LMFDB - Embedded newform 252.4.e.a.71.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(71,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("252.71");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.e (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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.9
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.88294 - 2.11058i) q^{2} +(-0.909099 + 7.94818i) q^{4} +21.8666i q^{5} +7.00000i q^{7} +(18.4870 - 13.0472i) q^{8} +(46.1512 - 41.1734i) q^{10} +66.1125 q^{11} -61.5090 q^{13} +(14.7741 - 13.1806i) q^{14} +(-62.3471 - 14.4514i) q^{16} +11.7720i q^{17} +87.9289i q^{19} +(-173.800 - 19.8789i) q^{20} +(-124.486 - 139.536i) q^{22} -13.2343 q^{23} -353.148 q^{25} +(115.818 + 129.820i) q^{26} +(-55.6372 - 6.36369i) q^{28} -7.53630i q^{29} -45.1117i q^{31} +(86.8949 + 158.800i) q^{32} +(24.8457 - 22.1659i) q^{34} -153.066 q^{35} +207.904 q^{37} +(185.581 - 165.565i) q^{38} +(285.298 + 404.249i) q^{40} +172.688i q^{41} -331.004i q^{43} +(-60.1028 + 525.474i) q^{44} +(24.9194 + 27.9322i) q^{46} -436.796 q^{47} -49.0000 q^{49} +(664.956 + 745.347i) q^{50} +(55.9177 - 488.884i) q^{52} +282.237i q^{53} +1445.66i q^{55} +(91.3303 + 129.409i) q^{56} +(-15.9060 + 14.1904i) q^{58} -553.350 q^{59} -262.257 q^{61} +(-95.2119 + 84.9425i) q^{62} +(171.542 - 482.408i) q^{64} -1344.99i q^{65} -89.8443i q^{67} +(-93.5658 - 10.7019i) q^{68} +(288.214 + 323.058i) q^{70} +891.802 q^{71} -506.529 q^{73} +(-391.470 - 438.798i) q^{74} +(-698.874 - 79.9360i) q^{76} +462.788i q^{77} +836.714i q^{79} +(316.002 - 1363.32i) q^{80} +(364.472 - 325.161i) q^{82} +114.691 q^{83} -257.413 q^{85} +(-698.610 + 623.259i) q^{86} +(1222.22 - 862.583i) q^{88} +162.452i q^{89} -430.563i q^{91} +(12.0313 - 105.189i) q^{92} +(822.460 + 921.894i) q^{94} -1922.71 q^{95} -1054.85 q^{97} +(92.2639 + 103.418i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64}+ \cdots + 5496 q^{94}+O(q^{100}) $ 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.88294	−	2.11058i	−0.665719	−	0.746203i
$2$	−1.88294	−	2.11058i	−0.665719	−	0.746203i
$3$		0			0
$3$		0			0
$4$	−0.909099	+	7.94818i	−0.113637	+	0.993522i
$5$			21.8666i			1.95581i	0.209055	+	0.977904i	$0.432961\pi$
$5$			21.8666i			1.95581i	−0.209055	+	0.977904i	$0.567039\pi$
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$	18.4870	−	13.0472i	0.817020	−	0.576610i
$9$		0			0
$10$	46.1512	−	41.1734i	1.45943	−	1.30202i
$11$	66.1125			1.81215			0.906076	−	0.423115i	$-0.139063\pi$
$11$	66.1125			1.81215			0.906076	+	0.423115i	$0.139063\pi$
$12$		0			0
$13$	−61.5090			−1.31227			−0.656135	−	0.754643i	$-0.727810\pi$
$13$	−61.5090			−1.31227			−0.656135	+	0.754643i	$0.727810\pi$
$14$	14.7741	−	13.1806i	0.282038	−	0.251618i
$15$		0			0
$16$	−62.3471	−	14.4514i	−0.974173	−	0.225802i
$17$			11.7720i			0.167949i	0.996468	+	0.0839743i	$0.0267614\pi$
$17$			11.7720i			0.167949i	−0.996468	+	0.0839743i	$0.973239\pi$
$18$		0			0
$19$			87.9289i			1.06170i	0.847466	+	0.530849i	$0.178127\pi$
$19$			87.9289i			1.06170i	−0.847466	+	0.530849i	$0.821873\pi$
$20$	−173.800	−	19.8789i	−1.94314	−	0.222253i
$21$		0			0
$22$	−124.486	−	139.536i	−1.20638	−	1.35223i
$23$	−13.2343			−0.119981			−0.0599903	−	0.998199i	$-0.519107\pi$
$23$	−13.2343			−0.119981			−0.0599903	+	0.998199i	$0.519107\pi$
$24$		0			0
$25$	−353.148			−2.82518
$26$	115.818	+	129.820i	0.873603	+	0.979220i
$27$		0			0
$28$	−55.6372	−	6.36369i	−0.375516	−	0.0429509i
$29$		−	7.53630i		−	0.0482571i	−0.999709	−	0.0241285i	$-0.992319\pi$
$29$		−	7.53630i		−	0.0482571i	0.999709	−	0.0241285i	$-0.00768110\pi$
$30$		0			0
$31$		−	45.1117i		−	0.261365i	−0.991424	−	0.130682i	$-0.958283\pi$
$31$		−	45.1117i		−	0.261365i	0.991424	−	0.130682i	$-0.0417168\pi$
$32$	86.8949	+	158.800i	0.480031	+	0.877252i
$33$		0			0
$34$	24.8457	−	22.1659i	0.125324	−	0.111806i
$35$	−153.066			−0.739226
$36$		0			0
$37$	207.904			0.923763			0.461881	−	0.886942i	$-0.347175\pi$
$37$	207.904			0.923763			0.461881	+	0.886942i	$0.347175\pi$
$38$	185.581	−	165.565i	0.792242	−	0.706792i
$39$		0			0
$40$	285.298	+	404.249i	1.12774	+	1.59793i
$41$			172.688i			0.657789i	0.944367	+	0.328894i	$0.106676\pi$
$41$			172.688i			0.657789i	−0.944367	+	0.328894i	$0.893324\pi$
$42$		0			0
$43$		−	331.004i		−	1.17390i	−0.809624	−	0.586949i	$-0.800329\pi$
$43$		−	331.004i		−	1.17390i	0.809624	−	0.586949i	$-0.199671\pi$
$44$	−60.1028	+	525.474i	−0.205928	+	1.80041i
$45$		0			0
$46$	24.9194	+	27.9322i	0.0798733	+	0.0895298i
$47$	−436.796			−1.35560			−0.677801	−	0.735246i	$-0.737067\pi$
$47$	−436.796			−1.35560			−0.677801	+	0.735246i	$0.737067\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	664.956	+	745.347i	1.88078	+	2.10816i
$51$		0			0
$52$	55.9177	−	488.884i	0.149123	−	1.30377i
$53$			282.237i			0.731477i	0.930718	+	0.365739i	$0.119184\pi$
$53$			282.237i			0.731477i	−0.930718	+	0.365739i	$0.880816\pi$
$54$		0			0
$55$			1445.66i			3.54422i
$56$	91.3303	+	129.409i	0.217938	+	0.308804i
$57$		0			0
$58$	−15.9060	+	14.1904i	−0.0360096	+	0.0321256i
$59$	−553.350			−1.22102			−0.610509	−	0.792009i	$-0.709035\pi$
$59$	−553.350			−1.22102			−0.610509	+	0.792009i	$0.709035\pi$
$60$		0			0
$61$	−262.257			−0.550468			−0.275234	−	0.961377i	$-0.588755\pi$
$61$	−262.257			−0.550468			−0.275234	+	0.961377i	$0.588755\pi$
$62$	−95.2119	+	84.9425i	−0.195031	+	0.173995i
$63$		0			0
$64$	171.542	−	482.408i	0.335042	−	0.942203i
$65$		−	1344.99i		−	2.56655i
$66$		0			0
$67$		−	89.8443i		−	0.163824i	−0.996640	−	0.0819121i	$-0.973897\pi$
$67$		−	89.8443i		−	0.163824i	0.996640	−	0.0819121i	$-0.0261027\pi$
$68$	−93.5658	−	10.7019i	−0.166861	−	0.0190852i
$69$		0			0
$70$	288.214	+	323.058i	0.492116	+	0.551612i
$71$	891.802			1.49067			0.745334	−	0.666691i	$-0.232290\pi$
$71$	891.802			1.49067			0.745334	+	0.666691i	$0.232290\pi$
$72$		0			0
$73$	−506.529			−0.812119			−0.406059	−	0.913847i	$-0.633097\pi$
$73$	−506.529			−0.812119			−0.406059	+	0.913847i	$0.633097\pi$
$74$	−391.470	−	438.798i	−0.614966	−	0.689314i
$75$		0			0
$76$	−698.874	−	79.9360i	−1.05482	−	0.120649i
$77$			462.788i			0.684929i
$78$		0			0
$79$			836.714i			1.19162i	0.803127	+	0.595808i	$0.203168\pi$
$79$			836.714i			1.19162i	−0.803127	+	0.595808i	$0.796832\pi$
$80$	316.002	−	1363.32i	0.441626	−	1.90530i
$81$		0			0
$82$	364.472	−	325.161i	0.490844	−	0.437902i
$83$	114.691			0.151674			0.0758369	−	0.997120i	$-0.475837\pi$
$83$	114.691			0.151674			0.0758369	+	0.997120i	$0.475837\pi$
$84$		0			0
$85$	−257.413			−0.328475
$86$	−698.610	+	623.259i	−0.875965	+	0.781485i
$87$		0			0
$88$	1222.22	−	862.583i	1.48056	−	1.04490i
$89$			162.452i			0.193482i	0.995310	+	0.0967410i	$0.0308419\pi$
$89$			162.452i			0.193482i	−0.995310	+	0.0967410i	$0.969158\pi$
$90$		0			0
$91$		−	430.563i		−	0.495992i
$92$	12.0313	−	105.189i	0.0136343	−	0.119203i
$93$		0			0
$94$	822.460	+	921.894i	0.902449	+	1.01155i
$95$	−1922.71			−2.07648
$96$		0			0
$97$	−1054.85			−1.10416			−0.552082	−	0.833790i	$-0.686167\pi$
$97$	−1054.85			−1.10416			−0.552082	+	0.833790i	$0.686167\pi$
$98$	92.2639	+	103.418i	0.0951027	+	0.106600i
$99$		0			0
$100$	321.046	−	2806.88i	0.321046	−	2.80688i
$101$			170.869i			0.168337i	0.996452	+	0.0841687i	$0.0268235\pi$
$101$			170.869i			0.168337i	−0.996452	+	0.0841687i	$0.973177\pi$
$102$		0			0
$103$			75.9945i			0.0726986i	0.999339	+	0.0363493i	$0.0115729\pi$
$103$			75.9945i			0.0726986i	−0.999339	+	0.0363493i	$0.988427\pi$
$104$	−1137.12	+	802.519i	−1.07215	+	0.756668i
$105$		0			0
$106$	595.685	−	531.435i	0.545830	−	0.486958i
$107$	1082.89			0.978385			0.489193	−	0.872176i	$-0.337291\pi$
$107$	1082.89			0.978385			0.489193	+	0.872176i	$0.337291\pi$
$108$		0			0
$109$	−701.186			−0.616160			−0.308080	−	0.951360i	$-0.599686\pi$
$109$	−701.186			−0.616160			−0.308080	+	0.951360i	$0.599686\pi$
$110$	3051.17	−	2722.08i	2.64471	−	2.35945i
$111$		0			0
$112$	101.159	−	436.430i	0.0853453	−	0.368203i
$113$		−	804.271i		−	0.669553i	−0.942298	−	0.334776i	$-0.891339\pi$
$113$		−	804.271i		−	0.669553i	0.942298	−	0.334776i	$-0.108661\pi$
$114$		0			0
$115$		−	289.390i		−	0.234659i
$116$	59.8998	+	6.85124i	0.0479445	+	0.00548381i
$117$		0			0
$118$	1041.92	+	1167.89i	0.812854	+	0.911127i
$119$	−82.4039			−0.0634786
$120$		0			0
$121$	3039.86			2.28389
$122$	493.813	+	553.514i	0.366457	+	0.410761i
$123$		0			0
$124$	358.556	+	41.0110i	0.259672	+	0.0297008i
$125$		−	4988.82i		−	3.56971i
$126$		0			0
$127$			1464.86i			1.02351i	0.859133	+	0.511753i	$0.171004\pi$
$127$			1464.86i			1.02351i	−0.859133	+	0.511753i	$0.828996\pi$
$128$	−1341.16	+	546.291i	−0.926118	+	0.377233i
$129$		0			0
$130$	−2838.71	+	2532.54i	−1.91517	+	1.70860i
$131$	2092.35			1.39549			0.697747	−	0.716344i	$-0.254186\pi$
$131$	2092.35			1.39549			0.697747	+	0.716344i	$0.254186\pi$
$132$		0			0
$133$	−615.502			−0.401284
$134$	−189.624	+	169.171i	−0.122246	+	0.109061i
$135$		0			0
$136$	153.591	+	217.629i	0.0968408	+	0.137217i
$137$		−	578.141i		−	0.360539i	−0.983617	−	0.180270i	$-0.942303\pi$
$137$		−	578.141i		−	0.360539i	0.983617	−	0.180270i	$-0.0576970\pi$
$138$		0			0
$139$		−	1529.70i		−	0.933433i	−0.884407	−	0.466716i	$-0.845437\pi$
$139$		−	1529.70i		−	0.933433i	0.884407	−	0.466716i	$-0.154563\pi$
$140$	139.152	−	1216.60i	0.0840037	−	0.734437i
$141$		0			0
$142$	−1679.21	−	1882.22i	−0.992366	−	1.11234i
$143$	−4066.51			−2.37803
$144$		0			0
$145$	164.793			0.0943816
$146$	953.761	+	1069.07i	0.540643	+	0.606005i
$147$		0			0
$148$	−189.005	+	1652.46i	−0.104974	+	0.917779i
$149$			1177.79i			0.647571i	0.946130	+	0.323786i	$0.104956\pi$
$149$			1177.79i			0.647571i	−0.946130	+	0.323786i	$0.895044\pi$
$150$		0			0
$151$			274.592i			0.147987i	0.997259	+	0.0739933i	$0.0235744\pi$
$151$			274.592i			0.147987i	−0.997259	+	0.0739933i	$0.976426\pi$
$152$	1147.22	+	1625.55i	0.612186	+	0.867428i
$153$		0			0
$154$	976.750	−	871.400i	0.511096	−	0.455970i
$155$	986.440			0.511179
$156$		0			0
$157$	803.908			0.408655			0.204328	−	0.978903i	$-0.434499\pi$
$157$	803.908			0.408655			0.204328	+	0.978903i	$0.434499\pi$
$158$	1765.95	−	1575.48i	0.889187	−	0.793281i
$159$		0			0
$160$	−3472.40	+	1900.09i	−1.71574	+	0.938848i
$161$		−	92.6404i		−	0.0453484i
$162$		0			0
$163$		−	1909.17i		−	0.917410i	−0.888589	−	0.458705i	$-0.848314\pi$
$163$		−	1909.17i		−	0.917410i	0.888589	−	0.458705i	$-0.151686\pi$
$164$	−1372.56	−	156.990i	−0.653528	−	0.0747494i
$165$		0			0
$166$	−215.955	−	242.064i	−0.100972	−	0.113179i
$167$	−531.691			−0.246368			−0.123184	−	0.992384i	$-0.539311\pi$
$167$	−531.691			−0.246368			−0.123184	+	0.992384i	$0.539311\pi$
$168$		0			0
$169$	1586.35			0.722055
$170$	484.693	+	543.291i	0.218672	+	0.245109i
$171$		0			0
$172$	2630.88	+	300.915i	1.16629	+	0.133399i
$173$			3717.57i			1.63377i	0.576804	+	0.816883i	$0.304300\pi$
$173$			3717.57i			1.63377i	−0.576804	+	0.816883i	$0.695700\pi$
$174$		0			0
$175$		−	2472.04i		−	1.06782i
$176$	−4121.92	−	955.415i	−1.76535	−	0.409188i
$177$		0			0
$178$	342.868	−	305.887i	0.144377	−	0.128805i
$179$	−2173.06			−0.907387			−0.453694	−	0.891158i	$-0.649894\pi$
$179$	−2173.06			−0.907387			−0.453694	+	0.891158i	$0.649894\pi$
$180$		0			0
$181$	2449.11			1.00575			0.502876	−	0.864358i	$-0.332275\pi$
$181$	2449.11			1.00575			0.502876	+	0.864358i	$0.332275\pi$
$182$	−908.738	+	810.723i	−0.370110	+	0.330191i
$183$		0			0
$184$	−244.664	+	172.671i	−0.0980265	+	0.0691820i
$185$			4546.15i			1.80670i
$186$		0			0
$187$			778.275i			0.304348i
$188$	397.091	−	3471.73i	0.154047	−	1.34682i
$189$		0			0
$190$	3620.33	+	4058.02i	1.38235	+	1.54947i
$191$	3122.32			1.18284			0.591421	−	0.806363i	$-0.298567\pi$
$191$	3122.32			1.18284			0.591421	+	0.806363i	$0.298567\pi$
$192$		0			0
$193$	−686.947			−0.256205			−0.128102	−	0.991761i	$-0.540889\pi$
$193$	−686.947			−0.256205			−0.128102	+	0.991761i	$0.540889\pi$
$194$	1986.22	+	2226.35i	0.735063	+	0.823931i
$195$		0			0
$196$	44.5458	−	389.461i	0.0162339	−	0.141932i
$197$			644.412i			0.233058i	0.993187	+	0.116529i	$0.0371768\pi$
$197$			644.412i			0.233058i	−0.993187	+	0.116529i	$0.962823\pi$
$198$		0			0
$199$			2749.76i			0.979523i	0.871856	+	0.489761i	$0.162916\pi$
$199$			2749.76i			0.979523i	−0.871856	+	0.489761i	$0.837084\pi$
$200$	−6528.66	+	4607.59i	−2.30823	+	1.62903i
$201$		0			0
$202$	360.632	−	321.735i	0.125614	−	0.112065i
$203$	52.7541			0.0182395
$204$		0			0
$205$	−3776.10			−1.28651
$206$	160.392	−	143.093i	0.0542479	−	0.0483968i
$207$		0			0
$208$	3834.91	+	888.888i	1.27838	+	0.296314i
$209$			5813.20i			1.92396i
$210$		0			0
$211$		−	15.7611i		−	0.00514235i	−0.999997	−	0.00257118i	$-0.999182\pi$
$211$		−	15.7611i		−	0.00514235i	0.999997	−	0.00257118i	$-0.000818432\pi$
$212$	−2243.27	−	256.582i	−0.726739	−	0.0831231i
$213$		0			0
$214$	−2039.02	−	2285.53i	−0.651329	−	0.730074i
$215$	7237.92			2.29592
$216$		0			0
$217$	315.782			0.0987866
$218$	1320.29	+	1479.91i	0.410189	+	0.459780i
$219$		0			0
$220$	−11490.3	−	1314.24i	−3.52126	−	0.402756i
$221$		−	724.083i		−	0.220394i
$222$		0			0
$223$			3774.33i			1.13340i	0.823925	+	0.566699i	$0.191780\pi$
$223$			3774.33i			1.13340i	−0.823925	+	0.566699i	$0.808220\pi$
$224$	−1111.60	+	608.264i	−0.331570	+	0.181435i
$225$		0			0
$226$	−1697.48	+	1514.39i	−0.499622	+	0.445734i
$227$	1031.00			0.301452			0.150726	−	0.988576i	$-0.451839\pi$
$227$	1031.00			0.301452			0.150726	+	0.988576i	$0.451839\pi$
$228$		0			0
$229$	2221.01			0.640910			0.320455	−	0.947264i	$-0.396164\pi$
$229$	2221.01			0.640910			0.320455	+	0.947264i	$0.396164\pi$
$230$	−610.781	+	544.903i	−0.175103	+	0.156217i
$231$		0			0
$232$	−98.3275	−	139.324i	−0.0278255	−	0.0394270i
$233$			4787.61i			1.34612i	0.739586	+	0.673062i	$0.235021\pi$
$233$			4787.61i			1.34612i	−0.739586	+	0.673062i	$0.764979\pi$
$234$		0			0
$235$		−	9551.25i		−	2.65130i
$236$	503.050	−	4398.13i	0.138753	−	1.21311i
$237$		0			0
$238$	155.161	+	173.920i	0.0422589	+	0.0473679i
$239$	5520.83			1.49420			0.747098	−	0.664714i	$-0.231446\pi$
$239$	5520.83			1.49420			0.747098	+	0.664714i	$0.231446\pi$
$240$		0			0
$241$	611.900			0.163552			0.0817758	−	0.996651i	$-0.473941\pi$
$241$	611.900			0.163552			0.0817758	+	0.996651i	$0.473941\pi$
$242$	−5723.87	−	6415.88i	−1.52043	−	1.70425i
$243$		0			0
$244$	238.417	−	2084.47i	0.0625538	−	0.546903i
$245$		−	1071.46i		−	0.279401i
$246$		0			0
$247$		−	5408.42i		−	1.39324i
$248$	−588.581	−	833.982i	−0.150705	−	0.213540i
$249$		0			0
$250$	−10529.3	+	9393.64i	−2.66373	+	2.37642i
$251$	5063.20			1.27325			0.636626	−	0.771173i	$-0.280329\pi$
$251$	5063.20			1.27325			0.636626	+	0.771173i	$0.280329\pi$
$252$		0			0
$253$	−874.956			−0.217423
$254$	3091.70	−	2758.24i	0.763743	−	0.681367i
$255$		0			0
$256$	3678.32	+	1802.00i	0.898027	+	0.439941i
$257$		−	6434.13i		−	1.56167i	−0.624735	−	0.780837i	$-0.714793\pi$
$257$		−	6434.13i		−	1.56167i	0.624735	−	0.780837i	$-0.285207\pi$
$258$		0			0
$259$			1455.33i			0.349149i
$260$	10690.2	+	1222.73i	2.54992	+	0.291656i
$261$		0			0
$262$	−3939.77	−	4416.08i	−0.929006	−	1.04132i
$263$	3816.92			0.894911			0.447455	−	0.894306i	$-0.352330\pi$
$263$	3816.92			0.894911			0.447455	+	0.894306i	$0.352330\pi$
$264$		0			0
$265$	−6171.57			−1.43063
$266$	1158.95	+	1299.07i	0.267142	+	0.299439i
$267$		0			0
$268$	714.099	+	81.6773i	0.162763	+	0.0186166i
$269$			2855.07i			0.647126i	0.946207	+	0.323563i	$0.104881\pi$
$269$			2855.07i			0.647126i	−0.946207	+	0.323563i	$0.895119\pi$
$270$		0			0
$271$			5572.22i			1.24903i	0.781011	+	0.624517i	$0.214704\pi$
$271$			5572.22i			1.24903i	−0.781011	+	0.624517i	$0.785296\pi$
$272$	170.121	−	733.949i	0.0379232	−	0.163611i
$273$		0			0
$274$	−1220.21	+	1088.60i	−0.269035	+	0.240018i
$275$	−23347.5			−5.11966
$276$		0			0
$277$	−1433.15			−0.310865			−0.155433	−	0.987846i	$-0.549677\pi$
$277$	−1433.15			−0.310865			−0.155433	+	0.987846i	$0.549677\pi$
$278$	−3228.55	+	2880.32i	−0.696530	+	0.621404i
$279$		0			0
$280$	−2829.74	+	1997.08i	−0.603962	+	0.426245i
$281$		−	1560.76i		−	0.331342i	−0.986181	−	0.165671i	$-0.947021\pi$
$281$		−	1560.76i		−	0.331342i	0.986181	−	0.165671i	$-0.0529789\pi$
$282$		0			0
$283$			557.943i			0.117195i	0.998282	+	0.0585976i	$0.0186629\pi$
$283$			557.943i			0.117195i	−0.998282	+	0.0585976i	$0.981337\pi$
$284$	−810.736	+	7088.20i	−0.169396	+	1.48101i
$285$		0			0
$286$	7656.99	+	8582.70i	1.58310	+	1.77450i
$287$	−1208.82			−0.248621
$288$		0			0
$289$	4774.42			0.971793
$290$	−310.295	−	347.809i	−0.0628316	−	0.0704278i
$291$		0			0
$292$	460.484	−	4025.98i	0.0922870	−	0.806858i
$293$			1422.60i			0.283649i	0.989892	+	0.141824i	$0.0452968\pi$
$293$			1422.60i			0.283649i	−0.989892	+	0.141824i	$0.954703\pi$
$294$		0			0
$295$		−	12099.9i		−	2.38808i
$296$	3843.53	−	2712.56i	0.754732	−	0.532651i
$297$		0			0
$298$	2485.82	−	2217.70i	0.483219	−	0.431100i
$299$	814.031			0.157447
$300$		0			0
$301$	2317.03			0.443691
$302$	579.549	−	517.040i	0.110428	−	0.0985175i
$303$		0			0
$304$	1270.69	−	5482.11i	0.239734	−	1.03428i
$305$		−	5734.67i		−	1.07661i
$306$		0			0
$307$		−	7600.14i		−	1.41291i	−0.707758	−	0.706455i	$-0.750293\pi$
$307$		−	7600.14i		−	1.41291i	0.707758	−	0.706455i	$-0.249707\pi$
$308$	−3678.32	−	420.720i	−0.680492	−	0.0778335i
$309$		0			0
$310$	−1857.40	−	2081.96i	−0.340301	−	0.381443i
$311$	4016.60			0.732349			0.366174	−	0.930546i	$-0.380667\pi$
$311$	4016.60			0.732349			0.366174	+	0.930546i	$0.380667\pi$
$312$		0			0
$313$	6789.33			1.22606			0.613028	−	0.790061i	$-0.289951\pi$
$313$	6789.33			1.22606			0.613028	+	0.790061i	$0.289951\pi$
$314$	−1513.71	−	1696.71i	−0.272049	−	0.304940i
$315$		0			0
$316$	−6650.35	−	760.655i	−1.18390	−	0.135412i
$317$			4680.61i			0.829303i	0.909980	+	0.414651i	$0.136096\pi$
$317$			4680.61i			0.829303i	−0.909980	+	0.414651i	$0.863904\pi$
$318$		0			0
$319$		−	498.244i		−	0.0874492i
$320$	10548.6	+	3751.03i	1.84277	+	0.655278i
$321$		0			0
$322$	−195.525	+	174.436i	−0.0338391	+	0.0301893i
$323$	−1035.10			−0.178311
$324$		0			0
$325$	21721.8			3.70741
$326$	−4029.46	+	3594.85i	−0.684574	+	0.610737i
$327$		0			0
$328$	2253.09	+	3192.49i	0.379288	+	0.537426i
$329$		−	3057.57i		−	0.512369i
$330$		0			0
$331$			5224.33i			0.867538i	0.901024	+	0.433769i	$0.142817\pi$
$331$			5224.33i			0.867538i	−0.901024	+	0.433769i	$0.857183\pi$
$332$	−104.265	+	911.582i	−0.0172358	+	0.150691i
$333$		0			0
$334$	1001.14	+	1122.18i	0.164012	+	0.183841i
$335$	1964.59			0.320409
$336$		0			0
$337$	−11037.2			−1.78408			−0.892038	−	0.451961i	$-0.850725\pi$
$337$	−11037.2			−1.78408			−0.892038	+	0.451961i	$0.850725\pi$
$338$	−2987.01	−	3348.13i	−0.480685	−	0.538799i
$339$		0			0
$340$	234.014	−	2045.97i	0.0373270	−	0.326347i
$341$		−	2982.45i		−	0.473633i
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	−4318.67	−	6119.28i	−0.676881	−	0.959097i
$345$		0			0
$346$	7846.23	−	6999.95i	1.21912	−	1.08763i
$347$	4831.11			0.747399			0.373699	−	0.927550i	$-0.378089\pi$
$347$	4831.11			0.747399			0.373699	+	0.927550i	$0.378089\pi$
$348$		0			0
$349$	−4994.72			−0.766079			−0.383039	−	0.923732i	$-0.625123\pi$
$349$	−4994.72			−0.766079			−0.383039	+	0.923732i	$0.625123\pi$
$350$	−5217.43	+	4654.69i	−0.796810	+	0.710867i
$351$		0			0
$352$	5744.84	+	10498.6i	0.869889	+	1.58971i
$353$		−	7932.09i		−	1.19598i	−0.801502	−	0.597992i	$-0.795965\pi$
$353$		−	7932.09i		−	1.19598i	0.801502	−	0.597992i	$-0.204035\pi$
$354$		0			0
$355$			19500.7i			2.91546i
$356$	−1291.20	−	147.685i	−0.192229	−	0.0219868i
$357$		0			0
$358$	4091.74	+	4586.42i	0.604065	+	0.677095i
$359$	−2834.37			−0.416692			−0.208346	−	0.978055i	$-0.566808\pi$
$359$	−2834.37			−0.416692			−0.208346	+	0.978055i	$0.566808\pi$
$360$		0			0
$361$	−872.488			−0.127203
$362$	−4611.53	−	5169.05i	−0.669548	−	0.750495i
$363$		0			0
$364$	3422.19	+	391.424i	0.492779	+	0.0563632i
$365$		−	11076.1i		−	1.58835i
$366$		0			0
$367$			5182.11i			0.737068i	0.929614	+	0.368534i	$0.120140\pi$
$367$			5182.11i			0.737068i	−0.929614	+	0.368534i	$0.879860\pi$
$368$	825.123	+	191.254i	0.116882	+	0.0270919i
$369$		0			0
$370$	9595.02	−	8560.12i	1.34817	−	1.20276i
$371$	−1975.66			−0.276472
$372$		0			0
$373$	−5714.61			−0.793274			−0.396637	−	0.917976i	$-0.629823\pi$
$373$	−5714.61			−0.793274			−0.396637	+	0.917976i	$0.629823\pi$
$374$	1642.61	−	1465.44i	0.227106	−	0.202610i
$375$		0			0
$376$	−8075.07	+	5698.96i	−1.10755	+	0.781653i
$377$			463.550i			0.0633264i
$378$		0			0
$379$			4307.45i			0.583796i	0.956449	+	0.291898i	$0.0942868\pi$
$379$			4307.45i			0.583796i	−0.956449	+	0.291898i	$0.905713\pi$
$380$	1747.93	−	15282.0i	0.235965	−	2.06303i
$381$		0			0
$382$	−5879.13	−	6589.90i	−0.787440	−	0.882640i
$383$	6878.76			0.917724			0.458862	−	0.888508i	$-0.348257\pi$
$383$	6878.76			0.917724			0.458862	+	0.888508i	$0.348257\pi$
$384$		0			0
$385$	−10119.6			−1.33959
$386$	1293.48	+	1449.86i	0.170560	+	0.191181i
$387$		0			0
$388$	958.965	−	8384.15i	0.125474	−	1.09701i
$389$			9982.91i			1.30117i	0.759435	+	0.650583i	$0.225476\pi$
$389$			9982.91i			1.30117i	−0.759435	+	0.650583i	$0.774524\pi$
$390$		0			0
$391$		−	155.795i		−	0.0201506i
$392$	−905.865	+	639.312i	−0.116717	+	0.0823728i
$393$		0			0
$394$	1360.08	−	1213.39i	0.173909	−	0.155151i
$395$	−18296.1			−2.33057
$396$		0			0
$397$	591.572			0.0747862			0.0373931	−	0.999301i	$-0.488095\pi$
$397$	591.572			0.0747862			0.0373931	+	0.999301i	$0.488095\pi$
$398$	5803.58	−	5177.62i	0.730923	−	0.652087i
$399$		0			0
$400$	22017.8	+	5103.47i	2.75222	+	0.637934i
$401$			8963.04i			1.11619i	0.829776	+	0.558096i	$0.188468\pi$
$401$			8963.04i			1.11619i	−0.829776	+	0.558096i	$0.811532\pi$
$402$		0			0
$403$			2774.78i			0.342981i
$404$	−1358.10	−	155.337i	−0.167247	−	0.0191294i
$405$		0			0
$406$	−99.3326	−	111.342i	−0.0121424	−	0.0136103i
$407$	13745.1			1.67400
$408$		0			0
$409$	1445.03			0.174700			0.0873500	−	0.996178i	$-0.472160\pi$
$409$	1445.03			0.174700			0.0873500	+	0.996178i	$0.472160\pi$
$410$	7110.16	+	7969.76i	0.856453	+	0.959997i
$411$		0			0
$412$	−604.018	−	69.0865i	−0.0722277	−	0.00826128i
$413$		−	3873.45i		−	0.461501i
$414$		0			0
$415$			2507.89i			0.296645i
$416$	−5344.81	−	9767.60i	−0.629930	−	1.15119i
$417$		0			0
$418$	12269.2	−	10945.9i	1.43566	−	1.28082i
$419$	−4787.43			−0.558190			−0.279095	−	0.960264i	$-0.590034\pi$
$419$	−4787.43			−0.558190			−0.279095	+	0.960264i	$0.590034\pi$
$420$		0			0
$421$	−13140.8			−1.52124			−0.760619	−	0.649198i	$-0.775104\pi$
$421$	−13140.8			−1.52124			−0.760619	+	0.649198i	$0.775104\pi$
$422$	−33.2650	+	29.6771i	−0.00383724	+	0.00342336i
$423$		0			0
$424$	3682.41	+	5217.74i	0.421777	+	0.597631i
$425$		−	4157.25i		−	0.474486i
$426$		0			0
$427$		−	1835.80i		−	0.208057i
$428$	−984.457	+	8607.03i	−0.111181	+	0.972048i
$429$		0			0
$430$	−13628.5	−	15276.2i	−1.52843	−	1.71322i
$431$	−8691.74			−0.971384			−0.485692	−	0.874130i	$-0.661432\pi$
$431$	−8691.74			−0.971384			−0.485692	+	0.874130i	$0.661432\pi$
$432$		0			0
$433$	17570.6			1.95009			0.975043	−	0.222016i	$-0.0712639\pi$
$433$	17570.6			1.95009			0.975043	+	0.222016i	$0.0712639\pi$
$434$	−594.598	−	666.483i	−0.0657641	−	0.0737148i
$435$		0			0
$436$	637.447	−	5573.15i	0.0700188	−	0.612169i
$437$		−	1163.68i		−	0.127383i
$438$		0			0
$439$			1150.20i			0.125048i	0.998043	+	0.0625238i	$0.0199149\pi$
$439$			1150.20i			0.125048i	−0.998043	+	0.0625238i	$0.980085\pi$
$440$	18861.7	+	26725.9i	2.04363	+	2.89570i
$441$		0			0
$442$	−1528.23	+	1363.40i	−0.164459	+	0.146720i
$443$	−863.626			−0.0926232			−0.0463116	−	0.998927i	$-0.514747\pi$
$443$	−863.626			−0.0926232			−0.0463116	+	0.998927i	$0.514747\pi$
$444$		0			0
$445$	−3552.28			−0.378414
$446$	7966.02	−	7106.82i	0.845744	−	0.754524i
$447$		0			0
$448$	3376.86	+	1200.79i	0.356119	+	0.126634i
$449$			10187.4i			1.07076i	0.844611	+	0.535381i	$0.179832\pi$
$449$			10187.4i			1.07076i	−0.844611	+	0.535381i	$0.820168\pi$
$450$		0			0
$451$			11416.8i			1.19201i
$452$	6392.49	+	731.162i	0.665216	+	0.0760862i
$453$		0			0
$454$	−1941.30	−	2176.00i	−0.200682	−	0.224944i
$455$	9414.95			0.970065
$456$		0			0
$457$	1094.43			0.112025			0.0560123	−	0.998430i	$-0.482161\pi$
$457$	1094.43			0.112025			0.0560123	+	0.998430i	$0.482161\pi$
$458$	−4182.02	−	4687.62i	−0.426666	−	0.478249i
$459$		0			0
$460$	2300.12	+	263.084i	0.233139	+	0.0266660i
$461$		−	5352.20i		−	0.540731i	−0.962758	−	0.270365i	$-0.912855\pi$
$461$		−	5352.20i		−	0.540731i	0.962758	−	0.270365i	$-0.0871445\pi$
$462$		0			0
$463$			14115.5i			1.41685i	0.705785	+	0.708426i	$0.250595\pi$
$463$			14115.5i			1.41685i	−0.705785	+	0.708426i	$0.749405\pi$
$464$	−108.910	+	469.866i	−0.0108966	+	0.0470108i
$465$		0			0
$466$	10104.6	−	9014.77i	1.00448	−	0.896140i
$467$	−10004.7			−0.991357			−0.495678	−	0.868506i	$-0.665081\pi$
$467$	−10004.7			−0.991357			−0.495678	+	0.868506i	$0.665081\pi$
$468$		0			0
$469$	628.910			0.0619198
$470$	−20158.7	+	17984.4i	−1.97840	+	1.76502i
$471$		0			0
$472$	−10229.8	+	7219.67i	−0.997596	+	0.704051i
$473$		−	21883.5i		−	2.12728i
$474$		0			0
$475$		−	31051.9i		−	2.99949i
$476$	74.9133	−	654.961i	0.00721354	−	0.0630674i
$477$		0			0
$478$	−10395.4	−	11652.2i	−0.994714	−	1.11497i
$479$	−5471.20			−0.521891			−0.260945	−	0.965354i	$-0.584034\pi$
$479$	−5471.20			−0.521891			−0.260945	+	0.965354i	$0.584034\pi$
$480$		0			0
$481$	−12788.0			−1.21223
$482$	−1152.17	−	1291.46i	−0.108879	−	0.122043i
$483$		0			0
$484$	−2763.54	+	24161.4i	−0.259536	+	2.26910i
$485$		−	23066.0i		−	2.15953i
$486$		0			0
$487$		−	14865.7i		−	1.38323i	−0.722268	−	0.691613i	$-0.756900\pi$
$487$		−	14865.7i		−	1.38323i	0.722268	−	0.691613i	$-0.243100\pi$
$488$	−4848.36	+	3421.72i	−0.449743	+	0.317405i
$489$		0			0
$490$	−2261.41	+	2017.50i	−0.208490	+	0.186003i
$491$	−19778.0			−1.81786			−0.908930	−	0.416950i	$-0.863099\pi$
$491$	−19778.0			−1.81786			−0.908930	+	0.416950i	$0.863099\pi$
$492$		0			0
$493$	88.7172			0.00810471
$494$	−11414.9	+	10183.7i	−1.03964	+	0.927503i
$495$		0			0
$496$	−651.926	+	2812.58i	−0.0590168	+	0.254614i
$497$			6242.62i			0.563420i
$498$		0			0
$499$			14497.9i			1.30063i	0.759663	+	0.650317i	$0.225364\pi$
$499$			14497.9i			1.30063i	−0.759663	+	0.650317i	$0.774636\pi$
$500$	39652.1	+	4535.33i	3.54659	+	0.405652i
$501$		0			0
$502$	−9533.69	−	10686.3i	−0.847628	−	0.950105i
$503$	11520.0			1.02118			0.510589	−	0.859825i	$-0.329427\pi$
$503$	11520.0			1.02118			0.510589	+	0.859825i	$0.329427\pi$
$504$		0			0
$505$	−3736.32			−0.329236
$506$	1647.49	+	1846.66i	0.144743	+	0.162242i
$507$		0			0
$508$	−11643.0	−	1331.70i	−1.01688	−	0.116309i
$509$			15531.3i			1.35248i	0.736683	+	0.676239i	$0.236391\pi$
$509$			15531.3i			1.35248i	−0.736683	+	0.676239i	$0.763609\pi$
$510$		0			0
$511$		−	3545.70i		−	0.306952i
$512$	−3122.77	−	11156.4i	−0.269548	−	0.962987i
$513$		0			0
$514$	−13579.8	+	12115.1i	−1.16533	+	1.03964i
$515$	−1661.74			−0.142185
$516$		0			0
$517$	−28877.7			−2.45656
$518$	3071.59	−	2740.29i	0.260536	−	0.232435i
$519$		0			0
$520$	−17548.4	−	24864.9i	−1.47990	−	2.09692i
$521$			17911.8i			1.50620i	0.657906	+	0.753100i	$0.271443\pi$
$521$			17911.8i			1.50620i	−0.657906	+	0.753100i	$0.728557\pi$
$522$		0			0
$523$		−	15173.0i		−	1.26859i	−0.773093	−	0.634293i	$-0.781291\pi$
$523$		−	15173.0i		−	1.26859i	0.773093	−	0.634293i	$-0.218709\pi$
$524$	−1902.15	+	16630.4i	−0.158580	+	1.38645i
$525$		0			0
$526$	−7187.02	−	8055.92i	−0.595759	−	0.667785i
$527$	531.055			0.0438958
$528$		0			0
$529$	−11991.9			−0.985605
$530$	11620.7	+	13025.6i	0.952397	+	1.06754i
$531$		0			0
$532$	559.552	−	4892.12i	0.0456009	−	0.398685i
$533$		−	10621.9i		−	0.863197i
$534$		0			0
$535$			23679.2i			1.91353i
$536$	−1172.22	−	1660.96i	−0.0944627	−	0.133848i
$537$		0			0
$538$	6025.86	−	5375.92i	0.482887	−	0.430804i
$539$	−3239.51			−0.258879
$540$		0			0
$541$	−8514.18			−0.676623			−0.338312	−	0.941034i	$-0.609856\pi$
$541$	−8514.18			−0.676623			−0.338312	+	0.941034i	$0.609856\pi$
$542$	11760.6	−	10492.1i	0.932033	−	0.831505i
$543$		0			0
$544$	−1869.39	+	1022.92i	−0.147333	+	0.0806205i
$545$		−	15332.6i		−	1.20509i
$546$		0			0
$547$			8321.92i			0.650493i	0.945629	+	0.325246i	$0.105447\pi$
$547$			8321.92i			0.650493i	−0.945629	+	0.325246i	$0.894553\pi$
$548$	4595.16	+	525.587i	0.358204	+	0.0409707i
$549$		0			0
$550$	43961.9	+	49276.8i	3.40826	+	3.82031i
$551$	662.658			0.0512345
$552$		0			0
$553$	−5856.99			−0.450388
$554$	2698.53	+	3024.78i	0.206949	+	0.231969i
$555$		0			0
$556$	12158.3	+	1390.65i	0.927386	+	0.106073i
$557$			2082.84i			0.158443i	0.996857	+	0.0792213i	$0.0252434\pi$
$557$			2082.84i			0.158443i	−0.996857	+	0.0792213i	$0.974757\pi$
$558$		0			0
$559$			20359.7i			1.54047i
$560$	9543.23	+	2212.01i	0.720134	+	0.166919i
$561$		0			0
$562$	−3294.11	+	2938.81i	−0.247248	+	0.220580i
$563$	−8425.49			−0.630714			−0.315357	−	0.948973i	$-0.602124\pi$
$563$	−8425.49			−0.630714			−0.315357	+	0.948973i	$0.602124\pi$
$564$		0			0
$565$	17586.7			1.30952
$566$	1177.58	−	1050.57i	0.0874514	−	0.0780191i
$567$		0			0
$568$	16486.8	−	11635.5i	1.21791	−	0.859534i
$569$			22690.3i			1.67175i	0.548919	+	0.835875i	$0.315039\pi$
$569$			22690.3i			1.67175i	−0.548919	+	0.835875i	$0.684961\pi$
$570$		0			0
$571$		−	23862.8i		−	1.74891i	−0.485109	−	0.874454i	$-0.661220\pi$
$571$		−	23862.8i		−	1.74891i	0.485109	−	0.874454i	$-0.338780\pi$
$572$	3696.86	−	32321.4i	0.270233	−	2.36263i
$573$		0			0
$574$	2276.13	+	2551.30i	0.165512	+	0.185522i
$575$	4673.68			0.338967
$576$		0			0
$577$	13667.8			0.986131			0.493066	−	0.869992i	$-0.335876\pi$
$577$	13667.8			0.986131			0.493066	+	0.869992i	$0.335876\pi$
$578$	−8989.93	−	10076.8i	−0.646941	−	0.725155i
$579$		0			0
$580$	−149.813	+	1309.81i	−0.0107253	+	0.0937702i
$581$			802.834i			0.0573273i
$582$		0			0
$583$			18659.4i			1.32555i
$584$	−9364.22	+	6608.77i	−0.663517	+	0.468276i
$585$		0			0
$586$	3002.51	−	2678.66i	0.211659	−	0.188830i
$587$	18696.1			1.31460			0.657301	−	0.753628i	$-0.271698\pi$
$587$	18696.1			1.31460			0.657301	+	0.753628i	$0.271698\pi$
$588$		0			0
$589$	3966.62			0.277490
$590$	−25537.8	+	22783.3i	−1.78199	+	1.58979i
$591$		0			0
$592$	−12962.2	−	3004.50i	−0.899905	−	0.208588i
$593$			12602.7i			0.872735i	0.899769	+	0.436367i	$0.143735\pi$
$593$			12602.7i			0.872735i	−0.899769	+	0.436367i	$0.856265\pi$
$594$		0			0
$595$		−	1801.89i		−	0.124152i
$596$	−9361.27	−	1070.73i	−0.643376	−	0.0735883i
$597$		0			0
$598$	−1532.77	−	1718.08i	−0.104815	−	0.117487i
$599$	28096.8			1.91653			0.958267	−	0.285876i	$-0.0922845\pi$
$599$	28096.8			1.91653			0.958267	+	0.285876i	$0.0922845\pi$
$600$		0			0
$601$	12077.8			0.819737			0.409869	−	0.912145i	$-0.365575\pi$
$601$	12077.8			0.819737			0.409869	+	0.912145i	$0.365575\pi$
$602$	−4362.81	−	4890.27i	−0.295374	−	0.331084i
$603$		0			0
$604$	−2182.51	−	249.631i	−0.147028	−	0.0168168i
$605$			66471.5i			4.46686i
$606$		0			0
$607$		−	8916.88i		−	0.596252i	−0.954527	−	0.298126i	$-0.903638\pi$
$607$		−	8916.88i		−	0.596252i	0.954527	−	0.298126i	$-0.0963616\pi$
$608$	−13963.1	+	7640.57i	−0.931377	+	0.509648i
$609$		0			0
$610$	−12103.5	+	10798.0i	−0.803370	+	0.716720i
$611$	26866.9			1.77892
$612$		0			0
$613$	−22083.1			−1.45502			−0.727510	−	0.686098i	$-0.759322\pi$
$613$	−22083.1			−1.45502			−0.727510	+	0.686098i	$0.759322\pi$
$614$	−16040.7	+	14310.6i	−1.05432	+	0.940600i
$615$		0			0
$616$	6038.08	+	8555.57i	0.394937	+	0.559600i
$617$		−	11370.8i		−	0.741930i	−0.928647	−	0.370965i	$-0.879027\pi$
$617$		−	11370.8i		−	0.741930i	0.928647	−	0.370965i	$-0.120973\pi$
$618$		0			0
$619$		−	9687.07i		−	0.629009i	−0.949256	−	0.314504i	$-0.898162\pi$
$619$		−	9687.07i		−	0.629009i	0.949256	−	0.314504i	$-0.101838\pi$
$620$	−896.771	+	7840.40i	−0.0580890	+	0.507868i
$621$		0			0
$622$	−7563.00	−	8477.35i	−0.487538	−	0.546481i
$623$	−1137.17			−0.0731293
$624$		0			0
$625$	64945.1			4.15648
$626$	−12783.9	−	14329.4i	−0.816209	−	0.914887i
$627$		0			0
$628$	−730.832	+	6389.61i	−0.0464385	+	0.406008i
$629$			2447.44i			0.155145i
$630$		0			0
$631$		−	25566.3i		−	1.61296i	−0.591259	−	0.806482i	$-0.701369\pi$
$631$		−	25566.3i		−	1.61296i	0.591259	−	0.806482i	$-0.298631\pi$
$632$	10916.8	+	15468.4i	0.687097	+	0.973573i
$633$		0			0
$634$	9878.79	−	8813.28i	0.618828	−	0.552082i
$635$	−32031.5			−2.00178
$636$		0			0
$637$	3013.94			0.187467
$638$	−1051.58	+	938.161i	−0.0652548	+	0.0582165i
$639$		0			0
$640$	−11945.5	−	29326.7i	−0.737795	−	1.81131i
$641$			7551.94i			0.465341i	0.972556	+	0.232671i	$0.0747464\pi$
$641$			7551.94i			0.465341i	−0.972556	+	0.232671i	$0.925254\pi$
$642$		0			0
$643$			11807.7i			0.724182i	0.932143	+	0.362091i	$0.117937\pi$
$643$			11807.7i			0.724182i	−0.932143	+	0.362091i	$0.882063\pi$
$644$	736.323	+	84.2193i	0.0450546	+	0.00515327i
$645$		0			0
$646$	1949.02	+	2184.66i	0.118705	+	0.133056i
$647$	−16918.7			−1.02804			−0.514020	−	0.857778i	$-0.671844\pi$
$647$	−16918.7			−1.02804			−0.514020	+	0.857778i	$0.671844\pi$
$648$		0			0
$649$	−36583.4			−2.21267
$650$	−40900.7	−	45845.6i	−2.46809	−	2.76648i
$651$		0			0
$652$	15174.4	+	1735.62i	0.911467	+	0.104252i
$653$		−	26856.9i		−	1.60948i	−0.593628	−	0.804740i	$-0.702305\pi$
$653$		−	26856.9i		−	1.60948i	0.593628	−	0.804740i	$-0.297695\pi$
$654$		0			0
$655$			45752.6i			2.72932i
$656$	2495.58	−	10766.6i	0.148530	−	0.640800i
$657$		0			0
$658$	−6453.25	+	5757.22i	−0.382331	+	0.341094i
$659$	17861.3			1.05581			0.527904	−	0.849304i	$-0.322978\pi$
$659$	17861.3			1.05581			0.527904	+	0.849304i	$0.322978\pi$
$660$		0			0
$661$	17592.6			1.03521			0.517603	−	0.855621i	$-0.326824\pi$
$661$	17592.6			1.03521			0.517603	+	0.855621i	$0.326824\pi$
$662$	11026.4	−	9837.08i	0.647359	−	0.577536i
$663$		0			0
$664$	2120.29	−	1496.39i	0.123921	−	0.0874567i
$665$		−	13458.9i		−	0.784835i
$666$		0			0
$667$			99.7380i			0.00578991i
$668$	483.359	−	4225.97i	0.0279966	−	0.244772i
$669$		0			0
$670$	−3699.20	−	4146.42i	−0.213302	−	0.239090i
$671$	−17338.5			−0.997532
$672$		0			0
$673$	1930.27			0.110559			0.0552795	−	0.998471i	$-0.482395\pi$
$673$	1930.27			0.110559			0.0552795	+	0.998471i	$0.482395\pi$
$674$	20782.3	+	23294.9i	1.18769	+	1.33128i
$675$		0			0
$676$	−1442.15	+	12608.6i	−0.0820524	+	0.717378i
$677$			7085.47i			0.402240i	0.979567	+	0.201120i	$0.0644582\pi$
$677$			7085.47i			0.402240i	−0.979567	+	0.201120i	$0.935542\pi$
$678$		0			0
$679$		−	7383.96i		−	0.417335i
$680$	−4758.81	+	3358.52i	−0.268371	+	0.189402i
$681$		0			0
$682$	−6294.70	+	5615.76i	−0.353426	+	0.315306i
$683$	−6132.11			−0.343541			−0.171770	−	0.985137i	$-0.554949\pi$
$683$	−6132.11			−0.343541			−0.171770	+	0.985137i	$0.554949\pi$
$684$		0			0
$685$	12642.0			0.705146
$686$	−723.929	+	645.847i	−0.0402912	+	0.0359454i
$687$		0			0
$688$	−4783.45	+	20637.1i	−0.265069	+	1.14358i
$689$		−	17360.1i		−	0.959896i
$690$		0			0
$691$		−	32430.8i		−	1.78542i	−0.450633	−	0.892710i	$-0.648802\pi$
$691$		−	32430.8i		−	1.78542i	0.450633	−	0.892710i	$-0.351198\pi$
$692$	−29547.9	−	3379.64i	−1.62318	−	0.185657i
$693$		0			0
$694$	−9096.67	−	10196.4i	−0.497557	−	0.557711i
$695$	33449.3			1.82562
$696$		0			0
$697$	−2032.88			−0.110475
$698$	9404.75	+	10541.8i	0.509993	+	0.571650i
$699$		0			0
$700$	19648.2	+	2247.33i	1.06090	+	0.121344i
$701$		−	36023.2i		−	1.94091i	−0.241283	−	0.970455i	$-0.577568\pi$
$701$		−	36023.2i		−	1.94091i	0.241283	−	0.970455i	$-0.422432\pi$
$702$		0			0
$703$			18280.8i			0.980757i
$704$	11341.0	−	31893.2i	0.607147	−	1.70742i
$705$		0			0
$706$	−16741.3	+	14935.6i	−0.892447	+	0.796189i
$707$	−1196.08			−0.0636256
$708$		0			0
$709$	2852.85			0.151116			0.0755579	−	0.997141i	$-0.475926\pi$
$709$	2852.85			0.151116			0.0755579	+	0.997141i	$0.475926\pi$
$710$	41157.8	−	36718.5i	2.17553	−	1.94088i
$711$		0			0
$712$	2119.54	+	3003.26i	0.111564	+	0.158079i
$713$			597.024i			0.0313587i
$714$		0			0
$715$		−	88920.8i		−	4.65098i
$716$	1975.53	−	17271.9i	0.103113	−	0.901510i
$717$		0			0
$718$	5336.94	+	5982.17i	0.277400	+	0.310937i
$719$	−18135.0			−0.940643			−0.470322	−	0.882495i	$-0.655862\pi$
$719$	−18135.0			−0.940643			−0.470322	+	0.882495i	$0.655862\pi$
$720$		0			0
$721$	−531.961			−0.0274775
$722$	1642.84	+	1841.46i	0.0846816	+	0.0949195i
$723$		0			0
$724$	−2226.49	+	19466.0i	−0.114291	+	0.999238i
$725$			2661.43i			0.136335i
$726$		0			0
$727$			2295.77i			0.117119i	0.998284	+	0.0585595i	$0.0186507\pi$
$727$			2295.77i			0.117119i	−0.998284	+	0.0585595i	$0.981349\pi$
$728$	−5617.64	−	7959.83i	−0.285994	−	0.405235i
$729$		0			0
$730$	−23376.9	+	20855.5i	−1.18523	+	1.05739i
$731$	3896.57			0.197154
$732$		0			0
$733$	37706.1			1.90001			0.950005	−	0.312234i	$-0.101077\pi$
$733$	37706.1			1.90001			0.950005	+	0.312234i	$0.101077\pi$
$734$	10937.3	−	9757.58i	0.550002	−	0.490680i
$735$		0			0
$736$	−1150.00	−	2101.61i	−0.0575944	−	0.105253i
$737$		−	5939.83i		−	0.296875i
$738$		0			0
$739$		−	30540.4i		−	1.52023i	−0.649791	−	0.760113i	$-0.725144\pi$
$739$		−	30540.4i		−	1.52023i	0.649791	−	0.760113i	$-0.274856\pi$
$740$	−36133.6	−	4132.90i	−1.79500	−	0.205309i
$741$		0			0
$742$	3720.05	+	4169.79i	0.184053	+	0.206305i
$743$	3816.22			0.188430			0.0942150	−	0.995552i	$-0.469966\pi$
$743$	3816.22			0.188430			0.0942150	+	0.995552i	$0.469966\pi$
$744$		0			0
$745$	−25754.2			−1.26652
$746$	10760.2	+	12061.1i	0.528097	+	0.591943i
$747$		0			0
$748$	−6185.87	−	707.529i	−0.302377	−	0.0345853i
$749$			7580.25i			0.369795i
$750$		0			0
$751$			3291.17i			0.159916i	0.996798	+	0.0799578i	$0.0254786\pi$
$751$			3291.17i			0.159916i	−0.996798	+	0.0799578i	$0.974521\pi$
$752$	27233.0	+	6312.30i	1.32059	+	0.306098i
$753$		0			0
$754$	978.360	−	872.835i	0.0472543	−	0.0421575i
$755$	−6004.39			−0.289434
$756$		0			0
$757$	4954.49			0.237878			0.118939	−	0.992902i	$-0.462051\pi$
$757$	4954.49			0.237878			0.118939	+	0.992902i	$0.462051\pi$
$758$	9091.21	−	8110.65i	0.435630	−	0.388644i
$759$		0			0
$760$	−35545.1	+	25085.9i	−1.69652	+	1.19732i
$761$		−	8155.76i		−	0.388497i	−0.980952	−	0.194248i	$-0.937773\pi$
$761$		−	8155.76i		−	0.388497i	0.980952	−	0.194248i	$-0.0622268\pi$
$762$		0			0
$763$		−	4908.30i		−	0.232887i
$764$	−2838.49	+	24816.7i	−0.134415	+	1.17518i
$765$		0			0
$766$	−12952.3	−	14518.2i	−0.610946	−	0.684808i
$767$	34036.0			1.60231
$768$		0			0
$769$	−19910.5			−0.933668			−0.466834	−	0.884345i	$-0.654605\pi$
$769$	−19910.5			−0.933668			−0.466834	+	0.884345i	$0.654605\pi$
$770$	19054.5	+	21358.2i	0.891790	+	0.999606i
$771$		0			0
$772$	624.503	−	5459.98i	0.0291144	−	0.254545i
$773$		−	13405.6i		−	0.623759i	−0.950122	−	0.311880i	$-0.899041\pi$
$773$		−	13405.6i		−	0.623759i	0.950122	−	0.311880i	$-0.100959\pi$
$774$		0			0
$775$			15931.1i			0.738404i
$776$	−19501.1	+	13762.9i	−0.902124	+	0.636672i
$777$		0			0
$778$	21069.7	−	18797.2i	0.970934	−	0.866211i
$779$	−15184.3			−0.698373
$780$		0			0
$781$	58959.3			2.70132
$782$	−328.817	+	293.351i	−0.0150364	+	0.0134146i
$783$		0			0
$784$	3055.01	+	708.116i	0.139168	+	0.0322575i
$785$			17578.7i			0.799251i
$786$		0			0
$787$		−	14037.3i		−	0.635800i	−0.948124	−	0.317900i	$-0.897022\pi$
$787$		−	14037.3i		−	0.635800i	0.948124	−	0.317900i	$-0.102978\pi$
$788$	−5121.90	−	585.834i	−0.231549	−	0.0264841i
$789$		0			0
$790$	34450.4	+	38615.3i	1.55150	+	1.73908i
$791$	5629.90			0.253067
$792$		0			0
$793$	16131.2			0.722364
$794$	−1113.89	−	1248.56i	−0.0497866	−	0.0558057i
$795$		0			0
$796$	−21855.6	−	2499.80i	−0.973178	−	0.111310i
$797$		−	36858.2i		−	1.63813i	−0.573704	−	0.819063i	$-0.694494\pi$
$797$		−	36858.2i		−	1.63813i	0.573704	−	0.819063i	$-0.305506\pi$
$798$		0			0
$799$		−	5141.96i		−	0.227671i
$800$	−30686.8	−	56079.7i	−1.35618	−	2.47840i
$801$		0			0
$802$	18917.2	−	16876.8i	0.832906	−	0.743070i
$803$	−33487.9			−1.47168
$804$		0			0
$805$	2025.73			0.0886927
$806$	5856.39	−	5224.73i	0.255934	−	0.228329i
$807$		0			0
$808$	2229.36	+	3158.86i	0.0970650	+	0.137535i
$809$		−	12429.2i		−	0.540156i	−0.962839	−	0.270078i	$-0.912951\pi$
$809$		−	12429.2i		−	0.540156i	0.962839	−	0.270078i	$-0.0870494\pi$
$810$		0			0
$811$			15370.2i			0.665501i	0.943015	+	0.332751i	$0.107977\pi$
$811$			15370.2i			0.665501i	−0.943015	+	0.332751i	$0.892023\pi$
$812$	−47.9587	+	419.299i	−0.00207268	+	0.0181213i
$813$		0			0
$814$	−25881.1	−	29010.0i	−1.11441	−	1.24914i
$815$	41747.1			1.79428
$816$		0			0
$817$	29104.8			1.24632
$818$	−2720.91	−	3049.86i	−0.116301	−	0.130362i
$819$		0			0
$820$	3432.85	−	30013.1i	0.146195	−	1.27818i
$821$			18477.9i			0.785486i	0.919648	+	0.392743i	$0.128474\pi$
$821$			18477.9i			0.785486i	−0.919648	+	0.392743i	$0.871526\pi$
$822$		0			0
$823$			10598.5i			0.448895i	0.974486	+	0.224448i	$0.0720578\pi$
$823$			10598.5i			0.448895i	−0.974486	+	0.224448i	$0.927942\pi$
$824$	991.515	+	1404.91i	0.0419188	+	0.0593962i
$825$		0			0
$826$	−8175.23	+	7293.46i	−0.344374	+	0.307230i
$827$	25115.2			1.05603			0.528017	−	0.849234i	$-0.322936\pi$
$827$	25115.2			1.05603			0.528017	+	0.849234i	$0.322936\pi$
$828$		0			0
$829$	25579.4			1.07166			0.535832	−	0.844324i	$-0.319998\pi$
$829$	25579.4			1.07166			0.535832	+	0.844324i	$0.319998\pi$
$830$	5293.11	−	4722.21i	0.221357	−	0.197482i
$831$		0			0
$832$	−10551.3	+	29672.4i	−0.439666	+	1.23643i
$833$		−	576.827i		−	0.0239927i
$834$		0			0
$835$		−	11626.3i		−	0.481849i
$836$	−46204.3	−	5284.77i	−1.91150	−	0.218634i
$837$		0			0
$838$	9014.44	+	10104.3i	0.371597	+	0.416523i
$839$	6978.90			0.287173			0.143587	−	0.989638i	$-0.454136\pi$
$839$	6978.90			0.287173			0.143587	+	0.989638i	$0.454136\pi$
$840$		0			0
$841$	24332.2			0.997671
$842$	24743.2	+	27734.6i	1.01272	+	1.13515i
$843$		0			0
$844$	125.272	+	14.3284i	0.00510904	+	0.000584363i
$845$			34688.2i			1.41220i
$846$		0			0
$847$			21279.0i			0.863231i
$848$	4078.71	−	17596.7i	0.165169	−	0.712586i
$849$		0			0
$850$	−8774.22	+	7827.85i	−0.354063	+	0.315874i
$851$	−2751.47			−0.110834
$852$		0			0
$853$	−44677.6			−1.79335			−0.896677	−	0.442685i	$-0.854026\pi$
$853$	−44677.6			−1.79335			−0.896677	+	0.442685i	$0.854026\pi$
$854$	−3874.60	+	3456.69i	−0.155253	+	0.138508i
$855$		0			0
$856$	20019.5	−	14128.7i	0.799360	−	0.564147i
$857$		−	25565.0i		−	1.01900i	−0.860470	−	0.509501i	$-0.829830\pi$
$857$		−	25565.0i		−	1.01900i	0.860470	−	0.509501i	$-0.170170\pi$
$858$		0			0
$859$		−	6461.94i		−	0.256669i	−0.991731	−	0.128334i	$-0.959037\pi$
$859$		−	6461.94i		−	0.256669i	0.991731	−	0.128334i	$-0.0409631\pi$
$860$	−6579.99	+	57528.3i	−0.260902	+	2.28105i
$861$		0			0
$862$	16366.0	+	18344.6i	0.646668	+	0.724849i
$863$	−27097.5			−1.06884			−0.534420	−	0.845219i	$-0.679470\pi$
$863$	−27097.5			−1.06884			−0.534420	+	0.845219i	$0.679470\pi$
$864$		0			0
$865$	−81290.6			−3.19533
$866$	−33084.3	−	37084.1i	−1.29821	−	1.45516i
$867$		0			0
$868$	−287.077	+	2509.89i	−0.0112258	+	0.0981467i
$869$			55317.2i			2.15939i
$870$		0			0
$871$			5526.23i			0.214982i
$872$	−12962.9	+	9148.51i	−0.503415	+	0.355284i
$873$		0			0
$874$	−2456.04	+	2191.14i	−0.0950537	+	0.0848013i
$875$	34921.8			1.34922
$876$		0			0
$877$	−40674.5			−1.56611			−0.783055	−	0.621952i	$-0.786340\pi$
$877$	−40674.5			−1.56611			−0.783055	+	0.621952i	$0.786340\pi$
$878$	2427.58	−	2165.75i	0.0933109	−	0.0832465i
$879$		0			0
$880$	20891.7	−	90132.4i	0.800294	−	3.45268i
$881$			36098.7i			1.38047i	0.723584	+	0.690237i	$0.242494\pi$
$881$			36098.7i			1.38047i	−0.723584	+	0.690237i	$0.757506\pi$
$882$		0			0
$883$			36446.8i			1.38905i	0.719467	+	0.694526i	$0.244386\pi$
$883$			36446.8i			1.38905i	−0.719467	+	0.694526i	$0.755614\pi$
$884$	5755.14	+	658.263i	0.218966	+	0.0250450i
$885$		0			0
$886$	1626.15	+	1822.75i	0.0616610	+	0.0691157i
$887$	−9088.36			−0.344033			−0.172016	−	0.985094i	$-0.555028\pi$
$887$	−9088.36			−0.344033			−0.172016	+	0.985094i	$0.555028\pi$
$888$		0			0
$889$	−10254.0			−0.386849
$890$	6688.71	+	7497.37i	0.251917	+	0.282373i
$891$		0			0
$892$	−29999.0	−	3431.23i	−1.12606	−	0.128796i
$893$		−	38407.0i		−	1.43924i
$894$		0			0
$895$		−	47517.5i		−	1.77468i
$896$	−3824.04	−	9388.14i	−0.142581	−	0.350040i
$897$		0			0
$898$	21501.3	−	19182.2i	0.799005	−	0.712826i
$899$	−339.975			−0.0126127
$900$		0			0
$901$	−3322.50			−0.122851
$902$	24096.2	−	21497.2i	0.889484	−	0.793546i
$903$		0			0
$904$	−10493.5	−	14868.6i	−0.386071	−	0.547038i
$905$			53553.8i			1.96706i
$906$		0			0
$907$			38031.8i			1.39231i	0.717892	+	0.696155i	$0.245107\pi$
$907$			38031.8i			1.39231i	−0.717892	+	0.696155i	$0.754893\pi$
$908$	−937.277	+	8194.54i	−0.0342562	+	0.299499i
$909$		0			0
$910$	−17727.7	−	19871.0i	−0.645790	−	0.723865i
$911$	−24648.4			−0.896419			−0.448209	−	0.893929i	$-0.647938\pi$
$911$	−24648.4			−0.896419			−0.448209	+	0.893929i	$0.647938\pi$
$912$		0			0
$913$	7582.49			0.274856
$914$	−2060.74	−	2309.88i	−0.0745769	−	0.0835931i
$915$		0			0
$916$	−2019.12	+	17653.0i	−0.0728313	+	0.636759i
$917$			14646.5i			0.527447i
$918$		0			0
$919$			21102.2i			0.757451i	0.925509	+	0.378726i	$0.123638\pi$
$919$			21102.2i			0.757451i	−0.925509	+	0.378726i	$0.876362\pi$
$920$	−3775.73	−	5349.97i	−0.135307	−	0.191721i
$921$		0			0
$922$	−11296.3	+	10077.9i	−0.403495	+	0.359975i
$923$	−54853.8			−1.95616
$924$		0			0
$925$	−73420.9			−2.60980
$926$	29791.9	−	26578.6i	1.05726	−	0.943225i
$927$		0			0
$928$	1196.76	−	654.866i	0.0423336	−	0.0231649i
$929$		−	13010.0i		−	0.459466i	−0.973254	−	0.229733i	$-0.926215\pi$
$929$		−	13010.0i		−	0.459466i	0.973254	−	0.229733i	$-0.0737854\pi$
$930$		0			0
$931$		−	4308.52i		−	0.151671i
$932$	−38052.8	−	4352.41i	−1.33740	−	0.152970i
$933$		0			0
$934$	18838.3	+	21115.8i	0.659965	+	0.739753i
$935$	−17018.2			−0.595247
$936$		0			0
$937$	6116.05			0.213237			0.106618	−	0.994300i	$-0.465998\pi$
$937$	6116.05			0.213237			0.106618	+	0.994300i	$0.465998\pi$
$938$	−1184.20	−	1327.37i	−0.0412211	−	0.0462047i
$939$		0			0
$940$	75915.0	+	8683.03i	2.63412	+	0.301286i
$941$			15615.5i			0.540969i	0.962724	+	0.270485i	$0.0871839\pi$
$941$			15615.5i			0.540969i	−0.962724	+	0.270485i	$0.912816\pi$
$942$		0			0
$943$		−	2285.41i		−	0.0789219i
$944$	34499.8	+	7996.66i	1.18948	+	0.275709i
$945$		0			0
$946$	−46186.8	+	41205.2i	−1.58738	+	1.41617i
$947$	33651.5			1.15473			0.577364	−	0.816487i	$-0.304081\pi$
$947$	33651.5			1.15473			0.577364	+	0.816487i	$0.304081\pi$
$948$		0			0
$949$	31156.1			1.06572
$950$	−65537.6	+	58468.8i	−2.23823	+	1.99682i
$951$		0			0
$952$	−1523.40	+	1075.14i	−0.0518633	+	0.0366024i
$953$			13028.5i			0.442847i	0.975178	+	0.221424i	$0.0710703\pi$
$953$			13028.5i			0.442847i	−0.975178	+	0.221424i	$0.928930\pi$
$954$		0			0
$955$			68274.5i			2.31341i
$956$	−5018.98	+	43880.6i	−0.169796	+	1.48452i
$957$		0			0
$958$	10301.9	+	11547.4i	0.347432	+	0.389436i
$959$	4046.98			0.136271
$960$		0			0
$961$	27755.9			0.931689
$962$	24078.9	+	26990.0i	0.807002	+	0.904567i
$963$		0			0
$964$	−556.277	+	4863.49i	−0.0185856	+	0.162492i
$965$		−	15021.2i		−	0.501088i
$966$		0			0
$967$			28818.4i			0.958363i	0.877716	+	0.479182i	$0.159066\pi$
$967$			28818.4i			0.958363i	−0.877716	+	0.479182i	$0.840934\pi$
$968$	56198.1	−	39661.7i	1.86599	−	1.31692i
$969$		0			0
$970$	−48682.7	+	43431.9i	−1.61145	+	1.43764i
$971$	57593.1			1.90345			0.951725	−	0.306952i	$-0.0993090\pi$
$971$	57593.1			1.90345			0.951725	+	0.306952i	$0.0993090\pi$
$972$		0			0
$973$	10707.9			0.352804
$974$	−31375.3	+	27991.3i	−1.03217	+	0.920839i
$975$		0			0
$976$	16351.0	+	3789.97i	0.536251	+	0.124297i
$977$			43479.4i			1.42378i	0.702293	+	0.711888i	$0.252159\pi$
$977$			43479.4i			1.42378i	−0.702293	+	0.711888i	$0.747841\pi$
$978$		0			0
$979$			10740.1i			0.350619i
$980$	8516.18	+	974.066i	0.277591	+	0.0317504i
$981$		0			0
$982$	37240.7	+	41743.1i	1.21018	+	1.35649i
$983$	−1724.27			−0.0559468			−0.0279734	−	0.999609i	$-0.508905\pi$
$983$	−1724.27			−0.0559468			−0.0279734	+	0.999609i	$0.508905\pi$
$984$		0			0
$985$	−14091.1			−0.455817
$986$	−167.049	−	187.245i	−0.00539546	−	0.00604776i
$987$		0			0
$988$	42987.1	+	4916.78i	1.38421	+	0.158324i
$989$			4380.62i			0.140845i
$990$		0			0
$991$		−	45591.3i		−	1.46141i	−0.682695	−	0.730703i	$-0.739192\pi$
$991$		−	45591.3i		−	1.46141i	0.682695	−	0.730703i	$-0.260808\pi$
$992$	7163.72	−	3919.98i	0.229283	−	0.125463i
$993$		0			0
$994$	13175.5	−	11754.5i	0.420425	−	0.375079i
$995$	−60127.8			−1.91576
$996$		0			0
$997$	58305.6			1.85211			0.926057	−	0.377384i	$-0.123176\pi$
$997$	58305.6			1.85211			0.926057	+	0.377384i	$0.123176\pi$
$998$	30599.0	−	27298.7i	0.970537	−	0.865857i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.9	✓	36
3.2	odd	2	inner	252.4.e.a.71.28	yes	36
4.3	odd	2	inner	252.4.e.a.71.27	yes	36
12.11	even	2	inner	252.4.e.a.71.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.9	✓	36	1.1	even	1	trivial
252.4.e.a.71.10	yes	36	12.11	even	2	inner
252.4.e.a.71.27	yes	36	4.3	odd	2	inner
252.4.e.a.71.28	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88294 - 2.11058i) q^{2} +(-0.909099 + 7.94818i) q^{4} +21.8666i q^{5} +7.00000i q^{7} +(18.4870 - 13.0472i) q^{8} +(46.1512 - 41.1734i) q^{10} +66.1125 q^{11} -61.5090 q^{13} +(14.7741 - 13.1806i) q^{14} +(-62.3471 - 14.4514i) q^{16} +11.7720i q^{17} +87.9289i q^{19} +(-173.800 - 19.8789i) q^{20} +(-124.486 - 139.536i) q^{22} -13.2343 q^{23} -353.148 q^{25} +(115.818 + 129.820i) q^{26} +(-55.6372 - 6.36369i) q^{28} -7.53630i q^{29} -45.1117i q^{31} +(86.8949 + 158.800i) q^{32} +(24.8457 - 22.1659i) q^{34} -153.066 q^{35} +207.904 q^{37} +(185.581 - 165.565i) q^{38} +(285.298 + 404.249i) q^{40} +172.688i q^{41} -331.004i q^{43} +(-60.1028 + 525.474i) q^{44} +(24.9194 + 27.9322i) q^{46} -436.796 q^{47} -49.0000 q^{49} +(664.956 + 745.347i) q^{50} +(55.9177 - 488.884i) q^{52} +282.237i q^{53} +1445.66i q^{55} +(91.3303 + 129.409i) q^{56} +(-15.9060 + 14.1904i) q^{58} -553.350 q^{59} -262.257 q^{61} +(-95.2119 + 84.9425i) q^{62} +(171.542 - 482.408i) q^{64} -1344.99i q^{65} -89.8443i q^{67} +(-93.5658 - 10.7019i) q^{68} +(288.214 + 323.058i) q^{70} +891.802 q^{71} -506.529 q^{73} +(-391.470 - 438.798i) q^{74} +(-698.874 - 79.9360i) q^{76} +462.788i q^{77} +836.714i q^{79} +(316.002 - 1363.32i) q^{80} +(364.472 - 325.161i) q^{82} +114.691 q^{83} -257.413 q^{85} +(-698.610 + 623.259i) q^{86} +(1222.22 - 862.583i) q^{88} +162.452i q^{89} -430.563i q^{91} +(12.0313 - 105.189i) q^{92} +(822.460 + 921.894i) q^{94} -1922.71 q^{95} -1054.85 q^{97} +(92.2639 + 103.418i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64}+ \cdots + 5496 q^{94}+O(q^{100}) \) 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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