LMFDB - Embedded newform 360.4.m.c.179.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.179");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.m (of order $2$, degree $1$, 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:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.7
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.79134 + 0.456513i) q^{2} +(7.58319 - 2.54857i) q^{4} +(-10.9564 + 2.22672i) q^{5} -9.98469 q^{7} +(-20.0038 + 10.5758i) q^{8} +O(q^{10})$	\(q+(-2.79134 + 0.456513i) q^{2} +(7.58319 - 2.54857i) q^{4} +(-10.9564 + 2.22672i) q^{5} -9.98469 q^{7} +(-20.0038 + 10.5758i) q^{8} +(29.5664 - 11.2173i) q^{10} -56.3249i q^{11} +69.5331 q^{13} +(27.8707 - 4.55815i) q^{14} +(51.0096 - 38.6526i) q^{16} -56.6848 q^{17} -72.8043 q^{19} +(-77.4092 + 44.8087i) q^{20} +(25.7131 + 157.222i) q^{22} +129.844i q^{23} +(115.083 - 48.7934i) q^{25} +(-194.091 + 31.7428i) q^{26} +(-75.7158 + 25.4467i) q^{28} +45.6362 q^{29} -124.113i q^{31} +(-124.740 + 131.179i) q^{32} +(158.227 - 25.8774i) q^{34} +(109.396 - 22.2331i) q^{35} +38.5467 q^{37} +(203.222 - 33.2361i) q^{38} +(195.620 - 160.415i) q^{40} -106.961i q^{41} +410.715i q^{43} +(-143.548 - 427.123i) q^{44} +(-59.2755 - 362.439i) q^{46} -117.432i q^{47} -243.306 q^{49} +(-298.963 + 188.736i) q^{50} +(527.283 - 177.210i) q^{52} +660.920i q^{53} +(125.420 + 617.116i) q^{55} +(199.732 - 105.596i) q^{56} +(-127.386 + 20.8336i) q^{58} +565.912i q^{59} +825.056i q^{61} +(56.6591 + 346.441i) q^{62} +(288.306 - 423.112i) q^{64} +(-761.829 + 154.830i) q^{65} -168.301i q^{67} +(-429.852 + 144.465i) q^{68} +(-295.212 + 112.001i) q^{70} +478.705 q^{71} -359.165i q^{73} +(-107.597 + 17.5971i) q^{74} +(-552.089 + 185.547i) q^{76} +562.387i q^{77} +752.089i q^{79} +(-472.811 + 537.075i) q^{80} +(48.8291 + 298.564i) q^{82} -910.621 q^{83} +(621.059 - 126.221i) q^{85} +(-187.497 - 1146.45i) q^{86} +(595.679 + 1126.71i) q^{88} +432.574i q^{89} -694.267 q^{91} +(330.916 + 984.631i) q^{92} +(53.6093 + 327.793i) q^{94} +(797.670 - 162.115i) q^{95} +1021.20i q^{97} +(679.150 - 111.072i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 76 q^{4}+O(q^{10}) $ 64 * q + 76 * q^4	$ 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) $ 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.79134	+	0.456513i	−0.986889	+	0.161402i
$2$	−2.79134	+	0.456513i	−0.986889	+	0.161402i
$3$		0			0
$3$		0			0
$4$	7.58319	−	2.54857i	0.947899	−	0.318571i
$5$	−10.9564	+	2.22672i	−0.979966	+	0.199164i
$5$	−10.9564	+	2.22672i	−0.979966	+	0.199164i
$6$		0			0
$7$	−9.98469			−0.539123			−0.269561	−	0.962983i	$-0.586879\pi$
$7$	−9.98469			−0.539123			−0.269561	+	0.962983i	$0.586879\pi$
$8$	−20.0038	+	10.5758i	−0.884053	+	0.467387i
$9$		0			0
$10$	29.5664	−	11.2173i	0.934972	−	0.354721i
$11$		−	56.3249i		−	1.54387i	−0.635700	−	0.771937i	$-0.719288\pi$
$11$		−	56.3249i		−	1.54387i	0.635700	−	0.771937i	$-0.280712\pi$
$12$		0			0
$13$	69.5331			1.48346			0.741731	−	0.670697i	$-0.234005\pi$
$13$	69.5331			1.48346			0.741731	+	0.670697i	$0.234005\pi$
$14$	27.8707	−	4.55815i	0.532054	−	0.0870154i
$15$		0			0
$16$	51.0096	−	38.6526i	0.797025	−	0.603947i
$17$	−56.6848			−0.808711			−0.404356	−	0.914602i	$-0.632504\pi$
$17$	−56.6848			−0.808711			−0.404356	+	0.914602i	$0.632504\pi$
$18$		0			0
$19$	−72.8043			−0.879077			−0.439538	−	0.898224i	$-0.644858\pi$
$19$	−72.8043			−0.879077			−0.439538	+	0.898224i	$0.644858\pi$
$20$	−77.4092	+	44.8087i	−0.865461	+	0.500976i
$21$		0			0
$22$	25.7131	+	157.222i	0.249184	+	1.52363i
$23$			129.844i			1.17714i	0.808445	+	0.588572i	$0.200310\pi$
$23$			129.844i			1.17714i	−0.808445	+	0.588572i	$0.799690\pi$
$24$		0			0
$25$	115.083	−	48.7934i	0.920668	−	0.390347i
$26$	−194.091	+	31.7428i	−1.46401	+	0.239434i
$27$		0			0
$28$	−75.7158	+	25.4467i	−0.511034	+	0.171749i
$29$	45.6362			0.292222			0.146111	−	0.989268i	$-0.453324\pi$
$29$	45.6362			0.292222			0.146111	+	0.989268i	$0.453324\pi$
$30$		0			0
$31$		−	124.113i		−	0.719074i	−0.933131	−	0.359537i	$-0.882935\pi$
$31$		−	124.113i		−	0.719074i	0.933131	−	0.359537i	$-0.117065\pi$
$32$	−124.740	+	131.179i	−0.689096	+	0.724670i
$33$		0			0
$34$	158.227	−	25.8774i	0.798108	−	0.130528i
$35$	109.396	−	22.2331i	0.528322	−	0.107374i
$36$		0			0
$37$	38.5467			0.171271			0.0856356	−	0.996327i	$-0.472708\pi$
$37$	38.5467			0.171271			0.0856356	+	0.996327i	$0.472708\pi$
$38$	203.222	−	33.2361i	0.867551	−	0.141885i
$39$		0			0
$40$	195.620	−	160.415i	0.773255	−	0.634095i
$41$		−	106.961i		−	0.407426i	−0.979031	−	0.203713i	$-0.934699\pi$
$41$		−	106.961i		−	0.407426i	0.979031	−	0.203713i	$-0.0653010\pi$
$42$		0			0
$43$			410.715i			1.45659i	0.685263	+	0.728296i	$0.259687\pi$
$43$			410.715i			1.45659i	−0.685263	+	0.728296i	$0.740313\pi$
$44$	−143.548	−	427.123i	−0.491834	−	1.46344i
$45$		0			0
$46$	−59.2755	−	362.439i	−0.189993	−	1.16171i
$47$		−	117.432i		−	0.364452i	−0.983257	−	0.182226i	$-0.941670\pi$
$47$		−	117.432i		−	0.364452i	0.983257	−	0.182226i	$-0.0583302\pi$
$48$		0			0
$49$	−243.306			−0.709347
$50$	−298.963	+	188.736i	−0.845594	+	0.533827i
$51$		0			0
$52$	527.283	−	177.210i	1.40617	−	0.472589i
$53$			660.920i			1.71291i	0.516219	+	0.856457i	$0.327339\pi$
$53$			660.920i			1.71291i	−0.516219	+	0.856457i	$0.672661\pi$
$54$		0			0
$55$	125.420	+	617.116i	0.307483	+	1.51294i
$56$	199.732	−	105.596i	0.476613	−	0.251979i
$57$		0			0
$58$	−127.386	+	20.8336i	−0.288391	+	0.0471652i
$59$			565.912i			1.24874i	0.781130	+	0.624368i	$0.214643\pi$
$59$			565.912i			1.24874i	−0.781130	+	0.624368i	$0.785357\pi$
$60$		0			0
$61$			825.056i			1.73176i	0.500249	+	0.865882i	$0.333242\pi$
$61$			825.056i			1.73176i	−0.500249	+	0.865882i	$0.666758\pi$
$62$	56.6591	+	346.441i	0.116060	+	0.709646i
$63$		0			0
$64$	288.306	−	423.112i	0.563099	−	0.826390i
$65$	−761.829	+	154.830i	−1.45374	+	0.295452i
$66$		0			0
$67$		−	168.301i		−	0.306884i	−0.988158	−	0.153442i	$-0.950964\pi$
$67$		−	168.301i		−	0.306884i	0.988158	−	0.153442i	$-0.0490358\pi$
$68$	−429.852	+	144.465i	−0.766577	+	0.257632i
$69$		0			0
$70$	−295.212	+	112.001i	−0.504065	+	0.191238i
$71$	478.705			0.800166			0.400083	−	0.916479i	$-0.368981\pi$
$71$	478.705			0.800166			0.400083	+	0.916479i	$0.368981\pi$
$72$		0			0
$73$		−	359.165i		−	0.575851i	−0.957653	−	0.287925i	$-0.907034\pi$
$73$		−	359.165i		−	0.575851i	0.957653	−	0.287925i	$-0.0929655\pi$
$74$	−107.597	+	17.5971i	−0.169026	+	0.0276435i
$75$		0			0
$76$	−552.089	+	185.547i	−0.833276	+	0.280049i
$77$			562.387i			0.832337i
$78$		0			0
$79$			752.089i			1.07110i	0.844505	+	0.535548i	$0.179895\pi$
$79$			752.089i			1.07110i	−0.844505	+	0.535548i	$0.820105\pi$
$80$	−472.811	+	537.075i	−0.660773	+	0.750586i
$81$		0			0
$82$	48.8291	+	298.564i	0.0657594	+	0.402084i
$83$	−910.621			−1.20426			−0.602130	−	0.798398i	$-0.705681\pi$
$83$	−910.621			−1.20426			−0.602130	+	0.798398i	$0.705681\pi$
$84$		0			0
$85$	621.059	−	126.221i	0.792510	−	0.161066i
$86$	−187.497	−	1146.45i	−0.235097	−	1.43749i
$87$		0			0
$88$	595.679	+	1126.71i	0.721586	+	1.36487i
$89$			432.574i			0.515200i	0.966252	+	0.257600i	$0.0829317\pi$
$89$			432.574i			0.515200i	−0.966252	+	0.257600i	$0.917068\pi$
$90$		0			0
$91$	−694.267			−0.799769
$92$	330.916	+	984.631i	0.375005	+	1.11581i
$93$		0			0
$94$	53.6093	+	327.793i	0.0588232	+	0.359673i
$95$	797.670	−	162.115i	0.861466	−	0.175080i
$96$		0			0
$97$			1021.20i			1.06894i	0.845188	+	0.534468i	$0.179488\pi$
$97$			1021.20i			1.06894i	−0.845188	+	0.534468i	$0.820512\pi$
$98$	679.150	−	111.072i	0.700046	−	0.114490i
$99$		0			0
$100$	748.347	−	663.308i	0.748347	−	0.663308i
$101$	1795.89			1.76928			0.884640	−	0.466275i	$-0.154404\pi$
$101$	1795.89			1.76928			0.884640	+	0.466275i	$0.154404\pi$
$102$		0			0
$103$	−1112.84			−1.06457			−0.532286	−	0.846564i	$-0.678667\pi$
$103$	−1112.84			−1.06457			−0.532286	+	0.846564i	$0.678667\pi$
$104$	−1390.93	+	735.366i	−1.31146	+	0.693351i
$105$		0			0
$106$	−301.719	−	1844.86i	−0.276467	−	1.69045i
$107$	1033.88			0.934102			0.467051	−	0.884230i	$-0.345316\pi$
$107$	1033.88			0.934102			0.467051	+	0.884230i	$0.345316\pi$
$108$		0			0
$109$			1901.48i			1.67090i	0.549563	+	0.835452i	$0.314794\pi$
$109$			1901.48i			1.67090i	−0.549563	+	0.835452i	$0.685206\pi$
$110$	−631.811	−	1665.33i	−0.547644	−	1.44348i
$111$		0			0
$112$	−509.315	+	385.934i	−0.429694	+	0.325602i
$113$	1470.23			1.22396			0.611981	−	0.790872i	$-0.290373\pi$
$113$	1470.23			1.22396			0.611981	+	0.790872i	$0.290373\pi$
$114$		0			0
$115$	−289.126	−	1422.62i	−0.234444	−	1.15356i
$116$	346.068	−	116.307i	0.276997	−	0.0930936i
$117$		0			0
$118$	−258.346	−	1579.65i	−0.201548	−	1.23236i
$119$	565.981			0.435995
$120$		0			0
$121$	−1841.50			−1.38354
$122$	−376.649	−	2303.01i	−0.279510	−	1.70906i
$123$		0			0
$124$	−316.310	−	941.170i	−0.229076	−	0.681610i
$125$	−1152.25	+	790.856i	−0.824480	+	0.565890i
$126$		0			0
$127$	−2240.64			−1.56555			−0.782775	−	0.622305i	$-0.786196\pi$
$127$	−2240.64			−1.56555			−0.782775	+	0.622305i	$0.786196\pi$
$128$	−611.606	+	1312.67i	−0.422335	+	0.906440i
$129$		0			0
$130$	2055.85	−	779.970i	1.38700	−	0.526215i
$131$		−	1227.95i		−	0.818981i	−0.912314	−	0.409491i	$-0.865706\pi$
$131$		−	1227.95i		−	0.818981i	0.912314	−	0.409491i	$-0.134294\pi$
$132$		0			0
$133$	726.929			0.473930
$134$	76.8316	+	469.785i	0.0495316	+	0.302860i
$135$		0			0
$136$	1133.91	−	599.486i	0.714944	−	0.377981i
$137$	173.005			0.107889			0.0539444	−	0.998544i	$-0.482821\pi$
$137$	173.005			0.107889			0.0539444	+	0.998544i	$0.482821\pi$
$138$		0			0
$139$	1563.18			0.953863			0.476932	−	0.878940i	$-0.341749\pi$
$139$	1563.18			0.953863			0.476932	+	0.878940i	$0.341749\pi$
$140$	772.907	−	447.401i	0.466590	−	0.270088i
$141$		0			0
$142$	−1336.23	+	218.535i	−0.789675	+	0.129148i
$143$		−	3916.45i		−	2.29028i
$144$		0			0
$145$	−500.007	+	101.619i	−0.286368	+	0.0582000i
$146$	163.964	+	1002.55i	0.0929434	+	0.568301i
$147$		0			0
$148$	292.307	−	98.2389i	0.162348	−	0.0545621i
$149$	267.275			0.146953			0.0734766	−	0.997297i	$-0.476591\pi$
$149$	267.275			0.146953			0.0734766	+	0.997297i	$0.476591\pi$
$150$		0			0
$151$			453.304i			0.244301i	0.992512	+	0.122150i	$0.0389790\pi$
$151$			453.304i			0.244301i	−0.992512	+	0.122150i	$0.961021\pi$
$152$	1456.37	−	769.961i	0.777150	−	0.410869i
$153$		0			0
$154$	−256.737	−	1569.82i	−0.134341	−	0.821424i
$155$	276.364	+	1359.82i	0.143213	+	0.704669i
$156$		0			0
$157$	46.0351			0.0234013			0.0117006	−	0.999932i	$-0.496275\pi$
$157$	46.0351			0.0234013			0.0117006	+	0.999932i	$0.496275\pi$
$158$	−343.339	−	2099.34i	−0.172877	−	1.05705i
$159$		0			0
$160$	1074.59	−	1715.01i	0.530963	−	0.847395i
$161$		−	1296.45i		−	0.634626i
$162$		0			0
$163$		−	2837.59i		−	1.36354i	−0.731566	−	0.681771i	$-0.761210\pi$
$163$		−	2837.59i		−	1.36354i	0.731566	−	0.681771i	$-0.238790\pi$
$164$	−272.597	−	811.105i	−0.129794	−	0.386199i
$165$		0			0
$166$	2541.85	−	415.711i	1.18847	−	0.194370i
$167$		−	2577.45i		−	1.19431i	−0.802127	−	0.597154i	$-0.796298\pi$
$167$		−	2577.45i		−	1.19431i	0.802127	−	0.597154i	$-0.203702\pi$
$168$		0			0
$169$	2637.85			1.20066
$170$	−1675.97	+	635.848i	−0.756123	+	0.286867i
$171$		0			0
$172$	1046.74	+	3114.53i	0.464029	+	1.38070i
$173$			1134.93i			0.498772i	0.968404	+	0.249386i	$0.0802287\pi$
$173$			1134.93i			0.498772i	−0.968404	+	0.249386i	$0.919771\pi$
$174$		0			0
$175$	−1149.07	+	487.187i	−0.496353	+	0.210445i
$176$	−2177.10	−	2873.11i	−0.932417	−	1.23050i
$177$		0			0
$178$	−197.476	−	1207.46i	−0.0831542	−	0.508445i
$179$			207.680i			0.0867192i	0.999060	+	0.0433596i	$0.0138061\pi$
$179$			207.680i			0.0867192i	−0.999060	+	0.0433596i	$0.986194\pi$
$180$		0			0
$181$		−	1998.14i		−	0.820556i	−0.911960	−	0.410278i	$-0.865432\pi$
$181$		−	1998.14i		−	0.820556i	0.911960	−	0.410278i	$-0.134568\pi$
$182$	1937.94	−	316.942i	0.789283	−	0.129084i
$183$		0			0
$184$	−1373.20	−	2597.38i	−0.550182	−	1.04066i
$185$	−422.331	+	85.8325i	−0.167840	+	0.0341110i
$186$		0			0
$187$			3192.77i			1.24855i
$188$	−299.284	−	890.510i	−0.116104	−	0.345463i
$189$		0			0
$190$	−2152.56	+	816.664i	−0.821912	+	0.311827i
$191$	3178.44			1.20411			0.602053	−	0.798456i	$-0.294350\pi$
$191$	3178.44			1.20411			0.602053	+	0.798456i	$0.294350\pi$
$192$		0			0
$193$		−	283.846i		−	0.105864i	−0.998598	−	0.0529318i	$-0.983143\pi$
$193$		−	283.846i		−	0.105864i	0.998598	−	0.0529318i	$-0.0168566\pi$
$194$	−466.190	−	2850.51i	−0.172528	−	1.05492i
$195$		0			0
$196$	−1845.03	+	620.082i	−0.672389	+	0.225978i
$197$			4926.74i			1.78180i	0.454195	+	0.890902i	$0.349927\pi$
$197$			4926.74i			1.78180i	−0.454195	+	0.890902i	$0.650073\pi$
$198$		0			0
$199$		−	2272.67i		−	0.809575i	−0.914411	−	0.404788i	$-0.867345\pi$
$199$		−	2272.67i		−	0.809575i	0.914411	−	0.404788i	$-0.132655\pi$
$200$	−1786.08	+	2193.15i	−0.631476	+	0.775396i
$201$		0			0
$202$	−5012.93	+	819.846i	−1.74608	+	0.285565i
$203$	−455.664			−0.157544
$204$		0			0
$205$	238.171	+	1171.90i	0.0811445	+	0.399264i
$206$	3106.31	−	508.025i	1.05062	−	0.171824i
$207$		0			0
$208$	3546.85	−	2687.64i	1.18236	−	0.895933i
$209$			4100.70i			1.35718i
$210$		0			0
$211$	−1710.14			−0.557967			−0.278984	−	0.960296i	$-0.589998\pi$
$211$	−1710.14			−0.557967			−0.278984	+	0.960296i	$0.589998\pi$
$212$	1684.40	+	5011.89i	0.545685	+	1.62367i
$213$		0			0
$214$	−2885.91	+	471.980i	−0.921855	+	0.150766i
$215$	−914.546	−	4499.94i	−0.290100	−	1.42741i
$216$		0			0
$217$			1239.23i			0.387669i
$218$	−868.050	−	5307.68i	−0.269687	−	1.64900i
$219$		0			0
$220$	2523.84	+	4360.07i	0.773444	+	1.33616i
$221$	−3941.47			−1.19969
$222$		0			0
$223$	−1105.19			−0.331878			−0.165939	−	0.986136i	$-0.553065\pi$
$223$	−1105.19			−0.331878			−0.165939	+	0.986136i	$0.553065\pi$
$224$	1245.49	−	1309.78i	0.371508	−	0.390686i
$225$		0			0
$226$	−4103.92	+	671.180i	−1.20791	+	0.197550i
$227$	4781.11			1.39795			0.698973	−	0.715148i	$-0.253641\pi$
$227$	4781.11			1.39795			0.698973	+	0.715148i	$0.253641\pi$
$228$		0			0
$229$			2154.90i			0.621832i	0.950437	+	0.310916i	$0.100636\pi$
$229$			2154.90i			0.621832i	−0.950437	+	0.310916i	$0.899364\pi$
$230$	1456.49	+	3839.02i	0.417558	+	1.10060i
$231$		0			0
$232$	−912.900	+	482.638i	−0.258340	+	0.136581i
$233$	−5855.26			−1.64631			−0.823157	−	0.567814i	$-0.807789\pi$
$233$	−5855.26			−1.64631			−0.823157	+	0.567814i	$0.807789\pi$
$234$		0			0
$235$	261.488	+	1286.63i	0.0725855	+	0.357150i
$236$	1442.27	+	4291.42i	0.397811	+	1.18368i
$237$		0			0
$238$	−1579.85	+	258.378i	−0.430278	+	0.0703704i
$239$	−2901.59			−0.785306			−0.392653	−	0.919687i	$-0.628443\pi$
$239$	−2901.59			−0.785306			−0.392653	+	0.919687i	$0.628443\pi$
$240$		0			0
$241$	2254.49			0.602591			0.301296	−	0.953531i	$-0.402581\pi$
$241$	2254.49			0.602591			0.301296	+	0.953531i	$0.402581\pi$
$242$	5140.25	−	840.668i	1.36540	−	0.223307i
$243$		0			0
$244$	2102.71	+	6256.55i	0.551690	+	1.64154i
$245$	2665.75	−	541.773i	0.695136	−	0.141276i
$246$		0			0
$247$	−5062.31			−1.30408
$248$	1312.59	+	2482.73i	0.336086	+	0.635700i
$249$		0			0
$250$	2855.28	−	2733.57i	0.722335	−	0.691544i
$251$			903.943i			0.227316i	0.993520	+	0.113658i	$0.0362569\pi$
$251$			903.943i			0.227316i	−0.993520	+	0.113658i	$0.963743\pi$
$252$		0			0
$253$	7313.45			1.81736
$254$	6254.40	−	1022.88i	1.54502	−	0.252683i
$255$		0			0
$256$	1107.95	−	3943.31i	0.270496	−	0.962721i
$257$	2563.95			0.622313			0.311157	−	0.950359i	$-0.399284\pi$
$257$	2563.95			0.622313			0.311157	+	0.950359i	$0.399284\pi$
$258$		0			0
$259$	−384.877			−0.0923362
$260$	−5382.50	+	3115.69i	−1.28388	+	0.743179i
$261$		0			0
$262$	560.576	+	3427.63i	0.132185	+	0.808243i
$263$		−	1011.41i		−	0.237134i	−0.992946	−	0.118567i	$-0.962170\pi$
$263$		−	1011.41i		−	0.237134i	0.992946	−	0.118567i	$-0.0378301\pi$
$264$		0			0
$265$	−1471.68	−	7241.28i	−0.341150	−	1.67860i
$266$	−2029.11	+	331.853i	−0.467717	+	0.0764932i
$267$		0			0
$268$	−428.927	−	1276.26i	−0.0977644	−	0.290895i
$269$	−2687.22			−0.609080			−0.304540	−	0.952500i	$-0.598503\pi$
$269$	−2687.22			−0.609080			−0.304540	+	0.952500i	$0.598503\pi$
$270$		0			0
$271$		−	365.036i		−	0.0818241i	−0.999163	−	0.0409121i	$-0.986974\pi$
$271$		−	365.036i		−	0.0818241i	0.999163	−	0.0409121i	$-0.0130263\pi$
$272$	−2891.47	+	2191.02i	−0.644563	+	0.488419i
$273$		0			0
$274$	−482.915	+	78.9789i	−0.106474	+	0.0174135i
$275$	−2748.28	−	6482.07i	−0.602646	−	1.42139i
$276$		0			0
$277$	4005.31			0.868793			0.434397	−	0.900722i	$-0.356962\pi$
$277$	4005.31			0.868793			0.434397	+	0.900722i	$0.356962\pi$
$278$	−4363.36	+	713.611i	−0.941357	+	0.153955i
$279$		0			0
$280$	−1953.20	+	1601.69i	−0.416880	+	0.341855i
$281$		−	4423.63i		−	0.939116i	−0.882902	−	0.469558i	$-0.844413\pi$
$281$		−	4423.63i		−	0.939116i	0.882902	−	0.469558i	$-0.155587\pi$
$282$		0			0
$283$		−	4991.23i		−	1.04840i	−0.851595	−	0.524201i	$-0.824364\pi$
$283$		−	4991.23i		−	1.04840i	0.851595	−	0.524201i	$-0.175636\pi$
$284$	3630.11	−	1220.01i	0.758476	−	0.254910i
$285$		0			0
$286$	1787.91	+	10932.1i	0.369655	+	2.26025i
$287$			1067.97i			0.219653i
$288$		0			0
$289$	−1699.83			−0.345986
$290$	1349.30	−	511.913i	0.273219	−	0.103657i
$291$		0			0
$292$	−915.358	−	2723.62i	−0.183450	−	0.545848i
$293$			5923.82i			1.18114i	0.806987	+	0.590569i	$0.201097\pi$
$293$			5923.82i			1.18114i	−0.806987	+	0.590569i	$0.798903\pi$
$294$		0			0
$295$	−1260.12	−	6200.33i	−0.248703	−	1.22372i
$296$	−771.081	+	407.660i	−0.151413	+	0.0800499i
$297$		0			0
$298$	−746.056	+	122.015i	−0.145026	+	0.0237185i
$299$			9028.45i			1.74625i
$300$		0			0
$301$		−	4100.86i		−	0.785282i
$302$	−206.940	−	1265.33i	−0.0394306	−	0.241097i
$303$		0			0
$304$	−3713.72	+	2814.08i	−0.700646	+	0.530916i
$305$	−1837.16	−	9039.60i	−0.344904	−	1.69707i
$306$		0			0
$307$			8861.87i			1.64747i	0.566974	+	0.823736i	$0.308114\pi$
$307$			8861.87i			1.64747i	−0.566974	+	0.823736i	$0.691886\pi$
$308$	1433.28	+	4264.69i	0.265159	+	0.788972i
$309$		0			0
$310$	−1392.20	−	3669.57i	−0.255070	−	0.672315i
$311$	−839.079			−0.152990			−0.0764949	−	0.997070i	$-0.524373\pi$
$311$	−839.079			−0.152990			−0.0764949	+	0.997070i	$0.524373\pi$
$312$		0			0
$313$			6644.93i			1.19998i	0.800008	+	0.599990i	$0.204829\pi$
$313$			6644.93i			1.19998i	−0.800008	+	0.599990i	$0.795171\pi$
$314$	−128.500	+	21.0156i	−0.0230945	+	0.00377701i
$315$		0			0
$316$	1916.75	+	5703.23i	0.341220	+	1.01529i
$317$			6259.34i			1.10902i	0.832177	+	0.554510i	$0.187094\pi$
$317$			6259.34i			1.10902i	−0.832177	+	0.554510i	$0.812906\pi$
$318$		0			0
$319$		−	2570.46i		−	0.451154i
$320$	−2216.64	+	5277.74i	−0.387231	+	0.921983i
$321$		0			0
$322$	591.848	+	3618.84i	0.102430	+	0.626305i
$323$	4126.90			0.710919
$324$		0			0
$325$	8002.11	−	3392.76i	1.36578	−	0.579065i
$326$	1295.40	+	7920.69i	0.220078	+	1.34566i
$327$		0			0
$328$	1131.19	+	2139.63i	0.190426	+	0.360186i
$329$			1172.52i			0.196484i
$330$		0			0
$331$	4943.81			0.820956			0.410478	−	0.911871i	$-0.365362\pi$
$331$	4943.81			0.820956			0.410478	+	0.911871i	$0.365362\pi$
$332$	−6905.41	+	2320.78i	−1.14152	+	0.383643i
$333$		0			0
$334$	1176.64	+	7194.56i	0.192763	+	1.17865i
$335$	374.758	+	1843.96i	0.0611201	+	0.300736i
$336$		0			0
$337$			6995.97i			1.13084i	0.824801	+	0.565422i	$0.191287\pi$
$337$			6995.97i			1.13084i	−0.824801	+	0.565422i	$0.808713\pi$
$338$	−7363.15	+	1204.22i	−1.18492	+	0.193789i
$339$		0			0
$340$	4387.93	−	2539.97i	0.699908	−	0.405145i
$341$	−6990.64			−1.11016
$342$		0			0
$343$	5854.09			0.921548
$344$	−4343.63	−	8215.87i	−0.680792	−	1.28770i
$345$		0			0
$346$	−518.113	−	3167.99i	−0.0805027	−	0.492232i
$347$	−5924.13			−0.916496			−0.458248	−	0.888824i	$-0.651523\pi$
$347$	−5924.13			−0.916496			−0.458248	+	0.888824i	$0.651523\pi$
$348$		0			0
$349$		−	8698.61i		−	1.33417i	−0.744981	−	0.667086i	$-0.767541\pi$
$349$		−	8698.61i		−	1.33417i	0.744981	−	0.667086i	$-0.232459\pi$
$350$	2985.05	−	1884.47i	0.455879	−	0.287798i
$351$		0			0
$352$	7388.66	+	7025.96i	1.11880	+	1.06388i
$353$	−136.609			−0.0205976			−0.0102988	−	0.999947i	$-0.503278\pi$
$353$	−136.609			−0.0205976			−0.0102988	+	0.999947i	$0.503278\pi$
$354$		0			0
$355$	−5244.86	+	1065.94i	−0.784136	+	0.159364i
$356$	1102.45	+	3280.29i	0.164128	+	0.488357i
$357$		0			0
$358$	−94.8088	−	579.707i	−0.0139966	−	0.0855822i
$359$	−7563.50			−1.11194			−0.555970	−	0.831202i	$-0.687653\pi$
$359$	−7563.50			−1.11194			−0.555970	+	0.831202i	$0.687653\pi$
$360$		0			0
$361$	−1558.53			−0.227224
$362$	912.178	+	5577.50i	0.132439	+	0.809798i
$363$		0			0
$364$	−5264.76	+	1769.39i	−0.758100	+	0.254783i
$365$	799.759	+	3935.14i	0.114688	+	0.564314i
$366$		0			0
$367$	3493.23			0.496853			0.248426	−	0.968651i	$-0.420087\pi$
$367$	3493.23			0.496853			0.248426	+	0.968651i	$0.420087\pi$
$368$	5018.80	+	6623.28i	0.710933	+	0.938213i
$369$		0			0
$370$	1139.69	−	432.388i	0.160134	−	0.0607534i
$371$		−	6599.09i		−	0.923471i
$372$		0			0
$373$	−8241.23			−1.14401			−0.572004	−	0.820251i	$-0.693834\pi$
$373$	−8241.23			−1.14401			−0.572004	+	0.820251i	$0.693834\pi$
$374$	−1457.54	−	8912.11i	−0.201518	−	1.23218i
$375$		0			0
$376$	1241.93	+	2349.09i	0.170340	+	0.322194i
$377$	3173.23			0.433500
$378$		0			0
$379$	13107.5			1.77648			0.888242	−	0.459376i	$-0.151927\pi$
$379$	13107.5			1.77648			0.888242	+	0.459376i	$0.151927\pi$
$380$	5635.72	−	3262.26i	0.760807	−	0.440396i
$381$		0			0
$382$	−8872.12	+	1451.00i	−1.18832	+	0.194345i
$383$		−	5261.29i		−	0.701930i	−0.936389	−	0.350965i	$-0.885854\pi$
$383$		−	5261.29i		−	0.701930i	0.936389	−	0.350965i	$-0.114146\pi$
$384$		0			0
$385$	−1252.28	−	6161.71i	−0.165771	−	0.815662i
$386$	129.580	+	792.312i	0.0170866	+	0.104476i
$387$		0			0
$388$	2602.59	+	7743.93i	0.340533	+	1.01324i
$389$	−11019.9			−1.43633			−0.718163	−	0.695875i	$-0.755017\pi$
$389$	−11019.9			−1.43633			−0.718163	+	0.695875i	$0.755017\pi$
$390$		0			0
$391$		−	7360.18i		−	0.951970i
$392$	4867.05	−	2573.15i	0.627100	−	0.331539i
$393$		0			0
$394$	−2249.12	−	13752.2i	−0.287587	−	1.75844i
$395$	−1674.69	−	8240.15i	−0.213323	−	1.04964i
$396$		0			0
$397$	−3819.53			−0.482864			−0.241432	−	0.970418i	$-0.577617\pi$
$397$	−3819.53			−0.482864			−0.241432	+	0.970418i	$0.577617\pi$
$398$	1037.51	+	6343.81i	0.130667	+	0.798961i
$399$		0			0
$400$	3984.37	−	6937.21i	0.498046	−	0.867151i
$401$			8354.64i			1.04043i	0.854036	+	0.520213i	$0.174148\pi$
$401$			8354.64i			1.04043i	−0.854036	+	0.520213i	$0.825852\pi$
$402$		0			0
$403$		−	8629.94i		−	1.06672i
$404$	13618.5	−	4576.94i	1.67710	−	0.563642i
$405$		0			0
$406$	1271.91	−	208.017i	0.155478	−	0.0254278i
$407$		−	2171.14i		−	0.264421i
$408$		0			0
$409$	15835.5			1.91447			0.957234	−	0.289315i	$-0.0934276\pi$
$409$	15835.5			1.91447			0.957234	+	0.289315i	$0.0934276\pi$
$410$	−1199.81	−	3162.45i	−0.144523	−	0.380932i
$411$		0			0
$412$	−8438.85	+	2836.14i	−1.00911	+	0.339142i
$413$		−	5650.45i		−	0.673222i
$414$		0			0
$415$	9977.09	−	2027.69i	1.18013	−	0.239845i
$416$	−8673.54	+	9121.30i	−1.02225	+	1.07502i
$417$		0			0
$418$	−1872.02	−	11446.5i	−0.219052	−	1.33939i
$419$			1015.69i			0.118424i	0.998245	+	0.0592119i	$0.0188588\pi$
$419$			1015.69i			0.118424i	−0.998245	+	0.0592119i	$0.981141\pi$
$420$		0			0
$421$			5843.58i			0.676481i	0.941060	+	0.338241i	$0.109832\pi$
$421$			5843.58i			0.676481i	−0.941060	+	0.338241i	$0.890168\pi$
$422$	4773.60	−	780.703i	0.550652	−	0.0900570i
$423$		0			0
$424$	−6989.74	−	13220.9i	−0.800594	−	1.51431i
$425$	−6523.49	+	2765.85i	−0.744555	+	0.315678i
$426$		0			0
$427$		−	8237.93i		−	0.933633i
$428$	7840.11	−	2634.92i	0.885435	−	0.297578i
$429$		0			0
$430$	4607.09	+	12143.4i	0.516683	+	1.36187i
$431$	−13829.0			−1.54552			−0.772762	−	0.634696i	$-0.781125\pi$
$431$	−13829.0			−1.54552			−0.772762	+	0.634696i	$0.781125\pi$
$432$		0			0
$433$			11541.2i			1.28091i	0.767996	+	0.640454i	$0.221254\pi$
$433$			11541.2i			1.28091i	−0.767996	+	0.640454i	$0.778746\pi$
$434$	−565.724	−	3459.11i	−0.0625706	−	0.382587i
$435$		0			0
$436$	4846.05	+	14419.3i	0.532302	+	1.58385i
$437$		−	9453.20i		−	1.03480i
$438$		0			0
$439$			5358.82i			0.582603i	0.956631	+	0.291301i	$0.0940883\pi$
$439$			5358.82i			0.582603i	−0.956631	+	0.291301i	$0.905912\pi$
$440$	−9035.35	−	11018.3i	−0.978962	−	1.19381i
$441$		0			0
$442$	11002.0	−	1799.34i	1.18396	−	0.193633i
$443$	−12378.9			−1.32763			−0.663814	−	0.747898i	$-0.731063\pi$
$443$	−12378.9			−1.32763			−0.663814	+	0.747898i	$0.731063\pi$
$444$		0			0
$445$	−963.220	−	4739.44i	−0.102609	−	0.504879i
$446$	3084.95	−	504.532i	0.327527	−	0.0535657i
$447$		0			0
$448$	−2878.65	+	4224.64i	−0.303579	+	0.445526i
$449$			7794.74i			0.819279i	0.912247	+	0.409640i	$0.134346\pi$
$449$			7794.74i			0.819279i	−0.912247	+	0.409640i	$0.865654\pi$
$450$		0			0
$451$	−6024.56			−0.629015
$452$	11149.0	−	3746.99i	1.16019	−	0.389919i
$453$		0			0
$454$	−13345.7	+	2182.64i	−1.37962	+	0.225631i
$455$	7606.63	−	1545.94i	0.783746	−	0.159285i
$456$		0			0
$457$		−	6684.54i		−	0.684222i	−0.939659	−	0.342111i	$-0.888858\pi$
$457$		−	6684.54i		−	0.684222i	0.939659	−	0.342111i	$-0.111142\pi$
$458$	−983.739	−	6015.05i	−0.100365	−	0.613679i
$459$		0			0
$460$	−5818.13	−	10051.1i	−0.589721	−	1.01877i
$461$	16144.0			1.63102			0.815511	−	0.578741i	$-0.196456\pi$
$461$	16144.0			1.63102			0.815511	+	0.578741i	$0.196456\pi$
$462$		0			0
$463$	−14282.5			−1.43362			−0.716809	−	0.697269i	$-0.754398\pi$
$463$	−14282.5			−1.43362			−0.716809	+	0.697269i	$0.754398\pi$
$464$	2327.89	−	1763.96i	0.232908	−	0.176487i
$465$		0			0
$466$	16344.0	−	2673.01i	1.62473	−	0.265718i
$467$	14273.2			1.41431			0.707156	−	0.707057i	$-0.249978\pi$
$467$	14273.2			1.41431			0.707156	+	0.707057i	$0.249978\pi$
$468$		0			0
$469$			1680.43i			0.165448i
$470$	−1317.27	−	3472.05i	−0.129279	−	0.340752i
$471$		0			0
$472$	−5984.95	−	11320.4i	−0.583643	−	1.10395i
$473$	23133.5			2.24879
$474$		0			0
$475$	−8378.57	+	3552.37i	−0.809338	+	0.343145i
$476$	4291.94	−	1442.44i	0.413279	−	0.138895i
$477$		0			0
$478$	8099.33	−	1324.61i	0.775010	−	0.126750i
$479$	18890.4			1.80193			0.900967	−	0.433887i	$-0.142858\pi$
$479$	18890.4			1.80193			0.900967	+	0.433887i	$0.142858\pi$
$480$		0			0
$481$	2680.27			0.254074
$482$	−6293.05	+	1029.20i	−0.594690	+	0.0972593i
$483$		0			0
$484$	−13964.4	+	4693.19i	−1.31146	+	0.440758i
$485$	−2273.92	−	11188.6i	−0.212893	−	1.04752i
$486$		0			0
$487$	−3394.04			−0.315808			−0.157904	−	0.987454i	$-0.550474\pi$
$487$	−3394.04			−0.315808			−0.157904	+	0.987454i	$0.550474\pi$
$488$	−8725.59	−	16504.3i	−0.809404	−	1.53097i
$489$		0			0
$490$	−7193.68	+	2729.22i	−0.663219	+	0.251620i
$491$			7878.06i			0.724097i	0.932159	+	0.362049i	$0.117923\pi$
$491$			7878.06i			0.724097i	−0.932159	+	0.362049i	$0.882077\pi$
$492$		0			0
$493$	−2586.88			−0.236323
$494$	14130.6	−	2311.01i	1.28698	−	0.210481i
$495$		0			0
$496$	−4797.28	−	6330.94i	−0.434283	−	0.573120i
$497$	−4779.72			−0.431388
$498$		0			0
$499$	3859.49			0.346241			0.173121	−	0.984901i	$-0.444615\pi$
$499$	3859.49			0.346241			0.173121	+	0.984901i	$0.444615\pi$
$500$	−6722.15	+	8933.79i	−0.601248	+	0.799063i
$501$		0			0
$502$	−412.662	−	2523.22i	−0.0366893	−	0.224336i
$503$			15327.2i			1.35866i	0.733835	+	0.679328i	$0.237729\pi$
$503$			15327.2i			1.35866i	−0.733835	+	0.679328i	$0.762271\pi$
$504$		0			0
$505$	−19676.4	+	3998.93i	−1.73383	+	0.352376i
$506$	−20414.3	+	3338.69i	−1.79353	+	0.293326i
$507$		0			0
$508$	−16991.2	+	5710.43i	−1.48398	+	0.498739i
$509$	8682.06			0.756042			0.378021	−	0.925797i	$-0.376605\pi$
$509$	8682.06			0.756042			0.378021	+	0.925797i	$0.376605\pi$
$510$		0			0
$511$			3586.15i			0.310454i
$512$	−1292.50	+	11512.9i	−0.111565	+	0.993757i
$513$		0			0
$514$	−7156.85	+	1170.48i	−0.614154	+	0.100443i
$515$	12192.6	−	2477.97i	1.04325	−	0.212024i
$516$		0			0
$517$	−6614.35			−0.562667
$518$	1074.32	−	175.701i	0.0911255	−	0.0149032i
$519$		0			0
$520$	13602.1	−	11154.1i	1.14710	−	0.940656i
$521$		−	3686.60i		−	0.310005i	−0.987914	−	0.155003i	$-0.950461\pi$
$521$		−	3686.60i		−	0.310005i	0.987914	−	0.155003i	$-0.0495386\pi$
$522$		0			0
$523$		−	1664.45i		−	0.139161i	−0.997576	−	0.0695806i	$-0.977834\pi$
$523$		−	1664.45i		−	0.139161i	0.997576	−	0.0695806i	$-0.0221661\pi$
$524$	−3129.52	−	9311.78i	−0.260904	−	0.776311i
$525$		0			0
$526$	461.723	+	2823.20i	0.0382739	+	0.234025i
$527$			7035.31i			0.581524i
$528$		0			0
$529$	−4692.44			−0.385670
$530$	7413.71	+	19541.1i	0.607606	+	1.60153i
$531$		0			0
$532$	5512.44	−	1852.63i	0.449238	−	0.150981i
$533$		−	7437.32i		−	0.604402i
$534$		0			0
$535$	−11327.6	+	2302.16i	−0.915389	+	0.186039i
$536$	1779.91	+	3366.66i	0.143434	+	0.271302i
$537$		0			0
$538$	7500.94	−	1226.75i	0.601094	−	0.0983066i
$539$			13704.2i			1.09514i
$540$		0			0
$541$			11177.4i			0.888270i	0.895960	+	0.444135i	$0.146489\pi$
$541$			11177.4i			0.888270i	−0.895960	+	0.444135i	$0.853511\pi$
$542$	166.644	+	1018.94i	0.0132066	+	0.0807513i
$543$		0			0
$544$	7070.85	−	7435.87i	0.557280	−	0.586049i
$545$	−4234.05	−	20833.3i	−0.332783	−	1.63743i
$546$		0			0
$547$			14146.6i			1.10579i	0.833252	+	0.552893i	$0.186476\pi$
$547$			14146.6i			1.10579i	−0.833252	+	0.552893i	$0.813524\pi$
$548$	1311.93	−	440.914i	0.102268	−	0.0343703i
$549$		0			0
$550$	10630.6	+	16839.0i	0.824161	+	1.30549i
$551$	−3322.52			−0.256886
$552$		0			0
$553$		−	7509.38i		−	0.577452i
$554$	−11180.2	+	1828.48i	−0.857402	+	0.140225i
$555$		0			0
$556$	11853.9	−	3983.87i	0.904166	−	0.303873i
$557$		−	21574.0i		−	1.64115i	−0.571540	−	0.820574i	$-0.693654\pi$
$557$		−	21574.0i		−	1.64115i	0.571540	−	0.820574i	$-0.306346\pi$
$558$		0			0
$559$			28558.3i			2.16080i
$560$	4720.87	−	5362.53i	0.356238	−	0.404658i
$561$		0			0
$562$	2019.45	+	12347.9i	0.151575	+	0.926803i
$563$	−24297.3			−1.81885			−0.909423	−	0.415872i	$-0.863477\pi$
$563$	−24297.3			−1.81885			−0.909423	+	0.415872i	$0.863477\pi$
$564$		0			0
$565$	−16108.4	+	3273.79i	−1.19944	+	0.243769i
$566$	2278.56	+	13932.2i	0.169214	+	1.03466i
$567$		0			0
$568$	−9575.92	+	5062.67i	−0.707389	+	0.373987i
$569$			11145.0i			0.821129i	0.911832	+	0.410565i	$0.134668\pi$
$569$			11145.0i			0.821129i	−0.911832	+	0.410565i	$0.865332\pi$
$570$		0			0
$571$	−113.162			−0.00829363			−0.00414681	−	0.999991i	$-0.501320\pi$
$571$	−113.162			−0.00829363			−0.00414681	+	0.999991i	$0.501320\pi$
$572$	−9981.34	−	29699.2i	−0.729617	−	2.17095i
$573$		0			0
$574$	−487.543	−	2981.07i	−0.0354524	−	0.216773i
$575$	6335.52	+	14942.9i	0.459495	+	1.08376i
$576$		0			0
$577$		−	24768.3i		−	1.78703i	−0.449032	−	0.893516i	$-0.648231\pi$
$577$		−	24768.3i		−	1.78703i	0.449032	−	0.893516i	$-0.351769\pi$
$578$	4744.80	−	775.995i	0.341450	−	0.0558428i
$579$		0			0
$580$	−3532.66	+	2044.90i	−0.252907	+	0.146396i
$581$	9092.27			0.649244
$582$		0			0
$583$	37226.3			2.64452
$584$	3798.45	+	7184.68i	0.269145	+	0.509082i
$585$		0			0
$586$	−2704.30	−	16535.4i	−0.190638	−	1.16565i
$587$	6494.87			0.456681			0.228341	−	0.973581i	$-0.426670\pi$
$587$	6494.87			0.456681			0.228341	+	0.973581i	$0.426670\pi$
$588$		0			0
$589$			9035.94i			0.632121i
$590$	6347.97	+	16732.0i	0.442952	+	1.16753i
$591$		0			0
$592$	1966.25	−	1489.93i	0.136507	−	0.103439i
$593$	12664.6			0.877019			0.438509	−	0.898727i	$-0.355507\pi$
$593$	12664.6			0.877019			0.438509	+	0.898727i	$0.355507\pi$
$594$		0			0
$595$	−6201.09	+	1260.28i	−0.427260	+	0.0868343i
$596$	2026.80	−	681.169i	0.139297	−	0.0468151i
$597$		0			0
$598$	−4121.61	−	25201.5i	−0.281848	−	1.72335i
$599$	−12713.6			−0.867216			−0.433608	−	0.901102i	$-0.642760\pi$
$599$	−12713.6			−0.867216			−0.433608	+	0.901102i	$0.642760\pi$
$600$		0			0
$601$	−21278.7			−1.44422			−0.722110	−	0.691778i	$-0.756828\pi$
$601$	−21278.7			−1.44422			−0.722110	+	0.691778i	$0.756828\pi$
$602$	1872.10	+	11446.9i	0.126746	+	0.774986i
$603$		0			0
$604$	1155.28	+	3437.49i	0.0778272	+	0.231572i
$605$	20176.1	−	4100.49i	1.35583	−	0.275552i
$606$		0			0
$607$	4284.76			0.286512			0.143256	−	0.989686i	$-0.454243\pi$
$607$	4284.76			0.286512			0.143256	+	0.989686i	$0.454243\pi$
$608$	9081.60	−	9550.41i	0.605769	−	0.637040i
$609$		0			0
$610$	9254.86	+	24393.9i	0.614292	+	1.61915i
$611$		−	8165.42i		−	0.540650i
$612$		0			0
$613$	−10809.2			−0.712199			−0.356099	−	0.934448i	$-0.615894\pi$
$613$	−10809.2			−0.712199			−0.356099	+	0.934448i	$0.615894\pi$
$614$	−4045.56	−	24736.5i	−0.265905	−	1.62587i
$615$		0			0
$616$	−5947.67	−	11249.9i	−0.389024	−	0.735830i
$617$	−19661.1			−1.28286			−0.641431	−	0.767181i	$-0.721659\pi$
$617$	−19661.1			−1.28286			−0.641431	+	0.767181i	$0.721659\pi$
$618$		0			0
$619$	−8709.77			−0.565550			−0.282775	−	0.959186i	$-0.591255\pi$
$619$	−8709.77			−0.565550			−0.282775	+	0.959186i	$0.591255\pi$
$620$	5561.33	+	9607.47i	0.360239	+	0.622331i
$621$		0			0
$622$	2342.16	−	383.051i	0.150984	−	0.0246928i
$623$		−	4319.12i		−	0.277756i
$624$		0			0
$625$	10863.4	−	11230.6i	0.695258	−	0.718760i
$626$	−3033.50	−	18548.3i	−0.193679	−	1.18425i
$627$		0			0
$628$	349.093	−	117.324i	0.0221820	−	0.00745498i
$629$	−2185.01			−0.138509
$630$		0			0
$631$		−	4196.65i		−	0.264764i	−0.991199	−	0.132382i	$-0.957737\pi$
$631$		−	4196.65i		−	0.264764i	0.991199	−	0.132382i	$-0.0422625\pi$
$632$	−7953.91	−	15044.7i	−0.500616	−	0.946905i
$633$		0			0
$634$	−2857.47	−	17472.0i	−0.178998	−	1.09448i
$635$	24549.3	−	4989.27i	1.53419	−	0.311800i
$636$		0			0
$637$	−16917.8			−1.05229
$638$	1173.45	+	7175.03i	0.0728170	+	0.445238i
$639$		0			0
$640$	3778.04	−	15743.9i	0.233344	−	0.972394i
$641$		−	17311.9i		−	1.06674i	−0.845883	−	0.533369i	$-0.820926\pi$
$641$		−	17311.9i		−	1.06674i	0.845883	−	0.533369i	$-0.179074\pi$
$642$		0			0
$643$		−	9788.09i		−	0.600318i	−0.953889	−	0.300159i	$-0.902960\pi$
$643$		−	9788.09i		−	0.600318i	0.953889	−	0.300159i	$-0.0970397\pi$
$644$	−3304.10	−	9831.24i	−0.202174	−	0.601561i
$645$		0			0
$646$	−11519.6	+	1883.99i	−0.701598	+	0.114744i
$647$			14375.1i			0.873482i	0.899587	+	0.436741i	$0.143867\pi$
$647$			14375.1i			0.873482i	−0.899587	+	0.436741i	$0.856133\pi$
$648$		0			0
$649$	31874.9			1.92789
$650$	−20787.8	+	13123.4i	−1.25441	+	0.791912i
$651$		0			0
$652$	−7231.80	−	21518.0i	−0.434385	−	1.29250i
$653$		−	2261.17i		−	0.135507i	−0.997702	−	0.0677537i	$-0.978417\pi$
$653$		−	2261.17i		−	0.135507i	0.997702	−	0.0677537i	$-0.0215832\pi$
$654$		0			0
$655$	2734.30	+	13453.9i	0.163111	+	0.802574i
$656$	−4134.32	−	5456.03i	−0.246064	−	0.324729i
$657$		0			0
$658$	−535.273	−	3272.91i	−0.0317129	−	0.193908i
$659$			23135.8i			1.36759i	0.729675	+	0.683794i	$0.239671\pi$
$659$			23135.8i			1.36759i	−0.729675	+	0.683794i	$0.760329\pi$
$660$		0			0
$661$			1210.89i			0.0712528i	0.999365	+	0.0356264i	$0.0113426\pi$
$661$			1210.89i			0.0712528i	−0.999365	+	0.0356264i	$0.988657\pi$
$662$	−13799.9	+	2256.92i	−0.810192	+	0.132504i
$663$		0			0
$664$	18215.9	−	9630.51i	1.06463	−	0.562856i
$665$	−7964.49	+	1618.66i	−0.464436	+	0.0943896i
$666$		0			0
$667$			5925.59i			0.343988i
$668$	−6568.82	−	19545.3i	−0.380472	−	1.13208i
$669$		0			0
$670$	−1887.87	−	4976.05i	−0.108858	−	0.286928i
$671$	46471.2			2.67362
$672$		0			0
$673$			12324.0i			0.705879i	0.935646	+	0.352940i	$0.114818\pi$
$673$			12324.0i			0.705879i	−0.935646	+	0.352940i	$0.885182\pi$
$674$	−3193.75	−	19528.1i	−0.182520	−	1.11602i
$675$		0			0
$676$	20003.3	−	6722.76i	1.13811	−	0.382496i
$677$			282.089i			0.0160141i	0.999968	+	0.00800707i	$0.00254876\pi$
$677$			282.089i			0.0160141i	−0.999968	+	0.00800707i	$0.997451\pi$
$678$		0			0
$679$		−	10196.3i		−	0.576288i
$680$	−11088.7	+	9093.08i	−0.625340	+	0.512800i
$681$		0			0
$682$	19513.3	−	3191.32i	1.09560	−	0.179182i
$683$	−11198.5			−0.627379			−0.313689	−	0.949526i	$-0.601565\pi$
$683$	−11198.5			−0.627379			−0.313689	+	0.949526i	$0.601565\pi$
$684$		0			0
$685$	−1895.50	+	385.232i	−0.105727	+	0.0214875i
$686$	−16340.8	+	2672.47i	−0.909465	+	0.148740i
$687$		0			0
$688$	15875.2	+	20950.4i	0.879704	+	1.16094i
$689$			45955.8i			2.54104i
$690$		0			0
$691$	−7199.54			−0.396358			−0.198179	−	0.980166i	$-0.563503\pi$
$691$	−7199.54			−0.396358			−0.198179	+	0.980166i	$0.563503\pi$
$692$	2892.46	+	8606.43i	0.158894	+	0.472785i
$693$		0			0
$694$	16536.3	−	2704.45i	0.904480	−	0.147924i
$695$	−17126.7	+	3480.75i	−0.934754	+	0.189975i
$696$		0			0
$697$			6063.06i			0.329490i
$698$	3971.03	+	24280.8i	0.215338	+	1.31668i
$699$		0			0
$700$	−7472.01	+	6622.93i	−0.403451	+	0.357604i
$701$	−6712.14			−0.361646			−0.180823	−	0.983516i	$-0.557876\pi$
$701$	−6712.14			−0.361646			−0.180823	+	0.983516i	$0.557876\pi$
$702$		0			0
$703$	−2806.36			−0.150560
$704$	−23831.7	−	16238.8i	−1.27584	−	0.869353i
$705$		0			0
$706$	381.322	−	62.3637i	0.0203275	−	0.00332449i
$707$	−17931.4			−0.953859
$708$		0			0
$709$			5725.29i			0.303269i	0.988437	+	0.151635i	$0.0484537\pi$
$709$			5725.29i			0.303269i	−0.988437	+	0.151635i	$0.951546\pi$
$710$	14153.6	−	5369.75i	0.748133	−	0.283835i
$711$		0			0
$712$	−4574.81	−	8653.15i	−0.240798	−	0.455464i
$713$	16115.3			0.846454
$714$		0			0
$715$	8720.82	+	42910.0i	0.456140	+	2.24440i
$716$	529.288	+	1574.88i	0.0276263	+	0.0822011i
$717$		0			0
$718$	21112.3	−	3452.84i	1.09736	−	0.179469i
$719$	−26935.0			−1.39709			−0.698544	−	0.715567i	$-0.746168\pi$
$719$	−26935.0			−1.39709			−0.698544	+	0.715567i	$0.746168\pi$
$720$		0			0
$721$	11111.3			0.573936
$722$	4350.39	−	711.490i	0.224245	−	0.0366744i
$723$		0			0
$724$	−5092.41	−	15152.3i	−0.261406	−	0.777804i
$725$	5251.98	−	2226.75i	0.269039	−	0.114068i
$726$		0			0
$727$	33480.6			1.70802			0.854008	−	0.520260i	$-0.174165\pi$
$727$	33480.6			1.70802			0.854008	+	0.520260i	$0.174165\pi$
$728$	13888.0	−	7342.40i	0.707038	−	0.373802i
$729$		0			0
$730$	−4028.85	−	10619.2i	−0.204266	−	0.538405i
$731$		−	23281.3i		−	1.17796i
$732$		0			0
$733$	−12021.9			−0.605783			−0.302891	−	0.953025i	$-0.597952\pi$
$733$	−12021.9			−0.605783			−0.302891	+	0.953025i	$0.597952\pi$
$734$	−9750.80	+	1594.71i	−0.490338	+	0.0801930i
$735$		0			0
$736$	−17032.8	−	16196.7i	−0.853041	−	0.811166i
$737$	−9479.53			−0.473790
$738$		0			0
$739$	17322.5			0.862270			0.431135	−	0.902288i	$-0.358113\pi$
$739$	17322.5			0.862270			0.431135	+	0.902288i	$0.358113\pi$
$740$	−2983.87	+	1727.22i	−0.148228	+	0.0858027i
$741$		0			0
$742$	3012.57	+	18420.3i	0.149050	+	0.911363i
$743$			33981.1i			1.67785i	0.544245	+	0.838926i	$0.316816\pi$
$743$			33981.1i			1.67785i	−0.544245	+	0.838926i	$0.683184\pi$
$744$		0			0
$745$	−2928.36	+	595.145i	−0.144009	+	0.0292677i
$746$	23004.1	−	3762.23i	1.12901	−	0.184645i
$747$		0			0
$748$	8137.00	+	24211.4i	0.397752	+	1.18350i
$749$	−10323.0			−0.503596
$750$		0			0
$751$			37073.6i			1.80138i	0.434463	+	0.900690i	$0.356938\pi$
$751$			37073.6i			1.80138i	−0.434463	+	0.900690i	$0.643062\pi$
$752$	−4539.05	−	5990.16i	−0.220109	−	0.290477i
$753$		0			0
$754$	−8857.57	+	1448.62i	−0.427817	+	0.0699678i
$755$	−1009.38	−	4966.56i	−0.0486558	−	0.239406i
$756$		0			0
$757$	29091.4			1.39676			0.698378	−	0.715729i	$-0.253906\pi$
$757$	29091.4			1.39676			0.698378	+	0.715729i	$0.253906\pi$
$758$	−36587.6	+	5983.75i	−1.75319	+	0.286728i
$759$		0			0
$760$	−14242.0	+	11678.9i	−0.679751	+	0.557418i
$761$		−	7879.37i		−	0.375331i	−0.982233	−	0.187666i	$-0.939908\pi$
$761$		−	7879.37i		−	0.375331i	0.982233	−	0.187666i	$-0.0600921\pi$
$762$		0			0
$763$		−	18985.7i		−	0.900822i
$764$	24102.7	−	8100.49i	1.14137	−	0.383593i
$765$		0			0
$766$	2401.85	+	14686.1i	0.113293	+	0.692727i
$767$			39349.6i			1.85245i
$768$		0			0
$769$	−33111.9			−1.55273			−0.776363	−	0.630286i	$-0.782938\pi$
$769$	−33111.9			−1.55273			−0.776363	+	0.630286i	$0.782938\pi$
$770$	6308.44	+	16627.8i	0.295247	+	0.778212i
$771$		0			0
$772$	−723.402	−	2152.46i	−0.0337251	−	0.100348i
$773$		−	13761.2i		−	0.640305i	−0.947366	−	0.320152i	$-0.896266\pi$
$773$		−	13761.2i		−	0.640305i	0.947366	−	0.320152i	$-0.103734\pi$
$774$		0			0
$775$	−6055.88	−	14283.3i	−0.280689	−	0.662029i
$776$	−10799.9	−	20427.9i	−0.499607	−	0.944997i
$777$		0			0
$778$	30760.3	−	5030.73i	1.41749	−	0.231826i
$779$			7787.21i			0.358159i
$780$		0			0
$781$		−	26963.0i		−	1.23535i
$782$	3360.02	+	20544.8i	0.153650	+	0.939489i
$783$		0			0
$784$	−12410.9	+	9404.40i	−0.565367	+	0.428408i
$785$	−504.377	+	102.507i	−0.0229325	+	0.00466068i
$786$		0			0
$787$		−	34649.3i		−	1.56940i	−0.619879	−	0.784698i	$-0.712818\pi$
$787$		−	34649.3i		−	1.56940i	0.619879	−	0.784698i	$-0.287182\pi$
$788$	12556.1	+	37360.4i	0.567632	+	1.68897i
$789$		0			0
$790$	8436.37	+	22236.6i	0.379940	+	1.00145i
$791$	−14679.8			−0.659866
$792$		0			0
$793$			57368.7i			2.56901i
$794$	10661.6	−	1743.67i	0.476533	−	0.0779351i
$795$		0			0
$796$	−5792.07	−	17234.1i	−0.257908	−	0.767396i
$797$		−	10582.2i		−	0.470314i	−0.971957	−	0.235157i	$-0.924440\pi$
$797$		−	10582.2i		−	0.470314i	0.971957	−	0.235157i	$-0.0755604\pi$
$798$		0			0
$799$			6656.62i			0.294736i
$800$	−7954.81	+	21183.0i	−0.351556	+	0.936167i
$801$		0			0
$802$	−3814.01	−	23320.7i	−0.167927	−	1.02679i
$803$	−20230.0			−0.889040
$804$		0			0
$805$	2886.83	+	14204.4i	0.126394	+	0.621912i
$806$	3939.68	+	24089.1i	0.172171	+	1.05273i
$807$		0			0
$808$	−35924.6	+	18992.9i	−1.56414	+	0.826939i
$809$		−	17843.7i		−	0.775467i	−0.921772	−	0.387733i	$-0.873258\pi$
$809$		−	17843.7i		−	0.775467i	0.921772	−	0.387733i	$-0.126742\pi$
$810$		0			0
$811$	−32908.9			−1.42489			−0.712445	−	0.701728i	$-0.752412\pi$
$811$	−32908.9			−1.42489			−0.712445	+	0.701728i	$0.752412\pi$
$812$	−3455.39	+	1161.29i	−0.149335	+	0.0501889i
$813$		0			0
$814$	991.153	+	6060.39i	0.0426780	+	0.260954i
$815$	6318.51	+	31089.7i	0.271568	+	1.33623i
$816$		0			0
$817$		−	29901.8i		−	1.28046i
$818$	−44202.4	+	7229.14i	−1.88937	+	0.308999i
$819$		0			0
$820$	4792.77	+	8279.75i	0.204111	+	0.352612i
$821$	18076.7			0.768432			0.384216	−	0.923243i	$-0.374472\pi$
$821$	18076.7			0.768432			0.384216	+	0.923243i	$0.374472\pi$
$822$		0			0
$823$	−6914.80			−0.292873			−0.146437	−	0.989220i	$-0.546780\pi$
$823$	−6914.80			−0.292873			−0.146437	+	0.989220i	$0.546780\pi$
$824$	22261.0	−	11769.1i	0.941139	−	0.497568i
$825$		0			0
$826$	2579.51	+	15772.4i	0.108659	+	0.664395i
$827$	−22804.8			−0.958887			−0.479444	−	0.877573i	$-0.659161\pi$
$827$	−22804.8			−0.958887			−0.479444	+	0.877573i	$0.659161\pi$
$828$		0			0
$829$			32176.2i			1.34804i	0.738713	+	0.674020i	$0.235434\pi$
$829$			32176.2i			1.34804i	−0.738713	+	0.674020i	$0.764566\pi$
$830$	−26923.8	+	10214.7i	−1.12595	+	0.427176i
$831$		0			0
$832$	20046.8	−	29420.3i	0.835336	−	1.22592i
$833$	13791.8			0.573657
$834$		0			0
$835$	5739.26	+	28239.5i	0.237862	+	1.17038i
$836$	10450.9	+	31096.4i	0.432360	+	1.28647i
$837$		0			0
$838$	−463.675	−	2835.13i	−0.0191138	−	0.116871i
$839$	9692.12			0.398819			0.199409	−	0.979916i	$-0.436098\pi$
$839$	9692.12			0.398819			0.199409	+	0.979916i	$0.436098\pi$
$840$		0			0
$841$	−22306.3			−0.914606
$842$	−2667.67	−	16311.4i	−0.109185	−	0.667612i
$843$		0			0
$844$	−12968.3	+	4358.42i	−0.528897	+	0.177752i
$845$	−28901.3	+	5873.75i	−1.17661	+	0.239128i
$846$		0			0
$847$	18386.8			0.745900
$848$	25546.3	+	33713.3i	1.03451	+	1.36523i
$849$		0			0
$850$	16946.6	−	10698.5i	0.683841	−	0.431712i
$851$			5005.05i			0.201611i
$852$		0			0
$853$	−20658.5			−0.829229			−0.414614	−	0.909997i	$-0.636084\pi$
$853$	−20658.5			−0.829229			−0.414614	+	0.909997i	$0.636084\pi$
$854$	3760.72	+	22994.9i	0.150690	+	0.921392i
$855$		0			0
$856$	−20681.6	+	10934.1i	−0.825796	+	0.436587i
$857$	4105.59			0.163645			0.0818227	−	0.996647i	$-0.473926\pi$
$857$	4105.59			0.163645			0.0818227	+	0.996647i	$0.473926\pi$
$858$		0			0
$859$	14592.0			0.579597			0.289799	−	0.957088i	$-0.406412\pi$
$859$	14592.0			0.579597			0.289799	+	0.957088i	$0.406412\pi$
$860$	−18403.6	−	31793.1i	−0.729718	−	1.26062i
$861$		0			0
$862$	38601.5	−	6313.13i	1.52526	−	0.249450i
$863$		−	20482.4i		−	0.807912i	−0.914778	−	0.403956i	$-0.867635\pi$
$863$		−	20482.4i		−	0.807912i	0.914778	−	0.403956i	$-0.132365\pi$
$864$		0			0
$865$	−2527.18	−	12434.7i	−0.0993371	−	0.488779i
$866$	−5268.70	−	32215.4i	−0.206741	−	1.26411i
$867$		0			0
$868$	3158.26	+	9397.30i	0.123500	+	0.367471i
$869$	42361.3			1.65364
$870$		0			0
$871$		−	11702.5i		−	0.455251i
$872$	−20109.6	−	38036.8i	−0.780959	−	1.47717i
$873$		0			0
$874$	4315.51	+	26387.1i	0.167019	+	1.02123i
$875$	11504.8	−	7896.45i	0.444496	−	0.305084i
$876$		0			0
$877$	13433.5			0.517235			0.258618	−	0.965980i	$-0.416733\pi$
$877$	13433.5			0.517235			0.258618	+	0.965980i	$0.416733\pi$
$878$	−2446.37	−	14958.3i	−0.0940332	−	0.574964i
$879$		0			0
$880$	30250.7	+	26631.0i	1.15881	+	1.02015i
$881$		−	13807.4i		−	0.528016i	−0.964520	−	0.264008i	$-0.914955\pi$
$881$		−	13807.4i		−	0.528016i	0.964520	−	0.264008i	$-0.0850446\pi$
$882$		0			0
$883$		−	47565.4i		−	1.81280i	−0.422419	−	0.906401i	$-0.638819\pi$
$883$		−	47565.4i		−	1.81280i	0.422419	−	0.906401i	$-0.361181\pi$
$884$	−29888.9	+	10045.1i	−1.13719	+	0.382188i
$885$		0			0
$886$	34553.7	−	5651.13i	1.31022	−	0.214282i
$887$		−	36694.6i		−	1.38905i	−0.719470	−	0.694524i	$-0.755615\pi$
$887$		−	36694.6i		−	1.38905i	0.719470	−	0.694524i	$-0.244385\pi$
$888$		0			0
$889$	22372.1			0.844023
$890$	4852.30	+	12789.7i	0.182752	+	0.481698i
$891$		0			0
$892$	−8380.84	+	2816.65i	−0.314587	+	0.105727i
$893$			8549.56i			0.320381i
$894$		0			0
$895$	−462.445	−	2275.42i	−0.0172713	−	0.0849819i
$896$	6106.70	−	13106.6i	0.227690	−	0.488682i
$897$		0			0
$898$	−3558.40	−	21757.8i	−0.132233	−	0.808538i
$899$		−	5664.04i		−	0.210129i
$900$		0			0
$901$		−	37464.2i		−	1.38525i
$902$	16816.6	−	2750.29i	0.620767	−	0.101524i
$903$		0			0
$904$	−29410.3	+	15548.8i	−1.08205	+	0.572064i
$905$	4449.29	+	21892.3i	0.163425	+	0.804117i
$906$		0			0
$907$			4090.11i			0.149735i	0.997193	+	0.0748677i	$0.0238534\pi$
$907$			4090.11i			0.149735i	−0.997193	+	0.0748677i	$0.976147\pi$
$908$	36256.1	−	12185.0i	1.32511	−	0.445346i
$909$		0			0
$910$	−20527.0	+	7787.77i	−0.747761	+	0.283694i
$911$	6881.32			0.250262			0.125131	−	0.992140i	$-0.460065\pi$
$911$	6881.32			0.250262			0.125131	+	0.992140i	$0.460065\pi$
$912$		0			0
$913$			51290.6i			1.85923i
$914$	3051.58	+	18658.8i	0.110435	+	0.675251i
$915$		0			0
$916$	5491.91	+	16341.0i	0.198098	+	0.589434i
$917$			12260.7i			0.441531i
$918$		0			0
$919$		−	39036.6i		−	1.40120i	−0.713556	−	0.700598i	$-0.752916\pi$
$919$		−	39036.6i		−	1.40120i	0.713556	−	0.700598i	$-0.247084\pi$
$920$	20828.9	+	25400.0i	0.746421	+	0.910233i
$921$		0			0
$922$	−45063.5	+	7369.96i	−1.60964	+	0.263250i
$923$	33285.8			1.18702
$924$		0			0
$925$	4436.08	−	1880.82i	0.157684	−	0.0668552i
$926$	39867.4	−	6520.17i	1.41482	−	0.231389i
$927$		0			0
$928$	−5692.65	+	5986.53i	−0.201369	+	0.211764i
$929$		−	5762.99i		−	0.203528i	−0.994809	−	0.101764i	$-0.967551\pi$
$929$		−	5762.99i		−	0.203528i	0.994809	−	0.101764i	$-0.0324487\pi$
$930$		0			0
$931$	17713.7			0.623570
$932$	−44401.6	+	14922.6i	−1.56054	+	0.524468i
$933$		0			0
$934$	−39841.3	+	6515.90i	−1.39577	+	0.228273i
$935$	−7109.39	−	34981.1i	−0.248665	−	1.22353i
$936$		0			0
$937$		−	42120.7i		−	1.46854i	−0.678857	−	0.734270i	$-0.737525\pi$
$937$		−	42120.7i		−	1.46854i	0.678857	−	0.734270i	$-0.262475\pi$
$938$	−767.140	−	4690.66i	−0.0267036	−	0.163279i
$939$		0			0
$940$	5261.97	+	9090.32i	0.182582	+	0.315419i
$941$	−22406.0			−0.776212			−0.388106	−	0.921615i	$-0.626871\pi$
$941$	−22406.0			−0.776212			−0.388106	+	0.921615i	$0.626871\pi$
$942$		0			0
$943$	13888.2			0.479600
$944$	21874.0	+	28866.9i	0.754170	+	0.995273i
$945$		0			0
$946$	−64573.5	+	10560.8i	−2.21931	+	0.362959i
$947$	−7130.41			−0.244675			−0.122338	−	0.992489i	$-0.539039\pi$
$947$	−7130.41			−0.244675			−0.122338	+	0.992489i	$0.539039\pi$
$948$		0			0
$949$		−	24973.9i		−	0.854253i
$950$	21765.8	−	13740.8i	0.743342	−	0.469275i
$951$		0			0
$952$	−11321.8	+	5985.68i	−0.385442	+	0.203778i
$953$	24036.1			0.817003			0.408502	−	0.912758i	$-0.366051\pi$
$953$	24036.1			0.817003			0.408502	+	0.912758i	$0.366051\pi$
$954$		0			0
$955$	−34824.2	+	7077.49i	−1.17998	+	0.239814i
$956$	−22003.3	+	7394.91i	−0.744391	+	0.250176i
$957$		0			0
$958$	−52729.7	+	8623.74i	−1.77831	+	0.290836i
$959$	−1727.40			−0.0581654
$960$		0			0
$961$	14387.0			0.482932
$962$	−7481.55	+	1223.58i	−0.250743	+	0.0410081i
$963$		0			0
$964$	17096.2	−	5745.73i	0.571195	−	0.191968i
$965$	632.045	+	3109.92i	0.0210842	+	0.103743i
$966$		0			0
$967$	−27089.6			−0.900873			−0.450436	−	0.892809i	$-0.648732\pi$
$967$	−27089.6			−0.900873			−0.450436	+	0.892809i	$0.648732\pi$
$968$	36837.0	−	19475.2i	1.22313	−	0.646651i
$969$		0			0
$970$	11455.0	+	30193.1i	0.379174	+	0.999426i
$971$		−	27491.4i		−	0.908589i	−0.890851	−	0.454295i	$-0.849891\pi$
$971$		−	27491.4i		−	0.908589i	0.890851	−	0.454295i	$-0.150109\pi$
$972$		0			0
$973$	−15607.8			−0.514249
$974$	9473.94	−	1549.43i	0.311668	−	0.0509721i
$975$		0			0
$976$	31890.5	+	42085.7i	1.04589	+	1.38026i
$977$	−26635.4			−0.872203			−0.436101	−	0.899898i	$-0.643641\pi$
$977$	−26635.4			−0.872203			−0.436101	+	0.899898i	$0.643641\pi$
$978$		0			0
$979$	24364.7			0.795403
$980$	18834.1	−	10902.2i	0.613912	−	0.355366i
$981$		0			0
$982$	−3596.44	−	21990.4i	−0.116871	−	0.714604i
$983$			1824.66i			0.0592042i	0.999562	+	0.0296021i	$0.00942401\pi$
$983$			1824.66i			0.0592042i	−0.999562	+	0.0296021i	$0.990576\pi$
$984$		0			0
$985$	−10970.4	−	53979.1i	−0.354870	−	1.74611i
$986$	7220.88	−	1180.95i	0.233225	−	0.0381430i
$987$		0			0
$988$	−38388.5	+	12901.7i	−1.23613	+	0.415442i
$989$	−53328.9			−1.71462
$990$		0			0
$991$		−	10688.0i		−	0.342599i	−0.985219	−	0.171299i	$-0.945203\pi$
$991$		−	10688.0i		−	0.342599i	0.985219	−	0.171299i	$-0.0547965\pi$
$992$	16281.0	+	15481.8i	0.521091	+	0.495512i
$993$		0			0
$994$	13341.8	−	2182.01i	0.425732	−	0.0696268i
$995$	5060.60	+	24900.2i	0.161238	+	0.793357i
$996$		0			0
$997$	−25338.8			−0.804904			−0.402452	−	0.915441i	$-0.631842\pi$
$997$	−25338.8			−0.804904			−0.402452	+	0.915441i	$0.631842\pi$
$998$	−10773.2	+	1761.91i	−0.341702	+	0.0558840i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.m.c.179.7	yes	64
3.2	odd	2	inner	360.4.m.c.179.58	yes	64
4.3	odd	2		1440.4.m.c.719.8		64
5.4	even	2	inner	360.4.m.c.179.57	yes	64
8.3	odd	2	inner	360.4.m.c.179.6	yes	64
8.5	even	2		1440.4.m.c.719.57		64
12.11	even	2		1440.4.m.c.719.58		64
15.14	odd	2	inner	360.4.m.c.179.8	yes	64
20.19	odd	2		1440.4.m.c.719.5		64
24.5	odd	2		1440.4.m.c.719.7		64
24.11	even	2	inner	360.4.m.c.179.59	yes	64
40.19	odd	2	inner	360.4.m.c.179.60	yes	64
40.29	even	2		1440.4.m.c.719.60		64
60.59	even	2		1440.4.m.c.719.59		64
120.29	odd	2		1440.4.m.c.719.6		64
120.59	even	2	inner	360.4.m.c.179.5	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.4.m.c.179.5	✓	64	120.59	even	2	inner
360.4.m.c.179.6	yes	64	8.3	odd	2	inner
360.4.m.c.179.7	yes	64	1.1	even	1	trivial
360.4.m.c.179.8	yes	64	15.14	odd	2	inner
360.4.m.c.179.57	yes	64	5.4	even	2	inner
360.4.m.c.179.58	yes	64	3.2	odd	2	inner
360.4.m.c.179.59	yes	64	24.11	even	2	inner
360.4.m.c.179.60	yes	64	40.19	odd	2	inner
1440.4.m.c.719.5		64	20.19	odd	2
1440.4.m.c.719.6		64	120.29	odd	2
1440.4.m.c.719.7		64	24.5	odd	2
1440.4.m.c.719.8		64	4.3	odd	2
1440.4.m.c.719.57		64	8.5	even	2
1440.4.m.c.719.58		64	12.11	even	2
1440.4.m.c.719.59		64	60.59	even	2
1440.4.m.c.719.60		64	40.29	even	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.79134 + 0.456513i) q^{2} +(7.58319 - 2.54857i) q^{4} +(-10.9564 + 2.22672i) q^{5} -9.98469 q^{7} +(-20.0038 + 10.5758i) q^{8} +O(q^{10})\)	\(q+(-2.79134 + 0.456513i) q^{2} +(7.58319 - 2.54857i) q^{4} +(-10.9564 + 2.22672i) q^{5} -9.98469 q^{7} +(-20.0038 + 10.5758i) q^{8} +(29.5664 - 11.2173i) q^{10} -56.3249i q^{11} +69.5331 q^{13} +(27.8707 - 4.55815i) q^{14} +(51.0096 - 38.6526i) q^{16} -56.6848 q^{17} -72.8043 q^{19} +(-77.4092 + 44.8087i) q^{20} +(25.7131 + 157.222i) q^{22} +129.844i q^{23} +(115.083 - 48.7934i) q^{25} +(-194.091 + 31.7428i) q^{26} +(-75.7158 + 25.4467i) q^{28} +45.6362 q^{29} -124.113i q^{31} +(-124.740 + 131.179i) q^{32} +(158.227 - 25.8774i) q^{34} +(109.396 - 22.2331i) q^{35} +38.5467 q^{37} +(203.222 - 33.2361i) q^{38} +(195.620 - 160.415i) q^{40} -106.961i q^{41} +410.715i q^{43} +(-143.548 - 427.123i) q^{44} +(-59.2755 - 362.439i) q^{46} -117.432i q^{47} -243.306 q^{49} +(-298.963 + 188.736i) q^{50} +(527.283 - 177.210i) q^{52} +660.920i q^{53} +(125.420 + 617.116i) q^{55} +(199.732 - 105.596i) q^{56} +(-127.386 + 20.8336i) q^{58} +565.912i q^{59} +825.056i q^{61} +(56.6591 + 346.441i) q^{62} +(288.306 - 423.112i) q^{64} +(-761.829 + 154.830i) q^{65} -168.301i q^{67} +(-429.852 + 144.465i) q^{68} +(-295.212 + 112.001i) q^{70} +478.705 q^{71} -359.165i q^{73} +(-107.597 + 17.5971i) q^{74} +(-552.089 + 185.547i) q^{76} +562.387i q^{77} +752.089i q^{79} +(-472.811 + 537.075i) q^{80} +(48.8291 + 298.564i) q^{82} -910.621 q^{83} +(621.059 - 126.221i) q^{85} +(-187.497 - 1146.45i) q^{86} +(595.679 + 1126.71i) q^{88} +432.574i q^{89} -694.267 q^{91} +(330.916 + 984.631i) q^{92} +(53.6093 + 327.793i) q^{94} +(797.670 - 162.115i) q^{95} +1021.20i q^{97} +(679.150 - 111.072i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 64 * q + 76 * q^4	\( 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) \) 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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