LMFDB - Embedded newform 91.2.r.a.25.4

Newspace parameters

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.r (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
Defining polynomial:	$x^{16} - 11 x^{14} + 85 x^{12} - 334 x^{10} + 952 x^{8} - 1050 x^{6} + 853 x^{4} - 93 x^{2} + 9$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.4
Root			$0.287846 + 0.166188i$ of defining polynomial
Character	$\chi$	$=$	91.25
Dual form			91.2.r.a.51.4

$q$-expansion

$f(q)$	$=$	$q+(-0.287846 + 0.166188i) q^{2} +(-0.729919 + 1.26426i) q^{3} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} -0.485214i q^{6} +(-2.26391 - 1.36920i) q^{7} -1.29278i q^{8} +(0.434437 + 0.752468i) q^{9} +O(q^{10})$	\(q+(-0.287846 + 0.166188i) q^{2} +(-0.729919 + 1.26426i) q^{3} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} -0.485214i q^{6} +(-2.26391 - 1.36920i) q^{7} -1.29278i q^{8} +(0.434437 + 0.752468i) q^{9} +(0.240245 - 0.416116i) q^{10} +(5.15732 + 2.97758i) q^{11} +(-1.37920 - 2.38885i) q^{12} +(1.88953 + 3.07078i) q^{13} +(0.879201 + 0.0178849i) q^{14} -2.11037i q^{15} +(-1.67468 - 2.90063i) q^{16} +(2.16436 - 3.74877i) q^{17} +(-0.250102 - 0.144396i) q^{18} +(-1.69527 + 0.978767i) q^{19} -2.73154i q^{20} +(3.38349 - 1.86276i) q^{21} -1.97935 q^{22} +(-0.270081 - 0.467795i) q^{23} +(1.63441 + 0.943626i) q^{24} +(-1.45509 + 2.52029i) q^{25} +(-1.05422 - 0.569894i) q^{26} -5.64793 q^{27} +(4.37939 - 2.41104i) q^{28} +7.15857 q^{29} +(0.350718 + 0.607461i) q^{30} +(-5.28968 - 3.05400i) q^{31} +(3.20327 + 1.84941i) q^{32} +(-7.52885 + 4.34678i) q^{33} +1.43876i q^{34} +(3.82396 + 0.0777879i) q^{35} -1.64176 q^{36} +(6.95316 - 4.01441i) q^{37} +(0.325318 - 0.563467i) q^{38} +(-5.26145 + 0.147426i) q^{39} +(0.934437 + 1.61849i) q^{40} +7.55362i q^{41} +(-0.664356 + 1.09848i) q^{42} -4.24839 q^{43} +(-9.74489 + 5.62622i) q^{44} +(-1.08778 - 0.628032i) q^{45} +(0.155483 + 0.0897684i) q^{46} +(5.42204 - 3.13042i) q^{47} +4.88953 q^{48} +(3.25057 + 6.19950i) q^{49} -0.967272i q^{50} +(3.15961 + 5.47260i) q^{51} +(-6.81011 + 0.190820i) q^{52} +(1.38953 - 2.40673i) q^{53} +(1.62573 - 0.938616i) q^{54} -8.60891 q^{55} +(-1.77008 + 2.92674i) q^{56} -2.85768i q^{57} +(-2.06056 + 1.18967i) q^{58} +(0.737119 + 0.425576i) q^{59} +(3.45337 + 1.99380i) q^{60} +(-3.38953 - 5.87083i) q^{61} +2.03015 q^{62} +(0.0467536 - 2.29835i) q^{63} +5.46933 q^{64} +(-4.58518 - 2.47868i) q^{65} +(1.44476 - 2.50240i) q^{66} +(-0.854859 - 0.493553i) q^{67} +(4.08961 + 7.08341i) q^{68} +0.788550 q^{69} +(-1.11364 + 0.613105i) q^{70} -3.76223i q^{71} +(0.972777 - 0.561633i) q^{72} +(7.91131 + 4.56760i) q^{73} +(-1.33429 + 2.31106i) q^{74} +(-2.12419 - 3.67921i) q^{75} -3.69881i q^{76} +(-7.59879 - 13.8024i) q^{77} +(1.48999 - 0.916825i) q^{78} +(0.0655625 + 0.113558i) q^{79} +(4.19322 + 2.42096i) q^{80} +(2.81922 - 4.88303i) q^{81} +(-1.25532 - 2.17428i) q^{82} -2.66812i q^{83} +(-0.148428 + 7.29653i) q^{84} +6.25768i q^{85} +(1.22288 - 0.706030i) q^{86} +(-5.22517 + 9.05026i) q^{87} +(3.84936 - 6.66729i) q^{88} +(8.41550 - 4.85869i) q^{89} +0.417485 q^{90} +(-0.0731980 - 9.53911i) q^{91} +1.02065 q^{92} +(7.72207 - 4.45834i) q^{93} +(-1.04047 + 1.80215i) q^{94} +(1.41493 - 2.45072i) q^{95} +(-4.67625 + 2.69983i) q^{96} -6.58319i q^{97} +(-1.96594 - 1.24429i) q^{98} +5.17429i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16q - 4q^{3} + 6q^{4} - 12q^{9} + O(q^{10}) $	$ 16q - 4q^{3} + 6q^{4} - 12q^{9} - 6q^{10} + 18q^{12} - 12q^{13} - 26q^{14} + 2q^{16} + 8q^{17} - 36q^{22} - 12q^{23} - 6q^{26} + 32q^{27} - 16q^{29} + 38q^{30} - 56q^{36} + 34q^{38} + 18q^{39} - 4q^{40} + 16q^{42} + 16q^{43} + 36q^{48} + 40q^{49} + 16q^{51} - 42q^{52} - 20q^{53} + 24q^{55} - 36q^{56} - 12q^{61} + 44q^{62} + 88q^{64} - 30q^{65} + 2q^{66} - 2q^{68} - 56q^{69} + 42q^{74} + 8q^{75} - 76q^{77} + 20q^{78} + 20q^{79} - 24q^{81} - 16q^{82} - 68q^{87} + 4q^{88} - 216q^{90} + 56q^{91} + 12q^{92} - 26q^{94} - 16q^{95} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.287846	+	0.166188i	−0.203538	+	0.117512i	−0.598304	−	0.801269i	$-0.704159\pi$
$2$	−0.287846	+	0.166188i	−0.203538	+	0.117512i	0.394767	+	0.918781i	$0.370825\pi$
$3$	−0.729919	+	1.26426i	−0.421419	+	0.729919i	−0.996079	−	0.0884737i	$-0.971801\pi$
$3$	−0.729919	+	1.26426i	−0.421419	+	0.729919i	0.574660	+	0.818392i	$0.305134\pi$
$4$	−0.944763	+	1.63638i	−0.472382	+	0.818189i
$5$	−1.25195	+	0.722811i	−0.559887	+	0.323251i	−0.753100	−	0.657906i	$-0.771442\pi$
$5$	−1.25195	+	0.722811i	−0.559887	+	0.323251i	0.193213	+	0.981157i	$0.438109\pi$
$6$		−	0.485214i		−	0.198088i
$7$	−2.26391	−	1.36920i	−0.855677	−	0.517510i
$7$	−2.26391	−	1.36920i	−0.855677	−	0.517510i
$8$		−	1.29278i		−	0.457068i
$9$	0.434437	+	0.752468i	0.144812	+	0.250823i
$10$	0.240245	−	0.416116i	0.0759720	−	0.131587i
$11$	5.15732	+	2.97758i	1.55499	+	0.897774i	0.997723	+	0.0674405i	$0.0214833\pi$
$11$	5.15732	+	2.97758i	1.55499	+	0.897774i	0.557267	+	0.830333i	$0.311850\pi$
$12$	−1.37920	−	2.38885i	−0.398141	−	0.689600i
$13$	1.88953	+	3.07078i	0.524060	+	0.851681i
$13$	1.88953	+	3.07078i	0.524060	+	0.851681i
$14$	0.879201	+	0.0178849i	0.234976	+	0.00477994i
$15$		−	2.11037i		−	0.544896i
$16$	−1.67468	−	2.90063i	−0.418670	−	0.725159i
$17$	2.16436	−	3.74877i	0.524933	−	0.909211i	−0.474645	−	0.880177i	$-0.657424\pi$
$17$	2.16436	−	3.74877i	0.524933	−	0.909211i	0.999578	−	0.0290341i	$-0.00924314\pi$
$18$	−0.250102	−	0.144396i	−0.0589496	−	0.0340345i
$19$	−1.69527	+	0.978767i	−0.388923	+	0.224545i	−0.681693	−	0.731638i	$-0.738756\pi$
$19$	−1.69527	+	0.978767i	−0.388923	+	0.224545i	0.292771	+	0.956183i	$0.405423\pi$
$20$		−	2.73154i		−	0.610791i
$21$	3.38349	−	1.86276i	0.738339	−	0.406486i
$22$	−1.97935			−0.421998
$23$	−0.270081	−	0.467795i	−0.0563158	−	0.0975419i	0.836493	−	0.547977i	$-0.184602\pi$
$23$	−0.270081	−	0.467795i	−0.0563158	−	0.0975419i	−0.892809	+	0.450436i	$0.851269\pi$
$24$	1.63441	+	0.943626i	0.333622	+	0.192617i
$25$	−1.45509	+	2.52029i	−0.291018	+	0.504058i
$26$	−1.05422	−	0.569894i	−0.206749	−	0.111765i
$27$	−5.64793			−1.08694
$28$	4.37939	−	2.41104i	0.827627	−	0.455644i
$29$	7.15857			1.32931			0.664656	−	0.747149i	$-0.268578\pi$
$29$	7.15857			1.32931			0.664656	+	0.747149i	$0.268578\pi$
$30$	0.350718	+	0.607461i	0.0640320	+	0.110907i
$31$	−5.28968	−	3.05400i	−0.950055	−	0.548514i	−0.0569568	−	0.998377i	$-0.518140\pi$
$31$	−5.28968	−	3.05400i	−0.950055	−	0.548514i	−0.893098	+	0.449862i	$0.851473\pi$
$32$	3.20327	+	1.84941i	0.566263	+	0.326932i
$33$	−7.52885	+	4.34678i	−1.31060	+	0.756678i
$34$			1.43876i			0.246745i
$35$	3.82396	+	0.0777879i	0.646368	+	0.0131486i
$36$	−1.64176			−0.273627
$37$	6.95316	−	4.01441i	1.14309	−	0.659964i	0.195897	−	0.980624i	$-0.437238\pi$
$37$	6.95316	−	4.01441i	1.14309	−	0.659964i	0.947194	+	0.320660i	$0.103905\pi$
$38$	0.325318	−	0.563467i	0.0527736	−	0.0914065i
$39$	−5.26145	+	0.147426i	−0.842507	+	0.0236071i
$40$	0.934437	+	1.61849i	0.147748	+	0.255906i
$41$			7.55362i			1.17968i	0.807521	+	0.589839i	$0.200809\pi$
$41$			7.55362i			1.17968i	−0.807521	+	0.589839i	$0.799191\pi$
$42$	−0.664356	+	1.09848i	−0.102512	+	0.169499i
$43$	−4.24839			−0.647873			−0.323936	−	0.946079i	$-0.605006\pi$
$43$	−4.24839			−0.647873			−0.323936	+	0.946079i	$0.605006\pi$
$44$	−9.74489	+	5.62622i	−1.46910	+	0.848184i
$45$	−1.08778	−	0.628032i	−0.162157	−	0.0936215i
$46$	0.155483	+	0.0897684i	0.0229248	+	0.0132356i
$47$	5.42204	−	3.13042i	0.790886	−	0.456618i	−0.0493882	−	0.998780i	$-0.515727\pi$
$47$	5.42204	−	3.13042i	0.790886	−	0.456618i	0.840274	+	0.542161i	$0.182394\pi$
$48$	4.88953			0.705742
$49$	3.25057	+	6.19950i	0.464367	+	0.885643i
$50$		−	0.967272i		−	0.136793i
$51$	3.15961	+	5.47260i	0.442434	+	0.766317i
$52$	−6.81011	+	0.190820i	−0.944393	+	0.0264619i
$53$	1.38953	−	2.40673i	0.190866	−	0.330590i	−0.754671	−	0.656103i	$-0.772204\pi$
$53$	1.38953	−	2.40673i	0.190866	−	0.330590i	0.945538	+	0.325513i	$0.105537\pi$
$54$	1.62573	−	0.938616i	0.221234	−	0.127729i
$55$	−8.60891			−1.16082
$56$	−1.77008	+	2.92674i	−0.236537	+	0.391103i
$57$		−	2.85768i		−	0.378509i
$58$	−2.06056	+	1.18967i	−0.270565	+	0.156211i
$59$	0.737119	+	0.425576i	0.0959647	+	0.0554053i	0.547214	−	0.836993i	$-0.315688\pi$
$59$	0.737119	+	0.425576i	0.0959647	+	0.0554053i	−0.451250	+	0.892398i	$0.649022\pi$
$60$	3.45337	+	1.99380i	0.445828	+	0.257399i
$61$	−3.38953	−	5.87083i	−0.433984	−	0.751683i	0.563228	−	0.826302i	$-0.309559\pi$
$61$	−3.38953	−	5.87083i	−0.433984	−	0.751683i	−0.997212	+	0.0746187i	$0.976226\pi$
$62$	2.03015			0.257829
$63$	0.0467536	−	2.29835i	0.00589039	−	0.289565i
$64$	5.46933			0.683667
$65$	−4.58518	−	2.47868i	−0.568721	−	0.307442i
$66$	1.44476	−	2.50240i	0.177838	−	0.308025i
$67$	−0.854859	−	0.493553i	−0.104438	−	0.0602971i	0.446871	−	0.894598i	$-0.352538\pi$
$67$	−0.854859	−	0.493553i	−0.104438	−	0.0602971i	−0.551309	+	0.834301i	$0.685871\pi$
$68$	4.08961	+	7.08341i	0.495938	+	0.858990i
$69$	0.788550			0.0949302
$70$	−1.11364	+	0.613105i	−0.133105	+	0.0732801i
$71$		−	3.76223i		−	0.446494i	−0.974762	−	0.223247i	$-0.928334\pi$
$71$		−	3.76223i		−	0.446494i	0.974762	−	0.223247i	$-0.0716657\pi$
$72$	0.972777	−	0.561633i	0.114643	−	0.0661891i
$73$	7.91131	+	4.56760i	0.925949	+	0.534597i	0.885528	−	0.464586i	$-0.153797\pi$
$73$	7.91131	+	4.56760i	0.925949	+	0.534597i	0.0404208	+	0.999183i	$0.487130\pi$
$74$	−1.33429	+	2.31106i	−0.155108	+	0.268655i
$75$	−2.12419	−	3.67921i	−0.245281	−	0.424839i
$76$		−	3.69881i		−	0.424283i
$77$	−7.59879	−	13.8024i	−0.865963	−	1.57293i
$78$	1.48999	−	0.916825i	0.168708	−	0.103810i
$79$	0.0655625	+	0.113558i	0.00737636	+	0.0127762i	0.869690	−	0.493598i	$-0.164319\pi$
$79$	0.0655625	+	0.113558i	0.00737636	+	0.0127762i	−0.862314	+	0.506375i	$0.830985\pi$
$80$	4.19322	+	2.42096i	0.468816	+	0.270671i
$81$	2.81922	−	4.88303i	0.313246	−	0.542558i
$82$	−1.25532	−	2.17428i	−0.138627	−	0.240109i
$83$		−	2.66812i		−	0.292865i	−0.989221	−	0.146432i	$-0.953221\pi$
$83$		−	2.66812i		−	0.292865i	0.989221	−	0.146432i	$-0.0467791\pi$
$84$	−0.148428	+	7.29653i	−0.0161948	+	0.796117i
$85$			6.25768i			0.678741i
$86$	1.22288	−	0.706030i	0.131866	−	0.0761331i
$87$	−5.22517	+	9.05026i	−0.560197	+	0.970290i
$88$	3.84936	−	6.66729i	0.410344	−	0.710736i
$89$	8.41550	−	4.85869i	0.892042	−	0.515021i	0.0174319	−	0.999848i	$-0.494451\pi$
$89$	8.41550	−	4.85869i	0.892042	−	0.515021i	0.874610	+	0.484828i	$0.161118\pi$
$90$	0.417485			0.0440068
$91$	−0.0731980	−	9.53911i	−0.00767324	−	0.999971i
$92$	1.02065			0.106410
$93$	7.72207	−	4.45834i	0.800742	−	0.462308i
$94$	−1.04047	+	1.80215i	−0.107317	+	0.185878i
$95$	1.41493	−	2.45072i	0.145168	−	0.251439i
$96$	−4.67625	+	2.69983i	−0.477267	+	0.275550i
$97$		−	6.58319i		−	0.668422i	−0.942498	−	0.334211i	$-0.891530\pi$
$97$		−	6.58319i		−	0.668422i	0.942498	−	0.334211i	$-0.108470\pi$
$98$	−1.96594	−	1.24429i	−0.198590	−	0.125693i
$99$			5.17429i			0.520036i
$100$	−2.74943	−	4.76215i	−0.274943	−	0.476215i
$101$	−0.0354144	+	0.0613396i	−0.00352387	+	0.00610352i	−0.867782	−	0.496945i	$-0.834455\pi$
$101$	−0.0354144	+	0.0613396i	−0.00352387	+	0.00610352i	0.864258	+	0.503049i	$0.167788\pi$
$102$	−1.81896	−	1.05018i	−0.180104	−	0.103983i
$103$	3.16910	+	5.48905i	0.312261	+	0.540852i	0.978852	−	0.204572i	$-0.0655803\pi$
$103$	3.16910	+	5.48905i	0.312261	+	0.540852i	−0.666590	+	0.745424i	$0.732247\pi$
$104$	3.96985	−	2.44275i	0.389276	−	0.239531i
$105$	−2.88953	+	4.77769i	−0.281989	+	0.466255i
$106$			0.923689i			0.0897166i
$107$	−3.87476	−	6.71129i	−0.374588	−	0.648805i	0.615678	−	0.787998i	$-0.288882\pi$
$107$	−3.87476	−	6.71129i	−0.374588	−	0.648805i	−0.990265	+	0.139193i	$0.955549\pi$
$108$	5.33596	−	9.24215i	0.513453	−	0.889326i
$109$	−0.0290658	−	0.0167811i	−0.00278400	−	0.00160734i	0.498607	−	0.866828i	$-0.333845\pi$
$109$	−0.0290658	−	0.0167811i	−0.00278400	−	0.00160734i	−0.501391	+	0.865221i	$0.667178\pi$
$110$	2.47804	−	1.43069i	0.236271	−	0.136411i
$111$			11.7208i			1.11249i
$112$	−0.180227	+	8.85975i	−0.0170298	+	0.837168i
$113$	−9.19987			−0.865451			−0.432725	−	0.901526i	$-0.642448\pi$
$113$	−9.19987			−0.865451			−0.432725	+	0.901526i	$0.642448\pi$
$114$	0.474911	+	0.822571i	0.0444795	+	0.0770408i
$115$	0.676254	+	0.390435i	0.0630610	+	0.0364083i
$116$	−6.76315	+	11.7141i	−0.627943	+	1.08763i
$117$	−1.48978	+	2.75587i	−0.137730	+	0.254780i
$118$	−0.282902			−0.0260432
$119$	−10.0327	+	5.52344i	−0.919699	+	0.506333i
$120$	−2.72825			−0.249054
$121$	12.2320	+	21.1864i	1.11200	+	1.92603i
$122$	1.95132	+	1.12660i	0.176664	+	0.101997i
$123$	−9.54971	−	5.51353i	−0.861068	−	0.497138i
$124$	9.99499	−	5.77061i	0.897577	−	0.518216i
$125$		−	11.4351i		−	1.02279i
$126$	0.368500	+	0.669340i	0.0328286	+	0.0596296i
$127$	−14.3952			−1.27737			−0.638683	−	0.769470i	$-0.720520\pi$
$127$	−14.3952			−1.27737			−0.638683	+	0.769470i	$0.720520\pi$
$128$	−7.98085	+	4.60775i	−0.705414	+	0.407271i
$129$	3.10098	−	5.37105i	0.273026	−	0.472895i
$130$	1.73175	−	0.0485237i	0.151884	−	0.00425581i
$131$	4.73414	+	8.19978i	0.413624	+	0.716418i	0.995283	−	0.0970151i	$-0.0309295\pi$
$131$	4.73414	+	8.19978i	0.413624	+	0.716418i	−0.581659	+	0.813433i	$0.697596\pi$
$132$		−	16.4267i		−	1.42976i
$133$	5.17808	+	0.105334i	0.448996	+	0.00913357i
$134$	0.328090			0.0283426
$135$	7.07090	−	4.08238i	0.608566	−	0.351356i
$136$	−4.84635	−	2.79804i	−0.415571	−	0.239930i
$137$	−14.3814	−	8.30313i	−1.22869	−	0.709384i	−0.261934	−	0.965086i	$-0.584360\pi$
$137$	−14.3814	−	8.30313i	−1.22869	−	0.709384i	−0.966756	+	0.255702i	$0.917693\pi$
$138$	−0.226980	+	0.131047i	−0.0193219	+	0.0111555i
$139$	18.4778			1.56726			0.783632	−	0.621225i	$-0.213365\pi$
$139$	18.4778			1.56726			0.783632	+	0.621225i	$0.213365\pi$
$140$	−3.74003	+	6.18396i	−0.316090	+	0.522640i
$141$			9.13980i			0.769710i
$142$	0.625236	+	1.08294i	0.0524687	+	0.0908784i
$143$	0.601400	+	21.4632i	0.0502916	+	1.79484i
$144$	1.45509	−	2.52029i	0.121257	−	0.210024i
$145$	−8.96213	+	5.17429i	−0.744264	+	0.429701i
$146$	−3.03631			−0.251287
$147$	−10.2104	−	0.415577i	−0.842140	−	0.0342762i
$148$			15.1707i			1.24702i
$149$	2.66805	−	1.54040i	0.218575	−	0.126195i	−0.386715	−	0.922199i	$-0.626390\pi$
$149$	2.66805	−	1.54040i	0.218575	−	0.126195i	0.605290	+	0.796005i	$0.293057\pi$
$150$	1.22288	+	0.706030i	0.0998477	+	0.0576471i
$151$	−2.20737	−	1.27442i	−0.179633	−	0.103711i	0.407487	−	0.913211i	$-0.366405\pi$
$151$	−2.20737	−	1.27442i	−0.179633	−	0.103711i	−0.587120	+	0.809500i	$0.699738\pi$
$152$	1.26533	+	2.19162i	0.102632	+	0.177764i
$153$	3.76111			0.304068
$154$	4.48106	+	2.71013i	0.361095	+	0.218388i
$155$	8.82985			0.709231
$156$	4.72958	−	8.74901i	0.378670	−	0.700481i
$157$	4.70452	−	8.14847i	0.375461	−	0.650318i	−0.614935	−	0.788578i	$-0.710818\pi$
$157$	4.70452	−	8.14847i	0.375461	−	0.650318i	0.990396	+	0.138260i	$0.0441509\pi$
$158$	−0.0377438	−	0.0217914i	−0.00300273	−	0.00173363i
$159$	2.02848	+	3.51344i	0.160869	+	0.278634i
$160$	−5.34708			−0.422724
$161$	−0.0290658	+	1.42884i	−0.00229070	+	0.112608i
$162$			1.87408i			0.147241i
$163$	0.602023	−	0.347578i	0.0471541	−	0.0272244i	−0.476238	−	0.879317i	$-0.658000\pi$
$163$	0.602023	−	0.347578i	0.0471541	−	0.0272244i	0.523392	+	0.852092i	$0.324666\pi$
$164$	−12.3606	−	7.13638i	−0.965199	−	0.557258i
$165$	6.28380	−	10.8839i	0.489193	−	0.847308i
$166$	0.443409	+	0.768007i	0.0344152	+	0.0596089i
$167$			13.9840i			1.08211i	0.840986	+	0.541056i	$0.181975\pi$
$167$			13.9840i			1.08211i	−0.840986	+	0.541056i	$0.818025\pi$
$168$	−2.40814	−	4.37412i	−0.185792	−	0.337471i
$169$	−5.85938	+	11.6046i	−0.450721	+	0.892665i
$170$	−1.03995	−	1.80125i	−0.0797605	−	0.138149i
$171$	−1.47298	−	0.850426i	−0.112642	−	0.0650337i
$172$	4.01372	−	6.95197i	0.306043	−	0.530083i
$173$	−2.71824	−	4.70813i	−0.206664	−	0.357952i	0.743998	−	0.668182i	$-0.232927\pi$
$173$	−2.71824	−	4.70813i	−0.206664	−	0.357952i	−0.950662	+	0.310230i	$0.899594\pi$
$174$		−	3.47344i		−	0.263321i
$175$	6.74497	−	3.71339i	0.509872	−	0.280706i
$176$		−	19.9460i		−	1.50349i
$177$	−1.07607	+	0.621272i	−0.0808827	+	0.0466976i
$178$	−1.61491	+	2.79711i	−0.121043	+	0.209652i
$179$	2.67912	−	4.64037i	0.200247	−	0.346838i	−0.748361	−	0.663292i	$-0.769159\pi$
$179$	2.67912	−	4.64037i	0.200247	−	0.346838i	0.948608	+	0.316454i	$0.102492\pi$
$180$	2.05540	−	1.18668i	0.153200	−	0.0884502i
$181$	−7.54016			−0.560456			−0.280228	−	0.959933i	$-0.590410\pi$
$181$	−7.54016			−0.560456			−0.280228	+	0.959933i	$0.590410\pi$
$182$	1.60635	+	2.73363i	0.119071	+	0.202630i
$183$	9.89632			0.731557
$184$	−0.604757	+	0.349157i	−0.0445833	+	0.0257402i
$185$	−5.80331	+	10.0516i	−0.426668	+	0.739011i
$186$	−1.48184	+	2.56663i	−0.108654	+	0.188194i
$187$	22.3245	−	12.8891i	1.63253	−	0.942543i
$188$			11.8300i			0.862793i
$189$	12.7864	+	7.73316i	0.930074	+	0.562504i
$190$			0.940574i			0.0682364i
$191$	−6.77316	−	11.7315i	−0.490089	−	0.848859i	0.509846	−	0.860266i	$-0.329702\pi$
$191$	−6.77316	−	11.7315i	−0.490089	−	0.848859i	−0.999935	+	0.0114067i	$0.996369\pi$
$192$	−3.99217	+	6.91464i	−0.288110	+	0.499021i
$193$	−16.0702	−	9.27812i	−1.15676	−	0.667853i	−0.206232	−	0.978503i	$-0.566120\pi$
$193$	−16.0702	−	9.27812i	−1.15676	−	0.667853i	−0.950524	+	0.310650i	$0.899453\pi$
$194$	1.09405	+	1.89494i	0.0785479	+	0.136049i
$195$	6.48049	−	3.98760i	0.464077	−	0.285558i
$196$	−13.2157	−	0.537898i	−0.943982	−	0.0384213i
$197$			2.66812i			0.190096i	0.995473	+	0.0950480i	$0.0303004\pi$
$197$			2.66812i			0.190096i	−0.995473	+	0.0950480i	$0.969700\pi$
$198$	−0.859903	−	1.48940i	−0.0611106	−	0.105847i
$199$	10.0999	−	17.4936i	0.715965	−	1.24009i	−0.246621	−	0.969112i	$-0.579320\pi$
$199$	10.0999	−	17.4936i	0.715965	−	1.24009i	0.962586	−	0.270976i	$-0.0873465\pi$
$200$	3.25819	+	1.88111i	0.230389	+	0.133015i
$201$	1.24795	−	0.720507i	0.0880239	−	0.0508206i
$202$		−	0.0235418i		−	0.00165639i
$203$	−16.2063	−	9.80152i	−1.13746	−	0.687932i
$204$	−11.9403			−0.835990
$205$	−5.45984	−	9.45672i	−0.381332	−	0.660486i
$206$	−1.82443	−	1.05333i	−0.127114	−	0.0733891i
$207$	0.234667	−	0.406455i	0.0163105	−	0.0282506i
$208$	5.74285	−	10.6234i	0.398195	−	0.736601i
$209$	−11.6574			−0.806361
$210$	0.0377438	−	1.85544i	0.00260457	−	0.128038i
$211$	13.1268			0.903683			0.451842	−	0.892098i	$-0.350767\pi$
$211$	13.1268			0.903683			0.451842	+	0.892098i	$0.350767\pi$
$212$	2.62555	+	4.54758i	0.180323	+	0.312329i
$213$	4.75642	+	2.74612i	0.325905	+	0.188161i
$214$	2.23067	+	1.28788i	0.152485	+	0.0880374i
$215$	5.31875	−	3.07078i	0.362736	−	0.209425i
$216$			7.30155i			0.496807i
$217$	7.79382	+	14.1566i	0.529079	+	0.961014i
$218$	0.0111553			0.000755530
$219$	−11.5492	+	6.66795i	−0.780424	+	0.450578i
$220$	8.13338	−	14.0874i	0.548352	−	0.949774i
$221$	15.6013	−	0.437148i	1.04946	−	0.0294058i
$222$	−1.94785	−	3.37377i	−0.130731	−	0.226433i
$223$			2.22334i			0.148886i	0.997225	+	0.0744428i	$0.0237178\pi$
$223$			2.22334i			0.148886i	−0.997225	+	0.0744428i	$0.976282\pi$
$224$	−4.71969	−	8.57281i	−0.315348	−	0.572795i
$225$	−2.52858			−0.168572
$226$	2.64814	−	1.52890i	0.176152	−	0.101701i
$227$	23.4732	+	13.5523i	1.55797	+	0.899495i	0.997451	+	0.0713539i	$0.0227320\pi$
$227$	23.4732	+	13.5523i	1.55797	+	0.899495i	0.560520	+	0.828141i	$0.310601\pi$
$228$	4.67625	+	2.69983i	0.309692	+	0.178801i
$229$	−16.4447	+	9.49437i	−1.08670	+	0.627406i	−0.932696	−	0.360665i	$-0.882550\pi$
$229$	−16.4447	+	9.49437i	−1.08670	+	0.627406i	−0.154003	+	0.988070i	$0.549217\pi$
$230$	−0.259542			−0.0171137
$231$	22.9962	+	0.467795i	1.51304	+	0.0307786i
$232$		−	9.25447i		−	0.607586i
$233$	10.8700	+	18.8274i	0.712118	+	1.23343i	0.964060	+	0.265683i	$0.0855974\pi$
$233$	10.8700	+	18.8274i	0.712118	+	1.23343i	−0.251942	+	0.967742i	$0.581069\pi$
$234$	−0.0291646	−	1.04085i	−0.00190655	−	0.0680424i
$235$	−4.52540	+	7.83822i	−0.295205	+	0.511309i
$236$	−1.39281	+	0.804137i	−0.0906639	+	0.0523449i
$237$	−0.191421			−0.0124342
$238$	1.96995	−	3.25722i	0.127693	−	0.211134i
$239$		−	19.9695i		−	1.29172i	−0.763455	−	0.645861i	$-0.776499\pi$
$239$		−	19.9695i		−	1.29172i	0.763455	−	0.645861i	$-0.223501\pi$
$240$	−6.12142	+	3.53420i	−0.395136	+	0.228132i
$241$	−2.79768	−	1.61524i	−0.180214	−	0.104047i	0.407179	−	0.913348i	$-0.366513\pi$
$241$	−2.79768	−	1.61524i	−0.180214	−	0.104047i	−0.587393	+	0.809302i	$0.699846\pi$
$242$	−7.04183	−	4.06560i	−0.452666	−	0.261347i
$243$	−4.35630	−	7.54533i	−0.279456	−	0.484033i
$244$	12.8092			0.820025
$245$	−8.55060	−	5.41188i	−0.546278	−	0.345753i
$246$	3.66512			0.233680
$247$	−6.20884	−	3.35641i	−0.395059	−	0.213563i
$248$	−3.94816	+	6.83841i	−0.250708	+	0.434239i
$249$	3.37319	+	1.94751i	0.213767	+	0.123419i
$250$	1.90038	+	3.29155i	0.120190	+	0.208176i
$251$	−12.4916			−0.788466			−0.394233	−	0.919011i	$-0.628990\pi$
$251$	−12.4916			−0.788466			−0.394233	+	0.919011i	$0.628990\pi$
$252$	3.71680	+	2.24790i	0.234136	+	0.141605i
$253$		−	3.21675i		−	0.202236i
$254$	4.14359	−	2.39230i	0.259992	−	0.150106i
$255$	−7.91131	−	4.56760i	−0.495425	−	0.286034i
$256$	−3.93783	+	6.82052i	−0.246114	+	0.426283i
$257$	2.91379	+	5.04682i	0.181757	+	0.314812i	0.942479	−	0.334266i	$-0.108488\pi$
$257$	2.91379	+	5.04682i	0.181757	+	0.314812i	−0.760722	+	0.649078i	$0.775155\pi$
$258$			2.06138i			0.128336i
$259$	−21.2378	−	0.432025i	−1.31966	−	0.0268447i
$260$	8.38796	−	5.16132i	0.520199	−	0.320091i
$261$	3.10995	+	5.38659i	0.192501	+	0.333422i
$262$	−2.72540	−	1.57351i	−0.168376	−	0.0972119i
$263$	−8.75736	+	15.1682i	−0.540002	+	0.935311i	0.458901	+	0.888487i	$0.348243\pi$
$263$	−8.75736	+	15.1682i	−0.540002	+	0.935311i	−0.998903	+	0.0468234i	$0.985090\pi$
$264$	5.61945	+	9.73316i	0.345853	+	0.599035i
$265$			4.01746i			0.246791i
$266$	−1.50799	+	0.830213i	−0.0924609	+	0.0509036i
$267$			14.1858i			0.868157i
$268$	1.61528	−	0.932581i	0.0986688	−	0.0569665i
$269$	−11.1644	+	19.3372i	−0.680703	+	1.17901i	0.294064	+	0.955786i	$0.404992\pi$
$269$	−11.1644	+	19.3372i	−0.680703	+	1.17901i	−0.974767	+	0.223226i	$0.928341\pi$
$270$	−1.35688	+	2.35019i	−0.0825773	+	0.143028i
$271$	−22.8366	+	13.1847i	−1.38723	+	0.800916i	−0.993002	−	0.118098i	$-0.962320\pi$
$271$	−22.8366	+	13.1847i	−1.38723	+	0.800916i	−0.394225	+	0.919014i	$0.628987\pi$
$272$	−14.4984			−0.879097
$273$	12.1133	+	6.87023i	0.733131	+	0.415805i
$274$	5.51951			0.333446
$275$	−15.0087	+	8.66529i	−0.905060	+	0.522536i
$276$	−0.744993	+	1.29037i	−0.0448433	+	0.0776709i
$277$	−4.68809	+	8.12001i	−0.281680	+	0.487884i	−0.971799	−	0.235812i	$-0.924225\pi$
$277$	−4.68809	+	8.12001i	−0.281680	+	0.487884i	0.690119	+	0.723696i	$0.257558\pi$
$278$	−5.31875	+	3.07078i	−0.318997	+	0.184173i
$279$		−	5.30709i		−	0.317727i
$280$	0.100563	−	4.94356i	0.00600978	−	0.295434i
$281$		−	17.7754i		−	1.06039i	−0.847876	−	0.530195i	$-0.822119\pi$
$281$		−	17.7754i		−	1.06039i	0.847876	−	0.530195i	$-0.177881\pi$
$282$	−1.51892	−	2.63085i	−0.0904505	−	0.156665i
$283$	−4.80331	+	8.31958i	−0.285527	+	0.494548i	−0.972737	−	0.231911i	$-0.925502\pi$
$283$	−4.80331	+	8.31958i	−0.285527	+	0.494548i	0.687210	+	0.726459i	$0.258835\pi$
$284$	6.15643	+	3.55442i	0.365317	+	0.210916i
$285$	2.06556	+	3.57766i	0.122353	+	0.211922i
$286$	−3.74003	−	6.07814i	−0.221153	−	0.359408i
$287$	10.3424	−	17.1007i	0.610494	−	1.00942i
$288$			3.21380i			0.189375i
$289$	−0.868875	−	1.50494i	−0.0511103	−	0.0885256i
$290$	1.71981	−	2.97879i	0.100990	−	0.174921i
$291$	8.32284	+	4.80519i	0.487894	+	0.281685i
$292$	−14.9486	+	8.63060i	−0.874803	+	0.505067i
$293$		−	11.6338i		−	0.679654i	−0.940488	−	0.339827i	$-0.889631\pi$
$293$		−	11.6338i		−	0.679654i	0.940488	−	0.339827i	$-0.110369\pi$
$294$	3.00808	−	1.57722i	0.175435	−	0.0919855i
$295$	−1.23044			−0.0716392
$296$	−5.18976	−	8.98892i	−0.301648	−	0.522470i
$297$	−29.1282	−	16.8172i	−1.69019	−	0.975830i
$298$	−0.511991	+	0.886795i	−0.0296588	+	0.0513706i
$299$	0.926168	−	1.71327i	0.0535617	−	0.0990810i
$300$	8.02744			0.463464
$301$	9.61796	+	5.81690i	0.554370	+	0.335281i
$302$	0.847174			0.0487494
$303$	−0.0516993	−	0.0895459i	−0.00297005	−	0.00514427i
$304$	5.67809	+	3.27825i	0.325661	+	0.188020i
$305$	8.48700	+	4.89997i	0.485964	+	0.280572i
$306$	−1.08262	+	0.625050i	−0.0618892	+	0.0357317i
$307$			13.8280i			0.789204i	0.918852	+	0.394602i	$0.129118\pi$
$307$			13.8280i			0.789204i	−0.918852	+	0.394602i	$0.870882\pi$
$308$	29.7650	+	0.605485i	1.69602	+	0.0345007i
$309$	−9.25275			−0.526371
$310$	−2.54163	+	1.46741i	−0.144355	+	0.0833435i
$311$	15.3572	−	26.5994i	0.870827	−	1.50832i	0.00968369	−	0.999953i	$-0.496918\pi$
$311$	15.3572	−	26.5994i	0.870827	−	1.50832i	0.861143	−	0.508363i	$-0.169749\pi$
$312$	0.190590	+	6.80192i	0.0107900	+	0.385083i
$313$	−5.54334	−	9.60135i	−0.313328	−	0.542701i	0.665752	−	0.746173i	$-0.268111\pi$
$313$	−5.54334	−	9.60135i	−0.313328	−	0.542701i	−0.979081	+	0.203472i	$0.934777\pi$
$314$			3.12733i			0.176486i
$315$	1.60274	+	2.91120i	0.0903042	+	0.164028i
$316$	−0.247764			−0.0139378
$317$	20.6836	−	11.9417i	1.16171	−	0.670712i	0.209994	−	0.977703i	$-0.432656\pi$
$317$	20.6836	−	11.9417i	1.16171	−	0.670712i	0.951712	+	0.306991i	$0.0993222\pi$
$318$	−1.16778	−	0.674218i	−0.0654858	−	0.0378083i
$319$	36.9190	+	21.3152i	2.06707	+	1.19342i
$320$	−6.84731	+	3.95329i	−0.382776	+	0.220996i
$321$	11.3130			0.631433
$322$	−0.229089	−	0.416116i	−0.0127666	−	0.0231892i
$323$			8.47360i			0.471484i
$324$	5.32698	+	9.22661i	0.295944	+	0.512589i
$325$	−10.4887	+	0.293893i	−0.581807	+	0.0163023i
$326$	−0.115526	+	0.200098i	−0.00639842	+	0.0110824i
$327$	0.0424313	−	0.0244977i	0.00234646	−	0.00135473i
$328$	9.76519			0.539192
$329$	−16.5612	−	0.336891i	−0.913048	−	0.0185734i
$330$			4.17716i			0.229945i
$331$	15.8690	−	9.16200i	0.872241	−	0.503589i	0.00414903	−	0.999991i	$-0.498679\pi$
$331$	15.8690	−	9.16200i	0.872241	−	0.503589i	0.868092	+	0.496403i	$0.165346\pi$
$332$	4.36606	+	2.52075i	0.239619	+	0.138344i
$333$	6.04142	+	3.48802i	0.331068	+	0.191142i
$334$	−2.32396	−	4.02522i	−0.127162	−	0.220250i
$335$	1.42698			0.0779643
$336$	−11.0694	−	6.69475i	−0.603888	−	0.365229i
$337$	7.21762			0.393169			0.196584	−	0.980487i	$-0.437015\pi$
$337$	7.21762			0.393169			0.196584	+	0.980487i	$0.437015\pi$
$338$	−0.241953	−	4.31410i	−0.0131605	−	0.234656i
$339$	6.71516	−	11.6310i	0.364717	−	0.631709i
$340$	−10.2399	−	5.91203i	−0.555338	−	0.320625i
$341$	−18.1870	−	31.5009i	−0.984884	−	1.70587i
$342$	0.565321			0.0305691
$343$	1.12937	−	18.4858i	0.0609804	−	0.998139i
$344$			5.49224i			0.296122i
$345$	−0.987221	+	0.569972i	−0.0531502	+	0.0306863i
$346$	1.56487	+	0.903476i	0.0841277	+	0.0485712i
$347$	10.5391	−	18.2543i	0.565770	−	0.979942i	−0.431208	−	0.902253i	$-0.641912\pi$
$347$	10.5391	−	18.2543i	0.565770	−	0.979942i	0.996978	−	0.0776892i	$-0.0247542\pi$
$348$	−9.87310	−	17.1007i	−0.529254	−	0.916694i
$349$		−	30.7629i		−	1.64670i	−0.567534	−	0.823350i	$-0.692102\pi$
$349$		−	30.7629i		−	1.64670i	0.567534	−	0.823350i	$-0.307898\pi$
$350$	−1.32439	+	2.18982i	−0.0707917	+	0.117051i
$351$	−10.6719	−	17.3435i	−0.569624	−	0.925730i
$352$	11.0135	+	19.0760i	0.587022	+	1.01675i
$353$	5.30157	+	3.06086i	0.282174	+	0.162913i	0.634407	−	0.772999i	$-0.281244\pi$
$353$	5.30157	+	3.06086i	0.282174	+	0.162913i	−0.352233	+	0.935912i	$0.614578\pi$
$354$	0.206495	−	0.357660i	0.0109751	−	0.0190094i
$355$	2.71938	+	4.71010i	0.144330	+	0.249986i
$356$			18.3613i			0.973145i
$357$	0.340033	−	16.7156i	0.0179964	−	0.884684i
$358$			1.78095i			0.0941259i
$359$	−16.8257	+	9.71433i	−0.888028	+	0.512703i	−0.873297	−	0.487189i	$-0.838022\pi$
$359$	−16.8257	+	9.71433i	−0.888028	+	0.512703i	−0.0147308	+	0.999891i	$0.504689\pi$
$360$	−0.811909	+	1.40627i	−0.0427914	+	0.0741168i
$361$	−7.58403	+	13.1359i	−0.399160	+	0.691365i
$362$	2.17040	−	1.25308i	0.114074	−	0.0658605i
$363$	−35.7133			−1.87446
$364$	15.6787	+	8.89242i	0.821790	+	0.466090i
$365$	−13.2060			−0.691235
$366$	−2.84861	+	1.64465i	−0.148899	+	0.0859670i
$367$	2.70234	−	4.68058i	0.141061	−	0.244324i	−0.786836	−	0.617163i	$-0.788282\pi$
$367$	2.70234	−	4.68058i	0.141061	−	0.244324i	0.927896	+	0.372838i	$0.121615\pi$
$368$	−0.904601	+	1.56681i	−0.0471556	+	0.0816758i
$369$	−5.68385	+	3.28158i	−0.295890	+	0.170832i
$370$		−	3.85776i		−	0.200555i
$371$	−6.44106	+	3.54608i	−0.334403	+	0.184103i
$372$			16.8483i			0.873544i
$373$	−8.12533	−	14.0735i	−0.420714	−	0.728698i	0.575296	−	0.817946i	$-0.304887\pi$
$373$	−8.12533	−	14.0735i	−0.420714	−	0.728698i	−0.996009	+	0.0892478i	$0.971554\pi$
$374$	−4.28401	+	7.42013i	−0.221521	+	0.383686i
$375$	14.4569	+	8.34671i	0.746553	+	0.431022i
$376$	−4.04695	−	7.00952i	−0.208706	−	0.361489i
$377$	13.5263	+	21.9824i	0.696640	+	1.13215i
$378$	−4.96566	−	0.101013i	−0.255406	−	0.00519553i
$379$		−	25.1730i		−	1.29305i	−0.762893	−	0.646525i	$-0.776222\pi$
$379$		−	25.1730i		−	1.29305i	0.762893	−	0.646525i	$-0.223778\pi$
$380$	2.67354	+	4.63071i	0.137150	+	0.237550i
$381$	10.5073	−	18.1992i	0.538306	−	0.932373i
$382$	3.89925	+	2.25123i	0.199503	+	0.115183i
$383$	−3.30335	+	1.90719i	−0.168793	+	0.0974529i	−0.582017	−	0.813177i	$-0.697736\pi$
$383$	−3.30335	+	1.90719i	−0.168793	+	0.0974529i	0.413223	+	0.910630i	$0.364403\pi$
$384$		−	13.4531i		−	0.686527i
$385$	19.4898	+	11.7873i	0.993291	+	0.600738i
$386$	6.16764			0.313924
$387$	−1.84566	−	3.19677i	−0.0938201	−	0.162501i
$388$	10.7726	+	6.21956i	0.546895	+	0.315750i
$389$	−1.43548	+	2.48632i	−0.0727817	+	0.126062i	−0.900119	−	0.435643i	$-0.856521\pi$
$389$	−1.43548	+	2.48632i	−0.0727817	+	0.126062i	0.827338	+	0.561705i	$0.189854\pi$
$390$	−1.20269	+	2.22479i	−0.0609005	+	0.112657i
$391$	−2.33821			−0.118248
$392$	8.01461	−	4.20228i	0.404799	−	0.212247i
$393$	−13.8222			−0.697236
$394$	−0.443409	−	0.768007i	−0.0223386	−	0.0386917i
$395$	−0.164161	−	0.0947786i	−0.00825986	−	0.00476883i
$396$	−8.46709	−	4.88848i	−0.425487	−	0.245655i
$397$	−16.5570	+	9.55919i	−0.830972	+	0.479762i	−0.854185	−	0.519968i	$-0.825944\pi$
$397$	−16.5570	+	9.55919i	−0.830972	+	0.479762i	0.0232131	+	0.999731i	$0.492610\pi$
$398$			6.71394i			0.336539i
$399$	−3.91274	+	6.46953i	−0.195882	+	0.323882i
$400$	9.74725			0.487362
$401$	2.59655	−	1.49912i	0.129666	−	0.0748625i	−0.433764	−	0.901026i	$-0.642815\pi$
$401$	2.59655	−	1.49912i	0.129666	−	0.0748625i	0.563430	+	0.826164i	$0.309482\pi$
$402$	−0.239479	+	0.414789i	−0.0119441	+	0.0206878i
$403$	−0.616835	−	22.0141i	−0.0307267	−	1.09660i
$404$	−0.0669165	−	0.115903i	−0.00332922	−	0.00576638i
$405$			8.15104i			0.405028i
$406$	6.29382	+	0.128030i	0.312357	+	0.00635403i
$407$	47.8129			2.37000
$408$	7.07489	−	4.08469i	0.350259	−	0.202222i
$409$	−29.5146	−	17.0403i	−1.45940	−	0.842587i	−0.460422	−	0.887700i	$-0.652302\pi$
$409$	−29.5146	−	17.0403i	−1.45940	−	0.842587i	−0.998982	+	0.0451127i	$0.985635\pi$
$410$	3.14318	+	1.81472i	0.155231	+	0.0896224i
$411$	20.9946	−	12.1212i	1.03559	−	0.597896i
$412$	−11.9762			−0.590026
$413$	−1.08607	−	1.97273i	−0.0534421	−	0.0970717i
$414$			0.155995i			0.00766674i
$415$	1.92855	+	3.34034i	0.0946687	+	0.163971i
$416$	0.373536	+	13.3310i	0.0183141	+	0.653607i
$417$	−13.4873	+	23.3606i	−0.660475	+	1.14398i
$418$	3.35554	−	1.93732i	0.164125	−	0.0947574i
$419$	34.7759			1.69891			0.849457	−	0.527657i	$-0.176929\pi$
$419$	34.7759			1.69891			0.849457	+	0.527657i	$0.176929\pi$
$420$	−5.08819	−	9.24215i	−0.248278	−	0.450971i
$421$			24.1400i			1.17651i	0.808674	+	0.588257i	$0.200186\pi$
$421$			24.1400i			1.17651i	−0.808674	+	0.588257i	$0.799814\pi$
$422$	−3.77848	+	2.18151i	−0.183933	+	0.106194i
$423$	4.71108	+	2.71994i	0.229060	+	0.132248i
$424$	−3.11138	−	1.79636i	−0.151102	−	0.0872388i
$425$	6.29866	+	10.9096i	0.305530	+	0.529193i
$426$	−1.82549			−0.0884451
$427$	−0.364776	+	17.9320i	−0.0176528	+	0.867789i
$428$	14.6429			0.707793
$429$	−27.5740	−	14.9061i	−1.33128	−	0.719672i
$430$	−1.02065	+	1.76782i	−0.0492202	+	0.0852519i
$431$	−4.12641	−	2.38238i	−0.198762	−	0.114755i	0.397316	−	0.917682i	$-0.369942\pi$
$431$	−4.12641	−	2.38238i	−0.198762	−	0.114755i	−0.596078	+	0.802927i	$0.703275\pi$
$432$	9.45848	+	16.3826i	0.455071	+	0.788207i
$433$	−22.0231			−1.05836			−0.529181	−	0.848509i	$-0.677501\pi$
$433$	−22.0231			−1.05836			−0.529181	+	0.848509i	$0.677501\pi$
$434$	−4.59607	−	2.77968i	−0.220618	−	0.133429i
$435$		−	15.1072i		−	0.724337i
$436$	0.0549206	−	0.0317084i	0.00263022	−	0.00151856i
$437$	0.915724	+	0.528693i	0.0438050	+	0.0252908i
$438$	2.21626	−	3.83868i	0.105897	−	0.183419i
$439$	1.71620	+	2.97254i	0.0819097	+	0.141872i	0.904070	−	0.427384i	$-0.140565\pi$
$439$	1.71620	+	2.97254i	0.0819097	+	0.141872i	−0.822161	+	0.569256i	$0.807231\pi$
$440$			11.1294i			0.530576i
$441$	−3.25275	+	5.13924i	−0.154893	+	0.244726i
$442$	−4.41811	+	2.71857i	−0.210148	+	0.129309i
$443$	4.35297	+	7.53957i	0.206816	+	0.358216i	0.950710	−	0.310082i	$-0.100357\pi$
$443$	4.35297	+	7.53957i	0.206816	+	0.358216i	−0.743894	+	0.668298i	$0.767023\pi$
$444$	−19.1796	−	11.0733i	−0.910223	−	0.525518i
$445$	−7.02383	+	12.1656i	−0.332962	+	0.576706i
$446$	−0.369491	−	0.639977i	−0.0174959	−	0.0303038i
$447$			4.49747i			0.212723i
$448$	−12.3821	−	7.48862i	−0.584998	−	0.353804i
$449$		−	17.6120i		−	0.831159i	−0.909557	−	0.415580i	$-0.863579\pi$
$449$		−	17.6120i		−	0.831159i	0.909557	−	0.415580i	$-0.136421\pi$
$450$	0.727841	−	0.420219i	0.0343107	−	0.0198093i
$451$	−22.4915	+	38.9564i	−1.05908	+	1.83439i
$452$	8.69170	−	15.0545i	0.408823	−	0.708102i
$453$	3.22240	−	1.86045i	0.151401	−	0.0874116i
$454$	−9.00887			−0.422807
$455$	6.98661	+	11.8895i	0.327537	+	0.557390i
$456$	−3.69436			−0.173004
$457$	−7.85717	+	4.53634i	−0.367543	+	0.212201i	−0.672384	−	0.740202i	$-0.734730\pi$
$457$	−7.85717	+	4.53634i	−0.367543	+	0.212201i	0.304842	+	0.952403i	$0.401396\pi$
$458$	3.15570	−	5.46583i	0.147456	−	0.255401i
$459$	−12.2241	+	21.1728i	−0.570573	+	0.988262i
$460$	−1.27780	+	0.737738i	−0.0595777	+	0.0343972i
$461$			6.58319i			0.306610i	0.988179	+	0.153305i	$0.0489917\pi$
$461$			6.58319i			0.306610i	−0.988179	+	0.153305i	$0.951008\pi$
$462$	−6.69711	+	3.68704i	−0.311578	+	0.171537i
$463$		−	3.47344i		−	0.161424i	−0.996737	−	0.0807121i	$-0.974281\pi$
$463$		−	3.47344i		−	0.161424i	0.996737	−	0.0807121i	$-0.0257194\pi$
$464$	−11.9883	−	20.7644i	−0.556544	−	0.963962i
$465$	−6.44507	+	11.1632i	−0.298883	+	0.517681i
$466$	−6.25777	−	3.61293i	−0.289886	−	0.167366i
$467$	14.8927	+	25.7949i	0.689152	+	1.19365i	0.972112	+	0.234515i	$0.0753502\pi$
$467$	14.8927	+	25.7949i	0.689152	+	1.19365i	−0.282960	+	0.959132i	$0.591316\pi$
$468$	−3.10215	−	5.04149i	−0.143397	−	0.233043i
$469$	1.25955	+	2.28783i	0.0581606	+	0.105642i
$470$		−	3.00826i		−	0.138761i
$471$	6.86783	+	11.8954i	0.316453	+	0.548113i
$472$	0.550177	−	0.952935i	0.0253240	−	0.0438624i
$473$	−21.9103	−	12.6499i	−1.00744	−	0.581643i
$474$	0.0550998	−	0.0318119i	0.00253082	−	0.00146117i
$475$		−	5.69677i		−	0.261386i
$476$	0.440118	−	21.6357i	0.0201728	−	0.991671i
$477$	2.41465			0.110559
$478$	3.31869	+	5.74814i	0.151793	+	0.262914i
$479$	30.4715	+	17.5927i	1.39228	+	0.803833i	0.993567	−	0.113243i	$-0.0361240\pi$
$479$	30.4715	+	17.5927i	1.39228	+	0.803833i	0.398712	+	0.917076i	$0.369457\pi$
$480$	3.90294	−	6.76008i	0.178144	−	0.308554i
$481$	25.4655	+	13.7663i	1.16113	+	0.627688i
$482$	1.07373			0.0489072
$483$	−1.78520	−	1.07968i	−0.0812296	−	0.0491273i
$484$	−46.2252			−2.10115
$485$	4.75840	+	8.24179i	0.216068	+	0.374241i
$486$	2.50788	+	1.44793i	0.113760	+	0.0656792i
$487$	1.56018	+	0.900769i	0.0706984	+	0.0408178i	0.534933	−	0.844895i	$-0.320337\pi$
$487$	1.56018	+	0.900769i	0.0706984	+	0.0408178i	−0.464234	+	0.885713i	$0.653670\pi$
$488$	−7.58971	+	4.38192i	−0.343570	+	0.198360i
$489$			1.01482i			0.0458916i
$490$	3.36064	+	0.136782i	0.151818	+	0.00617920i
$491$	8.19322			0.369755			0.184877	−	0.982762i	$-0.440811\pi$
$491$	8.19322			0.369755			0.184877	+	0.982762i	$0.440811\pi$
$492$	18.0444	−	10.4180i	0.813506	−	0.469678i
$493$	15.4937	−	26.8358i	0.697800	−	1.20863i
$494$	2.34498	−	0.0657065i	0.105506	−	0.00295627i
$495$	−3.74003	−	6.47792i	−0.168102	−	0.291161i
$496$			20.4579i			0.918587i
$497$	−5.15125	+	8.51734i	−0.231065	+	0.382055i
$498$	−1.29461			−0.0580129
$499$	−31.6242	+	18.2582i	−1.41569	+	0.817350i	−0.995917	−	0.0902781i	$-0.971224\pi$
$499$	−31.6242	+	18.2582i	−1.41569	+	0.817350i	−0.419775	+	0.907628i	$0.637891\pi$
$500$	18.7122	+	10.8035i	0.836834	+	0.483147i
$501$	−17.6793	−	10.2072i	−0.789854	−	0.456022i
$502$	3.59566	−	2.07596i	0.160482	−	0.0926545i
$503$	−3.02972			−0.135089			−0.0675443	−	0.997716i	$-0.521516\pi$
$503$	−3.02972			−0.135089			−0.0675443	+	0.997716i	$0.521516\pi$
$504$	−2.97127	−	0.0604422i	−0.132351	−	0.00269231i
$505$		−	0.102392i		−	0.00455637i
$506$	0.534585	+	0.925928i	0.0237652	+	0.0411625i
$507$	−10.3944	−	15.8782i	−0.461630	−	0.705176i
$508$	13.6000	−	23.5559i	0.603404	−	1.04513i
$509$	25.4133	−	14.6724i	1.12642	−	0.650341i	0.183391	−	0.983040i	$-0.441293\pi$
$509$	25.4133	−	14.6724i	1.12642	−	0.650341i	0.943033	+	0.332699i	$0.107959\pi$
$510$	3.03631			0.134450
$511$	−11.6565	−	21.1728i	−0.515654	−	0.936630i
$512$		−	21.0487i		−	0.930229i
$513$	9.57479	−	5.52800i	0.422737	−	0.244067i
$514$	−1.67744	−	0.968471i	−0.0739887	−	0.0427174i
$515$	−7.93509	−	4.58133i	−0.349662	−	0.201877i
$516$	5.85938	+	10.1487i	0.257945	+	0.446773i
$517$	37.2843			1.63976
$518$	6.18502	−	3.40511i	0.271754	−	0.149612i
$519$	7.93637			0.348368
$520$	−3.20439	+	5.92764i	−0.140522	+	0.259944i
$521$	14.8419	−	25.7069i	0.650236	−	1.12624i	−0.332830	−	0.942987i	$-0.608003\pi$
$521$	14.8419	−	25.7069i	0.650236	−	1.12624i	0.983066	−	0.183254i	$-0.0586632\pi$
$522$	−1.79037	−	1.03367i	−0.0783624	−	0.0452425i
$523$	−10.2864	−	17.8165i	−0.449791	−	0.779062i	0.548581	−	0.836098i	$-0.315168\pi$
$523$	−10.2864	−	17.8165i	−0.449791	−	0.779062i	−0.998372	+	0.0570361i	$0.981835\pi$
$524$	−17.8906			−0.781553
$525$	−0.228603	+	11.2379i	−0.00997704	+	0.490460i
$526$		−	5.82146i		−	0.253828i
$527$	−22.8975	+	13.2199i	−0.997431	+	0.575867i
$528$	25.2168	+	14.5590i	1.09742	+	0.633597i
$529$	11.3541	−	19.6659i	0.493657	−	0.855039i
$530$	−0.667652	−	1.15641i	−0.0290010	−	0.0502311i
$531$			0.739544i			0.0320935i
$532$	−5.06442	+	8.37377i	−0.219571	+	0.363049i
$533$	−23.1955	+	14.2728i	−1.00471	+	0.618222i
$534$	−2.35751	−	4.08332i	−0.102019	−	0.176703i
$535$	9.70198	+	5.60144i	0.419453	+	0.242171i
$536$	−0.638057	+	1.10515i	−0.0275599	+	0.0477351i
$537$	3.91108	+	6.77419i	0.168775	+	0.292328i
$538$		−	7.42151i		−	0.319964i
$539$	−1.69527	+	41.6516i	−0.0730206	+	1.79406i
$540$			15.4275i			0.663896i
$541$	29.5027	−	17.0334i	1.26842	−	0.732324i	0.293732	−	0.955888i	$-0.405103\pi$
$541$	29.5027	−	17.0334i	1.26842	−	0.732324i	0.974689	+	0.223564i	$0.0717692\pi$
$542$	4.38228	−	7.59034i	0.188235	−	0.326033i
$543$	5.50371	−	9.53270i	0.236187	−	0.409087i
$544$	13.8660	−	8.00555i	0.594500	−	0.343235i
$545$	0.0485183			0.00207830
$546$	−4.62851	+	0.0355167i	−0.198082	+	0.00151997i
$547$	−0.850931			−0.0363832			−0.0181916	−	0.999835i	$-0.505791\pi$
$547$	−0.850931			−0.0363832			−0.0181916	+	0.999835i	$0.505791\pi$
$548$	27.1741	−	15.6890i	1.16082	−	0.670200i
$549$	2.94507	−	5.10102i	0.125693	−	0.217706i
$550$	2.88013	−	4.98853i	0.122809	−	0.212712i
$551$	−12.1357	+	7.00657i	−0.516999	+	0.298490i
$552$		−	1.01942i		−	0.0433895i
$553$	0.00705575	−	0.346853i	0.000300041	−	0.0147497i
$554$		−	3.11641i		−	0.132404i
$555$	−8.47189	−	14.6737i	−0.359612	−	0.622866i
$556$	−17.4571	+	30.2366i	−0.740347	+	1.28232i
$557$	15.3530	+	8.86404i	0.650526	+	0.375581i	0.788658	−	0.614833i	$-0.210776\pi$
$557$	15.3530	+	8.86404i	0.650526	+	0.375581i	−0.138132	+	0.990414i	$0.544110\pi$
$558$	0.881972	+	1.52762i	0.0373369	+	0.0646694i
$559$	−8.02744	−	13.0459i	−0.339525	−	0.551781i
$560$	−6.17829	−	11.2222i	−0.261080	−	0.474224i
$561$			37.6319i			1.58882i
$562$	2.95405	+	5.11656i	0.124609	+	0.215829i
$563$	−12.0903	+	20.9410i	−0.509545	+	0.882558i	0.490394	+	0.871501i	$0.336853\pi$
$563$	−12.0903	+	20.9410i	−0.509545	+	0.882558i	−0.999939	+	0.0110571i	$0.996480\pi$
$564$	−14.9562	−	8.63495i	−0.629768	−	0.363597i
$565$	11.5177	−	6.64976i	0.484555	−	0.279758i
$566$		−	3.19301i		−	0.134212i
$567$	−13.0683	+	7.19465i	−0.548817	+	0.302147i
$568$	−4.86375			−0.204078
$569$	−21.3874	−	37.0441i	−0.896608	−	1.55297i	−0.831802	−	0.555073i	$-0.812690\pi$
$569$	−21.3874	−	37.0441i	−0.896608	−	1.55297i	−0.0648066	−	0.997898i	$-0.520643\pi$
$570$	−1.18913	−	0.686542i	−0.0498070	−	0.0287561i
$571$	3.68140	−	6.37637i	0.154062	−	0.266843i	−0.778655	−	0.627452i	$-0.784098\pi$
$571$	3.68140	−	6.37637i	0.154062	−	0.266843i	0.932717	+	0.360609i	$0.117431\pi$
$572$	−35.6901	−	19.2935i	−1.49228	−	0.806703i
$573$	19.7754			0.826131
$574$	−0.135096	+	6.64115i	−0.00563878	+	0.277196i
$575$	1.57197			0.0655557
$576$	2.37608	+	4.11550i	0.0990035	+	0.171479i
$577$	−7.09615	−	4.09696i	−0.295417	−	0.170559i	0.344965	−	0.938615i	$-0.387891\pi$
$577$	−7.09615	−	4.09696i	−0.295417	−	0.170559i	−0.640382	+	0.768057i	$0.721224\pi$
$578$	0.500204	+	0.288793i	0.0208057	+	0.0120122i
$579$	23.4598	−	13.5445i	0.974957	−	0.562892i
$580$		−	19.5539i		−	0.811932i
$581$	−3.65320	+	6.04039i	−0.151560	+	0.250598i
$582$	−3.19426			−0.132406
$583$	14.3325	−	8.27485i	0.593590	−	0.342709i
$584$	5.90491	−	10.2276i	0.244347	−	0.423221i
$585$	−0.126848	−	4.52703i	−0.00524450	−	0.187170i
$586$	1.93339	+	3.34874i	0.0798678	+	0.138335i
$587$		−	39.1141i		−	1.61441i	−0.590271	−	0.807205i	$-0.700979\pi$
$587$		−	39.1141i		−	1.61441i	0.590271	−	0.807205i	$-0.299021\pi$
$588$	10.3265	−	16.3155i	0.425856	−	0.672838i
$589$	11.9566			0.492664
$590$	0.354178	−	0.204485i	0.0145813	−	0.00841849i
$591$	−3.37319	−	1.94751i	−0.138755	−	0.0801100i
$592$	−23.2886	−	13.4457i	−0.957158	−	0.552615i
$593$	−1.05082	+	0.606691i	−0.0431520	+	0.0249138i	−0.521421	−	0.853300i	$-0.674598\pi$
$593$	−1.05082	+	0.606691i	−0.0431520	+	0.0249138i	0.478269	+	0.878213i	$0.341264\pi$
$594$	11.1792			0.458689
$595$	8.56803	−	14.1668i	0.351255	−	0.580783i
$596$			5.82125i			0.238448i
$597$	14.7443	+	25.5378i	0.603442	+	1.04519i
$598$	0.0181311	+	0.647075i	0.000741435	+	0.0264609i
$599$	−16.3319	+	28.2877i	−0.667303	+	1.15580i	0.311352	+	0.950295i	$0.399218\pi$
$599$	−16.3319	+	28.2877i	−0.667303	+	1.15580i	−0.978655	+	0.205508i	$0.934115\pi$
$600$	−4.75642	+	2.74612i	−0.194180	+	0.112110i
$601$	2.50114			0.102024			0.0510118	−	0.998698i	$-0.483755\pi$
$601$	2.50114			0.102024			0.0510118	+	0.998698i	$0.483755\pi$
$602$	−3.73519	−	0.0759819i	−0.152235	−	0.00309679i
$603$		−	0.857671i		−	0.0349271i
$604$	4.17088	−	2.40806i	0.169711	−	0.0979825i
$605$	−30.6275	−	17.6828i	−1.24518	−	0.718907i
$606$	0.0297628	+	0.0171836i	0.00120903	+	0.000698035i
$607$	−6.32282	−	10.9515i	−0.256635	−	0.444506i	0.708703	−	0.705507i	$-0.249281\pi$
$607$	−6.32282	−	10.9515i	−0.256635	−	0.444506i	−0.965338	+	0.261001i	$0.915947\pi$
$608$	−7.24055			−0.293643
$609$	24.2209	−	13.3347i	0.981482	−	0.540347i
$610$	−3.25726			−0.131883
$611$	19.8579	+	10.7349i	0.803365	+	0.434287i
$612$	−3.55336	+	6.15460i	−0.143636	+	0.248785i
$613$	17.3448	+	10.0140i	0.700548	+	0.404462i	0.807552	−	0.589797i	$-0.200792\pi$
$613$	17.3448	+	10.0140i	0.700548	+	0.404462i	−0.107003	+	0.994259i	$0.534126\pi$
$614$	−2.29804	−	3.98032i	−0.0927413	−	0.160633i
$615$	15.9409			0.642801
$616$	−17.8435	+	9.82359i	−0.718934	+	0.395804i
$617$			45.2926i			1.82341i	0.410846	+	0.911705i	$0.365233\pi$
$617$			45.2926i			1.82341i	−0.410846	+	0.911705i	$0.634767\pi$
$618$	2.66336	−	1.53769i	0.107136	−	0.0618551i
$619$	3.83922	+	2.21658i	0.154311	+	0.0890917i	0.575167	−	0.818036i	$-0.304937\pi$
$619$	3.83922	+	2.21658i	0.154311	+	0.0890917i	−0.420856	+	0.907127i	$0.638270\pi$
$620$	−8.34212	+	14.4490i	−0.335028	+	0.580285i
$621$	1.52540	+	2.64207i	0.0612122	+	0.106023i
$622$			10.2087i			0.409332i
$623$	−25.7045	−	0.522886i	−1.02983	−	0.0209490i
$624$	9.23889	+	15.0147i	0.369852	+	0.601067i
$625$	0.989985	+	1.71471i	0.0395994	+	0.0685882i
$626$	3.19125	+	1.84247i	0.127548	+	0.0736400i
$627$	8.50897	−	14.7380i	0.339816	−	0.588578i
$628$	8.88931	+	15.3967i	0.354722	+	0.614397i
$629$		−	34.7544i		−	1.38575i
$630$	−0.945148	−	0.571621i	−0.0376556	−	0.0227739i
$631$			19.7358i			0.785672i	0.919609	+	0.392836i	$0.128506\pi$
$631$			19.7358i			0.785672i	−0.919609	+	0.392836i	$0.871494\pi$
$632$	0.146805	−	0.0847581i	0.00583961	−	0.00337150i
$633$	−9.58147	+	16.5956i	−0.380829	+	0.659615i
$634$	−3.96912	+	6.87472i	−0.157634	+	0.273030i
$635$	18.0220	−	10.4050i	0.715180	−	0.412909i
$636$	−7.66574			−0.303967
$637$	−12.8953	+	21.6959i	−0.510929	+	0.859623i
$638$	−14.1693			−0.560968
$639$	2.83096	−	1.63445i	0.111991	−	0.0646580i
$640$	6.66106	−	11.5373i	0.263302	−	0.456052i
$641$	19.8213	−	34.3314i	0.782893	−	1.35601i	−0.147357	−	0.989083i	$-0.547077\pi$
$641$	19.8213	−	34.3314i	0.782893	−	1.35601i	0.930250	−	0.366926i	$-0.119590\pi$
$642$	−3.25641	+	1.88009i	−0.128520	+	0.0742012i
$643$			20.8300i			0.821453i	0.911759	+	0.410727i	$0.134725\pi$
$643$			20.8300i			0.821453i	−0.911759	+	0.410727i	$0.865275\pi$
$644$	−2.31066	−	1.39748i	−0.0910529	−	0.0550684i
$645$			8.96568i			0.353023i
$646$	−1.40821	−	2.43909i	−0.0554052	−	0.0959646i
$647$	−7.87206	+	13.6348i	−0.309482	+	0.536039i	−0.978249	−	0.207433i	$-0.933489\pi$
$647$	−7.87206	+	13.6348i	−0.309482	+	0.536039i	0.668767	+	0.743472i	$0.266822\pi$
$648$	−6.31269	−	3.64463i	−0.247986	−	0.143175i
$649$	2.53437	+	4.38966i	0.0994828	+	0.172309i
$650$	2.97028	−	1.82769i	0.116504	−	0.0716877i
$651$	−23.5864	−	0.479800i	−0.924426	−	0.0188049i
$652$			1.31352i			0.0514413i
$653$	13.5132	+	23.4055i	0.528812	+	0.915930i	0.999436	+	0.0335954i	$0.0106958\pi$
$653$	13.5132	+	23.4055i	0.528812	+	0.915930i	−0.470623	+	0.882334i	$0.655971\pi$
$654$	−0.00814244	+	0.0141031i	−0.000318395	+	0.000551476i
$655$	−11.8538	−	6.84378i	−0.463165	−	0.267409i
$656$	21.9103	−	12.6499i	0.855453	−	0.493896i
$657$			7.93734i			0.309665i
$658$	4.82305	−	2.65529i	0.188022	−	0.103514i
$659$	−6.79491			−0.264692			−0.132346	−	0.991204i	$-0.542251\pi$
$659$	−6.79491			−0.264692			−0.132346	+	0.991204i	$0.542251\pi$
$660$	11.8734	+	20.5653i	0.462172	+	0.800505i
$661$	6.23994	+	3.60263i	0.242705	+	0.140126i	0.616420	−	0.787418i	$-0.288583\pi$
$661$	6.23994	+	3.60263i	0.242705	+	0.140126i	−0.373714	+	0.927544i	$0.621916\pi$
$662$	−3.04522	+	5.27448i	−0.118356	+	0.204998i
$663$	−10.8350	+	20.0431i	−0.420796	+	0.778409i
$664$	−3.44930			−0.133859
$665$	−6.55880	+	3.61090i	−0.254339	+	0.140025i
$666$	−2.31866			−0.0898463
$667$	−1.93339	−	3.34874i	−0.0748613	−	0.129664i
$668$	−22.8831	−	13.2115i	−0.885372	−	0.511170i
$669$	−2.81087	−	1.62285i	−0.108674	−	0.0627432i
$670$	−0.410750	+	0.237147i	−0.0158687	+	0.00916178i
$671$		−	40.3703i		−	1.55848i
$672$	14.2832	+	0.290552i	0.550987	+	0.0112083i
$673$	−8.32130			−0.320763			−0.160381	−	0.987055i	$-0.551272\pi$
$673$	−8.32130			−0.320763			−0.160381	+	0.987055i	$0.551272\pi$
$674$	−2.07756	+	1.19948i	−0.0800246	+	0.0462022i
$675$	8.21824	−	14.2344i	0.316320	−	0.547883i
$676$	−13.4539	−	20.5518i	−0.517456	−	0.790454i
$677$	14.9978	+	25.9770i	0.576413	+	0.998376i	0.995887	+	0.0906086i	$0.0288812\pi$
$677$	14.9978	+	25.9770i	0.576413	+	0.998376i	−0.419474	+	0.907767i	$0.637785\pi$
$678$			4.46391i			0.171435i
$679$	−9.01372	+	14.9037i	−0.345915	+	0.571953i
$680$	8.08982			0.310231
$681$	−34.2671	+	19.7841i	−1.31312	+	0.758128i
$682$	10.4701	+	6.04493i	0.400922	+	0.231472i
$683$	−31.2496	−	18.0420i	−1.19573	−	0.690356i	−0.236132	−	0.971721i	$-0.575880\pi$
$683$	−31.2496	−	18.0420i	−1.19573	−	0.690356i	−0.959601	+	0.281365i	$0.909213\pi$
$684$	2.78324	−	1.60690i	0.106420	−	0.0614415i
$685$	24.0064			0.917236
$686$	2.74703	+	5.50874i	0.104882	+	0.210325i
$687$		−	27.7205i		−	1.05760i
$688$	7.11470	+	12.3230i	0.271245	+	0.469811i
$689$	10.0161	−	0.280651i	0.381583	−	0.0106920i
$690$	0.189445	−	0.328128i	0.00721204	−	0.0124916i
$691$	−22.3155	+	12.8838i	−0.848920	+	0.490124i	−0.860286	−	0.509811i	$-0.829715\pi$
$691$	−22.3155	+	12.8838i	−0.848920	+	0.490124i	0.0113665	+	0.999935i	$0.496382\pi$
$692$	10.2724			0.390497
$693$	7.08465	−	11.7141i	0.269123	−	0.444983i
$694$			7.00589i			0.265940i
$695$	−23.1332	+	13.3559i	−0.877491	+	0.506620i
$696$	11.7000	+	6.75501i	0.443488	+	0.256048i
$697$	28.3168	+	16.3487i	1.07258	+	0.619252i
$698$	5.11242	+	8.85496i	0.193508	+	0.335165i
$699$	−31.7369			−1.20040
$700$	−0.295890	+	14.5456i	−0.0111836	+	0.549772i
$701$	−41.7872			−1.57828			−0.789141	−	0.614213i	$-0.789474\pi$
$701$	−41.7872			−1.57828			−0.789141	+	0.614213i	$0.789474\pi$
$702$	5.95415	+	3.21872i	0.224725	+	0.121483i
$703$	−7.85834	+	13.6110i	−0.296383	+	0.513350i
$704$	28.2071	+	16.2854i	1.06310	+	0.613778i
$705$	−6.60635	−	11.4425i	−0.248809	−	0.430951i
$706$	−2.03471			−0.0765774
$707$	0.164161	−	0.0903778i	0.00617393	−	0.00339901i
$708$		−	2.34782i		−	0.0882364i
$709$	−0.297781	+	0.171924i	−0.0111834	+	0.00645673i	−0.505581	−	0.862779i	$-0.668722\pi$
$709$	−0.297781	+	0.171924i	−0.0111834	+	0.00645673i	0.494398	+	0.869236i	$0.335389\pi$
$710$	−1.56552	−	0.903855i	−0.0587530	−	0.0339211i
$711$	−0.0569657	+	0.0986674i	−0.00213638	+	0.00370032i
$712$	−6.28124	−	10.8794i	−0.235399	−	0.407724i
$713$			3.29931i			0.123560i
$714$	2.68005	+	4.86802i	0.100298	+	0.182181i
$715$	−16.2668	−	26.4361i	−0.608342	−	0.988652i
$716$	5.06227	+	8.76810i	0.189186	+	0.327679i
$717$	25.2466	+	14.5761i	0.942852	+	0.544356i
$718$	3.22881	−	5.59246i	0.120498	−	0.208709i
$719$	4.39005	+	7.60379i	0.163721	+	0.283574i	0.936200	−	0.351467i	$-0.114317\pi$
$719$	4.39005	+	7.60379i	0.163721	+	0.283574i	−0.772479	+	0.635040i	$0.780984\pi$
$720$			4.20702i			0.156786i
$721$	0.341055	−	16.7659i	0.0127015	−	0.624393i
$722$		−	5.04149i		−	0.187625i
$723$	4.08416	−	2.35799i	0.151891	−	0.0876946i
$724$	7.12367	−	12.3386i	0.264749	−	0.458559i
$725$	−10.4164	+	18.0416i	−0.386854	+	0.670050i
$726$	10.2799	−	5.93512i	0.381524	−	0.220273i
$727$	17.3658			0.644064			0.322032	−	0.946729i	$-0.395634\pi$
$727$	17.3658			0.644064			0.322032	+	0.946729i	$0.395634\pi$
$728$	−12.3320	+	0.0946291i	−0.457054	+	0.00350719i
$729$	29.6343			1.09757
$730$	3.80130	−	2.19468i	0.140692	−	0.0812288i
$731$	−9.19502	+	15.9262i	−0.340090	+	0.589053i
$732$	−9.34968	+	16.1941i	−0.345574	+	0.598552i
$733$	−7.84528	+	4.52947i	−0.289772	+	0.167300i	−0.637839	−	0.770170i	$-0.720172\pi$
$733$	−7.84528	+	4.52947i	−0.289772	+	0.167300i	0.348067	+	0.937470i	$0.386838\pi$
$734$			1.79638i			0.0663056i
$735$	13.0833	−	6.85991i	0.482583	−	0.253032i
$736$		−	1.99796i		−	0.0736458i
$737$	−2.93919	−	5.09082i	−0.108266	−	0.187523i
$738$	1.09071	−	1.88917i	0.0401498	−	0.0695414i
$739$	−6.13010	−	3.53921i	−0.225499	−	0.130192i	0.382995	−	0.923751i	$-0.374893\pi$
$739$	−6.13010	−	3.53921i	−0.225499	−	0.130192i	−0.608494	+	0.793558i	$0.708226\pi$
$740$	−10.9655	−	18.9928i	−0.403100	−	0.698190i
$741$	8.77531	−	5.39966i	0.322369	−	0.198362i
$742$	1.26472	−	2.09115i	0.0464292	−	0.0767685i
$743$		−	14.6779i		−	0.538479i	−0.963073	−	0.269240i	$-0.913228\pi$
$743$		−	14.6779i		−	0.538479i	0.963073	−	0.269240i	$-0.0867724\pi$
$744$	−5.76367	−	9.98297i	−0.211306	−	0.365993i
$745$	−2.22684	+	3.85699i	−0.0815849	+	0.141309i
$746$	4.67768	+	2.70066i	0.171262	+	0.0988782i
$747$	2.00768	−	1.15913i	0.0734571	−	0.0424105i
$748$			48.7085i			1.78096i
$749$	−0.416997	+	20.4991i	−0.0152367	+	0.749020i
$750$	−5.54848			−0.202602
$751$	−15.8556	−	27.4628i	−0.578580	−	1.00213i	−0.995643	−	0.0932523i	$-0.970274\pi$
$751$	−15.8556	−	27.4628i	−0.578580	−	1.00213i	0.417062	−	0.908878i	$-0.363060\pi$
$752$	−18.1604	−	10.4849i	−0.662241	−	0.382345i
$753$	9.11788	−	15.7926i	0.332274	−	0.575516i
$754$	−7.54669	−	4.07962i	−0.274834	−	0.148571i
$755$	3.68467			0.134099
$756$	−24.7345	+	13.6174i	−0.899585	+	0.495259i
$757$	15.5317			0.564510			0.282255	−	0.959339i	$-0.408918\pi$
$757$	15.5317			0.564510			0.282255	+	0.959339i	$0.408918\pi$
$758$	4.18344	+	7.24593i	0.151949	+	0.263184i
$759$	4.06680	+	2.34797i	0.147616	+	0.0852259i
$760$	−3.16825	−	1.82919i	−0.114925	−	0.0663518i
$761$	−0.216826	+	0.125185i	−0.00785993	+	0.00453794i	−0.503925	−	0.863748i	$-0.668111\pi$
$761$	−0.216826	+	0.125185i	−0.00785993	+	0.00453794i	0.496065	+	0.868285i	$0.334778\pi$
$762$			6.98474i			0.253030i
$763$	0.0428255	+	0.0777879i	0.00155039	+	0.00281611i
$764$	25.5961			0.926036
$765$	−4.70870	+	2.71857i	−0.170243	+	0.0982901i
$766$	0.633903	−	1.09795i	0.0229039	−	0.0396706i
$767$	0.0859562	+	3.06767i	0.00310370	+	0.110767i
$768$	−5.74859	−	9.95686i	−0.207435	−	0.359287i
$769$		−	24.0146i		−	0.865988i	−0.901397	−	0.432994i	$-0.857457\pi$
$769$		−	24.0146i		−	0.865988i	0.901397	−	0.432994i	$-0.142543\pi$
$770$	−7.56896	−	0.153969i	−0.272766	−	0.00554867i
$771$	−8.50731			−0.306383
$772$	30.3650	−	17.5312i	1.09286	−	0.630963i
$773$	−26.4192	−	15.2531i	−0.950231	−	0.548616i	−0.0570784	−	0.998370i	$-0.518179\pi$
$773$	−26.4192	−	15.2531i	−0.950231	−	0.548616i	−0.893153	+	0.449753i	$0.851512\pi$
$774$	1.06253	+	0.613451i	0.0381918	+	0.0220501i
$775$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.287846 + 0.166188i) q^{2} +(-0.729919 + 1.26426i) q^{3} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} -0.485214i q^{6} +(-2.26391 - 1.36920i) q^{7} -1.29278i q^{8} +(0.434437 + 0.752468i) q^{9} +O(q^{10})\)	\(q+(-0.287846 + 0.166188i) q^{2} +(-0.729919 + 1.26426i) q^{3} +(-0.944763 + 1.63638i) q^{4} +(-1.25195 + 0.722811i) q^{5} -0.485214i q^{6} +(-2.26391 - 1.36920i) q^{7} -1.29278i q^{8} +(0.434437 + 0.752468i) q^{9} +(0.240245 - 0.416116i) q^{10} +(5.15732 + 2.97758i) q^{11} +(-1.37920 - 2.38885i) q^{12} +(1.88953 + 3.07078i) q^{13} +(0.879201 + 0.0178849i) q^{14} -2.11037i q^{15} +(-1.67468 - 2.90063i) q^{16} +(2.16436 - 3.74877i) q^{17} +(-0.250102 - 0.144396i) q^{18} +(-1.69527 + 0.978767i) q^{19} -2.73154i q^{20} +(3.38349 - 1.86276i) q^{21} -1.97935 q^{22} +(-0.270081 - 0.467795i) q^{23} +(1.63441 + 0.943626i) q^{24} +(-1.45509 + 2.52029i) q^{25} +(-1.05422 - 0.569894i) q^{26} -5.64793 q^{27} +(4.37939 - 2.41104i) q^{28} +7.15857 q^{29} +(0.350718 + 0.607461i) q^{30} +(-5.28968 - 3.05400i) q^{31} +(3.20327 + 1.84941i) q^{32} +(-7.52885 + 4.34678i) q^{33} +1.43876i q^{34} +(3.82396 + 0.0777879i) q^{35} -1.64176 q^{36} +(6.95316 - 4.01441i) q^{37} +(0.325318 - 0.563467i) q^{38} +(-5.26145 + 0.147426i) q^{39} +(0.934437 + 1.61849i) q^{40} +7.55362i q^{41} +(-0.664356 + 1.09848i) q^{42} -4.24839 q^{43} +(-9.74489 + 5.62622i) q^{44} +(-1.08778 - 0.628032i) q^{45} +(0.155483 + 0.0897684i) q^{46} +(5.42204 - 3.13042i) q^{47} +4.88953 q^{48} +(3.25057 + 6.19950i) q^{49} -0.967272i q^{50} +(3.15961 + 5.47260i) q^{51} +(-6.81011 + 0.190820i) q^{52} +(1.38953 - 2.40673i) q^{53} +(1.62573 - 0.938616i) q^{54} -8.60891 q^{55} +(-1.77008 + 2.92674i) q^{56} -2.85768i q^{57} +(-2.06056 + 1.18967i) q^{58} +(0.737119 + 0.425576i) q^{59} +(3.45337 + 1.99380i) q^{60} +(-3.38953 - 5.87083i) q^{61} +2.03015 q^{62} +(0.0467536 - 2.29835i) q^{63} +5.46933 q^{64} +(-4.58518 - 2.47868i) q^{65} +(1.44476 - 2.50240i) q^{66} +(-0.854859 - 0.493553i) q^{67} +(4.08961 + 7.08341i) q^{68} +0.788550 q^{69} +(-1.11364 + 0.613105i) q^{70} -3.76223i q^{71} +(0.972777 - 0.561633i) q^{72} +(7.91131 + 4.56760i) q^{73} +(-1.33429 + 2.31106i) q^{74} +(-2.12419 - 3.67921i) q^{75} -3.69881i q^{76} +(-7.59879 - 13.8024i) q^{77} +(1.48999 - 0.916825i) q^{78} +(0.0655625 + 0.113558i) q^{79} +(4.19322 + 2.42096i) q^{80} +(2.81922 - 4.88303i) q^{81} +(-1.25532 - 2.17428i) q^{82} -2.66812i q^{83} +(-0.148428 + 7.29653i) q^{84} +6.25768i q^{85} +(1.22288 - 0.706030i) q^{86} +(-5.22517 + 9.05026i) q^{87} +(3.84936 - 6.66729i) q^{88} +(8.41550 - 4.85869i) q^{89} +0.417485 q^{90} +(-0.0731980 - 9.53911i) q^{91} +1.02065 q^{92} +(7.72207 - 4.45834i) q^{93} +(-1.04047 + 1.80215i) q^{94} +(1.41493 - 2.45072i) q^{95} +(-4.67625 + 2.69983i) q^{96} -6.58319i q^{97} +(-1.96594 - 1.24429i) q^{98} +5.17429i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16q - 4q^{3} + 6q^{4} - 12q^{9} + O(q^{10}) \)	\( 16q - 4q^{3} + 6q^{4} - 12q^{9} - 6q^{10} + 18q^{12} - 12q^{13} - 26q^{14} + 2q^{16} + 8q^{17} - 36q^{22} - 12q^{23} - 6q^{26} + 32q^{27} - 16q^{29} + 38q^{30} - 56q^{36} + 34q^{38} + 18q^{39} - 4q^{40} + 16q^{42} + 16q^{43} + 36q^{48} + 40q^{49} + 16q^{51} - 42q^{52} - 20q^{53} + 24q^{55} - 36q^{56} - 12q^{61} + 44q^{62} + 88q^{64} - 30q^{65} + 2q^{66} - 2q^{68} - 56q^{69} + 42q^{74} + 8q^{75} - 76q^{77} + 20q^{78} + 20q^{79} - 24q^{81} - 16q^{82} - 68q^{87} + 4q^{88} - 216q^{90} + 56q^{91} + 12q^{92} - 26q^{94} - 16q^{95} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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