LMFDB - Embedded newform 252.4.bm.a.173.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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, 1, 5]))

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

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (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			173.15
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.56423 - 4.51937i) q^{3} +17.7911 q^{5} +(-5.94198 - 17.5412i) q^{7} +(-13.8494 - 23.1774i) q^{9} +O(q^{10})$	\(q+(2.56423 - 4.51937i) q^{3} +17.7911 q^{5} +(-5.94198 - 17.5412i) q^{7} +(-13.8494 - 23.1774i) q^{9} +13.5659i q^{11} +(45.1112 - 26.0449i) q^{13} +(45.6205 - 80.4044i) q^{15} +(-6.56910 - 11.3780i) q^{17} +(-53.6675 - 30.9849i) q^{19} +(-94.5117 - 18.1257i) q^{21} +151.165i q^{23} +191.522 q^{25} +(-140.261 + 3.15817i) q^{27} +(133.122 + 76.8580i) q^{29} +(-83.7735 - 48.3666i) q^{31} +(61.3095 + 34.7863i) q^{33} +(-105.714 - 312.076i) q^{35} +(135.685 - 235.014i) q^{37} +(-2.03112 - 270.659i) q^{39} +(-171.369 - 296.821i) q^{41} +(-127.826 + 221.401i) q^{43} +(-246.396 - 412.352i) q^{45} +(-15.5635 - 26.9567i) q^{47} +(-272.386 + 208.459i) q^{49} +(-68.2662 + 0.512293i) q^{51} +(324.401 - 187.293i) q^{53} +241.353i q^{55} +(-277.648 + 163.090i) q^{57} +(331.586 - 574.325i) q^{59} +(530.280 - 306.157i) q^{61} +(-324.267 + 380.655i) q^{63} +(802.576 - 463.368i) q^{65} +(-298.821 + 517.573i) q^{67} +(683.171 + 387.623i) q^{69} +265.032i q^{71} +(-886.396 + 511.761i) q^{73} +(491.108 - 865.560i) q^{75} +(237.963 - 80.6086i) q^{77} +(582.924 + 1009.65i) q^{79} +(-345.388 + 641.988i) q^{81} +(177.198 - 306.916i) q^{83} +(-116.871 - 202.427i) q^{85} +(688.706 - 404.546i) q^{87} +(-677.048 + 1172.68i) q^{89} +(-724.909 - 636.544i) q^{91} +(-433.402 + 254.580i) q^{93} +(-954.802 - 551.255i) q^{95} +(326.661 + 188.598i) q^{97} +(314.424 - 187.880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	2.56423	−	4.51937i	0.493487	−	0.869753i
$3$	2.56423	−	4.51937i	0.493487	−	0.869753i
$4$		0			0
$5$	17.7911			1.59128			0.795641	−	0.605769i	$-0.207134\pi$
$5$	17.7911			1.59128			0.795641	+	0.605769i	$0.207134\pi$
$6$		0			0
$7$	−5.94198	−	17.5412i	−0.320837	−	0.947134i
$7$	−5.94198	−	17.5412i	−0.320837	−	0.947134i
$8$		0			0
$9$	−13.8494	−	23.1774i	−0.512941	−	0.858424i
$10$		0			0
$11$			13.5659i			0.371844i	0.982564	+	0.185922i	$0.0595272\pi$
$11$			13.5659i			0.371844i	−0.982564	+	0.185922i	$0.940473\pi$
$12$		0			0
$13$	45.1112	−	26.0449i	0.962430	−	0.555659i	0.0655098	−	0.997852i	$-0.479133\pi$
$13$	45.1112	−	26.0449i	0.962430	−	0.555659i	0.896920	+	0.442193i	$0.145799\pi$
$14$		0			0
$15$	45.6205	−	80.4044i	0.785277	−	1.38402i
$16$		0			0
$17$	−6.56910	−	11.3780i	−0.0937200	−	0.162328i	0.815354	−	0.578963i	$-0.196543\pi$
$17$	−6.56910	−	11.3780i	−0.0937200	−	0.162328i	−0.909074	+	0.416635i	$0.863209\pi$
$18$		0			0
$19$	−53.6675	−	30.9849i	−0.648008	−	0.374128i	0.139684	−	0.990196i	$-0.455391\pi$
$19$	−53.6675	−	30.9849i	−0.648008	−	0.374128i	−0.787693	+	0.616068i	$0.788725\pi$
$20$		0			0
$21$	−94.5117	−	18.1257i	−0.982102	−	0.188350i
$22$		0			0
$23$			151.165i			1.37044i	0.728337	+	0.685219i	$0.240294\pi$
$23$			151.165i			1.37044i	−0.728337	+	0.685219i	$0.759706\pi$
$24$		0			0
$25$	191.522			1.53218
$26$		0			0
$27$	−140.261	+	3.15817i	−0.999747	+	0.0225107i
$28$		0			0
$29$	133.122	+	76.8580i	0.852419	+	0.492144i	0.861466	−	0.507815i	$-0.169547\pi$
$29$	133.122	+	76.8580i	0.852419	+	0.492144i	−0.00904753	+	0.999959i	$0.502880\pi$
$30$		0			0
$31$	−83.7735	−	48.3666i	−0.485360	−	0.280223i	0.237287	−	0.971439i	$-0.423742\pi$
$31$	−83.7735	−	48.3666i	−0.485360	−	0.280223i	−0.722648	+	0.691217i	$0.757075\pi$
$32$		0			0
$33$	61.3095	+	34.7863i	0.323413	+	0.183500i
$34$		0			0
$35$	−105.714	−	312.076i	−0.510542	−	1.50716i
$36$		0			0
$37$	135.685	−	235.014i	0.602879	−	1.04422i	−0.389504	−	0.921025i	$-0.627353\pi$
$37$	135.685	−	235.014i	0.602879	−	1.04422i	0.992383	−	0.123192i	$-0.0393133\pi$
$38$		0			0
$39$	−2.03112	−	270.659i	−0.00833948	−	1.11129i
$40$		0			0
$41$	−171.369	−	296.821i	−0.652766	−	1.13062i	−0.982449	−	0.186532i	$-0.940275\pi$
$41$	−171.369	−	296.821i	−0.652766	−	1.13062i	0.329683	−	0.944092i	$-0.393058\pi$
$42$		0			0
$43$	−127.826	+	221.401i	−0.453331	+	0.785193i	−0.998591	−	0.0530747i	$-0.983098\pi$
$43$	−127.826	+	221.401i	−0.453331	+	0.785193i	0.545259	+	0.838267i	$0.316431\pi$
$44$		0			0
$45$	−246.396	−	412.352i	−0.816233	−	1.36599i
$46$		0			0
$47$	−15.5635	−	26.9567i	−0.0483014	−	0.0836605i	0.840864	−	0.541247i	$-0.182047\pi$
$47$	−15.5635	−	26.9567i	−0.0483014	−	0.0836605i	−0.889165	+	0.457586i	$0.848714\pi$
$48$		0			0
$49$	−272.386	+	208.459i	−0.794127	+	0.607751i
$50$		0			0
$51$	−68.2662	+	0.512293i	−0.187435	+	0.00140658i
$52$		0			0
$53$	324.401	−	187.293i	0.840753	−	0.485409i	−0.0167669	−	0.999859i	$-0.505337\pi$
$53$	324.401	−	187.293i	0.840753	−	0.485409i	0.857520	+	0.514450i	$0.172004\pi$
$54$		0			0
$55$			241.353i			0.591709i
$56$		0			0
$57$	−277.648	+	163.090i	−0.645183	+	0.378980i
$58$		0			0
$59$	331.586	−	574.325i	0.731676	−	1.26730i	−0.224490	−	0.974476i	$-0.572072\pi$
$59$	331.586	−	574.325i	0.731676	−	1.26730i	0.956166	−	0.292824i	$-0.0945949\pi$
$60$		0			0
$61$	530.280	−	306.157i	1.11304	−	0.642614i	0.173424	−	0.984847i	$-0.444517\pi$
$61$	530.280	−	306.157i	1.11304	−	0.642614i	0.939615	+	0.342234i	$0.111183\pi$
$62$		0			0
$63$	−324.267	+	380.655i	−0.648473	+	0.761238i
$64$		0			0
$65$	802.576	−	463.368i	1.53150	−	0.884210i
$66$		0			0
$67$	−298.821	+	517.573i	−0.544877	+	0.943755i	0.453737	+	0.891136i	$0.350090\pi$
$67$	−298.821	+	517.573i	−0.544877	+	0.943755i	−0.998615	+	0.0526198i	$0.983243\pi$
$68$		0			0
$69$	683.171	+	387.623i	1.19194	+	0.676294i
$70$		0			0
$71$			265.032i			0.443008i	0.975160	+	0.221504i	$0.0710965\pi$
$71$			265.032i			0.443008i	−0.975160	+	0.221504i	$0.928903\pi$
$72$		0			0
$73$	−886.396	+	511.761i	−1.42116	+	0.820508i	−0.996398	−	0.0847956i	$-0.972976\pi$
$73$	−886.396	+	511.761i	−1.42116	+	0.820508i	−0.424764	+	0.905304i	$0.639643\pi$
$74$		0			0
$75$	491.108	−	865.560i	0.756110	−	1.33262i
$76$		0			0
$77$	237.963	−	80.6086i	0.352187	−	0.119301i
$78$		0			0
$79$	582.924	+	1009.65i	0.830179	+	1.43791i	0.897896	+	0.440207i	$0.145095\pi$
$79$	582.924	+	1009.65i	0.830179	+	1.43791i	−0.0677174	+	0.997705i	$0.521572\pi$
$80$		0			0
$81$	−345.388	+	641.988i	−0.473783	+	0.880641i
$82$		0			0
$83$	177.198	−	306.916i	0.234338	−	0.405885i	−0.724742	−	0.689020i	$-0.758041\pi$
$83$	177.198	−	306.916i	0.234338	−	0.405885i	0.959080	+	0.283135i	$0.0913746\pi$
$84$		0			0
$85$	−116.871	−	202.427i	−0.149135	−	0.258309i
$86$		0			0
$87$	688.706	−	404.546i	0.848702	−	0.498527i
$88$		0			0
$89$	−677.048	+	1172.68i	−0.806370	+	1.39667i	0.108992	+	0.994043i	$0.465238\pi$
$89$	−677.048	+	1172.68i	−0.806370	+	1.39667i	−0.915362	+	0.402631i	$0.868096\pi$
$90$		0			0
$91$	−724.909	−	636.544i	−0.835067	−	0.733275i
$92$		0			0
$93$	−433.402	+	254.580i	−0.483244	+	0.283857i
$94$		0			0
$95$	−954.802	−	551.255i	−1.03116	−	0.595343i
$96$		0			0
$97$	326.661	+	188.598i	0.341932	+	0.197415i	0.661126	−	0.750275i	$-0.270079\pi$
$97$	326.661	+	188.598i	0.341932	+	0.197415i	−0.319194	+	0.947689i	$0.603412\pi$
$98$		0			0
$99$	314.424	−	187.880i	0.319200	−	0.190734i
$100$		0			0
$101$	803.364			0.791462			0.395731	−	0.918366i	$-0.370491\pi$
$101$	803.364			0.791462			0.395731	+	0.918366i	$0.370491\pi$
$102$		0			0
$103$			862.124i			0.824734i	0.911018	+	0.412367i	$0.135298\pi$
$103$			862.124i			0.824734i	−0.911018	+	0.412367i	$0.864702\pi$
$104$		0			0
$105$	−1681.46	−	322.475i	−1.56280	−	0.299718i
$106$		0			0
$107$	1704.57	+	984.134i	1.54007	+	0.889157i	0.998834	+	0.0482833i	$0.0153750\pi$
$107$	1704.57	+	984.134i	1.54007	+	0.889157i	0.541231	+	0.840874i	$0.317958\pi$
$108$		0			0
$109$	229.475	+	397.462i	0.201648	+	0.349265i	0.949060	−	0.315096i	$-0.102037\pi$
$109$	229.475	+	397.462i	0.201648	+	0.349265i	−0.747411	+	0.664362i	$0.768703\pi$
$110$		0			0
$111$	−714.186	−	1215.84i	−0.610698	−	1.03966i
$112$		0			0
$113$	631.086	−	364.357i	0.525376	−	0.303326i	−0.213755	−	0.976887i	$-0.568569\pi$
$113$	631.086	−	364.357i	0.525376	−	0.303326i	0.739132	+	0.673561i	$0.235236\pi$
$114$		0			0
$115$			2689.39i			2.18075i
$116$		0			0
$117$	−1228.42	−	684.855i	−0.970661	−	0.541153i
$118$		0			0
$119$	−160.550	+	182.838i	−0.123677	+	0.140846i
$120$		0			0
$121$	1146.97			0.861732
$122$		0			0
$123$	−1780.87	+	13.3643i	−1.30550	+	0.00979689i
$124$		0			0
$125$	1183.50			0.846845
$126$		0			0
$127$	−2470.13			−1.72589			−0.862947	−	0.505294i	$-0.831384\pi$
$127$	−2470.13			−1.72589			−0.862947	+	0.505294i	$0.831384\pi$
$128$		0			0
$129$	672.816	+	1145.41i	0.459211	+	0.781769i
$130$		0			0
$131$	−248.130			−0.165490			−0.0827450	−	0.996571i	$-0.526369\pi$
$131$	−248.130			−0.165490			−0.0827450	+	0.996571i	$0.526369\pi$
$132$		0			0
$133$	−224.621	+	1125.50i	−0.146444	+	0.733785i
$134$		0			0
$135$	−2495.39	+	56.1872i	−1.59088	+	0.0358209i
$136$		0			0
$137$			2395.79i			1.49406i	0.664792	+	0.747029i	$0.268520\pi$
$137$			2395.79i			1.49406i	−0.664792	+	0.747029i	$0.731480\pi$
$138$		0			0
$139$	1712.79	−	988.882i	1.04516	−	0.603424i	0.123870	−	0.992298i	$-0.460469\pi$
$139$	1712.79	−	988.882i	1.04516	−	0.603424i	0.921291	+	0.388875i	$0.127136\pi$
$140$		0			0
$141$	−161.736	+	1.21372i	−0.0966001	+	0.000724921i
$142$		0			0
$143$	353.324	+	611.976i	0.206619	+	0.357874i
$144$		0			0
$145$	2368.38	+	1367.39i	1.35644	+	0.783140i
$146$		0			0
$147$	243.641	+	1765.55i	0.136702	+	0.990612i
$148$		0			0
$149$			1019.87i			0.560743i	0.959892	+	0.280372i	$0.0904577\pi$
$149$			1019.87i			0.560743i	−0.959892	+	0.280372i	$0.909542\pi$
$150$		0			0
$151$	−411.016			−0.221510			−0.110755	−	0.993848i	$-0.535327\pi$
$151$	−411.016			−0.221510			−0.110755	+	0.993848i	$0.535327\pi$
$152$		0			0
$153$	−172.735	+	309.834i	−0.0912733	+	0.163716i
$154$		0			0
$155$	−1490.42	−	860.495i	−0.772345	−	0.445913i
$156$		0			0
$157$	1567.68	+	905.102i	0.796909	+	0.460095i	0.842389	−	0.538870i	$-0.181149\pi$
$157$	1567.68	+	905.102i	0.796909	+	0.460095i	−0.0454804	+	0.998965i	$0.514482\pi$
$158$		0			0
$159$	−14.6061	−	1946.35i	−0.00728515	−	0.970791i
$160$		0			0
$161$	2651.61	−	898.220i	1.29799	−	0.439687i
$162$		0			0
$163$	706.017	−	1222.86i	0.339261	−	0.587617i	−0.645033	−	0.764155i	$-0.723156\pi$
$163$	706.017	−	1222.86i	0.339261	−	0.587617i	0.984294	+	0.176538i	$0.0564898\pi$
$164$		0			0
$165$	1090.76	+	618.885i	0.514641	+	0.292001i
$166$		0			0
$167$	−1654.98	−	2866.52i	−0.766865	−	1.32825i	−0.939255	−	0.343221i	$-0.888482\pi$
$167$	−1654.98	−	2866.52i	−0.766865	−	1.32825i	0.172389	−	0.985029i	$-0.444851\pi$
$168$		0			0
$169$	258.178	−	447.178i	0.117514	−	0.203540i
$170$		0			0
$171$	25.1109	+	1673.00i	0.0112297	+	0.748171i
$172$		0			0
$173$	378.636	+	655.817i	0.166400	+	0.288213i	0.937151	−	0.348923i	$-0.113452\pi$
$173$	378.636	+	655.817i	0.166400	+	0.288213i	−0.770752	+	0.637136i	$0.780119\pi$
$174$		0			0
$175$	−1138.02	−	3359.53i	−0.491579	−	1.45118i
$176$		0			0
$177$	−1745.32	−	2971.26i	−0.741165	−	1.26177i
$178$		0			0
$179$	−603.705	+	348.550i	−0.252084	+	0.145541i	−0.620718	−	0.784034i	$-0.713159\pi$
$179$	−603.705	+	348.550i	−0.252084	+	0.145541i	0.368634	+	0.929575i	$0.379826\pi$
$180$		0			0
$181$			4664.90i			1.91569i	0.287289	+	0.957844i	$0.407246\pi$
$181$			4664.90i			1.91569i	−0.287289	+	0.957844i	$0.592754\pi$
$182$		0			0
$183$	−23.8758	−	3181.59i	−0.00964452	−	1.28519i
$184$		0			0
$185$	2413.99	−	4181.15i	0.959351	−	1.66164i
$186$		0			0
$187$	154.354	−	89.1161i	0.0603607	−	0.0348493i
$188$		0			0
$189$	888.824	+	2441.57i	0.342076	+	0.939672i
$190$		0			0
$191$	957.155	−	552.614i	0.362604	−	0.209349i	−0.307619	−	0.951510i	$-0.599532\pi$
$191$	957.155	−	552.614i	0.362604	−	0.209349i	0.670222	+	0.742160i	$0.266199\pi$
$192$		0			0
$193$	−1105.00	+	1913.91i	−0.412122	+	0.713816i	−0.995122	−	0.0986565i	$-0.968545\pi$
$193$	−1105.00	+	1913.91i	−0.412122	+	0.713816i	0.583000	+	0.812472i	$0.301879\pi$
$194$		0			0
$195$	−36.1358	−	4815.32i	−0.0132705	−	1.76837i
$196$		0			0
$197$		−	3666.81i		−	1.32614i	−0.748558	−	0.663069i	$-0.769254\pi$
$197$		−	3666.81i		−	1.32614i	0.748558	−	0.663069i	$-0.230746\pi$
$198$		0			0
$199$	470.426	−	271.600i	0.167576	−	0.0967500i	−0.413866	−	0.910338i	$-0.635822\pi$
$199$	470.426	−	271.600i	0.167576	−	0.0967500i	0.581442	+	0.813588i	$0.302489\pi$
$200$		0			0
$201$	1572.86	+	2677.66i	0.551944	+	0.939640i
$202$		0			0
$203$	557.172	−	2791.81i	0.192639	−	0.965253i
$204$		0			0
$205$	−3048.85	−	5280.76i	−1.03873	−	1.79914i
$206$		0			0
$207$	3503.62	−	2093.55i	1.17642	−	0.702954i
$208$		0			0
$209$	420.340	−	728.050i	0.139117	−	0.240958i
$210$		0			0
$211$	−2273.48	−	3937.79i	−0.741768	−	1.28478i	−0.951690	−	0.307062i	$-0.900654\pi$
$211$	−2273.48	−	3937.79i	−0.741768	−	1.28478i	0.209921	−	0.977718i	$-0.432679\pi$
$212$		0			0
$213$	1197.78	+	679.605i	0.385307	+	0.218619i
$214$		0			0
$215$	−2274.16	+	3938.96i	−0.721378	+	1.24946i
$216$		0			0
$217$	−350.627	+	1756.88i	−0.109687	+	0.549607i
$218$		0			0
$219$	39.9098	+	5318.23i	0.0123144	+	1.64097i
$220$		0			0
$221$	−592.679	−	342.184i	−0.180398	−	0.104153i
$222$		0			0
$223$	−1047.81	−	604.951i	−0.314647	−	0.181661i	0.334357	−	0.942446i	$-0.391481\pi$
$223$	−1047.81	−	604.951i	−0.314647	−	0.181661i	−0.649004	+	0.760785i	$0.724814\pi$
$224$		0			0
$225$	−2652.47	−	4439.00i	−0.785917	−	1.31526i
$226$		0			0
$227$	−678.746			−0.198458			−0.0992289	−	0.995065i	$-0.531638\pi$
$227$	−678.746			−0.198458			−0.0992289	+	0.995065i	$0.531638\pi$
$228$		0			0
$229$			2399.34i			0.692371i	0.938166	+	0.346185i	$0.112523\pi$
$229$			2399.34i			0.692371i	−0.938166	+	0.346185i	$0.887477\pi$
$230$		0			0
$231$	245.892	−	1282.14i	0.0700368	−	0.365189i
$232$		0			0
$233$	1763.67	+	1018.26i	0.495888	+	0.286301i	0.727014	−	0.686623i	$-0.240908\pi$
$233$	1763.67	+	1018.26i	0.495888	+	0.286301i	−0.231126	+	0.972924i	$0.574241\pi$
$234$		0			0
$235$	−276.891	−	479.589i	−0.0768611	−	0.133127i
$236$		0			0
$237$	6057.76	−	45.4595i	1.66031	−	0.0124596i
$238$		0			0
$239$	−503.492	+	290.691i	−0.136269	+	0.0786748i	−0.566585	−	0.824004i	$-0.691736\pi$
$239$	−503.492	+	290.691i	−0.136269	+	0.0786748i	0.430316	+	0.902678i	$0.358402\pi$
$240$		0			0
$241$			1236.12i			0.330396i	0.986260	+	0.165198i	$0.0528264\pi$
$241$			1236.12i			0.330396i	−0.986260	+	0.165198i	$0.947174\pi$
$242$		0			0
$243$	2015.72	+	3207.14i	0.532135	+	0.846660i
$244$		0			0
$245$	−4846.03	+	3708.70i	−1.26368	+	0.967104i
$246$		0			0
$247$	−3228.00			−0.831550
$248$		0			0
$249$	−932.690	−	1587.83i	−0.237377	−	0.404115i
$250$		0			0
$251$	5732.64			1.44160			0.720798	−	0.693145i	$-0.243775\pi$
$251$	5732.64			1.44160			0.720798	+	0.693145i	$0.243775\pi$
$252$		0			0
$253$	−2050.70			−0.509590
$254$		0			0
$255$	−1214.53	+	9.11424i	−0.298262	+	0.00223826i
$256$		0			0
$257$	−3522.65			−0.855007			−0.427504	−	0.904014i	$-0.640607\pi$
$257$	−3522.65			−0.855007			−0.427504	+	0.904014i	$0.640607\pi$
$258$		0			0
$259$	−4928.66	−	983.632i	−1.18244	−	0.235984i
$260$		0			0
$261$	−62.2876	−	4149.87i	−0.0147721	−	0.984177i
$262$		0			0
$263$			1264.38i			0.296445i	0.988954	+	0.148222i	$0.0473551\pi$
$263$			1264.38i			0.296445i	−0.988954	+	0.148222i	$0.952645\pi$
$264$		0			0
$265$	5771.44	−	3332.14i	1.33788	−	0.772423i
$266$		0			0
$267$	3563.67	+	6066.86i	0.816828	+	1.39058i
$268$		0			0
$269$	−3764.05	−	6519.52i	−0.853153	−	1.47770i	−0.878348	−	0.478021i	$-0.841354\pi$
$269$	−3764.05	−	6519.52i	−0.853153	−	1.47770i	0.0251959	−	0.999683i	$-0.491979\pi$
$270$		0			0
$271$	3138.73	+	1812.15i	0.703559	+	0.406200i	0.808672	−	0.588260i	$-0.200187\pi$
$271$	3138.73	+	1812.15i	0.703559	+	0.406200i	−0.105113	+	0.994460i	$0.533520\pi$
$272$		0			0
$273$	−4735.62	+	1643.88i	−1.04986	+	0.364440i
$274$		0			0
$275$			2598.18i			0.569732i
$276$		0			0
$277$	968.914			0.210167			0.105084	−	0.994463i	$-0.466489\pi$
$277$	968.914			0.210167			0.105084	+	0.994463i	$0.466489\pi$
$278$		0			0
$279$	39.1975	+	2611.50i	0.00841108	+	0.560382i
$280$		0			0
$281$	−6482.72	−	3742.80i	−1.37625	−	0.794579i	−0.384545	−	0.923106i	$-0.625642\pi$
$281$	−6482.72	−	3742.80i	−1.37625	−	0.794579i	−0.991706	+	0.128528i	$0.958975\pi$
$282$		0			0
$283$	−2481.99	−	1432.98i	−0.521338	−	0.300995i	0.216144	−	0.976362i	$-0.430652\pi$
$283$	−2481.99	−	1432.98i	−0.521338	−	0.300995i	−0.737482	+	0.675367i	$0.763985\pi$
$284$		0			0
$285$	−4939.66	+	2901.55i	−1.02667	+	0.603064i
$286$		0			0
$287$	−4188.31	+	4769.72i	−0.861421	+	0.981003i
$288$		0			0
$289$	2370.19	−	4105.30i	0.482433	−	0.835599i
$290$		0			0
$291$	1689.98	−	992.693i	0.340441	−	0.199975i
$292$		0			0
$293$	−118.540	−	205.318i	−0.0236355	−	0.0409378i	0.853966	−	0.520329i	$-0.174191\pi$
$293$	−118.540	−	205.318i	−0.0236355	−	0.0409378i	−0.877601	+	0.479391i	$0.840857\pi$
$294$		0			0
$295$	5899.28	−	10217.9i	1.16430	−	2.01663i
$296$		0			0
$297$	−42.8435	−	1902.77i	−0.00837048	−	0.371750i
$298$		0			0
$299$	3937.09	+	6819.23i	0.761497	+	1.31895i
$300$		0			0
$301$	4643.17	+	926.655i	0.889128	+	0.177447i
$302$		0			0
$303$	2060.01	−	3630.70i	0.390576	−	0.688377i
$304$		0			0
$305$	9434.25	−	5446.87i	1.77116	−	1.02258i
$306$		0			0
$307$		−	10160.1i		−	1.88882i	−0.328775	−	0.944408i	$-0.606636\pi$
$307$		−	10160.1i		−	1.88882i	0.328775	−	0.944408i	$-0.393364\pi$
$308$		0			0
$309$	3896.26	+	2210.69i	0.717315	+	0.406996i
$310$		0			0
$311$	−741.924	+	1285.05i	−0.135275	+	0.234304i	−0.925703	−	0.378252i	$-0.876525\pi$
$311$	−741.924	+	1285.05i	−0.135275	+	0.234304i	0.790427	+	0.612556i	$0.209859\pi$
$312$		0			0
$313$	−926.127	+	534.700i	−0.167245	+	0.0965591i	−0.581286	−	0.813699i	$-0.697450\pi$
$313$	−926.127	+	534.700i	−0.167245	+	0.0965591i	0.414041	+	0.910258i	$0.364117\pi$
$314$		0			0
$315$	−5769.05	+	6772.26i	−1.03190	+	1.21134i
$316$		0			0
$317$	−8810.36	+	5086.67i	−1.56101	+	0.901248i	−0.563852	+	0.825876i	$0.690681\pi$
$317$	−8810.36	+	5086.67i	−1.56101	+	0.901248i	−0.997155	+	0.0753723i	$0.975985\pi$
$318$		0			0
$319$	−1042.65	+	1805.93i	−0.183001	+	0.316967i
$320$		0			0
$321$	8818.58	−	5180.03i	1.53335	−	0.900689i
$322$		0			0
$323$			814.172i			0.140253i
$324$		0			0
$325$	8639.79	−	4988.19i	1.47461	−	0.851369i
$326$		0			0
$327$	2384.70	−	17.8956i	0.403285	−	0.00302639i
$328$		0			0
$329$	−380.375	+	433.178i	−0.0637409	+	0.0725893i
$330$		0			0
$331$	4326.42	+	7493.58i	0.718433	+	1.24436i	0.961620	+	0.274384i	$0.0884738\pi$
$331$	4326.42	+	7493.58i	0.718433	+	1.24436i	−0.243187	+	0.969979i	$0.578193\pi$
$332$		0			0
$333$	−7326.18	+	109.963i	−1.20562	+	0.0180958i
$334$		0			0
$335$	−5316.34	+	9208.18i	−0.867053	+	1.50178i
$336$		0			0
$337$	3097.68	+	5365.34i	0.500716	+	0.867266i	1.00000		0.000827331i	$0.000263348\pi$
$337$	3097.68	+	5365.34i	0.500716	+	0.867266i	−0.499283	+	0.866439i	$0.666403\pi$
$338$		0			0
$339$	−28.4145	−	3786.41i	−0.00455240	−	0.606635i
$340$		0			0
$341$	656.139	−	1136.47i	0.104199	−	0.180478i
$342$		0			0
$343$	5275.12	+	3539.31i	0.830408	+	0.557156i
$344$		0			0
$345$	12154.3	+	6896.22i	1.89672	+	1.07617i
$346$		0			0
$347$	8424.31	+	4863.78i	1.30329	+	0.752453i	0.980966	−	0.194178i	$-0.0622039\pi$
$347$	8424.31	+	4863.78i	1.30329	+	0.752453i	0.322320	+	0.946631i	$0.395537\pi$
$348$		0			0
$349$	−5034.21	−	2906.50i	−0.772135	−	0.445792i	0.0615008	−	0.998107i	$-0.480411\pi$
$349$	−5034.21	−	2906.50i	−0.772135	−	0.445792i	−0.833636	+	0.552315i	$0.813745\pi$
$350$		0			0
$351$	−6245.06	+	3795.55i	−0.949678	+	0.577183i
$352$		0			0
$353$	−2419.25			−0.364770			−0.182385	−	0.983227i	$-0.558382\pi$
$353$	−2419.25			−0.364770			−0.182385	+	0.983227i	$0.558382\pi$
$354$		0			0
$355$			4715.21i			0.704950i
$356$		0			0
$357$	414.622	+	1194.42i	0.0614682	+	0.177075i
$358$		0			0
$359$	−913.173	−	527.221i	−0.134249	−	0.0775088i	0.431371	−	0.902175i	$-0.358030\pi$
$359$	−913.173	−	527.221i	−0.134249	−	0.0775088i	−0.565620	+	0.824666i	$0.691363\pi$
$360$		0			0
$361$	−1509.37	−	2614.30i	−0.220057	−	0.381149i
$362$		0			0
$363$	2941.09	−	5183.56i	0.425254	−	0.749494i
$364$		0			0
$365$	−15769.9	+	9104.78i	−2.26147	+	1.30566i
$366$		0			0
$367$			3474.15i			0.494139i	0.968998	+	0.247069i	$0.0794676\pi$
$367$			3474.15i			0.494139i	−0.968998	+	0.247069i	$0.920532\pi$
$368$		0			0
$369$	−4506.18	+	8082.69i	−0.635724	+	1.14029i
$370$		0			0
$371$	−5212.93	−	4577.49i	−0.729492	−	0.640569i
$372$		0			0
$373$	−9068.20			−1.25880			−0.629402	−	0.777080i	$-0.716700\pi$
$373$	−9068.20			−1.25880			−0.629402	+	0.777080i	$0.716700\pi$
$374$		0			0
$375$	3034.78	−	5348.68i	0.417907	−	0.736546i
$376$		0			0
$377$	8007.05			1.09386
$378$		0			0
$379$	−14362.5			−1.94658			−0.973289	−	0.229585i	$-0.926263\pi$
$379$	−14362.5			−1.94658			−0.973289	+	0.229585i	$0.926263\pi$
$380$		0			0
$381$	−6333.99	+	11163.4i	−0.851707	+	1.50110i
$382$		0			0
$383$	−5587.94			−0.745510			−0.372755	−	0.927930i	$-0.621587\pi$
$383$	−5587.94			−0.745510			−0.372755	+	0.927930i	$0.621587\pi$
$384$		0			0
$385$	4233.61	−	1434.11i	0.560428	−	0.189842i
$386$		0			0
$387$	6901.81	−	103.593i	0.906560	−	0.0136071i
$388$		0			0
$389$			5942.97i			0.774603i	0.921953	+	0.387302i	$0.126593\pi$
$389$			5942.97i			0.774603i	−0.921953	+	0.387302i	$0.873407\pi$
$390$		0			0
$391$	1719.96	−	993.018i	0.222460	−	0.128438i
$392$		0			0
$393$	−636.263	+	1121.39i	−0.0816672	+	0.143935i
$394$		0			0
$395$	10370.9	+	17962.8i	1.32105	+	2.28812i
$396$		0			0
$397$	−9736.71	−	5621.49i	−1.23091	−	0.710667i	−0.263691	−	0.964607i	$-0.584940\pi$
$397$	−9736.71	−	5621.49i	−1.23091	−	0.710667i	−0.967220	+	0.253940i	$0.918273\pi$
$398$		0			0
$399$	4510.58	+	3901.20i	0.565943	+	0.489484i
$400$		0			0
$401$		−	12760.3i		−	1.58907i	−0.607216	−	0.794536i	$-0.707714\pi$
$401$		−	12760.3i		−	1.58907i	0.607216	−	0.794536i	$-0.292286\pi$
$402$		0			0
$403$	−5038.83			−0.622833
$404$		0			0
$405$	−6144.82	+	11421.6i	−0.753923	+	1.40135i
$406$		0			0
$407$	3188.19	+	1840.70i	0.388286	+	0.224177i
$408$		0			0
$409$	5289.19	+	3053.72i	0.639447	+	0.369185i	0.784401	−	0.620253i	$-0.212970\pi$
$409$	5289.19	+	3053.72i	0.639447	+	0.369185i	−0.144955	+	0.989438i	$0.546304\pi$
$410$		0			0
$411$	10827.4	+	6143.36i	1.29946	+	0.737298i
$412$		0			0
$413$	−12044.6	−	2403.79i	−1.43505	−	0.286399i
$414$		0			0
$415$	3152.54	−	5460.37i	0.372897	−	0.645877i
$416$		0			0
$417$	−77.1183	−	10276.5i	−0.00905635	−	1.20681i
$418$		0			0
$419$	−910.097	−	1576.33i	−0.106113	−	0.183792i	0.808080	−	0.589073i	$-0.200507\pi$
$419$	−910.097	−	1576.33i	−0.106113	−	0.183792i	−0.914192	+	0.405281i	$0.867174\pi$
$420$		0			0
$421$	6368.00	−	11029.7i	0.737190	−	1.27685i	−0.216565	−	0.976268i	$-0.569485\pi$
$421$	6368.00	−	11029.7i	0.737190	−	1.27685i	0.953756	−	0.300583i	$-0.0971813\pi$
$422$		0			0
$423$	−409.243	+	734.056i	−0.0470404	+	0.0843760i
$424$		0			0
$425$	−1258.13	−	2179.14i	−0.143596	−	0.248715i
$426$		0			0
$427$	−8521.27	−	7482.55i	−0.965746	−	0.848024i
$428$		0			0
$429$	3671.75	−	27.5541i	0.413226	−	0.00310099i
$430$		0			0
$431$	94.7887	−	54.7263i	0.0105935	−	0.00611618i	−0.494694	−	0.869067i	$-0.664720\pi$
$431$	94.7887	−	54.7263i	0.0105935	−	0.00611618i	0.505287	+	0.862951i	$0.331386\pi$
$432$		0			0
$433$			5455.80i			0.605518i	0.953067	+	0.302759i	$0.0979077\pi$
$433$			5455.80i			0.605518i	−0.953067	+	0.302759i	$0.902092\pi$
$434$		0			0
$435$	12252.8	−	7197.30i	1.35052	−	0.793297i
$436$		0			0
$437$	4683.84	−	8112.64i	0.512719	−	0.888056i
$438$		0			0
$439$	−961.619	+	555.191i	−0.104546	+	0.0603595i	−0.551361	−	0.834267i	$-0.685891\pi$
$439$	−961.619	+	555.191i	−0.104546	+	0.0603595i	0.446815	+	0.894626i	$0.352558\pi$
$440$		0			0
$441$	8603.92	+	3426.18i	0.929049	+	0.369958i
$442$		0			0
$443$	−9854.82	+	5689.68i	−1.05692	+	0.610214i	−0.924579	−	0.380989i	$-0.875583\pi$
$443$	−9854.82	+	5689.68i	−1.05692	+	0.610214i	−0.132343	+	0.991204i	$0.542250\pi$
$444$		0			0
$445$	−12045.4	+	20863.3i	−1.28316	+	2.22250i
$446$		0			0
$447$	4609.16	+	2615.18i	0.487708	+	0.276720i
$448$		0			0
$449$			5096.78i			0.535706i	0.963460	+	0.267853i	$0.0863141\pi$
$449$			5096.78i			0.535706i	−0.963460	+	0.267853i	$0.913686\pi$
$450$		0			0
$451$	4026.65	−	2324.79i	0.420416	−	0.242727i
$452$		0			0
$453$	−1053.94	+	1857.54i	−0.109312	+	0.192659i
$454$		0			0
$455$	−12896.9	−	11324.8i	−1.32883	−	1.16685i
$456$		0			0
$457$	3198.64	+	5540.21i	0.327409	+	0.567090i	0.981997	−	0.188896i	$-0.0604910\pi$
$457$	3198.64	+	5540.21i	0.327409	+	0.567090i	−0.654588	+	0.755986i	$0.727158\pi$
$458$		0			0
$459$	957.319	+	1575.14i	0.0973504	+	0.160177i
$460$		0			0
$461$	5030.14	−	8712.45i	0.508193	−	0.880216i	−0.491762	−	0.870729i	$-0.663647\pi$
$461$	5030.14	−	8712.45i	0.508193	−	0.880216i	0.999955	−	0.00948609i	$-0.00301956\pi$
$462$		0			0
$463$	−5074.24	−	8788.84i	−0.509330	−	0.882186i	−0.999942	−	0.0108072i	$-0.996560\pi$
$463$	−5074.24	−	8788.84i	−0.509330	−	0.882186i	0.490611	−	0.871378i	$-0.336773\pi$
$464$		0			0
$465$	−7710.68	+	4529.25i	−0.768977	+	0.451697i
$466$		0			0
$467$	7678.30	−	13299.2i	0.760834	−	1.31780i	−0.181587	−	0.983375i	$-0.558123\pi$
$467$	7678.30	−	13299.2i	0.760834	−	1.31780i	0.942421	−	0.334429i	$-0.108543\pi$
$468$		0			0
$469$	10854.4	+	2166.26i	1.06868	+	0.213281i
$470$		0			0
$471$	8110.39	−	4764.04i	0.793434	−	0.466063i
$472$		0			0
$473$	−3003.51	−	1734.08i	−0.291969	−	0.168569i
$474$		0			0
$475$	−10278.5	−	5934.30i	−0.992864	−	0.573230i
$476$		0			0
$477$	−8833.74	−	4924.89i	−0.847944	−	0.472737i
$478$		0			0
$479$	−7014.75			−0.669128			−0.334564	−	0.942373i	$-0.608589\pi$
$479$	−7014.75			−0.669128			−0.334564	+	0.942373i	$0.608589\pi$
$480$		0			0
$481$		−	14135.7i		−	1.33998i
$482$		0			0
$483$	2739.97	−	14286.9i	0.258122	−	1.34591i
$484$		0			0
$485$	5811.65	+	3355.36i	0.544110	+	0.314142i
$486$		0			0
$487$	1037.15	+	1796.39i	0.0965042	+	0.167150i	0.910235	−	0.414091i	$-0.135901\pi$
$487$	1037.15	+	1796.39i	0.0965042	+	0.167150i	−0.813731	+	0.581241i	$0.802567\pi$
$488$		0			0
$489$	−3716.15	−	6326.44i	−0.343661	−	0.585054i
$490$		0			0
$491$	13983.7	−	8073.52i	1.28529	−	0.742063i	0.307480	−	0.951555i	$-0.400514\pi$
$491$	13983.7	−	8073.52i	1.28529	−	0.742063i	0.977810	+	0.209492i	$0.0671810\pi$
$492$		0			0
$493$		−	2019.55i		−	0.184495i
$494$		0			0
$495$	5593.94	−	3342.59i	0.507937	−	0.303512i
$496$		0			0
$497$	4648.98	−	1574.82i	0.419588	−	0.142133i
$498$		0			0
$499$	−12904.0			−1.15764			−0.578818	−	0.815457i	$-0.696486\pi$
$499$	−12904.0			−1.15764			−0.578818	+	0.815457i	$0.696486\pi$
$500$		0			0
$501$	−17198.6	+	129.064i	−1.53369	+	0.0115093i
$502$		0			0
$503$	998.713			0.0885297			0.0442648	−	0.999020i	$-0.485905\pi$
$503$	998.713			0.0885297			0.0442648	+	0.999020i	$0.485905\pi$
$504$		0			0
$505$	14292.7			1.25944
$506$		0			0
$507$	−1358.93	−	2313.47i	−0.119038	−	0.202653i
$508$		0			0
$509$	22719.8			1.97846			0.989232	−	0.146355i	$-0.0467543\pi$
$509$	22719.8			1.97846			0.989232	+	0.146355i	$0.0467543\pi$
$510$		0			0
$511$	14243.8	+	12507.6i	1.23309	+	1.08278i
$512$		0			0
$513$	7625.28	+	4176.47i	0.656266	+	0.359446i
$514$		0			0
$515$			15338.1i			1.31238i
$516$		0			0
$517$	365.694	−	211.133i	0.0311087	−	0.0179606i
$518$		0			0
$519$	3934.79	−	29.5280i	0.332790	−	0.00249737i
$520$		0			0
$521$	−3887.46	−	6733.27i	−0.326895	−	0.566199i	0.654999	−	0.755630i	$-0.272669\pi$
$521$	−3887.46	−	6733.27i	−0.326895	−	0.566199i	−0.981894	+	0.189431i	$0.939336\pi$
$522$		0			0
$523$	−10863.1	−	6271.81i	−0.908241	−	0.524373i	−0.0283764	−	0.999597i	$-0.509034\pi$
$523$	−10863.1	−	6271.81i	−0.908241	−	0.524373i	−0.879865	+	0.475224i	$0.842367\pi$
$524$		0			0
$525$	−18101.1	−	3471.47i	−1.50475	−	0.288585i
$526$		0			0
$527$			1270.90i			0.105050i
$528$		0			0
$529$	−10683.9			−0.878102
$530$		0			0
$531$	−17903.7	+	268.726i	−1.46319	+	0.0219618i
$532$		0			0
$533$	−15461.3	−	8926.61i	−1.25648	−	0.725431i
$534$		0			0
$535$	30326.1	+	17508.8i	2.45068	+	1.41490i
$536$		0			0
$537$	27.1817	+	3622.13i	0.00218432	+	0.291074i
$538$		0			0
$539$	−2827.94	−	3695.17i	−0.225989	−	0.295292i
$540$		0			0
$541$	−6461.61	+	11191.8i	−0.513505	+	0.889417i	0.486372	+	0.873752i	$0.338320\pi$
$541$	−6461.61	+	11191.8i	−0.513505	+	0.889417i	−0.999877	+	0.0156650i	$0.995013\pi$
$542$		0			0
$543$	21082.4	+	11961.9i	1.66618	+	0.945367i
$544$		0			0
$545$	4082.60	+	7071.27i	0.320879	+	0.555780i
$546$		0			0
$547$	7092.76	−	12285.0i	0.554414	−	0.960274i	−0.443535	−	0.896257i	$-0.646276\pi$
$547$	7092.76	−	12285.0i	0.554414	−	0.960274i	0.997949	−	0.0640165i	$-0.0203910\pi$
$548$		0			0
$549$	−14440.0	−	8050.44i	−1.12256	−	0.625837i
$550$		0			0
$551$	−4762.88	−	8249.55i	−0.368250	−	0.637827i
$552$		0			0
$553$	14246.8	−	16224.5i	1.09554	−	1.24763i
$554$		0			0
$555$	−12706.1	−	21631.1i	−0.971793	−	1.65440i
$556$		0			0
$557$	291.861	−	168.506i	0.0222020	−	0.0128183i	−0.488858	−	0.872363i	$-0.662586\pi$
$557$	291.861	−	168.506i	0.0222020	−	0.0128183i	0.511060	+	0.859545i	$0.329253\pi$
$558$		0			0
$559$			13316.9i			1.00759i
$560$		0			0
$561$	−6.94974	−	926.095i	−0.000523027	−	0.0696966i
$562$		0			0
$563$	10465.6	−	18126.9i	0.783431	−	1.35694i	−0.146501	−	0.989211i	$-0.546801\pi$
$563$	10465.6	−	18126.9i	0.783431	−	1.35694i	0.929932	−	0.367732i	$-0.119866\pi$
$564$		0			0
$565$	11227.7	−	6482.31i	0.836022	−	0.482677i
$566$		0			0
$567$	13313.5	+	2243.83i	0.986093	+	0.166194i
$568$		0			0
$569$	7253.31	−	4187.70i	0.534401	−	0.308537i	−0.208406	−	0.978043i	$-0.566827\pi$
$569$	7253.31	−	4187.70i	0.534401	−	0.308537i	0.742807	+	0.669506i	$0.233494\pi$
$570$		0			0
$571$	−1441.81	+	2497.29i	−0.105670	+	0.183027i	−0.914012	−	0.405687i	$-0.867032\pi$
$571$	−1441.81	+	2497.29i	−0.105670	+	0.183027i	0.808341	+	0.588714i	$0.200366\pi$
$572$		0			0
$573$	−43.0957	−	5742.77i	−0.00314197	−	0.418687i
$574$		0			0
$575$			28951.5i			2.09976i
$576$		0			0
$577$	4937.05	−	2850.41i	0.356208	−	0.205657i	−0.311208	−	0.950342i	$-0.600734\pi$
$577$	4937.05	−	2850.41i	0.356208	−	0.205657i	0.667416	+	0.744685i	$0.267400\pi$
$578$		0			0
$579$	5816.20	+	9901.61i	0.417467	+	0.710703i
$580$		0			0
$581$	−6436.58	−	1284.57i	−0.459611	−	0.0917265i
$582$		0			0
$583$	2540.81	+	4400.81i	0.180497	+	0.312629i
$584$		0			0
$585$	−21854.9	−	12184.3i	−1.54459	−	0.861126i
$586$		0			0
$587$	−5664.99	+	9812.05i	−0.398329	+	0.689926i	−0.993520	−	0.113658i	$-0.963743\pi$
$587$	−5664.99	+	9812.05i	−0.398329	+	0.689926i	0.595191	+	0.803584i	$0.297076\pi$
$588$		0			0
$589$	2997.27	+	5191.43i	0.209678	+	0.363173i
$590$		0			0
$591$	−16571.7	−	9402.55i	−1.15341	−	0.654432i
$592$		0			0
$593$	13404.0	−	23216.5i	0.928225	−	1.60773i	0.141935	−	0.989876i	$-0.454668\pi$
$593$	13404.0	−	23216.5i	0.928225	−	1.60773i	0.786290	−	0.617857i	$-0.211999\pi$
$594$		0			0
$595$	−2856.36	+	3252.88i	−0.196806	+	0.224126i
$596$		0			0
$597$	−21.1808	−	2822.48i	−0.00145205	−	0.193495i
$598$		0			0
$599$	8198.13	+	4733.19i	0.559210	+	0.322860i	0.752828	−	0.658217i	$-0.228689\pi$
$599$	8198.13	+	4733.19i	0.559210	+	0.322860i	−0.193619	+	0.981077i	$0.562022\pi$
$600$		0			0
$601$	−12413.2	−	7166.76i	−0.842503	−	0.486420i	0.0156109	−	0.999878i	$-0.495031\pi$
$601$	−12413.2	−	7166.76i	−0.842503	−	0.486420i	−0.858114	+	0.513459i	$0.828364\pi$
$602$		0			0
$603$	16134.5	−	242.172i	1.08963	−	0.0163549i
$604$		0			0
$605$	20405.7			1.37126
$606$		0			0
$607$		−	17945.9i		−	1.20000i	−0.799999	−	0.600002i	$-0.795167\pi$
$607$		−	17945.9i		−	1.20000i	0.799999	−	0.600002i	$-0.204833\pi$
$608$		0			0
$609$	−11188.5	−	9676.91i	−0.744467	−	0.643889i
$610$		0			0
$611$	−1404.17	−	810.700i	−0.0929734	−	0.0536782i
$612$		0			0
$613$	−10054.6	−	17415.2i	−0.662485	−	1.14746i	−0.979961	−	0.199191i	$-0.936168\pi$
$613$	−10054.6	−	17415.2i	−0.662485	−	1.14746i	0.317475	−	0.948267i	$-0.397165\pi$
$614$		0			0
$615$	−31683.6	+	237.765i	−2.07741	+	0.0155896i
$616$		0			0
$617$	−14287.8	+	8249.06i	−0.932260	+	0.538241i	−0.887526	−	0.460758i	$-0.847578\pi$
$617$	−14287.8	+	8249.06i	−0.932260	+	0.538241i	−0.0447345	+	0.998999i	$0.514244\pi$
$618$		0			0
$619$			24117.6i			1.56602i	0.622007	+	0.783011i	$0.286317\pi$
$619$			24117.6i			1.56602i	−0.622007	+	0.783011i	$0.713683\pi$
$620$		0			0
$621$	−477.404	−	21202.5i	−0.0308496	−	1.37009i
$622$		0			0
$623$	24593.2	+	4908.17i	1.58155	+	0.315636i
$624$		0			0
$625$	−2884.51			−0.184609
$626$		0			0
$627$	−2212.48	−	3766.56i	−0.140922	−	0.239907i
$628$		0			0
$629$	−3565.32			−0.226007
$630$		0			0
$631$	−17867.2			−1.12723			−0.563614	−	0.826038i	$-0.690590\pi$
$631$	−17867.2			−1.12723			−0.563614	+	0.826038i	$0.690590\pi$
$632$		0			0
$633$	−23626.1	+	177.298i	−1.48349	+	0.0111327i
$634$		0			0
$635$	−43946.3			−2.74638
$636$		0			0
$637$	−6858.34	+	16498.1i	−0.426589	+	1.02618i
$638$		0			0
$639$	6142.77	−	3670.54i	0.380288	−	0.227237i
$640$		0			0
$641$		−	4557.22i		−	0.280810i	−0.990094	−	0.140405i	$-0.955160\pi$
$641$		−	4557.22i		−	0.280810i	0.990094	−	0.140405i	$-0.0448405\pi$
$642$		0			0
$643$	17264.3	−	9967.53i	1.05884	−	0.611324i	0.133731	−	0.991018i	$-0.457304\pi$
$643$	17264.3	−	9967.53i	1.05884	−	0.611324i	0.925112	+	0.379694i	$0.123971\pi$
$644$		0			0
$645$	11970.1	+	20378.2i	0.730734	+	1.24401i
$646$		0			0
$647$	−4177.66	−	7235.92i	−0.253850	−	0.439681i	0.710733	−	0.703462i	$-0.248364\pi$
$647$	−4177.66	−	7235.92i	−0.253850	−	0.439681i	−0.964582	+	0.263782i	$0.915030\pi$
$648$		0			0
$649$	7791.26	+	4498.28i	0.471238	+	0.272070i
$650$		0			0
$651$	7040.90	+	6089.66i	0.423893	+	0.366625i
$652$		0			0
$653$			7271.47i			0.435765i	0.975975	+	0.217882i	$0.0699149\pi$
$653$			7271.47i			0.435765i	−0.975975	+	0.217882i	$0.930085\pi$
$654$		0			0
$655$	−4414.49			−0.263341
$656$		0			0
$657$	24137.4	+	13456.8i	1.43332	+	0.799087i
$658$		0			0
$659$	12999.8	+	7505.46i	0.768440	+	0.443659i	0.832318	−	0.554299i	$-0.187014\pi$
$659$	12999.8	+	7505.46i	0.768440	+	0.443659i	−0.0638781	+	0.997958i	$0.520347\pi$
$660$		0			0
$661$	−6762.53	−	3904.35i	−0.397930	−	0.229745i	0.287660	−	0.957732i	$-0.407123\pi$
$661$	−6762.53	−	3904.35i	−0.397930	−	0.229745i	−0.685590	+	0.727987i	$0.740456\pi$
$662$		0			0
$663$	−3066.22	+	1801.10i	−0.179611	+	0.105504i
$664$		0			0
$665$	−3996.25	+	20023.9i	−0.233034	+	1.16766i
$666$		0			0
$667$	−11618.2	+	20123.4i	−0.674453	+	1.16819i
$668$		0			0
$669$	−5420.81	+	3184.18i	−0.313275	+	0.184017i
$670$		0			0
$671$	4153.31	+	7193.75i	0.238952	+	0.413877i
$672$		0			0
$673$	−9508.81	+	16469.7i	−0.544633	+	0.943332i	0.453997	+	0.891003i	$0.349998\pi$
$673$	−9508.81	+	16469.7i	−0.544633	+	0.943332i	−0.998630	+	0.0523285i	$0.983336\pi$
$674$		0			0
$675$	−26863.0	+	604.859i	−1.53179	+	0.0344904i
$676$		0			0
$677$	9631.20	+	16681.7i	0.546761	+	0.947018i	0.998494	+	0.0548645i	$0.0174727\pi$
$677$	9631.20	+	16681.7i	0.546761	+	0.947018i	−0.451733	+	0.892153i	$0.649194\pi$
$678$		0			0
$679$	1367.21	−	6850.66i	0.0772737	−	0.387193i
$680$		0			0
$681$	−1740.46	+	3067.50i	−0.0979364	+	0.172609i
$682$		0			0
$683$	27933.6	−	16127.5i	1.56494	−	0.903516i	0.568190	−	0.822897i	$-0.307644\pi$
$683$	27933.6	−	16127.5i	1.56494	−	0.903516i	0.996745	−	0.0806185i	$-0.0256896\pi$
$684$		0			0
$685$			42623.6i			2.37747i
$686$		0			0
$687$	10843.5	+	6152.47i	0.602191	+	0.341676i
$688$		0			0
$689$	9756.08	−	16898.0i	0.539444	−	0.934344i
$690$		0			0
$691$	−7760.38	+	4480.46i	−0.427234	+	0.246664i	−0.698168	−	0.715934i	$-0.746001\pi$
$691$	−7760.38	+	4480.46i	−0.427234	+	0.246664i	0.270933	+	0.962598i	$0.412668\pi$
$692$		0			0
$693$	−5163.94	−	4398.99i	−0.283062	−	0.241131i
$694$		0			0
$695$	30472.4	−	17593.3i	1.66315	−	0.960217i
$696$		0			0
$697$	−2251.49	+	3899.69i	−0.122354	+	0.211924i
$698$		0			0
$699$	9124.34	−	5359.64i	0.493726	−	0.290014i
$700$		0			0
$701$			1583.93i			0.0853413i	0.999089	+	0.0426707i	$0.0135866\pi$
$701$			1583.93i			0.0853413i	−0.999089	+	0.0426707i	$0.986413\pi$
$702$		0			0
$703$	−14563.8	+	8408.40i	−0.781342	+	0.451108i
$704$		0			0
$705$	−2877.45	+	21.5934i	−0.153718	+	0.00115355i
$706$		0			0
$707$	−4773.57	−	14091.9i	−0.253930	−	0.749621i
$708$		0			0
$709$	9234.49	+	15994.6i	0.489152	+	0.847236i	0.999922	−	0.0124813i	$-0.00397303\pi$
$709$	9234.49	+	15994.6i	0.489152	+	0.847236i	−0.510770	+	0.859717i	$0.670640\pi$
$710$		0			0
$711$	15328.1	−	27493.8i	0.808505	−	1.45021i
$712$		0			0
$713$	7311.35	−	12663.6i	0.384028	−	0.665156i
$714$		0			0
$715$	6286.02	+	10887.7i	0.328789	+	0.569478i
$716$		0			0
$717$	22.6697	+	3020.87i	0.00118077	+	0.157345i
$718$		0			0
$719$	−17456.3	+	30235.1i	−0.905436	+	1.56826i	−0.0851053	+	0.996372i	$0.527123\pi$
$719$	−17456.3	+	30235.1i	−0.905436	+	1.56826i	−0.820331	+	0.571889i	$0.806211\pi$
$720$		0			0
$721$	15122.7	−	5122.73i	0.781134	−	0.264605i
$722$		0			0
$723$	5586.49	+	3169.70i	0.287363	+	0.163046i
$724$		0			0
$725$	25495.8	+	14720.0i	1.30606	+	0.754052i
$726$		0			0
$727$	−3661.37	−	2113.89i	−0.186785	−	0.107840i	0.403692	−	0.914895i	$-0.367727\pi$
$727$	−3661.37	−	2113.89i	−0.186785	−	0.107840i	−0.590477	+	0.807055i	$0.701060\pi$
$728$		0			0
$729$	19663.1	−	885.932i	0.998987	−	0.0450100i
$730$		0			0
$731$	3358.80			0.169945
$732$		0			0
$733$			14318.7i			0.721521i	0.932659	+	0.360760i	$0.117483\pi$
$733$			14318.7i			0.721521i	−0.932659	+	0.360760i	$0.882517\pi$
$734$		0			0
$735$	4334.64	+	31411.0i	0.217531	+	1.57634i
$736$		0			0
$737$	−7021.37	−	4053.79i	−0.350930	−	0.202610i
$738$		0			0
$739$	17713.6	+	30680.8i	0.881737	+	1.52721i	0.849408	+	0.527737i	$0.176959\pi$
$739$	17713.6	+	30680.8i	0.881737	+	1.52721i	0.0323295	+	0.999477i	$0.489707\pi$
$740$		0			0
$741$	−8277.36	+	14588.5i	−0.410359	+	0.723243i
$742$		0			0
$743$	−5141.17	+	2968.25i	−0.253851	+	0.146561i	−0.621526	−	0.783393i	$-0.713487\pi$
$743$	−5141.17	+	2968.25i	−0.253851	+	0.146561i	0.367675	+	0.929954i	$0.380154\pi$
$744$		0			0
$745$			18144.5i			0.892301i
$746$		0			0
$747$	−9567.62	+	143.606i	−0.468622	+	0.00703381i
$748$		0			0
$749$	7134.34	−	35747.9i	0.348042	−	1.74392i
$750$		0			0
$751$	−6540.92			−0.317818			−0.158909	−	0.987293i	$-0.550798\pi$
$751$	−6540.92			−0.317818			−0.158909	+	0.987293i	$0.550798\pi$
$752$		0			0
$753$	14699.8	−	25907.9i	0.711409	−	1.25383i
$754$		0			0
$755$	−7312.42			−0.352485
$756$		0			0
$757$	−2644.76			−0.126982			−0.0634910	−	0.997982i	$-0.520223\pi$
$757$	−2644.76			−0.126982			−0.0634910	+	0.997982i	$0.520223\pi$
$758$		0			0
$759$	−5258.47	+	9267.86i	−0.251476	+	0.443217i
$760$		0			0
$761$	−7278.69			−0.346718			−0.173359	−	0.984859i	$-0.555462\pi$
$761$	−7278.69			−0.346718			−0.173359	+	0.984859i	$0.555462\pi$
$762$		0			0
$763$	5608.41	−	6386.96i	0.266105	−	0.303045i
$764$		0			0
$765$	−3073.14	+	5512.27i	−0.145242	+	0.260518i
$766$		0			0
$767$		−	34544.6i		−	1.62625i
$768$		0			0
$769$	−30341.8	+	17517.8i	−1.42282	+	0.821468i	−0.996539	−	0.0831215i	$-0.973511\pi$
$769$	−30341.8	+	17517.8i	−1.42282	+	0.821468i	−0.426284	+	0.904589i	$0.640178\pi$
$770$		0			0
$771$	−9032.90	+	15920.2i	−0.421935	+	0.743645i
$772$		0			0
$773$	−13199.1	−	22861.5i	−0.614149	−	1.06374i	−0.990533	−	0.137274i	$-0.956166\pi$
$773$	−13199.1	−	22861.5i	−0.614149	−	1.06374i	0.376384	−	0.926464i	$-0.377167\pi$
$774$		0			0
$775$	−16044.5	−	9263.29i	−0.743658	−	0.429351i
$776$		0			0
$777$	−17083.6	+	19752.2i	−0.788767	+	0.911976i
$778$		0			0
$779$			21239.5i			0.976872i
$780$		0			0
$781$	−3595.41			−0.164730
$782$		0			0
$783$	−18914.5	−	10359.7i	−0.863281	−	0.472831i
$784$		0			0
$785$	27890.7	+	16102.7i	1.26811	+	0.732141i
$786$		0			0
$787$	−7520.85	−	4342.16i	−0.340647	−	0.196673i	0.319911	−	0.947448i	$-0.396347\pi$
$787$	−7520.85	−	4342.16i	−0.340647	−	0.196673i	−0.660558	+	0.750775i	$0.729680\pi$
$788$		0			0
$789$	5714.20	+	3242.16i	0.257834	+	0.146292i
$790$		0			0
$791$	−10141.2	−	8904.98i	−0.455851	−	0.400284i
$792$		0			0
$793$	15947.7	−	27622.2i	0.714148	−	1.23694i
$794$		0			0
$795$	−259.858	−	34627.7i	−0.0115927	−	1.54480i
$796$		0			0
$797$	−12025.1	−	20828.2i	−0.534445	−	0.925686i	−0.999190	−	0.0402412i	$-0.987187\pi$
$797$	−12025.1	−	20828.2i	−0.534445	−	0.925686i	0.464745	−	0.885445i	$-0.346146\pi$
$798$		0			0
$799$	−204.476	+	354.163i	−0.00905362	+	0.0156813i
$800$		0			0
$801$	36556.5	−	548.696i	1.61256	−	0.0242038i
$802$		0			0
$803$	−6942.53	−	12024.8i	−0.305101	−	0.528451i
$804$		0			0
$805$	47175.0	−	15980.3i	2.06547	−	0.699666i
$806$		0			0
$807$	−39116.0	+	293.540i	−1.70626	+	0.0128043i
$808$		0			0
$809$	−1268.85	+	732.570i	−0.0551426	+	0.0318366i	−0.527318	−	0.849668i	$-0.676802\pi$
$809$	−1268.85	+	732.570i	−0.0551426	+	0.0318366i	0.472175	+	0.881505i	$0.343469\pi$
$810$		0			0
$811$		−	9657.92i		−	0.418169i	−0.977898	−	0.209085i	$-0.932952\pi$
$811$		−	9657.92i		−	0.418169i	0.977898	−	0.209085i	$-0.0670484\pi$
$812$		0			0
$813$	16238.2	−	9538.32i	0.700491	−	0.411468i
$814$		0			0
$815$	12560.8	−	21755.9i	0.539859	−	0.935064i
$816$		0			0
$817$	13720.2	−	7921.34i	0.587525	−	0.339208i
$818$		0			0
$819$	−4713.92	+	25617.3i	−0.201120	+	1.09297i
$820$		0			0
$821$	−8667.67	+	5004.28i	−0.368457	+	0.212729i	−0.672784	−	0.739839i	$-0.734902\pi$
$821$	−8667.67	+	5004.28i	−0.368457	+	0.212729i	0.304327	+	0.952568i	$0.401568\pi$
$822$		0			0
$823$	5684.20	−	9845.33i	0.240752	−	0.416995i	−0.720177	−	0.693791i	$-0.755939\pi$
$823$	5684.20	−	9845.33i	0.240752	−	0.416995i	0.960929	+	0.276796i	$0.0892726\pi$
$824$		0			0
$825$	11742.1	+	6662.34i	0.495526	+	0.281155i
$826$		0			0
$827$			41180.4i			1.73154i	0.500444	+	0.865769i	$0.333170\pi$
$827$			41180.4i			1.73154i	−0.500444	+	0.865769i	$0.666830\pi$
$828$		0			0
$829$	−19659.4	+	11350.4i	−0.823644	+	0.475531i	−0.851671	−	0.524076i	$-0.824411\pi$
$829$	−19659.4	+	11350.4i	−0.823644	+	0.475531i	0.0280278	+	0.999607i	$0.491077\pi$
$830$		0			0
$831$	2484.52	−	4378.88i	0.103715	−	0.182794i
$832$		0			0
$833$	4161.17	+	1729.82i	0.173081	+	0.0719505i
$834$		0			0
$835$	−29443.9	−	50998.4i	−1.22030	−	2.11362i
$836$		0			0
$837$	11902.9	+	6519.36i	0.491545	+	0.269226i
$838$		0			0
$839$	−15716.8	+	27222.3i	−0.646729	+	1.12017i	0.337171	+	0.941443i	$0.390530\pi$
$839$	−15716.8	+	27222.3i	−0.646729	+	1.12017i	−0.983899	+	0.178723i	$0.942803\pi$
$840$		0			0
$841$	−380.183	−	658.495i	−0.0155883	−	0.0269997i
$842$		0			0
$843$	−33538.3	+	19700.4i	−1.37025	+	0.804884i
$844$		0			0
$845$	4593.27	−	7955.78i	0.186998	−	0.323890i
$846$		0			0
$847$	−6815.25	−	20119.1i	−0.276475	−	0.816176i
$848$		0			0
$849$	−12840.5	+	7542.53i	−0.519065	+	0.304899i
$850$		0			0
$851$	35525.9	+	20510.9i	1.43104	+	0.826209i
$852$		0			0
$853$	29988.5	+	17313.8i	1.20373	+	0.694976i	0.961383	−	0.275213i	$-0.0887483\pi$
$853$	29988.5	+	17313.8i	1.20373	+	0.694976i	0.242351	+	0.970189i	$0.422082\pi$
$854$		0			0
$855$	446.750	+	29764.4i	0.0178696	+	1.19055i
$856$		0			0
$857$	−19466.3			−0.775912			−0.387956	−	0.921678i	$-0.626819\pi$
$857$	−19466.3			−0.775912			−0.387956	+	0.921678i	$0.626819\pi$
$858$		0			0
$859$			23148.3i			0.919451i	0.888061	+	0.459725i	$0.152052\pi$
$859$			23148.3i			0.919451i	−0.888061	+	0.459725i	$0.847948\pi$
$860$		0			0
$861$	10816.3	+	31159.2i	0.428130	+	1.23334i
$862$		0			0
$863$	6199.04	+	3579.02i	0.244517	+	0.141172i	0.617251	−	0.786766i	$-0.288246\pi$
$863$	6199.04	+	3579.02i	0.244517	+	0.141172i	−0.372734	+	0.927938i	$0.621580\pi$
$864$		0			0
$865$	6736.34	+	11667.7i	0.264789	+	0.458628i
$866$		0			0
$867$	−12475.6	−	21238.7i	−0.488690	−	0.831955i
$868$		0			0
$869$	−13696.9	+	7907.92i	−0.534679	+	0.308697i
$870$		0			0
$871$			31131.1i			1.21106i
$872$		0			0
$873$	−152.844	−	10183.1i	−0.00592554	−	0.394785i
$874$		0			0
$875$	−7032.35	−	20760.0i	−0.271699	−	0.802076i
$876$		0			0
$877$	−11407.3			−0.439221			−0.219610	−	0.975588i	$-0.570479\pi$
$877$	−11407.3			−0.439221			−0.219610	+	0.975588i	$0.570479\pi$
$878$		0			0
$879$	−1231.87	+	9.24439i	−0.0472696	+	0.000354727i
$880$		0			0
$881$	−9290.49			−0.355283			−0.177642	−	0.984095i	$-0.556847\pi$
$881$	−9290.49			−0.355283			−0.177642	+	0.984095i	$0.556847\pi$
$882$		0			0
$883$	−3743.77			−0.142682			−0.0713408	−	0.997452i	$-0.522728\pi$
$883$	−3743.77			−0.142682			−0.0713408	+	0.997452i	$0.522728\pi$
$884$		0			0
$885$	−31051.1	−	52862.0i	−1.17940	−	2.00784i
$886$		0			0
$887$	−9498.47			−0.359557			−0.179779	−	0.983707i	$-0.557538\pi$
$887$	−9498.47			−0.359557			−0.179779	+	0.983707i	$0.557538\pi$
$888$		0			0
$889$	14677.5	+	43329.0i	0.553731	+	1.63465i
$890$		0			0
$891$	−8709.17	−	4685.52i	−0.327461	−	0.176174i
$892$		0			0
$893$			1928.93i			0.0722836i
$894$		0			0
$895$	−10740.6	+	6201.07i	−0.401137	+	0.231597i
$896$		0			0
$897$	40914.2	−	307.035i	1.52295	−	0.0114288i
$898$		0			0
$899$	−7434.73	−	12877.3i	−0.275820	−	0.477734i
$900$		0			0
$901$	−4262.05	−	2460.69i	−0.157591	−	0.0909851i
$902$		0			0
$903$	16094.1	−	18608.0i	0.593108	−	0.685754i
$904$		0			0
$905$			82993.6i			3.04840i
$906$		0			0
$907$	−22817.3			−0.835320			−0.417660	−	0.908603i	$-0.637150\pi$
$907$	−22817.3			−0.835320			−0.417660	+	0.908603i	$0.637150\pi$
$908$		0			0
$909$	−11126.1	−	18619.9i	−0.405973	−	0.679410i
$910$		0			0
$911$	−27473.6	−	15861.9i	−0.999167	−	0.576869i	−0.0911650	−	0.995836i	$-0.529059\pi$
$911$	−27473.6	−	15861.9i	−0.999167	−	0.576869i	−0.908002	+	0.418967i	$0.862392\pi$
$912$		0			0
$913$	4163.61	+	2403.86i	0.150926	+	0.0871371i
$914$		0			0
$915$	−424.775	−	56603.9i	−0.0153472	−	2.04510i
$916$		0			0
$917$	1474.38	+	4352.49i	0.0530953	+	0.156741i
$918$		0			0
$919$	18308.5	−	31711.2i	0.657171	−	1.13825i	−0.324173	−	0.945998i	$-0.605086\pi$
$919$	18308.5	−	31711.2i	0.657171	−	1.13825i	0.981345	−	0.192256i	$-0.0615805\pi$
$920$		0			0
$921$	−45917.2	−	26052.8i	−1.64280	−	0.932107i
$922$		0			0
$923$	6902.75	+	11955.9i	0.246161	+	0.426364i
$924$		0			0
$925$	25986.8	−	45010.4i	0.923718	−	1.59993i
$926$		0			0
$927$	19981.8	−	11939.9i	0.707972	−	0.423040i
$928$		0			0
$929$	10508.1	+	18200.6i	0.371109	+	0.642780i	0.989736	−	0.142904i	$-0.0456442\pi$
$929$	10508.1	+	18200.6i	0.371109	+	0.642780i	−0.618627	+	0.785685i	$0.712311\pi$
$930$		0			0
$931$	21077.3	−	2747.60i	0.741978	−	0.0967228i
$932$		0			0
$933$	3905.15	+	6648.20i	0.137030	+	0.233282i
$934$		0			0
$935$	2746.11	−	1585.47i	0.0960509	−	0.0554550i
$936$		0			0
$937$		−	36585.5i		−	1.27556i	−0.770220	−	0.637779i	$-0.779853\pi$
$937$		−	36585.5i		−	1.27556i	0.770220	−	0.637779i	$-0.220147\pi$
$938$		0			0
$939$	41.6987	+	5556.60i	0.00144919	+	0.193113i
$940$		0			0
$941$	10222.6	−	17706.0i	0.354141	−	0.613389i	−0.632830	−	0.774291i	$-0.718107\pi$
$941$	10222.6	−	17706.0i	0.354141	−	0.613389i	0.986970	+	0.160901i	$0.0514401\pi$
$942$		0			0
$943$	44868.9	−	25905.1i	1.54945	−	0.894576i
$944$		0			0
$945$	15813.1	+	43438.1i	0.544340	+	1.49528i
$946$		0			0
$947$	−5157.86	+	2977.89i	−0.176988	+	0.102184i	−0.585877	−	0.810400i	$-0.699250\pi$
$947$	−5157.86	+	2977.89i	−0.176988	+	0.102184i	0.408889	+	0.912584i	$0.365916\pi$
$948$		0			0
$949$	−26657.6	+	46172.3i	−0.911846	+	1.57936i
$950$		0			0
$951$	396.685	+	52860.7i	0.0135262	+	1.80245i
$952$		0			0
$953$		−	29135.0i		−	0.990319i	−0.868802	−	0.495160i	$-0.835110\pi$
$953$		−	29135.0i		−	0.990319i	0.868802	−	0.495160i	$-0.164890\pi$
$954$		0			0
$955$	17028.8	−	9831.59i	0.577005	−	0.333134i
$956$		0			0
$957$	5488.04	+	9342.95i	0.185374	+	0.315585i
$958$		0			0
$959$	42024.9	−	14235.7i	1.41507	−	0.479349i
$960$		0			0
$961$	−10216.8	−	17696.1i	−0.342950	−	0.594007i
$962$		0			0
$963$	−797.566	−	53137.2i	−0.0266887	−	1.77811i
$964$		0			0
$965$	−19659.1	+	34050.6i	−0.655802	+	1.13588i
$966$		0			0
$967$	−23316.8	−	40385.9i	−0.775406	−	1.34304i	−0.934566	−	0.355790i	$-0.884212\pi$
$967$	−23316.8	−	40385.9i	−0.775406	−	1.34304i	0.159160	−	0.987253i	$-0.449121\pi$
$968$		0			0
$969$	3679.54	+	2087.73i	0.121986	+	0.0692131i
$970$		0			0
$971$	−18560.8	+	32148.2i	−0.613433	+	1.06250i	0.377224	+	0.926122i	$0.376879\pi$
$971$	−18560.8	+	32148.2i	−0.613433	+	1.06250i	−0.990657	+	0.136376i	$0.956455\pi$
$972$		0			0
$973$	−27523.6	−	24168.5i	−0.906849	−	0.796307i
$974$		0			0
$975$	−389.005	−	51837.3i	−0.0127776	−	1.70269i
$976$		0			0
$977$	1626.77	+	939.217i	0.0532702	+	0.0307556i	0.526399	−	0.850238i	$-0.323542\pi$
$977$	1626.77	+	939.217i	0.0532702	+	0.0307556i	−0.473128	+	0.880994i	$0.656875\pi$
$978$		0			0
$979$	−15908.5	−	9184.80i	−0.519345	−	0.299844i
$980$		0			0
$981$	6034.06	−	10823.2i	0.196384	−	0.352252i
$982$		0			0
$983$	9151.34			0.296930			0.148465	−	0.988918i	$-0.452567\pi$
$983$	9151.34			0.296930			0.148465	+	0.988918i	$0.452567\pi$
$984$		0			0
$985$		−	65236.4i		−	2.11026i
$986$		0			0
$987$	982.321	+	2829.82i	0.0316795	+	0.0912607i
$988$		0			0
$989$	−33468.0	−	19322.8i	−1.07606	−	0.621263i
$990$		0			0
$991$	−22232.1	−	38507.1i	−0.712639	−	1.23433i	−0.963863	−	0.266399i	$-0.914166\pi$
$991$	−22232.1	−	38507.1i	−0.712639	−	1.23433i	0.251224	−	0.967929i	$-0.419167\pi$
$992$		0			0
$993$	44960.2	−	337.397i	1.43683	−	0.0107824i
$994$		0			0
$995$	8369.38	−	4832.06i	0.266660	−	0.153956i
$996$		0			0
$997$		−	23468.3i		−	0.745484i	−0.927935	−	0.372742i	$-0.878418\pi$
$997$		−	23468.3i		−	0.745484i	0.927935	−	0.372742i	$-0.121582\pi$
$998$		0			0
$999$	−18289.1	+	33391.7i	−0.579220	+	1.05752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.15	yes	48
3.2	odd	2		756.4.bm.a.89.3		48
7.3	odd	6		252.4.w.a.101.24	yes	48
9.4	even	3		756.4.w.a.341.3		48
9.5	odd	6		252.4.w.a.5.24	✓	48
21.17	even	6		756.4.w.a.521.3		48
63.31	odd	6		756.4.bm.a.17.3		48
63.59	even	6	inner	252.4.bm.a.185.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.24	✓	48	9.5	odd	6
252.4.w.a.101.24	yes	48	7.3	odd	6
252.4.bm.a.173.15	yes	48	1.1	even	1	trivial
252.4.bm.a.185.15	yes	48	63.59	even	6	inner
756.4.w.a.341.3		48	9.4	even	3
756.4.w.a.521.3		48	21.17	even	6
756.4.bm.a.17.3		48	63.31	odd	6
756.4.bm.a.89.3		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.56423 - 4.51937i) q^{3} +17.7911 q^{5} +(-5.94198 - 17.5412i) q^{7} +(-13.8494 - 23.1774i) q^{9} +O(q^{10})\)	\(q+(2.56423 - 4.51937i) q^{3} +17.7911 q^{5} +(-5.94198 - 17.5412i) q^{7} +(-13.8494 - 23.1774i) q^{9} +13.5659i q^{11} +(45.1112 - 26.0449i) q^{13} +(45.6205 - 80.4044i) q^{15} +(-6.56910 - 11.3780i) q^{17} +(-53.6675 - 30.9849i) q^{19} +(-94.5117 - 18.1257i) q^{21} +151.165i q^{23} +191.522 q^{25} +(-140.261 + 3.15817i) q^{27} +(133.122 + 76.8580i) q^{29} +(-83.7735 - 48.3666i) q^{31} +(61.3095 + 34.7863i) q^{33} +(-105.714 - 312.076i) q^{35} +(135.685 - 235.014i) q^{37} +(-2.03112 - 270.659i) q^{39} +(-171.369 - 296.821i) q^{41} +(-127.826 + 221.401i) q^{43} +(-246.396 - 412.352i) q^{45} +(-15.5635 - 26.9567i) q^{47} +(-272.386 + 208.459i) q^{49} +(-68.2662 + 0.512293i) q^{51} +(324.401 - 187.293i) q^{53} +241.353i q^{55} +(-277.648 + 163.090i) q^{57} +(331.586 - 574.325i) q^{59} +(530.280 - 306.157i) q^{61} +(-324.267 + 380.655i) q^{63} +(802.576 - 463.368i) q^{65} +(-298.821 + 517.573i) q^{67} +(683.171 + 387.623i) q^{69} +265.032i q^{71} +(-886.396 + 511.761i) q^{73} +(491.108 - 865.560i) q^{75} +(237.963 - 80.6086i) q^{77} +(582.924 + 1009.65i) q^{79} +(-345.388 + 641.988i) q^{81} +(177.198 - 306.916i) q^{83} +(-116.871 - 202.427i) q^{85} +(688.706 - 404.546i) q^{87} +(-677.048 + 1172.68i) q^{89} +(-724.909 - 636.544i) q^{91} +(-433.402 + 254.580i) q^{93} +(-954.802 - 551.255i) q^{95} +(326.661 + 188.598i) q^{97} +(314.424 - 187.880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more