LMFDB - Embedded newform 405.4.e.m.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$23.8957735523$
Analytic rank:	$0$
Dimension:	$2$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.4.e.m.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50000 + 4.33013i) q^{2} +(-8.50000 + 14.7224i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-4.50000 - 7.79423i) q^{7} -45.0000 q^{8} +O(q^{10})$	\(q+(2.50000 + 4.33013i) q^{2} +(-8.50000 + 14.7224i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-4.50000 - 7.79423i) q^{7} -45.0000 q^{8} -25.0000 q^{10} +(4.00000 + 6.92820i) q^{11} +(-21.5000 + 37.2391i) q^{13} +(22.5000 - 38.9711i) q^{14} +(-44.5000 - 77.0763i) q^{16} -122.000 q^{17} -59.0000 q^{19} +(-42.5000 - 73.6122i) q^{20} +(-20.0000 + 34.6410i) q^{22} +(106.500 - 184.463i) q^{23} +(-12.5000 - 21.6506i) q^{25} -215.000 q^{26} +153.000 q^{28} +(-112.000 - 193.990i) q^{29} +(18.0000 - 31.1769i) q^{31} +(42.5000 - 73.6122i) q^{32} +(-305.000 - 528.275i) q^{34} +45.0000 q^{35} +206.000 q^{37} +(-147.500 - 255.477i) q^{38} +(112.500 - 194.856i) q^{40} +(-206.500 + 357.668i) q^{41} +(196.000 + 339.482i) q^{43} -136.000 q^{44} +1065.00 q^{46} +(155.500 + 269.334i) q^{47} +(131.000 - 226.899i) q^{49} +(62.5000 - 108.253i) q^{50} +(-365.500 - 633.065i) q^{52} -377.000 q^{53} -40.0000 q^{55} +(202.500 + 350.740i) q^{56} +(560.000 - 969.948i) q^{58} +(-168.500 + 291.851i) q^{59} +(-20.0000 - 34.6410i) q^{61} +180.000 q^{62} -287.000 q^{64} +(-107.500 - 186.195i) q^{65} +(-174.000 + 301.377i) q^{67} +(1037.00 - 1796.14i) q^{68} +(112.500 + 194.856i) q^{70} +62.0000 q^{71} -1214.00 q^{73} +(515.000 + 892.006i) q^{74} +(501.500 - 868.623i) q^{76} +(36.0000 - 62.3538i) q^{77} +(147.000 + 254.611i) q^{79} +445.000 q^{80} -2065.00 q^{82} +(-267.000 - 462.458i) q^{83} +(305.000 - 528.275i) q^{85} +(-980.000 + 1697.41i) q^{86} +(-180.000 - 311.769i) q^{88} -810.000 q^{89} +387.000 q^{91} +(1810.50 + 3135.88i) q^{92} +(-777.500 + 1346.67i) q^{94} +(147.500 - 255.477i) q^{95} +(464.000 + 803.672i) q^{97} +1310.00 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} - 9 q^{7} - 90 q^{8}+O(q^{10}) $ 2 * q + 5 * q^2 - 17 * q^4 - 5 * q^5 - 9 * q^7 - 90 * q^8	$ 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} - 9 q^{7} - 90 q^{8} - 50 q^{10} + 8 q^{11} - 43 q^{13} + 45 q^{14} - 89 q^{16} - 244 q^{17} - 118 q^{19} - 85 q^{20} - 40 q^{22} + 213 q^{23} - 25 q^{25} - 430 q^{26} + 306 q^{28} - 224 q^{29} + 36 q^{31} + 85 q^{32} - 610 q^{34} + 90 q^{35} + 412 q^{37} - 295 q^{38} + 225 q^{40} - 413 q^{41} + 392 q^{43} - 272 q^{44} + 2130 q^{46} + 311 q^{47} + 262 q^{49} + 125 q^{50} - 731 q^{52} - 754 q^{53} - 80 q^{55} + 405 q^{56} + 1120 q^{58} - 337 q^{59} - 40 q^{61} + 360 q^{62} - 574 q^{64} - 215 q^{65} - 348 q^{67} + 2074 q^{68} + 225 q^{70} + 124 q^{71} - 2428 q^{73} + 1030 q^{74} + 1003 q^{76} + 72 q^{77} + 294 q^{79} + 890 q^{80} - 4130 q^{82} - 534 q^{83} + 610 q^{85} - 1960 q^{86} - 360 q^{88} - 1620 q^{89} + 774 q^{91} + 3621 q^{92} - 1555 q^{94} + 295 q^{95} + 928 q^{97} + 2620 q^{98}+O(q^{100}) $ 2 * q + 5 * q^2 - 17 * q^4 - 5 * q^5 - 9 * q^7 - 90 * q^8 - 50 * q^10 + 8 * q^11 - 43 * q^13 + 45 * q^14 - 89 * q^16 - 244 * q^17 - 118 * q^19 - 85 * q^20 - 40 * q^22 + 213 * q^23 - 25 * q^25 - 430 * q^26 + 306 * q^28 - 224 * q^29 + 36 * q^31 + 85 * q^32 - 610 * q^34 + 90 * q^35 + 412 * q^37 - 295 * q^38 + 225 * q^40 - 413 * q^41 + 392 * q^43 - 272 * q^44 + 2130 * q^46 + 311 * q^47 + 262 * q^49 + 125 * q^50 - 731 * q^52 - 754 * q^53 - 80 * q^55 + 405 * q^56 + 1120 * q^58 - 337 * q^59 - 40 * q^61 + 360 * q^62 - 574 * q^64 - 215 * q^65 - 348 * q^67 + 2074 * q^68 + 225 * q^70 + 124 * q^71 - 2428 * q^73 + 1030 * q^74 + 1003 * q^76 + 72 * q^77 + 294 * q^79 + 890 * q^80 - 4130 * q^82 - 534 * q^83 + 610 * q^85 - 1960 * q^86 - 360 * q^88 - 1620 * q^89 + 774 * q^91 + 3621 * q^92 - 1555 * q^94 + 295 * q^95 + 928 * q^97 + 2620 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.50000	+	4.33013i	0.883883	+	1.53093i	0.846988	+	0.531612i	$0.178414\pi$
$2$	2.50000	+	4.33013i	0.883883	+	1.53093i	0.0368954	+	0.999319i	$0.488253\pi$
$3$		0			0
$3$		0			0
$4$	−8.50000	+	14.7224i	−1.06250	+	1.84030i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$		0			0
$7$	−4.50000	−	7.79423i	−0.242977	−	0.420849i	0.718584	−	0.695440i	$-0.244791\pi$
$7$	−4.50000	−	7.79423i	−0.242977	−	0.420849i	−0.961561	+	0.274592i	$0.911457\pi$
$8$	−45.0000			−1.98874
$9$		0			0
$10$	−25.0000			−0.790569
$11$	4.00000	+	6.92820i	0.109640	+	0.189903i	0.915625	−	0.402034i	$-0.131697\pi$
$11$	4.00000	+	6.92820i	0.109640	+	0.189903i	−0.805984	+	0.591937i	$0.798363\pi$
$12$		0			0
$13$	−21.5000	+	37.2391i	−0.458694	+	0.794482i	−0.998892	−	0.0470560i	$-0.985016\pi$
$13$	−21.5000	+	37.2391i	−0.458694	+	0.794482i	0.540198	+	0.841538i	$0.318349\pi$
$14$	22.5000	−	38.9711i	0.429527	−	0.743963i
$15$		0			0
$16$	−44.5000	−	77.0763i	−0.695312	−	1.20432i
$17$	−122.000			−1.74055			−0.870275	−	0.492566i	$-0.836059\pi$
$17$	−122.000			−1.74055			−0.870275	+	0.492566i	$0.836059\pi$
$18$		0			0
$19$	−59.0000			−0.712396			−0.356198	−	0.934410i	$-0.615927\pi$
$19$	−59.0000			−0.712396			−0.356198	+	0.934410i	$0.615927\pi$
$20$	−42.5000	−	73.6122i	−0.475164	−	0.823009i
$21$		0			0
$22$	−20.0000	+	34.6410i	−0.193819	+	0.335704i
$23$	106.500	−	184.463i	0.965512	−	1.67232i	0.257280	−	0.966337i	$-0.417174\pi$
$23$	106.500	−	184.463i	0.965512	−	1.67232i	0.708232	−	0.705980i	$-0.249493\pi$
$24$		0			0
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−215.000			−1.62173
$27$		0			0
$28$	153.000			1.03265
$29$	−112.000	−	193.990i	−0.717168	−	1.24217i	−0.962117	−	0.272636i	$-0.912105\pi$
$29$	−112.000	−	193.990i	−0.717168	−	1.24217i	0.244949	−	0.969536i	$-0.421229\pi$
$30$		0			0
$31$	18.0000	−	31.1769i	0.104287	−	0.180630i	−0.809160	−	0.587589i	$-0.800077\pi$
$31$	18.0000	−	31.1769i	0.104287	−	0.180630i	0.913447	+	0.406958i	$0.133411\pi$
$32$	42.5000	−	73.6122i	0.234782	−	0.406654i
$33$		0			0
$34$	−305.000	−	528.275i	−1.53844	−	2.66466i
$35$	45.0000			0.217325
$36$		0			0
$37$	206.000			0.915302			0.457651	−	0.889132i	$-0.348691\pi$
$37$	206.000			0.915302			0.457651	+	0.889132i	$0.348691\pi$
$38$	−147.500	−	255.477i	−0.629675	−	1.09063i
$39$		0			0
$40$	112.500	−	194.856i	0.444695	−	0.770235i
$41$	−206.500	+	357.668i	−0.786582	+	1.36240i	0.141467	+	0.989943i	$0.454818\pi$
$41$	−206.500	+	357.668i	−0.786582	+	1.36240i	−0.928049	+	0.372458i	$0.878515\pi$
$42$		0			0
$43$	196.000	+	339.482i	0.695110	+	1.20397i	0.970144	+	0.242531i	$0.0779776\pi$
$43$	196.000	+	339.482i	0.695110	+	1.20397i	−0.275034	+	0.961435i	$0.588689\pi$
$44$	−136.000			−0.465972
$45$		0			0
$46$	1065.00			3.41360
$47$	155.500	+	269.334i	0.482596	+	0.835881i	0.999800	−	0.0199813i	$-0.00636066\pi$
$47$	155.500	+	269.334i	0.482596	+	0.835881i	−0.517204	+	0.855862i	$0.673027\pi$
$48$		0			0
$49$	131.000	−	226.899i	0.381924	−	0.661512i
$50$	62.5000	−	108.253i	0.176777	−	0.306186i
$51$		0			0
$52$	−365.500	−	633.065i	−0.974726	−	1.68827i
$53$	−377.000			−0.977074			−0.488537	−	0.872543i	$-0.662469\pi$
$53$	−377.000			−0.977074			−0.488537	+	0.872543i	$0.662469\pi$
$54$		0			0
$55$	−40.0000			−0.0980654
$56$	202.500	+	350.740i	0.483218	+	0.836958i
$57$		0			0
$58$	560.000	−	969.948i	1.26779	−	2.19587i
$59$	−168.500	+	291.851i	−0.371811	+	0.643995i	−0.989844	−	0.142157i	$-0.954596\pi$
$59$	−168.500	+	291.851i	−0.371811	+	0.643995i	0.618033	+	0.786152i	$0.287930\pi$
$60$		0			0
$61$	−20.0000	−	34.6410i	−0.0419793	−	0.0727103i	0.844272	−	0.535914i	$-0.180033\pi$
$61$	−20.0000	−	34.6410i	−0.0419793	−	0.0727103i	−0.886252	+	0.463204i	$0.846700\pi$
$62$	180.000			0.368710
$63$		0			0
$64$	−287.000			−0.560547
$65$	−107.500	−	186.195i	−0.205134	−	0.355303i
$66$		0			0
$67$	−174.000	+	301.377i	−0.317276	+	0.549538i	−0.979919	−	0.199398i	$-0.936101\pi$
$67$	−174.000	+	301.377i	−0.317276	+	0.549538i	0.662643	+	0.748936i	$0.269435\pi$
$68$	1037.00	−	1796.14i	1.84933	−	3.20314i
$69$		0			0
$70$	112.500	+	194.856i	0.192090	+	0.332710i
$71$	62.0000			0.103634			0.0518172	−	0.998657i	$-0.483499\pi$
$71$	62.0000			0.103634			0.0518172	+	0.998657i	$0.483499\pi$
$72$		0			0
$73$	−1214.00			−1.94641			−0.973205	−	0.229939i	$-0.926147\pi$
$73$	−1214.00			−1.94641			−0.973205	+	0.229939i	$0.926147\pi$
$74$	515.000	+	892.006i	0.809021	+	1.40127i
$75$		0			0
$76$	501.500	−	868.623i	0.756921	−	1.31103i
$77$	36.0000	−	62.3538i	0.0532803	−	0.0922841i
$78$		0			0
$79$	147.000	+	254.611i	0.209352	+	0.362608i	0.951511	−	0.307616i	$-0.0995313\pi$
$79$	147.000	+	254.611i	0.209352	+	0.362608i	−0.742159	+	0.670224i	$0.766198\pi$
$80$	445.000			0.621906
$81$		0			0
$82$	−2065.00			−2.78099
$83$	−267.000	−	462.458i	−0.353097	−	0.611582i	0.633693	−	0.773584i	$-0.281538\pi$
$83$	−267.000	−	462.458i	−0.353097	−	0.611582i	−0.986790	+	0.162002i	$0.948205\pi$
$84$		0			0
$85$	305.000	−	528.275i	0.389199	−	0.674112i
$86$	−980.000	+	1697.41i	−1.22879	+	2.12833i
$87$		0			0
$88$	−180.000	−	311.769i	−0.218046	−	0.377667i
$89$	−810.000			−0.964717			−0.482359	−	0.875974i	$-0.660220\pi$
$89$	−810.000			−0.964717			−0.482359	+	0.875974i	$0.660220\pi$
$90$		0			0
$91$	387.000			0.445809
$92$	1810.50	+	3135.88i	2.05171	+	3.55367i
$93$		0			0
$94$	−777.500	+	1346.67i	−0.853117	+	1.47764i
$95$	147.500	−	255.477i	0.159297	−	0.275910i
$96$		0			0
$97$	464.000	+	803.672i	0.485691	+	0.841242i	0.999865	−	0.0164441i	$-0.00523456\pi$
$97$	464.000	+	803.672i	0.485691	+	0.841242i	−0.514173	+	0.857686i	$0.671901\pi$
$98$	1310.00			1.35031
$99$		0			0
$100$	425.000			0.425000
$101$	498.000	+	862.561i	0.490622	+	0.849783i	0.999942	−	0.0107948i	$-0.00343616\pi$
$101$	498.000	+	862.561i	0.490622	+	0.849783i	−0.509319	+	0.860578i	$0.670103\pi$
$102$		0			0
$103$	216.500	−	374.989i	0.207110	−	0.358726i	−0.743693	−	0.668522i	$-0.766927\pi$
$103$	216.500	−	374.989i	0.207110	−	0.358726i	0.950803	+	0.309796i	$0.100261\pi$
$104$	967.500	−	1675.76i	0.912223	−	1.58002i
$105$		0			0
$106$	−942.500	−	1632.46i	−0.863620	−	1.49583i
$107$	−1686.00			−1.52329			−0.761644	−	0.647996i	$-0.775607\pi$
$107$	−1686.00			−1.52329			−0.761644	+	0.647996i	$0.775607\pi$
$108$		0			0
$109$	656.000			0.576453			0.288227	−	0.957562i	$-0.406934\pi$
$109$	656.000			0.576453			0.288227	+	0.957562i	$0.406934\pi$
$110$	−100.000	−	173.205i	−0.0866784	−	0.150131i
$111$		0			0
$112$	−400.500	+	693.686i	−0.337890	+	0.585243i
$113$	−509.000	+	881.614i	−0.423741	+	0.733940i	−0.996302	−	0.0859216i	$-0.972617\pi$
$113$	−509.000	+	881.614i	−0.423741	+	0.733940i	0.572561	+	0.819862i	$0.305950\pi$
$114$		0			0
$115$	532.500	+	922.317i	0.431790	+	0.747883i
$116$	3808.00			3.04796
$117$		0			0
$118$	−1685.00			−1.31455
$119$	549.000	+	950.896i	0.422914	+	0.732508i
$120$		0			0
$121$	633.500	−	1097.25i	0.475958	−	0.824383i
$122$	100.000	−	173.205i	0.0742096	−	0.128535i
$123$		0			0
$124$	306.000	+	530.008i	0.221610	+	0.383839i
$125$	125.000			0.0894427
$126$		0			0
$127$	−1361.00			−0.950939			−0.475469	−	0.879732i	$-0.657722\pi$
$127$	−1361.00			−0.950939			−0.475469	+	0.879732i	$0.657722\pi$
$128$	−1057.50	−	1831.64i	−0.730240	−	1.26481i
$129$		0			0
$130$	537.500	−	930.977i	0.362630	−	0.628093i
$131$	−955.500	+	1654.97i	−0.637270	+	1.10378i	0.348759	+	0.937212i	$0.386603\pi$
$131$	−955.500	+	1654.97i	−0.637270	+	1.10378i	−0.986029	+	0.166572i	$0.946730\pi$
$132$		0			0
$133$	265.500	+	459.859i	0.173096	+	0.299811i
$134$	−1740.00			−1.12174
$135$		0			0
$136$	5490.00			3.46150
$137$	−327.000	−	566.381i	−0.203923	−	0.353206i	0.745866	−	0.666096i	$-0.232036\pi$
$137$	−327.000	−	566.381i	−0.203923	−	0.353206i	−0.949789	+	0.312891i	$0.898703\pi$
$138$		0			0
$139$	366.500	−	634.797i	0.223641	−	0.387358i	−0.732270	−	0.681015i	$-0.761539\pi$
$139$	366.500	−	634.797i	0.223641	−	0.387358i	0.955911	+	0.293657i	$0.0948723\pi$
$140$	−382.500	+	662.509i	−0.230908	+	0.399945i
$141$		0			0
$142$	155.000	+	268.468i	0.0916008	+	0.158657i
$143$	−344.000			−0.201166
$144$		0			0
$145$	1120.00			0.641455
$146$	−3035.00	−	5256.77i	−1.72040	−	2.97982i
$147$		0			0
$148$	−1751.00	+	3032.82i	−0.972509	+	1.68443i
$149$	563.000	−	975.145i	0.309549	−	0.536154i	−0.668715	−	0.743519i	$-0.733155\pi$
$149$	563.000	−	975.145i	0.309549	−	0.536154i	0.978264	+	0.207365i	$0.0664887\pi$
$150$		0			0
$151$	1273.00	+	2204.90i	0.686061	+	1.18829i	0.973102	+	0.230375i	$0.0739952\pi$
$151$	1273.00	+	2204.90i	0.686061	+	1.18829i	−0.287041	+	0.957918i	$0.592671\pi$
$152$	2655.00			1.41677
$153$		0			0
$154$	360.000			0.188374
$155$	90.0000	+	155.885i	0.0466385	+	0.0807803i
$156$		0			0
$157$	−611.500	+	1059.15i	−0.310847	+	0.538403i	−0.978546	−	0.206028i	$-0.933946\pi$
$157$	−611.500	+	1059.15i	−0.310847	+	0.538403i	0.667699	+	0.744432i	$0.267279\pi$
$158$	−735.000	+	1273.06i	−0.370085	+	0.641006i
$159$		0			0
$160$	212.500	+	368.061i	0.104998	+	0.181861i
$161$	−1917.00			−0.938390
$162$		0			0
$163$	3176.00			1.52616			0.763078	−	0.646306i	$-0.223687\pi$
$163$	3176.00			1.52616			0.763078	+	0.646306i	$0.223687\pi$
$164$	−3510.50	−	6080.36i	−1.67149	−	2.89510i
$165$		0			0
$166$	1335.00	−	2312.29i	0.624193	−	1.08113i
$167$	−66.0000	+	114.315i	−0.0305822	+	0.0529700i	−0.880911	−	0.473281i	$-0.843069\pi$
$167$	−66.0000	+	114.315i	−0.0305822	+	0.0529700i	0.850329	+	0.526251i	$0.176403\pi$
$168$		0			0
$169$	174.000	+	301.377i	0.0791989	+	0.137177i
$170$	3050.00			1.37603
$171$		0			0
$172$	−6664.00			−2.95422
$173$	496.500	+	859.963i	0.218198	+	0.377929i	0.954257	−	0.298988i	$-0.0966489\pi$
$173$	496.500	+	859.963i	0.218198	+	0.377929i	−0.736059	+	0.676917i	$0.763316\pi$
$174$		0			0
$175$	−112.500	+	194.856i	−0.0485954	+	0.0841698i
$176$	356.000	−	616.610i	0.152469	−	0.264084i
$177$		0			0
$178$	−2025.00	−	3507.40i	−0.852698	−	1.47692i
$179$	−3101.00			−1.29486			−0.647429	−	0.762126i	$-0.724156\pi$
$179$	−3101.00			−1.29486			−0.647429	+	0.762126i	$0.724156\pi$
$180$		0			0
$181$	2846.00			1.16874			0.584369	−	0.811488i	$-0.301342\pi$
$181$	2846.00			1.16874			0.584369	+	0.811488i	$0.301342\pi$
$182$	967.500	+	1675.76i	0.394043	+	0.682503i
$183$		0			0
$184$	−4792.50	+	8300.85i	−1.92015	+	3.32580i
$185$	−515.000	+	892.006i	−0.204668	+	0.354495i
$186$		0			0
$187$	−488.000	−	845.241i	−0.190835	−	0.330535i
$188$	−5287.00			−2.05103
$189$		0			0
$190$	1475.00			0.563199
$191$	−1540.00	−	2667.36i	−0.583406	−	1.01049i	−0.995072	−	0.0991537i	$-0.968386\pi$
$191$	−1540.00	−	2667.36i	−0.583406	−	1.01049i	0.411666	−	0.911335i	$-0.364947\pi$
$192$		0			0
$193$	−1294.00	+	2241.27i	−0.482612	+	0.835909i	−0.999801	−	0.0199626i	$-0.993645\pi$
$193$	−1294.00	+	2241.27i	−0.482612	+	0.835909i	0.517189	+	0.855872i	$0.326979\pi$
$194$	−2320.00	+	4018.36i	−0.858589	+	1.48712i
$195$		0			0
$196$	2227.00	+	3857.28i	0.811589	+	1.40571i
$197$	−1335.00			−0.482816			−0.241408	−	0.970424i	$-0.577609\pi$
$197$	−1335.00			−0.482816			−0.241408	+	0.970424i	$0.577609\pi$
$198$		0			0
$199$	−5204.00			−1.85378			−0.926889	−	0.375336i	$-0.877527\pi$
$199$	−5204.00			−1.85378			−0.926889	+	0.375336i	$0.877527\pi$
$200$	562.500	+	974.279i	0.198874	+	0.344459i
$201$		0			0
$202$	−2490.00	+	4312.81i	−0.867306	+	1.50222i
$203$	−1008.00	+	1745.91i	−0.348511	+	0.603639i
$204$		0			0
$205$	−1032.50	−	1788.34i	−0.351770	−	0.609284i
$206$	2165.00			0.732246
$207$		0			0
$208$	3827.00			1.27574
$209$	−236.000	−	408.764i	−0.0781075	−	0.135286i
$210$		0			0
$211$	−818.500	+	1417.68i	−0.267051	+	0.462547i	−0.968099	−	0.250568i	$-0.919383\pi$
$211$	−818.500	+	1417.68i	−0.267051	+	0.462547i	0.701048	+	0.713115i	$0.252716\pi$
$212$	3204.50	−	5550.36i	1.03814	−	1.79811i
$213$		0			0
$214$	−4215.00	−	7300.59i	−1.34641	−	2.33205i
$215$	−1960.00			−0.621725
$216$		0			0
$217$	−324.000			−0.101357
$218$	1640.00	+	2840.56i	0.509518	+	0.882510i
$219$		0			0
$220$	340.000	−	588.897i	0.104195	−	0.180470i
$221$	2623.00	−	4543.17i	0.798380	−	1.38284i
$222$		0			0
$223$	2240.00	+	3879.79i	0.672652	+	1.16507i	0.977149	+	0.212555i	$0.0681784\pi$
$223$	2240.00	+	3879.79i	0.672652	+	1.16507i	−0.304497	+	0.952513i	$0.598488\pi$
$224$	−765.000			−0.228186
$225$		0			0
$226$	−5090.00			−1.49815
$227$	1868.00	+	3235.47i	0.546183	+	0.946017i	0.998531	+	0.0541753i	$0.0172530\pi$
$227$	1868.00	+	3235.47i	0.546183	+	0.946017i	−0.452349	+	0.891841i	$0.649414\pi$
$228$		0			0
$229$	690.000	−	1195.12i	0.199111	−	0.344871i	−0.749129	−	0.662424i	$-0.769528\pi$
$229$	690.000	−	1195.12i	0.199111	−	0.344871i	0.948241	+	0.317553i	$0.102861\pi$
$230$	−2662.50	+	4611.59i	−0.763305	+	1.32208i
$231$		0			0
$232$	5040.00	+	8729.54i	1.42626	+	2.47035i
$233$	−2904.00			−0.816512			−0.408256	−	0.912867i	$-0.633863\pi$
$233$	−2904.00			−0.816512			−0.408256	+	0.912867i	$0.633863\pi$
$234$		0			0
$235$	−1555.00			−0.431647
$236$	−2864.50	−	4961.46i	−0.790098	−	1.36849i
$237$		0			0
$238$	−2745.00	+	4754.48i	−0.747613	+	1.29490i
$239$	2983.00	−	5166.71i	0.807340	−	1.39835i	−0.107360	−	0.994220i	$-0.534240\pi$
$239$	2983.00	−	5166.71i	0.807340	−	1.39835i	0.914700	−	0.404133i	$-0.132427\pi$
$240$		0			0
$241$	1609.00	+	2786.87i	0.430061	+	0.744888i	0.996878	−	0.0789557i	$-0.0251586\pi$
$241$	1609.00	+	2786.87i	0.430061	+	0.744888i	−0.566817	+	0.823844i	$0.691825\pi$
$242$	6335.00			1.68277
$243$		0			0
$244$	680.000			0.178412
$245$	655.000	+	1134.49i	0.170802	+	0.295837i
$246$		0			0
$247$	1268.50	−	2197.11i	0.326772	−	0.565986i
$248$	−810.000	+	1402.96i	−0.207399	+	0.359226i
$249$		0			0
$250$	312.500	+	541.266i	0.0790569	+	0.136931i
$251$	6123.00			1.53976			0.769881	−	0.638187i	$-0.220315\pi$
$251$	6123.00			1.53976			0.769881	+	0.638187i	$0.220315\pi$
$252$		0			0
$253$	1704.00			0.423437
$254$	−3402.50	−	5893.30i	−0.840519	−	1.45582i
$255$		0			0
$256$	4139.50	−	7169.82i	1.01062	−	1.75045i
$257$	699.000	−	1210.70i	0.169659	−	0.293858i	−0.768641	−	0.639681i	$-0.779067\pi$
$257$	699.000	−	1210.70i	0.169659	−	0.293858i	0.938300	+	0.345822i	$0.112400\pi$
$258$		0			0
$259$	−927.000	−	1605.61i	−0.222398	−	0.385204i
$260$	3655.00			0.871821
$261$		0			0
$262$	−9555.00			−2.25309
$263$	1605.50	+	2780.81i	0.376423	+	0.651985i	0.990539	−	0.137232i	$-0.0438205\pi$
$263$	1605.50	+	2780.81i	0.376423	+	0.651985i	−0.614116	+	0.789216i	$0.710487\pi$
$264$		0			0
$265$	942.500	−	1632.46i	0.218480	−	0.378419i
$266$	−1327.50	+	2299.30i	−0.305993	+	0.529996i
$267$		0			0
$268$	−2958.00	−	5123.41i	−0.674211	−	1.16777i
$269$	4018.00			0.910713			0.455356	−	0.890309i	$-0.349512\pi$
$269$	4018.00			0.910713			0.455356	+	0.890309i	$0.349512\pi$
$270$		0			0
$271$	2314.00			0.518692			0.259346	−	0.965784i	$-0.416493\pi$
$271$	2314.00			0.518692			0.259346	+	0.965784i	$0.416493\pi$
$272$	5429.00	+	9403.30i	1.21023	+	2.09617i
$273$		0			0
$274$	1635.00	−	2831.90i	0.360489	−	0.624385i
$275$	100.000	−	173.205i	0.0219281	−	0.0379806i
$276$		0			0
$277$	2173.50	+	3764.61i	0.471455	+	0.816584i	0.999467	−	0.0326534i	$-0.0103957\pi$
$277$	2173.50	+	3764.61i	0.471455	+	0.816584i	−0.528012	+	0.849237i	$0.677062\pi$
$278$	3665.00			0.790691
$279$		0			0
$280$	−2025.00			−0.432203
$281$	−775.500	−	1343.21i	−0.164635	−	0.285156i	0.771891	−	0.635755i	$-0.219311\pi$
$281$	−775.500	−	1343.21i	−0.164635	−	0.285156i	−0.936526	+	0.350599i	$0.885978\pi$
$282$		0			0
$283$	−2190.00	+	3793.19i	−0.460007	+	0.796756i	−0.998961	−	0.0455799i	$-0.985486\pi$
$283$	−2190.00	+	3793.19i	−0.460007	+	0.796756i	0.538954	+	0.842335i	$0.318820\pi$
$284$	−527.000	+	912.791i	−0.110112	+	0.190719i
$285$		0			0
$286$	−860.000	−	1489.56i	−0.177807	−	0.307971i
$287$	3717.00			0.764486
$288$		0			0
$289$	9971.00			2.02951
$290$	2800.00	+	4849.74i	0.566971	+	0.982023i
$291$		0			0
$292$	10319.0	−	17873.0i	2.06806	−	3.58199i
$293$	−2524.50	+	4372.56i	−0.503354	+	0.871836i	0.496638	+	0.867958i	$0.334568\pi$
$293$	−2524.50	+	4372.56i	−0.503354	+	0.871836i	−0.999992	+	0.00387777i	$0.998766\pi$
$294$		0			0
$295$	−842.500	−	1459.25i	−0.166279	−	0.288003i
$296$	−9270.00			−1.82030
$297$		0			0
$298$	5630.00			1.09442
$299$	4579.50	+	7931.93i	0.885750	+	1.53416i
$300$		0			0
$301$	1764.00	−	3055.34i	0.337792	−	0.585072i
$302$	−6365.00	+	11024.5i	−1.21280	+	2.10063i
$303$		0			0
$304$	2625.50	+	4547.50i	0.495338	+	0.857951i
$305$	200.000			0.0375474
$306$		0			0
$307$	5428.00			1.00910			0.504548	−	0.863384i	$-0.331659\pi$
$307$	5428.00			1.00910			0.504548	+	0.863384i	$0.331659\pi$
$308$	612.000	+	1060.02i	0.113221	+	0.196104i
$309$		0			0
$310$	−450.000	+	779.423i	−0.0824461	+	0.142801i
$311$	9.00000	−	15.5885i	0.00164097	−	0.00284225i	−0.865204	−	0.501420i	$-0.832811\pi$
$311$	9.00000	−	15.5885i	0.00164097	−	0.00284225i	0.866845	+	0.498578i	$0.166144\pi$
$312$		0			0
$313$	1058.00	+	1832.51i	0.191060	+	0.330925i	0.945602	−	0.325327i	$-0.105474\pi$
$313$	1058.00	+	1832.51i	0.191060	+	0.330925i	−0.754542	+	0.656252i	$0.772141\pi$
$314$	−6115.00			−1.09901
$315$		0			0
$316$	−4998.00			−0.889745
$317$	−2207.50	−	3823.50i	−0.391122	−	0.677443i	0.601476	−	0.798891i	$-0.294579\pi$
$317$	−2207.50	−	3823.50i	−0.391122	−	0.677443i	−0.992598	+	0.121448i	$0.961246\pi$
$318$		0			0
$319$	896.000	−	1551.92i	0.157261	−	0.272385i
$320$	717.500	−	1242.75i	0.125342	−	0.217099i
$321$		0			0
$322$	−4792.50	−	8300.85i	−0.829427	−	1.43661i
$323$	7198.00			1.23996
$324$		0			0
$325$	1075.00			0.183478
$326$	7940.00	+	13752.5i	1.34894	+	2.33644i
$327$		0			0
$328$	9292.50	−	16095.1i	1.56431	−	2.70946i
$329$	1399.50	−	2424.01i	0.234520	−	0.406200i
$330$		0			0
$331$	−1740.00	−	3013.77i	−0.288940	−	0.500458i	0.684617	−	0.728903i	$-0.259969\pi$
$331$	−1740.00	−	3013.77i	−0.288940	−	0.500458i	−0.973557	+	0.228445i	$0.926636\pi$
$332$	9078.00			1.50066
$333$		0			0
$334$	−660.000			−0.108125
$335$	−870.000	−	1506.88i	−0.141890	−	0.245761i
$336$		0			0
$337$	−3161.00	+	5475.01i	−0.510951	+	0.884994i	0.488968	+	0.872302i	$0.337373\pi$
$337$	−3161.00	+	5475.01i	−0.510951	+	0.884994i	−0.999919	+	0.0126922i	$0.995960\pi$
$338$	−870.000	+	1506.88i	−0.140005	+	0.242496i
$339$		0			0
$340$	5185.00	+	8980.68i	0.827047	+	1.43249i
$341$	288.000			0.0457363
$342$		0			0
$343$	−5445.00			−0.857150
$344$	−8820.00	−	15276.7i	−1.38239	−	2.39437i
$345$		0			0
$346$	−2482.50	+	4299.82i	−0.385723	+	0.668091i
$347$	5017.00	−	8689.70i	0.776158	−	1.34434i	−0.157984	−	0.987442i	$-0.550499\pi$
$347$	5017.00	−	8689.70i	0.776158	−	1.34434i	0.934142	−	0.356903i	$-0.116167\pi$
$348$		0			0
$349$	1255.00	+	2173.72i	0.192489	+	0.333400i	0.946074	−	0.323949i	$-0.105011\pi$
$349$	1255.00	+	2173.72i	0.192489	+	0.333400i	−0.753586	+	0.657350i	$0.771677\pi$
$350$	−1125.00			−0.171811
$351$		0			0
$352$	680.000			0.102966
$353$	−1863.00	−	3226.81i	−0.280899	−	0.486532i	0.690707	−	0.723135i	$-0.257299\pi$
$353$	−1863.00	−	3226.81i	−0.280899	−	0.486532i	−0.971607	+	0.236603i	$0.923966\pi$
$354$		0			0
$355$	−155.000	+	268.468i	−0.0231734	+	0.0401375i
$356$	6885.00	−	11925.2i	1.02501	−	1.77537i
$357$		0			0
$358$	−7752.50	−	13427.7i	−1.14450	−	1.98234i
$359$	−10710.0			−1.57452			−0.787259	−	0.616622i	$-0.788501\pi$
$359$	−10710.0			−1.57452			−0.787259	+	0.616622i	$0.788501\pi$
$360$		0			0
$361$	−3378.00			−0.492492
$362$	7115.00	+	12323.5i	1.03303	+	1.78926i
$363$		0			0
$364$	−3289.50	+	5697.58i	−0.473672	+	0.820424i
$365$	3035.00	−	5256.77i	0.435231	−	0.753841i
$366$		0			0
$367$	1080.00	+	1870.61i	0.153612	+	0.266063i	0.932553	−	0.361034i	$-0.117576\pi$
$367$	1080.00	+	1870.61i	0.153612	+	0.266063i	−0.778941	+	0.627097i	$0.784243\pi$
$368$	−18957.0			−2.68533
$369$		0			0
$370$	−5150.00			−0.723610
$371$	1696.50	+	2938.42i	0.237407	+	0.411200i
$372$		0			0
$373$	−1697.00	+	2939.29i	−0.235569	+	0.408018i	−0.959438	−	0.281920i	$-0.909029\pi$
$373$	−1697.00	+	2939.29i	−0.235569	+	0.408018i	0.723869	+	0.689938i	$0.242362\pi$
$374$	2440.00	−	4226.20i	0.337351	−	0.584310i
$375$		0			0
$376$	−6997.50	−	12120.0i	−0.959757	−	1.66235i
$377$	9632.00			1.31584
$378$		0			0
$379$	9031.00			1.22399			0.611994	−	0.790863i	$-0.290368\pi$
$379$	9031.00			1.22399			0.611994	+	0.790863i	$0.290368\pi$
$380$	2507.50	+	4343.12i	0.338505	+	0.586308i
$381$		0			0
$382$	7700.00	−	13336.8i	1.03133	−	1.78631i
$383$	5152.50	−	8924.39i	0.687416	−	1.19064i	−0.285255	−	0.958452i	$-0.592078\pi$
$383$	5152.50	−	8924.39i	0.687416	−	1.19064i	0.972671	−	0.232188i	$-0.0745885\pi$
$384$		0			0
$385$	180.000	+	311.769i	0.0238277	+	0.0412707i
$386$	−12940.0			−1.70629
$387$		0			0
$388$	−15776.0			−2.06419
$389$	1740.00	+	3013.77i	0.226790	+	0.392813i	0.956855	−	0.290565i	$-0.0938434\pi$
$389$	1740.00	+	3013.77i	0.226790	+	0.392813i	−0.730065	+	0.683378i	$0.760510\pi$
$390$		0			0
$391$	−12993.0	+	22504.5i	−1.68052	+	2.91075i
$392$	−5895.00	+	10210.4i	−0.759547	+	1.31557i
$393$		0			0
$394$	−3337.50	−	5780.72i	−0.426753	−	0.739158i
$395$	−1470.00			−0.187250
$396$		0			0
$397$	3706.00			0.468511			0.234255	−	0.972175i	$-0.424735\pi$
$397$	3706.00			0.468511			0.234255	+	0.972175i	$0.424735\pi$
$398$	−13010.0	−	22534.0i	−1.63852	−	2.83801i
$399$		0			0
$400$	−1112.50	+	1926.91i	−0.139063	+	0.240863i
$401$	−1339.50	+	2320.08i	−0.166812	+	0.288926i	−0.937297	−	0.348531i	$-0.886680\pi$
$401$	−1339.50	+	2320.08i	−0.166812	+	0.288926i	0.770486	+	0.637457i	$0.220014\pi$
$402$		0			0
$403$	774.000	+	1340.61i	0.0956717	+	0.165708i
$404$	−16932.0			−2.08514
$405$		0			0
$406$	−10080.0			−1.23217
$407$	824.000	+	1427.21i	0.100354	+	0.173819i
$408$		0			0
$409$	6249.50	−	10824.5i	0.755545	−	1.30864i	−0.189558	−	0.981870i	$-0.560706\pi$
$409$	6249.50	−	10824.5i	0.755545	−	1.30864i	0.945103	−	0.326773i	$-0.105961\pi$
$410$	5162.50	−	8941.71i	0.621848	−	1.07707i
$411$		0			0
$412$	3680.50	+	6374.81i	0.440110	+	0.762292i
$413$	3033.00			0.361366
$414$		0			0
$415$	2670.00			0.315820
$416$	1827.50	+	3165.32i	0.215386	+	0.373059i
$417$		0			0
$418$	1180.00	−	2043.82i	0.138076	−	0.239154i
$419$	464.000	−	803.672i	0.0541000	−	0.0937039i	−0.837707	−	0.546120i	$-0.816104\pi$
$419$	464.000	−	803.672i	0.0541000	−	0.0937039i	0.891807	+	0.452416i	$0.149438\pi$
$420$		0			0
$421$	−3785.00	−	6555.81i	−0.438170	−	0.758933i	0.559378	−	0.828912i	$-0.311040\pi$
$421$	−3785.00	−	6555.81i	−0.438170	−	0.758933i	−0.997548	+	0.0699796i	$0.977707\pi$
$422$	−8185.00			−0.944170
$423$		0			0
$424$	16965.0			1.94314
$425$	1525.00	+	2641.38i	0.174055	+	0.301472i
$426$		0			0
$427$	−180.000	+	311.769i	−0.0204000	+	0.0353339i
$428$	14331.0	−	24822.0i	1.61849	−	2.80331i
$429$		0			0
$430$	−4900.00	−	8487.05i	−0.549533	−	0.951818i
$431$	−2460.00			−0.274928			−0.137464	−	0.990507i	$-0.543895\pi$
$431$	−2460.00			−0.274928			−0.137464	+	0.990507i	$0.543895\pi$
$432$		0			0
$433$	1648.00			0.182905			0.0914525	−	0.995809i	$-0.470849\pi$
$433$	1648.00			0.182905			0.0914525	+	0.995809i	$0.470849\pi$
$434$	−810.000	−	1402.96i	−0.0895881	−	0.155171i
$435$		0			0
$436$	−5576.00	+	9657.92i	−0.612482	+	1.06085i
$437$	−6283.50	+	10883.3i	−0.687827	+	1.19135i
$438$		0			0
$439$	−7913.00	−	13705.7i	−0.860289	−	1.49006i	−0.871650	−	0.490129i	$-0.836950\pi$
$439$	−7913.00	−	13705.7i	−0.860289	−	1.49006i	0.0113610	−	0.999935i	$-0.496384\pi$
$440$	1800.00			0.195026
$441$		0			0
$442$	26230.0			2.82270
$443$	−6387.00	−	11062.6i	−0.685001	−	1.18646i	−0.973436	−	0.228957i	$-0.926468\pi$
$443$	−6387.00	−	11062.6i	−0.685001	−	1.18646i	0.288435	−	0.957499i	$-0.406865\pi$
$444$		0			0
$445$	2025.00	−	3507.40i	0.215717	−	0.373633i
$446$	−11200.0	+	19399.0i	−1.18909	+	2.05957i
$447$		0			0
$448$	1291.50	+	2236.94i	0.136200	+	0.235905i
$449$	8875.00			0.932822			0.466411	−	0.884568i	$-0.345547\pi$
$449$	8875.00			0.932822			0.466411	+	0.884568i	$0.345547\pi$
$450$		0			0
$451$	−3304.00			−0.344965
$452$	−8653.00	−	14987.4i	−0.900449	−	1.55962i
$453$		0			0
$454$	−9340.00	+	16177.4i	−0.965524	+	1.67234i
$455$	−967.500	+	1675.76i	−0.0996859	+	0.172661i
$456$		0			0
$457$	−5762.00	−	9980.08i	−0.589792	−	1.02155i	−0.994259	−	0.106997i	$-0.965876\pi$
$457$	−5762.00	−	9980.08i	−0.589792	−	1.02155i	0.404467	−	0.914553i	$-0.367457\pi$
$458$	6900.00			0.703965
$459$		0			0
$460$	−18105.0			−1.83511
$461$	4272.00	+	7399.32i	0.431598	+	0.747550i	0.997011	−	0.0772577i	$-0.0246164\pi$
$461$	4272.00	+	7399.32i	0.431598	+	0.747550i	−0.565413	+	0.824808i	$0.691283\pi$
$462$		0			0
$463$	−1261.50	+	2184.98i	−0.126624	+	0.219319i	−0.922367	−	0.386316i	$-0.873747\pi$
$463$	−1261.50	+	2184.98i	−0.126624	+	0.219319i	0.795743	+	0.605635i	$0.207081\pi$
$464$	−9968.00	+	17265.1i	−0.997312	+	1.72740i
$465$		0			0
$466$	−7260.00	−	12574.7i	−0.721702	−	1.25002i
$467$	−2902.00			−0.287556			−0.143778	−	0.989610i	$-0.545925\pi$
$467$	−2902.00			−0.287556			−0.143778	+	0.989610i	$0.545925\pi$
$468$		0			0
$469$	3132.00			0.308363
$470$	−3887.50	−	6733.35i	−0.381526	−	0.660822i
$471$		0			0
$472$	7582.50	−	13133.3i	0.739434	−	1.28074i
$473$	−1568.00	+	2715.86i	−0.152424	+	0.264007i
$474$		0			0
$475$	737.500	+	1277.39i	0.0712396	+	0.123391i
$476$	−18666.0			−1.79738
$477$		0			0
$478$	29830.0			2.85438
$479$	−2181.00	−	3777.60i	−0.208043	−	0.360340i	0.743055	−	0.669230i	$-0.233376\pi$
$479$	−2181.00	−	3777.60i	−0.208043	−	0.360340i	−0.951098	+	0.308890i	$0.900043\pi$
$480$		0			0
$481$	−4429.00	+	7671.25i	−0.419844	+	0.727191i
$482$	−8045.00	+	13934.3i	−0.760248	+	1.31679i
$483$		0			0
$484$	10769.5	+	18653.3i	1.01141	+	1.75181i
$485$	−4640.00			−0.434416
$486$		0			0
$487$	5723.00			0.532513			0.266257	−	0.963902i	$-0.414213\pi$
$487$	5723.00			0.532513			0.266257	+	0.963902i	$0.414213\pi$
$488$	900.000	+	1558.85i	0.0834858	+	0.144602i
$489$		0			0
$490$	−3275.00	+	5672.47i	−0.301938	+	0.522971i
$491$	6669.50	−	11551.9i	0.613015	−	1.06177i	−0.377714	−	0.925922i	$-0.623290\pi$
$491$	6669.50	−	11551.9i	0.613015	−	1.06177i	0.990729	−	0.135851i	$-0.0433768\pi$
$492$		0			0
$493$	13664.0	+	23666.7i	1.24827	+	2.16206i
$494$	12685.0			1.15531
$495$		0			0
$496$	−3204.00			−0.290048
$497$	−279.000	−	483.242i	−0.0251808	−	0.0436144i
$498$		0			0
$499$	9818.50	−	17006.1i	0.880835	−	1.52565i	0.0304198	−	0.999537i	$-0.490316\pi$
$499$	9818.50	−	17006.1i	0.880835	−	1.52565i	0.850415	−	0.526113i	$-0.176351\pi$
$500$	−1062.50	+	1840.30i	−0.0950329	+	0.164602i
$501$		0			0
$502$	15307.5	+	26513.4i	1.36097	+	2.35727i
$503$	−5416.00			−0.480094			−0.240047	−	0.970761i	$-0.577163\pi$
$503$	−5416.00			−0.480094			−0.240047	+	0.970761i	$0.577163\pi$
$504$		0			0
$505$	−4980.00			−0.438826
$506$	4260.00	+	7378.54i	0.374269	+	0.648253i
$507$		0			0
$508$	11568.5	−	20037.2i	1.01037	−	1.75002i
$509$	3055.00	−	5291.42i	0.266032	−	0.460782i	−0.701801	−	0.712373i	$-0.747621\pi$
$509$	3055.00	−	5291.42i	0.266032	−	0.460782i	0.967834	+	0.251591i	$0.0809538\pi$
$510$		0			0
$511$	5463.00	+	9462.19i	0.472933	+	0.819144i
$512$	24475.0			2.11260
$513$		0			0
$514$	6990.00			0.599836
$515$	1082.50	+	1874.94i	0.0926226	+	0.160427i
$516$		0			0
$517$	−1244.00	+	2154.67i	−0.105824	+	0.183293i
$518$	4635.00	−	8028.06i	0.393147	−	0.680951i
$519$		0			0
$520$	4837.50	+	8378.80i	0.407958	+	0.706605i
$521$	20375.0			1.71333			0.856665	−	0.515873i	$-0.172532\pi$
$521$	20375.0			1.71333			0.856665	+	0.515873i	$0.172532\pi$
$522$		0			0
$523$	−19010.0			−1.58939			−0.794693	−	0.607011i	$-0.792368\pi$
$523$	−19010.0			−1.58939			−0.794693	+	0.607011i	$0.792368\pi$
$524$	−16243.5	−	28134.6i	−1.35420	−	2.34554i
$525$		0			0
$526$	−8027.50	+	13904.0i	−0.665429	+	1.15256i
$527$	−2196.00	+	3803.58i	−0.181517	+	0.314396i
$528$		0			0
$529$	−16601.0	−	28753.8i	−1.36443	−	2.36326i
$530$	9425.00			0.772445
$531$		0			0
$532$	−9027.00			−0.735658
$533$	−8879.50	−	15379.7i	−0.721602	−	1.24985i
$534$		0			0
$535$	4215.00	−	7300.59i	0.340617	−	0.589967i
$536$	7830.00	−	13562.0i	0.630979	−	1.09289i
$537$		0			0
$538$	10045.0	+	17398.5i	0.804964	+	1.39424i
$539$	2096.00			0.167497
$540$		0			0
$541$	3288.00			0.261298			0.130649	−	0.991429i	$-0.458294\pi$
$541$	3288.00			0.261298			0.130649	+	0.991429i	$0.458294\pi$
$542$	5785.00	+	10019.9i	0.458463	+	0.794081i
$543$		0			0
$544$	−5185.00	+	8980.68i	−0.408649	+	0.707801i
$545$	−1640.00	+	2840.56i	−0.128899	+	0.223259i
$546$		0			0
$547$	−1628.00	−	2819.78i	−0.127255	−	0.220411i	0.795357	−	0.606141i	$-0.207283\pi$
$547$	−1628.00	−	2819.78i	−0.127255	−	0.220411i	−0.922612	+	0.385729i	$0.873950\pi$
$548$	11118.0			0.866674
$549$		0			0
$550$	1000.00			0.0775275
$551$	6608.00	+	11445.4i	0.510908	+	0.884918i
$552$		0			0
$553$	1323.00	−	2291.50i	0.101735	−	0.176211i
$554$	−10867.5	+	18823.1i	−0.833422	+	1.44353i
$555$		0			0
$556$	6230.50	+	10791.5i	0.475238	+	0.823136i
$557$	213.000			0.0162031			0.00810153	−	0.999967i	$-0.497421\pi$
$557$	213.000			0.0162031			0.00810153	+	0.999967i	$0.497421\pi$
$558$		0			0
$559$	−16856.0			−1.27537
$560$	−2002.50	−	3468.43i	−0.151109	−	0.261729i
$561$		0			0
$562$	3877.50	−	6716.03i	0.291036	−	0.504090i
$563$	−8694.00	+	15058.4i	−0.650814	+	1.12724i	0.332111	+	0.943240i	$0.392239\pi$
$563$	−8694.00	+	15058.4i	−0.650814	+	1.12724i	−0.982926	+	0.184003i	$0.941094\pi$
$564$		0			0
$565$	−2545.00	−	4408.07i	−0.189503	−	0.328228i
$566$	−21900.0			−1.62637
$567$		0			0
$568$	−2790.00			−0.206102
$569$	2176.50	+	3769.81i	0.160358	+	0.277748i	0.934997	−	0.354655i	$-0.115402\pi$
$569$	2176.50	+	3769.81i	0.160358	+	0.277748i	−0.774639	+	0.632403i	$0.782069\pi$
$570$		0			0
$571$	962.000	−	1666.23i	0.0705052	−	0.122119i	−0.828618	−	0.559815i	$-0.810872\pi$
$571$	962.000	−	1666.23i	0.0705052	−	0.122119i	0.899123	+	0.437696i	$0.144206\pi$
$572$	2924.00	−	5064.52i	0.213739	−	0.370206i
$573$		0			0
$574$	9292.50	+	16095.1i	0.675717	+	1.17038i
$575$	−5325.00			−0.386205
$576$		0			0
$577$	16832.0			1.21443			0.607214	−	0.794538i	$-0.292287\pi$
$577$	16832.0			1.21443			0.607214	+	0.794538i	$0.292287\pi$
$578$	24927.5	+	43175.7i	1.79385	+	3.10705i
$579$		0			0
$580$	−9520.00	+	16489.1i	−0.681546	+	1.18047i
$581$	−2403.00	+	4162.12i	−0.171589	+	0.297201i
$582$		0			0
$583$	−1508.00	−	2611.93i	−0.107127	−	0.185549i
$584$	54630.0			3.87090
$585$		0			0
$586$	−25245.0			−1.77963
$587$	1053.00	+	1823.85i	0.0740408	+	0.128242i	0.900669	−	0.434506i	$-0.143077\pi$
$587$	1053.00	+	1823.85i	0.0740408	+	0.128242i	−0.826628	+	0.562749i	$0.809744\pi$
$588$		0			0
$589$	−1062.00	+	1839.44i	−0.0742936	+	0.128680i
$590$	4212.50	−	7296.26i	0.293942	−	0.509123i
$591$		0			0
$592$	−9167.00	−	15877.7i	−0.636421	−	1.10231i
$593$	4694.00			0.325058			0.162529	−	0.986704i	$-0.448035\pi$
$593$	4694.00			0.325058			0.162529	+	0.986704i	$0.448035\pi$
$594$		0			0
$595$	−5490.00			−0.378266
$596$	9571.00	+	16577.5i	0.657791	+	1.13933i
$597$		0			0
$598$	−22897.5	+	39659.6i	−1.56580	+	2.71205i
$599$	−6613.00	+	11454.1i	−0.451085	+	0.781302i	−0.998454	−	0.0555895i	$-0.982296\pi$
$599$	−6613.00	+	11454.1i	−0.451085	+	0.781302i	0.547369	+	0.836892i	$0.315630\pi$
$600$		0			0
$601$	6645.50	+	11510.3i	0.451041	+	0.781226i	0.998451	−	0.0556387i	$-0.0177195\pi$
$601$	6645.50	+	11510.3i	0.451041	+	0.781226i	−0.547410	+	0.836865i	$0.684386\pi$
$602$	17640.0			1.19427
$603$		0			0
$604$	−43282.0			−2.91576
$605$	3167.50	+	5486.27i	0.212855	+	0.368675i
$606$		0			0
$607$	−3020.00	+	5230.79i	−0.201941	+	0.349772i	−0.949154	−	0.314813i	$-0.898058\pi$
$607$	−3020.00	+	5230.79i	−0.201941	+	0.349772i	0.747213	+	0.664585i	$0.231392\pi$
$608$	−2507.50	+	4343.12i	−0.167257	+	0.289698i
$609$		0			0
$610$	500.000	+	866.025i	0.0331876	+	0.0574825i
$611$	−13373.0			−0.885456
$612$		0			0
$613$	−23.0000			−0.00151543			−0.000757717	−	1.00000i	$-0.500241\pi$
$613$	−23.0000			−0.00151543			−0.000757717		1.00000i	$0.500241\pi$
$614$	13570.0	+	23503.9i	0.891923	+	1.54486i
$615$		0			0
$616$	−1620.00	+	2805.92i	−0.105960	+	0.183529i
$617$	1509.00	−	2613.66i	0.0984604	−	0.170538i	−0.812587	−	0.582840i	$-0.801942\pi$
$617$	1509.00	−	2613.66i	0.0984604	−	0.170538i	0.911048	+	0.412301i	$0.135275\pi$
$618$		0			0
$619$	4719.50	+	8174.41i	0.306450	+	0.530787i	0.977583	−	0.210550i	$-0.0675253\pi$
$619$	4719.50	+	8174.41i	0.306450	+	0.530787i	−0.671133	+	0.741337i	$0.734192\pi$
$620$	−3060.00			−0.198214
$621$		0			0
$622$	90.0000			0.00580172
$623$	3645.00	+	6313.33i	0.234404	+	0.406000i
$624$		0			0
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−5290.00	+	9162.55i	−0.337749	+	0.584999i
$627$		0			0
$628$	−10395.5	−	18005.5i	−0.660550	−	1.14411i
$629$	−25132.0			−1.59313
$630$		0			0
$631$	−9800.00			−0.618275			−0.309138	−	0.951017i	$-0.600040\pi$
$631$	−9800.00			−0.618275			−0.309138	+	0.951017i	$0.600040\pi$
$632$	−6615.00	−	11457.5i	−0.416346	−	0.721132i
$633$		0			0
$634$	11037.5	−	19117.5i	0.691412	−	1.19756i
$635$	3402.50	−	5893.30i	0.212636	−	0.368297i
$636$		0			0
$637$	5633.00	+	9756.64i	0.350373	+	0.606864i
$638$	8960.00			0.556003
$639$		0			0
$640$	10575.0			0.653146
$641$	−11721.0	−	20301.4i	−0.722233	−	1.25095i	−0.960103	−	0.279648i	$-0.909782\pi$
$641$	−11721.0	−	20301.4i	−0.722233	−	1.25095i	0.237869	−	0.971297i	$-0.423551\pi$
$642$		0			0
$643$	−15654.0	+	27113.5i	−0.960083	+	1.66291i	−0.237802	+	0.971314i	$0.576427\pi$
$643$	−15654.0	+	27113.5i	−0.960083	+	1.66291i	−0.722282	+	0.691599i	$0.756907\pi$
$644$	16294.5	−	28222.9i	0.997039	−	1.72692i
$645$		0			0
$646$	17995.0	+	31168.3i	1.09598	+	1.89829i
$647$	712.000			0.0432637			0.0216318	−	0.999766i	$-0.493114\pi$
$647$	712.000			0.0432637			0.0216318	+	0.999766i	$0.493114\pi$
$648$		0			0
$649$	−2696.00			−0.163062
$650$	2687.50	+	4654.89i	0.162173	+	0.280892i
$651$		0			0
$652$	−26996.0	+	46758.4i	−1.62154	+	2.80859i
$653$	−15739.0	+	27260.7i	−0.943208	+	1.63368i	−0.183907	+	0.982944i	$0.558875\pi$
$653$	−15739.0	+	27260.7i	−0.943208	+	1.63368i	−0.759301	+	0.650740i	$0.774459\pi$
$654$		0			0
$655$	−4777.50	−	8274.87i	−0.284996	−	0.493628i
$656$	36757.0			2.18768
$657$		0			0
$658$	13995.0			0.829152
$659$	8060.50	+	13961.2i	0.476468	+	0.825267i	0.999636	−	0.0269624i	$-0.00858343\pi$
$659$	8060.50	+	13961.2i	0.476468	+	0.825267i	−0.523168	+	0.852229i	$0.675250\pi$
$660$		0			0
$661$	9580.00	−	16593.0i	0.563720	−	0.976391i	−0.433448	−	0.901179i	$-0.642703\pi$
$661$	9580.00	−	16593.0i	0.563720	−	0.976391i	0.997168	−	0.0752127i	$-0.0239636\pi$
$662$	8700.00	−	15068.8i	0.510778	−	0.884694i
$663$		0			0
$664$	12015.0	+	20810.6i	0.702218	+	1.21628i
$665$	−2655.00			−0.154822
$666$		0			0
$667$	−47712.0			−2.76974
$668$	−1122.00	−	1943.36i	−0.0649873	−	0.112561i
$669$		0			0
$670$	4350.00	−	7534.42i	0.250829	−	0.434448i
$671$	160.000	−	277.128i	0.00920526	−	0.0159440i
$672$		0			0
$673$	6711.00	+	11623.8i	0.384383	+	0.665772i	0.991683	−	0.128701i	$-0.0410807\pi$
$673$	6711.00	+	11623.8i	0.384383	+	0.665772i	−0.607300	+	0.794473i	$0.707747\pi$
$674$	−31610.0			−1.80649
$675$		0			0
$676$	−5916.00			−0.336595
$677$	−12952.5	−	22434.4i	−0.735310	−	1.27359i	−0.954587	−	0.297932i	$-0.903703\pi$
$677$	−12952.5	−	22434.4i	−0.735310	−	1.27359i	0.219277	−	0.975663i	$-0.429630\pi$
$678$		0			0
$679$	4176.00	−	7233.04i	0.236024	−	0.408805i
$680$	−13725.0	+	23772.4i	−0.774014	+	1.34063i
$681$		0			0
$682$	720.000	+	1247.08i	0.0404255	+	0.0700191i
$683$	−9246.00			−0.517992			−0.258996	−	0.965878i	$-0.583392\pi$
$683$	−9246.00			−0.517992			−0.258996	+	0.965878i	$0.583392\pi$
$684$		0			0
$685$	3270.00			0.182395
$686$	−13612.5	−	23577.5i	−0.757621	−	1.31224i
$687$		0			0
$688$	17444.0	−	30213.9i	0.966637	−	1.67426i
$689$	8105.50	−	14039.1i	0.448178	−	0.776268i
$690$		0			0
$691$	−12519.5	−	21684.4i	−0.689239	−	1.19380i	−0.972084	−	0.234632i	$-0.924612\pi$
$691$	−12519.5	−	21684.4i	−0.689239	−	1.19380i	0.282845	−	0.959166i	$-0.408722\pi$
$692$	−16881.0			−0.927340
$693$		0			0
$694$	50170.0			2.74413
$695$	1832.50	+	3173.98i	0.100015	+	0.173232i
$696$		0			0
$697$	25193.0	−	43635.6i	1.36909	−	2.37133i
$698$	−6275.00	+	10868.6i	−0.340275	+	0.589374i
$699$		0			0
$700$	−1912.50	−	3312.55i	−0.103265	−	0.178861i
$701$	32930.0			1.77425			0.887125	−	0.461530i	$-0.152699\pi$
$701$	32930.0			1.77425			0.887125	+	0.461530i	$0.152699\pi$
$702$		0			0
$703$	−12154.0			−0.652058
$704$	−1148.00	−	1988.39i	−0.0614586	−	0.106449i
$705$		0			0
$706$	9315.00	−	16134.1i	0.496565	−	0.860075i
$707$	4482.00	−	7763.05i	0.238420	−	0.412956i
$708$		0			0
$709$	−941.000	−	1629.86i	−0.0498448	−	0.0863338i	0.840026	−	0.542545i	$-0.182539\pi$
$709$	−941.000	−	1629.86i	−0.0498448	−	0.0863338i	−0.889871	+	0.456212i	$0.849206\pi$
$710$	−1550.00			−0.0819302
$711$		0			0
$712$	36450.0			1.91857
$713$	−3834.00	−	6640.68i	−0.201381	−	0.348802i
$714$		0			0
$715$	860.000	−	1489.56i	0.0449821	−	0.0779112i
$716$	26358.5	−	45654.3i	1.37579	−	2.38293i
$717$		0			0
$718$	−26775.0	−	46375.7i	−1.39169	−	2.41048i
$719$	−1962.00			−0.101767			−0.0508833	−	0.998705i	$-0.516204\pi$
$719$	−1962.00			−0.101767			−0.0508833	+	0.998705i	$0.516204\pi$
$720$		0			0
$721$	−3897.00			−0.201292
$722$	−8445.00	−	14627.2i	−0.435305	−	0.753971i
$723$		0			0
$724$	−24191.0	+	41900.0i	−1.24178	+	2.15083i
$725$	−2800.00	+	4849.74i	−0.143434	+	0.248434i
$726$		0			0
$727$	6870.50	+	11900.1i	0.350499	+	0.607082i	0.986337	−	0.164741i	$-0.0526787\pi$
$727$	6870.50	+	11900.1i	0.350499	+	0.607082i	−0.635838	+	0.771823i	$0.719345\pi$
$728$	−17415.0			−0.886597
$729$		0			0
$730$	30350.0			1.53877
$731$	−23912.0	−	41416.8i	−1.20987	−	2.09556i
$732$		0			0
$733$	16229.0	−	28109.5i	0.817779	−	1.41643i	−0.0895367	−	0.995984i	$-0.528539\pi$
$733$	16229.0	−	28109.5i	0.817779	−	1.41643i	0.907315	−	0.420451i	$-0.138128\pi$
$734$	−5400.00	+	9353.07i	−0.271550	+	0.470338i
$735$		0			0
$736$	−9052.50	−	15679.4i	−0.453369	−	0.785258i
$737$	−2784.00			−0.139145
$738$		0			0
$739$	19612.0			0.976237			0.488118	−	0.872777i	$-0.337683\pi$
$739$	19612.0			0.976237			0.488118	+	0.872777i	$0.337683\pi$
$740$	−8755.00	−	15164.1i	−0.434919	−	0.753302i
$741$		0			0
$742$	−8482.50	+	14692.1i	−0.419680	+	0.726907i
$743$	−18368.0	+	31814.3i	−0.906940	+	1.57087i	−0.0886488	+	0.996063i	$0.528255\pi$
$743$	−18368.0	+	31814.3i	−0.906940	+	1.57087i	−0.818291	+	0.574804i	$0.805078\pi$
$744$		0			0
$745$	2815.00	+	4875.72i	0.138434	+	0.239775i
$746$	−16970.0			−0.832863
$747$		0			0
$748$	16592.0			0.811048
$749$	7587.00	+	13141.1i	0.370124	+	0.641074i
$750$		0			0
$751$	1873.00	−	3244.13i	0.0910076	−	0.157630i	−0.816928	−	0.576740i	$-0.804325\pi$
$751$	1873.00	−	3244.13i	0.0910076	−	0.157630i	0.907935	+	0.419110i	$0.137658\pi$
$752$	13839.5	−	23970.7i	0.671110	−	1.16240i
$753$		0			0
$754$	24080.0	+	41707.8i	1.16305	+	2.01447i
$755$	−12730.0			−0.613632
$756$		0			0
$757$	5725.00			0.274873			0.137436	−	0.990511i	$-0.456114\pi$
$757$	5725.00			0.274873			0.137436	+	0.990511i	$0.456114\pi$
$758$	22577.5	+	39105.4i	1.08186	+	1.87384i
$759$		0			0
$760$	−6637.50	+	11496.5i	−0.316799	+	0.548712i
$761$	−18661.5	+	32322.7i	−0.888934	+	1.53968i	−0.0477970	+	0.998857i	$0.515220\pi$
$761$	−18661.5	+	32322.7i	−0.888934	+	1.53968i	−0.841137	+	0.540822i	$0.818113\pi$
$762$		0			0
$763$	−2952.00	−	5113.01i	−0.140065	−	0.242600i
$764$	52360.0			2.47947
$765$		0			0
$766$	51525.0			2.43038
$767$	−7245.50	−	12549.6i	−0.341095	−	0.590794i
$768$		0			0
$769$	12293.0	−	21292.1i	0.576459	−	0.998456i	−0.419423	−	0.907791i	$-0.637767\pi$
$769$	12293.0	−	21292.1i	0.576459	−	0.998456i	0.995881	−	0.0906650i	$-0.0288993\pi$
$770$	−900.000	+	1558.85i	−0.0421218	+	0.0729570i
$771$		0			0
$772$	−21998.0	−	38101.7i	−1.02555	−	1.77631i
$773$	−3078.00			−0.143219			−0.0716093	−	0.997433i	$-0.522813\pi$
$773$	−3078.00			−0.143219			−0.0716093	+	0.997433i	$0.522813\pi$
$774$		0			0
$775$	−900.000			−0.0417148
$776$	−20880.0	−	36165.2i	−0.965913	−	1.67301i
$777$		0			0
$778$	−8700.00	+	15068.8i	−0.400913	+	0.694401i
$779$	12183.5	−	21102.4i	0.560358	−	0.970569i
$780$		0			0
$781$	248.000	+	429.549i	0.0113625	+	0.0196805i
$782$	−129930.			−5.94154
$783$		0			0
$784$	−23318.0			−1.06223
$785$	−3057.50	−	5295.75i	−0.139015	−	0.240781i
$786$		0			0
$787$	−20519.0	+	35540.0i	−0.929382	+	1.60974i	−0.145023	+	0.989428i	$0.546326\pi$
$787$	−20519.0	+	35540.0i	−0.929382	+	1.60974i	−0.784358	+	0.620308i	$0.787008\pi$
$788$	11347.5	−	19654.4i	0.512992	−	0.888529i
$789$		0			0
$790$	−3675.00	−	6365.29i	−0.165507	−	0.286667i
$791$	9162.00			0.411837
$792$		0			0
$793$	1720.00			0.0770227
$794$	9265.00	+	16047.5i	0.414109	+	0.717258i
$795$		0			0
$796$	44234.0	−	76615.5i	1.96964	−	3.41151i
$797$	−4681.00	+	8107.73i	−0.208042	+	0.360339i	−0.951098	−	0.308890i	$-0.900042\pi$
$797$	−4681.00	+	8107.73i	−0.208042	+	0.360339i	0.743056	+	0.669230i	$0.233376\pi$
$798$		0			0
$799$	−18971.0	−	32858.7i	−0.839982	−	1.45489i
$800$	−2125.00			−0.0939126
$801$		0			0
$802$	−13395.0			−0.589768
$803$	−4856.00	−	8410.84i	−0.213405	−	0.369629i
$804$		0			0
$805$	4792.50	−	8300.85i	0.209830	−	0.363437i
$806$	−3870.00	+	6703.04i	−0.169125	+	0.292933i
$807$		0			0
$808$	−22410.0	−	38815.3i	−0.975719	−	1.69000i
$809$	−45115.0			−1.96064			−0.980321	−	0.197411i	$-0.936747\pi$
$809$	−45115.0			−1.96064			−0.980321	+	0.197411i	$0.936747\pi$
$810$		0			0
$811$	−13512.0			−0.585044			−0.292522	−	0.956259i	$-0.594494\pi$
$811$	−13512.0			−0.585044			−0.292522	+	0.956259i	$0.594494\pi$
$812$	−17136.0	−	29680.4i	−0.740586	−	1.28273i
$813$		0			0
$814$	−4120.00	+	7136.05i	−0.177403	+	0.307271i
$815$	−7940.00	+	13752.5i	−0.341259	+	0.591078i
$816$		0			0
$817$	−11564.0	−	20029.4i	−0.495194	−	0.857700i
$818$	62495.0			2.67125
$819$		0			0
$820$	35105.0			1.49502
$821$	2265.00	+	3923.10i	0.0962839	+	0.166769i	0.910144	−	0.414293i	$-0.135971\pi$
$821$	2265.00	+	3923.10i	0.0962839	+	0.166769i	−0.813860	+	0.581061i	$0.802638\pi$
$822$		0			0
$823$	−15442.0	+	26746.3i	−0.654039	+	1.13283i	0.328095	+	0.944645i	$0.393594\pi$
$823$	−15442.0	+	26746.3i	−0.654039	+	1.13283i	−0.982134	+	0.188184i	$0.939740\pi$
$824$	−9742.50	+	16874.5i	−0.411888	+	0.713412i
$825$		0			0
$826$	7582.50	+	13133.3i	0.319405	+	0.553227i
$827$	12088.0			0.508272			0.254136	−	0.967168i	$-0.418209\pi$
$827$	12088.0			0.508272			0.254136	+	0.967168i	$0.418209\pi$
$828$		0			0
$829$	−14112.0			−0.591230			−0.295615	−	0.955307i	$-0.595525\pi$
$829$	−14112.0			−0.591230			−0.295615	+	0.955307i	$0.595525\pi$
$830$	6675.00	+	11561.4i	0.279148	+	0.483498i
$831$		0			0
$832$	6170.50	−	10687.6i	0.257120	−	0.445344i
$833$	−15982.0	+	27681.6i	−0.664758	+	1.15139i
$834$		0			0
$835$	−330.000	−	571.577i	−0.0136768	−	0.0236889i
$836$	8024.00			0.331957
$837$		0			0
$838$	4640.00			0.191272
$839$	−1930.00	−	3342.86i	−0.0794172	−	0.137555i	0.823581	−	0.567198i	$-0.191973\pi$
$839$	−1930.00	−	3342.86i	−0.0794172	−	0.137555i	−0.902999	+	0.429643i	$0.858639\pi$
$840$		0			0
$841$	−12893.5	+	22332.2i	−0.528660	+	0.915667i
$842$	18925.0	−	32779.1i	0.774583	−	1.34162i
$843$		0			0
$844$	−13914.5	−	24100.6i	−0.567484	−	0.982912i
$845$	−1740.00			−0.0708377
$846$		0			0
$847$	−11403.0			−0.462588
$848$	16776.5	+	29057.8i	0.679372	+	1.17671i
$849$		0			0
$850$	−7625.00	+	13206.9i	−0.307689	+	0.532932i
$851$	21939.0	−	37999.5i	0.883736	−	1.53068i
$852$		0			0
$853$	−1431.00	−	2478.56i	−0.0574402	−	0.0994894i	0.835875	−	0.548919i	$-0.184961\pi$
$853$	−1431.00	−	2478.56i	−0.0574402	−	0.0994894i	−0.893316	+	0.449430i	$0.851627\pi$
$854$	−1800.00			−0.0721250
$855$		0			0
$856$	75870.0			3.02942
$857$	16267.0	+	28175.3i	0.648390	+	1.12304i	0.983507	+	0.180868i	$0.0578906\pi$
$857$	16267.0	+	28175.3i	0.648390	+	1.12304i	−0.335118	+	0.942176i	$0.608776\pi$
$858$		0			0
$859$	250.000	−	433.013i	0.00993002	−	0.0171993i	−0.861018	−	0.508575i	$-0.830172\pi$
$859$	250.000	−	433.013i	0.00993002	−	0.0171993i	0.870948	+	0.491376i	$0.163506\pi$
$860$	16660.0	−	28856.0i	0.660583	−	1.14416i
$861$		0			0
$862$	−6150.00	−	10652.1i	−0.243004	−	0.420896i
$863$	−36595.0			−1.44346			−0.721731	−	0.692173i	$-0.756653\pi$
$863$	−36595.0			−1.44346			−0.721731	+	0.692173i	$0.756653\pi$
$864$		0			0
$865$	−4965.00			−0.195162
$866$	4120.00	+	7136.05i	0.161667	+	0.280015i
$867$		0			0
$868$	2754.00	−	4770.07i	0.107692	−	0.186528i
$869$	−1176.00	+	2036.89i	−0.0459069	+	0.0795130i
$870$		0			0
$871$	−7482.00	−	12959.2i	−0.291065	−	0.504140i
$872$	−29520.0			−1.14641
$873$		0			0
$874$	−62835.0			−2.43184
$875$	−562.500	−	974.279i	−0.0217325	−	0.0376419i
$876$		0			0
$877$	−20071.5	+	34764.9i	−0.772824	+	1.33857i	0.163186	+	0.986595i	$0.447823\pi$
$877$	−20071.5	+	34764.9i	−0.772824	+	1.33857i	−0.936010	+	0.351975i	$0.885510\pi$
$878$	39565.0	−	68528.6i	1.52079	−	2.63409i
$879$		0			0
$880$	1780.00	+	3083.05i	0.0681861	+	0.118102i
$881$	16414.0			0.627698			0.313849	−	0.949473i	$-0.398381\pi$
$881$	16414.0			0.627698			0.313849	+	0.949473i	$0.398381\pi$
$882$		0			0
$883$	−33478.0			−1.27591			−0.637953	−	0.770076i	$-0.720218\pi$
$883$	−33478.0			−1.27591			−0.637953	+	0.770076i	$0.720218\pi$
$884$	44591.0	+	77233.9i	1.69656	+	2.93853i
$885$		0			0
$886$	31935.0	−	55313.0i	1.21092	−	2.09738i
$887$	1816.50	−	3146.27i	0.0687622	−	0.119100i	−0.829594	−	0.558366i	$-0.811428\pi$
$887$	1816.50	−	3146.27i	0.0687622	−	0.119100i	0.898357	+	0.439267i	$0.144762\pi$
$888$		0			0
$889$	6124.50	+	10607.9i	0.231056	+	0.400201i
$890$	20250.0			0.762676
$891$		0			0
$892$	−76160.0			−2.85877
$893$	−9174.50	−	15890.7i	−0.343799	−	0.595478i
$894$		0			0
$895$	7752.50	−	13427.7i	0.289539	−	0.501496i
$896$	−9517.50	+	16484.8i	−0.354863	+	0.614641i
$897$		0			0
$898$	22187.5	+	38429.9i	0.824506	+	1.42809i
$899$	−8064.00			−0.299165
$900$		0			0
$901$	45994.0			1.70065
$902$	−8260.00	−	14306.7i	−0.304909	−	0.528118i
$903$		0			0
$904$	22905.0	−	39672.6i	0.842709	−	1.45961i
$905$	−7115.00	+	12323.5i	−0.261338	+	0.452650i
$906$		0			0
$907$	−10233.0	−	17724.1i	−0.374621	−	0.648862i	0.615649	−	0.788020i	$-0.288894\pi$
$907$	−10233.0	−	17724.1i	−0.374621	−	0.648862i	−0.990270	+	0.139158i	$0.955560\pi$
$908$	−63512.0			−2.32128
$909$		0			0
$910$	−9675.00			−0.352443
$911$	7537.00	+	13054.5i	0.274108	+	0.474768i	0.969910	−	0.243465i	$-0.0782842\pi$
$911$	7537.00	+	13054.5i	0.274108	+	0.474768i	−0.695802	+	0.718234i	$0.744951\pi$
$912$		0			0
$913$	2136.00	−	3699.66i	0.0774275	−	0.134108i
$914$	28810.0	−	49900.4i	1.04261	−	1.80586i
$915$		0			0
$916$	11730.0	+	20317.0i	0.423111	+	0.732851i
$917$	17199.0			0.619369
$918$		0			0
$919$	−36848.0			−1.32264			−0.661318	−	0.750105i	$-0.730003\pi$
$919$	−36848.0			−1.32264			−0.661318	+	0.750105i	$0.730003\pi$
$920$	−23962.5	−	41504.3i	−0.858718	−	1.48734i
$921$		0			0
$922$	−21360.0	+	36996.6i	−0.762965	+	1.32149i
$923$	−1333.00	+	2308.82i	−0.0475365	+	0.0823357i
$924$		0			0
$925$	−2575.00	−	4460.03i	−0.0915302	−	0.158535i
$926$	−12615.0			−0.447683
$927$		0			0
$928$	−19040.0			−0.673511
$929$	−17587.0	−	30461.6i	−0.621110	−	1.07579i	−0.989279	−	0.146035i	$-0.953349\pi$
$929$	−17587.0	−	30461.6i	−0.621110	−	1.07579i	0.368170	−	0.929759i	$-0.379984\pi$
$930$		0			0
$931$	−7729.00	+	13387.0i	−0.272081	+	0.471259i
$932$	24684.0	−	42753.9i	0.867544	−	1.50263i
$933$		0			0
$934$	−7255.00	−	12566.0i	−0.254166	−	0.440228i
$935$	4880.00			0.170688
$936$		0			0
$937$	−10092.0			−0.351858			−0.175929	−	0.984403i	$-0.556293\pi$
$937$	−10092.0			−0.351858			−0.175929	+	0.984403i	$0.556293\pi$
$938$	7830.00	+	13562.0i	0.272557	+	0.472083i
$939$		0			0
$940$	13217.5	−	22893.4i	0.458625	−	0.794361i
$941$	6455.00	−	11180.4i	0.223621	−	0.387322i	−0.732284	−	0.680999i	$-0.761546\pi$
$941$	6455.00	−	11180.4i	0.223621	−	0.387322i	0.955905	+	0.293677i	$0.0948790\pi$
$942$		0			0
$943$	43984.5	+	76183.4i	1.51891	+	2.63083i
$944$	29993.0			1.03410
$945$		0			0
$946$	−15680.0			−0.538901
$947$	24030.0	+	41621.2i	0.824572	+	1.42820i	0.902246	+	0.431222i	$0.141918\pi$
$947$	24030.0	+	41621.2i	0.824572	+	1.42820i	−0.0776732	+	0.996979i	$0.524749\pi$
$948$		0			0
$949$	26101.0	−	45208.3i	0.892807	−	1.54639i
$950$	−3687.50	+	6386.94i	−0.125935	+	0.218126i
$951$		0			0
$952$	−24705.0	−	42790.3i	−0.841065	−	1.45677i
$953$	6316.00			0.214686			0.107343	−	0.994222i	$-0.465766\pi$
$953$	6316.00			0.214686			0.107343	+	0.994222i	$0.465766\pi$
$954$		0			0
$955$	15400.0			0.521814
$956$	50711.0	+	87834.0i	1.71560	+	2.97150i
$957$		0			0
$958$	10905.0	−	18888.0i	0.367771	−	0.636998i
$959$	−2943.00	+	5097.43i	−0.0990974	+	0.171642i
$960$		0			0
$961$	14247.5	+	24677.4i	0.478248	+	0.828351i
$962$	−44290.0			−1.48437
$963$		0			0
$964$	−54706.0			−1.82776
$965$	−6470.00	−	11206.4i	−0.215831	−	0.373830i
$966$		0			0
$967$	−3880.00	+	6720.36i	−0.129030	+	0.223487i	−0.923301	−	0.384077i	$-0.874520\pi$
$967$	−3880.00	+	6720.36i	−0.129030	+	0.223487i	0.794271	+	0.607564i	$0.207853\pi$
$968$	−28507.5	+	49376.4i	−0.946556	+	1.63948i
$969$		0			0
$970$	−11600.0	−	20091.8i	−0.383973	−	0.665060i
$971$	22437.0			0.741542			0.370771	−	0.928724i	$-0.379093\pi$
$971$	22437.0			0.741542			0.370771	+	0.928724i	$0.379093\pi$
$972$		0			0
$973$	−6597.00			−0.217359
$974$	14307.5	+	24781.3i	0.470680	+	0.815241i
$975$		0			0
$976$	−1780.00	+	3083.05i	−0.0583775	+	0.101113i
$977$	1753.00	−	3036.29i	0.0574037	−	0.0994262i	−0.835896	−	0.548889i	$-0.815051\pi$
$977$	1753.00	−	3036.29i	0.0574037	−	0.0994262i	0.893299	+	0.449462i	$0.148384\pi$
$978$		0			0
$979$	−3240.00	−	5611.84i	−0.105772	−	0.183203i
$980$	−22270.0			−0.725907
$981$		0			0
$982$	66695.0			2.16734
$983$	15324.0	+	26541.9i	0.497212	+	0.861197i	0.999995	−	0.00321597i	$-0.00102368\pi$
$983$	15324.0	+	26541.9i	0.497212	+	0.861197i	−0.502783	+	0.864413i	$0.667690\pi$
$984$		0			0
$985$	3337.50	−	5780.72i	0.107961	−	0.186994i
$986$	−68320.0	+	118334.i	−2.20665	+	3.82202i
$987$		0			0
$988$	21564.5	+	37350.8i	0.694391	+	1.20272i
$989$	83496.0			2.68455
$990$		0			0
$991$	19232.0			0.616473			0.308236	−	0.951310i	$-0.400261\pi$
$991$	19232.0			0.616473			0.308236	+	0.951310i	$0.400261\pi$
$992$	−1530.00	−	2650.04i	−0.0489693	−	0.0848173i
$993$		0			0
$994$	1395.00	−	2416.21i	0.0445138	−	0.0771002i
$995$	13010.0	−	22534.0i	0.414517	−	0.717965i
$996$		0			0
$997$	−19207.5	−	33268.4i	−0.610138	−	1.05679i	−0.991217	−	0.132247i	$-0.957781\pi$
$997$	−19207.5	−	33268.4i	−0.610138	−	1.05679i	0.381079	−	0.924543i	$-0.375553\pi$
$998$	98185.0			3.11422
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.4.e.m.271.1		2
3.2	odd	2		405.4.e.a.271.1		2
9.2	odd	6		405.4.e.a.136.1		2
9.4	even	3		405.4.a.a.1.1	✓	1
9.5	odd	6		405.4.a.b.1.1	yes	1
9.7	even	3	inner	405.4.e.m.136.1		2
45.4	even	6		2025.4.a.f.1.1		1
45.14	odd	6		2025.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.4.a.a.1.1	✓	1	9.4	even	3
405.4.a.b.1.1	yes	1	9.5	odd	6
405.4.e.a.136.1		2	9.2	odd	6
405.4.e.a.271.1		2	3.2	odd	2
405.4.e.m.136.1		2	9.7	even	3	inner
405.4.e.m.271.1		2	1.1	even	1	trivial
2025.4.a.a.1.1		1	45.14	odd	6
2025.4.a.f.1.1		1	45.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.50000 + 4.33013i) q^{2} +(-8.50000 + 14.7224i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-4.50000 - 7.79423i) q^{7} -45.0000 q^{8} +O(q^{10})\)	\(q+(2.50000 + 4.33013i) q^{2} +(-8.50000 + 14.7224i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-4.50000 - 7.79423i) q^{7} -45.0000 q^{8} -25.0000 q^{10} +(4.00000 + 6.92820i) q^{11} +(-21.5000 + 37.2391i) q^{13} +(22.5000 - 38.9711i) q^{14} +(-44.5000 - 77.0763i) q^{16} -122.000 q^{17} -59.0000 q^{19} +(-42.5000 - 73.6122i) q^{20} +(-20.0000 + 34.6410i) q^{22} +(106.500 - 184.463i) q^{23} +(-12.5000 - 21.6506i) q^{25} -215.000 q^{26} +153.000 q^{28} +(-112.000 - 193.990i) q^{29} +(18.0000 - 31.1769i) q^{31} +(42.5000 - 73.6122i) q^{32} +(-305.000 - 528.275i) q^{34} +45.0000 q^{35} +206.000 q^{37} +(-147.500 - 255.477i) q^{38} +(112.500 - 194.856i) q^{40} +(-206.500 + 357.668i) q^{41} +(196.000 + 339.482i) q^{43} -136.000 q^{44} +1065.00 q^{46} +(155.500 + 269.334i) q^{47} +(131.000 - 226.899i) q^{49} +(62.5000 - 108.253i) q^{50} +(-365.500 - 633.065i) q^{52} -377.000 q^{53} -40.0000 q^{55} +(202.500 + 350.740i) q^{56} +(560.000 - 969.948i) q^{58} +(-168.500 + 291.851i) q^{59} +(-20.0000 - 34.6410i) q^{61} +180.000 q^{62} -287.000 q^{64} +(-107.500 - 186.195i) q^{65} +(-174.000 + 301.377i) q^{67} +(1037.00 - 1796.14i) q^{68} +(112.500 + 194.856i) q^{70} +62.0000 q^{71} -1214.00 q^{73} +(515.000 + 892.006i) q^{74} +(501.500 - 868.623i) q^{76} +(36.0000 - 62.3538i) q^{77} +(147.000 + 254.611i) q^{79} +445.000 q^{80} -2065.00 q^{82} +(-267.000 - 462.458i) q^{83} +(305.000 - 528.275i) q^{85} +(-980.000 + 1697.41i) q^{86} +(-180.000 - 311.769i) q^{88} -810.000 q^{89} +387.000 q^{91} +(1810.50 + 3135.88i) q^{92} +(-777.500 + 1346.67i) q^{94} +(147.500 - 255.477i) q^{95} +(464.000 + 803.672i) q^{97} +1310.00 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} - 9 q^{7} - 90 q^{8}+O(q^{10}) \) 2 * q + 5 * q^2 - 17 * q^4 - 5 * q^5 - 9 * q^7 - 90 * q^8	\( 2 q + 5 q^{2} - 17 q^{4} - 5 q^{5} - 9 q^{7} - 90 q^{8} - 50 q^{10} + 8 q^{11} - 43 q^{13} + 45 q^{14} - 89 q^{16} - 244 q^{17} - 118 q^{19} - 85 q^{20} - 40 q^{22} + 213 q^{23} - 25 q^{25} - 430 q^{26} + 306 q^{28} - 224 q^{29} + 36 q^{31} + 85 q^{32} - 610 q^{34} + 90 q^{35} + 412 q^{37} - 295 q^{38} + 225 q^{40} - 413 q^{41} + 392 q^{43} - 272 q^{44} + 2130 q^{46} + 311 q^{47} + 262 q^{49} + 125 q^{50} - 731 q^{52} - 754 q^{53} - 80 q^{55} + 405 q^{56} + 1120 q^{58} - 337 q^{59} - 40 q^{61} + 360 q^{62} - 574 q^{64} - 215 q^{65} - 348 q^{67} + 2074 q^{68} + 225 q^{70} + 124 q^{71} - 2428 q^{73} + 1030 q^{74} + 1003 q^{76} + 72 q^{77} + 294 q^{79} + 890 q^{80} - 4130 q^{82} - 534 q^{83} + 610 q^{85} - 1960 q^{86} - 360 q^{88} - 1620 q^{89} + 774 q^{91} + 3621 q^{92} - 1555 q^{94} + 295 q^{95} + 928 q^{97} + 2620 q^{98}+O(q^{100}) \) 2 * q + 5 * q^2 - 17 * q^4 - 5 * q^5 - 9 * q^7 - 90 * q^8 - 50 * q^10 + 8 * q^11 - 43 * q^13 + 45 * q^14 - 89 * q^16 - 244 * q^17 - 118 * q^19 - 85 * q^20 - 40 * q^22 + 213 * q^23 - 25 * q^25 - 430 * q^26 + 306 * q^28 - 224 * q^29 + 36 * q^31 + 85 * q^32 - 610 * q^34 + 90 * q^35 + 412 * q^37 - 295 * q^38 + 225 * q^40 - 413 * q^41 + 392 * q^43 - 272 * q^44 + 2130 * q^46 + 311 * q^47 + 262 * q^49 + 125 * q^50 - 731 * q^52 - 754 * q^53 - 80 * q^55 + 405 * q^56 + 1120 * q^58 - 337 * q^59 - 40 * q^61 + 360 * q^62 - 574 * q^64 - 215 * q^65 - 348 * q^67 + 2074 * q^68 + 225 * q^70 + 124 * q^71 - 2428 * q^73 + 1030 * q^74 + 1003 * q^76 + 72 * q^77 + 294 * q^79 + 890 * q^80 - 4130 * q^82 - 534 * q^83 + 610 * q^85 - 1960 * q^86 - 360 * q^88 - 1620 * q^89 + 774 * q^91 + 3621 * q^92 - 1555 * q^94 + 295 * q^95 + 928 * q^97 + 2620 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more