LMFDB - Embedded newform 91.2.k.b.23.1

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$1.21245 - 0.727987i$ of defining polynomial
Character	$\chi$	$=$	91.23
Dual form			91.2.k.b.4.6

$q$-expansion

$f(q)$	$=$	$q-2.30327i q^{2} +(0.736680 - 1.27597i) q^{3} -3.30504 q^{4} +(0.733776 + 0.423646i) q^{5} +(-2.93889 - 1.69677i) q^{6} +(-0.357777 + 2.62145i) q^{7} +3.00585i q^{8} +(0.414604 + 0.718115i) q^{9} +O(q^{10})$	\(q-2.30327i q^{2} +(0.736680 - 1.27597i) q^{3} -3.30504 q^{4} +(0.733776 + 0.423646i) q^{5} +(-2.93889 - 1.69677i) q^{6} +(-0.357777 + 2.62145i) q^{7} +3.00585i q^{8} +(0.414604 + 0.718115i) q^{9} +(0.975769 - 1.69008i) q^{10} +(1.30198 + 0.751701i) q^{11} +(-2.43476 + 4.21712i) q^{12} +(-2.92329 - 2.11054i) q^{13} +(6.03790 + 0.824057i) q^{14} +(1.08112 - 0.624183i) q^{15} +0.313194 q^{16} -2.07140 q^{17} +(1.65401 - 0.954943i) q^{18} +(0.0410731 - 0.0237136i) q^{19} +(-2.42516 - 1.40016i) q^{20} +(3.08132 + 2.38768i) q^{21} +(1.73137 - 2.99882i) q^{22} +7.81870 q^{23} +(3.83536 + 2.21435i) q^{24} +(-2.14105 - 3.70840i) q^{25} +(-4.86115 + 6.73311i) q^{26} +5.64180 q^{27} +(1.18247 - 8.66399i) q^{28} +(-0.679854 - 1.17754i) q^{29} +(-1.43766 - 2.49010i) q^{30} +(-6.80787 + 3.93052i) q^{31} +5.29033i q^{32} +(1.91829 - 1.10753i) q^{33} +4.77099i q^{34} +(-1.37309 + 1.77199i) q^{35} +(-1.37028 - 2.37340i) q^{36} +6.70219i q^{37} +(-0.0546187 - 0.0946024i) q^{38} +(-4.84652 + 2.17522i) q^{39} +(-1.27341 + 2.20562i) q^{40} +(-8.67622 + 5.00922i) q^{41} +(5.49947 - 7.09710i) q^{42} +(4.63283 - 8.02430i) q^{43} +(-4.30311 - 2.48440i) q^{44} +0.702581i q^{45} -18.0086i q^{46} +(-0.311781 - 0.180007i) q^{47} +(0.230724 - 0.399625i) q^{48} +(-6.74399 - 1.87579i) q^{49} +(-8.54144 + 4.93141i) q^{50} +(-1.52596 + 2.64304i) q^{51} +(9.66157 + 6.97543i) q^{52} +(-1.35591 - 2.34850i) q^{53} -12.9946i q^{54} +(0.636910 + 1.10316i) q^{55} +(-7.87968 - 1.07542i) q^{56} -0.0698773i q^{57} +(-2.71219 + 1.56588i) q^{58} +1.64120i q^{59} +(-3.57313 + 2.06295i) q^{60} +(-2.26097 - 3.91612i) q^{61} +(9.05305 + 15.6803i) q^{62} +(-2.03084 + 0.829938i) q^{63} +12.8114 q^{64} +(-1.25091 - 2.78711i) q^{65} +(-2.55093 - 4.41834i) q^{66} +(-1.76900 - 1.02133i) q^{67} +6.84606 q^{68} +(5.75988 - 9.97641i) q^{69} +(4.08136 + 3.16260i) q^{70} +(12.3096 + 7.10697i) q^{71} +(-2.15854 + 1.24624i) q^{72} +(5.85563 - 3.38075i) q^{73} +15.4369 q^{74} -6.30907 q^{75} +(-0.135748 + 0.0783743i) q^{76} +(-2.43637 + 3.14414i) q^{77} +(5.01012 + 11.1628i) q^{78} +(-5.82952 + 10.0970i) q^{79} +(0.229814 + 0.132683i) q^{80} +(2.91240 - 5.04442i) q^{81} +(11.5376 + 19.9837i) q^{82} -11.5362i q^{83} +(-10.1839 - 7.89138i) q^{84} +(-1.51994 - 0.877541i) q^{85} +(-18.4821 - 10.6706i) q^{86} -2.00334 q^{87} +(-2.25950 + 3.91357i) q^{88} -17.5112i q^{89} +1.61823 q^{90} +(6.57857 - 6.90814i) q^{91} -25.8411 q^{92} +11.5822i q^{93} +(-0.414604 + 0.718115i) q^{94} +0.0401846 q^{95} +(6.75029 + 3.89728i) q^{96} +(0.369125 + 0.213115i) q^{97} +(-4.32044 + 15.5332i) q^{98} +1.24663i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9	$ 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9} + 12 q^{10} + 12 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 34 q^{17} + 3 q^{18} + 9 q^{19} - 3 q^{20} + 21 q^{21} - 15 q^{22} - 6 q^{23} + 15 q^{24} - 5 q^{25} - 6 q^{26} + 12 q^{27} - 9 q^{28} - q^{29} + 11 q^{30} + 18 q^{31} - 6 q^{33} - 6 q^{35} - 13 q^{36} + 19 q^{38} - 4 q^{39} - q^{40} - 6 q^{41} - 8 q^{42} + 11 q^{43} - 33 q^{44} - 15 q^{47} + 19 q^{48} - 3 q^{49} + 18 q^{50} + 4 q^{51} - 7 q^{52} - 8 q^{53} - 15 q^{55} + 27 q^{56} - 24 q^{58} - 30 q^{60} + 5 q^{61} + 41 q^{62} - 30 q^{63} + 2 q^{64} + 21 q^{65} - 34 q^{66} + 15 q^{67} + 22 q^{68} + 7 q^{69} + 3 q^{70} + 30 q^{71} + 57 q^{72} + 42 q^{73} + 66 q^{74} - 2 q^{75} - 45 q^{76} - 19 q^{77} + 44 q^{78} - 35 q^{79} - 63 q^{80} + 14 q^{81} + 5 q^{82} - 12 q^{84} - 21 q^{85} - 57 q^{86} - 20 q^{87} - 14 q^{88} - 7 q^{91} - 66 q^{92} + q^{94} - 4 q^{95} + 21 q^{96} - 3 q^{97} - 18 q^{98}+O(q^{100}) $ 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9 + 12 * q^10 + 12 * q^11 - q^12 - 2 * q^13 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 34 * q^17 + 3 * q^18 + 9 * q^19 - 3 * q^20 + 21 * q^21 - 15 * q^22 - 6 * q^23 + 15 * q^24 - 5 * q^25 - 6 * q^26 + 12 * q^27 - 9 * q^28 - q^29 + 11 * q^30 + 18 * q^31 - 6 * q^33 - 6 * q^35 - 13 * q^36 + 19 * q^38 - 4 * q^39 - q^40 - 6 * q^41 - 8 * q^42 + 11 * q^43 - 33 * q^44 - 15 * q^47 + 19 * q^48 - 3 * q^49 + 18 * q^50 + 4 * q^51 - 7 * q^52 - 8 * q^53 - 15 * q^55 + 27 * q^56 - 24 * q^58 - 30 * q^60 + 5 * q^61 + 41 * q^62 - 30 * q^63 + 2 * q^64 + 21 * q^65 - 34 * q^66 + 15 * q^67 + 22 * q^68 + 7 * q^69 + 3 * q^70 + 30 * q^71 + 57 * q^72 + 42 * q^73 + 66 * q^74 - 2 * q^75 - 45 * q^76 - 19 * q^77 + 44 * q^78 - 35 * q^79 - 63 * q^80 + 14 * q^81 + 5 * q^82 - 12 * q^84 - 21 * q^85 - 57 * q^86 - 20 * q^87 - 14 * q^88 - 7 * q^91 - 66 * q^92 + q^94 - 4 * q^95 + 21 * q^96 - 3 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	2.30327i		−	1.62866i	−0.580405	−	0.814328i	$-0.697106\pi$
$2$		−	2.30327i		−	1.62866i	0.580405	−	0.814328i	$-0.302894\pi$
$3$	0.736680	−	1.27597i	0.425323	−	0.736680i	−0.571128	−	0.820861i	$-0.693494\pi$
$3$	0.736680	−	1.27597i	0.425323	−	0.736680i	0.996451	+	0.0841807i	$0.0268273\pi$
$4$	−3.30504			−1.65252
$5$	0.733776	+	0.423646i	0.328155	+	0.189460i	0.655022	−	0.755610i	$-0.272660\pi$
$5$	0.733776	+	0.423646i	0.328155	+	0.189460i	−0.326867	+	0.945070i	$0.605993\pi$
$6$	−2.93889	−	1.69677i	−1.19980	−	0.692704i
$7$	−0.357777	+	2.62145i	−0.135227	+	0.990815i
$7$	−0.357777	+	2.62145i	−0.135227	+	0.990815i
$8$			3.00585i			1.06273i
$9$	0.414604	+	0.718115i	0.138201	+	0.239372i
$10$	0.975769	−	1.69008i	0.308565	−	0.534451i
$11$	1.30198	+	0.751701i	0.392563	+	0.226646i	0.683270	−	0.730166i	$-0.260557\pi$
$11$	1.30198	+	0.751701i	0.392563	+	0.226646i	−0.290707	+	0.956812i	$0.593890\pi$
$12$	−2.43476	+	4.21712i	−0.702853	+	1.21738i
$13$	−2.92329	−	2.11054i	−0.810774	−	0.585360i
$13$	−2.92329	−	2.11054i	−0.810774	−	0.585360i
$14$	6.03790	+	0.824057i	1.61370	+	0.220238i
$15$	1.08112	−	0.624183i	0.279143	−	0.161163i
$16$	0.313194			0.0782985
$17$	−2.07140			−0.502389			−0.251194	−	0.967937i	$-0.580823\pi$
$17$	−2.07140			−0.502389			−0.251194	+	0.967937i	$0.580823\pi$
$18$	1.65401	−	0.954943i	0.389854	−	0.225082i
$19$	0.0410731	−	0.0237136i	0.00942282	−	0.00544027i	−0.495281	−	0.868733i	$-0.664935\pi$
$19$	0.0410731	−	0.0237136i	0.00942282	−	0.00544027i	0.504704	+	0.863292i	$0.331602\pi$
$20$	−2.42516	−	1.40016i	−0.542282	−	0.313086i
$21$	3.08132	+	2.38768i	0.672399	+	0.521035i
$22$	1.73137	−	2.99882i	0.369129	−	0.639350i
$23$	7.81870			1.63031			0.815156	−	0.579241i	$-0.196651\pi$
$23$	7.81870			1.63031			0.815156	+	0.579241i	$0.196651\pi$
$24$	3.83536	+	2.21435i	0.782891	+	0.452002i
$25$	−2.14105	−	3.70840i	−0.428210	−	0.741681i
$26$	−4.86115	+	6.73311i	−0.953349	+	1.32047i
$27$	5.64180			1.08577
$28$	1.18247	−	8.66399i	0.223465	−	1.63734i
$29$	−0.679854	−	1.17754i	−0.126246	−	0.218664i	0.795973	−	0.605331i	$-0.206959\pi$
$29$	−0.679854	−	1.17754i	−0.126246	−	0.218664i	−0.922219	+	0.386668i	$0.873626\pi$
$30$	−1.43766	−	2.49010i	−0.262480	−	0.454628i
$31$	−6.80787	+	3.93052i	−1.22273	+	0.705943i	−0.965499	−	0.260407i	$-0.916143\pi$
$31$	−6.80787	+	3.93052i	−1.22273	+	0.705943i	−0.257230	+	0.966350i	$0.582810\pi$
$32$			5.29033i			0.935206i
$33$	1.91829	−	1.10753i	0.333932	−	0.192796i
$34$			4.77099i			0.818218i
$35$	−1.37309	+	1.77199i	−0.232095	+	0.299520i
$36$	−1.37028	−	2.37340i	−0.228380	−	0.395566i
$37$			6.70219i			1.10183i	0.834560	+	0.550917i	$0.185722\pi$
$37$			6.70219i			1.10183i	−0.834560	+	0.550917i	$0.814278\pi$
$38$	−0.0546187	−	0.0946024i	−0.00886032	−	0.0153465i
$39$	−4.84652	+	2.17522i	−0.776064	+	0.348314i
$40$	−1.27341	+	2.20562i	−0.201345	+	0.348739i
$41$	−8.67622	+	5.00922i	−1.35500	+	0.782309i	−0.988945	−	0.148285i	$-0.952625\pi$
$41$	−8.67622	+	5.00922i	−1.35500	+	0.782309i	−0.366054	+	0.930594i	$0.619291\pi$
$42$	5.49947	−	7.09710i	0.848587	−	1.09511i
$43$	4.63283	−	8.02430i	0.706500	−	1.22369i	−0.259647	−	0.965704i	$-0.583606\pi$
$43$	4.63283	−	8.02430i	0.706500	−	1.22369i	0.966147	−	0.257991i	$-0.0830604\pi$
$44$	−4.30311	−	2.48440i	−0.648718	−	0.374537i
$45$			0.702581i			0.104735i
$46$		−	18.0086i		−	2.65522i
$47$	−0.311781	−	0.180007i	−0.0454779	−	0.0262567i	0.477089	−	0.878855i	$-0.341692\pi$
$47$	−0.311781	−	0.180007i	−0.0454779	−	0.0262567i	−0.522567	+	0.852598i	$0.675025\pi$
$48$	0.230724	−	0.399625i	0.0333021	−	0.0576810i
$49$	−6.74399	−	1.87579i	−0.963427	−	0.267970i
$50$	−8.54144	+	4.93141i	−1.20794	+	0.697406i
$51$	−1.52596	+	2.64304i	−0.213677	+	0.370100i
$52$	9.66157	+	6.97543i	1.33982	+	0.967318i
$53$	−1.35591	−	2.34850i	−0.186248	−	0.322591i	0.757748	−	0.652547i	$-0.226299\pi$
$53$	−1.35591	−	2.34850i	−0.186248	−	0.322591i	−0.943996	+	0.329956i	$0.892966\pi$
$54$		−	12.9946i		−	1.76834i
$55$	0.636910	+	1.10316i	0.0858809	+	0.148750i
$56$	−7.87968	−	1.07542i	−1.05297	−	0.143710i
$57$		−	0.0698773i		−	0.00925548i
$58$	−2.71219	+	1.56588i	−0.356128	+	0.205611i
$59$			1.64120i			0.213666i	0.994277	+	0.106833i	$0.0340709\pi$
$59$			1.64120i			0.213666i	−0.994277	+	0.106833i	$0.965929\pi$
$60$	−3.57313	+	2.06295i	−0.461289	+	0.266325i
$61$	−2.26097	−	3.91612i	−0.289488	−	0.501407i	0.684200	−	0.729295i	$-0.260152\pi$
$61$	−2.26097	−	3.91612i	−0.289488	−	0.501407i	−0.973688	+	0.227887i	$0.926818\pi$
$62$	9.05305	+	15.6803i	1.14974	+	1.99140i
$63$	−2.03084	+	0.829938i	−0.255861	+	0.104562i
$64$	12.8114			1.60143
$65$	−1.25091	−	2.78711i	−0.155157	−	0.345698i
$66$	−2.55093	−	4.41834i	−0.313998	−	0.543860i
$67$	−1.76900	−	1.02133i	−0.216117	−	0.124775i	0.388034	−	0.921645i	$-0.373154\pi$
$67$	−1.76900	−	1.02133i	−0.216117	−	0.124775i	−0.604151	+	0.796870i	$0.706488\pi$
$68$	6.84606			0.830206
$69$	5.75988	−	9.97641i	0.693409	−	1.20102i
$70$	4.08136	+	3.16260i	0.487815	+	0.378003i
$71$	12.3096	+	7.10697i	1.46088	+	0.843442i	0.999052	−	0.0435255i	$-0.0138590\pi$
$71$	12.3096	+	7.10697i	1.46088	+	0.843442i	0.461832	+	0.886967i	$0.347192\pi$
$72$	−2.15854	+	1.24624i	−0.254387	+	0.146870i
$73$	5.85563	−	3.38075i	0.685349	−	0.395687i	−0.116518	−	0.993189i	$-0.537173\pi$
$73$	5.85563	−	3.38075i	0.685349	−	0.395687i	0.801867	+	0.597502i	$0.203840\pi$
$74$	15.4369			1.79451
$75$	−6.30907			−0.728509
$76$	−0.135748	+	0.0783743i	−0.0155714	+	0.00899015i
$77$	−2.43637	+	3.14414i	−0.277650	+	0.358308i
$78$	5.01012	+	11.1628i	0.567284	+	1.26394i
$79$	−5.82952	+	10.0970i	−0.655873	+	1.13600i	0.325801	+	0.945438i	$0.394366\pi$
$79$	−5.82952	+	10.0970i	−0.655873	+	1.13600i	−0.981674	+	0.190567i	$0.938967\pi$
$80$	0.229814	+	0.132683i	0.0256940	+	0.0148344i
$81$	2.91240	−	5.04442i	0.323600	−	0.560491i
$82$	11.5376	+	19.9837i	1.27411	+	2.20683i
$83$		−	11.5362i		−	1.26627i	−0.774043	−	0.633133i	$-0.781768\pi$
$83$		−	11.5362i		−	1.26627i	0.774043	−	0.633133i	$-0.218232\pi$
$84$	−10.1839	−	7.89138i	−1.11115	−	0.861020i
$85$	−1.51994	−	0.877541i	−0.164861	−	0.0951826i
$86$	−18.4821	−	10.6706i	−1.99298	−	1.15065i
$87$	−2.00334			−0.214781
$88$	−2.25950	+	3.91357i	−0.240863	+	0.417188i
$89$		−	17.5112i		−	1.85619i	−0.372350	−	0.928093i	$-0.621448\pi$
$89$		−	17.5112i		−	1.85619i	0.372350	−	0.928093i	$-0.378552\pi$
$90$	1.61823			0.170576
$91$	6.57857	−	6.90814i	0.689622	−	0.724170i
$92$	−25.8411			−2.69412
$93$			11.5822i			1.20101i
$94$	−0.414604	+	0.718115i	−0.0427631	+	0.0740679i
$95$	0.0401846			0.00412286
$96$	6.75029	+	3.89728i	0.688948	+	0.397764i
$97$	0.369125	+	0.213115i	0.0374790	+	0.0216385i	0.518622	−	0.855003i	$-0.326445\pi$
$97$	0.369125	+	0.213115i	0.0374790	+	0.0216385i	−0.481143	+	0.876642i	$0.659778\pi$
$98$	−4.32044	+	15.5332i	−0.436431	+	1.56909i
$99$			1.24663i			0.125291i
$100$	7.07624	+	12.2564i	0.707624	+	1.22564i
$101$	4.83499	−	8.37444i	0.481099	−	0.833288i	−0.518666	−	0.854977i	$-0.673571\pi$
$101$	4.83499	−	8.37444i	0.481099	−	0.833288i	0.999765	+	0.0216891i	$0.00690441\pi$
$102$	6.08763	+	3.51469i	0.602765	+	0.348007i
$103$	−4.98912	+	8.64140i	−0.491592	+	0.851463i	−0.999953	−	0.00968129i	$-0.996918\pi$
$103$	−4.98912	+	8.64140i	−0.491592	+	0.851463i	0.508361	+	0.861144i	$0.330252\pi$
$104$	6.34397	−	8.78695i	0.622078	−	0.861631i
$105$	1.24947	+	3.05741i	0.121935	+	0.298373i
$106$	−5.40922	+	3.12301i	−0.525390	+	0.303334i
$107$	9.86223			0.953417			0.476709	−	0.879061i	$-0.341830\pi$
$107$	9.86223			0.953417			0.476709	+	0.879061i	$0.341830\pi$
$108$	−18.6464			−1.79425
$109$	−10.0507	+	5.80275i	−0.962679	+	0.555803i	−0.896996	−	0.442038i	$-0.854256\pi$
$109$	−10.0507	+	5.80275i	−0.962679	+	0.555803i	−0.0656822	+	0.997841i	$0.520922\pi$
$110$	2.54087	−	1.46697i	0.242263	−	0.139870i
$111$	8.55178	+	4.93737i	0.811699	+	0.468635i
$112$	−0.112054	+	0.821022i	−0.0105881	+	0.0775793i
$113$	1.73879	−	3.01167i	0.163572	−	0.283314i	−0.772576	−	0.634923i	$-0.781032\pi$
$113$	1.73879	−	3.01167i	0.163572	−	0.283314i	0.936147	+	0.351609i	$0.114365\pi$
$114$	−0.160946			−0.0150740
$115$	5.73718	+	3.31236i	0.534994	+	0.308879i
$116$	2.24694	+	3.89182i	0.208623	+	0.361346i
$117$	0.303608	−	2.97429i	0.0280686	−	0.274974i
$118$	3.78011			0.347987
$119$	0.741100	−	5.43007i	0.0679366	−	0.497774i
$120$	1.87620	+	3.24967i	0.171273	+	0.296653i
$121$	−4.36989	−	7.56887i	−0.397263	−	0.688079i
$122$	−9.01986	+	5.20762i	−0.816620	+	0.471476i
$123$			14.7608i			1.33093i
$124$	22.5003	−	12.9905i	2.02058	−	1.16658i
$125$		−	7.86464i		−	0.703435i
$126$	1.91157	+	4.67756i	0.170296	+	0.416710i
$127$	−7.84992	−	13.5965i	−0.696567	−	1.20649i	−0.969649	−	0.244499i	$-0.921376\pi$
$127$	−7.84992	−	13.5965i	−0.696567	−	1.20649i	0.273082	−	0.961991i	$-0.411957\pi$
$128$		−	18.9275i		−	1.67297i
$129$	−6.82583	−	11.8227i	−0.600981	−	1.04093i
$130$	−6.41945	+	2.88119i	−0.563023	+	0.252697i
$131$	1.27259	−	2.20418i	0.111186	−	0.192580i	−0.805063	−	0.593190i	$-0.797868\pi$
$131$	1.27259	−	2.20418i	0.111186	−	0.192580i	0.916249	+	0.400610i	$0.131202\pi$
$132$	−6.34003	+	3.66042i	−0.551829	+	0.318598i
$133$	0.0474689	+	0.116155i	0.00411608	+	0.0100719i
$134$	−2.35240	+	4.07447i	−0.203216	+	0.351981i
$135$	4.13982	+	2.39013i	0.356299	+	0.205709i
$136$		−	6.22632i		−	0.533902i
$137$		−	1.86472i		−	0.159314i	−0.996822	−	0.0796571i	$-0.974617\pi$
$137$		−	1.86472i		−	0.159314i	0.996822	−	0.0796571i	$-0.0253825\pi$
$138$	−22.9783	−	13.2665i	−1.95605	−	1.12932i
$139$	−7.80462	+	13.5180i	−0.661979	+	1.14658i	0.318116	+	0.948052i	$0.396950\pi$
$139$	−7.80462	+	13.5180i	−0.661979	+	1.14658i	−0.980095	+	0.198530i	$0.936383\pi$
$140$	4.53813	−	5.85648i	0.383542	−	0.494963i
$141$	−0.459366	+	0.265215i	−0.0386856	+	0.0223351i
$142$	16.3692	−	28.3524i	1.37368	−	2.37928i
$143$	−2.21957	−	4.94533i	−0.185610	−	0.413550i
$144$	0.129851	+	0.224909i	0.0108209	+	0.0187424i
$145$		−	1.15207i		−	0.0956741i
$146$	−7.78676	−	13.4871i	−0.644437	−	1.11620i
$147$	−7.36161	+	7.22326i	−0.607176	+	0.595764i
$148$		−	22.1510i		−	1.82080i
$149$	5.51106	−	3.18181i	0.451484	−	0.260664i	−0.256973	−	0.966419i	$-0.582725\pi$
$149$	5.51106	−	3.18181i	0.451484	−	0.260664i	0.708457	+	0.705754i	$0.249392\pi$
$150$			14.5315i			1.18649i
$151$	0.575122	−	0.332047i	0.0468028	−	0.0270216i	−0.476416	−	0.879220i	$-0.658064\pi$
$151$	0.575122	−	0.332047i	0.0468028	−	0.0270216i	0.523219	+	0.852198i	$0.324731\pi$
$152$	0.0712794	+	0.123460i	0.00578152	+	0.0100139i
$153$	−0.858811	−	1.48750i	−0.0694307	−	0.120258i
$154$	7.24180	+	5.61160i	0.583561	+	0.452196i
$155$	−6.66060			−0.534992
$156$	16.0179	−	7.18919i	1.28246	−	0.575596i
$157$	8.28798	+	14.3552i	0.661453	+	1.14567i	0.980234	+	0.197842i	$0.0633933\pi$
$157$	8.28798	+	14.3552i	0.661453	+	1.14567i	−0.318781	+	0.947828i	$0.603273\pi$
$158$	23.2562	+	13.4269i	1.85016	+	1.06819i
$159$	−3.99548			−0.316862
$160$	−2.24122	+	3.88191i	−0.177184	+	0.306892i
$161$	−2.79735	+	20.4963i	−0.220462	+	1.61534i
$162$	−11.6186	−	6.70802i	−0.912846	−	0.527032i
$163$	7.83863	−	4.52563i	0.613969	−	0.354475i	−0.160548	−	0.987028i	$-0.551326\pi$
$163$	7.83863	−	4.52563i	0.613969	−	0.354475i	0.774517	+	0.632553i	$0.217993\pi$
$164$	28.6752	−	16.5557i	2.23916	−	1.29278i
$165$	1.87680			0.146108
$166$	−26.5710			−2.06231
$167$	−2.30156	+	1.32880i	−0.178100	+	0.102826i	−0.586400	−	0.810022i	$-0.699455\pi$
$167$	−2.30156	+	1.32880i	−0.178100	+	0.102826i	0.408300	+	0.912848i	$0.366122\pi$
$168$	−7.17701	+	9.26197i	−0.553718	+	0.714576i
$169$	4.09120	+	12.3395i	0.314708	+	0.949189i
$170$	−2.02121	+	3.50084i	−0.155020	+	0.268502i
$171$	0.0340582	+	0.0196635i	0.00260449	+	0.00150370i
$172$	−15.3117	+	26.5206i	−1.16750	+	2.02218i
$173$	9.79352	+	16.9629i	0.744588	+	1.28966i	0.950387	+	0.311070i	$0.100687\pi$
$173$	9.79352	+	16.9629i	0.744588	+	1.28966i	−0.205799	+	0.978594i	$0.565979\pi$
$174$			4.61423i			0.349804i
$175$	10.4874	−	4.28587i	0.792774	−	0.323981i
$176$	0.407774	+	0.235428i	0.0307371	+	0.0177461i
$177$	2.09411	+	1.20904i	0.157403	+	0.0908768i
$178$	−40.3330			−3.02309
$179$	−1.44666	+	2.50569i	−0.108129	+	0.187284i	−0.915012	−	0.403426i	$-0.867819\pi$
$179$	−1.44666	+	2.50569i	−0.108129	+	0.187284i	0.806884	+	0.590711i	$0.201152\pi$
$180$		−	2.32205i		−	0.173076i
$181$	−1.36804			−0.101686			−0.0508429	−	0.998707i	$-0.516191\pi$
$181$	−1.36804			−0.101686			−0.0508429	+	0.998707i	$0.516191\pi$
$182$	−15.9113	−	15.1522i	−1.17942	−	1.12316i
$183$	−6.66245			−0.492503
$184$			23.5018i			1.73258i
$185$	−2.83936	+	4.91791i	−0.208754	+	0.361572i
$186$	26.6768			1.95604
$187$	−2.69693	−	1.55707i	−0.197219	−	0.113865i
$188$	1.03045	+	0.594929i	0.0751531	+	0.0433897i
$189$	−2.01851	+	14.7897i	−0.146825	+	1.07579i
$190$		−	0.0925559i		−	0.00671471i
$191$	0.756625	+	1.31051i	0.0547475	+	0.0948254i	0.892100	−	0.451837i	$-0.149231\pi$
$191$	0.756625	+	1.31051i	0.0547475	+	0.0948254i	−0.837353	+	0.546663i	$0.815898\pi$
$192$	9.43792	−	16.3470i	0.681123	−	1.17974i
$193$	−6.02229	−	3.47697i	−0.433494	−	0.250278i	0.267340	−	0.963602i	$-0.413855\pi$
$193$	−6.02229	−	3.47697i	−0.433494	−	0.250278i	−0.700834	+	0.713324i	$0.747189\pi$
$194$	0.490860	−	0.850194i	0.0352417	−	0.0610404i
$195$	−4.47778	−	0.457080i	−0.320661	−	0.0327322i
$196$	22.2891	+	6.19955i	1.59208	+	0.442825i
$197$	−13.4037	+	7.73860i	−0.954971	+	0.551353i	−0.894622	−	0.446825i	$-0.852555\pi$
$197$	−13.4037	+	7.73860i	−0.954971	+	0.551353i	−0.0603494	+	0.998177i	$0.519221\pi$
$198$	2.87133			0.204056
$199$	−6.61529			−0.468945			−0.234473	−	0.972123i	$-0.575336\pi$
$199$	−6.61529			−0.468945			−0.234473	+	0.972123i	$0.575336\pi$
$200$	11.1469	−	6.43566i	0.788205	−	0.455070i
$201$	−2.60637	+	1.50479i	−0.183839	+	0.106140i
$202$	−19.2886	−	11.1363i	−1.35714	−	0.783545i
$203$	3.33010	−	1.36090i	0.233727	−	0.0955168i
$204$	5.04336	−	8.73535i	0.353106	−	0.611597i
$205$	−8.48854			−0.592865
$206$	19.9035	+	11.4913i	1.38674	+	0.800634i
$207$	3.24166	+	5.61473i	0.225311	+	0.390250i
$208$	−0.915555	−	0.661010i	−0.0634823	−	0.0458328i
$209$	0.0713021			0.00493207
$210$	7.04203	−	2.87785i	0.485947	−	0.198591i
$211$	4.04714	+	7.00986i	0.278617	+	0.482578i	0.971041	−	0.238912i	$-0.0767907\pi$
$211$	4.04714	+	7.00986i	0.278617	+	0.482578i	−0.692424	+	0.721490i	$0.743457\pi$
$212$	4.48132	+	7.76187i	0.307778	+	0.533088i
$213$	18.1365	−	10.4711i	1.24269	−	0.717470i
$214$		−	22.7153i		−	1.55279i
$215$	6.79892	−	3.92536i	0.463683	−	0.267707i
$216$			16.9584i			1.15387i
$217$	−7.86797	−	19.2527i	−0.534113	−	1.30696i
$218$	13.3653	+	23.1493i	0.905211	+	1.56787i
$219$		−	9.96212i		−	0.673178i
$220$	−2.10501	−	3.64599i	−0.141920	−	0.245812i
$221$	6.05530	+	4.37178i	0.407323	+	0.294078i
$222$	11.3721	−	19.6970i	0.763244	−	1.32198i
$223$	13.9067	−	8.02903i	0.931261	−	0.537664i	0.0440506	−	0.999029i	$-0.485974\pi$
$223$	13.9067	−	8.02903i	0.931261	−	0.537664i	0.887210	+	0.461366i	$0.152640\pi$
$224$	−13.8683	−	1.89276i	−0.926616	−	0.126465i
$225$	1.77537	−	3.07504i	0.118358	−	0.205002i
$226$	−6.93668	−	4.00490i	−0.461421	−	0.266402i
$227$		−	1.29581i		−	0.0860057i	−0.999075	−	0.0430029i	$-0.986308\pi$
$227$		−	1.29581i		−	0.0860057i	0.999075	−	0.0430029i	$-0.0136925\pi$
$228$			0.230947i			0.0152948i
$229$	18.0285	+	10.4088i	1.19136	+	0.687831i	0.958614	−	0.284707i	$-0.0918965\pi$
$229$	18.0285	+	10.4088i	1.19136	+	0.687831i	0.232743	+	0.972538i	$0.425230\pi$
$230$	7.62925	−	13.2142i	0.503058	−	0.871322i
$231$	2.21700	+	5.42496i	0.145868	+	0.356936i
$232$	3.53951	−	2.04354i	0.232380	−	0.134165i
$233$	−6.65213	+	11.5218i	−0.435796	+	0.754820i	−0.997360	−	0.0726127i	$-0.976866\pi$
$233$	−6.65213	+	11.5218i	−0.435796	+	0.754820i	0.561565	+	0.827433i	$0.310200\pi$
$234$	−6.85059	−	0.699290i	−0.447837	−	0.0457140i
$235$	−0.152518	−	0.264169i	−0.00994920	−	0.0172325i
$236$		−	5.42421i		−	0.353086i
$237$	8.58899	+	14.8766i	0.557915	+	0.966337i
$238$	−12.5069	−	1.70695i	−0.810702	−	0.110645i
$239$		−	13.3652i		−	0.864525i	−0.901748	−	0.432263i	$-0.857715\pi$
$239$		−	13.3652i		−	0.864525i	0.901748	−	0.432263i	$-0.142285\pi$
$240$	0.338599	−	0.195490i	0.0218565	−	0.0126188i
$241$		−	0.834153i		−	0.0537325i	−0.999639	−	0.0268663i	$-0.991447\pi$
$241$		−	0.834153i		−	0.0537325i	0.999639	−	0.0268663i	$-0.00855282\pi$
$242$	−17.4331	+	10.0650i	−1.12064	+	0.647004i
$243$	4.17170	+	7.22559i	0.267614	+	0.463522i
$244$	7.47259	+	12.9429i	0.478384	+	0.828585i
$245$	−4.15391	−	4.23347i	−0.265383	−	0.270467i
$246$	33.9980			2.16763
$247$	−0.170117	−	0.0173651i	−0.0108243	−	0.00110491i
$248$	−11.8146	−	20.4634i	−0.750225	−	1.29943i
$249$	−14.7199	−	8.49852i	−0.932834	−	0.538572i
$250$	−18.1144			−1.14565
$251$	13.6360	−	23.6183i	0.860699	−	1.49078i	−0.0105555	−	0.999944i	$-0.503360\pi$
$251$	13.6360	−	23.6183i	0.860699	−	1.49078i	0.871255	−	0.490831i	$-0.163307\pi$
$252$	6.71199	−	2.74297i	0.422816	−	0.172791i
$253$	10.1798	+	5.87733i	0.640000	+	0.369504i
$254$	−31.3163	+	18.0804i	−1.96496	+	1.13447i
$255$	−2.23943	+	1.29293i	−0.140238	+	0.0809667i
$256$	−17.9721			−1.12326
$257$	−6.55188			−0.408695			−0.204348	−	0.978898i	$-0.565507\pi$
$257$	−6.55188			−0.408695			−0.204348	+	0.978898i	$0.565507\pi$
$258$	−27.2308	+	15.7217i	−1.69532	+	0.978791i
$259$	−17.5695	−	2.39789i	−1.09171	−	0.148998i
$260$	4.13432	+	9.21148i	0.256399	+	0.571272i
$261$	0.563740	−	0.976426i	0.0348946	−	0.0604393i
$262$	−5.07682	−	2.93110i	−0.313647	−	0.181084i
$263$	11.2945	−	19.5627i	0.696450	−	1.20629i	−0.273239	−	0.961946i	$-0.588095\pi$
$263$	11.2945	−	19.5627i	0.696450	−	1.20629i	0.969689	−	0.244341i	$-0.0785717\pi$
$264$	3.32906	+	5.76610i	0.204889	+	0.354879i
$265$		−	2.29770i		−	0.141146i
$266$	0.267537	−	0.109334i	0.0164037	−	0.00670367i
$267$	−22.3437	−	12.9002i	−1.36742	−	0.789478i
$268$	5.84660	+	3.37553i	0.357138	+	0.206194i
$269$	16.0013			0.975617			0.487808	−	0.872951i	$-0.337797\pi$
$269$	16.0013			0.975617			0.487808	+	0.872951i	$0.337797\pi$
$270$	5.50510	−	9.53511i	0.335030	−	0.580288i
$271$			8.75935i			0.532093i	0.963960	+	0.266046i	$0.0857174\pi$
$271$			8.75935i			0.532093i	−0.963960	+	0.266046i	$0.914283\pi$
$272$	−0.648750			−0.0393363
$273$	−3.96826	−	13.4831i	−0.240170	−	0.816037i
$274$	−4.29496			−0.259468
$275$		−	6.43771i		−	0.388209i
$276$	−19.0366	+	32.9724i	−1.14587	+	1.98471i
$277$	19.9183			1.19677			0.598387	−	0.801208i	$-0.295809\pi$
$277$	19.9183			1.19677			0.598387	+	0.801208i	$0.295809\pi$
$278$	31.1355	+	17.9761i	1.86739	+	1.07814i
$279$	−5.64514	−	3.25922i	−0.337965	−	0.195124i
$280$	−5.32632	−	4.12731i	−0.318308	−	0.246654i
$281$			14.0234i			0.836566i	0.908317	+	0.418283i	$0.137368\pi$
$281$			14.0234i			0.836566i	−0.908317	+	0.418283i	$0.862632\pi$
$282$	0.610861	+	1.05804i	0.0363762	+	0.0630055i
$283$	0.506295	−	0.876929i	0.0300961	−	0.0521280i	−0.850585	−	0.525838i	$-0.823752\pi$
$283$	0.506295	−	0.876929i	0.0300961	−	0.0521280i	0.880681	+	0.473710i	$0.157085\pi$
$284$	−40.6838	−	23.4888i	−2.41414	−	1.39380i
$285$	0.0296032	−	0.0512743i	0.00175354	−	0.00303723i
$286$	−11.3904	+	5.11227i	−0.673530	+	0.302295i
$287$	−10.0273	−	24.5365i	−0.591890	−	1.44834i
$288$	−3.79906	+	2.19339i	−0.223862	+	0.129247i
$289$	−12.7093			−0.747606
$290$	−2.65352			−0.155820
$291$	0.543855	−	0.313995i	0.0318813	−	0.0184067i
$292$	−19.3531	+	11.1735i	−1.13255	+	0.653879i
$293$	−0.172543	−	0.0996176i	−0.0100801	−	0.00581972i	0.494952	−	0.868921i	$-0.335186\pi$
$293$	−0.172543	−	0.0996176i	−0.0100801	−	0.00581972i	−0.505032	+	0.863101i	$0.668519\pi$
$294$	16.6371	+	16.9558i	0.970295	+	0.988880i
$295$	−0.695286	+	1.20427i	−0.0404811	+	0.0701153i
$296$	−20.1458			−1.17095
$297$	7.34554	+	4.24095i	0.426232	+	0.246085i
$298$	−7.32857	−	12.6935i	−0.424532	−	0.735312i
$299$	−22.8563	−	16.5017i	−1.32181	−	0.954319i
$300$	20.8517			1.20387
$301$	19.3778	+	15.0156i	1.11692	+	0.865487i
$302$	−0.764792	−	1.32466i	−0.0440088	−	0.0762256i
$303$	−7.12368	−	12.3386i	−0.409245	−	0.708833i
$304$	0.0128639	−	0.00742695i	0.000737793	−	0.000425965i
$305$		−	3.83140i		−	0.219386i
$306$	−3.42612	+	1.97807i	−0.195858	+	0.113079i
$307$			27.2004i			1.55241i	0.630482	+	0.776204i	$0.282857\pi$
$307$			27.2004i			1.55241i	−0.630482	+	0.776204i	$0.717143\pi$
$308$	8.05228	−	10.3915i	0.458821	−	0.592111i
$309$	7.35077	+	12.7319i	0.418171	+	0.724293i
$310$			15.3411i			0.871318i
$311$	13.5505	+	23.4701i	0.768376	+	1.33087i	0.938443	+	0.345434i	$0.112268\pi$
$311$	13.5505	+	23.4701i	0.768376	+	1.33087i	−0.170067	+	0.985432i	$0.554398\pi$
$312$	−6.53839	−	14.5679i	−0.370163	−	0.824744i
$313$	11.0392	−	19.1205i	0.623975	−	1.08076i	−0.364763	−	0.931100i	$-0.618850\pi$
$313$	11.0392	−	19.1205i	0.623975	−	1.08076i	0.988738	−	0.149656i	$-0.0478165\pi$
$314$	33.0639	−	19.0894i	1.86590	−	1.07728i
$315$	−1.84178	−	0.251367i	−0.103773	−	0.0141629i
$316$	19.2668	−	33.3711i	1.08384	−	1.87727i
$317$	−6.12126	−	3.53411i	−0.343804	−	0.198496i	0.318149	−	0.948041i	$-0.396939\pi$
$317$	−6.12126	−	3.53411i	−0.343804	−	0.198496i	−0.661953	+	0.749545i	$0.730272\pi$
$318$			9.20265i			0.516059i
$319$		−	2.04419i		−	0.114453i
$320$	9.40071	+	5.42750i	0.525516	+	0.303407i
$321$	7.26531	−	12.5839i	0.405510	−	0.702364i
$322$	47.2085	+	6.44305i	2.63083	+	0.359057i
$323$	−0.0850789	+	0.0491204i	−0.00473392	+	0.00273313i
$324$	−9.62558	+	16.6720i	−0.534754	+	0.926221i
$325$	−1.56786	+	15.3595i	−0.0869690	+	0.851992i
$326$	−10.4237	−	18.0544i	−0.577318	−	0.999943i
$327$			17.0991i			0.945582i
$328$	−15.0569	−	26.0794i	−0.831381	−	1.43999i
$329$	0.583427	−	0.752916i	0.0321654	−	0.0415096i
$330$		−	4.32276i		−	0.237960i
$331$	5.70588	−	3.29429i	0.313623	−	0.181071i	−0.334923	−	0.942245i	$-0.608710\pi$
$331$	5.70588	−	3.29429i	0.313623	−	0.181071i	0.648547	+	0.761175i	$0.275377\pi$
$332$			38.1277i			2.09253i
$333$	−4.81294	+	2.77875i	−0.263748	+	0.152275i
$334$	3.06059	+	5.30110i	0.167468	+	0.290063i
$335$	−0.865365	−	1.49886i	−0.0472799	−	0.0818912i
$336$	0.965050	+	0.747808i	0.0526478	+	0.0407963i
$337$	−4.22290			−0.230036			−0.115018	−	0.993363i	$-0.536693\pi$
$337$	−4.22290			−0.230036			−0.115018	+	0.993363i	$0.536693\pi$
$338$	28.4210	−	9.42313i	1.54590	−	0.512551i
$339$	−2.56187	−	4.43728i	−0.139141	−	0.241000i
$340$	5.02347	+	2.90030i	0.272436	+	0.157291i
$341$	−11.8183			−0.639998
$342$	0.0452902	−	0.0784450i	0.00244902	−	0.00424182i
$343$	7.33014	−	17.0079i	0.395790	−	0.918341i
$344$	24.1198	+	13.9256i	1.30045	+	0.750817i
$345$	8.45293	−	4.88030i	0.455091	−	0.262747i
$346$	39.0700	−	22.5571i	2.10042	−	1.21268i
$347$	−9.09478			−0.488233			−0.244117	−	0.969746i	$-0.578498\pi$
$347$	−9.09478			−0.488233			−0.244117	+	0.969746i	$0.578498\pi$
$348$	6.62111			0.354929
$349$	7.98521	−	4.61026i	0.427439	−	0.246782i	−0.270816	−	0.962631i	$-0.587294\pi$
$349$	7.98521	−	4.61026i	0.427439	−	0.246782i	0.698255	+	0.715849i	$0.253960\pi$
$350$	−9.87149	−	24.1553i	−0.527653	−	1.29116i
$351$	−16.4926	−	11.9073i	−0.880310	−	0.635564i
$352$	−3.97674	+	6.88792i	−0.211961	+	0.367127i
$353$	1.86584	+	1.07724i	0.0993087	+	0.0573359i	0.548832	−	0.835933i	$-0.315073\pi$
$353$	1.86584	+	1.07724i	0.0993087	+	0.0573359i	−0.449523	+	0.893269i	$0.648406\pi$
$354$	2.78473	−	4.82330i	0.148007	−	0.256356i
$355$	6.02167	+	10.4298i	0.319597	+	0.553559i
$356$			57.8752i			3.06738i
$357$	−6.38265	−	4.94585i	−0.337805	−	0.261762i
$358$	5.77128	+	3.33205i	0.305021	+	0.176104i
$359$	−7.41107	−	4.27878i	−0.391141	−	0.225825i	0.291513	−	0.956567i	$-0.405841\pi$
$359$	−7.41107	−	4.27878i	−0.391141	−	0.225825i	−0.682654	+	0.730741i	$0.739175\pi$
$360$	−2.11185			−0.111304
$361$	−9.49888	+	16.4525i	−0.499941	+	0.865923i
$362$			3.15096i			0.165611i
$363$	−12.8769			−0.675860
$364$	−21.7424	+	22.8317i	−1.13961	+	1.19670i
$365$	5.72896			0.299867
$366$			15.3454i			0.802117i
$367$	−1.14912	+	1.99033i	−0.0599833	+	0.103894i	−0.894458	−	0.447153i	$-0.852438\pi$
$367$	−1.14912	+	1.99033i	−0.0599833	+	0.103894i	0.834474	+	0.551047i	$0.185771\pi$
$368$	2.44877			0.127651
$369$	−7.19439	−	4.15368i	−0.374525	−	0.216232i
$370$	11.3273	+	6.53979i	0.588876	+	0.339988i
$371$	6.64158	−	2.71420i	0.344814	−	0.140914i
$372$		−	38.2795i		−	1.98470i
$373$	−5.88418	−	10.1917i	−0.304672	−	0.527707i	0.672517	−	0.740082i	$-0.265213\pi$
$373$	−5.88418	−	10.1917i	−0.304672	−	0.527707i	−0.977188	+	0.212375i	$0.931880\pi$
$374$	−3.58636	+	6.21175i	−0.185446	+	0.321202i
$375$	−10.0350	−	5.79373i	−0.518207	−	0.299187i
$376$	0.541073	−	0.937166i	0.0279037	−	0.0483307i
$377$	−0.497847	+	4.87715i	−0.0256404	+	0.251186i
$378$	34.0646	+	4.64917i	1.75210	+	0.239127i
$379$	−6.92034	+	3.99546i	−0.355474	+	0.205233i	−0.667094	−	0.744974i	$-0.732462\pi$
$379$	−6.92034	+	3.99546i	−0.355474	+	0.205233i	0.311619	+	0.950207i	$0.399129\pi$
$380$	−0.132812			−0.00681310
$381$	−23.1315			−1.18506
$382$	3.01846	−	1.74271i	0.154438	−	0.0891647i
$383$	−24.4605	+	14.1223i	−1.24988	+	0.721616i	−0.971084	−	0.238736i	$-0.923267\pi$
$383$	−24.4605	+	14.1223i	−1.24988	+	0.721616i	−0.278791	+	0.960352i	$0.589934\pi$
$384$	−24.1508	−	13.9435i	−1.23244	−	0.711551i
$385$	−3.11975	+	1.27494i	−0.158997	+	0.0649770i
$386$	−8.00839	+	13.8709i	−0.407616	+	0.706012i
$387$	7.68316			0.390557
$388$	−1.21997	−	0.704352i	−0.0619347	−	0.0357580i
$389$	3.84043	+	6.65182i	0.194717	+	0.337261i	0.946808	−	0.321799i	$-0.104288\pi$
$389$	3.84043	+	6.65182i	0.194717	+	0.337261i	−0.752090	+	0.659060i	$0.770954\pi$
$390$	−1.05278	+	10.3135i	−0.0533094	+	0.522246i
$391$	−16.1957			−0.819050
$392$	5.63834	−	20.2714i	0.284779	−	1.02386i
$393$	−1.87498	−	3.24756i	−0.0945801	−	0.163818i
$394$	17.8241	+	30.8722i	0.897964	+	1.55532i
$395$	−8.55513	+	4.93931i	−0.430455	+	0.248524i
$396$		−	4.12017i		−	0.207046i
$397$	6.45433	−	3.72641i	0.323933	−	0.187023i	−0.329211	−	0.944256i	$-0.606783\pi$
$397$	6.45433	−	3.72641i	0.323933	−	0.187023i	0.653144	+	0.757233i	$0.273449\pi$
$398$			15.2368i			0.763750i
$399$	0.183180	+	0.0250005i	0.00917046	+	0.00125159i
$400$	−0.670563	−	1.16145i	−0.0335282	−	0.0580725i
$401$			18.1982i			0.908777i	0.890804	+	0.454389i	$0.150142\pi$
$401$			18.1982i			0.908777i	−0.890804	+	0.454389i	$0.849858\pi$
$402$	3.46593	+	6.00316i	0.172865	+	0.299411i
$403$	28.1969	+	2.87826i	1.40459	+	0.143376i
$404$	−15.9798	+	27.6778i	−0.795025	+	1.37702i
$405$	4.27409	−	2.46765i	0.212381	−	0.122618i
$406$	−3.13453	−	7.67011i	−0.155564	−	0.380661i
$407$	−5.03804	+	8.72615i	−0.249727	+	0.432539i
$408$	−7.94458	−	4.58681i	−0.393315	−	0.227081i
$409$		−	29.2825i		−	1.44793i	−0.689838	−	0.723964i	$-0.742318\pi$
$409$		−	29.2825i		−	1.44793i	0.689838	−	0.723964i	$-0.257682\pi$
$410$			19.5514i			0.965573i
$411$	−2.37933	−	1.37371i	−0.117364	−	0.0677599i
$412$	16.4892	−	28.5602i	0.812365	−	1.40706i
$413$	−4.30231	−	0.587183i	−0.211703	−	0.0288934i
$414$	12.9322	−	7.46641i	0.635583	−	0.366954i
$415$	4.88728	−	8.46502i	0.239907	−	0.415531i
$416$	11.1655	−	15.4651i	0.547432	−	0.758241i
$417$	11.4990	+	19.9169i	0.563109	+	0.975334i
$418$		−	0.164228i		−	0.00803264i
$419$	10.3697	+	17.9608i	0.506591	+	0.877441i	0.999971	+	0.00762733i	$0.00242788\pi$
$419$	10.3697	+	17.9608i	0.506591	+	0.877441i	−0.493380	+	0.869814i	$0.664239\pi$
$420$	−4.12953	−	10.1049i	−0.201500	−	0.493067i
$421$			24.8696i			1.21207i	0.795437	+	0.606036i	$0.207241\pi$
$421$			24.8696i			1.21207i	−0.795437	+	0.606036i	$0.792759\pi$
$422$	16.1456	−	9.32165i	0.785954	−	0.453771i
$423$		−	0.298526i		−	0.0145148i
$424$	7.05923	−	4.07565i	0.342826	−	0.197931i
$425$	4.43497	+	7.68159i	0.215128	+	0.372612i
$426$	−24.1178	−	41.7733i	−1.16851	−	2.02392i
$427$	11.0748	−	4.52592i	0.535948	−	0.219025i
$428$	−32.5950			−1.57554
$429$	−7.94520	−	0.811025i	−0.383598	−	0.0391566i
$430$	−9.04115	−	15.6597i	−0.436003	−	0.755179i
$431$	−18.3327	−	10.5844i	−0.883055	−	0.509832i	−0.0113906	−	0.999935i	$-0.503626\pi$
$431$	−18.3327	−	10.5844i	−0.883055	−	0.509832i	−0.871665	+	0.490103i	$0.836959\pi$
$432$	1.76698			0.0850138
$433$	−11.7148	+	20.2906i	−0.562977	+	0.975105i	0.434258	+	0.900789i	$0.357011\pi$
$433$	−11.7148	+	20.2906i	−0.562977	+	0.975105i	−0.997235	+	0.0743163i	$0.976323\pi$
$434$	−44.3442	+	18.1220i	−2.12859	+	0.869885i
$435$	−1.47000	−	0.848707i	−0.0704813	−	0.0406924i
$436$	33.2178	−	19.1783i	1.59084	−	0.918474i
$437$	0.321139	−	0.185409i	0.0153621	−	0.00886934i
$438$	−22.9454			−1.09637
$439$	12.0384			0.574561			0.287280	−	0.957847i	$-0.407249\pi$
$439$	12.0384			0.574561			0.287280	+	0.957847i	$0.407249\pi$
$440$	−3.31593	+	1.91445i	−0.158081	+	0.0912680i
$441$	−1.44905	−	5.62067i	−0.0690025	−	0.267651i
$442$	10.0694	−	13.9470i	0.478952	−	0.663390i
$443$	−7.86656	+	13.6253i	−0.373752	+	0.647357i	−0.990139	−	0.140086i	$-0.955262\pi$
$443$	−7.86656	+	13.6253i	−0.373752	+	0.647357i	0.616388	+	0.787443i	$0.288595\pi$
$444$	−28.2640	−	16.3182i	−1.34135	−	0.774427i
$445$	7.41855	−	12.8493i	0.351673	−	0.609116i
$446$	−18.4930	−	32.0308i	−0.875669	−	1.51670i
$447$		−	9.37592i		−	0.443466i
$448$	−4.58363	+	33.5845i	−0.216556	+	1.58672i
$449$	22.5177	+	13.0006i	1.06268	+	0.613536i	0.926171	−	0.377104i	$-0.123080\pi$
$449$	22.5177	+	13.0006i	1.06268	+	0.613536i	0.136504	+	0.990640i	$0.456413\pi$
$450$	−7.08263	−	4.08916i	−0.333878	−	0.192765i
$451$	−15.0617			−0.709230
$452$	−5.74676	+	9.95369i	−0.270305	+	0.468182i
$453$		−	0.978449i		−	0.0459716i
$454$	−2.98459			−0.140074
$455$	7.75380	−	2.28204i	0.363504	−	0.106984i
$456$	0.210041			0.00983605
$457$		−	30.7958i		−	1.44057i	−0.693679	−	0.720284i	$-0.744011\pi$
$457$		−	30.7958i		−	1.44057i	0.693679	−	0.720284i	$-0.255989\pi$
$458$	23.9742	−	41.5245i	1.12024	−	1.94031i
$459$	−11.6864			−0.545476
$460$	−18.9616	−	10.9475i	−0.884088	−	0.510429i
$461$	−29.5278	−	17.0479i	−1.37525	−	0.794000i	−0.383665	−	0.923472i	$-0.625338\pi$
$461$	−29.5278	−	17.0479i	−1.37525	−	0.794000i	−0.991583	+	0.129472i	$0.958672\pi$
$462$	12.4951	−	5.10635i	0.581325	−	0.237569i
$463$		−	1.69184i		−	0.0786263i	−0.999227	−	0.0393131i	$-0.987483\pi$
$463$		−	1.69184i		−	0.0786263i	0.999227	−	0.0393131i	$-0.0125170\pi$
$464$	−0.212926	−	0.368799i	−0.00988485	−	0.0171211i
$465$	−4.90674	+	8.49871i	−0.227544	+	0.394118i
$466$	26.5378	+	15.3216i	1.22934	+	0.709761i
$467$	14.1762	−	24.5539i	0.655996	−	1.13622i	−0.325647	−	0.945491i	$-0.605582\pi$
$467$	14.1762	−	24.5539i	0.655996	−	1.13622i	0.981643	−	0.190727i	$-0.0610845\pi$
$468$	−1.00344	+	9.83015i	−0.0463838	+	0.454399i
$469$	3.31027	−	4.27192i	0.152854	−	0.197259i
$470$	−0.608453	+	0.351290i	−0.0280658	+	0.0162038i
$471$	24.4224			1.12532
$472$	−4.93318			−0.227068
$473$	12.0637	−	6.96501i	0.554692	−	0.320251i
$474$	34.2647	−	19.7827i	1.57383	−	0.908651i
$475$	−0.175879	−	0.101544i	−0.00806989	−	0.00465915i
$476$	−2.44936	+	17.9466i	−0.112266	+	0.822581i
$477$	1.12433	−	1.94739i	0.0514794	−	0.0891650i
$478$	−30.7837			−1.40801
$479$	5.44077	+	3.14123i	0.248595	+	0.143526i	0.619121	−	0.785296i	$-0.287489\pi$
$479$	5.44077	+	3.14123i	0.248595	+	0.143526i	−0.370526	+	0.928822i	$0.620822\pi$
$480$	3.30213	+	5.71946i	0.150721	+	0.261056i
$481$	14.1453	−	19.5924i	0.644969	−	0.893338i
$482$	−1.92128			−0.0875117
$483$	24.0919	+	18.6686i	1.09622	+	0.849450i
$484$	14.4427	+	25.0154i	0.656484	+	1.13706i
$485$	0.180570	+	0.312757i	0.00819927	+	0.0142016i
$486$	16.6425	−	9.60853i	0.754917	−	0.435852i
$487$		−	13.0176i		−	0.589883i	−0.955515	−	0.294942i	$-0.904700\pi$
$487$		−	13.0176i		−	0.589883i	0.955515	−	0.294942i	$-0.0953002\pi$
$488$	11.7712	−	6.79613i	0.532859	−	0.307647i
$489$		−	13.3358i		−	0.603065i
$490$	−9.75082	+	9.56756i	−0.440497	+	0.432218i
$491$	−6.17616	−	10.6974i	−0.278726	−	0.482768i	0.692342	−	0.721569i	$-0.256579\pi$
$491$	−6.17616	−	10.6974i	−0.278726	−	0.482768i	−0.971068	+	0.238801i	$0.923246\pi$
$492$		−	48.7849i		−	2.19939i
$493$	1.40825	+	2.43916i	0.0634244	+	0.109854i
$494$	−0.0399964	+	0.391825i	−0.00179952	+	0.0176290i
$495$	−0.528131	+	0.914749i	−0.0237377	+	0.0411149i
$496$	−2.13218	+	1.23102i	−0.0957378	+	0.0552743i
$497$	−23.0347	+	29.7264i	−1.03325	+	1.33341i
$498$	−19.5744	+	33.9038i	−0.877148	+	1.51926i
$499$	7.92708	+	4.57670i	0.354865	+	0.204881i	0.666826	−	0.745214i	$-0.267652\pi$
$499$	7.92708	+	4.57670i	0.354865	+	0.204881i	−0.311961	+	0.950095i	$0.600986\pi$
$500$			25.9929i			1.16244i
$501$			3.91562i			0.174937i
$502$	−54.3993	−	31.4074i	−2.42796	−	1.40178i
$503$	−11.2519	+	19.4888i	−0.501696	+	0.868963i	0.498302	+	0.867003i	$0.333957\pi$
$503$	−11.2519	+	19.4888i	−0.501696	+	0.868963i	−0.999998	+	0.00195935i	$0.999376\pi$
$504$	−2.49467	−	6.10439i	−0.111121	−	0.271911i
$505$	7.09559	−	4.09664i	0.315750	−	0.182298i
$506$	13.5370	−	23.4469i	0.601795	−	1.04234i
$507$	18.7587	+	3.86999i	0.833101	+	0.171872i
$508$	25.9443	+	44.9368i	1.15109	+	1.99375i
$509$			38.6606i			1.71360i	0.515649	+	0.856800i	$0.327551\pi$
$509$			38.6606i			1.71360i	−0.515649	+	0.856800i	$0.672449\pi$
$510$	2.97797	+	5.15800i	0.131867	+	0.228400i
$511$	6.76745	+	16.5598i	0.299374	+	0.732562i
$512$			3.53972i			0.156435i
$513$	0.231727	−	0.133787i	0.0102310	−	0.00590686i
$514$			15.0907i			0.665623i
$515$	−7.32179	+	4.22724i	−0.322637	+	0.186274i
$516$	22.5596	+	39.0744i	0.993132	+	1.72016i
$517$	−0.270623	−	0.468732i	−0.0119020	−	0.0206148i
$518$	−5.52298	+	40.4671i	−0.242666	+	1.77802i
$519$	28.8588			1.26676
$520$	8.37761	−	3.76006i	0.367383	−	0.164889i
$521$	−20.1176	−	34.8446i	−0.881366	−	1.52657i	−0.849823	−	0.527068i	$-0.823291\pi$
$521$	−20.1176	−	34.8446i	−0.881366	−	1.52657i	−0.0315430	−	0.999502i	$-0.510042\pi$
$522$	−2.24897	−	1.29844i	−0.0984348	−	0.0568313i
$523$	−0.732146			−0.0320145			−0.0160073	−	0.999872i	$-0.505095\pi$
$523$	−0.732146			−0.0320145			−0.0160073	+	0.999872i	$0.505095\pi$
$524$	−4.20594	+	7.28491i	−0.183737	+	0.318243i
$525$	2.25724	−	16.5389i	0.0985142	−	0.721818i
$526$	−45.0581	−	26.0143i	−1.96463	−	1.13428i
$527$	14.1018	−	8.14169i	0.614285	−	0.354658i
$528$	0.600798	−	0.346871i	0.0261464	−	0.0150956i
$529$	38.1321			1.65792
$530$	−5.29221			−0.229879
$531$	−1.17857	+	0.680446i	−0.0511455	+	0.0295288i
$532$	−0.156887	−	0.383898i	−0.00680189	−	0.0166441i
$533$	35.9353	+	3.66817i	1.55653	+	0.158886i
$534$	−29.7125	+	51.4636i	−1.28579	+	2.22705i
$535$	7.23667	+	4.17809i	0.312868	+	0.180635i
$536$	3.06996	−	5.31733i	0.132602	−	0.229674i
$537$	2.13146	+	3.69179i	0.0919791	+	0.159312i
$538$		−	36.8553i		−	1.58894i
$539$	−7.37054	−	7.51171i	−0.317472	−	0.323552i
$540$	−13.6823	−	7.89946i	−0.588791	−	0.339939i
$541$	−20.4847	−	11.8268i	−0.880705	−	0.508476i	−0.00981448	−	0.999952i	$-0.503124\pi$
$541$	−20.4847	−	11.8268i	−0.880705	−	0.508476i	−0.870891	+	0.491476i	$0.836457\pi$
$542$	20.1751			0.866595
$543$	−1.00781	+	1.74558i	−0.0432492	+	0.0749099i
$544$		−	10.9584i		−	0.469837i
$545$	−9.83325			−0.421210
$546$	−31.0553	+	9.13996i	−1.32904	+	0.391154i
$547$	−12.9472			−0.553582			−0.276791	−	0.960930i	$-0.589271\pi$
$547$	−12.9472			−0.553582			−0.276791	+	0.960930i	$0.589271\pi$
$548$			6.16298i			0.263270i
$549$	1.87481	−	3.24727i	0.0800151	−	0.138590i
$550$	−14.8278			−0.632258
$551$	−0.0558475	−	0.0322436i	−0.00237918	−	0.00137362i
$552$	29.9876	+	17.3133i	1.27636	+	0.736904i
$553$	−24.3832	−	18.8943i	−1.03688	−	0.803467i
$554$		−	45.8771i		−	1.94913i
$555$	4.18340	+	7.24585i	0.177575	+	0.307569i
$556$	25.7946	−	44.6775i	1.09393	−	1.89475i
$557$	5.54845	+	3.20340i	0.235096	+	0.135732i	0.612921	−	0.790145i	$-0.289995\pi$
$557$	5.54845	+	3.20340i	0.235096	+	0.135732i	−0.377825	+	0.925877i	$0.623328\pi$
$558$	−7.50685	+	13.0023i	−0.317790	+	0.550429i
$559$	−30.4787	+	13.6795i	−1.28911	+	0.578582i
$560$	−0.430045	+	0.554975i	−0.0181727	+	0.0234520i
$561$	−3.97355	+	2.29413i	−0.167764	+	0.0968584i
$562$	32.2996			1.36248
$563$	−7.32084			−0.308537			−0.154268	−	0.988029i	$-0.549302\pi$
$563$	−7.32084			−0.308537			−0.154268	+	0.988029i	$0.549302\pi$
$564$	1.51822	−	0.876546i	0.0639287	−	0.0369092i
$565$	2.55176	−	1.47326i	0.107354	−	0.0619806i
$566$	−2.01980	−	1.16613i	−0.0848986	−	0.0490162i
$567$	12.1817	+	9.43948i	0.511583	+	0.396421i
$568$	−21.3625	+	37.0009i	−0.896349	+	1.55252i
$569$	4.31743			0.180996			0.0904981	−	0.995897i	$-0.471154\pi$
$569$	4.31743			0.180996			0.0904981	+	0.995897i	$0.471154\pi$
$570$	−0.118098	−	0.0681842i	−0.00494660	−	0.00285592i
$571$	17.0847	+	29.5916i	0.714974	+	1.23837i	0.962970	+	0.269610i	$0.0868946\pi$
$571$	17.0847	+	29.5916i	0.714974	+	1.23837i	−0.247996	+	0.968761i	$0.579772\pi$
$572$	7.33577	+	16.3445i	0.306724	+	0.683398i
$573$	2.22956			0.0931413
$574$	−56.5140	+	23.0954i	−2.35885	+	0.963985i
$575$	−16.7402	−	28.9949i	−0.698115	−	1.20917i
$576$	5.31166	+	9.20007i	0.221319	+	0.383336i
$577$	−5.50494	+	3.17828i	−0.229174	+	0.132314i	−0.610191	−	0.792254i	$-0.708907\pi$
$577$	−5.50494	+	3.17828i	−0.229174	+	0.132314i	0.381017	+	0.924568i	$0.375574\pi$
$578$			29.2729i			1.21759i
$579$	−8.87301	+	5.12283i	−0.368750	+	0.212898i
$580$			3.80763i			0.158103i
$581$	30.2417	+	4.12740i	1.25464	+	0.171234i
$582$	−0.723214	−	1.25264i	−0.0299782	−	0.0519237i
$583$		−	4.07695i		−	0.168850i
$584$	10.1620	+	17.6011i	0.420507	+	0.728339i
$585$	1.48283	−	2.05384i	0.0613074	−	0.0849160i
$586$	−0.229446	+	0.397412i	−0.00947832	+	0.0164169i
$587$	27.2036	−	15.7060i	1.12281	−	0.648256i	0.180695	−	0.983539i	$-0.442165\pi$
$587$	27.2036	−	15.7060i	1.12281	−	0.648256i	0.942118	+	0.335283i	$0.108832\pi$
$588$	24.3304	−	23.8731i	1.00337	−	0.984511i
$589$	−0.186414	+	0.322878i	−0.00768104	+	0.0133040i
$590$	2.77376	+	1.60143i	0.114194	+	0.0659298i
$591$			22.8035i			0.938011i
$592$			2.09909i			0.0862719i
$593$	0.409641	+	0.236506i	0.0168219	+	0.00971215i	0.508387	−	0.861128i	$-0.330242\pi$
$593$	0.409641	+	0.236506i	0.0168219	+	0.00971215i	−0.491565	+	0.870841i	$0.663575\pi$
$594$	9.76804	−	16.9187i	0.400787	−	0.694184i
$595$	2.84423	−	3.67049i	0.116602	−	0.150476i
$596$	−18.2143	+	10.5160i	−0.746086	+	0.430753i
$597$	−4.87335	+	8.44089i	−0.199453	+	0.345463i
$598$	−38.0079	+	52.6442i	−1.55426	+	2.15278i
$599$	4.81348	+	8.33719i	0.196673	+	0.340648i	0.947448	−	0.319910i	$-0.103653\pi$
$599$	4.81348	+	8.33719i	0.196673	+	0.340648i	−0.750774	+	0.660559i	$0.770320\pi$
$600$		−	18.9641i		−	0.774207i
$601$	20.5399	+	35.5762i	0.837842	+	1.45118i	0.891696	+	0.452635i	$0.149516\pi$
$601$	20.5399	+	35.5762i	0.837842	+	1.45118i	−0.0538542	+	0.998549i	$0.517151\pi$
$602$	34.5850	−	44.6322i	1.40958	−	1.81907i
$603$		−	1.69379i		−	0.0689765i
$604$	−1.90080	+	1.09743i	−0.0773424	+	0.0446537i
$605$		−	7.40514i		−	0.301062i
$606$	−28.4190	+	16.4077i	−1.15444	+	0.666518i
$607$	−9.54289	−	16.5288i	−0.387334	−	0.670882i	0.604756	−	0.796411i	$-0.293271\pi$
$607$	−9.54289	−	16.5288i	−0.387334	−	0.670882i	−0.992090	+	0.125529i	$0.959937\pi$
$608$	0.125453	+	0.217290i	0.00508777	+	0.00881228i
$609$	0.716750	−	5.25166i	0.0290442	−	0.212808i
$610$	−8.82474			−0.357303
$611$	0.531513	+	1.18424i	0.0215027	+	0.0479092i
$612$	2.83840	+	4.91626i	0.114736	+	0.198728i
$613$	−32.9131	−	19.0024i	−1.32935	−	0.767500i	−0.344149	−	0.938915i	$-0.611833\pi$
$613$	−32.9131	−	19.0024i	−1.32935	−	0.767500i	−0.985199	+	0.171415i	$0.945166\pi$
$614$	62.6498			2.52834
$615$	−6.25334	+	10.8311i	−0.252159	+	0.436752i
$616$	−9.45082	−	7.32335i	−0.380784	−	0.295066i
$617$	7.20117	+	4.15759i	0.289908	+	0.167378i	0.637900	−	0.770119i	$-0.279803\pi$
$617$	7.20117	+	4.15759i	0.289908	+	0.167378i	−0.347992	+	0.937497i	$0.613136\pi$
$618$	29.3250	−	16.9308i	1.17962	−	0.681056i
$619$	−38.5146	+	22.2364i	−1.54803	+	0.893756i	−0.549739	+	0.835336i	$0.685273\pi$
$619$	−38.5146	+	22.2364i	−1.54803	+	0.893756i	−0.998292	+	0.0584199i	$0.981394\pi$
$620$	22.0135			0.884085
$621$	44.1116			1.77014
$622$	54.0579	−	31.2103i	2.16752	−	1.25142i
$623$	45.9048	+	6.26512i	1.83914	+	0.251007i
$624$	−1.51790	+	0.681266i	−0.0607646	+	0.0272725i
$625$	−7.37342	+	12.7711i	−0.294937	+	0.510845i
$626$	−44.0397	−	25.4263i	−1.76018	−	1.01624i
$627$	0.0525269	−	0.0909792i	0.00209772	−	0.00363336i
$628$	−27.3921	−	47.4445i	−1.09306	−	1.89324i
$629$		−	13.8829i		−	0.553549i
$630$	−0.578966	+	4.24211i	−0.0230666	+	0.169010i
$631$	−10.1779	−	5.87622i	−0.405177	−	0.233929i	0.283539	−	0.958961i	$-0.408492\pi$
$631$	−10.1779	−	5.87622i	−0.405177	−	0.233929i	−0.688715	+	0.725032i	$0.741825\pi$
$632$	−30.3501	−	17.5227i	−1.20726	−	0.697014i
$633$	11.9258			0.474008
$634$	−8.14001	+	14.0989i	−0.323281	+	0.559939i
$635$		−	13.3023i		−	0.527887i
$636$	13.2052			0.523620
$637$	15.7557	+	19.7170i	0.624263	+	0.781215i
$638$	−4.70831			−0.186404
$639$			11.7863i			0.466259i
$640$	8.01854	−	13.8885i	0.316961	−	0.548992i
$641$	−10.4868			−0.414205			−0.207102	−	0.978319i	$-0.566403\pi$
$641$	−10.4868			−0.414205			−0.207102	+	0.978319i	$0.566403\pi$
$642$	−28.9840	−	16.7339i	−1.14391	−	0.660436i
$643$	27.0912	+	15.6411i	1.06837	+	0.616825i	0.927736	−	0.373237i	$-0.121752\pi$
$643$	27.0912	+	15.6411i	1.06837	+	0.616825i	0.140635	+	0.990061i	$0.455085\pi$
$644$	9.24536	−	67.7411i	0.364318	−	2.66937i
$645$		−	11.5669i		−	0.455448i
$646$	0.113137	+	0.195959i	0.00445133	+	0.00770992i
$647$	−13.4337	+	23.2679i	−0.528135	+	0.914757i	0.471327	+	0.881959i	$0.343775\pi$
$647$	−13.4337	+	23.2679i	−0.528135	+	0.914757i	−0.999462	+	0.0327983i	$0.989558\pi$
$648$	15.1627	+	8.75422i	0.595649	+	0.343898i
$649$	−1.23369	+	2.13681i	−0.0484265	+	0.0838772i
$650$	35.3770	+	3.61119i	1.38760	+	0.141643i
$651$	−30.3621	−	4.14384i	−1.18998	−	0.162410i
$652$	−25.9070	+	14.9574i	−1.01459	+	0.585776i
$653$	−4.14161			−0.162074			−0.0810369	−	0.996711i	$-0.525823\pi$
$653$	−4.14161			−0.162074			−0.0810369	+	0.996711i	$0.525823\pi$
$654$	39.3838			1.54003
$655$	1.86759	−	1.07825i	0.0729726	−	0.0421308i
$656$	−2.71734	+	1.56886i	−0.106094	+	0.0612536i
$657$	4.85553	+	2.80334i	0.189432	+	0.109369i
$658$	−1.73417	−	1.34379i	−0.0676048	−	0.0523863i
$659$	−10.7276	+	18.5807i	−0.417887	+	0.723801i	−0.995727	−	0.0923492i	$-0.970562\pi$
$659$	−10.7276	+	18.5807i	−0.417887	+	0.723801i	0.577840	+	0.816150i	$0.303896\pi$
$660$	−6.20288			−0.241447
$661$	−36.7084	−	21.1936i	−1.42779	−	0.824335i	−0.430844	−	0.902426i	$-0.641784\pi$
$661$	−36.7084	−	21.1936i	−1.42779	−	0.824335i	−0.996946	+	0.0780909i	$0.975118\pi$
$662$	−7.58763	−	13.1422i	−0.294902	−	0.510785i
$663$	10.0391	−	4.50576i	0.389885	−	0.174989i
$664$	34.6762			1.34570
$665$	−0.0143772	+	0.105342i	−0.000557522	+	0.00408499i
$666$	6.40021	+	11.0855i	0.248003	+	0.429554i
$667$	−5.31558	−	9.20685i	−0.205820	−	0.356491i
$668$	7.60673	−	4.39175i	0.294313	−	0.169922i
$669$		−	23.6593i		−	0.914722i
$670$	−3.45226	+	1.99317i	−0.133373	+	0.0770027i
$671$		−	6.79830i		−	0.262445i
$672$	−12.6316	+	16.3012i	−0.487275	+	0.628831i
$673$	−14.7928	−	25.6219i	−0.570220	−	0.987650i	−0.996543	−	0.0830790i	$-0.973525\pi$
$673$	−14.7928	−	25.6219i	−0.570220	−	0.987650i	0.426323	−	0.904571i	$-0.359809\pi$
$674$			9.72645i			0.374649i
$675$	−12.0794	−	20.9221i	−0.464935	−	0.805292i
$676$	−13.5216	−	40.7823i	−0.520061	−	1.56855i
$677$	−16.0830	+	27.8565i	−0.618118	+	1.07061i	0.371711	+	0.928349i	$0.378771\pi$
$677$	−16.0830	+	27.8565i	−0.618118	+	1.07061i	−0.989829	+	0.142263i	$0.954562\pi$
$678$	−10.2202	+	5.90066i	−0.392506	+	0.226613i
$679$	−0.690734	+	0.891396i	−0.0265079	+	0.0342086i
$680$	2.63775	−	4.56872i	0.101153	−	0.175202i
$681$	−1.65341	−	0.954596i	−0.0633587	−	0.0365802i
$682$			27.2207i			1.04234i
$683$		−	8.60236i		−	0.329160i	−0.986364	−	0.164580i	$-0.947373\pi$
$683$		−	8.60236i		−	0.329160i	0.986364	−	0.164580i	$-0.0526269\pi$
$684$	−0.112563	−	0.0649885i	−0.00430397	−	0.00248490i
$685$	0.789983	−	1.36829i	0.0301837	−	0.0522797i
$686$	−39.1738	−	16.8833i	−1.49566	−	0.644606i
$687$	26.5625	−	15.3359i	1.01342	−	0.585100i
$688$	1.45097	−	2.51316i	0.0553179	−	0.0958134i
$689$	−0.992909	+	9.72704i	−0.0378268	+	0.370571i
$690$	−11.2406	−	19.4694i	−0.427924	−	0.741186i
$691$		−	20.4420i		−	0.777651i	−0.921311	−	0.388826i	$-0.872881\pi$
$691$		−	20.4420i		−	0.777651i	0.921311	−	0.388826i	$-0.127119\pi$
$692$	−32.3680	−	56.0629i	−1.23044	−	2.13119i
$693$	−3.26798	−	0.446017i	−0.124140	−	0.0169428i
$694$			20.9477i			0.795164i
$695$	−11.4537	+	6.61279i	−0.434463	+	0.250837i
$696$		−	6.02174i		−	0.228253i
$697$	17.9719	−	10.3761i	0.680736	−	0.393023i
$698$	−10.6187	−	18.3921i	−0.401922	−	0.696150i
$699$	9.80099	+	16.9758i	0.370708	+	0.642084i
$700$	−34.6613	+	14.1649i	−1.31007	+	0.535385i
$701$	−25.1373			−0.949422			−0.474711	−	0.880142i	$-0.657447\pi$
$701$	−25.1373			−0.949422			−0.474711	+	0.880142i	$0.657447\pi$
$702$	−27.4256	+	37.9869i	−1.03511	+	1.43372i
$703$	0.158933	+	0.275280i	0.00599427	+	0.0103824i
$704$	16.6803	+	9.63036i	0.628661	+	0.362958i
$705$	−0.449429			−0.0169265
$706$	2.48118	−	4.29753i	0.0933804	−	0.161740i
$707$	20.2233	+	15.6709i	0.760576	+	0.589363i
$708$	−6.92112	−	3.99591i	−0.260112	−	0.150176i
$709$	−25.5416	+	14.7464i	−0.959234	+	0.553814i	−0.895937	−	0.444181i	$-0.853495\pi$
$709$	−25.5416	+	14.7464i	−0.959234	+	0.553814i	−0.0632970	+	0.997995i	$0.520162\pi$
$710$	24.0227	−	13.8695i	0.901556	−	0.520514i
$711$	−9.66777			−0.362570
$712$	52.6360			1.97262
$713$	−53.2287	+	30.7316i	−1.99343	+	1.15091i
$714$	−11.3916	+	14.7009i	−0.426320	+	0.550169i
$715$	0.466399	−	4.56908i	0.0174423	−	0.170874i
$716$	4.78127	−	8.28140i	0.178684	−	0.309491i
$717$	−17.0536	−	9.84591i	−0.636879	−	0.367702i
$718$	−9.85518	+	17.0697i	−0.367792	+	0.637034i
$719$	−4.16576	−	7.21531i	−0.155357	−	0.269086i	0.777832	−	0.628472i	$-0.216319\pi$
$719$	−4.16576	−	7.21531i	−0.155357	−	0.269086i	−0.933189	+	0.359386i	$0.882986\pi$
$720$			0.220044i			0.00820055i
$721$	−20.8680	−	16.1704i	−0.777165	−	0.602218i
$722$	37.8946	+	21.8784i	1.41029	+	0.814231i
$723$	−1.06435	−	0.614504i	−0.0395837	−	0.0228537i
$724$	4.52143			0.168038
$725$	−2.91120	+	5.04235i	−0.108119	+	0.187268i
$726$			29.6588i			1.10074i
$727$	9.66141			0.358322			0.179161	−	0.983820i	$-0.442662\pi$
$727$	9.66141			0.358322			0.179161	+	0.983820i	$0.442662\pi$
$728$	20.7648	+	19.7742i	0.769595	+	0.732880i
$729$	29.7672			1.10249
$730$		−	13.1953i		−	0.488381i
$731$	−9.59645	+	16.6215i	−0.354938	+	0.614770i
$732$	22.0197			0.813870
$733$	−12.1398	−	7.00894i	−0.448395	−	0.258881i	0.258757	−	0.965942i	$-0.416687\pi$
$733$	−12.1398	−	7.00894i	−0.448395	−	0.258881i	−0.707152	+	0.707061i	$0.750020\pi$
$734$	4.58425	+	2.64672i	0.169208	+	0.0976921i
$735$	−8.46188	+	2.18154i	−0.312121	+	0.0804672i
$736$			41.3635i			1.52468i
$737$	−1.53547	−	2.65951i	−0.0565598	−	0.0979644i
$738$	−9.56704	+	16.5706i	−0.352168	+	0.609972i
$739$	33.6145	+	19.4073i	1.23653	+	0.713910i	0.968383	−	0.249468i	$-0.0802559\pi$
$739$	33.6145	+	19.4073i	1.23653	+	0.713910i	0.268146	+	0.963378i	$0.413589\pi$
$740$	9.38417	−	16.2539i	0.344969	−	0.597504i
$741$	−0.147479	+	0.204271i	−0.00541779	+	0.00750410i
$742$	−6.25153	−	15.2973i	−0.229501	−	0.561583i
$743$	29.7863	−	17.1971i	1.09275	−	0.630901i	0.158445	−	0.987368i	$-0.449352\pi$
$743$	29.7863	−	17.1971i	1.09275	−	0.630901i	0.934308	+	0.356467i	$0.116019\pi$
$744$	−34.8142			−1.27635
$745$	5.39185			0.197542
$746$	−23.4742	+	13.5528i	−0.859452	+	0.496205i
$747$	8.28434	−	4.78297i	0.303108	−	0.175000i
$748$	8.91346	+	5.14619i	0.325908	+	0.188163i
$749$	−3.52848	+	25.8533i	−0.128928	+	0.944660i
$750$	−13.3445	+	23.1134i	−0.487272	+	0.843980i
$751$	−48.1470			−1.75691			−0.878454	−	0.477827i	$-0.841425\pi$
$751$	−48.1470			−1.75691			−0.878454	+	0.477827i	$0.841425\pi$
$752$	−0.0976479	−	0.0563770i	−0.00356085	−	0.00205586i
$753$	−20.0908	−	34.7983i	−0.732150	−	1.26812i
$754$	11.2334	+	1.14667i	0.409096	+	0.0417594i
$755$	0.562681			0.0204781
$756$	6.67125	−	48.8805i	0.242631	−	1.77777i
$757$	3.45319	+	5.98110i	0.125508	+	0.217387i	0.921931	−	0.387353i	$-0.126611\pi$
$757$	3.45319	+	5.98110i	0.125508	+	0.217387i	−0.796423	+	0.604740i	$0.793277\pi$
$758$	9.20262	+	15.9394i	0.334254	+	0.578945i
$759$	14.9986	−	8.65942i	0.544413	−	0.314317i
$760$			0.120789i			0.00438147i
$761$	−27.6895	+	15.9865i	−1.00374	+	0.579511i	−0.909353	−	0.416025i	$-0.863423\pi$
$761$	−27.6895	+	15.9865i	−1.00374	+	0.579511i	−0.0943888	+	0.995535i	$0.530090\pi$
$762$			53.2781i			1.93006i
$763$	−11.6157	−	28.4234i	−0.420517	−	1.02900i
$764$	−2.50067	−	4.33129i	−0.0904712	−	0.156701i
$765$		−	1.45533i		−	0.0526174i
$766$	32.5274	+	56.3391i	1.17526	+	2.03562i
$767$	3.46382	−	4.79769i	0.125071	−	0.173234i
$768$	−13.2397	+	22.9319i	−0.477748	+	0.827483i
$769$	12.4665	−	7.19752i	0.449553	−	0.259549i	−0.258089	−	0.966121i	$-0.583093\pi$
$769$	12.4665	−	7.19752i	0.449553	−	0.259549i	0.707641	+	0.706572i	$0.249759\pi$
$770$	2.93653	+	7.18562i	0.105825	+	0.258952i
$771$	−4.82664	+	8.35999i	−0.173827	+	0.301078i
$772$	19.9039	+	11.4915i	0.716357	+	0.413589i

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.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.30327i q^{2} +(0.736680 - 1.27597i) q^{3} -3.30504 q^{4} +(0.733776 + 0.423646i) q^{5} +(-2.93889 - 1.69677i) q^{6} +(-0.357777 + 2.62145i) q^{7} +3.00585i q^{8} +(0.414604 + 0.718115i) q^{9} +O(q^{10})\)	\(q-2.30327i q^{2} +(0.736680 - 1.27597i) q^{3} -3.30504 q^{4} +(0.733776 + 0.423646i) q^{5} +(-2.93889 - 1.69677i) q^{6} +(-0.357777 + 2.62145i) q^{7} +3.00585i q^{8} +(0.414604 + 0.718115i) q^{9} +(0.975769 - 1.69008i) q^{10} +(1.30198 + 0.751701i) q^{11} +(-2.43476 + 4.21712i) q^{12} +(-2.92329 - 2.11054i) q^{13} +(6.03790 + 0.824057i) q^{14} +(1.08112 - 0.624183i) q^{15} +0.313194 q^{16} -2.07140 q^{17} +(1.65401 - 0.954943i) q^{18} +(0.0410731 - 0.0237136i) q^{19} +(-2.42516 - 1.40016i) q^{20} +(3.08132 + 2.38768i) q^{21} +(1.73137 - 2.99882i) q^{22} +7.81870 q^{23} +(3.83536 + 2.21435i) q^{24} +(-2.14105 - 3.70840i) q^{25} +(-4.86115 + 6.73311i) q^{26} +5.64180 q^{27} +(1.18247 - 8.66399i) q^{28} +(-0.679854 - 1.17754i) q^{29} +(-1.43766 - 2.49010i) q^{30} +(-6.80787 + 3.93052i) q^{31} +5.29033i q^{32} +(1.91829 - 1.10753i) q^{33} +4.77099i q^{34} +(-1.37309 + 1.77199i) q^{35} +(-1.37028 - 2.37340i) q^{36} +6.70219i q^{37} +(-0.0546187 - 0.0946024i) q^{38} +(-4.84652 + 2.17522i) q^{39} +(-1.27341 + 2.20562i) q^{40} +(-8.67622 + 5.00922i) q^{41} +(5.49947 - 7.09710i) q^{42} +(4.63283 - 8.02430i) q^{43} +(-4.30311 - 2.48440i) q^{44} +0.702581i q^{45} -18.0086i q^{46} +(-0.311781 - 0.180007i) q^{47} +(0.230724 - 0.399625i) q^{48} +(-6.74399 - 1.87579i) q^{49} +(-8.54144 + 4.93141i) q^{50} +(-1.52596 + 2.64304i) q^{51} +(9.66157 + 6.97543i) q^{52} +(-1.35591 - 2.34850i) q^{53} -12.9946i q^{54} +(0.636910 + 1.10316i) q^{55} +(-7.87968 - 1.07542i) q^{56} -0.0698773i q^{57} +(-2.71219 + 1.56588i) q^{58} +1.64120i q^{59} +(-3.57313 + 2.06295i) q^{60} +(-2.26097 - 3.91612i) q^{61} +(9.05305 + 15.6803i) q^{62} +(-2.03084 + 0.829938i) q^{63} +12.8114 q^{64} +(-1.25091 - 2.78711i) q^{65} +(-2.55093 - 4.41834i) q^{66} +(-1.76900 - 1.02133i) q^{67} +6.84606 q^{68} +(5.75988 - 9.97641i) q^{69} +(4.08136 + 3.16260i) q^{70} +(12.3096 + 7.10697i) q^{71} +(-2.15854 + 1.24624i) q^{72} +(5.85563 - 3.38075i) q^{73} +15.4369 q^{74} -6.30907 q^{75} +(-0.135748 + 0.0783743i) q^{76} +(-2.43637 + 3.14414i) q^{77} +(5.01012 + 11.1628i) q^{78} +(-5.82952 + 10.0970i) q^{79} +(0.229814 + 0.132683i) q^{80} +(2.91240 - 5.04442i) q^{81} +(11.5376 + 19.9837i) q^{82} -11.5362i q^{83} +(-10.1839 - 7.89138i) q^{84} +(-1.51994 - 0.877541i) q^{85} +(-18.4821 - 10.6706i) q^{86} -2.00334 q^{87} +(-2.25950 + 3.91357i) q^{88} -17.5112i q^{89} +1.61823 q^{90} +(6.57857 - 6.90814i) q^{91} -25.8411 q^{92} +11.5822i q^{93} +(-0.414604 + 0.718115i) q^{94} +0.0401846 q^{95} +(6.75029 + 3.89728i) q^{96} +(0.369125 + 0.213115i) q^{97} +(-4.32044 + 15.5332i) q^{98} +1.24663i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9	\( 12 q - 3 q^{3} - 8 q^{4} - 3 q^{5} - 9 q^{6} - 3 q^{7} - q^{9} + 12 q^{10} + 12 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - 12 q^{15} + 16 q^{16} - 34 q^{17} + 3 q^{18} + 9 q^{19} - 3 q^{20} + 21 q^{21} - 15 q^{22} - 6 q^{23} + 15 q^{24} - 5 q^{25} - 6 q^{26} + 12 q^{27} - 9 q^{28} - q^{29} + 11 q^{30} + 18 q^{31} - 6 q^{33} - 6 q^{35} - 13 q^{36} + 19 q^{38} - 4 q^{39} - q^{40} - 6 q^{41} - 8 q^{42} + 11 q^{43} - 33 q^{44} - 15 q^{47} + 19 q^{48} - 3 q^{49} + 18 q^{50} + 4 q^{51} - 7 q^{52} - 8 q^{53} - 15 q^{55} + 27 q^{56} - 24 q^{58} - 30 q^{60} + 5 q^{61} + 41 q^{62} - 30 q^{63} + 2 q^{64} + 21 q^{65} - 34 q^{66} + 15 q^{67} + 22 q^{68} + 7 q^{69} + 3 q^{70} + 30 q^{71} + 57 q^{72} + 42 q^{73} + 66 q^{74} - 2 q^{75} - 45 q^{76} - 19 q^{77} + 44 q^{78} - 35 q^{79} - 63 q^{80} + 14 q^{81} + 5 q^{82} - 12 q^{84} - 21 q^{85} - 57 q^{86} - 20 q^{87} - 14 q^{88} - 7 q^{91} - 66 q^{92} + q^{94} - 4 q^{95} + 21 q^{96} - 3 q^{97} - 18 q^{98}+O(q^{100}) \) 12 * q - 3 * q^3 - 8 * q^4 - 3 * q^5 - 9 * q^6 - 3 * q^7 - q^9 + 12 * q^10 + 12 * q^11 - q^12 - 2 * q^13 + 4 * q^14 - 12 * q^15 + 16 * q^16 - 34 * q^17 + 3 * q^18 + 9 * q^19 - 3 * q^20 + 21 * q^21 - 15 * q^22 - 6 * q^23 + 15 * q^24 - 5 * q^25 - 6 * q^26 + 12 * q^27 - 9 * q^28 - q^29 + 11 * q^30 + 18 * q^31 - 6 * q^33 - 6 * q^35 - 13 * q^36 + 19 * q^38 - 4 * q^39 - q^40 - 6 * q^41 - 8 * q^42 + 11 * q^43 - 33 * q^44 - 15 * q^47 + 19 * q^48 - 3 * q^49 + 18 * q^50 + 4 * q^51 - 7 * q^52 - 8 * q^53 - 15 * q^55 + 27 * q^56 - 24 * q^58 - 30 * q^60 + 5 * q^61 + 41 * q^62 - 30 * q^63 + 2 * q^64 + 21 * q^65 - 34 * q^66 + 15 * q^67 + 22 * q^68 + 7 * q^69 + 3 * q^70 + 30 * q^71 + 57 * q^72 + 42 * q^73 + 66 * q^74 - 2 * q^75 - 45 * q^76 - 19 * q^77 + 44 * q^78 - 35 * q^79 - 63 * q^80 + 14 * q^81 + 5 * q^82 - 12 * q^84 - 21 * q^85 - 57 * q^86 - 20 * q^87 - 14 * q^88 - 7 * q^91 - 66 * q^92 + q^94 - 4 * q^95 + 21 * q^96 - 3 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

Varieties

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