LMFDB - Embedded newform 1386.2.ba.a.989.16

Newspace parameters

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.ba (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			989.16
Character	$\chi$	$=$	1386.989
Dual form			1386.2.ba.a.1187.16

$q$-expansion

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(3.19684 + 1.84570i) q^{5} +(1.52985 + 2.15860i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(3.19684 + 1.84570i) q^{5} +(1.52985 + 2.15860i) q^{7} +1.00000 q^{8} +(-3.19684 + 1.84570i) q^{10} +(2.64375 + 2.00265i) q^{11} +5.60520i q^{13} +(-2.63433 + 0.245585i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.39461 - 2.41554i) q^{17} +(2.14631 + 1.23917i) q^{19} -3.69140i q^{20} +(-3.05622 + 1.28823i) q^{22} +(-3.26215 - 1.88340i) q^{23} +(4.31321 + 7.47069i) q^{25} +(-4.85424 - 2.80260i) q^{26} +(1.10448 - 2.40419i) q^{28} -1.51011 q^{29} +(-1.70296 - 2.94961i) q^{31} +(-0.500000 - 0.866025i) q^{32} +2.78923 q^{34} +(0.906550 + 9.72435i) q^{35} +(2.85865 - 4.95132i) q^{37} +(-2.14631 + 1.23917i) q^{38} +(3.19684 + 1.84570i) q^{40} -6.24731 q^{41} -7.72006i q^{43} +(0.412474 - 3.29088i) q^{44} +(3.26215 - 1.88340i) q^{46} +(-8.98162 - 5.18554i) q^{47} +(-2.31914 + 6.60467i) q^{49} -8.62641 q^{50} +(4.85424 - 2.80260i) q^{52} +(9.27677 - 5.35595i) q^{53} +(4.75535 + 11.2817i) q^{55} +(1.52985 + 2.15860i) q^{56} +(0.755057 - 1.30780i) q^{58} +(11.6232 - 6.71066i) q^{59} +(2.13230 + 1.23108i) q^{61} +3.40592 q^{62} +1.00000 q^{64} +(-10.3455 + 17.9189i) q^{65} +(5.66594 + 9.81369i) q^{67} +(-1.39461 + 2.41554i) q^{68} +(-8.87481 - 4.07708i) q^{70} -5.15087i q^{71} +(4.53946 - 2.62086i) q^{73} +(2.85865 + 4.95132i) q^{74} -2.47835i q^{76} +(-0.278403 + 8.77055i) q^{77} +(0.250209 + 0.144458i) q^{79} +(-3.19684 + 1.84570i) q^{80} +(3.12366 - 5.41033i) q^{82} -10.2522 q^{83} -10.2961i q^{85} +(6.68577 + 3.86003i) q^{86} +(2.64375 + 2.00265i) q^{88} +(-13.7391 - 7.93225i) q^{89} +(-12.0994 + 8.57509i) q^{91} +3.76681i q^{92} +(8.98162 - 5.18554i) q^{94} +(4.57428 + 7.92289i) q^{95} +4.58628 q^{97} +(-4.56024 - 5.31076i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) $	$ 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.19684	+	1.84570i	1.42967	+	0.825421i	0.997094	−	0.0761754i	$-0.0242709\pi$
$5$	3.19684	+	1.84570i	1.42967	+	0.825421i	0.432577	+	0.901597i	$0.357604\pi$
$6$		0			0
$7$	1.52985	+	2.15860i	0.578228	+	0.815875i
$7$	1.52985	+	2.15860i	0.578228	+	0.815875i
$8$	1.00000			0.353553
$9$		0			0
$10$	−3.19684	+	1.84570i	−1.01093	+	0.583661i
$11$	2.64375	+	2.00265i	0.797119	+	0.603822i
$11$	2.64375	+	2.00265i	0.797119	+	0.603822i
$12$		0			0
$13$			5.60520i			1.55460i	0.629129	+	0.777301i	$0.283412\pi$
$13$			5.60520i			1.55460i	−0.629129	+	0.777301i	$0.716588\pi$
$14$	−2.63433	+	0.245585i	−0.704054	+	0.0656352i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.39461	−	2.41554i	−0.338243	−	0.585855i	0.645859	−	0.763457i	$-0.276499\pi$
$17$	−1.39461	−	2.41554i	−0.338243	−	0.585855i	−0.984102	+	0.177602i	$0.943166\pi$
$18$		0			0
$19$	2.14631	+	1.23917i	0.492398	+	0.284286i	0.725569	−	0.688150i	$-0.241577\pi$
$19$	2.14631	+	1.23917i	0.492398	+	0.284286i	−0.233171	+	0.972436i	$0.574910\pi$
$20$		−	3.69140i		−	0.825421i
$21$		0			0
$22$	−3.05622	+	1.28823i	−0.651588	+	0.274651i
$23$	−3.26215	−	1.88340i	−0.680206	−	0.392717i	0.119727	−	0.992807i	$-0.461798\pi$
$23$	−3.26215	−	1.88340i	−0.680206	−	0.392717i	−0.799933	+	0.600090i	$0.795131\pi$
$24$		0			0
$25$	4.31321	+	7.47069i	0.862641	+	1.49414i
$26$	−4.85424	−	2.80260i	−0.951995	−	0.549635i
$27$		0			0
$28$	1.10448	−	2.40419i	0.208727	−	0.454349i
$29$	−1.51011			−0.280421			−0.140210	−	0.990122i	$-0.544778\pi$
$29$	−1.51011			−0.280421			−0.140210	+	0.990122i	$0.544778\pi$
$30$		0			0
$31$	−1.70296	−	2.94961i	−0.305860	−	0.529766i	0.671592	−	0.740921i	$-0.265611\pi$
$31$	−1.70296	−	2.94961i	−0.305860	−	0.529766i	−0.977453	+	0.211155i	$0.932277\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	2.78923			0.478348
$35$	0.906550	+	9.72435i	0.153235	+	1.64372i
$36$		0			0
$37$	2.85865	−	4.95132i	0.469959	−	0.813993i	−0.529451	−	0.848340i	$-0.677602\pi$
$37$	2.85865	−	4.95132i	0.469959	−	0.813993i	0.999410	+	0.0343479i	$0.0109354\pi$
$38$	−2.14631	+	1.23917i	−0.348178	+	0.201021i
$39$		0			0
$40$	3.19684	+	1.84570i	0.505465	+	0.291831i
$41$	−6.24731			−0.975666			−0.487833	−	0.872937i	$-0.662213\pi$
$41$	−6.24731			−0.975666			−0.487833	+	0.872937i	$0.662213\pi$
$42$		0			0
$43$		−	7.72006i		−	1.17730i	−0.808389	−	0.588649i	$-0.799660\pi$
$43$		−	7.72006i		−	1.17730i	0.808389	−	0.588649i	$-0.200340\pi$
$44$	0.412474	−	3.29088i	0.0621827	−	0.496118i
$45$		0			0
$46$	3.26215	−	1.88340i	0.480978	−	0.277693i
$47$	−8.98162	−	5.18554i	−1.31010	−	0.756389i	−0.327991	−	0.944681i	$-0.606371\pi$
$47$	−8.98162	−	5.18554i	−1.31010	−	0.756389i	−0.982113	+	0.188292i	$0.939705\pi$
$48$		0			0
$49$	−2.31914	+	6.60467i	−0.331305	+	0.943524i
$50$	−8.62641			−1.21996
$51$		0			0
$52$	4.85424	−	2.80260i	0.673162	−	0.388650i
$53$	9.27677	−	5.35595i	1.27426	−	0.735696i	0.298475	−	0.954417i	$-0.403522\pi$
$53$	9.27677	−	5.35595i	1.27426	−	0.735696i	0.975787	+	0.218721i	$0.0701886\pi$
$54$		0			0
$55$	4.75535	+	11.2817i	0.641211	+	1.52123i
$56$	1.52985	+	2.15860i	0.204434	+	0.288456i
$57$		0			0
$58$	0.755057	−	1.30780i	0.0991438	−	0.171722i
$59$	11.6232	−	6.71066i	1.51321	−	0.873654i	0.513333	−	0.858190i	$-0.328411\pi$
$59$	11.6232	−	6.71066i	1.51321	−	0.873654i	0.999880	−	0.0154644i	$-0.00492266\pi$
$60$		0			0
$61$	2.13230	+	1.23108i	0.273013	+	0.157624i	0.630256	−	0.776387i	$-0.282950\pi$
$61$	2.13230	+	1.23108i	0.273013	+	0.157624i	−0.357243	+	0.934011i	$0.616283\pi$
$62$	3.40592			0.432552
$63$		0			0
$64$	1.00000			0.125000
$65$	−10.3455	+	17.9189i	−1.28320	+	2.22257i
$66$		0			0
$67$	5.66594	+	9.81369i	0.692204	+	1.19893i	0.971114	+	0.238616i	$0.0766936\pi$
$67$	5.66594	+	9.81369i	0.692204	+	1.19893i	−0.278910	+	0.960317i	$0.589973\pi$
$68$	−1.39461	+	2.41554i	−0.169122	+	0.292927i
$69$		0			0
$70$	−8.87481	−	4.07708i	−1.06074	−	0.487304i
$71$		−	5.15087i		−	0.611296i	−0.952145	−	0.305648i	$-0.901127\pi$
$71$		−	5.15087i		−	0.611296i	0.952145	−	0.305648i	$-0.0988730\pi$
$72$		0			0
$73$	4.53946	−	2.62086i	0.531303	−	0.306748i	−0.210244	−	0.977649i	$-0.567426\pi$
$73$	4.53946	−	2.62086i	0.531303	−	0.306748i	0.741547	+	0.670901i	$0.234092\pi$
$74$	2.85865	+	4.95132i	0.332311	+	0.575580i
$75$		0			0
$76$		−	2.47835i		−	0.284286i
$77$	−0.278403	+	8.77055i	−0.0317270	+	0.999497i
$78$		0			0
$79$	0.250209	+	0.144458i	0.0281507	+	0.0162528i	0.514009	−	0.857785i	$-0.328160\pi$
$79$	0.250209	+	0.144458i	0.0281507	+	0.0162528i	−0.485859	+	0.874037i	$0.661493\pi$
$80$	−3.19684	+	1.84570i	−0.357418	+	0.206355i
$81$		0			0
$82$	3.12366	−	5.41033i	0.344950	−	0.597471i
$83$	−10.2522			−1.12533			−0.562664	−	0.826685i	$-0.690224\pi$
$83$	−10.2522			−1.12533			−0.562664	+	0.826685i	$0.690224\pi$
$84$		0			0
$85$		−	10.2961i		−	1.11677i
$86$	6.68577	+	3.86003i	0.720945	+	0.416238i
$87$		0			0
$88$	2.64375	+	2.00265i	0.281824	+	0.213483i
$89$	−13.7391	−	7.93225i	−1.45634	−	0.840816i	−0.457508	−	0.889205i	$-0.651258\pi$
$89$	−13.7391	−	7.93225i	−1.45634	−	0.840816i	−0.998829	+	0.0483889i	$0.984591\pi$
$90$		0			0
$91$	−12.0994	+	8.57509i	−1.26836	+	0.898914i
$92$			3.76681i			0.392717i
$93$		0			0
$94$	8.98162	−	5.18554i	0.926383	−	0.534848i
$95$	4.57428	+	7.92289i	0.469311	+	0.812871i
$96$		0			0
$97$	4.58628			0.465666			0.232833	−	0.972517i	$-0.425200\pi$
$97$	4.58628			0.465666			0.232833	+	0.972517i	$0.425200\pi$
$98$	−4.56024	−	5.31076i	−0.460654	−	0.536468i
$99$		0			0
$100$	4.31321	−	7.47069i	0.431321	−	0.747069i
$101$	−1.45801	−	2.52536i	−0.145078	−	0.251282i	0.784324	−	0.620351i	$-0.213010\pi$
$101$	−1.45801	−	2.52536i	−0.145078	−	0.251282i	−0.929402	+	0.369069i	$0.879677\pi$
$102$		0			0
$103$	−4.61616	+	7.99543i	−0.454844	+	0.787813i	−0.998679	−	0.0513790i	$-0.983638\pi$
$103$	−4.61616	+	7.99543i	−0.454844	+	0.787813i	0.543835	+	0.839192i	$0.316972\pi$
$104$			5.60520i			0.549635i
$105$		0			0
$106$			10.7119i			1.04043i
$107$	1.81237	−	3.13911i	0.175208	−	0.303469i	−0.765025	−	0.644000i	$-0.777274\pi$
$107$	1.81237	−	3.13911i	0.175208	−	0.303469i	0.940233	+	0.340531i	$0.110607\pi$
$108$		0			0
$109$	−13.9355	+	8.04565i	−1.33478	+	0.770634i	−0.986028	−	0.166583i	$-0.946727\pi$
$109$	−13.9355	+	8.04565i	−1.33478	+	0.770634i	−0.348749	+	0.937216i	$0.613393\pi$
$110$	−12.1479	−	1.52260i	−1.15826	−	0.145175i
$111$		0			0
$112$	−2.63433	+	0.245585i	−0.248921	+	0.0232056i
$113$			18.8371i			1.77204i	0.463643	+	0.886022i	$0.346542\pi$
$113$			18.8371i			1.77204i	−0.463643	+	0.886022i	$0.653458\pi$
$114$		0			0
$115$	−6.95239	−	12.0419i	−0.648314	−	1.12291i
$116$	0.755057	+	1.30780i	0.0701052	+	0.121426i
$117$		0			0
$118$			13.4213i			1.23553i
$119$	3.08065	−	6.70582i	0.282403	−	0.614722i
$120$		0			0
$121$	2.97878	+	10.5890i	0.270798	+	0.962636i
$122$	−2.13230	+	1.23108i	−0.193049	+	0.111457i
$123$		0			0
$124$	−1.70296	+	2.94961i	−0.152930	+	0.264883i
$125$			13.3865i			1.19733i
$126$		0			0
$127$			8.08283i			0.717235i	0.933485	+	0.358618i	$0.116752\pi$
$127$			8.08283i			0.717235i	−0.933485	+	0.358618i	$0.883248\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−10.3455	−	17.9189i	−0.907361	−	1.57159i
$131$	7.83557	−	13.5716i	0.684597	−	1.18576i	−0.288967	−	0.957339i	$-0.593312\pi$
$131$	7.83557	−	13.5716i	0.684597	−	1.18576i	0.973563	−	0.228417i	$-0.0733549\pi$
$132$		0			0
$133$	0.608644	+	6.52878i	0.0527761	+	0.566117i
$134$	−11.3319			−0.978925
$135$		0			0
$136$	−1.39461	−	2.41554i	−0.119587	−	0.207131i
$137$	2.55426	−	1.47471i	0.218226	−	0.125993i	−0.386903	−	0.922120i	$-0.626455\pi$
$137$	2.55426	−	1.47471i	0.218226	−	0.125993i	0.605128	+	0.796128i	$0.293122\pi$
$138$		0			0
$139$		−	4.00952i		−	0.340083i	−0.985437	−	0.170042i	$-0.945610\pi$
$139$		−	4.00952i		−	0.340083i	0.985437	−	0.170042i	$-0.0543902\pi$
$140$	7.96826	−	5.64727i	0.673441	−	0.477282i
$141$		0			0
$142$	4.46078	+	2.57543i	0.374341	+	0.216126i
$143$	−11.2253	+	14.8187i	−0.938703	+	1.23920i
$144$		0			0
$145$	−4.82759	−	2.78721i	−0.400910	−	0.231465i
$146$			5.24171i			0.433807i
$147$		0			0
$148$	−5.71730			−0.469959
$149$	3.23457	−	5.60244i	0.264986	−	0.458969i	−0.702574	−	0.711611i	$-0.747966\pi$
$149$	3.23457	−	5.60244i	0.264986	−	0.458969i	0.967560	+	0.252641i	$0.0812993\pi$
$150$		0			0
$151$	13.3957	−	7.73400i	1.09012	−	0.629384i	0.156515	−	0.987676i	$-0.449974\pi$
$151$	13.3957	−	7.73400i	1.09012	−	0.629384i	0.933610	+	0.358292i	$0.116641\pi$
$152$	2.14631	+	1.23917i	0.174089	+	0.100510i
$153$		0			0
$154$	−7.45631	−	4.62638i	−0.600847	−	0.372804i
$155$		−	12.5726i		−	1.00985i
$156$		0			0
$157$	9.34257	+	16.1818i	0.745618	+	1.29145i	0.949905	+	0.312538i	$0.101179\pi$
$157$	9.34257	+	16.1818i	0.745618	+	1.29145i	−0.204287	+	0.978911i	$0.565488\pi$
$158$	−0.250209	+	0.144458i	−0.0199056	+	0.0114925i
$159$		0			0
$160$		−	3.69140i		−	0.291831i
$161$	−0.925070	−	9.92301i	−0.0729057	−	0.782043i
$162$		0			0
$163$	4.62801	−	8.01595i	0.362494	−	0.627858i	−0.625877	−	0.779922i	$-0.715259\pi$
$163$	4.62801	−	8.01595i	0.362494	−	0.627858i	0.988371	+	0.152064i	$0.0485920\pi$
$164$	3.12366	+	5.41033i	0.243917	+	0.422476i
$165$		0			0
$166$	5.12612	−	8.87869i	0.397864	−	0.689120i
$167$	16.3875			1.26811			0.634053	−	0.773289i	$-0.281390\pi$
$167$	16.3875			1.26811			0.634053	+	0.773289i	$0.281390\pi$
$168$		0			0
$169$	−18.4182			−1.41679
$170$	8.91672	+	5.14807i	0.683881	+	0.394839i
$171$		0			0
$172$	−6.68577	+	3.86003i	−0.509785	+	0.294325i
$173$	−10.4622	+	18.1210i	−0.795424	+	1.37771i	0.127146	+	0.991884i	$0.459418\pi$
$173$	−10.4622	+	18.1210i	−0.795424	+	1.37771i	−0.922570	+	0.385831i	$0.873915\pi$
$174$		0			0
$175$	−9.52771	+	20.7395i	−0.720228	+	1.56776i
$176$	−3.05622	+	1.28823i	−0.230371	+	0.0971036i
$177$		0			0
$178$	13.7391	−	7.93225i	1.02979	−	0.594547i
$179$	12.9584	−	7.48153i	0.968555	−	0.559196i	0.0697596	−	0.997564i	$-0.477777\pi$
$179$	12.9584	−	7.48153i	0.968555	−	0.559196i	0.898795	+	0.438368i	$0.144443\pi$
$180$		0			0
$181$	−10.1125			−0.751657			−0.375828	−	0.926689i	$-0.622642\pi$
$181$	−10.1125			−0.751657			−0.375828	+	0.926689i	$0.622642\pi$
$182$	−1.37655	−	14.7659i	−0.102037	−	1.09452i
$183$		0			0
$184$	−3.26215	−	1.88340i	−0.240489	−	0.138846i
$185$	18.2773	−	10.5524i	1.34377	−	0.775828i
$186$		0			0
$187$	1.15048	−	9.17900i	0.0841316	−	0.671235i
$188$			10.3711i			0.756389i
$189$		0			0
$190$	−9.14856			−0.663707
$191$	4.57254	+	2.63995i	0.330857	+	0.191020i	0.656222	−	0.754568i	$-0.272154\pi$
$191$	4.57254	+	2.63995i	0.330857	+	0.191020i	−0.325364	+	0.945589i	$0.605487\pi$
$192$		0			0
$193$	−19.8361	+	11.4524i	−1.42784	+	0.824362i	−0.996950	−	0.0780447i	$-0.975132\pi$
$193$	−19.8361	+	11.4524i	−1.42784	+	0.824362i	−0.430886	+	0.902406i	$0.641799\pi$
$194$	−2.29314	+	3.97184i	−0.164638	+	0.285161i
$195$		0			0
$196$	6.87938	−	1.29390i	0.491384	−	0.0924215i
$197$	8.56673			0.610354			0.305177	−	0.952296i	$-0.401284\pi$
$197$	8.56673			0.610354			0.305177	+	0.952296i	$0.401284\pi$
$198$		0			0
$199$	2.28887	+	3.96444i	0.162254	+	0.281032i	0.935677	−	0.352859i	$-0.114790\pi$
$199$	2.28887	+	3.96444i	0.162254	+	0.281032i	−0.773423	+	0.633890i	$0.781457\pi$
$200$	4.31321	+	7.47069i	0.304990	+	0.528258i
$201$		0			0
$202$	2.91603			0.205171
$203$	−2.31024	−	3.25974i	−0.162147	−	0.228789i
$204$		0			0
$205$	−19.9717	−	11.5307i	−1.39488	−	0.805336i
$206$	−4.61616	−	7.99543i	−0.321623	−	0.557068i
$207$		0			0
$208$	−4.85424	−	2.80260i	−0.336581	−	0.194325i
$209$	3.19267	+	7.57437i	0.220842	+	0.523930i
$210$		0			0
$211$		−	10.0586i		−	0.692463i	−0.938149	−	0.346231i	$-0.887461\pi$
$211$		−	10.0586i		−	0.692463i	0.938149	−	0.346231i	$-0.112539\pi$
$212$	−9.27677	−	5.35595i	−0.637131	−	0.367848i
$213$		0			0
$214$	1.81237	+	3.13911i	0.123891	+	0.214585i
$215$	14.2489	−	24.6798i	0.971767	−	1.68315i
$216$		0			0
$217$	3.76177	−	8.18846i	0.255366	−	0.555869i
$218$		−	16.0913i		−	1.08984i
$219$		0			0
$220$	7.39258	−	9.75911i	0.498408	−	0.657959i
$221$	13.5396	−	7.81708i	0.910770	−	0.525834i
$222$		0			0
$223$	14.7430			0.987266			0.493633	−	0.869670i	$-0.335669\pi$
$223$	14.7430			0.987266			0.493633	+	0.869670i	$0.335669\pi$
$224$	1.10448	−	2.40419i	0.0737963	−	0.160637i
$225$		0			0
$226$	−16.3134	−	9.41854i	−1.08515	−	0.626512i
$227$	−9.41469	−	16.3067i	−0.624875	−	1.08232i	−0.988565	−	0.150795i	$-0.951817\pi$
$227$	−9.41469	−	16.3067i	−0.624875	−	1.08232i	0.363690	−	0.931520i	$-0.381517\pi$
$228$		0			0
$229$	−6.82233	+	11.8166i	−0.450832	+	0.780865i	−0.998438	−	0.0558720i	$-0.982206\pi$
$229$	−6.82233	+	11.8166i	−0.450832	+	0.780865i	0.547606	+	0.836737i	$0.315539\pi$
$230$	13.9048			0.916854
$231$		0			0
$232$	−1.51011			−0.0991438
$233$	−3.51518	+	6.08847i	−0.230287	+	0.398869i	−0.957893	−	0.287127i	$-0.907300\pi$
$233$	−3.51518	+	6.08847i	−0.230287	+	0.398869i	0.727606	+	0.685996i	$0.240633\pi$
$234$		0			0
$235$	−19.1419	−	33.1547i	−1.24868	−	2.16278i
$236$	−11.6232	−	6.71066i	−0.756607	−	0.436827i
$237$		0			0
$238$	4.26709	+	6.02083i	0.276594	+	0.390273i
$239$	−10.3908			−0.672126			−0.336063	−	0.941840i	$-0.609095\pi$
$239$	−10.3908			−0.672126			−0.336063	+	0.941840i	$0.609095\pi$
$240$		0			0
$241$	9.24972	−	5.34033i	0.595827	−	0.344001i	−0.171571	−	0.985172i	$-0.554884\pi$
$241$	9.24972	−	5.34033i	0.595827	−	0.344001i	0.767398	+	0.641171i	$0.221551\pi$
$242$	−10.6597	−	2.71480i	−0.685233	−	0.174514i
$243$		0			0
$244$		−	2.46216i		−	0.157624i
$245$	−19.6041	+	16.8337i	−1.25246	+	1.07546i
$246$		0			0
$247$	−6.94581	+	12.0305i	−0.441951	+	0.765482i
$248$	−1.70296	−	2.94961i	−0.108138	−	0.187300i
$249$		0			0
$250$	−11.5931	−	6.69326i	−0.733210	−	0.423319i
$251$			9.19949i			0.580667i	0.956926	+	0.290333i	$0.0937662\pi$
$251$			9.19949i			0.580667i	−0.956926	+	0.290333i	$0.906234\pi$
$252$		0			0
$253$	−4.85250	−	11.5122i	−0.305074	−	0.723765i
$254$	−6.99993	−	4.04141i	−0.439215	−	0.253581i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.8743	+	10.3197i	1.11497	+	0.643728i	0.940112	−	0.340865i	$-0.110720\pi$
$257$	17.8743	+	10.3197i	1.11497	+	0.643728i	0.174858	+	0.984594i	$0.444053\pi$
$258$		0			0
$259$	15.0612	−	1.40408i	0.935860	−	0.0872453i
$260$	20.6910			1.28320
$261$		0			0
$262$	7.83557	+	13.5716i	0.484083	+	0.838456i
$263$	−13.1613	−	22.7960i	−0.811561	−	1.40566i	−0.911771	−	0.410698i	$-0.865285\pi$
$263$	−13.1613	−	22.7960i	−0.811561	−	1.40566i	0.100211	−	0.994966i	$-0.468048\pi$
$264$		0			0
$265$	39.5419			2.42904
$266$	−5.95841	−	2.73729i	−0.365334	−	0.167834i
$267$		0			0
$268$	5.66594	−	9.81369i	0.346102	−	0.599467i
$269$	7.04033	−	4.06473i	0.429256	−	0.247831i	−0.269773	−	0.962924i	$-0.586949\pi$
$269$	7.04033	−	4.06473i	0.429256	−	0.247831i	0.699030	+	0.715093i	$0.253615\pi$
$270$		0			0
$271$	−12.6065	−	7.27836i	−0.765790	−	0.442129i	0.0655809	−	0.997847i	$-0.479110\pi$
$271$	−12.6065	−	7.27836i	−0.765790	−	0.442129i	−0.831371	+	0.555718i	$0.812443\pi$
$272$	2.78923			0.169122
$273$		0			0
$274$			2.94941i			0.178180i
$275$	−3.55817	+	28.3884i	−0.214566	+	1.71189i
$276$		0			0
$277$	25.9763	−	14.9974i	1.56077	−	0.901109i	0.563587	−	0.826057i	$-0.309421\pi$
$277$	25.9763	−	14.9974i	1.56077	−	0.901109i	0.997180	−	0.0750526i	$-0.0239125\pi$
$278$	3.47235	+	2.00476i	0.208258	+	0.120238i
$279$		0			0
$280$	0.906550	+	9.72435i	0.0541767	+	0.581141i
$281$	12.8423			0.766110			0.383055	−	0.923726i	$-0.374872\pi$
$281$	12.8423			0.766110			0.383055	+	0.923726i	$0.374872\pi$
$282$		0			0
$283$	6.35099	−	3.66675i	0.377527	−	0.217965i	−0.299215	−	0.954186i	$-0.596725\pi$
$283$	6.35099	−	3.66675i	0.377527	−	0.217965i	0.676742	+	0.736220i	$0.263391\pi$
$284$	−4.46078	+	2.57543i	−0.264699	+	0.152824i
$285$		0			0
$286$	−7.22076	−	17.1307i	−0.426972	−	1.01296i
$287$	−9.55743	−	13.4855i	−0.564157	−	0.796022i
$288$		0			0
$289$	4.61011	−	7.98495i	0.271183	−	0.469703i
$290$	4.82759	−	2.78721i	0.283486	−	0.163671i
$291$		0			0
$292$	−4.53946	−	2.62086i	−0.265652	−	0.153374i
$293$	−6.05343			−0.353645			−0.176823	−	0.984243i	$-0.556582\pi$
$293$	−6.05343			−0.353645			−0.176823	+	0.984243i	$0.556582\pi$
$294$		0			0
$295$	49.5434			2.88453
$296$	2.85865	−	4.95132i	0.166156	−	0.287790i
$297$		0			0
$298$	3.23457	+	5.60244i	0.187373	+	0.324540i
$299$	10.5569	−	18.2850i	0.610518	−	1.05745i
$300$		0			0
$301$	16.6646	−	11.8105i	0.960529	−	0.680747i
$302$			15.4680i			0.890083i
$303$		0			0
$304$	−2.14631	+	1.23917i	−0.123099	+	0.0710715i
$305$	4.54441	+	7.87116i	0.260212	+	0.450701i
$306$		0			0
$307$		−	6.24654i		−	0.356509i	−0.983984	−	0.178255i	$-0.942955\pi$
$307$		−	6.24654i		−	0.356509i	0.983984	−	0.178255i	$-0.0570450\pi$
$308$	7.73472	−	4.14417i	0.440726	−	0.236136i
$309$		0			0
$310$	10.8882	+	6.28629i	0.618407	+	0.357038i
$311$	8.45677	−	4.88252i	0.479539	−	0.276862i	−0.240685	−	0.970603i	$-0.577372\pi$
$311$	8.45677	−	4.88252i	0.479539	−	0.276862i	0.720225	+	0.693741i	$0.244039\pi$
$312$		0			0
$313$	−16.0158	+	27.7402i	−0.905266	+	1.56797i	−0.0847068	+	0.996406i	$0.526995\pi$
$313$	−16.0158	+	27.7402i	−0.905266	+	1.56797i	−0.820559	+	0.571561i	$0.806338\pi$
$314$	−18.6851			−1.05446
$315$		0			0
$316$		−	0.288917i		−	0.0162528i
$317$	18.5774	+	10.7256i	1.04341	+	0.602412i	0.920797	−	0.390042i	$-0.127540\pi$
$317$	18.5774	+	10.7256i	1.04341	+	0.602412i	0.122612	+	0.992455i	$0.460873\pi$
$318$		0			0
$319$	−3.99235	−	3.02423i	−0.223529	−	0.169324i
$320$	3.19684	+	1.84570i	0.178709	+	0.103178i
$321$		0			0
$322$	9.05612	+	4.16037i	0.504678	+	0.231848i
$323$		−	6.91267i		−	0.384631i
$324$		0			0
$325$	−41.8747	+	24.1764i	−2.32279	+	1.34106i
$326$	4.62801	+	8.01595i	0.256322	+	0.443963i
$327$		0			0
$328$	−6.24731			−0.344950
$329$	−2.54698	−	27.3208i	−0.140419	−	1.50625i
$330$		0			0
$331$	15.3327	−	26.5569i	0.842759	−	1.45970i	−0.0447947	−	0.998996i	$-0.514263\pi$
$331$	15.3327	−	26.5569i	0.842759	−	1.45970i	0.887553	−	0.460705i	$-0.152403\pi$
$332$	5.12612	+	8.87869i	0.281332	+	0.487282i
$333$		0			0
$334$	−8.19377	+	14.1920i	−0.448343	+	0.776554i
$335$			41.8304i			2.28544i
$336$		0			0
$337$		−	33.3731i		−	1.81795i	−0.416853	−	0.908974i	$-0.636867\pi$
$337$		−	33.3731i		−	1.81795i	0.416853	−	0.908974i	$-0.363133\pi$
$338$	9.20911	−	15.9507i	0.500910	−	0.867601i
$339$		0			0
$340$	−8.91672	+	5.14807i	−0.483577	+	0.279193i
$341$	1.40485	−	11.2084i	0.0760769	−	0.606972i
$342$		0			0
$343$	−17.8048	+	5.09803i	−0.961368	+	0.275268i
$344$		−	7.72006i		−	0.416238i
$345$		0			0
$346$	−10.4622	−	18.1210i	−0.562450	−	0.974191i
$347$	10.0767	+	17.4533i	0.540943	+	0.936941i	0.998850	+	0.0479408i	$0.0152659\pi$
$347$	10.0767	+	17.4533i	0.540943	+	0.936941i	−0.457907	+	0.889000i	$0.651401\pi$
$348$		0			0
$349$			25.8276i			1.38252i	0.722607	+	0.691259i	$0.242944\pi$
$349$			25.8276i			1.38252i	−0.722607	+	0.691259i	$0.757056\pi$
$350$	−13.1971	−	18.6210i	−0.705414	−	0.995334i
$351$		0			0
$352$	0.412474	−	3.29088i	0.0219849	−	0.175404i
$353$	8.21248	−	4.74148i	0.437106	−	0.252363i	−0.265263	−	0.964176i	$-0.585459\pi$
$353$	8.21248	−	4.74148i	0.437106	−	0.252363i	0.702369	+	0.711813i	$0.252125\pi$
$354$		0			0
$355$	9.50695	−	16.4665i	0.504577	−	0.873952i
$356$			15.8645i			0.840816i
$357$		0			0
$358$			14.9631i			0.790822i
$359$	−5.42112	+	9.38966i	−0.286116	+	0.495567i	−0.972879	−	0.231314i	$-0.925698\pi$
$359$	−5.42112	+	9.38966i	−0.286116	+	0.495567i	0.686763	+	0.726881i	$0.259031\pi$
$360$		0			0
$361$	−6.42890	−	11.1352i	−0.338363	−	0.586062i
$362$	5.05625	−	8.75769i	0.265751	−	0.460294i
$363$		0			0
$364$	13.4759	+	6.19084i	0.706331	+	0.324488i
$365$	19.3492			1.01279
$366$		0			0
$367$	4.46446	+	7.73268i	0.233043	+	0.403642i	0.958702	−	0.284412i	$-0.0917983\pi$
$367$	4.46446	+	7.73268i	0.233043	+	0.403642i	−0.725659	+	0.688054i	$0.758465\pi$
$368$	3.26215	−	1.88340i	0.170051	−	0.0981792i
$369$		0			0
$370$			21.1048i			1.09719i
$371$	25.7534	+	11.8311i	1.33705	+	0.614240i
$372$		0			0
$373$	12.8877	+	7.44073i	0.667301	+	0.385266i	0.795053	−	0.606540i	$-0.207443\pi$
$373$	12.8877	+	7.44073i	0.667301	+	0.385266i	−0.127752	+	0.991806i	$0.540776\pi$
$374$	7.37400	+	5.58584i	0.381301	+	0.288837i
$375$		0			0
$376$	−8.98162	−	5.18554i	−0.463192	−	0.267424i
$377$		−	8.46448i		−	0.435943i
$378$		0			0
$379$	30.2827			1.55552			0.777759	−	0.628563i	$-0.216356\pi$
$379$	30.2827			1.55552			0.777759	+	0.628563i	$0.216356\pi$
$380$	4.57428	−	7.92289i	0.234656	−	0.406436i
$381$		0			0
$382$	−4.57254	+	2.63995i	−0.233951	+	0.135072i
$383$	−18.4934	−	10.6772i	−0.944969	−	0.545578i	−0.0534545	−	0.998570i	$-0.517023\pi$
$383$	−18.4934	−	10.6772i	−0.944969	−	0.545578i	−0.891514	+	0.452992i	$0.850357\pi$
$384$		0			0
$385$	−17.0778	+	27.5242i	−0.870365	+	1.40276i
$386$		−	22.9048i		−	1.16582i
$387$		0			0
$388$	−2.29314	−	3.97184i	−0.116417	−	0.201639i
$389$	−6.05094	+	3.49351i	−0.306795	+	0.177128i	−0.645491	−	0.763768i	$-0.723347\pi$
$389$	−6.05094	+	3.49351i	−0.306795	+	0.177128i	0.338696	+	0.940896i	$0.390014\pi$
$390$		0			0
$391$			10.5065i			0.531335i
$392$	−2.31914	+	6.60467i	−0.117134	+	0.333586i
$393$		0			0
$394$	−4.28337	+	7.41901i	−0.215793	+	0.373764i
$395$	0.533253	+	0.923622i	0.0268309	+	0.0464725i
$396$		0			0
$397$	−5.27929	+	9.14400i	−0.264960	+	0.458924i	−0.967553	−	0.252668i	$-0.918692\pi$
$397$	−5.27929	+	9.14400i	−0.264960	+	0.458924i	0.702593	+	0.711592i	$0.252025\pi$
$398$	−4.57774			−0.229462
$399$		0			0
$400$	−8.62641			−0.431321
$401$	−8.21248	−	4.74148i	−0.410112	−	0.236778i	0.280726	−	0.959788i	$-0.409425\pi$
$401$	−8.21248	−	4.74148i	−0.410112	−	0.236778i	−0.690838	+	0.723010i	$0.742758\pi$
$402$		0			0
$403$	16.5331	−	9.54542i	0.823575	−	0.475491i
$404$	−1.45801	+	2.52536i	−0.0725389	+	0.125641i
$405$		0			0
$406$	3.97813	−	0.370860i	0.197431	−	0.0184055i
$407$	17.4733	−	7.36517i	0.866120	−	0.365078i
$408$		0			0
$409$	1.48918	−	0.859778i	0.0736351	−	0.0425133i	−0.462730	−	0.886499i	$-0.653130\pi$
$409$	1.48918	−	0.859778i	0.0736351	−	0.0425133i	0.536366	+	0.843986i	$0.319797\pi$
$410$	19.9717	−	11.5307i	0.986331	−	0.569459i
$411$		0			0
$412$	9.23233			0.454844
$413$	32.2674	+	14.8236i	1.58777	+	0.729422i
$414$		0			0
$415$	−32.7748	−	18.9225i	−1.60885	−	0.928870i
$416$	4.85424	−	2.80260i	0.237999	−	0.137409i
$417$		0			0
$418$	−8.15594	−	1.02225i	−0.398920	−	0.0500000i
$419$		−	5.34038i		−	0.260895i	−0.991455	−	0.130447i	$-0.958359\pi$
$419$		−	5.34038i		−	0.260895i	0.991455	−	0.130447i	$-0.0416414\pi$
$420$		0			0
$421$	−27.1036			−1.32095			−0.660475	−	0.750848i	$-0.729645\pi$
$421$	−27.1036			−1.32095			−0.660475	+	0.750848i	$0.729645\pi$
$422$	8.71101	+	5.02930i	0.424045	+	0.244823i
$423$		0			0
$424$	9.27677	−	5.35595i	0.450520	−	0.260108i
$425$	12.0305	−	20.8374i	0.583565	−	1.01076i
$426$		0			0
$427$	0.604670	+	6.48615i	0.0292620	+	0.313887i
$428$	−3.62473			−0.175208
$429$		0			0
$430$	14.2489	+	24.6798i	0.687143	+	1.19017i
$431$	3.80062	+	6.58286i	0.183069	+	0.317085i	0.942924	−	0.333007i	$-0.108063\pi$
$431$	3.80062	+	6.58286i	0.183069	+	0.317085i	−0.759855	+	0.650093i	$0.774730\pi$
$432$		0			0
$433$	−31.9514			−1.53549			−0.767744	−	0.640757i	$-0.778621\pi$
$433$	−31.9514			−1.53549			−0.767744	+	0.640757i	$0.778621\pi$
$434$	5.21053	+	7.35202i	0.250113	+	0.352908i
$435$		0			0
$436$	13.9355	+	8.04565i	0.667388	+	0.385317i
$437$	−4.66773	−	8.08475i	−0.223288	−	0.386746i
$438$		0			0
$439$	3.37246	+	1.94709i	0.160959	+	0.0929294i	0.578316	−	0.815813i	$-0.303710\pi$
$439$	3.37246	+	1.94709i	0.160959	+	0.0929294i	−0.417357	+	0.908743i	$0.637044\pi$
$440$	4.75535	+	11.2817i	0.226702	+	0.537835i
$441$		0			0
$442$			15.6342i			0.743641i
$443$	−4.84958	−	2.79991i	−0.230410	−	0.133028i	0.380351	−	0.924842i	$-0.375803\pi$
$443$	−4.84958	−	2.79991i	−0.230410	−	0.133028i	−0.610761	+	0.791815i	$0.709137\pi$
$444$		0			0
$445$	−29.2811	−	50.7163i	−1.38806	−	2.40418i
$446$	−7.37151	+	12.7678i	−0.349051	+	0.604575i
$447$		0			0
$448$	1.52985	+	2.15860i	0.0722785	+	0.101984i
$449$		−	19.7608i		−	0.932570i	−0.884635	−	0.466285i	$-0.845592\pi$
$449$		−	19.7608i		−	0.932570i	0.884635	−	0.466285i	$-0.154408\pi$
$450$		0			0
$451$	−16.5163	−	12.5112i	−0.777723	−	0.589129i
$452$	16.3134	−	9.41854i	0.767318	−	0.443011i
$453$		0			0
$454$	18.8294			0.883707
$455$	−54.5069	+	5.08139i	−2.55532	+	0.238219i
$456$		0			0
$457$	−16.7231	−	9.65507i	−0.782272	−	0.451645i	0.0549627	−	0.998488i	$-0.482496\pi$
$457$	−16.7231	−	9.65507i	−0.782272	−	0.451645i	−0.837235	+	0.546843i	$0.815829\pi$
$458$	−6.82233	−	11.8166i	−0.318787	−	0.552155i
$459$		0			0
$460$	−6.95239	+	12.0419i	−0.324157	+	0.561456i
$461$	6.95967			0.324144			0.162072	−	0.986779i	$-0.448182\pi$
$461$	6.95967			0.324144			0.162072	+	0.986779i	$0.448182\pi$
$462$		0			0
$463$	16.2724			0.756243			0.378121	−	0.925756i	$-0.376570\pi$
$463$	16.2724			0.756243			0.378121	+	0.925756i	$0.376570\pi$
$464$	0.755057	−	1.30780i	0.0350526	−	0.0607129i
$465$		0			0
$466$	−3.51518	−	6.08847i	−0.162837	−	0.282043i
$467$	1.39696	+	0.806535i	0.0646436	+	0.0373220i	0.531973	−	0.846761i	$-0.321451\pi$
$467$	1.39696	+	0.806535i	0.0646436	+	0.0373220i	−0.467330	+	0.884083i	$0.654784\pi$
$468$		0			0
$469$	−12.5158	+	27.2440i	−0.577928	+	1.25801i
$470$	38.2838			1.76590
$471$		0			0
$472$	11.6232	−	6.71066i	0.535002	−	0.308883i
$473$	15.4606	−	20.4099i	0.710878	−	0.938447i
$474$		0			0
$475$			21.3792i			0.980947i
$476$	−7.34774	+	0.684991i	−0.336783	+	0.0313965i
$477$		0			0
$478$	5.19541	−	8.99871i	0.237632	−	0.411591i
$479$	−16.9520	−	29.3616i	−0.774555	−	1.34157i	−0.935045	−	0.354530i	$-0.884641\pi$
$479$	−16.9520	−	29.3616i	−0.774555	−	1.34157i	0.160490	−	0.987037i	$-0.448693\pi$
$480$		0			0
$481$	27.7531	+	16.0233i	1.26543	+	0.730599i
$482$			10.6807i			0.486490i
$483$		0			0
$484$	7.68095	−	7.87420i	0.349134	−	0.357918i
$485$	14.6616	+	8.46489i	0.665750	+	0.384371i
$486$		0			0
$487$	−1.52594	−	2.64300i	−0.0691468	−	0.119766i	0.829379	−	0.558686i	$-0.188694\pi$
$487$	−1.52594	−	2.64300i	−0.0691468	−	0.119766i	−0.898526	+	0.438920i	$0.855361\pi$
$488$	2.13230	+	1.23108i	0.0965246	+	0.0557285i
$489$		0			0
$490$	−4.77630	−	25.3945i	−0.215771	−	1.14721i
$491$	−35.7449			−1.61315			−0.806573	−	0.591134i	$-0.798680\pi$
$491$	−35.7449			−1.61315			−0.806573	+	0.591134i	$0.798680\pi$
$492$		0			0
$493$	2.10602	+	3.64774i	0.0948505	+	0.164286i
$494$	−6.94581	−	12.0305i	−0.312507	−	0.541278i
$495$		0			0
$496$	3.40592			0.152930
$497$	11.1187	−	7.88004i	0.498741	−	0.353468i
$498$		0			0
$499$	−3.75597	+	6.50553i	−0.168140	+	0.291227i	−0.937766	−	0.347268i	$-0.887109\pi$
$499$	−3.75597	+	6.50553i	−0.168140	+	0.291227i	0.769626	+	0.638495i	$0.220443\pi$
$500$	11.5931	−	6.69326i	0.518458	−	0.299332i
$501$		0			0
$502$	−7.96699	−	4.59974i	−0.355584	−	0.205297i
$503$	−21.5419			−0.960507			−0.480253	−	0.877130i	$-0.659455\pi$
$503$	−21.5419			−0.960507			−0.480253	+	0.877130i	$0.659455\pi$
$504$		0			0
$505$		−	10.7642i		−	0.479002i
$506$	12.3961	+	1.55371i	0.551074	+	0.0690708i
$507$		0			0
$508$	6.99993	−	4.04141i	0.310572	−	0.179309i
$509$	26.1028	+	15.0705i	1.15699	+	0.667986i	0.950580	−	0.310480i	$-0.100490\pi$
$509$	26.1028	+	15.0705i	1.15699	+	0.667986i	0.206406	+	0.978466i	$0.433823\pi$
$510$		0			0
$511$	12.6021	+	5.78938i	0.557483	+	0.256107i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−17.8743	+	10.3197i	−0.788403	+	0.455185i
$515$	−29.5143	+	17.0401i	−1.30056	+	0.750876i
$516$		0			0
$517$	−13.3603	−	31.6963i	−0.587585	−	1.39400i
$518$	−6.31465	+	13.7455i	−0.277450	+	0.603941i
$519$		0			0
$520$	−10.3455	+	17.9189i	−0.453680	+	0.785797i
$521$	−27.8685	+	16.0899i	−1.22094	+	0.704909i	−0.965118	−	0.261815i	$-0.915679\pi$
$521$	−27.8685	+	16.0899i	−1.22094	+	0.704909i	−0.255821	+	0.966724i	$0.582346\pi$
$522$		0			0
$523$	−3.03873	−	1.75441i	−0.132874	−	0.0767149i	0.432089	−	0.901831i	$-0.357776\pi$
$523$	−3.03873	−	1.75441i	−0.132874	−	0.0767149i	−0.564964	+	0.825116i	$0.691110\pi$
$524$	−15.6711			−0.684597
$525$		0			0
$526$	26.3226			1.14772
$527$	−4.74993	+	8.22713i	−0.206910	+	0.358379i
$528$		0			0
$529$	−4.40558	−	7.63068i	−0.191547	−	0.331769i
$530$	−19.7709	+	34.2443i	−0.858794	+	1.48748i
$531$		0			0
$532$	5.34977	−	3.79149i	0.231942	−	0.164382i
$533$		−	35.0174i		−	1.51677i
$534$		0			0
$535$	11.5877	−	6.69016i	0.500980	−	0.289241i
$536$	5.66594	+	9.81369i	0.244731	+	0.423887i
$537$		0			0
$538$			8.12947i			0.350486i
$539$	−19.3580	+	12.8166i	−0.833810	+	0.552051i
$540$		0			0
$541$	3.92948	+	2.26869i	0.168942	+	0.0975385i	0.582087	−	0.813127i	$-0.302236\pi$
$541$	3.92948	+	2.26869i	0.168942	+	0.0975385i	−0.413145	+	0.910665i	$0.635570\pi$
$542$	12.6065	−	7.27836i	0.541495	−	0.312632i
$543$		0			0
$544$	−1.39461	+	2.41554i	−0.0597935	+	0.103565i
$545$	−59.3994			−2.54439
$546$		0			0
$547$			16.8271i			0.719477i	0.933053	+	0.359738i	$0.117134\pi$
$547$			16.8271i			0.719477i	−0.933053	+	0.359738i	$0.882866\pi$
$548$	−2.55426	−	1.47471i	−0.109113	−	0.0629963i
$549$		0			0
$550$	−22.8060	−	17.2757i	−0.972453	−	0.736638i
$551$	−3.24117	−	1.87129i	−0.138079	−	0.0797197i
$552$		0			0
$553$	0.0709535	+	0.761102i	0.00301725	+	0.0323653i
$554$			29.9949i			1.27436i
$555$		0			0
$556$	−3.47235	+	2.00476i	−0.147260	+	0.0850208i
$557$	−6.67157	−	11.5555i	−0.282684	−	0.489622i	0.689361	−	0.724418i	$-0.257891\pi$
$557$	−6.67157	−	11.5555i	−0.282684	−	0.489622i	−0.972045	+	0.234795i	$0.924558\pi$
$558$		0			0
$559$	43.2725			1.83023
$560$	−8.87481	−	4.07708i	−0.375029	−	0.172288i
$561$		0			0
$562$	−6.42117	+	11.1218i	−0.270861	+	0.469144i
$563$	16.4049	+	28.4141i	0.691384	+	1.19751i	0.971385	+	0.237512i	$0.0763318\pi$
$563$	16.4049	+	28.4141i	0.691384	+	1.19751i	−0.280001	+	0.960000i	$0.590335\pi$
$564$		0			0
$565$	−34.7676	+	60.2192i	−1.46268	+	2.53344i
$566$			7.33349i			0.308250i
$567$		0			0
$568$		−	5.15087i		−	0.216126i
$569$	2.97076	−	5.14551i	0.124541	−	0.215711i	−0.797012	−	0.603963i	$-0.793588\pi$
$569$	2.97076	−	5.14551i	0.124541	−	0.215711i	0.921553	+	0.388252i	$0.126921\pi$
$570$		0			0
$571$	31.8007	−	18.3601i	1.33082	−	0.768348i	0.345393	−	0.938458i	$-0.387746\pi$
$571$	31.8007	−	18.3601i	1.33082	−	0.768348i	0.985425	+	0.170110i	$0.0544124\pi$
$572$	18.4460	+	2.31200i	0.771266	+	0.0966694i
$573$		0			0
$574$	16.4575	−	1.53424i	0.686922	−	0.0640381i
$575$		−	32.4940i		−	1.35510i
$576$		0			0
$577$	0.409992	+	0.710127i	0.0170682	+	0.0295630i	0.874433	−	0.485146i	$-0.161233\pi$
$577$	0.409992	+	0.710127i	0.0170682	+	0.0295630i	−0.857365	+	0.514709i	$0.827900\pi$
$578$	4.61011	+	7.98495i	0.191755	+	0.332130i
$579$		0			0
$580$			5.57443i			0.231465i
$581$	−15.6843	−	22.1305i	−0.650696	−	0.918128i
$582$		0			0
$583$	35.2515	+	4.41837i	1.45997	+	0.182990i
$584$	4.53946	−	2.62086i	0.187844	−	0.108452i
$585$		0			0
$586$	3.02672	−	5.24243i	0.125032	−	0.216563i
$587$			42.0341i			1.73493i	0.497494	+	0.867467i	$0.334254\pi$
$587$			42.0341i			1.73493i	−0.497494	+	0.867467i	$0.665746\pi$
$588$		0			0
$589$		−	8.44105i		−	0.347807i
$590$	−24.7717	+	42.9059i	−1.01984	+	1.76641i
$591$		0			0
$592$	2.85865	+	4.95132i	0.117490	+	0.203498i
$593$	−13.1169	+	22.7191i	−0.538645	+	0.932960i	0.460333	+	0.887747i	$0.347730\pi$
$593$	−13.1169	+	22.7191i	−0.538645	+	0.932960i	−0.998977	+	0.0452135i	$0.985603\pi$
$594$		0			0
$595$	22.2253	−	15.7515i	0.911148	−	0.645749i
$596$	−6.46913			−0.264986
$597$		0			0
$598$	10.5569	+	18.2850i	0.431702	+	0.747729i
$599$	−22.7563	+	13.1384i	−0.929798	+	0.536819i	−0.886748	−	0.462254i	$-0.847041\pi$
$599$	−22.7563	+	13.1384i	−0.929798	+	0.536819i	−0.0430501	+	0.999073i	$0.513708\pi$
$600$		0			0
$601$		−	37.0989i		−	1.51329i	−0.653824	−	0.756647i	$-0.726836\pi$
$601$		−	37.0989i		−	1.51329i	0.653824	−	0.756647i	$-0.273164\pi$
$602$	1.89593	+	20.3372i	0.0772722	+	0.828882i
$603$		0			0
$604$	−13.3957	−	7.73400i	−0.545062	−	0.314692i
$605$	−10.0214	+	39.3493i	−0.407428	+	1.59978i
$606$		0			0
$607$	−1.72911	−	0.998300i	−0.0701822	−	0.0405197i	0.464498	−	0.885574i	$-0.346235\pi$
$607$	−1.72911	−	0.998300i	−0.0701822	−	0.0405197i	−0.534680	+	0.845054i	$0.679568\pi$
$608$		−	2.47835i		−	0.100510i
$609$		0			0
$610$	−9.08883			−0.367996
$611$	29.0660	−	50.3437i	1.17588	−	2.03669i
$612$		0			0
$613$	6.55742	−	3.78593i	0.264852	−	0.152912i	−0.361694	−	0.932297i	$-0.617801\pi$
$613$	6.55742	−	3.78593i	0.264852	−	0.152912i	0.626546	+	0.779385i	$0.284468\pi$
$614$	5.40966	+	3.12327i	0.218316	+	0.126045i
$615$		0			0
$616$	−0.278403	+	8.77055i	−0.0112172	+	0.353375i
$617$		−	17.2159i		−	0.693084i	−0.938034	−	0.346542i	$-0.887356\pi$
$617$		−	17.2159i		−	0.693084i	0.938034	−	0.346542i	$-0.112644\pi$
$618$		0			0
$619$	−18.3426	−	31.7703i	−0.737250	−	1.27695i	−0.953729	−	0.300667i	$-0.902791\pi$
$619$	−18.3426	−	31.7703i	−0.737250	−	1.27695i	0.216479	−	0.976287i	$-0.430543\pi$
$620$	−10.8882	+	6.28629i	−0.437280	+	0.252464i
$621$		0			0
$622$			9.76504i			0.391542i
$623$	−3.89607	−	41.7923i	−0.156093	−	1.67437i
$624$		0			0
$625$	−3.14145	+	5.44116i	−0.125658	+	0.217646i
$626$	−16.0158	−	27.7402i	−0.640120	−	1.10872i
$627$		0			0
$628$	9.34257	−	16.1818i	0.372809	−	0.645725i
$629$	−15.9468			−0.635842
$630$		0			0
$631$	−47.4286			−1.88810			−0.944051	−	0.329801i	$-0.893019\pi$
$631$	−47.4286			−1.88810			−0.944051	+	0.329801i	$0.893019\pi$
$632$	0.250209	+	0.144458i	0.00995279	+	0.00574625i
$633$		0			0
$634$	−18.5774	+	10.7256i	−0.737802	+	0.425970i
$635$	−14.9185	+	25.8395i	−0.592021	+	1.02541i
$636$		0			0
$637$	−37.0204	−	12.9992i	−1.46680	−	0.515048i
$638$	4.61524	−	1.94537i	0.182719	−	0.0770178i
$639$		0			0
$640$	−3.19684	+	1.84570i	−0.126366	+	0.0729576i
$641$	28.5801	−	16.5007i	1.12884	−	0.651739i	0.185200	−	0.982701i	$-0.440707\pi$
$641$	28.5801	−	16.5007i	1.12884	−	0.651739i	0.943644	+	0.330962i	$0.107373\pi$
$642$		0			0
$643$	−41.8847			−1.65177			−0.825885	−	0.563838i	$-0.809324\pi$
$643$	−41.8847			−1.65177			−0.825885	+	0.563838i	$0.809324\pi$
$644$	−8.13105	+	5.76264i	−0.320408	+	0.227080i
$645$		0			0
$646$	5.98655	+	3.45634i	0.235538	+	0.135988i
$647$	−17.9616	+	10.3701i	−0.706142	+	0.407691i	−0.809631	−	0.586939i	$-0.800333\pi$
$647$	−17.9616	+	10.3701i	−0.706142	+	0.407691i	0.103489	+	0.994631i	$0.466999\pi$
$648$		0			0
$649$	44.1679	+	5.53594i	1.73374	+	0.217305i
$650$		−	48.3527i		−	1.89655i
$651$		0			0
$652$	−9.25602			−0.362494
$653$	−6.73045	−	3.88583i	−0.263383	−	0.152064i	0.362494	−	0.931986i	$-0.381925\pi$
$653$	−6.73045	−	3.88583i	−0.263383	−	0.152064i	−0.625877	+	0.779922i	$0.715259\pi$
$654$		0			0
$655$	50.0982	−	28.9242i	1.95750	−	1.13016i
$656$	3.12366	−	5.41033i	0.121958	−	0.211238i
$657$		0			0
$658$	24.9340	+	11.4547i	0.972029	+	0.446549i
$659$	−44.6638			−1.73986			−0.869928	−	0.493180i	$-0.835835\pi$
$659$	−44.6638			−1.73986			−0.869928	+	0.493180i	$0.835835\pi$
$660$		0			0
$661$	3.14521	+	5.44767i	0.122335	+	0.211890i	0.920688	−	0.390300i	$-0.127629\pi$
$661$	3.14521	+	5.44767i	0.122335	+	0.211890i	−0.798353	+	0.602189i	$0.794295\pi$
$662$	15.3327	+	26.5569i	0.595920	+	1.03216i
$663$		0			0
$664$	−10.2522			−0.397864
$665$	−10.1044	+	21.9949i	−0.391833	+	0.852924i
$666$		0			0
$667$	4.92622	+	2.84415i	0.190744	+	0.110126i
$668$	−8.19377	−	14.1920i	−0.317027	−	0.549106i
$669$		0			0
$670$	−36.2262	−	20.9152i	−1.39954	−	0.808025i
$671$	3.17182	+	7.52491i	0.122447	+	0.290496i
$672$		0			0
$673$		−	4.96695i		−	0.191462i	−0.995407	−	0.0957309i	$-0.969481\pi$
$673$		−	4.96695i		−	0.191462i	0.995407	−	0.0957309i	$-0.0305188\pi$
$674$	28.9019	+	16.6865i	1.11326	+	0.642742i
$675$		0			0
$676$	9.20911	+	15.9507i	0.354197	+	0.613487i
$677$	−12.5168	+	21.6798i	−0.481061	+	0.833222i	−0.999764	−	0.0217327i	$-0.993082\pi$
$677$	−12.5168	+	21.6798i	−0.481061	+	0.833222i	0.518703	+	0.854955i	$0.326415\pi$
$678$		0			0
$679$	7.01631	+	9.89996i	0.269261	+	0.379926i
$680$		−	10.2961i		−	0.394839i
$681$		0			0
$682$	9.00438	+	6.82086i	0.344795	+	0.261184i
$683$	37.1556	−	21.4518i	1.42172	−	0.820831i	0.425275	−	0.905064i	$-0.360177\pi$
$683$	37.1556	−	21.4518i	1.42172	−	0.820831i	0.996446	+	0.0842334i	$0.0268441\pi$
$684$		0			0
$685$	10.8874			0.415988
$686$	4.48737	−	17.9684i	0.171328	−	0.686037i
$687$		0			0
$688$	6.68577	+	3.86003i	0.254893	+	0.147162i
$689$	30.0211	+	51.9981i	1.14371	+	1.98097i
$690$		0			0
$691$	−3.04518	+	5.27440i	−0.115844	+	0.200648i	−0.918117	−	0.396310i	$-0.870291\pi$
$691$	−3.04518	+	5.27440i	−0.115844	+	0.200648i	0.802273	+	0.596958i	$0.203624\pi$
$692$	20.9243			0.795424
$693$		0			0
$694$	−20.1533			−0.765009
$695$	7.40037	−	12.8178i	0.280712	−	0.486207i
$696$		0			0
$697$	8.71258	+	15.0906i	0.330013	+	0.571599i
$698$	−22.3673	−	12.9138i	−0.846616	−	0.488794i
$699$		0			0
$700$	22.7248	−	2.11851i	0.858917	−	0.0800723i
$701$	−49.6670			−1.87590			−0.937948	−	0.346777i	$-0.887276\pi$
$701$	−49.6670			−1.87590			−0.937948	+	0.346777i	$0.887276\pi$
$702$		0			0
$703$	12.2711	−	7.08472i	0.462813	−	0.267205i
$704$	2.64375	+	2.00265i	0.0996399	+	0.0754777i
$705$		0			0
$706$			9.48296i			0.356896i
$707$	3.22070	−	7.01068i	0.121127	−	0.263664i
$708$		0			0
$709$	−1.37833	+	2.38734i	−0.0517643	+	0.0896584i	−0.890746	−	0.454500i	$-0.849818\pi$
$709$	−1.37833	+	2.38734i	−0.0517643	+	0.0896584i	0.838982	+	0.544159i	$0.183151\pi$
$710$	9.50695	+	16.4665i	0.356789	+	0.617978i
$711$		0			0
$712$	−13.7391	−	7.93225i	−0.514893	−	0.297274i
$713$			12.8294i			0.480466i
$714$		0			0
$715$	−63.2362	+	26.6547i	−2.36490	+	0.996828i
$716$	−12.9584	−	7.48153i	−0.484278	−	0.279598i
$717$		0			0
$718$	−5.42112	−	9.38966i	−0.202314	−	0.350419i
$719$	−34.4448	−	19.8867i	−1.28457	−	0.741650i	−0.306894	−	0.951744i	$-0.599290\pi$
$719$	−34.4448	−	19.8867i	−1.28457	−	0.741650i	−0.977681	+	0.210094i	$0.932623\pi$
$720$		0			0
$721$	−24.3210	+	2.26732i	−0.905761	+	0.0844393i
$722$	12.8578			0.478518
$723$		0			0
$724$	5.05625	+	8.75769i	0.187914	+	0.325477i
$725$	−6.51343	−	11.2816i	−0.241903	−	0.418988i
$726$		0			0
$727$	25.4901			0.945376			0.472688	−	0.881230i	$-0.343284\pi$
$727$	25.4901			0.945376			0.472688	+	0.881230i	$0.343284\pi$
$728$	−12.0994	+	8.57509i	−0.448433	+	0.317814i
$729$		0			0
$730$	−9.67462	+	16.7569i	−0.358074	+	0.620202i
$731$	−18.6481	+	10.7665i	−0.689726	+	0.398213i
$732$		0			0
$733$	42.1323	+	24.3251i	1.55619	+	0.898467i	0.997616	+	0.0690128i	$0.0219849\pi$
$733$	42.1323	+	24.3251i	1.55619	+	0.898467i	0.558575	+	0.829454i	$0.311348\pi$
$734$	−8.92893			−0.329573
$735$		0			0
$736$			3.76681i			0.138846i
$737$	−4.67410	+	37.2918i	−0.172173	+	1.37366i
$738$		0			0
$739$	−10.9783	+	6.33835i	−0.403845	+	0.233160i	−0.688142	−	0.725576i	$-0.741573\pi$
$739$	−10.9783	+	6.33835i	−0.403845	+	0.233160i	0.284297	+	0.958736i	$0.408240\pi$
$740$	−18.2773	−	10.5524i	−0.671887	−	0.387914i
$741$		0			0
$742$	−23.1227	+	16.3876i	−0.848862	+	0.601606i
$743$	−18.4512			−0.676910			−0.338455	−	0.940983i	$-0.609904\pi$
$743$	−18.4512			−0.676910			−0.338455	+	0.940983i	$0.609904\pi$
$744$		0			0
$745$	20.6808	−	11.9401i	0.757686	−	0.437450i
$746$	−12.8877	+	7.44073i	−0.471853	+	0.272424i
$747$		0			0
$748$	−8.52448	+	3.59315i	−0.311686	+	0.131379i
$749$	9.54873	−	0.890178i	0.348903	−	0.0325264i
$750$		0			0
$751$	25.5428	−	44.2414i	0.932070	−	1.61439i	0.152293	−	0.988335i	$-0.451334\pi$
$751$	25.5428	−	44.2414i	0.932070	−	1.61439i	0.779777	−	0.626057i	$-0.215332\pi$
$752$	8.98162	−	5.18554i	0.327526	−	0.189097i
$753$		0			0
$754$	7.33046	+	4.23224i	0.266959	+	0.154129i
$755$	57.0985			2.07803
$756$		0			0
$757$	13.3898			0.486659			0.243329	−	0.969944i	$-0.421760\pi$
$757$	13.3898			0.486659			0.243329	+	0.969944i	$0.421760\pi$
$758$	−15.1414	+	26.2256i	−0.549959	+	0.952556i
$759$		0			0
$760$	4.57428	+	7.92289i	0.165927	+	0.287393i
$761$	3.48214	−	6.03125i	0.126228	−	0.218633i	−0.795985	−	0.605317i	$-0.793046\pi$
$761$	3.48214	−	6.03125i	0.126228	−	0.218633i	0.922212	+	0.386684i	$0.126380\pi$
$762$		0			0
$763$	−38.6865	−	17.7726i	−1.40055	−	0.643410i
$764$		−	5.27991i		−	0.191020i
$765$		0			0
$766$	18.4934	−	10.6772i	0.668194	−	0.385782i
$767$	37.6146	+	65.1504i	1.35818	+	2.35244i
$768$		0			0
$769$			2.40816i			0.0868404i	0.999057	+	0.0434202i	$0.0138254\pi$
$769$			2.40816i			0.0868404i	−0.999057	+	0.0434202i	$0.986175\pi$
$770$	−15.2978	−	28.5519i	−0.551294	−	1.02894i
$771$		0			0
$772$	19.8361	+	11.4524i	0.713918	+	0.412181i
$773$	−11.9339	+	6.89002i	−0.429231	+	0.247817i	−0.699019	−	0.715103i	$-0.746380\pi$
$773$	−11.9339	+	6.89002i	−0.429231	+	0.247817i	0.269788	+	0.962920i	$0.413046\pi$
$774$		0			0
$775$	14.6904	−	25.4445i	0.527695	−	0.913995i
$776$	4.58628			0.164638
$777$		0			0
$778$		−	6.98703i		−	0.250497i
$779$	−13.4087	−	7.74151i	−0.480416	−	0.277368i
$780$		0			0
$781$	10.3154	−	13.6176i	0.369114	−	0.487276i
$782$	−9.09888	−	5.25324i	−0.325375	−	0.187855i
$783$		0			0
$784$	−4.56024	−	5.31076i	−0.162866	−	0.189670i
$785$			68.9743i			2.46180i
$786$		0			0
$787$	−4.15993	+	2.40174i	−0.148285	+	0.0856127i	−0.572307	−	0.820039i	$-0.693951\pi$
$787$	−4.15993	+	2.40174i	−0.148285	+	0.0856127i	0.424022	+	0.905652i	$0.360618\pi$
$788$	−4.28337	−	7.41901i	−0.152589	−	0.264291i
$789$		0			0
$790$	−1.06651			−0.0379446
$791$	−40.6618	+	28.8179i

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.ba (of order \(6\), degree \(2\), minimal)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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