LMFDB - Embedded newform 52.4.h.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,4,Mod(17,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("52.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	52.h (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:	$3.06809932030$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 51x^{6} - 224x^{5} + 2520x^{4} - 5712x^{3} + 16675x^{2} + 9072x + 6561 $ x^8 + 51x^6 - 224x^5 + 2520x^4 - 5712x^3 + 16675x^2 + 9072x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$1.73860 + 3.01134i$ of defining polynomial
Character	$\chi$	$=$	52.49
Dual form			52.4.h.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.48104 - 7.76138i) q^{3} +11.8097i q^{5} +(-27.8750 - 16.0936i) q^{7} +(-26.6594 + 46.1754i) q^{9} +O(q^{10})$	\(q+(-4.48104 - 7.76138i) q^{3} +11.8097i q^{5} +(-27.8750 - 16.0936i) q^{7} +(-26.6594 + 46.1754i) q^{9} +(-10.4661 + 6.04263i) q^{11} +(-4.16590 - 46.6867i) q^{13} +(91.6593 - 52.9195i) q^{15} +(44.8791 - 77.7328i) q^{17} +(-16.6029 - 9.58572i) q^{19} +288.465i q^{21} +(7.88869 + 13.6636i) q^{23} -14.4680 q^{25} +235.870 q^{27} +(-131.197 - 227.240i) q^{29} +84.0297i q^{31} +(93.7982 + 54.1544i) q^{33} +(190.060 - 329.194i) q^{35} +(-234.864 + 135.599i) q^{37} +(-343.686 + 241.538i) q^{39} +(143.088 - 82.6122i) q^{41} +(135.153 - 234.092i) q^{43} +(-545.315 - 314.838i) q^{45} +238.811i q^{47} +(346.511 + 600.174i) q^{49} -804.419 q^{51} -94.2765 q^{53} +(-71.3613 - 123.601i) q^{55} +171.816i q^{57} +(-214.177 - 123.655i) q^{59} +(-101.847 + 176.404i) q^{61} +(1486.26 - 858.092i) q^{63} +(551.354 - 49.1978i) q^{65} +(-200.442 + 115.725i) q^{67} +(70.6990 - 122.454i) q^{69} +(649.282 + 374.863i) q^{71} -153.347i q^{73} +(64.8316 + 112.292i) q^{75} +388.991 q^{77} -881.413 q^{79} +(-337.140 - 583.944i) q^{81} -197.016i q^{83} +(917.998 + 530.006i) q^{85} +(-1175.80 + 2036.54i) q^{87} +(1204.33 - 695.321i) q^{89} +(-635.234 + 1368.44i) q^{91} +(652.186 - 376.540i) q^{93} +(113.204 - 196.075i) q^{95} +(-972.430 - 561.433i) q^{97} -644.370i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 36 q^{7} - 70 q^{9}+O(q^{10}) $ 8 * q - 36 * q^7 - 70 * q^9	$ 8 q - 36 q^{7} - 70 q^{9} + 72 q^{11} + 62 q^{13} + 96 q^{15} + 88 q^{17} - 144 q^{19} - 20 q^{23} - 84 q^{25} - 432 q^{27} - 484 q^{29} + 1038 q^{33} + 40 q^{35} + 996 q^{37} - 236 q^{39} + 156 q^{41} + 504 q^{43} - 1530 q^{45} + 922 q^{49} - 1808 q^{51} - 1164 q^{53} - 1128 q^{55} + 600 q^{59} - 1224 q^{61} + 6480 q^{63} + 670 q^{65} + 960 q^{67} + 1738 q^{69} - 2964 q^{71} + 1448 q^{75} - 3972 q^{77} - 3968 q^{79} - 4132 q^{81} + 3870 q^{85} - 1660 q^{87} + 5430 q^{89} - 1720 q^{91} + 3324 q^{93} + 2400 q^{95} - 3042 q^{97}+O(q^{100}) $ 8 * q - 36 * q^7 - 70 * q^9 + 72 * q^11 + 62 * q^13 + 96 * q^15 + 88 * q^17 - 144 * q^19 - 20 * q^23 - 84 * q^25 - 432 * q^27 - 484 * q^29 + 1038 * q^33 + 40 * q^35 + 996 * q^37 - 236 * q^39 + 156 * q^41 + 504 * q^43 - 1530 * q^45 + 922 * q^49 - 1808 * q^51 - 1164 * q^53 - 1128 * q^55 + 600 * q^59 - 1224 * q^61 + 6480 * q^63 + 670 * q^65 + 960 * q^67 + 1738 * q^69 - 2964 * q^71 + 1448 * q^75 - 3972 * q^77 - 3968 * q^79 - 4132 * q^81 + 3870 * q^85 - 1660 * q^87 + 5430 * q^89 - 1720 * q^91 + 3324 * q^93 + 2400 * q^95 - 3042 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−4.48104	−	7.76138i	−0.862376	−	1.49368i	−0.869630	−	0.493705i	$-0.835642\pi$
$3$	−4.48104	−	7.76138i	−0.862376	−	1.49368i	0.00725381	−	0.999974i	$-0.497691\pi$
$4$		0			0
$5$			11.8097i			1.05629i	0.849155	+	0.528144i	$0.177112\pi$
$5$			11.8097i			1.05629i	−0.849155	+	0.528144i	$0.822888\pi$
$6$		0			0
$7$	−27.8750	−	16.0936i	−1.50511	−	0.868975i	−0.999982	−	0.00592959i	$-0.998113\pi$
$7$	−27.8750	−	16.0936i	−1.50511	−	0.868975i	−0.505126	−	0.863045i	$-0.668554\pi$
$8$		0			0
$9$	−26.6594	+	46.1754i	−0.987384	+	1.71020i
$10$		0			0
$11$	−10.4661	+	6.04263i	−0.286878	+	0.165629i	−0.636533	−	0.771249i	$-0.719632\pi$
$11$	−10.4661	+	6.04263i	−0.286878	+	0.165629i	0.349655	+	0.936879i	$0.386299\pi$
$12$		0			0
$13$	−4.16590	−	46.6867i	−0.0888778	−	0.996043i
$13$	−4.16590	−	46.6867i	−0.0888778	−	0.996043i
$14$		0			0
$15$	91.6593	−	52.9195i	1.57775	−	0.910917i
$16$		0			0
$17$	44.8791	−	77.7328i	0.640281	−	1.10900i	−0.345089	−	0.938570i	$-0.612151\pi$
$17$	44.8791	−	77.7328i	0.640281	−	1.10900i	0.985370	−	0.170429i	$-0.0545153\pi$
$18$		0			0
$19$	−16.6029	−	9.58572i	−0.200473	−	0.115743i	0.396403	−	0.918076i	$-0.370258\pi$
$19$	−16.6029	−	9.58572i	−0.200473	−	0.115743i	−0.596876	+	0.802334i	$0.703592\pi$
$20$		0			0
$21$			288.465i			2.99753i
$22$		0			0
$23$	7.88869	+	13.6636i	0.0715176	+	0.123872i	0.899567	−	0.436784i	$-0.143882\pi$
$23$	7.88869	+	13.6636i	0.0715176	+	0.123872i	−0.828049	+	0.560656i	$0.810549\pi$
$24$		0			0
$25$	−14.4680			−0.115744
$26$		0			0
$27$	235.870			1.68123
$28$		0			0
$29$	−131.197	−	227.240i	−0.840093	−	1.45508i	−0.889815	−	0.456321i	$-0.849167\pi$
$29$	−131.197	−	227.240i	−0.840093	−	1.45508i	0.0497219	−	0.998763i	$-0.484166\pi$
$30$		0			0
$31$			84.0297i			0.486844i	0.969920	+	0.243422i	$0.0782700\pi$
$31$			84.0297i			0.486844i	−0.969920	+	0.243422i	$0.921730\pi$
$32$		0			0
$33$	93.7982	+	54.1544i	0.494793	+	0.285669i
$34$		0			0
$35$	190.060	−	329.194i	0.917888	−	1.58983i
$36$		0			0
$37$	−234.864	+	135.599i	−1.04355	+	0.602495i	−0.920837	−	0.389947i	$-0.872493\pi$
$37$	−234.864	+	135.599i	−1.04355	+	0.602495i	−0.122714	+	0.992442i	$0.539160\pi$
$38$		0			0
$39$	−343.686	+	241.538i	−1.41112	+	0.991718i
$40$		0			0
$41$	143.088	−	82.6122i	0.545041	−	0.314679i	−0.202079	−	0.979369i	$-0.564770\pi$
$41$	143.088	−	82.6122i	0.545041	−	0.314679i	0.747119	+	0.664690i	$0.231436\pi$
$42$		0			0
$43$	135.153	−	234.092i	0.479318	−	0.830204i	−0.520400	−	0.853922i	$-0.674217\pi$
$43$	135.153	−	234.092i	0.479318	−	0.830204i	0.999719	+	0.0237186i	$0.00755056\pi$
$44$		0			0
$45$	−545.315	−	314.838i	−1.80646	−	1.04296i
$46$		0			0
$47$			238.811i			0.741153i	0.928802	+	0.370577i	$0.120840\pi$
$47$			238.811i			0.741153i	−0.928802	+	0.370577i	$0.879160\pi$
$48$		0			0
$49$	346.511	+	600.174i	1.01024	+	1.74978i
$50$		0			0
$51$	−804.419			−2.20865
$52$		0			0
$53$	−94.2765			−0.244337			−0.122169	−	0.992509i	$-0.538985\pi$
$53$	−94.2765			−0.244337			−0.122169	+	0.992509i	$0.538985\pi$
$54$		0			0
$55$	−71.3613	−	123.601i	−0.174952	−	0.303026i
$56$		0			0
$57$			171.816i			0.399255i
$58$		0			0
$59$	−214.177	−	123.655i	−0.472601	−	0.272856i	0.244727	−	0.969592i	$-0.421302\pi$
$59$	−214.177	−	123.655i	−0.472601	−	0.272856i	−0.717328	+	0.696736i	$0.754635\pi$
$60$		0			0
$61$	−101.847	+	176.404i	−0.213774	+	0.370267i	−0.952893	−	0.303308i	$-0.901909\pi$
$61$	−101.847	+	176.404i	−0.213774	+	0.370267i	0.739119	+	0.673575i	$0.235242\pi$
$62$		0			0
$63$	1486.26	−	858.092i	2.97224	−	1.71602i
$64$		0			0
$65$	551.354	−	49.1978i	1.05211	−	0.0938806i
$66$		0			0
$67$	−200.442	+	115.725i	−0.365491	+	0.211016i	−0.671487	−	0.741016i	$-0.734344\pi$
$67$	−200.442	+	115.725i	−0.365491	+	0.211016i	0.305996	+	0.952033i	$0.401011\pi$
$68$		0			0
$69$	70.6990	−	122.454i	0.123350	−	0.213649i
$70$		0			0
$71$	649.282	+	374.863i	1.08529	+	0.626593i	0.932319	−	0.361638i	$-0.117782\pi$
$71$	649.282	+	374.863i	1.08529	+	0.626593i	0.152972	+	0.988231i	$0.451116\pi$
$72$		0			0
$73$		−	153.347i		−	0.245862i	−0.992415	−	0.122931i	$-0.960771\pi$
$73$		−	153.347i		−	0.245862i	0.992415	−	0.122931i	$-0.0392294\pi$
$74$		0			0
$75$	64.8316	+	112.292i	0.0998148	+	0.172884i
$76$		0			0
$77$	388.991			0.575710
$78$		0			0
$79$	−881.413			−1.25527			−0.627637	−	0.778506i	$-0.715978\pi$
$79$	−881.413			−1.25527			−0.627637	+	0.778506i	$0.715978\pi$
$80$		0			0
$81$	−337.140	−	583.944i	−0.462470	−	0.801021i
$82$		0			0
$83$		−	197.016i		−	0.260546i	−0.991478	−	0.130273i	$-0.958415\pi$
$83$		−	197.016i		−	0.260546i	0.991478	−	0.130273i	$-0.0415854\pi$
$84$		0			0
$85$	917.998	+	530.006i	1.17142	+	0.676321i
$86$		0			0
$87$	−1175.80	+	2036.54i	−1.44895	+	2.50966i
$88$		0			0
$89$	1204.33	−	695.321i	1.43437	−	0.828133i	0.436918	−	0.899501i	$-0.356070\pi$
$89$	1204.33	−	695.321i	1.43437	−	0.828133i	0.997450	+	0.0713683i	$0.0227366\pi$
$90$		0			0
$91$	−635.234	+	1368.44i	−0.731765	+	1.57639i
$92$		0			0
$93$	652.186	−	376.540i	0.727189	−	0.419843i
$94$		0			0
$95$	113.204	−	196.075i	0.122258	−	0.211757i
$96$		0			0
$97$	−972.430	−	561.433i	−1.01789	−	0.587679i	−0.104398	−	0.994536i	$-0.533291\pi$
$97$	−972.430	−	561.433i	−1.01789	−	0.587679i	−0.913492	+	0.406857i	$0.866625\pi$
$98$		0			0
$99$		−	644.370i		−	0.654158i
$100$		0			0
$101$	−596.702	−	1033.52i	−0.587862	−	1.01821i	−0.994512	−	0.104623i	$-0.966636\pi$
$101$	−596.702	−	1033.52i	−0.587862	−	1.01821i	0.406650	−	0.913584i	$-0.366697\pi$
$102$		0			0
$103$	1367.61			1.30830			0.654149	−	0.756366i	$-0.273027\pi$
$103$	1367.61			1.30830			0.654149	+	0.756366i	$0.273027\pi$
$104$		0			0
$105$	−3406.67			−3.16626
$106$		0			0
$107$	−868.434	−	1504.17i	−0.784623	−	1.35901i	−0.929224	−	0.369517i	$-0.879523\pi$
$107$	−868.434	−	1504.17i	−0.784623	−	1.35901i	0.144601	−	0.989490i	$-0.453810\pi$
$108$		0			0
$109$		−	946.465i		−	0.831697i	−0.909434	−	0.415848i	$-0.863485\pi$
$109$		−	946.465i		−	0.831697i	0.909434	−	0.415848i	$-0.136515\pi$
$110$		0			0
$111$	2104.87	+	1215.25i	1.79987	+	1.03915i
$112$		0			0
$113$	485.712	−	841.279i	0.404354	−	0.700361i	−0.589892	−	0.807482i	$-0.700830\pi$
$113$	485.712	−	841.279i	0.404354	−	0.700361i	0.994246	+	0.107121i	$0.0341631\pi$
$114$		0			0
$115$	−161.362	+	93.1627i	−0.130845	+	0.0755432i
$116$		0			0
$117$	2266.83	+	1052.28i	1.79119	+	0.831477i
$118$		0			0
$119$	−2502.01	+	1444.54i	−1.92738	+	1.11278i
$120$		0			0
$121$	−592.473	+	1026.19i	−0.445134	+	0.770995i
$122$		0			0
$123$	−1282.37	−	740.376i	−0.940060	−	0.542744i
$124$		0			0
$125$			1305.35i			0.934029i
$126$		0			0
$127$	−801.930	−	1388.98i	−0.560313	−	0.970491i	−0.997469	−	0.0711048i	$-0.977348\pi$
$127$	−801.930	−	1388.98i	−0.560313	−	0.970491i	0.437156	−	0.899386i	$-0.355986\pi$
$128$		0			0
$129$	−2422.51			−1.65341
$130$		0			0
$131$	1677.20			1.11861			0.559305	−	0.828962i	$-0.311068\pi$
$131$	1677.20			1.11861			0.559305	+	0.828962i	$0.311068\pi$
$132$		0			0
$133$	308.538	+	534.404i	0.201155	+	0.348411i
$134$		0			0
$135$			2785.55i			1.77586i
$136$		0			0
$137$	505.815	+	292.032i	0.315436	+	0.182117i	0.649356	−	0.760484i	$-0.275038\pi$
$137$	505.815	+	292.032i	0.315436	+	0.182117i	−0.333921	+	0.942601i	$0.608372\pi$
$138$		0			0
$139$	−78.3050	+	135.628i	−0.0477823	+	0.0827614i	−0.888927	−	0.458048i	$-0.848549\pi$
$139$	−78.3050	+	135.628i	−0.0477823	+	0.0827614i	0.841145	+	0.540810i	$0.181882\pi$
$140$		0			0
$141$	1853.51	−	1070.12i	1.10704	−	0.639153i
$142$		0			0
$143$	325.711	+	463.456i	0.190471	+	0.271022i
$144$		0			0
$145$	2683.63	−	1549.39i	1.53699	−	0.887380i
$146$		0			0
$147$	3105.45	−	5378.80i	1.74240	−	3.01793i
$148$		0			0
$149$	−1027.99	−	593.508i	−0.565207	−	0.326322i	0.190026	−	0.981779i	$-0.439143\pi$
$149$	−1027.99	−	593.508i	−0.565207	−	0.326322i	−0.755233	+	0.655457i	$0.772476\pi$
$150$		0			0
$151$		−	2022.29i		−	1.08988i	−0.838476	−	0.544939i	$-0.816553\pi$
$151$		−	2022.29i		−	1.08988i	0.838476	−	0.544939i	$-0.183447\pi$
$152$		0			0
$153$	2392.89	+	4144.62i	1.26441	+	2.19001i
$154$		0			0
$155$	−992.361			−0.514248
$156$		0			0
$157$	1429.86			0.726848			0.363424	−	0.931624i	$-0.381608\pi$
$157$	1429.86			0.726848			0.363424	+	0.931624i	$0.381608\pi$
$158$		0			0
$159$	422.457	+	731.716i	0.210711	+	0.364961i
$160$		0			0
$161$		−	507.831i		−	0.248588i
$162$		0			0
$163$	−961.889	−	555.347i	−0.462215	−	0.266860i	0.250760	−	0.968049i	$-0.419319\pi$
$163$	−961.889	−	555.347i	−0.462215	−	0.266860i	−0.712975	+	0.701189i	$0.752653\pi$
$164$		0			0
$165$	−639.545	+	1107.73i	−0.301749	+	0.522644i
$166$		0			0
$167$	−246.272	+	142.185i	−0.114115	+	0.0658841i	−0.555971	−	0.831202i	$-0.687653\pi$
$167$	−246.272	+	142.185i	−0.114115	+	0.0658841i	0.441856	+	0.897086i	$0.354320\pi$
$168$		0			0
$169$	−2162.29	+	388.984i	−0.984201	+	0.177052i
$170$		0			0
$171$	885.248	−	511.098i	0.395887	−	0.228565i
$172$		0			0
$173$	−2170.41	+	3759.26i	−0.953834	+	1.65209i	−0.216820	+	0.976212i	$0.569569\pi$
$173$	−2170.41	+	3759.26i	−0.953834	+	1.65209i	−0.737014	+	0.675878i	$0.763765\pi$
$174$		0			0
$175$	403.295	+	232.843i	0.174207	+	0.100579i
$176$		0			0
$177$			2216.41i			0.941219i
$178$		0			0
$179$	325.394	+	563.599i	0.135872	+	0.235337i	0.925930	−	0.377694i	$-0.123283\pi$
$179$	325.394	+	563.599i	0.135872	+	0.235337i	−0.790058	+	0.613032i	$0.789950\pi$
$180$		0			0
$181$	454.138			0.186496			0.0932482	−	0.995643i	$-0.470275\pi$
$181$	454.138			0.186496			0.0932482	+	0.995643i	$0.470275\pi$
$182$		0			0
$183$	1825.52			0.737413
$184$		0			0
$185$	−1601.38	−	2773.66i	−0.636408	−	1.10229i
$186$		0			0
$187$			1084.75i			0.424197i
$188$		0			0
$189$	−6574.88	−	3796.01i	−2.53044	−	1.46095i
$190$		0			0
$191$	1407.63	−	2438.09i	0.533259	−	0.923633i	−0.465986	−	0.884792i	$-0.654300\pi$
$191$	1407.63	−	2438.09i	0.533259	−	0.923633i	0.999245	−	0.0388404i	$-0.0123664\pi$
$192$		0			0
$193$	−999.023	+	576.786i	−0.372597	+	0.215119i	−0.674593	−	0.738190i	$-0.735681\pi$
$193$	−999.023	+	576.786i	−0.372597	+	0.215119i	0.301995	+	0.953309i	$0.402347\pi$
$194$		0			0
$195$	−2852.48	−	4058.81i	−1.04754	−	1.49055i
$196$		0			0
$197$	−352.175	+	203.329i	−0.127368	+	0.0735359i	−0.562330	−	0.826913i	$-0.690095\pi$
$197$	−352.175	+	203.329i	−0.127368	+	0.0735359i	0.434962	+	0.900449i	$0.356762\pi$
$198$		0			0
$199$	−404.699	+	700.960i	−0.144163	+	0.249697i	−0.929060	−	0.369929i	$-0.879382\pi$
$199$	−404.699	+	700.960i	−0.144163	+	0.249697i	0.784898	+	0.619626i	$0.212716\pi$
$200$		0			0
$201$	1796.38	+	1037.14i	0.630381	+	0.363951i
$202$		0			0
$203$			8445.76i			2.92008i
$204$		0			0
$205$	975.621	+	1689.83i	0.332392	+	0.575720i
$206$		0			0
$207$	−841.229			−0.282461
$208$		0			0
$209$	231.692			0.0766815
$210$		0			0
$211$	−1800.27	−	3118.16i	−0.587373	−	1.01736i	−0.994575	−	0.104021i	$-0.966829\pi$
$211$	−1800.27	−	3118.16i	−0.587373	−	1.01736i	0.407202	−	0.913338i	$-0.366504\pi$
$212$		0			0
$213$		−	6719.10i		−	2.16143i
$214$		0			0
$215$	2764.55	+	1596.11i	0.876934	+	0.506298i
$216$		0			0
$217$	1352.34	−	2342.33i	0.423055	−	0.732754i
$218$		0			0
$219$	−1190.19	+	687.155i	−0.367239	+	0.212026i
$220$		0			0
$221$	−3816.05	−	1771.43i	−1.16152	−	0.539181i
$222$		0			0
$223$	2261.02	−	1305.40i	0.678964	−	0.392000i	−0.120501	−	0.992713i	$-0.538450\pi$
$223$	2261.02	−	1305.40i	0.678964	−	0.392000i	0.799465	+	0.600713i	$0.205117\pi$
$224$		0			0
$225$	385.708	−	668.065i	0.114284	−	0.197945i
$226$		0			0
$227$	4036.43	+	2330.43i	1.18021	+	0.681394i	0.956063	−	0.293162i	$-0.0947076\pi$
$227$	4036.43	+	2330.43i	1.18021	+	0.681394i	0.224145	+	0.974556i	$0.428041\pi$
$228$		0			0
$229$			123.893i			0.0357515i	0.999840	+	0.0178757i	$0.00569032\pi$
$229$			123.893i			0.0357515i	−0.999840	+	0.0178757i	$0.994310\pi$
$230$		0			0
$231$	−1743.08	−	3019.11i	−0.496478	−	0.859926i
$232$		0			0
$233$	−1186.44			−0.333590			−0.166795	−	0.985992i	$-0.553342\pi$
$233$	−1186.44			−0.333590			−0.166795	+	0.985992i	$0.553342\pi$
$234$		0			0
$235$	−2820.28			−0.782871
$236$		0			0
$237$	3949.64	+	6840.98i	1.08252	+	1.87498i
$238$		0			0
$239$			4543.56i			1.22970i	0.788644	+	0.614850i	$0.210783\pi$
$239$			4543.56i			1.22970i	−0.788644	+	0.614850i	$0.789217\pi$
$240$		0			0
$241$	5442.24	+	3142.08i	1.45463	+	0.839831i	0.998739	−	0.0502054i	$-0.0159876\pi$
$241$	5442.24	+	3142.08i	1.45463	+	0.839831i	0.455890	+	0.890036i	$0.349321\pi$
$242$		0			0
$243$	162.773	−	281.931i	0.0429707	−	0.0744275i
$244$		0			0
$245$	−7087.85	+	4092.17i	−1.84827	+	1.06710i
$246$		0			0
$247$	−378.359	+	815.069i	−0.0974672	+	0.209966i
$248$		0			0
$249$	−1529.12	+	882.836i	−0.389172	+	0.224689i
$250$		0			0
$251$	462.404	−	800.908i	0.116282	−	0.201406i	−0.802010	−	0.597311i	$-0.796236\pi$
$251$	462.404	−	800.908i	0.116282	−	0.201406i	0.918291	+	0.395905i	$0.129569\pi$
$252$		0			0
$253$	−165.128	−	95.3368i	−0.0410337	−	0.0236908i
$254$		0			0
$255$		−	9499.91i		−	2.33297i
$256$		0			0
$257$	−271.205	−	469.741i	−0.0658261	−	0.114014i	0.831234	−	0.555923i	$-0.187635\pi$
$257$	−271.205	−	469.741i	−0.0658261	−	0.114014i	−0.897060	+	0.441908i	$0.854302\pi$
$258$		0			0
$259$	8729.11			2.09421
$260$		0			0
$261$	13990.5			3.31798
$262$		0			0
$263$	2624.40	+	4545.59i	0.615312	+	1.06575i	0.990330	+	0.138734i	$0.0443034\pi$
$263$	2624.40	+	4545.59i	0.615312	+	1.06575i	−0.375017	+	0.927018i	$0.622363\pi$
$264$		0			0
$265$		−	1113.37i		−	0.258091i
$266$		0			0
$267$	−10793.3	−	6231.51i	−2.47393	−	1.42832i
$268$		0			0
$269$	165.080	−	285.927i	0.0374168	−	0.0648078i	−0.846711	−	0.532054i	$-0.821420\pi$
$269$	165.080	−	285.927i	0.0374168	−	0.0648078i	0.884127	+	0.467246i	$0.154754\pi$
$270$		0			0
$271$	−1241.78	+	716.940i	−0.278349	+	0.160705i	−0.632676	−	0.774417i	$-0.718043\pi$
$271$	−1241.78	+	716.940i	−0.278349	+	0.160705i	0.354327	+	0.935122i	$0.384710\pi$
$272$		0			0
$273$	13467.5	−	1201.71i	2.98567	−	0.266414i
$274$		0			0
$275$	151.424	−	87.4247i	0.0332044	−	0.0191706i
$276$		0			0
$277$	−1070.54	+	1854.22i	−0.232211	+	0.402200i	−0.958458	−	0.285233i	$-0.907929\pi$
$277$	−1070.54	+	1854.22i	−0.232211	+	0.402200i	0.726248	+	0.687433i	$0.241262\pi$
$278$		0			0
$279$	−3880.10	−	2240.18i	−0.832600	−	0.480702i
$280$		0			0
$281$		−	5857.04i		−	1.24342i	−0.783246	−	0.621711i	$-0.786438\pi$
$281$		−	5857.04i		−	1.24342i	0.783246	−	0.621711i	$-0.213562\pi$
$282$		0			0
$283$	−853.748	−	1478.73i	−0.179329	−	0.310606i	0.762322	−	0.647198i	$-0.224059\pi$
$283$	−853.748	−	1478.73i	−0.179329	−	0.310606i	−0.941651	+	0.336591i	$0.890726\pi$
$284$		0			0
$285$	−2029.09			−0.421729
$286$		0			0
$287$	−5318.12			−1.09379
$288$		0			0
$289$	−1571.76	−	2722.37i	−0.319919	−	0.554116i
$290$		0			0
$291$			10063.2i			2.02720i
$292$		0			0
$293$	1544.37	+	891.643i	0.307929	+	0.177783i	0.645999	−	0.763338i	$-0.276441\pi$
$293$	1544.37	+	891.643i	0.307929	+	0.177783i	−0.338071	+	0.941121i	$0.609774\pi$
$294$		0			0
$295$	1460.32	−	2529.36i	0.288215	−	0.499203i
$296$		0			0
$297$	−2468.65	+	1425.28i	−0.482308	+	0.278461i
$298$		0			0
$299$	605.045	−	425.218i	0.117026	−	0.0822441i
$300$		0			0
$301$	−7534.80	+	4350.22i	−1.44285	+	0.833032i
$302$		0			0
$303$	−5347.69	+	9262.47i	−1.01392	+	1.75615i
$304$		0			0
$305$	−2083.28	−	1202.78i	−0.391108	−	0.225807i
$306$		0			0
$307$		−	4027.85i		−	0.748801i	−0.927267	−	0.374400i	$-0.877849\pi$
$307$		−	4027.85i		−	0.748801i	0.927267	−	0.374400i	$-0.122151\pi$
$308$		0			0
$309$	−6128.31	−	10614.5i	−1.12824	−	1.95418i
$310$		0			0
$311$	−80.6308			−0.0147014			−0.00735072	−	0.999973i	$-0.502340\pi$
$311$	−80.6308			−0.0147014			−0.00735072	+	0.999973i	$0.502340\pi$
$312$		0			0
$313$	−4628.22			−0.835790			−0.417895	−	0.908495i	$-0.637232\pi$
$313$	−4628.22			−0.835790			−0.417895	+	0.908495i	$0.637232\pi$
$314$		0			0
$315$	10133.8	+	17552.2i	1.81261	+	3.13954i
$316$		0			0
$317$		−	10723.3i		−	1.89993i	−0.312354	−	0.949966i	$-0.601118\pi$
$317$		−	10723.3i		−	1.89993i	0.312354	−	0.949966i	$-0.398882\pi$
$318$		0			0
$319$	2746.25	+	1585.55i	0.482009	+	0.278288i
$320$		0			0
$321$	−7782.97	+	13480.5i	−1.35328	+	2.34395i
$322$		0			0
$323$	−1490.25	+	860.396i	−0.256717	+	0.148216i
$324$		0			0
$325$	60.2722	+	675.463i	0.0102871	+	0.115286i
$326$		0			0
$327$	−7345.88	+	4241.15i	−1.24229	+	0.717235i
$328$		0			0
$329$	3843.34	−	6656.87i	0.644044	−	1.11552i
$330$		0			0
$331$	4496.86	+	2596.26i	0.746736	+	0.431128i	0.824513	−	0.565843i	$-0.191449\pi$
$331$	4496.86	+	2596.26i	0.746736	+	0.431128i	−0.0777775	+	0.996971i	$0.524782\pi$
$332$		0			0
$333$		−	14459.9i		−	2.37957i
$334$		0			0
$335$	−1366.68	−	2367.15i	−0.222894	−	0.386064i
$336$		0			0
$337$	2676.49			0.432635			0.216317	−	0.976323i	$-0.430595\pi$
$337$	2676.49			0.432635			0.216317	+	0.976323i	$0.430595\pi$
$338$		0			0
$339$	−8705.98			−1.39482
$340$		0			0
$341$	−507.760	−	879.466i	−0.0806356	−	0.139665i
$342$		0			0
$343$		−	11266.2i		−	1.77353i
$344$		0			0
$345$	1446.14	+	834.931i	0.225674	+	0.130293i
$346$		0			0
$347$	4924.23	−	8529.02i	0.761806	−	1.31949i	−0.180113	−	0.983646i	$-0.557646\pi$
$347$	4924.23	−	8529.02i	0.761806	−	1.31949i	0.941919	−	0.335840i	$-0.109020\pi$
$348$		0			0
$349$	−5638.99	+	3255.67i	−0.864894	+	0.499347i	−0.865648	−	0.500653i	$-0.833093\pi$
$349$	−5638.99	+	3255.67i	−0.864894	+	0.499347i	0.000754175		1.00000i	$0.499760\pi$
$350$		0			0
$351$	−982.611	−	11012.0i	−0.149424	−	1.67458i
$352$		0			0
$353$	9609.82	−	5548.23i	1.44895	−	0.836552i	0.450531	−	0.892761i	$-0.351235\pi$
$353$	9609.82	−	5548.23i	1.44895	−	0.836552i	0.998419	+	0.0562092i	$0.0179014\pi$
$354$		0			0
$355$	−4427.01	+	7667.80i	−0.661862	+	1.14638i
$356$		0			0
$357$	22423.2	+	12946.0i	3.32426	+	1.91926i
$358$		0			0
$359$			7844.27i			1.15322i	0.817021	+	0.576608i	$0.195624\pi$
$359$			7844.27i			1.15322i	−0.817021	+	0.576608i	$0.804376\pi$
$360$		0			0
$361$	−3245.73	−	5621.77i	−0.473207	−	0.819619i
$362$		0			0
$363$	10619.6			1.53549
$364$		0			0
$365$	1810.98			0.259701
$366$		0			0
$367$	−1637.80	−	2836.75i	−0.232949	−	0.403479i	0.725726	−	0.687984i	$-0.241504\pi$
$367$	−1637.80	−	2836.75i	−0.232949	−	0.403479i	−0.958675	+	0.284505i	$0.908171\pi$
$368$		0			0
$369$			8809.55i			1.24284i
$370$		0			0
$371$	2627.96	+	1517.25i	0.367754	+	0.212323i
$372$		0			0
$373$	812.650	−	1407.55i	0.112808	−	0.195389i	−0.804093	−	0.594503i	$-0.797349\pi$
$373$	812.650	−	1407.55i	0.112808	−	0.195389i	0.916901	+	0.399114i	$0.130682\pi$
$374$		0			0
$375$	10131.3	−	5849.30i	1.39514	−	0.805484i
$376$		0			0
$377$	−10062.5	+	7071.82i	−1.37466	+	0.966093i
$378$		0			0
$379$	−11188.2	+	6459.52i	−1.51636	+	0.875470i	−0.516542	+	0.856262i	$0.672781\pi$
$379$	−11188.2	+	6459.52i	−1.51636	+	0.875470i	−0.999816	+	0.0192081i	$0.993885\pi$
$380$		0			0
$381$	−7186.95	+	12448.2i	−0.966401	+	1.67386i
$382$		0			0
$383$	−4300.61	−	2482.96i	−0.573762	−	0.331261i	0.184889	−	0.982759i	$-0.440808\pi$
$383$	−4300.61	−	2482.96i	−0.573762	−	0.331261i	−0.758650	+	0.651498i	$0.774141\pi$
$384$		0			0
$385$			4593.86i			0.608116i
$386$		0			0
$387$	7206.20	+	12481.5i	0.946543	+	1.63946i
$388$		0			0
$389$	8704.29			1.13451			0.567256	−	0.823542i	$-0.308005\pi$
$389$	8704.29			1.13451			0.567256	+	0.823542i	$0.308005\pi$
$390$		0			0
$391$	1416.15			0.183165
$392$		0			0
$393$	−7515.61	−	13017.4i	−0.964662	−	1.67084i
$394$		0			0
$395$		−	10409.2i		−	1.32593i
$396$		0			0
$397$	−3805.52	−	2197.12i	−0.481092	−	0.277759i	0.239779	−	0.970827i	$-0.422925\pi$
$397$	−3805.52	−	2197.12i	−0.481092	−	0.277759i	−0.720871	+	0.693069i	$0.756258\pi$
$398$		0			0
$399$	2765.14	−	4789.36i	0.346943	−	0.600923i
$400$		0			0
$401$	−2814.32	+	1624.85i	−0.350475	+	0.202347i	−0.664894	−	0.746937i	$-0.731524\pi$
$401$	−2814.32	+	1624.85i	−0.350475	+	0.202347i	0.314419	+	0.949284i	$0.398190\pi$
$402$		0			0
$403$	3923.07	−	350.059i	0.484918	−	0.0432697i
$404$		0			0
$405$	6896.18	−	3981.51i	0.846109	−	0.488501i
$406$		0			0
$407$	1638.75	−	2838.39i	0.199581	−	0.345685i
$408$		0			0
$409$	5685.82	+	3282.71i	0.687398	+	0.396870i	0.802637	−	0.596468i	$-0.203430\pi$
$409$	5685.82	+	3282.71i	0.687398	+	0.396870i	−0.115238	+	0.993338i	$0.536763\pi$
$410$		0			0
$411$		−	5234.43i		−	0.628213i
$412$		0			0
$413$	3980.12	+	6893.77i	0.474211	+	0.821357i
$414$		0			0
$415$	2326.69			0.275212
$416$		0			0
$417$	1403.55			0.164825
$418$		0			0
$419$	5682.35	+	9842.12i	0.662532	+	1.14754i	0.979948	+	0.199253i	$0.0638516\pi$
$419$	5682.35	+	9842.12i	0.662532	+	1.14754i	−0.317416	+	0.948286i	$0.602815\pi$
$420$		0			0
$421$			3657.27i			0.423383i	0.977337	+	0.211692i	$0.0678972\pi$
$421$			3657.27i			0.423383i	−0.977337	+	0.211692i	$0.932103\pi$
$422$		0			0
$423$	−11027.2	−	6366.56i	−1.26752	−	0.731803i
$424$		0			0
$425$	−649.310	+	1124.64i	−0.0741086	+	0.128360i
$426$		0			0
$427$	5677.98	−	3278.18i	0.643505	−	0.371528i
$428$		0			0
$429$	2137.54	−	4604.73i	0.240562	−	0.518225i
$430$		0			0
$431$	11576.7	−	6683.84i	1.29381	−	0.746982i	0.314483	−	0.949263i	$-0.398169\pi$
$431$	11576.7	−	6683.84i	1.29381	−	0.746982i	0.979328	+	0.202281i	$0.0648355\pi$
$432$		0			0
$433$	3031.38	−	5250.50i	0.336440	−	0.582731i	−0.647320	−	0.762218i	$-0.724110\pi$
$433$	3031.38	−	5250.50i	0.336440	−	0.582731i	0.983760	+	0.179487i	$0.0574437\pi$
$434$		0			0
$435$	−24050.9	−	13885.8i	−2.65092	−	1.53051i
$436$		0			0
$437$		−	302.475i		−	0.0331106i
$438$		0			0
$439$	−855.711	−	1482.13i	−0.0930315	−	0.161135i	0.815754	−	0.578399i	$-0.196322\pi$
$439$	−855.711	−	1482.13i	−0.0930315	−	0.161135i	−0.908785	+	0.417264i	$0.862989\pi$
$440$		0			0
$441$	−36951.0			−3.98996
$442$		0			0
$443$	14253.1			1.52864			0.764320	−	0.644837i	$-0.223075\pi$
$443$	14253.1			1.52864			0.764320	+	0.644837i	$0.223075\pi$
$444$		0			0
$445$	8211.50	+	14222.7i	0.874747	+	1.51511i
$446$		0			0
$447$			10638.1i			1.12565i
$448$		0			0
$449$	−3059.23	−	1766.25i	−0.321546	−	0.185644i	0.330536	−	0.943793i	$-0.392771\pi$
$449$	−3059.23	−	1766.25i	−0.321546	−	0.185644i	−0.652081	+	0.758149i	$0.726104\pi$
$450$		0			0
$451$	−998.389	+	1729.26i	−0.104240	+	0.180549i
$452$		0			0
$453$	−15695.8	+	9061.95i	−1.62793	+	0.939884i
$454$		0			0
$455$	−16160.8	−	7501.90i	−1.66512	−	0.772955i
$456$		0			0
$457$	−4838.91	+	2793.74i	−0.495305	+	0.285965i	−0.726773	−	0.686878i	$-0.758981\pi$
$457$	−4838.91	+	2793.74i	−0.495305	+	0.285965i	0.231468	+	0.972843i	$0.425647\pi$
$458$		0			0
$459$	10585.6	−	18334.9i	1.07646	−	1.86448i
$460$		0			0
$461$	2328.04	+	1344.09i	0.235201	+	0.135793i	0.612969	−	0.790107i	$-0.289975\pi$
$461$	2328.04	+	1344.09i	0.235201	+	0.135793i	−0.377768	+	0.925900i	$0.623308\pi$
$462$		0			0
$463$			19314.2i			1.93868i	0.245723	+	0.969340i	$0.420975\pi$
$463$			19314.2i			1.93868i	−0.245723	+	0.969340i	$0.579025\pi$
$464$		0			0
$465$	4446.81	+	7702.10i	0.443475	+	0.768121i
$466$		0			0
$467$	−5482.16			−0.543221			−0.271611	−	0.962407i	$-0.587556\pi$
$467$	−5482.16			−0.543221			−0.271611	+	0.962407i	$0.587556\pi$
$468$		0			0
$469$	7449.77			0.733472
$470$		0			0
$471$	−6407.25	−	11097.7i	−0.626816	−	1.08568i
$472$		0			0
$473$			3266.72i			0.317556i
$474$		0			0
$475$	240.211	+	138.686i	0.0232035	+	0.0133965i
$476$		0			0
$477$	2513.35	−	4353.25i	0.241255	−	0.417865i
$478$		0			0
$479$	−4389.48	+	2534.27i	−0.418707	+	0.241740i	−0.694524	−	0.719470i	$-0.744385\pi$
$479$	−4389.48	+	2534.27i	−0.418707	+	0.241740i	0.275817	+	0.961210i	$0.411052\pi$
$480$		0			0
$481$	7309.08	+	10400.1i	0.692859	+	0.985873i
$482$		0			0
$483$	−3941.47	+	2275.61i	−0.371311	+	0.214376i
$484$		0			0
$485$	6630.33	−	11484.1i	0.620758	−	1.07518i
$486$		0			0
$487$	−11806.8	−	6816.65i	−1.09860	−	0.634275i	−0.162744	−	0.986668i	$-0.552035\pi$
$487$	−11806.8	−	6816.65i	−1.09860	−	0.634275i	−0.935852	+	0.352393i	$0.885368\pi$
$488$		0			0
$489$			9954.12i			0.920533i
$490$		0			0
$491$	332.094	+	575.204i	0.0305238	+	0.0528688i	0.880884	−	0.473333i	$-0.156949\pi$
$491$	332.094	+	575.204i	0.0305238	+	0.0528688i	−0.850360	+	0.526201i	$0.823616\pi$
$492$		0			0
$493$	−23552.0			−2.15158
$494$		0			0
$495$	7609.79			0.690979
$496$		0			0
$497$	−12065.8	−	20898.6i	−1.08899	−	1.88618i
$498$		0			0
$499$			14754.0i			1.32361i	0.749676	+	0.661805i	$0.230209\pi$
$499$			14754.0i			1.32361i	−0.749676	+	0.661805i	$0.769791\pi$
$500$		0			0
$501$	2207.11	+	1274.28i	0.196819	+	0.113634i
$502$		0			0
$503$	2641.84	−	4575.80i	0.234182	−	0.405616i	−0.724852	−	0.688904i	$-0.758092\pi$
$503$	2641.84	−	4575.80i	0.234182	−	0.405616i	0.959035	+	0.283288i	$0.0914253\pi$
$504$		0			0
$505$	12205.5	−	7046.85i	1.07552	−	0.620952i
$506$		0			0
$507$	12708.4	+	15039.3i	1.11321	+	1.31740i
$508$		0			0
$509$	6582.35	−	3800.32i	0.573197	−	0.330936i	−0.185228	−	0.982696i	$-0.559302\pi$
$509$	6582.35	−	3800.32i	0.573197	−	0.330936i	0.758425	+	0.651760i	$0.225969\pi$
$510$		0			0
$511$	−2467.92	+	4274.56i	−0.213648	+	0.370050i
$512$		0			0
$513$	−3916.14	−	2260.99i	−0.337041	−	0.194591i
$514$		0			0
$515$			16151.0i			1.38194i
$516$		0			0
$517$	−1443.05	−	2499.43i	−0.122757	−	0.212621i
$518$		0			0
$519$	38902.8			3.29025
$520$		0			0
$521$	10834.5			0.911074			0.455537	−	0.890217i	$-0.349447\pi$
$521$	10834.5			0.911074			0.455537	+	0.890217i	$0.349447\pi$
$522$		0			0
$523$	−4518.24	−	7825.83i	−0.377761	−	0.654301i	0.612975	−	0.790102i	$-0.289973\pi$
$523$	−4518.24	−	7825.83i	−0.377761	−	0.654301i	−0.990736	+	0.135801i	$0.956639\pi$
$524$		0			0
$525$		−	4173.51i		−	0.346946i
$526$		0			0
$527$	6531.86	+	3771.17i	0.539910	+	0.311717i
$528$		0			0
$529$	5959.04	−	10321.4i	0.489770	−	0.848307i
$530$		0			0
$531$	11419.6	−	6593.13i	0.933277	−	0.538828i
$532$		0			0
$533$	−4452.98	−	6336.17i	−0.361876	−	0.514916i
$534$		0			0
$535$	17763.7	−	10255.9i	1.43550	−	0.828788i
$536$		0			0
$537$	2916.21	−	5051.02i	0.234346	−	0.405899i
$538$		0			0
$539$	−7253.25	−	4187.67i	−0.579628	−	0.334649i
$540$		0			0
$541$		−	8389.76i		−	0.666735i	−0.942797	−	0.333368i	$-0.891815\pi$
$541$		−	8389.76i		−	0.666735i	0.942797	−	0.333368i	$-0.108185\pi$
$542$		0			0
$543$	−2035.01	−	3524.74i	−0.160830	−	0.278566i
$544$		0			0
$545$	11177.4			0.878511
$546$		0			0
$547$	−23840.9			−1.86355			−0.931777	−	0.363032i	$-0.881742\pi$
$547$	−23840.9			−1.86355			−0.931777	+	0.363032i	$0.881742\pi$
$548$		0			0
$549$	−5430.36	−	9405.66i	−0.422153	−	0.731191i
$550$		0			0
$551$			5030.48i			0.388939i
$552$		0			0
$553$	24569.4	+	14185.1i	1.88933	+	1.09080i
$554$		0			0
$555$	−14351.6	+	24857.8i	−1.09765	+	1.90118i
$556$		0			0
$557$	−16297.7	+	9409.46i	−1.23977	+	0.715784i	−0.969048	−	0.246873i	$-0.920597\pi$
$557$	−16297.7	+	9409.46i	−1.23977	+	0.715784i	−0.270726	+	0.962657i	$0.587264\pi$
$558$		0			0
$559$	−11492.0	−	5334.66i	−0.869519	−	0.403635i
$560$		0			0
$561$	8419.16	−	4860.80i	0.633613	−	0.365817i
$562$		0			0
$563$	−4276.04	+	7406.32i	−0.320095	+	0.554421i	−0.980507	−	0.196482i	$-0.937048\pi$
$563$	−4276.04	+	7406.32i	−0.320095	+	0.554421i	0.660412	+	0.750903i	$0.270382\pi$
$564$		0			0
$565$	9935.21	+	5736.10i	0.739783	+	0.427114i
$566$		0			0
$567$			21703.3i			1.60750i
$568$		0			0
$569$	13111.9	+	22710.4i	0.966041	+	1.67323i	0.706792	+	0.707422i	$0.250142\pi$
$569$	13111.9	+	22710.4i	0.966041	+	1.67323i	0.259250	+	0.965810i	$0.416525\pi$
$570$		0			0
$571$	−3528.25			−0.258586			−0.129293	−	0.991606i	$-0.541271\pi$
$571$	−3528.25			−0.258586			−0.129293	+	0.991606i	$0.541271\pi$
$572$		0			0
$573$	−25230.6			−1.83948
$574$		0			0
$575$	−114.133	−	197.685i	−0.00827773	−	0.0143375i
$576$		0			0
$577$		−	26672.4i		−	1.92441i	−0.272322	−	0.962206i	$-0.587792\pi$
$577$		−	26672.4i		−	1.92441i	0.272322	−	0.962206i	$-0.412208\pi$
$578$		0			0
$579$	8953.32	+	5169.20i	0.642638	+	0.371027i
$580$		0			0
$581$	−3170.71	+	5491.83i	−0.226408	+	0.392150i
$582$		0			0
$583$	986.711	−	569.678i	0.0700950	−	0.0404694i
$584$		0			0
$585$	−12427.0	+	26770.5i	−0.878280	+	1.89201i
$586$		0			0
$587$	4017.05	−	2319.24i	0.282455	−	0.163076i	−0.352079	−	0.935970i	$-0.614525\pi$
$587$	4017.05	−	2319.24i	0.282455	−	0.163076i	0.634534	+	0.772895i	$0.281192\pi$
$588$		0			0
$589$	805.484	−	1395.14i	0.0563487	−	0.0975989i
$590$		0			0
$591$	3156.22	+	1822.25i	0.219678	+	0.126831i
$592$		0			0
$593$			5932.05i			0.410793i	0.978679	+	0.205396i	$0.0658484\pi$
$593$			5932.05i			0.410793i	−0.978679	+	0.205396i	$0.934152\pi$
$594$		0			0
$595$	−17059.5	−	29547.9i	−1.17541	−	2.03587i
$596$		0			0
$597$	7253.89			0.497289
$598$		0			0
$599$	−8927.94			−0.608991			−0.304496	−	0.952514i	$-0.598488\pi$
$599$	−8927.94			−0.608991			−0.304496	+	0.952514i	$0.598488\pi$
$600$		0			0
$601$	−5217.26	−	9036.57i	−0.354104	−	0.613327i	0.632860	−	0.774266i	$-0.281881\pi$
$601$	−5217.26	−	9036.57i	−0.354104	−	0.613327i	−0.986964	+	0.160940i	$0.948548\pi$
$602$		0			0
$603$		−	12340.7i		−	0.833417i
$604$		0			0
$605$	−12119.0	−	6996.91i	−0.814392	−	0.470190i
$606$		0			0
$607$	−4468.87	+	7740.30i	−0.298823	+	0.517577i	−0.975867	−	0.218366i	$-0.929927\pi$
$607$	−4468.87	+	7740.30i	−0.298823	+	0.517577i	0.677044	+	0.735943i	$0.263261\pi$
$608$		0			0
$609$	65550.8	−	37845.8i	4.36166	−	2.51821i
$610$		0			0
$611$	11149.3	−	994.863i	0.738220	−	0.0658721i
$612$		0			0
$613$	−20757.2	+	11984.2i	−1.36766	+	0.789620i	−0.990629	−	0.136580i	$-0.956389\pi$
$613$	−20757.2	+	11984.2i	−1.36766	+	0.789620i	−0.377032	+	0.926200i	$0.623055\pi$
$614$		0			0
$615$	8743.59	−	15144.3i	0.573293	−	0.992973i
$616$		0			0
$617$	−11348.4	−	6551.98i	−0.740467	−	0.427509i	0.0817724	−	0.996651i	$-0.473942\pi$
$617$	−11348.4	−	6551.98i	−0.740467	−	0.427509i	−0.822239	+	0.569142i	$0.807275\pi$
$618$		0			0
$619$		−	25051.3i		−	1.62665i	−0.581810	−	0.813324i	$-0.697655\pi$
$619$		−	25051.3i		−	1.62665i	0.581810	−	0.813324i	$-0.302345\pi$
$620$		0			0
$621$	1860.71	+	3222.84i	0.120238	+	0.208258i
$622$		0			0
$623$	−44761.0			−2.87851
$624$		0			0
$625$	−17224.2			−1.10235
$626$		0			0
$627$	−1038.22	−	1798.25i	−0.0661283	−	0.114538i
$628$		0			0
$629$			24342.2i			1.54306i
$630$		0			0
$631$	48.2319	+	27.8467i	0.00304292	+	0.00175683i	0.501521	−	0.865146i	$-0.332774\pi$
$631$	48.2319	+	27.8467i	0.00304292	+	0.00175683i	−0.498478	+	0.866902i	$0.666107\pi$
$632$		0			0
$633$	−16134.1	+	27945.2i	−1.01307	+	1.75469i
$634$		0			0
$635$	16403.4	−	9470.51i	1.02512	−	0.591852i
$636$		0			0
$637$	26576.6	−	18677.7i	1.65307	−	1.16175i
$638$		0			0
$639$	−34618.9	+	19987.2i	−2.14320	+	1.23738i
$640$		0			0
$641$	−8949.61	+	15501.2i	−0.551464	+	0.955164i	0.446705	+	0.894681i	$0.352597\pi$
$641$	−8949.61	+	15501.2i	−0.551464	+	0.955164i	−0.998169	+	0.0604827i	$0.980736\pi$
$642$		0			0
$643$	22413.1	+	12940.2i	1.37463	+	0.793643i	0.991507	−	0.130054i	$-0.0415151\pi$
$643$	22413.1	+	12940.2i	1.37463	+	0.793643i	0.383123	+	0.923697i	$0.374848\pi$
$644$		0			0
$645$		−	28609.0i		−	1.74648i
$646$		0			0
$647$	−68.8528	−	119.257i	−0.00418375	−	0.00724646i	0.863926	−	0.503619i	$-0.167998\pi$
$647$	−68.8528	−	119.257i	−0.00418375	−	0.00724646i	−0.868110	+	0.496372i	$0.834665\pi$
$648$		0			0
$649$	2988.81			0.180772
$650$		0			0
$651$	−24239.6			−1.45933
$652$		0			0
$653$	−8047.59	−	13938.8i	−0.482277	−	0.835328i	0.517516	−	0.855673i	$-0.326857\pi$
$653$	−8047.59	−	13938.8i	−0.482277	−	0.835328i	−0.999793	+	0.0203456i	$0.993523\pi$
$654$		0			0
$655$			19807.2i			1.18157i
$656$		0			0
$657$	7080.87	+	4088.14i	0.420473	+	0.242760i
$658$		0			0
$659$	3527.57	−	6109.93i	0.208520	−	0.361167i	−0.742729	−	0.669593i	$-0.766469\pi$
$659$	3527.57	−	6109.93i	0.208520	−	0.361167i	0.951248	+	0.308426i	$0.0998021\pi$
$660$		0			0
$661$	3501.02	−	2021.31i	0.206012	−	0.118941i	−0.393445	−	0.919348i	$-0.628717\pi$
$661$	3501.02	−	2021.31i	0.206012	−	0.118941i	0.599457	+	0.800407i	$0.295383\pi$
$662$		0			0
$663$	3351.13	+	37555.6i	0.196300	+	2.19991i
$664$		0			0
$665$	−6311.13	+	3643.73i	−0.368022	+	0.212478i
$666$		0			0
$667$	2069.95	−	3585.25i	0.120163	−	0.208128i
$668$		0			0
$669$	−20263.4	−	11699.1i	−1.17104	−	0.676103i
$670$		0			0
$671$		−	2461.70i		−	0.141629i
$672$		0			0
$673$	11358.9	+	19674.2i	0.650598	+	1.12687i	0.982978	+	0.183724i	$0.0588151\pi$
$673$	11358.9	+	19674.2i	0.650598	+	1.12687i	−0.332380	+	0.943146i	$0.607852\pi$
$674$		0			0
$675$	−3412.57			−0.194592
$676$		0			0
$677$	19237.7			1.09212			0.546058	−	0.837747i	$-0.316128\pi$
$677$	19237.7			1.09212			0.546058	+	0.837747i	$0.316128\pi$
$678$		0			0
$679$	18071.0	+	31299.9i	1.02136	+	1.76904i
$680$		0			0
$681$		−	41771.0i		−	2.35047i
$682$		0			0
$683$	−21722.4	−	12541.5i	−1.21696	−	0.702614i	−0.252696	−	0.967546i	$-0.581317\pi$
$683$	−21722.4	−	12541.5i	−1.21696	−	0.702614i	−0.964267	+	0.264932i	$0.914651\pi$
$684$		0			0
$685$	−3448.80	+	5973.50i	−0.192368	+	0.333191i
$686$		0			0
$687$	961.581	−	555.169i	0.0534012	−	0.0308312i
$688$		0			0
$689$	392.746	+	4401.46i	0.0217162	+	0.243370i
$690$		0			0
$691$	9752.83	−	5630.80i	0.536925	−	0.309994i	−0.206907	−	0.978361i	$-0.566340\pi$
$691$	9752.83	−	5630.80i	0.536925	−	0.309994i	0.743832	+	0.668367i	$0.233006\pi$
$692$		0			0
$693$	−10370.3	+	17961.8i	−0.568447	+	0.984579i
$694$		0			0
$695$	−1601.72	−	924.755i	−0.0874198	−	0.0504719i
$696$		0			0
$697$		−	14830.2i		−	0.805933i
$698$		0			0
$699$	5316.50	+	9208.44i	0.287680	+	0.498276i
$700$		0			0
$701$	15678.7			0.844761			0.422381	−	0.906419i	$-0.361195\pi$
$701$	15678.7			0.844761			0.422381	+	0.906419i	$0.361195\pi$
$702$		0			0
$703$	5199.25			0.278938
$704$		0			0
$705$	12637.8	+	21889.3i	0.675129	+	1.16936i
$706$		0			0
$707$			38412.4i			2.04335i
$708$		0			0
$709$	15238.3	+	8797.84i	0.807174	+	0.466022i	0.845974	−	0.533225i	$-0.179020\pi$
$709$	15238.3	+	8797.84i	0.807174	+	0.466022i	−0.0387995	+	0.999247i	$0.512353\pi$
$710$		0			0
$711$	23497.9	−	40699.6i	1.23944	−	2.14677i
$712$		0			0
$713$	−1148.15	+	662.884i	−0.0603064	+	0.0348179i
$714$		0			0
$715$	−5473.26	+	3846.53i	−0.286277	+	0.201192i
$716$		0			0
$717$	35264.3	−	20359.8i	1.83678	−	1.06046i
$718$		0			0
$719$	8305.36	−	14385.3i	0.430790	−	0.746150i	−0.566152	−	0.824301i	$-0.691568\pi$
$719$	8305.36	−	14385.3i	0.430790	−	0.746150i	0.996942	+	0.0781513i	$0.0249017\pi$
$720$		0			0
$721$	−38122.1	−	22009.8i	−1.96913	−	1.13688i
$722$		0			0
$723$		−	56319.1i		−	2.89700i
$724$		0			0
$725$	1898.16	+	3287.71i	0.0972357	+	0.168417i
$726$		0			0
$727$	8614.24			0.439456			0.219728	−	0.975561i	$-0.429483\pi$
$727$	8614.24			0.439456			0.219728	+	0.975561i	$0.429483\pi$
$728$		0			0
$729$	−21123.1			−1.07317
$730$		0			0
$731$	−12131.1	−	21011.7i	−0.613797	−	1.06313i
$732$		0			0
$733$		−	22282.4i		−	1.12281i	−0.827541	−	0.561405i	$-0.810261\pi$
$733$		−	22282.4i		−	1.12281i	0.827541	−	0.561405i	$-0.189739\pi$
$734$		0			0
$735$	63521.8	+	36674.3i	3.18781	+	1.84048i
$736$		0			0
$737$	1398.57	−	2422.39i	0.0699009	−	0.121072i
$738$		0			0
$739$	23374.0	−	13495.0i	1.16350	−	0.671748i	0.211361	−	0.977408i	$-0.432210\pi$
$739$	23374.0	−	13495.0i	1.16350	−	0.671748i	0.952141	+	0.305660i	$0.0988771\pi$
$740$		0			0
$741$	8021.51	−	715.767i	0.397675	−	0.0354849i
$742$		0			0
$743$	−7976.16	+	4605.04i	−0.393832	+	0.227379i	−0.683819	−	0.729652i	$-0.739682\pi$
$743$	−7976.16	+	4605.04i	−0.393832	+	0.227379i	0.289987	+	0.957030i	$0.406349\pi$
$744$		0			0
$745$	7009.12	−	12140.2i	0.344690	−	0.597021i
$746$		0			0
$747$	9097.29	+	5252.32i	0.445586	+	0.257259i
$748$		0			0
$749$			55905.1i			2.72727i
$750$		0			0
$751$	11115.8	+	19253.2i	0.540109	+	0.935496i	0.998897	+	0.0469505i	$0.0149503\pi$
$751$	11115.8	+	19253.2i	0.540109	+	0.935496i	−0.458788	+	0.888546i	$0.651716\pi$
$752$		0			0
$753$	−8288.20			−0.401114
$754$		0			0
$755$	23882.5			1.15123
$756$		0			0
$757$	10967.4	+	18996.2i	0.526576	+	0.912057i	0.999520	+	0.0309645i	$0.00985788\pi$
$757$	10967.4	+	18996.2i	0.526576	+	0.912057i	−0.472944	+	0.881092i	$0.656809\pi$
$758$		0			0
$759$			1708.83i			0.0817215i
$760$		0			0
$761$	−20991.7	−	12119.6i	−0.999932	−	0.577311i	−0.0917041	−	0.995786i	$-0.529231\pi$
$761$	−20991.7	−	12119.6i	−0.999932	−	0.577311i	−0.908228	+	0.418475i	$0.862565\pi$
$762$		0			0
$763$	−15232.1	+	26382.7i	−0.722724	+	1.25179i
$764$		0			0
$765$	−48946.5	+	28259.3i	−2.31329	+	1.33558i
$766$		0			0
$767$	−4880.81	+	10514.3i	−0.229773	+	0.494982i
$768$		0			0
$769$	−26825.0	+	15487.4i	−1.25791	+	0.726256i	−0.972668	−	0.232199i	$-0.925408\pi$
$769$	−26825.0	+	15487.4i	−1.25791	+	0.726256i	−0.285243	+	0.958455i	$0.592074\pi$
$770$		0			0
$771$	−2430.56	+	4209.85i	−0.113534	+	0.196646i
$772$		0			0
$773$	27865.7	+	16088.3i	1.29658	+	0.748583i	0.979813	−	0.199918i	$-0.0640677\pi$
$773$	27865.7	+	16088.3i	1.29658	+	0.748583i	0.316772	+	0.948502i	$0.397401\pi$
$774$		0			0
$775$		−	1215.74i		−	0.0563493i
$776$		0			0
$777$	−39115.5	−	67750.0i	−1.80600	−	3.12808i
$778$		0			0
$779$	−3167.59			−0.145688
$780$		0			0
$781$	−9060.63			−0.415128
$782$		0			0
$783$	−30945.5	−	53599.2i	−1.41239	−	2.44633i
$784$		0			0
$785$			16886.1i			0.767760i
$786$		0			0
$787$	−22531.5	−	13008.6i	−1.02053	−	0.589206i	−0.106276	−	0.994337i	$-0.533893\pi$
$787$	−22531.5	−	13008.6i	−1.02053	−	0.589206i	−0.914259	+	0.405131i	$0.867226\pi$
$788$		0			0
$789$	23520.0	−	40737.9i	1.06126	−	1.83816i
$790$		0			0
$791$	−27078.5	+	15633.8i	−1.21719	+	0.702747i
$792$		0			0
$793$	8660.02	+	4020.02i	0.387801	+	0.180019i
$794$		0			0
$795$	−8641.32	+	4989.07i	−0.385504	+	0.222571i
$796$		0			0
$797$	−9450.96	+	16369.5i	−0.420038	+	0.727527i	−0.995943	−	0.0899897i	$-0.971317\pi$
$797$	−9450.96	+	16369.5i	−0.420038	+	0.727527i	0.575905	+	0.817517i	$0.304650\pi$
$798$		0			0
$799$	18563.5	+	10717.6i	0.821938	+	0.474546i
$800$		0			0
$801$			74147.2i			3.27074i
$802$		0			0
$803$	926.621	+	1604.95i	0.0407220	+	0.0705325i
$804$		0			0
$805$	5997.31			0.262580
$806$		0			0
$807$	−2958.92			−0.129069
$808$		0			0
$809$	−363.787	−	630.098i	−0.0158097	−	0.0273833i	0.858012	−	0.513629i	$-0.171699\pi$
$809$	−363.787	−	630.098i	−0.0158097	−	0.0273833i	−0.873822	+	0.486246i	$0.838366\pi$
$810$		0			0
$811$		−	23940.1i		−	1.03656i	−0.855210	−	0.518281i	$-0.826572\pi$
$811$		−	23940.1i		−	1.03656i	0.855210	−	0.518281i	$-0.173428\pi$
$812$		0			0
$813$	11128.9	+	6425.26i	0.480082	+	0.277176i
$814$		0			0
$815$	6558.46	−	11359.6i	0.281881	−	0.488232i
$816$		0			0
$817$	−4487.89	+	2591.08i	−0.192180	+	0.110955i
$818$		0			0
$819$	−46253.1	−	65813.8i	−1.97340	−	2.80796i
$820$		0			0
$821$	6548.34	−	3780.69i	0.278366	−	0.160715i	−0.354317	−	0.935125i	$-0.615287\pi$
$821$	6548.34	−	3780.69i	0.278366	−	0.160715i	0.632684	+	0.774410i	$0.281953\pi$
$822$		0			0
$823$	10413.0	−	18035.9i	0.441038	−	0.763901i	−0.556729	−	0.830695i	$-0.687944\pi$
$823$	10413.0	−	18035.9i	0.441038	−	0.763901i	0.997767	+	0.0667938i	$0.0212770\pi$
$824$		0			0
$825$	−1357.07	−	783.506i	−0.0572693	−	0.0330645i
$826$		0			0
$827$			34592.6i			1.45454i	0.686353	+	0.727268i	$0.259210\pi$
$827$			34592.6i			1.45454i	−0.686353	+	0.727268i	$0.740790\pi$
$828$		0			0
$829$	−10442.0	−	18086.1i	−0.437474	−	0.757727i	0.560020	−	0.828479i	$-0.310794\pi$
$829$	−10442.0	−	18086.1i	−0.437474	−	0.757727i	−0.997494	+	0.0707518i	$0.977460\pi$
$830$		0			0
$831$	19188.5			0.801011
$832$		0			0
$833$	62204.3			2.58734
$834$		0			0
$835$	−1679.16	−	2908.39i	−0.0695925	−	0.120538i
$836$		0			0
$837$			19820.1i			0.818498i
$838$		0			0
$839$	−38090.7	−	21991.7i	−1.56739	−	0.904932i	−0.996472	−	0.0839231i	$-0.973255\pi$
$839$	−38090.7	−	21991.7i	−1.56739	−	0.904932i	−0.570916	−	0.821009i	$-0.693412\pi$
$840$		0			0
$841$	−22230.9	+	38505.0i	−0.911513	+	1.57879i
$842$		0			0
$843$	−45458.7	+	26245.6i	−1.85727	+	1.07230i
$844$		0			0
$845$	−4593.76	−	25535.9i	−0.187018	−	1.03960i
$846$		0			0
$847$	33030.4	−	19070.1i	1.33995	−	0.773621i
$848$		0			0
$849$	−7651.35	+	13252.5i	−0.309297	+	0.535719i
$850$		0			0
$851$	−3705.54	−	2139.39i	−0.149265	−	0.0861779i
$852$		0			0
$853$		−	16552.4i		−	0.664412i	−0.943207	−	0.332206i	$-0.892207\pi$
$853$		−	16552.4i		−	0.664412i	0.943207	−	0.332206i	$-0.107793\pi$
$854$		0			0
$855$	6035.89	+	10454.5i	0.241431	+	0.418170i
$856$		0			0
$857$	−12869.9			−0.512983			−0.256492	−	0.966546i	$-0.582567\pi$
$857$	−12869.9			−0.512983			−0.256492	+	0.966546i	$0.582567\pi$
$858$		0			0
$859$	21172.2			0.840961			0.420481	−	0.907302i	$-0.361861\pi$
$859$	21172.2			0.840961			0.420481	+	0.907302i	$0.361861\pi$
$860$		0			0
$861$	23830.7	+	41276.0i	0.943261	+	1.63378i
$862$		0			0
$863$		−	47889.1i		−	1.88895i	−0.328584	−	0.944475i	$-0.606571\pi$
$863$		−	47889.1i		−	1.88895i	0.328584	−	0.944475i	$-0.393429\pi$
$864$		0			0
$865$	−44395.6	−	25631.8i	−1.74508	−	1.00752i
$866$		0			0
$867$	−14086.2	+	24398.1i	−0.551781	+	0.955712i
$868$		0			0
$869$	9224.99	−	5326.05i	0.360111	−	0.207910i
$870$		0			0
$871$	6237.85	+	8875.88i	0.242665	+	0.345290i
$872$		0			0
$873$	51848.7	−	29934.9i	2.01010	−	1.16053i
$874$		0			0
$875$	21007.8	−	36386.5i	0.811648	−	1.40582i
$876$		0			0
$877$	−37745.6	−	21792.4i	−1.45334	−	0.839085i	−0.454669	−	0.890660i	$-0.650243\pi$
$877$	−37745.6	−	21792.4i	−1.45334	−	0.839085i	−0.998669	+	0.0515750i	$0.983576\pi$
$878$		0			0
$879$		−	15981.9i		−	0.613262i
$880$		0			0
$881$	21279.2	+	36856.7i	0.813751	+	1.40946i	0.910221	+	0.414122i	$0.135911\pi$
$881$	21279.2	+	36856.7i	0.813751	+	1.40946i	−0.0964705	+	0.995336i	$0.530755\pi$
$882$		0			0
$883$	−22522.3			−0.858364			−0.429182	−	0.903218i	$-0.641198\pi$
$883$	−22522.3			−0.858364			−0.429182	+	0.903218i	$0.641198\pi$
$884$		0			0
$885$	−26175.1			−0.994198
$886$		0			0
$887$	3089.40	+	5351.00i	0.116947	+	0.202558i	0.918556	−	0.395290i	$-0.129356\pi$
$887$	3089.40	+	5351.00i	0.116947	+	0.202558i	−0.801609	+	0.597848i	$0.796023\pi$
$888$		0			0
$889$			51623.9i			1.94759i
$890$		0			0
$891$	7057.11	+	4074.43i	0.265345	+	0.153197i
$892$		0			0
$893$	2289.18	−	3964.97i	0.0857832	−	0.148581i
$894$		0			0
$895$	−6655.92	+	3842.79i	−0.248584	+	0.143520i
$896$		0			0
$897$	−6011.50	−	2790.57i	−0.223766	−	0.103873i
$898$		0			0
$899$	19094.9	−	11024.5i	0.708399	−	0.408995i
$900$		0			0
$901$	−4231.04	+	7328.38i	−0.156445	+	0.270970i
$902$		0			0
$903$	67527.4	+	38987.0i	2.48856	+	1.43677i
$904$		0			0
$905$			5363.22i			0.196994i
$906$		0			0
$907$	13077.7	+	22651.3i	0.478764	+	0.829244i	0.999703	−	0.0243499i	$-0.00775157\pi$
$907$	13077.7	+	22651.3i	0.478764	+	0.829244i	−0.520939	+	0.853594i	$0.674418\pi$
$908$		0			0
$909$	63630.8			2.32178
$910$		0			0
$911$	29386.6			1.06874			0.534369	−	0.845251i	$-0.320549\pi$
$911$	29386.6			1.06874			0.534369	+	0.845251i	$0.320549\pi$
$912$		0			0
$913$	1190.49	+	2062.00i	0.0431540	+	0.0747450i
$914$		0			0
$915$			21558.8i			0.778920i
$916$		0			0
$917$	−46752.0	−	26992.3i	−1.68363	−	0.972044i
$918$		0			0
$919$	−11348.9	+	19656.9i	−0.407363	+	0.705573i	−0.994593	−	0.103847i	$-0.966885\pi$
$919$	−11348.9	+	19656.9i	−0.407363	+	0.705573i	0.587231	+	0.809420i	$0.300218\pi$
$920$		0			0
$921$	−31261.7	+	18049.0i	−1.11847	+	0.645747i
$922$		0			0
$923$	14796.3	−	31874.5i	0.527655	−	1.13669i
$924$		0			0
$925$	3398.01	−	1961.84i	0.120785	−	0.0697351i
$926$		0			0
$927$	−36459.6	+	63149.9i	−1.29179	+	2.23745i
$928$		0			0
$929$	−35327.4	−	20396.3i	−1.24764	−	0.720324i	−0.277000	−	0.960870i	$-0.589340\pi$
$929$	−35327.4	−	20396.3i	−1.24764	−	0.720324i	−0.970638	+	0.240546i	$0.922673\pi$
$930$		0			0
$931$		−	13286.2i		−	0.467710i
$932$		0			0
$933$	361.309	+	625.806i	0.0126782	+	0.0219592i
$934$		0			0
$935$	−12810.5			−0.448074
$936$		0			0
$937$	22015.2			0.767560			0.383780	−	0.923424i	$-0.374622\pi$
$937$	22015.2			0.767560			0.383780	+	0.923424i	$0.374622\pi$
$938$		0			0
$939$	20739.2	+	35921.3i	0.720765	+	1.24840i
$940$		0			0
$941$		−	7774.05i		−	0.269316i	−0.990892	−	0.134658i	$-0.957006\pi$
$941$		−	7774.05i		−	0.269316i	0.990892	−	0.134658i	$-0.0429936\pi$
$942$		0			0
$943$	2257.56	+	1303.40i	0.0779600	+	0.0450102i
$944$		0			0
$945$	44829.6	−	77647.1i	1.54318	−	2.67287i
$946$		0			0
$947$	13746.3	−	7936.44i	0.471695	−	0.272333i	−0.245254	−	0.969459i	$-0.578871\pi$
$947$	13746.3	−	7936.44i	0.471695	−	0.272333i	0.716949	+	0.697126i	$0.245538\pi$
$948$		0			0
$949$	−7159.28	+	638.829i	−0.244889	+	0.0218517i
$950$		0			0
$951$	−83227.3	+	48051.3i	−2.83789	+	1.63845i
$952$		0			0
$953$	21907.7	−	37945.3i	0.744659	−	1.28979i	−0.205695	−	0.978616i	$-0.565945\pi$
$953$	21907.7	−	37945.3i	0.744659	−	1.28979i	0.950354	−	0.311171i	$-0.100721\pi$
$954$		0			0
$955$	28793.0	+	16623.6i	0.975622	+	0.563275i
$956$		0			0
$957$		−	28419.6i		−	0.959955i
$958$		0			0
$959$	−9399.73	−	16280.8i	−0.316510	−	0.548212i
$960$		0			0
$961$	22730.0			0.762983
$962$		0			0
$963$	92607.6			3.09890
$964$		0			0
$965$	−6811.65	−	11798.1i	−0.227228	−	0.393570i
$966$		0			0
$967$		−	6323.57i		−	0.210292i	−0.994457	−	0.105146i	$-0.966469\pi$
$967$		−	6323.57i		−	0.210292i	0.994457	−	0.105146i	$-0.0335310\pi$
$968$		0			0
$969$	13355.7	+	7710.93i	0.442774	+	0.255635i
$970$		0			0
$971$	24755.4	−	42877.5i	0.818164	−	1.41710i	−0.0888698	−	0.996043i	$-0.528326\pi$
$971$	24755.4	−	42877.5i	0.818164	−	1.41710i	0.907034	−	0.421058i	$-0.138341\pi$
$972$		0			0
$973$	4365.50	−	2520.42i	0.143835	−	0.0830433i
$974$		0			0
$975$	4972.44	−	3494.57i	0.163329	−	0.114785i
$976$		0			0
$977$	4897.51	−	2827.58i	0.160374	−	0.0925918i	−0.417665	−	0.908601i	$-0.637152\pi$
$977$	4897.51	−	2827.58i	0.160374	−	0.0925918i	0.578039	+	0.816009i	$0.303818\pi$
$978$		0			0
$979$	−8403.12	+	14554.6i	−0.274326	+	0.475146i
$980$		0			0
$981$	43703.4	+	25232.2i	1.42237	+	0.821204i
$982$		0			0
$983$		−	4051.62i		−	0.131461i	−0.997837	−	0.0657307i	$-0.979062\pi$
$983$		−	4051.62i		−	0.131461i	0.997837	−	0.0657307i	$-0.0209378\pi$
$984$		0			0
$985$	−2401.24	−	4159.07i	−0.0776750	−	0.134537i
$986$		0			0
$987$	−68888.6			−2.22163
$988$		0			0
$989$	4264.73			0.137119
$990$		0			0
$991$	10104.2	+	17500.9i	0.323884	+	0.560984i	0.981286	−	0.192556i	$-0.0616778\pi$
$991$	10104.2	+	17500.9i	0.323884	+	0.560984i	−0.657402	+	0.753540i	$0.728345\pi$
$992$		0			0
$993$		−	46535.7i		−	1.48718i
$994$		0			0
$995$	−8278.09	−	4779.36i	−0.263752	−	0.152277i
$996$		0			0
$997$	23139.1	−	40078.2i	0.735029	−	1.27311i	−0.219681	−	0.975572i	$-0.570502\pi$
$997$	23139.1	−	40078.2i	0.735029	−	1.27311i	0.954711	−	0.297536i	$-0.0961649\pi$
$998$		0			0
$999$	−55397.4	+	31983.7i	−1.75445	+	1.01293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.4.h.a.49.1	yes	8
3.2	odd	2		468.4.t.g.361.2		8
4.3	odd	2		208.4.w.c.49.4		8
13.2	odd	12		676.4.a.g.1.8		8
13.3	even	3		676.4.d.d.337.8		8
13.4	even	6	inner	52.4.h.a.17.1	✓	8
13.5	odd	4		676.4.e.h.653.2		16
13.6	odd	12		676.4.e.h.529.2		16
13.7	odd	12		676.4.e.h.529.1		16
13.8	odd	4		676.4.e.h.653.1		16
13.9	even	3		676.4.h.e.485.1		8
13.10	even	6		676.4.d.d.337.7		8
13.11	odd	12		676.4.a.g.1.7		8
13.12	even	2		676.4.h.e.361.1		8
39.17	odd	6		468.4.t.g.433.3		8
52.43	odd	6		208.4.w.c.17.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.4.h.a.17.1	✓	8	13.4	even	6	inner
52.4.h.a.49.1	yes	8	1.1	even	1	trivial
208.4.w.c.17.4		8	52.43	odd	6
208.4.w.c.49.4		8	4.3	odd	2
468.4.t.g.361.2		8	3.2	odd	2
468.4.t.g.433.3		8	39.17	odd	6
676.4.a.g.1.7		8	13.11	odd	12
676.4.a.g.1.8		8	13.2	odd	12
676.4.d.d.337.7		8	13.10	even	6
676.4.d.d.337.8		8	13.3	even	3
676.4.e.h.529.1		16	13.7	odd	12
676.4.e.h.529.2		16	13.6	odd	12
676.4.e.h.653.1		16	13.8	odd	4
676.4.e.h.653.2		16	13.5	odd	4
676.4.h.e.361.1		8	13.12	even	2
676.4.h.e.485.1		8	13.9	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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	52.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.48104 - 7.76138i) q^{3} +11.8097i q^{5} +(-27.8750 - 16.0936i) q^{7} +(-26.6594 + 46.1754i) q^{9} +O(q^{10})\)	\(q+(-4.48104 - 7.76138i) q^{3} +11.8097i q^{5} +(-27.8750 - 16.0936i) q^{7} +(-26.6594 + 46.1754i) q^{9} +(-10.4661 + 6.04263i) q^{11} +(-4.16590 - 46.6867i) q^{13} +(91.6593 - 52.9195i) q^{15} +(44.8791 - 77.7328i) q^{17} +(-16.6029 - 9.58572i) q^{19} +288.465i q^{21} +(7.88869 + 13.6636i) q^{23} -14.4680 q^{25} +235.870 q^{27} +(-131.197 - 227.240i) q^{29} +84.0297i q^{31} +(93.7982 + 54.1544i) q^{33} +(190.060 - 329.194i) q^{35} +(-234.864 + 135.599i) q^{37} +(-343.686 + 241.538i) q^{39} +(143.088 - 82.6122i) q^{41} +(135.153 - 234.092i) q^{43} +(-545.315 - 314.838i) q^{45} +238.811i q^{47} +(346.511 + 600.174i) q^{49} -804.419 q^{51} -94.2765 q^{53} +(-71.3613 - 123.601i) q^{55} +171.816i q^{57} +(-214.177 - 123.655i) q^{59} +(-101.847 + 176.404i) q^{61} +(1486.26 - 858.092i) q^{63} +(551.354 - 49.1978i) q^{65} +(-200.442 + 115.725i) q^{67} +(70.6990 - 122.454i) q^{69} +(649.282 + 374.863i) q^{71} -153.347i q^{73} +(64.8316 + 112.292i) q^{75} +388.991 q^{77} -881.413 q^{79} +(-337.140 - 583.944i) q^{81} -197.016i q^{83} +(917.998 + 530.006i) q^{85} +(-1175.80 + 2036.54i) q^{87} +(1204.33 - 695.321i) q^{89} +(-635.234 + 1368.44i) q^{91} +(652.186 - 376.540i) q^{93} +(113.204 - 196.075i) q^{95} +(-972.430 - 561.433i) q^{97} -644.370i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 36 q^{7} - 70 q^{9}+O(q^{10}) \) 8 * q - 36 * q^7 - 70 * q^9	\( 8 q - 36 q^{7} - 70 q^{9} + 72 q^{11} + 62 q^{13} + 96 q^{15} + 88 q^{17} - 144 q^{19} - 20 q^{23} - 84 q^{25} - 432 q^{27} - 484 q^{29} + 1038 q^{33} + 40 q^{35} + 996 q^{37} - 236 q^{39} + 156 q^{41} + 504 q^{43} - 1530 q^{45} + 922 q^{49} - 1808 q^{51} - 1164 q^{53} - 1128 q^{55} + 600 q^{59} - 1224 q^{61} + 6480 q^{63} + 670 q^{65} + 960 q^{67} + 1738 q^{69} - 2964 q^{71} + 1448 q^{75} - 3972 q^{77} - 3968 q^{79} - 4132 q^{81} + 3870 q^{85} - 1660 q^{87} + 5430 q^{89} - 1720 q^{91} + 3324 q^{93} + 2400 q^{95} - 3042 q^{97}+O(q^{100}) \) 8 * q - 36 * q^7 - 70 * q^9 + 72 * q^11 + 62 * q^13 + 96 * q^15 + 88 * q^17 - 144 * q^19 - 20 * q^23 - 84 * q^25 - 432 * q^27 - 484 * q^29 + 1038 * q^33 + 40 * q^35 + 996 * q^37 - 236 * q^39 + 156 * q^41 + 504 * q^43 - 1530 * q^45 + 922 * q^49 - 1808 * q^51 - 1164 * q^53 - 1128 * q^55 + 600 * q^59 - 1224 * q^61 + 6480 * q^63 + 670 * q^65 + 960 * q^67 + 1738 * q^69 - 2964 * q^71 + 1448 * q^75 - 3972 * q^77 - 3968 * q^79 - 4132 * q^81 + 3870 * q^85 - 1660 * q^87 + 5430 * q^89 - 1720 * q^91 + 3324 * q^93 + 2400 * q^95 - 3042 * q^97

Introduction

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