LMFDB - Embedded newform 252.4.e.a.71.14

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			71.14
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16208 + 2.57868i) q^{2} +(-5.29916 - 5.99324i) q^{4} +0.300247i q^{5} +7.00000i q^{7} +(21.6127 - 6.70021i) q^{8} +(-0.774240 - 0.348910i) q^{10} +9.71649 q^{11} -76.4714 q^{13} +(-18.0507 - 8.13454i) q^{14} +(-7.83789 + 63.5182i) q^{16} -93.2361i q^{17} -81.8849i q^{19} +(1.79945 - 1.59106i) q^{20} +(-11.2913 + 25.0557i) q^{22} +185.343 q^{23} +124.910 q^{25} +(88.8656 - 197.195i) q^{26} +(41.9527 - 37.0941i) q^{28} -159.193i q^{29} +139.107i q^{31} +(-154.685 - 94.0245i) q^{32} +(240.426 + 108.348i) q^{34} -2.10173 q^{35} +30.5025 q^{37} +(211.155 + 95.1565i) q^{38} +(2.01172 + 6.48914i) q^{40} -173.772i q^{41} -356.320i q^{43} +(-51.4892 - 58.2333i) q^{44} +(-215.382 + 477.939i) q^{46} +346.929 q^{47} -49.0000 q^{49} +(-145.155 + 322.102i) q^{50} +(405.234 + 458.312i) q^{52} +154.800i q^{53} +2.91735i q^{55} +(46.9015 + 151.289i) q^{56} +(410.508 + 184.995i) q^{58} +586.598 q^{59} +167.768 q^{61} +(-358.711 - 161.653i) q^{62} +(422.214 - 289.619i) q^{64} -22.9603i q^{65} -403.531i q^{67} +(-558.787 + 494.073i) q^{68} +(2.44237 - 5.41968i) q^{70} +156.489 q^{71} -565.672 q^{73} +(-35.4462 + 78.6561i) q^{74} +(-490.756 + 433.921i) q^{76} +68.0154i q^{77} -542.718i q^{79} +(-19.0712 - 2.35330i) q^{80} +(448.101 + 201.936i) q^{82} -791.534 q^{83} +27.9939 q^{85} +(918.834 + 414.071i) q^{86} +(209.999 - 65.1025i) q^{88} -809.418i q^{89} -535.300i q^{91} +(-982.160 - 1110.80i) q^{92} +(-403.158 + 894.618i) q^{94} +24.5857 q^{95} -192.401 q^{97} +(56.9418 - 126.355i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.16208	+	2.57868i	−0.410856	+	0.911700i
$2$	−1.16208	+	2.57868i	−0.410856	+	0.911700i
$3$		0			0
$3$		0			0
$4$	−5.29916	−	5.99324i	−0.662395	−	0.749155i
$5$			0.300247i			0.0268549i	0.999910	+	0.0134275i	$0.00427422\pi$
$5$			0.300247i			0.0268549i	−0.999910	+	0.0134275i	$0.995726\pi$
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$	21.6127	−	6.70021i	0.955154	−	0.296110i
$9$		0			0
$10$	−0.774240	−	0.348910i	−0.0244836	−	0.0110335i
$11$	9.71649			0.266330			0.133165	−	0.991094i	$-0.457486\pi$
$11$	9.71649			0.266330			0.133165	+	0.991094i	$0.457486\pi$
$12$		0			0
$13$	−76.4714			−1.63149			−0.815744	−	0.578413i	$-0.803672\pi$
$13$	−76.4714			−1.63149			−0.815744	+	0.578413i	$0.803672\pi$
$14$	−18.0507	−	8.13454i	−0.344590	−	0.155289i
$15$		0			0
$16$	−7.83789	+	63.5182i	−0.122467	+	0.992473i
$17$		−	93.2361i		−	1.33018i	−0.746763	−	0.665091i	$-0.768393\pi$
$17$		−	93.2361i		−	1.33018i	0.746763	−	0.665091i	$-0.231607\pi$
$18$		0			0
$19$		−	81.8849i		−	0.988720i	−0.869257	−	0.494360i	$-0.835402\pi$
$19$		−	81.8849i		−	0.988720i	0.869257	−	0.494360i	$-0.164598\pi$
$20$	1.79945	−	1.59106i	0.0201185	−	0.0177885i
$21$		0			0
$22$	−11.2913	+	25.0557i	−0.109423	+	0.242813i
$23$	185.343			1.68029			0.840144	−	0.542363i	$-0.182470\pi$
$23$	185.343			1.68029			0.840144	+	0.542363i	$0.182470\pi$
$24$		0			0
$25$	124.910			0.999279
$26$	88.8656	−	197.195i	0.670307	−	1.48743i
$27$		0			0
$28$	41.9527	−	37.0941i	0.283154	−	0.250362i
$29$		−	159.193i		−	1.01936i	−0.860364	−	0.509679i	$-0.829764\pi$
$29$		−	159.193i		−	1.01936i	0.860364	−	0.509679i	$-0.170236\pi$
$30$		0			0
$31$			139.107i			0.805945i	0.915212	+	0.402973i	$0.132023\pi$
$31$			139.107i			0.805945i	−0.915212	+	0.402973i	$0.867977\pi$
$32$	−154.685	−	94.0245i	−0.854521	−	0.519417i
$33$		0			0
$34$	240.426	+	108.348i	1.21273	+	0.546513i
$35$	−2.10173			−0.0101502
$36$		0			0
$37$	30.5025			0.135529			0.0677646	−	0.997701i	$-0.478413\pi$
$37$	30.5025			0.135529			0.0677646	+	0.997701i	$0.478413\pi$
$38$	211.155	+	95.1565i	0.901417	+	0.406222i
$39$		0			0
$40$	2.01172	+	6.48914i	0.00795201	+	0.0256506i
$41$		−	173.772i		−	0.661916i	−0.943645	−	0.330958i	$-0.892628\pi$
$41$		−	173.772i		−	0.661916i	0.943645	−	0.330958i	$-0.107372\pi$
$42$		0			0
$43$		−	356.320i		−	1.26368i	−0.775099	−	0.631840i	$-0.782300\pi$
$43$		−	356.320i		−	1.26368i	0.775099	−	0.631840i	$-0.217700\pi$
$44$	−51.4892	−	58.2333i	−0.176416	−	0.199523i
$45$		0			0
$46$	−215.382	+	477.939i	−0.690357	+	1.53192i
$47$	346.929			1.07670			0.538349	−	0.842722i	$-0.319048\pi$
$47$	346.929			1.07670			0.538349	+	0.842722i	$0.319048\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	−145.155	+	322.102i	−0.410560	+	0.911043i
$51$		0			0
$52$	405.234	+	458.312i	1.08069	+	1.22224i
$53$			154.800i			0.401197i	0.979674	+	0.200598i	$0.0642886\pi$
$53$			154.800i			0.401197i	−0.979674	+	0.200598i	$0.935711\pi$
$54$		0			0
$55$			2.91735i			0.00715228i
$56$	46.9015	+	151.289i	0.111919	+	0.361014i
$57$		0			0
$58$	410.508	+	184.995i	0.929350	+	0.418810i
$59$	586.598			1.29438			0.647192	−	0.762327i	$-0.275943\pi$
$59$	586.598			1.29438			0.647192	+	0.762327i	$0.275943\pi$
$60$		0			0
$61$	167.768			0.352140			0.176070	−	0.984378i	$-0.443662\pi$
$61$	167.768			0.352140			0.176070	+	0.984378i	$0.443662\pi$
$62$	−358.711	−	161.653i	−0.734780	−	0.331127i
$63$		0			0
$64$	422.214	−	289.619i	0.824637	−	0.565662i
$65$		−	22.9603i		−	0.0438135i
$66$		0			0
$67$		−	403.531i		−	0.735809i	−0.929864	−	0.367905i	$-0.880075\pi$
$67$		−	403.531i		−	0.735809i	0.929864	−	0.367905i	$-0.119925\pi$
$68$	−558.787	+	494.073i	−0.996512	+	0.881105i
$69$		0			0
$70$	2.44237	−	5.41968i	0.00417027	−	0.00925394i
$71$	156.489			0.261576			0.130788	−	0.991410i	$-0.458249\pi$
$71$	156.489			0.261576			0.130788	+	0.991410i	$0.458249\pi$
$72$		0			0
$73$	−565.672			−0.906944			−0.453472	−	0.891270i	$-0.649815\pi$
$73$	−565.672			−0.906944			−0.453472	+	0.891270i	$0.649815\pi$
$74$	−35.4462	+	78.6561i	−0.0556830	+	0.123562i
$75$		0			0
$76$	−490.756	+	433.921i	−0.740705	+	0.654923i
$77$			68.0154i			0.100663i
$78$		0			0
$79$		−	542.718i		−	0.772918i	−0.922307	−	0.386459i	$-0.873698\pi$
$79$		−	542.718i		−	0.772918i	0.922307	−	0.386459i	$-0.126302\pi$
$80$	−19.0712	−	2.35330i	−0.0266528	−	0.00328884i
$81$		0			0
$82$	448.101	+	201.936i	0.603469	+	0.271952i
$83$	−791.534			−1.04677			−0.523386	−	0.852095i	$-0.675332\pi$
$83$	−791.534			−1.04677			−0.523386	+	0.852095i	$0.675332\pi$
$84$		0			0
$85$	27.9939			0.0357219
$86$	918.834	+	414.071i	1.15210	+	0.519191i
$87$		0			0
$88$	209.999	−	65.1025i	0.254386	−	0.0788631i
$89$		−	809.418i		−	0.964024i	−0.876165	−	0.482012i	$-0.839906\pi$
$89$		−	809.418i		−	0.964024i	0.876165	−	0.482012i	$-0.160094\pi$
$90$		0			0
$91$		−	535.300i		−	0.616645i
$92$	−982.160	−	1110.80i	−1.11301	−	1.25880i
$93$		0			0
$94$	−403.158	+	894.618i	−0.442368	+	0.981626i
$95$	24.5857			0.0265520
$96$		0			0
$97$	−192.401			−0.201395			−0.100698	−	0.994917i	$-0.532107\pi$
$97$	−192.401			−0.201395			−0.100698	+	0.994917i	$0.532107\pi$
$98$	56.9418	−	126.355i	0.0586937	−	0.130243i
$99$		0			0
$100$	−661.917	−	748.615i	−0.661917	−	0.748615i
$101$		−	39.5093i		−	0.0389240i	−0.999811	−	0.0194620i	$-0.993805\pi$
$101$		−	39.5093i		−	0.0389240i	0.999811	−	0.0194620i	$-0.00619534\pi$
$102$		0			0
$103$		−	1420.94i		−	1.35932i	−0.733528	−	0.679659i	$-0.762128\pi$
$103$		−	1420.94i		−	1.35932i	0.733528	−	0.679659i	$-0.237872\pi$
$104$	−1652.75	+	512.374i	−1.55832	+	0.483100i
$105$		0			0
$106$	−399.179	−	179.889i	−0.365771	−	0.164834i
$107$	1455.04			1.31462			0.657310	−	0.753620i	$-0.271694\pi$
$107$	1455.04			1.31462			0.657310	+	0.753620i	$0.271694\pi$
$108$		0			0
$109$	−1904.97			−1.67397			−0.836984	−	0.547227i	$-0.815684\pi$
$109$	−1904.97			−1.67397			−0.836984	+	0.547227i	$0.815684\pi$
$110$	−7.52290	−	3.39018i	−0.00652073	−	0.00293856i
$111$		0			0
$112$	−444.628	−	54.8652i	−0.375119	−	0.0462882i
$113$			1236.88i			1.02970i	0.857281	+	0.514848i	$0.172152\pi$
$113$			1236.88i			1.02970i	−0.857281	+	0.514848i	$0.827848\pi$
$114$		0			0
$115$			55.6486i			0.0451240i
$116$	−954.083	+	843.589i	−0.763658	+	0.675218i
$117$		0			0
$118$	−681.672	+	1512.65i	−0.531805	+	1.18009i
$119$	652.653			0.502761
$120$		0			0
$121$	−1236.59			−0.929068
$122$	−194.960	+	432.620i	−0.144679	+	0.321046i
$123$		0			0
$124$	833.700	−	737.148i	0.603778	−	0.533854i
$125$			75.0347i			0.0536905i
$126$		0			0
$127$		−	2425.86i		−	1.69497i	−0.530823	−	0.847483i	$-0.678117\pi$
$127$		−	2425.86i		−	1.69497i	0.530823	−	0.847483i	$-0.321883\pi$
$128$	256.188	+	1425.31i	0.176906	+	0.984228i
$129$		0			0
$130$	59.2073	+	26.6816i	0.0399448	+	0.0180010i
$131$	−2516.53			−1.67840			−0.839198	−	0.543826i	$-0.816975\pi$
$131$	−2516.53			−1.67840			−0.839198	+	0.543826i	$0.816975\pi$
$132$		0			0
$133$	573.194			0.373701
$134$	1040.58	+	468.934i	0.670837	+	0.302312i
$135$		0			0
$136$	−624.702	−	2015.08i	−0.393880	−	1.27053i
$137$		−	228.393i		−	0.142430i	−0.997461	−	0.0712149i	$-0.977312\pi$
$137$		−	228.393i		−	0.142430i	0.997461	−	0.0712149i	$-0.0226876\pi$
$138$		0			0
$139$			1316.68i			0.803449i	0.915761	+	0.401724i	$0.131589\pi$
$139$			1316.68i			0.803449i	−0.915761	+	0.401724i	$0.868411\pi$
$140$	11.1374	+	12.5962i	0.00672344	+	0.00760408i
$141$		0			0
$142$	−181.853	+	403.535i	−0.107470	+	0.238478i
$143$	−743.034			−0.434515
$144$		0			0
$145$	47.7973			0.0273748
$146$	657.354	−	1458.69i	0.372624	−	0.826861i
$147$		0			0
$148$	−161.638	−	182.809i	−0.0897738	−	0.101532i
$149$			1186.97i			0.652622i	0.945262	+	0.326311i	$0.105806\pi$
$149$			1186.97i			0.652622i	−0.945262	+	0.326311i	$0.894194\pi$
$150$		0			0
$151$			3479.34i			1.87513i	0.347812	+	0.937564i	$0.386925\pi$
$151$			3479.34i			1.87513i	−0.347812	+	0.937564i	$0.613075\pi$
$152$	−548.646	−	1769.75i	−0.292770	−	0.944380i
$153$		0			0
$154$	−175.390	−	79.0392i	−0.0917748	−	0.0413582i
$155$	−41.7664			−0.0216436
$156$		0			0
$157$	−1045.32			−0.531372			−0.265686	−	0.964060i	$-0.585599\pi$
$157$	−1045.32			−0.531372			−0.265686	+	0.964060i	$0.585599\pi$
$158$	1399.49	+	630.680i	0.704670	+	0.317558i
$159$		0			0
$160$	28.2306	−	46.4437i	0.0139489	−	0.0229481i
$161$			1297.40i			0.635089i
$162$		0			0
$163$		−	318.248i		−	0.152927i	−0.997072	−	0.0764636i	$-0.975637\pi$
$163$		−	318.248i		−	0.152927i	0.997072	−	0.0764636i	$-0.0243629\pi$
$164$	−1041.46	+	920.843i	−0.495878	+	0.438450i
$165$		0			0
$166$	919.823	−	2041.11i	0.430073	−	0.954343i
$167$	−767.396			−0.355586			−0.177793	−	0.984068i	$-0.556896\pi$
$167$	−767.396			−0.355586			−0.177793	+	0.984068i	$0.556896\pi$
$168$		0			0
$169$	3650.88			1.66176
$170$	−32.5310	+	72.1872i	−0.0146766	+	0.0325677i
$171$		0			0
$172$	−2135.51	+	1888.19i	−0.946693	+	0.837055i
$173$		−	933.370i		−	0.410190i	−0.978742	−	0.205095i	$-0.934250\pi$
$173$		−	933.370i		−	0.410190i	0.978742	−	0.205095i	$-0.0657503\pi$
$174$		0			0
$175$			874.369i			0.377692i
$176$	−76.1568	+	617.175i	−0.0326167	+	0.264325i
$177$		0			0
$178$	2087.23	+	940.606i	0.878901	+	0.396075i
$179$	1371.81			0.572816			0.286408	−	0.958108i	$-0.407539\pi$
$179$	1371.81			0.572816			0.286408	+	0.958108i	$0.407539\pi$
$180$		0			0
$181$	1678.90			0.689455			0.344728	−	0.938703i	$-0.387971\pi$
$181$	1678.90			0.689455			0.344728	+	0.938703i	$0.387971\pi$
$182$	1380.37	+	622.059i	0.562195	+	0.253352i
$183$		0			0
$184$	4005.75	−	1241.84i	1.60493	−	0.497551i
$185$			9.15829i			0.00363963i
$186$		0			0
$187$		−	905.928i		−	0.354268i
$188$	−1838.43	−	2079.23i	−0.713199	−	0.806614i
$189$		0			0
$190$	−28.5705	+	63.3986i	−0.0109091	+	0.0242075i
$191$	−960.981			−0.364053			−0.182026	−	0.983294i	$-0.558266\pi$
$191$	−960.981			−0.364053			−0.182026	+	0.983294i	$0.558266\pi$
$192$		0			0
$193$	4482.75			1.67189			0.835947	−	0.548810i	$-0.184919\pi$
$193$	4482.75			1.67189			0.835947	+	0.548810i	$0.184919\pi$
$194$	223.585	−	496.140i	0.0827445	−	0.183612i
$195$		0			0
$196$	259.659	+	293.669i	0.0946278	+	0.107022i
$197$		−	4174.06i		−	1.50959i	−0.655961	−	0.754795i	$-0.727736\pi$
$197$		−	4174.06i		−	1.50959i	0.655961	−	0.754795i	$-0.272264\pi$
$198$		0			0
$199$			4302.61i			1.53268i	0.642433	+	0.766342i	$0.277925\pi$
$199$			4302.61i			1.53268i	−0.642433	+	0.766342i	$0.722075\pi$
$200$	2699.63	−	836.922i	0.954465	−	0.295897i
$201$		0			0
$202$	101.882	+	45.9129i	0.0354870	+	0.0159922i
$203$	1114.35			0.385281
$204$		0			0
$205$	52.1744			0.0177757
$206$	3664.16	+	1651.25i	1.23929	+	0.558484i
$207$		0			0
$208$	599.375	−	4857.33i	0.199804	−	1.61921i
$209$		−	795.634i		−	0.263326i
$210$		0			0
$211$			1832.00i			0.597725i	0.954296	+	0.298862i	$0.0966072\pi$
$211$			1832.00i			0.597725i	−0.954296	+	0.298862i	$0.903393\pi$
$212$	927.754	−	820.309i	0.300558	−	0.265750i
$213$		0			0
$214$	−1690.87	+	3752.09i	−0.540119	+	1.19854i
$215$	106.984			0.0339360
$216$		0			0
$217$	−973.747			−0.304619
$218$	2213.72	−	4912.29i	0.687760	−	1.52616i
$219$		0			0
$220$	17.4844	−	15.4595i	0.00535816	−	0.00473763i
$221$			7129.90i			2.17018i
$222$		0			0
$223$			3117.21i			0.936072i	0.883709	+	0.468036i	$0.155038\pi$
$223$			3117.21i			0.936072i	−0.883709	+	0.468036i	$0.844962\pi$
$224$	658.171	−	1082.79i	0.196321	−	0.322979i
$225$		0			0
$226$	−3189.51	−	1437.35i	−0.938775	−	0.423057i
$227$	−5108.49			−1.49367			−0.746833	−	0.665011i	$-0.768427\pi$
$227$	−5108.49			−1.49367			−0.746833	+	0.665011i	$0.768427\pi$
$228$		0			0
$229$	4443.04			1.28211			0.641057	−	0.767493i	$-0.278496\pi$
$229$	4443.04			1.28211			0.641057	+	0.767493i	$0.278496\pi$
$230$	−143.500	−	64.6679i	−0.0411396	−	0.0185395i
$231$		0			0
$232$	−1066.63	−	3440.59i	−0.301843	−	0.973645i
$233$			241.778i			0.0679801i	0.999422	+	0.0339901i	$0.0108215\pi$
$233$			241.778i			0.0679801i	−0.999422	+	0.0339901i	$0.989179\pi$
$234$		0			0
$235$			104.164i			0.0289146i
$236$	−3108.48	−	3515.63i	−0.857392	−	0.969694i
$237$		0			0
$238$	−758.433	+	1682.98i	−0.206563	+	0.458368i
$239$	758.452			0.205273			0.102636	−	0.994719i	$-0.467272\pi$
$239$	758.452			0.205273			0.102636	+	0.994719i	$0.467272\pi$
$240$		0			0
$241$	−5755.96			−1.53848			−0.769241	−	0.638958i	$-0.779366\pi$
$241$	−5755.96			−1.53848			−0.769241	+	0.638958i	$0.779366\pi$
$242$	1437.01	−	3188.77i	0.381713	−	0.847032i
$243$		0			0
$244$	−889.030	−	1005.48i	−0.233255	−	0.263807i
$245$		−	14.7121i		−	0.00383642i
$246$		0			0
$247$			6261.85i			1.61309i
$248$	932.044	+	3006.47i	0.238649	+	0.769801i
$249$		0			0
$250$	−193.490	−	87.1961i	−0.0489496	−	0.0220591i
$251$	−1275.64			−0.320787			−0.160394	−	0.987053i	$-0.551276\pi$
$251$	−1275.64			−0.320787			−0.160394	+	0.987053i	$0.551276\pi$
$252$		0			0
$253$	1800.88			0.447512
$254$	6255.52	+	2819.04i	1.54530	+	0.696387i
$255$		0			0
$256$	−3973.13	−	995.698i	−0.970004	−	0.243090i
$257$		−	7412.37i		−	1.79911i	−0.436810	−	0.899554i	$-0.643892\pi$
$257$		−	7412.37i		−	1.79911i	0.436810	−	0.899554i	$-0.356108\pi$
$258$		0			0
$259$			213.518i			0.0512252i
$260$	−137.607	+	121.670i	−0.0328231	+	0.0290218i
$261$		0			0
$262$	2924.40	−	6489.31i	0.689580	−	1.53019i
$263$	5386.10			1.26282			0.631409	−	0.775450i	$-0.282477\pi$
$263$	5386.10			1.26282			0.631409	+	0.775450i	$0.282477\pi$
$264$		0			0
$265$	−46.4782			−0.0107741
$266$	−666.096	+	1478.08i	−0.153537	+	0.340703i
$267$		0			0
$268$	−2418.46	+	2138.38i	−0.551235	+	0.487396i
$269$		−	5903.70i		−	1.33812i	−0.743207	−	0.669062i	$-0.766696\pi$
$269$		−	5903.70i		−	1.33812i	0.743207	−	0.669062i	$-0.233304\pi$
$270$		0			0
$271$		−	1486.67i		−	0.333242i	−0.986021	−	0.166621i	$-0.946714\pi$
$271$		−	1486.67i		−	0.333242i	0.986021	−	0.166621i	$-0.0532857\pi$
$272$	5922.20	+	730.774i	1.32017	+	0.162903i
$273$		0			0
$274$	588.951	+	265.410i	0.129853	+	0.0585182i
$275$	1213.69			0.266138
$276$		0			0
$277$	−91.0097			−0.0197410			−0.00987048	−	0.999951i	$-0.503142\pi$
$277$	−91.0097			−0.0197410			−0.00987048	+	0.999951i	$0.503142\pi$
$278$	−3395.30	−	1530.08i	−0.732505	−	0.330102i
$279$		0			0
$280$	−45.4240	+	14.0820i	−0.00969501	+	0.00300558i
$281$			7462.63i			1.58428i	0.610339	+	0.792140i	$0.291033\pi$
$281$			7462.63i			1.58428i	−0.610339	+	0.792140i	$0.708967\pi$
$282$		0			0
$283$			696.270i			0.146251i	0.997323	+	0.0731254i	$0.0232973\pi$
$283$			696.270i			0.146251i	−0.997323	+	0.0731254i	$0.976703\pi$
$284$	−829.261	−	937.878i	−0.173266	−	0.195961i
$285$		0			0
$286$	863.462	−	1916.04i	0.178523	−	0.396147i
$287$	1216.40			0.250181
$288$		0			0
$289$	−3779.98			−0.769382
$290$	−55.5441	+	123.254i	−0.0112471	+	0.0249576i
$291$		0			0
$292$	2997.59	+	3390.21i	0.600755	+	0.679442i
$293$		−	752.697i		−	0.150079i	−0.997181	−	0.0750393i	$-0.976092\pi$
$293$		−	752.697i		−	0.150079i	0.997181	−	0.0750393i	$-0.0239082\pi$
$294$		0			0
$295$			176.124i			0.0347606i
$296$	659.240	−	204.373i	0.129451	−	0.0401316i
$297$		0			0
$298$	−3060.82	−	1379.35i	−0.594996	−	0.268134i
$299$	−14173.4			−2.74137
$300$		0			0
$301$	2494.24			0.477626
$302$	−8972.09	−	4043.26i	−1.70955	−	0.770408i
$303$		0			0
$304$	5201.19	+	641.805i	0.981278	+	0.121086i
$305$			50.3719i			0.00945668i
$306$		0			0
$307$		−	7832.90i		−	1.45618i	−0.685482	−	0.728090i	$-0.740408\pi$
$307$		−	7832.90i		−	1.45618i	0.685482	−	0.728090i	$-0.259592\pi$
$308$	407.633	−	360.424i	0.0754125	−	0.0666789i
$309$		0			0
$310$	48.5357	−	107.702i	0.00889240	−	0.0197325i
$311$	8094.20			1.47582			0.737910	−	0.674899i	$-0.235813\pi$
$311$	8094.20			1.47582			0.737910	+	0.674899i	$0.235813\pi$
$312$		0			0
$313$	1194.07			0.215632			0.107816	−	0.994171i	$-0.465614\pi$
$313$	1194.07			0.215632			0.107816	+	0.994171i	$0.465614\pi$
$314$	1214.74	−	2695.54i	0.218318	−	0.484452i
$315$		0			0
$316$	−3252.64	+	2875.95i	−0.579036	+	0.511977i
$317$			558.918i			0.0990283i	0.998773	+	0.0495141i	$0.0157673\pi$
$317$			558.918i			0.0990283i	−0.998773	+	0.0495141i	$0.984233\pi$
$318$		0			0
$319$		−	1546.80i		−	0.271486i
$320$	86.9572	+	126.769i	0.0151908	+	0.0221456i
$321$		0			0
$322$	−3345.57	−	1507.68i	−0.579011	−	0.260930i
$323$	−7634.63			−1.31518
$324$		0			0
$325$	−9552.03			−1.63031
$326$	820.660	+	369.829i	0.139424	+	0.0628311i
$327$		0			0
$328$	−1164.31	−	3755.67i	−0.196000	−	0.632232i
$329$			2428.50i			0.406954i
$330$		0			0
$331$			4269.51i			0.708983i	0.935059	+	0.354491i	$0.115346\pi$
$331$			4269.51i			0.708983i	−0.935059	+	0.354491i	$0.884654\pi$
$332$	4194.46	+	4743.85i	0.693376	+	0.784195i
$333$		0			0
$334$	891.773	−	1978.87i	0.146095	−	0.324188i
$335$	121.159			0.0197601
$336$		0			0
$337$	5238.96			0.846837			0.423419	−	0.905934i	$-0.360830\pi$
$337$	5238.96			0.846837			0.423419	+	0.905934i	$0.360830\pi$
$338$	−4242.60	+	9414.44i	−0.682742	+	1.51502i
$339$		0			0
$340$	−148.344	−	167.774i	−0.0236620	−	0.0267613i
$341$			1351.63i			0.214648i
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	−2387.42	−	7701.02i	−0.374189	−	1.20701i
$345$		0			0
$346$	2406.86	+	1084.65i	0.373970	+	0.168529i
$347$	765.526			0.118431			0.0592156	−	0.998245i	$-0.481140\pi$
$347$	765.526			0.118431			0.0592156	+	0.998245i	$0.481140\pi$
$348$		0			0
$349$	12201.9			1.87149			0.935747	−	0.352672i	$-0.114727\pi$
$349$	12201.9			1.87149			0.935747	+	0.352672i	$0.114727\pi$
$350$	−2254.72	−	1016.08i	−0.344342	−	0.155177i
$351$		0			0
$352$	−1502.99	−	913.588i	−0.227585	−	0.138336i
$353$			4748.81i			0.716017i	0.933718	+	0.358008i	$0.116544\pi$
$353$			4748.81i			0.716017i	−0.933718	+	0.358008i	$0.883456\pi$
$354$		0			0
$355$			46.9855i			0.00702459i
$356$	−4851.04	+	4289.23i	−0.722204	+	0.638564i
$357$		0			0
$358$	−1594.15	+	3537.46i	−0.235345	+	0.522236i
$359$	2985.96			0.438977			0.219489	−	0.975615i	$-0.429561\pi$
$359$	2985.96			0.438977			0.219489	+	0.975615i	$0.429561\pi$
$360$		0			0
$361$	153.862			0.0224321
$362$	−1951.01	+	4329.33i	−0.283267	+	0.628577i
$363$		0			0
$364$	−3208.18	+	2836.64i	−0.461963	+	0.408462i
$365$		−	169.841i		−	0.0243559i
$366$		0			0
$367$			8144.25i			1.15838i	0.815192	+	0.579191i	$0.196632\pi$
$367$			8144.25i			1.15838i	−0.815192	+	0.579191i	$0.803368\pi$
$368$	−1452.70	+	11772.6i	−0.205780	+	1.66764i
$369$		0			0
$370$	−23.6163	−	10.6426i	−0.00331825	−	0.00149536i
$371$	−1083.60			−0.151638
$372$		0			0
$373$	−12379.6			−1.71847			−0.859236	−	0.511579i	$-0.829061\pi$
$373$	−12379.6			−1.71847			−0.859236	+	0.511579i	$0.829061\pi$
$374$	2336.10	+	1052.76i	0.322986	+	0.145553i
$375$		0			0
$376$	7498.06	−	2324.50i	1.02841	−	0.318821i
$377$			12173.7i			1.66307i
$378$		0			0
$379$		−	12503.2i		−	1.69458i	−0.531129	−	0.847291i	$-0.678232\pi$
$379$		−	12503.2i		−	1.69458i	0.531129	−	0.847291i	$-0.321768\pi$
$380$	−130.283	−	147.348i	−0.0175879	−	0.0198916i
$381$		0			0
$382$	1116.73	−	2478.06i	0.149573	−	0.331907i
$383$	246.082			0.0328308			0.0164154	−	0.999865i	$-0.494775\pi$
$383$	246.082			0.0328308			0.0164154	+	0.999865i	$0.494775\pi$
$384$		0			0
$385$	−20.4214			−0.00270331
$386$	−5209.30	+	11559.6i	−0.686908	+	1.52427i
$387$		0			0
$388$	1019.56	+	1153.10i	0.133403	+	0.150876i
$389$			10288.3i			1.34097i	0.741923	+	0.670485i	$0.233914\pi$
$389$			10288.3i			1.34097i	−0.741923	+	0.670485i	$0.766086\pi$
$390$		0			0
$391$		−	17280.6i		−	2.23509i
$392$	−1059.02	+	328.310i	−0.136451	+	0.0423015i
$393$		0			0
$394$	10763.5	+	4850.57i	1.37629	+	0.620224i
$395$	162.949			0.0207567
$396$		0			0
$397$	−11462.6			−1.44909			−0.724547	−	0.689225i	$-0.757951\pi$
$397$	−11462.6			−1.44909			−0.724547	+	0.689225i	$0.757951\pi$
$398$	−11095.1	−	4999.97i	−1.39735	−	0.629713i
$399$		0			0
$400$	−979.030	+	7934.05i	−0.122379	+	0.991757i
$401$		−	9125.36i		−	1.13641i	−0.822888	−	0.568203i	$-0.807639\pi$
$401$		−	9125.36i		−	1.13641i	0.822888	−	0.568203i	$-0.192361\pi$
$402$		0			0
$403$		−	10637.7i		−	1.31489i
$404$	−236.789	+	209.366i	−0.0291601	+	0.0257831i
$405$		0			0
$406$	−1294.96	+	2873.55i	−0.158295	+	0.351261i
$407$	296.377			0.0360955
$408$		0			0
$409$	−5019.52			−0.606844			−0.303422	−	0.952856i	$-0.598129\pi$
$409$	−5019.52			−0.606844			−0.303422	+	0.952856i	$0.598129\pi$
$410$	−60.6307	+	134.541i	−0.00730326	+	0.0162061i
$411$		0			0
$412$	−8516.06	+	7529.81i	−1.01834	+	0.900405i
$413$			4106.19i			0.489231i
$414$		0			0
$415$		−	237.656i		−	0.0281110i
$416$	11829.0	+	7190.18i	1.39414	+	0.847422i
$417$		0			0
$418$	2051.68	+	924.588i	0.240074	+	0.108189i
$419$	10727.8			1.25081			0.625403	−	0.780302i	$-0.284935\pi$
$419$	10727.8			1.25081			0.625403	+	0.780302i	$0.284935\pi$
$420$		0			0
$421$	8669.15			1.00358			0.501792	−	0.864989i	$-0.332674\pi$
$421$	8669.15			1.00358			0.501792	+	0.864989i	$0.332674\pi$
$422$	−4724.13	−	2128.92i	−0.544946	−	0.245579i
$423$		0			0
$424$	1037.19	+	3345.64i	0.118798	+	0.383204i
$425$		−	11646.1i		−	1.32922i
$426$		0			0
$427$			1174.38i			0.133096i
$428$	−7710.50	−	8720.42i	−0.870797	−	0.984854i
$429$		0			0
$430$	−124.324	+	275.877i	−0.0139428	+	0.0309395i
$431$	4819.01			0.538569			0.269285	−	0.963061i	$-0.413213\pi$
$431$	4819.01			0.538569			0.269285	+	0.963061i	$0.413213\pi$
$432$		0			0
$433$	−1274.56			−0.141458			−0.0707290	−	0.997496i	$-0.522533\pi$
$433$	−1274.56			−0.141458			−0.0707290	+	0.997496i	$0.522533\pi$
$434$	1131.57	−	2510.98i	0.125154	−	0.277721i
$435$		0			0
$436$	10094.7	+	11416.9i	1.10883	+	1.25406i
$437$		−	15176.8i		−	1.66134i
$438$		0			0
$439$			6189.10i			0.672869i	0.941707	+	0.336434i	$0.109221\pi$
$439$			6189.10i			0.672869i	−0.941707	+	0.336434i	$0.890779\pi$
$440$	19.5468	+	63.0517i	0.00211786	+	0.00683152i
$441$		0			0
$442$	−18385.7	−	8285.49i	−1.97855	−	0.891630i
$443$	−10421.5			−1.11770			−0.558848	−	0.829270i	$-0.688757\pi$
$443$	−10421.5			−1.11770			−0.558848	+	0.829270i	$0.688757\pi$
$444$		0			0
$445$	243.025			0.0258888
$446$	−8038.29	−	3622.44i	−0.853417	−	0.384591i
$447$		0			0
$448$	2027.33	+	2955.50i	0.213800	+	0.311684i
$449$		−	4319.61i		−	0.454020i	−0.973892	−	0.227010i	$-0.927105\pi$
$449$		−	4319.61i		−	0.454020i	0.973892	−	0.227010i	$-0.0728949\pi$
$450$		0			0
$451$		−	1688.45i		−	0.176288i
$452$	7412.91	−	6554.41i	0.771403	−	0.682065i
$453$		0			0
$454$	5936.45	−	13173.1i	0.613682	−	1.36178i
$455$	160.722			0.0165599
$456$		0			0
$457$	−6228.62			−0.637554			−0.318777	−	0.947830i	$-0.603272\pi$
$457$	−6228.62			−0.637554			−0.318777	+	0.947830i	$0.603272\pi$
$458$	−5163.15	+	11457.2i	−0.526764	+	1.16890i
$459$		0			0
$460$	333.516	−	294.891i	0.0338049	−	0.0298899i
$461$		−	3665.71i		−	0.370345i	−0.982706	−	0.185172i	$-0.940716\pi$
$461$		−	3665.71i		−	0.370345i	0.982706	−	0.185172i	$-0.0592844\pi$
$462$		0			0
$463$			1640.57i			0.164673i	0.996605	+	0.0823367i	$0.0262383\pi$
$463$			1640.57i			0.164673i	−0.996605	+	0.0823367i	$0.973762\pi$
$464$	10111.7	+	1247.74i	1.01169	+	0.124838i
$465$		0			0
$466$	−623.466	−	280.964i	−0.0619775	−	0.0279301i
$467$	15141.3			1.50034			0.750168	−	0.661247i	$-0.229972\pi$
$467$	15141.3			1.50034			0.750168	+	0.661247i	$0.229972\pi$
$468$		0			0
$469$	2824.72			0.278110
$470$	−268.607	−	121.047i	−0.0263615	−	0.0118798i
$471$		0			0
$472$	12678.0	−	3930.33i	1.23634	−	0.383280i
$473$		−	3462.18i		−	0.336556i
$474$		0			0
$475$		−	10228.2i		−	0.988007i
$476$	−3458.51	−	3911.51i	−0.333026	−	0.376646i
$477$		0			0
$478$	−881.379	+	1955.80i	−0.0843375	+	0.187147i
$479$	−430.774			−0.0410910			−0.0205455	−	0.999789i	$-0.506540\pi$
$479$	−430.774			−0.0410910			−0.0205455	+	0.999789i	$0.506540\pi$
$480$		0			0
$481$	−2332.57			−0.221114
$482$	6688.87	−	14842.8i	0.632095	−	1.40263i
$483$		0			0
$484$	6552.88	+	7411.18i	0.615410	+	0.696016i
$485$		−	57.7678i		−	0.00540845i
$486$		0			0
$487$		−	4431.53i		−	0.412344i	−0.978516	−	0.206172i	$-0.933899\pi$
$487$		−	4431.53i		−	0.412344i	0.978516	−	0.206172i	$-0.0661007\pi$
$488$	3625.92	−	1124.08i	0.336348	−	0.104272i
$489$		0			0
$490$	37.9378	+	17.0966i	0.00349766	+	0.00157622i
$491$	3768.32			0.346358			0.173179	−	0.984890i	$-0.444596\pi$
$491$	3768.32			0.346358			0.173179	+	0.984890i	$0.444596\pi$
$492$		0			0
$493$	−14842.5			−1.35593
$494$	−16147.3	−	7276.75i	−1.47065	−	0.662746i
$495$		0			0
$496$	−8835.81	−	1090.30i	−0.799878	−	0.0987017i
$497$			1095.42i			0.0988663i
$498$		0			0
$499$			10794.4i			0.968384i	0.874962	+	0.484192i	$0.160886\pi$
$499$			10794.4i			0.968384i	−0.874962	+	0.484192i	$0.839114\pi$
$500$	449.701	−	397.621i	0.0402225	−	0.0355643i
$501$		0			0
$502$	1482.39	−	3289.46i	0.131797	−	0.292462i
$503$	18367.1			1.62812			0.814062	−	0.580777i	$-0.197251\pi$
$503$	18367.1			1.62812			0.814062	+	0.580777i	$0.197251\pi$
$504$		0			0
$505$	11.8626			0.00104530
$506$	−2092.76	+	4643.89i	−0.183863	+	0.407996i
$507$		0			0
$508$	−14538.8	+	12855.0i	−1.26979	+	1.12274i
$509$		−	4154.17i		−	0.361749i	−0.983506	−	0.180875i	$-0.942107\pi$
$509$		−	4154.17i		−	0.361749i	0.983506	−	0.180875i	$-0.0578928\pi$
$510$		0			0
$511$		−	3959.71i		−	0.342793i
$512$	7184.67	−	9088.36i	0.620157	−	0.784477i
$513$		0			0
$514$	19114.1	+	8613.74i	1.64025	+	0.739174i
$515$	426.634			0.0365044
$516$		0			0
$517$	3370.93			0.286757
$518$	−550.593	−	248.124i	−0.0467020	−	0.0210462i
$519$		0			0
$520$	−153.839	−	496.234i	−0.0129736	−	0.0418486i
$521$		−	21474.8i		−	1.80581i	−0.429839	−	0.902905i	$-0.641430\pi$
$521$		−	21474.8i		−	1.80581i	0.429839	−	0.902905i	$-0.358570\pi$
$522$		0			0
$523$		−	16488.9i		−	1.37860i	−0.724474	−	0.689302i	$-0.757917\pi$
$523$		−	16488.9i		−	1.37860i	0.724474	−	0.689302i	$-0.242083\pi$
$524$	13335.5	+	15082.2i	1.11176	+	1.25738i
$525$		0			0
$526$	−6259.06	+	13889.0i	−0.518836	+	1.15131i
$527$	12969.8			1.07205
$528$		0			0
$529$	22184.9			1.82337
$530$	54.0113	−	119.852i	0.00442660	−	0.00982275i
$531$		0			0
$532$	−3037.45	−	3435.29i	−0.247538	−	0.279960i
$533$			13288.6i			1.07991i
$534$		0			0
$535$			436.872i			0.0353040i
$536$	−2703.75	−	8721.39i	−0.217881	−	0.702811i
$537$		0			0
$538$	15223.8	+	6860.56i	1.21997	+	0.549776i
$539$	−476.108			−0.0380472
$540$		0			0
$541$	−3208.96			−0.255017			−0.127508	−	0.991837i	$-0.540698\pi$
$541$	−3208.96			−0.255017			−0.127508	+	0.991837i	$0.540698\pi$
$542$	3833.64	+	1727.62i	0.303817	+	0.136915i
$543$		0			0
$544$	−8766.48	+	14422.2i	−0.690918	+	1.13667i
$545$		−	571.960i		−	0.0449543i
$546$		0			0
$547$		−	6448.31i		−	0.504040i	−0.967722	−	0.252020i	$-0.918905\pi$
$547$		−	6448.31i		−	0.504040i	0.967722	−	0.252020i	$-0.0810949\pi$
$548$	−1368.81	+	1210.29i	−0.106702	+	0.0943448i
$549$		0			0
$550$	−1410.40	+	3129.70i	−0.109344	+	0.242638i
$551$	−13035.5			−1.00786
$552$		0			0
$553$	3799.03			0.292136
$554$	105.760	−	234.685i	0.00811069	−	0.0179978i
$555$		0			0
$556$	7891.19	−	6977.30i	0.601908	−	0.532200i
$557$			1897.44i			0.144340i	0.997392	+	0.0721698i	$0.0229923\pi$
$557$			1897.44i			0.144340i	−0.997392	+	0.0721698i	$0.977008\pi$
$558$		0			0
$559$			27248.3i			2.06168i
$560$	16.4731	−	133.498i	0.00124307	−	0.0100738i
$561$		0			0
$562$	−19243.7	−	8672.14i	−1.44439	−	0.650911i
$563$	−9998.80			−0.748488			−0.374244	−	0.927330i	$-0.622098\pi$
$563$	−9998.80			−0.748488			−0.374244	+	0.927330i	$0.622098\pi$
$564$		0			0
$565$	−371.369			−0.0276524
$566$	−1795.46	−	809.119i	−0.133337	−	0.0600880i
$567$		0			0
$568$	3382.15	−	1048.51i	0.249845	−	0.0774552i
$569$		−	4882.81i		−	0.359750i	−0.983689	−	0.179875i	$-0.942431\pi$
$569$		−	4882.81i		−	0.359750i	0.983689	−	0.179875i	$-0.0575694\pi$
$570$		0			0
$571$		−	4778.99i		−	0.350253i	−0.984546	−	0.175126i	$-0.943967\pi$
$571$		−	4778.99i		−	0.350253i	0.984546	−	0.175126i	$-0.0560334\pi$
$572$	3937.45	+	4453.18i	0.287820	+	0.325519i
$573$		0			0
$574$	−1413.55	+	3136.71i	−0.102788	+	0.228090i
$575$	23151.1			1.67908
$576$		0			0
$577$	−24393.3			−1.75998			−0.879990	−	0.474993i	$-0.842451\pi$
$577$	−24393.3			−1.75998			−0.879990	+	0.474993i	$0.842451\pi$
$578$	4392.62	−	9747.34i	0.316105	−	0.701446i
$579$		0			0
$580$	−253.285	−	286.460i	−0.0181329	−	0.0205080i
$581$		−	5540.74i		−	0.395643i
$582$		0			0
$583$			1504.11i			0.106851i
$584$	−12225.7	+	3790.12i	−0.866271	+	0.268555i
$585$		0			0
$586$	1940.96	+	874.691i	0.136827	+	0.0616607i
$587$	−24922.9			−1.75243			−0.876217	−	0.481917i	$-0.839941\pi$
$587$	−24922.9			−1.75243			−0.876217	+	0.481917i	$0.839941\pi$
$588$		0			0
$589$	11390.7			0.796854
$590$	−454.168	−	204.670i	−0.0316912	−	0.0142816i
$591$		0			0
$592$	−239.075	+	1937.47i	−0.0165979	+	0.134509i
$593$			17621.1i			1.22025i	0.792304	+	0.610127i	$0.208882\pi$
$593$			17621.1i			1.22025i	−0.792304	+	0.610127i	$0.791118\pi$
$594$		0			0
$595$			195.957i			0.0135016i
$596$	7113.82	−	6289.96i	0.488915	−	0.432293i
$597$		0			0
$598$	16470.6	−	36548.7i	1.12631	−	2.49931i
$599$	26506.9			1.80809			0.904044	−	0.427440i	$-0.140585\pi$
$599$	26506.9			1.80809			0.904044	+	0.427440i	$0.140585\pi$
$600$		0			0
$601$	4960.07			0.336648			0.168324	−	0.985732i	$-0.446165\pi$
$601$	4960.07			0.336648			0.168324	+	0.985732i	$0.446165\pi$
$602$	−2898.50	+	6431.84i	−0.196236	+	0.435452i
$603$		0			0
$604$	20852.5	−	18437.5i	1.40476	−	1.24207i
$605$		−	371.282i		−	0.0249500i
$606$		0			0
$607$			22066.5i			1.47554i	0.675052	+	0.737770i	$0.264121\pi$
$607$			22066.5i			1.47554i	−0.675052	+	0.737770i	$0.735879\pi$
$608$	−7699.18	+	12666.4i	−0.513558	+	0.844882i
$609$		0			0
$610$	−129.893	−	58.5360i	−0.00862166	−	0.00388534i
$611$	−26530.2			−1.75662
$612$		0			0
$613$	26585.0			1.75165			0.875823	−	0.482632i	$-0.160319\pi$
$613$	26585.0			1.75165			0.875823	+	0.482632i	$0.160319\pi$
$614$	20198.5	+	9102.43i	1.32760	+	0.598280i
$615$		0			0
$616$	455.718	+	1469.99i	0.0298075	+	0.0961490i
$617$			10612.8i			0.692472i	0.938148	+	0.346236i	$0.112540\pi$
$617$			10612.8i			0.692472i	−0.938148	+	0.346236i	$0.887460\pi$
$618$		0			0
$619$			16881.1i			1.09614i	0.836433	+	0.548068i	$0.184637\pi$
$619$			16881.1i			1.09614i	−0.836433	+	0.548068i	$0.815363\pi$
$620$	221.327	+	250.316i	0.0143366	+	0.0162144i
$621$		0			0
$622$	−9406.08	+	20872.3i	−0.606350	+	1.34551i
$623$	5665.93			0.364367
$624$		0			0
$625$	15591.2			0.997837
$626$	−1387.60	+	3079.12i	−0.0885936	+	0.196591i
$627$		0			0
$628$	5539.30	+	6264.84i	0.351978	+	0.398080i
$629$		−	2843.94i		−	0.180278i
$630$		0			0
$631$			20426.2i			1.28868i	0.764741	+	0.644338i	$0.222867\pi$
$631$			20426.2i			1.28868i	−0.764741	+	0.644338i	$0.777133\pi$
$632$	−3636.32	−	11729.6i	−0.228869	−	0.738256i
$633$		0			0
$634$	−1441.27	−	649.505i	−0.0902841	−	0.0406864i
$635$	728.358			0.0455182
$636$		0			0
$637$	3747.10			0.233070
$638$	3988.69	+	1797.50i	0.247514	+	0.111542i
$639$		0			0
$640$	−427.946	+	76.9197i	−0.0264314	+	0.00475081i
$641$			21909.2i			1.35002i	0.737809	+	0.675010i	$0.235861\pi$
$641$			21909.2i			1.35002i	−0.737809	+	0.675010i	$0.764139\pi$
$642$		0			0
$643$		−	9377.07i		−	0.575110i	−0.957764	−	0.287555i	$-0.907158\pi$
$643$		−	9377.07i		−	0.575110i	0.957764	−	0.287555i	$-0.0928424\pi$
$644$	7775.63	−	6875.12i	0.475780	−	0.420680i
$645$		0			0
$646$	8872.03	−	19687.3i	0.540349	−	1.19905i
$647$	−23771.8			−1.44446			−0.722231	−	0.691651i	$-0.756883\pi$
$647$	−23771.8			−1.44446			−0.722231	+	0.691651i	$0.756883\pi$
$648$		0			0
$649$	5699.68			0.344733
$650$	11100.2	−	24631.6i	0.669824	−	1.48636i
$651$		0			0
$652$	−1907.34	+	1686.45i	−0.114566	+	0.101298i
$653$		−	19631.7i		−	1.17649i	−0.808682	−	0.588246i	$-0.799819\pi$
$653$		−	19631.7i		−	1.17649i	0.808682	−	0.588246i	$-0.200181\pi$
$654$		0			0
$655$		−	755.580i		−	0.0450732i
$656$	11037.7	+	1362.00i	0.656934	+	0.0810629i
$657$		0			0
$658$	−6262.33	−	2822.11i	−0.371020	−	0.167199i
$659$	−10907.1			−0.644732			−0.322366	−	0.946615i	$-0.604478\pi$
$659$	−10907.1			−0.644732			−0.322366	+	0.946615i	$0.604478\pi$
$660$		0			0
$661$	−9092.18			−0.535015			−0.267507	−	0.963556i	$-0.586200\pi$
$661$	−9092.18			−0.535015			−0.267507	+	0.963556i	$0.586200\pi$
$662$	−11009.7	−	4961.49i	−0.646380	−	0.291290i
$663$		0			0
$664$	−17107.2	+	5303.44i	−0.999829	+	0.309960i
$665$			172.100i			0.0100357i
$666$		0			0
$667$		−	29505.3i		−	1.71282i
$668$	4066.55	+	4599.19i	0.235538	+	0.266389i
$669$		0			0
$670$	−140.796	+	312.430i	−0.00811855	+	0.0180153i
$671$	1630.12			0.0937855
$672$		0			0
$673$	1978.31			0.113311			0.0566554	−	0.998394i	$-0.481956\pi$
$673$	1978.31			0.113311			0.0566554	+	0.998394i	$0.481956\pi$
$674$	−6088.07	+	13509.6i	−0.347928	+	0.772062i
$675$		0			0
$676$	−19346.6	−	21880.6i	−1.10074	−	1.24491i
$677$			8522.24i			0.483805i	0.970301	+	0.241903i	$0.0777715\pi$
$677$			8522.24i			0.483805i	−0.970301	+	0.241903i	$0.922229\pi$
$678$		0			0
$679$		−	1346.81i		−	0.0761203i
$680$	605.022	−	187.565i	0.0341199	−	0.0105776i
$681$		0			0
$682$	−3485.42	−	1570.70i	−0.195694	−	0.0881893i
$683$	−35190.8			−1.97150			−0.985752	−	0.168208i	$-0.946202\pi$
$683$	−35190.8			−1.97150			−0.985752	+	0.168208i	$0.946202\pi$
$684$		0			0
$685$	68.5742			0.00382494
$686$	884.486	+	398.592i	0.0492272	+	0.0221841i
$687$		0			0
$688$	22632.8	+	2792.79i	1.25417	+	0.154759i
$689$		−	11837.8i		−	0.654548i
$690$		0			0
$691$			16471.4i			0.906802i	0.891307	+	0.453401i	$0.149790\pi$
$691$			16471.4i			0.906802i	−0.891307	+	0.453401i	$0.850210\pi$
$692$	−5593.91	+	4946.07i	−0.307296	+	0.271707i
$693$		0			0
$694$	−889.600	+	1974.05i	−0.0486582	+	0.107974i
$695$	−395.330			−0.0215766
$696$		0			0
$697$	−16201.8			−0.880469
$698$	−14179.5	+	31464.7i	−0.768915	+	1.70624i
$699$		0			0
$700$	5240.30	−	4633.42i	0.282950	−	0.250181i
$701$			25256.3i			1.36080i	0.732843	+	0.680398i	$0.238193\pi$
$701$			25256.3i			1.36080i	−0.732843	+	0.680398i	$0.761807\pi$
$702$		0			0
$703$		−	2497.69i		−	0.134000i
$704$	4102.44	−	2814.08i	0.219626	−	0.150653i
$705$		0			0
$706$	−12245.7	−	5518.49i	−0.652792	−	0.294180i
$707$	276.565			0.0147119
$708$		0			0
$709$	−19712.2			−1.04416			−0.522079	−	0.852897i	$-0.674843\pi$
$709$	−19712.2			−1.04416			−0.522079	+	0.852897i	$0.674843\pi$
$710$	−121.160	−	54.6007i	−0.00640432	−	0.00288609i
$711$		0			0
$712$	−5423.27	−	17493.7i	−0.285457	−	0.920791i
$713$			25782.4i			1.35422i
$714$		0			0
$715$		−	223.094i		−	0.0116689i
$716$	−7269.44	−	8221.60i	−0.379430	−	0.429128i
$717$		0			0
$718$	−3469.91	+	7699.83i	−0.180357	+	0.400216i
$719$	31049.2			1.61049			0.805244	−	0.592944i	$-0.202034\pi$
$719$	31049.2			1.61049			0.805244	+	0.592944i	$0.202034\pi$
$720$		0			0
$721$	9946.61			0.513774
$722$	−178.799	+	396.760i	−0.00921638	+	0.0204514i
$723$		0			0
$724$	−8896.74	−	10062.0i	−0.456691	−	0.516509i
$725$		−	19884.8i		−	1.01862i
$726$		0			0
$727$			21491.9i			1.09641i	0.836343	+	0.548207i	$0.184689\pi$
$727$			21491.9i			1.09641i	−0.836343	+	0.548207i	$0.815311\pi$
$728$	−3586.62	−	11569.3i	−0.182595	−	0.588991i
$729$		0			0
$730$	437.966	+	197.369i	0.0222053	+	0.0100068i
$731$	−33221.9			−1.68092
$732$		0			0
$733$	−28172.7			−1.41962			−0.709811	−	0.704392i	$-0.751220\pi$
$733$	−28172.7			−1.41962			−0.709811	+	0.704392i	$0.751220\pi$
$734$	−21001.4	−	9464.24i	−1.05610	−	0.475928i
$735$		0			0
$736$	−28669.7	−	17426.7i	−1.43584	−	0.872770i
$737$		−	3920.91i		−	0.195968i
$738$		0			0
$739$			15944.0i			0.793651i	0.917894	+	0.396825i	$0.129888\pi$
$739$			15944.0i			0.793651i	−0.917894	+	0.396825i	$0.870112\pi$
$740$	54.8878	−	48.5312i	0.00272664	−	0.00241087i
$741$		0			0
$742$	1259.23	−	2794.26i	0.0623014	−	0.138248i
$743$	19257.0			0.950837			0.475419	−	0.879760i	$-0.342297\pi$
$743$	19257.0			0.950837			0.475419	+	0.879760i	$0.342297\pi$
$744$		0			0
$745$	−356.385			−0.0175261
$746$	14386.0	−	31922.9i	0.706045	−	1.56673i
$747$		0			0
$748$	−5429.45	+	4800.65i	−0.265401	+	0.234665i
$749$			10185.3i			0.496880i
$750$		0			0
$751$			3970.69i			0.192933i	0.995336	+	0.0964663i	$0.0307540\pi$
$751$			3970.69i			0.192933i	−0.995336	+	0.0964663i	$0.969246\pi$
$752$	−2719.19	+	22036.3i	−0.131860	+	1.06859i
$753$		0			0
$754$	−31392.1	−	14146.8i	−1.51622	−	0.683284i
$755$	−1044.66			−0.0503564
$756$		0			0
$757$	20546.9			0.986511			0.493255	−	0.869885i	$-0.335807\pi$
$757$	20546.9			0.986511			0.493255	+	0.869885i	$0.335807\pi$
$758$	32241.7	+	14529.7i	1.54495	+	0.696229i
$759$		0			0
$760$	531.363	−	164.729i	0.0253612	−	0.00786232i
$761$			12620.6i			0.601176i	0.953754	+	0.300588i	$0.0971829\pi$
$761$			12620.6i			0.601176i	−0.953754	+	0.300588i	$0.902817\pi$
$762$		0			0
$763$		−	13334.8i		−	0.632701i
$764$	5092.39	+	5759.39i	0.241147	+	0.272732i
$765$		0			0
$766$	−285.966	+	634.567i	−0.0134888	+	0.0299319i
$767$	−44858.0			−2.11177
$768$		0			0
$769$	10838.7			0.508261			0.254130	−	0.967170i	$-0.418211\pi$
$769$	10838.7			0.508261			0.254130	+	0.967170i	$0.418211\pi$
$770$	23.7313	−	52.6603i	0.00111067	−	0.00246460i
$771$		0			0
$772$	−23754.8	−	26866.2i	−1.10745	−	1.25251i
$773$			6610.44i			0.307582i	0.988103	+	0.153791i	$0.0491482\pi$
$773$			6610.44i			0.307582i	−0.988103	+	0.153791i	$0.950852\pi$
$774$		0			0
$775$			17375.8i			0.805364i
$776$	−4158.30	+	1289.13i	−0.192364	+	0.0596352i
$777$		0			0
$778$	−26530.2	−	11955.8i	−1.22256	−	0.550946i
$779$	−14229.3			−0.654450
$780$		0			0
$781$	1520.53			0.0696655
$782$	44561.2	+	20081.4i	2.03773	+	0.918300i
$783$		0			0
$784$	384.057	−	3112.39i	0.0174953	−	0.141782i
$785$		−	313.854i		−	0.0142700i
$786$		0			0
$787$		−	2544.84i		−	0.115265i	−0.998338	−	0.0576326i	$-0.981645\pi$
$787$		−	2544.84i		−	0.115265i	0.998338	−	0.0576326i	$-0.0183552\pi$
$788$	−25016.1	+	22119.0i	−1.13092	+	0.999944i
$789$		0			0
$790$	−189.360	+	420.194i	−0.00852800	+	0.0189238i
$791$	−8658.15			−0.389189
$792$		0			0
$793$	−12829.5			−0.574512
$794$	13320.4	−	29558.3i	0.595369	−	1.32114i
$795$		0			0
$796$	25786.6	−	22800.2i	1.14822	−	1.01524i
$797$			24488.2i			1.08835i	0.838971	+	0.544176i	$0.183157\pi$
$797$			24488.2i			1.08835i	−0.838971	+	0.544176i	$0.816843\pi$
$798$		0			0
$799$		−	32346.3i		−	1.43220i
$800$	−19321.7	−	11744.6i	−0.853905	−	0.519042i
$801$		0			0
$802$	23531.4	+	10604.4i	1.03606	+	0.466899i
$803$	−5496.35			−0.241547
$804$		0			0
$805$	−389.540			−0.0170553
$806$	27431.2	+	12361.8i	1.19879	+	0.540231i
$807$		0			0
$808$	−264.721	−	853.902i	−0.0115258	−	0.0371784i
$809$		−	13881.7i		−	0.603280i	−0.953422	−	0.301640i	$-0.902466\pi$
$809$		−	13881.7i		−	0.603280i	0.953422	−	0.301640i	$-0.0975341\pi$
$810$		0			0
$811$			26250.2i			1.13658i	0.822828	+	0.568291i	$0.192395\pi$
$811$			26250.2i			1.13658i	−0.822828	+	0.568291i	$0.807605\pi$
$812$	−5905.12	−	6678.58i	−0.255208	−	0.288636i
$813$		0			0
$814$	−344.413	+	764.262i	−0.0148301	+	0.0329083i
$815$	95.5532			0.00410685
$816$		0			0
$817$	−29177.2			−1.24943
$818$	5833.07	−	12943.7i	0.249326	−	0.553260i
$819$		0			0
$820$	−276.480	−	312.694i	−0.0117745	−	0.0133168i
$821$			17579.8i			0.747307i	0.927568	+	0.373653i	$0.121895\pi$
$821$			17579.8i			0.747307i	−0.927568	+	0.373653i	$0.878105\pi$
$822$		0			0
$823$			1245.89i			0.0527691i	0.999652	+	0.0263846i	$0.00839944\pi$
$823$			1245.89i			0.0527691i	−0.999652	+	0.0263846i	$0.991601\pi$
$824$	−9520.63	−	30710.4i	−0.402508	−	1.29836i
$825$		0			0
$826$	−10588.5	−	4771.71i	−0.446032	−	0.201004i
$827$	30172.3			1.26867			0.634337	−	0.773057i	$-0.281273\pi$
$827$	30172.3			1.26867			0.634337	+	0.773057i	$0.281273\pi$
$828$		0			0
$829$	21765.8			0.911891			0.455945	−	0.890008i	$-0.349301\pi$
$829$	21765.8			0.911891			0.455945	+	0.890008i	$0.349301\pi$
$830$	612.838	+	276.174i	0.0256288	+	0.0115496i
$831$		0			0
$832$	−32287.3	+	22147.6i	−1.34539	+	0.922871i
$833$			4568.57i			0.190026i
$834$		0			0
$835$		−	230.408i		−	0.00954923i
$836$	−4768.43	+	4216.19i	−0.197272	+	0.174426i
$837$		0			0
$838$	−12466.5	+	27663.6i	−0.513901	+	1.14036i
$839$	−5120.96			−0.210721			−0.105361	−	0.994434i	$-0.533600\pi$
$839$	−5120.96			−0.210721			−0.105361	+	0.994434i	$0.533600\pi$
$840$		0			0
$841$	−953.433			−0.0390927
$842$	−10074.2	+	22354.9i	−0.412328	+	0.914967i
$843$		0			0
$844$	10979.6	−	9708.04i	0.447789	−	0.395930i
$845$			1096.17i			0.0446263i
$846$		0			0
$847$		−	8656.13i		−	0.351155i
$848$	−9832.62	−	1213.31i	−0.398177	−	0.0491333i
$849$		0			0
$850$	30031.6	+	13533.7i	1.21185	+	0.546119i
$851$	5653.42			0.227728
$852$		0			0
$853$	−29483.3			−1.18346			−0.591729	−	0.806137i	$-0.701555\pi$
$853$	−29483.3			−1.18346			−0.591729	+	0.806137i	$0.701555\pi$
$854$	−3028.34	−	1364.72i	−0.121344	−	0.0546834i
$855$		0			0
$856$	31447.3	−	9749.09i	1.25566	−	0.389272i
$857$		−	47834.8i		−	1.90666i	−0.301936	−	0.953328i	$-0.597633\pi$
$857$		−	47834.8i		−	1.90666i	0.301936	−	0.953328i	$-0.402367\pi$
$858$		0			0
$859$		−	6519.42i		−	0.258952i	−0.991583	−	0.129476i	$-0.958671\pi$
$859$		−	6519.42i		−	0.258952i	0.991583	−	0.129476i	$-0.0413295\pi$
$860$	−566.925	−	641.181i	−0.0224790	−	0.0254233i
$861$		0			0
$862$	−5600.05	+	12426.7i	−0.221274	+	0.491014i
$863$	3991.43			0.157439			0.0787195	−	0.996897i	$-0.474917\pi$
$863$	3991.43			0.157439			0.0787195	+	0.996897i	$0.474917\pi$
$864$		0			0
$865$	280.242			0.0110156
$866$	1481.13	−	3286.67i	0.0581189	−	0.128967i
$867$		0			0
$868$	5160.04	+	5835.90i	0.201778	+	0.228207i
$869$		−	5273.31i		−	0.205852i
$870$		0			0
$871$			30858.6i			1.20046i
$872$	−41171.4	+	12763.7i	−1.59890	+	0.495679i
$873$		0			0
$874$	39136.0	+	17636.6i	1.51464	+	0.682570i
$875$	−525.243			−0.0202931
$876$		0			0
$877$	40731.8			1.56832			0.784158	−	0.620561i	$-0.213095\pi$
$877$	40731.8			1.56832			0.784158	+	0.620561i	$0.213095\pi$
$878$	−15959.7	−	7192.20i	−0.613455	−	0.276452i
$879$		0			0
$880$	−185.305	−	22.8659i	−0.00709844	−	0.000875918i
$881$		−	36733.9i		−	1.40476i	−0.711800	−	0.702382i	$-0.752120\pi$
$881$		−	36733.9i		−	1.40476i	0.711800	−	0.702382i	$-0.247880\pi$
$882$		0			0
$883$		−	8461.49i		−	0.322482i	−0.986915	−	0.161241i	$-0.948450\pi$
$883$		−	8461.49i		−	0.322482i	0.986915	−	0.161241i	$-0.0515497\pi$
$884$	42731.2	−	37782.4i	1.62580	−	1.43751i
$885$		0			0
$886$	12110.6	−	26873.6i	0.459213	−	1.01900i
$887$	38063.3			1.44086			0.720428	−	0.693529i	$-0.243945\pi$
$887$	38063.3			1.44086			0.720428	+	0.693529i	$0.243945\pi$
$888$		0			0
$889$	16981.0			0.640637
$890$	−282.414	+	626.684i	−0.0106366	+	0.0236028i
$891$		0			0
$892$	18682.2	−	16518.6i	0.701264	−	0.620049i
$893$		−	28408.3i		−	1.06455i
$894$		0			0
$895$			411.882i			0.0153829i
$896$	−9977.20	+	1793.32i	−0.372003	+	0.0668643i
$897$		0			0
$898$	11138.9	+	5019.71i	0.413930	+	0.186537i
$899$	22144.8			0.821547
$900$		0			0
$901$	14433.0			0.533664
$902$	4353.97	+	1962.11i	0.160722	+	0.0724291i
$903$		0			0
$904$	8287.34	+	26732.2i	0.304904	+	0.983519i
$905$			504.084i			0.0185153i
$906$		0			0
$907$		−	21480.7i		−	0.786387i	−0.919456	−	0.393194i	$-0.871370\pi$
$907$		−	21480.7i		−	0.786387i	0.919456	−	0.393194i	$-0.128630\pi$
$908$	27070.7	+	30616.4i	0.989396	+	1.11899i
$909$		0			0
$910$	−186.772	+	414.451i	−0.00680375	+	0.0150977i
$911$	−40098.6			−1.45832			−0.729158	−	0.684346i	$-0.760088\pi$
$911$	−40098.6			−1.45832			−0.729158	+	0.684346i	$0.760088\pi$
$912$		0			0
$913$	−7690.93			−0.278787
$914$	7238.13	−	16061.6i	0.261943	−	0.581258i
$915$		0			0
$916$	−23544.3	−	26628.2i	−0.849265	−	0.960502i
$917$		−	17615.7i		−	0.634374i
$918$		0			0
$919$			30820.2i			1.10627i	0.833091	+	0.553136i	$0.186569\pi$
$919$			30820.2i			1.10627i	−0.833091	+	0.553136i	$0.813431\pi$
$920$	372.857	+	1202.71i	0.0133617	+	0.0431004i
$921$		0			0
$922$	9452.67	+	4259.83i	0.337643	+	0.152158i
$923$	−11967.0			−0.426758
$924$		0			0
$925$	3810.06			0.135431
$926$	−4230.50	−	1906.47i	−0.150133	−	0.0676571i
$927$		0			0
$928$	−14968.0	+	24624.8i	−0.529472	+	0.871064i
$929$			32211.7i			1.13760i	0.822475	+	0.568801i	$0.192593\pi$
$929$			32211.7i			1.13760i	−0.822475	+	0.568801i	$0.807407\pi$
$930$		0			0
$931$			4012.36i			0.141246i
$932$	1449.03	−	1281.22i	0.0509277	−	0.0450297i
$933$		0			0
$934$	−17595.4	+	39044.6i	−0.616422	+	1.36786i
$935$	272.002			0.00951382
$936$		0			0
$937$	26750.4			0.932653			0.466327	−	0.884613i	$-0.345577\pi$
$937$	26750.4			0.932653			0.466327	+	0.884613i	$0.345577\pi$
$938$	−3282.54	+	7284.04i	−0.114263	+	0.253553i
$939$		0			0
$940$	624.283	−	551.984i	0.0216616	−	0.0191529i
$941$			30346.4i			1.05129i	0.850704	+	0.525645i	$0.176176\pi$
$941$			30346.4i			1.05129i	−0.850704	+	0.525645i	$0.823824\pi$
$942$		0			0
$943$		−	32207.3i		−	1.11221i
$944$	−4597.69	+	37259.7i	−0.158519	+	1.28464i
$945$		0			0
$946$	8927.84	+	4023.32i	0.306838	+	0.138276i
$947$	19938.9			0.684189			0.342095	−	0.939665i	$-0.388864\pi$
$947$	19938.9			0.684189			0.342095	+	0.939665i	$0.388864\pi$
$948$		0			0
$949$	43257.8			1.47967
$950$	26375.3	+	11886.0i	0.900766	+	0.405929i
$951$		0			0
$952$	14105.6	−	4372.91i	0.480214	−	0.148873i
$953$			33363.8i			1.13406i	0.823697	+	0.567031i	$0.191908\pi$
$953$			33363.8i			1.13406i	−0.823697	+	0.567031i	$0.808092\pi$
$954$		0			0
$955$		−	288.532i		−	0.00977661i
$956$	−4019.15	−	4545.58i	−0.135971	−	0.153781i
$957$		0			0
$958$	500.593	−	1110.83i	0.0168825	−	0.0374627i
$959$	1598.75			0.0538334
$960$		0			0
$961$	10440.3			0.350453
$962$	2710.62	−	6014.94i	0.0908462	−	0.201590i
$963$		0			0
$964$	30501.8	+	34496.9i	1.01908	+	1.15256i
$965$			1345.93i			0.0448986i
$966$		0			0
$967$			20192.7i			0.671513i	0.941949	+	0.335756i	$0.108992\pi$
$967$			20192.7i			0.671513i	−0.941949	+	0.335756i	$0.891008\pi$
$968$	−26726.0	+	8285.41i	−0.887403	+	0.275107i
$969$		0			0
$970$	148.965	+	67.1306i	0.00493089	+	0.00222210i
$971$	23232.6			0.767837			0.383918	−	0.923367i	$-0.374574\pi$
$971$	23232.6			0.767837			0.383918	+	0.923367i	$0.374574\pi$
$972$		0			0
$973$	−9216.76			−0.303675
$974$	11427.5	+	5149.78i	0.375935	+	0.169414i
$975$		0			0
$976$	−1314.95	+	10656.3i	−0.0431255	+	0.349489i
$977$			42470.8i			1.39075i	0.718648	+	0.695374i	$0.244761\pi$
$977$			42470.8i			1.39075i	−0.718648	+	0.695374i	$0.755239\pi$
$978$		0			0
$979$		−	7864.70i		−	0.256749i
$980$	−88.1732	+	77.9617i	−0.00287407	+	0.00254122i
$981$		0			0
$982$	−4379.07	+	9717.28i	−0.142303	+	0.315775i
$983$	53713.8			1.74283			0.871417	−	0.490544i	$-0.163202\pi$
$983$	53713.8			1.74283			0.871417	+	0.490544i	$0.163202\pi$
$984$		0			0
$985$	1253.25			0.0405399
$986$	17248.2	−	38274.1i	0.557093	−	1.23620i
$987$		0			0
$988$	37528.8	−	33182.5i	1.20845	−	1.06850i
$989$		−	66041.3i		−	2.12335i
$990$		0			0
$991$		−	1994.68i		−	0.0639385i	−0.999489	−	0.0319693i	$-0.989822\pi$
$991$		−	1994.68i		−	0.0639385i	0.999489	−	0.0319693i	$-0.0101779\pi$
$992$	13079.4	−	21517.7i	0.418621	−	0.688697i
$993$		0			0
$994$	−2824.75	−	1272.97i	−0.0901364	−	0.0406198i
$995$	−1291.85			−0.0411601
$996$		0			0
$997$	−48379.4			−1.53680			−0.768401	−	0.639969i	$-0.778947\pi$
$997$	−48379.4			−1.53680			−0.768401	+	0.639969i	$0.778947\pi$
$998$	−27835.3	−	12543.9i	−0.882876	−	0.397866i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.14	yes	36
3.2	odd	2	inner	252.4.e.a.71.23	yes	36
4.3	odd	2	inner	252.4.e.a.71.24	yes	36
12.11	even	2	inner	252.4.e.a.71.13	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.13	✓	36	12.11	even	2	inner
252.4.e.a.71.14	yes	36	1.1	even	1	trivial
252.4.e.a.71.23	yes	36	3.2	odd	2	inner
252.4.e.a.71.24	yes	36	4.3	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)

\(f(q)\)	\(=\)	\(q+(-1.16208 + 2.57868i) q^{2} +(-5.29916 - 5.99324i) q^{4} +0.300247i q^{5} +7.00000i q^{7} +(21.6127 - 6.70021i) q^{8} +(-0.774240 - 0.348910i) q^{10} +9.71649 q^{11} -76.4714 q^{13} +(-18.0507 - 8.13454i) q^{14} +(-7.83789 + 63.5182i) q^{16} -93.2361i q^{17} -81.8849i q^{19} +(1.79945 - 1.59106i) q^{20} +(-11.2913 + 25.0557i) q^{22} +185.343 q^{23} +124.910 q^{25} +(88.8656 - 197.195i) q^{26} +(41.9527 - 37.0941i) q^{28} -159.193i q^{29} +139.107i q^{31} +(-154.685 - 94.0245i) q^{32} +(240.426 + 108.348i) q^{34} -2.10173 q^{35} +30.5025 q^{37} +(211.155 + 95.1565i) q^{38} +(2.01172 + 6.48914i) q^{40} -173.772i q^{41} -356.320i q^{43} +(-51.4892 - 58.2333i) q^{44} +(-215.382 + 477.939i) q^{46} +346.929 q^{47} -49.0000 q^{49} +(-145.155 + 322.102i) q^{50} +(405.234 + 458.312i) q^{52} +154.800i q^{53} +2.91735i q^{55} +(46.9015 + 151.289i) q^{56} +(410.508 + 184.995i) q^{58} +586.598 q^{59} +167.768 q^{61} +(-358.711 - 161.653i) q^{62} +(422.214 - 289.619i) q^{64} -22.9603i q^{65} -403.531i q^{67} +(-558.787 + 494.073i) q^{68} +(2.44237 - 5.41968i) q^{70} +156.489 q^{71} -565.672 q^{73} +(-35.4462 + 78.6561i) q^{74} +(-490.756 + 433.921i) q^{76} +68.0154i q^{77} -542.718i q^{79} +(-19.0712 - 2.35330i) q^{80} +(448.101 + 201.936i) q^{82} -791.534 q^{83} +27.9939 q^{85} +(918.834 + 414.071i) q^{86} +(209.999 - 65.1025i) q^{88} -809.418i q^{89} -535.300i q^{91} +(-982.160 - 1110.80i) q^{92} +(-403.158 + 894.618i) q^{94} +24.5857 q^{95} -192.401 q^{97} +(56.9418 - 126.355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64}+ \cdots + 5496 q^{94}+O(q^{100}) \) 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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