LMFDB - Embedded newform 966.2.i.n.415.4

Newspace parameters

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.173309020416.2
Defining polynomial:	$ x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 $ x^8 - 5x^6 - 28x^5 - 4x^4 + 70x^3 + 51x^2 + 406x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.4
Root			$-1.75834 + 0.512349i$ of defining polynomial
Character	$\chi$	$=$	966.415
Dual form			966.2.i.n.277.4

$q$-expansion

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.44864 - 2.50912i) q^{5} +1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.44864 - 2.50912i) q^{5} +1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.44864 - 2.50912i) q^{10} +(-0.809697 - 1.40244i) q^{11} +(0.500000 - 0.866025i) q^{12} -3.02636 q^{13} -2.64575 q^{14} +2.89728 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.77152 - 4.80040i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.38410 + 2.39733i) q^{19} -2.89728 q^{20} +(1.32288 - 2.29129i) q^{21} -1.61939 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.69711 - 2.93948i) q^{25} +(-1.51318 + 2.62090i) q^{26} -1.00000 q^{27} +(-1.32288 + 2.29129i) q^{28} +1.76820 q^{29} +(1.44864 - 2.50912i) q^{30} +(0.802888 + 1.39064i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.809697 - 1.40244i) q^{33} -5.54303 q^{34} -7.66548 q^{35} +1.00000 q^{36} +(0.513179 - 0.888851i) q^{37} +(1.38410 + 2.39733i) q^{38} +(-1.51318 - 2.62090i) q^{39} +(-1.44864 + 2.50912i) q^{40} +6.76820 q^{41} +(-1.32288 - 2.29129i) q^{42} +2.00000 q^{43} +(-0.809697 + 1.40244i) q^{44} +(1.44864 + 2.50912i) q^{45} +(0.500000 + 0.866025i) q^{46} +(2.07772 - 3.59871i) q^{47} -1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} -3.39422 q^{50} +(2.77152 - 4.80040i) q^{51} +(1.51318 + 2.62090i) q^{52} +(-2.44864 - 4.24117i) q^{53} +(-0.500000 + 0.866025i) q^{54} -4.69184 q^{55} +(1.32288 + 2.29129i) q^{56} -2.76820 q^{57} +(0.884100 - 1.53131i) q^{58} +(3.47849 + 6.02492i) q^{59} +(-1.44864 - 2.50912i) q^{60} +(6.89728 - 11.9464i) q^{61} +1.60578 q^{62} +2.64575 q^{63} +1.00000 q^{64} +(-4.38410 + 7.59348i) q^{65} +(-0.809697 - 1.40244i) q^{66} +(-3.61939 - 6.26897i) q^{67} +(-2.77152 + 4.80040i) q^{68} -1.00000 q^{69} +(-3.83274 + 6.63850i) q^{70} +4.87092 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.56803 - 4.44796i) q^{73} +(-0.513179 - 0.888851i) q^{74} +(1.69711 - 2.93948i) q^{75} +2.76820 q^{76} +(-2.14226 + 3.71050i) q^{77} -3.02636 q^{78} +(3.44532 - 5.96748i) q^{79} +(1.44864 + 2.50912i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.38410 - 5.86143i) q^{82} +5.15544 q^{83} -2.64575 q^{84} -16.0597 q^{85} +(1.00000 - 1.73205i) q^{86} +(0.884100 + 1.53131i) q^{87} +(0.809697 + 1.40244i) q^{88} +(7.28138 - 12.6117i) q^{89} +2.89728 q^{90} +(4.00349 + 6.93426i) q^{91} +1.00000 q^{92} +(-0.802888 + 1.39064i) q^{93} +(-2.07772 - 3.59871i) q^{94} +(4.01012 + 6.94574i) q^{95} +(-0.500000 + 0.866025i) q^{96} -14.6988 q^{97} +(3.50000 + 6.06218i) q^{98} +1.61939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^15 - 4 * q^16 + 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 6 * q^25 - 2 * q^26 - 8 * q^27 - 20 * q^29 - 2 * q^30 + 14 * q^31 + 4 * q^32 + 6 * q^33 + 4 * q^34 + 8 * q^36 - 6 * q^37 - 6 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 + 16 * q^43 - 6 * q^44 - 2 * q^45 + 4 * q^46 + 10 * q^47 - 8 * q^48 - 28 * q^49 - 12 * q^50 - 2 * q^51 + 2 * q^52 - 6 * q^53 - 4 * q^54 + 44 * q^55 + 12 * q^57 - 10 * q^58 - 24 * q^59 + 2 * q^60 + 28 * q^61 + 28 * q^62 + 8 * q^64 - 18 * q^65 - 6 * q^66 - 28 * q^67 + 2 * q^68 - 8 * q^69 + 32 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 6 * q^75 - 12 * q^76 - 14 * q^77 - 4 * q^78 + 4 * q^79 - 2 * q^80 - 4 * q^81 + 10 * q^82 + 28 * q^83 - 52 * q^85 + 8 * q^86 - 10 * q^87 + 6 * q^88 + 14 * q^89 - 4 * q^90 + 14 * q^91 + 8 * q^92 - 14 * q^93 - 10 * q^94 + 34 * q^95 - 4 * q^96 + 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.44864	−	2.50912i	0.647851	−	1.12211i	−0.335784	−	0.941939i	$-0.609001\pi$
$5$	1.44864	−	2.50912i	0.647851	−	1.12211i	0.983635	−	0.180172i	$-0.0576655\pi$
$6$	1.00000			0.408248
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.44864	−	2.50912i	−0.458100	−	0.793452i
$11$	−0.809697	−	1.40244i	−0.244133	−	0.422851i	0.717755	−	0.696296i	$-0.245170\pi$
$11$	−0.809697	−	1.40244i	−0.244133	−	0.422851i	−0.961887	+	0.273446i	$0.911837\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−3.02636			−0.839360			−0.419680	−	0.907672i	$-0.637858\pi$
$13$	−3.02636			−0.839360			−0.419680	+	0.907672i	$0.637858\pi$
$14$	−2.64575			−0.707107
$15$	2.89728			0.748074
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.77152	−	4.80040i	−0.672191	−	1.16427i	−0.977281	−	0.211946i	$-0.932020\pi$
$17$	−2.77152	−	4.80040i	−0.672191	−	1.16427i	0.305090	−	0.952323i	$-0.401313\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.38410	+	2.39733i	−0.317534	+	0.549986i	−0.979973	−	0.199131i	$-0.936188\pi$
$19$	−1.38410	+	2.39733i	−0.317534	+	0.549986i	0.662439	+	0.749116i	$0.269522\pi$
$20$	−2.89728			−0.647851
$21$	1.32288	−	2.29129i	0.288675	−	0.500000i
$22$	−1.61939			−0.345256
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−1.69711	−	2.93948i	−0.339422	−	0.587897i
$26$	−1.51318	+	2.62090i	−0.296759	+	0.514001i
$27$	−1.00000			−0.192450
$28$	−1.32288	+	2.29129i	−0.250000	+	0.433013i
$29$	1.76820			0.328347			0.164173	−	0.986432i	$-0.447504\pi$
$29$	1.76820			0.328347			0.164173	+	0.986432i	$0.447504\pi$
$30$	1.44864	−	2.50912i	0.264484	−	0.458100i
$31$	0.802888	+	1.39064i	0.144203	+	0.249767i	0.929075	−	0.369891i	$-0.120605\pi$
$31$	0.802888	+	1.39064i	0.144203	+	0.249767i	−0.784872	+	0.619657i	$0.787272\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.809697	−	1.40244i	0.140950	−	0.244133i
$34$	−5.54303			−0.950622
$35$	−7.66548			−1.29570
$36$	1.00000			0.166667
$37$	0.513179	−	0.888851i	0.0843660	−	0.146126i	−0.820755	−	0.571281i	$-0.806447\pi$
$37$	0.513179	−	0.888851i	0.0843660	−	0.146126i	0.905121	+	0.425154i	$0.139780\pi$
$38$	1.38410	+	2.39733i	0.224531	+	0.388899i
$39$	−1.51318	−	2.62090i	−0.242302	−	0.419680i
$40$	−1.44864	+	2.50912i	−0.229050	+	0.396726i
$41$	6.76820			1.05702			0.528508	−	0.848929i	$-0.322752\pi$
$41$	6.76820			1.05702			0.528508	+	0.848929i	$0.322752\pi$
$42$	−1.32288	−	2.29129i	−0.204124	−	0.353553i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−0.809697	+	1.40244i	−0.122066	+	0.211425i
$45$	1.44864	+	2.50912i	0.215950	+	0.374037i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	2.07772	−	3.59871i	0.303066	−	0.524926i	−0.673763	−	0.738948i	$-0.735323\pi$
$47$	2.07772	−	3.59871i	0.303066	−	0.524926i	0.976829	+	0.214022i	$0.0686563\pi$
$48$	−1.00000			−0.144338
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	−3.39422			−0.480016
$51$	2.77152	−	4.80040i	0.388090	−	0.672191i
$52$	1.51318	+	2.62090i	0.209840	+	0.363454i
$53$	−2.44864	−	4.24117i	−0.336346	−	0.582569i	0.647396	−	0.762154i	$-0.275858\pi$
$53$	−2.44864	−	4.24117i	−0.336346	−	0.582569i	−0.983743	+	0.179585i	$0.942525\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−4.69184			−0.632647
$56$	1.32288	+	2.29129i	0.176777	+	0.306186i
$57$	−2.76820			−0.366657
$58$	0.884100	−	1.53131i	0.116088	−	0.201070i
$59$	3.47849	+	6.02492i	0.452861	+	0.784378i	0.998562	−	0.0536015i	$-0.0170701\pi$
$59$	3.47849	+	6.02492i	0.452861	+	0.784378i	−0.545701	+	0.837980i	$0.683737\pi$
$60$	−1.44864	−	2.50912i	−0.187019	−	0.323926i
$61$	6.89728	−	11.9464i	0.883106	−	1.52958i	0.0352369	−	0.999379i	$-0.488781\pi$
$61$	6.89728	−	11.9464i	0.883106	−	1.52958i	0.847869	−	0.530206i	$-0.177885\pi$
$62$	1.60578			0.203934
$63$	2.64575			0.333333
$64$	1.00000			0.125000
$65$	−4.38410	+	7.59348i	−0.543781	+	0.941856i
$66$	−0.809697	−	1.40244i	−0.0996668	−	0.172628i
$67$	−3.61939	−	6.26897i	−0.442179	−	0.765877i	0.555672	−	0.831402i	$-0.312461\pi$
$67$	−3.61939	−	6.26897i	−0.442179	−	0.765877i	−0.997851	+	0.0655248i	$0.979128\pi$
$68$	−2.77152	+	4.80040i	−0.336096	+	0.582135i
$69$	−1.00000			−0.120386
$70$	−3.83274	+	6.63850i	−0.458100	+	0.793452i
$71$	4.87092			0.578072			0.289036	−	0.957318i	$-0.406665\pi$
$71$	4.87092			0.578072			0.289036	+	0.957318i	$0.406665\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−2.56803	−	4.44796i	−0.300566	−	0.520595i	0.675699	−	0.737178i	$-0.263842\pi$
$73$	−2.56803	−	4.44796i	−0.300566	−	0.520595i	−0.976264	+	0.216583i	$0.930509\pi$
$74$	−0.513179	−	0.888851i	−0.0596558	−	0.103327i
$75$	1.69711	−	2.93948i	0.195966	−	0.339422i
$76$	2.76820			0.317534
$77$	−2.14226	+	3.71050i	−0.244133	+	0.422851i
$78$	−3.02636			−0.342667
$79$	3.44532	−	5.96748i	0.387629	−	0.671394i	−0.604501	−	0.796604i	$-0.706627\pi$
$79$	3.44532	−	5.96748i	0.387629	−	0.671394i	0.992130	+	0.125211i	$0.0399607\pi$
$80$	1.44864	+	2.50912i	0.161963	+	0.280528i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.38410	−	5.86143i	0.373711	−	0.647287i
$83$	5.15544			0.565883			0.282941	−	0.959137i	$-0.408690\pi$
$83$	5.15544			0.565883			0.282941	+	0.959137i	$0.408690\pi$
$84$	−2.64575			−0.288675
$85$	−16.0597			−1.74192
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	0.884100	+	1.53131i	0.0947855	+	0.164173i
$88$	0.809697	+	1.40244i	0.0863140	+	0.149500i
$89$	7.28138	−	12.6117i	0.771825	−	1.33684i	−0.164737	−	0.986337i	$-0.552678\pi$
$89$	7.28138	−	12.6117i	0.771825	−	1.33684i	0.936562	−	0.350502i	$-0.113989\pi$
$90$	2.89728			0.305400
$91$	4.00349	+	6.93426i	0.419680	+	0.726907i
$92$	1.00000			0.104257
$93$	−0.802888	+	1.39064i	−0.0832556	+	0.144203i
$94$	−2.07772	−	3.59871i	−0.214300	−	0.371179i
$95$	4.01012	+	6.94574i	0.411430	+	0.712618i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−14.6988			−1.49244			−0.746220	−	0.665700i	$-0.768133\pi$
$97$	−14.6988			−1.49244			−0.746220	+	0.665700i	$0.768133\pi$
$98$	3.50000	+	6.06218i	0.353553	+	0.612372i
$99$	1.61939			0.162755
$100$	−1.69711	+	2.93948i	−0.169711	+	0.293948i
$101$	1.69711	+	2.93948i	0.168869	+	0.292490i	0.938022	−	0.346574i	$-0.112655\pi$
$101$	1.69711	+	2.93948i	0.168869	+	0.292490i	−0.769154	+	0.639064i	$0.779322\pi$
$102$	−2.77152	−	4.80040i	−0.274421	−	0.475311i
$103$	5.50986	−	9.54336i	0.542903	−	0.940336i	−0.455833	−	0.890066i	$-0.650658\pi$
$103$	5.50986	−	9.54336i	0.542903	−	0.940336i	0.998736	−	0.0502701i	$-0.0160082\pi$
$104$	3.02636			0.296759
$105$	−3.83274	−	6.63850i	−0.374037	−	0.647851i
$106$	−4.89728			−0.475666
$107$	−4.57772	+	7.92884i	−0.442545	+	0.766510i	−0.997878	−	0.0651183i	$-0.979258\pi$
$107$	−4.57772	+	7.92884i	−0.442545	+	0.766510i	0.555333	+	0.831628i	$0.312591\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−5.28469	−	9.15336i	−0.506182	−	0.876733i	−0.999974	−	0.00715295i	$-0.997723\pi$
$109$	−5.28469	−	9.15336i	−0.506182	−	0.876733i	0.493793	−	0.869580i	$-0.335610\pi$
$110$	−2.34592	+	4.06325i	−0.223675	+	0.387416i
$111$	1.02636			0.0974175
$112$	2.64575			0.250000
$113$	3.76209			0.353908			0.176954	−	0.984219i	$-0.443376\pi$
$113$	3.76209			0.353908			0.176954	+	0.984219i	$0.443376\pi$
$114$	−1.38410	+	2.39733i	−0.129633	+	0.224531i
$115$	1.44864	+	2.50912i	0.135086	+	0.233976i
$116$	−0.884100	−	1.53131i	−0.0820866	−	0.142178i
$117$	1.51318	−	2.62090i	0.139893	−	0.242302i
$118$	6.95698			0.640442
$119$	−7.33274	+	12.7007i	−0.672191	+	1.16427i
$120$	−2.89728			−0.264484
$121$	4.18878	−	7.25518i	0.380798	−	0.659562i
$122$	−6.89728	−	11.9464i	−0.624450	−	1.08158i
$123$	3.38410	+	5.86143i	0.305134	+	0.528508i
$124$	0.802888	−	1.39064i	0.0721015	−	0.124883i
$125$	4.65238			0.416122
$126$	1.32288	−	2.29129i	0.117851	−	0.204124i
$127$	13.7252			1.21791			0.608956	−	0.793204i	$-0.291588\pi$
$127$	13.7252			1.21791			0.608956	+	0.793204i	$0.291588\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$	4.38410	+	7.59348i	0.384511	+	0.665993i
$131$	−1.45876	+	2.52665i	−0.127453	+	0.220755i	−0.922689	−	0.385545i	$-0.874013\pi$
$131$	−1.45876	+	2.52665i	−0.127453	+	0.220755i	0.795236	+	0.606300i	$0.207347\pi$
$132$	−1.61939			−0.140950
$133$	7.32397			0.635069
$134$	−7.23879			−0.625336
$135$	−1.44864	+	2.50912i	−0.124679	+	0.215950i
$136$	2.77152	+	4.80040i	0.237655	+	0.411631i
$137$	5.80137	+	10.0483i	0.495644	+	0.858481i	0.999987	−	0.00502238i	$-0.00159868\pi$
$137$	5.80137	+	10.0483i	0.495644	+	0.858481i	−0.504343	+	0.863503i	$0.668265\pi$
$138$	−0.500000	+	0.866025i	−0.0425628	+	0.0737210i
$139$	−0.155436			−0.0131839			−0.00659194	−	0.999978i	$-0.502098\pi$
$139$	−0.155436			−0.0131839			−0.00659194	+	0.999978i	$0.502098\pi$
$140$	3.83274	+	6.63850i	0.323926	+	0.561056i
$141$	4.15544			0.349951
$142$	2.43546	−	4.21834i	0.204379	−	0.353995i
$143$	2.45043	+	4.24427i	0.204915	+	0.354924i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.56148	−	4.43662i	0.212720	−	0.368441i
$146$	−5.13607			−0.425064
$147$	−7.00000			−0.577350
$148$	−1.02636			−0.0843660
$149$	−8.31786	+	14.4070i	−0.681426	+	1.18026i	0.293120	+	0.956076i	$0.405306\pi$
$149$	−8.31786	+	14.4070i	−0.681426	+	1.18026i	−0.974546	+	0.224188i	$0.928027\pi$
$150$	−1.69711	−	2.93948i	−0.138569	−	0.240008i
$151$	9.86259	+	17.0825i	0.802606	+	1.39015i	0.917895	+	0.396823i	$0.129887\pi$
$151$	9.86259	+	17.0825i	0.802606	+	1.39015i	−0.115289	+	0.993332i	$0.536779\pi$
$152$	1.38410	−	2.39733i	0.112265	−	0.194449i
$153$	5.54303			0.448127
$154$	2.14226	+	3.71050i	0.172628	+	0.299000i
$155$	4.65238			0.373688
$156$	−1.51318	+	2.62090i	−0.121151	+	0.209840i
$157$	−0.900593	−	1.55987i	−0.0718752	−	0.124491i	0.827848	−	0.560953i	$-0.189565\pi$
$157$	−0.900593	−	1.55987i	−0.0718752	−	0.124491i	−0.899723	+	0.436461i	$0.856232\pi$
$158$	−3.44532	−	5.96748i	−0.274095	−	0.474747i
$159$	2.44864	−	4.24117i	0.194190	−	0.336346i
$160$	2.89728			0.229050
$161$	2.64575			0.208514
$162$	−1.00000			−0.0785674
$163$	−4.43546	+	7.68244i	−0.347412	+	0.601735i	−0.985789	−	0.167989i	$-0.946273\pi$
$163$	−4.43546	+	7.68244i	−0.347412	+	0.601735i	0.638377	+	0.769724i	$0.279606\pi$
$164$	−3.38410	−	5.86143i	−0.264254	−	0.457701i
$165$	−2.34592	−	4.06325i	−0.182629	−	0.316324i
$166$	2.57772	−	4.46474i	0.200070	−	0.346531i
$167$	−1.26427			−0.0978319			−0.0489159	−	0.998803i	$-0.515577\pi$
$167$	−1.26427			−0.0978319			−0.0489159	+	0.998803i	$0.515577\pi$
$168$	−1.32288	+	2.29129i	−0.102062	+	0.176777i
$169$	−3.84116			−0.295474
$170$	−8.02985	+	13.9081i	−0.615861	+	1.06670i
$171$	−1.38410	−	2.39733i	−0.105845	−	0.183329i
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	0.431967	−	0.748188i	0.0328418	−	0.0568837i	−0.849137	−	0.528172i	$-0.822878\pi$
$173$	0.431967	−	0.748188i	0.0328418	−	0.0568837i	0.881979	+	0.471288i	$0.156211\pi$
$174$	1.76820			0.134047
$175$	−4.49014	+	7.77714i	−0.339422	+	0.587897i
$176$	1.61939			0.122066
$177$	−3.47849	+	6.02492i	−0.261459	+	0.452861i
$178$	−7.28138	−	12.6117i	−0.545762	−	0.945288i
$179$	8.93062	+	15.4683i	0.667506	+	1.15615i	0.978599	+	0.205775i	$0.0659716\pi$
$179$	8.93062	+	15.4683i	0.667506	+	1.15615i	−0.311093	+	0.950379i	$0.600695\pi$
$180$	1.44864	−	2.50912i	0.107975	−	0.187019i
$181$	5.30512			0.394327			0.197163	−	0.980371i	$-0.436827\pi$
$181$	5.30512			0.394327			0.197163	+	0.980371i	$0.436827\pi$
$182$	8.00699			0.593517
$183$	13.7946			1.01972
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−1.48682	−	2.57525i	−0.109313	−	0.189336i
$186$	0.802888	+	1.39064i	0.0588706	+	0.101967i
$187$	−4.48818	+	7.77375i	−0.328208	+	0.568473i
$188$	−4.15544			−0.303066
$189$	1.32288	+	2.29129i	0.0962250	+	0.166667i
$190$	8.02025			0.581850
$191$	−9.15230	+	15.8522i	−0.662237	+	1.14703i	0.317789	+	0.948161i	$0.397060\pi$
$191$	−9.15230	+	15.8522i	−0.662237	+	1.14703i	−0.980026	+	0.198867i	$0.936274\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−0.170755	−	0.295756i	−0.0122912	−	0.0212890i	0.859814	−	0.510607i	$-0.170579\pi$
$193$	−0.170755	−	0.295756i	−0.0122912	−	0.0212890i	−0.872106	+	0.489318i	$0.837246\pi$
$194$	−7.34941	+	12.7296i	−0.527657	+	0.913929i
$195$	−8.76820			−0.627904
$196$	7.00000			0.500000
$197$	20.2476			1.44258			0.721291	−	0.692632i	$-0.243549\pi$
$197$	20.2476			1.44258			0.721291	+	0.692632i	$0.243549\pi$
$198$	0.809697	−	1.40244i	0.0575427	−	0.0996668i
$199$	13.4471	+	23.2911i	0.953241	+	1.65106i	0.738343	+	0.674425i	$0.235608\pi$
$199$	13.4471	+	23.2911i	0.953241	+	1.65106i	0.214898	+	0.976637i	$0.431058\pi$
$200$	1.69711	+	2.93948i	0.120004	+	0.207853i
$201$	3.61939	−	6.26897i	0.255292	−	0.442179i
$202$	3.39422			0.238817
$203$	−2.33911	−	4.05146i	−0.164173	−	0.284356i
$204$	−5.54303			−0.388090
$205$	9.80468	−	16.9822i	0.684789	−	1.18609i
$206$	−5.50986	−	9.54336i	−0.383890	−	0.664918i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	1.51318	−	2.62090i	0.104920	−	0.181727i
$209$	4.48281			0.310082
$210$	−7.66548			−0.528968
$211$	6.41359			0.441530			0.220765	−	0.975327i	$-0.429145\pi$
$211$	6.41359			0.441530			0.220765	+	0.975327i	$0.429145\pi$
$212$	−2.44864	+	4.24117i	−0.168173	+	0.291285i
$213$	2.43546	+	4.21834i	0.166875	+	0.289036i
$214$	4.57772	+	7.92884i	0.312926	+	0.542004i
$215$	2.89728	−	5.01823i	0.197593	−	0.342241i
$216$	1.00000			0.0680414
$217$	2.12424	−	3.67930i	0.144203	−	0.249767i
$218$	−10.5694			−0.715849
$219$	2.56803	−	4.44796i	0.173532	−	0.300566i
$220$	2.34592	+	4.06325i	0.158162	+	0.273944i
$221$	8.38759	+	14.5277i	0.564211	+	0.977242i
$222$	0.513179	−	0.888851i	0.0344423	−	0.0596558i
$223$	−16.1888			−1.08408			−0.542040	−	0.840352i	$-0.682348\pi$
$223$	−16.1888			−1.08408			−0.542040	+	0.840352i	$0.682348\pi$
$224$	1.32288	−	2.29129i	0.0883883	−	0.153093i
$225$	3.39422			0.226282
$226$	1.88105	−	3.25807i	0.125125	−	0.216723i
$227$	−11.4554	−	19.8414i	−0.760325	−	1.31692i	−0.942683	−	0.333689i	$-0.891706\pi$
$227$	−11.4554	−	19.8414i	−0.760325	−	1.31692i	0.182358	−	0.983232i	$-0.441627\pi$
$228$	1.38410	+	2.39733i	0.0916643	+	0.158767i
$229$	2.58273	−	4.47343i	0.170672	−	0.295612i	−0.767983	−	0.640470i	$-0.778740\pi$
$229$	2.58273	−	4.47343i	0.170672	−	0.295612i	0.938655	+	0.344858i	$0.112073\pi$
$230$	2.89728			0.191041
$231$	−4.28451			−0.281900
$232$	−1.76820			−0.116088
$233$	−5.54652	+	9.60686i	−0.363365	+	0.629366i	−0.988512	−	0.151140i	$-0.951705\pi$
$233$	−5.54652	+	9.60686i	−0.363365	+	0.629366i	0.625147	+	0.780507i	$0.285039\pi$
$234$	−1.51318	−	2.62090i	−0.0989196	−	0.171334i
$235$	−6.01973	−	10.4265i	−0.392684	−	0.680148i
$236$	3.47849	−	6.02492i	0.226430	−	0.392189i
$237$	6.89065			0.447596
$238$	7.33274	+	12.7007i	0.475311	+	0.823263i
$239$	−5.63912			−0.364764			−0.182382	−	0.983228i	$-0.558381\pi$
$239$	−5.63912			−0.364764			−0.182382	+	0.983228i	$0.558381\pi$
$240$	−1.44864	+	2.50912i	−0.0935093	+	0.161963i
$241$	−12.0479	−	20.8675i	−0.776072	−	1.34420i	−0.934190	−	0.356776i	$-0.883876\pi$
$241$	−12.0479	−	20.8675i	−0.776072	−	1.34420i	0.158118	−	0.987420i	$-0.449457\pi$
$242$	−4.18878	−	7.25518i	−0.269265	−	0.466381i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−13.7946			−0.883106
$245$	10.1405	+	17.5638i	0.647851	+	1.12211i
$246$	6.76820			0.431525
$247$	4.18878	−	7.25518i	0.266526	−	0.461636i
$248$	−0.802888	−	1.39064i	−0.0509834	−	0.0883059i
$249$	2.57772	+	4.46474i	0.163356	+	0.282941i
$250$	2.32619	−	4.02908i	0.147121	−	0.254821i
$251$	17.9970			1.13596			0.567979	−	0.823043i	$-0.307726\pi$
$251$	17.9970			1.13596			0.567979	+	0.823043i	$0.307726\pi$
$252$	−1.32288	−	2.29129i	−0.0833333	−	0.144338i
$253$	1.61939			0.101810
$254$	6.86259	−	11.8864i	0.430597	−	0.745816i
$255$	−8.02985	−	13.9081i	−0.502849	−	0.870960i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.635628	+	1.10094i	−0.0396494	+	0.0686747i	−0.885169	−	0.465269i	$-0.845957\pi$
$257$	−0.635628	+	1.10094i	−0.0396494	+	0.0686747i	0.845520	+	0.533944i	$0.179291\pi$
$258$	2.00000			0.124515
$259$	−2.71549			−0.168732
$260$	8.76820			0.543781
$261$	−0.884100	+	1.53131i	−0.0547244	+	0.0947855i
$262$	1.45876	+	2.52665i	0.0901227	+	0.156097i
$263$	13.3639	+	23.1470i	0.824056	+	1.42731i	0.902639	+	0.430399i	$0.141627\pi$
$263$	13.3639	+	23.1470i	0.824056	+	1.42731i	−0.0785824	+	0.996908i	$0.525039\pi$
$264$	−0.809697	+	1.40244i	−0.0498334	+	0.0863140i
$265$	−14.1888			−0.871610
$266$	3.66198	−	6.34274i	0.224531	−	0.388899i
$267$	14.5628			0.891226
$268$	−3.61939	+	6.26897i	−0.221090	+	0.382939i
$269$	−12.5759	−	21.7822i	−0.766768	−	1.32808i	−0.939307	−	0.343079i	$-0.888530\pi$
$269$	−12.5759	−	21.7822i	−0.766768	−	1.32808i	0.172538	−	0.985003i	$-0.444803\pi$
$270$	1.44864	+	2.50912i	0.0881614	+	0.152700i
$271$	10.8429	−	18.7804i	0.658657	−	1.14083i	−0.322306	−	0.946635i	$-0.604458\pi$
$271$	10.8429	−	18.7804i	0.658657	−	1.14083i	0.980964	−	0.194192i	$-0.0622085\pi$
$272$	5.54303			0.336096
$273$	−4.00349	+	6.93426i	−0.242302	+	0.419680i
$274$	11.6027			0.700947
$275$	−2.74829	+	4.76018i	−0.165728	+	0.287050i
$276$	0.500000	+	0.866025i	0.0300965	+	0.0521286i
$277$	−4.88454	−	8.46027i	−0.293484	−	0.508328i	0.681147	−	0.732146i	$-0.261481\pi$
$277$	−4.88454	−	8.46027i	−0.293484	−	0.508328i	−0.974631	+	0.223818i	$0.928148\pi$
$278$	−0.0777178	+	0.134611i	−0.00466121	+	0.00807345i
$279$	−1.60578			−0.0961353
$280$	7.66548			0.458100
$281$	−2.80730			−0.167469			−0.0837346	−	0.996488i	$-0.526685\pi$
$281$	−2.80730			−0.167469			−0.0837346	+	0.996488i	$0.526685\pi$
$282$	2.07772	−	3.59871i	0.123726	−	0.214300i
$283$	−12.9570	−	22.4422i	−0.770213	−	1.33405i	−0.937446	−	0.348130i	$-0.886817\pi$
$283$	−12.9570	−	22.4422i	−0.770213	−	1.33405i	0.167234	−	0.985917i	$-0.446517\pi$
$284$	−2.43546	−	4.21834i	−0.144518	−	0.250313i
$285$	−4.01012	+	6.94574i	−0.237539	+	0.411430i
$286$	4.90087			0.289794
$287$	−8.95349	−	15.5079i	−0.528508	−	0.915402i
$288$	−1.00000			−0.0589256
$289$	−6.86259	+	11.8864i	−0.403682	+	0.699197i
$290$	−2.56148	−	4.43662i	−0.150416	−	0.260527i
$291$	−7.34941	−	12.7296i	−0.430830	−	0.746220i
$292$	−2.56803	+	4.44796i	−0.150283	+	0.260297i
$293$	31.3143			1.82940			0.914700	−	0.404133i	$-0.132427\pi$
$293$	31.3143			1.82940			0.914700	+	0.404133i	$0.132427\pi$
$294$	−3.50000	+	6.06218i	−0.204124	+	0.353553i
$295$	20.1563			1.17355
$296$	−0.513179	+	0.888851i	−0.0298279	+	0.0516634i
$297$	0.809697	+	1.40244i	0.0469834	+	0.0813776i
$298$	8.31786	+	14.4070i	0.481841	+	0.834573i
$299$	1.51318	−	2.62090i	0.0875094	−	0.151571i
$300$	−3.39422			−0.195966
$301$	−2.64575	−	4.58258i	−0.152499	−	0.264135i
$302$	19.7252			1.13506
$303$	−1.69711	+	2.93948i	−0.0974965	+	0.168869i
$304$	−1.38410	−	2.39733i	−0.0793836	−	0.137496i
$305$	−19.9833	−	34.6122i	−1.14424	−	1.98189i
$306$	2.77152	−	4.80040i	0.158437	−	0.274421i
$307$	−13.6067			−0.776573			−0.388286	−	0.921539i	$-0.626933\pi$
$307$	−13.6067			−0.776573			−0.388286	+	0.921539i	$0.626933\pi$
$308$	4.28451			0.244133
$309$	11.0197			0.626890
$310$	2.32619	−	4.02908i	0.132119	−	0.228836i
$311$	7.38545	+	12.7920i	0.418791	+	0.725367i	0.995818	−	0.0913580i	$-0.0291208\pi$
$311$	7.38545	+	12.7920i	0.418791	+	0.725367i	−0.577027	+	0.816725i	$0.695787\pi$
$312$	1.51318	+	2.62090i	0.0856669	+	0.148379i
$313$	−1.34242	+	2.32515i	−0.0758783	+	0.131425i	−0.901468	−	0.432846i	$-0.857509\pi$
$313$	−1.34242	+	2.32515i	−0.0758783	+	0.131425i	0.825590	+	0.564271i	$0.190843\pi$
$314$	−1.80119			−0.101647
$315$	3.83274	−	6.63850i	0.215950	−	0.374037i
$316$	−6.89065			−0.387629
$317$	−5.52151	+	9.56353i	−0.310119	+	0.537142i	−0.978388	−	0.206778i	$-0.933702\pi$
$317$	−5.52151	+	9.56353i	−0.310119	+	0.537142i	0.668269	+	0.743920i	$0.267036\pi$
$318$	−2.44864	−	4.24117i	−0.137313	−	0.237833i
$319$	−1.43171	−	2.47979i	−0.0801602	−	0.138841i
$320$	1.44864	−	2.50912i	0.0809814	−	0.140264i
$321$	−9.15544			−0.511007
$322$	1.32288	−	2.29129i	0.0737210	−	0.127688i
$323$	15.3442			0.853775
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	5.13607	+	8.89593i	0.284898	+	0.493457i
$326$	4.43546	+	7.68244i	0.245657	+	0.425491i
$327$	5.28469	−	9.15336i	0.292244	−	0.506182i
$328$	−6.76820			−0.373711
$329$	−10.9942			−0.606133
$330$	−4.69184			−0.258277
$331$	−4.14619	+	7.18141i	−0.227895	+	0.394726i	−0.957184	−	0.289480i	$-0.906518\pi$
$331$	−4.14619	+	7.18141i	−0.227895	+	0.394726i	0.729289	+	0.684206i	$0.239851\pi$
$332$	−2.57772	−	4.46474i	−0.141471	−	0.245034i
$333$	0.513179	+	0.888851i	0.0281220	+	0.0487088i
$334$	−0.632133	+	1.09489i	−0.0345888	+	0.0599095i
$335$	−20.9728			−1.14587
$336$	1.32288	+	2.29129i	0.0721688	+	0.125000i
$337$	−25.0624			−1.36524			−0.682618	−	0.730775i	$-0.739159\pi$
$337$	−25.0624			−1.36524			−0.682618	+	0.730775i	$0.739159\pi$
$338$	−1.92058	+	3.32654i	−0.104466	+	0.180940i
$339$	1.88105	+	3.25807i	0.102164	+	0.176954i
$340$	8.02985	+	13.9081i	0.435480	+	0.754273i
$341$	1.30019	−	2.25200i	0.0704094	−	0.121953i
$342$	−2.76820			−0.149687
$343$	18.5203			1.00000
$344$	−2.00000			−0.107833
$345$	−1.44864	+	2.50912i	−0.0779921	+	0.135086i
$346$	−0.431967	−	0.748188i	−0.0232227	−	0.0402228i
$347$	−3.39422	−	5.87897i	−0.182211	−	0.315600i	0.760422	−	0.649429i	$-0.224992\pi$
$347$	−3.39422	−	5.87897i	−0.182211	−	0.315600i	−0.942633	+	0.333830i	$0.891659\pi$
$348$	0.884100	−	1.53131i	0.0473927	−	0.0820866i
$349$	12.0070			0.642719			0.321360	−	0.946957i	$-0.395860\pi$
$349$	12.0070			0.642719			0.321360	+	0.946957i	$0.395860\pi$
$350$	4.49014	+	7.77714i	0.240008	+	0.415706i
$351$	3.02636			0.161535
$352$	0.809697	−	1.40244i	0.0431570	−	0.0747501i
$353$	−10.4632	−	18.1227i	−0.556898	−	0.964576i	−0.997753	−	0.0669979i	$-0.978658\pi$
$353$	−10.4632	−	18.1227i	−0.556898	−	0.964576i	0.440855	−	0.897578i	$-0.354675\pi$
$354$	3.47849	+	6.02492i	0.184880	+	0.320221i
$355$	7.05621	−	12.2217i	0.374505	−	0.648661i
$356$	−14.5628			−0.771825
$357$	−14.6655			−0.776179
$358$	17.8612			0.943996
$359$	5.01362	−	8.68384i	0.264609	−	0.458316i	−0.702852	−	0.711336i	$-0.748091\pi$
$359$	5.01362	−	8.68384i	0.264609	−	0.458316i	0.967461	+	0.253020i	$0.0814239\pi$
$360$	−1.44864	−	2.50912i	−0.0763500	−	0.132242i
$361$	5.66853	+	9.81819i	0.298344	+	0.516747i
$362$	2.65256	−	4.59437i	0.139415	−	0.241475i
$363$	8.37756			0.439708
$364$	4.00349	−	6.93426i	0.209840	−	0.363454i
$365$	−14.8806			−0.778887
$366$	6.89728	−	11.9464i	0.360527	−	0.624450i
$367$	12.1242	+	20.9998i	0.632880	+	1.09618i	0.986960	+	0.160966i	$0.0514608\pi$
$367$	12.1242	+	20.9998i	0.632880	+	1.09618i	−0.354080	+	0.935215i	$0.615206\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$	−3.38410	+	5.86143i	−0.176169	+	0.305134i
$370$	−2.97364			−0.154592
$371$	−6.47849	+	11.2211i	−0.336346	+	0.582569i
$372$	1.60578			0.0832556
$373$	−17.4599	+	30.2414i	−0.904037	+	1.56584i	−0.0818326	+	0.996646i	$0.526077\pi$
$373$	−17.4599	+	30.2414i	−0.904037	+	1.56584i	−0.822205	+	0.569192i	$0.807256\pi$
$374$	4.48818	+	7.77375i	0.232078	+	0.401971i
$375$	2.32619	+	4.02908i	0.120124	+	0.208061i
$376$	−2.07772	+	3.59871i	−0.107150	+	0.185589i
$377$	−5.35121			−0.275601
$378$	2.64575			0.136083
$379$	3.76732			0.193514			0.0967571	−	0.995308i	$-0.469153\pi$
$379$	3.76732			0.193514			0.0967571	+	0.995308i	$0.469153\pi$
$380$	4.01012	−	6.94574i	0.205715	−	0.356309i
$381$	6.86259	+	11.8864i	0.351581	+	0.608956i
$382$	9.15230	+	15.8522i	0.468272	+	0.811072i
$383$	−16.6826	+	28.8951i	−0.852441	+	1.47647i	0.0265587	+	0.999647i	$0.491545\pi$
$383$	−16.6826	+	28.8951i	−0.852441	+	1.47647i	−0.878999	+	0.476823i	$0.841788\pi$
$384$	1.00000			0.0510310
$385$	6.20672	+	10.7503i	0.316324	+	0.547888i
$386$	−0.341510			−0.0173824
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	7.34941	+	12.7296i	0.373110	+	0.646245i
$389$	13.1752	+	22.8201i	0.668007	+	1.15702i	0.978461	+	0.206434i	$0.0661858\pi$
$389$	13.1752	+	22.8201i	0.668007	+	1.15702i	−0.310453	+	0.950589i	$0.600481\pi$
$390$	−4.38410	+	7.59348i	−0.221998	+	0.384511i
$391$	5.54303			0.280323
$392$	3.50000	−	6.06218i	0.176777	−	0.306186i
$393$	−2.91753			−0.147170
$394$	10.1238	−	17.5349i	0.510030	−	0.883398i
$395$	−9.98207	−	17.2894i	−0.502252	−	0.869926i
$396$	−0.809697	−	1.40244i	−0.0406888	−	0.0704751i
$397$	6.39073	−	11.0691i	0.320742	−	0.555541i	−0.659900	−	0.751354i	$-0.729401\pi$
$397$	6.39073	−	11.0691i	0.320742	−	0.555541i	0.980641	+	0.195813i	$0.0627346\pi$
$398$	26.8942			1.34809
$399$	3.66198	+	6.34274i	0.183329	+	0.317534i
$400$	3.39422			0.169711
$401$	−3.61957	+	6.26929i	−0.180753	+	0.313073i	−0.942137	−	0.335228i	$-0.891187\pi$
$401$	−3.61957	+	6.26929i	−0.180753	+	0.313073i	0.761384	+	0.648301i	$0.224520\pi$
$402$	−3.61939	−	6.26897i	−0.180519	−	0.312668i
$403$	−2.42983	−	4.20858i	−0.121038	−	0.209644i
$404$	1.69711	−	2.93948i	0.0844345	−	0.146245i
$405$	−2.89728			−0.143967
$406$	−4.67822			−0.232176
$407$	−1.66208			−0.0823861
$408$	−2.77152	+	4.80040i	−0.137210	+	0.237655i
$409$	−14.1988	−	24.5931i	−0.702087	−	1.21605i	−0.967733	−	0.251979i	$-0.918919\pi$
$409$	−14.1988	−	24.5931i	−0.702087	−	1.21605i	0.265646	−	0.964071i	$-0.414415\pi$
$410$	−9.80468	−	16.9822i	−0.484219	−	0.838691i
$411$	−5.80137	+	10.0483i	−0.286160	+	0.495644i
$412$	−11.0197			−0.542903
$413$	9.20322	−	15.9404i	0.452861	−	0.784378i
$414$	−1.00000			−0.0491473
$415$	7.46837	−	12.9356i	0.366608	−	0.634983i
$416$	−1.51318	−	2.62090i	−0.0741897	−	0.128500i
$417$	−0.0777178	−	0.134611i	−0.00380586	−	0.00659194i
$418$	2.24140	−	3.88222i	0.109631	−	0.189886i
$419$	16.3112			0.796856			0.398428	−	0.917200i	$-0.369556\pi$
$419$	16.3112			0.796856			0.398428	+	0.917200i	$0.369556\pi$
$420$	−3.83274	+	6.63850i	−0.187019	+	0.323926i
$421$	−35.7221			−1.74099			−0.870495	−	0.492177i	$-0.836201\pi$
$421$	−35.7221			−1.74099			−0.870495	+	0.492177i	$0.836201\pi$
$422$	3.20680	−	5.55433i	0.156104	−	0.270381i
$423$	2.07772	+	3.59871i	0.101022	+	0.174975i
$424$	2.44864	+	4.24117i	0.118916	+	0.205969i
$425$	−9.40714	+	16.2936i	−0.456313	+	0.790358i
$426$	4.87092			0.235997
$427$	−36.4970			−1.76621
$428$	9.15544			0.442545
$429$	−2.45043	+	4.24427i	−0.118308	+	0.204915i
$430$	−2.89728	−	5.01823i	−0.139719	−	0.242001i
$431$	−12.7252	−	22.0407i	−0.612950	−	1.06166i	−0.990740	−	0.135770i	$-0.956649\pi$
$431$	−12.7252	−	22.0407i	−0.612950	−	1.06166i	0.377790	−	0.925891i	$-0.376684\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	35.4496			1.70360			0.851801	−	0.523866i	$-0.175511\pi$
$433$	35.4496			1.70360			0.851801	+	0.523866i	$0.175511\pi$
$434$	−2.12424	−	3.67930i	−0.101967	−	0.176612i
$435$	5.12297			0.245628
$436$	−5.28469	+	9.15336i	−0.253091	+	0.438366i
$437$	−1.38410	−	2.39733i	−0.0662105	−	0.114680i
$438$	−2.56803	−	4.44796i	−0.122705	−	0.212532i
$439$	−8.66378	+	15.0061i	−0.413500	+	0.716202i	−0.995270	−	0.0971510i	$-0.969027\pi$
$439$	−8.66378	+	15.0061i	−0.413500	+	0.716202i	0.581770	+	0.813353i	$0.302360\pi$
$440$	4.69184			0.223675
$441$	−3.50000	−	6.06218i	−0.166667	−	0.288675i
$442$	16.7752			0.797914
$443$	11.8924	−	20.5983i	0.565027	−	0.978655i	−0.432020	−	0.901864i	$-0.642199\pi$
$443$	11.8924	−	20.5983i	0.565027	−	0.978655i	0.997047	−	0.0767915i	$-0.0244676\pi$
$444$	−0.513179	−	0.888851i	−0.0243544	−	0.0421830i
$445$	−21.0962	−	36.5397i	−1.00006	−	1.73215i
$446$	−8.09439	+	14.0199i	−0.383281	+	0.663861i
$447$	−16.6357			−0.786843
$448$	−1.32288	−	2.29129i	−0.0625000	−	0.108253i
$449$	−30.3846			−1.43394			−0.716968	−	0.697106i	$-0.754471\pi$
$449$	−30.3846			−1.43394			−0.716968	+	0.697106i	$0.754471\pi$
$450$	1.69711	−	2.93948i	0.0800026	−	0.138569i
$451$	−5.48019	−	9.49197i	−0.258052	−	0.446959i
$452$	−1.88105	−	3.25807i	−0.0884769	−	0.153247i
$453$	−9.86259	+	17.0825i	−0.463385	+	0.802606i
$454$	−22.9109			−1.07526
$455$	23.1985			1.08756
$456$	2.76820			0.129633
$457$	−10.7103	+	18.5508i	−0.501006	+	0.867768i	0.498993	+	0.866606i	$0.333703\pi$
$457$	−10.7103	+	18.5508i	−0.501006	+	0.867768i	−0.999999	+	0.00116232i	$0.999630\pi$
$458$	−2.58273	−	4.47343i	−0.120683	−	0.209029i
$459$	2.77152	+	4.80040i	0.129363	+	0.224064i
$460$	1.44864	−	2.50912i	0.0675432	−	0.116988i
$461$	−19.1660			−0.892650			−0.446325	−	0.894871i	$-0.647267\pi$
$461$	−19.1660			−0.892650			−0.446325	+	0.894871i	$0.647267\pi$
$462$	−2.14226	+	3.71050i	−0.0996668	+	0.172628i
$463$	7.72787			0.359144			0.179572	−	0.983745i	$-0.442529\pi$
$463$	7.72787			0.359144			0.179572	+	0.983745i	$0.442529\pi$
$464$	−0.884100	+	1.53131i	−0.0410433	+	0.0710891i
$465$	2.32619	+	4.02908i	0.107874	+	0.186844i
$466$	5.54652	+	9.60686i	0.256938	+	0.445029i
$467$	−2.61259	+	4.52513i	−0.120896	+	0.209398i	−0.920121	−	0.391634i	$-0.871910\pi$
$467$	−2.61259	+	4.52513i	−0.120896	+	0.209398i	0.799225	+	0.601032i	$0.205243\pi$
$468$	−3.02636			−0.139893
$469$	−9.57602	+	16.5861i	−0.442179	+	0.765877i
$470$	−12.0395			−0.555339
$471$	0.900593	−	1.55987i	0.0414972	−	0.0718752i
$472$	−3.47849	−	6.02492i	−0.160111	−	0.277320i
$473$	−1.61939	−	2.80487i	−0.0744598	−	0.128968i
$474$	3.44532	−	5.96748i	0.158249	−	0.274095i
$475$	9.39589			0.431113
$476$	14.6655			0.672191
$477$	4.89728			0.224231
$478$	−2.81956	+	4.88362i	−0.128964	+	0.223372i
$479$	−7.38410	−	12.7896i	−0.337388	−	0.584373i	0.646552	−	0.762870i	$-0.276210\pi$
$479$	−7.38410	−	12.7896i	−0.337388	−	0.584373i	−0.983941	+	0.178496i	$0.942877\pi$
$480$	1.44864	+	2.50912i	0.0661210	+	0.114525i
$481$	−1.55306	+	2.68998i	−0.0708135	+	0.122653i
$482$	−24.0958			−1.09753
$483$	1.32288	+	2.29129i	0.0601929	+	0.104257i
$484$	−8.37756			−0.380798
$485$	−21.2933	+	36.8811i	−0.966879	+	1.67468i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−5.08077	−	8.80016i	−0.230232	−	0.398773i	0.727644	−	0.685954i	$-0.240615\pi$
$487$	−5.08077	−	8.80016i	−0.230232	−	0.398773i	−0.957876	+	0.287181i	$0.907282\pi$
$488$	−6.89728	+	11.9464i	−0.312225	+	0.540790i
$489$	−8.87092			−0.401157
$490$	20.2810			0.916200
$491$	7.02976			0.317249			0.158624	−	0.987339i	$-0.449294\pi$
$491$	7.02976			0.317249			0.158624	+	0.987339i	$0.449294\pi$
$492$	3.38410	−	5.86143i	0.152567	−	0.264254i
$493$	−4.90059	−	8.48808i	−0.220712	−	0.382284i
$494$	−4.18878	−	7.25518i	−0.188462	−	0.326426i
$495$	2.34592	−	4.06325i	0.105441	−	0.182629i
$496$	−1.60578			−0.0721015
$497$	−6.44362	−	11.1607i	−0.289036	−	0.500625i
$498$	5.15544			0.231021
$499$	−19.8293	+	34.3453i	−0.887679	+	1.53751i	−0.0450680	+	0.998984i	$0.514350\pi$
$499$	−19.8293	+	34.3453i	−0.887679	+	1.53751i	−0.842611	+	0.538522i	$0.818983\pi$
$500$	−2.32619	−	4.02908i	−0.104030	−	0.180186i
$501$	−0.632133	−	1.09489i	−0.0282416	−	0.0489159i
$502$	8.99848	−	15.5858i	0.401622	−	0.695629i
$503$	26.6752			1.18939			0.594694	−	0.803952i	$-0.297273\pi$
$503$	26.6752			1.18939			0.594694	+	0.803952i	$0.297273\pi$
$504$	−2.64575			−0.117851
$505$	9.83401			0.437608
$506$	0.809697	−	1.40244i	0.0359954	−	0.0623459i
$507$	−1.92058	−	3.32654i	−0.0852960	−	0.147737i
$508$	−6.86259	−	11.8864i	−0.304478	−	0.527372i
$509$	−18.3644	+	31.8080i	−0.813987	+	1.40987i	0.0960660	+	0.995375i	$0.469374\pi$
$509$	−18.3644	+	31.8080i	−0.813987	+	1.40987i	−0.910053	+	0.414492i	$0.863959\pi$
$510$	−16.0597			−0.711136
$511$	−6.79438	+	11.7682i	−0.300566	+	0.520595i
$512$	−1.00000			−0.0441942
$513$	1.38410	−	2.39733i	0.0611095	−	0.105845i
$514$	0.635628	+	1.10094i	0.0280363	+	0.0485603i
$515$	−15.9636	−	27.6498i	−0.703441	−	1.21840i
$516$	1.00000	−	1.73205i	0.0440225	−	0.0762493i
$517$	−6.72929			−0.295954
$518$	−1.35774	+	2.35168i	−0.0596558	+	0.103327i
$519$	0.863933			0.0379225
$520$	4.38410	−	7.59348i	0.192256	−	0.332996i
$521$	−4.39422	−	7.61102i	−0.192514	−	0.333445i	0.753568	−	0.657369i	$-0.228331\pi$
$521$	−4.39422	−	7.61102i	−0.192514	−	0.333445i	−0.946083	+	0.323925i	$0.894998\pi$
$522$	0.884100	+	1.53131i	0.0386960	+	0.0670235i
$523$	−19.2415	+	33.3272i	−0.841372	+	1.45730i	0.0473633	+	0.998878i	$0.484918\pi$
$523$	−19.2415	+	33.3272i	−0.841372	+	1.45730i	−0.888735	+	0.458421i	$0.848415\pi$
$524$	2.91753			0.127453
$525$	−8.98027			−0.391931
$526$	26.7279			1.16539
$527$	4.45043	−	7.70838i	0.193864	−	0.335782i
$528$	0.809697	+	1.40244i	0.0352375	+	0.0610332i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−7.09439	+	12.2878i	−0.308161	+	0.533750i
$531$	−6.95698			−0.301907
$532$	−3.66198	−	6.34274i	−0.158767	−	0.274993i
$533$	−20.4830			−0.887217
$534$	7.28138	−	12.6117i	0.315096	−	0.545762i
$535$	13.2629	+	22.9721i	0.573406	+	0.993169i
$536$	3.61939	+	6.26897i	0.156334	+	0.270778i
$537$	−8.93062	+	15.4683i	−0.385385	+	0.667506i
$538$	−25.1519			−1.08437
$539$	11.3358			0.488266
$540$	2.89728			0.124679
$541$	9.98988	−	17.3030i	0.429498	−	0.743913i	−0.567330	−	0.823490i	$-0.692024\pi$
$541$	9.98988	−	17.3030i	0.429498	−	0.743913i	0.996829	+	0.0795774i	$0.0253571\pi$
$542$	−10.8429	−	18.7804i	−0.465741	−	0.806687i
$543$	2.65256	+	4.59437i	0.113832	+	0.197163i
$544$	2.77152	−	4.80040i	0.118828	−	0.205816i
$545$	−30.6225			−1.31172
$546$	4.00349	+	6.93426i	0.171334	+	0.296759i
$547$	15.3485			0.656254			0.328127	−	0.944634i	$-0.393583\pi$
$547$	15.3485			0.656254			0.328127	+	0.944634i	$0.393583\pi$
$548$	5.80137	−	10.0483i	0.247822	−	0.429240i
$549$	6.89728	+	11.9464i	0.294369	+	0.509862i
$550$	2.74829	+	4.76018i	0.117188	+	0.202975i
$551$	−2.44737	+	4.23896i	−0.104261	+	0.180586i
$552$	1.00000			0.0425628
$553$	−18.2309			−0.775259
$554$	−9.76908			−0.415048
$555$	1.48682	−	2.57525i	0.0631121	−	0.109313i
$556$	0.0777178	+	0.134611i	0.00329597	+	0.00570879i
$557$	10.4320	+	18.0687i	0.442017	+	0.765596i	0.997839	−	0.0657053i	$-0.0209297\pi$
$557$	10.4320	+	18.0687i	0.442017	+	0.765596i	−0.555822	+	0.831301i	$0.687596\pi$
$558$	−0.802888	+	1.39064i	−0.0339890	+	0.0588706i
$559$	−6.05271			−0.256003
$560$	3.83274	−	6.63850i	0.161963	−	0.280528i
$561$	−8.97635			−0.378982
$562$	−1.40365	+	2.43119i	−0.0592093	+	0.102554i
$563$	−7.31938	−	12.6775i	−0.308475	−	0.534295i	0.669554	−	0.742764i	$-0.266485\pi$
$563$	−7.31938	−	12.6775i	−0.308475	−	0.534295i	−0.978029	+	0.208469i	$0.933152\pi$
$564$	−2.07772	−	3.59871i	−0.0874877	−	0.151533i
$565$	5.44991	−	9.43953i	0.229280	−	0.397124i
$566$	−25.9140			−1.08925
$567$	−1.32288	+	2.29129i	−0.0555556	+	0.0962250i
$568$	−4.87092			−0.204379
$569$	19.3512	−	33.5173i	0.811245	−	1.40512i	−0.100749	−	0.994912i	$-0.532124\pi$
$569$	19.3512	−	33.5173i	0.811245	−	1.40512i	0.911993	−	0.410205i	$-0.134543\pi$
$570$	4.01012	+	6.94574i	0.167966	+	0.290925i
$571$	−6.47320	−	11.2119i	−0.270895	−	0.469204i	0.698196	−	0.715906i	$-0.253986\pi$
$571$	−6.47320	−	11.2119i	−0.270895	−	0.469204i	−0.969091	+	0.246702i	$0.920653\pi$
$572$	2.45043	−	4.24427i	0.102458	−	0.177462i
$573$	−18.3046			−0.764686
$574$	−17.9070			−0.747423
$575$	3.39422			0.141549
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−3.92757	−	6.80275i	−0.163507	−	0.283202i	0.772617	−	0.634872i	$-0.218947\pi$
$577$	−3.92757	−	6.80275i	−0.163507	−	0.283202i	−0.936124	+	0.351670i	$0.885614\pi$
$578$	6.86259	+	11.8864i	0.285446	+	0.494407i
$579$	0.170755	−	0.295756i	0.00709633	−	0.0122912i
$580$	−5.12297			−0.212720
$581$	−6.82000	−	11.8126i	−0.282941	−	0.490069i
$582$	−14.6988			−0.609286
$583$	−3.96531	+	6.86812i	−0.164226	+	0.284449i
$584$	2.56803	+	4.44796i	0.106266	+	0.184058i
$585$	−4.38410	−	7.59348i	−0.181260	−	0.313952i
$586$	15.6571	−	27.1190i	0.646791	−	1.12027i
$587$	39.8243			1.64373			0.821863	−	0.569685i	$-0.192935\pi$
$587$	39.8243			1.64373			0.821863	+	0.569685i	$0.192935\pi$
$588$	3.50000	+	6.06218i	0.144338	+	0.250000i
$589$	−4.44511			−0.183158
$590$	10.0782	−	17.4559i	0.414911	−	0.718647i
$591$	10.1238	+	17.5349i	0.416438	+	0.721291i
$592$	0.513179	+	0.888851i	0.0210915	+	0.0365316i
$593$	13.0470	−	22.5980i	0.535775	−	0.927989i	−0.463351	−	0.886175i	$-0.653353\pi$
$593$	13.0470	−	22.5980i	0.535775	−	0.927989i	0.999125	−	0.0418139i	$-0.0133137\pi$
$594$	1.61939			0.0664445
$595$	21.2450	+	36.7974i	0.870960	+	1.50855i
$596$	16.6357			0.681426
$597$	−13.4471	+	23.2911i	−0.550354	+	0.953241i
$598$	−1.51318	−	2.62090i	−0.0618785	−	0.107177i
$599$	−18.9482	−	32.8193i	−0.774203	−	1.34096i	−0.935241	−	0.354011i	$-0.884818\pi$
$599$	−18.9482	−	32.8193i	−0.774203	−	1.34096i	0.161038	−	0.986948i	$-0.448516\pi$
$600$	−1.69711	+	2.93948i	−0.0692843	+	0.120004i
$601$	3.65849			0.149233			0.0746165	−	0.997212i	$-0.476227\pi$
$601$	3.65849			0.149233			0.0746165	+	0.997212i	$0.476227\pi$
$602$	−5.29150			−0.215666
$603$	7.23879			0.294786
$604$	9.86259	−	17.0825i	0.401303	−	0.695077i
$605$	−12.1361	−	21.0203i	−0.493401	−	0.854596i
$606$	1.69711	+	2.93948i	0.0689405	+	0.119408i
$607$	10.3323	−	17.8961i	0.419375	−	0.726379i	−0.576502	−	0.817096i	$-0.695583\pi$
$607$	10.3323	−	17.8961i	0.419375	−	0.726379i	0.995877	+	0.0907170i	$0.0289159\pi$
$608$	−2.76820			−0.112265
$609$	2.33911	−	4.05146i	0.0947855	−	0.164173i
$610$	−39.9667			−1.61820
$611$	−6.28792	+	10.8910i	−0.254382	+	0.440602i
$612$	−2.77152	−	4.80040i	−0.112032	−	0.194045i
$613$	−14.4269	−	24.9881i	−0.582696	−	1.00926i	−0.995158	−	0.0982842i	$-0.968665\pi$
$613$	−14.4269	−	24.9881i	−0.582696	−	1.00926i	0.412463	−	0.910975i	$-0.364669\pi$
$614$	−6.80333	+	11.7837i	−0.274560	+	0.475552i
$615$	19.6094			0.790726
$616$	2.14226	−	3.71050i	0.0863140	−	0.149500i
$617$	21.1524			0.851563			0.425782	−	0.904826i	$-0.359999\pi$
$617$	21.1524			0.851563			0.425782	+	0.904826i	$0.359999\pi$
$618$	5.50986	−	9.54336i	0.221639	−	0.383890i
$619$	10.6492	+	18.4450i	0.428029	+	0.741369i	0.996698	−	0.0811982i	$-0.0258747\pi$
$619$	10.6492	+	18.4450i	0.428029	+	0.741369i	−0.568669	+	0.822567i	$0.692541\pi$
$620$	−2.32619	−	4.02908i	−0.0934221	−	0.161812i
$621$	0.500000	−	0.866025i	0.0200643	−	0.0347524i
$622$	14.7709			0.592259
$623$	−38.5294			−1.54365
$624$	3.02636			0.121151
$625$	15.2252	−	26.3708i	0.609007	−	1.05483i
$626$	1.34242	+	2.32515i	0.0536540	+	0.0929315i
$627$	2.24140	+	3.88222i	0.0895130	+	0.155041i
$628$	−0.900593	+	1.55987i	−0.0359376	+	0.0622457i
$629$	−5.68913			−0.226840
$630$	−3.83274	−	6.63850i	−0.152700	−	0.264484i
$631$	41.4808			1.65133			0.825663	−	0.564164i	$-0.190801\pi$
$631$	41.4808			1.65133			0.825663	+	0.564164i	$0.190801\pi$
$632$	−3.44532	+	5.96748i	−0.137048	+	0.237373i
$633$	3.20680	+	5.55433i	0.127459	+	0.220765i
$634$	5.52151	+	9.56353i	0.219287	+	0.379816i
$635$	19.8828	−	34.4381i	0.789026	−	1.36663i
$636$	−4.89728			−0.194190
$637$	10.5923	−	18.3463i	0.419680	−	0.726907i
$638$	−2.86341			−0.113364
$639$	−2.43546	+	4.21834i	−0.0963453	+	0.166875i
$640$	−1.44864	−	2.50912i	−0.0572625	−	0.0991816i
$641$	1.60246	+	2.77554i	0.0632934	+	0.109627i	0.895936	−	0.444184i	$-0.146506\pi$
$641$	1.60246	+	2.77554i	0.0632934	+	0.109627i	−0.832642	+	0.553811i	$0.813173\pi$
$642$	−4.57772	+	7.92884i	−0.180668	+	0.312926i
$643$	−34.0131			−1.34135			−0.670673	−	0.741753i	$-0.733995\pi$
$643$	−34.0131			−1.34135			−0.670673	+	0.741753i	$0.733995\pi$
$644$	−1.32288	−	2.29129i	−0.0521286	−	0.0902894i
$645$	5.79456			0.228160
$646$	7.67211	−	13.2885i	0.301855	−	0.522828i
$647$	−5.75986	−	9.97637i	−0.226443	−	0.392211i	0.730308	−	0.683118i	$-0.239376\pi$
$647$	−5.75986	−	9.97637i	−0.226443	−	0.392211i	−0.956752	+	0.290906i	$0.906043\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	5.63305	−	9.75672i	0.221116	−	0.382985i
$650$	10.2721			0.402906
$651$	4.24848			0.166511
$652$	8.87092			0.347412
$653$	6.17560	−	10.6965i	0.241670	−	0.418585i	−0.719520	−	0.694472i	$-0.755638\pi$
$653$	6.17560	−	10.6965i	0.241670	−	0.418585i	0.961190	+	0.275887i	$0.0889715\pi$
$654$	−5.28469	−	9.15336i	−0.206648	−	0.357925i
$655$	4.22644	+	7.32041i	0.165141	+	0.286032i
$656$	−3.38410	+	5.86143i	−0.132127	+	0.228851i
$657$	5.13607			0.200377
$658$	−5.49712	+	9.52130i	−0.214300	+	0.371179i
$659$	−4.82754			−0.188054			−0.0940272	−	0.995570i	$-0.529974\pi$
$659$	−4.82754			−0.188054			−0.0940272	+	0.995570i	$0.529974\pi$
$660$	−2.34592	+	4.06325i	−0.0913147	+	0.158162i
$661$	7.73503	+	13.3975i	0.300858	+	0.521101i	0.976331	−	0.216284i	$-0.0693937\pi$
$661$	7.73503	+	13.3975i	0.300858	+	0.521101i	−0.675473	+	0.737385i	$0.736060\pi$
$662$	4.14619	+	7.18141i	0.161146	+	0.279114i
$663$	−8.38759	+	14.5277i	−0.325747	+	0.564211i
$664$	−5.15544			−0.200070
$665$	10.6098	−	18.3767i	0.411430	−	0.712618i
$666$	1.02636			0.0397705
$667$	−0.884100	+	1.53131i	−0.0342325	+	0.0592924i
$668$	0.632133	+	1.09489i	0.0244580	+	0.0423624i
$669$	−8.09439	−	14.0199i	−0.312947	−	0.542040i
$670$	−10.4864	+	18.1630i	−0.405125	+	0.701697i
$671$	−22.3388			−0.862381
$672$	2.64575			0.102062
$673$	15.3248			0.590729			0.295365	−	0.955385i	$-0.404559\pi$
$673$	15.3248			0.590729			0.295365	+	0.955385i	$0.404559\pi$
$674$	−12.5312	+	21.7047i	−0.482684	+	0.836033i
$675$	1.69711	+	2.93948i	0.0653219	+	0.113141i
$676$	1.92058	+	3.32654i	0.0738685	+	0.127944i
$677$	23.8126	−	41.2446i	0.915192	−	1.58516i	0.108572	−	0.994089i	$-0.465372\pi$
$677$	23.8126	−	41.2446i	0.915192	−	1.58516i	0.806620	−	0.591070i	$-0.201294\pi$
$678$	3.76209			0.144482
$679$	19.4447	+	33.6792i	0.746220	+	1.29249i
$680$	16.0597			0.615861
$681$	11.4554	−	19.8414i	0.438974	−	0.760325i
$682$	−1.30019	−	2.25200i	−0.0497869	−	0.0862335i
$683$	13.8091	+	23.9180i	0.528390	+	0.915199i	0.999452	+	0.0330984i	$0.0105375\pi$
$683$	13.8091	+	23.9180i	0.528390	+	0.915199i	−0.471062	+	0.882100i	$0.656129\pi$
$684$	−1.38410	+	2.39733i	−0.0529224	+	0.0916643i
$685$	33.6164			1.28441
$686$	9.26013	−	16.0390i	0.353553	−	0.612372i
$687$	5.16547			0.197075
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	7.41046	+	12.8353i	0.282316	+	0.488986i
$690$	1.44864	+	2.50912i	0.0551488	+	0.0955205i
$691$	−1.96487	+	3.40326i	−0.0747473	+	0.129466i	−0.900976	−	0.433868i	$-0.857148\pi$
$691$	−1.96487	+	3.40326i	−0.0747473	+	0.129466i	0.826229	+	0.563334i	$0.190482\pi$
$692$	−0.863933			−0.0328418
$693$	−2.14226	−	3.71050i	−0.0813776	−	0.140950i
$694$	−6.78845			−0.257686
$695$	−0.225170	+	0.390006i	−0.00854119	+	0.0147938i
$696$	−0.884100	−	1.53131i	−0.0335117	−	0.0580440i
$697$	−18.7582	−	32.4901i	−0.710516	−	1.23065i
$698$	6.00349	−	10.3984i	0.227236	−	0.393584i
$699$	−11.0930			−0.419578
$700$	8.98027			0.339422
$701$	13.5725			0.512624			0.256312	−	0.966594i	$-0.417492\pi$
$701$	13.5725			0.512624			0.256312	+	0.966594i	$0.417492\pi$
$702$	1.51318	−	2.62090i	0.0571112	−	0.0989196i
$703$	1.42058	+	2.46052i	0.0535782	+	0.0928002i
$704$	−0.809697	−	1.40244i	−0.0305166	−	0.0528563i
$705$	6.01973	−	10.4265i	0.226716	−	0.392684i
$706$	−20.9263			−0.787573
$707$	4.49014	−	7.77714i	0.168869	−	0.292490i
$708$	6.95698			0.261459
$709$	−6.24821	+	10.8222i	−0.234657	+	0.406437i	−0.959173	−	0.282821i	$-0.908730\pi$
$709$	−6.24821	+	10.8222i	−0.234657	+	0.406437i	0.724516	+	0.689258i	$0.242063\pi$
$710$	−7.05621	−	12.2217i	−0.264815	−	0.458673i
$711$	3.44532	+	5.96748i	0.129210	+	0.223798i
$712$	−7.28138	+	12.6117i	−0.272881	+	0.472644i
$713$	−1.60578			−0.0601368
$714$	−7.33274	+	12.7007i	−0.274421	+	0.475311i
$715$	14.1992			0.531019
$716$	8.93062	−	15.4683i	0.333753	−	0.578077i
$717$	−2.81956	−	4.88362i	−0.105298	−	0.182382i
$718$	−5.01362	−	8.68384i	−0.187107	−	0.324078i
$719$	25.7981	−	44.6837i	0.962108	−	1.66642i	0.244917	−	0.969544i	$-0.421239\pi$
$719$	25.7981	−	44.6837i	0.962108	−	1.66642i	0.717191	−	0.696877i	$-0.245428\pi$
$720$	−2.89728			−0.107975
$721$	−29.1555			−1.08581
$722$	11.3371			0.421922
$723$	12.0479	−	20.8675i	0.448065	−	0.776072i
$724$	−2.65256	−	4.59437i	−0.0985816	−	0.170748i
$725$	−3.00083	−	5.19760i	−0.111448	−	0.193034i
$726$	4.18878	−	7.25518i	0.155460	−	0.269265i
$727$	−41.3991			−1.53541			−0.767704	−	0.640804i	$-0.778601\pi$
$727$	−41.3991			−1.53541			−0.767704	+	0.640804i	$0.778601\pi$
$728$	−4.00349	−	6.93426i	−0.148379	−	0.257001i
$729$	1.00000			0.0370370
$730$	−7.44031	+	12.8870i	−0.275378	+	0.476969i
$731$	−5.54303	−	9.60081i	−0.205016	−	0.355099i
$732$	−6.89728	−	11.9464i	−0.254931	−	0.441553i
$733$	−12.0494	+	20.8702i	−0.445055	+	0.770857i	−0.998056	−	0.0623230i	$-0.980149\pi$
$733$	−12.0494	+	20.8702i	−0.445055	+	0.770857i	0.553001	+	0.833180i	$0.313482\pi$
$734$	24.2485			0.895028
$735$	−10.1405	+	17.5638i	−0.374037	+	0.647851i
$736$	−1.00000			−0.0368605
$737$	−5.86123	+	10.1519i	−0.215901	+	0.373952i
$738$	3.38410	+	5.86143i	0.124570	+	0.215762i
$739$	−7.79931	−	13.5088i	−0.286902	−	0.496929i	0.686166	−	0.727445i	$-0.259292\pi$
$739$	−7.79931	−	13.5088i	−0.286902	−	0.496929i	−0.973069	+	0.230515i	$0.925959\pi$
$740$	−1.48682	+	2.57525i	−0.0546566	+	0.0946681i
$741$	8.37756			0.307757
$742$	6.47849	+	11.2211i	0.237833	+	0.411939i
$743$	25.7488			0.944633			0.472317	−	0.881429i	$-0.343418\pi$
$743$	25.7488			0.944633			0.472317	+	0.881429i	$0.343418\pi$
$744$	0.802888	−	1.39064i	0.0294353	−	0.0509834i
$745$	24.0992	+	41.7410i	0.882925	+	1.52927i
$746$	17.4599	+	30.2414i	0.639251	+	1.10721i
$747$	−2.57772	+	4.46474i	−0.0943138	+	0.163356i
$748$	8.97635			0.328208
$749$	24.2230			0.885089
$750$	4.65238			0.169881
$751$	−11.2867	+	19.5491i	−0.411856	+	0.713356i	−0.995093	−	0.0989464i	$-0.968453\pi$
$751$	−11.2867	+	19.5491i	−0.411856	+	0.713356i	0.583236	+	0.812302i	$0.301786\pi$
$752$	2.07772	+	3.59871i	0.0757666	+	0.131232i
$753$	8.99848	+	15.5858i	0.327923	+	0.567979i
$754$	−2.67560	+	4.63428i	−0.0974397	+	0.168771i
$755$	57.1493			2.07988
$756$	1.32288	−	2.29129i	0.0481125	−	0.0833333i
$757$	15.4706			0.562289			0.281144	−	0.959665i	$-0.409286\pi$
$757$	15.4706			0.562289			0.281144	+	0.959665i	$0.409286\pi$
$758$	1.88366	−	3.26260i	0.0684176	−	0.118503i
$759$	0.809697	+	1.40244i	0.0293901	+	0.0509052i
$760$	−4.01012	−	6.94574i	−0.145462	−	0.251948i
$761$	−19.2520	+	33.3454i	−0.697884	+	1.20877i	0.271315	+	0.962491i	$0.412541\pi$
$761$	−19.2520	+	33.3454i	−0.697884	+	1.20877i	−0.969199	+	0.246279i	$0.920792\pi$
$762$	13.7252			0.497211
$763$	−13.9820	+	24.2175i	−0.506182	+	0.876733i
$764$	18.3046			0.662237
$765$	8.02985	−	13.9081i	0.290320	−	0.502849i
$766$	16.6826	+	28.8951i	0.602767	+	1.04402i
$767$	−10.5272	−	18.2336i	−0.380114	−	0.658376i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	10.9842			0.396101			0.198051	−	0.980192i	$-0.436539\pi$
$769$	10.9842			0.396101			0.198051	+	0.980192i	$0.436539\pi$
$770$	12.4134			0.447349
$771$	−1.27126			−0.0457831
$772$	−0.170755	+	0.295756i	−0.00614560	+	0.0106445i
$773$	9.53640	+	16.5175i	0.343000	+	0.594094i	0.984988	−	0.172620i	$-0.0552234\pi$
$773$	9.53640	+	16.5175i	0.343000	+	0.594094i	−0.641988	+	0.766715i	$0.721890\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$	2.72518	−	4.72015i	0.0978914	−	0.169553i
$776$	14.6988			0.527657

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.44864 - 2.50912i) q^{5} +1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.44864 - 2.50912i) q^{5} +1.00000 q^{6} +(-1.32288 - 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.44864 - 2.50912i) q^{10} +(-0.809697 - 1.40244i) q^{11} +(0.500000 - 0.866025i) q^{12} -3.02636 q^{13} -2.64575 q^{14} +2.89728 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.77152 - 4.80040i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.38410 + 2.39733i) q^{19} -2.89728 q^{20} +(1.32288 - 2.29129i) q^{21} -1.61939 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.69711 - 2.93948i) q^{25} +(-1.51318 + 2.62090i) q^{26} -1.00000 q^{27} +(-1.32288 + 2.29129i) q^{28} +1.76820 q^{29} +(1.44864 - 2.50912i) q^{30} +(0.802888 + 1.39064i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.809697 - 1.40244i) q^{33} -5.54303 q^{34} -7.66548 q^{35} +1.00000 q^{36} +(0.513179 - 0.888851i) q^{37} +(1.38410 + 2.39733i) q^{38} +(-1.51318 - 2.62090i) q^{39} +(-1.44864 + 2.50912i) q^{40} +6.76820 q^{41} +(-1.32288 - 2.29129i) q^{42} +2.00000 q^{43} +(-0.809697 + 1.40244i) q^{44} +(1.44864 + 2.50912i) q^{45} +(0.500000 + 0.866025i) q^{46} +(2.07772 - 3.59871i) q^{47} -1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} -3.39422 q^{50} +(2.77152 - 4.80040i) q^{51} +(1.51318 + 2.62090i) q^{52} +(-2.44864 - 4.24117i) q^{53} +(-0.500000 + 0.866025i) q^{54} -4.69184 q^{55} +(1.32288 + 2.29129i) q^{56} -2.76820 q^{57} +(0.884100 - 1.53131i) q^{58} +(3.47849 + 6.02492i) q^{59} +(-1.44864 - 2.50912i) q^{60} +(6.89728 - 11.9464i) q^{61} +1.60578 q^{62} +2.64575 q^{63} +1.00000 q^{64} +(-4.38410 + 7.59348i) q^{65} +(-0.809697 - 1.40244i) q^{66} +(-3.61939 - 6.26897i) q^{67} +(-2.77152 + 4.80040i) q^{68} -1.00000 q^{69} +(-3.83274 + 6.63850i) q^{70} +4.87092 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.56803 - 4.44796i) q^{73} +(-0.513179 - 0.888851i) q^{74} +(1.69711 - 2.93948i) q^{75} +2.76820 q^{76} +(-2.14226 + 3.71050i) q^{77} -3.02636 q^{78} +(3.44532 - 5.96748i) q^{79} +(1.44864 + 2.50912i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.38410 - 5.86143i) q^{82} +5.15544 q^{83} -2.64575 q^{84} -16.0597 q^{85} +(1.00000 - 1.73205i) q^{86} +(0.884100 + 1.53131i) q^{87} +(0.809697 + 1.40244i) q^{88} +(7.28138 - 12.6117i) q^{89} +2.89728 q^{90} +(4.00349 + 6.93426i) q^{91} +1.00000 q^{92} +(-0.802888 + 1.39064i) q^{93} +(-2.07772 - 3.59871i) q^{94} +(4.01012 + 6.94574i) q^{95} +(-0.500000 + 0.866025i) q^{96} -14.6988 q^{97} +(3.50000 + 6.06218i) q^{98} +1.61939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} - 2 q^{5} + 8 q^{6} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{13} - 4 q^{15} - 4 q^{16} + 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 6 q^{25} - 2 q^{26} - 8 q^{27} - 20 q^{29} - 2 q^{30} + 14 q^{31} + 4 q^{32} + 6 q^{33} + 4 q^{34} + 8 q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 2 q^{40} + 20 q^{41} + 16 q^{43} - 6 q^{44} - 2 q^{45} + 4 q^{46} + 10 q^{47} - 8 q^{48} - 28 q^{49} - 12 q^{50} - 2 q^{51} + 2 q^{52} - 6 q^{53} - 4 q^{54} + 44 q^{55} + 12 q^{57} - 10 q^{58} - 24 q^{59} + 2 q^{60} + 28 q^{61} + 28 q^{62} + 8 q^{64} - 18 q^{65} - 6 q^{66} - 28 q^{67} + 2 q^{68} - 8 q^{69} + 32 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 6 q^{75} - 12 q^{76} - 14 q^{77} - 4 q^{78} + 4 q^{79} - 2 q^{80} - 4 q^{81} + 10 q^{82} + 28 q^{83} - 52 q^{85} + 8 q^{86} - 10 q^{87} + 6 q^{88} + 14 q^{89} - 4 q^{90} + 14 q^{91} + 8 q^{92} - 14 q^{93} - 10 q^{94} + 34 q^{95} - 4 q^{96} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 - 2 * q^5 + 8 * q^6 - 8 * q^8 - 4 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 4 * q^13 - 4 * q^15 - 4 * q^16 + 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 6 * q^25 - 2 * q^26 - 8 * q^27 - 20 * q^29 - 2 * q^30 + 14 * q^31 + 4 * q^32 + 6 * q^33 + 4 * q^34 + 8 * q^36 - 6 * q^37 - 6 * q^38 - 2 * q^39 + 2 * q^40 + 20 * q^41 + 16 * q^43 - 6 * q^44 - 2 * q^45 + 4 * q^46 + 10 * q^47 - 8 * q^48 - 28 * q^49 - 12 * q^50 - 2 * q^51 + 2 * q^52 - 6 * q^53 - 4 * q^54 + 44 * q^55 + 12 * q^57 - 10 * q^58 - 24 * q^59 + 2 * q^60 + 28 * q^61 + 28 * q^62 + 8 * q^64 - 18 * q^65 - 6 * q^66 - 28 * q^67 + 2 * q^68 - 8 * q^69 + 32 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 6 * q^75 - 12 * q^76 - 14 * q^77 - 4 * q^78 + 4 * q^79 - 2 * q^80 - 4 * q^81 + 10 * q^82 + 28 * q^83 - 52 * q^85 + 8 * q^86 - 10 * q^87 + 6 * q^88 + 14 * q^89 - 4 * q^90 + 14 * q^91 + 8 * q^92 - 14 * q^93 - 10 * q^94 + 34 * q^95 - 4 * q^96 + 28 * q^98 + 12 * q^99

Introduction

L-functions

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