LMFDB - Embedded newform 252.4.w.a.5.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.20
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.80953 + 3.53377i) q^{3} +(-3.77250 - 6.53416i) q^{5} +(14.8160 - 11.1124i) q^{7} +(2.02498 + 26.9240i) q^{9} +O(q^{10})$	\(q+(3.80953 + 3.53377i) q^{3} +(-3.77250 - 6.53416i) q^{5} +(14.8160 - 11.1124i) q^{7} +(2.02498 + 26.9240i) q^{9} +(49.1821 + 28.3953i) q^{11} +(-41.0023 - 23.6727i) q^{13} +(8.71876 - 38.2232i) q^{15} +(-23.2821 - 40.3258i) q^{17} +(85.5255 + 49.3782i) q^{19} +(95.7106 + 10.0236i) q^{21} +(171.876 - 99.2327i) q^{23} +(34.0365 - 58.9530i) q^{25} +(-87.4288 + 109.723i) q^{27} +(151.458 - 87.4444i) q^{29} +94.3050i q^{31} +(87.0181 + 281.971i) q^{33} +(-128.503 - 54.8890i) q^{35} +(-216.629 + 375.212i) q^{37} +(-72.5455 - 235.074i) q^{39} +(-129.589 + 224.454i) q^{41} +(177.731 + 307.840i) q^{43} +(168.286 - 114.802i) q^{45} +468.923 q^{47} +(96.0304 - 329.283i) q^{49} +(53.8082 - 235.896i) q^{51} +(-83.4534 + 48.1818i) q^{53} -428.485i q^{55} +(151.321 + 490.335i) q^{57} -489.780 q^{59} -697.552i q^{61} +(329.191 + 376.404i) q^{63} +357.220i q^{65} -13.4143 q^{67} +(1005.43 + 229.340i) q^{69} -787.178i q^{71} +(-725.727 + 418.998i) q^{73} +(337.989 - 104.306i) q^{75} +(1044.22 - 125.824i) q^{77} -473.028 q^{79} +(-720.799 + 109.041i) q^{81} +(-216.914 - 375.705i) q^{83} +(-175.664 + 304.258i) q^{85} +(885.992 + 202.096i) q^{87} +(611.420 - 1059.01i) q^{89} +(-870.551 + 104.897i) q^{91} +(-333.252 + 359.257i) q^{93} -745.117i q^{95} +(-174.198 + 100.573i) q^{97} +(-664.921 + 1381.68i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	3.80953	+	3.53377i	0.733144	+	0.680074i
$3$	3.80953	+	3.53377i	0.733144	+	0.680074i
$4$		0			0
$5$	−3.77250	−	6.53416i	−0.337422	−	0.584433i	0.646525	−	0.762893i	$-0.276222\pi$
$5$	−3.77250	−	6.53416i	−0.337422	−	0.584433i	−0.983947	+	0.178460i	$0.942888\pi$
$6$		0			0
$7$	14.8160	−	11.1124i	0.799991	−	0.600012i
$7$	14.8160	−	11.1124i	0.799991	−	0.600012i
$8$		0			0
$9$	2.02498	+	26.9240i	0.0749992	+	0.997184i
$10$		0			0
$11$	49.1821	+	28.3953i	1.34809	+	0.778319i	0.987978	−	0.154592i	$-0.0494062\pi$
$11$	49.1821	+	28.3953i	1.34809	+	0.778319i	0.360109	+	0.932910i	$0.382740\pi$
$12$		0			0
$13$	−41.0023	−	23.6727i	−0.874768	−	0.505048i	−0.00583823	−	0.999983i	$-0.501858\pi$
$13$	−41.0023	−	23.6727i	−0.874768	−	0.505048i	−0.868930	+	0.494935i	$0.835192\pi$
$14$		0			0
$15$	8.71876	−	38.2232i	0.150078	−	0.657945i
$16$		0			0
$17$	−23.2821	−	40.3258i	−0.332161	−	0.575320i	0.650774	−	0.759271i	$-0.274445\pi$
$17$	−23.2821	−	40.3258i	−0.332161	−	0.575320i	−0.982935	+	0.183951i	$0.941111\pi$
$18$		0			0
$19$	85.5255	+	49.3782i	1.03268	+	0.596218i	0.917751	−	0.397156i	$-0.130003\pi$
$19$	85.5255	+	49.3782i	1.03268	+	0.596218i	0.114928	+	0.993374i	$0.463336\pi$
$20$		0			0
$21$	95.7106	+	10.0236i	0.994561	+	0.104158i
$22$		0			0
$23$	171.876	−	99.2327i	1.55820	−	0.899628i	0.560772	−	0.827970i	$-0.310504\pi$
$23$	171.876	−	99.2327i	1.55820	−	0.899628i	0.997429	−	0.0716582i	$-0.0228291\pi$
$24$		0			0
$25$	34.0365	−	58.9530i	0.272292	−	0.471624i
$26$		0			0
$27$	−87.4288	+	109.723i	−0.623173	+	0.782084i
$28$		0			0
$29$	151.458	−	87.4444i	0.969830	−	0.559932i	0.0706455	−	0.997501i	$-0.477494\pi$
$29$	151.458	−	87.4444i	0.969830	−	0.559932i	0.899184	+	0.437570i	$0.144161\pi$
$30$		0			0
$31$			94.3050i			0.546377i	0.961961	+	0.273188i	$0.0880783\pi$
$31$			94.3050i			0.546377i	−0.961961	+	0.273188i	$0.911922\pi$
$32$		0			0
$33$	87.0181	+	281.971i	0.459028	+	1.48742i
$34$		0			0
$35$	−128.503	−	54.8890i	−0.620602	−	0.265084i
$36$		0			0
$37$	−216.629	+	375.212i	−0.962528	+	1.66715i	−0.246413	+	0.969165i	$0.579252\pi$
$37$	−216.629	+	375.212i	−0.962528	+	1.66715i	−0.716115	+	0.697982i	$0.754081\pi$
$38$		0			0
$39$	−72.5455	−	235.074i	−0.297861	−	0.965179i
$40$		0			0
$41$	−129.589	+	224.454i	−0.493619	+	0.854973i	−0.999973	−	0.00735276i	$-0.997660\pi$
$41$	−129.589	+	224.454i	−0.493619	+	0.854973i	0.506354	+	0.862326i	$0.330993\pi$
$42$		0			0
$43$	177.731	+	307.840i	0.630321	+	1.09175i	0.987486	+	0.157707i	$0.0504100\pi$
$43$	177.731	+	307.840i	0.630321	+	1.09175i	−0.357165	+	0.934041i	$0.616257\pi$
$44$		0			0
$45$	168.286	−	114.802i	0.557480	−	0.380304i
$46$		0			0
$47$	468.923			1.45531			0.727653	−	0.685945i	$-0.240611\pi$
$47$	468.923			1.45531			0.727653	+	0.685945i	$0.240611\pi$
$48$		0			0
$49$	96.0304	−	329.283i	0.279972	−	0.960008i
$50$		0			0
$51$	53.8082	−	235.896i	0.147738	−	0.647687i
$52$		0			0
$53$	−83.4534	+	48.1818i	−0.216287	+	0.124873i	−0.604230	−	0.796810i	$-0.706519\pi$
$53$	−83.4534	+	48.1818i	−0.216287	+	0.124873i	0.387943	+	0.921683i	$0.373186\pi$
$54$		0			0
$55$		−	428.485i		−	1.05049i
$56$		0			0
$57$	151.321	+	490.335i	0.351630	+	1.13941i
$58$		0			0
$59$	−489.780			−1.08074			−0.540372	−	0.841426i	$-0.681717\pi$
$59$	−489.780			−1.08074			−0.540372	+	0.841426i	$0.681717\pi$
$60$		0			0
$61$		−	697.552i		−	1.46414i	−0.681231	−	0.732068i	$-0.738555\pi$
$61$		−	697.552i		−	1.46414i	0.681231	−	0.732068i	$-0.261445\pi$
$62$		0			0
$63$	329.191	+	376.404i	0.658321	+	0.752738i
$64$		0			0
$65$			357.220i			0.681658i
$66$		0			0
$67$	−13.4143			−0.0244600			−0.0122300	−	0.999925i	$-0.503893\pi$
$67$	−13.4143			−0.0244600			−0.0122300	+	0.999925i	$0.503893\pi$
$68$		0			0
$69$	1005.43	+	229.340i	1.75420	+	0.400136i
$70$		0			0
$71$		−	787.178i		−	1.31579i	−0.753111	−	0.657893i	$-0.771448\pi$
$71$		−	787.178i		−	1.31579i	0.753111	−	0.657893i	$-0.228552\pi$
$72$		0			0
$73$	−725.727	+	418.998i	−1.16356	+	0.671782i	−0.952155	−	0.305617i	$-0.901137\pi$
$73$	−725.727	+	418.998i	−1.16356	+	0.671782i	−0.211405	+	0.977398i	$0.567804\pi$
$74$		0			0
$75$	337.989	−	104.306i	0.520368	−	0.160589i
$76$		0			0
$77$	1044.22	−	125.824i	1.54546	−	0.186220i
$78$		0			0
$79$	−473.028			−0.673668			−0.336834	−	0.941564i	$-0.609356\pi$
$79$	−473.028			−0.673668			−0.336834	+	0.941564i	$0.609356\pi$
$80$		0			0
$81$	−720.799	+	109.041i	−0.988750	+	0.149576i
$82$		0			0
$83$	−216.914	−	375.705i	−0.286860	−	0.496856i	0.686199	−	0.727414i	$-0.259278\pi$
$83$	−216.914	−	375.705i	−0.286860	−	0.496856i	−0.973058	+	0.230558i	$0.925945\pi$
$84$		0			0
$85$	−175.664	+	304.258i	−0.224157	+	0.388252i
$86$		0			0
$87$	885.992	+	202.096i	1.09182	+	0.249046i
$88$		0			0
$89$	611.420	−	1059.01i	0.728206	−	1.26129i	−0.229435	−	0.973324i	$-0.573688\pi$
$89$	611.420	−	1059.01i	0.728206	−	1.26129i	0.957641	−	0.287966i	$-0.0929790\pi$
$90$		0			0
$91$	−870.551	+	104.897i	−1.00284	+	0.120837i
$92$		0			0
$93$	−333.252	+	359.257i	−0.371577	+	0.400573i
$94$		0			0
$95$		−	745.117i		−	0.804709i
$96$		0			0
$97$	−174.198	+	100.573i	−0.182341	+	0.105275i	−0.588392	−	0.808576i	$-0.700239\pi$
$97$	−174.198	+	100.573i	−0.182341	+	0.105275i	0.406051	+	0.913850i	$0.366906\pi$
$98$		0			0
$99$	−664.921	+	1381.68i	−0.675021	+	1.40266i
$100$		0			0
$101$	250.434	−	433.764i	0.246724	−	0.427338i	−0.715891	−	0.698212i	$-0.753979\pi$
$101$	250.434	−	433.764i	0.246724	−	0.427338i	0.962615	+	0.270874i	$0.0873127\pi$
$102$		0			0
$103$	−1618.98	+	934.717i	−1.54876	+	0.894179i	−0.550527	+	0.834818i	$0.685573\pi$
$103$	−1618.98	+	934.717i	−1.54876	+	0.894179i	−0.998237	+	0.0593611i	$0.981094\pi$
$104$		0			0
$105$	−295.573	−	663.202i	−0.274714	−	0.616399i
$106$		0			0
$107$	52.0731	+	30.0644i	0.0470476	+	0.0271630i	0.523339	−	0.852124i	$-0.324686\pi$
$107$	52.0731	+	30.0644i	0.0470476	+	0.0271630i	−0.476292	+	0.879287i	$0.658019\pi$
$108$		0			0
$109$	−874.873	−	1515.32i	−0.768785	−	1.33158i	−0.938222	−	0.346034i	$-0.887528\pi$
$109$	−874.873	−	1515.32i	−0.768785	−	1.33158i	0.169436	−	0.985541i	$-0.445805\pi$
$110$		0			0
$111$	−2151.16	+	663.864i	−1.83945	+	0.567668i
$112$		0			0
$113$	−236.459	−	136.520i	−0.196852	−	0.113652i	0.398335	−	0.917240i	$-0.369588\pi$
$113$	−236.459	−	136.520i	−0.196852	−	0.113652i	−0.595186	+	0.803588i	$0.702922\pi$
$114$		0			0
$115$	−1296.80	−	748.710i	−1.05154	−	0.607110i
$116$		0			0
$117$	554.333	−	1151.88i	0.438018	−	0.910182i
$118$		0			0
$119$	−793.064	−	338.750i	−0.610925	−	0.260951i
$120$		0			0
$121$	947.086	+	1640.40i	0.711560	+	1.23246i
$122$		0			0
$123$	−1286.84	+	397.128i	−0.943338	+	0.291121i
$124$		0			0
$125$	−1456.74			−1.04235
$126$		0			0
$127$	−919.086			−0.642171			−0.321085	−	0.947050i	$-0.604048\pi$
$127$	−919.086			−0.642171			−0.321085	+	0.947050i	$0.604048\pi$
$128$		0			0
$129$	−410.762	+	1800.79i	−0.280353	+	1.22907i
$130$		0			0
$131$	451.099	+	781.327i	0.300861	+	0.521106i	0.976331	−	0.216281i	$-0.0693928\pi$
$131$	451.099	+	781.327i	0.300861	+	0.521106i	−0.675471	+	0.737387i	$0.736059\pi$
$132$		0			0
$133$	1815.86	−	218.802i	1.18387	−	0.142651i
$134$		0			0
$135$	1046.77	+	157.343i	0.667348	+	0.100310i
$136$		0			0
$137$	976.413	+	563.733i	0.608910	+	0.351554i	0.772539	−	0.634968i	$-0.218987\pi$
$137$	976.413	+	563.733i	0.608910	+	0.351554i	−0.163629	+	0.986522i	$0.552320\pi$
$138$		0			0
$139$	−623.154	−	359.778i	−0.380253	−	0.219539i	0.297675	−	0.954667i	$-0.403789\pi$
$139$	−623.154	−	359.778i	−0.380253	−	0.219539i	−0.677929	+	0.735128i	$0.737122\pi$
$140$		0			0
$141$	1786.37	+	1657.06i	1.06695	+	0.989716i
$142$		0			0
$143$	−1344.39	−	2328.54i	−0.786176	−	1.36170i
$144$		0			0
$145$	−1142.75	−	659.768i	−0.654485	−	0.377867i
$146$		0			0
$147$	1529.44	−	915.062i	0.858136	−	0.513422i
$148$		0			0
$149$	−256.791	+	148.258i	−0.141189	+	0.0815153i	−0.568930	−	0.822386i	$-0.692643\pi$
$149$	−256.791	+	148.258i	−0.141189	+	0.0815153i	0.427742	+	0.903901i	$0.359309\pi$
$150$		0			0
$151$	−303.762	+	526.131i	−0.163707	+	0.283549i	−0.936195	−	0.351480i	$-0.885679\pi$
$151$	−303.762	+	526.131i	−0.163707	+	0.283549i	0.772488	+	0.635029i	$0.219012\pi$
$152$		0			0
$153$	1038.58	−	708.506i	0.548788	−	0.374374i
$154$		0			0
$155$	616.204	−	355.766i	0.319321	−	0.184360i
$156$		0			0
$157$			196.402i			0.0998383i	0.998753	+	0.0499191i	$0.0158964\pi$
$157$			196.402i			0.0998383i	−0.998753	+	0.0499191i	$0.984104\pi$
$158$		0			0
$159$	−488.181	−	111.355i	−0.243492	−	0.0555410i
$160$		0			0
$161$	1443.81	−	3380.19i	0.706760	−	1.65463i
$162$		0			0
$163$	−796.131	+	1378.94i	−0.382563	+	0.662619i	−0.991428	−	0.130655i	$-0.958292\pi$
$163$	−796.131	+	1378.94i	−0.382563	+	0.662619i	0.608865	+	0.793274i	$0.291625\pi$
$164$		0			0
$165$	1514.17	−	1632.32i	0.714410	−	0.770159i
$166$		0			0
$167$	−756.255	+	1309.87i	−0.350424	+	0.606951i	−0.986324	−	0.164820i	$-0.947296\pi$
$167$	−756.255	+	1309.87i	−0.350424	+	0.606951i	0.635900	+	0.771771i	$0.280629\pi$
$168$		0			0
$169$	22.2908	+	38.6088i	0.0101460	+	0.0175734i
$170$		0			0
$171$	−1156.27	+	2402.68i	−0.517088	+	1.07449i
$172$		0			0
$173$	−1177.69			−0.517561			−0.258781	−	0.965936i	$-0.583321\pi$
$173$	−1177.69			−0.517561			−0.258781	+	0.965936i	$0.583321\pi$
$174$		0			0
$175$	−150.821	−	1251.68i	−0.0651485	−	0.540673i
$176$		0			0
$177$	−1865.83	−	1730.77i	−0.792341	−	0.734986i
$178$		0			0
$179$	899.277	−	519.198i	0.375504	−	0.216797i	−0.300357	−	0.953827i	$-0.597106\pi$
$179$	899.277	−	519.198i	0.375504	−	0.216797i	0.675860	+	0.737030i	$0.263772\pi$
$180$		0			0
$181$			3190.62i			1.31026i	0.755516	+	0.655130i	$0.227386\pi$
$181$			3190.62i			1.31026i	−0.755516	+	0.655130i	$0.772614\pi$
$182$		0			0
$183$	2464.99	−	2657.34i	0.995721	−	1.07342i
$184$		0			0
$185$	3268.92			1.29911
$186$		0			0
$187$		−	2644.41i		−	1.03411i
$188$		0			0
$189$	−76.0625	+	2597.21i	−0.0292737	+	0.999571i
$190$		0			0
$191$		−	1872.31i		−	0.709296i	−0.935000	−	0.354648i	$-0.884601\pi$
$191$		−	1872.31i		−	0.709296i	0.935000	−	0.354648i	$-0.115399\pi$
$192$		0			0
$193$	1593.98			0.594493			0.297247	−	0.954801i	$-0.403932\pi$
$193$	1593.98			0.594493			0.297247	+	0.954801i	$0.403932\pi$
$194$		0			0
$195$	−1262.33	+	1360.84i	−0.463577	+	0.499753i
$196$		0			0
$197$			4318.76i			1.56192i	0.624580	+	0.780961i	$0.285270\pi$
$197$			4318.76i			1.56192i	−0.624580	+	0.780961i	$0.714730\pi$
$198$		0			0
$199$	2988.87	−	1725.63i	1.06470	−	0.614706i	0.137973	−	0.990436i	$-0.455941\pi$
$199$	2988.87	−	1725.63i	1.06470	−	0.614706i	0.926729	+	0.375730i	$0.122608\pi$
$200$		0			0
$201$	−51.1022	−	47.4031i	−0.0179327	−	0.0166346i
$202$		0			0
$203$	1272.30	−	2978.64i	0.439890	−	1.02985i
$204$		0			0
$205$	1955.49			0.666232
$206$		0			0
$207$	3019.78	+	4426.64i	1.01396	+	1.48634i
$208$		0			0
$209$	2804.22	+	4857.05i	0.928095	+	1.60751i
$210$		0			0
$211$	−1228.66	+	2128.11i	−0.400876	+	0.694337i	−0.993832	−	0.110898i	$-0.964627\pi$
$211$	−1228.66	+	2128.11i	−0.400876	+	0.694337i	0.592956	+	0.805235i	$0.297961\pi$
$212$		0			0
$213$	2781.70	−	2998.77i	0.894832	−	0.964660i
$214$		0			0
$215$	1340.98	−	2322.65i	0.425369	−	0.736760i
$216$		0			0
$217$	1047.95	+	1397.23i	0.327833	+	0.437097i
$218$		0			0
$219$	−4245.32	−	968.363i	−1.30992	−	0.298794i
$220$		0			0
$221$			2204.60i			0.671029i
$222$		0			0
$223$	−3304.21	+	1907.68i	−0.992225	+	0.572861i	−0.905938	−	0.423409i	$-0.860833\pi$
$223$	−3304.21	+	1907.68i	−0.992225	+	0.572861i	−0.0862860	+	0.996270i	$0.527500\pi$
$224$		0			0
$225$	1656.17	+	797.019i	0.490717	+	0.236154i
$226$		0			0
$227$	−1919.23	+	3324.20i	−0.561162	+	0.971961i	0.436233	+	0.899834i	$0.356312\pi$
$227$	−1919.23	+	3324.20i	−0.561162	+	0.971961i	−0.997395	+	0.0721277i	$0.977021\pi$
$228$		0			0
$229$	2230.42	−	1287.74i	0.643627	−	0.371598i	−0.142383	−	0.989812i	$-0.545477\pi$
$229$	2230.42	−	1287.74i	0.643627	−	0.371598i	0.786010	+	0.618213i	$0.212143\pi$
$230$		0			0
$231$	4422.63	+	3210.71i	1.25969	+	0.914500i
$232$		0			0
$233$	−3578.43	−	2066.01i	−1.00614	−	0.580896i	−0.0960817	−	0.995373i	$-0.530631\pi$
$233$	−3578.43	−	2066.01i	−1.00614	−	0.580896i	−0.910060	+	0.414478i	$0.863964\pi$
$234$		0			0
$235$	−1769.01	−	3064.01i	−0.491053	−	0.850529i
$236$		0			0
$237$	−1802.01	−	1671.57i	−0.493896	−	0.458144i
$238$		0			0
$239$	4518.49	+	2608.75i	1.22291	+	0.706050i	0.965538	−	0.260261i	$-0.0838087\pi$
$239$	4518.49	+	2608.75i	1.22291	+	0.706050i	0.257376	+	0.966311i	$0.417142\pi$
$240$		0			0
$241$	−4733.66	−	2732.98i	−1.26524	−	0.730484i	−0.291153	−	0.956676i	$-0.594039\pi$
$241$	−4733.66	−	2732.98i	−1.26524	−	0.730484i	−0.974083	+	0.226192i	$0.927372\pi$
$242$		0			0
$243$	−3131.23	−	2131.74i	−0.826619	−	0.562763i
$244$		0			0
$245$	−2513.86	+	614.741i	−0.655529	+	0.160304i
$246$		0			0
$247$	−2337.83	−	4049.24i	−0.602236	−	1.04310i
$248$		0			0
$249$	501.317	−	2197.78i	0.127589	−	0.559352i
$250$		0			0
$251$	−1445.51			−0.363505			−0.181752	−	0.983344i	$-0.558177\pi$
$251$	−1445.51			−0.363505			−0.181752	+	0.983344i	$0.558177\pi$
$252$		0			0
$253$	11271.0			2.80079
$254$		0			0
$255$	−1744.37	+	538.325i	−0.428380	+	0.132201i
$256$		0			0
$257$	−370.431	−	641.604i	−0.0899098	−	0.155728i	0.817563	−	0.575839i	$-0.195325\pi$
$257$	−370.431	−	641.604i	−0.0899098	−	0.155728i	−0.907473	+	0.420111i	$0.861991\pi$
$258$		0			0
$259$	959.914	+	7966.41i	0.230294	+	1.91123i
$260$		0			0
$261$	2661.05	+	3900.78i	0.631091	+	0.925104i
$262$		0			0
$263$	3153.75	+	1820.82i	0.739424	+	0.426907i	0.821860	−	0.569690i	$-0.192937\pi$
$263$	3153.75	+	1820.82i	0.739424	+	0.426907i	−0.0824358	+	0.996596i	$0.526270\pi$
$264$		0			0
$265$	629.655	+	363.532i	0.145960	+	0.0842701i
$266$		0			0
$267$	6071.51	−	1873.71i	1.39165	−	0.429473i
$268$		0			0
$269$	−1896.50	−	3284.83i	−0.429857	−	0.744535i	0.567003	−	0.823716i	$-0.308103\pi$
$269$	−1896.50	−	3284.83i	−0.429857	−	0.744535i	−0.996860	+	0.0791811i	$0.974769\pi$
$270$		0			0
$271$	−2612.92	−	1508.57i	−0.585696	−	0.338152i	0.177698	−	0.984085i	$-0.443135\pi$
$271$	−2612.92	−	1508.57i	−0.585696	−	0.338152i	−0.763394	+	0.645933i	$0.776468\pi$
$272$		0			0
$273$	−3687.07	−	2676.72i	−0.817405	−	0.593415i
$274$		0			0
$275$	3347.97	−	1932.95i	0.734147	−	0.423860i
$276$		0			0
$277$	1666.31	−	2886.13i	0.361439	−	0.626031i	−0.626759	−	0.779213i	$-0.715619\pi$
$277$	1666.31	−	2886.13i	0.361439	−	0.626031i	0.988198	+	0.153182i	$0.0489522\pi$
$278$		0			0
$279$	−2539.06	+	190.966i	−0.544838	+	0.0409778i
$280$		0			0
$281$	−4170.82	+	2408.02i	−0.885446	+	0.511212i	−0.872450	−	0.488703i	$-0.837470\pi$
$281$	−4170.82	+	2408.02i	−0.885446	+	0.511212i	−0.0129957	+	0.999916i	$0.504137\pi$
$282$		0			0
$283$		−	1535.22i		−	0.322472i	−0.986916	−	0.161236i	$-0.948452\pi$
$283$		−	1535.22i		−	0.322472i	0.986916	−	0.161236i	$-0.0515480\pi$
$284$		0			0
$285$	2633.07	−	2838.54i	0.547261	−	0.589967i
$286$		0			0
$287$	574.227	+	4765.57i	0.118103	+	0.980148i
$288$		0			0
$289$	1372.39	−	2377.04i	0.279338	−	0.483827i
$290$		0			0
$291$	−1019.01	−	232.438i	−0.205277	−	0.0468240i
$292$		0			0
$293$	−612.380	+	1060.67i	−0.122101	+	0.211485i	−0.920596	−	0.390516i	$-0.872297\pi$
$293$	−612.380	+	1060.67i	−0.122101	+	0.211485i	0.798495	+	0.602001i	$0.205630\pi$
$294$		0			0
$295$	1847.69	+	3200.30i	0.364667	+	0.631622i
$296$		0			0
$297$	−7415.56	+	2913.86i	−1.44880	+	0.569290i
$298$		0			0
$299$	−9396.41			−1.81742
$300$		0			0
$301$	6054.11	+	2585.95i	1.15931	+	0.495189i
$302$		0			0
$303$	2486.85	−	767.460i	0.471505	−	0.145510i
$304$		0			0
$305$	−4557.91	+	2631.51i	−0.855690	+	0.494033i
$306$		0			0
$307$			2685.67i			0.499280i	0.968339	+	0.249640i	$0.0803124\pi$
$307$			2685.67i			0.499280i	−0.968339	+	0.249640i	$0.919688\pi$
$308$		0			0
$309$	−9470.61	−	2160.26i	−1.74357	−	0.397712i
$310$		0			0
$311$	−509.831			−0.0929578			−0.0464789	−	0.998919i	$-0.514800\pi$
$311$	−509.831			−0.0929578			−0.0464789	+	0.998919i	$0.514800\pi$
$312$		0			0
$313$			2485.09i			0.448772i	0.974500	+	0.224386i	$0.0720377\pi$
$313$			2485.09i			0.448772i	−0.974500	+	0.224386i	$0.927962\pi$
$314$		0			0
$315$	1217.61	−	3570.97i	0.217793	−	0.638735i
$316$		0			0
$317$			7161.52i			1.26887i	0.772977	+	0.634434i	$0.218767\pi$
$317$			7161.52i			1.26887i	−0.772977	+	0.634434i	$0.781233\pi$
$318$		0			0
$319$	9932.04			1.74322
$320$		0			0
$321$	92.1332	+	298.545i	0.0160198	+	0.0519102i
$322$		0			0
$323$		−	4598.52i		−	0.792162i
$324$		0			0
$325$	−2791.15	+	1611.47i	−0.476385	+	0.275041i
$326$		0			0
$327$	2021.95	−	8864.26i	0.341939	−	1.49907i
$328$		0			0
$329$	6947.58	−	5210.84i	1.16423	−	0.873201i
$330$		0			0
$331$	7301.84			1.21252			0.606262	−	0.795265i	$-0.292668\pi$
$331$	7301.84			1.21252			0.606262	+	0.795265i	$0.292668\pi$
$332$		0			0
$333$	−10540.9	−	5072.71i	−1.73464	−	0.834782i
$334$		0			0
$335$	50.6055	+	87.6513i	0.00825336	+	0.0142952i
$336$		0			0
$337$	−2715.34	+	4703.10i	−0.438913	+	0.760220i	−0.997606	−	0.0691544i	$-0.977970\pi$
$337$	−2715.34	+	4703.10i	−0.438913	+	0.760220i	0.558692	+	0.829375i	$0.311303\pi$
$338$		0			0
$339$	−418.369	−	1355.67i	−0.0670285	−	0.217197i
$340$		0			0
$341$	−2677.82	+	4638.12i	−0.425255	+	0.736564i
$342$		0			0
$343$	−2236.32	−	5945.79i	−0.352041	−	0.935985i
$344$		0			0
$345$	−2294.44	−	7434.84i	−0.358054	−	1.16023i
$346$		0			0
$347$		−	3350.18i		−	0.518291i	−0.965838	−	0.259146i	$-0.916559\pi$
$347$		−	3350.18i		−	0.518291i	0.965838	−	0.259146i	$-0.0834410\pi$
$348$		0			0
$349$	823.653	−	475.536i	0.126330	−	0.0729366i	−0.435503	−	0.900187i	$-0.643430\pi$
$349$	823.653	−	475.536i	0.126330	−	0.0729366i	0.561833	+	0.827251i	$0.310096\pi$
$350$		0			0
$351$	6182.22	−	2429.23i	0.940122	−	0.369410i
$352$		0			0
$353$	−478.499	+	828.784i	−0.0721471	+	0.124962i	−0.899842	−	0.436216i	$-0.856318\pi$
$353$	−478.499	+	828.784i	−0.0721471	+	0.124962i	0.827695	+	0.561178i	$0.189652\pi$
$354$		0			0
$355$	−5143.54	+	2969.63i	−0.768989	+	0.443976i
$356$		0			0
$357$	−1824.14	−	4092.98i	−0.270430	−	0.606788i
$358$		0			0
$359$	4129.52	+	2384.18i	0.607097	+	0.350508i	0.771828	−	0.635831i	$-0.219342\pi$
$359$	4129.52	+	2384.18i	0.607097	+	0.350508i	−0.164732	+	0.986338i	$0.552676\pi$
$360$		0			0
$361$	1446.91	+	2506.13i	0.210951	+	0.365378i
$362$		0			0
$363$	−2188.85	+	9595.93i	−0.316487	+	1.38748i
$364$		0			0
$365$	5475.60	+	3161.34i	0.785222	+	0.453348i
$366$		0			0
$367$	−402.274	−	232.253i	−0.0572168	−	0.0330341i	0.471119	−	0.882070i	$-0.343850\pi$
$367$	−402.274	−	232.253i	−0.0572168	−	0.0330341i	−0.528335	+	0.849036i	$0.677184\pi$
$368$		0			0
$369$	−6305.61	−	3034.53i	−0.889586	−	0.428106i
$370$		0			0
$371$	−701.035	+	1641.23i	−0.0981022	+	0.229672i
$372$		0			0
$373$	−4414.52	−	7646.18i	−0.612803	−	1.06141i	−0.990766	−	0.135585i	$-0.956709\pi$
$373$	−4414.52	−	7646.18i	−0.612803	−	1.06141i	0.377963	−	0.925821i	$-0.376625\pi$
$374$		0			0
$375$	−5549.47	−	5147.76i	−0.764196	−	0.708878i
$376$		0			0
$377$	−8280.17			−1.13117
$378$		0			0
$379$	9957.69			1.34958			0.674792	−	0.738008i	$-0.264233\pi$
$379$	9957.69			1.34958			0.674792	+	0.738008i	$0.264233\pi$
$380$		0			0
$381$	−3501.28	−	3247.84i	−0.470804	−	0.436724i
$382$		0			0
$383$	−4183.98	−	7246.87i	−0.558203	−	0.966835i	−0.997647	−	0.0685654i	$-0.978158\pi$
$383$	−4183.98	−	7246.87i	−0.558203	−	0.966835i	0.439444	−	0.898270i	$-0.355175\pi$
$384$		0			0
$385$	−4761.48	−	6348.45i	−0.630306	−	0.840382i
$386$		0			0
$387$	−7928.37	+	5408.60i	−1.04140	+	0.710426i
$388$		0			0
$389$	−2449.32	−	1414.12i	−0.319243	−	0.184315i	0.331812	−	0.943346i	$-0.392340\pi$
$389$	−2449.32	−	1414.12i	−0.319243	−	0.184315i	−0.651055	+	0.759030i	$0.725673\pi$
$390$		0			0
$391$	−8003.28	−	4620.70i	−1.03515	−	0.597644i
$392$		0			0
$393$	−1042.55	+	4570.57i	−0.133816	+	0.586653i
$394$		0			0
$395$	1784.50	+	3090.84i	0.227311	+	0.393714i
$396$		0			0
$397$	7266.91	+	4195.55i	0.918680	+	0.530400i	0.883214	−	0.468971i	$-0.155375\pi$
$397$	7266.91	+	4195.55i	0.918680	+	0.530400i	0.0354662	+	0.999371i	$0.488708\pi$
$398$		0			0
$399$	7690.76	+	5583.29i	0.964961	+	0.700537i
$400$		0			0
$401$	−9824.80	+	5672.35i	−1.22351	+	0.706393i	−0.965664	−	0.259793i	$-0.916346\pi$
$401$	−9824.80	+	5672.35i	−1.22351	+	0.706393i	−0.257845	+	0.966186i	$0.583012\pi$
$402$		0			0
$403$	2232.45	−	3866.72i	0.275946	−	0.477953i
$404$		0			0
$405$	3431.70	+	4298.46i	0.421044	+	0.527388i
$406$		0			0
$407$	−21308.5	+	12302.5i	−2.59514	+	1.49831i
$408$		0			0
$409$		−	5561.60i		−	0.672380i	−0.941794	−	0.336190i	$-0.890862\pi$
$409$		−	5561.60i		−	0.672380i	0.941794	−	0.336190i	$-0.109138\pi$
$410$		0			0
$411$	1727.57	+	5597.97i	0.207335	+	0.671843i
$412$		0			0
$413$	−7256.60	+	5442.62i	−0.864586	+	0.648459i
$414$		0			0
$415$	−1636.61	+	2834.70i	−0.193586	+	0.335301i
$416$		0			0
$417$	−1102.55	−	3572.66i	−0.129477	−	0.419554i
$418$		0			0
$419$	2668.47	−	4621.92i	0.311129	−	0.538892i	−0.667478	−	0.744630i	$-0.732626\pi$
$419$	2668.47	−	4621.92i	0.311129	−	0.538892i	0.978607	+	0.205738i	$0.0659595\pi$
$420$		0			0
$421$	6734.22	+	11664.0i	0.779586	+	1.35028i	0.932180	+	0.361994i	$0.117904\pi$
$421$	6734.22	+	11664.0i	0.779586	+	1.35028i	−0.152594	+	0.988289i	$0.548763\pi$
$422$		0			0
$423$	949.558	+	12625.3i	0.109147	+	1.45121i
$424$		0			0
$425$	−3169.77			−0.361780
$426$		0			0
$427$	−7751.46	−	10335.0i	−0.878499	−	1.17130i
$428$		0			0
$429$	3107.06	−	13621.4i	0.349674	−	1.53298i
$430$		0			0
$431$	9288.24	−	5362.57i	1.03805	−	0.599318i	0.118769	−	0.992922i	$-0.462105\pi$
$431$	9288.24	−	5362.57i	1.03805	−	0.599318i	0.919280	+	0.393604i	$0.128772\pi$
$432$		0			0
$433$		−	4680.18i		−	0.519434i	−0.965685	−	0.259717i	$-0.916371\pi$
$433$		−	4680.18i		−	0.519434i	0.965685	−	0.259717i	$-0.0836293\pi$
$434$		0			0
$435$	−2021.87	−	6551.62i	−0.222854	−	0.722129i
$436$		0			0
$437$	19599.7			2.14550
$438$		0			0
$439$			2450.71i			0.266438i	0.991087	+	0.133219i	$0.0425313\pi$
$439$			2450.71i			0.266438i	−0.991087	+	0.133219i	$0.957469\pi$
$440$		0			0
$441$	9060.06	+	1918.73i	0.978302	+	0.207184i
$442$		0			0
$443$			10179.0i			1.09169i	0.837888	+	0.545843i	$0.183790\pi$
$443$			10179.0i			1.09169i	−0.837888	+	0.545843i	$0.816210\pi$
$444$		0			0
$445$	−9226.32			−0.982852
$446$		0			0
$447$	−1502.16	−	342.645i	−0.158948	−	0.0362563i
$448$		0			0
$449$		−	4048.85i		−	0.425561i	−0.977100	−	0.212780i	$-0.931748\pi$
$449$		−	4048.85i		−	0.425561i	0.977100	−	0.212780i	$-0.0682519\pi$
$450$		0			0
$451$	−12746.9	+	7359.43i	−1.33088	+	0.768385i
$452$		0			0
$453$	−3016.41	+	930.886i	−0.312855	+	0.0965493i
$454$		0			0
$455$	3969.57	+	5292.59i	0.409003	+	0.545320i
$456$		0			0
$457$	−1146.77			−0.117382			−0.0586910	−	0.998276i	$-0.518693\pi$
$457$	−1146.77			−0.117382			−0.0586910	+	0.998276i	$0.518693\pi$
$458$		0			0
$459$	6460.21	+	971.046i	0.656943	+	0.0987463i
$460$		0			0
$461$	811.579	+	1405.70i	0.0819935	+	0.142017i	0.904106	−	0.427308i	$-0.140538\pi$
$461$	811.579	+	1405.70i	0.0819935	+	0.142017i	−0.822113	+	0.569325i	$0.807205\pi$
$462$		0			0
$463$	1433.87	−	2483.54i	0.143926	−	0.249287i	−0.785046	−	0.619438i	$-0.787361\pi$
$463$	1433.87	−	2483.54i	0.143926	−	0.249287i	0.928972	+	0.370151i	$0.120694\pi$
$464$		0			0
$465$	3604.64	+	822.223i	0.359486	+	0.0819993i
$466$		0			0
$467$	7595.86	−	13156.4i	0.752665	−	1.30365i	−0.193862	−	0.981029i	$-0.562101\pi$
$467$	7595.86	−	13156.4i	0.752665	−	1.30365i	0.946527	−	0.322625i	$-0.104565\pi$
$468$		0			0
$469$	−198.747	+	149.065i	−0.0195678	+	0.0146763i
$470$		0			0
$471$	−694.040	+	748.200i	−0.0678974	+	0.0731958i
$472$		0			0
$473$			20187.0i			1.96236i
$474$		0			0
$475$	5821.98	−	3361.32i	0.562381	−	0.324691i
$476$		0			0
$477$	−1466.24	−	2149.33i	−0.140743	−	0.206312i
$478$		0			0
$479$	3938.22	−	6821.20i	0.375662	−	0.650665i	−0.614764	−	0.788711i	$-0.710749\pi$
$479$	3938.22	−	6821.20i	0.375662	−	0.650665i	0.990426	+	0.138046i	$0.0440821\pi$
$480$		0			0
$481$	17764.5	−	10256.4i	1.68398	−	0.972245i
$482$		0			0
$483$	17445.0	−	7774.81i	1.64343	−	0.732435i
$484$		0			0
$485$	1314.32	+	758.824i	0.123052	+	0.0710441i
$486$		0			0
$487$	1027.58	+	1779.82i	0.0956143	+	0.165609i	0.909865	−	0.414905i	$-0.136185\pi$
$487$	1027.58	+	1779.82i	0.0956143	+	0.165609i	−0.814251	+	0.580514i	$0.802852\pi$
$488$		0			0
$489$	−7905.73	+	2439.76i	−0.731104	+	0.225624i
$490$		0			0
$491$	−2541.83	−	1467.53i	−0.233628	−	0.134885i	0.378617	−	0.925554i	$-0.376400\pi$
$491$	−2541.83	−	1467.53i	−0.233628	−	0.134885i	−0.612245	+	0.790668i	$0.709733\pi$
$492$		0			0
$493$	−7052.53	−	4071.78i	−0.644280	−	0.371975i
$494$		0			0
$495$	11536.5	−	867.672i	1.04753	−	0.0787858i
$496$		0			0
$497$	−8747.41	−	11662.9i	−0.789487	−	1.05262i
$498$		0			0
$499$	8687.94	+	15047.9i	0.779410	+	1.34998i	0.932282	+	0.361731i	$0.117814\pi$
$499$	8687.94	+	15047.9i	0.779410	+	1.34998i	−0.152873	+	0.988246i	$0.548852\pi$
$500$		0			0
$501$	−7509.75	+	2317.56i	−0.669683	+	0.206669i
$502$		0			0
$503$	−6001.85			−0.532027			−0.266013	−	0.963969i	$-0.585707\pi$
$503$	−6001.85			−0.532027			−0.266013	+	0.963969i	$0.585707\pi$
$504$		0			0
$505$	−3779.04			−0.333000
$506$		0			0
$507$	−51.5172	+	225.852i	−0.00451274	+	0.0197839i
$508$		0			0
$509$	−3420.88	−	5925.14i	−0.297894	−	0.515967i	0.677760	−	0.735283i	$-0.262951\pi$
$509$	−3420.88	−	5925.14i	−0.297894	−	0.515967i	−0.975654	+	0.219316i	$0.929617\pi$
$510$		0			0
$511$	−6096.33	+	14272.4i	−0.527761	+	1.23557i
$512$		0			0
$513$	−12895.3	+	5067.07i	−1.10983	+	0.436095i
$514$		0			0
$515$	12215.2	+	7052.44i	1.04517	+	0.603432i
$516$		0			0
$517$	23062.6	+	13315.2i	1.96188	+	1.13269i
$518$		0			0
$519$	−4486.44	−	4161.68i	−0.379447	−	0.351980i
$520$		0			0
$521$	−3540.51	−	6132.35i	−0.297721	−	0.515668i	0.677893	−	0.735160i	$-0.262893\pi$
$521$	−3540.51	−	6132.35i	−0.297721	−	0.515668i	−0.975614	+	0.219493i	$0.929560\pi$
$522$		0			0
$523$	15657.2	+	9039.69i	1.30907	+	0.755790i	0.981940	−	0.189191i	$-0.0605866\pi$
$523$	15657.2	+	9039.69i	1.30907	+	0.755790i	0.327126	+	0.944981i	$0.393920\pi$
$524$		0			0
$525$	3848.58	−	5301.26i	0.319935	−	0.440697i
$526$		0			0
$527$	3802.93	−	2195.62i	0.314342	−	0.181485i
$528$		0			0
$529$	13610.8	−	23574.5i	1.11866	−	1.93758i
$530$		0			0
$531$	−991.794	−	13186.8i	−0.0810549	−	1.07770i
$532$		0			0
$533$	10626.9	−	6135.43i	0.863604	−	0.498602i
$534$		0			0
$535$		−	453.672i		−	0.0366616i
$536$		0			0
$537$	5260.55	+	1199.94i	0.422736	+	0.0964267i
$538$		0			0
$539$	14073.1	−	13468.0i	1.12462	−	1.07627i
$540$		0			0
$541$	−1588.46	+	2751.29i	−0.126235	+	0.218645i	−0.922215	−	0.386678i	$-0.873623\pi$
$541$	−1588.46	+	2751.29i	−0.126235	+	0.218645i	0.795980	+	0.605323i	$0.206956\pi$
$542$		0			0
$543$	−11274.9	+	12154.8i	−0.891074	+	0.960609i
$544$		0			0
$545$	−6600.91	+	11433.1i	−0.518811	+	0.898607i
$546$		0			0
$547$	1380.00	+	2390.24i	0.107870	+	0.186836i	0.914907	−	0.403665i	$-0.132264\pi$
$547$	1380.00	+	2390.24i	0.107870	+	0.186836i	−0.807037	+	0.590500i	$0.798930\pi$
$548$		0			0
$549$	18780.9	−	1412.53i	1.46001	−	0.109809i
$550$		0			0
$551$	17271.4			1.33536
$552$		0			0
$553$	−7008.40	+	5256.46i	−0.538929	+	0.404209i
$554$		0			0
$555$	12453.1	+	11551.6i	0.952437	+	0.883494i
$556$		0			0
$557$	−5282.58	+	3049.90i	−0.401849	+	0.232008i	−0.687282	−	0.726391i	$-0.741196\pi$
$557$	−5282.58	+	3049.90i	−0.401849	+	0.232008i	0.285432	+	0.958399i	$0.407863\pi$
$558$		0			0
$559$		−	16829.5i		−	1.27337i
$560$		0			0
$561$	9344.73	−	10074.0i	0.703271	−	0.758151i
$562$		0			0
$563$	22413.0			1.67779			0.838894	−	0.544294i	$-0.183203\pi$
$563$	22413.0			1.67779			0.838894	+	0.544294i	$0.183203\pi$
$564$		0			0
$565$			2060.08i			0.153395i
$566$		0			0
$567$	−9467.69	+	9625.34i	−0.701244	+	0.712921i
$568$		0			0
$569$			5204.40i			0.383444i	0.981449	+	0.191722i	$0.0614072\pi$
$569$			5204.40i			0.383444i	−0.981449	+	0.191722i	$0.938593\pi$
$570$		0			0
$571$	−12697.2			−0.930583			−0.465292	−	0.885158i	$-0.654050\pi$
$571$	−12697.2			−0.930583			−0.465292	+	0.885158i	$0.654050\pi$
$572$		0			0
$573$	6616.30	−	7132.61i	0.482373	−	0.520016i
$574$		0			0
$575$		−	13510.1i		−	0.979847i
$576$		0			0
$577$	3115.61	−	1798.80i	0.224792	−	0.129783i	−0.383375	−	0.923593i	$-0.625238\pi$
$577$	3115.61	−	1798.80i	0.224792	−	0.129783i	0.608167	+	0.793809i	$0.291905\pi$
$578$		0			0
$579$	6072.31	+	5632.76i	0.435849	+	0.404299i
$580$		0			0
$581$	−7388.78	−	3156.04i	−0.527605	−	0.225361i
$582$		0			0
$583$	−5472.55			−0.388765
$584$		0			0
$585$	−9617.79	+	723.363i	−0.679738	+	0.0511238i
$586$		0			0
$587$	1151.11	+	1993.78i	0.0809393	+	0.140191i	0.903654	−	0.428264i	$-0.140875\pi$
$587$	1151.11	+	1993.78i	0.0809393	+	0.140191i	−0.822714	+	0.568455i	$0.807541\pi$
$588$		0			0
$589$	−4656.61	+	8065.49i	−0.325760	+	0.564232i
$590$		0			0
$591$	−15261.5	+	16452.4i	−1.06222	+	1.14511i
$592$		0			0
$593$	−10090.0	+	17476.5i	−0.698732	+	1.21024i	0.270174	+	0.962812i	$0.412919\pi$
$593$	−10090.0	+	17476.5i	−0.698732	+	1.21024i	−0.968906	+	0.247428i	$0.920415\pi$
$594$		0			0
$595$	778.391	+	6459.94i	0.0536318	+	0.445095i
$596$		0			0
$597$	17484.2	+	3988.16i	1.19862	+	0.273408i
$598$		0			0
$599$			7886.74i			0.537969i	0.963144	+	0.268985i	$0.0866881\pi$
$599$			7886.74i			0.537969i	−0.963144	+	0.268985i	$0.913312\pi$
$600$		0			0
$601$	−17585.9	+	10153.2i	−1.19358	+	0.689115i	−0.959117	−	0.283009i	$-0.908667\pi$
$601$	−17585.9	+	10153.2i	−1.19358	+	0.689115i	−0.234465	+	0.972124i	$0.575334\pi$
$602$		0			0
$603$	−27.1637	−	361.167i	−0.00183448	−	0.0243911i
$604$		0			0
$605$	7145.76	−	12376.8i	0.480192	−	0.831718i
$606$		0			0
$607$	−17341.6	+	10012.2i	−1.15960	+	0.669494i	−0.951207	−	0.308552i	$-0.900155\pi$
$607$	−17341.6	+	10012.2i	−1.15960	+	0.669494i	−0.208389	+	0.978046i	$0.566822\pi$
$608$		0			0
$609$	15372.7	−	6851.21i	1.02288	−	0.455870i
$610$		0			0
$611$	−19226.9	−	11100.7i	−1.27306	−	0.734999i
$612$		0			0
$613$	−2502.05	−	4333.67i	−0.164856	−	0.285539i	0.771748	−	0.635928i	$-0.219383\pi$
$613$	−2502.05	−	4333.67i	−0.164856	−	0.285539i	−0.936604	+	0.350389i	$0.886049\pi$
$614$		0			0
$615$	7449.51	+	6910.26i	0.488444	+	0.453087i
$616$		0			0
$617$	−21325.2	−	12312.1i	−1.39144	−	0.803349i	−0.397966	−	0.917400i	$-0.630284\pi$
$617$	−21325.2	−	12312.1i	−1.39144	−	0.803349i	−0.993475	+	0.114052i	$0.963617\pi$
$618$		0			0
$619$	−14877.7	−	8589.64i	−0.966050	−	0.557749i	−0.0680204	−	0.997684i	$-0.521668\pi$
$619$	−14877.7	−	8589.64i	−0.966050	−	0.557749i	−0.898030	+	0.439935i	$0.855002\pi$
$620$		0			0
$621$	−4138.78	+	27534.6i	−0.267445	+	1.77927i
$622$		0			0
$623$	−2709.29	−	22484.7i	−0.174230	−	1.44595i
$624$		0			0
$625$	1240.97	+	2149.42i	0.0794218	+	0.137563i
$626$		0			0
$627$	−6480.93	+	28412.5i	−0.412797	+	1.80971i
$628$		0			0
$629$	20174.3			1.27886
$630$		0			0
$631$	−26068.5			−1.64464			−0.822321	−	0.569024i	$-0.807321\pi$
$631$	−26068.5			−1.64464			−0.822321	+	0.569024i	$0.807321\pi$
$632$		0			0
$633$	−12200.9	+	3765.27i	−0.766100	+	0.236424i
$634$		0			0
$635$	3467.25	+	6005.45i	0.216683	+	0.375306i
$636$		0			0
$637$	−11732.5	+	11228.0i	−0.729760	+	0.698385i
$638$		0			0
$639$	21193.9	−	1594.02i	1.31208	−	0.0986829i
$640$		0			0
$641$	4042.88	+	2334.16i	0.249117	+	0.143828i	0.619360	−	0.785107i	$-0.287392\pi$
$641$	4042.88	+	2334.16i	0.249117	+	0.143828i	−0.370243	+	0.928935i	$0.620726\pi$
$642$		0			0
$643$	13001.3	+	7506.30i	0.797388	+	0.460372i	0.842557	−	0.538607i	$-0.181049\pi$
$643$	13001.3	+	7506.30i	0.797388	+	0.460372i	−0.0451689	+	0.998979i	$0.514383\pi$
$644$		0			0
$645$	13316.2	−	4109.48i	0.812908	−	0.250869i
$646$		0			0
$647$	−6082.70	−	10535.5i	−0.369607	−	0.640177i	0.619897	−	0.784683i	$-0.287174\pi$
$647$	−6082.70	−	10535.5i	−0.369607	−	0.640177i	−0.989504	+	0.144506i	$0.953841\pi$
$648$		0			0
$649$	−24088.4	−	13907.4i	−1.45694	−	0.841163i
$650$		0			0
$651$	−945.274	+	9026.00i	−0.0569097	+	0.543405i
$652$		0			0
$653$	−6720.08	+	3879.84i	−0.402721	+	0.232511i	−0.687658	−	0.726035i	$-0.741361\pi$
$653$	−6720.08	+	3879.84i	−0.402721	+	0.232511i	0.284936	+	0.958546i	$0.408028\pi$
$654$		0			0
$655$	3403.54	−	5895.11i	0.203034	−	0.351666i
$656$		0			0
$657$	−12750.7	−	18691.0i	−0.757156	−	1.10990i
$658$		0			0
$659$	−11524.2	+	6653.50i	−0.681213	+	0.393298i	−0.800312	−	0.599584i	$-0.795333\pi$
$659$	−11524.2	+	6653.50i	−0.681213	+	0.393298i	0.119099	+	0.992882i	$0.461999\pi$
$660$		0			0
$661$		−	15551.5i		−	0.915105i	−0.889183	−	0.457552i	$-0.848726\pi$
$661$		−	15551.5i		−	0.915105i	0.889183	−	0.457552i	$-0.151274\pi$
$662$		0			0
$663$	−7790.54	+	8398.48i	−0.456349	+	0.491961i
$664$		0			0
$665$	−8280.01	−	11039.7i	−0.482835	−	0.643760i
$666$		0			0
$667$	17354.7	−	30059.2i	1.00746	−	1.74497i
$668$		0			0
$669$	−19328.8	−	4408.92i	−1.11703	−	0.254796i
$670$		0			0
$671$	19807.2	−	34307.1i	1.13956	−	1.97378i
$672$		0			0
$673$	−4487.12	−	7771.92i	−0.257007	−	0.445149i	0.708432	−	0.705779i	$-0.249403\pi$
$673$	−4487.12	−	7771.92i	−0.257007	−	0.445149i	−0.965439	+	0.260630i	$0.916070\pi$
$674$		0			0
$675$	3492.74	+	8888.79i	0.199164	+	0.506859i
$676$		0			0
$677$	22542.8			1.27975			0.639875	−	0.768479i	$-0.278986\pi$
$677$	22542.8			1.27975			0.639875	+	0.768479i	$0.278986\pi$
$678$		0			0
$679$	−1463.32	+	3425.85i	−0.0827053	+	0.193626i
$680$		0			0
$681$	−19058.3	+	5881.53i	−1.07242	+	0.330956i
$682$		0			0
$683$	15772.5	−	9106.24i	0.883626	−	0.510162i	0.0117740	−	0.999931i	$-0.496252\pi$
$683$	15772.5	−	9106.24i	0.883626	−	0.510162i	0.871852	+	0.489769i	$0.162919\pi$
$684$		0			0
$685$		−	8506.72i		−	0.474489i
$686$		0			0
$687$	13047.4	+	2976.14i	0.724585	+	0.165279i
$688$		0			0
$689$	4562.37			0.252268
$690$		0			0
$691$		−	3525.57i		−	0.194094i	−0.995280	−	0.0970469i	$-0.969060\pi$
$691$		−	3525.57i		−	0.194094i	0.995280	−	0.0970469i	$-0.0309397\pi$
$692$		0			0
$693$	5502.20	+	27859.8i	0.301604	+	1.52714i
$694$		0			0
$695$			5429.05i			0.296310i
$696$		0			0
$697$	12068.4			0.655844
$698$		0			0
$699$	−6331.34	−	20515.9i	−0.342594	−	1.11013i
$700$		0			0
$701$			20879.2i			1.12496i	0.826811	+	0.562480i	$0.190153\pi$
$701$			20879.2i			1.12496i	−0.826811	+	0.562480i	$0.809847\pi$
$702$		0			0
$703$	−37054.6	+	21393.5i	−1.98797	+	1.14775i
$704$		0			0
$705$	4088.43	−	17923.7i	0.218410	−	0.957512i
$706$		0			0
$707$	−1109.71	−	9209.58i	−0.0590310	−	0.489904i
$708$		0			0
$709$	29582.8			1.56700			0.783502	−	0.621389i	$-0.213431\pi$
$709$	29582.8			1.56700			0.783502	+	0.621389i	$0.213431\pi$
$710$		0			0
$711$	−957.871	−	12735.8i	−0.0505246	−	0.671771i
$712$		0			0
$713$	9358.14	+	16208.8i	0.491536	+	0.851365i
$714$		0			0
$715$	−10143.4	+	17568.8i	−0.530547	+	0.918934i
$716$		0			0
$717$	7994.58	+	25905.4i	0.416406	+	1.34931i
$718$		0			0
$719$	−6560.66	+	11363.4i	−0.340294	+	0.589406i	−0.984487	−	0.175456i	$-0.943860\pi$
$719$	−6560.66	+	11363.4i	−0.340294	+	0.589406i	0.644193	+	0.764863i	$0.277193\pi$
$720$		0			0
$721$	−13599.9	+	31839.5i	−0.702479	+	1.64461i
$722$		0			0
$723$	−8375.29	−	27139.0i	−0.430817	−	1.39600i
$724$		0			0
$725$		−	11905.2i		−	0.609860i
$726$		0			0
$727$	−4229.65	+	2441.99i	−0.215776	+	0.124578i	−0.603993	−	0.796990i	$-0.706424\pi$
$727$	−4229.65	+	2441.99i	−0.215776	+	0.124578i	0.388217	+	0.921568i	$0.373091\pi$
$728$		0			0
$729$	−4395.41	−	19186.0i	−0.223310	−	0.974747i
$730$		0			0
$731$	8275.93	−	14334.3i	0.418737	−	0.725273i
$732$		0			0
$733$	−8789.04	+	5074.36i	−0.442879	+	0.255697i	−0.704818	−	0.709388i	$-0.748971\pi$
$733$	−8789.04	+	5074.36i	−0.442879	+	0.255697i	0.261939	+	0.965084i	$0.415638\pi$
$734$		0			0
$735$	−11749.0	−	6541.52i	−0.589615	−	0.328283i
$736$		0			0
$737$	−659.745	−	380.904i	−0.0329742	−	0.0190377i
$738$		0			0
$739$	−10276.2	−	17799.0i	−0.511526	−	0.885989i	−0.999911	−	0.0133603i	$-0.995747\pi$
$739$	−10276.2	−	17799.0i	−0.511526	−	0.885989i	0.488385	−	0.872628i	$-0.337586\pi$
$740$		0			0
$741$	5403.04	−	23687.0i	0.267862	−	1.17431i
$742$		0			0
$743$	−23075.7	−	13322.7i	−1.13939	−	0.657825i	−0.193108	−	0.981178i	$-0.561857\pi$
$743$	−23075.7	−	13322.7i	−1.13939	−	0.657825i	−0.946279	+	0.323352i	$0.895190\pi$
$744$		0			0
$745$	1937.48	+	1118.61i	0.0952805	+	0.0550102i
$746$		0			0
$747$	9676.23	−	6600.97i	0.473942	−	0.323316i
$748$		0			0
$749$	1105.60	−	133.220i	0.0539358	−	0.00649900i
$750$		0			0
$751$	−4790.97	−	8298.21i	−0.232790	−	0.403204i	0.725838	−	0.687865i	$-0.241452\pi$
$751$	−4790.97	−	8298.21i	−0.232790	−	0.403204i	−0.958628	+	0.284662i	$0.908119\pi$
$752$		0			0
$753$	−5506.70	−	5108.09i	−0.266501	−	0.247210i
$754$		0			0
$755$	4583.76			0.220954
$756$		0			0
$757$	3537.16			0.169829			0.0849144	−	0.996388i	$-0.472938\pi$
$757$	3537.16			0.169829			0.0849144	+	0.996388i	$0.472938\pi$
$758$		0			0
$759$	42937.0	+	39829.0i	2.05338	+	1.90474i
$760$		0			0
$761$	−7689.31	−	13318.3i	−0.366277	−	0.634411i	0.622703	−	0.782458i	$-0.286035\pi$
$761$	−7689.31	−	13318.3i	−0.366277	−	0.634411i	−0.988980	+	0.148047i	$0.952701\pi$
$762$		0			0
$763$	−29801.0	−	12729.2i	−1.41398	−	0.603968i
$764$		0			0
$765$	−8547.55	−	4113.44i	−0.403970	−	0.194408i
$766$		0			0
$767$	20082.1	+	11594.4i	0.945401	+	0.545827i
$768$		0			0
$769$	3181.18	+	1836.65i	0.149176	+	0.0861267i	0.572730	−	0.819744i	$-0.305884\pi$
$769$	3181.18	+	1836.65i	0.149176	+	0.0861267i	−0.423554	+	0.905871i	$0.639218\pi$
$770$		0			0
$771$	856.116	−	3753.22i	0.0399900	−	0.175317i
$772$		0			0
$773$	−3149.06	−	5454.33i	−0.146525	−	0.253788i	0.783416	−	0.621498i	$-0.213475\pi$
$773$	−3149.06	−	5454.33i	−0.146525	−	0.253788i	−0.929941	+	0.367709i	$0.880142\pi$
$774$		0			0
$775$	5559.56	+	3209.81i	0.257684	+	0.148774i
$776$		0			0
$777$	−24494.6	+	33740.4i	−1.13094	+	1.55782i
$778$		0			0
$779$	−22166.3	+	12797.7i	−1.01950	+	0.588608i
$780$		0			0
$781$	22352.2	−	38715.1i	1.02410	−	1.77379i
$782$		0			0
$783$	−3647.11	+	24263.6i	−0.166459	+	1.10742i
$784$		0			0
$785$	1283.32	−	740.927i	0.0583488	−	0.0336877i
$786$		0			0
$787$		−	3822.89i		−	0.173153i	−0.996245	−	0.0865765i	$-0.972407\pi$
$787$		−	3822.89i		−	0.173153i	0.996245	−	0.0865765i	$-0.0275927\pi$
$788$		0			0
$789$	5579.94	+	18081.1i	0.251776	+	0.815847i
$790$		0			0
$791$	−5020.45	+	604.940i	−0.225672	+	0.0271924i
$792$		0			0
$793$	−16512.9	+	28601.2i	−0.739459	+	1.28078i
$794$		0			0
$795$	1114.05	+	3609.94i	0.0496998	+	0.161046i
$796$		0			0
$797$	−7152.20	+	12388.0i	−0.317872	+	0.550570i	−0.980044	−	0.198782i	$-0.936301\pi$
$797$	−7152.20	+	12388.0i	−0.317872	+	0.550570i	0.662172	+	0.749352i	$0.269635\pi$
$798$		0			0
$799$	−10917.5	−	18909.7i	−0.483397	−	0.837268i
$800$		0			0
$801$	29750.8	+	14317.4i	1.31235	+	0.631559i
$802$		0			0
$803$	−47590.3			−2.09144
$804$		0			0
$805$	−27533.5	+	3317.65i	−1.20550	+	0.145257i
$806$		0			0
$807$	4383.07	−	19215.4i	0.191191	−	0.838186i
$808$		0			0
$809$	−20679.9	+	11939.6i	−0.898724	+	0.518878i	−0.876786	−	0.480881i	$-0.840317\pi$
$809$	−20679.9	+	11939.6i	−0.898724	+	0.518878i	−0.0219379	+	0.999759i	$0.506984\pi$
$810$		0			0
$811$		−	28307.9i		−	1.22568i	−0.790208	−	0.612839i	$-0.790028\pi$
$811$		−	28307.9i		−	1.22568i	0.790208	−	0.612839i	$-0.209972\pi$
$812$		0			0
$813$	−4623.05	−	14980.4i	−0.199431	−	0.646230i
$814$		0			0
$815$	12013.6			0.516342
$816$		0			0
$817$			35104.2i			1.50323i
$818$		0			0
$819$	−4587.09	−	23226.3i	−0.195709	−	0.990954i
$820$		0			0
$821$		−	36809.7i		−	1.56476i	−0.622802	−	0.782380i	$-0.714006\pi$
$821$		−	36809.7i		−	1.56476i	0.622802	−	0.782380i	$-0.285994\pi$
$822$		0			0
$823$	3830.52			0.162240			0.0811201	−	0.996704i	$-0.474150\pi$
$823$	3830.52			0.162240			0.0811201	+	0.996704i	$0.474150\pi$
$824$		0			0
$825$	19584.8	+	4467.32i	0.826492	+	0.188524i
$826$		0			0
$827$		−	18522.9i		−	0.778843i	−0.921060	−	0.389422i	$-0.872675\pi$
$827$		−	18522.9i		−	0.778843i	0.921060	−	0.389422i	$-0.127325\pi$
$828$		0			0
$829$	2362.46	−	1363.97i	0.0989767	−	0.0571442i	−0.449695	−	0.893182i	$-0.648467\pi$
$829$	2362.46	−	1363.97i	0.0989767	−	0.0571442i	0.548671	+	0.836038i	$0.315134\pi$
$830$		0			0
$831$	16546.7	−	5106.44i	0.690734	−	0.213165i
$832$		0			0
$833$	−15514.4	+	3793.90i	−0.645308	+	0.157804i
$834$		0			0
$835$	11411.9			0.472963
$836$		0			0
$837$	−10347.5	−	8244.97i	−0.427312	−	0.340487i
$838$		0			0
$839$	−19190.7	−	33239.3i	−0.789675	−	1.36776i	−0.926166	−	0.377116i	$-0.876916\pi$
$839$	−19190.7	−	33239.3i	−0.789675	−	1.36776i	0.136491	−	0.990641i	$-0.456418\pi$
$840$		0			0
$841$	3098.54	−	5366.83i	0.127047	−	0.220051i
$842$		0			0
$843$	−24398.2	−	5565.28i	−0.996821	−	0.227376i
$844$		0			0
$845$	168.184	−	291.303i	0.00684699	−	0.0118593i
$846$		0			0
$847$	32260.8	+	13779.9i	1.30873	+	0.559011i
$848$		0			0
$849$	5425.12	−	5848.47i	0.219305	−	0.236418i
$850$		0			0
$851$			85986.6i			3.46367i
$852$		0			0
$853$	18992.7	−	10965.5i	0.762366	−	0.440152i	−0.0677784	−	0.997700i	$-0.521591\pi$
$853$	18992.7	−	10965.5i	0.762366	−	0.440152i	0.830145	+	0.557548i	$0.188258\pi$
$854$		0			0
$855$	20061.5	−	1508.84i	0.802443	−	0.0603525i
$856$		0			0
$857$	14458.2	−	25042.3i	0.576292	−	0.998167i	−0.419608	−	0.907705i	$-0.637833\pi$
$857$	14458.2	−	25042.3i	0.576292	−	0.998167i	0.995900	−	0.0904612i	$-0.0288341\pi$
$858$		0			0
$859$	−25092.2	+	14487.0i	−0.996664	+	0.575424i	−0.907259	−	0.420571i	$-0.861830\pi$
$859$	−25092.2	+	14487.0i	−0.996664	+	0.575424i	−0.0894041	+	0.995995i	$0.528496\pi$
$860$		0			0
$861$	−14652.9	+	20183.7i	−0.579986	+	0.798908i
$862$		0			0
$863$	38744.7	+	22369.2i	1.52825	+	0.882338i	0.999435	+	0.0336031i	$0.0106982\pi$
$863$	38744.7	+	22369.2i	1.52825	+	0.882338i	0.528819	+	0.848735i	$0.322635\pi$
$864$		0			0
$865$	4442.83	+	7695.21i	0.174637	+	0.302480i
$866$		0			0
$867$	13628.1	−	4205.71i	0.533833	−	0.164744i
$868$		0			0
$869$	−23264.5	−	13431.8i	−0.908164	−	0.524329i
$870$		0			0
$871$	550.018	+	317.553i	0.0213968	+	0.0123535i
$872$		0			0
$873$	−3060.57	−	4486.43i	−0.118654	−	0.173932i
$874$		0			0
$875$	−21583.1	+	16187.8i	−0.833875	+	0.625425i
$876$		0			0
$877$	3298.63	+	5713.40i	0.127009	+	0.219986i	0.922516	−	0.385958i	$-0.126129\pi$
$877$	3298.63	+	5713.40i	0.127009	+	0.219986i	−0.795507	+	0.605944i	$0.792796\pi$
$878$		0			0
$879$	−6081.05	+	1876.65i	−0.233343	+	0.0720113i
$880$		0			0
$881$	42441.4			1.62303			0.811513	−	0.584334i	$-0.198644\pi$
$881$	42441.4			1.62303			0.811513	+	0.584334i	$0.198644\pi$
$882$		0			0
$883$	36843.7			1.40418			0.702088	−	0.712090i	$-0.252251\pi$
$883$	36843.7			1.40418			0.702088	+	0.712090i	$0.252251\pi$
$884$		0			0
$885$	−4270.28	+	18720.9i	−0.162196	+	0.711071i
$886$		0			0
$887$	−8002.33	−	13860.4i	−0.302922	−	0.524676i	0.673874	−	0.738846i	$-0.264629\pi$
$887$	−8002.33	−	13860.4i	−0.302922	−	0.524676i	−0.976797	+	0.214169i	$0.931296\pi$
$888$		0			0
$889$	−13617.2	+	10213.2i	−0.513731	+	0.385310i
$890$		0			0
$891$	−38546.7	−	15104.4i	−1.44934	−	0.567921i
$892$		0			0
$893$	40104.9	+	23154.6i	1.50286	+	0.867679i
$894$		0			0
$895$	−6785.04	−	3917.35i	−0.253407	−	0.146304i
$896$		0			0
$897$	−35795.9	−	33204.7i	−1.33243	−	1.23598i
$898$		0			0
$899$	8246.45	+	14283.3i	0.305934	+	0.529893i
$900$		0			0
$901$	3885.94	+	2243.55i	0.143684	+	0.0829562i
$902$		0			0
$903$	13925.1	+	31245.1i	0.513178	+	1.15146i
$904$		0			0
$905$	20848.0	−	12036.6i	0.765759	−	0.442111i
$906$		0			0
$907$	−4646.36	+	8047.73i	−0.170099	+	0.294620i	−0.938454	−	0.345403i	$-0.887742\pi$
$907$	−4646.36	+	8047.73i	−0.170099	+	0.294620i	0.768355	+	0.640024i	$0.221075\pi$
$908$		0			0
$909$	12185.8	+	5864.30i	0.444638	+	0.213979i
$910$		0			0
$911$	−6700.78	+	3868.70i	−0.243696	+	0.140698i	−0.616874	−	0.787062i	$-0.711601\pi$
$911$	−6700.78	+	3868.70i	−0.243696	+	0.140698i	0.373178	+	0.927760i	$0.378268\pi$
$912$		0			0
$913$		−	24637.3i		−	0.893073i
$914$		0			0
$915$	−26662.6	−	6081.79i	−0.963322	−	0.219735i
$916$		0			0
$917$	15365.9	+	6563.39i	0.553355	+	0.236360i
$918$		0			0
$919$	1597.63	−	2767.18i	0.0573461	−	0.0993263i	−0.835927	−	0.548840i	$-0.815069\pi$
$919$	1597.63	−	2767.18i	0.0573461	−	0.0993263i	0.893273	+	0.449514i	$0.148403\pi$
$920$		0			0
$921$	−9490.52	+	10231.1i	−0.339548	+	0.366044i
$922$		0			0
$923$	−18634.6	+	32276.1i	−0.664535	+	1.15101i
$924$		0			0
$925$	14746.6	+	25541.8i	0.524178	+	0.907902i
$926$		0			0
$927$	−28444.7	−	41696.5i	−1.00782	−	1.47734i
$928$		0			0
$929$	44410.3			1.56841			0.784206	−	0.620500i	$-0.213070\pi$
$929$	44410.3			1.56841			0.784206	+	0.620500i	$0.213070\pi$
$930$		0			0
$931$	24472.4	−	23420.3i	0.861495	−	0.824456i
$932$		0			0
$933$	−1942.21	−	1801.62i	−0.0681514	−	0.0632182i
$934$		0			0
$935$	−17279.0	+	9976.04i	−0.604368	+	0.348932i
$936$		0			0
$937$			4561.31i			0.159030i	0.996834	+	0.0795152i	$0.0253372\pi$
$937$			4561.31i			0.159030i	−0.996834	+	0.0795152i	$0.974663\pi$
$938$		0			0
$939$	−8781.74	+	9467.03i	−0.305198	+	0.329015i
$940$		0			0
$941$	21459.0			0.743406			0.371703	−	0.928352i	$-0.378774\pi$
$941$	21459.0			0.743406			0.371703	+	0.928352i	$0.378774\pi$
$942$		0			0
$943$			51437.8i			1.77629i
$944$		0			0
$945$	17257.5	−	9300.95i	0.594060	−	0.320169i
$946$		0			0
$947$		−	53684.7i		−	1.84215i	−0.389384	−	0.921075i	$-0.627312\pi$
$947$		−	53684.7i		−	1.84215i	0.389384	−	0.921075i	$-0.372688\pi$
$948$		0			0
$949$	39675.3			1.35713
$950$		0			0
$951$	−25307.1	+	27282.0i	−0.862924	+	0.930262i
$952$		0			0
$953$		−	14243.0i		−	0.484131i	−0.970260	−	0.242065i	$-0.922175\pi$
$953$		−	14243.0i		−	0.484131i	0.970260	−	0.242065i	$-0.0778248\pi$
$954$		0			0
$955$	−12234.0	+	7063.28i	−0.414536	+	0.239332i
$956$		0			0
$957$	37836.4	+	35097.5i	1.27803	+	1.18552i
$958$		0			0
$959$	20731.0	−	2497.98i	0.698059	−	0.0841127i
$960$		0			0
$961$	20897.6			0.701472
$962$		0			0
$963$	−704.006	+	1462.89i	−0.0235579	+	0.0489523i
$964$		0			0
$965$	−6013.29	−	10415.3i	−0.200595	−	0.347442i
$966$		0			0
$967$	5390.06	−	9335.85i	0.179248	−	0.310466i	−0.762375	−	0.647135i	$-0.775967\pi$
$967$	5390.06	−	9335.85i	0.179248	−	0.310466i	0.941623	+	0.336669i	$0.109300\pi$
$968$		0			0
$969$	16250.1	−	17518.2i	0.538729	−	0.580768i
$970$		0			0
$971$	−21692.8	+	37573.0i	−0.716945	+	1.24179i	0.245259	+	0.969458i	$0.421127\pi$
$971$	−21692.8	+	37573.0i	−0.716945	+	1.24179i	−0.962204	+	0.272328i	$0.912206\pi$
$972$		0			0
$973$	−13230.7	+	1594.23i	−0.435926	+	0.0525269i
$974$		0			0
$975$	−16327.5	−	3724.33i	−0.536307	−	0.122332i
$976$		0			0
$977$		−	44004.2i		−	1.44096i	−0.693476	−	0.720480i	$-0.743922\pi$
$977$		−	44004.2i		−	1.44096i	0.693476	−	0.720480i	$-0.256078\pi$
$978$		0			0
$979$	60141.8	−	34722.9i	1.96337	−	1.13355i
$980$		0			0
$981$	39026.9	−	26623.5i	1.27017	−	0.866487i
$982$		0			0
$983$	7201.38	−	12473.2i	0.233661	−	0.404712i	−0.725222	−	0.688515i	$-0.758263\pi$
$983$	7201.38	−	12473.2i	0.233661	−	0.404712i	0.958883	+	0.283803i	$0.0915962\pi$
$984$		0			0
$985$	28219.4	−	16292.5i	0.912839	−	0.527028i
$986$		0			0
$987$	44880.9	+	4700.28i	1.44739	+	0.151582i
$988$		0			0
$989$	61095.6	+	35273.6i	1.96433	+	1.13411i
$990$		0			0
$991$	3574.74	+	6191.63i	0.114587	+	0.198470i	0.917614	−	0.397472i	$-0.130112\pi$
$991$	3574.74	+	6191.63i	0.114587	+	0.198470i	−0.803028	+	0.595942i	$0.796779\pi$
$992$		0			0
$993$	27816.5	+	25803.0i	0.888954	+	0.824606i
$994$		0			0
$995$	−22551.0	−	13019.8i	−0.718509	−	0.414831i
$996$		0			0
$997$	−36180.2	−	20888.7i	−1.14929	−	0.663541i	−0.200574	−	0.979679i	$-0.564281\pi$
$997$	−36180.2	−	20888.7i	−1.14929	−	0.663541i	−0.948713	+	0.316138i	$0.897614\pi$
$998$		0			0
$999$	−22229.9	−	56573.5i	−0.704027	−	1.79170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.20	✓	48
3.2	odd	2		756.4.w.a.341.17		48
7.3	odd	6		252.4.bm.a.185.12	yes	48
9.2	odd	6		252.4.bm.a.173.12	yes	48
9.7	even	3		756.4.bm.a.89.17		48
21.17	even	6		756.4.bm.a.17.17		48
63.38	even	6	inner	252.4.w.a.101.20	yes	48
63.52	odd	6		756.4.w.a.521.17		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.20	✓	48	1.1	even	1	trivial
252.4.w.a.101.20	yes	48	63.38	even	6	inner
252.4.bm.a.173.12	yes	48	9.2	odd	6
252.4.bm.a.185.12	yes	48	7.3	odd	6
756.4.w.a.341.17		48	3.2	odd	2
756.4.w.a.521.17		48	63.52	odd	6
756.4.bm.a.17.17		48	21.17	even	6
756.4.bm.a.89.17		48	9.7	even	3

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.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.80953 + 3.53377i) q^{3} +(-3.77250 - 6.53416i) q^{5} +(14.8160 - 11.1124i) q^{7} +(2.02498 + 26.9240i) q^{9} +O(q^{10})\)	\(q+(3.80953 + 3.53377i) q^{3} +(-3.77250 - 6.53416i) q^{5} +(14.8160 - 11.1124i) q^{7} +(2.02498 + 26.9240i) q^{9} +(49.1821 + 28.3953i) q^{11} +(-41.0023 - 23.6727i) q^{13} +(8.71876 - 38.2232i) q^{15} +(-23.2821 - 40.3258i) q^{17} +(85.5255 + 49.3782i) q^{19} +(95.7106 + 10.0236i) q^{21} +(171.876 - 99.2327i) q^{23} +(34.0365 - 58.9530i) q^{25} +(-87.4288 + 109.723i) q^{27} +(151.458 - 87.4444i) q^{29} +94.3050i q^{31} +(87.0181 + 281.971i) q^{33} +(-128.503 - 54.8890i) q^{35} +(-216.629 + 375.212i) q^{37} +(-72.5455 - 235.074i) q^{39} +(-129.589 + 224.454i) q^{41} +(177.731 + 307.840i) q^{43} +(168.286 - 114.802i) q^{45} +468.923 q^{47} +(96.0304 - 329.283i) q^{49} +(53.8082 - 235.896i) q^{51} +(-83.4534 + 48.1818i) q^{53} -428.485i q^{55} +(151.321 + 490.335i) q^{57} -489.780 q^{59} -697.552i q^{61} +(329.191 + 376.404i) q^{63} +357.220i q^{65} -13.4143 q^{67} +(1005.43 + 229.340i) q^{69} -787.178i q^{71} +(-725.727 + 418.998i) q^{73} +(337.989 - 104.306i) q^{75} +(1044.22 - 125.824i) q^{77} -473.028 q^{79} +(-720.799 + 109.041i) q^{81} +(-216.914 - 375.705i) q^{83} +(-175.664 + 304.258i) q^{85} +(885.992 + 202.096i) q^{87} +(611.420 - 1059.01i) q^{89} +(-870.551 + 104.897i) q^{91} +(-333.252 + 359.257i) q^{93} -745.117i q^{95} +(-174.198 + 100.573i) q^{97} +(-664.921 + 1381.68i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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