LMFDB - Embedded newform 261.3.s.a.73.1

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			73.1
Character	$\chi$	$=$	261.73
Dual form			261.3.s.a.118.1

$q$-expansion

$f(q)$	$=$	$q+(-2.58169 + 0.290886i) q^{2} +(2.68078 - 0.611870i) q^{4} +(2.49104 + 1.98654i) q^{5} +(1.30161 - 5.70272i) q^{7} +(3.06598 - 1.07283i) q^{8} +O(q^{10})$	\(q+(-2.58169 + 0.290886i) q^{2} +(2.68078 - 0.611870i) q^{4} +(2.49104 + 1.98654i) q^{5} +(1.30161 - 5.70272i) q^{7} +(3.06598 - 1.07283i) q^{8} +(-7.00893 - 4.40400i) q^{10} +(-16.1070 - 5.63608i) q^{11} +(2.84196 + 5.90140i) q^{13} +(-1.70150 + 15.1013i) q^{14} +(-17.5130 + 8.43380i) q^{16} +(14.7807 + 14.7807i) q^{17} +(9.65814 - 15.3708i) q^{19} +(7.89342 + 3.80127i) q^{20} +(43.2227 + 9.86529i) q^{22} +(-18.5750 - 23.2923i) q^{23} +(-3.30408 - 14.4761i) q^{25} +(-9.05369 - 14.4089i) q^{26} -16.0841i q^{28} +(19.9272 - 21.0691i) q^{29} +(-13.3687 + 1.50629i) q^{31} +(31.7582 - 19.9550i) q^{32} +(-42.4586 - 33.8596i) q^{34} +(14.5710 - 11.6200i) q^{35} +(17.2522 - 6.03682i) q^{37} +(-20.4631 + 42.4921i) q^{38} +(9.76869 + 3.41821i) q^{40} +(44.4102 - 44.4102i) q^{41} +(7.00239 - 62.1479i) q^{43} +(-46.6278 - 5.25369i) q^{44} +(54.7302 + 54.7302i) q^{46} +(16.6790 - 47.6658i) q^{47} +(13.3206 + 6.41487i) q^{49} +(12.7410 + 36.4117i) q^{50} +(11.2296 + 14.0814i) q^{52} +(-12.0961 + 15.1681i) q^{53} +(-28.9269 - 46.0368i) q^{55} +(-2.12736 - 18.8808i) q^{56} +(-45.3170 + 60.1904i) q^{58} -47.9911 q^{59} +(41.0683 - 25.8049i) q^{61} +(34.0756 - 7.77754i) q^{62} +(-15.3963 + 12.2781i) q^{64} +(-4.64390 + 20.3463i) q^{65} +(-6.15092 + 12.7725i) q^{67} +(48.6676 + 30.5799i) q^{68} +(-34.2377 + 34.2377i) q^{70} +(11.6321 + 24.1543i) q^{71} +(-12.2617 - 1.38156i) q^{73} +(-42.7839 + 20.6036i) q^{74} +(16.4864 - 47.1153i) q^{76} +(-53.1060 + 84.5178i) q^{77} +(33.5205 + 95.7961i) q^{79} +(-60.3795 - 13.7812i) q^{80} +(-101.735 + 127.571i) q^{82} +(9.73978 + 42.6728i) q^{83} +(7.45688 + 66.1816i) q^{85} +162.483i q^{86} -55.4303 q^{88} +(-53.9337 + 6.07686i) q^{89} +(37.3532 - 8.52561i) q^{91} +(-64.0472 - 51.0760i) q^{92} +(-29.1946 + 127.910i) q^{94} +(54.5935 - 19.1031i) q^{95} +(-124.213 - 78.0480i) q^{97} +(-36.2556 - 12.6864i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{27}{28}\right)$	$1$

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 $

$2$	−2.58169	+	0.290886i	−1.29084	+	0.145443i	−0.730554	−	0.682854i	$-0.760738\pi$
$2$	−2.58169	+	0.290886i	−1.29084	+	0.145443i	−0.560289	+	0.828298i	$0.689310\pi$
$3$		0			0
$3$		0			0
$4$	2.68078	−	0.611870i	0.670194	−	0.152967i
$5$	2.49104	+	1.98654i	0.498207	+	0.397307i	0.840100	−	0.542432i	$-0.182496\pi$
$5$	2.49104	+	1.98654i	0.498207	+	0.397307i	−0.341892	+	0.939739i	$0.611068\pi$
$6$		0			0
$7$	1.30161	−	5.70272i	0.185944	−	0.814675i	−0.792782	−	0.609505i	$-0.791368\pi$
$7$	1.30161	−	5.70272i	0.185944	−	0.814675i	0.978726	−	0.205170i	$-0.0657746\pi$
$8$	3.06598	−	1.07283i	0.383247	−	0.134104i
$9$		0			0
$10$	−7.00893	−	4.40400i	−0.700893	−	0.440400i
$11$	−16.1070	−	5.63608i	−1.46427	−	0.512371i	−0.523682	−	0.851914i	$-0.675442\pi$
$11$	−16.1070	−	5.63608i	−1.46427	−	0.512371i	−0.940591	+	0.339543i	$0.889728\pi$
$12$		0			0
$13$	2.84196	+	5.90140i	0.218613	+	0.453954i	0.981216	−	0.192913i	$-0.0617934\pi$
$13$	2.84196	+	5.90140i	0.218613	+	0.453954i	−0.762603	+	0.646866i	$0.776079\pi$
$14$	−1.70150	+	15.1013i	−0.121536	+	1.07866i
$15$		0			0
$16$	−17.5130	+	8.43380i	−1.09456	+	0.527112i
$17$	14.7807	+	14.7807i	0.869452	+	0.869452i	0.992412	−	0.122959i	$-0.0392385\pi$
$17$	14.7807	+	14.7807i	0.869452	+	0.869452i	−0.122959	+	0.992412i	$0.539238\pi$
$18$		0			0
$19$	9.65814	−	15.3708i	0.508323	−	0.808992i	−0.489697	−	0.871893i	$-0.662892\pi$
$19$	9.65814	−	15.3708i	0.508323	−	0.808992i	0.998020	+	0.0629012i	$0.0200353\pi$
$20$	7.89342	+	3.80127i	0.394671	+	0.190063i
$21$		0			0
$22$	43.2227	+	9.86529i	1.96467	+	0.448422i
$23$	−18.5750	−	23.2923i	−0.807608	−	1.01271i	−0.999510	−	0.0312943i	$-0.990037\pi$
$23$	−18.5750	−	23.2923i	−0.807608	−	1.01271i	0.191902	−	0.981414i	$-0.438534\pi$
$24$		0			0
$25$	−3.30408	−	14.4761i	−0.132163	−	0.579045i
$26$	−9.05369	−	14.4089i	−0.348219	−	0.554187i
$27$		0			0
$28$		−	16.0841i		−	0.574434i
$29$	19.9272	−	21.0691i	0.687144	−	0.726521i
$29$	19.9272	−	21.0691i	0.687144	−	0.726521i
$30$		0			0
$31$	−13.3687	+	1.50629i	−0.431249	+	0.0485900i	−0.324921	−	0.945741i	$-0.605338\pi$
$31$	−13.3687	+	1.50629i	−0.431249	+	0.0485900i	−0.106327	+	0.994331i	$0.533909\pi$
$32$	31.7582	−	19.9550i	0.992443	−	0.623593i
$33$		0			0
$34$	−42.4586	−	33.8596i	−1.24878	−	0.995871i
$35$	14.5710	−	11.6200i	0.416315	−	0.332000i
$36$		0			0
$37$	17.2522	−	6.03682i	0.466277	−	0.163157i	−0.0869071	−	0.996216i	$-0.527698\pi$
$37$	17.2522	−	6.03682i	0.466277	−	0.163157i	0.553184	+	0.833059i	$0.313413\pi$
$38$	−20.4631	+	42.4921i	−0.538503	+	1.11821i
$39$		0			0
$40$	9.76869	+	3.41821i	0.244217	+	0.0854553i
$41$	44.4102	−	44.4102i	1.08318	−	1.08318i	0.0869640	−	0.996211i	$-0.472283\pi$
$41$	44.4102	−	44.4102i	1.08318	−	1.08318i	0.996211	−	0.0869640i	$-0.0277165\pi$
$42$		0			0
$43$	7.00239	−	62.1479i	0.162846	−	1.44530i	−0.600663	−	0.799503i	$-0.705096\pi$
$43$	7.00239	−	62.1479i	0.162846	−	1.44530i	0.763509	−	0.645797i	$-0.223475\pi$
$44$	−46.6278	−	5.25369i	−1.05972	−	0.119402i
$45$		0			0
$46$	54.7302	+	54.7302i	1.18979	+	1.18979i
$47$	16.6790	−	47.6658i	0.354872	−	1.01417i	−0.618668	−	0.785652i	$-0.712327\pi$
$47$	16.6790	−	47.6658i	0.354872	−	1.01417i	0.973541	−	0.228515i	$-0.0733868\pi$
$48$		0			0
$49$	13.3206	+	6.41487i	0.271849	+	0.130916i
$50$	12.7410	+	36.4117i	0.254820	+	0.728234i
$51$		0			0
$52$	11.2296	+	14.0814i	0.215953	+	0.270796i
$53$	−12.0961	+	15.1681i	−0.228229	+	0.286190i	−0.882739	−	0.469863i	$-0.844303\pi$
$53$	−12.0961	+	15.1681i	−0.228229	+	0.286190i	0.654511	+	0.756053i	$0.272875\pi$
$54$		0			0
$55$	−28.9269	−	46.0368i	−0.525943	−	0.837033i
$56$	−2.12736	−	18.8808i	−0.0379886	−	0.337158i
$57$		0			0
$58$	−45.3170	+	60.1904i	−0.781327	+	1.03777i
$59$	−47.9911			−0.813408			−0.406704	−	0.913560i	$-0.633322\pi$
$59$	−47.9911			−0.813408			−0.406704	+	0.913560i	$0.633322\pi$
$60$		0			0
$61$	41.0683	−	25.8049i	0.673251	−	0.423031i	−0.151554	−	0.988449i	$-0.548428\pi$
$61$	41.0683	−	25.8049i	0.673251	−	0.423031i	0.824805	+	0.565417i	$0.191285\pi$
$62$	34.0756	−	7.77754i	0.549607	−	0.125444i
$63$		0			0
$64$	−15.3963	+	12.2781i	−0.240567	+	0.191846i
$65$	−4.64390	+	20.3463i	−0.0714446	+	0.313019i
$66$		0			0
$67$	−6.15092	+	12.7725i	−0.0918048	+	0.190635i	−0.941815	−	0.336132i	$-0.890881\pi$
$67$	−6.15092	+	12.7725i	−0.0918048	+	0.190635i	0.850010	+	0.526766i	$0.176596\pi$
$68$	48.6676	+	30.5799i	0.715700	+	0.449704i
$69$		0			0
$70$	−34.2377	+	34.2377i	−0.489110	+	0.489110i
$71$	11.6321	+	24.1543i	0.163832	+	0.340202i	0.966682	−	0.255980i	$-0.0823981\pi$
$71$	11.6321	+	24.1543i	0.163832	+	0.340202i	−0.802850	+	0.596182i	$0.796684\pi$
$72$		0			0
$73$	−12.2617	−	1.38156i	−0.167968	−	0.0189255i	0.0275798	−	0.999620i	$-0.491220\pi$
$73$	−12.2617	−	1.38156i	−0.167968	−	0.0189255i	−0.195548	+	0.980694i	$0.562649\pi$
$74$	−42.7839	+	20.6036i	−0.578160	+	0.278427i
$75$		0			0
$76$	16.4864	−	47.1153i	0.216926	−	0.619938i
$77$	−53.1060	+	84.5178i	−0.689689	+	1.09763i
$78$		0			0
$79$	33.5205	+	95.7961i	0.424310	+	1.21261i	0.935557	+	0.353175i	$0.114898\pi$
$79$	33.5205	+	95.7961i	0.424310	+	1.21261i	−0.511247	+	0.859434i	$0.670816\pi$
$80$	−60.3795	−	13.7812i	−0.754744	−	0.172265i
$81$		0			0
$82$	−101.735	+	127.571i	−1.24067	+	1.55575i
$83$	9.73978	+	42.6728i	0.117347	+	0.514130i	0.999100	+	0.0424187i	$0.0135063\pi$
$83$	9.73978	+	42.6728i	0.117347	+	0.514130i	−0.881753	+	0.471711i	$0.843637\pi$
$84$		0			0
$85$	7.45688	+	66.1816i	0.0877280	+	0.778607i
$86$			162.483i			1.88934i
$87$		0			0
$88$	−55.4303			−0.629890
$89$	−53.9337	+	6.07686i	−0.605996	+	0.0682794i	−0.409631	−	0.912251i	$-0.634342\pi$
$89$	−53.9337	+	6.07686i	−0.605996	+	0.0682794i	−0.196365	+	0.980531i	$0.562914\pi$
$90$		0			0
$91$	37.3532	−	8.52561i	0.410474	−	0.0936881i
$92$	−64.0472	−	51.0760i	−0.696165	−	0.555173i
$93$		0			0
$94$	−29.1946	+	127.910i	−0.310581	+	1.36074i
$95$	54.5935	−	19.1031i	0.574669	−	0.201085i
$96$		0			0
$97$	−124.213	−	78.0480i	−1.28054	−	0.804619i	−0.292126	−	0.956380i	$-0.594363\pi$
$97$	−124.213	−	78.0480i	−1.28054	−	0.804619i	−0.988417	+	0.151761i	$0.951506\pi$
$98$	−36.2556	−	12.6864i	−0.369955	−	0.129453i
$99$		0			0
$100$	−17.7150	−	36.7856i	−0.177150	−	0.367856i
$101$	15.1390	−	134.362i	0.149891	−	1.33032i	−0.663314	−	0.748342i	$-0.730850\pi$
$101$	15.1390	−	134.362i	0.149891	−	1.33032i	0.813205	−	0.581978i	$-0.197721\pi$
$102$		0			0
$103$	42.8611	−	20.6408i	0.416127	−	0.200396i	−0.214092	−	0.976813i	$-0.568679\pi$
$103$	42.8611	−	20.6408i	0.416127	−	0.200396i	0.630219	+	0.776417i	$0.282965\pi$
$104$	15.0446	+	15.0446i	0.144660	+	0.144660i
$105$		0			0
$106$	26.8162	−	42.6778i	0.252983	−	0.402620i
$107$	−119.175	−	57.3917i	−1.11379	−	0.536371i	−0.215818	−	0.976434i	$-0.569242\pi$
$107$	−119.175	−	57.3917i	−1.11379	−	0.536371i	−0.897967	+	0.440063i	$0.854956\pi$
$108$		0			0
$109$	−42.9080	−	9.79348i	−0.393652	−	0.0898485i	0.0211130	−	0.999777i	$-0.493279\pi$
$109$	−42.9080	−	9.79348i	−0.393652	−	0.0898485i	−0.414765	+	0.909929i	$0.636136\pi$
$110$	88.0715	+	110.438i	0.800650	+	1.00398i
$111$		0			0
$112$	25.3006	+	110.849i	0.225898	+	0.989724i
$113$	48.1620	+	76.6493i	0.426212	+	0.678313i	0.988938	−	0.148331i	$-0.0473901\pi$
$113$	48.1620	+	76.6493i	0.426212	+	0.678313i	−0.562726	+	0.826644i	$0.690247\pi$
$114$		0			0
$115$		−	94.9218i		−	0.825407i
$116$	40.5287	−	68.6744i	0.349386	−	0.592021i
$117$		0			0
$118$	123.898	−	13.9599i	1.04998	−	0.118305i
$119$	103.529	−	65.0515i	0.869991	−	0.546651i
$120$		0			0
$121$	133.068	+	106.119i	1.09974	+	0.877012i
$122$	−98.5191	+	78.5664i	−0.807534	+	0.643987i
$123$		0			0
$124$	−34.9169	+	12.2179i	−0.281588	+	0.0985317i
$125$	55.0873	−	114.390i	0.440698	−	0.915120i
$126$		0			0
$127$	−198.494	−	69.4561i	−1.56295	−	0.546898i	−0.596244	−	0.802804i	$-0.703341\pi$
$127$	−198.494	−	69.4561i	−1.56295	−	0.546898i	−0.966702	+	0.255905i	$0.917626\pi$
$128$	−69.9093	+	69.9093i	−0.546166	+	0.546166i
$129$		0			0
$130$	6.07065	−	53.8785i	0.0466973	−	0.414450i
$131$	164.999	+	18.5909i	1.25953	+	0.141915i	0.716375	−	0.697715i	$-0.245800\pi$
$131$	164.999	+	18.5909i	1.25953	+	0.141915i	0.543158	+	0.839631i	$0.317228\pi$
$132$		0			0
$133$	−75.0845	−	75.0845i	−0.564545	−	0.564545i
$134$	12.1644	−	34.7638i	0.0907791	−	0.259432i
$135$		0			0
$136$	61.1745	+	29.4601i	0.449813	+	0.216618i
$137$	56.9427	+	162.733i	0.415640	+	1.18783i	0.941428	+	0.337215i	$0.109485\pi$
$137$	56.9427	+	162.733i	0.415640	+	1.18783i	−0.525788	+	0.850616i	$0.676229\pi$
$138$		0			0
$139$	97.5376	+	122.308i	0.701709	+	0.879915i	0.997150	−	0.0754457i	$-0.0240379\pi$
$139$	97.5376	+	122.308i	0.701709	+	0.879915i	−0.295441	+	0.955361i	$0.595467\pi$
$140$	31.9517	−	40.0662i	0.228227	−	0.286187i
$141$		0			0
$142$	−37.0566	−	58.9752i	−0.260962	−	0.415319i
$143$	−12.5147	−	111.071i	−0.0875156	−	0.776723i
$144$		0			0
$145$	91.4939	−	12.8979i	0.630992	−	0.0889512i
$146$	32.0577			0.219573
$147$		0			0
$148$	42.5557	−	26.7395i	0.287538	−	0.180672i
$149$	−101.993	+	23.2793i	−0.684519	+	0.156237i	−0.550617	−	0.834758i	$-0.685608\pi$
$149$	−101.993	+	23.2793i	−0.684519	+	0.156237i	−0.133901	+	0.990995i	$0.542751\pi$
$150$		0			0
$151$	−87.2999	+	69.6194i	−0.578145	+	0.461055i	−0.868379	−	0.495900i	$-0.834838\pi$
$151$	−87.2999	+	69.6194i	−0.578145	+	0.461055i	0.290234	+	0.956956i	$0.406267\pi$
$152$	13.1213	−	57.4883i	0.0863245	−	0.378212i
$153$		0			0
$154$	112.518	−	233.646i	0.730637	−	1.51718i
$155$	−36.2942	−	22.8052i	−0.234156	−	0.147130i
$156$		0			0
$157$	154.052	−	154.052i	0.981223	−	0.981223i	−0.0186037	−	0.999827i	$-0.505922\pi$
$157$	154.052	−	154.052i	0.981223	−	0.981223i	0.999827	+	0.0186037i	$0.00592209\pi$
$158$	−114.405	−	237.565i	−0.724083	−	1.50357i
$159$		0			0
$160$	118.752	+	13.3801i	0.742201	+	0.0836259i
$161$	−157.007	+	75.6105i	−0.975198	+	0.469631i
$162$		0			0
$163$	−18.9751	+	54.2278i	−0.116412	+	0.332686i	−0.987316	−	0.158767i	$-0.949248\pi$
$163$	−18.9751	+	54.2278i	−0.116412	+	0.332686i	0.870904	+	0.491453i	$0.163534\pi$
$164$	91.8805	−	146.227i	0.560247	−	0.891628i
$165$		0			0
$166$	−37.5580	−	107.335i	−0.226253	−	0.646594i
$167$	−131.159	−	29.9362i	−0.785384	−	0.179259i	−0.189020	−	0.981973i	$-0.560531\pi$
$167$	−131.159	−	29.9362i	−0.785384	−	0.179259i	−0.596364	+	0.802714i	$0.703388\pi$
$168$		0			0
$169$	78.6200	−	98.5864i	0.465207	−	0.583352i
$170$	−38.5026	−	168.691i	−0.226486	−	0.992300i
$171$		0			0
$172$	−19.2546	−	170.889i	−0.111945	−	0.993542i
$173$		−	21.1826i		−	0.122443i	−0.998124	−	0.0612213i	$-0.980500\pi$
$173$		−	21.1826i		−	0.122443i	0.998124	−	0.0612213i	$-0.0194995\pi$
$174$		0			0
$175$	−86.8540			−0.496308
$176$	329.615	−	37.1387i	1.87281	−	0.211015i
$177$		0			0
$178$	137.472	−	31.3771i	0.772315	−	0.176276i
$179$	71.5446	+	57.0549i	0.399690	+	0.318742i	0.802622	−	0.596487i	$-0.203437\pi$
$179$	71.5446	+	57.0549i	0.399690	+	0.318742i	−0.402932	+	0.915230i	$0.632009\pi$
$180$		0			0
$181$	−43.7618	+	191.733i	−0.241778	+	1.05930i	0.697620	+	0.716468i	$0.254242\pi$
$181$	−43.7618	+	191.733i	−0.241778	+	1.05930i	−0.939398	+	0.342829i	$0.888615\pi$
$182$	−93.9541	+	32.8760i	−0.516232	+	0.180637i
$183$		0			0
$184$	−81.9393	−	51.4858i	−0.445322	−	0.279814i
$185$	54.9684	+	19.2343i	0.297126	+	0.103969i
$186$		0			0
$187$	−154.767	−	321.378i	−0.827633	−	1.71860i
$188$	15.5474	−	137.987i	0.0826988	−	0.733973i
$189$		0			0
$190$	−135.387	+	65.1987i	−0.712561	+	0.343151i
$191$	173.129	+	173.129i	0.906436	+	0.906436i	0.995983	−	0.0895465i	$-0.0285418\pi$
$191$	173.129	+	173.129i	0.906436	+	0.906436i	−0.0895465	+	0.995983i	$0.528542\pi$
$192$		0			0
$193$	−107.871	+	171.676i	−0.558917	+	0.889511i	−0.999968	−	0.00797056i	$-0.997463\pi$
$193$	−107.871	+	171.676i	−0.558917	+	0.889511i	0.441051	+	0.897482i	$0.354606\pi$
$194$	343.381	+	165.364i	1.77001	+	0.852390i
$195$		0			0
$196$	39.6346	+	9.04635i	0.202218	+	0.0461548i
$197$	−39.4510	−	49.4700i	−0.200259	−	0.251117i	0.671554	−	0.740956i	$-0.265627\pi$
$197$	−39.4510	−	49.4700i	−0.200259	−	0.251117i	−0.871813	+	0.489839i	$0.837056\pi$
$198$		0			0
$199$	−10.0083	−	43.8490i	−0.0502928	−	0.220347i	0.943536	−	0.331269i	$-0.107477\pi$
$199$	−10.0083	−	43.8490i	−0.0502928	−	0.220347i	−0.993829	+	0.110922i	$0.964620\pi$
$200$	−25.6607	−	40.8388i	−0.128304	−	0.204194i
$201$		0			0
$202$			351.285i			1.73903i
$203$	−94.2140	−	141.063i	−0.464108	−	0.694891i
$204$		0			0
$205$	198.850	−	22.4050i	0.970000	−	0.109293i
$206$	−104.650	+	65.7557i	−0.508008	+	0.319203i
$207$		0			0
$208$	−99.5424	−	79.3824i	−0.478569	−	0.381646i
$209$	−242.195	+	193.144i	−1.15883	+	0.924134i
$210$		0			0
$211$	267.044	−	93.4429i	1.26561	−	0.442857i	0.387748	−	0.921765i	$-0.373253\pi$
$211$	267.044	−	93.4429i	1.26561	−	0.442857i	0.877865	+	0.478908i	$0.158967\pi$
$212$	−23.1461	+	48.0634i	−0.109180	+	0.226714i
$213$		0			0
$214$	324.367	+	113.501i	1.51573	+	0.530378i
$215$	140.902	−	140.902i	0.655359	−	0.655359i
$216$		0			0
$217$	−8.81087	+	78.1986i	−0.0406031	+	0.360362i
$218$	113.624	+	12.8023i	0.521210	+	0.0587263i
$219$		0			0
$220$	−105.715	−	105.715i	−0.480523	−	0.480523i
$221$	−45.2205	+	129.233i	−0.204618	+	0.584764i
$222$		0			0
$223$	−9.38970	−	4.52184i	−0.0421063	−	0.0202773i	0.412712	−	0.910862i	$-0.364582\pi$
$223$	−9.38970	−	4.52184i	−0.0421063	−	0.0202773i	−0.454818	+	0.890584i	$0.650296\pi$
$224$	−72.4610	−	207.082i	−0.323487	−	0.924472i
$225$		0			0
$226$	−146.635	−	183.875i	−0.648829	−	0.813605i
$227$	−41.9912	+	52.6552i	−0.184983	+	0.231961i	−0.865673	−	0.500611i	$-0.833109\pi$
$227$	−41.9912	+	52.6552i	−0.184983	+	0.231961i	0.680690	+	0.732572i	$0.261680\pi$
$228$		0			0
$229$	−137.469	−	218.781i	−0.600303	−	0.955376i	−0.999262	−	0.0384078i	$-0.987771\pi$
$229$	−137.469	−	218.781i	−0.600303	−	0.955376i	0.398959	−	0.916969i	$-0.369371\pi$
$230$	27.6114	+	245.058i	0.120050	+	1.06547i
$231$		0			0
$232$	38.4927	−	85.9760i	0.165917	−	0.370586i
$233$	−139.905			−0.600452			−0.300226	−	0.953868i	$-0.597062\pi$
$233$	−139.905			−0.600452			−0.300226	+	0.953868i	$0.597062\pi$
$234$		0			0
$235$	136.238	−	85.6040i	0.579736	−	0.364272i
$236$	−128.653	+	29.3643i	−0.545141	+	0.124425i
$237$		0			0
$238$	−248.356	+	198.058i	−1.04351	+	0.832175i
$239$	−22.0091	+	96.4282i	−0.0920883	+	0.403465i	−0.999872	−	0.0159726i	$-0.994916\pi$
$239$	−22.0091	+	96.4282i	−0.0920883	+	0.403465i	0.907784	+	0.419438i	$0.137773\pi$
$240$		0			0
$241$	−158.413	+	328.947i	−0.657314	+	1.36493i	0.259552	+	0.965729i	$0.416425\pi$
$241$	−158.413	+	328.947i	−0.657314	+	1.36493i	−0.916865	+	0.399197i	$0.869289\pi$
$242$	−374.409	−	235.257i	−1.54715	−	0.972136i
$243$		0			0
$244$	94.3057	−	94.3057i	0.386499	−	0.386499i
$245$	20.4388	+	42.4415i	0.0834235	+	0.173231i
$246$		0			0
$247$	118.158	+	13.3132i	0.478371	+	0.0538994i
$248$	−39.3722	+	18.9606i	−0.158759	+	0.0764542i
$249$		0			0
$250$	−108.944	+	311.343i	−0.435775	+	1.24537i
$251$	−117.710	+	187.335i	−0.468965	+	0.746353i	−0.994536	−	0.104396i	$-0.966709\pi$
$251$	−117.710	+	187.335i	−0.468965	+	0.746353i	0.525571	+	0.850750i	$0.323852\pi$
$252$		0			0
$253$	167.910	+	479.859i	0.663676	+	1.89668i
$254$	532.653	+	121.575i	2.09706	+	0.478640i
$255$		0			0
$256$	209.261	−	262.405i	0.817425	−	1.02502i
$257$	29.0472	+	127.264i	0.113024	+	0.495191i	0.999476	+	0.0323701i	$0.0103055\pi$
$257$	29.0472	+	127.264i	0.113024	+	0.495191i	−0.886452	+	0.462821i	$0.846837\pi$
$258$		0			0
$259$	−11.9706	−	106.242i	−0.0462187	−	0.410202i
$260$			57.3852i			0.220712i
$261$		0			0
$262$	−431.383			−1.64650
$263$	−53.5898	+	6.03812i	−0.203763	+	0.0229586i	−0.213256	−	0.976996i	$-0.568407\pi$
$263$	−53.5898	+	6.03812i	−0.203763	+	0.0229586i	0.00949275	+	0.999955i	$0.496978\pi$
$264$		0			0
$265$	−60.2638	+	13.7548i	−0.227411	+	0.0519050i
$266$	215.686	+	172.004i	0.810849	+	0.646630i
$267$		0			0
$268$	−8.67412	+	38.0038i	−0.0323661	+	0.141805i
$269$	−23.6596	+	8.27885i	−0.0879538	+	0.0307764i	−0.373897	−	0.927470i	$-0.621979\pi$
$269$	−23.6596	+	8.27885i	−0.0879538	+	0.0307764i	0.285943	+	0.958246i	$0.407693\pi$
$270$		0			0
$271$	261.030	+	164.016i	0.963211	+	0.605226i	0.919194	−	0.393805i	$-0.128841\pi$
$271$	261.030	+	164.016i	0.963211	+	0.605226i	0.0440174	+	0.999031i	$0.485984\pi$
$272$	−383.511	−	134.196i	−1.40997	−	0.493369i
$273$		0			0
$274$	−194.345	−	403.561i	−0.709288	−	1.47285i
$275$	−28.3698	+	251.789i	−0.103163	+	0.915596i
$276$		0			0
$277$	−448.792	+	216.127i	−1.62019	+	0.780241i	−0.999991	−	0.00420714i	$-0.998661\pi$
$277$	−448.792	+	216.127i	−1.62019	+	0.780241i	−0.620195	+	0.784448i	$0.712947\pi$
$278$	−287.389	−	287.389i	−1.03377	−	1.03377i
$279$		0			0
$280$	32.2081	−	51.2590i	0.115029	−	0.183068i
$281$	360.665	+	173.687i	1.28350	+	0.618103i	0.946288	−	0.323325i	$-0.104801\pi$
$281$	360.665	+	173.687i	1.28350	+	0.618103i	0.337216	+	0.941427i	$0.390515\pi$
$282$		0			0
$283$	72.2136	+	16.4823i	0.255172	+	0.0582413i	0.348193	−	0.937423i	$-0.386795\pi$
$283$	72.2136	+	16.4823i	0.255172	+	0.0582413i	−0.0930214	+	0.995664i	$0.529652\pi$
$284$	45.9624	+	57.6350i	0.161839	+	0.202940i
$285$		0			0
$286$	64.6182	+	283.111i	0.225938	+	0.989898i
$287$	−195.454	−	311.064i	−0.681026	−	1.08385i
$288$		0			0
$289$			147.938i			0.511895i
$290$	−232.457	+	59.9127i	−0.801575	+	0.206596i
$291$		0			0
$292$	−33.7161	+	3.79890i	−0.115466	+	0.0130099i
$293$	381.722	−	239.852i	1.30281	−	0.818608i	0.311508	−	0.950243i	$-0.399166\pi$
$293$	381.722	−	239.852i	1.30281	−	0.818608i	0.991298	+	0.131636i	$0.0420230\pi$
$294$		0			0
$295$	−119.548	−	95.3360i	−0.405246	−	0.323173i
$296$	46.4185	−	37.0176i	0.156819	−	0.125059i
$297$		0			0
$298$	256.543	−	89.7683i	0.860882	−	0.301236i
$299$	84.6676	−	175.814i	0.283169	−	0.588007i
$300$		0			0
$301$	−345.298	−	120.825i	−1.14717	−	0.401412i
$302$	205.130	−	205.130i	0.679237	−	0.679237i
$303$		0			0
$304$	−39.5081	+	350.644i	−0.129961	+	1.15343i
$305$	153.565	+	17.3026i	0.503492	+	0.0567299i
$306$		0			0
$307$	−14.8497	−	14.8497i	−0.0483703	−	0.0483703i	0.682508	−	0.730878i	$-0.260889\pi$
$307$	−14.8497	−	14.8497i	−0.0483703	−	0.0483703i	−0.730878	+	0.682508i	$0.760889\pi$
$308$	−90.6515	+	259.067i	−0.294323	+	0.841127i
$309$		0			0
$310$	100.334	+	48.3183i	0.323658	+	0.155866i
$311$	−51.0039	−	145.761i	−0.164000	−	0.468684i	0.832330	−	0.554280i	$-0.187006\pi$
$311$	−51.0039	−	145.761i	−0.164000	−	0.468684i	−0.996330	+	0.0855959i	$0.972721\pi$
$312$		0			0
$313$	106.381	+	133.398i	0.339876	+	0.426191i	0.922169	−	0.386788i	$-0.126416\pi$
$313$	106.381	+	133.398i	0.339876	+	0.426191i	−0.582292	+	0.812979i	$0.697844\pi$
$314$	−352.902	+	442.526i	−1.12389	+	1.40932i
$315$		0			0
$316$	148.476	+	236.298i	0.469860	+	0.747777i
$317$	4.18683	+	37.1591i	0.0132077	+	0.117221i	0.998586	−	0.0531589i	$-0.0169290\pi$
$317$	4.18683	+	37.1591i	0.0132077	+	0.117221i	−0.985378	+	0.170380i	$0.945500\pi$
$318$		0			0
$319$	−439.714	+	227.049i	−1.37841	+	0.711753i
$320$	−62.7436			−0.196074
$321$		0			0
$322$	383.348	−	240.874i	1.19052	−	0.748055i
$323$	369.946	−	84.4377i	1.14534	−	0.261417i
$324$		0			0
$325$	76.0393	−	60.6393i	0.233967	−	0.186582i
$326$	33.2137	−	145.519i	0.101883	−	0.446377i
$327$		0			0
$328$	88.5161	−	183.805i	0.269866	−	0.560383i
$329$	−250.116	−	157.158i	−0.760230	−	0.477684i
$330$		0			0
$331$	195.213	−	195.213i	0.589768	−	0.589768i	−0.347800	−	0.937569i	$-0.613071\pi$
$331$	195.213	−	195.213i	0.589768	−	0.589768i	0.937569	+	0.347800i	$0.113071\pi$
$332$	52.2204	+	108.437i	0.157290	+	0.326616i
$333$		0			0
$334$	347.320	+	39.1335i	1.03988	+	0.117166i
$335$	−40.6952	+	19.5978i	−0.121478	+	0.0585009i
$336$		0			0
$337$	86.0626	−	245.953i	0.255379	−	0.729830i	−0.742801	−	0.669513i	$-0.766503\pi$
$337$	86.0626	−	245.953i	0.255379	−	0.729830i	0.998179	−	0.0603174i	$-0.0192113\pi$
$338$	−174.295	+	277.389i	−0.515665	+	0.820676i
$339$		0			0
$340$	60.4848	+	172.855i	0.177896	+	0.508398i
$341$	223.819	+	51.0853i	0.656362	+	0.149810i
$342$		0			0
$343$	232.625	−	291.702i	0.678207	−	0.850444i
$344$	−45.2051	−	198.057i	−0.131410	−	0.575746i
$345$		0			0
$346$	6.16172	+	54.6867i	0.0178084	+	0.158054i
$347$		−	75.7571i		−	0.218320i	−0.994024	−	0.109160i	$-0.965184\pi$
$347$		−	75.7571i		−	0.218320i	0.994024	−	0.109160i	$-0.0348161\pi$
$348$		0			0
$349$	−88.0863			−0.252396			−0.126198	−	0.992005i	$-0.540277\pi$
$349$	−88.0863			−0.252396			−0.126198	+	0.992005i	$0.540277\pi$
$350$	224.230	−	25.2646i	0.640656	−	0.0721846i
$351$		0			0
$352$	−623.997	+	142.423i	−1.77272	+	0.404611i
$353$	−333.963	−	266.327i	−0.946071	−	0.754467i	0.0233860	−	0.999727i	$-0.492555\pi$
$353$	−333.963	−	266.327i	−0.946071	−	0.754467i	−0.969457	+	0.245260i	$0.921127\pi$
$354$		0			0
$355$	−19.0074	+	83.2769i	−0.0535420	+	0.234583i
$356$	−140.866	+	49.2911i	−0.395691	+	0.138458i
$357$		0			0
$358$	−201.302	−	126.486i	−0.562296	−	0.353314i
$359$	−396.769	−	138.835i	−1.10521	−	0.386728i	−0.284845	−	0.958574i	$-0.591942\pi$
$359$	−396.769	−	138.835i	−1.10521	−	0.386728i	−0.820361	+	0.571845i	$0.806228\pi$
$360$		0			0
$361$	13.6489	+	28.3422i	0.0378086	+	0.0785103i
$362$	57.2067	−	507.723i	0.158030	−	1.40255i
$363$		0			0
$364$	94.9189	−	45.7105i	0.260766	−	0.125578i
$365$	−27.7998	−	27.7998i	−0.0761638	−	0.0761638i
$366$		0			0
$367$	−133.333	+	212.198i	−0.363305	+	0.578196i	−0.977494	−	0.210962i	$-0.932340\pi$
$367$	−133.333	+	212.198i	−0.363305	+	0.578196i	0.614189	+	0.789159i	$0.289483\pi$
$368$	521.746	+	251.259i	1.41779	+	0.682770i
$369$		0			0
$370$	−147.506	−	33.6673i	−0.398665	−	0.0909927i
$371$	70.7548	+	88.7237i	0.190714	+	0.239148i
$372$		0			0
$373$	109.293	+	478.845i	0.293012	+	1.28377i	0.880311	+	0.474397i	$0.157334\pi$
$373$	109.293	+	478.845i	0.293012	+	1.28377i	−0.587299	+	0.809370i	$0.699809\pi$
$374$	493.045	+	784.677i	1.31830	+	2.09807i
$375$		0			0
$376$		−	164.036i		−	0.436267i
$377$	180.970	+	57.7205i	0.480025	+	0.153105i
$378$		0			0
$379$	8.35834	−	0.941759i	0.0220537	−	0.00248485i	−0.100931	−	0.994893i	$-0.532182\pi$
$379$	8.35834	−	0.941759i	0.0220537	−	0.00248485i	0.122984	+	0.992409i	$0.460753\pi$
$380$	134.664	−	84.6153i	0.354380	−	0.222672i
$381$		0			0
$382$	−497.326	−	396.605i	−1.30190	−	1.03823i
$383$	81.7068	−	65.1590i	0.213334	−	0.170128i	−0.510993	−	0.859585i	$-0.670722\pi$
$383$	81.7068	−	65.1590i	0.213334	−	0.170128i	0.724327	+	0.689457i	$0.242151\pi$
$384$		0			0
$385$	−300.187	+	105.040i	−0.779706	+	0.272831i
$386$	228.551	−	474.591i	0.592101	−	1.22951i
$387$		0			0
$388$	−380.742	−	133.227i	−0.981293	−	0.343369i
$389$	−3.30195	+	3.30195i	−0.00848831	+	0.00848831i	−0.711338	−	0.702850i	$-0.751911\pi$
$389$	−3.30195	+	3.30195i	−0.00848831	+	0.00848831i	0.702850	+	0.711338i	$0.251911\pi$
$390$		0			0
$391$	69.7251	−	618.827i	0.178325	−	1.58268i
$392$	47.7228	+	5.37707i	0.121742	+	0.0137170i
$393$		0			0
$394$	116.240	+	116.240i	0.295026	+	0.295026i
$395$	−106.802	+	305.221i	−0.270384	+	0.772712i
$396$		0			0
$397$	596.541	+	287.279i	1.50262	+	0.723625i	0.990783	−	0.135457i	$-0.0432503\pi$
$397$	596.541	+	287.279i	1.50262	+	0.723625i	0.511839	+	0.859082i	$0.328965\pi$
$398$	38.5933	+	110.293i	0.0969680	+	0.277119i
$399$		0			0
$400$	179.953	+	225.654i	0.449883	+	0.564135i
$401$	297.015	−	372.445i	0.740687	−	0.928792i	−0.258622	−	0.965979i	$-0.583268\pi$
$401$	297.015	−	372.445i	0.740687	−	0.928792i	0.999308	+	0.0371871i	$0.0118398\pi$
$402$		0			0
$403$	−46.8826	−	74.6132i	−0.116334	−	0.185144i
$404$	−41.6279	−	369.458i	−0.103039	−	0.914501i
$405$		0			0
$406$	284.264	+	336.775i	0.700158	+	0.829494i
$407$	−311.906			−0.766354
$408$		0			0
$409$	−245.996	+	154.570i	−0.601458	+	0.377921i	−0.798074	−	0.602560i	$-0.794148\pi$
$409$	−245.996	+	154.570i	−0.601458	+	0.377921i	0.196616	+	0.980481i	$0.437005\pi$
$410$	−506.851	+	115.685i	−1.23622	+	0.282159i
$411$		0			0
$412$	102.271	−	81.5587i	0.248232	−	0.197958i
$413$	−62.4657	+	273.680i	−0.151249	+	0.662663i
$414$		0			0
$415$	−60.5088	+	125.648i	−0.145804	+	0.302766i
$416$	208.018	+	130.706i	0.500043	+	0.314198i
$417$		0			0
$418$	569.089	−	569.089i	1.36146	−	1.36146i
$419$	−148.802	−	308.990i	−0.355135	−	0.737446i	0.644496	−	0.764608i	$-0.277067\pi$
$419$	−148.802	−	308.990i	−0.355135	−	0.737446i	−0.999631	+	0.0271619i	$0.991353\pi$
$420$		0			0
$421$	528.745	+	59.5753i	1.25593	+	0.141509i	0.714738	−	0.699392i	$-0.246546\pi$
$421$	528.745	+	59.5753i	1.25593	+	0.141509i	0.541189	+	0.840901i	$0.317974\pi$
$422$	−662.244	+	318.920i	−1.56930	+	0.755734i
$423$		0			0
$424$	−20.8137	+	59.4821i	−0.0490889	+	0.140288i
$425$	165.131	−	262.804i	0.388542	−	0.618362i
$426$		0			0
$427$	−93.7034	−	267.789i	−0.219446	−	0.627141i
$428$	−354.598	−	80.9346i	−0.828500	−	0.189100i
$429$		0			0
$430$	−322.779	+	404.752i	−0.750649	+	0.941284i
$431$	125.008	+	547.695i	0.290041	+	1.27075i	0.884467	+	0.466604i	$0.154523\pi$
$431$	125.008	+	547.695i	0.290041	+	1.27075i	−0.594425	+	0.804151i	$0.702620\pi$
$432$		0			0
$433$	−14.0479	−	124.679i	−0.0324432	−	0.287942i	−0.999449	−	0.0331877i	$-0.989434\pi$
$433$	−14.0479	−	124.679i	−0.0324432	−	0.287942i	0.967006	−	0.254754i	$-0.0819945\pi$
$434$		−	204.447i		−	0.471077i
$435$		0			0
$436$	−121.019			−0.277567
$437$	−537.422	+	60.5529i	−1.22980	+	0.138565i
$438$		0			0
$439$	505.439	−	115.363i	1.15134	−	0.262786i	0.396084	−	0.918214i	$-0.370369\pi$
$439$	505.439	−	115.363i	1.15134	−	0.262786i	0.755258	+	0.655428i	$0.227512\pi$
$440$	−138.079	−	110.114i	−0.313816	−	0.250260i
$441$		0			0
$442$	79.1532	−	346.793i	0.179080	−	0.784599i
$443$	−57.1618	+	20.0018i	−0.129033	+	0.0451507i	−0.394023	−	0.919100i	$-0.628917\pi$
$443$	−57.1618	+	20.0018i	−0.129033	+	0.0451507i	0.264990	+	0.964251i	$0.414631\pi$
$444$		0			0
$445$	−146.423	−	92.0035i	−0.329040	−	0.206749i
$446$	25.5566	+	8.94264i	0.0573018	+	0.0200508i
$447$		0			0
$448$	49.9788	+	103.782i	0.111560	+	0.231656i
$449$	80.2125	−	711.905i	0.178647	−	1.58554i	−0.509829	−	0.860276i	$-0.670291\pi$
$449$	80.2125	−	711.905i	0.178647	−	1.58554i	0.688476	−	0.725260i	$-0.258280\pi$
$450$		0			0
$451$	−965.615	+	465.015i	−2.14105	+	1.03108i
$452$	176.011	+	176.011i	0.389405	+	0.389405i
$453$		0			0
$454$	93.0913	−	148.154i	0.205047	−	0.326330i
$455$	109.985	+	52.9658i	0.241724	+	0.116408i
$456$		0			0
$457$	−533.475	−	121.762i	−1.16734	−	0.266438i	−0.405435	−	0.914124i	$-0.632880\pi$
$457$	−533.475	−	121.762i	−1.16734	−	0.266438i	−0.761908	+	0.647686i	$0.775737\pi$
$458$	418.543	+	524.836i	0.913850	+	1.14593i
$459$		0			0
$460$	−58.0798	−	254.464i	−0.126260	−	0.553183i
$461$	313.897	+	499.564i	0.680904	+	1.08365i	0.991118	+	0.132985i	$0.0424564\pi$
$461$	313.897	+	499.564i	0.680904	+	1.08365i	−0.310214	+	0.950667i	$0.600401\pi$
$462$		0			0
$463$		−	75.7339i		−	0.163572i	−0.996650	−	0.0817861i	$-0.973938\pi$
$463$		−	75.7339i		−	0.163572i	0.996650	−	0.0817861i	$-0.0260624\pi$
$464$	−171.291	+	537.045i	−0.369162	+	1.15742i
$465$		0			0
$466$	361.192	−	40.6965i	0.775090	−	0.0873316i
$467$	146.168	−	91.8436i	0.312994	−	0.196667i	−0.366369	−	0.930470i	$-0.619399\pi$
$467$	146.168	−	91.8436i	0.312994	−	0.196667i	0.679363	+	0.733803i	$0.262256\pi$
$468$		0			0
$469$	64.8320	+	51.7018i	0.138235	+	0.110238i
$470$	−326.823	+	260.632i	−0.695367	+	0.554537i
$471$		0			0
$472$	−147.140	+	51.4864i	−0.311737	+	0.109081i
$473$	−463.058	+	961.550i	−0.978981	+	2.03288i
$474$		0			0
$475$	−254.422	−	89.0260i	−0.535624	−	0.187423i
$476$	237.735	−	237.735i	0.499443	−	0.499443i
$477$		0			0
$478$	28.7710	−	255.349i	0.0601903	−	0.534204i
$479$	14.8101	+	1.66870i	0.0309188	+	0.00348372i	0.127410	−	0.991850i	$-0.459333\pi$
$479$	14.8101	+	1.66870i	0.0309188	+	0.00348372i	−0.0964915	+	0.995334i	$0.530762\pi$
$480$		0			0
$481$	84.6559	+	84.6559i	0.176000	+	0.176000i
$482$	313.285	−	895.318i	0.649970	−	1.85751i
$483$		0			0
$484$	421.657	+	203.059i	0.871193	+	0.419544i
$485$	−154.373	−	441.174i	−0.318296	−	0.909636i
$486$		0			0
$487$	121.461	+	152.307i	0.249406	+	0.312745i	0.890737	−	0.454519i	$-0.150189\pi$
$487$	121.461	+	152.307i	0.249406	+	0.312745i	−0.641331	+	0.767264i	$0.721618\pi$
$488$	98.2302	−	123.177i	0.201291	−	0.252411i
$489$		0			0
$490$	−65.1121	−	103.625i	−0.132882	−	0.211480i
$491$	−4.56914	−	40.5522i	−0.00930578	−	0.0825911i	0.988201	−	0.153163i	$-0.0489461\pi$
$491$	−4.56914	−	40.5522i	−0.00930578	−	0.0825911i	−0.997507	+	0.0705722i	$0.977517\pi$
$492$		0			0
$493$	605.953	−	16.8788i	1.22911	−	0.0342370i
$494$	−308.918			−0.625341
$495$		0			0
$496$	221.422	−	139.129i	0.446415	−	0.280501i
$497$	152.886	−	34.8952i	0.307617	−	0.0702116i
$498$		0			0
$499$	510.903	−	407.432i	1.02385	−	0.816497i	0.0406810	−	0.999172i	$-0.487047\pi$
$499$	510.903	−	407.432i	1.02385	−	0.816497i	0.983173	+	0.182676i	$0.0584758\pi$
$500$	77.6850	−	340.360i	0.155370	−	0.680720i
$501$		0			0
$502$	249.398	−	517.880i	0.496808	−	1.03163i
$503$	543.585	+	341.557i	1.08069	+	0.679040i	0.949958	−	0.312379i	$-0.101126\pi$
$503$	543.585	+	341.557i	1.08069	+	0.679040i	0.130728	+	0.991418i	$0.458269\pi$
$504$		0			0
$505$	304.627	−	304.627i	0.603222	−	0.603222i
$506$	−573.075	−	1190.00i	−1.13256	−	2.35178i
$507$		0			0
$508$	−574.616	−	64.7437i	−1.13113	−	0.127448i
$509$	108.052	−	52.0353i	0.212284	−	0.102230i	−0.324720	−	0.945810i	$-0.605270\pi$
$509$	108.052	−	52.0353i	0.212284	−	0.102230i	0.537004	+	0.843580i	$0.319556\pi$
$510$		0			0
$511$	−23.8386	+	68.1267i	−0.0466508	+	0.133320i
$512$	−253.515	+	403.466i	−0.495146	+	0.788020i
$513$		0			0
$514$	−112.010	−	320.106i	−0.217918	−	0.622775i
$515$	147.772	+	33.7280i	0.286936	+	0.0654913i
$516$		0			0
$517$	−537.297	+	673.750i	−1.03926	+	1.30319i
$518$	61.8089	+	270.802i	0.119322	+	0.522785i
$519$		0			0
$520$	7.59003	+	67.3634i	0.0145962	+	0.129545i
$521$			424.304i			0.814404i	0.913338	+	0.407202i	$0.133495\pi$
$521$			424.304i			0.814404i	−0.913338	+	0.407202i	$0.866505\pi$
$522$		0			0
$523$	4.61578			0.00882558			0.00441279	−	0.999990i	$-0.498595\pi$
$523$	4.61578			0.00882558			0.00441279	+	0.999990i	$0.498595\pi$
$524$	453.700	−	51.1197i	0.865840	−	0.0975568i
$525$		0			0
$526$	136.596	−	31.1770i	0.259687	−	0.0592720i
$527$	−219.863	−	175.335i	−0.417197	−	0.332703i
$528$		0			0
$529$	−79.7873	+	349.571i	−0.150827	+	0.660815i
$530$	151.581	−	53.0405i	0.286002	−	0.100076i
$531$		0			0
$532$	−247.227	−	155.343i	−0.464712	−	0.291998i
$533$	388.294	+	135.870i	0.728507	+	0.254916i
$534$		0			0
$535$	−182.859	−	379.710i	−0.341792	−	0.709739i
$536$	−5.15582	+	45.7592i	−0.00961907	+	0.0853716i
$537$		0			0
$538$	58.6734	−	28.2556i	0.109058	−	0.0525198i
$539$	−178.400	−	178.400i	−0.330984	−	0.330984i
$540$		0			0
$541$	160.391	−	255.261i	0.296472	−	0.471833i	−0.664958	−	0.746880i	$-0.731551\pi$
$541$	160.391	−	255.261i	0.296472	−	0.471833i	0.961431	+	0.275048i	$0.0886936\pi$
$542$	−721.608	−	347.508i	−1.33138	−	0.641159i
$543$		0			0
$544$	764.356	+	174.459i	1.40507	+	0.320697i
$545$	−87.4304	−	109.634i	−0.160423	−	0.201164i
$546$		0			0
$547$	33.8389	+	148.258i	0.0618627	+	0.271038i	0.996394	−	0.0848416i	$-0.0270384\pi$
$547$	33.8389	+	148.258i	0.0618627	+	0.271038i	−0.934532	+	0.355880i	$0.884181\pi$
$548$	252.222	+	401.409i	0.460259	+	0.732498i
$549$		0			0
$550$		−	658.293i		−	1.19690i
$551$	−131.391	−	509.786i	−0.238459	−	0.925201i
$552$		0			0
$553$	589.929	−	66.4691i	1.06678	−	0.120197i
$554$	1095.77	−	688.518i	1.97793	−	1.24281i
$555$		0			0
$556$	336.313	+	268.201i	0.604880	+	0.482375i
$557$	24.5533	−	19.5806i	0.0440814	−	0.0351538i	−0.601201	−	0.799098i	$-0.705311\pi$
$557$	24.5533	−	19.5806i	0.0440814	−	0.0351538i	0.645283	+	0.763944i	$0.276740\pi$
$558$		0			0
$559$	386.660	−	135.298i	0.691699	−	0.242036i
$560$	−157.181	+	326.390i	−0.280680	+	0.582839i
$561$		0			0
$562$	−981.646	−	343.493i	−1.74670	−	0.611197i
$563$	667.667	−	667.667i	1.18591	−	1.18591i	0.207721	−	0.978188i	$-0.433395\pi$
$563$	667.667	−	667.667i	1.18591	−	1.18591i	0.978188	−	0.207721i	$-0.0666048\pi$
$564$		0			0
$565$	−32.2934	+	286.612i	−0.0571565	+	0.507278i
$566$	−191.227	−	21.5461i	−0.337857	−	0.0380674i
$567$		0			0
$568$	61.5773	+	61.5773i	0.108411	+	0.108411i
$569$	−296.283	+	846.727i	−0.520708	+	1.48810i	0.320428	+	0.947273i	$0.396173\pi$
$569$	−296.283	+	846.727i	−0.520708	+	1.48810i	−0.841136	+	0.540824i	$0.818112\pi$
$570$		0			0
$571$	−603.338	−	290.552i	−1.05663	−	0.508848i	−0.176858	−	0.984236i	$-0.556593\pi$
$571$	−603.338	−	290.552i	−1.05663	−	0.508848i	−0.879776	+	0.475388i	$0.842308\pi$
$572$	−101.510	−	290.100i	−0.177466	−	0.507168i
$573$		0			0
$574$	595.086	+	746.214i	1.03673	+	1.30002i
$575$	−275.809	+	345.853i	−0.479668	+	0.601484i
$576$		0			0
$577$	−4.39331	−	6.99192i	−0.00761406	−	0.0121177i	0.842895	−	0.538077i	$-0.180849\pi$
$577$	−4.39331	−	6.99192i	−0.00761406	−	0.0121177i	−0.850510	+	0.525960i	$0.823706\pi$
$578$	−43.0330	−	381.928i	−0.0744516	−	0.660776i
$579$		0			0
$580$	237.383	−	90.5588i	0.409281	−	0.156136i
$581$	256.028			0.440669
$582$		0			0
$583$	280.321	−	176.137i	0.480825	−	0.302122i
$584$	−39.0762	+	8.91890i	−0.0669114	+	0.0152721i
$585$		0			0
$586$	−915.717	+	730.260i	−1.56266	+	1.24618i
$587$	68.8550	−	301.673i	0.117300	−	0.513924i	−0.881805	−	0.471615i	$-0.843671\pi$
$587$	68.8550	−	301.673i	0.117300	−	0.513924i	0.999105	−	0.0423093i	$-0.0134715\pi$
$588$		0			0
$589$	−105.964	+	220.036i	−0.179905	+	0.373576i
$590$	336.366	+	211.353i	0.570112	+	0.358225i
$591$		0			0
$592$	−251.225	+	251.225i	−0.424366	+	0.424366i
$593$	−313.607	−	651.212i	−0.528849	−	1.09817i	−0.978744	−	0.205084i	$-0.934253\pi$
$593$	−313.607	−	651.212i	−0.528849	−	1.09817i	0.449896	−	0.893081i	$-0.351461\pi$
$594$		0			0
$595$	387.121	+	43.6181i	0.650624	+	0.0733077i
$596$	−259.177	+	124.813i	−0.434861	+	0.209418i
$597$		0			0
$598$	−167.443	+	478.526i	−0.280006	+	0.800210i
$599$	202.636	−	322.493i	0.338290	−	0.538386i	−0.633648	−	0.773621i	$-0.718443\pi$
$599$	202.636	−	322.493i	0.338290	−	0.538386i	0.971938	+	0.235235i	$0.0755861\pi$
$600$		0			0
$601$	−311.119	−	889.126i	−0.517668	−	1.47941i	−0.845137	−	0.534549i	$-0.820481\pi$
$601$	−311.119	−	889.126i	−0.517668	−	1.47941i	0.327469	−	0.944862i	$-0.393804\pi$
$602$	926.597	+	211.490i	1.53920	+	0.351312i
$603$		0			0
$604$	−191.434	+	240.050i	−0.316943	+	0.397434i
$605$	120.670	+	528.690i	0.199455	+	0.873868i
$606$		0			0
$607$	9.33482	+	82.8488i	0.0153786	+	0.136489i	0.999055	−	0.0434556i	$-0.0138367\pi$
$607$	9.33482	+	82.8488i	0.0153786	+	0.136489i	−0.983677	+	0.179945i	$0.942408\pi$
$608$		−	680.878i		−	1.11986i
$609$		0			0
$610$	−401.490			−0.658180
$611$	328.696	−	37.0352i	0.537964	−	0.0606140i
$612$		0			0
$613$	−730.866	+	166.815i	−1.19228	+	0.272129i	−0.772212	−	0.635365i	$-0.780850\pi$
$613$	−730.866	+	166.815i	−1.19228	+	0.272129i	−0.420065	+	0.907494i	$0.637993\pi$
$614$	42.6568	+	34.0177i	0.0694737	+	0.0554034i
$615$		0			0
$616$	−72.1486	+	316.104i	−0.117124	+	0.513155i
$617$	−516.148	+	180.608i	−0.836544	+	0.292719i	−0.714351	−	0.699787i	$-0.753278\pi$
$617$	−516.148	+	180.608i	−0.836544	+	0.292719i	−0.122192	+	0.992506i	$0.538992\pi$
$618$		0			0
$619$	−669.936	−	420.949i	−1.08229	−	0.680046i	−0.131947	−	0.991257i	$-0.542123\pi$
$619$	−669.936	−	420.949i	−1.08229	−	0.680046i	−0.950341	+	0.311211i	$0.899266\pi$
$620$	−111.251	−	38.9283i	−0.179436	−	0.0627875i
$621$		0			0
$622$	174.076	+	361.472i	0.279865	+	0.581145i
$623$	−35.5459	+	315.478i	−0.0570560	+	0.506386i
$624$		0			0
$625$	30.0154	−	14.4547i	0.0480247	−	0.0231275i
$626$	−313.447	−	313.447i	−0.500713	−	0.500713i
$627$		0			0
$628$	318.719	−	507.239i	0.507515	−	0.807705i
$629$	344.229	+	165.772i	0.547263	+	0.263548i
$630$		0			0
$631$	305.108	+	69.6389i	0.483531	+	0.110363i	0.457336	−	0.889294i	$-0.348804\pi$
$631$	305.108	+	69.6389i	0.483531	+	0.110363i	0.0261949	+	0.999657i	$0.491661\pi$
$632$	205.546	+	257.747i	0.325232	+	0.407828i
$633$		0			0
$634$	−21.6182	−	94.7153i	−0.0340980	−	0.149393i
$635$	−356.479	−	567.333i	−0.561384	−	0.893438i
$636$		0			0
$637$			96.8410i			0.152027i
$638$	1069.16	−	714.076i	1.67580	−	1.11924i
$639$		0			0
$640$	−313.024	+	35.2693i	−0.489100	+	0.0551083i
$641$	−166.181	+	104.418i	−0.259253	+	0.162899i	−0.655387	−	0.755293i	$-0.727494\pi$
$641$	−166.181	+	104.418i	−0.259253	+	0.162899i	0.396134	+	0.918193i	$0.370352\pi$
$642$		0			0
$643$	−28.9995	−	23.1263i	−0.0451003	−	0.0359663i	0.600680	−	0.799489i	$-0.294896\pi$
$643$	−28.9995	−	23.1263i	−0.0451003	−	0.0359663i	−0.645781	+	0.763523i	$0.723468\pi$
$644$	−374.636	+	298.763i	−0.581734	+	0.463917i
$645$		0			0
$646$	−930.522	+	325.604i	−1.44044	+	0.504030i
$647$	−341.548	+	709.232i	−0.527895	+	1.09619i	0.451132	+	0.892457i	$0.351020\pi$
$647$	−341.548	+	709.232i	−0.527895	+	1.09619i	−0.979027	+	0.203729i	$0.934694\pi$
$648$		0			0
$649$	772.992	+	270.482i	1.19105	+	0.416767i
$650$	−178.670	+	178.670i	−0.274878	+	0.274878i
$651$		0			0
$652$	−17.6877	+	156.983i	−0.0271284	+	0.240771i
$653$	−651.771	−	73.4370i	−0.998118	−	0.112461i	−0.402239	−	0.915535i	$-0.631768\pi$
$653$	−651.771	−	73.4370i	−0.998118	−	0.112461i	−0.595879	+	0.803074i	$0.703196\pi$
$654$		0			0
$655$	374.087	+	374.087i	0.571125	+	0.571125i
$656$	−403.207	+	1152.30i	−0.614646	+	1.75656i
$657$		0			0
$658$	691.435	+	332.978i	1.05081	+	0.506045i
$659$	49.7225	+	142.099i	0.0754514	+	0.215628i	0.975431	−	0.220304i	$-0.0707048\pi$
$659$	49.7225	+	142.099i	0.0754514	+	0.215628i	−0.899980	+	0.435931i	$0.856419\pi$
$660$		0			0
$661$	236.407	+	296.445i	0.357650	+	0.448479i	0.927809	−	0.373055i	$-0.121690\pi$
$661$	236.407	+	296.445i	0.357650	+	0.448479i	−0.570159	+	0.821534i	$0.693118\pi$
$662$	−447.195	+	560.764i	−0.675521	+	0.847076i
$663$		0			0
$664$	75.6427	+	120.385i	0.113920	+	0.181302i
$665$	−37.8803	−	336.197i	−0.0569628	−	0.505559i
$666$		0			0
$667$	−860.895	−	72.7909i	−1.29070	−	0.109132i
$668$	−369.925			−0.553780
$669$		0			0
$670$	99.3616	−	62.4330i	0.148301	−	0.0931836i
$671$	−806.926	+	184.176i	−1.20257	+	0.274479i
$672$		0			0
$673$	−387.895	+	309.336i	−0.576367	+	0.459637i	−0.867772	−	0.496963i	$-0.834449\pi$
$673$	−387.895	+	309.336i	−0.576367	+	0.459637i	0.291405	+	0.956600i	$0.405877\pi$
$674$	−150.642	+	660.007i	−0.223505	+	0.979239i
$675$		0			0
$676$	150.441	−	312.393i	0.222545	−	0.462120i
$677$	659.147	+	414.170i	0.973630	+	0.611772i	0.922122	−	0.386900i	$-0.126454\pi$
$677$	659.147	+	414.170i	0.973630	+	0.611772i	0.0515083	+	0.998673i	$0.483597\pi$
$678$		0			0
$679$	−606.763	+	606.763i	−0.893612	+	0.893612i
$680$	93.8645	+	194.912i	0.138036	+	0.286635i
$681$		0			0
$682$	−592.691	−	66.7803i	−0.869049	−	0.0979183i
$683$	−346.400	+	166.817i	−0.507174	+	0.244242i	−0.669930	−	0.742424i	$-0.733676\pi$
$683$	−346.400	+	166.817i	−0.507174	+	0.244242i	0.162756	+	0.986666i	$0.447962\pi$
$684$		0			0
$685$	−181.428	+	518.492i	−0.264859	+	0.756923i
$686$	−515.712	+	820.751i	−0.751767	+	1.19643i
$687$		0			0
$688$	401.510	+	1147.45i	0.583591	+	1.66781i
$689$	−123.889	−	28.2770i	−0.179811	−	0.0410406i
$690$		0			0
$691$	654.553	−	820.783i	0.947254	−	1.18782i	−0.0348332	−	0.999393i	$-0.511090\pi$
$691$	654.553	−	820.783i	0.947254	−	1.18782i	0.982087	−	0.188426i	$-0.0603386\pi$
$692$	−12.9610	−	56.7857i	−0.0187297	−	0.0820603i
$693$		0			0
$694$	22.0367	+	195.581i	0.0317532	+	0.281817i
$695$			498.436i			0.717175i
$696$		0			0
$697$	1312.83			1.88354
$698$	227.411	−	25.6231i	0.325804	−	0.0367093i
$699$		0			0
$700$	−232.836	+	53.1433i	−0.332623	+	0.0759190i
$701$	−70.4321	−	56.1677i	−0.100474	−	0.0801252i	0.571964	−	0.820278i	$-0.306182\pi$
$701$	−70.4321	−	56.1677i	−0.100474	−	0.0801252i	−0.672438	+	0.740153i	$0.734753\pi$
$702$		0			0
$703$	73.8336	−	323.486i	0.105026	−	0.460151i
$704$	317.188	−	110.989i	0.450552	−	0.157655i
$705$		0			0
$706$	939.659	+	590.427i	1.33096	+	0.836299i
$707$	−746.526	−	261.221i	−1.05591	−	0.369478i
$708$		0			0
$709$	−457.420	−	949.843i	−0.645162	−	1.33969i	−0.925118	−	0.379681i	$-0.876034\pi$
$709$	−457.420	−	949.843i	−0.645162	−	1.33969i	0.279955	−	0.960013i	$-0.409680\pi$
$710$	24.8471	−	220.524i	0.0349959	−	0.310597i
$711$		0			0
$712$	−158.840	+	76.4933i	−0.223090	+	0.107434i
$713$	283.408	+	283.408i	0.397487	+	0.397487i
$714$		0			0
$715$	189.473	−	301.544i	0.264997	−	0.421740i
$716$	226.705	+	109.175i	0.316627	+	0.152480i
$717$		0			0
$718$	1064.72	+	243.015i	1.48289	+	0.338461i
$719$	375.775	+	471.207i	0.522636	+	0.655364i	0.971166	−	0.238403i	$-0.0766240\pi$
$719$	375.775	+	471.207i	0.522636	+	0.655364i	−0.448531	+	0.893767i	$0.648053\pi$
$720$		0			0
$721$	−61.9204	−	271.291i	−0.0858813	−	0.376270i
$722$	−43.4815	−	69.2005i	−0.0602237	−	0.0958455i
$723$		0			0
$724$			540.769i			0.746919i
$725$	−370.840	−	218.854i	−0.511504	−	0.301868i
$726$		0			0
$727$	−652.396	+	73.5073i	−0.897380	+	0.101110i	−0.548591	−	0.836091i	$-0.684836\pi$
$727$	−652.396	+	73.5073i	−0.897380	+	0.101110i	−0.348789	+	0.937201i	$0.613407\pi$
$728$	105.377	−	66.2131i	0.144749	−	0.0909520i
$729$		0			0
$730$	79.8569	+	63.6837i	0.109393	+	0.0872380i
$731$	1022.09	−	815.089i	1.39821	−	1.11503i
$732$		0			0
$733$	−1069.34	+	374.177i	−1.45885	+	0.510473i	−0.939040	−	0.343809i	$-0.888283\pi$
$733$	−1069.34	+	374.177i	−1.45885	+	0.510473i	−0.519810	+	0.854282i	$0.673997\pi$
$734$	282.498	−	586.614i	0.384875	−	0.799201i
$735$		0			0
$736$	−1054.70	−	369.057i	−1.43302	−	0.501436i
$737$	171.060	−	171.060i	0.232103	−	0.232103i
$738$		0			0
$739$	72.0915	−	639.830i	0.0975527	−	0.865805i	−0.845684	−	0.533684i	$-0.820807\pi$
$739$	72.0915	−	639.830i	0.0975527	−	0.865805i	0.943237	−	0.332121i	$-0.107764\pi$
$740$	159.127	+	17.9293i	0.215036	+	0.0242288i
$741$		0			0
$742$	−208.475	−	208.475i	−0.280964	−	0.280964i
$743$	−147.582	+	421.766i	−0.198630	+	0.567653i	−0.999514	−	0.0311669i	$-0.990078\pi$
$743$	−147.582	+	421.766i	−0.198630	+	0.567653i	0.800884	+	0.598820i	$0.204363\pi$
$744$		0			0
$745$	−300.314	−	144.624i	−0.403106	−	0.194126i
$746$	−421.450	−	1204.44i	−0.564947	−	1.61453i
$747$		0			0
$748$	−611.538	−	766.844i	−0.817564	−	1.02519i
$749$	−482.408	+	604.921i	−0.644070	+	0.807638i
$750$		0			0
$751$	523.385	+	832.962i	0.696917	+	1.10914i	0.988299	+	0.152531i	$0.0487423\pi$
$751$	523.385	+	832.962i	0.696917	+	1.10914i	−0.291381	+	0.956607i	$0.594115\pi$
$752$	109.905	+	975.438i	0.146151	+	1.29712i
$753$		0			0
$754$	−483.997	−	96.3746i	−0.641905	−	0.127818i
$755$	−355.769			−0.471217
$756$		0			0
$757$	−315.734	+	198.389i	−0.417086	+	0.262073i	−0.724186	−	0.689605i	$-0.757784\pi$
$757$	−315.734	+	198.389i	−0.417086	+	0.262073i	0.307100	+	0.951677i	$0.400641\pi$
$758$	−21.3047	+	4.86265i	−0.0281064	+	0.00641511i
$759$		0			0
$760$	146.888	−	117.139i	0.193274	−	0.154131i
$761$	−0.0873012	+	0.382492i	−0.000114719	+	0.000502617i	−0.974985	−	0.222270i	$-0.928653\pi$
$761$	−0.0873012	+	0.382492i	−0.000114719	+	0.000502617i	0.974871	+	0.222772i	$0.0715106\pi$
$762$		0			0
$763$	−111.699	+	231.945i	−0.146395	+	0.303991i
$764$	570.053	+	358.188i	0.746143	+	0.468833i
$765$		0			0
$766$	−191.987	+	191.987i	−0.250636	+	0.250636i
$767$	−136.389	−	283.214i	−0.177821	−	0.369250i
$768$		0			0
$769$	1349.61	+	152.064i	1.75502	+	0.197743i	0.930049	−	0.367436i	$-0.119764\pi$
$769$	1349.61	+	152.064i	1.75502	+	0.197743i	0.824968	+	0.565179i	$0.191193\pi$
$770$	744.433	−	358.500i	0.966797	−	0.465585i
$771$		0			0
$772$	−184.135	+	526.227i	−0.238517	+	0.681641i
$773$	−392.849	+	625.216i	−0.508214	+	0.808818i	−0.998012	−	0.0630179i	$-0.979927\pi$
$773$	−392.849	+	625.216i	−0.508214	+	0.808818i	0.489798	+	0.871836i	$0.337070\pi$
$774$		0			0
$775$	65.9766	+	188.550i	0.0851310	+	0.243291i
$776$	−464.566	−	106.034i	−0.598668	−	0.136642i
$777$		0			0
$778$	7.56411	−	9.48510i	0.00972251	−	0.0121916i
$779$	−253.702	−	1111.54i	−0.325677	−	1.42688i
$780$		0			0
$781$	−51.2226	−	454.613i	−0.0655859	−	0.582091i
$782$			1617.90i			2.06893i
$783$		0			0
$784$	−287.385			−0.366563
$785$	689.779	−	77.7195i	0.878700	−	0.0990057i
$786$		0			0
$787$	161.929	−	36.9592i	0.205755	−	0.0469622i	−0.118401	−

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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