LMFDB - Embedded newform 261.3.s.a.37.1

Newspace parameters

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	261.s (of order $28$, degree $12$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.11173489980$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{28})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	261.37
Dual form			261.3.s.a.127.1

$q$-expansion

$f(q)$	$=$	$q+(-1.65381 - 0.578694i) q^{2} +(-0.727117 - 0.579856i) q^{4} +(0.825315 + 1.71379i) q^{5} +(-1.24782 - 1.56472i) q^{7} +(4.59573 + 7.31406i) q^{8} +O(q^{10})$	\(q+(-1.65381 - 0.578694i) q^{2} +(-0.727117 - 0.579856i) q^{4} +(0.825315 + 1.71379i) q^{5} +(-1.24782 - 1.56472i) q^{7} +(4.59573 + 7.31406i) q^{8} +(-0.373160 - 3.31188i) q^{10} +(6.63034 - 10.5521i) q^{11} +(-3.80625 + 0.868753i) q^{13} +(1.15817 + 3.30986i) q^{14} +(-2.54008 - 11.1288i) q^{16} +(-7.59392 - 7.59392i) q^{17} +(-0.137534 + 0.0154964i) q^{19} +(0.393648 - 1.72469i) q^{20} +(-17.0718 + 13.6143i) q^{22} +(-26.7367 - 12.8757i) q^{23} +(13.3313 - 16.7170i) q^{25} +(6.79757 + 0.765903i) q^{26} +1.86129i q^{28} +(-8.15475 + 27.8298i) q^{29} +(-54.1874 - 18.9610i) q^{31} +(1.62926 - 14.4601i) q^{32} +(8.16437 + 16.9535i) q^{34} +(1.65175 - 3.42989i) q^{35} +(-29.9166 - 47.6121i) q^{37} +(0.236424 + 0.0539622i) q^{38} +(-8.74180 + 13.9125i) q^{40} +(25.9162 - 25.9162i) q^{41} +(5.16003 + 14.7465i) q^{43} +(-10.9397 + 3.82798i) q^{44} +(36.7664 + 36.7664i) q^{46} +(-55.9924 - 35.1824i) q^{47} +(10.0122 - 43.8665i) q^{49} +(-31.7215 + 19.9320i) q^{50} +(3.27134 + 1.57540i) q^{52} +(-29.3541 + 14.1362i) q^{53} +(23.5562 + 2.65415i) q^{55} +(5.70980 - 16.3177i) q^{56} +(29.5914 - 41.3062i) q^{58} -0.396318 q^{59} +(-6.99907 + 62.1184i) q^{61} +(78.6432 + 62.7159i) q^{62} +(-30.8736 + 64.1097i) q^{64} +(-4.63022 - 5.80611i) q^{65} +(-21.7870 - 4.97273i) q^{67} +(1.11828 + 9.92505i) q^{68} +(-4.71654 + 4.71654i) q^{70} +(64.8290 - 14.7968i) q^{71} +(76.3640 - 26.7209i) q^{73} +(21.9237 + 96.0540i) q^{74} +(0.108989 + 0.0684824i) q^{76} +(-24.7846 + 2.79256i) q^{77} +(67.7630 - 42.5783i) q^{79} +(16.9760 - 13.5379i) q^{80} +(-57.8580 + 27.8629i) q^{82} +(68.4247 - 85.8019i) q^{83} +(6.74697 - 19.2817i) q^{85} -27.3741i q^{86} +107.650 q^{88} +(77.7390 + 27.2021i) q^{89} +(6.10889 + 4.87167i) q^{91} +(11.9746 + 24.8656i) q^{92} +(72.2411 + 90.5875i) q^{94} +(-0.140067 - 0.222915i) q^{95} +(19.5392 + 173.415i) q^{97} +(-41.9436 + 66.7529i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) $	$ 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{3}{28}\right)$	$1$

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 $

$2$	−1.65381	−	0.578694i	−0.826906	−	0.289347i	−0.116546	−	0.993185i	$-0.537182\pi$
$2$	−1.65381	−	0.578694i	−0.826906	−	0.289347i	−0.710360	+	0.703838i	$0.751468\pi$
$3$		0			0
$3$		0			0
$4$	−0.727117	−	0.579856i	−0.181779	−	0.144964i
$5$	0.825315	+	1.71379i	0.165063	+	0.342757i	0.967051	−	0.254583i	$-0.0819384\pi$
$5$	0.825315	+	1.71379i	0.165063	+	0.342757i	−0.801988	+	0.597341i	$0.796224\pi$
$6$		0			0
$7$	−1.24782	−	1.56472i	−0.178260	−	0.223531i	0.684671	−	0.728852i	$-0.259946\pi$
$7$	−1.24782	−	1.56472i	−0.178260	−	0.223531i	−0.862932	+	0.505320i	$0.831374\pi$
$8$	4.59573	+	7.31406i	0.574466	+	0.914257i
$9$		0			0
$10$	−0.373160	−	3.31188i	−0.0373160	−	0.331188i
$11$	6.63034	−	10.5521i	0.602758	−	0.959284i	−0.396392	−	0.918081i	$-0.629738\pi$
$11$	6.63034	−	10.5521i	0.602758	−	0.959284i	0.999151	−	0.0412032i	$-0.0131191\pi$
$12$		0			0
$13$	−3.80625	+	0.868753i	−0.292789	+	0.0668271i	−0.366392	−	0.930460i	$-0.619407\pi$
$13$	−3.80625	+	0.868753i	−0.292789	+	0.0668271i	0.0736036	+	0.997288i	$0.476550\pi$
$14$	1.15817	+	3.30986i	0.0827265	+	0.236419i
$15$		0			0
$16$	−2.54008	−	11.1288i	−0.158755	−	0.695550i
$17$	−7.59392	−	7.59392i	−0.446701	−	0.446701i	0.447555	−	0.894256i	$-0.352295\pi$
$17$	−7.59392	−	7.59392i	−0.446701	−	0.446701i	−0.894256	+	0.447555i	$0.852295\pi$
$18$		0			0
$19$	−0.137534	+	0.0154964i	−0.00723865	+	0.000815600i	−0.115583	−	0.993298i	$-0.536874\pi$
$19$	−0.137534	+	0.0154964i	−0.00723865	+	0.000815600i	0.108344	+	0.994113i	$0.465445\pi$
$20$	0.393648	−	1.72469i	0.0196824	−	0.0862343i
$21$		0			0
$22$	−17.0718	+	13.6143i	−0.775991	+	0.618832i
$23$	−26.7367	−	12.8757i	−1.16247	−	0.559814i	−0.249710	−	0.968321i	$-0.580335\pi$
$23$	−26.7367	−	12.8757i	−1.16247	−	0.559814i	−0.912755	+	0.408507i	$0.866050\pi$
$24$		0			0
$25$	13.3313	−	16.7170i	0.533253	−	0.668678i
$26$	6.79757	+	0.765903i	0.261445	+	0.0294578i
$27$		0			0
$28$			1.86129i			0.0664747i
$29$	−8.15475	+	27.8298i	−0.281198	+	0.959650i
$29$	−8.15475	+	27.8298i	−0.281198	+	0.959650i
$30$		0			0
$31$	−54.1874	−	18.9610i	−1.74798	−	0.611645i	−0.749264	−	0.662272i	$-0.769593\pi$
$31$	−54.1874	−	18.9610i	−1.74798	−	0.611645i	−0.998718	+	0.0506263i	$0.983878\pi$
$32$	1.62926	−	14.4601i	0.0509145	−	0.451879i
$33$		0			0
$34$	8.16437	+	16.9535i	0.240128	+	0.498632i
$35$	1.65175	−	3.42989i	0.0471928	−	0.0979968i
$36$		0			0
$37$	−29.9166	−	47.6121i	−0.808558	−	1.28681i	−0.954706	−	0.297550i	$-0.903831\pi$
$37$	−29.9166	−	47.6121i	−0.808558	−	1.28681i	0.146149	−	0.989263i	$-0.453312\pi$
$38$	0.236424	+	0.0539622i	0.00622167	+	0.00142006i
$39$		0			0
$40$	−8.74180	+	13.9125i	−0.218545	+	0.347812i
$41$	25.9162	−	25.9162i	0.632101	−	0.632101i	−0.316493	−	0.948595i	$-0.602506\pi$
$41$	25.9162	−	25.9162i	0.632101	−	0.632101i	0.948595	+	0.316493i	$0.102506\pi$
$42$		0			0
$43$	5.16003	+	14.7465i	0.120001	+	0.342943i	0.988178	−	0.153312i	$-0.0489940\pi$
$43$	5.16003	+	14.7465i	0.120001	+	0.342943i	−0.868177	+	0.496255i	$0.834708\pi$
$44$	−10.9397	+	3.82798i	−0.248631	+	0.0869996i
$45$		0			0
$46$	36.7664	+	36.7664i	0.799270	+	0.799270i
$47$	−55.9924	−	35.1824i	−1.19133	−	0.748561i	−0.217547	−	0.976050i	$-0.569806\pi$
$47$	−55.9924	−	35.1824i	−1.19133	−	0.748561i	−0.973781	+	0.227489i	$0.926948\pi$
$48$		0			0
$49$	10.0122	−	43.8665i	0.204331	−	0.895234i
$50$	−31.7215	+	19.9320i	−0.634431	+	0.398639i
$51$		0			0
$52$	3.27134	+	1.57540i	0.0629104	+	0.0302961i
$53$	−29.3541	+	14.1362i	−0.553851	+	0.266720i	−0.689806	−	0.723995i	$-0.742304\pi$
$53$	−29.3541	+	14.1362i	−0.553851	+	0.266720i	0.135955	+	0.990715i	$0.456590\pi$
$54$		0			0
$55$	23.5562	+	2.65415i	0.428295	+	0.0482572i
$56$	5.70980	−	16.3177i	0.101961	−	0.291387i
$57$		0			0
$58$	29.5914	−	41.3062i	0.510196	−	0.712176i
$59$	−0.396318			−0.00671725			−0.00335862	−	0.999994i	$-0.501069\pi$
$59$	−0.396318			−0.00671725			−0.00335862	+	0.999994i	$0.501069\pi$
$60$		0			0
$61$	−6.99907	+	62.1184i	−0.114739	+	1.01834i	0.795984	+	0.605317i	$0.206954\pi$
$61$	−6.99907	+	62.1184i	−0.114739	+	1.01834i	−0.910723	+	0.413018i	$0.864475\pi$
$62$	78.6432	+	62.7159i	1.26844	+	1.01155i
$63$		0			0
$64$	−30.8736	+	64.1097i	−0.482400	+	1.00171i
$65$	−4.63022	−	5.80611i	−0.0712341	−	0.0893247i
$66$		0			0
$67$	−21.7870	−	4.97273i	−0.325179	−	0.0742199i	0.0568153	−	0.998385i	$-0.481905\pi$
$67$	−21.7870	−	4.97273i	−0.325179	−	0.0742199i	−0.381994	+	0.924165i	$0.624763\pi$
$68$	1.11828	+	9.92505i	0.0164454	+	0.145957i
$69$		0			0
$70$	−4.71654	+	4.71654i	−0.0673791	+	0.0673791i
$71$	64.8290	−	14.7968i	0.913085	−	0.208406i	0.259928	−	0.965628i	$-0.416301\pi$
$71$	64.8290	−	14.7968i	0.913085	−	0.208406i	0.653157	+	0.757222i	$0.273444\pi$
$72$		0			0
$73$	76.3640	−	26.7209i	1.04608	−	0.366040i	0.248108	−	0.968732i	$-0.420191\pi$
$73$	76.3640	−	26.7209i	1.04608	−	0.366040i	0.797974	+	0.602692i	$0.205905\pi$
$74$	21.9237	+	96.0540i	0.296266	+	1.29803i
$75$		0			0
$76$	0.108989	+	0.0684824i	0.00143407	+	0.000901084i
$77$	−24.7846	+	2.79256i	−0.321878	+	0.0362670i
$78$		0			0
$79$	67.7630	−	42.5783i	0.857759	−	0.538966i	−0.0298547	−	0.999554i	$-0.509504\pi$
$79$	67.7630	−	42.5783i	0.857759	−	0.538966i	0.887614	+	0.460588i	$0.152362\pi$
$80$	16.9760	−	13.5379i	0.212200	−	0.169224i
$81$		0			0
$82$	−57.8580	+	27.8629i	−0.705585	+	0.339792i
$83$	68.4247	−	85.8019i	0.824394	−	1.03376i	−0.174401	−	0.984675i	$-0.555799\pi$
$83$	68.4247	−	85.8019i	0.824394	−	1.03376i	0.998795	−	0.0490825i	$-0.0156297\pi$
$84$		0			0
$85$	6.74697	−	19.2817i	0.0793761	−	0.226844i
$86$		−	27.3741i		−	0.318303i
$87$		0			0
$88$	107.650			1.22330
$89$	77.7390	+	27.2021i	0.873472	+	0.305641i	0.729533	−	0.683945i	$-0.239737\pi$
$89$	77.7390	+	27.2021i	0.873472	+	0.305641i	0.143939	+	0.989587i	$0.454023\pi$
$90$		0			0
$91$	6.10889	+	4.87167i	0.0671306	+	0.0535349i
$92$	11.9746	+	24.8656i	0.130159	+	0.270278i
$93$		0			0
$94$	72.2411	+	90.5875i	0.768522	+	0.963697i
$95$	−0.140067	−	0.222915i	−0.00147439	−	0.00234647i
$96$		0			0
$97$	19.5392	+	173.415i	0.201435	+	1.78778i	0.534794	+	0.844983i	$0.320389\pi$
$97$	19.5392	+	173.415i	0.201435	+	1.78778i	−0.333359	+	0.942800i	$0.608182\pi$
$98$	−41.9436	+	66.7529i	−0.427996	+	0.681152i
$99$		0			0
$100$	−19.3869	+	4.42492i	−0.193869	+	0.0442492i
$101$	1.74084	+	4.97504i	0.0172360	+	0.0492578i	0.952180	−	0.305538i	$-0.0988362\pi$
$101$	1.74084	+	4.97504i	0.0172360	+	0.0492578i	−0.934944	+	0.354795i	$0.884550\pi$
$102$		0			0
$103$	−15.5109	−	67.9577i	−0.150591	−	0.659783i	−0.992714	−	0.120497i	$-0.961551\pi$
$103$	−15.5109	−	67.9577i	−0.150591	−	0.659783i	0.842123	−	0.539286i	$-0.181306\pi$
$104$	−23.8466	−	23.8466i	−0.229294	−	0.229294i
$105$		0			0
$106$	56.7267	−	6.39156i	0.535157	−	0.0602977i
$107$	−18.2372	+	79.9024i	−0.170441	+	0.746751i	0.815377	+	0.578931i	$0.196530\pi$
$107$	−18.2372	+	79.9024i	−0.170441	+	0.746751i	−0.985818	+	0.167820i	$0.946327\pi$
$108$		0			0
$109$	−78.0488	+	62.2418i	−0.716044	+	0.571026i	−0.912298	−	0.409527i	$-0.865694\pi$
$109$	−78.0488	+	62.2418i	−0.716044	+	0.571026i	0.196254	+	0.980553i	$0.437122\pi$
$110$	−37.4216	−	18.0213i	−0.340196	−	0.163830i
$111$		0			0
$112$	−14.2439	+	17.8613i	−0.127178	+	0.159476i
$113$	−53.9781	−	6.08187i	−0.477683	−	0.0538219i	−0.130159	−	0.991493i	$-0.541549\pi$
$113$	−53.9781	−	6.08187i	−0.477683	−	0.0538219i	−0.347524	+	0.937671i	$0.612977\pi$
$114$		0			0
$115$		−	56.4475i		−	0.490848i
$116$	22.0668	−	15.5070i	0.190231	−	0.133681i
$117$		0			0
$118$	0.655435	+	0.229347i	0.00555453	+	0.00194362i
$119$	−2.40649	+	21.3582i	−0.0202226	+	0.179481i
$120$		0			0
$121$	−14.8860	−	30.9112i	−0.123025	−	0.255464i
$122$	47.5227	−	98.6819i	0.389530	−	0.808868i
$123$		0			0
$124$	28.4059	+	45.2078i	0.229080	+	0.364579i
$125$	86.0135	+	19.6320i	0.688108	+	0.157056i
$126$		0			0
$127$	47.8514	−	76.1551i	0.376783	−	0.599646i	−0.603472	−	0.797384i	$-0.706217\pi$
$127$	47.8514	−	76.1551i	0.376783	−	0.599646i	0.980255	+	0.197738i	$0.0633594\pi$
$128$	47.0009	−	47.0009i	0.367195	−	0.367195i
$129$		0			0
$130$	4.29755	+	12.2817i	0.0330581	+	0.0944746i
$131$	129.814	−	45.4240i	0.990949	−	0.346748i	0.214359	−	0.976755i	$-0.431234\pi$
$131$	129.814	−	45.4240i	0.990949	−	0.346748i	0.776590	+	0.630007i	$0.216948\pi$
$132$		0			0
$133$	0.195866	+	0.195866i	0.00147268	+	0.00147268i
$134$	33.1539	+	20.8320i	0.247417	+	0.155462i
$135$		0			0
$136$	20.6428	−	90.4420i	0.151785	−	0.665015i
$137$	−100.340	+	63.0480i	−0.732411	+	0.460204i	−0.845904	−	0.533335i	$-0.820939\pi$
$137$	−100.340	+	63.0480i	−0.732411	+	0.460204i	0.113494	+	0.993539i	$0.463796\pi$
$138$		0			0
$139$	−198.977	−	95.8224i	−1.43149	−	0.689370i	−0.452217	−	0.891908i	$-0.649367\pi$
$139$	−198.977	−	95.8224i	−1.43149	−	0.689370i	−0.979274	+	0.202538i	$0.935081\pi$
$140$	−3.18985	+	1.53615i	−0.0227847	+	0.0109725i
$141$		0			0
$142$	−115.778	−	13.0450i	−0.815337	−	0.0918665i
$143$	−16.0696	+	45.9242i	−0.112375	+	0.321148i
$144$		0			0
$145$	−54.4246	+	8.99291i	−0.375342	+	0.0620200i
$146$	−141.755			−0.970924
$147$		0			0
$148$	−5.85526	+	51.9669i	−0.0395626	+	0.351127i
$149$	−195.444	−	155.861i	−1.31170	−	1.04605i	−0.995241	−	0.0974435i	$-0.968933\pi$
$149$	−195.444	−	155.861i	−1.31170	−	1.04605i	−0.316462	−	0.948605i	$-0.602495\pi$
$150$		0			0
$151$	81.6119	−	169.469i	0.540476	−	1.12231i	−0.434638	−	0.900605i	$-0.643124\pi$
$151$	81.6119	−	169.469i	0.540476	−	1.12231i	0.975114	−	0.221705i	$-0.0711622\pi$
$152$	−0.745412	−	0.934717i	−0.00490402	−	0.00614945i
$153$		0			0
$154$	42.6052	+	9.72435i	0.276657	+	0.0631451i
$155$	−12.2266	−	108.514i	−0.0788815	−	0.700093i
$156$		0			0
$157$	25.4802	−	25.4802i	0.162294	−	0.162294i	−0.621288	−	0.783582i	$-0.713390\pi$
$157$	25.4802	−	25.4802i	0.162294	−	0.162294i	0.783582	+	0.621288i	$0.213390\pi$
$158$	−136.707	+	31.2025i	−0.865235	+	0.197484i
$159$		0			0
$160$	26.1262	−	9.14195i	0.163289	−	0.0571372i
$161$	13.2158	+	57.9021i	0.0820856	+	0.359640i
$162$		0			0
$163$	132.376	+	83.1771i	0.812120	+	0.510289i	0.872921	−	0.487861i	$-0.162223\pi$
$163$	132.376	+	83.1771i	0.812120	+	0.510289i	−0.0608014	+	0.998150i	$0.519366\pi$
$164$	−33.8717	+	3.81642i	−0.206535	+	0.0232709i
$165$		0			0
$166$	−162.815	+	102.303i	−0.980811	+	0.616284i
$167$	−159.364	+	127.089i	−0.954276	+	0.761010i	−0.971057	−	0.238849i	$-0.923230\pi$
$167$	−159.364	+	127.089i	−0.954276	+	0.761010i	0.0167802	+	0.999859i	$0.494658\pi$
$168$		0			0
$169$	−138.531	+	66.7130i	−0.819709	+	0.394751i
$170$	−22.3164	+	27.9839i	−0.131273	+	0.164611i
$171$		0			0
$172$	4.79892	−	13.7145i	0.0279007	−	0.0797356i
$173$		−	108.217i		−	0.625531i	−0.949830	−	0.312765i	$-0.898745\pi$
$173$		−	108.217i		−	0.625531i	0.949830	−	0.312765i	$-0.101255\pi$
$174$		0			0
$175$	−42.7925			−0.244529
$176$	−134.274	−	46.9845i	−0.762921	−	0.266958i
$177$		0			0
$178$	−112.824	−	89.9742i	−0.633843	−	0.505473i
$179$	50.0799	+	103.992i	0.279776	+	0.580961i	0.992746	−	0.120234i	$-0.0383645\pi$
$179$	50.0799	+	103.992i	0.279776	+	0.580961i	−0.712970	+	0.701195i	$0.752650\pi$
$180$		0			0
$181$	−59.6313	−	74.7753i	−0.329455	−	0.413123i	0.589324	−	0.807897i	$-0.299394\pi$
$181$	−59.6313	−	74.7753i	−0.329455	−	0.413123i	−0.918778	+	0.394774i	$0.870823\pi$
$182$	−7.28374	−	11.5920i	−0.0400206	−	0.0636924i
$183$		0			0
$184$	−28.7009	−	254.727i	−0.155983	−	1.38439i
$185$	56.9062	−	90.5657i	0.307601	−	0.489544i
$186$		0			0
$187$	−130.482	+	29.7817i	−0.697766	+	0.159261i
$188$	20.3123	+	58.0492i	0.108044	+	0.308772i
$189$		0			0
$190$	0.102645	+	0.449715i	0.000540234	+	0.00236692i
$191$	42.1854	+	42.1854i	0.220866	+	0.220866i	0.808863	−	0.587997i	$-0.200083\pi$
$191$	42.1854	+	42.1854i	0.220866	+	0.220866i	−0.587997	+	0.808863i	$0.700083\pi$
$192$		0			0
$193$	−304.307	+	34.2872i	−1.57672	+	0.177654i	−0.856521	−	0.516112i	$-0.827379\pi$
$193$	−304.307	+	34.2872i	−1.57672	+	0.177654i	−0.720201	+	0.693766i	$0.755950\pi$
$194$	68.0401	−	298.103i	0.350722	−	1.53661i
$195$		0			0
$196$	−32.7163	+	26.0904i	−0.166920	+	0.133114i
$197$	−66.4296	−	31.9908i	−0.337206	−	0.162390i	0.257616	−	0.966247i	$-0.417063\pi$
$197$	−66.4296	−	31.9908i	−0.337206	−	0.162390i	−0.594822	+	0.803858i	$0.702777\pi$
$198$		0			0
$199$	156.727	−	196.529i	0.787571	−	0.987583i	−0.212375	−	0.977188i	$-0.568120\pi$
$199$	156.727	−	196.529i	0.787571	−	0.987583i	0.999946	−	0.0103945i	$-0.00330874\pi$
$200$	183.536	+	20.6795i	0.917680	+	0.103398i
$201$		0			0
$202$		−	9.23519i		−	0.0457188i
$203$	53.7216	−	21.9668i	0.264638	−	0.108211i
$204$		0			0
$205$	65.8037	+	23.0257i	0.320994	+	0.112321i
$206$	−13.6746	+	121.365i	−0.0663815	+	0.589152i
$207$		0			0
$208$	19.3364	+	40.1524i	0.0929632	+	0.193040i
$209$	−0.748379	+	1.55403i	−0.00358076	+	0.00743553i
$210$		0			0
$211$	98.3713	+	156.557i	0.466215	+	0.741976i	0.994231	−	0.107258i	$-0.0342070\pi$
$211$	98.3713	+	156.557i	0.466215	+	0.741976i	−0.528017	+	0.849234i	$0.677064\pi$
$212$	29.5408	+	6.74249i	0.139343	+	0.0318042i
$213$		0			0
$214$	76.3999	−	121.590i	0.357009	−	0.568177i
$215$	−21.0137	+	21.0137i	−0.0977383	+	0.0977383i
$216$		0			0
$217$	37.9476	+	108.448i	0.174874	+	0.499761i
$218$	165.097	−	57.7700i	0.757326	−	0.265000i
$219$		0			0
$220$	−15.5891	−	15.5891i	−0.0708595	−	0.0708595i
$221$	35.5016	+	22.3072i	0.160641	+	0.100937i
$222$		0			0
$223$	−15.1512	+	66.3816i	−0.0679425	+	0.297676i	−0.997471	−	0.0710748i	$-0.977357\pi$
$223$	−15.1512	+	66.3816i	−0.0679425	+	0.297676i	0.929528	+	0.368750i	$0.120214\pi$
$224$	−24.6591	+	15.4943i	−0.110085	+	0.0691711i
$225$		0			0
$226$	85.7502	+	41.2951i	0.379426	+	0.182722i
$227$	−95.4082	+	45.9461i	−0.420300	+	0.202406i	−0.632066	−	0.774915i	$-0.717793\pi$
$227$	−95.4082	+	45.9461i	−0.420300	+	0.202406i	0.211766	+	0.977320i	$0.432079\pi$
$228$		0			0
$229$	316.964	+	35.7133i	1.38412	+	0.155953i	0.772408	−	0.635126i	$-0.219052\pi$
$229$	316.964	+	35.7133i	1.38412	+	0.155953i	0.611714	+	0.791079i	$0.290480\pi$
$230$	−32.6658	+	93.3536i	−0.142025	+	0.405885i
$231$		0			0
$232$	−241.026	+	68.2540i	−1.03891	+	0.294198i
$233$	279.358			1.19896			0.599481	−	0.800389i	$-0.295374\pi$
$233$	279.358			1.19896			0.599481	+	0.800389i	$0.295374\pi$
$234$		0			0
$235$	14.0836	−	124.995i	0.0599302	−	0.531896i
$236$	0.288169	+	0.229807i	0.00122106	+	0.000973759i
$237$		0			0
$238$	16.3398	−	33.9299i	0.0686545	−	0.142563i
$239$	0.0841531	+	0.105525i	0.000352105	+	0.000441525i	0.782008	−	0.623269i	$-0.214196\pi$
$239$	0.0841531	+	0.105525i	0.000352105	+	0.000441525i	−0.781655	+	0.623711i	$0.785624\pi$
$240$		0			0
$241$	457.706	+	104.468i	1.89919	+	0.433479i	0.999992	−	0.00405456i	$-0.00129061\pi$
$241$	457.706	+	104.468i	1.89919	+	0.433479i	0.899202	+	0.437533i	$0.144148\pi$
$242$	6.73061	+	59.7358i	0.0278124	+	0.246842i
$243$		0			0
$244$	41.1089	−	41.1089i	0.168479	−	0.168479i
$245$	83.4410	−	19.0449i	0.340575	−	0.0777341i
$246$		0			0
$247$	0.510028	−	0.178467i	0.00206489	−	0.000722536i
$248$	−110.349	−	483.470i	−0.444955	−	1.94947i
$249$		0			0
$250$	−130.889	−	82.2432i	−0.523557	−	0.328973i
$251$	275.015	−	30.9867i	1.09568	−	0.123453i	0.454426	−	0.890785i	$-0.349844\pi$
$251$	275.015	−	30.9867i	1.09568	−	0.123453i	0.641251	+	0.767331i	$0.278416\pi$
$252$		0			0
$253$	−313.140	+	196.759i	−1.23771	+	0.777703i
$254$	−123.208	+	98.2549i	−0.485070	+	0.386830i
$255$		0			0
$256$	151.509	−	72.9629i	0.591832	−	0.285011i
$257$	−256.872	+	322.107i	−0.999501	+	1.25333i	−0.0322581	+	0.999480i	$0.510270\pi$
$257$	−256.872	+	322.107i	−0.999501	+	1.25333i	−0.967242	+	0.253854i	$0.918302\pi$
$258$		0			0
$259$	−37.1689	+	106.223i	−0.143509	+	0.410126i
$260$			6.90658i			0.0265638i
$261$		0			0
$262$	−240.975			−0.919752
$263$	−80.4619	−	28.1548i	−0.305939	−	0.107053i	0.172943	−	0.984932i	$-0.444672\pi$
$263$	−80.4619	−	28.1548i	−0.305939	−	0.107053i	−0.478882	+	0.877879i	$0.658958\pi$
$264$		0			0
$265$	−48.4528	−	38.6398i	−0.182841	−	0.145811i
$266$	−0.210579	−	0.437272i	−0.000791651	−	0.00164388i
$267$		0			0
$268$	12.9582	+	16.2491i	0.0483515	+	0.0606309i
$269$	190.483	+	303.152i	0.708116	+	1.12696i	0.986064	+	0.166364i	$0.0532026\pi$
$269$	190.483	+	303.152i	0.708116	+	1.12696i	−0.277949	+	0.960596i	$0.589655\pi$
$270$		0			0
$271$	6.38164	+	56.6386i	0.0235485	+	0.208999i	0.999977	−	0.00684439i	$-0.00217865\pi$
$271$	6.38164	+	56.6386i	0.0235485	+	0.208999i	−0.976428	+	0.215843i	$0.930750\pi$
$272$	−65.2221	+	103.800i	−0.239787	+	0.381619i
$273$		0			0
$274$	202.429	−	46.2032i	0.738794	−	0.168625i
$275$	−88.0082	−	251.513i	−0.320030	−	0.914593i
$276$		0			0
$277$	49.3432	+	216.187i	0.178134	+	0.780458i	0.982491	+	0.186311i	$0.0596531\pi$
$277$	49.3432	+	216.187i	0.178134	+	0.780458i	−0.804357	+	0.594147i	$0.797490\pi$
$278$	273.619	+	273.619i	0.984242	+	0.984242i
$279$		0			0
$280$	32.6774	−	3.68186i	0.116705	−	0.0131495i
$281$	13.4153	−	58.7763i	0.0477413	−	0.209168i	−0.945431	−	0.325821i	$-0.894359\pi$
$281$	13.4153	−	58.7763i	0.0477413	−	0.209168i	0.993173	+	0.116653i	$0.0372164\pi$
$282$		0			0
$283$	86.1969	−	68.7397i	0.304583	−	0.242897i	−0.459256	−	0.888304i	$-0.651884\pi$
$283$	86.1969	−	68.7397i	0.304583	−	0.242897i	0.763838	+	0.645408i	$0.223312\pi$
$284$	−55.7183	−	26.8325i	−0.196191	−	0.0944807i
$285$		0			0
$286$	53.1521	−	66.6507i	0.185847	−	0.233044i
$287$	−72.8903	−	8.21276i	−0.253973	−	0.0286159i
$288$		0			0
$289$		−	173.665i		−	0.600916i
$290$	95.2123	+	16.6226i	0.328318	+	0.0573194i
$291$		0			0
$292$	−71.0198	−	24.8509i	−0.243218	−	0.0851058i
$293$	−27.3886	+	243.081i	−0.0934766	+	0.829628i	0.856253	+	0.516557i	$0.172786\pi$
$293$	−27.3886	+	243.081i	−0.0934766	+	0.829628i	−0.949730	+	0.313071i	$0.898642\pi$
$294$		0			0
$295$	−0.327087	−	0.679203i	−0.00110877	−	0.00230238i
$296$	210.749	−	437.624i	0.711989	−	1.47846i
$297$		0			0
$298$	233.031	+	370.867i	0.781985	+	1.24452i
$299$	112.953	+	25.7807i	0.377768	+	0.0862230i
$300$		0			0
$301$	16.6354	−	26.4751i	0.0552671	−	0.0879570i
$302$	−233.041	+	233.041i	−0.771660	+	0.771660i
$303$		0			0
$304$	0.521804	+	1.49123i	0.00171646	+	0.00490536i
$305$	−112.234	+	39.2724i	−0.367981	+	0.128762i
$306$		0			0
$307$	−94.4266	−	94.4266i	−0.307579	−	0.307579i	0.536391	−	0.843970i	$-0.319787\pi$
$307$	−94.4266	−	94.4266i	−0.307579	−	0.307579i	−0.843970	+	0.536391i	$0.819787\pi$
$308$	19.6406	+	12.3410i	0.0637681	+	0.0400682i
$309$		0			0
$310$	−42.5761	+	186.538i	−0.137342	+	0.601736i
$311$	147.871	−	92.9137i	0.475471	−	0.298758i	−0.272896	−	0.962044i	$-0.587981\pi$
$311$	147.871	−	92.9137i	0.475471	−	0.298758i	0.748366	+	0.663286i	$0.230839\pi$
$312$		0			0
$313$	−1.30805	−	0.629925i	−0.00417908	−	0.00201254i	0.431793	−	0.901973i	$-0.357881\pi$
$313$	−1.30805	−	0.629925i	−0.00417908	−	0.00201254i	−0.435972	+	0.899960i	$0.643595\pi$
$314$	−56.8847	+	27.3942i	−0.181161	+	0.0872428i
$315$		0			0
$316$	−73.9609	−	8.33339i	−0.234053	−	0.0263715i
$317$	28.4216	−	81.2242i	0.0896579	−	0.256228i	−0.890319	−	0.455336i	$-0.849519\pi$
$317$	28.4216	−	81.2242i	0.0896579	−	0.256228i	0.979977	+	0.199109i	$0.0638047\pi$
$318$		0			0
$319$	239.595	+	270.571i	0.751082	+	0.848186i
$320$	−135.351			−0.422971
$321$		0			0
$322$	11.6512	−	103.407i	0.0361838	−	0.321140i
$323$	1.16210	+	0.926746i	0.00359784	+	0.00286918i
$324$		0			0
$325$	−36.2195	+	75.2106i	−0.111445	+	0.231417i
$326$	−170.790	−	214.164i	−0.523897	−	0.656945i
$327$		0			0
$328$	308.656	+	70.4487i	0.941024	+	0.214783i
$329$	14.8180	+	131.514i	0.0450396	+	0.399738i
$330$		0			0
$331$	266.303	−	266.303i	0.804542	−	0.804542i	−0.179260	−	0.983802i	$-0.557370\pi$
$331$	266.303	−	266.303i	0.804542	−	0.804542i	0.983802	+	0.179260i	$0.0573702\pi$
$332$	−99.5055	+	22.7115i	−0.299715	+	0.0684080i
$333$		0			0
$334$	337.104	−	117.958i	1.00929	−	0.353167i
$335$	−9.45893	−	41.4423i	−0.0282356	−	0.123708i
$336$		0			0
$337$	298.132	+	187.329i	0.884665	+	0.555872i	0.895995	−	0.444064i	$-0.146464\pi$
$337$	298.132	+	187.329i	0.884665	+	0.555872i	−0.0113300	+	0.999936i	$0.503607\pi$
$338$	267.711	−	30.1637i	0.792043	−	0.0892418i
$339$		0			0
$340$	−16.0865	+	10.1078i	−0.0473131	+	0.0297288i
$341$	−559.360	+	446.075i	−1.64035	+	1.30814i
$342$		0			0
$343$	−169.487	+	81.6206i	−0.494131	+	0.237961i
$344$	−84.1429	+	105.512i	−0.244601	+	0.306720i
$345$		0			0
$346$	−62.6244	+	178.970i	−0.180995	+	0.517255i
$347$		−	641.193i		−	1.84782i	−0.382610	−	0.923910i	$-0.624975\pi$
$347$		−	641.193i		−	1.84782i	0.382610	−	0.923910i	$-0.375025\pi$
$348$		0			0
$349$	−467.597			−1.33982			−0.669910	−	0.742443i	$-0.733667\pi$
$349$	−467.597			−1.33982			−0.669910	+	0.742443i	$0.733667\pi$
$350$	70.7708	+	24.7638i	0.202202	+	0.0707536i
$351$		0			0
$352$	−141.782	−	113.068i	−0.402791	−	0.321215i
$353$	−89.7057	−	186.276i	−0.254124	−	0.527694i	0.734408	−	0.678709i	$-0.237460\pi$
$353$	−89.7057	−	186.276i	−0.254124	−	0.527694i	−0.988531	+	0.151015i	$0.951746\pi$
$354$		0			0
$355$	78.8630	+	98.8910i	0.222149	+	0.278566i
$356$	−40.7521	−	64.8565i	−0.114472	−	0.182181i
$357$		0			0
$358$	−22.6432	−	200.964i	−0.0632492	−	0.561353i
$359$	93.0423	−	148.076i	0.259171	−	0.412468i	−0.691639	−	0.722243i	$-0.743111\pi$
$359$	93.0423	−	148.076i	0.259171	−	0.412468i	0.950810	+	0.309775i	$0.100254\pi$
$360$		0			0
$361$	−351.930	+	80.3258i	−0.974876	+	0.222509i
$362$	55.3470	+	158.173i	0.152892	+	0.436941i
$363$		0			0
$364$	−1.61700	−	7.08455i	−0.00444231	−	0.0194630i
$365$	108.818	+	108.818i	0.298132	+	0.298132i
$366$		0			0
$367$	−272.112	+	30.6597i	−0.741450	+	0.0835413i	−0.474606	−	0.880198i	$-0.657409\pi$
$367$	−272.112	+	30.6597i	−0.741450	+	0.0835413i	−0.266844	+	0.963740i	$0.585981\pi$
$368$	−75.3781	+	330.253i	−0.204832	+	0.897426i
$369$		0			0
$370$	−146.522	+	116.847i	−0.396005	+	0.315804i
$371$	58.7479	+	28.2915i	0.158350	+	0.0762574i
$372$		0			0
$373$	30.4398	−	38.1703i	0.0816080	−	0.102333i	−0.739351	−	0.673320i	$-0.764868\pi$
$373$	30.4398	−	38.1703i	0.0816080	−	0.102333i	0.820959	+	0.570987i	$0.193439\pi$
$374$	233.028	+	26.2559i	0.623069	+	0.0702030i
$375$		0			0
$376$		−	571.220i		−	1.51920i
$377$	6.86181	−	113.012i	0.0182011	−	0.299766i
$378$		0			0
$379$	156.410	+	54.7303i	0.412692	+	0.144407i	0.528636	−	0.848849i	$-0.322704\pi$
$379$	156.410	+	54.7303i	0.412692	+	0.144407i	−0.115944	+	0.993256i	$0.536989\pi$
$380$	−0.0274137	+	0.243304i	−7.21414e−5	+	0.000640273i
$381$		0			0
$382$	−45.3543	−	94.1793i	−0.118729	−	0.246543i
$383$	−70.7762	+	146.968i	−0.184794	+	0.383729i	−0.972700	−	0.232067i	$-0.925451\pi$
$383$	−70.7762	+	146.968i	−0.184794	+	0.383729i	0.787906	+	0.615796i	$0.211165\pi$
$384$		0			0
$385$	−25.2410	−	40.1708i	−0.0655610	−	0.104340i
$386$	523.109	+	119.396i	1.35521	+	0.309317i
$387$		0			0
$388$	86.3484	−	137.423i	0.222548	−	0.354182i
$389$	309.216	−	309.216i	0.794899	−	0.794899i	−0.187387	−	0.982286i	$-0.560002\pi$
$389$	309.216	−	309.216i	0.794899	−	0.794899i	0.982286	+	0.187387i	$0.0600020\pi$
$390$		0			0
$391$	105.259	+	300.814i	0.269205	+	0.769345i
$392$	366.855	−	128.368i	0.935856	−	0.327470i
$393$		0			0
$394$	91.3492	+	91.3492i	0.231851	+	0.231851i
$395$	128.896	+	80.9907i	0.326319	+	0.205040i
$396$		0			0
$397$	−22.7855	+	99.8297i	−0.0573942	+	0.251460i	−0.995484	−	0.0949326i	$-0.969736\pi$
$397$	−22.7855	+	99.8297i	−0.0573942	+	0.251460i	0.938090	+	0.346393i	$0.112594\pi$
$398$	−372.927	+	234.325i	−0.937002	+	0.588757i
$399$		0			0
$400$	−219.902	−	105.899i	−0.549756	−	0.264748i
$401$	−122.533	+	59.0090i	−0.305569	+	0.147155i	−0.580384	−	0.814343i	$-0.697098\pi$
$401$	−122.533	+	59.0090i	−0.305569	+	0.147155i	0.274815	+	0.961497i	$0.411383\pi$
$402$		0			0
$403$	222.724	+	25.0949i	0.552664	+	0.0622703i
$404$	1.61901	−	4.62687i	0.00400745	−	0.0114526i
$405$		0			0
$406$	−101.558	+	5.24061i	−0.250142	+	0.0129079i
$407$	−700.766			−1.72178
$408$		0			0
$409$	−38.6381	+	342.922i	−0.0944696	+	0.838441i	0.853719	+	0.520734i	$0.174342\pi$
$409$	−38.6381	+	342.922i	−0.0944696	+	0.838441i	−0.948189	+	0.317708i	$0.897087\pi$
$410$	−95.5022	−	76.1604i	−0.232932	−	0.185757i
$411$		0			0
$412$	−28.1274	+	58.4072i	−0.0682705	+	0.141765i
$413$	0.494534	+	0.620126i	0.00119742	+	0.00150152i
$414$		0			0
$415$	203.518	+	46.4516i	0.490405	+	0.111932i
$416$	6.36087	+	56.4543i	0.0152906	+	0.135707i
$417$		0			0
$418$	2.13698	−	2.13698i	0.00511240	−	0.00511240i
$419$	−200.129	+	45.6781i	−0.477635	+	0.109017i	−0.454559	−	0.890717i	$-0.650203\pi$
$419$	−200.129	+	45.6781i	−0.477635	+	0.109017i	−0.0230758	+	0.999734i	$0.507346\pi$
$420$		0			0
$421$	−30.0377	+	10.5107i	−0.0713485	+	0.0249659i	−0.365717	−	0.930726i	$-0.619176\pi$
$421$	−30.0377	+	10.5107i	−0.0713485	+	0.0249659i	0.294369	+	0.955692i	$0.404891\pi$
$422$	−72.0891	−	315.843i	−0.170827	−	0.748443i
$423$		0			0
$424$	−238.296	−	149.731i	−0.562019	−	0.353140i
$425$	−228.184	+	25.7102i	−0.536904	+	0.0604946i
$426$		0			0
$427$	105.932	−	66.5612i	0.248083	−	0.155881i
$428$	59.5924	−	47.5234i	0.139235	−	0.111036i
$429$		0			0
$430$	46.9133	−	22.5922i	0.109101	−	0.0525401i
$431$	404.927	−	507.763i	0.939507	−	1.17810i	−0.0443267	−	0.999017i	$-0.514114\pi$
$431$	404.927	−	507.763i	0.939507	−	1.17810i	0.983833	−	0.179087i	$-0.0573143\pi$
$432$		0			0
$433$	98.3588	−	281.093i	0.227156	−	0.649176i	−0.772739	−	0.634724i	$-0.781114\pi$
$433$	98.3588	−	281.093i	0.227156	−	0.649176i	0.999896	−	0.0144521i	$-0.00460042\pi$
$434$		−	201.313i		−	0.463855i
$435$		0			0
$436$	92.8419			0.212940
$437$	3.87674	+	1.35653i	0.00887126	+	0.00310419i
$438$		0			0
$439$	−104.158	−	83.0632i	−0.237262	−	0.189210i	0.497640	−	0.867384i	$-0.334200\pi$
$439$	−104.158	−	83.0632i	−0.237262	−	0.189210i	−0.734902	+	0.678174i	$0.762772\pi$
$440$	88.8453	+	184.489i	0.201921	+	0.419294i
$441$		0			0
$442$	−45.8040	−	57.4364i	−0.103629	−	0.129947i
$443$	174.139	+	277.141i	0.393091	+	0.625601i	0.983373	−	0.181596i	$-0.0581263\pi$
$443$	174.139	+	277.141i	0.393091	+	0.625601i	−0.590282	+	0.807197i	$0.700983\pi$
$444$		0			0
$445$	17.5407	+	155.678i	0.0394174	+	0.349839i
$446$	63.4719	−	101.015i	0.142314	−	0.226491i
$447$		0			0
$448$	138.839	−	31.6890i	0.309908	−	0.0707344i
$449$	−73.6423	−	210.458i	−0.164014	−	0.468725i	0.832318	−	0.554299i	$-0.187013\pi$
$449$	−73.6423	−	210.458i	−0.164014	−	0.468725i	−0.996332	+	0.0855735i	$0.972728\pi$
$450$		0			0
$451$	−101.638	−	445.303i	−0.225361	−	0.987369i
$452$	35.7218	+	35.7218i	0.0790305	+	0.0790305i
$453$		0			0
$454$	184.376	−	20.7742i	0.406114	−	0.0457581i
$455$	−3.30724	+	14.4900i	−0.00726867	+	0.0318461i
$456$		0			0
$457$	−606.218	+	483.443i	−1.32652	+	1.05786i	−0.333150	+	0.942874i	$0.608112\pi$
$457$	−606.218	+	483.443i	−1.32652	+	1.05786i	−0.993367	+	0.114988i	$0.963317\pi$
$458$	−503.532	−	242.488i	−1.09941	−	0.529450i
$459$		0			0
$460$	−32.7314	+	41.0439i	−0.0711553	+	0.0892259i
$461$	485.426	+	54.6943i	1.05298	+	0.118643i	0.621450	−	0.783454i	$-0.286544\pi$
$461$	485.426	+	54.6943i	1.05298	+	0.118643i	0.431534	+	0.902097i	$0.357973\pi$
$462$		0			0
$463$		−	770.815i		−	1.66483i	−0.554155	−	0.832414i	$-0.686958\pi$
$463$		−	770.815i		−	1.66483i	0.554155	−	0.832414i	$-0.313042\pi$
$464$	330.426	+	20.0627i	0.712126	+	0.0432386i
$465$		0			0
$466$	−462.006	−	161.663i	−0.991429	−	0.346916i
$467$	−93.5969	+	830.696i	−0.200422	+	1.77879i	0.343003	+	0.939334i	$0.388556\pi$
$467$	−93.5969	+	830.696i	−0.200422	+	1.77879i	−0.543425	+	0.839458i	$0.682873\pi$
$468$		0			0
$469$	19.4053	+	40.2956i	0.0413760	+	0.0859182i
$470$	−95.6258	+	198.569i	−0.203459	+	0.422487i
$471$		0			0
$472$	−1.82137	−	2.89869i	−0.00385883	−	0.00614129i
$473$	189.820	+	43.3252i	0.401311	+	0.0915966i
$474$		0			0
$475$	−1.57446	+	2.50574i	−0.00331466	+	0.00527525i
$476$	14.1345	−	14.1345i	0.0296943	−	0.0296943i
$477$		0			0
$478$	−0.0781069	−	0.223217i	−0.000163404	−	0.000466981i
$479$	701.949	−	245.623i	1.46545	−	0.512782i	0.524522	−	0.851397i	$-0.324244\pi$
$479$	701.949	−	245.623i	1.46545	−	0.512782i	0.940925	+	0.338615i	$0.109958\pi$
$480$		0			0
$481$	155.233	+	155.233i	0.322731	+	0.322731i
$482$	−696.504	−	437.643i	−1.44503	−	0.907972i
$483$		0			0
$484$	−7.10015	+	31.1078i	−0.0146697	+	0.0642723i
$485$	−281.070	+	176.608i	−0.579526	+	0.364140i
$486$		0			0
$487$	−808.881	−	389.537i	−1.66095	−	0.799870i	−0.998721	−	0.0505653i	$-0.983898\pi$
$487$	−808.881	−	389.537i	−1.66095	−	0.799870i	−0.662226	−	0.749304i	$-0.730388\pi$
$488$	−486.504	+	234.288i	−0.996934	+	0.480098i
$489$		0			0
$490$	−149.017	−	16.7902i	−0.304116	−	0.0342657i
$491$	−144.911	+	414.132i	−0.295135	+	0.843446i	0.696865	+	0.717203i	$0.254578\pi$
$491$	−144.911	+	414.132i	−0.295135	+	0.843446i	−0.991999	+	0.126244i	$0.959708\pi$
$492$		0			0
$493$	273.264	−	149.411i	0.554288	−	0.303065i
$494$	−0.946768			−0.00191653
$495$		0			0
$496$	−73.3730	+	651.204i	−0.147929	+	1.31291i
$497$	−104.048	−	82.9755i	−0.209352	−	0.166953i
$498$		0			0
$499$	275.489	−	572.059i	0.552082	−	1.14641i	−0.419071	−	0.907954i	$-0.637644\pi$
$499$	275.489	−	572.059i	0.552082	−	1.14641i	0.971153	−	0.238457i	$-0.0766416\pi$
$500$	−51.1581	−	64.1502i	−0.102316	−	0.128300i
$501$		0			0
$502$	−472.755	−	107.903i	−0.941743	−	0.214947i
$503$	−87.3784	−	775.505i	−0.173714	−	1.54176i	−0.713921	−	0.700226i	$-0.753083\pi$
$503$	−87.3784	−	775.505i	−0.173714	−	1.54176i	0.540207	−	0.841532i	$-0.318346\pi$
$504$		0			0
$505$	−7.08940	+	7.08940i	−0.0140384	+	0.0140384i
$506$	631.738	−	144.190i	1.24849	−	0.284960i
$507$		0			0
$508$	−78.9526	+	27.6267i	−0.155418	+	0.0543833i
$509$	219.690	+	962.525i	0.431611	+	1.89101i	0.453511	+	0.891251i	$0.350171\pi$
$509$	219.690	+	962.525i	0.431611	+	1.89101i	−0.0218997	+	0.999760i	$0.506971\pi$
$510$		0			0
$511$	−137.099	−	86.1453i	−0.268296	−	0.168582i
$512$	−556.996	+	62.7584i	−1.08788	+	0.122575i
$513$		0			0
$514$	611.219	−	384.054i	1.18914	−	0.747187i
$515$	103.663	−	82.6688i	0.201288	−	0.160522i
$516$		0			0
$517$	−742.497	+	357.568i	−1.43617	+	0.691621i
$518$	122.941	−	154.163i	0.237337	−	0.297612i
$519$		0			0
$520$	21.1870	−	60.5490i	0.0407442	−	0.116440i
$521$		−	535.964i		−	1.02872i	−0.857574	−	0.514361i	$-0.828029\pi$
$521$		−	535.964i		−	1.02872i	0.857574	−	0.514361i	$-0.171971\pi$
$522$		0			0
$523$	915.345			1.75018			0.875091	−	0.483959i	$-0.160801\pi$
$523$	915.345			1.75018			0.875091	+	0.483959i	$0.160801\pi$
$524$	−120.729	−	42.2451i	−0.230400	−	0.0806204i
$525$		0			0
$526$	116.776	+	93.1257i	0.222007	+	0.177045i
$527$	267.507	+	555.483i	0.507603	+	1.05405i
$528$		0			0
$529$	219.241	+	274.920i	0.414445	+	0.519697i
$530$	57.7712	+	91.9423i	0.109002	+	0.173476i
$531$		0			0
$532$	−0.0288433	−	0.255991i	−5.42167e−5	−	0.000481187i
$533$	−76.1287	+	121.158i	−0.142831	+	0.227314i
$534$		0			0
$535$	−151.987	+	34.6900i	−0.284088	+	0.0648412i
$536$	−63.7561	−	182.205i	−0.118948	−	0.339934i
$537$		0			0
$538$	−139.591	−	611.588i	−0.259463	−	1.13678i
$539$	−396.500	−	396.500i	−0.735622	−	0.735622i
$540$		0			0
$541$	28.3793	−	3.19758i	0.0524572	−	0.00591051i	−0.0856969	−	0.996321i	$-0.527312\pi$
$541$	28.3793	−	3.19758i	0.0524572	−	0.00591051i	0.138154	+	0.990411i	$0.455883\pi$
$542$	22.2224	−	97.3627i	0.0410007	−	0.179636i
$543$		0			0
$544$	−122.181	+	97.4365i	−0.224598	+	0.179111i
$545$	−171.084	−	82.3897i	−0.313916	−	0.151174i
$546$		0			0
$547$	−73.0250	+	91.5704i	−0.133501	+	0.167405i	−0.844088	−	0.536204i	$-0.819858\pi$
$547$	−73.0250	+	91.5704i	−0.133501	+	0.167405i	0.710588	+	0.703609i	$0.248429\pi$
$548$	109.518	+	12.3397i	0.199850	+	0.0225177i
$549$		0			0
$550$			466.885i			0.848882i
$551$	0.690296	−	3.95393i	0.00125281	−	0.00717591i
$552$		0			0
$553$	−151.179	−	52.8999i	−0.273380	−	0.0956599i
$554$	43.5016	−	386.087i	0.0785227	−	0.696908i
$555$		0			0
$556$	89.1165	+	185.052i	0.160281	+	0.332828i
$557$	376.472	−	781.753i	0.675893	−	1.40351i	−0.227109	−	0.973869i	$-0.572927\pi$
$557$	376.472	−	781.753i	0.675893	−	1.40351i	0.903002	−	0.429636i	$-0.141358\pi$
$558$		0			0
$559$	−32.4515	−	51.6462i	−0.0580527	−	0.0923904i
$560$	−42.3661	−	9.66979i	−0.0756538	−	0.0172675i
$561$		0			0
$562$	−56.1999	+	89.4416i	−0.0999998	+	0.159149i
$563$	−66.7692	+	66.7692i	−0.118595	+	0.118595i	−0.763914	−	0.645318i	$-0.776725\pi$
$563$	−66.7692	+	66.7692i	−0.118595	+	0.118595i	0.645318	+	0.763914i	$0.276725\pi$
$564$		0			0
$565$	−34.1260	−	97.5264i	−0.0603999	−	0.172613i
$566$	−182.333	+	63.8010i	−0.322143	+	0.112723i
$567$		0			0
$568$	406.161	+	406.161i	0.715073	+	0.715073i
$569$	−586.687	−	368.640i	−1.03108	−	0.647873i	−0.0934960	−	0.995620i	$-0.529804\pi$
$569$	−586.687	−	368.640i	−1.03108	−	0.647873i	−0.937589	+	0.347746i	$0.886947\pi$
$570$		0			0
$571$	122.100	−	534.957i	0.213836	−	0.936877i	−0.748096	−	0.663590i	$-0.769032\pi$
$571$	122.100	−	534.957i	0.213836	−	0.936877i	0.961933	−	0.273287i	$-0.0881109\pi$
$572$	38.3139	−	24.0742i	0.0669823	−	0.0420878i
$573$		0			0
$574$	115.794	+	55.7635i	0.201732	+	0.0971490i
$575$	−571.679	+	275.306i	−0.994224	+	0.478793i
$576$		0			0
$577$	377.501	+	42.5342i	0.654248	+	0.0737161i	0.432848	−	0.901467i	$-0.357509\pi$
$577$	377.501	+	42.5342i	0.654248	+	0.0737161i	0.221400	+	0.975183i	$0.428937\pi$
$578$	−100.499	+	287.209i	−0.173873	+	0.496901i
$579$		0			0
$580$	44.7876	+	25.0196i	0.0772201	+	0.0431372i
$581$	−219.638			−0.378034
$582$		0			0
$583$	−45.4608	+	403.476i	−0.0779774	+	0.692068i
$584$	546.386	+	435.728i	0.935593	+	0.746110i
$585$		0			0
$586$	185.965	−	386.161i	0.317347	−	0.658977i
$587$	−227.442	−	285.204i	−0.387466	−	0.485867i	0.549398	−	0.835561i	$-0.314857\pi$
$587$	−227.442	−	285.204i	−0.387466	−	0.485867i	−0.936864	+	0.349694i	$0.886286\pi$
$588$		0			0
$589$	7.74646	+	1.76808i	0.0131519	+	0.00300183i
$590$	0.147890	+	1.31256i	0.000250661	+	0.00222468i
$591$		0			0
$592$	−453.875	+	453.875i	−0.766680	+	0.766680i
$593$	79.2074	−	18.0786i	0.133571	−	0.0304866i	−0.155213	−	0.987881i	$-0.549606\pi$
$593$	79.2074	−	18.0786i	0.133571	−	0.0304866i	0.288784	+	0.957394i	$0.406749\pi$
$594$		0			0
$595$	−38.5895	+	13.5031i	−0.0648564	+	0.0226942i
$596$	51.7333	+	226.659i	0.0868009	+	0.380300i
$597$		0			0
$598$	−171.883	−	108.001i	−0.287430	−	0.180604i
$599$	−110.418	+	12.4411i	−0.184337	+	0.0207698i	−0.203650	−	0.979044i	$-0.565281\pi$
$599$	−110.418	+	12.4411i	−0.184337	+	0.0207698i	0.0193132	+	0.999813i	$0.493852\pi$
$600$		0			0
$601$	−240.700	+	151.242i	−0.400499	+	0.251650i	−0.717189	−	0.696879i	$-0.754571\pi$
$601$	−240.700	+	151.242i	−0.400499	+	0.251650i	0.316690	+	0.948529i	$0.397429\pi$
$602$	−42.8328	+	34.1580i	−0.0711508	+	0.0567409i
$603$		0			0
$604$	−157.609	+	75.9005i	−0.260942	+	0.125663i
$605$	40.6895	−	51.0230i	0.0672553	−	0.0843355i
$606$		0			0
$607$	−103.263	+	295.109i	−0.170120	+	0.486176i	−0.997104	−	0.0760501i	$-0.975769\pi$
$607$	−103.263	+	295.109i	−0.170120	+	0.486176i	0.826984	+	0.562226i	$0.190055\pi$
$608$			2.01401i			0.00331252i
$609$		0			0
$610$	208.341			0.341542
$611$	243.686	+	85.2694i	0.398832	+	0.139557i
$612$		0			0
$613$	−109.428	−	87.2662i	−0.178513	−	0.142359i	0.530157	−	0.847899i	$-0.322133\pi$
$613$	−109.428	−	87.2662i	−0.178513	−	0.142359i	−0.708670	+	0.705540i	$0.750704\pi$
$614$	101.520	+	210.808i	0.165342	+	0.343336i
$615$		0			0
$616$	−134.328	−	168.442i	−0.218065	−	0.273445i
$617$	530.280	+	843.935i	0.859448	+	1.36780i	0.928943	+	0.370222i	$0.120718\pi$
$617$	530.280	+	843.935i	0.859448	+	1.36780i	−0.0694948	+	0.997582i	$0.522139\pi$
$618$		0			0
$619$	2.68832	+	23.8595i	0.00434301	+	0.0385452i	0.995697	−	0.0926708i	$-0.0295404\pi$
$619$	2.68832	+	23.8595i	0.00434301	+	0.0385452i	−0.991354	+	0.131216i	$0.958112\pi$
$620$	−54.0326	+	85.9923i	−0.0871493	+	0.138697i
$621$		0			0
$622$	−298.320	+	68.0896i	−0.479614	+	0.109469i
$623$	−54.4409	−	155.583i	−0.0873851	−	0.249732i
$624$		0			0
$625$	−81.6042	−	357.531i	−0.130567	−	0.572050i
$626$	1.79874	+	1.79874i	0.00287339	+	0.00287339i
$627$		0			0
$628$	−33.3019	+	3.75222i	−0.0530285	+	0.00597488i
$629$	−134.378	+	588.747i	−0.213637	+	0.936005i
$630$		0			0
$631$	−198.431	+	158.243i	−0.314470	+	0.250782i	−0.767986	−	0.640467i	$-0.778741\pi$
$631$	−198.431	+	158.243i	−0.314470	+	0.250782i	0.453516	+	0.891248i	$0.350170\pi$
$632$	622.840	+	299.944i	0.985507	+	0.474595i
$633$		0			0
$634$	−94.0079	+	117.882i	−0.148277	+	0.185934i
$635$	170.006	+	19.1551i	0.267726	+	0.0301655i
$636$		0			0
$637$			175.665i			0.275769i
$638$	−239.668	−	586.127i	−0.375655	−	0.918694i
$639$		0			0
$640$	119.340	+	41.7589i	0.186469	+	0.0652483i
$641$	38.2084	−	339.109i	0.0596075	−	0.529031i	−0.928056	−	0.372440i	$-0.878521\pi$
$641$	38.2084	−	339.109i	0.0596075	−	0.529031i	0.987664	−	0.156591i	$-0.0500503\pi$
$642$		0			0
$643$	251.743	+	522.750i	0.391513	+	0.812985i	0.999814	+	0.0192789i	$0.00613705\pi$
$643$	251.743	+	522.750i	0.391513	+	0.812985i	−0.608301	+	0.793706i	$0.708149\pi$
$644$	23.9655	−	49.7648i	0.0372135	−	0.0772746i
$645$		0			0
$646$	−1.38560	−	2.20517i	−0.00214489	−	0.00341357i
$647$	442.664	+	101.035i	0.684179	+	0.156160i	0.550462	−	0.834860i	$-0.314451\pi$
$647$	442.664	+	101.035i	0.684179	+	0.156160i	0.133717	+	0.991020i	$0.457309\pi$
$648$		0			0
$649$	−2.62772	+	4.18199i	−0.00404888	+	0.00644375i
$650$	103.424	−	103.424i	0.159114	−	0.159114i
$651$		0			0
$652$	−48.0217	−	137.238i	−0.0736529	−	0.210488i
$653$	551.878	−	193.110i	0.845142	−	0.295728i	0.127240	−	0.991872i	$-0.459388\pi$
$653$	551.878	−	193.110i	0.845142	−	0.295728i	0.717902	+	0.696144i	$0.245102\pi$
$654$		0			0
$655$	184.985	+	184.985i	0.282419	+	0.282419i
$656$	−354.245	−	222.587i	−0.540007	−	0.339309i
$657$		0			0
$658$	51.6000	−	226.074i	0.0784194	−	0.343578i
$659$	−761.337	+	478.379i	−1.15529	+	0.725917i	−0.966643	−	0.256128i	$-0.917553\pi$
$659$	−761.337	+	478.379i	−1.15529	+	0.725917i	−0.188648	+	0.982045i	$0.560410\pi$
$660$		0			0
$661$	992.160	+	477.799i	1.50100	+	0.722843i	0.990561	−	0.137072i	$-0.0437693\pi$
$661$	992.160	+	477.799i	1.50100	+	0.722843i	0.510437	+	0.859915i	$0.329484\pi$
$662$	−594.524	+	286.308i	−0.898073	+	0.432489i
$663$		0			0
$664$	942.021	+	106.140i	1.41871	+	0.159850i
$665$	−0.174021	+	0.497323i	−0.000261686	+	0.000747855i
$666$		0			0
$667$	576.360	−	639.080i	0.864109	−	0.958141i
$668$	189.569			0.283787
$669$		0			0
$670$	−8.33910	+	74.0116i	−0.0124464	+	0.110465i
$671$	609.076	+	485.722i	0.907713	+	0.723877i
$672$		0			0
$673$	−231.236	+	480.167i	−0.343590	+	0.713473i	−0.999131	−	0.0416874i	$-0.986727\pi$
$673$	−231.236	+	480.167i	−0.343590	+	0.713473i	0.655540	+	0.755160i	$0.272441\pi$
$674$	−384.649	−	482.334i	−0.570695	−	0.715629i
$675$		0			0
$676$	139.412	+	31.8199i	0.206231	+	0.0470708i
$677$	0.426844	+	3.78834i	0.000630493	+	0.00559578i	0.994024	−	0.109166i	$-0.0348181\pi$
$677$	0.426844	+	3.78834i	0.000630493	+	0.00559578i	−0.993393	+	0.114762i	$0.963389\pi$
$678$		0			0
$679$	246.964	−	246.964i	0.363718	−	0.363718i
$680$	172.035	−	39.2659i	0.252993	−	0.0577439i
$681$		0			0
$682$	1183.22	−	414.026i	1.73492	−	0.607076i
$683$	−122.389	−	536.221i	−0.179193	−	0.785096i	−0.982004	−	0.188862i	$-0.939520\pi$
$683$	−122.389	−	536.221i	−0.179193	−	0.785096i	0.802810	−	0.596234i	$-0.203337\pi$
$684$		0			0
$685$	−190.863	−	119.927i	−0.278632	−	0.175076i
$686$	327.533	−	36.9041i	0.477453	−	0.0537961i
$687$		0			0
$688$	151.004	−	94.8823i	0.219483	−	0.137910i
$689$	99.4483	−	79.3073i	0.144337	−	0.115105i
$690$		0			0
$691$	689.611	−	332.099i	0.997990	−	0.480606i	0.137734	−	0.990469i	$-0.456018\pi$
$691$	689.611	−	332.099i	0.997990	−	0.480606i	0.860256	+	0.509863i	$0.170304\pi$
$692$	−62.7502	+	78.6862i	−0.0906795	+	0.113708i
$693$		0			0
$694$	−371.055	+	1060.41i	−0.534661	+	1.52797i
$695$		−	420.088i		−	0.604443i
$696$		0			0
$697$	−393.610			−0.564721
$698$	773.318	+	270.596i	1.10790	+	0.387673i
$699$		0			0
$700$	31.1151	+	24.8135i	0.0444502	+	0.0354479i
$701$	−391.731	−	813.437i	−0.558817	−	1.16040i	−0.968695	−	0.248255i	$-0.920143\pi$
$701$	−391.731	−	813.437i	−0.558817	−	1.16040i	0.409878	−	0.912141i	$-0.365571\pi$
$702$		0			0
$703$	4.85238	+	6.08469i	0.00690239	+	0.00865532i
$704$	471.791	+	750.852i	0.670158	+	1.06655i
$705$		0			0
$706$	40.5597	+	359.978i	0.0574500	+	0.509883i
$707$	5.61228	−	8.93189i	0.00793816	−	0.0126335i
$708$		0			0
$709$	1016.73	−	232.062i	1.43403	−	0.327309i	0.566243	−	0.824238i	$-0.308396\pi$
$709$	1016.73	−	232.062i	1.43403	−	0.327309i	0.867791	+	0.496929i	$0.165539\pi$
$710$	−73.1969	−	209.185i	−0.103094	−	0.294626i
$711$		0			0
$712$	158.310	+	693.601i	0.222345	+	0.974159i
$713$	1204.66	+	1204.66i	1.68956	+	1.68956i
$714$		0			0
$715$	−91.9667	+	10.3622i	−0.128625	+	0.0144925i
$716$	23.8865	−	104.653i	0.0333610	−	0.146164i
$717$		0			0
$718$	−239.565	+	191.047i	−0.333656	+	0.266082i
$719$	−623.735	−	300.375i	−0.867504	−	0.417768i	−0.0534590	−	0.998570i	$-0.517025\pi$
$719$	−623.735	−	300.375i	−0.867504	−	0.417768i	−0.814045	+	0.580802i	$0.802739\pi$
$720$		0			0
$721$	−86.9799	+	109.069i	−0.120638	+	0.151275i
$722$	628.511	+	70.8162i	0.870514	+	0.0980833i
$723$		0			0
$724$			88.9479i			0.122856i
$725$	356.517	+	507.331i	0.491747	+	0.699768i
$726$		0			0
$727$	−280.613	−	98.1906i	−0.385987	−	0.135063i	0.130308	−	0.991474i	$-0.458403\pi$
$727$	−280.613	−	98.1906i	−0.385987	−	0.135063i	−0.516295	+	0.856411i	$0.672689\pi$
$728$	−7.55693	+	67.0696i	−0.0103804	+	0.0921286i
$729$		0			0
$730$	−116.993	−	242.938i	−0.160264	−	0.332791i
$731$	72.7991	−	151.169i	0.0995884	−	0.206797i
$732$		0			0
$733$	−270.527	−	430.541i	−0.369068	−	0.587369i	0.609627	−	0.792689i	$-0.291319\pi$
$733$	−270.527	−	430.541i	−0.369068	−	0.587369i	−0.978695	+	0.205320i	$0.934177\pi$
$734$	467.765	+	106.764i	0.637282	+	0.145455i
$735$		0			0
$736$	−229.746	+	365.638i	−0.312154	+	0.496791i
$737$	−196.928	+	196.928i	−0.267202	+	0.267202i
$738$		0			0
$739$	−123.481	−	352.888i	−0.167092	−	0.477521i	0.829640	−	0.558298i	$-0.188546\pi$
$739$	−123.481	−	352.888i	−0.167092	−	0.477521i	−0.996732	+	0.0807770i	$0.974260\pi$
$740$	−93.8925	+	32.8544i	−0.126882	+	0.0443978i
$741$		0			0
$742$	−80.7858	−	80.7858i	−0.108876	−	0.108876i
$743$	61.7282	+	38.7864i	0.0830797	+	0.0522024i	0.572931	−	0.819603i	$-0.305806\pi$
$743$	61.7282	+	38.7864i	0.0830797	+	0.0522024i	−0.489852	+	0.871806i	$0.662949\pi$
$744$		0			0
$745$	105.810	−	463.583i	0.142027	−	0.622260i
$746$	−72.4306	+	45.5112i	−0.0970920	+	0.0610069i
$747$		0			0
$748$	112.145	+	54.0062i	0.149926	+	0.0722008i
$749$	147.782	−	71.1679i	0.197305	−	0.0950172i
$750$		0			0
$751$	−690.638	−	77.8162i	−0.919624	−	0.103617i	−0.360555	−	0.932738i	$-0.617413\pi$
$751$	−690.638	−	77.8162i	−0.919624	−	0.103617i	−0.559069	+	0.829121i	$0.688841\pi$
$752$	−249.312	+	712.494i	−0.331533	+	0.947466i
$753$		0			0
$754$	−76.7475	+	182.930i	−0.101787	+	0.242612i
$755$	357.789			0.473892
$756$		0			0
$757$	−10.1618	+	90.1883i	−0.0134238	+	0.119139i	−0.998637	−	0.0521936i	$-0.983379\pi$
$757$	−10.1618	+	90.1883i	−0.0134238	+	0.119139i	0.985213	+	0.171333i	$0.0548073\pi$
$758$	−227.001	−	181.027i	−0.299474	−	0.238822i
$759$		0			0
$760$	0.986704	−	2.04891i	0.00129829	−	0.00269594i
$761$	−135.413	−	169.803i	−0.177941	−	0.223131i	0.684860	−	0.728675i	$-0.259863\pi$
$761$	−135.413	−	169.803i	−0.177941	−	0.223131i	−0.862801	+	0.505543i	$0.831292\pi$
$762$		0			0
$763$	194.782	+	44.4578i	0.255285	+	0.0582670i
$764$	−6.21225	−	55.1352i	−0.00813121	−	0.0721665i
$765$		0			0
$766$	202.100	−	202.100i	0.263838	−	0.263838i
$767$	1.50849	−	0.344302i	0.00196673	−	0.000448894i
$768$		0			0
$769$	768.761	−	269.001i	0.999689	−	0.349806i	0.219678	−	0.975572i	$-0.429499\pi$
$769$	768.761	−	269.001i	0.999689	−	0.349806i	0.780011	+	0.625766i	$0.215214\pi$
$770$	18.4972	+	81.0417i	0.0240224	+	0.105249i
$771$		0			0
$772$	241.149	+	151.524i	0.312369	+	0.196274i
$773$	−247.757	+	27.9155i	−0.320514	+	0.0361132i	−0.270756	−	0.962648i	$-0.587274\pi$
$773$	−247.757	+	27.9155i	−0.320514	+	0.0361132i	−0.0497581	+	0.998761i	$0.515845\pi$
$774$		0			0
$775$	−1039.36	+	653.074i	−1.34111	+	0.842676i
$776$	−1178.57	+	939.878i	−1.51878	+	1.21118i
$777$		0			0
$778$	−690.326	+	332.443i	−0.887308	+	0.427305i
$779$	−3.16275	+	3.96597i	−0.00406002	+	0.00509110i
$780$		0			0
$781$	273.701	−	782.192i	0.350449	−	1.00153i
$782$		−	558.402i		−	0.714070i
$783$		0			0
$784$	−513.613			−0.655119
$785$	64.6968	+	22.6384i	0.0824163	+	0.0288387i
$786$		0			0
$787$	−430.893	−	343.626i	−0.547513	−	0.436627i	0.310263	−	0.950651i

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	261.s (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65381 - 0.578694i) q^{2} +(-0.727117 - 0.579856i) q^{4} +(0.825315 + 1.71379i) q^{5} +(-1.24782 - 1.56472i) q^{7} +(4.59573 + 7.31406i) q^{8} +O(q^{10})\)	\(q+(-1.65381 - 0.578694i) q^{2} +(-0.727117 - 0.579856i) q^{4} +(0.825315 + 1.71379i) q^{5} +(-1.24782 - 1.56472i) q^{7} +(4.59573 + 7.31406i) q^{8} +(-0.373160 - 3.31188i) q^{10} +(6.63034 - 10.5521i) q^{11} +(-3.80625 + 0.868753i) q^{13} +(1.15817 + 3.30986i) q^{14} +(-2.54008 - 11.1288i) q^{16} +(-7.59392 - 7.59392i) q^{17} +(-0.137534 + 0.0154964i) q^{19} +(0.393648 - 1.72469i) q^{20} +(-17.0718 + 13.6143i) q^{22} +(-26.7367 - 12.8757i) q^{23} +(13.3313 - 16.7170i) q^{25} +(6.79757 + 0.765903i) q^{26} +1.86129i q^{28} +(-8.15475 + 27.8298i) q^{29} +(-54.1874 - 18.9610i) q^{31} +(1.62926 - 14.4601i) q^{32} +(8.16437 + 16.9535i) q^{34} +(1.65175 - 3.42989i) q^{35} +(-29.9166 - 47.6121i) q^{37} +(0.236424 + 0.0539622i) q^{38} +(-8.74180 + 13.9125i) q^{40} +(25.9162 - 25.9162i) q^{41} +(5.16003 + 14.7465i) q^{43} +(-10.9397 + 3.82798i) q^{44} +(36.7664 + 36.7664i) q^{46} +(-55.9924 - 35.1824i) q^{47} +(10.0122 - 43.8665i) q^{49} +(-31.7215 + 19.9320i) q^{50} +(3.27134 + 1.57540i) q^{52} +(-29.3541 + 14.1362i) q^{53} +(23.5562 + 2.65415i) q^{55} +(5.70980 - 16.3177i) q^{56} +(29.5914 - 41.3062i) q^{58} -0.396318 q^{59} +(-6.99907 + 62.1184i) q^{61} +(78.6432 + 62.7159i) q^{62} +(-30.8736 + 64.1097i) q^{64} +(-4.63022 - 5.80611i) q^{65} +(-21.7870 - 4.97273i) q^{67} +(1.11828 + 9.92505i) q^{68} +(-4.71654 + 4.71654i) q^{70} +(64.8290 - 14.7968i) q^{71} +(76.3640 - 26.7209i) q^{73} +(21.9237 + 96.0540i) q^{74} +(0.108989 + 0.0684824i) q^{76} +(-24.7846 + 2.79256i) q^{77} +(67.7630 - 42.5783i) q^{79} +(16.9760 - 13.5379i) q^{80} +(-57.8580 + 27.8629i) q^{82} +(68.4247 - 85.8019i) q^{83} +(6.74697 - 19.2817i) q^{85} -27.3741i q^{86} +107.650 q^{88} +(77.7390 + 27.2021i) q^{89} +(6.10889 + 4.87167i) q^{91} +(11.9746 + 24.8656i) q^{92} +(72.2411 + 90.5875i) q^{94} +(-0.140067 - 0.222915i) q^{95} +(19.5392 + 173.415i) q^{97} +(-41.9436 + 66.7529i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \)	\( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Introduction

L-functions

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