LMFDB - Embedded newform 126.4.g.d.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, 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:	$7.43424066072$
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 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.4.g.d.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-4.50000 + 7.79423i) q^{5} +(-14.0000 - 12.1244i) q^{7} -8.00000 q^{8} +(9.00000 + 15.5885i) q^{10} +(-28.5000 - 49.3634i) q^{11} -70.0000 q^{13} +(-35.0000 + 12.1244i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(25.5000 + 44.1673i) q^{17} +(-2.50000 + 4.33013i) q^{19} +36.0000 q^{20} -114.000 q^{22} +(34.5000 - 59.7558i) q^{23} +(22.0000 + 38.1051i) q^{25} +(-70.0000 + 121.244i) q^{26} +(-14.0000 + 72.7461i) q^{28} -114.000 q^{29} +(-11.5000 - 19.9186i) q^{31} +(16.0000 + 27.7128i) q^{32} +102.000 q^{34} +(157.500 - 54.5596i) q^{35} +(126.500 - 219.104i) q^{37} +(5.00000 + 8.66025i) q^{38} +(36.0000 - 62.3538i) q^{40} +42.0000 q^{41} -124.000 q^{43} +(-114.000 + 197.454i) q^{44} +(-69.0000 - 119.512i) q^{46} +(100.500 - 174.071i) q^{47} +(49.0000 + 339.482i) q^{49} +88.0000 q^{50} +(140.000 + 242.487i) q^{52} +(-196.500 - 340.348i) q^{53} +513.000 q^{55} +(112.000 + 96.9948i) q^{56} +(-114.000 + 197.454i) q^{58} +(109.500 + 189.660i) q^{59} +(354.500 - 614.012i) q^{61} -46.0000 q^{62} +64.0000 q^{64} +(315.000 - 545.596i) q^{65} +(-209.500 - 362.865i) q^{67} +(102.000 - 176.669i) q^{68} +(63.0000 - 327.358i) q^{70} +96.0000 q^{71} +(156.500 + 271.066i) q^{73} +(-253.000 - 438.209i) q^{74} +20.0000 q^{76} +(-199.500 + 1036.63i) q^{77} +(-230.500 + 399.238i) q^{79} +(-72.0000 - 124.708i) q^{80} +(42.0000 - 72.7461i) q^{82} +588.000 q^{83} -459.000 q^{85} +(-124.000 + 214.774i) q^{86} +(228.000 + 394.908i) q^{88} +(-508.500 + 880.748i) q^{89} +(980.000 + 848.705i) q^{91} -276.000 q^{92} +(-201.000 - 348.142i) q^{94} +(-22.5000 - 38.9711i) q^{95} -1834.00 q^{97} +(637.000 + 254.611i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{4} - 9 q^{5} - 28 q^{7} - 16 q^{8} + 18 q^{10} - 57 q^{11} - 140 q^{13} - 70 q^{14} - 16 q^{16} + 51 q^{17} - 5 q^{19} + 72 q^{20} - 228 q^{22} + 69 q^{23} + 44 q^{25} - 140 q^{26}+ \cdots + 1274 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^4 - 9 * q^5 - 28 * q^7 - 16 * q^8 + 18 * q^10 - 57 * q^11 - 140 * q^13 - 70 * q^14 - 16 * q^16 + 51 * q^17 - 5 * q^19 + 72 * q^20 - 228 * q^22 + 69 * q^23 + 44 * q^25 - 140 * q^26 - 28 * q^28 - 228 * q^29 - 23 * q^31 + 32 * q^32 + 204 * q^34 + 315 * q^35 + 253 * q^37 + 10 * q^38 + 72 * q^40 + 84 * q^41 - 248 * q^43 - 228 * q^44 - 138 * q^46 + 201 * q^47 + 98 * q^49 + 176 * q^50 + 280 * q^52 - 393 * q^53 + 1026 * q^55 + 224 * q^56 - 228 * q^58 + 219 * q^59 + 709 * q^61 - 92 * q^62 + 128 * q^64 + 630 * q^65 - 419 * q^67 + 204 * q^68 + 126 * q^70 + 192 * q^71 + 313 * q^73 - 506 * q^74 + 40 * q^76 - 399 * q^77 - 461 * q^79 - 144 * q^80 + 84 * q^82 + 1176 * q^83 - 918 * q^85 - 248 * q^86 + 456 * q^88 - 1017 * q^89 + 1960 * q^91 - 552 * q^92 - 402 * q^94 - 45 * q^95 - 3668 * q^97 + 1274 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−4.50000	+	7.79423i	−0.402492	+	0.697137i	−0.994026	−	0.109143i	$-0.965189\pi$
$5$	−4.50000	+	7.79423i	−0.402492	+	0.697137i	0.591534	+	0.806280i	$0.298523\pi$
$6$		0			0
$7$	−14.0000	−	12.1244i	−0.755929	−	0.654654i
$7$	−14.0000	−	12.1244i	−0.755929	−	0.654654i
$8$	−8.00000			−0.353553
$9$		0			0
$10$	9.00000	+	15.5885i	0.284605	+	0.492950i
$11$	−28.5000	−	49.3634i	−0.781188	−	1.35306i	−0.931250	−	0.364381i	$-0.881280\pi$
$11$	−28.5000	−	49.3634i	−0.781188	−	1.35306i	0.150061	−	0.988677i	$-0.452053\pi$
$12$		0			0
$13$	−70.0000			−1.49342			−0.746712	−	0.665148i	$-0.768369\pi$
$13$	−70.0000			−1.49342			−0.746712	+	0.665148i	$0.768369\pi$
$14$	−35.0000	+	12.1244i	−0.668153	+	0.231455i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	25.5000	+	44.1673i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	25.5000	+	44.1673i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.0301863	+	0.0522842i	−0.880724	−	0.473630i	$-0.842943\pi$
$19$	−2.50000	+	4.33013i	−0.0301863	+	0.0522842i	0.850538	+	0.525914i	$0.176277\pi$
$20$	36.0000			0.402492
$21$		0			0
$22$	−114.000			−1.10477
$23$	34.5000	−	59.7558i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	34.5000	−	59.7558i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	22.0000	+	38.1051i	0.176000	+	0.304841i
$26$	−70.0000	+	121.244i	−0.528005	+	0.914531i
$27$		0			0
$28$	−14.0000	+	72.7461i	−0.0944911	+	0.490990i
$29$	−114.000			−0.729975			−0.364987	−	0.931012i	$-0.618927\pi$
$29$	−114.000			−0.729975			−0.364987	+	0.931012i	$0.618927\pi$
$30$		0			0
$31$	−11.5000	−	19.9186i	−0.0666278	−	0.115403i	0.830787	−	0.556590i	$-0.187891\pi$
$31$	−11.5000	−	19.9186i	−0.0666278	−	0.115403i	−0.897415	+	0.441188i	$0.854557\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	102.000			0.514496
$35$	157.500	−	54.5596i	0.760639	−	0.263493i
$36$		0			0
$37$	126.500	−	219.104i	0.562067	−	0.973528i	−0.435249	−	0.900310i	$-0.643340\pi$
$37$	126.500	−	219.104i	0.562067	−	0.973528i	0.997316	−	0.0732182i	$-0.0233270\pi$
$38$	5.00000	+	8.66025i	0.0213449	+	0.0369705i
$39$		0			0
$40$	36.0000	−	62.3538i	0.142302	−	0.246475i
$41$	42.0000			0.159983			0.0799914	−	0.996796i	$-0.474511\pi$
$41$	42.0000			0.159983			0.0799914	+	0.996796i	$0.474511\pi$
$42$		0			0
$43$	−124.000			−0.439763			−0.219882	−	0.975527i	$-0.570567\pi$
$43$	−124.000			−0.439763			−0.219882	+	0.975527i	$0.570567\pi$
$44$	−114.000	+	197.454i	−0.390594	+	0.676529i
$45$		0			0
$46$	−69.0000	−	119.512i	−0.221163	−	0.383065i
$47$	100.500	−	174.071i	0.311903	−	0.540231i	−0.666871	−	0.745173i	$-0.732367\pi$
$47$	100.500	−	174.071i	0.311903	−	0.540231i	0.978774	+	0.204941i	$0.0657003\pi$
$48$		0			0
$49$	49.0000	+	339.482i	0.142857	+	0.989743i
$50$	88.0000			0.248902
$51$		0			0
$52$	140.000	+	242.487i	0.373356	+	0.646671i
$53$	−196.500	−	340.348i	−0.509271	−	0.882083i	−0.999942	−	0.0107383i	$-0.996582\pi$
$53$	−196.500	−	340.348i	−0.509271	−	0.882083i	0.490672	−	0.871345i	$-0.336751\pi$
$54$		0			0
$55$	513.000			1.25769
$56$	112.000	+	96.9948i	0.267261	+	0.231455i
$57$		0			0
$58$	−114.000	+	197.454i	−0.258085	+	0.447016i
$59$	109.500	+	189.660i	0.241622	+	0.418501i	0.961176	−	0.275935i	$-0.0889873\pi$
$59$	109.500	+	189.660i	0.241622	+	0.418501i	−0.719555	+	0.694436i	$0.755654\pi$
$60$		0			0
$61$	354.500	−	614.012i	0.744083	−	1.28879i	−0.206539	−	0.978438i	$-0.566220\pi$
$61$	354.500	−	614.012i	0.744083	−	1.28879i	0.950622	−	0.310351i	$-0.100447\pi$
$62$	−46.0000			−0.0942259
$63$		0			0
$64$	64.0000			0.125000
$65$	315.000	−	545.596i	0.601091	−	1.04112i
$66$		0			0
$67$	−209.500	−	362.865i	−0.382007	−	0.661656i	0.609342	−	0.792908i	$-0.291434\pi$
$67$	−209.500	−	362.865i	−0.382007	−	0.661656i	−0.991349	+	0.131251i	$0.958100\pi$
$68$	102.000	−	176.669i	0.181902	−	0.315063i
$69$		0			0
$70$	63.0000	−	327.358i	0.107571	−	0.558953i
$71$	96.0000			0.160466			0.0802331	−	0.996776i	$-0.474434\pi$
$71$	96.0000			0.160466			0.0802331	+	0.996776i	$0.474434\pi$
$72$		0			0
$73$	156.500	+	271.066i	0.250917	+	0.434601i	0.963779	−	0.266704i	$-0.0859346\pi$
$73$	156.500	+	271.066i	0.250917	+	0.434601i	−0.712862	+	0.701305i	$0.752601\pi$
$74$	−253.000	−	438.209i	−0.397441	−	0.688388i
$75$		0			0
$76$	20.0000			0.0301863
$77$	−199.500	+	1036.63i	−0.295261	+	1.53422i
$78$		0			0
$79$	−230.500	+	399.238i	−0.328269	+	0.568579i	−0.982169	−	0.188003i	$-0.939799\pi$
$79$	−230.500	+	399.238i	−0.328269	+	0.568579i	0.653899	+	0.756582i	$0.273132\pi$
$80$	−72.0000	−	124.708i	−0.100623	−	0.174284i
$81$		0			0
$82$	42.0000	−	72.7461i	0.0565625	−	0.0979691i
$83$	588.000			0.777607			0.388804	−	0.921321i	$-0.372888\pi$
$83$	588.000			0.777607			0.388804	+	0.921321i	$0.372888\pi$
$84$		0			0
$85$	−459.000			−0.585712
$86$	−124.000	+	214.774i	−0.155480	+	0.269299i
$87$		0			0
$88$	228.000	+	394.908i	0.276192	+	0.478378i
$89$	−508.500	+	880.748i	−0.605628	+	1.04898i	0.386324	+	0.922363i	$0.373745\pi$
$89$	−508.500	+	880.748i	−0.605628	+	1.04898i	−0.991952	+	0.126615i	$0.959589\pi$
$90$		0			0
$91$	980.000	+	848.705i	1.12892	+	0.977675i
$92$	−276.000			−0.312772
$93$		0			0
$94$	−201.000	−	348.142i	−0.220549	−	0.382001i
$95$	−22.5000	−	38.9711i	−0.0242995	−	0.0420879i
$96$		0			0
$97$	−1834.00			−1.91974			−0.959868	−	0.280451i	$-0.909516\pi$
$97$	−1834.00			−1.91974			−0.959868	+	0.280451i	$0.909516\pi$
$98$	637.000	+	254.611i	0.656599	+	0.262445i
$99$		0			0
$100$	88.0000	−	152.420i	0.0880000	−	0.152420i
$101$	−142.500	−	246.817i	−0.140389	−	0.243161i	0.787254	−	0.616629i	$-0.211502\pi$
$101$	−142.500	−	246.817i	−0.140389	−	0.243161i	−0.927643	+	0.373468i	$0.878169\pi$
$102$		0			0
$103$	249.500	−	432.147i	0.238679	−	0.413405i	−0.721656	−	0.692252i	$-0.756619\pi$
$103$	249.500	−	432.147i	0.238679	−	0.413405i	0.960336	+	0.278847i	$0.0899522\pi$
$104$	560.000			0.528005
$105$		0			0
$106$	−786.000			−0.720218
$107$	−553.500	+	958.690i	−0.500083	+	0.866169i	0.499917	+	0.866073i	$0.333364\pi$
$107$	−553.500	+	958.690i	−0.500083	+	0.866169i	−1.00000		9.56665e-5i	$0.999970\pi$
$108$		0			0
$109$	−461.500	−	799.341i	−0.405538	−	0.702413i	0.588846	−	0.808246i	$-0.299583\pi$
$109$	−461.500	−	799.341i	−0.405538	−	0.702413i	−0.994384	+	0.105832i	$0.966249\pi$
$110$	513.000	−	888.542i	0.444660	−	0.770174i
$111$		0			0
$112$	280.000	−	96.9948i	0.236228	−	0.0818317i
$113$	−1542.00			−1.28371			−0.641855	−	0.766826i	$-0.721835\pi$
$113$	−1542.00			−1.28371			−0.641855	+	0.766826i	$0.721835\pi$
$114$		0			0
$115$	310.500	+	537.802i	0.251776	+	0.436089i
$116$	228.000	+	394.908i	0.182494	+	0.316088i
$117$		0			0
$118$	438.000			0.341705
$119$	178.500	−	927.513i	0.137505	−	0.714496i
$120$		0			0
$121$	−959.000	+	1661.04i	−0.720511	+	1.24796i
$122$	−709.000	−	1228.02i	−0.526146	−	0.911312i
$123$		0			0
$124$	−46.0000	+	79.6743i	−0.0333139	+	0.0577013i
$125$	−1521.00			−1.08834
$126$		0			0
$127$	−2056.00			−1.43654			−0.718270	−	0.695765i	$-0.755066\pi$
$127$	−2056.00			−1.43654			−0.718270	+	0.695765i	$0.755066\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−630.000	−	1091.19i	−0.425036	−	0.736184i
$131$	1024.50	−	1774.49i	0.683290	−	1.18349i	−0.290681	−	0.956820i	$-0.593882\pi$
$131$	1024.50	−	1774.49i	0.683290	−	1.18349i	0.973971	−	0.226673i	$-0.0727848\pi$
$132$		0			0
$133$	87.5000	−	30.3109i	0.0570467	−	0.0197616i
$134$	−838.000			−0.540240
$135$		0			0
$136$	−204.000	−	353.338i	−0.128624	−	0.222783i
$137$	−70.5000	−	122.110i	−0.0439651	−	0.0761498i	0.843205	−	0.537591i	$-0.180666\pi$
$137$	−70.5000	−	122.110i	−0.0439651	−	0.0761498i	−0.887171	+	0.461442i	$0.847332\pi$
$138$		0			0
$139$	1484.00			0.905548			0.452774	−	0.891625i	$-0.350434\pi$
$139$	1484.00			0.905548			0.452774	+	0.891625i	$0.350434\pi$
$140$	−504.000	−	436.477i	−0.304256	−	0.263493i
$141$		0			0
$142$	96.0000	−	166.277i	0.0567334	−	0.0982651i
$143$	1995.00	+	3455.44i	1.16665	+	2.02069i
$144$		0			0
$145$	513.000	−	888.542i	0.293809	−	0.508892i
$146$	626.000			0.354850
$147$		0			0
$148$	−1012.00			−0.562067
$149$	−28.5000	+	49.3634i	−0.0156699	+	0.0271410i	−0.873754	−	0.486368i	$-0.838321\pi$
$149$	−28.5000	+	49.3634i	−0.0156699	+	0.0271410i	0.858084	+	0.513509i	$0.171655\pi$
$150$		0			0
$151$	−419.500	−	726.595i	−0.226082	−	0.391586i	0.730561	−	0.682847i	$-0.239258\pi$
$151$	−419.500	−	726.595i	−0.226082	−	0.391586i	−0.956644	+	0.291261i	$0.905925\pi$
$152$	20.0000	−	34.6410i	0.0106725	−	0.0184852i
$153$		0			0
$154$	1596.00	+	1382.18i	0.835126	+	0.723240i
$155$	207.000			0.107269
$156$		0			0
$157$	1416.50	+	2453.45i	0.720057	+	1.24718i	0.960976	+	0.276631i	$0.0892179\pi$
$157$	1416.50	+	2453.45i	0.720057	+	1.24718i	−0.240919	+	0.970545i	$0.577449\pi$
$158$	461.000	+	798.475i	0.232121	+	0.402046i
$159$		0			0
$160$	−288.000			−0.142302
$161$	−1207.50	+	418.290i	−0.591083	+	0.204757i
$162$		0			0
$163$	1155.50	−	2001.38i	0.555250	−	0.961721i	−0.442634	−	0.896702i	$-0.645956\pi$
$163$	1155.50	−	2001.38i	0.555250	−	0.961721i	0.997884	−	0.0650188i	$-0.0207107\pi$
$164$	−84.0000	−	145.492i	−0.0399957	−	0.0692746i
$165$		0			0
$166$	588.000	−	1018.45i	0.274926	−	0.476185i
$167$	−1260.00			−0.583843			−0.291921	−	0.956442i	$-0.594295\pi$
$167$	−1260.00			−0.583843			−0.291921	+	0.956442i	$0.594295\pi$
$168$		0			0
$169$	2703.00			1.23031
$170$	−459.000	+	795.011i	−0.207081	+	0.358674i
$171$		0			0
$172$	248.000	+	429.549i	0.109941	+	0.190423i
$173$	1633.50	−	2829.30i	0.717877	−	1.24340i	−0.243962	−	0.969785i	$-0.578447\pi$
$173$	1633.50	−	2829.30i	0.717877	−	1.24340i	0.961839	−	0.273615i	$-0.0882193\pi$
$174$		0			0
$175$	154.000	−	800.207i	0.0665217	−	0.345657i
$176$	912.000			0.390594
$177$		0			0
$178$	1017.00	+	1761.50i	0.428244	+	0.741740i
$179$	643.500	+	1114.57i	0.268701	+	0.465403i	0.968527	−	0.248910i	$-0.0800724\pi$
$179$	643.500	+	1114.57i	0.268701	+	0.465403i	−0.699826	+	0.714314i	$0.746739\pi$
$180$		0			0
$181$	−2674.00			−1.09810			−0.549052	−	0.835788i	$-0.685011\pi$
$181$	−2674.00			−1.09810			−0.549052	+	0.835788i	$0.685011\pi$
$182$	2450.00	−	848.705i	0.997836	−	0.345660i
$183$		0			0
$184$	−276.000	+	478.046i	−0.110581	+	0.191533i
$185$	1138.50	+	1971.94i	0.452455	+	0.783675i
$186$		0			0
$187$	1453.50	−	2517.54i	0.568398	−	0.984494i
$188$	−804.000			−0.311903
$189$		0			0
$190$	−90.0000			−0.0343647
$191$	2092.50	−	3624.32i	0.792712	−	1.37302i	−0.131570	−	0.991307i	$-0.542002\pi$
$191$	2092.50	−	3624.32i	0.792712	−	1.37302i	0.924282	−	0.381711i	$-0.124665\pi$
$192$		0			0
$193$	42.5000	+	73.6122i	0.0158509	+	0.0274545i	0.873842	−	0.486210i	$-0.161621\pi$
$193$	42.5000	+	73.6122i	0.0158509	+	0.0274545i	−0.857991	+	0.513664i	$0.828288\pi$
$194$	−1834.00	+	3176.58i	−0.678730	+	1.17559i
$195$		0			0
$196$	1078.00	−	848.705i	0.392857	−	0.309295i
$197$	390.000			0.141047			0.0705237	−	0.997510i	$-0.477533\pi$
$197$	390.000			0.141047			0.0705237	+	0.997510i	$0.477533\pi$
$198$		0			0
$199$	1416.50	+	2453.45i	0.504588	+	0.873972i	0.999986	+	0.00530596i	$0.00168895\pi$
$199$	1416.50	+	2453.45i	0.504588	+	0.873972i	−0.495398	+	0.868666i	$0.664978\pi$
$200$	−176.000	−	304.841i	−0.0622254	−	0.107778i
$201$		0			0
$202$	−570.000			−0.198540
$203$	1596.00	+	1382.18i	0.551809	+	0.477881i
$204$		0			0
$205$	−189.000	+	327.358i	−0.0643919	+	0.111530i
$206$	−499.000	−	864.293i	−0.168772	−	0.292321i
$207$		0			0
$208$	560.000	−	969.948i	0.186678	−	0.323336i
$209$	285.000			0.0943247
$210$		0			0
$211$	−124.000			−0.0404574			−0.0202287	−	0.999795i	$-0.506439\pi$
$211$	−124.000			−0.0404574			−0.0202287	+	0.999795i	$0.506439\pi$
$212$	−786.000	+	1361.39i	−0.254635	+	0.441041i
$213$		0			0
$214$	1107.00	+	1917.38i	0.353612	+	0.612474i
$215$	558.000	−	966.484i	0.177001	−	0.306575i
$216$		0			0
$217$	−80.5000	+	418.290i	−0.0251829	+	0.130854i
$218$	−1846.00			−0.573518
$219$		0			0
$220$	−1026.00	−	1777.08i	−0.314422	−	0.544595i
$221$	−1785.00	−	3091.71i	−0.543313	−	0.941045i
$222$		0			0
$223$	56.0000			0.0168163			0.00840816	−	0.999965i	$-0.497324\pi$
$223$	56.0000			0.0168163			0.00840816	+	0.999965i	$0.497324\pi$
$224$	112.000	−	581.969i	0.0334077	−	0.173591i
$225$		0			0
$226$	−1542.00	+	2670.82i	−0.453860	+	0.786108i
$227$	−1528.50	−	2647.44i	−0.446917	−	0.774083i	0.551267	−	0.834329i	$-0.314145\pi$
$227$	−1528.50	−	2647.44i	−0.446917	−	0.774083i	−0.998184	+	0.0602465i	$0.980811\pi$
$228$		0			0
$229$	480.500	−	832.250i	0.138656	−	0.240160i	−0.788332	−	0.615250i	$-0.789055\pi$
$229$	480.500	−	832.250i	0.138656	−	0.240160i	0.926988	+	0.375090i	$0.122388\pi$
$230$	1242.00			0.356065
$231$		0			0
$232$	912.000			0.258085
$233$	−1414.50	+	2449.99i	−0.397712	+	0.688858i	−0.993443	−	0.114326i	$-0.963529\pi$
$233$	−1414.50	+	2449.99i	−0.397712	+	0.688858i	0.595731	+	0.803184i	$0.296862\pi$
$234$		0			0
$235$	904.500	+	1566.64i	0.251077	+	0.434878i
$236$	438.000	−	758.638i	0.120811	−	0.209251i
$237$		0			0
$238$	−1428.00	−	1236.68i	−0.388922	−	0.336817i
$239$	3540.00			0.958090			0.479045	−	0.877790i	$-0.340983\pi$
$239$	3540.00			0.958090			0.479045	+	0.877790i	$0.340983\pi$
$240$		0			0
$241$	−2615.50	−	4530.18i	−0.699084	−	1.21085i	−0.968785	−	0.247904i	$-0.920258\pi$
$241$	−2615.50	−	4530.18i	−0.699084	−	1.21085i	0.269701	−	0.962944i	$-0.413075\pi$
$242$	1918.00	+	3322.07i	0.509478	+	0.882442i
$243$		0			0
$244$	−2836.00			−0.744083
$245$	−2866.50	−	1145.75i	−0.747486	−	0.298773i
$246$		0			0
$247$	175.000	−	303.109i	0.0450809	−	0.0780824i
$248$	92.0000	+	159.349i	0.0235565	+	0.0408010i
$249$		0			0
$250$	−1521.00	+	2634.45i	−0.384786	+	0.666469i
$251$	−5040.00			−1.26742			−0.633709	−	0.773571i	$-0.718468\pi$
$251$	−5040.00			−1.26742			−0.633709	+	0.773571i	$0.718468\pi$
$252$		0			0
$253$	−3933.00			−0.977334
$254$	−2056.00	+	3561.10i	−0.507893	+	0.879697i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−718.500	+	1244.48i	−0.174392	+	0.302056i	−0.939951	−	0.341310i	$-0.889129\pi$
$257$	−718.500	+	1244.48i	−0.174392	+	0.302056i	0.765559	+	0.643366i	$0.222463\pi$
$258$		0			0
$259$	−4427.50	+	1533.73i	−1.06221	+	0.367959i
$260$	−2520.00			−0.601091
$261$		0			0
$262$	−2049.00	−	3548.97i	−0.483159	−	0.836856i
$263$	−1162.50	−	2013.51i	−0.272558	−	0.472085i	0.696958	−	0.717112i	$-0.254536\pi$
$263$	−1162.50	−	2013.51i	−0.272558	−	0.472085i	−0.969516	+	0.245027i	$0.921203\pi$
$264$		0			0
$265$	3537.00			0.819910
$266$	35.0000	−	181.865i	0.00806762	−	0.0419206i
$267$		0			0
$268$	−838.000	+	1451.46i	−0.191004	+	0.330828i
$269$	−1192.50	−	2065.47i	−0.270290	−	0.468156i	0.698646	−	0.715467i	$-0.253786\pi$
$269$	−1192.50	−	2065.47i	−0.270290	−	0.468156i	−0.968936	+	0.247311i	$0.920453\pi$
$270$		0			0
$271$	165.500	−	286.654i	0.0370975	−	0.0642547i	−0.846881	−	0.531783i	$-0.821522\pi$
$271$	165.500	−	286.654i	0.0370975	−	0.0642547i	0.883978	+	0.467528i	$0.154855\pi$
$272$	−816.000			−0.181902
$273$		0			0
$274$	−282.000			−0.0621761
$275$	1254.00	−	2171.99i	0.274978	−	0.476276i
$276$		0			0
$277$	−2435.50	−	4218.41i	−0.528285	−	0.915017i	−0.999456	−	0.0329750i	$-0.989502\pi$
$277$	−2435.50	−	4218.41i	−0.528285	−	0.915017i	0.471171	−	0.882042i	$-0.343831\pi$
$278$	1484.00	−	2570.36i	0.320160	−	0.554533i
$279$		0			0
$280$	−1260.00	+	436.477i	−0.268926	+	0.0931589i
$281$	7026.00			1.49159			0.745794	−	0.666177i	$-0.232070\pi$
$281$	7026.00			1.49159			0.745794	+	0.666177i	$0.232070\pi$
$282$		0			0
$283$	2676.50	+	4635.83i	0.562196	+	0.973752i	0.997305	+	0.0733738i	$0.0233766\pi$
$283$	2676.50	+	4635.83i	0.562196	+	0.973752i	−0.435109	+	0.900378i	$0.643290\pi$
$284$	−192.000	−	332.554i	−0.0401166	−	0.0694839i
$285$		0			0
$286$	7980.00			1.64989
$287$	−588.000	−	509.223i	−0.120936	−	0.104733i
$288$		0			0
$289$	1156.00	−	2002.25i	0.235294	−	0.407541i
$290$	−1026.00	−	1777.08i	−0.207754	−	0.359841i
$291$		0			0
$292$	626.000	−	1084.26i	0.125458	−	0.217300i
$293$	−4158.00			−0.829054			−0.414527	−	0.910037i	$-0.636053\pi$
$293$	−4158.00			−0.829054			−0.414527	+	0.910037i	$0.636053\pi$
$294$		0			0
$295$	−1971.00			−0.389004
$296$	−1012.00	+	1752.84i	−0.198721	+	0.344194i
$297$		0			0
$298$	57.0000	+	98.7269i	0.0110803	+	0.0191916i
$299$	−2415.00	+	4182.90i	−0.467101	+	0.809042i
$300$		0			0
$301$	1736.00	+	1503.42i	0.332430	+	0.287893i
$302$	−1678.00			−0.319729
$303$		0			0
$304$	−40.0000	−	69.2820i	−0.00754657	−	0.0130710i
$305$	3190.50	+	5526.11i	0.598975	+	1.03746i
$306$		0			0
$307$	−9604.00			−1.78544			−0.892719	−	0.450615i	$-0.851205\pi$
$307$	−9604.00			−1.78544			−0.892719	+	0.450615i	$0.851205\pi$
$308$	3990.00	−	1382.18i	0.738154	−	0.255704i
$309$		0			0
$310$	207.000	−	358.535i	0.0379252	−	0.0656884i
$311$	5065.50	+	8773.70i	0.923595	+	1.59971i	0.793805	+	0.608173i	$0.208097\pi$
$311$	5065.50	+	8773.70i	0.923595	+	1.59971i	0.129791	+	0.991541i	$0.458570\pi$
$312$		0			0
$313$	−5399.50	+	9352.21i	−0.975073	+	1.68888i	−0.295378	+	0.955380i	$0.595446\pi$
$313$	−5399.50	+	9352.21i	−0.975073	+	1.68888i	−0.679695	+	0.733495i	$0.737888\pi$
$314$	5666.00			1.01831
$315$		0			0
$316$	1844.00			0.328269
$317$	265.500	−	459.859i	0.0470409	−	0.0814772i	−0.841546	−	0.540185i	$-0.818354\pi$
$317$	265.500	−	459.859i	0.0470409	−	0.0814772i	0.888587	+	0.458708i	$0.151688\pi$
$318$		0			0
$319$	3249.00	+	5627.43i	0.570248	+	0.987698i
$320$	−288.000	+	498.831i	−0.0503115	+	0.0871421i
$321$		0			0
$322$	−483.000	+	2509.74i	−0.0835917	+	0.434355i
$323$	−255.000			−0.0439275
$324$		0			0
$325$	−1540.00	−	2667.36i	−0.262843	−	0.455257i
$326$	−2311.00	−	4002.77i	−0.392621	−	0.680040i
$327$		0			0
$328$	−336.000			−0.0565625
$329$	−3517.50	+	1218.50i	−0.589441	+	0.204188i
$330$		0			0
$331$	3507.50	−	6075.17i	0.582446	−	1.00883i	−0.412743	−	0.910848i	$-0.635429\pi$
$331$	3507.50	−	6075.17i	0.582446	−	1.00883i	0.995189	−	0.0979784i	$-0.0312376\pi$
$332$	−1176.00	−	2036.89i	−0.194402	−	0.336714i
$333$		0			0
$334$	−1260.00	+	2182.38i	−0.206420	+	0.357529i
$335$	3771.00			0.615020
$336$		0			0
$337$	8990.00			1.45316			0.726582	−	0.687079i	$-0.241108\pi$
$337$	8990.00			1.45316			0.726582	+	0.687079i	$0.241108\pi$
$338$	2703.00	−	4681.73i	0.434982	−	0.753410i
$339$		0			0
$340$	918.000	+	1590.02i	0.146428	+	0.253621i
$341$	−655.500	+	1135.36i	−0.104098	+	0.180303i
$342$		0			0
$343$	3430.00	−	5346.84i	0.539949	−	0.841698i
$344$	992.000			0.155480
$345$		0			0
$346$	−3267.00	−	5658.61i	−0.507616	−	0.879216i
$347$	−4354.50	−	7542.22i	−0.673665	−	1.16682i	−0.976857	−	0.213893i	$-0.931386\pi$
$347$	−4354.50	−	7542.22i	−0.673665	−	1.16682i	0.303192	−	0.952929i	$-0.401948\pi$
$348$		0			0
$349$	6482.00			0.994193			0.497097	−	0.867695i	$-0.334399\pi$
$349$	6482.00			0.994193			0.497097	+	0.867695i	$0.334399\pi$
$350$	−1232.00	−	1066.94i	−0.188152	−	0.162944i
$351$		0			0
$352$	912.000	−	1579.63i	0.138096	−	0.239189i
$353$	−1066.50	−	1847.23i	−0.160805	−	0.278522i	0.774353	−	0.632754i	$-0.218076\pi$
$353$	−1066.50	−	1847.23i	−0.160805	−	0.278522i	−0.935158	+	0.354232i	$0.884742\pi$
$354$		0			0
$355$	−432.000	+	748.246i	−0.0645864	+	0.111867i
$356$	4068.00			0.605628
$357$		0			0
$358$	2574.00			0.380000
$359$	1924.50	−	3333.33i	0.282928	−	0.490046i	−0.689176	−	0.724594i	$-0.742028\pi$
$359$	1924.50	−	3333.33i	0.282928	−	0.490046i	0.972105	+	0.234548i	$0.0753608\pi$
$360$		0			0
$361$	3417.00	+	5918.42i	0.498178	+	0.862869i
$362$	−2674.00	+	4631.50i	−0.388238	+	0.672449i
$363$		0			0
$364$	980.000	−	5092.23i	0.141115	−	0.733256i
$365$	−2817.00			−0.403969
$366$		0			0
$367$	−3245.50	−	5621.37i	−0.461618	−	0.799545i	0.537424	−	0.843312i	$-0.319397\pi$
$367$	−3245.50	−	5621.37i	−0.461618	−	0.799545i	−0.999042	+	0.0437668i	$0.986064\pi$
$368$	552.000	+	956.092i	0.0781929	+	0.135434i
$369$		0			0
$370$	4554.00			0.639868
$371$	−1375.50	+	7147.31i	−0.192486	+	1.00019i
$372$		0			0
$373$	−461.500	+	799.341i	−0.0640632	+	0.110961i	−0.896278	−	0.443493i	$-0.853739\pi$
$373$	−461.500	+	799.341i	−0.0640632	+	0.110961i	0.832215	+	0.554453i	$0.187073\pi$
$374$	−2907.00	−	5035.07i	−0.401918	−	0.696143i
$375$		0			0
$376$	−804.000	+	1392.57i	−0.110274	+	0.191001i
$377$	7980.00			1.09016
$378$		0			0
$379$	6344.00			0.859814			0.429907	−	0.902873i	$-0.358546\pi$
$379$	6344.00			0.859814			0.429907	+	0.902873i	$0.358546\pi$
$380$	−90.0000	+	155.885i	−0.0121497	+	0.0210440i
$381$		0			0
$382$	−4185.00	−	7248.63i	−0.560532	−	0.970870i
$383$	−2503.50	+	4336.19i	−0.334002	+	0.578509i	−0.983293	−	0.182032i	$-0.941733\pi$
$383$	−2503.50	+	4336.19i	−0.334002	+	0.578509i	0.649290	+	0.760541i	$0.275066\pi$
$384$		0			0
$385$	−7182.00	−	6219.79i	−0.950724	−	0.823351i
$386$	170.000			0.0224165
$387$		0			0
$388$	3668.00	+	6353.16i	0.479934	+	0.831270i
$389$	6145.50	+	10644.3i	0.801001	+	1.38737i	0.918958	+	0.394355i	$0.129032\pi$
$389$	6145.50	+	10644.3i	0.801001	+	1.38737i	−0.117958	+	0.993019i	$0.537635\pi$
$390$		0			0
$391$	3519.00			0.455150
$392$	−392.000	−	2715.86i	−0.0505076	−	0.349927i
$393$		0			0
$394$	390.000	−	675.500i	0.0498678	−	0.0863736i
$395$	−2074.50	−	3593.14i	−0.264252	−	0.457697i
$396$		0			0
$397$	−443.500	+	768.165i	−0.0560671	+	0.0971110i	−0.892697	−	0.450658i	$-0.851189\pi$
$397$	−443.500	+	768.165i	−0.0560671	+	0.0971110i	0.836630	+	0.547769i	$0.184523\pi$
$398$	5666.00			0.713595
$399$		0			0
$400$	−704.000			−0.0880000
$401$	5977.50	−	10353.3i	0.744394	−	1.28933i	−0.206083	−	0.978535i	$-0.566072\pi$
$401$	5977.50	−	10353.3i	0.744394	−	1.28933i	0.950477	−	0.310794i	$-0.100595\pi$
$402$		0			0
$403$	805.000	+	1394.30i	0.0995035	+	0.172345i
$404$	−570.000	+	987.269i	−0.0701945	+	0.121580i
$405$		0			0
$406$	3990.00	−	1382.18i	0.487735	−	0.168956i
$407$	−14421.0			−1.75632
$408$		0			0
$409$	1710.50	+	2962.67i	0.206794	+	0.358178i	0.950703	−	0.310103i	$-0.100364\pi$
$409$	1710.50	+	2962.67i	0.206794	+	0.358178i	−0.743909	+	0.668281i	$0.767030\pi$
$410$	378.000	+	654.715i	0.0455319	+	0.0788636i
$411$		0			0
$412$	−1996.00			−0.238679
$413$	766.500	−	3982.85i	0.0913245	−	0.474536i
$414$		0			0
$415$	−2646.00	+	4583.01i	−0.312981	+	0.542099i
$416$	−1120.00	−	1939.90i	−0.132001	−	0.228633i
$417$		0			0
$418$	285.000	−	493.634i	0.0333488	−	0.0577618i
$419$	5460.00			0.636607			0.318304	−	0.947989i	$-0.396887\pi$
$419$	5460.00			0.636607			0.318304	+	0.947989i	$0.396887\pi$
$420$		0			0
$421$	7730.00			0.894863			0.447431	−	0.894318i	$-0.352339\pi$
$421$	7730.00			0.894863			0.447431	+	0.894318i	$0.352339\pi$
$422$	−124.000	+	214.774i	−0.0143039	+	0.0247750i
$423$		0			0
$424$	1572.00	+	2722.78i	0.180054	+	0.311863i
$425$	−1122.00	+	1943.36i	−0.128059	+	0.221804i
$426$		0			0
$427$	−12407.5	+	4298.08i	−1.40619	+	0.487117i
$428$	4428.00			0.500083
$429$		0			0
$430$	−1116.00	−	1932.97i	−0.125159	−	0.216781i
$431$	−5656.50	−	9797.35i	−0.632167	−	1.09495i	−0.987108	−	0.160057i	$-0.948832\pi$
$431$	−5656.50	−	9797.35i	−0.632167	−	1.09495i	0.354941	−	0.934889i	$-0.384501\pi$
$432$		0			0
$433$	4214.00			0.467695			0.233847	−	0.972273i	$-0.424868\pi$
$433$	4214.00			0.467695			0.233847	+	0.972273i	$0.424868\pi$
$434$	644.000	+	557.720i	0.0712281	+	0.0616853i
$435$		0			0
$436$	−1846.00	+	3197.37i	−0.202769	+	0.351207i
$437$	172.500	+	298.779i	0.0188828	+	0.0327060i
$438$		0			0
$439$	−8276.50	+	14335.3i	−0.899808	+	1.55851i	−0.0720696	+	0.997400i	$0.522960\pi$
$439$	−8276.50	+	14335.3i	−0.899808	+	1.55851i	−0.827739	+	0.561114i	$0.810373\pi$
$440$	−4104.00			−0.444660
$441$		0			0
$442$	−7140.00			−0.768360
$443$	−8197.50	+	14198.5i	−0.879176	+	1.52278i	−0.0269294	+	0.999637i	$0.508573\pi$
$443$	−8197.50	+	14198.5i	−0.879176	+	1.52278i	−0.852247	+	0.523140i	$0.824760\pi$
$444$		0			0
$445$	−4576.50	−	7926.73i	−0.487521	−	0.844411i
$446$	56.0000	−	96.9948i	0.00594546	−	0.0102978i
$447$		0			0
$448$	−896.000	−	775.959i	−0.0944911	−	0.0818317i
$449$	15090.0			1.58606			0.793030	−	0.609182i	$-0.208502\pi$
$449$	15090.0			1.58606			0.793030	+	0.609182i	$0.208502\pi$
$450$		0			0
$451$	−1197.00	−	2073.26i	−0.124977	−	0.216466i
$452$	3084.00	+	5341.64i	0.320927	+	0.555862i
$453$		0			0
$454$	−6114.00			−0.632036
$455$	−11025.0	+	3819.17i	−1.13596	+	0.393507i
$456$		0			0
$457$	7392.50	−	12804.2i	0.756688	−	1.31062i	−0.187842	−	0.982199i	$-0.560149\pi$
$457$	7392.50	−	12804.2i	0.756688	−	1.31062i	0.944531	−	0.328423i	$-0.106517\pi$
$458$	−961.000	−	1664.50i	−0.0980449	−	0.169819i
$459$		0			0
$460$	1242.00	−	2151.21i	0.125888	−	0.218045i
$461$	−2898.00			−0.292784			−0.146392	−	0.989227i	$-0.546766\pi$
$461$	−2898.00			−0.292784			−0.146392	+	0.989227i	$0.546766\pi$
$462$		0			0
$463$	464.000			0.0465743			0.0232872	−	0.999729i	$-0.492587\pi$
$463$	464.000			0.0465743			0.0232872	+	0.999729i	$0.492587\pi$
$464$	912.000	−	1579.63i	0.0912468	−	0.158044i
$465$		0			0
$466$	2829.00	+	4899.97i	0.281225	+	0.487096i
$467$	2116.50	−	3665.89i	0.209721	−	0.363248i	−0.741905	−	0.670505i	$-0.766078\pi$
$467$	2116.50	−	3665.89i	0.209721	−	0.363248i	0.951627	+	0.307256i	$0.0994109\pi$
$468$		0			0
$469$	−1466.50	+	7620.16i	−0.144385	+	0.750248i
$470$	3618.00			0.355076
$471$		0			0
$472$	−876.000	−	1517.28i	−0.0854262	−	0.147963i
$473$	3534.00	+	6121.07i	0.343538	+	0.595025i
$474$		0			0
$475$	−220.000			−0.0212511
$476$	−3570.00	+	1236.68i	−0.343762	+	0.119083i
$477$		0			0
$478$	3540.00	−	6131.46i	0.338736	−	0.586708i
$479$	1369.50	+	2372.04i	0.130635	+	0.226266i	0.923921	−	0.382582i	$-0.124965\pi$
$479$	1369.50	+	2372.04i	0.130635	+	0.226266i	−0.793287	+	0.608848i	$0.791632\pi$
$480$		0			0
$481$	−8855.00	+	15337.3i	−0.839404	+	1.45389i
$482$	−10462.0			−0.988654
$483$		0			0
$484$	7672.00			0.720511
$485$	8253.00	−	14294.6i	0.772679	−	1.33832i
$486$		0			0
$487$	−8525.50	−	14766.6i	−0.793280	−	1.37400i	−0.923926	−	0.382572i	$-0.875038\pi$
$487$	−8525.50	−	14766.6i	−0.793280	−	1.37400i	0.130646	−	0.991429i	$-0.458295\pi$
$488$	−2836.00	+	4912.10i	−0.263073	+	0.455656i
$489$		0			0
$490$	−4851.00	+	3819.17i	−0.447236	+	0.352107i
$491$	4296.00			0.394859			0.197429	−	0.980317i	$-0.436741\pi$
$491$	4296.00			0.394859			0.197429	+	0.980317i	$0.436741\pi$
$492$		0			0
$493$	−2907.00	−	5035.07i	−0.265567	−	0.459976i
$494$	−350.000	−	606.218i	−0.0318770	−	0.0552126i
$495$		0			0
$496$	368.000			0.0333139
$497$	−1344.00	−	1163.94i	−0.121301	−	0.105050i
$498$		0			0
$499$	−1700.50	+	2945.35i	−0.152555	+	0.264233i	−0.932166	−	0.362031i	$-0.882083\pi$
$499$	−1700.50	+	2945.35i	−0.152555	+	0.264233i	0.779611	+	0.626264i	$0.215417\pi$
$500$	3042.00	+	5268.90i	0.272085	+	0.471265i
$501$		0			0
$502$	−5040.00	+	8729.54i	−0.448100	+	0.776132i
$503$	−16800.0			−1.48921			−0.744607	−	0.667503i	$-0.767363\pi$
$503$	−16800.0			−1.48921			−0.744607	+	0.667503i	$0.767363\pi$
$504$		0			0
$505$	2565.00			0.226022
$506$	−3933.00	+	6812.16i	−0.345540	+	0.598493i
$507$		0			0
$508$	4112.00	+	7122.19i	0.359135	+	0.622040i
$509$	919.500	−	1592.62i	0.0800710	−	0.138687i	−0.823209	−	0.567738i	$-0.807819\pi$
$509$	919.500	−	1592.62i	0.0800710	−	0.138687i	0.903280	+	0.429051i	$0.141152\pi$
$510$		0			0
$511$	1095.50	−	5692.38i	0.0948377	−	0.492791i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	1437.00	+	2488.96i	0.123314	+	0.213586i
$515$	2245.50	+	3889.32i	0.192133	+	0.332784i
$516$		0			0
$517$	−11457.0			−0.974620
$518$	−1771.00	+	9202.39i	−0.150219	+	0.780559i
$519$		0			0
$520$	−2520.00	+	4364.77i	−0.212518	+	0.368092i
$521$	151.500	+	262.406i	0.0127396	+	0.0220656i	0.872325	−	0.488927i	$-0.162611\pi$
$521$	151.500	+	262.406i	0.0127396	+	0.0220656i	−0.859585	+	0.510992i	$0.829278\pi$
$522$		0			0
$523$	10833.5	−	18764.2i	0.905767	−	1.56883i	0.0858815	−	0.996305i	$-0.472629\pi$
$523$	10833.5	−	18764.2i	0.905767	−	1.56883i	0.819885	−	0.572528i	$-0.194037\pi$
$524$	−8196.00			−0.683290
$525$		0			0
$526$	−4650.00			−0.385456
$527$	586.500	−	1015.85i	0.0484788	−	0.0839678i
$528$		0			0
$529$	3703.00	+	6413.78i	0.304348	+	0.527146i
$530$	3537.00	−	6126.26i	0.289882	−	0.502090i
$531$		0			0
$532$	−280.000	−	242.487i	−0.0228187	−	0.0197616i
$533$	−2940.00			−0.238922
$534$		0			0
$535$	−4981.50	−	8628.21i	−0.402559	−	0.697253i
$536$	1676.00	+	2902.92i	0.135060	+	0.233931i
$537$		0			0
$538$	−4770.00			−0.382248
$539$	15361.5	−	12094.0i	1.22758	−	0.966470i
$540$		0			0
$541$	−2519.50	+	4363.90i	−0.200225	+	0.346800i	−0.948601	−	0.316475i	$-0.897501\pi$
$541$	−2519.50	+	4363.90i	−0.200225	+	0.346800i	0.748376	+	0.663275i	$0.230834\pi$
$542$	−331.000	−	573.309i	−0.0262319	−	0.0454349i
$543$		0			0
$544$	−816.000	+	1413.35i	−0.0643120	+	0.111392i
$545$	8307.00			0.652904
$546$		0			0
$547$	−2392.00			−0.186974			−0.0934868	−	0.995621i	$-0.529801\pi$
$547$	−2392.00			−0.186974			−0.0934868	+	0.995621i	$0.529801\pi$
$548$	−282.000	+	488.438i	−0.0219826	+	0.0380749i
$549$		0			0
$550$	−2508.00	−	4343.98i	−0.194439	−	0.336778i
$551$	285.000	−	493.634i	0.0220352	−	0.0381661i
$552$		0			0
$553$	8067.50	−	2794.66i	0.620371	−	0.214903i
$554$	−9742.00			−0.747108
$555$		0			0
$556$	−2968.00	−	5140.73i	−0.226387	−	0.392114i
$557$	−11074.5	−	19181.6i	−0.842445	−	1.45916i	−0.887822	−	0.460187i	$-0.847782\pi$
$557$	−11074.5	−	19181.6i	−0.842445	−	1.45916i	0.0453775	−	0.998970i	$-0.485551\pi$
$558$		0			0
$559$	8680.00			0.656753
$560$	−504.000	+	2618.86i	−0.0380319	+	0.197620i
$561$		0			0
$562$	7026.00	−	12169.4i	0.527356	−	0.913407i
$563$	−4174.50	−	7230.45i	−0.312494	−	0.541256i	0.666408	−	0.745588i	$-0.267831\pi$
$563$	−4174.50	−	7230.45i	−0.312494	−	0.541256i	−0.978902	+	0.204332i	$0.934498\pi$
$564$		0			0
$565$	6939.00	−	12018.7i	0.516683	−	0.894921i
$566$	10706.0			0.795065
$567$		0			0
$568$	−768.000			−0.0567334
$569$	−7672.50	+	13289.2i	−0.565286	+	0.979105i	0.431737	+	0.902000i	$0.357901\pi$
$569$	−7672.50	+	13289.2i	−0.565286	+	0.979105i	−0.997023	+	0.0771050i	$0.975432\pi$
$570$		0			0
$571$	5796.50	+	10039.8i	0.424827	+	0.735821i	0.996404	−	0.0847268i	$-0.0270017\pi$
$571$	5796.50	+	10039.8i	0.424827	+	0.735821i	−0.571578	+	0.820548i	$0.693668\pi$
$572$	7980.00	−	13821.8i	0.583323	−	1.01034i
$573$		0			0
$574$	−1470.00	+	509.223i	−0.106893	+	0.0370288i
$575$	3036.00			0.220191
$576$		0			0
$577$	7296.50	+	12637.9i	0.526442	+	0.911825i	0.999525	+	0.0308071i	$0.00980776\pi$
$577$	7296.50	+	12637.9i	0.526442	+	0.911825i	−0.473083	+	0.881018i	$0.656859\pi$
$578$	−2312.00	−	4004.50i	−0.166378	−	0.288175i
$579$		0			0
$580$	−4104.00			−0.293809
$581$	−8232.00	−	7129.12i	−0.587816	−	0.509063i
$582$		0			0
$583$	−11200.5	+	19399.8i	−0.795673	+	1.37815i
$584$	−1252.00	−	2168.53i	−0.0887125	−	0.153655i
$585$		0			0
$586$	−4158.00	+	7201.87i	−0.293115	+	0.507690i
$587$	15372.0			1.08087			0.540435	−	0.841386i	$-0.318260\pi$
$587$	15372.0			1.08087			0.540435	+	0.841386i	$0.318260\pi$
$588$		0			0
$589$	115.000			0.00804498
$590$	−1971.00	+	3413.87i	−0.137534	+	0.238215i
$591$		0			0
$592$	2024.00	+	3505.67i	0.140517	+	0.243382i
$593$	−7186.50	+	12447.4i	−0.497663	+	0.861978i	−0.999996	−	0.00269639i	$-0.999142\pi$
$593$	−7186.50	+	12447.4i	−0.497663	+	0.861978i	0.502333	+	0.864674i	$0.332475\pi$
$594$		0			0
$595$	6426.00	+	5565.08i	0.442757	+	0.383439i
$596$	228.000			0.0156699
$597$		0			0
$598$	4830.00	+	8365.81i	0.330290	+	0.572079i
$599$	1273.50	+	2205.77i	0.0868678	+	0.150459i	0.906186	−	0.422880i	$-0.138981\pi$
$599$	1273.50	+	2205.77i	0.0868678	+	0.150459i	−0.819318	+	0.573340i	$0.805648\pi$
$600$		0			0
$601$	−7042.00			−0.477952			−0.238976	−	0.971025i	$-0.576812\pi$
$601$	−7042.00			−0.477952			−0.238976	+	0.971025i	$0.576812\pi$
$602$	4340.00	−	1503.42i	0.293829	−	0.101785i
$603$		0			0
$604$	−1678.00	+	2906.38i	−0.113041	+	0.195793i
$605$	−8631.00	−	14949.3i	−0.580000	−	1.00459i
$606$		0			0
$607$	11295.5	−	19564.4i	0.755305	−	1.30823i	−0.189917	−	0.981800i	$-0.560822\pi$
$607$	11295.5	−	19564.4i	0.755305	−	1.30823i	0.945223	−	0.326427i	$-0.105845\pi$
$608$	−160.000			−0.0106725
$609$		0			0
$610$	12762.0			0.847079
$611$	−7035.00	+	12185.0i	−0.465803	+	0.806794i
$612$		0			0
$613$	4242.50	+	7348.23i	0.279532	+	0.484163i	0.971268	−	0.237987i	$-0.0764874\pi$
$613$	4242.50	+	7348.23i	0.279532	+	0.484163i	−0.691737	+	0.722150i	$0.743154\pi$
$614$	−9604.00	+	16634.6i	−0.631247	+	1.09335i
$615$		0			0
$616$	1596.00	−	8293.06i	0.104391	−	0.542430i
$617$	18282.0			1.19288			0.596439	−	0.802658i	$-0.296582\pi$
$617$	18282.0			1.19288			0.596439	+	0.802658i	$0.296582\pi$
$618$		0			0
$619$	−1145.50	−	1984.06i	−0.0743805	−	0.128831i	0.826436	−	0.563030i	$-0.190365\pi$
$619$	−1145.50	−	1984.06i	−0.0743805	−	0.128831i	−0.900817	+	0.434200i	$0.857031\pi$
$620$	−414.000	−	717.069i	−0.0268172	−	0.0464487i
$621$		0			0
$622$	20262.0			1.30616
$623$	17797.5	−	6165.23i	1.14453	−	0.396477i
$624$		0			0
$625$	4094.50	−	7091.88i	0.262048	−	0.453880i
$626$	10799.0	+	18704.4i	0.689481	+	1.19422i
$627$		0			0
$628$	5666.00	−	9813.80i	0.360029	−	0.623588i
$629$	12903.0			0.817927
$630$		0			0
$631$	−6928.00			−0.437083			−0.218541	−	0.975828i	$-0.570130\pi$
$631$	−6928.00			−0.437083			−0.218541	+	0.975828i	$0.570130\pi$
$632$	1844.00	−	3193.90i	0.116061	−	0.201023i
$633$		0			0
$634$	−531.000	−	919.719i	−0.0332629	−	0.0576131i
$635$	9252.00	−	16024.9i	0.578196	−	1.00146i
$636$		0			0
$637$	−3430.00	−	23763.7i	−0.213346	−	1.47811i
$638$	12996.0			0.806452
$639$		0			0
$640$	576.000	+	997.661i	0.0355756	+	0.0616188i
$641$	12487.5	+	21629.0i	0.769464	+	1.33275i	0.937854	+	0.347031i	$0.112810\pi$
$641$	12487.5	+	21629.0i	0.769464	+	1.33275i	−0.168390	+	0.985721i	$0.553857\pi$
$642$		0			0
$643$	9548.00			0.585593			0.292797	−	0.956175i	$-0.405414\pi$
$643$	9548.00			0.585593			0.292797	+	0.956175i	$0.405414\pi$
$644$	3864.00	+	3346.32i	0.236433	+	0.204757i
$645$		0			0
$646$	−255.000	+	441.673i	−0.0155307	+	0.0269000i
$647$	5065.50	+	8773.70i	0.307798	+	0.533122i	0.977880	−	0.209165i	$-0.0670745\pi$
$647$	5065.50	+	8773.70i	0.307798	+	0.533122i	−0.670082	+	0.742287i	$0.733741\pi$
$648$		0			0
$649$	6241.50	−	10810.6i	0.377504	−	0.653857i
$650$	−6160.00			−0.371716
$651$		0			0
$652$	−9244.00			−0.555250
$653$	8329.50	−	14427.1i	0.499171	−	0.864589i	−0.500829	−	0.865546i	$-0.666971\pi$
$653$	8329.50	−	14427.1i	0.499171	−	0.864589i	1.00000		0.000957229i	$0.000304695\pi$
$654$		0			0
$655$	9220.50	+	15970.4i	0.550038	+	0.952693i
$656$	−336.000	+	581.969i	−0.0199979	+	0.0346373i
$657$		0			0
$658$	−1407.00	+	7310.99i	−0.0833595	+	0.433149i
$659$	−29556.0			−1.74710			−0.873550	−	0.486735i	$-0.838188\pi$
$659$	−29556.0			−1.74710			−0.873550	+	0.486735i	$0.838188\pi$
$660$		0			0
$661$	−95.5000	−	165.411i	−0.00561955	−	0.00973334i	0.863202	−	0.504859i	$-0.168455\pi$
$661$	−95.5000	−	165.411i	−0.00561955	−	0.00973334i	−0.868822	+	0.495125i	$0.835122\pi$
$662$	−7015.00	−	12150.3i	−0.411852	−	0.713348i
$663$		0			0
$664$	−4704.00			−0.274926
$665$	−157.500	+	818.394i	−0.00918434	+	0.0477232i
$666$		0			0
$667$	−3933.00	+	6812.16i	−0.228315	+	0.395454i
$668$	2520.00	+	4364.77i	0.145961	+	0.252811i
$669$		0			0
$670$	3771.00	−	6531.56i	0.217442	−	0.376621i
$671$	−40413.0			−2.32508
$672$		0			0
$673$	2606.00			0.149263			0.0746314	−	0.997211i	$-0.476222\pi$
$673$	2606.00			0.149263			0.0746314	+	0.997211i	$0.476222\pi$
$674$	8990.00	−	15571.1i	0.513771	−	0.889878i
$675$		0			0
$676$	−5406.00	−	9363.47i	−0.307579	−	0.532742i
$677$	−2104.50	+	3645.10i	−0.119472	+	0.206931i	−0.919559	−	0.392953i	$-0.871453\pi$
$677$	−2104.50	+	3645.10i	−0.119472	+	0.206931i	0.800087	+	0.599885i	$0.204787\pi$
$678$		0			0
$679$	25676.0	+	22236.1i	1.45118	+	1.25676i
$680$	3672.00			0.207081
$681$		0			0
$682$	1311.00	+	2270.72i	0.0736082	+	0.127493i
$683$	12151.5	+	21047.0i	0.680768	+	1.17912i	0.974747	+	0.223312i	$0.0716869\pi$
$683$	12151.5	+	21047.0i	0.680768	+	1.17912i	−0.293979	+	0.955812i	$0.594980\pi$
$684$		0			0
$685$	1269.00			0.0707825
$686$	−5831.00	−	11287.8i	−0.324532	−	0.628235i
$687$		0			0
$688$	992.000	−	1718.19i	0.0549704	−	0.0952116i
$689$	13755.0	+	23824.4i	0.760557	+	1.31732i
$690$		0			0
$691$	−7520.50	+	13025.9i	−0.414028	+	0.717117i	−0.995326	−	0.0965734i	$-0.969212\pi$
$691$	−7520.50	+	13025.9i	−0.414028	+	0.717117i	0.581298	+	0.813691i	$0.302545\pi$
$692$	−13068.0			−0.717877
$693$		0			0
$694$	−17418.0			−0.952706
$695$	−6678.00	+	11566.6i	−0.364476	+	0.631291i
$696$		0			0
$697$	1071.00	+	1855.03i	0.0582023	+	0.100809i
$698$	6482.00	−	11227.2i	0.351500	−	0.608817i
$699$		0			0
$700$	−3080.00	+	1066.94i	−0.166304	+	0.0576095i
$701$	−24726.0			−1.33222			−0.666111	−	0.745852i	$-0.732042\pi$
$701$	−24726.0			−1.33222			−0.666111	+	0.745852i	$0.732042\pi$
$702$		0			0
$703$	632.500	+	1095.52i	0.0339334	+	0.0587744i
$704$	−1824.00	−	3159.26i	−0.0976486	−	0.169132i
$705$		0			0
$706$	−4266.00			−0.227412
$707$	−997.500	+	5183.16i	−0.0530620	+	0.275718i
$708$		0			0
$709$	2478.50	−	4292.89i	0.131286	−	0.227395i	−0.792886	−	0.609370i	$-0.791423\pi$
$709$	2478.50	−	4292.89i	0.131286	−	0.227395i	0.924173	+	0.381975i	$0.124756\pi$
$710$	864.000	+	1496.49i	0.0456695	+	0.0791019i
$711$		0			0
$712$	4068.00	−	7045.98i	0.214122	−	0.370870i
$713$	−1587.00			−0.0833571
$714$		0			0
$715$	−35910.0			−1.87826
$716$	2574.00	−	4458.30i	0.134350	−	0.232702i
$717$		0			0
$718$	−3849.00	−	6666.66i	−0.200060	−	0.346515i
$719$	13834.5	−	23962.1i	0.717580	−	1.24288i	−0.244376	−	0.969680i	$-0.578583\pi$
$719$	13834.5	−	23962.1i	0.717580	−	1.24288i	0.961956	−	0.273204i	$-0.0880834\pi$
$720$		0			0
$721$	−8732.50	+	3025.03i	−0.451061	+	0.156252i
$722$	13668.0			0.704529
$723$		0			0
$724$	5348.00	+	9263.01i	0.274526	+	0.475493i
$725$	−2508.00	−	4343.98i	−0.128476	−	0.222526i
$726$		0			0
$727$	−13888.0			−0.708497			−0.354249	−	0.935151i	$-0.615263\pi$
$727$	−13888.0			−0.708497			−0.354249	+	0.935151i	$0.615263\pi$
$728$	−7840.00	−	6789.64i	−0.399134	−	0.345660i
$729$		0			0
$730$	−2817.00	+	4879.19i	−0.142824	+	0.247379i
$731$	−3162.00	−	5476.74i	−0.159987	−	0.277106i
$732$		0			0
$733$	−7121.50	+	12334.8i	−0.358852	+	0.621550i	−0.987769	−	0.155922i	$-0.950165\pi$
$733$	−7121.50	+	12334.8i	−0.358852	+	0.621550i	0.628917	+	0.777472i	$0.283498\pi$
$734$	−12982.0			−0.652826
$735$		0			0
$736$	2208.00			0.110581
$737$	−11941.5	+	20683.3i	−0.596840	+	1.03376i
$738$		0			0
$739$	−18479.5	−	32007.4i	−0.919864	−	1.59325i	−0.799620	−	0.600507i	$-0.794966\pi$
$739$	−18479.5	−	32007.4i	−0.919864	−	1.59325i	−0.120244	−	0.992744i	$-0.538368\pi$
$740$	4554.00	−	7887.76i	0.226228	−	0.391838i
$741$		0			0
$742$	11004.0	+	9529.74i	0.544433	+	0.471493i
$743$	12528.0			0.618584			0.309292	−	0.950967i	$-0.399908\pi$
$743$	12528.0			0.618584			0.309292	+	0.950967i	$0.399908\pi$
$744$		0			0
$745$	−256.500	−	444.271i	−0.0126140	−	0.0218481i
$746$	923.000	+	1598.68i	0.0452995	+	0.0784610i
$747$		0			0
$748$	−11628.0			−0.568398
$749$	19372.5	−	6710.83i	0.945068	−	0.327381i
$750$		0			0
$751$	8883.50	−	15386.7i	0.431643	−	0.747627i	−0.565372	−	0.824836i	$-0.691268\pi$
$751$	8883.50	−	15386.7i	0.431643	−	0.747627i	0.997015	+	0.0772090i	$0.0246009\pi$
$752$	1608.00	+	2785.14i	0.0779757	+	0.135058i
$753$		0			0
$754$	7980.00	−	13821.8i	0.385430	−	0.667585i
$755$	7551.00			0.363985
$756$		0			0
$757$	−28726.0			−1.37921			−0.689606	−	0.724184i	$-0.742216\pi$
$757$	−28726.0			−1.37921			−0.689606	+	0.724184i	$0.742216\pi$
$758$	6344.00	−	10988.1i	0.303990	−	0.526526i
$759$		0			0
$760$	180.000	+	311.769i	0.00859117	+	0.0148803i
$761$	−13234.5	+	22922.8i	−0.630421	+	1.09192i	0.357045	+	0.934087i	$0.383784\pi$
$761$	−13234.5	+	22922.8i	−0.630421	+	1.09192i	−0.987466	+	0.157834i	$0.949549\pi$
$762$		0			0
$763$	−3230.50	+	16786.2i	−0.153279	+	0.796462i
$764$	−16740.0			−0.792712
$765$		0			0
$766$	5007.00	+	8672.38i	0.236175	+	0.409068i
$767$	−7665.00	−	13276.2i	−0.360844	−	0.625000i
$768$		0			0
$769$	5054.00			0.236999			0.118499	−	0.992954i	$-0.462192\pi$
$769$	5054.00			0.236999			0.118499	+	0.992954i	$0.462192\pi$
$770$	−17955.0	+	6219.79i	−0.840329	+	0.291098i
$771$		0			0
$772$	170.000	−	294.449i	0.00792543	−	0.0137273i
$773$	−17782.5	−	30800.2i	−0.827415	−	1.43313i	−0.900059	−	0.435767i	$-0.856477\pi$
$773$	−17782.5	−	30800.2i	−0.827415	−	1.43313i	0.0726439	−	0.997358i	$-0.476856\pi$
$774$		0			0
$775$	506.000	−	876.418i	0.0234530	−	0.0406217i
$776$	14672.0			0.678730
$777$		0			0
$778$	24582.0			1.13279
$779$	−105.000	+	181.865i	−0.00482929	+	0.00836457i
$780$		0			0
$781$	−2736.00	−	4738.89i	−0.125354	−	0.217120i
$782$	3519.00	−	6095.09i	0.160920	−	0.278721i
$783$		0			0
$784$	−5096.00	−	2036.89i	−0.232143	−	0.0927884i
$785$	−25497.0			−1.15927
$786$		0			0
$787$	4314.50	+	7472.93i	0.195420	+	0.338477i	0.947038	−	0.321121i	$-0.104060\pi$
$787$	4314.50	+	7472.93i	0.195420	+	0.338477i	−0.751618	+	0.659598i	$0.770726\pi$
$788$	−780.000	−	1351.00i	−0.0352619	−	0.0610753i
$789$		0			0
$790$	−8298.00			−0.373708
$791$	21588.0	+	18695.8i	0.970393	+	0.840385i
$792$		0			0
$793$	−24815.0	+	42980.8i	−1.11123	+	1.92471i
$794$	887.000	+	1536.33i	0.0396454	+	0.0686679i
$795$		0			0
$796$	5666.00	−	9813.80i	0.252294	−	0.436986i
$797$	−20706.0			−0.920256			−0.460128	−	0.887853i	$-0.652197\pi$
$797$	−20706.0			−0.920256			−0.460128	+	0.887853i	$0.652197\pi$
$798$		0			0
$799$	10251.0			0.453885
$800$	−704.000	+	1219.36i	−0.0311127	+	0.0538888i
$801$		0			0
$802$	−11955.0	−	20706.7i	−0.526366	−	0.911693i
$803$	8920.50	−	15450.8i	0.392027	−	0.679011i
$804$		0			0
$805$	2173.50	−	11293.8i	0.0951625	−	0.494479i
$806$	3220.00			0.140719
$807$		0			0
$808$	1140.00	+	1974.54i	0.0496350	+	0.0859703i
$809$	−8092.50	−	14016.6i	−0.351690	−	0.609145i	0.634856	−	0.772631i	$-0.281060\pi$
$809$	−8092.50	−	14016.6i	−0.351690	−	0.609145i	−0.986546	+	0.163486i	$0.947726\pi$
$810$		0			0
$811$	−11788.0			−0.510398			−0.255199	−	0.966889i	$-0.582141\pi$
$811$	−11788.0			−0.510398			−0.255199	+	0.966889i	$0.582141\pi$
$812$	1596.00	−	8293.06i	0.0689761	−	0.358411i
$813$		0			0
$814$	−14421.0	+	24977.9i	−0.620953	+	1.07552i
$815$	10399.5	+	18012.5i	0.446968	+	0.774171i
$816$		0			0
$817$	310.000	−	536.936i	0.0132748	−	0.0229927i
$818$	6842.00			0.292451
$819$		0			0
$820$	1512.00			0.0643919
$821$	−14896.5	+	25801.5i	−0.633242	+	1.09681i	0.353643	+	0.935380i	$0.384943\pi$
$821$	−14896.5	+	25801.5i	−0.633242	+	1.09681i	−0.986885	+	0.161426i	$0.948391\pi$
$822$		0			0
$823$	−15161.5	−	26260.5i	−0.642159	−	1.11225i	−0.984950	−	0.172840i	$-0.944706\pi$
$823$	−15161.5	−	26260.5i	−0.642159	−	1.11225i	0.342791	−	0.939412i	$-0.388628\pi$
$824$	−1996.00	+	3457.17i	−0.0843859	+	0.146161i
$825$		0			0
$826$	−6132.00	−	5310.47i	−0.258305	−	0.223698i
$827$	−21156.0			−0.889560			−0.444780	−	0.895640i	$-0.646718\pi$
$827$	−21156.0			−0.889560			−0.444780	+	0.895640i	$0.646718\pi$
$828$		0			0
$829$	2634.50	+	4563.09i	0.110374	+	0.191173i	0.915921	−	0.401358i	$-0.131462\pi$
$829$	2634.50	+	4563.09i	0.110374	+	0.191173i	−0.805547	+	0.592532i	$0.798129\pi$
$830$	5292.00	+	9166.01i	0.221311	+	0.383322i
$831$		0			0
$832$	−4480.00			−0.186678
$833$	−13744.5	+	10821.0i	−0.571691	+	0.450090i
$834$		0			0
$835$	5670.00	−	9820.73i	0.234992	−	0.407018i
$836$	−570.000	−	987.269i	−0.0235812	−	0.0408438i
$837$		0			0
$838$	5460.00	−	9457.00i	0.225075	−	0.389841i
$839$	39816.0			1.63838			0.819190	−	0.573522i	$-0.194423\pi$
$839$	39816.0			1.63838			0.819190	+	0.573522i	$0.194423\pi$
$840$		0			0
$841$	−11393.0			−0.467137
$842$	7730.00	−	13388.8i	0.316382	−	0.547989i
$843$		0			0
$844$	248.000	+	429.549i	0.0101144	+	0.0175186i
$845$	−12163.5	+	21067.8i	−0.495192	+	0.857697i
$846$		0			0
$847$	33565.0	−	11627.3i	1.36164	−	0.471685i
$848$	6288.00			0.254635
$849$		0			0
$850$	2244.00	+	3886.72i	0.0905513	+	0.156839i
$851$	−8728.50	−	15118.2i	−0.351597	−	0.608984i
$852$		0			0
$853$	14546.0			0.583875			0.291938	−	0.956437i	$-0.405700\pi$
$853$	14546.0			0.583875			0.291938	+	0.956437i	$0.405700\pi$
$854$	−4963.00	+	25788.5i	−0.198865	+	1.03333i
$855$		0			0
$856$	4428.00	−	7669.52i	0.176806	−	0.306237i
$857$	−15724.5	−	27235.6i	−0.626766	−	1.08559i	−0.988196	−	0.153192i	$-0.951045\pi$
$857$	−15724.5	−	27235.6i	−0.626766	−	1.08559i	0.361430	−	0.932399i	$-0.382289\pi$
$858$		0			0
$859$	12261.5	−	21237.5i	0.487028	−	0.843557i	−0.512861	−	0.858472i	$-0.671414\pi$
$859$	12261.5	−	21237.5i	0.487028	−	0.843557i	0.999889	+	0.0149147i	$0.00474766\pi$
$860$	−4464.00			−0.177001
$861$		0			0
$862$	−22626.0			−0.894019
$863$	−4081.50	+	7069.37i	−0.160992	+	0.278846i	−0.935225	−	0.354055i	$-0.884803\pi$
$863$	−4081.50	+	7069.37i	−0.160992	+	0.278846i	0.774233	+	0.632901i	$0.218136\pi$
$864$		0			0
$865$	14701.5	+	25463.7i	0.577880	+	1.00092i
$866$	4214.00	−	7298.86i	0.165355	−	0.286403i
$867$		0			0
$868$	1610.00	−	557.720i	0.0629573	−	0.0218091i
$869$	26277.0			1.02576
$870$		0			0
$871$	14665.0	+	25400.5i	0.570499	+	0.988133i
$872$	3692.00	+	6394.73i	0.143379	+	0.248341i
$873$		0			0
$874$	690.000			0.0267043
$875$	21294.0	+	18441.1i	0.822707	+	0.712485i
$876$		0			0
$877$	−2183.50	+	3781.93i	−0.0840725	+	0.145618i	−0.904996	−	0.425421i	$-0.860126\pi$
$877$	−2183.50	+	3781.93i	−0.0840725	+	0.145618i	0.820923	+	0.571039i	$0.193459\pi$
$878$	16553.0	+	28670.6i	0.636260	+	1.10204i
$879$		0			0
$880$	−4104.00	+	7108.34i	−0.157211	+	0.272298i
$881$	50190.0			1.91935			0.959673	−	0.281118i	$-0.0907053\pi$
$881$	50190.0			1.91935			0.959673	+	0.281118i	$0.0907053\pi$
$882$		0			0
$883$	12308.0			0.469079			0.234540	−	0.972107i	$-0.424642\pi$
$883$	12308.0			0.469079			0.234540	+	0.972107i	$0.424642\pi$
$884$	−7140.00	+	12366.8i	−0.271656	+	0.470523i
$885$		0			0
$886$	16395.0	+	28397.0i	0.621671	+	1.07677i
$887$	15808.5	−	27381.1i	0.598419	−	1.03649i	−0.394636	−	0.918838i	$-0.629129\pi$
$887$	15808.5	−	27381.1i	0.598419	−	1.03649i	0.993055	−	0.117654i	$-0.0375374\pi$
$888$		0			0
$889$	28784.0	+	24927.7i	1.08592	+	0.940436i
$890$	−18306.0			−0.689459
$891$		0			0
$892$	−112.000	−	193.990i	−0.00420408	−	0.00728168i
$893$	502.500	+	870.356i	0.0188304	+	0.0326152i
$894$		0			0
$895$	−11583.0			−0.432600
$896$	−2240.00	+	775.959i	−0.0835191	+	0.0289319i
$897$		0			0
$898$	15090.0	−	26136.6i	0.560757	−	0.971260i
$899$	1311.00	+	2270.72i	0.0486366	+	0.0842411i
$900$		0			0
$901$	10021.5	−	17357.7i	0.370549	−	0.641810i
$902$	−4788.00			−0.176744
$903$		0			0
$904$	12336.0			0.453860
$905$	12033.0	−	20841.8i	0.441978	−	0.765529i
$906$		0			0
$907$	6762.50	+	11713.0i	0.247569	+	0.428802i	0.962851	−	0.270034i	$-0.0870350\pi$
$907$	6762.50	+	11713.0i	0.247569	+	0.428802i	−0.715282	+	0.698836i	$0.753702\pi$
$908$	−6114.00	+	10589.8i	−0.223458	+	0.387041i
$909$		0			0
$910$	−4410.00	+	22915.0i	−0.160648	+	0.834754i
$911$	19248.0			0.700016			0.350008	−	0.936747i	$-0.386179\pi$
$911$	19248.0			0.700016			0.350008	+	0.936747i	$0.386179\pi$
$912$		0			0
$913$	−16758.0	−	29025.7i	−0.607458	−	1.05215i
$914$	−14785.0	−	25608.4i	−0.535059	−	0.926750i
$915$		0			0
$916$	−3844.00			−0.138656
$917$	−35857.5	+	12421.4i	−1.29130	+	0.447318i
$918$		0			0
$919$	4347.50	−	7530.09i	0.156051	−	0.270288i	−0.777390	−	0.629019i	$-0.783457\pi$
$919$	4347.50	−	7530.09i	0.156051	−	0.270288i	0.933441	+	0.358730i	$0.116790\pi$
$920$	−2484.00	−	4302.41i	−0.0890164	−	0.154181i
$921$		0			0
$922$	−2898.00	+	5019.48i	−0.103515	+	0.179293i
$923$	−6720.00			−0.239644
$924$		0			0
$925$	11132.0			0.395695
$926$	464.000	−	803.672i	0.0164665	−	0.0285208i
$927$		0			0
$928$	−1824.00	−	3159.26i	−0.0645213	−	0.111754i
$929$	9739.50	−	16869.3i	0.343964	−	0.595763i	−0.641201	−	0.767373i	$-0.721563\pi$
$929$	9739.50	−	16869.3i	0.343964	−	0.595763i	0.985165	+	0.171610i	$0.0548968\pi$
$930$		0			0
$931$	−1592.50	−	636.529i	−0.0560602	−	0.0224075i
$932$	11316.0			0.397712
$933$		0			0
$934$	−4233.00	−	7331.77i	−0.148295	−	0.256855i
$935$	13081.5	+	22657.8i	0.457552	+	0.792503i
$936$		0			0
$937$	−12502.0			−0.435883			−0.217942	−	0.975962i	$-0.569934\pi$
$937$	−12502.0			−0.435883			−0.217942	+	0.975962i	$0.569934\pi$
$938$	11732.0	+	10160.2i	0.408383	+	0.353670i
$939$		0			0
$940$	3618.00	−	6266.56i	0.125538	−	0.217439i
$941$	−7996.50	−	13850.3i	−0.277023	−	0.479818i	0.693621	−	0.720340i	$-0.256014\pi$
$941$	−7996.50	−	13850.3i	−0.277023	−	0.479818i	−0.970643	+	0.240523i	$0.922681\pi$
$942$		0			0
$943$	1449.00	−	2509.74i	0.0500381	−	0.0866685i
$944$	−3504.00			−0.120811
$945$		0			0
$946$	14136.0			0.485836
$947$	22000.5	−	38106.0i	0.754932	−	1.30758i	−0.190477	−	0.981692i	$-0.561003\pi$
$947$	22000.5	−	38106.0i	0.754932	−	1.30758i	0.945408	−	0.325888i	$-0.105663\pi$
$948$		0			0
$949$	−10955.0	−	18974.6i	−0.374725	−	0.649043i
$950$	−220.000	+	381.051i	−0.00751341	+	0.0130136i
$951$		0			0
$952$	−1428.00	+	7420.11i	−0.0486153	+	0.252612i
$953$	4002.00			0.136031			0.0680155	−	0.997684i	$-0.478333\pi$
$953$	4002.00			0.136031			0.0680155	+	0.997684i	$0.478333\pi$
$954$		0			0
$955$	18832.5	+	32618.8i	0.638121	+	1.10526i
$956$	−7080.00	−	12262.9i	−0.239523	−	0.414865i
$957$		0			0
$958$	5478.00			0.184745
$959$	−493.500	+	2564.30i	−0.0166173	+	0.0863458i
$960$		0			0
$961$	14631.0	−	25341.6i	0.491121	−	0.850647i
$962$	17710.0	+	30674.6i	0.593548	+	1.02806i
$963$		0			0
$964$	−10462.0	+	18120.7i	−0.349542	+	0.605424i
$965$	−765.000			−0.0255194
$966$		0			0
$967$	10544.0			0.350643			0.175322	−	0.984511i	$-0.443903\pi$
$967$	10544.0			0.350643			0.175322	+	0.984511i	$0.443903\pi$
$968$	7672.00	−	13288.3i	0.254739	−	0.441221i
$969$		0			0
$970$	−16506.0	−	28589.2i	−0.546367	−	0.946335i
$971$	−3091.50	+	5354.64i	−0.102174	+	0.176971i	−0.912580	−	0.408898i	$-0.865913\pi$
$971$	−3091.50	+	5354.64i	−0.102174	+	0.176971i	0.810406	+	0.585869i	$0.199247\pi$
$972$		0			0
$973$	−20776.0	−	17992.5i	−0.684530	−	0.592821i
$974$	−34102.0			−1.12187
$975$		0			0
$976$	5672.00	+	9824.19i	0.186021	+	0.322197i
$977$	1861.50	+	3224.21i	0.0609567	+	0.105580i	0.894893	−	0.446280i	$-0.147252\pi$
$977$	1861.50	+	3224.21i	0.0609567	+	0.105580i	−0.833937	+	0.551860i	$0.813918\pi$
$978$		0			0
$979$	57969.0			1.89244
$980$	1764.00	+	12221.4i	0.0574989	+	0.398364i
$981$		0			0
$982$	4296.00	−	7440.89i	0.139604	−	0.241801i
$983$	−22948.5	−	39748.0i	−0.744602	−	1.28969i	−0.950381	−	0.311089i	$-0.899306\pi$
$983$	−22948.5	−	39748.0i	−0.744602	−	1.28969i	0.205779	−	0.978599i	$-0.434027\pi$
$984$		0			0
$985$	−1755.00	+	3039.75i	−0.0567705	+	0.0983294i
$986$	−11628.0			−0.375569
$987$		0			0
$988$	−1400.00			−0.0450809
$989$	−4278.00	+	7409.71i	−0.137545	+	0.238236i
$990$		0			0
$991$	−3233.50	−	5600.59i	−0.103648	−	0.179524i	0.809537	−	0.587069i	$-0.199718\pi$
$991$	−3233.50	−	5600.59i	−0.103648	−	0.179524i	−0.913185	+	0.407545i	$0.866385\pi$
$992$	368.000	−	637.395i	0.0117782	−	0.0204005i
$993$		0			0
$994$	−3360.00	+	1163.94i	−0.107216	+	0.0371407i
$995$	−25497.0			−0.812371
$996$		0			0
$997$	−11519.5	−	19952.4i	−0.365924	−	0.633799i	0.623000	−	0.782222i	$-0.285914\pi$
$997$	−11519.5	−	19952.4i	−0.365924	−	0.633799i	−0.988924	+	0.148423i	$0.952580\pi$
$998$	3401.00	+	5890.70i	0.107873	+	0.186841i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.g.d.37.1		2
3.2	odd	2		14.4.c.a.9.1	✓	2
7.2	even	3		882.4.a.f.1.1		1
7.3	odd	6		882.4.g.u.361.1		2
7.4	even	3	inner	126.4.g.d.109.1		2
7.5	odd	6		882.4.a.c.1.1		1
7.6	odd	2		882.4.g.u.667.1		2
12.11	even	2		112.4.i.a.65.1		2
15.2	even	4		350.4.j.b.149.1		4
15.8	even	4		350.4.j.b.149.2		4
15.14	odd	2		350.4.e.e.51.1		2
21.2	odd	6		98.4.a.d.1.1		1
21.5	even	6		98.4.a.f.1.1		1
21.11	odd	6		14.4.c.a.11.1	yes	2
21.17	even	6		98.4.c.a.67.1		2
21.20	even	2		98.4.c.a.79.1		2
24.5	odd	2		448.4.i.b.65.1		2
24.11	even	2		448.4.i.e.65.1		2
84.11	even	6		112.4.i.a.81.1		2
84.23	even	6		784.4.a.p.1.1		1
84.47	odd	6		784.4.a.c.1.1		1
105.32	even	12		350.4.j.b.249.2		4
105.44	odd	6		2450.4.a.q.1.1		1
105.53	even	12		350.4.j.b.249.1		4
105.74	odd	6		350.4.e.e.151.1		2
105.89	even	6		2450.4.a.d.1.1		1
168.11	even	6		448.4.i.e.193.1		2
168.53	odd	6		448.4.i.b.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.a.9.1	✓	2	3.2	odd	2
14.4.c.a.11.1	yes	2	21.11	odd	6
98.4.a.d.1.1		1	21.2	odd	6
98.4.a.f.1.1		1	21.5	even	6
98.4.c.a.67.1		2	21.17	even	6
98.4.c.a.79.1		2	21.20	even	2
112.4.i.a.65.1		2	12.11	even	2
112.4.i.a.81.1		2	84.11	even	6
126.4.g.d.37.1		2	1.1	even	1	trivial
126.4.g.d.109.1		2	7.4	even	3	inner
350.4.e.e.51.1		2	15.14	odd	2
350.4.e.e.151.1		2	105.74	odd	6
350.4.j.b.149.1		4	15.2	even	4
350.4.j.b.149.2		4	15.8	even	4
350.4.j.b.249.1		4	105.53	even	12
350.4.j.b.249.2		4	105.32	even	12
448.4.i.b.65.1		2	24.5	odd	2
448.4.i.b.193.1		2	168.53	odd	6
448.4.i.e.65.1		2	24.11	even	2
448.4.i.e.193.1		2	168.11	even	6
784.4.a.c.1.1		1	84.47	odd	6
784.4.a.p.1.1		1	84.23	even	6
882.4.a.c.1.1		1	7.5	odd	6
882.4.a.f.1.1		1	7.2	even	3
882.4.g.u.361.1		2	7.3	odd	6
882.4.g.u.667.1		2	7.6	odd	2
2450.4.a.d.1.1		1	105.89	even	6
2450.4.a.q.1.1		1	105.44	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-4.50000 + 7.79423i) q^{5} +(-14.0000 - 12.1244i) q^{7} -8.00000 q^{8} +(9.00000 + 15.5885i) q^{10} +(-28.5000 - 49.3634i) q^{11} -70.0000 q^{13} +(-35.0000 + 12.1244i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(25.5000 + 44.1673i) q^{17} +(-2.50000 + 4.33013i) q^{19} +36.0000 q^{20} -114.000 q^{22} +(34.5000 - 59.7558i) q^{23} +(22.0000 + 38.1051i) q^{25} +(-70.0000 + 121.244i) q^{26} +(-14.0000 + 72.7461i) q^{28} -114.000 q^{29} +(-11.5000 - 19.9186i) q^{31} +(16.0000 + 27.7128i) q^{32} +102.000 q^{34} +(157.500 - 54.5596i) q^{35} +(126.500 - 219.104i) q^{37} +(5.00000 + 8.66025i) q^{38} +(36.0000 - 62.3538i) q^{40} +42.0000 q^{41} -124.000 q^{43} +(-114.000 + 197.454i) q^{44} +(-69.0000 - 119.512i) q^{46} +(100.500 - 174.071i) q^{47} +(49.0000 + 339.482i) q^{49} +88.0000 q^{50} +(140.000 + 242.487i) q^{52} +(-196.500 - 340.348i) q^{53} +513.000 q^{55} +(112.000 + 96.9948i) q^{56} +(-114.000 + 197.454i) q^{58} +(109.500 + 189.660i) q^{59} +(354.500 - 614.012i) q^{61} -46.0000 q^{62} +64.0000 q^{64} +(315.000 - 545.596i) q^{65} +(-209.500 - 362.865i) q^{67} +(102.000 - 176.669i) q^{68} +(63.0000 - 327.358i) q^{70} +96.0000 q^{71} +(156.500 + 271.066i) q^{73} +(-253.000 - 438.209i) q^{74} +20.0000 q^{76} +(-199.500 + 1036.63i) q^{77} +(-230.500 + 399.238i) q^{79} +(-72.0000 - 124.708i) q^{80} +(42.0000 - 72.7461i) q^{82} +588.000 q^{83} -459.000 q^{85} +(-124.000 + 214.774i) q^{86} +(228.000 + 394.908i) q^{88} +(-508.500 + 880.748i) q^{89} +(980.000 + 848.705i) q^{91} -276.000 q^{92} +(-201.000 - 348.142i) q^{94} +(-22.5000 - 38.9711i) q^{95} -1834.00 q^{97} +(637.000 + 254.611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{4} - 9 q^{5} - 28 q^{7} - 16 q^{8} + 18 q^{10} - 57 q^{11} - 140 q^{13} - 70 q^{14} - 16 q^{16} + 51 q^{17} - 5 q^{19} + 72 q^{20} - 228 q^{22} + 69 q^{23} + 44 q^{25} - 140 q^{26}+ \cdots + 1274 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^4 - 9 * q^5 - 28 * q^7 - 16 * q^8 + 18 * q^10 - 57 * q^11 - 140 * q^13 - 70 * q^14 - 16 * q^16 + 51 * q^17 - 5 * q^19 + 72 * q^20 - 228 * q^22 + 69 * q^23 + 44 * q^25 - 140 * q^26 - 28 * q^28 - 228 * q^29 - 23 * q^31 + 32 * q^32 + 204 * q^34 + 315 * q^35 + 253 * q^37 + 10 * q^38 + 72 * q^40 + 84 * q^41 - 248 * q^43 - 228 * q^44 - 138 * q^46 + 201 * q^47 + 98 * q^49 + 176 * q^50 + 280 * q^52 - 393 * q^53 + 1026 * q^55 + 224 * q^56 - 228 * q^58 + 219 * q^59 + 709 * q^61 - 92 * q^62 + 128 * q^64 + 630 * q^65 - 419 * q^67 + 204 * q^68 + 126 * q^70 + 192 * q^71 + 313 * q^73 - 506 * q^74 + 40 * q^76 - 399 * q^77 - 461 * q^79 - 144 * q^80 + 84 * q^82 + 1176 * q^83 - 918 * q^85 - 248 * q^86 + 456 * q^88 - 1017 * q^89 + 1960 * q^91 - 552 * q^92 - 402 * q^94 - 45 * q^95 - 3668 * q^97 + 1274 * q^98

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