LMFDB - Embedded newform 208.4.w.b.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(17,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("208.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.w (of order $6$, 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:	$12.2723972812$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	208.17
Dual form			208.4.w.b.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{3} -1.73205i q^{5} +(12.0000 - 6.92820i) q^{7} +(11.5000 + 19.9186i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{3} -1.73205i q^{5} +(12.0000 - 6.92820i) q^{7} +(11.5000 + 19.9186i) q^{9} +(-12.0000 - 6.92820i) q^{11} +(45.5000 + 11.2583i) q^{13} +(-3.00000 - 1.73205i) q^{15} +(-58.5000 - 101.325i) q^{17} +(99.0000 - 57.1577i) q^{19} -27.7128i q^{21} +(-39.0000 + 67.5500i) q^{23} +122.000 q^{25} +100.000 q^{27} +(70.5000 - 122.110i) q^{29} -155.885i q^{31} +(-24.0000 + 13.8564i) q^{33} +(-12.0000 - 20.7846i) q^{35} +(-124.500 - 71.8801i) q^{37} +(65.0000 - 67.5500i) q^{39} +(235.500 + 135.966i) q^{41} +(52.0000 + 90.0666i) q^{43} +(34.5000 - 19.9186i) q^{45} -301.377i q^{47} +(-75.5000 + 130.770i) q^{49} -234.000 q^{51} +93.0000 q^{53} +(-12.0000 + 20.7846i) q^{55} -228.631i q^{57} +(246.000 - 142.028i) q^{59} +(-72.5000 - 125.574i) q^{61} +(276.000 + 159.349i) q^{63} +(19.5000 - 78.8083i) q^{65} +(681.000 + 393.176i) q^{67} +(78.0000 + 135.100i) q^{69} +(-915.000 + 528.275i) q^{71} +458.993i q^{73} +(122.000 - 211.310i) q^{75} -192.000 q^{77} -1276.00 q^{79} +(-210.500 + 364.597i) q^{81} +789.815i q^{83} +(-175.500 + 101.325i) q^{85} +(-141.000 - 244.219i) q^{87} +(-846.000 - 488.438i) q^{89} +(624.000 - 180.133i) q^{91} +(-270.000 - 155.885i) q^{93} +(-99.0000 - 171.473i) q^{95} +(174.000 - 100.459i) q^{97} -318.697i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 24 q^{7} + 23 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 24 * q^7 + 23 * q^9	$ 2 q + 2 q^{3} + 24 q^{7} + 23 q^{9} - 24 q^{11} + 91 q^{13} - 6 q^{15} - 117 q^{17} + 198 q^{19} - 78 q^{23} + 244 q^{25} + 200 q^{27} + 141 q^{29} - 48 q^{33} - 24 q^{35} - 249 q^{37} + 130 q^{39} + 471 q^{41} + 104 q^{43} + 69 q^{45} - 151 q^{49} - 468 q^{51} + 186 q^{53} - 24 q^{55} + 492 q^{59} - 145 q^{61} + 552 q^{63} + 39 q^{65} + 1362 q^{67} + 156 q^{69} - 1830 q^{71} + 244 q^{75} - 384 q^{77} - 2552 q^{79} - 421 q^{81} - 351 q^{85} - 282 q^{87} - 1692 q^{89} + 1248 q^{91} - 540 q^{93} - 198 q^{95} + 348 q^{97}+O(q^{100}) $ 2 * q + 2 * q^3 + 24 * q^7 + 23 * q^9 - 24 * q^11 + 91 * q^13 - 6 * q^15 - 117 * q^17 + 198 * q^19 - 78 * q^23 + 244 * q^25 + 200 * q^27 + 141 * q^29 - 48 * q^33 - 24 * q^35 - 249 * q^37 + 130 * q^39 + 471 * q^41 + 104 * q^43 + 69 * q^45 - 151 * q^49 - 468 * q^51 + 186 * q^53 - 24 * q^55 + 492 * q^59 - 145 * q^61 + 552 * q^63 + 39 * q^65 + 1362 * q^67 + 156 * q^69 - 1830 * q^71 + 244 * q^75 - 384 * q^77 - 2552 * q^79 - 421 * q^81 - 351 * q^85 - 282 * q^87 - 1692 * q^89 + 1248 * q^91 - 540 * q^93 - 198 * q^95 + 348 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	1.00000	−	1.73205i	0.192450	−	0.333333i	−0.753612	−	0.657320i	$-0.771690\pi$
$3$	1.00000	−	1.73205i	0.192450	−	0.333333i	0.946062	+	0.323987i	$0.105023\pi$
$4$		0			0
$5$		−	1.73205i		−	0.154919i	−0.996995	−	0.0774597i	$-0.975319\pi$
$5$		−	1.73205i		−	0.154919i	0.996995	−	0.0774597i	$-0.0246809\pi$
$6$		0			0
$7$	12.0000	−	6.92820i	0.647939	−	0.374088i	−0.139727	−	0.990190i	$-0.544623\pi$
$7$	12.0000	−	6.92820i	0.647939	−	0.374088i	0.787666	+	0.616102i	$0.211289\pi$
$8$		0			0
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$		0			0
$11$	−12.0000	−	6.92820i	−0.328921	−	0.189903i	0.326441	−	0.945218i	$-0.394151\pi$
$11$	−12.0000	−	6.92820i	−0.328921	−	0.189903i	−0.655362	+	0.755315i	$0.727484\pi$
$12$		0			0
$13$	45.5000	+	11.2583i	0.970725	+	0.240192i
$13$	45.5000	+	11.2583i	0.970725	+	0.240192i
$14$		0			0
$15$	−3.00000	−	1.73205i	−0.0516398	−	0.0298142i
$16$		0			0
$17$	−58.5000	−	101.325i	−0.834608	−	1.44558i	−0.894349	−	0.447369i	$-0.852361\pi$
$17$	−58.5000	−	101.325i	−0.834608	−	1.44558i	0.0597414	−	0.998214i	$-0.480972\pi$
$18$		0			0
$19$	99.0000	−	57.1577i	1.19538	−	0.690151i	0.235856	−	0.971788i	$-0.424211\pi$
$19$	99.0000	−	57.1577i	1.19538	−	0.690151i	0.959521	+	0.281637i	$0.0908774\pi$
$20$		0			0
$21$		−	27.7128i		−	0.287973i
$22$		0			0
$23$	−39.0000	+	67.5500i	−0.353568	+	0.612398i	−0.986872	−	0.161506i	$-0.948365\pi$
$23$	−39.0000	+	67.5500i	−0.353568	+	0.612398i	0.633304	+	0.773903i	$0.281698\pi$
$24$		0			0
$25$	122.000			0.976000
$26$		0			0
$27$	100.000			0.712778
$28$		0			0
$29$	70.5000	−	122.110i	0.451432	−	0.781903i	−0.547043	−	0.837104i	$-0.684247\pi$
$29$	70.5000	−	122.110i	0.451432	−	0.781903i	0.998475	+	0.0552014i	$0.0175801\pi$
$30$		0			0
$31$		−	155.885i		−	0.903151i	−0.892233	−	0.451576i	$-0.850862\pi$
$31$		−	155.885i		−	0.903151i	0.892233	−	0.451576i	$-0.149138\pi$
$32$		0			0
$33$	−24.0000	+	13.8564i	−0.126602	+	0.0730937i
$34$		0			0
$35$	−12.0000	−	20.7846i	−0.0579534	−	0.100378i
$36$		0			0
$37$	−124.500	−	71.8801i	−0.553180	−	0.319379i	0.197223	−	0.980359i	$-0.436808\pi$
$37$	−124.500	−	71.8801i	−0.553180	−	0.319379i	−0.750404	+	0.660980i	$0.770141\pi$
$38$		0			0
$39$	65.0000	−	67.5500i	0.266880	−	0.277350i
$40$		0			0
$41$	235.500	+	135.966i	0.897047	+	0.517910i	0.876241	−	0.481873i	$-0.160043\pi$
$41$	235.500	+	135.966i	0.897047	+	0.517910i	0.0208059	+	0.999784i	$0.493377\pi$
$42$		0			0
$43$	52.0000	+	90.0666i	0.184417	+	0.319419i	0.943380	−	0.331714i	$-0.107627\pi$
$43$	52.0000	+	90.0666i	0.184417	+	0.319419i	−0.758963	+	0.651134i	$0.774294\pi$
$44$		0			0
$45$	34.5000	−	19.9186i	0.114288	−	0.0659842i
$46$		0			0
$47$		−	301.377i		−	0.935326i	−0.883907	−	0.467663i	$-0.845096\pi$
$47$		−	301.377i		−	0.935326i	0.883907	−	0.467663i	$-0.154904\pi$
$48$		0			0
$49$	−75.5000	+	130.770i	−0.220117	+	0.381253i
$50$		0			0
$51$	−234.000			−0.642481
$52$		0			0
$53$	93.0000			0.241029			0.120514	−	0.992712i	$-0.461546\pi$
$53$	93.0000			0.241029			0.120514	+	0.992712i	$0.461546\pi$
$54$		0			0
$55$	−12.0000	+	20.7846i	−0.0294196	+	0.0509563i
$56$		0			0
$57$		−	228.631i		−	0.531279i
$58$		0			0
$59$	246.000	−	142.028i	0.542822	−	0.313398i	−0.203400	−	0.979096i	$-0.565199\pi$
$59$	246.000	−	142.028i	0.542822	−	0.313398i	0.746222	+	0.665698i	$0.231866\pi$
$60$		0			0
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	0.779852	−	0.625964i	$-0.215294\pi$
$61$	−72.5000	−	125.574i	−0.152175	−	0.263575i	−0.932027	+	0.362389i	$0.881961\pi$
$62$		0			0
$63$	276.000	+	159.349i	0.551948	+	0.318667i
$64$		0			0
$65$	19.5000	−	78.8083i	0.0372104	−	0.150384i
$66$		0			0
$67$	681.000	+	393.176i	1.24175	+	0.716926i	0.969451	−	0.245286i	$-0.0788819\pi$
$67$	681.000	+	393.176i	1.24175	+	0.716926i	0.272301	+	0.962212i	$0.412215\pi$
$68$		0			0
$69$	78.0000	+	135.100i	0.136088	+	0.235712i
$70$		0			0
$71$	−915.000	+	528.275i	−1.52944	+	0.883025i	−0.530059	+	0.847961i	$0.677830\pi$
$71$	−915.000	+	528.275i	−1.52944	+	0.883025i	−0.999385	+	0.0350641i	$0.988836\pi$
$72$		0			0
$73$			458.993i			0.735906i	0.929844	+	0.367953i	$0.119941\pi$
$73$			458.993i			0.735906i	−0.929844	+	0.367953i	$0.880059\pi$
$74$		0			0
$75$	122.000	−	211.310i	0.187831	−	0.325333i
$76$		0			0
$77$	−192.000			−0.284161
$78$		0			0
$79$	−1276.00			−1.81723			−0.908615	−	0.417634i	$-0.862859\pi$
$79$	−1276.00			−1.81723			−0.908615	+	0.417634i	$0.862859\pi$
$80$		0			0
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$		0			0
$83$			789.815i			1.04450i	0.852793	+	0.522250i	$0.174907\pi$
$83$			789.815i			1.04450i	−0.852793	+	0.522250i	$0.825093\pi$
$84$		0			0
$85$	−175.500	+	101.325i	−0.223949	+	0.129297i
$86$		0			0
$87$	−141.000	−	244.219i	−0.173756	−	0.300955i
$88$		0			0
$89$	−846.000	−	488.438i	−1.00759	−	0.581734i	−0.0971073	−	0.995274i	$-0.530959\pi$
$89$	−846.000	−	488.438i	−1.00759	−	0.581734i	−0.910486	+	0.413540i	$0.864292\pi$
$90$		0			0
$91$	624.000	−	180.133i	0.718824	−	0.207507i
$92$		0			0
$93$	−270.000	−	155.885i	−0.301050	−	0.173812i
$94$		0			0
$95$	−99.0000	−	171.473i	−0.106918	−	0.185187i
$96$		0			0
$97$	174.000	−	100.459i	0.182134	−	0.105155i	−0.406161	−	0.913802i	$-0.633133\pi$
$97$	174.000	−	100.459i	0.182134	−	0.105155i	0.588295	+	0.808646i	$0.299799\pi$
$98$		0			0
$99$		−	318.697i		−	0.323538i
$100$		0			0
$101$	−214.500	+	371.525i	−0.211322	+	0.366021i	−0.952129	−	0.305698i	$-0.901110\pi$
$101$	−214.500	+	371.525i	−0.211322	+	0.366021i	0.740806	+	0.671719i	$0.234444\pi$
$102$		0			0
$103$	−182.000			−0.174107			−0.0870534	−	0.996204i	$-0.527745\pi$
$103$	−182.000			−0.174107			−0.0870534	+	0.996204i	$0.527745\pi$
$104$		0			0
$105$	−48.0000			−0.0446126
$106$		0			0
$107$	−753.000	+	1304.23i	−0.680330	+	1.17837i	0.294551	+	0.955636i	$0.404830\pi$
$107$	−753.000	+	1304.23i	−0.680330	+	1.17837i	−0.974880	+	0.222729i	$0.928503\pi$
$108$		0			0
$109$			1551.92i			1.36373i	0.731477	+	0.681866i	$0.238831\pi$
$109$			1551.92i			1.36373i	−0.731477	+	0.681866i	$0.761169\pi$
$110$		0			0
$111$	−249.000	+	143.760i	−0.212919	+	0.122929i
$112$		0			0
$113$	343.500	+	594.959i	0.285962	+	0.495302i	0.972842	−	0.231470i	$-0.0743534\pi$
$113$	343.500	+	594.959i	0.285962	+	0.495302i	−0.686880	+	0.726771i	$0.741020\pi$
$114$		0			0
$115$	117.000	+	67.5500i	0.0948722	+	0.0547745i
$116$		0			0
$117$	299.000	+	1035.77i	0.236261	+	0.818433i
$118$		0			0
$119$	−1404.00	−	810.600i	−1.08155	−	0.624433i
$120$		0			0
$121$	−569.500	−	986.403i	−0.427874	−	0.741099i
$122$		0			0
$123$	471.000	−	271.932i	0.345273	−	0.199344i
$124$		0			0
$125$		−	427.817i		−	0.306121i
$126$		0			0
$127$	143.000	−	247.683i	0.0999149	−	0.173058i	−0.811734	−	0.584027i	$-0.801476\pi$
$127$	143.000	−	247.683i	0.0999149	−	0.173058i	0.911649	+	0.410969i	$0.134810\pi$
$128$		0			0
$129$	208.000			0.141964
$130$		0			0
$131$	1974.00			1.31656			0.658279	−	0.752774i	$-0.271285\pi$
$131$	1974.00			1.31656			0.658279	+	0.752774i	$0.271285\pi$
$132$		0			0
$133$	792.000	−	1371.78i	0.516354	−	0.894352i
$134$		0			0
$135$		−	173.205i		−	0.110423i
$136$		0			0
$137$	−733.500	+	423.486i	−0.457424	+	0.264094i	−0.710961	−	0.703232i	$-0.751740\pi$
$137$	−733.500	+	423.486i	−0.457424	+	0.264094i	0.253536	+	0.967326i	$0.418406\pi$
$138$		0			0
$139$	118.000	+	204.382i	0.0720045	+	0.124716i	0.899780	−	0.436344i	$-0.143727\pi$
$139$	118.000	+	204.382i	0.0720045	+	0.124716i	−0.827775	+	0.561060i	$0.810394\pi$
$140$		0			0
$141$	−522.000	−	301.377i	−0.311775	−	0.180004i
$142$		0			0
$143$	−468.000	−	450.333i	−0.273679	−	0.263348i
$144$		0			0
$145$	−211.500	−	122.110i	−0.121132	−	0.0699355i
$146$		0			0
$147$	151.000	+	261.540i	0.0847229	+	0.146744i
$148$		0			0
$149$	−40.5000	+	23.3827i	−0.0222677	+	0.0128563i	−0.511093	−	0.859526i	$-0.670759\pi$
$149$	−40.5000	+	23.3827i	−0.0222677	+	0.0128563i	0.488825	+	0.872382i	$0.337426\pi$
$150$		0			0
$151$			1770.16i			0.953995i	0.878905	+	0.476998i	$0.158275\pi$
$151$			1770.16i			0.953995i	−0.878905	+	0.476998i	$0.841725\pi$
$152$		0			0
$153$	1345.50	−	2330.47i	0.710962	−	1.23142i
$154$		0			0
$155$	−270.000			−0.139916
$156$		0			0
$157$	1211.00			0.615594			0.307797	−	0.951452i	$-0.400408\pi$
$157$	1211.00			0.615594			0.307797	+	0.951452i	$0.400408\pi$
$158$		0			0
$159$	93.0000	−	161.081i	0.0463860	−	0.0803430i
$160$		0			0
$161$			1080.80i			0.529062i
$162$		0			0
$163$	870.000	−	502.295i	0.418059	−	0.241367i	−0.276187	−	0.961104i	$-0.589071\pi$
$163$	870.000	−	502.295i	0.418059	−	0.241367i	0.694247	+	0.719737i	$0.255738\pi$
$164$		0			0
$165$	24.0000	+	41.5692i	0.0113236	+	0.0196131i
$166$		0			0
$167$	−792.000	−	457.261i	−0.366987	−	0.211880i	0.305154	−	0.952303i	$-0.401292\pi$
$167$	−792.000	−	457.261i	−0.366987	−	0.211880i	−0.672141	+	0.740423i	$0.734625\pi$
$168$		0			0
$169$	1943.50	+	1024.51i	0.884615	+	0.466321i
$170$		0			0
$171$	2277.00	+	1314.63i	1.01828	+	0.587906i
$172$		0			0
$173$	−1287.00	−	2229.15i	−0.565600	−	0.979648i	−0.996994	−	0.0774841i	$-0.975311\pi$
$173$	−1287.00	−	2229.15i	−0.565600	−	0.979648i	0.431394	−	0.902164i	$-0.358022\pi$
$174$		0			0
$175$	1464.00	−	845.241i	0.632389	−	0.365110i
$176$		0			0
$177$		−	568.113i		−	0.241254i
$178$		0			0
$179$	1872.00	−	3242.40i	0.781675	−	1.35390i	−0.149290	−	0.988793i	$-0.547699\pi$
$179$	1872.00	−	3242.40i	0.781675	−	1.35390i	0.930965	−	0.365108i	$-0.118968\pi$
$180$		0			0
$181$	−637.000			−0.261590			−0.130795	−	0.991409i	$-0.541753\pi$
$181$	−637.000			−0.261590			−0.130795	+	0.991409i	$0.541753\pi$
$182$		0			0
$183$	−290.000			−0.117144
$184$		0			0
$185$	−124.500	+	215.640i	−0.0494780	+	0.0856983i
$186$		0			0
$187$			1621.20i			0.633978i
$188$		0			0
$189$	1200.00	−	692.820i	0.461837	−	0.266642i
$190$		0			0
$191$	−1299.00	−	2249.93i	−0.492106	−	0.852353i	0.507852	−	0.861444i	$-0.330440\pi$
$191$	−1299.00	−	2249.93i	−0.492106	−	0.852353i	−0.999959	+	0.00909077i	$0.997106\pi$
$192$		0			0
$193$	967.500	+	558.586i	0.360840	+	0.208331i	0.669449	−	0.742858i	$-0.266530\pi$
$193$	967.500	+	558.586i	0.360840	+	0.208331i	−0.308609	+	0.951189i	$0.599863\pi$
$194$		0			0
$195$	−117.000	−	112.583i	−0.0429669	−	0.0413449i
$196$		0			0
$197$	1776.00	+	1025.37i	0.642308	+	0.370837i	0.785503	−	0.618858i	$-0.212404\pi$
$197$	1776.00	+	1025.37i	0.642308	+	0.370837i	−0.143195	+	0.989695i	$0.545738\pi$
$198$		0			0
$199$	−1261.00	−	2184.12i	−0.449196	−	0.778030i	0.549138	−	0.835732i	$-0.314956\pi$
$199$	−1261.00	−	2184.12i	−0.449196	−	0.778030i	−0.998334	+	0.0577019i	$0.981623\pi$
$200$		0			0
$201$	1362.00	−	786.351i	0.477951	−	0.275945i
$202$		0			0
$203$		−	1953.75i		−	0.675500i
$204$		0			0
$205$	235.500	−	407.898i	0.0802343	−	0.138970i
$206$		0			0
$207$	−1794.00			−0.602375
$208$		0			0
$209$	−1584.00			−0.524247
$210$		0			0
$211$	521.000	−	902.398i	0.169986	−	0.294425i	−0.768428	−	0.639936i	$-0.778961\pi$
$211$	521.000	−	902.398i	0.169986	−	0.294425i	0.938415	+	0.345511i	$0.112294\pi$
$212$		0			0
$213$			2113.10i			0.679753i
$214$		0			0
$215$	156.000	−	90.0666i	0.0494842	−	0.0285697i
$216$		0			0
$217$	−1080.00	−	1870.61i	−0.337858	−	0.585187i
$218$		0			0
$219$	795.000	+	458.993i	0.245302	+	0.141625i
$220$		0			0
$221$	−1521.00	−	5268.90i	−0.462957	−	1.60373i
$222$		0			0
$223$	2085.00	+	1203.78i	0.626107	+	0.361483i	0.779243	−	0.626722i	$-0.215604\pi$
$223$	2085.00	+	1203.78i	0.626107	+	0.361483i	−0.153136	+	0.988205i	$0.548937\pi$
$224$		0			0
$225$	1403.00	+	2430.07i	0.415704	+	0.720020i
$226$		0			0
$227$	−2085.00	+	1203.78i	−0.609631	+	0.351971i	−0.772821	−	0.634624i	$-0.781155\pi$
$227$	−2085.00	+	1203.78i	−0.609631	+	0.351971i	0.163190	+	0.986595i	$0.447822\pi$
$228$		0			0
$229$			2508.01i			0.723729i	0.932231	+	0.361864i	$0.117860\pi$
$229$			2508.01i			0.723729i	−0.932231	+	0.361864i	$0.882140\pi$
$230$		0			0
$231$	−192.000	+	332.554i	−0.0546869	+	0.0947205i
$232$		0			0
$233$	−5850.00			−1.64483			−0.822417	−	0.568885i	$-0.807375\pi$
$233$	−5850.00			−1.64483			−0.822417	+	0.568885i	$0.807375\pi$
$234$		0			0
$235$	−522.000			−0.144900
$236$		0			0
$237$	−1276.00	+	2210.10i	−0.349726	+	0.605744i
$238$		0			0
$239$			5383.21i			1.45695i	0.685072	+	0.728475i	$0.259771\pi$
$239$			5383.21i			1.45695i	−0.685072	+	0.728475i	$0.740229\pi$
$240$		0			0
$241$	4258.50	−	2458.65i	1.13823	−	0.657159i	0.192240	−	0.981348i	$-0.438425\pi$
$241$	4258.50	−	2458.65i	1.13823	−	0.657159i	0.945992	+	0.324189i	$0.105091\pi$
$242$		0			0
$243$	1771.00	+	3067.46i	0.467530	+	0.809785i
$244$		0			0
$245$	226.500	+	130.770i	0.0590635	+	0.0341003i
$246$		0			0
$247$	5148.00	−	1486.10i	1.32615	−	0.382827i
$248$		0			0
$249$	1368.00	+	789.815i	0.348167	+	0.201014i
$250$		0			0
$251$	−1989.00	−	3445.05i	−0.500178	−	0.866333i	−1.00000		0.000205037i	$-0.999935\pi$
$251$	−1989.00	−	3445.05i	−0.500178	−	0.866333i	0.499822	−	0.866128i	$-0.333399\pi$
$252$		0			0
$253$	936.000	−	540.400i	0.232592	−	0.134287i
$254$		0			0
$255$			405.300i			0.0995328i
$256$		0			0
$257$	−1033.50	+	1790.07i	−0.250848	+	0.434482i	−0.963760	−	0.266772i	$-0.914043\pi$
$257$	−1033.50	+	1790.07i	−0.250848	+	0.434482i	0.712911	+	0.701254i	$0.247376\pi$
$258$		0			0
$259$	−1992.00			−0.477903
$260$		0			0
$261$	3243.00			0.769106
$262$		0			0
$263$	−1026.00	+	1777.08i	−0.240555	+	0.416653i	−0.960872	−	0.276991i	$-0.910663\pi$
$263$	−1026.00	+	1777.08i	−0.240555	+	0.416653i	0.720318	+	0.693644i	$0.243996\pi$
$264$		0			0
$265$		−	161.081i		−	0.0373400i
$266$		0			0
$267$	−1692.00	+	976.877i	−0.387823	+	0.223910i
$268$		0			0
$269$	−1665.00	−	2883.86i	−0.377386	−	0.653652i	0.613295	−	0.789854i	$-0.289844\pi$
$269$	−1665.00	−	2883.86i	−0.377386	−	0.653652i	−0.990681	+	0.136202i	$0.956510\pi$
$270$		0			0
$271$	−2430.00	−	1402.96i	−0.544694	−	0.314479i	0.202285	−	0.979327i	$-0.435163\pi$
$271$	−2430.00	−	1402.96i	−0.544694	−	0.314479i	−0.746979	+	0.664848i	$0.768496\pi$
$272$		0			0
$273$	312.000	−	1260.93i	0.0691689	−	0.279543i
$274$		0			0
$275$	−1464.00	−	845.241i	−0.321027	−	0.185345i
$276$		0			0
$277$	−188.500	−	326.492i	−0.0408876	−	0.0708194i	0.844857	−	0.534992i	$-0.179685\pi$
$277$	−188.500	−	326.492i	−0.0408876	−	0.0708194i	−0.885745	+	0.464172i	$0.846352\pi$
$278$		0			0
$279$	3105.00	−	1792.67i	0.666278	−	0.384676i
$280$		0			0
$281$		−	36.3731i		−	0.00772183i	−0.999993	−	0.00386092i	$-0.998771\pi$
$281$		−	36.3731i		−	0.00772183i	0.999993	−	0.00386092i	$-0.00122897\pi$
$282$		0			0
$283$	−3562.00	+	6169.56i	−0.748194	+	1.29591i	0.200493	+	0.979695i	$0.435745\pi$
$283$	−3562.00	+	6169.56i	−0.748194	+	1.29591i	−0.948688	+	0.316215i	$0.897588\pi$
$284$		0			0
$285$	−396.000			−0.0823053
$286$		0			0
$287$	3768.00			0.774976
$288$		0			0
$289$	−4388.00	+	7600.24i	−0.893141	+	1.54696i
$290$		0			0
$291$		−	401.836i		−	0.0809486i
$292$		0			0
$293$	−7207.50	+	4161.25i	−1.43709	+	0.829703i	−0.997646	−	0.0685685i	$-0.978157\pi$
$293$	−7207.50	+	4161.25i	−1.43709	+	0.829703i	−0.439441	+	0.898271i	$0.644823\pi$
$294$		0			0
$295$	−246.000	−	426.084i	−0.0485514	−	0.0840936i
$296$		0			0
$297$	−1200.00	−	692.820i	−0.234448	−	0.135359i
$298$		0			0
$299$	−2535.00	+	2634.45i	−0.490310	+	0.509546i
$300$		0			0
$301$	1248.00	+	720.533i	0.238982	+	0.137976i
$302$		0			0
$303$	429.000	+	743.050i	0.0813380	+	0.140882i
$304$		0			0
$305$	−217.500	+	125.574i	−0.0408328	+	0.0235748i
$306$		0			0
$307$			2220.49i			0.412801i	0.978468	+	0.206401i	$0.0661750\pi$
$307$			2220.49i			0.412801i	−0.978468	+	0.206401i	$0.933825\pi$
$308$		0			0
$309$	−182.000	+	315.233i	−0.0335069	+	0.0580356i
$310$		0			0
$311$	−4914.00			−0.895972			−0.447986	−	0.894041i	$-0.647859\pi$
$311$	−4914.00			−0.895972			−0.447986	+	0.894041i	$0.647859\pi$
$312$		0			0
$313$	−518.000			−0.0935434			−0.0467717	−	0.998906i	$-0.514893\pi$
$313$	−518.000			−0.0935434			−0.0467717	+	0.998906i	$0.514893\pi$
$314$		0			0
$315$	276.000	−	478.046i	0.0493677	−	0.0855074i
$316$		0			0
$317$			3916.17i			0.693861i	0.937891	+	0.346930i	$0.112776\pi$
$317$			3916.17i			0.693861i	−0.937891	+	0.346930i	$0.887224\pi$
$318$		0			0
$319$	−1692.00	+	976.877i	−0.296971	+	0.171456i
$320$		0			0
$321$	1506.00	+	2608.47i	0.261859	+	0.453553i
$322$		0			0
$323$	−11583.0	−	6687.45i	−1.99534	−	1.15201i
$324$		0			0
$325$	5551.00	+	1373.52i	0.947428	+	0.234428i
$326$		0			0
$327$	2688.00	+	1551.92i	0.454577	+	0.262450i
$328$		0			0
$329$	−2088.00	−	3616.52i	−0.349894	−	0.606034i
$330$		0			0
$331$	6456.00	−	3727.37i	1.07207	−	0.618958i	0.143321	−	0.989676i	$-0.454222\pi$
$331$	6456.00	−	3727.37i	1.07207	−	0.618958i	0.928745	+	0.370719i	$0.120889\pi$
$332$		0			0
$333$		−	3306.48i		−	0.544127i
$334$		0			0
$335$	681.000	−	1179.53i	0.111066	−	0.192371i
$336$		0			0
$337$	−3575.00			−0.577871			−0.288936	−	0.957349i	$-0.593301\pi$
$337$	−3575.00			−0.577871			−0.288936	+	0.957349i	$0.593301\pi$
$338$		0			0
$339$	1374.00			0.220134
$340$		0			0
$341$	−1080.00	+	1870.61i	−0.171511	+	0.297066i
$342$		0			0
$343$			6845.06i			1.07755i
$344$		0			0
$345$	234.000	−	135.100i	0.0365163	−	0.0210827i
$346$		0			0
$347$	−3483.00	−	6032.73i	−0.538839	−	0.933297i	−0.998967	−	0.0454442i	$-0.985530\pi$
$347$	−3483.00	−	6032.73i	−0.538839	−	0.933297i	0.460128	−	0.887853i	$-0.347804\pi$
$348$		0			0
$349$	−5760.00	−	3325.54i	−0.883455	−	0.510063i	−0.0116588	−	0.999932i	$-0.503711\pi$
$349$	−5760.00	−	3325.54i	−0.883455	−	0.510063i	−0.871796	+	0.489869i	$0.837045\pi$
$350$		0			0
$351$	4550.00	+	1125.83i	0.691912	+	0.171204i
$352$		0			0
$353$	4876.50	+	2815.45i	0.735269	+	0.424508i	0.820347	−	0.571867i	$-0.193781\pi$
$353$	4876.50	+	2815.45i	0.735269	+	0.424508i	−0.0850777	+	0.996374i	$0.527114\pi$
$354$		0			0
$355$	915.000	+	1584.83i	0.136798	+	0.236940i
$356$		0			0
$357$	−2808.00	+	1621.20i	−0.416289	+	0.240344i
$358$		0			0
$359$			7129.12i			1.04808i	0.851694	+	0.524040i	$0.175576\pi$
$359$			7129.12i			1.04808i	−0.851694	+	0.524040i	$0.824424\pi$
$360$		0			0
$361$	3104.50	−	5377.15i	0.452617	−	0.783956i
$362$		0			0
$363$	−2278.00			−0.329377
$364$		0			0
$365$	795.000			0.114006
$366$		0			0
$367$	1.00000	−	1.73205i	0.000142233	−	0.000246355i	−0.865954	−	0.500123i	$-0.833288\pi$
$367$	1.00000	−	1.73205i	0.000142233	−	0.000246355i	0.866097	+	0.499877i	$0.166621\pi$
$368$		0			0
$369$			6254.44i			0.882366i
$370$		0			0
$371$	1116.00	−	644.323i	0.156172	−	0.0901660i
$372$		0			0
$373$	−1749.50	−	3030.22i	−0.242857	−	0.420641i	0.718670	−	0.695351i	$-0.244751\pi$
$373$	−1749.50	−	3030.22i	−0.242857	−	0.420641i	−0.961527	+	0.274711i	$0.911418\pi$
$374$		0			0
$375$	−741.000	−	427.817i	−0.102040	−	0.0589129i
$376$		0			0
$377$	4582.50	−	4762.27i	0.626023	−	0.650582i
$378$		0			0
$379$	−4779.00	−	2759.16i	−0.647706	−	0.373953i	0.139871	−	0.990170i	$-0.455331\pi$
$379$	−4779.00	−	2759.16i	−0.647706	−	0.373953i	−0.787577	+	0.616216i	$0.788665\pi$
$380$		0			0
$381$	−286.000	−	495.367i	−0.0384573	−	0.0666100i
$382$		0			0
$383$	6378.00	−	3682.34i	0.850915	−	0.491276i	−0.0100443	−	0.999950i	$-0.503197\pi$
$383$	6378.00	−	3682.34i	0.850915	−	0.491276i	0.860960	+	0.508673i	$0.169864\pi$
$384$		0			0
$385$			332.554i			0.0440221i
$386$		0			0
$387$	−1196.00	+	2071.53i	−0.157096	+	0.272098i
$388$		0			0
$389$	−1209.00			−0.157580			−0.0787901	−	0.996891i	$-0.525106\pi$
$389$	−1209.00			−0.157580			−0.0787901	+	0.996891i	$0.525106\pi$
$390$		0			0
$391$	9126.00			1.18036
$392$		0			0
$393$	1974.00	−	3419.07i	0.253372	−	0.438853i
$394$		0			0
$395$			2210.10i			0.281524i
$396$		0			0
$397$	10128.0	−	5847.40i	1.28038	−	0.739226i	0.303460	−	0.952844i	$-0.401858\pi$
$397$	10128.0	−	5847.40i	1.28038	−	0.739226i	0.976917	+	0.213618i	$0.0685248\pi$
$398$		0			0
$399$	−1584.00	−	2743.57i	−0.198745	−	0.344236i
$400$		0			0
$401$	−2581.50	−	1490.43i	−0.321481	−	0.185607i	0.330571	−	0.943781i	$-0.392759\pi$
$401$	−2581.50	−	1490.43i	−0.321481	−	0.185607i	−0.652053	+	0.758174i	$0.726092\pi$
$402$		0			0
$403$	1755.00	−	7092.75i	0.216930	−	0.876712i
$404$		0			0
$405$	631.500	+	364.597i	0.0774802	+	0.0447332i
$406$		0			0
$407$	996.000	+	1725.12i	0.121302	+	0.210101i
$408$		0			0
$409$	37.5000	−	21.6506i	0.00453363	−	0.00261749i	−0.497731	−	0.867331i	$-0.665833\pi$
$409$	37.5000	−	21.6506i	0.00453363	−	0.00261749i	0.502265	+	0.864714i	$0.332500\pi$
$410$		0			0
$411$			1693.95i			0.203300i
$412$		0			0
$413$	1968.00	−	3408.68i	0.234477	−	0.406126i
$414$		0			0
$415$	1368.00			0.161813
$416$		0			0
$417$	472.000			0.0554291
$418$		0			0
$419$	−4731.00	+	8194.33i	−0.551610	+	0.955416i	0.446549	+	0.894759i	$0.352653\pi$
$419$	−4731.00	+	8194.33i	−0.551610	+	0.955416i	−0.998159	+	0.0606569i	$0.980680\pi$
$420$		0			0
$421$			7068.50i			0.818284i	0.912471	+	0.409142i	$0.134172\pi$
$421$			7068.50i			0.818284i	−0.912471	+	0.409142i	$0.865828\pi$
$422$		0			0
$423$	6003.00	−	3465.83i	0.690014	−	0.398380i
$424$		0			0
$425$	−7137.00	−	12361.6i	−0.814577	−	1.41089i
$426$		0			0
$427$	−1740.00	−	1004.59i	−0.197200	−	0.113854i
$428$		0			0
$429$	−1248.00	+	360.267i	−0.140452	+	0.0405451i
$430$		0			0
$431$	8598.00	+	4964.06i	0.960907	+	0.554780i	0.896452	−	0.443140i	$-0.146136\pi$
$431$	8598.00	+	4964.06i	0.960907	+	0.554780i	0.0644552	+	0.997921i	$0.479469\pi$
$432$		0			0
$433$	3308.50	+	5730.49i	0.367197	+	0.636004i	0.989126	−	0.147070i	$-0.0469841\pi$
$433$	3308.50	+	5730.49i	0.367197	+	0.636004i	−0.621929	+	0.783074i	$0.713651\pi$
$434$		0			0
$435$	−423.000	+	244.219i	−0.0466237	+	0.0269182i
$436$		0			0
$437$			8916.60i			0.976061i
$438$		0			0
$439$	6994.00	−	12114.0i	0.760377	−	1.31701i	−0.182280	−	0.983247i	$-0.558348\pi$
$439$	6994.00	−	12114.0i	0.760377	−	1.31701i	0.942656	−	0.333765i	$-0.108319\pi$
$440$		0			0
$441$	−3473.00			−0.375013
$442$		0			0
$443$	−2004.00			−0.214928			−0.107464	−	0.994209i	$-0.534273\pi$
$443$	−2004.00			−0.214928			−0.107464	+	0.994209i	$0.534273\pi$
$444$		0			0
$445$	−846.000	+	1465.31i	−0.0901219	+	0.156096i
$446$		0			0
$447$			93.5307i			0.00989676i
$448$		0			0
$449$	7866.00	−	4541.44i	0.826769	−	0.477336i	−0.0259758	−	0.999663i	$-0.508269\pi$
$449$	7866.00	−	4541.44i	0.826769	−	0.477336i	0.852745	+	0.522327i	$0.174936\pi$
$450$		0			0
$451$	−1884.00	−	3263.18i	−0.196705	−	0.340704i
$452$		0			0
$453$	3066.00	+	1770.16i	0.317998	+	0.183596i
$454$		0			0
$455$	−312.000	−	1080.80i	−0.0321468	−	0.111360i
$456$		0			0
$457$	2185.50	+	1261.80i	0.223705	+	0.129156i	0.607665	−	0.794194i	$-0.292106\pi$
$457$	2185.50	+	1261.80i	0.223705	+	0.129156i	−0.383959	+	0.923350i	$0.625440\pi$
$458$		0			0
$459$	−5850.00	−	10132.5i	−0.594890	−	1.03038i
$460$		0			0
$461$	16963.5	−	9793.88i	1.71382	−	0.989472i	0.784545	−	0.620072i	$-0.212897\pi$
$461$	16963.5	−	9793.88i	1.71382	−	0.989472i	0.929270	−	0.369400i	$-0.120437\pi$
$462$		0			0
$463$		−	8632.54i		−	0.866497i	−0.901274	−	0.433249i	$-0.857367\pi$
$463$		−	8632.54i		−	0.866497i	0.901274	−	0.433249i	$-0.142633\pi$
$464$		0			0
$465$	−270.000	+	467.654i	−0.0269268	+	0.0466385i
$466$		0			0
$467$	−5460.00			−0.541025			−0.270512	−	0.962716i	$-0.587193\pi$
$467$	−5460.00			−0.541025			−0.270512	+	0.962716i	$0.587193\pi$
$468$		0			0
$469$	10896.0			1.07277
$470$		0			0
$471$	1211.00	−	2097.51i	0.118471	−	0.205198i
$472$		0			0
$473$		−	1441.07i		−	0.140085i
$474$		0			0
$475$	12078.0	−	6973.24i	1.16669	−	0.673587i
$476$		0			0
$477$	1069.50	+	1852.43i	0.102660	+	0.177813i
$478$		0			0
$479$	2211.00	+	1276.52i	0.210904	+	0.121766i	0.601732	−	0.798698i	$-0.294478\pi$
$479$	2211.00	+	1276.52i	0.210904	+	0.121766i	−0.390827	+	0.920464i	$0.627811\pi$
$480$		0			0
$481$	−4855.50	−	4672.21i	−0.460274	−	0.442899i
$482$		0			0
$483$	1872.00	+	1080.80i	0.176354	+	0.101818i
$484$		0			0
$485$	−174.000	−	301.377i	−0.0162906	−	0.0282161i
$486$		0			0
$487$	−9378.00	+	5414.39i	−0.872603	+	0.503798i	−0.868212	−	0.496193i	$-0.834731\pi$
$487$	−9378.00	+	5414.39i	−0.872603	+	0.503798i	−0.00439074	+	0.999990i	$0.501398\pi$
$488$		0			0
$489$		−	2009.18i		−	0.185804i
$490$		0			0
$491$	5694.00	−	9862.30i	0.523354	−	0.906475i	−0.476277	−	0.879295i	$-0.658014\pi$
$491$	5694.00	−	9862.30i	0.523354	−	0.906475i	0.999631	−	0.0271797i	$-0.00865264\pi$
$492$		0			0
$493$	−16497.0			−1.50707
$494$		0			0
$495$	−552.000			−0.0501223
$496$		0			0
$497$	−7320.00	+	12678.6i	−0.660658	+	1.14429i
$498$		0			0
$499$			17677.3i			1.58586i	0.609311	+	0.792931i	$0.291446\pi$
$499$			17677.3i			1.58586i	−0.609311	+	0.792931i	$0.708554\pi$
$500$		0			0
$501$	−1584.00	+	914.523i	−0.141253	+	0.0815526i
$502$		0			0
$503$	1938.00	+	3356.71i	0.171792	+	0.297552i	0.939046	−	0.343791i	$-0.111711\pi$
$503$	1938.00	+	3356.71i	0.171792	+	0.297552i	−0.767255	+	0.641343i	$0.778378\pi$
$504$		0			0
$505$	643.500	+	371.525i	0.0567037	+	0.0327379i
$506$		0			0
$507$	3718.00	−	2341.73i	0.325685	−	0.205128i
$508$		0			0
$509$	−14779.5	−	8532.95i	−1.28701	−	0.743058i	−0.308893	−	0.951097i	$-0.599958\pi$
$509$	−14779.5	−	8532.95i	−1.28701	−	0.743058i	−0.978120	+	0.208039i	$0.933292\pi$
$510$		0			0
$511$	3180.00	+	5507.92i	0.275293	+	0.476822i
$512$		0			0
$513$	9900.00	−	5715.77i	0.852038	−	0.491925i
$514$		0			0
$515$			315.233i			0.0269725i
$516$		0			0
$517$	−2088.00	+	3616.52i	−0.177621	+	0.307649i
$518$		0			0
$519$	−5148.00			−0.435399
$520$		0			0
$521$	2121.00			0.178355			0.0891773	−	0.996016i	$-0.471576\pi$
$521$	2121.00			0.178355			0.0891773	+	0.996016i	$0.471576\pi$
$522$		0			0
$523$	−5732.00	+	9928.12i	−0.479241	+	0.830069i	−0.999717	−	0.0238072i	$-0.992421\pi$
$523$	−5732.00	+	9928.12i	−0.479241	+	0.830069i	0.520476	+	0.853876i	$0.325755\pi$
$524$		0			0
$525$		−	3380.96i		−	0.281062i
$526$		0			0
$527$	−15795.0	+	9119.25i	−1.30558	+	0.753777i
$528$		0			0
$529$	3041.50	+	5268.03i	0.249979	+	0.432977i
$530$		0			0
$531$	5658.00	+	3266.65i	0.462404	+	0.266969i
$532$		0			0
$533$	9184.50	+	8837.79i	0.746388	+	0.718212i
$534$		0			0
$535$	2259.00	+	1304.23i	0.182552	+	0.105396i
$536$		0			0
$537$	−3744.00	−	6484.80i	−0.300867	−	0.521117i
$538$		0			0
$539$	1812.00	−	1046.16i	0.144802	−	0.0836016i
$540$		0			0
$541$		−	4764.87i		−	0.378665i	−0.981913	−	0.189333i	$-0.939368\pi$
$541$		−	4764.87i		−	0.378665i	0.981913	−	0.189333i	$-0.0606324\pi$
$542$		0			0
$543$	−637.000	+	1103.32i	−0.0503431	+	0.0871968i
$544$		0			0
$545$	2688.00			0.211268
$546$		0			0
$547$	−6554.00			−0.512301			−0.256151	−	0.966637i	$-0.582454\pi$
$547$	−6554.00			−0.512301			−0.256151	+	0.966637i	$0.582454\pi$
$548$		0			0
$549$	1667.50	−	2888.19i	0.129631	−	0.224527i
$550$		0			0
$551$		−	16118.5i		−	1.24622i
$552$		0			0
$553$	−15312.0	+	8840.39i	−1.17745	+	0.679804i
$554$		0			0
$555$	249.000	+	431.281i	0.0190441	+	0.0329853i
$556$		0			0
$557$	−15685.5	−	9056.03i	−1.19321	−	0.688898i	−0.234174	−	0.972195i	$-0.575239\pi$
$557$	−15685.5	−	9056.03i	−1.19321	−	0.688898i	−0.959032	+	0.283297i	$0.908572\pi$
$558$		0			0
$559$	1352.00	+	4683.47i	0.102296	+	0.354364i
$560$		0			0
$561$	2808.00	+	1621.20i	0.211326	+	0.122009i
$562$		0			0
$563$	−6084.00	−	10537.8i	−0.455435	−	0.788837i	0.543278	−	0.839553i	$-0.317183\pi$
$563$	−6084.00	−	10537.8i	−0.455435	−	0.788837i	−0.998713	+	0.0507160i	$0.983850\pi$
$564$		0			0
$565$	1030.50	−	594.959i	0.0767318	−	0.0443011i
$566$		0			0
$567$			5833.55i			0.432074i
$568$		0			0
$569$	3861.00	−	6687.45i	0.284467	−	0.492711i	−0.688013	−	0.725698i	$-0.741517\pi$
$569$	3861.00	−	6687.45i	0.284467	−	0.492711i	0.972480	+	0.232988i	$0.0748502\pi$
$570$		0			0
$571$	−11440.0			−0.838440			−0.419220	−	0.907885i	$-0.637696\pi$
$571$	−11440.0			−0.838440			−0.419220	+	0.907885i	$0.637696\pi$
$572$		0			0
$573$	−5196.00			−0.378824
$574$		0			0
$575$	−4758.00	+	8241.10i	−0.345082	+	0.597700i
$576$		0			0
$577$			15444.7i			1.11433i	0.830400	+	0.557167i	$0.188112\pi$
$577$			15444.7i			1.11433i	−0.830400	+	0.557167i	$0.811888\pi$
$578$		0			0
$579$	1935.00	−	1117.17i	0.138887	−	0.0801867i
$580$		0			0
$581$	5472.00	+	9477.78i	0.390735	+	0.676772i
$582$		0			0
$583$	−1116.00	−	644.323i	−0.0792796	−	0.0457721i
$584$		0			0
$585$	1794.00	−	517.883i	0.126791	−	0.0366014i
$586$		0			0
$587$	12186.0	+	7035.59i	0.856848	+	0.494702i	0.862956	−	0.505280i	$-0.168611\pi$
$587$	12186.0	+	7035.59i	0.856848	+	0.494702i	−0.00610719	+	0.999981i	$0.501944\pi$
$588$		0			0
$589$	−8910.00	−	15432.6i	−0.623311	−	1.07961i
$590$		0			0
$591$	3552.00	−	2050.75i	0.247225	−	0.142735i
$592$		0			0
$593$			26938.6i			1.86549i	0.360538	+	0.932745i	$0.382593\pi$
$593$			26938.6i			1.86549i	−0.360538	+	0.932745i	$0.617407\pi$
$594$		0			0
$595$	−1404.00	+	2431.80i	−0.0967368	+	0.167553i
$596$		0			0
$597$	−5044.00			−0.345791
$598$		0			0
$599$	10554.0			0.719908			0.359954	−	0.932970i	$-0.382792\pi$
$599$	10554.0			0.719908			0.359954	+	0.932970i	$0.382792\pi$
$600$		0			0
$601$	7415.50	−	12844.0i	0.503302	−	0.871745i	−0.496691	−	0.867928i	$-0.665452\pi$
$601$	7415.50	−	12844.0i	0.503302	−	0.871745i	0.999993	−	0.00381713i	$-0.00121503\pi$
$602$		0			0
$603$			18086.1i			1.22143i
$604$		0			0
$605$	−1708.50	+	986.403i	−0.114811	+	0.0662859i
$606$		0			0
$607$	−3977.00	−	6888.37i	−0.265933	−	0.460610i	0.701874	−	0.712301i	$-0.252347\pi$
$607$	−3977.00	−	6888.37i	−0.265933	−	0.460610i	−0.967808	+	0.251691i	$0.919013\pi$
$608$		0			0
$609$	−3384.00	−	1953.75i	−0.225167	−	0.130000i
$610$		0			0
$611$	3393.00	−	13712.6i	0.224658	−	0.907945i
$612$		0			0
$613$	21841.5	+	12610.2i	1.43910	+	0.830866i	0.997787	−	0.0664859i	$-0.0211787\pi$
$613$	21841.5	+	12610.2i	1.43910	+	0.830866i	0.441315	+	0.897352i	$0.354512\pi$
$614$		0			0
$615$	−471.000	−	815.796i	−0.0308822	−	0.0534895i
$616$		0			0
$617$	−15055.5	+	8692.30i	−0.982353	+	0.567162i	−0.902980	−	0.429683i	$-0.858625\pi$
$617$	−15055.5	+	8692.30i	−0.982353	+	0.567162i	−0.0793731	+	0.996845i	$0.525292\pi$
$618$		0			0
$619$			8209.92i			0.533093i	0.963822	+	0.266547i	$0.0858826\pi$
$619$			8209.92i			0.533093i	−0.963822	+	0.266547i	$0.914117\pi$
$620$		0			0
$621$	−3900.00	+	6755.00i	−0.252015	+	0.436504i
$622$		0			0
$623$	−13536.0			−0.870479
$624$		0			0
$625$	14509.0			0.928576
$626$		0			0
$627$	−1584.00	+	2743.57i	−0.100891	+	0.174749i
$628$		0			0
$629$			16819.9i			1.06622i
$630$		0			0
$631$	−11142.0	+	6432.84i	−0.702941	+	0.405843i	−0.808442	−	0.588576i	$-0.799689\pi$
$631$	−11142.0	+	6432.84i	−0.702941	+	0.405843i	0.105501	+	0.994419i	$0.466355\pi$
$632$		0			0
$633$	−1042.00	−	1804.80i	−0.0654278	−	0.113324i
$634$		0			0
$635$	−429.000	−	247.683i	−0.0268100	−	0.0154788i
$636$		0			0
$637$	−4907.50	+	5100.02i	−0.305247	+	0.317222i
$638$		0			0
$639$	−21045.0	−	12150.3i	−1.30286	−	0.752206i
$640$		0			0
$641$	−3100.50	−	5370.22i	−0.191049	−	0.330907i	0.754549	−	0.656244i	$-0.227856\pi$
$641$	−3100.50	−	5370.22i	−0.191049	−	0.330907i	−0.945598	+	0.325337i	$0.894522\pi$
$642$		0			0
$643$	14568.0	−	8410.84i	0.893477	−	0.515849i	0.0183989	−	0.999831i	$-0.494143\pi$
$643$	14568.0	−	8410.84i	0.893477	−	0.515849i	0.875078	+	0.483981i	$0.160810\pi$
$644$		0			0
$645$		−	360.267i		−	0.0219930i
$646$		0			0
$647$	−6747.00	+	11686.1i	−0.409972	+	0.710092i	−0.994886	−	0.101003i	$-0.967795\pi$
$647$	−6747.00	+	11686.1i	−0.409972	+	0.710092i	0.584914	+	0.811095i	$0.301128\pi$
$648$		0			0
$649$	−3936.00			−0.238061
$650$		0			0
$651$	−4320.00			−0.260083
$652$		0			0
$653$	5667.00	−	9815.53i	0.339612	−	0.588226i	−0.644747	−	0.764396i	$-0.723037\pi$
$653$	5667.00	−	9815.53i	0.339612	−	0.588226i	0.984360	+	0.176170i	$0.0563708\pi$
$654$		0			0
$655$		−	3419.07i		−	0.203960i
$656$		0			0
$657$	−9142.50	+	5278.42i	−0.542896	+	0.313441i
$658$		0			0
$659$	6618.00	+	11462.7i	0.391200	+	0.677578i	0.992608	−	0.121364i	$-0.0387268\pi$
$659$	6618.00	+	11462.7i	0.391200	+	0.677578i	−0.601408	+	0.798942i	$0.705393\pi$
$660$		0			0
$661$	−10264.5	−	5926.21i	−0.603998	−	0.348718i	0.166615	−	0.986022i	$-0.446716\pi$
$661$	−10264.5	−	5926.21i	−0.603998	−	0.348718i	−0.770613	+	0.637304i	$0.780050\pi$
$662$		0			0
$663$	−10647.0	−	2634.45i	−0.623673	−	0.154319i
$664$		0			0
$665$	−2376.00	−	1371.78i	−0.138552	−	0.0799932i
$666$		0			0
$667$	5499.00	+	9524.55i	0.319224	+	0.552911i
$668$		0			0
$669$	4170.00	−	2407.55i	0.240989	−	0.139135i
$670$		0			0
$671$			2009.18i			0.115594i
$672$		0			0
$673$	−4010.50	+	6946.39i	−0.229708	+	0.397866i	−0.957722	−	0.287697i	$-0.907110\pi$
$673$	−4010.50	+	6946.39i	−0.229708	+	0.397866i	0.728014	+	0.685563i	$0.240444\pi$
$674$		0			0
$675$	12200.0			0.695671
$676$		0			0
$677$	−21630.0			−1.22793			−0.613965	−	0.789333i	$-0.710426\pi$
$677$	−21630.0			−1.22793			−0.613965	+	0.789333i	$0.710426\pi$
$678$		0			0
$679$	1392.00	−	2411.01i	0.0786746	−	0.136268i
$680$		0			0
$681$			4815.10i			0.270947i
$682$		0			0
$683$	22983.0	−	13269.2i	1.28758	−	0.743387i	0.309361	−	0.950945i	$-0.399885\pi$
$683$	22983.0	−	13269.2i	1.28758	−	0.743387i	0.978223	+	0.207557i	$0.0665514\pi$
$684$		0			0
$685$	733.500	+	1270.46i	0.0409133	+	0.0708639i
$686$		0			0
$687$	4344.00	+	2508.01i	0.241243	+	0.139282i
$688$		0			0
$689$	4231.50	+	1047.02i	0.233973	+	0.0578933i
$690$		0			0
$691$	720.000	+	415.692i	0.0396383	+	0.0228852i	0.519688	−	0.854356i	$-0.326048\pi$
$691$	720.000	+	415.692i	0.0396383	+	0.0228852i	−0.480050	+	0.877241i	$0.659381\pi$
$692$		0			0
$693$	−2208.00	−	3824.37i	−0.121032	−	0.209633i
$694$		0			0
$695$	354.000	−	204.382i	0.0193208	−	0.0111549i
$696$		0			0
$697$		−	31816.0i		−	1.72901i
$698$		0			0
$699$	−5850.00	+	10132.5i	−0.316548	+	0.548278i
$700$		0			0
$701$	30186.0			1.62640			0.813202	−	0.581981i	$-0.197722\pi$
$701$	30186.0			1.62640			0.813202	+	0.581981i	$0.197722\pi$
$702$		0			0
$703$	−16434.0			−0.881679
$704$		0			0
$705$	−522.000	+	904.131i	−0.0278860	+	0.0483000i
$706$		0			0
$707$			5944.40i			0.316212i
$708$		0			0
$709$	−10288.5	+	5940.07i	−0.544983	+	0.314646i	−0.747096	−	0.664716i	$-0.768552\pi$
$709$	−10288.5	+	5940.07i	−0.544983	+	0.314646i	0.202113	+	0.979362i	$0.435219\pi$
$710$		0			0
$711$	−14674.0	−	25416.1i	−0.774006	−	1.34062i
$712$		0			0
$713$	10530.0	+	6079.50i	0.553088	+	0.319325i
$714$		0			0
$715$	−780.000	+	810.600i	−0.0407977	+	0.0423982i
$716$		0			0
$717$	9324.00	+	5383.21i	0.485650	+	0.280390i
$718$		0			0
$719$	9204.00	+	15941.8i	0.477401	+	0.826883i	0.999665	−	0.0259014i	$-0.00824561\pi$
$719$	9204.00	+	15941.8i	0.477401	+	0.826883i	−0.522264	+	0.852784i	$0.674912\pi$
$720$		0			0
$721$	−2184.00	+	1260.93i	−0.112811	+	0.0651312i
$722$		0			0
$723$		−	9834.58i		−	0.505881i
$724$		0			0
$725$	8601.00	−	14897.4i	0.440597	−	0.763137i
$726$		0			0
$727$	−21112.0			−1.07703			−0.538515	−	0.842616i	$-0.681014\pi$
$727$	−21112.0			−1.07703			−0.538515	+	0.842616i	$0.681014\pi$
$728$		0			0
$729$	−4283.00			−0.217599
$730$		0			0
$731$	6084.00	−	10537.8i	0.307832	−	0.533180i
$732$		0			0
$733$		−	23959.5i		−	1.20732i	−0.797243	−	0.603658i	$-0.793709\pi$
$733$		−	23959.5i		−	1.20732i	0.797243	−	0.603658i	$-0.206291\pi$
$734$		0			0
$735$	453.000	−	261.540i	0.0227335	−	0.0131252i
$736$		0			0
$737$	−5448.00	−	9436.21i	−0.272293	−	0.471625i
$738$		0			0
$739$	−2742.00	−	1583.09i	−0.136490	−	0.0788025i	0.430200	−	0.902734i	$-0.358443\pi$
$739$	−2742.00	−	1583.09i	−0.136490	−	0.0788025i	−0.566690	+	0.823931i	$0.691776\pi$
$740$		0			0
$741$	2574.00	−	10402.7i	0.127609	−	0.515726i
$742$		0			0
$743$	26070.0	+	15051.5i	1.28723	+	0.743185i	0.978160	−	0.207852i	$-0.0666474\pi$
$743$	26070.0	+	15051.5i	1.28723	+	0.743185i	0.309075	+	0.951038i	$0.399981\pi$
$744$		0			0
$745$	40.5000	+	70.1481i	0.00199168	+	0.00344970i
$746$		0			0
$747$	−15732.0	+	9082.87i	−0.770554	+	0.444880i
$748$		0			0
$749$			20867.7i			1.01801i
$750$		0			0
$751$	14248.0	−	24678.3i	0.692299	−	1.19910i	−0.278783	−	0.960354i	$-0.589931\pi$
$751$	14248.0	−	24678.3i	0.692299	−	1.19910i	0.971083	−	0.238744i	$-0.0767356\pi$
$752$		0			0
$753$	−7956.00			−0.385037
$754$		0			0
$755$	3066.00			0.147792
$756$		0			0
$757$	−8711.00	+	15087.9i	−0.418239	+	0.724411i	−0.995762	−	0.0919633i	$-0.970686\pi$
$757$	−8711.00	+	15087.9i	−0.418239	+	0.724411i	0.577524	+	0.816374i	$0.304019\pi$
$758$		0			0
$759$		−	2161.60i		−	0.103374i
$760$		0			0
$761$	35790.0	−	20663.4i	1.70484	−	0.984292i	0.764149	−	0.645040i	$-0.223159\pi$
$761$	35790.0	−	20663.4i	1.70484	−	0.984292i	0.940695	−	0.339252i	$-0.110174\pi$
$762$		0			0
$763$	10752.0	+	18623.0i	0.510155	+	0.883615i
$764$		0			0
$765$	−4036.50	−	2330.47i	−0.190771	−	0.110142i
$766$		0			0
$767$	12792.0	−	3692.73i	0.602206	−	0.173842i
$768$		0			0
$769$	−12186.0	−	7035.59i	−0.571441	−	0.329922i	0.186283	−	0.982496i	$-0.440356\pi$
$769$	−12186.0	−	7035.59i	−0.571441	−	0.329922i	−0.757725	+	0.652574i	$0.773689\pi$
$770$		0			0
$771$	2067.00	+	3580.15i	0.0965515	+	0.167232i
$772$		0			0
$773$	174.000	−	100.459i	0.00809618	−	0.00467433i	−0.495946	−	0.868353i	$-0.665179\pi$
$773$	174.000	−	100.459i	0.00809618	−	0.00467433i	0.504043	+	0.863679i	$0.331845\pi$
$774$		0			0
$775$		−	19017.9i		−	0.881476i
$776$		0			0
$777$	−1992.00	+	3450.25i	−0.0919725	+	0.159301i
$778$		0			0
$779$	31086.0			1.42975
$780$		0			0
$781$	14640.0			0.670756
$782$		0			0
$783$	7050.00	−	12211.0i	0.321771	−	0.557323i
$784$		0			0
$785$		−	2097.51i		−	0.0953675i
$786$		0			0
$787$	5979.00	−	3451.98i	0.270811	−	0.156353i	−0.358445	−	0.933551i	$-0.616693\pi$
$787$	5979.00	−	3451.98i	0.270811	−	0.156353i	0.629256	+	0.777198i	$0.283360\pi$
$788$		0			0
$789$	2052.00	+	3554.17i	0.0925895	+	0.160370i
$790$		0			0
$791$	8244.00	+	4759.68i	0.370573	+	0.213950i
$792$		0			0
$793$	−1885.00	−	6529.83i	−0.0844115	−	0.292410i
$794$		0			0
$795$	−279.000	−	161.081i	−0.0124467	−	0.00718609i
$796$		0			0
$797$	15639.0	+	27087.5i	0.695059	+	1.20388i	0.970161	+	0.242462i	$0.0779550\pi$
$797$	15639.0	+	27087.5i	0.695059	+	1.20388i	−0.275102	+	0.961415i	$0.588712\pi$
$798$		0			0
$799$	−30537.0	+	17630.5i	−1.35209	+	0.780631i
$800$		0			0
$801$		−	22468.2i		−	0.991103i
$802$		0			0
$803$	3180.00	−	5507.92i	0.139751	−	0.242055i
$804$		0			0
$805$	1872.00			0.0819619
$806$		0			0
$807$	−6660.00			−0.290512
$808$		0			0
$809$	−4024.50	+	6970.64i	−0.174900	+	0.302935i	−0.940127	−	0.340826i	$-0.889293\pi$
$809$	−4024.50	+	6970.64i	−0.174900	+	0.302935i	0.765227	+	0.643761i	$0.222627\pi$
$810$		0			0
$811$		−	14026.1i		−	0.607305i	−0.952783	−	0.303653i	$-0.901794\pi$
$811$		−	14026.1i		−	0.607305i	0.952783	−	0.303653i	$-0.0982062\pi$
$812$		0			0
$813$	−4860.00	+	2805.92i	−0.209653	+	0.121043i
$814$		0			0
$815$	−870.000	−	1506.88i	−0.0373924	−	0.0647655i
$816$		0			0
$817$	10296.0	+	5944.40i	0.440895	+	0.254551i
$818$		0			0
$819$	10764.0	+	10357.7i	0.459249	+	0.441912i
$820$		0			0
$821$	−6960.00	−	4018.36i	−0.295866	−	0.170818i	0.344718	−	0.938706i	$-0.387974\pi$
$821$	−6960.00	−	4018.36i	−0.295866	−	0.170818i	−0.640584	+	0.767888i	$0.721308\pi$
$822$		0			0
$823$	−20150.0	−	34900.8i	−0.853445	−	1.47821i	−0.878081	−	0.478513i	$-0.841176\pi$
$823$	−20150.0	−	34900.8i	−0.853445	−	1.47821i	0.0246361	−	0.999696i	$-0.492157\pi$
$824$		0			0
$825$	−2928.00	+	1690.48i	−0.123563	+	0.0713394i
$826$		0			0
$827$		−	39525.4i		−	1.66195i	−0.556310	−	0.830975i	$-0.687783\pi$
$827$		−	39525.4i		−	1.66195i	0.556310	−	0.830975i	$-0.312217\pi$
$828$		0			0
$829$	6155.50	−	10661.6i	0.257888	−	0.446676i	−0.707788	−	0.706425i	$-0.750307\pi$
$829$	6155.50	−	10661.6i	0.257888	−	0.446676i	0.965676	+	0.259750i	$0.0836400\pi$
$830$		0			0
$831$	−754.000			−0.0314753
$832$		0			0
$833$	17667.0			0.734844
$834$		0			0
$835$	−792.000	+	1371.78i	−0.0328243	+	0.0568534i
$836$		0			0
$837$		−	15588.5i		−	0.643747i
$838$		0			0
$839$	−18591.0	+	10733.5i	−0.764997	+	0.441671i	−0.831087	−	0.556142i	$-0.812281\pi$
$839$	−18591.0	+	10733.5i	−0.764997	+	0.441671i	0.0660899	+	0.997814i	$0.478948\pi$
$840$		0			0
$841$	2254.00	+	3904.04i	0.0924187	+	0.160074i
$842$		0			0
$843$	−63.0000	−	36.3731i	−0.00257394	−	0.00148607i
$844$		0			0
$845$	1774.50	−	3366.24i	0.0722422	−	0.137044i
$846$		0			0
$847$	−13668.0	−	7891.22i	−0.554472	−	0.320125i
$848$		0			0
$849$	7124.00	+	12339.1i	0.287980	+	0.498796i
$850$		0			0
$851$	9711.00	−	5606.65i	0.391174	−	0.225844i
$852$		0			0
$853$			774.227i			0.0310774i	0.999879	+	0.0155387i	$0.00494632\pi$
$853$			774.227i			0.0310774i	−0.999879	+	0.0155387i	$0.995054\pi$
$854$		0			0
$855$	2277.00	−	3943.88i	0.0910781	−	0.157752i
$856$		0			0
$857$	13923.0			0.554960			0.277480	−	0.960731i	$-0.410501\pi$
$857$	13923.0			0.554960			0.277480	+	0.960731i	$0.410501\pi$
$858$		0			0
$859$	22358.0			0.888062			0.444031	−	0.896011i	$-0.353548\pi$
$859$	22358.0			0.888062			0.444031	+	0.896011i	$0.353548\pi$
$860$		0			0
$861$	3768.00	−	6526.37i	0.149144	−	0.258325i
$862$		0			0
$863$			2230.88i			0.0879955i	0.999032	+	0.0439977i	$0.0140094\pi$
$863$			2230.88i			0.0879955i	−0.999032	+	0.0439977i	$0.985991\pi$
$864$		0			0
$865$	−3861.00	+	2229.15i	−0.151766	+	0.0876224i
$866$		0			0
$867$	8776.00	+	15200.5i	0.343770	+	0.595427i
$868$		0			0
$869$	15312.0	+	8840.39i	0.597726	+	0.345097i
$870$		0			0
$871$	26559.0	+	25556.4i	1.03320	+	0.994197i
$872$		0			0
$873$	4002.00	+	2310.56i	0.155151	+	0.0895767i
$874$		0			0
$875$	−2964.00	−	5133.80i	−0.114516	−	0.198348i
$876$		0			0
$877$	−14509.5	+	8377.06i	−0.558667	+	0.322547i	−0.752610	−	0.658466i	$-0.771206\pi$
$877$	−14509.5	+	8377.06i	−0.558667	+	0.322547i	0.193943	+	0.981013i	$0.437872\pi$
$878$		0			0
$879$			16645.0i			0.638706i
$880$		0			0
$881$	−8677.50	+	15029.9i	−0.331842	+	0.574766i	−0.982873	−	0.184284i	$-0.941003\pi$
$881$	−8677.50	+	15029.9i	−0.331842	+	0.574766i	0.651031	+	0.759051i	$0.274337\pi$
$882$		0			0
$883$	46982.0			1.79057			0.895283	−	0.445497i	$-0.146973\pi$
$883$	46982.0			1.79057			0.895283	+	0.445497i	$0.146973\pi$
$884$		0			0
$885$	−984.000			−0.0373749
$886$		0			0
$887$	−4458.00	+	7721.48i	−0.168754	+	0.292291i	−0.937982	−	0.346684i	$-0.887308\pi$
$887$	−4458.00	+	7721.48i	−0.168754	+	0.292291i	0.769228	+	0.638975i	$0.220641\pi$
$888$		0			0
$889$		−	3962.93i		−	0.149508i
$890$		0			0
$891$	5052.00	−	2916.77i	0.189953	−	0.109670i
$892$		0			0
$893$	−17226.0	−	29836.3i	−0.645516	−	1.11807i
$894$		0			0
$895$	−5616.00	−	3242.40i	−0.209745	−	0.121097i
$896$		0			0
$897$	2028.00	+	7025.20i	0.0754882	+	0.261499i
$898$		0			0
$899$	−19035.0	−	10989.9i	−0.706177	−	0.407711i
$900$		0			0
$901$	−5440.50	−	9423.22i	−0.201165	−	0.348427i
$902$		0			0
$903$	2496.00	−	1441.07i	0.0919841	−	0.0531071i
$904$		0			0
$905$			1103.32i			0.0405254i
$906$		0			0
$907$	−15418.0	+	26704.8i	−0.564439	+	0.977637i	0.432662	+	0.901556i	$0.357574\pi$
$907$	−15418.0	+	26704.8i	−0.564439	+	0.977637i	−0.997102	+	0.0760813i	$0.975759\pi$
$908$		0			0
$909$	−9867.00			−0.360031
$910$		0			0
$911$	27480.0			0.999400			0.499700	−	0.866199i	$-0.333444\pi$
$911$	27480.0			0.999400			0.499700	+	0.866199i	$0.333444\pi$
$912$		0			0
$913$	5472.00	−	9477.78i	0.198354	−	0.343558i
$914$		0			0
$915$			502.295i			0.0181479i
$916$		0			0
$917$	23688.0	−	13676.3i	0.853050	−	0.492509i
$918$		0			0
$919$	−14221.0	−	24631.5i	−0.510454	−	0.884133i	−0.999927	−	0.0121140i	$-0.996144\pi$
$919$	−14221.0	−	24631.5i	−0.510454	−	0.884133i	0.489472	−	0.872019i	$-0.337189\pi$
$920$		0			0
$921$	3846.00	+	2220.49i	0.137600	+	0.0794437i
$922$		0			0
$923$	−47580.0	+	13735.2i	−1.69677	+	0.489814i
$924$		0			0
$925$	−15189.0	−	8769.37i	−0.539904	−	0.311714i
$926$		0			0
$927$	−2093.00	−	3625.18i	−0.0741566	−	0.128443i
$928$		0			0
$929$	6043.50	−	3489.22i	0.213435	−	0.123227i	−0.389472	−	0.921038i	$-0.627342\pi$
$929$	6043.50	−	3489.22i	0.213435	−	0.123227i	0.602907	+	0.797812i	$0.294009\pi$
$930$		0			0
$931$			17261.6i			0.607655i
$932$		0			0
$933$	−4914.00	+	8511.30i	−0.172430	+	0.298657i
$934$		0			0
$935$	2808.00			0.0982154
$936$		0			0
$937$	−38465.0			−1.34109			−0.670543	−	0.741871i	$-0.733939\pi$
$937$	−38465.0			−1.34109			−0.670543	+	0.741871i	$0.733939\pi$
$938$		0			0
$939$	−518.000	+	897.202i	−0.0180024	+	0.0311811i
$940$		0			0
$941$			4884.38i			0.169210i	0.996415	+	0.0846049i	$0.0269628\pi$
$941$			4884.38i			0.169210i	−0.996415	+	0.0846049i	$0.973037\pi$
$942$		0			0
$943$	−18369.0	+	10605.3i	−0.634334	+	0.366233i
$944$		0			0
$945$	−1200.00	−	2078.46i	−0.0413079	−	0.0715475i
$946$		0			0
$947$	−18849.0	−	10882.5i	−0.646790	−	0.373424i	0.140435	−	0.990090i	$-0.455150\pi$
$947$	−18849.0	−	10882.5i	−0.646790	−	0.373424i	−0.787225	+	0.616665i	$0.788483\pi$
$948$		0			0
$949$	−5167.50	+	20884.2i	−0.176759	+	0.714362i
$950$		0			0
$951$	6783.00	+	3916.17i	0.231287	+	0.133534i
$952$		0			0
$953$	−3237.00	−	5606.65i	−0.110028	−	0.190574i	0.805753	−	0.592251i	$-0.201761\pi$
$953$	−3237.00	−	5606.65i	−0.110028	−	0.190574i	−0.915781	+	0.401677i	$0.868427\pi$
$954$		0			0
$955$	−3897.00	+	2249.93i	−0.132046	+	0.0762368i
$956$		0			0
$957$			3907.51i			0.131987i
$958$		0			0
$959$	−5868.00	+	10163.7i	−0.197589	+	0.342234i
$960$		0			0
$961$	5491.00			0.184317
$962$		0			0
$963$	−34638.0			−1.15908
$964$		0			0
$965$	967.500	−	1675.76i	0.0322745	−	0.0559011i
$966$		0			0
$967$		−	7541.35i		−	0.250789i	−0.992107	−	0.125395i	$-0.959980\pi$
$967$		−	7541.35i		−	0.250789i	0.992107	−	0.125395i	$-0.0400197\pi$
$968$		0			0
$969$	−23166.0	+	13374.9i	−0.768007	+	0.443409i
$970$		0			0
$971$	17499.0	+	30309.2i	0.578342	+	1.00172i	0.995670	+	0.0929611i	$0.0296332\pi$
$971$	17499.0	+	30309.2i	0.578342	+	1.00172i	−0.417328	+	0.908756i	$0.637033\pi$
$972$		0			0
$973$	2832.00	+	1635.06i	0.0933091	+	0.0538720i
$974$		0			0
$975$	7930.00	−	8241.10i	0.260475	−	0.270694i
$976$		0			0
$977$	−21838.5	−	12608.5i	−0.715123	−	0.412877i	0.0978318	−	0.995203i	$-0.468809\pi$
$977$	−21838.5	−	12608.5i	−0.715123	−	0.412877i	−0.812955	+	0.582326i	$0.802143\pi$
$978$		0			0
$979$	6768.00	+	11722.5i	0.220946	+	0.382690i
$980$		0			0
$981$	−30912.0	+	17847.1i	−1.00606	+	0.580849i
$982$		0			0
$983$			56440.6i			1.83131i	0.401967	+	0.915654i	$0.368327\pi$
$983$			56440.6i			1.83131i	−0.401967	+	0.915654i	$0.631673\pi$
$984$		0			0
$985$	1776.00	−	3076.12i	0.0574498	−	0.0995060i
$986$		0			0
$987$	−8352.00			−0.269349
$988$		0			0
$989$	−8112.00			−0.260816
$990$		0			0
$991$	29641.0	−	51339.7i	0.950129	−	1.64567i	0.204987	−	0.978765i	$-0.434285\pi$
$991$	29641.0	−	51339.7i	0.950129	−	1.64567i	0.745142	−	0.666906i	$-0.232382\pi$
$992$		0			0
$993$		−	14909.5i		−	0.476474i
$994$		0			0
$995$	−3783.00	+	2184.12i	−0.120532	+	0.0695891i
$996$		0			0
$997$	18855.5	+	32658.7i	0.598957	+	1.03742i	0.992975	+	0.118321i	$0.0377511\pi$
$997$	18855.5	+	32658.7i	0.598957	+	1.03742i	−0.394019	+	0.919102i	$0.628916\pi$
$998$		0			0
$999$	−12450.0	−	7188.01i	−0.394295	−	0.227646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.w.b.17.1		2
4.3	odd	2		13.4.e.b.4.1	✓	2
12.11	even	2		117.4.q.a.82.1		2
13.10	even	6	inner	208.4.w.b.49.1		2
52.3	odd	6		169.4.e.a.23.1		2
52.7	even	12		169.4.a.i.1.2		2
52.11	even	12		169.4.c.h.146.1		4
52.15	even	12		169.4.c.h.146.2		4
52.19	even	12		169.4.a.i.1.1		2
52.23	odd	6		13.4.e.b.10.1	yes	2
52.31	even	4		169.4.c.h.22.2		4
52.35	odd	6		169.4.b.d.168.1		2
52.43	odd	6		169.4.b.d.168.2		2
52.47	even	4		169.4.c.h.22.1		4
52.51	odd	2		169.4.e.a.147.1		2
156.23	even	6		117.4.q.a.10.1		2
156.59	odd	12		1521.4.a.o.1.1		2
156.71	odd	12		1521.4.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.e.b.4.1	✓	2	4.3	odd	2
13.4.e.b.10.1	yes	2	52.23	odd	6
117.4.q.a.10.1		2	156.23	even	6
117.4.q.a.82.1		2	12.11	even	2
169.4.a.i.1.1		2	52.19	even	12
169.4.a.i.1.2		2	52.7	even	12
169.4.b.d.168.1		2	52.35	odd	6
169.4.b.d.168.2		2	52.43	odd	6
169.4.c.h.22.1		4	52.47	even	4
169.4.c.h.22.2		4	52.31	even	4
169.4.c.h.146.1		4	52.11	even	12
169.4.c.h.146.2		4	52.15	even	12
169.4.e.a.23.1		2	52.3	odd	6
169.4.e.a.147.1		2	52.51	odd	2
208.4.w.b.17.1		2	1.1	even	1	trivial
208.4.w.b.49.1		2	13.10	even	6	inner
1521.4.a.o.1.1		2	156.59	odd	12
1521.4.a.o.1.2		2	156.71	odd	12

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{3} -1.73205i q^{5} +(12.0000 - 6.92820i) q^{7} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{3} -1.73205i q^{5} +(12.0000 - 6.92820i) q^{7} +(11.5000 + 19.9186i) q^{9} +(-12.0000 - 6.92820i) q^{11} +(45.5000 + 11.2583i) q^{13} +(-3.00000 - 1.73205i) q^{15} +(-58.5000 - 101.325i) q^{17} +(99.0000 - 57.1577i) q^{19} -27.7128i q^{21} +(-39.0000 + 67.5500i) q^{23} +122.000 q^{25} +100.000 q^{27} +(70.5000 - 122.110i) q^{29} -155.885i q^{31} +(-24.0000 + 13.8564i) q^{33} +(-12.0000 - 20.7846i) q^{35} +(-124.500 - 71.8801i) q^{37} +(65.0000 - 67.5500i) q^{39} +(235.500 + 135.966i) q^{41} +(52.0000 + 90.0666i) q^{43} +(34.5000 - 19.9186i) q^{45} -301.377i q^{47} +(-75.5000 + 130.770i) q^{49} -234.000 q^{51} +93.0000 q^{53} +(-12.0000 + 20.7846i) q^{55} -228.631i q^{57} +(246.000 - 142.028i) q^{59} +(-72.5000 - 125.574i) q^{61} +(276.000 + 159.349i) q^{63} +(19.5000 - 78.8083i) q^{65} +(681.000 + 393.176i) q^{67} +(78.0000 + 135.100i) q^{69} +(-915.000 + 528.275i) q^{71} +458.993i q^{73} +(122.000 - 211.310i) q^{75} -192.000 q^{77} -1276.00 q^{79} +(-210.500 + 364.597i) q^{81} +789.815i q^{83} +(-175.500 + 101.325i) q^{85} +(-141.000 - 244.219i) q^{87} +(-846.000 - 488.438i) q^{89} +(624.000 - 180.133i) q^{91} +(-270.000 - 155.885i) q^{93} +(-99.0000 - 171.473i) q^{95} +(174.000 - 100.459i) q^{97} -318.697i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 24 q^{7} + 23 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 24 * q^7 + 23 * q^9	\( 2 q + 2 q^{3} + 24 q^{7} + 23 q^{9} - 24 q^{11} + 91 q^{13} - 6 q^{15} - 117 q^{17} + 198 q^{19} - 78 q^{23} + 244 q^{25} + 200 q^{27} + 141 q^{29} - 48 q^{33} - 24 q^{35} - 249 q^{37} + 130 q^{39} + 471 q^{41} + 104 q^{43} + 69 q^{45} - 151 q^{49} - 468 q^{51} + 186 q^{53} - 24 q^{55} + 492 q^{59} - 145 q^{61} + 552 q^{63} + 39 q^{65} + 1362 q^{67} + 156 q^{69} - 1830 q^{71} + 244 q^{75} - 384 q^{77} - 2552 q^{79} - 421 q^{81} - 351 q^{85} - 282 q^{87} - 1692 q^{89} + 1248 q^{91} - 540 q^{93} - 198 q^{95} + 348 q^{97}+O(q^{100}) \) 2 * q + 2 * q^3 + 24 * q^7 + 23 * q^9 - 24 * q^11 + 91 * q^13 - 6 * q^15 - 117 * q^17 + 198 * q^19 - 78 * q^23 + 244 * q^25 + 200 * q^27 + 141 * q^29 - 48 * q^33 - 24 * q^35 - 249 * q^37 + 130 * q^39 + 471 * q^41 + 104 * q^43 + 69 * q^45 - 151 * q^49 - 468 * q^51 + 186 * q^53 - 24 * q^55 + 492 * q^59 - 145 * q^61 + 552 * q^63 + 39 * q^65 + 1362 * q^67 + 156 * q^69 - 1830 * q^71 + 244 * q^75 - 384 * q^77 - 2552 * q^79 - 421 * q^81 - 351 * q^85 - 282 * q^87 - 1692 * q^89 + 1248 * q^91 - 540 * q^93 - 198 * q^95 + 348 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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