233i
$975$		0			0
$976$	−2896.00	+	5016.02i	−0.0949782	+	0.164507i
$977$	−12999.0	+	22514.9i	−0.425665	+	0.737274i	−0.996482	−	0.0838035i	$-0.973293\pi$
$977$	−12999.0	+	22514.9i	−0.425665	+	0.737274i	0.570817	+	0.821077i	$0.306627\pi$
$978$		0			0
$979$	2916.00	+	5050.66i	0.0951949	+	0.164882i
$980$	2940.00			0.0958315
$981$		0			0
$982$	−468.000			−0.0152082
$983$	−7308.00	−	12657.8i	−0.237120	−	0.410704i	0.722767	−	0.691092i	$-0.242870\pi$
$983$	−7308.00	−	12657.8i	−0.237120	−	0.410704i	−0.959887	+	0.280388i	$0.909537\pi$
$984$		0			0
$985$	−9015.00	+	15614.4i	−0.291616	+	0.505094i
$986$	9828.00	−	17022.6i	0.317431	−	0.549807i
$987$		0			0
$988$	−5984.00	−	10364.6i	−0.192689	−	0.333747i
$989$	12480.0			0.401255
$990$		0			0
$991$	−2968.00			−0.0951379			−0.0475689	−	0.998868i	$-0.515147\pi$
$991$	−2968.00			−0.0951379			−0.0475689	+	0.998868i	$0.515147\pi$
$992$	−3904.00	−	6761.93i	−0.124952	−	0.216423i
$993$		0			0
$994$	−13608.0	+	23569.7i	−0.434225	+	0.752100i
$995$	6740.00	−	11674.0i	0.214746	−	0.371951i
$996$		0			0
$997$	4526.00	+	7839.26i	0.143771	+	0.249019i	0.928914	−	0.370296i	$-0.120744\pi$
$997$	4526.00	+	7839.26i	0.143771	+	0.249019i	−0.785143	+	0.619315i	$0.787410\pi$
$998$	−28408.0			−0.901042
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.4.e.u.271.1		2
3.2	odd	2		810.4.e.a.271.1		2
9.2	odd	6		810.4.e.a.541.1		2
9.4	even	3		90.4.a.b.1.1	✓	1
9.5	odd	6		90.4.a.e.1.1	yes	1
9.7	even	3	inner	810.4.e.u.541.1		2
36.23	even	6		720.4.a.t.1.1		1
36.31	odd	6		720.4.a.e.1.1		1
45.4	even	6		450.4.a.m.1.1		1
45.13	odd	12		450.4.c.g.199.2		2
45.14	odd	6		450.4.a.c.1.1		1
45.22	odd	12		450.4.c.g.199.1		2
45.23	even	12		450.4.c.f.199.1		2
45.32	even	12		450.4.c.f.199.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.4.a.b.1.1	✓	1	9.4	even	3
90.4.a.e.1.1	yes	1	9.5	odd	6
450.4.a.c.1.1		1	45.14	odd	6
450.4.a.m.1.1		1	45.4	even	6
450.4.c.f.199.1		2	45.23	even	12
450.4.c.f.199.2		2	45.32	even	12
450.4.c.g.199.1		2	45.22	odd	12
450.4.c.g.199.2		2	45.13	odd	12
720.4.a.e.1.1		1	36.31	odd	6
720.4.a.t.1.1		1	36.23	even	6
810.4.e.a.271.1		2	3.2	odd	2
810.4.e.a.541.1		2	9.2	odd	6
810.4.e.u.271.1		2	1.1	even	1	trivial
810.4.e.u.541.1		2	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(-7.00000 - 12.1244i) q^{7} -8.00000 q^{8} +10.0000 q^{10} +(-3.00000 - 5.19615i) q^{11} +(-34.0000 + 58.8897i) q^{13} +(14.0000 - 24.2487i) q^{14} +(-8.00000 - 13.8564i) q^{16} +78.0000 q^{17} +44.0000 q^{19} +(10.0000 + 17.3205i) q^{20} +(6.00000 - 10.3923i) q^{22} +(-60.0000 + 103.923i) q^{23} +(-12.5000 - 21.6506i) q^{25} -136.000 q^{26} +56.0000 q^{28} +(-63.0000 - 109.119i) q^{29} +(122.000 - 211.310i) q^{31} +(16.0000 - 27.7128i) q^{32} +(78.0000 + 135.100i) q^{34} -70.0000 q^{35} -304.000 q^{37} +(44.0000 + 76.2102i) q^{38} +(-20.0000 + 34.6410i) q^{40} +(240.000 - 415.692i) q^{41} +(-52.0000 - 90.0666i) q^{43} +24.0000 q^{44} -240.000 q^{46} +(-300.000 - 519.615i) q^{47} +(73.5000 - 127.306i) q^{49} +(25.0000 - 43.3013i) q^{50} +(-136.000 - 235.559i) q^{52} -258.000 q^{53} -30.0000 q^{55} +(56.0000 + 96.9948i) q^{56} +(126.000 - 218.238i) q^{58} +(-267.000 + 462.458i) q^{59} +(-181.000 - 313.501i) q^{61} +488.000 q^{62} +64.0000 q^{64} +(170.000 + 294.449i) q^{65} +(134.000 - 232.095i) q^{67} +(-156.000 + 270.200i) q^{68} +(-70.0000 - 121.244i) q^{70} -972.000 q^{71} +470.000 q^{73} +(-304.000 - 526.543i) q^{74} +(-88.0000 + 152.420i) q^{76} +(-42.0000 + 72.7461i) q^{77} +(-622.000 - 1077.34i) q^{79} -80.0000 q^{80} +960.000 q^{82} +(-198.000 - 342.946i) q^{83} +(195.000 - 337.750i) q^{85} +(104.000 - 180.133i) q^{86} +(24.0000 + 41.5692i) q^{88} -972.000 q^{89} +952.000 q^{91} +(-240.000 - 415.692i) q^{92} +(600.000 - 1039.23i) q^{94} +(110.000 - 190.526i) q^{95} +(23.0000 + 39.8372i) q^{97} +294.000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} - 14 q^{7} - 16 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^4 + 5 * q^5 - 14 * q^7 - 16 * q^8	\( 2 q + 2 q^{2} - 4 q^{4} + 5 q^{5} - 14 q^{7} - 16 q^{8} + 20 q^{10} - 6 q^{11} - 68 q^{13} + 28 q^{14} - 16 q^{16} + 156 q^{17} + 88 q^{19} + 20 q^{20} + 12 q^{22} - 120 q^{23} - 25 q^{25} - 272 q^{26} + 112 q^{28} - 126 q^{29} + 244 q^{31} + 32 q^{32} + 156 q^{34} - 140 q^{35} - 608 q^{37} + 88 q^{38} - 40 q^{40} + 480 q^{41} - 104 q^{43} + 48 q^{44} - 480 q^{46} - 600 q^{47} + 147 q^{49} + 50 q^{50} - 272 q^{52} - 516 q^{53} - 60 q^{55} + 112 q^{56} + 252 q^{58} - 534 q^{59} - 362 q^{61} + 976 q^{62} + 128 q^{64} + 340 q^{65} + 268 q^{67} - 312 q^{68} - 140 q^{70} - 1944 q^{71} + 940 q^{73} - 608 q^{74} - 176 q^{76} - 84 q^{77} - 1244 q^{79} - 160 q^{80} + 1920 q^{82} - 396 q^{83} + 390 q^{85} + 208 q^{86} + 48 q^{88} - 1944 q^{89} + 1904 q^{91} - 480 q^{92} + 1200 q^{94} + 220 q^{95} + 46 q^{97} + 588 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 + 5 * q^5 - 14 * q^7 - 16 * q^8 + 20 * q^10 - 6 * q^11 - 68 * q^13 + 28 * q^14 - 16 * q^16 + 156 * q^17 + 88 * q^19 + 20 * q^20 + 12 * q^22 - 120 * q^23 - 25 * q^25 - 272 * q^26 + 112 * q^28 - 126 * q^29 + 244 * q^31 + 32 * q^32 + 156 * q^34 - 140 * q^35 - 608 * q^37 + 88 * q^38 - 40 * q^40 + 480 * q^41 - 104 * q^43 + 48 * q^44 - 480 * q^46 - 600 * q^47 + 147 * q^49 + 50 * q^50 - 272 * q^52 - 516 * q^53 - 60 * q^55 + 112 * q^56 + 252 * q^58 - 534 * q^59 - 362 * q^61 + 976 * q^62 + 128 * q^64 + 340 * q^65 + 268 * q^67 - 312 * q^68 - 140 * q^70 - 1944 * q^71 + 940 * q^73 - 608 * q^74 - 176 * q^76 - 84 * q^77 - 1244 * q^79 - 160 * q^80 + 1920 * q^82 - 396 * q^83 + 390 * q^85 + 208 * q^86 + 48 * q^88 - 1944 * q^89 + 1904 * q^91 - 480 * q^92 + 1200 * q^94 + 220 * q^95 + 46 * q^97 + 588 * q^98

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